diff options
| author | Gabriel Dos Reis <gdr@axiomatics.org> | 2016-01-17 22:53:01 -0800 |
|---|---|---|
| committer | Gabriel Dos Reis <gdr@axiomatics.org> | 2016-01-17 22:53:01 -0800 |
| commit | d07fc9735f40e545edda456e15dbab783c500f6a (patch) | |
| tree | 4d9fab82a7085b73a4b00d23389935503fdfc90d /src | |
| parent | 5437d438937eb25eb320fef6e4fd6ebc91ca6dc9 (diff) | |
| download | open-axiom-d07fc9735f40e545edda456e15dbab783c500f6a.tar.gz | |
subtractIfCan$CancellationAbelianMonoid: return the more principled Maybe %
Diffstat (limited to 'src')
| -rw-r--r-- | src/algebra/Makefile.am | 3 | ||||
| -rw-r--r-- | src/algebra/Makefile.in | 3 | ||||
| -rw-r--r-- | src/algebra/catdef.spad.pamphlet | 6 | ||||
| -rw-r--r-- | src/algebra/gbeuclid.spad.pamphlet | 10 | ||||
| -rw-r--r-- | src/algebra/gbintern.spad.pamphlet | 8 | ||||
| -rw-r--r-- | src/algebra/idecomp.spad.pamphlet | 9 | ||||
| -rw-r--r-- | src/algebra/indexedp.spad.pamphlet | 20 | ||||
| -rw-r--r-- | src/algebra/integer.spad.pamphlet | 4 | ||||
| -rw-r--r-- | src/algebra/newpoly.spad.pamphlet | 14 | ||||
| -rw-r--r-- | src/algebra/ore.spad.pamphlet | 6 | ||||
| -rw-r--r-- | src/algebra/polset.spad.pamphlet | 4 | ||||
| -rw-r--r-- | src/algebra/poly.spad.pamphlet | 22 | ||||
| -rw-r--r-- | src/algebra/product.spad.pamphlet | 8 | ||||
| -rw-r--r-- | src/algebra/prtition.spad.pamphlet | 17 | ||||
| -rw-r--r-- | src/algebra/updivp.spad.pamphlet | 2 | ||||
| -rw-r--r-- | src/algebra/vector.spad.pamphlet | 8 | ||||
| -rw-r--r-- | src/share/algebra/browse.daase | 626 | ||||
| -rw-r--r-- | src/share/algebra/category.daase | 39 | ||||
| -rw-r--r-- | src/share/algebra/interp.daase | 652 | ||||
| -rw-r--r-- | src/share/algebra/operation.daase | 2242 |
20 files changed, 1794 insertions, 1909 deletions
diff --git a/src/algebra/Makefile.am b/src/algebra/Makefile.am index 88c3a9fc..30385bcc 100644 --- a/src/algebra/Makefile.am +++ b/src/algebra/Makefile.am @@ -516,7 +516,8 @@ strap-1/OASGP.$(FASLEXT): strap-1/ORDSET.$(FASLEXT) strap-1/OAMONS.$(FASLEXT): strap-1/OCAMON.$(FASLEXT) strap-1/ABELGRP.$(FASLEXT): strap-1/CABMON.$(FASLEXT) \ - strap-1/LLINSET.$(FASLEXT) + strap-1/LLINSET.$(FASLEXT) \ + strap-1/MAYBE.$(FASLEXT) strap-1/OAGROUP.$(FASLEXT): strap-1/OCAMON.$(FASLEXT) \ strap-1/ABELGRP.$(FASLEXT) diff --git a/src/algebra/Makefile.in b/src/algebra/Makefile.in index 25cd01a2..fdfb8d04 100644 --- a/src/algebra/Makefile.in +++ b/src/algebra/Makefile.in @@ -2027,7 +2027,8 @@ strap-1/OASGP.$(FASLEXT): strap-1/ORDSET.$(FASLEXT) strap-1/OAMONS.$(FASLEXT): strap-1/OCAMON.$(FASLEXT) strap-1/ABELGRP.$(FASLEXT): strap-1/CABMON.$(FASLEXT) \ - strap-1/LLINSET.$(FASLEXT) + strap-1/LLINSET.$(FASLEXT) \ + strap-1/MAYBE.$(FASLEXT) strap-1/OAGROUP.$(FASLEXT): strap-1/OCAMON.$(FASLEXT) \ strap-1/ABELGRP.$(FASLEXT) diff --git a/src/algebra/catdef.spad.pamphlet b/src/algebra/catdef.spad.pamphlet index 1e9370df..ee556b91 100644 --- a/src/algebra/catdef.spad.pamphlet +++ b/src/algebra/catdef.spad.pamphlet @@ -240,7 +240,7 @@ AbelianGroup(): Category == Join(CancellationAbelianMonoid, LeftLinearSet Intege ++ and \spad{y} i.e. \spad{x + (-y)}. add (x:% - y:%):% == x+(-y) - subtractIfCan(x:%, y:%):Union(%, "failed") == (x-y) :: Union(%,"failed") + subtractIfCan(x:%, y:%) == just(x-y) n:NonNegativeInteger * x:% == (n::Integer) * x import RepeatedDoubling(%) if not (% has Ring) then @@ -514,9 +514,9 @@ BiModule(R:Ring,S:Ring):Category == ++ \spad{c = a+b <=> c-b = a} CancellationAbelianMonoid(): Category == AbelianMonoid with --operations - subtractIfCan: (%,%) -> Union(%,"failed") + subtractIfCan: (%,%) -> Maybe % ++ subtractIfCan(x, y) returns an element z such that \spad{z+y=x} - ++ or "failed" if no such element exists. + ++ or \spad{nothing} if no such element exists. @ diff --git a/src/algebra/gbeuclid.spad.pamphlet b/src/algebra/gbeuclid.spad.pamphlet index 963e210b..5b708afc 100644 --- a/src/algebra/gbeuclid.spad.pamphlet +++ b/src/algebra/gbeuclid.spad.pamphlet @@ -389,9 +389,8 @@ EuclideanGroebnerBasisPackage(Dom, Expon, VarSet, Dpol): T == C where ds:= degree s lf1:= leadingCoefficient(f1) ls:= leadingCoefficient(s) - e: Union(Expon, "failed") - (((e:= subtractIfCan(ds, degree f1)) case "failed" ) or sizeLess?(ls, lf1) ) => - eRed(s, rest(H), Hh) + e := subtractIfCan(ds, degree f1) + ((e case nothing) or sizeLess?(ls, lf1) ) => eRed(s, rest(H), Hh) sdf1:= divide(ls, lf1) q1:= sdf1.quotient sdf1.remainder = 0 => @@ -414,9 +413,8 @@ EuclideanGroebnerBasisPackage(Dom, Expon, VarSet, Dpol): T == C where --- crit M - true, if lcm#2 multiple of lcm#1 ecritM(e1: Expon, c1: Dom, e2: Expon, c2: Dom) == - en: Union(Expon, "failed") - ((en:=subtractIfCan(e2, e1)) case "failed") or - ((c2 exquo c1) case "failed") => false + en := subtractIfCan(e2, e1) + (en case nothing) or ((c2 exquo c1) case "failed") => false true ---------------------------- diff --git a/src/algebra/gbintern.spad.pamphlet b/src/algebra/gbintern.spad.pamphlet index 77e72e6f..d6d37fd9 100644 --- a/src/algebra/gbintern.spad.pamphlet +++ b/src/algebra/gbintern.spad.pamphlet @@ -264,8 +264,8 @@ GroebnerInternalPackage(Dom, Expon, VarSet, Dpol): T == C where while not ( s = 0 or null F ) repeat f1:= first(F) s1:= degree(s) - e: Union(Expon, "failed") - (e:= subtractIfCan(s1, degree(f1))) case Expon => + e := subtractIfCan(s1, degree(f1)) + e case Expon => cc:=gcdCo(leadingCoefficient f1, leadingCoefficient s) s:=cc.co1*reductum(s) - monomial(cc.co2,e)*reductum(f1) m := m*cc.co1 @@ -286,8 +286,8 @@ GroebnerInternalPackage(Dom, Expon, VarSet, Dpol): T == C where --- crit M - true, if lcm#2 multiple of lcm#1 critM(e1: Expon, e2: Expon) == - en: Union(Expon, "failed") - (en:=subtractIfCan(e2, e1)) case Expon + en := subtractIfCan(e2, e1) + en case Expon ---------------------------- diff --git a/src/algebra/idecomp.spad.pamphlet b/src/algebra/idecomp.spad.pamphlet index 51ff3a62..9e53d263 100644 --- a/src/algebra/idecomp.spad.pamphlet +++ b/src/algebra/idecomp.spad.pamphlet @@ -298,15 +298,16 @@ IdealDecompositionPackage(vl,nv) : C == T -- take away nv, now doesn't Jd:=generators(groebner J) not one?(#(factors factor Jd.last)) => return false i:=subtractIfCan(#truelist,1) - (i case "failed") => return true + (i case nothing) => return true + k: NNI := i JR:=(reverse Jd);JM:=groebnerIdeal([JR.first]);JP:List(DPoly):=[] for f in JR.rest repeat - if not ismonic(f,truelist.i) then + if not ismonic(f,truelist.k) then if not inRadical?(f,JM) then return false JP:=cons(f,JP) else - x:=truelist.i - i:=(i-1)::NNI + x:=truelist.k + k := (k-1)::NNI if not testPower(univariate(f,x),x,JM) then return false JM :=groebnerIdeal(append(cons(f,JP),generators JM)) true diff --git a/src/algebra/indexedp.spad.pamphlet b/src/algebra/indexedp.spad.pamphlet index beee92ac..e4dd5805 100644 --- a/src/algebra/indexedp.spad.pamphlet +++ b/src/algebra/indexedp.spad.pamphlet @@ -293,19 +293,19 @@ IndexedDirectProductOrderedAbelianMonoidSup(A:OrderedAbelianMonoidSup,S:OrderedS s: S subtractIfCan(x,y) == - empty? y => x - empty? x => "failed" - x.first.k < y.first.k => "failed" + empty? y => just x + empty? x => nothing + x.first.k < y.first.k => nothing x.first.k > y.first.k => t:= subtractIfCan(x.rest, y) - t case "failed" => "failed" - cons( x.first, t) - u:=subtractIfCan(x.first.c, y.first.c) - u case "failed" => "failed" + t case nothing => nothing + just cons( x.first, t) + u := subtractIfCan(x.first.c, y.first.c) + u case nothing => nothing zero? u => subtractIfCan(x.rest, y.rest) - t:= subtractIfCan(x.rest, y.rest) - t case "failed" => "failed" - cons([x.first.k,u],t) + t := subtractIfCan(x.rest, y.rest) + t case nothing => nothing + just cons([x.first.k,u],t) sup(x,y) == empty? y => x diff --git a/src/algebra/integer.spad.pamphlet b/src/algebra/integer.spad.pamphlet index a91b6d63..fde8ef88 100644 --- a/src/algebra/integer.spad.pamphlet +++ b/src/algebra/integer.spad.pamphlet @@ -251,8 +251,8 @@ NonNegativeInteger: Join(OrderedAbelianMonoidSup,Monoid) with shift(x:%, n:Integer):% == ASH(x,n)$Lisp subtractIfCan(x, y) == c:Integer := rep x - rep y - negative? c => "failed" - per c + negative? c => nothing + just per c @ diff --git a/src/algebra/newpoly.spad.pamphlet b/src/algebra/newpoly.spad.pamphlet index 65bdcde7..d695d8ee 100644 --- a/src/algebra/newpoly.spad.pamphlet +++ b/src/algebra/newpoly.spad.pamphlet @@ -120,7 +120,7 @@ NewSparseUnivariatePolynomial(R): Exports == Implementation where e := yy.first.k; y := per(yy.rest) -- while (not empty? xx) repeat repeat - if (u:=subtractIfCan(xx.first.k,e)) case "failed" then break + if (u:=subtractIfCan(xx.first.k,e)) case nothing then break xx:= rep fmecg(per rest(xx), u, xx.first.c, y) if empty? xx then break per xx @@ -134,7 +134,7 @@ NewSparseUnivariatePolynomial(R): Exports == Implementation where empty? xx => [x, co, 0] pow: NNI := 0; e := yy.first.k; y := per(yy.rest); repeat - if (u:=subtractIfCan(xx.first.k,e)) case "failed" then break + if (u:=subtractIfCan(xx.first.k,e)) case nothing then break xx:= rep fmecg(co * per rest(xx), u, xx.first.c, y) pow := pow + 1 if empty? xx then break @@ -151,7 +151,7 @@ NewSparseUnivariatePolynomial(R): Exports == Implementation where (co = -1) => - monicModulo(-x,-y) xx:= rep x; e := yy.first.k; y := per(yy.rest) repeat - if (u:=subtractIfCan(xx.first.k,e)) case "failed" then break + if (u:=subtractIfCan(xx.first.k,e)) case nothing then break xx:= rep fmecg(co * per rest(xx), u, xx.first.c, y) if empty? xx then break per xx @@ -167,7 +167,7 @@ NewSparseUnivariatePolynomial(R): Exports == Implementation where pow: NNI := subtractIfCan(xx.first.k,e)::NNI + 1 qq: Rep := []; y := per(yy.rest) repeat - if (u:=subtractIfCan(xx.first.k,e)) case "failed" then break + if (u:=subtractIfCan(xx.first.k,e)) case nothing then break qq := cons([u::NNI, xx.first.c]$Term, rep (co * per qq)) xx := rep fmecg(co * per rest(xx), u, xx.first.c, y) pow := subtractIfCan(pow,1)::NNI @@ -183,7 +183,7 @@ NewSparseUnivariatePolynomial(R): Exports == Implementation where (empty? xx) or (xx.first.k < e) => 0 qq: Rep := []; co := yy.first.c; y := per(yy.rest) repeat - if (u:=subtractIfCan(xx.first.k,e)) case "failed" then break + if (u:=subtractIfCan(xx.first.k,e)) case nothing then break qq := cons([u::NNI, xx.first.c]$Term, rep (co * per qq)) xx := rep fmecg(co * per rest(xx), u, xx.first.c, y) if empty? xx then break @@ -236,7 +236,7 @@ NewSparseUnivariatePolynomial(R): Exports == Implementation where pow: NNI := subtractIfCan(xx.first.k,e)::NNI + 1 qq: Rep := []; y := per(yy.rest) repeat - if (u:=subtractIfCan(xx.first.k,e)) case "failed" then break + if (u:=subtractIfCan(xx.first.k,e)) case nothing then break qq := cons([u::NNI, xx.first.c]$Term, rep (co * per qq)) xx := rep fmecg(co * per rest(xx), u, xx.first.c, y) pow := subtractIfCan(pow,1)::NNI @@ -257,7 +257,7 @@ NewSparseUnivariatePolynomial(R): Exports == Implementation where pow: NNI := subtractIfCan(xx.first.k,e)::NNI + 1 qq: Rep := []; co := yy.first.c; y := per(yy.rest) repeat - if (u:=subtractIfCan(xx.first.k,e)) case "failed" then break + if (u:=subtractIfCan(xx.first.k,e)) case nothing then break qq := cons([u::NNI, xx.first.c]$Term, rep (co * per qq)) xx := rep fmecg(co * per rest(xx), u, xx.first.c, y) pow := subtractIfCan(pow,1)::NNI diff --git a/src/algebra/ore.spad.pamphlet b/src/algebra/ore.spad.pamphlet index 3aaeab04..1167ea57 100644 --- a/src/algebra/ore.spad.pamphlet +++ b/src/algebra/ore.spad.pamphlet @@ -400,7 +400,7 @@ UnivariateSkewPolynomialCategoryOps(R, C): Exports == Implementation where termPoly(a, n, y, sigma, delta) == zero? y => 0 - (u := subtractIfCan(n, 1)) case "failed" => a * y + (u := subtractIfCan(n, 1)) case nothing => a * y n1 := u::N z:C := 0 while y ~= 0 repeat @@ -424,7 +424,7 @@ UnivariateSkewPolynomialCategoryOps(R, C): Exports == Implementation where localLeftDivide(a, b, sigma, b1) == zero? b => error "leftDivide: division by 0" zero? a or - (n := subtractIfCan(degree(a),(m := degree b))) case "failed" => + (n := subtractIfCan(degree(a),(m := degree b))) case nothing => [0,a] q := monomial((sigma**(-m))(b1 * leadingCoefficient a), n::N) qr := localLeftDivide(a - b * q, b, sigma, b1) @@ -435,7 +435,7 @@ UnivariateSkewPolynomialCategoryOps(R, C): Exports == Implementation where localRightDivide(a, b, sigma, b1) == zero? b => error "rightDivide: division by 0" zero? a or - (n := subtractIfCan(degree(a),(m := degree b))) case "failed" => + (n := subtractIfCan(degree(a),(m := degree b))) case nothing => [0,a] q := monomial(leadingCoefficient(a) * (sigma**n) b1, n::N) qr := localRightDivide(a - q * b, b, sigma, b1) diff --git a/src/algebra/polset.spad.pamphlet b/src/algebra/polset.spad.pamphlet index 2752335c..bcd9bfc3 100644 --- a/src/algebra/polset.spad.pamphlet +++ b/src/algebra/polset.spad.pamphlet @@ -268,10 +268,10 @@ PolynomialSetCategory(R:Ring, E:OrderedAbelianMonoidSup,_ r : R := 1$R lp1 := sort(localInf?, reverse elements(ps)) lp2 := lp1 - e : Union(E, "failed") while (not zero? a) and (not empty? lp2) repeat p := first lp2 - if ((e:= subtractIfCan(degree(a),degree(p))) case E) + e := subtractIfCan(degree(a),degree(p)) + if e case E then g := gcd((lca := leadingCoefficient(a)),(lcp := leadingCoefficient(p)))$R (lca,lcp) := (exactQuo(lca,g),exactQuo(lcp,g)) diff --git a/src/algebra/poly.spad.pamphlet b/src/algebra/poly.spad.pamphlet index aeca4bf1..c9f16e71 100644 --- a/src/algebra/poly.spad.pamphlet +++ b/src/algebra/poly.spad.pamphlet @@ -331,8 +331,8 @@ PolynomialRing(R:Ring,E:OrderedAbelianMonoid): T == C while not null p1 repeat (a:= p1.first.c exquo p2.first.c) a case "failed" => return "failed" - ee:= subtractIfCan(p1.first.k, p2.first.k) - ee case "failed" => return "failed" + ee := subtractIfCan(p1.first.k, p2.first.k) + ee case nothing => return "failed" p1:= fmecg(p1.rest, ee, a, p2.rest) rout:= [[ee,a], :rout] null p1 => reverse(rout)::% -- nreverse? @@ -346,8 +346,8 @@ PolynomialRing(R:Ring,E:OrderedAbelianMonoid): T == C while not null p1 repeat (a:= p1.first.c exquo p2.first.c) a case "failed" => return "failed" - ee:= subtractIfCan(p1.first.k, p2.first.k) - ee case "failed" => return "failed" + ee := subtractIfCan(p1.first.k, p2.first.k) + ee case nothing => return "failed" p1:= fmecg(p1.rest, ee, a, p2.rest) rout:= [[ee,a], :rout] null p1 => reverse(rout)::% -- nreverse? @@ -539,8 +539,8 @@ SparseUnivariatePolynomial(R:Ring): UnivariatePolynomialCategory(R) with while not null p1 repeat (a:= p1.first.c exquo p2.first.c) a case "failed" => return "failed" - ee:= subtractIfCan(p1.first.k, p2.first.k) - ee case "failed" => return "failed" + ee := subtractIfCan(p1.first.k, p2.first.k) + ee case nothing => return "failed" p1:= fmecg(p1.rest, ee, a, p2.rest) rout:= [[ee,a], :rout] null p1 => reverse(rout)::% -- nreverse? @@ -554,8 +554,8 @@ SparseUnivariatePolynomial(R:Ring): UnivariatePolynomialCategory(R) with while not null p1 repeat (a:= p1.first.c exquo p2.first.c) a case "failed" => return "failed" - ee:= subtractIfCan(p1.first.k, p2.first.k) - ee case "failed" => return "failed" + ee := subtractIfCan(p1.first.k, p2.first.k) + ee case nothing => return "failed" p1:= fmecg(p1.rest, ee, a, p2.rest) rout:= [[ee,a], :rout] null p1 => reverse(rout)::% -- nreverse? @@ -581,7 +581,7 @@ SparseUnivariatePolynomial(R:Ring): UnivariatePolynomialCategory(R) with p2:=p2.rest; e1:=max(p1.first.k:Integer-e+1,0):NonNegativeInteger while not null p1 repeat - if (u:=subtractIfCan(p1.first.k,e)) case "failed" then leave + if (u:=subtractIfCan(p1.first.k,e)) case nothing then leave p1:=fmecg(co * p1.rest, u, p1.first.c, p2) e1:= (e1 - 1):NonNegativeInteger e1 = 0 => p1 @@ -628,7 +628,7 @@ SparseUnivariatePolynomial(R:Ring): UnivariatePolynomialCategory(R) with rout:Rep := [] p2 := p2.rest while not null p1 repeat - (u:=subtractIfCan(p1.first.k, n)) case "failed" => leave + (u:=subtractIfCan(p1.first.k, n)) case nothing => leave rout:=[[u, p1.first.c], :rout] p1:=fmecg(p1.rest, rout.first.k, rout.first.c, p2) [reverse!(rout),p1] @@ -697,7 +697,7 @@ SparseUnivariatePolynomial(R:Ring): UnivariatePolynomialCategory(R) with p2:=p2.rest rout:=empty()$List(Term) while p1 ~= 0 repeat - (u:=subtractIfCan(p1.first.k, n)) case "failed" => leave + (u:=subtractIfCan(p1.first.k, n)) case nothing => leave rout:=[[u, ct * p1.first.c], :rout] p1:=fmecg(p1.rest, rout.first.k, rout.first.c, p2) [reverse!(rout),p1] diff --git a/src/algebra/product.spad.pamphlet b/src/algebra/product.spad.pamphlet index e10d11a8..94635e44 100644 --- a/src/algebra/product.spad.pamphlet +++ b/src/algebra/product.spad.pamphlet @@ -80,10 +80,10 @@ Product (A:SetCategory,B:SetCategory) : C == T if A has CancellationAbelianMonoid and B has CancellationAbelianMonoid then - subtractIfCan(x, y) : Union(%,"failed") == - (na:= subtractIfCan(x.acomp, y.acomp)) case "failed" => "failed" - (nb:= subtractIfCan(x.bcomp, y.bcomp)) case "failed" => "failed" - [na::A,nb::B] + subtractIfCan(x, y) == + (na:= subtractIfCan(x.acomp, y.acomp)) case nothing => nothing + (nb:= subtractIfCan(x.bcomp, y.bcomp)) case nothing => nothing + just [na::A,nb::B] if A has AbelianGroup and B has AbelianGroup then - x == [- x.acomp,-x.bcomp] diff --git a/src/algebra/prtition.spad.pamphlet b/src/algebra/prtition.spad.pamphlet index 6fc92821..56acfbda 100644 --- a/src/algebra/prtition.spad.pamphlet +++ b/src/algebra/prtition.spad.pamphlet @@ -91,17 +91,18 @@ Partition(): Exports == Implementation where zero? n => 0 x + (subtractIfCan(n,1) :: NNI) * x - remv(i: PI,x: %): UN == - member?(i,rep x) => per remove(i, rep x)$Rep - "failed" + remv(i: PI,x: %): Maybe % == + member?(i,rep x) => just per remove(i, rep x)$Rep + nothing subtractIfCan(x, y) == zero? x => - zero? y => 0 - "failed" - zero? y => x - (aa := remv(first rep y,x)) case "failed" => "failed" - subtractIfCan((aa :: %), per rest rep y) + zero? y => just 0 + nothing + zero? y => just x + aa := remv(first rep y,x) + aa case nothing => nothing + subtractIfCan(aa@%, per rest rep y) powers x == l := rep x diff --git a/src/algebra/updivp.spad.pamphlet b/src/algebra/updivp.spad.pamphlet index efeb3cca..0ceeefb3 100644 --- a/src/algebra/updivp.spad.pamphlet +++ b/src/algebra/updivp.spad.pamphlet @@ -43,7 +43,7 @@ UnivariatePolynomialDivisionPackage(R,UP): Exports == Implementation where zero? p2 => error "divideIfCan: division by zero" one? (lc := leadingCoefficient p2) => monicDivide(p1,p2) q: UP := 0 - while not ((e := subtractIfCan(degree(p1),degree(p2))) case "failed") + while not ((e := subtractIfCan(degree(p1),degree(p2))) case nothing) repeat c := leadingCoefficient(p1) exquo lc c case "failed" => return "failed" diff --git a/src/algebra/vector.spad.pamphlet b/src/algebra/vector.spad.pamphlet index 7d143b7a..38b14e15 100644 --- a/src/algebra/vector.spad.pamphlet +++ b/src/algebra/vector.spad.pamphlet @@ -340,13 +340,13 @@ DirectProduct(dim:NonNegativeInteger, R:Type): if R has CancellationAbelianMonoid then - subtractIfCan(u:%, v:%):Union(%,"failed") == + subtractIfCan(u:%, v:%) == w := new(dim,0)$Vector(R) for i in 1..dim repeat - (c := subtractIfCan(qelt(rep u, i), qelt(rep v,i))) case "failed" => - return "failed" + (c := subtractIfCan(qelt(rep u, i), qelt(rep v,i))) case nothing => + return nothing qsetelt!(w, i, c::R) - per w + just per w if R has Ring then diff --git a/src/share/algebra/browse.daase b/src/share/algebra/browse.daase index f4e6e265..c5762f0e 100644 --- a/src/share/algebra/browse.daase +++ b/src/share/algebra/browse.daase @@ -1,5 +1,5 @@ -(1915153 . 3581079092) +(1891991 . 3662084402) (|OneDimensionalArrayAggregate&| A S) ((|constructor| (NIL "One-dimensional-array aggregates serves as models for one-dimensional arrays. Categorically,{} these aggregates are finite linear aggregates with the shallowly mutable property,{} that is,{} any component of the array may be changed without affecting the identity of the overall array. Array data structures are typically represented by a fixed area in storage and therefore cannot efficiently grow or shrink on demand as can list structures (see however \\spadtype{FlexibleArray} for a data structure which is a cross between a list and an array). Iteration over,{} and access to,{} elements of arrays is extremely fast (and often can be optimized to open-code). Insertion and deletion however is generally slow since an entirely new data structure must be created for the result."))) NIL @@ -38,7 +38,7 @@ NIL NIL (|AlgebraicallyClosedField|) ((|constructor| (NIL "Model for algebraically closed fields.")) (|zerosOf| (((|List| $) (|SparseUnivariatePolynomial| $) (|Symbol|)) "\\spad{zerosOf(p, y)} returns \\spad{[y1,...,yn]} such that \\spad{p(yi) = 0}. The \\spad{yi}'s are expressed in radicals if possible,{} and otherwise as implicit algebraic quantities which display as \\spad{'yi}. The returned symbols \\spad{y1},{}...,{}yn are bound in the interpreter to respective root values.") (((|List| $) (|SparseUnivariatePolynomial| $)) "\\spad{zerosOf(p)} returns \\spad{[y1,...,yn]} such that \\spad{p(yi) = 0}. The \\spad{yi}'s are expressed in radicals if possible,{} and otherwise as implicit algebraic quantities. The returned symbols \\spad{y1},{}...,{}yn are bound in the interpreter to respective root values.") (((|List| $) (|Polynomial| $)) "\\spad{zerosOf(p)} returns \\spad{[y1,...,yn]} such that \\spad{p(yi) = 0}. The \\spad{yi}'s are expressed in radicals if possible. Otherwise they are implicit algebraic quantities. The returned symbols \\spad{y1},{}...,{}yn are bound in the interpreter to respective root values. Error: if \\spad{p} has more than one variable \\spad{y}.")) (|zeroOf| (($ (|SparseUnivariatePolynomial| $) (|Symbol|)) "\\spad{zeroOf(p, y)} returns \\spad{y} such that \\spad{p(y) = 0}; if possible,{} \\spad{y} is expressed in terms of radicals. Otherwise it is an implicit algebraic quantity which displays as \\spad{'y}.") (($ (|SparseUnivariatePolynomial| $)) "\\spad{zeroOf(p)} returns \\spad{y} such that \\spad{p(y) = 0}; if possible,{} \\spad{y} is expressed in terms of radicals. Otherwise it is an implicit algebraic quantity.") (($ (|Polynomial| $)) "\\spad{zeroOf(p)} returns \\spad{y} such that \\spad{p(y) = 0}. If possible,{} \\spad{y} is expressed in terms of radicals. Otherwise it is an implicit algebraic quantity. Error: if \\spad{p} has more than one variable \\spad{y}.")) (|rootsOf| (((|List| $) (|SparseUnivariatePolynomial| $) (|Symbol|)) "\\spad{rootsOf(p, y)} returns \\spad{[y1,...,yn]} such that \\spad{p(yi) = 0}; The returned roots display as \\spad{'y1},{}...,{}\\spad{'yn}. Note: the returned symbols \\spad{y1},{}...,{}yn are bound in the interpreter to respective root values.") (((|List| $) (|SparseUnivariatePolynomial| $)) "\\spad{rootsOf(p)} returns \\spad{[y1,...,yn]} such that \\spad{p(yi) = 0}. Note: the returned symbols \\spad{y1},{}...,{}yn are bound in the interpreter to respective root values.") (((|List| $) (|Polynomial| $)) "\\spad{rootsOf(p)} returns \\spad{[y1,...,yn]} such that \\spad{p(yi) = 0}. Note: the returned symbols \\spad{y1},{}...,{}yn are bound in the interpreter to respective root values. Error: if \\spad{p} has more than one variable \\spad{y}.")) (|rootOf| (($ (|SparseUnivariatePolynomial| $) (|Symbol|)) "\\spad{rootOf(p, y)} returns \\spad{y} such that \\spad{p(y) = 0}. The object returned displays as \\spad{'y}.") (($ (|SparseUnivariatePolynomial| $)) "\\spad{rootOf(p)} returns \\spad{y} such that \\spad{p(y) = 0}.") (($ (|Polynomial| $)) "\\spad{rootOf(p)} returns \\spad{y} such that \\spad{p(y) = 0}. Error: if \\spad{p} has more than one variable \\spad{y}."))) -((|canonicalsClosed| . T) (|canonicalUnitNormal| . T) (|noZeroDivisors| . T) ((|commutative| "*") . T) (|rightUnitary| . T) (|leftUnitary| . T) (|unitsKnown| . T)) +((|canonicalUnitNormal| . T) (|noZeroDivisors| . T) ((|commutative| "*") . T)) NIL (|AlgebraicallyClosedFunctionSpace&| S R) ((|constructor| (NIL "Model for algebraically closed function spaces.")) (|zerosOf| (((|List| $) $ (|Symbol|)) "\\spad{zerosOf(p, y)} returns \\spad{[y1,...,yn]} such that \\spad{p(yi) = 0}. The \\spad{yi}'s are expressed in radicals if possible,{} and otherwise as implicit algebraic quantities which display as \\spad{'yi}. The returned symbols \\spad{y1},{}...,{}yn are bound in the interpreter to respective root values.") (((|List| $) $) "\\spad{zerosOf(p)} returns \\spad{[y1,...,yn]} such that \\spad{p(yi) = 0}. The \\spad{yi}'s are expressed in radicals if possible. The returned symbols \\spad{y1},{}...,{}yn are bound in the interpreter to respective root values. Error: if \\spad{p} has more than one variable.")) (|zeroOf| (($ $ (|Symbol|)) "\\spad{zeroOf(p, y)} returns \\spad{y} such that \\spad{p(y) = 0}. The value \\spad{y} is expressed in terms of radicals if possible,{}and otherwise as an implicit algebraic quantity which displays as \\spad{'y}.") (($ $) "\\spad{zeroOf(p)} returns \\spad{y} such that \\spad{p(y) = 0}. The value \\spad{y} is expressed in terms of radicals if possible,{}and otherwise as an implicit algebraic quantity. Error: if \\spad{p} has more than one variable.")) (|rootsOf| (((|List| $) $ (|Symbol|)) "\\spad{rootsOf(p, y)} returns \\spad{[y1,...,yn]} such that \\spad{p(yi) = 0}; The returned roots display as \\spad{'y1},{}...,{}\\spad{'yn}. Note: the returned symbols \\spad{y1},{}...,{}yn are bound in the interpreter to respective root values.") (((|List| $) $) "\\spad{rootsOf(p, y)} returns \\spad{[y1,...,yn]} such that \\spad{p(yi) = 0}; Note: the returned symbols \\spad{y1},{}...,{}yn are bound in the interpreter to respective root values. Error: if \\spad{p} has more than one variable \\spad{y}.")) (|rootOf| (($ $ (|Symbol|)) "\\spad{rootOf(p,y)} returns \\spad{y} such that \\spad{p(y) = 0}. The object returned displays as \\spad{'y}.") (($ $) "\\spad{rootOf(p)} returns \\spad{y} such that \\spad{p(y) = 0}. Error: if \\spad{p} has more than one variable \\spad{y}."))) @@ -46,7 +46,7 @@ NIL NIL (|AlgebraicallyClosedFunctionSpace| R) ((|constructor| (NIL "Model for algebraically closed function spaces.")) (|zerosOf| (((|List| $) $ (|Symbol|)) "\\spad{zerosOf(p, y)} returns \\spad{[y1,...,yn]} such that \\spad{p(yi) = 0}. The \\spad{yi}'s are expressed in radicals if possible,{} and otherwise as implicit algebraic quantities which display as \\spad{'yi}. The returned symbols \\spad{y1},{}...,{}yn are bound in the interpreter to respective root values.") (((|List| $) $) "\\spad{zerosOf(p)} returns \\spad{[y1,...,yn]} such that \\spad{p(yi) = 0}. The \\spad{yi}'s are expressed in radicals if possible. The returned symbols \\spad{y1},{}...,{}yn are bound in the interpreter to respective root values. Error: if \\spad{p} has more than one variable.")) (|zeroOf| (($ $ (|Symbol|)) "\\spad{zeroOf(p, y)} returns \\spad{y} such that \\spad{p(y) = 0}. The value \\spad{y} is expressed in terms of radicals if possible,{}and otherwise as an implicit algebraic quantity which displays as \\spad{'y}.") (($ $) "\\spad{zeroOf(p)} returns \\spad{y} such that \\spad{p(y) = 0}. The value \\spad{y} is expressed in terms of radicals if possible,{}and otherwise as an implicit algebraic quantity. Error: if \\spad{p} has more than one variable.")) (|rootsOf| (((|List| $) $ (|Symbol|)) "\\spad{rootsOf(p, y)} returns \\spad{[y1,...,yn]} such that \\spad{p(yi) = 0}; The returned roots display as \\spad{'y1},{}...,{}\\spad{'yn}. Note: the returned symbols \\spad{y1},{}...,{}yn are bound in the interpreter to respective root values.") (((|List| $) $) "\\spad{rootsOf(p, y)} returns \\spad{[y1,...,yn]} such that \\spad{p(yi) = 0}; Note: the returned symbols \\spad{y1},{}...,{}yn are bound in the interpreter to respective root values. Error: if \\spad{p} has more than one variable \\spad{y}.")) (|rootOf| (($ $ (|Symbol|)) "\\spad{rootOf(p,y)} returns \\spad{y} such that \\spad{p(y) = 0}. The object returned displays as \\spad{'y}.") (($ $) "\\spad{rootOf(p)} returns \\spad{y} such that \\spad{p(y) = 0}. Error: if \\spad{p} has more than one variable \\spad{y}."))) -((|unitsKnown| . T) (|leftUnitary| . T) (|rightUnitary| . T) ((|commutative| "*") . T) (|noZeroDivisors| . T) (|canonicalUnitNormal| . T) (|canonicalsClosed| . T)) +(((|commutative| "*") . T) (|noZeroDivisors| . T) (|canonicalUnitNormal| . T)) NIL (|PlaneAlgebraicCurvePlot|) ((|refine| (($ $ (|DoubleFloat|)) "\\spad{refine(p,x)} \\undocumented{}")) (|makeSketch| (($ (|Polynomial| (|Integer|)) (|Symbol|) (|Symbol|) (|Segment| (|Fraction| (|Integer|))) (|Segment| (|Fraction| (|Integer|)))) "\\spad{makeSketch(p,x,y,a..b,c..d)} creates an ACPLOT of the curve \\spad{p = 0} in the region {\\em a <= x <= b, c <= y <= d}. More specifically,{} 'makeSketch' plots a non-singular algebraic curve \\spad{p = 0} in an rectangular region {\\em xMin <= x <= xMax},{} {\\em yMin <= y <= yMax}. The user inputs \\spad{makeSketch(p,x,y,xMin..xMax,yMin..yMax)}. Here \\spad{p} is a polynomial in the variables \\spad{x} and \\spad{y} with integer coefficients (\\spad{p} belongs to the domain \\spad{Polynomial Integer}). The case where \\spad{p} is a polynomial in only one of the variables is allowed. The variables \\spad{x} and \\spad{y} are input to specify the the coordinate axes. The horizontal axis is the \\spad{x}-axis and the vertical axis is the \\spad{y}-axis. The rational numbers xMin,{}...,{}yMax specify the boundaries of the region in which the curve is to be plotted."))) @@ -82,7 +82,7 @@ NIL NIL (|Algebra| R) ((|constructor| (NIL "The category of associative algebras (modules which are themselves rings). \\blankline"))) -((|rightUnitary| . T) (|leftUnitary| . T) (|unitsKnown| . T)) +NIL NIL (|AlgFactor| UP) ((|constructor| (NIL "Factorization of univariate polynomials with coefficients in \\spadtype{AlgebraicNumber}.")) (|doublyTransitive?| (((|Boolean|) |#1|) "\\spad{doublyTransitive?(p)} is \\spad{true} if \\spad{p} is irreducible over over the field \\spad{K} generated by its coefficients,{} and if \\spad{p(X) / (X - a)} is irreducible over \\spad{K(a)} where \\spad{p(a) = 0}.")) (|split| (((|Factored| |#1|) |#1|) "\\spad{split(p)} returns a prime factorisation of \\spad{p} over its splitting field.")) (|factor| (((|Factored| |#1|) |#1|) "\\spad{factor(p)} returns a prime factorisation of \\spad{p} over the field generated by its coefficients.") (((|Factored| |#1|) |#1| (|List| (|AlgebraicNumber|))) "\\spad{factor(p, [a1,...,an])} returns a prime factorisation of \\spad{p} over the field generated by its coefficients and \\spad{a1},{}...,{}an."))) @@ -90,8 +90,8 @@ NIL NIL (|AlgebraicFunctionField| F UP UPUP |modulus|) ((|constructor| (NIL "Function field defined by \\spad{f}(\\spad{x},{} \\spad{y}) = 0.")) (|knownInfBasis| (((|Void|) (|NonNegativeInteger|)) "\\spad{knownInfBasis(n)} \\undocumented{}"))) -((|noZeroDivisors| |has| #1=(|Fraction| |#2|) . #2=((|Field|))) (|canonicalUnitNormal| |has| #1# . #2#) (|canonicalsClosed| |has| #1# . #2#) ((|commutative| "*") . T) (|rightUnitary| . T) (|leftUnitary| . T) (|unitsKnown| . T)) -((|HasCategory| #1=(|Fraction| |#2|) (QUOTE (|CharacteristicNonZero|))) (|HasCategory| #1# (QUOTE (|CharacteristicZero|))) #2=(|HasCategory| #1# (QUOTE (|FiniteFieldCategory|))) (OR #3=(|HasCategory| #1# #4=(QUOTE (|Field|))) #2#) #3# (|HasCategory| #1# #5=(QUOTE (|Finite|))) (OR #6=(AND (|HasCategory| #1# (QUOTE (|DifferentialRing|))) #3#) #2#) (OR #6# #7=(AND (|HasCategory| #1# (QUOTE (|DifferentialSpace|))) #3#) #2#) (OR #8=(AND #3# #9=(|HasCategory| #1# (QUOTE (|PartialDifferentialRing| #10=(|Symbol|))))) (AND #2# #9#)) (OR #8# #11=(AND #3# (|HasCategory| #1# (QUOTE (|PartialDifferentialSpace| #10#))))) (|HasCategory| #1# (QUOTE (|LinearlyExplicitRingOver| #12=(|Integer|)))) (OR #3# #13=(|HasCategory| #1# (QUOTE (|RetractableTo| (|Fraction| #12#))))) #13# (|HasCategory| #1# (QUOTE (|RetractableTo| #12#))) (|HasCategory| |#1| #4#) (|HasCategory| |#1| #5#) #7# #11# #6# #8#) +((|noZeroDivisors| |has| #1=(|Fraction| |#2|) . #2=((|Field|))) (|canonicalUnitNormal| |has| #1# . #2#) ((|commutative| "*") . T)) +((|HasCategory| #1=(|Fraction| |#2|) (QUOTE (|CharacteristicNonZero|))) (|HasCategory| #1# (QUOTE (|CharacteristicZero|))) #2=(|HasCategory| #1# (QUOTE (|FiniteFieldCategory|))) (OR #3=(|HasCategory| #1# #4=(QUOTE (|Field|))) #2#) #3# (|HasCategory| #1# #5=(QUOTE (|Finite|))) (OR #6=(AND (|HasCategory| #1# (QUOTE (|DifferentialRing|))) #3#) #2#) (OR #6# #7=(AND (|HasCategory| #1# (QUOTE (|DifferentialSpace|))) #3#) #2#) (OR #8=(AND #3# #9=(|HasCategory| #1# (QUOTE (|PartialDifferentialRing| #10=(|Symbol|))))) (AND #2# #9#)) (OR #8# #11=(AND #3# (|HasCategory| #1# (QUOTE (|PartialDifferentialSpace| #10#))))) (|HasCategory| #1# (QUOTE (|LinearlyExplicitRingOver| #12=(|Integer|)))) (OR #3# #13=(|HasCategory| #1# (QUOTE (|RetractableTo| (|Fraction| #12#))))) #13# (|HasCategory| #1# (QUOTE (|RetractableTo| #12#))) (|HasCategory| |#1| #4#) (|HasCategory| |#1| #5#) #11# #7# #6# #8#) (|AlgebraicManipulations| R F) ((|constructor| (NIL "AlgebraicManipulations provides functions to simplify and expand expressions involving algebraic operators.")) (|rootKerSimp| ((|#2| (|BasicOperator|) |#2| (|NonNegativeInteger|)) "\\spad{rootKerSimp(op,f,n)} should be local but conditional.")) (|rootSimp| ((|#2| |#2|) "\\spad{rootSimp(f)} transforms every radical of the form \\spad{(a * b**(q*n+r))**(1/n)} appearing in \\spad{f} into \\spad{b**q * (a * b**r)**(1/n)}. This transformation is not in general valid for all complex numbers \\spad{b}.")) (|rootProduct| ((|#2| |#2|) "\\spad{rootProduct(f)} combines every product of the form \\spad{(a**(1/n))**m * (a**(1/s))**t} into a single power of a root of \\spad{a},{} and transforms every radical power of the form \\spad{(a**(1/n))**m} into a simpler form.")) (|rootPower| ((|#2| |#2|) "\\spad{rootPower(f)} transforms every radical power of the form \\spad{(a**(1/n))**m} into a simpler form if \\spad{m} and \\spad{n} have a common factor.")) (|ratPoly| (((|SparseUnivariatePolynomial| |#2|) |#2|) "\\spad{ratPoly(f)} returns a polynomial \\spad{p} such that \\spad{p} has no algebraic coefficients,{} and \\spad{p(f) = 0}.")) (|ratDenom| ((|#2| |#2| (|List| (|Kernel| |#2|))) "\\spad{ratDenom(f, [a1,...,an])} removes the \\spad{ai}'s which are algebraic from the denominators in \\spad{f}.") ((|#2| |#2| (|List| |#2|)) "\\spad{ratDenom(f, [a1,...,an])} removes the \\spad{ai}'s which are algebraic kernels from the denominators in \\spad{f}.") ((|#2| |#2| |#2|) "\\spad{ratDenom(f, a)} removes \\spad{a} from the denominators in \\spad{f} if \\spad{a} is an algebraic kernel.") ((|#2| |#2|) "\\spad{ratDenom(f)} rationalizes the denominators appearing in \\spad{f} by moving all the algebraic quantities into the numerators.")) (|rootSplit| ((|#2| |#2|) "\\spad{rootSplit(f)} transforms every radical of the form \\spad{(a/b)**(1/n)} appearing in \\spad{f} into \\spad{a**(1/n) / b**(1/n)}. This transformation is not in general valid for all complex numbers \\spad{a} and \\spad{b}.")) (|coerce| (($ (|SparseMultivariatePolynomial| |#1| (|Kernel| $))) "\\spad{coerce(x)} \\undocumented")) (|denom| (((|SparseMultivariatePolynomial| |#1| (|Kernel| $)) $) "\\spad{denom(x)} \\undocumented")) (|numer| (((|SparseMultivariatePolynomial| |#1| (|Kernel| $)) $) "\\spad{numer(x)} \\undocumented"))) NIL @@ -106,8 +106,8 @@ NIL ((|HasCategory| |#1| (QUOTE (|EuclideanDomain|)))) (|AlgebraGivenByStructuralConstants| R |n| |ls| |gamma|) ((|constructor| (NIL "AlgebraGivenByStructuralConstants implements finite rank algebras over a commutative ring,{} given by the structural constants \\spad{gamma} with respect to a fixed basis \\spad{[a1,..,an]},{} where \\spad{gamma} is an \\spad{n}-vector of \\spad{n} by \\spad{n} matrices \\spad{[(gammaijk) for k in 1..rank()]} defined by \\spad{ai * aj = gammaij1 * a1 + ... + gammaijn * an}. The symbols for the fixed basis have to be given as a list of symbols.")) (|coerce| (($ (|Vector| |#1|)) "\\spad{coerce(v)} converts a vector to a member of the algebra by forming a linear combination with the basis element. Note: the vector is assumed to have length equal to the dimension of the algebra."))) -((|unitsKnown| |has| |#1| (|IntegralDomain|)) (|leftUnitary| . T) (|rightUnitary| . T)) -((|HasCategory| |#1| (QUOTE (|Field|))) (|HasCategory| |#1| (QUOTE (|IntegralDomain|)))) +NIL +((|HasCategory| |#1| (QUOTE (|IntegralDomain|))) (|HasCategory| |#1| (QUOTE (|Field|)))) (|AssociationList| |Key| |Entry|) ((|constructor| (NIL "\\spadtype{AssociationList} implements association lists. These may be viewed as lists of pairs where the first part is a key and the second is the stored value. For example,{} the key might be a string with a persons employee identification number and the value might be a record with personnel data."))) NIL @@ -118,11 +118,11 @@ NIL ((|HasCategory| |#2| (QUOTE (|Algebra| (|Fraction| (|Integer|))))) (|HasCategory| |#2| (QUOTE (|IntegralDomain|))) (|HasCategory| |#2| (QUOTE (|CharacteristicNonZero|))) (|HasCategory| |#2| (QUOTE (|CharacteristicZero|))) (|HasCategory| |#2| (QUOTE (|CommutativeRing|))) (|HasCategory| |#2| (QUOTE (|Field|)))) (|AbelianMonoidRing| R E) ((|constructor| (NIL "Abelian monoid ring elements (not necessarily of finite support) of this ring are of the form formal SUM (r_i * e_i) where the r_i are coefficents and the e_i,{} elements of the ordered abelian monoid,{} are thought of as exponents or monomials. The monomials commute with each other,{} and with the coefficients (which themselves may or may not be commutative). See \\spadtype{FiniteAbelianMonoidRing} for the case of finite support a useful common model for polynomials and power series. Conceptually at least,{} only the non-zero terms are ever operated on.")) (/ (($ $ |#1|) "\\spad{p/c} divides \\spad{p} by the coefficient \\spad{c}.")) (|coefficient| ((|#1| $ |#2|) "\\spad{coefficient(p,e)} extracts the coefficient of the monomial with exponent \\spad{e} from polynomial \\spad{p},{} or returns zero if exponent is not present.")) (|reductum| (($ $) "\\spad{reductum(u)} returns \\spad{u} minus its leading monomial returns zero if handed the zero element.")) (|monomial| (($ |#1| |#2|) "\\spad{monomial(r,e)} makes a term from a coefficient \\spad{r} and an exponent \\spad{e}.")) (|monomial?| (((|Boolean|) $) "\\spad{monomial?(p)} tests if \\spad{p} is a single monomial.")) (|degree| ((|#2| $) "\\spad{degree(p)} returns the maximum of the exponents of the terms of \\spad{p}.")) (|leadingMonomial| (($ $) "\\spad{leadingMonomial(p)} returns the monomial of \\spad{p} with the highest degree.")) (|leadingCoefficient| ((|#1| $) "\\spad{leadingCoefficient(p)} returns the coefficient highest degree term of \\spad{p}."))) -(((|commutative| "*") |has| |#1| (|CommutativeRing|)) (|noZeroDivisors| |has| |#1| (|IntegralDomain|)) (|rightUnitary| . T) (|leftUnitary| . T) (|unitsKnown| . T)) +(((|commutative| "*") |has| |#1| (|CommutativeRing|)) (|noZeroDivisors| |has| |#1| (|IntegralDomain|))) NIL (|AlgebraicNumber|) ((|constructor| (NIL "Algebraic closure of the rational numbers,{} with mathematical =")) (|norm| (($ $ (|List| (|Kernel| $))) "\\spad{norm(f,l)} computes the norm of the algebraic number \\spad{f} with respect to the extension generated by kernels \\spad{l}") (($ $ (|Kernel| $)) "\\spad{norm(f,k)} computes the norm of the algebraic number \\spad{f} with respect to the extension generated by kernel \\spad{k}") (((|SparseUnivariatePolynomial| $) (|SparseUnivariatePolynomial| $) (|List| (|Kernel| $))) "\\spad{norm(p,l)} computes the norm of the polynomial \\spad{p} with respect to the extension generated by kernels \\spad{l}") (((|SparseUnivariatePolynomial| $) (|SparseUnivariatePolynomial| $) (|Kernel| $)) "\\spad{norm(p,k)} computes the norm of the polynomial \\spad{p} with respect to the extension generated by kernel \\spad{k}")) (|reduce| (($ $) "\\spad{reduce(f)} simplifies all the unreduced algebraic numbers present in \\spad{f} by applying their defining relations.")) (|denom| (((|SparseMultivariatePolynomial| (|Integer|) (|Kernel| $)) $) "\\spad{denom(f)} returns the denominator of \\spad{f} viewed as a polynomial in the kernels over \\spad{Z}.")) (|numer| (((|SparseMultivariatePolynomial| (|Integer|) (|Kernel| $)) $) "\\spad{numer(f)} returns the numerator of \\spad{f} viewed as a polynomial in the kernels over \\spad{Z}."))) -((|canonicalsClosed| . T) (|canonicalUnitNormal| . T) (|noZeroDivisors| . T) ((|commutative| "*") . T) (|rightUnitary| . T) (|leftUnitary| . T) (|unitsKnown| . T)) +((|canonicalUnitNormal| . T) (|noZeroDivisors| . T) ((|commutative| "*") . T)) ((|HasCategory| $ (QUOTE (|Ring|))) (|HasCategory| $ (QUOTE (|RetractableTo| (|Integer|))))) (|AnonymousFunction|) ((|constructor| (NIL "This domain implements anonymous functions")) (|body| (((|Syntax|) $) "\\spad{body(f)} returns the body of the unnamed function `f'.")) (|parameters| (((|List| (|Identifier|)) $) "\\spad{parameters(f)} returns the list of parameters bound by `f'."))) @@ -130,7 +130,7 @@ NIL NIL (|AntiSymm| R |lVar|) ((|constructor| (NIL "The domain of antisymmetric polynomials.")) (|degree| (((|NonNegativeInteger|) $) "\\spad{degree(p)} returns the homogeneous degree of \\spad{p}.")) (|retractable?| (((|Boolean|) $) "\\spad{retractable?(p)} tests if \\spad{p} is a 0-form,{} \\spadignore{i.e.} if degree(\\spad{p}) = 0.")) (|homogeneous?| (((|Boolean|) $) "\\spad{homogeneous?(p)} tests if all of the terms of \\spad{p} have the same degree.")) (|exp| (($ (|List| (|Integer|))) "\\spad{exp([i1,...in])} returns \\spad{u_1\\^{i_1} ... u_n\\^{i_n}}")) (|generator| (($ (|NonNegativeInteger|)) "\\spad{generator(n)} returns the \\spad{n}th multiplicative generator,{} a basis term.")) (|coefficient| ((|#1| $ $) "\\spad{coefficient(p,u)} returns the coefficient of the term in \\spad{p} containing the basis term \\spad{u} if such a term exists,{} and 0 otherwise. Error: if the second argument \\spad{u} is not a basis element.")) (|reductum| (($ $) "\\spad{reductum(p)},{} where \\spad{p} is an antisymmetric polynomial,{} returns \\spad{p} minus the leading term of \\spad{p} if \\spad{p} has at least two terms,{} and 0 otherwise.")) (|leadingBasisTerm| (($ $) "\\spad{leadingBasisTerm(p)} returns the leading basis term of antisymmetric polynomial \\spad{p}.")) (|leadingCoefficient| ((|#1| $) "\\spad{leadingCoefficient(p)} returns the leading coefficient of antisymmetric polynomial \\spad{p}."))) -((|unitsKnown| . T)) +NIL NIL (|Any|) ((|constructor| (NIL "\\spadtype{Any} implements a type that packages up objects and their types in objects of \\spadtype{Any}. Roughly speaking that means that if \\spad{s : S} then when converted to \\spadtype{Any},{} the new object will include both the original object and its type. This is a way of converting arbitrary objects into a single type without losing any of the original information. Any object can be converted to one of \\spadtype{Any}. The original object can be recovered by `is-case' pattern matching as exemplified here and \\spad{AnyFunctions1}.")) (|obj| (((|None|) $) "\\spad{obj(a)} essentially returns the original object that was converted to \\spadtype{Any} except that the type is forced to be \\spadtype{None}.")) (|dom| (((|SExpression|) $) "\\spad{dom(a)} returns a \\spadgloss{LISP} form of the type of the original object that was converted to \\spadtype{Any}.")) (|any| (($ (|SExpression|) (|None|)) "\\spad{any(type,object)} is a technical function for creating an \\spad{object} of \\spadtype{Any}. Arugment \\spad{type} is a \\spadgloss{LISP} form for the \\spad{type} of \\spad{object}."))) @@ -201,12 +201,12 @@ NIL NIL NIL (|AttributeRegistry|) -((|constructor| (NIL "This category exports the attributes in the AXIOM Library")) (|canonical| ((|attribute|) "\\spad{canonical} is \\spad{true} if and only if distinct elements have distinct data structures. For example,{} a domain of mathematical objects which has the \\spad{canonical} attribute means that two objects are mathematically equal if and only if their data structures are equal.")) (|multiplicativeValuation| ((|attribute|) "\\spad{multiplicativeValuation} implies \\spad{euclideanSize(a*b)=euclideanSize(a)*euclideanSize(b)}.")) (|additiveValuation| ((|attribute|) "\\spad{additiveValuation} implies \\spad{euclideanSize(a*b)=euclideanSize(a)+euclideanSize(b)}.")) (|noetherian| ((|attribute|) "\\spad{noetherian} is \\spad{true} if all of its ideals are finitely generated.")) (|central| ((|attribute|) "\\spad{central} is \\spad{true} if,{} given an algebra over a ring \\spad{R},{} the image of \\spad{R} is the center of the algebra,{} \\spadignore{i.e.} the set of members of the algebra which commute with all others is precisely the image of \\spad{R} in the algebra.")) (|partiallyOrderedSet| ((|attribute|) "\\spad{partiallyOrderedSet} is \\spad{true} if a set with \\spadop{<} which is transitive,{} but \\spad{not(a < b or a = b)} does not necessarily imply \\spad{b<a}.")) (|arbitraryPrecision| ((|attribute|) "\\spad{arbitraryPrecision} means the user can set the precision for subsequent calculations.")) (|canonicalsClosed| ((|attribute|) "\\spad{canonicalsClosed} is \\spad{true} if \\spad{unitCanonical(a)*unitCanonical(b) = unitCanonical(a*b)}.")) (|canonicalUnitNormal| ((|attribute|) "\\spad{canonicalUnitNormal} is \\spad{true} if we can choose a canonical representative for each class of associate elements,{} that is \\spad{associates?(a,b)} returns \\spad{true} if and only if \\spad{unitCanonical(a) = unitCanonical(b)}.")) (|noZeroDivisors| ((|attribute|) "\\spad{noZeroDivisors} is \\spad{true} if \\spad{x * y \\~~= 0} implies both \\spad{x} and \\spad{y} are non-zero.")) (|rightUnitary| ((|attribute|) "\\spad{rightUnitary} is \\spad{true} if \\spad{x * 1 = x} for all \\spad{x}.")) (|leftUnitary| ((|attribute|) "\\spad{leftUnitary} is \\spad{true} if \\spad{1 * x = x} for all \\spad{x}.")) (|unitsKnown| ((|attribute|) "\\spad{unitsKnown} is \\spad{true} if a monoid (a multiplicative semigroup with a 1) has \\spad{unitsKnown} means that the operation \\spadfun{recip} can only return \"failed\" if its argument is not a unit.")) (|commutative| ((|attribute| "*") "\\spad{commutative(\"*\")} is \\spad{true} if it has an operation \\spad{\"*\": (D,D) -> D} which is commutative."))) -(((|commutative| "*") . T) (|unitsKnown| . T) (|leftUnitary| . T) (|rightUnitary| . T) (|noZeroDivisors| . T) (|canonicalUnitNormal| . T) (|canonicalsClosed| . T) (|arbitraryPrecision| . T) (|partiallyOrderedSet| . T) (|central| . T) (|noetherian| . T) (|additiveValuation| . T) (|multiplicativeValuation| . T) (|NullSquare| . T) (|JacobiIdentity| . T) (|canonical| . T)) +((|constructor| (NIL "This category exports the attributes in the AXIOM Library")) (|canonical| ((|attribute|) "\\spad{canonical} is \\spad{true} if and only if distinct elements have distinct data structures. For example,{} a domain of mathematical objects which has the \\spad{canonical} attribute means that two objects are mathematically equal if and only if their data structures are equal.")) (|multiplicativeValuation| ((|attribute|) "\\spad{multiplicativeValuation} implies \\spad{euclideanSize(a*b)=euclideanSize(a)*euclideanSize(b)}.")) (|additiveValuation| ((|attribute|) "\\spad{additiveValuation} implies \\spad{euclideanSize(a*b)=euclideanSize(a)+euclideanSize(b)}.")) (|partiallyOrderedSet| ((|attribute|) "\\spad{partiallyOrderedSet} is \\spad{true} if a set with \\spadop{<} which is transitive,{} but \\spad{not(a < b or a = b)} does not necessarily imply \\spad{b<a}.")) (|canonicalUnitNormal| ((|attribute|) "\\spad{canonicalUnitNormal} is \\spad{true} if we can choose a canonical representative for each class of associate elements,{} that is \\spad{associates?(a,b)} returns \\spad{true} if and only if \\spad{unitCanonical(a) = unitCanonical(b)}.")) (|noZeroDivisors| ((|attribute|) "\\spad{noZeroDivisors} is \\spad{true} if \\spad{x * y \\~~= 0} implies both \\spad{x} and \\spad{y} are non-zero.")) (|commutative| ((|attribute| "*") "\\spad{commutative(\"*\")} is \\spad{true} if it has an operation \\spad{\"*\": (D,D) -> D} which is commutative."))) +(((|commutative| "*") . T) (|noZeroDivisors| . T) (|canonicalUnitNormal| . T) (|partiallyOrderedSet| . T) (|additiveValuation| . T) (|multiplicativeValuation| . T) (|canonical| . T)) NIL (|Automorphism| R) ((|constructor| (NIL "Automorphism \\spad{R} is the multiplicative group of automorphisms of \\spad{R}.")) (|morphism| (($ (|Mapping| |#1| |#1| (|Integer|))) "\\spad{morphism(f)} returns the morphism given by \\spad{f^n(x) = f(x,n)}.") (($ (|Mapping| |#1| |#1|) (|Mapping| |#1| |#1|)) "\\spad{morphism(f, g)} returns the invertible morphism given by \\spad{f},{} where \\spad{g} is the inverse of \\spad{f}..") (($ (|Mapping| |#1| |#1|)) "\\spad{morphism(f)} returns the non-invertible morphism given by \\spad{f}."))) -((|unitsKnown| . T)) +NIL NIL (|BalancedFactorisation| R UP) ((|constructor| (NIL "This package provides balanced factorisations of polynomials.")) (|balancedFactorisation| (((|Factored| |#2|) |#2| (|List| |#2|)) "\\spad{balancedFactorisation(a, [b1,...,bn])} returns a factorisation \\spad{a = p1^e1 ... pm^em} such that each \\spad{pi} is balanced with respect to \\spad{[b1,...,bm]}.") (((|Factored| |#2|) |#2| |#2|) "\\spad{balancedFactorisation(a, b)} returns a factorisation \\spad{a = p1^e1 ... pm^em} such that each \\spad{pi} is balanced with respect to \\spad{b}."))) @@ -238,8 +238,8 @@ NIL NIL (|BinaryExpansion|) ((|constructor| (NIL "This domain allows rational numbers to be presented as repeating binary expansions.")) (|binary| (($ (|Fraction| (|Integer|))) "\\spad{binary(r)} converts a rational number to a binary expansion.")) (|fractionPart| (((|Fraction| (|Integer|)) $) "\\spad{fractionPart(b)} returns the fractional part of a binary expansion."))) -((|canonicalsClosed| . T) (|canonicalUnitNormal| . T) (|noZeroDivisors| . T) ((|commutative| "*") . T) (|rightUnitary| . T) (|leftUnitary| . T) (|unitsKnown| . T)) -(#1=(|HasCategory| #2=(|Integer|) (QUOTE (|PolynomialFactorizationExplicit|))) (|HasCategory| #2# (QUOTE (|RetractableTo| #3=(|Symbol|)))) #4=(|HasCategory| #2# #5=(QUOTE (|CharacteristicNonZero|))) (|HasCategory| #2# (QUOTE (|CharacteristicZero|))) (|HasCategory| #2# (QUOTE (|ConvertibleTo| (|InputForm|)))) (|HasCategory| #2# (QUOTE (|RealConstant|))) #6=(|HasCategory| #2# (QUOTE (|OrderedIntegralDomain|))) #7=(|HasCategory| #2# (QUOTE (|OrderedSet|))) (OR #6# #7#) (|HasCategory| #2# (QUOTE (|RetractableTo| #2#))) (|HasCategory| #2# (QUOTE (|StepThrough|))) (|HasCategory| #2# (QUOTE (|PatternMatchable| #8=(|Float|)))) (|HasCategory| #2# (QUOTE (|PatternMatchable| #2#))) (|HasCategory| #2# (QUOTE (|ConvertibleTo| (|Pattern| #8#)))) (|HasCategory| #2# (QUOTE (|ConvertibleTo| (|Pattern| #2#)))) (|HasCategory| #2# (QUOTE (|DifferentialSpace|))) (|HasCategory| #2# (QUOTE (|PartialDifferentialSpace| #3#))) (|HasCategory| #2# (QUOTE (|DifferentialRing|))) (|HasCategory| #2# (QUOTE (|PartialDifferentialRing| #3#))) (|HasCategory| #2# (QUOTE (|InnerEvalable| #3# #2#))) (|HasCategory| #2# (QUOTE (|Evalable| #2#))) (|HasCategory| #2# (QUOTE (|Eltable| #2# #2#))) (|HasCategory| #2# (QUOTE (|EuclideanDomain|))) (|HasCategory| #2# (QUOTE (|IntegerNumberSystem|))) (|HasCategory| #2# (QUOTE (|LinearlyExplicitRingOver| #2#))) #9=(AND (|HasCategory| $ #5#) #1#) (OR #9# #4#)) +((|canonicalUnitNormal| . T) (|noZeroDivisors| . T) ((|commutative| "*") . T)) +(#1=(|HasCategory| #2=(|Integer|) (QUOTE (|PolynomialFactorizationExplicit|))) (|HasCategory| #2# (QUOTE (|RetractableTo| #3=(|Symbol|)))) #4=(|HasCategory| #2# #5=(QUOTE (|CharacteristicNonZero|))) (|HasCategory| #2# (QUOTE (|CharacteristicZero|))) (|HasCategory| #2# (QUOTE (|ConvertibleTo| (|InputForm|)))) (|HasCategory| #2# (QUOTE (|RealConstant|))) #6=(|HasCategory| #2# (QUOTE (|OrderedIntegralDomain|))) #7=(|HasCategory| #2# (QUOTE (|OrderedSet|))) (OR #6# #7#) (|HasCategory| #2# (QUOTE (|RetractableTo| #2#))) (|HasCategory| #2# (QUOTE (|StepThrough|))) (|HasCategory| #2# (QUOTE (|PatternMatchable| #8=(|Float|)))) (|HasCategory| #2# (QUOTE (|PatternMatchable| #2#))) (|HasCategory| #2# (QUOTE (|ConvertibleTo| (|Pattern| #8#)))) (|HasCategory| #2# (QUOTE (|ConvertibleTo| (|Pattern| #2#)))) (|HasCategory| #2# (QUOTE (|PartialDifferentialSpace| #3#))) (|HasCategory| #2# (QUOTE (|DifferentialSpace|))) (|HasCategory| #2# (QUOTE (|DifferentialRing|))) (|HasCategory| #2# (QUOTE (|PartialDifferentialRing| #3#))) (|HasCategory| #2# (QUOTE (|InnerEvalable| #3# #2#))) (|HasCategory| #2# (QUOTE (|Evalable| #2#))) (|HasCategory| #2# (QUOTE (|Eltable| #2# #2#))) (|HasCategory| #2# (QUOTE (|EuclideanDomain|))) (|HasCategory| #2# (QUOTE (|IntegerNumberSystem|))) (|HasCategory| #2# (QUOTE (|LinearlyExplicitRingOver| #2#))) #9=(AND (|HasCategory| $ #5#) #1#) (OR #9# #4#)) (|Binding|) ((|constructor| (NIL "\\indented{1}{Author: Gabriel Dos Reis} Date Created: October 24,{} 2007 Date Last Modified: January 18,{} 2008. A `Binding' is a name asosciated with a collection of properties.")) (|binding| (($ (|Identifier|) (|List| (|Property|))) "\\spad{binding(n,props)} constructs a binding with name `n' and property list `props'.")) (|properties| (((|List| (|Property|)) $) "\\spad{properties(b)} returns the properties associated with binding \\spad{b}.")) (|name| (((|Identifier|) $) "\\spad{name(b)} returns the name of binding \\spad{b}"))) NIL @@ -257,8 +257,8 @@ NIL NIL ((AND (|HasCategory| #1=(|Boolean|) (QUOTE (|Evalable| #1#))) #2=(|HasCategory| #1# (QUOTE (|SetCategory|)))) (|HasCategory| #1# (QUOTE (|ConvertibleTo| (|InputForm|)))) #3=(|HasCategory| #1# #4=(QUOTE (|OrderedSet|))) (|HasCategory| (|Integer|) #4#) #5=(|HasCategory| #1# (QUOTE (|BasicType|))) (|HasCategory| #1# (QUOTE (|CoercibleTo| (|OutputForm|)))) #2# (AND #6=(|HasCategory| $ (QUOTE (|ShallowlyMutableAggregate| #1#))) #3#) #7=(|HasCategory| $ (QUOTE (|FiniteAggregate| #1#))) (AND #7# #5#) #6#) (|BiModule| R S) -((|constructor| (NIL "A \\spadtype{BiModule} is both a left and right module with respect to potentially different rings. \\blankline")) (|rightUnitary| ((|attribute|) "\\spad{x * 1 = x}")) (|leftUnitary| ((|attribute|) "\\spad{1 * x = x}"))) -((|leftUnitary| . T) (|rightUnitary| . T)) +((|constructor| (NIL "A \\spadtype{BiModule} is both a left and right module with respect to potentially different rings. \\blankline"))) +NIL NIL (|BooleanLogic&| S) ((|constructor| (NIL "This is the category of Boolean logic structures.")) (|or| (($ $ $) "\\spad{x or y} returns the disjunction of \\spad{x} and \\spad{y}.")) (|and| (($ $ $) "\\spad{x and y} returns the conjunction of \\spad{x} and \\spad{y}.")) (|not| (($ $) "\\spad{not x} returns the complement or negation of \\spad{x}."))) @@ -286,12 +286,12 @@ NIL NIL (|BalancedPAdicInteger| |p|) ((|constructor| (NIL "Stream-based implementation of Zp: \\spad{p}-adic numbers are represented as sum(\\spad{i} = 0..,{} a[\\spad{i}] * p^i),{} where the a[\\spad{i}] lie in -(\\spad{p} - 1)\\spad{/2},{}...,{}(\\spad{p} - 1)\\spad{/2}."))) -((|noZeroDivisors| . T) ((|commutative| "*") . T) (|rightUnitary| . T) (|leftUnitary| . T) (|unitsKnown| . T)) +((|noZeroDivisors| . T) ((|commutative| "*") . T)) NIL (|BalancedPAdicRational| |p|) ((|constructor| (NIL "Stream-based implementation of Qp: numbers are represented as sum(\\spad{i} = \\spad{k}..,{} a[\\spad{i}] * p^i),{} where the a[\\spad{i}] lie in -(\\spad{p} - 1)\\spad{/2},{}...,{}(\\spad{p} - 1)\\spad{/2}."))) -((|canonicalsClosed| . T) (|canonicalUnitNormal| . T) (|noZeroDivisors| . T) ((|commutative| "*") . T) (|rightUnitary| . T) (|leftUnitary| . T) (|unitsKnown| . T)) -(#1=(|HasCategory| #2=(|BalancedPAdicInteger| |#1|) (QUOTE (|PolynomialFactorizationExplicit|))) (|HasCategory| #2# (QUOTE (|RetractableTo| #3=(|Symbol|)))) #4=(|HasCategory| #2# #5=(QUOTE (|CharacteristicNonZero|))) (|HasCategory| #2# (QUOTE (|CharacteristicZero|))) (|HasCategory| #2# (QUOTE (|ConvertibleTo| (|InputForm|)))) (|HasCategory| #2# (QUOTE (|RealConstant|))) #6=(|HasCategory| #2# (QUOTE (|OrderedIntegralDomain|))) #7=(|HasCategory| #2# (QUOTE (|OrderedSet|))) (OR #6# #7#) (|HasCategory| #2# (QUOTE (|RetractableTo| #8=(|Integer|)))) (|HasCategory| #2# (QUOTE (|StepThrough|))) (|HasCategory| #2# (QUOTE (|PatternMatchable| #9=(|Float|)))) (|HasCategory| #2# (QUOTE (|PatternMatchable| #8#))) (|HasCategory| #2# (QUOTE (|ConvertibleTo| (|Pattern| #9#)))) (|HasCategory| #2# (QUOTE (|ConvertibleTo| (|Pattern| #8#)))) (|HasCategory| #2# (QUOTE (|LinearlyExplicitRingOver| #8#))) (|HasCategory| #2# (QUOTE (|DifferentialSpace|))) (|HasCategory| #2# (QUOTE (|PartialDifferentialSpace| #3#))) (|HasCategory| #2# (QUOTE (|DifferentialRing|))) (|HasCategory| #2# (QUOTE (|PartialDifferentialRing| #3#))) (|HasCategory| #2# (|%list| (QUOTE |InnerEvalable|) (QUOTE #3#) #10=(|%list| (QUOTE |BalancedPAdicInteger|) (|devaluate| |#1|)))) (|HasCategory| #2# (|%list| (QUOTE |Evalable|) #10#)) (|HasCategory| #2# (|%list| (QUOTE |Eltable|) #10# #10#)) (|HasCategory| #2# (QUOTE (|EuclideanDomain|))) (|HasCategory| #2# (QUOTE (|IntegerNumberSystem|))) #11=(AND (|HasCategory| $ #5#) #1#) (OR #11# #4#)) +((|canonicalUnitNormal| . T) (|noZeroDivisors| . T) ((|commutative| "*") . T)) +(#1=(|HasCategory| #2=(|BalancedPAdicInteger| |#1|) (QUOTE (|PolynomialFactorizationExplicit|))) (|HasCategory| #2# (QUOTE (|RetractableTo| #3=(|Symbol|)))) #4=(|HasCategory| #2# #5=(QUOTE (|CharacteristicNonZero|))) (|HasCategory| #2# (QUOTE (|CharacteristicZero|))) (|HasCategory| #2# (QUOTE (|ConvertibleTo| (|InputForm|)))) (|HasCategory| #2# (QUOTE (|RealConstant|))) #6=(|HasCategory| #2# (QUOTE (|OrderedIntegralDomain|))) #7=(|HasCategory| #2# (QUOTE (|OrderedSet|))) (OR #6# #7#) (|HasCategory| #2# (QUOTE (|RetractableTo| #8=(|Integer|)))) (|HasCategory| #2# (QUOTE (|StepThrough|))) (|HasCategory| #2# (QUOTE (|PatternMatchable| #9=(|Float|)))) (|HasCategory| #2# (QUOTE (|PatternMatchable| #8#))) (|HasCategory| #2# (QUOTE (|ConvertibleTo| (|Pattern| #9#)))) (|HasCategory| #2# (QUOTE (|ConvertibleTo| (|Pattern| #8#)))) (|HasCategory| #2# (QUOTE (|LinearlyExplicitRingOver| #8#))) (|HasCategory| #2# (QUOTE (|PartialDifferentialSpace| #3#))) (|HasCategory| #2# (QUOTE (|DifferentialSpace|))) (|HasCategory| #2# (QUOTE (|DifferentialRing|))) (|HasCategory| #2# (QUOTE (|PartialDifferentialRing| #3#))) (|HasCategory| #2# (|%list| (QUOTE |InnerEvalable|) (QUOTE #3#) #10=(|%list| (QUOTE |BalancedPAdicInteger|) (|devaluate| |#1|)))) (|HasCategory| #2# (|%list| (QUOTE |Evalable|) #10#)) (|HasCategory| #2# (|%list| (QUOTE |Eltable|) #10# #10#)) (|HasCategory| #2# (QUOTE (|EuclideanDomain|))) (|HasCategory| #2# (QUOTE (|IntegerNumberSystem|))) #11=(AND (|HasCategory| $ #5#) #1#) (OR #11# #4#)) (|BinaryRecursiveAggregate&| A S) ((|constructor| (NIL "A binary-recursive aggregate has 0,{} 1 or 2 children and serves as a model for a binary tree or a doubly-linked aggregate structure")) (|setright!| (($ $ $) "\\spad{setright!(a,x)} sets the right child of \\spad{t} to be \\spad{x}.")) (|setleft!| (($ $ $) "\\spad{setleft!(a,b)} sets the left child of \\axiom{a} to be \\spad{b}.")) (|setelt| (($ $ "right" $) "\\spad{setelt(a,\"right\",b)} (also written \\axiom{\\spad{b} . right := \\spad{b}}) is equivalent to \\axiom{setright!(a,{}\\spad{b})}.") (($ $ "left" $) "\\spad{setelt(a,\"left\",b)} (also written \\axiom{a . left := \\spad{b}}) is equivalent to \\axiom{setleft!(a,{}\\spad{b})}.")) (|right| (($ $) "\\spad{right(a)} returns the right child.")) (|elt| (($ $ "right") "\\spad{elt(a,\"right\")} (also written: \\axiom{a . right}) is equivalent to \\axiom{right(a)}.") (($ $ "left") "\\spad{elt(u,\"left\")} (also written: \\axiom{a . left}) is equivalent to \\axiom{left(a)}.")) (|left| (($ $) "\\spad{left(u)} returns the left child."))) NIL @@ -345,7 +345,7 @@ NIL NIL NIL (|CancellationAbelianMonoid|) -((|constructor| (NIL "This is an \\spadtype{AbelianMonoid} with the cancellation property,{} \\spadignore{i.e.} \\spad{ a+b = a+c => b=c }. This is formalised by the partial subtraction operator,{} which satisfies the axioms listed below: \\blankline")) (|subtractIfCan| (((|Union| $ "failed") $ $) "\\spad{subtractIfCan(x, y)} returns an element \\spad{z} such that \\spad{z+y=x} or \"failed\" if no such element exists."))) +((|constructor| (NIL "This is an \\spadtype{AbelianMonoid} with the cancellation property,{} \\spadignore{i.e.} \\spad{ a+b = a+c => b=c }. This is formalised by the partial subtraction operator,{} which satisfies the axioms listed below: \\blankline")) (|subtractIfCan| (((|Maybe| $) $ $) "\\spad{subtractIfCan(x, y)} returns an element \\spad{z} such that \\spad{z+y=x} or \\spad{nothing} if no such element exists."))) NIL NIL (|CachableSet|) @@ -402,7 +402,7 @@ NIL NIL (|CharacteristicNonZero|) ((|constructor| (NIL "Rings of Characteristic Non Zero")) (|charthRoot| (((|Maybe| $) $) "\\spad{charthRoot(x)} returns the \\spad{p}th root of \\spad{x} where \\spad{p} is the characteristic of the ring."))) -((|unitsKnown| . T)) +NIL NIL (|CharacteristicPolynomialPackage| R) ((|constructor| (NIL "This package provides a characteristicPolynomial function for any matrix over a commutative ring.")) (|characteristicPolynomial| ((|#1| (|Matrix| |#1|) |#1|) "\\spad{characteristicPolynomial(m,r)} computes the characteristic polynomial of the matrix \\spad{m} evaluated at the point \\spad{r}. In particular,{} if \\spad{r} is the polynomial 'x,{} then it returns the characteristic polynomial expressed as a polynomial in 'x."))) @@ -410,7 +410,7 @@ NIL NIL (|CharacteristicZero|) ((|constructor| (NIL "Rings of Characteristic Zero."))) -((|unitsKnown| . T)) +NIL NIL (|ChangeOfVariable| F UP UPUP) ((|constructor| (NIL "Tools to send a point to infinity on an algebraic curve.")) (|chvar| (((|Record| (|:| |func| |#3|) (|:| |poly| |#3|) (|:| |c1| (|Fraction| |#2|)) (|:| |c2| (|Fraction| |#2|)) (|:| |deg| (|NonNegativeInteger|))) |#3| |#3|) "\\spad{chvar(f(x,y), p(x,y))} returns \\spad{[g(z,t), q(z,t), c1(z), c2(z), n]} such that under the change of variable \\spad{x = c1(z)},{} \\spad{y = t * c2(z)},{} one gets \\spad{f(x,y) = g(z,t)}. The algebraic relation between \\spad{x} and \\spad{y} is \\spad{p(x, y) = 0}. The algebraic relation between \\spad{z} and \\spad{t} is \\spad{q(z, t) = 0}.")) (|eval| ((|#3| |#3| (|Fraction| |#2|) (|Fraction| |#2|)) "\\spad{eval(p(x,y), f(x), g(x))} returns \\spad{p(f(x), y * g(x))}.")) (|goodPoint| ((|#1| |#3| |#3|) "\\spad{goodPoint(p, q)} returns an integer a such that a is neither a pole of \\spad{p(x,y)} nor a branch point of \\spad{q(x,y) = 0}.")) (|rootPoly| (((|Record| (|:| |exponent| (|NonNegativeInteger|)) (|:| |coef| (|Fraction| |#2|)) (|:| |radicand| |#2|)) (|Fraction| |#2|) (|NonNegativeInteger|)) "\\spad{rootPoly(g, n)} returns \\spad{[m, c, P]} such that \\spad{c * g ** (1/n) = P ** (1/m)} thus if \\spad{y**n = g},{} then \\spad{z**m = P} where \\spad{z = c * y}.")) (|radPoly| (((|Union| (|Record| (|:| |radicand| (|Fraction| |#2|)) (|:| |deg| (|NonNegativeInteger|))) "failed") |#3|) "\\spad{radPoly(p(x, y))} returns \\spad{[c(x), n]} if \\spad{p} is of the form \\spad{y**n - c(x)},{} \"failed\" otherwise.")) (|mkIntegral| (((|Record| (|:| |coef| (|Fraction| |#2|)) (|:| |poly| |#3|)) |#3|) "\\spad{mkIntegral(p(x,y))} returns \\spad{[c(x), q(x,z)]} such that \\spad{z = c * y} is integral. The algebraic relation between \\spad{x} and \\spad{y} is \\spad{p(x, y) = 0}. The algebraic relation between \\spad{x} and \\spad{z} is \\spad{q(x, z) = 0}."))) @@ -429,8 +429,8 @@ NIL NIL NIL (|CliffordAlgebra| |n| K Q) -((|constructor| (NIL "CliffordAlgebra(\\spad{n},{} \\spad{K},{} \\spad{Q}) defines a vector space of dimension \\spad{2**n} over \\spad{K},{} given a quadratic form \\spad{Q} on \\spad{K**n}. \\blankline If \\spad{e[i]},{} \\spad{1<=i<=n} is a basis for \\spad{K**n} then \\indented{3}{1,{} \\spad{e[i]} (\\spad{1<=i<=n}),{} \\spad{e[i1]*e[i2]}} (\\spad{1<=i1<i2<=n}),{}...,{}\\spad{e[1]*e[2]*..*e[n]} is a basis for the Clifford Algebra. \\blankline The algebra is defined by the relations \\indented{3}{\\spad{e[i]*e[j] = -e[j]*e[i]}\\space{2}(\\spad{i \\~~= j}),{}} \\indented{3}{\\spad{e[i]*e[i] = Q(e[i])}} \\blankline Examples of Clifford Algebras are: gaussians,{} quaternions,{} exterior algebras and spin algebras.")) (|recip| (((|Union| $ "failed") $) "\\spad{recip(x)} computes the multiplicative inverse of \\spad{x} or \"failed\" if \\spad{x} is not invertible.")) (|coefficient| ((|#2| $ (|List| (|PositiveInteger|))) "\\spad{coefficient(x,[i1,i2,...,iN])} extracts the coefficient of \\spad{e(i1)*e(i2)*...*e(iN)} in \\spad{x}.")) (|monomial| (($ |#2| (|List| (|PositiveInteger|))) "\\spad{monomial(c,[i1,i2,...,iN])} produces the value given by \\spad{c*e(i1)*e(i2)*...*e(iN)}.")) (|e| (($ (|PositiveInteger|)) "\\spad{e(n)} produces the appropriate unit element."))) -((|leftUnitary| . T) (|rightUnitary| . T) (|unitsKnown| . T)) +((|constructor| (NIL "CliffordAlgebra(\\spad{n},{} \\spad{K},{} \\spad{Q}) defines a vector space of dimension \\spad{2**n} over \\spad{K},{} given a quadratic form \\spad{Q} on \\spad{K**n}. \\blankline If \\spad{e[i]},{} \\spad{1<=i<=n} is a basis for \\spad{K**n} then \\indented{3}{1,{} \\spad{e[i]} (\\spad{1<=i<=n}),{} \\spad{e[i1]*e[i2]}} (\\spad{1<=i1<i2<=n}),{}...,{}\\spad{e[1]*e[2]*..*e[n]} is a basis for the Clifford Algebra. \\blankline The algebra is defined by the relations \\indented{3}{\\spad{e[i]*e[j] = -e[j]*e[i]}\\space{2}(\\spad{i \\~~= j}),{}} \\indented{3}{\\spad{e[i]*e[i] = Q(e[i])}} \\blankline Examples of Clifford Algebras are: gaussians,{} quaternions,{} exterior algebras and spin algebras.")) (|coefficient| ((|#2| $ (|List| (|PositiveInteger|))) "\\spad{coefficient(x,[i1,i2,...,iN])} extracts the coefficient of \\spad{e(i1)*e(i2)*...*e(iN)} in \\spad{x}.")) (|monomial| (($ |#2| (|List| (|PositiveInteger|))) "\\spad{monomial(c,[i1,i2,...,iN])} produces the value given by \\spad{c*e(i1)*e(i2)*...*e(iN)}.")) (|e| (($ (|PositiveInteger|)) "\\spad{e(n)} produces the appropriate unit element."))) +NIL NIL (|TwoDimensionalPlotClipping|) ((|constructor| (NIL "\\indented{1}{The purpose of this package is to provide reasonable plots of} functions with singularities.")) (|clipWithRanges| (((|Record| (|:| |brans| (|List| (|List| (|Point| (|DoubleFloat|))))) (|:| |xValues| (|Segment| (|DoubleFloat|))) (|:| |yValues| (|Segment| (|DoubleFloat|)))) (|List| (|List| (|Point| (|DoubleFloat|)))) (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|)) "\\spad{clipWithRanges(pointLists,xMin,xMax,yMin,yMax)} performs clipping on a list of lists of points,{} \\spad{pointLists}. Clipping is done within the specified ranges of \\spad{xMin},{} \\spad{xMax} and \\spad{yMin},{} \\spad{yMax}. This function is used internally by the \\fakeAxiomFun{iClipParametric} subroutine in this package.")) (|clipParametric| (((|Record| (|:| |brans| (|List| (|List| (|Point| (|DoubleFloat|))))) (|:| |xValues| (|Segment| (|DoubleFloat|))) (|:| |yValues| (|Segment| (|DoubleFloat|)))) (|Plot|) (|Fraction| (|Integer|)) (|Fraction| (|Integer|))) "\\spad{clipParametric(p,frac,sc)} performs two-dimensional clipping on a plot,{} \\spad{p},{} from the domain \\spadtype{Plot} for the parametric curve \\spad{x = f(t)},{} \\spad{y = g(t)}; the fraction parameter is specified by \\spad{frac} and the scale parameter is specified by \\spad{sc} for use in the \\fakeAxiomFun{iClipParametric} subroutine,{} which is called by this function.") (((|Record| (|:| |brans| (|List| (|List| (|Point| (|DoubleFloat|))))) (|:| |xValues| (|Segment| (|DoubleFloat|))) (|:| |yValues| (|Segment| (|DoubleFloat|)))) (|Plot|)) "\\spad{clipParametric(p)} performs two-dimensional clipping on a plot,{} \\spad{p},{} from the domain \\spadtype{Plot} for the parametric curve \\spad{x = f(t)},{} \\spad{y = g(t)}; the default parameters \\spad{1/2} for the fraction and \\spad{5/1} for the scale are used in the \\fakeAxiomFun{iClipParametric} subroutine,{} which is called by this function.")) (|clip| (((|Record| (|:| |brans| (|List| (|List| (|Point| (|DoubleFloat|))))) (|:| |xValues| (|Segment| (|DoubleFloat|))) (|:| |yValues| (|Segment| (|DoubleFloat|)))) (|List| (|List| (|Point| (|DoubleFloat|))))) "\\spad{clip(ll)} performs two-dimensional clipping on a list of lists of points,{} \\spad{ll}; the default parameters \\spad{1/2} for the fraction and \\spad{5/1} for the scale are used in the \\fakeAxiomFun{iClipParametric} subroutine,{} which is called by this function.") (((|Record| (|:| |brans| (|List| (|List| (|Point| (|DoubleFloat|))))) (|:| |xValues| (|Segment| (|DoubleFloat|))) (|:| |yValues| (|Segment| (|DoubleFloat|)))) (|List| (|Point| (|DoubleFloat|)))) "\\spad{clip(l)} performs two-dimensional clipping on a curve \\spad{l},{} which is a list of points; the default parameters \\spad{1/2} for the fraction and \\spad{5/1} for the scale are used in the \\fakeAxiomFun{iClipParametric} subroutine,{} which is called by this function.") (((|Record| (|:| |brans| (|List| (|List| (|Point| (|DoubleFloat|))))) (|:| |xValues| (|Segment| (|DoubleFloat|))) (|:| |yValues| (|Segment| (|DoubleFloat|)))) (|Plot|) (|Fraction| (|Integer|)) (|Fraction| (|Integer|))) "\\spad{clip(p,frac,sc)} performs two-dimensional clipping on a plot,{} \\spad{p},{} from the domain \\spadtype{Plot} for the graph of one variable \\spad{y = f(x)}; the fraction parameter is specified by \\spad{frac} and the scale parameter is specified by \\spad{sc} for use in the \\spadfun{clip} function.") (((|Record| (|:| |brans| (|List| (|List| (|Point| (|DoubleFloat|))))) (|:| |xValues| (|Segment| (|DoubleFloat|))) (|:| |yValues| (|Segment| (|DoubleFloat|)))) (|Plot|)) "\\spad{clip(p)} performs two-dimensional clipping on a plot,{} \\spad{p},{} from the domain \\spadtype{Plot} for the graph of one variable,{} \\spad{y = f(x)}; the default parameters \\spad{1/4} for the fraction and \\spad{5/1} for the scale are used in the \\spadfun{clip} function."))) @@ -494,7 +494,7 @@ NIL ((|HasCategory| |#2| (QUOTE (|PolynomialFactorizationExplicit|))) (|HasCategory| |#2| (QUOTE (|IntegerNumberSystem|))) (|HasCategory| |#2| (QUOTE (|RadicalCategory|))) (|HasCategory| |#2| (QUOTE (|TranscendentalFunctionCategory|))) (|HasCategory| |#2| (QUOTE (|RealNumberSystem|))) (|HasCategory| |#2| (QUOTE (|RealConstant|))) (|HasCategory| |#2| (QUOTE (|CharacteristicNonZero|))) (|HasCategory| |#2| (QUOTE (|CharacteristicZero|))) (|HasCategory| |#2| (QUOTE (|ConvertibleTo| (|InputForm|)))) (|HasCategory| |#2| (QUOTE (|Field|))) (|HasAttribute| |#2| (QUOTE |additiveValuation|)) (|HasAttribute| |#2| (QUOTE |multiplicativeValuation|)) (|HasCategory| |#2| (QUOTE (|EuclideanDomain|))) (|HasCategory| |#2| (QUOTE (|IntegralDomain|)))) (|ComplexCategory| R) ((|constructor| (NIL "This category represents the extension of a ring by a square root of \\spad{-1}.")) (|rationalIfCan| (((|Union| (|Fraction| (|Integer|)) "failed") $) "\\spad{rationalIfCan(x)} returns \\spad{x} as a rational number,{} or \"failed\" if \\spad{x} is not a rational number.")) (|rational| (((|Fraction| (|Integer|)) $) "\\spad{rational(x)} returns \\spad{x} as a rational number. Error: if \\spad{x} is not a rational number.")) (|rational?| (((|Boolean|) $) "\\spad{rational?(x)} tests if \\spad{x} is a rational number.")) (|polarCoordinates| (((|Record| (|:| |r| |#1|) (|:| |phi| |#1|)) $) "\\spad{polarCoordinates(x)} returns (\\spad{r},{} phi) such that \\spad{x} = \\spad{r} * exp(\\%\\spad{i} * phi).")) (|argument| ((|#1| $) "\\spad{argument(x)} returns the angle made by (0,{}1) and (0,{}\\spad{x}).")) (|abs| (($ $) "\\spad{abs(x)} returns the absolute value of \\spad{x} = sqrt(norm(\\spad{x})).")) (|exquo| (((|Union| $ "failed") $ |#1|) "\\spad{exquo(x, r)} returns the exact quotient of \\spad{x} by \\spad{r},{} or \"failed\" if \\spad{r} does not divide \\spad{x} exactly.")) (|norm| ((|#1| $) "\\spad{norm(x)} returns \\spad{x} * conjugate(\\spad{x})")) (|real| ((|#1| $) "\\spad{real(x)} returns real part of \\spad{x}.")) (|imag| ((|#1| $) "\\spad{imag(x)} returns imaginary part of \\spad{x}.")) (|conjugate| (($ $) "\\spad{conjugate(x + \\%i y)} returns \\spad{x} - \\%\\spad{i} \\spad{y}.")) (|imaginary| (($) "\\spad{imaginary()} = sqrt(\\spad{-1}) = \\%\\spad{i}.")) (|complex| (($ |#1| |#1|) "\\spad{complex(x,y)} constructs \\spad{x} + \\%i*y.") ((|attribute|) "indicates that \\% has sqrt(\\spad{-1})"))) -((|noZeroDivisors| OR (|has| |#1| (|IntegralDomain|)) (AND (|has| |#1| (|EuclideanDomain|)) (|has| |#1| (|PolynomialFactorizationExplicit|)))) (|canonicalUnitNormal| |has| |#1| . #1=((|Field|))) (|canonicalsClosed| |has| |#1| . #1#) (|additiveValuation| |has| |#1| (ATTRIBUTE |additiveValuation|)) (|multiplicativeValuation| |has| |#1| (ATTRIBUTE |multiplicativeValuation|)) (|complex| . T) ((|commutative| "*") . T) (|rightUnitary| . T) (|leftUnitary| . T) (|unitsKnown| . T)) +((|noZeroDivisors| OR (|has| |#1| (|IntegralDomain|)) (AND (|has| |#1| (|EuclideanDomain|)) (|has| |#1| (|PolynomialFactorizationExplicit|)))) (|canonicalUnitNormal| |has| |#1| (|Field|)) (|additiveValuation| |has| |#1| (ATTRIBUTE |additiveValuation|)) (|multiplicativeValuation| |has| |#1| (ATTRIBUTE |multiplicativeValuation|)) (|complex| . T) ((|commutative| "*") . T)) NIL (|ComplexFactorization| RR PR) ((|constructor| (NIL "\\indented{1}{Author:} Date Created: Date Last Updated: Basic Functions: Related Constructors: Complex,{} UnivariatePolynomial Also See: AMS Classifications: Keywords: complex,{} polynomial factorization,{} factor References:")) (|factor| (((|Factored| |#2|) |#2|) "\\spad{factor(p)} factorizes the polynomial \\spad{p} with complex coefficients."))) @@ -506,8 +506,8 @@ NIL NIL (|Complex| R) ((|constructor| (NIL "\\spadtype {Complex(R)} creates the domain of elements of the form \\spad{a + b * i} where \\spad{a} and \\spad{b} come from the ring \\spad{R},{} and \\spad{i} is a new element such that \\spad{i**2 = -1}."))) -((|noZeroDivisors| OR (|has| |#1| (|IntegralDomain|)) (AND (|has| |#1| (|EuclideanDomain|)) (|has| |#1| (|PolynomialFactorizationExplicit|)))) (|canonicalUnitNormal| |has| |#1| . #1=((|Field|))) (|canonicalsClosed| |has| |#1| . #1#) (|additiveValuation| |has| |#1| (ATTRIBUTE |additiveValuation|)) (|multiplicativeValuation| |has| |#1| (ATTRIBUTE |multiplicativeValuation|)) (|complex| . T) ((|commutative| "*") . T) (|rightUnitary| . T) (|leftUnitary| . T) (|unitsKnown| . T)) -(#1=(|HasCategory| |#1| #2=(QUOTE (|CharacteristicNonZero|))) (|HasCategory| |#1| (QUOTE (|CharacteristicZero|))) #3=(|HasCategory| |#1| (QUOTE (|FiniteFieldCategory|))) (OR #4=(|HasCategory| |#1| (QUOTE (|Field|))) #3#) #5=(|HasCategory| |#1| (QUOTE (|IntegralDomain|))) #4# (|HasCategory| |#1| (QUOTE (|Finite|))) (OR #6=(|HasCategory| |#1| (QUOTE (|DifferentialRing|))) #3#) (OR #7=(AND #6# #4#) #8=(|HasCategory| |#1| (QUOTE (|DifferentialSpace|))) #3#) #9=(|HasCategory| |#1| (QUOTE (|PartialDifferentialRing| #10=(|Symbol|)))) (OR #11=(AND #4# #9#) #12=(|HasCategory| |#1| (QUOTE (|PartialDifferentialSpace| #10#)))) (|HasCategory| |#1| (QUOTE (|LinearlyExplicitRingOver| #13=(|Integer|)))) (OR #4# #14=(|HasCategory| |#1| (QUOTE (|RetractableTo| (|Fraction| #13#))))) #14# (|HasCategory| |#1| (QUOTE (|RetractableTo| #13#))) (OR #15=(AND #16=(|HasCategory| |#1| (QUOTE (|EuclideanDomain|))) #17=(|HasCategory| |#1| (QUOTE (|PolynomialFactorizationExplicit|)))) #18=(AND #3# #17#) #4#) (OR #15# (AND #4# #17#) #18#) (OR #4# #5#) (AND (|HasCategory| |#1| (QUOTE (|RadicalCategory|))) #19=(|HasCategory| |#1| (QUOTE (|TranscendentalFunctionCategory|)))) #19# (|HasCategory| |#1| (QUOTE (|RealConstant|))) (|HasCategory| |#1| (QUOTE (|ConvertibleTo| (|InputForm|)))) (OR #16# #4# #3# #5#) (OR #16# #4# #3#) (|HasCategory| |#1| (QUOTE (|ConvertibleTo| (|Pattern| #20=(|Float|))))) (|HasCategory| |#1| (QUOTE (|ConvertibleTo| (|Pattern| #13#)))) (|HasCategory| |#1| (QUOTE (|PatternMatchable| #20#))) (|HasCategory| |#1| (QUOTE (|PatternMatchable| #13#))) (|HasCategory| |#1| (|%list| (QUOTE |InnerEvalable|) (QUOTE #10#) #21=(|devaluate| |#1|))) (|HasCategory| |#1| (|%list| (QUOTE |Evalable|) #21#)) (|HasCategory| |#1| (|%list| (QUOTE |Eltable|) #21# #21#)) #22=(|HasCategory| |#1| (QUOTE (|RealNumberSystem|))) (AND #22# #19#) (|HasCategory| |#1| (QUOTE (|IntegerNumberSystem|))) #16# #17# (OR #15# #4#) (OR #15# #5#) (OR #7# #8#) #8# #12# #6# #15# (|HasAttribute| |#1| (QUOTE |additiveValuation|)) (|HasAttribute| |#1| (QUOTE |multiplicativeValuation|)) (AND #8# #4#) (AND #4# #12#) #7# #11# (OR #23=(AND #16# #17# (|HasCategory| $ #2#)) #3#) (OR #23# #1#)) +((|noZeroDivisors| OR (|has| |#1| (|IntegralDomain|)) (AND (|has| |#1| (|EuclideanDomain|)) (|has| |#1| (|PolynomialFactorizationExplicit|)))) (|canonicalUnitNormal| |has| |#1| (|Field|)) (|additiveValuation| |has| |#1| (ATTRIBUTE |additiveValuation|)) (|multiplicativeValuation| |has| |#1| (ATTRIBUTE |multiplicativeValuation|)) (|complex| . T) ((|commutative| "*") . T)) +(#1=(|HasCategory| |#1| #2=(QUOTE (|CharacteristicNonZero|))) (|HasCategory| |#1| (QUOTE (|CharacteristicZero|))) #3=(|HasCategory| |#1| (QUOTE (|FiniteFieldCategory|))) (OR #4=(|HasCategory| |#1| (QUOTE (|Field|))) #3#) #5=(|HasCategory| |#1| (QUOTE (|IntegralDomain|))) #4# (|HasCategory| |#1| (QUOTE (|Finite|))) (OR #6=(|HasCategory| |#1| (QUOTE (|DifferentialRing|))) #3#) (OR #7=(AND #6# #4#) #8=(|HasCategory| |#1| (QUOTE (|DifferentialSpace|))) #3#) #9=(|HasCategory| |#1| (QUOTE (|PartialDifferentialRing| #10=(|Symbol|)))) (OR #11=(AND #4# #9#) #12=(|HasCategory| |#1| (QUOTE (|PartialDifferentialSpace| #10#)))) (|HasCategory| |#1| (QUOTE (|LinearlyExplicitRingOver| #13=(|Integer|)))) (OR #4# #14=(|HasCategory| |#1| (QUOTE (|RetractableTo| (|Fraction| #13#))))) #14# (|HasCategory| |#1| (QUOTE (|RetractableTo| #13#))) (OR #15=(AND #16=(|HasCategory| |#1| (QUOTE (|EuclideanDomain|))) #17=(|HasCategory| |#1| (QUOTE (|PolynomialFactorizationExplicit|)))) #18=(AND #3# #17#) #4#) (OR #15# (AND #4# #17#) #18#) (OR #4# #5#) (AND (|HasCategory| |#1| (QUOTE (|RadicalCategory|))) #19=(|HasCategory| |#1| (QUOTE (|TranscendentalFunctionCategory|)))) #19# (|HasCategory| |#1| (QUOTE (|RealConstant|))) (|HasCategory| |#1| (QUOTE (|ConvertibleTo| (|InputForm|)))) (OR #16# #4# #3# #5#) (OR #16# #4# #3#) (|HasCategory| |#1| (QUOTE (|ConvertibleTo| (|Pattern| #20=(|Float|))))) (|HasCategory| |#1| (QUOTE (|ConvertibleTo| (|Pattern| #13#)))) (|HasCategory| |#1| (QUOTE (|PatternMatchable| #20#))) (|HasCategory| |#1| (QUOTE (|PatternMatchable| #13#))) (|HasCategory| |#1| (|%list| (QUOTE |InnerEvalable|) (QUOTE #10#) #21=(|devaluate| |#1|))) (|HasCategory| |#1| (|%list| (QUOTE |Evalable|) #21#)) (|HasCategory| |#1| (|%list| (QUOTE |Eltable|) #21# #21#)) #22=(|HasCategory| |#1| (QUOTE (|RealNumberSystem|))) (AND #22# #19#) (|HasCategory| |#1| (QUOTE (|IntegerNumberSystem|))) #16# #17# (OR #15# #4#) (OR #15# #5#) (OR #7# #8#) #12# #8# #6# #15# (|HasAttribute| |#1| (QUOTE |additiveValuation|)) (|HasAttribute| |#1| (QUOTE |multiplicativeValuation|)) (AND #4# #12#) (AND #8# #4#) #7# #11# (OR #23=(AND #16# #17# (|HasCategory| $ #2#)) #3#) (OR #23# #1#)) (|ComplexFunctions2| R S) ((|constructor| (NIL "This package extends maps from underlying rings to maps between complex over those rings.")) (|map| (((|Complex| |#2|) (|Mapping| |#2| |#1|) (|Complex| |#1|)) "\\spad{map(f,u)} maps \\spad{f} onto real and imaginary parts of \\spad{u}."))) NIL @@ -522,7 +522,7 @@ NIL NIL (|CommutativeRing|) ((|constructor| (NIL "The category of commutative rings with unity,{} \\spadignore{i.e.} rings where \\spadop{*} is commutative,{} and which have a multiplicative identity. element.")) (|commutative| ((|attribute| "*") "multiplication is commutative."))) -(((|commutative| "*") . T) (|rightUnitary| . T) (|leftUnitary| . T) (|unitsKnown| . T)) +(((|commutative| "*") . T)) NIL (|Conduit|) ((|constructor| (NIL "This category is the root of the I/O conduits.")) (|close!| (($ $) "\\spad{close!(c)} closes the conduit \\spad{c},{} changing its state to one that is invalid for future read or write operations."))) @@ -530,7 +530,7 @@ NIL NIL (|ContinuedFraction| R) ((|constructor| (NIL "\\spadtype{ContinuedFraction} implements general \\indented{1}{continued fractions.\\space{2}This version is not restricted to simple,{}} \\indented{1}{finite fractions and uses the \\spadtype{Stream} as a} \\indented{1}{representation.\\space{2}The arithmetic functions assume that the} \\indented{1}{approximants alternate below/above the convergence point.} \\indented{1}{This is enforced by ensuring the partial numerators and partial} \\indented{1}{denominators are greater than 0 in the Euclidean domain view of \\spad{R}} \\indented{1}{(\\spadignore{i.e.} \\spad{sizeLess?(0, x)}).}")) (|complete| (($ $) "\\spad{complete(x)} causes all entries in \\spadvar{\\spad{x}} to be computed. Normally entries are only computed as needed. If \\spadvar{\\spad{x}} is an infinite continued fraction,{} a user-initiated interrupt is necessary to stop the computation.")) (|extend| (($ $ (|Integer|)) "\\spad{extend(x,n)} causes the first \\spadvar{\\spad{n}} entries in the continued fraction \\spadvar{\\spad{x}} to be computed. Normally entries are only computed as needed.")) (|denominators| (((|Stream| |#1|) $) "\\spad{denominators(x)} returns the stream of denominators of the approximants of the continued fraction \\spadvar{\\spad{x}}. If the continued fraction is finite,{} then the stream will be finite.")) (|numerators| (((|Stream| |#1|) $) "\\spad{numerators(x)} returns the stream of numerators of the approximants of the continued fraction \\spadvar{\\spad{x}}. If the continued fraction is finite,{} then the stream will be finite.")) (|convergents| (((|Stream| (|Fraction| |#1|)) $) "\\spad{convergents(x)} returns the stream of the convergents of the continued fraction \\spadvar{\\spad{x}}. If the continued fraction is finite,{} then the stream will be finite.")) (|approximants| (((|Stream| (|Fraction| |#1|)) $) "\\spad{approximants(x)} returns the stream of approximants of the continued fraction \\spadvar{\\spad{x}}. If the continued fraction is finite,{} then the stream will be infinite and periodic with period 1.")) (|reducedForm| (($ $) "\\spad{reducedForm(x)} puts the continued fraction \\spadvar{\\spad{x}} in reduced form,{} \\spadignore{i.e.} the function returns an equivalent continued fraction of the form \\spad{continuedFraction(b0,[1,1,1,...],[b1,b2,b3,...])}.")) (|wholePart| ((|#1| $) "\\spad{wholePart(x)} extracts the whole part of \\spadvar{\\spad{x}}. That is,{} if \\spad{x = continuedFraction(b0, [a1,a2,a3,...], [b1,b2,b3,...])},{} then \\spad{wholePart(x) = b0}.")) (|partialQuotients| (((|Stream| |#1|) $) "\\spad{partialQuotients(x)} extracts the partial quotients in \\spadvar{\\spad{x}}. That is,{} if \\spad{x = continuedFraction(b0, [a1,a2,a3,...], [b1,b2,b3,...])},{} then \\spad{partialQuotients(x) = [b0,b1,b2,b3,...]}.")) (|partialDenominators| (((|Stream| |#1|) $) "\\spad{partialDenominators(x)} extracts the denominators in \\spadvar{\\spad{x}}. That is,{} if \\spad{x = continuedFraction(b0, [a1,a2,a3,...], [b1,b2,b3,...])},{} then \\spad{partialDenominators(x) = [b1,b2,b3,...]}.")) (|partialNumerators| (((|Stream| |#1|) $) "\\spad{partialNumerators(x)} extracts the numerators in \\spadvar{\\spad{x}}. That is,{} if \\spad{x = continuedFraction(b0, [a1,a2,a3,...], [b1,b2,b3,...])},{} then \\spad{partialNumerators(x) = [a1,a2,a3,...]}.")) (|reducedContinuedFraction| (($ |#1| (|Stream| |#1|)) "\\spad{reducedContinuedFraction(b0,b)} constructs a continued fraction in the following way: if \\spad{b = [b1,b2,...]} then the result is the continued fraction \\spad{b0 + 1/(b1 + 1/(b2 + ...))}. That is,{} the result is the same as \\spad{continuedFraction(b0,[1,1,1,...],[b1,b2,b3,...])}.")) (|continuedFraction| (($ |#1| (|Stream| |#1|) (|Stream| |#1|)) "\\spad{continuedFraction(b0,a,b)} constructs a continued fraction in the following way: if \\spad{a = [a1,a2,...]} and \\spad{b = [b1,b2,...]} then the result is the continued fraction \\spad{b0 + a1/(b1 + a2/(b2 + ...))}.") (($ (|Fraction| |#1|)) "\\spad{continuedFraction(r)} converts the fraction \\spadvar{\\spad{r}} with components of type \\spad{R} to a continued fraction over \\spad{R}."))) -(((|commutative| "*") . T) (|noZeroDivisors| . T) (|canonicalUnitNormal| . T) (|canonicalsClosed| . T) (|rightUnitary| . T) (|leftUnitary| . T) (|unitsKnown| . T)) +((|canonicalUnitNormal| . T) (|noZeroDivisors| . T) ((|commutative| "*") . T)) NIL (|Contour|) ((|constructor| (NIL "\\indented{1}{Author: Gabriel Dos Reis} Date Created: October 24,{} 2007 Date Last Modified: January 18,{} 2008. A `Contour' a list of bindings making up a `virtual scope'.")) (|findBinding| (((|Maybe| (|Binding|)) (|Identifier|) $) "\\spad{findBinding(c,n)} returns the first binding associated with `n'. Otherwise `nothing.")) (|push| (($ (|Binding|) $) "\\spad{push(c,b)} augments the contour with binding `b'.")) (|bindings| (((|List| (|Binding|)) $) "\\spad{bindings(c)} returns the list of bindings in countour \\spad{c}."))) @@ -622,8 +622,8 @@ NIL NIL (|DecimalExpansion|) ((|constructor| (NIL "This domain allows rational numbers to be presented as repeating decimal expansions.")) (|decimal| (($ (|Fraction| (|Integer|))) "\\spad{decimal(r)} converts a rational number to a decimal expansion.")) (|fractionPart| (((|Fraction| (|Integer|)) $) "\\spad{fractionPart(d)} returns the fractional part of a decimal expansion."))) -((|canonicalsClosed| . T) (|canonicalUnitNormal| . T) (|noZeroDivisors| . T) ((|commutative| "*") . T) (|rightUnitary| . T) (|leftUnitary| . T) (|unitsKnown| . T)) -(#1=(|HasCategory| #2=(|Integer|) (QUOTE (|PolynomialFactorizationExplicit|))) (|HasCategory| #2# (QUOTE (|RetractableTo| #3=(|Symbol|)))) #4=(|HasCategory| #2# #5=(QUOTE (|CharacteristicNonZero|))) (|HasCategory| #2# (QUOTE (|CharacteristicZero|))) (|HasCategory| #2# (QUOTE (|ConvertibleTo| (|InputForm|)))) (|HasCategory| #2# (QUOTE (|RealConstant|))) #6=(|HasCategory| #2# (QUOTE (|OrderedIntegralDomain|))) #7=(|HasCategory| #2# (QUOTE (|OrderedSet|))) (OR #6# #7#) (|HasCategory| #2# (QUOTE (|RetractableTo| #2#))) (|HasCategory| #2# (QUOTE (|StepThrough|))) (|HasCategory| #2# (QUOTE (|PatternMatchable| #8=(|Float|)))) (|HasCategory| #2# (QUOTE (|PatternMatchable| #2#))) (|HasCategory| #2# (QUOTE (|ConvertibleTo| (|Pattern| #8#)))) (|HasCategory| #2# (QUOTE (|ConvertibleTo| (|Pattern| #2#)))) (|HasCategory| #2# (QUOTE (|DifferentialSpace|))) (|HasCategory| #2# (QUOTE (|PartialDifferentialSpace| #3#))) (|HasCategory| #2# (QUOTE (|DifferentialRing|))) (|HasCategory| #2# (QUOTE (|PartialDifferentialRing| #3#))) (|HasCategory| #2# (QUOTE (|InnerEvalable| #3# #2#))) (|HasCategory| #2# (QUOTE (|Evalable| #2#))) (|HasCategory| #2# (QUOTE (|Eltable| #2# #2#))) (|HasCategory| #2# (QUOTE (|EuclideanDomain|))) (|HasCategory| #2# (QUOTE (|IntegerNumberSystem|))) (|HasCategory| #2# (QUOTE (|LinearlyExplicitRingOver| #2#))) #9=(AND (|HasCategory| $ #5#) #1#) (OR #9# #4#)) +((|canonicalUnitNormal| . T) (|noZeroDivisors| . T) ((|commutative| "*") . T)) +(#1=(|HasCategory| #2=(|Integer|) (QUOTE (|PolynomialFactorizationExplicit|))) (|HasCategory| #2# (QUOTE (|RetractableTo| #3=(|Symbol|)))) #4=(|HasCategory| #2# #5=(QUOTE (|CharacteristicNonZero|))) (|HasCategory| #2# (QUOTE (|CharacteristicZero|))) (|HasCategory| #2# (QUOTE (|ConvertibleTo| (|InputForm|)))) (|HasCategory| #2# (QUOTE (|RealConstant|))) #6=(|HasCategory| #2# (QUOTE (|OrderedIntegralDomain|))) #7=(|HasCategory| #2# (QUOTE (|OrderedSet|))) (OR #6# #7#) (|HasCategory| #2# (QUOTE (|RetractableTo| #2#))) (|HasCategory| #2# (QUOTE (|StepThrough|))) (|HasCategory| #2# (QUOTE (|PatternMatchable| #8=(|Float|)))) (|HasCategory| #2# (QUOTE (|PatternMatchable| #2#))) (|HasCategory| #2# (QUOTE (|ConvertibleTo| (|Pattern| #8#)))) (|HasCategory| #2# (QUOTE (|ConvertibleTo| (|Pattern| #2#)))) (|HasCategory| #2# (QUOTE (|PartialDifferentialSpace| #3#))) (|HasCategory| #2# (QUOTE (|DifferentialSpace|))) (|HasCategory| #2# (QUOTE (|DifferentialRing|))) (|HasCategory| #2# (QUOTE (|PartialDifferentialRing| #3#))) (|HasCategory| #2# (QUOTE (|InnerEvalable| #3# #2#))) (|HasCategory| #2# (QUOTE (|Evalable| #2#))) (|HasCategory| #2# (QUOTE (|Eltable| #2# #2#))) (|HasCategory| #2# (QUOTE (|EuclideanDomain|))) (|HasCategory| #2# (QUOTE (|IntegerNumberSystem|))) (|HasCategory| #2# (QUOTE (|LinearlyExplicitRingOver| #2#))) #9=(AND (|HasCategory| $ #5#) #1#) (OR #9# #4#)) (|DefinitionAst|) ((|constructor| (NIL "This domain represents the syntax of a definition.")) (|body| (((|SpadAst|) $) "\\spad{body(d)} returns the right hand side of the definition `d'.")) (|signature| (((|Signature|) $) "\\spad{signature(d)} returns the signature of the operation being defined. Note that this list may be partial in that it contains only the types actually specified in the definition.")) (|head| (((|HeadAst|) $) "\\spad{head(d)} returns the head of the definition `d'. This is a list of identifiers starting with the name of the operation followed by the name of the parameters,{} if any."))) NIL @@ -646,7 +646,7 @@ NIL ((AND #1=(|HasCategory| |#1| (QUOTE (|SetCategory|))) (|HasCategory| |#1| (|%list| (QUOTE |Evalable|) (|devaluate| |#1|)))) #1# (OR #2=(|HasCategory| |#1| (QUOTE (|BasicType|))) #1#) (|HasCategory| |#1| (QUOTE (|CoercibleTo| (|OutputForm|)))) #2#) (|DeRhamComplex| |CoefRing| |listIndVar|) ((|constructor| (NIL "The deRham complex of Euclidean space,{} that is,{} the class of differential forms of arbitary degree over a coefficient ring. See Flanders,{} Harley,{} Differential Forms,{} With Applications to the Physical Sciences,{} New York,{} Academic Press,{} 1963.")) (|exteriorDifferential| (($ $) "\\spad{exteriorDifferential(df)} returns the exterior derivative (gradient,{} curl,{} divergence,{} ...) of the differential form \\spad{df}.")) (|totalDifferential| (($ (|Expression| |#1|)) "\\spad{totalDifferential(x)} returns the total differential (gradient) form for element \\spad{x}.")) (|degree| (((|Integer|) $) "\\spad{degree(df)} returns the homogeneous degree of differential form \\spad{df}.")) (|retractable?| (((|Boolean|) $) "\\spad{retractable?(df)} tests if differential form \\spad{df} is a 0-form,{} \\spadignore{i.e.} if degree(\\spad{df}) = 0.")) (|homogeneous?| (((|Boolean|) $) "\\spad{homogeneous?(df)} tests if all of the terms of differential form \\spad{df} have the same degree.")) (|generator| (($ (|NonNegativeInteger|)) "\\spad{generator(n)} returns the \\spad{n}th basis term for a differential form.")) (|coefficient| (((|Expression| |#1|) $ $) "\\spad{coefficient(df,u)},{} where \\spad{df} is a differential form,{} returns the coefficient of \\spad{df} containing the basis term \\spad{u} if such a term exists,{} and 0 otherwise.")) (|reductum| (($ $) "\\spad{reductum(df)},{} where \\spad{df} is a differential form,{} returns \\spad{df} minus the leading term of \\spad{df} if \\spad{df} has two or more terms,{} and 0 otherwise.")) (|leadingBasisTerm| (($ $) "\\spad{leadingBasisTerm(df)} returns the leading basis term of differential form \\spad{df}.")) (|leadingCoefficient| (((|Expression| |#1|) $) "\\spad{leadingCoefficient(df)} returns the leading coefficient of differential form \\spad{df}."))) -((|unitsKnown| . T)) +NIL NIL (|DefiniteIntegrationTools| R F) ((|constructor| (NIL "\\spadtype{DefiniteIntegrationTools} provides common tools used by the definite integration of both rational and elementary functions.")) (|checkForZero| (((|Union| (|Boolean|) "failed") (|SparseUnivariatePolynomial| |#2|) (|OrderedCompletion| |#2|) (|OrderedCompletion| |#2|) (|Boolean|)) "\\spad{checkForZero(p, a, b, incl?)} is \\spad{true} if \\spad{p} has a zero between a and \\spad{b},{} \\spad{false} otherwise,{} \"failed\" if this cannot be determined. Check for a and \\spad{b} inclusive if incl? is \\spad{true},{} exclusive otherwise.") (((|Union| (|Boolean|) "failed") (|Polynomial| |#1|) (|Symbol|) (|OrderedCompletion| |#2|) (|OrderedCompletion| |#2|) (|Boolean|)) "\\spad{checkForZero(p, x, a, b, incl?)} is \\spad{true} if \\spad{p} has a zero for \\spad{x} between a and \\spad{b},{} \\spad{false} otherwise,{} \"failed\" if this cannot be determined. Check for a and \\spad{b} inclusive if incl? is \\spad{true},{} exclusive otherwise.")) (|computeInt| (((|Union| (|OrderedCompletion| |#2|) "failed") (|Kernel| |#2|) |#2| (|OrderedCompletion| |#2|) (|OrderedCompletion| |#2|) (|Boolean|)) "\\spad{computeInt(x, g, a, b, eval?)} returns the integral of \\spad{f} for \\spad{x} between a and \\spad{b},{} assuming that \\spad{g} is an indefinite integral of \\spad{f} and \\spad{f} has no pole between a and \\spad{b}. If \\spad{eval?} is \\spad{true},{} then \\spad{g} can be evaluated safely at \\spad{a} and \\spad{b},{} provided that they are finite values. Otherwise,{} limits must be computed.")) (|ignore?| (((|Boolean|) (|String|)) "\\spad{ignore?(s)} is \\spad{true} if \\spad{s} is the string that tells the integrator to assume that the function has no pole in the integration interval."))) @@ -654,7 +654,7 @@ NIL NIL (|DoubleFloat|) ((|constructor| (NIL "\\indented{1}{\\spadtype{DoubleFloat} is intended to make accessible} hardware floating point arithmetic in \\Language{},{} either native double precision,{} or IEEE. On most machines,{} there will be hardware support for the arithmetic operations: \\spadfunFrom{+}{DoubleFloat},{} \\spadfunFrom{*}{DoubleFloat},{} \\spadfunFrom{/}{DoubleFloat} and possibly also the \\spadfunFrom{sqrt}{DoubleFloat} operation. The operations \\spadfunFrom{exp}{DoubleFloat},{} \\spadfunFrom{log}{DoubleFloat},{} \\spadfunFrom{sin}{DoubleFloat},{} \\spadfunFrom{cos}{DoubleFloat},{} \\spadfunFrom{atan}{DoubleFloat} are normally coded in software based on minimax polynomial/rational approximations. Note that under Lisp/VM,{} \\spadfunFrom{atan}{DoubleFloat} is not available at this time. Some general comments about the accuracy of the operations: the operations \\spadfunFrom{+}{DoubleFloat},{} \\spadfunFrom{*}{DoubleFloat},{} \\spadfunFrom{/}{DoubleFloat} and \\spadfunFrom{sqrt}{DoubleFloat} are expected to be fully accurate. The operations \\spadfunFrom{exp}{DoubleFloat},{} \\spadfunFrom{log}{DoubleFloat},{} \\spadfunFrom{sin}{DoubleFloat},{} \\spadfunFrom{cos}{DoubleFloat} and \\spadfunFrom{atan}{DoubleFloat} are not expected to be fully accurate. In particular,{} \\spadfunFrom{sin}{DoubleFloat} and \\spadfunFrom{cos}{DoubleFloat} will lose all precision for large arguments. \\blankline The \\spadtype{Float} domain provides an alternative to the \\spad{DoubleFloat} domain. It provides an arbitrary precision model of floating point arithmetic. This means that accuracy problems like those above are eliminated by increasing the working precision where necessary. \\spadtype{Float} provides some special functions such as \\spadfunFrom{erf}{DoubleFloat},{} the error function in addition to the elementary functions. The disadvantage of \\spadtype{Float} is that it is much more expensive than small floats when the latter can be used.")) (|nan?| (((|Boolean|) $) "\\spad{nan? x} holds if \\spad{x} is a Not a Number floating point data in the IEEE 754 sense.")) (|rationalApproximation| (((|Fraction| (|Integer|)) $ (|NonNegativeInteger|) (|NonNegativeInteger|)) "\\spad{rationalApproximation(f, n, b)} computes a rational approximation \\spad{r} to \\spad{f} with relative error \\spad{< b**(-n)} (that is,{} \\spad{|(r-f)/f| < b**(-n)}).") (((|Fraction| (|Integer|)) $ (|NonNegativeInteger|)) "\\spad{rationalApproximation(f, n)} computes a rational approximation \\spad{r} to \\spad{f} with relative error \\spad{< 10**(-n)}.")) (|Beta| (($ $ $) "\\spad{Beta(x,y)} is \\spad{Gamma(x) * Gamma(y)/Gamma(x+y)}.")) (|Gamma| (($ $) "\\spad{Gamma(x)} is the Euler Gamma function.")) (|atan| (($ $ $) "\\spad{atan(x,y)} computes the arc tangent from \\spad{x} with phase \\spad{y}.")) (|log10| (($ $) "\\spad{log10(x)} computes the logarithm with base 10 for \\spad{x}.")) (|log2| (($ $) "\\spad{log2(x)} computes the logarithm with base 2 for \\spad{x}.")) (|exp1| (($) "\\spad{exp1()} returns the natural log base \\spad{2.718281828...}.")) (** (($ $ $) "\\spad{x ** y} returns the \\spad{y}th power of \\spad{x} (equal to \\spad{exp(y log x)}).")) (/ (($ $ (|Integer|)) "\\spad{x / i} computes the division from \\spad{x} by an integer \\spad{i}."))) -((|approximate| . T) (|canonicalsClosed| . T) (|canonicalUnitNormal| . T) (|noZeroDivisors| . T) ((|commutative| "*") . T) (|rightUnitary| . T) (|leftUnitary| . T) (|unitsKnown| . T)) +((|approximate| . T) (|canonicalUnitNormal| . T) (|noZeroDivisors| . T) ((|commutative| "*") . T)) NIL (|DoubleFloatSpecialFunctions|) ((|constructor| (NIL "This package provides special functions for double precision real and complex floating point.")) (|hypergeometric0F1| (((|Complex| (|DoubleFloat|)) (|Complex| (|DoubleFloat|)) (|Complex| (|DoubleFloat|))) "\\spad{hypergeometric0F1(c,z)} is the hypergeometric function \\spad{0F1(; c; z)}.") (((|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|)) "\\spad{hypergeometric0F1(c,z)} is the hypergeometric function \\spad{0F1(; c; z)}.")) (|airyBi| (((|Complex| (|DoubleFloat|)) (|Complex| (|DoubleFloat|))) "\\spad{airyBi(x)} is the Airy function \\spad{Bi(x)}. This function satisfies the differential equation: \\indented{2}{\\spad{Bi''(x) - x * Bi(x) = 0}.}") (((|DoubleFloat|) (|DoubleFloat|)) "\\spad{airyBi(x)} is the Airy function \\spad{Bi(x)}. This function satisfies the differential equation: \\indented{2}{\\spad{Bi''(x) - x * Bi(x) = 0}.}")) (|airyAi| (((|DoubleFloat|) (|DoubleFloat|)) "\\spad{airyAi(x)} is the Airy function \\spad{Ai(x)}. This function satisfies the differential equation: \\indented{2}{\\spad{Ai''(x) - x * Ai(x) = 0}.}") (((|Complex| (|DoubleFloat|)) (|Complex| (|DoubleFloat|))) "\\spad{airyAi(x)} is the Airy function \\spad{Ai(x)}. This function satisfies the differential equation: \\indented{2}{\\spad{Ai''(x) - x * Ai(x) = 0}.}")) (|besselK| (((|Complex| (|DoubleFloat|)) (|Complex| (|DoubleFloat|)) (|Complex| (|DoubleFloat|))) "\\spad{besselK(v,x)} is the modified Bessel function of the first kind,{} \\spad{K(v,x)}. This function satisfies the differential equation: \\indented{2}{\\spad{x^2 w''(x) + x w'(x) - (x^2+v^2)w(x) = 0}.} Note: The default implmentation uses the relation \\indented{2}{\\spad{K(v,x) = \\%pi/2*(I(-v,x) - I(v,x))/sin(v*\\%pi)}} so is not valid for integer values of \\spad{v}.") (((|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|)) "\\spad{besselK(v,x)} is the modified Bessel function of the first kind,{} \\spad{K(v,x)}. This function satisfies the differential equation: \\indented{2}{\\spad{x^2 w''(x) + x w'(x) - (x^2+v^2)w(x) = 0}.} Note: The default implmentation uses the relation \\indented{2}{\\spad{K(v,x) = \\%pi/2*(I(-v,x) - I(v,x))/sin(v*\\%pi)}.} so is not valid for integer values of \\spad{v}.")) (|besselI| (((|Complex| (|DoubleFloat|)) (|Complex| (|DoubleFloat|)) (|Complex| (|DoubleFloat|))) "\\spad{besselI(v,x)} is the modified Bessel function of the first kind,{} \\spad{I(v,x)}. This function satisfies the differential equation: \\indented{2}{\\spad{x^2 w''(x) + x w'(x) - (x^2+v^2)w(x) = 0}.}") (((|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|)) "\\spad{besselI(v,x)} is the modified Bessel function of the first kind,{} \\spad{I(v,x)}. This function satisfies the differential equation: \\indented{2}{\\spad{x^2 w''(x) + x w'(x) - (x^2+v^2)w(x) = 0}.}")) (|besselY| (((|Complex| (|DoubleFloat|)) (|Complex| (|DoubleFloat|)) (|Complex| (|DoubleFloat|))) "\\spad{besselY(v,x)} is the Bessel function of the second kind,{} \\spad{Y(v,x)}. This function satisfies the differential equation: \\indented{2}{\\spad{x^2 w''(x) + x w'(x) + (x^2-v^2)w(x) = 0}.} Note: The default implmentation uses the relation \\indented{2}{\\spad{Y(v,x) = (J(v,x) cos(v*\\%pi) - J(-v,x))/sin(v*\\%pi)}} so is not valid for integer values of \\spad{v}.") (((|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|)) "\\spad{besselY(v,x)} is the Bessel function of the second kind,{} \\spad{Y(v,x)}. This function satisfies the differential equation: \\indented{2}{\\spad{x^2 w''(x) + x w'(x) + (x^2-v^2)w(x) = 0}.} Note: The default implmentation uses the relation \\indented{2}{\\spad{Y(v,x) = (J(v,x) cos(v*\\%pi) - J(-v,x))/sin(v*\\%pi)}} so is not valid for integer values of \\spad{v}.")) (|besselJ| (((|Complex| (|DoubleFloat|)) (|Complex| (|DoubleFloat|)) (|Complex| (|DoubleFloat|))) "\\spad{besselJ(v,x)} is the Bessel function of the first kind,{} \\spad{J(v,x)}. This function satisfies the differential equation: \\indented{2}{\\spad{x^2 w''(x) + x w'(x) + (x^2-v^2)w(x) = 0}.}") (((|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|)) "\\spad{besselJ(v,x)} is the Bessel function of the first kind,{} \\spad{J(v,x)}. This function satisfies the differential equation: \\indented{2}{\\spad{x^2 w''(x) + x w'(x) + (x^2-v^2)w(x) = 0}.}")) (|polygamma| (((|Complex| (|DoubleFloat|)) (|NonNegativeInteger|) (|Complex| (|DoubleFloat|))) "\\spad{polygamma(n, x)} is the \\spad{n}-th derivative of \\spad{digamma(x)}.") (((|DoubleFloat|) (|NonNegativeInteger|) (|DoubleFloat|)) "\\spad{polygamma(n, x)} is the \\spad{n}-th derivative of \\spad{digamma(x)}.")) (|digamma| (((|Complex| (|DoubleFloat|)) (|Complex| (|DoubleFloat|))) "\\spad{digamma(x)} is the function,{} \\spad{psi(x)},{} defined by \\indented{2}{\\spad{psi(x) = Gamma'(x)/Gamma(x)}.}") (((|DoubleFloat|) (|DoubleFloat|)) "\\spad{digamma(x)} is the function,{} \\spad{psi(x)},{} defined by \\indented{2}{\\spad{psi(x) = Gamma'(x)/Gamma(x)}.}")) (|logGamma| (((|Complex| (|DoubleFloat|)) (|Complex| (|DoubleFloat|))) "\\spad{logGamma(x)} is the natural log of \\spad{Gamma(x)}. This can often be computed even if \\spad{Gamma(x)} cannot.") (((|DoubleFloat|) (|DoubleFloat|)) "\\spad{logGamma(x)} is the natural log of \\spad{Gamma(x)}. This can often be computed even if \\spad{Gamma(x)} cannot.")) (|Beta| (((|Complex| (|DoubleFloat|)) (|Complex| (|DoubleFloat|)) (|Complex| (|DoubleFloat|))) "\\spad{Beta(x, y)} is the Euler beta function,{} \\spad{B(x,y)},{} defined by \\indented{2}{\\spad{Beta(x,y) = integrate(t^(x-1)*(1-t)^(y-1), t=0..1)}.} This is related to \\spad{Gamma(x)} by \\indented{2}{\\spad{Beta(x,y) = Gamma(x)*Gamma(y) / Gamma(x + y)}.}") (((|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|)) "\\spad{Beta(x, y)} is the Euler beta function,{} \\spad{B(x,y)},{} defined by \\indented{2}{\\spad{Beta(x,y) = integrate(t^(x-1)*(1-t)^(y-1), t=0..1)}.} This is related to \\spad{Gamma(x)} by \\indented{2}{\\spad{Beta(x,y) = Gamma(x)*Gamma(y) / Gamma(x + y)}.}")) (|Gamma| (((|Complex| (|DoubleFloat|)) (|Complex| (|DoubleFloat|))) "\\spad{Gamma(x)} is the Euler gamma function,{} \\spad{Gamma(x)},{} defined by \\indented{2}{\\spad{Gamma(x) = integrate(t^(x-1)*exp(-t), t=0..\\%infinity)}.}") (((|DoubleFloat|) (|DoubleFloat|)) "\\spad{Gamma(x)} is the Euler gamma function,{} \\spad{Gamma(x)},{} defined by \\indented{2}{\\spad{Gamma(x) = integrate(t^(x-1)*exp(-t), t=0..\\%infinity)}.}"))) @@ -674,7 +674,7 @@ NIL NIL (|DifferentialExtension| R) ((|constructor| (NIL "Differential extensions of a ring \\spad{R}. Given a differentiation on \\spad{R},{} extend it to a differentiation on \\%."))) -((|unitsKnown| . T)) +NIL NIL (|DifferentialDomain&| S T$) ((|constructor| (NIL "This category captures the interface of domains with a distinguished operation named \\spad{differentiate}. Usually,{} additional properties are wanted. For example,{} that it obeys the usual Leibniz identity of differentiation of product,{} in case of differential rings. One could also want \\spad{differentiate} to obey the chain rule when considering differential manifolds. The lack of specific requirement in this category is an implicit admission that currently \\Language{} is not expressive enough to express the most general notion of differentiation in an adequate manner,{} suitable for computational purposes.")) (D ((|#2| $) "\\spad{D x} is a shorthand for \\spad{differentiate x}")) (|differentiate| ((|#2| $) "\\spad{differentiate x} compute the derivative of \\spad{x}."))) @@ -686,7 +686,7 @@ NIL NIL (|DifferentialModule| R) ((|constructor| (NIL "An \\spad{R}-module equipped with a distinguised differential operator. If \\spad{R} is a differential ring,{} then differentiation on the module should extend differentiation on the differential ring \\spad{R}. The latter can be the null operator. In that case,{} the differentiation operator on the module is just an \\spad{R}-linear operator. For that reason,{} we do not require that the ring \\spad{R} be a DifferentialRing; \\blankline"))) -((|leftUnitary| . T) (|rightUnitary| . T)) +NIL NIL (|DifferentialSpace&| S) ((|constructor| (NIL "This category is like \\spadtype{DifferentialDomain} where the target of the differentiation operator is the same as its source.")) (D (($ $ (|NonNegativeInteger|)) "\\spad{D(x, n)} returns the \\spad{n}\\spad{-}th derivative of \\spad{x}.")) (|differentiate| (($ $ (|NonNegativeInteger|)) "\\spad{differentiate(x,n)} returns the \\spad{n}\\spad{-}th derivative of \\spad{x}."))) @@ -698,7 +698,7 @@ NIL NIL (|DifferentialRing|) ((|constructor| (NIL "An ordinary differential ring,{} that is,{} a ring with an operation \\spadfun{differentiate}. \\blankline"))) -((|unitsKnown| . T)) +NIL NIL (|Dioid|) ((|constructor| (NIL "Dioid is the class of semirings where the addition operation induces a canonical order relation."))) @@ -719,15 +719,15 @@ NIL (|DirectProductCategory&| S |dim| R) ((|constructor| (NIL "\\indented{2}{This category represents a finite cartesian product of a given type.} Many categorical properties are preserved under this construction.")) (|dot| ((|#3| $ $) "\\spad{dot(x,y)} computes the inner product of the vectors \\spad{x} and \\spad{y}.")) (|unitVector| (($ (|PositiveInteger|)) "\\spad{unitVector(n)} produces a vector with 1 in position \\spad{n} and zero elsewhere.")) (|directProduct| (($ (|Vector| |#3|)) "\\spad{directProduct(v)} converts the vector \\spad{v} to become a direct product. Error: if the length of \\spad{v} is different from dim."))) NIL -((|HasCategory| |#3| (QUOTE (|Field|))) (|HasCategory| |#3| (QUOTE (|OrderedAbelianMonoidSup|))) (|HasCategory| |#3| (QUOTE (|OrderedSet|))) (|HasAttribute| |#3| (QUOTE |unitsKnown|)) (|HasCategory| |#3| (QUOTE (|CommutativeRing|))) (|HasCategory| |#3| (QUOTE (|Finite|))) (|HasCategory| |#3| (QUOTE (|Monoid|))) (|HasCategory| |#3| (QUOTE (|AbelianGroup|))) (|HasCategory| |#3| (QUOTE (|AbelianMonoid|))) (|HasCategory| |#3| (QUOTE (|CancellationAbelianMonoid|))) (|HasCategory| |#3| (QUOTE (|AbelianSemiGroup|))) (|HasCategory| |#3| (QUOTE (|Ring|))) (|HasCategory| |#3| (QUOTE (|SetCategory|)))) +((|HasCategory| |#3| (QUOTE (|Field|))) (|HasCategory| |#3| (QUOTE (|OrderedAbelianMonoidSup|))) (|HasCategory| |#3| (QUOTE (|OrderedSet|))) (|HasCategory| |#3| (QUOTE (|CommutativeRing|))) (|HasCategory| |#3| (QUOTE (|Finite|))) (|HasCategory| |#3| (QUOTE (|Monoid|))) (|HasCategory| |#3| (QUOTE (|AbelianGroup|))) (|HasCategory| |#3| (QUOTE (|AbelianMonoid|))) (|HasCategory| |#3| (QUOTE (|CancellationAbelianMonoid|))) (|HasCategory| |#3| (QUOTE (|AbelianSemiGroup|))) (|HasCategory| |#3| (QUOTE (|Ring|))) (|HasCategory| |#3| (QUOTE (|SetCategory|)))) (|DirectProductCategory| |dim| R) ((|constructor| (NIL "\\indented{2}{This category represents a finite cartesian product of a given type.} Many categorical properties are preserved under this construction.")) (|dot| ((|#2| $ $) "\\spad{dot(x,y)} computes the inner product of the vectors \\spad{x} and \\spad{y}.")) (|unitVector| (($ (|PositiveInteger|)) "\\spad{unitVector(n)} produces a vector with 1 in position \\spad{n} and zero elsewhere.")) (|directProduct| (($ (|Vector| |#2|)) "\\spad{directProduct(v)} converts the vector \\spad{v} to become a direct product. Error: if the length of \\spad{v} is different from dim."))) -((|rightUnitary| |has| |#2| . #1=((|Ring|))) (|leftUnitary| |has| |#2| . #1#) (|unitsKnown| |has| |#2| (ATTRIBUTE |unitsKnown|))) +NIL NIL (|DirectProduct| |dim| R) ((|constructor| (NIL "\\indented{2}{This type represents the finite direct or cartesian product of an} underlying component type. This contrasts with simple vectors in that the members can be viewed as having constant length. Thus many categorical properties can by lifted from the underlying component type. Component extraction operations are provided but no updating operations. Thus new direct product elements can either be created by converting vector elements using the \\spadfun{directProduct} function or by taking appropriate linear combinations of basis vectors provided by the \\spad{unitVector} operation."))) -((|rightUnitary| |has| |#2| . #1=((|Ring|))) (|leftUnitary| |has| |#2| . #1#) (|unitsKnown| |has| |#2| (ATTRIBUTE |unitsKnown|))) -((OR (AND #1=(|HasCategory| |#2| (QUOTE (|AbelianGroup|))) #2=(|HasCategory| |#2| (|%list| (QUOTE |Evalable|) #3=(|devaluate| |#2|)))) (AND #4=(|HasCategory| |#2| (QUOTE (|AbelianMonoid|))) #2#) (AND #5=(|HasCategory| |#2| (QUOTE (|AbelianSemiGroup|))) #2#) (AND #6=(|HasCategory| |#2| (QUOTE (|CancellationAbelianMonoid|))) #2#) (AND #7=(|HasCategory| |#2| (QUOTE (|CommutativeRing|))) #2#) (AND #8=(|HasCategory| |#2| (QUOTE (|DifferentialRing|))) #2#) (AND #9=(|HasCategory| |#2| (QUOTE (|Field|))) #2#) (AND #10=(|HasCategory| |#2| (QUOTE (|Finite|))) #2#) (AND #11=(|HasCategory| |#2| (QUOTE (|Monoid|))) #2#) (AND #12=(|HasCategory| |#2| (QUOTE (|OrderedAbelianMonoidSup|))) #2#) (AND #13=(|HasCategory| |#2| #14=(QUOTE (|OrderedSet|))) #2#) (AND #15=(|HasCategory| |#2| (QUOTE (|PartialDifferentialRing| #16=(|Symbol|)))) #2#) (AND #17=(|HasCategory| |#2| (QUOTE (|Ring|))) #2#) #18=(AND #19=(|HasCategory| |#2| (QUOTE (|SetCategory|))) #2#)) (|HasCategory| |#2| (QUOTE (|CoercibleTo| (|OutputForm|)))) #9# (OR #7# #9# #17#) (OR #7# #9#) #1# #17# #11# #12# (OR #12# #13#) #13# #10# (OR (AND #7# #20=(|HasCategory| |#2| (QUOTE (|LinearlyExplicitRingOver| #21=(|Integer|))))) (AND #8# #20#) (AND #9# #20#) (AND #20# #15#) #22=(AND #20# #17#)) #15# (OR #1# #4# #5# #23=(|HasCategory| |#2| (QUOTE (|BasicType|))) #6# #7# #8# #9# #10# #11# #12# #13# #15# #17# #19#) (OR #1# #4# #5# #6# #7# #8# #9# #10# #11# #12# #13# #15# #17# #19#) (OR #1# #4# #5# #6# #7# #8# #9# #15# #17#) (OR #1# #4# #6# #7# #8# #9# #15# #17#) (OR #1# #6# #7# #8# #9# #15# #17#) (OR #1# #7# #8# #9# #15# #17#) (OR #8# #15# #17#) #8# (OR #8# #24=(AND (|HasCategory| |#2| (QUOTE (|DifferentialSpace|))) #17#)) (OR #25=(AND (|HasCategory| |#2| (QUOTE (|PartialDifferentialSpace| #16#))) #17#) #15#) #19# (OR (AND #1# #26=(|HasCategory| |#2| (QUOTE (|RetractableTo| (|Fraction| #21#))))) (AND #4# #26#) (AND #5# #26#) (AND #6# #26#) (AND #7# #26#) (AND #8# #26#) (AND #9# #26#) (AND #10# #26#) (AND #11# #26#) (AND #12# #26#) (AND #13# #26#) (AND #15# #26#) (AND #26# #17#) #27=(AND #26# #19#)) (OR #28=(AND #1# #29=(|HasCategory| |#2| (QUOTE (|RetractableTo| #21#)))) #30=(AND #4# #29#) #31=(AND #5# #29#) #32=(AND #6# #29#) #33=(AND #7# #29#) #34=(AND #8# #29#) #35=(AND #12# #29#) #36=(AND #13# #29#) #37=(AND #15# #29#) #38=(AND #29# #19#) #39=(AND #9# #29#) #40=(AND #10# #29#) #41=(AND #11# #29#) #17#) (OR #28# #30# #31# #32# #33# #34# #35# #36# #37# #38# #39# #40# #41# (AND #29# #17#)) #23# (|HasCategory| #21# #14#) #22# #24# #25# (OR #38# #17#) #38# #27# (|HasAttribute| |#2| (QUOTE |unitsKnown|)) (AND #8# #17#) (AND #15# #17#) #7# #4# #6# #5# #18# (AND #23# (|HasCategory| $ (|%list| (QUOTE |FiniteAggregate|) #3#))) (|HasCategory| $ (|%list| (QUOTE |ShallowlyMutableAggregate|) #3#))) +NIL +((OR (AND #1=(|HasCategory| |#2| (QUOTE (|AbelianGroup|))) #2=(|HasCategory| |#2| (|%list| (QUOTE |Evalable|) #3=(|devaluate| |#2|)))) (AND #4=(|HasCategory| |#2| (QUOTE (|AbelianMonoid|))) #2#) (AND #5=(|HasCategory| |#2| (QUOTE (|AbelianSemiGroup|))) #2#) (AND #6=(|HasCategory| |#2| (QUOTE (|CancellationAbelianMonoid|))) #2#) (AND #7=(|HasCategory| |#2| (QUOTE (|CommutativeRing|))) #2#) (AND #8=(|HasCategory| |#2| (QUOTE (|DifferentialRing|))) #2#) (AND #9=(|HasCategory| |#2| (QUOTE (|Field|))) #2#) (AND #10=(|HasCategory| |#2| (QUOTE (|Finite|))) #2#) (AND #11=(|HasCategory| |#2| (QUOTE (|Monoid|))) #2#) (AND #12=(|HasCategory| |#2| (QUOTE (|OrderedAbelianMonoidSup|))) #2#) (AND #13=(|HasCategory| |#2| #14=(QUOTE (|OrderedSet|))) #2#) (AND #15=(|HasCategory| |#2| (QUOTE (|PartialDifferentialRing| #16=(|Symbol|)))) #2#) (AND #17=(|HasCategory| |#2| (QUOTE (|Ring|))) #2#) #18=(AND #19=(|HasCategory| |#2| (QUOTE (|SetCategory|))) #2#)) (|HasCategory| |#2| (QUOTE (|CoercibleTo| (|OutputForm|)))) #9# (OR #7# #9# #17#) (OR #7# #9#) #1# #17# #11# #12# (OR #12# #13#) #13# #10# (OR (AND #7# #20=(|HasCategory| |#2| (QUOTE (|LinearlyExplicitRingOver| #21=(|Integer|))))) (AND #8# #20#) (AND #9# #20#) (AND #20# #15#) #22=(AND #20# #17#)) #15# (OR #1# #4# #5# #23=(|HasCategory| |#2| (QUOTE (|BasicType|))) #6# #7# #8# #9# #10# #11# #12# #13# #15# #17# #19#) (OR #1# #4# #5# #6# #7# #8# #9# #10# #11# #12# #13# #15# #17# #19#) (OR #1# #4# #5# #6# #7# #8# #9# #15# #17#) (OR #1# #4# #6# #7# #8# #9# #15# #17#) (OR #1# #6# #7# #8# #9# #15# #17#) (OR #1# #7# #8# #9# #15# #17#) (OR #8# #15# #17#) #8# (OR #8# #24=(AND (|HasCategory| |#2| (QUOTE (|DifferentialSpace|))) #17#)) (OR #25=(AND (|HasCategory| |#2| (QUOTE (|PartialDifferentialSpace| #16#))) #17#) #15#) #19# (OR (AND #1# #26=(|HasCategory| |#2| (QUOTE (|RetractableTo| (|Fraction| #21#))))) (AND #4# #26#) (AND #5# #26#) (AND #6# #26#) (AND #7# #26#) (AND #8# #26#) (AND #9# #26#) (AND #10# #26#) (AND #11# #26#) (AND #12# #26#) (AND #13# #26#) (AND #15# #26#) (AND #26# #17#) #27=(AND #26# #19#)) (OR #28=(AND #1# #29=(|HasCategory| |#2| (QUOTE (|RetractableTo| #21#)))) #30=(AND #4# #29#) #31=(AND #5# #29#) #32=(AND #6# #29#) #33=(AND #7# #29#) #34=(AND #8# #29#) #35=(AND #12# #29#) #36=(AND #13# #29#) #37=(AND #15# #29#) #38=(AND #29# #19#) #39=(AND #9# #29#) #40=(AND #10# #29#) #41=(AND #11# #29#) #17#) (OR #28# #30# #31# #32# #33# #34# #35# #36# #37# #38# #39# #40# #41# (AND #29# #17#)) #23# (|HasCategory| #21# #14#) #22# #24# #25# (OR #38# #17#) #38# #27# (AND #8# #17#) (AND #15# #17#) #7# #4# #6# #5# #18# (AND #23# (|HasCategory| $ (|%list| (QUOTE |FiniteAggregate|) #3#))) (|HasCategory| $ (|%list| (QUOTE |ShallowlyMutableAggregate|) #3#))) (|DirectProductFunctions2| |dim| A B) ((|constructor| (NIL "\\indented{2}{This package provides operations which all take as arguments} direct products of elements of some type \\spad{A} and functions from \\spad{A} to another type \\spad{B}. The operations all iterate over their vector argument and either return a value of type \\spad{B} or a direct product over \\spad{B}.")) (|map| (((|DirectProduct| |#1| |#3|) (|Mapping| |#3| |#2|) (|DirectProduct| |#1| |#2|)) "\\spad{map(f, v)} applies the function \\spad{f} to every element of the vector \\spad{v} producing a new vector containing the values.")) (|reduce| ((|#3| (|Mapping| |#3| |#2| |#3|) (|DirectProduct| |#1| |#2|) |#3|) "\\spad{reduce(func,vec,ident)} combines the elements in \\spad{vec} using the binary function \\spad{func}. Argument \\spad{ident} is returned if the vector is empty.")) (|scan| (((|DirectProduct| |#1| |#3|) (|Mapping| |#3| |#2| |#3|) (|DirectProduct| |#1| |#2|) |#3|) "\\spad{scan(func,vec,ident)} creates a new vector whose elements are the result of applying reduce to the binary function \\spad{func},{} increasing initial subsequences of the vector \\spad{vec},{} and the element \\spad{ident}."))) NIL @@ -742,7 +742,7 @@ NIL NIL (|DivisionRing|) ((|constructor| (NIL "A division ring (sometimes called a skew field),{} \\spadignore{i.e.} a not necessarily commutative ring where all non-zero elements have multiplicative inverses.")) (|inv| (($ $) "\\spad{inv x} returns the multiplicative inverse of \\spad{x}. Error: if \\spad{x} is 0.")) (** (($ $ (|Integer|)) "\\spad{x**n} returns \\spad{x} raised to the integer power \\spad{n}."))) -((|noZeroDivisors| . T) (|rightUnitary| . T) (|leftUnitary| . T) (|unitsKnown| . T)) +((|noZeroDivisors| . T)) NIL (|DoublyLinkedAggregate| S) ((|constructor| (NIL "A doubly-linked aggregate serves as a model for a doubly-linked list,{} that is,{} a list which can has links to both next and previous nodes and thus can be efficiently traversed in both directions.")) (|setnext!| (($ $ $) "\\spad{setnext!(u,v)} destructively sets the next node of doubly-linked aggregate \\spad{u} to \\spad{v},{} returning \\spad{v}.")) (|setprevious!| (($ $ $) "\\spad{setprevious!(u,v)} destructively sets the previous node of doubly-linked aggregate \\spad{u} to \\spad{v},{} returning \\spad{v}.")) (|concat!| (($ $ $) "\\spad{concat!(u,v)} destructively concatenates doubly-linked aggregate \\spad{v} to the end of doubly-linked aggregate \\spad{u}.")) (|next| (($ $) "\\spad{next(l)} returns the doubly-linked aggregate beginning with its next element. Error: if \\spad{l} has no next element. Note: \\axiom{next(\\spad{l}) = rest(\\spad{l})} and \\axiom{previous(next(\\spad{l})) = \\spad{l}}.")) (|previous| (($ $) "\\spad{previous(l)} returns the doubly-link list beginning with its previous element. Error: if \\spad{l} has no previous element. Note: \\axiom{next(previous(\\spad{l})) = \\spad{l}}.")) (|tail| (($ $) "\\spad{tail(l)} returns the doubly-linked aggregate \\spad{l} starting at its second element. Error: if \\spad{l} is empty.")) (|head| (($ $) "\\spad{head(l)} returns the first element of a doubly-linked aggregate \\spad{l}. Error: if \\spad{l} is empty.")) (|last| ((|#1| $) "\\spad{last(l)} returns the last element of a doubly-linked aggregate \\spad{l}. Error: if \\spad{l} is empty."))) @@ -758,12 +758,12 @@ NIL NIL (|DifferentialModuleExtension| R) ((|constructor| (NIL "Category of modules that extend differential rings. \\blankline"))) -((|leftUnitary| . T) (|rightUnitary| . T)) +NIL NIL (|DistributedMultivariatePolynomial| |vl| R) ((|constructor| (NIL "\\indented{2}{This type supports distributed multivariate polynomials} whose variables are from a user specified list of symbols. The coefficient ring may be non commutative,{} but the variables are assumed to commute. The term ordering is lexicographic specified by the variable list parameter with the most significant variable first in the list.")) (|reorder| (($ $ (|List| (|Integer|))) "\\spad{reorder(p, perm)} applies the permutation perm to the variables in a polynomial and returns the new correctly ordered polynomial"))) -(((|commutative| "*") |has| |#2| (|CommutativeRing|)) (|noZeroDivisors| |has| |#2| (|IntegralDomain|)) (|canonicalUnitNormal| |has| |#2| (ATTRIBUTE |canonicalUnitNormal|)) (|leftUnitary| . T) (|rightUnitary| . T) (|unitsKnown| . T)) -(#1=(|HasCategory| |#2| (QUOTE (|PolynomialFactorizationExplicit|))) (OR #2=(|HasCategory| |#2| (QUOTE (|CommutativeRing|))) #3=(|HasCategory| |#2| (QUOTE (|GcdDomain|))) #4=(|HasCategory| |#2| (QUOTE (|IntegralDomain|))) #1#) (OR #3# #4# #1#) (OR #3# #1#) #4# #2# (OR #2# #4#) (AND (|HasCategory| |#2| #5=(QUOTE (|PatternMatchable| #6=(|Float|)))) (|HasCategory| #7=(|OrderedVariableList| |#1|) #5#)) (AND (|HasCategory| |#2| #8=(QUOTE (|PatternMatchable| #9=(|Integer|)))) (|HasCategory| #7# #8#)) (AND (|HasCategory| |#2| #10=(QUOTE (|ConvertibleTo| (|Pattern| #6#)))) (|HasCategory| #7# #10#)) (AND (|HasCategory| |#2| #11=(QUOTE (|ConvertibleTo| (|Pattern| #9#)))) (|HasCategory| #7# #11#)) (AND (|HasCategory| |#2| #12=(QUOTE (|ConvertibleTo| (|InputForm|)))) (|HasCategory| #7# #12#)) (|HasCategory| |#2| (QUOTE (|LinearlyExplicitRingOver| #9#))) (|HasCategory| |#2| (QUOTE (|CharacteristicZero|))) #13=(|HasCategory| |#2| #14=(QUOTE (|CharacteristicNonZero|))) #15=(|HasCategory| |#2| (QUOTE (|Algebra| #16=(|Fraction| #9#)))) (|HasCategory| |#2| (QUOTE (|RetractableTo| #9#))) (OR #15# #17=(|HasCategory| |#2| (QUOTE (|RetractableTo| #16#)))) #17# (|HasCategory| |#2| (QUOTE (|Field|))) (|HasAttribute| |#2| (QUOTE |canonicalUnitNormal|)) #3# #18=(AND #1# (|HasCategory| $ #14#)) (OR #18# #13#)) +(((|commutative| "*") |has| |#2| (|CommutativeRing|)) (|noZeroDivisors| |has| |#2| (|IntegralDomain|)) (|canonicalUnitNormal| |has| |#2| (ATTRIBUTE |canonicalUnitNormal|))) +(#1=(|HasCategory| |#2| (QUOTE (|PolynomialFactorizationExplicit|))) (OR #2=(|HasCategory| |#2| (QUOTE (|CommutativeRing|))) #3=(|HasCategory| |#2| (QUOTE (|GcdDomain|))) #4=(|HasCategory| |#2| (QUOTE (|IntegralDomain|))) #1#) (OR #3# #4# #1#) (OR #3# #1#) #4# #2# (OR #2# #4#) (AND (|HasCategory| |#2| #5=(QUOTE (|PatternMatchable| #6=(|Float|)))) (|HasCategory| #7=(|OrderedVariableList| |#1|) #5#)) (AND (|HasCategory| |#2| #8=(QUOTE (|PatternMatchable| #9=(|Integer|)))) (|HasCategory| #7# #8#)) (AND (|HasCategory| |#2| #10=(QUOTE (|ConvertibleTo| (|Pattern| #6#)))) (|HasCategory| #7# #10#)) (AND (|HasCategory| |#2| #11=(QUOTE (|ConvertibleTo| (|Pattern| #9#)))) (|HasCategory| #7# #11#)) (AND (|HasCategory| |#2| #12=(QUOTE (|ConvertibleTo| (|InputForm|)))) (|HasCategory| #7# #12#)) (|HasCategory| |#2| (QUOTE (|LinearlyExplicitRingOver| #9#))) #13=(|HasCategory| |#2| (QUOTE (|Algebra| #14=(|Fraction| #9#)))) #15=(|HasCategory| |#2| #16=(QUOTE (|CharacteristicNonZero|))) (|HasCategory| |#2| (QUOTE (|CharacteristicZero|))) (|HasCategory| |#2| (QUOTE (|RetractableTo| #9#))) (OR #13# #17=(|HasCategory| |#2| (QUOTE (|RetractableTo| #14#)))) #17# (|HasCategory| |#2| (QUOTE (|Field|))) (|HasAttribute| |#2| (QUOTE |canonicalUnitNormal|)) #3# #18=(AND #1# (|HasCategory| $ #16#)) (OR #18# #15#)) (|Domain|) ((|showSummary| (((|Void|) $) "\\spad{showSummary(d)} prints out implementation detail information of domain `d'.")) (|reflect| (($ (|ConstructorCall| (|DomainConstructor|))) "\\spad{reflect cc} returns the domain object designated by the ConstructorCall syntax `cc'. The constructor implied by `cc' must be known to the system since it is instantiated.")) (|reify| (((|ConstructorCall| (|DomainConstructor|)) $) "\\spad{reify(d)} returns the abstract syntax for the domain `x'.")) (|constructor| (NIL "\\indented{1}{Author: Gabriel Dos Reis} Date Create: October 18,{} 2007. Date Last Updated: December 20,{} 2008. Basic Operations: coerce,{} reify Related Constructors: Type,{} Syntax,{} OutputForm Also See: Type,{} ConstructorCall") (((|DomainConstructor|) $) "\\spad{constructor(d)} returns the domain constructor that is instantiated to the domain object `d'."))) NIL @@ -778,19 +778,19 @@ NIL NIL (|DirectProductMatrixModule| |n| R M S) ((|constructor| (NIL "This constructor provides a direct product type with a left matrix-module view."))) -((|unitsKnown| OR (|and| #1=(|has| |#4| #2=(|Ring|)) (|has| |#4| (|DifferentialRing|))) (|has| |#4| (ATTRIBUTE |unitsKnown|)) (|and| #1# (|has| |#4| (|PartialDifferentialRing| (|Symbol|))))) (|rightUnitary| |has| |#4| . #3=(#2#)) (|leftUnitary| |has| |#4| . #3#)) -((OR (AND #1=(|HasCategory| |#4| (QUOTE (|AbelianGroup|))) #2=(|HasCategory| |#4| (|%list| (QUOTE |Evalable|) #3=(|devaluate| |#4|)))) (AND #4=(|HasCategory| |#4| (QUOTE (|CommutativeRing|))) #2#) (AND #5=(|HasCategory| |#4| (QUOTE (|DifferentialRing|))) #2#) (AND #6=(|HasCategory| |#4| (QUOTE (|Field|))) #2#) (AND #7=(|HasCategory| |#4| (QUOTE (|Finite|))) #2#) (AND #8=(|HasCategory| |#4| (QUOTE (|Monoid|))) #2#) (AND #9=(|HasCategory| |#4| (QUOTE (|OrderedAbelianMonoidSup|))) #2#) (AND #10=(|HasCategory| |#4| #11=(QUOTE (|OrderedSet|))) #2#) (AND #12=(|HasCategory| |#4| (QUOTE (|PartialDifferentialRing| #13=(|Symbol|)))) #2#) (AND #14=(|HasCategory| |#4| (QUOTE (|Ring|))) #2#) #15=(AND #16=(|HasCategory| |#4| (QUOTE (|SetCategory|))) #2#)) #6# (OR #4# #6# #14#) (OR #4# #6#) #14# #8# #9# (OR #9# #10#) #10# #7# (OR (AND #4# #17=(|HasCategory| |#4| (QUOTE (|LinearlyExplicitRingOver| #18=(|Integer|))))) (AND #5# #17#) (AND #6# #17#) (AND #17# #12#) #19=(AND #17# #14#)) #12# (OR #5# #12# #14#) #5# (OR #5# #20=(AND (|HasCategory| |#4| (QUOTE (|DifferentialSpace|))) #14#)) (OR #21=(AND (|HasCategory| |#4| (QUOTE (|PartialDifferentialSpace| #13#))) #14#) #12#) #16# (OR (AND #1# #22=(|HasCategory| |#4| (QUOTE (|RetractableTo| (|Fraction| #18#))))) (AND #4# #22#) (AND #5# #22#) (AND #6# #22#) (AND #7# #22#) (AND #8# #22#) (AND #9# #22#) (AND #10# #22#) (AND #12# #22#) (AND #22# #14#) #23=(AND #22# #16#)) (OR #24=(AND #1# #25=(|HasCategory| |#4| (QUOTE (|RetractableTo| #18#)))) #26=(AND #4# #25#) #27=(AND #5# #25#) #28=(AND #9# #25#) #29=(AND #10# #25#) #30=(AND #12# #25#) #31=(AND #25# #16#) #32=(AND #6# #25#) #33=(AND #7# #25#) #34=(AND #8# #25#) #14#) (OR #24# #26# #27# #28# #29# #30# #31# #32# #33# #34# (AND #25# #14#)) #35=(|HasCategory| |#4| (QUOTE (|BasicType|))) (|HasCategory| #18# #11#) #19# (OR #36=(AND #12# #14#) #21#) (OR #37=(AND #5# #14#) #20#) #31# (OR #31# #14#) #23# (OR #36# (|HasAttribute| |#4| (QUOTE |unitsKnown|)) #37#) #20# #21# #4# #1# (|HasCategory| |#4| (QUOTE (|AbelianMonoid|))) (|HasCategory| |#4| (QUOTE (|CancellationAbelianMonoid|))) (|HasCategory| |#4| (QUOTE (|AbelianSemiGroup|))) (|HasCategory| |#4| (QUOTE (|CoercibleTo| (|OutputForm|)))) #15# (AND #35# (|HasCategory| $ (|%list| (QUOTE |FiniteAggregate|) #3#))) (|HasCategory| $ (|%list| (QUOTE |ShallowlyMutableAggregate|) #3#))) +NIL +((OR (AND #1=(|HasCategory| |#4| (QUOTE (|AbelianGroup|))) #2=(|HasCategory| |#4| (|%list| (QUOTE |Evalable|) #3=(|devaluate| |#4|)))) (AND #4=(|HasCategory| |#4| (QUOTE (|CommutativeRing|))) #2#) (AND #5=(|HasCategory| |#4| (QUOTE (|DifferentialRing|))) #2#) (AND #6=(|HasCategory| |#4| (QUOTE (|Field|))) #2#) (AND #7=(|HasCategory| |#4| (QUOTE (|Finite|))) #2#) (AND #8=(|HasCategory| |#4| (QUOTE (|Monoid|))) #2#) (AND #9=(|HasCategory| |#4| (QUOTE (|OrderedAbelianMonoidSup|))) #2#) (AND #10=(|HasCategory| |#4| #11=(QUOTE (|OrderedSet|))) #2#) (AND #12=(|HasCategory| |#4| (QUOTE (|PartialDifferentialRing| #13=(|Symbol|)))) #2#) (AND #14=(|HasCategory| |#4| (QUOTE (|Ring|))) #2#) #15=(AND #16=(|HasCategory| |#4| (QUOTE (|SetCategory|))) #2#)) #6# (OR #4# #6# #14#) (OR #4# #6#) #14# #8# #9# (OR #9# #10#) #10# #7# (OR (AND #4# #17=(|HasCategory| |#4| (QUOTE (|LinearlyExplicitRingOver| #18=(|Integer|))))) (AND #5# #17#) (AND #6# #17#) (AND #17# #12#) #19=(AND #17# #14#)) #12# (OR #5# #12# #14#) #5# (OR #5# #20=(AND (|HasCategory| |#4| (QUOTE (|DifferentialSpace|))) #14#)) (OR #21=(AND (|HasCategory| |#4| (QUOTE (|PartialDifferentialSpace| #13#))) #14#) #12#) #16# (OR (AND #1# #22=(|HasCategory| |#4| (QUOTE (|RetractableTo| (|Fraction| #18#))))) (AND #4# #22#) (AND #5# #22#) (AND #6# #22#) (AND #7# #22#) (AND #8# #22#) (AND #9# #22#) (AND #10# #22#) (AND #12# #22#) (AND #22# #14#) #23=(AND #22# #16#)) (OR #24=(AND #1# #25=(|HasCategory| |#4| (QUOTE (|RetractableTo| #18#)))) #26=(AND #4# #25#) #27=(AND #5# #25#) #28=(AND #9# #25#) #29=(AND #10# #25#) #30=(AND #12# #25#) #31=(AND #25# #16#) #32=(AND #6# #25#) #33=(AND #7# #25#) #34=(AND #8# #25#) #14#) (OR #24# #26# #27# #28# #29# #30# #31# #32# #33# #34# (AND #25# #14#)) #35=(|HasCategory| |#4| (QUOTE (|BasicType|))) (|HasCategory| #18# #11#) #19# (OR (AND #5# #14#) #20#) (OR (AND #12# #14#) #21#) #31# (OR #31# #14#) #23# #21# #20# #4# #1# (|HasCategory| |#4| (QUOTE (|AbelianMonoid|))) (|HasCategory| |#4| (QUOTE (|CancellationAbelianMonoid|))) (|HasCategory| |#4| (QUOTE (|AbelianSemiGroup|))) (|HasCategory| |#4| (QUOTE (|CoercibleTo| (|OutputForm|)))) #15# (AND #35# (|HasCategory| $ (|%list| (QUOTE |FiniteAggregate|) #3#))) (|HasCategory| $ (|%list| (QUOTE |ShallowlyMutableAggregate|) #3#))) (|DirectProductModule| |n| R S) ((|constructor| (NIL "This constructor provides a direct product of \\spad{R}-modules with an \\spad{R}-module view."))) -((|unitsKnown| OR (|and| #1=(|has| |#3| #2=(|Ring|)) (|has| |#3| (|DifferentialRing|))) (|has| |#3| (ATTRIBUTE |unitsKnown|)) (|and| #1# (|has| |#3| (|PartialDifferentialRing| (|Symbol|))))) (|rightUnitary| |has| |#3| . #3=(#2#)) (|leftUnitary| |has| |#3| . #3#)) -((OR (AND #1=(|HasCategory| |#3| (QUOTE (|AbelianGroup|))) #2=(|HasCategory| |#3| (|%list| (QUOTE |Evalable|) #3=(|devaluate| |#3|)))) (AND #4=(|HasCategory| |#3| (QUOTE (|CommutativeRing|))) #2#) (AND #5=(|HasCategory| |#3| (QUOTE (|DifferentialRing|))) #2#) (AND #6=(|HasCategory| |#3| (QUOTE (|Field|))) #2#) (AND #7=(|HasCategory| |#3| (QUOTE (|Finite|))) #2#) (AND #8=(|HasCategory| |#3| (QUOTE (|Monoid|))) #2#) (AND #9=(|HasCategory| |#3| (QUOTE (|OrderedAbelianMonoidSup|))) #2#) (AND #10=(|HasCategory| |#3| #11=(QUOTE (|OrderedSet|))) #2#) (AND #12=(|HasCategory| |#3| (QUOTE (|PartialDifferentialRing| #13=(|Symbol|)))) #2#) (AND #14=(|HasCategory| |#3| (QUOTE (|Ring|))) #2#) #15=(AND #16=(|HasCategory| |#3| (QUOTE (|SetCategory|))) #2#)) #6# (OR #4# #6# #14#) (OR #4# #6#) #14# #8# #9# (OR #9# #10#) #10# #7# (OR (AND #4# #17=(|HasCategory| |#3| (QUOTE (|LinearlyExplicitRingOver| #18=(|Integer|))))) (AND #5# #17#) (AND #6# #17#) (AND #17# #12#) #19=(AND #17# #14#)) #12# (OR #5# #12# #14#) #5# (OR #5# #20=(AND (|HasCategory| |#3| (QUOTE (|DifferentialSpace|))) #14#)) (OR #21=(AND (|HasCategory| |#3| (QUOTE (|PartialDifferentialSpace| #13#))) #14#) #12#) #16# (OR (AND #1# #22=(|HasCategory| |#3| (QUOTE (|RetractableTo| (|Fraction| #18#))))) (AND #4# #22#) (AND #5# #22#) (AND #6# #22#) (AND #7# #22#) (AND #8# #22#) (AND #9# #22#) (AND #10# #22#) (AND #12# #22#) (AND #22# #14#) #23=(AND #22# #16#)) (OR #24=(AND #1# #25=(|HasCategory| |#3| (QUOTE (|RetractableTo| #18#)))) #26=(AND #4# #25#) #27=(AND #5# #25#) #28=(AND #9# #25#) #29=(AND #10# #25#) #30=(AND #12# #25#) #31=(AND #25# #16#) #32=(AND #6# #25#) #33=(AND #7# #25#) #34=(AND #8# #25#) #14#) (OR #24# #26# #27# #28# #29# #30# #31# #32# #33# #34# (AND #25# #14#)) #35=(|HasCategory| |#3| (QUOTE (|BasicType|))) (|HasCategory| #18# #11#) #19# (OR #36=(AND #12# #14#) #21#) (OR #37=(AND #5# #14#) #20#) #31# (OR #31# #14#) #23# (OR #36# (|HasAttribute| |#3| (QUOTE |unitsKnown|)) #37#) #20# #21# #4# #1# (|HasCategory| |#3| (QUOTE (|AbelianMonoid|))) (|HasCategory| |#3| (QUOTE (|CancellationAbelianMonoid|))) (|HasCategory| |#3| (QUOTE (|AbelianSemiGroup|))) (|HasCategory| |#3| (QUOTE (|CoercibleTo| (|OutputForm|)))) #15# (AND #35# (|HasCategory| $ (|%list| (QUOTE |FiniteAggregate|) #3#))) (|HasCategory| $ (|%list| (QUOTE |ShallowlyMutableAggregate|) #3#))) +NIL +((OR (AND #1=(|HasCategory| |#3| (QUOTE (|AbelianGroup|))) #2=(|HasCategory| |#3| (|%list| (QUOTE |Evalable|) #3=(|devaluate| |#3|)))) (AND #4=(|HasCategory| |#3| (QUOTE (|CommutativeRing|))) #2#) (AND #5=(|HasCategory| |#3| (QUOTE (|DifferentialRing|))) #2#) (AND #6=(|HasCategory| |#3| (QUOTE (|Field|))) #2#) (AND #7=(|HasCategory| |#3| (QUOTE (|Finite|))) #2#) (AND #8=(|HasCategory| |#3| (QUOTE (|Monoid|))) #2#) (AND #9=(|HasCategory| |#3| (QUOTE (|OrderedAbelianMonoidSup|))) #2#) (AND #10=(|HasCategory| |#3| #11=(QUOTE (|OrderedSet|))) #2#) (AND #12=(|HasCategory| |#3| (QUOTE (|PartialDifferentialRing| #13=(|Symbol|)))) #2#) (AND #14=(|HasCategory| |#3| (QUOTE (|Ring|))) #2#) #15=(AND #16=(|HasCategory| |#3| (QUOTE (|SetCategory|))) #2#)) #6# (OR #4# #6# #14#) (OR #4# #6#) #14# #8# #9# (OR #9# #10#) #10# #7# (OR (AND #4# #17=(|HasCategory| |#3| (QUOTE (|LinearlyExplicitRingOver| #18=(|Integer|))))) (AND #5# #17#) (AND #6# #17#) (AND #17# #12#) #19=(AND #17# #14#)) #12# (OR #5# #12# #14#) #5# (OR #5# #20=(AND (|HasCategory| |#3| (QUOTE (|DifferentialSpace|))) #14#)) (OR #21=(AND (|HasCategory| |#3| (QUOTE (|PartialDifferentialSpace| #13#))) #14#) #12#) #16# (OR (AND #1# #22=(|HasCategory| |#3| (QUOTE (|RetractableTo| (|Fraction| #18#))))) (AND #4# #22#) (AND #5# #22#) (AND #6# #22#) (AND #7# #22#) (AND #8# #22#) (AND #9# #22#) (AND #10# #22#) (AND #12# #22#) (AND #22# #14#) #23=(AND #22# #16#)) (OR #24=(AND #1# #25=(|HasCategory| |#3| (QUOTE (|RetractableTo| #18#)))) #26=(AND #4# #25#) #27=(AND #5# #25#) #28=(AND #9# #25#) #29=(AND #10# #25#) #30=(AND #12# #25#) #31=(AND #25# #16#) #32=(AND #6# #25#) #33=(AND #7# #25#) #34=(AND #8# #25#) #14#) (OR #24# #26# #27# #28# #29# #30# #31# #32# #33# #34# (AND #25# #14#)) #35=(|HasCategory| |#3| (QUOTE (|BasicType|))) (|HasCategory| #18# #11#) #19# (OR (AND #5# #14#) #20#) (OR (AND #12# #14#) #21#) #31# (OR #31# #14#) #23# #21# #20# #4# #1# (|HasCategory| |#3| (QUOTE (|AbelianMonoid|))) (|HasCategory| |#3| (QUOTE (|CancellationAbelianMonoid|))) (|HasCategory| |#3| (QUOTE (|AbelianSemiGroup|))) (|HasCategory| |#3| (QUOTE (|CoercibleTo| (|OutputForm|)))) #15# (AND #35# (|HasCategory| $ (|%list| (QUOTE |FiniteAggregate|) #3#))) (|HasCategory| $ (|%list| (QUOTE |ShallowlyMutableAggregate|) #3#))) (|DifferentialPolynomialCategory&| A R S V E) ((|constructor| (NIL "\\spadtype{DifferentialPolynomialCategory} is a category constructor specifying basic functions in an ordinary differential polynomial ring with a given ordered set of differential indeterminates. In addition,{} it implements defaults for the basic functions. The functions \\spadfun{order} and \\spadfun{weight} are extended from the set of derivatives of differential indeterminates to the set of differential polynomials. Other operations provided on differential polynomials are \\spadfun{leader},{} \\spadfun{initial},{} \\spadfun{separant},{} \\spadfun{differentialVariables},{} and \\spadfun{isobaric?}. Furthermore,{} if the ground ring is a differential ring,{} then evaluation (substitution of differential indeterminates by elements of the ground ring or by differential polynomials) is provided by \\spadfun{eval}. A convenient way of referencing derivatives is provided by the functions \\spadfun{makeVariable}. \\blankline To construct a domain using this constructor,{} one needs to provide a ground ring \\spad{R},{} an ordered set \\spad{S} of differential indeterminates,{} a ranking \\spad{V} on the set of derivatives of the differential indeterminates,{} and a set \\spad{E} of exponents in bijection with the set of differential monomials in the given differential indeterminates. \\blankline")) (|separant| (($ $) "\\spad{separant(p)} returns the partial derivative of the differential polynomial \\spad{p} with respect to its leader.")) (|initial| (($ $) "\\spad{initial(p)} returns the leading coefficient when the differential polynomial \\spad{p} is written as a univariate polynomial in its leader.")) (|leader| ((|#4| $) "\\spad{leader(p)} returns the derivative of the highest rank appearing in the differential polynomial \\spad{p} Note: an error occurs if \\spad{p} is in the ground ring.")) (|isobaric?| (((|Boolean|) $) "\\spad{isobaric?(p)} returns \\spad{true} if every differential monomial appearing in the differential polynomial \\spad{p} has same weight,{} and returns \\spad{false} otherwise.")) (|weight| (((|NonNegativeInteger|) $ |#3|) "\\spad{weight(p, s)} returns the maximum weight of all differential monomials appearing in the differential polynomial \\spad{p} when \\spad{p} is viewed as a differential polynomial in the differential indeterminate \\spad{s} alone.") (((|NonNegativeInteger|) $) "\\spad{weight(p)} returns the maximum weight of all differential monomials appearing in the differential polynomial \\spad{p}.")) (|weights| (((|List| (|NonNegativeInteger|)) $ |#3|) "\\spad{weights(p, s)} returns a list of weights of differential monomials appearing in the differential polynomial \\spad{p} when \\spad{p} is viewed as a differential polynomial in the differential indeterminate \\spad{s} alone.") (((|List| (|NonNegativeInteger|)) $) "\\spad{weights(p)} returns a list of weights of differential monomials appearing in differential polynomial \\spad{p}.")) (|degree| (((|NonNegativeInteger|) $ |#3|) "\\spad{degree(p, s)} returns the maximum degree of the differential polynomial \\spad{p} viewed as a differential polynomial in the differential indeterminate \\spad{s} alone.")) (|order| (((|NonNegativeInteger|) $) "\\spad{order(p)} returns the order of the differential polynomial \\spad{p},{} which is the maximum number of differentiations of a differential indeterminate,{} among all those appearing in \\spad{p}.") (((|NonNegativeInteger|) $ |#3|) "\\spad{order(p,s)} returns the order of the differential polynomial \\spad{p} in differential indeterminate \\spad{s}.")) (|differentialVariables| (((|List| |#3|) $) "\\spad{differentialVariables(p)} returns a list of differential indeterminates occurring in a differential polynomial \\spad{p}.")) (|makeVariable| (((|Mapping| $ (|NonNegativeInteger|)) $) "\\spad{makeVariable(p)} views \\spad{p} as an element of a differential ring,{} in such a way that the \\spad{n}-th derivative of \\spad{p} may be simply referenced as \\spad{z}.\\spad{n} where \\spad{z} := makeVariable(\\spad{p}). Note: In the interpreter,{} \\spad{z} is given as an internal map,{} which may be ignored.") (((|Mapping| $ (|NonNegativeInteger|)) |#3|) "\\spad{makeVariable(s)} views \\spad{s} as a differential indeterminate,{} in such a way that the \\spad{n}-th derivative of \\spad{s} may be simply referenced as \\spad{z}.\\spad{n} where \\spad{z} :=makeVariable(\\spad{s}). Note: In the interpreter,{} \\spad{z} is given as an internal map,{} which may be ignored."))) NIL ((|HasCategory| |#2| (QUOTE (|DifferentialRing|)))) (|DifferentialPolynomialCategory| R S V E) ((|constructor| (NIL "\\spadtype{DifferentialPolynomialCategory} is a category constructor specifying basic functions in an ordinary differential polynomial ring with a given ordered set of differential indeterminates. In addition,{} it implements defaults for the basic functions. The functions \\spadfun{order} and \\spadfun{weight} are extended from the set of derivatives of differential indeterminates to the set of differential polynomials. Other operations provided on differential polynomials are \\spadfun{leader},{} \\spadfun{initial},{} \\spadfun{separant},{} \\spadfun{differentialVariables},{} and \\spadfun{isobaric?}. Furthermore,{} if the ground ring is a differential ring,{} then evaluation (substitution of differential indeterminates by elements of the ground ring or by differential polynomials) is provided by \\spadfun{eval}. A convenient way of referencing derivatives is provided by the functions \\spadfun{makeVariable}. \\blankline To construct a domain using this constructor,{} one needs to provide a ground ring \\spad{R},{} an ordered set \\spad{S} of differential indeterminates,{} a ranking \\spad{V} on the set of derivatives of the differential indeterminates,{} and a set \\spad{E} of exponents in bijection with the set of differential monomials in the given differential indeterminates. \\blankline")) (|separant| (($ $) "\\spad{separant(p)} returns the partial derivative of the differential polynomial \\spad{p} with respect to its leader.")) (|initial| (($ $) "\\spad{initial(p)} returns the leading coefficient when the differential polynomial \\spad{p} is written as a univariate polynomial in its leader.")) (|leader| ((|#3| $) "\\spad{leader(p)} returns the derivative of the highest rank appearing in the differential polynomial \\spad{p} Note: an error occurs if \\spad{p} is in the ground ring.")) (|isobaric?| (((|Boolean|) $) "\\spad{isobaric?(p)} returns \\spad{true} if every differential monomial appearing in the differential polynomial \\spad{p} has same weight,{} and returns \\spad{false} otherwise.")) (|weight| (((|NonNegativeInteger|) $ |#2|) "\\spad{weight(p, s)} returns the maximum weight of all differential monomials appearing in the differential polynomial \\spad{p} when \\spad{p} is viewed as a differential polynomial in the differential indeterminate \\spad{s} alone.") (((|NonNegativeInteger|) $) "\\spad{weight(p)} returns the maximum weight of all differential monomials appearing in the differential polynomial \\spad{p}.")) (|weights| (((|List| (|NonNegativeInteger|)) $ |#2|) "\\spad{weights(p, s)} returns a list of weights of differential monomials appearing in the differential polynomial \\spad{p} when \\spad{p} is viewed as a differential polynomial in the differential indeterminate \\spad{s} alone.") (((|List| (|NonNegativeInteger|)) $) "\\spad{weights(p)} returns a list of weights of differential monomials appearing in differential polynomial \\spad{p}.")) (|degree| (((|NonNegativeInteger|) $ |#2|) "\\spad{degree(p, s)} returns the maximum degree of the differential polynomial \\spad{p} viewed as a differential polynomial in the differential indeterminate \\spad{s} alone.")) (|order| (((|NonNegativeInteger|) $) "\\spad{order(p)} returns the order of the differential polynomial \\spad{p},{} which is the maximum number of differentiations of a differential indeterminate,{} among all those appearing in \\spad{p}.") (((|NonNegativeInteger|) $ |#2|) "\\spad{order(p,s)} returns the order of the differential polynomial \\spad{p} in differential indeterminate \\spad{s}.")) (|differentialVariables| (((|List| |#2|) $) "\\spad{differentialVariables(p)} returns a list of differential indeterminates occurring in a differential polynomial \\spad{p}.")) (|makeVariable| (((|Mapping| $ (|NonNegativeInteger|)) $) "\\spad{makeVariable(p)} views \\spad{p} as an element of a differential ring,{} in such a way that the \\spad{n}-th derivative of \\spad{p} may be simply referenced as \\spad{z}.\\spad{n} where \\spad{z} := makeVariable(\\spad{p}). Note: In the interpreter,{} \\spad{z} is given as an internal map,{} which may be ignored.") (((|Mapping| $ (|NonNegativeInteger|)) |#2|) "\\spad{makeVariable(s)} views \\spad{s} as a differential indeterminate,{} in such a way that the \\spad{n}-th derivative of \\spad{s} may be simply referenced as \\spad{z}.\\spad{n} where \\spad{z} :=makeVariable(\\spad{s}). Note: In the interpreter,{} \\spad{z} is given as an internal map,{} which may be ignored."))) -(((|commutative| "*") |has| |#1| (|CommutativeRing|)) (|noZeroDivisors| |has| |#1| (|IntegralDomain|)) (|canonicalUnitNormal| |has| |#1| (ATTRIBUTE |canonicalUnitNormal|)) (|leftUnitary| . T) (|rightUnitary| . T) (|unitsKnown| . T)) +(((|commutative| "*") |has| |#1| (|CommutativeRing|)) (|noZeroDivisors| |has| |#1| (|IntegralDomain|)) (|canonicalUnitNormal| |has| |#1| (ATTRIBUTE |canonicalUnitNormal|))) NIL (|DequeueAggregate| S) ((|constructor| (NIL "A dequeue is a doubly ended stack,{} that is,{} a bag where first items inserted are the first items extracted,{} at either the front or the back end of the data structure.")) (|reverse!| (($ $) "\\spad{reverse!(d)} destructively replaces \\spad{d} by its reverse dequeue,{} \\spadignore{i.e.} the top (front) element is now the bottom (back) element,{} and so on.")) (|extractBottom!| ((|#1| $) "\\spad{extractBottom!(d)} destructively extracts the bottom (back) element from the dequeue \\spad{d}. Error: if \\spad{d} is empty.")) (|extractTop!| ((|#1| $) "\\spad{extractTop!(d)} destructively extracts the top (front) element from the dequeue \\spad{d}. Error: if \\spad{d} is empty.")) (|insertBottom!| ((|#1| |#1| $) "\\spad{insertBottom!(x,d)} destructively inserts \\spad{x} into the dequeue \\spad{d} at the bottom (back) of the dequeue.")) (|insertTop!| ((|#1| |#1| $) "\\spad{insertTop!(x,d)} destructively inserts \\spad{x} into the dequeue \\spad{d},{} that is,{} at the top (front) of the dequeue. The element previously at the top of the dequeue becomes the second in the dequeue,{} and so on.")) (|bottom!| ((|#1| $) "\\spad{bottom!(d)} returns the element at the bottom (back) of the dequeue.")) (|top!| ((|#1| $) "\\spad{top!(d)} returns the element at the top (front) of the dequeue.")) (|height| (((|NonNegativeInteger|) $) "\\spad{height(d)} returns the number of elements in dequeue \\spad{d}. Note: \\axiom{height(\\spad{d}) = \\# \\spad{d}}.")) (|dequeue| (($ (|List| |#1|)) "\\spad{dequeue([x,y,...,z])} creates a dequeue with first (top or front) element \\spad{x},{} second element \\spad{y},{}...,{}and last (bottom or back) element \\spad{z}.") (($) "\\spad{dequeue()}\\$\\spad{D} creates an empty dequeue of type \\spad{D}."))) @@ -842,8 +842,8 @@ NIL NIL (|DifferentialSparseMultivariatePolynomial| R S V) ((|constructor| (NIL "\\spadtype{DifferentialSparseMultivariatePolynomial} implements an ordinary differential polynomial ring by combining a domain belonging to the category \\spadtype{DifferentialVariableCategory} with the domain \\spadtype{SparseMultivariatePolynomial}. \\blankline"))) -(((|commutative| "*") |has| |#1| (|CommutativeRing|)) (|noZeroDivisors| |has| |#1| (|IntegralDomain|)) (|canonicalUnitNormal| |has| |#1| (ATTRIBUTE |canonicalUnitNormal|)) (|leftUnitary| . T) (|rightUnitary| . T) (|unitsKnown| . T)) -(#1=(|HasCategory| |#1| (QUOTE (|PolynomialFactorizationExplicit|))) (OR #2=(|HasCategory| |#1| (QUOTE (|CommutativeRing|))) #3=(|HasCategory| |#1| (QUOTE (|GcdDomain|))) #4=(|HasCategory| |#1| (QUOTE (|IntegralDomain|))) #1#) (OR #3# #4# #1#) (OR #3# #1#) #4# #2# (OR #2# #4#) (AND (|HasCategory| |#1| #5=(QUOTE (|PatternMatchable| #6=(|Float|)))) (|HasCategory| |#3| #5#)) (AND (|HasCategory| |#1| #7=(QUOTE (|PatternMatchable| #8=(|Integer|)))) (|HasCategory| |#3| #7#)) (AND (|HasCategory| |#1| #9=(QUOTE (|ConvertibleTo| (|Pattern| #6#)))) (|HasCategory| |#3| #9#)) (AND (|HasCategory| |#1| #10=(QUOTE (|ConvertibleTo| (|Pattern| #8#)))) (|HasCategory| |#3| #10#)) (AND (|HasCategory| |#1| #11=(QUOTE (|ConvertibleTo| (|InputForm|)))) (|HasCategory| |#3| #11#)) (|HasCategory| |#1| (QUOTE (|LinearlyExplicitRingOver| #8#))) (|HasCategory| |#1| (QUOTE (|CharacteristicZero|))) #12=(|HasCategory| |#1| #13=(QUOTE (|CharacteristicNonZero|))) #14=(|HasCategory| |#1| (QUOTE (|Algebra| #15=(|Fraction| #8#)))) (|HasCategory| |#1| (QUOTE (|RetractableTo| #8#))) (OR #14# #16=(|HasCategory| |#1| (QUOTE (|RetractableTo| #15#)))) #16# (|HasCategory| |#1| (QUOTE (|DifferentialRing|))) (|HasCategory| |#1| (QUOTE (|DifferentialSpace|))) (|HasCategory| |#1| (QUOTE (|PartialDifferentialSpace| #17=(|Symbol|)))) (|HasCategory| |#1| (QUOTE (|PartialDifferentialRing| #17#))) (|HasCategory| |#1| (QUOTE (|Field|))) (|HasAttribute| |#1| (QUOTE |canonicalUnitNormal|)) #3# #18=(AND #1# (|HasCategory| $ #13#)) (OR #18# #12#)) +(((|commutative| "*") |has| |#1| (|CommutativeRing|)) (|noZeroDivisors| |has| |#1| (|IntegralDomain|)) (|canonicalUnitNormal| |has| |#1| (ATTRIBUTE |canonicalUnitNormal|))) +(#1=(|HasCategory| |#1| (QUOTE (|PolynomialFactorizationExplicit|))) (OR #2=(|HasCategory| |#1| (QUOTE (|CommutativeRing|))) #3=(|HasCategory| |#1| (QUOTE (|GcdDomain|))) #4=(|HasCategory| |#1| (QUOTE (|IntegralDomain|))) #1#) (OR #3# #4# #1#) (OR #3# #1#) #4# #2# (OR #2# #4#) (AND (|HasCategory| |#1| #5=(QUOTE (|PatternMatchable| #6=(|Float|)))) (|HasCategory| |#3| #5#)) (AND (|HasCategory| |#1| #7=(QUOTE (|PatternMatchable| #8=(|Integer|)))) (|HasCategory| |#3| #7#)) (AND (|HasCategory| |#1| #9=(QUOTE (|ConvertibleTo| (|Pattern| #6#)))) (|HasCategory| |#3| #9#)) (AND (|HasCategory| |#1| #10=(QUOTE (|ConvertibleTo| (|Pattern| #8#)))) (|HasCategory| |#3| #10#)) (AND (|HasCategory| |#1| #11=(QUOTE (|ConvertibleTo| (|InputForm|)))) (|HasCategory| |#3| #11#)) (|HasCategory| |#1| (QUOTE (|LinearlyExplicitRingOver| #8#))) #12=(|HasCategory| |#1| (QUOTE (|Algebra| #13=(|Fraction| #8#)))) #14=(|HasCategory| |#1| #15=(QUOTE (|CharacteristicNonZero|))) (|HasCategory| |#1| (QUOTE (|CharacteristicZero|))) (|HasCategory| |#1| (QUOTE (|RetractableTo| #8#))) (OR #12# #16=(|HasCategory| |#1| (QUOTE (|RetractableTo| #13#)))) #16# (|HasCategory| |#1| (QUOTE (|DifferentialRing|))) (|HasCategory| |#1| (QUOTE (|PartialDifferentialSpace| #17=(|Symbol|)))) (|HasCategory| |#1| (QUOTE (|DifferentialSpace|))) (|HasCategory| |#1| (QUOTE (|PartialDifferentialRing| #17#))) (|HasCategory| |#1| (QUOTE (|Field|))) (|HasAttribute| |#1| (QUOTE |canonicalUnitNormal|)) #3# #18=(AND #1# (|HasCategory| $ #15#)) (OR #18# #14#)) (|DifferentialVariableCategory&| A S) ((|constructor| (NIL "\\spadtype{DifferentialVariableCategory} constructs the set of derivatives of a given set of (ordinary) differential indeterminates. If \\spad{x},{}...,{}\\spad{y} is an ordered set of differential indeterminates,{} and the prime notation is used for differentiation,{} then the set of derivatives (including zero-th order) of the differential indeterminates is \\spad{x},{}\\spad{x'},{}\\spad{x''},{}...,{} \\spad{y},{}\\spad{y'},{}\\spad{y''},{}... (Note: in the interpreter,{} the \\spad{n}-th derivative of \\spad{y} is displayed as \\spad{y} with a subscript \\spad{n}.) This set is viewed as a set of algebraic indeterminates,{} totally ordered in a way compatible with differentiation and the given order on the differential indeterminates. Such a total order is called a ranking of the differential indeterminates. \\blankline A domain in this category is needed to construct a differential polynomial domain. Differential polynomials are ordered by a ranking on the derivatives,{} and by an order (extending the ranking) on on the set of differential monomials. One may thus associate a domain in this category with a ranking of the differential indeterminates,{} just as one associates a domain in the category \\spadtype{OrderedAbelianMonoidSup} with an ordering of the set of monomials in a set of algebraic indeterminates. The ranking is specified through the binary relation \\spadfun{<}. For example,{} one may define one derivative to be less than another by lexicographically comparing first the \\spadfun{order},{} then the given order of the differential indeterminates appearing in the derivatives. This is the default implementation. \\blankline The notion of weight generalizes that of degree. A polynomial domain may be made into a graded ring if a weight function is given on the set of indeterminates,{} Very often,{} a grading is the first step in ordering the set of monomials. For differential polynomial domains,{} this constructor provides a function \\spadfun{weight},{} which allows the assignment of a non-negative number to each derivative of a differential indeterminate. For example,{} one may define the weight of a derivative to be simply its \\spadfun{order} (this is the default assignment). This weight function can then be extended to the set of all differential polynomials,{} providing a graded ring structure.")) (|weight| (((|NonNegativeInteger|) $) "\\spad{weight(v)} returns the weight of the derivative \\spad{v}.")) (|variable| ((|#2| $) "\\spad{variable(v)} returns \\spad{s} if \\spad{v} is any derivative of the differential indeterminate \\spad{s}.")) (|order| (((|NonNegativeInteger|) $) "\\spad{order(v)} returns \\spad{n} if \\spad{v} is the \\spad{n}-th derivative of any differential indeterminate.")) (|makeVariable| (($ |#2| (|NonNegativeInteger|)) "\\spad{makeVariable(s, n)} returns the \\spad{n}-th derivative of a differential indeterminate \\spad{s} as an algebraic indeterminate."))) NIL @@ -913,8 +913,8 @@ NIL NIL NIL (|EuclideanModularRing| S R |Mod| |reduction| |merge| |exactQuo|) -((|constructor| (NIL "These domains are used for the factorization and gcds of univariate polynomials over the integers in order to work modulo different primes. See \\spadtype{ModularRing},{} \\spadtype{ModularField}")) (|inv| (($ $) "\\spad{inv(x)} \\undocumented")) (|recip| (((|Union| $ "failed") $) "\\spad{recip(x)} \\undocumented")) (|exQuo| (((|Union| $ "failed") $ $) "\\spad{exQuo(x,y)} \\undocumented")) (|reduce| (($ |#2| |#3|) "\\spad{reduce(r,m)} \\undocumented")) (|coerce| ((|#2| $) "\\spad{coerce(x)} \\undocumented")) (|modulus| ((|#3| $) "\\spad{modulus(x)} \\undocumented"))) -((|noZeroDivisors| . T) ((|commutative| "*") . T) (|rightUnitary| . T) (|leftUnitary| . T) (|unitsKnown| . T)) +((|constructor| (NIL "These domains are used for the factorization and gcds of univariate polynomials over the integers in order to work modulo different primes. See \\spadtype{ModularRing},{} \\spadtype{ModularField}")) (|inv| (($ $) "\\spad{inv(x)} \\undocumented")) (|exQuo| (((|Union| $ "failed") $ $) "\\spad{exQuo(x,y)} \\undocumented")) (|reduce| (($ |#2| |#3|) "\\spad{reduce(r,m)} \\undocumented")) (|modulus| ((|#3| $) "\\spad{modulus(x)} \\undocumented"))) +((|noZeroDivisors| . T) ((|commutative| "*") . T)) NIL (|EntireRing&| S) ((|constructor| (NIL "Entire Rings (non-commutative Integral Domains),{} \\spadignore{i.e.} a ring not necessarily commutative which has no zero divisors. \\blankline")) (|noZeroDivisors| ((|attribute|) "if a product is zero then one of the factors must be zero."))) @@ -922,7 +922,7 @@ NIL NIL (|EntireRing|) ((|constructor| (NIL "Entire Rings (non-commutative Integral Domains),{} \\spadignore{i.e.} a ring not necessarily commutative which has no zero divisors. \\blankline")) (|noZeroDivisors| ((|attribute|) "if a product is zero then one of the factors must be zero."))) -((|noZeroDivisors| . T) (|rightUnitary| . T) (|leftUnitary| . T) (|unitsKnown| . T)) +((|noZeroDivisors| . T)) NIL (|Environment|) ((|constructor| (NIL "\\indented{1}{Author: Gabriel Dos Reis} Date Created: October 24,{} 2007 Date Last Modified: March 18,{} 2010. An `Environment' is a stack of scope.")) (|categoryFrame| (($) "the current category environment in the interpreter.")) (|interactiveEnv| (($) "the current interactive environment in effect.")) (|currentEnv| (($) "the current normal environment in effect.")) (|putProperties| (($ (|Identifier|) (|List| (|Property|)) $) "\\spad{putProperties(n,props,e)} set the list of properties of \\spad{n} to \\spad{props} in \\spad{e}.")) (|getProperties| (((|List| (|Property|)) (|Identifier|) $) "\\spad{getBinding(n,e)} returns the list of properties of \\spad{n} in \\spad{e}.")) (|putProperty| (($ (|Identifier|) (|Identifier|) (|SExpression|) $) "\\spad{putProperty(n,p,v,e)} binds the property \\spad{(p,v)} to \\spad{n} in the topmost scope of \\spad{e}.")) (|getProperty| (((|Maybe| (|SExpression|)) (|Identifier|) (|Identifier|) $) "\\spad{getProperty(n,p,e)} returns the value of property with name \\spad{p} for the symbol \\spad{n} in environment \\spad{e}. Otherwise,{} \\spad{nothing}.")) (|scopes| (((|List| (|Scope|)) $) "\\spad{scopes(e)} returns the stack of scopes in environment \\spad{e}.")) (|empty| (($) "\\spad{empty()} constructs an empty environment"))) @@ -934,8 +934,8 @@ NIL NIL (|Equation| S) ((|constructor| (NIL "Equations as mathematical objects. All properties of the basis domain,{} \\spadignore{e.g.} being an abelian group are carried over the equation domain,{} by performing the structural operations on the left and on the right hand side.")) (|subst| (($ $ $) "\\spad{subst(eq1,eq2)} substitutes \\spad{eq2} into both sides of \\spad{eq1} the lhs of \\spad{eq2} should be a kernel")) (|inv| (($ $) "\\spad{inv(x)} returns the multiplicative inverse of \\spad{x}.")) (/ (($ $ $) "\\spad{e1/e2} produces a new equation by dividing the left and right hand sides of equations \\spad{e1} and \\spad{e2}.")) (|factorAndSplit| (((|List| $) $) "\\spad{factorAndSplit(eq)} make the right hand side 0 and factors the new left hand side. Each factor is equated to 0 and put into the resulting list without repetitions.")) (|rightOne| (((|Union| $ "failed") $) "\\spad{rightOne(eq)} divides by the right hand side.") (((|Union| $ "failed") $) "\\spad{rightOne(eq)} divides by the right hand side,{} if possible.")) (|leftOne| (((|Union| $ "failed") $) "\\spad{leftOne(eq)} divides by the left hand side.") (((|Union| $ "failed") $) "\\spad{leftOne(eq)} divides by the left hand side,{} if possible.")) (* (($ $ |#1|) "\\spad{eqn*x} produces a new equation by multiplying both sides of equation eqn by \\spad{x}.") (($ |#1| $) "\\spad{x*eqn} produces a new equation by multiplying both sides of equation eqn by \\spad{x}.")) (- (($ $ |#1|) "\\spad{eqn-x} produces a new equation by subtracting \\spad{x} from both sides of equation eqn.") (($ |#1| $) "\\spad{x-eqn} produces a new equation by subtracting both sides of equation eqn from \\spad{x}.")) (|rightZero| (($ $) "\\spad{rightZero(eq)} subtracts the right hand side.")) (|leftZero| (($ $) "\\spad{leftZero(eq)} subtracts the left hand side.")) (+ (($ $ |#1|) "\\spad{eqn+x} produces a new equation by adding \\spad{x} to both sides of equation eqn.") (($ |#1| $) "\\spad{x+eqn} produces a new equation by adding \\spad{x} to both sides of equation eqn.")) (|eval| (($ $ (|List| $)) "\\spad{eval(eqn, [x1=v1, ... xn=vn])} replaces \\spad{xi} by \\spad{vi} in equation \\spad{eqn}.") (($ $ $) "\\spad{eval(eqn, x=f)} replaces \\spad{x} by \\spad{f} in equation \\spad{eqn}.")) (|rhs| ((|#1| $) "\\spad{rhs(eqn)} returns the right hand side of equation \\spad{eqn}.")) (|lhs| ((|#1| $) "\\spad{lhs(eqn)} returns the left hand side of equation \\spad{eqn}.")) (|swap| (($ $) "\\spad{swap(eq)} interchanges left and right hand side of equation \\spad{eq}.")) (|equation| (($ |#1| |#1|) "\\spad{equation(a,b)} creates an equation.")) (= (($ |#1| |#1|) "\\spad{a=b} creates an equation."))) -((|unitsKnown| OR (|has| |#1| #1=(|Ring|)) (|has| |#1| (|Group|))) (|rightUnitary| |has| |#1| . #2=(#1#)) (|leftUnitary| |has| |#1| . #2#)) -(#1=(|HasCategory| |#1| (QUOTE (|Field|))) (OR #2=(|HasCategory| |#1| (QUOTE (|CommutativeRing|))) #1# #3=(|HasCategory| |#1| (QUOTE (|Ring|)))) (OR #2# #1#) #4=(|HasCategory| |#1| (QUOTE (|AbelianGroup|))) #3# #5=(|HasCategory| |#1| (QUOTE (|SetCategory|))) #2# #6=(|HasCategory| |#1| (QUOTE (|PartialDifferentialRing| #7=(|Symbol|)))) (OR #6# #3#) (OR #4# #8=(|HasCategory| |#1| (QUOTE (|AbelianSemiGroup|))) #2# #1# #6# #3#) (OR #4# #2# #1# #6# #3#) (OR #2# #3#) (OR #9=(|HasCategory| |#1| (QUOTE (|Group|))) #10=(|HasCategory| |#1| (QUOTE (|Monoid|)))) #9# (OR #4# #8# #2# #1# #9# #10# #6# #3# #11=(|HasCategory| |#1| (QUOTE (|SemiGroup|))) #5#) (OR #9# #10# #11#) (|HasCategory| |#1| (|%list| (QUOTE |InnerEvalable|) (QUOTE #7#) #12=(|devaluate| |#1|))) (AND #5# (|HasCategory| |#1| (|%list| (QUOTE |Evalable|) #12#))) (|HasCategory| |#1| (QUOTE (|IntegralDomain|))) (|HasCategory| |#1| (QUOTE (|ExpressionSpace|))) (OR #1# #9#) (OR #4# #10#) (OR #9# #3#) #8# #11# #10#) +NIL +(#1=(|HasCategory| |#1| (QUOTE (|Field|))) (OR #2=(|HasCategory| |#1| (QUOTE (|CommutativeRing|))) #1# #3=(|HasCategory| |#1| (QUOTE (|Ring|)))) (OR #2# #1#) #4=(|HasCategory| |#1| (QUOTE (|AbelianGroup|))) #3# #5=(|HasCategory| |#1| (QUOTE (|SetCategory|))) #2# #6=(|HasCategory| |#1| (QUOTE (|PartialDifferentialRing| #7=(|Symbol|)))) (OR #6# #3#) (OR #4# #8=(|HasCategory| |#1| (QUOTE (|AbelianSemiGroup|))) #2# #1# #6# #3#) (OR #4# #2# #1# #6# #3#) (OR #2# #3#) (OR #9=(|HasCategory| |#1| (QUOTE (|Group|))) #10=(|HasCategory| |#1| (QUOTE (|Monoid|)))) #9# (OR #4# #8# #2# #1# #9# #10# #6# #3# #11=(|HasCategory| |#1| (QUOTE (|SemiGroup|))) #5#) (OR #9# #10# #11#) (|HasCategory| |#1| (|%list| (QUOTE |InnerEvalable|) (QUOTE #7#) #12=(|devaluate| |#1|))) (AND #5# (|HasCategory| |#1| (|%list| (QUOTE |Evalable|) #12#))) (|HasCategory| |#1| (QUOTE (|IntegralDomain|))) (|HasCategory| |#1| (QUOTE (|ExpressionSpace|))) (OR #1# #9#) (OR #4# #10#) #8# #11# #10#) (|EquationFunctions2| S R) ((|constructor| (NIL "This package provides operations for mapping the sides of equations.")) (|map| (((|Equation| |#2|) (|Mapping| |#2| |#1|) (|Equation| |#1|)) "\\spad{map(f,eq)} returns an equation where \\spad{f} is applied to the sides of \\spad{eq}"))) NIL @@ -970,7 +970,7 @@ NIL NIL (|EuclideanDomain|) ((|constructor| (NIL "A constructive euclidean domain,{} \\spadignore{i.e.} one can divide producing a quotient and a remainder where the remainder is either zero or is smaller (\\spadfun{euclideanSize}) than the divisor. \\blankline Conditional attributes: \\indented{2}{multiplicativeValuation\\tab{25}\\spad{Size(a*b)=Size(a)*Size(b)}} \\indented{2}{additiveValuation\\tab{25}\\spad{Size(a*b)=Size(a)+Size(b)}}")) (|multiEuclidean| (((|Union| (|List| $) "failed") (|List| $) $) "\\spad{multiEuclidean([f1,...,fn],z)} returns a list of coefficients \\spad{[a1, ..., an]} such that \\spad{ z / prod fi = sum aj/fj}. If no such list of coefficients exists,{} \"failed\" is returned.")) (|extendedEuclidean| (((|Union| (|Record| (|:| |coef1| $) (|:| |coef2| $)) "failed") $ $ $) "\\spad{extendedEuclidean(x,y,z)} either returns a record rec where \\spad{rec.coef1*x+rec.coef2*y=z} or returns \"failed\" if \\spad{z} cannot be expressed as a linear combination of \\spad{x} and \\spad{y}.") (((|Record| (|:| |coef1| $) (|:| |coef2| $) (|:| |generator| $)) $ $) "\\spad{extendedEuclidean(x,y)} returns a record rec where \\spad{rec.coef1*x+rec.coef2*y = rec.generator} and rec.generator is a gcd of \\spad{x} and \\spad{y}. The gcd is unique only up to associates if \\spadatt{canonicalUnitNormal} is not asserted. \\spadfun{principalIdeal} provides a version of this operation which accepts an arbitrary length list of arguments.")) (|rem| (($ $ $) "\\spad{x rem y} is the same as \\spad{divide(x,y).remainder}. See \\spadfunFrom{divide}{EuclideanDomain}.")) (|quo| (($ $ $) "\\spad{x quo y} is the same as \\spad{divide(x,y).quotient}. See \\spadfunFrom{divide}{EuclideanDomain}.")) (|divide| (((|Record| (|:| |quotient| $) (|:| |remainder| $)) $ $) "\\spad{divide(x,y)} divides \\spad{x} by \\spad{y} producing a record containing a \\spad{quotient} and \\spad{remainder},{} where the remainder is smaller (see \\spadfunFrom{sizeLess?}{EuclideanDomain}) than the divisor \\spad{y}.")) (|euclideanSize| (((|NonNegativeInteger|) $) "\\spad{euclideanSize(x)} returns the euclidean size of the element \\spad{x}. Error: if \\spad{x} is zero.")) (|sizeLess?| (((|Boolean|) $ $) "\\spad{sizeLess?(x,y)} tests whether \\spad{x} is strictly smaller than \\spad{y} with respect to the \\spadfunFrom{euclideanSize}{EuclideanDomain}."))) -((|noZeroDivisors| . T) ((|commutative| "*") . T) (|rightUnitary| . T) (|leftUnitary| . T) (|unitsKnown| . T)) +((|noZeroDivisors| . T) ((|commutative| "*") . T)) NIL (|Evalable&| S R) ((|constructor| (NIL "This category provides \\spadfun{eval} operations. A domain may belong to this category if it is possible to make ``evaluation'' substitutions.")) (|eval| (($ $ (|List| (|Equation| |#2|))) "\\spad{eval(f, [x1 = v1,...,xn = vn])} replaces \\spad{xi} by \\spad{vi} in \\spad{f}.") (($ $ (|Equation| |#2|)) "\\spad{eval(f,x = v)} replaces \\spad{x} by \\spad{v} in \\spad{f}."))) @@ -994,12 +994,12 @@ NIL NIL (|ExponentialExpansion| R FE |var| |cen|) ((|constructor| (NIL "UnivariatePuiseuxSeriesWithExponentialSingularity is a domain used to represent essential singularities of functions. Objects in this domain are quotients of sums,{} where each term in the sum is a univariate Puiseux series times the exponential of a univariate Puiseux series.")) (|coerce| (($ (|UnivariatePuiseuxSeries| |#2| |#3| |#4|)) "\\spad{coerce(f)} converts a \\spadtype{UnivariatePuiseuxSeries} to an \\spadtype{ExponentialExpansion}.")) (|limitPlus| (((|Union| (|OrderedCompletion| |#2|) "failed") $) "\\spad{limitPlus(f(var))} returns \\spad{limit(var -> a+,f(var))}."))) -((|canonicalsClosed| . T) (|canonicalUnitNormal| . T) (|noZeroDivisors| . T) ((|commutative| "*") . T) (|rightUnitary| . T) (|leftUnitary| . T) (|unitsKnown| . T)) -(#1=(|HasCategory| #2=(|UnivariatePuiseuxSeriesWithExponentialSingularity| |#1| |#2| |#3| |#4|) (QUOTE (|PolynomialFactorizationExplicit|))) (|HasCategory| #2# (QUOTE (|RetractableTo| #3=(|Symbol|)))) #4=(|HasCategory| #2# #5=(QUOTE (|CharacteristicNonZero|))) (|HasCategory| #2# (QUOTE (|CharacteristicZero|))) (|HasCategory| #2# (QUOTE (|ConvertibleTo| (|InputForm|)))) (|HasCategory| #2# (QUOTE (|RealConstant|))) #6=(|HasCategory| #2# (QUOTE (|OrderedIntegralDomain|))) #7=(|HasCategory| #2# (QUOTE (|OrderedSet|))) (OR #6# #7#) (|HasCategory| #2# (QUOTE (|RetractableTo| #8=(|Integer|)))) (|HasCategory| #2# (QUOTE (|StepThrough|))) (|HasCategory| #2# (QUOTE (|PatternMatchable| #9=(|Float|)))) (|HasCategory| #2# (QUOTE (|PatternMatchable| #8#))) (|HasCategory| #2# (QUOTE (|ConvertibleTo| (|Pattern| #9#)))) (|HasCategory| #2# (QUOTE (|ConvertibleTo| (|Pattern| #8#)))) (|HasCategory| #2# (QUOTE (|LinearlyExplicitRingOver| #8#))) (|HasCategory| #2# (QUOTE (|DifferentialSpace|))) (|HasCategory| #2# (QUOTE (|PartialDifferentialSpace| #3#))) (|HasCategory| #2# (QUOTE (|DifferentialRing|))) (|HasCategory| #2# (QUOTE (|PartialDifferentialRing| #3#))) (|HasCategory| #2# (|%list| (QUOTE |InnerEvalable|) (QUOTE #3#) #10=(|%list| (QUOTE |UnivariatePuiseuxSeriesWithExponentialSingularity|) (|devaluate| |#1|) (|devaluate| |#2|) (|devaluate| |#3|) (|devaluate| |#4|)))) (|HasCategory| #2# (|%list| (QUOTE |Evalable|) #10#)) (|HasCategory| #2# (|%list| (QUOTE |Eltable|) #10# #10#)) (|HasCategory| #2# (QUOTE (|EuclideanDomain|))) (|HasCategory| #2# (QUOTE (|IntegerNumberSystem|))) #11=(AND (|HasCategory| $ #5#) #1#) (OR #11# #4#)) +((|canonicalUnitNormal| . T) (|noZeroDivisors| . T) ((|commutative| "*") . T)) +(#1=(|HasCategory| #2=(|UnivariatePuiseuxSeriesWithExponentialSingularity| |#1| |#2| |#3| |#4|) (QUOTE (|PolynomialFactorizationExplicit|))) (|HasCategory| #2# (QUOTE (|RetractableTo| #3=(|Symbol|)))) #4=(|HasCategory| #2# #5=(QUOTE (|CharacteristicNonZero|))) (|HasCategory| #2# (QUOTE (|CharacteristicZero|))) (|HasCategory| #2# (QUOTE (|ConvertibleTo| (|InputForm|)))) (|HasCategory| #2# (QUOTE (|RealConstant|))) #6=(|HasCategory| #2# (QUOTE (|OrderedIntegralDomain|))) #7=(|HasCategory| #2# (QUOTE (|OrderedSet|))) (OR #6# #7#) (|HasCategory| #2# (QUOTE (|RetractableTo| #8=(|Integer|)))) (|HasCategory| #2# (QUOTE (|StepThrough|))) (|HasCategory| #2# (QUOTE (|PatternMatchable| #9=(|Float|)))) (|HasCategory| #2# (QUOTE (|PatternMatchable| #8#))) (|HasCategory| #2# (QUOTE (|ConvertibleTo| (|Pattern| #9#)))) (|HasCategory| #2# (QUOTE (|ConvertibleTo| (|Pattern| #8#)))) (|HasCategory| #2# (QUOTE (|LinearlyExplicitRingOver| #8#))) (|HasCategory| #2# (QUOTE (|PartialDifferentialSpace| #3#))) (|HasCategory| #2# (QUOTE (|DifferentialSpace|))) (|HasCategory| #2# (QUOTE (|DifferentialRing|))) (|HasCategory| #2# (QUOTE (|PartialDifferentialRing| #3#))) (|HasCategory| #2# (|%list| (QUOTE |InnerEvalable|) (QUOTE #3#) #10=(|%list| (QUOTE |UnivariatePuiseuxSeriesWithExponentialSingularity|) (|devaluate| |#1|) (|devaluate| |#2|) (|devaluate| |#3|) (|devaluate| |#4|)))) (|HasCategory| #2# (|%list| (QUOTE |Evalable|) #10#)) (|HasCategory| #2# (|%list| (QUOTE |Eltable|) #10# #10#)) (|HasCategory| #2# (QUOTE (|EuclideanDomain|))) (|HasCategory| #2# (QUOTE (|IntegerNumberSystem|))) #11=(AND (|HasCategory| $ #5#) #1#) (OR #11# #4#)) (|Expression| R) ((|constructor| (NIL "Expressions involving symbolic functions.")) (|squareFreePolynomial| (((|Factored| (|SparseUnivariatePolynomial| $)) (|SparseUnivariatePolynomial| $)) "\\spad{squareFreePolynomial(p)} \\undocumented{}")) (|factorPolynomial| (((|Factored| (|SparseUnivariatePolynomial| $)) (|SparseUnivariatePolynomial| $)) "\\spad{factorPolynomial(p)} \\undocumented{}")) (|simplifyPower| (($ $ (|Integer|)) "simplifyPower?(\\spad{f},{}\\spad{n}) \\undocumented{}")) (|number?| (((|Boolean|) $) "\\spad{number?(f)} tests if \\spad{f} is rational")) (|reduce| (($ $) "\\spad{reduce(f)} simplifies all the unreduced algebraic quantities present in \\spad{f} by applying their defining relations."))) -((|unitsKnown| OR (AND (|has| |#1| #1=(|IntegralDomain|)) (OR #2=(|has| |#1| (|Ring|)) #3=(|has| |#1| (|Group|)))) #2# #3#) (|leftUnitary| |has| |#1| . #4=((|CommutativeRing|))) (|rightUnitary| |has| |#1| . #4#) ((|commutative| "*") |has| |#1| . #5=(#1#)) (|noZeroDivisors| |has| |#1| . #5#) (|canonicalUnitNormal| |has| |#1| . #5#) (|canonicalsClosed| |has| |#1| . #5#)) -((OR #1=(AND #2=(|HasCategory| |#1| (QUOTE (|IntegralDomain|))) #3=(|HasCategory| |#1| #4=(QUOTE (|RetractableTo| #5=(|Integer|))))) #6=(|HasCategory| |#1| (QUOTE (|RetractableTo| (|Fraction| #5#))))) #2# (OR #2# #7=(|HasCategory| |#1| #8=(QUOTE (|Ring|)))) #7# #9=(|HasCategory| |#1| (QUOTE (|AbelianGroup|))) (OR #2# #6#) #10=(|HasCategory| |#1| (QUOTE (|CommutativeRing|))) #11=(|HasCategory| |#1| (QUOTE (|CharacteristicNonZero|))) #12=(|HasCategory| |#1| (QUOTE (|CharacteristicZero|))) (OR #10# #7#) (OR (AND #11# #13=(|HasCategory| |#1| (QUOTE (|LinearlyExplicitRingOver| #5#)))) (AND #12# #13#) (AND #10# #13#) (AND #2# #13#) #14=(AND #13# #7#)) (OR #15=(|HasCategory| |#1| (QUOTE (|Group|))) #16=(|HasCategory| |#1| (QUOTE (|SemiGroup|)))) #15# (|HasCategory| |#1| (QUOTE (|ConvertibleTo| (|InputForm|)))) (OR #3# #7#) #3# (|HasCategory| |#1| (QUOTE (|PatternMatchable| #17=(|Float|)))) (|HasCategory| |#1| (QUOTE (|PatternMatchable| #5#))) (|HasCategory| |#1| (QUOTE (|ConvertibleTo| (|Pattern| #17#)))) (|HasCategory| |#1| (QUOTE (|ConvertibleTo| (|Pattern| #5#)))) #1# (OR #9# #18=(|HasCategory| |#1| (QUOTE (|AbelianSemiGroup|))) #11# #12# #10# #2# #7#) (OR #9# #11# #12# #10# #2# #7#) (OR #11# #12# #10# #2# #7#) (AND (|HasCategory| |#1| (QUOTE (|GcdDomain|))) #2#) (OR #15# #2#) #14# (OR #14# #9#) (OR #14# #18# #16#) (OR #14# #18#) (OR #15# #7#) (OR (AND #2# #6#) #1#) #18# #16# #6# (|HasCategory| $ #8#) (|HasCategory| $ #4#)) +(((|commutative| "*") |has| |#1| . #1=((|IntegralDomain|))) (|noZeroDivisors| |has| |#1| . #1#) (|canonicalUnitNormal| |has| |#1| . #1#)) +((OR #1=(AND #2=(|HasCategory| |#1| (QUOTE (|IntegralDomain|))) #3=(|HasCategory| |#1| #4=(QUOTE (|RetractableTo| #5=(|Integer|))))) #6=(|HasCategory| |#1| (QUOTE (|RetractableTo| (|Fraction| #5#))))) #2# (OR #2# #7=(|HasCategory| |#1| #8=(QUOTE (|Ring|)))) #7# #9=(|HasCategory| |#1| (QUOTE (|AbelianGroup|))) (OR #2# #6#) #10=(|HasCategory| |#1| (QUOTE (|CommutativeRing|))) #11=(|HasCategory| |#1| (QUOTE (|CharacteristicNonZero|))) #12=(|HasCategory| |#1| (QUOTE (|CharacteristicZero|))) (OR #10# #7#) (OR (AND #11# #13=(|HasCategory| |#1| (QUOTE (|LinearlyExplicitRingOver| #5#)))) (AND #12# #13#) (AND #10# #13#) (AND #2# #13#) #14=(AND #13# #7#)) (OR #15=(|HasCategory| |#1| (QUOTE (|Group|))) #16=(|HasCategory| |#1| (QUOTE (|SemiGroup|)))) #15# (|HasCategory| |#1| (QUOTE (|ConvertibleTo| (|InputForm|)))) (OR #3# #7#) #3# (|HasCategory| |#1| (QUOTE (|PatternMatchable| #17=(|Float|)))) (|HasCategory| |#1| (QUOTE (|PatternMatchable| #5#))) (|HasCategory| |#1| (QUOTE (|ConvertibleTo| (|Pattern| #17#)))) (|HasCategory| |#1| (QUOTE (|ConvertibleTo| (|Pattern| #5#)))) #1# (OR #9# #18=(|HasCategory| |#1| (QUOTE (|AbelianSemiGroup|))) #11# #12# #10# #2# #7#) (OR #9# #11# #12# #10# #2# #7#) (OR #11# #12# #10# #2# #7#) (AND (|HasCategory| |#1| (QUOTE (|GcdDomain|))) #2#) (OR #15# #2#) #14# (OR #14# #9#) (OR #14# #18# #16#) (OR #14# #18#) (OR (AND #2# #6#) #1#) #18# #16# #6# (|HasCategory| $ #8#) (|HasCategory| $ #4#)) (|ExpressionFunctions2| R S) ((|constructor| (NIL "Lifting of maps to Expressions. Date Created: 16 Jan 1989 Date Last Updated: 22 Jan 1990")) (|map| (((|Expression| |#2|) (|Mapping| |#2| |#1|) (|Expression| |#1|)) "\\spad{map(f, e)} applies \\spad{f} to all the constants appearing in \\spad{e}."))) NIL @@ -1018,7 +1018,7 @@ NIL NIL (|ExponentialOfUnivariatePuiseuxSeries| FE |var| |cen|) ((|constructor| (NIL "ExponentialOfUnivariatePuiseuxSeries is a domain used to represent essential singularities of functions. An object in this domain is a function of the form \\spad{exp(f(x))},{} where \\spad{f(x)} is a Puiseux series with no terms of non-negative degree. Objects are ordered according to order of singularity,{} with functions which tend more rapidly to zero or infinity considered to be larger. Thus,{} if \\spad{order(f(x)) < order(g(x))},{} \\spadignore{i.e.} the first non-zero term of \\spad{f(x)} has lower degree than the first non-zero term of \\spad{g(x)},{} then \\spad{exp(f(x)) > exp(g(x))}. If \\spad{order(f(x)) = order(g(x))},{} then the ordering is essentially random. This domain is used in computing limits involving functions with essential singularities.")) (|exponentialOrder| (((|Fraction| (|Integer|)) $) "\\spad{exponentialOrder(exp(c * x **(-n) + ...))} returns \\spad{-n}. exponentialOrder(0) returns \\spad{0}.")) (|exponent| (((|UnivariatePuiseuxSeries| |#1| |#2| |#3|) $) "\\spad{exponent(exp(f(x)))} returns \\spad{f(x)}")) (|exponential| (($ (|UnivariatePuiseuxSeries| |#1| |#2| |#3|)) "\\spad{exponential(f(x))} returns \\spad{exp(f(x))}. Note: the function does NOT check that \\spad{f(x)} has no non-negative terms."))) -(((|commutative| "*") |has| |#1| (|CommutativeRing|)) (|noZeroDivisors| |has| |#1| (|IntegralDomain|)) (|canonicalUnitNormal| |has| |#1| . #1=((|Field|))) (|canonicalsClosed| |has| |#1| . #1#) (|rightUnitary| . T) (|leftUnitary| . T) (|unitsKnown| . T)) +(((|commutative| "*") |has| |#1| (|CommutativeRing|)) (|noZeroDivisors| |has| |#1| (|IntegralDomain|)) (|canonicalUnitNormal| |has| |#1| (|Field|))) (#1=(|HasCategory| |#1| (QUOTE (|Algebra| #2=(|Fraction| #3=(|Integer|))))) #4=(|HasCategory| |#1| (QUOTE (|IntegralDomain|))) #5=(|HasCategory| |#1| (QUOTE (|CommutativeRing|))) (OR #5# #4#) (|HasCategory| |#1| (QUOTE (|CharacteristicNonZero|))) (|HasCategory| |#1| (QUOTE (|CharacteristicZero|))) (AND (|HasCategory| |#1| (QUOTE (|PartialDifferentialRing| #6=(|Symbol|)))) #7=(|HasSignature| |#1| (|%list| (QUOTE *) (|%list| #8=(|devaluate| |#1|) #9=(|%list| (QUOTE |Fraction|) (QUOTE #3#)) #8#)))) #7# (|HasCategory| #2# (QUOTE (|SemiGroup|))) #10=(|HasCategory| |#1| (QUOTE (|Field|))) (OR #5# #10# #4#) (OR #10# #4#) (AND #11=(|HasSignature| |#1| (|%list| (QUOTE **) (|%list| #8# #8# #9#))) (|HasSignature| |#1| (|%list| (QUOTE |coerce|) (|%list| #8# #12=(QUOTE #6#))))) #11# (OR (AND #1# (|HasCategory| |#1| (QUOTE (|AlgebraicallyClosedFunctionSpace| #3#))) (|HasCategory| |#1| (QUOTE (|PrimitiveFunctionCategory|))) (|HasCategory| |#1| (QUOTE (|TranscendentalFunctionCategory|)))) (AND #1# (|HasSignature| |#1| (|%list| (QUOTE |integrate|) (|%list| #8# #8# #12#))) (|HasSignature| |#1| (|%list| (QUOTE |variables|) (|%list| (|%list| (QUOTE |List|) #12#) #8#)))))) (|FactoredFunctions| M) ((|constructor| (NIL "computes various functions on factored arguments.")) (|log| (((|List| (|Record| (|:| |coef| (|NonNegativeInteger|)) (|:| |logand| |#1|))) (|Factored| |#1|)) "\\spad{log(f)} returns \\spad{[(a1,b1),...,(am,bm)]} such that the logarithm of \\spad{f} is equal to \\spad{a1*log(b1) + ... + am*log(bm)}.")) (|nthRoot| (((|Record| (|:| |exponent| (|NonNegativeInteger|)) (|:| |coef| |#1|) (|:| |radicand| (|List| |#1|))) (|Factored| |#1|) (|NonNegativeInteger|)) "\\spad{nthRoot(f, n)} returns \\spad{(p, r, [r1,...,rm])} such that the \\spad{n}th-root of \\spad{f} is equal to \\spad{r * \\spad{p}th-root(r1 * ... * rm)},{} where \\spad{r1},{}...,{}rm are distinct factors of \\spad{f},{} each of which has an exponent smaller than \\spad{p} in \\spad{f}."))) @@ -1030,7 +1030,7 @@ NIL NIL (|FreeAbelianGroup| S) ((|constructor| (NIL "The free abelian group on a set \\spad{S} is the monoid of finite sums of the form \\spad{reduce(+,[ni * si])} where the \\spad{si}'s are in \\spad{S},{} and the \\spad{ni}'s are integers. The operation is commutative."))) -((|leftUnitary| . T) (|rightUnitary| . T)) +NIL ((|HasCategory| |#1| (QUOTE (|OrderedSet|))) (|HasCategory| (|Integer|) (QUOTE (|OrderedAbelianMonoid|)))) (|FreeAbelianMonoidCategory| S E) ((|constructor| (NIL "A free abelian monoid on a set \\spad{S} is the monoid of finite sums of the form \\spad{reduce(+,[ni * si])} where the \\spad{si}'s are in \\spad{S},{} and the \\spad{ni}'s are in a given abelian monoid. The operation is commutative.")) (|highCommonTerms| (($ $ $) "\\spad{highCommonTerms(e1 a1 + ... + en an, f1 b1 + ... + fm bm)} returns \\indented{2}{\\spad{reduce(+,[max(ei, fi) ci])}} where \\spad{ci} ranges in the intersection of \\spad{{a1,...,an}} and \\spad{{b1,...,bm}}.")) (|mapGen| (($ (|Mapping| |#1| |#1|) $) "\\spad{mapGen(f, e1 a1 +...+ en an)} returns \\spad{e1 f(a1) +...+ en f(an)}.")) (|mapCoef| (($ (|Mapping| |#2| |#2|) $) "\\spad{mapCoef(f, e1 a1 +...+ en an)} returns \\spad{f(e1) a1 +...+ f(en) an}.")) (|coefficient| ((|#2| |#1| $) "\\spad{coefficient(s, e1 a1 + ... + en an)} returns \\spad{ei} such that \\spad{ai} = \\spad{s},{} or 0 if \\spad{s} is not one of the \\spad{ai}'s.")) (|nthFactor| ((|#1| $ (|Integer|)) "\\spad{nthFactor(x, n)} returns the factor of the n^th term of \\spad{x}.")) (|nthCoef| ((|#2| $ (|Integer|)) "\\spad{nthCoef(x, n)} returns the coefficient of the n^th term of \\spad{x}.")) (|terms| (((|List| (|Record| (|:| |gen| |#1|) (|:| |exp| |#2|))) $) "\\spad{terms(e1 a1 + ... + en an)} returns \\spad{[[a1, e1],...,[an, en]]}.")) (|size| (((|NonNegativeInteger|) $) "\\spad{size(x)} returns the number of terms in \\spad{x}. mapGen(\\spad{f},{} \\spad{a1}\\^\\spad{e1} ... an\\^en) returns \\spad{f(a1)\\^e1 ... f(an)\\^en}.")) (* (($ |#2| |#1|) "\\spad{e * s} returns \\spad{e} times \\spad{s}.")) (+ (($ |#1| $) "\\spad{s + x} returns the sum of \\spad{s} and \\spad{x}."))) @@ -1046,7 +1046,7 @@ NIL ((|HasCategory| |#2| (QUOTE (|GcdDomain|))) (|HasCategory| |#2| (QUOTE (|IntegralDomain|))) (|HasCategory| |#2| (QUOTE (|CommutativeRing|)))) (|FiniteAbelianMonoidRing| R E) ((|constructor| (NIL "This category is similar to AbelianMonoidRing,{} except that the sum is assumed to be finite. It is a useful model for polynomials,{} but is somewhat more general.")) (|primitivePart| (($ $) "\\spad{primitivePart(p)} returns the unit normalized form of polynomial \\spad{p} divided by the content of \\spad{p}.")) (|content| ((|#1| $) "\\spad{content(p)} gives the gcd of the coefficients of polynomial \\spad{p}.")) (|exquo| (((|Union| $ "failed") $ |#1|) "\\spad{exquo(p,r)} returns the exact quotient of polynomial \\spad{p} by \\spad{r},{} or \"failed\" if none exists.")) (|binomThmExpt| (($ $ $ (|NonNegativeInteger|)) "\\spad{binomThmExpt(p,q,n)} returns \\spad{(x+y)^n} by means of the binomial theorem trick.")) (|pomopo!| (($ $ |#1| |#2| $) "\\spad{pomopo!(p1,r,e,p2)} returns \\spad{p1 + monomial(e,r) * p2} and may use \\spad{p1} as workspace. The constaant \\spad{r} is assumed to be nonzero.")) (|mapExponents| (($ (|Mapping| |#2| |#2|) $) "\\spad{mapExponents(fn,u)} maps function \\spad{fn} onto the exponents of the non-zero monomials of polynomial \\spad{u}.")) (|minimumDegree| ((|#2| $) "\\spad{minimumDegree(p)} gives the least exponent of a non-zero term of polynomial \\spad{p}. Error: if applied to 0.")) (|numberOfMonomials| (((|NonNegativeInteger|) $) "\\spad{numberOfMonomials(p)} gives the number of non-zero monomials in polynomial \\spad{p}.")) (|coefficients| (((|List| |#1|) $) "\\spad{coefficients(p)} gives the list of non-zero coefficients of polynomial \\spad{p}.")) (|ground| ((|#1| $) "\\spad{ground(p)} retracts polynomial \\spad{p} to the coefficient ring.")) (|ground?| (((|Boolean|) $) "\\spad{ground?(p)} tests if polynomial \\spad{p} is a member of the coefficient ring."))) -(((|commutative| "*") |has| |#1| (|CommutativeRing|)) (|noZeroDivisors| |has| |#1| (|IntegralDomain|)) (|rightUnitary| . T) (|leftUnitary| . T) (|unitsKnown| . T)) +(((|commutative| "*") |has| |#1| (|CommutativeRing|)) (|noZeroDivisors| |has| |#1| (|IntegralDomain|))) NIL (|FlexibleArray| S) ((|constructor| (NIL "\\indented{1}{A FlexibleArray is the notion of an array intended to allow for growth} at the end only. Hence the following efficient operations \\indented{2}{\\spad{append(x,a)} meaning append item \\spad{x} at the end of the array \\spad{a}} \\indented{2}{\\spad{delete(a,n)} meaning delete the last item from the array \\spad{a}} Flexible arrays support the other operations inherited from \\spadtype{ExtensibleLinearAggregate}. However,{} these are not efficient. Flexible arrays combine the \\spad{O(1)} access time property of arrays with growing and shrinking at the end in \\spad{O(1)} (average) time. This is done by using an ordinary array which may have zero or more empty slots at the end. When the array becomes full it is copied into a new larger (50\\% larger) array. Conversely,{} when the array becomes less than 1/2 full,{} it is copied into a smaller array. Flexible arrays provide for an efficient implementation of many data structures in particular heaps,{} stacks and sets."))) @@ -1058,7 +1058,7 @@ NIL ((|HasCategory| |#2| (QUOTE (|Finite|)))) (|FiniteAlgebraicExtensionField| F) ((|constructor| (NIL "FiniteAlgebraicExtensionField {\\em F} is the category of fields which are finite algebraic extensions of the field {\\em F}. If {\\em F} is finite then any finite algebraic extension of {\\em F} is finite,{} too. Let {\\em K} be a finite algebraic extension of the finite field {\\em F}. The exponentiation of elements of {\\em K} defines a \\spad{Z}-module structure on the multiplicative group of {\\em K}. The additive group of {\\em K} becomes a module over the ring of polynomials over {\\em F} via the operation \\spadfun{linearAssociatedExp}(a:K,{}f:SparseUnivariatePolynomial \\spad{F}) which is linear over {\\em F},{} \\spadignore{i.e.} for elements {\\em a} from {\\em K},{} {\\em c,d} from {\\em F} and {\\em f,g} univariate polynomials over {\\em F} we have \\spadfun{linearAssociatedExp}(a,{}cf+dg) equals {\\em c} times \\spadfun{linearAssociatedExp}(a,{}\\spad{f}) plus {\\em d} times \\spadfun{linearAssociatedExp}(a,{}\\spad{g}). Therefore \\spadfun{linearAssociatedExp} is defined completely by its action on monomials from {\\em F[X]}: \\spadfun{linearAssociatedExp}(a,{}monomial(1,{}\\spad{k})\\$SUP(\\spad{F})) is defined to be \\spadfun{Frobenius}(a,{}\\spad{k}) which is {\\em a**(q**k)} where {\\em q=size()\\$F}. The operations order and discreteLog associated with the multiplicative exponentiation have additive analogues associated to the operation \\spadfun{linearAssociatedExp}. These are the functions \\spadfun{linearAssociatedOrder} and \\spadfun{linearAssociatedLog},{} respectively.")) (|linearAssociatedLog| (((|Union| (|SparseUnivariatePolynomial| |#1|) "failed") $ $) "\\spad{linearAssociatedLog(b,a)} returns a polynomial {\\em g},{} such that the \\spadfun{linearAssociatedExp}(\\spad{b},{}\\spad{g}) equals {\\em a}. If there is no such polynomial {\\em g},{} then \\spadfun{linearAssociatedLog} fails.") (((|SparseUnivariatePolynomial| |#1|) $) "\\spad{linearAssociatedLog(a)} returns a polynomial {\\em g},{} such that \\spadfun{linearAssociatedExp}(normalElement(),{}\\spad{g}) equals {\\em a}.")) (|linearAssociatedOrder| (((|SparseUnivariatePolynomial| |#1|) $) "\\spad{linearAssociatedOrder(a)} retruns the monic polynomial {\\em g} of least degree,{} such that \\spadfun{linearAssociatedExp}(a,{}\\spad{g}) is 0.")) (|linearAssociatedExp| (($ $ (|SparseUnivariatePolynomial| |#1|)) "\\spad{linearAssociatedExp(a,f)} is linear over {\\em F},{} \\spadignore{i.e.} for elements {\\em a} from {\\em \\$},{} {\\em c,d} form {\\em F} and {\\em f,g} univariate polynomials over {\\em F} we have \\spadfun{linearAssociatedExp}(a,{}cf+dg) equals {\\em c} times \\spadfun{linearAssociatedExp}(a,{}\\spad{f}) plus {\\em d} times \\spadfun{linearAssociatedExp}(a,{}\\spad{g}). Therefore \\spadfun{linearAssociatedExp} is defined completely by its action on monomials from {\\em F[X]}: \\spadfun{linearAssociatedExp}(a,{}monomial(1,{}\\spad{k})\\$SUP(\\spad{F})) is defined to be \\spadfun{Frobenius}(a,{}\\spad{k}) which is {\\em a**(q**k)},{} where {\\em q=size()\\$F}.")) (|generator| (($) "\\spad{generator()} returns a root of the defining polynomial. This element generates the field as an algebra over the ground field.")) (|normal?| (((|Boolean|) $) "\\spad{normal?(a)} tests whether the element \\spad{a} is normal over the ground field \\spad{F},{} \\spadignore{i.e.} \\spad{a**(q**i), 0 <= i <= extensionDegree()-1} is an \\spad{F}-basis,{} where \\spad{q = size()\\$F}. Implementation according to Lidl/Niederreiter: Theorem 2.39.")) (|normalElement| (($) "\\spad{normalElement()} returns a element,{} normal over the ground field \\spad{F},{} \\spadignore{i.e.} \\spad{a**(q**i), 0 <= i < extensionDegree()} is an \\spad{F}-basis,{} where \\spad{q = size()\\$F}. At the first call,{} the element is computed by \\spadfunFrom{createNormalElement}{FiniteAlgebraicExtensionField} then cached in a global variable. On subsequent calls,{} the element is retrieved by referencing the global variable.")) (|createNormalElement| (($) "\\spad{createNormalElement()} computes a normal element over the ground field \\spad{F},{} that is,{} \\spad{a**(q**i), 0 <= i < extensionDegree()} is an \\spad{F}-basis,{} where \\spad{q = size()\\$F}. Reference: Such an element exists Lidl/Niederreiter: Theorem 2.35.")) (|trace| (($ $ (|PositiveInteger|)) "\\spad{trace(a,d)} computes the trace of \\spad{a} with respect to the field of extension degree \\spad{d} over the ground field of size \\spad{q}. Error: if \\spad{d} does not divide the extension degree of \\spad{a}. Note: \\spad{trace(a,d) = reduce(+,[a**(q**(d*i)) for i in 0..n/d])}.") ((|#1| $) "\\spad{trace(a)} computes the trace of \\spad{a} with respect to the field considered as an algebra with 1 over the ground field \\spad{F}.")) (|norm| (($ $ (|PositiveInteger|)) "\\spad{norm(a,d)} computes the norm of \\spad{a} with respect to the field of extension degree \\spad{d} over the ground field of size. Error: if \\spad{d} does not divide the extension degree of \\spad{a}. Note: norm(a,{}\\spad{d}) = reduce(*,{}[a**(q**(d*i)) for \\spad{i} in 0..n/d])") ((|#1| $) "\\spad{norm(a)} computes the norm of \\spad{a} with respect to the field considered as an algebra with 1 over the ground field \\spad{F}.")) (|degree| (((|PositiveInteger|) $) "\\spad{degree(a)} returns the degree of the minimal polynomial of an element \\spad{a} over the ground field \\spad{F}.")) (|extensionDegree| (((|PositiveInteger|)) "\\spad{extensionDegree()} returns the degree of field extension.")) (|definingPolynomial| (((|SparseUnivariatePolynomial| |#1|)) "\\spad{definingPolynomial()} returns the polynomial used to define the field extension.")) (|minimalPolynomial| (((|SparseUnivariatePolynomial| $) $ (|PositiveInteger|)) "\\spad{minimalPolynomial(x,n)} computes the minimal polynomial of \\spad{x} over the field of extension degree \\spad{n} over the ground field \\spad{F}.") (((|SparseUnivariatePolynomial| |#1|) $) "\\spad{minimalPolynomial(a)} returns the minimal polynomial of an element \\spad{a} over the ground field \\spad{F}.")) (|represents| (($ (|Vector| |#1|)) "\\spad{represents([a1,..,an])} returns \\spad{a1*v1 + ... + an*vn},{} where \\spad{v1},{}...,{}vn are the elements of the fixed basis.")) (|coordinates| (((|Matrix| |#1|) (|Vector| $)) "\\spad{coordinates([v1,...,vm])} returns the coordinates of the \\spad{vi}'s with to the fixed basis. The coordinates of \\spad{vi} are contained in the \\spad{i}th row of the matrix returned by this function.") (((|Vector| |#1|) $) "\\spad{coordinates(a)} returns the coordinates of \\spad{a} with respect to the fixed \\spad{F}-vectorspace basis.")) (|basis| (((|Vector| $) (|PositiveInteger|)) "\\spad{basis(n)} returns a fixed basis of a subfield of \\$ as \\spad{F}-vectorspace.") (((|Vector| $)) "\\spad{basis()} returns a fixed basis of \\$ as \\spad{F}-vectorspace."))) -((|canonicalsClosed| . T) (|canonicalUnitNormal| . T) (|noZeroDivisors| . T) ((|commutative| "*") . T) (|rightUnitary| . T) (|leftUnitary| . T) (|unitsKnown| . T)) +((|canonicalUnitNormal| . T) (|noZeroDivisors| . T) ((|commutative| "*") . T)) NIL (|FourierComponent| E) ((|constructor| (NIL "\\indented{1}{Author: James Davenport} Date Created: 17 April 1992 Date Last Updated: 12 June 1992 Basic Functions: Related Constructors: Also See: AMS Classifications: Keywords: References: Description:")) (|argument| ((|#1| $) "\\spad{argument(x)} returns the argument of a given sin/cos expressions")) (|sin?| (((|Boolean|) $) "\\spad{sin?(x)} returns \\spad{true} if term is a sin,{} otherwise \\spad{false}")) (|cos| (($ |#1|) "\\spad{cos(x)} makes a cos kernel for use in Fourier series")) (|sin| (($ |#1|) "\\spad{sin(x)} makes a sin kernel for use in Fourier series"))) @@ -1094,7 +1094,7 @@ NIL NIL (|FiniteField| |p| |n|) ((|constructor| (NIL "FiniteField(\\spad{p},{}\\spad{n}) implements finite fields with p**n elements. This packages checks that \\spad{p} is prime. For a non-checking version,{} see \\spadtype{InnerFiniteField}."))) -((|canonicalsClosed| . T) (|canonicalUnitNormal| . T) (|noZeroDivisors| . T) ((|commutative| "*") . T) (|rightUnitary| . T) (|leftUnitary| . T) (|unitsKnown| . T)) +((|canonicalUnitNormal| . T) (|noZeroDivisors| . T) ((|commutative| "*") . T)) ((OR #1=(|HasCategory| #2=(|PrimeField| |#1|) (QUOTE (|CharacteristicNonZero|))) #3=(|HasCategory| #2# (QUOTE (|Finite|)))) (|HasCategory| #2# (QUOTE (|CharacteristicZero|))) #3# #1#) (|FunctionFieldCategory&| S F UP UPUP) ((|constructor| (NIL "This category is a model for the function field of a plane algebraic curve.")) (|rationalPoints| (((|List| (|List| |#2|))) "\\spad{rationalPoints()} returns the list of all the affine rational points.")) (|nonSingularModel| (((|List| (|Polynomial| |#2|)) (|Symbol|)) "\\spad{nonSingularModel(u)} returns the equations in \\spad{u1},{}...,{}un of an affine non-singular model for the curve.")) (|algSplitSimple| (((|Record| (|:| |num| $) (|:| |den| |#3|) (|:| |derivden| |#3|) (|:| |gd| |#3|)) $ (|Mapping| |#3| |#3|)) "\\spad{algSplitSimple(f, D)} returns \\spad{[h,d,d',g]} such that \\spad{f=h/d},{} \\spad{h} is integral at all the normal places \\spad{w}.\\spad{r}.\\spad{t}. \\spad{D},{} \\spad{d' = Dd},{} \\spad{g = gcd(d, discriminant())} and \\spad{D} is the derivation to use. \\spad{f} must have at most simple finite poles.")) (|hyperelliptic| (((|Union| |#3| "failed")) "\\spad{hyperelliptic()} returns \\spad{p(x)} if the curve is the hyperelliptic defined by \\spad{y**2 = p(x)},{} \"failed\" otherwise.")) (|elliptic| (((|Union| |#3| "failed")) "\\spad{elliptic()} returns \\spad{p(x)} if the curve is the elliptic defined by \\spad{y**2 = p(x)},{} \"failed\" otherwise.")) (|elt| ((|#2| $ |#2| |#2|) "\\spad{elt(f,a,b)} or \\spad{f}(a,{} \\spad{b}) returns the value of \\spad{f} at the point \\spad{(x = a, y = b)} if it is not singular.")) (|primitivePart| (($ $) "\\spad{primitivePart(f)} removes the content of the denominator and the common content of the numerator of \\spad{f}.")) (|differentiate| (($ $ (|Mapping| |#3| |#3|)) "\\spad{differentiate(x, d)} extends the derivation \\spad{d} from UP to \\$ and applies it to \\spad{x}.")) (|integralDerivationMatrix| (((|Record| (|:| |num| (|Matrix| |#3|)) (|:| |den| |#3|)) (|Mapping| |#3| |#3|)) "\\spad{integralDerivationMatrix(d)} extends the derivation \\spad{d} from UP to \\$ and returns (\\spad{M},{} \\spad{Q}) such that the i^th row of \\spad{M} divided by \\spad{Q} form the coordinates of \\spad{d(wi)} with respect to \\spad{(w1,...,wn)} where \\spad{(w1,...,wn)} is the integral basis returned by integralBasis().")) (|integralRepresents| (($ (|Vector| |#3|) |#3|) "\\spad{integralRepresents([A1,...,An], D)} returns \\spad{(A1 w1+...+An wn)/D} where \\spad{(w1,...,wn)} is the integral basis of \\spad{integralBasis()}.")) (|integralCoordinates| (((|Record| (|:| |num| (|Vector| |#3|)) (|:| |den| |#3|)) $) "\\spad{integralCoordinates(f)} returns \\spad{[[A1,...,An], D]} such that \\spad{f = (A1 w1 +...+ An wn) / D} where \\spad{(w1,...,wn)} is the integral basis returned by \\spad{integralBasis()}.")) (|represents| (($ (|Vector| |#3|) |#3|) "\\spad{represents([A0,...,A(n-1)],D)} returns \\spad{(A0 + A1 y +...+ A(n-1)*y**(n-1))/D}.")) (|yCoordinates| (((|Record| (|:| |num| (|Vector| |#3|)) (|:| |den| |#3|)) $) "\\spad{yCoordinates(f)} returns \\spad{[[A1,...,An], D]} such that \\spad{f = (A1 + A2 y +...+ An y**(n-1)) / D}.")) (|inverseIntegralMatrixAtInfinity| (((|Matrix| (|Fraction| |#3|))) "\\spad{inverseIntegralMatrixAtInfinity()} returns \\spad{M} such that \\spad{M (v1,...,vn) = (1, y, ..., y**(n-1))} where \\spad{(v1,...,vn)} is the local integral basis at infinity returned by \\spad{infIntBasis()}.")) (|integralMatrixAtInfinity| (((|Matrix| (|Fraction| |#3|))) "\\spad{integralMatrixAtInfinity()} returns \\spad{M} such that \\spad{(v1,...,vn) = M (1, y, ..., y**(n-1))} where \\spad{(v1,...,vn)} is the local integral basis at infinity returned by \\spad{infIntBasis()}.")) (|inverseIntegralMatrix| (((|Matrix| (|Fraction| |#3|))) "\\spad{inverseIntegralMatrix()} returns \\spad{M} such that \\spad{M (w1,...,wn) = (1, y, ..., y**(n-1))} where \\spad{(w1,...,wn)} is the integral basis of \\spadfunFrom{integralBasis}{FunctionFieldCategory}.")) (|integralMatrix| (((|Matrix| (|Fraction| |#3|))) "\\spad{integralMatrix()} returns \\spad{M} such that \\spad{(w1,...,wn) = M (1, y, ..., y**(n-1))},{} where \\spad{(w1,...,wn)} is the integral basis of \\spadfunFrom{integralBasis}{FunctionFieldCategory}.")) (|reduceBasisAtInfinity| (((|Vector| $) (|Vector| $)) "\\spad{reduceBasisAtInfinity(b1,...,bn)} returns \\spad{(x**i * bj)} for all \\spad{i},{}\\spad{j} such that \\spad{x**i*bj} is locally integral at infinity.")) (|normalizeAtInfinity| (((|Vector| $) (|Vector| $)) "\\spad{normalizeAtInfinity(v)} makes \\spad{v} normal at infinity.")) (|complementaryBasis| (((|Vector| $) (|Vector| $)) "\\spad{complementaryBasis(b1,...,bn)} returns the complementary basis \\spad{(b1',...,bn')} of \\spad{(b1,...,bn)}.")) (|integral?| (((|Boolean|) $ |#3|) "\\spad{integral?(f, p)} tests whether \\spad{f} is locally integral at \\spad{p(x) = 0}.") (((|Boolean|) $ |#2|) "\\spad{integral?(f, a)} tests whether \\spad{f} is locally integral at \\spad{x = a}.") (((|Boolean|) $) "\\spad{integral?()} tests if \\spad{f} is integral over \\spad{k[x]}.")) (|integralAtInfinity?| (((|Boolean|) $) "\\spad{integralAtInfinity?()} tests if \\spad{f} is locally integral at infinity.")) (|integralBasisAtInfinity| (((|Vector| $)) "\\spad{integralBasisAtInfinity()} returns the local integral basis at infinity.")) (|integralBasis| (((|Vector| $)) "\\spad{integralBasis()} returns the integral basis for the curve.")) (|ramified?| (((|Boolean|) |#3|) "\\spad{ramified?(p)} tests whether \\spad{p(x) = 0} is ramified.") (((|Boolean|) |#2|) "\\spad{ramified?(a)} tests whether \\spad{x = a} is ramified.")) (|ramifiedAtInfinity?| (((|Boolean|)) "\\spad{ramifiedAtInfinity?()} tests if infinity is ramified.")) (|singular?| (((|Boolean|) |#3|) "\\spad{singular?(p)} tests whether \\spad{p(x) = 0} is singular.") (((|Boolean|) |#2|) "\\spad{singular?(a)} tests whether \\spad{x = a} is singular.")) (|singularAtInfinity?| (((|Boolean|)) "\\spad{singularAtInfinity?()} tests if there is a singularity at infinity.")) (|branchPoint?| (((|Boolean|) |#3|) "\\spad{branchPoint?(p)} tests whether \\spad{p(x) = 0} is a branch point.") (((|Boolean|) |#2|) "\\spad{branchPoint?(a)} tests whether \\spad{x = a} is a branch point.")) (|branchPointAtInfinity?| (((|Boolean|)) "\\spad{branchPointAtInfinity?()} tests if there is a branch point at infinity.")) (|rationalPoint?| (((|Boolean|) |#2| |#2|) "\\spad{rationalPoint?(a, b)} tests if \\spad{(x=a,y=b)} is on the curve.")) (|absolutelyIrreducible?| (((|Boolean|)) "\\spad{absolutelyIrreducible?()} tests if the curve absolutely irreducible?")) (|genus| (((|NonNegativeInteger|)) "\\spad{genus()} returns the genus of one absolutely irreducible component")) (|numberOfComponents| (((|NonNegativeInteger|)) "\\spad{numberOfComponents()} returns the number of absolutely irreducible components."))) @@ -1102,7 +1102,7 @@ NIL ((|HasCategory| |#2| (QUOTE (|Finite|))) (|HasCategory| |#2| (QUOTE (|Field|)))) (|FunctionFieldCategory| F UP UPUP) ((|constructor| (NIL "This category is a model for the function field of a plane algebraic curve.")) (|rationalPoints| (((|List| (|List| |#1|))) "\\spad{rationalPoints()} returns the list of all the affine rational points.")) (|nonSingularModel| (((|List| (|Polynomial| |#1|)) (|Symbol|)) "\\spad{nonSingularModel(u)} returns the equations in \\spad{u1},{}...,{}un of an affine non-singular model for the curve.")) (|algSplitSimple| (((|Record| (|:| |num| $) (|:| |den| |#2|) (|:| |derivden| |#2|) (|:| |gd| |#2|)) $ (|Mapping| |#2| |#2|)) "\\spad{algSplitSimple(f, D)} returns \\spad{[h,d,d',g]} such that \\spad{f=h/d},{} \\spad{h} is integral at all the normal places \\spad{w}.\\spad{r}.\\spad{t}. \\spad{D},{} \\spad{d' = Dd},{} \\spad{g = gcd(d, discriminant())} and \\spad{D} is the derivation to use. \\spad{f} must have at most simple finite poles.")) (|hyperelliptic| (((|Union| |#2| "failed")) "\\spad{hyperelliptic()} returns \\spad{p(x)} if the curve is the hyperelliptic defined by \\spad{y**2 = p(x)},{} \"failed\" otherwise.")) (|elliptic| (((|Union| |#2| "failed")) "\\spad{elliptic()} returns \\spad{p(x)} if the curve is the elliptic defined by \\spad{y**2 = p(x)},{} \"failed\" otherwise.")) (|elt| ((|#1| $ |#1| |#1|) "\\spad{elt(f,a,b)} or \\spad{f}(a,{} \\spad{b}) returns the value of \\spad{f} at the point \\spad{(x = a, y = b)} if it is not singular.")) (|primitivePart| (($ $) "\\spad{primitivePart(f)} removes the content of the denominator and the common content of the numerator of \\spad{f}.")) (|differentiate| (($ $ (|Mapping| |#2| |#2|)) "\\spad{differentiate(x, d)} extends the derivation \\spad{d} from UP to \\$ and applies it to \\spad{x}.")) (|integralDerivationMatrix| (((|Record| (|:| |num| (|Matrix| |#2|)) (|:| |den| |#2|)) (|Mapping| |#2| |#2|)) "\\spad{integralDerivationMatrix(d)} extends the derivation \\spad{d} from UP to \\$ and returns (\\spad{M},{} \\spad{Q}) such that the i^th row of \\spad{M} divided by \\spad{Q} form the coordinates of \\spad{d(wi)} with respect to \\spad{(w1,...,wn)} where \\spad{(w1,...,wn)} is the integral basis returned by integralBasis().")) (|integralRepresents| (($ (|Vector| |#2|) |#2|) "\\spad{integralRepresents([A1,...,An], D)} returns \\spad{(A1 w1+...+An wn)/D} where \\spad{(w1,...,wn)} is the integral basis of \\spad{integralBasis()}.")) (|integralCoordinates| (((|Record| (|:| |num| (|Vector| |#2|)) (|:| |den| |#2|)) $) "\\spad{integralCoordinates(f)} returns \\spad{[[A1,...,An], D]} such that \\spad{f = (A1 w1 +...+ An wn) / D} where \\spad{(w1,...,wn)} is the integral basis returned by \\spad{integralBasis()}.")) (|represents| (($ (|Vector| |#2|) |#2|) "\\spad{represents([A0,...,A(n-1)],D)} returns \\spad{(A0 + A1 y +...+ A(n-1)*y**(n-1))/D}.")) (|yCoordinates| (((|Record| (|:| |num| (|Vector| |#2|)) (|:| |den| |#2|)) $) "\\spad{yCoordinates(f)} returns \\spad{[[A1,...,An], D]} such that \\spad{f = (A1 + A2 y +...+ An y**(n-1)) / D}.")) (|inverseIntegralMatrixAtInfinity| (((|Matrix| (|Fraction| |#2|))) "\\spad{inverseIntegralMatrixAtInfinity()} returns \\spad{M} such that \\spad{M (v1,...,vn) = (1, y, ..., y**(n-1))} where \\spad{(v1,...,vn)} is the local integral basis at infinity returned by \\spad{infIntBasis()}.")) (|integralMatrixAtInfinity| (((|Matrix| (|Fraction| |#2|))) "\\spad{integralMatrixAtInfinity()} returns \\spad{M} such that \\spad{(v1,...,vn) = M (1, y, ..., y**(n-1))} where \\spad{(v1,...,vn)} is the local integral basis at infinity returned by \\spad{infIntBasis()}.")) (|inverseIntegralMatrix| (((|Matrix| (|Fraction| |#2|))) "\\spad{inverseIntegralMatrix()} returns \\spad{M} such that \\spad{M (w1,...,wn) = (1, y, ..., y**(n-1))} where \\spad{(w1,...,wn)} is the integral basis of \\spadfunFrom{integralBasis}{FunctionFieldCategory}.")) (|integralMatrix| (((|Matrix| (|Fraction| |#2|))) "\\spad{integralMatrix()} returns \\spad{M} such that \\spad{(w1,...,wn) = M (1, y, ..., y**(n-1))},{} where \\spad{(w1,...,wn)} is the integral basis of \\spadfunFrom{integralBasis}{FunctionFieldCategory}.")) (|reduceBasisAtInfinity| (((|Vector| $) (|Vector| $)) "\\spad{reduceBasisAtInfinity(b1,...,bn)} returns \\spad{(x**i * bj)} for all \\spad{i},{}\\spad{j} such that \\spad{x**i*bj} is locally integral at infinity.")) (|normalizeAtInfinity| (((|Vector| $) (|Vector| $)) "\\spad{normalizeAtInfinity(v)} makes \\spad{v} normal at infinity.")) (|complementaryBasis| (((|Vector| $) (|Vector| $)) "\\spad{complementaryBasis(b1,...,bn)} returns the complementary basis \\spad{(b1',...,bn')} of \\spad{(b1,...,bn)}.")) (|integral?| (((|Boolean|) $ |#2|) "\\spad{integral?(f, p)} tests whether \\spad{f} is locally integral at \\spad{p(x) = 0}.") (((|Boolean|) $ |#1|) "\\spad{integral?(f, a)} tests whether \\spad{f} is locally integral at \\spad{x = a}.") (((|Boolean|) $) "\\spad{integral?()} tests if \\spad{f} is integral over \\spad{k[x]}.")) (|integralAtInfinity?| (((|Boolean|) $) "\\spad{integralAtInfinity?()} tests if \\spad{f} is locally integral at infinity.")) (|integralBasisAtInfinity| (((|Vector| $)) "\\spad{integralBasisAtInfinity()} returns the local integral basis at infinity.")) (|integralBasis| (((|Vector| $)) "\\spad{integralBasis()} returns the integral basis for the curve.")) (|ramified?| (((|Boolean|) |#2|) "\\spad{ramified?(p)} tests whether \\spad{p(x) = 0} is ramified.") (((|Boolean|) |#1|) "\\spad{ramified?(a)} tests whether \\spad{x = a} is ramified.")) (|ramifiedAtInfinity?| (((|Boolean|)) "\\spad{ramifiedAtInfinity?()} tests if infinity is ramified.")) (|singular?| (((|Boolean|) |#2|) "\\spad{singular?(p)} tests whether \\spad{p(x) = 0} is singular.") (((|Boolean|) |#1|) "\\spad{singular?(a)} tests whether \\spad{x = a} is singular.")) (|singularAtInfinity?| (((|Boolean|)) "\\spad{singularAtInfinity?()} tests if there is a singularity at infinity.")) (|branchPoint?| (((|Boolean|) |#2|) "\\spad{branchPoint?(p)} tests whether \\spad{p(x) = 0} is a branch point.") (((|Boolean|) |#1|) "\\spad{branchPoint?(a)} tests whether \\spad{x = a} is a branch point.")) (|branchPointAtInfinity?| (((|Boolean|)) "\\spad{branchPointAtInfinity?()} tests if there is a branch point at infinity.")) (|rationalPoint?| (((|Boolean|) |#1| |#1|) "\\spad{rationalPoint?(a, b)} tests if \\spad{(x=a,y=b)} is on the curve.")) (|absolutelyIrreducible?| (((|Boolean|)) "\\spad{absolutelyIrreducible?()} tests if the curve absolutely irreducible?")) (|genus| (((|NonNegativeInteger|)) "\\spad{genus()} returns the genus of one absolutely irreducible component")) (|numberOfComponents| (((|NonNegativeInteger|)) "\\spad{numberOfComponents()} returns the number of absolutely irreducible components."))) -((|noZeroDivisors| |has| (|Fraction| |#2|) . #1=((|Field|))) (|canonicalUnitNormal| |has| (|Fraction| |#2|) . #1#) (|canonicalsClosed| |has| (|Fraction| |#2|) . #1#) ((|commutative| "*") . T) (|rightUnitary| . T) (|leftUnitary| . T) (|unitsKnown| . T)) +((|noZeroDivisors| |has| (|Fraction| |#2|) . #1=((|Field|))) (|canonicalUnitNormal| |has| (|Fraction| |#2|) . #1#) ((|commutative| "*") . T)) NIL (|FunctionFieldCategoryFunctions2| R1 UP1 UPUP1 F1 R2 UP2 UPUP2 F2) ((|constructor| (NIL "Lifts a map from rings to function fields over them.")) (|map| ((|#8| (|Mapping| |#5| |#1|) |#4|) "\\spad{map(f, p)} lifts \\spad{f} to \\spad{F1} and applies it to \\spad{p}."))) @@ -1110,15 +1110,15 @@ NIL NIL (|FiniteFieldCyclicGroup| |p| |extdeg|) ((|constructor| (NIL "FiniteFieldCyclicGroup(\\spad{p},{}\\spad{n}) implements a finite field extension of degee \\spad{n} over the prime field with \\spad{p} elements. Its elements are represented by powers of a primitive element,{} \\spadignore{i.e.} a generator of the multiplicative (cyclic) group. As primitive element we choose the root of the extension polynomial,{} which is created by {\\em createPrimitivePoly} from \\spadtype{FiniteFieldPolynomialPackage}. The Zech logarithms are stored in a table of size half of the field size,{} and use \\spadtype{SingleInteger} for representing field elements,{} hence,{} there are restrictions on the size of the field.")) (|getZechTable| (((|PrimitiveArray| (|SingleInteger|))) "\\spad{getZechTable()} returns the zech logarithm table of the field. This table is used to perform additions in the field quickly."))) -((|canonicalsClosed| . T) (|canonicalUnitNormal| . T) (|noZeroDivisors| . T) ((|commutative| "*") . T) (|rightUnitary| . T) (|leftUnitary| . T) (|unitsKnown| . T)) +((|canonicalUnitNormal| . T) (|noZeroDivisors| . T) ((|commutative| "*") . T)) ((OR #1=(|HasCategory| #2=(|PrimeField| |#1|) (QUOTE (|CharacteristicNonZero|))) #3=(|HasCategory| #2# (QUOTE (|Finite|)))) (|HasCategory| #2# (QUOTE (|CharacteristicZero|))) #3# #1#) (|FiniteFieldCyclicGroupExtensionByPolynomial| GF |defpol|) ((|constructor| (NIL "FiniteFieldCyclicGroupExtensionByPolynomial(GF,{}defpol) implements a finite extension field of the ground field {\\em GF}. Its elements are represented by powers of a primitive element,{} \\spadignore{i.e.} a generator of the multiplicative (cyclic) group. As primitive element we choose the root of the extension polynomial {\\em defpol},{} which MUST be primitive (user responsibility). Zech logarithms are stored in a table of size half of the field size,{} and use \\spadtype{SingleInteger} for representing field elements,{} hence,{} there are restrictions on the size of the field.")) (|getZechTable| (((|PrimitiveArray| (|SingleInteger|))) "\\spad{getZechTable()} returns the zech logarithm table of the field it is used to perform additions in the field quickly."))) -((|canonicalsClosed| . T) (|canonicalUnitNormal| . T) (|noZeroDivisors| . T) ((|commutative| "*") . T) (|rightUnitary| . T) (|leftUnitary| . T) (|unitsKnown| . T)) +((|canonicalUnitNormal| . T) (|noZeroDivisors| . T) ((|commutative| "*") . T)) ((OR #1=(|HasCategory| |#1| (QUOTE (|CharacteristicNonZero|))) #2=(|HasCategory| |#1| (QUOTE (|Finite|)))) (|HasCategory| |#1| (QUOTE (|CharacteristicZero|))) #2# #1#) (|FiniteFieldCyclicGroupExtension| GF |extdeg|) ((|constructor| (NIL "FiniteFieldCyclicGroupExtension(GF,{}\\spad{n}) implements a extension of degree \\spad{n} over the ground field {\\em GF}. Its elements are represented by powers of a primitive element,{} \\spadignore{i.e.} a generator of the multiplicative (cyclic) group. As primitive element we choose the root of the extension polynomial,{} which is created by {\\em createPrimitivePoly} from \\spadtype{FiniteFieldPolynomialPackage}. Zech logarithms are stored in a table of size half of the field size,{} and use \\spadtype{SingleInteger} for representing field elements,{} hence,{} there are restrictions on the size of the field.")) (|getZechTable| (((|PrimitiveArray| (|SingleInteger|))) "\\spad{getZechTable()} returns the zech logarithm table of the field. This table is used to perform additions in the field quickly."))) -((|canonicalsClosed| . T) (|canonicalUnitNormal| . T) (|noZeroDivisors| . T) ((|commutative| "*") . T) (|rightUnitary| . T) (|leftUnitary| . T) (|unitsKnown| . T)) +((|canonicalUnitNormal| . T) (|noZeroDivisors| . T) ((|commutative| "*") . T)) ((OR #1=(|HasCategory| |#1| (QUOTE (|CharacteristicNonZero|))) #2=(|HasCategory| |#1| (QUOTE (|Finite|)))) (|HasCategory| |#1| (QUOTE (|CharacteristicZero|))) #2# #1#) (|FiniteFieldFunctions| GF) ((|constructor| (NIL "FiniteFieldFunctions(GF) is a package with functions concerning finite extension fields of the finite ground field {\\em GF},{} \\spadignore{e.g.} Zech logarithms.")) (|createLowComplexityNormalBasis| (((|Union| (|SparseUnivariatePolynomial| |#1|) (|Vector| (|List| (|Record| (|:| |value| |#1|) (|:| |index| (|SingleInteger|)))))) (|PositiveInteger|)) "\\spad{createLowComplexityNormalBasis(n)} tries to find a a low complexity normal basis of degree {\\em n} over {\\em GF} and returns its multiplication matrix If no low complexity basis is found it calls \\axiomFunFrom{createNormalPoly}{FiniteFieldPolynomialPackage}(\\spad{n}) to produce a normal polynomial of degree {\\em n} over {\\em GF}")) (|createLowComplexityTable| (((|Union| (|Vector| (|List| (|Record| (|:| |value| |#1|) (|:| |index| (|SingleInteger|))))) "failed") (|PositiveInteger|)) "\\spad{createLowComplexityTable(n)} tries to find a low complexity normal basis of degree {\\em n} over {\\em GF} and returns its multiplication matrix Fails,{} if it does not find a low complexity basis")) (|sizeMultiplication| (((|NonNegativeInteger|) (|Vector| (|List| (|Record| (|:| |value| |#1|) (|:| |index| (|SingleInteger|)))))) "\\spad{sizeMultiplication(m)} returns the number of entries of the multiplication table {\\em m}.")) (|createMultiplicationMatrix| (((|Matrix| |#1|) (|Vector| (|List| (|Record| (|:| |value| |#1|) (|:| |index| (|SingleInteger|)))))) "\\spad{createMultiplicationMatrix(m)} forms the multiplication table {\\em m} into a matrix over the ground field.")) (|createMultiplicationTable| (((|Vector| (|List| (|Record| (|:| |value| |#1|) (|:| |index| (|SingleInteger|))))) (|SparseUnivariatePolynomial| |#1|)) "\\spad{createMultiplicationTable(f)} generates a multiplication table for the normal basis of the field extension determined by {\\em f}. This is needed to perform multiplications between elements represented as coordinate vectors to this basis. See \\spadtype{FFNBP},{} \\spadtype{FFNBX}.")) (|createZechTable| (((|PrimitiveArray| (|SingleInteger|)) (|SparseUnivariatePolynomial| |#1|)) "\\spad{createZechTable(f)} generates a Zech logarithm table for the cyclic group representation of a extension of the ground field by the primitive polynomial {\\em f(x)},{} \\spadignore{i.e.} \\spad{Z(i)},{} defined by {\\em x**Z(i) = 1+x**i} is stored at index \\spad{i}. This is needed in particular to perform addition of field elements in finite fields represented in this way. See \\spadtype{FFCGP},{} \\spadtype{FFCGX}."))) @@ -1134,7 +1134,7 @@ NIL NIL (|FiniteFieldCategory|) ((|constructor| (NIL "FiniteFieldCategory is the category of finite fields")) (|representationType| (((|Union| "prime" "polynomial" "normal" "cyclic")) "\\spad{representationType()} returns the type of the representation,{} one of: \\spad{prime},{} \\spad{polynomial},{} \\spad{normal},{} or \\spad{cyclic}.")) (|order| (((|PositiveInteger|) $) "\\spad{order(b)} computes the order of an element \\spad{b} in the multiplicative group of the field. Error: if \\spad{b} equals 0.")) (|discreteLog| (((|NonNegativeInteger|) $) "\\spad{discreteLog(a)} computes the discrete logarithm of \\spad{a} with respect to \\spad{primitiveElement()} of the field.")) (|primitive?| (((|Boolean|) $) "\\spad{primitive?(b)} tests whether the element \\spad{b} is a generator of the (cyclic) multiplicative group of the field,{} \\spadignore{i.e.} is a primitive element. Implementation Note: see ch.IX.1.3,{} th.2 in \\spad{D}. Lipson.")) (|primitiveElement| (($) "\\spad{primitiveElement()} returns a primitive element stored in a global variable in the domain. At first call,{} the primitive element is computed by calling \\spadfun{createPrimitiveElement}.")) (|createPrimitiveElement| (($) "\\spad{createPrimitiveElement()} computes a generator of the (cyclic) multiplicative group of the field.")) (|tableForDiscreteLogarithm| (((|Table| (|PositiveInteger|) (|NonNegativeInteger|)) (|Integer|)) "\\spad{tableForDiscreteLogarithm(a,n)} returns a table of the discrete logarithms of \\spad{a**0} up to \\spad{a**(n-1)} which,{} called with key \\spad{lookup(a**i)} returns \\spad{i} for \\spad{i} in \\spad{0..n-1}. Error: if not called for prime divisors of order of \\indented{7}{multiplicative group.}")) (|factorsOfCyclicGroupSize| (((|List| (|Record| (|:| |factor| (|Integer|)) (|:| |exponent| (|Integer|))))) "\\spad{factorsOfCyclicGroupSize()} returns the factorization of size()\\spad{-1}")) (|conditionP| (((|Union| (|Vector| $) "failed") (|Matrix| $)) "\\spad{conditionP(mat)},{} given a matrix representing a homogeneous system of equations,{} returns a vector whose characteristic'th powers is a non-trivial solution,{} or \"failed\" if no such vector exists.")) (|charthRoot| (($ $) "\\spad{charthRoot(a)} takes the characteristic'th root of {\\em a}. Note: such a root is alway defined in finite fields."))) -((|canonicalsClosed| . T) (|canonicalUnitNormal| . T) (|noZeroDivisors| . T) ((|commutative| "*") . T) (|rightUnitary| . T) (|leftUnitary| . T) (|unitsKnown| . T)) +((|canonicalUnitNormal| . T) (|noZeroDivisors| . T) ((|commutative| "*") . T)) NIL (|FunctionFieldIntegralBasis| R UP F) ((|constructor| (NIL "In this package \\spad{R} is a Euclidean domain and \\spad{F} is a framed algebra over \\spad{R}. The package provides functions to compute the integral closure of \\spad{R} in the quotient field of \\spad{F}. It is assumed that \\spad{char(R/P) = char(R)} for any prime \\spad{P} of \\spad{R}. A typical instance of this is when \\spad{R = K[x]} and \\spad{F} is a function field over \\spad{R}.")) (|localIntegralBasis| (((|Record| (|:| |basis| (|Matrix| |#1|)) (|:| |basisDen| |#1|) (|:| |basisInv| (|Matrix| |#1|))) |#1|) "\\spad{integralBasis(p)} returns a record \\spad{[basis,basisDen,basisInv]} containing information regarding the local integral closure of \\spad{R} at the prime \\spad{p} in the quotient field of \\spad{F},{} where \\spad{F} is a framed algebra with \\spad{R}-module basis \\spad{w1,w2,...,wn}. If \\spad{basis} is the matrix \\spad{(aij, i = 1..n, j = 1..n)},{} then the \\spad{i}th element of the local integral basis is \\spad{vi = (1/basisDen) * sum(aij * wj, j = 1..n)},{} \\spadignore{i.e.} the \\spad{i}th row of \\spad{basis} contains the coordinates of the \\spad{i}th basis vector. Similarly,{} the \\spad{i}th row of the matrix \\spad{basisInv} contains the coordinates of \\spad{wi} with respect to the basis \\spad{v1,...,vn}: if \\spad{basisInv} is the matrix \\spad{(bij, i = 1..n, j = 1..n)},{} then \\spad{wi = sum(bij * vj, j = 1..n)}.")) (|integralBasis| (((|Record| (|:| |basis| (|Matrix| |#1|)) (|:| |basisDen| |#1|) (|:| |basisInv| (|Matrix| |#1|)))) "\\spad{integralBasis()} returns a record \\spad{[basis,basisDen,basisInv]} containing information regarding the integral closure of \\spad{R} in the quotient field of \\spad{F},{} where \\spad{F} is a framed algebra with \\spad{R}-module basis \\spad{w1,w2,...,wn}. If \\spad{basis} is the matrix \\spad{(aij, i = 1..n, j = 1..n)},{} then the \\spad{i}th element of the integral basis is \\spad{vi = (1/basisDen) * sum(aij * wj, j = 1..n)},{} \\spadignore{i.e.} the \\spad{i}th row of \\spad{basis} contains the coordinates of the \\spad{i}th basis vector. Similarly,{} the \\spad{i}th row of the matrix \\spad{basisInv} contains the coordinates of \\spad{wi} with respect to the basis \\spad{v1,...,vn}: if \\spad{basisInv} is the matrix \\spad{(bij, i = 1..n, j = 1..n)},{} then \\spad{wi = sum(bij * vj, j = 1..n)}.")) (|squareFree| (((|Factored| $) $) "\\spad{squareFree(x)} returns a square-free factorisation of \\spad{x}"))) @@ -1142,19 +1142,19 @@ NIL NIL (|FiniteFieldNormalBasis| |p| |extdeg|) ((|constructor| (NIL "FiniteFieldNormalBasis(\\spad{p},{}\\spad{n}) implements a finite extension field of degree \\spad{n} over the prime field with \\spad{p} elements. The elements are represented by coordinate vectors with respect to a normal basis,{} \\spadignore{i.e.} a basis consisting of the conjugates (\\spad{q}-powers) of an element,{} in this case called normal element. This is chosen as a root of the extension polynomial created by \\spadfunFrom{createNormalPoly}{FiniteFieldPolynomialPackage}.")) (|sizeMultiplication| (((|NonNegativeInteger|)) "\\spad{sizeMultiplication()} returns the number of entries in the multiplication table of the field. Note: The time of multiplication of field elements depends on this size.")) (|getMultiplicationMatrix| (((|Matrix| (|PrimeField| |#1|))) "\\spad{getMultiplicationMatrix()} returns the multiplication table in form of a matrix.")) (|getMultiplicationTable| (((|Vector| (|List| (|Record| (|:| |value| (|PrimeField| |#1|)) (|:| |index| (|SingleInteger|)))))) "\\spad{getMultiplicationTable()} returns the multiplication table for the normal basis of the field. This table is used to perform multiplications between field elements."))) -((|canonicalsClosed| . T) (|canonicalUnitNormal| . T) (|noZeroDivisors| . T) ((|commutative| "*") . T) (|rightUnitary| . T) (|leftUnitary| . T) (|unitsKnown| . T)) +((|canonicalUnitNormal| . T) (|noZeroDivisors| . T) ((|commutative| "*") . T)) ((OR #1=(|HasCategory| #2=(|PrimeField| |#1|) (QUOTE (|CharacteristicNonZero|))) #3=(|HasCategory| #2# (QUOTE (|Finite|)))) (|HasCategory| #2# (QUOTE (|CharacteristicZero|))) #3# #1#) (|FiniteFieldNormalBasisExtensionByPolynomial| GF |uni|) ((|constructor| (NIL "FiniteFieldNormalBasisExtensionByPolynomial(GF,{}uni) implements a finite extension of the ground field {\\em GF}. The elements are represented by coordinate vectors with respect to. a normal basis,{} \\spadignore{i.e.} a basis consisting of the conjugates (\\spad{q}-powers) of an element,{} in this case called normal element,{} where \\spad{q} is the size of {\\em GF}. The normal element is chosen as a root of the extension polynomial,{} which MUST be normal over {\\em GF} (user responsibility)")) (|sizeMultiplication| (((|NonNegativeInteger|)) "\\spad{sizeMultiplication()} returns the number of entries in the multiplication table of the field. Note: the time of multiplication of field elements depends on this size.")) (|getMultiplicationMatrix| (((|Matrix| |#1|)) "\\spad{getMultiplicationMatrix()} returns the multiplication table in form of a matrix.")) (|getMultiplicationTable| (((|Vector| (|List| (|Record| (|:| |value| |#1|) (|:| |index| (|SingleInteger|)))))) "\\spad{getMultiplicationTable()} returns the multiplication table for the normal basis of the field. This table is used to perform multiplications between field elements."))) -((|canonicalsClosed| . T) (|canonicalUnitNormal| . T) (|noZeroDivisors| . T) ((|commutative| "*") . T) (|rightUnitary| . T) (|leftUnitary| . T) (|unitsKnown| . T)) +((|canonicalUnitNormal| . T) (|noZeroDivisors| . T) ((|commutative| "*") . T)) ((OR #1=(|HasCategory| |#1| (QUOTE (|CharacteristicNonZero|))) #2=(|HasCategory| |#1| (QUOTE (|Finite|)))) (|HasCategory| |#1| (QUOTE (|CharacteristicZero|))) #2# #1#) (|FiniteFieldNormalBasisExtension| GF |extdeg|) ((|constructor| (NIL "FiniteFieldNormalBasisExtensionByPolynomial(GF,{}\\spad{n}) implements a finite extension field of degree \\spad{n} over the ground field {\\em GF}. The elements are represented by coordinate vectors with respect to a normal basis,{} \\spadignore{i.e.} a basis consisting of the conjugates (\\spad{q}-powers) of an element,{} in this case called normal element. This is chosen as a root of the extension polynomial,{} created by {\\em createNormalPoly} from \\spadtype{FiniteFieldPolynomialPackage}")) (|sizeMultiplication| (((|NonNegativeInteger|)) "\\spad{sizeMultiplication()} returns the number of entries in the multiplication table of the field. Note: the time of multiplication of field elements depends on this size.")) (|getMultiplicationMatrix| (((|Matrix| |#1|)) "\\spad{getMultiplicationMatrix()} returns the multiplication table in form of a matrix.")) (|getMultiplicationTable| (((|Vector| (|List| (|Record| (|:| |value| |#1|) (|:| |index| (|SingleInteger|)))))) "\\spad{getMultiplicationTable()} returns the multiplication table for the normal basis of the field. This table is used to perform multiplications between field elements."))) -((|canonicalsClosed| . T) (|canonicalUnitNormal| . T) (|noZeroDivisors| . T) ((|commutative| "*") . T) (|rightUnitary| . T) (|leftUnitary| . T) (|unitsKnown| . T)) +((|canonicalUnitNormal| . T) (|noZeroDivisors| . T) ((|commutative| "*") . T)) ((OR #1=(|HasCategory| |#1| (QUOTE (|CharacteristicNonZero|))) #2=(|HasCategory| |#1| (QUOTE (|Finite|)))) (|HasCategory| |#1| (QUOTE (|CharacteristicZero|))) #2# #1#) (|FiniteFieldExtensionByPolynomial| GF |defpol|) ((|constructor| (NIL "FiniteFieldExtensionByPolynomial(GF,{} defpol) implements the extension of the finite field {\\em GF} generated by the extension polynomial {\\em defpol} which MUST be irreducible. Note: the user has the responsibility to ensure that {\\em defpol} is irreducible."))) -((|canonicalsClosed| . T) (|canonicalUnitNormal| . T) (|noZeroDivisors| . T) ((|commutative| "*") . T) (|rightUnitary| . T) (|leftUnitary| . T) (|unitsKnown| . T)) +((|canonicalUnitNormal| . T) (|noZeroDivisors| . T) ((|commutative| "*") . T)) ((OR #1=(|HasCategory| |#1| (QUOTE (|CharacteristicNonZero|))) #2=(|HasCategory| |#1| (QUOTE (|Finite|)))) (|HasCategory| |#1| (QUOTE (|CharacteristicZero|))) #2# #1#) (|FiniteFieldPolynomialPackage| GF) ((|constructor| (NIL "This package provides a number of functions for generating,{} counting and testing irreducible,{} normal,{} primitive,{} random polynomials over finite fields.")) (|reducedQPowers| (((|PrimitiveArray| (|SparseUnivariatePolynomial| |#1|)) (|SparseUnivariatePolynomial| |#1|)) "\\spad{reducedQPowers(f)} generates \\spad{[x,x**q,x**(q**2),...,x**(q**(n-1))]} reduced modulo \\spad{f} where \\spad{q = size()\\$GF} and \\spad{n = degree f}.")) (|leastAffineMultiple| (((|SparseUnivariatePolynomial| |#1|) (|SparseUnivariatePolynomial| |#1|)) "\\spad{leastAffineMultiple(f)} computes the least affine polynomial which is divisible by the polynomial \\spad{f} over the finite field {\\em GF},{} \\spadignore{i.e.} a polynomial whose exponents are 0 or a power of \\spad{q},{} the size of {\\em GF}.")) (|random| (((|SparseUnivariatePolynomial| |#1|) (|PositiveInteger|) (|PositiveInteger|)) "\\spad{random(m,n)}\\$FFPOLY(GF) generates a random monic polynomial of degree \\spad{d} over the finite field {\\em GF},{} \\spad{d} between \\spad{m} and \\spad{n}.") (((|SparseUnivariatePolynomial| |#1|) (|PositiveInteger|)) "\\spad{random(n)}\\$FFPOLY(GF) generates a random monic polynomial of degree \\spad{n} over the finite field {\\em GF}.")) (|nextPrimitiveNormalPoly| (((|Union| (|SparseUnivariatePolynomial| |#1|) "failed") (|SparseUnivariatePolynomial| |#1|)) "\\spad{nextPrimitiveNormalPoly(f)} yields the next primitive normal polynomial over a finite field {\\em GF} of the same degree as \\spad{f} in the following order,{} or \"failed\" if there are no greater ones. Error: if \\spad{f} has degree 0. Note: the input polynomial \\spad{f} is made monic. Also,{} \\spad{f < g} if the {\\em lookup} of the constant term of \\spad{f} is less than this number for \\spad{g} or,{} in case these numbers are equal,{} if the {\\em lookup} of the coefficient of the term of degree {\\em n-1} of \\spad{f} is less than this number for \\spad{g}. If these numbers are equals,{} \\spad{f < g} if the number of monomials of \\spad{f} is less than that for \\spad{g},{} or if the lists of exponents for \\spad{f} are lexicographically less than those for \\spad{g}. If these lists are also equal,{} the lists of coefficients are coefficients according to the lexicographic ordering induced by the ordering of the elements of {\\em GF} given by {\\em lookup}. This operation is equivalent to nextNormalPrimitivePoly(\\spad{f}).")) (|nextNormalPrimitivePoly| (((|Union| (|SparseUnivariatePolynomial| |#1|) "failed") (|SparseUnivariatePolynomial| |#1|)) "\\spad{nextNormalPrimitivePoly(f)} yields the next normal primitive polynomial over a finite field {\\em GF} of the same degree as \\spad{f} in the following order,{} or \"failed\" if there are no greater ones. Error: if \\spad{f} has degree 0. Note: the input polynomial \\spad{f} is made monic. Also,{} \\spad{f < g} if the {\\em lookup} of the constant term of \\spad{f} is less than this number for \\spad{g} or if {\\em lookup} of the coefficient of the term of degree {\\em n-1} of \\spad{f} is less than this number for \\spad{g}. Otherwise,{} \\spad{f < g} if the number of monomials of \\spad{f} is less than that for \\spad{g} or if the lists of exponents for \\spad{f} are lexicographically less than those for \\spad{g}. If these lists are also equal,{} the lists of coefficients are compared according to the lexicographic ordering induced by the ordering of the elements of {\\em GF} given by {\\em lookup}. This operation is equivalent to nextPrimitiveNormalPoly(\\spad{f}).")) (|nextNormalPoly| (((|Union| (|SparseUnivariatePolynomial| |#1|) "failed") (|SparseUnivariatePolynomial| |#1|)) "\\spad{nextNormalPoly(f)} yields the next normal polynomial over a finite field {\\em GF} of the same degree as \\spad{f} in the following order,{} or \"failed\" if there are no greater ones. Error: if \\spad{f} has degree 0. Note: the input polynomial \\spad{f} is made monic. Also,{} \\spad{f < g} if the {\\em lookup} of the coefficient of the term of degree {\\em n-1} of \\spad{f} is less than that for \\spad{g}. In case these numbers are equal,{} \\spad{f < g} if if the number of monomials of \\spad{f} is less that for \\spad{g} or if the list of exponents of \\spad{f} are lexicographically less than the corresponding list for \\spad{g}. If these lists are also equal,{} the lists of coefficients are compared according to the lexicographic ordering induced by the ordering of the elements of {\\em GF} given by {\\em lookup}.")) (|nextPrimitivePoly| (((|Union| (|SparseUnivariatePolynomial| |#1|) "failed") (|SparseUnivariatePolynomial| |#1|)) "\\spad{nextPrimitivePoly(f)} yields the next primitive polynomial over a finite field {\\em GF} of the same degree as \\spad{f} in the following order,{} or \"failed\" if there are no greater ones. Error: if \\spad{f} has degree 0. Note: the input polynomial \\spad{f} is made monic. Also,{} \\spad{f < g} if the {\\em lookup} of the constant term of \\spad{f} is less than this number for \\spad{g}. If these values are equal,{} then \\spad{f < g} if if the number of monomials of \\spad{f} is less than that for \\spad{g} or if the lists of exponents of \\spad{f} are lexicographically less than the corresponding list for \\spad{g}. If these lists are also equal,{} the lists of coefficients are compared according to the lexicographic ordering induced by the ordering of the elements of {\\em GF} given by {\\em lookup}.")) (|nextIrreduciblePoly| (((|Union| (|SparseUnivariatePolynomial| |#1|) "failed") (|SparseUnivariatePolynomial| |#1|)) "\\spad{nextIrreduciblePoly(f)} yields the next monic irreducible polynomial over a finite field {\\em GF} of the same degree as \\spad{f} in the following order,{} or \"failed\" if there are no greater ones. Error: if \\spad{f} has degree 0. Note: the input polynomial \\spad{f} is made monic. Also,{} \\spad{f < g} if the number of monomials of \\spad{f} is less than this number for \\spad{g}. If \\spad{f} and \\spad{g} have the same number of monomials,{} the lists of exponents are compared lexicographically. If these lists are also equal,{} the lists of coefficients are compared according to the lexicographic ordering induced by the ordering of the elements of {\\em GF} given by {\\em lookup}.")) (|createPrimitiveNormalPoly| (((|SparseUnivariatePolynomial| |#1|) (|PositiveInteger|)) "\\spad{createPrimitiveNormalPoly(n)}\\$FFPOLY(GF) generates a normal and primitive polynomial of degree \\spad{n} over the field {\\em GF}. polynomial of degree \\spad{n} over the field {\\em GF}.")) (|createNormalPrimitivePoly| (((|SparseUnivariatePolynomial| |#1|) (|PositiveInteger|)) "\\spad{createNormalPrimitivePoly(n)}\\$FFPOLY(GF) generates a normal and primitive polynomial of degree \\spad{n} over the field {\\em GF}. Note: this function is equivalent to createPrimitiveNormalPoly(\\spad{n})")) (|createNormalPoly| (((|SparseUnivariatePolynomial| |#1|) (|PositiveInteger|)) "\\spad{createNormalPoly(n)}\\$FFPOLY(GF) generates a normal polynomial of degree \\spad{n} over the finite field {\\em GF}.")) (|createPrimitivePoly| (((|SparseUnivariatePolynomial| |#1|) (|PositiveInteger|)) "\\spad{createPrimitivePoly(n)}\\$FFPOLY(GF) generates a primitive polynomial of degree \\spad{n} over the finite field {\\em GF}.")) (|createIrreduciblePoly| (((|SparseUnivariatePolynomial| |#1|) (|PositiveInteger|)) "\\spad{createIrreduciblePoly(n)}\\$FFPOLY(GF) generates a monic irreducible univariate polynomial of degree \\spad{n} over the finite field {\\em GF}.")) (|numberOfNormalPoly| (((|PositiveInteger|) (|PositiveInteger|)) "\\spad{numberOfNormalPoly(n)}\\$FFPOLY(GF) yields the number of normal polynomials of degree \\spad{n} over the finite field {\\em GF}.")) (|numberOfPrimitivePoly| (((|PositiveInteger|) (|PositiveInteger|)) "\\spad{numberOfPrimitivePoly(n)}\\$FFPOLY(GF) yields the number of primitive polynomials of degree \\spad{n} over the finite field {\\em GF}.")) (|numberOfIrreduciblePoly| (((|PositiveInteger|) (|PositiveInteger|)) "\\spad{numberOfIrreduciblePoly(n)}\\$FFPOLY(GF) yields the number of monic irreducible univariate polynomials of degree \\spad{n} over the finite field {\\em GF}.")) (|normal?| (((|Boolean|) (|SparseUnivariatePolynomial| |#1|)) "\\spad{normal?(f)} tests whether the polynomial \\spad{f} over a finite field is normal,{} \\spadignore{i.e.} its roots are linearly independent over the field.")) (|primitive?| (((|Boolean|) (|SparseUnivariatePolynomial| |#1|)) "\\spad{primitive?(f)} tests whether the polynomial \\spad{f} over a finite field is primitive,{} \\spadignore{i.e.} all its roots are primitive."))) @@ -1170,7 +1170,7 @@ NIL NIL (|FiniteFieldExtension| GF |n|) ((|constructor| (NIL "FiniteFieldExtensionByPolynomial(GF,{} \\spad{n}) implements an extension of the finite field {\\em GF} of degree \\spad{n} generated by the extension polynomial constructed by \\spadfunFrom{createIrreduciblePoly}{FiniteFieldPolynomialPackage} from \\spadtype{FiniteFieldPolynomialPackage}."))) -((|canonicalsClosed| . T) (|canonicalUnitNormal| . T) (|noZeroDivisors| . T) ((|commutative| "*") . T) (|rightUnitary| . T) (|leftUnitary| . T) (|unitsKnown| . T)) +((|canonicalUnitNormal| . T) (|noZeroDivisors| . T) ((|commutative| "*") . T)) ((OR #1=(|HasCategory| |#1| (QUOTE (|CharacteristicNonZero|))) #2=(|HasCategory| |#1| (QUOTE (|Finite|)))) (|HasCategory| |#1| (QUOTE (|CharacteristicZero|))) #2# #1#) (|FGLMIfCanPackage| R |ls|) ((|constructor| (NIL "This is just an interface between several packages and domains. The goal is to compute lexicographical Groebner bases of sets of polynomial with type \\spadtype{Polynomial R} by the {\\em FGLM} algorithm if this is possible (\\spadignore{i.e.} if the input system generates a zero-dimensional ideal).")) (|groebner| (((|List| (|Polynomial| |#1|)) (|List| (|Polynomial| |#1|))) "\\axiom{groebner(\\spad{lq1})} returns the lexicographical Groebner basis of \\axiom{\\spad{lq1}}. If \\axiom{\\spad{lq1}} generates a zero-dimensional ideal then the {\\em FGLM} strategy is used,{} otherwise the {\\em Sugar} strategy is used.")) (|fglmIfCan| (((|Union| (|List| (|Polynomial| |#1|)) "failed") (|List| (|Polynomial| |#1|))) "\\axiom{fglmIfCan(\\spad{lq1})} returns the lexicographical Groebner basis of \\axiom{\\spad{lq1}} by using the {\\em FGLM} strategy,{} if \\axiom{zeroDimensional?(\\spad{lq1})} holds.")) (|zeroDimensional?| (((|Boolean|) (|List| (|Polynomial| |#1|))) "\\axiom{zeroDimensional?(\\spad{lq1})} returns \\spad{true} iff \\axiom{\\spad{lq1}} generates a zero-dimensional ideal \\spad{w}.\\spad{r}.\\spad{t}. the variables of \\axiom{ls}."))) @@ -1178,15 +1178,15 @@ NIL NIL (|FreeGroup| S) ((|constructor| (NIL "The free group on a set \\spad{S} is the group of finite products of the form \\spad{reduce(*,[si ** ni])} where the \\spad{si}'s are in \\spad{S},{} and the \\spad{ni}'s are integers. The multiplication is not commutative.")) (|factors| (((|List| (|Record| (|:| |gen| |#1|) (|:| |exp| (|Integer|)))) $) "\\spad{factors(a1\\^e1,...,an\\^en)} returns \\spad{[[a1, e1],...,[an, en]]}.")) (|mapGen| (($ (|Mapping| |#1| |#1|) $) "\\spad{mapGen(f, a1\\^e1 ... an\\^en)} returns \\spad{f(a1)\\^e1 ... f(an)\\^en}.")) (|mapExpon| (($ (|Mapping| (|Integer|) (|Integer|)) $) "\\spad{mapExpon(f, a1\\^e1 ... an\\^en)} returns \\spad{a1\\^f(e1) ... an\\^f(en)}.")) (|nthFactor| ((|#1| $ (|Integer|)) "\\spad{nthFactor(x, n)} returns the factor of the n^th monomial of \\spad{x}.")) (|nthExpon| (((|Integer|) $ (|Integer|)) "\\spad{nthExpon(x, n)} returns the exponent of the n^th monomial of \\spad{x}.")) (|size| (((|NonNegativeInteger|) $) "\\spad{size(x)} returns the number of monomials in \\spad{x}.")) (** (($ |#1| (|Integer|)) "\\spad{s ** n} returns the product of \\spad{s} by itself \\spad{n} times.")) (* (($ $ |#1|) "\\spad{x * s} returns the product of \\spad{x} by \\spad{s} on the right.") (($ |#1| $) "\\spad{s * x} returns the product of \\spad{x} by \\spad{s} on the left."))) -((|unitsKnown| . T)) +NIL NIL (|Field&| S) -((|constructor| (NIL "The category of commutative fields,{} \\spadignore{i.e.} commutative rings where all non-zero elements have multiplicative inverses. The \\spadfun{factor} operation while trivial is useful to have defined. \\blankline")) (|canonicalsClosed| ((|attribute|) "since \\spad{0*0=0},{} \\spad{1*1=1}")) (|canonicalUnitNormal| ((|attribute|) "either 0 or 1.")) (/ (($ $ $) "\\spad{x/y} divides the element \\spad{x} by the element \\spad{y}. Error: if \\spad{y} is 0."))) +((|constructor| (NIL "The category of commutative fields,{} \\spadignore{i.e.} commutative rings where all non-zero elements have multiplicative inverses. The \\spadfun{factor} operation while trivial is useful to have defined. \\blankline")) (|canonicalUnitNormal| ((|attribute|) "either 0 or 1.")) (/ (($ $ $) "\\spad{x/y} divides the element \\spad{x} by the element \\spad{y}. Error: if \\spad{y} is 0."))) NIL NIL (|Field|) -((|constructor| (NIL "The category of commutative fields,{} \\spadignore{i.e.} commutative rings where all non-zero elements have multiplicative inverses. The \\spadfun{factor} operation while trivial is useful to have defined. \\blankline")) (|canonicalsClosed| ((|attribute|) "since \\spad{0*0=0},{} \\spad{1*1=1}")) (|canonicalUnitNormal| ((|attribute|) "either 0 or 1.")) (/ (($ $ $) "\\spad{x/y} divides the element \\spad{x} by the element \\spad{y}. Error: if \\spad{y} is 0."))) -((|canonicalsClosed| . T) (|canonicalUnitNormal| . T) (|noZeroDivisors| . T) ((|commutative| "*") . T) (|rightUnitary| . T) (|leftUnitary| . T) (|unitsKnown| . T)) +((|constructor| (NIL "The category of commutative fields,{} \\spadignore{i.e.} commutative rings where all non-zero elements have multiplicative inverses. The \\spadfun{factor} operation while trivial is useful to have defined. \\blankline")) (|canonicalUnitNormal| ((|attribute|) "either 0 or 1.")) (/ (($ $ $) "\\spad{x/y} divides the element \\spad{x} by the element \\spad{y}. Error: if \\spad{y} is 0."))) +((|canonicalUnitNormal| . T) (|noZeroDivisors| . T) ((|commutative| "*") . T)) NIL (|File| S) ((|constructor| (NIL "This domain provides a basic model of files to save arbitrary values. The operations provide sequential access to the contents.")) (|readIfCan!| (((|Union| |#1| "failed") $) "\\spad{readIfCan!(f)} returns a value from the file \\spad{f},{} if possible. If \\spad{f} is not open for reading,{} or if \\spad{f} is at the end of file then \\spad{\"failed\"} is the result."))) @@ -1197,12 +1197,12 @@ NIL NIL NIL (|FiniteRankNonAssociativeAlgebra&| S R) -((|constructor| (NIL "A FiniteRankNonAssociativeAlgebra is a non associative algebra over a commutative ring \\spad{R} which is a free \\spad{R}-module of finite rank.")) (|unitsKnown| ((|attribute|) "unitsKnown means that \\spadfun{recip} truly yields reciprocal or \\spad{\"failed\"} if not a unit,{} similarly for \\spadfun{leftRecip} and \\spadfun{rightRecip}. The reason is that we use left,{} respectively right,{} minimal polynomials to decide this question.")) (|unit| (((|Union| $ "failed")) "\\spad{unit()} returns a unit of the algebra (necessarily unique),{} or \\spad{\"failed\"} if there is none.")) (|rightUnit| (((|Union| $ "failed")) "\\spad{rightUnit()} returns a right unit of the algebra (not necessarily unique),{} or \\spad{\"failed\"} if there is none.")) (|leftUnit| (((|Union| $ "failed")) "\\spad{leftUnit()} returns a left unit of the algebra (not necessarily unique),{} or \\spad{\"failed\"} if there is none.")) (|rightUnits| (((|Union| (|Record| (|:| |particular| $) (|:| |basis| (|List| $))) "failed")) "\\spad{rightUnits()} returns the affine space of all right units of the algebra,{} or \\spad{\"failed\"} if there is none.")) (|leftUnits| (((|Union| (|Record| (|:| |particular| $) (|:| |basis| (|List| $))) "failed")) "\\spad{leftUnits()} returns the affine space of all left units of the algebra,{} or \\spad{\"failed\"} if there is none.")) (|rightMinimalPolynomial| (((|SparseUnivariatePolynomial| |#2|) $) "\\spad{rightMinimalPolynomial(a)} returns the polynomial determined by the smallest non-trivial linear combination of right powers of \\spad{a}. Note: the polynomial never has a constant term as in general the algebra has no unit.")) (|leftMinimalPolynomial| (((|SparseUnivariatePolynomial| |#2|) $) "\\spad{leftMinimalPolynomial(a)} returns the polynomial determined by the smallest non-trivial linear combination of left powers of \\spad{a}. Note: the polynomial never has a constant term as in general the algebra has no unit.")) (|associatorDependence| (((|List| (|Vector| |#2|))) "\\spad{associatorDependence()} looks for the associator identities,{} \\spadignore{i.e.} finds a basis of the solutions of the linear combinations of the six permutations of \\spad{associator(a,b,c)} which yield 0,{} for all \\spad{a},{}\\spad{b},{}\\spad{c} in the algebra. The order of the permutations is \\spad{123 231 312 132 321 213}.")) (|rightRecip| (((|Union| $ "failed") $) "\\spad{rightRecip(a)} returns an element,{} which is a right inverse of \\spad{a},{} or \\spad{\"failed\"} if there is no unit element,{} if such an element doesn't exist or cannot be determined (see unitsKnown).")) (|leftRecip| (((|Union| $ "failed") $) "\\spad{leftRecip(a)} returns an element,{} which is a left inverse of \\spad{a},{} or \\spad{\"failed\"} if there is no unit element,{} if such an element doesn't exist or cannot be determined (see unitsKnown).")) (|recip| (((|Union| $ "failed") $) "\\spad{recip(a)} returns an element,{} which is both a left and a right inverse of \\spad{a},{} or \\spad{\"failed\"} if there is no unit element,{} if such an element doesn't exist or cannot be determined (see unitsKnown).")) (|lieAlgebra?| (((|Boolean|)) "\\spad{lieAlgebra?()} tests if the algebra is anticommutative and \\spad{(a*b)*c + (b*c)*a + (c*a)*b = 0} for all \\spad{a},{}\\spad{b},{}\\spad{c} in the algebra (Jacobi identity). Example: for every associative algebra \\spad{(A,+,@)} we can construct a Lie algebra \\spad{(A,+,*)},{} where \\spad{a*b := a@b-b@a}.")) (|jordanAlgebra?| (((|Boolean|)) "\\spad{jordanAlgebra?()} tests if the algebra is commutative,{} characteristic is not 2,{} and \\spad{(a*b)*a**2 - a*(b*a**2) = 0} for all \\spad{a},{}\\spad{b},{}\\spad{c} in the algebra (Jordan identity). Example: for every associative algebra \\spad{(A,+,@)} we can construct a Jordan algebra \\spad{(A,+,*)},{} where \\spad{a*b := (a@b+b@a)/2}.")) (|noncommutativeJordanAlgebra?| (((|Boolean|)) "\\spad{noncommutativeJordanAlgebra?()} tests if the algebra is flexible and Jordan admissible.")) (|jordanAdmissible?| (((|Boolean|)) "\\spad{jordanAdmissible?()} tests if 2 is invertible in the coefficient domain and the multiplication defined by \\spad{(1/2)(a*b+b*a)} determines a Jordan algebra,{} \\spadignore{i.e.} satisfies the Jordan identity. The property of \\spadatt{commutative(\"*\")} follows from by definition.")) (|lieAdmissible?| (((|Boolean|)) "\\spad{lieAdmissible?()} tests if the algebra defined by the commutators is a Lie algebra,{} \\spadignore{i.e.} satisfies the Jacobi identity. The property of anticommutativity follows from definition.")) (|jacobiIdentity?| (((|Boolean|)) "\\spad{jacobiIdentity?()} tests if \\spad{(a*b)*c + (b*c)*a + (c*a)*b = 0} for all \\spad{a},{}\\spad{b},{}\\spad{c} in the algebra. For example,{} this holds for crossed products of 3-dimensional vectors.")) (|powerAssociative?| (((|Boolean|)) "\\spad{powerAssociative?()} tests if all subalgebras generated by a single element are associative.")) (|alternative?| (((|Boolean|)) "\\spad{alternative?()} tests if \\spad{2*associator(a,a,b) = 0 = 2*associator(a,b,b)} for all \\spad{a},{} \\spad{b} in the algebra. Note: we only can test this; in general we don't know whether \\spad{2*a=0} implies \\spad{a=0}.")) (|flexible?| (((|Boolean|)) "\\spad{flexible?()} tests if \\spad{2*associator(a,b,a) = 0} for all \\spad{a},{} \\spad{b} in the algebra. Note: we only can test this; in general we don't know whether \\spad{2*a=0} implies \\spad{a=0}.")) (|rightAlternative?| (((|Boolean|)) "\\spad{rightAlternative?()} tests if \\spad{2*associator(a,b,b) = 0} for all \\spad{a},{} \\spad{b} in the algebra. Note: we only can test this; in general we don't know whether \\spad{2*a=0} implies \\spad{a=0}.")) (|leftAlternative?| (((|Boolean|)) "\\spad{leftAlternative?()} tests if \\spad{2*associator(a,a,b) = 0} for all \\spad{a},{} \\spad{b} in the algebra. Note: we only can test this; in general we don't know whether \\spad{2*a=0} implies \\spad{a=0}.")) (|antiAssociative?| (((|Boolean|)) "\\spad{antiAssociative?()} tests if multiplication in algebra is anti-associative,{} \\spadignore{i.e.} \\spad{(a*b)*c + a*(b*c) = 0} for all \\spad{a},{}\\spad{b},{}\\spad{c} in the algebra.")) (|associative?| (((|Boolean|)) "\\spad{associative?()} tests if multiplication in algebra is associative.")) (|antiCommutative?| (((|Boolean|)) "\\spad{antiCommutative?()} tests if \\spad{a*a = 0} for all \\spad{a} in the algebra. Note: this implies \\spad{a*b + b*a = 0} for all \\spad{a} and \\spad{b}.")) (|commutative?| (((|Boolean|)) "\\spad{commutative?()} tests if multiplication in the algebra is commutative.")) (|rightCharacteristicPolynomial| (((|SparseUnivariatePolynomial| |#2|) $) "\\spad{rightCharacteristicPolynomial(a)} returns the characteristic polynomial of the right regular representation of \\spad{a} with respect to any basis.")) (|leftCharacteristicPolynomial| (((|SparseUnivariatePolynomial| |#2|) $) "\\spad{leftCharacteristicPolynomial(a)} returns the characteristic polynomial of the left regular representation of \\spad{a} with respect to any basis.")) (|rightTraceMatrix| (((|Matrix| |#2|) (|Vector| $)) "\\spad{rightTraceMatrix([v1,...,vn])} is the \\spad{n}-by-\\spad{n} matrix whose element at the \\spad{i}\\spad{-}th row and \\spad{j}\\spad{-}th column is given by the right trace of the product \\spad{vi*vj}.")) (|leftTraceMatrix| (((|Matrix| |#2|) (|Vector| $)) "\\spad{leftTraceMatrix([v1,...,vn])} is the \\spad{n}-by-\\spad{n} matrix whose element at the \\spad{i}\\spad{-}th row and \\spad{j}\\spad{-}th column is given by the left trace of the product \\spad{vi*vj}.")) (|rightDiscriminant| ((|#2| (|Vector| $)) "\\spad{rightDiscriminant([v1,...,vn])} returns the determinant of the \\spad{n}-by-\\spad{n} matrix whose element at the \\spad{i}\\spad{-}th row and \\spad{j}\\spad{-}th column is given by the right trace of the product \\spad{vi*vj}. Note: the same as \\spad{determinant(rightTraceMatrix([v1,...,vn]))}.")) (|leftDiscriminant| ((|#2| (|Vector| $)) "\\spad{leftDiscriminant([v1,...,vn])} returns the determinant of the \\spad{n}-by-\\spad{n} matrix whose element at the \\spad{i}\\spad{-}th row and \\spad{j}\\spad{-}th column is given by the left trace of the product \\spad{vi*vj}. Note: the same as \\spad{determinant(leftTraceMatrix([v1,...,vn]))}.")) (|represents| (($ (|Vector| |#2|) (|Vector| $)) "\\spad{represents([a1,...,am],[v1,...,vm])} returns the linear combination \\spad{a1*vm + ... + an*vm}.")) (|coordinates| (((|Matrix| |#2|) (|Vector| $) (|Vector| $)) "\\spad{coordinates([a1,...,am],[v1,...,vn])} returns a matrix whose \\spad{i}-th row is formed by the coordinates of \\spad{ai} with respect to the \\spad{R}-module basis \\spad{v1},{}...,{}\\spad{vn}.") (((|Vector| |#2|) $ (|Vector| $)) "\\spad{coordinates(a,[v1,...,vn])} returns the coordinates of \\spad{a} with respect to the \\spad{R}-module basis \\spad{v1},{}...,{}\\spad{vn}.")) (|rightNorm| ((|#2| $) "\\spad{rightNorm(a)} returns the determinant of the right regular representation of \\spad{a}.")) (|leftNorm| ((|#2| $) "\\spad{leftNorm(a)} returns the determinant of the left regular representation of \\spad{a}.")) (|rightTrace| ((|#2| $) "\\spad{rightTrace(a)} returns the trace of the right regular representation of \\spad{a}.")) (|leftTrace| ((|#2| $) "\\spad{leftTrace(a)} returns the trace of the left regular representation of \\spad{a}.")) (|rightRegularRepresentation| (((|Matrix| |#2|) $ (|Vector| $)) "\\spad{rightRegularRepresentation(a,[v1,...,vn])} returns the matrix of the linear map defined by right multiplication by \\spad{a} with respect to the \\spad{R}-module basis \\spad{[v1,...,vn]}.")) (|leftRegularRepresentation| (((|Matrix| |#2|) $ (|Vector| $)) "\\spad{leftRegularRepresentation(a,[v1,...,vn])} returns the matrix of the linear map defined by left multiplication by \\spad{a} with respect to the \\spad{R}-module basis \\spad{[v1,...,vn]}.")) (|structuralConstants| (((|Vector| (|Matrix| |#2|)) (|Vector| $)) "\\spad{structuralConstants([v1,v2,...,vm])} calculates the structural constants \\spad{[(gammaijk) for k in 1..m]} defined by \\spad{vi * vj = gammaij1 * v1 + ... + gammaijm * vm},{} where \\spad{[v1,...,vm]} is an \\spad{R}-module basis of a subalgebra.")) (|conditionsForIdempotents| (((|List| (|Polynomial| |#2|)) (|Vector| $)) "\\spad{conditionsForIdempotents([v1,...,vn])} determines a complete list of polynomial equations for the coefficients of idempotents with respect to the \\spad{R}-module basis \\spad{v1},{}...,{}\\spad{vn}.")) (|rank| (((|PositiveInteger|)) "\\spad{rank()} returns the rank of the algebra as \\spad{R}-module.")) (|someBasis| (((|Vector| $)) "\\spad{someBasis()} returns some \\spad{R}-module basis."))) +((|constructor| (NIL "A FiniteRankNonAssociativeAlgebra is a non associative algebra over a commutative ring \\spad{R} which is a free \\spad{R}-module of finite rank.")) (|unit| (((|Union| $ "failed")) "\\spad{unit()} returns a unit of the algebra (necessarily unique),{} or \\spad{\"failed\"} if there is none.")) (|rightUnit| (((|Union| $ "failed")) "\\spad{rightUnit()} returns a right unit of the algebra (not necessarily unique),{} or \\spad{\"failed\"} if there is none.")) (|leftUnit| (((|Union| $ "failed")) "\\spad{leftUnit()} returns a left unit of the algebra (not necessarily unique),{} or \\spad{\"failed\"} if there is none.")) (|rightUnits| (((|Union| (|Record| (|:| |particular| $) (|:| |basis| (|List| $))) "failed")) "\\spad{rightUnits()} returns the affine space of all right units of the algebra,{} or \\spad{\"failed\"} if there is none.")) (|leftUnits| (((|Union| (|Record| (|:| |particular| $) (|:| |basis| (|List| $))) "failed")) "\\spad{leftUnits()} returns the affine space of all left units of the algebra,{} or \\spad{\"failed\"} if there is none.")) (|rightMinimalPolynomial| (((|SparseUnivariatePolynomial| |#2|) $) "\\spad{rightMinimalPolynomial(a)} returns the polynomial determined by the smallest non-trivial linear combination of right powers of \\spad{a}. Note: the polynomial never has a constant term as in general the algebra has no unit.")) (|leftMinimalPolynomial| (((|SparseUnivariatePolynomial| |#2|) $) "\\spad{leftMinimalPolynomial(a)} returns the polynomial determined by the smallest non-trivial linear combination of left powers of \\spad{a}. Note: the polynomial never has a constant term as in general the algebra has no unit.")) (|associatorDependence| (((|List| (|Vector| |#2|))) "\\spad{associatorDependence()} looks for the associator identities,{} \\spadignore{i.e.} finds a basis of the solutions of the linear combinations of the six permutations of \\spad{associator(a,b,c)} which yield 0,{} for all \\spad{a},{}\\spad{b},{}\\spad{c} in the algebra. The order of the permutations is \\spad{123 231 312 132 321 213}.")) (|rightRecip| (((|Union| $ "failed") $) "\\spad{rightRecip(a)} returns an element,{} which is a right inverse of \\spad{a},{} or \\spad{\"failed\"} if there is no unit element,{} if such an element doesn't exist or cannot be determined.")) (|leftRecip| (((|Union| $ "failed") $) "\\spad{leftRecip(a)} returns an element,{} which is a left inverse of \\spad{a},{} or \\spad{\"failed\"} if there is no unit element,{} if such an element doesn't exist or cannot be determined.")) (|recip| (((|Union| $ "failed") $) "\\spad{recip(a)} returns an element,{} which is both a left and a right inverse of \\spad{a},{} or \\spad{\"failed\"} if there is no unit element,{} if such an element doesn't exist or cannot be determined.")) (|lieAlgebra?| (((|Boolean|)) "\\spad{lieAlgebra?()} tests if the algebra is anticommutative and \\spad{(a*b)*c + (b*c)*a + (c*a)*b = 0} for all \\spad{a},{}\\spad{b},{}\\spad{c} in the algebra (Jacobi identity). Example: for every associative algebra \\spad{(A,+,@)} we can construct a Lie algebra \\spad{(A,+,*)},{} where \\spad{a*b := a@b-b@a}.")) (|jordanAlgebra?| (((|Boolean|)) "\\spad{jordanAlgebra?()} tests if the algebra is commutative,{} characteristic is not 2,{} and \\spad{(a*b)*a**2 - a*(b*a**2) = 0} for all \\spad{a},{}\\spad{b},{}\\spad{c} in the algebra (Jordan identity). Example: for every associative algebra \\spad{(A,+,@)} we can construct a Jordan algebra \\spad{(A,+,*)},{} where \\spad{a*b := (a@b+b@a)/2}.")) (|noncommutativeJordanAlgebra?| (((|Boolean|)) "\\spad{noncommutativeJordanAlgebra?()} tests if the algebra is flexible and Jordan admissible.")) (|jordanAdmissible?| (((|Boolean|)) "\\spad{jordanAdmissible?()} tests if 2 is invertible in the coefficient domain and the multiplication defined by \\spad{(1/2)(a*b+b*a)} determines a Jordan algebra,{} \\spadignore{i.e.} satisfies the Jordan identity. The property of \\spadatt{commutative(\"*\")} follows from by definition.")) (|lieAdmissible?| (((|Boolean|)) "\\spad{lieAdmissible?()} tests if the algebra defined by the commutators is a Lie algebra,{} \\spadignore{i.e.} satisfies the Jacobi identity. The property of anticommutativity follows from definition.")) (|jacobiIdentity?| (((|Boolean|)) "\\spad{jacobiIdentity?()} tests if \\spad{(a*b)*c + (b*c)*a + (c*a)*b = 0} for all \\spad{a},{}\\spad{b},{}\\spad{c} in the algebra. For example,{} this holds for crossed products of 3-dimensional vectors.")) (|powerAssociative?| (((|Boolean|)) "\\spad{powerAssociative?()} tests if all subalgebras generated by a single element are associative.")) (|alternative?| (((|Boolean|)) "\\spad{alternative?()} tests if \\spad{2*associator(a,a,b) = 0 = 2*associator(a,b,b)} for all \\spad{a},{} \\spad{b} in the algebra. Note: we only can test this; in general we don't know whether \\spad{2*a=0} implies \\spad{a=0}.")) (|flexible?| (((|Boolean|)) "\\spad{flexible?()} tests if \\spad{2*associator(a,b,a) = 0} for all \\spad{a},{} \\spad{b} in the algebra. Note: we only can test this; in general we don't know whether \\spad{2*a=0} implies \\spad{a=0}.")) (|rightAlternative?| (((|Boolean|)) "\\spad{rightAlternative?()} tests if \\spad{2*associator(a,b,b) = 0} for all \\spad{a},{} \\spad{b} in the algebra. Note: we only can test this; in general we don't know whether \\spad{2*a=0} implies \\spad{a=0}.")) (|leftAlternative?| (((|Boolean|)) "\\spad{leftAlternative?()} tests if \\spad{2*associator(a,a,b) = 0} for all \\spad{a},{} \\spad{b} in the algebra. Note: we only can test this; in general we don't know whether \\spad{2*a=0} implies \\spad{a=0}.")) (|antiAssociative?| (((|Boolean|)) "\\spad{antiAssociative?()} tests if multiplication in algebra is anti-associative,{} \\spadignore{i.e.} \\spad{(a*b)*c + a*(b*c) = 0} for all \\spad{a},{}\\spad{b},{}\\spad{c} in the algebra.")) (|associative?| (((|Boolean|)) "\\spad{associative?()} tests if multiplication in algebra is associative.")) (|antiCommutative?| (((|Boolean|)) "\\spad{antiCommutative?()} tests if \\spad{a*a = 0} for all \\spad{a} in the algebra. Note: this implies \\spad{a*b + b*a = 0} for all \\spad{a} and \\spad{b}.")) (|commutative?| (((|Boolean|)) "\\spad{commutative?()} tests if multiplication in the algebra is commutative.")) (|rightCharacteristicPolynomial| (((|SparseUnivariatePolynomial| |#2|) $) "\\spad{rightCharacteristicPolynomial(a)} returns the characteristic polynomial of the right regular representation of \\spad{a} with respect to any basis.")) (|leftCharacteristicPolynomial| (((|SparseUnivariatePolynomial| |#2|) $) "\\spad{leftCharacteristicPolynomial(a)} returns the characteristic polynomial of the left regular representation of \\spad{a} with respect to any basis.")) (|rightTraceMatrix| (((|Matrix| |#2|) (|Vector| $)) "\\spad{rightTraceMatrix([v1,...,vn])} is the \\spad{n}-by-\\spad{n} matrix whose element at the \\spad{i}\\spad{-}th row and \\spad{j}\\spad{-}th column is given by the right trace of the product \\spad{vi*vj}.")) (|leftTraceMatrix| (((|Matrix| |#2|) (|Vector| $)) "\\spad{leftTraceMatrix([v1,...,vn])} is the \\spad{n}-by-\\spad{n} matrix whose element at the \\spad{i}\\spad{-}th row and \\spad{j}\\spad{-}th column is given by the left trace of the product \\spad{vi*vj}.")) (|rightDiscriminant| ((|#2| (|Vector| $)) "\\spad{rightDiscriminant([v1,...,vn])} returns the determinant of the \\spad{n}-by-\\spad{n} matrix whose element at the \\spad{i}\\spad{-}th row and \\spad{j}\\spad{-}th column is given by the right trace of the product \\spad{vi*vj}. Note: the same as \\spad{determinant(rightTraceMatrix([v1,...,vn]))}.")) (|leftDiscriminant| ((|#2| (|Vector| $)) "\\spad{leftDiscriminant([v1,...,vn])} returns the determinant of the \\spad{n}-by-\\spad{n} matrix whose element at the \\spad{i}\\spad{-}th row and \\spad{j}\\spad{-}th column is given by the left trace of the product \\spad{vi*vj}. Note: the same as \\spad{determinant(leftTraceMatrix([v1,...,vn]))}.")) (|represents| (($ (|Vector| |#2|) (|Vector| $)) "\\spad{represents([a1,...,am],[v1,...,vm])} returns the linear combination \\spad{a1*vm + ... + an*vm}.")) (|coordinates| (((|Matrix| |#2|) (|Vector| $) (|Vector| $)) "\\spad{coordinates([a1,...,am],[v1,...,vn])} returns a matrix whose \\spad{i}-th row is formed by the coordinates of \\spad{ai} with respect to the \\spad{R}-module basis \\spad{v1},{}...,{}\\spad{vn}.") (((|Vector| |#2|) $ (|Vector| $)) "\\spad{coordinates(a,[v1,...,vn])} returns the coordinates of \\spad{a} with respect to the \\spad{R}-module basis \\spad{v1},{}...,{}\\spad{vn}.")) (|rightNorm| ((|#2| $) "\\spad{rightNorm(a)} returns the determinant of the right regular representation of \\spad{a}.")) (|leftNorm| ((|#2| $) "\\spad{leftNorm(a)} returns the determinant of the left regular representation of \\spad{a}.")) (|rightTrace| ((|#2| $) "\\spad{rightTrace(a)} returns the trace of the right regular representation of \\spad{a}.")) (|leftTrace| ((|#2| $) "\\spad{leftTrace(a)} returns the trace of the left regular representation of \\spad{a}.")) (|rightRegularRepresentation| (((|Matrix| |#2|) $ (|Vector| $)) "\\spad{rightRegularRepresentation(a,[v1,...,vn])} returns the matrix of the linear map defined by right multiplication by \\spad{a} with respect to the \\spad{R}-module basis \\spad{[v1,...,vn]}.")) (|leftRegularRepresentation| (((|Matrix| |#2|) $ (|Vector| $)) "\\spad{leftRegularRepresentation(a,[v1,...,vn])} returns the matrix of the linear map defined by left multiplication by \\spad{a} with respect to the \\spad{R}-module basis \\spad{[v1,...,vn]}.")) (|structuralConstants| (((|Vector| (|Matrix| |#2|)) (|Vector| $)) "\\spad{structuralConstants([v1,v2,...,vm])} calculates the structural constants \\spad{[(gammaijk) for k in 1..m]} defined by \\spad{vi * vj = gammaij1 * v1 + ... + gammaijm * vm},{} where \\spad{[v1,...,vm]} is an \\spad{R}-module basis of a subalgebra.")) (|conditionsForIdempotents| (((|List| (|Polynomial| |#2|)) (|Vector| $)) "\\spad{conditionsForIdempotents([v1,...,vn])} determines a complete list of polynomial equations for the coefficients of idempotents with respect to the \\spad{R}-module basis \\spad{v1},{}...,{}\\spad{vn}.")) (|rank| (((|PositiveInteger|)) "\\spad{rank()} returns the rank of the algebra as \\spad{R}-module.")) (|someBasis| (((|Vector| $)) "\\spad{someBasis()} returns some \\spad{R}-module basis."))) NIL ((|HasCategory| |#2| (QUOTE (|IntegralDomain|)))) (|FiniteRankNonAssociativeAlgebra| R) -((|constructor| (NIL "A FiniteRankNonAssociativeAlgebra is a non associative algebra over a commutative ring \\spad{R} which is a free \\spad{R}-module of finite rank.")) (|unitsKnown| ((|attribute|) "unitsKnown means that \\spadfun{recip} truly yields reciprocal or \\spad{\"failed\"} if not a unit,{} similarly for \\spadfun{leftRecip} and \\spadfun{rightRecip}. The reason is that we use left,{} respectively right,{} minimal polynomials to decide this question.")) (|unit| (((|Union| $ "failed")) "\\spad{unit()} returns a unit of the algebra (necessarily unique),{} or \\spad{\"failed\"} if there is none.")) (|rightUnit| (((|Union| $ "failed")) "\\spad{rightUnit()} returns a right unit of the algebra (not necessarily unique),{} or \\spad{\"failed\"} if there is none.")) (|leftUnit| (((|Union| $ "failed")) "\\spad{leftUnit()} returns a left unit of the algebra (not necessarily unique),{} or \\spad{\"failed\"} if there is none.")) (|rightUnits| (((|Union| (|Record| (|:| |particular| $) (|:| |basis| (|List| $))) "failed")) "\\spad{rightUnits()} returns the affine space of all right units of the algebra,{} or \\spad{\"failed\"} if there is none.")) (|leftUnits| (((|Union| (|Record| (|:| |particular| $) (|:| |basis| (|List| $))) "failed")) "\\spad{leftUnits()} returns the affine space of all left units of the algebra,{} or \\spad{\"failed\"} if there is none.")) (|rightMinimalPolynomial| (((|SparseUnivariatePolynomial| |#1|) $) "\\spad{rightMinimalPolynomial(a)} returns the polynomial determined by the smallest non-trivial linear combination of right powers of \\spad{a}. Note: the polynomial never has a constant term as in general the algebra has no unit.")) (|leftMinimalPolynomial| (((|SparseUnivariatePolynomial| |#1|) $) "\\spad{leftMinimalPolynomial(a)} returns the polynomial determined by the smallest non-trivial linear combination of left powers of \\spad{a}. Note: the polynomial never has a constant term as in general the algebra has no unit.")) (|associatorDependence| (((|List| (|Vector| |#1|))) "\\spad{associatorDependence()} looks for the associator identities,{} \\spadignore{i.e.} finds a basis of the solutions of the linear combinations of the six permutations of \\spad{associator(a,b,c)} which yield 0,{} for all \\spad{a},{}\\spad{b},{}\\spad{c} in the algebra. The order of the permutations is \\spad{123 231 312 132 321 213}.")) (|rightRecip| (((|Union| $ "failed") $) "\\spad{rightRecip(a)} returns an element,{} which is a right inverse of \\spad{a},{} or \\spad{\"failed\"} if there is no unit element,{} if such an element doesn't exist or cannot be determined (see unitsKnown).")) (|leftRecip| (((|Union| $ "failed") $) "\\spad{leftRecip(a)} returns an element,{} which is a left inverse of \\spad{a},{} or \\spad{\"failed\"} if there is no unit element,{} if such an element doesn't exist or cannot be determined (see unitsKnown).")) (|recip| (((|Union| $ "failed") $) "\\spad{recip(a)} returns an element,{} which is both a left and a right inverse of \\spad{a},{} or \\spad{\"failed\"} if there is no unit element,{} if such an element doesn't exist or cannot be determined (see unitsKnown).")) (|lieAlgebra?| (((|Boolean|)) "\\spad{lieAlgebra?()} tests if the algebra is anticommutative and \\spad{(a*b)*c + (b*c)*a + (c*a)*b = 0} for all \\spad{a},{}\\spad{b},{}\\spad{c} in the algebra (Jacobi identity). Example: for every associative algebra \\spad{(A,+,@)} we can construct a Lie algebra \\spad{(A,+,*)},{} where \\spad{a*b := a@b-b@a}.")) (|jordanAlgebra?| (((|Boolean|)) "\\spad{jordanAlgebra?()} tests if the algebra is commutative,{} characteristic is not 2,{} and \\spad{(a*b)*a**2 - a*(b*a**2) = 0} for all \\spad{a},{}\\spad{b},{}\\spad{c} in the algebra (Jordan identity). Example: for every associative algebra \\spad{(A,+,@)} we can construct a Jordan algebra \\spad{(A,+,*)},{} where \\spad{a*b := (a@b+b@a)/2}.")) (|noncommutativeJordanAlgebra?| (((|Boolean|)) "\\spad{noncommutativeJordanAlgebra?()} tests if the algebra is flexible and Jordan admissible.")) (|jordanAdmissible?| (((|Boolean|)) "\\spad{jordanAdmissible?()} tests if 2 is invertible in the coefficient domain and the multiplication defined by \\spad{(1/2)(a*b+b*a)} determines a Jordan algebra,{} \\spadignore{i.e.} satisfies the Jordan identity. The property of \\spadatt{commutative(\"*\")} follows from by definition.")) (|lieAdmissible?| (((|Boolean|)) "\\spad{lieAdmissible?()} tests if the algebra defined by the commutators is a Lie algebra,{} \\spadignore{i.e.} satisfies the Jacobi identity. The property of anticommutativity follows from definition.")) (|jacobiIdentity?| (((|Boolean|)) "\\spad{jacobiIdentity?()} tests if \\spad{(a*b)*c + (b*c)*a + (c*a)*b = 0} for all \\spad{a},{}\\spad{b},{}\\spad{c} in the algebra. For example,{} this holds for crossed products of 3-dimensional vectors.")) (|powerAssociative?| (((|Boolean|)) "\\spad{powerAssociative?()} tests if all subalgebras generated by a single element are associative.")) (|alternative?| (((|Boolean|)) "\\spad{alternative?()} tests if \\spad{2*associator(a,a,b) = 0 = 2*associator(a,b,b)} for all \\spad{a},{} \\spad{b} in the algebra. Note: we only can test this; in general we don't know whether \\spad{2*a=0} implies \\spad{a=0}.")) (|flexible?| (((|Boolean|)) "\\spad{flexible?()} tests if \\spad{2*associator(a,b,a) = 0} for all \\spad{a},{} \\spad{b} in the algebra. Note: we only can test this; in general we don't know whether \\spad{2*a=0} implies \\spad{a=0}.")) (|rightAlternative?| (((|Boolean|)) "\\spad{rightAlternative?()} tests if \\spad{2*associator(a,b,b) = 0} for all \\spad{a},{} \\spad{b} in the algebra. Note: we only can test this; in general we don't know whether \\spad{2*a=0} implies \\spad{a=0}.")) (|leftAlternative?| (((|Boolean|)) "\\spad{leftAlternative?()} tests if \\spad{2*associator(a,a,b) = 0} for all \\spad{a},{} \\spad{b} in the algebra. Note: we only can test this; in general we don't know whether \\spad{2*a=0} implies \\spad{a=0}.")) (|antiAssociative?| (((|Boolean|)) "\\spad{antiAssociative?()} tests if multiplication in algebra is anti-associative,{} \\spadignore{i.e.} \\spad{(a*b)*c + a*(b*c) = 0} for all \\spad{a},{}\\spad{b},{}\\spad{c} in the algebra.")) (|associative?| (((|Boolean|)) "\\spad{associative?()} tests if multiplication in algebra is associative.")) (|antiCommutative?| (((|Boolean|)) "\\spad{antiCommutative?()} tests if \\spad{a*a = 0} for all \\spad{a} in the algebra. Note: this implies \\spad{a*b + b*a = 0} for all \\spad{a} and \\spad{b}.")) (|commutative?| (((|Boolean|)) "\\spad{commutative?()} tests if multiplication in the algebra is commutative.")) (|rightCharacteristicPolynomial| (((|SparseUnivariatePolynomial| |#1|) $) "\\spad{rightCharacteristicPolynomial(a)} returns the characteristic polynomial of the right regular representation of \\spad{a} with respect to any basis.")) (|leftCharacteristicPolynomial| (((|SparseUnivariatePolynomial| |#1|) $) "\\spad{leftCharacteristicPolynomial(a)} returns the characteristic polynomial of the left regular representation of \\spad{a} with respect to any basis.")) (|rightTraceMatrix| (((|Matrix| |#1|) (|Vector| $)) "\\spad{rightTraceMatrix([v1,...,vn])} is the \\spad{n}-by-\\spad{n} matrix whose element at the \\spad{i}\\spad{-}th row and \\spad{j}\\spad{-}th column is given by the right trace of the product \\spad{vi*vj}.")) (|leftTraceMatrix| (((|Matrix| |#1|) (|Vector| $)) "\\spad{leftTraceMatrix([v1,...,vn])} is the \\spad{n}-by-\\spad{n} matrix whose element at the \\spad{i}\\spad{-}th row and \\spad{j}\\spad{-}th column is given by the left trace of the product \\spad{vi*vj}.")) (|rightDiscriminant| ((|#1| (|Vector| $)) "\\spad{rightDiscriminant([v1,...,vn])} returns the determinant of the \\spad{n}-by-\\spad{n} matrix whose element at the \\spad{i}\\spad{-}th row and \\spad{j}\\spad{-}th column is given by the right trace of the product \\spad{vi*vj}. Note: the same as \\spad{determinant(rightTraceMatrix([v1,...,vn]))}.")) (|leftDiscriminant| ((|#1| (|Vector| $)) "\\spad{leftDiscriminant([v1,...,vn])} returns the determinant of the \\spad{n}-by-\\spad{n} matrix whose element at the \\spad{i}\\spad{-}th row and \\spad{j}\\spad{-}th column is given by the left trace of the product \\spad{vi*vj}. Note: the same as \\spad{determinant(leftTraceMatrix([v1,...,vn]))}.")) (|represents| (($ (|Vector| |#1|) (|Vector| $)) "\\spad{represents([a1,...,am],[v1,...,vm])} returns the linear combination \\spad{a1*vm + ... + an*vm}.")) (|coordinates| (((|Matrix| |#1|) (|Vector| $) (|Vector| $)) "\\spad{coordinates([a1,...,am],[v1,...,vn])} returns a matrix whose \\spad{i}-th row is formed by the coordinates of \\spad{ai} with respect to the \\spad{R}-module basis \\spad{v1},{}...,{}\\spad{vn}.") (((|Vector| |#1|) $ (|Vector| $)) "\\spad{coordinates(a,[v1,...,vn])} returns the coordinates of \\spad{a} with respect to the \\spad{R}-module basis \\spad{v1},{}...,{}\\spad{vn}.")) (|rightNorm| ((|#1| $) "\\spad{rightNorm(a)} returns the determinant of the right regular representation of \\spad{a}.")) (|leftNorm| ((|#1| $) "\\spad{leftNorm(a)} returns the determinant of the left regular representation of \\spad{a}.")) (|rightTrace| ((|#1| $) "\\spad{rightTrace(a)} returns the trace of the right regular representation of \\spad{a}.")) (|leftTrace| ((|#1| $) "\\spad{leftTrace(a)} returns the trace of the left regular representation of \\spad{a}.")) (|rightRegularRepresentation| (((|Matrix| |#1|) $ (|Vector| $)) "\\spad{rightRegularRepresentation(a,[v1,...,vn])} returns the matrix of the linear map defined by right multiplication by \\spad{a} with respect to the \\spad{R}-module basis \\spad{[v1,...,vn]}.")) (|leftRegularRepresentation| (((|Matrix| |#1|) $ (|Vector| $)) "\\spad{leftRegularRepresentation(a,[v1,...,vn])} returns the matrix of the linear map defined by left multiplication by \\spad{a} with respect to the \\spad{R}-module basis \\spad{[v1,...,vn]}.")) (|structuralConstants| (((|Vector| (|Matrix| |#1|)) (|Vector| $)) "\\spad{structuralConstants([v1,v2,...,vm])} calculates the structural constants \\spad{[(gammaijk) for k in 1..m]} defined by \\spad{vi * vj = gammaij1 * v1 + ... + gammaijm * vm},{} where \\spad{[v1,...,vm]} is an \\spad{R}-module basis of a subalgebra.")) (|conditionsForIdempotents| (((|List| (|Polynomial| |#1|)) (|Vector| $)) "\\spad{conditionsForIdempotents([v1,...,vn])} determines a complete list of polynomial equations for the coefficients of idempotents with respect to the \\spad{R}-module basis \\spad{v1},{}...,{}\\spad{vn}.")) (|rank| (((|PositiveInteger|)) "\\spad{rank()} returns the rank of the algebra as \\spad{R}-module.")) (|someBasis| (((|Vector| $)) "\\spad{someBasis()} returns some \\spad{R}-module basis."))) -((|unitsKnown| |has| |#1| (|IntegralDomain|)) (|leftUnitary| . T) (|rightUnitary| . T)) +((|constructor| (NIL "A FiniteRankNonAssociativeAlgebra is a non associative algebra over a commutative ring \\spad{R} which is a free \\spad{R}-module of finite rank.")) (|unit| (((|Union| $ "failed")) "\\spad{unit()} returns a unit of the algebra (necessarily unique),{} or \\spad{\"failed\"} if there is none.")) (|rightUnit| (((|Union| $ "failed")) "\\spad{rightUnit()} returns a right unit of the algebra (not necessarily unique),{} or \\spad{\"failed\"} if there is none.")) (|leftUnit| (((|Union| $ "failed")) "\\spad{leftUnit()} returns a left unit of the algebra (not necessarily unique),{} or \\spad{\"failed\"} if there is none.")) (|rightUnits| (((|Union| (|Record| (|:| |particular| $) (|:| |basis| (|List| $))) "failed")) "\\spad{rightUnits()} returns the affine space of all right units of the algebra,{} or \\spad{\"failed\"} if there is none.")) (|leftUnits| (((|Union| (|Record| (|:| |particular| $) (|:| |basis| (|List| $))) "failed")) "\\spad{leftUnits()} returns the affine space of all left units of the algebra,{} or \\spad{\"failed\"} if there is none.")) (|rightMinimalPolynomial| (((|SparseUnivariatePolynomial| |#1|) $) "\\spad{rightMinimalPolynomial(a)} returns the polynomial determined by the smallest non-trivial linear combination of right powers of \\spad{a}. Note: the polynomial never has a constant term as in general the algebra has no unit.")) (|leftMinimalPolynomial| (((|SparseUnivariatePolynomial| |#1|) $) "\\spad{leftMinimalPolynomial(a)} returns the polynomial determined by the smallest non-trivial linear combination of left powers of \\spad{a}. Note: the polynomial never has a constant term as in general the algebra has no unit.")) (|associatorDependence| (((|List| (|Vector| |#1|))) "\\spad{associatorDependence()} looks for the associator identities,{} \\spadignore{i.e.} finds a basis of the solutions of the linear combinations of the six permutations of \\spad{associator(a,b,c)} which yield 0,{} for all \\spad{a},{}\\spad{b},{}\\spad{c} in the algebra. The order of the permutations is \\spad{123 231 312 132 321 213}.")) (|rightRecip| (((|Union| $ "failed") $) "\\spad{rightRecip(a)} returns an element,{} which is a right inverse of \\spad{a},{} or \\spad{\"failed\"} if there is no unit element,{} if such an element doesn't exist or cannot be determined.")) (|leftRecip| (((|Union| $ "failed") $) "\\spad{leftRecip(a)} returns an element,{} which is a left inverse of \\spad{a},{} or \\spad{\"failed\"} if there is no unit element,{} if such an element doesn't exist or cannot be determined.")) (|recip| (((|Union| $ "failed") $) "\\spad{recip(a)} returns an element,{} which is both a left and a right inverse of \\spad{a},{} or \\spad{\"failed\"} if there is no unit element,{} if such an element doesn't exist or cannot be determined.")) (|lieAlgebra?| (((|Boolean|)) "\\spad{lieAlgebra?()} tests if the algebra is anticommutative and \\spad{(a*b)*c + (b*c)*a + (c*a)*b = 0} for all \\spad{a},{}\\spad{b},{}\\spad{c} in the algebra (Jacobi identity). Example: for every associative algebra \\spad{(A,+,@)} we can construct a Lie algebra \\spad{(A,+,*)},{} where \\spad{a*b := a@b-b@a}.")) (|jordanAlgebra?| (((|Boolean|)) "\\spad{jordanAlgebra?()} tests if the algebra is commutative,{} characteristic is not 2,{} and \\spad{(a*b)*a**2 - a*(b*a**2) = 0} for all \\spad{a},{}\\spad{b},{}\\spad{c} in the algebra (Jordan identity). Example: for every associative algebra \\spad{(A,+,@)} we can construct a Jordan algebra \\spad{(A,+,*)},{} where \\spad{a*b := (a@b+b@a)/2}.")) (|noncommutativeJordanAlgebra?| (((|Boolean|)) "\\spad{noncommutativeJordanAlgebra?()} tests if the algebra is flexible and Jordan admissible.")) (|jordanAdmissible?| (((|Boolean|)) "\\spad{jordanAdmissible?()} tests if 2 is invertible in the coefficient domain and the multiplication defined by \\spad{(1/2)(a*b+b*a)} determines a Jordan algebra,{} \\spadignore{i.e.} satisfies the Jordan identity. The property of \\spadatt{commutative(\"*\")} follows from by definition.")) (|lieAdmissible?| (((|Boolean|)) "\\spad{lieAdmissible?()} tests if the algebra defined by the commutators is a Lie algebra,{} \\spadignore{i.e.} satisfies the Jacobi identity. The property of anticommutativity follows from definition.")) (|jacobiIdentity?| (((|Boolean|)) "\\spad{jacobiIdentity?()} tests if \\spad{(a*b)*c + (b*c)*a + (c*a)*b = 0} for all \\spad{a},{}\\spad{b},{}\\spad{c} in the algebra. For example,{} this holds for crossed products of 3-dimensional vectors.")) (|powerAssociative?| (((|Boolean|)) "\\spad{powerAssociative?()} tests if all subalgebras generated by a single element are associative.")) (|alternative?| (((|Boolean|)) "\\spad{alternative?()} tests if \\spad{2*associator(a,a,b) = 0 = 2*associator(a,b,b)} for all \\spad{a},{} \\spad{b} in the algebra. Note: we only can test this; in general we don't know whether \\spad{2*a=0} implies \\spad{a=0}.")) (|flexible?| (((|Boolean|)) "\\spad{flexible?()} tests if \\spad{2*associator(a,b,a) = 0} for all \\spad{a},{} \\spad{b} in the algebra. Note: we only can test this; in general we don't know whether \\spad{2*a=0} implies \\spad{a=0}.")) (|rightAlternative?| (((|Boolean|)) "\\spad{rightAlternative?()} tests if \\spad{2*associator(a,b,b) = 0} for all \\spad{a},{} \\spad{b} in the algebra. Note: we only can test this; in general we don't know whether \\spad{2*a=0} implies \\spad{a=0}.")) (|leftAlternative?| (((|Boolean|)) "\\spad{leftAlternative?()} tests if \\spad{2*associator(a,a,b) = 0} for all \\spad{a},{} \\spad{b} in the algebra. Note: we only can test this; in general we don't know whether \\spad{2*a=0} implies \\spad{a=0}.")) (|antiAssociative?| (((|Boolean|)) "\\spad{antiAssociative?()} tests if multiplication in algebra is anti-associative,{} \\spadignore{i.e.} \\spad{(a*b)*c + a*(b*c) = 0} for all \\spad{a},{}\\spad{b},{}\\spad{c} in the algebra.")) (|associative?| (((|Boolean|)) "\\spad{associative?()} tests if multiplication in algebra is associative.")) (|antiCommutative?| (((|Boolean|)) "\\spad{antiCommutative?()} tests if \\spad{a*a = 0} for all \\spad{a} in the algebra. Note: this implies \\spad{a*b + b*a = 0} for all \\spad{a} and \\spad{b}.")) (|commutative?| (((|Boolean|)) "\\spad{commutative?()} tests if multiplication in the algebra is commutative.")) (|rightCharacteristicPolynomial| (((|SparseUnivariatePolynomial| |#1|) $) "\\spad{rightCharacteristicPolynomial(a)} returns the characteristic polynomial of the right regular representation of \\spad{a} with respect to any basis.")) (|leftCharacteristicPolynomial| (((|SparseUnivariatePolynomial| |#1|) $) "\\spad{leftCharacteristicPolynomial(a)} returns the characteristic polynomial of the left regular representation of \\spad{a} with respect to any basis.")) (|rightTraceMatrix| (((|Matrix| |#1|) (|Vector| $)) "\\spad{rightTraceMatrix([v1,...,vn])} is the \\spad{n}-by-\\spad{n} matrix whose element at the \\spad{i}\\spad{-}th row and \\spad{j}\\spad{-}th column is given by the right trace of the product \\spad{vi*vj}.")) (|leftTraceMatrix| (((|Matrix| |#1|) (|Vector| $)) "\\spad{leftTraceMatrix([v1,...,vn])} is the \\spad{n}-by-\\spad{n} matrix whose element at the \\spad{i}\\spad{-}th row and \\spad{j}\\spad{-}th column is given by the left trace of the product \\spad{vi*vj}.")) (|rightDiscriminant| ((|#1| (|Vector| $)) "\\spad{rightDiscriminant([v1,...,vn])} returns the determinant of the \\spad{n}-by-\\spad{n} matrix whose element at the \\spad{i}\\spad{-}th row and \\spad{j}\\spad{-}th column is given by the right trace of the product \\spad{vi*vj}. Note: the same as \\spad{determinant(rightTraceMatrix([v1,...,vn]))}.")) (|leftDiscriminant| ((|#1| (|Vector| $)) "\\spad{leftDiscriminant([v1,...,vn])} returns the determinant of the \\spad{n}-by-\\spad{n} matrix whose element at the \\spad{i}\\spad{-}th row and \\spad{j}\\spad{-}th column is given by the left trace of the product \\spad{vi*vj}. Note: the same as \\spad{determinant(leftTraceMatrix([v1,...,vn]))}.")) (|represents| (($ (|Vector| |#1|) (|Vector| $)) "\\spad{represents([a1,...,am],[v1,...,vm])} returns the linear combination \\spad{a1*vm + ... + an*vm}.")) (|coordinates| (((|Matrix| |#1|) (|Vector| $) (|Vector| $)) "\\spad{coordinates([a1,...,am],[v1,...,vn])} returns a matrix whose \\spad{i}-th row is formed by the coordinates of \\spad{ai} with respect to the \\spad{R}-module basis \\spad{v1},{}...,{}\\spad{vn}.") (((|Vector| |#1|) $ (|Vector| $)) "\\spad{coordinates(a,[v1,...,vn])} returns the coordinates of \\spad{a} with respect to the \\spad{R}-module basis \\spad{v1},{}...,{}\\spad{vn}.")) (|rightNorm| ((|#1| $) "\\spad{rightNorm(a)} returns the determinant of the right regular representation of \\spad{a}.")) (|leftNorm| ((|#1| $) "\\spad{leftNorm(a)} returns the determinant of the left regular representation of \\spad{a}.")) (|rightTrace| ((|#1| $) "\\spad{rightTrace(a)} returns the trace of the right regular representation of \\spad{a}.")) (|leftTrace| ((|#1| $) "\\spad{leftTrace(a)} returns the trace of the left regular representation of \\spad{a}.")) (|rightRegularRepresentation| (((|Matrix| |#1|) $ (|Vector| $)) "\\spad{rightRegularRepresentation(a,[v1,...,vn])} returns the matrix of the linear map defined by right multiplication by \\spad{a} with respect to the \\spad{R}-module basis \\spad{[v1,...,vn]}.")) (|leftRegularRepresentation| (((|Matrix| |#1|) $ (|Vector| $)) "\\spad{leftRegularRepresentation(a,[v1,...,vn])} returns the matrix of the linear map defined by left multiplication by \\spad{a} with respect to the \\spad{R}-module basis \\spad{[v1,...,vn]}.")) (|structuralConstants| (((|Vector| (|Matrix| |#1|)) (|Vector| $)) "\\spad{structuralConstants([v1,v2,...,vm])} calculates the structural constants \\spad{[(gammaijk) for k in 1..m]} defined by \\spad{vi * vj = gammaij1 * v1 + ... + gammaijm * vm},{} where \\spad{[v1,...,vm]} is an \\spad{R}-module basis of a subalgebra.")) (|conditionsForIdempotents| (((|List| (|Polynomial| |#1|)) (|Vector| $)) "\\spad{conditionsForIdempotents([v1,...,vn])} determines a complete list of polynomial equations for the coefficients of idempotents with respect to the \\spad{R}-module basis \\spad{v1},{}...,{}\\spad{vn}.")) (|rank| (((|PositiveInteger|)) "\\spad{rank()} returns the rank of the algebra as \\spad{R}-module.")) (|someBasis| (((|Vector| $)) "\\spad{someBasis()} returns some \\spad{R}-module basis."))) +NIL NIL (|FiniteAggregate&| A S) ((|constructor| (NIL "A finite aggregate is a homogeneous aggregate with a finite number of elements.")) (|member?| (((|Boolean|) |#2| $) "\\spad{member?(x,u)} tests if \\spad{x} is a member of \\spad{u}. For collections,{} \\axiom{member?(\\spad{x},{}\\spad{u}) = reduce(or,{}[x=y for \\spad{y} in \\spad{u}],{}\\spad{false})}.")) (|find| (((|Union| |#2| "failed") (|Mapping| (|Boolean|) |#2|) $) "\\spad{find(p,u)} returns the first \\spad{x} in \\spad{u} such that \\spad{p(x)} is \\spad{true},{} and \\spad{\"failed\"} otherwise.")) (|reduce| ((|#2| (|Mapping| |#2| |#2| |#2|) $ |#2| |#2|) "\\spad{reduce(f,u,x,z)} reduces the binary operation \\spad{f} across \\spad{u},{} stopping when an \"absorbing element\" \\spad{z} is encountered. As for \\spad{reduce(f,u,x)},{} \\spad{x} is the identity operation of \\spad{f}. Same as \\spad{reduce(f,u,x)} when \\spad{u} contains no element \\spad{z}. Thus the third argument \\spad{x} is returned when \\spad{u} is empty.") ((|#2| (|Mapping| |#2| |#2| |#2|) $ |#2|) "\\spad{reduce(f,u,x)} reduces the binary operation \\spad{f} across \\spad{u},{} where \\spad{x} is the starting value,{} usually the identity operation of \\spad{f}. Same as \\spad{reduce(f,u)} if \\spad{u} has 2 or more elements. Returns \\spad{f(x,y)} if \\spad{u} has one element \\spad{y},{} \\spad{x} if \\spad{u} is empty. For example,{} \\spad{reduce(+,u,0)} returns the sum of the elements of \\spad{u}.") ((|#2| (|Mapping| |#2| |#2| |#2|) $) "\\spad{reduce(f,u)} reduces the binary operation \\spad{f} across \\spad{u}. For example,{} if \\spad{u} is \\spad{[x,y,...,z]} then \\spad{reduce(f,u)} returns \\spad{f(..f(f(x,y),...),z)}. Note: if \\spad{u} has one element \\spad{x},{} \\spad{reduce(f,u)} returns \\spad{x}. Error: if \\spad{u} is empty.")) (|members| (((|List| |#2|) $) "\\spad{members(u)} returns a list of the consecutive elements of \\spad{u}. For collections,{} \\axiom{members([\\spad{x},{}\\spad{y},{}...,{}\\spad{z}]) = (\\spad{x},{}\\spad{y},{}...,{}\\spad{z})}.")) (|count| (((|NonNegativeInteger|) |#2| $) "\\spad{count(x,u)} returns the number of occurrences of \\spad{x} in \\spad{u}. For collections,{} \\axiom{count(\\spad{x},{}\\spad{u}) = reduce(+,{}[x=y for \\spad{y} in \\spad{u}],{}0)}.") (((|NonNegativeInteger|) (|Mapping| (|Boolean|) |#2|) $) "\\spad{count(p,u)} returns the number of elements \\spad{x} \\indented{1}{in \\spad{u} such that \\axiom{\\spad{p}(\\spad{x})} holds. For collections,{}} \\axiom{count(\\spad{p},{}\\spad{u}) = reduce(+,{}[1 for \\spad{x} in \\spad{u} | \\spad{p}(\\spad{x})],{}0)}.")) (|every?| (((|Boolean|) (|Mapping| (|Boolean|) |#2|) $) "\\spad{every?(f,u)} tests if \\spad{p}(\\spad{x}) holds for all elements \\spad{x} of \\spad{u}. Note: for collections,{} \\axiom{every?(\\spad{p},{}\\spad{u}) = reduce(and,{}map(\\spad{f},{}\\spad{u}),{}\\spad{true},{}\\spad{false})}.")) (|any?| (((|Boolean|) (|Mapping| (|Boolean|) |#2|) $) "\\spad{any?(p,u)} tests if \\spad{p(x)} is \\spad{true} for any element \\spad{x} of \\spad{u}. Note: for collections,{} \\axiom{any?(\\spad{p},{}\\spad{u}) = reduce(or,{}map(\\spad{f},{}\\spad{u}),{}\\spad{false},{}\\spad{true})}.")) (|#| (((|NonNegativeInteger|) $) "\\spad{\\#u} returns the number of items in \\spad{u}."))) @@ -1226,7 +1226,7 @@ NIL ((|HasCategory| |#2| (QUOTE (|CharacteristicNonZero|))) (|HasCategory| |#2| (QUOTE (|CharacteristicZero|))) (|HasCategory| |#2| (QUOTE (|Field|)))) (|FiniteRankAlgebra| R UP) ((|constructor| (NIL "A FiniteRankAlgebra is an algebra over a commutative ring \\spad{R} which is a free \\spad{R}-module of finite rank.")) (|minimalPolynomial| ((|#2| $) "\\spad{minimalPolynomial(a)} returns the minimal polynomial of \\spad{a}.")) (|characteristicPolynomial| ((|#2| $) "\\spad{characteristicPolynomial(a)} returns the characteristic polynomial of the regular representation of \\spad{a} with respect to any basis.")) (|traceMatrix| (((|Matrix| |#1|) (|Vector| $)) "\\spad{traceMatrix([v1,..,vn])} is the \\spad{n}-by-\\spad{n} matrix ( Tr(\\spad{vi} * vj) )")) (|discriminant| ((|#1| (|Vector| $)) "\\spad{discriminant([v1,..,vn])} returns \\spad{determinant(traceMatrix([v1,..,vn]))}.")) (|represents| (($ (|Vector| |#1|) (|Vector| $)) "\\spad{represents([a1,..,an],[v1,..,vn])} returns \\spad{a1*v1 + ... + an*vn}.")) (|coordinates| (((|Matrix| |#1|) (|Vector| $) (|Vector| $)) "\\spad{coordinates([v1,...,vm], basis)} returns the coordinates of the \\spad{vi}'s with to the basis \\spad{basis}. The coordinates of \\spad{vi} are contained in the \\spad{i}th row of the matrix returned by this function.") (((|Vector| |#1|) $ (|Vector| $)) "\\spad{coordinates(a,basis)} returns the coordinates of \\spad{a} with respect to the \\spad{basis} \\spad{basis}.")) (|norm| ((|#1| $) "\\spad{norm(a)} returns the determinant of the regular representation of \\spad{a} with respect to any basis.")) (|trace| ((|#1| $) "\\spad{trace(a)} returns the trace of the regular representation of \\spad{a} with respect to any basis.")) (|regularRepresentation| (((|Matrix| |#1|) $ (|Vector| $)) "\\spad{regularRepresentation(a,basis)} returns the matrix of the linear map defined by left multiplication by \\spad{a} with respect to the \\spad{basis} \\spad{basis}.")) (|rank| (((|PositiveInteger|)) "\\spad{rank()} returns the rank of the algebra."))) -((|rightUnitary| . T) (|leftUnitary| . T) (|unitsKnown| . T)) +NIL NIL (|FiniteLinearAggregate&| A S) ((|constructor| (NIL "A finite linear aggregate is a linear aggregate of finite length. The finite property of the aggregate adds several exports to the list of exports from \\spadtype{LinearAggregate} such as \\spadfun{reverse},{} \\spadfun{sort},{} and so on.")) (|sort!| (($ $) "\\spad{sort!(u)} returns \\spad{u} with its elements in ascending order.") (($ (|Mapping| (|Boolean|) |#2| |#2|) $) "\\spad{sort!(p,u)} returns \\spad{u} with its elements ordered by \\spad{p}.")) (|reverse!| (($ $) "\\spad{reverse!(u)} returns \\spad{u} with its elements in reverse order.")) (|copyInto!| (($ $ $ (|Integer|)) "\\spad{copyInto!(u,v,i)} returns aggregate \\spad{u} containing a copy of \\spad{v} inserted at element \\spad{i}.")) (|position| (((|Integer|) |#2| $ (|Integer|)) "\\spad{position(x,a,n)} returns the index \\spad{i} of the first occurrence of \\spad{x} in \\axiom{a} where \\axiom{\\spad{i} >= \\spad{n}},{} and \\axiom{minIndex(a) - 1} if no such \\spad{x} is found.") (((|Integer|) |#2| $) "\\spad{position(x,a)} returns the index \\spad{i} of the first occurrence of \\spad{x} in a,{} and \\axiom{minIndex(a) - 1} if there is no such \\spad{x}.") (((|Integer|) (|Mapping| (|Boolean|) |#2|) $) "\\spad{position(p,a)} returns the index \\spad{i} of the first \\spad{x} in \\axiom{a} such that \\axiom{\\spad{p}(\\spad{x})} is \\spad{true},{} and \\axiom{minIndex(a) - 1} if there is no such \\spad{x}.")) (|sorted?| (((|Boolean|) $) "\\spad{sorted?(u)} tests if the elements of \\spad{u} are in ascending order.") (((|Boolean|) (|Mapping| (|Boolean|) |#2| |#2|) $) "\\spad{sorted?(p,a)} tests if \\axiom{a} is sorted according to predicate \\spad{p}.")) (|sort| (($ $) "\\spad{sort(u)} returns an \\spad{u} with elements in ascending order. Note: \\axiom{sort(\\spad{u}) = sort(<=,{}\\spad{u})}.") (($ (|Mapping| (|Boolean|) |#2| |#2|) $) "\\spad{sort(p,a)} returns a copy of \\axiom{a} sorted using total ordering predicate \\spad{p}.")) (|reverse| (($ $) "\\spad{reverse(a)} returns a copy of \\axiom{a} with elements in reverse order.")) (|merge| (($ $ $) "\\spad{merge(u,v)} merges \\spad{u} and \\spad{v} in ascending order. Note: \\axiom{merge(\\spad{u},{}\\spad{v}) = merge(<=,{}\\spad{u},{}\\spad{v})}.") (($ (|Mapping| (|Boolean|) |#2| |#2|) $ $) "\\spad{merge(p,a,b)} returns an aggregate \\spad{c} which merges \\axiom{a} and \\spad{b}. The result is produced by examining each element \\spad{x} of \\axiom{a} and \\spad{y} of \\spad{b} successively. If \\axiom{\\spad{p}(\\spad{x},{}\\spad{y})} is \\spad{true},{} then \\spad{x} is inserted into the result; otherwise \\spad{y} is inserted. If \\spad{x} is chosen,{} the next element of \\axiom{a} is examined,{} and so on. When all the elements of one aggregate are examined,{} the remaining elements of the other are appended. For example,{} \\axiom{merge(<,{}[1,{}3],{}[2,{}7,{}5])} returns \\axiom{[1,{}2,{}3,{}7,{}5]}."))) @@ -1241,8 +1241,8 @@ NIL NIL NIL (|FreeLieAlgebra| |VarSet| R) -((|constructor| (NIL "The category of free Lie algebras. It is used by domains of non-commutative algebra: \\spadtype{LiePolynomial} and \\spadtype{XPBWPolynomial}. \\newline Author: Michel Petitot (petitot@lifl.fr)")) (|eval| (($ $ (|List| |#1|) (|List| $)) "\\axiom{eval(\\spad{p},{} [\\spad{x1},{}...,{}xn],{} [\\spad{v1},{}...,{}vn])} replaces \\axiom{\\spad{xi}} by \\axiom{\\spad{vi}} in \\axiom{\\spad{p}}.") (($ $ |#1| $) "\\axiom{eval(\\spad{p},{} \\spad{x},{} \\spad{v})} replaces \\axiom{\\spad{x}} by \\axiom{\\spad{v}} in \\axiom{\\spad{p}}.")) (|varList| (((|List| |#1|) $) "\\axiom{varList(\\spad{x})} returns the list of distinct entries of \\axiom{\\spad{x}}.")) (|trunc| (($ $ (|NonNegativeInteger|)) "\\axiom{trunc(\\spad{p},{}\\spad{n})} returns the polynomial \\axiom{\\spad{p}} truncated at order \\axiom{\\spad{n}}.")) (|mirror| (($ $) "\\axiom{mirror(\\spad{x})} returns \\axiom{Sum(r_i mirror(w_i))} if \\axiom{\\spad{x}} is \\axiom{Sum(r_i w_i)}.")) (|LiePoly| (($ (|LyndonWord| |#1|)) "\\axiom{LiePoly(\\spad{l})} returns the bracketed form of \\axiom{\\spad{l}} as a Lie polynomial.")) (|rquo| (((|XRecursivePolynomial| |#1| |#2|) (|XRecursivePolynomial| |#1| |#2|) $) "\\axiom{rquo(\\spad{x},{}\\spad{y})} returns the right simplification of \\axiom{\\spad{x}} by \\axiom{\\spad{y}}.")) (|lquo| (((|XRecursivePolynomial| |#1| |#2|) (|XRecursivePolynomial| |#1| |#2|) $) "\\axiom{lquo(\\spad{x},{}\\spad{y})} returns the left simplification of \\axiom{\\spad{x}} by \\axiom{\\spad{y}}.")) (|degree| (((|NonNegativeInteger|) $) "\\axiom{degree(\\spad{x})} returns the greatest length of a word in the support of \\axiom{\\spad{x}}.")) (|coerce| (((|XRecursivePolynomial| |#1| |#2|) $) "\\axiom{coerce(\\spad{x})} returns \\axiom{\\spad{x}} as a recursive polynomial.") (((|XDistributedPolynomial| |#1| |#2|) $) "\\axiom{coerce(\\spad{x})} returns \\axiom{\\spad{x}} as distributed polynomial.") (($ |#1|) "\\axiom{coerce(\\spad{x})} returns \\axiom{\\spad{x}} as a Lie polynomial.")) (|coef| ((|#2| (|XRecursivePolynomial| |#1| |#2|) $) "\\axiom{coef(\\spad{x},{}\\spad{y})} returns the scalar product of \\axiom{\\spad{x}} by \\axiom{\\spad{y}},{} the set of words being regarded as an orthogonal basis."))) -((|JacobiIdentity| . T) (|NullSquare| . T) (|leftUnitary| . T) (|rightUnitary| . T)) +((|constructor| (NIL "The category of free Lie algebras. It is used by domains of non-commutative algebra: \\spadtype{LiePolynomial} and \\spadtype{XPBWPolynomial}. \\newline Author: Michel Petitot (petitot@lifl.fr)")) (|eval| (($ $ (|List| |#1|) (|List| $)) "\\axiom{eval(\\spad{p},{} [\\spad{x1},{}...,{}xn],{} [\\spad{v1},{}...,{}vn])} replaces \\axiom{\\spad{xi}} by \\axiom{\\spad{vi}} in \\axiom{\\spad{p}}.") (($ $ |#1| $) "\\axiom{eval(\\spad{p},{} \\spad{x},{} \\spad{v})} replaces \\axiom{\\spad{x}} by \\axiom{\\spad{v}} in \\axiom{\\spad{p}}.")) (|varList| (((|List| |#1|) $) "\\axiom{varList(\\spad{x})} returns the list of distinct entries of \\axiom{\\spad{x}}.")) (|trunc| (($ $ (|NonNegativeInteger|)) "\\axiom{trunc(\\spad{p},{}\\spad{n})} returns the polynomial \\axiom{\\spad{p}} truncated at order \\axiom{\\spad{n}}.")) (|mirror| (($ $) "\\axiom{mirror(\\spad{x})} returns \\axiom{Sum(r_i mirror(w_i))} if \\axiom{\\spad{x}} is \\axiom{Sum(r_i w_i)}.")) (|LiePoly| (($ (|LyndonWord| |#1|)) "\\axiom{LiePoly(\\spad{l})} returns the bracketed form of \\axiom{\\spad{l}} as a Lie polynomial.")) (|rquo| (((|XRecursivePolynomial| |#1| |#2|) (|XRecursivePolynomial| |#1| |#2|) $) "\\axiom{rquo(\\spad{x},{}\\spad{y})} returns the right simplification of \\axiom{\\spad{x}} by \\axiom{\\spad{y}}.")) (|lquo| (((|XRecursivePolynomial| |#1| |#2|) (|XRecursivePolynomial| |#1| |#2|) $) "\\axiom{lquo(\\spad{x},{}\\spad{y})} returns the left simplification of \\axiom{\\spad{x}} by \\axiom{\\spad{y}}.")) (|degree| (((|NonNegativeInteger|) $) "\\axiom{degree(\\spad{x})} returns the greatest length of a word in the support of \\axiom{\\spad{x}}.")) (|coerce| (($ |#1|) "\\axiom{coerce(\\spad{x})} returns \\axiom{\\spad{x}} as a Lie polynomial.")) (|coef| ((|#2| (|XRecursivePolynomial| |#1| |#2|) $) "\\axiom{coef(\\spad{x},{}\\spad{y})} returns the scalar product of \\axiom{\\spad{x}} by \\axiom{\\spad{y}},{} the set of words being regarded as an orthogonal basis."))) +NIL NIL (|FiniteLinearAggregateSort| S V) ((|constructor| (NIL "This package exports 3 sorting algorithms which work over FiniteLinearAggregates.")) (|shellSort| ((|#2| (|Mapping| (|Boolean|) |#1| |#1|) |#2|) "\\spad{shellSort(f, agg)} sorts the aggregate agg with the ordering function \\spad{f} using the shellSort algorithm.")) (|heapSort| ((|#2| (|Mapping| (|Boolean|) |#1| |#1|) |#2|) "\\spad{heapSort(f, agg)} sorts the aggregate agg with the ordering function \\spad{f} using the heapsort algorithm.")) (|quickSort| ((|#2| (|Mapping| (|Boolean|) |#1| |#1|) |#2|) "\\spad{quickSort(f, agg)} sorts the aggregate agg with the ordering function \\spad{f} using the quicksort algorithm."))) @@ -1258,7 +1258,7 @@ NIL NIL (|Float|) ((|outputSpacing| (((|Void|) (|NonNegativeInteger|)) "\\spad{outputSpacing(n)} inserts a space after \\spad{n} (default 10) digits on output; outputSpacing(0) means no spaces are inserted.")) (|outputGeneral| (((|Void|) (|NonNegativeInteger|)) "\\spad{outputGeneral(n)} sets the output mode to general notation with \\spad{n} significant digits displayed.") (((|Void|)) "\\spad{outputGeneral()} sets the output mode (default mode) to general notation; numbers will be displayed in either fixed or floating (scientific) notation depending on the magnitude.")) (|outputFixed| (((|Void|) (|NonNegativeInteger|)) "\\spad{outputFixed(n)} sets the output mode to fixed point notation,{} with \\spad{n} digits displayed after the decimal point.") (((|Void|)) "\\spad{outputFixed()} sets the output mode to fixed point notation; the output will contain a decimal point.")) (|outputFloating| (((|Void|) (|NonNegativeInteger|)) "\\spad{outputFloating(n)} sets the output mode to floating (scientific) notation with \\spad{n} significant digits displayed after the decimal point.") (((|Void|)) "\\spad{outputFloating()} sets the output mode to floating (scientific) notation,{} \\spadignore{i.e.} \\spad{mantissa * 10 exponent} is displayed as \\spad{0.mantissa E exponent}.")) (|atan| (($ $ $) "\\spad{atan(x,y)} computes the arc tangent from \\spad{x} with phase \\spad{y}.")) (|exp1| (($) "\\spad{exp1()} returns exp 1: \\spad{2.7182818284...}.")) (|log10| (($ $) "\\spad{log10(x)} computes the logarithm for \\spad{x} to base 10.") (($) "\\spad{log10()} returns \\spad{ln 10}: \\spad{2.3025809299...}.")) (|log2| (($ $) "\\spad{log2(x)} computes the logarithm for \\spad{x} to base 2.") (($) "\\spad{log2()} returns \\spad{ln 2},{} \\spadignore{i.e.} \\spad{0.6931471805...}.")) (|rationalApproximation| (((|Fraction| (|Integer|)) $ (|NonNegativeInteger|) (|NonNegativeInteger|)) "\\spad{rationalApproximation(f, n, b)} computes a rational approximation \\spad{r} to \\spad{f} with relative error \\spad{< b**(-n)},{} that is \\spad{|(r-f)/f| < b**(-n)}.") (((|Fraction| (|Integer|)) $ (|NonNegativeInteger|)) "\\spad{rationalApproximation(f, n)} computes a rational approximation \\spad{r} to \\spad{f} with relative error \\spad{< 10**(-n)}.")) (|shift| (($ $ (|Integer|)) "\\spad{shift(x,n)} adds \\spad{n} to the exponent of float \\spad{x}.")) (|relerror| (((|Integer|) $ $) "\\spad{relerror(x,y)} computes the absolute value of \\spad{x - y} divided by \\spad{y},{} when \\spad{y \\~= 0}.")) (|normalize| (($ $) "\\spad{normalize(x)} normalizes \\spad{x} at current precision.")) (** (($ $ $) "\\spad{x ** y} computes \\spad{exp(y log x)} where \\spad{x >= 0}.")) (/ (($ $ (|Integer|)) "\\spad{x / i} computes the division from \\spad{x} by an integer \\spad{i}."))) -((|arbitraryExponent| . T) (|arbitraryPrecision| . T) (|approximate| . T) (|canonicalsClosed| . T) (|canonicalUnitNormal| . T) (|noZeroDivisors| . T) ((|commutative| "*") . T) (|rightUnitary| . T) (|leftUnitary| . T) (|unitsKnown| . T)) +((|arbitraryExponent| . T) (|arbitraryPrecision| . T) (|approximate| . T) (|canonicalUnitNormal| . T) (|noZeroDivisors| . T) ((|commutative| "*") . T)) NIL (|FloatingComplexPackage| |Par|) ((|constructor| (NIL "\\indented{3}{This is a package for the approximation of complex solutions for} systems of equations of rational functions with complex rational coefficients. The results are expressed as either complex rational numbers or complex floats depending on the type of the precision parameter which can be either a rational number or a floating point number.")) (|complexRoots| (((|List| (|List| (|Complex| |#1|))) (|List| (|Fraction| (|Polynomial| (|Complex| (|Integer|))))) (|List| (|Symbol|)) |#1|) "\\spad{complexRoots(lrf, lv, eps)} finds all the complex solutions of a list of rational functions with rational number coefficients with respect the the variables appearing in \\spad{lv}. Each solution is computed to precision eps and returned as list corresponding to the order of variables in \\spad{lv}.") (((|List| (|Complex| |#1|)) (|Fraction| (|Polynomial| (|Complex| (|Integer|)))) |#1|) "\\spad{complexRoots(rf, eps)} finds all the complex solutions of a univariate rational function with rational number coefficients. The solutions are computed to precision eps.")) (|complexSolve| (((|List| (|Equation| (|Polynomial| (|Complex| |#1|)))) (|Equation| (|Fraction| (|Polynomial| (|Complex| (|Integer|))))) |#1|) "\\spad{complexSolve(eq,eps)} finds all the complex solutions of the equation \\spad{eq} of rational functions with rational rational coefficients with respect to all the variables appearing in \\spad{eq},{} with precision \\spad{eps}.") (((|List| (|Equation| (|Polynomial| (|Complex| |#1|)))) (|Fraction| (|Polynomial| (|Complex| (|Integer|)))) |#1|) "\\spad{complexSolve(p,eps)} find all the complex solutions of the rational function \\spad{p} with complex rational coefficients with respect to all the variables appearing in \\spad{p},{} with precision \\spad{eps}.") (((|List| (|List| (|Equation| (|Polynomial| (|Complex| |#1|))))) (|List| (|Equation| (|Fraction| (|Polynomial| (|Complex| (|Integer|)))))) |#1|) "\\spad{complexSolve(leq,eps)} finds all the complex solutions to precision \\spad{eps} of the system \\spad{leq} of equations of rational functions over complex rationals with respect to all the variables appearing in lp.") (((|List| (|List| (|Equation| (|Polynomial| (|Complex| |#1|))))) (|List| (|Fraction| (|Polynomial| (|Complex| (|Integer|))))) |#1|) "\\spad{complexSolve(lp,eps)} finds all the complex solutions to precision \\spad{eps} of the system \\spad{lp} of rational functions over the complex rationals with respect to all the variables appearing in \\spad{lp}."))) @@ -1270,15 +1270,19 @@ NIL NIL (|FreeModule| R S) ((|constructor| (NIL "A \\spad{bi}-module is a free module over a ring with generators indexed by an ordered set. Each element can be expressed as a finite linear combination of generators. Only non-zero terms are stored."))) -((|leftUnitary| . T) (|rightUnitary| . T)) +NIL ((|HasCategory| |#1| (QUOTE (|CommutativeRing|))) (AND (|HasCategory| |#1| #1=(QUOTE (|SetCategory|))) (|HasCategory| |#2| #1#))) (|FreeModule1| R S) ((|constructor| (NIL "This domain implements linear combinations of elements from the domain \\spad{S} with coefficients in the domain \\spad{R} where \\spad{S} is an ordered set and \\spad{R} is a ring (which may be non-commutative). This domain is used by domains of non-commutative algebra such as: \\indented{4}{\\spadtype{XDistributedPolynomial},{}} \\indented{4}{\\spadtype{XRecursivePolynomial}.} Author: Michel Petitot (petitot@lifl.fr)")) (* (($ |#2| |#1|) "\\spad{s*r} returns the product \\spad{r*s} used by \\spadtype{XRecursivePolynomial}"))) -((|leftUnitary| . T) (|rightUnitary| . T)) +NIL ((|HasCategory| |#1| (QUOTE (|CommutativeRing|)))) +(|FreeMagma| |VarSet|) +((|constructor| (NIL "This type is the basic representation of parenthesized words (binary trees over arbitrary symbols) useful in \\spadtype{LiePolynomial}. \\newline Author: Michel Petitot (petitot@lifl.fr).")) (|varList| (((|List| |#1|) $) "\\axiom{varList(\\spad{x})} returns the list of distinct entries of \\axiom{\\spad{x}}.")) (|right| (($ $) "\\axiom{right(\\spad{x})} returns right subtree of \\axiom{\\spad{x}} or error if \\axiomOpFrom{retractable?}{FreeMagma}(\\axiom{\\spad{x}}) is \\spad{true}.")) (|retractable?| (((|Boolean|) $) "\\axiom{retractable?(\\spad{x})} tests if \\axiom{\\spad{x}} is a tree with only one entry.")) (|rest| (($ $) "\\axiom{rest(\\spad{x})} return \\axiom{\\spad{x}} without the first entry or error if \\axiomOpFrom{retractable?}{FreeMagma}(\\axiom{\\spad{x}}) is \\spad{true}.")) (|mirror| (($ $) "\\axiom{mirror(\\spad{x})} returns the reversed word of \\axiom{\\spad{x}}. That is \\axiom{\\spad{x}} itself if \\axiomOpFrom{retractable?}{FreeMagma}(\\axiom{\\spad{x}}) is \\spad{true} and \\axiom{mirror(\\spad{z}) * mirror(\\spad{y})} if \\axiom{\\spad{x}} is \\axiom{y*z}.")) (|lexico| (((|Boolean|) $ $) "\\axiom{lexico(\\spad{x},{}\\spad{y})} returns \\axiom{\\spad{true}} iff \\axiom{\\spad{x}} is smaller than \\axiom{\\spad{y}} \\spad{w}.\\spad{r}.\\spad{t}. the lexicographical ordering induced by \\axiom{VarSet}. \\spad{N}.\\spad{B}. This operation does not take into account the tree structure of its arguments. Thus this is not a total ordering.")) (|length| (((|PositiveInteger|) $) "\\axiom{length(\\spad{x})} returns the number of entries in \\axiom{\\spad{x}}.")) (|left| (($ $) "\\axiom{left(\\spad{x})} returns left subtree of \\axiom{\\spad{x}} or error if \\axiomOpFrom{retractable?}{FreeMagma}(\\axiom{\\spad{x}}) is \\spad{true}.")) (|first| ((|#1| $) "\\axiom{first(\\spad{x})} returns the first entry of the tree \\axiom{\\spad{x}}.")) (* (($ $ $) "\\axiom{x*y} returns the tree \\axiom{[\\spad{x},{}\\spad{y}]}."))) +NIL +NIL (|FreeModuleCat| R |Basis|) ((|constructor| (NIL "A domain of this category implements formal linear combinations of elements from a domain \\spad{Basis} with coefficients in a domain \\spad{R}. The domain \\spad{Basis} needs only to belong to the category \\spadtype{SetCategory} and \\spad{R} to the category \\spadtype{Ring}. Thus the coefficient ring may be non-commutative. See the \\spadtype{XDistributedPolynomial} constructor for examples of domains built with the \\spadtype{FreeModuleCat} category constructor. Author: Michel Petitot (petitot@lifl.fr)")) (|reductum| (($ $) "\\spad{reductum(x)} returns \\spad{x} minus its leading term.")) (|leadingTerm| (((|Record| (|:| |k| |#2|) (|:| |c| |#1|)) $) "\\spad{leadingTerm(x)} returns the first term which appears in \\spad{ListOfTerms(x)}.")) (|leadingCoefficient| ((|#1| $) "\\spad{leadingCoefficient(x)} returns the first coefficient which appears in \\spad{ListOfTerms(x)}.")) (|leadingMonomial| ((|#2| $) "\\spad{leadingMonomial(x)} returns the first element from \\spad{Basis} which appears in \\spad{ListOfTerms(x)}.")) (|numberOfMonomials| (((|NonNegativeInteger|) $) "\\spad{numberOfMonomials(x)} returns the number of monomials of \\spad{x}.")) (|monomials| (((|List| $) $) "\\spad{monomials(x)} returns the list of \\spad{r_i*b_i} whose sum is \\spad{x}.")) (|coefficients| (((|List| |#1|) $) "\\spad{coefficients(x)} returns the list of coefficients of \\spad{x}.")) (|ListOfTerms| (((|List| (|Record| (|:| |k| |#2|) (|:| |c| |#1|))) $) "\\spad{ListOfTerms(x)} returns a list \\spad{lt} of terms with type \\spad{Record(k: Basis, c: R)} such that \\spad{x} equals \\spad{reduce(+, map(x +-> monom(x.k, x.c), lt))}.")) (|monomial?| (((|Boolean|) $) "\\spad{monomial?(x)} returns \\spad{true} if \\spad{x} contains a single monomial.")) (|monom| (($ |#2| |#1|) "\\spad{monom(b,r)} returns the element with the single monomial \\indented{1}{\\spad{b} and coefficient \\spad{r}.}")) (|coefficient| ((|#1| $ |#2|) "\\spad{coefficient(x,b)} returns the coefficient of \\spad{b} in \\spad{x}.")) (* (($ |#1| |#2|) "\\spad{r*b} returns the product of \\spad{r} by \\spad{b}."))) -((|leftUnitary| . T) (|rightUnitary| . T)) +NIL NIL (|FreeMonoidCategory| S) ((|constructor| (NIL "A free monoid on a set \\spad{S} is the monoid of finite products of the form \\spad{reduce(*,[si ** ni])} where the \\spad{si}'s are in \\spad{S},{} and the \\spad{ni}'s are nonnegative integers. The multiplication is not commutative.")) (|mapGen| (($ (|Mapping| |#1| |#1|) $) "\\spad{mapGen(f, a1\\^e1 ... an\\^en)} returns \\spad{f(a1)\\^e1 ... f(an)\\^en}.")) (|mapExpon| (($ (|Mapping| (|NonNegativeInteger|) (|NonNegativeInteger|)) $) "\\spad{mapExpon(f, a1\\^e1 ... an\\^en)} returns \\spad{a1\\^f(e1) ... an\\^f(en)}.")) (|nthFactor| ((|#1| $ (|Integer|)) "\\spad{nthFactor(x, n)} returns the factor of the n^th monomial of \\spad{x}.")) (|nthExpon| (((|NonNegativeInteger|) $ (|Integer|)) "\\spad{nthExpon(x, n)} returns the exponent of the n^th monomial of \\spad{x}.")) (|factors| (((|List| (|Record| (|:| |gen| |#1|) (|:| |exp| (|NonNegativeInteger|)))) $) "\\spad{factors(a1\\^e1,...,an\\^en)} returns \\spad{[[a1, e1],...,[an, en]]}.")) (|size| (((|NonNegativeInteger|) $) "\\spad{size(x)} returns the number of monomials in \\spad{x}.")) (|overlap| (((|Record| (|:| |lm| $) (|:| |mm| $) (|:| |rm| $)) $ $) "\\spad{overlap(x, y)} returns \\spad{[l, m, r]} such that \\spad{x = l * m},{} \\spad{y = m * r} and \\spad{l} and \\spad{r} have no overlap,{} \\spadignore{i.e.} \\spad{overlap(l, r) = [l, 1, r]}.")) (|divide| (((|Union| (|Record| (|:| |lm| $) (|:| |rm| $)) "failed") $ $) "\\spad{divide(x, y)} returns the left and right exact quotients of \\spad{x} by \\spad{y},{} \\spadignore{i.e.} \\spad{[l, r]} such that \\spad{x = l * y * r},{} \"failed\" if \\spad{x} is not of the form \\spad{l * y * r}.")) (|rquo| (((|Union| $ "failed") $ $) "\\spad{rquo(x, y)} returns the exact right quotient of \\spad{x} by \\spad{y} \\spadignore{i.e.} \\spad{q} such that \\spad{x = q * y},{} \"failed\" if \\spad{x} is not of the form \\spad{q * y}.")) (|lquo| (((|Union| $ "failed") $ $) "\\spad{lquo(x, y)} returns the exact left quotient of \\spad{x} by \\spad{y} \\spadignore{i.e.} \\spad{q} such that \\spad{x = y * q},{} \"failed\" if \\spad{x} is not of the form \\spad{y * q}.")) (|hcrf| (($ $ $) "\\spad{hcrf(x, y)} returns the highest common right factor of \\spad{x} and \\spad{y},{} \\spadignore{i.e.} the largest \\spad{d} such that \\spad{x = a d} and \\spad{y = b d}.")) (|hclf| (($ $ $) "\\spad{hclf(x, y)} returns the highest common left factor of \\spad{x} and \\spad{y},{} \\spadignore{i.e.} the largest \\spad{d} such that \\spad{x = d a} and \\spad{y = d b}.")) (** (($ |#1| (|NonNegativeInteger|)) "\\spad{s ** n} returns the product of \\spad{s} by itself \\spad{n} times.")) (* (($ $ |#1|) "\\spad{x * s} returns the product of \\spad{x} by \\spad{s} on the right.") (($ |#1| $) "\\spad{s * x} returns the product of \\spad{x} by \\spad{s} on the left."))) @@ -1298,7 +1302,7 @@ NIL NIL (|FreeNilpotentLie| |n| |class| R) ((|constructor| (NIL "Generate the Free Lie Algebra over a ring \\spad{R} with identity; A \\spad{P}. Hall basis is generated by a package call to HallBasis.")) (|generator| (($ (|NonNegativeInteger|)) "\\spad{generator(i)} is the \\spad{i}th Hall Basis element")) (|shallowExpand| (((|OutputForm|) $) "\\spad{shallowExpand(x)} \\undocumented{}")) (|deepExpand| (((|OutputForm|) $) "\\spad{deepExpand(x)} \\undocumented{}")) (|dimension| (((|NonNegativeInteger|)) "\\spad{dimension()} is the rank of this Lie algebra"))) -((|leftUnitary| . T) (|rightUnitary| . T)) +NIL NIL (|FindOrderFinite| F UP UPUP R) ((|constructor| (NIL "\\indented{1}{Finds the order of a divisor over a finite field} Author: Manuel Bronstein Date Created: 1988 Date Last Updated: 11 Jul 1990")) (|order| (((|NonNegativeInteger|) (|FiniteDivisor| |#1| |#2| |#3| |#4|)) "\\spad{order(x)} \\undocumented"))) @@ -1318,7 +1322,7 @@ NIL NIL (|FieldOfPrimeCharacteristic|) ((|constructor| (NIL "FieldOfPrimeCharacteristic is the category of fields of prime characteristic,{} \\spadignore{e.g.} finite fields,{} algebraic closures of fields of prime characteristic,{} transcendental extensions of of fields of prime characteristic.")) (|primeFrobenius| (($ $ (|NonNegativeInteger|)) "\\spad{primeFrobenius(a,s)} returns \\spad{a**(p**s)} where \\spad{p} is the characteristic.") (($ $) "\\spad{primeFrobenius(a)} returns \\spad{a ** p} where \\spad{p} is the characteristic.")) (|discreteLog| (((|Union| (|NonNegativeInteger|) "failed") $ $) "\\spad{discreteLog(b,a)} computes \\spad{s} with \\spad{b**s = a} if such an \\spad{s} exists.")) (|order| (((|OnePointCompletion| (|PositiveInteger|)) $) "\\spad{order(a)} computes the order of an element in the multiplicative group of the field. Error: if \\spad{a} is 0."))) -((|canonicalsClosed| . T) (|canonicalUnitNormal| . T) (|noZeroDivisors| . T) ((|commutative| "*") . T) (|rightUnitary| . T) (|leftUnitary| . T) (|unitsKnown| . T)) +((|canonicalUnitNormal| . T) (|noZeroDivisors| . T) ((|commutative| "*") . T)) NIL (|FloatingPointSystem&| S) ((|constructor| (NIL "This category is intended as a model for floating point systems. A floating point system is a model for the real numbers. In fact,{} it is an approximation in the sense that not all real numbers are exactly representable by floating point numbers. A floating point system is characterized by the following: \\blankline \\indented{2}{1: \\spadfunFrom{base}{FloatingPointSystem} of the \\spadfunFrom{exponent}{FloatingPointSystem}.} \\indented{9}{(actual implemenations are usually binary or decimal)} \\indented{2}{2: \\spadfunFrom{precision}{FloatingPointSystem} of the \\spadfunFrom{mantissa}{FloatingPointSystem} (arbitrary or fixed)} \\indented{2}{3: rounding error for operations} \\blankline Because a Float is an approximation to the real numbers,{} even though it is defined to be a join of a Field and OrderedRing,{} some of the attributes do not hold. In particular associative(\"+\") does not hold. Algorithms defined over a field need special considerations when the field is a floating point system.")) (|max| (($) "\\spad{max()} returns the maximum floating point number.")) (|min| (($) "\\spad{min()} returns the minimum floating point number.")) (|decreasePrecision| (((|PositiveInteger|) (|Integer|)) "\\spad{decreasePrecision(n)} decreases the current \\spadfunFrom{precision}{FloatingPointSystem} precision by \\spad{n} decimal digits.")) (|increasePrecision| (((|PositiveInteger|) (|Integer|)) "\\spad{increasePrecision(n)} increases the current \\spadfunFrom{precision}{FloatingPointSystem} by \\spad{n} decimal digits.")) (|precision| (((|PositiveInteger|) (|PositiveInteger|)) "\\spad{precision(n)} set the precision in the base to \\spad{n} decimal digits.") (((|PositiveInteger|)) "\\spad{precision()} returns the precision in digits base.")) (|digits| (((|PositiveInteger|) (|PositiveInteger|)) "\\spad{digits(d)} set the \\spadfunFrom{precision}{FloatingPointSystem} to \\spad{d} digits.") (((|PositiveInteger|)) "\\spad{digits()} returns ceiling's precision in decimal digits.")) (|bits| (((|PositiveInteger|) (|PositiveInteger|)) "\\spad{bits(n)} set the \\spadfunFrom{precision}{FloatingPointSystem} to \\spad{n} bits.") (((|PositiveInteger|)) "\\spad{bits()} returns ceiling's precision in bits.")) (|mantissa| (((|Integer|) $) "\\spad{mantissa(x)} returns the mantissa part of \\spad{x}.")) (|exponent| (((|Integer|) $) "\\spad{exponent(x)} returns the \\spadfunFrom{exponent}{FloatingPointSystem} part of \\spad{x}.")) (|base| (((|PositiveInteger|)) "\\spad{base()} returns the base of the \\spadfunFrom{exponent}{FloatingPointSystem}.")) (|order| (((|Integer|) $) "\\spad{order x} is the order of magnitude of \\spad{x}. Note: \\spad{base ** order x <= |x| < base ** (1 + order x)}.")) (|float| (($ (|Integer|) (|Integer|) (|PositiveInteger|)) "\\spad{float(a,e,b)} returns \\spad{a * b ** e}.") (($ (|Integer|) (|Integer|)) "\\spad{float(a,e)} returns \\spad{a * base() ** e}.")) (|approximate| ((|attribute|) "\\spad{approximate} means \"is an approximation to the real numbers\"."))) @@ -1326,20 +1330,20 @@ NIL ((|HasAttribute| |#1| (QUOTE |arbitraryExponent|)) (|HasAttribute| |#1| (QUOTE |arbitraryPrecision|))) (|FloatingPointSystem|) ((|constructor| (NIL "This category is intended as a model for floating point systems. A floating point system is a model for the real numbers. In fact,{} it is an approximation in the sense that not all real numbers are exactly representable by floating point numbers. A floating point system is characterized by the following: \\blankline \\indented{2}{1: \\spadfunFrom{base}{FloatingPointSystem} of the \\spadfunFrom{exponent}{FloatingPointSystem}.} \\indented{9}{(actual implemenations are usually binary or decimal)} \\indented{2}{2: \\spadfunFrom{precision}{FloatingPointSystem} of the \\spadfunFrom{mantissa}{FloatingPointSystem} (arbitrary or fixed)} \\indented{2}{3: rounding error for operations} \\blankline Because a Float is an approximation to the real numbers,{} even though it is defined to be a join of a Field and OrderedRing,{} some of the attributes do not hold. In particular associative(\"+\") does not hold. Algorithms defined over a field need special considerations when the field is a floating point system.")) (|max| (($) "\\spad{max()} returns the maximum floating point number.")) (|min| (($) "\\spad{min()} returns the minimum floating point number.")) (|decreasePrecision| (((|PositiveInteger|) (|Integer|)) "\\spad{decreasePrecision(n)} decreases the current \\spadfunFrom{precision}{FloatingPointSystem} precision by \\spad{n} decimal digits.")) (|increasePrecision| (((|PositiveInteger|) (|Integer|)) "\\spad{increasePrecision(n)} increases the current \\spadfunFrom{precision}{FloatingPointSystem} by \\spad{n} decimal digits.")) (|precision| (((|PositiveInteger|) (|PositiveInteger|)) "\\spad{precision(n)} set the precision in the base to \\spad{n} decimal digits.") (((|PositiveInteger|)) "\\spad{precision()} returns the precision in digits base.")) (|digits| (((|PositiveInteger|) (|PositiveInteger|)) "\\spad{digits(d)} set the \\spadfunFrom{precision}{FloatingPointSystem} to \\spad{d} digits.") (((|PositiveInteger|)) "\\spad{digits()} returns ceiling's precision in decimal digits.")) (|bits| (((|PositiveInteger|) (|PositiveInteger|)) "\\spad{bits(n)} set the \\spadfunFrom{precision}{FloatingPointSystem} to \\spad{n} bits.") (((|PositiveInteger|)) "\\spad{bits()} returns ceiling's precision in bits.")) (|mantissa| (((|Integer|) $) "\\spad{mantissa(x)} returns the mantissa part of \\spad{x}.")) (|exponent| (((|Integer|) $) "\\spad{exponent(x)} returns the \\spadfunFrom{exponent}{FloatingPointSystem} part of \\spad{x}.")) (|base| (((|PositiveInteger|)) "\\spad{base()} returns the base of the \\spadfunFrom{exponent}{FloatingPointSystem}.")) (|order| (((|Integer|) $) "\\spad{order x} is the order of magnitude of \\spad{x}. Note: \\spad{base ** order x <= |x| < base ** (1 + order x)}.")) (|float| (($ (|Integer|) (|Integer|) (|PositiveInteger|)) "\\spad{float(a,e,b)} returns \\spad{a * b ** e}.") (($ (|Integer|) (|Integer|)) "\\spad{float(a,e)} returns \\spad{a * base() ** e}.")) (|approximate| ((|attribute|) "\\spad{approximate} means \"is an approximation to the real numbers\"."))) -((|approximate| . T) (|canonicalsClosed| . T) (|canonicalUnitNormal| . T) (|noZeroDivisors| . T) ((|commutative| "*") . T) (|rightUnitary| . T) (|leftUnitary| . T) (|unitsKnown| . T)) +((|approximate| . T) (|canonicalUnitNormal| . T) (|noZeroDivisors| . T) ((|commutative| "*") . T)) NIL (|Factored| R) ((|constructor| (NIL "\\spadtype{Factored} creates a domain whose objects are kept in factored form as long as possible. Thus certain operations like multiplication and gcd are relatively easy to do. Others,{} like addition require somewhat more work,{} and unless the argument domain provides a factor function,{} the result may not be completely factored. Each object consists of a unit and a list of factors,{} where a factor has a member of \\spad{R} (the \"base\"),{} and exponent and a flag indicating what is known about the base. A flag may be one of \"nil\",{} \"sqfr\",{} \"irred\" or \"prime\",{} which respectively mean that nothing is known about the base,{} it is square-free,{} it is irreducible,{} or it is prime. The current restriction to integral domains allows simplification to be performed without worrying about multiplication order.")) (|rationalIfCan| (((|Union| (|Fraction| (|Integer|)) "failed") $) "\\spad{rationalIfCan(u)} returns a rational number if \\spad{u} really is one,{} and \"failed\" otherwise.")) (|rational| (((|Fraction| (|Integer|)) $) "\\spad{rational(u)} assumes spadvar{\\spad{u}} is actually a rational number and does the conversion to rational number (see \\spadtype{Fraction Integer}).")) (|rational?| (((|Boolean|) $) "\\spad{rational?(u)} tests if \\spadvar{\\spad{u}} is actually a rational number (see \\spadtype{Fraction Integer}).")) (|unitNormalize| (($ $) "\\spad{unitNormalize(u)} normalizes the unit part of the factorization. For example,{} when working with factored integers,{} this operation will ensure that the bases are all positive integers.")) (|unit| ((|#1| $) "\\spad{unit(u)} extracts the unit part of the factorization.")) (|flagFactor| (($ |#1| (|Integer|) (|Union| #1="nil" #2="sqfr" #3="irred" #4="prime")) "\\spad{flagFactor(base,exponent,flag)} creates a factored object with a single factor whose \\spad{base} is asserted to be properly described by the information \\spad{flag}.")) (|sqfrFactor| (($ |#1| (|Integer|)) "\\spad{sqfrFactor(base,exponent)} creates a factored object with a single factor whose \\spad{base} is asserted to be square-free (flag = \"sqfr\").")) (|primeFactor| (($ |#1| (|Integer|)) "\\spad{primeFactor(base,exponent)} creates a factored object with a single factor whose \\spad{base} is asserted to be prime (flag = \"prime\").")) (|numberOfFactors| (((|NonNegativeInteger|) $) "\\spad{numberOfFactors(u)} returns the number of factors in \\spadvar{\\spad{u}}.")) (|nthFlag| (((|Union| #1# #2# #3# #4#) $ (|Integer|)) "\\spad{nthFlag(u,n)} returns the information flag of the \\spad{n}th factor of \\spadvar{\\spad{u}}. If \\spadvar{\\spad{n}} is not a valid index for a factor (for example,{} less than 1 or too big),{} \"nil\" is returned.")) (|nthFactor| ((|#1| $ (|Integer|)) "\\spad{nthFactor(u,n)} returns the base of the \\spad{n}th factor of \\spadvar{\\spad{u}}. If \\spadvar{\\spad{n}} is not a valid index for a factor (for example,{} less than 1 or too big),{} 1 is returned. If \\spadvar{\\spad{u}} consists only of a unit,{} the unit is returned.")) (|nthExponent| (((|Integer|) $ (|Integer|)) "\\spad{nthExponent(u,n)} returns the exponent of the \\spad{n}th factor of \\spadvar{\\spad{u}}. If \\spadvar{\\spad{n}} is not a valid index for a factor (for example,{} less than 1 or too big),{} 0 is returned.")) (|irreducibleFactor| (($ |#1| (|Integer|)) "\\spad{irreducibleFactor(base,exponent)} creates a factored object with a single factor whose \\spad{base} is asserted to be irreducible (flag = \"irred\").")) (|factors| (((|List| (|Record| (|:| |factor| |#1|) (|:| |exponent| (|Integer|)))) $) "\\spad{factors(u)} returns a list of the factors in a form suitable for iteration. That is,{} it returns a list where each element is a record containing a base and exponent. The original object is the product of all the factors and the unit (which can be extracted by \\axiom{unit(\\spad{u})}).")) (|nilFactor| (($ |#1| (|Integer|)) "\\spad{nilFactor(base,exponent)} creates a factored object with a single factor with no information about the kind of \\spad{base} (flag = \"nil\").")) (|factorList| (((|List| (|Record| (|:| |flg| (|Union| #1# #2# #3# #4#)) (|:| |fctr| |#1|) (|:| |xpnt| (|Integer|)))) $) "\\spad{factorList(u)} returns the list of factors with flags (for use by factoring code).")) (|makeFR| (($ |#1| (|List| (|Record| (|:| |flg| (|Union| #1# #2# #3# #4#)) (|:| |fctr| |#1|) (|:| |xpnt| (|Integer|))))) "\\spad{makeFR(unit,listOfFactors)} creates a factored object (for use by factoring code).")) (|exponent| (((|Integer|) $) "\\spad{exponent(u)} returns the exponent of the first factor of \\spadvar{\\spad{u}},{} or 0 if the factored form consists solely of a unit.")) (|expand| ((|#1| $) "\\spad{expand(f)} multiplies the unit and factors together,{} yielding an \"unfactored\" object. Note: this is purposely not called \\spadfun{coerce} which would cause the interpreter to do this automatically."))) -((|noZeroDivisors| . T) ((|commutative| "*") . T) (|rightUnitary| . T) (|leftUnitary| . T) (|unitsKnown| . T)) -((|HasCategory| |#1| (QUOTE (|InnerEvalable| #1=(|Symbol|) $))) (|HasCategory| |#1| (QUOTE (|Evalable| $))) (|HasCategory| |#1| (QUOTE (|Eltable| $ $))) (|HasCategory| |#1| (QUOTE (|ConvertibleTo| (|InputForm|)))) #2=(|HasCategory| |#1| (QUOTE (|UniqueFactorizationDomain|))) (OR #3=(|HasCategory| |#1| (QUOTE (|GcdDomain|))) #2#) (|HasCategory| |#1| (QUOTE (|RealConstant|))) (|HasCategory| |#1| (QUOTE (|RetractableTo| (|Fraction| #4=(|Integer|))))) (|HasCategory| |#1| (QUOTE (|RetractableTo| #4#))) (|HasCategory| |#1| (|%list| (QUOTE |InnerEvalable|) (QUOTE #1#) #5=(|devaluate| |#1|))) (|HasCategory| |#1| (|%list| (QUOTE |Evalable|) #5#)) (|HasCategory| |#1| (|%list| (QUOTE |Eltable|) #5# #5#)) (|HasCategory| |#1| (QUOTE (|DifferentialSpace|))) (|HasCategory| |#1| (QUOTE (|PartialDifferentialSpace| #1#))) (|HasCategory| |#1| (QUOTE (|DifferentialRing|))) (|HasCategory| |#1| (QUOTE (|PartialDifferentialRing| #1#))) (|HasCategory| |#1| (QUOTE (|IntegerNumberSystem|))) #3#) +((|noZeroDivisors| . T) ((|commutative| "*") . T)) +((|HasCategory| |#1| (QUOTE (|InnerEvalable| #1=(|Symbol|) $))) (|HasCategory| |#1| (QUOTE (|Evalable| $))) (|HasCategory| |#1| (QUOTE (|Eltable| $ $))) (|HasCategory| |#1| (QUOTE (|ConvertibleTo| (|InputForm|)))) #2=(|HasCategory| |#1| (QUOTE (|UniqueFactorizationDomain|))) (OR #3=(|HasCategory| |#1| (QUOTE (|GcdDomain|))) #2#) (|HasCategory| |#1| (QUOTE (|RealConstant|))) (|HasCategory| |#1| (QUOTE (|RetractableTo| (|Fraction| #4=(|Integer|))))) (|HasCategory| |#1| (QUOTE (|RetractableTo| #4#))) (|HasCategory| |#1| (|%list| (QUOTE |InnerEvalable|) (QUOTE #1#) #5=(|devaluate| |#1|))) (|HasCategory| |#1| (|%list| (QUOTE |Evalable|) #5#)) (|HasCategory| |#1| (|%list| (QUOTE |Eltable|) #5# #5#)) (|HasCategory| |#1| (QUOTE (|PartialDifferentialSpace| #1#))) (|HasCategory| |#1| (QUOTE (|DifferentialSpace|))) (|HasCategory| |#1| (QUOTE (|DifferentialRing|))) (|HasCategory| |#1| (QUOTE (|PartialDifferentialRing| #1#))) (|HasCategory| |#1| (QUOTE (|IntegerNumberSystem|))) #3#) (|FactoredFunctions2| R S) ((|constructor| (NIL "\\spadtype{FactoredFunctions2} contains functions that involve factored objects whose underlying domains may not be the same. For example,{} \\spadfun{map} might be used to coerce an object of type \\spadtype{Factored(Integer)} to \\spadtype{Factored(Complex(Integer))}.")) (|map| (((|Factored| |#2|) (|Mapping| |#2| |#1|) (|Factored| |#1|)) "\\spad{map(fn,u)} is used to apply the function \\userfun{\\spad{fn}} to every factor of \\spadvar{\\spad{u}}. The new factored object will have all its information flags set to \"nil\". This function is used,{} for example,{} to coerce every factor base to another type."))) NIL NIL (|Fraction| S) ((|constructor| (NIL "Fraction takes an IntegralDomain \\spad{S} and produces the domain of Fractions with numerators and denominators from \\spad{S}. If \\spad{S} is also a GcdDomain,{} then gcd's between numerator and denominator will be cancelled during all operations.")) (|canonical| ((|attribute|) "\\spad{canonical} means that equal elements are in fact identical."))) -((|canonical| AND (|has| |#1| (ATTRIBUTE |canonicalUnitNormal|)) (|has| |#1| (|GcdDomain|)) (|has| |#1| (ATTRIBUTE |canonical|))) (|canonicalsClosed| . T) (|canonicalUnitNormal| . T) (|noZeroDivisors| . T) ((|commutative| "*") . T) (|rightUnitary| . T) (|leftUnitary| . T) (|unitsKnown| . T)) -(#1=(|HasCategory| |#1| (QUOTE (|PolynomialFactorizationExplicit|))) (|HasCategory| |#1| (QUOTE (|RetractableTo| #2=(|Symbol|)))) #3=(|HasCategory| |#1| #4=(QUOTE (|CharacteristicNonZero|))) (|HasCategory| |#1| (QUOTE (|CharacteristicZero|))) (|HasCategory| |#1| (QUOTE (|ConvertibleTo| (|InputForm|)))) (|HasCategory| |#1| (QUOTE (|RealConstant|))) #5=(|HasCategory| |#1| (QUOTE (|OrderedIntegralDomain|))) #6=(|HasCategory| |#1| (QUOTE (|OrderedSet|))) (OR #5# #6#) (|HasCategory| |#1| (QUOTE (|RetractableTo| #7=(|Integer|)))) (|HasCategory| |#1| (QUOTE (|StepThrough|))) (|HasCategory| |#1| (QUOTE (|PatternMatchable| #8=(|Float|)))) (|HasCategory| |#1| (QUOTE (|PatternMatchable| #7#))) (|HasCategory| |#1| (QUOTE (|ConvertibleTo| (|Pattern| #8#)))) (|HasCategory| |#1| (QUOTE (|ConvertibleTo| (|Pattern| #7#)))) (|HasCategory| |#1| (QUOTE (|LinearlyExplicitRingOver| #7#))) (|HasCategory| |#1| (QUOTE (|DifferentialSpace|))) (|HasCategory| |#1| (QUOTE (|PartialDifferentialSpace| #2#))) (|HasCategory| |#1| (QUOTE (|DifferentialRing|))) (|HasCategory| |#1| (QUOTE (|PartialDifferentialRing| #2#))) (|HasCategory| |#1| (|%list| (QUOTE |InnerEvalable|) (QUOTE #2#) #9=(|devaluate| |#1|))) (|HasCategory| |#1| (|%list| (QUOTE |Evalable|) #9#)) (|HasCategory| |#1| (|%list| (QUOTE |Eltable|) #9# #9#)) (|HasCategory| |#1| (QUOTE (|EuclideanDomain|))) (|HasCategory| |#1| (QUOTE (|IntegerNumberSystem|))) (AND (|HasAttribute| |#1| (QUOTE |canonical|)) (|HasAttribute| |#1| (QUOTE |canonicalUnitNormal|)) (|HasCategory| |#1| (QUOTE (|GcdDomain|)))) #10=(AND #1# (|HasCategory| $ #4#)) (OR #10# #3#)) +((|canonical| AND (|has| |#1| (ATTRIBUTE |canonicalUnitNormal|)) (|has| |#1| (|GcdDomain|)) (|has| |#1| (ATTRIBUTE |canonical|))) (|canonicalUnitNormal| . T) (|noZeroDivisors| . T) ((|commutative| "*") . T)) +(#1=(|HasCategory| |#1| (QUOTE (|PolynomialFactorizationExplicit|))) (|HasCategory| |#1| (QUOTE (|RetractableTo| #2=(|Symbol|)))) #3=(|HasCategory| |#1| #4=(QUOTE (|CharacteristicNonZero|))) (|HasCategory| |#1| (QUOTE (|CharacteristicZero|))) (|HasCategory| |#1| (QUOTE (|ConvertibleTo| (|InputForm|)))) (|HasCategory| |#1| (QUOTE (|RealConstant|))) #5=(|HasCategory| |#1| (QUOTE (|OrderedIntegralDomain|))) #6=(|HasCategory| |#1| (QUOTE (|OrderedSet|))) (OR #5# #6#) (|HasCategory| |#1| (QUOTE (|RetractableTo| #7=(|Integer|)))) (|HasCategory| |#1| (QUOTE (|StepThrough|))) (|HasCategory| |#1| (QUOTE (|PatternMatchable| #8=(|Float|)))) (|HasCategory| |#1| (QUOTE (|PatternMatchable| #7#))) (|HasCategory| |#1| (QUOTE (|ConvertibleTo| (|Pattern| #8#)))) (|HasCategory| |#1| (QUOTE (|ConvertibleTo| (|Pattern| #7#)))) (|HasCategory| |#1| (QUOTE (|LinearlyExplicitRingOver| #7#))) (|HasCategory| |#1| (QUOTE (|PartialDifferentialSpace| #2#))) (|HasCategory| |#1| (QUOTE (|DifferentialSpace|))) (|HasCategory| |#1| (QUOTE (|DifferentialRing|))) (|HasCategory| |#1| (QUOTE (|PartialDifferentialRing| #2#))) (|HasCategory| |#1| (|%list| (QUOTE |InnerEvalable|) (QUOTE #2#) #9=(|devaluate| |#1|))) (|HasCategory| |#1| (|%list| (QUOTE |Evalable|) #9#)) (|HasCategory| |#1| (|%list| (QUOTE |Eltable|) #9# #9#)) (|HasCategory| |#1| (QUOTE (|EuclideanDomain|))) (|HasCategory| |#1| (QUOTE (|IntegerNumberSystem|))) (AND (|HasAttribute| |#1| (QUOTE |canonical|)) (|HasAttribute| |#1| (QUOTE |canonicalUnitNormal|)) (|HasCategory| |#1| (QUOTE (|GcdDomain|)))) #10=(AND #1# (|HasCategory| $ #4#)) (OR #10# #3#)) (|FractionFunctions2| A B) ((|constructor| (NIL "This package extends a map between integral domains to a map between Fractions over those domains by applying the map to the numerators and denominators.")) (|map| (((|Fraction| |#2|) (|Mapping| |#2| |#1|) (|Fraction| |#1|)) "\\spad{map(func,frac)} applies the function \\spad{func} to the numerator and denominator of the fraction \\spad{frac}."))) NIL @@ -1350,7 +1354,7 @@ NIL NIL (|FramedAlgebra| R UP) ((|constructor| (NIL "A \\spadtype{FramedAlgebra} is a \\spadtype{FiniteRankAlgebra} together with a fixed \\spad{R}-module basis.")) (|regularRepresentation| (((|Matrix| |#1|) $) "\\spad{regularRepresentation(a)} returns the matrix of the linear map defined by left multiplication by \\spad{a} with respect to the fixed basis.")) (|discriminant| ((|#1|) "\\spad{discriminant()} = determinant(traceMatrix()).")) (|traceMatrix| (((|Matrix| |#1|)) "\\spad{traceMatrix()} is the \\spad{n}-by-\\spad{n} matrix ( \\spad{Tr(vi * vj)} ),{} where \\spad{v1},{} ...,{} vn are the elements of the fixed basis.")) (|convert| (($ (|Vector| |#1|)) "\\spad{convert([a1,..,an])} returns \\spad{a1*v1 + ... + an*vn},{} where \\spad{v1},{} ...,{} vn are the elements of the fixed basis.") (((|Vector| |#1|) $) "\\spad{convert(a)} returns the coordinates of \\spad{a} with respect to the fixed \\spad{R}-module basis.")) (|represents| (($ (|Vector| |#1|)) "\\spad{represents([a1,..,an])} returns \\spad{a1*v1 + ... + an*vn},{} where \\spad{v1},{} ...,{} vn are the elements of the fixed basis.")) (|coordinates| (((|Matrix| |#1|) (|Vector| $)) "\\spad{coordinates([v1,...,vm])} returns the coordinates of the \\spad{vi}'s with to the fixed basis. The coordinates of \\spad{vi} are contained in the \\spad{i}th row of the matrix returned by this function.") (((|Vector| |#1|) $) "\\spad{coordinates(a)} returns the coordinates of \\spad{a} with respect to the fixed \\spad{R}-module basis.")) (|basis| (((|Vector| $)) "\\spad{basis()} returns the fixed \\spad{R}-module basis."))) -((|rightUnitary| . T) (|leftUnitary| . T) (|unitsKnown| . T)) +NIL NIL (|FullyRetractableTo&| A S) ((|constructor| (NIL "\\indented{2}{A is fully retractable to \\spad{B} means that A is retractable to \\spad{B},{} and,{}} \\indented{2}{in addition,{} if \\spad{B} is retractable to the integers or rational} \\indented{2}{numbers then so is A.} \\indented{2}{In particular,{} what we are asserting is that there are no integers} \\indented{2}{(rationals) in A which don't retract into \\spad{B}.} Date Created: March 1990 Date Last Updated: 9 April 1991"))) @@ -1362,7 +1366,7 @@ NIL NIL (|FractionalIdeal| R F UP A) ((|constructor| (NIL "Fractional ideals in a framed algebra.")) (|randomLC| ((|#4| (|NonNegativeInteger|) (|Vector| |#4|)) "\\spad{randomLC(n,x)} should be local but conditional.")) (|minimize| (($ $) "\\spad{minimize(I)} returns a reduced set of generators for \\spad{I}.")) (|denom| ((|#1| $) "\\spad{denom(1/d * (f1,...,fn))} returns \\spad{d}.")) (|numer| (((|Vector| |#4|) $) "\\spad{numer(1/d * (f1,...,fn))} = the vector \\spad{[f1,...,fn]}.")) (|norm| ((|#2| $) "\\spad{norm(I)} returns the norm of the ideal \\spad{I}.")) (|basis| (((|Vector| |#4|) $) "\\spad{basis((f1,...,fn))} returns the vector \\spad{[f1,...,fn]}.")) (|ideal| (($ (|Vector| |#4|)) "\\spad{ideal([f1,...,fn])} returns the ideal \\spad{(f1,...,fn)}."))) -((|unitsKnown| . T)) +NIL NIL (|FractionalIdealFunctions2| R1 F1 U1 A1 R2 F2 U2 A2) ((|constructor| (NIL "\\indented{1}{Lifting of morphisms to fractional ideals.} Author: Manuel Bronstein Date Created: 1 Feb 1989 Date Last Updated: 27 Feb 1990 Keywords: ideal,{} algebra,{} module.")) (|map| (((|FractionalIdeal| |#5| |#6| |#7| |#8|) (|Mapping| |#5| |#1|) (|FractionalIdeal| |#1| |#2| |#3| |#4|)) "\\spad{map(f,i)} \\undocumented{}"))) @@ -1382,7 +1386,7 @@ NIL ((|HasCategory| |#2| (QUOTE (|Field|)))) (|FramedNonAssociativeAlgebra| R) ((|constructor| (NIL "FramedNonAssociativeAlgebra(\\spad{R}) is a \\spadtype{FiniteRankNonAssociativeAlgebra} (\\spadignore{i.e.} a non associative algebra over \\spad{R} which is a free \\spad{R}-module of finite rank) over a commutative ring \\spad{R} together with a fixed \\spad{R}-module basis.")) (|apply| (($ (|Matrix| |#1|) $) "\\spad{apply(m,a)} defines a left operation of \\spad{n} by \\spad{n} matrices where \\spad{n} is the rank of the algebra in terms of matrix-vector multiplication,{} this is a substitute for a left module structure. Error: if shape of matrix doesn't fit.")) (|rightRankPolynomial| (((|SparseUnivariatePolynomial| (|Polynomial| |#1|))) "\\spad{rightRankPolynomial()} calculates the right minimal polynomial of the generic element in the algebra,{} defined by the same structural constants over the polynomial ring in symbolic coefficients with respect to the fixed basis.")) (|leftRankPolynomial| (((|SparseUnivariatePolynomial| (|Polynomial| |#1|))) "\\spad{leftRankPolynomial()} calculates the left minimal polynomial of the generic element in the algebra,{} defined by the same structural constants over the polynomial ring in symbolic coefficients with respect to the fixed basis.")) (|rightRegularRepresentation| (((|Matrix| |#1|) $) "\\spad{rightRegularRepresentation(a)} returns the matrix of the linear map defined by right multiplication by \\spad{a} with respect to the fixed \\spad{R}-module basis.")) (|leftRegularRepresentation| (((|Matrix| |#1|) $) "\\spad{leftRegularRepresentation(a)} returns the matrix of the linear map defined by left multiplication by \\spad{a} with respect to the fixed \\spad{R}-module basis.")) (|rightTraceMatrix| (((|Matrix| |#1|)) "\\spad{rightTraceMatrix()} is the \\spad{n}-by-\\spad{n} matrix whose element at the \\spad{i}\\spad{-}th row and \\spad{j}\\spad{-}th column is given by the right trace of the product \\spad{vi*vj},{} where \\spad{v1},{}...,{}\\spad{vn} are the elements of the fixed \\spad{R}-module basis.")) (|leftTraceMatrix| (((|Matrix| |#1|)) "\\spad{leftTraceMatrix()} is the \\spad{n}-by-\\spad{n} matrix whose element at the \\spad{i}\\spad{-}th row and \\spad{j}\\spad{-}th column is given by left trace of the product \\spad{vi*vj},{} where \\spad{v1},{}...,{}\\spad{vn} are the elements of the fixed \\spad{R}-module basis.")) (|rightDiscriminant| ((|#1|) "\\spad{rightDiscriminant()} returns the determinant of the \\spad{n}-by-\\spad{n} matrix whose element at the \\spad{i}\\spad{-}th row and \\spad{j}\\spad{-}th column is given by the right trace of the product \\spad{vi*vj},{} where \\spad{v1},{}...,{}\\spad{vn} are the elements of the fixed \\spad{R}-module basis. Note: the same as \\spad{determinant(rightTraceMatrix())}.")) (|leftDiscriminant| ((|#1|) "\\spad{leftDiscriminant()} returns the determinant of the \\spad{n}-by-\\spad{n} matrix whose element at the \\spad{i}\\spad{-}th row and \\spad{j}\\spad{-}th column is given by the left trace of the product \\spad{vi*vj},{} where \\spad{v1},{}...,{}\\spad{vn} are the elements of the fixed \\spad{R}-module basis. Note: the same as \\spad{determinant(leftTraceMatrix())}.")) (|convert| (($ (|Vector| |#1|)) "\\spad{convert([a1,...,an])} returns \\spad{a1*v1 + ... + an*vn},{} where \\spad{v1},{} ...,{} \\spad{vn} are the elements of the fixed \\spad{R}-module basis.") (((|Vector| |#1|) $) "\\spad{convert(a)} returns the coordinates of \\spad{a} with respect to the fixed \\spad{R}-module basis.")) (|represents| (($ (|Vector| |#1|)) "\\spad{represents([a1,...,an])} returns \\spad{a1*v1 + ... + an*vn},{} where \\spad{v1},{} ...,{} \\spad{vn} are the elements of the fixed \\spad{R}-module basis.")) (|conditionsForIdempotents| (((|List| (|Polynomial| |#1|))) "\\spad{conditionsForIdempotents()} determines a complete list of polynomial equations for the coefficients of idempotents with respect to the fixed \\spad{R}-module basis.")) (|structuralConstants| (((|Vector| (|Matrix| |#1|))) "\\spad{structuralConstants()} calculates the structural constants \\spad{[(gammaijk) for k in 1..rank()]} defined by \\spad{vi * vj = gammaij1 * v1 + ... + gammaijn * vn},{} where \\spad{v1},{}...,{}\\spad{vn} is the fixed \\spad{R}-module basis.")) (|coordinates| (((|Matrix| |#1|) (|Vector| $)) "\\spad{coordinates([a1,...,am])} returns a matrix whose \\spad{i}-th row is formed by the coordinates of \\spad{ai} with respect to the fixed \\spad{R}-module basis.") (((|Vector| |#1|) $) "\\spad{coordinates(a)} returns the coordinates of \\spad{a} with respect to the fixed \\spad{R}-module basis.")) (|basis| (((|Vector| $)) "\\spad{basis()} returns the fixed \\spad{R}-module basis."))) -((|unitsKnown| |has| |#1| (|IntegralDomain|)) (|leftUnitary| . T) (|rightUnitary| . T)) +NIL NIL (|FactoredFunctionUtilities| R) ((|constructor| (NIL "\\spadtype{FactoredFunctionUtilities} implements some utility functions for manipulating factored objects.")) (|mergeFactors| (((|Factored| |#1|) (|Factored| |#1|) (|Factored| |#1|)) "\\spad{mergeFactors(u,v)} is used when the factorizations of \\spadvar{\\spad{u}} and \\spadvar{\\spad{v}} are known to be disjoint,{} \\spadignore{e.g.} resulting from a content/primitive part split. Essentially,{} it creates a new factored object by multiplying the units together and appending the lists of factors.")) (|refine| (((|Factored| |#1|) (|Factored| |#1|) (|Mapping| (|Factored| |#1|) |#1|)) "\\spad{refine(u,fn)} is used to apply the function \\userfun{\\spad{fn}} to each factor of \\spadvar{\\spad{u}} and then build a new factored object from the results. For example,{} if \\spadvar{\\spad{u}} were created by calling \\spad{nilFactor(10,2)} then \\spad{refine(u,factor)} would create a factored object equal to that created by \\spad{factor(100)} or \\spad{primeFactor(2,2) * primeFactor(5,2)}."))) @@ -1394,7 +1398,7 @@ NIL ((|HasCategory| |#2| (QUOTE (|RetractableTo| (|Integer|)))) (|HasCategory| |#2| (QUOTE (|IntegralDomain|))) (|HasCategory| |#2| (QUOTE (|CommutativeRing|))) (|HasCategory| |#2| (QUOTE (|CharacteristicNonZero|))) (|HasCategory| |#2| (QUOTE (|CharacteristicZero|))) (|HasCategory| |#2| (QUOTE (|Ring|))) (|HasCategory| |#2| (QUOTE (|AbelianGroup|))) (|HasCategory| |#2| (QUOTE (|AbelianSemiGroup|))) (|HasCategory| |#2| (QUOTE (|Group|))) (|HasCategory| |#2| (QUOTE (|SemiGroup|))) (|HasCategory| |#2| (QUOTE (|ConvertibleTo| (|InputForm|))))) (|FunctionSpace| R) ((|constructor| (NIL "A space of formal functions with arguments in an arbitrary ordered set.")) (|univariate| (((|Fraction| (|SparseUnivariatePolynomial| $)) $ (|Kernel| $)) "\\spad{univariate(f, k)} returns \\spad{f} viewed as a univariate fraction in \\spad{k}.")) (/ (($ (|SparseMultivariatePolynomial| |#1| (|Kernel| $)) (|SparseMultivariatePolynomial| |#1| (|Kernel| $))) "\\spad{p1/p2} returns the quotient of \\spad{p1} and \\spad{p2} as an element of \\%.")) (|denominator| (($ $) "\\spad{denominator(f)} returns the denominator of \\spad{f} converted to \\%.")) (|denom| (((|SparseMultivariatePolynomial| |#1| (|Kernel| $)) $) "\\spad{denom(f)} returns the denominator of \\spad{f} viewed as a polynomial in the kernels over \\spad{R}.")) (|convert| (($ (|Factored| $)) "\\spad{convert(f1\\^e1 ... fm\\^em)} returns \\spad{(f1)\\^e1 ... (fm)\\^em} as an element of \\%,{} using formal kernels created using a \\spadfunFrom{paren}{ExpressionSpace}.")) (|isPower| (((|Union| (|Record| (|:| |val| $) (|:| |exponent| (|Integer|))) "failed") $) "\\spad{isPower(p)} returns \\spad{[x, n]} if \\spad{p = x**n} and \\spad{n <> 0}.")) (|numerator| (($ $) "\\spad{numerator(f)} returns the numerator of \\spad{f} converted to \\%.")) (|numer| (((|SparseMultivariatePolynomial| |#1| (|Kernel| $)) $) "\\spad{numer(f)} returns the numerator of \\spad{f} viewed as a polynomial in the kernels over \\spad{R} if \\spad{R} is an integral domain. If not,{} then numer(\\spad{f}) = \\spad{f} viewed as a polynomial in the kernels over \\spad{R}.")) (|coerce| (($ (|Fraction| (|Polynomial| (|Fraction| |#1|)))) "\\spad{coerce(f)} returns \\spad{f} as an element of \\%.") (($ (|Polynomial| (|Fraction| |#1|))) "\\spad{coerce(p)} returns \\spad{p} as an element of \\%.") (($ (|Fraction| |#1|)) "\\spad{coerce(q)} returns \\spad{q} as an element of \\%.") (($ (|SparseMultivariatePolynomial| |#1| (|Kernel| $))) "\\spad{coerce(p)} returns \\spad{p} as an element of \\%.")) (|isMult| (((|Union| (|Record| (|:| |coef| (|Integer|)) (|:| |var| (|Kernel| $))) "failed") $) "\\spad{isMult(p)} returns \\spad{[n, x]} if \\spad{p = n * x} and \\spad{n <> 0}.")) (|isPlus| (((|Union| (|List| $) "failed") $) "\\spad{isPlus(p)} returns \\spad{[m1,...,mn]} if \\spad{p = m1 +...+ mn} and \\spad{n > 1}.")) (|isExpt| (((|Union| (|Record| (|:| |var| (|Kernel| $)) (|:| |exponent| (|Integer|))) "failed") $ (|Symbol|)) "\\spad{isExpt(p,f)} returns \\spad{[x, n]} if \\spad{p = x**n} and \\spad{n <> 0} and \\spad{x = f(a)}.") (((|Union| (|Record| (|:| |var| (|Kernel| $)) (|:| |exponent| (|Integer|))) "failed") $ (|BasicOperator|)) "\\spad{isExpt(p,op)} returns \\spad{[x, n]} if \\spad{p = x**n} and \\spad{n <> 0} and \\spad{x = op(a)}.") (((|Union| (|Record| (|:| |var| (|Kernel| $)) (|:| |exponent| (|Integer|))) "failed") $) "\\spad{isExpt(p)} returns \\spad{[x, n]} if \\spad{p = x**n} and \\spad{n <> 0}.")) (|isTimes| (((|Union| (|List| $) "failed") $) "\\spad{isTimes(p)} returns \\spad{[a1,...,an]} if \\spad{p = a1*...*an} and \\spad{n > 1}.")) (** (($ $ (|NonNegativeInteger|)) "\\spad{x**n} returns \\spad{x} * \\spad{x} * \\spad{x} * ... * \\spad{x} (\\spad{n} times).")) (|eval| (($ $ (|Symbol|) (|NonNegativeInteger|) (|Mapping| $ $)) "\\spad{eval(x, s, n, f)} replaces every \\spad{s(a)**n} in \\spad{x} by \\spad{f(a)} for any \\spad{a}.") (($ $ (|Symbol|) (|NonNegativeInteger|) (|Mapping| $ (|List| $))) "\\spad{eval(x, s, n, f)} replaces every \\spad{s(a1,...,am)**n} in \\spad{x} by \\spad{f(a1,...,am)} for any \\spad{a1},{}...,{}am.") (($ $ (|List| (|Symbol|)) (|List| (|NonNegativeInteger|)) (|List| (|Mapping| $ (|List| $)))) "\\spad{eval(x, [s1,...,sm], [n1,...,nm], [f1,...,fm])} replaces every \\spad{si(a1,...,an)**ni} in \\spad{x} by \\spad{fi(a1,...,an)} for any \\spad{a1},{}...,{}am.") (($ $ (|List| (|Symbol|)) (|List| (|NonNegativeInteger|)) (|List| (|Mapping| $ $))) "\\spad{eval(x, [s1,...,sm], [n1,...,nm], [f1,...,fm])} replaces every \\spad{si(a)**ni} in \\spad{x} by \\spad{fi(a)} for any \\spad{a}.") (($ $ (|List| (|BasicOperator|)) (|List| $) (|Symbol|)) "\\spad{eval(x, [s1,...,sm], [f1,...,fm], y)} replaces every \\spad{si(a)} in \\spad{x} by \\spad{fi(y)} with \\spad{y} replaced by \\spad{a} for any \\spad{a}.") (($ $ (|BasicOperator|) $ (|Symbol|)) "\\spad{eval(x, s, f, y)} replaces every \\spad{s(a)} in \\spad{x} by \\spad{f(y)} with \\spad{y} replaced by \\spad{a} for any \\spad{a}.") (($ $) "\\spad{eval(f)} unquotes all the quoted operators in \\spad{f}.") (($ $ (|List| (|Symbol|))) "\\spad{eval(f, [foo1,...,foon])} unquotes all the \\spad{fooi}'s in \\spad{f}.") (($ $ (|Symbol|)) "\\spad{eval(f, foo)} unquotes all the foo's in \\spad{f}.")) (|applyQuote| (($ (|Symbol|) (|List| $)) "\\spad{applyQuote(foo, [x1,...,xn])} returns \\spad{'foo(x1,...,xn)}.") (($ (|Symbol|) $ $ $ $) "\\spad{applyQuote(foo, x, y, z, t)} returns \\spad{'foo(x,y,z,t)}.") (($ (|Symbol|) $ $ $) "\\spad{applyQuote(foo, x, y, z)} returns \\spad{'foo(x,y,z)}.") (($ (|Symbol|) $ $) "\\spad{applyQuote(foo, x, y)} returns \\spad{'foo(x,y)}.") (($ (|Symbol|) $) "\\spad{applyQuote(foo, x)} returns \\spad{'foo(x)}.")) (|variables| (((|List| (|Symbol|)) $) "\\spad{variables(f)} returns the list of all the variables of \\spad{f}.")) (|ground| ((|#1| $) "\\spad{ground(f)} returns \\spad{f} as an element of \\spad{R}. An error occurs if \\spad{f} is not an element of \\spad{R}.")) (|ground?| (((|Boolean|) $) "\\spad{ground?(f)} tests if \\spad{f} is an element of \\spad{R}."))) -((|unitsKnown| OR (|has| |#1| (|Ring|)) (|has| |#1| (|Group|))) (|leftUnitary| |has| |#1| . #1=((|CommutativeRing|))) (|rightUnitary| |has| |#1| . #1#) ((|commutative| "*") |has| |#1| . #2=((|IntegralDomain|))) (|noZeroDivisors| |has| |#1| . #2#) (|canonicalUnitNormal| |has| |#1| . #2#) (|canonicalsClosed| |has| |#1| . #2#)) +(((|commutative| "*") |has| |#1| . #1=((|IntegralDomain|))) (|noZeroDivisors| |has| |#1| . #1#) (|canonicalUnitNormal| |has| |#1| . #1#)) NIL (|FunctionSpaceFunctions2| R A S B) ((|constructor| (NIL "This package allows a mapping \\spad{R} -> \\spad{S} to be lifted to a mapping from a function space over \\spad{R} to a function space over \\spad{S}.")) (|map| ((|#4| (|Mapping| |#3| |#1|) |#2|) "\\spad{map(f, a)} applies \\spad{f} to all the constants in \\spad{R} appearing in \\spad{a}."))) @@ -1426,7 +1430,7 @@ NIL NIL (|FourierSeries| R E) ((|constructor| (NIL "\\indented{1}{Author: James Davenport} Date Created: 17 April 1992 Date Last Updated: Basic Functions: Related Constructors: Also See: AMS Classifications: Keywords: References: Description:")) (|makeCos| (($ |#2| |#1|) "\\spad{makeCos(e,r)} makes a sin expression with given argument and coefficient")) (|makeSin| (($ |#2| |#1|) "\\spad{makeSin(e,r)} makes a sin expression with given argument and coefficient")) (|coerce| (($ (|FourierComponent| |#2|)) "\\spad{coerce(c)} converts sin/cos terms into Fourier Series") (($ |#1|) "\\spad{coerce(r)} converts coefficients into Fourier Series"))) -((|canonical| AND (|has| |#1| #1=(ATTRIBUTE |canonical|)) (|has| |#2| #1#)) (|rightUnitary| . T) (|leftUnitary| . T) (|unitsKnown| . T)) +((|canonical| AND (|has| |#1| #1=(ATTRIBUTE |canonical|)) (|has| |#2| #1#))) ((AND (|HasAttribute| |#1| #1=(QUOTE |canonical|)) (|HasAttribute| |#2| #1#))) (|FunctionSpaceIntegration| R F) ((|constructor| (NIL "\\spadtype{FunctionSpaceIntegration} provides functions for the indefinite integration of real-valued functions.")) (|integrate| (((|Union| |#2| (|List| |#2|)) |#2| (|Symbol|)) "\\spad{integrate(f, x)} returns the integral of \\spad{f(x)dx} where \\spad{x} is viewed as a real variable."))) @@ -1445,7 +1449,7 @@ NIL NIL NIL (|FortranScalarType|) -((|constructor| (NIL "Creates and manipulates objects which correspond to the basic FORTRAN data types: REAL,{} INTEGER,{} COMPLEX,{} LOGICAL and CHARACTER")) (= (((|Boolean|) $ $) "\\spad{x=y} tests for equality")) (|logical?| (((|Boolean|) $) "\\spad{logical?(t)} tests whether \\spad{t} is equivalent to the FORTRAN type LOGICAL.")) (|character?| (((|Boolean|) $) "\\spad{character?(t)} tests whether \\spad{t} is equivalent to the FORTRAN type CHARACTER.")) (|doubleComplex?| (((|Boolean|) $) "\\spad{doubleComplex?(t)} tests whether \\spad{t} is equivalent to the (non-standard) FORTRAN type DOUBLE COMPLEX.")) (|complex?| (((|Boolean|) $) "\\spad{complex?(t)} tests whether \\spad{t} is equivalent to the FORTRAN type COMPLEX.")) (|integer?| (((|Boolean|) $) "\\spad{integer?(t)} tests whether \\spad{t} is equivalent to the FORTRAN type INTEGER.")) (|double?| (((|Boolean|) $) "\\spad{double?(t)} tests whether \\spad{t} is equivalent to the FORTRAN type DOUBLE PRECISION")) (|real?| (((|Boolean|) $) "\\spad{real?(t)} tests whether \\spad{t} is equivalent to the FORTRAN type REAL.")) (|coerce| (((|SExpression|) $) "\\spad{coerce(x)} returns the \\spad{s}-expression associated with \\spad{x}") (((|Symbol|) $) "\\spad{coerce(x)} returns the symbol associated with \\spad{x}") (($ (|Symbol|)) "\\spad{coerce(s)} transforms the symbol \\spad{s} into an element of FortranScalarType provided \\spad{s} is one of real,{} complex,{}double precision,{} logical,{} integer,{} character,{} REAL,{} COMPLEX,{} LOGICAL,{} INTEGER,{} CHARACTER,{} DOUBLE PRECISION") (($ (|String|)) "\\spad{coerce(s)} transforms the string \\spad{s} into an element of FortranScalarType provided \\spad{s} is one of \"real\",{} \"double precision\",{} \"complex\",{} \"logical\",{} \"integer\",{} \"character\",{} \"REAL\",{} \"COMPLEX\",{} \"LOGICAL\",{} \"INTEGER\",{} \"CHARACTER\",{} \"DOUBLE PRECISION\""))) +((|constructor| (NIL "Creates and manipulates objects which correspond to the basic FORTRAN data types: REAL,{} INTEGER,{} COMPLEX,{} LOGICAL and CHARACTER")) (= (((|Boolean|) $ $) "\\spad{x=y} tests for equality")) (|logical?| (((|Boolean|) $) "\\spad{logical?(t)} tests whether \\spad{t} is equivalent to the FORTRAN type LOGICAL.")) (|character?| (((|Boolean|) $) "\\spad{character?(t)} tests whether \\spad{t} is equivalent to the FORTRAN type CHARACTER.")) (|doubleComplex?| (((|Boolean|) $) "\\spad{doubleComplex?(t)} tests whether \\spad{t} is equivalent to the (non-standard) FORTRAN type DOUBLE COMPLEX.")) (|complex?| (((|Boolean|) $) "\\spad{complex?(t)} tests whether \\spad{t} is equivalent to the FORTRAN type COMPLEX.")) (|integer?| (((|Boolean|) $) "\\spad{integer?(t)} tests whether \\spad{t} is equivalent to the FORTRAN type INTEGER.")) (|double?| (((|Boolean|) $) "\\spad{double?(t)} tests whether \\spad{t} is equivalent to the FORTRAN type DOUBLE PRECISION")) (|real?| (((|Boolean|) $) "\\spad{real?(t)} tests whether \\spad{t} is equivalent to the FORTRAN type REAL.")) (|coerce| (($ (|Symbol|)) "\\spad{coerce(s)} transforms the symbol \\spad{s} into an element of FortranScalarType provided \\spad{s} is one of real,{} complex,{}double precision,{} logical,{} integer,{} character,{} REAL,{} COMPLEX,{} LOGICAL,{} INTEGER,{} CHARACTER,{} DOUBLE PRECISION") (($ (|String|)) "\\spad{coerce(s)} transforms the string \\spad{s} into an element of FortranScalarType provided \\spad{s} is one of \"real\",{} \"double precision\",{} \"complex\",{} \"logical\",{} \"integer\",{} \"character\",{} \"REAL\",{} \"COMPLEX\",{} \"LOGICAL\",{} \"INTEGER\",{} \"CHARACTER\",{} \"DOUBLE PRECISION\""))) NIL NIL (|FunctionSpaceUnivariatePolynomialFactor| R F UP) @@ -1510,16 +1514,16 @@ NIL NIL (|GcdDomain|) ((|constructor| (NIL "This category describes domains where \\spadfun{gcd} can be computed but where there is no guarantee of the existence of \\spadfun{factor} operation for factorisation into irreducibles. However,{} if such a \\spadfun{factor} operation exist,{} factorization will be unique up to order and units.")) (|lcm| (($ (|List| $)) "\\spad{lcm(l)} returns the least common multiple of the elements of the list \\spad{l}.") (($ $ $) "\\spad{lcm(x,y)} returns the least common multiple of \\spad{x} and \\spad{y}.")) (|gcd| (($ (|List| $)) "\\spad{gcd(l)} returns the common gcd of the elements in the list \\spad{l}.") (($ $ $) "\\spad{gcd(x,y)} returns the greatest common divisor of \\spad{x} and \\spad{y}."))) -((|noZeroDivisors| . T) ((|commutative| "*") . T) (|rightUnitary| . T) (|leftUnitary| . T) (|unitsKnown| . T)) +((|noZeroDivisors| . T) ((|commutative| "*") . T)) NIL (|GenericNonAssociativeAlgebra| R |n| |ls| |gamma|) ((|constructor| (NIL "AlgebraGenericElementPackage allows you to create generic elements of an algebra,{} \\spadignore{i.e.} the scalars are extended to include symbolic coefficients")) (|conditionsForIdempotents| (((|List| (|Polynomial| |#1|))) "\\spad{conditionsForIdempotents()} determines a complete list of polynomial equations for the coefficients of idempotents with respect to the fixed \\spad{R}-module basis") (((|List| (|Polynomial| |#1|)) (|Vector| $)) "\\spad{conditionsForIdempotents([v1,...,vn])} determines a complete list of polynomial equations for the coefficients of idempotents with respect to the \\spad{R}-module basis \\spad{v1},{}...,{}\\spad{vn}")) (|genericRightDiscriminant| (((|Fraction| (|Polynomial| |#1|))) "\\spad{genericRightDiscriminant()} is the determinant of the generic left trace forms of all products of basis element,{} if the generic left trace form is associative,{} an algebra is separable if the generic left discriminant is invertible,{} if it is non-zero,{} there is some ring extension which makes the algebra separable")) (|genericRightTraceForm| (((|Fraction| (|Polynomial| |#1|)) $ $) "\\spad{genericRightTraceForm (a,b)} is defined to be \\spadfun{genericRightTrace (a*b)},{} this defines a symmetric bilinear form on the algebra")) (|genericLeftDiscriminant| (((|Fraction| (|Polynomial| |#1|))) "\\spad{genericLeftDiscriminant()} is the determinant of the generic left trace forms of all products of basis element,{} if the generic left trace form is associative,{} an algebra is separable if the generic left discriminant is invertible,{} if it is non-zero,{} there is some ring extension which makes the algebra separable")) (|genericLeftTraceForm| (((|Fraction| (|Polynomial| |#1|)) $ $) "\\spad{genericLeftTraceForm (a,b)} is defined to be \\spad{genericLeftTrace (a*b)},{} this defines a symmetric bilinear form on the algebra")) (|genericRightNorm| (((|Fraction| (|Polynomial| |#1|)) $) "\\spad{genericRightNorm(a)} substitutes the coefficients of \\spad{a} for the generic coefficients into the coefficient of the constant term in \\spadfun{rightRankPolynomial} and changes the sign if the degree of this polynomial is odd")) (|genericRightTrace| (((|Fraction| (|Polynomial| |#1|)) $) "\\spad{genericRightTrace(a)} substitutes the coefficients of \\spad{a} for the generic coefficients into the coefficient of the second highest term in \\spadfun{rightRankPolynomial} and changes the sign")) (|genericRightMinimalPolynomial| (((|SparseUnivariatePolynomial| (|Fraction| (|Polynomial| |#1|))) $) "\\spad{genericRightMinimalPolynomial(a)} substitutes the coefficients of \\spad{a} for the generic coefficients in \\spadfun{rightRankPolynomial}")) (|rightRankPolynomial| (((|SparseUnivariatePolynomial| (|Fraction| (|Polynomial| |#1|)))) "\\spad{rightRankPolynomial()} returns the right minimimal polynomial of the generic element")) (|genericLeftNorm| (((|Fraction| (|Polynomial| |#1|)) $) "\\spad{genericLeftNorm(a)} substitutes the coefficients of \\spad{a} for the generic coefficients into the coefficient of the constant term in \\spadfun{leftRankPolynomial} and changes the sign if the degree of this polynomial is odd. This is a form of degree \\spad{k}")) (|genericLeftTrace| (((|Fraction| (|Polynomial| |#1|)) $) "\\spad{genericLeftTrace(a)} substitutes the coefficients of \\spad{a} for the generic coefficients into the coefficient of the second highest term in \\spadfun{leftRankPolynomial} and changes the sign. \\indented{1}{This is a linear form}")) (|genericLeftMinimalPolynomial| (((|SparseUnivariatePolynomial| (|Fraction| (|Polynomial| |#1|))) $) "\\spad{genericLeftMinimalPolynomial(a)} substitutes the coefficients of {em a} for the generic coefficients in \\spad{leftRankPolynomial()}")) (|leftRankPolynomial| (((|SparseUnivariatePolynomial| (|Fraction| (|Polynomial| |#1|)))) "\\spad{leftRankPolynomial()} returns the left minimimal polynomial of the generic element")) (|generic| (($ (|Vector| (|Symbol|)) (|Vector| $)) "\\spad{generic(vs,ve)} returns a generic element,{} \\spadignore{i.e.} the linear combination of \\spad{ve} with the symbolic coefficients \\spad{vs} error,{} if the vector of symbols is shorter than the vector of elements") (($ (|Symbol|) (|Vector| $)) "\\spad{generic(s,v)} returns a generic element,{} \\spadignore{i.e.} the linear combination of \\spad{v} with the symbolic coefficients \\spad{s1,s2,..}") (($ (|Vector| $)) "\\spad{generic(ve)} returns a generic element,{} \\spadignore{i.e.} the linear combination of \\spad{ve} basis with the symbolic coefficients \\spad{\\%x1,\\%x2,..}") (($ (|Vector| (|Symbol|))) "\\spad{generic(vs)} returns a generic element,{} \\spadignore{i.e.} the linear combination of the fixed basis with the symbolic coefficients \\spad{vs}; error,{} if the vector of symbols is too short") (($ (|Symbol|)) "\\spad{generic(s)} returns a generic element,{} \\spadignore{i.e.} the linear combination of the fixed basis with the symbolic coefficients \\spad{s1,s2,..}") (($) "\\spad{generic()} returns a generic element,{} \\spadignore{i.e.} the linear combination of the fixed basis with the symbolic coefficients \\spad{\\%x1,\\%x2,..}")) (|rightUnits| (((|Union| (|Record| (|:| |particular| $) (|:| |basis| (|List| $))) "failed")) "\\spad{rightUnits()} returns the affine space of all right units of the algebra,{} or \\spad{\"failed\"} if there is none")) (|leftUnits| (((|Union| (|Record| (|:| |particular| $) (|:| |basis| (|List| $))) "failed")) "\\spad{leftUnits()} returns the affine space of all left units of the algebra,{} or \\spad{\"failed\"} if there is none")) (|coerce| (($ (|Vector| (|Fraction| (|Polynomial| |#1|)))) "\\spad{coerce(v)} assumes that it is called with a vector of length equal to the dimension of the algebra,{} then a linear combination with the basis element is formed"))) -((|unitsKnown| |has| (|Fraction| (|Polynomial| |#1|)) (|IntegralDomain|)) (|leftUnitary| . T) (|rightUnitary| . T)) -((|HasCategory| #1=(|Fraction| (|Polynomial| |#1|)) (QUOTE (|Field|))) (|HasCategory| |#1| #2=(QUOTE (|IntegralDomain|))) (|HasCategory| #1# #2#)) +NIL +((|HasCategory| #1=(|Fraction| (|Polynomial| |#1|)) #2=(QUOTE (|IntegralDomain|))) (|HasCategory| #1# (QUOTE (|Field|))) (|HasCategory| |#1| #2#)) (|GeneralDistributedMultivariatePolynomial| |vl| R E) ((|constructor| (NIL "\\indented{2}{This type supports distributed multivariate polynomials} whose variables are from a user specified list of symbols. The coefficient ring may be non commutative,{} but the variables are assumed to commute. The term ordering is specified by its third parameter. Suggested types which define term orderings include: \\spadtype{DirectProduct},{} \\spadtype{HomogeneousDirectProduct},{} \\spadtype{SplitHomogeneousDirectProduct} and finally \\spadtype{OrderedDirectProduct} which accepts an arbitrary user function to define a term ordering.")) (|reorder| (($ $ (|List| (|Integer|))) "\\spad{reorder(p, perm)} applies the permutation perm to the variables in a polynomial and returns the new correctly ordered polynomial"))) -(((|commutative| "*") |has| |#2| (|CommutativeRing|)) (|noZeroDivisors| |has| |#2| (|IntegralDomain|)) (|canonicalUnitNormal| |has| |#2| (ATTRIBUTE |canonicalUnitNormal|)) (|leftUnitary| . T) (|rightUnitary| . T) (|unitsKnown| . T)) -(#1=(|HasCategory| |#2| (QUOTE (|PolynomialFactorizationExplicit|))) (OR #2=(|HasCategory| |#2| (QUOTE (|CommutativeRing|))) #3=(|HasCategory| |#2| (QUOTE (|GcdDomain|))) #4=(|HasCategory| |#2| (QUOTE (|IntegralDomain|))) #1#) (OR #3# #4# #1#) (OR #3# #1#) #4# #2# (OR #2# #4#) (AND (|HasCategory| |#2| #5=(QUOTE (|PatternMatchable| #6=(|Float|)))) (|HasCategory| #7=(|OrderedVariableList| |#1|) #5#)) (AND (|HasCategory| |#2| #8=(QUOTE (|PatternMatchable| #9=(|Integer|)))) (|HasCategory| #7# #8#)) (AND (|HasCategory| |#2| #10=(QUOTE (|ConvertibleTo| (|Pattern| #6#)))) (|HasCategory| #7# #10#)) (AND (|HasCategory| |#2| #11=(QUOTE (|ConvertibleTo| (|Pattern| #9#)))) (|HasCategory| #7# #11#)) (AND (|HasCategory| |#2| #12=(QUOTE (|ConvertibleTo| (|InputForm|)))) (|HasCategory| #7# #12#)) (|HasCategory| |#2| (QUOTE (|LinearlyExplicitRingOver| #9#))) (|HasCategory| |#2| (QUOTE (|CharacteristicZero|))) #13=(|HasCategory| |#2| #14=(QUOTE (|CharacteristicNonZero|))) #15=(|HasCategory| |#2| (QUOTE (|Algebra| #16=(|Fraction| #9#)))) (|HasCategory| |#2| (QUOTE (|RetractableTo| #9#))) (OR #15# #17=(|HasCategory| |#2| (QUOTE (|RetractableTo| #16#)))) #17# (|HasCategory| |#2| (QUOTE (|Field|))) (|HasAttribute| |#2| (QUOTE |canonicalUnitNormal|)) #3# #18=(AND #1# (|HasCategory| $ #14#)) (OR #18# #13#)) +(((|commutative| "*") |has| |#2| (|CommutativeRing|)) (|noZeroDivisors| |has| |#2| (|IntegralDomain|)) (|canonicalUnitNormal| |has| |#2| (ATTRIBUTE |canonicalUnitNormal|))) +(#1=(|HasCategory| |#2| (QUOTE (|PolynomialFactorizationExplicit|))) (OR #2=(|HasCategory| |#2| (QUOTE (|CommutativeRing|))) #3=(|HasCategory| |#2| (QUOTE (|GcdDomain|))) #4=(|HasCategory| |#2| (QUOTE (|IntegralDomain|))) #1#) (OR #3# #4# #1#) (OR #3# #1#) #4# #2# (OR #2# #4#) (AND (|HasCategory| |#2| #5=(QUOTE (|PatternMatchable| #6=(|Float|)))) (|HasCategory| #7=(|OrderedVariableList| |#1|) #5#)) (AND (|HasCategory| |#2| #8=(QUOTE (|PatternMatchable| #9=(|Integer|)))) (|HasCategory| #7# #8#)) (AND (|HasCategory| |#2| #10=(QUOTE (|ConvertibleTo| (|Pattern| #6#)))) (|HasCategory| #7# #10#)) (AND (|HasCategory| |#2| #11=(QUOTE (|ConvertibleTo| (|Pattern| #9#)))) (|HasCategory| #7# #11#)) (AND (|HasCategory| |#2| #12=(QUOTE (|ConvertibleTo| (|InputForm|)))) (|HasCategory| #7# #12#)) (|HasCategory| |#2| (QUOTE (|LinearlyExplicitRingOver| #9#))) #13=(|HasCategory| |#2| (QUOTE (|Algebra| #14=(|Fraction| #9#)))) #15=(|HasCategory| |#2| #16=(QUOTE (|CharacteristicNonZero|))) (|HasCategory| |#2| (QUOTE (|CharacteristicZero|))) (|HasCategory| |#2| (QUOTE (|RetractableTo| #9#))) (OR #13# #17=(|HasCategory| |#2| (QUOTE (|RetractableTo| #14#)))) #17# (|HasCategory| |#2| (QUOTE (|Field|))) (|HasAttribute| |#2| (QUOTE |canonicalUnitNormal|)) #3# #18=(AND #1# (|HasCategory| $ #16#)) (OR #18# #15#)) (|GenExEuclid| R BP) ((|constructor| (NIL "\\indented{1}{Author : \\spad{P}.Gianni.} January 1990 The equation \\spad{Af+Bg=h} and its generalization to \\spad{n} polynomials is solved for solutions over the \\spad{R},{} euclidean domain. A table containing the solutions of \\spad{Af+Bg=x**k} is used. The operations are performed modulus a prime which are in principle big enough,{} but the solutions are tested and,{} in case of failure,{} a hensel lifting process is used to get to the right solutions. It will be used in the factorization of multivariate polynomials over finite field,{} with \\spad{R=F[x]}.")) (|testModulus| (((|Boolean|) |#1| (|List| |#2|)) "\\spad{testModulus(p,lp)} returns \\spad{true} if the the prime \\spad{p} is valid for the list of polynomials \\spad{lp},{} \\spadignore{i.e.} preserves the degree and they remain relatively prime.")) (|solveid| (((|Union| (|List| |#2|) "failed") |#2| |#1| (|Vector| (|List| |#2|))) "\\spad{solveid(h,table)} computes the coefficients of the extended euclidean algorithm for a list of polynomials whose tablePow is \\spad{table} and with right side \\spad{h}.")) (|tablePow| (((|Union| (|Vector| (|List| |#2|)) "failed") (|NonNegativeInteger|) |#1| (|List| |#2|)) "\\spad{tablePow(maxdeg,prime,lpol)} constructs the table with the coefficients of the Extended Euclidean Algorithm for \\spad{lpol}. Here the right side is \\spad{x**k},{} for \\spad{k} less or equal to \\spad{maxdeg}. The operation returns \"failed\" when the elements are not coprime modulo \\spad{prime}.")) (|compBound| (((|NonNegativeInteger|) |#2| (|List| |#2|)) "\\spad{compBound(p,lp)} computes a bound for the coefficients of the solution polynomials. Given a polynomial right hand side \\spad{p},{} and a list \\spad{lp} of left hand side polynomials. Exported because it depends on the valuation.")) (|reduction| ((|#2| |#2| |#1|) "\\spad{reduction(p,prime)} reduces the polynomial \\spad{p} modulo \\spad{prime} of \\spad{R}. Note: this function is exported only because it's conditional."))) NIL @@ -1546,7 +1550,7 @@ NIL NIL (|GeneralModulePolynomial| |vl| R IS E |ff| P) ((|constructor| (NIL "This package \\undocumented")) (* (($ |#6| $) "\\spad{p*x} \\undocumented")) (|multMonom| (($ |#2| |#4| $) "\\spad{multMonom(r,e,x)} \\undocumented")) (|build| (($ |#2| |#3| |#4|) "\\spad{build(r,i,e)} \\undocumented")) (|unitVector| (($ |#3|) "\\spad{unitVector(x)} \\undocumented")) (|monomial| (($ |#2| (|ModuleMonomial| |#3| |#4| |#5|)) "\\spad{monomial(r,x)} \\undocumented")) (|reductum| (($ $) "\\spad{reductum(x)} \\undocumented")) (|leadingIndex| ((|#3| $) "\\spad{leadingIndex(x)} \\undocumented")) (|leadingExponent| ((|#4| $) "\\spad{leadingExponent(x)} \\undocumented")) (|leadingMonomial| (((|ModuleMonomial| |#3| |#4| |#5|) $) "\\spad{leadingMonomial(x)} \\undocumented")) (|leadingCoefficient| ((|#2| $) "\\spad{leadingCoefficient(x)} \\undocumented"))) -((|leftUnitary| . T) (|rightUnitary| . T)) +NIL NIL (|GosperSummationMethod| E V R P Q) ((|constructor| (NIL "Gosper's summation algorithm.")) (|GospersMethod| (((|Union| |#5| "failed") |#5| |#2| (|Mapping| |#2|)) "\\spad{GospersMethod(b, n, new)} returns a rational function \\spad{rf(n)} such that \\spad{a(n) * rf(n)} is the indefinite sum of \\spad{a(n)} with respect to upward difference on \\spad{n},{} \\spadignore{i.e.} \\spad{a(n+1) * rf(n+1) - a(n) * rf(n) = a(n)},{} where \\spad{b(n) = a(n)/a(n-1)} is a rational function. Returns \"failed\" if no such rational function \\spad{rf(n)} exists. Note: \\spad{new} is a nullary function returning a new \\spad{V} every time. The condition on \\spad{a(n)} is that \\spad{a(n)/a(n-1)} is a rational function of \\spad{n}."))) @@ -1573,7 +1577,7 @@ NIL NIL NIL (|GraphImage|) -((|constructor| (NIL "TwoDimensionalGraph creates virtual two dimensional graphs (to be displayed on TwoDimensionalViewports).")) (|putColorInfo| (((|List| (|List| (|Point| (|DoubleFloat|)))) (|List| (|List| (|Point| (|DoubleFloat|)))) (|List| (|Palette|))) "\\spad{putColorInfo(llp,lpal)} takes a list of list of points,{} \\spad{llp},{} and returns the points with their hue and shade components set according to the list of palette colors,{} \\spad{lpal}.")) (|coerce| (((|OutputForm|) $) "\\spad{coerce(gi)} returns the indicated graph,{} \\spad{gi},{} of domain \\spadtype{GraphImage} as output of the domain \\spadtype{OutputForm}.") (($ (|List| (|List| (|Point| (|DoubleFloat|))))) "\\spad{coerce(llp)} component(\\spad{gi},{}pt) creates and returns a graph of the domain \\spadtype{GraphImage} which is composed of the list of list of points given by \\spad{llp},{} and whose point colors,{} line colors and point sizes are determined by the default functions \\spadfun{pointColorDefault},{} \\spadfun{lineColorDefault},{} and \\spadfun{pointSizeDefault}. The graph data is then sent to the viewport manager where it waits to be included in a two-dimensional viewport window.")) (|point| (((|Void|) $ (|Point| (|DoubleFloat|)) (|Palette|)) "\\spad{point(gi,pt,pal)} modifies the graph \\spad{gi} of the domain \\spadtype{GraphImage} to contain one point component,{} \\spad{pt} whose point color is set to be the palette color \\spad{pal},{} and whose line color and point size are determined by the default functions \\spadfun{lineColorDefault} and \\spadfun{pointSizeDefault}.")) (|appendPoint| (((|Void|) $ (|Point| (|DoubleFloat|))) "\\spad{appendPoint(gi,pt)} appends the point \\spad{pt} to the end of the list of points component for the graph,{} \\spad{gi},{} which is of the domain \\spadtype{GraphImage}.")) (|component| (((|Void|) $ (|Point| (|DoubleFloat|)) (|Palette|) (|Palette|) (|PositiveInteger|)) "\\spad{component(gi,pt,pal1,pal2,ps)} modifies the graph \\spad{gi} of the domain \\spadtype{GraphImage} to contain one point component,{} \\spad{pt} whose point color is set to the palette color \\spad{pal1},{} line color is set to the palette color \\spad{pal2},{} and point size is set to the positive integer \\spad{ps}.") (((|Void|) $ (|Point| (|DoubleFloat|))) "\\spad{component(gi,pt)} modifies the graph \\spad{gi} of the domain \\spadtype{GraphImage} to contain one point component,{} \\spad{pt} whose point color,{} line color and point size are determined by the default functions \\spadfun{pointColorDefault},{} \\spadfun{lineColorDefault},{} and \\spadfun{pointSizeDefault}.") (((|Void|) $ (|List| (|Point| (|DoubleFloat|))) (|Palette|) (|Palette|) (|PositiveInteger|)) "\\spad{component(gi,lp,pal1,pal2,p)} sets the components of the graph,{} \\spad{gi} of the domain \\spadtype{GraphImage},{} to the values given. The point list for \\spad{gi} is set to the list \\spad{lp},{} the color of the points in \\spad{lp} is set to the palette color \\spad{pal1},{} the color of the lines which connect the points \\spad{lp} is set to the palette color \\spad{pal2},{} and the size of the points in \\spad{lp} is given by the integer \\spad{p}.")) (|units| (((|List| (|Float|)) $ (|List| (|Float|))) "\\spad{units(gi,lu)} modifies the list of unit increments for the \\spad{x} and \\spad{y} axes of the given graph,{} \\spad{gi} of the domain \\spadtype{GraphImage},{} to be that of the list of unit increments,{} \\spad{lu},{} and returns the new list of units for \\spad{gi}.") (((|List| (|Float|)) $) "\\spad{units(gi)} returns the list of unit increments for the \\spad{x} and \\spad{y} axes of the indicated graph,{} \\spad{gi},{} of the domain \\spadtype{GraphImage}.")) (|ranges| (((|List| (|Segment| (|Float|))) $ (|List| (|Segment| (|Float|)))) "\\spad{ranges(gi,lr)} modifies the list of ranges for the given graph,{} \\spad{gi} of the domain \\spadtype{GraphImage},{} to be that of the list of range segments,{} \\spad{lr},{} and returns the new range list for \\spad{gi}.") (((|List| (|Segment| (|Float|))) $) "\\spad{ranges(gi)} returns the list of ranges of the point components from the indicated graph,{} \\spad{gi},{} of the domain \\spadtype{GraphImage}.")) (|key| (((|Integer|) $) "\\spad{key(gi)} returns the process ID of the given graph,{} \\spad{gi},{} of the domain \\spadtype{GraphImage}.")) (|pointLists| (((|List| (|List| (|Point| (|DoubleFloat|)))) $) "\\spad{pointLists(gi)} returns the list of lists of points which compose the given graph,{} \\spad{gi},{} of the domain \\spadtype{GraphImage}.")) (|makeGraphImage| (($ (|List| (|List| (|Point| (|DoubleFloat|)))) (|List| (|Palette|)) (|List| (|Palette|)) (|List| (|PositiveInteger|)) (|List| (|DrawOption|))) "\\spad{makeGraphImage(llp,lpal1,lpal2,lp,lopt)} returns a graph of the domain \\spadtype{GraphImage} which is composed of the points and lines from the list of lists of points,{} \\spad{llp},{} whose point colors are indicated by the list of palette colors,{} \\spad{lpal1},{} and whose lines are colored according to the list of palette colors,{} \\spad{lpal2}. The paramater \\spad{lp} is a list of integers which denote the size of the data points,{} and \\spad{lopt} is the list of draw command options. The graph data is then sent to the viewport manager where it waits to be included in a two-dimensional viewport window.") (($ (|List| (|List| (|Point| (|DoubleFloat|)))) (|List| (|Palette|)) (|List| (|Palette|)) (|List| (|PositiveInteger|))) "\\spad{makeGraphImage(llp,lpal1,lpal2,lp)} returns a graph of the domain \\spadtype{GraphImage} which is composed of the points and lines from the list of lists of points,{} \\spad{llp},{} whose point colors are indicated by the list of palette colors,{} \\spad{lpal1},{} and whose lines are colored according to the list of palette colors,{} \\spad{lpal2}. The paramater \\spad{lp} is a list of integers which denote the size of the data points. The graph data is then sent to the viewport manager where it waits to be included in a two-dimensional viewport window.") (($ (|List| (|List| (|Point| (|DoubleFloat|))))) "\\spad{makeGraphImage(llp)} returns a graph of the domain \\spadtype{GraphImage} which is composed of the points and lines from the list of lists of points,{} \\spad{llp},{} with default point size and default point and line colours. The graph data is then sent to the viewport manager where it waits to be included in a two-dimensional viewport window.") (($ $) "\\spad{makeGraphImage(gi)} takes the given graph,{} \\spad{gi} of the domain \\spadtype{GraphImage},{} and sends it's data to the viewport manager where it waits to be included in a two-dimensional viewport window. \\spad{gi} cannot be an empty graph,{} and it's elements must have been created using the \\spadfun{point} or \\spadfun{component} functions,{} not by a previous \\spadfun{makeGraphImage}.")) (|graphImage| (($) "\\spad{graphImage()} returns an empty graph with 0 point lists of the domain \\spadtype{GraphImage}. A graph image contains the graph data component of a two dimensional viewport."))) +((|constructor| (NIL "TwoDimensionalGraph creates virtual two dimensional graphs (to be displayed on TwoDimensionalViewports).")) (|putColorInfo| (((|List| (|List| (|Point| (|DoubleFloat|)))) (|List| (|List| (|Point| (|DoubleFloat|)))) (|List| (|Palette|))) "\\spad{putColorInfo(llp,lpal)} takes a list of list of points,{} \\spad{llp},{} and returns the points with their hue and shade components set according to the list of palette colors,{} \\spad{lpal}.")) (|coerce| (($ (|List| (|List| (|Point| (|DoubleFloat|))))) "\\spad{coerce(llp)} component(\\spad{gi},{}pt) creates and returns a graph of the domain \\spadtype{GraphImage} which is composed of the list of list of points given by \\spad{llp},{} and whose point colors,{} line colors and point sizes are determined by the default functions \\spadfun{pointColorDefault},{} \\spadfun{lineColorDefault},{} and \\spadfun{pointSizeDefault}. The graph data is then sent to the viewport manager where it waits to be included in a two-dimensional viewport window.")) (|point| (((|Void|) $ (|Point| (|DoubleFloat|)) (|Palette|)) "\\spad{point(gi,pt,pal)} modifies the graph \\spad{gi} of the domain \\spadtype{GraphImage} to contain one point component,{} \\spad{pt} whose point color is set to be the palette color \\spad{pal},{} and whose line color and point size are determined by the default functions \\spadfun{lineColorDefault} and \\spadfun{pointSizeDefault}.")) (|appendPoint| (((|Void|) $ (|Point| (|DoubleFloat|))) "\\spad{appendPoint(gi,pt)} appends the point \\spad{pt} to the end of the list of points component for the graph,{} \\spad{gi},{} which is of the domain \\spadtype{GraphImage}.")) (|component| (((|Void|) $ (|Point| (|DoubleFloat|)) (|Palette|) (|Palette|) (|PositiveInteger|)) "\\spad{component(gi,pt,pal1,pal2,ps)} modifies the graph \\spad{gi} of the domain \\spadtype{GraphImage} to contain one point component,{} \\spad{pt} whose point color is set to the palette color \\spad{pal1},{} line color is set to the palette color \\spad{pal2},{} and point size is set to the positive integer \\spad{ps}.") (((|Void|) $ (|Point| (|DoubleFloat|))) "\\spad{component(gi,pt)} modifies the graph \\spad{gi} of the domain \\spadtype{GraphImage} to contain one point component,{} \\spad{pt} whose point color,{} line color and point size are determined by the default functions \\spadfun{pointColorDefault},{} \\spadfun{lineColorDefault},{} and \\spadfun{pointSizeDefault}.") (((|Void|) $ (|List| (|Point| (|DoubleFloat|))) (|Palette|) (|Palette|) (|PositiveInteger|)) "\\spad{component(gi,lp,pal1,pal2,p)} sets the components of the graph,{} \\spad{gi} of the domain \\spadtype{GraphImage},{} to the values given. The point list for \\spad{gi} is set to the list \\spad{lp},{} the color of the points in \\spad{lp} is set to the palette color \\spad{pal1},{} the color of the lines which connect the points \\spad{lp} is set to the palette color \\spad{pal2},{} and the size of the points in \\spad{lp} is given by the integer \\spad{p}.")) (|units| (((|List| (|Float|)) $ (|List| (|Float|))) "\\spad{units(gi,lu)} modifies the list of unit increments for the \\spad{x} and \\spad{y} axes of the given graph,{} \\spad{gi} of the domain \\spadtype{GraphImage},{} to be that of the list of unit increments,{} \\spad{lu},{} and returns the new list of units for \\spad{gi}.") (((|List| (|Float|)) $) "\\spad{units(gi)} returns the list of unit increments for the \\spad{x} and \\spad{y} axes of the indicated graph,{} \\spad{gi},{} of the domain \\spadtype{GraphImage}.")) (|ranges| (((|List| (|Segment| (|Float|))) $ (|List| (|Segment| (|Float|)))) "\\spad{ranges(gi,lr)} modifies the list of ranges for the given graph,{} \\spad{gi} of the domain \\spadtype{GraphImage},{} to be that of the list of range segments,{} \\spad{lr},{} and returns the new range list for \\spad{gi}.") (((|List| (|Segment| (|Float|))) $) "\\spad{ranges(gi)} returns the list of ranges of the point components from the indicated graph,{} \\spad{gi},{} of the domain \\spadtype{GraphImage}.")) (|key| (((|Integer|) $) "\\spad{key(gi)} returns the process ID of the given graph,{} \\spad{gi},{} of the domain \\spadtype{GraphImage}.")) (|pointLists| (((|List| (|List| (|Point| (|DoubleFloat|)))) $) "\\spad{pointLists(gi)} returns the list of lists of points which compose the given graph,{} \\spad{gi},{} of the domain \\spadtype{GraphImage}.")) (|makeGraphImage| (($ (|List| (|List| (|Point| (|DoubleFloat|)))) (|List| (|Palette|)) (|List| (|Palette|)) (|List| (|PositiveInteger|)) (|List| (|DrawOption|))) "\\spad{makeGraphImage(llp,lpal1,lpal2,lp,lopt)} returns a graph of the domain \\spadtype{GraphImage} which is composed of the points and lines from the list of lists of points,{} \\spad{llp},{} whose point colors are indicated by the list of palette colors,{} \\spad{lpal1},{} and whose lines are colored according to the list of palette colors,{} \\spad{lpal2}. The paramater \\spad{lp} is a list of integers which denote the size of the data points,{} and \\spad{lopt} is the list of draw command options. The graph data is then sent to the viewport manager where it waits to be included in a two-dimensional viewport window.") (($ (|List| (|List| (|Point| (|DoubleFloat|)))) (|List| (|Palette|)) (|List| (|Palette|)) (|List| (|PositiveInteger|))) "\\spad{makeGraphImage(llp,lpal1,lpal2,lp)} returns a graph of the domain \\spadtype{GraphImage} which is composed of the points and lines from the list of lists of points,{} \\spad{llp},{} whose point colors are indicated by the list of palette colors,{} \\spad{lpal1},{} and whose lines are colored according to the list of palette colors,{} \\spad{lpal2}. The paramater \\spad{lp} is a list of integers which denote the size of the data points. The graph data is then sent to the viewport manager where it waits to be included in a two-dimensional viewport window.") (($ (|List| (|List| (|Point| (|DoubleFloat|))))) "\\spad{makeGraphImage(llp)} returns a graph of the domain \\spadtype{GraphImage} which is composed of the points and lines from the list of lists of points,{} \\spad{llp},{} with default point size and default point and line colours. The graph data is then sent to the viewport manager where it waits to be included in a two-dimensional viewport window.") (($ $) "\\spad{makeGraphImage(gi)} takes the given graph,{} \\spad{gi} of the domain \\spadtype{GraphImage},{} and sends it's data to the viewport manager where it waits to be included in a two-dimensional viewport window. \\spad{gi} cannot be an empty graph,{} and it's elements must have been created using the \\spadfun{point} or \\spadfun{component} functions,{} not by a previous \\spadfun{makeGraphImage}.")) (|graphImage| (($) "\\spad{graphImage()} returns an empty graph with 0 point lists of the domain \\spadtype{GraphImage}. A graph image contains the graph data component of a two dimensional viewport."))) NIL NIL (|GradedModule&| S R E) @@ -1589,16 +1593,16 @@ NIL NIL NIL (|Group&| S) -((|constructor| (NIL "The class of multiplicative groups,{} \\spadignore{i.e.} monoids with multiplicative inverses. \\blankline")) (|commutator| (($ $ $) "\\spad{commutator(p,q)} computes \\spad{inv(p) * inv(q) * p * q}.")) (|conjugate| (($ $ $) "\\spad{conjugate(p,q)} computes \\spad{inv(q) * p * q}; this is 'right action by conjugation'.")) (|unitsKnown| ((|attribute|) "unitsKnown asserts that recip only returns \"failed\" for non-units.")) (** (($ $ (|Integer|)) "\\spad{x**n} returns \\spad{x} raised to the integer power \\spad{n}.")) (/ (($ $ $) "\\spad{x/y} is the same as \\spad{x} times the inverse of \\spad{y}.")) (|inv| (($ $) "\\spad{inv(x)} returns the inverse of \\spad{x}."))) +((|constructor| (NIL "The class of multiplicative groups,{} \\spadignore{i.e.} monoids with multiplicative inverses. \\blankline")) (|commutator| (($ $ $) "\\spad{commutator(p,q)} computes \\spad{inv(p) * inv(q) * p * q}.")) (|conjugate| (($ $ $) "\\spad{conjugate(p,q)} computes \\spad{inv(q) * p * q}; this is 'right action by conjugation'.")) (** (($ $ (|Integer|)) "\\spad{x**n} returns \\spad{x} raised to the integer power \\spad{n}.")) (/ (($ $ $) "\\spad{x/y} is the same as \\spad{x} times the inverse of \\spad{y}.")) (|inv| (($ $) "\\spad{inv(x)} returns the inverse of \\spad{x}."))) NIL NIL (|Group|) -((|constructor| (NIL "The class of multiplicative groups,{} \\spadignore{i.e.} monoids with multiplicative inverses. \\blankline")) (|commutator| (($ $ $) "\\spad{commutator(p,q)} computes \\spad{inv(p) * inv(q) * p * q}.")) (|conjugate| (($ $ $) "\\spad{conjugate(p,q)} computes \\spad{inv(q) * p * q}; this is 'right action by conjugation'.")) (|unitsKnown| ((|attribute|) "unitsKnown asserts that recip only returns \"failed\" for non-units.")) (** (($ $ (|Integer|)) "\\spad{x**n} returns \\spad{x} raised to the integer power \\spad{n}.")) (/ (($ $ $) "\\spad{x/y} is the same as \\spad{x} times the inverse of \\spad{y}.")) (|inv| (($ $) "\\spad{inv(x)} returns the inverse of \\spad{x}."))) -((|unitsKnown| . T)) +((|constructor| (NIL "The class of multiplicative groups,{} \\spadignore{i.e.} monoids with multiplicative inverses. \\blankline")) (|commutator| (($ $ $) "\\spad{commutator(p,q)} computes \\spad{inv(p) * inv(q) * p * q}.")) (|conjugate| (($ $ $) "\\spad{conjugate(p,q)} computes \\spad{inv(q) * p * q}; this is 'right action by conjugation'.")) (** (($ $ (|Integer|)) "\\spad{x**n} returns \\spad{x} raised to the integer power \\spad{n}.")) (/ (($ $ $) "\\spad{x/y} is the same as \\spad{x} times the inverse of \\spad{y}.")) (|inv| (($ $) "\\spad{inv(x)} returns the inverse of \\spad{x}."))) +NIL NIL (|GeneralUnivariatePowerSeries| |Coef| |var| |cen|) ((|constructor| (NIL "This is a category of univariate Puiseux series constructed from univariate Laurent series. A Puiseux series is represented by a pair \\spad{[r,f(x)]},{} where \\spad{r} is a positive rational number and \\spad{f(x)} is a Laurent series. This pair represents the Puiseux series \\spad{f(x\\^r)}.")) (|integrate| (($ $ (|Variable| |#2|)) "\\spad{integrate(f(x))} returns an anti-derivative of the power series \\spad{f(x)} with constant coefficient 0. We may integrate a series when we can divide coefficients by integers.")) (|coerce| (($ (|UnivariatePuiseuxSeries| |#1| |#2| |#3|)) "\\spad{coerce(f)} converts a Puiseux series to a general power series.") (($ (|Variable| |#2|)) "\\spad{coerce(var)} converts the series variable \\spad{var} into a Puiseux series."))) -(((|commutative| "*") |has| |#1| (|CommutativeRing|)) (|noZeroDivisors| |has| |#1| (|IntegralDomain|)) (|canonicalUnitNormal| |has| |#1| . #1=((|Field|))) (|canonicalsClosed| |has| |#1| . #1#) (|rightUnitary| . T) (|leftUnitary| . T) (|unitsKnown| . T)) +(((|commutative| "*") |has| |#1| (|CommutativeRing|)) (|noZeroDivisors| |has| |#1| (|IntegralDomain|)) (|canonicalUnitNormal| |has| |#1| (|Field|))) (#1=(|HasCategory| |#1| (QUOTE (|Algebra| #2=(|Fraction| #3=(|Integer|))))) #4=(|HasCategory| |#1| (QUOTE (|IntegralDomain|))) #5=(|HasCategory| |#1| (QUOTE (|CommutativeRing|))) (OR #5# #4#) (|HasCategory| |#1| (QUOTE (|CharacteristicNonZero|))) (|HasCategory| |#1| (QUOTE (|CharacteristicZero|))) (AND (|HasCategory| |#1| (QUOTE (|PartialDifferentialRing| #6=(|Symbol|)))) #7=(|HasSignature| |#1| (|%list| (QUOTE *) (|%list| #8=(|devaluate| |#1|) #9=(|%list| (QUOTE |Fraction|) (QUOTE #3#)) #8#)))) #7# (|HasCategory| #2# (QUOTE (|SemiGroup|))) #10=(|HasCategory| |#1| (QUOTE (|Field|))) (OR #5# #10# #4#) (OR #10# #4#) (AND #11=(|HasSignature| |#1| (|%list| (QUOTE **) (|%list| #8# #8# #9#))) (|HasSignature| |#1| (|%list| (QUOTE |coerce|) (|%list| #8# #12=(QUOTE #6#))))) #11# (OR (AND #1# (|HasCategory| |#1| (QUOTE (|AlgebraicallyClosedFunctionSpace| #3#))) (|HasCategory| |#1| (QUOTE (|PrimitiveFunctionCategory|))) (|HasCategory| |#1| (QUOTE (|TranscendentalFunctionCategory|)))) (AND #1# (|HasSignature| |#1| (|%list| (QUOTE |integrate|) (|%list| #8# #8# #12#))) (|HasSignature| |#1| (|%list| (QUOTE |variables|) (|%list| (|%list| (QUOTE |List|) #12#) #8#)))))) (|GeneralSparseTable| |Key| |Entry| |Tbl| |dent|) ((|constructor| (NIL "A sparse table has a default entry,{} which is returned if no other value has been explicitly stored for a key."))) @@ -1610,7 +1614,7 @@ NIL ((AND #1=(|HasCategory| |#4| (QUOTE (|SetCategory|))) (|HasCategory| |#4| (|%list| (QUOTE |Evalable|) #2=(|devaluate| |#4|)))) (|HasCategory| |#4| (QUOTE (|ConvertibleTo| (|InputForm|)))) #3=(|HasCategory| |#4| (QUOTE (|BasicType|))) (|HasCategory| |#1| (QUOTE (|IntegralDomain|))) (|HasCategory| |#3| (QUOTE (|Finite|))) (|HasCategory| |#4| (QUOTE (|CoercibleTo| (|OutputForm|)))) #1# (AND #3# #4=(|HasCategory| $ (|%list| (QUOTE |FiniteAggregate|) #2#))) #4#) (|Pi|) ((|constructor| (NIL "\\indented{1}{Symbolic fractions in \\%\\spad{pi} with integer coefficients;} \\indented{1}{The point for using \\spad{Pi} as the default domain for those fractions} \\indented{1}{is that \\spad{Pi} is coercible to the float types,{} and not Expression.} Date Created: 21 Feb 1990 Date Last Updated: 12 Mai 1992")) (|pi| (($) "\\spad{pi()} returns the symbolic \\%\\spad{pi}."))) -((|canonicalsClosed| . T) (|canonicalUnitNormal| . T) (|noZeroDivisors| . T) ((|commutative| "*") . T) (|rightUnitary| . T) (|leftUnitary| . T) (|unitsKnown| . T)) +((|canonicalUnitNormal| . T) (|noZeroDivisors| . T) ((|commutative| "*") . T)) NIL (|HasAst|) ((|constructor| (NIL "This domain represents a `has' expression.")) (|rhs| (((|SpadAst|) $) "\\spad{rhs(e)} returns the right hand side of the case expression `e'.")) (|lhs| (((|SpadAst|) $) "\\spad{lhs(e)} returns the left hand side of the has expression `e'."))) @@ -1626,12 +1630,12 @@ NIL NIL (|HomogeneousDistributedMultivariatePolynomial| |vl| R) ((|constructor| (NIL "\\indented{2}{This type supports distributed multivariate polynomials} whose variables are from a user specified list of symbols. The coefficient ring may be non commutative,{} but the variables are assumed to commute. The term ordering is total degree ordering refined by reverse lexicographic ordering with respect to the position that the variables appear in the list of variables parameter.")) (|reorder| (($ $ (|List| (|Integer|))) "\\spad{reorder(p, perm)} applies the permutation perm to the variables in a polynomial and returns the new correctly ordered polynomial"))) -(((|commutative| "*") |has| |#2| (|CommutativeRing|)) (|noZeroDivisors| |has| |#2| (|IntegralDomain|)) (|canonicalUnitNormal| |has| |#2| (ATTRIBUTE |canonicalUnitNormal|)) (|leftUnitary| . T) (|rightUnitary| . T) (|unitsKnown| . T)) -(#1=(|HasCategory| |#2| (QUOTE (|PolynomialFactorizationExplicit|))) (OR #2=(|HasCategory| |#2| (QUOTE (|CommutativeRing|))) #3=(|HasCategory| |#2| (QUOTE (|GcdDomain|))) #4=(|HasCategory| |#2| (QUOTE (|IntegralDomain|))) #1#) (OR #3# #4# #1#) (OR #3# #1#) #4# #2# (OR #2# #4#) (AND (|HasCategory| |#2| #5=(QUOTE (|PatternMatchable| #6=(|Float|)))) (|HasCategory| #7=(|OrderedVariableList| |#1|) #5#)) (AND (|HasCategory| |#2| #8=(QUOTE (|PatternMatchable| #9=(|Integer|)))) (|HasCategory| #7# #8#)) (AND (|HasCategory| |#2| #10=(QUOTE (|ConvertibleTo| (|Pattern| #6#)))) (|HasCategory| #7# #10#)) (AND (|HasCategory| |#2| #11=(QUOTE (|ConvertibleTo| (|Pattern| #9#)))) (|HasCategory| #7# #11#)) (AND (|HasCategory| |#2| #12=(QUOTE (|ConvertibleTo| (|InputForm|)))) (|HasCategory| #7# #12#)) (|HasCategory| |#2| (QUOTE (|LinearlyExplicitRingOver| #9#))) (|HasCategory| |#2| (QUOTE (|CharacteristicZero|))) #13=(|HasCategory| |#2| #14=(QUOTE (|CharacteristicNonZero|))) #15=(|HasCategory| |#2| (QUOTE (|Algebra| #16=(|Fraction| #9#)))) (|HasCategory| |#2| (QUOTE (|RetractableTo| #9#))) (OR #15# #17=(|HasCategory| |#2| (QUOTE (|RetractableTo| #16#)))) #17# (|HasCategory| |#2| (QUOTE (|Field|))) (|HasAttribute| |#2| (QUOTE |canonicalUnitNormal|)) #3# #18=(AND #1# (|HasCategory| $ #14#)) (OR #18# #13#)) +(((|commutative| "*") |has| |#2| (|CommutativeRing|)) (|noZeroDivisors| |has| |#2| (|IntegralDomain|)) (|canonicalUnitNormal| |has| |#2| (ATTRIBUTE |canonicalUnitNormal|))) +(#1=(|HasCategory| |#2| (QUOTE (|PolynomialFactorizationExplicit|))) (OR #2=(|HasCategory| |#2| (QUOTE (|CommutativeRing|))) #3=(|HasCategory| |#2| (QUOTE (|GcdDomain|))) #4=(|HasCategory| |#2| (QUOTE (|IntegralDomain|))) #1#) (OR #3# #4# #1#) (OR #3# #1#) #4# #2# (OR #2# #4#) (AND (|HasCategory| |#2| #5=(QUOTE (|PatternMatchable| #6=(|Float|)))) (|HasCategory| #7=(|OrderedVariableList| |#1|) #5#)) (AND (|HasCategory| |#2| #8=(QUOTE (|PatternMatchable| #9=(|Integer|)))) (|HasCategory| #7# #8#)) (AND (|HasCategory| |#2| #10=(QUOTE (|ConvertibleTo| (|Pattern| #6#)))) (|HasCategory| #7# #10#)) (AND (|HasCategory| |#2| #11=(QUOTE (|ConvertibleTo| (|Pattern| #9#)))) (|HasCategory| #7# #11#)) (AND (|HasCategory| |#2| #12=(QUOTE (|ConvertibleTo| (|InputForm|)))) (|HasCategory| #7# #12#)) (|HasCategory| |#2| (QUOTE (|LinearlyExplicitRingOver| #9#))) #13=(|HasCategory| |#2| (QUOTE (|Algebra| #14=(|Fraction| #9#)))) #15=(|HasCategory| |#2| #16=(QUOTE (|CharacteristicNonZero|))) (|HasCategory| |#2| (QUOTE (|CharacteristicZero|))) (|HasCategory| |#2| (QUOTE (|RetractableTo| #9#))) (OR #13# #17=(|HasCategory| |#2| (QUOTE (|RetractableTo| #14#)))) #17# (|HasCategory| |#2| (QUOTE (|Field|))) (|HasAttribute| |#2| (QUOTE |canonicalUnitNormal|)) #3# #18=(AND #1# (|HasCategory| $ #16#)) (OR #18# #15#)) (|HomogeneousDirectProduct| |dim| S) ((|constructor| (NIL "\\indented{2}{This type represents the finite direct or cartesian product of an} underlying ordered component type. The vectors are ordered first by the sum of their components,{} and then refined using a reverse lexicographic ordering. This type is a suitable third argument for \\spadtype{GeneralDistributedMultivariatePolynomial}."))) -((|rightUnitary| |has| |#2| . #1=((|Ring|))) (|leftUnitary| |has| |#2| . #1#) (|unitsKnown| |has| |#2| (ATTRIBUTE |unitsKnown|))) -((OR (AND #1=(|HasCategory| |#2| (QUOTE (|AbelianGroup|))) #2=(|HasCategory| |#2| (|%list| (QUOTE |Evalable|) #3=(|devaluate| |#2|)))) (AND #4=(|HasCategory| |#2| (QUOTE (|AbelianMonoid|))) #2#) (AND #5=(|HasCategory| |#2| (QUOTE (|AbelianSemiGroup|))) #2#) (AND #6=(|HasCategory| |#2| (QUOTE (|CancellationAbelianMonoid|))) #2#) (AND #7=(|HasCategory| |#2| (QUOTE (|CommutativeRing|))) #2#) (AND #8=(|HasCategory| |#2| (QUOTE (|DifferentialRing|))) #2#) (AND #9=(|HasCategory| |#2| (QUOTE (|Field|))) #2#) (AND #10=(|HasCategory| |#2| (QUOTE (|Finite|))) #2#) (AND #11=(|HasCategory| |#2| (QUOTE (|Monoid|))) #2#) (AND #12=(|HasCategory| |#2| (QUOTE (|OrderedAbelianMonoidSup|))) #2#) (AND #13=(|HasCategory| |#2| #14=(QUOTE (|OrderedSet|))) #2#) (AND #15=(|HasCategory| |#2| (QUOTE (|PartialDifferentialRing| #16=(|Symbol|)))) #2#) (AND #17=(|HasCategory| |#2| (QUOTE (|Ring|))) #2#) #18=(AND #19=(|HasCategory| |#2| (QUOTE (|SetCategory|))) #2#)) (|HasCategory| |#2| (QUOTE (|CoercibleTo| (|OutputForm|)))) #9# (OR #7# #9# #17#) (OR #7# #9#) #1# #17# #11# #12# (OR #12# #13#) #13# #10# (OR (AND #7# #20=(|HasCategory| |#2| (QUOTE (|LinearlyExplicitRingOver| #21=(|Integer|))))) (AND #8# #20#) (AND #9# #20#) (AND #20# #15#) #22=(AND #20# #17#)) #15# (OR #1# #4# #5# #23=(|HasCategory| |#2| (QUOTE (|BasicType|))) #6# #7# #8# #9# #10# #11# #12# #13# #15# #17# #19#) (OR #1# #4# #5# #6# #7# #8# #9# #10# #11# #12# #13# #15# #17# #19#) (OR #1# #4# #5# #6# #7# #8# #9# #15# #17#) (OR #1# #4# #6# #7# #8# #9# #15# #17#) (OR #1# #6# #7# #8# #9# #15# #17#) (OR #1# #7# #8# #9# #15# #17#) (OR #8# #15# #17#) #8# (OR #8# #24=(AND (|HasCategory| |#2| (QUOTE (|DifferentialSpace|))) #17#)) (OR #25=(AND (|HasCategory| |#2| (QUOTE (|PartialDifferentialSpace| #16#))) #17#) #15#) #19# (OR (AND #1# #26=(|HasCategory| |#2| (QUOTE (|RetractableTo| (|Fraction| #21#))))) (AND #4# #26#) (AND #5# #26#) (AND #6# #26#) (AND #7# #26#) (AND #8# #26#) (AND #9# #26#) (AND #10# #26#) (AND #11# #26#) (AND #12# #26#) (AND #13# #26#) (AND #15# #26#) (AND #26# #17#) #27=(AND #26# #19#)) (OR #28=(AND #1# #29=(|HasCategory| |#2| (QUOTE (|RetractableTo| #21#)))) #30=(AND #4# #29#) #31=(AND #5# #29#) #32=(AND #6# #29#) #33=(AND #7# #29#) #34=(AND #8# #29#) #35=(AND #12# #29#) #36=(AND #13# #29#) #37=(AND #15# #29#) #38=(AND #29# #19#) #39=(AND #9# #29#) #40=(AND #10# #29#) #41=(AND #11# #29#) #17#) (OR #28# #30# #31# #32# #33# #34# #35# #36# #37# #38# #39# #40# #41# (AND #29# #17#)) #23# (|HasCategory| #21# #14#) #22# #24# #25# (OR #38# #17#) #38# #27# (|HasAttribute| |#2| (QUOTE |unitsKnown|)) (AND #8# #17#) (AND #15# #17#) #7# #4# #6# #5# #18# (AND #23# (|HasCategory| $ (|%list| (QUOTE |FiniteAggregate|) #3#))) (|HasCategory| $ (|%list| (QUOTE |ShallowlyMutableAggregate|) #3#))) +NIL +((OR (AND #1=(|HasCategory| |#2| (QUOTE (|AbelianGroup|))) #2=(|HasCategory| |#2| (|%list| (QUOTE |Evalable|) #3=(|devaluate| |#2|)))) (AND #4=(|HasCategory| |#2| (QUOTE (|AbelianMonoid|))) #2#) (AND #5=(|HasCategory| |#2| (QUOTE (|AbelianSemiGroup|))) #2#) (AND #6=(|HasCategory| |#2| (QUOTE (|CancellationAbelianMonoid|))) #2#) (AND #7=(|HasCategory| |#2| (QUOTE (|CommutativeRing|))) #2#) (AND #8=(|HasCategory| |#2| (QUOTE (|DifferentialRing|))) #2#) (AND #9=(|HasCategory| |#2| (QUOTE (|Field|))) #2#) (AND #10=(|HasCategory| |#2| (QUOTE (|Finite|))) #2#) (AND #11=(|HasCategory| |#2| (QUOTE (|Monoid|))) #2#) (AND #12=(|HasCategory| |#2| (QUOTE (|OrderedAbelianMonoidSup|))) #2#) (AND #13=(|HasCategory| |#2| #14=(QUOTE (|OrderedSet|))) #2#) (AND #15=(|HasCategory| |#2| (QUOTE (|PartialDifferentialRing| #16=(|Symbol|)))) #2#) (AND #17=(|HasCategory| |#2| (QUOTE (|Ring|))) #2#) #18=(AND #19=(|HasCategory| |#2| (QUOTE (|SetCategory|))) #2#)) (|HasCategory| |#2| (QUOTE (|CoercibleTo| (|OutputForm|)))) #9# (OR #7# #9# #17#) (OR #7# #9#) #1# #17# #11# #12# (OR #12# #13#) #13# #10# (OR (AND #7# #20=(|HasCategory| |#2| (QUOTE (|LinearlyExplicitRingOver| #21=(|Integer|))))) (AND #8# #20#) (AND #9# #20#) (AND #20# #15#) #22=(AND #20# #17#)) #15# (OR #1# #4# #5# #23=(|HasCategory| |#2| (QUOTE (|BasicType|))) #6# #7# #8# #9# #10# #11# #12# #13# #15# #17# #19#) (OR #1# #4# #5# #6# #7# #8# #9# #10# #11# #12# #13# #15# #17# #19#) (OR #1# #4# #5# #6# #7# #8# #9# #15# #17#) (OR #1# #4# #6# #7# #8# #9# #15# #17#) (OR #1# #6# #7# #8# #9# #15# #17#) (OR #1# #7# #8# #9# #15# #17#) (OR #8# #15# #17#) #8# (OR #8# #24=(AND (|HasCategory| |#2| (QUOTE (|DifferentialSpace|))) #17#)) (OR #25=(AND (|HasCategory| |#2| (QUOTE (|PartialDifferentialSpace| #16#))) #17#) #15#) #19# (OR (AND #1# #26=(|HasCategory| |#2| (QUOTE (|RetractableTo| (|Fraction| #21#))))) (AND #4# #26#) (AND #5# #26#) (AND #6# #26#) (AND #7# #26#) (AND #8# #26#) (AND #9# #26#) (AND #10# #26#) (AND #11# #26#) (AND #12# #26#) (AND #13# #26#) (AND #15# #26#) (AND #26# #17#) #27=(AND #26# #19#)) (OR #28=(AND #1# #29=(|HasCategory| |#2| (QUOTE (|RetractableTo| #21#)))) #30=(AND #4# #29#) #31=(AND #5# #29#) #32=(AND #6# #29#) #33=(AND #7# #29#) #34=(AND #8# #29#) #35=(AND #12# #29#) #36=(AND #13# #29#) #37=(AND #15# #29#) #38=(AND #29# #19#) #39=(AND #9# #29#) #40=(AND #10# #29#) #41=(AND #11# #29#) #17#) (OR #28# #30# #31# #32# #33# #34# #35# #36# #37# #38# #39# #40# #41# (AND #29# #17#)) #23# (|HasCategory| #21# #14#) #22# #24# #25# (OR #38# #17#) #38# #27# (AND #8# #17#) (AND #15# #17#) #7# #4# #6# #5# #18# (AND #23# (|HasCategory| $ (|%list| (QUOTE |FiniteAggregate|) #3#))) (|HasCategory| $ (|%list| (QUOTE |ShallowlyMutableAggregate|) #3#))) (|HeadAst|) ((|constructor| (NIL "This domain represents the header of a definition.")) (|parameters| (((|List| (|ParameterAst|)) $) "\\spad{parameters(h)} gives the parameters specified in the definition header `h'.")) (|name| (((|Identifier|) $) "\\spad{name(h)} returns the name of the operation defined defined.")) (|headAst| (($ (|Identifier|) (|List| (|ParameterAst|))) "\\spad{headAst(f,[x1,..,xn])} constructs a function definition header."))) NIL @@ -1650,8 +1654,8 @@ NIL NIL (|HexadecimalExpansion|) ((|constructor| (NIL "This domain allows rational numbers to be presented as repeating hexadecimal expansions.")) (|hex| (($ (|Fraction| (|Integer|))) "\\spad{hex(r)} converts a rational number to a hexadecimal expansion.")) (|fractionPart| (((|Fraction| (|Integer|)) $) "\\spad{fractionPart(h)} returns the fractional part of a hexadecimal expansion."))) -((|canonicalsClosed| . T) (|canonicalUnitNormal| . T) (|noZeroDivisors| . T) ((|commutative| "*") . T) (|rightUnitary| . T) (|leftUnitary| . T) (|unitsKnown| . T)) -(#1=(|HasCategory| #2=(|Integer|) (QUOTE (|PolynomialFactorizationExplicit|))) (|HasCategory| #2# (QUOTE (|RetractableTo| #3=(|Symbol|)))) #4=(|HasCategory| #2# #5=(QUOTE (|CharacteristicNonZero|))) (|HasCategory| #2# (QUOTE (|CharacteristicZero|))) (|HasCategory| #2# (QUOTE (|ConvertibleTo| (|InputForm|)))) (|HasCategory| #2# (QUOTE (|RealConstant|))) #6=(|HasCategory| #2# (QUOTE (|OrderedIntegralDomain|))) #7=(|HasCategory| #2# (QUOTE (|OrderedSet|))) (OR #6# #7#) (|HasCategory| #2# (QUOTE (|RetractableTo| #2#))) (|HasCategory| #2# (QUOTE (|StepThrough|))) (|HasCategory| #2# (QUOTE (|PatternMatchable| #8=(|Float|)))) (|HasCategory| #2# (QUOTE (|PatternMatchable| #2#))) (|HasCategory| #2# (QUOTE (|ConvertibleTo| (|Pattern| #8#)))) (|HasCategory| #2# (QUOTE (|ConvertibleTo| (|Pattern| #2#)))) (|HasCategory| #2# (QUOTE (|DifferentialSpace|))) (|HasCategory| #2# (QUOTE (|PartialDifferentialSpace| #3#))) (|HasCategory| #2# (QUOTE (|DifferentialRing|))) (|HasCategory| #2# (QUOTE (|PartialDifferentialRing| #3#))) (|HasCategory| #2# (QUOTE (|InnerEvalable| #3# #2#))) (|HasCategory| #2# (QUOTE (|Evalable| #2#))) (|HasCategory| #2# (QUOTE (|Eltable| #2# #2#))) (|HasCategory| #2# (QUOTE (|EuclideanDomain|))) (|HasCategory| #2# (QUOTE (|IntegerNumberSystem|))) (|HasCategory| #2# (QUOTE (|LinearlyExplicitRingOver| #2#))) #9=(AND (|HasCategory| $ #5#) #1#) (OR #9# #4#)) +((|canonicalUnitNormal| . T) (|noZeroDivisors| . T) ((|commutative| "*") . T)) +(#1=(|HasCategory| #2=(|Integer|) (QUOTE (|PolynomialFactorizationExplicit|))) (|HasCategory| #2# (QUOTE (|RetractableTo| #3=(|Symbol|)))) #4=(|HasCategory| #2# #5=(QUOTE (|CharacteristicNonZero|))) (|HasCategory| #2# (QUOTE (|CharacteristicZero|))) (|HasCategory| #2# (QUOTE (|ConvertibleTo| (|InputForm|)))) (|HasCategory| #2# (QUOTE (|RealConstant|))) #6=(|HasCategory| #2# (QUOTE (|OrderedIntegralDomain|))) #7=(|HasCategory| #2# (QUOTE (|OrderedSet|))) (OR #6# #7#) (|HasCategory| #2# (QUOTE (|RetractableTo| #2#))) (|HasCategory| #2# (QUOTE (|StepThrough|))) (|HasCategory| #2# (QUOTE (|PatternMatchable| #8=(|Float|)))) (|HasCategory| #2# (QUOTE (|PatternMatchable| #2#))) (|HasCategory| #2# (QUOTE (|ConvertibleTo| (|Pattern| #8#)))) (|HasCategory| #2# (QUOTE (|ConvertibleTo| (|Pattern| #2#)))) (|HasCategory| #2# (QUOTE (|PartialDifferentialSpace| #3#))) (|HasCategory| #2# (QUOTE (|DifferentialSpace|))) (|HasCategory| #2# (QUOTE (|DifferentialRing|))) (|HasCategory| #2# (QUOTE (|PartialDifferentialRing| #3#))) (|HasCategory| #2# (QUOTE (|InnerEvalable| #3# #2#))) (|HasCategory| #2# (QUOTE (|Evalable| #2#))) (|HasCategory| #2# (QUOTE (|Eltable| #2# #2#))) (|HasCategory| #2# (QUOTE (|EuclideanDomain|))) (|HasCategory| #2# (QUOTE (|IntegerNumberSystem|))) (|HasCategory| #2# (QUOTE (|LinearlyExplicitRingOver| #2#))) #9=(AND (|HasCategory| $ #5#) #1#) (OR #9# #4#)) (|HomogeneousAggregate&| A S) ((|constructor| (NIL "\\indented{2}{A homogeneous aggregate is an aggregate of elements all of the} \\indented{2}{same type,{} and is functorial in stored elements..} In the current system,{} all aggregates are homogeneous. Two attributes characterize classes of aggregates."))) NIL @@ -1682,7 +1686,7 @@ NIL NIL (|InnerAlgebraicNumber|) ((|constructor| (NIL "Algebraic closure of the rational numbers.")) (|norm| (($ $ (|List| (|Kernel| $))) "\\spad{norm(f,l)} computes the norm of the algebraic number \\spad{f} with respect to the extension generated by kernels \\spad{l}") (($ $ (|Kernel| $)) "\\spad{norm(f,k)} computes the norm of the algebraic number \\spad{f} with respect to the extension generated by kernel \\spad{k}") (((|SparseUnivariatePolynomial| $) (|SparseUnivariatePolynomial| $) (|List| (|Kernel| $))) "\\spad{norm(p,l)} computes the norm of the polynomial \\spad{p} with respect to the extension generated by kernels \\spad{l}") (((|SparseUnivariatePolynomial| $) (|SparseUnivariatePolynomial| $) (|Kernel| $)) "\\spad{norm(p,k)} computes the norm of the polynomial \\spad{p} with respect to the extension generated by kernel \\spad{k}")) (|trueEqual| (((|Boolean|) $ $) "\\spad{trueEqual(x,y)} tries to determine if the two numbers are equal")) (|reduce| (($ $) "\\spad{reduce(f)} simplifies all the unreduced algebraic numbers present in \\spad{f} by applying their defining relations.")) (|denom| (((|SparseMultivariatePolynomial| (|Integer|) (|Kernel| $)) $) "\\spad{denom(f)} returns the denominator of \\spad{f} viewed as a polynomial in the kernels over \\spad{Z}.")) (|numer| (((|SparseMultivariatePolynomial| (|Integer|) (|Kernel| $)) $) "\\spad{numer(f)} returns the numerator of \\spad{f} viewed as a polynomial in the kernels over \\spad{Z}."))) -((|canonicalsClosed| . T) (|canonicalUnitNormal| . T) (|noZeroDivisors| . T) ((|commutative| "*") . T) (|rightUnitary| . T) (|leftUnitary| . T) (|unitsKnown| . T)) +((|canonicalUnitNormal| . T) (|noZeroDivisors| . T) ((|commutative| "*") . T)) ((|HasCategory| $ (QUOTE (|Ring|))) (|HasCategory| $ (QUOTE (|RetractableTo| (|Integer|))))) (|IndexedOneDimensionalArray| S |mn|) ((|constructor| (NIL "\\indented{1}{Author Micheal Monagan \\spad{Aug/87}} This is the basic one dimensional array data type."))) @@ -1782,7 +1786,7 @@ NIL NIL (|InnerFiniteField| |p| |n|) ((|constructor| (NIL "InnerFiniteField(\\spad{p},{}\\spad{n}) implements finite fields with \\spad{p**n} elements where \\spad{p} is assumed prime but does not check. For a version which checks that \\spad{p} is prime,{} see \\spadtype{FiniteField}."))) -((|canonicalsClosed| . T) (|canonicalUnitNormal| . T) (|noZeroDivisors| . T) ((|commutative| "*") . T) (|rightUnitary| . T) (|leftUnitary| . T) (|unitsKnown| . T)) +((|canonicalUnitNormal| . T) (|noZeroDivisors| . T) ((|commutative| "*") . T)) ((OR #1=(|HasCategory| #2=(|InnerPrimeField| |#1|) (QUOTE (|CharacteristicNonZero|))) #3=(|HasCategory| #2# (QUOTE (|Finite|)))) (|HasCategory| #2# (QUOTE (|CharacteristicZero|))) #3# #1#) (|InnerMatrixLinearAlgebraFunctions| R |Row| |Col| M) ((|constructor| (NIL "\\spadtype{InnerMatrixLinearAlgebraFunctions} is an internal package which provides standard linear algebra functions on domains in \\spad{MatrixCategory}")) (|inverse| (((|Union| |#4| "failed") |#4|) "\\spad{inverse(m)} returns the inverse of the matrix \\spad{m}. If the matrix is not invertible,{} \"failed\" is returned. Error: if the matrix is not square.")) (|generalizedInverse| ((|#4| |#4|) "\\spad{generalizedInverse(m)} returns the generalized (Moore--Penrose) inverse of the matrix \\spad{m},{} \\spadignore{i.e.} the matrix \\spad{h} such that m*h*m=h,{} h*m*h=m,{} m*h and h*m are both symmetric matrices.")) (|determinant| ((|#1| |#4|) "\\spad{determinant(m)} returns the determinant of the matrix \\spad{m}. an error message is returned if the matrix is not square.")) (|nullSpace| (((|List| |#3|) |#4|) "\\spad{nullSpace(m)} returns a basis for the null space of the matrix \\spad{m}.")) (|nullity| (((|NonNegativeInteger|) |#4|) "\\spad{nullity(m)} returns the mullity of the matrix \\spad{m}. This is the dimension of the null space of the matrix \\spad{m}.")) (|rank| (((|NonNegativeInteger|) |#4|) "\\spad{rank(m)} returns the rank of the matrix \\spad{m}.")) (|rowEchelon| ((|#4| |#4|) "\\spad{rowEchelon(m)} returns the row echelon form of the matrix \\spad{m}."))) @@ -1878,11 +1882,11 @@ NIL NIL (|IntegerNumberSystem|) ((|constructor| (NIL "An \\spad{IntegerNumberSystem} is a model for the integers.")) (|invmod| (($ $ $) "\\spad{invmod(a,b)},{} \\spad{0<=a<b>1},{} \\spad{(a,b)=1} means \\spad{1/a mod b}.")) (|powmod| (($ $ $ $) "\\spad{powmod(a,b,p)},{} \\spad{0<=a,b<p>1},{} means \\spad{a**b mod p}.")) (|mulmod| (($ $ $ $) "\\spad{mulmod(a,b,p)},{} \\spad{0<=a,b<p>1},{} means \\spad{a*b mod p}.")) (|submod| (($ $ $ $) "\\spad{submod(a,b,p)},{} \\spad{0<=a,b<p>1},{} means \\spad{a-b mod p}.")) (|addmod| (($ $ $ $) "\\spad{addmod(a,b,p)},{} \\spad{0<=a,b<p>1},{} means \\spad{a+b mod p}.")) (|mask| (($ $) "\\spad{mask(n)} returns \\spad{2**n-1} (an \\spad{n} bit mask).")) (|dec| (($ $) "\\spad{dec(x)} returns \\spad{x - 1}.")) (|inc| (($ $) "\\spad{inc(x)} returns \\spad{x + 1}.")) (|copy| (($ $) "\\spad{copy(n)} gives a copy of \\spad{n}.")) (|random| (($ $) "\\spad{random(a)} creates a random element from 0 to \\spad{a-1}.") (($) "\\spad{random()} creates a random element.")) (|rationalIfCan| (((|Union| (|Fraction| (|Integer|)) "failed") $) "\\spad{rationalIfCan(n)} creates a rational number,{} or returns \"failed\" if this is not possible.")) (|rational| (((|Fraction| (|Integer|)) $) "\\spad{rational(n)} creates a rational number (see \\spadtype{Fraction Integer})..")) (|rational?| (((|Boolean|) $) "\\spad{rational?(n)} tests if \\spad{n} is a rational number (see \\spadtype{Fraction Integer}).")) (|symmetricRemainder| (($ $ $) "\\spad{symmetricRemainder(a,b)} (where \\spad{b > 1}) yields \\spad{r} where \\spad{ -b/2 <= r < b/2 }.")) (|positiveRemainder| (($ $ $) "\\spad{positiveRemainder(a,b)} (where \\spad{b > 1}) yields \\spad{r} where \\spad{0 <= r < b} and \\spad{r == a rem b}.")) (|bit?| (((|Boolean|) $ $) "\\spad{bit?(n,i)} returns \\spad{true} if and only if \\spad{i}-th bit of \\spad{n} is a 1.")) (|shift| (($ $ $) "\\spad{shift(a,i)} shift \\spad{a} by \\spad{i} digits.")) (|length| (($ $) "\\spad{length(a)} length of \\spad{a} in digits.")) (|base| (($) "\\spad{base()} returns the base for the operations of \\spad{IntegerNumberSystem}.")) (|multiplicativeValuation| ((|attribute|) "euclideanSize(a*b) returns \\spad{euclideanSize(a)*euclideanSize(b)}.")) (|even?| (((|Boolean|) $) "\\spad{even?(n)} returns \\spad{true} if and only if \\spad{n} is even.")) (|odd?| (((|Boolean|) $) "\\spad{odd?(n)} returns \\spad{true} if and only if \\spad{n} is odd."))) -((|canonicalUnitNormal| . T) (|multiplicativeValuation| . T) (|noZeroDivisors| . T) ((|commutative| "*") . T) (|rightUnitary| . T) (|leftUnitary| . T) (|unitsKnown| . T)) +((|canonicalUnitNormal| . T) (|multiplicativeValuation| . T) (|noZeroDivisors| . T) ((|commutative| "*") . T)) NIL (|Integer|) -((|constructor| (NIL "\\spadtype{Integer} provides the domain of arbitrary precision integers.")) (|noetherian| ((|attribute|) "ascending chain condition on ideals.")) (|canonicalsClosed| ((|attribute|) "two positives multiply to give positive.")) (|canonical| ((|attribute|) "mathematical equality is data structure equality."))) -((|noetherian| . T) (|canonicalsClosed| . T) (|canonical| . T) (|canonicalUnitNormal| . T) (|multiplicativeValuation| . T) (|noZeroDivisors| . T) ((|commutative| "*") . T) (|rightUnitary| . T) (|leftUnitary| . T) (|unitsKnown| . T)) +((|constructor| (NIL "\\spadtype{Integer} provides the domain of arbitrary precision integers.")) (|canonical| ((|attribute|) "mathematical equality is data structure equality."))) +((|canonical| . T) (|canonicalUnitNormal| . T) (|multiplicativeValuation| . T) (|noZeroDivisors| . T) ((|commutative| "*") . T)) NIL (|Int16|) ((|constructor| (NIL "This domain is a datatype for (signed) integer values of precision 16 bits."))) @@ -1918,15 +1922,15 @@ NIL NIL (|IntervalCategory| R) ((|constructor| (NIL "\\indented{1}{+ Author: Mike Dewar} + Date Created: November 1996 + Date Last Updated: + Basic Functions: + Related Constructors: + Also See: + AMS Classifications: + Keywords: + References: + Description: + This category implements of interval arithmetic and transcendental + functions over intervals.")) (|contains?| (((|Boolean|) $ |#1|) "\\spad{contains?(i,f)} returns \\spad{true} if \\axiom{\\spad{f}} is contained within the interval \\axiom{\\spad{i}},{} \\spad{false} otherwise.")) (|negative?| (((|Boolean|) $) "\\spad{negative?(u)} returns \\axiom{\\spad{true}} if every element of \\spad{u} is negative,{} \\axiom{\\spad{false}} otherwise.")) (|positive?| (((|Boolean|) $) "\\spad{positive?(u)} returns \\axiom{\\spad{true}} if every element of \\spad{u} is positive,{} \\axiom{\\spad{false}} otherwise.")) (|width| ((|#1| $) "\\spad{width(u)} returns \\axiom{sup(\\spad{u}) - inf(\\spad{u})}.")) (|sup| ((|#1| $) "\\spad{sup(u)} returns the supremum of \\axiom{\\spad{u}}.")) (|inf| ((|#1| $) "\\spad{inf(u)} returns the infinum of \\axiom{\\spad{u}}.")) (|qinterval| (($ |#1| |#1|) "\\spad{qinterval(inf,sup)} creates a new interval \\axiom{[\\spad{inf},{}\\spad{sup}]},{} without checking the ordering on the elements.")) (|interval| (($ (|Fraction| (|Integer|))) "\\spad{interval(f)} creates a new interval around \\spad{f}.") (($ |#1|) "\\spad{interval(f)} creates a new interval around \\spad{f}.") (($ |#1| |#1|) "\\spad{interval(inf,sup)} creates a new interval,{} either \\axiom{[\\spad{inf},{}\\spad{sup}]} if \\axiom{\\spad{inf} <= \\spad{sup}} or \\axiom{[\\spad{sup},{}in]} otherwise."))) -((|approximate| . T) (|noZeroDivisors| . T) ((|commutative| "*") . T) (|rightUnitary| . T) (|leftUnitary| . T) (|unitsKnown| . T)) +((|approximate| . T) (|noZeroDivisors| . T) ((|commutative| "*") . T)) NIL (|IntegralDomain&| S) -((|constructor| (NIL "The category of commutative integral domains,{} \\spadignore{i.e.} commutative rings with no zero divisors. \\blankline Conditional attributes: \\indented{2}{canonicalUnitNormal\\tab{20}the canonical field is the same for all associates} \\indented{2}{canonicalsClosed\\tab{20}the product of two canonicals is itself canonical}")) (|unit?| (((|Boolean|) $) "\\spad{unit?(x)} tests whether \\spad{x} is a unit,{} \\spadignore{i.e.} is invertible.")) (|associates?| (((|Boolean|) $ $) "\\spad{associates?(x,y)} tests whether \\spad{x} and \\spad{y} are associates,{} \\spadignore{i.e.} differ by a unit factor.")) (|unitCanonical| (($ $) "\\spad{unitCanonical(x)} returns \\spad{unitNormal(x).canonical}.")) (|unitNormal| (((|Record| (|:| |unit| $) (|:| |canonical| $) (|:| |associate| $)) $) "\\spad{unitNormal(x)} tries to choose a canonical element from the associate class of \\spad{x}. The attribute canonicalUnitNormal,{} if asserted,{} means that the \"canonical\" element is the same across all associates of \\spad{x} if \\spad{unitNormal(x) = [u,c,a]} then \\spad{u*c = x},{} \\spad{a*u = 1}.")) (|exquo| (((|Union| $ "failed") $ $) "\\spad{exquo(a,b)} either returns an element \\spad{c} such that \\spad{c*b=a} or \"failed\" if no such element can be found."))) +((|constructor| (NIL "The category of commutative integral domains,{} \\spadignore{i.e.} commutative rings with no zero divisors. \\blankline Conditional attributes: \\indented{2}{canonicalUnitNormal\\tab{20}the canonical field is the same for all associates}")) (|unit?| (((|Boolean|) $) "\\spad{unit?(x)} tests whether \\spad{x} is a unit,{} \\spadignore{i.e.} is invertible.")) (|associates?| (((|Boolean|) $ $) "\\spad{associates?(x,y)} tests whether \\spad{x} and \\spad{y} are associates,{} \\spadignore{i.e.} differ by a unit factor.")) (|unitCanonical| (($ $) "\\spad{unitCanonical(x)} returns \\spad{unitNormal(x).canonical}.")) (|unitNormal| (((|Record| (|:| |unit| $) (|:| |canonical| $) (|:| |associate| $)) $) "\\spad{unitNormal(x)} tries to choose a canonical element from the associate class of \\spad{x}. The attribute canonicalUnitNormal,{} if asserted,{} means that the \"canonical\" element is the same across all associates of \\spad{x} if \\spad{unitNormal(x) = [u,c,a]} then \\spad{u*c = x},{} \\spad{a*u = 1}.")) (|exquo| (((|Union| $ "failed") $ $) "\\spad{exquo(a,b)} either returns an element \\spad{c} such that \\spad{c*b=a} or \"failed\" if no such element can be found."))) NIL NIL (|IntegralDomain|) -((|constructor| (NIL "The category of commutative integral domains,{} \\spadignore{i.e.} commutative rings with no zero divisors. \\blankline Conditional attributes: \\indented{2}{canonicalUnitNormal\\tab{20}the canonical field is the same for all associates} \\indented{2}{canonicalsClosed\\tab{20}the product of two canonicals is itself canonical}")) (|unit?| (((|Boolean|) $) "\\spad{unit?(x)} tests whether \\spad{x} is a unit,{} \\spadignore{i.e.} is invertible.")) (|associates?| (((|Boolean|) $ $) "\\spad{associates?(x,y)} tests whether \\spad{x} and \\spad{y} are associates,{} \\spadignore{i.e.} differ by a unit factor.")) (|unitCanonical| (($ $) "\\spad{unitCanonical(x)} returns \\spad{unitNormal(x).canonical}.")) (|unitNormal| (((|Record| (|:| |unit| $) (|:| |canonical| $) (|:| |associate| $)) $) "\\spad{unitNormal(x)} tries to choose a canonical element from the associate class of \\spad{x}. The attribute canonicalUnitNormal,{} if asserted,{} means that the \"canonical\" element is the same across all associates of \\spad{x} if \\spad{unitNormal(x) = [u,c,a]} then \\spad{u*c = x},{} \\spad{a*u = 1}.")) (|exquo| (((|Union| $ "failed") $ $) "\\spad{exquo(a,b)} either returns an element \\spad{c} such that \\spad{c*b=a} or \"failed\" if no such element can be found."))) -((|noZeroDivisors| . T) ((|commutative| "*") . T) (|rightUnitary| . T) (|leftUnitary| . T) (|unitsKnown| . T)) +((|constructor| (NIL "The category of commutative integral domains,{} \\spadignore{i.e.} commutative rings with no zero divisors. \\blankline Conditional attributes: \\indented{2}{canonicalUnitNormal\\tab{20}the canonical field is the same for all associates}")) (|unit?| (((|Boolean|) $) "\\spad{unit?(x)} tests whether \\spad{x} is a unit,{} \\spadignore{i.e.} is invertible.")) (|associates?| (((|Boolean|) $ $) "\\spad{associates?(x,y)} tests whether \\spad{x} and \\spad{y} are associates,{} \\spadignore{i.e.} differ by a unit factor.")) (|unitCanonical| (($ $) "\\spad{unitCanonical(x)} returns \\spad{unitNormal(x).canonical}.")) (|unitNormal| (((|Record| (|:| |unit| $) (|:| |canonical| $) (|:| |associate| $)) $) "\\spad{unitNormal(x)} tries to choose a canonical element from the associate class of \\spad{x}. The attribute canonicalUnitNormal,{} if asserted,{} means that the \"canonical\" element is the same across all associates of \\spad{x} if \\spad{unitNormal(x) = [u,c,a]} then \\spad{u*c = x},{} \\spad{a*u = 1}.")) (|exquo| (((|Union| $ "failed") $ $) "\\spad{exquo(a,b)} either returns an element \\spad{c} such that \\spad{c*b=a} or \"failed\" if no such element can be found."))) +((|noZeroDivisors| . T) ((|commutative| "*") . T)) NIL (|ElementaryIntegration| R F) ((|constructor| (NIL "This package provides functions for integration,{} limited integration,{} extended integration and the risch differential equation for elemntary functions.")) (|lfextlimint| (((|Union| (|Record| (|:| |ratpart| |#2|) (|:| |coeff| |#2|)) #1="failed") |#2| (|Symbol|) (|Kernel| |#2|) (|List| (|Kernel| |#2|))) "\\spad{lfextlimint(f,x,k,[k1,...,kn])} returns functions \\spad{[h, c]} such that \\spad{dh/dx = f - c dk/dx}. Value \\spad{h} is looked for in a field containing \\spad{f} and \\spad{k1},{}...,{}kn (the \\spad{ki}'s must be logs).")) (|lfintegrate| (((|IntegrationResult| |#2|) |#2| (|Symbol|)) "\\spad{lfintegrate(f, x)} = \\spad{g} such that \\spad{dg/dx = f}.")) (|lfinfieldint| (((|Union| |#2| "failed") |#2| (|Symbol|)) "\\spad{lfinfieldint(f, x)} returns a function \\spad{g} such that \\spad{dg/dx = f} if \\spad{g} exists,{} \"failed\" otherwise.")) (|lflimitedint| (((|Union| (|Record| (|:| |mainpart| |#2|) (|:| |limitedlogs| (|List| (|Record| (|:| |coeff| |#2|) (|:| |logand| |#2|))))) "failed") |#2| (|Symbol|) (|List| |#2|)) "\\spad{lflimitedint(f,x,[g1,...,gn])} returns functions \\spad{[h,[[ci, gi]]]} such that the \\spad{gi}'s are among \\spad{[g1,...,gn]},{} and \\spad{d(h+sum(ci log(gi)))/dx = f},{} if possible,{} \"failed\" otherwise.")) (|lfextendedint| (((|Union| (|Record| (|:| |ratpart| |#2|) (|:| |coeff| |#2|)) #1#) |#2| (|Symbol|) |#2|) "\\spad{lfextendedint(f, x, g)} returns functions \\spad{[h, c]} such that \\spad{dh/dx = f - cg},{} if (\\spad{h},{} \\spad{c}) exist,{} \"failed\" otherwise."))) @@ -1974,7 +1978,7 @@ NIL NIL (|Interval| R) ((|constructor| (NIL "\\indented{1}{+ Author: Mike Dewar} + Date Created: November 1996 + Date Last Updated: + Basic Functions: + Related Constructors: + Also See: + AMS Classifications: + Keywords: + References: + Description: + This domain is an implementation of interval arithmetic and transcendental + functions over intervals."))) -((|approximate| . T) (|noZeroDivisors| . T) ((|commutative| "*") . T) (|rightUnitary| . T) (|leftUnitary| . T) (|unitsKnown| . T)) +((|approximate| . T) (|noZeroDivisors| . T) ((|commutative| "*") . T)) NIL (|IntegerSolveLinearPolynomialEquation|) ((|constructor| (NIL "This package provides the implementation for the \\spadfun{solveLinearPolynomialEquation} operation over the integers. It uses a lifting technique from the package GenExEuclid")) (|solveLinearPolynomialEquation| (((|Union| (|List| (|SparseUnivariatePolynomial| (|Integer|))) "failed") (|List| (|SparseUnivariatePolynomial| (|Integer|))) (|SparseUnivariatePolynomial| (|Integer|))) "\\spad{solveLinearPolynomialEquation([f1, ..., fn], g)} (where the \\spad{fi} are relatively prime to each other) returns a list of \\spad{ai} such that \\spad{g/prod fi = sum ai/fi} or returns \"failed\" if no such list of \\spad{ai}'s exists."))) @@ -2010,11 +2014,11 @@ NIL NIL (|InnerPAdicInteger| |p| |unBalanced?|) ((|constructor| (NIL "This domain implements Zp,{} the \\spad{p}-adic completion of the integers. This is an internal domain."))) -((|noZeroDivisors| . T) ((|commutative| "*") . T) (|rightUnitary| . T) (|leftUnitary| . T) (|unitsKnown| . T)) +((|noZeroDivisors| . T) ((|commutative| "*") . T)) NIL (|InnerPrimeField| |p|) ((|constructor| (NIL "InnerPrimeField(\\spad{p}) implements the field with \\spad{p} elements. Note: argument \\spad{p} MUST be a prime (this domain does not check). See \\spadtype{PrimeField} for a domain that does check."))) -((|canonicalsClosed| . T) (|canonicalUnitNormal| . T) (|noZeroDivisors| . T) ((|commutative| "*") . T) (|rightUnitary| . T) (|leftUnitary| . T) (|unitsKnown| . T)) +((|canonicalUnitNormal| . T) (|noZeroDivisors| . T) ((|commutative| "*") . T)) ((|HasCategory| $ (QUOTE (|CharacteristicZero|))) (|HasCategory| $ (QUOTE (|CharacteristicNonZero|))) (|HasCategory| $ (QUOTE (|Finite|)))) (|InternalPrintPackage|) ((|constructor| (NIL "A package to print strings without line-feed nor carriage-return.")) (|iprint| (((|Void|) (|String|)) "\\axiom{iprint(\\spad{s})} prints \\axiom{\\spad{s}} at the current position of the cursor."))) @@ -2022,7 +2026,7 @@ NIL NIL (|IntegrationResult| F) ((|constructor| (NIL "If a function \\spad{f} has an elementary integral \\spad{g},{} then \\spad{g} can be written in the form \\spad{g = h + c1 log(u1) + c2 log(u2) + ... + cn log(un)} where \\spad{h},{} which is in the same field than \\spad{f},{} is called the rational part of the integral,{} and \\spad{c1 log(u1) + ... cn log(un)} is called the logarithmic part of the integral. This domain manipulates integrals represented in that form,{} by keeping both parts separately. The logs are not explicitly computed.")) (|differentiate| ((|#1| $ (|Symbol|)) "\\spad{differentiate(ir,x)} differentiates \\spad{ir} with respect to \\spad{x}") ((|#1| $ (|Mapping| |#1| |#1|)) "\\spad{differentiate(ir,D)} differentiates \\spad{ir} with respect to the derivation \\spad{D}.")) (|integral| (($ |#1| (|Symbol|)) "\\spad{integral(f,x)} returns the formal integral of \\spad{f} with respect to \\spad{x}") (($ |#1| |#1|) "\\spad{integral(f,x)} returns the formal integral of \\spad{f} with respect to \\spad{x}")) (|elem?| (((|Boolean|) $) "\\spad{elem?(ir)} tests if an integration result is elementary over F?")) (|notelem| (((|List| (|Record| (|:| |integrand| |#1|) (|:| |intvar| |#1|))) $) "\\spad{notelem(ir)} returns the non-elementary part of an integration result")) (|logpart| (((|List| (|Record| (|:| |scalar| (|Fraction| (|Integer|))) (|:| |coeff| (|SparseUnivariatePolynomial| |#1|)) (|:| |logand| (|SparseUnivariatePolynomial| |#1|)))) $) "\\spad{logpart(ir)} returns the logarithmic part of an integration result")) (|ratpart| ((|#1| $) "\\spad{ratpart(ir)} returns the rational part of an integration result")) (|mkAnswer| (($ |#1| (|List| (|Record| (|:| |scalar| (|Fraction| (|Integer|))) (|:| |coeff| (|SparseUnivariatePolynomial| |#1|)) (|:| |logand| (|SparseUnivariatePolynomial| |#1|)))) (|List| (|Record| (|:| |integrand| |#1|) (|:| |intvar| |#1|)))) "\\spad{mkAnswer(r,l,ne)} creates an integration result from a rational part \\spad{r},{} a logarithmic part \\spad{l},{} and a non-elementary part \\spad{ne}."))) -((|leftUnitary| . T) (|rightUnitary| . T)) +NIL ((|HasCategory| |#1| (QUOTE (|PartialDifferentialRing| #1=(|Symbol|)))) (|HasCategory| |#1| (QUOTE (|RetractableTo| #1#)))) (|IntegrationResultFunctions2| E F) ((|constructor| (NIL "\\indented{1}{Internally used by the integration packages} Author: Manuel Bronstein Date Created: 1987 Date Last Updated: 12 August 1992 Keywords: integration.")) (|map| (((|Union| (|Record| (|:| |mainpart| |#2|) (|:| |limitedlogs| (|List| (|Record| (|:| |coeff| |#2|) (|:| |logand| |#2|))))) "failed") (|Mapping| |#2| |#1|) (|Union| (|Record| (|:| |mainpart| |#1|) (|:| |limitedlogs| (|List| (|Record| (|:| |coeff| |#1|) (|:| |logand| |#1|))))) "failed")) "\\spad{map(f,ufe)} \\undocumented") (((|Union| |#2| "failed") (|Mapping| |#2| |#1|) (|Union| |#1| "failed")) "\\spad{map(f,ue)} \\undocumented") (((|Union| (|Record| (|:| |ratpart| |#2|) (|:| |coeff| |#2|)) "failed") (|Mapping| |#2| |#1|) (|Union| (|Record| (|:| |ratpart| |#1|) (|:| |coeff| |#1|)) "failed")) "\\spad{map(f,ure)} \\undocumented") (((|IntegrationResult| |#2|) (|Mapping| |#2| |#1|) (|IntegrationResult| |#1|)) "\\spad{map(f,ire)} \\undocumented"))) @@ -2066,11 +2070,11 @@ NIL NIL (|InnerSparseUnivariatePowerSeries| |Coef|) ((|constructor| (NIL "InnerSparseUnivariatePowerSeries is an internal domain \\indented{2}{used for creating sparse Taylor and Laurent series.}")) (|cAcsch| (($ $) "\\spad{cAcsch(f)} computes the inverse hyperbolic cosecant of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cAsech| (($ $) "\\spad{cAsech(f)} computes the inverse hyperbolic secant of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cAcoth| (($ $) "\\spad{cAcoth(f)} computes the inverse hyperbolic cotangent of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cAtanh| (($ $) "\\spad{cAtanh(f)} computes the inverse hyperbolic tangent of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cAcosh| (($ $) "\\spad{cAcosh(f)} computes the inverse hyperbolic cosine of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cAsinh| (($ $) "\\spad{cAsinh(f)} computes the inverse hyperbolic sine of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cCsch| (($ $) "\\spad{cCsch(f)} computes the hyperbolic cosecant of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cSech| (($ $) "\\spad{cSech(f)} computes the hyperbolic secant of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cCoth| (($ $) "\\spad{cCoth(f)} computes the hyperbolic cotangent of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cTanh| (($ $) "\\spad{cTanh(f)} computes the hyperbolic tangent of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cCosh| (($ $) "\\spad{cCosh(f)} computes the hyperbolic cosine of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cSinh| (($ $) "\\spad{cSinh(f)} computes the hyperbolic sine of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cAcsc| (($ $) "\\spad{cAcsc(f)} computes the arccosecant of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cAsec| (($ $) "\\spad{cAsec(f)} computes the arcsecant of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cAcot| (($ $) "\\spad{cAcot(f)} computes the arccotangent of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cAtan| (($ $) "\\spad{cAtan(f)} computes the arctangent of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cAcos| (($ $) "\\spad{cAcos(f)} computes the arccosine of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cAsin| (($ $) "\\spad{cAsin(f)} computes the arcsine of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cCsc| (($ $) "\\spad{cCsc(f)} computes the cosecant of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cSec| (($ $) "\\spad{cSec(f)} computes the secant of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cCot| (($ $) "\\spad{cCot(f)} computes the cotangent of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cTan| (($ $) "\\spad{cTan(f)} computes the tangent of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cCos| (($ $) "\\spad{cCos(f)} computes the cosine of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cSin| (($ $) "\\spad{cSin(f)} computes the sine of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cLog| (($ $) "\\spad{cLog(f)} computes the logarithm of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cExp| (($ $) "\\spad{cExp(f)} computes the exponential of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cRationalPower| (($ $ (|Fraction| (|Integer|))) "\\spad{cRationalPower(f,r)} computes \\spad{f^r}. For use when the coefficient ring is commutative.")) (|cPower| (($ $ |#1|) "\\spad{cPower(f,r)} computes \\spad{f^r},{} where \\spad{f} has constant coefficient 1. For use when the coefficient ring is commutative.")) (|integrate| (($ $) "\\spad{integrate(f(x))} returns an anti-derivative of the power series \\spad{f(x)} with constant coefficient 0. Warning: function does not check for a term of degree \\spad{-1}.")) (|seriesToOutputForm| (((|OutputForm|) (|Stream| (|Record| (|:| |k| (|Integer|)) (|:| |c| |#1|))) (|Reference| (|OrderedCompletion| (|Integer|))) (|Symbol|) |#1| (|Fraction| (|Integer|))) "\\spad{seriesToOutputForm(st,refer,var,cen,r)} prints the series \\spad{f((var - cen)^r)}.")) (|iCompose| (($ $ $) "\\spad{iCompose(f,g)} returns \\spad{f(g(x))}. This is an internal function which should only be called for Taylor series \\spad{f(x)} and \\spad{g(x)} such that the constant coefficient of \\spad{g(x)} is zero.")) (|taylorQuoByVar| (($ $) "\\spad{taylorQuoByVar(a0 + a1 x + a2 x**2 + ...)} returns \\spad{a1 + a2 x + a3 x**2 + ...}")) (|iExquo| (((|Union| $ "failed") $ $ (|Boolean|)) "\\spad{iExquo(f,g,taylor?)} is the quotient of the power series \\spad{f} and \\spad{g}. If \\spad{taylor?} is \\spad{true},{} then we must have \\spad{order(f) >= order(g)}.")) (|multiplyCoefficients| (($ (|Mapping| |#1| (|Integer|)) $) "\\spad{multiplyCoefficients(fn,f)} returns the series \\spad{sum(fn(n) * an * x^n,n = n0..)},{} where \\spad{f} is the series \\spad{sum(an * x^n,n = n0..)}.")) (|monomial?| (((|Boolean|) $) "\\spad{monomial?(f)} tests if \\spad{f} is a single monomial.")) (|series| (($ (|Stream| (|Record| (|:| |k| (|Integer|)) (|:| |c| |#1|)))) "\\spad{series(st)} creates a series from a stream of non-zero terms,{} where a term is an exponent-coefficient pair. The terms in the stream should be ordered by increasing order of exponents.")) (|getStream| (((|Stream| (|Record| (|:| |k| (|Integer|)) (|:| |c| |#1|))) $) "\\spad{getStream(f)} returns the stream of terms representing the series \\spad{f}.")) (|getRef| (((|Reference| (|OrderedCompletion| (|Integer|))) $) "\\spad{getRef(f)} returns a reference containing the order to which the terms of \\spad{f} have been computed.")) (|makeSeries| (($ (|Reference| (|OrderedCompletion| (|Integer|))) (|Stream| (|Record| (|:| |k| (|Integer|)) (|:| |c| |#1|)))) "\\spad{makeSeries(refer,str)} creates a power series from the reference \\spad{refer} and the stream \\spad{str}."))) -(((|commutative| "*") |has| |#1| (|CommutativeRing|)) (|noZeroDivisors| |has| |#1| (|IntegralDomain|)) (|rightUnitary| . T) (|leftUnitary| . T) (|unitsKnown| . T)) +(((|commutative| "*") |has| |#1| (|CommutativeRing|)) (|noZeroDivisors| |has| |#1| (|IntegralDomain|))) ((|HasCategory| |#1| (QUOTE (|Algebra| (|Fraction| #1=(|Integer|))))) #2=(|HasCategory| |#1| (QUOTE (|IntegralDomain|))) (OR #3=(|HasCategory| |#1| (QUOTE (|CommutativeRing|))) #2#) #3# (|HasCategory| |#1| (QUOTE (|CharacteristicNonZero|))) (|HasCategory| |#1| (QUOTE (|CharacteristicZero|))) (AND (|HasCategory| |#1| (QUOTE (|PartialDifferentialRing| #4=(|Symbol|)))) #5=(|HasSignature| |#1| (|%list| (QUOTE *) (|%list| #6=(|devaluate| |#1|) #7=(QUOTE #1#) #6#)))) #5# (|HasCategory| #1# (QUOTE (|SemiGroup|))) (|HasCategory| |#1| (QUOTE (|Field|))) (AND #8=(|HasSignature| |#1| (|%list| (QUOTE **) (|%list| #6# #6# #7#))) (|HasSignature| |#1| (|%list| (QUOTE |coerce|) (|%list| #6# (QUOTE #4#))))) #8#) (|InnerTaylorSeries| |Coef|) ((|constructor| (NIL "Internal package for dense Taylor series. This is an internal Taylor series type in which Taylor series are represented by a \\spadtype{Stream} of \\spadtype{Ring} elements. For univariate series,{} the \\spad{Stream} elements are the Taylor coefficients. For multivariate series,{} the \\spad{n}th Stream element is a form of degree \\spad{n} in the power series variables.")) (* (($ $ (|Integer|)) "\\spad{x*i} returns the product of integer \\spad{i} and the series \\spad{x}.")) (|order| (((|NonNegativeInteger|) $ (|NonNegativeInteger|)) "\\spad{order(x,n)} returns the minimum of \\spad{n} and the order of \\spad{x}.") (((|NonNegativeInteger|) $) "\\spad{order(x)} returns the order of a power series \\spad{x},{} \\indented{1}{\\spadignore{i.e.} the degree of the first non-zero term of the series.}")) (|pole?| (((|Boolean|) $) "\\spad{pole?(x)} tests if the series \\spad{x} has a pole. \\indented{1}{Note: this is \\spad{false} when \\spad{x} is a Taylor series.}")) (|series| (($ (|Stream| |#1|)) "\\spad{series(s)} creates a power series from a stream of \\indented{1}{ring elements.} \\indented{1}{For univariate series types,{} the stream \\spad{s} should be a stream} \\indented{1}{of Taylor coefficients. For multivariate series types,{} the} \\indented{1}{stream \\spad{s} should be a stream of forms the \\spad{n}th element} \\indented{1}{of which is a} \\indented{1}{form of degree \\spad{n} in the power series variables.}")) (|coefficients| (((|Stream| |#1|) $) "\\spad{coefficients(x)} returns a stream of ring elements. \\indented{1}{When \\spad{x} is a univariate series,{} this is a stream of Taylor} \\indented{1}{coefficients. When \\spad{x} is a multivariate series,{} the} \\indented{1}{\\spad{n}th element of the stream is a form of} \\indented{1}{degree \\spad{n} in the power series variables.}"))) -(((|commutative| "*") |has| |#1| . #1=((|IntegralDomain|))) (|noZeroDivisors| |has| |#1| . #1#) (|rightUnitary| . T) (|leftUnitary| . T) (|unitsKnown| . T)) +(((|commutative| "*") |has| |#1| . #1=((|IntegralDomain|))) (|noZeroDivisors| |has| |#1| . #1#)) ((|HasCategory| |#1| (QUOTE (|IntegralDomain|)))) (|InternalTypeForm|) ((|constructor| (NIL "This domain provides representations for internal type form.")) (|mappingMode| (($ $ (|List| $)) "\\spad{mappingMode(r,ts)} returns a mapping mode with return mode \\spad{r},{} and parameter modes \\spad{ts}.")) (|categoryMode| (($) "\\spad{categoryMode} is a constant mode denoting Category.")) (|voidMode| (($) "\\spad{voidMode} is a constant mode denoting Void.")) (|noValueMode| (($) "\\spad{noValueMode} is a constant mode that indicates that the value of an expression is to be ignored.")) (|jokerMode| (($) "\\spad{jokerMode} is a constant that stands for any mode in a type inference context"))) @@ -2106,7 +2110,7 @@ NIL NIL (|AssociatedJordanAlgebra| R A) ((|constructor| (NIL "\\indented{1}{AssociatedJordanAlgebra takes an algebra \\spad{A} and uses \\spadfun{*\\$A}} \\indented{1}{to define the new multiplications \\spad{a*b := (a *\\$A b + b *\\$A a)/2}} \\indented{1}{(anticommutator).} \\indented{1}{The usual notation \\spad{{a,b}_+} cannot be used due to} \\indented{1}{restrictions in the current language.} \\indented{1}{This domain only gives a Jordan algebra if the} \\indented{1}{Jordan-identity \\spad{(a*b)*c + (b*c)*a + (c*a)*b = 0} holds} \\indented{1}{for all \\spad{a},{}\\spad{b},{}\\spad{c} in \\spad{A}.} \\indented{1}{This relation can be checked by} \\indented{1}{\\spadfun{jordanAdmissible?()\\$A}.} \\blankline If the underlying algebra is of type \\spadtype{FramedNonAssociativeAlgebra(R)} (\\spadignore{i.e.} a non associative algebra over \\spad{R} which is a free \\spad{R}-module of finite rank,{} together with a fixed \\spad{R}-module basis),{} then the same is \\spad{true} for the associated Jordan algebra. Moreover,{} if the underlying algebra is of type \\spadtype{FiniteRankNonAssociativeAlgebra(R)} (\\spadignore{i.e.} a non associative algebra over \\spad{R} which is a free \\spad{R}-module of finite rank),{} then the same \\spad{true} for the associated Jordan algebra.")) (|coerce| (($ |#2|) "\\spad{coerce(a)} coerces the element \\spad{a} of the algebra \\spad{A} to an element of the Jordan algebra \\spadtype{AssociatedJordanAlgebra}(\\spad{R},{}A)."))) -((|unitsKnown| OR (|and| (|has| |#2| (|FiniteRankNonAssociativeAlgebra| |#1|)) #1=(|has| |#1| (|IntegralDomain|))) (AND (|has| |#2| (|FramedNonAssociativeAlgebra| |#1|)) #1#)) (|leftUnitary| . T) (|rightUnitary| . T)) +NIL ((OR #1=(|HasCategory| |#2| (|%list| (QUOTE |FiniteRankNonAssociativeAlgebra|) #2=(|devaluate| |#1|))) #3=(|HasCategory| |#2| (|%list| (QUOTE |FramedNonAssociativeAlgebra|) #2#))) #3# (AND (|HasCategory| |#1| (QUOTE (|Field|))) #3#) (OR (AND #4=(|HasCategory| |#1| (QUOTE (|IntegralDomain|))) #1#) (AND #4# #3#)) #1#) (|JVMBytecode|) ((|constructor| (NIL "This is the datatype for the JVM bytecodes."))) @@ -2178,7 +2182,7 @@ NIL NIL (|LocalAlgebra| A R S) ((|constructor| (NIL "LocalAlgebra produces the localization of an algebra,{} \\spadignore{i.e.} fractions whose numerators come from some \\spad{R} algebra.")) (|denom| ((|#3| $) "\\spad{denom x} returns the denominator of \\spad{x}.")) (|numer| ((|#1| $) "\\spad{numer x} returns the numerator of \\spad{x}.")) (/ (($ |#1| |#3|) "\\spad{a / d} divides the element \\spad{a} by \\spad{d}.") (($ $ |#3|) "\\spad{x / d} divides the element \\spad{x} by \\spad{d}."))) -((|rightUnitary| . T) (|leftUnitary| . T) (|unitsKnown| . T)) +NIL ((|HasCategory| |#1| (QUOTE (|OrderedRing|)))) (|LeftAlgebra&| S R) ((|constructor| (NIL "The category of all left algebras over an arbitrary ring.")) (|coerce| (($ |#2|) "\\spad{coerce(r)} returns \\spad{r} * 1 where 1 is the identity of the left algebra."))) @@ -2186,7 +2190,7 @@ NIL NIL (|LeftAlgebra| R) ((|constructor| (NIL "The category of all left algebras over an arbitrary ring.")) (|coerce| (($ |#1|) "\\spad{coerce(r)} returns \\spad{r} * 1 where 1 is the identity of the left algebra."))) -((|unitsKnown| . T)) +NIL NIL (|LaplaceTransform| R F) ((|constructor| (NIL "This package computes the forward Laplace Transform.")) (|laplace| ((|#2| |#2| (|Symbol|) (|Symbol|)) "\\spad{laplace(f, t, s)} returns the Laplace transform of \\spad{f(t)} using \\spad{s} as the new variable. This is \\spad{integral(exp(-s*t)*f(t), t = 0..\\%plusInfinity)}. Returns the formal object \\spad{laplace(f, t, s)} if it cannot compute the transform."))) @@ -2194,7 +2198,7 @@ NIL NIL (|LaurentPolynomial| R UP) ((|constructor| (NIL "\\indented{1}{Univariate polynomials with negative and positive exponents.} Author: Manuel Bronstein Date Created: May 1988 Date Last Updated: 26 Apr 1990")) (|separate| (((|Record| (|:| |polyPart| $) (|:| |fracPart| (|Fraction| |#2|))) (|Fraction| |#2|)) "\\spad{separate(x)} \\undocumented")) (|monomial| (($ |#1| (|Integer|)) "\\spad{monomial(x,n)} \\undocumented")) (|coefficient| ((|#1| $ (|Integer|)) "\\spad{coefficient(x,n)} \\undocumented")) (|trailingCoefficient| ((|#1| $) "\\spad{trailingCoefficient }\\undocumented")) (|leadingCoefficient| ((|#1| $) "\\spad{leadingCoefficient }\\undocumented")) (|reductum| (($ $) "\\spad{reductum(x)} \\undocumented")) (|order| (((|Integer|) $) "\\spad{order(x)} \\undocumented")) (|degree| (((|Integer|) $) "\\spad{degree(x)} \\undocumented")) (|monomial?| (((|Boolean|) $) "\\spad{monomial?(x)} \\undocumented"))) -((|leftUnitary| . T) (|rightUnitary| . T) ((|commutative| "*") . T) (|noZeroDivisors| . T) (|unitsKnown| . T)) +(((|commutative| "*") . T) (|noZeroDivisors| . T)) ((|HasCategory| |#2| (QUOTE (|PartialDifferentialRing| #1=(|Symbol|)))) (|HasCategory| |#2| (QUOTE (|PartialDifferentialSpace| #1#))) (|HasCategory| |#2| (QUOTE (|DifferentialRing|))) (|HasCategory| |#2| (QUOTE (|DifferentialSpace|))) (|HasCategory| |#1| (QUOTE (|Field|))) (|HasCategory| |#1| (QUOTE (|CharacteristicNonZero|))) (|HasCategory| |#1| (QUOTE (|CharacteristicZero|))) (|HasCategory| |#1| (QUOTE (|RetractableTo| (|Fraction| #2=(|Integer|))))) (|HasCategory| |#1| (QUOTE (|RetractableTo| #2#)))) (|LazardSetSolvingPackage| R E V P TS ST) ((|constructor| (NIL "A package for solving polynomial systems by means of Lazard triangular sets [1]. This package provides two operations. One for solving in the sense of the regular zeros,{} and the other for solving in the sense of the Zariski closure. Both produce square-free regular sets. Moreover,{} the decompositions do not contain any redundant component. However,{} only zero-dimensional regular sets are normalized,{} since normalization may be time consumming in positive dimension. The decomposition process is that of [2].\\newline References : \\indented{1}{[1] \\spad{D}. LAZARD \"A new method for solving algebraic systems of} \\indented{5}{positive dimension\" Discr. App. Math. 33:147-160,{}1991} \\indented{1}{[2] \\spad{M}. MORENO MAZA \"A new algorithm for computing triangular} \\indented{5}{decomposition of algebraic varieties\" NAG Tech. Rep. 4/98.}")) (|zeroSetSplit| (((|List| |#6|) (|List| |#4|) (|Boolean|)) "\\axiom{zeroSetSplit(lp,{}clos?)} has the same specifications as \\axiomOpFrom{zeroSetSplit(lp,{}clos?)}{RegularTriangularSetCategory}.")) (|normalizeIfCan| ((|#6| |#6|) "\\axiom{normalizeIfCan(ts)} returns \\axiom{ts} in an normalized shape if \\axiom{ts} is zero-dimensional."))) @@ -2209,8 +2213,8 @@ NIL NIL NIL (|LieExponentials| |VarSet| R |Order|) -((|constructor| (NIL "Management of the Lie Group associated with a free nilpotent Lie algebra. Every Lie bracket with length greater than \\axiom{Order} are assumed to be null. The implementation inherits from the \\spadtype{XPBWPolynomial} domain constructor: Lyndon coordinates are exponential coordinates of the second kind. \\newline Author: Michel Petitot (petitot@lifl.fr).")) (|identification| (((|List| (|Equation| |#2|)) $ $) "\\axiom{identification(\\spad{g},{}\\spad{h})} returns the list of equations \\axiom{g_i = h_i},{} where \\axiom{g_i} (resp. \\axiom{h_i}) are exponential coordinates of \\axiom{\\spad{g}} (resp. \\axiom{\\spad{h}}).")) (|LyndonCoordinates| (((|List| (|Record| (|:| |k| (|LyndonWord| |#1|)) (|:| |c| |#2|))) $) "\\axiom{LyndonCoordinates(\\spad{g})} returns the exponential coordinates of \\axiom{\\spad{g}}.")) (|LyndonBasis| (((|List| (|LiePolynomial| |#1| |#2|)) (|List| |#1|)) "\\axiom{LyndonBasis(lv)} returns the Lyndon basis of the nilpotent free Lie algebra.")) (|varList| (((|List| |#1|) $) "\\axiom{varList(\\spad{g})} returns the list of variables of \\axiom{\\spad{g}}.")) (|mirror| (($ $) "\\axiom{mirror(\\spad{g})} is the mirror of the internal representation of \\axiom{\\spad{g}}.")) (|coerce| (((|XPBWPolynomial| |#1| |#2|) $) "\\axiom{coerce(\\spad{g})} returns the internal representation of \\axiom{\\spad{g}}.") (((|XDistributedPolynomial| |#1| |#2|) $) "\\axiom{coerce(\\spad{g})} returns the internal representation of \\axiom{\\spad{g}}.")) (|ListOfTerms| (((|List| (|Record| (|:| |k| (|PoincareBirkhoffWittLyndonBasis| |#1|)) (|:| |c| |#2|))) $) "\\axiom{ListOfTerms(\\spad{p})} returns the internal representation of \\axiom{\\spad{p}}.")) (|log| (((|LiePolynomial| |#1| |#2|) $) "\\axiom{log(\\spad{p})} returns the logarithm of \\axiom{\\spad{p}}.")) (|exp| (($ (|LiePolynomial| |#1| |#2|)) "\\axiom{exp(\\spad{p})} returns the exponential of \\axiom{\\spad{p}}."))) -((|unitsKnown| . T)) +((|constructor| (NIL "Management of the Lie Group associated with a free nilpotent Lie algebra. Every Lie bracket with length greater than \\axiom{Order} are assumed to be null. The implementation inherits from the \\spadtype{XPBWPolynomial} domain constructor: Lyndon coordinates are exponential coordinates of the second kind. \\newline Author: Michel Petitot (petitot@lifl.fr).")) (|identification| (((|List| (|Equation| |#2|)) $ $) "\\axiom{identification(\\spad{g},{}\\spad{h})} returns the list of equations \\axiom{g_i = h_i},{} where \\axiom{g_i} (resp. \\axiom{h_i}) are exponential coordinates of \\axiom{\\spad{g}} (resp. \\axiom{\\spad{h}}).")) (|LyndonCoordinates| (((|List| (|Record| (|:| |k| (|LyndonWord| |#1|)) (|:| |c| |#2|))) $) "\\axiom{LyndonCoordinates(\\spad{g})} returns the exponential coordinates of \\axiom{\\spad{g}}.")) (|LyndonBasis| (((|List| (|LiePolynomial| |#1| |#2|)) (|List| |#1|)) "\\axiom{LyndonBasis(lv)} returns the Lyndon basis of the nilpotent free Lie algebra.")) (|varList| (((|List| |#1|) $) "\\axiom{varList(\\spad{g})} returns the list of variables of \\axiom{\\spad{g}}.")) (|mirror| (($ $) "\\axiom{mirror(\\spad{g})} is the mirror of the internal representation of \\axiom{\\spad{g}}.")) (|ListOfTerms| (((|List| (|Record| (|:| |k| (|PoincareBirkhoffWittLyndonBasis| |#1|)) (|:| |c| |#2|))) $) "\\axiom{ListOfTerms(\\spad{p})} returns the internal representation of \\axiom{\\spad{p}}.")) (|log| (((|LiePolynomial| |#1| |#2|) $) "\\axiom{log(\\spad{p})} returns the logarithm of \\axiom{\\spad{p}}.")) (|exp| (($ (|LiePolynomial| |#1| |#2|)) "\\axiom{exp(\\spad{p})} returns the exponential of \\axiom{\\spad{p}}."))) +NIL NIL (|LexTriangularPackage| R |ls|) ((|constructor| (NIL "A package for solving polynomial systems with finitely many solutions. The decompositions are given by means of regular triangular sets. The computations use lexicographical Groebner bases. The main operations are \\axiomOpFrom{lexTriangular}{LexTriangularPackage} and \\axiomOpFrom{squareFreeLexTriangular}{LexTriangularPackage}. The second one provide decompositions by means of square-free regular triangular sets. Both are based on the {\\em lexTriangular} method described in [1]. They differ from the algorithm described in [2] by the fact that multiciplities of the roots are not kept. With the \\axiomOpFrom{squareFreeLexTriangular}{LexTriangularPackage} operation all multiciplities are removed. With the other operation some multiciplities may remain. Both operations admit an optional argument to produce normalized triangular sets. \\newline")) (|zeroSetSplit| (((|List| (|SquareFreeRegularTriangularSet| |#1| (|IndexedExponents| (|OrderedVariableList| |#2|)) (|OrderedVariableList| |#2|) (|NewSparseMultivariatePolynomial| |#1| (|OrderedVariableList| |#2|)))) (|List| (|NewSparseMultivariatePolynomial| |#1| (|OrderedVariableList| |#2|))) (|Boolean|)) "\\axiom{zeroSetSplit(lp,{} norm?)} decomposes the variety associated with \\axiom{lp} into square-free regular chains. Thus a point belongs to this variety iff it is a regular zero of a regular set in in the output. Note that \\axiom{lp} needs to generate a zero-dimensional ideal. If \\axiom{norm?} is \\axiom{\\spad{true}} then the regular sets are normalized.") (((|List| (|RegularChain| |#1| |#2|)) (|List| (|NewSparseMultivariatePolynomial| |#1| (|OrderedVariableList| |#2|))) (|Boolean|)) "\\axiom{zeroSetSplit(lp,{} norm?)} decomposes the variety associated with \\axiom{lp} into regular chains. Thus a point belongs to this variety iff it is a regular zero of a regular set in in the output. Note that \\axiom{lp} needs to generate a zero-dimensional ideal. If \\axiom{norm?} is \\axiom{\\spad{true}} then the regular sets are normalized.")) (|squareFreeLexTriangular| (((|List| (|SquareFreeRegularTriangularSet| |#1| (|IndexedExponents| (|OrderedVariableList| |#2|)) (|OrderedVariableList| |#2|) (|NewSparseMultivariatePolynomial| |#1| (|OrderedVariableList| |#2|)))) (|List| (|NewSparseMultivariatePolynomial| |#1| (|OrderedVariableList| |#2|))) (|Boolean|)) "\\axiom{squareFreeLexTriangular(base,{} norm?)} decomposes the variety associated with \\axiom{base} into square-free regular chains. Thus a point belongs to this variety iff it is a regular zero of a regular set in in the output. Note that \\axiom{base} needs to be a lexicographical Groebner basis of a zero-dimensional ideal. If \\axiom{norm?} is \\axiom{\\spad{true}} then the regular sets are normalized.")) (|lexTriangular| (((|List| (|RegularChain| |#1| |#2|)) (|List| (|NewSparseMultivariatePolynomial| |#1| (|OrderedVariableList| |#2|))) (|Boolean|)) "\\axiom{lexTriangular(base,{} norm?)} decomposes the variety associated with \\axiom{base} into regular chains. Thus a point belongs to this variety iff it is a regular zero of a regular set in in the output. Note that \\axiom{base} needs to be a lexicographical Groebner basis of a zero-dimensional ideal. If \\axiom{norm?} is \\axiom{\\spad{true}} then the regular sets are normalized.")) (|groebner| (((|List| (|NewSparseMultivariatePolynomial| |#1| (|OrderedVariableList| |#2|))) (|List| (|NewSparseMultivariatePolynomial| |#1| (|OrderedVariableList| |#2|)))) "\\axiom{groebner(lp)} returns the lexicographical Groebner basis of \\axiom{lp}. If \\axiom{lp} generates a zero-dimensional ideal then the {\\em FGLM} strategy is used,{} otherwise the {\\em Sugar} strategy is used.")) (|fglmIfCan| (((|Union| (|List| (|NewSparseMultivariatePolynomial| |#1| (|OrderedVariableList| |#2|))) "failed") (|List| (|NewSparseMultivariatePolynomial| |#1| (|OrderedVariableList| |#2|)))) "\\axiom{fglmIfCan(lp)} returns the lexicographical Groebner basis of \\axiom{lp} by using the {\\em FGLM} strategy,{} if \\axiom{zeroDimensional?(lp)} holds .")) (|zeroDimensional?| (((|Boolean|) (|List| (|NewSparseMultivariatePolynomial| |#1| (|OrderedVariableList| |#2|)))) "\\axiom{zeroDimensional?(lp)} returns \\spad{true} iff \\axiom{lp} generates a zero-dimensional ideal \\spad{w}.\\spad{r}.\\spad{t}. the variables involved in \\axiom{lp}."))) @@ -2234,15 +2238,15 @@ NIL ((AND (|HasCategory| #1=(|Record| (|:| |key| #2=(|String|)) (|:| |entry| #3=(|Any|))) (QUOTE (|Evalable| #1#))) #4=(|HasCategory| #1# #5=(QUOTE (|SetCategory|)))) (OR #6=(|HasCategory| #3# #5#) #4#) (OR #7=(|HasCategory| #3# #8=(QUOTE (|BasicType|))) #6# #9=(|HasCategory| #1# #8#) #4#) (OR #10=(|HasCategory| #1# #11=(QUOTE (|CoercibleTo| (|OutputForm|)))) #12=(|HasCategory| #3# #11#)) (|HasCategory| #1# (QUOTE (|ConvertibleTo| (|InputForm|)))) (AND (|HasCategory| #3# (QUOTE (|Evalable| #3#))) #6#) #9# (|HasCategory| #2# (QUOTE (|OrderedSet|))) #7# (OR #7# #9#) #6# #12# #10# #4# (AND #13=(|HasCategory| $ (QUOTE (|FiniteAggregate| #1#))) #9#) #13# (AND (|HasCategory| $ (QUOTE (|FiniteAggregate| #3#))) #7#) (|HasCategory| $ (QUOTE (|ShallowlyMutableAggregate| #3#)))) (|AssociatedLieAlgebra| R A) ((|constructor| (NIL "AssociatedLieAlgebra takes an algebra \\spad{A} and uses \\spadfun{*\\$A} to define the Lie bracket \\spad{a*b := (a *\\$A b - b *\\$A a)} (commutator). Note that the notation \\spad{[a,b]} cannot be used due to restrictions of the current compiler. This domain only gives a Lie algebra if the Jacobi-identity \\spad{(a*b)*c + (b*c)*a + (c*a)*b = 0} holds for all \\spad{a},{}\\spad{b},{}\\spad{c} in \\spad{A}. This relation can be checked by \\spad{lieAdmissible?()\\$A}. \\blankline If the underlying algebra is of type \\spadtype{FramedNonAssociativeAlgebra(R)} (\\spadignore{i.e.} a non associative algebra over \\spad{R} which is a free \\spad{R}-module of finite rank,{} together with a fixed \\spad{R}-module basis),{} then the same is \\spad{true} for the associated Lie algebra. Also,{} if the underlying algebra is of type \\spadtype{FiniteRankNonAssociativeAlgebra(R)} (\\spadignore{i.e.} a non associative algebra over \\spad{R} which is a free \\spad{R}-module of finite rank),{} then the same is \\spad{true} for the associated Lie algebra.")) (|coerce| (($ |#2|) "\\spad{coerce(a)} coerces the element \\spad{a} of the algebra \\spad{A} to an element of the Lie algebra \\spadtype{AssociatedLieAlgebra}(\\spad{R},{}A)."))) -((|unitsKnown| OR (|and| (|has| |#2| (|FiniteRankNonAssociativeAlgebra| |#1|)) #1=(|has| |#1| (|IntegralDomain|))) (AND (|has| |#2| (|FramedNonAssociativeAlgebra| |#1|)) #1#)) (|leftUnitary| . T) (|rightUnitary| . T)) +NIL ((OR #1=(|HasCategory| |#2| (|%list| (QUOTE |FiniteRankNonAssociativeAlgebra|) #2=(|devaluate| |#1|))) #3=(|HasCategory| |#2| (|%list| (QUOTE |FramedNonAssociativeAlgebra|) #2#))) #3# (AND (|HasCategory| |#1| (QUOTE (|Field|))) #3#) (OR (AND #4=(|HasCategory| |#1| (QUOTE (|IntegralDomain|))) #1#) (AND #4# #3#)) #1#) (|LieAlgebra&| S R) -((|constructor| (NIL "\\axiom{JacobiIdentity} means that \\axiom{[\\spad{x},{}[\\spad{y},{}\\spad{z}]]+[\\spad{y},{}[\\spad{z},{}\\spad{x}]]+[\\spad{z},{}[\\spad{x},{}\\spad{y}]] = 0} holds.")) (/ (($ $ |#2|) "\\axiom{x/r} returns the division of \\axiom{\\spad{x}} by \\axiom{\\spad{r}}.")) (|construct| (($ $ $) "\\axiom{construct(\\spad{x},{}\\spad{y})} returns the Lie bracket of \\axiom{\\spad{x}} and \\axiom{\\spad{y}}."))) +((|constructor| (NIL "The category of Lie Algebras. It is used by the following domains of non-commutative algebra: \\axiomType{LiePolynomial} and \\axiomType{XPBWPolynomial}. \\newline Author : Michel Petitot (petitot@lifl.fr).")) (/ (($ $ |#2|) "\\axiom{x/r} returns the division of \\axiom{\\spad{x}} by \\axiom{\\spad{r}}.")) (|construct| (($ $ $) "\\axiom{construct(\\spad{x},{}\\spad{y})} returns the Lie bracket of \\axiom{\\spad{x}} and \\axiom{\\spad{y}}."))) NIL ((|HasCategory| |#2| (QUOTE (|Field|)))) (|LieAlgebra| R) -((|constructor| (NIL "\\axiom{JacobiIdentity} means that \\axiom{[\\spad{x},{}[\\spad{y},{}\\spad{z}]]+[\\spad{y},{}[\\spad{z},{}\\spad{x}]]+[\\spad{z},{}[\\spad{x},{}\\spad{y}]] = 0} holds.")) (/ (($ $ |#1|) "\\axiom{x/r} returns the division of \\axiom{\\spad{x}} by \\axiom{\\spad{r}}.")) (|construct| (($ $ $) "\\axiom{construct(\\spad{x},{}\\spad{y})} returns the Lie bracket of \\axiom{\\spad{x}} and \\axiom{\\spad{y}}."))) -((|JacobiIdentity| . T) (|NullSquare| . T) (|leftUnitary| . T) (|rightUnitary| . T)) +((|constructor| (NIL "The category of Lie Algebras. It is used by the following domains of non-commutative algebra: \\axiomType{LiePolynomial} and \\axiomType{XPBWPolynomial}. \\newline Author : Michel Petitot (petitot@lifl.fr).")) (/ (($ $ |#1|) "\\axiom{x/r} returns the division of \\axiom{\\spad{x}} by \\axiom{\\spad{r}}.")) (|construct| (($ $ $) "\\axiom{construct(\\spad{x},{}\\spad{y})} returns the Lie bracket of \\axiom{\\spad{x}} and \\axiom{\\spad{y}}."))) +NIL NIL (|PowerSeriesLimitPackage| R FE) ((|constructor| (NIL "PowerSeriesLimitPackage implements limits of expressions in one or more variables as one of the variables approaches a limiting value. Included are two-sided limits,{} left- and right- hand limits,{} and limits at plus or minus infinity.")) (|complexLimit| (((|Union| (|OnePointCompletion| |#2|) "failed") |#2| (|Equation| (|OnePointCompletion| |#2|))) "\\spad{complexLimit(f(x),x = a)} computes the complex limit \\spad{lim(x -> a,f(x))}.")) (|limit| (((|Union| (|OrderedCompletion| |#2|) #1="failed") |#2| (|Equation| |#2|) (|String|)) "\\spad{limit(f(x),x=a,\"left\")} computes the left hand real limit \\spad{lim(x -> a-,f(x))}; \\spad{limit(f(x),x=a,\"right\")} computes the right hand real limit \\spad{lim(x -> a+,f(x))}.") (((|Union| (|OrderedCompletion| |#2|) (|Record| (|:| |leftHandLimit| (|Union| (|OrderedCompletion| |#2|) #1#)) (|:| |rightHandLimit| (|Union| (|OrderedCompletion| |#2|) #1#))) "failed") |#2| (|Equation| (|OrderedCompletion| |#2|))) "\\spad{limit(f(x),x = a)} computes the real limit \\spad{lim(x -> a,f(x))}."))) @@ -2262,7 +2266,7 @@ NIL ((|not| #1=(|HasCategory| |#1| (QUOTE (|Field|)))) #1#) (|LinearElement| K B) ((|constructor| (NIL "A simple data structure for elements that form a vector space of finite dimension over a given field,{} with a given symbolic basis.")) (|coordinates| (((|Vector| |#1|) $) "\\spad{coordinates x} returns the coordinates of the linear element with respect to the basis \\spad{B}.")) (|linearElement| (($ (|List| |#1|)) "\\spad{linearElement [x1,..,xn]} returns a linear element \\indented{1}{with coordinates \\spad{[x1,..,xn]} with respect to} the basis elements \\spad{B}."))) -((|leftUnitary| . T) (|rightUnitary| . T)) +NIL ((AND (|HasCategory| |#1| #1=(QUOTE (|SetCategory|))) (|HasCategory| (|LinearBasis| |#2|) #1#))) (|LinearlyExplicitRingOver| R) ((|constructor| (NIL "An extension of left-module with an explicit linear dependence test.")) (|reducedSystem| (((|Record| (|:| |mat| (|Matrix| |#1|)) (|:| |vec| (|Vector| |#1|))) (|Matrix| $) (|Vector| $)) "\\spad{reducedSystem(A, v)} returns a matrix \\spad{B} and a vector \\spad{w} such that \\spad{A x = v} and \\spad{B x = w} have the same solutions in \\spad{R}.") (((|Matrix| |#1|) (|Matrix| $)) "\\spad{reducedSystem(A)} returns a matrix \\spad{B} such that \\spad{A x = 0} and \\spad{B x = 0} have the same solutions in \\spad{R}.")) (|leftReducedSystem| (((|Record| (|:| |mat| (|Matrix| |#1|)) (|:| |vec| (|Vector| |#1|))) (|Vector| $) $) "\\spad{reducedSystem([v1,...,vn],u)} returns a matrix \\spad{M} with coefficients in \\spad{R} and a vector \\spad{w} such that the system of equations \\spad{c1*v1 + ... + cn*vn = u} has the same solution as \\spad{c * M = w} where \\spad{c} is the row vector \\spad{[c1,...cn]}.") (((|Matrix| |#1|) (|Vector| $)) "\\spad{leftReducedSystem [v1,...,vn]} returns a matrix \\spad{M} with coefficients in \\spad{R} such that the system of equations \\spad{c1*v1 + ... + cn*vn = 0\\$\\%} has the same solution as \\spad{c * M = 0} where \\spad{c} is the row vector \\spad{[c1,...cn]}."))) @@ -2270,7 +2274,7 @@ NIL NIL (|LinearForm| K B) ((|constructor| (NIL "A simple data structure for linear forms on a vector space of finite dimension over a given field,{} with a given symbolic basis.")) (|coordinates| (((|Vector| |#1|) $) "\\spad{coordinates x} returns the coordinates of the linear form with respect to the basis \\spad{DualBasis B}.")) (|linearForm| (($ (|List| |#1|)) "\\spad{linearForm [x1,..,xn]} constructs a linear form with coordinates \\spad{[x1,..,xn]} with respect to the basis elements \\spad{DualBasis B}."))) -((|leftUnitary| . T) (|rightUnitary| . T)) +NIL NIL (|LinearSet| S) ((|constructor| (NIL "\\indented{2}{A set is an \\spad{S}-linear set if it is stable by dilation} \\indented{2}{by elements in the semigroup \\spad{S}.} See Also: LeftLinearSet,{} RightLinearSet."))) @@ -2322,7 +2326,7 @@ NIL NIL (|Localize| M R S) ((|constructor| (NIL "Localize(\\spad{M},{}\\spad{R},{}\\spad{S}) produces fractions with numerators from an \\spad{R} module \\spad{M} and denominators from some multiplicative subset \\spad{D} of \\spad{R}.")) (|denom| ((|#3| $) "\\spad{denom x} returns the denominator of \\spad{x}.")) (|numer| ((|#1| $) "\\spad{numer x} returns the numerator of \\spad{x}.")) (/ (($ |#1| |#3|) "\\spad{m / d} divides the element \\spad{m} by \\spad{d}.") (($ $ |#3|) "\\spad{x / d} divides the element \\spad{x} by \\spad{d}."))) -((|leftUnitary| . T) (|rightUnitary| . T)) +NIL ((|HasCategory| |#1| (QUOTE (|OrderedAbelianGroup|)))) (|ElementaryFunctionLODESolver| R F L) ((|constructor| (NIL "\\spad{ElementaryFunctionLODESolver} provides the top-level functions for finding closed form solutions of linear ordinary differential equations and initial value problems.")) (|solve| (((|Union| |#2| "failed") |#3| |#2| (|Symbol|) |#2| (|List| |#2|)) "\\spad{solve(op, g, x, a, [y0,...,ym])} returns either the solution of the initial value problem \\spad{op y = g, y(a) = y0, y'(a) = y1,...} or \"failed\" if the solution cannot be found; \\spad{x} is the dependent variable.") (((|Union| (|Record| (|:| |particular| |#2|) (|:| |basis| (|List| |#2|))) "failed") |#3| |#2| (|Symbol|)) "\\spad{solve(op, g, x)} returns either a solution of the ordinary differential equation \\spad{op y = g} or \"failed\" if no non-trivial solution can be found; When found,{} the solution is returned in the form \\spad{[h, [b1,...,bm]]} where \\spad{h} is a particular solution and and \\spad{[b1,...bm]} are linearly independent solutions of the associated homogenuous equation \\spad{op y = 0}. A full basis for the solutions of the homogenuous equation is not always returned,{} only the solutions which were found; \\spad{x} is the dependent variable."))) @@ -2330,15 +2334,15 @@ NIL NIL (|LinearOrdinaryDifferentialOperator| A |diff|) ((|constructor| (NIL "\\spad{LinearOrdinaryDifferentialOperator} defines a ring of differential operators with coefficients in a ring A with a given derivation. Multiplication of operators corresponds to functional composition: \\indented{4}{\\spad{(L1 * L2).(f) = L1 L2 f}}"))) -((|rightUnitary| . T) (|leftUnitary| . T) (|unitsKnown| . T)) +NIL ((|HasCategory| |#1| (QUOTE (|CommutativeRing|))) (|HasCategory| |#1| (QUOTE (|RetractableTo| (|Fraction| #1=(|Integer|))))) (|HasCategory| |#1| (QUOTE (|RetractableTo| #1#))) (|HasCategory| |#1| (QUOTE (|IntegralDomain|))) (|HasCategory| |#1| (QUOTE (|GcdDomain|))) (|HasCategory| |#1| (QUOTE (|Field|)))) (|LinearOrdinaryDifferentialOperator1| A) ((|constructor| (NIL "\\spad{LinearOrdinaryDifferentialOperator1} defines a ring of differential operators with coefficients in a differential ring A. Multiplication of operators corresponds to functional composition: \\indented{4}{\\spad{(L1 * L2).(f) = L1 L2 f}}"))) -((|rightUnitary| . T) (|leftUnitary| . T) (|unitsKnown| . T)) +NIL ((|HasCategory| |#1| (QUOTE (|CommutativeRing|))) (|HasCategory| |#1| (QUOTE (|RetractableTo| (|Fraction| #1=(|Integer|))))) (|HasCategory| |#1| (QUOTE (|RetractableTo| #1#))) (|HasCategory| |#1| (QUOTE (|IntegralDomain|))) (|HasCategory| |#1| (QUOTE (|GcdDomain|))) (|HasCategory| |#1| (QUOTE (|Field|)))) (|LinearOrdinaryDifferentialOperator2| A M) ((|constructor| (NIL "\\spad{LinearOrdinaryDifferentialOperator2} defines a ring of differential operators with coefficients in a differential ring A and acting on an A-module \\spad{M}. Multiplication of operators corresponds to functional composition: \\indented{4}{\\spad{(L1 * L2).(f) = L1 L2 f}}")) (|differentiate| (($ $) "\\spad{differentiate(x)} returns the derivative of \\spad{x}"))) -((|rightUnitary| . T) (|leftUnitary| . T) (|unitsKnown| . T)) +NIL ((|HasCategory| |#1| (QUOTE (|CommutativeRing|))) (|HasCategory| |#1| (QUOTE (|RetractableTo| (|Fraction| #1=(|Integer|))))) (|HasCategory| |#1| (QUOTE (|RetractableTo| #1#))) (|HasCategory| |#1| (QUOTE (|IntegralDomain|))) (|HasCategory| |#1| (QUOTE (|GcdDomain|))) (|HasCategory| |#1| (QUOTE (|Field|)))) (|LinearOrdinaryDifferentialOperatorCategory&| S A) ((|constructor| (NIL "\\spad{LinearOrdinaryDifferentialOperatorCategory} is the category of differential operators with coefficients in a ring A with a given derivation. Multiplication of operators corresponds to functional composition: \\indented{4}{\\spad{(L1 * L2).(f) = L1 L2 f}}")) (|directSum| (($ $ $) "\\spad{directSum(a,b)} computes an operator \\spad{c} of minimal order such that the nullspace of \\spad{c} is generated by all the sums of a solution of \\spad{a} by a solution of \\spad{b}.")) (|symmetricSquare| (($ $) "\\spad{symmetricSquare(a)} computes \\spad{symmetricProduct(a,a)} using a more efficient method.")) (|symmetricPower| (($ $ (|NonNegativeInteger|)) "\\spad{symmetricPower(a,n)} computes an operator \\spad{c} of minimal order such that the nullspace of \\spad{c} is generated by all the products of \\spad{n} solutions of \\spad{a}.")) (|symmetricProduct| (($ $ $) "\\spad{symmetricProduct(a,b)} computes an operator \\spad{c} of minimal order such that the nullspace of \\spad{c} is generated by all the products of a solution of \\spad{a} by a solution of \\spad{b}.")) (|adjoint| (($ $) "\\spad{adjoint(a)} returns the adjoint operator of a.")) (D (($) "\\spad{D()} provides the operator corresponding to a derivation in the ring \\spad{A}."))) @@ -2346,7 +2350,7 @@ NIL ((|HasCategory| |#2| (QUOTE (|Field|)))) (|LinearOrdinaryDifferentialOperatorCategory| A) ((|constructor| (NIL "\\spad{LinearOrdinaryDifferentialOperatorCategory} is the category of differential operators with coefficients in a ring A with a given derivation. Multiplication of operators corresponds to functional composition: \\indented{4}{\\spad{(L1 * L2).(f) = L1 L2 f}}")) (|directSum| (($ $ $) "\\spad{directSum(a,b)} computes an operator \\spad{c} of minimal order such that the nullspace of \\spad{c} is generated by all the sums of a solution of \\spad{a} by a solution of \\spad{b}.")) (|symmetricSquare| (($ $) "\\spad{symmetricSquare(a)} computes \\spad{symmetricProduct(a,a)} using a more efficient method.")) (|symmetricPower| (($ $ (|NonNegativeInteger|)) "\\spad{symmetricPower(a,n)} computes an operator \\spad{c} of minimal order such that the nullspace of \\spad{c} is generated by all the products of \\spad{n} solutions of \\spad{a}.")) (|symmetricProduct| (($ $ $) "\\spad{symmetricProduct(a,b)} computes an operator \\spad{c} of minimal order such that the nullspace of \\spad{c} is generated by all the products of a solution of \\spad{a} by a solution of \\spad{b}.")) (|adjoint| (($ $) "\\spad{adjoint(a)} returns the adjoint operator of a.")) (D (($) "\\spad{D()} provides the operator corresponding to a derivation in the ring \\spad{A}."))) -((|rightUnitary| . T) (|leftUnitary| . T) (|unitsKnown| . T)) +NIL NIL (|LinearOrdinaryDifferentialOperatorFactorizer| F UP) ((|constructor| (NIL "\\spadtype{LinearOrdinaryDifferentialOperatorFactorizer} provides a factorizer for linear ordinary differential operators whose coefficients are rational functions.")) (|factor1| (((|List| (|LinearOrdinaryDifferentialOperator1| (|Fraction| |#2|))) (|LinearOrdinaryDifferentialOperator1| (|Fraction| |#2|))) "\\spad{factor1(a)} returns the factorisation of a,{} assuming that a has no first-order right factor.")) (|factor| (((|List| (|LinearOrdinaryDifferentialOperator1| (|Fraction| |#2|))) (|LinearOrdinaryDifferentialOperator1| (|Fraction| |#2|))) "\\spad{factor(a)} returns the factorisation of a.") (((|List| (|LinearOrdinaryDifferentialOperator1| (|Fraction| |#2|))) (|LinearOrdinaryDifferentialOperator1| (|Fraction| |#2|)) (|Mapping| (|List| |#1|) |#2|)) "\\spad{factor(a, zeros)} returns the factorisation of a. \\spad{zeros} is a zero finder in \\spad{UP}."))) @@ -2370,7 +2374,7 @@ NIL NIL (|LiePolynomial| |VarSet| R) ((|constructor| (NIL "This type supports Lie polynomials in Lyndon basis see Free Lie Algebras by \\spad{C}. Reutenauer (Oxford science publications). \\newline Author: Michel Petitot (petitot@lifl.fr).")) (|construct| (($ $ (|LyndonWord| |#1|)) "\\axiom{construct(\\spad{x},{}\\spad{y})} returns the Lie bracket \\axiom{[\\spad{x},{}\\spad{y}]}.") (($ (|LyndonWord| |#1|) $) "\\axiom{construct(\\spad{x},{}\\spad{y})} returns the Lie bracket \\axiom{[\\spad{x},{}\\spad{y}]}.") (($ (|LyndonWord| |#1|) (|LyndonWord| |#1|)) "\\axiom{construct(\\spad{x},{}\\spad{y})} returns the Lie bracket \\axiom{[\\spad{x},{}\\spad{y}]}.")) (|LiePolyIfCan| (((|Union| $ "failed") (|XDistributedPolynomial| |#1| |#2|)) "\\axiom{LiePolyIfCan(\\spad{p})} returns \\axiom{\\spad{p}} in Lyndon basis if \\axiom{\\spad{p}} is a Lie polynomial,{} otherwise \\axiom{\"failed\"} is returned."))) -((|JacobiIdentity| . T) (|NullSquare| . T) (|leftUnitary| . T) (|rightUnitary| . T)) +NIL ((|HasCategory| |#2| (QUOTE (|Field|))) (|HasCategory| |#2| (QUOTE (|CommutativeRing|)))) (|ListAggregate&| A S) ((|constructor| (NIL "A list aggregate is a model for a linked list data structure. A linked list is a versatile data structure. Insertion and deletion are efficient and searching is a linear operation.")) (|list| (($ |#2|) "\\spad{list(x)} returns the list of one element \\spad{x}."))) @@ -2394,14 +2398,14 @@ NIL NIL (|LieSquareMatrix| |n| R) ((|constructor| (NIL "LieSquareMatrix(\\spad{n},{}\\spad{R}) implements the Lie algebra of the \\spad{n} by \\spad{n} matrices over the commutative ring \\spad{R}. The Lie bracket (commutator) of the algebra is given by \\spad{a*b := (a *\\$SQMATRIX(n,R) b - b *\\$SQMATRIX(n,R) a)},{} where \\spadfun{*\\$SQMATRIX(\\spad{n},{}\\spad{R})} is the usual matrix multiplication."))) -((|unitsKnown| . T) (|rightUnitary| . T) (|leftUnitary| . T)) -(#1=(|HasCategory| |#2| (QUOTE (|PartialDifferentialRing| #2=(|Symbol|)))) (|HasCategory| |#2| (QUOTE (|PartialDifferentialSpace| #2#))) #3=(|HasCategory| |#2| (QUOTE (|DifferentialRing|))) (|HasCategory| |#2| (QUOTE (|DifferentialSpace|))) #4=(|HasAttribute| |#2| (QUOTE (|commutative| "*"))) #5=(|HasCategory| |#2| (QUOTE (|LinearlyExplicitRingOver| #6=(|Integer|)))) (|HasCategory| |#2| (QUOTE (|RetractableTo| (|Fraction| #6#)))) (|HasCategory| |#2| (QUOTE (|RetractableTo| #6#))) (OR (AND #3# #7=(|HasCategory| |#2| (|%list| (QUOTE |Evalable|) (|devaluate| |#2|)))) (AND #5# #7#) (AND #1# #7#) #8=(AND #9=(|HasCategory| |#2| (QUOTE (|SetCategory|))) #7#)) (|HasCategory| |#2| (QUOTE (|EuclideanDomain|))) (|HasCategory| |#2| (QUOTE (|Field|))) (|HasCategory| |#2| (QUOTE (|IntegralDomain|))) (OR #4# #3# #1#) (|HasCategory| |#2| (QUOTE (|CoercibleTo| (|OutputForm|)))) (|HasCategory| |#2| (QUOTE (|BasicType|))) #9# #8# (|HasCategory| |#2| (QUOTE (|CommutativeRing|)))) +NIL +(#1=(|HasCategory| |#2| (QUOTE (|PartialDifferentialRing| #2=(|Symbol|)))) (|HasCategory| |#2| (QUOTE (|PartialDifferentialSpace| #2#))) #3=(|HasCategory| |#2| (QUOTE (|DifferentialRing|))) (|HasCategory| |#2| (QUOTE (|DifferentialSpace|))) (|HasAttribute| |#2| (QUOTE (|commutative| "*"))) #4=(|HasCategory| |#2| (QUOTE (|LinearlyExplicitRingOver| #5=(|Integer|)))) (|HasCategory| |#2| (QUOTE (|RetractableTo| (|Fraction| #5#)))) (|HasCategory| |#2| (QUOTE (|RetractableTo| #5#))) (OR (AND #3# #6=(|HasCategory| |#2| (|%list| (QUOTE |Evalable|) (|devaluate| |#2|)))) (AND #4# #6#) (AND #1# #6#) #7=(AND #8=(|HasCategory| |#2| (QUOTE (|SetCategory|))) #6#)) (|HasCategory| |#2| (QUOTE (|EuclideanDomain|))) (|HasCategory| |#2| (QUOTE (|Field|))) (|HasCategory| |#2| (QUOTE (|IntegralDomain|))) #7# #8# (|HasCategory| |#2| (QUOTE (|BasicType|))) (|HasCategory| |#2| (QUOTE (|CoercibleTo| (|OutputForm|)))) (|HasCategory| |#2| (QUOTE (|CommutativeRing|)))) (|ConstructAst|) ((|constructor| (NIL "This domain represents `literal sequence' syntax.")) (|elements| (((|List| (|SpadAst|)) $) "\\spad{elements(e)} returns the list of expressions in the `literal' list `e'."))) NIL NIL (|LyndonWord| |VarSet|) -((|constructor| (NIL "Lyndon words over arbitrary (ordered) symbols: see Free Lie Algebras by \\spad{C}. Reutenauer (Oxford science publications). A Lyndon word is a word which is smaller than any of its right factors \\spad{w}.\\spad{r}.\\spad{t}. the pure lexicographical ordering. If \\axiom{a} and \\axiom{\\spad{b}} are two Lyndon words such that \\axiom{a < \\spad{b}} holds \\spad{w}.\\spad{r}.\\spad{t} lexicographical ordering then \\axiom{a*b} is a Lyndon word. Parenthesized Lyndon words can be generated from symbols by using the following rule: \\axiom{[[a,{}\\spad{b}],{}\\spad{c}]} is a Lyndon word iff \\axiom{a*b < \\spad{c} <= \\spad{b}} holds. Lyndon words are internally represented by binary trees using the \\spadtype{Magma} domain constructor. Two ordering are provided: lexicographic and length-lexicographic. \\newline Author : Michel Petitot (petitot@lifl.fr).")) (|LyndonWordsList| (((|List| $) (|List| |#1|) (|PositiveInteger|)) "\\axiom{LyndonWordsList(vl,{} \\spad{n})} returns the list of Lyndon words over the alphabet \\axiom{vl},{} up to order \\axiom{\\spad{n}}.")) (|LyndonWordsList1| (((|OneDimensionalArray| (|List| $)) (|List| |#1|) (|PositiveInteger|)) "\\axiom{\\spad{LyndonWordsList1}(vl,{} \\spad{n})} returns an array of lists of Lyndon words over the alphabet \\axiom{vl},{} up to order \\axiom{\\spad{n}}.")) (|varList| (((|List| |#1|) $) "\\axiom{varList(\\spad{x})} returns the list of distinct entries of \\axiom{\\spad{x}}.")) (|lyndonIfCan| (((|Union| $ "failed") (|OrderedFreeMonoid| |#1|)) "\\axiom{lyndonIfCan(\\spad{w})} convert \\axiom{\\spad{w}} into a Lyndon word.")) (|lyndon| (($ (|OrderedFreeMonoid| |#1|)) "\\axiom{lyndon(\\spad{w})} convert \\axiom{\\spad{w}} into a Lyndon word,{} error if \\axiom{\\spad{w}} is not a Lyndon word.")) (|lyndon?| (((|Boolean|) (|OrderedFreeMonoid| |#1|)) "\\axiom{lyndon?(\\spad{w})} test if \\axiom{\\spad{w}} is a Lyndon word.")) (|factor| (((|List| $) (|OrderedFreeMonoid| |#1|)) "\\axiom{factor(\\spad{x})} returns the decreasing factorization into Lyndon words.")) (|coerce| (((|Magma| |#1|) $) "\\axiom{coerce(\\spad{x})} returns the element of \\axiomType{Magma}(VarSet) corresponding to \\axiom{\\spad{x}}.") (((|OrderedFreeMonoid| |#1|) $) "\\axiom{coerce(\\spad{x})} returns the element of \\axiomType{OrderedFreeMonoid}(VarSet) corresponding to \\axiom{\\spad{x}}.")) (|lexico| (((|Boolean|) $ $) "\\axiom{lexico(\\spad{x},{}\\spad{y})} returns \\axiom{\\spad{true}} iff \\axiom{\\spad{x}} is smaller than \\axiom{\\spad{y}} \\spad{w}.\\spad{r}.\\spad{t}. the lexicographical ordering induced by \\axiom{VarSet}.")) (|length| (((|PositiveInteger|) $) "\\axiom{length(\\spad{x})} returns the number of entries in \\axiom{\\spad{x}}.")) (|right| (($ $) "\\axiom{right(\\spad{x})} returns right subtree of \\axiom{\\spad{x}} or error if \\axiomOpFrom{retractable?}{LyndonWord}(\\axiom{\\spad{x}}) is \\spad{true}.")) (|left| (($ $) "\\axiom{left(\\spad{x})} returns left subtree of \\axiom{\\spad{x}} or error if \\axiomOpFrom{retractable?}{LyndonWord}(\\axiom{\\spad{x}}) is \\spad{true}.")) (|retractable?| (((|Boolean|) $) "\\axiom{retractable?(\\spad{x})} tests if \\axiom{\\spad{x}} is a tree with only one entry."))) +((|constructor| (NIL "Lyndon words over arbitrary (ordered) symbols: see Free Lie Algebras by \\spad{C}. Reutenauer (Oxford science publications). A Lyndon word is a word which is smaller than any of its right factors \\spad{w}.\\spad{r}.\\spad{t}. the pure lexicographical ordering. If \\axiom{a} and \\axiom{\\spad{b}} are two Lyndon words such that \\axiom{a < \\spad{b}} holds \\spad{w}.\\spad{r}.\\spad{t} lexicographical ordering then \\axiom{a*b} is a Lyndon word. Parenthesized Lyndon words can be generated from symbols by using the following rule: \\axiom{[[a,{}\\spad{b}],{}\\spad{c}]} is a Lyndon word iff \\axiom{a*b < \\spad{c} <= \\spad{b}} holds. Lyndon words are internally represented by binary trees using the \\spadtype{FreeMagma} domain constructor. Two ordering are provided: lexicographic and length-lexicographic. \\newline Author : Michel Petitot (petitot@lifl.fr).")) (|LyndonWordsList| (((|List| $) (|List| |#1|) (|PositiveInteger|)) "\\axiom{LyndonWordsList(vl,{} \\spad{n})} returns the list of Lyndon words over the alphabet \\axiom{vl},{} up to order \\axiom{\\spad{n}}.")) (|LyndonWordsList1| (((|OneDimensionalArray| (|List| $)) (|List| |#1|) (|PositiveInteger|)) "\\axiom{\\spad{LyndonWordsList1}(vl,{} \\spad{n})} returns an array of lists of Lyndon words over the alphabet \\axiom{vl},{} up to order \\axiom{\\spad{n}}.")) (|varList| (((|List| |#1|) $) "\\axiom{varList(\\spad{x})} returns the list of distinct entries of \\axiom{\\spad{x}}.")) (|lyndonIfCan| (((|Union| $ "failed") (|OrderedFreeMonoid| |#1|)) "\\axiom{lyndonIfCan(\\spad{w})} convert \\axiom{\\spad{w}} into a Lyndon word.")) (|lyndon| (($ (|OrderedFreeMonoid| |#1|)) "\\axiom{lyndon(\\spad{w})} convert \\axiom{\\spad{w}} into a Lyndon word,{} error if \\axiom{\\spad{w}} is not a Lyndon word.")) (|lyndon?| (((|Boolean|) (|OrderedFreeMonoid| |#1|)) "\\axiom{lyndon?(\\spad{w})} test if \\axiom{\\spad{w}} is a Lyndon word.")) (|factor| (((|List| $) (|OrderedFreeMonoid| |#1|)) "\\axiom{factor(\\spad{x})} returns the decreasing factorization into Lyndon words.")) (|lexico| (((|Boolean|) $ $) "\\axiom{lexico(\\spad{x},{}\\spad{y})} returns \\axiom{\\spad{true}} iff \\axiom{\\spad{x}} is smaller than \\axiom{\\spad{y}} \\spad{w}.\\spad{r}.\\spad{t}. the lexicographical ordering induced by \\axiom{VarSet}.")) (|length| (((|PositiveInteger|) $) "\\axiom{length(\\spad{x})} returns the number of entries in \\axiom{\\spad{x}}.")) (|right| (($ $) "\\axiom{right(\\spad{x})} returns right subtree of \\axiom{\\spad{x}} or error if \\axiomOpFrom{retractable?}{LyndonWord}(\\axiom{\\spad{x}}) is \\spad{true}.")) (|left| (($ $) "\\axiom{left(\\spad{x})} returns left subtree of \\axiom{\\spad{x}} or error if \\axiomOpFrom{retractable?}{LyndonWord}(\\axiom{\\spad{x}}) is \\spad{true}.")) (|retractable?| (((|Boolean|) $) "\\axiom{retractable?(\\spad{x})} tests if \\axiom{\\spad{x}} is a tree with only one entry."))) NIL NIL (|LazyStreamAggregate&| A S) @@ -2416,10 +2420,6 @@ NIL ((|constructor| (NIL "This domain represents the syntax of a macro definition.")) (|body| (((|SpadAst|) $) "\\spad{body(m)} returns the right hand side of the definition `m'.")) (|head| (((|HeadAst|) $) "\\spad{head(m)} returns the head of the macro definition `m'. This is a list of identifiers starting with the name of the macro followed by the name of the parameters,{} if any."))) NIL NIL -(|Magma| |VarSet|) -((|constructor| (NIL "This type is the basic representation of parenthesized words (binary trees over arbitrary symbols) useful in \\spadtype{LiePolynomial}. \\newline Author: Michel Petitot (petitot@lifl.fr).")) (|varList| (((|List| |#1|) $) "\\axiom{varList(\\spad{x})} returns the list of distinct entries of \\axiom{\\spad{x}}.")) (|right| (($ $) "\\axiom{right(\\spad{x})} returns right subtree of \\axiom{\\spad{x}} or error if \\axiomOpFrom{retractable?}{Magma}(\\axiom{\\spad{x}}) is \\spad{true}.")) (|retractable?| (((|Boolean|) $) "\\axiom{retractable?(\\spad{x})} tests if \\axiom{\\spad{x}} is a tree with only one entry.")) (|rest| (($ $) "\\axiom{rest(\\spad{x})} return \\axiom{\\spad{x}} without the first entry or error if \\axiomOpFrom{retractable?}{Magma}(\\axiom{\\spad{x}}) is \\spad{true}.")) (|mirror| (($ $) "\\axiom{mirror(\\spad{x})} returns the reversed word of \\axiom{\\spad{x}}. That is \\axiom{\\spad{x}} itself if \\axiomOpFrom{retractable?}{Magma}(\\axiom{\\spad{x}}) is \\spad{true} and \\axiom{mirror(\\spad{z}) * mirror(\\spad{y})} if \\axiom{\\spad{x}} is \\axiom{y*z}.")) (|lexico| (((|Boolean|) $ $) "\\axiom{lexico(\\spad{x},{}\\spad{y})} returns \\axiom{\\spad{true}} iff \\axiom{\\spad{x}} is smaller than \\axiom{\\spad{y}} \\spad{w}.\\spad{r}.\\spad{t}. the lexicographical ordering induced by \\axiom{VarSet}. \\spad{N}.\\spad{B}. This operation does not take into account the tree structure of its arguments. Thus this is not a total ordering.")) (|length| (((|PositiveInteger|) $) "\\axiom{length(\\spad{x})} returns the number of entries in \\axiom{\\spad{x}}.")) (|left| (($ $) "\\axiom{left(\\spad{x})} returns left subtree of \\axiom{\\spad{x}} or error if \\axiomOpFrom{retractable?}{Magma}(\\axiom{\\spad{x}}) is \\spad{true}.")) (|first| ((|#1| $) "\\axiom{first(\\spad{x})} returns the first entry of the tree \\axiom{\\spad{x}}.")) (|coerce| (((|OrderedFreeMonoid| |#1|) $) "\\axiom{coerce(\\spad{x})} returns the element of \\axiomType{OrderedFreeMonoid}(VarSet) corresponding to \\axiom{\\spad{x}} by removing parentheses.")) (* (($ $ $) "\\axiom{x*y} returns the tree \\axiom{[\\spad{x},{}\\spad{y}]}."))) -NIL -NIL (|MappingPackageInternalHacks1| A) ((|constructor| (NIL "various Currying operations.")) (|recur| ((|#1| (|Mapping| |#1| (|NonNegativeInteger|) |#1|) (|NonNegativeInteger|) |#1|) "\\spad{recur(n,g,x)} is \\spad{g(n,g(n-1,..g(1,x)..))}.")) (|iter| ((|#1| (|Mapping| |#1| |#1|) (|NonNegativeInteger|) |#1|) "\\spad{iter(f,n,x)} applies \\spad{f n} times to \\spad{x}."))) NIL @@ -2475,7 +2475,7 @@ NIL (|Maybe| T$) ((|constructor| (NIL "This domain implements the notion of optional value,{} where a computation may fail to produce expected value.")) (|nothing| (($) "\\spad{nothing} represents failure or absence of value.")) (|autoCoerce| ((|#1| $) "\\spad{autoCoerce} is a courtesy coercion function used by the compiler in case it knows that `x' really is a \\spadtype{T}.")) (|case| (((|Boolean|) $ (|[\|\|]| |nothing|)) "\\spad{x case nothing} holds if the value for \\spad{x} is missing.") (((|Boolean|) $ (|[\|\|]| |#1|)) "\\spad{x case T} returns \\spad{true} if \\spad{x} is actually a data of type \\spad{T}.")) (|just| (($ |#1|) "\\spad{just x} injects the value `x' into \\%."))) NIL -NIL +((|HasCategory| |#1| (QUOTE (|CoercibleTo| (|OutputForm|))))) (|MatrixCommonDenominator| R Q) ((|constructor| (NIL "MatrixCommonDenominator provides functions to compute the common denominator of a matrix of elements of the quotient field of an integral domain.")) (|splitDenominator| (((|Record| (|:| |num| (|Matrix| |#1|)) (|:| |den| |#1|)) (|Matrix| |#2|)) "\\spad{splitDenominator(q)} returns \\spad{[p, d]} such that \\spad{q = p/d} and \\spad{d} is a common denominator for the elements of \\spad{q}.")) (|clearDenominator| (((|Matrix| |#1|) (|Matrix| |#2|)) "\\spad{clearDenominator(q)} returns \\spad{p} such that \\spad{q = p/d} where \\spad{d} is a common denominator for the elements of \\spad{q}.")) (|commonDenominator| ((|#1| (|Matrix| |#2|)) "\\spad{commonDenominator(q)} returns a common denominator \\spad{d} for the elements of \\spad{q}."))) NIL @@ -2526,7 +2526,7 @@ NIL NIL (|MonogenicLinearOperator| R) ((|constructor| (NIL "This is the category of linear operator rings with one generator. The generator is not named by the category but can always be constructed as \\spad{monomial(1,1)}. \\blankline For convenience,{} call the generator \\spad{G}. Then each value is equal to \\indented{4}{\\spad{sum(a(i)*G**i, i = 0..n)}} for some unique \\spad{n} and \\spad{a(i)} in \\spad{R}. \\blankline Note that multiplication is not necessarily commutative. In fact,{} if \\spad{a} is in \\spad{R},{} it is quite normal to have \\spad{a*G \\~= G*a}.")) (|monomial| (($ |#1| (|NonNegativeInteger|)) "\\spad{monomial(c,k)} produces \\spad{c} times the \\spad{k}-th power of the generating operator,{} \\spad{monomial(1,1)}.")) (|coefficient| ((|#1| $ (|NonNegativeInteger|)) "\\spad{coefficient(l,k)} is \\spad{a(k)} if \\indented{2}{\\spad{l = sum(monomial(a(i),i), i = 0..n)}.}")) (|reductum| (($ $) "\\spad{reductum(l)} is \\spad{l - monomial(a(n),n)} if \\indented{2}{\\spad{l = sum(monomial(a(i),i), i = 0..n)}.}")) (|leadingCoefficient| ((|#1| $) "\\spad{leadingCoefficient(l)} is \\spad{a(n)} if \\indented{2}{\\spad{l = sum(monomial(a(i),i), i = 0..n)}.}")) (|minimumDegree| (((|NonNegativeInteger|) $) "\\spad{minimumDegree(l)} is the smallest \\spad{k} such that \\spad{a(k) \\~= 0} if \\indented{2}{\\spad{l = sum(monomial(a(i),i), i = 0..n)}.}")) (|degree| (((|NonNegativeInteger|) $) "\\spad{degree(l)} is \\spad{n} if \\indented{2}{\\spad{l = sum(monomial(a(i),i), i = 0..n)}.}"))) -((|rightUnitary| . T) (|leftUnitary| . T) (|unitsKnown| . T)) +NIL NIL (|MultipleMap| R1 UP1 UPUP1 R2 UP2 UPUP2) ((|constructor| (NIL "Lifting of a map through 2 levels of polynomials.")) (|map| ((|#6| (|Mapping| |#4| |#1|) |#3|) "\\spad{map(f, p)} lifts \\spad{f} to the domain of \\spad{p} then applies it to \\spad{p}."))) @@ -2537,24 +2537,24 @@ NIL NIL NIL (|ModularField| R |Mod| |reduction| |merge| |exactQuo|) -((|constructor| (NIL "\\indented{1}{These domains are used for the factorization and gcds} of univariate polynomials over the integers in order to work modulo different primes. See \\spadtype{ModularRing},{} \\spadtype{EuclideanModularRing}")) (|exQuo| (((|Union| $ "failed") $ $) "\\spad{exQuo(x,y)} \\undocumented")) (|reduce| (($ |#1| |#2|) "\\spad{reduce(r,m)} \\undocumented")) (|coerce| ((|#1| $) "\\spad{coerce(x)} \\undocumented")) (|modulus| ((|#2| $) "\\spad{modulus(x)} \\undocumented"))) -((|canonicalsClosed| . T) (|canonicalUnitNormal| . T) (|noZeroDivisors| . T) ((|commutative| "*") . T) (|rightUnitary| . T) (|leftUnitary| . T) (|unitsKnown| . T)) +((|constructor| (NIL "\\indented{1}{These domains are used for the factorization and gcds} of univariate polynomials over the integers in order to work modulo different primes. See \\spadtype{ModularRing},{} \\spadtype{EuclideanModularRing}")) (|exQuo| (((|Union| $ "failed") $ $) "\\spad{exQuo(x,y)} \\undocumented")) (|reduce| (($ |#1| |#2|) "\\spad{reduce(r,m)} \\undocumented")) (|modulus| ((|#2| $) "\\spad{modulus(x)} \\undocumented"))) +((|canonicalUnitNormal| . T) (|noZeroDivisors| . T) ((|commutative| "*") . T)) NIL (|ModMonic| R P) ((|constructor| (NIL "This package \\undocumented")) (|frobenius| (($ $) "\\spad{frobenius(x)} \\undocumented")) (|computePowers| (((|PrimitiveArray| $)) "\\spad{computePowers()} \\undocumented")) (|pow| (((|PrimitiveArray| $)) "\\spad{pow()} \\undocumented")) (|An| (((|Vector| |#1|) $) "\\spad{An(x)} \\undocumented")) (|UnVectorise| (($ (|Vector| |#1|)) "\\spad{UnVectorise(v)} \\undocumented")) (|Vectorise| (((|Vector| |#1|) $) "\\spad{Vectorise(x)} \\undocumented")) (|lift| ((|#2| $) "\\spad{lift(x)} \\undocumented")) (|reduce| (($ |#2|) "\\spad{reduce(x)} \\undocumented")) (|modulus| ((|#2|) "\\spad{modulus()} \\undocumented")) (|setPoly| ((|#2| |#2|) "\\spad{setPoly(x)} \\undocumented"))) -(((|commutative| "*") |has| |#1| (|CommutativeRing|)) (|noZeroDivisors| |has| |#1| (|IntegralDomain|)) (|additiveValuation| |has| |#1| (|Field|)) (|canonicalUnitNormal| |has| |#1| (ATTRIBUTE |canonicalUnitNormal|)) (|leftUnitary| . T) (|rightUnitary| . T) (|unitsKnown| . T)) -(#1=(|HasCategory| |#1| (QUOTE (|PolynomialFactorizationExplicit|))) #2=(|HasCategory| |#1| (QUOTE (|IntegralDomain|))) #3=(|HasCategory| |#1| (QUOTE (|CommutativeRing|))) (OR #3# #2#) (AND (|HasCategory| |#1| #4=(QUOTE (|PatternMatchable| #5=(|Float|)))) (|HasCategory| #6=(|SingletonAsOrderedSet|) #4#)) (AND (|HasCategory| |#1| #7=(QUOTE (|PatternMatchable| #8=(|Integer|)))) (|HasCategory| #6# #7#)) (AND (|HasCategory| |#1| #9=(QUOTE (|ConvertibleTo| (|Pattern| #5#)))) (|HasCategory| #6# #9#)) (AND (|HasCategory| |#1| #10=(QUOTE (|ConvertibleTo| (|Pattern| #8#)))) (|HasCategory| #6# #10#)) (AND (|HasCategory| |#1| #11=(QUOTE (|ConvertibleTo| (|InputForm|)))) (|HasCategory| #6# #11#)) (|HasCategory| |#1| (QUOTE (|LinearlyExplicitRingOver| #8#))) (|HasCategory| |#1| (QUOTE (|CharacteristicZero|))) #12=(|HasCategory| |#1| #13=(QUOTE (|CharacteristicNonZero|))) #14=(|HasCategory| |#1| (QUOTE (|Algebra| #15=(|Fraction| #8#)))) (|HasCategory| |#1| (QUOTE (|RetractableTo| #8#))) (OR #14# #16=(|HasCategory| |#1| (QUOTE (|RetractableTo| #15#)))) #16# (OR #3# #17=(|HasCategory| |#1| (QUOTE (|Field|))) #18=(|HasCategory| |#1| (QUOTE (|GcdDomain|))) #2# #1#) (OR #17# #18# #2# #1#) (OR #17# #18# #1#) #17# (|HasCategory| |#1| (QUOTE (|StepThrough|))) (|HasCategory| |#1| (QUOTE (|PartialDifferentialSpace| #19=(|Symbol|)))) (|HasCategory| |#1| (QUOTE (|PartialDifferentialRing| #19#))) (|HasCategory| |#1| (QUOTE (|Finite|))) (|HasCategory| |#1| (QUOTE (|FiniteFieldCategory|))) (|HasCategory| |#1| (QUOTE (|DifferentialSpace|))) (|HasCategory| |#1| (QUOTE (|DifferentialRing|))) (|HasAttribute| |#1| (QUOTE |canonicalUnitNormal|)) #18# #20=(AND #1# (|HasCategory| $ #13#)) (OR #20# #12#)) +(((|commutative| "*") |has| |#1| (|CommutativeRing|)) (|noZeroDivisors| |has| |#1| (|IntegralDomain|)) (|additiveValuation| |has| |#1| (|Field|)) (|canonicalUnitNormal| |has| |#1| (ATTRIBUTE |canonicalUnitNormal|))) +(#1=(|HasCategory| |#1| (QUOTE (|PolynomialFactorizationExplicit|))) #2=(|HasCategory| |#1| (QUOTE (|IntegralDomain|))) #3=(|HasCategory| |#1| (QUOTE (|CommutativeRing|))) (OR #3# #2#) (AND (|HasCategory| |#1| #4=(QUOTE (|PatternMatchable| #5=(|Float|)))) (|HasCategory| #6=(|SingletonAsOrderedSet|) #4#)) (AND (|HasCategory| |#1| #7=(QUOTE (|PatternMatchable| #8=(|Integer|)))) (|HasCategory| #6# #7#)) (AND (|HasCategory| |#1| #9=(QUOTE (|ConvertibleTo| (|Pattern| #5#)))) (|HasCategory| #6# #9#)) (AND (|HasCategory| |#1| #10=(QUOTE (|ConvertibleTo| (|Pattern| #8#)))) (|HasCategory| #6# #10#)) (AND (|HasCategory| |#1| #11=(QUOTE (|ConvertibleTo| (|InputForm|)))) (|HasCategory| #6# #11#)) (|HasCategory| |#1| (QUOTE (|LinearlyExplicitRingOver| #8#))) #12=(|HasCategory| |#1| (QUOTE (|Algebra| #13=(|Fraction| #8#)))) #14=(|HasCategory| |#1| #15=(QUOTE (|CharacteristicNonZero|))) (|HasCategory| |#1| (QUOTE (|CharacteristicZero|))) (|HasCategory| |#1| (QUOTE (|RetractableTo| #8#))) (OR #12# #16=(|HasCategory| |#1| (QUOTE (|RetractableTo| #13#)))) #16# (OR #3# #17=(|HasCategory| |#1| (QUOTE (|Field|))) #18=(|HasCategory| |#1| (QUOTE (|GcdDomain|))) #2# #1#) (OR #17# #18# #2# #1#) (OR #17# #18# #1#) #17# (|HasCategory| |#1| (QUOTE (|StepThrough|))) (|HasCategory| |#1| (QUOTE (|PartialDifferentialSpace| #19=(|Symbol|)))) (|HasCategory| |#1| (QUOTE (|PartialDifferentialRing| #19#))) (|HasCategory| |#1| (QUOTE (|Finite|))) (|HasCategory| |#1| (QUOTE (|FiniteFieldCategory|))) (|HasCategory| |#1| (QUOTE (|DifferentialSpace|))) (|HasCategory| |#1| (QUOTE (|DifferentialRing|))) (|HasAttribute| |#1| (QUOTE |canonicalUnitNormal|)) #18# #20=(AND #1# (|HasCategory| $ #15#)) (OR #20# #14#)) (|ModuleMonomial| IS E |ff|) ((|constructor| (NIL "This package \\undocumented")) (|construct| (($ |#1| |#2|) "\\spad{construct(i,e)} \\undocumented")) (|index| ((|#1| $) "\\spad{index(x)} \\undocumented")) (|exponent| ((|#2| $) "\\spad{exponent(x)} \\undocumented"))) NIL NIL (|ModuleOperator| R M) ((|constructor| (NIL "Algebra of ADDITIVE operators on a module.")) (|makeop| (($ |#1| (|FreeGroup| (|BasicOperator|))) "\\spad{makeop should} be local but conditional")) (|opeval| ((|#2| (|BasicOperator|) |#2|) "\\spad{opeval should} be local but conditional")) (** (($ $ (|Integer|)) "\\spad{op**n} \\undocumented") (($ (|BasicOperator|) (|Integer|)) "\\spad{op**n} \\undocumented")) (|evaluateInverse| (($ $ (|Mapping| |#2| |#2|)) "\\spad{evaluateInverse(x,f)} \\undocumented")) (|evaluate| (($ $ (|Mapping| |#2| |#2|)) "\\spad{evaluate(f, u +-> g u)} attaches the map \\spad{g} to \\spad{f}. \\spad{f} must be a basic operator \\spad{g} MUST be additive,{} \\spadignore{i.e.} \\spad{g(a + b) = g(a) + g(b)} for any \\spad{a},{} \\spad{b} in \\spad{M}. This implies that \\spad{g(n a) = n g(a)} for any \\spad{a} in \\spad{M} and integer \\spad{n > 0}.")) (|conjug| ((|#1| |#1|) "\\spad{conjug(x)}should be local but conditional")) (|adjoint| (($ $ $) "\\spad{adjoint(op1, op2)} sets the adjoint of \\spad{op1} to be \\spad{op2}. \\spad{op1} must be a basic operator") (($ $) "\\spad{adjoint(op)} returns the adjoint of the operator \\spad{op}."))) -((|leftUnitary| |has| |#1| . #1=((|CommutativeRing|))) (|rightUnitary| |has| |#1| . #1#) (|unitsKnown| . T)) +NIL ((|HasCategory| |#1| (QUOTE (|CommutativeRing|))) (|HasCategory| |#1| (QUOTE (|CharacteristicNonZero|))) (|HasCategory| |#1| (QUOTE (|CharacteristicZero|)))) (|ModularRing| R |Mod| |reduction| |merge| |exactQuo|) -((|constructor| (NIL "These domains are used for the factorization and gcds of univariate polynomials over the integers in order to work modulo different primes. See \\spadtype{EuclideanModularRing} ,{}\\spadtype{ModularField}")) (|inv| (($ $) "\\spad{inv(x)} \\undocumented")) (|recip| (((|Union| $ "failed") $) "\\spad{recip(x)} \\undocumented")) (|exQuo| (((|Union| $ "failed") $ $) "\\spad{exQuo(x,y)} \\undocumented")) (|reduce| (($ |#1| |#2|) "\\spad{reduce(r,m)} \\undocumented")) (|coerce| ((|#1| $) "\\spad{coerce(x)} \\undocumented")) (|modulus| ((|#2| $) "\\spad{modulus(x)} \\undocumented"))) -((|unitsKnown| . T)) +((|constructor| (NIL "These domains are used for the factorization and gcds of univariate polynomials over the integers in order to work modulo different primes. See \\spadtype{EuclideanModularRing} ,{}\\spadtype{ModularField}")) (|inv| (($ $) "\\spad{inv(x)} \\undocumented")) (|exQuo| (((|Union| $ "failed") $ $) "\\spad{exQuo(x,y)} \\undocumented")) (|reduce| (($ |#1| |#2|) "\\spad{reduce(r,m)} \\undocumented")) (|modulus| ((|#2| $) "\\spad{modulus(x)} \\undocumented"))) +NIL NIL (|Module&| S R) ((|constructor| (NIL "The category of modules over a commutative ring. \\blankline"))) @@ -2562,11 +2562,11 @@ NIL NIL (|Module| R) ((|constructor| (NIL "The category of modules over a commutative ring. \\blankline"))) -((|leftUnitary| . T) (|rightUnitary| . T)) +NIL NIL (|MoebiusTransform| F) ((|constructor| (NIL "\\indented{1}{MoebiusTransform(\\spad{F}) is the domain of fractional linear (Moebius)} transformations over \\spad{F}.")) (|eval| (((|OnePointCompletion| |#1|) $ (|OnePointCompletion| |#1|)) "\\spad{eval(m,x)} returns \\spad{(a*x + b)/(c*x + d)} where \\spad{m = moebius(a,b,c,d)} (see \\spadfunFrom{moebius}{MoebiusTransform}).") ((|#1| $ |#1|) "\\spad{eval(m,x)} returns \\spad{(a*x + b)/(c*x + d)} where \\spad{m = moebius(a,b,c,d)} (see \\spadfunFrom{moebius}{MoebiusTransform}).")) (|recip| (($ $) "\\spad{recip(m)} = recip() * \\spad{m}") (($) "\\spad{recip()} returns \\spad{matrix [[0,1],[1,0]]} representing the map \\spad{x -> 1 / x}.")) (|scale| (($ $ |#1|) "\\spad{scale(m,h)} returns \\spad{scale(h) * m} (see \\spadfunFrom{shift}{MoebiusTransform}).") (($ |#1|) "\\spad{scale(k)} returns \\spad{matrix [[k,0],[0,1]]} representing the map \\spad{x -> k * x}.")) (|shift| (($ $ |#1|) "\\spad{shift(m,h)} returns \\spad{shift(h) * m} (see \\spadfunFrom{shift}{MoebiusTransform}).") (($ |#1|) "\\spad{shift(k)} returns \\spad{matrix [[1,k],[0,1]]} representing the map \\spad{x -> x + k}.")) (|moebius| (($ |#1| |#1| |#1| |#1|) "\\spad{moebius(a,b,c,d)} returns \\spad{matrix [[a,b],[c,d]]}."))) -((|unitsKnown| . T)) +NIL NIL (|Monad&| S) ((|constructor| (NIL "Monad is the class of all multiplicative monads,{} \\spadignore{i.e.} sets with a binary operation.")) (** (($ $ (|PositiveInteger|)) "\\spad{a**n} returns the \\spad{n}\\spad{-}th power of \\spad{a},{} defined by repeated squaring.")) (|leftPower| (($ $ (|PositiveInteger|)) "\\spad{leftPower(a,n)} returns the \\spad{n}\\spad{-}th left power of \\spad{a},{} \\spadignore{i.e.} \\spad{leftPower(a,n) := a * leftPower(a,n-1)} and \\spad{leftPower(a,1) := a}.")) (|rightPower| (($ $ (|PositiveInteger|)) "\\spad{rightPower(a,n)} returns the \\spad{n}\\spad{-}th right power of \\spad{a},{} \\spadignore{i.e.} \\spad{rightPower(a,n) := rightPower(a,n-1) * a} and \\spad{rightPower(a,1) := a}.")) (* (($ $ $) "\\spad{a*b} is the product of \\spad{a} and \\spad{b} in a set with a binary operation."))) @@ -2577,11 +2577,11 @@ NIL NIL NIL (|MonadWithUnit&| S) -((|constructor| (NIL "\\indented{1}{MonadWithUnit is the class of multiplicative monads with unit,{}} \\indented{1}{\\spadignore{i.e.} sets with a binary operation and a unit element.} Axioms \\indented{3}{leftIdentity(\"*\":(\\%,{}\\%)->\\%,{}1)\\space{3}\\tab{30} 1*x=x} \\indented{3}{rightIdentity(\"*\":(\\%,{}\\%)->\\%,{}1)\\space{2}\\tab{30} x*1=x} Common Additional Axioms \\indented{3}{unitsKnown---if \"recip\" says \"failed\",{} that PROVES input wasn't a unit}")) (|rightRecip| (((|Union| $ "failed") $) "\\spad{rightRecip(a)} returns an element,{} which is a right inverse of \\spad{a},{} or \\spad{\"failed\"} if such an element doesn't exist or cannot be determined (see unitsKnown).")) (|leftRecip| (((|Union| $ "failed") $) "\\spad{leftRecip(a)} returns an element,{} which is a left inverse of \\spad{a},{} or \\spad{\"failed\"} if such an element doesn't exist or cannot be determined (see unitsKnown).")) (|recip| (((|Union| $ "failed") $) "\\spad{recip(a)} returns an element,{} which is both a left and a right inverse of \\spad{a},{} or \\spad{\"failed\"} if such an element doesn't exist or cannot be determined (see unitsKnown).")) (** (($ $ (|NonNegativeInteger|)) "\\spad{a**n} returns the \\spad{n}\\spad{-}th power of \\spad{a},{} defined by repeated squaring.")) (|leftPower| (($ $ (|NonNegativeInteger|)) "\\spad{leftPower(a,n)} returns the \\spad{n}\\spad{-}th left power of \\spad{a},{} \\spadignore{i.e.} \\spad{leftPower(a,n) := a * leftPower(a,n-1)} and \\spad{leftPower(a,0) := 1}.")) (|rightPower| (($ $ (|NonNegativeInteger|)) "\\spad{rightPower(a,n)} returns the \\spad{n}\\spad{-}th right power of \\spad{a},{} \\spadignore{i.e.} \\spad{rightPower(a,n) := rightPower(a,n-1) * a} and \\spad{rightPower(a,0) := 1}.")) (|one?| (((|Boolean|) $) "\\spad{one?(a)} tests whether \\spad{a} is the unit 1.")) (|One| (($) "1 returns the unit element,{} denoted by 1."))) +((|constructor| (NIL "\\indented{1}{MonadWithUnit is the class of multiplicative monads with unit,{}} \\indented{1}{\\spadignore{i.e.} sets with a binary operation and a unit element.} Axioms \\indented{3}{leftIdentity(\"*\":(\\%,{}\\%)->\\%,{}1)\\space{3}\\tab{30} 1*x=x} \\indented{3}{rightIdentity(\"*\":(\\%,{}\\%)->\\%,{}1)\\space{2}\\tab{30} x*1=x}")) (|rightRecip| (((|Union| $ "failed") $) "\\spad{rightRecip(a)} returns an element,{} which is a right inverse of \\spad{a},{} or \\spad{\"failed\"} if such an element doesn't exist or cannot be determined.")) (|leftRecip| (((|Union| $ "failed") $) "\\spad{leftRecip(a)} returns an element,{} which is a left inverse of \\spad{a},{} or \\spad{\"failed\"} if such an element doesn't exist or cannot be determined.")) (|recip| (((|Union| $ "failed") $) "\\spad{recip(a)} returns an element,{} which is both a left and a right inverse of \\spad{a},{} or \\spad{\"failed\"} if such an element doesn't exist or cannot be determined.")) (** (($ $ (|NonNegativeInteger|)) "\\spad{a**n} returns the \\spad{n}\\spad{-}th power of \\spad{a},{} defined by repeated squaring.")) (|leftPower| (($ $ (|NonNegativeInteger|)) "\\spad{leftPower(a,n)} returns the \\spad{n}\\spad{-}th left power of \\spad{a},{} \\spadignore{i.e.} \\spad{leftPower(a,n) := a * leftPower(a,n-1)} and \\spad{leftPower(a,0) := 1}.")) (|rightPower| (($ $ (|NonNegativeInteger|)) "\\spad{rightPower(a,n)} returns the \\spad{n}\\spad{-}th right power of \\spad{a},{} \\spadignore{i.e.} \\spad{rightPower(a,n) := rightPower(a,n-1) * a} and \\spad{rightPower(a,0) := 1}.")) (|one?| (((|Boolean|) $) "\\spad{one?(a)} tests whether \\spad{a} is the unit 1.")) (|One| (($) "1 returns the unit element,{} denoted by 1."))) NIL NIL (|MonadWithUnit|) -((|constructor| (NIL "\\indented{1}{MonadWithUnit is the class of multiplicative monads with unit,{}} \\indented{1}{\\spadignore{i.e.} sets with a binary operation and a unit element.} Axioms \\indented{3}{leftIdentity(\"*\":(\\%,{}\\%)->\\%,{}1)\\space{3}\\tab{30} 1*x=x} \\indented{3}{rightIdentity(\"*\":(\\%,{}\\%)->\\%,{}1)\\space{2}\\tab{30} x*1=x} Common Additional Axioms \\indented{3}{unitsKnown---if \"recip\" says \"failed\",{} that PROVES input wasn't a unit}")) (|rightRecip| (((|Union| $ "failed") $) "\\spad{rightRecip(a)} returns an element,{} which is a right inverse of \\spad{a},{} or \\spad{\"failed\"} if such an element doesn't exist or cannot be determined (see unitsKnown).")) (|leftRecip| (((|Union| $ "failed") $) "\\spad{leftRecip(a)} returns an element,{} which is a left inverse of \\spad{a},{} or \\spad{\"failed\"} if such an element doesn't exist or cannot be determined (see unitsKnown).")) (|recip| (((|Union| $ "failed") $) "\\spad{recip(a)} returns an element,{} which is both a left and a right inverse of \\spad{a},{} or \\spad{\"failed\"} if such an element doesn't exist or cannot be determined (see unitsKnown).")) (** (($ $ (|NonNegativeInteger|)) "\\spad{a**n} returns the \\spad{n}\\spad{-}th power of \\spad{a},{} defined by repeated squaring.")) (|leftPower| (($ $ (|NonNegativeInteger|)) "\\spad{leftPower(a,n)} returns the \\spad{n}\\spad{-}th left power of \\spad{a},{} \\spadignore{i.e.} \\spad{leftPower(a,n) := a * leftPower(a,n-1)} and \\spad{leftPower(a,0) := 1}.")) (|rightPower| (($ $ (|NonNegativeInteger|)) "\\spad{rightPower(a,n)} returns the \\spad{n}\\spad{-}th right power of \\spad{a},{} \\spadignore{i.e.} \\spad{rightPower(a,n) := rightPower(a,n-1) * a} and \\spad{rightPower(a,0) := 1}.")) (|one?| (((|Boolean|) $) "\\spad{one?(a)} tests whether \\spad{a} is the unit 1.")) (|One| (($) "1 returns the unit element,{} denoted by 1."))) +((|constructor| (NIL "\\indented{1}{MonadWithUnit is the class of multiplicative monads with unit,{}} \\indented{1}{\\spadignore{i.e.} sets with a binary operation and a unit element.} Axioms \\indented{3}{leftIdentity(\"*\":(\\%,{}\\%)->\\%,{}1)\\space{3}\\tab{30} 1*x=x} \\indented{3}{rightIdentity(\"*\":(\\%,{}\\%)->\\%,{}1)\\space{2}\\tab{30} x*1=x}")) (|rightRecip| (((|Union| $ "failed") $) "\\spad{rightRecip(a)} returns an element,{} which is a right inverse of \\spad{a},{} or \\spad{\"failed\"} if such an element doesn't exist or cannot be determined.")) (|leftRecip| (((|Union| $ "failed") $) "\\spad{leftRecip(a)} returns an element,{} which is a left inverse of \\spad{a},{} or \\spad{\"failed\"} if such an element doesn't exist or cannot be determined.")) (|recip| (((|Union| $ "failed") $) "\\spad{recip(a)} returns an element,{} which is both a left and a right inverse of \\spad{a},{} or \\spad{\"failed\"} if such an element doesn't exist or cannot be determined.")) (** (($ $ (|NonNegativeInteger|)) "\\spad{a**n} returns the \\spad{n}\\spad{-}th power of \\spad{a},{} defined by repeated squaring.")) (|leftPower| (($ $ (|NonNegativeInteger|)) "\\spad{leftPower(a,n)} returns the \\spad{n}\\spad{-}th left power of \\spad{a},{} \\spadignore{i.e.} \\spad{leftPower(a,n) := a * leftPower(a,n-1)} and \\spad{leftPower(a,0) := 1}.")) (|rightPower| (($ $ (|NonNegativeInteger|)) "\\spad{rightPower(a,n)} returns the \\spad{n}\\spad{-}th right power of \\spad{a},{} \\spadignore{i.e.} \\spad{rightPower(a,n) := rightPower(a,n-1) * a} and \\spad{rightPower(a,0) := 1}.")) (|one?| (((|Boolean|) $) "\\spad{one?(a)} tests whether \\spad{a} is the unit 1.")) (|One| (($) "1 returns the unit element,{} denoted by 1."))) NIL NIL (|MonogenicAlgebra&| S R UP) @@ -2590,14 +2590,14 @@ NIL ((|HasCategory| |#2| (QUOTE (|FiniteFieldCategory|))) (|HasCategory| |#2| (QUOTE (|Field|))) (|HasCategory| |#2| (QUOTE (|Finite|)))) (|MonogenicAlgebra| R UP) ((|constructor| (NIL "A \\spadtype{MonogenicAlgebra} is an algebra of finite rank which can be generated by a single element.")) (|derivationCoordinates| (((|Matrix| |#1|) (|Vector| $) (|Mapping| |#1| |#1|)) "\\spad{derivationCoordinates(b, ')} returns \\spad{M} such that \\spad{b' = M b}.")) (|lift| ((|#2| $) "\\spad{lift(z)} returns a minimal degree univariate polynomial up such that \\spad{z=reduce up}.")) (|convert| (($ |#2|) "\\spad{convert(up)} converts the univariate polynomial \\spad{up} to an algebra element,{} reducing by the \\spad{definingPolynomial()} if necessary.")) (|reduce| (((|Union| $ "failed") (|Fraction| |#2|)) "\\spad{reduce(frac)} converts the fraction \\spad{frac} to an algebra element.") (($ |#2|) "\\spad{reduce(up)} converts the univariate polynomial \\spad{up} to an algebra element,{} reducing by the \\spad{definingPolynomial()} if necessary.")) (|definingPolynomial| ((|#2|) "\\spad{definingPolynomial()} returns the minimal polynomial which \\spad{generator()} satisfies.")) (|generator| (($) "\\spad{generator()} returns the generator for this domain."))) -((|noZeroDivisors| |has| |#1| . #1=((|Field|))) (|canonicalUnitNormal| |has| |#1| . #1#) (|canonicalsClosed| |has| |#1| . #1#) ((|commutative| "*") . T) (|rightUnitary| . T) (|leftUnitary| . T) (|unitsKnown| . T)) +((|noZeroDivisors| |has| |#1| . #1=((|Field|))) (|canonicalUnitNormal| |has| |#1| . #1#) ((|commutative| "*") . T)) NIL (|Monoid&| S) -((|constructor| (NIL "The class of multiplicative monoids,{} \\spadignore{i.e.} semigroups with a multiplicative identity element. \\blankline")) (|recip| (((|Union| $ "failed") $) "\\spad{recip(x)} tries to compute the multiplicative inverse for \\spad{x} or \"failed\" if it cannot find the inverse (see unitsKnown).")) (** (($ $ (|NonNegativeInteger|)) "\\spad{x**n} returns the repeated product of \\spad{x} \\spad{n} times,{} \\spadignore{i.e.} exponentiation.")) (|one?| (((|Boolean|) $) "\\spad{one?(x)} tests if \\spad{x} is equal to 1.")) (|sample| (($) "\\spad{sample yields} a value of type \\%")) (|One| (($) "1 is the multiplicative identity."))) +((|constructor| (NIL "The class of multiplicative monoids,{} \\spadignore{i.e.} semigroups with a multiplicative identity element. \\blankline")) (|recip| (((|Union| $ "failed") $) "\\spad{recip(x)} tries to compute the multiplicative inverse for \\spad{x} or \"failed\" if it cannot find the inverse.")) (** (($ $ (|NonNegativeInteger|)) "\\spad{x**n} returns the repeated product of \\spad{x} \\spad{n} times,{} \\spadignore{i.e.} exponentiation.")) (|one?| (((|Boolean|) $) "\\spad{one?(x)} tests if \\spad{x} is equal to 1.")) (|sample| (($) "\\spad{sample yields} a value of type \\%")) (|One| (($) "1 is the multiplicative identity."))) NIL NIL (|Monoid|) -((|constructor| (NIL "The class of multiplicative monoids,{} \\spadignore{i.e.} semigroups with a multiplicative identity element. \\blankline")) (|recip| (((|Union| $ "failed") $) "\\spad{recip(x)} tries to compute the multiplicative inverse for \\spad{x} or \"failed\" if it cannot find the inverse (see unitsKnown).")) (** (($ $ (|NonNegativeInteger|)) "\\spad{x**n} returns the repeated product of \\spad{x} \\spad{n} times,{} \\spadignore{i.e.} exponentiation.")) (|one?| (((|Boolean|) $) "\\spad{one?(x)} tests if \\spad{x} is equal to 1.")) (|sample| (($) "\\spad{sample yields} a value of type \\%")) (|One| (($) "1 is the multiplicative identity."))) +((|constructor| (NIL "The class of multiplicative monoids,{} \\spadignore{i.e.} semigroups with a multiplicative identity element. \\blankline")) (|recip| (((|Union| $ "failed") $) "\\spad{recip(x)} tries to compute the multiplicative inverse for \\spad{x} or \"failed\" if it cannot find the inverse.")) (** (($ $ (|NonNegativeInteger|)) "\\spad{x**n} returns the repeated product of \\spad{x} \\spad{n} times,{} \\spadignore{i.e.} exponentiation.")) (|one?| (((|Boolean|) $) "\\spad{one?(x)} tests if \\spad{x} is equal to 1.")) (|sample| (($) "\\spad{sample yields} a value of type \\%")) (|One| (($) "1 is the multiplicative identity."))) NIL NIL (|MonoidOperation| T$) @@ -2626,8 +2626,8 @@ NIL NIL (|MultivariatePolynomial| |vl| R) ((|constructor| (NIL "\\indented{2}{This type is the basic representation of sparse recursive multivariate} polynomials whose variables are from a user specified list of symbols. The ordering is specified by the position of the variable in the list. The coefficient ring may be non commutative,{} but the variables are assumed to commute."))) -(((|commutative| "*") |has| |#2| (|CommutativeRing|)) (|noZeroDivisors| |has| |#2| (|IntegralDomain|)) (|canonicalUnitNormal| |has| |#2| (ATTRIBUTE |canonicalUnitNormal|)) (|leftUnitary| . T) (|rightUnitary| . T) (|unitsKnown| . T)) -(#1=(|HasCategory| |#2| (QUOTE (|PolynomialFactorizationExplicit|))) (OR #2=(|HasCategory| |#2| (QUOTE (|CommutativeRing|))) #3=(|HasCategory| |#2| (QUOTE (|GcdDomain|))) #4=(|HasCategory| |#2| (QUOTE (|IntegralDomain|))) #1#) (OR #3# #4# #1#) (OR #3# #1#) #4# #2# (OR #2# #4#) (AND (|HasCategory| |#2| #5=(QUOTE (|PatternMatchable| #6=(|Float|)))) (|HasCategory| #7=(|OrderedVariableList| |#1|) #5#)) (AND (|HasCategory| |#2| #8=(QUOTE (|PatternMatchable| #9=(|Integer|)))) (|HasCategory| #7# #8#)) (AND (|HasCategory| |#2| #10=(QUOTE (|ConvertibleTo| (|Pattern| #6#)))) (|HasCategory| #7# #10#)) (AND (|HasCategory| |#2| #11=(QUOTE (|ConvertibleTo| (|Pattern| #9#)))) (|HasCategory| #7# #11#)) (AND (|HasCategory| |#2| #12=(QUOTE (|ConvertibleTo| (|InputForm|)))) (|HasCategory| #7# #12#)) (|HasCategory| |#2| (QUOTE (|LinearlyExplicitRingOver| #9#))) (|HasCategory| |#2| (QUOTE (|CharacteristicZero|))) #13=(|HasCategory| |#2| #14=(QUOTE (|CharacteristicNonZero|))) #15=(|HasCategory| |#2| (QUOTE (|Algebra| #16=(|Fraction| #9#)))) (|HasCategory| |#2| (QUOTE (|RetractableTo| #9#))) (OR #15# #17=(|HasCategory| |#2| (QUOTE (|RetractableTo| #16#)))) #17# (|HasCategory| |#2| (QUOTE (|Field|))) (|HasAttribute| |#2| (QUOTE |canonicalUnitNormal|)) #3# #18=(AND #1# (|HasCategory| $ #14#)) (OR #18# #13#)) +(((|commutative| "*") |has| |#2| (|CommutativeRing|)) (|noZeroDivisors| |has| |#2| (|IntegralDomain|)) (|canonicalUnitNormal| |has| |#2| (ATTRIBUTE |canonicalUnitNormal|))) +(#1=(|HasCategory| |#2| (QUOTE (|PolynomialFactorizationExplicit|))) (OR #2=(|HasCategory| |#2| (QUOTE (|CommutativeRing|))) #3=(|HasCategory| |#2| (QUOTE (|GcdDomain|))) #4=(|HasCategory| |#2| (QUOTE (|IntegralDomain|))) #1#) (OR #3# #4# #1#) (OR #3# #1#) #4# #2# (OR #2# #4#) (AND (|HasCategory| |#2| #5=(QUOTE (|PatternMatchable| #6=(|Float|)))) (|HasCategory| #7=(|OrderedVariableList| |#1|) #5#)) (AND (|HasCategory| |#2| #8=(QUOTE (|PatternMatchable| #9=(|Integer|)))) (|HasCategory| #7# #8#)) (AND (|HasCategory| |#2| #10=(QUOTE (|ConvertibleTo| (|Pattern| #6#)))) (|HasCategory| #7# #10#)) (AND (|HasCategory| |#2| #11=(QUOTE (|ConvertibleTo| (|Pattern| #9#)))) (|HasCategory| #7# #11#)) (AND (|HasCategory| |#2| #12=(QUOTE (|ConvertibleTo| (|InputForm|)))) (|HasCategory| #7# #12#)) (|HasCategory| |#2| (QUOTE (|LinearlyExplicitRingOver| #9#))) #13=(|HasCategory| |#2| (QUOTE (|Algebra| #14=(|Fraction| #9#)))) #15=(|HasCategory| |#2| #16=(QUOTE (|CharacteristicNonZero|))) (|HasCategory| |#2| (QUOTE (|CharacteristicZero|))) (|HasCategory| |#2| (QUOTE (|RetractableTo| #9#))) (OR #13# #17=(|HasCategory| |#2| (QUOTE (|RetractableTo| #14#)))) #17# (|HasCategory| |#2| (QUOTE (|Field|))) (|HasAttribute| |#2| (QUOTE |canonicalUnitNormal|)) #3# #18=(AND #1# (|HasCategory| $ #16#)) (OR #18# #15#)) (|MPolyCatRationalFunctionFactorizer| E OV R PRF) ((|constructor| (NIL "\\indented{3}{This package exports a factor operation for multivariate polynomials} with coefficients which are rational functions over some ring \\spad{R} over which we can factor. It is used internally by packages such as primary decomposition which need to work with polynomials with rational function coefficients,{} \\spadignore{i.e.} themselves fractions of polynomials.")) (|factor| (((|Factored| |#4|) |#4|) "\\spad{factor(prf)} factors a polynomial with rational function coefficients.")) (|pushuconst| ((|#4| (|Fraction| (|Polynomial| |#3|)) |#2|) "\\spad{pushuconst(r,var)} takes a rational function and raises all occurances of the variable \\spad{var} to the polynomial level.")) (|pushucoef| ((|#4| (|SparseUnivariatePolynomial| (|Polynomial| |#3|)) |#2|) "\\spad{pushucoef(upoly,var)} converts the anonymous univariate polynomial \\spad{upoly} to a polynomial in \\spad{var} over rational functions.")) (|pushup| ((|#4| |#4| |#2|) "\\spad{pushup(prf,var)} raises all occurences of the variable \\spad{var} in the coefficients of the polynomial \\spad{prf} back to the polynomial level.")) (|pushdterm| ((|#4| (|SparseUnivariatePolynomial| |#4|) |#2|) "\\spad{pushdterm(monom,var)} pushes all top level occurences of the variable \\spad{var} into the coefficient domain for the monomial \\spad{monom}.")) (|pushdown| ((|#4| |#4| |#2|) "\\spad{pushdown(prf,var)} pushes all top level occurences of the variable \\spad{var} into the coefficient domain for the polynomial \\spad{prf}.")) (|totalfract| (((|Record| (|:| |sup| (|Polynomial| |#3|)) (|:| |inf| (|Polynomial| |#3|))) |#4|) "\\spad{totalfract(prf)} takes a polynomial whose coefficients are themselves fractions of polynomials and returns a record containing the numerator and denominator resulting from putting \\spad{prf} over a common denominator.")) (|convert| (((|Symbol|) $) "\\spad{convert(x)} converts \\spad{x} to a symbol"))) NIL @@ -2642,7 +2642,7 @@ NIL NIL (|MonoidRing| R M) ((|constructor| (NIL "\\spadtype{MonoidRing}(\\spad{R},{}\\spad{M}),{} implements the algebra of all maps from the monoid \\spad{M} to the commutative ring \\spad{R} with finite support. Multiplication of two maps \\spad{f} and \\spad{g} is defined to map an element \\spad{c} of \\spad{M} to the (convolution) sum over {\\em f(a)g(b)} such that {\\em ab = c}. Thus \\spad{M} can be identified with a canonical basis and the maps can also be considered as formal linear combinations of the elements in \\spad{M}. Scalar multiples of a basis element are called monomials. A prominent example is the class of polynomials where the monoid is a direct product of the natural numbers with pointwise addition. When \\spad{M} is \\spadtype{FreeMonoid Symbol},{} one gets polynomials in infinitely many non-commuting variables. Another application area is representation theory of finite groups \\spad{G},{} where modules over \\spadtype{MonoidRing}(\\spad{R},{}\\spad{G}) are studied.")) (|reductum| (($ $) "\\spad{reductum(f)} is \\spad{f} minus its leading monomial.")) (|leadingCoefficient| ((|#1| $) "\\spad{leadingCoefficient(f)} gives the coefficient of \\spad{f},{} whose corresponding monoid element is the greatest among all those with non-zero coefficients.")) (|leadingMonomial| ((|#2| $) "\\spad{leadingMonomial(f)} gives the monomial of \\spad{f} whose corresponding monoid element is the greatest among all those with non-zero coefficients.")) (|numberOfMonomials| (((|NonNegativeInteger|) $) "\\spad{numberOfMonomials(f)} is the number of non-zero coefficients with respect to the canonical basis.")) (|monomials| (((|List| $) $) "\\spad{monomials(f)} gives the list of all monomials whose sum is \\spad{f}.")) (|coefficients| (((|List| |#1|) $) "\\spad{coefficients(f)} lists all non-zero coefficients.")) (|monomial?| (((|Boolean|) $) "\\spad{monomial?(f)} tests if \\spad{f} is a single monomial.")) (|terms| (((|List| (|Record| (|:| |coef| |#1|) (|:| |monom| |#2|))) $) "\\spad{terms(f)} gives the list of non-zero coefficients combined with their corresponding basis element as records. This is the internal representation.")) (|coerce| (($ (|List| (|Record| (|:| |coef| |#1|) (|:| |monom| |#2|)))) "\\spad{coerce(lt)} converts a list of terms and coefficients to a member of the domain.")) (|coefficient| ((|#1| $ |#2|) "\\spad{coefficient(f,m)} extracts the coefficient of \\spad{m} in \\spad{f} with respect to the canonical basis \\spad{M}.")) (|monomial| (($ |#1| |#2|) "\\spad{monomial(r,m)} creates a scalar multiple of the basis element \\spad{m}."))) -((|leftUnitary| |has| |#1| . #1=((|CommutativeRing|))) (|rightUnitary| |has| |#1| . #1#) (|unitsKnown| . T)) +NIL ((AND (|HasCategory| |#1| #1=(QUOTE (|Finite|))) (|HasCategory| |#2| #1#)) (|HasCategory| |#1| (QUOTE (|CommutativeRing|))) (|HasCategory| |#1| (QUOTE (|CharacteristicNonZero|))) (|HasCategory| |#1| (QUOTE (|CharacteristicZero|))) (|HasCategory| |#2| (QUOTE (|OrderedSet|)))) (|Multiset| S) ((|constructor| (NIL "A multiset is a set with multiplicities.")) (|remove!| (($ (|Mapping| (|Boolean|) |#1|) $ (|Integer|)) "\\spad{remove!(p,ms,number)} removes destructively at most \\spad{number} copies of elements \\spad{x} such that \\spad{p(x)} is \\spadfun{\\spad{true}} if \\spad{number} is positive,{} all of them if \\spad{number} equals zero,{} and all but at most \\spad{-number} if \\spad{number} is negative.") (($ |#1| $ (|Integer|)) "\\spad{remove!(x,ms,number)} removes destructively at most \\spad{number} copies of element \\spad{x} if \\spad{number} is positive,{} all of them if \\spad{number} equals zero,{} and all but at most \\spad{-number} if \\spad{number} is negative.")) (|remove| (($ (|Mapping| (|Boolean|) |#1|) $ (|Integer|)) "\\spad{remove(p,ms,number)} removes at most \\spad{number} copies of elements \\spad{x} such that \\spad{p(x)} is \\spadfun{\\spad{true}} if \\spad{number} is positive,{} all of them if \\spad{number} equals zero,{} and all but at most \\spad{-number} if \\spad{number} is negative.") (($ |#1| $ (|Integer|)) "\\spad{remove(x,ms,number)} removes at most \\spad{number} copies of element \\spad{x} if \\spad{number} is positive,{} all of them if \\spad{number} equals zero,{} and all but at most \\spad{-number} if \\spad{number} is negative.")) (|unique| (((|List| |#1|) $) "\\spad{unique ms} returns a list of the elements of \\spad{ms} {\\em without} their multiplicity. See also \\spadfun{members}.")) (|multiset| (($ (|List| |#1|)) "\\spad{multiset(ls)} creates a multiset with elements from \\spad{ls}.") (($ |#1|) "\\spad{multiset(s)} creates a multiset with singleton \\spad{s}.") (($) "\\spad{multiset()}\\$\\spad{D} creates an empty multiset of domain \\spad{D}."))) @@ -2662,7 +2662,7 @@ NIL NIL (|MultivariateTaylorSeriesCategory| |Coef| |Var|) ((|constructor| (NIL "\\spadtype{MultivariateTaylorSeriesCategory} is the most general multivariate Taylor series category.")) (|integrate| (($ $ |#2|) "\\spad{integrate(f,x)} returns the anti-derivative of the power series \\spad{f(x)} with respect to the variable \\spad{x} with constant coefficient 1. We may integrate a series when we can divide coefficients by integers.")) (|polynomial| (((|Polynomial| |#1|) $ (|NonNegativeInteger|) (|NonNegativeInteger|)) "\\spad{polynomial(f,k1,k2)} returns a polynomial consisting of the sum of all terms of \\spad{f} of degree \\spad{d} with \\spad{k1 <= d <= k2}.") (((|Polynomial| |#1|) $ (|NonNegativeInteger|)) "\\spad{polynomial(f,k)} returns a polynomial consisting of the sum of all terms of \\spad{f} of degree \\spad{<= k}.")) (|order| (((|NonNegativeInteger|) $ |#2| (|NonNegativeInteger|)) "\\spad{order(f,x,n)} returns \\spad{min(n,order(f,x))}.") (((|NonNegativeInteger|) $ |#2|) "\\spad{order(f,x)} returns the order of \\spad{f} viewed as a series in \\spad{x} may result in an infinite loop if \\spad{f} has no non-zero terms.")) (|monomial| (($ $ (|List| |#2|) (|List| (|NonNegativeInteger|))) "\\spad{monomial(a,[x1,x2,...,xk],[n1,n2,...,nk])} returns \\spad{a * x1^n1 * ... * xk^nk}.") (($ $ |#2| (|NonNegativeInteger|)) "\\spad{monomial(a,x,n)} returns \\spad{a*x^n}.")) (|extend| (($ $ (|NonNegativeInteger|)) "\\spad{extend(f,n)} causes all terms of \\spad{f} of degree \\spad{<= n} to be computed.")) (|coefficient| (($ $ (|List| |#2|) (|List| (|NonNegativeInteger|))) "\\spad{coefficient(f,[x1,x2,...,xk],[n1,n2,...,nk])} returns the coefficient of \\spad{x1^n1 * ... * xk^nk} in \\spad{f}.") (($ $ |#2| (|NonNegativeInteger|)) "\\spad{coefficient(f,x,n)} returns the coefficient of \\spad{x^n} in \\spad{f}."))) -(((|commutative| "*") |has| |#1| (|CommutativeRing|)) (|noZeroDivisors| |has| |#1| (|IntegralDomain|)) (|leftUnitary| . T) (|rightUnitary| . T) (|unitsKnown| . T)) +(((|commutative| "*") |has| |#1| (|CommutativeRing|)) (|noZeroDivisors| |has| |#1| (|IntegralDomain|))) NIL (|MultivariateFactorize| OV E R P) ((|constructor| (NIL "\\indented{2}{This is the top level package for doing multivariate factorization} over basic domains like \\spadtype{Integer} or \\spadtype{Fraction Integer}.")) (|factor| (((|Factored| (|SparseUnivariatePolynomial| |#4|)) (|SparseUnivariatePolynomial| |#4|)) "\\spad{factor(p)} factors the multivariate polynomial \\spad{p} over its coefficient domain where \\spad{p} is represented as a univariate polynomial with multivariate coefficients") (((|Factored| |#4|) |#4|) "\\spad{factor(p)} factors the multivariate polynomial \\spad{p} over its coefficient domain"))) @@ -2678,7 +2678,7 @@ NIL NIL (|NonAssociativeAlgebra| R) ((|constructor| (NIL "NonAssociativeAlgebra is the category of non associative algebras (modules which are themselves non associative rngs). Axioms \\indented{3}{r*(a*b) = (r*a)*b = a*(r*b)}")) (|plenaryPower| (($ $ (|PositiveInteger|)) "\\spad{plenaryPower(a,n)} is recursively defined to be \\spad{plenaryPower(a,n-1)*plenaryPower(a,n-1)} for \\spad{n>1} and \\spad{a} for \\spad{n=1}."))) -((|leftUnitary| . T) (|rightUnitary| . T)) +NIL NIL (|NonAssociativeRng&| S) ((|constructor| (NIL "NonAssociativeRng is a basic ring-type structure,{} not necessarily commutative or associative,{} and not necessarily with unit. Axioms \\indented{2}{x*(y+z) = x*y + x*z} \\indented{2}{(x+y)*z = x*z + y*z} Common Additional Axioms \\indented{2}{noZeroDivisors\\space{2}ab = 0 => \\spad{a=0} or \\spad{b=0}}")) (|antiCommutator| (($ $ $) "\\spad{antiCommutator(a,b)} returns \\spad{a*b+b*a}.")) (|commutator| (($ $ $) "\\spad{commutator(a,b)} returns \\spad{a*b-b*a}.")) (|associator| (($ $ $ $) "\\spad{associator(a,b,c)} returns \\spad{(a*b)*c-a*(b*c)}."))) @@ -2758,12 +2758,12 @@ NIL NIL (|NewSparseMultivariatePolynomial| R |VarSet|) ((|constructor| (NIL "A post-facto extension for \\axiomType{SMP} in order to speed up operations related to pseudo-division and gcd. This domain is based on the \\axiomType{NSUP} constructor which is itself a post-facto extension of the \\axiomType{SUP} constructor."))) -(((|commutative| "*") |has| |#1| (|CommutativeRing|)) (|noZeroDivisors| |has| |#1| (|IntegralDomain|)) (|canonicalUnitNormal| |has| |#1| (ATTRIBUTE |canonicalUnitNormal|)) (|leftUnitary| . T) (|rightUnitary| . T) (|unitsKnown| . T)) -(#1=(|HasCategory| |#1| (QUOTE (|PolynomialFactorizationExplicit|))) (OR #2=(|HasCategory| |#1| (QUOTE (|CommutativeRing|))) #3=(|HasCategory| |#1| (QUOTE (|GcdDomain|))) #4=(|HasCategory| |#1| (QUOTE (|IntegralDomain|))) #1#) (OR #3# #4# #1#) (OR #3# #1#) #4# #2# (OR #2# #4#) (AND (|HasCategory| |#1| #5=(QUOTE (|PatternMatchable| #6=(|Float|)))) (|HasCategory| |#2| #5#)) (AND (|HasCategory| |#1| #7=(QUOTE (|PatternMatchable| #8=(|Integer|)))) (|HasCategory| |#2| #7#)) (AND (|HasCategory| |#1| #9=(QUOTE (|ConvertibleTo| (|Pattern| #6#)))) (|HasCategory| |#2| #9#)) (AND (|HasCategory| |#1| #10=(QUOTE (|ConvertibleTo| (|Pattern| #8#)))) (|HasCategory| |#2| #10#)) (AND (|HasCategory| |#1| #11=(QUOTE (|ConvertibleTo| (|InputForm|)))) (|HasCategory| |#2| #11#)) (|HasCategory| |#1| (QUOTE (|LinearlyExplicitRingOver| #8#))) (|HasCategory| |#1| (QUOTE (|CharacteristicZero|))) #12=(|HasCategory| |#1| #13=(QUOTE (|CharacteristicNonZero|))) #14=(|HasCategory| |#1| (QUOTE (|Algebra| #15=(|Fraction| #8#)))) #16=(|HasCategory| |#1| (QUOTE (|RetractableTo| #8#))) (OR #14# #17=(|HasCategory| |#1| (QUOTE (|RetractableTo| #15#)))) #17# (AND #16# #18=(|HasCategory| |#2| (QUOTE (|ConvertibleTo| (|Symbol|))))) #18# (|HasCategory| |#1| (QUOTE (|Field|))) #19=(AND #14# #18#) (OR (AND #20=(|HasCategory| |#1| (QUOTE (|Algebra| #8#))) #18# #21=(|not| #14#)) #19#) (OR (AND #18# #21# (|not| #20#)) (AND #20# #18# #21# (|not| (|HasCategory| |#1| (QUOTE (|IntegerNumberSystem|))))) (AND #14# #18# (|not| (|HasCategory| |#1| (QUOTE (|QuotientFieldCategory| #8#)))))) (|HasAttribute| |#1| (QUOTE |canonicalUnitNormal|)) #3# #22=(AND #1# (|HasCategory| $ #13#)) (OR #22# #12#)) +(((|commutative| "*") |has| |#1| (|CommutativeRing|)) (|noZeroDivisors| |has| |#1| (|IntegralDomain|)) (|canonicalUnitNormal| |has| |#1| (ATTRIBUTE |canonicalUnitNormal|))) +(#1=(|HasCategory| |#1| (QUOTE (|PolynomialFactorizationExplicit|))) (OR #2=(|HasCategory| |#1| (QUOTE (|CommutativeRing|))) #3=(|HasCategory| |#1| (QUOTE (|GcdDomain|))) #4=(|HasCategory| |#1| (QUOTE (|IntegralDomain|))) #1#) (OR #3# #4# #1#) (OR #3# #1#) #4# #2# (OR #2# #4#) (AND (|HasCategory| |#1| #5=(QUOTE (|PatternMatchable| #6=(|Float|)))) (|HasCategory| |#2| #5#)) (AND (|HasCategory| |#1| #7=(QUOTE (|PatternMatchable| #8=(|Integer|)))) (|HasCategory| |#2| #7#)) (AND (|HasCategory| |#1| #9=(QUOTE (|ConvertibleTo| (|Pattern| #6#)))) (|HasCategory| |#2| #9#)) (AND (|HasCategory| |#1| #10=(QUOTE (|ConvertibleTo| (|Pattern| #8#)))) (|HasCategory| |#2| #10#)) (AND (|HasCategory| |#1| #11=(QUOTE (|ConvertibleTo| (|InputForm|)))) (|HasCategory| |#2| #11#)) (|HasCategory| |#1| (QUOTE (|LinearlyExplicitRingOver| #8#))) #12=(|HasCategory| |#1| (QUOTE (|Algebra| #13=(|Fraction| #8#)))) #14=(|HasCategory| |#1| #15=(QUOTE (|CharacteristicNonZero|))) (|HasCategory| |#1| (QUOTE (|CharacteristicZero|))) #16=(|HasCategory| |#1| (QUOTE (|RetractableTo| #8#))) (OR #12# #17=(|HasCategory| |#1| (QUOTE (|RetractableTo| #13#)))) #17# (AND #16# #18=(|HasCategory| |#2| (QUOTE (|ConvertibleTo| (|Symbol|))))) #18# (|HasCategory| |#1| (QUOTE (|Field|))) #19=(AND #12# #18#) (OR (AND #20=(|HasCategory| |#1| (QUOTE (|Algebra| #8#))) #18# #21=(|not| #12#)) #19#) (OR (AND #18# #21# (|not| #20#)) (AND #20# #18# #21# (|not| (|HasCategory| |#1| (QUOTE (|IntegerNumberSystem|))))) (AND #12# #18# (|not| (|HasCategory| |#1| (QUOTE (|QuotientFieldCategory| #8#)))))) (|HasAttribute| |#1| (QUOTE |canonicalUnitNormal|)) #3# #22=(AND #1# (|HasCategory| $ #15#)) (OR #22# #14#)) (|NewSparseUnivariatePolynomial| R) ((|constructor| (NIL "A post-facto extension for \\axiomType{SUP} in order to speed up operations related to pseudo-division and gcd for both \\axiomType{SUP} and,{} consequently,{} \\axiomType{NSMP}.")) (|halfExtendedResultant2| (((|Record| (|:| |resultant| |#1|) (|:| |coef2| $)) $ $) "\\axiom{\\spad{halfExtendedResultant2}(a,{}\\spad{b})} returns \\axiom{[\\spad{r},{}ca]} such that \\axiom{extendedResultant(a,{}\\spad{b})} returns \\axiom{[\\spad{r},{}ca,{} cb]}")) (|halfExtendedResultant1| (((|Record| (|:| |resultant| |#1|) (|:| |coef1| $)) $ $) "\\axiom{\\spad{halfExtendedResultant1}(a,{}\\spad{b})} returns \\axiom{[\\spad{r},{}ca]} such that \\axiom{extendedResultant(a,{}\\spad{b})} returns \\axiom{[\\spad{r},{}ca,{} cb]}")) (|extendedResultant| (((|Record| (|:| |resultant| |#1|) (|:| |coef1| $) (|:| |coef2| $)) $ $) "\\axiom{extendedResultant(a,{}\\spad{b})} returns \\axiom{[\\spad{r},{}ca,{}cb]} such that \\axiom{\\spad{r}} is the resultant of \\axiom{a} and \\axiom{\\spad{b}} and \\axiom{\\spad{r} = ca * a + cb * \\spad{b}}")) (|halfExtendedSubResultantGcd2| (((|Record| (|:| |gcd| $) (|:| |coef2| $)) $ $) "\\axiom{\\spad{halfExtendedSubResultantGcd2}(a,{}\\spad{b})} returns \\axiom{[\\spad{g},{}cb]} such that \\axiom{extendedSubResultantGcd(a,{}\\spad{b})} returns \\axiom{[\\spad{g},{}ca,{} cb]}")) (|halfExtendedSubResultantGcd1| (((|Record| (|:| |gcd| $) (|:| |coef1| $)) $ $) "\\axiom{\\spad{halfExtendedSubResultantGcd1}(a,{}\\spad{b})} returns \\axiom{[\\spad{g},{}ca]} such that \\axiom{extendedSubResultantGcd(a,{}\\spad{b})} returns \\axiom{[\\spad{g},{}ca,{} cb]}")) (|extendedSubResultantGcd| (((|Record| (|:| |gcd| $) (|:| |coef1| $) (|:| |coef2| $)) $ $) "\\axiom{extendedSubResultantGcd(a,{}\\spad{b})} returns \\axiom{[\\spad{g},{}ca,{} cb]} such that \\axiom{\\spad{g}} is a gcd of \\axiom{a} and \\axiom{\\spad{b}} in \\axiom{R^(\\spad{-1}) \\spad{P}} and \\axiom{\\spad{g} = ca * a + cb * \\spad{b}}")) (|lastSubResultant| (($ $ $) "\\axiom{lastSubResultant(a,{}\\spad{b})} returns \\axiom{resultant(a,{}\\spad{b})} if \\axiom{a} and \\axiom{\\spad{b}} has no non-trivial gcd in \\axiom{R^(\\spad{-1}) \\spad{P}} otherwise the non-zero sub-resultant with smallest index.")) (|subResultantsChain| (((|List| $) $ $) "\\axiom{subResultantsChain(a,{}\\spad{b})} returns the list of the non-zero sub-resultants of \\axiom{a} and \\axiom{\\spad{b}} sorted by increasing degree.")) (|lazyPseudoQuotient| (($ $ $) "\\axiom{lazyPseudoQuotient(a,{}\\spad{b})} returns \\axiom{\\spad{q}} if \\axiom{lazyPseudoDivide(a,{}\\spad{b})} returns \\axiom{[\\spad{c},{}\\spad{g},{}\\spad{q},{}\\spad{r}]}")) (|lazyPseudoDivide| (((|Record| (|:| |coef| |#1|) (|:| |gap| (|NonNegativeInteger|)) (|:| |quotient| $) (|:| |remainder| $)) $ $) "\\axiom{lazyPseudoDivide(a,{}\\spad{b})} returns \\axiom{[\\spad{c},{}\\spad{g},{}\\spad{q},{}\\spad{r}]} such that \\axiom{c^n * a = q*b +r} and \\axiom{lazyResidueClass(a,{}\\spad{b})} returns \\axiom{[\\spad{r},{}\\spad{c},{}\\spad{n}]} where \\axiom{\\spad{n} + \\spad{g} = max(0,{} degree(\\spad{b}) - degree(a) + 1)}.")) (|lazyPseudoRemainder| (($ $ $) "\\axiom{lazyPseudoRemainder(a,{}\\spad{b})} returns \\axiom{\\spad{r}} if \\axiom{lazyResidueClass(a,{}\\spad{b})} returns \\axiom{[\\spad{r},{}\\spad{c},{}\\spad{n}]}. This lazy pseudo-remainder is computed by means of the \\axiomOpFrom{fmecg}{NewSparseUnivariatePolynomial} operation.")) (|lazyResidueClass| (((|Record| (|:| |polnum| $) (|:| |polden| |#1|) (|:| |power| (|NonNegativeInteger|))) $ $) "\\axiom{lazyResidueClass(a,{}\\spad{b})} returns \\axiom{[\\spad{r},{}\\spad{c},{}\\spad{n}]} such that \\axiom{\\spad{r}} is reduced \\spad{w}.\\spad{r}.\\spad{t}. \\axiom{\\spad{b}} and \\axiom{\\spad{b}} divides \\axiom{c^n * a - \\spad{r}} where \\axiom{\\spad{c}} is \\axiom{leadingCoefficient(\\spad{b})} and \\axiom{\\spad{n}} is as small as possible with the previous properties.")) (|monicModulo| (($ $ $) "\\axiom{monicModulo(a,{}\\spad{b})} returns \\axiom{\\spad{r}} such that \\axiom{\\spad{r}} is reduced \\spad{w}.\\spad{r}.\\spad{t}. \\axiom{\\spad{b}} and \\axiom{\\spad{b}} divides \\axiom{a -r} where \\axiom{\\spad{b}} is monic.")) (|fmecg| (($ $ (|NonNegativeInteger|) |#1| $) "\\axiom{fmecg(\\spad{p1},{}\\spad{e},{}\\spad{r},{}\\spad{p2})} returns \\axiom{\\spad{p1} - \\spad{r} * X**e * \\spad{p2}} where \\axiom{\\spad{X}} is \\axiom{monomial(1,{}1)}"))) -(((|commutative| "*") |has| |#1| (|CommutativeRing|)) (|noZeroDivisors| |has| |#1| (|IntegralDomain|)) (|additiveValuation| |has| |#1| (|Field|)) (|canonicalUnitNormal| |has| |#1| (ATTRIBUTE |canonicalUnitNormal|)) (|leftUnitary| . T) (|rightUnitary| . T) (|unitsKnown| . T)) -(#1=(|HasCategory| |#1| (QUOTE (|PolynomialFactorizationExplicit|))) #2=(|HasCategory| |#1| (QUOTE (|IntegralDomain|))) #3=(|HasCategory| |#1| (QUOTE (|CommutativeRing|))) (OR #3# #2#) (AND (|HasCategory| |#1| #4=(QUOTE (|PatternMatchable| #5=(|Float|)))) (|HasCategory| #6=(|SingletonAsOrderedSet|) #4#)) (AND (|HasCategory| |#1| #7=(QUOTE (|PatternMatchable| #8=(|Integer|)))) (|HasCategory| #6# #7#)) (AND (|HasCategory| |#1| #9=(QUOTE (|ConvertibleTo| (|Pattern| #5#)))) (|HasCategory| #6# #9#)) (AND (|HasCategory| |#1| #10=(QUOTE (|ConvertibleTo| (|Pattern| #8#)))) (|HasCategory| #6# #10#)) (AND (|HasCategory| |#1| #11=(QUOTE (|ConvertibleTo| (|InputForm|)))) (|HasCategory| #6# #11#)) (|HasCategory| |#1| (QUOTE (|LinearlyExplicitRingOver| #8#))) (|HasCategory| |#1| (QUOTE (|CharacteristicZero|))) #12=(|HasCategory| |#1| #13=(QUOTE (|CharacteristicNonZero|))) #14=(|HasCategory| |#1| (QUOTE (|Algebra| #15=(|Fraction| #8#)))) (|HasCategory| |#1| (QUOTE (|RetractableTo| #8#))) (OR #14# #16=(|HasCategory| |#1| (QUOTE (|RetractableTo| #15#)))) #16# (OR #3# #17=(|HasCategory| |#1| (QUOTE (|Field|))) #18=(|HasCategory| |#1| (QUOTE (|GcdDomain|))) #2# #1#) (OR #17# #18# #2# #1#) (OR #17# #18# #1#) #17# (|HasCategory| |#1| (QUOTE (|StepThrough|))) (|HasCategory| |#1| (QUOTE (|PartialDifferentialSpace| #19=(|Symbol|)))) (|HasCategory| |#1| (QUOTE (|PartialDifferentialRing| #19#))) (|HasCategory| |#1| (QUOTE (|DifferentialSpace|))) (|HasCategory| |#1| (QUOTE (|DifferentialRing|))) (|HasAttribute| |#1| (QUOTE |canonicalUnitNormal|)) #18# #20=(AND #1# (|HasCategory| $ #13#)) (OR #20# #12#)) +(((|commutative| "*") |has| |#1| (|CommutativeRing|)) (|noZeroDivisors| |has| |#1| (|IntegralDomain|)) (|additiveValuation| |has| |#1| (|Field|)) (|canonicalUnitNormal| |has| |#1| (ATTRIBUTE |canonicalUnitNormal|))) +(#1=(|HasCategory| |#1| (QUOTE (|PolynomialFactorizationExplicit|))) #2=(|HasCategory| |#1| (QUOTE (|IntegralDomain|))) #3=(|HasCategory| |#1| (QUOTE (|CommutativeRing|))) (OR #3# #2#) (AND (|HasCategory| |#1| #4=(QUOTE (|PatternMatchable| #5=(|Float|)))) (|HasCategory| #6=(|SingletonAsOrderedSet|) #4#)) (AND (|HasCategory| |#1| #7=(QUOTE (|PatternMatchable| #8=(|Integer|)))) (|HasCategory| #6# #7#)) (AND (|HasCategory| |#1| #9=(QUOTE (|ConvertibleTo| (|Pattern| #5#)))) (|HasCategory| #6# #9#)) (AND (|HasCategory| |#1| #10=(QUOTE (|ConvertibleTo| (|Pattern| #8#)))) (|HasCategory| #6# #10#)) (AND (|HasCategory| |#1| #11=(QUOTE (|ConvertibleTo| (|InputForm|)))) (|HasCategory| #6# #11#)) (|HasCategory| |#1| (QUOTE (|LinearlyExplicitRingOver| #8#))) #12=(|HasCategory| |#1| (QUOTE (|Algebra| #13=(|Fraction| #8#)))) #14=(|HasCategory| |#1| #15=(QUOTE (|CharacteristicNonZero|))) (|HasCategory| |#1| (QUOTE (|CharacteristicZero|))) (|HasCategory| |#1| (QUOTE (|RetractableTo| #8#))) (OR #12# #16=(|HasCategory| |#1| (QUOTE (|RetractableTo| #13#)))) #16# (OR #3# #17=(|HasCategory| |#1| (QUOTE (|Field|))) #18=(|HasCategory| |#1| (QUOTE (|GcdDomain|))) #2# #1#) (OR #17# #18# #2# #1#) (OR #17# #18# #1#) #17# (|HasCategory| |#1| (QUOTE (|StepThrough|))) (|HasCategory| |#1| (QUOTE (|PartialDifferentialSpace| #19=(|Symbol|)))) (|HasCategory| |#1| (QUOTE (|PartialDifferentialRing| #19#))) (|HasCategory| |#1| (QUOTE (|DifferentialSpace|))) (|HasCategory| |#1| (QUOTE (|DifferentialRing|))) (|HasAttribute| |#1| (QUOTE |canonicalUnitNormal|)) #18# #20=(AND #1# (|HasCategory| $ #15#)) (OR #20# #14#)) (|NewSparseUnivariatePolynomialFunctions2| R S) ((|constructor| (NIL "This package lifts a mapping from coefficient rings \\spad{R} to \\spad{S} to a mapping from sparse univariate polynomial over \\spad{R} to a sparse univariate polynomial over \\spad{S}. Note that the mapping is assumed to send zero to zero,{} since it will only be applied to the non-zero coefficients of the polynomial.")) (|map| (((|NewSparseUnivariatePolynomial| |#2|) (|Mapping| |#2| |#1|) (|NewSparseUnivariatePolynomial| |#1|)) "\\axiom{map(func,{} poly)} creates a new polynomial by applying func to every non-zero coefficient of the polynomial poly."))) NIL @@ -2826,7 +2826,7 @@ NIL ((|HasCategory| |#2| (QUOTE (|Field|))) (|HasCategory| |#2| (QUOTE (|IntegerNumberSystem|))) (|HasCategory| |#2| (QUOTE (|RealNumberSystem|))) (|HasCategory| |#2| (QUOTE (|CharacteristicNonZero|))) (|HasCategory| |#2| (QUOTE (|CharacteristicZero|))) (|HasCategory| |#2| (QUOTE (|ConvertibleTo| (|InputForm|)))) (|HasCategory| |#2| (QUOTE (|OrderedSet|))) (|HasCategory| |#2| (QUOTE (|Finite|)))) (|OctonionCategory| R) ((|constructor| (NIL "OctonionCategory gives the categorial frame for the octonions,{} and eight-dimensional non-associative algebra,{} doubling the the quaternions in the same way as doubling the Complex numbers to get the quaternions.")) (|inv| (($ $) "\\spad{inv(o)} returns the inverse of \\spad{o} if it exists.")) (|rationalIfCan| (((|Union| (|Fraction| (|Integer|)) "failed") $) "\\spad{rationalIfCan(o)} returns the real part if all seven imaginary parts are 0,{} and \"failed\" otherwise.")) (|rational| (((|Fraction| (|Integer|)) $) "\\spad{rational(o)} returns the real part if all seven imaginary parts are 0. Error: if \\spad{o} is not rational.")) (|rational?| (((|Boolean|) $) "\\spad{rational?(o)} tests if \\spad{o} is rational,{} \\spadignore{i.e.} that all seven imaginary parts are 0.")) (|abs| ((|#1| $) "\\spad{abs(o)} computes the absolute value of an octonion,{} equal to the square root of the \\spadfunFrom{norm}{Octonion}.")) (|octon| (($ |#1| |#1| |#1| |#1| |#1| |#1| |#1| |#1|) "\\spad{octon(re,ri,rj,rk,rE,rI,rJ,rK)} constructs an octonion from scalars.")) (|norm| ((|#1| $) "\\spad{norm(o)} returns the norm of an octonion,{} equal to the sum of the squares of its coefficients.")) (|imagK| ((|#1| $) "\\spad{imagK(o)} extracts the imaginary \\spad{K} part of octonion \\spad{o}.")) (|imagJ| ((|#1| $) "\\spad{imagJ(o)} extracts the imaginary \\spad{J} part of octonion \\spad{o}.")) (|imagI| ((|#1| $) "\\spad{imagI(o)} extracts the imaginary \\spad{I} part of octonion \\spad{o}.")) (|imagE| ((|#1| $) "\\spad{imagE(o)} extracts the imaginary \\spad{E} part of octonion \\spad{o}.")) (|imagk| ((|#1| $) "\\spad{imagk(o)} extracts the \\spad{k} part of octonion \\spad{o}.")) (|imagj| ((|#1| $) "\\spad{imagj(o)} extracts the \\spad{j} part of octonion \\spad{o}.")) (|imagi| ((|#1| $) "\\spad{imagi(o)} extracts the \\spad{i} part of octonion \\spad{o}.")) (|real| ((|#1| $) "\\spad{real(o)} extracts real part of octonion \\spad{o}.")) (|conjugate| (($ $) "\\spad{conjugate(o)} negates the imaginary parts \\spad{i},{}\\spad{j},{}\\spad{k},{}\\spad{E},{}\\spad{I},{}\\spad{J},{}\\spad{K} of octonian \\spad{o}."))) -((|rightUnitary| . T) (|leftUnitary| . T) (|unitsKnown| . T)) +NIL NIL (|OrderedCancellationAbelianMonoid|) ((|constructor| (NIL "Ordered sets which are also abelian cancellation monoids,{} such that the addition preserves the ordering."))) @@ -2834,8 +2834,8 @@ NIL NIL (|Octonion| R) ((|constructor| (NIL "Octonion implements octonions (Cayley-Dixon algebra) over a commutative ring,{} an eight-dimensional non-associative algebra,{} doubling the quaternions in the same way as doubling the complex numbers to get the quaternions the main constructor function is {\\em octon} which takes 8 arguments: the real part,{} the \\spad{i} imaginary part,{} the \\spad{j} imaginary part,{} the \\spad{k} imaginary part,{} (as with quaternions) and in addition the imaginary parts \\spad{E},{} \\spad{I},{} \\spad{J},{} \\spad{K}.")) (|octon| (($ (|Quaternion| |#1|) (|Quaternion| |#1|)) "\\spad{octon(qe,qE)} constructs an octonion from two quaternions using the relation {\\em O = Q + QE}."))) -((|rightUnitary| . T) (|leftUnitary| . T) (|unitsKnown| . T)) -((|HasCategory| |#1| (QUOTE (|CharacteristicNonZero|))) (|HasCategory| |#1| (QUOTE (|CharacteristicZero|))) (|HasCategory| |#1| (QUOTE (|ConvertibleTo| (|InputForm|)))) (|HasCategory| |#1| (QUOTE (|OrderedSet|))) (|HasCategory| |#1| (QUOTE (|Finite|))) (|HasCategory| |#1| (|%list| (QUOTE |InnerEvalable|) (QUOTE (|Symbol|)) #1=(|devaluate| |#1|))) (|HasCategory| |#1| (|%list| (QUOTE |Evalable|) #1#)) (|HasCategory| |#1| (|%list| (QUOTE |Eltable|) #1# #1#)) (OR #2=(|HasCategory| |#1| #3=(QUOTE (|RetractableTo| (|Fraction| #4=(|Integer|))))) #5=(|HasCategory| #6=(|Quaternion| |#1|) #3#)) (OR #7=(|HasCategory| |#1| #8=(QUOTE (|RetractableTo| #4#))) #9=(|HasCategory| #6# #8#)) (|HasCategory| |#1| (QUOTE (|RealNumberSystem|))) (|HasCategory| |#1| (QUOTE (|IntegerNumberSystem|))) (|HasCategory| |#1| (QUOTE (|Field|))) #5# #9# #2# #7#) +NIL +((|HasCategory| |#1| (QUOTE (|CharacteristicNonZero|))) (|HasCategory| |#1| (QUOTE (|CharacteristicZero|))) (|HasCategory| |#1| (QUOTE (|ConvertibleTo| (|InputForm|)))) (|HasCategory| |#1| (QUOTE (|OrderedSet|))) (|HasCategory| |#1| (QUOTE (|Finite|))) (|HasCategory| |#1| (|%list| (QUOTE |InnerEvalable|) (QUOTE (|Symbol|)) #1=(|devaluate| |#1|))) (|HasCategory| |#1| (|%list| (QUOTE |Evalable|) #1#)) (|HasCategory| |#1| (|%list| (QUOTE |Eltable|) #1# #1#)) (OR #2=(|HasCategory| |#1| #3=(QUOTE (|RetractableTo| (|Fraction| #4=(|Integer|))))) #5=(|HasCategory| #6=(|Quaternion| |#1|) #3#)) (OR #7=(|HasCategory| |#1| #8=(QUOTE (|RetractableTo| #4#))) #9=(|HasCategory| #6# #8#)) (|HasCategory| |#1| (QUOTE (|RealNumberSystem|))) (|HasCategory| |#1| (QUOTE (|IntegerNumberSystem|))) (|HasCategory| |#1| (QUOTE (|Field|))) #5# #9# #7# #2#) (|OctonionCategoryFunctions2| OR R OS S) ((|constructor| (NIL "\\spad{OctonionCategoryFunctions2} implements functions between two octonion domains defined over different rings. The function map is used to coerce between octonion types.")) (|map| ((|#3| (|Mapping| |#4| |#2|) |#1|) "\\spad{map(f,u)} maps \\spad{f} onto the component parts of the octonion \\spad{u}."))) NIL @@ -2886,15 +2886,15 @@ NIL NIL (|OrderedDirectProduct| |dim| S |f|) ((|constructor| (NIL "\\indented{2}{This type represents the finite direct or cartesian product of an} underlying ordered component type. The ordering on the type is determined by its third argument which represents the less than function on vectors. This type is a suitable third argument for \\spadtype{GeneralDistributedMultivariatePolynomial}."))) -((|rightUnitary| |has| |#2| . #1=((|Ring|))) (|leftUnitary| |has| |#2| . #1#) (|unitsKnown| |has| |#2| (ATTRIBUTE |unitsKnown|))) -((OR (AND #1=(|HasCategory| |#2| (QUOTE (|AbelianGroup|))) #2=(|HasCategory| |#2| (|%list| (QUOTE |Evalable|) #3=(|devaluate| |#2|)))) (AND #4=(|HasCategory| |#2| (QUOTE (|AbelianMonoid|))) #2#) (AND #5=(|HasCategory| |#2| (QUOTE (|AbelianSemiGroup|))) #2#) (AND #6=(|HasCategory| |#2| (QUOTE (|CancellationAbelianMonoid|))) #2#) (AND #7=(|HasCategory| |#2| (QUOTE (|CommutativeRing|))) #2#) (AND #8=(|HasCategory| |#2| (QUOTE (|DifferentialRing|))) #2#) (AND #9=(|HasCategory| |#2| (QUOTE (|Field|))) #2#) (AND #10=(|HasCategory| |#2| (QUOTE (|Finite|))) #2#) (AND #11=(|HasCategory| |#2| (QUOTE (|Monoid|))) #2#) (AND #12=(|HasCategory| |#2| (QUOTE (|OrderedAbelianMonoidSup|))) #2#) (AND #13=(|HasCategory| |#2| #14=(QUOTE (|OrderedSet|))) #2#) (AND #15=(|HasCategory| |#2| (QUOTE (|PartialDifferentialRing| #16=(|Symbol|)))) #2#) (AND #17=(|HasCategory| |#2| (QUOTE (|Ring|))) #2#) #18=(AND #19=(|HasCategory| |#2| (QUOTE (|SetCategory|))) #2#)) (|HasCategory| |#2| (QUOTE (|CoercibleTo| (|OutputForm|)))) #9# (OR #7# #9# #17#) (OR #7# #9#) #1# #17# #11# #12# (OR #12# #13#) #13# #10# (OR (AND #7# #20=(|HasCategory| |#2| (QUOTE (|LinearlyExplicitRingOver| #21=(|Integer|))))) (AND #8# #20#) (AND #9# #20#) (AND #20# #15#) #22=(AND #20# #17#)) #15# (OR #1# #4# #5# #23=(|HasCategory| |#2| (QUOTE (|BasicType|))) #6# #7# #8# #9# #10# #11# #12# #13# #15# #17# #19#) (OR #1# #4# #5# #6# #7# #8# #9# #10# #11# #12# #13# #15# #17# #19#) (OR #1# #4# #5# #6# #7# #8# #9# #15# #17#) (OR #1# #4# #6# #7# #8# #9# #15# #17#) (OR #1# #6# #7# #8# #9# #15# #17#) (OR #1# #7# #8# #9# #15# #17#) (OR #8# #15# #17#) #8# (OR #8# #24=(AND (|HasCategory| |#2| (QUOTE (|DifferentialSpace|))) #17#)) (OR #25=(AND (|HasCategory| |#2| (QUOTE (|PartialDifferentialSpace| #16#))) #17#) #15#) #19# (OR (AND #1# #26=(|HasCategory| |#2| (QUOTE (|RetractableTo| (|Fraction| #21#))))) (AND #4# #26#) (AND #5# #26#) (AND #6# #26#) (AND #7# #26#) (AND #8# #26#) (AND #9# #26#) (AND #10# #26#) (AND #11# #26#) (AND #12# #26#) (AND #13# #26#) (AND #15# #26#) (AND #26# #17#) #27=(AND #26# #19#)) (OR #28=(AND #1# #29=(|HasCategory| |#2| (QUOTE (|RetractableTo| #21#)))) #30=(AND #4# #29#) #31=(AND #5# #29#) #32=(AND #6# #29#) #33=(AND #7# #29#) #34=(AND #8# #29#) #35=(AND #12# #29#) #36=(AND #13# #29#) #37=(AND #15# #29#) #38=(AND #29# #19#) #39=(AND #9# #29#) #40=(AND #10# #29#) #41=(AND #11# #29#) #17#) (OR #28# #30# #31# #32# #33# #34# #35# #36# #37# #38# #39# #40# #41# (AND #29# #17#)) #23# (|HasCategory| #21# #14#) #22# #24# #25# (OR #38# #17#) #38# #27# (|HasAttribute| |#2| (QUOTE |unitsKnown|)) (AND #8# #17#) (AND #15# #17#) #7# #4# #6# #5# #18# (AND #23# (|HasCategory| $ (|%list| (QUOTE |FiniteAggregate|) #3#))) (|HasCategory| $ (|%list| (QUOTE |ShallowlyMutableAggregate|) #3#))) +NIL +((OR (AND #1=(|HasCategory| |#2| (QUOTE (|AbelianGroup|))) #2=(|HasCategory| |#2| (|%list| (QUOTE |Evalable|) #3=(|devaluate| |#2|)))) (AND #4=(|HasCategory| |#2| (QUOTE (|AbelianMonoid|))) #2#) (AND #5=(|HasCategory| |#2| (QUOTE (|AbelianSemiGroup|))) #2#) (AND #6=(|HasCategory| |#2| (QUOTE (|CancellationAbelianMonoid|))) #2#) (AND #7=(|HasCategory| |#2| (QUOTE (|CommutativeRing|))) #2#) (AND #8=(|HasCategory| |#2| (QUOTE (|DifferentialRing|))) #2#) (AND #9=(|HasCategory| |#2| (QUOTE (|Field|))) #2#) (AND #10=(|HasCategory| |#2| (QUOTE (|Finite|))) #2#) (AND #11=(|HasCategory| |#2| (QUOTE (|Monoid|))) #2#) (AND #12=(|HasCategory| |#2| (QUOTE (|OrderedAbelianMonoidSup|))) #2#) (AND #13=(|HasCategory| |#2| #14=(QUOTE (|OrderedSet|))) #2#) (AND #15=(|HasCategory| |#2| (QUOTE (|PartialDifferentialRing| #16=(|Symbol|)))) #2#) (AND #17=(|HasCategory| |#2| (QUOTE (|Ring|))) #2#) #18=(AND #19=(|HasCategory| |#2| (QUOTE (|SetCategory|))) #2#)) (|HasCategory| |#2| (QUOTE (|CoercibleTo| (|OutputForm|)))) #9# (OR #7# #9# #17#) (OR #7# #9#) #1# #17# #11# #12# (OR #12# #13#) #13# #10# (OR (AND #7# #20=(|HasCategory| |#2| (QUOTE (|LinearlyExplicitRingOver| #21=(|Integer|))))) (AND #8# #20#) (AND #9# #20#) (AND #20# #15#) #22=(AND #20# #17#)) #15# (OR #1# #4# #5# #23=(|HasCategory| |#2| (QUOTE (|BasicType|))) #6# #7# #8# #9# #10# #11# #12# #13# #15# #17# #19#) (OR #1# #4# #5# #6# #7# #8# #9# #10# #11# #12# #13# #15# #17# #19#) (OR #1# #4# #5# #6# #7# #8# #9# #15# #17#) (OR #1# #4# #6# #7# #8# #9# #15# #17#) (OR #1# #6# #7# #8# #9# #15# #17#) (OR #1# #7# #8# #9# #15# #17#) (OR #8# #15# #17#) #8# (OR #8# #24=(AND (|HasCategory| |#2| (QUOTE (|DifferentialSpace|))) #17#)) (OR #25=(AND (|HasCategory| |#2| (QUOTE (|PartialDifferentialSpace| #16#))) #17#) #15#) #19# (OR (AND #1# #26=(|HasCategory| |#2| (QUOTE (|RetractableTo| (|Fraction| #21#))))) (AND #4# #26#) (AND #5# #26#) (AND #6# #26#) (AND #7# #26#) (AND #8# #26#) (AND #9# #26#) (AND #10# #26#) (AND #11# #26#) (AND #12# #26#) (AND #13# #26#) (AND #15# #26#) (AND #26# #17#) #27=(AND #26# #19#)) (OR #28=(AND #1# #29=(|HasCategory| |#2| (QUOTE (|RetractableTo| #21#)))) #30=(AND #4# #29#) #31=(AND #5# #29#) #32=(AND #6# #29#) #33=(AND #7# #29#) #34=(AND #8# #29#) #35=(AND #12# #29#) #36=(AND #13# #29#) #37=(AND #15# #29#) #38=(AND #29# #19#) #39=(AND #9# #29#) #40=(AND #10# #29#) #41=(AND #11# #29#) #17#) (OR #28# #30# #31# #32# #33# #34# #35# #36# #37# #38# #39# #40# #41# (AND #29# #17#)) #23# (|HasCategory| #21# #14#) #22# #24# #25# (OR #38# #17#) #38# #27# (AND #8# #17#) (AND #15# #17#) #7# #4# #6# #5# #18# (AND #23# (|HasCategory| $ (|%list| (QUOTE |FiniteAggregate|) #3#))) (|HasCategory| $ (|%list| (QUOTE |ShallowlyMutableAggregate|) #3#))) (|OrderlyDifferentialPolynomial| R) ((|constructor| (NIL "\\spadtype{OrderlyDifferentialPolynomial} implements an ordinary differential polynomial ring in arbitrary number of differential indeterminates,{} with coefficients in a ring. The ranking on the differential indeterminate is orderly. This is analogous to the domain \\spadtype{Polynomial}. \\blankline"))) -(((|commutative| "*") |has| |#1| (|CommutativeRing|)) (|noZeroDivisors| |has| |#1| (|IntegralDomain|)) (|canonicalUnitNormal| |has| |#1| (ATTRIBUTE |canonicalUnitNormal|)) (|leftUnitary| . T) (|rightUnitary| . T) (|unitsKnown| . T)) -(#1=(|HasCategory| |#1| (QUOTE (|PolynomialFactorizationExplicit|))) (OR #2=(|HasCategory| |#1| (QUOTE (|CommutativeRing|))) #3=(|HasCategory| |#1| (QUOTE (|GcdDomain|))) #4=(|HasCategory| |#1| (QUOTE (|IntegralDomain|))) #1#) (OR #3# #4# #1#) (OR #3# #1#) #4# #2# (OR #2# #4#) (AND (|HasCategory| |#1| #5=(QUOTE (|PatternMatchable| #6=(|Float|)))) (|HasCategory| #7=(|OrderlyDifferentialVariable| #8=(|Symbol|)) #5#)) (AND (|HasCategory| |#1| #9=(QUOTE (|PatternMatchable| #10=(|Integer|)))) (|HasCategory| #7# #9#)) (AND (|HasCategory| |#1| #11=(QUOTE (|ConvertibleTo| (|Pattern| #6#)))) (|HasCategory| #7# #11#)) (AND (|HasCategory| |#1| #12=(QUOTE (|ConvertibleTo| (|Pattern| #10#)))) (|HasCategory| #7# #12#)) (AND (|HasCategory| |#1| #13=(QUOTE (|ConvertibleTo| (|InputForm|)))) (|HasCategory| #7# #13#)) (|HasCategory| |#1| (QUOTE (|LinearlyExplicitRingOver| #10#))) (|HasCategory| |#1| (QUOTE (|CharacteristicZero|))) #14=(|HasCategory| |#1| #15=(QUOTE (|CharacteristicNonZero|))) #16=(|HasCategory| |#1| (QUOTE (|Algebra| #17=(|Fraction| #10#)))) (|HasCategory| |#1| (QUOTE (|RetractableTo| #10#))) (OR #16# #18=(|HasCategory| |#1| (QUOTE (|RetractableTo| #17#)))) #18# (|HasCategory| |#1| (QUOTE (|DifferentialRing|))) (|HasCategory| |#1| (QUOTE (|DifferentialSpace|))) (|HasCategory| |#1| (QUOTE (|PartialDifferentialSpace| #8#))) (|HasCategory| |#1| (QUOTE (|PartialDifferentialRing| #8#))) (|HasCategory| |#1| (QUOTE (|Field|))) (|HasAttribute| |#1| (QUOTE |canonicalUnitNormal|)) #3# #19=(AND #1# (|HasCategory| $ #15#)) (OR #19# #14#)) +(((|commutative| "*") |has| |#1| (|CommutativeRing|)) (|noZeroDivisors| |has| |#1| (|IntegralDomain|)) (|canonicalUnitNormal| |has| |#1| (ATTRIBUTE |canonicalUnitNormal|))) +(#1=(|HasCategory| |#1| (QUOTE (|PolynomialFactorizationExplicit|))) (OR #2=(|HasCategory| |#1| (QUOTE (|CommutativeRing|))) #3=(|HasCategory| |#1| (QUOTE (|GcdDomain|))) #4=(|HasCategory| |#1| (QUOTE (|IntegralDomain|))) #1#) (OR #3# #4# #1#) (OR #3# #1#) #4# #2# (OR #2# #4#) (AND (|HasCategory| |#1| #5=(QUOTE (|PatternMatchable| #6=(|Float|)))) (|HasCategory| #7=(|OrderlyDifferentialVariable| #8=(|Symbol|)) #5#)) (AND (|HasCategory| |#1| #9=(QUOTE (|PatternMatchable| #10=(|Integer|)))) (|HasCategory| #7# #9#)) (AND (|HasCategory| |#1| #11=(QUOTE (|ConvertibleTo| (|Pattern| #6#)))) (|HasCategory| #7# #11#)) (AND (|HasCategory| |#1| #12=(QUOTE (|ConvertibleTo| (|Pattern| #10#)))) (|HasCategory| #7# #12#)) (AND (|HasCategory| |#1| #13=(QUOTE (|ConvertibleTo| (|InputForm|)))) (|HasCategory| #7# #13#)) (|HasCategory| |#1| (QUOTE (|LinearlyExplicitRingOver| #10#))) #14=(|HasCategory| |#1| (QUOTE (|Algebra| #15=(|Fraction| #10#)))) #16=(|HasCategory| |#1| #17=(QUOTE (|CharacteristicNonZero|))) (|HasCategory| |#1| (QUOTE (|CharacteristicZero|))) (|HasCategory| |#1| (QUOTE (|RetractableTo| #10#))) (OR #14# #18=(|HasCategory| |#1| (QUOTE (|RetractableTo| #15#)))) #18# (|HasCategory| |#1| (QUOTE (|DifferentialRing|))) (|HasCategory| |#1| (QUOTE (|PartialDifferentialSpace| #8#))) (|HasCategory| |#1| (QUOTE (|DifferentialSpace|))) (|HasCategory| |#1| (QUOTE (|PartialDifferentialRing| #8#))) (|HasCategory| |#1| (QUOTE (|Field|))) (|HasAttribute| |#1| (QUOTE |canonicalUnitNormal|)) #3# #19=(AND #1# (|HasCategory| $ #17#)) (OR #19# #16#)) (|OrdinaryDifferentialRing| |Kernels| R |var|) ((|constructor| (NIL "This constructor produces an ordinary differential ring from a partial differential ring by specifying a variable."))) -(((|commutative| "*") |has| |#2| . #1=((|Field|))) (|noZeroDivisors| |has| |#2| . #1#) (|canonicalUnitNormal| |has| |#2| . #1#) (|canonicalsClosed| |has| |#2| . #1#) (|unitsKnown| . T) (|leftUnitary| . T) (|rightUnitary| . T)) +(((|commutative| "*") |has| |#2| . #1=((|Field|))) (|noZeroDivisors| |has| |#2| . #1#) (|canonicalUnitNormal| |has| |#2| . #1#)) ((|HasCategory| |#2| (QUOTE (|Field|)))) (|OrderlyDifferentialVariable| S) ((|constructor| (NIL "\\spadtype{OrderlyDifferentialVariable} adds a commonly used orderly ranking to the set of derivatives of an ordered list of differential indeterminates. An orderly ranking is a ranking \\spadfun{<} of the derivatives with the property that for two derivatives \\spad{u} and \\spad{v},{} \\spad{u} \\spadfun{<} \\spad{v} if the \\spadfun{order} of \\spad{u} is less than that of \\spad{v}. This domain belongs to \\spadtype{DifferentialVariableCategory}. It defines \\spadfun{weight} to be just \\spadfun{order},{} and it defines an orderly ranking \\spadfun{<} on derivatives \\spad{u} via the lexicographic order on the pair (\\spadfun{order}(\\spad{u}),{} \\spadfun{variable}(\\spad{u}))."))) @@ -2906,11 +2906,11 @@ NIL ((|HasCategory| |#1| (QUOTE (|OrderedSet|)))) (|OrderedIntegralDomain|) ((|constructor| (NIL "The category of ordered commutative integral domains,{} where ordering and the arithmetic operations are compatible \\blankline"))) -((|noZeroDivisors| . T) ((|commutative| "*") . T) (|rightUnitary| . T) (|leftUnitary| . T) (|unitsKnown| . T)) +((|noZeroDivisors| . T) ((|commutative| "*") . T)) NIL (|OppositeMonogenicLinearOperator| P R) ((|constructor| (NIL "This constructor creates the \\spadtype{MonogenicLinearOperator} domain which is ``opposite'' in the ring sense to \\spad{P}. That is,{} as sets \\spad{P = \\$} but \\spad{a * b} in \\spad{\\$} is equal to \\spad{b * a} in \\spad{P}.")) (|po| ((|#1| $) "\\spad{po(q)} creates a value in \\spad{P} equal to \\spad{q} in \\$.")) (|op| (($ |#1|) "\\spad{op(p)} creates a value in \\$ equal to \\spad{p} in \\spad{P}."))) -((|rightUnitary| . T) (|leftUnitary| . T) (|unitsKnown| . T)) +NIL ((|HasCategory| |#2| (QUOTE (|CommutativeRing|))) (|HasCategory| |#1| (QUOTE (|DifferentialRing|)))) (|OrderedMultisetAggregate| S) ((|constructor| (NIL "to become an in order iterator")) (|min| ((|#1| $) "\\spad{min(u)} returns the smallest entry in the multiset aggregate \\spad{u}."))) @@ -2918,7 +2918,7 @@ NIL NIL (|OnePointCompletion| R) ((|constructor| (NIL "Adjunction of a complex infinity to a set. Date Created: 4 Oct 1989 Date Last Updated: 1 Nov 1989")) (|rationalIfCan| (((|Union| (|Fraction| (|Integer|)) "failed") $) "\\spad{rationalIfCan(x)} returns \\spad{x} as a finite rational number if it is one,{} \"failed\" otherwise.")) (|rational| (((|Fraction| (|Integer|)) $) "\\spad{rational(x)} returns \\spad{x} as a finite rational number. Error: if \\spad{x} is not a rational number.")) (|rational?| (((|Boolean|) $) "\\spad{rational?(x)} tests if \\spad{x} is a finite rational number.")) (|infinite?| (((|Boolean|) $) "\\spad{infinite?(x)} tests if \\spad{x} is infinite.")) (|finite?| (((|Boolean|) $) "\\spad{finite?(x)} tests if \\spad{x} is finite.")) (|infinity| (($) "\\spad{infinity()} returns infinity."))) -((|unitsKnown| |has| |#1| (|OrderedRing|))) +NIL (#1=(|HasCategory| |#1| (QUOTE (|OrderedRing|))) #2=(|HasCategory| |#1| (QUOTE (|AbelianGroup|))) (OR #2# #1#) (|HasCategory| |#1| (QUOTE (|RetractableTo| (|Fraction| #3=(|Integer|))))) (OR #1# #4=(|HasCategory| |#1| (QUOTE (|RetractableTo| #3#)))) #4# (|HasCategory| |#1| (QUOTE (|IntegerNumberSystem|)))) (|OnePointCompletionFunctions2| R S) ((|constructor| (NIL "Lifting of maps to one-point completions. Date Created: 4 Oct 1989 Date Last Updated: 4 Oct 1989")) (|map| (((|OnePointCompletion| |#2|) (|Mapping| |#2| |#1|) (|OnePointCompletion| |#1|) (|OnePointCompletion| |#2|)) "\\spad{map(f, r, i)} lifts \\spad{f} and applies it to \\spad{r},{} assuming that \\spad{f}(infinity) = \\spad{i}.") (((|OnePointCompletion| |#2|) (|Mapping| |#2| |#1|) (|OnePointCompletion| |#1|)) "\\spad{map(f, r)} lifts \\spad{f} and applies it to \\spad{r},{} assuming that \\spad{f}(infinity) = infinity."))) @@ -2926,7 +2926,7 @@ NIL NIL (|Operator| R) ((|constructor| (NIL "Algebra of ADDITIVE operators over a ring."))) -((|leftUnitary| |has| |#1| . #1=((|CommutativeRing|))) (|rightUnitary| |has| |#1| . #1#) (|unitsKnown| . T)) +NIL ((|HasCategory| |#1| (QUOTE (|CommutativeRing|))) (|HasCategory| |#1| (QUOTE (|CharacteristicNonZero|))) (|HasCategory| |#1| (QUOTE (|CharacteristicZero|)))) (|OperatorCategory&| A S) ((|constructor| (NIL "This category specifies the interface for operators used to build terms,{} in the sense of Universal Algebra. The domain parameter \\spad{S} provides representation for the `external name' of an operator.")) (|is?| (((|Boolean|) $ |#2|) "\\spad{is?(op,n)} holds if the name of the operator \\spad{op} is \\spad{n}.")) (|arity| (((|Arity|) $) "\\spad{arity(op)} returns the arity of the operator \\spad{op}.")) (|name| ((|#2| $) "\\spad{name(op)} returns the externam name of \\spad{op}."))) @@ -2946,7 +2946,7 @@ NIL NIL (|OrderedCompletion| R) ((|constructor| (NIL "Adjunction of two real infinites quantities to a set. Date Created: 4 Oct 1989 Date Last Updated: 1 Nov 1989")) (|rationalIfCan| (((|Union| (|Fraction| (|Integer|)) "failed") $) "\\spad{rationalIfCan(x)} returns \\spad{x} as a finite rational number if it is one and \"failed\" otherwise.")) (|rational| (((|Fraction| (|Integer|)) $) "\\spad{rational(x)} returns \\spad{x} as a finite rational number. Error: if \\spad{x} cannot be so converted.")) (|rational?| (((|Boolean|) $) "\\spad{rational?(x)} tests if \\spad{x} is a finite rational number.")) (|whatInfinity| (((|SingleInteger|) $) "\\spad{whatInfinity(x)} returns 0 if \\spad{x} is finite,{} 1 if \\spad{x} is +infinity,{} and \\spad{-1} if \\spad{x} is -infinity.")) (|infinite?| (((|Boolean|) $) "\\spad{infinite?(x)} tests if \\spad{x} is +infinity or -infinity,{}")) (|finite?| (((|Boolean|) $) "\\spad{finite?(x)} tests if \\spad{x} is finite.")) (|minusInfinity| (($) "\\spad{minusInfinity()} returns -infinity.")) (|plusInfinity| (($) "\\spad{plusInfinity()} returns +infinity."))) -((|unitsKnown| |has| |#1| (|OrderedRing|))) +NIL (#1=(|HasCategory| |#1| (QUOTE (|OrderedRing|))) #2=(|HasCategory| |#1| (QUOTE (|AbelianGroup|))) (OR #2# #1#) (|HasCategory| |#1| (QUOTE (|RetractableTo| (|Fraction| #3=(|Integer|))))) (OR #1# #4=(|HasCategory| |#1| (QUOTE (|RetractableTo| #3#)))) #4# (|HasCategory| |#1| (QUOTE (|IntegerNumberSystem|)))) (|OrderedCompletionFunctions2| R S) ((|constructor| (NIL "Lifting of maps to ordered completions. Date Created: 4 Oct 1989 Date Last Updated: 4 Oct 1989")) (|map| (((|OrderedCompletion| |#2|) (|Mapping| |#2| |#1|) (|OrderedCompletion| |#1|) (|OrderedCompletion| |#2|) (|OrderedCompletion| |#2|)) "\\spad{map(f, r, p, m)} lifts \\spad{f} and applies it to \\spad{r},{} assuming that \\spad{f}(plusInfinity) = \\spad{p} and that \\spad{f}(minusInfinity) = \\spad{m}.") (((|OrderedCompletion| |#2|) (|Mapping| |#2| |#1|) (|OrderedCompletion| |#1|)) "\\spad{map(f, r)} lifts \\spad{f} and applies it to \\spad{r},{} assuming that \\spad{f}(plusInfinity) = plusInfinity and that \\spad{f}(minusInfinity) = minusInfinity."))) @@ -2966,7 +2966,7 @@ NIL NIL (|OrderedRing|) ((|constructor| (NIL "Ordered sets which are also rings,{} that is,{} domains where the ring operations are compatible with the ordering. \\blankline"))) -((|unitsKnown| . T)) +NIL NIL (|OrderedSet|) ((|constructor| (NIL "The class of totally ordered sets,{} that is,{} sets such that for each pair of elements \\spad{(a,b)} exactly one of the following relations holds \\spad{a<b or a=b or b<a} and the relation is transitive,{} \\spadignore{i.e.} \\spad{a<b and b<c => a<c}."))) @@ -2990,7 +2990,7 @@ NIL ((|HasCategory| |#2| (QUOTE (|Field|))) (|HasCategory| |#2| (QUOTE (|GcdDomain|))) (|HasCategory| |#2| (QUOTE (|IntegralDomain|))) (|HasCategory| |#2| (QUOTE (|CommutativeRing|)))) (|UnivariateSkewPolynomialCategory| R) ((|constructor| (NIL "This is the category of univariate skew polynomials over an Ore coefficient ring. The multiplication is given by \\spad{x a = \\sigma(a) x + \\delta a}. This category is an evolution of the types \\indented{2}{MonogenicLinearOperator,{} OppositeMonogenicLinearOperator,{} and} \\indented{2}{NonCommutativeOperatorDivision} developped by Jean Della Dora and Stephen \\spad{M}. Watt.")) (|leftLcm| (($ $ $) "\\spad{leftLcm(a,b)} computes the value \\spad{m} of lowest degree such that \\spad{m = aa*a = bb*b} for some values \\spad{aa} and \\spad{bb}. The value \\spad{m} is computed using right-division.")) (|rightExtendedGcd| (((|Record| (|:| |coef1| $) (|:| |coef2| $) (|:| |generator| $)) $ $) "\\spad{rightExtendedGcd(a,b)} returns \\spad{[c,d]} such that \\spad{g = c * a + d * b = rightGcd(a, b)}.")) (|rightGcd| (($ $ $) "\\spad{rightGcd(a,b)} computes the value \\spad{g} of highest degree such that \\indented{3}{\\spad{a = aa*g}} \\indented{3}{\\spad{b = bb*g}} for some values \\spad{aa} and \\spad{bb}. The value \\spad{g} is computed using right-division.")) (|rightExactQuotient| (((|Union| $ "failed") $ $) "\\spad{rightExactQuotient(a,b)} computes the value \\spad{q},{} if it exists such that \\spad{a = q*b}.")) (|rightRemainder| (($ $ $) "\\spad{rightRemainder(a,b)} computes the pair \\spad{[q,r]} such that \\spad{a = q*b + r} and the degree of \\spad{r} is less than the degree of \\spad{b}. The value \\spad{r} is returned.")) (|rightQuotient| (($ $ $) "\\spad{rightQuotient(a,b)} computes the pair \\spad{[q,r]} such that \\spad{a = q*b + r} and the degree of \\spad{r} is less than the degree of \\spad{b}. The value \\spad{q} is returned.")) (|rightDivide| (((|Record| (|:| |quotient| $) (|:| |remainder| $)) $ $) "\\spad{rightDivide(a,b)} returns the pair \\spad{[q,r]} such that \\spad{a = q*b + r} and the degree of \\spad{r} is less than the degree of \\spad{b}. This process is called ``right division''.")) (|rightLcm| (($ $ $) "\\spad{rightLcm(a,b)} computes the value \\spad{m} of lowest degree such that \\spad{m = a*aa = b*bb} for some values \\spad{aa} and \\spad{bb}. The value \\spad{m} is computed using left-division.")) (|leftExtendedGcd| (((|Record| (|:| |coef1| $) (|:| |coef2| $) (|:| |generator| $)) $ $) "\\spad{leftExtendedGcd(a,b)} returns \\spad{[c,d]} such that \\spad{g = a * c + b * d = leftGcd(a, b)}.")) (|leftGcd| (($ $ $) "\\spad{leftGcd(a,b)} computes the value \\spad{g} of highest degree such that \\indented{3}{\\spad{a = g*aa}} \\indented{3}{\\spad{b = g*bb}} for some values \\spad{aa} and \\spad{bb}. The value \\spad{g} is computed using left-division.")) (|leftExactQuotient| (((|Union| $ "failed") $ $) "\\spad{leftExactQuotient(a,b)} computes the value \\spad{q},{} if it exists,{} \\indented{1}{such that \\spad{a = b*q}.}")) (|leftRemainder| (($ $ $) "\\spad{leftRemainder(a,b)} computes the pair \\spad{[q,r]} such that \\spad{a = b*q + r} and the degree of \\spad{r} is less than the degree of \\spad{b}. The value \\spad{r} is returned.")) (|leftQuotient| (($ $ $) "\\spad{leftQuotient(a,b)} computes the pair \\spad{[q,r]} such that \\spad{a = b*q + r} and the degree of \\spad{r} is less than the degree of \\spad{b}. The value \\spad{q} is returned.")) (|leftDivide| (((|Record| (|:| |quotient| $) (|:| |remainder| $)) $ $) "\\spad{leftDivide(a,b)} returns the pair \\spad{[q,r]} such that \\spad{a = b*q + r} and the degree of \\spad{r} is less than the degree of \\spad{b}. This process is called ``left division''.")) (|primitivePart| (($ $) "\\spad{primitivePart(l)} returns \\spad{l0} such that \\spad{l = a * l0} for some a in \\spad{R},{} and \\spad{content(l0) = 1}.")) (|content| ((|#1| $) "\\spad{content(l)} returns the gcd of all the coefficients of \\spad{l}.")) (|monicRightDivide| (((|Record| (|:| |quotient| $) (|:| |remainder| $)) $ $) "\\spad{monicRightDivide(a,b)} returns the pair \\spad{[q,r]} such that \\spad{a = q*b + r} and the degree of \\spad{r} is less than the degree of \\spad{b}. \\spad{b} must be monic. This process is called ``right division''.")) (|monicLeftDivide| (((|Record| (|:| |quotient| $) (|:| |remainder| $)) $ $) "\\spad{monicLeftDivide(a,b)} returns the pair \\spad{[q,r]} such that \\spad{a = b*q + r} and the degree of \\spad{r} is less than the degree of \\spad{b}. \\spad{b} must be monic. This process is called ``left division''.")) (|exquo| (((|Union| $ "failed") $ |#1|) "\\spad{exquo(l, a)} returns the exact quotient of \\spad{l} by a,{} returning \\axiom{\"failed\"} if this is not possible.")) (|apply| ((|#1| $ |#1| |#1|) "\\spad{apply(p, c, m)} returns \\spad{p(m)} where the action is given by \\spad{x m = c sigma(m) + delta(m)}.")) (|coefficients| (((|List| |#1|) $) "\\spad{coefficients(l)} returns the list of all the nonzero coefficients of \\spad{l}.")) (|monomial| (($ |#1| (|NonNegativeInteger|)) "\\spad{monomial(c,k)} produces \\spad{c} times the \\spad{k}-th power of the generating operator,{} \\spad{monomial(1,1)}.")) (|coefficient| ((|#1| $ (|NonNegativeInteger|)) "\\spad{coefficient(l,k)} is \\spad{a(k)} if \\indented{2}{\\spad{l = sum(monomial(a(i),i), i = 0..n)}.}")) (|reductum| (($ $) "\\spad{reductum(l)} is \\spad{l - monomial(a(n),n)} if \\indented{2}{\\spad{l = sum(monomial(a(i),i), i = 0..n)}.}")) (|leadingCoefficient| ((|#1| $) "\\spad{leadingCoefficient(l)} is \\spad{a(n)} if \\indented{2}{\\spad{l = sum(monomial(a(i),i), i = 0..n)}.}")) (|minimumDegree| (((|NonNegativeInteger|) $) "\\spad{minimumDegree(l)} is the smallest \\spad{k} such that \\spad{a(k) ~= 0} if \\indented{2}{\\spad{l = sum(monomial(a(i),i), i = 0..n)}.}")) (|degree| (((|NonNegativeInteger|) $) "\\spad{degree(l)} is \\spad{n} if \\indented{2}{\\spad{l = sum(monomial(a(i),i), i = 0..n)}.}"))) -((|rightUnitary| . T) (|leftUnitary| . T) (|unitsKnown| . T)) +NIL NIL (|UnivariateSkewPolynomialCategoryOps| R C) ((|constructor| (NIL "\\spad{UnivariateSkewPolynomialCategoryOps} provides products and \\indented{1}{divisions of univariate skew polynomials.}")) (|rightDivide| (((|Record| (|:| |quotient| |#2|) (|:| |remainder| |#2|)) |#2| |#2| (|Automorphism| |#1|)) "\\spad{rightDivide(a, b, sigma)} returns the pair \\spad{[q,r]} such that \\spad{a = q*b + r} and the degree of \\spad{r} is less than the degree of \\spad{b}. This process is called ``right division''. \\spad{\\sigma} is the morphism to use.")) (|leftDivide| (((|Record| (|:| |quotient| |#2|) (|:| |remainder| |#2|)) |#2| |#2| (|Automorphism| |#1|)) "\\spad{leftDivide(a, b, sigma)} returns the pair \\spad{[q,r]} such that \\spad{a = b*q + r} and the degree of \\spad{r} is less than the degree of \\spad{b}. This process is called ``left division''. \\spad{\\sigma} is the morphism to use.")) (|monicRightDivide| (((|Record| (|:| |quotient| |#2|) (|:| |remainder| |#2|)) |#2| |#2| (|Automorphism| |#1|)) "\\spad{monicRightDivide(a, b, sigma)} returns the pair \\spad{[q,r]} such that \\spad{a = q*b + r} and the degree of \\spad{r} is less than the degree of \\spad{b}. \\spad{b} must be monic. This process is called ``right division''. \\spad{\\sigma} is the morphism to use.")) (|monicLeftDivide| (((|Record| (|:| |quotient| |#2|) (|:| |remainder| |#2|)) |#2| |#2| (|Automorphism| |#1|)) "\\spad{monicLeftDivide(a, b, sigma)} returns the pair \\spad{[q,r]} such that \\spad{a = b*q + r} and the degree of \\spad{r} is less than the degree of \\spad{b}. \\spad{b} must be monic. This process is called ``left division''. \\spad{\\sigma} is the morphism to use.")) (|apply| ((|#1| |#2| |#1| |#1| (|Automorphism| |#1|) (|Mapping| |#1| |#1|)) "\\spad{apply(p, c, m, sigma, delta)} returns \\spad{p(m)} where the action is given by \\spad{x m = c sigma(m) + delta(m)}.")) (|times| ((|#2| |#2| |#2| (|Automorphism| |#1|) (|Mapping| |#1| |#1|)) "\\spad{times(p, q, sigma, delta)} returns \\spad{p * q}. \\spad{\\sigma} and \\spad{\\delta} are the maps to use."))) @@ -2998,11 +2998,11 @@ NIL ((|HasCategory| |#1| (QUOTE (|Field|))) (|HasCategory| |#1| (QUOTE (|IntegralDomain|)))) (|SparseUnivariateSkewPolynomial| R |sigma| |delta|) ((|constructor| (NIL "This is the domain of sparse univariate skew polynomials over an Ore coefficient field. The multiplication is given by \\spad{x a = \\sigma(a) x + \\delta a}.")) (|outputForm| (((|OutputForm|) $ (|OutputForm|)) "\\spad{outputForm(p, x)} returns the output form of \\spad{p} using \\spad{x} for the otherwise anonymous variable."))) -((|rightUnitary| . T) (|leftUnitary| . T) (|unitsKnown| . T)) +NIL ((|HasCategory| |#1| (QUOTE (|CommutativeRing|))) (|HasCategory| |#1| (QUOTE (|RetractableTo| (|Fraction| #1=(|Integer|))))) (|HasCategory| |#1| (QUOTE (|RetractableTo| #1#))) (|HasCategory| |#1| (QUOTE (|IntegralDomain|))) (|HasCategory| |#1| (QUOTE (|GcdDomain|))) (|HasCategory| |#1| (QUOTE (|Field|)))) (|UnivariateSkewPolynomial| |x| R |sigma| |delta|) ((|constructor| (NIL "This is the domain of univariate skew polynomials over an Ore coefficient field in a named variable. The multiplication is given by \\spad{x a = \\sigma(a) x + \\delta a}."))) -((|rightUnitary| . T) (|leftUnitary| . T) (|unitsKnown| . T)) +NIL ((|HasCategory| |#2| (QUOTE (|CommutativeRing|))) (|HasCategory| |#2| (QUOTE (|RetractableTo| (|Fraction| #1=(|Integer|))))) (|HasCategory| |#2| (QUOTE (|RetractableTo| #1#))) (|HasCategory| |#2| (QUOTE (|IntegralDomain|))) (|HasCategory| |#2| (QUOTE (|GcdDomain|))) (|HasCategory| |#2| (QUOTE (|Field|)))) (|OrthogonalPolynomialFunctions| R) ((|constructor| (NIL "This package provides orthogonal polynomials as functions on a ring.")) (|legendreP| ((|#1| (|NonNegativeInteger|) |#1|) "\\spad{legendreP(n,x)} is the \\spad{n}-th Legendre polynomial,{} \\spad{P[n](x)}. These are defined by \\spad{1/sqrt(1-2*x*t+t**2) = sum(P[n](x)*t**n, n = 0..)}.")) (|laguerreL| ((|#1| (|NonNegativeInteger|) (|NonNegativeInteger|) |#1|) "\\spad{laguerreL(m,n,x)} is the associated Laguerre polynomial,{} \\spad{L<m>[n](x)}. This is the \\spad{m}-th derivative of \\spad{L[n](x)}.") ((|#1| (|NonNegativeInteger|) |#1|) "\\spad{laguerreL(n,x)} is the \\spad{n}-th Laguerre polynomial,{} \\spad{L[n](x)}. These are defined by \\spad{exp(-t*x/(1-t))/(1-t) = sum(L[n](x)*t**n/n!, n = 0..)}.")) (|hermiteH| ((|#1| (|NonNegativeInteger|) |#1|) "\\spad{hermiteH(n,x)} is the \\spad{n}-th Hermite polynomial,{} \\spad{H[n](x)}. These are defined by \\spad{exp(2*t*x-t**2) = sum(H[n](x)*t**n/n!, n = 0..)}.")) (|chebyshevU| ((|#1| (|NonNegativeInteger|) |#1|) "\\spad{chebyshevU(n,x)} is the \\spad{n}-th Chebyshev polynomial of the second kind,{} \\spad{U[n](x)}. These are defined by \\spad{1/(1-2*t*x+t**2) = sum(T[n](x) *t**n, n = 0..)}.")) (|chebyshevT| ((|#1| (|NonNegativeInteger|) |#1|) "\\spad{chebyshevT(n,x)} is the \\spad{n}-th Chebyshev polynomial of the first kind,{} \\spad{T[n](x)}. These are defined by \\spad{(1-t*x)/(1-2*t*x+t**2) = sum(T[n](x) *t**n, n = 0..)}."))) @@ -3046,7 +3046,7 @@ NIL NIL (|OrdinaryWeightedPolynomials| R |vl| |wl| |wtlevel|) ((|constructor| (NIL "This domain represents truncated weighted polynomials over the \"Polynomial\" type. The variables must be specified,{} as must the weights. The representation is sparse in the sense that only non-zero terms are represented.")) (|changeWeightLevel| (((|Void|) (|NonNegativeInteger|)) "\\spad{changeWeightLevel(n)} This changes the weight level to the new value given: NB: previously calculated terms are not affected")) (/ (((|Union| $ "failed") $ $) "\\spad{x/y} division (only works if minimum weight of divisor is zero,{} and if \\spad{R} is a Field)"))) -((|leftUnitary| |has| |#1| . #1=((|CommutativeRing|))) (|rightUnitary| |has| |#1| . #1#) (|unitsKnown| . T)) +NIL ((|HasCategory| |#1| (QUOTE (|CommutativeRing|))) (|HasCategory| |#1| (QUOTE (|Field|)))) (|PadeApproximants| R PS UP) ((|constructor| (NIL "\\indented{1}{This package computes reliable Pad&ea. approximants using} a generalized Viskovatov continued fraction algorithm. Authors: Burge,{} Hassner & Watt. Date Created: April 1987 Date Last Updated: 12 April 1990 Keywords: Pade,{} series Examples: References: \\indented{2}{\"Pade Approximants,{} Part I: Basic Theory\",{} Baker & Graves-Morris.}")) (|padecf| (((|Union| (|ContinuedFraction| |#3|) "failed") (|NonNegativeInteger|) (|NonNegativeInteger|) |#2| |#2|) "\\spad{padecf(nd,dd,ns,ds)} computes the approximant as a continued fraction of polynomials (if it exists) for arguments \\spad{nd} (numerator degree of approximant),{} \\spad{dd} (denominator degree of approximant),{} \\spad{ns} (numerator series of function),{} and \\spad{ds} (denominator series of function).")) (|pade| (((|Union| (|Fraction| |#3|) "failed") (|NonNegativeInteger|) (|NonNegativeInteger|) |#2| |#2|) "\\spad{pade(nd,dd,ns,ds)} computes the approximant as a quotient of polynomials (if it exists) for arguments \\spad{nd} (numerator degree of approximant),{} \\spad{dd} (denominator degree of approximant),{} \\spad{ns} (numerator series of function),{} and \\spad{ds} (denominator series of function)."))) @@ -3058,20 +3058,20 @@ NIL NIL (|PAdicInteger| |p|) ((|constructor| (NIL "Stream-based implementation of Zp: \\spad{p}-adic numbers are represented as sum(\\spad{i} = 0..,{} a[\\spad{i}] * p^i),{} where the a[\\spad{i}] lie in 0,{}1,{}...,{}(\\spad{p} - 1)."))) -((|noZeroDivisors| . T) ((|commutative| "*") . T) (|rightUnitary| . T) (|leftUnitary| . T) (|unitsKnown| . T)) +((|noZeroDivisors| . T) ((|commutative| "*") . T)) NIL (|PAdicIntegerCategory| |p|) ((|constructor| (NIL "This is the catefory of stream-based representations of \\indented{2}{the \\spad{p}-adic integers.}")) (|root| (($ (|SparseUnivariatePolynomial| (|Integer|)) (|Integer|)) "\\spad{root(f,a)} returns a root of the polynomial \\spad{f}. Argument \\spad{a} must be a root of \\spad{f} \\spad{(mod p)}.")) (|sqrt| (($ $ (|Integer|)) "\\spad{sqrt(b,a)} returns a square root of \\spad{b}. Argument \\spad{a} is a square root of \\spad{b} \\spad{(mod p)}.")) (|approximate| (((|Integer|) $ (|Integer|)) "\\spad{approximate(x,n)} returns an integer \\spad{y} such that \\spad{y = x (mod p^n)} when \\spad{n} is positive,{} and 0 otherwise.")) (|quotientByP| (($ $) "\\spad{quotientByP(x)} returns \\spad{b},{} where \\spad{x = a + b p}.")) (|moduloP| (((|Integer|) $) "\\spad{modulo(x)} returns a,{} where \\spad{x = a + b p}.")) (|modulus| (((|Integer|)) "\\spad{modulus()} returns the value of \\spad{p}.")) (|complete| (($ $) "\\spad{complete(x)} forces the computation of all digits.")) (|extend| (($ $ (|Integer|)) "\\spad{extend(x,n)} forces the computation of digits up to order \\spad{n}.")) (|order| (((|NonNegativeInteger|) $) "\\spad{order(x)} returns the exponent of the highest power of \\spad{p} dividing \\spad{x}.")) (|digits| (((|Stream| (|Integer|)) $) "\\spad{digits(x)} returns a stream of \\spad{p}-adic digits of \\spad{x}."))) -((|noZeroDivisors| . T) ((|commutative| "*") . T) (|rightUnitary| . T) (|leftUnitary| . T) (|unitsKnown| . T)) +((|noZeroDivisors| . T) ((|commutative| "*") . T)) NIL (|PAdicRational| |p|) ((|constructor| (NIL "Stream-based implementation of Qp: numbers are represented as sum(\\spad{i} = \\spad{k}..,{} a[\\spad{i}] * p^i) where the a[\\spad{i}] lie in 0,{}1,{}...,{}(\\spad{p} - 1)."))) -((|canonicalsClosed| . T) (|canonicalUnitNormal| . T) (|noZeroDivisors| . T) ((|commutative| "*") . T) (|rightUnitary| . T) (|leftUnitary| . T) (|unitsKnown| . T)) -(#1=(|HasCategory| #2=(|PAdicInteger| |#1|) (QUOTE (|PolynomialFactorizationExplicit|))) (|HasCategory| #2# (QUOTE (|RetractableTo| #3=(|Symbol|)))) #4=(|HasCategory| #2# #5=(QUOTE (|CharacteristicNonZero|))) (|HasCategory| #2# (QUOTE (|CharacteristicZero|))) (|HasCategory| #2# (QUOTE (|ConvertibleTo| (|InputForm|)))) (|HasCategory| #2# (QUOTE (|RealConstant|))) #6=(|HasCategory| #2# (QUOTE (|OrderedIntegralDomain|))) #7=(|HasCategory| #2# (QUOTE (|OrderedSet|))) (OR #6# #7#) (|HasCategory| #2# (QUOTE (|RetractableTo| #8=(|Integer|)))) (|HasCategory| #2# (QUOTE (|StepThrough|))) (|HasCategory| #2# (QUOTE (|PatternMatchable| #9=(|Float|)))) (|HasCategory| #2# (QUOTE (|PatternMatchable| #8#))) (|HasCategory| #2# (QUOTE (|ConvertibleTo| (|Pattern| #9#)))) (|HasCategory| #2# (QUOTE (|ConvertibleTo| (|Pattern| #8#)))) (|HasCategory| #2# (QUOTE (|LinearlyExplicitRingOver| #8#))) (|HasCategory| #2# (QUOTE (|DifferentialSpace|))) (|HasCategory| #2# (QUOTE (|PartialDifferentialSpace| #3#))) (|HasCategory| #2# (QUOTE (|DifferentialRing|))) (|HasCategory| #2# (QUOTE (|PartialDifferentialRing| #3#))) (|HasCategory| #2# (|%list| (QUOTE |InnerEvalable|) (QUOTE #3#) #10=(|%list| (QUOTE |PAdicInteger|) (|devaluate| |#1|)))) (|HasCategory| #2# (|%list| (QUOTE |Evalable|) #10#)) (|HasCategory| #2# (|%list| (QUOTE |Eltable|) #10# #10#)) (|HasCategory| #2# (QUOTE (|EuclideanDomain|))) (|HasCategory| #2# (QUOTE (|IntegerNumberSystem|))) #11=(AND (|HasCategory| $ #5#) #1#) (OR #11# #4#)) +((|canonicalUnitNormal| . T) (|noZeroDivisors| . T) ((|commutative| "*") . T)) +(#1=(|HasCategory| #2=(|PAdicInteger| |#1|) (QUOTE (|PolynomialFactorizationExplicit|))) (|HasCategory| #2# (QUOTE (|RetractableTo| #3=(|Symbol|)))) #4=(|HasCategory| #2# #5=(QUOTE (|CharacteristicNonZero|))) (|HasCategory| #2# (QUOTE (|CharacteristicZero|))) (|HasCategory| #2# (QUOTE (|ConvertibleTo| (|InputForm|)))) (|HasCategory| #2# (QUOTE (|RealConstant|))) #6=(|HasCategory| #2# (QUOTE (|OrderedIntegralDomain|))) #7=(|HasCategory| #2# (QUOTE (|OrderedSet|))) (OR #6# #7#) (|HasCategory| #2# (QUOTE (|RetractableTo| #8=(|Integer|)))) (|HasCategory| #2# (QUOTE (|StepThrough|))) (|HasCategory| #2# (QUOTE (|PatternMatchable| #9=(|Float|)))) (|HasCategory| #2# (QUOTE (|PatternMatchable| #8#))) (|HasCategory| #2# (QUOTE (|ConvertibleTo| (|Pattern| #9#)))) (|HasCategory| #2# (QUOTE (|ConvertibleTo| (|Pattern| #8#)))) (|HasCategory| #2# (QUOTE (|LinearlyExplicitRingOver| #8#))) (|HasCategory| #2# (QUOTE (|PartialDifferentialSpace| #3#))) (|HasCategory| #2# (QUOTE (|DifferentialSpace|))) (|HasCategory| #2# (QUOTE (|DifferentialRing|))) (|HasCategory| #2# (QUOTE (|PartialDifferentialRing| #3#))) (|HasCategory| #2# (|%list| (QUOTE |InnerEvalable|) (QUOTE #3#) #10=(|%list| (QUOTE |PAdicInteger|) (|devaluate| |#1|)))) (|HasCategory| #2# (|%list| (QUOTE |Evalable|) #10#)) (|HasCategory| #2# (|%list| (QUOTE |Eltable|) #10# #10#)) (|HasCategory| #2# (QUOTE (|EuclideanDomain|))) (|HasCategory| #2# (QUOTE (|IntegerNumberSystem|))) #11=(AND (|HasCategory| $ #5#) #1#) (OR #11# #4#)) (|PAdicRationalConstructor| |p| PADIC) ((|constructor| (NIL "This is the category of stream-based representations of Qp.")) (|removeZeroes| (($ (|Integer|) $) "\\spad{removeZeroes(n,x)} removes up to \\spad{n} leading zeroes from the \\spad{p}-adic rational \\spad{x}.") (($ $) "\\spad{removeZeroes(x)} removes leading zeroes from the representation of the \\spad{p}-adic rational \\spad{x}. A \\spad{p}-adic rational is represented by (1) an exponent and (2) a \\spad{p}-adic integer which may have leading zero digits. When the \\spad{p}-adic integer has a leading zero digit,{} a 'leading zero' is removed from the \\spad{p}-adic rational as follows: the number is rewritten by increasing the exponent by 1 and dividing the \\spad{p}-adic integer by \\spad{p}. Note: \\spad{removeZeroes(f)} removes all leading zeroes from \\spad{f}.")) (|continuedFraction| (((|ContinuedFraction| (|Fraction| (|Integer|))) $) "\\spad{continuedFraction(x)} converts the \\spad{p}-adic rational number \\spad{x} to a continued fraction.")) (|approximate| (((|Fraction| (|Integer|)) $ (|Integer|)) "\\spad{approximate(x,n)} returns a rational number \\spad{y} such that \\spad{y = x (mod p^n)}."))) -((|canonicalsClosed| . T) (|canonicalUnitNormal| . T) (|noZeroDivisors| . T) ((|commutative| "*") . T) (|rightUnitary| . T) (|leftUnitary| . T) (|unitsKnown| . T)) -(#1=(|HasCategory| |#2| (QUOTE (|PolynomialFactorizationExplicit|))) (|HasCategory| |#2| (QUOTE (|RetractableTo| #2=(|Symbol|)))) #3=(|HasCategory| |#2| #4=(QUOTE (|CharacteristicNonZero|))) (|HasCategory| |#2| (QUOTE (|CharacteristicZero|))) (|HasCategory| |#2| (QUOTE (|ConvertibleTo| (|InputForm|)))) (|HasCategory| |#2| (QUOTE (|RealConstant|))) #5=(|HasCategory| |#2| (QUOTE (|OrderedIntegralDomain|))) #6=(|HasCategory| |#2| (QUOTE (|OrderedSet|))) (OR #5# #6#) (|HasCategory| |#2| (QUOTE (|RetractableTo| #7=(|Integer|)))) (|HasCategory| |#2| (QUOTE (|StepThrough|))) (|HasCategory| |#2| (QUOTE (|PatternMatchable| #8=(|Float|)))) (|HasCategory| |#2| (QUOTE (|PatternMatchable| #7#))) (|HasCategory| |#2| (QUOTE (|ConvertibleTo| (|Pattern| #8#)))) (|HasCategory| |#2| (QUOTE (|ConvertibleTo| (|Pattern| #7#)))) (|HasCategory| |#2| (QUOTE (|LinearlyExplicitRingOver| #7#))) (|HasCategory| |#2| (QUOTE (|DifferentialSpace|))) (|HasCategory| |#2| (QUOTE (|PartialDifferentialSpace| #2#))) (|HasCategory| |#2| (QUOTE (|DifferentialRing|))) (|HasCategory| |#2| (QUOTE (|PartialDifferentialRing| #2#))) (|HasCategory| |#2| (|%list| (QUOTE |InnerEvalable|) (QUOTE #2#) #9=(|devaluate| |#2|))) (|HasCategory| |#2| (|%list| (QUOTE |Evalable|) #9#)) (|HasCategory| |#2| (|%list| (QUOTE |Eltable|) #9# #9#)) (|HasCategory| |#2| (QUOTE (|EuclideanDomain|))) (|HasCategory| |#2| (QUOTE (|IntegerNumberSystem|))) #10=(AND #1# (|HasCategory| $ #4#)) (OR #10# #3#)) +((|canonicalUnitNormal| . T) (|noZeroDivisors| . T) ((|commutative| "*") . T)) +(#1=(|HasCategory| |#2| (QUOTE (|PolynomialFactorizationExplicit|))) (|HasCategory| |#2| (QUOTE (|RetractableTo| #2=(|Symbol|)))) #3=(|HasCategory| |#2| #4=(QUOTE (|CharacteristicNonZero|))) (|HasCategory| |#2| (QUOTE (|CharacteristicZero|))) (|HasCategory| |#2| (QUOTE (|ConvertibleTo| (|InputForm|)))) (|HasCategory| |#2| (QUOTE (|RealConstant|))) #5=(|HasCategory| |#2| (QUOTE (|OrderedIntegralDomain|))) #6=(|HasCategory| |#2| (QUOTE (|OrderedSet|))) (OR #5# #6#) (|HasCategory| |#2| (QUOTE (|RetractableTo| #7=(|Integer|)))) (|HasCategory| |#2| (QUOTE (|StepThrough|))) (|HasCategory| |#2| (QUOTE (|PatternMatchable| #8=(|Float|)))) (|HasCategory| |#2| (QUOTE (|PatternMatchable| #7#))) (|HasCategory| |#2| (QUOTE (|ConvertibleTo| (|Pattern| #8#)))) (|HasCategory| |#2| (QUOTE (|ConvertibleTo| (|Pattern| #7#)))) (|HasCategory| |#2| (QUOTE (|LinearlyExplicitRingOver| #7#))) (|HasCategory| |#2| (QUOTE (|PartialDifferentialSpace| #2#))) (|HasCategory| |#2| (QUOTE (|DifferentialSpace|))) (|HasCategory| |#2| (QUOTE (|DifferentialRing|))) (|HasCategory| |#2| (QUOTE (|PartialDifferentialRing| #2#))) (|HasCategory| |#2| (|%list| (QUOTE |InnerEvalable|) (QUOTE #2#) #9=(|devaluate| |#2|))) (|HasCategory| |#2| (|%list| (QUOTE |Evalable|) #9#)) (|HasCategory| |#2| (|%list| (QUOTE |Eltable|) #9# #9#)) (|HasCategory| |#2| (QUOTE (|EuclideanDomain|))) (|HasCategory| |#2| (QUOTE (|IntegerNumberSystem|))) #10=(AND #1# (|HasCategory| $ #4#)) (OR #10# #3#)) (|Pair| S T$) ((|constructor| (NIL "\\indented{1}{This domain provides a very simple representation} of the notion of `pair of objects'. It does not try to achieve all possible imaginable things.")) (|second| ((|#2| $) "\\spad{second(p)} extracts the second components of `p'.")) (|first| ((|#1| $) "\\spad{first(p)} extracts the first component of `p'.")) (|construct| (($ |#1| |#2|) "\\spad{construct(s,t)} is same as pair(\\spad{s},{}\\spad{t}),{} with syntactic sugar.")) (|pair| (($ |#1| |#2|) "\\spad{pair(s,t)} returns a pair object composed of `s' and `t'."))) NIL @@ -3157,7 +3157,7 @@ NIL NIL NIL (|PoincareBirkhoffWittLyndonBasis| |VarSet|) -((|constructor| (NIL "This domain provides the internal representation of polynomials in non-commutative variables written over the Poincare-Birkhoff-Witt basis. See the \\spadtype{XPBWPolynomial} domain constructor. See Free Lie Algebras by \\spad{C}. Reutenauer (Oxford science publications). \\newline Author: Michel Petitot (petitot@lifl.fr).")) (|varList| (((|List| |#1|) $) "\\spad{varList([l1]*[l2]*...[ln])} returns the list of variables in the word \\spad{l1*l2*...*ln}.")) (|retractable?| (((|Boolean|) $) "\\spad{retractable?([l1]*[l2]*...[ln])} returns \\spad{true} iff \\spad{n} equals \\spad{1}.")) (|rest| (($ $) "\\spad{rest([l1]*[l2]*...[ln])} returns the list \\spad{l2, .... ln}.")) (|ListOfTerms| (((|List| (|LyndonWord| |#1|)) $) "\\spad{ListOfTerms([l1]*[l2]*...[ln])} returns the list of words \\spad{l1, l2, .... ln}.")) (|length| (((|NonNegativeInteger|) $) "\\spad{length([l1]*[l2]*...[ln])} returns the length of the word \\spad{l1*l2*...*ln}.")) (|first| (((|LyndonWord| |#1|) $) "\\spad{first([l1]*[l2]*...[ln])} returns the Lyndon word \\spad{l1}.")) (|coerce| (($ |#1|) "\\spad{coerce(v)} return \\spad{v}") (((|OrderedFreeMonoid| |#1|) $) "\\spad{coerce([l1]*[l2]*...[ln])} returns the word \\spad{l1*l2*...*ln},{} where \\spad{[l_i]} is the backeted form of the Lyndon word \\spad{l_i}.")) (|One| (($) "\\spad{1} returns the empty list."))) +((|constructor| (NIL "This domain provides the internal representation of polynomials in non-commutative variables written over the Poincare-Birkhoff-Witt basis. See the \\spadtype{XPBWPolynomial} domain constructor. See Free Lie Algebras by \\spad{C}. Reutenauer (Oxford science publications). \\newline Author: Michel Petitot (petitot@lifl.fr).")) (|varList| (((|List| |#1|) $) "\\spad{varList([l1]*[l2]*...[ln])} returns the list of variables in the word \\spad{l1*l2*...*ln}.")) (|retractable?| (((|Boolean|) $) "\\spad{retractable?([l1]*[l2]*...[ln])} returns \\spad{true} iff \\spad{n} equals \\spad{1}.")) (|rest| (($ $) "\\spad{rest([l1]*[l2]*...[ln])} returns the list \\spad{l2, .... ln}.")) (|ListOfTerms| (((|List| (|LyndonWord| |#1|)) $) "\\spad{ListOfTerms([l1]*[l2]*...[ln])} returns the list of words \\spad{l1, l2, .... ln}.")) (|length| (((|NonNegativeInteger|) $) "\\spad{length([l1]*[l2]*...[ln])} returns the length of the word \\spad{l1*l2*...*ln}.")) (|first| (((|LyndonWord| |#1|) $) "\\spad{first([l1]*[l2]*...[ln])} returns the Lyndon word \\spad{l1}.")) (|coerce| (($ |#1|) "\\spad{coerce(v)} return \\spad{v}")) (|One| (($) "\\spad{1} returns the empty list."))) NIL NIL (|PolynomialComposition| UP R) @@ -3178,11 +3178,11 @@ NIL NIL (|PartialDifferentialModule| R S) ((|constructor| (NIL "A partial differential \\spad{R}-module with differentiations indexed by a parameter type \\spad{S}. \\blankline"))) -((|leftUnitary| . T) (|rightUnitary| . T)) +NIL NIL (|PartialDifferentialRing| S) ((|constructor| (NIL "A partial differential ring with differentiations indexed by a parameter type \\spad{S}. \\blankline"))) -((|unitsKnown| . T)) +NIL NIL (|PartialDifferentialSpace&| A S) ((|constructor| (NIL "\\indented{2}{This category captures the interface of domains stable by partial} \\indented{2}{differentiation with respect to variables from some domain.} See Also: \\indented{2}{PartialDifferentialDomain}")) (D (($ $ (|List| |#2|) (|List| (|NonNegativeInteger|))) "\\spad{D(x,[s1,...,sn],[n1,...,nn])} is a shorthand for \\spad{differentiate(x,[s1,...,sn],[n1,...,nn])}.") (($ $ |#2| (|NonNegativeInteger|)) "\\spad{D(x,s,n)} is a shorthand for \\spad{differentiate(x,s,n)}.") (($ $ (|List| |#2|)) "\\spad{D(x,[s1,...sn])} is a shorthand for \\spad{differentiate(x,[s1,...sn])}.")) (|differentiate| (($ $ (|List| |#2|) (|List| (|NonNegativeInteger|))) "\\spad{differentiate(x,[s1,...,sn],[n1,...,nn])} computes multiple partial derivatives,{} \\spadignore{i.e.}") (($ $ |#2| (|NonNegativeInteger|)) "\\spad{differentiate(x,s,n)} computes multiple partial derivatives,{} \\spadignore{i.e.} \\spad{n}\\spad{-}th derivative of \\spad{x} with respect to \\spad{s}.") (($ $ (|List| |#2|)) "\\spad{differentiate(x,[s1,...sn])} computes successive partial derivatives,{} \\spadignore{i.e.} \\spad{differentiate(...differentiate(x, s1)..., sn)}."))) @@ -3198,23 +3198,23 @@ NIL ((AND #1=(|HasCategory| |#1| (QUOTE (|SetCategory|))) (|HasCategory| |#1| (|%list| (QUOTE |Evalable|) #2=(|devaluate| |#1|)))) #1# (OR #3=(|HasCategory| |#1| (QUOTE (|BasicType|))) #1#) (|HasCategory| |#1| (QUOTE (|CoercibleTo| (|OutputForm|)))) #3# (|HasCategory| $ (|%list| (QUOTE |ShallowlyMutableAggregate|) #2#))) (|Permutation| S) ((|constructor| (NIL "Permutation(\\spad{S}) implements the group of all bijections \\indented{2}{on a set \\spad{S},{} which move only a finite number of points.} \\indented{2}{A permutation is considered as a map from \\spad{S} into \\spad{S}. In particular} \\indented{2}{multiplication is defined as composition of maps:} \\indented{2}{{\\em pi1 * pi2 = pi1 o pi2}.} \\indented{2}{The internal representation of permuatations are two lists} \\indented{2}{of equal length representing preimages and images.}")) (|coerceImages| (($ (|List| |#1|)) "\\spad{coerceImages(ls)} coerces the list {\\em ls} to a permutation whose image is given by {\\em ls} and the preimage is fixed to be {\\em [1,...,n]}. Note: {coerceImages(\\spad{ls})=coercePreimagesImages([1,{}...,{}\\spad{n}],{}\\spad{ls})}. We assume that both preimage and image do not contain repetitions.")) (|fixedPoints| (((|Set| |#1|) $) "\\spad{fixedPoints(p)} returns the points fixed by the permutation \\spad{p}.")) (|sort| (((|List| $) (|List| $)) "\\spad{sort(lp)} sorts a list of permutations {\\em lp} according to cycle structure first according to length of cycles,{} second,{} if \\spad{S} has \\spadtype{Finite} or \\spad{S} has \\spadtype{OrderedSet} according to lexicographical order of entries in cycles of equal length.")) (|odd?| (((|Boolean|) $) "\\spad{odd?(p)} returns \\spad{true} if and only if \\spad{p} is an odd permutation \\spadignore{i.e.} {\\em sign(p)} is {\\em -1}.")) (|even?| (((|Boolean|) $) "\\spad{even?(p)} returns \\spad{true} if and only if \\spad{p} is an even permutation,{} \\spadignore{i.e.} {\\em sign(p)} is 1.")) (|sign| (((|Integer|) $) "\\spad{sign(p)} returns the signum of the permutation \\spad{p},{} \\spad{+1} or \\spad{-1}.")) (|numberOfCycles| (((|NonNegativeInteger|) $) "\\spad{numberOfCycles(p)} returns the number of non-trivial cycles of the permutation \\spad{p}.")) (|order| (((|NonNegativeInteger|) $) "\\spad{order(p)} returns the order of a permutation \\spad{p} as a group element.")) (|cyclePartition| (((|Partition|) $) "\\spad{cyclePartition(p)} returns the cycle structure of a permutation \\spad{p} including cycles of length 1 only if \\spad{S} is finite.")) (|degree| (((|NonNegativeInteger|) $) "\\spad{degree(p)} retuns the number of points moved by the permutation \\spad{p}.")) (|coerceListOfPairs| (($ (|List| (|List| |#1|))) "\\spad{coerceListOfPairs(lls)} coerces a list of pairs {\\em lls} to a permutation. Error: if not consistent,{} \\spadignore{i.e.} the set of the first elements coincides with the set of second elements. coerce(\\spad{p}) generates output of the permutation \\spad{p} with domain OutputForm.")) (|coerce| (($ (|List| |#1|)) "\\spad{coerce(ls)} coerces a cycle {\\em ls},{} \\spadignore{i.e.} a list with not repetitions to a permutation,{} which maps {\\em ls.i} to {\\em ls.i+1},{} indices modulo the length of the list. Error: if repetitions occur.") (($ (|List| (|List| |#1|))) "\\spad{coerce(lls)} coerces a list of cycles {\\em lls} to a permutation,{} each cycle being a list with no repetitions,{} is coerced to the permutation,{} which maps {\\em ls.i} to {\\em ls.i+1},{} indices modulo the length of the list,{} then these permutations are mutiplied. Error: if repetitions occur in one cycle.")) (|coercePreimagesImages| (($ (|List| (|List| |#1|))) "\\spad{coercePreimagesImages(lls)} coerces the representation {\\em lls} of a permutation as a list of preimages and images to a permutation. We assume that both preimage and image do not contain repetitions.")) (|listRepresentation| (((|Record| (|:| |preimage| (|List| |#1|)) (|:| |image| (|List| |#1|))) $) "\\spad{listRepresentation(p)} produces a representation {\\em rep} of the permutation \\spad{p} as a list of preimages and images,{} \\spad{i}.\\spad{e} \\spad{p} maps {\\em (rep.preimage).k} to {\\em (rep.image).k} for all indices \\spad{k}. Elements of \\spad{S} not in {\\em (rep.preimage).k} are fixed points,{} and these are the only fixed points of the permutation."))) -((|unitsKnown| . T)) -((OR #1=(|HasCategory| |#1| (QUOTE (|Finite|))) #2=(|HasCategory| |#1| (QUOTE (|OrderedSet|)))) #1# #2#) +NIL +((OR #1=(|HasCategory| |#1| (QUOTE (|Finite|))) #2=(|HasCategory| |#1| (QUOTE (|OrderedSet|)))) #2# #1#) (|Permanent| |n| R) ((|constructor| (NIL "Permanent implements the functions {\\em permanent},{} the permanent for square matrices.")) (|permanent| ((|#2| (|SquareMatrix| |#1| |#2|)) "\\spad{permanent(x)} computes the permanent of a square matrix \\spad{x}. The {\\em permanent} is equivalent to the \\spadfun{determinant} except that coefficients have no change of sign. This function is much more difficult to compute than the {\\em determinant}. The formula used is by \\spad{H}.\\spad{J}. Ryser,{} improved by [Nijenhuis and Wilf,{} Ch. 19]. Note: permanent(\\spad{x}) choose one of three algorithms,{} depending on the underlying ring \\spad{R} and on \\spad{n},{} the number of rows (and columns) of x:\\begin{items} \\item 1. if 2 has an inverse in \\spad{R} we can use the algorithm of \\indented{3}{[Nijenhuis and Wilf,{} ch.19,{}\\spad{p}.158]; if 2 has no inverse,{}} \\indented{3}{some modifications are necessary:} \\item 2. if {\\em n > 6} and \\spad{R} is an integral domain with characteristic \\indented{3}{different from 2 (the algorithm works if and only 2 is not a} \\indented{3}{zero-divisor of \\spad{R} and {\\em characteristic()\\$R ~= 2},{}} \\indented{3}{but how to check that for any given \\spad{R} ?),{}} \\indented{3}{the local function {\\em permanent2} is called;} \\item 3. else,{} the local function {\\em permanent3} is called \\indented{3}{(works for all commutative rings \\spad{R}).} \\end{items}"))) NIL NIL (|PermutationCategory| S) ((|constructor| (NIL "PermutationCategory provides a categorial environment \\indented{1}{for subgroups of bijections of a set (\\spadignore{i.e.} permutations)}")) (< (((|Boolean|) $ $) "\\spad{p < q} is an order relation on permutations. Note: this order is only total if and only if \\spad{S} is totally ordered or \\spad{S} is finite.")) (|orbit| (((|Set| |#1|) $ |#1|) "\\spad{orbit(p, el)} returns the orbit of {\\em el} under the permutation \\spad{p},{} \\spadignore{i.e.} the set which is given by applications of the powers of \\spad{p} to {\\em el}.")) (|support| (((|Set| |#1|) $) "\\spad{support p} returns the set of points not fixed by the permutation \\spad{p}.")) (|cycles| (($ (|List| (|List| |#1|))) "\\spad{cycles(lls)} coerces a list list of cycles {\\em lls} to a permutation,{} each cycle being a list with not repetitions,{} is coerced to the permutation,{} which maps {\\em ls.i} to {\\em ls.i+1},{} indices modulo the length of the list,{} then these permutations are mutiplied. Error: if repetitions occur in one cycle.")) (|cycle| (($ (|List| |#1|)) "\\spad{cycle(ls)} coerces a cycle {\\em ls},{} \\spadignore{i.e.} a list with not repetitions to a permutation,{} which maps {\\em ls.i} to {\\em ls.i+1},{} indices modulo the length of the list. Error: if repetitions occur."))) -((|unitsKnown| . T)) +NIL NIL (|PermutationGroup| S) -((|constructor| (NIL "PermutationGroup implements permutation groups acting on a set \\spad{S},{} \\spadignore{i.e.} all subgroups of the symmetric group of \\spad{S},{} represented as a list of permutations (generators). Note that therefore the objects are not members of the \\Language category \\spadtype{Group}. Using the idea of base and strong generators by Sims,{} basic routines and algorithms are implemented so that the word problem for permutation groups can be solved.")) (|initializeGroupForWordProblem| (((|Void|) $ (|Integer|) (|Integer|)) "\\spad{initializeGroupForWordProblem(gp,m,n)} initializes the group {\\em gp} for the word problem. Notes: (1) with a small integer you get shorter words,{} but the routine takes longer than the standard routine for longer words. (2) be careful: invoking this routine will destroy the possibly stored information about your group (but will recompute it again). (3) users need not call this function normally for the soultion of the word problem.") (((|Void|) $) "\\spad{initializeGroupForWordProblem(gp)} initializes the group {\\em gp} for the word problem. Notes: it calls the other function of this name with parameters 0 and 1: {\\em initializeGroupForWordProblem(gp,0,1)}. Notes: (1) be careful: invoking this routine will destroy the possibly information about your group (but will recompute it again) (2) users need not call this function normally for the soultion of the word problem.")) (<= (((|Boolean|) $ $) "\\spad{gp1 <= gp2} returns \\spad{true} if and only if {\\em gp1} is a subgroup of {\\em gp2}. Note: because of a bug in the parser you have to call this function explicitly by {\\em gp1 <=\\$(PERMGRP S) gp2}.")) (< (((|Boolean|) $ $) "\\spad{gp1 < gp2} returns \\spad{true} if and only if {\\em gp1} is a proper subgroup of {\\em gp2}.")) (|support| (((|Set| |#1|) $) "\\spad{support(gp)} returns the points moved by the group {\\em gp}.")) (|wordInGenerators| (((|List| (|NonNegativeInteger|)) (|Permutation| |#1|) $) "\\spad{wordInGenerators(p,gp)} returns the word for the permutation \\spad{p} in the original generators of the group {\\em gp},{} represented by the indices of the list,{} given by {\\em generators}.")) (|wordInStrongGenerators| (((|List| (|NonNegativeInteger|)) (|Permutation| |#1|) $) "\\spad{wordInStrongGenerators(p,gp)} returns the word for the permutation \\spad{p} in the strong generators of the group {\\em gp},{} represented by the indices of the list,{} given by {\\em strongGenerators}.")) (|member?| (((|Boolean|) (|Permutation| |#1|) $) "\\spad{member?(pp,gp)} answers the question,{} whether the permutation {\\em pp} is in the group {\\em gp} or not.")) (|orbits| (((|Set| (|Set| |#1|)) $) "\\spad{orbits(gp)} returns the orbits of the group {\\em gp},{} \\spadignore{i.e.} it partitions the (finite) of all moved points.")) (|orbit| (((|Set| (|List| |#1|)) $ (|List| |#1|)) "\\spad{orbit(gp,ls)} returns the orbit of the ordered list {\\em ls} under the group {\\em gp}. Note: return type is \\spad{L} \\spad{L} \\spad{S} temporarily because FSET \\spad{L} \\spad{S} has an error.") (((|Set| (|Set| |#1|)) $ (|Set| |#1|)) "\\spad{orbit(gp,els)} returns the orbit of the unordered set {\\em els} under the group {\\em gp}.") (((|Set| |#1|) $ |#1|) "\\spad{orbit(gp,el)} returns the orbit of the element {\\em el} under the group {\\em gp},{} \\spadignore{i.e.} the set of all points gained by applying each group element to {\\em el}.")) (|permutationGroup| (($ (|List| (|Permutation| |#1|))) "\\spad{permutationGroup(ls)} coerces a list of permutations {\\em ls} to the group generated by this list.")) (|wordsForStrongGenerators| (((|List| (|List| (|NonNegativeInteger|))) $) "\\spad{wordsForStrongGenerators(gp)} returns the words for the strong generators of the group {\\em gp} in the original generators of {\\em gp},{} represented by their indices in the list,{} given by {\\em generators}.")) (|strongGenerators| (((|List| (|Permutation| |#1|)) $) "\\spad{strongGenerators(gp)} returns strong generators for the group {\\em gp}.")) (|base| (((|List| |#1|) $) "\\spad{base(gp)} returns a base for the group {\\em gp}.")) (|degree| (((|NonNegativeInteger|) $) "\\spad{degree(gp)} returns the number of points moved by all permutations of the group {\\em gp}.")) (|order| (((|NonNegativeInteger|) $) "\\spad{order(gp)} returns the order of the group {\\em gp}.")) (|random| (((|Permutation| |#1|) $) "\\spad{random(gp)} returns a random product of maximal 20 generators of the group {\\em gp}. Note: {\\em random(gp)=random(gp,20)}.") (((|Permutation| |#1|) $ (|Integer|)) "\\spad{random(gp,i)} returns a random product of maximal \\spad{i} generators of the group {\\em gp}.")) (|elt| (((|Permutation| |#1|) $ (|NonNegativeInteger|)) "\\spad{elt(gp,i)} returns the \\spad{i}-th generator of the group {\\em gp}.")) (|generators| (((|List| (|Permutation| |#1|)) $) "\\spad{generators(gp)} returns the generators of the group {\\em gp}.")) (|coerce| (($ (|List| (|Permutation| |#1|))) "\\spad{coerce(ls)} coerces a list of permutations {\\em ls} to the group generated by this list.") (((|List| (|Permutation| |#1|)) $) "\\spad{coerce(gp)} returns the generators of the group {\\em gp}."))) +((|constructor| (NIL "PermutationGroup implements permutation groups acting on a set \\spad{S},{} \\spadignore{i.e.} all subgroups of the symmetric group of \\spad{S},{} represented as a list of permutations (generators). Note that therefore the objects are not members of the \\Language category \\spadtype{Group}. Using the idea of base and strong generators by Sims,{} basic routines and algorithms are implemented so that the word problem for permutation groups can be solved.")) (|initializeGroupForWordProblem| (((|Void|) $ (|Integer|) (|Integer|)) "\\spad{initializeGroupForWordProblem(gp,m,n)} initializes the group {\\em gp} for the word problem. Notes: (1) with a small integer you get shorter words,{} but the routine takes longer than the standard routine for longer words. (2) be careful: invoking this routine will destroy the possibly stored information about your group (but will recompute it again). (3) users need not call this function normally for the soultion of the word problem.") (((|Void|) $) "\\spad{initializeGroupForWordProblem(gp)} initializes the group {\\em gp} for the word problem. Notes: it calls the other function of this name with parameters 0 and 1: {\\em initializeGroupForWordProblem(gp,0,1)}. Notes: (1) be careful: invoking this routine will destroy the possibly information about your group (but will recompute it again) (2) users need not call this function normally for the soultion of the word problem.")) (<= (((|Boolean|) $ $) "\\spad{gp1 <= gp2} returns \\spad{true} if and only if {\\em gp1} is a subgroup of {\\em gp2}. Note: because of a bug in the parser you have to call this function explicitly by {\\em gp1 <=\\$(PERMGRP S) gp2}.")) (< (((|Boolean|) $ $) "\\spad{gp1 < gp2} returns \\spad{true} if and only if {\\em gp1} is a proper subgroup of {\\em gp2}.")) (|support| (((|Set| |#1|) $) "\\spad{support(gp)} returns the points moved by the group {\\em gp}.")) (|wordInGenerators| (((|List| (|NonNegativeInteger|)) (|Permutation| |#1|) $) "\\spad{wordInGenerators(p,gp)} returns the word for the permutation \\spad{p} in the original generators of the group {\\em gp},{} represented by the indices of the list,{} given by {\\em generators}.")) (|wordInStrongGenerators| (((|List| (|NonNegativeInteger|)) (|Permutation| |#1|) $) "\\spad{wordInStrongGenerators(p,gp)} returns the word for the permutation \\spad{p} in the strong generators of the group {\\em gp},{} represented by the indices of the list,{} given by {\\em strongGenerators}.")) (|member?| (((|Boolean|) (|Permutation| |#1|) $) "\\spad{member?(pp,gp)} answers the question,{} whether the permutation {\\em pp} is in the group {\\em gp} or not.")) (|orbits| (((|Set| (|Set| |#1|)) $) "\\spad{orbits(gp)} returns the orbits of the group {\\em gp},{} \\spadignore{i.e.} it partitions the (finite) of all moved points.")) (|orbit| (((|Set| (|List| |#1|)) $ (|List| |#1|)) "\\spad{orbit(gp,ls)} returns the orbit of the ordered list {\\em ls} under the group {\\em gp}. Note: return type is \\spad{L} \\spad{L} \\spad{S} temporarily because FSET \\spad{L} \\spad{S} has an error.") (((|Set| (|Set| |#1|)) $ (|Set| |#1|)) "\\spad{orbit(gp,els)} returns the orbit of the unordered set {\\em els} under the group {\\em gp}.") (((|Set| |#1|) $ |#1|) "\\spad{orbit(gp,el)} returns the orbit of the element {\\em el} under the group {\\em gp},{} \\spadignore{i.e.} the set of all points gained by applying each group element to {\\em el}.")) (|permutationGroup| (($ (|List| (|Permutation| |#1|))) "\\spad{permutationGroup(ls)} coerces a list of permutations {\\em ls} to the group generated by this list.")) (|wordsForStrongGenerators| (((|List| (|List| (|NonNegativeInteger|))) $) "\\spad{wordsForStrongGenerators(gp)} returns the words for the strong generators of the group {\\em gp} in the original generators of {\\em gp},{} represented by their indices in the list,{} given by {\\em generators}.")) (|strongGenerators| (((|List| (|Permutation| |#1|)) $) "\\spad{strongGenerators(gp)} returns strong generators for the group {\\em gp}.")) (|base| (((|List| |#1|) $) "\\spad{base(gp)} returns a base for the group {\\em gp}.")) (|degree| (((|NonNegativeInteger|) $) "\\spad{degree(gp)} returns the number of points moved by all permutations of the group {\\em gp}.")) (|order| (((|NonNegativeInteger|) $) "\\spad{order(gp)} returns the order of the group {\\em gp}.")) (|random| (((|Permutation| |#1|) $) "\\spad{random(gp)} returns a random product of maximal 20 generators of the group {\\em gp}. Note: {\\em random(gp)=random(gp,20)}.") (((|Permutation| |#1|) $ (|Integer|)) "\\spad{random(gp,i)} returns a random product of maximal \\spad{i} generators of the group {\\em gp}.")) (|elt| (((|Permutation| |#1|) $ (|NonNegativeInteger|)) "\\spad{elt(gp,i)} returns the \\spad{i}-th generator of the group {\\em gp}.")) (|generators| (((|List| (|Permutation| |#1|)) $) "\\spad{generators(gp)} returns the generators of the group {\\em gp}."))) NIL NIL (|PrimeField| |p|) ((|constructor| (NIL "PrimeField(\\spad{p}) implements the field with \\spad{p} elements if \\spad{p} is a prime number. Error: if \\spad{p} is not prime. Note: this domain does not check that argument is a prime."))) -((|canonicalsClosed| . T) (|canonicalUnitNormal| . T) (|noZeroDivisors| . T) ((|commutative| "*") . T) (|rightUnitary| . T) (|leftUnitary| . T) (|unitsKnown| . T)) +((|canonicalUnitNormal| . T) (|noZeroDivisors| . T) ((|commutative| "*") . T)) ((|HasCategory| $ (QUOTE (|CharacteristicZero|))) (|HasCategory| $ (QUOTE (|CharacteristicNonZero|))) (|HasCategory| $ (QUOTE (|Finite|)))) (|PolynomialFactorizationByRecursion| R E |VarSet| S) ((|constructor| (NIL "PolynomialFactorizationByRecursion(\\spad{R},{}\\spad{E},{}\\spad{VarSet},{}\\spad{S}) is used for factorization of sparse univariate polynomials over a domain \\spad{S} of multivariate polynomials over \\spad{R}.")) (|factorSFBRlcUnit| (((|Factored| (|SparseUnivariatePolynomial| |#4|)) (|List| |#3|) (|SparseUnivariatePolynomial| |#4|)) "\\spad{factorSFBRlcUnit(p)} returns the square free factorization of polynomial \\spad{p} (see \\spadfun{factorSquareFreeByRecursion}{PolynomialFactorizationByRecursionUnivariate}) in the case where the leading coefficient of \\spad{p} is a unit.")) (|bivariateSLPEBR| (((|Union| (|List| (|SparseUnivariatePolynomial| |#4|)) "failed") (|List| (|SparseUnivariatePolynomial| |#4|)) (|SparseUnivariatePolynomial| |#4|) |#3|) "\\spad{bivariateSLPEBR(lp,p,v)} implements the bivariate case of \\spadfunFrom{solveLinearPolynomialEquationByRecursion}{PolynomialFactorizationByRecursionUnivariate}; its implementation depends on \\spad{R}")) (|randomR| ((|#1|) "\\spad{randomR produces} a random element of \\spad{R}")) (|factorSquareFreeByRecursion| (((|Factored| (|SparseUnivariatePolynomial| |#4|)) (|SparseUnivariatePolynomial| |#4|)) "\\spad{factorSquareFreeByRecursion(p)} returns the square free factorization of \\spad{p}. This functions performs the recursion step for factorSquareFreePolynomial,{} as defined in \\spadfun{PolynomialFactorizationExplicit} category (see \\spadfun{factorSquareFreePolynomial}).")) (|factorByRecursion| (((|Factored| (|SparseUnivariatePolynomial| |#4|)) (|SparseUnivariatePolynomial| |#4|)) "\\spad{factorByRecursion(p)} factors polynomial \\spad{p}. This function performs the recursion step for factorPolynomial,{} as defined in \\spadfun{PolynomialFactorizationExplicit} category (see \\spadfun{factorPolynomial})")) (|solveLinearPolynomialEquationByRecursion| (((|Union| (|List| (|SparseUnivariatePolynomial| |#4|)) "failed") (|List| (|SparseUnivariatePolynomial| |#4|)) (|SparseUnivariatePolynomial| |#4|)) "\\spad{solveLinearPolynomialEquationByRecursion([p1,...,pn],p)} returns the list of polynomials \\spad{[q1,...,qn]} such that \\spad{sum qi/pi = p / prod pi},{} a recursion step for solveLinearPolynomialEquation as defined in \\spadfun{PolynomialFactorizationExplicit} category (see \\spadfun{solveLinearPolynomialEquation}). If no such list of \\spad{qi} exists,{} then \"failed\" is returned."))) @@ -3230,7 +3230,7 @@ NIL ((|HasCategory| |#1| (QUOTE (|CharacteristicNonZero|)))) (|PolynomialFactorizationExplicit|) ((|constructor| (NIL "This is the category of domains that know \"enough\" about themselves in order to factor univariate polynomials over themselves. This will be used in future releases for supporting factorization over finitely generated coefficient fields,{} it is not yet available in the current release of axiom.")) (|charthRoot| (((|Maybe| $) $) "\\spad{charthRoot(r)} returns the \\spad{p}\\spad{-}th root of \\spad{r},{} or \\spad{nothing} if none exists in the domain.")) (|conditionP| (((|Union| (|Vector| $) "failed") (|Matrix| $)) "\\spad{conditionP(m)} returns a vector of elements,{} not all zero,{} whose \\spad{p}\\spad{-}th powers (\\spad{p} is the characteristic of the domain) are a solution of the homogenous linear system represented by \\spad{m},{} or \"failed\" is there is no such vector.")) (|solveLinearPolynomialEquation| (((|Union| (|List| (|SparseUnivariatePolynomial| $)) "failed") (|List| (|SparseUnivariatePolynomial| $)) (|SparseUnivariatePolynomial| $)) "\\spad{solveLinearPolynomialEquation([f1, ..., fn], g)} (where the \\spad{fi} are relatively prime to each other) returns a list of \\spad{ai} such that \\spad{g/prod fi = sum ai/fi} or returns \"failed\" if no such list of \\spad{ai}'s exists.")) (|gcdPolynomial| (((|SparseUnivariatePolynomial| $) (|SparseUnivariatePolynomial| $) (|SparseUnivariatePolynomial| $)) "\\spad{gcdPolynomial(p,q)} returns the gcd of the univariate polynomials \\spad{p} qnd \\spad{q}.")) (|factorSquareFreePolynomial| (((|Factored| (|SparseUnivariatePolynomial| $)) (|SparseUnivariatePolynomial| $)) "\\spad{factorSquareFreePolynomial(p)} factors the univariate polynomial \\spad{p} into irreducibles where \\spad{p} is known to be square free and primitive with respect to its main variable.")) (|factorPolynomial| (((|Factored| (|SparseUnivariatePolynomial| $)) (|SparseUnivariatePolynomial| $)) "\\spad{factorPolynomial(p)} returns the factorization into irreducibles of the univariate polynomial \\spad{p}.")) (|squareFreePolynomial| (((|Factored| (|SparseUnivariatePolynomial| $)) (|SparseUnivariatePolynomial| $)) "\\spad{squareFreePolynomial(p)} returns the square-free factorization of the univariate polynomial \\spad{p}."))) -((|noZeroDivisors| . T) ((|commutative| "*") . T) (|rightUnitary| . T) (|leftUnitary| . T) (|unitsKnown| . T)) +((|noZeroDivisors| . T) ((|commutative| "*") . T)) NIL (|PointsOfFiniteOrder| R0 F UP UPUP R) ((|constructor| (NIL "This package provides function for testing whether a divisor on a curve is a torsion divisor.")) (|torsionIfCan| (((|Union| (|Record| (|:| |order| (|NonNegativeInteger|)) (|:| |function| |#5|)) "failed") (|FiniteDivisor| |#2| |#3| |#4| |#5|)) "\\spad{torsionIfCan(f)}\\\\ undocumented")) (|torsion?| (((|Boolean|) (|FiniteDivisor| |#2| |#3| |#4| |#5|)) "\\spad{torsion?(f)} \\undocumented")) (|order| (((|Union| (|NonNegativeInteger|) "failed") (|FiniteDivisor| |#2| |#3| |#4| |#5|)) "\\spad{order(f)} \\undocumented"))) @@ -3245,8 +3245,8 @@ NIL NIL NIL (|PartialFraction| R) -((|constructor| (NIL "The domain \\spadtype{PartialFraction} implements partial fractions over a euclidean domain \\spad{R}. This requirement on the argument domain allows us to normalize the fractions. Of particular interest are the 2 forms for these fractions. The ``compact'' form has only one fractional term per prime in the denominator,{} while the ``p-adic'' form expands each numerator \\spad{p}-adically via the prime \\spad{p} in the denominator. For computational efficiency,{} the compact form is used,{} though the \\spad{p}-adic form may be gotten by calling the function \\spadfunFrom{padicFraction}{PartialFraction}. For a general euclidean domain,{} it is not known how to factor the denominator. Thus the function \\spadfunFrom{partialFraction}{PartialFraction} takes as its second argument an element of \\spadtype{Factored(R)}.")) (|wholePart| ((|#1| $) "\\spad{wholePart(p)} extracts the whole part of the partial fraction \\spad{p}.")) (|partialFraction| (($ |#1| (|Factored| |#1|)) "\\spad{partialFraction(numer,denom)} is the main function for constructing partial fractions. The second argument is the denominator and should be factored.")) (|padicFraction| (($ $) "\\spad{padicFraction(q)} expands the fraction \\spad{p}-adically in the primes \\spad{p} in the denominator of \\spad{q}. For example,{} \\spad{padicFraction(3/(2**2)) = 1/2 + 1/(2**2)}. Use \\spadfunFrom{compactFraction}{PartialFraction} to return to compact form.")) (|padicallyExpand| (((|SparseUnivariatePolynomial| |#1|) |#1| |#1|) "\\spad{padicallyExpand(p,x)} is a utility function that expands the second argument \\spad{x} ``p-adically'' in the first.")) (|numberOfFractionalTerms| (((|Integer|) $) "\\spad{numberOfFractionalTerms(p)} computes the number of fractional terms in \\spad{p}. This returns 0 if there is no fractional part.")) (|nthFractionalTerm| (($ $ (|Integer|)) "\\spad{nthFractionalTerm(p,n)} extracts the \\spad{n}th fractional term from the partial fraction \\spad{p}. This returns 0 if the index \\spad{n} is out of range.")) (|firstNumer| ((|#1| $) "\\spad{firstNumer(p)} extracts the numerator of the first fractional term. This returns 0 if there is no fractional part (use \\spadfunFrom{wholePart}{PartialFraction} to get the whole part).")) (|firstDenom| (((|Factored| |#1|) $) "\\spad{firstDenom(p)} extracts the denominator of the first fractional term. This returns 1 if there is no fractional part (use \\spadfunFrom{wholePart}{PartialFraction} to get the whole part).")) (|compactFraction| (($ $) "\\spad{compactFraction(p)} normalizes the partial fraction \\spad{p} to the compact representation. In this form,{} the partial fraction has only one fractional term per prime in the denominator.")) (|coerce| (($ (|Fraction| (|Factored| |#1|))) "\\spad{coerce(f)} takes a fraction with numerator and denominator in factored form and creates a partial fraction. It is necessary for the parts to be factored because it is not known in general how to factor elements of \\spad{R} and this is needed to decompose into partial fractions.") (((|Fraction| |#1|) $) "\\spad{coerce(p)} sums up the components of the partial fraction and returns a single fraction."))) -((|canonicalsClosed| . T) (|canonicalUnitNormal| . T) (|noZeroDivisors| . T) ((|commutative| "*") . T) (|rightUnitary| . T) (|leftUnitary| . T) (|unitsKnown| . T)) +((|constructor| (NIL "The domain \\spadtype{PartialFraction} implements partial fractions over a euclidean domain \\spad{R}. This requirement on the argument domain allows us to normalize the fractions. Of particular interest are the 2 forms for these fractions. The ``compact'' form has only one fractional term per prime in the denominator,{} while the ``p-adic'' form expands each numerator \\spad{p}-adically via the prime \\spad{p} in the denominator. For computational efficiency,{} the compact form is used,{} though the \\spad{p}-adic form may be gotten by calling the function \\spadfunFrom{padicFraction}{PartialFraction}. For a general euclidean domain,{} it is not known how to factor the denominator. Thus the function \\spadfunFrom{partialFraction}{PartialFraction} takes as its second argument an element of \\spadtype{Factored(R)}.")) (|wholePart| ((|#1| $) "\\spad{wholePart(p)} extracts the whole part of the partial fraction \\spad{p}.")) (|partialFraction| (($ |#1| (|Factored| |#1|)) "\\spad{partialFraction(numer,denom)} is the main function for constructing partial fractions. The second argument is the denominator and should be factored.")) (|padicFraction| (($ $) "\\spad{padicFraction(q)} expands the fraction \\spad{p}-adically in the primes \\spad{p} in the denominator of \\spad{q}. For example,{} \\spad{padicFraction(3/(2**2)) = 1/2 + 1/(2**2)}. Use \\spadfunFrom{compactFraction}{PartialFraction} to return to compact form.")) (|padicallyExpand| (((|SparseUnivariatePolynomial| |#1|) |#1| |#1|) "\\spad{padicallyExpand(p,x)} is a utility function that expands the second argument \\spad{x} ``p-adically'' in the first.")) (|numberOfFractionalTerms| (((|Integer|) $) "\\spad{numberOfFractionalTerms(p)} computes the number of fractional terms in \\spad{p}. This returns 0 if there is no fractional part.")) (|nthFractionalTerm| (($ $ (|Integer|)) "\\spad{nthFractionalTerm(p,n)} extracts the \\spad{n}th fractional term from the partial fraction \\spad{p}. This returns 0 if the index \\spad{n} is out of range.")) (|firstNumer| ((|#1| $) "\\spad{firstNumer(p)} extracts the numerator of the first fractional term. This returns 0 if there is no fractional part (use \\spadfunFrom{wholePart}{PartialFraction} to get the whole part).")) (|firstDenom| (((|Factored| |#1|) $) "\\spad{firstDenom(p)} extracts the denominator of the first fractional term. This returns 1 if there is no fractional part (use \\spadfunFrom{wholePart}{PartialFraction} to get the whole part).")) (|compactFraction| (($ $) "\\spad{compactFraction(p)} normalizes the partial fraction \\spad{p} to the compact representation. In this form,{} the partial fraction has only one fractional term per prime in the denominator.")) (|coerce| (($ (|Fraction| (|Factored| |#1|))) "\\spad{coerce(f)} takes a fraction with numerator and denominator in factored form and creates a partial fraction. It is necessary for the parts to be factored because it is not known in general how to factor elements of \\spad{R} and this is needed to decompose into partial fractions."))) +((|canonicalUnitNormal| . T) (|noZeroDivisors| . T) ((|commutative| "*") . T)) NIL (|PartialFractionPackage| R) ((|constructor| (NIL "The package \\spadtype{PartialFractionPackage} gives an easier to use interfact the domain \\spadtype{PartialFraction}. The user gives a fraction of polynomials,{} and a variable and the package converts it to the proper datatype for the \\spadtype{PartialFraction} domain.")) (|partialFraction| (((|Any|) (|Polynomial| |#1|) (|Factored| (|Polynomial| |#1|)) (|Symbol|)) "\\spad{partialFraction(num, facdenom, var)} returns the partial fraction decomposition of the rational function whose numerator is \\spad{num} and whose factored denominator is \\spad{facdenom} with respect to the variable var.") (((|Any|) (|Fraction| (|Polynomial| |#1|)) (|Symbol|)) "\\spad{partialFraction(rf, var)} returns the partial fraction decomposition of the rational function \\spad{rf} with respect to the variable var."))) @@ -3274,7 +3274,7 @@ NIL NIL (|PrincipalIdealDomain|) ((|constructor| (NIL "The category of constructive principal ideal domains,{} \\spadignore{i.e.} where a single generator can be constructively found for any ideal given by a finite set of generators. Note that this constructive definition only implies that finitely generated ideals are principal. It is not clear what we would mean by an infinitely generated ideal.")) (|expressIdealMember| (((|Maybe| (|List| $)) (|List| $) $) "\\spad{expressIdealMember([f1,...,fn],h)} returns a representation of \\spad{h} as a linear combination of the \\spad{fi} or \\spad{nothing} if \\spad{h} is not in the ideal generated by the \\spad{fi}.")) (|principalIdeal| (((|Record| (|:| |coef| (|List| $)) (|:| |generator| $)) (|List| $)) "\\spad{principalIdeal([f1,...,fn])} returns a record whose generator component is a generator of the ideal generated by \\spad{[f1,...,fn]} whose coef component satisfies \\spad{generator = sum (input.i * coef.i)}"))) -((|noZeroDivisors| . T) ((|commutative| "*") . T) (|rightUnitary| . T) (|leftUnitary| . T) (|unitsKnown| . T)) +((|noZeroDivisors| . T) ((|commutative| "*") . T)) NIL (|PolynomialInterpolation| |xx| F) ((|constructor| (NIL "This package exports interpolation algorithms")) (|interpolate| (((|SparseUnivariatePolynomial| |#2|) (|List| |#2|) (|List| |#2|)) "\\spad{interpolate(lf,lg)} \\undocumented") (((|UnivariatePolynomial| |#1| |#2|) (|UnivariatePolynomial| |#1| |#2|) (|List| |#2|) (|List| |#2|)) "\\spad{interpolate(u,lf,lg)} \\undocumented"))) @@ -3374,8 +3374,8 @@ NIL ((|HasCategory| |#1| (QUOTE (|OrderedRing|)))) (|Polynomial| R) ((|constructor| (NIL "\\indented{2}{This type is the basic representation of sparse recursive multivariate} polynomials whose variables are arbitrary symbols. The ordering is alphabetic determined by the Symbol type. The coefficient ring may be non commutative,{} but the variables are assumed to commute.")) (|integrate| (($ $ (|Symbol|)) "\\spad{integrate(p,x)} computes the integral of \\spad{p*dx},{} \\spadignore{i.e.} integrates the polynomial \\spad{p} with respect to the variable \\spad{x}."))) -(((|commutative| "*") |has| |#1| (|CommutativeRing|)) (|noZeroDivisors| |has| |#1| (|IntegralDomain|)) (|canonicalUnitNormal| |has| |#1| (ATTRIBUTE |canonicalUnitNormal|)) (|leftUnitary| . T) (|rightUnitary| . T) (|unitsKnown| . T)) -(#1=(|HasCategory| |#1| (QUOTE (|PolynomialFactorizationExplicit|))) (OR #2=(|HasCategory| |#1| (QUOTE (|CommutativeRing|))) #3=(|HasCategory| |#1| (QUOTE (|GcdDomain|))) #4=(|HasCategory| |#1| (QUOTE (|IntegralDomain|))) #1#) (OR #3# #4# #1#) (OR #3# #1#) #4# #2# (OR #2# #4#) (AND (|HasCategory| |#1| #5=(QUOTE (|PatternMatchable| #6=(|Float|)))) (|HasCategory| #7=(|Symbol|) #5#)) (AND (|HasCategory| |#1| #8=(QUOTE (|PatternMatchable| #9=(|Integer|)))) (|HasCategory| #7# #8#)) (AND (|HasCategory| |#1| #10=(QUOTE (|ConvertibleTo| (|Pattern| #6#)))) (|HasCategory| #7# #10#)) (AND (|HasCategory| |#1| #11=(QUOTE (|ConvertibleTo| (|Pattern| #9#)))) (|HasCategory| #7# #11#)) (AND (|HasCategory| |#1| #12=(QUOTE (|ConvertibleTo| (|InputForm|)))) (|HasCategory| #7# #12#)) (|HasCategory| |#1| (QUOTE (|LinearlyExplicitRingOver| #9#))) (|HasCategory| |#1| (QUOTE (|CharacteristicZero|))) #13=(|HasCategory| |#1| #14=(QUOTE (|CharacteristicNonZero|))) #15=(|HasCategory| |#1| (QUOTE (|Algebra| #16=(|Fraction| #9#)))) (|HasCategory| |#1| (QUOTE (|RetractableTo| #9#))) (OR #15# #17=(|HasCategory| |#1| (QUOTE (|RetractableTo| #16#)))) #17# (|HasCategory| |#1| (QUOTE (|Field|))) (|HasAttribute| |#1| (QUOTE |canonicalUnitNormal|)) #3# #18=(AND #1# (|HasCategory| $ #14#)) (OR #18# #13#)) +(((|commutative| "*") |has| |#1| (|CommutativeRing|)) (|noZeroDivisors| |has| |#1| (|IntegralDomain|)) (|canonicalUnitNormal| |has| |#1| (ATTRIBUTE |canonicalUnitNormal|))) +(#1=(|HasCategory| |#1| (QUOTE (|PolynomialFactorizationExplicit|))) (OR #2=(|HasCategory| |#1| (QUOTE (|CommutativeRing|))) #3=(|HasCategory| |#1| (QUOTE (|GcdDomain|))) #4=(|HasCategory| |#1| (QUOTE (|IntegralDomain|))) #1#) (OR #3# #4# #1#) (OR #3# #1#) #4# #2# (OR #2# #4#) (AND (|HasCategory| |#1| #5=(QUOTE (|PatternMatchable| #6=(|Float|)))) (|HasCategory| #7=(|Symbol|) #5#)) (AND (|HasCategory| |#1| #8=(QUOTE (|PatternMatchable| #9=(|Integer|)))) (|HasCategory| #7# #8#)) (AND (|HasCategory| |#1| #10=(QUOTE (|ConvertibleTo| (|Pattern| #6#)))) (|HasCategory| #7# #10#)) (AND (|HasCategory| |#1| #11=(QUOTE (|ConvertibleTo| (|Pattern| #9#)))) (|HasCategory| #7# #11#)) (AND (|HasCategory| |#1| #12=(QUOTE (|ConvertibleTo| (|InputForm|)))) (|HasCategory| #7# #12#)) (|HasCategory| |#1| (QUOTE (|LinearlyExplicitRingOver| #9#))) #13=(|HasCategory| |#1| (QUOTE (|Algebra| #14=(|Fraction| #9#)))) #15=(|HasCategory| |#1| #16=(QUOTE (|CharacteristicNonZero|))) (|HasCategory| |#1| (QUOTE (|CharacteristicZero|))) (|HasCategory| |#1| (QUOTE (|RetractableTo| #9#))) (OR #13# #17=(|HasCategory| |#1| (QUOTE (|RetractableTo| #14#)))) #17# (|HasCategory| |#1| (QUOTE (|Field|))) (|HasAttribute| |#1| (QUOTE |canonicalUnitNormal|)) #3# #18=(AND #1# (|HasCategory| $ #16#)) (OR #18# #15#)) (|PolynomialFunctions2| R S) ((|constructor| (NIL "\\indented{2}{This package takes a mapping between coefficient rings,{} and lifts} it to a mapping between polynomials over those rings.")) (|map| (((|Polynomial| |#2|) (|Mapping| |#2| |#1|) (|Polynomial| |#1|)) "\\spad{map(f, p)} produces a new polynomial as a result of applying the function \\spad{f} to every coefficient of the polynomial \\spad{p}."))) NIL @@ -3390,7 +3390,7 @@ NIL ((|HasCategory| |#2| (QUOTE (|PolynomialFactorizationExplicit|))) (|HasAttribute| |#2| (QUOTE |canonicalUnitNormal|)) (|HasCategory| |#2| (QUOTE (|GcdDomain|))) (|HasCategory| |#2| (QUOTE (|CommutativeRing|))) (|HasCategory| |#4| #1=(QUOTE (|PatternMatchable| #2=(|Float|)))) (|HasCategory| |#2| #1#) (|HasCategory| |#4| #3=(QUOTE (|PatternMatchable| #4=(|Integer|)))) (|HasCategory| |#2| #3#) (|HasCategory| |#4| #5=(QUOTE (|ConvertibleTo| (|Pattern| #2#)))) (|HasCategory| |#2| #5#) (|HasCategory| |#4| #6=(QUOTE (|ConvertibleTo| (|Pattern| #4#)))) (|HasCategory| |#2| #6#) (|HasCategory| |#4| #7=(QUOTE (|ConvertibleTo| (|InputForm|)))) (|HasCategory| |#2| #7#)) (|PolynomialCategory| R E |VarSet|) ((|constructor| (NIL "The category for general multi-variate polynomials over a ring \\spad{R},{} in variables from VarSet,{} with exponents from the \\spadtype{OrderedAbelianMonoidSup}.")) (|canonicalUnitNormal| ((|attribute|) "we can choose a unique representative for each associate class. This normalization is chosen to be normalization of leading coefficient (by default).")) (|squareFreePart| (($ $) "\\spad{squareFreePart(p)} returns product of all the irreducible factors of polynomial \\spad{p} each taken with multiplicity one.")) (|squareFree| (((|Factored| $) $) "\\spad{squareFree(p)} returns the square free factorization of the polynomial \\spad{p}.")) (|primitivePart| (($ $ |#3|) "\\spad{primitivePart(p,v)} returns the unitCanonical associate of the polynomial \\spad{p} with its content with respect to the variable \\spad{v} divided out.") (($ $) "\\spad{primitivePart(p)} returns the unitCanonical associate of the polynomial \\spad{p} with its content divided out.")) (|content| (($ $ |#3|) "\\spad{content(p,v)} is the gcd of the coefficients of the polynomial \\spad{p} when \\spad{p} is viewed as a univariate polynomial with respect to the variable \\spad{v}. Thus,{} for polynomial 7*x**2*y + 14*x*y**2,{} the gcd of the coefficients with respect to \\spad{x} is 7*y.")) (|discriminant| (($ $ |#3|) "\\spad{discriminant(p,v)} returns the disriminant of the polynomial \\spad{p} with respect to the variable \\spad{v}.")) (|resultant| (($ $ $ |#3|) "\\spad{resultant(p,q,v)} returns the resultant of the polynomials \\spad{p} and \\spad{q} with respect to the variable \\spad{v}.")) (|primitiveMonomials| (((|List| $) $) "\\spad{primitiveMonomials(p)} gives the list of monomials of the polynomial \\spad{p} with their coefficients removed. Note: \\spad{primitiveMonomials(sum(a_(i) X^(i))) = [X^(1),...,X^(n)]}.")) (|variables| (((|List| |#3|) $) "\\spad{variables(p)} returns the list of those variables actually appearing in the polynomial \\spad{p}.")) (|totalDegree| (((|NonNegativeInteger|) $ (|List| |#3|)) "\\spad{totalDegree(p, lv)} returns the maximum sum (over all monomials of polynomial \\spad{p}) of the variables in the list lv.") (((|NonNegativeInteger|) $) "\\spad{totalDegree(p)} returns the largest sum over all monomials of all exponents of a monomial.")) (|isExpt| (((|Union| (|Record| (|:| |var| |#3|) (|:| |exponent| (|NonNegativeInteger|))) "failed") $) "\\spad{isExpt(p)} returns \\spad{[x, n]} if polynomial \\spad{p} has the form \\spad{x**n} and \\spad{n > 0}.")) (|isTimes| (((|Union| (|List| $) "failed") $) "\\spad{isTimes(p)} returns \\spad{[a1,...,an]} if polynomial \\spad{p = a1 ... an} and \\spad{n >= 2},{} and,{} for each \\spad{i},{} \\spad{ai} is either a nontrivial constant in \\spad{R} or else of the form \\spad{x**e},{} where \\spad{e > 0} is an integer and \\spad{x} in a member of VarSet.")) (|isPlus| (((|Union| (|List| $) "failed") $) "\\spad{isPlus(p)} returns \\spad{[m1,...,mn]} if polynomial \\spad{p = m1 + ... + mn} and \\spad{n >= 2} and each \\spad{mi} is a nonzero monomial.")) (|multivariate| (($ (|SparseUnivariatePolynomial| $) |#3|) "\\spad{multivariate(sup,v)} converts an anonymous univariable polynomial \\spad{sup} to a polynomial in the variable \\spad{v}.") (($ (|SparseUnivariatePolynomial| |#1|) |#3|) "\\spad{multivariate(sup,v)} converts an anonymous univariable polynomial \\spad{sup} to a polynomial in the variable \\spad{v}.")) (|monomial| (($ $ (|List| |#3|) (|List| (|NonNegativeInteger|))) "\\spad{monomial(a,[v1..vn],[e1..en])} returns \\spad{a*prod(vi**ei)}.") (($ $ |#3| (|NonNegativeInteger|)) "\\spad{monomial(a,x,n)} creates the monomial \\spad{a*x**n} where \\spad{a} is a polynomial,{} \\spad{x} is a variable and \\spad{n} is a nonnegative integer.")) (|monicDivide| (((|Record| (|:| |quotient| $) (|:| |remainder| $)) $ $ |#3|) "\\spad{monicDivide(a,b,v)} divides the polynomial a by the polynomial \\spad{b},{} with each viewed as a univariate polynomial in \\spad{v} returning both the quotient and remainder. Error: if \\spad{b} is not monic with respect to \\spad{v}.")) (|minimumDegree| (((|List| (|NonNegativeInteger|)) $ (|List| |#3|)) "\\spad{minimumDegree(p, lv)} gives the list of minimum degrees of the polynomial \\spad{p} with respect to each of the variables in the list lv") (((|NonNegativeInteger|) $ |#3|) "\\spad{minimumDegree(p,v)} gives the minimum degree of polynomial \\spad{p} with respect to \\spad{v},{} \\spadignore{i.e.} viewed a univariate polynomial in \\spad{v}")) (|mainVariable| (((|Union| |#3| "failed") $) "\\spad{mainVariable(p)} returns the biggest variable which actually occurs in the polynomial \\spad{p},{} or \"failed\" if no variables are present. fails precisely if polynomial satisfies ground?")) (|univariate| (((|SparseUnivariatePolynomial| |#1|) $) "\\spad{univariate(p)} converts the multivariate polynomial \\spad{p},{} which should actually involve only one variable,{} into a univariate polynomial in that variable,{} whose coefficients are in the ground ring. Error: if polynomial is genuinely multivariate") (((|SparseUnivariatePolynomial| $) $ |#3|) "\\spad{univariate(p,v)} converts the multivariate polynomial \\spad{p} into a univariate polynomial in \\spad{v},{} whose coefficients are still multivariate polynomials (in all the other variables).")) (|monomials| (((|List| $) $) "\\spad{monomials(p)} returns the list of non-zero monomials of polynomial \\spad{p},{} \\spadignore{i.e.} \\spad{monomials(sum(a_(i) X^(i))) = [a_(1) X^(1),...,a_(n) X^(n)]}.")) (|coefficient| (($ $ (|List| |#3|) (|List| (|NonNegativeInteger|))) "\\spad{coefficient(p, lv, ln)} views the polynomial \\spad{p} as a polynomial in the variables of \\spad{lv} and returns the coefficient of the term \\spad{lv**ln},{} \\spadignore{i.e.} \\spad{prod(lv_i ** ln_i)}.") (($ $ |#3| (|NonNegativeInteger|)) "\\spad{coefficient(p,v,n)} views the polynomial \\spad{p} as a univariate polynomial in \\spad{v} and returns the coefficient of the \\spad{v**n} term.")) (|degree| (((|List| (|NonNegativeInteger|)) $ (|List| |#3|)) "\\spad{degree(p,lv)} gives the list of degrees of polynomial \\spad{p} with respect to each of the variables in the list \\spad{lv}.") (((|NonNegativeInteger|) $ |#3|) "\\spad{degree(p,v)} gives the degree of polynomial \\spad{p} with respect to the variable \\spad{v}."))) -(((|commutative| "*") |has| |#1| (|CommutativeRing|)) (|noZeroDivisors| |has| |#1| (|IntegralDomain|)) (|canonicalUnitNormal| |has| |#1| (ATTRIBUTE |canonicalUnitNormal|)) (|leftUnitary| . T) (|rightUnitary| . T) (|unitsKnown| . T)) +(((|commutative| "*") |has| |#1| (|CommutativeRing|)) (|noZeroDivisors| |has| |#1| (|IntegralDomain|)) (|canonicalUnitNormal| |has| |#1| (ATTRIBUTE |canonicalUnitNormal|))) NIL (|PolynomialCategoryQuotientFunctions| E V R P F) ((|constructor| (NIL "This package transforms multivariate polynomials or fractions into univariate polynomials or fractions,{} and back.")) (|isPower| (((|Union| (|Record| (|:| |val| |#5|) (|:| |exponent| (|Integer|))) "failed") |#5|) "\\spad{isPower(p)} returns \\spad{[x, n]} if \\spad{p = x**n} and \\spad{n <> 0},{} \"failed\" otherwise.")) (|isExpt| (((|Union| (|Record| (|:| |var| |#2|) (|:| |exponent| (|Integer|))) "failed") |#5|) "\\spad{isExpt(p)} returns \\spad{[x, n]} if \\spad{p = x**n} and \\spad{n <> 0},{} \"failed\" otherwise.")) (|isTimes| (((|Union| (|List| |#5|) "failed") |#5|) "\\spad{isTimes(p)} returns \\spad{[a1,...,an]} if \\spad{p = a1 ... an} and \\spad{n > 1},{} \"failed\" otherwise.")) (|isPlus| (((|Union| (|List| |#5|) "failed") |#5|) "\\spad{isPlus(p)} returns [\\spad{m1},{}...,{}mn] if \\spad{p = m1 + ... + mn} and \\spad{n > 1},{} \"failed\" otherwise.")) (|multivariate| ((|#5| (|Fraction| (|SparseUnivariatePolynomial| |#5|)) |#2|) "\\spad{multivariate(f, v)} applies both the numerator and denominator of \\spad{f} to \\spad{v}.")) (|univariate| (((|SparseUnivariatePolynomial| |#5|) |#5| |#2| (|SparseUnivariatePolynomial| |#5|)) "\\spad{univariate(f, x, p)} returns \\spad{f} viewed as a univariate polynomial in \\spad{x},{} using the side-condition \\spad{p(x) = 0}.") (((|Fraction| (|SparseUnivariatePolynomial| |#5|)) |#5| |#2|) "\\spad{univariate(f, v)} returns \\spad{f} viewed as a univariate rational function in \\spad{v}.")) (|mainVariable| (((|Union| |#2| "failed") |#5|) "\\spad{mainVariable(f)} returns the highest variable appearing in the numerator or the denominator of \\spad{f},{} \"failed\" if \\spad{f} has no variables.")) (|variables| (((|List| |#2|) |#5|) "\\spad{variables(f)} returns the list of variables appearing in the numerator or the denominator of \\spad{f}."))) @@ -3414,7 +3414,7 @@ NIL NIL (|PolynomialRing| R E) ((|constructor| (NIL "This domain represents generalized polynomials with coefficients (from a not necessarily commutative ring),{} and terms indexed by their exponents (from an arbitrary ordered abelian monoid). This type is used,{} for example,{} by the \\spadtype{DistributedMultivariatePolynomial} domain where the exponent domain is a direct product of non negative integers.")) (|canonicalUnitNormal| ((|attribute|) "canonicalUnitNormal guarantees that the function unitCanonical returns the same representative for all associates of any particular element.")) (|fmecg| (($ $ |#2| |#1| $) "\\spad{fmecg(p1,e,r,p2)} finds \\spad{X} : \\spad{p1} - \\spad{r} * X**e * \\spad{p2}"))) -(((|commutative| "*") |has| |#1| (|CommutativeRing|)) (|noZeroDivisors| |has| |#1| (|IntegralDomain|)) (|canonicalUnitNormal| |has| |#1| (ATTRIBUTE |canonicalUnitNormal|)) (|rightUnitary| . T) (|leftUnitary| . T) (|unitsKnown| . T)) +(((|commutative| "*") |has| |#1| (|CommutativeRing|)) (|noZeroDivisors| |has| |#1| (|IntegralDomain|)) (|canonicalUnitNormal| |has| |#1| (ATTRIBUTE |canonicalUnitNormal|))) (#1=(|HasCategory| |#1| (QUOTE (|Algebra| #2=(|Fraction| #3=(|Integer|))))) #4=(|HasCategory| |#1| (QUOTE (|IntegralDomain|))) (OR #5=(|HasCategory| |#1| (QUOTE (|CommutativeRing|))) #4#) #5# (|HasCategory| |#1| (QUOTE (|CharacteristicNonZero|))) (|HasCategory| |#1| (QUOTE (|CharacteristicZero|))) (OR #1# #6=(|HasCategory| |#1| (QUOTE (|RetractableTo| #2#)))) #6# (|HasCategory| |#1| (QUOTE (|RetractableTo| #3#))) (|HasCategory| |#1| (QUOTE (|Field|))) (|HasCategory| |#1| (QUOTE (|GcdDomain|))) (AND #4# (|HasCategory| |#2| (QUOTE (|CancellationAbelianMonoid|)))) (|HasAttribute| |#1| (QUOTE |canonicalUnitNormal|))) (|PrecomputedAssociatedEquations| R L) ((|constructor| (NIL "\\spadtype{PrecomputedAssociatedEquations} stores some generic precomputations which speed up the computations of the associated equations needed for factoring operators.")) (|firstUncouplingMatrix| (((|Union| (|Matrix| |#1|) "failed") |#2| (|PositiveInteger|)) "\\spad{firstUncouplingMatrix(op, m)} returns the matrix A such that \\spad{A w = (W',W'',...,W^N)} in the corresponding associated equations for right-factors of order \\spad{m} of \\spad{op}. Returns \"failed\" if the matrix A has not been precomputed for the particular combination \\spad{degree(L), m}."))) @@ -3446,7 +3446,7 @@ NIL NIL (|Product| A B) ((|constructor| (NIL "This domain implements cartesian product")) (|selectsecond| ((|#2| $) "\\spad{selectsecond(x)} \\undocumented")) (|selectfirst| ((|#1| $) "\\spad{selectfirst(x)} \\undocumented")) (|makeprod| (($ |#1| |#2|) "\\spad{makeprod(a,b)} \\undocumented"))) -((|unitsKnown| AND (|has| |#2| #1=(|Group|)) (|has| |#1| #1#))) +NIL ((OR #1=(AND (|HasCategory| |#1| #2=(QUOTE (|OrderedAbelianMonoidSup|))) (|HasCategory| |#2| #2#)) #3=(AND (|HasCategory| |#1| #4=(QUOTE (|OrderedSet|))) (|HasCategory| |#2| #4#))) #1# (OR #5=(AND (|HasCategory| |#1| #6=(QUOTE (|CancellationAbelianMonoid|))) (|HasCategory| |#2| #6#)) #1# #7=(AND (|HasCategory| |#1| #8=(QUOTE (|AbelianGroup|))) (|HasCategory| |#2| #8#))) #7# (OR #5# #1# #7# #9=(AND (|HasCategory| |#1| #10=(QUOTE (|AbelianMonoid|))) (|HasCategory| |#2| #10#))) #11=(AND (|HasCategory| |#1| #12=(QUOTE (|Group|))) (|HasCategory| |#2| #12#)) (OR #11# #13=(AND (|HasCategory| |#1| #14=(QUOTE (|Monoid|))) (|HasCategory| |#2| #14#))) (AND (|HasCategory| |#1| #15=(QUOTE (|Finite|))) (|HasCategory| |#2| #15#)) (OR #5# #1# #7# #9# #11# #13#) #13# #9# #5# #3#) (|Property|) ((|constructor| (NIL "\\indented{1}{Author: Gabriel Dos Reis} Date Created: October 24,{} 2007 Date Last Modified: January 18,{} 2008. An `Property' is a pair of name and value.")) (|property| (($ (|Identifier|) (|SExpression|)) "\\spad{property(n,val)} constructs a property with name `n' and value `val'.")) (|value| (((|SExpression|) $) "\\spad{value(p)} returns value of property \\spad{p}")) (|name| (((|Identifier|) $) "\\spad{name(p)} returns the name of property \\spad{p}"))) @@ -3490,7 +3490,7 @@ NIL NIL (|PowerSeriesCategory| |Coef| |Expon| |Var|) ((|constructor| (NIL "\\spadtype{PowerSeriesCategory} is the most general power series category with exponents in an ordered abelian monoid.")) (|complete| (($ $) "\\spad{complete(f)} causes all terms of \\spad{f} to be computed. Note: this results in an infinite loop if \\spad{f} has infinitely many terms.")) (|pole?| (((|Boolean|) $) "\\spad{pole?(f)} determines if the power series \\spad{f} has a pole.")) (|variables| (((|List| |#3|) $) "\\spad{variables(f)} returns a list of the variables occuring in the power series \\spad{f}.")) (|degree| ((|#2| $) "\\spad{degree(f)} returns the exponent of the lowest order term of \\spad{f}.")) (|leadingCoefficient| ((|#1| $) "\\spad{leadingCoefficient(f)} returns the coefficient of the lowest order term of \\spad{f}")) (|leadingMonomial| (($ $) "\\spad{leadingMonomial(f)} returns the monomial of \\spad{f} of lowest order.")) (|monomial| (($ $ (|List| |#3|) (|List| |#2|)) "\\spad{monomial(a,[x1,..,xk],[n1,..,nk])} computes \\spad{a * x1**n1 * .. * xk**nk}.") (($ $ |#3| |#2|) "\\spad{monomial(a,x,n)} computes \\spad{a*x**n}."))) -(((|commutative| "*") |has| |#1| (|CommutativeRing|)) (|noZeroDivisors| |has| |#1| (|IntegralDomain|)) (|rightUnitary| . T) (|leftUnitary| . T) (|unitsKnown| . T)) +(((|commutative| "*") |has| |#1| (|CommutativeRing|)) (|noZeroDivisors| |has| |#1| (|IntegralDomain|))) NIL (|PlottableSpaceCurveCategory|) ((|constructor| (NIL "PlottableSpaceCurveCategory is the category of curves in 3-space which may be plotted via the graphics facilities. Functions are provided for obtaining lists of lists of points,{} representing the branches of the curve,{} and for determining the ranges of the x-,{} y-,{} and \\spad{z}-coordinates of the points on the curve.")) (|zRange| (((|Segment| (|DoubleFloat|)) $) "\\spad{zRange(c)} returns the range of the \\spad{z}-coordinates of the points on the curve \\spad{c}.")) (|yRange| (((|Segment| (|DoubleFloat|)) $) "\\spad{yRange(c)} returns the range of the \\spad{y}-coordinates of the points on the curve \\spad{c}.")) (|xRange| (((|Segment| (|DoubleFloat|)) $) "\\spad{xRange(c)} returns the range of the \\spad{x}-coordinates of the points on the curve \\spad{c}.")) (|listBranches| (((|List| (|List| (|Point| (|DoubleFloat|)))) $) "\\spad{listBranches(c)} returns a list of lists of points,{} representing the branches of the curve \\spad{c}."))) @@ -3562,7 +3562,7 @@ NIL ((|HasCategory| |#2| (QUOTE (|PolynomialFactorizationExplicit|))) (|HasCategory| |#2| (QUOTE (|IntegerNumberSystem|))) (|HasCategory| |#2| (QUOTE (|EuclideanDomain|))) (|HasCategory| |#2| (QUOTE (|RetractableTo| (|Symbol|)))) (|HasCategory| |#2| (QUOTE (|CharacteristicNonZero|))) (|HasCategory| |#2| (QUOTE (|CharacteristicZero|))) (|HasCategory| |#2| (QUOTE (|ConvertibleTo| (|InputForm|)))) (|HasCategory| |#2| (QUOTE (|RealConstant|))) (|HasCategory| |#2| (QUOTE (|OrderedIntegralDomain|))) (|HasCategory| |#2| (QUOTE (|OrderedSet|))) (|HasCategory| |#2| (QUOTE (|RetractableTo| (|Integer|)))) (|HasCategory| |#2| (QUOTE (|StepThrough|)))) (|QuotientFieldCategory| S) ((|constructor| (NIL "QuotientField(\\spad{S}) is the category of fractions of an Integral Domain \\spad{S}.")) (|floor| ((|#1| $) "\\spad{floor(x)} returns the largest integral element below \\spad{x}.")) (|ceiling| ((|#1| $) "\\spad{ceiling(x)} returns the smallest integral element above \\spad{x}.")) (|random| (($) "\\spad{random()} returns a random fraction.")) (|fractionPart| (($ $) "\\spad{fractionPart(x)} returns the fractional part of \\spad{x}. \\spad{x} = wholePart(\\spad{x}) + fractionPart(\\spad{x})")) (|wholePart| ((|#1| $) "\\spad{wholePart(x)} returns the whole part of the fraction \\spad{x} \\spadignore{i.e.} the truncated quotient of the numerator by the denominator.")) (|denominator| (($ $) "\\spad{denominator(x)} is the denominator of the fraction \\spad{x} converted to \\%.")) (|numerator| (($ $) "\\spad{numerator(x)} is the numerator of the fraction \\spad{x} converted to \\%.")) (|denom| ((|#1| $) "\\spad{denom(x)} returns the denominator of the fraction \\spad{x}.")) (|numer| ((|#1| $) "\\spad{numer(x)} returns the numerator of the fraction \\spad{x}.")) (/ (($ |#1| |#1|) "\\spad{d1 / d2} returns the fraction \\spad{d1} divided by \\spad{d2}."))) -((|canonicalsClosed| . T) (|canonicalUnitNormal| . T) (|noZeroDivisors| . T) ((|commutative| "*") . T) (|rightUnitary| . T) (|leftUnitary| . T) (|unitsKnown| . T)) +((|canonicalUnitNormal| . T) (|noZeroDivisors| . T) ((|commutative| "*") . T)) NIL (|QuotientFieldCategoryFunctions2| A B R S) ((|constructor| (NIL "This package extends a function between integral domains to a mapping between their quotient fields.")) (|map| ((|#4| (|Mapping| |#2| |#1|) |#3|) "\\spad{map(func,frac)} applies the function \\spad{func} to the numerator and denominator of \\spad{frac}."))) @@ -3582,15 +3582,15 @@ NIL NIL (|Quaternion| R) ((|constructor| (NIL "\\spadtype{Quaternion} implements quaternions over a \\indented{2}{commutative ring. The main constructor function is \\spadfun{quatern}} \\indented{2}{which takes 4 arguments: the real part,{} the \\spad{i} imaginary part,{} the \\spad{j}} \\indented{2}{imaginary part and the \\spad{k} imaginary part.}"))) -((|noZeroDivisors| |has| |#1| (|EntireRing|)) (|rightUnitary| . T) (|leftUnitary| . T) (|unitsKnown| . T)) -((|HasCategory| |#1| (QUOTE (|CharacteristicNonZero|))) (|HasCategory| |#1| (QUOTE (|CharacteristicZero|))) (|HasCategory| |#1| (QUOTE (|ConvertibleTo| (|InputForm|)))) #1=(|HasCategory| |#1| (QUOTE (|Field|))) (OR #2=(|HasCategory| |#1| (QUOTE (|EntireRing|))) #1#) #2# (|HasCategory| |#1| (QUOTE (|OrderedSet|))) (|HasCategory| |#1| (QUOTE (|LinearlyExplicitRingOver| #3=(|Integer|)))) (|HasCategory| |#1| (|%list| (QUOTE |InnerEvalable|) (QUOTE #4=(|Symbol|)) #5=(|devaluate| |#1|))) (|HasCategory| |#1| (|%list| (QUOTE |Evalable|) #5#)) (|HasCategory| |#1| (|%list| (QUOTE |Eltable|) #5# #5#)) (|HasCategory| |#1| (QUOTE (|DifferentialSpace|))) (|HasCategory| |#1| (QUOTE (|PartialDifferentialSpace| #4#))) (|HasCategory| |#1| (QUOTE (|DifferentialRing|))) (|HasCategory| |#1| (QUOTE (|PartialDifferentialRing| #4#))) (OR #1# #6=(|HasCategory| |#1| (QUOTE (|RetractableTo| (|Fraction| #3#))))) #6# (|HasCategory| |#1| (QUOTE (|RetractableTo| #3#))) (|HasCategory| |#1| (QUOTE (|RealNumberSystem|))) (|HasCategory| |#1| (QUOTE (|IntegerNumberSystem|)))) +((|noZeroDivisors| |has| |#1| (|EntireRing|))) +((|HasCategory| |#1| (QUOTE (|CharacteristicNonZero|))) (|HasCategory| |#1| (QUOTE (|CharacteristicZero|))) (|HasCategory| |#1| (QUOTE (|ConvertibleTo| (|InputForm|)))) #1=(|HasCategory| |#1| (QUOTE (|Field|))) (OR #2=(|HasCategory| |#1| (QUOTE (|EntireRing|))) #1#) #2# (|HasCategory| |#1| (QUOTE (|OrderedSet|))) (|HasCategory| |#1| (QUOTE (|LinearlyExplicitRingOver| #3=(|Integer|)))) (|HasCategory| |#1| (|%list| (QUOTE |InnerEvalable|) (QUOTE #4=(|Symbol|)) #5=(|devaluate| |#1|))) (|HasCategory| |#1| (|%list| (QUOTE |Evalable|) #5#)) (|HasCategory| |#1| (|%list| (QUOTE |Eltable|) #5# #5#)) (|HasCategory| |#1| (QUOTE (|PartialDifferentialSpace| #4#))) (|HasCategory| |#1| (QUOTE (|DifferentialSpace|))) (|HasCategory| |#1| (QUOTE (|DifferentialRing|))) (|HasCategory| |#1| (QUOTE (|PartialDifferentialRing| #4#))) (OR #1# #6=(|HasCategory| |#1| (QUOTE (|RetractableTo| (|Fraction| #3#))))) #6# (|HasCategory| |#1| (QUOTE (|RetractableTo| #3#))) (|HasCategory| |#1| (QUOTE (|RealNumberSystem|))) (|HasCategory| |#1| (QUOTE (|IntegerNumberSystem|)))) (|QuaternionCategory&| S R) ((|constructor| (NIL "\\spadtype{QuaternionCategory} describes the category of quaternions and implements functions that are not representation specific.")) (|rationalIfCan| (((|Union| (|Fraction| (|Integer|)) "failed") $) "\\spad{rationalIfCan(q)} returns \\spad{q} as a rational number,{} or \"failed\" if this is not possible. Note: if \\spad{rational?(q)} is \\spad{true},{} the conversion can be done and the rational number will be returned.")) (|rational| (((|Fraction| (|Integer|)) $) "\\spad{rational(q)} tries to convert \\spad{q} into a rational number. Error: if this is not possible. If \\spad{rational?(q)} is \\spad{true},{} the conversion will be done and the rational number returned.")) (|rational?| (((|Boolean|) $) "\\spad{rational?(q)} returns {\\it \\spad{true}} if all the imaginary parts of \\spad{q} are zero and the real part can be converted into a rational number,{} and {\\it \\spad{false}} otherwise.")) (|abs| ((|#2| $) "\\spad{abs(q)} computes the absolute value of quaternion \\spad{q} (sqrt of norm).")) (|real| ((|#2| $) "\\spad{real(q)} extracts the real part of quaternion \\spad{q}.")) (|quatern| (($ |#2| |#2| |#2| |#2|) "\\spad{quatern(r,i,j,k)} constructs a quaternion from scalars.")) (|norm| ((|#2| $) "\\spad{norm(q)} computes the norm of \\spad{q} (the sum of the squares of the components).")) (|imagK| ((|#2| $) "\\spad{imagK(q)} extracts the imaginary \\spad{k} part of quaternion \\spad{q}.")) (|imagJ| ((|#2| $) "\\spad{imagJ(q)} extracts the imaginary \\spad{j} part of quaternion \\spad{q}.")) (|imagI| ((|#2| $) "\\spad{imagI(q)} extracts the imaginary \\spad{i} part of quaternion \\spad{q}.")) (|conjugate| (($ $) "\\spad{conjugate(q)} negates the imaginary parts of quaternion \\spad{q}."))) NIL ((|HasCategory| |#2| (QUOTE (|IntegerNumberSystem|))) (|HasCategory| |#2| (QUOTE (|RealNumberSystem|))) (|HasCategory| |#2| (QUOTE (|CharacteristicNonZero|))) (|HasCategory| |#2| (QUOTE (|CharacteristicZero|))) (|HasCategory| |#2| (QUOTE (|ConvertibleTo| (|InputForm|)))) (|HasCategory| |#2| (QUOTE (|Field|))) (|HasCategory| |#2| (QUOTE (|OrderedSet|))) (|HasCategory| |#2| (QUOTE (|EntireRing|)))) (|QuaternionCategory| R) ((|constructor| (NIL "\\spadtype{QuaternionCategory} describes the category of quaternions and implements functions that are not representation specific.")) (|rationalIfCan| (((|Union| (|Fraction| (|Integer|)) "failed") $) "\\spad{rationalIfCan(q)} returns \\spad{q} as a rational number,{} or \"failed\" if this is not possible. Note: if \\spad{rational?(q)} is \\spad{true},{} the conversion can be done and the rational number will be returned.")) (|rational| (((|Fraction| (|Integer|)) $) "\\spad{rational(q)} tries to convert \\spad{q} into a rational number. Error: if this is not possible. If \\spad{rational?(q)} is \\spad{true},{} the conversion will be done and the rational number returned.")) (|rational?| (((|Boolean|) $) "\\spad{rational?(q)} returns {\\it \\spad{true}} if all the imaginary parts of \\spad{q} are zero and the real part can be converted into a rational number,{} and {\\it \\spad{false}} otherwise.")) (|abs| ((|#1| $) "\\spad{abs(q)} computes the absolute value of quaternion \\spad{q} (sqrt of norm).")) (|real| ((|#1| $) "\\spad{real(q)} extracts the real part of quaternion \\spad{q}.")) (|quatern| (($ |#1| |#1| |#1| |#1|) "\\spad{quatern(r,i,j,k)} constructs a quaternion from scalars.")) (|norm| ((|#1| $) "\\spad{norm(q)} computes the norm of \\spad{q} (the sum of the squares of the components).")) (|imagK| ((|#1| $) "\\spad{imagK(q)} extracts the imaginary \\spad{k} part of quaternion \\spad{q}.")) (|imagJ| ((|#1| $) "\\spad{imagJ(q)} extracts the imaginary \\spad{j} part of quaternion \\spad{q}.")) (|imagI| ((|#1| $) "\\spad{imagI(q)} extracts the imaginary \\spad{i} part of quaternion \\spad{q}.")) (|conjugate| (($ $) "\\spad{conjugate(q)} negates the imaginary parts of quaternion \\spad{q}."))) -((|noZeroDivisors| |has| |#1| (|EntireRing|)) (|rightUnitary| . T) (|leftUnitary| . T) (|unitsKnown| . T)) +((|noZeroDivisors| |has| |#1| (|EntireRing|))) NIL (|QuaternionCategoryFunctions2| QR R QS S) ((|constructor| (NIL "\\spadtype{QuaternionCategoryFunctions2} implements functions between two quaternion domains. The function \\spadfun{map} is used by the system interpreter to coerce between quaternion types.")) (|map| ((|#3| (|Mapping| |#4| |#2|) |#1|) "\\spad{map(f,u)} maps \\spad{f} onto the component parts of the quaternion \\spad{u}."))) @@ -3610,12 +3610,12 @@ NIL NIL (|RadicalFunctionField| F UP UPUP |radicnd| |n|) ((|constructor| (NIL "Function field defined by y**n = \\spad{f}(\\spad{x})."))) -((|noZeroDivisors| |has| #1=(|Fraction| |#2|) . #2=((|Field|))) (|canonicalUnitNormal| |has| #1# . #2#) (|canonicalsClosed| |has| #1# . #2#) ((|commutative| "*") . T) (|rightUnitary| . T) (|leftUnitary| . T) (|unitsKnown| . T)) -((|HasCategory| #1=(|Fraction| |#2|) (QUOTE (|CharacteristicNonZero|))) (|HasCategory| #1# (QUOTE (|CharacteristicZero|))) #2=(|HasCategory| #1# (QUOTE (|FiniteFieldCategory|))) (OR #3=(|HasCategory| #1# #4=(QUOTE (|Field|))) #2#) #3# (|HasCategory| #1# #5=(QUOTE (|Finite|))) (OR #6=(AND (|HasCategory| #1# (QUOTE (|DifferentialRing|))) #3#) #2#) (OR #6# #7=(AND (|HasCategory| #1# (QUOTE (|DifferentialSpace|))) #3#) #2#) (OR #8=(AND #3# #9=(|HasCategory| #1# (QUOTE (|PartialDifferentialRing| #10=(|Symbol|))))) (AND #2# #9#)) (OR #8# #11=(AND #3# (|HasCategory| #1# (QUOTE (|PartialDifferentialSpace| #10#))))) (|HasCategory| #1# (QUOTE (|LinearlyExplicitRingOver| #12=(|Integer|)))) (OR #3# #13=(|HasCategory| #1# (QUOTE (|RetractableTo| (|Fraction| #12#))))) #13# (|HasCategory| #1# (QUOTE (|RetractableTo| #12#))) (|HasCategory| |#1| #4#) (|HasCategory| |#1| #5#) #7# #11# #6# #8#) +((|noZeroDivisors| |has| #1=(|Fraction| |#2|) . #2=((|Field|))) (|canonicalUnitNormal| |has| #1# . #2#) ((|commutative| "*") . T)) +((|HasCategory| #1=(|Fraction| |#2|) (QUOTE (|CharacteristicNonZero|))) (|HasCategory| #1# (QUOTE (|CharacteristicZero|))) #2=(|HasCategory| #1# (QUOTE (|FiniteFieldCategory|))) (OR #3=(|HasCategory| #1# #4=(QUOTE (|Field|))) #2#) #3# (|HasCategory| #1# #5=(QUOTE (|Finite|))) (OR #6=(AND (|HasCategory| #1# (QUOTE (|DifferentialRing|))) #3#) #2#) (OR #6# #7=(AND (|HasCategory| #1# (QUOTE (|DifferentialSpace|))) #3#) #2#) (OR #8=(AND #3# #9=(|HasCategory| #1# (QUOTE (|PartialDifferentialRing| #10=(|Symbol|))))) (AND #2# #9#)) (OR #8# #11=(AND #3# (|HasCategory| #1# (QUOTE (|PartialDifferentialSpace| #10#))))) (|HasCategory| #1# (QUOTE (|LinearlyExplicitRingOver| #12=(|Integer|)))) (OR #3# #13=(|HasCategory| #1# (QUOTE (|RetractableTo| (|Fraction| #12#))))) #13# (|HasCategory| #1# (QUOTE (|RetractableTo| #12#))) (|HasCategory| |#1| #4#) (|HasCategory| |#1| #5#) #11# #7# #6# #8#) (|RadixExpansion| |bb|) ((|constructor| (NIL "This domain allows rational numbers to be presented as repeating decimal expansions or more generally as repeating expansions in any base.")) (|fractRadix| (($ (|List| (|Integer|)) (|List| (|Integer|))) "\\spad{fractRadix(pre,cyc)} creates a fractional radix expansion from a list of prefix ragits and a list of cyclic ragits. For example,{} \\spad{fractRadix([1],[6])} will return \\spad{0.16666666...}.")) (|wholeRadix| (($ (|List| (|Integer|))) "\\spad{wholeRadix(l)} creates an integral radix expansion from a list of ragits. For example,{} \\spad{wholeRadix([1,3,4])} will return \\spad{134}.")) (|cycleRagits| (((|List| (|Integer|)) $) "\\spad{cycleRagits(rx)} returns the cyclic part of the ragits of the fractional part of a radix expansion. For example,{} if \\spad{x = 3/28 = 0.10 714285 714285 ...},{} then \\spad{cycleRagits(x) = [7,1,4,2,8,5]}.")) (|prefixRagits| (((|List| (|Integer|)) $) "\\spad{prefixRagits(rx)} returns the non-cyclic part of the ragits of the fractional part of a radix expansion. For example,{} if \\spad{x = 3/28 = 0.10 714285 714285 ...},{} then \\spad{prefixRagits(x)=[1,0]}.")) (|fractRagits| (((|Stream| (|Integer|)) $) "\\spad{fractRagits(rx)} returns the ragits of the fractional part of a radix expansion.")) (|wholeRagits| (((|List| (|Integer|)) $) "\\spad{wholeRagits(rx)} returns the ragits of the integer part of a radix expansion.")) (|fractionPart| (((|Fraction| (|Integer|)) $) "\\spad{fractionPart(rx)} returns the fractional part of a radix expansion."))) -((|canonicalsClosed| . T) (|canonicalUnitNormal| . T) (|noZeroDivisors| . T) ((|commutative| "*") . T) (|rightUnitary| . T) (|leftUnitary| . T) (|unitsKnown| . T)) -(#1=(|HasCategory| #2=(|Integer|) (QUOTE (|PolynomialFactorizationExplicit|))) (|HasCategory| #2# (QUOTE (|RetractableTo| #3=(|Symbol|)))) #4=(|HasCategory| #2# #5=(QUOTE (|CharacteristicNonZero|))) (|HasCategory| #2# (QUOTE (|CharacteristicZero|))) (|HasCategory| #2# (QUOTE (|ConvertibleTo| (|InputForm|)))) (|HasCategory| #2# (QUOTE (|RealConstant|))) #6=(|HasCategory| #2# (QUOTE (|OrderedIntegralDomain|))) #7=(|HasCategory| #2# (QUOTE (|OrderedSet|))) (OR #6# #7#) (|HasCategory| #2# (QUOTE (|RetractableTo| #2#))) (|HasCategory| #2# (QUOTE (|StepThrough|))) (|HasCategory| #2# (QUOTE (|PatternMatchable| #8=(|Float|)))) (|HasCategory| #2# (QUOTE (|PatternMatchable| #2#))) (|HasCategory| #2# (QUOTE (|ConvertibleTo| (|Pattern| #8#)))) (|HasCategory| #2# (QUOTE (|ConvertibleTo| (|Pattern| #2#)))) (|HasCategory| #2# (QUOTE (|DifferentialSpace|))) (|HasCategory| #2# (QUOTE (|PartialDifferentialSpace| #3#))) (|HasCategory| #2# (QUOTE (|DifferentialRing|))) (|HasCategory| #2# (QUOTE (|PartialDifferentialRing| #3#))) (|HasCategory| #2# (QUOTE (|InnerEvalable| #3# #2#))) (|HasCategory| #2# (QUOTE (|Evalable| #2#))) (|HasCategory| #2# (QUOTE (|Eltable| #2# #2#))) (|HasCategory| #2# (QUOTE (|EuclideanDomain|))) (|HasCategory| #2# (QUOTE (|IntegerNumberSystem|))) (|HasCategory| #2# (QUOTE (|LinearlyExplicitRingOver| #2#))) #9=(AND (|HasCategory| $ #5#) #1#) (OR #9# #4#)) +((|canonicalUnitNormal| . T) (|noZeroDivisors| . T) ((|commutative| "*") . T)) +(#1=(|HasCategory| #2=(|Integer|) (QUOTE (|PolynomialFactorizationExplicit|))) (|HasCategory| #2# (QUOTE (|RetractableTo| #3=(|Symbol|)))) #4=(|HasCategory| #2# #5=(QUOTE (|CharacteristicNonZero|))) (|HasCategory| #2# (QUOTE (|CharacteristicZero|))) (|HasCategory| #2# (QUOTE (|ConvertibleTo| (|InputForm|)))) (|HasCategory| #2# (QUOTE (|RealConstant|))) #6=(|HasCategory| #2# (QUOTE (|OrderedIntegralDomain|))) #7=(|HasCategory| #2# (QUOTE (|OrderedSet|))) (OR #6# #7#) (|HasCategory| #2# (QUOTE (|RetractableTo| #2#))) (|HasCategory| #2# (QUOTE (|StepThrough|))) (|HasCategory| #2# (QUOTE (|PatternMatchable| #8=(|Float|)))) (|HasCategory| #2# (QUOTE (|PatternMatchable| #2#))) (|HasCategory| #2# (QUOTE (|ConvertibleTo| (|Pattern| #8#)))) (|HasCategory| #2# (QUOTE (|ConvertibleTo| (|Pattern| #2#)))) (|HasCategory| #2# (QUOTE (|PartialDifferentialSpace| #3#))) (|HasCategory| #2# (QUOTE (|DifferentialSpace|))) (|HasCategory| #2# (QUOTE (|DifferentialRing|))) (|HasCategory| #2# (QUOTE (|PartialDifferentialRing| #3#))) (|HasCategory| #2# (QUOTE (|InnerEvalable| #3# #2#))) (|HasCategory| #2# (QUOTE (|Evalable| #2#))) (|HasCategory| #2# (QUOTE (|Eltable| #2# #2#))) (|HasCategory| #2# (QUOTE (|EuclideanDomain|))) (|HasCategory| #2# (QUOTE (|IntegerNumberSystem|))) (|HasCategory| #2# (QUOTE (|LinearlyExplicitRingOver| #2#))) #9=(AND (|HasCategory| $ #5#) #1#) (OR #9# #4#)) (|RadixUtilities|) ((|constructor| (NIL "This package provides tools for creating radix expansions.")) (|radix| (((|Any|) (|Fraction| (|Integer|)) (|Integer|)) "\\spad{radix(x,b)} converts \\spad{x} to a radix expansion in base \\spad{b}."))) NIL @@ -3646,7 +3646,7 @@ NIL NIL (|RealClosedField|) ((|constructor| (NIL "\\axiomType{RealClosedField} provides common acces functions for all real closed fields.")) (|approximate| (((|Fraction| (|Integer|)) $ $) "\\axiom{approximate(\\spad{n},{}\\spad{p})} gives an approximation of \\axiom{\\spad{n}} that has precision \\axiom{\\spad{p}}")) (|rename| (($ $ (|OutputForm|)) "\\axiom{rename(\\spad{x},{}name)} gives a new number that prints as name")) (|rename!| (($ $ (|OutputForm|)) "\\axiom{rename!(\\spad{x},{}name)} changes the way \\axiom{\\spad{x}} is printed")) (|sqrt| (($ (|Integer|)) "\\axiom{sqrt(\\spad{x})} is \\axiom{\\spad{x} ** (1/2)}") (($ (|Fraction| (|Integer|))) "\\axiom{sqrt(\\spad{x})} is \\axiom{\\spad{x} ** (1/2)}") (($ $) "\\axiom{sqrt(\\spad{x})} is \\axiom{\\spad{x} ** (1/2)}") (($ $ (|PositiveInteger|)) "\\axiom{sqrt(\\spad{x},{}\\spad{n})} is \\axiom{\\spad{x} ** (1/n)}")) (|allRootsOf| (((|List| $) (|Polynomial| (|Integer|))) "\\axiom{allRootsOf(pol)} creates all the roots of \\axiom{pol} naming each uniquely") (((|List| $) (|Polynomial| (|Fraction| (|Integer|)))) "\\axiom{allRootsOf(pol)} creates all the roots of \\axiom{pol} naming each uniquely") (((|List| $) (|Polynomial| $)) "\\axiom{allRootsOf(pol)} creates all the roots of \\axiom{pol} naming each uniquely") (((|List| $) (|SparseUnivariatePolynomial| (|Integer|))) "\\axiom{allRootsOf(pol)} creates all the roots of \\axiom{pol} naming each uniquely") (((|List| $) (|SparseUnivariatePolynomial| (|Fraction| (|Integer|)))) "\\axiom{allRootsOf(pol)} creates all the roots of \\axiom{pol} naming each uniquely") (((|List| $) (|SparseUnivariatePolynomial| $)) "\\axiom{allRootsOf(pol)} creates all the roots of \\axiom{pol} naming each uniquely")) (|rootOf| (((|Union| $ "failed") (|SparseUnivariatePolynomial| $) (|PositiveInteger|)) "\\axiom{rootOf(pol,{}\\spad{n})} creates the \\spad{n}th root for the order of \\axiom{pol} and gives it unique name") (((|Union| $ "failed") (|SparseUnivariatePolynomial| $) (|PositiveInteger|) (|OutputForm|)) "\\axiom{rootOf(pol,{}\\spad{n},{}name)} creates the \\spad{n}th root for the order of \\axiom{pol} and names it \\axiom{name}")) (|mainValue| (((|Union| (|SparseUnivariatePolynomial| $) "failed") $) "\\axiom{mainValue(\\spad{x})} is the expression of \\axiom{\\spad{x}} in terms of \\axiom{SparseUnivariatePolynomial(\\$)}")) (|mainDefiningPolynomial| (((|Union| (|SparseUnivariatePolynomial| $) "failed") $) "\\axiom{mainDefiningPolynomial(\\spad{x})} is the defining polynomial for the main algebraic quantity of \\axiom{\\spad{x}}")) (|mainForm| (((|Union| (|OutputForm|) "failed") $) "\\axiom{mainForm(\\spad{x})} is the main algebraic quantity name of \\axiom{\\spad{x}}"))) -((|noZeroDivisors| . T) (|canonicalUnitNormal| . T) (|canonicalsClosed| . T) (|leftUnitary| . T) (|rightUnitary| . T) ((|commutative| "*") . T) (|unitsKnown| . T)) +((|noZeroDivisors| . T) (|canonicalUnitNormal| . T) ((|commutative| "*") . T)) NIL (|ElementaryRischDE| R F) ((|constructor| (NIL "\\indented{1}{Risch differential equation,{} elementary case.} Author: Manuel Bronstein Date Created: 1 February 1988 Date Last Updated: 2 November 1995 Keywords: elementary,{} function,{} integration.")) (|rischDE| (((|Record| (|:| |ans| |#2|) (|:| |right| |#2|) (|:| |sol?| (|Boolean|))) (|Integer|) |#2| |#2| (|Symbol|) (|Mapping| (|Union| (|Record| (|:| |mainpart| |#2|) (|:| |limitedlogs| (|List| (|Record| (|:| |coeff| |#2|) (|:| |logand| |#2|))))) "failed") |#2| (|List| |#2|)) (|Mapping| (|Union| (|Record| (|:| |ratpart| |#2|) (|:| |coeff| |#2|)) "failed") |#2| |#2|)) "\\spad{rischDE(n, f, g, x, lim, ext)} returns \\spad{[y, h, b]} such that \\spad{dy/dx + n df/dx y = h} and \\spad{b := h = g}. The equation \\spad{dy/dx + n df/dx y = g} has no solution if \\spad{h \\~~= g} (\\spad{y} is a partial solution in that case). Notes: \\spad{lim} is a limited integration function,{} and ext is an extended integration function."))) @@ -3694,7 +3694,7 @@ NIL NIL (|RealClosure| |TheField|) ((|constructor| (NIL "This domain implements the real closure of an ordered field.")) (|relativeApprox| (((|Fraction| (|Integer|)) $ $) "\\axiom{relativeApprox(\\spad{n},{}\\spad{p})} gives a relative approximation of \\axiom{\\spad{n}} that has precision \\axiom{\\spad{p}}")) (|mainCharacterization| (((|Union| (|RightOpenIntervalRootCharacterization| $ (|SparseUnivariatePolynomial| $)) "failed") $) "\\axiom{mainCharacterization(\\spad{x})} is the main algebraic quantity of \\axiom{\\spad{x}} (\\axiom{SEG})")) (|algebraicOf| (($ (|RightOpenIntervalRootCharacterization| $ (|SparseUnivariatePolynomial| $)) (|OutputForm|)) "\\axiom{algebraicOf(char)} is the external number"))) -((|noZeroDivisors| . T) (|canonicalUnitNormal| . T) (|canonicalsClosed| . T) (|leftUnitary| . T) (|rightUnitary| . T) ((|commutative| "*") . T) (|unitsKnown| . T)) +((|noZeroDivisors| . T) (|canonicalUnitNormal| . T) ((|commutative| "*") . T)) ((OR #1=(|HasCategory| |#1| #2=(QUOTE (|RetractableTo| #3=(|Integer|)))) #4=(|HasCategory| #5=(|Fraction| #3#) #2#)) (|HasCategory| |#1| #6=(QUOTE (|RetractableTo| #5#))) #1# (|HasCategory| #5# #6#) #4#) (|ReductionOfOrder| F L) ((|constructor| (NIL "\\spadtype{ReductionOfOrder} provides functions for reducing the order of linear ordinary differential equations once some solutions are known.")) (|ReduceOrder| (((|Record| (|:| |eq| |#2|) (|:| |op| (|List| |#1|))) |#2| (|List| |#1|)) "\\spad{ReduceOrder(op, [f1,...,fk])} returns \\spad{[op1,[g1,...,gk]]} such that for any solution \\spad{z} of \\spad{op1 z = 0},{} \\spad{y = gk \\int(g_{k-1} \\int(... \\int(g1 \\int z)...)} is a solution of \\spad{op y = 0}. Each \\spad{fi} must satisfy \\spad{op fi = 0}.") ((|#2| |#2| |#1|) "\\spad{ReduceOrder(op, s)} returns \\spad{op1} such that for any solution \\spad{z} of \\spad{op1 z = 0},{} \\spad{y = s \\int z} is a solution of \\spad{op y = 0}. \\spad{s} must satisfy \\spad{op s = 0}."))) @@ -3734,7 +3734,7 @@ NIL NIL (|ResidueRing| F |Expon| |VarSet| |FPol| |LFPol|) ((|constructor| (NIL "ResidueRing is the quotient of a polynomial ring by an ideal. The ideal is given as a list of generators. The elements of the domain are equivalence classes expressed in terms of reduced elements")) (|lift| ((|#4| $) "\\spad{lift(x)} return the canonical representative of the equivalence class \\spad{x}")) (|coerce| (($ |#4|) "\\spad{coerce(f)} produces the equivalence class of \\spad{f} in the residue ring")) (|reduce| (($ |#4|) "\\spad{reduce(f)} produces the equivalence class of \\spad{f} in the residue ring"))) -(((|commutative| "*") . T) (|rightUnitary| . T) (|leftUnitary| . T) (|unitsKnown| . T)) +(((|commutative| "*") . T)) NIL (|ReturnAst|) ((|constructor| (NIL "This domain represents `return' expressions.")) (|expression| (((|SpadAst|) $) "\\spad{expression(e)} returns the expression returned by `e'."))) @@ -3785,12 +3785,12 @@ NIL NIL NIL (|Ring&| S) -((|constructor| (NIL "The category of rings with unity,{} always associative,{} but not necessarily commutative.")) (|unitsKnown| ((|attribute|) "recip truly yields reciprocal or \"failed\" if not a unit. Note: \\spad{recip(0) = \"failed\"}.")) (|characteristic| (((|NonNegativeInteger|)) "\\spad{characteristic()} returns the characteristic of the ring this is the smallest positive integer \\spad{n} such that \\spad{n*x=0} for all \\spad{x} in the ring,{} or zero if no such \\spad{n} exists."))) +((|constructor| (NIL "The category of rings with unity,{} always associative,{} but not necessarily commutative.")) (|characteristic| (((|NonNegativeInteger|)) "\\spad{characteristic()} returns the characteristic of the ring this is the smallest positive integer \\spad{n} such that \\spad{n*x=0} for all \\spad{x} in the ring,{} or zero if no such \\spad{n} exists."))) NIL NIL (|Ring|) -((|constructor| (NIL "The category of rings with unity,{} always associative,{} but not necessarily commutative.")) (|unitsKnown| ((|attribute|) "recip truly yields reciprocal or \"failed\" if not a unit. Note: \\spad{recip(0) = \"failed\"}.")) (|characteristic| (((|NonNegativeInteger|)) "\\spad{characteristic()} returns the characteristic of the ring this is the smallest positive integer \\spad{n} such that \\spad{n*x=0} for all \\spad{x} in the ring,{} or zero if no such \\spad{n} exists."))) -((|unitsKnown| . T)) +((|constructor| (NIL "The category of rings with unity,{} always associative,{} but not necessarily commutative.")) (|characteristic| (((|NonNegativeInteger|)) "\\spad{characteristic()} returns the characteristic of the ring this is the smallest positive integer \\spad{n} such that \\spad{n*x=0} for all \\spad{x} in the ring,{} or zero if no such \\spad{n} exists."))) +NIL NIL (|RationalInterpolation| |xx| F) ((|constructor| (NIL "This package exports rational interpolation algorithms"))) @@ -3806,12 +3806,12 @@ NIL ((|HasCategory| |#4| (QUOTE (|EuclideanDomain|))) (|HasCategory| |#4| (QUOTE (|Field|))) (|HasCategory| |#4| (QUOTE (|IntegralDomain|))) (|HasCategory| |#4| (QUOTE (|CommutativeRing|)))) (|RectangularMatrixCategory| |m| |n| R |Row| |Col|) ((|constructor| (NIL "\\spadtype{RectangularMatrixCategory} is a category of matrices of fixed dimensions. The dimensions of the matrix will be parameters of the domain. Domains in this category will be \\spad{R}-modules and will be non-mutable.")) (|nullSpace| (((|List| |#5|) $) "\\spad{nullSpace(m)}+ returns a basis for the null space of the matrix \\spad{m}.")) (|nullity| (((|NonNegativeInteger|) $) "\\spad{nullity(m)} returns the nullity of the matrix \\spad{m}. This is the dimension of the null space of the matrix \\spad{m}.")) (|rank| (((|NonNegativeInteger|) $) "\\spad{rank(m)} returns the rank of the matrix \\spad{m}.")) (|rowEchelon| (($ $) "\\spad{rowEchelon(m)} returns the row echelon form of the matrix \\spad{m}.")) (/ (($ $ |#3|) "\\spad{m/r} divides the elements of \\spad{m} by \\spad{r}. Error: if \\spad{r = 0}.")) (|exquo| (((|Union| $ "failed") $ |#3|) "\\spad{exquo(m,r)} computes the exact quotient of the elements of \\spad{m} by \\spad{r},{} returning \\axiom{\"failed\"} if this is not possible.")) (|map| (($ (|Mapping| |#3| |#3| |#3|) $ $) "\\spad{map(f,a,b)} returns \\spad{c},{} where \\spad{c} is such that \\spad{c(i,j) = f(a(i,j),b(i,j))} for all \\spad{i},{} \\spad{j}.")) (|column| ((|#5| $ (|Integer|)) "\\spad{column(m,j)} returns the \\spad{j}th column of the matrix \\spad{m}. Error: if the index outside the proper range.")) (|row| ((|#4| $ (|Integer|)) "\\spad{row(m,i)} returns the \\spad{i}th row of the matrix \\spad{m}. Error: if the index is outside the proper range.")) (|qelt| ((|#3| $ (|Integer|) (|Integer|)) "\\spad{qelt(m,i,j)} returns the element in the \\spad{i}th row and \\spad{j}th column of the matrix \\spad{m}. Note: there is NO error check to determine if indices are in the proper ranges.")) (|elt| ((|#3| $ (|Integer|) (|Integer|) |#3|) "\\spad{elt(m,i,j,r)} returns the element in the \\spad{i}th row and \\spad{j}th column of the matrix \\spad{m},{} if \\spad{m} has an \\spad{i}th row and a \\spad{j}th column,{} and returns \\spad{r} otherwise.") ((|#3| $ (|Integer|) (|Integer|)) "\\spad{elt(m,i,j)} returns the element in the \\spad{i}th row and \\spad{j}th column of the matrix \\spad{m}. Error: if indices are outside the proper ranges.")) (|listOfLists| (((|List| (|List| |#3|)) $) "\\spad{listOfLists(m)} returns the rows of the matrix \\spad{m} as a list of lists.")) (|ncols| (((|NonNegativeInteger|) $) "\\spad{ncols(m)} returns the number of columns in the matrix \\spad{m}.")) (|nrows| (((|NonNegativeInteger|) $) "\\spad{nrows(m)} returns the number of rows in the matrix \\spad{m}.")) (|maxColIndex| (((|Integer|) $) "\\spad{maxColIndex(m)} returns the index of the 'last' column of the matrix \\spad{m}.")) (|minColIndex| (((|Integer|) $) "\\spad{minColIndex(m)} returns the index of the 'first' column of the matrix \\spad{m}.")) (|maxRowIndex| (((|Integer|) $) "\\spad{maxRowIndex(m)} returns the index of the 'last' row of the matrix \\spad{m}.")) (|minRowIndex| (((|Integer|) $) "\\spad{minRowIndex(m)} returns the index of the 'first' row of the matrix \\spad{m}.")) (|antisymmetric?| (((|Boolean|) $) "\\spad{antisymmetric?(m)} returns \\spad{true} if the matrix \\spad{m} is square and antisymmetric (\\spadignore{i.e.} \\spad{m[i,j] = -m[j,i]} for all \\spad{i} and \\spad{j}) and \\spad{false} otherwise.")) (|symmetric?| (((|Boolean|) $) "\\spad{symmetric?(m)} returns \\spad{true} if the matrix \\spad{m} is square and symmetric (\\spadignore{i.e.} \\spad{m[i,j] = m[j,i]} for all \\spad{i} and \\spad{j}) and \\spad{false} otherwise.")) (|diagonal?| (((|Boolean|) $) "\\spad{diagonal?(m)} returns \\spad{true} if the matrix \\spad{m} is square and diagonal (\\spadignore{i.e.} all entries of \\spad{m} not on the diagonal are zero) and \\spad{false} otherwise.")) (|square?| (((|Boolean|) $) "\\spad{square?(m)} returns \\spad{true} if \\spad{m} is a square matrix (\\spadignore{i.e.} if \\spad{m} has the same number of rows as columns) and \\spad{false} otherwise.")) (|matrix| (($ (|List| (|List| |#3|))) "\\spad{matrix(l)} converts the list of lists \\spad{l} to a matrix,{} where the list of lists is viewed as a list of the rows of the matrix."))) -((|leftUnitary| . T) (|rightUnitary| . T)) +NIL NIL (|RectangularMatrix| |m| |n| R) ((|constructor| (NIL "\\spadtype{RectangularMatrix} is a matrix domain where the number of rows and the number of columns are parameters of the domain.")) (|rectangularMatrix| (($ (|Matrix| |#3|)) "\\spad{rectangularMatrix(m)} converts a matrix of type \\spadtype{Matrix} to a matrix of type \\spad{RectangularMatrix}."))) -((|leftUnitary| . T) (|rightUnitary| . T)) -(#1=(|HasCategory| |#3| (QUOTE (|CommutativeRing|))) (OR (AND #1# #2=(|HasCategory| |#3| (|%list| (QUOTE |Evalable|) (|devaluate| |#3|)))) (AND #3=(|HasCategory| |#3| (QUOTE (|Field|))) #2#) #4=(AND #5=(|HasCategory| |#3| (QUOTE (|SetCategory|))) #2#)) (|HasCategory| |#3| (QUOTE (|ConvertibleTo| (|InputForm|)))) (OR #1# #3#) #3# (|HasCategory| |#3| (QUOTE (|EuclideanDomain|))) (|HasCategory| |#3| (QUOTE (|IntegralDomain|))) #4# #5# (|HasCategory| |#3| (QUOTE (|BasicType|))) (|HasCategory| |#3| (QUOTE (|CoercibleTo| (|OutputForm|))))) +NIL +(#1=(|HasCategory| |#3| (QUOTE (|CommutativeRing|))) (OR (AND #1# #2=(|HasCategory| |#3| (|%list| (QUOTE |Evalable|) (|devaluate| |#3|)))) (AND #3=(|HasCategory| |#3| (QUOTE (|Field|))) #2#) #4=(AND #5=(|HasCategory| |#3| (QUOTE (|SetCategory|))) #2#)) (|HasCategory| |#3| (QUOTE (|ConvertibleTo| (|InputForm|)))) (OR #1# #3#) #3# (|HasCategory| |#3| (QUOTE (|EuclideanDomain|))) (|HasCategory| |#3| (QUOTE (|IntegralDomain|))) (|HasCategory| |#3| (QUOTE (|CoercibleTo| (|OutputForm|)))) (|HasCategory| |#3| (QUOTE (|BasicType|))) #5# #4#) (|RectangularMatrixCategoryFunctions2| |m| |n| R1 |Row1| |Col1| M1 R2 |Row2| |Col2| M2) ((|constructor| (NIL "\\spadtype{RectangularMatrixCategoryFunctions2} provides functions between two matrix domains. The functions provided are \\spadfun{map} and \\spadfun{reduce}.")) (|reduce| ((|#7| (|Mapping| |#7| |#3| |#7|) |#6| |#7|) "\\spad{reduce(f,m,r)} returns a matrix \\spad{n} where \\spad{n[i,j] = f(m[i,j],r)} for all indices spad{\\spad{i}} and \\spad{j}.")) (|map| ((|#10| (|Mapping| |#7| |#3|) |#6|) "\\spad{map(f,m)} applies the function \\spad{f} to the elements of the matrix \\spad{m}."))) NIL @@ -3838,15 +3838,15 @@ NIL NIL (|RealNumberSystem|) ((|constructor| (NIL "The real number system category is intended as a model for the real numbers. The real numbers form an ordered normed field. Note that we have purposely not included \\spadtype{DifferentialRing} or the elementary functions (see \\spadtype{TranscendentalFunctionCategory}) in the definition.")) (|round| (($ $) "\\spad{round x} computes the integer closest to \\spad{x}.")) (|truncate| (($ $) "\\spad{truncate x} returns the integer between \\spad{x} and 0 closest to \\spad{x}.")) (|fractionPart| (($ $) "\\spad{fractionPart x} returns the fractional part of \\spad{x}.")) (|wholePart| (((|Integer|) $) "\\spad{wholePart x} returns the integer part of \\spad{x}.")) (|floor| (($ $) "\\spad{floor x} returns the largest integer \\spad{<= x}.")) (|ceiling| (($ $) "\\spad{ceiling x} returns the small integer \\spad{>= x}.")) (|norm| (($ $) "\\spad{norm x} returns the same as absolute value."))) -((|canonicalsClosed| . T) (|canonicalUnitNormal| . T) (|noZeroDivisors| . T) ((|commutative| "*") . T) (|rightUnitary| . T) (|leftUnitary| . T) (|unitsKnown| . T)) +((|canonicalUnitNormal| . T) (|noZeroDivisors| . T) ((|commutative| "*") . T)) NIL (|RightOpenIntervalRootCharacterization| |TheField| |ThePolDom|) ((|constructor| (NIL "\\axiomType{RightOpenIntervalRootCharacterization} provides work with interval root coding.")) (|relativeApprox| ((|#1| |#2| $ |#1|) "\\axiom{relativeApprox(exp,{}\\spad{c},{}\\spad{p}) = a} is relatively close to exp as a polynomial in \\spad{c} ip to precision \\spad{p}")) (|mightHaveRoots| (((|Boolean|) |#2| $) "\\axiom{mightHaveRoots(\\spad{p},{}\\spad{r})} is \\spad{false} if \\axiom{\\spad{p}.\\spad{r}} is not 0")) (|refine| (($ $) "\\axiom{refine(rootChar)} shrinks isolating interval around \\axiom{rootChar}")) (|middle| ((|#1| $) "\\axiom{middle(rootChar)} is the middle of the isolating interval")) (|size| ((|#1| $) "The size of the isolating interval")) (|right| ((|#1| $) "\\axiom{right(rootChar)} is the right bound of the isolating interval")) (|left| ((|#1| $) "\\axiom{left(rootChar)} is the left bound of the isolating interval"))) NIL NIL (|RomanNumeral|) -((|constructor| (NIL "\\spadtype{RomanNumeral} provides functions for converting \\indented{1}{integers to roman numerals.}")) (|roman| (($ (|Integer|)) "\\spad{roman(n)} creates a roman numeral for \\spad{n}.") (($ (|Symbol|)) "\\spad{roman(n)} creates a roman numeral for symbol \\spad{n}.")) (|noetherian| ((|attribute|) "ascending chain condition on ideals.")) (|canonicalsClosed| ((|attribute|) "two positives multiply to give positive.")) (|canonical| ((|attribute|) "mathematical equality is data structure equality."))) -((|noetherian| . T) (|canonicalsClosed| . T) (|canonical| . T) (|canonicalUnitNormal| . T) (|multiplicativeValuation| . T) (|noZeroDivisors| . T) ((|commutative| "*") . T) (|rightUnitary| . T) (|leftUnitary| . T) (|unitsKnown| . T)) +((|constructor| (NIL "\\spadtype{RomanNumeral} provides functions for converting \\indented{1}{integers to roman numerals.}")) (|roman| (($ (|Integer|)) "\\spad{roman(n)} creates a roman numeral for \\spad{n}.") (($ (|Symbol|)) "\\spad{roman(n)} creates a roman numeral for symbol \\spad{n}.")) (|canonical| ((|attribute|) "mathematical equality is data structure equality."))) +((|canonical| . T) (|canonicalUnitNormal| . T) (|multiplicativeValuation| . T) (|noZeroDivisors| . T) ((|commutative| "*") . T)) NIL (|RecursivePolynomialCategory&| S R E V) ((|constructor| (NIL "A category for general multi-variate polynomials with coefficients in a ring,{} variables in an ordered set,{} and exponents from an ordered abelian monoid,{} with a \\axiomOp{sup} operation. When not constant,{} such a polynomial is viewed as a univariate polynomial in its main variable \\spad{w}. \\spad{r}. \\spad{t}. to the total ordering on the elements in the ordered set,{} so that some operations usually defined for univariate polynomials make sense here.")) (|mainSquareFreePart| (($ $) "\\axiom{mainSquareFreePart(\\spad{p})} returns the square free part of \\axiom{\\spad{p}} viewed as a univariate polynomial in its main variable and with coefficients in the polynomial ring generated by its other variables over \\axiom{\\spad{R}}.")) (|mainPrimitivePart| (($ $) "\\axiom{mainPrimitivePart(\\spad{p})} returns the primitive part of \\axiom{\\spad{p}} viewed as a univariate polynomial in its main variable and with coefficients in the polynomial ring generated by its other variables over \\axiom{\\spad{R}}.")) (|mainContent| (($ $) "\\axiom{mainContent(\\spad{p})} returns the content of \\axiom{\\spad{p}} viewed as a univariate polynomial in its main variable and with coefficients in the polynomial ring generated by its other variables over \\axiom{\\spad{R}}.")) (|primitivePart!| (($ $) "\\axiom{primitivePart!(\\spad{p})} replaces \\axiom{\\spad{p}} by its primitive part.")) (|gcd| ((|#2| |#2| $) "\\axiom{gcd(\\spad{r},{}\\spad{p})} returns the gcd of \\axiom{\\spad{r}} and the content of \\axiom{\\spad{p}}.")) (|nextsubResultant2| (($ $ $ $ $) "\\axiom{\\spad{nextsubResultant2}(\\spad{p},{}\\spad{q},{}\\spad{z},{}\\spad{s})} is the multivariate version of the operation \\axiomOpFrom{\\spad{next_sousResultant2}}{PseudoRemainderSequence} from the \\axiomType{PseudoRemainderSequence} constructor.")) (|LazardQuotient2| (($ $ $ $ (|NonNegativeInteger|)) "\\axiom{\\spad{LazardQuotient2}(\\spad{p},{}a,{}\\spad{b},{}\\spad{n})} returns \\axiom{(a**(\\spad{n}-1) * \\spad{p}) exquo b**(\\spad{n}-1)} assuming that this quotient does not fail.")) (|LazardQuotient| (($ $ $ (|NonNegativeInteger|)) "\\axiom{LazardQuotient(a,{}\\spad{b},{}\\spad{n})} returns \\axiom{a**n exquo b**(\\spad{n}-1)} assuming that this quotient does not fail.")) (|lastSubResultant| (($ $ $) "\\axiom{lastSubResultant(a,{}\\spad{b})} returns the last non-zero subresultant of \\axiom{a} and \\axiom{\\spad{b}} where \\axiom{a} and \\axiom{\\spad{b}} are assumed to have the same main variable \\axiom{\\spad{v}} and are viewed as univariate polynomials in \\axiom{\\spad{v}}.")) (|subResultantChain| (((|List| $) $ $) "\\axiom{subResultantChain(a,{}\\spad{b})},{} where \\axiom{a} and \\axiom{\\spad{b}} are not contant polynomials with the same main variable,{} returns the subresultant chain of \\axiom{a} and \\axiom{\\spad{b}}.")) (|resultant| (($ $ $) "\\axiom{resultant(a,{}\\spad{b})} computes the resultant of \\axiom{a} and \\axiom{\\spad{b}} where \\axiom{a} and \\axiom{\\spad{b}} are assumed to have the same main variable \\axiom{\\spad{v}} and are viewed as univariate polynomials in \\axiom{\\spad{v}}.")) (|halfExtendedSubResultantGcd2| (((|Record| (|:| |gcd| $) (|:| |coef2| $)) $ $) "\\axiom{\\spad{halfExtendedSubResultantGcd2}(a,{}\\spad{b})} returns \\axiom{[\\spad{g},{}cb]} if \\axiom{extendedSubResultantGcd(a,{}\\spad{b})} returns \\axiom{[\\spad{g},{}ca,{}cb]} otherwise produces an error.")) (|halfExtendedSubResultantGcd1| (((|Record| (|:| |gcd| $) (|:| |coef1| $)) $ $) "\\axiom{\\spad{halfExtendedSubResultantGcd1}(a,{}\\spad{b})} returns \\axiom{[\\spad{g},{}ca]} if \\axiom{extendedSubResultantGcd(a,{}\\spad{b})} returns \\axiom{[\\spad{g},{}ca,{}cb]} otherwise produces an error.")) (|extendedSubResultantGcd| (((|Record| (|:| |gcd| $) (|:| |coef1| $) (|:| |coef2| $)) $ $) "\\axiom{extendedSubResultantGcd(a,{}\\spad{b})} returns \\axiom{[ca,{}cb,{}\\spad{r}]} such that \\axiom{\\spad{r}} is \\axiom{subResultantGcd(a,{}\\spad{b})} and we have \\axiom{ca * a + cb * cb = \\spad{r}} .")) (|subResultantGcd| (($ $ $) "\\axiom{subResultantGcd(a,{}\\spad{b})} computes a gcd of \\axiom{a} and \\axiom{\\spad{b}} where \\axiom{a} and \\axiom{\\spad{b}} are assumed to have the same main variable \\axiom{\\spad{v}} and are viewed as univariate polynomials in \\axiom{\\spad{v}} with coefficients in the fraction field of the polynomial ring generated by their other variables over \\axiom{\\spad{R}}.")) (|exactQuotient!| (($ $ $) "\\axiom{exactQuotient!(a,{}\\spad{b})} replaces \\axiom{a} by \\axiom{exactQuotient(a,{}\\spad{b})}") (($ $ |#2|) "\\axiom{exactQuotient!(\\spad{p},{}\\spad{r})} replaces \\axiom{\\spad{p}} by \\axiom{exactQuotient(\\spad{p},{}\\spad{r})}.")) (|exactQuotient| (($ $ $) "\\axiom{exactQuotient(a,{}\\spad{b})} computes the exact quotient of \\axiom{a} by \\axiom{\\spad{b}},{} which is assumed to be a divisor of \\axiom{a}. No error is returned if this exact quotient fails!") (($ $ |#2|) "\\axiom{exactQuotient(\\spad{p},{}\\spad{r})} computes the exact quotient of \\axiom{\\spad{p}} by \\axiom{\\spad{r}},{} which is assumed to be a divisor of \\axiom{\\spad{p}}. No error is returned if this exact quotient fails!")) (|primPartElseUnitCanonical!| (($ $) "\\axiom{primPartElseUnitCanonical!(\\spad{p})} replaces \\axiom{\\spad{p}} by \\axiom{primPartElseUnitCanonical(\\spad{p})}.")) (|primPartElseUnitCanonical| (($ $) "\\axiom{primPartElseUnitCanonical(\\spad{p})} returns \\axiom{primitivePart(\\spad{p})} if \\axiom{\\spad{R}} is a gcd-domain,{} otherwise \\axiom{unitCanonical(\\spad{p})}.")) (|convert| (($ (|Polynomial| |#2|)) "\\axiom{convert(\\spad{p})} returns \\axiom{\\spad{p}} as an element of the current domain if all its variables belong to \\axiom{\\spad{V}},{} otherwise an error is produced.") (($ (|Polynomial| (|Integer|))) "\\axiom{convert(\\spad{p})} returns the same as \\axiom{retract(\\spad{p})}.") (($ (|Polynomial| (|Integer|))) "\\axiom{convert(\\spad{p})} returns the same as \\axiom{retract(\\spad{p})}") (($ (|Polynomial| (|Fraction| (|Integer|)))) "\\axiom{convert(\\spad{p})} returns the same as \\axiom{retract(\\spad{p})}.")) (|retract| (($ (|Polynomial| |#2|)) "\\axiom{retract(\\spad{p})} returns \\axiom{\\spad{p}} as an element of the current domain if \\axiom{retractIfCan(\\spad{p})} does not return \"failed\",{} otherwise an error is produced.") (($ (|Polynomial| |#2|)) "\\axiom{retract(\\spad{p})} returns \\axiom{\\spad{p}} as an element of the current domain if \\axiom{retractIfCan(\\spad{p})} does not return \"failed\",{} otherwise an error is produced.") (($ (|Polynomial| (|Integer|))) "\\axiom{retract(\\spad{p})} returns \\axiom{\\spad{p}} as an element of the current domain if \\axiom{retractIfCan(\\spad{p})} does not return \"failed\",{} otherwise an error is produced.") (($ (|Polynomial| |#2|)) "\\axiom{retract(\\spad{p})} returns \\axiom{\\spad{p}} as an element of the current domain if \\axiom{retractIfCan(\\spad{p})} does not return \"failed\",{} otherwise an error is produced.") (($ (|Polynomial| (|Integer|))) "\\axiom{retract(\\spad{p})} returns \\axiom{\\spad{p}} as an element of the current domain if \\axiom{retractIfCan(\\spad{p})} does not return \"failed\",{} otherwise an error is produced.") (($ (|Polynomial| (|Fraction| (|Integer|)))) "\\axiom{retract(\\spad{p})} returns \\axiom{\\spad{p}} as an element of the current domain if \\axiom{retractIfCan(\\spad{p})} does not return \"failed\",{} otherwise an error is produced.")) (|retractIfCan| (((|Union| $ "failed") (|Polynomial| |#2|)) "\\axiom{retractIfCan(\\spad{p})} returns \\axiom{\\spad{p}} as an element of the current domain if all its variables belong to \\axiom{\\spad{V}}.") (((|Union| $ "failed") (|Polynomial| |#2|)) "\\axiom{retractIfCan(\\spad{p})} returns \\axiom{\\spad{p}} as an element of the current domain if all its variables belong to \\axiom{\\spad{V}}.") (((|Union| $ "failed") (|Polynomial| (|Integer|))) "\\axiom{retractIfCan(\\spad{p})} returns \\axiom{\\spad{p}} as an element of the current domain if all its variables belong to \\axiom{\\spad{V}}.") (((|Union| $ "failed") (|Polynomial| |#2|)) "\\axiom{retractIfCan(\\spad{p})} returns \\axiom{\\spad{p}} as an element of the current domain if all its variables belong to \\axiom{\\spad{V}}.") (((|Union| $ "failed") (|Polynomial| (|Integer|))) "\\axiom{retractIfCan(\\spad{p})} returns \\axiom{\\spad{p}} as an element of the current domain if all its variables belong to \\axiom{\\spad{V}}.") (((|Union| $ "failed") (|Polynomial| (|Fraction| (|Integer|)))) "\\axiom{retractIfCan(\\spad{p})} returns \\axiom{\\spad{p}} as an element of the current domain if all its variables belong to \\axiom{\\spad{V}}.")) (|initiallyReduce| (($ $ $) "\\axiom{initiallyReduce(a,{}\\spad{b})} returns a polynomial \\axiom{\\spad{r}} such that \\axiom{initiallyReduced?(\\spad{r},{}\\spad{b})} holds and there exists an integer \\axiom{\\spad{e}} such that \\axiom{init(\\spad{b})^e a - \\spad{r}} is zero modulo \\axiom{\\spad{b}}.")) (|headReduce| (($ $ $) "\\axiom{headReduce(a,{}\\spad{b})} returns a polynomial \\axiom{\\spad{r}} such that \\axiom{headReduced?(\\spad{r},{}\\spad{b})} holds and there exists an integer \\axiom{\\spad{e}} such that \\axiom{init(\\spad{b})^e a - \\spad{r}} is zero modulo \\axiom{\\spad{b}}.")) (|lazyResidueClass| (((|Record| (|:| |polnum| $) (|:| |polden| $) (|:| |power| (|NonNegativeInteger|))) $ $) "\\axiom{lazyResidueClass(a,{}\\spad{b})} returns \\axiom{[\\spad{p},{}\\spad{q},{}\\spad{n}]} where \\axiom{\\spad{p} / q**n} represents the residue class of \\axiom{a} modulo \\axiom{\\spad{b}} and \\axiom{\\spad{p}} is reduced \\spad{w}.\\spad{r}.\\spad{t}. \\axiom{\\spad{b}} and \\axiom{\\spad{q}} is \\axiom{init(\\spad{b})}.")) (|monicModulo| (($ $ $) "\\axiom{monicModulo(a,{}\\spad{b})} computes \\axiom{a mod \\spad{b}},{} if \\axiom{\\spad{b}} is monic as univariate polynomial in its main variable.")) (|pseudoDivide| (((|Record| (|:| |quotient| $) (|:| |remainder| $)) $ $) "\\axiom{pseudoDivide(a,{}\\spad{b})} computes \\axiom{[pquo(a,{}\\spad{b}),{}prem(a,{}\\spad{b})]},{} both polynomials viewed as univariate polynomials in the main variable of \\axiom{\\spad{b}},{} if \\axiom{\\spad{b}} is not a constant polynomial.")) (|lazyPseudoDivide| (((|Record| (|:| |coef| $) (|:| |gap| (|NonNegativeInteger|)) (|:| |quotient| $) (|:| |remainder| $)) $ $ |#4|) "\\axiom{lazyPseudoDivide(a,{}\\spad{b},{}\\spad{v})} returns \\axiom{[\\spad{c},{}\\spad{g},{}\\spad{q},{}\\spad{r}]} such that \\axiom{\\spad{r} = lazyPrem(a,{}\\spad{b},{}\\spad{v})},{} \\axiom{(c**g)*r = prem(a,{}\\spad{b},{}\\spad{v})} and \\axiom{\\spad{q}} is the pseudo-quotient computed in this lazy pseudo-division.") (((|Record| (|:| |coef| $) (|:| |gap| (|NonNegativeInteger|)) (|:| |quotient| $) (|:| |remainder| $)) $ $) "\\axiom{lazyPseudoDivide(a,{}\\spad{b})} returns \\axiom{[\\spad{c},{}\\spad{g},{}\\spad{q},{}\\spad{r}]} such that \\axiom{[\\spad{c},{}\\spad{g},{}\\spad{r}] = lazyPremWithDefault(a,{}\\spad{b})} and \\axiom{\\spad{q}} is the pseudo-quotient computed in this lazy pseudo-division.")) (|lazyPremWithDefault| (((|Record| (|:| |coef| $) (|:| |gap| (|NonNegativeInteger|)) (|:| |remainder| $)) $ $ |#4|) "\\axiom{lazyPremWithDefault(a,{}\\spad{b},{}\\spad{v})} returns \\axiom{[\\spad{c},{}\\spad{g},{}\\spad{r}]} such that \\axiom{\\spad{r} = lazyPrem(a,{}\\spad{b},{}\\spad{v})} and \\axiom{(c**g)*r = prem(a,{}\\spad{b},{}\\spad{v})}.") (((|Record| (|:| |coef| $) (|:| |gap| (|NonNegativeInteger|)) (|:| |remainder| $)) $ $) "\\axiom{lazyPremWithDefault(a,{}\\spad{b})} returns \\axiom{[\\spad{c},{}\\spad{g},{}\\spad{r}]} such that \\axiom{\\spad{r} = lazyPrem(a,{}\\spad{b})} and \\axiom{(c**g)*r = prem(a,{}\\spad{b})}.")) (|lazyPquo| (($ $ $ |#4|) "\\axiom{lazyPquo(a,{}\\spad{b},{}\\spad{v})} returns the polynomial \\axiom{\\spad{q}} such that \\axiom{lazyPseudoDivide(a,{}\\spad{b},{}\\spad{v})} returns \\axiom{[\\spad{c},{}\\spad{g},{}\\spad{q},{}\\spad{r}]}.") (($ $ $) "\\axiom{lazyPquo(a,{}\\spad{b})} returns the polynomial \\axiom{\\spad{q}} such that \\axiom{lazyPseudoDivide(a,{}\\spad{b})} returns \\axiom{[\\spad{c},{}\\spad{g},{}\\spad{q},{}\\spad{r}]}.")) (|lazyPrem| (($ $ $ |#4|) "\\axiom{lazyPrem(a,{}\\spad{b},{}\\spad{v})} returns the polynomial \\axiom{\\spad{r}} reduced \\spad{w}.\\spad{r}.\\spad{t}. \\axiom{\\spad{b}} viewed as univariate polynomials in the variable \\axiom{\\spad{v}} such that \\axiom{\\spad{b}} divides \\axiom{init(\\spad{b})^e a - \\spad{r}} where \\axiom{\\spad{e}} is the number of steps of this pseudo-division.") (($ $ $) "\\axiom{lazyPrem(a,{}\\spad{b})} returns the polynomial \\axiom{\\spad{r}} reduced \\spad{w}.\\spad{r}.\\spad{t}. \\axiom{\\spad{b}} and such that \\axiom{\\spad{b}} divides \\axiom{init(\\spad{b})^e a - \\spad{r}} where \\axiom{\\spad{e}} is the number of steps of this pseudo-division.")) (|pquo| (($ $ $ |#4|) "\\axiom{pquo(a,{}\\spad{b},{}\\spad{v})} computes the pseudo-quotient of \\axiom{a} by \\axiom{\\spad{b}},{} both viewed as univariate polynomials in \\axiom{\\spad{v}}.") (($ $ $) "\\axiom{pquo(a,{}\\spad{b})} computes the pseudo-quotient of \\axiom{a} by \\axiom{\\spad{b}},{} both viewed as univariate polynomials in the main variable of \\axiom{\\spad{b}}.")) (|prem| (($ $ $ |#4|) "\\axiom{prem(a,{}\\spad{b},{}\\spad{v})} computes the pseudo-remainder of \\axiom{a} by \\axiom{\\spad{b}},{} both viewed as univariate polynomials in \\axiom{\\spad{v}}.") (($ $ $) "\\axiom{prem(a,{}\\spad{b})} computes the pseudo-remainder of \\axiom{a} by \\axiom{\\spad{b}},{} both viewed as univariate polynomials in the main variable of \\axiom{\\spad{b}}.")) (|normalized?| (((|Boolean|) $ (|List| $)) "\\axiom{normalized?(\\spad{q},{}lp)} returns \\spad{true} iff \\axiom{normalized?(\\spad{q},{}\\spad{p})} holds for every \\axiom{\\spad{p}} in \\axiom{lp}.") (((|Boolean|) $ $) "\\axiom{normalized?(a,{}\\spad{b})} returns \\spad{true} iff \\axiom{a} and its iterated initials have degree zero \\spad{w}.\\spad{r}.\\spad{t}. the main variable of \\axiom{\\spad{b}}")) (|initiallyReduced?| (((|Boolean|) $ (|List| $)) "\\axiom{initiallyReduced?(\\spad{q},{}lp)} returns \\spad{true} iff \\axiom{initiallyReduced?(\\spad{q},{}\\spad{p})} holds for every \\axiom{\\spad{p}} in \\axiom{lp}.") (((|Boolean|) $ $) "\\axiom{initiallyReduced?(a,{}\\spad{b})} returns \\spad{false} iff there exists an iterated initial of \\axiom{a} which is not reduced \\spad{w}.\\spad{r}.\\spad{t} \\axiom{\\spad{b}}.")) (|headReduced?| (((|Boolean|) $ (|List| $)) "\\axiom{headReduced?(\\spad{q},{}lp)} returns \\spad{true} iff \\axiom{headReduced?(\\spad{q},{}\\spad{p})} holds for every \\axiom{\\spad{p}} in \\axiom{lp}.") (((|Boolean|) $ $) "\\axiom{headReduced?(a,{}\\spad{b})} returns \\spad{true} iff \\axiom{degree(head(a),{}mvar(\\spad{b})) < mdeg(\\spad{b})}.")) (|reduced?| (((|Boolean|) $ (|List| $)) "\\axiom{reduced?(\\spad{q},{}lp)} returns \\spad{true} iff \\axiom{reduced?(\\spad{q},{}\\spad{p})} holds for every \\axiom{\\spad{p}} in \\axiom{lp}.") (((|Boolean|) $ $) "\\axiom{reduced?(a,{}\\spad{b})} returns \\spad{true} iff \\axiom{degree(a,{}mvar(\\spad{b})) < mdeg(\\spad{b})}.")) (|supRittWu?| (((|Boolean|) $ $) "\\axiom{supRittWu?(a,{}\\spad{b})} returns \\spad{true} if \\axiom{a} is greater than \\axiom{\\spad{b}} \\spad{w}.\\spad{r}.\\spad{t}. the Ritt and Wu Wen Tsun ordering using the refinement of Lazard.")) (|infRittWu?| (((|Boolean|) $ $) "\\axiom{infRittWu?(a,{}\\spad{b})} returns \\spad{true} if \\axiom{a} is less than \\axiom{\\spad{b}} \\spad{w}.\\spad{r}.\\spad{t}. the Ritt and Wu Wen Tsun ordering using the refinement of Lazard.")) (|RittWuCompare| (((|Union| (|Boolean|) "failed") $ $) "\\axiom{RittWuCompare(a,{}\\spad{b})} returns \\axiom{\"failed\"} if \\axiom{a} and \\axiom{\\spad{b}} have same rank \\spad{w}.\\spad{r}.\\spad{t}. Ritt and Wu Wen Tsun ordering using the refinement of Lazard,{} otherwise returns \\axiom{infRittWu?(a,{}\\spad{b})}.")) (|mainMonomials| (((|List| $) $) "\\axiom{mainMonomials(\\spad{p})} returns an error if \\axiom{\\spad{p}} is \\axiom{\\spad{O}},{} otherwise,{} if \\axiom{\\spad{p}} belongs to \\axiom{\\spad{R}} returns [1],{} otherwise returns the list of the monomials of \\axiom{\\spad{p}},{} where \\axiom{\\spad{p}} is viewed as a univariate polynomial in its main variable.")) (|mainCoefficients| (((|List| $) $) "\\axiom{mainCoefficients(\\spad{p})} returns an error if \\axiom{\\spad{p}} is \\axiom{\\spad{O}},{} otherwise,{} if \\axiom{\\spad{p}} belongs to \\axiom{\\spad{R}} returns [\\spad{p}],{} otherwise returns the list of the coefficients of \\axiom{\\spad{p}},{} where \\axiom{\\spad{p}} is viewed as a univariate polynomial in its main variable.")) (|leastMonomial| (($ $) "\\axiom{leastMonomial(\\spad{p})} returns an error if \\axiom{\\spad{p}} is \\axiom{\\spad{O}},{} otherwise,{} if \\axiom{\\spad{p}} belongs to \\axiom{\\spad{R}} returns \\axiom{1},{} otherwise,{} the monomial of \\axiom{\\spad{p}} with lowest degree,{} where \\axiom{\\spad{p}} is viewed as a univariate polynomial in its main variable.")) (|mainMonomial| (($ $) "\\axiom{mainMonomial(\\spad{p})} returns an error if \\axiom{\\spad{p}} is \\axiom{\\spad{O}},{} otherwise,{} if \\axiom{\\spad{p}} belongs to \\axiom{\\spad{R}} returns \\axiom{1},{} otherwise,{} \\axiom{mvar(\\spad{p})} raised to the power \\axiom{mdeg(\\spad{p})}.")) (|quasiMonic?| (((|Boolean|) $) "\\axiom{quasiMonic?(\\spad{p})} returns \\spad{false} if \\axiom{\\spad{p}} belongs to \\axiom{\\spad{R}},{} otherwise returns \\spad{true} iff the initial of \\axiom{\\spad{p}} lies in the base ring \\axiom{\\spad{R}}.")) (|monic?| (((|Boolean|) $) "\\axiom{monic?(\\spad{p})} returns \\spad{false} if \\axiom{\\spad{p}} belongs to \\axiom{\\spad{R}},{} otherwise returns \\spad{true} iff \\axiom{\\spad{p}} is monic as a univariate polynomial in its main variable.")) (|reductum| (($ $ |#4|) "\\axiom{reductum(\\spad{p},{}\\spad{v})} returns the reductum of \\axiom{\\spad{p}},{} where \\axiom{\\spad{p}} is viewed as a univariate polynomial in \\axiom{\\spad{v}}.")) (|leadingCoefficient| (($ $ |#4|) "\\axiom{leadingCoefficient(\\spad{p},{}\\spad{v})} returns the leading coefficient of \\axiom{\\spad{p}},{} where \\axiom{\\spad{p}} is viewed as A univariate polynomial in \\axiom{\\spad{v}}.")) (|deepestInitial| (($ $) "\\axiom{deepestInitial(\\spad{p})} returns an error if \\axiom{\\spad{p}} belongs to \\axiom{\\spad{R}},{} otherwise returns the last term of \\axiom{iteratedInitials(\\spad{p})}.")) (|iteratedInitials| (((|List| $) $) "\\axiom{iteratedInitials(\\spad{p})} returns \\axiom{[]} if \\axiom{\\spad{p}} belongs to \\axiom{\\spad{R}},{} otherwise returns the list of the iterated initials of \\axiom{\\spad{p}}.")) (|deepestTail| (($ $) "\\axiom{deepestTail(\\spad{p})} returns \\axiom{0} if \\axiom{\\spad{p}} belongs to \\axiom{\\spad{R}},{} otherwise returns tail(\\spad{p}),{} if \\axiom{tail(\\spad{p})} belongs to \\axiom{\\spad{R}} or \\axiom{mvar(tail(\\spad{p})) < mvar(\\spad{p})},{} otherwise returns \\axiom{deepestTail(tail(\\spad{p}))}.")) (|tail| (($ $) "\\axiom{tail(\\spad{p})} returns its reductum,{} where \\axiom{\\spad{p}} is viewed as a univariate polynomial in its main variable.")) (|head| (($ $) "\\axiom{head(\\spad{p})} returns \\axiom{\\spad{p}} if \\axiom{\\spad{p}} belongs to \\axiom{\\spad{R}},{} otherwise returns its leading term (monomial in the AXIOM sense),{} where \\axiom{\\spad{p}} is viewed as a univariate polynomial in its main variable.")) (|init| (($ $) "\\axiom{init(\\spad{p})} returns an error if \\axiom{\\spad{p}} belongs to \\axiom{\\spad{R}},{} otherwise returns its leading coefficient,{} where \\axiom{\\spad{p}} is viewed as a univariate polynomial in its main variable.")) (|mdeg| (((|NonNegativeInteger|) $) "\\axiom{mdeg(\\spad{p})} returns an error if \\axiom{\\spad{p}} is \\axiom{0},{} otherwise,{} if \\axiom{\\spad{p}} belongs to \\axiom{\\spad{R}} returns \\axiom{0},{} otherwise,{} returns the degree of \\axiom{\\spad{p}} in its main variable.")) (|mvar| ((|#4| $) "\\axiom{mvar(\\spad{p})} returns an error if \\axiom{\\spad{p}} belongs to \\axiom{\\spad{R}},{} otherwise returns its main variable \\spad{w}. \\spad{r}. \\spad{t}. to the total ordering on the elements in \\axiom{\\spad{V}}."))) @@ -3854,7 +3854,7 @@ NIL ((|HasCategory| |#2| (QUOTE (|GcdDomain|))) (|HasCategory| |#2| (QUOTE (|IntegralDomain|))) (|HasCategory| |#2| (QUOTE (|RetractableTo| #1=(|Integer|)))) (|HasCategory| |#2| (QUOTE (|IntegerNumberSystem|))) (|HasCategory| |#2| (QUOTE (|Algebra| #1#))) (|HasCategory| |#2| (QUOTE (|QuotientFieldCategory| #1#))) (|HasCategory| |#2| (QUOTE (|Algebra| (|Fraction| #1#)))) (|HasCategory| |#4| (QUOTE (|ConvertibleTo| (|Symbol|))))) (|RecursivePolynomialCategory| R E V) ((|constructor| (NIL "A category for general multi-variate polynomials with coefficients in a ring,{} variables in an ordered set,{} and exponents from an ordered abelian monoid,{} with a \\axiomOp{sup} operation. When not constant,{} such a polynomial is viewed as a univariate polynomial in its main variable \\spad{w}. \\spad{r}. \\spad{t}. to the total ordering on the elements in the ordered set,{} so that some operations usually defined for univariate polynomials make sense here.")) (|mainSquareFreePart| (($ $) "\\axiom{mainSquareFreePart(\\spad{p})} returns the square free part of \\axiom{\\spad{p}} viewed as a univariate polynomial in its main variable and with coefficients in the polynomial ring generated by its other variables over \\axiom{\\spad{R}}.")) (|mainPrimitivePart| (($ $) "\\axiom{mainPrimitivePart(\\spad{p})} returns the primitive part of \\axiom{\\spad{p}} viewed as a univariate polynomial in its main variable and with coefficients in the polynomial ring generated by its other variables over \\axiom{\\spad{R}}.")) (|mainContent| (($ $) "\\axiom{mainContent(\\spad{p})} returns the content of \\axiom{\\spad{p}} viewed as a univariate polynomial in its main variable and with coefficients in the polynomial ring generated by its other variables over \\axiom{\\spad{R}}.")) (|primitivePart!| (($ $) "\\axiom{primitivePart!(\\spad{p})} replaces \\axiom{\\spad{p}} by its primitive part.")) (|gcd| ((|#1| |#1| $) "\\axiom{gcd(\\spad{r},{}\\spad{p})} returns the gcd of \\axiom{\\spad{r}} and the content of \\axiom{\\spad{p}}.")) (|nextsubResultant2| (($ $ $ $ $) "\\axiom{\\spad{nextsubResultant2}(\\spad{p},{}\\spad{q},{}\\spad{z},{}\\spad{s})} is the multivariate version of the operation \\axiomOpFrom{\\spad{next_sousResultant2}}{PseudoRemainderSequence} from the \\axiomType{PseudoRemainderSequence} constructor.")) (|LazardQuotient2| (($ $ $ $ (|NonNegativeInteger|)) "\\axiom{\\spad{LazardQuotient2}(\\spad{p},{}a,{}\\spad{b},{}\\spad{n})} returns \\axiom{(a**(\\spad{n}-1) * \\spad{p}) exquo b**(\\spad{n}-1)} assuming that this quotient does not fail.")) (|LazardQuotient| (($ $ $ (|NonNegativeInteger|)) "\\axiom{LazardQuotient(a,{}\\spad{b},{}\\spad{n})} returns \\axiom{a**n exquo b**(\\spad{n}-1)} assuming that this quotient does not fail.")) (|lastSubResultant| (($ $ $) "\\axiom{lastSubResultant(a,{}\\spad{b})} returns the last non-zero subresultant of \\axiom{a} and \\axiom{\\spad{b}} where \\axiom{a} and \\axiom{\\spad{b}} are assumed to have the same main variable \\axiom{\\spad{v}} and are viewed as univariate polynomials in \\axiom{\\spad{v}}.")) (|subResultantChain| (((|List| $) $ $) "\\axiom{subResultantChain(a,{}\\spad{b})},{} where \\axiom{a} and \\axiom{\\spad{b}} are not contant polynomials with the same main variable,{} returns the subresultant chain of \\axiom{a} and \\axiom{\\spad{b}}.")) (|resultant| (($ $ $) "\\axiom{resultant(a,{}\\spad{b})} computes the resultant of \\axiom{a} and \\axiom{\\spad{b}} where \\axiom{a} and \\axiom{\\spad{b}} are assumed to have the same main variable \\axiom{\\spad{v}} and are viewed as univariate polynomials in \\axiom{\\spad{v}}.")) (|halfExtendedSubResultantGcd2| (((|Record| (|:| |gcd| $) (|:| |coef2| $)) $ $) "\\axiom{\\spad{halfExtendedSubResultantGcd2}(a,{}\\spad{b})} returns \\axiom{[\\spad{g},{}cb]} if \\axiom{extendedSubResultantGcd(a,{}\\spad{b})} returns \\axiom{[\\spad{g},{}ca,{}cb]} otherwise produces an error.")) (|halfExtendedSubResultantGcd1| (((|Record| (|:| |gcd| $) (|:| |coef1| $)) $ $) "\\axiom{\\spad{halfExtendedSubResultantGcd1}(a,{}\\spad{b})} returns \\axiom{[\\spad{g},{}ca]} if \\axiom{extendedSubResultantGcd(a,{}\\spad{b})} returns \\axiom{[\\spad{g},{}ca,{}cb]} otherwise produces an error.")) (|extendedSubResultantGcd| (((|Record| (|:| |gcd| $) (|:| |coef1| $) (|:| |coef2| $)) $ $) "\\axiom{extendedSubResultantGcd(a,{}\\spad{b})} returns \\axiom{[ca,{}cb,{}\\spad{r}]} such that \\axiom{\\spad{r}} is \\axiom{subResultantGcd(a,{}\\spad{b})} and we have \\axiom{ca * a + cb * cb = \\spad{r}} .")) (|subResultantGcd| (($ $ $) "\\axiom{subResultantGcd(a,{}\\spad{b})} computes a gcd of \\axiom{a} and \\axiom{\\spad{b}} where \\axiom{a} and \\axiom{\\spad{b}} are assumed to have the same main variable \\axiom{\\spad{v}} and are viewed as univariate polynomials in \\axiom{\\spad{v}} with coefficients in the fraction field of the polynomial ring generated by their other variables over \\axiom{\\spad{R}}.")) (|exactQuotient!| (($ $ $) "\\axiom{exactQuotient!(a,{}\\spad{b})} replaces \\axiom{a} by \\axiom{exactQuotient(a,{}\\spad{b})}") (($ $ |#1|) "\\axiom{exactQuotient!(\\spad{p},{}\\spad{r})} replaces \\axiom{\\spad{p}} by \\axiom{exactQuotient(\\spad{p},{}\\spad{r})}.")) (|exactQuotient| (($ $ $) "\\axiom{exactQuotient(a,{}\\spad{b})} computes the exact quotient of \\axiom{a} by \\axiom{\\spad{b}},{} which is assumed to be a divisor of \\axiom{a}. No error is returned if this exact quotient fails!") (($ $ |#1|) "\\axiom{exactQuotient(\\spad{p},{}\\spad{r})} computes the exact quotient of \\axiom{\\spad{p}} by \\axiom{\\spad{r}},{} which is assumed to be a divisor of \\axiom{\\spad{p}}. No error is returned if this exact quotient fails!")) (|primPartElseUnitCanonical!| (($ $) "\\axiom{primPartElseUnitCanonical!(\\spad{p})} replaces \\axiom{\\spad{p}} by \\axiom{primPartElseUnitCanonical(\\spad{p})}.")) (|primPartElseUnitCanonical| (($ $) "\\axiom{primPartElseUnitCanonical(\\spad{p})} returns \\axiom{primitivePart(\\spad{p})} if \\axiom{\\spad{R}} is a gcd-domain,{} otherwise \\axiom{unitCanonical(\\spad{p})}.")) (|convert| (($ (|Polynomial| |#1|)) "\\axiom{convert(\\spad{p})} returns \\axiom{\\spad{p}} as an element of the current domain if all its variables belong to \\axiom{\\spad{V}},{} otherwise an error is produced.") (($ (|Polynomial| (|Integer|))) "\\axiom{convert(\\spad{p})} returns the same as \\axiom{retract(\\spad{p})}.") (($ (|Polynomial| (|Integer|))) "\\axiom{convert(\\spad{p})} returns the same as \\axiom{retract(\\spad{p})}") (($ (|Polynomial| (|Fraction| (|Integer|)))) "\\axiom{convert(\\spad{p})} returns the same as \\axiom{retract(\\spad{p})}.")) (|retract| (($ (|Polynomial| |#1|)) "\\axiom{retract(\\spad{p})} returns \\axiom{\\spad{p}} as an element of the current domain if \\axiom{retractIfCan(\\spad{p})} does not return \"failed\",{} otherwise an error is produced.") (($ (|Polynomial| |#1|)) "\\axiom{retract(\\spad{p})} returns \\axiom{\\spad{p}} as an element of the current domain if \\axiom{retractIfCan(\\spad{p})} does not return \"failed\",{} otherwise an error is produced.") (($ (|Polynomial| (|Integer|))) "\\axiom{retract(\\spad{p})} returns \\axiom{\\spad{p}} as an element of the current domain if \\axiom{retractIfCan(\\spad{p})} does not return \"failed\",{} otherwise an error is produced.") (($ (|Polynomial| |#1|)) "\\axiom{retract(\\spad{p})} returns \\axiom{\\spad{p}} as an element of the current domain if \\axiom{retractIfCan(\\spad{p})} does not return \"failed\",{} otherwise an error is produced.") (($ (|Polynomial| (|Integer|))) "\\axiom{retract(\\spad{p})} returns \\axiom{\\spad{p}} as an element of the current domain if \\axiom{retractIfCan(\\spad{p})} does not return \"failed\",{} otherwise an error is produced.") (($ (|Polynomial| (|Fraction| (|Integer|)))) "\\axiom{retract(\\spad{p})} returns \\axiom{\\spad{p}} as an element of the current domain if \\axiom{retractIfCan(\\spad{p})} does not return \"failed\",{} otherwise an error is produced.")) (|retractIfCan| (((|Union| $ "failed") (|Polynomial| |#1|)) "\\axiom{retractIfCan(\\spad{p})} returns \\axiom{\\spad{p}} as an element of the current domain if all its variables belong to \\axiom{\\spad{V}}.") (((|Union| $ "failed") (|Polynomial| |#1|)) "\\axiom{retractIfCan(\\spad{p})} returns \\axiom{\\spad{p}} as an element of the current domain if all its variables belong to \\axiom{\\spad{V}}.") (((|Union| $ "failed") (|Polynomial| (|Integer|))) "\\axiom{retractIfCan(\\spad{p})} returns \\axiom{\\spad{p}} as an element of the current domain if all its variables belong to \\axiom{\\spad{V}}.") (((|Union| $ "failed") (|Polynomial| |#1|)) "\\axiom{retractIfCan(\\spad{p})} returns \\axiom{\\spad{p}} as an element of the current domain if all its variables belong to \\axiom{\\spad{V}}.") (((|Union| $ "failed") (|Polynomial| (|Integer|))) "\\axiom{retractIfCan(\\spad{p})} returns \\axiom{\\spad{p}} as an element of the current domain if all its variables belong to \\axiom{\\spad{V}}.") (((|Union| $ "failed") (|Polynomial| (|Fraction| (|Integer|)))) "\\axiom{retractIfCan(\\spad{p})} returns \\axiom{\\spad{p}} as an element of the current domain if all its variables belong to \\axiom{\\spad{V}}.")) (|initiallyReduce| (($ $ $) "\\axiom{initiallyReduce(a,{}\\spad{b})} returns a polynomial \\axiom{\\spad{r}} such that \\axiom{initiallyReduced?(\\spad{r},{}\\spad{b})} holds and there exists an integer \\axiom{\\spad{e}} such that \\axiom{init(\\spad{b})^e a - \\spad{r}} is zero modulo \\axiom{\\spad{b}}.")) (|headReduce| (($ $ $) "\\axiom{headReduce(a,{}\\spad{b})} returns a polynomial \\axiom{\\spad{r}} such that \\axiom{headReduced?(\\spad{r},{}\\spad{b})} holds and there exists an integer \\axiom{\\spad{e}} such that \\axiom{init(\\spad{b})^e a - \\spad{r}} is zero modulo \\axiom{\\spad{b}}.")) (|lazyResidueClass| (((|Record| (|:| |polnum| $) (|:| |polden| $) (|:| |power| (|NonNegativeInteger|))) $ $) "\\axiom{lazyResidueClass(a,{}\\spad{b})} returns \\axiom{[\\spad{p},{}\\spad{q},{}\\spad{n}]} where \\axiom{\\spad{p} / q**n} represents the residue class of \\axiom{a} modulo \\axiom{\\spad{b}} and \\axiom{\\spad{p}} is reduced \\spad{w}.\\spad{r}.\\spad{t}. \\axiom{\\spad{b}} and \\axiom{\\spad{q}} is \\axiom{init(\\spad{b})}.")) (|monicModulo| (($ $ $) "\\axiom{monicModulo(a,{}\\spad{b})} computes \\axiom{a mod \\spad{b}},{} if \\axiom{\\spad{b}} is monic as univariate polynomial in its main variable.")) (|pseudoDivide| (((|Record| (|:| |quotient| $) (|:| |remainder| $)) $ $) "\\axiom{pseudoDivide(a,{}\\spad{b})} computes \\axiom{[pquo(a,{}\\spad{b}),{}prem(a,{}\\spad{b})]},{} both polynomials viewed as univariate polynomials in the main variable of \\axiom{\\spad{b}},{} if \\axiom{\\spad{b}} is not a constant polynomial.")) (|lazyPseudoDivide| (((|Record| (|:| |coef| $) (|:| |gap| (|NonNegativeInteger|)) (|:| |quotient| $) (|:| |remainder| $)) $ $ |#3|) "\\axiom{lazyPseudoDivide(a,{}\\spad{b},{}\\spad{v})} returns \\axiom{[\\spad{c},{}\\spad{g},{}\\spad{q},{}\\spad{r}]} such that \\axiom{\\spad{r} = lazyPrem(a,{}\\spad{b},{}\\spad{v})},{} \\axiom{(c**g)*r = prem(a,{}\\spad{b},{}\\spad{v})} and \\axiom{\\spad{q}} is the pseudo-quotient computed in this lazy pseudo-division.") (((|Record| (|:| |coef| $) (|:| |gap| (|NonNegativeInteger|)) (|:| |quotient| $) (|:| |remainder| $)) $ $) "\\axiom{lazyPseudoDivide(a,{}\\spad{b})} returns \\axiom{[\\spad{c},{}\\spad{g},{}\\spad{q},{}\\spad{r}]} such that \\axiom{[\\spad{c},{}\\spad{g},{}\\spad{r}] = lazyPremWithDefault(a,{}\\spad{b})} and \\axiom{\\spad{q}} is the pseudo-quotient computed in this lazy pseudo-division.")) (|lazyPremWithDefault| (((|Record| (|:| |coef| $) (|:| |gap| (|NonNegativeInteger|)) (|:| |remainder| $)) $ $ |#3|) "\\axiom{lazyPremWithDefault(a,{}\\spad{b},{}\\spad{v})} returns \\axiom{[\\spad{c},{}\\spad{g},{}\\spad{r}]} such that \\axiom{\\spad{r} = lazyPrem(a,{}\\spad{b},{}\\spad{v})} and \\axiom{(c**g)*r = prem(a,{}\\spad{b},{}\\spad{v})}.") (((|Record| (|:| |coef| $) (|:| |gap| (|NonNegativeInteger|)) (|:| |remainder| $)) $ $) "\\axiom{lazyPremWithDefault(a,{}\\spad{b})} returns \\axiom{[\\spad{c},{}\\spad{g},{}\\spad{r}]} such that \\axiom{\\spad{r} = lazyPrem(a,{}\\spad{b})} and \\axiom{(c**g)*r = prem(a,{}\\spad{b})}.")) (|lazyPquo| (($ $ $ |#3|) "\\axiom{lazyPquo(a,{}\\spad{b},{}\\spad{v})} returns the polynomial \\axiom{\\spad{q}} such that \\axiom{lazyPseudoDivide(a,{}\\spad{b},{}\\spad{v})} returns \\axiom{[\\spad{c},{}\\spad{g},{}\\spad{q},{}\\spad{r}]}.") (($ $ $) "\\axiom{lazyPquo(a,{}\\spad{b})} returns the polynomial \\axiom{\\spad{q}} such that \\axiom{lazyPseudoDivide(a,{}\\spad{b})} returns \\axiom{[\\spad{c},{}\\spad{g},{}\\spad{q},{}\\spad{r}]}.")) (|lazyPrem| (($ $ $ |#3|) "\\axiom{lazyPrem(a,{}\\spad{b},{}\\spad{v})} returns the polynomial \\axiom{\\spad{r}} reduced \\spad{w}.\\spad{r}.\\spad{t}. \\axiom{\\spad{b}} viewed as univariate polynomials in the variable \\axiom{\\spad{v}} such that \\axiom{\\spad{b}} divides \\axiom{init(\\spad{b})^e a - \\spad{r}} where \\axiom{\\spad{e}} is the number of steps of this pseudo-division.") (($ $ $) "\\axiom{lazyPrem(a,{}\\spad{b})} returns the polynomial \\axiom{\\spad{r}} reduced \\spad{w}.\\spad{r}.\\spad{t}. \\axiom{\\spad{b}} and such that \\axiom{\\spad{b}} divides \\axiom{init(\\spad{b})^e a - \\spad{r}} where \\axiom{\\spad{e}} is the number of steps of this pseudo-division.")) (|pquo| (($ $ $ |#3|) "\\axiom{pquo(a,{}\\spad{b},{}\\spad{v})} computes the pseudo-quotient of \\axiom{a} by \\axiom{\\spad{b}},{} both viewed as univariate polynomials in \\axiom{\\spad{v}}.") (($ $ $) "\\axiom{pquo(a,{}\\spad{b})} computes the pseudo-quotient of \\axiom{a} by \\axiom{\\spad{b}},{} both viewed as univariate polynomials in the main variable of \\axiom{\\spad{b}}.")) (|prem| (($ $ $ |#3|) "\\axiom{prem(a,{}\\spad{b},{}\\spad{v})} computes the pseudo-remainder of \\axiom{a} by \\axiom{\\spad{b}},{} both viewed as univariate polynomials in \\axiom{\\spad{v}}.") (($ $ $) "\\axiom{prem(a,{}\\spad{b})} computes the pseudo-remainder of \\axiom{a} by \\axiom{\\spad{b}},{} both viewed as univariate polynomials in the main variable of \\axiom{\\spad{b}}.")) (|normalized?| (((|Boolean|) $ (|List| $)) "\\axiom{normalized?(\\spad{q},{}lp)} returns \\spad{true} iff \\axiom{normalized?(\\spad{q},{}\\spad{p})} holds for every \\axiom{\\spad{p}} in \\axiom{lp}.") (((|Boolean|) $ $) "\\axiom{normalized?(a,{}\\spad{b})} returns \\spad{true} iff \\axiom{a} and its iterated initials have degree zero \\spad{w}.\\spad{r}.\\spad{t}. the main variable of \\axiom{\\spad{b}}")) (|initiallyReduced?| (((|Boolean|) $ (|List| $)) "\\axiom{initiallyReduced?(\\spad{q},{}lp)} returns \\spad{true} iff \\axiom{initiallyReduced?(\\spad{q},{}\\spad{p})} holds for every \\axiom{\\spad{p}} in \\axiom{lp}.") (((|Boolean|) $ $) "\\axiom{initiallyReduced?(a,{}\\spad{b})} returns \\spad{false} iff there exists an iterated initial of \\axiom{a} which is not reduced \\spad{w}.\\spad{r}.\\spad{t} \\axiom{\\spad{b}}.")) (|headReduced?| (((|Boolean|) $ (|List| $)) "\\axiom{headReduced?(\\spad{q},{}lp)} returns \\spad{true} iff \\axiom{headReduced?(\\spad{q},{}\\spad{p})} holds for every \\axiom{\\spad{p}} in \\axiom{lp}.") (((|Boolean|) $ $) "\\axiom{headReduced?(a,{}\\spad{b})} returns \\spad{true} iff \\axiom{degree(head(a),{}mvar(\\spad{b})) < mdeg(\\spad{b})}.")) (|reduced?| (((|Boolean|) $ (|List| $)) "\\axiom{reduced?(\\spad{q},{}lp)} returns \\spad{true} iff \\axiom{reduced?(\\spad{q},{}\\spad{p})} holds for every \\axiom{\\spad{p}} in \\axiom{lp}.") (((|Boolean|) $ $) "\\axiom{reduced?(a,{}\\spad{b})} returns \\spad{true} iff \\axiom{degree(a,{}mvar(\\spad{b})) < mdeg(\\spad{b})}.")) (|supRittWu?| (((|Boolean|) $ $) "\\axiom{supRittWu?(a,{}\\spad{b})} returns \\spad{true} if \\axiom{a} is greater than \\axiom{\\spad{b}} \\spad{w}.\\spad{r}.\\spad{t}. the Ritt and Wu Wen Tsun ordering using the refinement of Lazard.")) (|infRittWu?| (((|Boolean|) $ $) "\\axiom{infRittWu?(a,{}\\spad{b})} returns \\spad{true} if \\axiom{a} is less than \\axiom{\\spad{b}} \\spad{w}.\\spad{r}.\\spad{t}. the Ritt and Wu Wen Tsun ordering using the refinement of Lazard.")) (|RittWuCompare| (((|Union| (|Boolean|) "failed") $ $) "\\axiom{RittWuCompare(a,{}\\spad{b})} returns \\axiom{\"failed\"} if \\axiom{a} and \\axiom{\\spad{b}} have same rank \\spad{w}.\\spad{r}.\\spad{t}. Ritt and Wu Wen Tsun ordering using the refinement of Lazard,{} otherwise returns \\axiom{infRittWu?(a,{}\\spad{b})}.")) (|mainMonomials| (((|List| $) $) "\\axiom{mainMonomials(\\spad{p})} returns an error if \\axiom{\\spad{p}} is \\axiom{\\spad{O}},{} otherwise,{} if \\axiom{\\spad{p}} belongs to \\axiom{\\spad{R}} returns [1],{} otherwise returns the list of the monomials of \\axiom{\\spad{p}},{} where \\axiom{\\spad{p}} is viewed as a univariate polynomial in its main variable.")) (|mainCoefficients| (((|List| $) $) "\\axiom{mainCoefficients(\\spad{p})} returns an error if \\axiom{\\spad{p}} is \\axiom{\\spad{O}},{} otherwise,{} if \\axiom{\\spad{p}} belongs to \\axiom{\\spad{R}} returns [\\spad{p}],{} otherwise returns the list of the coefficients of \\axiom{\\spad{p}},{} where \\axiom{\\spad{p}} is viewed as a univariate polynomial in its main variable.")) (|leastMonomial| (($ $) "\\axiom{leastMonomial(\\spad{p})} returns an error if \\axiom{\\spad{p}} is \\axiom{\\spad{O}},{} otherwise,{} if \\axiom{\\spad{p}} belongs to \\axiom{\\spad{R}} returns \\axiom{1},{} otherwise,{} the monomial of \\axiom{\\spad{p}} with lowest degree,{} where \\axiom{\\spad{p}} is viewed as a univariate polynomial in its main variable.")) (|mainMonomial| (($ $) "\\axiom{mainMonomial(\\spad{p})} returns an error if \\axiom{\\spad{p}} is \\axiom{\\spad{O}},{} otherwise,{} if \\axiom{\\spad{p}} belongs to \\axiom{\\spad{R}} returns \\axiom{1},{} otherwise,{} \\axiom{mvar(\\spad{p})} raised to the power \\axiom{mdeg(\\spad{p})}.")) (|quasiMonic?| (((|Boolean|) $) "\\axiom{quasiMonic?(\\spad{p})} returns \\spad{false} if \\axiom{\\spad{p}} belongs to \\axiom{\\spad{R}},{} otherwise returns \\spad{true} iff the initial of \\axiom{\\spad{p}} lies in the base ring \\axiom{\\spad{R}}.")) (|monic?| (((|Boolean|) $) "\\axiom{monic?(\\spad{p})} returns \\spad{false} if \\axiom{\\spad{p}} belongs to \\axiom{\\spad{R}},{} otherwise returns \\spad{true} iff \\axiom{\\spad{p}} is monic as a univariate polynomial in its main variable.")) (|reductum| (($ $ |#3|) "\\axiom{reductum(\\spad{p},{}\\spad{v})} returns the reductum of \\axiom{\\spad{p}},{} where \\axiom{\\spad{p}} is viewed as a univariate polynomial in \\axiom{\\spad{v}}.")) (|leadingCoefficient| (($ $ |#3|) "\\axiom{leadingCoefficient(\\spad{p},{}\\spad{v})} returns the leading coefficient of \\axiom{\\spad{p}},{} where \\axiom{\\spad{p}} is viewed as A univariate polynomial in \\axiom{\\spad{v}}.")) (|deepestInitial| (($ $) "\\axiom{deepestInitial(\\spad{p})} returns an error if \\axiom{\\spad{p}} belongs to \\axiom{\\spad{R}},{} otherwise returns the last term of \\axiom{iteratedInitials(\\spad{p})}.")) (|iteratedInitials| (((|List| $) $) "\\axiom{iteratedInitials(\\spad{p})} returns \\axiom{[]} if \\axiom{\\spad{p}} belongs to \\axiom{\\spad{R}},{} otherwise returns the list of the iterated initials of \\axiom{\\spad{p}}.")) (|deepestTail| (($ $) "\\axiom{deepestTail(\\spad{p})} returns \\axiom{0} if \\axiom{\\spad{p}} belongs to \\axiom{\\spad{R}},{} otherwise returns tail(\\spad{p}),{} if \\axiom{tail(\\spad{p})} belongs to \\axiom{\\spad{R}} or \\axiom{mvar(tail(\\spad{p})) < mvar(\\spad{p})},{} otherwise returns \\axiom{deepestTail(tail(\\spad{p}))}.")) (|tail| (($ $) "\\axiom{tail(\\spad{p})} returns its reductum,{} where \\axiom{\\spad{p}} is viewed as a univariate polynomial in its main variable.")) (|head| (($ $) "\\axiom{head(\\spad{p})} returns \\axiom{\\spad{p}} if \\axiom{\\spad{p}} belongs to \\axiom{\\spad{R}},{} otherwise returns its leading term (monomial in the AXIOM sense),{} where \\axiom{\\spad{p}} is viewed as a univariate polynomial in its main variable.")) (|init| (($ $) "\\axiom{init(\\spad{p})} returns an error if \\axiom{\\spad{p}} belongs to \\axiom{\\spad{R}},{} otherwise returns its leading coefficient,{} where \\axiom{\\spad{p}} is viewed as a univariate polynomial in its main variable.")) (|mdeg| (((|NonNegativeInteger|) $) "\\axiom{mdeg(\\spad{p})} returns an error if \\axiom{\\spad{p}} is \\axiom{0},{} otherwise,{} if \\axiom{\\spad{p}} belongs to \\axiom{\\spad{R}} returns \\axiom{0},{} otherwise,{} returns the degree of \\axiom{\\spad{p}} in its main variable.")) (|mvar| ((|#3| $) "\\axiom{mvar(\\spad{p})} returns an error if \\axiom{\\spad{p}} belongs to \\axiom{\\spad{R}},{} otherwise returns its main variable \\spad{w}. \\spad{r}. \\spad{t}. to the total ordering on the elements in \\axiom{\\spad{V}}."))) -(((|commutative| "*") |has| |#1| (|CommutativeRing|)) (|noZeroDivisors| |has| |#1| (|IntegralDomain|)) (|canonicalUnitNormal| |has| |#1| (ATTRIBUTE |canonicalUnitNormal|)) (|leftUnitary| . T) (|rightUnitary| . T) (|unitsKnown| . T)) +(((|commutative| "*") |has| |#1| (|CommutativeRing|)) (|noZeroDivisors| |has| |#1| (|IntegralDomain|)) (|canonicalUnitNormal| |has| |#1| (ATTRIBUTE |canonicalUnitNormal|))) NIL (|RepeatAst|) ((|constructor| (NIL "This domain represents the `repeat' iterator syntax.")) (|body| (((|SpadAst|) $) "\\spad{body(e)} returns the body of the loop `e'.")) (|iterators| (((|List| (|SpadAst|)) $) "\\spad{iterators(e)} returns the list of iterators controlling the loop `e'."))) @@ -3910,7 +3910,7 @@ NIL NIL (|SimpleAlgebraicExtension| R UP M) ((|constructor| (NIL "Domain which represents simple algebraic extensions of arbitrary rings. The first argument to the domain,{} \\spad{R},{} is the underlying ring,{} the second argument is a domain of univariate polynomials over \\spad{K},{} while the last argument specifies the defining minimal polynomial. The elements of the domain are canonically represented as polynomials of degree less than that of the minimal polynomial with coefficients in \\spad{R}. The second argument is both the type of the third argument and the underlying representation used by \\spadtype{SAE} itself."))) -((|noZeroDivisors| |has| |#1| . #1=((|Field|))) (|canonicalUnitNormal| |has| |#1| . #1#) (|canonicalsClosed| |has| |#1| . #1#) ((|commutative| "*") . T) (|rightUnitary| . T) (|leftUnitary| . T) (|unitsKnown| . T)) +((|noZeroDivisors| |has| |#1| . #1=((|Field|))) (|canonicalUnitNormal| |has| |#1| . #1#) ((|commutative| "*") . T)) ((|HasCategory| |#1| (QUOTE (|CharacteristicNonZero|))) (|HasCategory| |#1| (QUOTE (|CharacteristicZero|))) #1=(|HasCategory| |#1| (QUOTE (|FiniteFieldCategory|))) (OR #2=(|HasCategory| |#1| (QUOTE (|Field|))) #1#) #2# (|HasCategory| |#1| (QUOTE (|Finite|))) (OR #3=(AND (|HasCategory| |#1| (QUOTE (|DifferentialRing|))) #2#) #1#) (OR #3# #4=(AND (|HasCategory| |#1| (QUOTE (|DifferentialSpace|))) #2#) #1#) (OR #5=(AND #2# #6=(|HasCategory| |#1| (QUOTE (|PartialDifferentialRing| #7=(|Symbol|))))) (AND #1# #6#)) (OR #5# #8=(AND #2# (|HasCategory| |#1| (QUOTE (|PartialDifferentialSpace| #7#))))) (|HasCategory| |#1| (QUOTE (|LinearlyExplicitRingOver| #9=(|Integer|)))) (OR #2# #10=(|HasCategory| |#1| (QUOTE (|RetractableTo| (|Fraction| #9#))))) #10# (|HasCategory| |#1| (QUOTE (|RetractableTo| #9#))) (OR #4# #1#) #8# #4# #3# #5#) (|SimpleAlgebraicExtensionAlgFactor| UP SAE UPA) ((|constructor| (NIL "Factorization of univariate polynomials with coefficients in an algebraic extension of the rational numbers (\\spadtype{Fraction Integer}).")) (|factor| (((|Factored| |#3|) |#3|) "\\spad{factor(p)} returns a prime factorisation of \\spad{p}."))) @@ -3942,8 +3942,8 @@ NIL NIL (|SequentialDifferentialPolynomial| R) ((|constructor| (NIL "\\spadtype{SequentialDifferentialPolynomial} implements an ordinary differential polynomial ring in arbitrary number of differential indeterminates,{} with coefficients in a ring. The ranking on the differential indeterminate is sequential. \\blankline"))) -(((|commutative| "*") |has| |#1| (|CommutativeRing|)) (|noZeroDivisors| |has| |#1| (|IntegralDomain|)) (|canonicalUnitNormal| |has| |#1| (ATTRIBUTE |canonicalUnitNormal|)) (|leftUnitary| . T) (|rightUnitary| . T) (|unitsKnown| . T)) -(#1=(|HasCategory| |#1| (QUOTE (|PolynomialFactorizationExplicit|))) (OR #2=(|HasCategory| |#1| (QUOTE (|CommutativeRing|))) #3=(|HasCategory| |#1| (QUOTE (|GcdDomain|))) #4=(|HasCategory| |#1| (QUOTE (|IntegralDomain|))) #1#) (OR #3# #4# #1#) (OR #3# #1#) #4# #2# (OR #2# #4#) (AND (|HasCategory| |#1| #5=(QUOTE (|PatternMatchable| #6=(|Float|)))) (|HasCategory| #7=(|SequentialDifferentialVariable| #8=(|Symbol|)) #5#)) (AND (|HasCategory| |#1| #9=(QUOTE (|PatternMatchable| #10=(|Integer|)))) (|HasCategory| #7# #9#)) (AND (|HasCategory| |#1| #11=(QUOTE (|ConvertibleTo| (|Pattern| #6#)))) (|HasCategory| #7# #11#)) (AND (|HasCategory| |#1| #12=(QUOTE (|ConvertibleTo| (|Pattern| #10#)))) (|HasCategory| #7# #12#)) (AND (|HasCategory| |#1| #13=(QUOTE (|ConvertibleTo| (|InputForm|)))) (|HasCategory| #7# #13#)) (|HasCategory| |#1| (QUOTE (|LinearlyExplicitRingOver| #10#))) (|HasCategory| |#1| (QUOTE (|CharacteristicZero|))) #14=(|HasCategory| |#1| #15=(QUOTE (|CharacteristicNonZero|))) #16=(|HasCategory| |#1| (QUOTE (|Algebra| #17=(|Fraction| #10#)))) (|HasCategory| |#1| (QUOTE (|RetractableTo| #10#))) (OR #16# #18=(|HasCategory| |#1| (QUOTE (|RetractableTo| #17#)))) #18# (|HasCategory| |#1| (QUOTE (|DifferentialRing|))) (|HasCategory| |#1| (QUOTE (|DifferentialSpace|))) (|HasCategory| |#1| (QUOTE (|PartialDifferentialSpace| #8#))) (|HasCategory| |#1| (QUOTE (|PartialDifferentialRing| #8#))) (|HasCategory| |#1| (QUOTE (|Field|))) (|HasAttribute| |#1| (QUOTE |canonicalUnitNormal|)) #3# #19=(AND #1# (|HasCategory| $ #15#)) (OR #19# #14#)) +(((|commutative| "*") |has| |#1| (|CommutativeRing|)) (|noZeroDivisors| |has| |#1| (|IntegralDomain|)) (|canonicalUnitNormal| |has| |#1| (ATTRIBUTE |canonicalUnitNormal|))) +(#1=(|HasCategory| |#1| (QUOTE (|PolynomialFactorizationExplicit|))) (OR #2=(|HasCategory| |#1| (QUOTE (|CommutativeRing|))) #3=(|HasCategory| |#1| (QUOTE (|GcdDomain|))) #4=(|HasCategory| |#1| (QUOTE (|IntegralDomain|))) #1#) (OR #3# #4# #1#) (OR #3# #1#) #4# #2# (OR #2# #4#) (AND (|HasCategory| |#1| #5=(QUOTE (|PatternMatchable| #6=(|Float|)))) (|HasCategory| #7=(|SequentialDifferentialVariable| #8=(|Symbol|)) #5#)) (AND (|HasCategory| |#1| #9=(QUOTE (|PatternMatchable| #10=(|Integer|)))) (|HasCategory| #7# #9#)) (AND (|HasCategory| |#1| #11=(QUOTE (|ConvertibleTo| (|Pattern| #6#)))) (|HasCategory| #7# #11#)) (AND (|HasCategory| |#1| #12=(QUOTE (|ConvertibleTo| (|Pattern| #10#)))) (|HasCategory| #7# #12#)) (AND (|HasCategory| |#1| #13=(QUOTE (|ConvertibleTo| (|InputForm|)))) (|HasCategory| #7# #13#)) (|HasCategory| |#1| (QUOTE (|LinearlyExplicitRingOver| #10#))) #14=(|HasCategory| |#1| (QUOTE (|Algebra| #15=(|Fraction| #10#)))) #16=(|HasCategory| |#1| #17=(QUOTE (|CharacteristicNonZero|))) (|HasCategory| |#1| (QUOTE (|CharacteristicZero|))) (|HasCategory| |#1| (QUOTE (|RetractableTo| #10#))) (OR #14# #18=(|HasCategory| |#1| (QUOTE (|RetractableTo| #15#)))) #18# (|HasCategory| |#1| (QUOTE (|DifferentialRing|))) (|HasCategory| |#1| (QUOTE (|PartialDifferentialSpace| #8#))) (|HasCategory| |#1| (QUOTE (|DifferentialSpace|))) (|HasCategory| |#1| (QUOTE (|PartialDifferentialRing| #8#))) (|HasCategory| |#1| (QUOTE (|Field|))) (|HasAttribute| |#1| (QUOTE |canonicalUnitNormal|)) #3# #19=(AND #1# (|HasCategory| $ #17#)) (OR #19# #16#)) (|SequentialDifferentialVariable| S) ((|constructor| (NIL "\\spadtype{OrderlyDifferentialVariable} adds a commonly used sequential ranking to the set of derivatives of an ordered list of differential indeterminates. A sequential ranking is a ranking \\spadfun{<} of the derivatives with the property that for any derivative \\spad{v},{} there are only a finite number of derivatives \\spad{u} with \\spad{u} \\spadfun{<} \\spad{v}. This domain belongs to \\spadtype{DifferentialVariableCategory}. It defines \\spadfun{weight} to be just \\spadfun{order},{} and it defines a sequential ranking \\spadfun{<} on derivatives \\spad{u} by the lexicographic order on the pair (\\spadfun{variable}(\\spad{u}),{} \\spadfun{order}(\\spad{u}))."))) NIL @@ -4050,8 +4050,8 @@ NIL NIL (|SplitHomogeneousDirectProduct| |dimtot| |dim1| S) ((|constructor| (NIL "\\indented{2}{This type represents the finite direct or cartesian product of an} underlying ordered component type. The vectors are ordered as if they were split into two blocks. The \\spad{dim1} parameter specifies the length of the first block. The ordering is lexicographic between the blocks but acts like \\spadtype{HomogeneousDirectProduct} within each block. This type is a suitable third argument for \\spadtype{GeneralDistributedMultivariatePolynomial}."))) -((|rightUnitary| |has| |#3| . #1=((|Ring|))) (|leftUnitary| |has| |#3| . #1#) (|unitsKnown| |has| |#3| (ATTRIBUTE |unitsKnown|))) -((OR (AND #1=(|HasCategory| |#3| (QUOTE (|AbelianGroup|))) #2=(|HasCategory| |#3| (|%list| (QUOTE |Evalable|) #3=(|devaluate| |#3|)))) (AND #4=(|HasCategory| |#3| (QUOTE (|AbelianMonoid|))) #2#) (AND #5=(|HasCategory| |#3| (QUOTE (|AbelianSemiGroup|))) #2#) (AND #6=(|HasCategory| |#3| (QUOTE (|CancellationAbelianMonoid|))) #2#) (AND #7=(|HasCategory| |#3| (QUOTE (|CommutativeRing|))) #2#) (AND #8=(|HasCategory| |#3| (QUOTE (|DifferentialRing|))) #2#) (AND #9=(|HasCategory| |#3| (QUOTE (|Field|))) #2#) (AND #10=(|HasCategory| |#3| (QUOTE (|Finite|))) #2#) (AND #11=(|HasCategory| |#3| (QUOTE (|Monoid|))) #2#) (AND #12=(|HasCategory| |#3| (QUOTE (|OrderedAbelianMonoidSup|))) #2#) (AND #13=(|HasCategory| |#3| #14=(QUOTE (|OrderedSet|))) #2#) (AND #15=(|HasCategory| |#3| (QUOTE (|PartialDifferentialRing| #16=(|Symbol|)))) #2#) (AND #17=(|HasCategory| |#3| (QUOTE (|Ring|))) #2#) #18=(AND #19=(|HasCategory| |#3| (QUOTE (|SetCategory|))) #2#)) (|HasCategory| |#3| (QUOTE (|CoercibleTo| (|OutputForm|)))) #9# (OR #7# #9# #17#) (OR #7# #9#) #1# #17# #11# #12# (OR #12# #13#) #13# #10# (OR (AND #7# #20=(|HasCategory| |#3| (QUOTE (|LinearlyExplicitRingOver| #21=(|Integer|))))) (AND #8# #20#) (AND #9# #20#) (AND #20# #15#) #22=(AND #20# #17#)) #15# (OR #1# #4# #5# #23=(|HasCategory| |#3| (QUOTE (|BasicType|))) #6# #7# #8# #9# #10# #11# #12# #13# #15# #17# #19#) (OR #1# #4# #5# #6# #7# #8# #9# #10# #11# #12# #13# #15# #17# #19#) (OR #1# #4# #5# #6# #7# #8# #9# #15# #17#) (OR #1# #4# #6# #7# #8# #9# #15# #17#) (OR #1# #6# #7# #8# #9# #15# #17#) (OR #1# #7# #8# #9# #15# #17#) (OR #8# #15# #17#) #8# (OR #8# #24=(AND (|HasCategory| |#3| (QUOTE (|DifferentialSpace|))) #17#)) (OR #25=(AND (|HasCategory| |#3| (QUOTE (|PartialDifferentialSpace| #16#))) #17#) #15#) #19# (OR (AND #1# #26=(|HasCategory| |#3| (QUOTE (|RetractableTo| (|Fraction| #21#))))) (AND #4# #26#) (AND #5# #26#) (AND #6# #26#) (AND #7# #26#) (AND #8# #26#) (AND #9# #26#) (AND #10# #26#) (AND #11# #26#) (AND #12# #26#) (AND #13# #26#) (AND #15# #26#) (AND #26# #17#) #27=(AND #26# #19#)) (OR #28=(AND #1# #29=(|HasCategory| |#3| (QUOTE (|RetractableTo| #21#)))) #30=(AND #4# #29#) #31=(AND #5# #29#) #32=(AND #6# #29#) #33=(AND #7# #29#) #34=(AND #8# #29#) #35=(AND #12# #29#) #36=(AND #13# #29#) #37=(AND #15# #29#) #38=(AND #29# #19#) #39=(AND #9# #29#) #40=(AND #10# #29#) #41=(AND #11# #29#) #17#) (OR #28# #30# #31# #32# #33# #34# #35# #36# #37# #38# #39# #40# #41# (AND #29# #17#)) #23# (|HasCategory| #21# #14#) #22# #24# #25# (OR #38# #17#) #38# #27# (|HasAttribute| |#3| (QUOTE |unitsKnown|)) (AND #8# #17#) (AND #15# #17#) #7# #4# #6# #5# #18# (AND #23# (|HasCategory| $ (|%list| (QUOTE |FiniteAggregate|) #3#))) (|HasCategory| $ (|%list| (QUOTE |ShallowlyMutableAggregate|) #3#))) +NIL +((OR (AND #1=(|HasCategory| |#3| (QUOTE (|AbelianGroup|))) #2=(|HasCategory| |#3| (|%list| (QUOTE |Evalable|) #3=(|devaluate| |#3|)))) (AND #4=(|HasCategory| |#3| (QUOTE (|AbelianMonoid|))) #2#) (AND #5=(|HasCategory| |#3| (QUOTE (|AbelianSemiGroup|))) #2#) (AND #6=(|HasCategory| |#3| (QUOTE (|CancellationAbelianMonoid|))) #2#) (AND #7=(|HasCategory| |#3| (QUOTE (|CommutativeRing|))) #2#) (AND #8=(|HasCategory| |#3| (QUOTE (|DifferentialRing|))) #2#) (AND #9=(|HasCategory| |#3| (QUOTE (|Field|))) #2#) (AND #10=(|HasCategory| |#3| (QUOTE (|Finite|))) #2#) (AND #11=(|HasCategory| |#3| (QUOTE (|Monoid|))) #2#) (AND #12=(|HasCategory| |#3| (QUOTE (|OrderedAbelianMonoidSup|))) #2#) (AND #13=(|HasCategory| |#3| #14=(QUOTE (|OrderedSet|))) #2#) (AND #15=(|HasCategory| |#3| (QUOTE (|PartialDifferentialRing| #16=(|Symbol|)))) #2#) (AND #17=(|HasCategory| |#3| (QUOTE (|Ring|))) #2#) #18=(AND #19=(|HasCategory| |#3| (QUOTE (|SetCategory|))) #2#)) (|HasCategory| |#3| (QUOTE (|CoercibleTo| (|OutputForm|)))) #9# (OR #7# #9# #17#) (OR #7# #9#) #1# #17# #11# #12# (OR #12# #13#) #13# #10# (OR (AND #7# #20=(|HasCategory| |#3| (QUOTE (|LinearlyExplicitRingOver| #21=(|Integer|))))) (AND #8# #20#) (AND #9# #20#) (AND #20# #15#) #22=(AND #20# #17#)) #15# (OR #1# #4# #5# #23=(|HasCategory| |#3| (QUOTE (|BasicType|))) #6# #7# #8# #9# #10# #11# #12# #13# #15# #17# #19#) (OR #1# #4# #5# #6# #7# #8# #9# #10# #11# #12# #13# #15# #17# #19#) (OR #1# #4# #5# #6# #7# #8# #9# #15# #17#) (OR #1# #4# #6# #7# #8# #9# #15# #17#) (OR #1# #6# #7# #8# #9# #15# #17#) (OR #1# #7# #8# #9# #15# #17#) (OR #8# #15# #17#) #8# (OR #8# #24=(AND (|HasCategory| |#3| (QUOTE (|DifferentialSpace|))) #17#)) (OR #25=(AND (|HasCategory| |#3| (QUOTE (|PartialDifferentialSpace| #16#))) #17#) #15#) #19# (OR (AND #1# #26=(|HasCategory| |#3| (QUOTE (|RetractableTo| (|Fraction| #21#))))) (AND #4# #26#) (AND #5# #26#) (AND #6# #26#) (AND #7# #26#) (AND #8# #26#) (AND #9# #26#) (AND #10# #26#) (AND #11# #26#) (AND #12# #26#) (AND #13# #26#) (AND #15# #26#) (AND #26# #17#) #27=(AND #26# #19#)) (OR #28=(AND #1# #29=(|HasCategory| |#3| (QUOTE (|RetractableTo| #21#)))) #30=(AND #4# #29#) #31=(AND #5# #29#) #32=(AND #6# #29#) #33=(AND #7# #29#) #34=(AND #8# #29#) #35=(AND #12# #29#) #36=(AND #13# #29#) #37=(AND #15# #29#) #38=(AND #29# #19#) #39=(AND #9# #29#) #40=(AND #10# #29#) #41=(AND #11# #29#) #17#) (OR #28# #30# #31# #32# #33# #34# #35# #36# #37# #38# #39# #40# #41# (AND #29# #17#)) #23# (|HasCategory| #21# #14#) #22# #24# #25# (OR #38# #17#) #38# #27# (AND #8# #17#) (AND #15# #17#) #7# #4# #6# #5# #18# (AND #23# (|HasCategory| $ (|%list| (QUOTE |FiniteAggregate|) #3#))) (|HasCategory| $ (|%list| (QUOTE |ShallowlyMutableAggregate|) #3#))) (|SturmHabichtPackage| R |x|) ((|constructor| (NIL "This package produces functions for counting etc. real roots of univariate polynomials in \\spad{x} over \\spad{R},{} which must be an OrderedIntegralDomain")) (|countRealRootsMultiple| (((|Integer|) (|UnivariatePolynomial| |#2| |#1|)) "\\spad{countRealRootsMultiple(p)} says how many real roots \\spad{p} has,{} counted with multiplicity")) (|SturmHabichtMultiple| (((|Integer|) (|UnivariatePolynomial| |#2| |#1|) (|UnivariatePolynomial| |#2| |#1|)) "\\spad{SturmHabichtMultiple(p1,p2)} computes c_{+}-c_{-} where c_{+} is the number of real roots of \\spad{p1} with \\spad{p2>0} and c_{-} is the number of real roots of \\spad{p1} with \\spad{p2<0}. If \\spad{p2=1} what you get is the number of real roots of \\spad{p1}.")) (|countRealRoots| (((|Integer|) (|UnivariatePolynomial| |#2| |#1|)) "\\spad{countRealRoots(p)} says how many real roots \\spad{p} has")) (|SturmHabicht| (((|Integer|) (|UnivariatePolynomial| |#2| |#1|) (|UnivariatePolynomial| |#2| |#1|)) "\\spad{SturmHabicht(p1,p2)} computes c_{+}-c_{-} where c_{+} is the number of real roots of \\spad{p1} with \\spad{p2>0} and c_{-} is the number of real roots of \\spad{p1} with \\spad{p2<0}. If \\spad{p2=1} what you get is the number of real roots of \\spad{p1}.")) (|SturmHabichtCoefficients| (((|List| |#1|) (|UnivariatePolynomial| |#2| |#1|) (|UnivariatePolynomial| |#2| |#1|)) "\\spad{SturmHabichtCoefficients(p1,p2)} computes the principal Sturm-Habicht coefficients of \\spad{p1} and \\spad{p2}")) (|SturmHabichtSequence| (((|List| (|UnivariatePolynomial| |#2| |#1|)) (|UnivariatePolynomial| |#2| |#1|) (|UnivariatePolynomial| |#2| |#1|)) "\\spad{SturmHabichtSequence(p1,p2)} computes the Sturm-Habicht sequence of \\spad{p1} and \\spad{p2}")) (|subresultantSequence| (((|List| (|UnivariatePolynomial| |#2| |#1|)) (|UnivariatePolynomial| |#2| |#1|) (|UnivariatePolynomial| |#2| |#1|)) "\\spad{subresultantSequence(p1,p2)} computes the (standard) subresultant sequence of \\spad{p1} and \\spad{p2}"))) NIL @@ -4077,8 +4077,8 @@ NIL NIL NIL (|SingleInteger|) -((|constructor| (NIL "SingleInteger is intended to support machine integer arithmetic.")) (|xor| (($ $ $) "\\spad{xor(n,m)} returns the bit-by-bit logical {\\em xor} of the single integers \\spad{n} and \\spad{m}.")) (|noetherian| ((|attribute|) "\\spad{noetherian} all ideals are finitely generated (in fact principal).")) (|canonicalsClosed| ((|attribute|) "\\spad{canonicalClosed} means two positives multiply to give positive.")) (|canonical| ((|attribute|) "\\spad{canonical} means that mathematical equality is implied by data structure equality."))) -((|noetherian| . T) (|canonicalsClosed| . T) (|canonical| . T) (|canonicalUnitNormal| . T) (|multiplicativeValuation| . T) (|noZeroDivisors| . T) ((|commutative| "*") . T) (|rightUnitary| . T) (|leftUnitary| . T) (|unitsKnown| . T)) +((|constructor| (NIL "SingleInteger is intended to support machine integer arithmetic.")) (|xor| (($ $ $) "\\spad{xor(n,m)} returns the bit-by-bit logical {\\em xor} of the single integers \\spad{n} and \\spad{m}.")) (|canonical| ((|attribute|) "\\spad{canonical} means that mathematical equality is implied by data structure equality."))) +((|canonical| . T) (|canonicalUnitNormal| . T) (|multiplicativeValuation| . T) (|noZeroDivisors| . T) ((|commutative| "*") . T)) NIL (|StackAggregate| S) ((|constructor| (NIL "A stack is a bag where the last item inserted is the first item extracted.")) (|depth| (((|NonNegativeInteger|) $) "\\spad{depth(s)} returns the number of elements of stack \\spad{s}. Note: \\axiom{depth(\\spad{s}) = \\#s}.")) (|top| ((|#1| $) "\\spad{top(s)} returns the top element \\spad{x} from \\spad{s}; \\spad{s} remains unchanged. Note: Use \\axiom{pop!(\\spad{s})} to obtain \\spad{x} and remove it from \\spad{s}.")) (|pop!| ((|#1| $) "\\spad{pop!(s)} returns the top element \\spad{x},{} destructively removing \\spad{x} from \\spad{s}. Note: Use \\axiom{top(\\spad{s})} to obtain \\spad{x} without removing it from \\spad{s}. Error: if \\spad{s} is empty.")) (|push!| ((|#1| |#1| $) "\\spad{push!(x,s)} pushes \\spad{x} onto stack \\spad{s},{} \\spadignore{i.e.} destructively changing \\spad{s} so as to have a new first (top) element \\spad{x}. Afterwards,{} pop!(\\spad{s}) produces \\spad{x} and pop!(\\spad{s}) produces the original \\spad{s}."))) @@ -4094,7 +4094,7 @@ NIL ((|HasCategory| |#3| (QUOTE (|Field|))) (|HasAttribute| |#3| (QUOTE (|commutative| "*"))) (|HasCategory| |#3| (QUOTE (|CommutativeRing|)))) (|SquareMatrixCategory| |ndim| R |Row| |Col|) ((|constructor| (NIL "\\spadtype{SquareMatrixCategory} is a general square matrix category which allows different representations and indexing schemes. Rows and columns may be extracted with rows returned as objects of type Row and colums returned as objects of type Col.")) (** (($ $ (|Integer|)) "\\spad{m**n} computes an integral power of the matrix \\spad{m}. Error: if the matrix is not invertible.")) (|inverse| (((|Union| $ "failed") $) "\\spad{inverse(m)} returns the inverse of the matrix \\spad{m},{} if that matrix is invertible and returns \"failed\" otherwise.")) (|minordet| ((|#2| $) "\\spad{minordet(m)} computes the determinant of the matrix \\spad{m} using minors.")) (|determinant| ((|#2| $) "\\spad{determinant(m)} returns the determinant of the matrix \\spad{m}.")) (* ((|#3| |#3| $) "\\spad{r * x} is the product of the row vector \\spad{r} and the matrix \\spad{x}. Error: if the dimensions are incompatible.") ((|#4| $ |#4|) "\\spad{x * c} is the product of the matrix \\spad{x} and the column vector \\spad{c}. Error: if the dimensions are incompatible.")) (|diagonalProduct| ((|#2| $) "\\spad{diagonalProduct(m)} returns the product of the elements on the diagonal of the matrix \\spad{m}.")) (|trace| ((|#2| $) "\\spad{trace(m)} returns the trace of the matrix \\spad{m}. this is the sum of the elements on the diagonal of the matrix \\spad{m}.")) (|diagonal| ((|#3| $) "\\spad{diagonal(m)} returns a row consisting of the elements on the diagonal of the matrix \\spad{m}.")) (|diagonalMatrix| (($ (|List| |#2|)) "\\spad{diagonalMatrix(l)} returns a diagonal matrix with the elements of \\spad{l} on the diagonal.")) (|scalarMatrix| (($ |#2|) "\\spad{scalarMatrix(r)} returns an \\spad{n}-by-\\spad{n} matrix with \\spad{r}'s on the diagonal and zeroes elsewhere."))) -((|rightUnitary| . T) (|leftUnitary| . T) (|unitsKnown| . T)) +NIL NIL (|SmithNormalForm| R |Row| |Col| M) ((|constructor| (NIL "\\spadtype{SmithNormalForm} is a package which provides some standard canonical forms for matrices.")) (|diophantineSystem| (((|Record| (|:| |particular| (|Union| |#3| "failed")) (|:| |basis| (|List| |#3|))) |#4| |#3|) "\\spad{diophantineSystem(A,B)} returns a particular integer solution and an integer basis of the equation \\spad{AX = B}.")) (|completeSmith| (((|Record| (|:| |Smith| |#4|) (|:| |leftEqMat| |#4|) (|:| |rightEqMat| |#4|)) |#4|) "\\spad{completeSmith} returns a record that contains the Smith normal form \\spad{H} of the matrix and the left and right equivalence matrices \\spad{U} and \\spad{V} such that U*m*v = \\spad{H}")) (|smith| ((|#4| |#4|) "\\spad{smith(m)} returns the Smith Normal form of the matrix \\spad{m}.")) (|completeHermite| (((|Record| (|:| |Hermite| |#4|) (|:| |eqMat| |#4|)) |#4|) "\\spad{completeHermite} returns a record that contains the Hermite normal form \\spad{H} of the matrix and the equivalence matrix \\spad{U} such that U*m = \\spad{H}")) (|hermite| ((|#4| |#4|) "\\spad{hermite(m)} returns the Hermite normal form of the matrix \\spad{m}."))) @@ -4102,12 +4102,12 @@ NIL NIL (|SparseMultivariatePolynomial| R |VarSet|) ((|constructor| (NIL "\\indented{2}{This type is the basic representation of sparse recursive multivariate} polynomials. It is parameterized by the coefficient ring and the variable set which may be infinite. The variable ordering is determined by the variable set parameter. The coefficient ring may be non-commutative,{} but the variables are assumed to commute."))) -(((|commutative| "*") |has| |#1| (|CommutativeRing|)) (|noZeroDivisors| |has| |#1| (|IntegralDomain|)) (|canonicalUnitNormal| |has| |#1| (ATTRIBUTE |canonicalUnitNormal|)) (|leftUnitary| . T) (|rightUnitary| . T) (|unitsKnown| . T)) -(#1=(|HasCategory| |#1| (QUOTE (|PolynomialFactorizationExplicit|))) (OR #2=(|HasCategory| |#1| (QUOTE (|CommutativeRing|))) #3=(|HasCategory| |#1| (QUOTE (|GcdDomain|))) #4=(|HasCategory| |#1| (QUOTE (|IntegralDomain|))) #1#) (OR #3# #4# #1#) (OR #3# #1#) #4# #2# (OR #2# #4#) (AND (|HasCategory| |#1| #5=(QUOTE (|PatternMatchable| #6=(|Float|)))) (|HasCategory| |#2| #5#)) (AND (|HasCategory| |#1| #7=(QUOTE (|PatternMatchable| #8=(|Integer|)))) (|HasCategory| |#2| #7#)) (AND (|HasCategory| |#1| #9=(QUOTE (|ConvertibleTo| (|Pattern| #6#)))) (|HasCategory| |#2| #9#)) (AND (|HasCategory| |#1| #10=(QUOTE (|ConvertibleTo| (|Pattern| #8#)))) (|HasCategory| |#2| #10#)) (AND (|HasCategory| |#1| #11=(QUOTE (|ConvertibleTo| (|InputForm|)))) (|HasCategory| |#2| #11#)) (|HasCategory| |#1| (QUOTE (|LinearlyExplicitRingOver| #8#))) (|HasCategory| |#1| (QUOTE (|CharacteristicZero|))) #12=(|HasCategory| |#1| #13=(QUOTE (|CharacteristicNonZero|))) #14=(|HasCategory| |#1| (QUOTE (|Algebra| #15=(|Fraction| #8#)))) (|HasCategory| |#1| (QUOTE (|RetractableTo| #8#))) (OR #14# #16=(|HasCategory| |#1| (QUOTE (|RetractableTo| #15#)))) #16# (|HasCategory| |#1| (QUOTE (|Field|))) (|HasAttribute| |#1| (QUOTE |canonicalUnitNormal|)) #3# #17=(AND #1# (|HasCategory| $ #13#)) (OR #17# #12#)) +(((|commutative| "*") |has| |#1| (|CommutativeRing|)) (|noZeroDivisors| |has| |#1| (|IntegralDomain|)) (|canonicalUnitNormal| |has| |#1| (ATTRIBUTE |canonicalUnitNormal|))) +(#1=(|HasCategory| |#1| (QUOTE (|PolynomialFactorizationExplicit|))) (OR #2=(|HasCategory| |#1| (QUOTE (|CommutativeRing|))) #3=(|HasCategory| |#1| (QUOTE (|GcdDomain|))) #4=(|HasCategory| |#1| (QUOTE (|IntegralDomain|))) #1#) (OR #3# #4# #1#) (OR #3# #1#) #4# #2# (OR #2# #4#) (AND (|HasCategory| |#1| #5=(QUOTE (|PatternMatchable| #6=(|Float|)))) (|HasCategory| |#2| #5#)) (AND (|HasCategory| |#1| #7=(QUOTE (|PatternMatchable| #8=(|Integer|)))) (|HasCategory| |#2| #7#)) (AND (|HasCategory| |#1| #9=(QUOTE (|ConvertibleTo| (|Pattern| #6#)))) (|HasCategory| |#2| #9#)) (AND (|HasCategory| |#1| #10=(QUOTE (|ConvertibleTo| (|Pattern| #8#)))) (|HasCategory| |#2| #10#)) (AND (|HasCategory| |#1| #11=(QUOTE (|ConvertibleTo| (|InputForm|)))) (|HasCategory| |#2| #11#)) (|HasCategory| |#1| (QUOTE (|LinearlyExplicitRingOver| #8#))) #12=(|HasCategory| |#1| (QUOTE (|Algebra| #13=(|Fraction| #8#)))) #14=(|HasCategory| |#1| #15=(QUOTE (|CharacteristicNonZero|))) (|HasCategory| |#1| (QUOTE (|CharacteristicZero|))) (|HasCategory| |#1| (QUOTE (|RetractableTo| #8#))) (OR #12# #16=(|HasCategory| |#1| (QUOTE (|RetractableTo| #13#)))) #16# (|HasCategory| |#1| (QUOTE (|Field|))) (|HasAttribute| |#1| (QUOTE |canonicalUnitNormal|)) #3# #17=(AND #1# (|HasCategory| $ #15#)) (OR #17# #14#)) (|SparseMultivariateTaylorSeries| |Coef| |Var| SMP) ((|constructor| (NIL "This domain provides multivariate Taylor series with variables from an arbitrary ordered set. A Taylor series is represented by a stream of polynomials from the polynomial domain SMP. The \\spad{n}th element of the stream is a form of degree \\spad{n}. SMTS is an internal domain.")) (|fintegrate| (($ (|Mapping| $) |#2| |#1|) "\\spad{fintegrate(f,v,c)} is the integral of \\spad{f()} with respect \\indented{1}{to \\spad{v} and having \\spad{c} as the constant of integration.} \\indented{1}{The evaluation of \\spad{f()} is delayed.}")) (|integrate| (($ $ |#2| |#1|) "\\spad{integrate(s,v,c)} is the integral of \\spad{s} with respect \\indented{1}{to \\spad{v} and having \\spad{c} as the constant of integration.}")) (|csubst| (((|Mapping| (|Stream| |#3|) |#3|) (|List| |#2|) (|List| (|Stream| |#3|))) "\\spad{csubst(a,b)} is for internal use only")) (* (($ |#3| $) "\\spad{smp*ts} multiplies a TaylorSeries by a monomial SMP.")) (|coerce| (($ |#3|) "\\spad{coerce(poly)} regroups the terms by total degree and forms a series.") (($ |#2|) "\\spad{coerce(var)} converts a variable to a Taylor series")) (|coefficient| ((|#3| $ (|NonNegativeInteger|)) "\\spad{coefficient(s, n)} gives the terms of total degree \\spad{n}."))) -(((|commutative| "*") |has| |#1| (|CommutativeRing|)) (|noZeroDivisors| |has| |#1| (|IntegralDomain|)) (|leftUnitary| . T) (|rightUnitary| . T) (|unitsKnown| . T)) -((|HasCategory| |#1| (QUOTE (|Algebra| (|Fraction| (|Integer|))))) #1=(|HasCategory| |#1| (QUOTE (|CommutativeRing|))) (|HasCategory| |#1| (QUOTE (|CharacteristicZero|))) (|HasCategory| |#1| (QUOTE (|CharacteristicNonZero|))) (OR #1# #2=(|HasCategory| |#1| (QUOTE (|IntegralDomain|)))) #2# (|HasCategory| |#1| (QUOTE (|Field|)))) +(((|commutative| "*") |has| |#1| (|CommutativeRing|)) (|noZeroDivisors| |has| |#1| (|IntegralDomain|))) +((|HasCategory| |#1| (QUOTE (|Algebra| (|Fraction| (|Integer|))))) #1=(|HasCategory| |#1| (QUOTE (|IntegralDomain|))) #2=(|HasCategory| |#1| (QUOTE (|CommutativeRing|))) (OR #2# #1#) (|HasCategory| |#1| (QUOTE (|CharacteristicNonZero|))) (|HasCategory| |#1| (QUOTE (|CharacteristicZero|))) (|HasCategory| |#1| (QUOTE (|Field|)))) (|SquareFreeNormalizedTriangularSetCategory| R E V P) ((|constructor| (NIL "The category of square-free and normalized triangular sets. Thus,{} up to the primitivity axiom of [1],{} these sets are Lazard triangular sets.\\newline References : \\indented{1}{[1] \\spad{D}. LAZARD \"A new method for solving algebraic systems of} \\indented{5}{positive dimension\" Discr. App. Math. 33:147-160,{}1991}"))) NIL @@ -4137,7 +4137,7 @@ NIL NIL NIL (|ThreeSpaceCategory| R) -((|constructor| (NIL "The category ThreeSpaceCategory is used for creating three dimensional objects using functions for defining points,{} curves,{} polygons,{} constructs and the subspaces containing them.")) (|coerce| (((|OutputForm|) $) "\\spad{coerce(s)} returns the \\spadtype{ThreeSpace} \\spad{s} to Output format.")) (|subspace| (((|SubSpace| 3 |#1|) $) "\\spad{subspace(s)} returns the \\spadtype{SubSpace} which holds all the point information in the \\spadtype{ThreeSpace},{} \\spad{s}.")) (|check| (($ $) "\\spad{check(s)} returns lllpt,{} list of lists of lists of point information about the \\spadtype{ThreeSpace} \\spad{s}.")) (|objects| (((|Record| (|:| |points| (|NonNegativeInteger|)) (|:| |curves| (|NonNegativeInteger|)) (|:| |polygons| (|NonNegativeInteger|)) (|:| |constructs| (|NonNegativeInteger|))) $) "\\spad{objects(s)} returns the \\spadtype{ThreeSpace},{} \\spad{s},{} in the form of a 3D object record containing information on the number of points,{} curves,{} polygons and constructs comprising the \\spadtype{ThreeSpace}..")) (|lprop| (((|List| (|SubSpaceComponentProperty|)) $) "\\spad{lprop(s)} checks to see if the \\spadtype{ThreeSpace},{} \\spad{s},{} is composed of a list of subspace component properties,{} and if so,{} returns the list; An error is signaled otherwise.")) (|llprop| (((|List| (|List| (|SubSpaceComponentProperty|))) $) "\\spad{llprop(s)} checks to see if the \\spadtype{ThreeSpace},{} \\spad{s},{} is composed of a list of curves which are lists of the subspace component properties of the curves,{} and if so,{} returns the list of lists; An error is signaled otherwise.")) (|lllp| (((|List| (|List| (|List| (|Point| |#1|)))) $) "\\spad{lllp(s)} checks to see if the \\spadtype{ThreeSpace},{} \\spad{s},{} is composed of a list of components,{} which are lists of curves,{} which are lists of points,{} and if so,{} returns the list of lists of lists; An error is signaled otherwise.")) (|lllip| (((|List| (|List| (|List| (|NonNegativeInteger|)))) $) "\\spad{lllip(s)} checks to see if the \\spadtype{ThreeSpace},{} \\spad{s},{} is composed of a list of components,{} which are lists of curves,{} which are lists of indices to points,{} and if so,{} returns the list of lists of lists; An error is signaled otherwise.")) (|lp| (((|List| (|Point| |#1|)) $) "\\spad{lp(s)} returns the list of points component which the \\spadtype{ThreeSpace},{} \\spad{s},{} contains; these points are used by reference,{} \\spadignore{i.e.} the component holds indices referring to the points rather than the points themselves. This allows for sharing of the points.")) (|mesh?| (((|Boolean|) $) "\\spad{mesh?(s)} returns \\spad{true} if the \\spadtype{ThreeSpace} \\spad{s} is composed of one component,{} a mesh comprising a list of curves which are lists of points,{} or returns \\spad{false} if otherwise")) (|mesh| (((|List| (|List| (|Point| |#1|))) $) "\\spad{mesh(s)} checks to see if the \\spadtype{ThreeSpace},{} \\spad{s},{} is composed of a single surface component defined by a list curves which contain lists of points,{} and if so,{} returns the list of lists of points; An error is signaled otherwise.") (($ (|List| (|List| (|Point| |#1|))) (|Boolean|) (|Boolean|)) "\\spad{mesh([[p0],[p1],...,[pn]], close1, close2)} creates a surface defined over a list of curves,{} \\spad{p0} through pn,{} which are lists of points; the booleans \\spad{close1} and \\spad{close2} indicate how the surface is to be closed: \\spad{close1} set to \\spad{true} means that each individual list (a curve) is to be closed (that is,{} the last point of the list is to be connected to the first point); \\spad{close2} set to \\spad{true} means that the boundary at one end of the surface is to be connected to the boundary at the other end (the boundaries are defined as the first list of points (curve) and the last list of points (curve)); the \\spadtype{ThreeSpace} containing this surface is returned.") (($ (|List| (|List| (|Point| |#1|)))) "\\spad{mesh([[p0],[p1],...,[pn]])} creates a surface defined by a list of curves which are lists,{} \\spad{p0} through pn,{} of points,{} and returns a \\spadtype{ThreeSpace} whose component is the surface.") (($ $ (|List| (|List| (|List| |#1|))) (|Boolean|) (|Boolean|)) "\\spad{mesh(s,[ [[r10]...,[r1m]], [[r20]...,[r2m]],..., [[rn0]...,[rnm]] ], close1, close2)} adds a surface component to the \\spadtype{ThreeSpace} \\spad{s},{} which is defined over a rectangular domain of size WxH where \\spad{W} is the number of lists of points from the domain \\spad{PointDomain(R)} and \\spad{H} is the number of elements in each of those lists; the booleans \\spad{close1} and \\spad{close2} indicate how the surface is to be closed: if \\spad{close1} is \\spad{true} this means that each individual list (a curve) is to be closed (\\spadignore{i.e.} the last point of the list is to be connected to the first point); if \\spad{close2} is \\spad{true},{} this means that the boundary at one end of the surface is to be connected to the boundary at the other end (the boundaries are defined as the first list of points (curve) and the last list of points (curve)).") (($ $ (|List| (|List| (|Point| |#1|))) (|Boolean|) (|Boolean|)) "\\spad{mesh(s,[[p0],[p1],...,[pn]], close1, close2)} adds a surface component to the \\spadtype{ThreeSpace},{} which is defined over a list of curves,{} in which each of these curves is a list of points. The boolean arguments \\spad{close1} and \\spad{close2} indicate how the surface is to be closed. Argument \\spad{close1} equal \\spad{true} means that each individual list (a curve) is to be closed,{} \\spadignore{i.e.} the last point of the list is to be connected to the first point. Argument \\spad{close2} equal \\spad{true} means that the boundary at one end of the surface is to be connected to the boundary at the other end,{} \\spadignore{i.e.} the boundaries are defined as the first list of points (curve) and the last list of points (curve).") (($ $ (|List| (|List| (|List| |#1|))) (|List| (|SubSpaceComponentProperty|)) (|SubSpaceComponentProperty|)) "\\spad{mesh(s,[ [[r10]...,[r1m]], [[r20]...,[r2m]],..., [[rn0]...,[rnm]] ], [props], prop)} adds a surface component to the \\spadtype{ThreeSpace} \\spad{s},{} which is defined over a rectangular domain of size WxH where \\spad{W} is the number of lists of points from the domain \\spad{PointDomain(R)} and \\spad{H} is the number of elements in each of those lists; lprops is the list of the subspace component properties for each curve list,{} and prop is the subspace component property by which the points are defined.") (($ $ (|List| (|List| (|Point| |#1|))) (|List| (|SubSpaceComponentProperty|)) (|SubSpaceComponentProperty|)) "\\spad{mesh(s,[[p0],[p1],...,[pn]],[props],prop)} adds a surface component,{} defined over a list curves which contains lists of points,{} to the \\spadtype{ThreeSpace} \\spad{s}; props is a list which contains the subspace component properties for each surface parameter,{} and \\spad{prop} is the subspace component property by which the points are defined.")) (|polygon?| (((|Boolean|) $) "\\spad{polygon?(s)} returns \\spad{true} if the \\spadtype{ThreeSpace} \\spad{s} contains a single polygon component,{} or \\spad{false} otherwise.")) (|polygon| (((|List| (|Point| |#1|)) $) "\\spad{polygon(s)} checks to see if the \\spadtype{ThreeSpace},{} \\spad{s},{} is composed of a single polygon component defined by a list of points,{} and if so,{} returns the list of points; An error is signaled otherwise.") (($ (|List| (|Point| |#1|))) "\\spad{polygon([p0,p1,...,pn])} creates a polygon defined by a list of points,{} \\spad{p0} through pn,{} and returns a \\spadtype{ThreeSpace} whose component is the polygon.") (($ $ (|List| (|List| |#1|))) "\\spad{polygon(s,[[r0],[r1],...,[rn]])} adds a polygon component defined by a list of points \\spad{r0} through \\spad{rn},{} which are lists of elements from the domain \\spad{PointDomain(m,R)} to the \\spadtype{ThreeSpace} \\spad{s},{} where \\spad{m} is the dimension of the points and \\spad{R} is the \\spadtype{Ring} over which the points are defined.") (($ $ (|List| (|Point| |#1|))) "\\spad{polygon(s,[p0,p1,...,pn])} adds a polygon component defined by a list of points,{} \\spad{p0} throught pn,{} to the \\spadtype{ThreeSpace} \\spad{s}.")) (|closedCurve?| (((|Boolean|) $) "\\spad{closedCurve?(s)} returns \\spad{true} if the \\spadtype{ThreeSpace} \\spad{s} contains a single closed curve component,{} \\spadignore{i.e.} the first element of the curve is also the last element,{} or \\spad{false} otherwise.")) (|closedCurve| (((|List| (|Point| |#1|)) $) "\\spad{closedCurve(s)} checks to see if the \\spadtype{ThreeSpace},{} \\spad{s},{} is composed of a single closed curve component defined by a list of points in which the first point is also the last point,{} all of which are from the domain \\spad{PointDomain(m,R)} and if so,{} returns the list of points. An error is signaled otherwise.") (($ (|List| (|Point| |#1|))) "\\spad{closedCurve(lp)} sets a list of points defined by the first element of \\spad{lp} through the last element of \\spad{lp} and back to the first elelment again and returns a \\spadtype{ThreeSpace} whose component is the closed curve defined by \\spad{lp}.") (($ $ (|List| (|List| |#1|))) "\\spad{closedCurve(s,[[lr0],[lr1],...,[lrn],[lr0]])} adds a closed curve component defined by a list of points \\spad{lr0} through \\spad{lrn},{} which are lists of elements from the domain \\spad{PointDomain(m,R)},{} where \\spad{R} is the \\spadtype{Ring} over which the point elements are defined and \\spad{m} is the dimension of the points,{} in which the last element of the list of points contains a copy of the first element list,{} \\spad{lr0}. The closed curve is added to the \\spadtype{ThreeSpace},{} \\spad{s}.") (($ $ (|List| (|Point| |#1|))) "\\spad{closedCurve(s,[p0,p1,...,pn,p0])} adds a closed curve component which is a list of points defined by the first element \\spad{p0} through the last element \\spad{pn} and back to the first element \\spad{p0} again,{} to the \\spadtype{ThreeSpace} \\spad{s}.")) (|curve?| (((|Boolean|) $) "\\spad{curve?(s)} queries whether the \\spadtype{ThreeSpace},{} \\spad{s},{} is a curve,{} \\spadignore{i.e.} has one component,{} a list of list of points,{} and returns \\spad{true} if it is,{} or \\spad{false} otherwise.")) (|curve| (((|List| (|Point| |#1|)) $) "\\spad{curve(s)} checks to see if the \\spadtype{ThreeSpace},{} \\spad{s},{} is composed of a single curve defined by a list of points and if so,{} returns the curve,{} \\spadignore{i.e.} list of points. An error is signaled otherwise.") (($ (|List| (|Point| |#1|))) "\\spad{curve([p0,p1,p2,...,pn])} creates a space curve defined by the list of points \\spad{p0} through \\spad{pn},{} and returns the \\spadtype{ThreeSpace} whose component is the curve.") (($ $ (|List| (|List| |#1|))) "\\spad{curve(s,[[p0],[p1],...,[pn]])} adds a space curve which is a list of points \\spad{p0} through pn defined by lists of elements from the domain \\spad{PointDomain(m,R)},{} where \\spad{R} is the \\spadtype{Ring} over which the point elements are defined and \\spad{m} is the dimension of the points,{} to the \\spadtype{ThreeSpace} \\spad{s}.") (($ $ (|List| (|Point| |#1|))) "\\spad{curve(s,[p0,p1,...,pn])} adds a space curve component defined by a list of points \\spad{p0} through \\spad{pn},{} to the \\spadtype{ThreeSpace} \\spad{s}.")) (|point?| (((|Boolean|) $) "\\spad{point?(s)} queries whether the \\spadtype{ThreeSpace},{} \\spad{s},{} is composed of a single component which is a point and returns the boolean result.")) (|point| (((|Point| |#1|) $) "\\spad{point(s)} checks to see if the \\spadtype{ThreeSpace},{} \\spad{s},{} is composed of only a single point and if so,{} returns the point. An error is signaled otherwise.") (($ (|Point| |#1|)) "\\spad{point(p)} returns a \\spadtype{ThreeSpace} object which is composed of one component,{} the point \\spad{p}.") (($ $ (|NonNegativeInteger|)) "\\spad{point(s,i)} adds a point component which is placed into a component list of the \\spadtype{ThreeSpace},{} \\spad{s},{} at the index given by \\spad{i}.") (($ $ (|List| |#1|)) "\\spad{point(s,[x,y,z])} adds a point component defined by a list of elements which are from the \\spad{PointDomain(R)} to the \\spadtype{ThreeSpace},{} \\spad{s},{} where \\spad{R} is the \\spadtype{Ring} over which the point elements are defined.") (($ $ (|Point| |#1|)) "\\spad{point(s,p)} adds a point component defined by the point,{} \\spad{p},{} specified as a list from \\spad{List(R)},{} to the \\spadtype{ThreeSpace},{} \\spad{s},{} where \\spad{R} is the \\spadtype{Ring} over which the point is defined.")) (|modifyPointData| (($ $ (|NonNegativeInteger|) (|Point| |#1|)) "\\spad{modifyPointData(s,i,p)} changes the point at the indexed location \\spad{i} in the \\spadtype{ThreeSpace},{} \\spad{s},{} to that of point \\spad{p}. This is useful for making changes to a point which has been transformed.")) (|enterPointData| (((|NonNegativeInteger|) $ (|List| (|Point| |#1|))) "\\spad{enterPointData(s,[p0,p1,...,pn])} adds a list of points from \\spad{p0} through pn to the \\spadtype{ThreeSpace},{} \\spad{s},{} and returns the index,{} to the starting point of the list.")) (|copy| (($ $) "\\spad{copy(s)} returns a new \\spadtype{ThreeSpace} that is an exact copy of \\spad{s}.")) (|composites| (((|List| $) $) "\\spad{composites(s)} takes the \\spadtype{ThreeSpace} \\spad{s},{} and creates a list containing a unique \\spadtype{ThreeSpace} for each single composite of \\spad{s}. If \\spad{s} has no composites defined (composites need to be explicitly created),{} the list returned is empty. Note that not all the components need to be part of a composite.")) (|components| (((|List| $) $) "\\spad{components(s)} takes the \\spadtype{ThreeSpace} \\spad{s},{} and creates a list containing a unique \\spadtype{ThreeSpace} for each single component of \\spad{s}. If \\spad{s} has no components defined,{} the list returned is empty.")) (|composite| (($ (|List| $)) "\\spad{composite([s1,s2,...,sn])} will create a new \\spadtype{ThreeSpace} that is a union of all the components from each \\spadtype{ThreeSpace} in the parameter list,{} grouped as a composite.")) (|merge| (($ $ $) "\\spad{merge(s1,s2)} will create a new \\spadtype{ThreeSpace} that has the components of \\spad{s1} and \\spad{s2}; Groupings of components into composites are maintained.") (($ (|List| $)) "\\spad{merge([s1,s2,...,sn])} will create a new \\spadtype{ThreeSpace} that has the components of all the ones in the list; Groupings of components into composites are maintained.")) (|numberOfComposites| (((|NonNegativeInteger|) $) "\\spad{numberOfComposites(s)} returns the number of supercomponents,{} or composites,{} in the \\spadtype{ThreeSpace},{} \\spad{s}; Composites are arbitrary groupings of otherwise distinct and unrelated components; A \\spadtype{ThreeSpace} need not have any composites defined at all and,{} outside of the requirement that no component can belong to more than one composite at a time,{} the definition and interpretation of composites are unrestricted.")) (|numberOfComponents| (((|NonNegativeInteger|) $) "\\spad{numberOfComponents(s)} returns the number of distinct object components in the indicated \\spadtype{ThreeSpace},{} \\spad{s},{} such as points,{} curves,{} polygons,{} and constructs.")) (|create3Space| (($ (|SubSpace| 3 |#1|)) "\\spad{create3Space(s)} creates a \\spadtype{ThreeSpace} object containing objects pre-defined within some \\spadtype{SubSpace} \\spad{s}.") (($) "\\spad{create3Space()} creates a \\spadtype{ThreeSpace} object capable of holding point,{} curve,{} mesh components and any combination."))) +((|constructor| (NIL "The category ThreeSpaceCategory is used for creating three dimensional objects using functions for defining points,{} curves,{} polygons,{} constructs and the subspaces containing them.")) (|subspace| (((|SubSpace| 3 |#1|) $) "\\spad{subspace(s)} returns the \\spadtype{SubSpace} which holds all the point information in the \\spadtype{ThreeSpace},{} \\spad{s}.")) (|check| (($ $) "\\spad{check(s)} returns lllpt,{} list of lists of lists of point information about the \\spadtype{ThreeSpace} \\spad{s}.")) (|objects| (((|Record| (|:| |points| (|NonNegativeInteger|)) (|:| |curves| (|NonNegativeInteger|)) (|:| |polygons| (|NonNegativeInteger|)) (|:| |constructs| (|NonNegativeInteger|))) $) "\\spad{objects(s)} returns the \\spadtype{ThreeSpace},{} \\spad{s},{} in the form of a 3D object record containing information on the number of points,{} curves,{} polygons and constructs comprising the \\spadtype{ThreeSpace}..")) (|lprop| (((|List| (|SubSpaceComponentProperty|)) $) "\\spad{lprop(s)} checks to see if the \\spadtype{ThreeSpace},{} \\spad{s},{} is composed of a list of subspace component properties,{} and if so,{} returns the list; An error is signaled otherwise.")) (|llprop| (((|List| (|List| (|SubSpaceComponentProperty|))) $) "\\spad{llprop(s)} checks to see if the \\spadtype{ThreeSpace},{} \\spad{s},{} is composed of a list of curves which are lists of the subspace component properties of the curves,{} and if so,{} returns the list of lists; An error is signaled otherwise.")) (|lllp| (((|List| (|List| (|List| (|Point| |#1|)))) $) "\\spad{lllp(s)} checks to see if the \\spadtype{ThreeSpace},{} \\spad{s},{} is composed of a list of components,{} which are lists of curves,{} which are lists of points,{} and if so,{} returns the list of lists of lists; An error is signaled otherwise.")) (|lllip| (((|List| (|List| (|List| (|NonNegativeInteger|)))) $) "\\spad{lllip(s)} checks to see if the \\spadtype{ThreeSpace},{} \\spad{s},{} is composed of a list of components,{} which are lists of curves,{} which are lists of indices to points,{} and if so,{} returns the list of lists of lists; An error is signaled otherwise.")) (|lp| (((|List| (|Point| |#1|)) $) "\\spad{lp(s)} returns the list of points component which the \\spadtype{ThreeSpace},{} \\spad{s},{} contains; these points are used by reference,{} \\spadignore{i.e.} the component holds indices referring to the points rather than the points themselves. This allows for sharing of the points.")) (|mesh?| (((|Boolean|) $) "\\spad{mesh?(s)} returns \\spad{true} if the \\spadtype{ThreeSpace} \\spad{s} is composed of one component,{} a mesh comprising a list of curves which are lists of points,{} or returns \\spad{false} if otherwise")) (|mesh| (((|List| (|List| (|Point| |#1|))) $) "\\spad{mesh(s)} checks to see if the \\spadtype{ThreeSpace},{} \\spad{s},{} is composed of a single surface component defined by a list curves which contain lists of points,{} and if so,{} returns the list of lists of points; An error is signaled otherwise.") (($ (|List| (|List| (|Point| |#1|))) (|Boolean|) (|Boolean|)) "\\spad{mesh([[p0],[p1],...,[pn]], close1, close2)} creates a surface defined over a list of curves,{} \\spad{p0} through pn,{} which are lists of points; the booleans \\spad{close1} and \\spad{close2} indicate how the surface is to be closed: \\spad{close1} set to \\spad{true} means that each individual list (a curve) is to be closed (that is,{} the last point of the list is to be connected to the first point); \\spad{close2} set to \\spad{true} means that the boundary at one end of the surface is to be connected to the boundary at the other end (the boundaries are defined as the first list of points (curve) and the last list of points (curve)); the \\spadtype{ThreeSpace} containing this surface is returned.") (($ (|List| (|List| (|Point| |#1|)))) "\\spad{mesh([[p0],[p1],...,[pn]])} creates a surface defined by a list of curves which are lists,{} \\spad{p0} through pn,{} of points,{} and returns a \\spadtype{ThreeSpace} whose component is the surface.") (($ $ (|List| (|List| (|List| |#1|))) (|Boolean|) (|Boolean|)) "\\spad{mesh(s,[ [[r10]...,[r1m]], [[r20]...,[r2m]],..., [[rn0]...,[rnm]] ], close1, close2)} adds a surface component to the \\spadtype{ThreeSpace} \\spad{s},{} which is defined over a rectangular domain of size WxH where \\spad{W} is the number of lists of points from the domain \\spad{PointDomain(R)} and \\spad{H} is the number of elements in each of those lists; the booleans \\spad{close1} and \\spad{close2} indicate how the surface is to be closed: if \\spad{close1} is \\spad{true} this means that each individual list (a curve) is to be closed (\\spadignore{i.e.} the last point of the list is to be connected to the first point); if \\spad{close2} is \\spad{true},{} this means that the boundary at one end of the surface is to be connected to the boundary at the other end (the boundaries are defined as the first list of points (curve) and the last list of points (curve)).") (($ $ (|List| (|List| (|Point| |#1|))) (|Boolean|) (|Boolean|)) "\\spad{mesh(s,[[p0],[p1],...,[pn]], close1, close2)} adds a surface component to the \\spadtype{ThreeSpace},{} which is defined over a list of curves,{} in which each of these curves is a list of points. The boolean arguments \\spad{close1} and \\spad{close2} indicate how the surface is to be closed. Argument \\spad{close1} equal \\spad{true} means that each individual list (a curve) is to be closed,{} \\spadignore{i.e.} the last point of the list is to be connected to the first point. Argument \\spad{close2} equal \\spad{true} means that the boundary at one end of the surface is to be connected to the boundary at the other end,{} \\spadignore{i.e.} the boundaries are defined as the first list of points (curve) and the last list of points (curve).") (($ $ (|List| (|List| (|List| |#1|))) (|List| (|SubSpaceComponentProperty|)) (|SubSpaceComponentProperty|)) "\\spad{mesh(s,[ [[r10]...,[r1m]], [[r20]...,[r2m]],..., [[rn0]...,[rnm]] ], [props], prop)} adds a surface component to the \\spadtype{ThreeSpace} \\spad{s},{} which is defined over a rectangular domain of size WxH where \\spad{W} is the number of lists of points from the domain \\spad{PointDomain(R)} and \\spad{H} is the number of elements in each of those lists; lprops is the list of the subspace component properties for each curve list,{} and prop is the subspace component property by which the points are defined.") (($ $ (|List| (|List| (|Point| |#1|))) (|List| (|SubSpaceComponentProperty|)) (|SubSpaceComponentProperty|)) "\\spad{mesh(s,[[p0],[p1],...,[pn]],[props],prop)} adds a surface component,{} defined over a list curves which contains lists of points,{} to the \\spadtype{ThreeSpace} \\spad{s}; props is a list which contains the subspace component properties for each surface parameter,{} and \\spad{prop} is the subspace component property by which the points are defined.")) (|polygon?| (((|Boolean|) $) "\\spad{polygon?(s)} returns \\spad{true} if the \\spadtype{ThreeSpace} \\spad{s} contains a single polygon component,{} or \\spad{false} otherwise.")) (|polygon| (((|List| (|Point| |#1|)) $) "\\spad{polygon(s)} checks to see if the \\spadtype{ThreeSpace},{} \\spad{s},{} is composed of a single polygon component defined by a list of points,{} and if so,{} returns the list of points; An error is signaled otherwise.") (($ (|List| (|Point| |#1|))) "\\spad{polygon([p0,p1,...,pn])} creates a polygon defined by a list of points,{} \\spad{p0} through pn,{} and returns a \\spadtype{ThreeSpace} whose component is the polygon.") (($ $ (|List| (|List| |#1|))) "\\spad{polygon(s,[[r0],[r1],...,[rn]])} adds a polygon component defined by a list of points \\spad{r0} through \\spad{rn},{} which are lists of elements from the domain \\spad{PointDomain(m,R)} to the \\spadtype{ThreeSpace} \\spad{s},{} where \\spad{m} is the dimension of the points and \\spad{R} is the \\spadtype{Ring} over which the points are defined.") (($ $ (|List| (|Point| |#1|))) "\\spad{polygon(s,[p0,p1,...,pn])} adds a polygon component defined by a list of points,{} \\spad{p0} throught pn,{} to the \\spadtype{ThreeSpace} \\spad{s}.")) (|closedCurve?| (((|Boolean|) $) "\\spad{closedCurve?(s)} returns \\spad{true} if the \\spadtype{ThreeSpace} \\spad{s} contains a single closed curve component,{} \\spadignore{i.e.} the first element of the curve is also the last element,{} or \\spad{false} otherwise.")) (|closedCurve| (((|List| (|Point| |#1|)) $) "\\spad{closedCurve(s)} checks to see if the \\spadtype{ThreeSpace},{} \\spad{s},{} is composed of a single closed curve component defined by a list of points in which the first point is also the last point,{} all of which are from the domain \\spad{PointDomain(m,R)} and if so,{} returns the list of points. An error is signaled otherwise.") (($ (|List| (|Point| |#1|))) "\\spad{closedCurve(lp)} sets a list of points defined by the first element of \\spad{lp} through the last element of \\spad{lp} and back to the first elelment again and returns a \\spadtype{ThreeSpace} whose component is the closed curve defined by \\spad{lp}.") (($ $ (|List| (|List| |#1|))) "\\spad{closedCurve(s,[[lr0],[lr1],...,[lrn],[lr0]])} adds a closed curve component defined by a list of points \\spad{lr0} through \\spad{lrn},{} which are lists of elements from the domain \\spad{PointDomain(m,R)},{} where \\spad{R} is the \\spadtype{Ring} over which the point elements are defined and \\spad{m} is the dimension of the points,{} in which the last element of the list of points contains a copy of the first element list,{} \\spad{lr0}. The closed curve is added to the \\spadtype{ThreeSpace},{} \\spad{s}.") (($ $ (|List| (|Point| |#1|))) "\\spad{closedCurve(s,[p0,p1,...,pn,p0])} adds a closed curve component which is a list of points defined by the first element \\spad{p0} through the last element \\spad{pn} and back to the first element \\spad{p0} again,{} to the \\spadtype{ThreeSpace} \\spad{s}.")) (|curve?| (((|Boolean|) $) "\\spad{curve?(s)} queries whether the \\spadtype{ThreeSpace},{} \\spad{s},{} is a curve,{} \\spadignore{i.e.} has one component,{} a list of list of points,{} and returns \\spad{true} if it is,{} or \\spad{false} otherwise.")) (|curve| (((|List| (|Point| |#1|)) $) "\\spad{curve(s)} checks to see if the \\spadtype{ThreeSpace},{} \\spad{s},{} is composed of a single curve defined by a list of points and if so,{} returns the curve,{} \\spadignore{i.e.} list of points. An error is signaled otherwise.") (($ (|List| (|Point| |#1|))) "\\spad{curve([p0,p1,p2,...,pn])} creates a space curve defined by the list of points \\spad{p0} through \\spad{pn},{} and returns the \\spadtype{ThreeSpace} whose component is the curve.") (($ $ (|List| (|List| |#1|))) "\\spad{curve(s,[[p0],[p1],...,[pn]])} adds a space curve which is a list of points \\spad{p0} through pn defined by lists of elements from the domain \\spad{PointDomain(m,R)},{} where \\spad{R} is the \\spadtype{Ring} over which the point elements are defined and \\spad{m} is the dimension of the points,{} to the \\spadtype{ThreeSpace} \\spad{s}.") (($ $ (|List| (|Point| |#1|))) "\\spad{curve(s,[p0,p1,...,pn])} adds a space curve component defined by a list of points \\spad{p0} through \\spad{pn},{} to the \\spadtype{ThreeSpace} \\spad{s}.")) (|point?| (((|Boolean|) $) "\\spad{point?(s)} queries whether the \\spadtype{ThreeSpace},{} \\spad{s},{} is composed of a single component which is a point and returns the boolean result.")) (|point| (((|Point| |#1|) $) "\\spad{point(s)} checks to see if the \\spadtype{ThreeSpace},{} \\spad{s},{} is composed of only a single point and if so,{} returns the point. An error is signaled otherwise.") (($ (|Point| |#1|)) "\\spad{point(p)} returns a \\spadtype{ThreeSpace} object which is composed of one component,{} the point \\spad{p}.") (($ $ (|NonNegativeInteger|)) "\\spad{point(s,i)} adds a point component which is placed into a component list of the \\spadtype{ThreeSpace},{} \\spad{s},{} at the index given by \\spad{i}.") (($ $ (|List| |#1|)) "\\spad{point(s,[x,y,z])} adds a point component defined by a list of elements which are from the \\spad{PointDomain(R)} to the \\spadtype{ThreeSpace},{} \\spad{s},{} where \\spad{R} is the \\spadtype{Ring} over which the point elements are defined.") (($ $ (|Point| |#1|)) "\\spad{point(s,p)} adds a point component defined by the point,{} \\spad{p},{} specified as a list from \\spad{List(R)},{} to the \\spadtype{ThreeSpace},{} \\spad{s},{} where \\spad{R} is the \\spadtype{Ring} over which the point is defined.")) (|modifyPointData| (($ $ (|NonNegativeInteger|) (|Point| |#1|)) "\\spad{modifyPointData(s,i,p)} changes the point at the indexed location \\spad{i} in the \\spadtype{ThreeSpace},{} \\spad{s},{} to that of point \\spad{p}. This is useful for making changes to a point which has been transformed.")) (|enterPointData| (((|NonNegativeInteger|) $ (|List| (|Point| |#1|))) "\\spad{enterPointData(s,[p0,p1,...,pn])} adds a list of points from \\spad{p0} through pn to the \\spadtype{ThreeSpace},{} \\spad{s},{} and returns the index,{} to the starting point of the list.")) (|copy| (($ $) "\\spad{copy(s)} returns a new \\spadtype{ThreeSpace} that is an exact copy of \\spad{s}.")) (|composites| (((|List| $) $) "\\spad{composites(s)} takes the \\spadtype{ThreeSpace} \\spad{s},{} and creates a list containing a unique \\spadtype{ThreeSpace} for each single composite of \\spad{s}. If \\spad{s} has no composites defined (composites need to be explicitly created),{} the list returned is empty. Note that not all the components need to be part of a composite.")) (|components| (((|List| $) $) "\\spad{components(s)} takes the \\spadtype{ThreeSpace} \\spad{s},{} and creates a list containing a unique \\spadtype{ThreeSpace} for each single component of \\spad{s}. If \\spad{s} has no components defined,{} the list returned is empty.")) (|composite| (($ (|List| $)) "\\spad{composite([s1,s2,...,sn])} will create a new \\spadtype{ThreeSpace} that is a union of all the components from each \\spadtype{ThreeSpace} in the parameter list,{} grouped as a composite.")) (|merge| (($ $ $) "\\spad{merge(s1,s2)} will create a new \\spadtype{ThreeSpace} that has the components of \\spad{s1} and \\spad{s2}; Groupings of components into composites are maintained.") (($ (|List| $)) "\\spad{merge([s1,s2,...,sn])} will create a new \\spadtype{ThreeSpace} that has the components of all the ones in the list; Groupings of components into composites are maintained.")) (|numberOfComposites| (((|NonNegativeInteger|) $) "\\spad{numberOfComposites(s)} returns the number of supercomponents,{} or composites,{} in the \\spadtype{ThreeSpace},{} \\spad{s}; Composites are arbitrary groupings of otherwise distinct and unrelated components; A \\spadtype{ThreeSpace} need not have any composites defined at all and,{} outside of the requirement that no component can belong to more than one composite at a time,{} the definition and interpretation of composites are unrestricted.")) (|numberOfComponents| (((|NonNegativeInteger|) $) "\\spad{numberOfComponents(s)} returns the number of distinct object components in the indicated \\spadtype{ThreeSpace},{} \\spad{s},{} such as points,{} curves,{} polygons,{} and constructs.")) (|create3Space| (($ (|SubSpace| 3 |#1|)) "\\spad{create3Space(s)} creates a \\spadtype{ThreeSpace} object containing objects pre-defined within some \\spadtype{SubSpace} \\spad{s}.") (($) "\\spad{create3Space()} creates a \\spadtype{ThreeSpace} object capable of holding point,{} curve,{} mesh components and any combination."))) NIL NIL (|SpadAst|) @@ -4169,9 +4169,9 @@ NIL NIL ((AND (|HasCategory| #1=(|SplittingNode| |#1| |#2|) (|%list| (QUOTE |Evalable|) #2=(|%list| (QUOTE |SplittingNode|) (|devaluate| |#1|) (|devaluate| |#2|)))) #3=(|HasCategory| #1# (QUOTE (|SetCategory|)))) #3# (OR #4=(|HasCategory| #1# (QUOTE (|BasicType|))) #3#) (|HasCategory| #1# (QUOTE (|CoercibleTo| (|OutputForm|)))) #4# (|HasCategory| $ (|%list| (QUOTE |ShallowlyMutableAggregate|) #2#))) (|SquareMatrix| |ndim| R) -((|constructor| (NIL "\\spadtype{SquareMatrix} is a matrix domain of square matrices,{} where the number of rows (= number of columns) is a parameter of the type.")) (|unitsKnown| ((|attribute|) "the invertible matrices are simply the matrices whose determinants are units in the Ring \\spad{R}.")) (|central| ((|attribute|) "the elements of the Ring \\spad{R},{} viewed as diagonal matrices,{} commute with all matrices and,{} indeed,{} are the only matrices which commute with all matrices.")) (|squareMatrix| (($ (|Matrix| |#2|)) "\\spad{squareMatrix(m)} converts a matrix of type \\spadtype{Matrix} to a matrix of type \\spadtype{SquareMatrix}.")) (|transpose| (($ $) "\\spad{transpose(m)} returns the transpose of the matrix \\spad{m}.")) (|new| (($ |#2|) "\\spad{new(c)} constructs a new \\spadtype{SquareMatrix} object of dimension \\spad{ndim} with initial entries equal to \\spad{c}."))) -((|unitsKnown| . T) (|central| |has| |#2| (ATTRIBUTE (|commutative| "*"))) (|rightUnitary| . T) (|leftUnitary| . T)) -(#1=(|HasCategory| |#2| (QUOTE (|PartialDifferentialRing| #2=(|Symbol|)))) (|HasCategory| |#2| (QUOTE (|PartialDifferentialSpace| #2#))) #3=(|HasCategory| |#2| (QUOTE (|DifferentialRing|))) (|HasCategory| |#2| (QUOTE (|DifferentialSpace|))) #4=(|HasAttribute| |#2| (QUOTE (|commutative| "*"))) #5=(|HasCategory| |#2| (QUOTE (|LinearlyExplicitRingOver| #6=(|Integer|)))) (|HasCategory| |#2| (QUOTE (|RetractableTo| (|Fraction| #6#)))) (|HasCategory| |#2| (QUOTE (|RetractableTo| #6#))) (OR (AND #3# #7=(|HasCategory| |#2| (|%list| (QUOTE |Evalable|) (|devaluate| |#2|)))) (AND #5# #7#) (AND #1# #7#) #8=(AND #9=(|HasCategory| |#2| (QUOTE (|SetCategory|))) #7#)) (|HasCategory| |#2| (QUOTE (|ConvertibleTo| (|InputForm|)))) (|HasCategory| |#2| (QUOTE (|EuclideanDomain|))) (|HasCategory| |#2| (QUOTE (|IntegralDomain|))) (|HasCategory| |#2| (QUOTE (|Field|))) (OR #4# #3# #1#) (|HasCategory| |#2| (QUOTE (|CoercibleTo| (|OutputForm|)))) (|HasCategory| |#2| (QUOTE (|BasicType|))) #9# #8# (|HasCategory| |#2| (QUOTE (|CommutativeRing|)))) +((|constructor| (NIL "\\spadtype{SquareMatrix} is a matrix domain of square matrices,{} where the number of rows (= number of columns) is a parameter of the type.")) (|squareMatrix| (($ (|Matrix| |#2|)) "\\spad{squareMatrix(m)} converts a matrix of type \\spadtype{Matrix} to a matrix of type \\spadtype{SquareMatrix}.")) (|transpose| (($ $) "\\spad{transpose(m)} returns the transpose of the matrix \\spad{m}.")) (|new| (($ |#2|) "\\spad{new(c)} constructs a new \\spadtype{SquareMatrix} object of dimension \\spad{ndim} with initial entries equal to \\spad{c}."))) +NIL +(#1=(|HasCategory| |#2| (QUOTE (|PartialDifferentialRing| #2=(|Symbol|)))) (|HasCategory| |#2| (QUOTE (|PartialDifferentialSpace| #2#))) #3=(|HasCategory| |#2| (QUOTE (|DifferentialRing|))) (|HasCategory| |#2| (QUOTE (|DifferentialSpace|))) (|HasAttribute| |#2| (QUOTE (|commutative| "*"))) #4=(|HasCategory| |#2| (QUOTE (|LinearlyExplicitRingOver| #5=(|Integer|)))) (|HasCategory| |#2| (QUOTE (|RetractableTo| (|Fraction| #5#)))) (|HasCategory| |#2| (QUOTE (|RetractableTo| #5#))) (OR (AND #3# #6=(|HasCategory| |#2| (|%list| (QUOTE |Evalable|) (|devaluate| |#2|)))) (AND #4# #6#) (AND #1# #6#) #7=(AND #8=(|HasCategory| |#2| (QUOTE (|SetCategory|))) #6#)) (|HasCategory| |#2| (QUOTE (|ConvertibleTo| (|InputForm|)))) (|HasCategory| |#2| (QUOTE (|EuclideanDomain|))) (|HasCategory| |#2| (QUOTE (|IntegralDomain|))) (|HasCategory| |#2| (QUOTE (|Field|))) #7# #8# (|HasCategory| |#2| (QUOTE (|BasicType|))) (|HasCategory| |#2| (QUOTE (|CoercibleTo| (|OutputForm|)))) (|HasCategory| |#2| (QUOTE (|CommutativeRing|)))) (|StringAggregate&| S) ((|constructor| (NIL "A string aggregate is a category for strings,{} that is,{} one dimensional arrays of characters.")) (|elt| (($ $ $) "\\spad{elt(s,t)} returns the concatenation of \\spad{s} and \\spad{t}. It is provided to allow juxtaposition of strings to work as concatenation. For example,{} \\axiom{\"smoo\" \"shed\"} returns \\axiom{\"smooshed\"}.")) (|rightTrim| (($ $ (|CharacterClass|)) "\\spad{rightTrim(s,cc)} returns \\spad{s} with all trailing occurences of characters in \\spad{cc} deleted. For example,{} \\axiom{rightTrim(\"(abc)\",{} charClass \"()\")} returns \\axiom{\"(abc\"}.") (($ $ (|Character|)) "\\spad{rightTrim(s,c)} returns \\spad{s} with all trailing occurrences of \\spad{c} deleted. For example,{} \\axiom{rightTrim(\" abc \",{} char \" \")} returns \\axiom{\" abc\"}.")) (|leftTrim| (($ $ (|CharacterClass|)) "\\spad{leftTrim(s,cc)} returns \\spad{s} with all leading characters in \\spad{cc} deleted. For example,{} \\axiom{leftTrim(\"(abc)\",{} charClass \"()\")} returns \\axiom{\"abc)\"}.") (($ $ (|Character|)) "\\spad{leftTrim(s,c)} returns \\spad{s} with all leading characters \\spad{c} deleted. For example,{} \\axiom{leftTrim(\" abc \",{} char \" \")} returns \\axiom{\"abc \"}.")) (|trim| (($ $ (|CharacterClass|)) "\\spad{trim(s,cc)} returns \\spad{s} with all characters in \\spad{cc} deleted from right and left ends. For example,{} \\axiom{trim(\"(abc)\",{} charClass \"()\")} returns \\axiom{\"abc\"}.") (($ $ (|Character|)) "\\spad{trim(s,c)} returns \\spad{s} with all characters \\spad{c} deleted from right and left ends. For example,{} \\axiom{trim(\" abc \",{} char \" \")} returns \\axiom{\"abc\"}.")) (|split| (((|List| $) $ (|CharacterClass|)) "\\spad{split(s,cc)} returns a list of substrings delimited by characters in \\spad{cc}.") (((|List| $) $ (|Character|)) "\\spad{split(s,c)} returns a list of substrings delimited by character \\spad{c}.")) (|coerce| (($ (|Character|)) "\\spad{coerce(c)} returns \\spad{c} as a string \\spad{s} with the character \\spad{c}.")) (|position| (((|Integer|) (|CharacterClass|) $ (|Integer|)) "\\spad{position(cc,t,i)} returns the position \\axiom{\\spad{j} >= \\spad{i}} in \\spad{t} of the first character belonging to \\spad{cc}.") (((|Integer|) $ $ (|Integer|)) "\\spad{position(s,t,i)} returns the position \\spad{j} of the substring \\spad{s} in string \\spad{t},{} where \\axiom{\\spad{j} >= \\spad{i}} is required.")) (|replace| (($ $ (|UniversalSegment| (|Integer|)) $) "\\spad{replace(s,i..j,t)} replaces the substring \\axiom{\\spad{s}(\\spad{i}..\\spad{j})} of \\spad{s} by string \\spad{t}.")) (|match?| (((|Boolean|) $ $ (|Character|)) "\\spad{match?(s,t,c)} tests if \\spad{s} matches \\spad{t} except perhaps for multiple and consecutive occurrences of character \\spad{c}. Typically \\spad{c} is the blank character.")) (|match| (((|NonNegativeInteger|) $ $ (|Character|)) "\\spad{match(p,s,wc)} tests if pattern \\axiom{\\spad{p}} matches subject \\axiom{\\spad{s}} where \\axiom{\\spad{wc}} is a wild card character. If no match occurs,{} the index \\axiom{0} is returned; otheriwse,{} the value returned is the first index of the first character in the subject matching the subject (excluding that matched by an initial wild-card). For example,{} \\axiom{match(\"*to*\",{}\"yorktown\",{}\"*\")} returns \\axiom{5} indicating a successful match starting at index \\axiom{5} of \\axiom{\"yorktown\"}.")) (|substring?| (((|Boolean|) $ $ (|Integer|)) "\\spad{substring?(s,t,i)} tests if \\spad{s} is a substring of \\spad{t} beginning at index \\spad{i}. Note: \\axiom{substring?(\\spad{s},{}\\spad{t},{}0) = prefix?(\\spad{s},{}\\spad{t})}.")) (|suffix?| (((|Boolean|) $ $) "\\spad{suffix?(s,t)} tests if the string \\spad{s} is the final substring of \\spad{t}. Note: \\axiom{suffix?(\\spad{s},{}\\spad{t}) == reduce(and,{}[\\spad{s}.\\spad{i} = \\spad{t}.(\\spad{n} - \\spad{m} + \\spad{i}) for \\spad{i} in 0..maxIndex \\spad{s}])} where \\spad{m} and \\spad{n} denote the maxIndex of \\spad{s} and \\spad{t} respectively.")) (|prefix?| (((|Boolean|) $ $) "\\spad{prefix?(s,t)} tests if the string \\spad{s} is the initial substring of \\spad{t}. Note: \\axiom{prefix?(\\spad{s},{}\\spad{t}) == reduce(and,{}[\\spad{s}.\\spad{i} = \\spad{t}.\\spad{i} for \\spad{i} in 0..maxIndex \\spad{s}])}.")) (|upperCase!| (($ $) "\\spad{upperCase!(s)} destructively replaces the alphabetic characters in \\spad{s} by upper case characters.")) (|upperCase| (($ $) "\\spad{upperCase(s)} returns the string with all characters in upper case.")) (|lowerCase!| (($ $) "\\spad{lowerCase!(s)} destructively replaces the alphabetic characters in \\spad{s} by lower case.")) (|lowerCase| (($ $) "\\spad{lowerCase(s)} returns the string with all characters in lower case."))) NIL @@ -4274,8 +4274,8 @@ NIL NIL (|SparseUnivariateLaurentSeries| |Coef| |var| |cen|) ((|constructor| (NIL "Sparse Laurent series in one variable \\indented{2}{\\spadtype{SparseUnivariateLaurentSeries} is a domain representing Laurent} \\indented{2}{series in one variable with coefficients in an arbitrary ring.\\space{2}The} \\indented{2}{parameters of the type specify the coefficient ring,{} the power series} \\indented{2}{variable,{} and the center of the power series expansion.\\space{2}For example,{}} \\indented{2}{\\spad{SparseUnivariateLaurentSeries(Integer,x,3)} represents Laurent} \\indented{2}{series in \\spad{(x - 3)} with integer coefficients.}")) (|integrate| (($ $ (|Variable| |#2|)) "\\spad{integrate(f(x))} returns an anti-derivative of the power series \\spad{f(x)} with constant coefficient 0. We may integrate a series when we can divide coefficients by integers.")) (|coerce| (($ (|Variable| |#2|)) "\\spad{coerce(var)} converts the series variable \\spad{var} into a Laurent series."))) -(((|commutative| "*") OR #1=(|and| #2=(|has| |#1| #3=(|Field|)) (|has| #4=(|SparseUnivariateTaylorSeries| |#1| |#2| |#3|) (|OrderedIntegralDomain|))) (|has| |#1| (|CommutativeRing|)) #5=(|and| #2# (|has| #4# (|PolynomialFactorizationExplicit|)))) (|noZeroDivisors| OR #1# (|has| |#1| (|IntegralDomain|)) #5#) (|canonicalUnitNormal| |has| |#1| . #6=(#3#)) (|canonicalsClosed| |has| |#1| . #6#) (|rightUnitary| . T) (|leftUnitary| . T) (|unitsKnown| . T)) -(#1=(|HasCategory| |#1| (QUOTE (|Algebra| (|Fraction| #2=(|Integer|))))) #3=(|HasCategory| |#1| (QUOTE (|IntegralDomain|))) #4=(|HasCategory| |#1| (QUOTE (|CommutativeRing|))) (OR #4# #3#) (OR #5=(AND #6=(|HasCategory| |#1| (QUOTE (|Field|))) #7=(|HasCategory| #8=(|SparseUnivariateTaylorSeries| |#1| |#2| |#3|) #9=(QUOTE (|CharacteristicNonZero|)))) #10=(|HasCategory| |#1| #9#)) (OR #11=(AND #6# (|HasCategory| #8# (QUOTE (|OrderedIntegralDomain|)))) #12=(AND #6# (|HasCategory| #8# #13=(QUOTE (|CharacteristicZero|)))) #14=(|HasCategory| |#1| #13#)) (OR #15=(AND #6# (|HasCategory| #8# #16=(QUOTE (|PartialDifferentialRing| #17=(|Symbol|))))) #18=(AND (|HasCategory| |#1| #16#) #19=(|HasSignature| |#1| (|%list| (QUOTE *) (|%list| #20=(|devaluate| |#1|) #21=(QUOTE #2#) #20#))))) (OR #15# #22=(AND #6# (|HasCategory| #8# (QUOTE (|PartialDifferentialSpace| #17#)))) #18#) (OR #23=(AND #6# (|HasCategory| #8# (QUOTE (|DifferentialRing|)))) #19#) (OR #23# #24=(AND #6# (|HasCategory| #8# (QUOTE (|DifferentialSpace|)))) #19#) (|HasCategory| #2# (QUOTE (|SemiGroup|))) (OR #6# #3#) #6# #25=(AND #6# #26=(|HasCategory| #8# (QUOTE (|PolynomialFactorizationExplicit|)))) (AND #6# (|HasCategory| #8# (QUOTE (|RetractableTo| #17#)))) (AND #6# (|HasCategory| #8# (QUOTE (|ConvertibleTo| (|InputForm|))))) (AND #6# (|HasCategory| #8# (QUOTE (|RealConstant|)))) (OR #4# #6# #3#) #11# (OR #11# #27=(AND #6# (|HasCategory| #8# (QUOTE (|OrderedSet|))))) (OR #28=(AND #6# (|HasCategory| #8# (QUOTE (|RetractableTo| #2#)))) #1#) #28# (AND #6# (|HasCategory| #8# (QUOTE (|StepThrough|)))) (AND #6# (|HasCategory| #8# (|%list| (QUOTE |Eltable|) #29=(|%list| (QUOTE |SparseUnivariateTaylorSeries|) #20# (|devaluate| |#2|) (|devaluate| |#3|)) #29#))) (AND #6# (|HasCategory| #8# (|%list| (QUOTE |Evalable|) #29#))) (AND #6# (|HasCategory| #8# (|%list| (QUOTE |InnerEvalable|) #30=(QUOTE #17#) #29#))) (AND #6# (|HasCategory| #8# (QUOTE (|LinearlyExplicitRingOver| #2#)))) (AND #6# (|HasCategory| #8# (QUOTE (|ConvertibleTo| (|Pattern| #2#))))) (AND #6# (|HasCategory| #8# (QUOTE (|ConvertibleTo| (|Pattern| #31=(|Float|)))))) (AND #6# (|HasCategory| #8# (QUOTE (|PatternMatchable| #2#)))) (AND #6# (|HasCategory| #8# (QUOTE (|PatternMatchable| #31#)))) (AND #32=(|HasSignature| |#1| (|%list| (QUOTE **) (|%list| #20# #20# #21#))) (|HasSignature| |#1| (|%list| (QUOTE |coerce|) (|%list| #20# #30#)))) #32# (OR (AND #1# (|HasCategory| |#1| (QUOTE (|AlgebraicallyClosedFunctionSpace| #2#))) (|HasCategory| |#1| (QUOTE (|PrimitiveFunctionCategory|))) (|HasCategory| |#1| (QUOTE (|TranscendentalFunctionCategory|)))) (AND #1# (|HasSignature| |#1| (|%list| (QUOTE |integrate|) (|%list| #20# #20# #30#))) (|HasSignature| |#1| (|%list| (QUOTE |variables|) (|%list| (|%list| (QUOTE |List|) #30#) #20#))))) (AND #6# (|HasCategory| #8# (QUOTE (|IntegerNumberSystem|)))) (AND #6# (|HasCategory| #8# (QUOTE (|EuclideanDomain|)))) #26# #7# #10# (OR #11# #25# #3#) (OR #11# #25# #4#) #22# #24# #27# (OR #12# #14#) #33=(AND #6# (|HasCategory| $ #9#) #26#) (OR #5# #33# #10#)) +(((|commutative| "*") OR #1=(|and| #2=(|has| |#1| #3=(|Field|)) (|has| #4=(|SparseUnivariateTaylorSeries| |#1| |#2| |#3|) (|OrderedIntegralDomain|))) (|has| |#1| (|CommutativeRing|)) #5=(|and| #2# (|has| #4# (|PolynomialFactorizationExplicit|)))) (|noZeroDivisors| OR #1# (|has| |#1| (|IntegralDomain|)) #5#) (|canonicalUnitNormal| |has| |#1| #3#)) +(#1=(|HasCategory| |#1| (QUOTE (|Algebra| (|Fraction| #2=(|Integer|))))) #3=(|HasCategory| |#1| (QUOTE (|IntegralDomain|))) #4=(|HasCategory| |#1| (QUOTE (|CommutativeRing|))) (OR #4# #3#) (OR #5=(AND #6=(|HasCategory| |#1| (QUOTE (|Field|))) #7=(|HasCategory| #8=(|SparseUnivariateTaylorSeries| |#1| |#2| |#3|) #9=(QUOTE (|CharacteristicNonZero|)))) #10=(|HasCategory| |#1| #9#)) (OR #11=(AND #6# (|HasCategory| #8# (QUOTE (|OrderedIntegralDomain|)))) #12=(AND #6# (|HasCategory| #8# #13=(QUOTE (|CharacteristicZero|)))) #14=(|HasCategory| |#1| #13#)) (OR #15=(AND #6# (|HasCategory| #8# #16=(QUOTE (|PartialDifferentialRing| #17=(|Symbol|))))) #18=(AND (|HasCategory| |#1| #16#) #19=(|HasSignature| |#1| (|%list| (QUOTE *) (|%list| #20=(|devaluate| |#1|) #21=(QUOTE #2#) #20#))))) (OR #15# #22=(AND #6# (|HasCategory| #8# (QUOTE (|PartialDifferentialSpace| #17#)))) #18#) (OR #23=(AND #6# (|HasCategory| #8# (QUOTE (|DifferentialRing|)))) #19#) (OR #23# #24=(AND #6# (|HasCategory| #8# (QUOTE (|DifferentialSpace|)))) #19#) (|HasCategory| #2# (QUOTE (|SemiGroup|))) (OR #6# #3#) #6# #25=(AND #6# #26=(|HasCategory| #8# (QUOTE (|PolynomialFactorizationExplicit|)))) (AND #6# (|HasCategory| #8# (QUOTE (|RetractableTo| #17#)))) (AND #6# (|HasCategory| #8# (QUOTE (|ConvertibleTo| (|InputForm|))))) (AND #6# (|HasCategory| #8# (QUOTE (|RealConstant|)))) (OR #4# #6# #3#) #11# (OR #11# #27=(AND #6# (|HasCategory| #8# (QUOTE (|OrderedSet|))))) (OR #28=(AND #6# (|HasCategory| #8# (QUOTE (|RetractableTo| #2#)))) #1#) #28# (AND #6# (|HasCategory| #8# (QUOTE (|StepThrough|)))) (AND #6# (|HasCategory| #8# (|%list| (QUOTE |Eltable|) #29=(|%list| (QUOTE |SparseUnivariateTaylorSeries|) #20# (|devaluate| |#2|) (|devaluate| |#3|)) #29#))) (AND #6# (|HasCategory| #8# (|%list| (QUOTE |Evalable|) #29#))) (AND #6# (|HasCategory| #8# (|%list| (QUOTE |InnerEvalable|) #30=(QUOTE #17#) #29#))) (AND #6# (|HasCategory| #8# (QUOTE (|LinearlyExplicitRingOver| #2#)))) (AND #6# (|HasCategory| #8# (QUOTE (|ConvertibleTo| (|Pattern| #2#))))) (AND #6# (|HasCategory| #8# (QUOTE (|ConvertibleTo| (|Pattern| #31=(|Float|)))))) (AND #6# (|HasCategory| #8# (QUOTE (|PatternMatchable| #2#)))) (AND #6# (|HasCategory| #8# (QUOTE (|PatternMatchable| #31#)))) (AND #32=(|HasSignature| |#1| (|%list| (QUOTE **) (|%list| #20# #20# #21#))) (|HasSignature| |#1| (|%list| (QUOTE |coerce|) (|%list| #20# #30#)))) #32# (OR (AND #1# (|HasCategory| |#1| (QUOTE (|AlgebraicallyClosedFunctionSpace| #2#))) (|HasCategory| |#1| (QUOTE (|PrimitiveFunctionCategory|))) (|HasCategory| |#1| (QUOTE (|TranscendentalFunctionCategory|)))) (AND #1# (|HasSignature| |#1| (|%list| (QUOTE |integrate|) (|%list| #20# #20# #30#))) (|HasSignature| |#1| (|%list| (QUOTE |variables|) (|%list| (|%list| (QUOTE |List|) #30#) #20#))))) (AND #6# (|HasCategory| #8# (QUOTE (|IntegerNumberSystem|)))) (AND #6# (|HasCategory| #8# (QUOTE (|EuclideanDomain|)))) #26# #7# #10# (OR #11# #25# #3#) (OR #11# #25# #4#) #24# #22# #27# (OR #12# #14#) #33=(AND #6# (|HasCategory| $ #9#) #26#) (OR #5# #33# #10#)) (|FunctionSpaceSum| R F) ((|constructor| (NIL "computes sums of top-level expressions.")) (|sum| ((|#2| |#2| (|SegmentBinding| |#2|)) "\\spad{sum(f(n), n = a..b)} returns \\spad{f}(a) + \\spad{f}(\\spad{a+1}) + ... + \\spad{f}(\\spad{b}).") ((|#2| |#2| (|Symbol|)) "\\spad{sum(a(n), n)} returns A(\\spad{n}) such that A(\\spad{n+1}) - A(\\spad{n}) = a(\\spad{n})."))) NIL @@ -4286,8 +4286,8 @@ NIL NIL (|SparseUnivariatePolynomial| R) ((|constructor| (NIL "This domain represents univariate polynomials over arbitrary (not necessarily commutative) coefficient rings. The variable is unspecified so that the variable displays as \\spad{?} on output. If it is necessary to specify the variable name,{} use type \\spadtype{UnivariatePolynomial}. The representation is sparse in the sense that only non-zero terms are represented.")) (|fmecg| (($ $ (|NonNegativeInteger|) |#1| $) "\\spad{fmecg(p1,e,r,p2)} finds \\spad{X} : \\spad{p1} - \\spad{r} * X**e * \\spad{p2}")) (|outputForm| (((|OutputForm|) $ (|OutputForm|)) "\\spad{outputForm(p,var)} converts the SparseUnivariatePolynomial \\spad{p} to an output form (see \\spadtype{OutputForm}) printed as a polynomial in the output form variable."))) -(((|commutative| "*") |has| |#1| (|CommutativeRing|)) (|noZeroDivisors| |has| |#1| (|IntegralDomain|)) (|additiveValuation| |has| |#1| (|Field|)) (|canonicalUnitNormal| |has| |#1| (ATTRIBUTE |canonicalUnitNormal|)) (|leftUnitary| . T) (|rightUnitary| . T) (|unitsKnown| . T)) -(#1=(|HasCategory| |#1| (QUOTE (|PolynomialFactorizationExplicit|))) #2=(|HasCategory| |#1| (QUOTE (|IntegralDomain|))) #3=(|HasCategory| |#1| (QUOTE (|CommutativeRing|))) (OR #3# #2#) (AND (|HasCategory| |#1| #4=(QUOTE (|PatternMatchable| #5=(|Float|)))) (|HasCategory| #6=(|SingletonAsOrderedSet|) #4#)) (AND (|HasCategory| |#1| #7=(QUOTE (|PatternMatchable| #8=(|Integer|)))) (|HasCategory| #6# #7#)) (AND (|HasCategory| |#1| #9=(QUOTE (|ConvertibleTo| (|Pattern| #5#)))) (|HasCategory| #6# #9#)) (AND (|HasCategory| |#1| #10=(QUOTE (|ConvertibleTo| (|Pattern| #8#)))) (|HasCategory| #6# #10#)) (AND (|HasCategory| |#1| #11=(QUOTE (|ConvertibleTo| (|InputForm|)))) (|HasCategory| #6# #11#)) (|HasCategory| |#1| (QUOTE (|LinearlyExplicitRingOver| #8#))) (|HasCategory| |#1| (QUOTE (|CharacteristicZero|))) #12=(|HasCategory| |#1| #13=(QUOTE (|CharacteristicNonZero|))) #14=(|HasCategory| |#1| (QUOTE (|Algebra| #15=(|Fraction| #8#)))) (|HasCategory| |#1| (QUOTE (|RetractableTo| #8#))) (OR #14# #16=(|HasCategory| |#1| (QUOTE (|RetractableTo| #15#)))) #16# (OR #3# #17=(|HasCategory| |#1| (QUOTE (|Field|))) #18=(|HasCategory| |#1| (QUOTE (|GcdDomain|))) #2# #1#) (OR #17# #18# #2# #1#) (OR #17# #18# #1#) #17# (|HasCategory| |#1| (QUOTE (|StepThrough|))) (|HasCategory| |#1| (QUOTE (|PartialDifferentialSpace| #19=(|Symbol|)))) (|HasCategory| |#1| (QUOTE (|PartialDifferentialRing| #19#))) (|HasCategory| |#1| (QUOTE (|DifferentialSpace|))) (|HasCategory| |#1| (QUOTE (|DifferentialRing|))) (|HasAttribute| |#1| (QUOTE |canonicalUnitNormal|)) #18# #20=(AND #1# (|HasCategory| $ #13#)) (OR #20# #12#)) +(((|commutative| "*") |has| |#1| (|CommutativeRing|)) (|noZeroDivisors| |has| |#1| (|IntegralDomain|)) (|additiveValuation| |has| |#1| (|Field|)) (|canonicalUnitNormal| |has| |#1| (ATTRIBUTE |canonicalUnitNormal|))) +(#1=(|HasCategory| |#1| (QUOTE (|PolynomialFactorizationExplicit|))) #2=(|HasCategory| |#1| (QUOTE (|IntegralDomain|))) #3=(|HasCategory| |#1| (QUOTE (|CommutativeRing|))) (OR #3# #2#) (AND (|HasCategory| |#1| #4=(QUOTE (|PatternMatchable| #5=(|Float|)))) (|HasCategory| #6=(|SingletonAsOrderedSet|) #4#)) (AND (|HasCategory| |#1| #7=(QUOTE (|PatternMatchable| #8=(|Integer|)))) (|HasCategory| #6# #7#)) (AND (|HasCategory| |#1| #9=(QUOTE (|ConvertibleTo| (|Pattern| #5#)))) (|HasCategory| #6# #9#)) (AND (|HasCategory| |#1| #10=(QUOTE (|ConvertibleTo| (|Pattern| #8#)))) (|HasCategory| #6# #10#)) (AND (|HasCategory| |#1| #11=(QUOTE (|ConvertibleTo| (|InputForm|)))) (|HasCategory| #6# #11#)) (|HasCategory| |#1| (QUOTE (|LinearlyExplicitRingOver| #8#))) #12=(|HasCategory| |#1| (QUOTE (|Algebra| #13=(|Fraction| #8#)))) #14=(|HasCategory| |#1| #15=(QUOTE (|CharacteristicNonZero|))) (|HasCategory| |#1| (QUOTE (|CharacteristicZero|))) (|HasCategory| |#1| (QUOTE (|RetractableTo| #8#))) (OR #12# #16=(|HasCategory| |#1| (QUOTE (|RetractableTo| #13#)))) #16# (OR #3# #17=(|HasCategory| |#1| (QUOTE (|Field|))) #18=(|HasCategory| |#1| (QUOTE (|GcdDomain|))) #2# #1#) (OR #17# #18# #2# #1#) (OR #17# #18# #1#) #17# (|HasCategory| |#1| (QUOTE (|StepThrough|))) (|HasCategory| |#1| (QUOTE (|PartialDifferentialSpace| #19=(|Symbol|)))) (|HasCategory| |#1| (QUOTE (|PartialDifferentialRing| #19#))) (|HasCategory| |#1| (QUOTE (|DifferentialSpace|))) (|HasCategory| |#1| (QUOTE (|DifferentialRing|))) (|HasAttribute| |#1| (QUOTE |canonicalUnitNormal|)) #18# #20=(AND #1# (|HasCategory| $ #15#)) (OR #20# #14#)) (|SparseUnivariatePolynomialFunctions2| R S) ((|constructor| (NIL "This package lifts a mapping from coefficient rings \\spad{R} to \\spad{S} to a mapping from sparse univariate polynomial over \\spad{R} to a sparse univariate polynomial over \\spad{S}. Note that the mapping is assumed to send zero to zero,{} since it will only be applied to the non-zero coefficients of the polynomial.")) (|map| (((|SparseUnivariatePolynomial| |#2|) (|Mapping| |#2| |#1|) (|SparseUnivariatePolynomial| |#1|)) "\\spad{map(func, poly)} creates a new polynomial by applying \\spad{func} to every non-zero coefficient of the polynomial poly."))) NIL @@ -4298,11 +4298,11 @@ NIL NIL (|SparseUnivariatePuiseuxSeries| |Coef| |var| |cen|) ((|constructor| (NIL "Sparse Puiseux series in one variable \\indented{2}{\\spadtype{SparseUnivariatePuiseuxSeries} is a domain representing Puiseux} \\indented{2}{series in one variable with coefficients in an arbitrary ring.\\space{2}The} \\indented{2}{parameters of the type specify the coefficient ring,{} the power series} \\indented{2}{variable,{} and the center of the power series expansion.\\space{2}For example,{}} \\indented{2}{\\spad{SparseUnivariatePuiseuxSeries(Integer,x,3)} represents Puiseux} \\indented{2}{series in \\spad{(x - 3)} with \\spadtype{Integer} coefficients.}")) (|integrate| (($ $ (|Variable| |#2|)) "\\spad{integrate(f(x))} returns an anti-derivative of the power series \\spad{f(x)} with constant coefficient 0. We may integrate a series when we can divide coefficients by integers."))) -(((|commutative| "*") |has| |#1| (|CommutativeRing|)) (|noZeroDivisors| |has| |#1| (|IntegralDomain|)) (|canonicalUnitNormal| |has| |#1| . #1=((|Field|))) (|canonicalsClosed| |has| |#1| . #1#) (|rightUnitary| . T) (|leftUnitary| . T) (|unitsKnown| . T)) +(((|commutative| "*") |has| |#1| (|CommutativeRing|)) (|noZeroDivisors| |has| |#1| (|IntegralDomain|)) (|canonicalUnitNormal| |has| |#1| (|Field|))) (#1=(|HasCategory| |#1| (QUOTE (|Algebra| #2=(|Fraction| #3=(|Integer|))))) #4=(|HasCategory| |#1| (QUOTE (|IntegralDomain|))) #5=(|HasCategory| |#1| (QUOTE (|CommutativeRing|))) (OR #5# #4#) (|HasCategory| |#1| (QUOTE (|CharacteristicNonZero|))) (|HasCategory| |#1| (QUOTE (|CharacteristicZero|))) (AND (|HasCategory| |#1| (QUOTE (|PartialDifferentialRing| #6=(|Symbol|)))) #7=(|HasSignature| |#1| (|%list| (QUOTE *) (|%list| #8=(|devaluate| |#1|) #9=(|%list| (QUOTE |Fraction|) (QUOTE #3#)) #8#)))) #7# (|HasCategory| #2# (QUOTE (|SemiGroup|))) #10=(|HasCategory| |#1| (QUOTE (|Field|))) (OR #5# #10# #4#) (OR #10# #4#) (AND #11=(|HasSignature| |#1| (|%list| (QUOTE **) (|%list| #8# #8# #9#))) (|HasSignature| |#1| (|%list| (QUOTE |coerce|) (|%list| #8# #12=(QUOTE #6#))))) #11# (OR (AND #1# (|HasCategory| |#1| (QUOTE (|AlgebraicallyClosedFunctionSpace| #3#))) (|HasCategory| |#1| (QUOTE (|PrimitiveFunctionCategory|))) (|HasCategory| |#1| (QUOTE (|TranscendentalFunctionCategory|)))) (AND #1# (|HasSignature| |#1| (|%list| (QUOTE |integrate|) (|%list| #8# #8# #12#))) (|HasSignature| |#1| (|%list| (QUOTE |variables|) (|%list| (|%list| (QUOTE |List|) #12#) #8#)))))) (|SparseUnivariateTaylorSeries| |Coef| |var| |cen|) ((|constructor| (NIL "Sparse Taylor series in one variable \\indented{2}{\\spadtype{SparseUnivariateTaylorSeries} is a domain representing Taylor} \\indented{2}{series in one variable with coefficients in an arbitrary ring.\\space{2}The} \\indented{2}{parameters of the type specify the coefficient ring,{} the power series} \\indented{2}{variable,{} and the center of the power series expansion.\\space{2}For example,{}} \\indented{2}{\\spadtype{SparseUnivariateTaylorSeries}(Integer,{}\\spad{x},{}3) represents Taylor} \\indented{2}{series in \\spad{(x - 3)} with \\spadtype{Integer} coefficients.}")) (|integrate| (($ $ (|Variable| |#2|)) "\\spad{integrate(f(x),x)} returns an anti-derivative of the power series \\spad{f(x)} with constant coefficient 0. We may integrate a series when we can divide coefficients by integers.")) (|univariatePolynomial| (((|UnivariatePolynomial| |#2| |#1|) $ (|NonNegativeInteger|)) "\\spad{univariatePolynomial(f,k)} returns a univariate polynomial \\indented{1}{consisting of the sum of all terms of \\spad{f} of degree \\spad{<= k}.}")) (|coerce| (($ (|Variable| |#2|)) "\\spad{coerce(var)} converts the series variable \\spad{var} into a \\indented{1}{Taylor series.}") (($ (|UnivariatePolynomial| |#2| |#1|)) "\\spad{coerce(p)} converts a univariate polynomial \\spad{p} in the variable \\spad{var} to a univariate Taylor series in \\spad{var}."))) -(((|commutative| "*") |has| |#1| (|CommutativeRing|)) (|noZeroDivisors| |has| |#1| (|IntegralDomain|)) (|rightUnitary| . T) (|leftUnitary| . T) (|unitsKnown| . T)) +(((|commutative| "*") |has| |#1| (|CommutativeRing|)) (|noZeroDivisors| |has| |#1| (|IntegralDomain|))) (#1=(|HasCategory| |#1| (QUOTE (|Algebra| (|Fraction| #2=(|Integer|))))) #3=(|HasCategory| |#1| (QUOTE (|IntegralDomain|))) (OR #4=(|HasCategory| |#1| (QUOTE (|CommutativeRing|))) #3#) #4# (|HasCategory| |#1| (QUOTE (|CharacteristicNonZero|))) (|HasCategory| |#1| (QUOTE (|CharacteristicZero|))) (AND (|HasCategory| |#1| (QUOTE (|PartialDifferentialRing| #5=(|Symbol|)))) #6=(|HasSignature| |#1| (|%list| (QUOTE *) (|%list| #7=(|devaluate| |#1|) #8=(QUOTE #9=(|NonNegativeInteger|)) #7#)))) #6# (|HasCategory| #9# (QUOTE (|SemiGroup|))) (AND #10=(|HasSignature| |#1| (|%list| (QUOTE **) (|%list| #7# #7# #8#))) (|HasSignature| |#1| (|%list| (QUOTE |coerce|) (|%list| #7# #11=(QUOTE #5#))))) #10# (|HasCategory| |#1| (QUOTE (|Field|))) (OR (AND #1# (|HasCategory| |#1| (QUOTE (|AlgebraicallyClosedFunctionSpace| #2#))) (|HasCategory| |#1| (QUOTE (|PrimitiveFunctionCategory|))) (|HasCategory| |#1| (QUOTE (|TranscendentalFunctionCategory|)))) (AND #1# (|HasSignature| |#1| (|%list| (QUOTE |integrate|) (|%list| #7# #7# #11#))) (|HasSignature| |#1| (|%list| (QUOTE |variables|) (|%list| (|%list| (QUOTE |List|) #11#) #7#)))))) (|Symbol|) ((|constructor| (NIL "Basic and scripted symbols.")) (|sample| (($) "\\spad{sample()} returns a sample of \\%")) (|list| (((|List| $) $) "\\spad{list(sy)} takes a scripted symbol and produces a list of the name followed by the scripts.")) (|string| (((|String|) $) "\\spad{string(s)} converts the symbol \\spad{s} to a string. Error: if the symbol is subscripted.")) (|elt| (($ $ (|List| (|OutputForm|))) "\\spad{elt(s,[a1,...,an])} or \\spad{s}([\\spad{a1},{}...,{}an]) returns \\spad{s} subscripted by \\spad{[a1,...,an]}.")) (|argscript| (($ $ (|List| (|OutputForm|))) "\\spad{argscript(s, [a1,...,an])} returns \\spad{s} arg-scripted by \\spad{[a1,...,an]}.")) (|superscript| (($ $ (|List| (|OutputForm|))) "\\spad{superscript(s, [a1,...,an])} returns \\spad{s} superscripted by \\spad{[a1,...,an]}.")) (|subscript| (($ $ (|List| (|OutputForm|))) "\\spad{subscript(s, [a1,...,an])} returns \\spad{s} subscripted by \\spad{[a1,...,an]}.")) (|script| (($ $ (|Record| (|:| |sub| (|List| (|OutputForm|))) (|:| |sup| (|List| (|OutputForm|))) (|:| |presup| (|List| (|OutputForm|))) (|:| |presub| (|List| (|OutputForm|))) (|:| |args| (|List| (|OutputForm|))))) "\\spad{script(s, [a,b,c,d,e])} returns \\spad{s} with subscripts a,{} superscripts \\spad{b},{} pre-superscripts \\spad{c},{} pre-subscripts \\spad{d},{} and argument-scripts \\spad{e}.") (($ $ (|List| (|List| (|OutputForm|)))) "\\spad{script(s, [a,b,c,d,e])} returns \\spad{s} with subscripts a,{} superscripts \\spad{b},{} pre-superscripts \\spad{c},{} pre-subscripts \\spad{d},{} and argument-scripts \\spad{e}. Omitted components are taken to be empty. For example,{} \\spad{script(s, [a,b,c])} is equivalent to \\spad{script(s,[a,b,c,[],[]])}.")) (|scripts| (((|Record| (|:| |sub| (|List| (|OutputForm|))) (|:| |sup| (|List| (|OutputForm|))) (|:| |presup| (|List| (|OutputForm|))) (|:| |presub| (|List| (|OutputForm|))) (|:| |args| (|List| (|OutputForm|)))) $) "\\spad{scripts(s)} returns all the scripts of \\spad{s}.")) (|scripted?| (((|Boolean|) $) "\\spad{scripted?(s)} is \\spad{true} if \\spad{s} has been given any scripts.")) (|name| (($ $) "\\spad{name(s)} returns \\spad{s} without its scripts.")) (|resetNew| (((|Void|)) "\\spad{resetNew()} resets the internals counters that new() and new(\\spad{s}) use to return distinct symbols every time.")) (|new| (($ $) "\\spad{new(s)} returns a new symbol whose name starts with \\%\\spad{s}.") (($) "\\spad{new()} returns a new symbol whose name starts with \\%."))) @@ -4314,14 +4314,14 @@ NIL NIL (|SymmetricPolynomial| R) ((|constructor| (NIL "This domain implements symmetric polynomial"))) -(((|commutative| "*") |has| |#1| (|CommutativeRing|)) (|noZeroDivisors| |has| |#1| (|IntegralDomain|)) (|canonicalUnitNormal| |has| |#1| (ATTRIBUTE |canonicalUnitNormal|)) (|rightUnitary| . T) (|leftUnitary| . T) (|unitsKnown| . T)) +(((|commutative| "*") |has| |#1| (|CommutativeRing|)) (|noZeroDivisors| |has| |#1| (|IntegralDomain|)) (|canonicalUnitNormal| |has| |#1| (ATTRIBUTE |canonicalUnitNormal|))) (#1=(|HasCategory| |#1| (QUOTE (|Algebra| #2=(|Fraction| #3=(|Integer|))))) #4=(|HasCategory| |#1| (QUOTE (|IntegralDomain|))) (OR #5=(|HasCategory| |#1| (QUOTE (|CommutativeRing|))) #4#) #5# (|HasCategory| |#1| (QUOTE (|CharacteristicNonZero|))) (|HasCategory| |#1| (QUOTE (|CharacteristicZero|))) (OR #1# #6=(|HasCategory| |#1| (QUOTE (|RetractableTo| #2#)))) #6# (|HasCategory| |#1| (QUOTE (|RetractableTo| #3#))) (|HasCategory| |#1| (QUOTE (|Field|))) (|HasCategory| |#1| (QUOTE (|GcdDomain|))) (AND #4# (|HasCategory| (|Partition|) (QUOTE (|CancellationAbelianMonoid|)))) (|HasAttribute| |#1| (QUOTE |canonicalUnitNormal|))) (|TheSymbolTable|) ((|constructor| (NIL "Creates and manipulates one global symbol table for FORTRAN code generation,{} containing details of types,{} dimensions,{} and argument lists.")) (|symbolTableOf| (((|SymbolTable|) (|Symbol|) $) "\\spad{symbolTableOf(f,tab)} returns the symbol table of \\spad{f}")) (|argumentListOf| (((|List| (|Symbol|)) (|Symbol|) $) "\\spad{argumentListOf(f,tab)} returns the argument list of \\spad{f}")) (|returnTypeOf| (((|Union| (|:| |fst| (|FortranScalarType|)) (|:| |void| #1="void")) (|Symbol|) $) "\\spad{returnTypeOf(f,tab)} returns the type of the object returned by \\spad{f}")) (|empty| (($) "\\spad{empty()} creates a new,{} empty symbol table.")) (|printTypes| (((|Void|) (|Symbol|)) "\\spad{printTypes(tab)} produces FORTRAN type declarations from \\spad{tab},{} on the current FORTRAN output stream")) (|printHeader| (((|Void|)) "\\spad{printHeader()} produces the FORTRAN header for the current subprogram in the global symbol table on the current FORTRAN output stream.") (((|Void|) (|Symbol|)) "\\spad{printHeader(f)} produces the FORTRAN header for subprogram \\spad{f} in the global symbol table on the current FORTRAN output stream.") (((|Void|) (|Symbol|) $) "\\spad{printHeader(f,tab)} produces the FORTRAN header for subprogram \\spad{f} in symbol table \\spad{tab} on the current FORTRAN output stream.")) (|returnType!| (((|Void|) (|Union| (|:| |fst| (|FortranScalarType|)) (|:| |void| #1#))) "\\spad{returnType!(t)} declares that the return type of he current subprogram in the global symbol table is \\spad{t}.") (((|Void|) (|Symbol|) (|Union| (|:| |fst| (|FortranScalarType|)) (|:| |void| #1#))) "\\spad{returnType!(f,t)} declares that the return type of subprogram \\spad{f} in the global symbol table is \\spad{t}.") (((|Void|) (|Symbol|) (|Union| (|:| |fst| (|FortranScalarType|)) (|:| |void| #1#)) $) "\\spad{returnType!(f,t,tab)} declares that the return type of subprogram \\spad{f} in symbol table \\spad{tab} is \\spad{t}.")) (|argumentList!| (((|Void|) (|List| (|Symbol|))) "\\spad{argumentList!(l)} declares that the argument list for the current subprogram in the global symbol table is \\spad{l}.") (((|Void|) (|Symbol|) (|List| (|Symbol|))) "\\spad{argumentList!(f,l)} declares that the argument list for subprogram \\spad{f} in the global symbol table is \\spad{l}.") (((|Void|) (|Symbol|) (|List| (|Symbol|)) $) "\\spad{argumentList!(f,l,tab)} declares that the argument list for subprogram \\spad{f} in symbol table \\spad{tab} is \\spad{l}.")) (|endSubProgram| (((|Symbol|)) "\\spad{endSubProgram()} asserts that we are no longer processing the current subprogram.")) (|currentSubProgram| (((|Symbol|)) "\\spad{currentSubProgram()} returns the name of the current subprogram being processed")) (|newSubProgram| (((|Void|) (|Symbol|)) "\\spad{newSubProgram(f)} asserts that from now on type declarations are part of subprogram \\spad{f}.")) (|declare!| (((|FortranType|) (|Symbol|) (|FortranType|) (|Symbol|)) "\\spad{declare!(u,t,asp)} declares the parameter \\spad{u} to have type \\spad{t} in \\spad{asp}.") (((|FortranType|) (|Symbol|) (|FortranType|)) "\\spad{declare!(u,t)} declares the parameter \\spad{u} to have type \\spad{t} in the current level of the symbol table.") (((|FortranType|) (|List| (|Symbol|)) (|FortranType|) (|Symbol|) $) "\\spad{declare!(u,t,asp,tab)} declares the parameters \\spad{u} of subprogram \\spad{asp} to have type \\spad{t} in symbol table \\spad{tab}.") (((|FortranType|) (|Symbol|) (|FortranType|) (|Symbol|) $) "\\spad{declare!(u,t,asp,tab)} declares the parameter \\spad{u} of subprogram \\spad{asp} to have type \\spad{t} in symbol table \\spad{tab}.")) (|clearTheSymbolTable| (((|Void|) (|Symbol|)) "\\spad{clearTheSymbolTable(x)} removes the symbol \\spad{x} from the table") (((|Void|)) "\\spad{clearTheSymbolTable()} clears the current symbol table.")) (|showTheSymbolTable| (($) "\\spad{showTheSymbolTable()} returns the current symbol table."))) NIL NIL (|SymbolTable|) -((|constructor| (NIL "Create and manipulate a symbol table for generated FORTRAN code")) (|symbolTable| (($ (|List| (|Record| (|:| |key| (|Symbol|)) (|:| |entry| (|FortranType|))))) "\\spad{symbolTable(l)} creates a symbol table from the elements of \\spad{l}.")) (|printTypes| (((|Void|) $) "\\spad{printTypes(tab)} produces FORTRAN type declarations from \\spad{tab},{} on the current FORTRAN output stream")) (|newTypeLists| (((|SExpression|) $) "\\spad{newTypeLists(x)} \\undocumented")) (|typeLists| (((|List| (|List| (|Union| (|:| |name| (|Symbol|)) (|:| |bounds| (|List| (|Union| (|:| S (|Symbol|)) (|:| P (|Polynomial| (|Integer|))))))))) $) "\\spad{typeLists(tab)} returns a list of lists of types of objects in \\spad{tab}")) (|externalList| (((|List| (|Symbol|)) $) "\\spad{externalList(tab)} returns a list of all the external symbols in \\spad{tab}")) (|typeList| (((|List| (|Union| (|:| |name| (|Symbol|)) (|:| |bounds| (|List| (|Union| (|:| S (|Symbol|)) (|:| P (|Polynomial| (|Integer|)))))))) (|FortranScalarType|) $) "\\spad{typeList(t,tab)} returns a list of all the objects of type \\spad{t} in \\spad{tab}")) (|parametersOf| (((|List| (|Symbol|)) $) "\\spad{parametersOf(tab)} returns a list of all the symbols declared in \\spad{tab}")) (|fortranTypeOf| (((|FortranType|) (|Symbol|) $) "\\spad{fortranTypeOf(u,tab)} returns the type of \\spad{u} in \\spad{tab}")) (|declare!| (((|FortranType|) (|Symbol|) (|FortranType|) $) "\\spad{declare!(u,t,tab)} creates a new entry in \\spad{tab},{} declaring \\spad{u} to be of type \\spad{t}") (((|FortranType|) (|List| (|Symbol|)) (|FortranType|) $) "\\spad{declare!(l,t,tab)} creates new entrys in \\spad{tab},{} declaring each of \\spad{l} to be of type \\spad{t}")) (|empty| (($) "\\spad{empty()} returns a new,{} empty symbol table")) (|coerce| (((|Table| (|Symbol|) (|FortranType|)) $) "\\spad{coerce(x)} returns a table view of \\spad{x}"))) +((|constructor| (NIL "Create and manipulate a symbol table for generated FORTRAN code")) (|symbolTable| (($ (|List| (|Record| (|:| |key| (|Symbol|)) (|:| |entry| (|FortranType|))))) "\\spad{symbolTable(l)} creates a symbol table from the elements of \\spad{l}.")) (|printTypes| (((|Void|) $) "\\spad{printTypes(tab)} produces FORTRAN type declarations from \\spad{tab},{} on the current FORTRAN output stream")) (|newTypeLists| (((|SExpression|) $) "\\spad{newTypeLists(x)} \\undocumented")) (|typeLists| (((|List| (|List| (|Union| (|:| |name| (|Symbol|)) (|:| |bounds| (|List| (|Union| (|:| S (|Symbol|)) (|:| P (|Polynomial| (|Integer|))))))))) $) "\\spad{typeLists(tab)} returns a list of lists of types of objects in \\spad{tab}")) (|externalList| (((|List| (|Symbol|)) $) "\\spad{externalList(tab)} returns a list of all the external symbols in \\spad{tab}")) (|typeList| (((|List| (|Union| (|:| |name| (|Symbol|)) (|:| |bounds| (|List| (|Union| (|:| S (|Symbol|)) (|:| P (|Polynomial| (|Integer|)))))))) (|FortranScalarType|) $) "\\spad{typeList(t,tab)} returns a list of all the objects of type \\spad{t} in \\spad{tab}")) (|parametersOf| (((|List| (|Symbol|)) $) "\\spad{parametersOf(tab)} returns a list of all the symbols declared in \\spad{tab}")) (|fortranTypeOf| (((|FortranType|) (|Symbol|) $) "\\spad{fortranTypeOf(u,tab)} returns the type of \\spad{u} in \\spad{tab}")) (|declare!| (((|FortranType|) (|Symbol|) (|FortranType|) $) "\\spad{declare!(u,t,tab)} creates a new entry in \\spad{tab},{} declaring \\spad{u} to be of type \\spad{t}") (((|FortranType|) (|List| (|Symbol|)) (|FortranType|) $) "\\spad{declare!(l,t,tab)} creates new entrys in \\spad{tab},{} declaring each of \\spad{l} to be of type \\spad{t}")) (|empty| (($) "\\spad{empty()} returns a new,{} empty symbol table"))) NIL NIL (|Syntax|) @@ -4357,7 +4357,7 @@ NIL NIL ((AND (|HasCategory| #1=(|Record| (|:| |key| |#1|) (|:| |entry| |#2|)) (|%list| #2=(QUOTE |Evalable|) #3=(|%list| (QUOTE |Record|) (|%list| #4=(QUOTE |:|) (QUOTE |key|) (|devaluate| |#1|)) (|%list| #4# (QUOTE |entry|) #5=(|devaluate| |#2|))))) #6=(|HasCategory| #1# #7=(QUOTE (|SetCategory|)))) (OR #8=(|HasCategory| |#2| #7#) #6#) (OR #9=(|HasCategory| |#2| #10=(QUOTE (|BasicType|))) #8# #11=(|HasCategory| #1# #10#) #6#) (OR #12=(|HasCategory| #1# #13=(QUOTE (|CoercibleTo| (|OutputForm|)))) #14=(|HasCategory| |#2| #13#)) (|HasCategory| #1# (QUOTE (|ConvertibleTo| (|InputForm|)))) (AND #8# (|HasCategory| |#2| (|%list| #2# #5#))) #11# (|HasCategory| |#1| (QUOTE (|OrderedSet|))) #9# (OR #9# #11#) #8# #14# #12# #6# (AND #15=(|HasCategory| $ (|%list| #16=(QUOTE |FiniteAggregate|) #3#)) #11#) #15# (AND #9# (|HasCategory| $ (|%list| #16# #5#))) (|HasCategory| $ (|%list| (QUOTE |ShallowlyMutableAggregate|) #5#))) (|Tableau| S) -((|constructor| (NIL "\\indented{1}{The tableau domain is for printing Young tableaux,{} and} coercions to and from List List \\spad{S} where \\spad{S} is a set.")) (|coerce| (((|OutputForm|) $) "\\spad{coerce(t)} converts a tableau \\spad{t} to an output form.")) (|listOfLists| (((|List| (|List| |#1|)) $) "\\spad{listOfLists t} converts a tableau \\spad{t} to a list of lists.")) (|tableau| (($ (|List| (|List| |#1|))) "\\spad{tableau(ll)} converts a list of lists \\spad{ll} to a tableau."))) +((|constructor| (NIL "\\indented{1}{The tableau domain is for printing Young tableaux,{} and} coercions to and from List List \\spad{S} where \\spad{S} is a set.")) (|listOfLists| (((|List| (|List| |#1|)) $) "\\spad{listOfLists t} converts a tableau \\spad{t} to a list of lists.")) (|tableau| (($ (|List| (|List| |#1|))) "\\spad{tableau(ll)} converts a list of lists \\spad{ll} to a tableau."))) NIL NIL (|TermAlgebraOperator| S) @@ -4434,8 +4434,8 @@ NIL ((AND (|HasCategory| |#1| #1=(|%list| (QUOTE |ConvertibleTo|) (|%list| (QUOTE |Pattern|) #2=(|devaluate| |#1|)))) (|HasCategory| |#1| #3=(|%list| (QUOTE |PatternMatchable|) #2#)) (|HasCategory| |#2| #1#) (|HasCategory| |#2| #3#))) (|TaylorSeries| |Coef|) ((|constructor| (NIL "\\spadtype{TaylorSeries} is a general multivariate Taylor series domain over the ring Coef and with variables of type Symbol.")) (|fintegrate| (($ (|Mapping| $) (|Symbol|) |#1|) "\\spad{fintegrate(f,v,c)} is the integral of \\spad{f()} with respect \\indented{1}{to \\spad{v} and having \\spad{c} as the constant of integration.} \\indented{1}{The evaluation of \\spad{f()} is delayed.}")) (|integrate| (($ $ (|Symbol|) |#1|) "\\spad{integrate(s,v,c)} is the integral of \\spad{s} with respect \\indented{1}{to \\spad{v} and having \\spad{c} as the constant of integration.}")) (|coerce| (($ (|Polynomial| |#1|)) "\\spad{coerce(s)} regroups terms of \\spad{s} by total degree \\indented{1}{and forms a series.}") (($ (|Symbol|)) "\\spad{coerce(s)} converts a variable to a Taylor series")) (|coefficient| (((|Polynomial| |#1|) $ (|NonNegativeInteger|)) "\\spad{coefficient(s, n)} gives the terms of total degree \\spad{n}."))) -(((|commutative| "*") |has| |#1| (|CommutativeRing|)) (|noZeroDivisors| |has| |#1| (|IntegralDomain|)) (|leftUnitary| . T) (|rightUnitary| . T) (|unitsKnown| . T)) -((|HasCategory| |#1| (QUOTE (|Algebra| (|Fraction| (|Integer|))))) #1=(|HasCategory| |#1| (QUOTE (|CommutativeRing|))) (|HasCategory| |#1| (QUOTE (|CharacteristicZero|))) (|HasCategory| |#1| (QUOTE (|CharacteristicNonZero|))) (OR #1# #2=(|HasCategory| |#1| (QUOTE (|IntegralDomain|)))) #2# (|HasCategory| |#1| (QUOTE (|Field|)))) +(((|commutative| "*") |has| |#1| (|CommutativeRing|)) (|noZeroDivisors| |has| |#1| (|IntegralDomain|))) +((|HasCategory| |#1| (QUOTE (|Algebra| (|Fraction| (|Integer|))))) #1=(|HasCategory| |#1| (QUOTE (|IntegralDomain|))) #2=(|HasCategory| |#1| (QUOTE (|CommutativeRing|))) (OR #2# #1#) (|HasCategory| |#1| (QUOTE (|CharacteristicNonZero|))) (|HasCategory| |#1| (QUOTE (|CharacteristicZero|))) (|HasCategory| |#1| (QUOTE (|Field|)))) (|TriangularSetCategory&| S R E V P) ((|constructor| (NIL "The category of triangular sets of multivariate polynomials with coefficients in an integral domain. Let \\axiom{\\spad{R}} be an integral domain and \\axiom{\\spad{V}} a finite ordered set of variables,{} say \\axiom{\\spad{X1} < \\spad{X2} < ... < Xn}. A set \\axiom{\\spad{S}} of polynomials in \\axiom{\\spad{R}[\\spad{X1},{}\\spad{X2},{}...,{}Xn]} is triangular if no elements of \\axiom{\\spad{S}} lies in \\axiom{\\spad{R}},{} and if two distinct elements of \\axiom{\\spad{S}} have distinct main variables. Note that the empty set is a triangular set. A triangular set is not necessarily a (lexicographical) Groebner basis and the notion of reduction related to triangular sets is based on the recursive view of polynomials. We recall this notion here and refer to [1] for more details. A polynomial \\axiom{\\spad{P}} is reduced \\spad{w}.\\spad{r}.\\spad{t} a non-constant polynomial \\axiom{\\spad{Q}} if the degree of \\axiom{\\spad{P}} in the main variable of \\axiom{\\spad{Q}} is less than the main degree of \\axiom{\\spad{Q}}. A polynomial \\axiom{\\spad{P}} is reduced \\spad{w}.\\spad{r}.\\spad{t} a triangular set \\axiom{\\spad{T}} if it is reduced \\spad{w}.\\spad{r}.\\spad{t}. every polynomial of \\axiom{\\spad{T}}. \\newline References : \\indented{1}{[1] \\spad{P}. AUBRY,{} \\spad{D}. LAZARD and \\spad{M}. MORENO MAZA \"On the Theories} \\indented{5}{of Triangular Sets\" Journal of Symbol. Comp. (to appear)}")) (|coHeight| (((|NonNegativeInteger|) $) "\\axiom{coHeight(ts)} returns \\axiom{size()\\$\\spad{V}} minus \\axiom{\\#ts}.")) (|extend| (($ $ |#5|) "\\axiom{extend(ts,{}\\spad{p})} returns a triangular set which encodes the simple extension by \\axiom{\\spad{p}} of the extension of the base field defined by \\axiom{ts},{} according to the properties of triangular sets of the current category If the required properties do not hold an error is returned.")) (|extendIfCan| (((|Union| $ "failed") $ |#5|) "\\axiom{extendIfCan(ts,{}\\spad{p})} returns a triangular set which encodes the simple extension by \\axiom{\\spad{p}} of the extension of the base field defined by \\axiom{ts},{} according to the properties of triangular sets of the current domain. If the required properties do not hold then \"failed\" is returned. This operation encodes in some sense the properties of the triangular sets of the current category. Is is used to implement the \\axiom{construct} operation to guarantee that every triangular set build from a list of polynomials has the required properties.")) (|select| (((|Union| |#5| "failed") $ |#4|) "\\axiom{select(ts,{}\\spad{v})} returns the polynomial of \\axiom{ts} with \\axiom{\\spad{v}} as main variable,{} if any.")) (|algebraic?| (((|Boolean|) |#4| $) "\\axiom{algebraic?(\\spad{v},{}ts)} returns \\spad{true} iff \\axiom{\\spad{v}} is the main variable of some polynomial in \\axiom{ts}.")) (|algebraicVariables| (((|List| |#4|) $) "\\axiom{algebraicVariables(ts)} returns the decreasingly sorted list of the main variables of the polynomials of \\axiom{ts}.")) (|rest| (((|Union| $ "failed") $) "\\axiom{rest(ts)} returns the polynomials of \\axiom{ts} with smaller main variable than \\axiom{mvar(ts)} if \\axiom{ts} is not empty,{} otherwise returns \"failed\"")) (|last| (((|Union| |#5| "failed") $) "\\axiom{last(ts)} returns the polynomial of \\axiom{ts} with smallest main variable if \\axiom{ts} is not empty,{} otherwise returns \\axiom{\"failed\"}.")) (|first| (((|Union| |#5| "failed") $) "\\axiom{first(ts)} returns the polynomial of \\axiom{ts} with greatest main variable if \\axiom{ts} is not empty,{} otherwise returns \\axiom{\"failed\"}.")) (|zeroSetSplitIntoTriangularSystems| (((|List| (|Record| (|:| |close| $) (|:| |open| (|List| |#5|)))) (|List| |#5|)) "\\axiom{zeroSetSplitIntoTriangularSystems(lp)} returns a list of triangular systems \\axiom{[[\\spad{ts1},{}\\spad{qs1}],{}...,{}[tsn,{}qsn]]} such that the zero set of \\axiom{lp} is the union of the closures of the \\axiom{W_i} where \\axiom{W_i} consists of the zeros of \\axiom{ts} which do not cancel any polynomial in \\axiom{qsi}.")) (|zeroSetSplit| (((|List| $) (|List| |#5|)) "\\axiom{zeroSetSplit(lp)} returns a list \\axiom{lts} of triangular sets such that the zero set of \\axiom{lp} is the union of the closures of the regular zero sets of the members of \\axiom{lts}.")) (|reduceByQuasiMonic| ((|#5| |#5| $) "\\axiom{reduceByQuasiMonic(\\spad{p},{}ts)} returns the same as \\axiom{remainder(\\spad{p},{}collectQuasiMonic(ts)).polnum}.")) (|collectQuasiMonic| (($ $) "\\axiom{collectQuasiMonic(ts)} returns the subset of \\axiom{ts} consisting of the polynomials with initial in \\axiom{\\spad{R}}.")) (|removeZero| ((|#5| |#5| $) "\\axiom{removeZero(\\spad{p},{}ts)} returns \\axiom{0} if \\axiom{\\spad{p}} reduces to \\axiom{0} by pseudo-division \\spad{w}.\\spad{r}.\\spad{t} \\axiom{ts} otherwise returns a polynomial \\axiom{\\spad{q}} computed from \\axiom{\\spad{p}} by removing any coefficient in \\axiom{\\spad{p}} reducing to \\axiom{0}.")) (|initiallyReduce| ((|#5| |#5| $) "\\axiom{initiallyReduce(\\spad{p},{}ts)} returns a polynomial \\axiom{\\spad{r}} such that \\axiom{initiallyReduced?(\\spad{r},{}ts)} holds and there exists some product \\axiom{\\spad{h}} of \\axiom{initials(ts)} such that \\axiom{h*p - \\spad{r}} lies in the ideal generated by \\axiom{ts}.")) (|headReduce| ((|#5| |#5| $) "\\axiom{headReduce(\\spad{p},{}ts)} returns a polynomial \\axiom{\\spad{r}} such that \\axiom{headReduce?(\\spad{r},{}ts)} holds and there exists some product \\axiom{\\spad{h}} of \\axiom{initials(ts)} such that \\axiom{h*p - \\spad{r}} lies in the ideal generated by \\axiom{ts}.")) (|stronglyReduce| ((|#5| |#5| $) "\\axiom{stronglyReduce(\\spad{p},{}ts)} returns a polynomial \\axiom{\\spad{r}} such that \\axiom{stronglyReduced?(\\spad{r},{}ts)} holds and there exists some product \\axiom{\\spad{h}} of \\axiom{initials(ts)} such that \\axiom{h*p - \\spad{r}} lies in the ideal generated by \\axiom{ts}.")) (|rewriteSetWithReduction| (((|List| |#5|) (|List| |#5|) $ (|Mapping| |#5| |#5| |#5|) (|Mapping| (|Boolean|) |#5| |#5|)) "\\axiom{rewriteSetWithReduction(lp,{}ts,{}redOp,{}redOp?)} returns a list \\axiom{lq} of polynomials such that \\axiom{[reduce(\\spad{p},{}ts,{}redOp,{}redOp?) for \\spad{p} in lp]} and \\axiom{lp} have the same zeros inside the regular zero set of \\axiom{ts}. Moreover,{} for every polynomial \\axiom{\\spad{q}} in \\axiom{lq} and every polynomial \\axiom{\\spad{t}} in \\axiom{ts} \\axiom{redOp?(\\spad{q},{}\\spad{t})} holds and there exists a polynomial \\axiom{\\spad{p}} in the ideal generated by \\axiom{lp} and a product \\axiom{\\spad{h}} of \\axiom{initials(ts)} such that \\axiom{h*p - \\spad{r}} lies in the ideal generated by \\axiom{ts}. The operation \\axiom{redOp} must satisfy the following conditions. For every \\axiom{\\spad{p}} and \\axiom{\\spad{q}} we have \\axiom{redOp?(redOp(\\spad{p},{}\\spad{q}),{}\\spad{q})} and there exists an integer \\axiom{\\spad{e}} and a polynomial \\axiom{\\spad{f}} such that \\axiom{init(\\spad{q})^e*p = f*q + redOp(\\spad{p},{}\\spad{q})}.")) (|reduce| ((|#5| |#5| $ (|Mapping| |#5| |#5| |#5|) (|Mapping| (|Boolean|) |#5| |#5|)) "\\axiom{reduce(\\spad{p},{}ts,{}redOp,{}redOp?)} returns a polynomial \\axiom{\\spad{r}} such that \\axiom{redOp?(\\spad{r},{}\\spad{p})} holds for every \\axiom{\\spad{p}} of \\axiom{ts} and there exists some product \\axiom{\\spad{h}} of the initials of the members of \\axiom{ts} such that \\axiom{h*p - \\spad{r}} lies in the ideal generated by \\axiom{ts}. The operation \\axiom{redOp} must satisfy the following conditions. For every \\axiom{\\spad{p}} and \\axiom{\\spad{q}} we have \\axiom{redOp?(redOp(\\spad{p},{}\\spad{q}),{}\\spad{q})} and there exists an integer \\axiom{\\spad{e}} and a polynomial \\axiom{\\spad{f}} such that \\axiom{init(\\spad{q})^e*p = f*q + redOp(\\spad{p},{}\\spad{q})}.")) (|autoReduced?| (((|Boolean|) $ (|Mapping| (|Boolean|) |#5| (|List| |#5|))) "\\axiom{autoReduced?(ts,{}redOp?)} returns \\spad{true} iff every element of \\axiom{ts} is reduced \\spad{w}.\\spad{r}.\\spad{t} to every other in the sense of \\axiom{redOp?}")) (|initiallyReduced?| (((|Boolean|) $) "\\spad{initiallyReduced?(ts)} returns \\spad{true} iff for every element \\axiom{\\spad{p}} of \\axiom{\\spad{ts}} \\axiom{\\spad{p}} and all its iterated initials are reduced \\spad{w}.\\spad{r}.\\spad{t}. to the other elements of \\axiom{\\spad{ts}} with the same main variable.") (((|Boolean|) |#5| $) "\\axiom{initiallyReduced?(\\spad{p},{}ts)} returns \\spad{true} iff \\axiom{\\spad{p}} and all its iterated initials are reduced \\spad{w}.\\spad{r}.\\spad{t}. to the elements of \\axiom{ts} with the same main variable.")) (|headReduced?| (((|Boolean|) $) "\\spad{headReduced?(ts)} returns \\spad{true} iff the head of every element of \\axiom{\\spad{ts}} is reduced \\spad{w}.\\spad{r}.\\spad{t} to any other element of \\axiom{\\spad{ts}}.") (((|Boolean|) |#5| $) "\\axiom{headReduced?(\\spad{p},{}ts)} returns \\spad{true} iff the head of \\axiom{\\spad{p}} is reduced \\spad{w}.\\spad{r}.\\spad{t}. \\axiom{ts}.")) (|stronglyReduced?| (((|Boolean|) $) "\\axiom{stronglyReduced?(ts)} returns \\spad{true} iff every element of \\axiom{ts} is reduced \\spad{w}.\\spad{r}.\\spad{t} to any other element of \\axiom{ts}.") (((|Boolean|) |#5| $) "\\axiom{stronglyReduced?(\\spad{p},{}ts)} returns \\spad{true} iff \\axiom{\\spad{p}} is reduced \\spad{w}.\\spad{r}.\\spad{t}. \\axiom{ts}.")) (|reduced?| (((|Boolean|) |#5| $ (|Mapping| (|Boolean|) |#5| |#5|)) "\\axiom{reduced?(\\spad{p},{}ts,{}redOp?)} returns \\spad{true} iff \\axiom{\\spad{p}} is reduced \\spad{w}.\\spad{r}.\\spad{t}. in the sense of the operation \\axiom{redOp?},{} that is if for every \\axiom{\\spad{t}} in \\axiom{ts} \\axiom{redOp?(\\spad{p},{}\\spad{t})} holds.")) (|normalized?| (((|Boolean|) $) "\\axiom{normalized?(ts)} returns \\spad{true} iff for every axiom{\\spad{p}} in axiom{ts} we have \\axiom{normalized?(\\spad{p},{}us)} where \\axiom{us} is \\axiom{collectUnder(ts,{}mvar(\\spad{p}))}.") (((|Boolean|) |#5| $) "\\axiom{normalized?(\\spad{p},{}ts)} returns \\spad{true} iff \\axiom{\\spad{p}} and all its iterated initials have degree zero \\spad{w}.\\spad{r}.\\spad{t}. the main variables of the polynomials of \\axiom{ts}")) (|quasiComponent| (((|Record| (|:| |close| (|List| |#5|)) (|:| |open| (|List| |#5|))) $) "\\axiom{quasiComponent(ts)} returns \\axiom{[lp,{}lq]} where \\axiom{lp} is the list of the members of \\axiom{ts} and \\axiom{lq}is \\axiom{initials(ts)}.")) (|degree| (((|NonNegativeInteger|) $) "\\axiom{degree(ts)} returns the product of main degrees of the members of \\axiom{ts}.")) (|initials| (((|List| |#5|) $) "\\axiom{initials(ts)} returns the list of the non-constant initials of the members of \\axiom{ts}.")) (|basicSet| (((|Union| (|Record| (|:| |bas| $) (|:| |top| (|List| |#5|))) "failed") (|List| |#5|) (|Mapping| (|Boolean|) |#5|) (|Mapping| (|Boolean|) |#5| |#5|)) "\\axiom{basicSet(ps,{}pred?,{}redOp?)} returns the same as \\axiom{basicSet(qs,{}redOp?)} where \\axiom{qs} consists of the polynomials of \\axiom{ps} satisfying property \\axiom{pred?}.") (((|Union| (|Record| (|:| |bas| $) (|:| |top| (|List| |#5|))) "failed") (|List| |#5|) (|Mapping| (|Boolean|) |#5| |#5|)) "\\axiom{basicSet(ps,{}redOp?)} returns \\axiom{[bs,{}ts]} where \\axiom{concat(bs,{}ts)} is \\axiom{ps} and \\axiom{bs} is a basic set in Wu Wen Tsun sense of \\axiom{ps} \\spad{w}.\\spad{r}.\\spad{t} the reduction-test \\axiom{redOp?},{} if no non-zero constant polynomial lie in \\axiom{ps},{} otherwise \\axiom{\"failed\"} is returned.")) (|infRittWu?| (((|Boolean|) $ $) "\\axiom{infRittWu?(\\spad{ts1},{}\\spad{ts2})} returns \\spad{true} iff \\axiom{\\spad{ts2}} has higher rank than \\axiom{\\spad{ts1}} in Wu Wen Tsun sense."))) NIL @@ -4482,7 +4482,7 @@ NIL NIL (|UniqueFactorizationDomain|) ((|constructor| (NIL "A constructive unique factorization domain,{} \\spadignore{i.e.} where we can constructively factor members into a product of a finite number of irreducible elements.")) (|factor| (((|Factored| $) $) "\\spad{factor(x)} returns the factorization of \\spad{x} into irreducibles.")) (|squareFreePart| (($ $) "\\spad{squareFreePart(x)} returns a product of prime factors of \\spad{x} each taken with multiplicity one.")) (|squareFree| (((|Factored| $) $) "\\spad{squareFree(x)} returns the square-free factorization of \\spad{x} \\spadignore{i.e.} such that the factors are pairwise relatively prime and each has multiple prime factors.")) (|prime?| (((|Boolean|) $) "\\spad{prime?(x)} tests if \\spad{x} can never be written as the product of two non-units of the ring,{} \\spadignore{i.e.} \\spad{x} is an irreducible element."))) -((|noZeroDivisors| . T) ((|commutative| "*") . T) (|rightUnitary| . T) (|leftUnitary| . T) (|unitsKnown| . T)) +((|noZeroDivisors| . T) ((|commutative| "*") . T)) NIL (|UInt16|) ((|constructor| (NIL "This domain is a datatype for (unsigned) integer values of precision 16 bits."))) @@ -4502,15 +4502,15 @@ NIL NIL (|UnivariateLaurentSeries| |Coef| |var| |cen|) ((|constructor| (NIL "Dense Laurent series in one variable \\indented{2}{\\spadtype{UnivariateLaurentSeries} is a domain representing Laurent} \\indented{2}{series in one variable with coefficients in an arbitrary ring.\\space{2}The} \\indented{2}{parameters of the type specify the coefficient ring,{} the power series} \\indented{2}{variable,{} and the center of the power series expansion.\\space{2}For example,{}} \\indented{2}{\\spad{UnivariateLaurentSeries(Integer,x,3)} represents Laurent series in} \\indented{2}{\\spad{(x - 3)} with integer coefficients.}")) (|integrate| (($ $ (|Variable| |#2|)) "\\spad{integrate(f(x))} returns an anti-derivative of the power series \\spad{f(x)} with constant coefficient 0. We may integrate a series when we can divide coefficients by integers.")) (|coerce| (($ (|Variable| |#2|)) "\\spad{coerce(var)} converts the series variable \\spad{var} into a Laurent series."))) -(((|commutative| "*") OR #1=(|and| #2=(|has| |#1| #3=(|Field|)) (|has| #4=(|UnivariateTaylorSeries| |#1| |#2| |#3|) (|OrderedIntegralDomain|))) (|has| |#1| (|CommutativeRing|)) #5=(|and| #2# (|has| #4# (|PolynomialFactorizationExplicit|)))) (|noZeroDivisors| OR #1# (|has| |#1| (|IntegralDomain|)) #5#) (|canonicalUnitNormal| |has| |#1| . #6=(#3#)) (|canonicalsClosed| |has| |#1| . #6#) (|rightUnitary| . T) (|leftUnitary| . T) (|unitsKnown| . T)) -(#1=(|HasCategory| |#1| (QUOTE (|Algebra| (|Fraction| #2=(|Integer|))))) #3=(|HasCategory| |#1| (QUOTE (|IntegralDomain|))) #4=(|HasCategory| |#1| (QUOTE (|CommutativeRing|))) (OR #4# #3#) (OR #5=(AND #6=(|HasCategory| |#1| (QUOTE (|Field|))) #7=(|HasCategory| #8=(|UnivariateTaylorSeries| |#1| |#2| |#3|) #9=(QUOTE (|CharacteristicNonZero|)))) #10=(|HasCategory| |#1| #9#)) (OR #11=(AND #6# (|HasCategory| #8# #12=(QUOTE (|CharacteristicZero|)))) #13=(AND #6# (|HasCategory| #8# (QUOTE (|OrderedIntegralDomain|)))) #14=(|HasCategory| |#1| #12#)) (OR #15=(AND #6# (|HasCategory| #8# #16=(QUOTE (|PartialDifferentialRing| #17=(|Symbol|))))) #18=(AND (|HasCategory| |#1| #16#) #19=(|HasSignature| |#1| (|%list| (QUOTE *) (|%list| #20=(|devaluate| |#1|) #21=(QUOTE #2#) #20#))))) (OR #15# #22=(AND #6# (|HasCategory| #8# (QUOTE (|PartialDifferentialSpace| #17#)))) #18#) (OR #23=(AND #6# (|HasCategory| #8# (QUOTE (|DifferentialRing|)))) #19#) (OR #23# #24=(AND #6# (|HasCategory| #8# (QUOTE (|DifferentialSpace|)))) #19#) (|HasCategory| #2# (QUOTE (|SemiGroup|))) (OR #6# #3#) #6# #25=(AND #6# #26=(|HasCategory| #8# (QUOTE (|PolynomialFactorizationExplicit|)))) (AND #6# (|HasCategory| #8# (QUOTE (|RetractableTo| #17#)))) (AND #6# (|HasCategory| #8# (QUOTE (|ConvertibleTo| (|InputForm|))))) (AND #6# (|HasCategory| #8# (QUOTE (|RealConstant|)))) (OR #4# #6# #3#) #13# (OR #13# #27=(AND #6# (|HasCategory| #8# (QUOTE (|OrderedSet|))))) (OR #28=(AND #6# (|HasCategory| #8# (QUOTE (|RetractableTo| #2#)))) #1#) #28# (AND #6# (|HasCategory| #8# (QUOTE (|StepThrough|)))) (AND #6# (|HasCategory| #8# (|%list| (QUOTE |Eltable|) #29=(|%list| (QUOTE |UnivariateTaylorSeries|) #20# (|devaluate| |#2|) (|devaluate| |#3|)) #29#))) (AND #6# (|HasCategory| #8# (|%list| (QUOTE |Evalable|) #29#))) (AND #6# (|HasCategory| #8# (|%list| (QUOTE |InnerEvalable|) #30=(QUOTE #17#) #29#))) (AND #6# (|HasCategory| #8# (QUOTE (|LinearlyExplicitRingOver| #2#)))) (AND #6# (|HasCategory| #8# (QUOTE (|ConvertibleTo| (|Pattern| #2#))))) (AND #6# (|HasCategory| #8# (QUOTE (|ConvertibleTo| (|Pattern| #31=(|Float|)))))) (AND #6# (|HasCategory| #8# (QUOTE (|PatternMatchable| #2#)))) (AND #6# (|HasCategory| #8# (QUOTE (|PatternMatchable| #31#)))) (AND #32=(|HasSignature| |#1| (|%list| (QUOTE **) (|%list| #20# #20# #21#))) (|HasSignature| |#1| (|%list| (QUOTE |coerce|) (|%list| #20# #30#)))) #32# (OR (AND #1# (|HasCategory| |#1| (QUOTE (|AlgebraicallyClosedFunctionSpace| #2#))) (|HasCategory| |#1| (QUOTE (|PrimitiveFunctionCategory|))) (|HasCategory| |#1| (QUOTE (|TranscendentalFunctionCategory|)))) (AND #1# (|HasSignature| |#1| (|%list| (QUOTE |integrate|) (|%list| #20# #20# #30#))) (|HasSignature| |#1| (|%list| (QUOTE |variables|) (|%list| (|%list| (QUOTE |List|) #30#) #20#))))) (AND #6# (|HasCategory| #8# (QUOTE (|IntegerNumberSystem|)))) (AND #6# (|HasCategory| #8# (QUOTE (|EuclideanDomain|)))) #26# #7# #10# (OR #25# #13# #3#) (OR #25# #13# #4#) #22# #24# #27# (OR #11# #14#) #33=(AND #6# (|HasCategory| $ #9#) #26#) (OR #5# #33# #10#)) +(((|commutative| "*") OR #1=(|and| #2=(|has| |#1| #3=(|Field|)) (|has| #4=(|UnivariateTaylorSeries| |#1| |#2| |#3|) (|OrderedIntegralDomain|))) (|has| |#1| (|CommutativeRing|)) #5=(|and| #2# (|has| #4# (|PolynomialFactorizationExplicit|)))) (|noZeroDivisors| OR #1# (|has| |#1| (|IntegralDomain|)) #5#) (|canonicalUnitNormal| |has| |#1| #3#)) +(#1=(|HasCategory| |#1| (QUOTE (|Algebra| (|Fraction| #2=(|Integer|))))) #3=(|HasCategory| |#1| (QUOTE (|IntegralDomain|))) #4=(|HasCategory| |#1| (QUOTE (|CommutativeRing|))) (OR #4# #3#) (OR #5=(AND #6=(|HasCategory| |#1| (QUOTE (|Field|))) #7=(|HasCategory| #8=(|UnivariateTaylorSeries| |#1| |#2| |#3|) #9=(QUOTE (|CharacteristicNonZero|)))) #10=(|HasCategory| |#1| #9#)) (OR #11=(AND #6# (|HasCategory| #8# #12=(QUOTE (|CharacteristicZero|)))) #13=(AND #6# (|HasCategory| #8# (QUOTE (|OrderedIntegralDomain|)))) #14=(|HasCategory| |#1| #12#)) (OR #15=(AND #6# (|HasCategory| #8# #16=(QUOTE (|PartialDifferentialRing| #17=(|Symbol|))))) #18=(AND (|HasCategory| |#1| #16#) #19=(|HasSignature| |#1| (|%list| (QUOTE *) (|%list| #20=(|devaluate| |#1|) #21=(QUOTE #2#) #20#))))) (OR #15# #22=(AND #6# (|HasCategory| #8# (QUOTE (|PartialDifferentialSpace| #17#)))) #18#) (OR #23=(AND #6# (|HasCategory| #8# (QUOTE (|DifferentialRing|)))) #19#) (OR #23# #24=(AND #6# (|HasCategory| #8# (QUOTE (|DifferentialSpace|)))) #19#) (|HasCategory| #2# (QUOTE (|SemiGroup|))) (OR #6# #3#) #6# #25=(AND #6# #26=(|HasCategory| #8# (QUOTE (|PolynomialFactorizationExplicit|)))) (AND #6# (|HasCategory| #8# (QUOTE (|RetractableTo| #17#)))) (AND #6# (|HasCategory| #8# (QUOTE (|ConvertibleTo| (|InputForm|))))) (AND #6# (|HasCategory| #8# (QUOTE (|RealConstant|)))) (OR #4# #6# #3#) #13# (OR #13# #27=(AND #6# (|HasCategory| #8# (QUOTE (|OrderedSet|))))) (OR #28=(AND #6# (|HasCategory| #8# (QUOTE (|RetractableTo| #2#)))) #1#) #28# (AND #6# (|HasCategory| #8# (QUOTE (|StepThrough|)))) (AND #6# (|HasCategory| #8# (|%list| (QUOTE |Eltable|) #29=(|%list| (QUOTE |UnivariateTaylorSeries|) #20# (|devaluate| |#2|) (|devaluate| |#3|)) #29#))) (AND #6# (|HasCategory| #8# (|%list| (QUOTE |Evalable|) #29#))) (AND #6# (|HasCategory| #8# (|%list| (QUOTE |InnerEvalable|) #30=(QUOTE #17#) #29#))) (AND #6# (|HasCategory| #8# (QUOTE (|LinearlyExplicitRingOver| #2#)))) (AND #6# (|HasCategory| #8# (QUOTE (|ConvertibleTo| (|Pattern| #2#))))) (AND #6# (|HasCategory| #8# (QUOTE (|ConvertibleTo| (|Pattern| #31=(|Float|)))))) (AND #6# (|HasCategory| #8# (QUOTE (|PatternMatchable| #2#)))) (AND #6# (|HasCategory| #8# (QUOTE (|PatternMatchable| #31#)))) (AND #32=(|HasSignature| |#1| (|%list| (QUOTE **) (|%list| #20# #20# #21#))) (|HasSignature| |#1| (|%list| (QUOTE |coerce|) (|%list| #20# #30#)))) #32# (OR (AND #1# (|HasCategory| |#1| (QUOTE (|AlgebraicallyClosedFunctionSpace| #2#))) (|HasCategory| |#1| (QUOTE (|PrimitiveFunctionCategory|))) (|HasCategory| |#1| (QUOTE (|TranscendentalFunctionCategory|)))) (AND #1# (|HasSignature| |#1| (|%list| (QUOTE |integrate|) (|%list| #20# #20# #30#))) (|HasSignature| |#1| (|%list| (QUOTE |variables|) (|%list| (|%list| (QUOTE |List|) #30#) #20#))))) (AND #6# (|HasCategory| #8# (QUOTE (|IntegerNumberSystem|)))) (AND #6# (|HasCategory| #8# (QUOTE (|EuclideanDomain|)))) #26# #7# #10# (OR #25# #13# #3#) (OR #25# #13# #4#) #24# #22# #27# (OR #11# #14#) #33=(AND #6# (|HasCategory| $ #9#) #26#) (OR #5# #33# #10#)) (|UnivariateLaurentSeriesFunctions2| |Coef1| |Coef2| |var1| |var2| |cen1| |cen2|) ((|constructor| (NIL "Mapping package for univariate Laurent series \\indented{2}{This package allows one to apply a function to the coefficients of} \\indented{2}{a univariate Laurent series.}")) (|map| (((|UnivariateLaurentSeries| |#2| |#4| |#6|) (|Mapping| |#2| |#1|) (|UnivariateLaurentSeries| |#1| |#3| |#5|)) "\\spad{map(f,g(x))} applies the map \\spad{f} to the coefficients of the Laurent series \\spad{g(x)}."))) NIL NIL (|UnivariateLaurentSeriesCategory| |Coef|) ((|constructor| (NIL "\\spadtype{UnivariateLaurentSeriesCategory} is the category of Laurent series in one variable.")) (|integrate| (($ $ (|Symbol|)) "\\spad{integrate(f(x),y)} returns an anti-derivative of the power series \\spad{f(x)} with respect to the variable \\spad{y}.") (($ $ (|Symbol|)) "\\spad{integrate(f(x),y)} returns an anti-derivative of the power series \\spad{f(x)} with respect to the variable \\spad{y}.") (($ $) "\\spad{integrate(f(x))} returns an anti-derivative of the power series \\spad{f(x)} with constant coefficient 1. We may integrate a series when we can divide coefficients by integers.")) (|rationalFunction| (((|Fraction| (|Polynomial| |#1|)) $ (|Integer|) (|Integer|)) "\\spad{rationalFunction(f,k1,k2)} returns a rational function consisting of the sum of all terms of \\spad{f} of degree \\spad{d} with \\spad{k1 <= d <= k2}.") (((|Fraction| (|Polynomial| |#1|)) $ (|Integer|)) "\\spad{rationalFunction(f,k)} returns a rational function consisting of the sum of all terms of \\spad{f} of degree <= \\spad{k}.")) (|multiplyCoefficients| (($ (|Mapping| |#1| (|Integer|)) $) "\\spad{multiplyCoefficients(f,sum(n = n0..infinity,a[n] * x**n)) = sum(n = 0..infinity,f(n) * a[n] * x**n)}. This function is used when Puiseux series are represented by a Laurent series and an exponent.")) (|series| (($ (|Stream| (|Record| (|:| |k| (|Integer|)) (|:| |c| |#1|)))) "\\spad{series(st)} creates a series from a stream of non-zero terms,{} where a term is an exponent-coefficient pair. The terms in the stream should be ordered by increasing order of exponents."))) -(((|commutative| "*") |has| |#1| (|CommutativeRing|)) (|noZeroDivisors| |has| |#1| (|IntegralDomain|)) (|canonicalUnitNormal| |has| |#1| . #1=((|Field|))) (|canonicalsClosed| |has| |#1| . #1#) (|rightUnitary| . T) (|leftUnitary| . T) (|unitsKnown| . T)) +(((|commutative| "*") |has| |#1| (|CommutativeRing|)) (|noZeroDivisors| |has| |#1| (|IntegralDomain|)) (|canonicalUnitNormal| |has| |#1| (|Field|))) NIL (|UnivariateLaurentSeriesConstructorCategory&| S |Coef| UTS) ((|constructor| (NIL "This is a category of univariate Laurent series constructed from univariate Taylor series. A Laurent series is represented by a pair \\spad{[n,f(x)]},{} where \\spad{n} is an arbitrary integer and \\spad{f(x)} is a Taylor series. This pair represents the Laurent series \\spad{x**n * f(x)}.")) (|taylorIfCan| (((|Union| |#3| "failed") $) "\\spad{taylorIfCan(f(x))} converts the Laurent series \\spad{f(x)} to a Taylor series,{} if possible. If this is not possible,{} \"failed\" is returned.")) (|taylor| ((|#3| $) "\\spad{taylor(f(x))} converts the Laurent series \\spad{f}(\\spad{x}) to a Taylor series,{} if possible. Error: if this is not possible.")) (|removeZeroes| (($ (|Integer|) $) "\\spad{removeZeroes(n,f(x))} removes up to \\spad{n} leading zeroes from the Laurent series \\spad{f(x)}. A Laurent series is represented by (1) an exponent and (2) a Taylor series which may have leading zero coefficients. When the Taylor series has a leading zero coefficient,{} the 'leading zero' is removed from the Laurent series as follows: the series is rewritten by increasing the exponent by 1 and dividing the Taylor series by its variable.") (($ $) "\\spad{removeZeroes(f(x))} removes leading zeroes from the representation of the Laurent series \\spad{f(x)}. A Laurent series is represented by (1) an exponent and (2) a Taylor series which may have leading zero coefficients. When the Taylor series has a leading zero coefficient,{} the 'leading zero' is removed from the Laurent series as follows: the series is rewritten by increasing the exponent by 1 and dividing the Taylor series by its variable. Note: \\spad{removeZeroes(f)} removes all leading zeroes from \\spad{f}")) (|taylorRep| ((|#3| $) "\\spad{taylorRep(f(x))} returns \\spad{g(x)},{} where \\spad{f = x**n * g(x)} is represented by \\spad{[n,g(x)]}.")) (|degree| (((|Integer|) $) "\\spad{degree(f(x))} returns the degree of the lowest order term of \\spad{f(x)},{} which may have zero as a coefficient.")) (|laurent| (($ (|Integer|) |#3|) "\\spad{laurent(n,f(x))} returns \\spad{x**n * f(x)}."))) @@ -4518,12 +4518,12 @@ NIL ((|HasCategory| |#2| (QUOTE (|Field|)))) (|UnivariateLaurentSeriesConstructorCategory| |Coef| UTS) ((|constructor| (NIL "This is a category of univariate Laurent series constructed from univariate Taylor series. A Laurent series is represented by a pair \\spad{[n,f(x)]},{} where \\spad{n} is an arbitrary integer and \\spad{f(x)} is a Taylor series. This pair represents the Laurent series \\spad{x**n * f(x)}.")) (|taylorIfCan| (((|Union| |#2| "failed") $) "\\spad{taylorIfCan(f(x))} converts the Laurent series \\spad{f(x)} to a Taylor series,{} if possible. If this is not possible,{} \"failed\" is returned.")) (|taylor| ((|#2| $) "\\spad{taylor(f(x))} converts the Laurent series \\spad{f}(\\spad{x}) to a Taylor series,{} if possible. Error: if this is not possible.")) (|removeZeroes| (($ (|Integer|) $) "\\spad{removeZeroes(n,f(x))} removes up to \\spad{n} leading zeroes from the Laurent series \\spad{f(x)}. A Laurent series is represented by (1) an exponent and (2) a Taylor series which may have leading zero coefficients. When the Taylor series has a leading zero coefficient,{} the 'leading zero' is removed from the Laurent series as follows: the series is rewritten by increasing the exponent by 1 and dividing the Taylor series by its variable.") (($ $) "\\spad{removeZeroes(f(x))} removes leading zeroes from the representation of the Laurent series \\spad{f(x)}. A Laurent series is represented by (1) an exponent and (2) a Taylor series which may have leading zero coefficients. When the Taylor series has a leading zero coefficient,{} the 'leading zero' is removed from the Laurent series as follows: the series is rewritten by increasing the exponent by 1 and dividing the Taylor series by its variable. Note: \\spad{removeZeroes(f)} removes all leading zeroes from \\spad{f}")) (|taylorRep| ((|#2| $) "\\spad{taylorRep(f(x))} returns \\spad{g(x)},{} where \\spad{f = x**n * g(x)} is represented by \\spad{[n,g(x)]}.")) (|degree| (((|Integer|) $) "\\spad{degree(f(x))} returns the degree of the lowest order term of \\spad{f(x)},{} which may have zero as a coefficient.")) (|laurent| (($ (|Integer|) |#2|) "\\spad{laurent(n,f(x))} returns \\spad{x**n * f(x)}."))) -(((|commutative| "*") |has| |#1| (|CommutativeRing|)) (|noZeroDivisors| |has| |#1| (|IntegralDomain|)) (|canonicalUnitNormal| |has| |#1| . #1=((|Field|))) (|canonicalsClosed| |has| |#1| . #1#) (|rightUnitary| . T) (|leftUnitary| . T) (|unitsKnown| . T)) +(((|commutative| "*") |has| |#1| (|CommutativeRing|)) (|noZeroDivisors| |has| |#1| (|IntegralDomain|)) (|canonicalUnitNormal| |has| |#1| (|Field|))) NIL (|UnivariateLaurentSeriesConstructor| |Coef| UTS) ((|constructor| (NIL "This package enables one to construct a univariate Laurent series domain from a univariate Taylor series domain. Univariate Laurent series are represented by a pair \\spad{[n,f(x)]},{} where \\spad{n} is an arbitrary integer and \\spad{f(x)} is a Taylor series. This pair represents the Laurent series \\spad{x**n * f(x)}."))) -(((|commutative| "*") |has| |#1| (|CommutativeRing|)) (|noZeroDivisors| |has| |#1| (|IntegralDomain|)) (|canonicalUnitNormal| |has| |#1| . #1=((|Field|))) (|canonicalsClosed| |has| |#1| . #1#) (|rightUnitary| . T) (|leftUnitary| . T) (|unitsKnown| . T)) -(#1=(|HasCategory| |#1| (QUOTE (|Algebra| (|Fraction| #2=(|Integer|))))) #3=(|HasCategory| |#1| (QUOTE (|IntegralDomain|))) #4=(|HasCategory| |#1| (QUOTE (|CommutativeRing|))) (OR #4# #3#) (OR #5=(|HasCategory| |#1| #6=(QUOTE (|CharacteristicNonZero|))) #7=(AND #8=(|HasCategory| |#1| (QUOTE (|Field|))) #9=(|HasCategory| |#2| #6#))) (OR #10=(|HasCategory| |#1| #11=(QUOTE (|CharacteristicZero|))) #12=(AND #8# (|HasCategory| |#2| #11#)) #13=(AND #8# (|HasCategory| |#2| (QUOTE (|OrderedIntegralDomain|))))) (OR #14=(AND #8# (|HasCategory| |#2| #15=(QUOTE (|PartialDifferentialRing| #16=(|Symbol|))))) #17=(AND (|HasCategory| |#1| #15#) #18=(|HasSignature| |#1| (|%list| (QUOTE *) (|%list| #19=(|devaluate| |#1|) #20=(QUOTE #2#) #19#))))) (OR #14# #21=(AND #8# (|HasCategory| |#2| (QUOTE (|PartialDifferentialSpace| #16#)))) #17#) (OR #18# #22=(AND #8# (|HasCategory| |#2| (QUOTE (|DifferentialRing|))))) (OR #18# #22# #23=(AND #8# (|HasCategory| |#2| (QUOTE (|DifferentialSpace|))))) (|HasCategory| #2# (QUOTE (|SemiGroup|))) (OR #8# #3#) #8# (AND #8# #24=(|HasCategory| |#2| (QUOTE (|PolynomialFactorizationExplicit|)))) (AND #8# (|HasCategory| |#2| (QUOTE (|RetractableTo| #16#)))) (AND #8# (|HasCategory| |#2| (QUOTE (|ConvertibleTo| (|InputForm|))))) (AND #8# (|HasCategory| |#2| (QUOTE (|RealConstant|)))) (OR #4# #8# #3#) #13# (OR #13# #25=(AND #8# (|HasCategory| |#2| (QUOTE (|OrderedSet|))))) (OR #1# #26=(AND #8# (|HasCategory| |#2| (QUOTE (|RetractableTo| #2#))))) #26# (AND #8# (|HasCategory| |#2| (QUOTE (|StepThrough|)))) (AND #8# (|HasCategory| |#2| (|%list| (QUOTE |Eltable|) #27=(|devaluate| |#2|) #27#))) (AND #8# (|HasCategory| |#2| (|%list| (QUOTE |Evalable|) #27#))) (AND #8# (|HasCategory| |#2| (|%list| (QUOTE |InnerEvalable|) #28=(QUOTE #16#) #27#))) (AND #8# (|HasCategory| |#2| (QUOTE (|LinearlyExplicitRingOver| #2#)))) (AND #8# (|HasCategory| |#2| (QUOTE (|ConvertibleTo| (|Pattern| #2#))))) (AND #8# (|HasCategory| |#2| (QUOTE (|ConvertibleTo| (|Pattern| #29=(|Float|)))))) (AND #8# (|HasCategory| |#2| (QUOTE (|PatternMatchable| #2#)))) (AND #8# (|HasCategory| |#2| (QUOTE (|PatternMatchable| #29#)))) (AND #30=(|HasSignature| |#1| (|%list| (QUOTE **) (|%list| #19# #19# #20#))) (|HasSignature| |#1| (|%list| (QUOTE |coerce|) (|%list| #19# #28#)))) #30# (OR (AND #1# (|HasCategory| |#1| (QUOTE (|AlgebraicallyClosedFunctionSpace| #2#))) (|HasCategory| |#1| (QUOTE (|PrimitiveFunctionCategory|))) (|HasCategory| |#1| (QUOTE (|TranscendentalFunctionCategory|)))) (AND #1# (|HasSignature| |#1| (|%list| (QUOTE |integrate|) (|%list| #19# #19# #28#))) (|HasSignature| |#1| (|%list| (QUOTE |variables|) (|%list| (|%list| (QUOTE |List|) #28#) #19#))))) #25# #24# (AND #8# (|HasCategory| |#2| (QUOTE (|IntegerNumberSystem|)))) (AND #8# (|HasCategory| |#2| (QUOTE (|EuclideanDomain|)))) #5# #9# (OR #18# #23#) (OR #21# #17#) #21# #23# (OR #10# #12#) #31=(AND #8# #24# (|HasCategory| $ #6#)) (OR #31# #5# #7#)) +(((|commutative| "*") |has| |#1| (|CommutativeRing|)) (|noZeroDivisors| |has| |#1| (|IntegralDomain|)) (|canonicalUnitNormal| |has| |#1| (|Field|))) +(#1=(|HasCategory| |#1| (QUOTE (|Algebra| (|Fraction| #2=(|Integer|))))) #3=(|HasCategory| |#1| (QUOTE (|IntegralDomain|))) #4=(|HasCategory| |#1| (QUOTE (|CommutativeRing|))) (OR #4# #3#) (OR #5=(|HasCategory| |#1| #6=(QUOTE (|CharacteristicNonZero|))) #7=(AND #8=(|HasCategory| |#1| (QUOTE (|Field|))) #9=(|HasCategory| |#2| #6#))) (OR #10=(|HasCategory| |#1| #11=(QUOTE (|CharacteristicZero|))) #12=(AND #8# (|HasCategory| |#2| #11#)) #13=(AND #8# (|HasCategory| |#2| (QUOTE (|OrderedIntegralDomain|))))) (OR #14=(AND #8# (|HasCategory| |#2| #15=(QUOTE (|PartialDifferentialRing| #16=(|Symbol|))))) #17=(AND (|HasCategory| |#1| #15#) #18=(|HasSignature| |#1| (|%list| (QUOTE *) (|%list| #19=(|devaluate| |#1|) #20=(QUOTE #2#) #19#))))) (OR #14# #21=(AND #8# (|HasCategory| |#2| (QUOTE (|PartialDifferentialSpace| #16#)))) #17#) (OR #18# #22=(AND #8# (|HasCategory| |#2| (QUOTE (|DifferentialRing|))))) (OR #18# #22# #23=(AND #8# (|HasCategory| |#2| (QUOTE (|DifferentialSpace|))))) (|HasCategory| #2# (QUOTE (|SemiGroup|))) (OR #8# #3#) #8# (AND #8# #24=(|HasCategory| |#2| (QUOTE (|PolynomialFactorizationExplicit|)))) (AND #8# (|HasCategory| |#2| (QUOTE (|RetractableTo| #16#)))) (AND #8# (|HasCategory| |#2| (QUOTE (|ConvertibleTo| (|InputForm|))))) (AND #8# (|HasCategory| |#2| (QUOTE (|RealConstant|)))) (OR #4# #8# #3#) #13# (OR #13# #25=(AND #8# (|HasCategory| |#2| (QUOTE (|OrderedSet|))))) (OR #1# #26=(AND #8# (|HasCategory| |#2| (QUOTE (|RetractableTo| #2#))))) #26# (AND #8# (|HasCategory| |#2| (QUOTE (|StepThrough|)))) (AND #8# (|HasCategory| |#2| (|%list| (QUOTE |Eltable|) #27=(|devaluate| |#2|) #27#))) (AND #8# (|HasCategory| |#2| (|%list| (QUOTE |Evalable|) #27#))) (AND #8# (|HasCategory| |#2| (|%list| (QUOTE |InnerEvalable|) #28=(QUOTE #16#) #27#))) (AND #8# (|HasCategory| |#2| (QUOTE (|LinearlyExplicitRingOver| #2#)))) (AND #8# (|HasCategory| |#2| (QUOTE (|ConvertibleTo| (|Pattern| #2#))))) (AND #8# (|HasCategory| |#2| (QUOTE (|ConvertibleTo| (|Pattern| #29=(|Float|)))))) (AND #8# (|HasCategory| |#2| (QUOTE (|PatternMatchable| #2#)))) (AND #8# (|HasCategory| |#2| (QUOTE (|PatternMatchable| #29#)))) (AND #30=(|HasSignature| |#1| (|%list| (QUOTE **) (|%list| #19# #19# #20#))) (|HasSignature| |#1| (|%list| (QUOTE |coerce|) (|%list| #19# #28#)))) #30# (OR (AND #1# (|HasCategory| |#1| (QUOTE (|AlgebraicallyClosedFunctionSpace| #2#))) (|HasCategory| |#1| (QUOTE (|PrimitiveFunctionCategory|))) (|HasCategory| |#1| (QUOTE (|TranscendentalFunctionCategory|)))) (AND #1# (|HasSignature| |#1| (|%list| (QUOTE |integrate|) (|%list| #19# #19# #28#))) (|HasSignature| |#1| (|%list| (QUOTE |variables|) (|%list| (|%list| (QUOTE |List|) #28#) #19#))))) #25# #24# (AND #8# (|HasCategory| |#2| (QUOTE (|IntegerNumberSystem|)))) (AND #8# (|HasCategory| |#2| (QUOTE (|EuclideanDomain|)))) #5# #9# (OR #18# #23#) (OR #21# #17#) #23# #21# (OR #10# #12#) #31=(AND #8# #24# (|HasCategory| $ #6#)) (OR #31# #5# #7#)) (|UnivariateFactorize| ZP) ((|constructor| (NIL "Package for the factorization of univariate polynomials with integer coefficients. The factorization is done by \"lifting\" (HENSEL) the factorization over a finite field.")) (|henselFact| (((|Record| (|:| |contp| (|Integer|)) (|:| |factors| (|List| (|Record| (|:| |irr| |#1|) (|:| |pow| (|Integer|)))))) |#1| (|Boolean|)) "\\spad{henselFact(m,flag)} returns the factorization of \\spad{m},{} FinalFact is a Record \\spad{s}.\\spad{t}. FinalFact.contp=content \\spad{m},{} FinalFact.factors=List of irreducible factors of \\spad{m} with exponent ,{} if \\spad{flag} =true the polynomial is assumed square free.")) (|factorSquareFree| (((|Factored| |#1|) |#1|) "\\spad{factorSquareFree(m)} returns the factorization of \\spad{m} square free polynomial")) (|factor| (((|Factored| |#1|) |#1|) "\\spad{factor(m)} returns the factorization of \\spad{m}"))) NIL @@ -4538,8 +4538,8 @@ NIL ((|HasCategory| |#1| (QUOTE (|OrderedRing|)))) (|UnivariatePolynomial| |x| R) ((|constructor| (NIL "This domain represents univariate polynomials in some symbol over arbitrary (not necessarily commutative) coefficient rings. The representation is sparse in the sense that only non-zero terms are represented.")) (|fmecg| (($ $ (|NonNegativeInteger|) |#2| $) "\\spad{fmecg(p1,e,r,p2)} finds \\spad{X} : \\spad{p1} - \\spad{r} * X**e * \\spad{p2}"))) -(((|commutative| "*") |has| |#2| (|CommutativeRing|)) (|noZeroDivisors| |has| |#2| (|IntegralDomain|)) (|additiveValuation| |has| |#2| (|Field|)) (|canonicalUnitNormal| |has| |#2| (ATTRIBUTE |canonicalUnitNormal|)) (|leftUnitary| . T) (|rightUnitary| . T) (|unitsKnown| . T)) -(#1=(|HasCategory| |#2| (QUOTE (|PolynomialFactorizationExplicit|))) #2=(|HasCategory| |#2| (QUOTE (|IntegralDomain|))) #3=(|HasCategory| |#2| (QUOTE (|CommutativeRing|))) (OR #3# #2#) (AND (|HasCategory| |#2| #4=(QUOTE (|PatternMatchable| #5=(|Float|)))) (|HasCategory| #6=(|SingletonAsOrderedSet|) #4#)) (AND (|HasCategory| |#2| #7=(QUOTE (|PatternMatchable| #8=(|Integer|)))) (|HasCategory| #6# #7#)) (AND (|HasCategory| |#2| #9=(QUOTE (|ConvertibleTo| (|Pattern| #5#)))) (|HasCategory| #6# #9#)) (AND (|HasCategory| |#2| #10=(QUOTE (|ConvertibleTo| (|Pattern| #8#)))) (|HasCategory| #6# #10#)) (AND (|HasCategory| |#2| #11=(QUOTE (|ConvertibleTo| (|InputForm|)))) (|HasCategory| #6# #11#)) (|HasCategory| |#2| (QUOTE (|LinearlyExplicitRingOver| #8#))) (|HasCategory| |#2| (QUOTE (|CharacteristicZero|))) #12=(|HasCategory| |#2| #13=(QUOTE (|CharacteristicNonZero|))) #14=(|HasCategory| |#2| (QUOTE (|Algebra| #15=(|Fraction| #8#)))) (|HasCategory| |#2| (QUOTE (|RetractableTo| #8#))) (OR #14# #16=(|HasCategory| |#2| (QUOTE (|RetractableTo| #15#)))) #16# (OR #3# #17=(|HasCategory| |#2| (QUOTE (|Field|))) #18=(|HasCategory| |#2| (QUOTE (|GcdDomain|))) #2# #1#) (OR #17# #18# #2# #1#) (OR #17# #18# #1#) #17# (|HasCategory| |#2| (QUOTE (|StepThrough|))) (|HasCategory| |#2| (QUOTE (|PartialDifferentialSpace| #19=(|Symbol|)))) (|HasCategory| |#2| (QUOTE (|PartialDifferentialRing| #19#))) (|HasCategory| |#2| (QUOTE (|DifferentialSpace|))) (|HasCategory| |#2| (QUOTE (|DifferentialRing|))) (|HasAttribute| |#2| (QUOTE |canonicalUnitNormal|)) #18# #20=(AND #1# (|HasCategory| $ #13#)) (OR #20# #12#)) +(((|commutative| "*") |has| |#2| (|CommutativeRing|)) (|noZeroDivisors| |has| |#2| (|IntegralDomain|)) (|additiveValuation| |has| |#2| (|Field|)) (|canonicalUnitNormal| |has| |#2| (ATTRIBUTE |canonicalUnitNormal|))) +(#1=(|HasCategory| |#2| (QUOTE (|PolynomialFactorizationExplicit|))) #2=(|HasCategory| |#2| (QUOTE (|IntegralDomain|))) #3=(|HasCategory| |#2| (QUOTE (|CommutativeRing|))) (OR #3# #2#) (AND (|HasCategory| |#2| #4=(QUOTE (|PatternMatchable| #5=(|Float|)))) (|HasCategory| #6=(|SingletonAsOrderedSet|) #4#)) (AND (|HasCategory| |#2| #7=(QUOTE (|PatternMatchable| #8=(|Integer|)))) (|HasCategory| #6# #7#)) (AND (|HasCategory| |#2| #9=(QUOTE (|ConvertibleTo| (|Pattern| #5#)))) (|HasCategory| #6# #9#)) (AND (|HasCategory| |#2| #10=(QUOTE (|ConvertibleTo| (|Pattern| #8#)))) (|HasCategory| #6# #10#)) (AND (|HasCategory| |#2| #11=(QUOTE (|ConvertibleTo| (|InputForm|)))) (|HasCategory| #6# #11#)) (|HasCategory| |#2| (QUOTE (|LinearlyExplicitRingOver| #8#))) #12=(|HasCategory| |#2| (QUOTE (|Algebra| #13=(|Fraction| #8#)))) #14=(|HasCategory| |#2| #15=(QUOTE (|CharacteristicNonZero|))) (|HasCategory| |#2| (QUOTE (|CharacteristicZero|))) (|HasCategory| |#2| (QUOTE (|RetractableTo| #8#))) (OR #12# #16=(|HasCategory| |#2| (QUOTE (|RetractableTo| #13#)))) #16# (OR #3# #17=(|HasCategory| |#2| (QUOTE (|Field|))) #18=(|HasCategory| |#2| (QUOTE (|GcdDomain|))) #2# #1#) (OR #17# #18# #2# #1#) (OR #17# #18# #1#) #17# (|HasCategory| |#2| (QUOTE (|StepThrough|))) (|HasCategory| |#2| (QUOTE (|PartialDifferentialSpace| #19=(|Symbol|)))) (|HasCategory| |#2| (QUOTE (|PartialDifferentialRing| #19#))) (|HasCategory| |#2| (QUOTE (|DifferentialSpace|))) (|HasCategory| |#2| (QUOTE (|DifferentialRing|))) (|HasAttribute| |#2| (QUOTE |canonicalUnitNormal|)) #18# #20=(AND #1# (|HasCategory| $ #15#)) (OR #20# #14#)) (|UnivariatePolynomialFunctions2| |x| R |y| S) ((|constructor| (NIL "This package lifts a mapping from coefficient rings \\spad{R} to \\spad{S} to a mapping from \\spadtype{UnivariatePolynomial}(\\spad{x},{}\\spad{R}) to \\spadtype{UnivariatePolynomial}(\\spad{y},{}\\spad{S}). Note that the mapping is assumed to send zero to zero,{} since it will only be applied to the non-zero coefficients of the polynomial.")) (|map| (((|UnivariatePolynomial| |#3| |#4|) (|Mapping| |#4| |#2|) (|UnivariatePolynomial| |#1| |#2|)) "\\spad{map(func, poly)} creates a new polynomial by applying \\spad{func} to every non-zero coefficient of the polynomial poly."))) NIL @@ -4566,7 +4566,7 @@ NIL ((|HasCategory| |#2| (QUOTE (|Algebra| (|Fraction| (|Integer|))))) (|HasCategory| |#2| (QUOTE (|Field|))) (|HasCategory| |#2| (QUOTE (|GcdDomain|))) (|HasCategory| |#2| (QUOTE (|IntegralDomain|))) (|HasCategory| |#2| (QUOTE (|CommutativeRing|))) (|HasCategory| |#2| (QUOTE (|StepThrough|)))) (|UnivariatePolynomialCategory| R) ((|constructor| (NIL "The category of univariate polynomials over a ring \\spad{R}. No particular model is assumed - implementations can be either sparse or dense.")) (|integrate| (($ $) "\\spad{integrate(p)} integrates the univariate polynomial \\spad{p} with respect to its distinguished variable.")) (|additiveValuation| ((|attribute|) "euclideanSize(a*b) = euclideanSize(a) + euclideanSize(\\spad{b})")) (|separate| (((|Record| (|:| |primePart| $) (|:| |commonPart| $)) $ $) "\\spad{separate(p, q)} returns \\spad{[a, b]} such that polynomial \\spad{p = a b} and \\spad{a} is relatively prime to \\spad{q}.")) (|pseudoDivide| (((|Record| (|:| |coef| |#1|) (|:| |quotient| $) (|:| |remainder| $)) $ $) "\\spad{pseudoDivide(p,q)} returns \\spad{[c, q, r]},{} when \\spad{p' := p*lc(q)**(deg p - deg q + 1) = c * p} is pseudo right-divided by \\spad{q},{} \\spadignore{i.e.} \\spad{p' = s q + r}.")) (|pseudoQuotient| (($ $ $) "\\spad{pseudoQuotient(p,q)} returns \\spad{r},{} the quotient when \\spad{p' := p*lc(q)**(deg p - deg q + 1)} is pseudo right-divided by \\spad{q},{} \\spadignore{i.e.} \\spad{p' = s q + r}.")) (|composite| (((|Union| (|Fraction| $) "failed") (|Fraction| $) $) "\\spad{composite(f, q)} returns \\spad{h} if \\spad{f} = \\spad{h}(\\spad{q}),{} and \"failed\" is no such \\spad{h} exists.") (((|Union| $ "failed") $ $) "\\spad{composite(p, q)} returns \\spad{h} if \\spad{p = h(q)},{} and \"failed\" no such \\spad{h} exists.")) (|subResultantGcd| (($ $ $) "\\spad{subResultantGcd(p,q)} computes the gcd of the polynomials \\spad{p} and \\spad{q} using the SubResultant GCD algorithm.")) (|order| (((|NonNegativeInteger|) $ $) "\\spad{order(p, q)} returns the largest \\spad{n} such that \\spad{q**n} divides polynomial \\spad{p} \\spadignore{i.e.} the order of \\spad{p(x)} at \\spad{q(x)=0}.")) (|elt| ((|#1| (|Fraction| $) |#1|) "\\spad{elt(a,r)} evaluates the fraction of univariate polynomials \\spad{a} with the distinguished variable replaced by the constant \\spad{r}.") (((|Fraction| $) (|Fraction| $) (|Fraction| $)) "\\spad{elt(a,b)} evaluates the fraction of univariate polynomials \\spad{a} with the distinguished variable replaced by \\spad{b}.")) (|resultant| ((|#1| $ $) "\\spad{resultant(p,q)} returns the resultant of the polynomials \\spad{p} and \\spad{q}.")) (|discriminant| ((|#1| $) "\\spad{discriminant(p)} returns the discriminant of the polynomial \\spad{p}.")) (|differentiate| (($ $ (|Mapping| |#1| |#1|) $) "\\spad{differentiate(p, d, x')} extends the \\spad{R}-derivation \\spad{d} to an extension \\spad{D} in \\spad{R[x]} where Dx is given by x',{} and returns \\spad{Dp}.")) (|pseudoRemainder| (($ $ $) "\\spad{pseudoRemainder(p,q)} = \\spad{r},{} for polynomials \\spad{p} and \\spad{q},{} returns the remainder when \\spad{p' := p*lc(q)**(deg p - deg q + 1)} is pseudo right-divided by \\spad{q},{} \\spadignore{i.e.} \\spad{p' = s q + r}.")) (|shiftLeft| (($ $ (|NonNegativeInteger|)) "\\spad{shiftLeft(p,n)} returns \\spad{p * monomial(1,n)}")) (|shiftRight| (($ $ (|NonNegativeInteger|)) "\\spad{shiftRight(p,n)} returns \\spad{monicDivide(p,monomial(1,n)).quotient}")) (|karatsubaDivide| (((|Record| (|:| |quotient| $) (|:| |remainder| $)) $ (|NonNegativeInteger|)) "\\spad{karatsubaDivide(p,n)} returns the same as \\spad{monicDivide(p,monomial(1,n))}")) (|monicDivide| (((|Record| (|:| |quotient| $) (|:| |remainder| $)) $ $) "\\spad{monicDivide(p,q)} divide the polynomial \\spad{p} by the monic polynomial \\spad{q},{} returning the pair \\spad{[quotient, remainder]}. Error: if \\spad{q} isn't monic.")) (|divideExponents| (((|Union| $ "failed") $ (|NonNegativeInteger|)) "\\spad{divideExponents(p,n)} returns a new polynomial resulting from dividing all exponents of the polynomial \\spad{p} by the non negative integer \\spad{n},{} or \"failed\" if some exponent is not exactly divisible by \\spad{n}.")) (|multiplyExponents| (($ $ (|NonNegativeInteger|)) "\\spad{multiplyExponents(p,n)} returns a new polynomial resulting from multiplying all exponents of the polynomial \\spad{p} by the non negative integer \\spad{n}.")) (|unmakeSUP| (($ (|SparseUnivariatePolynomial| |#1|)) "\\spad{unmakeSUP(sup)} converts \\spad{sup} of type \\spadtype{SparseUnivariatePolynomial(R)} to be a member of the given type. Note: converse of makeSUP.")) (|makeSUP| (((|SparseUnivariatePolynomial| |#1|) $) "\\spad{makeSUP(p)} converts the polynomial \\spad{p} to be of type SparseUnivariatePolynomial over the same coefficients.")) (|vectorise| (((|Vector| |#1|) $ (|NonNegativeInteger|)) "\\spad{vectorise(p, n)} returns \\spad{[a0,...,a(n-1)]} where \\spad{p = a0 + a1*x + ... + a(n-1)*x**(n-1)} + higher order terms. The degree of polynomial \\spad{p} can be different from \\spad{n-1}."))) -(((|commutative| "*") |has| |#1| (|CommutativeRing|)) (|noZeroDivisors| |has| |#1| (|IntegralDomain|)) (|additiveValuation| |has| |#1| (|Field|)) (|canonicalUnitNormal| |has| |#1| (ATTRIBUTE |canonicalUnitNormal|)) (|leftUnitary| . T) (|rightUnitary| . T) (|unitsKnown| . T)) +(((|commutative| "*") |has| |#1| (|CommutativeRing|)) (|noZeroDivisors| |has| |#1| (|IntegralDomain|)) (|additiveValuation| |has| |#1| (|Field|)) (|canonicalUnitNormal| |has| |#1| (ATTRIBUTE |canonicalUnitNormal|))) NIL (|UnivariatePolynomialCategoryFunctions2| R PR S PS) ((|constructor| (NIL "Mapping from polynomials over \\spad{R} to polynomials over \\spad{S} given a map from \\spad{R} to \\spad{S} assumed to send zero to zero.")) (|map| ((|#4| (|Mapping| |#3| |#1|) |#2|) "\\spad{map(f, p)} takes a function \\spad{f} from \\spad{R} to \\spad{S},{} and applies it to each (non-zero) coefficient of a polynomial \\spad{p} over \\spad{R},{} getting a new polynomial over \\spad{S}. Note: since the map is not applied to zero elements,{} it may map zero to zero."))) @@ -4578,7 +4578,7 @@ NIL ((|HasCategory| |#2| (QUOTE (|PartialDifferentialRing| #1=(|Symbol|)))) (|HasSignature| |#2| (|%list| (QUOTE *) (|%list| #2=(|devaluate| |#2|) #3=(|devaluate| |#3|) #2#))) (|HasCategory| |#3| (QUOTE (|SemiGroup|))) (|HasSignature| |#2| (|%list| (QUOTE **) (|%list| #2# #2# #3#))) (|HasSignature| |#2| (|%list| (QUOTE |coerce|) (|%list| #2# (QUOTE #1#))))) (|UnivariatePowerSeriesCategory| |Coef| |Expon|) ((|constructor| (NIL "\\spadtype{UnivariatePowerSeriesCategory} is the most general univariate power series category with exponents in an ordered abelian monoid. Note: this category exports a substitution function if it is possible to multiply exponents. Note: this category exports a derivative operation if it is possible to multiply coefficients by exponents.")) (|eval| (((|Stream| |#1|) $ |#1|) "\\spad{eval(f,a)} evaluates a power series at a value in the ground ring by returning a stream of partial sums.")) (|extend| (($ $ |#2|) "\\spad{extend(f,n)} causes all terms of \\spad{f} of degree <= \\spad{n} to be computed.")) (|approximate| ((|#1| $ |#2|) "\\spad{approximate(f)} returns a truncated power series with the series variable viewed as an element of the coefficient domain.")) (|truncate| (($ $ |#2| |#2|) "\\spad{truncate(f,k1,k2)} returns a (finite) power series consisting of the sum of all terms of \\spad{f} of degree \\spad{d} with \\spad{k1 <= d <= k2}.") (($ $ |#2|) "\\spad{truncate(f,k)} returns a (finite) power series consisting of the sum of all terms of \\spad{f} of degree \\spad{<= k}.")) (|order| ((|#2| $ |#2|) "\\spad{order(f,n) = min(m,n)},{} where \\spad{m} is the degree of the lowest order non-zero term in \\spad{f}.") ((|#2| $) "\\spad{order(f)} is the degree of the lowest order non-zero term in \\spad{f}. This will result in an infinite loop if \\spad{f} has no non-zero terms.")) (|multiplyExponents| (($ $ (|PositiveInteger|)) "\\spad{multiplyExponents(f,n)} multiplies all exponents of the power series \\spad{f} by the positive integer \\spad{n}.")) (|center| ((|#1| $) "\\spad{center(f)} returns the point about which the series \\spad{f} is expanded.")) (|variable| (((|Symbol|) $) "\\spad{variable(f)} returns the (unique) power series variable of the power series \\spad{f}.")) (|terms| (((|Stream| (|Record| (|:| |k| |#2|) (|:| |c| |#1|))) $) "\\spad{terms(f(x))} returns a stream of non-zero terms,{} where a a term is an exponent-coefficient pair. The terms in the stream are ordered by increasing order of exponents."))) -(((|commutative| "*") |has| |#1| (|CommutativeRing|)) (|noZeroDivisors| |has| |#1| (|IntegralDomain|)) (|rightUnitary| . T) (|leftUnitary| . T) (|unitsKnown| . T)) +(((|commutative| "*") |has| |#1| (|CommutativeRing|)) (|noZeroDivisors| |has| |#1| (|IntegralDomain|))) NIL (|UnivariatePolynomialSquareFree| RC P) ((|constructor| (NIL "This package provides for square-free decomposition of univariate polynomials over arbitrary rings,{} \\spadignore{i.e.} a partial factorization such that each factor is a product of irreducibles with multiplicity one and the factors are pairwise relatively prime. If the ring has characteristic zero,{} the result is guaranteed to satisfy this condition. If the ring is an infinite ring of finite characteristic,{} then it may not be possible to decide when polynomials contain factors which are \\spad{p}th powers. In this case,{} the flag associated with that polynomial is set to \"nil\" (meaning that that polynomials are not guaranteed to be square-free).")) (|BumInSepFFE| (((|Record| (|:| |flg| (|Union| #1="nil" #2="sqfr" #3="irred" #4="prime")) (|:| |fctr| |#2|) (|:| |xpnt| (|Integer|))) (|Record| (|:| |flg| (|Union| #1# #2# #3# #4#)) (|:| |fctr| |#2|) (|:| |xpnt| (|Integer|)))) "\\spad{BumInSepFFE(f)} is a local function,{} exported only because it has multiple conditional definitions.")) (|squareFreePart| ((|#2| |#2|) "\\spad{squareFreePart(p)} returns a polynomial which has the same irreducible factors as the univariate polynomial \\spad{p},{} but each factor has multiplicity one.")) (|squareFree| (((|Factored| |#2|) |#2|) "\\spad{squareFree(p)} computes the square-free factorization of the univariate polynomial \\spad{p}. Each factor has no repeated roots,{} and the factors are pairwise relatively prime.")) (|gcd| (($ $ $) "\\spad{gcd(p,q)} computes the greatest-common-divisor of \\spad{p} and \\spad{q}."))) @@ -4586,7 +4586,7 @@ NIL NIL (|UnivariatePuiseuxSeries| |Coef| |var| |cen|) ((|constructor| (NIL "Dense Puiseux series in one variable \\indented{2}{\\spadtype{UnivariatePuiseuxSeries} is a domain representing Puiseux} \\indented{2}{series in one variable with coefficients in an arbitrary ring.\\space{2}The} \\indented{2}{parameters of the type specify the coefficient ring,{} the power series} \\indented{2}{variable,{} and the center of the power series expansion.\\space{2}For example,{}} \\indented{2}{\\spad{UnivariatePuiseuxSeries(Integer,x,3)} represents Puiseux series in} \\indented{2}{\\spad{(x - 3)} with \\spadtype{Integer} coefficients.}")) (|integrate| (($ $ (|Variable| |#2|)) "\\spad{integrate(f(x))} returns an anti-derivative of the power series \\spad{f(x)} with constant coefficient 0. We may integrate a series when we can divide coefficients by integers."))) -(((|commutative| "*") |has| |#1| (|CommutativeRing|)) (|noZeroDivisors| |has| |#1| (|IntegralDomain|)) (|canonicalUnitNormal| |has| |#1| . #1=((|Field|))) (|canonicalsClosed| |has| |#1| . #1#) (|rightUnitary| . T) (|leftUnitary| . T) (|unitsKnown| . T)) +(((|commutative| "*") |has| |#1| (|CommutativeRing|)) (|noZeroDivisors| |has| |#1| (|IntegralDomain|)) (|canonicalUnitNormal| |has| |#1| (|Field|))) (#1=(|HasCategory| |#1| (QUOTE (|Algebra| #2=(|Fraction| #3=(|Integer|))))) #4=(|HasCategory| |#1| (QUOTE (|IntegralDomain|))) #5=(|HasCategory| |#1| (QUOTE (|CommutativeRing|))) (OR #5# #4#) (|HasCategory| |#1| (QUOTE (|CharacteristicNonZero|))) (|HasCategory| |#1| (QUOTE (|CharacteristicZero|))) (AND (|HasCategory| |#1| (QUOTE (|PartialDifferentialRing| #6=(|Symbol|)))) #7=(|HasSignature| |#1| (|%list| (QUOTE *) (|%list| #8=(|devaluate| |#1|) #9=(|%list| (QUOTE |Fraction|) (QUOTE #3#)) #8#)))) #7# (|HasCategory| #2# (QUOTE (|SemiGroup|))) #10=(|HasCategory| |#1| (QUOTE (|Field|))) (OR #5# #10# #4#) (OR #10# #4#) (AND #11=(|HasSignature| |#1| (|%list| (QUOTE **) (|%list| #8# #8# #9#))) (|HasSignature| |#1| (|%list| (QUOTE |coerce|) (|%list| #8# #12=(QUOTE #6#))))) #11# (OR (AND #1# (|HasCategory| |#1| (QUOTE (|AlgebraicallyClosedFunctionSpace| #3#))) (|HasCategory| |#1| (QUOTE (|PrimitiveFunctionCategory|))) (|HasCategory| |#1| (QUOTE (|TranscendentalFunctionCategory|)))) (AND #1# (|HasSignature| |#1| (|%list| (QUOTE |integrate|) (|%list| #8# #8# #12#))) (|HasSignature| |#1| (|%list| (QUOTE |variables|) (|%list| (|%list| (QUOTE |List|) #12#) #8#)))))) (|UnivariatePuiseuxSeriesFunctions2| |Coef1| |Coef2| |var1| |var2| |cen1| |cen2|) ((|constructor| (NIL "Mapping package for univariate Puiseux series. This package allows one to apply a function to the coefficients of a univariate Puiseux series.")) (|map| (((|UnivariatePuiseuxSeries| |#2| |#4| |#6|) (|Mapping| |#2| |#1|) (|UnivariatePuiseuxSeries| |#1| |#3| |#5|)) "\\spad{map(f,g(x))} applies the map \\spad{f} to the coefficients of the Puiseux series \\spad{g(x)}."))) @@ -4594,7 +4594,7 @@ NIL NIL (|UnivariatePuiseuxSeriesCategory| |Coef|) ((|constructor| (NIL "\\spadtype{UnivariatePuiseuxSeriesCategory} is the category of Puiseux series in one variable.")) (|integrate| (($ $ (|Symbol|)) "\\spad{integrate(f(x),y)} returns an anti-derivative of the power series \\spad{f(x)} with respect to the variable \\spad{y}.") (($ $ (|Symbol|)) "\\spad{integrate(f(x),var)} returns an anti-derivative of the power series \\spad{f(x)} with respect to the variable \\spad{var}.") (($ $) "\\spad{integrate(f(x))} returns an anti-derivative of the power series \\spad{f(x)} with constant coefficient 1. We may integrate a series when we can divide coefficients by rational numbers.")) (|multiplyExponents| (($ $ (|Fraction| (|Integer|))) "\\spad{multiplyExponents(f,r)} multiplies all exponents of the power series \\spad{f} by the positive rational number \\spad{r}.")) (|series| (($ (|NonNegativeInteger|) (|Stream| (|Record| (|:| |k| (|Fraction| (|Integer|))) (|:| |c| |#1|)))) "\\spad{series(n,st)} creates a series from a common denomiator and a stream of non-zero terms,{} where a term is an exponent-coefficient pair. The terms in the stream should be ordered by increasing order of exponents and \\spad{n} should be a common denominator for the exponents in the stream of terms."))) -(((|commutative| "*") |has| |#1| (|CommutativeRing|)) (|noZeroDivisors| |has| |#1| (|IntegralDomain|)) (|canonicalUnitNormal| |has| |#1| . #1=((|Field|))) (|canonicalsClosed| |has| |#1| . #1#) (|rightUnitary| . T) (|leftUnitary| . T) (|unitsKnown| . T)) +(((|commutative| "*") |has| |#1| (|CommutativeRing|)) (|noZeroDivisors| |has| |#1| (|IntegralDomain|)) (|canonicalUnitNormal| |has| |#1| (|Field|))) NIL (|UnivariatePuiseuxSeriesConstructorCategory&| S |Coef| ULS) ((|constructor| (NIL "This is a category of univariate Puiseux series constructed from univariate Laurent series. A Puiseux series is represented by a pair \\spad{[r,f(x)]},{} where \\spad{r} is a positive rational number and \\spad{f(x)} is a Laurent series. This pair represents the Puiseux series \\spad{f(x^r)}.")) (|laurentIfCan| (((|Union| |#3| "failed") $) "\\spad{laurentIfCan(f(x))} converts the Puiseux series \\spad{f(x)} to a Laurent series if possible. If this is not possible,{} \"failed\" is returned.")) (|laurent| ((|#3| $) "\\spad{laurent(f(x))} converts the Puiseux series \\spad{f(x)} to a Laurent series if possible. Error: if this is not possible.")) (|degree| (((|Fraction| (|Integer|)) $) "\\spad{degree(f(x))} returns the degree of the leading term of the Puiseux series \\spad{f(x)},{} which may have zero as a coefficient.")) (|laurentRep| ((|#3| $) "\\spad{laurentRep(f(x))} returns \\spad{g(x)} where the Puiseux series \\spad{f(x) = g(x^r)} is represented by \\spad{[r,g(x)]}.")) (|rationalPower| (((|Fraction| (|Integer|)) $) "\\spad{rationalPower(f(x))} returns \\spad{r} where the Puiseux series \\spad{f(x) = g(x^r)}.")) (|puiseux| (($ (|Fraction| (|Integer|)) |#3|) "\\spad{puiseux(r,f(x))} returns \\spad{f(x^r)}."))) @@ -4602,15 +4602,15 @@ NIL NIL (|UnivariatePuiseuxSeriesConstructorCategory| |Coef| ULS) ((|constructor| (NIL "This is a category of univariate Puiseux series constructed from univariate Laurent series. A Puiseux series is represented by a pair \\spad{[r,f(x)]},{} where \\spad{r} is a positive rational number and \\spad{f(x)} is a Laurent series. This pair represents the Puiseux series \\spad{f(x^r)}.")) (|laurentIfCan| (((|Union| |#2| "failed") $) "\\spad{laurentIfCan(f(x))} converts the Puiseux series \\spad{f(x)} to a Laurent series if possible. If this is not possible,{} \"failed\" is returned.")) (|laurent| ((|#2| $) "\\spad{laurent(f(x))} converts the Puiseux series \\spad{f(x)} to a Laurent series if possible. Error: if this is not possible.")) (|degree| (((|Fraction| (|Integer|)) $) "\\spad{degree(f(x))} returns the degree of the leading term of the Puiseux series \\spad{f(x)},{} which may have zero as a coefficient.")) (|laurentRep| ((|#2| $) "\\spad{laurentRep(f(x))} returns \\spad{g(x)} where the Puiseux series \\spad{f(x) = g(x^r)} is represented by \\spad{[r,g(x)]}.")) (|rationalPower| (((|Fraction| (|Integer|)) $) "\\spad{rationalPower(f(x))} returns \\spad{r} where the Puiseux series \\spad{f(x) = g(x^r)}.")) (|puiseux| (($ (|Fraction| (|Integer|)) |#2|) "\\spad{puiseux(r,f(x))} returns \\spad{f(x^r)}."))) -(((|commutative| "*") |has| |#1| (|CommutativeRing|)) (|noZeroDivisors| |has| |#1| (|IntegralDomain|)) (|canonicalUnitNormal| |has| |#1| . #1=((|Field|))) (|canonicalsClosed| |has| |#1| . #1#) (|rightUnitary| . T) (|leftUnitary| . T) (|unitsKnown| . T)) +(((|commutative| "*") |has| |#1| (|CommutativeRing|)) (|noZeroDivisors| |has| |#1| (|IntegralDomain|)) (|canonicalUnitNormal| |has| |#1| (|Field|))) NIL (|UnivariatePuiseuxSeriesConstructor| |Coef| ULS) ((|constructor| (NIL "This package enables one to construct a univariate Puiseux series domain from a univariate Laurent series domain. Univariate Puiseux series are represented by a pair \\spad{[r,f(x)]},{} where \\spad{r} is a positive rational number and \\spad{f(x)} is a Laurent series. This pair represents the Puiseux series \\spad{f(x^r)}."))) -(((|commutative| "*") |has| |#1| (|CommutativeRing|)) (|noZeroDivisors| |has| |#1| (|IntegralDomain|)) (|canonicalUnitNormal| |has| |#1| . #1=((|Field|))) (|canonicalsClosed| |has| |#1| . #1#) (|rightUnitary| . T) (|leftUnitary| . T) (|unitsKnown| . T)) +(((|commutative| "*") |has| |#1| (|CommutativeRing|)) (|noZeroDivisors| |has| |#1| (|IntegralDomain|)) (|canonicalUnitNormal| |has| |#1| (|Field|))) (#1=(|HasCategory| |#1| (QUOTE (|IntegralDomain|))) #2=(|HasCategory| |#1| (QUOTE (|CommutativeRing|))) (OR #2# #1#) (|HasCategory| |#1| (QUOTE (|CharacteristicNonZero|))) (|HasCategory| |#1| (QUOTE (|CharacteristicZero|))) (AND (|HasCategory| |#1| (QUOTE (|PartialDifferentialRing| #3=(|Symbol|)))) #4=(|HasSignature| |#1| (|%list| (QUOTE *) (|%list| #5=(|devaluate| |#1|) #6=(|%list| (QUOTE |Fraction|) (QUOTE #7=(|Integer|))) #5#)))) #4# (|HasCategory| #8=(|Fraction| #7#) (QUOTE (|SemiGroup|))) #9=(|HasCategory| |#1| (QUOTE (|Field|))) (OR #2# #9# #1#) (OR #9# #1#) (AND #10=(|HasSignature| |#1| (|%list| (QUOTE **) (|%list| #5# #5# #6#))) (|HasSignature| |#1| (|%list| (QUOTE |coerce|) (|%list| #5# #11=(QUOTE #3#))))) #10# (OR (AND #12=(|HasCategory| |#1| (QUOTE (|Algebra| #8#))) (|HasCategory| |#1| (QUOTE (|AlgebraicallyClosedFunctionSpace| #7#))) (|HasCategory| |#1| (QUOTE (|PrimitiveFunctionCategory|))) (|HasCategory| |#1| (QUOTE (|TranscendentalFunctionCategory|)))) (AND #12# (|HasSignature| |#1| (|%list| (QUOTE |integrate|) (|%list| #5# #5# #11#))) (|HasSignature| |#1| (|%list| (QUOTE |variables|) (|%list| (|%list| (QUOTE |List|) #11#) #5#))))) #12#) (|UnivariatePuiseuxSeriesWithExponentialSingularity| R FE |var| |cen|) ((|constructor| (NIL "UnivariatePuiseuxSeriesWithExponentialSingularity is a domain used to represent functions with essential singularities. Objects in this domain are sums,{} where each term in the sum is a univariate Puiseux series times the exponential of a univariate Puiseux series. Thus,{} the elements of this domain are sums of expressions of the form \\spad{g(x) * exp(f(x))},{} where \\spad{g}(\\spad{x}) is a univariate Puiseux series and \\spad{f}(\\spad{x}) is a univariate Puiseux series with no terms of non-negative degree.")) (|dominantTerm| (((|Union| (|Record| (|:| |%term| (|Record| (|:| |%coef| (|UnivariatePuiseuxSeries| |#2| |#3| |#4|)) (|:| |%expon| (|ExponentialOfUnivariatePuiseuxSeries| |#2| |#3| |#4|)) (|:| |%expTerms| (|List| (|Record| (|:| |k| (|Fraction| (|Integer|))) (|:| |c| |#2|)))))) (|:| |%type| (|String|))) "failed") $) "\\spad{dominantTerm(f(var))} returns the term that dominates the limiting behavior of \\spad{f(var)} as \\spad{var -> cen+} together with a \\spadtype{String} which briefly describes that behavior. The value of the \\spadtype{String} will be \\spad{\"zero\"} (resp. \\spad{\"infinity\"}) if the term tends to zero (resp. infinity) exponentially and will \\spad{\"series\"} if the term is a Puiseux series.")) (|limitPlus| (((|Union| (|OrderedCompletion| |#2|) "failed") $) "\\spad{limitPlus(f(var))} returns \\spad{limit(var -> cen+,f(var))}."))) -(((|commutative| "*") |has| #1=(|UnivariatePuiseuxSeries| |#2| |#3| |#4|) (|CommutativeRing|)) (|noZeroDivisors| |has| #1# (|IntegralDomain|)) (|rightUnitary| . T) (|leftUnitary| . T) (|unitsKnown| . T)) +(((|commutative| "*") |has| #1=(|UnivariatePuiseuxSeries| |#2| |#3| |#4|) (|CommutativeRing|)) (|noZeroDivisors| |has| #1# (|IntegralDomain|))) (#1=(|HasCategory| #2=(|UnivariatePuiseuxSeries| |#2| |#3| |#4|) (QUOTE (|Algebra| #3=(|Fraction| #4=(|Integer|))))) (|HasCategory| #2# (QUOTE (|CharacteristicNonZero|))) (|HasCategory| #2# (QUOTE (|CharacteristicZero|))) (|HasCategory| #2# (QUOTE (|CommutativeRing|))) (OR #1# #5=(|HasCategory| #2# (QUOTE (|RetractableTo| #3#)))) #5# (|HasCategory| #2# (QUOTE (|RetractableTo| #4#))) (|HasCategory| #2# (QUOTE (|Field|))) (|HasCategory| #2# (QUOTE (|GcdDomain|))) (|HasCategory| #2# (QUOTE (|IntegralDomain|)))) (|UnaryRecursiveAggregate&| A S) ((|constructor| (NIL "A unary-recursive aggregate is a one where nodes may have either 0 or 1 children. This aggregate models,{} though not precisely,{} a linked list possibly with a single cycle. A node with one children models a non-empty list,{} with the \\spadfun{value} of the list designating the head,{} or \\spadfun{first},{} of the list,{} and the child designating the tail,{} or \\spadfun{rest},{} of the list. A node with no child then designates the empty list. Since these aggregates are recursive aggregates,{} they may be cyclic.")) (|split!| (($ $ (|Integer|)) "\\spad{split!(u,n)} splits \\spad{u} into two aggregates: \\axiom{\\spad{v} = rest(\\spad{u},{}\\spad{n})} and \\axiom{\\spad{w} = first(\\spad{u},{}\\spad{n})},{} returning \\axiom{\\spad{v}}. Note: afterwards \\axiom{rest(\\spad{u},{}\\spad{n})} returns \\axiom{empty()}.")) (|setlast!| ((|#2| $ |#2|) "\\spad{setlast!(u,x)} destructively changes the last element of \\spad{u} to \\spad{x}.")) (|setrest!| (($ $ $) "\\spad{setrest!(u,v)} destructively changes the rest of \\spad{u} to \\spad{v}.")) (|setelt| ((|#2| $ "last" |#2|) "\\spad{setelt(u,\"last\",x)} (also written: \\axiom{\\spad{u}.last := \\spad{b}}) is equivalent to \\axiom{setlast!(\\spad{u},{}\\spad{v})}.") (($ $ "rest" $) "\\spad{setelt(u,\"rest\",v)} (also written: \\axiom{\\spad{u}.rest := \\spad{v}}) is equivalent to \\axiom{setrest!(\\spad{u},{}\\spad{v})}.") ((|#2| $ "first" |#2|) "\\spad{setelt(u,\"first\",x)} (also written: \\axiom{\\spad{u}.first := \\spad{x}}) is equivalent to \\axiom{setfirst!(\\spad{u},{}\\spad{x})}.")) (|setfirst!| ((|#2| $ |#2|) "\\spad{setfirst!(u,x)} destructively changes the first element of a to \\spad{x}.")) (|cycleSplit!| (($ $) "\\spad{cycleSplit!(u)} splits the aggregate by dropping off the cycle. The value returned is the cycle entry,{} or nil if none exists. For example,{} if \\axiom{\\spad{w} = concat(\\spad{u},{}\\spad{v})} is the cyclic list where \\spad{v} is the head of the cycle,{} \\axiom{cycleSplit!(\\spad{w})} will drop \\spad{v} off \\spad{w} thus destructively changing \\spad{w} to \\spad{u},{} and returning \\spad{v}.")) (|concat!| (($ $ |#2|) "\\spad{concat!(u,x)} destructively adds element \\spad{x} to the end of \\spad{u}. Note: \\axiom{concat!(a,{}\\spad{x}) = setlast!(a,{}[\\spad{x}])}.") (($ $ $) "\\spad{concat!(u,v)} destructively concatenates \\spad{v} to the end of \\spad{u}. Note: \\axiom{concat!(\\spad{u},{}\\spad{v}) = setlast!(\\spad{u},{}\\spad{v})}.")) (|cycleTail| (($ $) "\\spad{cycleTail(u)} returns the last node in the cycle,{} or empty if none exists.")) (|cycleLength| (((|NonNegativeInteger|) $) "\\spad{cycleLength(u)} returns the length of a top-level cycle contained in aggregate \\spad{u},{} or 0 is \\spad{u} has no such cycle.")) (|cycleEntry| (($ $) "\\spad{cycleEntry(u)} returns the head of a top-level cycle contained in aggregate \\spad{u},{} or \\axiom{empty()} if none exists.")) (|third| ((|#2| $) "\\spad{third(u)} returns the third element of \\spad{u}. Note: \\axiom{third(\\spad{u}) = first(rest(rest(\\spad{u})))}.")) (|second| ((|#2| $) "\\spad{second(u)} returns the second element of \\spad{u}. Note: \\axiom{second(\\spad{u}) = first(rest(\\spad{u}))}.")) (|tail| (($ $) "\\spad{tail(u)} returns the last node of \\spad{u}. Note: if \\spad{u} is \\axiom{shallowlyMutable},{} \\axiom{setrest(tail(\\spad{u}),{}\\spad{v}) = concat(\\spad{u},{}\\spad{v})}.")) (|last| (($ $ (|NonNegativeInteger|)) "\\spad{last(u,n)} returns a copy of the last \\spad{n} (\\axiom{\\spad{n} >= 0}) nodes of \\spad{u}. Note: \\axiom{last(\\spad{u},{}\\spad{n})} is a list of \\spad{n} elements.") ((|#2| $) "\\spad{last(u)} resturn the last element of \\spad{u}. Note: for lists,{} \\axiom{last(\\spad{u}) = \\spad{u} . (maxIndex \\spad{u}) = \\spad{u} . (\\# \\spad{u} - 1)}.")) (|rest| (($ $ (|NonNegativeInteger|)) "\\spad{rest(u,n)} returns the \\axiom{\\spad{n}}th (\\spad{n} >= 0) node of \\spad{u}. Note: \\axiom{rest(\\spad{u},{}0) = \\spad{u}}.") (($ $) "\\spad{rest(u)} returns an aggregate consisting of all but the first element of \\spad{u} (equivalently,{} the next node of \\spad{u}).")) (|elt| ((|#2| $ "last") "\\spad{elt(u,\"last\")} (also written: \\axiom{\\spad{u} . last}) is equivalent to last \\spad{u}.") (($ $ "rest") "\\spad{elt(\\%,\"rest\")} (also written: \\axiom{\\spad{u}.rest}) is equivalent to \\axiom{rest \\spad{u}}.") ((|#2| $ "first") "\\spad{elt(u,\"first\")} (also written: \\axiom{\\spad{u} . first}) is equivalent to first \\spad{u}.")) (|first| (($ $ (|NonNegativeInteger|)) "\\spad{first(u,n)} returns a copy of the first \\spad{n} (\\axiom{\\spad{n} >= 0}) elements of \\spad{u}.") ((|#2| $) "\\spad{first(u)} returns the first element of \\spad{u} (equivalently,{} the value at the current node).")) (|concat| (($ |#2| $) "\\spad{concat(x,u)} returns aggregate consisting of \\spad{x} followed by the elements of \\spad{u}. Note: if \\axiom{\\spad{v} = concat(\\spad{x},{}\\spad{u})} then \\axiom{\\spad{x} = first \\spad{v}} and \\axiom{\\spad{u} = rest \\spad{v}}.") (($ $ $) "\\spad{concat(u,v)} returns an aggregate \\spad{w} consisting of the elements of \\spad{u} followed by the elements of \\spad{v}. Note: \\axiom{\\spad{v} = rest(\\spad{w},{}\\#a)}."))) @@ -4622,7 +4622,7 @@ NIL NIL (|UnivariateTaylorSeries| |Coef| |var| |cen|) ((|constructor| (NIL "Dense Taylor series in one variable \\spadtype{UnivariateTaylorSeries} is a domain representing Taylor series in one variable with coefficients in an arbitrary ring. The parameters of the type specify the coefficient ring,{} the power series variable,{} and the center of the power series expansion. For example,{} \\spadtype{UnivariateTaylorSeries}(Integer,{}\\spad{x},{}3) represents Taylor series in \\spad{(x - 3)} with \\spadtype{Integer} coefficients.")) (|integrate| (($ $ (|Variable| |#2|)) "\\spad{integrate(f(x),x)} returns an anti-derivative of the power series \\spad{f(x)} with constant coefficient 0. We may integrate a series when we can divide coefficients by integers.")) (|invmultisect| (($ (|Integer|) (|Integer|) $) "\\spad{invmultisect(a,b,f(x))} substitutes \\spad{x^((a+b)*n)} \\indented{1}{for \\spad{x^n} and multiples by \\spad{x^b}.}")) (|multisect| (($ (|Integer|) (|Integer|) $) "\\spad{multisect(a,b,f(x))} selects the coefficients of \\indented{1}{\\spad{x^((a+b)*n+a)},{} and changes this monomial to \\spad{x^n}.}")) (|revert| (($ $) "\\spad{revert(f(x))} returns a Taylor series \\spad{g(x)} such that \\spad{f(g(x)) = g(f(x)) = x}. Series \\spad{f(x)} should have constant coefficient 0 and invertible 1st order coefficient.")) (|generalLambert| (($ $ (|Integer|) (|Integer|)) "\\spad{generalLambert(f(x),a,d)} returns \\spad{f(x^a) + f(x^(a + d)) + \\indented{1}{f(x^(a + 2 d)) + ... }. \\spad{f(x)} should have zero constant} \\indented{1}{coefficient and \\spad{a} and \\spad{d} should be positive.}")) (|evenlambert| (($ $) "\\spad{evenlambert(f(x))} returns \\spad{f(x^2) + f(x^4) + f(x^6) + ...}. \\indented{1}{\\spad{f(x)} should have a zero constant coefficient.} \\indented{1}{This function is used for computing infinite products.} \\indented{1}{If \\spad{f(x)} is a Taylor series with constant term 1,{} then} \\indented{1}{\\spad{product(n=1..infinity,f(x^(2*n))) = exp(log(evenlambert(f(x))))}.}")) (|oddlambert| (($ $) "\\spad{oddlambert(f(x))} returns \\spad{f(x) + f(x^3) + f(x^5) + ...}. \\indented{1}{\\spad{f(x)} should have a zero constant coefficient.} \\indented{1}{This function is used for computing infinite products.} \\indented{1}{If \\spad{f(x)} is a Taylor series with constant term 1,{} then} \\indented{1}{\\spad{product(n=1..infinity,f(x^(2*n-1)))=exp(log(oddlambert(f(x))))}.}")) (|lambert| (($ $) "\\spad{lambert(f(x))} returns \\spad{f(x) + f(x^2) + f(x^3) + ...}. \\indented{1}{This function is used for computing infinite products.} \\indented{1}{\\spad{f(x)} should have zero constant coefficient.} \\indented{1}{If \\spad{f(x)} is a Taylor series with constant term 1,{} then} \\indented{1}{\\spad{product(n = 1..infinity,f(x^n)) = exp(log(lambert(f(x))))}.}")) (|lagrange| (($ $) "\\spad{lagrange(g(x))} produces the Taylor series for \\spad{f(x)} \\indented{1}{where \\spad{f(x)} is implicitly defined as \\spad{f(x) = x*g(f(x))}.}")) (|univariatePolynomial| (((|UnivariatePolynomial| |#2| |#1|) $ (|NonNegativeInteger|)) "\\spad{univariatePolynomial(f,k)} returns a univariate polynomial \\indented{1}{consisting of the sum of all terms of \\spad{f} of degree \\spad{<= k}.}")) (|coerce| (($ (|Variable| |#2|)) "\\spad{coerce(var)} converts the series variable \\spad{var} into a \\indented{1}{Taylor series.}") (($ (|UnivariatePolynomial| |#2| |#1|)) "\\spad{coerce(p)} converts a univariate polynomial \\spad{p} in the variable \\spad{var} to a univariate Taylor series in \\spad{var}."))) -(((|commutative| "*") |has| |#1| (|CommutativeRing|)) (|noZeroDivisors| |has| |#1| (|IntegralDomain|)) (|rightUnitary| . T) (|leftUnitary| . T) (|unitsKnown| . T)) +(((|commutative| "*") |has| |#1| (|CommutativeRing|)) (|noZeroDivisors| |has| |#1| (|IntegralDomain|))) (#1=(|HasCategory| |#1| (QUOTE (|Algebra| (|Fraction| #2=(|Integer|))))) #3=(|HasCategory| |#1| (QUOTE (|IntegralDomain|))) (OR #4=(|HasCategory| |#1| (QUOTE (|CommutativeRing|))) #3#) #4# (|HasCategory| |#1| (QUOTE (|CharacteristicNonZero|))) (|HasCategory| |#1| (QUOTE (|CharacteristicZero|))) (AND (|HasCategory| |#1| (QUOTE (|PartialDifferentialRing| #5=(|Symbol|)))) #6=(|HasSignature| |#1| (|%list| (QUOTE *) (|%list| #7=(|devaluate| |#1|) #8=(QUOTE #9=(|NonNegativeInteger|)) #7#)))) #6# (|HasCategory| #9# (QUOTE (|SemiGroup|))) (AND #10=(|HasSignature| |#1| (|%list| (QUOTE **) (|%list| #7# #7# #8#))) (|HasSignature| |#1| (|%list| (QUOTE |coerce|) (|%list| #7# #11=(QUOTE #5#))))) #10# (|HasCategory| |#1| (QUOTE (|Field|))) (OR (AND #1# (|HasCategory| |#1| (QUOTE (|AlgebraicallyClosedFunctionSpace| #2#))) (|HasCategory| |#1| (QUOTE (|PrimitiveFunctionCategory|))) (|HasCategory| |#1| (QUOTE (|TranscendentalFunctionCategory|)))) (AND #1# (|HasSignature| |#1| (|%list| (QUOTE |integrate|) (|%list| #7# #7# #11#))) (|HasSignature| |#1| (|%list| (QUOTE |variables|) (|%list| (|%list| (QUOTE |List|) #11#) #7#)))))) (|UnivariateTaylorSeriesFunctions2| |Coef1| |Coef2| UTS1 UTS2) ((|constructor| (NIL "Mapping package for univariate Taylor series. \\indented{2}{This package allows one to apply a function to the coefficients of} \\indented{2}{a univariate Taylor series.}")) (|map| ((|#4| (|Mapping| |#2| |#1|) |#3|) "\\spad{map(f,g(x))} applies the map \\spad{f} to the coefficients of \\indented{1}{the Taylor series \\spad{g(x)}.}"))) @@ -4634,7 +4634,7 @@ NIL ((|HasCategory| |#2| (QUOTE (|AlgebraicallyClosedFunctionSpace| #1=(|Integer|)))) (|HasCategory| |#2| (QUOTE (|PrimitiveFunctionCategory|))) (|HasCategory| |#2| (QUOTE (|TranscendentalFunctionCategory|))) (|HasSignature| |#2| (|%list| (QUOTE |variables|) (|%list| (|%list| (QUOTE |List|) #2=(QUOTE (|Symbol|))) #3=(|devaluate| |#2|)))) (|HasSignature| |#2| (|%list| (QUOTE |integrate|) (|%list| #3# #3# #2#))) (|HasCategory| |#2| (QUOTE (|Algebra| (|Fraction| #1#)))) (|HasCategory| |#2| (QUOTE (|Field|)))) (|UnivariateTaylorSeriesCategory| |Coef|) ((|constructor| (NIL "\\spadtype{UnivariateTaylorSeriesCategory} is the category of Taylor series in one variable.")) (|integrate| (($ $ (|Symbol|)) "\\spad{integrate(f(x),y)} returns an anti-derivative of the power series \\spad{f(x)} with respect to the variable \\spad{y}.") (($ $ (|Symbol|)) "\\spad{integrate(f(x),y)} returns an anti-derivative of the power series \\spad{f(x)} with respect to the variable \\spad{y}.") (($ $) "\\spad{integrate(f(x))} returns an anti-derivative of the power series \\spad{f(x)} with constant coefficient 0. We may integrate a series when we can divide coefficients by integers.")) (** (($ $ |#1|) "\\spad{f(x) ** a} computes a power of a power series. When the coefficient ring is a field,{} we may raise a series to an exponent from the coefficient ring provided that the constant coefficient of the series is 1.")) (|polynomial| (((|Polynomial| |#1|) $ (|NonNegativeInteger|) (|NonNegativeInteger|)) "\\spad{polynomial(f,k1,k2)} returns a polynomial consisting of the sum of all terms of \\spad{f} of degree \\spad{d} with \\spad{k1 <= d <= k2}.") (((|Polynomial| |#1|) $ (|NonNegativeInteger|)) "\\spad{polynomial(f,k)} returns a polynomial consisting of the sum of all terms of \\spad{f} of degree \\spad{<= k}.")) (|multiplyCoefficients| (($ (|Mapping| |#1| (|Integer|)) $) "\\spad{multiplyCoefficients(f,sum(n = 0..infinity,a[n] * x**n))} returns \\spad{sum(n = 0..infinity,f(n) * a[n] * x**n)}. This function is used when Laurent series are represented by a Taylor series and an order.")) (|quoByVar| (($ $) "\\spad{quoByVar(a0 + a1 x + a2 x**2 + ...)} returns \\spad{a1 + a2 x + a3 x**2 + ...} Thus,{} this function substracts the constant term and divides by the series variable. This function is used when Laurent series are represented by a Taylor series and an order.")) (|coefficients| (((|Stream| |#1|) $) "\\spad{coefficients(a0 + a1 x + a2 x**2 + ...)} returns a stream of coefficients: \\spad{[a0,a1,a2,...]}. The entries of the stream may be zero.")) (|series| (($ (|Stream| |#1|)) "\\spad{series([a0,a1,a2,...])} is the Taylor series \\spad{a0 + a1 x + a2 x**2 + ...}.") (($ (|Stream| (|Record| (|:| |k| (|NonNegativeInteger|)) (|:| |c| |#1|)))) "\\spad{series(st)} creates a series from a stream of non-zero terms,{} where a term is an exponent-coefficient pair. The terms in the stream should be ordered by increasing order of exponents."))) -(((|commutative| "*") |has| |#1| (|CommutativeRing|)) (|noZeroDivisors| |has| |#1| (|IntegralDomain|)) (|rightUnitary| . T) (|leftUnitary| . T) (|unitsKnown| . T)) +(((|commutative| "*") |has| |#1| (|CommutativeRing|)) (|noZeroDivisors| |has| |#1| (|IntegralDomain|))) NIL (|UnivariateTaylorSeriesODESolver| |Coef| UTS) ((|constructor| (NIL "\\indented{1}{This package provides Taylor series solutions to regular} linear or non-linear ordinary differential equations of arbitrary order.")) (|mpsode| (((|List| |#2|) (|List| |#1|) (|List| (|Mapping| |#2| (|List| |#2|)))) "\\spad{mpsode(r,f)} solves the system of differential equations \\spad{dy[i]/dx =f[i] [x,y[1],y[2],...,y[n]]},{} \\spad{y[i](a) = r[i]} for \\spad{i} in 1..\\spad{n}.")) (|ode| ((|#2| (|Mapping| |#2| (|List| |#2|)) (|List| |#1|)) "\\spad{ode(f,cl)} is the solution to \\spad{y<n>=f(y,y',..,y<n-1>)} such that \\spad{y<i>(a) = cl.i} for \\spad{i} in 1..\\spad{n}.")) (|ode2| ((|#2| (|Mapping| |#2| |#2| |#2|) |#1| |#1|) "\\spad{ode2(f,c0,c1)} is the solution to \\spad{y'' = f(y,y')} such that \\spad{y(a) = c0} and \\spad{y'(a) = c1}.")) (|ode1| ((|#2| (|Mapping| |#2| |#2|) |#1|) "\\spad{ode1(f,c)} is the solution to \\spad{y' = f(y)} such that \\spad{y(a) = c}.")) (|fixedPointExquo| ((|#2| |#2| |#2|) "\\spad{fixedPointExquo(f,g)} computes the exact quotient of \\spad{f} and \\spad{g} using a fixed point computation.")) (|stFuncN| (((|Mapping| (|Stream| |#1|) (|List| (|Stream| |#1|))) (|Mapping| |#2| (|List| |#2|))) "\\spad{stFuncN(f)} is a local function xported due to compiler problem. This function is of no interest to the top-level user.")) (|stFunc2| (((|Mapping| (|Stream| |#1|) (|Stream| |#1|) (|Stream| |#1|)) (|Mapping| |#2| |#2| |#2|)) "\\spad{stFunc2(f)} is a local function exported due to compiler problem. This function is of no interest to the top-level user.")) (|stFunc1| (((|Mapping| (|Stream| |#1|) (|Stream| |#1|)) (|Mapping| |#2| |#2|)) "\\spad{stFunc1(f)} is a local function exported due to compiler problem. This function is of no interest to the top-level user."))) @@ -4649,7 +4649,7 @@ NIL NIL NIL (|Variable| |sym|) -((|constructor| (NIL "This domain implements variables")) (|variable| (((|Symbol|)) "\\spad{variable()} returns the symbol")) (|coerce| (((|Symbol|) $) "\\spad{coerce(x)} returns the symbol"))) +((|constructor| (NIL "This domain implements variables")) (|variable| (((|Symbol|)) "\\spad{variable()} returns the symbol"))) NIL NIL (|VectorCategory&| S R) @@ -4673,7 +4673,7 @@ NIL NIL NIL (|TwoDimensionalViewport|) -((|constructor| (NIL "TwoDimensionalViewport creates viewports to display graphs.")) (|coerce| (((|OutputForm|) $) "\\spad{coerce(v)} returns the given two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport} as output of the domain \\spadtype{OutputForm}.")) (|key| (((|Integer|) $) "\\spad{key(v)} returns the process ID number of the given two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport}.")) (|reset| (((|Void|) $) "\\spad{reset(v)} sets the current state of the graph characteristics of the given two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport},{} back to their initial settings.")) (|write| (((|String|) $ (|String|) (|List| (|String|))) "\\spad{write(v,s,lf)} takes the given two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport},{} and creates a directory indicated by \\spad{s},{} which contains the graph data files for \\spad{v} and the optional file types indicated by the list \\spad{lf}.") (((|String|) $ (|String|) (|String|)) "\\spad{write(v,s,f)} takes the given two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport},{} and creates a directory indicated by \\spad{s},{} which contains the graph data files for \\spad{v} and an optional file type \\spad{f}.") (((|String|) $ (|String|)) "\\spad{write(v,s)} takes the given two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport},{} and creates a directory indicated by \\spad{s},{} which contains the graph data files for \\spad{v}.")) (|resize| (((|Void|) $ (|PositiveInteger|) (|PositiveInteger|)) "\\spad{resize(v,w,h)} displays the two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport},{} with a width of \\spad{w} and a height of \\spad{h},{} keeping the upper left-hand corner position unchanged.")) (|update| (((|Void|) $ (|GraphImage|) (|PositiveInteger|)) "\\spad{update(v,gr,n)} drops the graph \\spad{gr} in slot \\spad{n} of viewport \\spad{v}. The graph \\spad{gr} must have been transmitted already and acquired an integer key.")) (|move| (((|Void|) $ (|NonNegativeInteger|) (|NonNegativeInteger|)) "\\spad{move(v,x,y)} displays the two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport},{} with the upper left-hand corner of the viewport window at the screen coordinate position \\spad{x},{} \\spad{y}.")) (|show| (((|Void|) $ (|PositiveInteger|) (|String|)) "\\spad{show(v,n,s)} displays the graph in field \\spad{n} of the given two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport},{} if \\spad{s} is \"on\",{} or does not display the graph if \\spad{s} is \"off\".")) (|translate| (((|Void|) $ (|PositiveInteger|) (|Float|) (|Float|)) "\\spad{translate(v,n,dx,dy)} displays the graph in field \\spad{n} of the given two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport},{} translated by \\spad{dx} in the \\spad{x}-coordinate direction from the center of the viewport,{} and by \\spad{dy} in the \\spad{y}-coordinate direction from the center. Setting \\spad{dx} and \\spad{dy} to \\spad{0} places the center of the graph at the center of the viewport.")) (|scale| (((|Void|) $ (|PositiveInteger|) (|Float|) (|Float|)) "\\spad{scale(v,n,sx,sy)} displays the graph in field \\spad{n} of the given two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport},{} scaled by the factor \\spad{sx} in the \\spad{x}-coordinate direction and by the factor \\spad{sy} in the \\spad{y}-coordinate direction.")) (|dimensions| (((|Void|) $ (|NonNegativeInteger|) (|NonNegativeInteger|) (|PositiveInteger|) (|PositiveInteger|)) "\\spad{dimensions(v,x,y,width,height)} sets the position of the upper left-hand corner of the two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport},{} to the window coordinate \\spad{x},{} \\spad{y},{} and sets the dimensions of the window to that of \\spad{width},{} \\spad{height}. The new dimensions are not displayed until the function \\spadfun{makeViewport2D} is executed again for \\spad{v}.")) (|close| (((|Void|) $) "\\spad{close(v)} closes the viewport window of the given two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport},{} and terminates the corresponding process ID.")) (|controlPanel| (((|Void|) $ (|String|)) "\\spad{controlPanel(v,s)} displays the control panel of the given two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport},{} if \\spad{s} is \"on\",{} or hides the control panel if \\spad{s} is \"off\".")) (|connect| (((|Void|) $ (|PositiveInteger|) (|String|)) "\\spad{connect(v,n,s)} displays the lines connecting the graph points in field \\spad{n} of the given two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport},{} if \\spad{s} is \"on\",{} or does not display the lines if \\spad{s} is \"off\".")) (|region| (((|Void|) $ (|PositiveInteger|) (|String|)) "\\spad{region(v,n,s)} displays the bounding box of the graph in field \\spad{n} of the given two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport},{} if \\spad{s} is \"on\",{} or does not display the bounding box if \\spad{s} is \"off\".")) (|points| (((|Void|) $ (|PositiveInteger|) (|String|)) "\\spad{points(v,n,s)} displays the points of the graph in field \\spad{n} of the given two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport},{} if \\spad{s} is \"on\",{} or does not display the points if \\spad{s} is \"off\".")) (|units| (((|Void|) $ (|PositiveInteger|) (|Palette|)) "\\spad{units(v,n,c)} displays the units of the graph in field \\spad{n} of the given two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport},{} with the units color set to the given palette color \\spad{c}.") (((|Void|) $ (|PositiveInteger|) (|String|)) "\\spad{units(v,n,s)} displays the units of the graph in field \\spad{n} of the given two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport},{} if \\spad{s} is \"on\",{} or does not display the units if \\spad{s} is \"off\".")) (|axes| (((|Void|) $ (|PositiveInteger|) (|Palette|)) "\\spad{axes(v,n,c)} displays the axes of the graph in field \\spad{n} of the given two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport},{} with the axes color set to the given palette color \\spad{c}.") (((|Void|) $ (|PositiveInteger|) (|String|)) "\\spad{axes(v,n,s)} displays the axes of the graph in field \\spad{n} of the given two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport},{} if \\spad{s} is \"on\",{} or does not display the axes if \\spad{s} is \"off\".")) (|getGraph| (((|GraphImage|) $ (|PositiveInteger|)) "\\spad{getGraph(v,n)} returns the graph which is of the domain \\spadtype{GraphImage} which is located in graph field \\spad{n} of the given two-dimensional viewport,{} \\spad{v},{} which is of the domain \\spadtype{TwoDimensionalViewport}.")) (|putGraph| (((|Void|) $ (|GraphImage|) (|PositiveInteger|)) "\\spad{putGraph(v,gi,n)} sets the graph field indicated by \\spad{n},{} of the indicated two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport},{} to be the graph,{} \\spad{gi} of domain \\spadtype{GraphImage}. The contents of viewport,{} \\spad{v},{} will contain \\spad{gi} when the function \\spadfun{makeViewport2D} is called to create the an updated viewport \\spad{v}.")) (|title| (((|Void|) $ (|String|)) "\\spad{title(v,s)} changes the title which is shown in the two-dimensional viewport window,{} \\spad{v} of domain \\spadtype{TwoDimensionalViewport}.")) (|graphs| (((|Vector| (|Union| (|GraphImage|) "undefined")) $) "\\spad{graphs(v)} returns a vector,{} or list,{} which is a union of all the graphs,{} of the domain \\spadtype{GraphImage},{} which are allocated for the two-dimensional viewport,{} \\spad{v},{} of domain \\spadtype{TwoDimensionalViewport}. Those graphs which have no data are labeled \"undefined\",{} otherwise their contents are shown.")) (|graphStates| (((|Vector| (|Record| (|:| |scaleX| (|DoubleFloat|)) (|:| |scaleY| (|DoubleFloat|)) (|:| |deltaX| (|DoubleFloat|)) (|:| |deltaY| (|DoubleFloat|)) (|:| |points| (|Integer|)) (|:| |connect| (|Integer|)) (|:| |spline| (|Integer|)) (|:| |axes| (|Integer|)) (|:| |axesColor| (|Palette|)) (|:| |units| (|Integer|)) (|:| |unitsColor| (|Palette|)) (|:| |showing| (|Integer|)))) $) "\\spad{graphStates(v)} returns and shows a listing of a record containing the current state of the characteristics of each of the ten graph records in the given two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport}.")) (|graphState| (((|Void|) $ (|PositiveInteger|) (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|) (|Integer|) (|Integer|) (|Integer|) (|Integer|) (|Palette|) (|Integer|) (|Palette|) (|Integer|)) "\\spad{graphState(v,num,sX,sY,dX,dY,pts,lns,box,axes,axesC,un,unC,cP)} sets the state of the characteristics for the graph indicated by \\spad{num} in the given two-dimensional viewport \\spad{v},{} of domain \\spadtype{TwoDimensionalViewport},{} to the values given as parameters. The scaling of the graph in the \\spad{x} and \\spad{y} component directions is set to be \\spad{sX} and \\spad{sY}; the window translation in the \\spad{x} and \\spad{y} component directions is set to be \\spad{dX} and \\spad{dY}; The graph points,{} lines,{} bounding \\spad{box},{} \\spad{axes},{} or units will be shown in the viewport if their given parameters \\spad{pts},{} \\spad{lns},{} \\spad{box},{} \\spad{axes} or \\spad{un} are set to be \\spad{1},{} but will not be shown if they are set to \\spad{0}. The color of the \\spad{axes} and the color of the units are indicated by the palette colors \\spad{axesC} and \\spad{unC} respectively. To display the control panel when the viewport window is displayed,{} set \\spad{cP} to \\spad{1},{} otherwise set it to \\spad{0}.")) (|options| (($ $ (|List| (|DrawOption|))) "\\spad{options(v,lopt)} takes the given two-dimensional viewport,{} \\spad{v},{} of the domain \\spadtype{TwoDimensionalViewport} and returns \\spad{v} with it's draw options modified to be those which are indicated in the given list,{} \\spad{lopt} of domain \\spadtype{DrawOption}.") (((|List| (|DrawOption|)) $) "\\spad{options(v)} takes the given two-dimensional viewport,{} \\spad{v},{} of the domain \\spadtype{TwoDimensionalViewport} and returns a list containing the draw options from the domain \\spadtype{DrawOption} for \\spad{v}.")) (|makeViewport2D| (($ (|GraphImage|) (|List| (|DrawOption|))) "\\spad{makeViewport2D(gi,lopt)} creates and displays a viewport window of the domain \\spadtype{TwoDimensionalViewport} whose graph field is assigned to be the given graph,{} \\spad{gi},{} of domain \\spadtype{GraphImage},{} and whose options field is set to be the list of options,{} \\spad{lopt} of domain \\spadtype{DrawOption}.") (($ $) "\\spad{makeViewport2D(v)} takes the given two-dimensional viewport,{} \\spad{v},{} of the domain \\spadtype{TwoDimensionalViewport} and displays a viewport window on the screen which contains the contents of \\spad{v}.")) (|viewport2D| (($) "\\spad{viewport2D()} returns an undefined two-dimensional viewport of the domain \\spadtype{TwoDimensionalViewport} whose contents are empty.")) (|getPickedPoints| (((|List| (|Point| (|DoubleFloat|))) $) "\\spad{getPickedPoints(x)} returns a list of small floats for the points the user interactively picked on the viewport for full integration into the system,{} some design issues need to be addressed: \\spadignore{e.g.} how to go through the GraphImage interface,{} how to default to graphs,{} etc."))) +((|constructor| (NIL "TwoDimensionalViewport creates viewports to display graphs.")) (|key| (((|Integer|) $) "\\spad{key(v)} returns the process ID number of the given two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport}.")) (|reset| (((|Void|) $) "\\spad{reset(v)} sets the current state of the graph characteristics of the given two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport},{} back to their initial settings.")) (|write| (((|String|) $ (|String|) (|List| (|String|))) "\\spad{write(v,s,lf)} takes the given two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport},{} and creates a directory indicated by \\spad{s},{} which contains the graph data files for \\spad{v} and the optional file types indicated by the list \\spad{lf}.") (((|String|) $ (|String|) (|String|)) "\\spad{write(v,s,f)} takes the given two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport},{} and creates a directory indicated by \\spad{s},{} which contains the graph data files for \\spad{v} and an optional file type \\spad{f}.") (((|String|) $ (|String|)) "\\spad{write(v,s)} takes the given two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport},{} and creates a directory indicated by \\spad{s},{} which contains the graph data files for \\spad{v}.")) (|resize| (((|Void|) $ (|PositiveInteger|) (|PositiveInteger|)) "\\spad{resize(v,w,h)} displays the two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport},{} with a width of \\spad{w} and a height of \\spad{h},{} keeping the upper left-hand corner position unchanged.")) (|update| (((|Void|) $ (|GraphImage|) (|PositiveInteger|)) "\\spad{update(v,gr,n)} drops the graph \\spad{gr} in slot \\spad{n} of viewport \\spad{v}. The graph \\spad{gr} must have been transmitted already and acquired an integer key.")) (|move| (((|Void|) $ (|NonNegativeInteger|) (|NonNegativeInteger|)) "\\spad{move(v,x,y)} displays the two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport},{} with the upper left-hand corner of the viewport window at the screen coordinate position \\spad{x},{} \\spad{y}.")) (|show| (((|Void|) $ (|PositiveInteger|) (|String|)) "\\spad{show(v,n,s)} displays the graph in field \\spad{n} of the given two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport},{} if \\spad{s} is \"on\",{} or does not display the graph if \\spad{s} is \"off\".")) (|translate| (((|Void|) $ (|PositiveInteger|) (|Float|) (|Float|)) "\\spad{translate(v,n,dx,dy)} displays the graph in field \\spad{n} of the given two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport},{} translated by \\spad{dx} in the \\spad{x}-coordinate direction from the center of the viewport,{} and by \\spad{dy} in the \\spad{y}-coordinate direction from the center. Setting \\spad{dx} and \\spad{dy} to \\spad{0} places the center of the graph at the center of the viewport.")) (|scale| (((|Void|) $ (|PositiveInteger|) (|Float|) (|Float|)) "\\spad{scale(v,n,sx,sy)} displays the graph in field \\spad{n} of the given two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport},{} scaled by the factor \\spad{sx} in the \\spad{x}-coordinate direction and by the factor \\spad{sy} in the \\spad{y}-coordinate direction.")) (|dimensions| (((|Void|) $ (|NonNegativeInteger|) (|NonNegativeInteger|) (|PositiveInteger|) (|PositiveInteger|)) "\\spad{dimensions(v,x,y,width,height)} sets the position of the upper left-hand corner of the two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport},{} to the window coordinate \\spad{x},{} \\spad{y},{} and sets the dimensions of the window to that of \\spad{width},{} \\spad{height}. The new dimensions are not displayed until the function \\spadfun{makeViewport2D} is executed again for \\spad{v}.")) (|close| (((|Void|) $) "\\spad{close(v)} closes the viewport window of the given two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport},{} and terminates the corresponding process ID.")) (|controlPanel| (((|Void|) $ (|String|)) "\\spad{controlPanel(v,s)} displays the control panel of the given two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport},{} if \\spad{s} is \"on\",{} or hides the control panel if \\spad{s} is \"off\".")) (|connect| (((|Void|) $ (|PositiveInteger|) (|String|)) "\\spad{connect(v,n,s)} displays the lines connecting the graph points in field \\spad{n} of the given two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport},{} if \\spad{s} is \"on\",{} or does not display the lines if \\spad{s} is \"off\".")) (|region| (((|Void|) $ (|PositiveInteger|) (|String|)) "\\spad{region(v,n,s)} displays the bounding box of the graph in field \\spad{n} of the given two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport},{} if \\spad{s} is \"on\",{} or does not display the bounding box if \\spad{s} is \"off\".")) (|points| (((|Void|) $ (|PositiveInteger|) (|String|)) "\\spad{points(v,n,s)} displays the points of the graph in field \\spad{n} of the given two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport},{} if \\spad{s} is \"on\",{} or does not display the points if \\spad{s} is \"off\".")) (|units| (((|Void|) $ (|PositiveInteger|) (|Palette|)) "\\spad{units(v,n,c)} displays the units of the graph in field \\spad{n} of the given two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport},{} with the units color set to the given palette color \\spad{c}.") (((|Void|) $ (|PositiveInteger|) (|String|)) "\\spad{units(v,n,s)} displays the units of the graph in field \\spad{n} of the given two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport},{} if \\spad{s} is \"on\",{} or does not display the units if \\spad{s} is \"off\".")) (|axes| (((|Void|) $ (|PositiveInteger|) (|Palette|)) "\\spad{axes(v,n,c)} displays the axes of the graph in field \\spad{n} of the given two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport},{} with the axes color set to the given palette color \\spad{c}.") (((|Void|) $ (|PositiveInteger|) (|String|)) "\\spad{axes(v,n,s)} displays the axes of the graph in field \\spad{n} of the given two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport},{} if \\spad{s} is \"on\",{} or does not display the axes if \\spad{s} is \"off\".")) (|getGraph| (((|GraphImage|) $ (|PositiveInteger|)) "\\spad{getGraph(v,n)} returns the graph which is of the domain \\spadtype{GraphImage} which is located in graph field \\spad{n} of the given two-dimensional viewport,{} \\spad{v},{} which is of the domain \\spadtype{TwoDimensionalViewport}.")) (|putGraph| (((|Void|) $ (|GraphImage|) (|PositiveInteger|)) "\\spad{putGraph(v,gi,n)} sets the graph field indicated by \\spad{n},{} of the indicated two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport},{} to be the graph,{} \\spad{gi} of domain \\spadtype{GraphImage}. The contents of viewport,{} \\spad{v},{} will contain \\spad{gi} when the function \\spadfun{makeViewport2D} is called to create the an updated viewport \\spad{v}.")) (|title| (((|Void|) $ (|String|)) "\\spad{title(v,s)} changes the title which is shown in the two-dimensional viewport window,{} \\spad{v} of domain \\spadtype{TwoDimensionalViewport}.")) (|graphs| (((|Vector| (|Union| (|GraphImage|) "undefined")) $) "\\spad{graphs(v)} returns a vector,{} or list,{} which is a union of all the graphs,{} of the domain \\spadtype{GraphImage},{} which are allocated for the two-dimensional viewport,{} \\spad{v},{} of domain \\spadtype{TwoDimensionalViewport}. Those graphs which have no data are labeled \"undefined\",{} otherwise their contents are shown.")) (|graphStates| (((|Vector| (|Record| (|:| |scaleX| (|DoubleFloat|)) (|:| |scaleY| (|DoubleFloat|)) (|:| |deltaX| (|DoubleFloat|)) (|:| |deltaY| (|DoubleFloat|)) (|:| |points| (|Integer|)) (|:| |connect| (|Integer|)) (|:| |spline| (|Integer|)) (|:| |axes| (|Integer|)) (|:| |axesColor| (|Palette|)) (|:| |units| (|Integer|)) (|:| |unitsColor| (|Palette|)) (|:| |showing| (|Integer|)))) $) "\\spad{graphStates(v)} returns and shows a listing of a record containing the current state of the characteristics of each of the ten graph records in the given two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport}.")) (|graphState| (((|Void|) $ (|PositiveInteger|) (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|) (|Integer|) (|Integer|) (|Integer|) (|Integer|) (|Palette|) (|Integer|) (|Palette|) (|Integer|)) "\\spad{graphState(v,num,sX,sY,dX,dY,pts,lns,box,axes,axesC,un,unC,cP)} sets the state of the characteristics for the graph indicated by \\spad{num} in the given two-dimensional viewport \\spad{v},{} of domain \\spadtype{TwoDimensionalViewport},{} to the values given as parameters. The scaling of the graph in the \\spad{x} and \\spad{y} component directions is set to be \\spad{sX} and \\spad{sY}; the window translation in the \\spad{x} and \\spad{y} component directions is set to be \\spad{dX} and \\spad{dY}; The graph points,{} lines,{} bounding \\spad{box},{} \\spad{axes},{} or units will be shown in the viewport if their given parameters \\spad{pts},{} \\spad{lns},{} \\spad{box},{} \\spad{axes} or \\spad{un} are set to be \\spad{1},{} but will not be shown if they are set to \\spad{0}. The color of the \\spad{axes} and the color of the units are indicated by the palette colors \\spad{axesC} and \\spad{unC} respectively. To display the control panel when the viewport window is displayed,{} set \\spad{cP} to \\spad{1},{} otherwise set it to \\spad{0}.")) (|options| (($ $ (|List| (|DrawOption|))) "\\spad{options(v,lopt)} takes the given two-dimensional viewport,{} \\spad{v},{} of the domain \\spadtype{TwoDimensionalViewport} and returns \\spad{v} with it's draw options modified to be those which are indicated in the given list,{} \\spad{lopt} of domain \\spadtype{DrawOption}.") (((|List| (|DrawOption|)) $) "\\spad{options(v)} takes the given two-dimensional viewport,{} \\spad{v},{} of the domain \\spadtype{TwoDimensionalViewport} and returns a list containing the draw options from the domain \\spadtype{DrawOption} for \\spad{v}.")) (|makeViewport2D| (($ (|GraphImage|) (|List| (|DrawOption|))) "\\spad{makeViewport2D(gi,lopt)} creates and displays a viewport window of the domain \\spadtype{TwoDimensionalViewport} whose graph field is assigned to be the given graph,{} \\spad{gi},{} of domain \\spadtype{GraphImage},{} and whose options field is set to be the list of options,{} \\spad{lopt} of domain \\spadtype{DrawOption}.") (($ $) "\\spad{makeViewport2D(v)} takes the given two-dimensional viewport,{} \\spad{v},{} of the domain \\spadtype{TwoDimensionalViewport} and displays a viewport window on the screen which contains the contents of \\spad{v}.")) (|viewport2D| (($) "\\spad{viewport2D()} returns an undefined two-dimensional viewport of the domain \\spadtype{TwoDimensionalViewport} whose contents are empty.")) (|getPickedPoints| (((|List| (|Point| (|DoubleFloat|))) $) "\\spad{getPickedPoints(x)} returns a list of small floats for the points the user interactively picked on the viewport for full integration into the system,{} some design issues need to be addressed: \\spadignore{e.g.} how to go through the GraphImage interface,{} how to default to graphs,{} etc."))) NIL NIL (|ThreeDimensionalViewport|) @@ -4694,7 +4694,7 @@ NIL NIL (|VectorSpace| S) ((|constructor| (NIL "Vector Spaces (not necessarily finite dimensional) over a field.")) (|dimension| (((|CardinalNumber|)) "\\spad{dimension()} returns the dimensionality of the vector space.")) (/ (($ $ |#1|) "\\spad{x/y} divides the vector \\spad{x} by the scalar \\spad{y}."))) -((|leftUnitary| . T) (|rightUnitary| . T)) +NIL NIL (|WeierstrassPreparation| R) ((|constructor| (NIL "This package implements the Weierstrass preparation theorem \\spad{f} or multivariate power series. weierstrass(\\spad{v},{}\\spad{p}) where \\spad{v} is a variable,{} and \\spad{p} is a TaylorSeries(\\spad{R}) in which the terms of lowest degree \\spad{s} must include c*v**s where \\spad{c} is a constant,{}\\spad{s>0},{} is a list of TaylorSeries coefficients A[\\spad{i}] of the equivalent polynomial A = A[0] + A[1]*v + A[2]\\spad{*v**2} + ... + A[\\spad{s}-1]*v**(\\spad{s}-1) + v**s such that p=A*B ,{} \\spad{B} being a TaylorSeries of minimum degree 0")) (|qqq| (((|Mapping| (|Stream| (|TaylorSeries| |#1|)) (|Stream| (|TaylorSeries| |#1|))) (|NonNegativeInteger|) (|TaylorSeries| |#1|) (|Stream| (|TaylorSeries| |#1|))) "\\spad{qqq(n,s,st)} is used internally.")) (|weierstrass| (((|List| (|TaylorSeries| |#1|)) (|Symbol|) (|TaylorSeries| |#1|)) "\\spad{weierstrass(v,ts)} where \\spad{v} is a variable and \\spad{ts} is \\indented{1}{a TaylorSeries,{} impements the Weierstrass Preparation} \\indented{1}{Theorem. The result is a list of TaylorSeries that} \\indented{1}{are the coefficients of the equivalent series.}")) (|clikeUniv| (((|Mapping| (|SparseUnivariatePolynomial| (|Polynomial| |#1|)) (|Polynomial| |#1|)) (|Symbol|)) "\\spad{clikeUniv(v)} is used internally.")) (|sts2stst| (((|Stream| (|Stream| (|Polynomial| |#1|))) (|Symbol|) (|Stream| (|Polynomial| |#1|))) "\\spad{sts2stst(v,s)} is used internally.")) (|cfirst| (((|Mapping| (|Stream| (|Polynomial| |#1|)) (|Stream| (|Polynomial| |#1|))) (|NonNegativeInteger|)) "\\spad{cfirst n} is used internally.")) (|crest| (((|Mapping| (|Stream| (|Polynomial| |#1|)) (|Stream| (|Polynomial| |#1|))) (|NonNegativeInteger|)) "\\spad{crest n} is used internally."))) @@ -4714,7 +4714,7 @@ NIL NIL (|WeightedPolynomials| R |VarSet| E P |vl| |wl| |wtlevel|) ((|constructor| (NIL "This domain represents truncated weighted polynomials over a general (not necessarily commutative) polynomial type. The variables must be specified,{} as must the weights. The representation is sparse in the sense that only non-zero terms are represented.")) (|changeWeightLevel| (((|Void|) (|NonNegativeInteger|)) "\\spad{changeWeightLevel(n)} changes the weight level to the new value given: NB: previously calculated terms are not affected")) (/ (((|Union| $ "failed") $ $) "\\spad{x/y} division (only works if minimum weight of divisor is zero,{} and if \\spad{R} is a Field)"))) -((|leftUnitary| |has| |#1| . #1=((|CommutativeRing|))) (|rightUnitary| |has| |#1| . #1#) (|unitsKnown| . T)) +NIL ((|HasCategory| |#1| (QUOTE (|CommutativeRing|))) (|HasCategory| |#1| (QUOTE (|Field|)))) (|WuWenTsunTriangularSet| R E V P) ((|constructor| (NIL "A domain constructor of the category \\axiomType{GeneralTriangularSet}. The only requirement for a list of polynomials to be a member of such a domain is the following: no polynomial is constant and two distinct polynomials have distinct main variables. Such a triangular set may not be auto-reduced or consistent. The \\axiomOpFrom{construct}{WuWenTsunTriangularSet} operation does not check the previous requirement. Triangular sets are stored as sorted lists \\spad{w}.\\spad{r}.\\spad{t}. the main variables of their members. Furthermore,{} this domain exports operations dealing with the characteristic set method of Wu Wen Tsun and some optimizations mainly proposed by Dong Ming Wang.\\newline References : \\indented{1}{[1] \\spad{W}. \\spad{T}. WU \"A Zero Structure Theorem for polynomial equations solving\"} \\indented{6}{MM Research Preprints,{} 1987.} \\indented{1}{[2] \\spad{D}. \\spad{M}. WANG \"An implementation of the characteristic set method in Maple\"} \\indented{6}{Proc. \\spad{DISCO'92}. Bath,{} England.}")) (|characteristicSerie| (((|List| $) (|List| |#4|)) "\\axiom{characteristicSerie(ps)} returns the same as \\axiom{characteristicSerie(ps,{}initiallyReduced?,{}initiallyReduce)}.") (((|List| $) (|List| |#4|) (|Mapping| (|Boolean|) |#4| |#4|) (|Mapping| |#4| |#4| |#4|)) "\\axiom{characteristicSerie(ps,{}redOp?,{}redOp)} returns a list \\axiom{lts} of triangular sets such that the zero set of \\axiom{ps} is the union of the regular zero sets of the members of \\axiom{lts}. This is made by the Ritt and Wu Wen Tsun process applying the operation \\axiom{characteristicSet(ps,{}redOp?,{}redOp)} to compute characteristic sets in Wu Wen Tsun sense.")) (|characteristicSet| (((|Union| $ "failed") (|List| |#4|)) "\\axiom{characteristicSet(ps)} returns the same as \\axiom{characteristicSet(ps,{}initiallyReduced?,{}initiallyReduce)}.") (((|Union| $ "failed") (|List| |#4|) (|Mapping| (|Boolean|) |#4| |#4|) (|Mapping| |#4| |#4| |#4|)) "\\axiom{characteristicSet(ps,{}redOp?,{}redOp)} returns a non-contradictory characteristic set of \\axiom{ps} in Wu Wen Tsun sense \\spad{w}.\\spad{r}.\\spad{t} the reduction-test \\axiom{redOp?} (using \\axiom{redOp} to reduce polynomials \\spad{w}.\\spad{r}.\\spad{t} a \\axiom{redOp?} basic set),{} if no non-zero constant polynomial appear during those reductions,{} else \\axiom{\"failed\"} is returned. The operations \\axiom{redOp} and \\axiom{redOp?} must satisfy the following conditions: \\axiom{redOp?(redOp(\\spad{p},{}\\spad{q}),{}\\spad{q})} holds for every polynomials \\axiom{\\spad{p},{}\\spad{q}} and there exists an integer \\axiom{\\spad{e}} and a polynomial \\axiom{\\spad{f}} such that we have \\axiom{init(\\spad{q})^e*p = f*q + redOp(\\spad{p},{}\\spad{q})}.")) (|medialSet| (((|Union| $ "failed") (|List| |#4|)) "\\axiom{medial(ps)} returns the same as \\axiom{medialSet(ps,{}initiallyReduced?,{}initiallyReduce)}.") (((|Union| $ "failed") (|List| |#4|) (|Mapping| (|Boolean|) |#4| |#4|) (|Mapping| |#4| |#4| |#4|)) "\\axiom{medialSet(ps,{}redOp?,{}redOp)} returns \\axiom{bs} a basic set (in Wu Wen Tsun sense \\spad{w}.\\spad{r}.\\spad{t} the reduction-test \\axiom{redOp?}) of some set generating the same ideal as \\axiom{ps} (with rank not higher than any basic set of \\axiom{ps}),{} if no non-zero constant polynomials appear during the computatioms,{} else \\axiom{\"failed\"} is returned. In the former case,{} \\axiom{bs} has to be understood as a candidate for being a characteristic set of \\axiom{ps}. In the original algorithm,{} \\axiom{bs} is simply a basic set of \\axiom{ps}."))) @@ -4722,11 +4722,11 @@ NIL ((AND #1=(|HasCategory| |#4| (QUOTE (|SetCategory|))) (|HasCategory| |#4| (|%list| (QUOTE |Evalable|) #2=(|devaluate| |#4|)))) (|HasCategory| |#4| (QUOTE (|ConvertibleTo| (|InputForm|)))) #3=(|HasCategory| |#4| (QUOTE (|BasicType|))) (|HasCategory| |#1| (QUOTE (|IntegralDomain|))) (|HasCategory| |#3| (QUOTE (|Finite|))) (|HasCategory| |#4| (QUOTE (|CoercibleTo| (|OutputForm|)))) #1# (AND #3# #4=(|HasCategory| $ (|%list| (QUOTE |FiniteAggregate|) #2#))) #4#) (|XAlgebra| R) ((|constructor| (NIL "This is the category of algebras over non-commutative rings. It is used by constructors of non-commutative algebras such as: \\indented{4}{\\spadtype{XPolynomialRing}.} \\indented{4}{\\spadtype{XFreeAlgebra}} Author: Michel Petitot (petitot@lifl.fr)"))) -((|rightUnitary| . T) (|leftUnitary| . T) (|unitsKnown| . T)) +NIL NIL (|XDistributedPolynomial| |vl| R) ((|constructor| (NIL "\\indented{2}{This type supports distributed multivariate polynomials} whose variables do not commute. The coefficient ring may be non-commutative too. However,{} coefficients and variables commute."))) -((|unitsKnown| . T) (|noZeroDivisors| |has| |#2| (ATTRIBUTE |noZeroDivisors|)) (|leftUnitary| . T) (|rightUnitary| . T)) +((|noZeroDivisors| |has| |#2| (ATTRIBUTE |noZeroDivisors|))) ((|HasCategory| |#2| (QUOTE (|CommutativeRing|))) (|HasAttribute| |#2| (QUOTE |noZeroDivisors|))) (|XExponentialPackage| R |VarSet| XPOLY) ((|constructor| (NIL "This package provides computations of logarithms and exponentials for polynomials in non-commutative variables. \\newline Author: Michel Petitot (petitot@lifl.fr).")) (|Hausdorff| ((|#3| |#3| |#3| (|NonNegativeInteger|)) "\\axiom{Hausdorff(a,{}\\spad{b},{}\\spad{n})} returns log(exp(a)*exp(\\spad{b})) truncated at order \\axiom{\\spad{n}}.")) (|log| ((|#3| |#3| (|NonNegativeInteger|)) "\\axiom{log(\\spad{p},{} \\spad{n})} returns the logarithm of \\axiom{\\spad{p}} truncated at order \\axiom{\\spad{n}}.")) (|exp| ((|#3| |#3| (|NonNegativeInteger|)) "\\axiom{exp(\\spad{p},{} \\spad{n})} returns the exponential of \\axiom{\\spad{p}} truncated at order \\axiom{\\spad{n}}."))) @@ -4738,31 +4738,31 @@ NIL ((|HasCategory| |#2| (QUOTE (|Finite|))) (|HasCategory| |#2| (QUOTE (|CharacteristicNonZero|))) (|HasCategory| |#2| (QUOTE (|CharacteristicZero|)))) (|ExtensionField| F) ((|constructor| (NIL "ExtensionField {\\em F} is the category of fields which extend the field \\spad{F}")) (|Frobenius| (($ $ (|NonNegativeInteger|)) "\\spad{Frobenius(a,s)} returns \\spad{a**(q**s)} where \\spad{q} is the size()\\$\\spad{F}.") (($ $) "\\spad{Frobenius(a)} returns \\spad{a ** q} where \\spad{q} is the \\spad{size()\\$F}.")) (|transcendenceDegree| (((|NonNegativeInteger|)) "\\spad{transcendenceDegree()} returns the transcendence degree of the field extension,{} 0 if the extension is algebraic.")) (|extensionDegree| (((|OnePointCompletion| (|PositiveInteger|))) "\\spad{extensionDegree()} returns the degree of the field extension if the extension is algebraic,{} and \\spad{infinity} if it is not.")) (|degree| (((|OnePointCompletion| (|PositiveInteger|)) $) "\\spad{degree(a)} returns the degree of minimal polynomial of an element \\spad{a} if \\spad{a} is algebraic with respect to the ground field \\spad{F},{} and \\spad{infinity} otherwise.")) (|inGroundField?| (((|Boolean|) $) "\\spad{inGroundField?(a)} tests whether an element \\spad{a} is already in the ground field \\spad{F}.")) (|transcendent?| (((|Boolean|) $) "\\spad{transcendent?(a)} tests whether an element \\spad{a} is transcendent with respect to the ground field \\spad{F}.")) (|algebraic?| (((|Boolean|) $) "\\spad{algebraic?(a)} tests whether an element \\spad{a} is algebraic with respect to the ground field \\spad{F}."))) -((|canonicalsClosed| . T) (|canonicalUnitNormal| . T) (|noZeroDivisors| . T) ((|commutative| "*") . T) (|rightUnitary| . T) (|leftUnitary| . T) (|unitsKnown| . T)) +((|canonicalUnitNormal| . T) (|noZeroDivisors| . T) ((|commutative| "*") . T)) NIL (|XFreeAlgebra| |vl| R) ((|constructor| (NIL "This category specifies opeations for polynomials and formal series with non-commutative variables.")) (|varList| (((|List| |#1|) $) "\\spad{varList(x)} returns the list of variables which appear in \\spad{x}.")) (|sh| (($ $ (|NonNegativeInteger|)) "\\spad{sh(x,n)} returns the shuffle power of \\spad{x} to the \\spad{n}.") (($ $ $) "\\spad{sh(x,y)} returns the shuffle-product of \\spad{x} by \\spad{y}. This multiplication is associative and commutative.")) (|quasiRegular| (($ $) "\\spad{quasiRegular(x)} return \\spad{x} minus its constant term.")) (|quasiRegular?| (((|Boolean|) $) "\\spad{quasiRegular?(x)} return \\spad{true} if \\spad{constant(x)} is zero.")) (|constant| ((|#2| $) "\\spad{constant(x)} returns the constant term of \\spad{x}.")) (|constant?| (((|Boolean|) $) "\\spad{constant?(x)} returns \\spad{true} if \\spad{x} is constant.")) (|coerce| (($ |#1|) "\\spad{coerce(v)} returns \\spad{v}.")) (|mirror| (($ $) "\\spad{mirror(x)} returns \\spad{Sum(r_i mirror(w_i))} if \\spad{x} writes \\spad{Sum(r_i w_i)}.")) (|monomial?| (((|Boolean|) $) "\\spad{monomial?(x)} returns \\spad{true} if \\spad{x} is a monomial")) (|monom| (($ (|OrderedFreeMonoid| |#1|) |#2|) "\\spad{monom(w,r)} returns the product of the word \\spad{w} by the coefficient \\spad{r}.")) (|rquo| (($ $ $) "\\spad{rquo(x,y)} returns the right simplification of \\spad{x} by \\spad{y}.") (($ $ (|OrderedFreeMonoid| |#1|)) "\\spad{rquo(x,w)} returns the right simplification of \\spad{x} by \\spad{w}.") (($ $ |#1|) "\\spad{rquo(x,v)} returns the right simplification of \\spad{x} by the variable \\spad{v}.")) (|lquo| (($ $ $) "\\spad{lquo(x,y)} returns the left simplification of \\spad{x} by \\spad{y}.") (($ $ (|OrderedFreeMonoid| |#1|)) "\\spad{lquo(x,w)} returns the left simplification of \\spad{x} by the word \\spad{w}.") (($ $ |#1|) "\\spad{lquo(x,v)} returns the left simplification of \\spad{x} by the variable \\spad{v}.")) (|coef| ((|#2| $ $) "\\spad{coef(x,y)} returns scalar product of \\spad{x} by \\spad{y},{} the set of words being regarded as an orthogonal basis.") ((|#2| $ (|OrderedFreeMonoid| |#1|)) "\\spad{coef(x,w)} returns the coefficient of the word \\spad{w} in \\spad{x}.")) (|mindegTerm| (((|Record| (|:| |k| (|OrderedFreeMonoid| |#1|)) (|:| |c| |#2|)) $) "\\spad{mindegTerm(x)} returns the term whose word is \\spad{mindeg(x)}.")) (|mindeg| (((|OrderedFreeMonoid| |#1|) $) "\\spad{mindeg(x)} returns the little word which appears in \\spad{x}. Error if \\spad{x=0}.")) (* (($ $ |#2|) "\\spad{x * r} returns the product of \\spad{x} by \\spad{r}. Usefull if \\spad{R} is a non-commutative Ring.") (($ |#1| $) "\\spad{v * x} returns the product of a variable \\spad{x} by \\spad{x}."))) -((|noZeroDivisors| |has| |#2| (ATTRIBUTE |noZeroDivisors|)) (|leftUnitary| . T) (|rightUnitary| . T) (|unitsKnown| . T)) +((|noZeroDivisors| |has| |#2| (ATTRIBUTE |noZeroDivisors|))) NIL (|XPBWPolynomial| |VarSet| R) -((|constructor| (NIL "This domain constructor implements polynomials in non-commutative variables written in the Poincare-Birkhoff-Witt basis from the Lyndon basis. These polynomials can be used to compute Baker-Campbell-Hausdorff relations. \\newline Author: Michel Petitot (petitot@lifl.fr).")) (|log| (($ $ (|NonNegativeInteger|)) "\\axiom{log(\\spad{p},{}\\spad{n})} returns the logarithm of \\axiom{\\spad{p}} (truncated up to order \\axiom{\\spad{n}}).")) (|exp| (($ $ (|NonNegativeInteger|)) "\\axiom{exp(\\spad{p},{}\\spad{n})} returns the exponential of \\axiom{\\spad{p}} (truncated up to order \\axiom{\\spad{n}}).")) (|product| (($ $ $ (|NonNegativeInteger|)) "\\axiom{product(a,{}\\spad{b},{}\\spad{n})} returns \\axiom{a*b} (truncated up to order \\axiom{\\spad{n}}).")) (|LiePolyIfCan| (((|Union| (|LiePolynomial| |#1| |#2|) "failed") $) "\\axiom{LiePolyIfCan(\\spad{p})} return \\axiom{\\spad{p}} if \\axiom{\\spad{p}} is a Lie polynomial.")) (|coerce| (((|XRecursivePolynomial| |#1| |#2|) $) "\\axiom{coerce(\\spad{p})} returns \\axiom{\\spad{p}} as a recursive polynomial.") (((|XDistributedPolynomial| |#1| |#2|) $) "\\axiom{coerce(\\spad{p})} returns \\axiom{\\spad{p}} as a distributed polynomial.") (($ (|LiePolynomial| |#1| |#2|)) "\\axiom{coerce(\\spad{p})} returns \\axiom{\\spad{p}}."))) -((|noZeroDivisors| |has| |#2| (ATTRIBUTE |noZeroDivisors|)) (|leftUnitary| . T) (|rightUnitary| . T) (|unitsKnown| . T)) +((|constructor| (NIL "This domain constructor implements polynomials in non-commutative variables written in the Poincare-Birkhoff-Witt basis from the Lyndon basis. These polynomials can be used to compute Baker-Campbell-Hausdorff relations. \\newline Author: Michel Petitot (petitot@lifl.fr).")) (|log| (($ $ (|NonNegativeInteger|)) "\\axiom{log(\\spad{p},{}\\spad{n})} returns the logarithm of \\axiom{\\spad{p}} (truncated up to order \\axiom{\\spad{n}}).")) (|exp| (($ $ (|NonNegativeInteger|)) "\\axiom{exp(\\spad{p},{}\\spad{n})} returns the exponential of \\axiom{\\spad{p}} (truncated up to order \\axiom{\\spad{n}}).")) (|product| (($ $ $ (|NonNegativeInteger|)) "\\axiom{product(a,{}\\spad{b},{}\\spad{n})} returns \\axiom{a*b} (truncated up to order \\axiom{\\spad{n}}).")) (|LiePolyIfCan| (((|Union| (|LiePolynomial| |#1| |#2|) "failed") $) "\\axiom{LiePolyIfCan(\\spad{p})} return \\axiom{\\spad{p}} if \\axiom{\\spad{p}} is a Lie polynomial.")) (|coerce| (($ (|LiePolynomial| |#1| |#2|)) "\\axiom{coerce(\\spad{p})} returns \\axiom{\\spad{p}}."))) +((|noZeroDivisors| |has| |#2| (ATTRIBUTE |noZeroDivisors|))) ((|HasCategory| |#2| (QUOTE (|CommutativeRing|))) (|HasCategory| |#2| (QUOTE (|Module| (|Fraction| (|Integer|))))) (|HasAttribute| |#2| (QUOTE |noZeroDivisors|))) (|XPolynomial| R) ((|constructor| (NIL "\\indented{2}{This type supports multivariate polynomials} whose set of variables is \\spadtype{Symbol}. The representation is recursive. The coefficient ring may be non-commutative and the variables do not commute. However,{} coefficients and variables commute."))) -((|noZeroDivisors| |has| |#1| (ATTRIBUTE |noZeroDivisors|)) (|leftUnitary| . T) (|rightUnitary| . T) (|unitsKnown| . T)) +((|noZeroDivisors| |has| |#1| (ATTRIBUTE |noZeroDivisors|))) ((|HasCategory| |#1| (QUOTE (|CommutativeRing|))) (|HasAttribute| |#1| (QUOTE |noZeroDivisors|))) (|XPolynomialsCat| |vl| R) ((|constructor| (NIL "The Category of polynomial rings with non-commutative variables. The coefficient ring may be non-commutative too. However coefficients commute with vaiables.")) (|trunc| (($ $ (|NonNegativeInteger|)) "\\spad{trunc(p,n)} returns the polynomial \\spad{p} truncated at order \\spad{n}.")) (|degree| (((|NonNegativeInteger|) $) "\\spad{degree(p)} returns the degree of \\spad{p}. \\indented{1}{Note that the degree of a word is its length.}")) (|maxdeg| (((|OrderedFreeMonoid| |#1|) $) "\\spad{maxdeg(p)} returns the greatest leading word in the support of \\spad{p}."))) -((|noZeroDivisors| |has| |#2| (ATTRIBUTE |noZeroDivisors|)) (|leftUnitary| . T) (|rightUnitary| . T) (|unitsKnown| . T)) +((|noZeroDivisors| |has| |#2| (ATTRIBUTE |noZeroDivisors|))) NIL (|XPolynomialRing| R E) ((|constructor| (NIL "This domain represents generalized polynomials with coefficients (from a not necessarily commutative ring),{} and words belonging to an arbitrary \\spadtype{OrderedMonoid}. This type is used,{} for instance,{} by the \\spadtype{XDistributedPolynomial} domain constructor where the Monoid is free.")) (|canonicalUnitNormal| ((|attribute|) "canonicalUnitNormal guarantees that the function unitCanonical returns the same representative for all associates of any particular element.")) (/ (($ $ |#1|) "\\spad{p/r} returns \\spad{p*(1/r)}.")) (|quasiRegular| (($ $) "\\spad{quasiRegular(x)} return \\spad{x} minus its constant term.")) (|quasiRegular?| (((|Boolean|) $) "\\spad{quasiRegular?(x)} return \\spad{true} if \\spad{constant(p)} is zero.")) (|constant| ((|#1| $) "\\spad{constant(p)} return the constant term of \\spad{p}.")) (|constant?| (((|Boolean|) $) "\\spad{constant?(p)} tests whether the polynomial \\spad{p} belongs to the coefficient ring.")) (|coef| ((|#1| $ |#2|) "\\spad{coef(p,e)} extracts the coefficient of the monomial \\spad{e}. Returns zero if \\spad{e} is not present.")) (|reductum| (($ $) "\\spad{reductum(p)} returns \\spad{p} minus its leading term. An error is produced if \\spad{p} is zero.")) (|mindeg| ((|#2| $) "\\spad{mindeg(p)} returns the smallest word occurring in the polynomial \\spad{p} with a non-zero coefficient. An error is produced if \\spad{p} is zero.")) (|maxdeg| ((|#2| $) "\\spad{maxdeg(p)} returns the greatest word occurring in the polynomial \\spad{p} with a non-zero coefficient. An error is produced if \\spad{p} is zero.")) (|#| (((|NonNegativeInteger|) $) "\\spad{\\# p} returns the number of terms in \\spad{p}.")) (* (($ $ |#1|) "\\spad{p*r} returns the product of \\spad{p} by \\spad{r}."))) -((|unitsKnown| . T) (|canonicalUnitNormal| |has| |#1| (ATTRIBUTE |canonicalUnitNormal|)) (|noZeroDivisors| |has| |#1| (ATTRIBUTE |noZeroDivisors|)) (|leftUnitary| . T) (|rightUnitary| . T)) -((|HasCategory| |#1| (QUOTE (|CommutativeRing|))) (|HasCategory| |#1| (QUOTE (|Field|))) (|HasAttribute| |#1| (QUOTE |unitsKnown|)) (|HasAttribute| |#1| (QUOTE |canonicalUnitNormal|)) (|HasAttribute| |#1| (QUOTE |noZeroDivisors|))) +((|canonicalUnitNormal| |has| |#1| (ATTRIBUTE |canonicalUnitNormal|)) (|noZeroDivisors| |has| |#1| (ATTRIBUTE |noZeroDivisors|))) +((|HasCategory| |#1| (QUOTE (|CommutativeRing|))) (|HasCategory| |#1| (QUOTE (|Field|))) (|HasAttribute| |#1| (QUOTE |canonicalUnitNormal|)) (|HasAttribute| |#1| (QUOTE |noZeroDivisors|))) (|XRecursivePolynomial| |VarSet| R) ((|constructor| (NIL "\\indented{2}{This type supports multivariate polynomials} whose variables do not commute. The representation is recursive. The coefficient ring may be non-commutative. Coefficients and variables commute.")) (|RemainderList| (((|List| (|Record| (|:| |k| |#1|) (|:| |c| $))) $) "\\spad{RemainderList(p)} returns the regular part of \\spad{p} as a list of terms.")) (|unexpand| (($ (|XDistributedPolynomial| |#1| |#2|)) "\\spad{unexpand(p)} returns \\spad{p} in recursive form.")) (|expand| (((|XDistributedPolynomial| |#1| |#2|) $) "\\spad{expand(p)} returns \\spad{p} in distributed form."))) -((|noZeroDivisors| |has| |#2| (ATTRIBUTE |noZeroDivisors|)) (|leftUnitary| . T) (|rightUnitary| . T) (|unitsKnown| . T)) +((|noZeroDivisors| |has| |#2| (ATTRIBUTE |noZeroDivisors|))) ((|HasCategory| |#2| (QUOTE (|CommutativeRing|))) (|HasAttribute| |#2| (QUOTE |noZeroDivisors|))) (|YoungDiagram|) ((|constructor| (NIL "This domain provides representations of Young diagrams.")) (|shape| (((|Partition|) $) "\\spad{shape x} returns the partition shaping \\spad{x}.")) (|youngDiagram| (($ (|List| (|PositiveInteger|))) "\\spad{youngDiagram l} returns an object representing a Young diagram with shape given by the list of integers \\spad{l}"))) @@ -4782,7 +4782,7 @@ NIL NIL (|IntegerMod| |p|) ((|constructor| (NIL "IntegerMod(\\spad{n}) creates the ring of integers reduced modulo the integer \\spad{n}."))) -(((|commutative| "*") . T) (|rightUnitary| . T) (|leftUnitary| . T) (|unitsKnown| . T)) +(((|commutative| "*") . T)) NIL NIL NIL @@ -4800,4 +4800,4 @@ NIL NIL NIL NIL -((|Union| NIL 1915133 1915138 1915143 1915148) (|Record| NIL 1915113 1915118 1915123 1915128) (|Mapping| NIL 1915093 1915098 1915103 1915108) (|Enumeration| NIL 1915073 1915078 1915083 1915088) (|IntegerMod| "ZMOD.spad" 1914843 1914863 1914979 1915068) (|IntegerLinearDependence| "ZLINDEP.spad" 1913921 1913952 1914833 1914838) (|ZeroDimensionalSolvePackage| "ZDSOLVE.spad" 1903858 1903904 1913911 1913916) (|ParadoxicalCombinatorsForStreams| "YSTREAM.spad" 1903324 1903364 1903848 1903853) (|YoungDiagram| "YDIAGRAM.spad" 1902949 1902967 1903314 1903319) (|XRecursivePolynomial| "XRPOLY.spad" 1902075 1902112 1902728 1902850) (|XPolynomialRing| "XPR.spad" 1899849 1899874 1901651 1901842) (|XPolynomialsCat| "XPOLYC.spad" 1899103 1899131 1899722 1899844) (|XPolynomial| "XPOLY.spad" 1898573 1898592 1898882 1899004) (|XPBWPolynomial| "XPBWPOLY.spad" 1896941 1896972 1898287 1898409) (|XFreeAlgebra| "XFALG.spad" 1894060 1894085 1896814 1896936) (|ExtensionField| "XF.spad" 1892444 1892466 1893890 1894055) (|ExtensionField&| "XF.spad" 1890840 1890865 1892289 1892294) (|XExponentialPackage| "XEXPPKG.spad" 1890083 1890125 1890830 1890835) (|XDistributedPolynomial| "XDPOLY.spad" 1889601 1889636 1889862 1889984) (|XAlgebra| "XALG.spad" 1889240 1889256 1889533 1889596) (|WuWenTsunTriangularSet| "WUTSET.spad" 1885122 1885158 1888772 1888777) (|WeightedPolynomials| "WP.spad" 1884254 1884314 1884921 1885031) (|WhileAst| "WHILEAST.spad" 1884047 1884061 1884244 1884249) (|WhereAst| "WHEREAST.spad" 1883713 1883727 1884037 1884042) (|WildFunctionFieldIntegralBasis| "WFFINTBS.spad" 1881353 1881398 1883703 1883708) (|WeierstrassPreparation| "WEIER.spad" 1879556 1879586 1881343 1881348) (|VectorSpace| "VSPACE.spad" 1879204 1879223 1879507 1879551) (|VectorSpace&| "VSPACE.spad" 1878888 1878910 1879194 1879199) (|Void| "VOID.spad" 1878564 1878574 1878878 1878883) (|ViewDefaultsPackage| "VIEWDEF.spad" 1873749 1873774 1878554 1878559) (|ThreeDimensionalViewport| "VIEW3D.spad" 1857689 1857719 1873739 1873744) (|TwoDimensionalViewport| "VIEW2D.spad" 1845569 1845597 1857679 1857684) (|ViewportPackage| "VIEW.spad" 1843277 1843298 1845559 1845564) (|VectorFunctions2| "VECTOR2.spad" 1841903 1841929 1843267 1843272) (|Vector| "VECTOR.spad" 1840758 1840772 1841012 1841017) (|VectorCategory| "VECTCAT.spad" 1838681 1838703 1840748 1840753) (|VectorCategory&| "VECTCAT.spad" 1836333 1836358 1838403 1838408) (|Variable| "VARIABLE.spad" 1836108 1836128 1836323 1836328) (|UnionType| "UTYPE.spad" 1835746 1835761 1836098 1836103) (|UTSodetools| "UTSODETL.spad" 1835025 1835053 1835690 1835695) (|UnivariateTaylorSeriesODESolver| "UTSODE.spad" 1833213 1833261 1835015 1835020) (|UnivariateTaylorSeriesCategory| "UTSCAT.spad" 1830597 1830640 1833043 1833208) (|UnivariateTaylorSeriesCategory&| "UTSCAT.spad" 1827634 1827680 1830083 1830088) (|UnivariateTaylorSeriesFunctions2| "UTS2.spad" 1827200 1827264 1827624 1827629) (|UnivariateTaylorSeries| "UTS.spad" 1822370 1822417 1825909 1826074) (|UnaryRecursiveAggregate| "URAGG.spad" 1817071 1817102 1822360 1822365) (|UnaryRecursiveAggregate&| "URAGG.spad" 1811685 1811719 1816977 1816982) (|UnivariatePuiseuxSeriesWithExponentialSingularity| "UPXSSING.spad" 1809483 1809555 1810965 1811170) (|UnivariatePuiseuxSeriesConstructor| "UPXSCONS.spad" 1807652 1807703 1808056 1808311) (|UnivariatePuiseuxSeriesConstructorCategory| "UPXSCCA.spad" 1806078 1806137 1807392 1807647) (|UnivariatePuiseuxSeriesConstructorCategory&| "UPXSCCA.spad" 1804751 1804813 1806068 1806073) (|UnivariatePuiseuxSeriesCategory| "UPXSCAT.spad" 1803206 1803250 1804491 1804746) (|UnivariatePuiseuxSeriesFunctions2| "UPXS2.spad" 1802719 1802802 1803196 1803201) (|UnivariatePuiseuxSeries| "UPXS.spad" 1800436 1800484 1801292 1801547) (|UnivariatePolynomialSquareFree| "UPSQFREE.spad" 1798824 1798865 1800426 1800431) (|UnivariatePowerSeriesCategory| "UPSCAT.spad" 1796525 1796575 1798654 1798819) (|UnivariatePowerSeriesCategory&| "UPSCAT.spad" 1794031 1794084 1796163 1796168) (|UnivariatePolynomialCategoryFunctions2| "UPOLYC2.spad" 1793467 1793521 1794021 1794026) (|UnivariatePolynomialCategory| "UPOLYC.spad" 1788398 1788434 1793185 1793462) (|UnivariatePolynomialCategory&| "UPOLYC.spad" 1783310 1783349 1788100 1788105) (|UnivariatePolynomialMultiplicationPackage| "UPMP.spad" 1782204 1782255 1783300 1783305) (|UnivariatePolynomialDivisionPackage| "UPDIVP.spad" 1781737 1781783 1782194 1782199) (|UnivariatePolynomialDecompositionPackage| "UPDECOMP.spad" 1779961 1780012 1781727 1781732) (|UnivariatePolynomialCommonDenominator| "UPCDEN.spad" 1779144 1779194 1779951 1779956) (|UnivariatePolynomialFunctions2| "UP2.spad" 1778481 1778529 1779134 1779139) (|UnivariatePolynomial| "UP.spad" 1776195 1776227 1776599 1776876) (|UniversalSegmentFunctions2| "UNISEG2.spad" 1775660 1775696 1776142 1776147) (|UniversalSegment| "UNISEG.spad" 1774983 1775007 1775562 1775567) (|UnivariateFactorize| "UNIFACT.spad" 1774070 1774098 1774973 1774978) (|UnivariateLaurentSeriesConstructor| "ULSCONS.spad" 1770482 1770533 1770883 1771138) (|UnivariateLaurentSeriesConstructorCategory| "ULSCCAT.spad" 1768074 1768133 1770222 1770477) (|UnivariateLaurentSeriesConstructorCategory&| "ULSCCAT.spad" 1765876 1765938 1768027 1768032) (|UnivariateLaurentSeriesCategory| "ULSCAT.spad" 1763982 1764026 1765616 1765871) (|UnivariateLaurentSeriesFunctions2| "ULS2.spad" 1763466 1763549 1763972 1763977) (|UnivariateLaurentSeries| "ULS.spad" 1759021 1759069 1759986 1760435) (|UInt8| "UINT8.spad" 1758896 1758907 1759011 1759016) (|UInt64| "UINT64.spad" 1758769 1758781 1758886 1758891) (|UInt32| "UINT32.spad" 1758642 1758654 1758759 1758764) (|UInt16| "UINT16.spad" 1758515 1758527 1758632 1758637) (|UniqueFactorizationDomain| "UFD.spad" 1757515 1757546 1758398 1758510) (|UniqueFactorizationDomain&| "UFD.spad" 1756619 1756653 1757505 1757510) (|UserDefinedVariableOrdering| "UDVO.spad" 1755476 1755509 1756609 1756614) (|UserDefinedPartialOrdering| "UDPO.spad" 1753026 1753060 1755424 1755429) (|TypeAst| "TYPEAST.spad" 1752941 1752954 1753016 1753021) (|Type| "TYPE.spad" 1752872 1752882 1752931 1752936) (|TwoFactorize| "TWOFACT.spad" 1751519 1751539 1752862 1752867) (|Tuple| "TUPLE.spad" 1750999 1751012 1751406 1751411) (|TubePlotTools| "TUBETOOL.spad" 1747856 1747875 1750989 1750994) (|TubePlot| "TUBE.spad" 1746498 1746520 1747846 1747851) (|TriangularSetCategory| "TSETCAT.spad" 1734573 1734608 1746488 1746493) (|TriangularSetCategory&| "TSETCAT.spad" 1722607 1722645 1734525 1734530) (|TaylorSeries| "TS.spad" 1721136 1721161 1722111 1722276) (|TranscendentalManipulations| "TRMANIP.spad" 1715555 1715592 1720899 1720904) (|TriangularMatrixOperations| "TRIMAT.spad" 1714495 1714543 1715545 1715550) (|TrigonometricManipulations| "TRIGMNIP.spad" 1713003 1713039 1714485 1714490) (|TrigonometricFunctionCategory| "TRIGCAT.spad" 1712489 1712524 1712993 1712998) (|TrigonometricFunctionCategory&| "TRIGCAT.spad" 1711972 1712010 1712479 1712484) (|Tree| "TREE.spad" 1710614 1710626 1711647 1711652) (|TranscendentalFunctionCategory| "TRANFUN.spad" 1710426 1710462 1710604 1710609) (|TranscendentalFunctionCategory&| "TRANFUN.spad" 1710235 1710274 1710416 1710421) (|TopLevelThreeSpace| "TOPSP.spad" 1709894 1709918 1710225 1710230) (|ToolsForSign| "TOOLSIGN.spad" 1709548 1709568 1709884 1709889) (|TextFile| "TEXTFILE.spad" 1708104 1708118 1709538 1709543) (|TexFormat1| "TEX1.spad" 1707653 1707671 1708094 1708099) (|TexFormat| "TEX.spad" 1704841 1704856 1707643 1707648) (|TabulatedComputationPackage| "TBCMPPK.spad" 1702918 1702965 1704831 1704836) (|TableAggregate| "TBAGG.spad" 1702172 1702206 1702908 1702913) (|TableAggregate&| "TBAGG.spad" 1701423 1701460 1702162 1702167) (|TangentExpansions| "TANEXP.spad" 1700817 1700842 1701413 1701418) (|TermAlgebraOperator| "TALGOP.spad" 1700525 1700552 1700807 1700812) (|Tableau| "TABLEAU.spad" 1700002 1700017 1700515 1700520) (|Table| "TABLE.spad" 1698806 1698831 1699078 1699083) (|TableauxBumpers| "TABLBUMP.spad" 1695573 1695596 1698796 1698801) (|System| "SYSTEM.spad" 1694798 1694810 1695563 1695568) (|SystemSolvePackage| "SYSSOLP.spad" 1692266 1692292 1694788 1694793) (|SystemPointer| "SYSPTR.spad" 1692155 1692174 1692256 1692261) (|SystemNonNegativeInteger| "SYSNNI.spad" 1691357 1691389 1692145 1692150) (|SystemInteger| "SYSINT.spad" 1690751 1690772 1691347 1691352) (|Syntax| "SYNTAX.spad" 1687082 1687094 1690741 1690746) (|SymbolTable| "SYMTAB.spad" 1685142 1685159 1687072 1687077) (|TheSymbolTable| "SYMS.spad" 1681160 1681180 1685132 1685137) (|SymmetricPolynomial| "SYMPOLY.spad" 1680197 1680224 1680295 1680529) (|SymmetricFunctions| "SYMFUNC.spad" 1679683 1679709 1680187 1680192) (|Symbol| "SYMBOL.spad" 1677175 1677187 1679673 1679678) (|SparseUnivariateTaylorSeries| "SUTS.spad" 1674440 1674493 1675884 1676049) (|SparseUnivariatePuiseuxSeries| "SUPXS.spad" 1672138 1672192 1673013 1673268) 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1636947 1636952) (|String| "STRING.spad" 1635831 1635843 1636219 1636224) (|StreamFunctions3| "STREAM3.spad" 1635391 1635419 1635821 1635826) (|StreamFunctions2| "STREAM2.spad" 1634506 1634532 1635381 1635386) (|StreamFunctions1| "STREAM1.spad" 1634199 1634223 1634496 1634501) (|Stream| "STREAM.spad" 1631200 1631214 1633694 1633699) (|StreamInfiniteProduct| "STINPROD.spad" 1630118 1630152 1631190 1631195) (|StepAst| "STEPAST.spad" 1629348 1629361 1630108 1630113) (|StepThrough| "STEP.spad" 1628657 1628674 1629338 1629343) (|SparseTable| "STBL.spad" 1627558 1627594 1627733 1627738) (|StreamAggregate| "STAGG.spad" 1626245 1626268 1627548 1627553) (|StreamAggregate&| "STAGG.spad" 1624929 1624955 1626235 1626240) (|Stack| "STACK.spad" 1624423 1624436 1624675 1624680) (|SemiRing| "SRING.spad" 1624178 1624192 1624413 1624418) (|SquareFreeRegularTriangularSet| "SREGSET.spad" 1621781 1621825 1623710 1623715) (|SquareFreeRegularSetDecompositionPackage| "SRDCMPK.spad" 1620321 1620378 1621771 1621776) (|StringAggregate| "SRAGG.spad" 1615514 1615535 1620311 1620316) (|StringAggregate&| "SRAGG.spad" 1610704 1610728 1615504 1615509) (|SquareMatrix| "SQMATRIX.spad" 1608624 1608651 1609549 1609667) (|SplittingTree| "SPLTREE.spad" 1603417 1603440 1608223 1608228) (|SplittingNode| "SPLNODE.spad" 1600027 1600050 1603407 1603412) (|SpecialFunctionCategory| "SPFCAT.spad" 1598816 1598845 1600017 1600022) (|SpecialOutputPackage| "SPECOUT.spad" 1597351 1597377 1598806 1598811) (|SpadAstExports| "SPADXPT.spad" 1589431 1589451 1597341 1597346) (|SpadParser| "spad-parser.spad" 1588889 1588905 1589421 1589426) (|SpadAst| "SPADAST.spad" 1588586 1588599 1588879 1588884) (|ThreeSpaceCategory| "SPACEC.spad" 1572786 1572812 1588576 1588581) (|ThreeSpace| "SPACE3.spad" 1572555 1572573 1572776 1572781) (|SortPackage| "SORTPAK.spad" 1572088 1572109 1572503 1572508) (|TransSolvePackage| "SOLVETRA.spad" 1569837 1569862 1572078 1572083) (|TransSolvePackageService| "SOLVESER.spad" 1568272 1568304 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"ROIRC.spad" 1422514 1422580 1423458 1423463) (|RealNumberSystem| "RNS.spad" 1421405 1421427 1422344 1422509) (|RealNumberSystem&| "RNS.spad" 1420453 1420478 1421395 1421400) (|RangeBinding| "RNGBIND.spad" 1419596 1419619 1420400 1420405) (|Rng| "RNG.spad" 1419204 1419213 1419586 1419591) (|Rng&| "RNG.spad" 1418809 1418821 1419194 1419199) (|RightModule| "RMODULE.spad" 1418582 1418601 1418799 1418804) (|RectangularMatrixCategoryFunctions2| "RMCAT2.spad" 1417970 1418059 1418572 1418577) (|RectangularMatrix| "RMATRIX.spad" 1417028 1417061 1417385 1417429) (|RectangularMatrixCategory| "RMATCAT.spad" 1412770 1412823 1416979 1417023) (|RectangularMatrixCategory&| "RMATCAT.spad" 1408365 1408421 1412577 1412582) (|RightLinearSet| "RLINSET.spad" 1408058 1408080 1408355 1408360) (|RationalInterpolation| "RINTERP.spad" 1407932 1407966 1408048 1408053) (|Ring| "RING.spad" 1407394 1407404 1407905 1407927) (|Ring&| "RING.spad" 1406870 1406883 1407384 1407389) (|RandomIntegerDistributions| "RIDIST.spad" 1406239 1406271 1406860 1406865) (|RegularChain| "RGCHAIN.spad" 1404691 1404716 1405594 1405599) (|RGBColorSpace| "RGBCSPC.spad" 1404470 1404492 1404681 1404686) (|RGBColorModel| "RGBCMDL.spad" 1404022 1404044 1404460 1404465) (|RationalFunctionFactorizer| "RFFACTOR.spad" 1403461 1403495 1404012 1404017) (|RationalFunctionFactor| "RFFACT.spad" 1403177 1403208 1403451 1403456) (|RandomFloatDistributions| "RFDIST.spad" 1402152 1402182 1403167 1403172) (|RationalFunction| "RF.spad" 1399813 1399837 1402142 1402147) (|RetractSolvePackage| "RETSOL.spad" 1399216 1399245 1399803 1399808) (|RetractableTo| "RETRACT.spad" 1398634 1398655 1399206 1399211) (|RetractableTo&| "RETRACT.spad" 1398049 1398073 1398624 1398629) (|ReturnAst| "RETAST.spad" 1397855 1397870 1398039 1398044) (|ResidueRing| "RESRING.spad" 1397166 1397217 1397761 1397850) (|ResolveLatticeCompletion| "RESLATC.spad" 1396469 1396501 1397156 1397161) (|RepeatedSquaring| "REPSQ.spad" 1396187 1396211 1396459 1396464) 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"RADCAT.spad" 1343154 1343175 1343561 1343566) (|RadicalCategory&| "RADCAT.spad" 1342734 1342758 1343144 1343149) (|Queue| "QUEUE.spad" 1342219 1342232 1342480 1342485) (|QuaternionCategoryFunctions2| "QUATCT2.spad" 1341814 1341858 1342209 1342214) (|QuaternionCategory| "QUATCAT.spad" 1339926 1339952 1341701 1341809) (|QuaternionCategory&| "QUATCAT.spad" 1337742 1337771 1339520 1339525) (|Quaternion| "QUAT.spad" 1336226 1336244 1336576 1336684) (|QueueAggregate| "QUAGG.spad" 1335070 1335092 1336216 1336221) (|QuasiquoteAst| "QQUTAST.spad" 1334828 1334847 1335060 1335065) (|QuadraticForm| "QFORM.spad" 1334436 1334461 1334818 1334823) (|QuotientFieldCategoryFunctions2| "QFCAT2.spad" 1334100 1334145 1334426 1334431) (|QuotientFieldCategory| "QFCAT.spad" 1332712 1332741 1333930 1334095) (|QuotientFieldCategory&| "QFCAT.spad" 1330841 1330873 1332062 1332067) (|QueryEquation| "QEQUAT.spad" 1330389 1330408 1330831 1330836) (|QuasiComponentPackage| "QCMPACK.spad" 1325285 1325323 1330379 1330384) (|QuasiAlgebraicSet2| "QALGSET2.spad" 1323265 1323299 1325275 1325280) (|QuasiAlgebraicSet| "QALGSET.spad" 1319326 1319373 1323150 1323155) (|PAdicWildFunctionFieldIntegralBasis| "PWFFINTB.spad" 1316713 1316763 1319316 1319321) (|PushVariables| "PUSHVAR.spad" 1316041 1316071 1316703 1316708) (|PartialTranscendentalFunctions| "PTRANFN.spad" 1312149 1312187 1316031 1316036) (|PointPackage| "PTPACK.spad" 1309227 1309247 1312139 1312144) (|PointFunctions2| "PTFUNC2.spad" 1309037 1309064 1309217 1309222) (|PointCategory| "PTCAT.spad" 1308303 1308324 1309027 1309032) (|PolynomialSquareFree| "PSQFR.spad" 1307600 1307642 1308293 1308298) (|PseudoLinearNormalForm| "PSEUDLIN.spad" 1306466 1306496 1307590 1307595) (|PolynomialSetUtilitiesPackage| "PSETPK.spad" 1293108 1293151 1306308 1306313) (|PolynomialSetCategory| "PSETCAT.spad" 1287499 1287541 1293098 1293103) (|PolynomialSetCategory&| "PSETCAT.spad" 1281841 1281886 1287443 1287448) (|PlottableSpaceCurveCategory| "PSCURVE.spad" 1280815 1280848 1281831 1281836) (|PowerSeriesCategory| "PSCAT.spad" 1279513 1279559 1280645 1280810) (|PowerSeriesCategory&| "PSCAT.spad" 1278368 1278417 1279503 1279508) (|Partition| "PRTITION.spad" 1277059 1277074 1278358 1278363) (|PretendAst| "PRTDAST.spad" 1276770 1276786 1277049 1277054) (|PseudoRemainderSequence| "PRS.spad" 1266360 1266398 1276719 1276724) (|PriorityQueueAggregate| "PRQAGG.spad" 1265797 1265827 1266350 1266355) (|PropositionalLogic| "PROPLOG.spad" 1265385 1265409 1265787 1265792) (|PropositionalFormulaFunctions2| "PROPFUN2.spad" 1264980 1265021 1265375 1265380) (|PropositionalFormulaFunctions1| "PROPFUN1.spad" 1264358 1264397 1264970 1264975) (|PropositionalFormula| "PROPFRML.spad" 1262908 1262937 1264348 1264353) (|Property| "PROPERTY.spad" 1262398 1262412 1262898 1262903) (|Product| "PRODUCT.spad" 1261269 1261286 1261558 1261623) (|PrintPackage| "PRINT.spad" 1261011 1261029 1261259 1261264) (|IntegerPrimesPackage| "PRIMES.spad" 1259254 1259282 1261001 1261006) (|PrimitiveElement| "PRIMELT.spad" 1257365 1257389 1259244 1259249) (|PrimitiveFunctionCategory| "PRIMCAT.spad" 1256985 1257016 1257355 1257360) (|PrimitiveArrayFunctions2| "PRIMARR2.spad" 1255730 1255764 1256975 1256980) (|PrimitiveArray| "PRIMARR.spad" 1254942 1254964 1255124 1255129) (|PrecomputedAssociatedEquations| "PREASSOC.spad" 1254296 1254336 1254932 1254937) (|PolynomialRing| "PR.spad" 1252729 1252753 1253440 1253674) (|PlottablePlaneCurveCategory| "PPCURVE.spad" 1251841 1251874 1252719 1252724) (|PortNumber| "PORTNUM.spad" 1251624 1251640 1251831 1251836) (|PolynomialRoots| "POLYROOT.spad" 1250457 1250488 1251573 1251578) (|PolynomialCategoryLifting| "POLYLIFT.spad" 1249699 1249745 1250447 1250452) (|PolynomialCategoryQuotientFunctions| "POLYCATQ.spad" 1247796 1247847 1249689 1249694) (|PolynomialCategory| "POLYCAT.spad" 1241175 1241212 1247557 1247791) (|PolynomialCategory&| "POLYCAT.spad" 1234118 1234158 1240503 1240508) (|PolynomialToUnivariatePolynomial| "POLY2UP.spad" 1233540 1233584 1234108 1234113) (|PolynomialFunctions2| "POLY2.spad" 1233119 1233149 1233530 1233535) (|Polynomial| "POLY.spad" 1231074 1231092 1231597 1231831) (|RealPolynomialUtilitiesPackage| "POLUTIL.spad" 1230002 1230059 1231021 1231026) (|PolToPol| "POLTOPOL.spad" 1228744 1228765 1229992 1229997) (|Point| "POINT.spad" 1227763 1227776 1227853 1227858) (|PolynomialNumberTheoryFunctions| "PNTHEORY.spad" 1224436 1224473 1227753 1227758) (|PatternMatchTools| "PMTOOLS.spad" 1223196 1223225 1224426 1224431) (|PatternMatchSymbol| "PMSYM.spad" 1222729 1222755 1223186 1223191) (|PatternMatchQuotientFieldCategory| "PMQFCAT.spad" 1222289 1222334 1222719 1222724) (|FunctionSpaceAttachPredicates| "PMPREDFS.spad" 1221732 1221773 1222279 1222284) (|AttachPredicates| "PMPRED.spad" 1221209 1221233 1221722 1221727) (|PatternMatchPolynomialCategory| "PMPLCAT.spad" 1220244 1220290 1221124 1221129) (|PatternMatchListAggregate| "PMLSAGG.spad" 1219806 1219843 1220234 1220239) (|PatternMatchKernel| "PMKERNEL.spad" 1219369 1219397 1219796 1219801) (|PatternMatchIntegerNumberSystem| "PMINS.spad" 1218920 1218959 1219359 1219364) (|PatternMatchFunctionSpace| "PMFS.spad" 1218478 1218515 1218910 1218915) (|PatternMatchPushDown| "PMDOWN.spad" 1217750 1217782 1218468 1218473) (|FunctionSpaceAssertions| "PMASSFS.spad" 1216708 1216741 1217740 1217745) (|PatternMatchAssertions| "PMASS.spad" 1215706 1215734 1216698 1216703) (|PlotTools| "PLOTTOOL.spad" 1215479 1215494 1215696 1215701) (|Plot3D| "PLOT3D.spad" 1211939 1211951 1215469 1215474) (|PlotFunctions1| "PLOT1.spad" 1211100 1211122 1211929 1211934) (|Plot| "PLOT.spad" 1206021 1206031 1211090 1211095) (|ParametricLinearEquations| "PLEQN.spad" 1193400 1193450 1206011 1206016) (|PolynomialInterpolationAlgorithms| "PINTERPA.spad" 1193157 1193200 1193390 1193395) (|PolynomialInterpolation| "PINTERP.spad" 1192762 1192798 1193147 1193152) (|PrincipalIdealDomain| "PID.spad" 1191675 1191701 1192645 1192757) (|PiCoercions| 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1216641 1216646) (|Polynomial| "multpoly.spad" 1214245 1214263 1214768 1214942) (|RealPolynomialUtilitiesPackage| "reclos.spad" 1213173 1213230 1214192 1214197) (|PolToPol| "poltopol.spad" 1211915 1211936 1213163 1213168) (|Point| "newpoint.spad" 1210934 1210947 1211024 1211029) (|PolynomialNumberTheoryFunctions| "numtheor.spad" 1207607 1207644 1210924 1210929) (|PatternMatchTools| "patmatch1.spad" 1206367 1206396 1207597 1207602) (|PatternMatchSymbol| "patmatch1.spad" 1205900 1205926 1206357 1206362) (|PatternMatchQuotientFieldCategory| "patmatch2.spad" 1205460 1205505 1205890 1205895) (|FunctionSpaceAttachPredicates| "expr.spad" 1204903 1204944 1205450 1205455) (|AttachPredicates| "expr.spad" 1204380 1204404 1204893 1204898) (|PatternMatchPolynomialCategory| "patmatch2.spad" 1203415 1203461 1204295 1204300) (|PatternMatchListAggregate| "patmatch1.spad" 1202977 1203014 1203405 1203410) (|PatternMatchKernel| "patmatch1.spad" 1202540 1202568 1202967 1202972) 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1147901) (|PermutationGroup| "permgrps.spad" 1142588 1142612 1147572 1147577) (|PermutationCategory| "perm.spad" 1141242 1141269 1142578 1142583) (|Permanent| "perman.spad" 1139791 1139812 1141232 1141237) (|Permutation| "perm.spad" 1135648 1135667 1139680 1139685) (|PendantTree| "tree.spad" 1135034 1135053 1135323 1135328) (|PartialDifferentialSpace| "catdef.spad" 1133825 1133857 1135024 1135029) (|PartialDifferentialSpace&| "catdef.spad" 1132613 1132648 1133815 1133820) (|PartialDifferentialRing| "catdef.spad" 1132444 1132475 1132603 1132608) (|PartialDifferentialModule| "catdef.spad" 1132259 1132294 1132434 1132439) (|PolynomialDecomposition| "pdecomp.spad" 1131712 1131746 1132249 1132254) (|PartialDifferentialDomain| "catdef.spad" 1131127 1131163 1131702 1131707) (|PartialDifferentialDomain&| "catdef.spad" 1130539 1130578 1131117 1131122) (|PolynomialComposition| "pdecomp.spad" 1130373 1130405 1130529 1130534) (|PoincareBirkhoffWittLyndonBasis| "xlpoly.spad" 1129125 1129171 1130363 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927101 927112 927934 927939) (|Monad&| "naalgc.spad" 926255 926269 927091 927096) (|MoebiusTransform| "moebius.spad" 924991 925015 926245 926250) (|Module| "catdef.spad" 924879 924893 924981 924986) (|Module&| "catdef.spad" 924764 924781 924869 924874) (|ModularRing| "modring.spad" 924220 924276 924754 924759) (|ModuleOperator| "opalg.spad" 922879 922903 924056 924061) (|ModuleMonomial| "modmonom.spad" 922598 922628 922869 922874) (|ModMonic| "modmon.spad" 919962 919980 920683 920900) (|ModularField| "modring.spad" 919376 919433 919877 919957) (|MathMLFormat| "mathml.spad" 918226 918244 919366 919371) (|MultipleMap| "curve.spad" 917959 918002 918216 918221) (|MonogenicLinearOperator| "lodop.spad" 916431 916462 917949 917954) (|MultivariateLifting| "mlift.spad" 915026 915060 916421 916426) (|MakeUnaryCompiledFunction| "mkfunc.spad" 914542 914579 915016 915021) (|MakeRecord| "mkrecord.spad" 914122 914143 914532 914537) (|MakeFunction| "mkfunc.spad" 913519 913539 914112 914117) 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861895 861929 864062 864067) (|LinearSystemMatrixPackage| "solvelin.spad" 860733 860780 861885 861890) (|ListAggregate| "aggcat.spad" 860413 860434 860723 860728) (|ListAggregate&| "aggcat.spad" 860090 860114 860403 860408) (|LiePolynomial| "xlpoly.spad" 859089 859119 859994 859999) (|LinearPolynomialEquationByFractions| "fraction.spad" 858327 858370 859079 859084) (|Logic| "logic.spad" 857866 857877 858317 858322) (|Logic&| "logic.spad" 857402 857416 857856 857861) (|LinearOrdinaryDifferentialOperatorsOps| "lodo.spad" 856296 856344 857392 857397) (|LinearOrdinaryDifferentialOperatorFactorizer| "lodof.spad" 855281 855336 856230 856235) (|LinearOrdinaryDifferentialOperatorCategory| "lodo.spad" 853941 853991 855271 855276) (|LinearOrdinaryDifferentialOperatorCategory&| "lodo.spad" 852561 852614 853894 853899) (|LinearOrdinaryDifferentialOperator2| "lodo.spad" 851808 851853 852248 852253) (|LinearOrdinaryDifferentialOperator1| "lodo.spad" 851182 851225 851495 851500) (|LinearOrdinaryDifferentialOperator| "lodo.spad" 850540 850589 850869 850874) (|ElementaryFunctionLODESolver| "odeef.spad" 849320 849360 850530 850535) (|Localize| "fraction.spad" 848720 848740 849259 849264) (|LinearAggregate| "aggcat.spad" 844894 844917 848710 848715) (|LinearAggregate&| "aggcat.spad" 840981 841007 844800 844805) (|ListMonoidOps| "free.spad" 837738 837766 840971 840976) (|LeftModule| "catdef.spad" 837514 837532 837728 837733) (|ListMultiDictionary| "lmdict.spad" 836856 836883 837121 837126) (|LeftLinearSet| "catdef.spad" 836552 836573 836846 836851) (|Literal| "syntax.spad" 836453 836469 836542 836547) (|ListFunctions3| "list.spad" 835752 835778 836443 836448) (|ListToMap| "list.spad" 832672 832691 835742 835747) (|ListFunctions2| "list.spad" 831362 831386 832662 832667) (|List| "list.spad" 829411 829423 830756 830761) (|LinearSet| "catdef.spad" 829183 829200 829401 829406) (|LinearForm| "vector.spad" 828660 828680 829173 829178) (|LinearlyExplicitRingOver| 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717879 717884) (|Int64| "data.spad" 717643 717654 717757 717762) (|Int32| "data.spad" 717519 717530 717633 717638) (|Int16| "data.spad" 717395 717406 717509 717514) (|Integer| "integer.spad" 717065 717078 717260 717390) (|IntegerNumberSystem| "si.spad" 714532 714557 716948 717060) (|IntegerNumberSystem&| "si.spad" 712103 712131 714522 714527) (|InnerPolySign| "sign.spad" 711562 711586 712093 712098) (|InfiniteProductPrimeField| "infprod.spad" 710635 710677 711552 711557) (|InfiniteProductFiniteField| "infprod.spad" 709699 709747 710625 710630) (|InnerMultFact| "multfact.spad" 708663 708691 709689 709694) (|InnerModularGcd| "modgcd.spad" 708154 708197 708653 708658) (|InnerNumericFloatSolvePackage| "numsolve.spad" 706428 706473 708144 708149) (|InfiniteProductCharacteristicZero| "infprod.spad" 705477 705527 706418 706423) (|InputFormFunctions1| "mkfunc.spad" 705085 705112 705467 705472) (|InputForm| "mkfunc.spad" 702289 702304 705075 705080) (|Infinity| "complet.spad" 701835 701849 702279 702284) (|InetClientStreamSocket| "net.spad" 701792 701820 701825 701830) (|InnerNumericEigenPackage| "numeigen.spad" 700320 700360 701782 701787) (|IndexedExponents| "multpoly.spad" 699940 699971 700215 700220) (|IncrementingMaps| "seg.spad" 699363 699387 699930 699935) (|InputBinaryFile| "net.spad" 698446 698467 699353 699358) (|InnerNormalBasisFieldFunctions| "ffnb.spad" 694268 694307 698436 698441) (|InputByteConduit| "net.spad" 692520 692542 694258 694263) (|InputByteConduit&| "net.spad" 690769 690794 692510 692515) (|InAst| "syntax.spad" 690427 690438 690759 690764) (|ImportAst| "syntax.spad" 690128 690143 690417 690422) (|InnerMatrixQuotientFieldFunctions| "matfuns.spad" 689141 689216 690034 690039) (|InnerMatrixLinearAlgebraFunctions| "matfuns.spad" 687681 687736 689047 689052) (|InnerFiniteField| "ffp.spad" 687126 687156 687411 687491) (|IfAst| "syntax.spad" 686737 686748 687116 687121) (|IndexedFlexibleArray| "array1.spad" 684415 684448 686131 686136) 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"defintrf.spad" 182912 182946 184689 184694) (|DeRhamComplex| "derham.spad" 180998 181041 182902 182907) (|Dequeue| "bags.spad" 180456 180471 180744 180749) (|DegreeReductionPackage| "degred.spad" 180053 180087 180446 180451) (|RationalFunctionDefiniteIntegration| "defintrf.spad" 177602 177645 180043 180048) (|ElementaryFunctionDefiniteIntegration| "defintef.spad" 176109 176156 177592 177597) (|DefinitionAst| "syntax.spad" 175482 175501 176099 176104) (|DecimalExpansion| "radix.spad" 173645 173667 174020 174100) (|DistinctDegreeFactorize| "ddfact.spad" 171449 171483 173635 173640) (|DoubleResultantPackage| "intalg.spad" 171033 171073 171439 171444) (|DualBasis| "vector.spad" 170652 170674 171023 171028) (|Database| "alql.spad" 169310 169326 170642 170647) (|DataArray| "data.spad" 168789 168809 169300 169305) (|CyclotomicPolynomialPackage| "cyclotom.spad" 168270 168303 168779 168784) (|CycleIndicators| "cycles.spad" 165040 165061 168260 168265) (|CoerceVectorMatrixPackage| "generic.spad" 164434 164467 165030 165035) (|ComplexTrigonometricManipulations| "efstruc.spad" 162907 162950 164424 164429) (|ConstructorKind| "domain.spad" 162497 162518 162897 162902) (|ConstructorCategory| "domain.spad" 161721 161746 162487 162492) (|ConstructorCategory&| "domain.spad" 160942 160970 161711 161716) (|ConstructorCall| "domain.spad" 160518 160541 160932 160937) (|Constructor| "domain.spad" 160200 160217 160508 160513) (|CyclicStreamTools| "stream.spad" 159430 159458 160190 160195) (|ComplexRootFindingPackage| "crfp.spad" 153179 153215 159420 159425) (|CoerceAst| "syntax.spad" 152892 152907 153169 153174) (|CRApackage| "cra.spad" 151951 151969 152882 152887) (|ComplexPatternMatch| "gaussian.spad" 151413 151445 151851 151856) (|CharacteristicPolynomialInMonogenicalAlgebra| "algcat.spad" 151076 151137 151403 151408) (|CoordinateSystems| "coordsys.spad" 146070 146095 151066 151071) (|Contour| "any.spad" 145492 145505 146060 146065) (|ContinuedFraction| "contfrac.spad" 141240 141265 145407 145487) (|Conduit| "net.spad" 140993 141006 141230 141235) (|CommutativeRing| "catdef.spad" 140682 140703 140959 140988) (|SubSpaceComponentProperty| "newpoint.spad" 140177 140208 140672 140677) (|ComplexPattern| "gaussian.spad" 139932 139959 140167 140172) (|ComplexFunctions2| "gaussian.spad" 139632 139659 139922 139927) (|Complex| "gaussian.spad" 136844 136859 137093 137467) (|CompilerPackage| "compiler.spad" 136380 136401 136834 136839) (|ComplexFactorization| "gaussian.spad" 135964 135996 136370 136375) (|ComplexCategory| "gaussian.spad" 133910 133933 135585 135959) (|ComplexCategory&| "gaussian.spad" 131487 131513 133165 133170) (|CommutativeOperatorCategory| "catdef.spad" 131209 131245 131347 131482) (|CommutativeOperation| "catdef.spad" 130781 130810 131069 131204) (|CommuteUnivariatePolynomialCategory| "polycat.spad" 130496 130547 130771 130776) (|CommonOperators| "op.spad" 130016 130037 130486 130491) (|CommaAst| "syntax.spad" 129773 129787 130006 130011) (|Commutator| "fnla.spad" 129576 129592 129763 129768) (|CombinatorialOpsCategory| "combfunc.spad" 128477 128507 129566 129571) (|IntegerCombinatoricFunctions| "combinat.spad" 127218 127254 128467 128472) (|CombinatorialFunction| "combfunc.spad" 124625 124656 127208 127213) (|Color| "color.spad" 123459 123470 124615 124620) (|ColonAst| "syntax.spad" 123119 123133 123449 123454) (|ComplexRootPackage| "cmplxrt.spad" 122814 122847 123109 123114) (|CollectAst| "syntax.spad" 122468 122484 122804 122809) (|TwoDimensionalPlotClipping| "clip.spad" 118552 118584 122458 122463) (|CliffordAlgebra| "clifford.spad" 117379 117408 118542 118547) (|Collection| "aggcat.spad" 115577 115595 117369 117374) (|Collection&| "aggcat.spad" 113594 113615 115389 115394) (|ComplexIntegerSolveLinearPolynomialEquation| "gaussian.spad" 112908 112962 113584 113589) (|ChangeOfVariable| "curve.spad" 111036 111068 112898 112903) (|CharacteristicZero| "catdef.spad" 110945 110969 111026 111031) (|CharacteristicPolynomialPackage| "eigen.spad" 110442 110481 110935 110940) (|CharacteristicNonZero| "catdef.spad" 110195 110222 110432 110437) (|Character| "string.spad" 107556 107571 110185 110190) (|CombinatorialFunctionCategory| "trigcat.spad" 106857 106892 107546 107551) (|CommonDenominator| "cden.spad" 106062 106091 106847 106852) (|CharacterClass| "string.spad" 104294 104314 105568 105599) (|Category| "domain.spad" 103362 103376 104284 104289) (|CategoryConstructor| "domain.spad" 103236 103261 103352 103357) (|CategoryAst| "syntax.spad" 102853 102870 103226 103231) (|CaseAst| "syntax.spad" 102562 102575 102843 102848) (|CartesianTensorFunctions2| "carten.spad" 101929 101979 102552 102557) (|CartesianTensor| "carten.spad" 97668 97705 101919 101924) (|CardinalNumber| "card.spad" 94943 94963 97634 97663) (|CapsuleAst| "syntax.spad" 94717 94733 94933 94938) (|CachableSet| "kl.spad" 94332 94349 94707 94712) (|CancellationAbelianMonoid| "catdef.spad" 93868 93899 94322 94327) (|ByteOrder| "data.spad" 93536 93551 93858 93863) (|ByteBuffer| "data.spad" 91756 91772 92970 92975) (|Byte| "data.spad" 91229 91239 91746 91751) (|BinaryTree| "tree.spad" 90362 90380 90904 90909) (|BinaryTournament| "tree.spad" 89421 89445 90037 90042) (|BinaryTreeCategory| "tree.spad" 88984 89010 89411 89416) (|BinaryTreeCategory&| "tree.spad" 88544 88573 88974 88979) (|BitAggregate| "aggcat.spad" 88022 88040 88534 88539) (|BitAggregate&| "aggcat.spad" 87497 87518 88012 88017) (|BinarySearchTree| "tree.spad" 86292 86316 87172 87177) (|BrillhartTests| "brill.spad" 84485 84508 86282 86287) (|BinaryRecursiveAggregate| "aggcat.spad" 83419 83451 84475 84480) (|BinaryRecursiveAggregate&| "aggcat.spad" 82266 82301 83325 83330) (|BalancedPAdicRational| "padic.spad" 80412 80443 80678 80758) (|BalancedPAdicInteger| "padic.spad" 80083 80113 80355 80407) (|BoundIntegerRoots| "oderf.spad" 79728 79756 80073 80078) (|BasicOperatorFunctions1| "op.spad" 77165 77196 79718 79723) (|BasicOperator| "op.spad" 72296 72315 77155 77160) (|Boolean| "boolean.spad" 71839 71852 72286 72291) (|BooleanLogic| "logic.spad" 71479 71497 71829 71834) (|BooleanLogic&| "logic.spad" 71116 71137 71469 71474) (|BiModule| "catdef.spad" 70949 70967 71106 71111) (|Bits| "boolean.spad" 70222 70232 70439 70444) (|BinaryOperatorCategory| "catdef.spad" 70084 70115 70212 70217) (|BinaryOperation| "catdef.spad" 69821 69845 70074 70079) (|Binding| "any.spad" 69237 69250 69811 69816) (|BinaryExpansion| "radix.spad" 67406 67427 67775 67855) (|BagAggregate| "aggcat.spad" 66725 66745 67396 67401) (|BagAggregate&| "aggcat.spad" 66041 66064 66715 66720) (|BezoutMatrix| "bezout.spad" 65163 65200 65983 65988) (|BalancedBinaryTree| "tree.spad" 62092 62118 64838 64843) (|BasicType| "catdef.spad" 61584 61599 62082 62087) (|BasicType&| "catdef.spad" 61073 61091 61574 61579) (|BalancedFactorisation| "oderf.spad" 60513 60545 61063 61068) (|Automorphism| "ore.spad" 59963 59983 60503 60508) (|AttributeRegistry| "attreg.spad" 58271 58294 59774 59958) (|AttributeAst| "syntax.spad" 57977 57995 58261 58266) (|ArcTrigonometricFunctionCategory| "trigcat.spad" 57416 57454 57967 57972) (|ArcTrigonometricFunctionCategory&| "trigcat.spad" 56852 56893 57406 57411) (|AbstractSyntaxCategory| "syntax.spad" 56735 56763 56842 56847) (|AbstractSyntaxCategory&| "syntax.spad" 56615 56646 56725 56730) (|ArrayStack| "bags.spad" 56084 56102 56361 56366) (|AssociatedEquations| "lodof.spad" 54897 54926 56037 56042) (|TwoDimensionalArray| "array2.spad" 54476 54503 54643 54648) (|OneDimensionalArrayFunctions2| "array1.spad" 53161 53200 54466 54471) (|OneDimensionalArray| "array1.spad" 52191 52218 52555 52560) (|TwoDimensionalArrayCategory| "array2.spad" 48474 48521 52181 52186) (|TwoDimensionalArrayCategory&| "array2.spad" 44754 44804 48464 48469) (|Arity| "term.spad" 44122 44133 44744 44749) (|ApplyRules| "rule.spad" 43401 43428 44112 44117) (|ApplyUnivariateSkewPolynomial| "ore.spad" 42992 43033 43391 43396) (|AnyFunctions1| "any.spad" 42051 42072 42982 42987) (|Any| "any.spad" 40900 40909 42041 42046) (|AntiSymm| "derham.spad" 39476 39499 40890 40895) (|AnonymousFunction| "variable.spad" 39169 39192 39466 39471) (|AlgebraicNumber| "constant.spad" 37618 37639 38995 39075) (|AbelianMonoidRing| "polycat.spad" 35924 35951 37508 37613) (|AbelianMonoidRing&| "polycat.spad" 34020 34050 35607 35612) (|AssociationList| "list.spad" 32544 32579 32908 32913) (|AlgebraGivenByStructuralConstants| "naalg.spad" 31680 31738 32449 32454) (|AlgebraPackage| "naalg.spad" 27437 27461 31623 31628) (|AlgebraicMultFact| "multfact.spad" 26614 26644 27427 27432) (|AlgebraicManipulations| "manip.spad" 24064 24096 26424 26429) (|AlgebraicFunctionField| "curve.spad" 22804 22852 23042 23174) (|AlgFactor| "algfact.spad" 21915 21933 22794 22799) (|Algebra| "catdef.spad" 21776 21791 21905 21910) (|Algebra&| "catdef.spad" 21634 21652 21766 21771) (|AssociationListAggregate| "aggcat.spad" 21149 21193 21624 21629) (|ArcHyperbolicFunctionCategory| "trigcat.spad" 20502 20537 21139 21144) (|Aggregate| "aggcat.spad" 19401 19416 20492 20497) (|Aggregate&| "aggcat.spad" 18297 18315 19391 19396) (|AlgebraicFunction| "algfunc.spad" 16714 16741 18230 18235) (|AddAst| "syntax.spad" 16395 16407 16704 16709) (|PlaneAlgebraicCurvePlot| "acplot.spad" 15250 15279 16385 16390) (|AlgebraicallyClosedFunctionSpace| "algfunc.spad" 13089 13129 15165 15245) (|AlgebraicallyClosedFunctionSpace&| "algfunc.spad" 11000 11043 13079 13084) (|AlgebraicallyClosedField| "algfunc.spad" 7744 7774 10915 10995) (|AlgebraicallyClosedField&| "algfunc.spad" 4560 4593 7734 7739) (|AbelianSemiGroup| "catdef.spad" 4086 4108 4550 4555) (|AbelianSemiGroup&| "catdef.spad" 3609 3634 4076 4081) (|AbelianMonoid| "catdef.spad" 3025 3044 3599 3604) (|AbelianMonoid&| "catdef.spad" 2438 2460 3015 3020) (|AbelianGroup| "catdef.spad" 2092 2110 2428 2433) (|AbelianGroup&| "catdef.spad" 1743 1764 2082 2087) (|OneDimensionalArrayAggregate| "aggcat.spad" 888 924 1733 1738) (|OneDimensionalArrayAggregate&| "aggcat.spad" 30 69 878 883))
\ No newline at end of file diff --git a/src/share/algebra/category.daase b/src/share/algebra/category.daase index e1dabd36..834af7d6 100644 --- a/src/share/algebra/category.daase +++ b/src/share/algebra/category.daase @@ -1,5 +1,5 @@ -(283263 . 3581079094) +(283984 . 3662084404) ((((|OutputForm|)) . T)) ((((|OutputForm|)) . T)) ((((|OutputForm|)) . T)) @@ -741,7 +741,7 @@ ((($) . T)) ((($) . T)) ((($) . T)) -((((|OutputForm|)) . T)) +(((|#2|) . T) (((|OutputForm|)) . T)) ((($) . T) (((|Integer|)) . T)) ((($) . T)) ((($) . T)) @@ -1191,6 +1191,9 @@ (((|#2|) . T)) (((|#2|) . T)) (((|#1| |#2|) . T)) +(((|#1|) . T)) +(((|#1|) . T)) +((((|OrderedFreeMonoid| |#1|)) . T) (((|OutputForm|)) . T)) ((((|OutputForm|)) . T)) (|has| |#1| (|OrderedSet|)) (|has| |#1| (|OrderedSet|)) @@ -1297,7 +1300,7 @@ (((|#1|) . T) (($) . T)) (((|#1|) . T) (((|Integer|)) . T)) (((|#1|) . T)) -((((|OutputForm|)) . T)) +((((|SExpression|)) . T) (((|Symbol|)) . T) (((|OutputForm|)) . T)) ((((|OutputForm|)) . T)) ((((|OutputForm|)) . T)) ((((|OutputForm|)) . T)) @@ -1961,7 +1964,7 @@ ((((|Syntax|)) . T)) ((((|OutputForm|)) . T) (((|Syntax|)) . T)) ((((|Syntax|)) . T)) -((((|OutputForm|)) . T)) +((((|XPBWPolynomial| |#1| |#2|)) . T) (((|XDistributedPolynomial| |#1| |#2|)) . T) (((|OutputForm|)) . T)) ((((|Record| (|:| |key| (|String|)) (|:| |entry| (|Any|)))) . T)) ((((|OutputForm|)) . T)) ((((|String|) (|Any|)) . T)) @@ -2125,7 +2128,7 @@ (((|#2| |#2|) . T)) (((|#2|) . T)) (((|#2|) . T)) -((((|OutputForm|)) . T)) +((((|XDistributedPolynomial| |#1| |#2|)) . T) (((|XRecursivePolynomial| |#1| |#2|)) . T) (((|OutputForm|)) . T)) ((((|Integer|)) . T) ((|#2|) . T)) (((|#2|) . T)) (((|#2|) . T)) @@ -2169,13 +2172,10 @@ ((((|Syntax|)) . T)) (((|#1|) . T)) (((|#1|) . T)) -((((|OutputForm|)) . T)) +((((|FreeMagma| |#1|)) . T) (((|OrderedFreeMonoid| |#1|)) . T) (((|OutputForm|)) . T)) ((((|Syntax|)) . T)) ((((|OutputForm|)) . T) (((|Syntax|)) . T)) ((((|Syntax|)) . T)) -(((|#1|) . T)) -(((|#1|) . T)) -((((|OutputForm|)) . T)) ((((|Syntax|)) . T)) ((((|TypeAst|)) . T) (((|OutputForm|)) . T) (((|Syntax|)) . T)) ((((|Syntax|)) . T)) @@ -2191,11 +2191,11 @@ (OR (|has| |#1| (|BasicType|)) (|has| |#1| (|SetCategory|))) (((|#1|) . T)) (((|#1| #1=(|Vector| |#1|) #1#) . T)) -((((|OutputForm|)) . T)) +((#1=((|OutputForm|)) |has| |#1| (|CoercibleTo| . #1#))) (((|#1|) . T)) (((|#1|) . T)) ((((|OutputForm|)) . T)) -((((|OutputForm|)) . T)) +(((|#1|) . T) (((|OutputForm|)) . T)) ((($) . T) (((|Fraction| (|Integer|))) . T)) ((($) . T) (((|Fraction| (|Integer|))) . T)) ((($ $) . T) ((#1=(|Fraction| (|Integer|)) #1#) . T)) @@ -2264,7 +2264,7 @@ (((|#1|) |has| |#1| (|CommutativeRing|)) (($) . T) (((|Integer|)) . T)) ((((|Integer|)) . T)) ((($) . T)) -((((|OutputForm|)) . T)) +(((|#1|) . T) (((|OutputForm|)) . T)) ((($) . T) (((|Integer|)) . T)) ((((|OutputForm|)) . T)) ((((|SemiGroupOperation| |#1|)) . T) (((|OutputForm|)) . T)) @@ -2763,7 +2763,7 @@ ((((|OutputForm|)) . T)) ((((|LyndonWord| |#1|)) . T)) ((((|LyndonWord| |#1|)) . T)) -((((|OutputForm|)) . T)) +((((|OrderedFreeMonoid| |#1|)) . T) (((|OutputForm|)) . T)) (((|#1|) . T)) (OR (|has| |#1| (|BasicType|)) (|has| |#1| (|SetCategory|))) ((((|Tree| |#1|)) . T) (((|OutputForm|)) OR (|has| |#1| (|CoercibleTo| (|OutputForm|))) (|has| |#1| (|SetCategory|)))) @@ -2778,7 +2778,9 @@ (OR (|has| |#1| (|Finite|)) (|has| |#1| (|OrderedSet|))) (OR (|has| |#1| (|Finite|)) (|has| |#1| (|OrderedSet|))) (((|#1|) . T)) -((((|OutputForm|)) . T)) +((((|List| (|Permutation| |#1|))) . T)) +((((|List| (|Permutation| |#1|))) . T)) +((((|List| (|Permutation| |#1|))) . T) (((|OutputForm|)) . T)) ((((|Integer|)) . T)) ((($) . T)) ((($) . T)) @@ -2796,7 +2798,7 @@ ((((|Fraction| (|Integer|))) . T) (($) . T)) ((((|Fraction| (|Integer|))) . T) (($) . T)) ((((|Integer|)) . T) (((|Fraction| (|Integer|))) . T) (($) . T)) -((((|OutputForm|)) . T)) +((((|Fraction| |#1|)) . T) (((|OutputForm|)) . T)) (((|#1|) . T) (($) . T) (((|Fraction| (|Integer|))) . T)) (((|#1|) . T) (($) . T) (((|Fraction| (|Integer|))) . T)) (((|#1| |#1|) . T) (($ $) . T) ((#1=(|Fraction| (|Integer|)) #1#) . T)) @@ -3730,7 +3732,7 @@ (((|#1|) . T) (((|Integer|)) |has| |#1| (|RetractableTo| (|Integer|))) (((|Fraction| (|Integer|))) |has| |#1| (|RetractableTo| (|Fraction| (|Integer|))))) (((|#1| (|Partition|)) . T)) ((((|OutputForm|)) . T)) -((((|OutputForm|)) . T)) +((((|Table| (|Symbol|) (|FortranType|))) . T) (((|OutputForm|)) . T)) ((((|String|)) . T) (((|Identifier|)) . T) (((|DoubleFloat|)) . T) (((|Integer|)) . T)) ((((|String|)) . T) (((|Identifier|)) . T) (((|DoubleFloat|)) . T) (((|Integer|)) . T)) ((((|InputForm|)) . T) (((|OutputForm|)) . T)) @@ -3754,6 +3756,7 @@ ((((|Record| (|:| |key| |#1|) (|:| |entry| |#2|))) . T)) (((|#1| |#2|) . T)) ((((|OutputForm|)) . T)) +((((|OutputForm|)) . T)) (((|#1|) . T)) ((((|OutputForm|)) . T)) ((((|OutputForm|)) . T)) @@ -4191,7 +4194,7 @@ (((|#2|) |has| |#2| (|CommutativeRing|))) (((|#2|) . T)) (((|#2|) . T) (($) . T)) -((((|OutputForm|)) . T)) +((((|XRecursivePolynomial| |#1| |#2|)) . T) (((|XDistributedPolynomial| |#1| |#2|)) . T) (((|OutputForm|)) . T)) (((|#2|) . T) (($) . T) (((|Integer|)) . T)) ((((|PoincareBirkhoffWittLyndonBasis| |#1|)) . T) ((|#2|) . T) (((|Integer|)) . T) (((|OrderedFreeMonoid| |#1|)) . T)) ((((|PoincareBirkhoffWittLyndonBasis| |#1|)) . T) (((|OrderedFreeMonoid| |#1|)) . T)) @@ -4252,4 +4255,4 @@ ((((|Integer|)) . T) (($) . T)) ((($) . T)) ((((|Integer|)) . T)) -(((|IntegerMod| . |CommutativeRing|) T) ((|IntegerMod| . |CoercibleFrom|) 283240) ((|IntegerMod| . |Rng|) T) ((|IntegerMod| . |SemiGroup|) T) ((|IntegerMod| . |SemiRing|) T) ((|IntegerMod| . |Monoid|) T) ((|IntegerMod| . |Ring|) T) ((|IntegerMod| . |LeftModule|) 283227) ((|IntegerMod| . |LeftLinearSet|) 283194) ((|IntegerMod| . |CancellationAbelianMonoid|) T) ((|IntegerMod| . |AbelianSemiGroup|) T) ((|IntegerMod| . |BasicType|) T) ((|IntegerMod| . |Join|) T) ((|IntegerMod| . |Type|) T) ((|IntegerMod| . |CoercibleTo|) 283168) ((|IntegerMod| . |SetCategory|) T) ((|IntegerMod| . |AbelianMonoid|) T) ((|IntegerMod| . |AbelianGroup|) T) ((|IntegerMod| . |RightModule|) 283155) ((|IntegerMod| . |RightLinearSet|) 283142) ((|IntegerMod| . |BiModule|) 283127) ((|IntegerMod| . |Finite|) T) ((|IntegerMod| . |ConvertibleTo|) 283104) ((|IntegerMod| . |StepThrough|) T) ((|YoungDiagram| . |SetCategory|) T) ((|YoungDiagram| . |CoercibleTo|) 283056) ((|YoungDiagram| . |Type|) T) ((|YoungDiagram| . |Join|) T) ((|YoungDiagram| . |BasicType|) T) ((|YoungDiagram| . |HomotopicTo|) 283031) ((|YoungDiagram| . |CoercibleFrom|) 283006) ((|XRecursivePolynomial| . |XPolynomialsCat|) 282985) ((|XRecursivePolynomial| . |Functorial|) 282969) ((|XRecursivePolynomial| . |Join|) T) ((|XRecursivePolynomial| . |Type|) T) ((|XRecursivePolynomial| . |RetractableTo|) 282931) ((|XRecursivePolynomial| . |CoercibleFrom|) 282860) ((|XRecursivePolynomial| . |Ring|) T) ((|XRecursivePolynomial| . |Monoid|) T) ((|XRecursivePolynomial| . |SemiRing|) T) ((|XRecursivePolynomial| . |SemiGroup|) T) ((|XRecursivePolynomial| . |Rng|) T) ((|XRecursivePolynomial| . |AbelianGroup|) T) ((|XRecursivePolynomial| . |LeftLinearSet|) 282814) ((|XRecursivePolynomial| . |AbelianMonoid|) T) ((|XRecursivePolynomial| . |SetCategory|) T) ((|XRecursivePolynomial| . |CoercibleTo|) 282788) ((|XRecursivePolynomial| . |BasicType|) T) ((|XRecursivePolynomial| . |AbelianSemiGroup|) T) ((|XRecursivePolynomial| . |CancellationAbelianMonoid|) T) ((|XRecursivePolynomial| . |LeftModule|) 282762) ((|XRecursivePolynomial| . |XAlgebra|) 282746) ((|XRecursivePolynomial| . |Module|) 282703) ((|XRecursivePolynomial| . |LinearSet|) 282660) ((|XRecursivePolynomial| . |RightModule|) 282644) ((|XRecursivePolynomial| . |RightLinearSet|) 282628) ((|XRecursivePolynomial| . |BiModule|) 282607) ((|XRecursivePolynomial| . |Algebra|) 282564) ((|XRecursivePolynomial| . |XFreeAlgebra|) 282543) ((|XPolynomialRing| . |Ring|) T) ((|XPolynomialRing| . |Monoid|) T) ((|XPolynomialRing| . |SemiRing|) T) ((|XPolynomialRing| . |SemiGroup|) T) ((|XPolynomialRing| . |Rng|) T) ((|XPolynomialRing| . |AbelianGroup|) T) ((|XPolynomialRing| . |LeftLinearSet|) 282497) ((|XPolynomialRing| . |AbelianMonoid|) T) ((|XPolynomialRing| . |SetCategory|) T) ((|XPolynomialRing| . |CoercibleTo|) 282471) ((|XPolynomialRing| . |Type|) T) ((|XPolynomialRing| . |Join|) T) ((|XPolynomialRing| . |BasicType|) T) ((|XPolynomialRing| . |AbelianSemiGroup|) T) ((|XPolynomialRing| . |CancellationAbelianMonoid|) T) ((|XPolynomialRing| . |LeftModule|) 282445) ((|XPolynomialRing| . |CoercibleFrom|) 282396) ((|XPolynomialRing| . |XAlgebra|) 282380) ((|XPolynomialRing| . |Module|) 282337) ((|XPolynomialRing| . |LinearSet|) 282294) ((|XPolynomialRing| . |RightModule|) 282278) ((|XPolynomialRing| . |RightLinearSet|) 282262) ((|XPolynomialRing| . |BiModule|) 282241) ((|XPolynomialRing| . |Algebra|) 282198) ((|XPolynomialRing| . |FreeModuleCat|) 282177) ((|XPolynomialRing| . |RetractableTo|) 282161) ((|XPolynomialRing| . |Functorial|) 282145) ((|XPolynomial| . |XPolynomialsCat|) 282118) ((|XPolynomial| . |Functorial|) 282102) ((|XPolynomial| . |Join|) T) ((|XPolynomial| . |Type|) T) ((|XPolynomial| . |RetractableTo|) 282058) ((|XPolynomial| . |CoercibleFrom|) 281981) ((|XPolynomial| . |Ring|) T) ((|XPolynomial| . |Monoid|) T) ((|XPolynomial| . |SemiRing|) T) ((|XPolynomial| . |SemiGroup|) T) ((|XPolynomial| . |Rng|) T) 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|Algebra|) 279823) ((|WeightedPolynomials| . |BiModule|) 279775) ((|WeightedPolynomials| . |RightLinearSet|) 279732) ((|WeightedPolynomials| . |RightModule|) 279689) ((|WeightedPolynomials| . |LinearSet|) 279646) ((|WeightedPolynomials| . |Module|) 279603) ((|WhileAst| . |SpadSyntaxCategory|) T) ((|WhileAst| . |HomotopicTo|) 279581) ((|WhileAst| . |CoercibleTo|) 279536) ((|WhileAst| . |CoercibleFrom|) 279514) ((|WhileAst| . |SetCategory|) T) ((|WhileAst| . |Type|) T) ((|WhileAst| . |Join|) T) ((|WhileAst| . |BasicType|) T) ((|WhileAst| . |AbstractSyntaxCategory|) T) ((|WhereAst| . |SpadSyntaxCategory|) T) ((|WhereAst| . |HomotopicTo|) 279492) ((|WhereAst| . |CoercibleTo|) 279447) ((|WhereAst| . |CoercibleFrom|) 279425) ((|WhereAst| . |SetCategory|) T) ((|WhereAst| . |Type|) T) ((|WhereAst| . |Join|) T) ((|WhereAst| . |BasicType|) T) ((|WhereAst| . |AbstractSyntaxCategory|) T) ((|Void| . |CoercibleTo|) 279399) ((|ThreeDimensionalViewport| . |SetCategory|) T) ((|ThreeDimensionalViewport| 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|BasicType|) 278566) ((|Vector| . |Type|) T) ((|Vector| . |Join|) T) ((|Vector| . |Aggregate|) T) ((|Vector| . |FiniteAggregate|) 278550) ((|Vector| . |ShallowlyMutableAggregate|) 278534) ((|Vector| . |OneDimensionalArrayAggregate|) 278518) ((|Variable| . |SetCategory|) T) ((|Variable| . |CoercibleTo|) 278473) ((|Variable| . |Type|) T) ((|Variable| . |Join|) T) ((|Variable| . |BasicType|) T) ((|UnivariateTaylorSeries| . |UnivariateTaylorSeriesCategory|) 278457) ((|UnivariateTaylorSeries| . |DifferentialRing|) 278394) ((|UnivariateTaylorSeries| . |CoercibleFrom|) 278218) ((|UnivariateTaylorSeries| . |LeftModule|) 278115) ((|UnivariateTaylorSeries| . |LeftLinearSet|) 277992) ((|UnivariateTaylorSeries| . |CancellationAbelianMonoid|) T) ((|UnivariateTaylorSeries| . |AbelianSemiGroup|) T) ((|UnivariateTaylorSeries| . |BasicType|) T) ((|UnivariateTaylorSeries| . |CoercibleTo|) 277966) ((|UnivariateTaylorSeries| . |SetCategory|) T) ((|UnivariateTaylorSeries| . |AbelianMonoid|) T) ((|UnivariateTaylorSeries| . |AbelianGroup|) T) ((|UnivariateTaylorSeries| . |Rng|) T) ((|UnivariateTaylorSeries| . |SemiGroup|) T) ((|UnivariateTaylorSeries| . |SemiRing|) T) ((|UnivariateTaylorSeries| . |Monoid|) T) ((|UnivariateTaylorSeries| . |Ring|) T) ((|UnivariateTaylorSeries| . |DifferentialDomain|) 277897) ((|UnivariateTaylorSeries| . |Join|) T) ((|UnivariateTaylorSeries| . |Type|) T) ((|UnivariateTaylorSeries| . |DifferentialSpace|) 277834) ((|UnivariateTaylorSeries| . |Eltable|) 277783) ((|UnivariateTaylorSeries| . |PartialDifferentialRing|) 277647) ((|UnivariateTaylorSeries| . |PartialDifferentialDomain|) 277481) ((|UnivariateTaylorSeries| . |PartialDifferentialSpace|) 277345) ((|UnivariateTaylorSeries| . |PowerSeriesCategory|) 277280) ((|UnivariateTaylorSeries| . |Algebra|) 277124) ((|UnivariateTaylorSeries| . |BiModule|) 276943) ((|UnivariateTaylorSeries| . |RightLinearSet|) 276776) ((|UnivariateTaylorSeries| . |RightModule|) 276609) ((|UnivariateTaylorSeries| . |LinearSet|) 276453) ((|UnivariateTaylorSeries| . |Module|) 276297) ((|UnivariateTaylorSeries| . |CharacteristicNonZero|) 276257) ((|UnivariateTaylorSeries| . |CharacteristicZero|) 276220) ((|UnivariateTaylorSeries| . |CommutativeRing|) 276149) ((|UnivariateTaylorSeries| . |Functorial|) 276133) ((|UnivariateTaylorSeries| . |IntegralDomain|) 276100) ((|UnivariateTaylorSeries| . |EntireRing|) 276067) ((|UnivariateTaylorSeries| . |AbelianMonoidRing|) 276028) ((|UnivariateTaylorSeries| . |UnivariatePowerSeriesCategory|) 275989) ((|UnivariateTaylorSeries| . |ArcHyperbolicFunctionCategory|) 275938) ((|UnivariateTaylorSeries| . |ArcTrigonometricFunctionCategory|) 275887) ((|UnivariateTaylorSeries| . |ElementaryFunctionCategory|) 275836) ((|UnivariateTaylorSeries| . |HyperbolicFunctionCategory|) 275785) ((|UnivariateTaylorSeries| . |TrigonometricFunctionCategory|) 275734) ((|UnivariateTaylorSeries| . |TranscendentalFunctionCategory|) 275683) ((|UnivariateTaylorSeries| . |RadicalCategory|) 275632) ((|UnivariatePuiseuxSeriesWithExponentialSingularity| . |FiniteAbelianMonoidRing|) 275522) ((|UnivariatePuiseuxSeriesWithExponentialSingularity| . |RetractableTo|) 275468) ((|UnivariatePuiseuxSeriesWithExponentialSingularity| . |FullyRetractableTo|) 275414) ((|UnivariatePuiseuxSeriesWithExponentialSingularity| . |Algebra|) 275245) ((|UnivariatePuiseuxSeriesWithExponentialSingularity| . |CoercibleFrom|) 275046) ((|UnivariatePuiseuxSeriesWithExponentialSingularity| . |LeftModule|) 274903) ((|UnivariatePuiseuxSeriesWithExponentialSingularity| . |LeftLinearSet|) 274740) ((|UnivariatePuiseuxSeriesWithExponentialSingularity| . |Rng|) T) ((|UnivariatePuiseuxSeriesWithExponentialSingularity| . |SemiGroup|) T) ((|UnivariatePuiseuxSeriesWithExponentialSingularity| . |SemiRing|) T) ((|UnivariatePuiseuxSeriesWithExponentialSingularity| . |Monoid|) T) ((|UnivariatePuiseuxSeriesWithExponentialSingularity| . |Ring|) T) ((|UnivariatePuiseuxSeriesWithExponentialSingularity| . |BiModule|) 274584) ((|UnivariatePuiseuxSeriesWithExponentialSingularity| . |RightLinearSet|) 274441) ((|UnivariatePuiseuxSeriesWithExponentialSingularity| . |RightModule|) 274298) ((|UnivariatePuiseuxSeriesWithExponentialSingularity| . |AbelianGroup|) T) ((|UnivariatePuiseuxSeriesWithExponentialSingularity| . |AbelianMonoid|) T) ((|UnivariatePuiseuxSeriesWithExponentialSingularity| . |SetCategory|) T) ((|UnivariatePuiseuxSeriesWithExponentialSingularity| . |CoercibleTo|) 274272) ((|UnivariatePuiseuxSeriesWithExponentialSingularity| . |Type|) T) ((|UnivariatePuiseuxSeriesWithExponentialSingularity| . |Join|) T) ((|UnivariatePuiseuxSeriesWithExponentialSingularity| . |BasicType|) T) ((|UnivariatePuiseuxSeriesWithExponentialSingularity| . |AbelianSemiGroup|) T) ((|UnivariatePuiseuxSeriesWithExponentialSingularity| . |CancellationAbelianMonoid|) T) ((|UnivariatePuiseuxSeriesWithExponentialSingularity| . |LinearSet|) 274103) ((|UnivariatePuiseuxSeriesWithExponentialSingularity| . |Module|) 273934) ((|UnivariatePuiseuxSeriesWithExponentialSingularity| . |CharacteristicNonZero|) 273856) ((|UnivariatePuiseuxSeriesWithExponentialSingularity| . |CharacteristicZero|) 273781) ((|UnivariatePuiseuxSeriesWithExponentialSingularity| . |CommutativeRing|) T) ((|UnivariatePuiseuxSeriesWithExponentialSingularity| . |Functorial|) 273727) ((|UnivariatePuiseuxSeriesWithExponentialSingularity| . |IntegralDomain|) T) ((|UnivariatePuiseuxSeriesWithExponentialSingularity| . |EntireRing|) T) ((|UnivariatePuiseuxSeriesWithExponentialSingularity| . |AbelianMonoidRing|) 273617) ((|UnivariatePuiseuxSeriesConstructor| . |UnivariatePuiseuxSeriesConstructorCategory|) 273596) ((|UnivariatePuiseuxSeriesConstructor| . |Field|) 273572) ((|UnivariatePuiseuxSeriesConstructor| . |UniqueFactorizationDomain|) 273548) ((|UnivariatePuiseuxSeriesConstructor| . |PrincipalIdealDomain|) 273524) ((|UnivariatePuiseuxSeriesConstructor| . |IntegralDomain|) 273463) ((|UnivariatePuiseuxSeriesConstructor| . |CommutativeRing|) 273369) ((|UnivariatePuiseuxSeriesConstructor| . |CoercibleFrom|) 273124) ((|UnivariatePuiseuxSeriesConstructor| . |Module|) 272912) ((|UnivariatePuiseuxSeriesConstructor| . |LinearSet|) 272700) ((|UnivariatePuiseuxSeriesConstructor| . |Algebra|) 272488) ((|UnivariatePuiseuxSeriesConstructor| . |GcdDomain|) 272464) ((|UnivariatePuiseuxSeriesConstructor| . |EuclideanDomain|) 272440) ((|UnivariatePuiseuxSeriesConstructor| . |LeftModule|) 272309) ((|UnivariatePuiseuxSeriesConstructor| . |LeftLinearSet|) 272158) ((|UnivariatePuiseuxSeriesConstructor| . |Rng|) T) ((|UnivariatePuiseuxSeriesConstructor| . |SemiGroup|) T) ((|UnivariatePuiseuxSeriesConstructor| . |SemiRing|) T) ((|UnivariatePuiseuxSeriesConstructor| . |Monoid|) T) ((|UnivariatePuiseuxSeriesConstructor| . |Ring|) T) ((|UnivariatePuiseuxSeriesConstructor| . |BiModule|) 271926) ((|UnivariatePuiseuxSeriesConstructor| . |RightLinearSet|) 271708) ((|UnivariatePuiseuxSeriesConstructor| . |RightModule|) 271490) ((|UnivariatePuiseuxSeriesConstructor| . |AbelianGroup|) T) ((|UnivariatePuiseuxSeriesConstructor| . |AbelianMonoid|) T) ((|UnivariatePuiseuxSeriesConstructor| . |SetCategory|) T) ((|UnivariatePuiseuxSeriesConstructor| . |CoercibleTo|) 271464) ((|UnivariatePuiseuxSeriesConstructor| . |Type|) T) ((|UnivariatePuiseuxSeriesConstructor| . |Join|) T) ((|UnivariatePuiseuxSeriesConstructor| . |BasicType|) T) ((|UnivariatePuiseuxSeriesConstructor| . |AbelianSemiGroup|) T) ((|UnivariatePuiseuxSeriesConstructor| . |CancellationAbelianMonoid|) T) ((|UnivariatePuiseuxSeriesConstructor| . |EntireRing|) 271403) ((|UnivariatePuiseuxSeriesConstructor| . |DivisionRing|) 271379) ((|UnivariatePuiseuxSeriesConstructor| . |RadicalCategory|) 271328) ((|UnivariatePuiseuxSeriesConstructor| . |TranscendentalFunctionCategory|) 271277) ((|UnivariatePuiseuxSeriesConstructor| . |TrigonometricFunctionCategory|) 271226) ((|UnivariatePuiseuxSeriesConstructor| . |HyperbolicFunctionCategory|) 271175) ((|UnivariatePuiseuxSeriesConstructor| . |ElementaryFunctionCategory|) 271124) ((|UnivariatePuiseuxSeriesConstructor| . |ArcTrigonometricFunctionCategory|) 271073) ((|UnivariatePuiseuxSeriesConstructor| . |ArcHyperbolicFunctionCategory|) 271022) ((|UnivariatePuiseuxSeriesConstructor| . |UnivariatePowerSeriesCategory|) 270981) ((|UnivariatePuiseuxSeriesConstructor| . |AbelianMonoidRing|) 270940) ((|UnivariatePuiseuxSeriesConstructor| . |Functorial|) 270924) ((|UnivariatePuiseuxSeriesConstructor| . |CharacteristicZero|) 270887) ((|UnivariatePuiseuxSeriesConstructor| . |CharacteristicNonZero|) 270847) ((|UnivariatePuiseuxSeriesConstructor| . |PowerSeriesCategory|) 270780) ((|UnivariatePuiseuxSeriesConstructor| . |PartialDifferentialSpace|) 270642) ((|UnivariatePuiseuxSeriesConstructor| . |PartialDifferentialDomain|) 270502) ((|UnivariatePuiseuxSeriesConstructor| . |PartialDifferentialRing|) 270364) ((|UnivariatePuiseuxSeriesConstructor| . |Eltable|) 270311) ((|UnivariatePuiseuxSeriesConstructor| . |DifferentialSpace|) 270246) ((|UnivariatePuiseuxSeriesConstructor| . |DifferentialDomain|) 270175) ((|UnivariatePuiseuxSeriesConstructor| . |DifferentialRing|) 270110) ((|UnivariatePuiseuxSeriesConstructor| . |UnivariatePuiseuxSeriesCategory|) 270094) ((|UnivariatePuiseuxSeriesConstructor| . |RetractableTo|) 270078) ((|UnivariatePuiseuxSeries| . |UnivariatePuiseuxSeriesConstructorCategory|) 270019) ((|UnivariatePuiseuxSeries| . |Field|) 269995) ((|UnivariatePuiseuxSeries| . |UniqueFactorizationDomain|) 269971) ((|UnivariatePuiseuxSeries| . |PrincipalIdealDomain|) 269947) ((|UnivariatePuiseuxSeries| . |IntegralDomain|) 269886) ((|UnivariatePuiseuxSeries| . |CommutativeRing|) 269792) ((|UnivariatePuiseuxSeries| . |CoercibleFrom|) 269433) ((|UnivariatePuiseuxSeries| . |Module|) 269221) ((|UnivariatePuiseuxSeries| . |LinearSet|) 269009) ((|UnivariatePuiseuxSeries| . |Algebra|) 268797) ((|UnivariatePuiseuxSeries| . |GcdDomain|) 268773) ((|UnivariatePuiseuxSeries| . |EuclideanDomain|) 268749) ((|UnivariatePuiseuxSeries| . |LeftModule|) 268618) ((|UnivariatePuiseuxSeries| . |LeftLinearSet|) 268467) ((|UnivariatePuiseuxSeries| . |Rng|) T) ((|UnivariatePuiseuxSeries| . |SemiGroup|) T) ((|UnivariatePuiseuxSeries| . |SemiRing|) T) ((|UnivariatePuiseuxSeries| . |Monoid|) T) ((|UnivariatePuiseuxSeries| . |Ring|) T) ((|UnivariatePuiseuxSeries| . |BiModule|) 268235) ((|UnivariatePuiseuxSeries| . |RightLinearSet|) 268017) ((|UnivariatePuiseuxSeries| . |RightModule|) 267799) ((|UnivariatePuiseuxSeries| . |AbelianGroup|) T) ((|UnivariatePuiseuxSeries| . |AbelianMonoid|) T) ((|UnivariatePuiseuxSeries| . |SetCategory|) T) ((|UnivariatePuiseuxSeries| . |CoercibleTo|) 267773) ((|UnivariatePuiseuxSeries| . |Type|) T) ((|UnivariatePuiseuxSeries| . |Join|) T) ((|UnivariatePuiseuxSeries| . |BasicType|) T) ((|UnivariatePuiseuxSeries| . |AbelianSemiGroup|) T) ((|UnivariatePuiseuxSeries| . |CancellationAbelianMonoid|) T) ((|UnivariatePuiseuxSeries| . |EntireRing|) 267712) ((|UnivariatePuiseuxSeries| . |DivisionRing|) 267688) ((|UnivariatePuiseuxSeries| . |RadicalCategory|) 267637) ((|UnivariatePuiseuxSeries| . |TranscendentalFunctionCategory|) 267586) ((|UnivariatePuiseuxSeries| . |TrigonometricFunctionCategory|) 267535) ((|UnivariatePuiseuxSeries| . |HyperbolicFunctionCategory|) 267484) ((|UnivariatePuiseuxSeries| . |ElementaryFunctionCategory|) 267433) ((|UnivariatePuiseuxSeries| . |ArcTrigonometricFunctionCategory|) 267382) ((|UnivariatePuiseuxSeries| . |ArcHyperbolicFunctionCategory|) 267331) ((|UnivariatePuiseuxSeries| . |UnivariatePowerSeriesCategory|) 267290) ((|UnivariatePuiseuxSeries| . |AbelianMonoidRing|) 267249) ((|UnivariatePuiseuxSeries| . |Functorial|) 267233) ((|UnivariatePuiseuxSeries| . |CharacteristicZero|) 267196) ((|UnivariatePuiseuxSeries| . |CharacteristicNonZero|) 267156) ((|UnivariatePuiseuxSeries| . |PowerSeriesCategory|) 267089) ((|UnivariatePuiseuxSeries| . |PartialDifferentialSpace|) 266951) ((|UnivariatePuiseuxSeries| . |PartialDifferentialDomain|) 266783) ((|UnivariatePuiseuxSeries| . |PartialDifferentialRing|) 266645) ((|UnivariatePuiseuxSeries| . |Eltable|) 266592) ((|UnivariatePuiseuxSeries| . |DifferentialSpace|) 266527) ((|UnivariatePuiseuxSeries| . |DifferentialDomain|) 266456) ((|UnivariatePuiseuxSeries| . |DifferentialRing|) 266391) ((|UnivariatePuiseuxSeries| . |UnivariatePuiseuxSeriesCategory|) 266375) ((|UnivariatePuiseuxSeries| . |RetractableTo|) 266271) ((|UnivariatePolynomial| . |UnivariatePolynomialCategory|) 266255) ((|UnivariatePolynomial| . |StepThrough|) 266225) ((|UnivariatePolynomial| . |ConvertibleTo|) NIL) ((|UnivariatePolynomial| . |Evalable|) 266212) ((|UnivariatePolynomial| . |InnerEvalable|) 266141) ((|UnivariatePolynomial| . |FiniteAbelianMonoidRing|) 266102) ((|UnivariatePolynomial| . |RetractableTo|) 265912) ((|UnivariatePolynomial| . |FullyRetractableTo|) 265896) ((|UnivariatePolynomial| . |Algebra|) 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|Type|) T) ((|UInt8| . |Join|) T) ((|UInt8| . |BasicType|) T) ((|UInt8| . |Finite|) T) ((|UInt8| . |Logic|) T) ((|UInt64| . |OrderedFinite|) T) ((|UInt64| . |OrderedType|) T) ((|UInt64| . |OrderedSet|) T) ((|UInt64| . |SetCategory|) T) ((|UInt64| . |CoercibleTo|) 247644) ((|UInt64| . |Type|) T) ((|UInt64| . |Join|) T) ((|UInt64| . |BasicType|) T) ((|UInt64| . |Finite|) T) ((|UInt64| . |Logic|) T) ((|UInt32| . |OrderedFinite|) T) ((|UInt32| . |OrderedType|) T) ((|UInt32| . |OrderedSet|) T) ((|UInt32| . |SetCategory|) T) ((|UInt32| . |CoercibleTo|) 247618) ((|UInt32| . |Type|) T) ((|UInt32| . |Join|) T) ((|UInt32| . |BasicType|) T) ((|UInt32| . |Finite|) T) ((|UInt32| . |Logic|) T) ((|UInt16| . |OrderedFinite|) T) ((|UInt16| . |OrderedType|) T) ((|UInt16| . |OrderedSet|) T) ((|UInt16| . |SetCategory|) T) ((|UInt16| . |CoercibleTo|) 247592) ((|UInt16| . |Type|) T) ((|UInt16| . |Join|) T) ((|UInt16| . |BasicType|) T) ((|UInt16| . |Finite|) T) ((|UInt16| . |Logic|) T) ((|TypeAst| . 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((|TaylorSeries| . |AbelianMonoidRing|) 246791) ((|TaylorSeries| . |Algebra|) 246635) ((|TaylorSeries| . |LinearSet|) 246479) ((|TaylorSeries| . |Module|) 246323) ((|TaylorSeries| . |CoercibleFrom|) 246147) ((|TaylorSeries| . |EntireRing|) 246114) ((|TaylorSeries| . |IntegralDomain|) 246081) ((|TaylorSeries| . |Functorial|) 246065) ((|TaylorSeries| . |BiModule|) 245884) ((|TaylorSeries| . |RightLinearSet|) 245717) ((|TaylorSeries| . |RightModule|) 245550) ((|TaylorSeries| . |CommutativeRing|) 245479) ((|TaylorSeries| . |CharacteristicZero|) 245442) ((|TaylorSeries| . |CharacteristicNonZero|) 245402) ((|TaylorSeries| . |LeftModule|) 245299) ((|TaylorSeries| . |LeftLinearSet|) 245176) ((|TaylorSeries| . |PowerSeriesCategory|) 245121) ((|TaylorSeries| . |PartialDifferentialSpace|) 245099) ((|TaylorSeries| . |Type|) T) ((|TaylorSeries| . |Join|) T) ((|TaylorSeries| . |PartialDifferentialDomain|) 245075) ((|TaylorSeries| . |Ring|) T) ((|TaylorSeries| . |Monoid|) T) ((|TaylorSeries| . 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|BasicType|) T) ((|TextFile| . |Join|) T) ((|TextFile| . |Type|) T) ((|TextFile| . |CoercibleTo|) 244490) ((|TextFile| . |SetCategory|) T) ((|TexFormat| . |SetCategory|) T) ((|TexFormat| . |CoercibleTo|) 244464) ((|TexFormat| . |Type|) T) ((|TexFormat| . |Join|) T) ((|TexFormat| . |BasicType|) T) ((|TexFormat| . |CoercibleFrom|) 244438) ((|TermAlgebraOperator| . |OperatorCategory|) 244422) ((|TermAlgebraOperator| . |BasicType|) T) ((|TermAlgebraOperator| . |Join|) T) ((|TermAlgebraOperator| . |Type|) T) ((|TermAlgebraOperator| . |CoercibleTo|) 244396) ((|TermAlgebraOperator| . |SetCategory|) T) ((|Table| . |TableAggregate|) 244375) ((|Table| . |Dictionary|) 244317) ((|Table| . |BagAggregate|) 244259) ((|Table| . |ShallowlyMutableAggregate|) 244188) ((|Table| . |Collection|) 244130) ((|Table| . |ConvertibleTo|) NIL) ((|Table| . |DictionaryOperations|) 244072) ((|Table| . |IndexedAggregate|) 244051) ((|Table| . |Evalable|) 243811) ((|Table| . |InnerEvalable|) 243559) ((|Table| . 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|CharacteristicZero|) 210386) ((|SparseMultivariatePolynomial| . |CharacteristicNonZero|) 210346) ((|SparseMultivariatePolynomial| . |LeftLinearSet|) 210223) ((|SparseMultivariatePolynomial| . |CancellationAbelianMonoid|) T) ((|SparseMultivariatePolynomial| . |AbelianSemiGroup|) T) ((|SparseMultivariatePolynomial| . |BasicType|) T) ((|SparseMultivariatePolynomial| . |Join|) T) ((|SparseMultivariatePolynomial| . |Type|) T) ((|SparseMultivariatePolynomial| . |CoercibleTo|) 210197) ((|SparseMultivariatePolynomial| . |SetCategory|) T) ((|SparseMultivariatePolynomial| . |AbelianMonoid|) T) ((|SparseMultivariatePolynomial| . |AbelianGroup|) T) ((|SparseMultivariatePolynomial| . |Ring|) T) ((|SparseMultivariatePolynomial| . |Monoid|) T) ((|SparseMultivariatePolynomial| . |SemiRing|) T) ((|SparseMultivariatePolynomial| . |SemiGroup|) T) ((|SparseMultivariatePolynomial| . |Rng|) T) ((|SparseMultivariatePolynomial| . |FullyRetractableTo|) 210181) ((|SparseMultivariatePolynomial| . |FiniteAbelianMonoidRing|) 210139) ((|SparseMultivariatePolynomial| . |Evalable|) 210126) ((|SparseMultivariatePolynomial| . |ConvertibleTo|) 209733) ((|SingleInteger| . |IntegerNumberSystem|) T) ((|SingleInteger| . |UniqueFactorizationDomain|) T) ((|SingleInteger| . |StepThrough|) T) ((|SingleInteger| . |RetractableTo|) 209710) ((|SingleInteger| . |ConvertibleTo|) 209596) ((|SingleInteger| . |RealConstant|) T) ((|SingleInteger| . |PatternMatchable|) 209573) ((|SingleInteger| . |OrderedRing|) T) ((|SingleInteger| . |OrderedCancellationAbelianMonoid|) T) ((|SingleInteger| . |OrderedAbelianSemiGroup|) T) ((|SingleInteger| . |OrderedType|) T) ((|SingleInteger| . |OrderedSet|) T) ((|SingleInteger| . |OrderedAbelianMonoid|) T) ((|SingleInteger| . |OrderedAbelianGroup|) T) ((|SingleInteger| . |OrderedIntegralDomain|) T) ((|SingleInteger| . |LeftModule|) 209540) ((|SingleInteger| . |LinearlyExplicitRingOver|) 209517) ((|SingleInteger| . |PrincipalIdealDomain|) T) ((|SingleInteger| . |IntegralDomain|) T) ((|SingleInteger| . |EntireRing|) T) ((|SingleInteger| . |CommutativeRing|) T) ((|SingleInteger| . |CoercibleFrom|) 209484) ((|SingleInteger| . |Module|) 209471) ((|SingleInteger| . |LinearSet|) 209458) ((|SingleInteger| . |RightModule|) 209445) ((|SingleInteger| . |RightLinearSet|) 209432) ((|SingleInteger| . |BiModule|) 209417) ((|SingleInteger| . |Algebra|) 209404) ((|SingleInteger| . |GcdDomain|) T) ((|SingleInteger| . |EuclideanDomain|) T) ((|SingleInteger| . |DifferentialSpace|) T) ((|SingleInteger| . |DifferentialDomain|) 209391) ((|SingleInteger| . |DifferentialRing|) T) ((|SingleInteger| . |CombinatorialFunctionCategory|) T) ((|SingleInteger| . |Ring|) T) ((|SingleInteger| . |Monoid|) T) ((|SingleInteger| . |SemiRing|) T) ((|SingleInteger| . |SemiGroup|) T) ((|SingleInteger| . |Rng|) T) ((|SingleInteger| . |AbelianGroup|) T) ((|SingleInteger| . |LeftLinearSet|) 209358) ((|SingleInteger| . |AbelianMonoid|) T) ((|SingleInteger| . |SetCategory|) T) ((|SingleInteger| . |CoercibleTo|) 209332) ((|SingleInteger| . |Type|) T) ((|SingleInteger| . |Join|) T) ((|SingleInteger| . |BasicType|) T) ((|SingleInteger| . |AbelianSemiGroup|) T) ((|SingleInteger| . |CancellationAbelianMonoid|) T) ((|SingleInteger| . |CharacteristicZero|) T) ((|SingleInteger| . |OrderedFinite|) T) ((|SingleInteger| . |Finite|) T) ((|SingleInteger| . |BooleanLogic|) T) ((|SingleInteger| . |Logic|) T) ((|SignatureAst| . |SpadSyntaxCategory|) T) ((|SignatureAst| . |HomotopicTo|) 209310) ((|SignatureAst| . |CoercibleTo|) 209265) ((|SignatureAst| . |CoercibleFrom|) 209243) ((|SignatureAst| . |SetCategory|) T) ((|SignatureAst| . |Type|) T) ((|SignatureAst| . |Join|) T) ((|SignatureAst| . |BasicType|) T) ((|SignatureAst| . |AbstractSyntaxCategory|) T) ((|Signature| . |SetCategory|) T) ((|Signature| . |CoercibleTo|) 209217) ((|Signature| . |Type|) T) ((|Signature| . |Join|) T) ((|Signature| . |BasicType|) T) ((|SplitHomogeneousDirectProduct| . |DirectProductCategory|) 209196) ((|SplitHomogeneousDirectProduct| . |VectorSpace|) 209163) ((|SplitHomogeneousDirectProduct| . |OrderedCancellationAbelianMonoid|) 209121) ((|SplitHomogeneousDirectProduct| . |OrderedAbelianSemiGroup|) 209079) ((|SplitHomogeneousDirectProduct| . |OrderedType|) 209004) ((|SplitHomogeneousDirectProduct| . |OrderedSet|) 208929) ((|SplitHomogeneousDirectProduct| . |OrderedAbelianMonoid|) 208887) ((|SplitHomogeneousDirectProduct| . |OrderedAbelianMonoidSup|) 208845) ((|SplitHomogeneousDirectProduct| . |Module|) 208774) ((|SplitHomogeneousDirectProduct| . |LinearSet|) 208679) ((|SplitHomogeneousDirectProduct| . |EltableAggregate|) 208651) ((|SplitHomogeneousDirectProduct| . |Eltable|) 208623) ((|SplitHomogeneousDirectProduct| . |IndexedAggregate|) 208595) ((|SplitHomogeneousDirectProduct| . |RetractableTo|) 208346) ((|SplitHomogeneousDirectProduct| . |CoercibleFrom|) 208070) ((|SplitHomogeneousDirectProduct| . |FullyRetractableTo|) 208031) ((|SplitHomogeneousDirectProduct| . |LinearlyExplicitRingOver|) 207903) ((|SplitHomogeneousDirectProduct| . |LeftModule|) 207688) ((|SplitHomogeneousDirectProduct| . |FullyLinearlyExplicitRingOver|) 207656) ((|SplitHomogeneousDirectProduct| . |HomogeneousAggregate|) 207640) ((|SplitHomogeneousDirectProduct| . |Functorial|) 207624) ((|SplitHomogeneousDirectProduct| . |InnerEvalable|) 207543) ((|SplitHomogeneousDirectProduct| . |Evalable|) 207467) ((|SplitHomogeneousDirectProduct| . |Aggregate|) T) ((|SplitHomogeneousDirectProduct| . |FiniteAggregate|) 207451) ((|SplitHomogeneousDirectProduct| . |Finite|) 207426) ((|SplitHomogeneousDirectProduct| . |DifferentialRing|) 207363) ((|SplitHomogeneousDirectProduct| . |LeftLinearSet|) 207093) ((|SplitHomogeneousDirectProduct| . |Rng|) 207070) ((|SplitHomogeneousDirectProduct| . |SemiGroup|) 207047) ((|SplitHomogeneousDirectProduct| . |SemiRing|) 207024) ((|SplitHomogeneousDirectProduct| . |Monoid|) 207001) ((|SplitHomogeneousDirectProduct| . |Ring|) 206978) ((|SplitHomogeneousDirectProduct| . |DifferentialDomain|) 206841) ((|SplitHomogeneousDirectProduct| . |DifferentialSpace|) 206710) ((|SplitHomogeneousDirectProduct| . |DifferentialSpaceExtension|) 206678) ((|SplitHomogeneousDirectProduct| . |PartialDifferentialDomain|) 206494) ((|SplitHomogeneousDirectProduct| . |PartialDifferentialSpace|) 206312) ((|SplitHomogeneousDirectProduct| . |PartialDifferentialRing|) 206216) ((|SplitHomogeneousDirectProduct| . |DifferentialExtension|) 206184) ((|SplitHomogeneousDirectProduct| . |CoercibleTo|) 205729) ((|SplitHomogeneousDirectProduct| . |RightModule|) 205636) ((|SplitHomogeneousDirectProduct| . |RightLinearSet|) 205519) ((|SplitHomogeneousDirectProduct| . |BiModule|) 205421) ((|SplitHomogeneousDirectProduct| . |CancellationAbelianMonoid|) 205223) ((|SplitHomogeneousDirectProduct| . |AbelianSemiGroup|) 204960) ((|SplitHomogeneousDirectProduct| . |BasicType|) 204565) ((|SplitHomogeneousDirectProduct| . |Join|) T) ((|SplitHomogeneousDirectProduct| . |Type|) T) ((|SplitHomogeneousDirectProduct| . |SetCategory|) 204197) ((|SplitHomogeneousDirectProduct| . |AbelianMonoid|) 203968) ((|SplitHomogeneousDirectProduct| . |AbelianGroup|) 203854) ((|SemiGroupOperation| . |SemiGroupOperatorCategory|) 203838) ((|SemiGroupOperation| . |MappingCategory|) 203812) ((|SemiGroupOperation| . |Type|) T) ((|SemiGroupOperation| . |BinaryOperatorCategory|) 203796) ((|SemiGroupOperation| . |SetCategory|) T) ((|SemiGroupOperation| . |CoercibleTo|) 203770) ((|SemiGroupOperation| . |Join|) T) ((|SemiGroupOperation| . |BasicType|) T) ((|SExpressionOf| . |SExpressionCategory|) 203734) ((|SExpressionOf| . |BasicType|) T) ((|SExpressionOf| . |CoercibleTo|) 203708) ((|SExpressionOf| . |SetCategory|) T) ((|SExpressionOf| . |Eltable|) 203652) ((|SExpressionOf| . |Type|) T) ((|SExpressionOf| . |Join|) T) ((|SExpressionOf| . |ConvertibleFrom|) 203565) ((|SExpression| . |SExpressionCategory|) 203489) ((|SExpression| . |BasicType|) T) ((|SExpression| . |CoercibleTo|) 203463) ((|SExpression| . |SetCategory|) T) ((|SExpression| . |Eltable|) 203407) ((|SExpression| . |Type|) T) ((|SExpression| . |Join|) T) ((|SExpression| . |ConvertibleFrom|) 203280) ((|SetOfMIntegersInOneToN| . |Finite|) T) ((|SetOfMIntegersInOneToN| . |BasicType|) T) ((|SetOfMIntegersInOneToN| . |Join|) T) ((|SetOfMIntegersInOneToN| . |Type|) T) ((|SetOfMIntegersInOneToN| . |CoercibleTo|) 203254) ((|SetOfMIntegersInOneToN| . |SetCategory|) T) ((|Set| . |FiniteSetAggregate|) 203238) ((|Set| . |SetAggregate|) 203222) ((|Set| . |FiniteAggregate|) 203206) ((|Set| . |Finite|) 203181) ((|Set| . |DictionaryOperations|) 203165) ((|Set| . |ConvertibleTo|) 203101) ((|Set| . |Collection|) 203085) ((|Set| . |HomogeneousAggregate|) 203069) ((|Set| . |SetCategory|) T) ((|Set| . |Functorial|) 203053) ((|Set| . |InnerEvalable|) 202972) ((|Set| . |Evalable|) 202896) ((|Set| . |CoercibleTo|) 202870) ((|Set| . |BasicType|) T) ((|Set| . |Type|) T) ((|Set| . |Join|) T) ((|Set| . 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T) ((|SequentialDifferentialPolynomial| . |DifferentialPolynomialCategory|) 202061) ((|SequentialDifferentialPolynomial| . |CoercibleFrom|) 201651) ((|SequentialDifferentialPolynomial| . |RetractableTo|) 201376) ((|SequentialDifferentialPolynomial| . |ConvertibleTo|) NIL) ((|SequentialDifferentialPolynomial| . |FiniteAbelianMonoidRing|) 201293) ((|SequentialDifferentialPolynomial| . |FullyRetractableTo|) 201277) ((|SequentialDifferentialPolynomial| . |Algebra|) 201040) ((|SequentialDifferentialPolynomial| . |BiModule|) 200783) ((|SequentialDifferentialPolynomial| . |RightLinearSet|) 200540) ((|SequentialDifferentialPolynomial| . |RightModule|) 200297) ((|SequentialDifferentialPolynomial| . |LeftLinearSet|) 200174) ((|SequentialDifferentialPolynomial| . |LeftModule|) 200003) ((|SequentialDifferentialPolynomial| . |LinearSet|) 199766) ((|SequentialDifferentialPolynomial| . |Module|) 199529) ((|SequentialDifferentialPolynomial| . |CharacteristicNonZero|) 199489) ((|SequentialDifferentialPolynomial| . |CharacteristicZero|) 199452) ((|SequentialDifferentialPolynomial| . |CommutativeRing|) 199305) ((|SequentialDifferentialPolynomial| . |Functorial|) 199289) ((|SequentialDifferentialPolynomial| . |IntegralDomain|) 199175) ((|SequentialDifferentialPolynomial| . |EntireRing|) 199061) ((|SequentialDifferentialPolynomial| . |AbelianMonoidRing|) 198978) ((|SequentialDifferentialPolynomial| . |FullyLinearlyExplicitRingOver|) 198962) ((|SequentialDifferentialPolynomial| . |LinearlyExplicitRingOver|) 198878) ((|SequentialDifferentialPolynomial| . |GcdDomain|) 198796) ((|SequentialDifferentialPolynomial| . |InnerEvalable|) 198623) ((|SequentialDifferentialPolynomial| . |PartialDifferentialRing|) 198501) ((|SequentialDifferentialPolynomial| . |PartialDifferentialDomain|) 198317) ((|SequentialDifferentialPolynomial| . |PartialDifferentialSpace|) 198137) ((|SequentialDifferentialPolynomial| . |PatternMatchable|) NIL) ((|SequentialDifferentialPolynomial| . |PolynomialFactorizationExplicit|) 198087) ((|SequentialDifferentialPolynomial| . |UniqueFactorizationDomain|) 198037) ((|SequentialDifferentialPolynomial| . |PolynomialCategory|) 197947) ((|SequentialDifferentialPolynomial| . |Evalable|) 197934) ((|SequentialDifferentialPolynomial| . |DifferentialRing|) 197899) ((|SequentialDifferentialPolynomial| . |CancellationAbelianMonoid|) T) ((|SequentialDifferentialPolynomial| . |AbelianSemiGroup|) T) ((|SequentialDifferentialPolynomial| . |BasicType|) T) ((|SequentialDifferentialPolynomial| . |CoercibleTo|) 197873) ((|SequentialDifferentialPolynomial| . |SetCategory|) T) ((|SequentialDifferentialPolynomial| . |AbelianMonoid|) T) ((|SequentialDifferentialPolynomial| . |AbelianGroup|) T) ((|SequentialDifferentialPolynomial| . |Rng|) T) ((|SequentialDifferentialPolynomial| . |SemiGroup|) T) ((|SequentialDifferentialPolynomial| . |SemiRing|) T) ((|SequentialDifferentialPolynomial| . |Monoid|) T) ((|SequentialDifferentialPolynomial| . |Ring|) T) ((|SequentialDifferentialPolynomial| . |DifferentialDomain|) 197792) ((|SequentialDifferentialPolynomial| . |Join|) T) ((|SequentialDifferentialPolynomial| . |Type|) T) ((|SequentialDifferentialPolynomial| . |DifferentialSpace|) 197717) ((|SequentialDifferentialPolynomial| . |DifferentialSpaceExtension|) 197701) ((|SequentialDifferentialPolynomial| . |DifferentialExtension|) 197685) ((|Scope| . |CoercibleTo|) 197659) ((|SingletonAsOrderedSet| . |OrderedSet|) T) ((|SingletonAsOrderedSet| . |CoercibleTo|) 197633) ((|SingletonAsOrderedSet| . |SetCategory|) T) ((|SingletonAsOrderedSet| . |BasicType|) T) ((|SingletonAsOrderedSet| . |Join|) T) ((|SingletonAsOrderedSet| . |Type|) T) ((|SingletonAsOrderedSet| . |OrderedType|) T) ((|SingletonAsOrderedSet| . |ConvertibleTo|) 197611) ((|SimpleAlgebraicExtension| . |MonogenicAlgebra|) 197590) ((|SimpleAlgebraicExtension| . |RetractableTo|) 197434) ((|SimpleAlgebraicExtension| . |FullyRetractableTo|) 197418) ((|SimpleAlgebraicExtension| . |LinearlyExplicitRingOver|) 197334) ((|SimpleAlgebraicExtension| . |LeftModule|) 197148) ((|SimpleAlgebraicExtension| . |FullyLinearlyExplicitRingOver|) 197132) ((|SimpleAlgebraicExtension| . |FiniteRankAlgebra|) 197111) ((|SimpleAlgebraicExtension| . |CharacteristicZero|) 197074) ((|SimpleAlgebraicExtension| . |CoercibleFrom|) 196821) ((|SimpleAlgebraicExtension| . |Module|) 196644) ((|SimpleAlgebraicExtension| . |LinearSet|) 196467) ((|SimpleAlgebraicExtension| . |LeftLinearSet|) 196329) ((|SimpleAlgebraicExtension| . |RightModule|) 196211) ((|SimpleAlgebraicExtension| . |RightLinearSet|) 196093) ((|SimpleAlgebraicExtension| . |BiModule|) 195961) ((|SimpleAlgebraicExtension| . |Algebra|) 195784) ((|SimpleAlgebraicExtension| . |FramedAlgebra|) 195763) ((|SimpleAlgebraicExtension| . |FieldOfPrimeCharacteristic|) 195725) ((|SimpleAlgebraicExtension| . |CharacteristicNonZero|) 195643) ((|SimpleAlgebraicExtension| . |StepThrough|) 195605) ((|SimpleAlgebraicExtension| . |FiniteFieldCategory|) 195567) ((|SimpleAlgebraicExtension| . |Finite|) 195500) ((|SimpleAlgebraicExtension| . |DivisionRing|) 195434) ((|SimpleAlgebraicExtension| . |EntireRing|) 195368) ((|SimpleAlgebraicExtension| . |EuclideanDomain|) 195302) ((|SimpleAlgebraicExtension| . |GcdDomain|) 195236) ((|SimpleAlgebraicExtension| . |IntegralDomain|) 195170) ((|SimpleAlgebraicExtension| . |PrincipalIdealDomain|) 195104) ((|SimpleAlgebraicExtension| . |UniqueFactorizationDomain|) 195038) ((|SimpleAlgebraicExtension| . |Field|) 194972) ((|SimpleAlgebraicExtension| . |DifferentialRing|) 194866) ((|SimpleAlgebraicExtension| . |DifferentialDomain|) 194690) ((|SimpleAlgebraicExtension| . |DifferentialSpace|) 194520) ((|SimpleAlgebraicExtension| . |DifferentialSpaceExtension|) 194487) ((|SimpleAlgebraicExtension| . |PartialDifferentialDomain|) 194301) ((|SimpleAlgebraicExtension| . |PartialDifferentialSpace|) 194117) ((|SimpleAlgebraicExtension| . |PartialDifferentialRing|) 194020) ((|SimpleAlgebraicExtension| . |DifferentialExtension|) 193987) ((|SimpleAlgebraicExtension| . |ConvertibleTo|) 193971) ((|SimpleAlgebraicExtension| . |AbelianGroup|) T) ((|SimpleAlgebraicExtension| . |AbelianMonoid|) T) ((|SimpleAlgebraicExtension| . |SetCategory|) T) ((|SimpleAlgebraicExtension| . |CoercibleTo|) 193945) ((|SimpleAlgebraicExtension| . |Type|) T) ((|SimpleAlgebraicExtension| . |Join|) T) ((|SimpleAlgebraicExtension| . |BasicType|) T) ((|SimpleAlgebraicExtension| . |AbelianSemiGroup|) T) ((|SimpleAlgebraicExtension| . |CancellationAbelianMonoid|) T) ((|SimpleAlgebraicExtension| . |Ring|) T) ((|SimpleAlgebraicExtension| . |Monoid|) T) ((|SimpleAlgebraicExtension| . |SemiRing|) T) ((|SimpleAlgebraicExtension| . |SemiGroup|) T) ((|SimpleAlgebraicExtension| . |Rng|) T) ((|SimpleAlgebraicExtension| . |CommutativeRing|) T) ((|Ruleset| . |SetCategory|) T) ((|Ruleset| . |CoercibleTo|) 193919) ((|Ruleset| . |Type|) T) ((|Ruleset| . |Join|) T) ((|Ruleset| . |BasicType|) T) ((|Ruleset| . |Eltable|) 193898) ((|RuleCalled| . |SetCategory|) T) ((|RuleCalled| . |CoercibleTo|) 193872) ((|RuleCalled| . |Type|) T) ((|RuleCalled| . |Join|) T) ((|RuleCalled| . |BasicType|) T) ((|RewriteRule| . |SetCategory|) T) ((|RewriteRule| . |CoercibleTo|) 193846) ((|RewriteRule| . |Type|) T) ((|RewriteRule| . |Join|) T) ((|RewriteRule| . |BasicType|) T) ((|RewriteRule| . |Eltable|) 193825) ((|RewriteRule| . |RetractableTo|) 193796) ((|RewriteRule| . |CoercibleFrom|) 193767) ((|RuntimeValue| . |Type|) T) ((|RuntimeValue| . |Join|) T) ((|RestrictAst| . |SpadSyntaxCategory|) T) ((|RestrictAst| . |HomotopicTo|) 193745) ((|RestrictAst| . |CoercibleTo|) 193700) ((|RestrictAst| . |CoercibleFrom|) 193678) ((|RestrictAst| . |SetCategory|) T) ((|RestrictAst| . |Type|) T) ((|RestrictAst| . |Join|) T) ((|RestrictAst| . |BasicType|) T) ((|RestrictAst| . |AbstractSyntaxCategory|) T) ((|RepeatAst| . |SpadSyntaxCategory|) T) ((|RepeatAst| . |HomotopicTo|) 193656) ((|RepeatAst| . |CoercibleTo|) 193611) ((|RepeatAst| . |CoercibleFrom|) 193589) ((|RepeatAst| . |SetCategory|) T) ((|RepeatAst| . |Type|) T) ((|RepeatAst| . |Join|) T) ((|RepeatAst| . |BasicType|) T) ((|RepeatAst| . |AbstractSyntaxCategory|) T) ((|RomanNumeral| . |IntegerNumberSystem|) T) ((|RomanNumeral| . |UniqueFactorizationDomain|) T) ((|RomanNumeral| . |StepThrough|) T) ((|RomanNumeral| . |RetractableTo|) 193566) ((|RomanNumeral| . |ConvertibleTo|) 193452) ((|RomanNumeral| . |RealConstant|) T) ((|RomanNumeral| . |PatternMatchable|) 193429) ((|RomanNumeral| . |OrderedRing|) T) ((|RomanNumeral| . |OrderedCancellationAbelianMonoid|) T) ((|RomanNumeral| . |OrderedAbelianSemiGroup|) T) ((|RomanNumeral| . |OrderedType|) T) ((|RomanNumeral| . |OrderedSet|) T) ((|RomanNumeral| . |OrderedAbelianMonoid|) T) ((|RomanNumeral| . |OrderedAbelianGroup|) T) ((|RomanNumeral| . |OrderedIntegralDomain|) T) ((|RomanNumeral| . |LeftModule|) 193396) ((|RomanNumeral| . |LinearlyExplicitRingOver|) 193373) ((|RomanNumeral| . |PrincipalIdealDomain|) T) ((|RomanNumeral| . |IntegralDomain|) T) ((|RomanNumeral| . |EntireRing|) T) ((|RomanNumeral| . |CommutativeRing|) T) ((|RomanNumeral| . |CoercibleFrom|) 193340) ((|RomanNumeral| . |Module|) 193327) ((|RomanNumeral| . |LinearSet|) 193314) ((|RomanNumeral| . |RightModule|) 193301) ((|RomanNumeral| . |RightLinearSet|) 193288) ((|RomanNumeral| . |BiModule|) 193273) ((|RomanNumeral| . |Algebra|) 193260) ((|RomanNumeral| . |GcdDomain|) T) ((|RomanNumeral| . |EuclideanDomain|) T) ((|RomanNumeral| . |DifferentialSpace|) T) ((|RomanNumeral| . |DifferentialDomain|) 193247) ((|RomanNumeral| . |DifferentialRing|) T) ((|RomanNumeral| . |CombinatorialFunctionCategory|) T) ((|RomanNumeral| . |Ring|) T) ((|RomanNumeral| . |Monoid|) T) ((|RomanNumeral| . |SemiRing|) T) ((|RomanNumeral| . |SemiGroup|) T) ((|RomanNumeral| . |Rng|) T) ((|RomanNumeral| . |AbelianGroup|) T) ((|RomanNumeral| . |LeftLinearSet|) 193214) ((|RomanNumeral| . |AbelianMonoid|) T) ((|RomanNumeral| . |SetCategory|) T) ((|RomanNumeral| . |CoercibleTo|) 193188) ((|RomanNumeral| . |Type|) T) ((|RomanNumeral| . |Join|) T) ((|RomanNumeral| . |BasicType|) T) ((|RomanNumeral| . |AbelianSemiGroup|) T) ((|RomanNumeral| . |CancellationAbelianMonoid|) T) ((|RomanNumeral| . |CharacteristicZero|) T) ((|RomanNumeral| . |ConvertibleFrom|) 193166) ((|RightOpenIntervalRootCharacterization| . |RealRootCharacterizationCategory|) 193145) ((|RightOpenIntervalRootCharacterization| . |BasicType|) T) ((|RightOpenIntervalRootCharacterization| . |Join|) T) ((|RightOpenIntervalRootCharacterization| . |Type|) T) ((|RightOpenIntervalRootCharacterization| . |CoercibleTo|) 193119) ((|RightOpenIntervalRootCharacterization| . |SetCategory|) T) ((|RangeBinding| . |Type|) T) ((|RangeBinding| . |Join|) T) ((|RangeBinding| . |SetCategory|) 193089) ((|RangeBinding| . |CoercibleTo|) 193040) ((|RangeBinding| . |BasicType|) 193010) ((|RectangularMatrix| . |RectangularMatrixCategory|) 192928) ((|RectangularMatrix| . |LinearSet|) 192857) ((|RectangularMatrix| . |Module|) 192786) ((|RectangularMatrix| . |HomogeneousAggregate|) 192770) ((|RectangularMatrix| . |Functorial|) 192754) ((|RectangularMatrix| . |InnerEvalable|) 192673) ((|RectangularMatrix| . |Evalable|) 192597) ((|RectangularMatrix| . |Aggregate|) T) ((|RectangularMatrix| . |FiniteAggregate|) 192581) ((|RectangularMatrix| . |LeftModule|) 192565) ((|RectangularMatrix| . |LeftLinearSet|) 192529) ((|RectangularMatrix| . |CancellationAbelianMonoid|) T) ((|RectangularMatrix| . |AbelianSemiGroup|) T) ((|RectangularMatrix| . |BasicType|) T) ((|RectangularMatrix| . |Join|) T) ((|RectangularMatrix| . |Type|) T) ((|RectangularMatrix| . |CoercibleTo|) 192479) ((|RectangularMatrix| . |SetCategory|) T) ((|RectangularMatrix| . |AbelianMonoid|) T) ((|RectangularMatrix| . |AbelianGroup|) T) ((|RectangularMatrix| . |RightModule|) 192463) ((|RectangularMatrix| . |RightLinearSet|) 192447) ((|RectangularMatrix| . |BiModule|) 192426) ((|RectangularMatrix| . |VectorSpace|) 192393) ((|RectangularMatrix| . |ConvertibleTo|) 192334) ((|RegularChain| . |RegularTriangularSetCategory|) 192216) ((|RegularChain| . |PolynomialSetCategory|) 192098) ((|RegularChain| . |FiniteAggregate|) 192017) ((|RegularChain| . |ConvertibleTo|) 191888) ((|RegularChain| . |HomogeneousAggregate|) 191807) ((|RegularChain| . |SetCategory|) T) ((|RegularChain| . |Functorial|) 191726) ((|RegularChain| . |InnerEvalable|) 191483) ((|RegularChain| . |Evalable|) 191247) ((|RegularChain| . |CoercibleTo|) 191134) ((|RegularChain| . |BasicType|) T) ((|RegularChain| . |Type|) T) ((|RegularChain| . |Join|) T) ((|RegularChain| . |Aggregate|) T) ((|RegularChain| . |Collection|) 191053) ((|RegularChain| . |ShallowlyMutableAggregate|) 190972) ((|RegularChain| . |TriangularSetCategory|) 190854) ((|ReturnAst| . |SpadSyntaxCategory|) T) ((|ReturnAst| . |HomotopicTo|) 190832) ((|ReturnAst| . |CoercibleTo|) 190787) ((|ReturnAst| . |CoercibleFrom|) 190765) ((|ReturnAst| . |SetCategory|) T) ((|ReturnAst| . |Type|) T) ((|ReturnAst| . |Join|) T) ((|ReturnAst| . |BasicType|) T) ((|ReturnAst| . |AbstractSyntaxCategory|) T) ((|ResidueRing| . |CommutativeRing|) T) ((|ResidueRing| . |CoercibleFrom|) 190729) ((|ResidueRing| . |Rng|) T) ((|ResidueRing| . |SemiGroup|) T) ((|ResidueRing| . |SemiRing|) T) ((|ResidueRing| . |Monoid|) T) ((|ResidueRing| . |Ring|) T) ((|ResidueRing| . |LeftModule|) 190703) ((|ResidueRing| . |LeftLinearSet|) 190657) ((|ResidueRing| . |CancellationAbelianMonoid|) T) ((|ResidueRing| . |AbelianSemiGroup|) T) ((|ResidueRing| . |BasicType|) T) ((|ResidueRing| . |Join|) T) ((|ResidueRing| . |Type|) T) ((|ResidueRing| . |CoercibleTo|) 190631) ((|ResidueRing| . |SetCategory|) T) ((|ResidueRing| . |AbelianMonoid|) T) ((|ResidueRing| . |AbelianGroup|) T) ((|ResidueRing| . |RightModule|) 190605) ((|ResidueRing| . |RightLinearSet|) 190579) ((|ResidueRing| . |BiModule|) 190546) ((|ResidueRing| . |Algebra|) 190530) ((|ResidueRing| . |LinearSet|) 190514) ((|ResidueRing| . |Module|) 190498) ((|RegularTriangularSet| . |RegularTriangularSetCategory|) 190467) ((|RegularTriangularSet| . |PolynomialSetCategory|) 190436) ((|RegularTriangularSet| . |FiniteAggregate|) 190420) ((|RegularTriangularSet| . |ConvertibleTo|) 190356) ((|RegularTriangularSet| . |HomogeneousAggregate|) 190340) ((|RegularTriangularSet| . |SetCategory|) T) ((|RegularTriangularSet| . |Functorial|) 190324) ((|RegularTriangularSet| . |InnerEvalable|) 190243) ((|RegularTriangularSet| . |Evalable|) 190167) ((|RegularTriangularSet| . |CoercibleTo|) 190119) ((|RegularTriangularSet| . |BasicType|) T) ((|RegularTriangularSet| . |Type|) T) ((|RegularTriangularSet| . |Join|) T) ((|RegularTriangularSet| . |Aggregate|) T) ((|RegularTriangularSet| . |Collection|) 190103) ((|RegularTriangularSet| . |ShallowlyMutableAggregate|) 190087) ((|RegularTriangularSet| . |TriangularSetCategory|) 190056) ((|Reference| . |SetCategory|) T) ((|Reference| . |CoercibleTo|) 190030) ((|Reference| . |Type|) T) ((|Reference| . |Join|) T) ((|Reference| . |BasicType|) T) ((|RealClosure| . |RealClosedField|) T) ((|RealClosure| . |RadicalCategory|) T) ((|RealClosure| . |OrderedAbelianGroup|) T) ((|RealClosure| . |OrderedAbelianMonoid|) T) ((|RealClosure| . |OrderedSet|) T) ((|RealClosure| . |OrderedType|) T) ((|RealClosure| . |OrderedAbelianSemiGroup|) T) ((|RealClosure| . |OrderedCancellationAbelianMonoid|) T) ((|RealClosure| . |OrderedRing|) T) ((|RealClosure| . |RetractableTo|) 189856) ((|RealClosure| . |FullyRetractableTo|) 189807) ((|RealClosure| . |DivisionRing|) T) ((|RealClosure| . |EntireRing|) T) ((|RealClosure| . |EuclideanDomain|) T) ((|RealClosure| . |GcdDomain|) T) ((|RealClosure| . |Algebra|) 189728) ((|RealClosure| . |LinearSet|) 189649) ((|RealClosure| . |Module|) 189570) ((|RealClosure| . |CoercibleFrom|) 189491) ((|RealClosure| . |IntegralDomain|) T) ((|RealClosure| . |PrincipalIdealDomain|) T) ((|RealClosure| . |UniqueFactorizationDomain|) T) ((|RealClosure| . |Field|) T) ((|RealClosure| . |BiModule|) 189391) ((|RealClosure| . |RightLinearSet|) 189312) ((|RealClosure| . |RightModule|) 189233) ((|RealClosure| . |CommutativeRing|) T) ((|RealClosure| . |CharacteristicZero|) T) ((|RealClosure| . |LeftModule|) 189154) ((|RealClosure| . |LeftLinearSet|) 189075) ((|RealClosure| . |CancellationAbelianMonoid|) T) ((|RealClosure| . |AbelianSemiGroup|) T) ((|RealClosure| . |BasicType|) T) ((|RealClosure| . |Join|) T) ((|RealClosure| . |Type|) T) ((|RealClosure| . |CoercibleTo|) 189049) ((|RealClosure| . |SetCategory|) T) ((|RealClosure| . |AbelianMonoid|) T) ((|RealClosure| . |AbelianGroup|) T) ((|RealClosure| . |Ring|) T) ((|RealClosure| . |Monoid|) T) ((|RealClosure| . |SemiRing|) T) ((|RealClosure| . |SemiGroup|) T) ((|RealClosure| . |Rng|) T) ((|ReduceAst| . |SpadSyntaxCategory|) T) ((|ReduceAst| . |HomotopicTo|) 189027) ((|ReduceAst| . |CoercibleTo|) 188982) ((|ReduceAst| . |CoercibleFrom|) 188960) ((|ReduceAst| . |SetCategory|) T) ((|ReduceAst| . |Type|) T) ((|ReduceAst| . |Join|) T) ((|ReduceAst| . |BasicType|) T) ((|ReduceAst| . |AbstractSyntaxCategory|) T) ((|RadixExpansion| . |QuotientFieldCategory|) 188937) ((|RadixExpansion| . |StepThrough|) T) ((|RadixExpansion| . |CoercibleFrom|) 188871) ((|RadixExpansion| . |RetractableTo|) 188815) ((|RadixExpansion| . |ConvertibleTo|) 188716) ((|RadixExpansion| . |RealConstant|) T) ((|RadixExpansion| . |PolynomialFactorizationExplicit|) NIL) ((|RadixExpansion| . |Patternable|) 188693) ((|RadixExpansion| . |OrderedRing|) T) ((|RadixExpansion| . |OrderedCancellationAbelianMonoid|) T) ((|RadixExpansion| . |OrderedAbelianSemiGroup|) T) ((|RadixExpansion| . |OrderedType|) T) ((|RadixExpansion| . |OrderedSet|) T) ((|RadixExpansion| . |OrderedAbelianMonoid|) T) ((|RadixExpansion| . |OrderedAbelianGroup|) T) ((|RadixExpansion| . |OrderedIntegralDomain|) T) ((|RadixExpansion| . |PatternMatchable|) 188670) ((|RadixExpansion| . |FullyPatternMatchable|) 188647) ((|RadixExpansion| . |LinearlyExplicitRingOver|) 188624) ((|RadixExpansion| . |FullyLinearlyExplicitRingOver|) 188601) ((|RadixExpansion| . |Eltable|) NIL) ((|RadixExpansion| . |Evalable|) NIL) ((|RadixExpansion| . |InnerEvalable|) NIL) ((|RadixExpansion| . |Functorial|) 188578) ((|RadixExpansion| . |FullyEvalableOver|) 188555) ((|RadixExpansion| . |DivisionRing|) T) ((|RadixExpansion| . |BiModule|) 188473) ((|RadixExpansion| . |RightLinearSet|) 188407) ((|RadixExpansion| . |RightModule|) 188341) ((|RadixExpansion| . |EntireRing|) T) ((|RadixExpansion| . |Module|) 188275) ((|RadixExpansion| . |LinearSet|) 188209) ((|RadixExpansion| . |LeftModule|) 188143) ((|RadixExpansion| . |LeftLinearSet|) 188077) ((|RadixExpansion| . |Algebra|) 188011) ((|RadixExpansion| . |EuclideanDomain|) T) ((|RadixExpansion| . |GcdDomain|) T) ((|RadixExpansion| . |CommutativeRing|) T) ((|RadixExpansion| . |IntegralDomain|) T) ((|RadixExpansion| . |PrincipalIdealDomain|) T) ((|RadixExpansion| . |UniqueFactorizationDomain|) T) ((|RadixExpansion| . |Field|) T) ((|RadixExpansion| . |DifferentialRing|) T) ((|RadixExpansion| . |DifferentialDomain|) 187998) ((|RadixExpansion| . |DifferentialSpace|) T) ((|RadixExpansion| . |DifferentialSpaceExtension|) 187975) ((|RadixExpansion| . |PartialDifferentialDomain|) NIL) ((|RadixExpansion| . |PartialDifferentialSpace|) NIL) ((|RadixExpansion| . |PartialDifferentialRing|) NIL) ((|RadixExpansion| . |DifferentialExtension|) 187952) ((|RadixExpansion| . |CharacteristicZero|) T) ((|RadixExpansion| . |CharacteristicNonZero|) NIL) ((|RadixExpansion| . |CancellationAbelianMonoid|) T) ((|RadixExpansion| . |AbelianSemiGroup|) T) ((|RadixExpansion| . |BasicType|) T) ((|RadixExpansion| . |Join|) T) ((|RadixExpansion| . |Type|) T) ((|RadixExpansion| . |CoercibleTo|) 187893) ((|RadixExpansion| . |SetCategory|) T) ((|RadixExpansion| . |AbelianMonoid|) T) ((|RadixExpansion| . |AbelianGroup|) T) ((|RadixExpansion| . |Ring|) T) ((|RadixExpansion| . |Monoid|) T) ((|RadixExpansion| . |SemiRing|) T) ((|RadixExpansion| . |SemiGroup|) T) ((|RadixExpansion| . |Rng|) T) ((|RadicalFunctionField| . |FunctionFieldCategory|) 187867) ((|RadicalFunctionField| . |CommutativeRing|) T) ((|RadicalFunctionField| . |CoercibleFrom|) 187775) ((|RadicalFunctionField| . |Rng|) T) ((|RadicalFunctionField| . |SemiGroup|) T) ((|RadicalFunctionField| . |SemiRing|) T) ((|RadicalFunctionField| . |Monoid|) T) ((|RadicalFunctionField| . |Ring|) T) ((|RadicalFunctionField| . |LeftModule|) 187633) ((|RadicalFunctionField| . |LeftLinearSet|) 187541) ((|RadicalFunctionField| . |CancellationAbelianMonoid|) T) ((|RadicalFunctionField| . |AbelianSemiGroup|) T) ((|RadicalFunctionField| . |BasicType|) T) ((|RadicalFunctionField| . |Join|) T) ((|RadicalFunctionField| . |Type|) T) ((|RadicalFunctionField| . |CoercibleTo|) 187515) ((|RadicalFunctionField| . |SetCategory|) T) ((|RadicalFunctionField| . |AbelianMonoid|) T) ((|RadicalFunctionField| . |AbelianGroup|) T) ((|RadicalFunctionField| . |RightModule|) 187443) ((|RadicalFunctionField| . |RightLinearSet|) 187371) ((|RadicalFunctionField| . |BiModule|) 187283) ((|RadicalFunctionField| . |ConvertibleTo|) 187267) ((|RadicalFunctionField| . |DifferentialExtension|) 187238) ((|RadicalFunctionField| . |PartialDifferentialRing|) 187157) ((|RadicalFunctionField| . |PartialDifferentialSpace|) 187005) ((|RadicalFunctionField| . |PartialDifferentialDomain|) 186851) ((|RadicalFunctionField| . |DifferentialSpaceExtension|) 186822) ((|RadicalFunctionField| . |DifferentialSpace|) 186721) ((|RadicalFunctionField| . |DifferentialDomain|) 186614) ((|RadicalFunctionField| . |DifferentialRing|) 186566) ((|RadicalFunctionField| . |Field|) T) ((|RadicalFunctionField| . |UniqueFactorizationDomain|) T) ((|RadicalFunctionField| . |PrincipalIdealDomain|) T) ((|RadicalFunctionField| . |IntegralDomain|) T) ((|RadicalFunctionField| . |Module|) 186494) ((|RadicalFunctionField| . |LinearSet|) 186422) ((|RadicalFunctionField| . |Algebra|) 186350) ((|RadicalFunctionField| . |GcdDomain|) T) ((|RadicalFunctionField| . |EuclideanDomain|) T) ((|RadicalFunctionField| . |EntireRing|) T) ((|RadicalFunctionField| . |DivisionRing|) T) ((|RadicalFunctionField| . |Finite|) NIL) ((|RadicalFunctionField| . |FiniteFieldCategory|) NIL) ((|RadicalFunctionField| . |StepThrough|) NIL) ((|RadicalFunctionField| . |CharacteristicNonZero|) 186297) ((|RadicalFunctionField| . |FieldOfPrimeCharacteristic|) NIL) ((|RadicalFunctionField| . |FramedAlgebra|) 186263) ((|RadicalFunctionField| . |CharacteristicZero|) 186213) ((|RadicalFunctionField| . |FiniteRankAlgebra|) 186179) ((|RadicalFunctionField| . |FullyLinearlyExplicitRingOver|) 186150) ((|RadicalFunctionField| . |LinearlyExplicitRingOver|) 186051) ((|RadicalFunctionField| . |FullyRetractableTo|) 186022) ((|RadicalFunctionField| . |RetractableTo|) 185852) ((|RadicalFunctionField| . |MonogenicAlgebra|) 185818) ((|Queue| . |QueueAggregate|) 185802) ((|Queue| . |FiniteAggregate|) 185786) ((|Queue| . |HomogeneousAggregate|) 185770) ((|Queue| . |SetCategory|) 185740) ((|Queue| . |Functorial|) 185724) ((|Queue| . |InnerEvalable|) 185643) ((|Queue| . |Evalable|) 185567) ((|Queue| . |CoercibleTo|) 185469) ((|Queue| . |BasicType|) 185407) ((|Queue| . |Type|) T) ((|Queue| . |Join|) T) ((|Queue| . |Aggregate|) T) ((|Queue| . |ShallowlyMutableAggregate|) 185391) ((|Queue| . |BagAggregate|) 185375) ((|Quaternion| . |QuaternionCategory|) 185359) ((|Quaternion| . |OrderedType|) 185330) ((|Quaternion| . |OrderedSet|) 185301) ((|Quaternion| . |RetractableTo|) 185145) ((|Quaternion| . |FullyRetractableTo|) 185129) ((|Quaternion| . |LinearlyExplicitRingOver|) 185045) ((|Quaternion| . |LeftModule|) 184901) ((|Quaternion| . |FullyLinearlyExplicitRingOver|) 184885) ((|Quaternion| . |Eltable|) 184838) ((|Quaternion| . |Evalable|) 184797) ((|Quaternion| . |InnerEvalable|) 184686) ((|Quaternion| . |Functorial|) 184670) ((|Quaternion| . |FullyEvalableOver|) 184654) ((|Quaternion| . |Algebra|) 184588) ((|Quaternion| . |BiModule|) 184448) ((|Quaternion| . |RightLinearSet|) 184322) ((|Quaternion| . |RightModule|) 184196) ((|Quaternion| . |LeftLinearSet|) 184100) ((|Quaternion| . |LinearSet|) 184034) ((|Quaternion| . |Module|) 183968) ((|Quaternion| . |CoercibleFrom|) 183821) ((|Quaternion| . |EntireRing|) 183764) ((|Quaternion| . |DivisionRing|) 183740) ((|Quaternion| . |DifferentialRing|) 183705) ((|Quaternion| . |DifferentialDomain|) 183624) ((|Quaternion| . |DifferentialSpace|) 183549) ((|Quaternion| . |DifferentialSpaceExtension|) 183533) ((|Quaternion| . |PartialDifferentialDomain|) 183405) ((|Quaternion| . |PartialDifferentialSpace|) 183279) ((|Quaternion| . |PartialDifferentialRing|) 183211) ((|Quaternion| . |DifferentialExtension|) 183195) ((|Quaternion| . |ConvertibleTo|) 183131) ((|Quaternion| . |CharacteristicZero|) 183094) ((|Quaternion| . |CharacteristicNonZero|) 183054) ((|Quaternion| . |CancellationAbelianMonoid|) T) ((|Quaternion| . |AbelianSemiGroup|) T) ((|Quaternion| . |BasicType|) T) ((|Quaternion| . |Join|) T) ((|Quaternion| . |Type|) T) ((|Quaternion| . |CoercibleTo|) 183028) ((|Quaternion| . |SetCategory|) T) ((|Quaternion| . |AbelianMonoid|) T) ((|Quaternion| . |AbelianGroup|) T) ((|Quaternion| . |Ring|) T) ((|Quaternion| . |Monoid|) T) ((|Quaternion| . |SemiRing|) T) ((|Quaternion| . |SemiGroup|) T) ((|Quaternion| . |Rng|) T) ((|QuasiquoteAst| . |SpadSyntaxCategory|) T) ((|QuasiquoteAst| . |HomotopicTo|) 183006) ((|QuasiquoteAst| . |CoercibleTo|) 182961) ((|QuasiquoteAst| . |CoercibleFrom|) 182939) ((|QuasiquoteAst| . |SetCategory|) T) ((|QuasiquoteAst| . |Type|) T) ((|QuasiquoteAst| . |Join|) T) ((|QuasiquoteAst| . |BasicType|) T) ((|QuasiquoteAst| . |AbstractSyntaxCategory|) T) ((|QuadraticForm| . |AbelianGroup|) T) ((|QuadraticForm| . |LeftLinearSet|) 182916) ((|QuadraticForm| . |AbelianMonoid|) T) ((|QuadraticForm| . |SetCategory|) T) ((|QuadraticForm| . |CoercibleTo|) 182890) ((|QuadraticForm| . |Type|) T) ((|QuadraticForm| . |Join|) T) ((|QuadraticForm| . |BasicType|) T) ((|QuadraticForm| . |AbelianSemiGroup|) T) ((|QuadraticForm| . |CancellationAbelianMonoid|) T) ((|QuadraticForm| . |Eltable|) 182846) ((|QueryEquation| . |CoercibleTo|) 182820) ((|QuasiAlgebraicSet| . |SetCategory|) T) ((|QuasiAlgebraicSet| . |CoercibleTo|) 182794) ((|QuasiAlgebraicSet| . |Type|) T) ((|QuasiAlgebraicSet| . |Join|) T) ((|QuasiAlgebraicSet| . |BasicType|) T) ((|Partition| . |OrderedCancellationAbelianMonoid|) T) ((|Partition| . |OrderedAbelianSemiGroup|) T) ((|Partition| . |OrderedType|) T) ((|Partition| . |OrderedSet|) T) ((|Partition| . |OrderedAbelianMonoid|) T) ((|Partition| . |AbelianMonoid|) T) ((|Partition| . |SetCategory|) T) ((|Partition| . |CoercibleTo|) 182731) ((|Partition| . |Type|) T) ((|Partition| . |Join|) T) ((|Partition| . |BasicType|) T) ((|Partition| . |AbelianSemiGroup|) T) ((|Partition| . |CancellationAbelianMonoid|) T) ((|PretendAst| . |SpadSyntaxCategory|) T) ((|PretendAst| . |HomotopicTo|) 182709) ((|PretendAst| . |CoercibleTo|) 182664) ((|PretendAst| . |CoercibleFrom|) 182642) ((|PretendAst| . |SetCategory|) T) ((|PretendAst| . |Type|) T) ((|PretendAst| . |Join|) T) ((|PretendAst| . |BasicType|) T) ((|PretendAst| . |AbstractSyntaxCategory|) T) ((|PropositionalFormula| . |PropositionalLogic|) T) ((|PropositionalFormula| . |BasicType|) T) ((|PropositionalFormula| . |CoercibleTo|) 182616) ((|PropositionalFormula| . |SetCategory|) T) ((|PropositionalFormula| . |Logic|) T) ((|PropositionalFormula| . |Join|) T) ((|PropositionalFormula| . |Type|) T) ((|PropositionalFormula| . |BooleanLogic|) T) ((|PropositionalFormula| . |CoercibleFrom|) 182600) ((|Property| . |CoercibleTo|) 182574) ((|Product| . |SetCategory|) T) ((|Product| . |CoercibleTo|) 182548) ((|Product| . |Type|) T) ((|Product| . |Join|) T) ((|Product| . |BasicType|) T) ((|Product| . |Finite|) 182493) ((|Product| . |Monoid|) 182381) ((|Product| . |SemiGroup|) 182269) ((|Product| . |AbelianMonoid|) 181949) ((|Product| . |AbelianSemiGroup|) 181629) ((|Product| . |CancellationAbelianMonoid|) 181377) ((|Product| . |Group|) 181324) ((|Product| . |AbelianGroup|) 181257) ((|Product| . |LeftLinearSet|) 181174) ((|Product| . |OrderedAbelianMonoidSup|) 181085) ((|Product| . |OrderedAbelianMonoid|) 180996) ((|Product| . |OrderedSet|) 180840) ((|Product| . |OrderedType|) 180684) ((|Product| . |OrderedAbelianSemiGroup|) 180595) ((|Product| . |OrderedCancellationAbelianMonoid|) 180506) ((|PrimitiveArray| . |OneDimensionalArrayAggregate|) 180490) ((|PrimitiveArray| . |ShallowlyMutableAggregate|) 180474) ((|PrimitiveArray| . |FiniteAggregate|) 180458) ((|PrimitiveArray| . |Aggregate|) T) ((|PrimitiveArray| . |Join|) T) ((|PrimitiveArray| . |Type|) T) ((|PrimitiveArray| . |BasicType|) 180368) ((|PrimitiveArray| . |CoercibleTo|) 180242) ((|PrimitiveArray| . |Evalable|) 180166) ((|PrimitiveArray| . |InnerEvalable|) 180085) ((|PrimitiveArray| . |Functorial|) 180069) ((|PrimitiveArray| . |SetCategory|) 180006) ((|PrimitiveArray| . |HomogeneousAggregate|) 179990) ((|PrimitiveArray| . |LinearAggregate|) 179974) ((|PrimitiveArray| . |EltableAggregate|) 179946) ((|PrimitiveArray| . |Eltable|) 179875) ((|PrimitiveArray| . |IndexedAggregate|) 179847) ((|PrimitiveArray| . |ConvertibleTo|) 179783) ((|PrimitiveArray| . |Collection|) 179767) ((|PrimitiveArray| . |OrderedSet|) 179738) ((|PrimitiveArray| . |OrderedType|) 179709) ((|PrimitiveArray| . |FiniteLinearAggregate|) 179693) ((|PolynomialRing| . |FiniteAbelianMonoidRing|) 179672) ((|PolynomialRing| . |RetractableTo|) 179516) ((|PolynomialRing| . |FullyRetractableTo|) 179500) ((|PolynomialRing| . |Algebra|) 179344) ((|PolynomialRing| . |CoercibleFrom|) 179134) ((|PolynomialRing| . |LeftModule|) 179031) ((|PolynomialRing| . |LeftLinearSet|) 178908) ((|PolynomialRing| . |Rng|) T) ((|PolynomialRing| . |SemiGroup|) T) ((|PolynomialRing| . |SemiRing|) T) ((|PolynomialRing| . |Monoid|) T) ((|PolynomialRing| . |Ring|) T) ((|PolynomialRing| . |BiModule|) 178727) ((|PolynomialRing| . |RightLinearSet|) 178560) ((|PolynomialRing| . |RightModule|) 178393) ((|PolynomialRing| . |AbelianGroup|) T) ((|PolynomialRing| . |AbelianMonoid|) T) ((|PolynomialRing| . |SetCategory|) T) ((|PolynomialRing| . |CoercibleTo|) 178367) ((|PolynomialRing| . |Type|) T) ((|PolynomialRing| . |Join|) T) ((|PolynomialRing| . |BasicType|) T) ((|PolynomialRing| . |AbelianSemiGroup|) T) ((|PolynomialRing| . |CancellationAbelianMonoid|) T) ((|PolynomialRing| . |LinearSet|) 178211) ((|PolynomialRing| . |Module|) 178055) ((|PolynomialRing| . |CharacteristicNonZero|) 178015) ((|PolynomialRing| . |CharacteristicZero|) 177978) ((|PolynomialRing| . |CommutativeRing|) 177907) ((|PolynomialRing| . |Functorial|) 177891) ((|PolynomialRing| . |IntegralDomain|) 177858) ((|PolynomialRing| . |EntireRing|) 177825) ((|PolynomialRing| . |AbelianMonoidRing|) 177804) ((|PortNumber| . |SetCategory|) T) ((|PortNumber| . |CoercibleTo|) 177752) ((|PortNumber| . |Type|) T) ((|PortNumber| . |Join|) T) ((|PortNumber| . |BasicType|) T) ((|Polynomial| . |PolynomialCategory|) 177697) ((|Polynomial| . |CoercibleFrom|) 177387) ((|Polynomial| . |RetractableTo|) 177212) ((|Polynomial| . |UniqueFactorizationDomain|) 177162) ((|Polynomial| . |PolynomialFactorizationExplicit|) 177112) ((|Polynomial| . |PatternMatchable|) 176993) ((|Polynomial| . |PartialDifferentialSpace|) 176971) ((|Polynomial| . |PartialDifferentialDomain|) 176947) ((|Polynomial| . |PartialDifferentialRing|) 176925) ((|Polynomial| . |InnerEvalable|) 176869) ((|Polynomial| . |GcdDomain|) 176787) ((|Polynomial| . |LinearlyExplicitRingOver|) 176703) ((|Polynomial| . |LeftModule|) 176532) ((|Polynomial| . |FullyLinearlyExplicitRingOver|) 176516) ((|Polynomial| . |AbelianMonoidRing|) 176468) ((|Polynomial| . |Algebra|) 176231) ((|Polynomial| . |LinearSet|) 175994) ((|Polynomial| . |Module|) 175757) ((|Polynomial| . |EntireRing|) 175643) ((|Polynomial| . |IntegralDomain|) 175529) ((|Polynomial| . |Functorial|) 175513) ((|Polynomial| . |BiModule|) 175256) ((|Polynomial| . |RightLinearSet|) 175013) ((|Polynomial| . |RightModule|) 174770) ((|Polynomial| . |CommutativeRing|) 174623) ((|Polynomial| . |CharacteristicZero|) 174586) ((|Polynomial| . |CharacteristicNonZero|) 174546) ((|Polynomial| . |LeftLinearSet|) 174423) ((|Polynomial| . |CancellationAbelianMonoid|) T) ((|Polynomial| . |AbelianSemiGroup|) T) ((|Polynomial| . |BasicType|) T) ((|Polynomial| . |Join|) T) ((|Polynomial| . |Type|) T) ((|Polynomial| . |CoercibleTo|) 174397) ((|Polynomial| . |SetCategory|) T) ((|Polynomial| . |AbelianMonoid|) T) ((|Polynomial| . |AbelianGroup|) T) ((|Polynomial| . |Ring|) T) ((|Polynomial| . |Monoid|) T) ((|Polynomial| . |SemiRing|) T) ((|Polynomial| . |SemiGroup|) T) ((|Polynomial| . |Rng|) T) ((|Polynomial| . |FullyRetractableTo|) 174381) ((|Polynomial| . |FiniteAbelianMonoidRing|) 174333) ((|Polynomial| . |Evalable|) 174320) ((|Polynomial| . |ConvertibleTo|) 174098) ((|Point| . |PointCategory|) 174082) ((|Point| . |OneDimensionalArrayAggregate|) 174066) ((|Point| . |ShallowlyMutableAggregate|) 174050) ((|Point| . |FiniteAggregate|) 174034) ((|Point| . |Aggregate|) T) ((|Point| . |Join|) T) ((|Point| . |Type|) T) ((|Point| . |BasicType|) 173944) ((|Point| . |CoercibleTo|) 173818) ((|Point| . |Evalable|) 173742) ((|Point| . |InnerEvalable|) 173661) ((|Point| . |Functorial|) 173645) ((|Point| . |SetCategory|) 173582) ((|Point| . |HomogeneousAggregate|) 173566) ((|Point| . |LinearAggregate|) 173550) ((|Point| . |EltableAggregate|) 173522) ((|Point| . |Eltable|) 173451) ((|Point| . |IndexedAggregate|) 173423) ((|Point| . |ConvertibleTo|) 173359) ((|Point| . |Collection|) 173343) ((|Point| . |OrderedSet|) 173314) ((|Point| . |OrderedType|) 173285) ((|Point| . |FiniteLinearAggregate|) 173269) ((|Point| . |VectorCategory|) 173253) ((|Point| . |ConvertibleFrom|) 173228) ((|Plot3D| . |PlottableSpaceCurveCategory|) T) ((|Plot3D| . |CoercibleTo|) 173202) ((|Plot| . |PlottablePlaneCurveCategory|) T) ((|Plot| . |CoercibleTo|) 173176) ((|PositiveInteger| . |OrderedAbelianSemiGroup|) T) ((|PositiveInteger| . |OrderedType|) T) ((|PositiveInteger| . |OrderedSet|) T) ((|PositiveInteger| . |SetCategory|) T) ((|PositiveInteger| . |CoercibleTo|) 173150) ((|PositiveInteger| . |Type|) T) ((|PositiveInteger| . |Join|) T) ((|PositiveInteger| . |BasicType|) T) ((|PositiveInteger| . |AbelianSemiGroup|) T) ((|PositiveInteger| . |Monoid|) T) ((|PositiveInteger| . |SemiGroup|) T) ((|PartialFraction| . |Field|) T) ((|PartialFraction| . |UniqueFactorizationDomain|) T) ((|PartialFraction| . |PrincipalIdealDomain|) T) ((|PartialFraction| . |IntegralDomain|) T) ((|PartialFraction| . |CommutativeRing|) T) ((|PartialFraction| . |CoercibleFrom|) 173071) ((|PartialFraction| . |Module|) 173012) ((|PartialFraction| . |LinearSet|) 172953) ((|PartialFraction| . |Algebra|) 172894) ((|PartialFraction| . |GcdDomain|) T) ((|PartialFraction| . |EuclideanDomain|) T) ((|PartialFraction| . |LeftModule|) 172835) ((|PartialFraction| . |LeftLinearSet|) 172756) ((|PartialFraction| . |Rng|) T) ((|PartialFraction| . |SemiGroup|) T) ((|PartialFraction| . |SemiRing|) T) ((|PartialFraction| . |Monoid|) T) ((|PartialFraction| . |Ring|) T) ((|PartialFraction| . |BiModule|) 172683) ((|PartialFraction| . |RightLinearSet|) 172624) ((|PartialFraction| . |RightModule|) 172565) ((|PartialFraction| . |AbelianGroup|) T) ((|PartialFraction| . |AbelianMonoid|) T) ((|PartialFraction| . |SetCategory|) T) ((|PartialFraction| . |CoercibleTo|) 172539) ((|PartialFraction| . |Type|) T) ((|PartialFraction| . |Join|) T) ((|PartialFraction| . |BasicType|) T) ((|PartialFraction| . |AbelianSemiGroup|) T) ((|PartialFraction| . |CancellationAbelianMonoid|) T) ((|PartialFraction| . |EntireRing|) T) ((|PartialFraction| . |DivisionRing|) T) ((|PrimeField| . |FiniteFieldCategory|) T) ((|PrimeField| . |StepThrough|) T) ((|PrimeField| . |Finite|) T) ((|PrimeField| . |CharacteristicNonZero|) T) ((|PrimeField| . |Field|) T) ((|PrimeField| . |UniqueFactorizationDomain|) T) ((|PrimeField| . |PrincipalIdealDomain|) T) ((|PrimeField| . |IntegralDomain|) T) ((|PrimeField| . |CommutativeRing|) T) ((|PrimeField| . |CoercibleFrom|) 172473) ((|PrimeField| . |Module|) 172427) ((|PrimeField| . |LinearSet|) 172381) ((|PrimeField| . |Algebra|) 172335) ((|PrimeField| . |GcdDomain|) T) ((|PrimeField| . |EuclideanDomain|) T) ((|PrimeField| . |BiModule|) 172280) ((|PrimeField| . |RightLinearSet|) 172234) ((|PrimeField| . |RightModule|) 172188) ((|PrimeField| . |LeftLinearSet|) 172122) ((|PrimeField| . |LeftModule|) 172076) ((|PrimeField| . |EntireRing|) T) ((|PrimeField| . |DivisionRing|) T) ((|PrimeField| . |FieldOfPrimeCharacteristic|) T) ((|PrimeField| . |DifferentialSpace|) T) ((|PrimeField| . |Type|) T) ((|PrimeField| . |Join|) T) ((|PrimeField| . |DifferentialDomain|) 172063) ((|PrimeField| . |Ring|) T) ((|PrimeField| . |Monoid|) T) ((|PrimeField| . |SemiRing|) T) ((|PrimeField| . |SemiGroup|) T) ((|PrimeField| . |Rng|) T) ((|PrimeField| . |AbelianGroup|) T) ((|PrimeField| . |AbelianMonoid|) T) ((|PrimeField| . |SetCategory|) T) ((|PrimeField| . |CoercibleTo|) 172037) ((|PrimeField| . |BasicType|) T) ((|PrimeField| . |AbelianSemiGroup|) T) ((|PrimeField| . |CancellationAbelianMonoid|) T) ((|PrimeField| . |DifferentialRing|) T) ((|PrimeField| . |FiniteAlgebraicExtensionField|) 172024) ((|PrimeField| . |CharacteristicZero|) 171990) ((|PrimeField| . |RetractableTo|) 171977) ((|PrimeField| . |VectorSpace|) 171964) ((|PrimeField| . |ExtensionField|) 171951) ((|PrimeField| . |ConvertibleTo|) 171928) ((|PermutationGroup| . |SetCategory|) T) ((|PermutationGroup| . |CoercibleTo|) 171902) ((|PermutationGroup| . |Type|) T) ((|PermutationGroup| . |Join|) T) ((|PermutationGroup| . |BasicType|) T) ((|Permutation| . |PermutationCategory|) 171886) ((|Permutation| . |OrderedType|) 171828) ((|Permutation| . |OrderedSet|) 171770) ((|Permutation| . |Monoid|) T) ((|Permutation| . |SetCategory|) T) ((|Permutation| . |CoercibleTo|) 171744) ((|Permutation| . |BasicType|) T) ((|Permutation| . |SemiGroup|) T) ((|Permutation| . |Group|) T) ((|Permutation| . |Type|) T) ((|Permutation| . |Join|) T) ((|Permutation| . |Eltable|) 171723) ((|PendantTree| . |BinaryRecursiveAggregate|) 171707) ((|PendantTree| . |HomogeneousAggregate|) 171691) ((|PendantTree| . |SetCategory|) 171661) ((|PendantTree| . |Functorial|) 171645) ((|PendantTree| . |InnerEvalable|) 171564) ((|PendantTree| . |Evalable|) 171488) ((|PendantTree| . |CoercibleTo|) 171368) ((|PendantTree| . |BasicType|) 171306) ((|PendantTree| . |Type|) T) ((|PendantTree| . |Join|) T) ((|PendantTree| . |Aggregate|) T) ((|PendantTree| . |RecursiveAggregate|) 171290) ((|PoincareBirkhoffWittLyndonBasis| . |OrderedSet|) T) ((|PoincareBirkhoffWittLyndonBasis| . |CoercibleTo|) 171264) ((|PoincareBirkhoffWittLyndonBasis| . |SetCategory|) T) ((|PoincareBirkhoffWittLyndonBasis| . |BasicType|) T) ((|PoincareBirkhoffWittLyndonBasis| . |Join|) T) ((|PoincareBirkhoffWittLyndonBasis| . |Type|) T) ((|PoincareBirkhoffWittLyndonBasis| . |OrderedType|) T) ((|PoincareBirkhoffWittLyndonBasis| . |RetractableTo|) 171233) ((|PoincareBirkhoffWittLyndonBasis| . |CoercibleFrom|) 171202) ((|Pattern| . |SetCategory|) T) ((|Pattern| . |CoercibleTo|) 171176) ((|Pattern| . |Type|) T) ((|Pattern| . |Join|) T) ((|Pattern| . |BasicType|) T) ((|Pattern| . |RetractableTo|) 171141) ((|Pattern| . |CoercibleFrom|) 171106) ((|PatternMatchResult| . |SetCategory|) T) ((|PatternMatchResult| . |CoercibleTo|) 171080) ((|PatternMatchResult| . |Type|) T) ((|PatternMatchResult| . |Join|) T) ((|PatternMatchResult| . |BasicType|) T) ((|PatternMatchListResult| . |SetCategory|) T) ((|PatternMatchListResult| . |CoercibleTo|) 171054) ((|PatternMatchListResult| . |Type|) T) ((|PatternMatchListResult| . |Join|) T) ((|PatternMatchListResult| . |BasicType|) T) ((|ParameterAst| . |SpadSyntaxCategory|) T) ((|ParameterAst| . |HomotopicTo|) 171032) ((|ParameterAst| . |CoercibleTo|) 170987) ((|ParameterAst| . |CoercibleFrom|) 170965) ((|ParameterAst| . |SetCategory|) T) ((|ParameterAst| . |Type|) T) ((|ParameterAst| . |Join|) T) ((|ParameterAst| . |BasicType|) T) ((|ParameterAst| . |AbstractSyntaxCategory|) T) ((|ParameterAst| . |UnionType|) T) ((|Palette| . |SetCategory|) T) ((|Palette| . |CoercibleTo|) 170939) ((|Palette| . |Type|) T) ((|Palette| . |Join|) T) ((|Palette| . |BasicType|) T) ((|Palette| . |CoercibleFrom|) 170918) ((|Pair| . |Type|) T) ((|Pair| . |Join|) T) ((|Pair| . |CoercibleTo|) 170735) ((|Pair| . |SetCategory|) 170670) ((|Pair| . |BasicType|) 170605) ((|PAdicRationalConstructor| . |QuotientFieldCategory|) 170589) ((|PAdicRationalConstructor| . |StepThrough|) 170559) ((|PAdicRationalConstructor| . |RetractableTo|) 170378) ((|PAdicRationalConstructor| . |CoercibleFrom|) 170244) ((|PAdicRationalConstructor| . |ConvertibleTo|) 169947) ((|PAdicRationalConstructor| . |RealConstant|) 169916) ((|PAdicRationalConstructor| . |PolynomialFactorizationExplicit|) 169866) ((|PAdicRationalConstructor| . |Patternable|) 169850) ((|PAdicRationalConstructor| . |OrderedRing|) 169810) ((|PAdicRationalConstructor| . |OrderedCancellationAbelianMonoid|) 169770) ((|PAdicRationalConstructor| . |OrderedAbelianSemiGroup|) 169730) ((|PAdicRationalConstructor| . |OrderedType|) 169657) ((|PAdicRationalConstructor| . |OrderedSet|) 169584) ((|PAdicRationalConstructor| . |OrderedAbelianMonoid|) 169544) ((|PAdicRationalConstructor| . |OrderedAbelianGroup|) 169504) ((|PAdicRationalConstructor| . |OrderedIntegralDomain|) 169464) ((|PAdicRationalConstructor| . |PatternMatchable|) 169345) ((|PAdicRationalConstructor| . |FullyPatternMatchable|) 169329) ((|PAdicRationalConstructor| . |LinearlyExplicitRingOver|) 169245) ((|PAdicRationalConstructor| . |LeftModule|) 169118) ((|PAdicRationalConstructor| . |FullyLinearlyExplicitRingOver|) 169102) ((|PAdicRationalConstructor| . |Eltable|) 169055) ((|PAdicRationalConstructor| . |Evalable|) 169014) ((|PAdicRationalConstructor| . |InnerEvalable|) 168903) ((|PAdicRationalConstructor| . |Functorial|) 168887) ((|PAdicRationalConstructor| . |FullyEvalableOver|) 168871) ((|PAdicRationalConstructor| . |DivisionRing|) T) ((|PAdicRationalConstructor| . |BiModule|) 168798) ((|PAdicRationalConstructor| . |RightLinearSet|) 168739) ((|PAdicRationalConstructor| . |RightModule|) 168680) ((|PAdicRationalConstructor| . |EntireRing|) T) ((|PAdicRationalConstructor| . |Module|) 168621) ((|PAdicRationalConstructor| . |LinearSet|) 168562) ((|PAdicRationalConstructor| . |LeftLinearSet|) 168483) ((|PAdicRationalConstructor| . |Algebra|) 168424) ((|PAdicRationalConstructor| . |EuclideanDomain|) T) ((|PAdicRationalConstructor| . |GcdDomain|) T) ((|PAdicRationalConstructor| . |CommutativeRing|) T) ((|PAdicRationalConstructor| . |IntegralDomain|) T) ((|PAdicRationalConstructor| . |PrincipalIdealDomain|) T) ((|PAdicRationalConstructor| . |UniqueFactorizationDomain|) T) ((|PAdicRationalConstructor| . |Field|) T) ((|PAdicRationalConstructor| . |DifferentialRing|) 168389) ((|PAdicRationalConstructor| . |DifferentialDomain|) 168308) ((|PAdicRationalConstructor| . |DifferentialSpace|) 168233) ((|PAdicRationalConstructor| . |DifferentialSpaceExtension|) 168217) ((|PAdicRationalConstructor| . |PartialDifferentialDomain|) 168089) ((|PAdicRationalConstructor| . |PartialDifferentialSpace|) 167963) ((|PAdicRationalConstructor| . |PartialDifferentialRing|) 167895) ((|PAdicRationalConstructor| . |DifferentialExtension|) 167879) ((|PAdicRationalConstructor| . |CharacteristicZero|) 167798) ((|PAdicRationalConstructor| . |CharacteristicNonZero|) 167758) ((|PAdicRationalConstructor| . |CancellationAbelianMonoid|) T) ((|PAdicRationalConstructor| . |AbelianSemiGroup|) T) ((|PAdicRationalConstructor| . |BasicType|) T) ((|PAdicRationalConstructor| . |Join|) T) ((|PAdicRationalConstructor| . |Type|) T) ((|PAdicRationalConstructor| . |CoercibleTo|) 167732) ((|PAdicRationalConstructor| . |SetCategory|) T) ((|PAdicRationalConstructor| . |AbelianMonoid|) T) ((|PAdicRationalConstructor| . |AbelianGroup|) T) ((|PAdicRationalConstructor| . |Ring|) T) ((|PAdicRationalConstructor| . |Monoid|) T) ((|PAdicRationalConstructor| . |SemiRing|) T) ((|PAdicRationalConstructor| . |SemiGroup|) T) ((|PAdicRationalConstructor| . |Rng|) T) ((|PAdicRational| . |QuotientFieldCategory|) 167699) ((|PAdicRational| . |StepThrough|) NIL) ((|PAdicRational| . |RetractableTo|) 167666) ((|PAdicRational| . |CoercibleFrom|) 167570) ((|PAdicRational| . |ConvertibleTo|) NIL) ((|PAdicRational| . |RealConstant|) NIL) ((|PAdicRational| . |PolynomialFactorizationExplicit|) NIL) ((|PAdicRational| . |Patternable|) 167537) ((|PAdicRational| . |OrderedRing|) NIL) ((|PAdicRational| . |OrderedCancellationAbelianMonoid|) NIL) ((|PAdicRational| . |OrderedAbelianSemiGroup|) NIL) ((|PAdicRational| . |OrderedType|) NIL) ((|PAdicRational| . |OrderedSet|) NIL) ((|PAdicRational| . |OrderedAbelianMonoid|) NIL) ((|PAdicRational| . |OrderedAbelianGroup|) NIL) ((|PAdicRational| . |OrderedIntegralDomain|) NIL) ((|PAdicRational| . |PatternMatchable|) NIL) ((|PAdicRational| . |FullyPatternMatchable|) 167504) ((|PAdicRational| . |LinearlyExplicitRingOver|) 167471) ((|PAdicRational| . |LeftModule|) 167395) ((|PAdicRational| . |FullyLinearlyExplicitRingOver|) 167362) ((|PAdicRational| . |Eltable|) 167298) ((|PAdicRational| . |Evalable|) 167239) ((|PAdicRational| . |InnerEvalable|) 167114) ((|PAdicRational| . |Functorial|) 167081) ((|PAdicRational| . |FullyEvalableOver|) 167048) ((|PAdicRational| . |DivisionRing|) T) ((|PAdicRational| . |BiModule|) 166956) ((|PAdicRational| . |RightLinearSet|) 166880) ((|PAdicRational| . |RightModule|) 166804) ((|PAdicRational| . |EntireRing|) T) ((|PAdicRational| . |Module|) 166728) ((|PAdicRational| . |LinearSet|) 166652) ((|PAdicRational| . |LeftLinearSet|) 166556) ((|PAdicRational| . |Algebra|) 166480) ((|PAdicRational| . |EuclideanDomain|) T) ((|PAdicRational| . |GcdDomain|) T) ((|PAdicRational| . |CommutativeRing|) T) ((|PAdicRational| . |IntegralDomain|) T) ((|PAdicRational| . |PrincipalIdealDomain|) T) ((|PAdicRational| . |UniqueFactorizationDomain|) T) ((|PAdicRational| . |Field|) T) ((|PAdicRational| . |DifferentialRing|) NIL) ((|PAdicRational| . |DifferentialDomain|) NIL) ((|PAdicRational| . |DifferentialSpace|) NIL) ((|PAdicRational| . |DifferentialSpaceExtension|) 166447) ((|PAdicRational| . |PartialDifferentialDomain|) NIL) ((|PAdicRational| . |PartialDifferentialSpace|) NIL) ((|PAdicRational| . |PartialDifferentialRing|) NIL) ((|PAdicRational| . |DifferentialExtension|) 166414) ((|PAdicRational| . |CharacteristicZero|) T) ((|PAdicRational| . |CharacteristicNonZero|) NIL) ((|PAdicRational| . |CancellationAbelianMonoid|) T) ((|PAdicRational| . |AbelianSemiGroup|) T) ((|PAdicRational| . |BasicType|) T) ((|PAdicRational| . |Join|) T) ((|PAdicRational| . |Type|) T) ((|PAdicRational| . |CoercibleTo|) 166388) ((|PAdicRational| . |SetCategory|) T) ((|PAdicRational| . |AbelianMonoid|) T) ((|PAdicRational| . |AbelianGroup|) T) ((|PAdicRational| . |Ring|) T) ((|PAdicRational| . |Monoid|) T) ((|PAdicRational| . |SemiRing|) T) ((|PAdicRational| . |SemiGroup|) T) ((|PAdicRational| . |Rng|) T) ((|PAdicInteger| . |PAdicIntegerCategory|) 166372) ((|PAdicInteger| . |PrincipalIdealDomain|) T) ((|PAdicInteger| . |IntegralDomain|) T) ((|PAdicInteger| . |EntireRing|) T) ((|PAdicInteger| . |CommutativeRing|) T) ((|PAdicInteger| . |CoercibleFrom|) 166339) ((|PAdicInteger| . |Module|) 166326) ((|PAdicInteger| . |LinearSet|) 166313) ((|PAdicInteger| . |RightModule|) 166300) ((|PAdicInteger| . |RightLinearSet|) 166287) ((|PAdicInteger| . |BiModule|) 166272) ((|PAdicInteger| . |Algebra|) 166259) ((|PAdicInteger| . |GcdDomain|) T) ((|PAdicInteger| . |EuclideanDomain|) T) ((|PAdicInteger| . |Ring|) T) ((|PAdicInteger| . |Monoid|) T) ((|PAdicInteger| . |SemiRing|) T) ((|PAdicInteger| . |SemiGroup|) T) ((|PAdicInteger| . |Rng|) T) ((|PAdicInteger| . |AbelianGroup|) T) ((|PAdicInteger| . |LeftLinearSet|) 166226) ((|PAdicInteger| . |AbelianMonoid|) T) ((|PAdicInteger| . |SetCategory|) T) ((|PAdicInteger| . |CoercibleTo|) 166200) ((|PAdicInteger| . |Type|) T) ((|PAdicInteger| . |Join|) T) ((|PAdicInteger| . |BasicType|) T) ((|PAdicInteger| . |AbelianSemiGroup|) T) ((|PAdicInteger| . |CancellationAbelianMonoid|) T) ((|PAdicInteger| . |LeftModule|) 166187) ((|PAdicInteger| . |CharacteristicZero|) T) ((|OrdinaryWeightedPolynomials| . |Ring|) T) ((|OrdinaryWeightedPolynomials| . |Monoid|) T) ((|OrdinaryWeightedPolynomials| . |SemiRing|) T) ((|OrdinaryWeightedPolynomials| . |SemiGroup|) T) ((|OrdinaryWeightedPolynomials| . |Rng|) T) ((|OrdinaryWeightedPolynomials| . |AbelianGroup|) T) ((|OrdinaryWeightedPolynomials| . |LeftLinearSet|) 166114) ((|OrdinaryWeightedPolynomials| . |AbelianMonoid|) T) ((|OrdinaryWeightedPolynomials| . |SetCategory|) T) ((|OrdinaryWeightedPolynomials| . |CoercibleTo|) 166060) ((|OrdinaryWeightedPolynomials| . |Type|) T) ((|OrdinaryWeightedPolynomials| . |Join|) T) ((|OrdinaryWeightedPolynomials| . |BasicType|) T) ((|OrdinaryWeightedPolynomials| . |AbelianSemiGroup|) T) ((|OrdinaryWeightedPolynomials| . |CancellationAbelianMonoid|) T) ((|OrdinaryWeightedPolynomials| . |LeftModule|) 166007) ((|OrdinaryWeightedPolynomials| . |CoercibleFrom|) 165916) ((|OrdinaryWeightedPolynomials| . |HomotopicTo|) 165885) ((|OrdinaryWeightedPolynomials| . |Algebra|) 165842) ((|OrdinaryWeightedPolynomials| . |BiModule|) 165794) ((|OrdinaryWeightedPolynomials| . |RightLinearSet|) 165751) ((|OrdinaryWeightedPolynomials| . |RightModule|) 165708) ((|OrdinaryWeightedPolynomials| . |LinearSet|) 165665) ((|OrdinaryWeightedPolynomials| . |Module|) 165622) ((|OverloadSet| . |SetCategory|) T) ((|OverloadSet| . |CoercibleTo|) 165596) ((|OverloadSet| . |Type|) T) ((|OverloadSet| . |Join|) T) ((|OverloadSet| . |BasicType|) T) ((|OrderedVariableList| . |OrderedFinite|) T) ((|OrderedVariableList| . |OrderedType|) T) ((|OrderedVariableList| . |OrderedSet|) T) ((|OrderedVariableList| . |SetCategory|) T) ((|OrderedVariableList| . |CoercibleTo|) 165570) ((|OrderedVariableList| . |Type|) T) ((|OrderedVariableList| . |Join|) T) ((|OrderedVariableList| . |BasicType|) T) ((|OrderedVariableList| . |Finite|) T) ((|OrderedVariableList| . |ConvertibleTo|) 165464) ((|OutputForm| . |SetCategory|) T) ((|OutputForm| . |CoercibleTo|) 165438) ((|OutputForm| . |Type|) T) ((|OutputForm| . |Join|) T) ((|OutputForm| . |BasicType|) T) ((|OutputBinaryFile| . |OutputByteConduit|) T) ((|OutputBinaryFile| . |Conduit|) T) ((|OutputBinaryFile| . |CoercibleTo|) 165412) ((|OrdSetInts| . |OrderedSet|) T) ((|OrdSetInts| . |CoercibleTo|) 165386) ((|OrdSetInts| . |SetCategory|) T) ((|OrdSetInts| . |BasicType|) T) ((|OrdSetInts| . |Join|) T) ((|OrdSetInts| . |Type|) T) ((|OrdSetInts| . |OrderedType|) T) ((|UnivariateSkewPolynomial| . |UnivariateSkewPolynomialCategory|) 165370) ((|UnivariateSkewPolynomial| . |RetractableTo|) 165214) ((|UnivariateSkewPolynomial| . |CoercibleFrom|) 165069) ((|UnivariateSkewPolynomial| . |FullyRetractableTo|) 165053) ((|UnivariateSkewPolynomial| . |Module|) 165010) ((|UnivariateSkewPolynomial| . |LinearSet|) 164967) ((|UnivariateSkewPolynomial| . |LeftModule|) 164941) ((|UnivariateSkewPolynomial| . |LeftLinearSet|) 164895) ((|UnivariateSkewPolynomial| . |CancellationAbelianMonoid|) T) ((|UnivariateSkewPolynomial| . |AbelianSemiGroup|) T) ((|UnivariateSkewPolynomial| . |BasicType|) T) ((|UnivariateSkewPolynomial| . |Join|) T) ((|UnivariateSkewPolynomial| . |Type|) T) ((|UnivariateSkewPolynomial| . |CoercibleTo|) 164869) ((|UnivariateSkewPolynomial| . |SetCategory|) T) ((|UnivariateSkewPolynomial| . |AbelianMonoid|) T) ((|UnivariateSkewPolynomial| . |AbelianGroup|) T) ((|UnivariateSkewPolynomial| . |RightModule|) 164853) ((|UnivariateSkewPolynomial| . |RightLinearSet|) 164837) ((|UnivariateSkewPolynomial| . |BiModule|) 164816) ((|UnivariateSkewPolynomial| . |Ring|) T) ((|UnivariateSkewPolynomial| . |Monoid|) T) ((|UnivariateSkewPolynomial| . |SemiRing|) T) ((|UnivariateSkewPolynomial| . |SemiGroup|) T) ((|UnivariateSkewPolynomial| . |Rng|) T) ((|UnivariateSkewPolynomial| . |Algebra|) 164773) ((|SparseUnivariateSkewPolynomial| . |UnivariateSkewPolynomialCategory|) 164757) ((|SparseUnivariateSkewPolynomial| . |RetractableTo|) 164601) ((|SparseUnivariateSkewPolynomial| . |CoercibleFrom|) 164482) ((|SparseUnivariateSkewPolynomial| . |FullyRetractableTo|) 164466) ((|SparseUnivariateSkewPolynomial| . |Module|) 164423) ((|SparseUnivariateSkewPolynomial| . |LinearSet|) 164380) ((|SparseUnivariateSkewPolynomial| . |LeftModule|) 164354) ((|SparseUnivariateSkewPolynomial| . |LeftLinearSet|) 164308) ((|SparseUnivariateSkewPolynomial| . |CancellationAbelianMonoid|) T) ((|SparseUnivariateSkewPolynomial| . |AbelianSemiGroup|) T) ((|SparseUnivariateSkewPolynomial| . |BasicType|) T) ((|SparseUnivariateSkewPolynomial| . |Join|) T) ((|SparseUnivariateSkewPolynomial| . |Type|) T) ((|SparseUnivariateSkewPolynomial| . |CoercibleTo|) 164282) ((|SparseUnivariateSkewPolynomial| . |SetCategory|) T) ((|SparseUnivariateSkewPolynomial| . |AbelianMonoid|) T) ((|SparseUnivariateSkewPolynomial| . |AbelianGroup|) T) ((|SparseUnivariateSkewPolynomial| . |RightModule|) 164266) ((|SparseUnivariateSkewPolynomial| . |RightLinearSet|) 164250) ((|SparseUnivariateSkewPolynomial| . |BiModule|) 164229) ((|SparseUnivariateSkewPolynomial| . |Ring|) T) ((|SparseUnivariateSkewPolynomial| . |Monoid|) T) ((|SparseUnivariateSkewPolynomial| . |SemiRing|) T) ((|SparseUnivariateSkewPolynomial| . |SemiGroup|) T) ((|SparseUnivariateSkewPolynomial| . |Rng|) T) ((|SparseUnivariateSkewPolynomial| . |Algebra|) 164186) ((|OrderedStructure| . |OrderedType|) T) ((|OrderedStructure| . |Type|) T) ((|OrderedStructure| . |Join|) T) ((|OrderedStructure| . |BasicType|) T) ((|OrderedStructure| . |HomotopicTo|) 164170) ((|OrderedStructure| . |CoercibleTo|) 164099) ((|OrderedStructure| . |CoercibleFrom|) 164083) ((|OrderedCompletion| . |SetCategory|) T) ((|OrderedCompletion| . |CoercibleTo|) 164057) ((|OrderedCompletion| . |Type|) T) ((|OrderedCompletion| . |Join|) T) ((|OrderedCompletion| . |BasicType|) T) ((|OrderedCompletion| . |FullyRetractableTo|) 164041) ((|OrderedCompletion| . |CoercibleFrom|) 163851) ((|OrderedCompletion| . |RetractableTo|) 163695) ((|OrderedCompletion| . |AbelianGroup|) 163630) ((|OrderedCompletion| . |LeftLinearSet|) 163516) ((|OrderedCompletion| . |AbelianMonoid|) 163451) ((|OrderedCompletion| . |AbelianSemiGroup|) 163386) ((|OrderedCompletion| . |CancellationAbelianMonoid|) 163321) ((|OrderedCompletion| . |OrderedRing|) 163291) ((|OrderedCompletion| . |OrderedCancellationAbelianMonoid|) 163261) ((|OrderedCompletion| . |OrderedAbelianSemiGroup|) 163231) ((|OrderedCompletion| . |OrderedType|) 163201) ((|OrderedCompletion| . |OrderedSet|) 163171) ((|OrderedCompletion| . |OrderedAbelianMonoid|) 163141) ((|OrderedCompletion| . |OrderedAbelianGroup|) 163111) ((|OrderedCompletion| . |Ring|) 163081) ((|OrderedCompletion| . |Monoid|) 163051) ((|OrderedCompletion| . |SemiRing|) 163021) ((|OrderedCompletion| . |SemiGroup|) 162991) ((|OrderedCompletion| . |Rng|) 162961) ((|OrderedCompletion| . |LeftModule|) 162925) ((|OrderedCompletion| . |CharacteristicZero|) 162895) ((|OperatorSignature| . |OperatorCategory|) 162869) ((|OperatorSignature| . |BasicType|) T) ((|OperatorSignature| . |Join|) T) ((|OperatorSignature| . |Type|) T) ((|OperatorSignature| . |CoercibleTo|) 162843) ((|OperatorSignature| . |SetCategory|) T) ((|Operator| . |Ring|) T) ((|Operator| . |Monoid|) T) ((|Operator| . |SemiRing|) T) ((|Operator| . |SemiGroup|) T) ((|Operator| . |Rng|) T) ((|Operator| . |AbelianGroup|) T) ((|Operator| . |LeftLinearSet|) 162770) ((|Operator| . |AbelianMonoid|) T) ((|Operator| . |SetCategory|) T) ((|Operator| . |CoercibleTo|) 162744) ((|Operator| . |Type|) T) ((|Operator| . |Join|) T) ((|Operator| . |BasicType|) T) ((|Operator| . |AbelianSemiGroup|) T) ((|Operator| . |CancellationAbelianMonoid|) T) ((|Operator| . |LeftModule|) 162691) ((|Operator| . |CoercibleFrom|) 162629) ((|Operator| . |RetractableTo|) 162587) ((|Operator| . |Eltable|) 162566) ((|Operator| . |CharacteristicZero|) 162529) ((|Operator| . |CharacteristicNonZero|) 162489) ((|Operator| . |Algebra|) 162446) ((|Operator| . |BiModule|) 162398) ((|Operator| . |RightLinearSet|) 162355) ((|Operator| . |RightModule|) 162312) ((|Operator| . |LinearSet|) 162269) ((|Operator| . |Module|) 162226) ((|OnePointCompletion| . |SetCategory|) T) ((|OnePointCompletion| . |CoercibleTo|) 162200) ((|OnePointCompletion| . |Type|) T) ((|OnePointCompletion| . |Join|) T) ((|OnePointCompletion| . |BasicType|) T) ((|OnePointCompletion| . |FullyRetractableTo|) 162184) ((|OnePointCompletion| . |CoercibleFrom|) 161994) ((|OnePointCompletion| . |RetractableTo|) 161838) ((|OnePointCompletion| . |AbelianGroup|) 161773) ((|OnePointCompletion| . |LeftLinearSet|) 161659) ((|OnePointCompletion| . |AbelianMonoid|) 161594) ((|OnePointCompletion| . |AbelianSemiGroup|) 161529) ((|OnePointCompletion| . |CancellationAbelianMonoid|) 161464) ((|OnePointCompletion| . |OrderedRing|) 161434) ((|OnePointCompletion| . |OrderedCancellationAbelianMonoid|) 161404) ((|OnePointCompletion| . |OrderedAbelianSemiGroup|) 161374) ((|OnePointCompletion| . |OrderedType|) 161344) ((|OnePointCompletion| . |OrderedSet|) 161314) ((|OnePointCompletion| . |OrderedAbelianMonoid|) 161284) ((|OnePointCompletion| . |OrderedAbelianGroup|) 161254) ((|OnePointCompletion| . |Ring|) 161224) ((|OnePointCompletion| . |Monoid|) 161194) ((|OnePointCompletion| . |SemiRing|) 161164) ((|OnePointCompletion| . |SemiGroup|) 161134) ((|OnePointCompletion| . |Rng|) 161104) ((|OnePointCompletion| . |LeftModule|) 161068) ((|OnePointCompletion| . |CharacteristicZero|) 161038) ((|OppositeMonogenicLinearOperator| . |MonogenicLinearOperator|) 161022) ((|OppositeMonogenicLinearOperator| . |CoercibleFrom|) 160959) ((|OppositeMonogenicLinearOperator| . |Module|) 160916) ((|OppositeMonogenicLinearOperator| . |LinearSet|) 160873) ((|OppositeMonogenicLinearOperator| . |LeftModule|) 160847) ((|OppositeMonogenicLinearOperator| . |LeftLinearSet|) 160801) ((|OppositeMonogenicLinearOperator| . |CancellationAbelianMonoid|) T) ((|OppositeMonogenicLinearOperator| . |AbelianSemiGroup|) T) ((|OppositeMonogenicLinearOperator| . |BasicType|) T) ((|OppositeMonogenicLinearOperator| . |Join|) T) ((|OppositeMonogenicLinearOperator| . |Type|) T) ((|OppositeMonogenicLinearOperator| . |CoercibleTo|) 160775) ((|OppositeMonogenicLinearOperator| . |SetCategory|) T) ((|OppositeMonogenicLinearOperator| . |AbelianMonoid|) T) ((|OppositeMonogenicLinearOperator| . |AbelianGroup|) T) ((|OppositeMonogenicLinearOperator| . |RightModule|) 160759) ((|OppositeMonogenicLinearOperator| . |RightLinearSet|) 160743) ((|OppositeMonogenicLinearOperator| . |BiModule|) 160722) ((|OppositeMonogenicLinearOperator| . |Ring|) T) ((|OppositeMonogenicLinearOperator| . |Monoid|) T) ((|OppositeMonogenicLinearOperator| . |SemiRing|) T) ((|OppositeMonogenicLinearOperator| . |SemiGroup|) T) ((|OppositeMonogenicLinearOperator| . |Rng|) T) ((|OppositeMonogenicLinearOperator| . |Algebra|) 160679) ((|OppositeMonogenicLinearOperator| . |DifferentialRing|) 160644) ((|OppositeMonogenicLinearOperator| . |DifferentialDomain|) 160603) ((|OppositeMonogenicLinearOperator| . |DifferentialSpace|) 160568) ((|OrderedFreeMonoid| . |FreeMonoidCategory|) 160552) ((|OrderedFreeMonoid| . |CoercibleFrom|) 160536) ((|OrderedFreeMonoid| . |RetractableTo|) 160520) ((|OrderedFreeMonoid| . |OrderedType|) T) ((|OrderedFreeMonoid| . |OrderedSet|) T) ((|OrderedFreeMonoid| . |SemiGroup|) T) ((|OrderedFreeMonoid| . |BasicType|) T) ((|OrderedFreeMonoid| . |Join|) T) ((|OrderedFreeMonoid| . |Type|) T) ((|OrderedFreeMonoid| . |CoercibleTo|) 160494) ((|OrderedFreeMonoid| . |SetCategory|) T) ((|OrderedFreeMonoid| . |Monoid|) T) ((|OrderedFreeMonoid| . |OrderedMonoid|) T) ((|OrderedFreeMonoid| . |OrderedSemiGroup|) T) ((|OrderlyDifferentialVariable| . |DifferentialVariableCategory|) 160478) ((|OrderlyDifferentialVariable| . |CoercibleFrom|) 160462) ((|OrderlyDifferentialVariable| . |RetractableTo|) 160446) ((|OrderlyDifferentialVariable| . |OrderedType|) T) ((|OrderlyDifferentialVariable| . |BasicType|) T) ((|OrderlyDifferentialVariable| . |SetCategory|) T) ((|OrderlyDifferentialVariable| . |CoercibleTo|) 160420) ((|OrderlyDifferentialVariable| . |OrderedSet|) T) ((|OrderlyDifferentialVariable| . |DifferentialDomain|) 160407) ((|OrderlyDifferentialVariable| . |Join|) T) ((|OrderlyDifferentialVariable| . |Type|) T) ((|OrderlyDifferentialVariable| . |DifferentialSpace|) T) ((|OrdinaryDifferentialRing| . |BiModule|) 160335) ((|OrdinaryDifferentialRing| . |RightLinearSet|) 160272) ((|OrdinaryDifferentialRing| . |RightModule|) 160209) ((|OrdinaryDifferentialRing| . |AbelianGroup|) T) ((|OrdinaryDifferentialRing| . |LeftLinearSet|) 160126) ((|OrdinaryDifferentialRing| . |AbelianMonoid|) T) ((|OrdinaryDifferentialRing| . |SetCategory|) T) ((|OrdinaryDifferentialRing| . |CoercibleTo|) 160087) ((|OrdinaryDifferentialRing| . |Type|) T) ((|OrdinaryDifferentialRing| . |Join|) T) ((|OrdinaryDifferentialRing| . |BasicType|) T) ((|OrdinaryDifferentialRing| . |AbelianSemiGroup|) T) ((|OrdinaryDifferentialRing| . |CancellationAbelianMonoid|) T) ((|OrdinaryDifferentialRing| . |LeftModule|) 160024) ((|OrdinaryDifferentialRing| . |DifferentialRing|) T) ((|OrdinaryDifferentialRing| . |CoercibleFrom|) 159919) ((|OrdinaryDifferentialRing| . |Rng|) T) ((|OrdinaryDifferentialRing| . |SemiGroup|) T) ((|OrdinaryDifferentialRing| . |SemiRing|) T) ((|OrdinaryDifferentialRing| . |Monoid|) T) ((|OrdinaryDifferentialRing| . |Ring|) T) ((|OrdinaryDifferentialRing| . |DifferentialDomain|) 159906) ((|OrdinaryDifferentialRing| . |DifferentialSpace|) T) ((|OrdinaryDifferentialRing| . |HomotopicTo|) 159890) ((|OrdinaryDifferentialRing| . |Field|) 159866) ((|OrdinaryDifferentialRing| . |UniqueFactorizationDomain|) 159842) ((|OrdinaryDifferentialRing| . |PrincipalIdealDomain|) 159818) ((|OrdinaryDifferentialRing| . |IntegralDomain|) 159794) ((|OrdinaryDifferentialRing| . |CommutativeRing|) 159770) ((|OrdinaryDifferentialRing| . |Module|) 159698) ((|OrdinaryDifferentialRing| . |LinearSet|) 159626) ((|OrdinaryDifferentialRing| . |Algebra|) 159554) ((|OrdinaryDifferentialRing| . |GcdDomain|) 159530) ((|OrdinaryDifferentialRing| . |EuclideanDomain|) 159506) ((|OrdinaryDifferentialRing| . |EntireRing|) 159482) ((|OrdinaryDifferentialRing| . |DivisionRing|) 159458) ((|OrderlyDifferentialPolynomial| . |DifferentialPolynomialCategory|) 159364) ((|OrderlyDifferentialPolynomial| . |CoercibleFrom|) 158957) ((|OrderlyDifferentialPolynomial| . |RetractableTo|) 158685) ((|OrderlyDifferentialPolynomial| . |ConvertibleTo|) NIL) ((|OrderlyDifferentialPolynomial| . |FiniteAbelianMonoidRing|) 158605) ((|OrderlyDifferentialPolynomial| . |FullyRetractableTo|) 158589) ((|OrderlyDifferentialPolynomial| . |Algebra|) 158352) ((|OrderlyDifferentialPolynomial| . |BiModule|) 158095) ((|OrderlyDifferentialPolynomial| . |RightLinearSet|) 157852) ((|OrderlyDifferentialPolynomial| . |RightModule|) 157609) ((|OrderlyDifferentialPolynomial| . |LeftLinearSet|) 157486) ((|OrderlyDifferentialPolynomial| . |LeftModule|) 157315) ((|OrderlyDifferentialPolynomial| . |LinearSet|) 157078) ((|OrderlyDifferentialPolynomial| . |Module|) 156841) ((|OrderlyDifferentialPolynomial| . |CharacteristicNonZero|) 156801) ((|OrderlyDifferentialPolynomial| . |CharacteristicZero|) 156764) ((|OrderlyDifferentialPolynomial| . |CommutativeRing|) 156617) ((|OrderlyDifferentialPolynomial| . |Functorial|) 156601) ((|OrderlyDifferentialPolynomial| . |IntegralDomain|) 156487) ((|OrderlyDifferentialPolynomial| . |EntireRing|) 156373) ((|OrderlyDifferentialPolynomial| . |AbelianMonoidRing|) 156293) ((|OrderlyDifferentialPolynomial| . |FullyLinearlyExplicitRingOver|) 156277) ((|OrderlyDifferentialPolynomial| . |LinearlyExplicitRingOver|) 156193) ((|OrderlyDifferentialPolynomial| . |GcdDomain|) 156111) ((|OrderlyDifferentialPolynomial| . |InnerEvalable|) 155941) ((|OrderlyDifferentialPolynomial| . |PartialDifferentialRing|) 155822) ((|OrderlyDifferentialPolynomial| . |PartialDifferentialDomain|) 155641) ((|OrderlyDifferentialPolynomial| . |PartialDifferentialSpace|) 155464) ((|OrderlyDifferentialPolynomial| . |PatternMatchable|) NIL) ((|OrderlyDifferentialPolynomial| . |PolynomialFactorizationExplicit|) 155414) ((|OrderlyDifferentialPolynomial| . |UniqueFactorizationDomain|) 155364) ((|OrderlyDifferentialPolynomial| . |PolynomialCategory|) 155277) ((|OrderlyDifferentialPolynomial| . |Evalable|) 155264) ((|OrderlyDifferentialPolynomial| . |DifferentialRing|) 155229) ((|OrderlyDifferentialPolynomial| . |CancellationAbelianMonoid|) T) ((|OrderlyDifferentialPolynomial| . |AbelianSemiGroup|) T) ((|OrderlyDifferentialPolynomial| . |BasicType|) T) ((|OrderlyDifferentialPolynomial| . |CoercibleTo|) 155203) ((|OrderlyDifferentialPolynomial| . |SetCategory|) T) ((|OrderlyDifferentialPolynomial| . |AbelianMonoid|) T) ((|OrderlyDifferentialPolynomial| . |AbelianGroup|) T) ((|OrderlyDifferentialPolynomial| . |Rng|) T) ((|OrderlyDifferentialPolynomial| . |SemiGroup|) T) ((|OrderlyDifferentialPolynomial| . |SemiRing|) T) ((|OrderlyDifferentialPolynomial| . |Monoid|) T) ((|OrderlyDifferentialPolynomial| . |Ring|) T) ((|OrderlyDifferentialPolynomial| . |DifferentialDomain|) 155122) ((|OrderlyDifferentialPolynomial| . |Join|) T) ((|OrderlyDifferentialPolynomial| . |Type|) T) ((|OrderlyDifferentialPolynomial| . |DifferentialSpace|) 155047) ((|OrderlyDifferentialPolynomial| . |DifferentialSpaceExtension|) 155031) ((|OrderlyDifferentialPolynomial| . |DifferentialExtension|) 155015) ((|OrderedDirectProduct| . |DirectProductCategory|) 154994) ((|OrderedDirectProduct| . |VectorSpace|) 154961) ((|OrderedDirectProduct| . |OrderedCancellationAbelianMonoid|) 154919) ((|OrderedDirectProduct| . |OrderedAbelianSemiGroup|) 154877) ((|OrderedDirectProduct| . |OrderedType|) 154802) ((|OrderedDirectProduct| . |OrderedSet|) 154727) ((|OrderedDirectProduct| . |OrderedAbelianMonoid|) 154685) ((|OrderedDirectProduct| . |OrderedAbelianMonoidSup|) 154643) ((|OrderedDirectProduct| . |Module|) 154572) ((|OrderedDirectProduct| . |LinearSet|) 154477) ((|OrderedDirectProduct| . |EltableAggregate|) 154449) ((|OrderedDirectProduct| . |Eltable|) 154421) ((|OrderedDirectProduct| . |IndexedAggregate|) 154393) ((|OrderedDirectProduct| . |RetractableTo|) 154144) ((|OrderedDirectProduct| . |CoercibleFrom|) 153868) ((|OrderedDirectProduct| . |FullyRetractableTo|) 153829) ((|OrderedDirectProduct| . |LinearlyExplicitRingOver|) 153701) ((|OrderedDirectProduct| . |LeftModule|) 153486) ((|OrderedDirectProduct| . |FullyLinearlyExplicitRingOver|) 153454) ((|OrderedDirectProduct| . |HomogeneousAggregate|) 153438) ((|OrderedDirectProduct| . |Functorial|) 153422) ((|OrderedDirectProduct| . |InnerEvalable|) 153341) ((|OrderedDirectProduct| . |Evalable|) 153265) ((|OrderedDirectProduct| . |Aggregate|) T) ((|OrderedDirectProduct| . |FiniteAggregate|) 153249) ((|OrderedDirectProduct| . |Finite|) 153224) ((|OrderedDirectProduct| . |DifferentialRing|) 153161) ((|OrderedDirectProduct| . |LeftLinearSet|) 152891) ((|OrderedDirectProduct| . |Rng|) 152868) ((|OrderedDirectProduct| . |SemiGroup|) 152845) ((|OrderedDirectProduct| . |SemiRing|) 152822) ((|OrderedDirectProduct| . |Monoid|) 152799) ((|OrderedDirectProduct| . |Ring|) 152776) ((|OrderedDirectProduct| . |DifferentialDomain|) 152639) ((|OrderedDirectProduct| . |DifferentialSpace|) 152508) ((|OrderedDirectProduct| . |DifferentialSpaceExtension|) 152476) ((|OrderedDirectProduct| . |PartialDifferentialDomain|) 152292) ((|OrderedDirectProduct| . |PartialDifferentialSpace|) 152110) ((|OrderedDirectProduct| . |PartialDifferentialRing|) 152014) ((|OrderedDirectProduct| . |DifferentialExtension|) 151982) ((|OrderedDirectProduct| . |CoercibleTo|) 151527) ((|OrderedDirectProduct| . |RightModule|) 151434) ((|OrderedDirectProduct| . |RightLinearSet|) 151317) ((|OrderedDirectProduct| . |BiModule|) 151219) ((|OrderedDirectProduct| . |CancellationAbelianMonoid|) 151021) ((|OrderedDirectProduct| . |AbelianSemiGroup|) 150758) ((|OrderedDirectProduct| . |BasicType|) 150363) ((|OrderedDirectProduct| . |Join|) T) ((|OrderedDirectProduct| . |Type|) T) ((|OrderedDirectProduct| . |SetCategory|) 149995) ((|OrderedDirectProduct| . |AbelianMonoid|) 149766) ((|OrderedDirectProduct| . |AbelianGroup|) 149652) ((|Octonion| . |OctonionCategory|) 149636) ((|Octonion| . |OrderedType|) 149607) ((|Octonion| . |OrderedSet|) 149578) ((|Octonion| . |RetractableTo|) 149255) ((|Octonion| . |CoercibleFrom|) 149032) ((|Octonion| . |FullyRetractableTo|) 148988) ((|Octonion| . |Eltable|) 148941) ((|Octonion| . |Evalable|) 148900) ((|Octonion| . |InnerEvalable|) 148789) ((|Octonion| . |Functorial|) 148773) ((|Octonion| . |FullyEvalableOver|) 148757) ((|Octonion| . |Finite|) 148732) ((|Octonion| . |ConvertibleTo|) 148668) ((|Octonion| . |CharacteristicZero|) 148631) ((|Octonion| . |CharacteristicNonZero|) 148591) ((|Octonion| . |Module|) 148575) ((|Octonion| . |LinearSet|) 148559) ((|Octonion| . |LeftModule|) 148533) ((|Octonion| . |LeftLinearSet|) 148487) ((|Octonion| . |CancellationAbelianMonoid|) T) ((|Octonion| . |AbelianSemiGroup|) T) ((|Octonion| . |BasicType|) T) ((|Octonion| . |Join|) T) ((|Octonion| . |Type|) T) ((|Octonion| . |CoercibleTo|) 148461) ((|Octonion| . |SetCategory|) T) ((|Octonion| . |AbelianMonoid|) T) ((|Octonion| . |AbelianGroup|) T) ((|Octonion| . |RightModule|) 148445) ((|Octonion| . |RightLinearSet|) 148429) ((|Octonion| . |BiModule|) 148408) ((|Octonion| . |Ring|) T) ((|Octonion| . |Monoid|) T) ((|Octonion| . |SemiRing|) T) ((|Octonion| . |SemiGroup|) T) ((|Octonion| . |Rng|) T) ((|Octonion| . |Algebra|) 148392) ((|NewSparseUnivariatePolynomial| . |UnivariatePolynomialCategory|) 148376) ((|NewSparseUnivariatePolynomial| . |StepThrough|) 148346) ((|NewSparseUnivariatePolynomial| . |ConvertibleTo|) NIL) ((|NewSparseUnivariatePolynomial| . |Evalable|) 148333) ((|NewSparseUnivariatePolynomial| . |InnerEvalable|) 148262) ((|NewSparseUnivariatePolynomial| . |FiniteAbelianMonoidRing|) 148223) ((|NewSparseUnivariatePolynomial| . |RetractableTo|) 147989) ((|NewSparseUnivariatePolynomial| . |FullyRetractableTo|) 147973) ((|NewSparseUnivariatePolynomial| . |Algebra|) 147713) ((|NewSparseUnivariatePolynomial| . |BiModule|) 147433) ((|NewSparseUnivariatePolynomial| . |RightLinearSet|) 147167) ((|NewSparseUnivariatePolynomial| . |RightModule|) 146901) ((|NewSparseUnivariatePolynomial| . |LeftLinearSet|) 146778) ((|NewSparseUnivariatePolynomial| . |LeftModule|) 146607) ((|NewSparseUnivariatePolynomial| . |LinearSet|) 146347) ((|NewSparseUnivariatePolynomial| . |Module|) 146087) ((|NewSparseUnivariatePolynomial| . |CoercibleFrom|) 145695) ((|NewSparseUnivariatePolynomial| . |CharacteristicNonZero|) 145655) ((|NewSparseUnivariatePolynomial| . |CharacteristicZero|) 145618) ((|NewSparseUnivariatePolynomial| . |Functorial|) 145602) ((|NewSparseUnivariatePolynomial| . |AbelianMonoidRing|) 145563) ((|NewSparseUnivariatePolynomial| . |FullyLinearlyExplicitRingOver|) 145547) ((|NewSparseUnivariatePolynomial| . |LinearlyExplicitRingOver|) 145463) ((|NewSparseUnivariatePolynomial| . |PartialDifferentialRing|) 145361) ((|NewSparseUnivariatePolynomial| . |PartialDifferentialDomain|) 145197) ((|NewSparseUnivariatePolynomial| . |PartialDifferentialSpace|) 145037) ((|NewSparseUnivariatePolynomial| . |PatternMatchable|) NIL) ((|NewSparseUnivariatePolynomial| . |PolynomialFactorizationExplicit|) 144987) ((|NewSparseUnivariatePolynomial| . |UniqueFactorizationDomain|) 144937) ((|NewSparseUnivariatePolynomial| . |PolynomialCategory|) 144872) ((|NewSparseUnivariatePolynomial| . |PrincipalIdealDomain|) 144848) ((|NewSparseUnivariatePolynomial| . |IntegralDomain|) 144711) ((|NewSparseUnivariatePolynomial| . |EntireRing|) 144574) ((|NewSparseUnivariatePolynomial| . |CommutativeRing|) 144404) ((|NewSparseUnivariatePolynomial| . |GcdDomain|) 144299) ((|NewSparseUnivariatePolynomial| . |EuclideanDomain|) 144275) ((|NewSparseUnivariatePolynomial| . |Eltable|) 144178) ((|NewSparseUnivariatePolynomial| . |DifferentialRing|) T) ((|NewSparseUnivariatePolynomial| . |CancellationAbelianMonoid|) T) ((|NewSparseUnivariatePolynomial| . |AbelianSemiGroup|) T) ((|NewSparseUnivariatePolynomial| . |BasicType|) T) ((|NewSparseUnivariatePolynomial| . |CoercibleTo|) 144108) ((|NewSparseUnivariatePolynomial| . |SetCategory|) T) ((|NewSparseUnivariatePolynomial| . |AbelianMonoid|) T) ((|NewSparseUnivariatePolynomial| . |AbelianGroup|) T) ((|NewSparseUnivariatePolynomial| . |Rng|) T) ((|NewSparseUnivariatePolynomial| . |SemiGroup|) T) ((|NewSparseUnivariatePolynomial| . |SemiRing|) T) ((|NewSparseUnivariatePolynomial| . |Monoid|) T) ((|NewSparseUnivariatePolynomial| . |Ring|) T) ((|NewSparseUnivariatePolynomial| . |DifferentialDomain|) 144095) ((|NewSparseUnivariatePolynomial| . |Join|) T) ((|NewSparseUnivariatePolynomial| . |Type|) T) ((|NewSparseUnivariatePolynomial| . |DifferentialSpace|) T) ((|NewSparseUnivariatePolynomial| . |DifferentialSpaceExtension|) 144079) ((|NewSparseUnivariatePolynomial| . |DifferentialExtension|) 144063) ((|NewSparseMultivariatePolynomial| . |RecursivePolynomialCategory|) 144016) ((|NewSparseMultivariatePolynomial| . |ConvertibleTo|) 143455) ((|NewSparseMultivariatePolynomial| . |Evalable|) 143442) ((|NewSparseMultivariatePolynomial| . |InnerEvalable|) 143394) ((|NewSparseMultivariatePolynomial| . |FiniteAbelianMonoidRing|) 143352) ((|NewSparseMultivariatePolynomial| . |RetractableTo|) 143132) ((|NewSparseMultivariatePolynomial| . |FullyRetractableTo|) 143116) ((|NewSparseMultivariatePolynomial| . |Algebra|) 142879) ((|NewSparseMultivariatePolynomial| . |CoercibleFrom|) 142524) ((|NewSparseMultivariatePolynomial| . |LeftModule|) 142353) ((|NewSparseMultivariatePolynomial| . |LeftLinearSet|) 142230) ((|NewSparseMultivariatePolynomial| . |Rng|) T) ((|NewSparseMultivariatePolynomial| . |SemiGroup|) T) ((|NewSparseMultivariatePolynomial| . |SemiRing|) T) ((|NewSparseMultivariatePolynomial| . |Monoid|) T) ((|NewSparseMultivariatePolynomial| . |Ring|) T) ((|NewSparseMultivariatePolynomial| . |BiModule|) 141973) ((|NewSparseMultivariatePolynomial| . |RightLinearSet|) 141730) ((|NewSparseMultivariatePolynomial| . |RightModule|) 141487) ((|NewSparseMultivariatePolynomial| . |AbelianGroup|) T) ((|NewSparseMultivariatePolynomial| . |AbelianMonoid|) T) ((|NewSparseMultivariatePolynomial| . |SetCategory|) T) ((|NewSparseMultivariatePolynomial| . |CoercibleTo|) 141346) ((|NewSparseMultivariatePolynomial| . |Type|) T) ((|NewSparseMultivariatePolynomial| . |Join|) T) ((|NewSparseMultivariatePolynomial| . |BasicType|) T) ((|NewSparseMultivariatePolynomial| . |AbelianSemiGroup|) T) ((|NewSparseMultivariatePolynomial| . |CancellationAbelianMonoid|) T) ((|NewSparseMultivariatePolynomial| . |LinearSet|) 141109) ((|NewSparseMultivariatePolynomial| . |Module|) 140872) ((|NewSparseMultivariatePolynomial| . |CharacteristicNonZero|) 140832) ((|NewSparseMultivariatePolynomial| . |CharacteristicZero|) 140795) ((|NewSparseMultivariatePolynomial| . |CommutativeRing|) 140648) ((|NewSparseMultivariatePolynomial| . |Functorial|) 140632) ((|NewSparseMultivariatePolynomial| . |IntegralDomain|) 140518) ((|NewSparseMultivariatePolynomial| . |EntireRing|) 140404) ((|NewSparseMultivariatePolynomial| . |AbelianMonoidRing|) 140362) ((|NewSparseMultivariatePolynomial| . |FullyLinearlyExplicitRingOver|) 140346) ((|NewSparseMultivariatePolynomial| . |LinearlyExplicitRingOver|) 140262) ((|NewSparseMultivariatePolynomial| . |GcdDomain|) 140180) ((|NewSparseMultivariatePolynomial| . |PartialDifferentialRing|) 140164) ((|NewSparseMultivariatePolynomial| . |PartialDifferentialDomain|) 140146) ((|NewSparseMultivariatePolynomial| . |PartialDifferentialSpace|) 140130) ((|NewSparseMultivariatePolynomial| . |PatternMatchable|) 139909) ((|NewSparseMultivariatePolynomial| . |PolynomialFactorizationExplicit|) 139859) ((|NewSparseMultivariatePolynomial| . |UniqueFactorizationDomain|) 139809) ((|NewSparseMultivariatePolynomial| . |PolynomialCategory|) 139762) ((|None| . |SetCategory|) T) ((|None| . |CoercibleTo|) 139736) ((|None| . |Type|) T) ((|None| . |Join|) T) ((|None| . |BasicType|) T) ((|NonNegativeInteger| . |OrderedAbelianMonoidSup|) T) ((|NonNegativeInteger| . |CancellationAbelianMonoid|) T) ((|NonNegativeInteger| . |AbelianSemiGroup|) T) ((|NonNegativeInteger| . |BasicType|) T) ((|NonNegativeInteger| . |Join|) T) ((|NonNegativeInteger| . |Type|) T) ((|NonNegativeInteger| . |CoercibleTo|) 139710) ((|NonNegativeInteger| . |SetCategory|) T) ((|NonNegativeInteger| . |AbelianMonoid|) T) ((|NonNegativeInteger| . |OrderedAbelianMonoid|) T) ((|NonNegativeInteger| . |OrderedSet|) T) ((|NonNegativeInteger| . |OrderedType|) T) ((|NonNegativeInteger| . |OrderedAbelianSemiGroup|) T) ((|NonNegativeInteger| . |OrderedCancellationAbelianMonoid|) T) ((|NonNegativeInteger| . |Monoid|) T) ((|NonNegativeInteger| . |SemiGroup|) T) ((|Multiset| . |MultisetAggregate|) 139694) ((|Multiset| . |SetAggregate|) 139678) ((|Multiset| . |DictionaryOperations|) 139662) ((|Multiset| . |ConvertibleTo|) 139598) ((|Multiset| . |Collection|) 139582) ((|Multiset| . |HomogeneousAggregate|) 139566) ((|Multiset| . |SetCategory|) T) ((|Multiset| . |Functorial|) 139550) ((|Multiset| . |InnerEvalable|) 139469) ((|Multiset| . |Evalable|) 139393) ((|Multiset| . |CoercibleTo|) 139367) ((|Multiset| . |BasicType|) T) ((|Multiset| . |Type|) T) ((|Multiset| . |Join|) T) ((|Multiset| . |Aggregate|) T) ((|Multiset| . |ShallowlyMutableAggregate|) 139351) ((|Multiset| . |BagAggregate|) 139335) ((|Multiset| . |MultiDictionary|) 139319) ((|Multiset| . |FiniteAggregate|) 139303) ((|MonoidRing| . |Ring|) T) ((|MonoidRing| . |Monoid|) T) ((|MonoidRing| . |SemiRing|) T) ((|MonoidRing| . |SemiGroup|) T) ((|MonoidRing| . |Rng|) T) ((|MonoidRing| . |AbelianGroup|) T) ((|MonoidRing| . |LeftLinearSet|) 139230) ((|MonoidRing| . |AbelianMonoid|) T) ((|MonoidRing| . |SetCategory|) T) ((|MonoidRing| . |CoercibleTo|) 139204) ((|MonoidRing| . |Type|) T) ((|MonoidRing| . |Join|) T) ((|MonoidRing| . |BasicType|) T) ((|MonoidRing| . |AbelianSemiGroup|) T) ((|MonoidRing| . |CancellationAbelianMonoid|) T) ((|MonoidRing| . |LeftModule|) 139151) ((|MonoidRing| . |CoercibleFrom|) 139102) ((|MonoidRing| . |RetractableTo|) 139073) ((|MonoidRing| . |Functorial|) 139057) ((|MonoidRing| . |CharacteristicZero|) 139020) ((|MonoidRing| . |CharacteristicNonZero|) 138980) ((|MonoidRing| . |Algebra|) 138937) ((|MonoidRing| . |BiModule|) 138889) ((|MonoidRing| . |RightLinearSet|) 138846) ((|MonoidRing| . |RightModule|) 138803) ((|MonoidRing| . |LinearSet|) 138760) ((|MonoidRing| . |Module|) 138717) ((|MonoidRing| . |Finite|) 138662) ((|MultivariatePolynomial| . |PolynomialCategory|) 138589) ((|MultivariatePolynomial| . |CoercibleFrom|) 138261) ((|MultivariatePolynomial| . |RetractableTo|) 138068) ((|MultivariatePolynomial| . |UniqueFactorizationDomain|) 138018) ((|MultivariatePolynomial| . |PolynomialFactorizationExplicit|) 137968) ((|MultivariatePolynomial| . |PatternMatchable|) NIL) ((|MultivariatePolynomial| . |PartialDifferentialSpace|) 137928) ((|MultivariatePolynomial| . |PartialDifferentialDomain|) 137886) ((|MultivariatePolynomial| . |PartialDifferentialRing|) 137846) ((|MultivariatePolynomial| . |InnerEvalable|) 137772) ((|MultivariatePolynomial| . |GcdDomain|) 137690) ((|MultivariatePolynomial| . |LinearlyExplicitRingOver|) 137606) ((|MultivariatePolynomial| . |LeftModule|) 137435) ((|MultivariatePolynomial| . |FullyLinearlyExplicitRingOver|) 137419) ((|MultivariatePolynomial| . |AbelianMonoidRing|) 137353) ((|MultivariatePolynomial| . |Algebra|) 137116) ((|MultivariatePolynomial| . |LinearSet|) 136879) ((|MultivariatePolynomial| . |Module|) 136642) ((|MultivariatePolynomial| . |EntireRing|) 136528) ((|MultivariatePolynomial| . |IntegralDomain|) 136414) ((|MultivariatePolynomial| . |Functorial|) 136398) ((|MultivariatePolynomial| . |BiModule|) 136141) ((|MultivariatePolynomial| . |RightLinearSet|) 135898) ((|MultivariatePolynomial| . |RightModule|) 135655) ((|MultivariatePolynomial| . |CommutativeRing|) 135508) ((|MultivariatePolynomial| . |CharacteristicZero|) 135471) ((|MultivariatePolynomial| . |CharacteristicNonZero|) 135431) ((|MultivariatePolynomial| . |LeftLinearSet|) 135308) ((|MultivariatePolynomial| . |CancellationAbelianMonoid|) T) ((|MultivariatePolynomial| . |AbelianSemiGroup|) T) ((|MultivariatePolynomial| . |BasicType|) T) ((|MultivariatePolynomial| . |Join|) T) ((|MultivariatePolynomial| . |Type|) T) ((|MultivariatePolynomial| . |CoercibleTo|) 135282) ((|MultivariatePolynomial| . |SetCategory|) T) ((|MultivariatePolynomial| . |AbelianMonoid|) T) ((|MultivariatePolynomial| . |AbelianGroup|) T) ((|MultivariatePolynomial| . |Ring|) T) ((|MultivariatePolynomial| . |Monoid|) T) ((|MultivariatePolynomial| . |SemiRing|) T) ((|MultivariatePolynomial| . |SemiGroup|) T) ((|MultivariatePolynomial| . |Rng|) T) ((|MultivariatePolynomial| . |FullyRetractableTo|) 135266) ((|MultivariatePolynomial| . |FiniteAbelianMonoidRing|) 135200) ((|MultivariatePolynomial| . |Evalable|) 135187) ((|MultivariatePolynomial| . |ConvertibleTo|) 134965) ((|MonoidOperation| . |MonoidOperatorCategory|) 134949) ((|MonoidOperation| . |BinaryOperatorCategory|) 134933) ((|MonoidOperation| . |Type|) T) ((|MonoidOperation| . |MappingCategory|) 134907) ((|MonoidOperation| . |SemiGroupOperatorCategory|) 134891) ((|MonoidOperation| . |SetCategory|) T) ((|MonoidOperation| . |CoercibleTo|) 134829) ((|MonoidOperation| . |Join|) T) ((|MonoidOperation| . |BasicType|) T) ((|MoebiusTransform| . |Group|) T) ((|MoebiusTransform| . |SemiGroup|) T) ((|MoebiusTransform| . |BasicType|) T) ((|MoebiusTransform| . |Join|) T) ((|MoebiusTransform| . |Type|) T) ((|MoebiusTransform| . |CoercibleTo|) 134803) ((|MoebiusTransform| . |SetCategory|) T) ((|MoebiusTransform| . |Monoid|) T) ((|ModularRing| . |Ring|) T) ((|ModularRing| . |Monoid|) T) ((|ModularRing| . |SemiRing|) T) ((|ModularRing| . |SemiGroup|) T) ((|ModularRing| . |Rng|) T) ((|ModularRing| . |AbelianGroup|) T) ((|ModularRing| . |LeftLinearSet|) 134770) ((|ModularRing| . |AbelianMonoid|) T) ((|ModularRing| . |SetCategory|) T) ((|ModularRing| . |CoercibleTo|) 134744) ((|ModularRing| . |Type|) T) ((|ModularRing| . |Join|) T) ((|ModularRing| . |BasicType|) T) ((|ModularRing| . |AbelianSemiGroup|) T) ((|ModularRing| . |CancellationAbelianMonoid|) T) ((|ModularRing| . |LeftModule|) 134731) ((|ModularRing| . |CoercibleFrom|) 134708) ((|ModuleOperator| . |Ring|) T) ((|ModuleOperator| . |Monoid|) T) ((|ModuleOperator| . |SemiRing|) T) ((|ModuleOperator| . |SemiGroup|) T) ((|ModuleOperator| . |Rng|) T) ((|ModuleOperator| . |AbelianGroup|) T) ((|ModuleOperator| . |LeftLinearSet|) 134635) ((|ModuleOperator| . |AbelianMonoid|) T) ((|ModuleOperator| . |SetCategory|) T) ((|ModuleOperator| . |CoercibleTo|) 134609) ((|ModuleOperator| . |Type|) T) ((|ModuleOperator| . |Join|) T) ((|ModuleOperator| . |BasicType|) T) ((|ModuleOperator| . |AbelianSemiGroup|) T) ((|ModuleOperator| . |CancellationAbelianMonoid|) T) ((|ModuleOperator| . |LeftModule|) 134556) ((|ModuleOperator| . |CoercibleFrom|) 134494) ((|ModuleOperator| . |RetractableTo|) 134452) ((|ModuleOperator| . |Eltable|) 134431) ((|ModuleOperator| . |CharacteristicZero|) 134394) ((|ModuleOperator| . |CharacteristicNonZero|) 134354) ((|ModuleOperator| . |Algebra|) 134311) ((|ModuleOperator| . |BiModule|) 134263) ((|ModuleOperator| . |RightLinearSet|) 134220) ((|ModuleOperator| . |RightModule|) 134177) ((|ModuleOperator| . |LinearSet|) 134134) ((|ModuleOperator| . |Module|) 134091) ((|ModuleMonomial| . |OrderedSet|) T) ((|ModuleMonomial| . |CoercibleTo|) 134005) ((|ModuleMonomial| . |SetCategory|) T) ((|ModuleMonomial| . |BasicType|) T) ((|ModuleMonomial| . |Join|) T) ((|ModuleMonomial| . |Type|) T) ((|ModuleMonomial| . |OrderedType|) T) ((|ModuleMonomial| . |HomotopicTo|) 133942) ((|ModuleMonomial| . |CoercibleFrom|) 133879) ((|ModMonic| . |UnivariatePolynomialCategory|) 133863) ((|ModMonic| . |StepThrough|) 133833) ((|ModMonic| . |ConvertibleTo|) NIL) ((|ModMonic| . |Evalable|) 133820) ((|ModMonic| . |InnerEvalable|) 133749) ((|ModMonic| . |FiniteAbelianMonoidRing|) 133710) ((|ModMonic| . |RetractableTo|) 133520) ((|ModMonic| . |FullyRetractableTo|) 133504) ((|ModMonic| . |Algebra|) 133244) ((|ModMonic| . |BiModule|) 132964) ((|ModMonic| . |RightLinearSet|) 132698) ((|ModMonic| . |RightModule|) 132432) ((|ModMonic| . |LeftLinearSet|) 132309) ((|ModMonic| . |LeftModule|) 132138) ((|ModMonic| . |LinearSet|) 131878) ((|ModMonic| . |Module|) 131618) ((|ModMonic| . |CoercibleFrom|) 131257) ((|ModMonic| . |CharacteristicNonZero|) 131217) ((|ModMonic| . |CharacteristicZero|) 131180) ((|ModMonic| . |Functorial|) 131164) ((|ModMonic| . |AbelianMonoidRing|) 131125) ((|ModMonic| . |FullyLinearlyExplicitRingOver|) 131109) ((|ModMonic| . |LinearlyExplicitRingOver|) 131025) ((|ModMonic| . |PartialDifferentialRing|) 130923) ((|ModMonic| . |PartialDifferentialDomain|) 130759) ((|ModMonic| . |PartialDifferentialSpace|) 130599) ((|ModMonic| . |PatternMatchable|) NIL) ((|ModMonic| . |PolynomialFactorizationExplicit|) 130549) ((|ModMonic| . |UniqueFactorizationDomain|) 130499) ((|ModMonic| . |PolynomialCategory|) 130434) ((|ModMonic| . |PrincipalIdealDomain|) 130410) ((|ModMonic| . |IntegralDomain|) 130273) ((|ModMonic| . |EntireRing|) 130136) ((|ModMonic| . |CommutativeRing|) 129966) ((|ModMonic| . |GcdDomain|) 129861) ((|ModMonic| . |EuclideanDomain|) 129837) ((|ModMonic| . |Eltable|) 129740) ((|ModMonic| . |DifferentialRing|) T) ((|ModMonic| . |CancellationAbelianMonoid|) T) ((|ModMonic| . |AbelianSemiGroup|) T) ((|ModMonic| . |BasicType|) T) ((|ModMonic| . |CoercibleTo|) 129714) ((|ModMonic| . |SetCategory|) T) ((|ModMonic| . |AbelianMonoid|) T) ((|ModMonic| . |AbelianGroup|) T) ((|ModMonic| . |Rng|) T) ((|ModMonic| . |SemiGroup|) T) ((|ModMonic| . |SemiRing|) T) ((|ModMonic| . |Monoid|) T) ((|ModMonic| . |Ring|) T) ((|ModMonic| . |DifferentialDomain|) 129701) ((|ModMonic| . |Join|) T) ((|ModMonic| . |Type|) T) ((|ModMonic| . |DifferentialSpace|) T) ((|ModMonic| . |DifferentialSpaceExtension|) 129685) ((|ModMonic| . |DifferentialExtension|) 129669) ((|ModMonic| . |Finite|) 129644) ((|ModularField| . |Field|) T) ((|ModularField| . |UniqueFactorizationDomain|) T) ((|ModularField| . |PrincipalIdealDomain|) T) ((|ModularField| . |IntegralDomain|) T) ((|ModularField| . |CommutativeRing|) T) ((|ModularField| . |CoercibleFrom|) 129578) ((|ModularField| . |Module|) 129532) ((|ModularField| . |LinearSet|) 129486) ((|ModularField| . |Algebra|) 129440) ((|ModularField| . |GcdDomain|) T) ((|ModularField| . |EuclideanDomain|) T) ((|ModularField| . |LeftModule|) 129394) ((|ModularField| . |LeftLinearSet|) 129328) ((|ModularField| . |Rng|) T) ((|ModularField| . |SemiGroup|) T) ((|ModularField| . |SemiRing|) T) ((|ModularField| . |Monoid|) T) ((|ModularField| . |Ring|) T) ((|ModularField| . |BiModule|) 129273) ((|ModularField| . |RightLinearSet|) 129227) ((|ModularField| . |RightModule|) 129181) ((|ModularField| . |AbelianGroup|) T) ((|ModularField| . |AbelianMonoid|) T) ((|ModularField| . |SetCategory|) T) ((|ModularField| . |CoercibleTo|) 129155) ((|ModularField| . |Type|) T) ((|ModularField| . |Join|) T) ((|ModularField| . |BasicType|) T) ((|ModularField| . |AbelianSemiGroup|) T) ((|ModularField| . |CancellationAbelianMonoid|) T) ((|ModularField| . |EntireRing|) T) ((|ModularField| . |DivisionRing|) T) ((|MathMLFormat| . |SetCategory|) T) ((|MathMLFormat| . |CoercibleTo|) 129129) ((|MathMLFormat| . |Type|) T) ((|MathMLFormat| . |Join|) T) ((|MathMLFormat| . |BasicType|) T) ((|Maybe| . |UnionType|) T) ((|Maybe| . |RetractableTo|) 129113) ((|Maybe| . |CoercibleFrom|) 129097) ((|Maybe| . |CoercibleTo|) 129071) ((|Matrix| . |MatrixCategory|) 129032) ((|Matrix| . |FiniteAggregate|) 129016) ((|Matrix| . |Aggregate|) T) ((|Matrix| . |Join|) T) ((|Matrix| . |Type|) T) ((|Matrix| . |BasicType|) 128954) ((|Matrix| . |CoercibleTo|) 128856) ((|Matrix| . |Evalable|) 128780) ((|Matrix| . |InnerEvalable|) 128699) ((|Matrix| . |Functorial|) 128683) ((|Matrix| . |SetCategory|) 128653) ((|Matrix| . |HomogeneousAggregate|) 128637) ((|Matrix| . |ShallowlyMutableAggregate|) 128621) ((|Matrix| . |TwoDimensionalArrayCategory|) 128582) ((|Matrix| . |ConvertibleTo|) 128523) ((|MappingAst| . |SpadSyntaxCategory|) T) ((|MappingAst| . |HomotopicTo|) 128501) ((|MappingAst| . |CoercibleTo|) 128436) ((|MappingAst| . |CoercibleFrom|) 128414) ((|MappingAst| . |SetCategory|) T) ((|MappingAst| . |Type|) T) ((|MappingAst| . |Join|) T) ((|MappingAst| . |BasicType|) T) ((|MappingAst| . |AbstractSyntaxCategory|) T) ((|Magma| . |OrderedSet|) T) ((|Magma| . |CoercibleTo|) 128388) ((|Magma| . |SetCategory|) T) ((|Magma| . |BasicType|) T) ((|Magma| . |Join|) T) ((|Magma| . |Type|) T) ((|Magma| . |OrderedType|) T) ((|Magma| . |RetractableTo|) 128372) ((|Magma| . |CoercibleFrom|) 128356) ((|MacroAst| . |SpadSyntaxCategory|) T) ((|MacroAst| . |HomotopicTo|) 128334) ((|MacroAst| . |CoercibleTo|) 128289) ((|MacroAst| . |CoercibleFrom|) 128267) ((|MacroAst| . |SetCategory|) T) ((|MacroAst| . |Type|) T) ((|MacroAst| . |Join|) T) ((|MacroAst| . |BasicType|) T) ((|MacroAst| . |AbstractSyntaxCategory|) T) ((|LyndonWord| . |OrderedSet|) T) ((|LyndonWord| . |CoercibleTo|) 128241) ((|LyndonWord| . |SetCategory|) T) ((|LyndonWord| . |BasicType|) T) ((|LyndonWord| . |Join|) T) ((|LyndonWord| . |Type|) T) ((|LyndonWord| . |OrderedType|) T) ((|LyndonWord| . |RetractableTo|) 128225) ((|LyndonWord| . |CoercibleFrom|) 128209) ((|ConstructAst| . |SpadSyntaxCategory|) T) ((|ConstructAst| . |HomotopicTo|) 128187) ((|ConstructAst| . |CoercibleTo|) 128142) ((|ConstructAst| . |CoercibleFrom|) 128120) ((|ConstructAst| . |SetCategory|) T) ((|ConstructAst| . |Type|) T) ((|ConstructAst| . |Join|) T) ((|ConstructAst| . |BasicType|) T) ((|ConstructAst| . |AbstractSyntaxCategory|) T) ((|LieSquareMatrix| . |SquareMatrixCategory|) 128064) ((|LieSquareMatrix| . |FiniteAggregate|) 128048) ((|LieSquareMatrix| . |Aggregate|) T) ((|LieSquareMatrix| . |Evalable|) 127972) ((|LieSquareMatrix| . |InnerEvalable|) 127891) ((|LieSquareMatrix| . |Functorial|) 127875) ((|LieSquareMatrix| . |HomogeneousAggregate|) 127859) ((|LieSquareMatrix| . |RectangularMatrixCategory|) 127798) ((|LieSquareMatrix| . |RetractableTo|) 127642) ((|LieSquareMatrix| . |CoercibleFrom|) 127523) ((|LieSquareMatrix| . |FullyRetractableTo|) 127507) ((|LieSquareMatrix| . |LinearlyExplicitRingOver|) 127423) ((|LieSquareMatrix| . |LeftModule|) 127329) ((|LieSquareMatrix| . |FullyLinearlyExplicitRingOver|) 127313) ((|LieSquareMatrix| . |DifferentialRing|) 127278) ((|LieSquareMatrix| . |DifferentialDomain|) 127197) ((|LieSquareMatrix| . |DifferentialSpace|) 127122) ((|LieSquareMatrix| . |DifferentialSpaceExtension|) 127106) ((|LieSquareMatrix| . |PartialDifferentialDomain|) 126978) ((|LieSquareMatrix| . |PartialDifferentialSpace|) 126852) ((|LieSquareMatrix| . |PartialDifferentialRing|) 126784) ((|LieSquareMatrix| . |DifferentialExtension|) 126768) ((|LieSquareMatrix| . |Module|) 126752) ((|LieSquareMatrix| . |LinearSet|) 126736) ((|LieSquareMatrix| . |LeftLinearSet|) 126690) ((|LieSquareMatrix| . |CancellationAbelianMonoid|) T) ((|LieSquareMatrix| . |AbelianSemiGroup|) T) ((|LieSquareMatrix| . |BasicType|) T) ((|LieSquareMatrix| . |Join|) T) ((|LieSquareMatrix| . |Type|) T) ((|LieSquareMatrix| . |CoercibleTo|) 126640) ((|LieSquareMatrix| . |SetCategory|) T) ((|LieSquareMatrix| . |AbelianMonoid|) T) ((|LieSquareMatrix| . |AbelianGroup|) T) ((|LieSquareMatrix| . |RightModule|) 126624) ((|LieSquareMatrix| . |RightLinearSet|) 126608) ((|LieSquareMatrix| . |BiModule|) 126587) ((|LieSquareMatrix| . |Ring|) T) ((|LieSquareMatrix| . |Monoid|) T) ((|LieSquareMatrix| . |SemiRing|) T) ((|LieSquareMatrix| . |SemiGroup|) T) ((|LieSquareMatrix| . |Rng|) T) ((|LieSquareMatrix| . |Algebra|) 126532) ((|LieSquareMatrix| . |FramedNonAssociativeAlgebra|) 126516) ((|LieSquareMatrix| . |NonAssociativeAlgebra|) 126500) ((|LieSquareMatrix| . |Monad|) T) ((|LieSquareMatrix| . |NonAssociativeRng|) T) ((|LieSquareMatrix| . |FiniteRankNonAssociativeAlgebra|) 126484) ((|LieSquareMatrix| . |Eltable|) 126456) ((|LiePolynomial| . |FreeLieAlgebra|) 126435) ((|LiePolynomial| . |Module|) 126419) ((|LiePolynomial| . |LinearSet|) 126403) ((|LiePolynomial| . |LeftModule|) 126387) ((|LiePolynomial| . |LeftLinearSet|) 126351) ((|LiePolynomial| . |CancellationAbelianMonoid|) T) ((|LiePolynomial| . |AbelianSemiGroup|) T) ((|LiePolynomial| . |BasicType|) T) ((|LiePolynomial| . |Join|) T) ((|LiePolynomial| . |Type|) T) ((|LiePolynomial| . |CoercibleTo|) 126325) ((|LiePolynomial| . |SetCategory|) T) ((|LiePolynomial| . |AbelianMonoid|) T) ((|LiePolynomial| . |AbelianGroup|) T) ((|LiePolynomial| . |RightModule|) 126309) ((|LiePolynomial| . |RightLinearSet|) 126293) ((|LiePolynomial| . |BiModule|) 126272) ((|LiePolynomial| . |LieAlgebra|) 126256) ((|LiePolynomial| . |FreeModuleCat|) 126220) ((|LiePolynomial| . |CoercibleFrom|) 126189) ((|LiePolynomial| . |RetractableTo|) 126158) ((|LiePolynomial| . |Functorial|) 126142) ((|LinearOrdinaryDifferentialOperator2| . |LinearOrdinaryDifferentialOperatorCategory|) 126126) ((|LinearOrdinaryDifferentialOperator2| . |Algebra|) 126083) ((|LinearOrdinaryDifferentialOperator2| . |CoercibleFrom|) 125964) ((|LinearOrdinaryDifferentialOperator2| . |LeftModule|) 125938) ((|LinearOrdinaryDifferentialOperator2| . |LeftLinearSet|) 125892) ((|LinearOrdinaryDifferentialOperator2| . |Rng|) T) ((|LinearOrdinaryDifferentialOperator2| . |SemiGroup|) T) ((|LinearOrdinaryDifferentialOperator2| . |SemiRing|) T) ((|LinearOrdinaryDifferentialOperator2| . |Monoid|) T) ((|LinearOrdinaryDifferentialOperator2| . |Ring|) T) ((|LinearOrdinaryDifferentialOperator2| . |BiModule|) 125871) ((|LinearOrdinaryDifferentialOperator2| . |RightLinearSet|) 125855) ((|LinearOrdinaryDifferentialOperator2| . |RightModule|) 125839) ((|LinearOrdinaryDifferentialOperator2| . |AbelianGroup|) T) ((|LinearOrdinaryDifferentialOperator2| . |AbelianMonoid|) T) ((|LinearOrdinaryDifferentialOperator2| . |SetCategory|) T) ((|LinearOrdinaryDifferentialOperator2| . |CoercibleTo|) 125813) ((|LinearOrdinaryDifferentialOperator2| . |BasicType|) T) ((|LinearOrdinaryDifferentialOperator2| . |AbelianSemiGroup|) T) ((|LinearOrdinaryDifferentialOperator2| . |CancellationAbelianMonoid|) T) ((|LinearOrdinaryDifferentialOperator2| . |LinearSet|) 125770) ((|LinearOrdinaryDifferentialOperator2| . |Module|) 125727) ((|LinearOrdinaryDifferentialOperator2| . |FullyRetractableTo|) 125711) ((|LinearOrdinaryDifferentialOperator2| . |RetractableTo|) 125555) ((|LinearOrdinaryDifferentialOperator2| . |UnivariateSkewPolynomialCategory|) 125539) ((|LinearOrdinaryDifferentialOperator2| . |Type|) T) ((|LinearOrdinaryDifferentialOperator2| . |Join|) T) ((|LinearOrdinaryDifferentialOperator2| . |Eltable|) 125500) ((|LinearOrdinaryDifferentialOperator1| . |LinearOrdinaryDifferentialOperatorCategory|) 125484) ((|LinearOrdinaryDifferentialOperator1| . |Algebra|) 125441) ((|LinearOrdinaryDifferentialOperator1| . |CoercibleFrom|) 125322) ((|LinearOrdinaryDifferentialOperator1| . |LeftModule|) 125296) ((|LinearOrdinaryDifferentialOperator1| . |LeftLinearSet|) 125250) ((|LinearOrdinaryDifferentialOperator1| . |Rng|) T) ((|LinearOrdinaryDifferentialOperator1| . |SemiGroup|) T) ((|LinearOrdinaryDifferentialOperator1| . |SemiRing|) T) ((|LinearOrdinaryDifferentialOperator1| . |Monoid|) T) ((|LinearOrdinaryDifferentialOperator1| . |Ring|) T) ((|LinearOrdinaryDifferentialOperator1| . |BiModule|) 125229) ((|LinearOrdinaryDifferentialOperator1| . |RightLinearSet|) 125213) ((|LinearOrdinaryDifferentialOperator1| . |RightModule|) 125197) ((|LinearOrdinaryDifferentialOperator1| . |AbelianGroup|) T) ((|LinearOrdinaryDifferentialOperator1| . |AbelianMonoid|) T) ((|LinearOrdinaryDifferentialOperator1| . |SetCategory|) T) ((|LinearOrdinaryDifferentialOperator1| . |CoercibleTo|) 125171) ((|LinearOrdinaryDifferentialOperator1| . |BasicType|) T) ((|LinearOrdinaryDifferentialOperator1| . |AbelianSemiGroup|) T) ((|LinearOrdinaryDifferentialOperator1| . |CancellationAbelianMonoid|) T) ((|LinearOrdinaryDifferentialOperator1| . |LinearSet|) 125128) ((|LinearOrdinaryDifferentialOperator1| . |Module|) 125085) ((|LinearOrdinaryDifferentialOperator1| . |FullyRetractableTo|) 125069) ((|LinearOrdinaryDifferentialOperator1| . |RetractableTo|) 124913) ((|LinearOrdinaryDifferentialOperator1| . |UnivariateSkewPolynomialCategory|) 124897) ((|LinearOrdinaryDifferentialOperator1| . |Type|) T) ((|LinearOrdinaryDifferentialOperator1| . |Join|) T) ((|LinearOrdinaryDifferentialOperator1| . |Eltable|) 124876) ((|LinearOrdinaryDifferentialOperator| . |LinearOrdinaryDifferentialOperatorCategory|) 124860) ((|LinearOrdinaryDifferentialOperator| . |Algebra|) 124817) ((|LinearOrdinaryDifferentialOperator| . |CoercibleFrom|) 124698) ((|LinearOrdinaryDifferentialOperator| . |LeftModule|) 124672) ((|LinearOrdinaryDifferentialOperator| . |LeftLinearSet|) 124626) ((|LinearOrdinaryDifferentialOperator| . |Rng|) T) ((|LinearOrdinaryDifferentialOperator| . |SemiGroup|) T) ((|LinearOrdinaryDifferentialOperator| . |SemiRing|) T) ((|LinearOrdinaryDifferentialOperator| . |Monoid|) T) ((|LinearOrdinaryDifferentialOperator| . |Ring|) T) ((|LinearOrdinaryDifferentialOperator| . |BiModule|) 124605) ((|LinearOrdinaryDifferentialOperator| . |RightLinearSet|) 124589) ((|LinearOrdinaryDifferentialOperator| . |RightModule|) 124573) ((|LinearOrdinaryDifferentialOperator| . |AbelianGroup|) T) ((|LinearOrdinaryDifferentialOperator| . |AbelianMonoid|) T) ((|LinearOrdinaryDifferentialOperator| . |SetCategory|) T) ((|LinearOrdinaryDifferentialOperator| . |CoercibleTo|) 124547) ((|LinearOrdinaryDifferentialOperator| . |BasicType|) T) ((|LinearOrdinaryDifferentialOperator| . |AbelianSemiGroup|) T) ((|LinearOrdinaryDifferentialOperator| . |CancellationAbelianMonoid|) T) ((|LinearOrdinaryDifferentialOperator| . |LinearSet|) 124504) ((|LinearOrdinaryDifferentialOperator| . |Module|) 124461) ((|LinearOrdinaryDifferentialOperator| . |FullyRetractableTo|) 124445) ((|LinearOrdinaryDifferentialOperator| . |RetractableTo|) 124289) ((|LinearOrdinaryDifferentialOperator| . |UnivariateSkewPolynomialCategory|) 124273) ((|LinearOrdinaryDifferentialOperator| . |Type|) T) ((|LinearOrdinaryDifferentialOperator| . |Join|) T) ((|LinearOrdinaryDifferentialOperator| . |Eltable|) 124252) ((|Localize| . |Module|) 124236) ((|Localize| . |LinearSet|) 124220) ((|Localize| . |LeftModule|) 124204) ((|Localize| . |LeftLinearSet|) 124168) ((|Localize| . |CancellationAbelianMonoid|) T) ((|Localize| . |AbelianSemiGroup|) T) ((|Localize| . |BasicType|) T) ((|Localize| . |Join|) T) ((|Localize| . |Type|) T) ((|Localize| . |CoercibleTo|) 124142) ((|Localize| . |SetCategory|) T) ((|Localize| . |AbelianMonoid|) T) ((|Localize| . |AbelianGroup|) T) ((|Localize| . |RightModule|) 124126) ((|Localize| . |RightLinearSet|) 124110) ((|Localize| . |BiModule|) 124089) ((|Localize| . |OrderedAbelianGroup|) 124051) ((|Localize| . |OrderedAbelianMonoid|) 124013) ((|Localize| . |OrderedSet|) 123975) ((|Localize| . |OrderedType|) 123937) ((|Localize| . |OrderedAbelianSemiGroup|) 123899) ((|Localize| . |OrderedCancellationAbelianMonoid|) 123861) ((|ListMonoidOps| . |SetCategory|) T) ((|ListMonoidOps| . |CoercibleTo|) 123835) ((|ListMonoidOps| . |Type|) T) ((|ListMonoidOps| . |Join|) T) ((|ListMonoidOps| . |BasicType|) T) ((|ListMonoidOps| . |RetractableTo|) 123819) ((|ListMonoidOps| . |CoercibleFrom|) 123803) ((|ListMultiDictionary| . |MultiDictionary|) 123787) ((|ListMultiDictionary| . |BagAggregate|) 123771) ((|ListMultiDictionary| . |ShallowlyMutableAggregate|) 123755) ((|ListMultiDictionary| . |Aggregate|) T) ((|ListMultiDictionary| . |Join|) T) ((|ListMultiDictionary| . |Type|) T) ((|ListMultiDictionary| . |BasicType|) 123693) ((|ListMultiDictionary| . |CoercibleTo|) 123595) ((|ListMultiDictionary| . |Evalable|) 123519) ((|ListMultiDictionary| . |InnerEvalable|) 123438) ((|ListMultiDictionary| . |Functorial|) 123422) ((|ListMultiDictionary| . |SetCategory|) 123392) ((|ListMultiDictionary| . |HomogeneousAggregate|) 123376) ((|ListMultiDictionary| . |Collection|) 123360) ((|ListMultiDictionary| . |ConvertibleTo|) 123296) ((|ListMultiDictionary| . |DictionaryOperations|) 123280) ((|ListMultiDictionary| . |FiniteAggregate|) 123264) ((|Literal| . |SpadSyntaxCategory|) T) ((|Literal| . |HomotopicTo|) 123242) ((|Literal| . |CoercibleTo|) 123184) ((|Literal| . |CoercibleFrom|) 123162) ((|Literal| . |SetCategory|) T) ((|Literal| . |Type|) T) ((|Literal| . |Join|) T) ((|Literal| . |BasicType|) T) ((|Literal| . |AbstractSyntaxCategory|) T) ((|List| . |ListAggregate|) 123146) ((|List| . |UnaryRecursiveAggregate|) 123130) ((|List| . |RecursiveAggregate|) 123114) ((|List| . |StreamAggregate|) 123098) ((|List| . |FiniteAggregate|) 123082) ((|List| . |OrderedSet|) 123053) ((|List| . |OrderedType|) 123024) ((|List| . |FiniteLinearAggregate|) 123008) ((|List| . |LinearAggregate|) 122992) ((|List| . |EltableAggregate|) 122964) ((|List| . |Eltable|) 122893) ((|List| . |IndexedAggregate|) 122865) ((|List| . |ConvertibleTo|) 122801) ((|List| . |HomogeneousAggregate|) 122785) ((|List| . |SetCategory|) 122722) ((|List| . |Functorial|) 122706) ((|List| . |InnerEvalable|) 122625) ((|List| . |Evalable|) 122549) ((|List| . |CoercibleTo|) 122423) ((|List| . |BasicType|) 122333) ((|List| . |Type|) T) ((|List| . |Join|) T) ((|List| . |Aggregate|) T) ((|List| . |Collection|) 122317) ((|List| . |ShallowlyMutableAggregate|) 122301) ((|List| . |ExtensibleLinearAggregate|) 122285) ((|LinearForm| . |VectorSpace|) 122269) ((|LinearForm| . |BiModule|) 122248) ((|LinearForm| . |RightLinearSet|) 122232) ((|LinearForm| . |RightModule|) 122216) ((|LinearForm| . |AbelianGroup|) T) ((|LinearForm| . |LeftLinearSet|) 122180) ((|LinearForm| . |AbelianMonoid|) T) ((|LinearForm| . |SetCategory|) T) ((|LinearForm| . |CoercibleTo|) 122154) ((|LinearForm| . |Type|) T) ((|LinearForm| . |Join|) T) ((|LinearForm| . |BasicType|) T) ((|LinearForm| . |AbelianSemiGroup|) T) ((|LinearForm| . |CancellationAbelianMonoid|) T) ((|LinearForm| . |LeftModule|) 122138) ((|LinearForm| . |LinearSet|) 122122) ((|LinearForm| . |Module|) 122106) ((|LinearForm| . |Eltable|) 122062) ((|LinearElement| . |VectorSpace|) 122046) ((|LinearElement| . |BiModule|) 122025) ((|LinearElement| . |RightLinearSet|) 122009) ((|LinearElement| . |RightModule|) 121993) ((|LinearElement| . |AbelianGroup|) T) ((|LinearElement| . |LeftLinearSet|) 121957) ((|LinearElement| . |AbelianMonoid|) T) ((|LinearElement| . |SetCategory|) T) ((|LinearElement| . |CoercibleTo|) 121931) ((|LinearElement| . |Type|) T) ((|LinearElement| . |Join|) T) ((|LinearElement| . |BasicType|) T) ((|LinearElement| . |AbelianSemiGroup|) T) ((|LinearElement| . |CancellationAbelianMonoid|) T) ((|LinearElement| . |LeftModule|) 121915) ((|LinearElement| . |LinearSet|) 121899) ((|LinearElement| . |Module|) 121883) ((|LinearElement| . |CoercibleFrom|) 121851) ((|LinearElement| . |IndexedDirectProductCategory|) 121814) ((|LinearElement| . |Functorial|) 121798) ((|LinearElement| . |ConvertibleFrom|) 121729) ((|LinearBasis| . |OrderedFinite|) T) ((|LinearBasis| . |OrderedType|) T) ((|LinearBasis| . |OrderedSet|) T) ((|LinearBasis| . |SetCategory|) T) ((|LinearBasis| . |CoercibleTo|) 121703) ((|LinearBasis| . |Type|) T) ((|LinearBasis| . |Join|) T) ((|LinearBasis| . |BasicType|) T) ((|LinearBasis| . |Finite|) T) ((|LinearBasis| . |CoercibleFrom|) 121663) ((|AssociatedLieAlgebra| . |NonAssociativeAlgebra|) 121647) ((|AssociatedLieAlgebra| . |Monad|) T) ((|AssociatedLieAlgebra| . |NonAssociativeRng|) T) ((|AssociatedLieAlgebra| . |BiModule|) 121626) ((|AssociatedLieAlgebra| . |RightLinearSet|) 121610) ((|AssociatedLieAlgebra| . |RightModule|) 121594) ((|AssociatedLieAlgebra| . |AbelianGroup|) T) ((|AssociatedLieAlgebra| . |LeftLinearSet|) 121558) ((|AssociatedLieAlgebra| . |AbelianMonoid|) T) ((|AssociatedLieAlgebra| . |SetCategory|) T) ((|AssociatedLieAlgebra| . |CoercibleTo|) 121519) ((|AssociatedLieAlgebra| . |Type|) T) ((|AssociatedLieAlgebra| . |Join|) T) 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. |EltableAggregate|) 120161) ((|Library| . |KeyedDictionary|) 120131) ((|Library| . |SetCategory|) T) ((|Library| . |CoercibleTo|) 120105) ((|Library| . |BasicType|) T) ((|Library| . |Type|) T) ((|Library| . |Join|) T) ((|Library| . |Aggregate|) T) ((|Library| . |FiniteAggregate|) 120038) ((|LieExponentials| . |Group|) T) ((|LieExponentials| . |SemiGroup|) T) ((|LieExponentials| . |BasicType|) T) ((|LieExponentials| . |Join|) T) ((|LieExponentials| . |Type|) T) ((|LieExponentials| . |CoercibleTo|) 120012) ((|LieExponentials| . |SetCategory|) T) ((|LieExponentials| . |Monoid|) T) ((|LetAst| . |SpadSyntaxCategory|) T) ((|LetAst| . |HomotopicTo|) 119990) ((|LetAst| . |CoercibleTo|) 119945) ((|LetAst| . |CoercibleFrom|) 119923) ((|LetAst| . |SetCategory|) T) ((|LetAst| . |Type|) T) ((|LetAst| . |Join|) T) ((|LetAst| . |BasicType|) T) ((|LetAst| . |AbstractSyntaxCategory|) T) ((|LaurentPolynomial| . |DifferentialExtension|) 119907) ((|LaurentPolynomial| . |PartialDifferentialRing|) 119839) ((|LaurentPolynomial| . |PartialDifferentialSpace|) 119713) ((|LaurentPolynomial| . |PartialDifferentialDomain|) 119585) ((|LaurentPolynomial| . |DifferentialSpaceExtension|) 119569) ((|LaurentPolynomial| . |DifferentialSpace|) 119494) ((|LaurentPolynomial| . |Type|) T) ((|LaurentPolynomial| . |Join|) T) ((|LaurentPolynomial| . |DifferentialDomain|) 119413) ((|LaurentPolynomial| . |Ring|) T) ((|LaurentPolynomial| . |Monoid|) T) ((|LaurentPolynomial| . |SemiRing|) T) ((|LaurentPolynomial| . |SemiGroup|) T) ((|LaurentPolynomial| . |Rng|) T) ((|LaurentPolynomial| . |AbelianGroup|) T) ((|LaurentPolynomial| . |LeftLinearSet|) 119380) ((|LaurentPolynomial| . |AbelianMonoid|) T) ((|LaurentPolynomial| . |SetCategory|) T) ((|LaurentPolynomial| . |CoercibleTo|) 119354) ((|LaurentPolynomial| . |BasicType|) T) ((|LaurentPolynomial| . |AbelianSemiGroup|) T) ((|LaurentPolynomial| . |CancellationAbelianMonoid|) T) ((|LaurentPolynomial| . |LeftModule|) 119341) ((|LaurentPolynomial| . |CoercibleFrom|) 119199) ((|LaurentPolynomial| . |DifferentialRing|) 119164) ((|LaurentPolynomial| . |IntegralDomain|) T) ((|LaurentPolynomial| . |EntireRing|) T) ((|LaurentPolynomial| . |CommutativeRing|) T) ((|LaurentPolynomial| . |Module|) 119151) ((|LaurentPolynomial| . |LinearSet|) 119138) ((|LaurentPolynomial| . |RightModule|) 119125) ((|LaurentPolynomial| . |RightLinearSet|) 119112) ((|LaurentPolynomial| . |BiModule|) 119097) ((|LaurentPolynomial| . |Algebra|) 119084) ((|LaurentPolynomial| . |ConvertibleTo|) 119055) ((|LaurentPolynomial| . |FullyRetractableTo|) 119039) ((|LaurentPolynomial| . |RetractableTo|) 118870) ((|LaurentPolynomial| . |CharacteristicZero|) 118833) ((|LaurentPolynomial| . |CharacteristicNonZero|) 118793) ((|LaurentPolynomial| . |EuclideanDomain|) 118769) ((|LaurentPolynomial| . |GcdDomain|) 118745) ((|LaurentPolynomial| . |PrincipalIdealDomain|) 118721) ((|LocalAlgebra| . |Algebra|) 118705) ((|LocalAlgebra| . |CoercibleFrom|) 118669) ((|LocalAlgebra| . |LeftModule|) 118643) ((|LocalAlgebra| . |LeftLinearSet|) 118597) ((|LocalAlgebra| . |Rng|) T) ((|LocalAlgebra| . |SemiGroup|) T) ((|LocalAlgebra| . |SemiRing|) T) ((|LocalAlgebra| . |Monoid|) T) ((|LocalAlgebra| . |Ring|) T) ((|LocalAlgebra| . |BiModule|) 118576) ((|LocalAlgebra| . |RightLinearSet|) 118560) ((|LocalAlgebra| . |RightModule|) 118544) ((|LocalAlgebra| . |AbelianGroup|) T) ((|LocalAlgebra| . |AbelianMonoid|) T) ((|LocalAlgebra| . |SetCategory|) T) ((|LocalAlgebra| . |CoercibleTo|) 118518) ((|LocalAlgebra| . |Type|) T) ((|LocalAlgebra| . |Join|) T) ((|LocalAlgebra| . |BasicType|) T) ((|LocalAlgebra| . |AbelianSemiGroup|) T) ((|LocalAlgebra| . |CancellationAbelianMonoid|) T) ((|LocalAlgebra| . |LinearSet|) 118502) ((|LocalAlgebra| . |Module|) 118486) ((|LocalAlgebra| . |OrderedRing|) 118456) ((|LocalAlgebra| . |OrderedCancellationAbelianMonoid|) 118426) ((|LocalAlgebra| . |OrderedAbelianSemiGroup|) 118396) ((|LocalAlgebra| . |OrderedType|) 118366) ((|LocalAlgebra| . |OrderedSet|) 118336) ((|LocalAlgebra| . |OrderedAbelianMonoid|) 118306) ((|LocalAlgebra| . |OrderedAbelianGroup|) 118276) ((|LocalAlgebra| . |CharacteristicZero|) 118246) ((|KleeneTrivalentLogic| . |PropositionalLogic|) T) ((|KleeneTrivalentLogic| . |BasicType|) T) ((|KleeneTrivalentLogic| . |CoercibleTo|) 118220) ((|KleeneTrivalentLogic| . |SetCategory|) T) ((|KleeneTrivalentLogic| . |Logic|) T) ((|KleeneTrivalentLogic| . |Join|) T) ((|KleeneTrivalentLogic| . |Type|) T) ((|KleeneTrivalentLogic| . |BooleanLogic|) T) ((|KleeneTrivalentLogic| . |Finite|) T) ((|Kernel| . |CachableSet|) T) ((|Kernel| . |BasicType|) T) ((|Kernel| . |Join|) T) ((|Kernel| . |Type|) T) ((|Kernel| . |CoercibleTo|) 118194) ((|Kernel| . |SetCategory|) T) ((|Kernel| . |OrderedSet|) T) ((|Kernel| . |OrderedType|) T) ((|Kernel| . |Patternable|) 118178) ((|Kernel| . |ConvertibleTo|) 117961) ((|KeyedAccessFile| . |FileCategory|) 117884) ((|KeyedAccessFile| . |BasicType|) T) ((|KeyedAccessFile| . |Join|) T) ((|KeyedAccessFile| . |Type|) T) ((|KeyedAccessFile| . |CoercibleTo|) 117858) ((|KeyedAccessFile| . |SetCategory|) T) ((|KeyedAccessFile| . |TableAggregate|) 117831) ((|KeyedAccessFile| . |Dictionary|) 117767) ((|KeyedAccessFile| . |BagAggregate|) 117703) ((|KeyedAccessFile| . |ShallowlyMutableAggregate|) 117626) ((|KeyedAccessFile| . |Collection|) 117562) ((|KeyedAccessFile| . |ConvertibleTo|) NIL) ((|KeyedAccessFile| . |DictionaryOperations|) 117498) ((|KeyedAccessFile| . |IndexedAggregate|) 117471) ((|KeyedAccessFile| . |Evalable|) 117213) ((|KeyedAccessFile| . |InnerEvalable|) 116943) ((|KeyedAccessFile| . |Functorial|) 116866) ((|KeyedAccessFile| . |HomogeneousAggregate|) 116789) ((|KeyedAccessFile| . |Eltable|) 116762) ((|KeyedAccessFile| . |EltableAggregate|) 116735) ((|KeyedAccessFile| . |KeyedDictionary|) 116708) ((|KeyedAccessFile| . |Aggregate|) T) ((|KeyedAccessFile| . |FiniteAggregate|) 116644) ((|JVMOpcode| . |SetCategory|) T) ((|JVMOpcode| . |CoercibleTo|) 116577) ((|JVMOpcode| . |Type|) T) 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T) ((|JVMBytecode| . |SetCategory|) T) ((|JVMBytecode| . |CoercibleTo|) 116325) ((|JVMBytecode| . |Type|) T) ((|JVMBytecode| . |Join|) T) ((|JVMBytecode| . |BasicType|) T) ((|JVMBytecode| . |HomotopicTo|) 116305) ((|JVMBytecode| . |CoercibleFrom|) 116285) ((|AssociatedJordanAlgebra| . |NonAssociativeAlgebra|) 116269) ((|AssociatedJordanAlgebra| . |Monad|) T) ((|AssociatedJordanAlgebra| . |NonAssociativeRng|) T) ((|AssociatedJordanAlgebra| . |BiModule|) 116248) ((|AssociatedJordanAlgebra| . |RightLinearSet|) 116232) ((|AssociatedJordanAlgebra| . |RightModule|) 116216) ((|AssociatedJordanAlgebra| . |AbelianGroup|) T) ((|AssociatedJordanAlgebra| . |LeftLinearSet|) 116180) ((|AssociatedJordanAlgebra| . |AbelianMonoid|) T) ((|AssociatedJordanAlgebra| . |SetCategory|) T) ((|AssociatedJordanAlgebra| . |CoercibleTo|) 116141) ((|AssociatedJordanAlgebra| . |Type|) T) ((|AssociatedJordanAlgebra| . |Join|) T) ((|AssociatedJordanAlgebra| . |BasicType|) T) ((|AssociatedJordanAlgebra| . |AbelianSemiGroup|) T) ((|AssociatedJordanAlgebra| . |CancellationAbelianMonoid|) T) ((|AssociatedJordanAlgebra| . |LeftModule|) 116125) ((|AssociatedJordanAlgebra| . |LinearSet|) 116109) ((|AssociatedJordanAlgebra| . |Module|) 116093) ((|AssociatedJordanAlgebra| . |FramedNonAssociativeAlgebra|) 116029) ((|AssociatedJordanAlgebra| . |FiniteRankNonAssociativeAlgebra|) 115910) ((|AssociatedJordanAlgebra| . |Eltable|) 115838) ((|JoinAst| . |SpadSyntaxCategory|) T) ((|JoinAst| . |HomotopicTo|) 115816) ((|JoinAst| . |CoercibleTo|) 115751) ((|JoinAst| . |CoercibleFrom|) 115729) ((|JoinAst| . |SetCategory|) T) ((|JoinAst| . |Type|) T) ((|JoinAst| . |Join|) T) ((|JoinAst| . |BasicType|) T) ((|JoinAst| . |AbstractSyntaxCategory|) T) ((|InfiniteTuple| . |Functorial|) 115713) ((|InfiniteTuple| . |Join|) T) ((|InfiniteTuple| . |Type|) T) ((|InfiniteTuple| . |CoercibleTo|) 115687) ((|InternalTypeForm| . |SetCategory|) T) ((|InternalTypeForm| . |CoercibleTo|) 115642) ((|InternalTypeForm| . |Type|) T) ((|InternalTypeForm| . |Join|) T) ((|InternalTypeForm| . |BasicType|) T) ((|InternalTypeForm| . |HomotopicTo|) 115620) ((|InternalTypeForm| . |CoercibleFrom|) 115598) ((|InnerTaylorSeries| . |Ring|) T) ((|InnerTaylorSeries| . |Monoid|) T) ((|InnerTaylorSeries| . |SemiRing|) T) ((|InnerTaylorSeries| . |SemiGroup|) T) ((|InnerTaylorSeries| . |Rng|) T) ((|InnerTaylorSeries| . |AbelianGroup|) T) ((|InnerTaylorSeries| . |LeftLinearSet|) 115552) ((|InnerTaylorSeries| . |AbelianMonoid|) T) ((|InnerTaylorSeries| . |SetCategory|) T) ((|InnerTaylorSeries| . |CoercibleTo|) 115526) ((|InnerTaylorSeries| . |Type|) T) ((|InnerTaylorSeries| . |Join|) T) ((|InnerTaylorSeries| . |BasicType|) T) ((|InnerTaylorSeries| . |AbelianSemiGroup|) T) ((|InnerTaylorSeries| . |CancellationAbelianMonoid|) T) ((|InnerTaylorSeries| . |LeftModule|) 115500) ((|InnerTaylorSeries| . |CoercibleFrom|) 115441) ((|InnerTaylorSeries| . |BiModule|) 115382) ((|InnerTaylorSeries| . |RightLinearSet|) 115330) ((|InnerTaylorSeries| . |RightModule|) 115278) ((|InnerTaylorSeries| . |IntegralDomain|) 115245) ((|InnerTaylorSeries| . |EntireRing|) 115212) ((|InnerTaylorSeries| . |CommutativeRing|) 115179) ((|InnerTaylorSeries| . |Module|) 115140) ((|InnerTaylorSeries| . |LinearSet|) 115101) ((|InnerTaylorSeries| . |Algebra|) 115062) ((|InnerSparseUnivariatePowerSeries| . |UnivariatePowerSeriesCategory|) 115034) ((|InnerSparseUnivariatePowerSeries| . |AbelianMonoidRing|) 115006) ((|InnerSparseUnivariatePowerSeries| . |Algebra|) 114850) ((|InnerSparseUnivariatePowerSeries| . |LinearSet|) 114694) ((|InnerSparseUnivariatePowerSeries| . |Module|) 114538) ((|InnerSparseUnivariatePowerSeries| . |CoercibleFrom|) 114362) ((|InnerSparseUnivariatePowerSeries| . |EntireRing|) 114329) ((|InnerSparseUnivariatePowerSeries| . |IntegralDomain|) 114296) ((|InnerSparseUnivariatePowerSeries| . |Functorial|) 114280) ((|InnerSparseUnivariatePowerSeries| . |BiModule|) 114099) ((|InnerSparseUnivariatePowerSeries| . |RightLinearSet|) 113932) ((|InnerSparseUnivariatePowerSeries| . |RightModule|) 113765) ((|InnerSparseUnivariatePowerSeries| . |CommutativeRing|) 113694) ((|InnerSparseUnivariatePowerSeries| . |CharacteristicZero|) 113657) ((|InnerSparseUnivariatePowerSeries| . |CharacteristicNonZero|) 113617) ((|InnerSparseUnivariatePowerSeries| . |LeftModule|) 113514) ((|InnerSparseUnivariatePowerSeries| . |LeftLinearSet|) 113391) ((|InnerSparseUnivariatePowerSeries| . |PowerSeriesCategory|) 113337) ((|InnerSparseUnivariatePowerSeries| . |PartialDifferentialSpace|) 113212) ((|InnerSparseUnivariatePowerSeries| . |PartialDifferentialDomain|) 113085) ((|InnerSparseUnivariatePowerSeries| . |PartialDifferentialRing|) 112960) ((|InnerSparseUnivariatePowerSeries| . |Eltable|) 112920) ((|InnerSparseUnivariatePowerSeries| . |DifferentialSpace|) 112868) ((|InnerSparseUnivariatePowerSeries| . |Type|) T) ((|InnerSparseUnivariatePowerSeries| . |Join|) T) ((|InnerSparseUnivariatePowerSeries| . |DifferentialDomain|) 112810) ((|InnerSparseUnivariatePowerSeries| . |Ring|) T) ((|InnerSparseUnivariatePowerSeries| . |Monoid|) T) ((|InnerSparseUnivariatePowerSeries| . |SemiRing|) T) ((|InnerSparseUnivariatePowerSeries| . |SemiGroup|) T) ((|InnerSparseUnivariatePowerSeries| . |Rng|) T) ((|InnerSparseUnivariatePowerSeries| . |AbelianGroup|) T) ((|InnerSparseUnivariatePowerSeries| . |AbelianMonoid|) T) ((|InnerSparseUnivariatePowerSeries| . |SetCategory|) T) ((|InnerSparseUnivariatePowerSeries| . |CoercibleTo|) 112784) ((|InnerSparseUnivariatePowerSeries| . |BasicType|) T) ((|InnerSparseUnivariatePowerSeries| . |AbelianSemiGroup|) T) ((|InnerSparseUnivariatePowerSeries| . |CancellationAbelianMonoid|) T) ((|InnerSparseUnivariatePowerSeries| . |DifferentialRing|) 112732) ((|IsAst| . |SpadSyntaxCategory|) T) ((|IsAst| . |HomotopicTo|) 112710) ((|IsAst| . |CoercibleTo|) 112665) ((|IsAst| . |CoercibleFrom|) 112643) ((|IsAst| . |SetCategory|) T) ((|IsAst| . |Type|) T) ((|IsAst| . |Join|) T) ((|IsAst| . |BasicType|) T) ((|IsAst| . |AbstractSyntaxCategory|) T) ((|InternalRepresentationForm| . |SetCategory|) T) ((|InternalRepresentationForm| . |CoercibleTo|) 112598) ((|InternalRepresentationForm| . |Type|) T) ((|InternalRepresentationForm| . |Join|) T) ((|InternalRepresentationForm| . |BasicType|) T) ((|InternalRepresentationForm| . |HomotopicTo|) 112576) ((|InternalRepresentationForm| . |CoercibleFrom|) 112554) ((|IntegrationResult| . |Module|) 112518) ((|IntegrationResult| . |LinearSet|) 112482) ((|IntegrationResult| . |LeftModule|) 112446) ((|IntegrationResult| . |LeftLinearSet|) 112390) ((|IntegrationResult| . |CancellationAbelianMonoid|) T) ((|IntegrationResult| . |AbelianSemiGroup|) T) ((|IntegrationResult| . |BasicType|) T) ((|IntegrationResult| . |Join|) T) ((|IntegrationResult| . |Type|) T) ((|IntegrationResult| . |CoercibleTo|) 112364) ((|IntegrationResult| . |SetCategory|) T) ((|IntegrationResult| . |AbelianMonoid|) T) ((|IntegrationResult| . |AbelianGroup|) T) ((|IntegrationResult| . |RightModule|) 112328) ((|IntegrationResult| . |RightLinearSet|) 112292) ((|IntegrationResult| . |BiModule|) 112249) ((|IntegrationResult| . |RetractableTo|) 112233) ((|IntegrationResult| . |CoercibleFrom|) 112217) ((|InnerPrimeField| . |FiniteFieldCategory|) T) ((|InnerPrimeField| . |StepThrough|) T) ((|InnerPrimeField| . |Finite|) T) ((|InnerPrimeField| . |CharacteristicNonZero|) T) ((|InnerPrimeField| . |Field|) T) ((|InnerPrimeField| . |UniqueFactorizationDomain|) T) ((|InnerPrimeField| . |PrincipalIdealDomain|) T) ((|InnerPrimeField| . |IntegralDomain|) T) ((|InnerPrimeField| . |CommutativeRing|) T) ((|InnerPrimeField| . |CoercibleFrom|) 112151) ((|InnerPrimeField| . |Module|) 112105) ((|InnerPrimeField| . |LinearSet|) 112059) ((|InnerPrimeField| . |Algebra|) 112013) ((|InnerPrimeField| . |GcdDomain|) T) ((|InnerPrimeField| . |EuclideanDomain|) T) ((|InnerPrimeField| . |BiModule|) 111958) ((|InnerPrimeField| . |RightLinearSet|) 111912) ((|InnerPrimeField| . |RightModule|) 111866) ((|InnerPrimeField| . |LeftLinearSet|) 111800) ((|InnerPrimeField| . |LeftModule|) 111754) ((|InnerPrimeField| . |EntireRing|) T) ((|InnerPrimeField| . |DivisionRing|) T) ((|InnerPrimeField| . |FieldOfPrimeCharacteristic|) T) ((|InnerPrimeField| . |DifferentialSpace|) T) ((|InnerPrimeField| . |Type|) T) ((|InnerPrimeField| . |Join|) T) ((|InnerPrimeField| . |DifferentialDomain|) 111741) ((|InnerPrimeField| . |Ring|) T) ((|InnerPrimeField| . |Monoid|) T) ((|InnerPrimeField| . |SemiRing|) T) ((|InnerPrimeField| . |SemiGroup|) T) ((|InnerPrimeField| . |Rng|) T) ((|InnerPrimeField| . |AbelianGroup|) T) ((|InnerPrimeField| . |AbelianMonoid|) T) ((|InnerPrimeField| . |SetCategory|) T) ((|InnerPrimeField| . |CoercibleTo|) 111715) ((|InnerPrimeField| . |BasicType|) T) ((|InnerPrimeField| . |AbelianSemiGroup|) T) ((|InnerPrimeField| . |CancellationAbelianMonoid|) T) ((|InnerPrimeField| . |DifferentialRing|) T) ((|InnerPrimeField| . |FiniteAlgebraicExtensionField|) 111702) ((|InnerPrimeField| . |CharacteristicZero|) 111668) ((|InnerPrimeField| . |RetractableTo|) 111655) ((|InnerPrimeField| . |VectorSpace|) 111642) ((|InnerPrimeField| . |ExtensionField|) 111629) ((|InnerPrimeField| . |ConvertibleTo|) 111606) ((|InnerPAdicInteger| . |PAdicIntegerCategory|) 111590) ((|InnerPAdicInteger| . |PrincipalIdealDomain|) T) ((|InnerPAdicInteger| . |IntegralDomain|) T) ((|InnerPAdicInteger| . |EntireRing|) T) ((|InnerPAdicInteger| . |CommutativeRing|) T) ((|InnerPAdicInteger| . |CoercibleFrom|) 111557) ((|InnerPAdicInteger| . |Module|) 111544) ((|InnerPAdicInteger| . |LinearSet|) 111531) ((|InnerPAdicInteger| . |RightModule|) 111518) ((|InnerPAdicInteger| . |RightLinearSet|) 111505) ((|InnerPAdicInteger| . |BiModule|) 111490) ((|InnerPAdicInteger| . |Algebra|) 111477) ((|InnerPAdicInteger| . |GcdDomain|) T) ((|InnerPAdicInteger| . |EuclideanDomain|) T) ((|InnerPAdicInteger| . |Ring|) T) ((|InnerPAdicInteger| . |Monoid|) T) ((|InnerPAdicInteger| . |SemiRing|) T) ((|InnerPAdicInteger| . |SemiGroup|) T) ((|InnerPAdicInteger| . |Rng|) T) ((|InnerPAdicInteger| . |AbelianGroup|) T) ((|InnerPAdicInteger| . |LeftLinearSet|) 111444) ((|InnerPAdicInteger| . |AbelianMonoid|) T) ((|InnerPAdicInteger| . |SetCategory|) T) ((|InnerPAdicInteger| . |CoercibleTo|) 111418) ((|InnerPAdicInteger| . |Type|) T) ((|InnerPAdicInteger| . |Join|) T) ((|InnerPAdicInteger| . |BasicType|) T) ((|InnerPAdicInteger| . |AbelianSemiGroup|) T) ((|InnerPAdicInteger| . |CancellationAbelianMonoid|) T) ((|InnerPAdicInteger| . |LeftModule|) 111405) ((|InnerPAdicInteger| . |CharacteristicZero|) T) ((|IP4Address| . |SetCategory|) T) ((|IP4Address| . |CoercibleTo|) 111379) ((|IP4Address| . |Type|) T) ((|IP4Address| . |Join|) T) ((|IP4Address| . |BasicType|) T) ((|IOMode| . |SetCategory|) T) ((|IOMode| . |CoercibleTo|) 111353) ((|IOMode| . |Type|) T) ((|IOMode| . |Join|) T) ((|IOMode| . |BasicType|) T) ((|InputOutputBinaryFile| . |InputOutputByteConduit|) T) ((|InputOutputBinaryFile| . |OutputByteConduit|) T) ((|InputOutputBinaryFile| . |Conduit|) T) ((|InputOutputBinaryFile| . |InputByteConduit|) T) ((|InputOutputBinaryFile| . |CoercibleTo|) 111327) ((|Interval| . |IntervalCategory|) 111311) ((|Interval| . |ArcHyperbolicFunctionCategory|) T) ((|Interval| . |ArcTrigonometricFunctionCategory|) T) ((|Interval| . |ElementaryFunctionCategory|) T) ((|Interval| . |HyperbolicFunctionCategory|) T) ((|Interval| . |TrigonometricFunctionCategory|) T) ((|Interval| . |TranscendentalFunctionCategory|) T) ((|Interval| . |RetractableTo|) 111288) ((|Interval| . |RadicalCategory|) T) ((|Interval| . |OrderedType|) T) ((|Interval| . |OrderedSet|) T) ((|Interval| . |IntegralDomain|) T) ((|Interval| . |EntireRing|) T) ((|Interval| . |CommutativeRing|) T) ((|Interval| . |CoercibleFrom|) 111255) ((|Interval| . |Module|) 111242) ((|Interval| . |LinearSet|) 111229) ((|Interval| . |LeftModule|) 111216) ((|Interval| . |LeftLinearSet|) 111183) ((|Interval| . |CancellationAbelianMonoid|) T) ((|Interval| . |AbelianSemiGroup|) T) ((|Interval| . |BasicType|) T) ((|Interval| . |Join|) T) ((|Interval| . |Type|) T) ((|Interval| . |CoercibleTo|) 111157) ((|Interval| . |SetCategory|) T) ((|Interval| . |AbelianMonoid|) T) ((|Interval| . |AbelianGroup|) T) ((|Interval| . |RightModule|) 111144) ((|Interval| . |RightLinearSet|) 111131) ((|Interval| . |BiModule|) 111116) ((|Interval| . |Ring|) T) ((|Interval| . |Monoid|) T) ((|Interval| . |SemiRing|) T) ((|Interval| . |SemiGroup|) T) ((|Interval| . |Rng|) T) ((|Interval| . |Algebra|) 111103) ((|Interval| . |GcdDomain|) T) ((|InnerTable| . |TableAggregate|) 111082) ((|InnerTable| . |Dictionary|) 111024) ((|InnerTable| . |BagAggregate|) 110966) ((|InnerTable| . |ShallowlyMutableAggregate|) 110895) ((|InnerTable| . |Collection|) 110837) ((|InnerTable| . |ConvertibleTo|) NIL) ((|InnerTable| . |DictionaryOperations|) 110779) ((|InnerTable| . |IndexedAggregate|) 110758) ((|InnerTable| . |Evalable|) 110518) ((|InnerTable| . |InnerEvalable|) 110266) ((|InnerTable| . |Functorial|) 110195) ((|InnerTable| . |HomogeneousAggregate|) 110124) ((|InnerTable| . |Eltable|) 110103) ((|InnerTable| . |EltableAggregate|) 110082) ((|InnerTable| . |KeyedDictionary|) 110061) ((|InnerTable| . |SetCategory|) T) ((|InnerTable| . |CoercibleTo|) 110035) ((|InnerTable| . |BasicType|) T) ((|InnerTable| . |Type|) T) ((|InnerTable| . |Join|) T) ((|InnerTable| . |Aggregate|) T) ((|InnerTable| . |FiniteAggregate|) 109977) ((|Int8| . |OrderedFinite|) T) ((|Int8| . |OrderedType|) T) ((|Int8| . |OrderedSet|) T) ((|Int8| . |SetCategory|) T) ((|Int8| . |CoercibleTo|) 109951) ((|Int8| . |Type|) T) ((|Int8| . |Join|) T) ((|Int8| . |BasicType|) T) ((|Int8| . |Finite|) T) ((|Int64| . |OrderedFinite|) T) ((|Int64| . |OrderedType|) T) ((|Int64| . |OrderedSet|) T) ((|Int64| . |SetCategory|) T) ((|Int64| . |CoercibleTo|) 109925) ((|Int64| . |Type|) T) ((|Int64| . |Join|) T) ((|Int64| . |BasicType|) T) ((|Int64| . |Finite|) T) ((|Int32| . |OrderedFinite|) T) ((|Int32| . |OrderedType|) T) ((|Int32| . |OrderedSet|) T) ((|Int32| . |SetCategory|) T) ((|Int32| . |CoercibleTo|) 109899) ((|Int32| . |Type|) T) ((|Int32| . |Join|) T) ((|Int32| . |BasicType|) T) ((|Int32| . |Finite|) T) ((|Int16| . |OrderedFinite|) T) ((|Int16| . |OrderedType|) T) ((|Int16| . |OrderedSet|) T) ((|Int16| . |SetCategory|) T) ((|Int16| . |CoercibleTo|) 109873) ((|Int16| . |Type|) T) ((|Int16| . |Join|) T) ((|Int16| . |BasicType|) T) ((|Int16| . |Finite|) T) ((|Integer| . |IntegerNumberSystem|) T) ((|Integer| . |UniqueFactorizationDomain|) T) ((|Integer| . |StepThrough|) T) ((|Integer| . |RetractableTo|) 109850) ((|Integer| . |ConvertibleTo|) 109736) ((|Integer| . |RealConstant|) T) ((|Integer| . |PatternMatchable|) 109713) ((|Integer| . |OrderedRing|) T) ((|Integer| . |OrderedCancellationAbelianMonoid|) T) ((|Integer| . |OrderedAbelianSemiGroup|) T) ((|Integer| . |OrderedType|) T) ((|Integer| . |OrderedSet|) T) ((|Integer| . |OrderedAbelianMonoid|) T) ((|Integer| . |OrderedAbelianGroup|) T) ((|Integer| . |OrderedIntegralDomain|) T) ((|Integer| . |LeftModule|) 109680) ((|Integer| . |LinearlyExplicitRingOver|) 109657) ((|Integer| . |PrincipalIdealDomain|) T) ((|Integer| . |IntegralDomain|) T) ((|Integer| . |EntireRing|) T) ((|Integer| . |CommutativeRing|) T) ((|Integer| . |CoercibleFrom|) 109624) ((|Integer| . |Module|) 109611) ((|Integer| . |LinearSet|) 109598) ((|Integer| . |RightModule|) 109585) ((|Integer| . |RightLinearSet|) 109572) ((|Integer| . |BiModule|) 109557) ((|Integer| . |Algebra|) 109544) ((|Integer| . |GcdDomain|) T) ((|Integer| . |EuclideanDomain|) T) ((|Integer| . |DifferentialSpace|) T) ((|Integer| . |DifferentialDomain|) 109531) ((|Integer| . |DifferentialRing|) T) ((|Integer| . |CombinatorialFunctionCategory|) T) ((|Integer| . |Ring|) T) ((|Integer| . |Monoid|) T) ((|Integer| . |SemiRing|) T) ((|Integer| . |SemiGroup|) T) ((|Integer| . |Rng|) T) ((|Integer| . |AbelianGroup|) T) ((|Integer| . |LeftLinearSet|) 109498) ((|Integer| . |AbelianMonoid|) T) ((|Integer| . |SetCategory|) T) ((|Integer| . |CoercibleTo|) 109472) ((|Integer| . |Type|) T) ((|Integer| . |Join|) T) ((|Integer| . |BasicType|) T) ((|Integer| . |AbelianSemiGroup|) T) ((|Integer| . |CancellationAbelianMonoid|) T) ((|Integer| . |CharacteristicZero|) T) ((|InputForm| . |SExpressionCategory|) 109396) ((|InputForm| . |BasicType|) T) ((|InputForm| . |CoercibleTo|) 109370) ((|InputForm| . |SetCategory|) T) ((|InputForm| . |Eltable|) 109314) ((|InputForm| . |Type|) T) ((|InputForm| . |Join|) T) ((|InputForm| . |ConvertibleFrom|) 109187) ((|InputForm| . |ConvertibleTo|) 109160) ((|InetClientStreamSocket| . |NetworkClientSocket|) 109134) ((|InetClientStreamSocket| . |InputByteConduit|) T) ((|InetClientStreamSocket| . |Conduit|) T) ((|InetClientStreamSocket| . |OutputByteConduit|) T) ((|InetClientStreamSocket| . |InputOutputByteConduit|) T) ((|InetClientStreamSocket| . |CoercibleTo|) 109108) ((|IndexedExponents| . |OrderedAbelianMonoidSup|) T) ((|IndexedExponents| . |CancellationAbelianMonoid|) T) ((|IndexedExponents| . |AbelianSemiGroup|) T) ((|IndexedExponents| . |BasicType|) T) ((|IndexedExponents| . |Join|) T) ((|IndexedExponents| . |Type|) T) ((|IndexedExponents| . |CoercibleTo|) 109082) ((|IndexedExponents| . |SetCategory|) T) ((|IndexedExponents| . |AbelianMonoid|) T) ((|IndexedExponents| . |OrderedAbelianMonoid|) T) ((|IndexedExponents| . |OrderedSet|) T) ((|IndexedExponents| . |OrderedType|) T) ((|IndexedExponents| . |OrderedAbelianSemiGroup|) T) ((|IndexedExponents| . |OrderedCancellationAbelianMonoid|) T) ((|IndexedExponents| . |IndexedDirectProductCategory|) 109043) ((|IndexedExponents| . |Functorial|) 109009) ((|IndexedExponents| . |ConvertibleFrom|) 108938) ((|InputBinaryFile| . |InputByteConduit|) T) ((|InputBinaryFile| . |Conduit|) T) ((|InputBinaryFile| . |CoercibleTo|) 108912) ((|InAst| . |SpadSyntaxCategory|) T) ((|InAst| . |HomotopicTo|) 108890) ((|InAst| . |CoercibleTo|) 108845) ((|InAst| . |CoercibleFrom|) 108823) ((|InAst| . |SetCategory|) T) ((|InAst| . |Type|) T) ((|InAst| . |Join|) T) ((|InAst| . |BasicType|) T) ((|InAst| . |AbstractSyntaxCategory|) T) ((|ImportAst| . |SpadSyntaxCategory|) T) ((|ImportAst| . |HomotopicTo|) 108801) ((|ImportAst| . |CoercibleTo|) 108756) ((|ImportAst| . |CoercibleFrom|) 108734) ((|ImportAst| . |SetCategory|) T) ((|ImportAst| . |Type|) T) ((|ImportAst| . |Join|) T) ((|ImportAst| . |BasicType|) T) ((|ImportAst| . |AbstractSyntaxCategory|) T) ((|InnerFiniteField| . |FiniteAlgebraicExtensionField|) 108698) ((|InnerFiniteField| . |DifferentialRing|) T) ((|InnerFiniteField| . |DifferentialDomain|) 108685) ((|InnerFiniteField| . |DifferentialSpace|) T) ((|InnerFiniteField| . |Finite|) T) ((|InnerFiniteField| . |StepThrough|) T) ((|InnerFiniteField| . |FiniteFieldCategory|) T) ((|InnerFiniteField| . |CharacteristicZero|) 108651) ((|InnerFiniteField| . |CoercibleFrom|) 108552) ((|InnerFiniteField| . |LeftModule|) 108473) ((|InnerFiniteField| . |LeftLinearSet|) 108374) ((|InnerFiniteField| . |CancellationAbelianMonoid|) T) ((|InnerFiniteField| . |AbelianSemiGroup|) T) ((|InnerFiniteField| . |BasicType|) T) ((|InnerFiniteField| . |Join|) T) ((|InnerFiniteField| . |Type|) T) ((|InnerFiniteField| . |CoercibleTo|) 108348) ((|InnerFiniteField| . |SetCategory|) T) ((|InnerFiniteField| . |AbelianMonoid|) T) ((|InnerFiniteField| . |AbelianGroup|) T) ((|InnerFiniteField| . |Rng|) T) ((|InnerFiniteField| . |SemiGroup|) T) ((|InnerFiniteField| . |SemiRing|) T) ((|InnerFiniteField| . |Monoid|) T) ((|InnerFiniteField| . |Ring|) T) ((|InnerFiniteField| . |Field|) T) ((|InnerFiniteField| . |UniqueFactorizationDomain|) T) ((|InnerFiniteField| . |PrincipalIdealDomain|) T) ((|InnerFiniteField| . |IntegralDomain|) T) ((|InnerFiniteField| . |CommutativeRing|) T) ((|InnerFiniteField| . |Module|) 108269) ((|InnerFiniteField| . |LinearSet|) 108190) ((|InnerFiniteField| . |Algebra|) 108144) ((|InnerFiniteField| . |GcdDomain|) T) ((|InnerFiniteField| . |EuclideanDomain|) T) ((|InnerFiniteField| . |BiModule|) 108049) ((|InnerFiniteField| . |RightLinearSet|) 107970) ((|InnerFiniteField| . |RightModule|) 107891) ((|InnerFiniteField| . |EntireRing|) T) ((|InnerFiniteField| . |DivisionRing|) T) ((|InnerFiniteField| . |FieldOfPrimeCharacteristic|) T) ((|InnerFiniteField| . |CharacteristicNonZero|) T) ((|InnerFiniteField| . |RetractableTo|) 107855) ((|InnerFiniteField| . |VectorSpace|) 107819) ((|InnerFiniteField| . |ExtensionField|) 107783) ((|IfAst| . |SpadSyntaxCategory|) T) ((|IfAst| . |HomotopicTo|) 107761) ((|IfAst| . |CoercibleTo|) 107716) ((|IfAst| . |CoercibleFrom|) 107694) ((|IfAst| . |SetCategory|) T) ((|IfAst| . |Type|) T) ((|IfAst| . |Join|) T) ((|IfAst| . |BasicType|) T) ((|IfAst| . |AbstractSyntaxCategory|) T) ((|IndexedFlexibleArray| . |OneDimensionalArrayAggregate|) 107678) ((|IndexedFlexibleArray| . |ShallowlyMutableAggregate|) 107662) ((|IndexedFlexibleArray| . |FiniteAggregate|) 107646) ((|IndexedFlexibleArray| . |Aggregate|) T) ((|IndexedFlexibleArray| . |Join|) T) ((|IndexedFlexibleArray| . |Type|) T) ((|IndexedFlexibleArray| . |BasicType|) 107556) ((|IndexedFlexibleArray| . |CoercibleTo|) 107430) ((|IndexedFlexibleArray| . |Evalable|) 107354) ((|IndexedFlexibleArray| . |InnerEvalable|) 107273) ((|IndexedFlexibleArray| . |Functorial|) 107257) ((|IndexedFlexibleArray| . |SetCategory|) 107194) ((|IndexedFlexibleArray| . |HomogeneousAggregate|) 107178) ((|IndexedFlexibleArray| . |LinearAggregate|) 107162) ((|IndexedFlexibleArray| . |EltableAggregate|) 107134) ((|IndexedFlexibleArray| . |Eltable|) 107063) ((|IndexedFlexibleArray| . |IndexedAggregate|) 107035) ((|IndexedFlexibleArray| . |ConvertibleTo|) 106971) ((|IndexedFlexibleArray| . |Collection|) 106955) ((|IndexedFlexibleArray| . |OrderedSet|) 106926) ((|IndexedFlexibleArray| . |OrderedType|) 106897) ((|IndexedFlexibleArray| . |FiniteLinearAggregate|) 106881) ((|IndexedFlexibleArray| . |ExtensibleLinearAggregate|) 106865) ((|InnerFreeAbelianMonoid| . |FreeAbelianMonoidCategory|) 106844) ((|InnerFreeAbelianMonoid| . |CoercibleFrom|) 106828) ((|InnerFreeAbelianMonoid| . |RetractableTo|) 106812) ((|InnerFreeAbelianMonoid| . |AbelianMonoid|) T) ((|InnerFreeAbelianMonoid| . |SetCategory|) T) ((|InnerFreeAbelianMonoid| . |CoercibleTo|) 106786) ((|InnerFreeAbelianMonoid| . |Type|) T) ((|InnerFreeAbelianMonoid| . |Join|) T) ((|InnerFreeAbelianMonoid| . |BasicType|) T) ((|InnerFreeAbelianMonoid| . |AbelianSemiGroup|) T) ((|InnerFreeAbelianMonoid| . |CancellationAbelianMonoid|) T) ((|IndexedProductTerm| . |BasicType|) T) ((|IndexedProductTerm| . |Join|) T) ((|IndexedProductTerm| . |Type|) T) ((|IndexedProductTerm| . |CoercibleTo|) 106756) ((|IndexedDirectProductOrderedAbelianMonoidSup| . |OrderedAbelianMonoidSup|) T) ((|IndexedDirectProductOrderedAbelianMonoidSup| . |CancellationAbelianMonoid|) T) ((|IndexedDirectProductOrderedAbelianMonoidSup| . |AbelianSemiGroup|) T) ((|IndexedDirectProductOrderedAbelianMonoidSup| . |BasicType|) T) ((|IndexedDirectProductOrderedAbelianMonoidSup| . |Join|) T) ((|IndexedDirectProductOrderedAbelianMonoidSup| . |Type|) T) ((|IndexedDirectProductOrderedAbelianMonoidSup| . |CoercibleTo|) 106730) ((|IndexedDirectProductOrderedAbelianMonoidSup| . |SetCategory|) T) ((|IndexedDirectProductOrderedAbelianMonoidSup| . |AbelianMonoid|) T) ((|IndexedDirectProductOrderedAbelianMonoidSup| . |OrderedAbelianMonoid|) T) ((|IndexedDirectProductOrderedAbelianMonoidSup| . |OrderedSet|) T) ((|IndexedDirectProductOrderedAbelianMonoidSup| . |OrderedType|) T) ((|IndexedDirectProductOrderedAbelianMonoidSup| . |OrderedAbelianSemiGroup|) T) ((|IndexedDirectProductOrderedAbelianMonoidSup| . |OrderedCancellationAbelianMonoid|) T) ((|IndexedDirectProductOrderedAbelianMonoidSup| . |IndexedDirectProductCategory|) 106709) ((|IndexedDirectProductOrderedAbelianMonoidSup| . |Functorial|) 106693) ((|IndexedDirectProductOrderedAbelianMonoidSup| . |ConvertibleFrom|) 106640) ((|IndexedDirectProductOrderedAbelianMonoid| . |OrderedAbelianMonoid|) T) ((|IndexedDirectProductOrderedAbelianMonoid| . |OrderedSet|) T) ((|IndexedDirectProductOrderedAbelianMonoid| . |OrderedType|) T) ((|IndexedDirectProductOrderedAbelianMonoid| . |OrderedAbelianSemiGroup|) T) ((|IndexedDirectProductOrderedAbelianMonoid| . |AbelianSemiGroup|) T) ((|IndexedDirectProductOrderedAbelianMonoid| . |BasicType|) T) ((|IndexedDirectProductOrderedAbelianMonoid| . |Join|) T) ((|IndexedDirectProductOrderedAbelianMonoid| . |Type|) T) ((|IndexedDirectProductOrderedAbelianMonoid| . |CoercibleTo|) 106614) ((|IndexedDirectProductOrderedAbelianMonoid| . |SetCategory|) T) ((|IndexedDirectProductOrderedAbelianMonoid| . |AbelianMonoid|) T) ((|IndexedDirectProductOrderedAbelianMonoid| . |IndexedDirectProductCategory|) 106593) ((|IndexedDirectProductOrderedAbelianMonoid| . |Functorial|) 106577) ((|IndexedDirectProductOrderedAbelianMonoid| . |ConvertibleFrom|) 106524) ((|IndexedDirectProductObject| . |IndexedDirectProductCategory|) 106503) ((|IndexedDirectProductObject| . |CoercibleTo|) 106419) ((|IndexedDirectProductObject| . |SetCategory|) 106354) ((|IndexedDirectProductObject| . |Functorial|) 106338) ((|IndexedDirectProductObject| . |ConvertibleFrom|) 106285) ((|IndexedDirectProductObject| . |Type|) T) ((|IndexedDirectProductObject| . |Join|) T) ((|IndexedDirectProductObject| . |BasicType|) T) ((|IndexedDirectProductAbelianMonoid| . |AbelianMonoid|) T) ((|IndexedDirectProductAbelianMonoid| . |SetCategory|) T) ((|IndexedDirectProductAbelianMonoid| . |CoercibleTo|) 106259) ((|IndexedDirectProductAbelianMonoid| . |Type|) T) ((|IndexedDirectProductAbelianMonoid| . |Join|) T) ((|IndexedDirectProductAbelianMonoid| . |BasicType|) T) ((|IndexedDirectProductAbelianMonoid| . |AbelianSemiGroup|) T) ((|IndexedDirectProductAbelianMonoid| . |IndexedDirectProductCategory|) 106238) ((|IndexedDirectProductAbelianMonoid| . |Functorial|) 106222) ((|IndexedDirectProductAbelianMonoid| . |ConvertibleFrom|) 106169) ((|IndexedDirectProductAbelianGroup| . |AbelianGroup|) T) ((|IndexedDirectProductAbelianGroup| . |LeftLinearSet|) 106146) ((|IndexedDirectProductAbelianGroup| . |AbelianMonoid|) T) ((|IndexedDirectProductAbelianGroup| . |SetCategory|) T) ((|IndexedDirectProductAbelianGroup| . |CoercibleTo|) 106120) ((|IndexedDirectProductAbelianGroup| . |Type|) T) ((|IndexedDirectProductAbelianGroup| . |Join|) T) ((|IndexedDirectProductAbelianGroup| . |BasicType|) T) ((|IndexedDirectProductAbelianGroup| . |AbelianSemiGroup|) T) ((|IndexedDirectProductAbelianGroup| . |CancellationAbelianMonoid|) T) ((|IndexedDirectProductAbelianGroup| . |IndexedDirectProductCategory|) 106099) ((|IndexedDirectProductAbelianGroup| . |Functorial|) 106083) ((|IndexedDirectProductAbelianGroup| . |ConvertibleFrom|) 106030) ((|Identifier| . |SetCategory|) T) ((|Identifier| . |CoercibleTo|) 106004) ((|Identifier| . |Type|) T) ((|Identifier| . |Join|) T) ((|Identifier| . |BasicType|) T) ((|PolynomialIdeals| . |SetCategory|) T) ((|PolynomialIdeals| . |CoercibleTo|) 105978) ((|PolynomialIdeals| . |Type|) T) ((|PolynomialIdeals| . |Join|) T) ((|PolynomialIdeals| . |BasicType|) T) ((|IndexCard| . |OrderedSet|) T) ((|IndexCard| . |CoercibleTo|) 105952) ((|IndexCard| . |SetCategory|) T) ((|IndexCard| . |BasicType|) T) ((|IndexCard| . |Join|) T) ((|IndexCard| . |Type|) T) ((|IndexCard| . |OrderedType|) T) ((|IndexCard| . |CoercibleFrom|) 105930) ((|IndexedBits| . |BitAggregate|) T) ((|IndexedBits| . |FiniteLinearAggregate|) 105907) ((|IndexedBits| . |OrderedType|) T) ((|IndexedBits| . |OrderedSet|) T) ((|IndexedBits| . |Collection|) 105884) ((|IndexedBits| . |ConvertibleTo|) 105859) ((|IndexedBits| . |Eltable|) 105781) ((|IndexedBits| . |IndexedAggregate|) 105746) ((|IndexedBits| . |EltableAggregate|) 105711) ((|IndexedBits| . |LinearAggregate|) 105688) ((|IndexedBits| . |HomogeneousAggregate|) 105665) ((|IndexedBits| . |SetCategory|) T) ((|IndexedBits| . |Functorial|) 105642) ((|IndexedBits| . |InnerEvalable|) NIL) ((|IndexedBits| . |Evalable|) NIL) ((|IndexedBits| . |CoercibleTo|) 105616) ((|IndexedBits| . |BasicType|) T) ((|IndexedBits| . |Aggregate|) T) ((|IndexedBits| . |FiniteAggregate|) 105593) ((|IndexedBits| . |ShallowlyMutableAggregate|) 105570) ((|IndexedBits| . |OneDimensionalArrayAggregate|) 105547) ((|IndexedBits| . |Logic|) T) ((|IndexedBits| . |Join|) T) ((|IndexedBits| . |Type|) T) ((|IndexedBits| . |BooleanLogic|) T) ((|InnerTwoDimensionalArray| . |TwoDimensionalArrayCategory|) 105521) ((|InnerTwoDimensionalArray| . |ShallowlyMutableAggregate|) 105505) ((|InnerTwoDimensionalArray| . |HomogeneousAggregate|) 105489) ((|InnerTwoDimensionalArray| . |SetCategory|) 105459) ((|InnerTwoDimensionalArray| . |Functorial|) 105443) ((|InnerTwoDimensionalArray| . |InnerEvalable|) 105362) ((|InnerTwoDimensionalArray| . |Evalable|) 105286) ((|InnerTwoDimensionalArray| . |CoercibleTo|) 105188) ((|InnerTwoDimensionalArray| . |BasicType|) 105126) ((|InnerTwoDimensionalArray| . |Type|) T) ((|InnerTwoDimensionalArray| . |Join|) T) ((|InnerTwoDimensionalArray| . |Aggregate|) T) ((|InnerTwoDimensionalArray| . |FiniteAggregate|) 105110) ((|IndexedOneDimensionalArray| . |OneDimensionalArrayAggregate|) 105094) ((|IndexedOneDimensionalArray| . |ShallowlyMutableAggregate|) 105078) ((|IndexedOneDimensionalArray| . |FiniteAggregate|) 105062) ((|IndexedOneDimensionalArray| . |Aggregate|) T) ((|IndexedOneDimensionalArray| . |Join|) T) ((|IndexedOneDimensionalArray| . |Type|) T) ((|IndexedOneDimensionalArray| . |BasicType|) 104972) ((|IndexedOneDimensionalArray| . |CoercibleTo|) 104846) ((|IndexedOneDimensionalArray| . |Evalable|) 104770) ((|IndexedOneDimensionalArray| . |InnerEvalable|) 104689) ((|IndexedOneDimensionalArray| . |Functorial|) 104673) ((|IndexedOneDimensionalArray| . |SetCategory|) 104610) ((|IndexedOneDimensionalArray| . |HomogeneousAggregate|) 104594) ((|IndexedOneDimensionalArray| . |LinearAggregate|) 104578) ((|IndexedOneDimensionalArray| . |EltableAggregate|) 104550) ((|IndexedOneDimensionalArray| . |Eltable|) 104479) ((|IndexedOneDimensionalArray| . |IndexedAggregate|) 104451) ((|IndexedOneDimensionalArray| . |ConvertibleTo|) 104387) ((|IndexedOneDimensionalArray| . |Collection|) 104371) ((|IndexedOneDimensionalArray| . |OrderedSet|) 104342) ((|IndexedOneDimensionalArray| . |OrderedType|) 104313) ((|IndexedOneDimensionalArray| . |FiniteLinearAggregate|) 104297) ((|InnerAlgebraicNumber| . |ExpressionSpace|) T) ((|InnerAlgebraicNumber| . |BasicType|) T) ((|InnerAlgebraicNumber| . |Join|) T) ((|InnerAlgebraicNumber| . |Type|) T) ((|InnerAlgebraicNumber| . |CoercibleTo|) 104271) ((|InnerAlgebraicNumber| . |SetCategory|) T) ((|InnerAlgebraicNumber| . |CoercibleFrom|) 104118) ((|InnerAlgebraicNumber| . |RetractableTo|) 104046) ((|InnerAlgebraicNumber| . |InnerEvalable|) 104008) ((|InnerAlgebraicNumber| . |Evalable|) 103995) ((|InnerAlgebraicNumber| . |AlgebraicallyClosedField|) T) ((|InnerAlgebraicNumber| . |RadicalCategory|) T) ((|InnerAlgebraicNumber| . |DivisionRing|) T) ((|InnerAlgebraicNumber| . |BiModule|) 103940) ((|InnerAlgebraicNumber| . |RightLinearSet|) 103894) ((|InnerAlgebraicNumber| . |RightModule|) 103848) ((|InnerAlgebraicNumber| . |EntireRing|) T) ((|InnerAlgebraicNumber| . |Module|) 103802) ((|InnerAlgebraicNumber| . |LinearSet|) 103756) ((|InnerAlgebraicNumber| . |LeftModule|) 103690) ((|InnerAlgebraicNumber| . |LeftLinearSet|) 103624) ((|InnerAlgebraicNumber| . |CancellationAbelianMonoid|) T) ((|InnerAlgebraicNumber| . |AbelianSemiGroup|) T) ((|InnerAlgebraicNumber| . |AbelianMonoid|) T) ((|InnerAlgebraicNumber| . |AbelianGroup|) T) ((|InnerAlgebraicNumber| . |Ring|) T) ((|InnerAlgebraicNumber| . |Monoid|) T) ((|InnerAlgebraicNumber| . |SemiRing|) T) ((|InnerAlgebraicNumber| . |SemiGroup|) T) ((|InnerAlgebraicNumber| . |Rng|) T) ((|InnerAlgebraicNumber| . |Algebra|) 103578) ((|InnerAlgebraicNumber| . |EuclideanDomain|) T) ((|InnerAlgebraicNumber| . |GcdDomain|) T) ((|InnerAlgebraicNumber| . |CommutativeRing|) T) ((|InnerAlgebraicNumber| . |IntegralDomain|) T) ((|InnerAlgebraicNumber| . |PrincipalIdealDomain|) T) ((|InnerAlgebraicNumber| . |UniqueFactorizationDomain|) T) ((|InnerAlgebraicNumber| . |Field|) T) ((|InnerAlgebraicNumber| . |LinearlyExplicitRingOver|) 103527) ((|InnerAlgebraicNumber| . |RealConstant|) T) ((|InnerAlgebraicNumber| . |ConvertibleTo|) 103452) ((|InnerAlgebraicNumber| . |CharacteristicZero|) T) ((|InnerAlgebraicNumber| . |DifferentialRing|) T) ((|InnerAlgebraicNumber| . |DifferentialDomain|) 103439) ((|InnerAlgebraicNumber| . |DifferentialSpace|) T) ((|Hostname| . |SetCategory|) T) ((|Hostname| . |CoercibleTo|) 103394) ((|Hostname| . |Type|) T) ((|Hostname| . |Join|) T) ((|Hostname| . |BasicType|) T) ((|HexadecimalExpansion| . |QuotientFieldCategory|) 103371) ((|HexadecimalExpansion| . |StepThrough|) T) ((|HexadecimalExpansion| . |CoercibleFrom|) 103305) ((|HexadecimalExpansion| . |RetractableTo|) 103249) ((|HexadecimalExpansion| . |ConvertibleTo|) 103150) ((|HexadecimalExpansion| . |RealConstant|) T) ((|HexadecimalExpansion| . |PolynomialFactorizationExplicit|) NIL) ((|HexadecimalExpansion| . |Patternable|) 103127) ((|HexadecimalExpansion| . |OrderedRing|) T) ((|HexadecimalExpansion| . |OrderedCancellationAbelianMonoid|) T) ((|HexadecimalExpansion| . |OrderedAbelianSemiGroup|) T) ((|HexadecimalExpansion| . |OrderedType|) T) ((|HexadecimalExpansion| . |OrderedSet|) T) ((|HexadecimalExpansion| . |OrderedAbelianMonoid|) T) ((|HexadecimalExpansion| . |OrderedAbelianGroup|) T) ((|HexadecimalExpansion| . |OrderedIntegralDomain|) T) ((|HexadecimalExpansion| . |PatternMatchable|) 103104) ((|HexadecimalExpansion| . |FullyPatternMatchable|) 103081) ((|HexadecimalExpansion| . |LinearlyExplicitRingOver|) 103058) ((|HexadecimalExpansion| . |FullyLinearlyExplicitRingOver|) 103035) ((|HexadecimalExpansion| . |Eltable|) NIL) ((|HexadecimalExpansion| . |Evalable|) NIL) ((|HexadecimalExpansion| . |InnerEvalable|) NIL) ((|HexadecimalExpansion| . |Functorial|) 103012) ((|HexadecimalExpansion| . |FullyEvalableOver|) 102989) ((|HexadecimalExpansion| . |DivisionRing|) T) ((|HexadecimalExpansion| . |BiModule|) 102907) ((|HexadecimalExpansion| . |RightLinearSet|) 102841) ((|HexadecimalExpansion| . |RightModule|) 102775) ((|HexadecimalExpansion| . |EntireRing|) T) ((|HexadecimalExpansion| . |Module|) 102709) ((|HexadecimalExpansion| . |LinearSet|) 102643) ((|HexadecimalExpansion| . |LeftModule|) 102577) ((|HexadecimalExpansion| . |LeftLinearSet|) 102511) ((|HexadecimalExpansion| . |Algebra|) 102445) ((|HexadecimalExpansion| . |EuclideanDomain|) T) ((|HexadecimalExpansion| . |GcdDomain|) T) ((|HexadecimalExpansion| . |CommutativeRing|) T) ((|HexadecimalExpansion| . |IntegralDomain|) T) ((|HexadecimalExpansion| . |PrincipalIdealDomain|) T) ((|HexadecimalExpansion| . |UniqueFactorizationDomain|) T) ((|HexadecimalExpansion| . |Field|) T) ((|HexadecimalExpansion| . |DifferentialRing|) T) ((|HexadecimalExpansion| . |DifferentialDomain|) 102432) ((|HexadecimalExpansion| . |DifferentialSpace|) T) ((|HexadecimalExpansion| . |DifferentialSpaceExtension|) 102409) ((|HexadecimalExpansion| . |PartialDifferentialDomain|) NIL) ((|HexadecimalExpansion| . |PartialDifferentialSpace|) NIL) ((|HexadecimalExpansion| . |PartialDifferentialRing|) NIL) ((|HexadecimalExpansion| . |DifferentialExtension|) 102386) ((|HexadecimalExpansion| . |CharacteristicZero|) T) ((|HexadecimalExpansion| . |CharacteristicNonZero|) NIL) ((|HexadecimalExpansion| . |CancellationAbelianMonoid|) T) ((|HexadecimalExpansion| . |AbelianSemiGroup|) T) ((|HexadecimalExpansion| . |BasicType|) T) ((|HexadecimalExpansion| . |Join|) T) ((|HexadecimalExpansion| . |Type|) T) ((|HexadecimalExpansion| . |CoercibleTo|) 102297) ((|HexadecimalExpansion| . |SetCategory|) T) ((|HexadecimalExpansion| . |AbelianMonoid|) T) ((|HexadecimalExpansion| . |AbelianGroup|) T) ((|HexadecimalExpansion| . |Ring|) T) ((|HexadecimalExpansion| . |Monoid|) T) ((|HexadecimalExpansion| . |SemiRing|) T) ((|HexadecimalExpansion| . |SemiGroup|) T) ((|HexadecimalExpansion| . |Rng|) T) ((|HyperellipticFiniteDivisor| . |FiniteDivisorCategory|) 102266) ((|HyperellipticFiniteDivisor| . |CancellationAbelianMonoid|) T) ((|HyperellipticFiniteDivisor| . |AbelianSemiGroup|) T) ((|HyperellipticFiniteDivisor| . |BasicType|) T) ((|HyperellipticFiniteDivisor| . |Join|) T) ((|HyperellipticFiniteDivisor| . |Type|) T) ((|HyperellipticFiniteDivisor| . |CoercibleTo|) 102240) ((|HyperellipticFiniteDivisor| . |SetCategory|) T) ((|HyperellipticFiniteDivisor| . |AbelianMonoid|) T) ((|HyperellipticFiniteDivisor| . |LeftLinearSet|) 102217) ((|HyperellipticFiniteDivisor| . |AbelianGroup|) T) ((|Heap| . |PriorityQueueAggregate|) 102201) ((|Heap| . |FiniteAggregate|) 102185) ((|Heap| . |HomogeneousAggregate|) 102169) ((|Heap| . |SetCategory|) 102139) ((|Heap| . |Functorial|) 102123) ((|Heap| . |InnerEvalable|) 102042) ((|Heap| . |Evalable|) 101966) ((|Heap| . |CoercibleTo|) 101868) ((|Heap| . |BasicType|) 101806) ((|Heap| . |Type|) T) ((|Heap| . |Join|) T) ((|Heap| . |Aggregate|) T) ((|Heap| . |ShallowlyMutableAggregate|) 101790) ((|Heap| . |BagAggregate|) 101774) ((|HeadAst| . |SpadSyntaxCategory|) T) ((|HeadAst| . |HomotopicTo|) 101752) ((|HeadAst| . |CoercibleTo|) 101707) ((|HeadAst| . |CoercibleFrom|) 101685) ((|HeadAst| . |SetCategory|) T) ((|HeadAst| . |Type|) T) ((|HeadAst| . |Join|) T) ((|HeadAst| . |BasicType|) T) ((|HeadAst| . |AbstractSyntaxCategory|) T) ((|HomogeneousDirectProduct| . |DirectProductCategory|) 101664) ((|HomogeneousDirectProduct| . |VectorSpace|) 101631) ((|HomogeneousDirectProduct| . |OrderedCancellationAbelianMonoid|) 101589) ((|HomogeneousDirectProduct| . |OrderedAbelianSemiGroup|) 101547) ((|HomogeneousDirectProduct| . |OrderedType|) 101472) ((|HomogeneousDirectProduct| . |OrderedSet|) 101397) ((|HomogeneousDirectProduct| . |OrderedAbelianMonoid|) 101355) ((|HomogeneousDirectProduct| . |OrderedAbelianMonoidSup|) 101313) ((|HomogeneousDirectProduct| . |Module|) 101242) ((|HomogeneousDirectProduct| . |LinearSet|) 101147) ((|HomogeneousDirectProduct| . |EltableAggregate|) 101119) ((|HomogeneousDirectProduct| . |Eltable|) 101091) ((|HomogeneousDirectProduct| . |IndexedAggregate|) 101063) ((|HomogeneousDirectProduct| . |RetractableTo|) 100814) ((|HomogeneousDirectProduct| . |CoercibleFrom|) 100538) ((|HomogeneousDirectProduct| . |FullyRetractableTo|) 100499) ((|HomogeneousDirectProduct| . |LinearlyExplicitRingOver|) 100371) ((|HomogeneousDirectProduct| . |LeftModule|) 100156) ((|HomogeneousDirectProduct| . |FullyLinearlyExplicitRingOver|) 100124) ((|HomogeneousDirectProduct| . |HomogeneousAggregate|) 100108) ((|HomogeneousDirectProduct| . |Functorial|) 100092) ((|HomogeneousDirectProduct| . |InnerEvalable|) 100011) ((|HomogeneousDirectProduct| . |Evalable|) 99935) ((|HomogeneousDirectProduct| . |Aggregate|) T) ((|HomogeneousDirectProduct| . |FiniteAggregate|) 99919) ((|HomogeneousDirectProduct| . |Finite|) 99894) ((|HomogeneousDirectProduct| . |DifferentialRing|) 99831) ((|HomogeneousDirectProduct| . |LeftLinearSet|) 99561) ((|HomogeneousDirectProduct| . |Rng|) 99538) ((|HomogeneousDirectProduct| . |SemiGroup|) 99515) ((|HomogeneousDirectProduct| . |SemiRing|) 99492) ((|HomogeneousDirectProduct| . |Monoid|) 99469) ((|HomogeneousDirectProduct| . |Ring|) 99446) ((|HomogeneousDirectProduct| . |DifferentialDomain|) 99309) ((|HomogeneousDirectProduct| . |DifferentialSpace|) 99178) ((|HomogeneousDirectProduct| . |DifferentialSpaceExtension|) 99146) ((|HomogeneousDirectProduct| . |PartialDifferentialDomain|) 98962) ((|HomogeneousDirectProduct| . |PartialDifferentialSpace|) 98780) ((|HomogeneousDirectProduct| . |PartialDifferentialRing|) 98684) ((|HomogeneousDirectProduct| . |DifferentialExtension|) 98652) ((|HomogeneousDirectProduct| . |CoercibleTo|) 98197) ((|HomogeneousDirectProduct| . |RightModule|) 98104) ((|HomogeneousDirectProduct| . |RightLinearSet|) 97987) ((|HomogeneousDirectProduct| . |BiModule|) 97889) ((|HomogeneousDirectProduct| . |CancellationAbelianMonoid|) 97691) ((|HomogeneousDirectProduct| . |AbelianSemiGroup|) 97428) ((|HomogeneousDirectProduct| . |BasicType|) 97033) ((|HomogeneousDirectProduct| . |Join|) T) ((|HomogeneousDirectProduct| . |Type|) T) ((|HomogeneousDirectProduct| . |SetCategory|) 96665) ((|HomogeneousDirectProduct| . |AbelianMonoid|) 96436) ((|HomogeneousDirectProduct| . |AbelianGroup|) 96322) ((|HomogeneousDistributedMultivariatePolynomial| . |PolynomialCategory|) 96214) ((|HomogeneousDistributedMultivariatePolynomial| . |CoercibleFrom|) 95886) ((|HomogeneousDistributedMultivariatePolynomial| . |RetractableTo|) 95693) ((|HomogeneousDistributedMultivariatePolynomial| . |UniqueFactorizationDomain|) 95643) ((|HomogeneousDistributedMultivariatePolynomial| . |PolynomialFactorizationExplicit|) 95593) ((|HomogeneousDistributedMultivariatePolynomial| . |PatternMatchable|) NIL) ((|HomogeneousDistributedMultivariatePolynomial| . |PartialDifferentialSpace|) 95553) ((|HomogeneousDistributedMultivariatePolynomial| . |PartialDifferentialDomain|) 95511) ((|HomogeneousDistributedMultivariatePolynomial| . |PartialDifferentialRing|) 95471) ((|HomogeneousDistributedMultivariatePolynomial| . |InnerEvalable|) 95397) ((|HomogeneousDistributedMultivariatePolynomial| . |GcdDomain|) 95315) ((|HomogeneousDistributedMultivariatePolynomial| . |LinearlyExplicitRingOver|) 95231) ((|HomogeneousDistributedMultivariatePolynomial| . |LeftModule|) 95060) ((|HomogeneousDistributedMultivariatePolynomial| . |FullyLinearlyExplicitRingOver|) 95044) ((|HomogeneousDistributedMultivariatePolynomial| . |AbelianMonoidRing|) 94965) ((|HomogeneousDistributedMultivariatePolynomial| . |Algebra|) 94728) ((|HomogeneousDistributedMultivariatePolynomial| . |LinearSet|) 94491) ((|HomogeneousDistributedMultivariatePolynomial| . |Module|) 94254) ((|HomogeneousDistributedMultivariatePolynomial| . |EntireRing|) 94140) ((|HomogeneousDistributedMultivariatePolynomial| . |IntegralDomain|) 94026) ((|HomogeneousDistributedMultivariatePolynomial| . |Functorial|) 94010) ((|HomogeneousDistributedMultivariatePolynomial| . |BiModule|) 93753) ((|HomogeneousDistributedMultivariatePolynomial| . |RightLinearSet|) 93510) ((|HomogeneousDistributedMultivariatePolynomial| . |RightModule|) 93267) ((|HomogeneousDistributedMultivariatePolynomial| . |CommutativeRing|) 93120) ((|HomogeneousDistributedMultivariatePolynomial| . |CharacteristicZero|) 93083) ((|HomogeneousDistributedMultivariatePolynomial| . |CharacteristicNonZero|) 93043) ((|HomogeneousDistributedMultivariatePolynomial| . |LeftLinearSet|) 92920) ((|HomogeneousDistributedMultivariatePolynomial| . |CancellationAbelianMonoid|) T) ((|HomogeneousDistributedMultivariatePolynomial| . |AbelianSemiGroup|) T) ((|HomogeneousDistributedMultivariatePolynomial| . |BasicType|) T) ((|HomogeneousDistributedMultivariatePolynomial| . |Join|) T) ((|HomogeneousDistributedMultivariatePolynomial| . |Type|) T) ((|HomogeneousDistributedMultivariatePolynomial| . |CoercibleTo|) 92894) ((|HomogeneousDistributedMultivariatePolynomial| . |SetCategory|) T) ((|HomogeneousDistributedMultivariatePolynomial| . |AbelianMonoid|) T) ((|HomogeneousDistributedMultivariatePolynomial| . |AbelianGroup|) T) ((|HomogeneousDistributedMultivariatePolynomial| . |Ring|) T) ((|HomogeneousDistributedMultivariatePolynomial| . |Monoid|) T) ((|HomogeneousDistributedMultivariatePolynomial| . |SemiRing|) T) ((|HomogeneousDistributedMultivariatePolynomial| . |SemiGroup|) T) ((|HomogeneousDistributedMultivariatePolynomial| . |Rng|) T) ((|HomogeneousDistributedMultivariatePolynomial| . |FullyRetractableTo|) 92878) ((|HomogeneousDistributedMultivariatePolynomial| . |FiniteAbelianMonoidRing|) 92799) ((|HomogeneousDistributedMultivariatePolynomial| . |Evalable|) 92786) ((|HomogeneousDistributedMultivariatePolynomial| . |ConvertibleTo|) 92564) ((|HashTable| . |TableAggregate|) 92543) ((|HashTable| . |Dictionary|) 92485) ((|HashTable| . |BagAggregate|) 92427) ((|HashTable| . |ShallowlyMutableAggregate|) 92356) ((|HashTable| . |Collection|) 92298) ((|HashTable| . |ConvertibleTo|) NIL) ((|HashTable| . |DictionaryOperations|) 92240) ((|HashTable| . |IndexedAggregate|) 92219) ((|HashTable| . |Evalable|) 91979) ((|HashTable| . |InnerEvalable|) 91727) ((|HashTable| . |Functorial|) 91656) ((|HashTable| . |HomogeneousAggregate|) 91585) ((|HashTable| . |Eltable|) 91564) ((|HashTable| . |EltableAggregate|) 91543) ((|HashTable| . |KeyedDictionary|) 91522) ((|HashTable| . |SetCategory|) T) ((|HashTable| . |CoercibleTo|) 91496) ((|HashTable| . |BasicType|) T) ((|HashTable| . |Type|) T) ((|HashTable| . |Join|) T) ((|HashTable| . |Aggregate|) T) ((|HashTable| . |FiniteAggregate|) 91438) ((|HasAst| . |SpadSyntaxCategory|) T) ((|HasAst| . |HomotopicTo|) 91416) ((|HasAst| . |CoercibleTo|) 91371) ((|HasAst| . |CoercibleFrom|) 91349) ((|HasAst| . |SetCategory|) T) ((|HasAst| . |Type|) T) ((|HasAst| . |Join|) T) ((|HasAst| . |BasicType|) T) ((|HasAst| . |AbstractSyntaxCategory|) T) ((|Pi| . |Field|) T) ((|Pi| . |UniqueFactorizationDomain|) T) ((|Pi| . |PrincipalIdealDomain|) T) ((|Pi| . |IntegralDomain|) T) ((|Pi| . |CommutativeRing|) T) ((|Pi| . |CoercibleFrom|) 91283) ((|Pi| . |Module|) 91237) ((|Pi| . |LinearSet|) 91191) ((|Pi| . |Algebra|) 91145) ((|Pi| . |GcdDomain|) T) ((|Pi| . |EuclideanDomain|) T) ((|Pi| . |LeftModule|) 91099) ((|Pi| . |LeftLinearSet|) 91033) ((|Pi| . |Rng|) T) ((|Pi| . |SemiGroup|) T) ((|Pi| . |SemiRing|) T) ((|Pi| . |Monoid|) T) ((|Pi| . |Ring|) T) ((|Pi| . |BiModule|) 90978) ((|Pi| . |RightLinearSet|) 90932) ((|Pi| . |RightModule|) 90886) ((|Pi| . |AbelianGroup|) T) ((|Pi| . |AbelianMonoid|) T) ((|Pi| . |SetCategory|) T) ((|Pi| . |CoercibleTo|) 90818) ((|Pi| . |Type|) T) ((|Pi| . |Join|) T) ((|Pi| . |BasicType|) T) ((|Pi| . |AbelianSemiGroup|) T) ((|Pi| . |CancellationAbelianMonoid|) T) ((|Pi| . |EntireRing|) T) ((|Pi| . |DivisionRing|) T) ((|Pi| . |CharacteristicZero|) T) ((|Pi| . |RetractableTo|) 90767) ((|Pi| . |RealConstant|) T) ((|Pi| . |ConvertibleTo|) 90636) ((|GeneralTriangularSet| . |TriangularSetCategory|) 90605) ((|GeneralTriangularSet| . |ShallowlyMutableAggregate|) 90589) ((|GeneralTriangularSet| . |CoercibleTo|) 90541) ((|GeneralTriangularSet| . |Collection|) 90525) ((|GeneralTriangularSet| . |Aggregate|) T) ((|GeneralTriangularSet| . |Join|) T) ((|GeneralTriangularSet| . |Type|) T) ((|GeneralTriangularSet| . |BasicType|) T) ((|GeneralTriangularSet| . |Evalable|) 90449) ((|GeneralTriangularSet| . |InnerEvalable|) 90368) ((|GeneralTriangularSet| . |Functorial|) 90352) ((|GeneralTriangularSet| . |SetCategory|) T) ((|GeneralTriangularSet| . |HomogeneousAggregate|) 90336) ((|GeneralTriangularSet| . |ConvertibleTo|) 90272) ((|GeneralTriangularSet| . |FiniteAggregate|) 90256) ((|GeneralTriangularSet| . |PolynomialSetCategory|) 90225) ((|GeneralSparseTable| . |TableAggregate|) 90204) ((|GeneralSparseTable| . |Dictionary|) 90146) ((|GeneralSparseTable| . |BagAggregate|) 90088) ((|GeneralSparseTable| . |ShallowlyMutableAggregate|) 90017) ((|GeneralSparseTable| . |Collection|) 89959) ((|GeneralSparseTable| . |ConvertibleTo|) NIL) ((|GeneralSparseTable| . |DictionaryOperations|) 89901) ((|GeneralSparseTable| . |IndexedAggregate|) 89880) ((|GeneralSparseTable| . |Evalable|) 89640) ((|GeneralSparseTable| . |InnerEvalable|) 89388) ((|GeneralSparseTable| . |Functorial|) 89317) ((|GeneralSparseTable| . |HomogeneousAggregate|) 89246) ((|GeneralSparseTable| . |Eltable|) 89225) ((|GeneralSparseTable| . |EltableAggregate|) 89204) ((|GeneralSparseTable| . |KeyedDictionary|) 89183) ((|GeneralSparseTable| . |SetCategory|) T) ((|GeneralSparseTable| . |CoercibleTo|) 89157) ((|GeneralSparseTable| . |BasicType|) T) ((|GeneralSparseTable| . |Type|) T) ((|GeneralSparseTable| . |Join|) T) ((|GeneralSparseTable| . |Aggregate|) T) ((|GeneralSparseTable| . |FiniteAggregate|) 89099) ((|GeneralUnivariatePowerSeries| . |UnivariatePuiseuxSeriesCategory|) 89083) ((|GeneralUnivariatePowerSeries| . |DifferentialRing|) 89018) ((|GeneralUnivariatePowerSeries| . |DifferentialDomain|) 88947) ((|GeneralUnivariatePowerSeries| . |DifferentialSpace|) 88882) ((|GeneralUnivariatePowerSeries| . |Eltable|) 88829) ((|GeneralUnivariatePowerSeries| . |PartialDifferentialRing|) 88691) ((|GeneralUnivariatePowerSeries| . |PartialDifferentialDomain|) 88523) ((|GeneralUnivariatePowerSeries| . |PartialDifferentialSpace|) 88385) ((|GeneralUnivariatePowerSeries| . |PowerSeriesCategory|) 88318) ((|GeneralUnivariatePowerSeries| . |Algebra|) 88106) ((|GeneralUnivariatePowerSeries| . |BiModule|) 87874) ((|GeneralUnivariatePowerSeries| . |RightLinearSet|) 87656) ((|GeneralUnivariatePowerSeries| . |RightModule|) 87438) ((|GeneralUnivariatePowerSeries| . |LeftLinearSet|) 87287) 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((|GeneralModulePolynomial| . |BiModule|) 84917) ((|GeneralDistributedMultivariatePolynomial| . |PolynomialCategory|) 84867) ((|GeneralDistributedMultivariatePolynomial| . |CoercibleFrom|) 84539) ((|GeneralDistributedMultivariatePolynomial| . |RetractableTo|) 84346) ((|GeneralDistributedMultivariatePolynomial| . |UniqueFactorizationDomain|) 84296) ((|GeneralDistributedMultivariatePolynomial| . |PolynomialFactorizationExplicit|) 84246) ((|GeneralDistributedMultivariatePolynomial| . |PatternMatchable|) NIL) ((|GeneralDistributedMultivariatePolynomial| . |PartialDifferentialSpace|) 84206) ((|GeneralDistributedMultivariatePolynomial| . |PartialDifferentialDomain|) 84164) ((|GeneralDistributedMultivariatePolynomial| . |PartialDifferentialRing|) 84124) ((|GeneralDistributedMultivariatePolynomial| . |InnerEvalable|) 84050) ((|GeneralDistributedMultivariatePolynomial| . |GcdDomain|) 83968) ((|GeneralDistributedMultivariatePolynomial| . |LinearlyExplicitRingOver|) 83884) 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T) ((|FortranType| . |SetCategory|) T) ((|FortranType| . |CoercibleTo|) 80632) ((|FortranType| . |Type|) T) ((|FortranType| . |Join|) T) ((|FortranType| . |BasicType|) T) ((|FortranScalarType| . |CoercibleTo|) 80606) ((|FourierSeries| . |Algebra|) 80590) ((|FourierSeries| . |CoercibleFrom|) 80554) ((|FourierSeries| . |LeftModule|) 80528) ((|FourierSeries| . |LeftLinearSet|) 80482) ((|FourierSeries| . |Rng|) T) ((|FourierSeries| . |SemiGroup|) T) ((|FourierSeries| . |SemiRing|) T) ((|FourierSeries| . |Monoid|) T) ((|FourierSeries| . |Ring|) T) ((|FourierSeries| . |BiModule|) 80461) ((|FourierSeries| . |RightLinearSet|) 80445) ((|FourierSeries| . |RightModule|) 80429) ((|FourierSeries| . |AbelianGroup|) T) ((|FourierSeries| . |AbelianMonoid|) T) ((|FourierSeries| . |SetCategory|) T) ((|FourierSeries| . |CoercibleTo|) 80403) ((|FourierSeries| . |Type|) T) ((|FourierSeries| . |Join|) T) ((|FourierSeries| . |BasicType|) T) ((|FourierSeries| . |AbelianSemiGroup|) T) ((|FourierSeries| . 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|OrderedRing|) 79524) ((|Fraction| . |OrderedCancellationAbelianMonoid|) 79484) ((|Fraction| . |OrderedAbelianSemiGroup|) 79444) ((|Fraction| . |OrderedType|) 79371) ((|Fraction| . |OrderedSet|) 79298) ((|Fraction| . |OrderedAbelianMonoid|) 79258) ((|Fraction| . |OrderedAbelianGroup|) 79218) ((|Fraction| . |OrderedIntegralDomain|) 79178) ((|Fraction| . |PatternMatchable|) 79059) ((|Fraction| . |FullyPatternMatchable|) 79043) ((|Fraction| . |LinearlyExplicitRingOver|) 78959) ((|Fraction| . |LeftModule|) 78832) ((|Fraction| . |FullyLinearlyExplicitRingOver|) 78816) ((|Fraction| . |Eltable|) 78769) ((|Fraction| . |Evalable|) 78728) ((|Fraction| . |InnerEvalable|) 78617) ((|Fraction| . |Functorial|) 78601) ((|Fraction| . |FullyEvalableOver|) 78585) ((|Fraction| . |DivisionRing|) T) ((|Fraction| . |BiModule|) 78512) ((|Fraction| . |RightLinearSet|) 78453) ((|Fraction| . |RightModule|) 78394) ((|Fraction| . |EntireRing|) T) ((|Fraction| . |Module|) 78335) ((|Fraction| . |LinearSet|) 78276) ((|Fraction| . |LeftLinearSet|) 78197) ((|Fraction| . |Algebra|) 78138) ((|Fraction| . |EuclideanDomain|) T) ((|Fraction| . |GcdDomain|) T) ((|Fraction| . |CommutativeRing|) T) ((|Fraction| . |IntegralDomain|) T) ((|Fraction| . |PrincipalIdealDomain|) T) ((|Fraction| . |UniqueFactorizationDomain|) T) ((|Fraction| . |Field|) T) ((|Fraction| . |DifferentialRing|) 78103) ((|Fraction| . |DifferentialDomain|) 78022) ((|Fraction| . |DifferentialSpace|) 77947) ((|Fraction| . |DifferentialSpaceExtension|) 77931) ((|Fraction| . |PartialDifferentialDomain|) 77803) ((|Fraction| . |PartialDifferentialSpace|) 77677) ((|Fraction| . |PartialDifferentialRing|) 77609) ((|Fraction| . |DifferentialExtension|) 77593) ((|Fraction| . |CharacteristicZero|) 77512) ((|Fraction| . |CharacteristicNonZero|) 77472) ((|Fraction| . |CancellationAbelianMonoid|) T) ((|Fraction| . |AbelianSemiGroup|) T) ((|Fraction| . |BasicType|) T) ((|Fraction| . |Join|) T) ((|Fraction| . |Type|) T) ((|Fraction| . |CoercibleTo|) 77446) ((|Fraction| . |SetCategory|) T) ((|Fraction| . |AbelianMonoid|) T) ((|Fraction| . |AbelianGroup|) T) ((|Fraction| . |Ring|) T) ((|Fraction| . |Monoid|) T) ((|Fraction| . |SemiRing|) T) ((|Fraction| . |SemiGroup|) T) ((|Fraction| . |Rng|) T) ((|Factored| . |IntegralDomain|) T) ((|Factored| . |EntireRing|) T) ((|Factored| . |CommutativeRing|) T) ((|Factored| . |CoercibleFrom|) 77317) ((|Factored| . |Module|) 77291) ((|Factored| . |LinearSet|) 77265) ((|Factored| . |LeftModule|) 77239) ((|Factored| . |LeftLinearSet|) 77193) ((|Factored| . |CancellationAbelianMonoid|) T) ((|Factored| . |AbelianSemiGroup|) T) ((|Factored| . |BasicType|) T) ((|Factored| . |Join|) T) ((|Factored| . |Type|) T) ((|Factored| . |CoercibleTo|) 77167) ((|Factored| . |SetCategory|) T) ((|Factored| . |AbelianMonoid|) T) ((|Factored| . |AbelianGroup|) T) ((|Factored| . |RightModule|) 77141) ((|Factored| . |RightLinearSet|) 77115) ((|Factored| . |BiModule|) 77082) ((|Factored| . |Ring|) T) ((|Factored| . |Monoid|) T) ((|Factored| . |SemiRing|) T) ((|Factored| . |SemiGroup|) T) ((|Factored| . |Rng|) T) ((|Factored| . |Algebra|) 77056) ((|Factored| . |DifferentialExtension|) 77040) ((|Factored| . |PartialDifferentialRing|) 76972) ((|Factored| . |PartialDifferentialSpace|) 76846) ((|Factored| . |PartialDifferentialDomain|) 76718) ((|Factored| . |DifferentialSpaceExtension|) 76702) ((|Factored| . |DifferentialSpace|) 76627) ((|Factored| . |DifferentialDomain|) 76546) ((|Factored| . |DifferentialRing|) 76511) ((|Factored| . |FullyEvalableOver|) 76495) ((|Factored| . |InnerEvalable|) 76295) ((|Factored| . |Functorial|) 76279) ((|Factored| . |Evalable|) 76199) ((|Factored| . |Eltable|) 76112) ((|Factored| . |FullyRetractableTo|) 76096) ((|Factored| . |RetractableTo|) 75940) ((|Factored| . |GcdDomain|) 75864) ((|Factored| . |RealConstant|) 75833) ((|Factored| . |ConvertibleTo|) 75699) ((|Factored| . |UniqueFactorizationDomain|) 75655) ((|FullPartialFractionExpansion| . |SetCategory|) T) ((|FullPartialFractionExpansion| . |CoercibleTo|) 75629) ((|FullPartialFractionExpansion| . |Type|) T) ((|FullPartialFractionExpansion| . |Join|) T) ((|FullPartialFractionExpansion| . |BasicType|) T) ((|FullPartialFractionExpansion| . |DifferentialSpace|) T) ((|FullPartialFractionExpansion| . |DifferentialDomain|) 75616) ((|FullPartialFractionExpansion| . |ConvertibleTo|) 75587) ((|FreeNilpotentLie| . |NonAssociativeAlgebra|) 75571) ((|FreeNilpotentLie| . |Monad|) T) ((|FreeNilpotentLie| . |NonAssociativeRng|) T) ((|FreeNilpotentLie| . |BiModule|) 75550) ((|FreeNilpotentLie| . |RightLinearSet|) 75534) ((|FreeNilpotentLie| . |RightModule|) 75518) ((|FreeNilpotentLie| . |AbelianGroup|) T) ((|FreeNilpotentLie| . |LeftLinearSet|) 75482) ((|FreeNilpotentLie| . |AbelianMonoid|) T) ((|FreeNilpotentLie| . |SetCategory|) T) ((|FreeNilpotentLie| . |CoercibleTo|) 75456) ((|FreeNilpotentLie| . |Type|) T) ((|FreeNilpotentLie| . |Join|) T) ((|FreeNilpotentLie| . |BasicType|) T) ((|FreeNilpotentLie| . |AbelianSemiGroup|) T) ((|FreeNilpotentLie| . |CancellationAbelianMonoid|) T) ((|FreeNilpotentLie| . |LeftModule|) 75440) ((|FreeNilpotentLie| . |LinearSet|) 75424) ((|FreeNilpotentLie| . |Module|) 75408) ((|FileName| . |FileNameCategory|) T) ((|FileName| . |BasicType|) T) ((|FileName| . |Join|) T) ((|FileName| . |Type|) T) ((|FileName| . |CoercibleTo|) 75363) ((|FileName| . |SetCategory|) T) ((|FileName| . |CoercibleFrom|) 75341) ((|FileName| . |HomotopicTo|) 75319) ((|FreeMonoid| . |FreeMonoidCategory|) 75303) ((|FreeMonoid| . |CoercibleFrom|) 75287) ((|FreeMonoid| . |RetractableTo|) 75271) ((|FreeMonoid| . |OrderedType|) 75242) ((|FreeMonoid| . |OrderedSet|) 75213) ((|FreeMonoid| . |SemiGroup|) T) ((|FreeMonoid| . |BasicType|) T) ((|FreeMonoid| . |Join|) T) ((|FreeMonoid| . |Type|) T) ((|FreeMonoid| . |CoercibleTo|) 75187) ((|FreeMonoid| . |SetCategory|) T) ((|FreeMonoid| . |Monoid|) T) ((|FreeModule1| . |FreeModuleCat|) 75166) ((|FreeModule1| . |CoercibleFrom|) 75150) ((|FreeModule1| . |RetractableTo|) 75134) ((|FreeModule1| . |LinearSet|) 75091) ((|FreeModule1| . |Module|) 75048) ((|FreeModule1| . |Functorial|) 75032) ((|FreeModule1| . |LeftModule|) 75016) ((|FreeModule1| . |LeftLinearSet|) 74980) ((|FreeModule1| . |CancellationAbelianMonoid|) T) ((|FreeModule1| . |AbelianSemiGroup|) T) ((|FreeModule1| . |BasicType|) T) ((|FreeModule1| . |Join|) T) ((|FreeModule1| . |Type|) T) ((|FreeModule1| . |CoercibleTo|) 74954) ((|FreeModule1| . |SetCategory|) T) ((|FreeModule1| . |AbelianMonoid|) T) ((|FreeModule1| . |AbelianGroup|) T) ((|FreeModule1| . |RightModule|) 74938) ((|FreeModule1| . |RightLinearSet|) 74922) ((|FreeModule1| . |BiModule|) 74901) ((|FreeModule| . |BiModule|) 74880) ((|FreeModule| . |RightLinearSet|) 74864) ((|FreeModule| . |RightModule|) 74848) ((|FreeModule| . |AbelianGroup|) T) ((|FreeModule| . |LeftLinearSet|) 74812) ((|FreeModule| . |AbelianMonoid|) T) ((|FreeModule| . |SetCategory|) T) ((|FreeModule| . |CoercibleTo|) 74786) 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T) ((|FiniteFieldNormalBasisExtensionByPolynomial| . |AbelianGroup|) T) ((|FiniteFieldNormalBasisExtensionByPolynomial| . |Rng|) T) ((|FiniteFieldNormalBasisExtensionByPolynomial| . |SemiGroup|) T) ((|FiniteFieldNormalBasisExtensionByPolynomial| . |SemiRing|) T) ((|FiniteFieldNormalBasisExtensionByPolynomial| . |Monoid|) T) ((|FiniteFieldNormalBasisExtensionByPolynomial| . |Ring|) T) ((|FiniteFieldNormalBasisExtensionByPolynomial| . |Field|) T) ((|FiniteFieldNormalBasisExtensionByPolynomial| . |UniqueFactorizationDomain|) T) ((|FiniteFieldNormalBasisExtensionByPolynomial| . |PrincipalIdealDomain|) T) ((|FiniteFieldNormalBasisExtensionByPolynomial| . |IntegralDomain|) T) ((|FiniteFieldNormalBasisExtensionByPolynomial| . |CommutativeRing|) T) ((|FiniteFieldNormalBasisExtensionByPolynomial| . |Module|) 70250) ((|FiniteFieldNormalBasisExtensionByPolynomial| . |LinearSet|) 70191) ((|FiniteFieldNormalBasisExtensionByPolynomial| . |Algebra|) 70145) 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|DifferentialRing|) 67843) ((|FiniteFieldCyclicGroupExtensionByPolynomial| . |DifferentialDomain|) 67812) ((|FiniteFieldCyclicGroupExtensionByPolynomial| . |DifferentialSpace|) 67787) ((|FiniteFieldCyclicGroupExtensionByPolynomial| . |Finite|) 67762) ((|FiniteFieldCyclicGroupExtensionByPolynomial| . |StepThrough|) 67737) ((|FiniteFieldCyclicGroupExtensionByPolynomial| . |FiniteFieldCategory|) 67712) ((|FiniteFieldCyclicGroupExtensionByPolynomial| . |CharacteristicZero|) 67675) ((|FiniteFieldCyclicGroupExtensionByPolynomial| . |CoercibleFrom|) 67596) ((|FiniteFieldCyclicGroupExtensionByPolynomial| . |LeftModule|) 67537) ((|FiniteFieldCyclicGroupExtensionByPolynomial| . |LeftLinearSet|) 67458) ((|FiniteFieldCyclicGroupExtensionByPolynomial| . |CancellationAbelianMonoid|) T) ((|FiniteFieldCyclicGroupExtensionByPolynomial| . |AbelianSemiGroup|) T) ((|FiniteFieldCyclicGroupExtensionByPolynomial| . |BasicType|) T) ((|FiniteFieldCyclicGroupExtensionByPolynomial| . |Join|) T) 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T) ((|FreeAbelianGroup| . |CancellationAbelianMonoid|) T) ((|FreeAbelianGroup| . |Module|) 63979) ((|FreeAbelianGroup| . |LinearSet|) 63956) ((|FreeAbelianGroup| . |LeftModule|) 63933) ((|FreeAbelianGroup| . |RightModule|) 63910) ((|FreeAbelianGroup| . |RightLinearSet|) 63887) ((|FreeAbelianGroup| . |BiModule|) 63857) ((|FreeAbelianGroup| . |FreeAbelianMonoidCategory|) 63829) ((|FreeAbelianGroup| . |CoercibleFrom|) 63813) ((|FreeAbelianGroup| . |RetractableTo|) 63797) ((|FreeAbelianGroup| . |OrderedSet|) 63768) ((|FreeAbelianGroup| . |OrderedType|) 63739) ((|ExponentialOfUnivariatePuiseuxSeries| . |UnivariatePuiseuxSeriesCategory|) 63723) ((|ExponentialOfUnivariatePuiseuxSeries| . |DifferentialRing|) 63658) ((|ExponentialOfUnivariatePuiseuxSeries| . |DifferentialDomain|) 63587) ((|ExponentialOfUnivariatePuiseuxSeries| . |DifferentialSpace|) 63522) ((|ExponentialOfUnivariatePuiseuxSeries| . |Eltable|) 63469) ((|ExponentialOfUnivariatePuiseuxSeries| . |PartialDifferentialRing|) 63331) 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58559) ((|Expression| . |LinearlyExplicitRingOver|) 58431) ((|Expression| . |LeftModule|) 58035) ((|Expression| . |FullyLinearlyExplicitRingOver|) 58003) ((|Expression| . |DivisionRing|) 57970) ((|Expression| . |BiModule|) 57818) ((|Expression| . |RightLinearSet|) 57680) ((|Expression| . |RightModule|) 57542) ((|Expression| . |EntireRing|) 57509) ((|Expression| . |Module|) 57371) ((|Expression| . |LinearSet|) 57233) ((|Expression| . |LeftLinearSet|) 56722) ((|Expression| . |Algebra|) 56584) ((|Expression| . |EuclideanDomain|) 56551) ((|Expression| . |GcdDomain|) 56518) ((|Expression| . |CommutativeRing|) 56485) ((|Expression| . |IntegralDomain|) 56452) ((|Expression| . |PrincipalIdealDomain|) 56419) ((|Expression| . |UniqueFactorizationDomain|) 56386) ((|Expression| . |Field|) 56353) ((|Expression| . |Evalable|) 56340) ((|Expression| . |InnerEvalable|) 56302) ((|Expression| . |ExpressionSpace|) T) ((|Expression| . |CharacteristicZero|) 56265) ((|Expression| . |CharacteristicNonZero|) 56225) ((|Expression| . |Ring|) 56057) ((|Expression| . |Monoid|) 55839) ((|Expression| . |SemiRing|) 55671) ((|Expression| . |SemiGroup|) 55453) ((|Expression| . |Rng|) 55285) ((|Expression| . |CancellationAbelianMonoid|) 55087) ((|Expression| . |AbelianSemiGroup|) 54855) ((|Expression| . |BasicType|) T) ((|Expression| . |Join|) T) ((|Expression| . |Type|) T) ((|Expression| . |CoercibleTo|) 54829) ((|Expression| . |SetCategory|) T) ((|Expression| . |AbelianMonoid|) 54597) ((|Expression| . |AbelianGroup|) 54399) ((|Expression| . |AlgebraicallyClosedFunctionSpace|) 54357) ((|Expression| . |RadicalCategory|) 54324) ((|Expression| . |AlgebraicallyClosedField|) 54291) ((|Expression| . |TranscendentalFunctionCategory|) 54258) ((|Expression| . |TrigonometricFunctionCategory|) 54225) ((|Expression| . |HyperbolicFunctionCategory|) 54192) ((|Expression| . |ElementaryFunctionCategory|) 54159) ((|Expression| . |ArcTrigonometricFunctionCategory|) 54126) ((|Expression| . |ArcHyperbolicFunctionCategory|) 54093) ((|Expression| . |CombinatorialOpsCategory|) 54060) ((|Expression| . |CombinatorialFunctionCategory|) 54027) ((|Expression| . |LiouvillianFunctionCategory|) 53994) ((|Expression| . |PrimitiveFunctionCategory|) 53961) ((|Expression| . |SpecialFunctionCategory|) 53928) ((|ExponentialExpansion| . |QuotientFieldCategory|) 53843) ((|ExponentialExpansion| . |StepThrough|) NIL) ((|ExponentialExpansion| . |RetractableTo|) 53707) ((|ExponentialExpansion| . |CoercibleFrom|) 53508) ((|ExponentialExpansion| . |ConvertibleTo|) NIL) ((|ExponentialExpansion| . |RealConstant|) NIL) ((|ExponentialExpansion| . |PolynomialFactorizationExplicit|) NIL) ((|ExponentialExpansion| . |Patternable|) 53423) ((|ExponentialExpansion| . |OrderedRing|) NIL) ((|ExponentialExpansion| . |OrderedCancellationAbelianMonoid|) NIL) ((|ExponentialExpansion| . |OrderedAbelianSemiGroup|) NIL) ((|ExponentialExpansion| . |OrderedType|) NIL) ((|ExponentialExpansion| . |OrderedSet|) NIL) ((|ExponentialExpansion| . |OrderedAbelianMonoid|) NIL) ((|ExponentialExpansion| . |OrderedAbelianGroup|) NIL) ((|ExponentialExpansion| . |OrderedIntegralDomain|) NIL) ((|ExponentialExpansion| . |PatternMatchable|) NIL) ((|ExponentialExpansion| . |FullyPatternMatchable|) 53338) ((|ExponentialExpansion| . |LinearlyExplicitRingOver|) 53253) ((|ExponentialExpansion| . |LeftModule|) 53125) ((|ExponentialExpansion| . |FullyLinearlyExplicitRingOver|) 53040) ((|ExponentialExpansion| . |Eltable|) 52924) ((|ExponentialExpansion| . |Evalable|) 52813) ((|ExponentialExpansion| . |InnerEvalable|) 52636) ((|ExponentialExpansion| . |Functorial|) 52551) ((|ExponentialExpansion| . |FullyEvalableOver|) 52466) ((|ExponentialExpansion| . |DivisionRing|) T) ((|ExponentialExpansion| . |BiModule|) 52322) ((|ExponentialExpansion| . |RightLinearSet|) 52194) ((|ExponentialExpansion| . |RightModule|) 52066) ((|ExponentialExpansion| . |EntireRing|) T) ((|ExponentialExpansion| . |Module|) 51938) 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51258) ((|ExponentialExpansion| . |CharacteristicNonZero|) 51149) ((|ExponentialExpansion| . |CancellationAbelianMonoid|) T) ((|ExponentialExpansion| . |AbelianSemiGroup|) T) ((|ExponentialExpansion| . |BasicType|) T) ((|ExponentialExpansion| . |Join|) T) ((|ExponentialExpansion| . |Type|) T) ((|ExponentialExpansion| . |CoercibleTo|) 51123) ((|ExponentialExpansion| . |SetCategory|) T) ((|ExponentialExpansion| . |AbelianMonoid|) T) ((|ExponentialExpansion| . |AbelianGroup|) T) ((|ExponentialExpansion| . |Ring|) T) ((|ExponentialExpansion| . |Monoid|) T) ((|ExponentialExpansion| . |SemiRing|) T) ((|ExponentialExpansion| . |SemiGroup|) T) ((|ExponentialExpansion| . |Rng|) T) ((|ExitAst| . |SpadSyntaxCategory|) T) ((|ExitAst| . |HomotopicTo|) 51101) ((|ExitAst| . |CoercibleTo|) 51056) ((|ExitAst| . |CoercibleFrom|) 51034) ((|ExitAst| . |SetCategory|) T) ((|ExitAst| . |Type|) T) ((|ExitAst| . |Join|) T) ((|ExitAst| . |BasicType|) T) ((|ExitAst| . |AbstractSyntaxCategory|) T) ((|Exit| . |SetCategory|) T) ((|Exit| . |CoercibleTo|) 51008) ((|Exit| . |Type|) T) ((|Exit| . |Join|) T) ((|Exit| . |BasicType|) T) ((|EqTable| . |TableAggregate|) 50987) ((|EqTable| . |Dictionary|) 50929) ((|EqTable| . |BagAggregate|) 50871) ((|EqTable| . |ShallowlyMutableAggregate|) 50800) ((|EqTable| . |Collection|) 50742) ((|EqTable| . |ConvertibleTo|) NIL) ((|EqTable| . |DictionaryOperations|) 50684) ((|EqTable| . |IndexedAggregate|) 50663) ((|EqTable| . |Evalable|) 50423) ((|EqTable| . |InnerEvalable|) 50171) ((|EqTable| . |Functorial|) 50100) ((|EqTable| . |HomogeneousAggregate|) 50029) ((|EqTable| . |Eltable|) 50008) ((|EqTable| . |EltableAggregate|) 49987) ((|EqTable| . |KeyedDictionary|) 49966) ((|EqTable| . |SetCategory|) T) ((|EqTable| . |CoercibleTo|) 49940) ((|EqTable| . |BasicType|) T) ((|EqTable| . |Type|) T) ((|EqTable| . |Join|) T) ((|EqTable| . |Aggregate|) T) ((|EqTable| . |FiniteAggregate|) 49882) ((|Equation| . |Functorial|) 49866) ((|Equation| . |Join|) T) ((|Equation| . 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((|Environment| . |CoercibleTo|) 46283) ((|EuclideanModularRing| . |EuclideanDomain|) T) ((|EuclideanModularRing| . |GcdDomain|) T) ((|EuclideanModularRing| . |Algebra|) 46270) ((|EuclideanModularRing| . |CoercibleFrom|) 46237) ((|EuclideanModularRing| . |Rng|) T) ((|EuclideanModularRing| . |SemiGroup|) T) ((|EuclideanModularRing| . |SemiRing|) T) ((|EuclideanModularRing| . |Monoid|) T) ((|EuclideanModularRing| . |Ring|) T) ((|EuclideanModularRing| . |BiModule|) 46222) ((|EuclideanModularRing| . |RightLinearSet|) 46209) ((|EuclideanModularRing| . |RightModule|) 46196) ((|EuclideanModularRing| . |AbelianGroup|) T) ((|EuclideanModularRing| . |LeftLinearSet|) 46163) ((|EuclideanModularRing| . |AbelianMonoid|) T) ((|EuclideanModularRing| . |SetCategory|) T) ((|EuclideanModularRing| . |CoercibleTo|) 46137) ((|EuclideanModularRing| . |Type|) T) ((|EuclideanModularRing| . |Join|) T) ((|EuclideanModularRing| . |BasicType|) T) ((|EuclideanModularRing| . |AbelianSemiGroup|) T) 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((|DifferentialSparseMultivariatePolynomial| . |ConvertibleTo|) 44953) ((|DifferentialSparseMultivariatePolynomial| . |FiniteAbelianMonoidRing|) 44911) ((|DifferentialSparseMultivariatePolynomial| . |FullyRetractableTo|) 44895) ((|DifferentialSparseMultivariatePolynomial| . |Algebra|) 44658) ((|DifferentialSparseMultivariatePolynomial| . |BiModule|) 44401) ((|DifferentialSparseMultivariatePolynomial| . |RightLinearSet|) 44158) ((|DifferentialSparseMultivariatePolynomial| . |RightModule|) 43915) ((|DifferentialSparseMultivariatePolynomial| . |LeftLinearSet|) 43792) ((|DifferentialSparseMultivariatePolynomial| . |LeftModule|) 43621) ((|DifferentialSparseMultivariatePolynomial| . |LinearSet|) 43384) ((|DifferentialSparseMultivariatePolynomial| . |Module|) 43147) ((|DifferentialSparseMultivariatePolynomial| . |CharacteristicNonZero|) 43107) ((|DifferentialSparseMultivariatePolynomial| . |CharacteristicZero|) 43070) ((|DifferentialSparseMultivariatePolynomial| . |CommutativeRing|) 42923) ((|DifferentialSparseMultivariatePolynomial| . |Functorial|) 42907) ((|DifferentialSparseMultivariatePolynomial| . |IntegralDomain|) 42793) ((|DifferentialSparseMultivariatePolynomial| . |EntireRing|) 42679) ((|DifferentialSparseMultivariatePolynomial| . |AbelianMonoidRing|) 42637) ((|DifferentialSparseMultivariatePolynomial| . |FullyLinearlyExplicitRingOver|) 42621) ((|DifferentialSparseMultivariatePolynomial| . |LinearlyExplicitRingOver|) 42537) ((|DifferentialSparseMultivariatePolynomial| . |GcdDomain|) 42455) ((|DifferentialSparseMultivariatePolynomial| . |InnerEvalable|) 42326) ((|DifferentialSparseMultivariatePolynomial| . |PartialDifferentialRing|) 42245) ((|DifferentialSparseMultivariatePolynomial| . |PartialDifferentialDomain|) 42102) ((|DifferentialSparseMultivariatePolynomial| . |PartialDifferentialSpace|) 41963) ((|DifferentialSparseMultivariatePolynomial| . |PatternMatchable|) 41742) ((|DifferentialSparseMultivariatePolynomial| . |PolynomialFactorizationExplicit|) 41692) ((|DifferentialSparseMultivariatePolynomial| . |UniqueFactorizationDomain|) 41642) ((|DifferentialSparseMultivariatePolynomial| . |PolynomialCategory|) 41595) ((|DifferentialSparseMultivariatePolynomial| . |Evalable|) 41582) ((|DifferentialSparseMultivariatePolynomial| . |DifferentialRing|) 41547) ((|DifferentialSparseMultivariatePolynomial| . |CancellationAbelianMonoid|) T) ((|DifferentialSparseMultivariatePolynomial| . |AbelianSemiGroup|) T) ((|DifferentialSparseMultivariatePolynomial| . |BasicType|) T) ((|DifferentialSparseMultivariatePolynomial| . |CoercibleTo|) 41521) ((|DifferentialSparseMultivariatePolynomial| . |SetCategory|) T) ((|DifferentialSparseMultivariatePolynomial| . |AbelianMonoid|) T) ((|DifferentialSparseMultivariatePolynomial| . |AbelianGroup|) T) ((|DifferentialSparseMultivariatePolynomial| . |Rng|) T) ((|DifferentialSparseMultivariatePolynomial| . |SemiGroup|) T) ((|DifferentialSparseMultivariatePolynomial| . |SemiRing|) T) ((|DifferentialSparseMultivariatePolynomial| . |Monoid|) T) ((|DifferentialSparseMultivariatePolynomial| . |Ring|) T) ((|DifferentialSparseMultivariatePolynomial| . |DifferentialDomain|) 41440) ((|DifferentialSparseMultivariatePolynomial| . |Join|) T) ((|DifferentialSparseMultivariatePolynomial| . |Type|) T) ((|DifferentialSparseMultivariatePolynomial| . |DifferentialSpace|) 41365) ((|DifferentialSparseMultivariatePolynomial| . |DifferentialSpaceExtension|) 41349) ((|DifferentialSparseMultivariatePolynomial| . |DifferentialExtension|) 41333) ((|DrawOption| . |SetCategory|) T) ((|DrawOption| . |CoercibleTo|) 41307) ((|DrawOption| . |Type|) T) ((|DrawOption| . |Join|) T) ((|DrawOption| . |BasicType|) T) ((|DirectProductModule| . |DirectProductCategory|) 41286) ((|DirectProductModule| . |VectorSpace|) 41253) ((|DirectProductModule| . |OrderedCancellationAbelianMonoid|) 41211) ((|DirectProductModule| . |OrderedAbelianSemiGroup|) 41169) ((|DirectProductModule| . |OrderedType|) 41094) ((|DirectProductModule| . |OrderedSet|) 41019) ((|DirectProductModule| . |OrderedAbelianMonoid|) 40977) ((|DirectProductModule| . |OrderedAbelianMonoidSup|) 40935) ((|DirectProductModule| . |Module|) 40864) ((|DirectProductModule| . |LinearSet|) 40769) ((|DirectProductModule| . |EltableAggregate|) 40741) ((|DirectProductModule| . |Eltable|) 40713) ((|DirectProductModule| . |IndexedAggregate|) 40685) ((|DirectProductModule| . |RetractableTo|) 40436) ((|DirectProductModule| . |CoercibleFrom|) 40160) ((|DirectProductModule| . |FullyRetractableTo|) 40121) ((|DirectProductModule| . |LinearlyExplicitRingOver|) 39993) ((|DirectProductModule| . |LeftModule|) 39765) ((|DirectProductModule| . |FullyLinearlyExplicitRingOver|) 39733) ((|DirectProductModule| . |HomogeneousAggregate|) 39717) ((|DirectProductModule| . |Functorial|) 39701) ((|DirectProductModule| . |InnerEvalable|) 39620) ((|DirectProductModule| . |Evalable|) 39544) ((|DirectProductModule| . |Aggregate|) T) ((|DirectProductModule| . |FiniteAggregate|) 39528) ((|DirectProductModule| . |Finite|) 39503) ((|DirectProductModule| . |DifferentialRing|) 39440) ((|DirectProductModule| . |LeftLinearSet|) 39264) ((|DirectProductModule| . |Rng|) 39241) ((|DirectProductModule| . |SemiGroup|) 39218) ((|DirectProductModule| . |SemiRing|) 39195) ((|DirectProductModule| . |Monoid|) 39172) ((|DirectProductModule| . |Ring|) 39149) ((|DirectProductModule| . |DifferentialDomain|) 39012) ((|DirectProductModule| . |DifferentialSpace|) 38881) ((|DirectProductModule| . |DifferentialSpaceExtension|) 38849) ((|DirectProductModule| . |PartialDifferentialDomain|) 38665) ((|DirectProductModule| . |PartialDifferentialSpace|) 38483) ((|DirectProductModule| . |PartialDifferentialRing|) 38387) ((|DirectProductModule| . |DifferentialExtension|) 38355) ((|DirectProductModule| . |CoercibleTo|) 38305) ((|DirectProductModule| . |RightModule|) 38212) ((|DirectProductModule| . |RightLinearSet|) 38095) ((|DirectProductModule| . |BiModule|) 37997) ((|DirectProductModule| . |CancellationAbelianMonoid|) T) ((|DirectProductModule| . |AbelianSemiGroup|) T) ((|DirectProductModule| . |BasicType|) T) ((|DirectProductModule| . |Join|) T) ((|DirectProductModule| . |Type|) T) ((|DirectProductModule| . |SetCategory|) T) ((|DirectProductModule| . |AbelianMonoid|) T) ((|DirectProductModule| . |AbelianGroup|) T) ((|DirectProductMatrixModule| . |DirectProductCategory|) 37976) ((|DirectProductMatrixModule| . |VectorSpace|) 37943) ((|DirectProductMatrixModule| . |OrderedCancellationAbelianMonoid|) 37901) ((|DirectProductMatrixModule| . |OrderedAbelianSemiGroup|) 37859) ((|DirectProductMatrixModule| . |OrderedType|) 37784) ((|DirectProductMatrixModule| . |OrderedSet|) 37709) ((|DirectProductMatrixModule| . |OrderedAbelianMonoid|) 37667) ((|DirectProductMatrixModule| . |OrderedAbelianMonoidSup|) 37625) ((|DirectProductMatrixModule| . |Module|) 37554) ((|DirectProductMatrixModule| . |LinearSet|) 37459) ((|DirectProductMatrixModule| . |EltableAggregate|) 37431) ((|DirectProductMatrixModule| . |Eltable|) 37403) ((|DirectProductMatrixModule| . |IndexedAggregate|) 37375) ((|DirectProductMatrixModule| . |RetractableTo|) 37126) ((|DirectProductMatrixModule| . |CoercibleFrom|) 36850) ((|DirectProductMatrixModule| . |FullyRetractableTo|) 36811) ((|DirectProductMatrixModule| . |LinearlyExplicitRingOver|) 36683) ((|DirectProductMatrixModule| . |LeftModule|) 36442) ((|DirectProductMatrixModule| . |FullyLinearlyExplicitRingOver|) 36410) ((|DirectProductMatrixModule| . |HomogeneousAggregate|) 36394) ((|DirectProductMatrixModule| . |Functorial|) 36378) ((|DirectProductMatrixModule| . |InnerEvalable|) 36297) ((|DirectProductMatrixModule| . |Evalable|) 36221) ((|DirectProductMatrixModule| . |Aggregate|) T) ((|DirectProductMatrixModule| . |FiniteAggregate|) 36205) ((|DirectProductMatrixModule| . |Finite|) 36180) ((|DirectProductMatrixModule| . |DifferentialRing|) 36117) ((|DirectProductMatrixModule| . |LeftLinearSet|) 35928) ((|DirectProductMatrixModule| . |Rng|) 35905) ((|DirectProductMatrixModule| . |SemiGroup|) 35882) ((|DirectProductMatrixModule| . |SemiRing|) 35859) ((|DirectProductMatrixModule| . |Monoid|) 35836) ((|DirectProductMatrixModule| . |Ring|) 35813) ((|DirectProductMatrixModule| . |DifferentialDomain|) 35676) ((|DirectProductMatrixModule| . |DifferentialSpace|) 35545) ((|DirectProductMatrixModule| . |DifferentialSpaceExtension|) 35513) ((|DirectProductMatrixModule| . |PartialDifferentialDomain|) 35329) ((|DirectProductMatrixModule| . |PartialDifferentialSpace|) 35147) ((|DirectProductMatrixModule| . |PartialDifferentialRing|) 35051) ((|DirectProductMatrixModule| . |DifferentialExtension|) 35019) ((|DirectProductMatrixModule| . |CoercibleTo|) 34969) ((|DirectProductMatrixModule| . |RightModule|) 34876) ((|DirectProductMatrixModule| . |RightLinearSet|) 34759) ((|DirectProductMatrixModule| . |BiModule|) 34661) ((|DirectProductMatrixModule| . |CancellationAbelianMonoid|) T) ((|DirectProductMatrixModule| . |AbelianSemiGroup|) T) ((|DirectProductMatrixModule| . |BasicType|) T) ((|DirectProductMatrixModule| . |Join|) T) ((|DirectProductMatrixModule| . |Type|) T) ((|DirectProductMatrixModule| . |SetCategory|) T) ((|DirectProductMatrixModule| . |AbelianMonoid|) T) ((|DirectProductMatrixModule| . |AbelianGroup|) T) ((|DomainTemplate| . |SetCategory|) T) ((|DomainTemplate| . |CoercibleTo|) 34635) ((|DomainTemplate| . |Type|) T) ((|DomainTemplate| . |Join|) T) ((|DomainTemplate| . |BasicType|) T) ((|DomainTemplate| . |Eltable|) 34590) ((|DomainConstructor| . |ConstructorCategory|) T) ((|DomainConstructor| . |SetCategory|) T) ((|DomainConstructor| . |CoercibleTo|) 34540) ((|DomainConstructor| . |Type|) T) ((|DomainConstructor| . |Join|) T) ((|DomainConstructor| . |BasicType|) T) ((|DomainConstructor| . |OperatorCategory|) 34514) ((|Domain| . |SetCategory|) T) ((|Domain| . |CoercibleTo|) 34488) ((|Domain| . |Type|) T) ((|Domain| . |Join|) T) ((|Domain| . |BasicType|) T) ((|DistributedMultivariatePolynomial| . |PolynomialCategory|) 34391) ((|DistributedMultivariatePolynomial| . |CoercibleFrom|) 34063) ((|DistributedMultivariatePolynomial| . |RetractableTo|) 33870) ((|DistributedMultivariatePolynomial| . |UniqueFactorizationDomain|) 33820) ((|DistributedMultivariatePolynomial| . |PolynomialFactorizationExplicit|) 33770) ((|DistributedMultivariatePolynomial| . |PatternMatchable|) NIL) ((|DistributedMultivariatePolynomial| . |PartialDifferentialSpace|) 33730) ((|DistributedMultivariatePolynomial| . |PartialDifferentialDomain|) 33688) ((|DistributedMultivariatePolynomial| . |PartialDifferentialRing|) 33648) ((|DistributedMultivariatePolynomial| . |InnerEvalable|) 33574) ((|DistributedMultivariatePolynomial| . |GcdDomain|) 33492) ((|DistributedMultivariatePolynomial| . |LinearlyExplicitRingOver|) 33408) ((|DistributedMultivariatePolynomial| . |LeftModule|) 33237) ((|DistributedMultivariatePolynomial| . |FullyLinearlyExplicitRingOver|) 33221) ((|DistributedMultivariatePolynomial| . |AbelianMonoidRing|) 33153) ((|DistributedMultivariatePolynomial| . |Algebra|) 32916) ((|DistributedMultivariatePolynomial| . |LinearSet|) 32679) ((|DistributedMultivariatePolynomial| . |Module|) 32442) ((|DistributedMultivariatePolynomial| . |EntireRing|) 32328) ((|DistributedMultivariatePolynomial| . |IntegralDomain|) 32214) ((|DistributedMultivariatePolynomial| . |Functorial|) 32198) ((|DistributedMultivariatePolynomial| . |BiModule|) 31941) ((|DistributedMultivariatePolynomial| . |RightLinearSet|) 31698) ((|DistributedMultivariatePolynomial| . |RightModule|) 31455) ((|DistributedMultivariatePolynomial| . |CommutativeRing|) 31308) ((|DistributedMultivariatePolynomial| . |CharacteristicZero|) 31271) ((|DistributedMultivariatePolynomial| . |CharacteristicNonZero|) 31231) ((|DistributedMultivariatePolynomial| . |LeftLinearSet|) 31108) ((|DistributedMultivariatePolynomial| . |CancellationAbelianMonoid|) T) ((|DistributedMultivariatePolynomial| . |AbelianSemiGroup|) T) ((|DistributedMultivariatePolynomial| . |BasicType|) T) ((|DistributedMultivariatePolynomial| . |Join|) T) ((|DistributedMultivariatePolynomial| . |Type|) T) ((|DistributedMultivariatePolynomial| . |CoercibleTo|) 31082) ((|DistributedMultivariatePolynomial| . |SetCategory|) T) ((|DistributedMultivariatePolynomial| . |AbelianMonoid|) T) ((|DistributedMultivariatePolynomial| . |AbelianGroup|) T) ((|DistributedMultivariatePolynomial| . |Ring|) T) ((|DistributedMultivariatePolynomial| . |Monoid|) T) ((|DistributedMultivariatePolynomial| . |SemiRing|) T) ((|DistributedMultivariatePolynomial| . |SemiGroup|) T) ((|DistributedMultivariatePolynomial| . |Rng|) T) ((|DistributedMultivariatePolynomial| . |FullyRetractableTo|) 31066) ((|DistributedMultivariatePolynomial| . |FiniteAbelianMonoidRing|) 30998) ((|DistributedMultivariatePolynomial| . |Evalable|) 30985) ((|DistributedMultivariatePolynomial| . |ConvertibleTo|) 30763) ((|DataList| . |ListAggregate|) 30747) ((|DataList| . |UnaryRecursiveAggregate|) 30731) ((|DataList| . |RecursiveAggregate|) 30715) ((|DataList| . |StreamAggregate|) 30699) ((|DataList| . |FiniteAggregate|) 30683) ((|DataList| . |OrderedSet|) 30654) ((|DataList| . |OrderedType|) 30625) ((|DataList| . |FiniteLinearAggregate|) 30609) ((|DataList| . |LinearAggregate|) 30593) ((|DataList| . |EltableAggregate|) 30565) ((|DataList| . |Eltable|) 30494) ((|DataList| . |IndexedAggregate|) 30466) ((|DataList| . |ConvertibleTo|) 30402) ((|DataList| . |HomogeneousAggregate|) 30386) ((|DataList| . |SetCategory|) 30323) ((|DataList| . |Functorial|) 30307) ((|DataList| . |InnerEvalable|) 30226) ((|DataList| . |Evalable|) 30150) ((|DataList| . |CoercibleTo|) 30002) ((|DataList| . |BasicType|) 29912) ((|DataList| . |Type|) T) ((|DataList| . |Join|) T) ((|DataList| . |Aggregate|) T) ((|DataList| . |Collection|) 29896) ((|DataList| . |ShallowlyMutableAggregate|) 29880) ((|DataList| . |ExtensibleLinearAggregate|) 29864) ((|DataList| . |HomotopicTo|) 29839) ((|DataList| . |CoercibleFrom|) 29814) ((|DirectProduct| . |DirectProductCategory|) 29793) ((|DirectProduct| . |VectorSpace|) 29760) ((|DirectProduct| . |OrderedCancellationAbelianMonoid|) 29718) ((|DirectProduct| . |OrderedAbelianSemiGroup|) 29676) ((|DirectProduct| . |OrderedType|) 29601) ((|DirectProduct| . |OrderedSet|) 29526) ((|DirectProduct| . |OrderedAbelianMonoid|) 29484) ((|DirectProduct| . |OrderedAbelianMonoidSup|) 29442) ((|DirectProduct| . |Module|) 29371) ((|DirectProduct| . |LinearSet|) 29276) ((|DirectProduct| . |EltableAggregate|) 29248) ((|DirectProduct| . |Eltable|) 29220) ((|DirectProduct| . |IndexedAggregate|) 29192) ((|DirectProduct| . |RetractableTo|) 28943) ((|DirectProduct| . |CoercibleFrom|) 28667) ((|DirectProduct| . |FullyRetractableTo|) 28628) ((|DirectProduct| . |LinearlyExplicitRingOver|) 28500) ((|DirectProduct| . |LeftModule|) 28285) ((|DirectProduct| . |FullyLinearlyExplicitRingOver|) 28253) ((|DirectProduct| . |HomogeneousAggregate|) 28237) ((|DirectProduct| . |Functorial|) 28221) ((|DirectProduct| . |InnerEvalable|) 28140) ((|DirectProduct| . |Evalable|) 28064) ((|DirectProduct| . |Aggregate|) T) ((|DirectProduct| . |FiniteAggregate|) 28048) ((|DirectProduct| . |Finite|) 28023) ((|DirectProduct| . |DifferentialRing|) 27960) ((|DirectProduct| . |LeftLinearSet|) 27690) ((|DirectProduct| . |Rng|) 27667) ((|DirectProduct| . |SemiGroup|) 27644) ((|DirectProduct| . |SemiRing|) 27621) ((|DirectProduct| . |Monoid|) 27598) ((|DirectProduct| . |Ring|) 27575) ((|DirectProduct| . |DifferentialDomain|) 27438) ((|DirectProduct| . |DifferentialSpace|) 27307) ((|DirectProduct| . |DifferentialSpaceExtension|) 27275) ((|DirectProduct| . |PartialDifferentialDomain|) 27091) ((|DirectProduct| . |PartialDifferentialSpace|) 26909) ((|DirectProduct| . |PartialDifferentialRing|) 26813) ((|DirectProduct| . |DifferentialExtension|) 26781) ((|DirectProduct| . |CoercibleTo|) 26326) ((|DirectProduct| . |RightModule|) 26233) ((|DirectProduct| . |RightLinearSet|) 26116) ((|DirectProduct| . |BiModule|) 26018) ((|DirectProduct| . |CancellationAbelianMonoid|) 25820) ((|DirectProduct| . |AbelianSemiGroup|) 25557) ((|DirectProduct| . |BasicType|) 25162) ((|DirectProduct| . |Join|) T) ((|DirectProduct| . |Type|) T) ((|DirectProduct| . |SetCategory|) 24794) ((|DirectProduct| . |AbelianMonoid|) 24565) ((|DirectProduct| . |AbelianGroup|) 24451) ((|DenavitHartenbergMatrix| . |MatrixCategory|) 24412) ((|DenavitHartenbergMatrix| . |FiniteAggregate|) 24396) ((|DenavitHartenbergMatrix| . |Aggregate|) T) ((|DenavitHartenbergMatrix| . |Join|) T) ((|DenavitHartenbergMatrix| . |Type|) T) ((|DenavitHartenbergMatrix| . |BasicType|) 24334) ((|DenavitHartenbergMatrix| . |CoercibleTo|) 24236) ((|DenavitHartenbergMatrix| . |Evalable|) 24160) ((|DenavitHartenbergMatrix| . |InnerEvalable|) 24079) ((|DenavitHartenbergMatrix| . |Functorial|) 24063) ((|DenavitHartenbergMatrix| . |SetCategory|) 24033) ((|DenavitHartenbergMatrix| . |HomogeneousAggregate|) 24017) ((|DenavitHartenbergMatrix| . |ShallowlyMutableAggregate|) 24001) ((|DenavitHartenbergMatrix| . |TwoDimensionalArrayCategory|) 23962) ((|DoubleFloat| . |FloatingPointSystem|) T) ((|DoubleFloat| . |CharacteristicZero|) T) ((|DoubleFloat| . |CoercibleFrom|) 23896) ((|DoubleFloat| . |LeftModule|) 23850) ((|DoubleFloat| . |LeftLinearSet|) 23784) ((|DoubleFloat| . |CancellationAbelianMonoid|) T) ((|DoubleFloat| . |AbelianSemiGroup|) T) ((|DoubleFloat| . |BasicType|) T) ((|DoubleFloat| . |Join|) T) ((|DoubleFloat| . |Type|) T) ((|DoubleFloat| . |CoercibleTo|) 23758) ((|DoubleFloat| . |SetCategory|) T) ((|DoubleFloat| . |AbelianMonoid|) T) ((|DoubleFloat| . |AbelianGroup|) T) ((|DoubleFloat| . |Rng|) T) ((|DoubleFloat| . |SemiGroup|) T) ((|DoubleFloat| . |SemiRing|) T) ((|DoubleFloat| . |Monoid|) T) ((|DoubleFloat| . |Ring|) T) ((|DoubleFloat| . |ConvertibleTo|) 23661) ((|DoubleFloat| . |Field|) T) ((|DoubleFloat| . |UniqueFactorizationDomain|) T) ((|DoubleFloat| . |PrincipalIdealDomain|) T) ((|DoubleFloat| . |IntegralDomain|) T) ((|DoubleFloat| . |CommutativeRing|) T) ((|DoubleFloat| . |Module|) 23615) ((|DoubleFloat| . |LinearSet|) 23569) ((|DoubleFloat| . |Algebra|) 23523) ((|DoubleFloat| . |GcdDomain|) T) ((|DoubleFloat| . |EuclideanDomain|) T) ((|DoubleFloat| . |BiModule|) 23468) ((|DoubleFloat| . |RightLinearSet|) 23422) ((|DoubleFloat| . |RightModule|) 23376) ((|DoubleFloat| . |EntireRing|) T) ((|DoubleFloat| . |DivisionRing|) T) ((|DoubleFloat| . |OrderedRing|) T) ((|DoubleFloat| . |OrderedCancellationAbelianMonoid|) T) ((|DoubleFloat| . |OrderedAbelianSemiGroup|) T) ((|DoubleFloat| . |OrderedType|) T) ((|DoubleFloat| . |OrderedSet|) T) ((|DoubleFloat| . |OrderedAbelianMonoid|) T) ((|DoubleFloat| . |OrderedAbelianGroup|) T) ((|DoubleFloat| . |PatternMatchable|) 23355) ((|DoubleFloat| . |RadicalCategory|) T) ((|DoubleFloat| . |RealConstant|) T) ((|DoubleFloat| . |RetractableTo|) 23304) ((|DoubleFloat| . |RealNumberSystem|) T) ((|DoubleFloat| . |DifferentialRing|) T) ((|DoubleFloat| . |DifferentialDomain|) 23291) ((|DoubleFloat| . |DifferentialSpace|) T) ((|DoubleFloat| . |TranscendentalFunctionCategory|) T) ((|DoubleFloat| . |TrigonometricFunctionCategory|) T) ((|DoubleFloat| . |HyperbolicFunctionCategory|) T) ((|DoubleFloat| . |ElementaryFunctionCategory|) T) ((|DoubleFloat| . |ArcTrigonometricFunctionCategory|) T) ((|DoubleFloat| . |ArcHyperbolicFunctionCategory|) T) ((|DeRhamComplex| . |LeftAlgebra|) 23260) ((|DeRhamComplex| . |CoercibleFrom|) 23209) ((|DeRhamComplex| . |LeftModule|) 23168) ((|DeRhamComplex| . |LeftLinearSet|) 23107) ((|DeRhamComplex| . |Rng|) T) ((|DeRhamComplex| . |SemiGroup|) T) ((|DeRhamComplex| . |SemiRing|) T) ((|DeRhamComplex| . |Monoid|) T) ((|DeRhamComplex| . |Ring|) T) ((|DeRhamComplex| . |AbelianGroup|) T) ((|DeRhamComplex| . |AbelianMonoid|) T) ((|DeRhamComplex| . |SetCategory|) T) ((|DeRhamComplex| . |CoercibleTo|) 23081) ((|DeRhamComplex| . |Type|) T) ((|DeRhamComplex| . |Join|) T) ((|DeRhamComplex| . |BasicType|) T) ((|DeRhamComplex| . |AbelianSemiGroup|) T) ((|DeRhamComplex| . |CancellationAbelianMonoid|) T) ((|DeRhamComplex| . |RetractableTo|) 23050) ((|DeRhamComplex| . |Functorial|) 23019) ((|Dequeue| . |DequeueAggregate|) 23003) ((|Dequeue| . |StackAggregate|) 22987) ((|Dequeue| . |BagAggregate|) 22971) ((|Dequeue| . |ShallowlyMutableAggregate|) 22955) ((|Dequeue| . |Aggregate|) T) ((|Dequeue| . |Join|) T) ((|Dequeue| . |Type|) T) ((|Dequeue| . |BasicType|) 22893) ((|Dequeue| . |CoercibleTo|) 22795) ((|Dequeue| . |Evalable|) 22719) ((|Dequeue| . |InnerEvalable|) 22638) ((|Dequeue| . |Functorial|) 22622) ((|Dequeue| . |SetCategory|) 22592) ((|Dequeue| . |HomogeneousAggregate|) 22576) ((|Dequeue| . |FiniteAggregate|) 22560) ((|Dequeue| . |QueueAggregate|) 22544) ((|DefinitionAst| . |SpadSyntaxCategory|) T) ((|DefinitionAst| . |HomotopicTo|) 22522) ((|DefinitionAst| . |CoercibleTo|) 22477) ((|DefinitionAst| . |CoercibleFrom|) 22455) ((|DefinitionAst| . |SetCategory|) T) ((|DefinitionAst| . |Type|) T) ((|DefinitionAst| . |Join|) T) ((|DefinitionAst| . |BasicType|) T) ((|DefinitionAst| . |AbstractSyntaxCategory|) T) ((|DecimalExpansion| . |QuotientFieldCategory|) 22432) ((|DecimalExpansion| . |StepThrough|) T) ((|DecimalExpansion| . |CoercibleFrom|) 22366) ((|DecimalExpansion| . |RetractableTo|) 22310) ((|DecimalExpansion| . |ConvertibleTo|) 22211) ((|DecimalExpansion| . |RealConstant|) T) ((|DecimalExpansion| . |PolynomialFactorizationExplicit|) NIL) ((|DecimalExpansion| . |Patternable|) 22188) ((|DecimalExpansion| . |OrderedRing|) T) ((|DecimalExpansion| . |OrderedCancellationAbelianMonoid|) T) ((|DecimalExpansion| . |OrderedAbelianSemiGroup|) T) ((|DecimalExpansion| . |OrderedType|) T) ((|DecimalExpansion| . |OrderedSet|) T) ((|DecimalExpansion| . |OrderedAbelianMonoid|) T) ((|DecimalExpansion| . |OrderedAbelianGroup|) T) ((|DecimalExpansion| . |OrderedIntegralDomain|) T) ((|DecimalExpansion| . 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((|DecimalExpansion| . |IntegralDomain|) T) ((|DecimalExpansion| . |PrincipalIdealDomain|) T) ((|DecimalExpansion| . |UniqueFactorizationDomain|) T) ((|DecimalExpansion| . |Field|) T) ((|DecimalExpansion| . |DifferentialRing|) T) ((|DecimalExpansion| . |DifferentialDomain|) 21493) ((|DecimalExpansion| . |DifferentialSpace|) T) ((|DecimalExpansion| . |DifferentialSpaceExtension|) 21470) ((|DecimalExpansion| . |PartialDifferentialDomain|) NIL) ((|DecimalExpansion| . |PartialDifferentialSpace|) NIL) ((|DecimalExpansion| . |PartialDifferentialRing|) NIL) ((|DecimalExpansion| . |DifferentialExtension|) 21447) ((|DecimalExpansion| . |CharacteristicZero|) T) ((|DecimalExpansion| . |CharacteristicNonZero|) NIL) ((|DecimalExpansion| . |CancellationAbelianMonoid|) T) ((|DecimalExpansion| . |AbelianSemiGroup|) T) ((|DecimalExpansion| . |BasicType|) T) ((|DecimalExpansion| . |Join|) T) ((|DecimalExpansion| . |Type|) T) ((|DecimalExpansion| . |CoercibleTo|) 21358) ((|DecimalExpansion| . 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21229) ((|ConstructorKind| . |Type|) T) ((|ConstructorKind| . |Join|) T) ((|ConstructorKind| . |BasicType|) T) ((|ConstructorCall| . |SetCategory|) T) ((|ConstructorCall| . |CoercibleTo|) 21203) ((|ConstructorCall| . |Type|) T) ((|ConstructorCall| . |Join|) T) ((|ConstructorCall| . |BasicType|) T) ((|Constructor| . |ConstructorCategory|) T) ((|Constructor| . |SetCategory|) T) ((|Constructor| . |CoercibleTo|) 21177) ((|Constructor| . |Type|) T) ((|Constructor| . |Join|) T) ((|Constructor| . |BasicType|) T) ((|Constructor| . |OperatorCategory|) 21151) ((|CoerceAst| . |SpadSyntaxCategory|) T) ((|CoerceAst| . |HomotopicTo|) 21129) ((|CoerceAst| . |CoercibleTo|) 21084) ((|CoerceAst| . |CoercibleFrom|) 21062) ((|CoerceAst| . |SetCategory|) T) ((|CoerceAst| . |Type|) T) ((|CoerceAst| . |Join|) T) ((|CoerceAst| . |BasicType|) T) ((|CoerceAst| . |AbstractSyntaxCategory|) T) ((|Contour| . |CoercibleTo|) 21036) ((|ContinuedFraction| . |Algebra|) 20951) ((|ContinuedFraction| . |CoercibleFrom|) 20846) ((|ContinuedFraction| . |LeftModule|) 20761) ((|ContinuedFraction| . |LeftLinearSet|) 20656) ((|ContinuedFraction| . |Rng|) T) ((|ContinuedFraction| . |SemiGroup|) T) ((|ContinuedFraction| . |SemiRing|) T) ((|ContinuedFraction| . |Monoid|) T) ((|ContinuedFraction| . |Ring|) T) ((|ContinuedFraction| . |BiModule|) 20550) ((|ContinuedFraction| . |RightLinearSet|) 20465) ((|ContinuedFraction| . |RightModule|) 20380) ((|ContinuedFraction| . |AbelianGroup|) T) ((|ContinuedFraction| . |AbelianMonoid|) T) ((|ContinuedFraction| . |SetCategory|) T) ((|ContinuedFraction| . |CoercibleTo|) 20354) ((|ContinuedFraction| . |Type|) T) ((|ContinuedFraction| . |Join|) T) ((|ContinuedFraction| . |BasicType|) T) ((|ContinuedFraction| . |AbelianSemiGroup|) T) ((|ContinuedFraction| . |CancellationAbelianMonoid|) T) ((|ContinuedFraction| . |LinearSet|) 20269) ((|ContinuedFraction| . |Module|) 20184) ((|ContinuedFraction| . |Field|) T) ((|ContinuedFraction| . |UniqueFactorizationDomain|) T) ((|ContinuedFraction| . |PrincipalIdealDomain|) T) ((|ContinuedFraction| . |IntegralDomain|) T) ((|ContinuedFraction| . |CommutativeRing|) T) ((|ContinuedFraction| . |GcdDomain|) T) ((|ContinuedFraction| . |EuclideanDomain|) T) ((|ContinuedFraction| . |EntireRing|) T) ((|ContinuedFraction| . |DivisionRing|) T) ((|SubSpaceComponentProperty| . |SetCategory|) T) ((|SubSpaceComponentProperty| . |CoercibleTo|) 20158) ((|SubSpaceComponentProperty| . |Type|) T) ((|SubSpaceComponentProperty| . |Join|) T) ((|SubSpaceComponentProperty| . |BasicType|) T) ((|Complex| . |ComplexCategory|) 20142) ((|Complex| . |ArcHyperbolicFunctionCategory|) 20093) ((|Complex| . |ArcTrigonometricFunctionCategory|) 20044) ((|Complex| . |ElementaryFunctionCategory|) 19995) ((|Complex| . |HyperbolicFunctionCategory|) 19946) ((|Complex| . |TrigonometricFunctionCategory|) 19897) ((|Complex| . |TranscendentalFunctionCategory|) 19848) ((|Complex| . |RadicalCategory|) 19760) ((|Complex| . |PolynomialFactorizationExplicit|) 19671) ((|Complex| . |ConvertibleTo|) 19295) ((|Complex| . |Patternable|) 19279) ((|Complex| . |Finite|) 19212) ((|Complex| . |FiniteFieldCategory|) 19174) ((|Complex| . |StepThrough|) 19136) ((|Complex| . |FieldOfPrimeCharacteristic|) 19098) ((|Complex| . |FramedAlgebra|) 19046) ((|Complex| . |Algebra|) 18804) ((|Complex| . |BiModule|) 18672) ((|Complex| . |RightLinearSet|) 18554) ((|Complex| . |RightModule|) 18436) ((|Complex| . |LinearSet|) 18194) ((|Complex| . |Module|) 17952) ((|Complex| . |FiniteRankAlgebra|) 17900) ((|Complex| . |MonogenicAlgebra|) 17848) ((|Complex| . |RetractableTo|) 17692) ((|Complex| . |CoercibleFrom|) 17374) ((|Complex| . |FullyRetractableTo|) 17358) ((|Complex| . |PatternMatchable|) 17239) ((|Complex| . |FullyPatternMatchable|) 17223) ((|Complex| . |LinearlyExplicitRingOver|) 17139) ((|Complex| . |LeftModule|) 16953) ((|Complex| . |LeftLinearSet|) 16815) ((|Complex| . |FullyLinearlyExplicitRingOver|) 16799) ((|Complex| . |Eltable|) 16752) ((|Complex| . |Evalable|) 16711) ((|Complex| . |InnerEvalable|) 16600) ((|Complex| . |Functorial|) 16584) ((|Complex| . |FullyEvalableOver|) 16568) ((|Complex| . |DivisionRing|) 16502) ((|Complex| . |UniqueFactorizationDomain|) 16348) ((|Complex| . |Field|) 16282) ((|Complex| . |PrincipalIdealDomain|) 16183) ((|Complex| . |IntegralDomain|) 16052) ((|Complex| . |EntireRing|) 15921) ((|Complex| . |GcdDomain|) 15822) ((|Complex| . |EuclideanDomain|) 15723) ((|Complex| . |DifferentialRing|) 15646) ((|Complex| . |DifferentialDomain|) 15528) ((|Complex| . |DifferentialSpace|) 15416) ((|Complex| . |DifferentialSpaceExtension|) 15400) ((|Complex| . |PartialDifferentialDomain|) 15272) ((|Complex| . |PartialDifferentialSpace|) 15146) ((|Complex| . |PartialDifferentialRing|) 15078) ((|Complex| . |DifferentialExtension|) 15062) ((|Complex| . |CommutativeRing|) T) ((|Complex| . |CharacteristicZero|) 15025) ((|Complex| . |Ring|) T) ((|Complex| . |Monoid|) T) ((|Complex| . |SemiRing|) T) ((|Complex| . |SemiGroup|) T) ((|Complex| . |Rng|) T) ((|Complex| . |AbelianGroup|) T) ((|Complex| . |AbelianMonoid|) T) ((|Complex| . |SetCategory|) T) ((|Complex| . |CoercibleTo|) 14999) ((|Complex| . |Type|) T) ((|Complex| . |Join|) T) ((|Complex| . |BasicType|) T) ((|Complex| . |AbelianSemiGroup|) T) ((|Complex| . |CancellationAbelianMonoid|) T) ((|Complex| . |CharacteristicNonZero|) 14917) ((|CommutativeOperation| . |CommutativeOperatorCategory|) 14901) ((|CommutativeOperation| . |MappingCategory|) 14875) ((|CommutativeOperation| . |Type|) T) ((|CommutativeOperation| . |BinaryOperatorCategory|) 14859) ((|CommutativeOperation| . |CoercibleTo|) 14823) ((|CommaAst| . |SpadSyntaxCategory|) T) ((|CommaAst| . |HomotopicTo|) 14801) ((|CommaAst| . |CoercibleTo|) 14756) ((|CommaAst| . |CoercibleFrom|) 14734) ((|CommaAst| . |SetCategory|) T) ((|CommaAst| . |Type|) T) ((|CommaAst| . |Join|) T) ((|CommaAst| . |BasicType|) T) ((|CommaAst| . |AbstractSyntaxCategory|) T) ((|Commutator| . |SetCategory|) T) ((|Commutator| . |CoercibleTo|) 14708) ((|Commutator| . |Type|) T) ((|Commutator| . |Join|) T) ((|Commutator| . |BasicType|) T) ((|Color| . |AbelianSemiGroup|) T) ((|Color| . |BasicType|) T) ((|Color| . |Join|) T) ((|Color| . |Type|) T) ((|Color| . |CoercibleTo|) 14682) ((|Color| . |SetCategory|) T) ((|ColonAst| . |SpadSyntaxCategory|) T) ((|ColonAst| . |HomotopicTo|) 14660) ((|ColonAst| . |CoercibleTo|) 14615) ((|ColonAst| . |CoercibleFrom|) 14593) ((|ColonAst| . |SetCategory|) T) ((|ColonAst| . |Type|) T) ((|ColonAst| . |Join|) T) ((|ColonAst| . |BasicType|) T) ((|ColonAst| . |AbstractSyntaxCategory|) T) ((|CollectAst| . |SpadSyntaxCategory|) T) ((|CollectAst| . |HomotopicTo|) 14571) ((|CollectAst| . |CoercibleTo|) 14526) ((|CollectAst| . |CoercibleFrom|) 14504) ((|CollectAst| . |SetCategory|) T) ((|CollectAst| . |Type|) T) ((|CollectAst| . |Join|) T) ((|CollectAst| . |BasicType|) T) ((|CollectAst| . |AbstractSyntaxCategory|) T) ((|CliffordAlgebra| . |Ring|) T) ((|CliffordAlgebra| . |Monoid|) T) ((|CliffordAlgebra| . |SemiRing|) T) ((|CliffordAlgebra| . |SemiGroup|) T) ((|CliffordAlgebra| . |Rng|) T) ((|CliffordAlgebra| . |AbelianGroup|) T) ((|CliffordAlgebra| . |LeftLinearSet|) 14458) ((|CliffordAlgebra| . |AbelianMonoid|) T) ((|CliffordAlgebra| . |SetCategory|) T) ((|CliffordAlgebra| . |CoercibleTo|) 14432) ((|CliffordAlgebra| . |Type|) T) ((|CliffordAlgebra| . |Join|) T) ((|CliffordAlgebra| . |BasicType|) T) ((|CliffordAlgebra| . |AbelianSemiGroup|) T) ((|CliffordAlgebra| . |CancellationAbelianMonoid|) T) ((|CliffordAlgebra| . |LeftModule|) 14406) ((|CliffordAlgebra| . |CoercibleFrom|) 14370) ((|CliffordAlgebra| . |Algebra|) 14354) ((|CliffordAlgebra| . |BiModule|) 14333) ((|CliffordAlgebra| . |RightLinearSet|) 14317) ((|CliffordAlgebra| . |RightModule|) 14301) ((|CliffordAlgebra| . |LinearSet|) 14285) ((|CliffordAlgebra| . |Module|) 14269) ((|CliffordAlgebra| . |VectorSpace|) 14253) ((|Character| . |OrderedFinite|) T) ((|Character| . |OrderedType|) T) ((|Character| . |OrderedSet|) T) ((|Character| . |SetCategory|) T) ((|Character| . |CoercibleTo|) 14227) ((|Character| . |Type|) T) ((|Character| . |Join|) T) ((|Character| . |BasicType|) T) ((|Character| . |Finite|) T) ((|CharacterClass| . |SetCategory|) T) ((|CharacterClass| . |CoercibleTo|) 14201) ((|CharacterClass| . |Type|) T) ((|CharacterClass| . |Join|) T) ((|CharacterClass| . |BasicType|) T) ((|CharacterClass| . |ConvertibleTo|) 14148) ((|CharacterClass| . |FiniteSetAggregate|) 14123) ((|CharacterClass| . |SetAggregate|) 14098) ((|CharacterClass| . |FiniteAggregate|) 14073) ((|CharacterClass| . |Finite|) T) ((|CharacterClass| . |DictionaryOperations|) 14048) ((|CharacterClass| . |Collection|) 14023) ((|CharacterClass| . |HomogeneousAggregate|) 13998) ((|CharacterClass| . |Functorial|) 13973) ((|CharacterClass| . |InnerEvalable|) NIL) ((|CharacterClass| . |Evalable|) NIL) ((|CharacterClass| . |Aggregate|) T) ((|CharacterClass| . |ShallowlyMutableAggregate|) 13948) ((|CharacterClass| . |BagAggregate|) 13923) ((|CharacterClass| . |Dictionary|) 13898) ((|Category| . |CoercibleTo|) 13872) ((|CategoryConstructor| . |ConstructorCategory|) T) ((|CategoryConstructor| . |SetCategory|) T) ((|CategoryConstructor| . |CoercibleTo|) 13822) ((|CategoryConstructor| . |Type|) T) ((|CategoryConstructor| . |Join|) T) ((|CategoryConstructor| . |BasicType|) T) ((|CategoryConstructor| . |OperatorCategory|) 13796) ((|CategoryAst| . |SpadSyntaxCategory|) T) ((|CategoryAst| . |HomotopicTo|) 13774) ((|CategoryAst| . |CoercibleTo|) 13729) ((|CategoryAst| . |CoercibleFrom|) 13707) ((|CategoryAst| . |SetCategory|) T) ((|CategoryAst| . |Type|) T) ((|CategoryAst| . |Join|) T) ((|CategoryAst| . |BasicType|) T) ((|CategoryAst| . |AbstractSyntaxCategory|) T) ((|CaseAst| . |SpadSyntaxCategory|) T) ((|CaseAst| . |HomotopicTo|) 13685) ((|CaseAst| . |CoercibleTo|) 13640) ((|CaseAst| . |CoercibleFrom|) 13618) ((|CaseAst| . |SetCategory|) T) ((|CaseAst| . |Type|) T) ((|CaseAst| . |Join|) T) ((|CaseAst| . |BasicType|) T) ((|CaseAst| . |AbstractSyntaxCategory|) T) ((|CartesianTensor| . |GradedAlgebra|) 13579) ((|CartesianTensor| . |CoercibleFrom|) 13451) ((|CartesianTensor| . |RetractableTo|) 13435) ((|CartesianTensor| . |SetCategory|) T) ((|CartesianTensor| . |CoercibleTo|) 13409) ((|CartesianTensor| . |Type|) T) ((|CartesianTensor| . |Join|) T) ((|CartesianTensor| . |BasicType|) T) ((|CartesianTensor| . |GradedModule|) 13343) ((|CartesianTensor| . |Eltable|) 13315) ((|CardinalNumber| . |OrderedSet|) T) ((|CardinalNumber| . |CoercibleTo|) 13289) ((|CardinalNumber| . |SetCategory|) T) ((|CardinalNumber| . |BasicType|) T) ((|CardinalNumber| . |Join|) T) ((|CardinalNumber| . |Type|) T) ((|CardinalNumber| . |OrderedType|) T) ((|CardinalNumber| . |AbelianMonoid|) T) ((|CardinalNumber| . |AbelianSemiGroup|) T) ((|CardinalNumber| . |Monoid|) T) ((|CardinalNumber| . |SemiGroup|) T) ((|CardinalNumber| . |RetractableTo|) 13255) ((|CardinalNumber| . |CoercibleFrom|) 13221) ((|CapsuleAst| . |SpadSyntaxCategory|) T) ((|CapsuleAst| . |HomotopicTo|) 13199) ((|CapsuleAst| . |CoercibleTo|) 13154) ((|CapsuleAst| . |CoercibleFrom|) 13132) ((|CapsuleAst| . |SetCategory|) T) ((|CapsuleAst| . |Type|) T) ((|CapsuleAst| . |Join|) T) ((|CapsuleAst| . |BasicType|) T) ((|CapsuleAst| . |AbstractSyntaxCategory|) T) ((|ByteOrder| . |SetCategory|) T) ((|ByteOrder| . |CoercibleTo|) 13106) ((|ByteOrder| . |Type|) T) ((|ByteOrder| . |Join|) T) ((|ByteOrder| . |BasicType|) T) ((|ByteBuffer| . |OneDimensionalArrayAggregate|) 13086) ((|ByteBuffer| . |ShallowlyMutableAggregate|) 13066) ((|ByteBuffer| . |FiniteAggregate|) 13046) ((|ByteBuffer| . |Aggregate|) T) ((|ByteBuffer| . |Join|) T) ((|ByteBuffer| . |Type|) T) ((|ByteBuffer| . |BasicType|) T) ((|ByteBuffer| . |CoercibleTo|) 12965) ((|ByteBuffer| . |Evalable|) NIL) ((|ByteBuffer| . |InnerEvalable|) NIL) ((|ByteBuffer| . |Functorial|) 12945) ((|ByteBuffer| . |SetCategory|) T) ((|ByteBuffer| . |HomogeneousAggregate|) 12925) ((|ByteBuffer| . |LinearAggregate|) 12905) ((|ByteBuffer| . |EltableAggregate|) 12873) ((|ByteBuffer| . |Eltable|) 12798) ((|ByteBuffer| . |IndexedAggregate|) 12766) ((|ByteBuffer| . |ConvertibleTo|) NIL) ((|ByteBuffer| . |Collection|) 12746) ((|ByteBuffer| . |OrderedSet|) T) ((|ByteBuffer| . |OrderedType|) T) ((|ByteBuffer| . |FiniteLinearAggregate|) 12726) ((|Byte| . |OrderedFinite|) T) ((|Byte| . |OrderedType|) T) ((|Byte| . |OrderedSet|) T) ((|Byte| . |SetCategory|) T) ((|Byte| . |CoercibleTo|) 12700) ((|Byte| . |Type|) T) ((|Byte| . |Join|) T) ((|Byte| . |BasicType|) T) ((|Byte| . |Finite|) T) ((|Byte| . |Logic|) T) ((|BinaryTree| . |BinaryTreeCategory|) 12684) ((|BinaryTree| . |ShallowlyMutableAggregate|) 12668) ((|BinaryTree| . |FiniteAggregate|) 12652) ((|BinaryTree| . |RecursiveAggregate|) 12636) ((|BinaryTree| . |Aggregate|) T) ((|BinaryTree| . |Join|) T) ((|BinaryTree| . |Type|) T) ((|BinaryTree| . |BasicType|) 12574) ((|BinaryTree| . |CoercibleTo|) 12476) ((|BinaryTree| . |Evalable|) 12400) ((|BinaryTree| . |InnerEvalable|) 12319) ((|BinaryTree| . |Functorial|) 12303) ((|BinaryTree| . |SetCategory|) 12273) ((|BinaryTree| . |HomogeneousAggregate|) 12257) ((|BinaryTree| . |BinaryRecursiveAggregate|) 12241) ((|BinaryTournament| . |BinaryTreeCategory|) 12225) ((|BinaryTournament| . |ShallowlyMutableAggregate|) 12209) ((|BinaryTournament| . |FiniteAggregate|) 12193) ((|BinaryTournament| . |RecursiveAggregate|) 12177) ((|BinaryTournament| . |Aggregate|) T) ((|BinaryTournament| . |Join|) T) ((|BinaryTournament| . |Type|) T) ((|BinaryTournament| . |BasicType|) 12115) ((|BinaryTournament| . |CoercibleTo|) 12017) ((|BinaryTournament| . |Evalable|) 11941) ((|BinaryTournament| . |InnerEvalable|) 11860) ((|BinaryTournament| . |Functorial|) 11844) ((|BinaryTournament| . |SetCategory|) 11814) ((|BinaryTournament| . |HomogeneousAggregate|) 11798) ((|BinaryTournament| . |BinaryRecursiveAggregate|) 11782) ((|BinarySearchTree| . |BinaryTreeCategory|) 11766) ((|BinarySearchTree| . |ShallowlyMutableAggregate|) 11750) ((|BinarySearchTree| . |FiniteAggregate|) 11734) ((|BinarySearchTree| . |RecursiveAggregate|) 11718) ((|BinarySearchTree| . |Aggregate|) T) ((|BinarySearchTree| . |Join|) T) ((|BinarySearchTree| . |Type|) T) ((|BinarySearchTree| . |BasicType|) 11656) ((|BinarySearchTree| . |CoercibleTo|) 11558) ((|BinarySearchTree| . |Evalable|) 11482) ((|BinarySearchTree| . |InnerEvalable|) 11401) ((|BinarySearchTree| . |Functorial|) 11385) ((|BinarySearchTree| . |SetCategory|) 11355) ((|BinarySearchTree| . |HomogeneousAggregate|) 11339) ((|BinarySearchTree| . |BinaryRecursiveAggregate|) 11323) ((|BalancedPAdicRational| . |QuotientFieldCategory|) 11282) ((|BalancedPAdicRational| . |StepThrough|) NIL) ((|BalancedPAdicRational| . |RetractableTo|) 11241) ((|BalancedPAdicRational| . |CoercibleFrom|) 11137) ((|BalancedPAdicRational| . |ConvertibleTo|) NIL) ((|BalancedPAdicRational| . |RealConstant|) NIL) ((|BalancedPAdicRational| . |PolynomialFactorizationExplicit|) NIL) ((|BalancedPAdicRational| . |Patternable|) 11096) ((|BalancedPAdicRational| . |OrderedRing|) NIL) ((|BalancedPAdicRational| . |OrderedCancellationAbelianMonoid|) NIL) ((|BalancedPAdicRational| . |OrderedAbelianSemiGroup|) NIL) ((|BalancedPAdicRational| . |OrderedType|) NIL) ((|BalancedPAdicRational| . |OrderedSet|) NIL) ((|BalancedPAdicRational| . |OrderedAbelianMonoid|) NIL) ((|BalancedPAdicRational| . |OrderedAbelianGroup|) NIL) ((|BalancedPAdicRational| . |OrderedIntegralDomain|) NIL) ((|BalancedPAdicRational| . |PatternMatchable|) NIL) ((|BalancedPAdicRational| . |FullyPatternMatchable|) 11055) ((|BalancedPAdicRational| . |LinearlyExplicitRingOver|) 11014) ((|BalancedPAdicRational| . |LeftModule|) 10930) ((|BalancedPAdicRational| . |FullyLinearlyExplicitRingOver|) 10889) ((|BalancedPAdicRational| . |Eltable|) 10817) ((|BalancedPAdicRational| . |Evalable|) 10750) ((|BalancedPAdicRational| . |InnerEvalable|) 10617) ((|BalancedPAdicRational| . |Functorial|) 10576) 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((|BalancedPAdicRational| . |DifferentialSpaceExtension|) 9870) ((|BalancedPAdicRational| . |PartialDifferentialDomain|) NIL) ((|BalancedPAdicRational| . |PartialDifferentialSpace|) NIL) ((|BalancedPAdicRational| . |PartialDifferentialRing|) NIL) ((|BalancedPAdicRational| . |DifferentialExtension|) 9829) ((|BalancedPAdicRational| . |CharacteristicZero|) T) ((|BalancedPAdicRational| . |CharacteristicNonZero|) NIL) ((|BalancedPAdicRational| . |CancellationAbelianMonoid|) T) ((|BalancedPAdicRational| . |AbelianSemiGroup|) T) ((|BalancedPAdicRational| . |BasicType|) T) ((|BalancedPAdicRational| . |Join|) T) ((|BalancedPAdicRational| . |Type|) T) ((|BalancedPAdicRational| . |CoercibleTo|) 9803) ((|BalancedPAdicRational| . |SetCategory|) T) ((|BalancedPAdicRational| . |AbelianMonoid|) T) ((|BalancedPAdicRational| . |AbelianGroup|) T) ((|BalancedPAdicRational| . |Ring|) T) ((|BalancedPAdicRational| . |Monoid|) T) ((|BalancedPAdicRational| . |SemiRing|) T) ((|BalancedPAdicRational| . |SemiGroup|) T) ((|BalancedPAdicRational| . |Rng|) T) ((|BalancedPAdicInteger| . |PAdicIntegerCategory|) 9787) ((|BalancedPAdicInteger| . |PrincipalIdealDomain|) T) ((|BalancedPAdicInteger| . |IntegralDomain|) T) ((|BalancedPAdicInteger| . |EntireRing|) T) ((|BalancedPAdicInteger| . |CommutativeRing|) T) ((|BalancedPAdicInteger| . |CoercibleFrom|) 9754) ((|BalancedPAdicInteger| . |Module|) 9741) ((|BalancedPAdicInteger| . |LinearSet|) 9728) ((|BalancedPAdicInteger| . |RightModule|) 9715) ((|BalancedPAdicInteger| . |RightLinearSet|) 9702) ((|BalancedPAdicInteger| . |BiModule|) 9687) ((|BalancedPAdicInteger| . |Algebra|) 9674) ((|BalancedPAdicInteger| . |GcdDomain|) T) ((|BalancedPAdicInteger| . |EuclideanDomain|) T) ((|BalancedPAdicInteger| . |Ring|) T) ((|BalancedPAdicInteger| . |Monoid|) T) ((|BalancedPAdicInteger| . |SemiRing|) T) ((|BalancedPAdicInteger| . |SemiGroup|) T) ((|BalancedPAdicInteger| . |Rng|) T) ((|BalancedPAdicInteger| . |AbelianGroup|) T) ((|BalancedPAdicInteger| . |LeftLinearSet|) 9641) ((|BalancedPAdicInteger| . |AbelianMonoid|) T) ((|BalancedPAdicInteger| . |SetCategory|) T) ((|BalancedPAdicInteger| . |CoercibleTo|) 9615) ((|BalancedPAdicInteger| . |Type|) T) ((|BalancedPAdicInteger| . |Join|) T) ((|BalancedPAdicInteger| . |BasicType|) T) ((|BalancedPAdicInteger| . |AbelianSemiGroup|) T) ((|BalancedPAdicInteger| . |CancellationAbelianMonoid|) T) ((|BalancedPAdicInteger| . |LeftModule|) 9602) ((|BalancedPAdicInteger| . |CharacteristicZero|) T) ((|BasicOperator| . |OrderedSet|) T) ((|BasicOperator| . |CoercibleTo|) 9576) ((|BasicOperator| . |SetCategory|) T) ((|BasicOperator| . |BasicType|) T) ((|BasicOperator| . |Join|) T) ((|BasicOperator| . |Type|) T) ((|BasicOperator| . |OrderedType|) T) ((|BasicOperator| . |OperatorCategory|) 9554) ((|Boolean| . |OrderedFinite|) T) ((|Boolean| . |OrderedType|) T) ((|Boolean| . |OrderedSet|) T) ((|Boolean| . |SetCategory|) T) ((|Boolean| . |CoercibleTo|) 9528) ((|Boolean| . |Type|) T) ((|Boolean| . |Join|) T) ((|Boolean| . |BasicType|) T) ((|Boolean| . |Finite|) T) ((|Boolean| . |PropositionalLogic|) T) ((|Boolean| . |Logic|) T) ((|Boolean| . |BooleanLogic|) T) ((|Boolean| . |ConvertibleTo|) 9503) ((|Bits| . |BitAggregate|) T) ((|Bits| . |FiniteLinearAggregate|) 9480) ((|Bits| . |OrderedType|) T) ((|Bits| . |OrderedSet|) T) ((|Bits| . |Collection|) 9457) ((|Bits| . |ConvertibleTo|) 9432) ((|Bits| . |Eltable|) 9354) ((|Bits| . |IndexedAggregate|) 9319) ((|Bits| . |EltableAggregate|) 9284) ((|Bits| . |LinearAggregate|) 9261) ((|Bits| . |HomogeneousAggregate|) 9238) ((|Bits| . |SetCategory|) T) ((|Bits| . |Functorial|) 9215) ((|Bits| . |InnerEvalable|) NIL) ((|Bits| . |Evalable|) NIL) ((|Bits| . |CoercibleTo|) 9189) ((|Bits| . |BasicType|) T) ((|Bits| . |Aggregate|) T) ((|Bits| . |FiniteAggregate|) 9166) ((|Bits| . |ShallowlyMutableAggregate|) 9143) ((|Bits| . |OneDimensionalArrayAggregate|) 9120) ((|Bits| . |Logic|) T) ((|Bits| . |Join|) T) ((|Bits| . |Type|) T) ((|Bits| . |BooleanLogic|) T) ((|BinaryOperation| . |BinaryOperatorCategory|) 9104) ((|BinaryOperation| . |Type|) T) ((|BinaryOperation| . |MappingCategory|) 9078) ((|BinaryOperation| . |SetCategory|) T) ((|BinaryOperation| . |CoercibleTo|) 9052) ((|BinaryOperation| . |Join|) T) ((|BinaryOperation| . |BasicType|) T) ((|Binding| . |CoercibleTo|) 9026) ((|BinaryExpansion| . |QuotientFieldCategory|) 9003) ((|BinaryExpansion| . |StepThrough|) T) ((|BinaryExpansion| . |CoercibleFrom|) 8937) ((|BinaryExpansion| . |RetractableTo|) 8881) ((|BinaryExpansion| . |ConvertibleTo|) 8782) ((|BinaryExpansion| . |RealConstant|) T) ((|BinaryExpansion| . |PolynomialFactorizationExplicit|) NIL) ((|BinaryExpansion| . |Patternable|) 8759) ((|BinaryExpansion| . |OrderedRing|) T) ((|BinaryExpansion| . |OrderedCancellationAbelianMonoid|) T) ((|BinaryExpansion| . |OrderedAbelianSemiGroup|) T) ((|BinaryExpansion| . |OrderedType|) T) ((|BinaryExpansion| . |OrderedSet|) T) ((|BinaryExpansion| . |OrderedAbelianMonoid|) T) ((|BinaryExpansion| . |OrderedAbelianGroup|) T) ((|BinaryExpansion| . |OrderedIntegralDomain|) T) ((|BinaryExpansion| . |PatternMatchable|) 8736) ((|BinaryExpansion| . |FullyPatternMatchable|) 8713) ((|BinaryExpansion| . |LinearlyExplicitRingOver|) 8690) ((|BinaryExpansion| . |FullyLinearlyExplicitRingOver|) 8667) ((|BinaryExpansion| . |Eltable|) NIL) ((|BinaryExpansion| . |Evalable|) NIL) ((|BinaryExpansion| . |InnerEvalable|) NIL) ((|BinaryExpansion| . |Functorial|) 8644) ((|BinaryExpansion| . |FullyEvalableOver|) 8621) ((|BinaryExpansion| . |DivisionRing|) T) ((|BinaryExpansion| . |BiModule|) 8539) ((|BinaryExpansion| . |RightLinearSet|) 8473) ((|BinaryExpansion| . |RightModule|) 8407) ((|BinaryExpansion| . |EntireRing|) T) ((|BinaryExpansion| . |Module|) 8341) ((|BinaryExpansion| . |LinearSet|) 8275) ((|BinaryExpansion| . |LeftModule|) 8209) ((|BinaryExpansion| . |LeftLinearSet|) 8143) ((|BinaryExpansion| . |Algebra|) 8077) ((|BinaryExpansion| . |EuclideanDomain|) T) ((|BinaryExpansion| . |GcdDomain|) T) ((|BinaryExpansion| . |CommutativeRing|) T) ((|BinaryExpansion| . |IntegralDomain|) T) ((|BinaryExpansion| . |PrincipalIdealDomain|) T) ((|BinaryExpansion| . |UniqueFactorizationDomain|) T) ((|BinaryExpansion| . |Field|) T) ((|BinaryExpansion| . |DifferentialRing|) T) ((|BinaryExpansion| . |DifferentialDomain|) 8064) ((|BinaryExpansion| . |DifferentialSpace|) T) ((|BinaryExpansion| . |DifferentialSpaceExtension|) 8041) ((|BinaryExpansion| . |PartialDifferentialDomain|) NIL) ((|BinaryExpansion| . |PartialDifferentialSpace|) NIL) ((|BinaryExpansion| . |PartialDifferentialRing|) NIL) ((|BinaryExpansion| . |DifferentialExtension|) 8018) ((|BinaryExpansion| . |CharacteristicZero|) T) ((|BinaryExpansion| . |CharacteristicNonZero|) NIL) ((|BinaryExpansion| . |CancellationAbelianMonoid|) T) ((|BinaryExpansion| . |AbelianSemiGroup|) T) ((|BinaryExpansion| . |BasicType|) T) ((|BinaryExpansion| . |Join|) T) ((|BinaryExpansion| . |Type|) T) ((|BinaryExpansion| . |CoercibleTo|) 7930) ((|BinaryExpansion| . |SetCategory|) T) ((|BinaryExpansion| . |AbelianMonoid|) T) ((|BinaryExpansion| . |AbelianGroup|) T) ((|BinaryExpansion| . |Ring|) T) ((|BinaryExpansion| . |Monoid|) T) ((|BinaryExpansion| . |SemiRing|) T) ((|BinaryExpansion| . |SemiGroup|) T) ((|BinaryExpansion| . |Rng|) T) ((|BalancedBinaryTree| . |BinaryTreeCategory|) 7914) ((|BalancedBinaryTree| . |ShallowlyMutableAggregate|) 7898) ((|BalancedBinaryTree| . |FiniteAggregate|) 7882) ((|BalancedBinaryTree| . |RecursiveAggregate|) 7866) ((|BalancedBinaryTree| . |Aggregate|) T) ((|BalancedBinaryTree| . |Join|) T) ((|BalancedBinaryTree| . |Type|) T) ((|BalancedBinaryTree| . |BasicType|) 7804) ((|BalancedBinaryTree| . |CoercibleTo|) 7706) ((|BalancedBinaryTree| . |Evalable|) 7630) ((|BalancedBinaryTree| . |InnerEvalable|) 7549) ((|BalancedBinaryTree| . |Functorial|) 7533) ((|BalancedBinaryTree| . |SetCategory|) 7503) ((|BalancedBinaryTree| . |HomogeneousAggregate|) 7487) ((|BalancedBinaryTree| . |BinaryRecursiveAggregate|) 7471) ((|Automorphism| . |Group|) T) ((|Automorphism| . |SemiGroup|) T) ((|Automorphism| . |BasicType|) T) ((|Automorphism| . |Join|) T) ((|Automorphism| . |Type|) T) ((|Automorphism| . |CoercibleTo|) 7445) ((|Automorphism| . |SetCategory|) T) ((|Automorphism| . |Monoid|) T) ((|Automorphism| . |Eltable|) 7424) ((|AttributeAst| . |SpadSyntaxCategory|) T) ((|AttributeAst| . |HomotopicTo|) 7402) ((|AttributeAst| . |CoercibleTo|) 7357) ((|AttributeAst| . |CoercibleFrom|) 7335) ((|AttributeAst| . |SetCategory|) T) ((|AttributeAst| . |Type|) T) ((|AttributeAst| . |Join|) T) ((|AttributeAst| . |BasicType|) T) ((|AttributeAst| . |AbstractSyntaxCategory|) T) ((|ArrayStack| . |StackAggregate|) 7319) ((|ArrayStack| . |FiniteAggregate|) 7303) ((|ArrayStack| . |HomogeneousAggregate|) 7287) ((|ArrayStack| . |SetCategory|) 7257) ((|ArrayStack| . |Functorial|) 7241) ((|ArrayStack| . |InnerEvalable|) 7160) ((|ArrayStack| . |Evalable|) 7084) ((|ArrayStack| . |CoercibleTo|) 6986) ((|ArrayStack| . |BasicType|) 6924) ((|ArrayStack| . |Type|) T) ((|ArrayStack| . |Join|) T) ((|ArrayStack| . |Aggregate|) T) ((|ArrayStack| . |ShallowlyMutableAggregate|) 6908) ((|ArrayStack| . |BagAggregate|) 6892) ((|TwoDimensionalArray| . |TwoDimensionalArrayCategory|) 6840) ((|TwoDimensionalArray| . |ShallowlyMutableAggregate|) 6824) ((|TwoDimensionalArray| . |HomogeneousAggregate|) 6808) ((|TwoDimensionalArray| . |SetCategory|) 6778) ((|TwoDimensionalArray| . |Functorial|) 6762) ((|TwoDimensionalArray| . |InnerEvalable|) 6681) ((|TwoDimensionalArray| . |Evalable|) 6605) ((|TwoDimensionalArray| . |CoercibleTo|) 6507) ((|TwoDimensionalArray| . |BasicType|) 6445) ((|TwoDimensionalArray| . |Type|) T) ((|TwoDimensionalArray| . |Join|) T) ((|TwoDimensionalArray| . |Aggregate|) T) ((|TwoDimensionalArray| . |FiniteAggregate|) 6429) ((|OneDimensionalArray| . |OneDimensionalArrayAggregate|) 6413) ((|OneDimensionalArray| . |ShallowlyMutableAggregate|) 6397) ((|OneDimensionalArray| . |FiniteAggregate|) 6381) ((|OneDimensionalArray| . |Aggregate|) T) ((|OneDimensionalArray| . |Join|) T) ((|OneDimensionalArray| . |Type|) T) ((|OneDimensionalArray| . |BasicType|) 6291) ((|OneDimensionalArray| . |CoercibleTo|) 6165) ((|OneDimensionalArray| . |Evalable|) 6089) ((|OneDimensionalArray| . |InnerEvalable|) 6008) ((|OneDimensionalArray| . |Functorial|) 5992) ((|OneDimensionalArray| . |SetCategory|) 5929) ((|OneDimensionalArray| . |HomogeneousAggregate|) 5913) ((|OneDimensionalArray| . |LinearAggregate|) 5897) ((|OneDimensionalArray| . |EltableAggregate|) 5869) ((|OneDimensionalArray| . |Eltable|) 5798) ((|OneDimensionalArray| . |IndexedAggregate|) 5770) ((|OneDimensionalArray| . |ConvertibleTo|) 5706) ((|OneDimensionalArray| . |Collection|) 5690) ((|OneDimensionalArray| . |OrderedSet|) 5661) ((|OneDimensionalArray| . |OrderedType|) 5632) ((|OneDimensionalArray| . |FiniteLinearAggregate|) 5616) ((|Arity| . |SetCategory|) T) ((|Arity| . |CoercibleTo|) 5590) ((|Arity| . |Type|) T) ((|Arity| . |Join|) T) ((|Arity| . |BasicType|) T) ((|Arity| . |RetractableTo|) 5556) ((|Arity| . |CoercibleFrom|) 5522) ((|Any| . |SetCategory|) T) ((|Any| . |CoercibleTo|) 5496) ((|Any| . |Type|) T) ((|Any| . |Join|) T) ((|Any| . |BasicType|) T) ((|AntiSymm| . |LeftAlgebra|) 5480) ((|AntiSymm| . |CoercibleFrom|) 5444) ((|AntiSymm| . |LeftModule|) 5418) ((|AntiSymm| . |LeftLinearSet|) 5372) ((|AntiSymm| . |Rng|) T) ((|AntiSymm| . |SemiGroup|) T) ((|AntiSymm| . |SemiRing|) T) ((|AntiSymm| . |Monoid|) T) ((|AntiSymm| . |Ring|) T) ((|AntiSymm| . |AbelianGroup|) T) ((|AntiSymm| . |AbelianMonoid|) T) ((|AntiSymm| . |SetCategory|) T) ((|AntiSymm| . |CoercibleTo|) 5346) ((|AntiSymm| . |Type|) T) ((|AntiSymm| . |Join|) T) ((|AntiSymm| . |BasicType|) T) ((|AntiSymm| . |AbelianSemiGroup|) T) ((|AntiSymm| . |CancellationAbelianMonoid|) T) ((|AntiSymm| . |RetractableTo|) 5330) ((|AntiSymm| . |Functorial|) 5314) ((|AnonymousFunction| . |SetCategory|) T) ((|AnonymousFunction| . |CoercibleTo|) 5288) ((|AnonymousFunction| . |Type|) T) ((|AnonymousFunction| . |Join|) T) ((|AnonymousFunction| . |BasicType|) T) ((|AlgebraicNumber| . |ExpressionSpace|) T) ((|AlgebraicNumber| . |BasicType|) T) ((|AlgebraicNumber| . |Join|) T) ((|AlgebraicNumber| . |Type|) T) ((|AlgebraicNumber| . |CoercibleTo|) 5262) ((|AlgebraicNumber| . |SetCategory|) T) ((|AlgebraicNumber| . |CoercibleFrom|) 5109) ((|AlgebraicNumber| . |RetractableTo|) 5037) ((|AlgebraicNumber| . |InnerEvalable|) 4999) ((|AlgebraicNumber| . |Evalable|) 4986) ((|AlgebraicNumber| . |AlgebraicallyClosedField|) T) ((|AlgebraicNumber| . |RadicalCategory|) T) ((|AlgebraicNumber| . |DivisionRing|) T) ((|AlgebraicNumber| . |BiModule|) 4931) ((|AlgebraicNumber| . |RightLinearSet|) 4885) ((|AlgebraicNumber| . |RightModule|) 4839) ((|AlgebraicNumber| . |EntireRing|) T) ((|AlgebraicNumber| . |Module|) 4793) ((|AlgebraicNumber| . |LinearSet|) 4747) ((|AlgebraicNumber| . |LeftModule|) 4681) ((|AlgebraicNumber| . |LeftLinearSet|) 4615) ((|AlgebraicNumber| . |CancellationAbelianMonoid|) T) ((|AlgebraicNumber| . |AbelianSemiGroup|) T) ((|AlgebraicNumber| . |AbelianMonoid|) T) ((|AlgebraicNumber| . |AbelianGroup|) T) ((|AlgebraicNumber| . |Ring|) T) ((|AlgebraicNumber| . |Monoid|) T) ((|AlgebraicNumber| . |SemiRing|) T) ((|AlgebraicNumber| . |SemiGroup|) T) ((|AlgebraicNumber| . |Rng|) T) ((|AlgebraicNumber| . |Algebra|) 4569) ((|AlgebraicNumber| . |EuclideanDomain|) T) ((|AlgebraicNumber| . |GcdDomain|) T) ((|AlgebraicNumber| . |CommutativeRing|) T) ((|AlgebraicNumber| . |IntegralDomain|) T) ((|AlgebraicNumber| . |PrincipalIdealDomain|) T) ((|AlgebraicNumber| . |UniqueFactorizationDomain|) T) ((|AlgebraicNumber| . |Field|) T) ((|AlgebraicNumber| . |LinearlyExplicitRingOver|) 4518) ((|AlgebraicNumber| . |RealConstant|) T) ((|AlgebraicNumber| . |ConvertibleTo|) 4443) ((|AlgebraicNumber| . |CharacteristicZero|) T) ((|AlgebraicNumber| . |DifferentialRing|) T) ((|AlgebraicNumber| . |DifferentialDomain|) 4430) ((|AlgebraicNumber| . |DifferentialSpace|) T) ((|AssociationList| . |AssociationListAggregate|) 4409) ((|AssociationList| . |KeyedDictionary|) 4388) ((|AssociationList| . |EltableAggregate|) 4300) ((|AssociationList| . |Eltable|) 4169) ((|AssociationList| . |HomogeneousAggregate|) 4098) ((|AssociationList| . |Functorial|) 4027) ((|AssociationList| . |InnerEvalable|) 3775) ((|AssociationList| . |Evalable|) 3535) ((|AssociationList| . |IndexedAggregate|) 3447) ((|AssociationList| . |DictionaryOperations|) 3389) ((|AssociationList| . |BagAggregate|) 3331) ((|AssociationList| . |Dictionary|) 3273) ((|AssociationList| . |TableAggregate|) 3252) ((|AssociationList| . |ShallowlyMutableAggregate|) 3181) ((|AssociationList| . |ExtensibleLinearAggregate|) 3123) ((|AssociationList| . |Collection|) 3065) ((|AssociationList| . |Aggregate|) T) ((|AssociationList| . |Join|) T) ((|AssociationList| . |Type|) T) ((|AssociationList| . |BasicType|) T) ((|AssociationList| . |CoercibleTo|) 3039) ((|AssociationList| . |SetCategory|) T) ((|AssociationList| . |ConvertibleTo|) NIL) ((|AssociationList| . |LinearAggregate|) 2981) ((|AssociationList| . |FiniteLinearAggregate|) 2923) ((|AssociationList| . |OrderedType|) NIL) ((|AssociationList| . |OrderedSet|) NIL) ((|AssociationList| . |FiniteAggregate|) 2865) ((|AssociationList| . |StreamAggregate|) 2807) ((|AssociationList| . |RecursiveAggregate|) 2749) ((|AssociationList| . |UnaryRecursiveAggregate|) 2691) ((|AssociationList| . |ListAggregate|) 2633) ((|AlgebraGivenByStructuralConstants| . |FramedNonAssociativeAlgebra|) 2617) ((|AlgebraGivenByStructuralConstants| . |NonAssociativeAlgebra|) 2601) ((|AlgebraGivenByStructuralConstants| . |Monad|) T) ((|AlgebraGivenByStructuralConstants| . |NonAssociativeRng|) T) ((|AlgebraGivenByStructuralConstants| . |BiModule|) 2580) ((|AlgebraGivenByStructuralConstants| . |RightLinearSet|) 2564) ((|AlgebraGivenByStructuralConstants| . |RightModule|) 2548) ((|AlgebraGivenByStructuralConstants| . |AbelianGroup|) T) ((|AlgebraGivenByStructuralConstants| . |LeftLinearSet|) 2477) ((|AlgebraGivenByStructuralConstants| . |AbelianMonoid|) T) ((|AlgebraGivenByStructuralConstants| . |SetCategory|) T) ((|AlgebraGivenByStructuralConstants| . |CoercibleTo|) 2451) ((|AlgebraGivenByStructuralConstants| . |BasicType|) T) ((|AlgebraGivenByStructuralConstants| . |AbelianSemiGroup|) T) ((|AlgebraGivenByStructuralConstants| . |CancellationAbelianMonoid|) T) ((|AlgebraGivenByStructuralConstants| . |LeftModule|) 2400) ((|AlgebraGivenByStructuralConstants| . |LinearSet|) 2384) ((|AlgebraGivenByStructuralConstants| . |Module|) 2368) ((|AlgebraGivenByStructuralConstants| . |FiniteRankNonAssociativeAlgebra|) 2352) ((|AlgebraGivenByStructuralConstants| . |Type|) T) ((|AlgebraGivenByStructuralConstants| . |Join|) T) ((|AlgebraGivenByStructuralConstants| . |Eltable|) 2324) ((|AlgebraicFunctionField| . |FunctionFieldCategory|) 2298) ((|AlgebraicFunctionField| . |CommutativeRing|) T) ((|AlgebraicFunctionField| . |CoercibleFrom|) 2206) ((|AlgebraicFunctionField| . |Rng|) T) ((|AlgebraicFunctionField| . |SemiGroup|) T) ((|AlgebraicFunctionField| . |SemiRing|) T) ((|AlgebraicFunctionField| . |Monoid|) T) ((|AlgebraicFunctionField| . |Ring|) T) ((|AlgebraicFunctionField| . |LeftModule|) 2064) ((|AlgebraicFunctionField| . |LeftLinearSet|) 1972) ((|AlgebraicFunctionField| . |CancellationAbelianMonoid|) T) ((|AlgebraicFunctionField| . |AbelianSemiGroup|) T) ((|AlgebraicFunctionField| . |BasicType|) T) ((|AlgebraicFunctionField| . |Join|) T) ((|AlgebraicFunctionField| . |Type|) T) ((|AlgebraicFunctionField| . |CoercibleTo|) 1946) ((|AlgebraicFunctionField| . |SetCategory|) T) ((|AlgebraicFunctionField| . |AbelianMonoid|) T) ((|AlgebraicFunctionField| . |AbelianGroup|) T) ((|AlgebraicFunctionField| . |RightModule|) 1874) ((|AlgebraicFunctionField| . |RightLinearSet|) 1802) ((|AlgebraicFunctionField| . |BiModule|) 1714) ((|AlgebraicFunctionField| . |ConvertibleTo|) 1698) ((|AlgebraicFunctionField| . |DifferentialExtension|) 1669) ((|AlgebraicFunctionField| . |PartialDifferentialRing|) 1588) ((|AlgebraicFunctionField| . |PartialDifferentialSpace|) 1436) ((|AlgebraicFunctionField| . |PartialDifferentialDomain|) 1282) ((|AlgebraicFunctionField| . |DifferentialSpaceExtension|) 1253) ((|AlgebraicFunctionField| . |DifferentialSpace|) 1152) ((|AlgebraicFunctionField| . |DifferentialDomain|) 1045) ((|AlgebraicFunctionField| . |DifferentialRing|) 997) ((|AlgebraicFunctionField| . |Field|) T) ((|AlgebraicFunctionField| . |UniqueFactorizationDomain|) T) ((|AlgebraicFunctionField| . |PrincipalIdealDomain|) T) ((|AlgebraicFunctionField| . |IntegralDomain|) T) ((|AlgebraicFunctionField| . |Module|) 925) ((|AlgebraicFunctionField| . |LinearSet|) 853) ((|AlgebraicFunctionField| . |Algebra|) 781) ((|AlgebraicFunctionField| . |GcdDomain|) T) ((|AlgebraicFunctionField| . |EuclideanDomain|) T) ((|AlgebraicFunctionField| . |EntireRing|) T) ((|AlgebraicFunctionField| . |DivisionRing|) T) ((|AlgebraicFunctionField| . |Finite|) NIL) ((|AlgebraicFunctionField| . |FiniteFieldCategory|) NIL) ((|AlgebraicFunctionField| . |StepThrough|) NIL) ((|AlgebraicFunctionField| . |CharacteristicNonZero|) 728) ((|AlgebraicFunctionField| . |FieldOfPrimeCharacteristic|) NIL) ((|AlgebraicFunctionField| . |FramedAlgebra|) 694) ((|AlgebraicFunctionField| . |CharacteristicZero|) 644) ((|AlgebraicFunctionField| . |FiniteRankAlgebra|) 610) ((|AlgebraicFunctionField| . |FullyLinearlyExplicitRingOver|) 581) ((|AlgebraicFunctionField| . |LinearlyExplicitRingOver|) 482) ((|AlgebraicFunctionField| . |FullyRetractableTo|) 453) ((|AlgebraicFunctionField| . |RetractableTo|) 283) ((|AlgebraicFunctionField| . |MonogenicAlgebra|) 249) ((|AddAst| . |SpadSyntaxCategory|) T) ((|AddAst| . |HomotopicTo|) 227) ((|AddAst| . |CoercibleTo|) 182) ((|AddAst| . |CoercibleFrom|) 160) ((|AddAst| . |SetCategory|) T) ((|AddAst| . |Type|) T) ((|AddAst| . |Join|) T) ((|AddAst| . |BasicType|) T) ((|AddAst| . |AbstractSyntaxCategory|) T) ((|PlaneAlgebraicCurvePlot| . |PlottablePlaneCurveCategory|) T) ((|PlaneAlgebraicCurvePlot| . |CoercibleTo|) 134) ((|Enumeration| . |EnumerationCategory|) T) ((|Enumeration| . |CoercibleTo|) 108) ((|Enumeration| . |SetCategory|) T) ((|Enumeration| . |BasicType|) T) ((|Enumeration| . |Type|) T) ((|Record| . |RecordCategory|) T) ((|Record| . |CoercibleTo|) 82) ((|Record| . |SetCategory|) T) ((|Record| . |BasicType|) T) ((|Record| . |Type|) T) ((|Union| . |UnionCategory|) T) ((|Union| . |CoercibleTo|) 56) ((|Union| . |SetCategory|) T) ((|Union| . |BasicType|) T) ((|Union| . |Type|) T) ((|Mapping| . |SetCategory|) T) ((|Mapping| . |CoercibleTo|) 30) ((|Mapping| . |Type|) T) ((|Mapping| . |Join|) T) ((|Mapping| . |BasicType|) T))
\ No newline at end of file +(((|IntegerMod| . |CommutativeRing|) T) ((|IntegerMod| . |CoercibleFrom|) 283961) ((|IntegerMod| . |Rng|) T) ((|IntegerMod| . |SemiGroup|) T) ((|IntegerMod| . |SemiRing|) T) ((|IntegerMod| . |Monoid|) T) ((|IntegerMod| . |Ring|) T) ((|IntegerMod| . |LeftModule|) 283948) ((|IntegerMod| . |LeftLinearSet|) 283915) ((|IntegerMod| . |CancellationAbelianMonoid|) T) ((|IntegerMod| . |AbelianSemiGroup|) T) ((|IntegerMod| . |BasicType|) T) ((|IntegerMod| . |Join|) T) ((|IntegerMod| . |Type|) T) ((|IntegerMod| . |CoercibleTo|) 283889) ((|IntegerMod| . |SetCategory|) T) ((|IntegerMod| . |AbelianMonoid|) T) ((|IntegerMod| . |AbelianGroup|) T) ((|IntegerMod| . |RightModule|) 283876) ((|IntegerMod| . |RightLinearSet|) 283863) ((|IntegerMod| . |BiModule|) 283848) ((|IntegerMod| . |Finite|) T) ((|IntegerMod| . |ConvertibleTo|) 283825) ((|IntegerMod| . |StepThrough|) T) ((|YoungDiagram| . |SetCategory|) T) ((|YoungDiagram| . |CoercibleTo|) 283777) ((|YoungDiagram| . |Type|) T) ((|YoungDiagram| . |Join|) T) ((|YoungDiagram| . |BasicType|) T) ((|YoungDiagram| . |HomotopicTo|) 283752) ((|YoungDiagram| . |CoercibleFrom|) 283727) ((|XRecursivePolynomial| . |XPolynomialsCat|) 283706) ((|XRecursivePolynomial| . |Functorial|) 283690) ((|XRecursivePolynomial| . |Join|) T) ((|XRecursivePolynomial| . |Type|) T) ((|XRecursivePolynomial| . |RetractableTo|) 283652) ((|XRecursivePolynomial| . |CoercibleFrom|) 283581) ((|XRecursivePolynomial| . |Ring|) T) ((|XRecursivePolynomial| . |Monoid|) T) ((|XRecursivePolynomial| . |SemiRing|) T) ((|XRecursivePolynomial| . |SemiGroup|) T) ((|XRecursivePolynomial| . |Rng|) T) ((|XRecursivePolynomial| . |AbelianGroup|) T) ((|XRecursivePolynomial| . |LeftLinearSet|) 283535) ((|XRecursivePolynomial| . |AbelianMonoid|) T) ((|XRecursivePolynomial| . |SetCategory|) T) ((|XRecursivePolynomial| . |CoercibleTo|) 283509) ((|XRecursivePolynomial| . |BasicType|) T) ((|XRecursivePolynomial| . |AbelianSemiGroup|) T) ((|XRecursivePolynomial| . |CancellationAbelianMonoid|) T) ((|XRecursivePolynomial| . |LeftModule|) 283483) ((|XRecursivePolynomial| . |XAlgebra|) 283467) ((|XRecursivePolynomial| . |Module|) 283424) ((|XRecursivePolynomial| . |LinearSet|) 283381) ((|XRecursivePolynomial| . |RightModule|) 283365) ((|XRecursivePolynomial| . |RightLinearSet|) 283349) ((|XRecursivePolynomial| . |BiModule|) 283328) ((|XRecursivePolynomial| . |Algebra|) 283285) ((|XRecursivePolynomial| . |XFreeAlgebra|) 283264) ((|XPolynomialRing| . |Ring|) T) ((|XPolynomialRing| . |Monoid|) T) ((|XPolynomialRing| . |SemiRing|) T) ((|XPolynomialRing| . |SemiGroup|) T) ((|XPolynomialRing| . |Rng|) T) ((|XPolynomialRing| . |AbelianGroup|) T) ((|XPolynomialRing| . |LeftLinearSet|) 283218) ((|XPolynomialRing| . |AbelianMonoid|) T) ((|XPolynomialRing| . |SetCategory|) T) ((|XPolynomialRing| . |CoercibleTo|) 283192) ((|XPolynomialRing| . |Type|) T) ((|XPolynomialRing| . |Join|) T) ((|XPolynomialRing| . |BasicType|) T) ((|XPolynomialRing| . |AbelianSemiGroup|) T) ((|XPolynomialRing| . |CancellationAbelianMonoid|) T) ((|XPolynomialRing| . |LeftModule|) 283166) ((|XPolynomialRing| . |CoercibleFrom|) 283117) ((|XPolynomialRing| . |XAlgebra|) 283101) ((|XPolynomialRing| . |Module|) 283058) ((|XPolynomialRing| . |LinearSet|) 283015) ((|XPolynomialRing| . |RightModule|) 282999) ((|XPolynomialRing| . |RightLinearSet|) 282983) ((|XPolynomialRing| . |BiModule|) 282962) ((|XPolynomialRing| . |Algebra|) 282919) ((|XPolynomialRing| . |FreeModuleCat|) 282898) ((|XPolynomialRing| . |RetractableTo|) 282882) ((|XPolynomialRing| . |Functorial|) 282866) ((|XPolynomial| . |XPolynomialsCat|) 282839) ((|XPolynomial| . |Functorial|) 282823) ((|XPolynomial| . |Join|) T) ((|XPolynomial| . |Type|) T) ((|XPolynomial| . |RetractableTo|) 282779) ((|XPolynomial| . |CoercibleFrom|) 282702) ((|XPolynomial| . |Ring|) T) ((|XPolynomial| . |Monoid|) T) ((|XPolynomial| . |SemiRing|) T) ((|XPolynomial| . |SemiGroup|) T) ((|XPolynomial| . |Rng|) T) ((|XPolynomial| . |AbelianGroup|) T) ((|XPolynomial| . |LeftLinearSet|) 282656) ((|XPolynomial| . |AbelianMonoid|) T) ((|XPolynomial| . |SetCategory|) T) ((|XPolynomial| . |CoercibleTo|) 282630) ((|XPolynomial| . |BasicType|) T) ((|XPolynomial| . |AbelianSemiGroup|) T) ((|XPolynomial| . |CancellationAbelianMonoid|) T) ((|XPolynomial| . |LeftModule|) 282604) ((|XPolynomial| . |XAlgebra|) 282588) ((|XPolynomial| . |Module|) 282545) ((|XPolynomial| . |LinearSet|) 282502) ((|XPolynomial| . |RightModule|) 282486) ((|XPolynomial| . |RightLinearSet|) 282470) ((|XPolynomial| . |BiModule|) 282449) ((|XPolynomial| . |Algebra|) 282406) ((|XPolynomial| . |XFreeAlgebra|) 282379) ((|XPBWPolynomial| . |XPolynomialsCat|) 282358) ((|XPBWPolynomial| . |Functorial|) 282342) ((|XPBWPolynomial| . |Join|) T) ((|XPBWPolynomial| . |Type|) T) ((|XPBWPolynomial| . |RetractableTo|) 282255) ((|XPBWPolynomial| . |CoercibleFrom|) 282135) ((|XPBWPolynomial| . |Ring|) T) ((|XPBWPolynomial| . |Monoid|) T) ((|XPBWPolynomial| . |SemiRing|) T) ((|XPBWPolynomial| . |SemiGroup|) T) ((|XPBWPolynomial| . |Rng|) T) ((|XPBWPolynomial| . |AbelianGroup|) T) ((|XPBWPolynomial| . |LeftLinearSet|) 282089) ((|XPBWPolynomial| . |AbelianMonoid|) T) ((|XPBWPolynomial| . |SetCategory|) T) ((|XPBWPolynomial| . |CoercibleTo|) 281975) ((|XPBWPolynomial| . |BasicType|) T) ((|XPBWPolynomial| . |AbelianSemiGroup|) T) ((|XPBWPolynomial| . |CancellationAbelianMonoid|) T) ((|XPBWPolynomial| . |LeftModule|) 281949) ((|XPBWPolynomial| . |XAlgebra|) 281933) ((|XPBWPolynomial| . |Module|) 281890) ((|XPBWPolynomial| . |LinearSet|) 281847) ((|XPBWPolynomial| . |RightModule|) 281831) ((|XPBWPolynomial| . |RightLinearSet|) 281815) ((|XPBWPolynomial| . |BiModule|) 281794) ((|XPBWPolynomial| . |Algebra|) 281751) ((|XPBWPolynomial| . |XFreeAlgebra|) 281730) ((|XPBWPolynomial| . |FreeModuleCat|) 281673) ((|XDistributedPolynomial| . |FreeModuleCat|) 281630) ((|XDistributedPolynomial| . |CoercibleFrom|) 281559) ((|XDistributedPolynomial| . |RetractableTo|) 281521) ((|XDistributedPolynomial| . |LinearSet|) 281478) ((|XDistributedPolynomial| . |Module|) 281435) ((|XDistributedPolynomial| . |Functorial|) 281419) ((|XDistributedPolynomial| . |LeftModule|) 281393) ((|XDistributedPolynomial| . |LeftLinearSet|) 281347) ((|XDistributedPolynomial| . |CancellationAbelianMonoid|) T) ((|XDistributedPolynomial| . |AbelianSemiGroup|) T) ((|XDistributedPolynomial| . |BasicType|) T) ((|XDistributedPolynomial| . |Join|) T) ((|XDistributedPolynomial| . |Type|) T) ((|XDistributedPolynomial| . |CoercibleTo|) 281321) ((|XDistributedPolynomial| . |SetCategory|) T) ((|XDistributedPolynomial| . |AbelianMonoid|) T) ((|XDistributedPolynomial| . |AbelianGroup|) T) ((|XDistributedPolynomial| . |RightModule|) 281305) ((|XDistributedPolynomial| . |RightLinearSet|) 281289) ((|XDistributedPolynomial| . |BiModule|) 281268) ((|XDistributedPolynomial| . |XPolynomialsCat|) 281247) ((|XDistributedPolynomial| . |Ring|) T) ((|XDistributedPolynomial| . |Monoid|) T) ((|XDistributedPolynomial| . |SemiRing|) T) ((|XDistributedPolynomial| . |SemiGroup|) T) ((|XDistributedPolynomial| . |Rng|) T) ((|XDistributedPolynomial| . |XAlgebra|) 281231) ((|XDistributedPolynomial| . |Algebra|) 281188) ((|XDistributedPolynomial| . |XFreeAlgebra|) 281167) ((|WuWenTsunTriangularSet| . |TriangularSetCategory|) 281136) ((|WuWenTsunTriangularSet| . |ShallowlyMutableAggregate|) 281120) ((|WuWenTsunTriangularSet| . |CoercibleTo|) 281072) ((|WuWenTsunTriangularSet| . |Collection|) 281056) ((|WuWenTsunTriangularSet| . |Aggregate|) T) ((|WuWenTsunTriangularSet| . |Join|) T) ((|WuWenTsunTriangularSet| . |Type|) T) ((|WuWenTsunTriangularSet| . |BasicType|) T) ((|WuWenTsunTriangularSet| . |Evalable|) 280980) ((|WuWenTsunTriangularSet| . |InnerEvalable|) 280899) ((|WuWenTsunTriangularSet| . |Functorial|) 280883) ((|WuWenTsunTriangularSet| . |SetCategory|) T) ((|WuWenTsunTriangularSet| . |HomogeneousAggregate|) 280867) ((|WuWenTsunTriangularSet| . |ConvertibleTo|) 280803) ((|WuWenTsunTriangularSet| . |FiniteAggregate|) 280787) ((|WuWenTsunTriangularSet| . |PolynomialSetCategory|) 280756) ((|WeightedPolynomials| . |Ring|) T) ((|WeightedPolynomials| . |Monoid|) T) ((|WeightedPolynomials| . |SemiRing|) T) ((|WeightedPolynomials| . |SemiGroup|) T) ((|WeightedPolynomials| . |Rng|) T) ((|WeightedPolynomials| . |AbelianGroup|) T) ((|WeightedPolynomials| . |LeftLinearSet|) 280683) ((|WeightedPolynomials| . |AbelianMonoid|) T) ((|WeightedPolynomials| . |SetCategory|) T) ((|WeightedPolynomials| . |CoercibleTo|) 280644) ((|WeightedPolynomials| . |Type|) T) ((|WeightedPolynomials| . |Join|) T) ((|WeightedPolynomials| . |BasicType|) T) ((|WeightedPolynomials| . |AbelianSemiGroup|) T) ((|WeightedPolynomials| . |CancellationAbelianMonoid|) T) ((|WeightedPolynomials| . |LeftModule|) 280591) ((|WeightedPolynomials| . |CoercibleFrom|) 280515) ((|WeightedPolynomials| . |HomotopicTo|) 280499) ((|WeightedPolynomials| . |Algebra|) 280456) ((|WeightedPolynomials| . |BiModule|) 280408) ((|WeightedPolynomials| . |RightLinearSet|) 280365) ((|WeightedPolynomials| . |RightModule|) 280322) ((|WeightedPolynomials| . |LinearSet|) 280279) ((|WeightedPolynomials| . |Module|) 280236) ((|WhileAst| . |SpadSyntaxCategory|) T) ((|WhileAst| . |HomotopicTo|) 280214) ((|WhileAst| . |CoercibleTo|) 280169) ((|WhileAst| . |CoercibleFrom|) 280147) ((|WhileAst| . |SetCategory|) T) ((|WhileAst| . |Type|) T) ((|WhileAst| . |Join|) T) ((|WhileAst| . |BasicType|) T) ((|WhileAst| . |AbstractSyntaxCategory|) T) ((|WhereAst| . |SpadSyntaxCategory|) T) ((|WhereAst| . |HomotopicTo|) 280125) ((|WhereAst| . |CoercibleTo|) 280080) ((|WhereAst| . |CoercibleFrom|) 280058) ((|WhereAst| . |SetCategory|) T) ((|WhereAst| . |Type|) T) ((|WhereAst| . |Join|) T) ((|WhereAst| . |BasicType|) T) ((|WhereAst| . |AbstractSyntaxCategory|) T) ((|Void| . |CoercibleTo|) 280032) ((|ThreeDimensionalViewport| . |SetCategory|) T) ((|ThreeDimensionalViewport| . |CoercibleTo|) 280006) ((|ThreeDimensionalViewport| . |Type|) T) ((|ThreeDimensionalViewport| . |Join|) T) ((|ThreeDimensionalViewport| . |BasicType|) T) ((|TwoDimensionalViewport| . |SetCategory|) T) ((|TwoDimensionalViewport| . |CoercibleTo|) 279980) ((|TwoDimensionalViewport| . |Type|) T) ((|TwoDimensionalViewport| . |Join|) T) ((|TwoDimensionalViewport| . |BasicType|) T) ((|Vector| . |VectorCategory|) 279964) ((|Vector| . |FiniteLinearAggregate|) 279948) ((|Vector| . |OrderedType|) 279919) ((|Vector| . |OrderedSet|) 279890) ((|Vector| . |Collection|) 279874) ((|Vector| . |ConvertibleTo|) 279810) ((|Vector| . |Eltable|) 279739) ((|Vector| . |IndexedAggregate|) 279711) ((|Vector| . |EltableAggregate|) 279683) ((|Vector| . |LinearAggregate|) 279667) ((|Vector| . |HomogeneousAggregate|) 279651) ((|Vector| . |SetCategory|) 279588) ((|Vector| . |Functorial|) 279572) ((|Vector| . |InnerEvalable|) 279491) ((|Vector| . |Evalable|) 279415) ((|Vector| . |CoercibleTo|) 279289) ((|Vector| . |BasicType|) 279199) ((|Vector| . |Type|) T) ((|Vector| . |Join|) T) ((|Vector| . |Aggregate|) T) ((|Vector| . |FiniteAggregate|) 279183) ((|Vector| . |ShallowlyMutableAggregate|) 279167) ((|Vector| . |OneDimensionalArrayAggregate|) 279151) ((|Variable| . |SetCategory|) T) ((|Variable| . |CoercibleTo|) 279106) ((|Variable| . |Type|) T) ((|Variable| . |Join|) T) ((|Variable| . |BasicType|) T) ((|UnivariateTaylorSeries| . |UnivariateTaylorSeriesCategory|) 279090) ((|UnivariateTaylorSeries| . |DifferentialRing|) 279027) ((|UnivariateTaylorSeries| . |CoercibleFrom|) 278851) ((|UnivariateTaylorSeries| . |LeftModule|) 278748) ((|UnivariateTaylorSeries| . |LeftLinearSet|) 278625) ((|UnivariateTaylorSeries| . |CancellationAbelianMonoid|) T) ((|UnivariateTaylorSeries| . |AbelianSemiGroup|) T) ((|UnivariateTaylorSeries| . |BasicType|) T) ((|UnivariateTaylorSeries| . |CoercibleTo|) 278599) ((|UnivariateTaylorSeries| . |SetCategory|) T) ((|UnivariateTaylorSeries| . |AbelianMonoid|) T) ((|UnivariateTaylorSeries| . |AbelianGroup|) T) ((|UnivariateTaylorSeries| . |Rng|) T) ((|UnivariateTaylorSeries| . |SemiGroup|) T) ((|UnivariateTaylorSeries| . |SemiRing|) T) ((|UnivariateTaylorSeries| . |Monoid|) T) ((|UnivariateTaylorSeries| . |Ring|) T) ((|UnivariateTaylorSeries| . |DifferentialDomain|) 278530) ((|UnivariateTaylorSeries| . |Join|) T) ((|UnivariateTaylorSeries| . |Type|) T) ((|UnivariateTaylorSeries| . |DifferentialSpace|) 278467) ((|UnivariateTaylorSeries| . |Eltable|) 278416) ((|UnivariateTaylorSeries| . |PartialDifferentialRing|) 278280) ((|UnivariateTaylorSeries| . |PartialDifferentialDomain|) 278114) ((|UnivariateTaylorSeries| . |PartialDifferentialSpace|) 277978) ((|UnivariateTaylorSeries| . |PowerSeriesCategory|) 277913) ((|UnivariateTaylorSeries| . |Algebra|) 277757) ((|UnivariateTaylorSeries| . |BiModule|) 277576) ((|UnivariateTaylorSeries| . |RightLinearSet|) 277409) ((|UnivariateTaylorSeries| . |RightModule|) 277242) ((|UnivariateTaylorSeries| . |LinearSet|) 277086) ((|UnivariateTaylorSeries| . |Module|) 276930) ((|UnivariateTaylorSeries| . |CharacteristicNonZero|) 276890) ((|UnivariateTaylorSeries| . |CharacteristicZero|) 276853) ((|UnivariateTaylorSeries| . |CommutativeRing|) 276782) ((|UnivariateTaylorSeries| . |Functorial|) 276766) ((|UnivariateTaylorSeries| . |IntegralDomain|) 276733) ((|UnivariateTaylorSeries| . |EntireRing|) 276700) ((|UnivariateTaylorSeries| . |AbelianMonoidRing|) 276661) ((|UnivariateTaylorSeries| . |UnivariatePowerSeriesCategory|) 276622) ((|UnivariateTaylorSeries| . |ArcHyperbolicFunctionCategory|) 276571) ((|UnivariateTaylorSeries| . |ArcTrigonometricFunctionCategory|) 276520) ((|UnivariateTaylorSeries| . |ElementaryFunctionCategory|) 276469) ((|UnivariateTaylorSeries| . |HyperbolicFunctionCategory|) 276418) ((|UnivariateTaylorSeries| . |TrigonometricFunctionCategory|) 276367) ((|UnivariateTaylorSeries| . |TranscendentalFunctionCategory|) 276316) ((|UnivariateTaylorSeries| . |RadicalCategory|) 276265) ((|UnivariatePuiseuxSeriesWithExponentialSingularity| . |FiniteAbelianMonoidRing|) 276155) ((|UnivariatePuiseuxSeriesWithExponentialSingularity| . |RetractableTo|) 276101) ((|UnivariatePuiseuxSeriesWithExponentialSingularity| . |FullyRetractableTo|) 276047) ((|UnivariatePuiseuxSeriesWithExponentialSingularity| . |Algebra|) 275878) ((|UnivariatePuiseuxSeriesWithExponentialSingularity| . |CoercibleFrom|) 275679) ((|UnivariatePuiseuxSeriesWithExponentialSingularity| . |LeftModule|) 275536) ((|UnivariatePuiseuxSeriesWithExponentialSingularity| . |LeftLinearSet|) 275373) ((|UnivariatePuiseuxSeriesWithExponentialSingularity| . |Rng|) T) ((|UnivariatePuiseuxSeriesWithExponentialSingularity| . |SemiGroup|) T) ((|UnivariatePuiseuxSeriesWithExponentialSingularity| . |SemiRing|) T) ((|UnivariatePuiseuxSeriesWithExponentialSingularity| . |Monoid|) T) ((|UnivariatePuiseuxSeriesWithExponentialSingularity| . |Ring|) T) ((|UnivariatePuiseuxSeriesWithExponentialSingularity| . |BiModule|) 275217) ((|UnivariatePuiseuxSeriesWithExponentialSingularity| . |RightLinearSet|) 275074) ((|UnivariatePuiseuxSeriesWithExponentialSingularity| . |RightModule|) 274931) ((|UnivariatePuiseuxSeriesWithExponentialSingularity| . |AbelianGroup|) T) ((|UnivariatePuiseuxSeriesWithExponentialSingularity| . |AbelianMonoid|) T) ((|UnivariatePuiseuxSeriesWithExponentialSingularity| . |SetCategory|) T) ((|UnivariatePuiseuxSeriesWithExponentialSingularity| . |CoercibleTo|) 274905) ((|UnivariatePuiseuxSeriesWithExponentialSingularity| . |Type|) T) ((|UnivariatePuiseuxSeriesWithExponentialSingularity| . |Join|) T) ((|UnivariatePuiseuxSeriesWithExponentialSingularity| . |BasicType|) T) ((|UnivariatePuiseuxSeriesWithExponentialSingularity| . |AbelianSemiGroup|) T) ((|UnivariatePuiseuxSeriesWithExponentialSingularity| . |CancellationAbelianMonoid|) T) ((|UnivariatePuiseuxSeriesWithExponentialSingularity| . |LinearSet|) 274736) ((|UnivariatePuiseuxSeriesWithExponentialSingularity| . |Module|) 274567) ((|UnivariatePuiseuxSeriesWithExponentialSingularity| . |CharacteristicNonZero|) 274489) ((|UnivariatePuiseuxSeriesWithExponentialSingularity| . |CharacteristicZero|) 274414) ((|UnivariatePuiseuxSeriesWithExponentialSingularity| . |CommutativeRing|) T) ((|UnivariatePuiseuxSeriesWithExponentialSingularity| . |Functorial|) 274360) ((|UnivariatePuiseuxSeriesWithExponentialSingularity| . |IntegralDomain|) T) ((|UnivariatePuiseuxSeriesWithExponentialSingularity| . |EntireRing|) T) ((|UnivariatePuiseuxSeriesWithExponentialSingularity| . |AbelianMonoidRing|) 274250) ((|UnivariatePuiseuxSeriesConstructor| . |UnivariatePuiseuxSeriesConstructorCategory|) 274229) ((|UnivariatePuiseuxSeriesConstructor| . |Field|) 274205) ((|UnivariatePuiseuxSeriesConstructor| . |UniqueFactorizationDomain|) 274181) ((|UnivariatePuiseuxSeriesConstructor| . |PrincipalIdealDomain|) 274157) ((|UnivariatePuiseuxSeriesConstructor| . |IntegralDomain|) 274096) ((|UnivariatePuiseuxSeriesConstructor| . |CommutativeRing|) 274002) ((|UnivariatePuiseuxSeriesConstructor| . |CoercibleFrom|) 273757) ((|UnivariatePuiseuxSeriesConstructor| . |Module|) 273545) ((|UnivariatePuiseuxSeriesConstructor| . |LinearSet|) 273333) ((|UnivariatePuiseuxSeriesConstructor| . |Algebra|) 273121) ((|UnivariatePuiseuxSeriesConstructor| . |GcdDomain|) 273097) ((|UnivariatePuiseuxSeriesConstructor| . |EuclideanDomain|) 273073) ((|UnivariatePuiseuxSeriesConstructor| . |LeftModule|) 272942) ((|UnivariatePuiseuxSeriesConstructor| . |LeftLinearSet|) 272791) ((|UnivariatePuiseuxSeriesConstructor| . |Rng|) T) ((|UnivariatePuiseuxSeriesConstructor| . |SemiGroup|) T) ((|UnivariatePuiseuxSeriesConstructor| . |SemiRing|) T) ((|UnivariatePuiseuxSeriesConstructor| . |Monoid|) T) ((|UnivariatePuiseuxSeriesConstructor| . |Ring|) T) ((|UnivariatePuiseuxSeriesConstructor| . |BiModule|) 272559) ((|UnivariatePuiseuxSeriesConstructor| . |RightLinearSet|) 272341) ((|UnivariatePuiseuxSeriesConstructor| . |RightModule|) 272123) ((|UnivariatePuiseuxSeriesConstructor| . |AbelianGroup|) T) ((|UnivariatePuiseuxSeriesConstructor| . |AbelianMonoid|) T) ((|UnivariatePuiseuxSeriesConstructor| . |SetCategory|) T) ((|UnivariatePuiseuxSeriesConstructor| . |CoercibleTo|) 272097) ((|UnivariatePuiseuxSeriesConstructor| . |Type|) T) ((|UnivariatePuiseuxSeriesConstructor| . |Join|) T) ((|UnivariatePuiseuxSeriesConstructor| . |BasicType|) T) ((|UnivariatePuiseuxSeriesConstructor| . |AbelianSemiGroup|) T) ((|UnivariatePuiseuxSeriesConstructor| . |CancellationAbelianMonoid|) T) ((|UnivariatePuiseuxSeriesConstructor| . |EntireRing|) 272036) ((|UnivariatePuiseuxSeriesConstructor| . |DivisionRing|) 272012) ((|UnivariatePuiseuxSeriesConstructor| . |RadicalCategory|) 271961) ((|UnivariatePuiseuxSeriesConstructor| . |TranscendentalFunctionCategory|) 271910) ((|UnivariatePuiseuxSeriesConstructor| . |TrigonometricFunctionCategory|) 271859) ((|UnivariatePuiseuxSeriesConstructor| . |HyperbolicFunctionCategory|) 271808) ((|UnivariatePuiseuxSeriesConstructor| . |ElementaryFunctionCategory|) 271757) ((|UnivariatePuiseuxSeriesConstructor| . |ArcTrigonometricFunctionCategory|) 271706) ((|UnivariatePuiseuxSeriesConstructor| . |ArcHyperbolicFunctionCategory|) 271655) ((|UnivariatePuiseuxSeriesConstructor| . |UnivariatePowerSeriesCategory|) 271614) ((|UnivariatePuiseuxSeriesConstructor| . |AbelianMonoidRing|) 271573) ((|UnivariatePuiseuxSeriesConstructor| . |Functorial|) 271557) ((|UnivariatePuiseuxSeriesConstructor| . |CharacteristicZero|) 271520) ((|UnivariatePuiseuxSeriesConstructor| . |CharacteristicNonZero|) 271480) ((|UnivariatePuiseuxSeriesConstructor| . |PowerSeriesCategory|) 271413) ((|UnivariatePuiseuxSeriesConstructor| . |PartialDifferentialSpace|) 271275) ((|UnivariatePuiseuxSeriesConstructor| . |PartialDifferentialDomain|) 271135) ((|UnivariatePuiseuxSeriesConstructor| . |PartialDifferentialRing|) 270997) ((|UnivariatePuiseuxSeriesConstructor| . |Eltable|) 270944) ((|UnivariatePuiseuxSeriesConstructor| . |DifferentialSpace|) 270879) ((|UnivariatePuiseuxSeriesConstructor| . |DifferentialDomain|) 270808) ((|UnivariatePuiseuxSeriesConstructor| . |DifferentialRing|) 270743) ((|UnivariatePuiseuxSeriesConstructor| . |UnivariatePuiseuxSeriesCategory|) 270727) ((|UnivariatePuiseuxSeriesConstructor| . |RetractableTo|) 270711) ((|UnivariatePuiseuxSeries| . |UnivariatePuiseuxSeriesConstructorCategory|) 270652) ((|UnivariatePuiseuxSeries| . |Field|) 270628) ((|UnivariatePuiseuxSeries| . |UniqueFactorizationDomain|) 270604) ((|UnivariatePuiseuxSeries| . |PrincipalIdealDomain|) 270580) ((|UnivariatePuiseuxSeries| . |IntegralDomain|) 270519) ((|UnivariatePuiseuxSeries| . |CommutativeRing|) 270425) ((|UnivariatePuiseuxSeries| . |CoercibleFrom|) 270066) ((|UnivariatePuiseuxSeries| . |Module|) 269854) ((|UnivariatePuiseuxSeries| . |LinearSet|) 269642) ((|UnivariatePuiseuxSeries| . |Algebra|) 269430) ((|UnivariatePuiseuxSeries| . |GcdDomain|) 269406) ((|UnivariatePuiseuxSeries| . |EuclideanDomain|) 269382) ((|UnivariatePuiseuxSeries| . |LeftModule|) 269251) ((|UnivariatePuiseuxSeries| . |LeftLinearSet|) 269100) ((|UnivariatePuiseuxSeries| . |Rng|) T) ((|UnivariatePuiseuxSeries| . |SemiGroup|) T) ((|UnivariatePuiseuxSeries| . |SemiRing|) T) ((|UnivariatePuiseuxSeries| . |Monoid|) T) ((|UnivariatePuiseuxSeries| . |Ring|) T) ((|UnivariatePuiseuxSeries| . |BiModule|) 268868) ((|UnivariatePuiseuxSeries| . |RightLinearSet|) 268650) ((|UnivariatePuiseuxSeries| . |RightModule|) 268432) ((|UnivariatePuiseuxSeries| . |AbelianGroup|) T) ((|UnivariatePuiseuxSeries| . |AbelianMonoid|) T) ((|UnivariatePuiseuxSeries| . |SetCategory|) T) ((|UnivariatePuiseuxSeries| . |CoercibleTo|) 268406) ((|UnivariatePuiseuxSeries| . |Type|) T) ((|UnivariatePuiseuxSeries| . |Join|) T) ((|UnivariatePuiseuxSeries| . |BasicType|) T) ((|UnivariatePuiseuxSeries| . |AbelianSemiGroup|) T) ((|UnivariatePuiseuxSeries| . |CancellationAbelianMonoid|) T) ((|UnivariatePuiseuxSeries| . |EntireRing|) 268345) ((|UnivariatePuiseuxSeries| . |DivisionRing|) 268321) ((|UnivariatePuiseuxSeries| . |RadicalCategory|) 268270) ((|UnivariatePuiseuxSeries| . |TranscendentalFunctionCategory|) 268219) ((|UnivariatePuiseuxSeries| . |TrigonometricFunctionCategory|) 268168) ((|UnivariatePuiseuxSeries| . |HyperbolicFunctionCategory|) 268117) ((|UnivariatePuiseuxSeries| . |ElementaryFunctionCategory|) 268066) ((|UnivariatePuiseuxSeries| . |ArcTrigonometricFunctionCategory|) 268015) ((|UnivariatePuiseuxSeries| . |ArcHyperbolicFunctionCategory|) 267964) ((|UnivariatePuiseuxSeries| . |UnivariatePowerSeriesCategory|) 267923) ((|UnivariatePuiseuxSeries| . |AbelianMonoidRing|) 267882) ((|UnivariatePuiseuxSeries| . |Functorial|) 267866) ((|UnivariatePuiseuxSeries| . |CharacteristicZero|) 267829) ((|UnivariatePuiseuxSeries| . |CharacteristicNonZero|) 267789) ((|UnivariatePuiseuxSeries| . |PowerSeriesCategory|) 267722) ((|UnivariatePuiseuxSeries| . |PartialDifferentialSpace|) 267584) ((|UnivariatePuiseuxSeries| . |PartialDifferentialDomain|) 267416) ((|UnivariatePuiseuxSeries| . |PartialDifferentialRing|) 267278) ((|UnivariatePuiseuxSeries| . |Eltable|) 267225) ((|UnivariatePuiseuxSeries| . |DifferentialSpace|) 267160) ((|UnivariatePuiseuxSeries| . |DifferentialDomain|) 267089) ((|UnivariatePuiseuxSeries| . |DifferentialRing|) 267024) ((|UnivariatePuiseuxSeries| . |UnivariatePuiseuxSeriesCategory|) 267008) ((|UnivariatePuiseuxSeries| . |RetractableTo|) 266904) ((|UnivariatePolynomial| . |UnivariatePolynomialCategory|) 266888) ((|UnivariatePolynomial| . |StepThrough|) 266858) ((|UnivariatePolynomial| . |ConvertibleTo|) NIL) ((|UnivariatePolynomial| . |Evalable|) 266845) ((|UnivariatePolynomial| . |InnerEvalable|) 266774) ((|UnivariatePolynomial| . |FiniteAbelianMonoidRing|) 266735) ((|UnivariatePolynomial| . |RetractableTo|) 266545) ((|UnivariatePolynomial| . |FullyRetractableTo|) 266529) ((|UnivariatePolynomial| . |Algebra|) 266269) ((|UnivariatePolynomial| . |BiModule|) 265989) ((|UnivariatePolynomial| . |RightLinearSet|) 265723) ((|UnivariatePolynomial| . |RightModule|) 265457) ((|UnivariatePolynomial| . |LeftLinearSet|) 265334) ((|UnivariatePolynomial| . |LeftModule|) 265163) ((|UnivariatePolynomial| . |LinearSet|) 264903) ((|UnivariatePolynomial| . |Module|) 264643) ((|UnivariatePolynomial| . |CoercibleFrom|) 264269) ((|UnivariatePolynomial| . |CharacteristicNonZero|) 264229) ((|UnivariatePolynomial| . |CharacteristicZero|) 264192) ((|UnivariatePolynomial| . |Functorial|) 264176) ((|UnivariatePolynomial| . |AbelianMonoidRing|) 264137) ((|UnivariatePolynomial| . |FullyLinearlyExplicitRingOver|) 264121) ((|UnivariatePolynomial| . |LinearlyExplicitRingOver|) 264037) ((|UnivariatePolynomial| . |PartialDifferentialRing|) 263935) ((|UnivariatePolynomial| . |PartialDifferentialDomain|) 263771) ((|UnivariatePolynomial| . |PartialDifferentialSpace|) 263611) ((|UnivariatePolynomial| . |PatternMatchable|) NIL) ((|UnivariatePolynomial| . |PolynomialFactorizationExplicit|) 263561) ((|UnivariatePolynomial| . |UniqueFactorizationDomain|) 263511) ((|UnivariatePolynomial| . |PolynomialCategory|) 263446) ((|UnivariatePolynomial| . |PrincipalIdealDomain|) 263422) ((|UnivariatePolynomial| . |IntegralDomain|) 263285) ((|UnivariatePolynomial| . |EntireRing|) 263148) ((|UnivariatePolynomial| . |CommutativeRing|) 262978) ((|UnivariatePolynomial| . |GcdDomain|) 262873) ((|UnivariatePolynomial| . |EuclideanDomain|) 262849) ((|UnivariatePolynomial| . |Eltable|) 262752) ((|UnivariatePolynomial| . |DifferentialRing|) T) ((|UnivariatePolynomial| . |CancellationAbelianMonoid|) T) ((|UnivariatePolynomial| . |AbelianSemiGroup|) T) ((|UnivariatePolynomial| . |BasicType|) T) ((|UnivariatePolynomial| . |CoercibleTo|) 262726) ((|UnivariatePolynomial| . |SetCategory|) T) ((|UnivariatePolynomial| . |AbelianMonoid|) T) ((|UnivariatePolynomial| . |AbelianGroup|) T) ((|UnivariatePolynomial| . |Rng|) T) ((|UnivariatePolynomial| . |SemiGroup|) T) ((|UnivariatePolynomial| . |SemiRing|) T) ((|UnivariatePolynomial| . |Monoid|) T) ((|UnivariatePolynomial| . |Ring|) T) ((|UnivariatePolynomial| . |DifferentialDomain|) 262713) ((|UnivariatePolynomial| . |Join|) T) ((|UnivariatePolynomial| . |Type|) T) ((|UnivariatePolynomial| . |DifferentialSpace|) T) ((|UnivariatePolynomial| . |DifferentialSpaceExtension|) 262697) ((|UnivariatePolynomial| . |DifferentialExtension|) 262681) ((|UniversalSegment| . |SegmentCategory|) 262665) ((|UniversalSegment| . |ConvertibleFrom|) 262649) ((|UniversalSegment| . |SetCategory|) 262619) ((|UniversalSegment| . |CoercibleTo|) 262570) ((|UniversalSegment| . |Type|) 262540) ((|UniversalSegment| . |Join|) 262510) ((|UniversalSegment| . |BasicType|) 262480) ((|UniversalSegment| . |SegmentExpansionCategory|) 262425) ((|UnivariateLaurentSeriesConstructor| . |UnivariateLaurentSeriesConstructorCategory|) 262404) ((|UnivariateLaurentSeriesConstructor| . |RadicalCategory|) 262353) ((|UnivariateLaurentSeriesConstructor| . |TranscendentalFunctionCategory|) 262302) ((|UnivariateLaurentSeriesConstructor| . |TrigonometricFunctionCategory|) 262251) ((|UnivariateLaurentSeriesConstructor| . |HyperbolicFunctionCategory|) 262200) ((|UnivariateLaurentSeriesConstructor| . |ElementaryFunctionCategory|) 262149) ((|UnivariateLaurentSeriesConstructor| . |ArcTrigonometricFunctionCategory|) 262098) ((|UnivariateLaurentSeriesConstructor| . |ArcHyperbolicFunctionCategory|) 262047) ((|UnivariateLaurentSeriesConstructor| . |UnivariatePowerSeriesCategory|) 262019) ((|UnivariateLaurentSeriesConstructor| . |AbelianMonoidRing|) 261991) ((|UnivariateLaurentSeriesConstructor| . |Functorial|) 261945) ((|UnivariateLaurentSeriesConstructor| . |CoercibleFrom|) 261616) ((|UnivariateLaurentSeriesConstructor| . |Module|) 261374) ((|UnivariateLaurentSeriesConstructor| . |LinearSet|) 261132) ((|UnivariateLaurentSeriesConstructor| . |LeftModule|) 260874) ((|UnivariateLaurentSeriesConstructor| . |LeftLinearSet|) 260693) ((|UnivariateLaurentSeriesConstructor| . |RightModule|) 260445) ((|UnivariateLaurentSeriesConstructor| . |RightLinearSet|) 260197) ((|UnivariateLaurentSeriesConstructor| . |BiModule|) 259930) ((|UnivariateLaurentSeriesConstructor| . |Algebra|) 259688) ((|UnivariateLaurentSeriesConstructor| . |PowerSeriesCategory|) 259634) ((|UnivariateLaurentSeriesConstructor| . |Eltable|) 259521) ((|UnivariateLaurentSeriesConstructor| . |UnivariateLaurentSeriesCategory|) 259505) ((|UnivariateLaurentSeriesConstructor| . |Rng|) T) ((|UnivariateLaurentSeriesConstructor| . |SemiGroup|) T) ((|UnivariateLaurentSeriesConstructor| . |SemiRing|) T) ((|UnivariateLaurentSeriesConstructor| . |Monoid|) T) ((|UnivariateLaurentSeriesConstructor| . |Ring|) T) ((|UnivariateLaurentSeriesConstructor| . |AbelianGroup|) T) ((|UnivariateLaurentSeriesConstructor| . |AbelianMonoid|) T) ((|UnivariateLaurentSeriesConstructor| . |SetCategory|) T) ((|UnivariateLaurentSeriesConstructor| . |CoercibleTo|) 259479) ((|UnivariateLaurentSeriesConstructor| . |Type|) T) ((|UnivariateLaurentSeriesConstructor| . |Join|) T) ((|UnivariateLaurentSeriesConstructor| . |BasicType|) T) ((|UnivariateLaurentSeriesConstructor| . |AbelianSemiGroup|) T) ((|UnivariateLaurentSeriesConstructor| . |CancellationAbelianMonoid|) T) ((|UnivariateLaurentSeriesConstructor| . |CharacteristicNonZero|) 259366) ((|UnivariateLaurentSeriesConstructor| . |CharacteristicZero|) 259191) ((|UnivariateLaurentSeriesConstructor| . |ConvertibleTo|) 258734) ((|UnivariateLaurentSeriesConstructor| . |DifferentialExtension|) 258701) ((|UnivariateLaurentSeriesConstructor| . |PartialDifferentialRing|) 258490) ((|UnivariateLaurentSeriesConstructor| . |PartialDifferentialSpace|) 258197) ((|UnivariateLaurentSeriesConstructor| . |PartialDifferentialDomain|) 257902) ((|UnivariateLaurentSeriesConstructor| . |DifferentialSpaceExtension|) 257869) ((|UnivariateLaurentSeriesConstructor| . |DifferentialSpace|) 257685) ((|UnivariateLaurentSeriesConstructor| . |DifferentialDomain|) 257495) ((|UnivariateLaurentSeriesConstructor| . |DifferentialRing|) 257375) ((|UnivariateLaurentSeriesConstructor| . |Field|) 257351) ((|UnivariateLaurentSeriesConstructor| . |UniqueFactorizationDomain|) 257327) ((|UnivariateLaurentSeriesConstructor| . |PrincipalIdealDomain|) 257303) ((|UnivariateLaurentSeriesConstructor| . |IntegralDomain|) 257242) ((|UnivariateLaurentSeriesConstructor| . |CommutativeRing|) 257148) ((|UnivariateLaurentSeriesConstructor| . |GcdDomain|) 257124) ((|UnivariateLaurentSeriesConstructor| . |EuclideanDomain|) 257100) ((|UnivariateLaurentSeriesConstructor| . |EntireRing|) 257039) ((|UnivariateLaurentSeriesConstructor| . |DivisionRing|) 257015) ((|UnivariateLaurentSeriesConstructor| . |FullyEvalableOver|) 256982) ((|UnivariateLaurentSeriesConstructor| . |InnerEvalable|) 256813) ((|UnivariateLaurentSeriesConstructor| . |Evalable|) 256743) ((|UnivariateLaurentSeriesConstructor| . |FullyLinearlyExplicitRingOver|) 256710) ((|UnivariateLaurentSeriesConstructor| . |LinearlyExplicitRingOver|) 256580) ((|UnivariateLaurentSeriesConstructor| . |FullyPatternMatchable|) 256547) ((|UnivariateLaurentSeriesConstructor| . |PatternMatchable|) 256370) ((|UnivariateLaurentSeriesConstructor| . |OrderedIntegralDomain|) 256301) ((|UnivariateLaurentSeriesConstructor| . |OrderedAbelianGroup|) 256232) ((|UnivariateLaurentSeriesConstructor| . |OrderedAbelianMonoid|) 256163) ((|UnivariateLaurentSeriesConstructor| . |OrderedSet|) 256032) ((|UnivariateLaurentSeriesConstructor| . |OrderedType|) 255901) ((|UnivariateLaurentSeriesConstructor| . |OrderedAbelianSemiGroup|) 255832) ((|UnivariateLaurentSeriesConstructor| . |OrderedCancellationAbelianMonoid|) 255763) ((|UnivariateLaurentSeriesConstructor| . |OrderedRing|) 255694) ((|UnivariateLaurentSeriesConstructor| . |Patternable|) 255661) ((|UnivariateLaurentSeriesConstructor| . |PolynomialFactorizationExplicit|) 255582) ((|UnivariateLaurentSeriesConstructor| . |RealConstant|) 255522) ((|UnivariateLaurentSeriesConstructor| . |RetractableTo|) 255237) ((|UnivariateLaurentSeriesConstructor| . |StepThrough|) 255178) ((|UnivariateLaurentSeriesConstructor| . |QuotientFieldCategory|) 255145) ((|UnivariateLaurentSeries| . |UnivariateLaurentSeriesConstructorCategory|) 255087) ((|UnivariateLaurentSeries| . |RadicalCategory|) 255036) ((|UnivariateLaurentSeries| . |TranscendentalFunctionCategory|) 254985) ((|UnivariateLaurentSeries| . |TrigonometricFunctionCategory|) 254934) ((|UnivariateLaurentSeries| . |HyperbolicFunctionCategory|) 254883) ((|UnivariateLaurentSeries| . |ElementaryFunctionCategory|) 254832) ((|UnivariateLaurentSeries| . |ArcTrigonometricFunctionCategory|) 254781) ((|UnivariateLaurentSeries| . |ArcHyperbolicFunctionCategory|) 254730) ((|UnivariateLaurentSeries| . |UnivariatePowerSeriesCategory|) 254702) ((|UnivariateLaurentSeries| . |AbelianMonoidRing|) 254674) ((|UnivariateLaurentSeries| . |Functorial|) 254591) ((|UnivariateLaurentSeries| . |CoercibleFrom|) 254309) ((|UnivariateLaurentSeries| . |Module|) 254030) ((|UnivariateLaurentSeries| . |LinearSet|) 253751) ((|UnivariateLaurentSeries| . |LeftModule|) 253553) ((|UnivariateLaurentSeries| . |LeftLinearSet|) 253335) ((|UnivariateLaurentSeries| . |RightModule|) 253050) ((|UnivariateLaurentSeries| . |RightLinearSet|) 252765) ((|UnivariateLaurentSeries| . |BiModule|) 252459) ((|UnivariateLaurentSeries| . |Algebra|) 252180) ((|UnivariateLaurentSeries| . |PowerSeriesCategory|) 252126) ((|UnivariateLaurentSeries| . |Eltable|) 251865) ((|UnivariateLaurentSeries| . |UnivariateLaurentSeriesCategory|) 251849) ((|UnivariateLaurentSeries| . |Rng|) T) ((|UnivariateLaurentSeries| . |SemiGroup|) T) ((|UnivariateLaurentSeries| . |SemiRing|) T) ((|UnivariateLaurentSeries| . |Monoid|) T) ((|UnivariateLaurentSeries| . |Ring|) T) ((|UnivariateLaurentSeries| . |AbelianGroup|) T) ((|UnivariateLaurentSeries| . |AbelianMonoid|) T) ((|UnivariateLaurentSeries| . |SetCategory|) T) ((|UnivariateLaurentSeries| . |CoercibleTo|) 251823) ((|UnivariateLaurentSeries| . |Type|) T) ((|UnivariateLaurentSeries| . |Join|) T) ((|UnivariateLaurentSeries| . |BasicType|) T) ((|UnivariateLaurentSeries| . |AbelianSemiGroup|) T) ((|UnivariateLaurentSeries| . |CancellationAbelianMonoid|) T) ((|UnivariateLaurentSeries| . |CharacteristicNonZero|) 251673) ((|UnivariateLaurentSeries| . |CharacteristicZero|) 251529) ((|UnivariateLaurentSeries| . |ConvertibleTo|) NIL) ((|UnivariateLaurentSeries| . |DifferentialExtension|) 251459) ((|UnivariateLaurentSeries| . |PartialDifferentialRing|) 251211) ((|UnivariateLaurentSeries| . |PartialDifferentialSpace|) 250844) ((|UnivariateLaurentSeries| . |PartialDifferentialDomain|) 250447) ((|UnivariateLaurentSeries| . |DifferentialSpaceExtension|) 250377) ((|UnivariateLaurentSeries| . |DifferentialSpace|) 250119) ((|UnivariateLaurentSeries| . |DifferentialDomain|) 249855) ((|UnivariateLaurentSeries| . |DifferentialRing|) 249698) ((|UnivariateLaurentSeries| . |Field|) 249674) ((|UnivariateLaurentSeries| . |UniqueFactorizationDomain|) 249650) ((|UnivariateLaurentSeries| . |PrincipalIdealDomain|) 249626) ((|UnivariateLaurentSeries| . |IntegralDomain|) 249565) ((|UnivariateLaurentSeries| . |CommutativeRing|) 249471) ((|UnivariateLaurentSeries| . |GcdDomain|) 249447) ((|UnivariateLaurentSeries| . |EuclideanDomain|) 249423) ((|UnivariateLaurentSeries| . |EntireRing|) 249362) ((|UnivariateLaurentSeries| . |DivisionRing|) 249338) ((|UnivariateLaurentSeries| . |FullyEvalableOver|) 249268) ((|UnivariateLaurentSeries| . |InnerEvalable|) 248913) ((|UnivariateLaurentSeries| . |Evalable|) 248732) ((|UnivariateLaurentSeries| . |FullyLinearlyExplicitRingOver|) 248662) ((|UnivariateLaurentSeries| . |LinearlyExplicitRingOver|) 248592) ((|UnivariateLaurentSeries| . |FullyPatternMatchable|) 248522) ((|UnivariateLaurentSeries| . |PatternMatchable|) NIL) ((|UnivariateLaurentSeries| . |OrderedIntegralDomain|) NIL) ((|UnivariateLaurentSeries| . |OrderedAbelianGroup|) NIL) ((|UnivariateLaurentSeries| . |OrderedAbelianMonoid|) NIL) ((|UnivariateLaurentSeries| . |OrderedSet|) NIL) ((|UnivariateLaurentSeries| . |OrderedType|) NIL) ((|UnivariateLaurentSeries| . |OrderedAbelianSemiGroup|) NIL) ((|UnivariateLaurentSeries| . |OrderedCancellationAbelianMonoid|) NIL) ((|UnivariateLaurentSeries| . |OrderedRing|) NIL) ((|UnivariateLaurentSeries| . |Patternable|) 248452) ((|UnivariateLaurentSeries| . |PolynomialFactorizationExplicit|) NIL) ((|UnivariateLaurentSeries| . |RealConstant|) NIL) ((|UnivariateLaurentSeries| . |RetractableTo|) 248399) ((|UnivariateLaurentSeries| . |StepThrough|) NIL) ((|UnivariateLaurentSeries| . |QuotientFieldCategory|) 248329) ((|UInt8| . |OrderedFinite|) T) ((|UInt8| . |OrderedType|) T) ((|UInt8| . |OrderedSet|) T) ((|UInt8| . |SetCategory|) T) ((|UInt8| . |CoercibleTo|) 248303) ((|UInt8| . |Type|) T) ((|UInt8| . |Join|) T) ((|UInt8| . |BasicType|) T) ((|UInt8| . |Finite|) T) ((|UInt8| . |Logic|) T) ((|UInt64| . |OrderedFinite|) T) ((|UInt64| . |OrderedType|) T) ((|UInt64| . |OrderedSet|) T) ((|UInt64| . |SetCategory|) T) ((|UInt64| . |CoercibleTo|) 248277) ((|UInt64| . |Type|) T) ((|UInt64| . |Join|) T) ((|UInt64| . |BasicType|) T) ((|UInt64| . |Finite|) T) ((|UInt64| . |Logic|) T) ((|UInt32| . |OrderedFinite|) T) ((|UInt32| . |OrderedType|) T) ((|UInt32| . |OrderedSet|) T) ((|UInt32| . |SetCategory|) T) ((|UInt32| . |CoercibleTo|) 248251) ((|UInt32| . |Type|) T) ((|UInt32| . |Join|) T) ((|UInt32| . |BasicType|) T) ((|UInt32| . |Finite|) T) ((|UInt32| . |Logic|) T) ((|UInt16| . |OrderedFinite|) T) ((|UInt16| . |OrderedType|) T) ((|UInt16| . |OrderedSet|) T) ((|UInt16| . |SetCategory|) T) ((|UInt16| . |CoercibleTo|) 248225) ((|UInt16| . |Type|) T) ((|UInt16| . |Join|) T) ((|UInt16| . |BasicType|) T) ((|UInt16| . |Finite|) T) ((|UInt16| . |Logic|) T) ((|TypeAst| . |SpadSyntaxCategory|) T) ((|TypeAst| . |HomotopicTo|) 248203) ((|TypeAst| . |CoercibleTo|) 248158) ((|TypeAst| . |CoercibleFrom|) 248136) ((|TypeAst| . |SetCategory|) T) ((|TypeAst| . |Type|) T) ((|TypeAst| . |Join|) T) ((|TypeAst| . |BasicType|) T) ((|TypeAst| . |AbstractSyntaxCategory|) T) ((|Tuple| . |HomotopicTo|) 248101) ((|Tuple| . |CoercibleTo|) 248011) ((|Tuple| . |CoercibleFrom|) 247976) ((|Tuple| . |SetCategory|) 247946) ((|Tuple| . |Type|) 247916) ((|Tuple| . |Join|) 247886) ((|Tuple| . |BasicType|) 247856) ((|TaylorSeries| . |MultivariateTaylorSeriesCategory|) 247829) ((|TaylorSeries| . |ArcHyperbolicFunctionCategory|) 247778) ((|TaylorSeries| . |ArcTrigonometricFunctionCategory|) 247727) ((|TaylorSeries| . |ElementaryFunctionCategory|) 247676) ((|TaylorSeries| . |HyperbolicFunctionCategory|) 247625) ((|TaylorSeries| . |TrigonometricFunctionCategory|) 247574) ((|TaylorSeries| . |TranscendentalFunctionCategory|) 247523) ((|TaylorSeries| . |RadicalCategory|) 247472) ((|TaylorSeries| . |AbelianMonoidRing|) 247424) ((|TaylorSeries| . |Algebra|) 247268) ((|TaylorSeries| . |LinearSet|) 247112) ((|TaylorSeries| . |Module|) 246956) ((|TaylorSeries| . |CoercibleFrom|) 246780) ((|TaylorSeries| . |EntireRing|) 246747) ((|TaylorSeries| . |IntegralDomain|) 246714) ((|TaylorSeries| . |Functorial|) 246698) ((|TaylorSeries| . |BiModule|) 246517) ((|TaylorSeries| . |RightLinearSet|) 246350) ((|TaylorSeries| . |RightModule|) 246183) ((|TaylorSeries| . |CommutativeRing|) 246112) ((|TaylorSeries| . |CharacteristicZero|) 246075) ((|TaylorSeries| . |CharacteristicNonZero|) 246035) ((|TaylorSeries| . |LeftModule|) 245932) ((|TaylorSeries| . |LeftLinearSet|) 245809) ((|TaylorSeries| . |PowerSeriesCategory|) 245754) ((|TaylorSeries| . |PartialDifferentialSpace|) 245732) ((|TaylorSeries| . |Type|) T) ((|TaylorSeries| . |Join|) T) ((|TaylorSeries| . |PartialDifferentialDomain|) 245708) ((|TaylorSeries| . |Ring|) T) ((|TaylorSeries| . |Monoid|) T) ((|TaylorSeries| . 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|ConvertibleFrom|) 204127) ((|SExpression| . |SExpressionCategory|) 204051) ((|SExpression| . |BasicType|) T) ((|SExpression| . |CoercibleTo|) 204025) ((|SExpression| . |SetCategory|) T) ((|SExpression| . |Eltable|) 203969) ((|SExpression| . |Type|) T) ((|SExpression| . |Join|) T) ((|SExpression| . |ConvertibleFrom|) 203842) ((|SetOfMIntegersInOneToN| . |Finite|) T) ((|SetOfMIntegersInOneToN| . |BasicType|) T) ((|SetOfMIntegersInOneToN| . |Join|) T) ((|SetOfMIntegersInOneToN| . |Type|) T) ((|SetOfMIntegersInOneToN| . |CoercibleTo|) 203816) ((|SetOfMIntegersInOneToN| . |SetCategory|) T) ((|Set| . |FiniteSetAggregate|) 203800) ((|Set| . |SetAggregate|) 203784) ((|Set| . |FiniteAggregate|) 203768) ((|Set| . |Finite|) 203743) ((|Set| . |DictionaryOperations|) 203727) ((|Set| . |ConvertibleTo|) 203663) ((|Set| . |Collection|) 203647) ((|Set| . |HomogeneousAggregate|) 203631) ((|Set| . |SetCategory|) T) ((|Set| . |Functorial|) 203615) ((|Set| . |InnerEvalable|) 203534) ((|Set| . |Evalable|) 203458) ((|Set| . |CoercibleTo|) 203432) ((|Set| . |BasicType|) T) ((|Set| . |Type|) T) ((|Set| . |Join|) T) ((|Set| . |Aggregate|) T) ((|Set| . |ShallowlyMutableAggregate|) 203416) ((|Set| . |BagAggregate|) 203400) ((|Set| . |Dictionary|) 203384) ((|SequenceAst| . |SpadSyntaxCategory|) T) ((|SequenceAst| . |HomotopicTo|) 203362) ((|SequenceAst| . |CoercibleTo|) 203317) ((|SequenceAst| . |CoercibleFrom|) 203295) ((|SequenceAst| . |SetCategory|) T) ((|SequenceAst| . |Type|) T) ((|SequenceAst| . |Join|) T) ((|SequenceAst| . |BasicType|) T) ((|SequenceAst| . |AbstractSyntaxCategory|) T) ((|SegmentBinding| . |Type|) T) ((|SegmentBinding| . |Join|) T) ((|SegmentBinding| . |SetCategory|) 203253) ((|SegmentBinding| . |CoercibleTo|) 203192) ((|SegmentBinding| . |BasicType|) 203150) ((|SegmentAst| . |SpadSyntaxCategory|) T) ((|SegmentAst| . |HomotopicTo|) 203128) ((|SegmentAst| . |CoercibleTo|) 203083) ((|SegmentAst| . |CoercibleFrom|) 203061) ((|SegmentAst| . |SetCategory|) T) ((|SegmentAst| . |Type|) T) ((|SegmentAst| . |Join|) T) ((|SegmentAst| . |BasicType|) T) ((|SegmentAst| . |AbstractSyntaxCategory|) T) ((|Segment| . |SegmentCategory|) 203045) ((|Segment| . |ConvertibleFrom|) 203029) ((|Segment| . |SetCategory|) 202999) ((|Segment| . |CoercibleTo|) 202950) ((|Segment| . |Type|) 202920) ((|Segment| . |Join|) 202890) ((|Segment| . |BasicType|) 202860) ((|Segment| . |SegmentExpansionCategory|) 202807) ((|SequentialDifferentialVariable| . |DifferentialVariableCategory|) 202791) ((|SequentialDifferentialVariable| . |CoercibleFrom|) 202775) ((|SequentialDifferentialVariable| . |RetractableTo|) 202759) ((|SequentialDifferentialVariable| . |OrderedType|) T) ((|SequentialDifferentialVariable| . |BasicType|) T) ((|SequentialDifferentialVariable| . |SetCategory|) T) ((|SequentialDifferentialVariable| . |CoercibleTo|) 202733) ((|SequentialDifferentialVariable| . |OrderedSet|) T) ((|SequentialDifferentialVariable| . |DifferentialDomain|) 202720) ((|SequentialDifferentialVariable| . |Join|) T) ((|SequentialDifferentialVariable| . |Type|) T) ((|SequentialDifferentialVariable| . |DifferentialSpace|) T) ((|SequentialDifferentialPolynomial| . |DifferentialPolynomialCategory|) 202623) ((|SequentialDifferentialPolynomial| . |CoercibleFrom|) 202213) ((|SequentialDifferentialPolynomial| . |RetractableTo|) 201938) ((|SequentialDifferentialPolynomial| . |ConvertibleTo|) NIL) ((|SequentialDifferentialPolynomial| . |FiniteAbelianMonoidRing|) 201855) ((|SequentialDifferentialPolynomial| . |FullyRetractableTo|) 201839) ((|SequentialDifferentialPolynomial| . |Algebra|) 201602) ((|SequentialDifferentialPolynomial| . |BiModule|) 201345) ((|SequentialDifferentialPolynomial| . |RightLinearSet|) 201102) ((|SequentialDifferentialPolynomial| . |RightModule|) 200859) ((|SequentialDifferentialPolynomial| . |LeftLinearSet|) 200736) ((|SequentialDifferentialPolynomial| . |LeftModule|) 200565) ((|SequentialDifferentialPolynomial| . |LinearSet|) 200328) ((|SequentialDifferentialPolynomial| . |Module|) 200091) ((|SequentialDifferentialPolynomial| . |CharacteristicNonZero|) 200051) ((|SequentialDifferentialPolynomial| . |CharacteristicZero|) 200014) ((|SequentialDifferentialPolynomial| . |CommutativeRing|) 199867) ((|SequentialDifferentialPolynomial| . |Functorial|) 199851) ((|SequentialDifferentialPolynomial| . |IntegralDomain|) 199737) ((|SequentialDifferentialPolynomial| . |EntireRing|) 199623) ((|SequentialDifferentialPolynomial| . |AbelianMonoidRing|) 199540) ((|SequentialDifferentialPolynomial| . |FullyLinearlyExplicitRingOver|) 199524) ((|SequentialDifferentialPolynomial| . |LinearlyExplicitRingOver|) 199440) ((|SequentialDifferentialPolynomial| . |GcdDomain|) 199358) ((|SequentialDifferentialPolynomial| . |InnerEvalable|) 199185) ((|SequentialDifferentialPolynomial| . |PartialDifferentialRing|) 199063) ((|SequentialDifferentialPolynomial| . |PartialDifferentialDomain|) 198879) ((|SequentialDifferentialPolynomial| . |PartialDifferentialSpace|) 198699) ((|SequentialDifferentialPolynomial| . |PatternMatchable|) NIL) ((|SequentialDifferentialPolynomial| . |PolynomialFactorizationExplicit|) 198649) ((|SequentialDifferentialPolynomial| . |UniqueFactorizationDomain|) 198599) ((|SequentialDifferentialPolynomial| . |PolynomialCategory|) 198509) ((|SequentialDifferentialPolynomial| . |Evalable|) 198496) ((|SequentialDifferentialPolynomial| . |DifferentialRing|) 198461) ((|SequentialDifferentialPolynomial| . |CancellationAbelianMonoid|) T) ((|SequentialDifferentialPolynomial| . |AbelianSemiGroup|) T) ((|SequentialDifferentialPolynomial| . |BasicType|) T) ((|SequentialDifferentialPolynomial| . |CoercibleTo|) 198435) ((|SequentialDifferentialPolynomial| . |SetCategory|) T) ((|SequentialDifferentialPolynomial| . |AbelianMonoid|) T) ((|SequentialDifferentialPolynomial| . |AbelianGroup|) T) ((|SequentialDifferentialPolynomial| . |Rng|) T) ((|SequentialDifferentialPolynomial| . |SemiGroup|) T) ((|SequentialDifferentialPolynomial| . |SemiRing|) T) ((|SequentialDifferentialPolynomial| . |Monoid|) T) ((|SequentialDifferentialPolynomial| . |Ring|) T) ((|SequentialDifferentialPolynomial| . |DifferentialDomain|) 198354) ((|SequentialDifferentialPolynomial| . |Join|) T) ((|SequentialDifferentialPolynomial| . |Type|) T) ((|SequentialDifferentialPolynomial| . |DifferentialSpace|) 198279) ((|SequentialDifferentialPolynomial| . |DifferentialSpaceExtension|) 198263) ((|SequentialDifferentialPolynomial| . |DifferentialExtension|) 198247) ((|Scope| . |CoercibleTo|) 198221) ((|SingletonAsOrderedSet| . |OrderedSet|) T) ((|SingletonAsOrderedSet| . |CoercibleTo|) 198195) ((|SingletonAsOrderedSet| . |SetCategory|) T) ((|SingletonAsOrderedSet| . |BasicType|) T) ((|SingletonAsOrderedSet| . |Join|) T) ((|SingletonAsOrderedSet| . |Type|) T) ((|SingletonAsOrderedSet| . |OrderedType|) T) ((|SingletonAsOrderedSet| . |ConvertibleTo|) 198173) ((|SimpleAlgebraicExtension| . |MonogenicAlgebra|) 198152) ((|SimpleAlgebraicExtension| . |RetractableTo|) 197996) ((|SimpleAlgebraicExtension| . |FullyRetractableTo|) 197980) ((|SimpleAlgebraicExtension| . |LinearlyExplicitRingOver|) 197896) ((|SimpleAlgebraicExtension| . |LeftModule|) 197710) ((|SimpleAlgebraicExtension| . |FullyLinearlyExplicitRingOver|) 197694) ((|SimpleAlgebraicExtension| . |FiniteRankAlgebra|) 197673) ((|SimpleAlgebraicExtension| . |CharacteristicZero|) 197636) ((|SimpleAlgebraicExtension| . |CoercibleFrom|) 197383) ((|SimpleAlgebraicExtension| . |Module|) 197206) ((|SimpleAlgebraicExtension| . |LinearSet|) 197029) ((|SimpleAlgebraicExtension| . |LeftLinearSet|) 196891) ((|SimpleAlgebraicExtension| . |RightModule|) 196773) ((|SimpleAlgebraicExtension| . |RightLinearSet|) 196655) ((|SimpleAlgebraicExtension| . |BiModule|) 196523) ((|SimpleAlgebraicExtension| . |Algebra|) 196346) ((|SimpleAlgebraicExtension| . |FramedAlgebra|) 196325) ((|SimpleAlgebraicExtension| . |FieldOfPrimeCharacteristic|) 196287) ((|SimpleAlgebraicExtension| . |CharacteristicNonZero|) 196205) ((|SimpleAlgebraicExtension| . |StepThrough|) 196167) ((|SimpleAlgebraicExtension| . |FiniteFieldCategory|) 196129) ((|SimpleAlgebraicExtension| . |Finite|) 196062) ((|SimpleAlgebraicExtension| . |DivisionRing|) 195996) ((|SimpleAlgebraicExtension| . |EntireRing|) 195930) ((|SimpleAlgebraicExtension| . |EuclideanDomain|) 195864) ((|SimpleAlgebraicExtension| . |GcdDomain|) 195798) ((|SimpleAlgebraicExtension| . |IntegralDomain|) 195732) ((|SimpleAlgebraicExtension| . |PrincipalIdealDomain|) 195666) ((|SimpleAlgebraicExtension| . |UniqueFactorizationDomain|) 195600) ((|SimpleAlgebraicExtension| . |Field|) 195534) ((|SimpleAlgebraicExtension| . |DifferentialRing|) 195428) ((|SimpleAlgebraicExtension| . |DifferentialDomain|) 195252) ((|SimpleAlgebraicExtension| . |DifferentialSpace|) 195082) ((|SimpleAlgebraicExtension| . |DifferentialSpaceExtension|) 195049) ((|SimpleAlgebraicExtension| . |PartialDifferentialDomain|) 194863) ((|SimpleAlgebraicExtension| . |PartialDifferentialSpace|) 194679) ((|SimpleAlgebraicExtension| . |PartialDifferentialRing|) 194582) ((|SimpleAlgebraicExtension| . |DifferentialExtension|) 194549) ((|SimpleAlgebraicExtension| . |ConvertibleTo|) 194533) ((|SimpleAlgebraicExtension| . |AbelianGroup|) T) ((|SimpleAlgebraicExtension| . |AbelianMonoid|) T) ((|SimpleAlgebraicExtension| . |SetCategory|) T) ((|SimpleAlgebraicExtension| . |CoercibleTo|) 194507) ((|SimpleAlgebraicExtension| . |Type|) T) ((|SimpleAlgebraicExtension| . |Join|) T) ((|SimpleAlgebraicExtension| . |BasicType|) T) ((|SimpleAlgebraicExtension| . |AbelianSemiGroup|) T) ((|SimpleAlgebraicExtension| . |CancellationAbelianMonoid|) T) ((|SimpleAlgebraicExtension| . |Ring|) T) ((|SimpleAlgebraicExtension| . |Monoid|) T) ((|SimpleAlgebraicExtension| . |SemiRing|) T) ((|SimpleAlgebraicExtension| . |SemiGroup|) T) ((|SimpleAlgebraicExtension| . |Rng|) T) ((|SimpleAlgebraicExtension| . |CommutativeRing|) T) ((|Ruleset| . |SetCategory|) T) ((|Ruleset| . |CoercibleTo|) 194481) ((|Ruleset| . |Type|) T) ((|Ruleset| . |Join|) T) ((|Ruleset| . |BasicType|) T) ((|Ruleset| . |Eltable|) 194460) ((|RuleCalled| . |SetCategory|) T) ((|RuleCalled| . |CoercibleTo|) 194434) ((|RuleCalled| . |Type|) T) ((|RuleCalled| . |Join|) T) ((|RuleCalled| . |BasicType|) T) ((|RewriteRule| . |SetCategory|) T) ((|RewriteRule| . |CoercibleTo|) 194408) ((|RewriteRule| . |Type|) T) ((|RewriteRule| . |Join|) T) ((|RewriteRule| . |BasicType|) T) ((|RewriteRule| . |Eltable|) 194387) ((|RewriteRule| . |RetractableTo|) 194358) ((|RewriteRule| . |CoercibleFrom|) 194329) ((|RuntimeValue| . |Type|) T) ((|RuntimeValue| . |Join|) T) ((|RestrictAst| . |SpadSyntaxCategory|) T) ((|RestrictAst| . |HomotopicTo|) 194307) ((|RestrictAst| . |CoercibleTo|) 194262) ((|RestrictAst| . |CoercibleFrom|) 194240) ((|RestrictAst| . |SetCategory|) T) ((|RestrictAst| . |Type|) T) ((|RestrictAst| . |Join|) T) ((|RestrictAst| . |BasicType|) T) ((|RestrictAst| . |AbstractSyntaxCategory|) T) ((|RepeatAst| . |SpadSyntaxCategory|) T) ((|RepeatAst| . |HomotopicTo|) 194218) ((|RepeatAst| . |CoercibleTo|) 194173) ((|RepeatAst| . |CoercibleFrom|) 194151) ((|RepeatAst| . |SetCategory|) T) ((|RepeatAst| . |Type|) T) ((|RepeatAst| . |Join|) T) ((|RepeatAst| . |BasicType|) T) ((|RepeatAst| . |AbstractSyntaxCategory|) T) ((|RomanNumeral| . |IntegerNumberSystem|) T) ((|RomanNumeral| . |UniqueFactorizationDomain|) T) ((|RomanNumeral| . |StepThrough|) T) ((|RomanNumeral| . |RetractableTo|) 194128) ((|RomanNumeral| . |ConvertibleTo|) 194014) ((|RomanNumeral| . |RealConstant|) T) ((|RomanNumeral| . |PatternMatchable|) 193991) ((|RomanNumeral| . |OrderedRing|) T) ((|RomanNumeral| . |OrderedCancellationAbelianMonoid|) T) ((|RomanNumeral| . |OrderedAbelianSemiGroup|) T) ((|RomanNumeral| . |OrderedType|) T) ((|RomanNumeral| . |OrderedSet|) T) ((|RomanNumeral| . |OrderedAbelianMonoid|) T) ((|RomanNumeral| . |OrderedAbelianGroup|) T) ((|RomanNumeral| . |OrderedIntegralDomain|) T) ((|RomanNumeral| . |LeftModule|) 193958) ((|RomanNumeral| . |LinearlyExplicitRingOver|) 193935) ((|RomanNumeral| . |PrincipalIdealDomain|) T) ((|RomanNumeral| . |IntegralDomain|) T) ((|RomanNumeral| . |EntireRing|) T) ((|RomanNumeral| . |CommutativeRing|) T) ((|RomanNumeral| . |CoercibleFrom|) 193902) ((|RomanNumeral| . |Module|) 193889) ((|RomanNumeral| . |LinearSet|) 193876) ((|RomanNumeral| . |RightModule|) 193863) ((|RomanNumeral| . |RightLinearSet|) 193850) ((|RomanNumeral| . |BiModule|) 193835) ((|RomanNumeral| . |Algebra|) 193822) ((|RomanNumeral| . |GcdDomain|) T) ((|RomanNumeral| . |EuclideanDomain|) T) ((|RomanNumeral| . |DifferentialSpace|) T) ((|RomanNumeral| . |DifferentialDomain|) 193809) ((|RomanNumeral| . |DifferentialRing|) T) ((|RomanNumeral| . |CombinatorialFunctionCategory|) T) ((|RomanNumeral| . |Ring|) T) ((|RomanNumeral| . |Monoid|) T) ((|RomanNumeral| . |SemiRing|) T) ((|RomanNumeral| . |SemiGroup|) T) ((|RomanNumeral| . |Rng|) T) ((|RomanNumeral| . |AbelianGroup|) T) ((|RomanNumeral| . |LeftLinearSet|) 193776) ((|RomanNumeral| . |AbelianMonoid|) T) ((|RomanNumeral| . |SetCategory|) T) ((|RomanNumeral| . |CoercibleTo|) 193750) ((|RomanNumeral| . |Type|) T) ((|RomanNumeral| . |Join|) T) ((|RomanNumeral| . |BasicType|) T) ((|RomanNumeral| . |AbelianSemiGroup|) T) ((|RomanNumeral| . |CancellationAbelianMonoid|) T) ((|RomanNumeral| . |CharacteristicZero|) T) ((|RomanNumeral| . |ConvertibleFrom|) 193728) ((|RightOpenIntervalRootCharacterization| . |RealRootCharacterizationCategory|) 193707) ((|RightOpenIntervalRootCharacterization| . |BasicType|) T) ((|RightOpenIntervalRootCharacterization| . |Join|) T) ((|RightOpenIntervalRootCharacterization| . |Type|) T) ((|RightOpenIntervalRootCharacterization| . |CoercibleTo|) 193681) ((|RightOpenIntervalRootCharacterization| . |SetCategory|) T) ((|RangeBinding| . |Type|) T) ((|RangeBinding| . |Join|) T) ((|RangeBinding| . |SetCategory|) 193651) ((|RangeBinding| . |CoercibleTo|) 193602) ((|RangeBinding| . |BasicType|) 193572) ((|RectangularMatrix| . |RectangularMatrixCategory|) 193490) ((|RectangularMatrix| . |LinearSet|) 193419) ((|RectangularMatrix| . |Module|) 193348) ((|RectangularMatrix| . |HomogeneousAggregate|) 193332) ((|RectangularMatrix| . |Functorial|) 193316) ((|RectangularMatrix| . |InnerEvalable|) 193235) ((|RectangularMatrix| . |Evalable|) 193159) ((|RectangularMatrix| . |Aggregate|) T) ((|RectangularMatrix| . |FiniteAggregate|) 193143) ((|RectangularMatrix| . |LeftModule|) 193127) ((|RectangularMatrix| . |LeftLinearSet|) 193091) ((|RectangularMatrix| . |CancellationAbelianMonoid|) T) ((|RectangularMatrix| . |AbelianSemiGroup|) T) ((|RectangularMatrix| . |BasicType|) T) ((|RectangularMatrix| . |Join|) T) ((|RectangularMatrix| . |Type|) T) ((|RectangularMatrix| . |CoercibleTo|) 193041) ((|RectangularMatrix| . |SetCategory|) T) ((|RectangularMatrix| . |AbelianMonoid|) T) ((|RectangularMatrix| . |AbelianGroup|) T) ((|RectangularMatrix| . |RightModule|) 193025) ((|RectangularMatrix| . |RightLinearSet|) 193009) ((|RectangularMatrix| . |BiModule|) 192988) ((|RectangularMatrix| . |VectorSpace|) 192955) ((|RectangularMatrix| . |ConvertibleTo|) 192896) ((|RegularChain| . |RegularTriangularSetCategory|) 192778) ((|RegularChain| . |PolynomialSetCategory|) 192660) ((|RegularChain| . |FiniteAggregate|) 192579) ((|RegularChain| . |ConvertibleTo|) 192450) ((|RegularChain| . |HomogeneousAggregate|) 192369) ((|RegularChain| . |SetCategory|) T) ((|RegularChain| . |Functorial|) 192288) ((|RegularChain| . |InnerEvalable|) 192045) ((|RegularChain| . |Evalable|) 191809) ((|RegularChain| . |CoercibleTo|) 191696) ((|RegularChain| . |BasicType|) T) ((|RegularChain| . |Type|) T) ((|RegularChain| . |Join|) T) ((|RegularChain| . |Aggregate|) T) ((|RegularChain| . |Collection|) 191615) ((|RegularChain| . |ShallowlyMutableAggregate|) 191534) ((|RegularChain| . |TriangularSetCategory|) 191416) ((|ReturnAst| . |SpadSyntaxCategory|) T) ((|ReturnAst| . |HomotopicTo|) 191394) ((|ReturnAst| . |CoercibleTo|) 191349) ((|ReturnAst| . |CoercibleFrom|) 191327) ((|ReturnAst| . |SetCategory|) T) ((|ReturnAst| . |Type|) T) ((|ReturnAst| . |Join|) T) ((|ReturnAst| . |BasicType|) T) ((|ReturnAst| . |AbstractSyntaxCategory|) T) ((|ResidueRing| . |CommutativeRing|) T) ((|ResidueRing| . |CoercibleFrom|) 191291) ((|ResidueRing| . |Rng|) T) ((|ResidueRing| . |SemiGroup|) T) ((|ResidueRing| . |SemiRing|) T) ((|ResidueRing| . |Monoid|) T) ((|ResidueRing| . |Ring|) T) ((|ResidueRing| . |LeftModule|) 191265) ((|ResidueRing| . |LeftLinearSet|) 191219) ((|ResidueRing| . |CancellationAbelianMonoid|) T) ((|ResidueRing| . |AbelianSemiGroup|) T) ((|ResidueRing| . |BasicType|) T) ((|ResidueRing| . |Join|) T) ((|ResidueRing| . |Type|) T) ((|ResidueRing| . |CoercibleTo|) 191193) ((|ResidueRing| . |SetCategory|) T) ((|ResidueRing| . |AbelianMonoid|) T) ((|ResidueRing| . |AbelianGroup|) T) ((|ResidueRing| . |RightModule|) 191167) ((|ResidueRing| . |RightLinearSet|) 191141) ((|ResidueRing| . |BiModule|) 191108) ((|ResidueRing| . |Algebra|) 191092) ((|ResidueRing| . |LinearSet|) 191076) ((|ResidueRing| . |Module|) 191060) ((|RegularTriangularSet| . |RegularTriangularSetCategory|) 191029) ((|RegularTriangularSet| . |PolynomialSetCategory|) 190998) ((|RegularTriangularSet| . |FiniteAggregate|) 190982) ((|RegularTriangularSet| . |ConvertibleTo|) 190918) ((|RegularTriangularSet| . |HomogeneousAggregate|) 190902) ((|RegularTriangularSet| . |SetCategory|) T) ((|RegularTriangularSet| . |Functorial|) 190886) ((|RegularTriangularSet| . |InnerEvalable|) 190805) ((|RegularTriangularSet| . |Evalable|) 190729) ((|RegularTriangularSet| . |CoercibleTo|) 190681) ((|RegularTriangularSet| . |BasicType|) T) ((|RegularTriangularSet| . |Type|) T) ((|RegularTriangularSet| . |Join|) T) ((|RegularTriangularSet| . |Aggregate|) T) ((|RegularTriangularSet| . |Collection|) 190665) ((|RegularTriangularSet| . |ShallowlyMutableAggregate|) 190649) ((|RegularTriangularSet| . |TriangularSetCategory|) 190618) ((|Reference| . |SetCategory|) T) ((|Reference| . |CoercibleTo|) 190592) ((|Reference| . |Type|) T) ((|Reference| . |Join|) T) ((|Reference| . |BasicType|) T) ((|RealClosure| . |RealClosedField|) T) ((|RealClosure| . |RadicalCategory|) T) ((|RealClosure| . |OrderedAbelianGroup|) T) ((|RealClosure| . |OrderedAbelianMonoid|) T) ((|RealClosure| . |OrderedSet|) T) ((|RealClosure| . |OrderedType|) T) ((|RealClosure| . |OrderedAbelianSemiGroup|) T) ((|RealClosure| . |OrderedCancellationAbelianMonoid|) T) ((|RealClosure| . |OrderedRing|) T) ((|RealClosure| . |RetractableTo|) 190418) ((|RealClosure| . |FullyRetractableTo|) 190369) ((|RealClosure| . |DivisionRing|) T) ((|RealClosure| . |EntireRing|) T) ((|RealClosure| . |EuclideanDomain|) T) ((|RealClosure| . |GcdDomain|) T) ((|RealClosure| . |Algebra|) 190290) ((|RealClosure| . |LinearSet|) 190211) ((|RealClosure| . |Module|) 190132) ((|RealClosure| . |CoercibleFrom|) 190053) ((|RealClosure| . |IntegralDomain|) T) ((|RealClosure| . |PrincipalIdealDomain|) T) ((|RealClosure| . |UniqueFactorizationDomain|) T) ((|RealClosure| . |Field|) T) ((|RealClosure| . |BiModule|) 189953) ((|RealClosure| . |RightLinearSet|) 189874) ((|RealClosure| . |RightModule|) 189795) ((|RealClosure| . |CommutativeRing|) T) ((|RealClosure| . |CharacteristicZero|) T) ((|RealClosure| . |LeftModule|) 189716) ((|RealClosure| . |LeftLinearSet|) 189637) ((|RealClosure| . |CancellationAbelianMonoid|) T) ((|RealClosure| . |AbelianSemiGroup|) T) ((|RealClosure| . |BasicType|) T) ((|RealClosure| . |Join|) T) ((|RealClosure| . |Type|) T) ((|RealClosure| . |CoercibleTo|) 189611) ((|RealClosure| . |SetCategory|) T) ((|RealClosure| . |AbelianMonoid|) T) ((|RealClosure| . |AbelianGroup|) T) ((|RealClosure| . |Ring|) T) ((|RealClosure| . |Monoid|) T) ((|RealClosure| . |SemiRing|) T) ((|RealClosure| . |SemiGroup|) T) ((|RealClosure| . |Rng|) T) ((|ReduceAst| . |SpadSyntaxCategory|) T) ((|ReduceAst| . |HomotopicTo|) 189589) ((|ReduceAst| . |CoercibleTo|) 189544) ((|ReduceAst| . |CoercibleFrom|) 189522) ((|ReduceAst| . |SetCategory|) T) ((|ReduceAst| . |Type|) T) ((|ReduceAst| . |Join|) T) ((|ReduceAst| . |BasicType|) T) ((|ReduceAst| . |AbstractSyntaxCategory|) T) ((|RadixExpansion| . |QuotientFieldCategory|) 189499) ((|RadixExpansion| . |StepThrough|) T) ((|RadixExpansion| . |CoercibleFrom|) 189433) ((|RadixExpansion| . |RetractableTo|) 189377) ((|RadixExpansion| . |ConvertibleTo|) 189278) ((|RadixExpansion| . |RealConstant|) T) ((|RadixExpansion| . |PolynomialFactorizationExplicit|) NIL) ((|RadixExpansion| . |Patternable|) 189255) ((|RadixExpansion| . |OrderedRing|) T) ((|RadixExpansion| . |OrderedCancellationAbelianMonoid|) T) ((|RadixExpansion| . |OrderedAbelianSemiGroup|) T) ((|RadixExpansion| . |OrderedType|) T) ((|RadixExpansion| . |OrderedSet|) T) ((|RadixExpansion| . |OrderedAbelianMonoid|) T) ((|RadixExpansion| . |OrderedAbelianGroup|) T) ((|RadixExpansion| . |OrderedIntegralDomain|) T) ((|RadixExpansion| . |PatternMatchable|) 189232) ((|RadixExpansion| . |FullyPatternMatchable|) 189209) ((|RadixExpansion| . |LinearlyExplicitRingOver|) 189186) ((|RadixExpansion| . |FullyLinearlyExplicitRingOver|) 189163) ((|RadixExpansion| . |Eltable|) NIL) ((|RadixExpansion| . |Evalable|) NIL) ((|RadixExpansion| . |InnerEvalable|) NIL) ((|RadixExpansion| . |Functorial|) 189140) ((|RadixExpansion| . |FullyEvalableOver|) 189117) ((|RadixExpansion| . |DivisionRing|) T) ((|RadixExpansion| . |BiModule|) 189035) ((|RadixExpansion| . |RightLinearSet|) 188969) ((|RadixExpansion| . |RightModule|) 188903) ((|RadixExpansion| . |EntireRing|) T) ((|RadixExpansion| . |Module|) 188837) ((|RadixExpansion| . |LinearSet|) 188771) ((|RadixExpansion| . |LeftModule|) 188705) ((|RadixExpansion| . |LeftLinearSet|) 188639) ((|RadixExpansion| . |Algebra|) 188573) ((|RadixExpansion| . |EuclideanDomain|) T) ((|RadixExpansion| . |GcdDomain|) T) ((|RadixExpansion| . |CommutativeRing|) T) ((|RadixExpansion| . |IntegralDomain|) T) ((|RadixExpansion| . |PrincipalIdealDomain|) T) ((|RadixExpansion| . |UniqueFactorizationDomain|) T) ((|RadixExpansion| . |Field|) T) ((|RadixExpansion| . |DifferentialRing|) T) ((|RadixExpansion| . |DifferentialDomain|) 188560) ((|RadixExpansion| . |DifferentialSpace|) T) ((|RadixExpansion| . |DifferentialSpaceExtension|) 188537) ((|RadixExpansion| . |PartialDifferentialDomain|) NIL) ((|RadixExpansion| . |PartialDifferentialSpace|) NIL) ((|RadixExpansion| . |PartialDifferentialRing|) NIL) ((|RadixExpansion| . |DifferentialExtension|) 188514) ((|RadixExpansion| . |CharacteristicZero|) T) ((|RadixExpansion| . |CharacteristicNonZero|) NIL) ((|RadixExpansion| . |CancellationAbelianMonoid|) T) ((|RadixExpansion| . |AbelianSemiGroup|) T) ((|RadixExpansion| . |BasicType|) T) ((|RadixExpansion| . |Join|) T) ((|RadixExpansion| . |Type|) T) ((|RadixExpansion| . |CoercibleTo|) 188455) ((|RadixExpansion| . |SetCategory|) T) ((|RadixExpansion| . |AbelianMonoid|) T) ((|RadixExpansion| . |AbelianGroup|) T) ((|RadixExpansion| . |Ring|) T) ((|RadixExpansion| . |Monoid|) T) ((|RadixExpansion| . |SemiRing|) T) ((|RadixExpansion| . |SemiGroup|) T) ((|RadixExpansion| . |Rng|) T) ((|RadicalFunctionField| . |FunctionFieldCategory|) 188429) ((|RadicalFunctionField| . |CommutativeRing|) T) ((|RadicalFunctionField| . |CoercibleFrom|) 188337) ((|RadicalFunctionField| . |Rng|) T) ((|RadicalFunctionField| . |SemiGroup|) T) ((|RadicalFunctionField| . |SemiRing|) T) ((|RadicalFunctionField| . |Monoid|) T) ((|RadicalFunctionField| . |Ring|) T) ((|RadicalFunctionField| . |LeftModule|) 188195) ((|RadicalFunctionField| . |LeftLinearSet|) 188103) ((|RadicalFunctionField| . |CancellationAbelianMonoid|) T) ((|RadicalFunctionField| . |AbelianSemiGroup|) T) ((|RadicalFunctionField| . |BasicType|) T) ((|RadicalFunctionField| . |Join|) T) ((|RadicalFunctionField| . |Type|) T) ((|RadicalFunctionField| . |CoercibleTo|) 188077) ((|RadicalFunctionField| . |SetCategory|) T) ((|RadicalFunctionField| . |AbelianMonoid|) T) ((|RadicalFunctionField| . |AbelianGroup|) T) ((|RadicalFunctionField| . |RightModule|) 188005) ((|RadicalFunctionField| . |RightLinearSet|) 187933) ((|RadicalFunctionField| . |BiModule|) 187845) ((|RadicalFunctionField| . |ConvertibleTo|) 187829) ((|RadicalFunctionField| . |DifferentialExtension|) 187800) ((|RadicalFunctionField| . |PartialDifferentialRing|) 187719) ((|RadicalFunctionField| . |PartialDifferentialSpace|) 187567) ((|RadicalFunctionField| . |PartialDifferentialDomain|) 187413) ((|RadicalFunctionField| . |DifferentialSpaceExtension|) 187384) ((|RadicalFunctionField| . |DifferentialSpace|) 187283) ((|RadicalFunctionField| . |DifferentialDomain|) 187176) ((|RadicalFunctionField| . |DifferentialRing|) 187128) ((|RadicalFunctionField| . |Field|) T) ((|RadicalFunctionField| . |UniqueFactorizationDomain|) T) ((|RadicalFunctionField| . |PrincipalIdealDomain|) T) ((|RadicalFunctionField| . |IntegralDomain|) T) ((|RadicalFunctionField| . |Module|) 187056) ((|RadicalFunctionField| . |LinearSet|) 186984) ((|RadicalFunctionField| . |Algebra|) 186912) ((|RadicalFunctionField| . |GcdDomain|) T) ((|RadicalFunctionField| . |EuclideanDomain|) T) ((|RadicalFunctionField| . |EntireRing|) T) ((|RadicalFunctionField| . |DivisionRing|) T) ((|RadicalFunctionField| . |Finite|) NIL) ((|RadicalFunctionField| . |FiniteFieldCategory|) NIL) ((|RadicalFunctionField| . |StepThrough|) NIL) ((|RadicalFunctionField| . |CharacteristicNonZero|) 186859) ((|RadicalFunctionField| . |FieldOfPrimeCharacteristic|) NIL) ((|RadicalFunctionField| . |FramedAlgebra|) 186825) ((|RadicalFunctionField| . |CharacteristicZero|) 186775) ((|RadicalFunctionField| . |FiniteRankAlgebra|) 186741) ((|RadicalFunctionField| . |FullyLinearlyExplicitRingOver|) 186712) ((|RadicalFunctionField| . |LinearlyExplicitRingOver|) 186613) ((|RadicalFunctionField| . |FullyRetractableTo|) 186584) ((|RadicalFunctionField| . |RetractableTo|) 186414) ((|RadicalFunctionField| . |MonogenicAlgebra|) 186380) ((|Queue| . |QueueAggregate|) 186364) ((|Queue| . |FiniteAggregate|) 186348) ((|Queue| . |HomogeneousAggregate|) 186332) ((|Queue| . |SetCategory|) 186302) ((|Queue| . |Functorial|) 186286) ((|Queue| . |InnerEvalable|) 186205) ((|Queue| . |Evalable|) 186129) ((|Queue| . |CoercibleTo|) 186031) ((|Queue| . |BasicType|) 185969) ((|Queue| . |Type|) T) ((|Queue| . |Join|) T) ((|Queue| . |Aggregate|) T) ((|Queue| . |ShallowlyMutableAggregate|) 185953) ((|Queue| . |BagAggregate|) 185937) ((|Quaternion| . |QuaternionCategory|) 185921) ((|Quaternion| . |OrderedType|) 185892) ((|Quaternion| . |OrderedSet|) 185863) ((|Quaternion| . |RetractableTo|) 185707) ((|Quaternion| . |FullyRetractableTo|) 185691) ((|Quaternion| . |LinearlyExplicitRingOver|) 185607) ((|Quaternion| . |LeftModule|) 185463) ((|Quaternion| . |FullyLinearlyExplicitRingOver|) 185447) ((|Quaternion| . |Eltable|) 185400) ((|Quaternion| . |Evalable|) 185359) ((|Quaternion| . |InnerEvalable|) 185248) ((|Quaternion| . |Functorial|) 185232) ((|Quaternion| . |FullyEvalableOver|) 185216) ((|Quaternion| . |Algebra|) 185150) ((|Quaternion| . |BiModule|) 185010) ((|Quaternion| . |RightLinearSet|) 184884) ((|Quaternion| . |RightModule|) 184758) ((|Quaternion| . |LeftLinearSet|) 184662) ((|Quaternion| . |LinearSet|) 184596) ((|Quaternion| . |Module|) 184530) ((|Quaternion| . |CoercibleFrom|) 184383) ((|Quaternion| . |EntireRing|) 184326) ((|Quaternion| . |DivisionRing|) 184302) ((|Quaternion| . |DifferentialRing|) 184267) ((|Quaternion| . |DifferentialDomain|) 184186) ((|Quaternion| . |DifferentialSpace|) 184111) ((|Quaternion| . |DifferentialSpaceExtension|) 184095) ((|Quaternion| . |PartialDifferentialDomain|) 183967) ((|Quaternion| . |PartialDifferentialSpace|) 183841) ((|Quaternion| . |PartialDifferentialRing|) 183773) ((|Quaternion| . |DifferentialExtension|) 183757) ((|Quaternion| . |ConvertibleTo|) 183693) ((|Quaternion| . |CharacteristicZero|) 183656) ((|Quaternion| . |CharacteristicNonZero|) 183616) ((|Quaternion| . |CancellationAbelianMonoid|) T) ((|Quaternion| . |AbelianSemiGroup|) T) ((|Quaternion| . |BasicType|) T) ((|Quaternion| . |Join|) T) ((|Quaternion| . |Type|) T) ((|Quaternion| . |CoercibleTo|) 183590) ((|Quaternion| . |SetCategory|) T) ((|Quaternion| . |AbelianMonoid|) T) ((|Quaternion| . |AbelianGroup|) T) ((|Quaternion| . |Ring|) T) ((|Quaternion| . |Monoid|) T) ((|Quaternion| . |SemiRing|) T) ((|Quaternion| . |SemiGroup|) T) ((|Quaternion| . |Rng|) T) ((|QuasiquoteAst| . |SpadSyntaxCategory|) T) ((|QuasiquoteAst| . |HomotopicTo|) 183568) ((|QuasiquoteAst| . |CoercibleTo|) 183523) ((|QuasiquoteAst| . |CoercibleFrom|) 183501) ((|QuasiquoteAst| . |SetCategory|) T) ((|QuasiquoteAst| . |Type|) T) ((|QuasiquoteAst| . |Join|) T) ((|QuasiquoteAst| . |BasicType|) T) ((|QuasiquoteAst| . |AbstractSyntaxCategory|) T) ((|QuadraticForm| . |AbelianGroup|) T) ((|QuadraticForm| . |LeftLinearSet|) 183478) ((|QuadraticForm| . |AbelianMonoid|) T) ((|QuadraticForm| . |SetCategory|) T) ((|QuadraticForm| . |CoercibleTo|) 183452) ((|QuadraticForm| . |Type|) T) ((|QuadraticForm| . |Join|) T) ((|QuadraticForm| . |BasicType|) T) ((|QuadraticForm| . |AbelianSemiGroup|) T) ((|QuadraticForm| . |CancellationAbelianMonoid|) T) ((|QuadraticForm| . |Eltable|) 183408) ((|QueryEquation| . |CoercibleTo|) 183382) ((|QuasiAlgebraicSet| . |SetCategory|) T) ((|QuasiAlgebraicSet| . |CoercibleTo|) 183356) ((|QuasiAlgebraicSet| . |Type|) T) ((|QuasiAlgebraicSet| . |Join|) T) ((|QuasiAlgebraicSet| . |BasicType|) T) ((|Partition| . |OrderedCancellationAbelianMonoid|) T) ((|Partition| . |OrderedAbelianSemiGroup|) T) ((|Partition| . |OrderedType|) T) ((|Partition| . |OrderedSet|) T) ((|Partition| . |OrderedAbelianMonoid|) T) ((|Partition| . |AbelianMonoid|) T) ((|Partition| . |SetCategory|) T) ((|Partition| . |CoercibleTo|) 183293) ((|Partition| . |Type|) T) ((|Partition| . |Join|) T) ((|Partition| . |BasicType|) T) ((|Partition| . |AbelianSemiGroup|) T) ((|Partition| . |CancellationAbelianMonoid|) T) ((|PretendAst| . |SpadSyntaxCategory|) T) ((|PretendAst| . |HomotopicTo|) 183271) ((|PretendAst| . |CoercibleTo|) 183226) ((|PretendAst| . |CoercibleFrom|) 183204) ((|PretendAst| . |SetCategory|) T) ((|PretendAst| . |Type|) T) ((|PretendAst| . |Join|) T) ((|PretendAst| . |BasicType|) T) ((|PretendAst| . |AbstractSyntaxCategory|) T) ((|PropositionalFormula| . |PropositionalLogic|) T) ((|PropositionalFormula| . |BasicType|) T) ((|PropositionalFormula| . |CoercibleTo|) 183178) ((|PropositionalFormula| . |SetCategory|) T) ((|PropositionalFormula| . |Logic|) T) ((|PropositionalFormula| . |Join|) T) ((|PropositionalFormula| . |Type|) T) ((|PropositionalFormula| . |BooleanLogic|) T) ((|PropositionalFormula| . |CoercibleFrom|) 183162) ((|Property| . |CoercibleTo|) 183136) ((|Product| . |SetCategory|) T) ((|Product| . |CoercibleTo|) 183110) ((|Product| . |Type|) T) ((|Product| . |Join|) T) ((|Product| . |BasicType|) T) ((|Product| . |Finite|) 183055) ((|Product| . |Monoid|) 182943) ((|Product| . |SemiGroup|) 182831) ((|Product| . |AbelianMonoid|) 182511) ((|Product| . |AbelianSemiGroup|) 182191) ((|Product| . |CancellationAbelianMonoid|) 181939) ((|Product| . |Group|) 181886) ((|Product| . |AbelianGroup|) 181819) ((|Product| . |LeftLinearSet|) 181736) ((|Product| . |OrderedAbelianMonoidSup|) 181647) ((|Product| . |OrderedAbelianMonoid|) 181558) ((|Product| . |OrderedSet|) 181402) ((|Product| . |OrderedType|) 181246) ((|Product| . |OrderedAbelianSemiGroup|) 181157) ((|Product| . |OrderedCancellationAbelianMonoid|) 181068) ((|PrimitiveArray| . |OneDimensionalArrayAggregate|) 181052) ((|PrimitiveArray| . |ShallowlyMutableAggregate|) 181036) ((|PrimitiveArray| . |FiniteAggregate|) 181020) ((|PrimitiveArray| . |Aggregate|) T) ((|PrimitiveArray| . |Join|) T) ((|PrimitiveArray| . |Type|) T) ((|PrimitiveArray| . |BasicType|) 180930) ((|PrimitiveArray| . |CoercibleTo|) 180804) ((|PrimitiveArray| . |Evalable|) 180728) ((|PrimitiveArray| . |InnerEvalable|) 180647) ((|PrimitiveArray| . |Functorial|) 180631) ((|PrimitiveArray| . |SetCategory|) 180568) ((|PrimitiveArray| . |HomogeneousAggregate|) 180552) ((|PrimitiveArray| . |LinearAggregate|) 180536) ((|PrimitiveArray| . |EltableAggregate|) 180508) ((|PrimitiveArray| . |Eltable|) 180437) ((|PrimitiveArray| . |IndexedAggregate|) 180409) ((|PrimitiveArray| . |ConvertibleTo|) 180345) ((|PrimitiveArray| . |Collection|) 180329) ((|PrimitiveArray| . |OrderedSet|) 180300) ((|PrimitiveArray| . |OrderedType|) 180271) ((|PrimitiveArray| . |FiniteLinearAggregate|) 180255) ((|PolynomialRing| . |FiniteAbelianMonoidRing|) 180234) ((|PolynomialRing| . |RetractableTo|) 180078) ((|PolynomialRing| . |FullyRetractableTo|) 180062) ((|PolynomialRing| . |Algebra|) 179906) ((|PolynomialRing| . |CoercibleFrom|) 179696) ((|PolynomialRing| . |LeftModule|) 179593) ((|PolynomialRing| . |LeftLinearSet|) 179470) ((|PolynomialRing| . |Rng|) T) ((|PolynomialRing| . |SemiGroup|) T) ((|PolynomialRing| . |SemiRing|) T) ((|PolynomialRing| . |Monoid|) T) ((|PolynomialRing| . |Ring|) T) ((|PolynomialRing| . |BiModule|) 179289) ((|PolynomialRing| . |RightLinearSet|) 179122) ((|PolynomialRing| . |RightModule|) 178955) ((|PolynomialRing| . |AbelianGroup|) T) ((|PolynomialRing| . |AbelianMonoid|) T) ((|PolynomialRing| . |SetCategory|) T) ((|PolynomialRing| . |CoercibleTo|) 178929) ((|PolynomialRing| . |Type|) T) ((|PolynomialRing| . |Join|) T) ((|PolynomialRing| . |BasicType|) T) ((|PolynomialRing| . |AbelianSemiGroup|) T) ((|PolynomialRing| . |CancellationAbelianMonoid|) T) ((|PolynomialRing| . |LinearSet|) 178773) ((|PolynomialRing| . |Module|) 178617) ((|PolynomialRing| . |CharacteristicNonZero|) 178577) ((|PolynomialRing| . |CharacteristicZero|) 178540) ((|PolynomialRing| . |CommutativeRing|) 178469) ((|PolynomialRing| . |Functorial|) 178453) ((|PolynomialRing| . |IntegralDomain|) 178420) ((|PolynomialRing| . |EntireRing|) 178387) ((|PolynomialRing| . |AbelianMonoidRing|) 178366) ((|PortNumber| . |SetCategory|) T) ((|PortNumber| . |CoercibleTo|) 178314) ((|PortNumber| . |Type|) T) ((|PortNumber| . |Join|) T) ((|PortNumber| . |BasicType|) T) ((|Polynomial| . |PolynomialCategory|) 178259) ((|Polynomial| . |CoercibleFrom|) 177949) ((|Polynomial| . |RetractableTo|) 177774) ((|Polynomial| . |UniqueFactorizationDomain|) 177724) ((|Polynomial| . |PolynomialFactorizationExplicit|) 177674) ((|Polynomial| . |PatternMatchable|) 177555) ((|Polynomial| . |PartialDifferentialSpace|) 177533) ((|Polynomial| . |PartialDifferentialDomain|) 177509) ((|Polynomial| . |PartialDifferentialRing|) 177487) ((|Polynomial| . |InnerEvalable|) 177431) ((|Polynomial| . |GcdDomain|) 177349) ((|Polynomial| . |LinearlyExplicitRingOver|) 177265) ((|Polynomial| . |LeftModule|) 177094) ((|Polynomial| . |FullyLinearlyExplicitRingOver|) 177078) ((|Polynomial| . |AbelianMonoidRing|) 177030) ((|Polynomial| . |Algebra|) 176793) ((|Polynomial| . |LinearSet|) 176556) ((|Polynomial| . |Module|) 176319) ((|Polynomial| . |EntireRing|) 176205) ((|Polynomial| . |IntegralDomain|) 176091) ((|Polynomial| . |Functorial|) 176075) ((|Polynomial| . |BiModule|) 175818) ((|Polynomial| . |RightLinearSet|) 175575) ((|Polynomial| . |RightModule|) 175332) ((|Polynomial| . |CommutativeRing|) 175185) ((|Polynomial| . |CharacteristicZero|) 175148) ((|Polynomial| . |CharacteristicNonZero|) 175108) ((|Polynomial| . |LeftLinearSet|) 174985) ((|Polynomial| . |CancellationAbelianMonoid|) T) ((|Polynomial| . |AbelianSemiGroup|) T) ((|Polynomial| . |BasicType|) T) ((|Polynomial| . |Join|) T) ((|Polynomial| . |Type|) T) ((|Polynomial| . |CoercibleTo|) 174959) ((|Polynomial| . |SetCategory|) T) ((|Polynomial| . |AbelianMonoid|) T) ((|Polynomial| . |AbelianGroup|) T) ((|Polynomial| . |Ring|) T) ((|Polynomial| . |Monoid|) T) ((|Polynomial| . |SemiRing|) T) ((|Polynomial| . |SemiGroup|) T) ((|Polynomial| . |Rng|) T) ((|Polynomial| . |FullyRetractableTo|) 174943) ((|Polynomial| . |FiniteAbelianMonoidRing|) 174895) ((|Polynomial| . |Evalable|) 174882) ((|Polynomial| . |ConvertibleTo|) 174660) ((|Point| . |PointCategory|) 174644) ((|Point| . |OneDimensionalArrayAggregate|) 174628) ((|Point| . |ShallowlyMutableAggregate|) 174612) ((|Point| . |FiniteAggregate|) 174596) ((|Point| . |Aggregate|) T) ((|Point| . |Join|) T) ((|Point| . |Type|) T) ((|Point| . |BasicType|) 174506) ((|Point| . |CoercibleTo|) 174380) ((|Point| . |Evalable|) 174304) ((|Point| . |InnerEvalable|) 174223) ((|Point| . |Functorial|) 174207) ((|Point| . |SetCategory|) 174144) ((|Point| . |HomogeneousAggregate|) 174128) ((|Point| . |LinearAggregate|) 174112) ((|Point| . |EltableAggregate|) 174084) ((|Point| . |Eltable|) 174013) ((|Point| . |IndexedAggregate|) 173985) ((|Point| . |ConvertibleTo|) 173921) ((|Point| . |Collection|) 173905) ((|Point| . |OrderedSet|) 173876) ((|Point| . |OrderedType|) 173847) ((|Point| . |FiniteLinearAggregate|) 173831) ((|Point| . |VectorCategory|) 173815) ((|Point| . |ConvertibleFrom|) 173790) ((|Plot3D| . |PlottableSpaceCurveCategory|) T) ((|Plot3D| . |CoercibleTo|) 173764) ((|Plot| . |PlottablePlaneCurveCategory|) T) ((|Plot| . |CoercibleTo|) 173738) ((|PositiveInteger| . |OrderedAbelianSemiGroup|) T) ((|PositiveInteger| . |OrderedType|) T) ((|PositiveInteger| . |OrderedSet|) T) ((|PositiveInteger| . |SetCategory|) T) ((|PositiveInteger| . |CoercibleTo|) 173712) ((|PositiveInteger| . |Type|) T) ((|PositiveInteger| . |Join|) T) ((|PositiveInteger| . |BasicType|) T) ((|PositiveInteger| . |AbelianSemiGroup|) T) ((|PositiveInteger| . |Monoid|) T) ((|PositiveInteger| . |SemiGroup|) T) ((|PartialFraction| . |Field|) T) ((|PartialFraction| . |UniqueFactorizationDomain|) T) ((|PartialFraction| . |PrincipalIdealDomain|) T) ((|PartialFraction| . |IntegralDomain|) T) ((|PartialFraction| . |CommutativeRing|) T) ((|PartialFraction| . |CoercibleFrom|) 173633) ((|PartialFraction| . |Module|) 173574) ((|PartialFraction| . |LinearSet|) 173515) ((|PartialFraction| . |Algebra|) 173456) ((|PartialFraction| . |GcdDomain|) T) ((|PartialFraction| . |EuclideanDomain|) T) ((|PartialFraction| . |LeftModule|) 173397) ((|PartialFraction| . |LeftLinearSet|) 173318) ((|PartialFraction| . |Rng|) T) ((|PartialFraction| . |SemiGroup|) T) ((|PartialFraction| . |SemiRing|) T) ((|PartialFraction| . |Monoid|) T) ((|PartialFraction| . |Ring|) T) ((|PartialFraction| . |BiModule|) 173245) ((|PartialFraction| . |RightLinearSet|) 173186) ((|PartialFraction| . |RightModule|) 173127) ((|PartialFraction| . |AbelianGroup|) T) ((|PartialFraction| . |AbelianMonoid|) T) ((|PartialFraction| . |SetCategory|) T) ((|PartialFraction| . |CoercibleTo|) 173075) ((|PartialFraction| . |Type|) T) ((|PartialFraction| . |Join|) T) ((|PartialFraction| . |BasicType|) T) ((|PartialFraction| . |AbelianSemiGroup|) T) ((|PartialFraction| . |CancellationAbelianMonoid|) T) ((|PartialFraction| . |EntireRing|) T) ((|PartialFraction| . |DivisionRing|) T) ((|PrimeField| . |FiniteFieldCategory|) T) ((|PrimeField| . |StepThrough|) T) ((|PrimeField| . |Finite|) T) ((|PrimeField| . |CharacteristicNonZero|) T) ((|PrimeField| . |Field|) T) ((|PrimeField| . |UniqueFactorizationDomain|) T) ((|PrimeField| . |PrincipalIdealDomain|) T) ((|PrimeField| . |IntegralDomain|) T) ((|PrimeField| . |CommutativeRing|) T) ((|PrimeField| . |CoercibleFrom|) 173009) ((|PrimeField| . |Module|) 172963) ((|PrimeField| . |LinearSet|) 172917) ((|PrimeField| . |Algebra|) 172871) ((|PrimeField| . |GcdDomain|) T) ((|PrimeField| . |EuclideanDomain|) T) ((|PrimeField| . |BiModule|) 172816) ((|PrimeField| . |RightLinearSet|) 172770) ((|PrimeField| . |RightModule|) 172724) ((|PrimeField| . |LeftLinearSet|) 172658) ((|PrimeField| . |LeftModule|) 172612) ((|PrimeField| . |EntireRing|) T) ((|PrimeField| . |DivisionRing|) T) ((|PrimeField| . |FieldOfPrimeCharacteristic|) T) ((|PrimeField| . |DifferentialSpace|) T) ((|PrimeField| . |Type|) T) ((|PrimeField| . |Join|) T) ((|PrimeField| . |DifferentialDomain|) 172599) ((|PrimeField| . |Ring|) T) ((|PrimeField| . |Monoid|) T) ((|PrimeField| . |SemiRing|) T) ((|PrimeField| . |SemiGroup|) T) ((|PrimeField| . |Rng|) T) ((|PrimeField| . |AbelianGroup|) T) ((|PrimeField| . |AbelianMonoid|) T) ((|PrimeField| . |SetCategory|) T) ((|PrimeField| . |CoercibleTo|) 172573) ((|PrimeField| . |BasicType|) T) ((|PrimeField| . |AbelianSemiGroup|) T) ((|PrimeField| . |CancellationAbelianMonoid|) T) ((|PrimeField| . |DifferentialRing|) T) ((|PrimeField| . |FiniteAlgebraicExtensionField|) 172560) ((|PrimeField| . |CharacteristicZero|) 172526) ((|PrimeField| . |RetractableTo|) 172513) ((|PrimeField| . |VectorSpace|) 172500) ((|PrimeField| . |ExtensionField|) 172487) ((|PrimeField| . |ConvertibleTo|) 172464) ((|PermutationGroup| . |SetCategory|) T) ((|PermutationGroup| . |CoercibleTo|) 172400) ((|PermutationGroup| . |Type|) T) ((|PermutationGroup| . |Join|) T) ((|PermutationGroup| . |BasicType|) T) ((|PermutationGroup| . |HomotopicTo|) 172359) ((|PermutationGroup| . |CoercibleFrom|) 172318) ((|Permutation| . |PermutationCategory|) 172302) ((|Permutation| . |OrderedType|) 172244) ((|Permutation| . |OrderedSet|) 172186) ((|Permutation| . |Monoid|) T) ((|Permutation| . |SetCategory|) T) ((|Permutation| . |CoercibleTo|) 172160) ((|Permutation| . |BasicType|) T) ((|Permutation| . |SemiGroup|) T) ((|Permutation| . |Group|) T) ((|Permutation| . |Type|) T) ((|Permutation| . |Join|) T) ((|Permutation| . |Eltable|) 172139) ((|PendantTree| . |BinaryRecursiveAggregate|) 172123) ((|PendantTree| . |HomogeneousAggregate|) 172107) ((|PendantTree| . |SetCategory|) 172077) ((|PendantTree| . |Functorial|) 172061) ((|PendantTree| . |InnerEvalable|) 171980) ((|PendantTree| . |Evalable|) 171904) ((|PendantTree| . |CoercibleTo|) 171784) ((|PendantTree| . |BasicType|) 171722) ((|PendantTree| . |Type|) T) ((|PendantTree| . |Join|) T) ((|PendantTree| . |Aggregate|) T) ((|PendantTree| . |RecursiveAggregate|) 171706) ((|PoincareBirkhoffWittLyndonBasis| . |OrderedSet|) T) ((|PoincareBirkhoffWittLyndonBasis| . |CoercibleTo|) 171645) ((|PoincareBirkhoffWittLyndonBasis| . |SetCategory|) T) ((|PoincareBirkhoffWittLyndonBasis| . |BasicType|) T) ((|PoincareBirkhoffWittLyndonBasis| . |Join|) T) ((|PoincareBirkhoffWittLyndonBasis| . |Type|) T) ((|PoincareBirkhoffWittLyndonBasis| . |OrderedType|) T) ((|PoincareBirkhoffWittLyndonBasis| . |RetractableTo|) 171614) ((|PoincareBirkhoffWittLyndonBasis| . |CoercibleFrom|) 171583) ((|Pattern| . |SetCategory|) T) ((|Pattern| . |CoercibleTo|) 171557) ((|Pattern| . |Type|) T) ((|Pattern| . |Join|) T) ((|Pattern| . |BasicType|) T) ((|Pattern| . |RetractableTo|) 171522) ((|Pattern| . |CoercibleFrom|) 171487) ((|PatternMatchResult| . |SetCategory|) T) ((|PatternMatchResult| . |CoercibleTo|) 171461) ((|PatternMatchResult| . |Type|) T) ((|PatternMatchResult| . |Join|) T) ((|PatternMatchResult| . |BasicType|) T) ((|PatternMatchListResult| . |SetCategory|) T) ((|PatternMatchListResult| . |CoercibleTo|) 171435) ((|PatternMatchListResult| . |Type|) T) ((|PatternMatchListResult| . |Join|) T) ((|PatternMatchListResult| . |BasicType|) T) ((|ParameterAst| . |SpadSyntaxCategory|) T) ((|ParameterAst| . |HomotopicTo|) 171413) ((|ParameterAst| . |CoercibleTo|) 171368) ((|ParameterAst| . |CoercibleFrom|) 171346) ((|ParameterAst| . |SetCategory|) T) ((|ParameterAst| . |Type|) T) ((|ParameterAst| . |Join|) T) ((|ParameterAst| . |BasicType|) T) ((|ParameterAst| . |AbstractSyntaxCategory|) T) ((|ParameterAst| . |UnionType|) T) ((|Palette| . |SetCategory|) T) ((|Palette| . |CoercibleTo|) 171320) ((|Palette| . |Type|) T) ((|Palette| . |Join|) T) ((|Palette| . |BasicType|) T) ((|Palette| . |CoercibleFrom|) 171299) ((|Pair| . |Type|) T) ((|Pair| . |Join|) T) ((|Pair| . |CoercibleTo|) 171116) ((|Pair| . |SetCategory|) 171051) ((|Pair| . |BasicType|) 170986) ((|PAdicRationalConstructor| . |QuotientFieldCategory|) 170970) ((|PAdicRationalConstructor| . |StepThrough|) 170940) ((|PAdicRationalConstructor| . |RetractableTo|) 170759) ((|PAdicRationalConstructor| . |CoercibleFrom|) 170625) ((|PAdicRationalConstructor| . |ConvertibleTo|) 170328) ((|PAdicRationalConstructor| . |RealConstant|) 170297) ((|PAdicRationalConstructor| . |PolynomialFactorizationExplicit|) 170247) ((|PAdicRationalConstructor| . |Patternable|) 170231) ((|PAdicRationalConstructor| . |OrderedRing|) 170191) ((|PAdicRationalConstructor| . |OrderedCancellationAbelianMonoid|) 170151) ((|PAdicRationalConstructor| . |OrderedAbelianSemiGroup|) 170111) ((|PAdicRationalConstructor| . |OrderedType|) 170038) ((|PAdicRationalConstructor| . |OrderedSet|) 169965) ((|PAdicRationalConstructor| . |OrderedAbelianMonoid|) 169925) ((|PAdicRationalConstructor| . |OrderedAbelianGroup|) 169885) ((|PAdicRationalConstructor| . |OrderedIntegralDomain|) 169845) ((|PAdicRationalConstructor| . |PatternMatchable|) 169726) ((|PAdicRationalConstructor| . |FullyPatternMatchable|) 169710) ((|PAdicRationalConstructor| . |LinearlyExplicitRingOver|) 169626) ((|PAdicRationalConstructor| . |LeftModule|) 169499) ((|PAdicRationalConstructor| . |FullyLinearlyExplicitRingOver|) 169483) ((|PAdicRationalConstructor| . |Eltable|) 169436) ((|PAdicRationalConstructor| . |Evalable|) 169395) ((|PAdicRationalConstructor| . |InnerEvalable|) 169284) ((|PAdicRationalConstructor| . |Functorial|) 169268) ((|PAdicRationalConstructor| . |FullyEvalableOver|) 169252) ((|PAdicRationalConstructor| . |DivisionRing|) T) ((|PAdicRationalConstructor| . |BiModule|) 169179) ((|PAdicRationalConstructor| . |RightLinearSet|) 169120) ((|PAdicRationalConstructor| . |RightModule|) 169061) ((|PAdicRationalConstructor| . |EntireRing|) T) ((|PAdicRationalConstructor| . |Module|) 169002) ((|PAdicRationalConstructor| . |LinearSet|) 168943) ((|PAdicRationalConstructor| . |LeftLinearSet|) 168864) ((|PAdicRationalConstructor| . |Algebra|) 168805) ((|PAdicRationalConstructor| . |EuclideanDomain|) T) ((|PAdicRationalConstructor| . |GcdDomain|) T) ((|PAdicRationalConstructor| . |CommutativeRing|) T) ((|PAdicRationalConstructor| . |IntegralDomain|) T) ((|PAdicRationalConstructor| . |PrincipalIdealDomain|) T) ((|PAdicRationalConstructor| . |UniqueFactorizationDomain|) T) ((|PAdicRationalConstructor| . |Field|) T) ((|PAdicRationalConstructor| . |DifferentialRing|) 168770) ((|PAdicRationalConstructor| . |DifferentialDomain|) 168689) ((|PAdicRationalConstructor| . |DifferentialSpace|) 168614) ((|PAdicRationalConstructor| . |DifferentialSpaceExtension|) 168598) ((|PAdicRationalConstructor| . |PartialDifferentialDomain|) 168470) ((|PAdicRationalConstructor| . |PartialDifferentialSpace|) 168344) ((|PAdicRationalConstructor| . |PartialDifferentialRing|) 168276) ((|PAdicRationalConstructor| . |DifferentialExtension|) 168260) ((|PAdicRationalConstructor| . |CharacteristicZero|) 168179) ((|PAdicRationalConstructor| . |CharacteristicNonZero|) 168139) ((|PAdicRationalConstructor| . |CancellationAbelianMonoid|) T) ((|PAdicRationalConstructor| . |AbelianSemiGroup|) T) ((|PAdicRationalConstructor| . |BasicType|) T) ((|PAdicRationalConstructor| . |Join|) T) ((|PAdicRationalConstructor| . |Type|) T) ((|PAdicRationalConstructor| . |CoercibleTo|) 168113) ((|PAdicRationalConstructor| . |SetCategory|) T) ((|PAdicRationalConstructor| . |AbelianMonoid|) T) ((|PAdicRationalConstructor| . |AbelianGroup|) T) ((|PAdicRationalConstructor| . |Ring|) T) ((|PAdicRationalConstructor| . |Monoid|) T) ((|PAdicRationalConstructor| . |SemiRing|) T) ((|PAdicRationalConstructor| . |SemiGroup|) T) ((|PAdicRationalConstructor| . |Rng|) T) ((|PAdicRational| . |QuotientFieldCategory|) 168080) ((|PAdicRational| . |StepThrough|) NIL) ((|PAdicRational| . |RetractableTo|) 168047) ((|PAdicRational| . |CoercibleFrom|) 167951) ((|PAdicRational| . |ConvertibleTo|) NIL) ((|PAdicRational| . |RealConstant|) NIL) ((|PAdicRational| . |PolynomialFactorizationExplicit|) NIL) ((|PAdicRational| . |Patternable|) 167918) ((|PAdicRational| . |OrderedRing|) NIL) ((|PAdicRational| . |OrderedCancellationAbelianMonoid|) NIL) ((|PAdicRational| . |OrderedAbelianSemiGroup|) NIL) ((|PAdicRational| . |OrderedType|) NIL) ((|PAdicRational| . |OrderedSet|) NIL) ((|PAdicRational| . |OrderedAbelianMonoid|) NIL) ((|PAdicRational| . |OrderedAbelianGroup|) NIL) ((|PAdicRational| . |OrderedIntegralDomain|) NIL) ((|PAdicRational| . |PatternMatchable|) NIL) ((|PAdicRational| . |FullyPatternMatchable|) 167885) ((|PAdicRational| . |LinearlyExplicitRingOver|) 167852) ((|PAdicRational| . |LeftModule|) 167776) ((|PAdicRational| . |FullyLinearlyExplicitRingOver|) 167743) ((|PAdicRational| . |Eltable|) 167679) ((|PAdicRational| . |Evalable|) 167620) ((|PAdicRational| . |InnerEvalable|) 167495) ((|PAdicRational| . |Functorial|) 167462) ((|PAdicRational| . |FullyEvalableOver|) 167429) ((|PAdicRational| . |DivisionRing|) T) ((|PAdicRational| . |BiModule|) 167337) ((|PAdicRational| . |RightLinearSet|) 167261) ((|PAdicRational| . |RightModule|) 167185) ((|PAdicRational| . |EntireRing|) T) ((|PAdicRational| . |Module|) 167109) ((|PAdicRational| . |LinearSet|) 167033) ((|PAdicRational| . |LeftLinearSet|) 166937) ((|PAdicRational| . |Algebra|) 166861) ((|PAdicRational| . |EuclideanDomain|) T) ((|PAdicRational| . |GcdDomain|) T) ((|PAdicRational| . |CommutativeRing|) T) ((|PAdicRational| . |IntegralDomain|) T) ((|PAdicRational| . |PrincipalIdealDomain|) T) ((|PAdicRational| . |UniqueFactorizationDomain|) T) ((|PAdicRational| . |Field|) T) ((|PAdicRational| . |DifferentialRing|) NIL) ((|PAdicRational| . |DifferentialDomain|) NIL) ((|PAdicRational| . |DifferentialSpace|) NIL) ((|PAdicRational| . |DifferentialSpaceExtension|) 166828) ((|PAdicRational| . |PartialDifferentialDomain|) NIL) ((|PAdicRational| . |PartialDifferentialSpace|) NIL) ((|PAdicRational| . |PartialDifferentialRing|) NIL) ((|PAdicRational| . |DifferentialExtension|) 166795) ((|PAdicRational| . |CharacteristicZero|) T) ((|PAdicRational| . |CharacteristicNonZero|) NIL) ((|PAdicRational| . |CancellationAbelianMonoid|) T) ((|PAdicRational| . |AbelianSemiGroup|) T) ((|PAdicRational| . |BasicType|) T) ((|PAdicRational| . |Join|) T) ((|PAdicRational| . |Type|) T) ((|PAdicRational| . |CoercibleTo|) 166769) ((|PAdicRational| . |SetCategory|) T) ((|PAdicRational| . |AbelianMonoid|) T) ((|PAdicRational| . |AbelianGroup|) T) ((|PAdicRational| . |Ring|) T) ((|PAdicRational| . |Monoid|) T) ((|PAdicRational| . |SemiRing|) T) ((|PAdicRational| . |SemiGroup|) T) ((|PAdicRational| . |Rng|) T) ((|PAdicInteger| . |PAdicIntegerCategory|) 166753) ((|PAdicInteger| . |PrincipalIdealDomain|) T) ((|PAdicInteger| . |IntegralDomain|) T) ((|PAdicInteger| . |EntireRing|) T) ((|PAdicInteger| . |CommutativeRing|) T) ((|PAdicInteger| . |CoercibleFrom|) 166720) ((|PAdicInteger| . |Module|) 166707) ((|PAdicInteger| . |LinearSet|) 166694) ((|PAdicInteger| . |RightModule|) 166681) ((|PAdicInteger| . |RightLinearSet|) 166668) ((|PAdicInteger| . |BiModule|) 166653) ((|PAdicInteger| . |Algebra|) 166640) ((|PAdicInteger| . |GcdDomain|) T) ((|PAdicInteger| . |EuclideanDomain|) T) ((|PAdicInteger| . |Ring|) T) ((|PAdicInteger| . |Monoid|) T) ((|PAdicInteger| . |SemiRing|) T) ((|PAdicInteger| . |SemiGroup|) T) ((|PAdicInteger| . |Rng|) T) ((|PAdicInteger| . |AbelianGroup|) T) ((|PAdicInteger| . |LeftLinearSet|) 166607) ((|PAdicInteger| . |AbelianMonoid|) T) ((|PAdicInteger| . |SetCategory|) T) ((|PAdicInteger| . |CoercibleTo|) 166581) ((|PAdicInteger| . |Type|) T) ((|PAdicInteger| . |Join|) T) ((|PAdicInteger| . |BasicType|) T) ((|PAdicInteger| . |AbelianSemiGroup|) T) ((|PAdicInteger| . |CancellationAbelianMonoid|) T) ((|PAdicInteger| . |LeftModule|) 166568) ((|PAdicInteger| . |CharacteristicZero|) T) ((|OrdinaryWeightedPolynomials| . |Ring|) T) ((|OrdinaryWeightedPolynomials| . |Monoid|) T) ((|OrdinaryWeightedPolynomials| . |SemiRing|) T) ((|OrdinaryWeightedPolynomials| . |SemiGroup|) T) ((|OrdinaryWeightedPolynomials| . |Rng|) T) ((|OrdinaryWeightedPolynomials| . |AbelianGroup|) T) ((|OrdinaryWeightedPolynomials| . |LeftLinearSet|) 166495) ((|OrdinaryWeightedPolynomials| . |AbelianMonoid|) T) ((|OrdinaryWeightedPolynomials| . |SetCategory|) T) ((|OrdinaryWeightedPolynomials| . |CoercibleTo|) 166441) ((|OrdinaryWeightedPolynomials| . |Type|) T) ((|OrdinaryWeightedPolynomials| . |Join|) T) ((|OrdinaryWeightedPolynomials| . |BasicType|) T) ((|OrdinaryWeightedPolynomials| . |AbelianSemiGroup|) T) ((|OrdinaryWeightedPolynomials| . |CancellationAbelianMonoid|) T) ((|OrdinaryWeightedPolynomials| . |LeftModule|) 166388) ((|OrdinaryWeightedPolynomials| . |CoercibleFrom|) 166297) ((|OrdinaryWeightedPolynomials| . |HomotopicTo|) 166266) ((|OrdinaryWeightedPolynomials| . |Algebra|) 166223) ((|OrdinaryWeightedPolynomials| . |BiModule|) 166175) ((|OrdinaryWeightedPolynomials| . |RightLinearSet|) 166132) ((|OrdinaryWeightedPolynomials| . |RightModule|) 166089) ((|OrdinaryWeightedPolynomials| . |LinearSet|) 166046) ((|OrdinaryWeightedPolynomials| . |Module|) 166003) ((|OverloadSet| . |SetCategory|) T) ((|OverloadSet| . |CoercibleTo|) 165977) ((|OverloadSet| . |Type|) T) ((|OverloadSet| . |Join|) T) ((|OverloadSet| . |BasicType|) T) ((|OrderedVariableList| . |OrderedFinite|) T) ((|OrderedVariableList| . |OrderedType|) T) ((|OrderedVariableList| . |OrderedSet|) T) ((|OrderedVariableList| . |SetCategory|) T) ((|OrderedVariableList| . |CoercibleTo|) 165951) ((|OrderedVariableList| . |Type|) T) ((|OrderedVariableList| . |Join|) T) ((|OrderedVariableList| . |BasicType|) T) ((|OrderedVariableList| . |Finite|) T) ((|OrderedVariableList| . |ConvertibleTo|) 165845) ((|OutputForm| . |SetCategory|) T) ((|OutputForm| . |CoercibleTo|) 165819) ((|OutputForm| . |Type|) T) ((|OutputForm| . |Join|) T) ((|OutputForm| . |BasicType|) T) ((|OutputBinaryFile| . |OutputByteConduit|) T) ((|OutputBinaryFile| . |Conduit|) T) ((|OutputBinaryFile| . |CoercibleTo|) 165793) ((|OrdSetInts| . |OrderedSet|) T) ((|OrdSetInts| . |CoercibleTo|) 165767) ((|OrdSetInts| . |SetCategory|) T) ((|OrdSetInts| . |BasicType|) T) ((|OrdSetInts| . |Join|) T) ((|OrdSetInts| . |Type|) T) ((|OrdSetInts| . |OrderedType|) T) ((|UnivariateSkewPolynomial| . |UnivariateSkewPolynomialCategory|) 165751) ((|UnivariateSkewPolynomial| . |RetractableTo|) 165595) ((|UnivariateSkewPolynomial| . |CoercibleFrom|) 165450) ((|UnivariateSkewPolynomial| . |FullyRetractableTo|) 165434) ((|UnivariateSkewPolynomial| . |Module|) 165391) ((|UnivariateSkewPolynomial| . |LinearSet|) 165348) ((|UnivariateSkewPolynomial| . |LeftModule|) 165322) ((|UnivariateSkewPolynomial| . |LeftLinearSet|) 165276) ((|UnivariateSkewPolynomial| . |CancellationAbelianMonoid|) T) ((|UnivariateSkewPolynomial| . |AbelianSemiGroup|) T) ((|UnivariateSkewPolynomial| . |BasicType|) T) ((|UnivariateSkewPolynomial| . |Join|) T) ((|UnivariateSkewPolynomial| . |Type|) T) ((|UnivariateSkewPolynomial| . |CoercibleTo|) 165250) ((|UnivariateSkewPolynomial| . |SetCategory|) T) ((|UnivariateSkewPolynomial| . |AbelianMonoid|) T) ((|UnivariateSkewPolynomial| . |AbelianGroup|) T) ((|UnivariateSkewPolynomial| . |RightModule|) 165234) ((|UnivariateSkewPolynomial| . |RightLinearSet|) 165218) ((|UnivariateSkewPolynomial| . |BiModule|) 165197) ((|UnivariateSkewPolynomial| . |Ring|) T) ((|UnivariateSkewPolynomial| . |Monoid|) T) ((|UnivariateSkewPolynomial| . |SemiRing|) T) ((|UnivariateSkewPolynomial| . |SemiGroup|) T) ((|UnivariateSkewPolynomial| . |Rng|) T) ((|UnivariateSkewPolynomial| . |Algebra|) 165154) ((|SparseUnivariateSkewPolynomial| . |UnivariateSkewPolynomialCategory|) 165138) ((|SparseUnivariateSkewPolynomial| . |RetractableTo|) 164982) ((|SparseUnivariateSkewPolynomial| . |CoercibleFrom|) 164863) ((|SparseUnivariateSkewPolynomial| . |FullyRetractableTo|) 164847) ((|SparseUnivariateSkewPolynomial| . |Module|) 164804) ((|SparseUnivariateSkewPolynomial| . |LinearSet|) 164761) ((|SparseUnivariateSkewPolynomial| . |LeftModule|) 164735) ((|SparseUnivariateSkewPolynomial| . |LeftLinearSet|) 164689) ((|SparseUnivariateSkewPolynomial| . |CancellationAbelianMonoid|) T) ((|SparseUnivariateSkewPolynomial| . |AbelianSemiGroup|) T) ((|SparseUnivariateSkewPolynomial| . |BasicType|) T) ((|SparseUnivariateSkewPolynomial| . |Join|) T) ((|SparseUnivariateSkewPolynomial| . |Type|) T) ((|SparseUnivariateSkewPolynomial| . |CoercibleTo|) 164663) ((|SparseUnivariateSkewPolynomial| . |SetCategory|) T) ((|SparseUnivariateSkewPolynomial| . |AbelianMonoid|) T) ((|SparseUnivariateSkewPolynomial| . |AbelianGroup|) T) ((|SparseUnivariateSkewPolynomial| . |RightModule|) 164647) ((|SparseUnivariateSkewPolynomial| . |RightLinearSet|) 164631) ((|SparseUnivariateSkewPolynomial| . |BiModule|) 164610) ((|SparseUnivariateSkewPolynomial| . |Ring|) T) ((|SparseUnivariateSkewPolynomial| . |Monoid|) T) ((|SparseUnivariateSkewPolynomial| . |SemiRing|) T) ((|SparseUnivariateSkewPolynomial| . |SemiGroup|) T) ((|SparseUnivariateSkewPolynomial| . |Rng|) T) ((|SparseUnivariateSkewPolynomial| . |Algebra|) 164567) ((|OrderedStructure| . |OrderedType|) T) ((|OrderedStructure| . |Type|) T) ((|OrderedStructure| . |Join|) T) ((|OrderedStructure| . |BasicType|) T) ((|OrderedStructure| . |HomotopicTo|) 164551) ((|OrderedStructure| . |CoercibleTo|) 164480) ((|OrderedStructure| . |CoercibleFrom|) 164464) ((|OrderedCompletion| . |SetCategory|) T) ((|OrderedCompletion| . |CoercibleTo|) 164438) ((|OrderedCompletion| . |Type|) T) ((|OrderedCompletion| . |Join|) T) ((|OrderedCompletion| . |BasicType|) T) ((|OrderedCompletion| . |FullyRetractableTo|) 164422) ((|OrderedCompletion| . |CoercibleFrom|) 164232) ((|OrderedCompletion| . |RetractableTo|) 164076) ((|OrderedCompletion| . |AbelianGroup|) 164011) ((|OrderedCompletion| . |LeftLinearSet|) 163897) ((|OrderedCompletion| . |AbelianMonoid|) 163832) ((|OrderedCompletion| . |AbelianSemiGroup|) 163767) ((|OrderedCompletion| . |CancellationAbelianMonoid|) 163702) ((|OrderedCompletion| . |OrderedRing|) 163672) ((|OrderedCompletion| . |OrderedCancellationAbelianMonoid|) 163642) ((|OrderedCompletion| . |OrderedAbelianSemiGroup|) 163612) ((|OrderedCompletion| . |OrderedType|) 163582) ((|OrderedCompletion| . |OrderedSet|) 163552) ((|OrderedCompletion| . |OrderedAbelianMonoid|) 163522) ((|OrderedCompletion| . |OrderedAbelianGroup|) 163492) ((|OrderedCompletion| . |Ring|) 163462) ((|OrderedCompletion| . |Monoid|) 163432) ((|OrderedCompletion| . |SemiRing|) 163402) ((|OrderedCompletion| . |SemiGroup|) 163372) ((|OrderedCompletion| . |Rng|) 163342) ((|OrderedCompletion| . |LeftModule|) 163306) ((|OrderedCompletion| . |CharacteristicZero|) 163276) ((|OperatorSignature| . |OperatorCategory|) 163250) ((|OperatorSignature| . |BasicType|) T) ((|OperatorSignature| . |Join|) T) ((|OperatorSignature| . |Type|) T) ((|OperatorSignature| . |CoercibleTo|) 163224) ((|OperatorSignature| . |SetCategory|) T) ((|Operator| . |Ring|) T) ((|Operator| . |Monoid|) T) ((|Operator| . |SemiRing|) T) ((|Operator| . |SemiGroup|) T) ((|Operator| . |Rng|) T) ((|Operator| . |AbelianGroup|) T) ((|Operator| . |LeftLinearSet|) 163151) ((|Operator| . |AbelianMonoid|) T) ((|Operator| . |SetCategory|) T) ((|Operator| . |CoercibleTo|) 163125) ((|Operator| . |Type|) T) ((|Operator| . |Join|) T) ((|Operator| . |BasicType|) T) ((|Operator| . |AbelianSemiGroup|) T) ((|Operator| . |CancellationAbelianMonoid|) T) ((|Operator| . |LeftModule|) 163072) ((|Operator| . |CoercibleFrom|) 163010) ((|Operator| . |RetractableTo|) 162968) ((|Operator| . |Eltable|) 162947) ((|Operator| . |CharacteristicZero|) 162910) ((|Operator| . |CharacteristicNonZero|) 162870) ((|Operator| . |Algebra|) 162827) ((|Operator| . |BiModule|) 162779) ((|Operator| . |RightLinearSet|) 162736) ((|Operator| . |RightModule|) 162693) ((|Operator| . |LinearSet|) 162650) ((|Operator| . |Module|) 162607) ((|OnePointCompletion| . |SetCategory|) T) ((|OnePointCompletion| . |CoercibleTo|) 162581) ((|OnePointCompletion| . |Type|) T) ((|OnePointCompletion| . |Join|) T) ((|OnePointCompletion| . |BasicType|) T) ((|OnePointCompletion| . |FullyRetractableTo|) 162565) ((|OnePointCompletion| . |CoercibleFrom|) 162375) ((|OnePointCompletion| . |RetractableTo|) 162219) ((|OnePointCompletion| . |AbelianGroup|) 162154) ((|OnePointCompletion| . |LeftLinearSet|) 162040) ((|OnePointCompletion| . |AbelianMonoid|) 161975) ((|OnePointCompletion| . |AbelianSemiGroup|) 161910) ((|OnePointCompletion| . |CancellationAbelianMonoid|) 161845) ((|OnePointCompletion| . |OrderedRing|) 161815) ((|OnePointCompletion| . |OrderedCancellationAbelianMonoid|) 161785) ((|OnePointCompletion| . |OrderedAbelianSemiGroup|) 161755) ((|OnePointCompletion| . |OrderedType|) 161725) ((|OnePointCompletion| . |OrderedSet|) 161695) ((|OnePointCompletion| . |OrderedAbelianMonoid|) 161665) ((|OnePointCompletion| . |OrderedAbelianGroup|) 161635) ((|OnePointCompletion| . |Ring|) 161605) ((|OnePointCompletion| . |Monoid|) 161575) ((|OnePointCompletion| . |SemiRing|) 161545) ((|OnePointCompletion| . |SemiGroup|) 161515) ((|OnePointCompletion| . |Rng|) 161485) ((|OnePointCompletion| . |LeftModule|) 161449) ((|OnePointCompletion| . |CharacteristicZero|) 161419) ((|OppositeMonogenicLinearOperator| . |MonogenicLinearOperator|) 161403) ((|OppositeMonogenicLinearOperator| . |CoercibleFrom|) 161340) ((|OppositeMonogenicLinearOperator| . |Module|) 161297) ((|OppositeMonogenicLinearOperator| . |LinearSet|) 161254) ((|OppositeMonogenicLinearOperator| . |LeftModule|) 161228) ((|OppositeMonogenicLinearOperator| . |LeftLinearSet|) 161182) ((|OppositeMonogenicLinearOperator| . |CancellationAbelianMonoid|) T) ((|OppositeMonogenicLinearOperator| . |AbelianSemiGroup|) T) ((|OppositeMonogenicLinearOperator| . |BasicType|) T) ((|OppositeMonogenicLinearOperator| . |Join|) T) ((|OppositeMonogenicLinearOperator| . |Type|) T) ((|OppositeMonogenicLinearOperator| . |CoercibleTo|) 161156) ((|OppositeMonogenicLinearOperator| . |SetCategory|) T) ((|OppositeMonogenicLinearOperator| . |AbelianMonoid|) T) ((|OppositeMonogenicLinearOperator| . |AbelianGroup|) T) ((|OppositeMonogenicLinearOperator| . |RightModule|) 161140) ((|OppositeMonogenicLinearOperator| . |RightLinearSet|) 161124) ((|OppositeMonogenicLinearOperator| . |BiModule|) 161103) ((|OppositeMonogenicLinearOperator| . |Ring|) T) ((|OppositeMonogenicLinearOperator| . |Monoid|) T) ((|OppositeMonogenicLinearOperator| . |SemiRing|) T) ((|OppositeMonogenicLinearOperator| . |SemiGroup|) T) ((|OppositeMonogenicLinearOperator| . |Rng|) T) ((|OppositeMonogenicLinearOperator| . |Algebra|) 161060) ((|OppositeMonogenicLinearOperator| . |DifferentialRing|) 161025) ((|OppositeMonogenicLinearOperator| . |DifferentialDomain|) 160984) ((|OppositeMonogenicLinearOperator| . |DifferentialSpace|) 160949) ((|OrderedFreeMonoid| . |FreeMonoidCategory|) 160933) ((|OrderedFreeMonoid| . |CoercibleFrom|) 160917) ((|OrderedFreeMonoid| . |RetractableTo|) 160901) ((|OrderedFreeMonoid| . |OrderedType|) T) ((|OrderedFreeMonoid| . |OrderedSet|) T) ((|OrderedFreeMonoid| . |SemiGroup|) T) ((|OrderedFreeMonoid| . |BasicType|) T) ((|OrderedFreeMonoid| . |Join|) T) ((|OrderedFreeMonoid| . |Type|) T) ((|OrderedFreeMonoid| . |CoercibleTo|) 160875) ((|OrderedFreeMonoid| . |SetCategory|) T) ((|OrderedFreeMonoid| . |Monoid|) T) ((|OrderedFreeMonoid| . |OrderedMonoid|) T) ((|OrderedFreeMonoid| . |OrderedSemiGroup|) T) ((|OrderlyDifferentialVariable| . |DifferentialVariableCategory|) 160859) ((|OrderlyDifferentialVariable| . |CoercibleFrom|) 160843) ((|OrderlyDifferentialVariable| . |RetractableTo|) 160827) ((|OrderlyDifferentialVariable| . |OrderedType|) T) ((|OrderlyDifferentialVariable| . |BasicType|) T) ((|OrderlyDifferentialVariable| . |SetCategory|) T) ((|OrderlyDifferentialVariable| . |CoercibleTo|) 160801) ((|OrderlyDifferentialVariable| . |OrderedSet|) T) ((|OrderlyDifferentialVariable| . |DifferentialDomain|) 160788) ((|OrderlyDifferentialVariable| . |Join|) T) ((|OrderlyDifferentialVariable| . |Type|) T) ((|OrderlyDifferentialVariable| . |DifferentialSpace|) T) ((|OrdinaryDifferentialRing| . |BiModule|) 160716) ((|OrdinaryDifferentialRing| . |RightLinearSet|) 160653) ((|OrdinaryDifferentialRing| . |RightModule|) 160590) ((|OrdinaryDifferentialRing| . |AbelianGroup|) T) ((|OrdinaryDifferentialRing| . |LeftLinearSet|) 160507) ((|OrdinaryDifferentialRing| . |AbelianMonoid|) T) ((|OrdinaryDifferentialRing| . |SetCategory|) T) ((|OrdinaryDifferentialRing| . |CoercibleTo|) 160468) ((|OrdinaryDifferentialRing| . |Type|) T) ((|OrdinaryDifferentialRing| . |Join|) T) ((|OrdinaryDifferentialRing| . |BasicType|) T) ((|OrdinaryDifferentialRing| . |AbelianSemiGroup|) T) ((|OrdinaryDifferentialRing| . |CancellationAbelianMonoid|) T) ((|OrdinaryDifferentialRing| . |LeftModule|) 160405) ((|OrdinaryDifferentialRing| . |DifferentialRing|) T) ((|OrdinaryDifferentialRing| . |CoercibleFrom|) 160300) ((|OrdinaryDifferentialRing| . |Rng|) T) ((|OrdinaryDifferentialRing| . |SemiGroup|) T) ((|OrdinaryDifferentialRing| . |SemiRing|) T) ((|OrdinaryDifferentialRing| . |Monoid|) T) ((|OrdinaryDifferentialRing| . |Ring|) T) ((|OrdinaryDifferentialRing| . |DifferentialDomain|) 160287) ((|OrdinaryDifferentialRing| . |DifferentialSpace|) T) ((|OrdinaryDifferentialRing| . |HomotopicTo|) 160271) ((|OrdinaryDifferentialRing| . |Field|) 160247) ((|OrdinaryDifferentialRing| . |UniqueFactorizationDomain|) 160223) ((|OrdinaryDifferentialRing| . |PrincipalIdealDomain|) 160199) ((|OrdinaryDifferentialRing| . |IntegralDomain|) 160175) ((|OrdinaryDifferentialRing| . |CommutativeRing|) 160151) ((|OrdinaryDifferentialRing| . |Module|) 160079) ((|OrdinaryDifferentialRing| . |LinearSet|) 160007) ((|OrdinaryDifferentialRing| . |Algebra|) 159935) ((|OrdinaryDifferentialRing| . |GcdDomain|) 159911) ((|OrdinaryDifferentialRing| . |EuclideanDomain|) 159887) ((|OrdinaryDifferentialRing| . |EntireRing|) 159863) ((|OrdinaryDifferentialRing| . |DivisionRing|) 159839) ((|OrderlyDifferentialPolynomial| . |DifferentialPolynomialCategory|) 159745) ((|OrderlyDifferentialPolynomial| . |CoercibleFrom|) 159338) ((|OrderlyDifferentialPolynomial| . |RetractableTo|) 159066) ((|OrderlyDifferentialPolynomial| . |ConvertibleTo|) NIL) ((|OrderlyDifferentialPolynomial| . |FiniteAbelianMonoidRing|) 158986) ((|OrderlyDifferentialPolynomial| . |FullyRetractableTo|) 158970) ((|OrderlyDifferentialPolynomial| . |Algebra|) 158733) ((|OrderlyDifferentialPolynomial| . |BiModule|) 158476) ((|OrderlyDifferentialPolynomial| . |RightLinearSet|) 158233) ((|OrderlyDifferentialPolynomial| . |RightModule|) 157990) ((|OrderlyDifferentialPolynomial| . |LeftLinearSet|) 157867) ((|OrderlyDifferentialPolynomial| . |LeftModule|) 157696) ((|OrderlyDifferentialPolynomial| . |LinearSet|) 157459) ((|OrderlyDifferentialPolynomial| . |Module|) 157222) ((|OrderlyDifferentialPolynomial| . |CharacteristicNonZero|) 157182) ((|OrderlyDifferentialPolynomial| . |CharacteristicZero|) 157145) ((|OrderlyDifferentialPolynomial| . |CommutativeRing|) 156998) ((|OrderlyDifferentialPolynomial| . |Functorial|) 156982) ((|OrderlyDifferentialPolynomial| . |IntegralDomain|) 156868) ((|OrderlyDifferentialPolynomial| . |EntireRing|) 156754) ((|OrderlyDifferentialPolynomial| . |AbelianMonoidRing|) 156674) ((|OrderlyDifferentialPolynomial| . |FullyLinearlyExplicitRingOver|) 156658) ((|OrderlyDifferentialPolynomial| . |LinearlyExplicitRingOver|) 156574) ((|OrderlyDifferentialPolynomial| . |GcdDomain|) 156492) ((|OrderlyDifferentialPolynomial| . |InnerEvalable|) 156322) ((|OrderlyDifferentialPolynomial| . |PartialDifferentialRing|) 156203) ((|OrderlyDifferentialPolynomial| . |PartialDifferentialDomain|) 156022) ((|OrderlyDifferentialPolynomial| . |PartialDifferentialSpace|) 155845) ((|OrderlyDifferentialPolynomial| . |PatternMatchable|) NIL) ((|OrderlyDifferentialPolynomial| . |PolynomialFactorizationExplicit|) 155795) ((|OrderlyDifferentialPolynomial| . |UniqueFactorizationDomain|) 155745) ((|OrderlyDifferentialPolynomial| . |PolynomialCategory|) 155658) ((|OrderlyDifferentialPolynomial| . |Evalable|) 155645) ((|OrderlyDifferentialPolynomial| . |DifferentialRing|) 155610) ((|OrderlyDifferentialPolynomial| . |CancellationAbelianMonoid|) T) ((|OrderlyDifferentialPolynomial| . |AbelianSemiGroup|) T) ((|OrderlyDifferentialPolynomial| . |BasicType|) T) ((|OrderlyDifferentialPolynomial| . |CoercibleTo|) 155584) ((|OrderlyDifferentialPolynomial| . |SetCategory|) T) ((|OrderlyDifferentialPolynomial| . |AbelianMonoid|) T) ((|OrderlyDifferentialPolynomial| . |AbelianGroup|) T) ((|OrderlyDifferentialPolynomial| . |Rng|) T) ((|OrderlyDifferentialPolynomial| . |SemiGroup|) T) ((|OrderlyDifferentialPolynomial| . |SemiRing|) T) ((|OrderlyDifferentialPolynomial| . |Monoid|) T) ((|OrderlyDifferentialPolynomial| . |Ring|) T) ((|OrderlyDifferentialPolynomial| . |DifferentialDomain|) 155503) ((|OrderlyDifferentialPolynomial| . |Join|) T) ((|OrderlyDifferentialPolynomial| . |Type|) T) ((|OrderlyDifferentialPolynomial| . |DifferentialSpace|) 155428) ((|OrderlyDifferentialPolynomial| . |DifferentialSpaceExtension|) 155412) ((|OrderlyDifferentialPolynomial| . |DifferentialExtension|) 155396) ((|OrderedDirectProduct| . |DirectProductCategory|) 155375) ((|OrderedDirectProduct| . |VectorSpace|) 155342) ((|OrderedDirectProduct| . |OrderedCancellationAbelianMonoid|) 155300) ((|OrderedDirectProduct| . |OrderedAbelianSemiGroup|) 155258) ((|OrderedDirectProduct| . |OrderedType|) 155183) ((|OrderedDirectProduct| . |OrderedSet|) 155108) ((|OrderedDirectProduct| . |OrderedAbelianMonoid|) 155066) ((|OrderedDirectProduct| . |OrderedAbelianMonoidSup|) 155024) ((|OrderedDirectProduct| . |Module|) 154953) ((|OrderedDirectProduct| . |LinearSet|) 154858) ((|OrderedDirectProduct| . |EltableAggregate|) 154830) ((|OrderedDirectProduct| . |Eltable|) 154802) ((|OrderedDirectProduct| . |IndexedAggregate|) 154774) ((|OrderedDirectProduct| . |RetractableTo|) 154525) ((|OrderedDirectProduct| . |CoercibleFrom|) 154249) ((|OrderedDirectProduct| . |FullyRetractableTo|) 154210) ((|OrderedDirectProduct| . |LinearlyExplicitRingOver|) 154082) ((|OrderedDirectProduct| . |LeftModule|) 153867) ((|OrderedDirectProduct| . |FullyLinearlyExplicitRingOver|) 153835) ((|OrderedDirectProduct| . |HomogeneousAggregate|) 153819) ((|OrderedDirectProduct| . |Functorial|) 153803) ((|OrderedDirectProduct| . |InnerEvalable|) 153722) ((|OrderedDirectProduct| . |Evalable|) 153646) ((|OrderedDirectProduct| . |Aggregate|) T) ((|OrderedDirectProduct| . |FiniteAggregate|) 153630) ((|OrderedDirectProduct| . |Finite|) 153605) ((|OrderedDirectProduct| . |DifferentialRing|) 153542) ((|OrderedDirectProduct| . |LeftLinearSet|) 153272) ((|OrderedDirectProduct| . |Rng|) 153249) ((|OrderedDirectProduct| . |SemiGroup|) 153226) ((|OrderedDirectProduct| . |SemiRing|) 153203) ((|OrderedDirectProduct| . |Monoid|) 153180) ((|OrderedDirectProduct| . |Ring|) 153157) ((|OrderedDirectProduct| . |DifferentialDomain|) 153020) ((|OrderedDirectProduct| . |DifferentialSpace|) 152889) ((|OrderedDirectProduct| . |DifferentialSpaceExtension|) 152857) ((|OrderedDirectProduct| . |PartialDifferentialDomain|) 152673) ((|OrderedDirectProduct| . |PartialDifferentialSpace|) 152491) ((|OrderedDirectProduct| . |PartialDifferentialRing|) 152395) ((|OrderedDirectProduct| . |DifferentialExtension|) 152363) ((|OrderedDirectProduct| . |CoercibleTo|) 151908) ((|OrderedDirectProduct| . |RightModule|) 151815) ((|OrderedDirectProduct| . |RightLinearSet|) 151698) ((|OrderedDirectProduct| . |BiModule|) 151600) ((|OrderedDirectProduct| . |CancellationAbelianMonoid|) 151402) ((|OrderedDirectProduct| . |AbelianSemiGroup|) 151139) ((|OrderedDirectProduct| . |BasicType|) 150744) ((|OrderedDirectProduct| . |Join|) T) ((|OrderedDirectProduct| . |Type|) T) ((|OrderedDirectProduct| . |SetCategory|) 150376) ((|OrderedDirectProduct| . |AbelianMonoid|) 150147) ((|OrderedDirectProduct| . |AbelianGroup|) 150033) ((|Octonion| . |OctonionCategory|) 150017) ((|Octonion| . |OrderedType|) 149988) ((|Octonion| . |OrderedSet|) 149959) ((|Octonion| . |RetractableTo|) 149636) ((|Octonion| . |CoercibleFrom|) 149413) ((|Octonion| . |FullyRetractableTo|) 149369) ((|Octonion| . |Eltable|) 149322) ((|Octonion| . |Evalable|) 149281) ((|Octonion| . |InnerEvalable|) 149170) ((|Octonion| . |Functorial|) 149154) ((|Octonion| . |FullyEvalableOver|) 149138) ((|Octonion| . |Finite|) 149113) ((|Octonion| . |ConvertibleTo|) 149049) ((|Octonion| . |CharacteristicZero|) 149012) ((|Octonion| . |CharacteristicNonZero|) 148972) ((|Octonion| . |Module|) 148956) ((|Octonion| . |LinearSet|) 148940) ((|Octonion| . |LeftModule|) 148914) ((|Octonion| . |LeftLinearSet|) 148868) ((|Octonion| . |CancellationAbelianMonoid|) T) ((|Octonion| . |AbelianSemiGroup|) T) ((|Octonion| . |BasicType|) T) ((|Octonion| . |Join|) T) ((|Octonion| . |Type|) T) ((|Octonion| . |CoercibleTo|) 148842) ((|Octonion| . |SetCategory|) T) ((|Octonion| . |AbelianMonoid|) T) ((|Octonion| . |AbelianGroup|) T) ((|Octonion| . |RightModule|) 148826) ((|Octonion| . |RightLinearSet|) 148810) ((|Octonion| . |BiModule|) 148789) ((|Octonion| . |Ring|) T) ((|Octonion| . |Monoid|) T) ((|Octonion| . |SemiRing|) T) ((|Octonion| . |SemiGroup|) T) ((|Octonion| . |Rng|) T) ((|Octonion| . |Algebra|) 148773) ((|NewSparseUnivariatePolynomial| . |UnivariatePolynomialCategory|) 148757) ((|NewSparseUnivariatePolynomial| . |StepThrough|) 148727) ((|NewSparseUnivariatePolynomial| . |ConvertibleTo|) NIL) ((|NewSparseUnivariatePolynomial| . |Evalable|) 148714) ((|NewSparseUnivariatePolynomial| . |InnerEvalable|) 148643) ((|NewSparseUnivariatePolynomial| . |FiniteAbelianMonoidRing|) 148604) ((|NewSparseUnivariatePolynomial| . |RetractableTo|) 148370) ((|NewSparseUnivariatePolynomial| . |FullyRetractableTo|) 148354) ((|NewSparseUnivariatePolynomial| . |Algebra|) 148094) ((|NewSparseUnivariatePolynomial| . |BiModule|) 147814) ((|NewSparseUnivariatePolynomial| . |RightLinearSet|) 147548) ((|NewSparseUnivariatePolynomial| . |RightModule|) 147282) ((|NewSparseUnivariatePolynomial| . |LeftLinearSet|) 147159) ((|NewSparseUnivariatePolynomial| . |LeftModule|) 146988) ((|NewSparseUnivariatePolynomial| . |LinearSet|) 146728) ((|NewSparseUnivariatePolynomial| . |Module|) 146468) ((|NewSparseUnivariatePolynomial| . |CoercibleFrom|) 146076) ((|NewSparseUnivariatePolynomial| . |CharacteristicNonZero|) 146036) ((|NewSparseUnivariatePolynomial| . |CharacteristicZero|) 145999) ((|NewSparseUnivariatePolynomial| . |Functorial|) 145983) ((|NewSparseUnivariatePolynomial| . |AbelianMonoidRing|) 145944) ((|NewSparseUnivariatePolynomial| . |FullyLinearlyExplicitRingOver|) 145928) ((|NewSparseUnivariatePolynomial| . |LinearlyExplicitRingOver|) 145844) ((|NewSparseUnivariatePolynomial| . |PartialDifferentialRing|) 145742) ((|NewSparseUnivariatePolynomial| . |PartialDifferentialDomain|) 145578) ((|NewSparseUnivariatePolynomial| . |PartialDifferentialSpace|) 145418) ((|NewSparseUnivariatePolynomial| . |PatternMatchable|) NIL) ((|NewSparseUnivariatePolynomial| . |PolynomialFactorizationExplicit|) 145368) ((|NewSparseUnivariatePolynomial| . |UniqueFactorizationDomain|) 145318) ((|NewSparseUnivariatePolynomial| . |PolynomialCategory|) 145253) ((|NewSparseUnivariatePolynomial| . |PrincipalIdealDomain|) 145229) ((|NewSparseUnivariatePolynomial| . |IntegralDomain|) 145092) ((|NewSparseUnivariatePolynomial| . |EntireRing|) 144955) ((|NewSparseUnivariatePolynomial| . |CommutativeRing|) 144785) ((|NewSparseUnivariatePolynomial| . |GcdDomain|) 144680) ((|NewSparseUnivariatePolynomial| . |EuclideanDomain|) 144656) ((|NewSparseUnivariatePolynomial| . |Eltable|) 144559) ((|NewSparseUnivariatePolynomial| . |DifferentialRing|) T) ((|NewSparseUnivariatePolynomial| . |CancellationAbelianMonoid|) T) ((|NewSparseUnivariatePolynomial| . |AbelianSemiGroup|) T) ((|NewSparseUnivariatePolynomial| . |BasicType|) T) ((|NewSparseUnivariatePolynomial| . |CoercibleTo|) 144489) ((|NewSparseUnivariatePolynomial| . |SetCategory|) T) ((|NewSparseUnivariatePolynomial| . |AbelianMonoid|) T) ((|NewSparseUnivariatePolynomial| . |AbelianGroup|) T) ((|NewSparseUnivariatePolynomial| . |Rng|) T) ((|NewSparseUnivariatePolynomial| . |SemiGroup|) T) ((|NewSparseUnivariatePolynomial| . |SemiRing|) T) ((|NewSparseUnivariatePolynomial| . |Monoid|) T) ((|NewSparseUnivariatePolynomial| . |Ring|) T) ((|NewSparseUnivariatePolynomial| . |DifferentialDomain|) 144476) ((|NewSparseUnivariatePolynomial| . |Join|) T) ((|NewSparseUnivariatePolynomial| . |Type|) T) ((|NewSparseUnivariatePolynomial| . |DifferentialSpace|) T) ((|NewSparseUnivariatePolynomial| . |DifferentialSpaceExtension|) 144460) ((|NewSparseUnivariatePolynomial| . |DifferentialExtension|) 144444) ((|NewSparseMultivariatePolynomial| . |RecursivePolynomialCategory|) 144397) ((|NewSparseMultivariatePolynomial| . |ConvertibleTo|) 143836) ((|NewSparseMultivariatePolynomial| . |Evalable|) 143823) ((|NewSparseMultivariatePolynomial| . |InnerEvalable|) 143775) ((|NewSparseMultivariatePolynomial| . |FiniteAbelianMonoidRing|) 143733) ((|NewSparseMultivariatePolynomial| . |RetractableTo|) 143513) ((|NewSparseMultivariatePolynomial| . |FullyRetractableTo|) 143497) ((|NewSparseMultivariatePolynomial| . |Algebra|) 143260) ((|NewSparseMultivariatePolynomial| . |CoercibleFrom|) 142905) ((|NewSparseMultivariatePolynomial| . |LeftModule|) 142734) ((|NewSparseMultivariatePolynomial| . |LeftLinearSet|) 142611) ((|NewSparseMultivariatePolynomial| . |Rng|) T) ((|NewSparseMultivariatePolynomial| . |SemiGroup|) T) ((|NewSparseMultivariatePolynomial| . |SemiRing|) T) ((|NewSparseMultivariatePolynomial| . |Monoid|) T) ((|NewSparseMultivariatePolynomial| . |Ring|) T) ((|NewSparseMultivariatePolynomial| . |BiModule|) 142354) ((|NewSparseMultivariatePolynomial| . |RightLinearSet|) 142111) ((|NewSparseMultivariatePolynomial| . |RightModule|) 141868) ((|NewSparseMultivariatePolynomial| . |AbelianGroup|) T) ((|NewSparseMultivariatePolynomial| . |AbelianMonoid|) T) ((|NewSparseMultivariatePolynomial| . |SetCategory|) T) ((|NewSparseMultivariatePolynomial| . |CoercibleTo|) 141727) ((|NewSparseMultivariatePolynomial| . |Type|) T) ((|NewSparseMultivariatePolynomial| . |Join|) T) ((|NewSparseMultivariatePolynomial| . |BasicType|) T) ((|NewSparseMultivariatePolynomial| . |AbelianSemiGroup|) T) ((|NewSparseMultivariatePolynomial| . |CancellationAbelianMonoid|) T) ((|NewSparseMultivariatePolynomial| . |LinearSet|) 141490) ((|NewSparseMultivariatePolynomial| . |Module|) 141253) ((|NewSparseMultivariatePolynomial| . |CharacteristicNonZero|) 141213) ((|NewSparseMultivariatePolynomial| . |CharacteristicZero|) 141176) ((|NewSparseMultivariatePolynomial| . |CommutativeRing|) 141029) ((|NewSparseMultivariatePolynomial| . |Functorial|) 141013) ((|NewSparseMultivariatePolynomial| . |IntegralDomain|) 140899) ((|NewSparseMultivariatePolynomial| . |EntireRing|) 140785) ((|NewSparseMultivariatePolynomial| . |AbelianMonoidRing|) 140743) ((|NewSparseMultivariatePolynomial| . |FullyLinearlyExplicitRingOver|) 140727) ((|NewSparseMultivariatePolynomial| . |LinearlyExplicitRingOver|) 140643) ((|NewSparseMultivariatePolynomial| . |GcdDomain|) 140561) ((|NewSparseMultivariatePolynomial| . |PartialDifferentialRing|) 140545) ((|NewSparseMultivariatePolynomial| . |PartialDifferentialDomain|) 140527) ((|NewSparseMultivariatePolynomial| . |PartialDifferentialSpace|) 140511) ((|NewSparseMultivariatePolynomial| . |PatternMatchable|) 140290) ((|NewSparseMultivariatePolynomial| . |PolynomialFactorizationExplicit|) 140240) ((|NewSparseMultivariatePolynomial| . |UniqueFactorizationDomain|) 140190) ((|NewSparseMultivariatePolynomial| . |PolynomialCategory|) 140143) ((|None| . |SetCategory|) T) ((|None| . |CoercibleTo|) 140117) ((|None| . |Type|) T) ((|None| . |Join|) T) ((|None| . |BasicType|) T) ((|NonNegativeInteger| . |OrderedAbelianMonoidSup|) T) ((|NonNegativeInteger| . |CancellationAbelianMonoid|) T) ((|NonNegativeInteger| . |AbelianSemiGroup|) T) ((|NonNegativeInteger| . |BasicType|) T) ((|NonNegativeInteger| . |Join|) T) ((|NonNegativeInteger| . |Type|) T) ((|NonNegativeInteger| . |CoercibleTo|) 140091) ((|NonNegativeInteger| . |SetCategory|) T) ((|NonNegativeInteger| . |AbelianMonoid|) T) ((|NonNegativeInteger| . |OrderedAbelianMonoid|) T) ((|NonNegativeInteger| . |OrderedSet|) T) ((|NonNegativeInteger| . |OrderedType|) T) ((|NonNegativeInteger| . |OrderedAbelianSemiGroup|) T) ((|NonNegativeInteger| . |OrderedCancellationAbelianMonoid|) T) ((|NonNegativeInteger| . |Monoid|) T) ((|NonNegativeInteger| . |SemiGroup|) T) ((|Multiset| . |MultisetAggregate|) 140075) ((|Multiset| . |SetAggregate|) 140059) ((|Multiset| . |DictionaryOperations|) 140043) ((|Multiset| . |ConvertibleTo|) 139979) ((|Multiset| . |Collection|) 139963) ((|Multiset| . |HomogeneousAggregate|) 139947) ((|Multiset| . |SetCategory|) T) ((|Multiset| . |Functorial|) 139931) ((|Multiset| . |InnerEvalable|) 139850) ((|Multiset| . |Evalable|) 139774) ((|Multiset| . |CoercibleTo|) 139748) ((|Multiset| . |BasicType|) T) ((|Multiset| . |Type|) T) ((|Multiset| . |Join|) T) ((|Multiset| . |Aggregate|) T) ((|Multiset| . |ShallowlyMutableAggregate|) 139732) ((|Multiset| . |BagAggregate|) 139716) ((|Multiset| . |MultiDictionary|) 139700) ((|Multiset| . |FiniteAggregate|) 139684) ((|MonoidRing| . |Ring|) T) ((|MonoidRing| . |Monoid|) T) ((|MonoidRing| . |SemiRing|) T) ((|MonoidRing| . |SemiGroup|) T) ((|MonoidRing| . |Rng|) T) ((|MonoidRing| . |AbelianGroup|) T) ((|MonoidRing| . |LeftLinearSet|) 139611) ((|MonoidRing| . |AbelianMonoid|) T) ((|MonoidRing| . |SetCategory|) T) ((|MonoidRing| . |CoercibleTo|) 139585) ((|MonoidRing| . |Type|) T) ((|MonoidRing| . |Join|) T) ((|MonoidRing| . |BasicType|) T) ((|MonoidRing| . |AbelianSemiGroup|) T) ((|MonoidRing| . |CancellationAbelianMonoid|) T) ((|MonoidRing| . |LeftModule|) 139532) ((|MonoidRing| . |CoercibleFrom|) 139483) ((|MonoidRing| . |RetractableTo|) 139454) ((|MonoidRing| . |Functorial|) 139438) ((|MonoidRing| . |CharacteristicZero|) 139401) ((|MonoidRing| . |CharacteristicNonZero|) 139361) ((|MonoidRing| . |Algebra|) 139318) ((|MonoidRing| . |BiModule|) 139270) ((|MonoidRing| . |RightLinearSet|) 139227) ((|MonoidRing| . |RightModule|) 139184) ((|MonoidRing| . |LinearSet|) 139141) ((|MonoidRing| . |Module|) 139098) ((|MonoidRing| . |Finite|) 139043) ((|MultivariatePolynomial| . |PolynomialCategory|) 138970) ((|MultivariatePolynomial| . |CoercibleFrom|) 138642) ((|MultivariatePolynomial| . |RetractableTo|) 138449) ((|MultivariatePolynomial| . |UniqueFactorizationDomain|) 138399) ((|MultivariatePolynomial| . |PolynomialFactorizationExplicit|) 138349) ((|MultivariatePolynomial| . |PatternMatchable|) NIL) ((|MultivariatePolynomial| . |PartialDifferentialSpace|) 138309) ((|MultivariatePolynomial| . |PartialDifferentialDomain|) 138267) ((|MultivariatePolynomial| . |PartialDifferentialRing|) 138227) ((|MultivariatePolynomial| . |InnerEvalable|) 138153) ((|MultivariatePolynomial| . |GcdDomain|) 138071) ((|MultivariatePolynomial| . |LinearlyExplicitRingOver|) 137987) ((|MultivariatePolynomial| . |LeftModule|) 137816) ((|MultivariatePolynomial| . |FullyLinearlyExplicitRingOver|) 137800) ((|MultivariatePolynomial| . |AbelianMonoidRing|) 137734) ((|MultivariatePolynomial| . |Algebra|) 137497) ((|MultivariatePolynomial| . |LinearSet|) 137260) ((|MultivariatePolynomial| . |Module|) 137023) ((|MultivariatePolynomial| . |EntireRing|) 136909) ((|MultivariatePolynomial| . |IntegralDomain|) 136795) ((|MultivariatePolynomial| . |Functorial|) 136779) ((|MultivariatePolynomial| . |BiModule|) 136522) ((|MultivariatePolynomial| . |RightLinearSet|) 136279) ((|MultivariatePolynomial| . |RightModule|) 136036) ((|MultivariatePolynomial| . |CommutativeRing|) 135889) ((|MultivariatePolynomial| . |CharacteristicZero|) 135852) ((|MultivariatePolynomial| . |CharacteristicNonZero|) 135812) ((|MultivariatePolynomial| . |LeftLinearSet|) 135689) ((|MultivariatePolynomial| . |CancellationAbelianMonoid|) T) ((|MultivariatePolynomial| . |AbelianSemiGroup|) T) ((|MultivariatePolynomial| . |BasicType|) T) ((|MultivariatePolynomial| . |Join|) T) ((|MultivariatePolynomial| . |Type|) T) ((|MultivariatePolynomial| . |CoercibleTo|) 135663) ((|MultivariatePolynomial| . |SetCategory|) T) ((|MultivariatePolynomial| . |AbelianMonoid|) T) ((|MultivariatePolynomial| . |AbelianGroup|) T) ((|MultivariatePolynomial| . |Ring|) T) ((|MultivariatePolynomial| . |Monoid|) T) ((|MultivariatePolynomial| . |SemiRing|) T) ((|MultivariatePolynomial| . |SemiGroup|) T) ((|MultivariatePolynomial| . |Rng|) T) ((|MultivariatePolynomial| . |FullyRetractableTo|) 135647) ((|MultivariatePolynomial| . |FiniteAbelianMonoidRing|) 135581) ((|MultivariatePolynomial| . |Evalable|) 135568) ((|MultivariatePolynomial| . |ConvertibleTo|) 135346) ((|MonoidOperation| . |MonoidOperatorCategory|) 135330) ((|MonoidOperation| . |BinaryOperatorCategory|) 135314) ((|MonoidOperation| . |Type|) T) ((|MonoidOperation| . |MappingCategory|) 135288) ((|MonoidOperation| . |SemiGroupOperatorCategory|) 135272) ((|MonoidOperation| . |SetCategory|) T) ((|MonoidOperation| . |CoercibleTo|) 135210) ((|MonoidOperation| . |Join|) T) ((|MonoidOperation| . |BasicType|) T) ((|MoebiusTransform| . |Group|) T) ((|MoebiusTransform| . |SemiGroup|) T) ((|MoebiusTransform| . |BasicType|) T) ((|MoebiusTransform| . |Join|) T) ((|MoebiusTransform| . |Type|) T) ((|MoebiusTransform| . |CoercibleTo|) 135184) ((|MoebiusTransform| . |SetCategory|) T) ((|MoebiusTransform| . |Monoid|) T) ((|ModularRing| . |Ring|) T) ((|ModularRing| . |Monoid|) T) ((|ModularRing| . |SemiRing|) T) ((|ModularRing| . |SemiGroup|) T) ((|ModularRing| . |Rng|) T) ((|ModularRing| . |AbelianGroup|) T) ((|ModularRing| . |LeftLinearSet|) 135151) ((|ModularRing| . |AbelianMonoid|) T) ((|ModularRing| . |SetCategory|) T) ((|ModularRing| . |CoercibleTo|) 135112) ((|ModularRing| . |Type|) T) ((|ModularRing| . |Join|) T) ((|ModularRing| . |BasicType|) T) ((|ModularRing| . |AbelianSemiGroup|) T) ((|ModularRing| . |CancellationAbelianMonoid|) T) ((|ModularRing| . |LeftModule|) 135099) ((|ModularRing| . |CoercibleFrom|) 135076) ((|ModuleOperator| . |Ring|) T) ((|ModuleOperator| . |Monoid|) T) ((|ModuleOperator| . |SemiRing|) T) ((|ModuleOperator| . |SemiGroup|) T) ((|ModuleOperator| . |Rng|) T) ((|ModuleOperator| . |AbelianGroup|) T) ((|ModuleOperator| . |LeftLinearSet|) 135003) ((|ModuleOperator| . |AbelianMonoid|) T) ((|ModuleOperator| . |SetCategory|) T) ((|ModuleOperator| . |CoercibleTo|) 134977) ((|ModuleOperator| . |Type|) T) ((|ModuleOperator| . |Join|) T) ((|ModuleOperator| . |BasicType|) T) ((|ModuleOperator| . |AbelianSemiGroup|) T) ((|ModuleOperator| . |CancellationAbelianMonoid|) T) ((|ModuleOperator| . |LeftModule|) 134924) ((|ModuleOperator| . |CoercibleFrom|) 134862) ((|ModuleOperator| . |RetractableTo|) 134820) ((|ModuleOperator| . |Eltable|) 134799) ((|ModuleOperator| . |CharacteristicZero|) 134762) ((|ModuleOperator| . |CharacteristicNonZero|) 134722) ((|ModuleOperator| . |Algebra|) 134679) ((|ModuleOperator| . |BiModule|) 134631) ((|ModuleOperator| . |RightLinearSet|) 134588) ((|ModuleOperator| . |RightModule|) 134545) ((|ModuleOperator| . |LinearSet|) 134502) ((|ModuleOperator| . |Module|) 134459) ((|ModuleMonomial| . |OrderedSet|) T) ((|ModuleMonomial| . |CoercibleTo|) 134373) ((|ModuleMonomial| . |SetCategory|) T) ((|ModuleMonomial| . |BasicType|) T) ((|ModuleMonomial| . |Join|) T) ((|ModuleMonomial| . |Type|) T) ((|ModuleMonomial| . |OrderedType|) T) ((|ModuleMonomial| . |HomotopicTo|) 134310) ((|ModuleMonomial| . |CoercibleFrom|) 134247) ((|ModMonic| . |UnivariatePolynomialCategory|) 134231) ((|ModMonic| . |StepThrough|) 134201) ((|ModMonic| . |ConvertibleTo|) NIL) ((|ModMonic| . |Evalable|) 134188) ((|ModMonic| . |InnerEvalable|) 134117) ((|ModMonic| . |FiniteAbelianMonoidRing|) 134078) ((|ModMonic| . |RetractableTo|) 133888) ((|ModMonic| . |FullyRetractableTo|) 133872) ((|ModMonic| . |Algebra|) 133612) ((|ModMonic| . |BiModule|) 133332) ((|ModMonic| . |RightLinearSet|) 133066) ((|ModMonic| . |RightModule|) 132800) ((|ModMonic| . |LeftLinearSet|) 132677) ((|ModMonic| . |LeftModule|) 132506) ((|ModMonic| . |LinearSet|) 132246) ((|ModMonic| . |Module|) 131986) ((|ModMonic| . |CoercibleFrom|) 131625) ((|ModMonic| . |CharacteristicNonZero|) 131585) ((|ModMonic| . |CharacteristicZero|) 131548) ((|ModMonic| . |Functorial|) 131532) ((|ModMonic| . |AbelianMonoidRing|) 131493) ((|ModMonic| . |FullyLinearlyExplicitRingOver|) 131477) ((|ModMonic| . |LinearlyExplicitRingOver|) 131393) ((|ModMonic| . |PartialDifferentialRing|) 131291) ((|ModMonic| . |PartialDifferentialDomain|) 131127) ((|ModMonic| . |PartialDifferentialSpace|) 130967) ((|ModMonic| . |PatternMatchable|) NIL) ((|ModMonic| . |PolynomialFactorizationExplicit|) 130917) ((|ModMonic| . |UniqueFactorizationDomain|) 130867) ((|ModMonic| . |PolynomialCategory|) 130802) ((|ModMonic| . |PrincipalIdealDomain|) 130778) ((|ModMonic| . |IntegralDomain|) 130641) ((|ModMonic| . |EntireRing|) 130504) ((|ModMonic| . |CommutativeRing|) 130334) ((|ModMonic| . |GcdDomain|) 130229) ((|ModMonic| . |EuclideanDomain|) 130205) ((|ModMonic| . |Eltable|) 130108) ((|ModMonic| . |DifferentialRing|) T) ((|ModMonic| . |CancellationAbelianMonoid|) T) ((|ModMonic| . |AbelianSemiGroup|) T) ((|ModMonic| . |BasicType|) T) ((|ModMonic| . |CoercibleTo|) 130082) ((|ModMonic| . |SetCategory|) T) ((|ModMonic| . |AbelianMonoid|) T) ((|ModMonic| . |AbelianGroup|) T) ((|ModMonic| . |Rng|) T) ((|ModMonic| . |SemiGroup|) T) ((|ModMonic| . |SemiRing|) T) ((|ModMonic| . |Monoid|) T) ((|ModMonic| . |Ring|) T) ((|ModMonic| . |DifferentialDomain|) 130069) ((|ModMonic| . |Join|) T) ((|ModMonic| . |Type|) T) ((|ModMonic| . |DifferentialSpace|) T) ((|ModMonic| . |DifferentialSpaceExtension|) 130053) ((|ModMonic| . |DifferentialExtension|) 130037) ((|ModMonic| . |Finite|) 130012) ((|ModularField| . |Field|) T) ((|ModularField| . |UniqueFactorizationDomain|) T) ((|ModularField| . |PrincipalIdealDomain|) T) ((|ModularField| . |IntegralDomain|) T) ((|ModularField| . |CommutativeRing|) T) ((|ModularField| . |CoercibleFrom|) 129946) ((|ModularField| . |Module|) 129900) ((|ModularField| . |LinearSet|) 129854) ((|ModularField| . |Algebra|) 129808) ((|ModularField| . |GcdDomain|) T) ((|ModularField| . |EuclideanDomain|) T) ((|ModularField| . |LeftModule|) 129762) ((|ModularField| . |LeftLinearSet|) 129696) ((|ModularField| . |Rng|) T) ((|ModularField| . |SemiGroup|) T) ((|ModularField| . |SemiRing|) T) ((|ModularField| . |Monoid|) T) ((|ModularField| . |Ring|) T) ((|ModularField| . |BiModule|) 129641) ((|ModularField| . |RightLinearSet|) 129595) ((|ModularField| . |RightModule|) 129549) ((|ModularField| . |AbelianGroup|) T) ((|ModularField| . |AbelianMonoid|) T) ((|ModularField| . |SetCategory|) T) ((|ModularField| . |CoercibleTo|) 129510) ((|ModularField| . |Type|) T) ((|ModularField| . |Join|) T) ((|ModularField| . |BasicType|) T) ((|ModularField| . |AbelianSemiGroup|) T) ((|ModularField| . |CancellationAbelianMonoid|) T) ((|ModularField| . |EntireRing|) T) ((|ModularField| . |DivisionRing|) T) ((|MathMLFormat| . |SetCategory|) T) ((|MathMLFormat| . |CoercibleTo|) 129484) ((|MathMLFormat| . |Type|) T) ((|MathMLFormat| . |Join|) T) ((|MathMLFormat| . |BasicType|) T) ((|Maybe| . |UnionType|) T) ((|Maybe| . |RetractableTo|) 129468) ((|Maybe| . |CoercibleFrom|) 129452) ((|Maybe| . |CoercibleTo|) 129394) ((|Matrix| . |MatrixCategory|) 129355) ((|Matrix| . |FiniteAggregate|) 129339) ((|Matrix| . |Aggregate|) T) ((|Matrix| . |Join|) T) ((|Matrix| . |Type|) T) ((|Matrix| . |BasicType|) 129277) ((|Matrix| . |CoercibleTo|) 129179) ((|Matrix| . |Evalable|) 129103) ((|Matrix| . |InnerEvalable|) 129022) ((|Matrix| . |Functorial|) 129006) ((|Matrix| . |SetCategory|) 128976) ((|Matrix| . |HomogeneousAggregate|) 128960) ((|Matrix| . |ShallowlyMutableAggregate|) 128944) ((|Matrix| . |TwoDimensionalArrayCategory|) 128905) ((|Matrix| . |ConvertibleTo|) 128846) ((|MappingAst| . |SpadSyntaxCategory|) T) ((|MappingAst| . |HomotopicTo|) 128824) ((|MappingAst| . |CoercibleTo|) 128759) ((|MappingAst| . |CoercibleFrom|) 128737) ((|MappingAst| . |SetCategory|) T) ((|MappingAst| . |Type|) T) ((|MappingAst| . |Join|) T) ((|MappingAst| . |BasicType|) T) ((|MappingAst| . |AbstractSyntaxCategory|) T) ((|MacroAst| . |SpadSyntaxCategory|) T) ((|MacroAst| . |HomotopicTo|) 128715) ((|MacroAst| . |CoercibleTo|) 128670) ((|MacroAst| . |CoercibleFrom|) 128648) ((|MacroAst| . |SetCategory|) T) ((|MacroAst| . |Type|) T) ((|MacroAst| . |Join|) T) ((|MacroAst| . |BasicType|) T) ((|MacroAst| . |AbstractSyntaxCategory|) T) ((|LyndonWord| . |OrderedSet|) T) ((|LyndonWord| . |CoercibleTo|) 128560) ((|LyndonWord| . |SetCategory|) T) ((|LyndonWord| . |BasicType|) T) ((|LyndonWord| . |Join|) T) ((|LyndonWord| . |Type|) T) ((|LyndonWord| . |OrderedType|) T) ((|LyndonWord| . |RetractableTo|) 128544) ((|LyndonWord| . |CoercibleFrom|) 128528) ((|ConstructAst| . |SpadSyntaxCategory|) T) ((|ConstructAst| . |HomotopicTo|) 128506) ((|ConstructAst| . |CoercibleTo|) 128461) ((|ConstructAst| . |CoercibleFrom|) 128439) ((|ConstructAst| . |SetCategory|) T) ((|ConstructAst| . |Type|) T) ((|ConstructAst| . |Join|) T) ((|ConstructAst| . |BasicType|) T) ((|ConstructAst| . |AbstractSyntaxCategory|) T) ((|LieSquareMatrix| . |SquareMatrixCategory|) 128383) ((|LieSquareMatrix| . |FiniteAggregate|) 128367) ((|LieSquareMatrix| . |Aggregate|) T) ((|LieSquareMatrix| . |Evalable|) 128291) ((|LieSquareMatrix| . |InnerEvalable|) 128210) ((|LieSquareMatrix| . |Functorial|) 128194) ((|LieSquareMatrix| . |HomogeneousAggregate|) 128178) ((|LieSquareMatrix| . |RectangularMatrixCategory|) 128117) ((|LieSquareMatrix| . |RetractableTo|) 127961) ((|LieSquareMatrix| . |CoercibleFrom|) 127842) ((|LieSquareMatrix| . |FullyRetractableTo|) 127826) ((|LieSquareMatrix| . |LinearlyExplicitRingOver|) 127742) ((|LieSquareMatrix| . |LeftModule|) 127648) ((|LieSquareMatrix| . |FullyLinearlyExplicitRingOver|) 127632) ((|LieSquareMatrix| . |DifferentialRing|) 127597) ((|LieSquareMatrix| . |DifferentialDomain|) 127516) ((|LieSquareMatrix| . |DifferentialSpace|) 127441) ((|LieSquareMatrix| . |DifferentialSpaceExtension|) 127425) ((|LieSquareMatrix| . |PartialDifferentialDomain|) 127297) ((|LieSquareMatrix| . |PartialDifferentialSpace|) 127171) ((|LieSquareMatrix| . |PartialDifferentialRing|) 127103) ((|LieSquareMatrix| . |DifferentialExtension|) 127087) ((|LieSquareMatrix| . |Module|) 127071) ((|LieSquareMatrix| . |LinearSet|) 127055) ((|LieSquareMatrix| . |LeftLinearSet|) 127009) ((|LieSquareMatrix| . |CancellationAbelianMonoid|) T) ((|LieSquareMatrix| . |AbelianSemiGroup|) T) ((|LieSquareMatrix| . |BasicType|) T) ((|LieSquareMatrix| . |Join|) T) ((|LieSquareMatrix| . |Type|) T) ((|LieSquareMatrix| . |CoercibleTo|) 126959) ((|LieSquareMatrix| . |SetCategory|) T) ((|LieSquareMatrix| . |AbelianMonoid|) T) ((|LieSquareMatrix| . |AbelianGroup|) T) ((|LieSquareMatrix| . |RightModule|) 126943) ((|LieSquareMatrix| . |RightLinearSet|) 126927) ((|LieSquareMatrix| . |BiModule|) 126906) ((|LieSquareMatrix| . |Ring|) T) ((|LieSquareMatrix| . |Monoid|) T) ((|LieSquareMatrix| . |SemiRing|) T) ((|LieSquareMatrix| . |SemiGroup|) T) ((|LieSquareMatrix| . |Rng|) T) ((|LieSquareMatrix| . |Algebra|) 126851) ((|LieSquareMatrix| . |FramedNonAssociativeAlgebra|) 126835) ((|LieSquareMatrix| . |NonAssociativeAlgebra|) 126819) ((|LieSquareMatrix| . |Monad|) T) ((|LieSquareMatrix| . |NonAssociativeRng|) T) ((|LieSquareMatrix| . |FiniteRankNonAssociativeAlgebra|) 126803) ((|LieSquareMatrix| . |Eltable|) 126775) ((|LiePolynomial| . |FreeLieAlgebra|) 126754) ((|LiePolynomial| . |Module|) 126738) ((|LiePolynomial| . |LinearSet|) 126722) ((|LiePolynomial| . |LeftModule|) 126706) ((|LiePolynomial| . |LeftLinearSet|) 126670) ((|LiePolynomial| . |CancellationAbelianMonoid|) T) ((|LiePolynomial| . |AbelianSemiGroup|) T) ((|LiePolynomial| . |BasicType|) T) ((|LiePolynomial| . |Join|) T) ((|LiePolynomial| . |Type|) T) ((|LiePolynomial| . |CoercibleTo|) 126556) ((|LiePolynomial| . |SetCategory|) T) ((|LiePolynomial| . |AbelianMonoid|) T) ((|LiePolynomial| . |AbelianGroup|) T) ((|LiePolynomial| . |RightModule|) 126540) ((|LiePolynomial| . |RightLinearSet|) 126524) ((|LiePolynomial| . |BiModule|) 126503) ((|LiePolynomial| . |LieAlgebra|) 126487) ((|LiePolynomial| . |FreeModuleCat|) 126451) ((|LiePolynomial| . |CoercibleFrom|) 126420) ((|LiePolynomial| . |RetractableTo|) 126389) ((|LiePolynomial| . |Functorial|) 126373) ((|LinearOrdinaryDifferentialOperator2| . |LinearOrdinaryDifferentialOperatorCategory|) 126357) ((|LinearOrdinaryDifferentialOperator2| . |Algebra|) 126314) ((|LinearOrdinaryDifferentialOperator2| . |CoercibleFrom|) 126195) ((|LinearOrdinaryDifferentialOperator2| . |LeftModule|) 126169) ((|LinearOrdinaryDifferentialOperator2| . |LeftLinearSet|) 126123) ((|LinearOrdinaryDifferentialOperator2| . |Rng|) T) ((|LinearOrdinaryDifferentialOperator2| . |SemiGroup|) T) ((|LinearOrdinaryDifferentialOperator2| . |SemiRing|) T) ((|LinearOrdinaryDifferentialOperator2| . |Monoid|) T) ((|LinearOrdinaryDifferentialOperator2| . |Ring|) T) ((|LinearOrdinaryDifferentialOperator2| . |BiModule|) 126102) ((|LinearOrdinaryDifferentialOperator2| . |RightLinearSet|) 126086) ((|LinearOrdinaryDifferentialOperator2| . |RightModule|) 126070) ((|LinearOrdinaryDifferentialOperator2| . |AbelianGroup|) T) ((|LinearOrdinaryDifferentialOperator2| . |AbelianMonoid|) T) ((|LinearOrdinaryDifferentialOperator2| . |SetCategory|) T) ((|LinearOrdinaryDifferentialOperator2| . |CoercibleTo|) 126044) ((|LinearOrdinaryDifferentialOperator2| . |BasicType|) T) ((|LinearOrdinaryDifferentialOperator2| . |AbelianSemiGroup|) T) ((|LinearOrdinaryDifferentialOperator2| . |CancellationAbelianMonoid|) T) ((|LinearOrdinaryDifferentialOperator2| . |LinearSet|) 126001) ((|LinearOrdinaryDifferentialOperator2| . |Module|) 125958) ((|LinearOrdinaryDifferentialOperator2| . |FullyRetractableTo|) 125942) ((|LinearOrdinaryDifferentialOperator2| . |RetractableTo|) 125786) ((|LinearOrdinaryDifferentialOperator2| . |UnivariateSkewPolynomialCategory|) 125770) ((|LinearOrdinaryDifferentialOperator2| . |Type|) T) ((|LinearOrdinaryDifferentialOperator2| . |Join|) T) ((|LinearOrdinaryDifferentialOperator2| . |Eltable|) 125731) ((|LinearOrdinaryDifferentialOperator1| . |LinearOrdinaryDifferentialOperatorCategory|) 125715) ((|LinearOrdinaryDifferentialOperator1| . |Algebra|) 125672) ((|LinearOrdinaryDifferentialOperator1| . |CoercibleFrom|) 125553) ((|LinearOrdinaryDifferentialOperator1| . |LeftModule|) 125527) ((|LinearOrdinaryDifferentialOperator1| . |LeftLinearSet|) 125481) ((|LinearOrdinaryDifferentialOperator1| . |Rng|) T) ((|LinearOrdinaryDifferentialOperator1| . |SemiGroup|) T) ((|LinearOrdinaryDifferentialOperator1| . |SemiRing|) T) ((|LinearOrdinaryDifferentialOperator1| . |Monoid|) T) ((|LinearOrdinaryDifferentialOperator1| . |Ring|) T) ((|LinearOrdinaryDifferentialOperator1| . |BiModule|) 125460) ((|LinearOrdinaryDifferentialOperator1| . |RightLinearSet|) 125444) ((|LinearOrdinaryDifferentialOperator1| . |RightModule|) 125428) ((|LinearOrdinaryDifferentialOperator1| . |AbelianGroup|) T) ((|LinearOrdinaryDifferentialOperator1| . |AbelianMonoid|) T) ((|LinearOrdinaryDifferentialOperator1| . |SetCategory|) T) ((|LinearOrdinaryDifferentialOperator1| . |CoercibleTo|) 125402) ((|LinearOrdinaryDifferentialOperator1| . |BasicType|) T) ((|LinearOrdinaryDifferentialOperator1| . |AbelianSemiGroup|) T) ((|LinearOrdinaryDifferentialOperator1| . |CancellationAbelianMonoid|) T) ((|LinearOrdinaryDifferentialOperator1| . |LinearSet|) 125359) ((|LinearOrdinaryDifferentialOperator1| . |Module|) 125316) ((|LinearOrdinaryDifferentialOperator1| . |FullyRetractableTo|) 125300) ((|LinearOrdinaryDifferentialOperator1| . |RetractableTo|) 125144) ((|LinearOrdinaryDifferentialOperator1| . |UnivariateSkewPolynomialCategory|) 125128) ((|LinearOrdinaryDifferentialOperator1| . |Type|) T) ((|LinearOrdinaryDifferentialOperator1| . |Join|) T) ((|LinearOrdinaryDifferentialOperator1| . |Eltable|) 125107) ((|LinearOrdinaryDifferentialOperator| . |LinearOrdinaryDifferentialOperatorCategory|) 125091) ((|LinearOrdinaryDifferentialOperator| . |Algebra|) 125048) ((|LinearOrdinaryDifferentialOperator| . |CoercibleFrom|) 124929) ((|LinearOrdinaryDifferentialOperator| . |LeftModule|) 124903) ((|LinearOrdinaryDifferentialOperator| . |LeftLinearSet|) 124857) ((|LinearOrdinaryDifferentialOperator| . |Rng|) T) ((|LinearOrdinaryDifferentialOperator| . |SemiGroup|) T) ((|LinearOrdinaryDifferentialOperator| . |SemiRing|) T) ((|LinearOrdinaryDifferentialOperator| . |Monoid|) T) ((|LinearOrdinaryDifferentialOperator| . |Ring|) T) ((|LinearOrdinaryDifferentialOperator| . |BiModule|) 124836) ((|LinearOrdinaryDifferentialOperator| . |RightLinearSet|) 124820) ((|LinearOrdinaryDifferentialOperator| . |RightModule|) 124804) ((|LinearOrdinaryDifferentialOperator| . |AbelianGroup|) T) ((|LinearOrdinaryDifferentialOperator| . |AbelianMonoid|) T) ((|LinearOrdinaryDifferentialOperator| . |SetCategory|) T) ((|LinearOrdinaryDifferentialOperator| . |CoercibleTo|) 124778) ((|LinearOrdinaryDifferentialOperator| . |BasicType|) T) ((|LinearOrdinaryDifferentialOperator| . |AbelianSemiGroup|) T) ((|LinearOrdinaryDifferentialOperator| . |CancellationAbelianMonoid|) T) ((|LinearOrdinaryDifferentialOperator| . |LinearSet|) 124735) ((|LinearOrdinaryDifferentialOperator| . |Module|) 124692) ((|LinearOrdinaryDifferentialOperator| . |FullyRetractableTo|) 124676) ((|LinearOrdinaryDifferentialOperator| . |RetractableTo|) 124520) ((|LinearOrdinaryDifferentialOperator| . |UnivariateSkewPolynomialCategory|) 124504) ((|LinearOrdinaryDifferentialOperator| . |Type|) T) ((|LinearOrdinaryDifferentialOperator| . |Join|) T) ((|LinearOrdinaryDifferentialOperator| . |Eltable|) 124483) ((|Localize| . |Module|) 124467) ((|Localize| . |LinearSet|) 124451) ((|Localize| . |LeftModule|) 124435) ((|Localize| . |LeftLinearSet|) 124399) ((|Localize| . |CancellationAbelianMonoid|) T) ((|Localize| . |AbelianSemiGroup|) T) ((|Localize| . |BasicType|) T) ((|Localize| . |Join|) T) ((|Localize| . |Type|) T) ((|Localize| . |CoercibleTo|) 124373) ((|Localize| . |SetCategory|) T) ((|Localize| . |AbelianMonoid|) T) ((|Localize| . |AbelianGroup|) T) ((|Localize| . |RightModule|) 124357) ((|Localize| . |RightLinearSet|) 124341) ((|Localize| . |BiModule|) 124320) ((|Localize| . |OrderedAbelianGroup|) 124282) ((|Localize| . |OrderedAbelianMonoid|) 124244) ((|Localize| . |OrderedSet|) 124206) ((|Localize| . |OrderedType|) 124168) ((|Localize| . |OrderedAbelianSemiGroup|) 124130) ((|Localize| . |OrderedCancellationAbelianMonoid|) 124092) ((|ListMonoidOps| . |SetCategory|) T) ((|ListMonoidOps| . |CoercibleTo|) 124066) ((|ListMonoidOps| . |Type|) T) ((|ListMonoidOps| . |Join|) T) ((|ListMonoidOps| . |BasicType|) T) ((|ListMonoidOps| . |RetractableTo|) 124050) ((|ListMonoidOps| . |CoercibleFrom|) 124034) ((|ListMultiDictionary| . |MultiDictionary|) 124018) ((|ListMultiDictionary| . |BagAggregate|) 124002) ((|ListMultiDictionary| . |ShallowlyMutableAggregate|) 123986) ((|ListMultiDictionary| . |Aggregate|) T) ((|ListMultiDictionary| . |Join|) T) ((|ListMultiDictionary| . |Type|) T) ((|ListMultiDictionary| . |BasicType|) 123924) ((|ListMultiDictionary| . |CoercibleTo|) 123826) ((|ListMultiDictionary| . |Evalable|) 123750) ((|ListMultiDictionary| . |InnerEvalable|) 123669) ((|ListMultiDictionary| . |Functorial|) 123653) ((|ListMultiDictionary| . |SetCategory|) 123623) ((|ListMultiDictionary| . |HomogeneousAggregate|) 123607) ((|ListMultiDictionary| . |Collection|) 123591) ((|ListMultiDictionary| . |ConvertibleTo|) 123527) ((|ListMultiDictionary| . |DictionaryOperations|) 123511) ((|ListMultiDictionary| . |FiniteAggregate|) 123495) ((|Literal| . |SpadSyntaxCategory|) T) ((|Literal| . |HomotopicTo|) 123473) ((|Literal| . |CoercibleTo|) 123415) ((|Literal| . |CoercibleFrom|) 123393) ((|Literal| . |SetCategory|) T) ((|Literal| . |Type|) T) ((|Literal| . |Join|) T) ((|Literal| . |BasicType|) T) ((|Literal| . |AbstractSyntaxCategory|) T) ((|List| . |ListAggregate|) 123377) ((|List| . |UnaryRecursiveAggregate|) 123361) ((|List| . |RecursiveAggregate|) 123345) ((|List| . |StreamAggregate|) 123329) ((|List| . |FiniteAggregate|) 123313) ((|List| . |OrderedSet|) 123284) ((|List| . |OrderedType|) 123255) ((|List| . |FiniteLinearAggregate|) 123239) ((|List| . |LinearAggregate|) 123223) ((|List| . |EltableAggregate|) 123195) ((|List| . |Eltable|) 123124) ((|List| . |IndexedAggregate|) 123096) ((|List| . |ConvertibleTo|) 123032) ((|List| . |HomogeneousAggregate|) 123016) ((|List| . |SetCategory|) 122953) ((|List| . |Functorial|) 122937) ((|List| . |InnerEvalable|) 122856) ((|List| . |Evalable|) 122780) ((|List| . |CoercibleTo|) 122654) ((|List| . |BasicType|) 122564) ((|List| . |Type|) T) ((|List| . |Join|) T) ((|List| . |Aggregate|) T) ((|List| . |Collection|) 122548) ((|List| . |ShallowlyMutableAggregate|) 122532) ((|List| . |ExtensibleLinearAggregate|) 122516) ((|LinearForm| . |VectorSpace|) 122500) ((|LinearForm| . |BiModule|) 122479) ((|LinearForm| . |RightLinearSet|) 122463) ((|LinearForm| . |RightModule|) 122447) ((|LinearForm| . |AbelianGroup|) T) ((|LinearForm| . |LeftLinearSet|) 122411) ((|LinearForm| . |AbelianMonoid|) T) ((|LinearForm| . |SetCategory|) T) ((|LinearForm| . |CoercibleTo|) 122385) ((|LinearForm| . |Type|) T) ((|LinearForm| . |Join|) T) ((|LinearForm| . |BasicType|) T) ((|LinearForm| . |AbelianSemiGroup|) T) ((|LinearForm| . |CancellationAbelianMonoid|) T) ((|LinearForm| . |LeftModule|) 122369) ((|LinearForm| . |LinearSet|) 122353) ((|LinearForm| . |Module|) 122337) ((|LinearForm| . |Eltable|) 122293) ((|LinearElement| . |VectorSpace|) 122277) ((|LinearElement| . |BiModule|) 122256) ((|LinearElement| . |RightLinearSet|) 122240) ((|LinearElement| . |RightModule|) 122224) ((|LinearElement| . |AbelianGroup|) T) ((|LinearElement| . |LeftLinearSet|) 122188) ((|LinearElement| . |AbelianMonoid|) T) ((|LinearElement| . |SetCategory|) T) ((|LinearElement| . |CoercibleTo|) 122162) ((|LinearElement| . |Type|) T) ((|LinearElement| . |Join|) T) ((|LinearElement| . |BasicType|) T) ((|LinearElement| . |AbelianSemiGroup|) T) ((|LinearElement| . |CancellationAbelianMonoid|) T) ((|LinearElement| . |LeftModule|) 122146) ((|LinearElement| . |LinearSet|) 122130) ((|LinearElement| . |Module|) 122114) ((|LinearElement| . |CoercibleFrom|) 122082) ((|LinearElement| . |IndexedDirectProductCategory|) 122045) ((|LinearElement| . |Functorial|) 122029) ((|LinearElement| . |ConvertibleFrom|) 121960) ((|LinearBasis| . |OrderedFinite|) T) ((|LinearBasis| . |OrderedType|) T) ((|LinearBasis| . |OrderedSet|) T) ((|LinearBasis| . |SetCategory|) T) ((|LinearBasis| . |CoercibleTo|) 121934) ((|LinearBasis| . |Type|) T) ((|LinearBasis| . |Join|) T) ((|LinearBasis| . |BasicType|) T) ((|LinearBasis| . |Finite|) T) ((|LinearBasis| . |CoercibleFrom|) 121894) ((|AssociatedLieAlgebra| . |NonAssociativeAlgebra|) 121878) ((|AssociatedLieAlgebra| . |Monad|) T) ((|AssociatedLieAlgebra| . |NonAssociativeRng|) T) ((|AssociatedLieAlgebra| . |BiModule|) 121857) ((|AssociatedLieAlgebra| . |RightLinearSet|) 121841) ((|AssociatedLieAlgebra| . |RightModule|) 121825) ((|AssociatedLieAlgebra| . |AbelianGroup|) T) ((|AssociatedLieAlgebra| . |LeftLinearSet|) 121789) ((|AssociatedLieAlgebra| . |AbelianMonoid|) T) ((|AssociatedLieAlgebra| . |SetCategory|) T) ((|AssociatedLieAlgebra| . |CoercibleTo|) 121750) ((|AssociatedLieAlgebra| . |Type|) T) ((|AssociatedLieAlgebra| . |Join|) T) ((|AssociatedLieAlgebra| . |BasicType|) T) ((|AssociatedLieAlgebra| . |AbelianSemiGroup|) T) ((|AssociatedLieAlgebra| . |CancellationAbelianMonoid|) T) ((|AssociatedLieAlgebra| . |LeftModule|) 121734) ((|AssociatedLieAlgebra| . |LinearSet|) 121718) ((|AssociatedLieAlgebra| . |Module|) 121702) ((|AssociatedLieAlgebra| . |FramedNonAssociativeAlgebra|) 121638) ((|AssociatedLieAlgebra| . |FiniteRankNonAssociativeAlgebra|) 121519) ((|AssociatedLieAlgebra| . |Eltable|) 121447) ((|Library| . |TableAggregate|) 121417) ((|Library| . |Dictionary|) 121350) ((|Library| . |BagAggregate|) 121283) ((|Library| . |ShallowlyMutableAggregate|) 121201) ((|Library| . |Collection|) 121134) ((|Library| . |ConvertibleTo|) NIL) ((|Library| . |DictionaryOperations|) 121067) ((|Library| . |IndexedAggregate|) 121037) ((|Library| . |Evalable|) 120843) ((|Library| . |InnerEvalable|) 120642) ((|Library| . |Functorial|) 120560) ((|Library| . |HomogeneousAggregate|) 120478) ((|Library| . |Eltable|) 120422) ((|Library| . |EltableAggregate|) 120392) ((|Library| . |KeyedDictionary|) 120362) ((|Library| . |SetCategory|) T) ((|Library| . |CoercibleTo|) 120336) ((|Library| . |BasicType|) T) ((|Library| . |Type|) T) ((|Library| . |Join|) T) ((|Library| . |Aggregate|) T) ((|Library| . |FiniteAggregate|) 120269) ((|LieExponentials| . |Group|) T) ((|LieExponentials| . |SemiGroup|) T) ((|LieExponentials| . |BasicType|) T) ((|LieExponentials| . |Join|) T) ((|LieExponentials| . |Type|) T) ((|LieExponentials| . |CoercibleTo|) 120161) ((|LieExponentials| . |SetCategory|) T) ((|LieExponentials| . |Monoid|) T) ((|LetAst| . |SpadSyntaxCategory|) T) ((|LetAst| . |HomotopicTo|) 120139) ((|LetAst| . |CoercibleTo|) 120094) ((|LetAst| . |CoercibleFrom|) 120072) ((|LetAst| . |SetCategory|) T) ((|LetAst| . |Type|) T) ((|LetAst| . |Join|) T) ((|LetAst| . |BasicType|) T) ((|LetAst| . |AbstractSyntaxCategory|) T) ((|LaurentPolynomial| . |DifferentialExtension|) 120056) ((|LaurentPolynomial| . |PartialDifferentialRing|) 119988) ((|LaurentPolynomial| . |PartialDifferentialSpace|) 119862) ((|LaurentPolynomial| . |PartialDifferentialDomain|) 119734) ((|LaurentPolynomial| . |DifferentialSpaceExtension|) 119718) ((|LaurentPolynomial| . |DifferentialSpace|) 119643) ((|LaurentPolynomial| . |Type|) T) ((|LaurentPolynomial| . |Join|) T) ((|LaurentPolynomial| . |DifferentialDomain|) 119562) ((|LaurentPolynomial| . |Ring|) T) ((|LaurentPolynomial| . |Monoid|) T) ((|LaurentPolynomial| . |SemiRing|) T) ((|LaurentPolynomial| . |SemiGroup|) T) ((|LaurentPolynomial| . |Rng|) T) ((|LaurentPolynomial| . |AbelianGroup|) T) ((|LaurentPolynomial| . |LeftLinearSet|) 119529) ((|LaurentPolynomial| . |AbelianMonoid|) T) ((|LaurentPolynomial| . |SetCategory|) T) ((|LaurentPolynomial| . |CoercibleTo|) 119503) ((|LaurentPolynomial| . |BasicType|) T) ((|LaurentPolynomial| . |AbelianSemiGroup|) T) ((|LaurentPolynomial| . |CancellationAbelianMonoid|) T) ((|LaurentPolynomial| . |LeftModule|) 119490) ((|LaurentPolynomial| . |CoercibleFrom|) 119348) ((|LaurentPolynomial| . |DifferentialRing|) 119313) ((|LaurentPolynomial| . |IntegralDomain|) T) ((|LaurentPolynomial| . |EntireRing|) T) ((|LaurentPolynomial| . |CommutativeRing|) T) ((|LaurentPolynomial| . |Module|) 119300) ((|LaurentPolynomial| . |LinearSet|) 119287) ((|LaurentPolynomial| . |RightModule|) 119274) ((|LaurentPolynomial| . |RightLinearSet|) 119261) ((|LaurentPolynomial| . |BiModule|) 119246) ((|LaurentPolynomial| . |Algebra|) 119233) ((|LaurentPolynomial| . |ConvertibleTo|) 119204) ((|LaurentPolynomial| . |FullyRetractableTo|) 119188) ((|LaurentPolynomial| . |RetractableTo|) 119019) ((|LaurentPolynomial| . |CharacteristicZero|) 118982) ((|LaurentPolynomial| . |CharacteristicNonZero|) 118942) ((|LaurentPolynomial| . |EuclideanDomain|) 118918) ((|LaurentPolynomial| . |GcdDomain|) 118894) ((|LaurentPolynomial| . |PrincipalIdealDomain|) 118870) ((|LocalAlgebra| . |Algebra|) 118854) ((|LocalAlgebra| . |CoercibleFrom|) 118818) ((|LocalAlgebra| . |LeftModule|) 118792) ((|LocalAlgebra| . |LeftLinearSet|) 118746) ((|LocalAlgebra| . |Rng|) T) ((|LocalAlgebra| . |SemiGroup|) T) ((|LocalAlgebra| . |SemiRing|) T) ((|LocalAlgebra| . |Monoid|) T) ((|LocalAlgebra| . |Ring|) T) ((|LocalAlgebra| . |BiModule|) 118725) ((|LocalAlgebra| . |RightLinearSet|) 118709) ((|LocalAlgebra| . |RightModule|) 118693) ((|LocalAlgebra| . |AbelianGroup|) T) ((|LocalAlgebra| . |AbelianMonoid|) T) ((|LocalAlgebra| . |SetCategory|) T) ((|LocalAlgebra| . |CoercibleTo|) 118667) ((|LocalAlgebra| . |Type|) T) ((|LocalAlgebra| . |Join|) T) ((|LocalAlgebra| . |BasicType|) T) ((|LocalAlgebra| . |AbelianSemiGroup|) T) ((|LocalAlgebra| . |CancellationAbelianMonoid|) T) ((|LocalAlgebra| . |LinearSet|) 118651) ((|LocalAlgebra| . |Module|) 118635) ((|LocalAlgebra| . |OrderedRing|) 118605) ((|LocalAlgebra| . |OrderedCancellationAbelianMonoid|) 118575) ((|LocalAlgebra| . |OrderedAbelianSemiGroup|) 118545) ((|LocalAlgebra| . |OrderedType|) 118515) ((|LocalAlgebra| . |OrderedSet|) 118485) ((|LocalAlgebra| . |OrderedAbelianMonoid|) 118455) ((|LocalAlgebra| . |OrderedAbelianGroup|) 118425) ((|LocalAlgebra| . |CharacteristicZero|) 118395) ((|KleeneTrivalentLogic| . |PropositionalLogic|) T) ((|KleeneTrivalentLogic| . |BasicType|) T) ((|KleeneTrivalentLogic| . |CoercibleTo|) 118369) ((|KleeneTrivalentLogic| . |SetCategory|) T) ((|KleeneTrivalentLogic| . |Logic|) T) ((|KleeneTrivalentLogic| . |Join|) T) ((|KleeneTrivalentLogic| . |Type|) T) ((|KleeneTrivalentLogic| . |BooleanLogic|) T) ((|KleeneTrivalentLogic| . |Finite|) T) ((|Kernel| . |CachableSet|) T) ((|Kernel| . |BasicType|) T) ((|Kernel| . |Join|) T) ((|Kernel| . |Type|) T) ((|Kernel| . |CoercibleTo|) 118343) ((|Kernel| . |SetCategory|) T) ((|Kernel| . |OrderedSet|) T) ((|Kernel| . |OrderedType|) T) ((|Kernel| . |Patternable|) 118327) ((|Kernel| . |ConvertibleTo|) 118110) ((|KeyedAccessFile| . |FileCategory|) 118033) ((|KeyedAccessFile| . |BasicType|) T) ((|KeyedAccessFile| . |Join|) T) ((|KeyedAccessFile| . |Type|) T) ((|KeyedAccessFile| . |CoercibleTo|) 118007) ((|KeyedAccessFile| . |SetCategory|) T) ((|KeyedAccessFile| . |TableAggregate|) 117980) ((|KeyedAccessFile| . |Dictionary|) 117916) ((|KeyedAccessFile| . |BagAggregate|) 117852) ((|KeyedAccessFile| . |ShallowlyMutableAggregate|) 117775) ((|KeyedAccessFile| . |Collection|) 117711) ((|KeyedAccessFile| . |ConvertibleTo|) NIL) ((|KeyedAccessFile| . |DictionaryOperations|) 117647) ((|KeyedAccessFile| . |IndexedAggregate|) 117620) ((|KeyedAccessFile| . |Evalable|) 117362) ((|KeyedAccessFile| . |InnerEvalable|) 117092) ((|KeyedAccessFile| . |Functorial|) 117015) ((|KeyedAccessFile| . |HomogeneousAggregate|) 116938) ((|KeyedAccessFile| . |Eltable|) 116911) ((|KeyedAccessFile| . |EltableAggregate|) 116884) ((|KeyedAccessFile| . |KeyedDictionary|) 116857) ((|KeyedAccessFile| . |Aggregate|) T) ((|KeyedAccessFile| . |FiniteAggregate|) 116793) ((|JVMOpcode| . |SetCategory|) T) ((|JVMOpcode| . |CoercibleTo|) 116726) ((|JVMOpcode| . |Type|) T) ((|JVMOpcode| . |Join|) T) ((|JVMOpcode| . |BasicType|) T) ((|JVMOpcode| . |HomotopicTo|) 116682) ((|JVMOpcode| . |CoercibleFrom|) 116638) ((|JVMMethodAccess| . |SetCategory|) T) ((|JVMMethodAccess| . |CoercibleTo|) 116612) ((|JVMMethodAccess| . |Type|) T) ((|JVMMethodAccess| . |Join|) T) ((|JVMMethodAccess| . |BasicType|) T) ((|JVMMethodAccess| . |Logic|) T) ((|JVMFieldAccess| . |SetCategory|) T) ((|JVMFieldAccess| . |CoercibleTo|) 116586) ((|JVMFieldAccess| . |Type|) T) ((|JVMFieldAccess| . |Join|) T) ((|JVMFieldAccess| . |BasicType|) T) ((|JVMFieldAccess| . |Logic|) T) ((|JVMConstantTag| . |SetCategory|) T) ((|JVMConstantTag| . |CoercibleTo|) 116543) ((|JVMConstantTag| . |Type|) T) ((|JVMConstantTag| . |Join|) T) ((|JVMConstantTag| . |BasicType|) T) ((|JVMClassFileAccess| . |SetCategory|) T) ((|JVMClassFileAccess| . |CoercibleTo|) 116517) ((|JVMClassFileAccess| . |Type|) T) ((|JVMClassFileAccess| . |Join|) T) ((|JVMClassFileAccess| . |BasicType|) T) ((|JVMClassFileAccess| . |Logic|) T) ((|JVMBytecode| . |SetCategory|) T) ((|JVMBytecode| . |CoercibleTo|) 116474) ((|JVMBytecode| . |Type|) T) ((|JVMBytecode| . |Join|) T) ((|JVMBytecode| . |BasicType|) T) ((|JVMBytecode| . |HomotopicTo|) 116454) ((|JVMBytecode| . |CoercibleFrom|) 116434) ((|AssociatedJordanAlgebra| . |NonAssociativeAlgebra|) 116418) ((|AssociatedJordanAlgebra| . |Monad|) T) ((|AssociatedJordanAlgebra| . |NonAssociativeRng|) T) ((|AssociatedJordanAlgebra| . |BiModule|) 116397) ((|AssociatedJordanAlgebra| . |RightLinearSet|) 116381) ((|AssociatedJordanAlgebra| . |RightModule|) 116365) ((|AssociatedJordanAlgebra| . |AbelianGroup|) T) ((|AssociatedJordanAlgebra| . |LeftLinearSet|) 116329) ((|AssociatedJordanAlgebra| . |AbelianMonoid|) T) ((|AssociatedJordanAlgebra| . |SetCategory|) T) ((|AssociatedJordanAlgebra| . |CoercibleTo|) 116290) ((|AssociatedJordanAlgebra| . |Type|) T) ((|AssociatedJordanAlgebra| . |Join|) T) ((|AssociatedJordanAlgebra| . |BasicType|) T) ((|AssociatedJordanAlgebra| . |AbelianSemiGroup|) T) ((|AssociatedJordanAlgebra| . |CancellationAbelianMonoid|) T) ((|AssociatedJordanAlgebra| . |LeftModule|) 116274) ((|AssociatedJordanAlgebra| . |LinearSet|) 116258) ((|AssociatedJordanAlgebra| . |Module|) 116242) ((|AssociatedJordanAlgebra| . |FramedNonAssociativeAlgebra|) 116178) ((|AssociatedJordanAlgebra| . |FiniteRankNonAssociativeAlgebra|) 116059) ((|AssociatedJordanAlgebra| . |Eltable|) 115987) ((|JoinAst| . |SpadSyntaxCategory|) T) ((|JoinAst| . |HomotopicTo|) 115965) ((|JoinAst| . |CoercibleTo|) 115900) ((|JoinAst| . |CoercibleFrom|) 115878) ((|JoinAst| . |SetCategory|) T) ((|JoinAst| . |Type|) T) ((|JoinAst| . |Join|) T) ((|JoinAst| . |BasicType|) T) ((|JoinAst| . |AbstractSyntaxCategory|) T) ((|InfiniteTuple| . |Functorial|) 115862) ((|InfiniteTuple| . |Join|) T) ((|InfiniteTuple| . |Type|) T) ((|InfiniteTuple| . |CoercibleTo|) 115836) ((|InternalTypeForm| . |SetCategory|) T) ((|InternalTypeForm| . |CoercibleTo|) 115791) ((|InternalTypeForm| . |Type|) T) ((|InternalTypeForm| . |Join|) T) ((|InternalTypeForm| . |BasicType|) T) ((|InternalTypeForm| . |HomotopicTo|) 115769) ((|InternalTypeForm| . |CoercibleFrom|) 115747) ((|InnerTaylorSeries| . |Ring|) T) ((|InnerTaylorSeries| . |Monoid|) T) ((|InnerTaylorSeries| . |SemiRing|) T) ((|InnerTaylorSeries| . |SemiGroup|) T) ((|InnerTaylorSeries| . |Rng|) T) ((|InnerTaylorSeries| . |AbelianGroup|) T) ((|InnerTaylorSeries| . |LeftLinearSet|) 115701) ((|InnerTaylorSeries| . |AbelianMonoid|) T) ((|InnerTaylorSeries| . |SetCategory|) T) ((|InnerTaylorSeries| . |CoercibleTo|) 115675) ((|InnerTaylorSeries| . |Type|) T) ((|InnerTaylorSeries| . |Join|) T) ((|InnerTaylorSeries| . |BasicType|) T) ((|InnerTaylorSeries| . |AbelianSemiGroup|) T) ((|InnerTaylorSeries| . |CancellationAbelianMonoid|) T) ((|InnerTaylorSeries| . |LeftModule|) 115649) ((|InnerTaylorSeries| . |CoercibleFrom|) 115590) ((|InnerTaylorSeries| . |BiModule|) 115531) ((|InnerTaylorSeries| . |RightLinearSet|) 115479) ((|InnerTaylorSeries| . |RightModule|) 115427) ((|InnerTaylorSeries| . |IntegralDomain|) 115394) ((|InnerTaylorSeries| . |EntireRing|) 115361) ((|InnerTaylorSeries| . |CommutativeRing|) 115328) ((|InnerTaylorSeries| . |Module|) 115289) ((|InnerTaylorSeries| . |LinearSet|) 115250) ((|InnerTaylorSeries| . |Algebra|) 115211) ((|InnerSparseUnivariatePowerSeries| . |UnivariatePowerSeriesCategory|) 115183) ((|InnerSparseUnivariatePowerSeries| . |AbelianMonoidRing|) 115155) ((|InnerSparseUnivariatePowerSeries| . |Algebra|) 114999) ((|InnerSparseUnivariatePowerSeries| . |LinearSet|) 114843) ((|InnerSparseUnivariatePowerSeries| . |Module|) 114687) ((|InnerSparseUnivariatePowerSeries| . |CoercibleFrom|) 114511) ((|InnerSparseUnivariatePowerSeries| . |EntireRing|) 114478) ((|InnerSparseUnivariatePowerSeries| . |IntegralDomain|) 114445) ((|InnerSparseUnivariatePowerSeries| . |Functorial|) 114429) ((|InnerSparseUnivariatePowerSeries| . |BiModule|) 114248) ((|InnerSparseUnivariatePowerSeries| . |RightLinearSet|) 114081) ((|InnerSparseUnivariatePowerSeries| . |RightModule|) 113914) ((|InnerSparseUnivariatePowerSeries| . |CommutativeRing|) 113843) ((|InnerSparseUnivariatePowerSeries| . |CharacteristicZero|) 113806) ((|InnerSparseUnivariatePowerSeries| . |CharacteristicNonZero|) 113766) ((|InnerSparseUnivariatePowerSeries| . |LeftModule|) 113663) ((|InnerSparseUnivariatePowerSeries| . |LeftLinearSet|) 113540) ((|InnerSparseUnivariatePowerSeries| . |PowerSeriesCategory|) 113486) ((|InnerSparseUnivariatePowerSeries| . |PartialDifferentialSpace|) 113361) ((|InnerSparseUnivariatePowerSeries| . |PartialDifferentialDomain|) 113234) ((|InnerSparseUnivariatePowerSeries| . |PartialDifferentialRing|) 113109) ((|InnerSparseUnivariatePowerSeries| . |Eltable|) 113069) ((|InnerSparseUnivariatePowerSeries| . |DifferentialSpace|) 113017) ((|InnerSparseUnivariatePowerSeries| . |Type|) T) ((|InnerSparseUnivariatePowerSeries| . |Join|) T) ((|InnerSparseUnivariatePowerSeries| . |DifferentialDomain|) 112959) ((|InnerSparseUnivariatePowerSeries| . |Ring|) T) ((|InnerSparseUnivariatePowerSeries| . |Monoid|) T) ((|InnerSparseUnivariatePowerSeries| . |SemiRing|) T) ((|InnerSparseUnivariatePowerSeries| . |SemiGroup|) T) ((|InnerSparseUnivariatePowerSeries| . |Rng|) T) ((|InnerSparseUnivariatePowerSeries| . |AbelianGroup|) T) ((|InnerSparseUnivariatePowerSeries| . |AbelianMonoid|) T) ((|InnerSparseUnivariatePowerSeries| . |SetCategory|) T) ((|InnerSparseUnivariatePowerSeries| . |CoercibleTo|) 112933) ((|InnerSparseUnivariatePowerSeries| . |BasicType|) T) ((|InnerSparseUnivariatePowerSeries| . |AbelianSemiGroup|) T) ((|InnerSparseUnivariatePowerSeries| . |CancellationAbelianMonoid|) T) ((|InnerSparseUnivariatePowerSeries| . |DifferentialRing|) 112881) ((|IsAst| . |SpadSyntaxCategory|) T) ((|IsAst| . |HomotopicTo|) 112859) ((|IsAst| . |CoercibleTo|) 112814) ((|IsAst| . |CoercibleFrom|) 112792) ((|IsAst| . |SetCategory|) T) ((|IsAst| . |Type|) T) ((|IsAst| . |Join|) T) ((|IsAst| . |BasicType|) T) ((|IsAst| . |AbstractSyntaxCategory|) T) ((|InternalRepresentationForm| . |SetCategory|) T) ((|InternalRepresentationForm| . |CoercibleTo|) 112747) ((|InternalRepresentationForm| . |Type|) T) ((|InternalRepresentationForm| . |Join|) T) ((|InternalRepresentationForm| . |BasicType|) T) ((|InternalRepresentationForm| . |HomotopicTo|) 112725) ((|InternalRepresentationForm| . |CoercibleFrom|) 112703) ((|IntegrationResult| . |Module|) 112667) ((|IntegrationResult| . |LinearSet|) 112631) ((|IntegrationResult| . |LeftModule|) 112595) ((|IntegrationResult| . |LeftLinearSet|) 112539) ((|IntegrationResult| . |CancellationAbelianMonoid|) T) ((|IntegrationResult| . |AbelianSemiGroup|) T) ((|IntegrationResult| . |BasicType|) T) ((|IntegrationResult| . |Join|) T) ((|IntegrationResult| . |Type|) T) ((|IntegrationResult| . |CoercibleTo|) 112513) ((|IntegrationResult| . |SetCategory|) T) ((|IntegrationResult| . |AbelianMonoid|) T) ((|IntegrationResult| . |AbelianGroup|) T) ((|IntegrationResult| . |RightModule|) 112477) ((|IntegrationResult| . |RightLinearSet|) 112441) ((|IntegrationResult| . |BiModule|) 112398) ((|IntegrationResult| . |RetractableTo|) 112382) ((|IntegrationResult| . |CoercibleFrom|) 112366) ((|InnerPrimeField| . |FiniteFieldCategory|) T) ((|InnerPrimeField| . |StepThrough|) T) ((|InnerPrimeField| . |Finite|) T) ((|InnerPrimeField| . |CharacteristicNonZero|) T) ((|InnerPrimeField| . |Field|) T) ((|InnerPrimeField| . |UniqueFactorizationDomain|) T) ((|InnerPrimeField| . |PrincipalIdealDomain|) T) ((|InnerPrimeField| . |IntegralDomain|) T) ((|InnerPrimeField| . |CommutativeRing|) T) ((|InnerPrimeField| . |CoercibleFrom|) 112300) ((|InnerPrimeField| . |Module|) 112254) ((|InnerPrimeField| . |LinearSet|) 112208) ((|InnerPrimeField| . |Algebra|) 112162) ((|InnerPrimeField| . |GcdDomain|) T) ((|InnerPrimeField| . |EuclideanDomain|) T) ((|InnerPrimeField| . |BiModule|) 112107) ((|InnerPrimeField| . |RightLinearSet|) 112061) ((|InnerPrimeField| . |RightModule|) 112015) ((|InnerPrimeField| . |LeftLinearSet|) 111949) ((|InnerPrimeField| . |LeftModule|) 111903) ((|InnerPrimeField| . |EntireRing|) T) ((|InnerPrimeField| . |DivisionRing|) T) ((|InnerPrimeField| . |FieldOfPrimeCharacteristic|) T) ((|InnerPrimeField| . |DifferentialSpace|) T) ((|InnerPrimeField| . |Type|) T) ((|InnerPrimeField| . |Join|) T) ((|InnerPrimeField| . |DifferentialDomain|) 111890) ((|InnerPrimeField| . |Ring|) T) ((|InnerPrimeField| . |Monoid|) T) ((|InnerPrimeField| . |SemiRing|) T) ((|InnerPrimeField| . |SemiGroup|) T) ((|InnerPrimeField| . |Rng|) T) ((|InnerPrimeField| . |AbelianGroup|) T) ((|InnerPrimeField| . |AbelianMonoid|) T) ((|InnerPrimeField| . |SetCategory|) T) ((|InnerPrimeField| . |CoercibleTo|) 111864) ((|InnerPrimeField| . |BasicType|) T) ((|InnerPrimeField| . |AbelianSemiGroup|) T) ((|InnerPrimeField| . |CancellationAbelianMonoid|) T) ((|InnerPrimeField| . |DifferentialRing|) T) ((|InnerPrimeField| . |FiniteAlgebraicExtensionField|) 111851) ((|InnerPrimeField| . |CharacteristicZero|) 111817) ((|InnerPrimeField| . |RetractableTo|) 111804) ((|InnerPrimeField| . |VectorSpace|) 111791) ((|InnerPrimeField| . |ExtensionField|) 111778) ((|InnerPrimeField| . |ConvertibleTo|) 111755) ((|InnerPAdicInteger| . |PAdicIntegerCategory|) 111739) ((|InnerPAdicInteger| . |PrincipalIdealDomain|) T) ((|InnerPAdicInteger| . |IntegralDomain|) T) ((|InnerPAdicInteger| . |EntireRing|) T) ((|InnerPAdicInteger| . |CommutativeRing|) T) ((|InnerPAdicInteger| . |CoercibleFrom|) 111706) ((|InnerPAdicInteger| . |Module|) 111693) ((|InnerPAdicInteger| . |LinearSet|) 111680) ((|InnerPAdicInteger| . |RightModule|) 111667) ((|InnerPAdicInteger| . |RightLinearSet|) 111654) ((|InnerPAdicInteger| . |BiModule|) 111639) ((|InnerPAdicInteger| . |Algebra|) 111626) ((|InnerPAdicInteger| . |GcdDomain|) T) ((|InnerPAdicInteger| . |EuclideanDomain|) T) ((|InnerPAdicInteger| . |Ring|) T) ((|InnerPAdicInteger| . |Monoid|) T) ((|InnerPAdicInteger| . |SemiRing|) T) ((|InnerPAdicInteger| . |SemiGroup|) T) ((|InnerPAdicInteger| . |Rng|) T) ((|InnerPAdicInteger| . |AbelianGroup|) T) ((|InnerPAdicInteger| . |LeftLinearSet|) 111593) ((|InnerPAdicInteger| . |AbelianMonoid|) T) ((|InnerPAdicInteger| . |SetCategory|) T) ((|InnerPAdicInteger| . |CoercibleTo|) 111567) ((|InnerPAdicInteger| . |Type|) T) ((|InnerPAdicInteger| . |Join|) T) ((|InnerPAdicInteger| . |BasicType|) T) ((|InnerPAdicInteger| . |AbelianSemiGroup|) T) ((|InnerPAdicInteger| . |CancellationAbelianMonoid|) T) ((|InnerPAdicInteger| . |LeftModule|) 111554) ((|InnerPAdicInteger| . |CharacteristicZero|) T) ((|IP4Address| . |SetCategory|) T) ((|IP4Address| . |CoercibleTo|) 111528) ((|IP4Address| . |Type|) T) ((|IP4Address| . |Join|) T) ((|IP4Address| . |BasicType|) T) ((|IOMode| . |SetCategory|) T) ((|IOMode| . |CoercibleTo|) 111502) ((|IOMode| . |Type|) T) ((|IOMode| . |Join|) T) ((|IOMode| . |BasicType|) T) ((|InputOutputBinaryFile| . |InputOutputByteConduit|) T) ((|InputOutputBinaryFile| . |OutputByteConduit|) T) ((|InputOutputBinaryFile| . |Conduit|) T) ((|InputOutputBinaryFile| . |InputByteConduit|) T) ((|InputOutputBinaryFile| . |CoercibleTo|) 111476) ((|Interval| . |IntervalCategory|) 111460) ((|Interval| . |ArcHyperbolicFunctionCategory|) T) ((|Interval| . |ArcTrigonometricFunctionCategory|) T) ((|Interval| . |ElementaryFunctionCategory|) T) ((|Interval| . |HyperbolicFunctionCategory|) T) ((|Interval| . |TrigonometricFunctionCategory|) T) ((|Interval| . |TranscendentalFunctionCategory|) T) ((|Interval| . |RetractableTo|) 111437) ((|Interval| . |RadicalCategory|) T) ((|Interval| . |OrderedType|) T) ((|Interval| . |OrderedSet|) T) ((|Interval| . |IntegralDomain|) T) ((|Interval| . |EntireRing|) T) ((|Interval| . |CommutativeRing|) T) ((|Interval| . |CoercibleFrom|) 111404) ((|Interval| . |Module|) 111391) ((|Interval| . |LinearSet|) 111378) ((|Interval| . |LeftModule|) 111365) ((|Interval| . |LeftLinearSet|) 111332) ((|Interval| . |CancellationAbelianMonoid|) T) ((|Interval| . |AbelianSemiGroup|) T) ((|Interval| . |BasicType|) T) ((|Interval| . |Join|) T) ((|Interval| . |Type|) T) ((|Interval| . |CoercibleTo|) 111306) ((|Interval| . |SetCategory|) T) ((|Interval| . |AbelianMonoid|) T) ((|Interval| . |AbelianGroup|) T) ((|Interval| . |RightModule|) 111293) ((|Interval| . |RightLinearSet|) 111280) ((|Interval| . |BiModule|) 111265) ((|Interval| . |Ring|) T) ((|Interval| . |Monoid|) T) ((|Interval| . |SemiRing|) T) ((|Interval| . |SemiGroup|) T) ((|Interval| . |Rng|) T) ((|Interval| . |Algebra|) 111252) ((|Interval| . |GcdDomain|) T) ((|InnerTable| . |TableAggregate|) 111231) ((|InnerTable| . |Dictionary|) 111173) ((|InnerTable| . |BagAggregate|) 111115) ((|InnerTable| . |ShallowlyMutableAggregate|) 111044) ((|InnerTable| . |Collection|) 110986) ((|InnerTable| . |ConvertibleTo|) NIL) ((|InnerTable| . |DictionaryOperations|) 110928) ((|InnerTable| . |IndexedAggregate|) 110907) ((|InnerTable| . |Evalable|) 110667) ((|InnerTable| . |InnerEvalable|) 110415) ((|InnerTable| . |Functorial|) 110344) ((|InnerTable| . |HomogeneousAggregate|) 110273) ((|InnerTable| . |Eltable|) 110252) ((|InnerTable| . |EltableAggregate|) 110231) ((|InnerTable| . |KeyedDictionary|) 110210) ((|InnerTable| . |SetCategory|) T) ((|InnerTable| . |CoercibleTo|) 110184) ((|InnerTable| . |BasicType|) T) ((|InnerTable| . |Type|) T) ((|InnerTable| . |Join|) T) ((|InnerTable| . |Aggregate|) T) ((|InnerTable| . |FiniteAggregate|) 110126) ((|Int8| . |OrderedFinite|) T) ((|Int8| . |OrderedType|) T) ((|Int8| . |OrderedSet|) T) ((|Int8| . |SetCategory|) T) ((|Int8| . |CoercibleTo|) 110100) ((|Int8| . |Type|) T) ((|Int8| . |Join|) T) ((|Int8| . |BasicType|) T) ((|Int8| . |Finite|) T) ((|Int64| . |OrderedFinite|) T) ((|Int64| . |OrderedType|) T) ((|Int64| . |OrderedSet|) T) ((|Int64| . |SetCategory|) T) ((|Int64| . |CoercibleTo|) 110074) ((|Int64| . |Type|) T) ((|Int64| . |Join|) T) ((|Int64| . |BasicType|) T) ((|Int64| . |Finite|) T) ((|Int32| . |OrderedFinite|) T) ((|Int32| . |OrderedType|) T) ((|Int32| . |OrderedSet|) T) ((|Int32| . |SetCategory|) T) ((|Int32| . |CoercibleTo|) 110048) ((|Int32| . |Type|) T) ((|Int32| . |Join|) T) ((|Int32| . |BasicType|) T) ((|Int32| . |Finite|) T) ((|Int16| . |OrderedFinite|) T) ((|Int16| . |OrderedType|) T) ((|Int16| . |OrderedSet|) T) ((|Int16| . |SetCategory|) T) ((|Int16| . |CoercibleTo|) 110022) ((|Int16| . |Type|) T) ((|Int16| . |Join|) T) ((|Int16| . |BasicType|) T) ((|Int16| . |Finite|) T) ((|Integer| . |IntegerNumberSystem|) T) ((|Integer| . |UniqueFactorizationDomain|) T) ((|Integer| . |StepThrough|) T) ((|Integer| . |RetractableTo|) 109999) ((|Integer| . |ConvertibleTo|) 109885) ((|Integer| . |RealConstant|) T) ((|Integer| . |PatternMatchable|) 109862) ((|Integer| . |OrderedRing|) T) ((|Integer| . |OrderedCancellationAbelianMonoid|) T) ((|Integer| . |OrderedAbelianSemiGroup|) T) ((|Integer| . |OrderedType|) T) ((|Integer| . |OrderedSet|) T) ((|Integer| . |OrderedAbelianMonoid|) T) ((|Integer| . |OrderedAbelianGroup|) T) ((|Integer| . |OrderedIntegralDomain|) T) ((|Integer| . |LeftModule|) 109829) ((|Integer| . |LinearlyExplicitRingOver|) 109806) ((|Integer| . |PrincipalIdealDomain|) T) ((|Integer| . |IntegralDomain|) T) ((|Integer| . |EntireRing|) T) ((|Integer| . |CommutativeRing|) T) ((|Integer| . |CoercibleFrom|) 109773) ((|Integer| . |Module|) 109760) ((|Integer| . |LinearSet|) 109747) ((|Integer| . |RightModule|) 109734) ((|Integer| . |RightLinearSet|) 109721) ((|Integer| . |BiModule|) 109706) ((|Integer| . |Algebra|) 109693) ((|Integer| . |GcdDomain|) T) ((|Integer| . |EuclideanDomain|) T) ((|Integer| . |DifferentialSpace|) T) ((|Integer| . |DifferentialDomain|) 109680) ((|Integer| . |DifferentialRing|) T) ((|Integer| . |CombinatorialFunctionCategory|) T) ((|Integer| . |Ring|) T) ((|Integer| . |Monoid|) T) ((|Integer| . |SemiRing|) T) ((|Integer| . |SemiGroup|) T) ((|Integer| . |Rng|) T) ((|Integer| . |AbelianGroup|) T) ((|Integer| . |LeftLinearSet|) 109647) ((|Integer| . |AbelianMonoid|) T) ((|Integer| . |SetCategory|) T) ((|Integer| . |CoercibleTo|) 109621) ((|Integer| . |Type|) T) ((|Integer| . |Join|) T) ((|Integer| . |BasicType|) T) ((|Integer| . |AbelianSemiGroup|) T) ((|Integer| . |CancellationAbelianMonoid|) T) ((|Integer| . |CharacteristicZero|) T) ((|InputForm| . |SExpressionCategory|) 109545) ((|InputForm| . |BasicType|) T) ((|InputForm| . |CoercibleTo|) 109519) ((|InputForm| . |SetCategory|) T) ((|InputForm| . |Eltable|) 109463) ((|InputForm| . |Type|) T) ((|InputForm| . |Join|) T) ((|InputForm| . |ConvertibleFrom|) 109336) ((|InputForm| . |ConvertibleTo|) 109309) ((|InetClientStreamSocket| . |NetworkClientSocket|) 109283) ((|InetClientStreamSocket| . |InputByteConduit|) T) ((|InetClientStreamSocket| . |Conduit|) T) ((|InetClientStreamSocket| . |OutputByteConduit|) T) ((|InetClientStreamSocket| . |InputOutputByteConduit|) T) ((|InetClientStreamSocket| . |CoercibleTo|) 109257) ((|IndexedExponents| . |OrderedAbelianMonoidSup|) T) ((|IndexedExponents| . |CancellationAbelianMonoid|) T) ((|IndexedExponents| . |AbelianSemiGroup|) T) ((|IndexedExponents| . |BasicType|) T) ((|IndexedExponents| . |Join|) T) ((|IndexedExponents| . |Type|) T) ((|IndexedExponents| . |CoercibleTo|) 109231) ((|IndexedExponents| . |SetCategory|) T) ((|IndexedExponents| . |AbelianMonoid|) T) ((|IndexedExponents| . |OrderedAbelianMonoid|) T) ((|IndexedExponents| . |OrderedSet|) T) ((|IndexedExponents| . |OrderedType|) T) ((|IndexedExponents| . |OrderedAbelianSemiGroup|) T) ((|IndexedExponents| . |OrderedCancellationAbelianMonoid|) T) ((|IndexedExponents| . |IndexedDirectProductCategory|) 109192) ((|IndexedExponents| . |Functorial|) 109158) ((|IndexedExponents| . |ConvertibleFrom|) 109087) ((|InputBinaryFile| . |InputByteConduit|) T) ((|InputBinaryFile| . |Conduit|) T) ((|InputBinaryFile| . |CoercibleTo|) 109061) ((|InAst| . |SpadSyntaxCategory|) T) ((|InAst| . |HomotopicTo|) 109039) ((|InAst| . |CoercibleTo|) 108994) ((|InAst| . |CoercibleFrom|) 108972) ((|InAst| . |SetCategory|) T) ((|InAst| . |Type|) T) ((|InAst| . |Join|) T) ((|InAst| . |BasicType|) T) ((|InAst| . |AbstractSyntaxCategory|) T) ((|ImportAst| . |SpadSyntaxCategory|) T) ((|ImportAst| . |HomotopicTo|) 108950) ((|ImportAst| . |CoercibleTo|) 108905) ((|ImportAst| . |CoercibleFrom|) 108883) ((|ImportAst| . |SetCategory|) T) ((|ImportAst| . |Type|) T) ((|ImportAst| . |Join|) T) ((|ImportAst| . |BasicType|) T) ((|ImportAst| . |AbstractSyntaxCategory|) T) ((|InnerFiniteField| . |FiniteAlgebraicExtensionField|) 108847) ((|InnerFiniteField| . |DifferentialRing|) T) ((|InnerFiniteField| . |DifferentialDomain|) 108834) ((|InnerFiniteField| . |DifferentialSpace|) T) ((|InnerFiniteField| . |Finite|) T) ((|InnerFiniteField| . |StepThrough|) T) ((|InnerFiniteField| . |FiniteFieldCategory|) T) ((|InnerFiniteField| . |CharacteristicZero|) 108800) ((|InnerFiniteField| . |CoercibleFrom|) 108701) ((|InnerFiniteField| . |LeftModule|) 108622) ((|InnerFiniteField| . |LeftLinearSet|) 108523) ((|InnerFiniteField| . |CancellationAbelianMonoid|) T) ((|InnerFiniteField| . |AbelianSemiGroup|) T) ((|InnerFiniteField| . |BasicType|) T) ((|InnerFiniteField| . |Join|) T) ((|InnerFiniteField| . |Type|) T) ((|InnerFiniteField| . |CoercibleTo|) 108497) ((|InnerFiniteField| . |SetCategory|) T) ((|InnerFiniteField| . |AbelianMonoid|) T) ((|InnerFiniteField| . |AbelianGroup|) T) ((|InnerFiniteField| . |Rng|) T) ((|InnerFiniteField| . |SemiGroup|) T) ((|InnerFiniteField| . |SemiRing|) T) ((|InnerFiniteField| . |Monoid|) T) ((|InnerFiniteField| . |Ring|) T) ((|InnerFiniteField| . |Field|) T) ((|InnerFiniteField| . |UniqueFactorizationDomain|) T) ((|InnerFiniteField| . |PrincipalIdealDomain|) T) ((|InnerFiniteField| . |IntegralDomain|) T) ((|InnerFiniteField| . |CommutativeRing|) T) ((|InnerFiniteField| . |Module|) 108418) ((|InnerFiniteField| . |LinearSet|) 108339) ((|InnerFiniteField| . |Algebra|) 108293) ((|InnerFiniteField| . |GcdDomain|) T) ((|InnerFiniteField| . |EuclideanDomain|) T) ((|InnerFiniteField| . |BiModule|) 108198) ((|InnerFiniteField| . |RightLinearSet|) 108119) ((|InnerFiniteField| . |RightModule|) 108040) ((|InnerFiniteField| . |EntireRing|) T) ((|InnerFiniteField| . |DivisionRing|) T) ((|InnerFiniteField| . |FieldOfPrimeCharacteristic|) T) ((|InnerFiniteField| . |CharacteristicNonZero|) T) ((|InnerFiniteField| . |RetractableTo|) 108004) ((|InnerFiniteField| . |VectorSpace|) 107968) ((|InnerFiniteField| . |ExtensionField|) 107932) ((|IfAst| . |SpadSyntaxCategory|) T) ((|IfAst| . |HomotopicTo|) 107910) ((|IfAst| . |CoercibleTo|) 107865) ((|IfAst| . |CoercibleFrom|) 107843) ((|IfAst| . |SetCategory|) T) ((|IfAst| . |Type|) T) ((|IfAst| . |Join|) T) ((|IfAst| . |BasicType|) T) ((|IfAst| . |AbstractSyntaxCategory|) T) ((|IndexedFlexibleArray| . |OneDimensionalArrayAggregate|) 107827) ((|IndexedFlexibleArray| . |ShallowlyMutableAggregate|) 107811) ((|IndexedFlexibleArray| . |FiniteAggregate|) 107795) ((|IndexedFlexibleArray| . |Aggregate|) T) ((|IndexedFlexibleArray| . |Join|) T) ((|IndexedFlexibleArray| . |Type|) T) ((|IndexedFlexibleArray| . |BasicType|) 107705) ((|IndexedFlexibleArray| . |CoercibleTo|) 107579) ((|IndexedFlexibleArray| . |Evalable|) 107503) ((|IndexedFlexibleArray| . |InnerEvalable|) 107422) ((|IndexedFlexibleArray| . |Functorial|) 107406) ((|IndexedFlexibleArray| . |SetCategory|) 107343) ((|IndexedFlexibleArray| . |HomogeneousAggregate|) 107327) ((|IndexedFlexibleArray| . |LinearAggregate|) 107311) ((|IndexedFlexibleArray| . |EltableAggregate|) 107283) ((|IndexedFlexibleArray| . |Eltable|) 107212) ((|IndexedFlexibleArray| . |IndexedAggregate|) 107184) ((|IndexedFlexibleArray| . |ConvertibleTo|) 107120) ((|IndexedFlexibleArray| . |Collection|) 107104) ((|IndexedFlexibleArray| . |OrderedSet|) 107075) ((|IndexedFlexibleArray| . |OrderedType|) 107046) ((|IndexedFlexibleArray| . |FiniteLinearAggregate|) 107030) ((|IndexedFlexibleArray| . |ExtensibleLinearAggregate|) 107014) ((|InnerFreeAbelianMonoid| . |FreeAbelianMonoidCategory|) 106993) ((|InnerFreeAbelianMonoid| . |CoercibleFrom|) 106977) ((|InnerFreeAbelianMonoid| . |RetractableTo|) 106961) ((|InnerFreeAbelianMonoid| . |AbelianMonoid|) T) ((|InnerFreeAbelianMonoid| . |SetCategory|) T) ((|InnerFreeAbelianMonoid| . |CoercibleTo|) 106935) ((|InnerFreeAbelianMonoid| . |Type|) T) ((|InnerFreeAbelianMonoid| . |Join|) T) ((|InnerFreeAbelianMonoid| . |BasicType|) T) ((|InnerFreeAbelianMonoid| . |AbelianSemiGroup|) T) ((|InnerFreeAbelianMonoid| . |CancellationAbelianMonoid|) T) ((|IndexedProductTerm| . |BasicType|) T) ((|IndexedProductTerm| . |Join|) T) ((|IndexedProductTerm| . |Type|) T) ((|IndexedProductTerm| . |CoercibleTo|) 106905) ((|IndexedDirectProductOrderedAbelianMonoidSup| . |OrderedAbelianMonoidSup|) T) ((|IndexedDirectProductOrderedAbelianMonoidSup| . |CancellationAbelianMonoid|) T) ((|IndexedDirectProductOrderedAbelianMonoidSup| . |AbelianSemiGroup|) T) ((|IndexedDirectProductOrderedAbelianMonoidSup| . |BasicType|) T) ((|IndexedDirectProductOrderedAbelianMonoidSup| . |Join|) T) ((|IndexedDirectProductOrderedAbelianMonoidSup| . |Type|) T) ((|IndexedDirectProductOrderedAbelianMonoidSup| . |CoercibleTo|) 106879) ((|IndexedDirectProductOrderedAbelianMonoidSup| . |SetCategory|) T) ((|IndexedDirectProductOrderedAbelianMonoidSup| . |AbelianMonoid|) T) ((|IndexedDirectProductOrderedAbelianMonoidSup| . |OrderedAbelianMonoid|) T) ((|IndexedDirectProductOrderedAbelianMonoidSup| . |OrderedSet|) T) ((|IndexedDirectProductOrderedAbelianMonoidSup| . |OrderedType|) T) ((|IndexedDirectProductOrderedAbelianMonoidSup| . |OrderedAbelianSemiGroup|) T) ((|IndexedDirectProductOrderedAbelianMonoidSup| . |OrderedCancellationAbelianMonoid|) T) ((|IndexedDirectProductOrderedAbelianMonoidSup| . |IndexedDirectProductCategory|) 106858) ((|IndexedDirectProductOrderedAbelianMonoidSup| . |Functorial|) 106842) ((|IndexedDirectProductOrderedAbelianMonoidSup| . |ConvertibleFrom|) 106789) ((|IndexedDirectProductOrderedAbelianMonoid| . |OrderedAbelianMonoid|) T) ((|IndexedDirectProductOrderedAbelianMonoid| . |OrderedSet|) T) ((|IndexedDirectProductOrderedAbelianMonoid| . |OrderedType|) T) ((|IndexedDirectProductOrderedAbelianMonoid| . |OrderedAbelianSemiGroup|) T) ((|IndexedDirectProductOrderedAbelianMonoid| . |AbelianSemiGroup|) T) ((|IndexedDirectProductOrderedAbelianMonoid| . |BasicType|) T) ((|IndexedDirectProductOrderedAbelianMonoid| . |Join|) T) ((|IndexedDirectProductOrderedAbelianMonoid| . |Type|) T) ((|IndexedDirectProductOrderedAbelianMonoid| . |CoercibleTo|) 106763) ((|IndexedDirectProductOrderedAbelianMonoid| . |SetCategory|) T) ((|IndexedDirectProductOrderedAbelianMonoid| . |AbelianMonoid|) T) ((|IndexedDirectProductOrderedAbelianMonoid| . |IndexedDirectProductCategory|) 106742) ((|IndexedDirectProductOrderedAbelianMonoid| . |Functorial|) 106726) ((|IndexedDirectProductOrderedAbelianMonoid| . |ConvertibleFrom|) 106673) ((|IndexedDirectProductObject| . |IndexedDirectProductCategory|) 106652) ((|IndexedDirectProductObject| . |CoercibleTo|) 106568) ((|IndexedDirectProductObject| . |SetCategory|) 106503) ((|IndexedDirectProductObject| . |Functorial|) 106487) ((|IndexedDirectProductObject| . |ConvertibleFrom|) 106434) ((|IndexedDirectProductObject| . |Type|) T) ((|IndexedDirectProductObject| . |Join|) T) ((|IndexedDirectProductObject| . |BasicType|) T) ((|IndexedDirectProductAbelianMonoid| . |AbelianMonoid|) T) ((|IndexedDirectProductAbelianMonoid| . |SetCategory|) T) ((|IndexedDirectProductAbelianMonoid| . |CoercibleTo|) 106408) ((|IndexedDirectProductAbelianMonoid| . |Type|) T) ((|IndexedDirectProductAbelianMonoid| . |Join|) T) ((|IndexedDirectProductAbelianMonoid| . |BasicType|) T) ((|IndexedDirectProductAbelianMonoid| . |AbelianSemiGroup|) T) ((|IndexedDirectProductAbelianMonoid| . |IndexedDirectProductCategory|) 106387) ((|IndexedDirectProductAbelianMonoid| . |Functorial|) 106371) ((|IndexedDirectProductAbelianMonoid| . |ConvertibleFrom|) 106318) ((|IndexedDirectProductAbelianGroup| . |AbelianGroup|) T) ((|IndexedDirectProductAbelianGroup| . |LeftLinearSet|) 106295) ((|IndexedDirectProductAbelianGroup| . |AbelianMonoid|) T) ((|IndexedDirectProductAbelianGroup| . |SetCategory|) T) ((|IndexedDirectProductAbelianGroup| . |CoercibleTo|) 106269) ((|IndexedDirectProductAbelianGroup| . |Type|) T) ((|IndexedDirectProductAbelianGroup| . |Join|) T) ((|IndexedDirectProductAbelianGroup| . |BasicType|) T) ((|IndexedDirectProductAbelianGroup| . |AbelianSemiGroup|) T) ((|IndexedDirectProductAbelianGroup| . |CancellationAbelianMonoid|) T) ((|IndexedDirectProductAbelianGroup| . |IndexedDirectProductCategory|) 106248) ((|IndexedDirectProductAbelianGroup| . |Functorial|) 106232) ((|IndexedDirectProductAbelianGroup| . |ConvertibleFrom|) 106179) ((|Identifier| . |SetCategory|) T) ((|Identifier| . |CoercibleTo|) 106153) ((|Identifier| . |Type|) T) ((|Identifier| . |Join|) T) ((|Identifier| . |BasicType|) T) ((|PolynomialIdeals| . |SetCategory|) T) ((|PolynomialIdeals| . |CoercibleTo|) 106127) ((|PolynomialIdeals| . |Type|) T) ((|PolynomialIdeals| . |Join|) T) ((|PolynomialIdeals| . |BasicType|) T) ((|IndexCard| . |OrderedSet|) T) ((|IndexCard| . |CoercibleTo|) 106101) ((|IndexCard| . |SetCategory|) T) ((|IndexCard| . |BasicType|) T) ((|IndexCard| . |Join|) T) ((|IndexCard| . |Type|) T) ((|IndexCard| . |OrderedType|) T) ((|IndexCard| . |CoercibleFrom|) 106079) ((|IndexedBits| . |BitAggregate|) T) ((|IndexedBits| . |FiniteLinearAggregate|) 106056) ((|IndexedBits| . |OrderedType|) T) ((|IndexedBits| . |OrderedSet|) T) ((|IndexedBits| . |Collection|) 106033) ((|IndexedBits| . |ConvertibleTo|) 106008) ((|IndexedBits| . |Eltable|) 105930) ((|IndexedBits| . |IndexedAggregate|) 105895) ((|IndexedBits| . |EltableAggregate|) 105860) ((|IndexedBits| . |LinearAggregate|) 105837) ((|IndexedBits| . |HomogeneousAggregate|) 105814) ((|IndexedBits| . |SetCategory|) T) ((|IndexedBits| . |Functorial|) 105791) ((|IndexedBits| . |InnerEvalable|) NIL) ((|IndexedBits| . |Evalable|) NIL) ((|IndexedBits| . |CoercibleTo|) 105765) ((|IndexedBits| . |BasicType|) T) ((|IndexedBits| . |Aggregate|) T) ((|IndexedBits| . |FiniteAggregate|) 105742) ((|IndexedBits| . |ShallowlyMutableAggregate|) 105719) ((|IndexedBits| . |OneDimensionalArrayAggregate|) 105696) ((|IndexedBits| . |Logic|) T) ((|IndexedBits| . |Join|) T) ((|IndexedBits| . |Type|) T) ((|IndexedBits| . |BooleanLogic|) T) ((|InnerTwoDimensionalArray| . |TwoDimensionalArrayCategory|) 105670) ((|InnerTwoDimensionalArray| . |ShallowlyMutableAggregate|) 105654) ((|InnerTwoDimensionalArray| . |HomogeneousAggregate|) 105638) ((|InnerTwoDimensionalArray| . |SetCategory|) 105608) ((|InnerTwoDimensionalArray| . |Functorial|) 105592) ((|InnerTwoDimensionalArray| . |InnerEvalable|) 105511) ((|InnerTwoDimensionalArray| . |Evalable|) 105435) ((|InnerTwoDimensionalArray| . |CoercibleTo|) 105337) ((|InnerTwoDimensionalArray| . |BasicType|) 105275) ((|InnerTwoDimensionalArray| . |Type|) T) ((|InnerTwoDimensionalArray| . |Join|) T) ((|InnerTwoDimensionalArray| . |Aggregate|) T) ((|InnerTwoDimensionalArray| . |FiniteAggregate|) 105259) ((|IndexedOneDimensionalArray| . |OneDimensionalArrayAggregate|) 105243) ((|IndexedOneDimensionalArray| . |ShallowlyMutableAggregate|) 105227) ((|IndexedOneDimensionalArray| . |FiniteAggregate|) 105211) ((|IndexedOneDimensionalArray| . |Aggregate|) T) ((|IndexedOneDimensionalArray| . |Join|) T) ((|IndexedOneDimensionalArray| . |Type|) T) ((|IndexedOneDimensionalArray| . |BasicType|) 105121) ((|IndexedOneDimensionalArray| . |CoercibleTo|) 104995) ((|IndexedOneDimensionalArray| . |Evalable|) 104919) ((|IndexedOneDimensionalArray| . |InnerEvalable|) 104838) ((|IndexedOneDimensionalArray| . |Functorial|) 104822) ((|IndexedOneDimensionalArray| . |SetCategory|) 104759) ((|IndexedOneDimensionalArray| . |HomogeneousAggregate|) 104743) ((|IndexedOneDimensionalArray| . |LinearAggregate|) 104727) ((|IndexedOneDimensionalArray| . |EltableAggregate|) 104699) ((|IndexedOneDimensionalArray| . |Eltable|) 104628) ((|IndexedOneDimensionalArray| . |IndexedAggregate|) 104600) ((|IndexedOneDimensionalArray| . |ConvertibleTo|) 104536) ((|IndexedOneDimensionalArray| . |Collection|) 104520) ((|IndexedOneDimensionalArray| . |OrderedSet|) 104491) ((|IndexedOneDimensionalArray| . |OrderedType|) 104462) ((|IndexedOneDimensionalArray| . |FiniteLinearAggregate|) 104446) ((|InnerAlgebraicNumber| . |ExpressionSpace|) T) ((|InnerAlgebraicNumber| . |BasicType|) T) ((|InnerAlgebraicNumber| . |Join|) T) ((|InnerAlgebraicNumber| . |Type|) T) ((|InnerAlgebraicNumber| . |CoercibleTo|) 104420) ((|InnerAlgebraicNumber| . |SetCategory|) T) ((|InnerAlgebraicNumber| . |CoercibleFrom|) 104267) ((|InnerAlgebraicNumber| . |RetractableTo|) 104195) ((|InnerAlgebraicNumber| . |InnerEvalable|) 104157) ((|InnerAlgebraicNumber| . |Evalable|) 104144) ((|InnerAlgebraicNumber| . |AlgebraicallyClosedField|) T) ((|InnerAlgebraicNumber| . |RadicalCategory|) T) ((|InnerAlgebraicNumber| . |DivisionRing|) T) ((|InnerAlgebraicNumber| . |BiModule|) 104089) ((|InnerAlgebraicNumber| . |RightLinearSet|) 104043) ((|InnerAlgebraicNumber| . |RightModule|) 103997) ((|InnerAlgebraicNumber| . |EntireRing|) T) ((|InnerAlgebraicNumber| . |Module|) 103951) ((|InnerAlgebraicNumber| . |LinearSet|) 103905) ((|InnerAlgebraicNumber| . |LeftModule|) 103839) ((|InnerAlgebraicNumber| . |LeftLinearSet|) 103773) ((|InnerAlgebraicNumber| . |CancellationAbelianMonoid|) T) ((|InnerAlgebraicNumber| . |AbelianSemiGroup|) T) ((|InnerAlgebraicNumber| . |AbelianMonoid|) T) ((|InnerAlgebraicNumber| . |AbelianGroup|) T) ((|InnerAlgebraicNumber| . |Ring|) T) ((|InnerAlgebraicNumber| . |Monoid|) T) ((|InnerAlgebraicNumber| . |SemiRing|) T) ((|InnerAlgebraicNumber| . |SemiGroup|) T) ((|InnerAlgebraicNumber| . |Rng|) T) ((|InnerAlgebraicNumber| . |Algebra|) 103727) ((|InnerAlgebraicNumber| . |EuclideanDomain|) T) ((|InnerAlgebraicNumber| . |GcdDomain|) T) ((|InnerAlgebraicNumber| . |CommutativeRing|) T) ((|InnerAlgebraicNumber| . |IntegralDomain|) T) ((|InnerAlgebraicNumber| . |PrincipalIdealDomain|) T) ((|InnerAlgebraicNumber| . |UniqueFactorizationDomain|) T) ((|InnerAlgebraicNumber| . |Field|) T) ((|InnerAlgebraicNumber| . |LinearlyExplicitRingOver|) 103676) ((|InnerAlgebraicNumber| . |RealConstant|) T) ((|InnerAlgebraicNumber| . |ConvertibleTo|) 103601) ((|InnerAlgebraicNumber| . |CharacteristicZero|) T) ((|InnerAlgebraicNumber| . |DifferentialRing|) T) ((|InnerAlgebraicNumber| . |DifferentialDomain|) 103588) ((|InnerAlgebraicNumber| . |DifferentialSpace|) T) ((|Hostname| . |SetCategory|) T) ((|Hostname| . |CoercibleTo|) 103543) ((|Hostname| . |Type|) T) ((|Hostname| . |Join|) T) ((|Hostname| . |BasicType|) T) ((|HexadecimalExpansion| . |QuotientFieldCategory|) 103520) ((|HexadecimalExpansion| . |StepThrough|) T) ((|HexadecimalExpansion| . |CoercibleFrom|) 103454) ((|HexadecimalExpansion| . |RetractableTo|) 103398) ((|HexadecimalExpansion| . |ConvertibleTo|) 103299) ((|HexadecimalExpansion| . |RealConstant|) T) ((|HexadecimalExpansion| . |PolynomialFactorizationExplicit|) NIL) ((|HexadecimalExpansion| . |Patternable|) 103276) ((|HexadecimalExpansion| . |OrderedRing|) T) ((|HexadecimalExpansion| . |OrderedCancellationAbelianMonoid|) T) ((|HexadecimalExpansion| . |OrderedAbelianSemiGroup|) T) ((|HexadecimalExpansion| . |OrderedType|) T) ((|HexadecimalExpansion| . |OrderedSet|) T) ((|HexadecimalExpansion| . |OrderedAbelianMonoid|) T) ((|HexadecimalExpansion| . |OrderedAbelianGroup|) T) ((|HexadecimalExpansion| . |OrderedIntegralDomain|) T) ((|HexadecimalExpansion| . |PatternMatchable|) 103253) ((|HexadecimalExpansion| . |FullyPatternMatchable|) 103230) ((|HexadecimalExpansion| . |LinearlyExplicitRingOver|) 103207) ((|HexadecimalExpansion| . |FullyLinearlyExplicitRingOver|) 103184) ((|HexadecimalExpansion| . |Eltable|) NIL) ((|HexadecimalExpansion| . |Evalable|) NIL) ((|HexadecimalExpansion| . |InnerEvalable|) NIL) ((|HexadecimalExpansion| . |Functorial|) 103161) ((|HexadecimalExpansion| . |FullyEvalableOver|) 103138) ((|HexadecimalExpansion| . |DivisionRing|) T) ((|HexadecimalExpansion| . |BiModule|) 103056) ((|HexadecimalExpansion| . |RightLinearSet|) 102990) ((|HexadecimalExpansion| . |RightModule|) 102924) ((|HexadecimalExpansion| . |EntireRing|) T) ((|HexadecimalExpansion| . |Module|) 102858) ((|HexadecimalExpansion| . |LinearSet|) 102792) ((|HexadecimalExpansion| . |LeftModule|) 102726) ((|HexadecimalExpansion| . |LeftLinearSet|) 102660) ((|HexadecimalExpansion| . |Algebra|) 102594) ((|HexadecimalExpansion| . |EuclideanDomain|) T) ((|HexadecimalExpansion| . |GcdDomain|) T) ((|HexadecimalExpansion| . |CommutativeRing|) T) ((|HexadecimalExpansion| . |IntegralDomain|) T) ((|HexadecimalExpansion| . |PrincipalIdealDomain|) T) ((|HexadecimalExpansion| . |UniqueFactorizationDomain|) T) ((|HexadecimalExpansion| . |Field|) T) ((|HexadecimalExpansion| . |DifferentialRing|) T) ((|HexadecimalExpansion| . |DifferentialDomain|) 102581) ((|HexadecimalExpansion| . |DifferentialSpace|) T) ((|HexadecimalExpansion| . |DifferentialSpaceExtension|) 102558) ((|HexadecimalExpansion| . |PartialDifferentialDomain|) NIL) ((|HexadecimalExpansion| . |PartialDifferentialSpace|) NIL) ((|HexadecimalExpansion| . |PartialDifferentialRing|) NIL) ((|HexadecimalExpansion| . |DifferentialExtension|) 102535) ((|HexadecimalExpansion| . |CharacteristicZero|) T) ((|HexadecimalExpansion| . |CharacteristicNonZero|) NIL) ((|HexadecimalExpansion| . |CancellationAbelianMonoid|) T) ((|HexadecimalExpansion| . |AbelianSemiGroup|) T) ((|HexadecimalExpansion| . |BasicType|) T) ((|HexadecimalExpansion| . |Join|) T) ((|HexadecimalExpansion| . |Type|) T) ((|HexadecimalExpansion| . |CoercibleTo|) 102446) ((|HexadecimalExpansion| . |SetCategory|) T) ((|HexadecimalExpansion| . |AbelianMonoid|) T) ((|HexadecimalExpansion| . |AbelianGroup|) T) ((|HexadecimalExpansion| . |Ring|) T) ((|HexadecimalExpansion| . |Monoid|) T) ((|HexadecimalExpansion| . |SemiRing|) T) ((|HexadecimalExpansion| . |SemiGroup|) T) ((|HexadecimalExpansion| . |Rng|) T) ((|HyperellipticFiniteDivisor| . |FiniteDivisorCategory|) 102415) ((|HyperellipticFiniteDivisor| . |CancellationAbelianMonoid|) T) ((|HyperellipticFiniteDivisor| . |AbelianSemiGroup|) T) ((|HyperellipticFiniteDivisor| . |BasicType|) T) ((|HyperellipticFiniteDivisor| . |Join|) T) ((|HyperellipticFiniteDivisor| . |Type|) T) ((|HyperellipticFiniteDivisor| . |CoercibleTo|) 102389) ((|HyperellipticFiniteDivisor| . |SetCategory|) T) ((|HyperellipticFiniteDivisor| . |AbelianMonoid|) T) ((|HyperellipticFiniteDivisor| . |LeftLinearSet|) 102366) ((|HyperellipticFiniteDivisor| . |AbelianGroup|) T) ((|Heap| . |PriorityQueueAggregate|) 102350) ((|Heap| . |FiniteAggregate|) 102334) ((|Heap| . |HomogeneousAggregate|) 102318) ((|Heap| . |SetCategory|) 102288) ((|Heap| . |Functorial|) 102272) ((|Heap| . |InnerEvalable|) 102191) ((|Heap| . |Evalable|) 102115) ((|Heap| . |CoercibleTo|) 102017) ((|Heap| . |BasicType|) 101955) ((|Heap| . |Type|) T) ((|Heap| . |Join|) T) ((|Heap| . |Aggregate|) T) ((|Heap| . |ShallowlyMutableAggregate|) 101939) ((|Heap| . |BagAggregate|) 101923) ((|HeadAst| . |SpadSyntaxCategory|) T) ((|HeadAst| . |HomotopicTo|) 101901) ((|HeadAst| . |CoercibleTo|) 101856) ((|HeadAst| . |CoercibleFrom|) 101834) ((|HeadAst| . |SetCategory|) T) ((|HeadAst| . |Type|) T) ((|HeadAst| . |Join|) T) ((|HeadAst| . |BasicType|) T) ((|HeadAst| . |AbstractSyntaxCategory|) T) ((|HomogeneousDirectProduct| . |DirectProductCategory|) 101813) ((|HomogeneousDirectProduct| . |VectorSpace|) 101780) ((|HomogeneousDirectProduct| . |OrderedCancellationAbelianMonoid|) 101738) ((|HomogeneousDirectProduct| . |OrderedAbelianSemiGroup|) 101696) ((|HomogeneousDirectProduct| . |OrderedType|) 101621) ((|HomogeneousDirectProduct| . |OrderedSet|) 101546) ((|HomogeneousDirectProduct| . |OrderedAbelianMonoid|) 101504) ((|HomogeneousDirectProduct| . |OrderedAbelianMonoidSup|) 101462) ((|HomogeneousDirectProduct| . |Module|) 101391) ((|HomogeneousDirectProduct| . |LinearSet|) 101296) ((|HomogeneousDirectProduct| . |EltableAggregate|) 101268) ((|HomogeneousDirectProduct| . |Eltable|) 101240) ((|HomogeneousDirectProduct| . |IndexedAggregate|) 101212) ((|HomogeneousDirectProduct| . |RetractableTo|) 100963) ((|HomogeneousDirectProduct| . |CoercibleFrom|) 100687) ((|HomogeneousDirectProduct| . |FullyRetractableTo|) 100648) ((|HomogeneousDirectProduct| . |LinearlyExplicitRingOver|) 100520) ((|HomogeneousDirectProduct| . |LeftModule|) 100305) ((|HomogeneousDirectProduct| . |FullyLinearlyExplicitRingOver|) 100273) ((|HomogeneousDirectProduct| . |HomogeneousAggregate|) 100257) ((|HomogeneousDirectProduct| . |Functorial|) 100241) ((|HomogeneousDirectProduct| . |InnerEvalable|) 100160) ((|HomogeneousDirectProduct| . |Evalable|) 100084) ((|HomogeneousDirectProduct| . |Aggregate|) T) ((|HomogeneousDirectProduct| . |FiniteAggregate|) 100068) ((|HomogeneousDirectProduct| . |Finite|) 100043) ((|HomogeneousDirectProduct| . |DifferentialRing|) 99980) ((|HomogeneousDirectProduct| . |LeftLinearSet|) 99710) ((|HomogeneousDirectProduct| . |Rng|) 99687) ((|HomogeneousDirectProduct| . |SemiGroup|) 99664) ((|HomogeneousDirectProduct| . |SemiRing|) 99641) ((|HomogeneousDirectProduct| . |Monoid|) 99618) ((|HomogeneousDirectProduct| . |Ring|) 99595) ((|HomogeneousDirectProduct| . |DifferentialDomain|) 99458) ((|HomogeneousDirectProduct| . |DifferentialSpace|) 99327) ((|HomogeneousDirectProduct| . |DifferentialSpaceExtension|) 99295) ((|HomogeneousDirectProduct| . |PartialDifferentialDomain|) 99111) ((|HomogeneousDirectProduct| . |PartialDifferentialSpace|) 98929) ((|HomogeneousDirectProduct| . |PartialDifferentialRing|) 98833) ((|HomogeneousDirectProduct| . |DifferentialExtension|) 98801) ((|HomogeneousDirectProduct| . |CoercibleTo|) 98346) ((|HomogeneousDirectProduct| . |RightModule|) 98253) ((|HomogeneousDirectProduct| . |RightLinearSet|) 98136) ((|HomogeneousDirectProduct| . |BiModule|) 98038) ((|HomogeneousDirectProduct| . |CancellationAbelianMonoid|) 97840) ((|HomogeneousDirectProduct| . |AbelianSemiGroup|) 97577) ((|HomogeneousDirectProduct| . |BasicType|) 97182) ((|HomogeneousDirectProduct| . |Join|) T) ((|HomogeneousDirectProduct| . |Type|) T) ((|HomogeneousDirectProduct| . |SetCategory|) 96814) ((|HomogeneousDirectProduct| . |AbelianMonoid|) 96585) ((|HomogeneousDirectProduct| . |AbelianGroup|) 96471) ((|HomogeneousDistributedMultivariatePolynomial| . |PolynomialCategory|) 96363) ((|HomogeneousDistributedMultivariatePolynomial| . |CoercibleFrom|) 96035) ((|HomogeneousDistributedMultivariatePolynomial| . |RetractableTo|) 95842) ((|HomogeneousDistributedMultivariatePolynomial| . |UniqueFactorizationDomain|) 95792) ((|HomogeneousDistributedMultivariatePolynomial| . |PolynomialFactorizationExplicit|) 95742) ((|HomogeneousDistributedMultivariatePolynomial| . |PatternMatchable|) NIL) ((|HomogeneousDistributedMultivariatePolynomial| . |PartialDifferentialSpace|) 95702) ((|HomogeneousDistributedMultivariatePolynomial| . |PartialDifferentialDomain|) 95660) ((|HomogeneousDistributedMultivariatePolynomial| . |PartialDifferentialRing|) 95620) ((|HomogeneousDistributedMultivariatePolynomial| . |InnerEvalable|) 95546) ((|HomogeneousDistributedMultivariatePolynomial| . |GcdDomain|) 95464) ((|HomogeneousDistributedMultivariatePolynomial| . |LinearlyExplicitRingOver|) 95380) ((|HomogeneousDistributedMultivariatePolynomial| . |LeftModule|) 95209) ((|HomogeneousDistributedMultivariatePolynomial| . |FullyLinearlyExplicitRingOver|) 95193) ((|HomogeneousDistributedMultivariatePolynomial| . |AbelianMonoidRing|) 95114) ((|HomogeneousDistributedMultivariatePolynomial| . |Algebra|) 94877) ((|HomogeneousDistributedMultivariatePolynomial| . |LinearSet|) 94640) ((|HomogeneousDistributedMultivariatePolynomial| . |Module|) 94403) ((|HomogeneousDistributedMultivariatePolynomial| . |EntireRing|) 94289) ((|HomogeneousDistributedMultivariatePolynomial| . |IntegralDomain|) 94175) ((|HomogeneousDistributedMultivariatePolynomial| . |Functorial|) 94159) ((|HomogeneousDistributedMultivariatePolynomial| . |BiModule|) 93902) ((|HomogeneousDistributedMultivariatePolynomial| . |RightLinearSet|) 93659) ((|HomogeneousDistributedMultivariatePolynomial| . |RightModule|) 93416) ((|HomogeneousDistributedMultivariatePolynomial| . |CommutativeRing|) 93269) ((|HomogeneousDistributedMultivariatePolynomial| . |CharacteristicZero|) 93232) ((|HomogeneousDistributedMultivariatePolynomial| . |CharacteristicNonZero|) 93192) ((|HomogeneousDistributedMultivariatePolynomial| . |LeftLinearSet|) 93069) ((|HomogeneousDistributedMultivariatePolynomial| . |CancellationAbelianMonoid|) T) ((|HomogeneousDistributedMultivariatePolynomial| . |AbelianSemiGroup|) T) ((|HomogeneousDistributedMultivariatePolynomial| . |BasicType|) T) ((|HomogeneousDistributedMultivariatePolynomial| . |Join|) T) ((|HomogeneousDistributedMultivariatePolynomial| . |Type|) T) ((|HomogeneousDistributedMultivariatePolynomial| . |CoercibleTo|) 93043) ((|HomogeneousDistributedMultivariatePolynomial| . |SetCategory|) T) ((|HomogeneousDistributedMultivariatePolynomial| . |AbelianMonoid|) T) ((|HomogeneousDistributedMultivariatePolynomial| . |AbelianGroup|) T) ((|HomogeneousDistributedMultivariatePolynomial| . |Ring|) T) ((|HomogeneousDistributedMultivariatePolynomial| . |Monoid|) T) ((|HomogeneousDistributedMultivariatePolynomial| . |SemiRing|) T) ((|HomogeneousDistributedMultivariatePolynomial| . |SemiGroup|) T) ((|HomogeneousDistributedMultivariatePolynomial| . |Rng|) T) ((|HomogeneousDistributedMultivariatePolynomial| . |FullyRetractableTo|) 93027) ((|HomogeneousDistributedMultivariatePolynomial| . |FiniteAbelianMonoidRing|) 92948) ((|HomogeneousDistributedMultivariatePolynomial| . |Evalable|) 92935) ((|HomogeneousDistributedMultivariatePolynomial| . |ConvertibleTo|) 92713) ((|HashTable| . |TableAggregate|) 92692) ((|HashTable| . |Dictionary|) 92634) ((|HashTable| . |BagAggregate|) 92576) ((|HashTable| . |ShallowlyMutableAggregate|) 92505) ((|HashTable| . |Collection|) 92447) ((|HashTable| . |ConvertibleTo|) NIL) ((|HashTable| . |DictionaryOperations|) 92389) ((|HashTable| . |IndexedAggregate|) 92368) ((|HashTable| . |Evalable|) 92128) ((|HashTable| . |InnerEvalable|) 91876) ((|HashTable| . |Functorial|) 91805) ((|HashTable| . |HomogeneousAggregate|) 91734) ((|HashTable| . |Eltable|) 91713) ((|HashTable| . |EltableAggregate|) 91692) ((|HashTable| . |KeyedDictionary|) 91671) ((|HashTable| . |SetCategory|) T) ((|HashTable| . |CoercibleTo|) 91645) ((|HashTable| . |BasicType|) T) ((|HashTable| . |Type|) T) ((|HashTable| . |Join|) T) ((|HashTable| . |Aggregate|) T) ((|HashTable| . |FiniteAggregate|) 91587) ((|HasAst| . |SpadSyntaxCategory|) T) ((|HasAst| . |HomotopicTo|) 91565) 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T) ((|FortranType| . |SetCategory|) T) ((|FortranType| . |CoercibleTo|) 80781) ((|FortranType| . |Type|) T) ((|FortranType| . |Join|) T) ((|FortranType| . |BasicType|) T) ((|FortranScalarType| . |CoercibleTo|) 80712) ((|FourierSeries| . |Algebra|) 80696) ((|FourierSeries| . |CoercibleFrom|) 80660) ((|FourierSeries| . |LeftModule|) 80634) ((|FourierSeries| . |LeftLinearSet|) 80588) ((|FourierSeries| . |Rng|) T) ((|FourierSeries| . |SemiGroup|) T) ((|FourierSeries| . |SemiRing|) T) ((|FourierSeries| . |Monoid|) T) ((|FourierSeries| . |Ring|) T) ((|FourierSeries| . |BiModule|) 80567) ((|FourierSeries| . |RightLinearSet|) 80551) ((|FourierSeries| . |RightModule|) 80535) ((|FourierSeries| . |AbelianGroup|) T) ((|FourierSeries| . |AbelianMonoid|) T) ((|FourierSeries| . |SetCategory|) T) ((|FourierSeries| . |CoercibleTo|) 80509) ((|FourierSeries| . |Type|) T) ((|FourierSeries| . |Join|) T) ((|FourierSeries| . |BasicType|) T) ((|FourierSeries| . |AbelianSemiGroup|) T) ((|FourierSeries| . 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((|Fraction| . |LeftLinearSet|) 78303) ((|Fraction| . |Algebra|) 78244) ((|Fraction| . |EuclideanDomain|) T) ((|Fraction| . |GcdDomain|) T) ((|Fraction| . |CommutativeRing|) T) ((|Fraction| . |IntegralDomain|) T) ((|Fraction| . |PrincipalIdealDomain|) T) ((|Fraction| . |UniqueFactorizationDomain|) T) ((|Fraction| . |Field|) T) ((|Fraction| . |DifferentialRing|) 78209) ((|Fraction| . |DifferentialDomain|) 78128) ((|Fraction| . |DifferentialSpace|) 78053) ((|Fraction| . |DifferentialSpaceExtension|) 78037) ((|Fraction| . |PartialDifferentialDomain|) 77909) ((|Fraction| . |PartialDifferentialSpace|) 77783) ((|Fraction| . |PartialDifferentialRing|) 77715) ((|Fraction| . |DifferentialExtension|) 77699) ((|Fraction| . |CharacteristicZero|) 77618) ((|Fraction| . |CharacteristicNonZero|) 77578) ((|Fraction| . |CancellationAbelianMonoid|) T) ((|Fraction| . |AbelianSemiGroup|) T) ((|Fraction| . |BasicType|) T) ((|Fraction| . |Join|) T) ((|Fraction| . |Type|) T) ((|Fraction| . |CoercibleTo|) 77552) ((|Fraction| . |SetCategory|) T) ((|Fraction| . |AbelianMonoid|) T) ((|Fraction| . |AbelianGroup|) T) ((|Fraction| . |Ring|) T) ((|Fraction| . |Monoid|) T) ((|Fraction| . |SemiRing|) T) ((|Fraction| . |SemiGroup|) T) ((|Fraction| . |Rng|) T) ((|Factored| . |IntegralDomain|) T) ((|Factored| . |EntireRing|) T) ((|Factored| . |CommutativeRing|) T) ((|Factored| . |CoercibleFrom|) 77423) ((|Factored| . |Module|) 77397) ((|Factored| . |LinearSet|) 77371) ((|Factored| . |LeftModule|) 77345) ((|Factored| . |LeftLinearSet|) 77299) ((|Factored| . |CancellationAbelianMonoid|) T) ((|Factored| . |AbelianSemiGroup|) T) ((|Factored| . |BasicType|) T) ((|Factored| . |Join|) T) ((|Factored| . |Type|) T) ((|Factored| . |CoercibleTo|) 77273) ((|Factored| . |SetCategory|) T) ((|Factored| . |AbelianMonoid|) T) ((|Factored| . |AbelianGroup|) T) ((|Factored| . |RightModule|) 77247) ((|Factored| . |RightLinearSet|) 77221) ((|Factored| . |BiModule|) 77188) ((|Factored| . |Ring|) T) ((|Factored| . 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((|FiniteFieldExtension| . |RightModule|) 72946) ((|FiniteFieldExtension| . |EntireRing|) T) ((|FiniteFieldExtension| . |DivisionRing|) T) ((|FiniteFieldExtension| . |FieldOfPrimeCharacteristic|) 72877) ((|FiniteFieldExtension| . |CharacteristicNonZero|) 72808) ((|FiniteFieldExtension| . |RetractableTo|) 72792) ((|FiniteFieldExtension| . |VectorSpace|) 72776) ((|FiniteFieldExtension| . |ExtensionField|) 72760) ((|FiniteFieldExtensionByPolynomial| . |FiniteAlgebraicExtensionField|) 72744) ((|FiniteFieldExtensionByPolynomial| . |DifferentialRing|) 72719) ((|FiniteFieldExtensionByPolynomial| . |DifferentialDomain|) 72688) ((|FiniteFieldExtensionByPolynomial| . |DifferentialSpace|) 72663) ((|FiniteFieldExtensionByPolynomial| . |Finite|) 72638) ((|FiniteFieldExtensionByPolynomial| . |StepThrough|) 72613) ((|FiniteFieldExtensionByPolynomial| . |FiniteFieldCategory|) 72588) ((|FiniteFieldExtensionByPolynomial| . |CharacteristicZero|) 72551) ((|FiniteFieldExtensionByPolynomial| . 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T) ((|FiniteFieldNormalBasisExtension| . |Module|) 71256) ((|FiniteFieldNormalBasisExtension| . |LinearSet|) 71197) ((|FiniteFieldNormalBasisExtension| . |Algebra|) 71151) ((|FiniteFieldNormalBasisExtension| . |GcdDomain|) T) ((|FiniteFieldNormalBasisExtension| . |EuclideanDomain|) T) ((|FiniteFieldNormalBasisExtension| . |BiModule|) 71078) ((|FiniteFieldNormalBasisExtension| . |RightLinearSet|) 71019) ((|FiniteFieldNormalBasisExtension| . |RightModule|) 70960) ((|FiniteFieldNormalBasisExtension| . |EntireRing|) T) ((|FiniteFieldNormalBasisExtension| . |DivisionRing|) T) ((|FiniteFieldNormalBasisExtension| . |FieldOfPrimeCharacteristic|) 70891) ((|FiniteFieldNormalBasisExtension| . |CharacteristicNonZero|) 70822) ((|FiniteFieldNormalBasisExtension| . |RetractableTo|) 70806) ((|FiniteFieldNormalBasisExtension| . |VectorSpace|) 70790) ((|FiniteFieldNormalBasisExtension| . |ExtensionField|) 70774) ((|FiniteFieldNormalBasisExtensionByPolynomial| . |FiniteAlgebraicExtensionField|) 70758) 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|Join|) T) ((|FiniteFieldNormalBasis| . |Type|) T) ((|FiniteFieldNormalBasis| . |CoercibleTo|) 69415) ((|FiniteFieldNormalBasis| . |SetCategory|) T) ((|FiniteFieldNormalBasis| . |AbelianMonoid|) T) ((|FiniteFieldNormalBasis| . |AbelianGroup|) T) ((|FiniteFieldNormalBasis| . |Rng|) T) ((|FiniteFieldNormalBasis| . |SemiGroup|) T) ((|FiniteFieldNormalBasis| . |SemiRing|) T) ((|FiniteFieldNormalBasis| . |Monoid|) T) ((|FiniteFieldNormalBasis| . |Ring|) T) ((|FiniteFieldNormalBasis| . |Field|) T) ((|FiniteFieldNormalBasis| . |UniqueFactorizationDomain|) T) ((|FiniteFieldNormalBasis| . |PrincipalIdealDomain|) T) ((|FiniteFieldNormalBasis| . |IntegralDomain|) T) ((|FiniteFieldNormalBasis| . |CommutativeRing|) T) ((|FiniteFieldNormalBasis| . |Module|) 69341) ((|FiniteFieldNormalBasis| . |LinearSet|) 69267) ((|FiniteFieldNormalBasis| . |Algebra|) 69221) ((|FiniteFieldNormalBasis| . |GcdDomain|) T) ((|FiniteFieldNormalBasis| . |EuclideanDomain|) T) ((|FiniteFieldNormalBasis| . |BiModule|) 69131) ((|FiniteFieldNormalBasis| . |RightLinearSet|) 69057) ((|FiniteFieldNormalBasis| . |RightModule|) 68983) ((|FiniteFieldNormalBasis| . |EntireRing|) T) ((|FiniteFieldNormalBasis| . |DivisionRing|) T) ((|FiniteFieldNormalBasis| . |FieldOfPrimeCharacteristic|) T) ((|FiniteFieldNormalBasis| . |CharacteristicNonZero|) T) ((|FiniteFieldNormalBasis| . |RetractableTo|) 68952) ((|FiniteFieldNormalBasis| . |VectorSpace|) 68921) ((|FiniteFieldNormalBasis| . |ExtensionField|) 68890) ((|FiniteFieldCyclicGroupExtension| . |FiniteAlgebraicExtensionField|) 68874) ((|FiniteFieldCyclicGroupExtension| . |DifferentialRing|) 68849) ((|FiniteFieldCyclicGroupExtension| . |DifferentialDomain|) 68818) ((|FiniteFieldCyclicGroupExtension| . |DifferentialSpace|) 68793) ((|FiniteFieldCyclicGroupExtension| . |Finite|) 68768) ((|FiniteFieldCyclicGroupExtension| . |StepThrough|) 68743) ((|FiniteFieldCyclicGroupExtension| . |FiniteFieldCategory|) 68718) ((|FiniteFieldCyclicGroupExtension| . |CharacteristicZero|) 68681) ((|FiniteFieldCyclicGroupExtension| . |CoercibleFrom|) 68602) ((|FiniteFieldCyclicGroupExtension| . |LeftModule|) 68543) ((|FiniteFieldCyclicGroupExtension| . |LeftLinearSet|) 68464) ((|FiniteFieldCyclicGroupExtension| . |CancellationAbelianMonoid|) T) ((|FiniteFieldCyclicGroupExtension| . |AbelianSemiGroup|) T) ((|FiniteFieldCyclicGroupExtension| . |BasicType|) T) ((|FiniteFieldCyclicGroupExtension| . |Join|) T) ((|FiniteFieldCyclicGroupExtension| . |Type|) T) ((|FiniteFieldCyclicGroupExtension| . |CoercibleTo|) 68438) ((|FiniteFieldCyclicGroupExtension| . |SetCategory|) T) ((|FiniteFieldCyclicGroupExtension| . |AbelianMonoid|) T) ((|FiniteFieldCyclicGroupExtension| . |AbelianGroup|) T) ((|FiniteFieldCyclicGroupExtension| . |Rng|) T) ((|FiniteFieldCyclicGroupExtension| . |SemiGroup|) T) ((|FiniteFieldCyclicGroupExtension| . |SemiRing|) T) ((|FiniteFieldCyclicGroupExtension| . |Monoid|) T) ((|FiniteFieldCyclicGroupExtension| . |Ring|) T) ((|FiniteFieldCyclicGroupExtension| . 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|SetCategory|) T) ((|DifferentialSparseMultivariatePolynomial| . |AbelianMonoid|) T) ((|DifferentialSparseMultivariatePolynomial| . |AbelianGroup|) T) ((|DifferentialSparseMultivariatePolynomial| . |Rng|) T) ((|DifferentialSparseMultivariatePolynomial| . |SemiGroup|) T) ((|DifferentialSparseMultivariatePolynomial| . |SemiRing|) T) ((|DifferentialSparseMultivariatePolynomial| . |Monoid|) T) ((|DifferentialSparseMultivariatePolynomial| . |Ring|) T) ((|DifferentialSparseMultivariatePolynomial| . |DifferentialDomain|) 41440) ((|DifferentialSparseMultivariatePolynomial| . |Join|) T) ((|DifferentialSparseMultivariatePolynomial| . |Type|) T) ((|DifferentialSparseMultivariatePolynomial| . |DifferentialSpace|) 41365) ((|DifferentialSparseMultivariatePolynomial| . |DifferentialSpaceExtension|) 41349) ((|DifferentialSparseMultivariatePolynomial| . |DifferentialExtension|) 41333) ((|DrawOption| . |SetCategory|) T) ((|DrawOption| . |CoercibleTo|) 41307) ((|DrawOption| . |Type|) T) ((|DrawOption| . |Join|) T) ((|DrawOption| . |BasicType|) T) ((|DirectProductModule| . |DirectProductCategory|) 41286) ((|DirectProductModule| . |VectorSpace|) 41253) ((|DirectProductModule| . |OrderedCancellationAbelianMonoid|) 41211) ((|DirectProductModule| . |OrderedAbelianSemiGroup|) 41169) ((|DirectProductModule| . |OrderedType|) 41094) ((|DirectProductModule| . |OrderedSet|) 41019) ((|DirectProductModule| . |OrderedAbelianMonoid|) 40977) ((|DirectProductModule| . |OrderedAbelianMonoidSup|) 40935) ((|DirectProductModule| . |Module|) 40864) ((|DirectProductModule| . |LinearSet|) 40769) ((|DirectProductModule| . |EltableAggregate|) 40741) ((|DirectProductModule| . |Eltable|) 40713) ((|DirectProductModule| . |IndexedAggregate|) 40685) ((|DirectProductModule| . |RetractableTo|) 40436) ((|DirectProductModule| . |CoercibleFrom|) 40160) ((|DirectProductModule| . |FullyRetractableTo|) 40121) ((|DirectProductModule| . |LinearlyExplicitRingOver|) 39993) ((|DirectProductModule| . |LeftModule|) 39765) ((|DirectProductModule| . |FullyLinearlyExplicitRingOver|) 39733) ((|DirectProductModule| . |HomogeneousAggregate|) 39717) ((|DirectProductModule| . |Functorial|) 39701) ((|DirectProductModule| . |InnerEvalable|) 39620) ((|DirectProductModule| . |Evalable|) 39544) ((|DirectProductModule| . |Aggregate|) T) ((|DirectProductModule| . |FiniteAggregate|) 39528) ((|DirectProductModule| . |Finite|) 39503) ((|DirectProductModule| . |DifferentialRing|) 39440) ((|DirectProductModule| . |LeftLinearSet|) 39264) ((|DirectProductModule| . |Rng|) 39241) ((|DirectProductModule| . |SemiGroup|) 39218) ((|DirectProductModule| . |SemiRing|) 39195) ((|DirectProductModule| . |Monoid|) 39172) ((|DirectProductModule| . |Ring|) 39149) ((|DirectProductModule| . |DifferentialDomain|) 39012) ((|DirectProductModule| . |DifferentialSpace|) 38881) ((|DirectProductModule| . |DifferentialSpaceExtension|) 38849) ((|DirectProductModule| . |PartialDifferentialDomain|) 38665) ((|DirectProductModule| . |PartialDifferentialSpace|) 38483) ((|DirectProductModule| . |PartialDifferentialRing|) 38387) ((|DirectProductModule| . |DifferentialExtension|) 38355) ((|DirectProductModule| . |CoercibleTo|) 38305) ((|DirectProductModule| . |RightModule|) 38212) ((|DirectProductModule| . |RightLinearSet|) 38095) ((|DirectProductModule| . |BiModule|) 37997) ((|DirectProductModule| . |CancellationAbelianMonoid|) T) ((|DirectProductModule| . |AbelianSemiGroup|) T) ((|DirectProductModule| . |BasicType|) T) ((|DirectProductModule| . |Join|) T) ((|DirectProductModule| . |Type|) T) ((|DirectProductModule| . |SetCategory|) T) ((|DirectProductModule| . |AbelianMonoid|) T) ((|DirectProductModule| . |AbelianGroup|) T) ((|DirectProductMatrixModule| . |DirectProductCategory|) 37976) ((|DirectProductMatrixModule| . |VectorSpace|) 37943) ((|DirectProductMatrixModule| . |OrderedCancellationAbelianMonoid|) 37901) ((|DirectProductMatrixModule| . |OrderedAbelianSemiGroup|) 37859) ((|DirectProductMatrixModule| . |OrderedType|) 37784) ((|DirectProductMatrixModule| . |OrderedSet|) 37709) ((|DirectProductMatrixModule| . |OrderedAbelianMonoid|) 37667) ((|DirectProductMatrixModule| . |OrderedAbelianMonoidSup|) 37625) ((|DirectProductMatrixModule| . |Module|) 37554) ((|DirectProductMatrixModule| . |LinearSet|) 37459) ((|DirectProductMatrixModule| . |EltableAggregate|) 37431) ((|DirectProductMatrixModule| . |Eltable|) 37403) ((|DirectProductMatrixModule| . |IndexedAggregate|) 37375) ((|DirectProductMatrixModule| . |RetractableTo|) 37126) ((|DirectProductMatrixModule| . |CoercibleFrom|) 36850) ((|DirectProductMatrixModule| . |FullyRetractableTo|) 36811) ((|DirectProductMatrixModule| . |LinearlyExplicitRingOver|) 36683) ((|DirectProductMatrixModule| . |LeftModule|) 36442) ((|DirectProductMatrixModule| . |FullyLinearlyExplicitRingOver|) 36410) ((|DirectProductMatrixModule| . |HomogeneousAggregate|) 36394) ((|DirectProductMatrixModule| . |Functorial|) 36378) ((|DirectProductMatrixModule| . |InnerEvalable|) 36297) ((|DirectProductMatrixModule| . |Evalable|) 36221) ((|DirectProductMatrixModule| . |Aggregate|) T) ((|DirectProductMatrixModule| . |FiniteAggregate|) 36205) ((|DirectProductMatrixModule| . |Finite|) 36180) ((|DirectProductMatrixModule| . |DifferentialRing|) 36117) ((|DirectProductMatrixModule| . |LeftLinearSet|) 35928) ((|DirectProductMatrixModule| . |Rng|) 35905) ((|DirectProductMatrixModule| . |SemiGroup|) 35882) ((|DirectProductMatrixModule| . |SemiRing|) 35859) ((|DirectProductMatrixModule| . |Monoid|) 35836) ((|DirectProductMatrixModule| . |Ring|) 35813) ((|DirectProductMatrixModule| . |DifferentialDomain|) 35676) ((|DirectProductMatrixModule| . |DifferentialSpace|) 35545) ((|DirectProductMatrixModule| . |DifferentialSpaceExtension|) 35513) ((|DirectProductMatrixModule| . |PartialDifferentialDomain|) 35329) ((|DirectProductMatrixModule| . |PartialDifferentialSpace|) 35147) ((|DirectProductMatrixModule| . |PartialDifferentialRing|) 35051) ((|DirectProductMatrixModule| . |DifferentialExtension|) 35019) ((|DirectProductMatrixModule| . |CoercibleTo|) 34969) ((|DirectProductMatrixModule| . |RightModule|) 34876) ((|DirectProductMatrixModule| . |RightLinearSet|) 34759) ((|DirectProductMatrixModule| . |BiModule|) 34661) ((|DirectProductMatrixModule| . |CancellationAbelianMonoid|) T) ((|DirectProductMatrixModule| . |AbelianSemiGroup|) T) ((|DirectProductMatrixModule| . |BasicType|) T) ((|DirectProductMatrixModule| . |Join|) T) ((|DirectProductMatrixModule| . |Type|) T) ((|DirectProductMatrixModule| . |SetCategory|) T) ((|DirectProductMatrixModule| . |AbelianMonoid|) T) ((|DirectProductMatrixModule| . |AbelianGroup|) T) ((|DomainTemplate| . |SetCategory|) T) ((|DomainTemplate| . |CoercibleTo|) 34635) ((|DomainTemplate| . |Type|) T) ((|DomainTemplate| . |Join|) T) ((|DomainTemplate| . |BasicType|) T) ((|DomainTemplate| . |Eltable|) 34590) ((|DomainConstructor| . |ConstructorCategory|) T) ((|DomainConstructor| . |SetCategory|) T) ((|DomainConstructor| . |CoercibleTo|) 34540) ((|DomainConstructor| . |Type|) T) ((|DomainConstructor| . |Join|) T) ((|DomainConstructor| . |BasicType|) T) ((|DomainConstructor| . |OperatorCategory|) 34514) ((|Domain| . |SetCategory|) T) ((|Domain| . |CoercibleTo|) 34488) ((|Domain| . |Type|) T) ((|Domain| . |Join|) T) ((|Domain| . |BasicType|) T) ((|DistributedMultivariatePolynomial| . |PolynomialCategory|) 34391) ((|DistributedMultivariatePolynomial| . |CoercibleFrom|) 34063) ((|DistributedMultivariatePolynomial| . |RetractableTo|) 33870) ((|DistributedMultivariatePolynomial| . |UniqueFactorizationDomain|) 33820) ((|DistributedMultivariatePolynomial| . |PolynomialFactorizationExplicit|) 33770) ((|DistributedMultivariatePolynomial| . |PatternMatchable|) NIL) ((|DistributedMultivariatePolynomial| . |PartialDifferentialSpace|) 33730) ((|DistributedMultivariatePolynomial| . |PartialDifferentialDomain|) 33688) ((|DistributedMultivariatePolynomial| . |PartialDifferentialRing|) 33648) ((|DistributedMultivariatePolynomial| . |InnerEvalable|) 33574) ((|DistributedMultivariatePolynomial| . |GcdDomain|) 33492) ((|DistributedMultivariatePolynomial| . |LinearlyExplicitRingOver|) 33408) ((|DistributedMultivariatePolynomial| . |LeftModule|) 33237) ((|DistributedMultivariatePolynomial| . |FullyLinearlyExplicitRingOver|) 33221) ((|DistributedMultivariatePolynomial| . |AbelianMonoidRing|) 33153) ((|DistributedMultivariatePolynomial| . |Algebra|) 32916) ((|DistributedMultivariatePolynomial| . |LinearSet|) 32679) ((|DistributedMultivariatePolynomial| . |Module|) 32442) ((|DistributedMultivariatePolynomial| . |EntireRing|) 32328) ((|DistributedMultivariatePolynomial| . |IntegralDomain|) 32214) ((|DistributedMultivariatePolynomial| . |Functorial|) 32198) ((|DistributedMultivariatePolynomial| . |BiModule|) 31941) ((|DistributedMultivariatePolynomial| . |RightLinearSet|) 31698) ((|DistributedMultivariatePolynomial| . |RightModule|) 31455) ((|DistributedMultivariatePolynomial| . |CommutativeRing|) 31308) ((|DistributedMultivariatePolynomial| . |CharacteristicZero|) 31271) ((|DistributedMultivariatePolynomial| . |CharacteristicNonZero|) 31231) ((|DistributedMultivariatePolynomial| . |LeftLinearSet|) 31108) ((|DistributedMultivariatePolynomial| . |CancellationAbelianMonoid|) T) ((|DistributedMultivariatePolynomial| . |AbelianSemiGroup|) T) ((|DistributedMultivariatePolynomial| . |BasicType|) T) ((|DistributedMultivariatePolynomial| . |Join|) T) ((|DistributedMultivariatePolynomial| . |Type|) T) ((|DistributedMultivariatePolynomial| . |CoercibleTo|) 31082) ((|DistributedMultivariatePolynomial| . |SetCategory|) T) ((|DistributedMultivariatePolynomial| . |AbelianMonoid|) T) ((|DistributedMultivariatePolynomial| . |AbelianGroup|) T) ((|DistributedMultivariatePolynomial| . |Ring|) T) ((|DistributedMultivariatePolynomial| . |Monoid|) T) ((|DistributedMultivariatePolynomial| . |SemiRing|) T) ((|DistributedMultivariatePolynomial| . |SemiGroup|) T) ((|DistributedMultivariatePolynomial| . |Rng|) T) ((|DistributedMultivariatePolynomial| . |FullyRetractableTo|) 31066) ((|DistributedMultivariatePolynomial| . |FiniteAbelianMonoidRing|) 30998) ((|DistributedMultivariatePolynomial| . |Evalable|) 30985) ((|DistributedMultivariatePolynomial| . |ConvertibleTo|) 30763) ((|DataList| . |ListAggregate|) 30747) ((|DataList| . |UnaryRecursiveAggregate|) 30731) ((|DataList| . |RecursiveAggregate|) 30715) ((|DataList| . |StreamAggregate|) 30699) ((|DataList| . |FiniteAggregate|) 30683) ((|DataList| . |OrderedSet|) 30654) ((|DataList| . |OrderedType|) 30625) ((|DataList| . |FiniteLinearAggregate|) 30609) ((|DataList| . |LinearAggregate|) 30593) ((|DataList| . |EltableAggregate|) 30565) ((|DataList| . |Eltable|) 30494) ((|DataList| . |IndexedAggregate|) 30466) ((|DataList| . |ConvertibleTo|) 30402) ((|DataList| . |HomogeneousAggregate|) 30386) ((|DataList| . |SetCategory|) 30323) ((|DataList| . |Functorial|) 30307) ((|DataList| . |InnerEvalable|) 30226) ((|DataList| . |Evalable|) 30150) ((|DataList| . |CoercibleTo|) 30002) ((|DataList| . |BasicType|) 29912) ((|DataList| . |Type|) T) ((|DataList| . |Join|) T) ((|DataList| . |Aggregate|) T) ((|DataList| . |Collection|) 29896) ((|DataList| . |ShallowlyMutableAggregate|) 29880) ((|DataList| . |ExtensibleLinearAggregate|) 29864) ((|DataList| . |HomotopicTo|) 29839) ((|DataList| . |CoercibleFrom|) 29814) ((|DirectProduct| . |DirectProductCategory|) 29793) ((|DirectProduct| . |VectorSpace|) 29760) ((|DirectProduct| . |OrderedCancellationAbelianMonoid|) 29718) ((|DirectProduct| . |OrderedAbelianSemiGroup|) 29676) ((|DirectProduct| . |OrderedType|) 29601) ((|DirectProduct| . |OrderedSet|) 29526) ((|DirectProduct| . |OrderedAbelianMonoid|) 29484) ((|DirectProduct| . |OrderedAbelianMonoidSup|) 29442) ((|DirectProduct| . |Module|) 29371) ((|DirectProduct| . |LinearSet|) 29276) ((|DirectProduct| . |EltableAggregate|) 29248) ((|DirectProduct| . |Eltable|) 29220) ((|DirectProduct| . |IndexedAggregate|) 29192) ((|DirectProduct| . |RetractableTo|) 28943) ((|DirectProduct| . |CoercibleFrom|) 28667) ((|DirectProduct| . |FullyRetractableTo|) 28628) ((|DirectProduct| . |LinearlyExplicitRingOver|) 28500) ((|DirectProduct| . |LeftModule|) 28285) ((|DirectProduct| . |FullyLinearlyExplicitRingOver|) 28253) ((|DirectProduct| . |HomogeneousAggregate|) 28237) ((|DirectProduct| . |Functorial|) 28221) ((|DirectProduct| . |InnerEvalable|) 28140) ((|DirectProduct| . |Evalable|) 28064) ((|DirectProduct| . |Aggregate|) T) ((|DirectProduct| . |FiniteAggregate|) 28048) ((|DirectProduct| . |Finite|) 28023) ((|DirectProduct| . |DifferentialRing|) 27960) ((|DirectProduct| . |LeftLinearSet|) 27690) ((|DirectProduct| . |Rng|) 27667) ((|DirectProduct| . |SemiGroup|) 27644) ((|DirectProduct| . |SemiRing|) 27621) ((|DirectProduct| . |Monoid|) 27598) ((|DirectProduct| . |Ring|) 27575) ((|DirectProduct| . |DifferentialDomain|) 27438) ((|DirectProduct| . |DifferentialSpace|) 27307) ((|DirectProduct| . |DifferentialSpaceExtension|) 27275) ((|DirectProduct| . |PartialDifferentialDomain|) 27091) ((|DirectProduct| . |PartialDifferentialSpace|) 26909) ((|DirectProduct| . |PartialDifferentialRing|) 26813) ((|DirectProduct| . |DifferentialExtension|) 26781) ((|DirectProduct| . |CoercibleTo|) 26326) ((|DirectProduct| . |RightModule|) 26233) ((|DirectProduct| . |RightLinearSet|) 26116) ((|DirectProduct| . |BiModule|) 26018) ((|DirectProduct| . |CancellationAbelianMonoid|) 25820) ((|DirectProduct| . |AbelianSemiGroup|) 25557) ((|DirectProduct| . |BasicType|) 25162) ((|DirectProduct| . |Join|) T) ((|DirectProduct| . |Type|) T) ((|DirectProduct| . |SetCategory|) 24794) ((|DirectProduct| . |AbelianMonoid|) 24565) ((|DirectProduct| . |AbelianGroup|) 24451) ((|DenavitHartenbergMatrix| . |MatrixCategory|) 24412) ((|DenavitHartenbergMatrix| . |FiniteAggregate|) 24396) ((|DenavitHartenbergMatrix| . |Aggregate|) T) ((|DenavitHartenbergMatrix| . |Join|) T) 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|LeftLinearSet|) 23107) ((|DeRhamComplex| . |Rng|) T) ((|DeRhamComplex| . |SemiGroup|) T) ((|DeRhamComplex| . |SemiRing|) T) ((|DeRhamComplex| . |Monoid|) T) ((|DeRhamComplex| . |Ring|) T) ((|DeRhamComplex| . |AbelianGroup|) T) ((|DeRhamComplex| . |AbelianMonoid|) T) ((|DeRhamComplex| . |SetCategory|) T) ((|DeRhamComplex| . |CoercibleTo|) 23081) ((|DeRhamComplex| . |Type|) T) ((|DeRhamComplex| . |Join|) T) ((|DeRhamComplex| . |BasicType|) T) ((|DeRhamComplex| . |AbelianSemiGroup|) T) ((|DeRhamComplex| . |CancellationAbelianMonoid|) T) ((|DeRhamComplex| . |RetractableTo|) 23050) ((|DeRhamComplex| . |Functorial|) 23019) ((|Dequeue| . |DequeueAggregate|) 23003) ((|Dequeue| . |StackAggregate|) 22987) ((|Dequeue| . |BagAggregate|) 22971) ((|Dequeue| . |ShallowlyMutableAggregate|) 22955) ((|Dequeue| . |Aggregate|) T) ((|Dequeue| . |Join|) T) ((|Dequeue| . |Type|) T) ((|Dequeue| . |BasicType|) 22893) ((|Dequeue| . |CoercibleTo|) 22795) ((|Dequeue| . |Evalable|) 22719) ((|Dequeue| . |InnerEvalable|) 22638) ((|Dequeue| . |Functorial|) 22622) ((|Dequeue| . |SetCategory|) 22592) ((|Dequeue| . |HomogeneousAggregate|) 22576) ((|Dequeue| . |FiniteAggregate|) 22560) ((|Dequeue| . |QueueAggregate|) 22544) ((|DefinitionAst| . |SpadSyntaxCategory|) T) ((|DefinitionAst| . |HomotopicTo|) 22522) ((|DefinitionAst| . |CoercibleTo|) 22477) ((|DefinitionAst| . |CoercibleFrom|) 22455) ((|DefinitionAst| . |SetCategory|) T) ((|DefinitionAst| . |Type|) T) ((|DefinitionAst| . |Join|) T) ((|DefinitionAst| . |BasicType|) T) ((|DefinitionAst| . |AbstractSyntaxCategory|) T) ((|DecimalExpansion| . |QuotientFieldCategory|) 22432) ((|DecimalExpansion| . |StepThrough|) T) ((|DecimalExpansion| . |CoercibleFrom|) 22366) ((|DecimalExpansion| . |RetractableTo|) 22310) ((|DecimalExpansion| . |ConvertibleTo|) 22211) ((|DecimalExpansion| . |RealConstant|) T) ((|DecimalExpansion| . |PolynomialFactorizationExplicit|) NIL) ((|DecimalExpansion| . |Patternable|) 22188) ((|DecimalExpansion| . |OrderedRing|) T) ((|DecimalExpansion| . |OrderedCancellationAbelianMonoid|) T) ((|DecimalExpansion| . |OrderedAbelianSemiGroup|) T) ((|DecimalExpansion| . |OrderedType|) T) ((|DecimalExpansion| . |OrderedSet|) T) ((|DecimalExpansion| . |OrderedAbelianMonoid|) T) ((|DecimalExpansion| . |OrderedAbelianGroup|) T) ((|DecimalExpansion| . |OrderedIntegralDomain|) T) ((|DecimalExpansion| . |PatternMatchable|) 22165) ((|DecimalExpansion| . |FullyPatternMatchable|) 22142) ((|DecimalExpansion| . |LinearlyExplicitRingOver|) 22119) ((|DecimalExpansion| . |FullyLinearlyExplicitRingOver|) 22096) ((|DecimalExpansion| . |Eltable|) NIL) ((|DecimalExpansion| . |Evalable|) NIL) ((|DecimalExpansion| . |InnerEvalable|) NIL) ((|DecimalExpansion| . |Functorial|) 22073) ((|DecimalExpansion| . |FullyEvalableOver|) 22050) ((|DecimalExpansion| . |DivisionRing|) T) ((|DecimalExpansion| . |BiModule|) 21968) ((|DecimalExpansion| . |RightLinearSet|) 21902) ((|DecimalExpansion| . |RightModule|) 21836) 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|CoercibleTo|) 21306) ((|Database| . |Type|) T) ((|Database| . |Join|) T) ((|Database| . |BasicType|) T) ((|Database| . |CoercibleFrom|) 21281) ((|DataArray| . |SetCategory|) T) ((|DataArray| . |CoercibleTo|) 21255) ((|DataArray| . |Type|) T) ((|DataArray| . |Join|) T) ((|DataArray| . |BasicType|) T) ((|ConstructorKind| . |SetCategory|) T) ((|ConstructorKind| . |CoercibleTo|) 21229) ((|ConstructorKind| . |Type|) T) ((|ConstructorKind| . |Join|) T) ((|ConstructorKind| . |BasicType|) T) ((|ConstructorCall| . |SetCategory|) T) ((|ConstructorCall| . |CoercibleTo|) 21203) ((|ConstructorCall| . |Type|) T) ((|ConstructorCall| . |Join|) T) ((|ConstructorCall| . |BasicType|) T) ((|Constructor| . |ConstructorCategory|) T) ((|Constructor| . |SetCategory|) T) ((|Constructor| . |CoercibleTo|) 21177) ((|Constructor| . |Type|) T) ((|Constructor| . |Join|) T) ((|Constructor| . |BasicType|) T) ((|Constructor| . |OperatorCategory|) 21151) ((|CoerceAst| . |SpadSyntaxCategory|) T) ((|CoerceAst| . |HomotopicTo|) 21129) ((|CoerceAst| . |CoercibleTo|) 21084) ((|CoerceAst| . |CoercibleFrom|) 21062) ((|CoerceAst| . |SetCategory|) T) ((|CoerceAst| . |Type|) T) ((|CoerceAst| . |Join|) T) ((|CoerceAst| . |BasicType|) T) ((|CoerceAst| . |AbstractSyntaxCategory|) T) ((|Contour| . |CoercibleTo|) 21036) ((|ContinuedFraction| . |Algebra|) 20951) ((|ContinuedFraction| . |CoercibleFrom|) 20846) ((|ContinuedFraction| . |LeftModule|) 20761) ((|ContinuedFraction| . |LeftLinearSet|) 20656) ((|ContinuedFraction| . |Rng|) T) ((|ContinuedFraction| . |SemiGroup|) T) ((|ContinuedFraction| . |SemiRing|) T) ((|ContinuedFraction| . |Monoid|) T) ((|ContinuedFraction| . |Ring|) T) ((|ContinuedFraction| . |BiModule|) 20550) ((|ContinuedFraction| . |RightLinearSet|) 20465) ((|ContinuedFraction| . |RightModule|) 20380) ((|ContinuedFraction| . |AbelianGroup|) T) ((|ContinuedFraction| . |AbelianMonoid|) T) ((|ContinuedFraction| . |SetCategory|) T) ((|ContinuedFraction| . |CoercibleTo|) 20354) ((|ContinuedFraction| . |Type|) T) ((|ContinuedFraction| . |Join|) T) ((|ContinuedFraction| . |BasicType|) T) ((|ContinuedFraction| . |AbelianSemiGroup|) T) ((|ContinuedFraction| . |CancellationAbelianMonoid|) T) ((|ContinuedFraction| . |LinearSet|) 20269) ((|ContinuedFraction| . |Module|) 20184) ((|ContinuedFraction| . |Field|) T) ((|ContinuedFraction| . |UniqueFactorizationDomain|) T) ((|ContinuedFraction| . |PrincipalIdealDomain|) T) ((|ContinuedFraction| . |IntegralDomain|) T) ((|ContinuedFraction| . |CommutativeRing|) T) ((|ContinuedFraction| . |GcdDomain|) T) ((|ContinuedFraction| . |EuclideanDomain|) T) ((|ContinuedFraction| . |EntireRing|) T) ((|ContinuedFraction| . |DivisionRing|) T) ((|SubSpaceComponentProperty| . |SetCategory|) T) ((|SubSpaceComponentProperty| . |CoercibleTo|) 20158) ((|SubSpaceComponentProperty| . |Type|) T) ((|SubSpaceComponentProperty| . |Join|) T) ((|SubSpaceComponentProperty| . |BasicType|) T) ((|Complex| . |ComplexCategory|) 20142) ((|Complex| . |ArcHyperbolicFunctionCategory|) 20093) ((|Complex| . |ArcTrigonometricFunctionCategory|) 20044) ((|Complex| . |ElementaryFunctionCategory|) 19995) ((|Complex| . |HyperbolicFunctionCategory|) 19946) ((|Complex| . |TrigonometricFunctionCategory|) 19897) ((|Complex| . |TranscendentalFunctionCategory|) 19848) ((|Complex| . |RadicalCategory|) 19760) ((|Complex| . |PolynomialFactorizationExplicit|) 19671) ((|Complex| . |ConvertibleTo|) 19295) ((|Complex| . |Patternable|) 19279) ((|Complex| . |Finite|) 19212) ((|Complex| . |FiniteFieldCategory|) 19174) ((|Complex| . |StepThrough|) 19136) ((|Complex| . |FieldOfPrimeCharacteristic|) 19098) ((|Complex| . |FramedAlgebra|) 19046) ((|Complex| . |Algebra|) 18804) ((|Complex| . |BiModule|) 18672) ((|Complex| . |RightLinearSet|) 18554) ((|Complex| . |RightModule|) 18436) ((|Complex| . |LinearSet|) 18194) ((|Complex| . |Module|) 17952) ((|Complex| . |FiniteRankAlgebra|) 17900) ((|Complex| . |MonogenicAlgebra|) 17848) ((|Complex| . |RetractableTo|) 17692) ((|Complex| . |CoercibleFrom|) 17374) ((|Complex| . |FullyRetractableTo|) 17358) ((|Complex| . |PatternMatchable|) 17239) ((|Complex| . |FullyPatternMatchable|) 17223) ((|Complex| . |LinearlyExplicitRingOver|) 17139) ((|Complex| . |LeftModule|) 16953) ((|Complex| . |LeftLinearSet|) 16815) ((|Complex| . |FullyLinearlyExplicitRingOver|) 16799) ((|Complex| . |Eltable|) 16752) ((|Complex| . |Evalable|) 16711) ((|Complex| . |InnerEvalable|) 16600) ((|Complex| . |Functorial|) 16584) ((|Complex| . |FullyEvalableOver|) 16568) ((|Complex| . |DivisionRing|) 16502) ((|Complex| . |UniqueFactorizationDomain|) 16348) ((|Complex| . |Field|) 16282) ((|Complex| . |PrincipalIdealDomain|) 16183) ((|Complex| . |IntegralDomain|) 16052) ((|Complex| . |EntireRing|) 15921) ((|Complex| . |GcdDomain|) 15822) ((|Complex| . |EuclideanDomain|) 15723) ((|Complex| . |DifferentialRing|) 15646) ((|Complex| . |DifferentialDomain|) 15528) ((|Complex| . |DifferentialSpace|) 15416) ((|Complex| . |DifferentialSpaceExtension|) 15400) ((|Complex| . |PartialDifferentialDomain|) 15272) ((|Complex| . |PartialDifferentialSpace|) 15146) ((|Complex| . |PartialDifferentialRing|) 15078) ((|Complex| . |DifferentialExtension|) 15062) ((|Complex| . |CommutativeRing|) T) ((|Complex| . |CharacteristicZero|) 15025) ((|Complex| . |Ring|) T) ((|Complex| . |Monoid|) T) ((|Complex| . |SemiRing|) T) ((|Complex| . |SemiGroup|) T) ((|Complex| . |Rng|) T) ((|Complex| . |AbelianGroup|) T) ((|Complex| . |AbelianMonoid|) T) ((|Complex| . |SetCategory|) T) ((|Complex| . |CoercibleTo|) 14999) ((|Complex| . |Type|) T) ((|Complex| . |Join|) T) ((|Complex| . |BasicType|) T) ((|Complex| . |AbelianSemiGroup|) T) ((|Complex| . |CancellationAbelianMonoid|) T) ((|Complex| . |CharacteristicNonZero|) 14917) ((|CommutativeOperation| . |CommutativeOperatorCategory|) 14901) ((|CommutativeOperation| . |MappingCategory|) 14875) ((|CommutativeOperation| . |Type|) T) ((|CommutativeOperation| . |BinaryOperatorCategory|) 14859) ((|CommutativeOperation| . |CoercibleTo|) 14823) ((|CommaAst| . |SpadSyntaxCategory|) T) ((|CommaAst| . |HomotopicTo|) 14801) ((|CommaAst| . |CoercibleTo|) 14756) ((|CommaAst| . |CoercibleFrom|) 14734) ((|CommaAst| . |SetCategory|) T) ((|CommaAst| . |Type|) T) ((|CommaAst| . |Join|) T) ((|CommaAst| . |BasicType|) T) ((|CommaAst| . |AbstractSyntaxCategory|) T) ((|Commutator| . |SetCategory|) T) ((|Commutator| . |CoercibleTo|) 14708) ((|Commutator| . |Type|) T) ((|Commutator| . |Join|) T) ((|Commutator| . |BasicType|) T) ((|Color| . |AbelianSemiGroup|) T) ((|Color| . |BasicType|) T) ((|Color| . |Join|) T) ((|Color| . |Type|) T) ((|Color| . |CoercibleTo|) 14682) ((|Color| . |SetCategory|) T) ((|ColonAst| . |SpadSyntaxCategory|) T) ((|ColonAst| . |HomotopicTo|) 14660) ((|ColonAst| . |CoercibleTo|) 14615) ((|ColonAst| . |CoercibleFrom|) 14593) ((|ColonAst| . |SetCategory|) T) ((|ColonAst| . |Type|) T) ((|ColonAst| . |Join|) T) ((|ColonAst| . |BasicType|) T) ((|ColonAst| . |AbstractSyntaxCategory|) T) ((|CollectAst| . |SpadSyntaxCategory|) T) ((|CollectAst| . |HomotopicTo|) 14571) ((|CollectAst| . |CoercibleTo|) 14526) ((|CollectAst| . |CoercibleFrom|) 14504) ((|CollectAst| . |SetCategory|) T) ((|CollectAst| . |Type|) T) ((|CollectAst| . |Join|) T) ((|CollectAst| . |BasicType|) T) ((|CollectAst| . |AbstractSyntaxCategory|) T) ((|CliffordAlgebra| . |Ring|) T) ((|CliffordAlgebra| . |Monoid|) T) ((|CliffordAlgebra| . |SemiRing|) T) ((|CliffordAlgebra| . |SemiGroup|) T) ((|CliffordAlgebra| . |Rng|) T) ((|CliffordAlgebra| . |AbelianGroup|) T) ((|CliffordAlgebra| . |LeftLinearSet|) 14458) ((|CliffordAlgebra| . |AbelianMonoid|) T) ((|CliffordAlgebra| . |SetCategory|) T) ((|CliffordAlgebra| . |CoercibleTo|) 14432) ((|CliffordAlgebra| . |Type|) T) ((|CliffordAlgebra| . |Join|) T) ((|CliffordAlgebra| . |BasicType|) T) ((|CliffordAlgebra| . |AbelianSemiGroup|) T) ((|CliffordAlgebra| . |CancellationAbelianMonoid|) T) ((|CliffordAlgebra| . |LeftModule|) 14406) ((|CliffordAlgebra| . |CoercibleFrom|) 14370) ((|CliffordAlgebra| . |Algebra|) 14354) ((|CliffordAlgebra| . |BiModule|) 14333) ((|CliffordAlgebra| . |RightLinearSet|) 14317) ((|CliffordAlgebra| . |RightModule|) 14301) ((|CliffordAlgebra| . |LinearSet|) 14285) ((|CliffordAlgebra| . |Module|) 14269) ((|CliffordAlgebra| . |VectorSpace|) 14253) ((|Character| . |OrderedFinite|) T) ((|Character| . |OrderedType|) T) ((|Character| . |OrderedSet|) T) ((|Character| . |SetCategory|) T) ((|Character| . |CoercibleTo|) 14227) ((|Character| . |Type|) T) ((|Character| . |Join|) T) ((|Character| . |BasicType|) T) ((|Character| . |Finite|) T) ((|CharacterClass| . |SetCategory|) T) ((|CharacterClass| . |CoercibleTo|) 14201) ((|CharacterClass| . |Type|) T) ((|CharacterClass| . |Join|) T) ((|CharacterClass| . |BasicType|) T) ((|CharacterClass| . |ConvertibleTo|) 14148) ((|CharacterClass| . |FiniteSetAggregate|) 14123) ((|CharacterClass| . |SetAggregate|) 14098) ((|CharacterClass| . |FiniteAggregate|) 14073) ((|CharacterClass| . |Finite|) T) ((|CharacterClass| . |DictionaryOperations|) 14048) ((|CharacterClass| . |Collection|) 14023) ((|CharacterClass| . |HomogeneousAggregate|) 13998) ((|CharacterClass| . |Functorial|) 13973) ((|CharacterClass| . |InnerEvalable|) NIL) ((|CharacterClass| . |Evalable|) NIL) ((|CharacterClass| . |Aggregate|) T) ((|CharacterClass| . |ShallowlyMutableAggregate|) 13948) ((|CharacterClass| . |BagAggregate|) 13923) ((|CharacterClass| . |Dictionary|) 13898) ((|Category| . |CoercibleTo|) 13872) ((|CategoryConstructor| . |ConstructorCategory|) T) ((|CategoryConstructor| . |SetCategory|) T) ((|CategoryConstructor| . |CoercibleTo|) 13822) ((|CategoryConstructor| . |Type|) T) ((|CategoryConstructor| . |Join|) T) ((|CategoryConstructor| . |BasicType|) T) ((|CategoryConstructor| . |OperatorCategory|) 13796) ((|CategoryAst| . |SpadSyntaxCategory|) T) ((|CategoryAst| . |HomotopicTo|) 13774) ((|CategoryAst| . |CoercibleTo|) 13729) ((|CategoryAst| . |CoercibleFrom|) 13707) ((|CategoryAst| . |SetCategory|) T) ((|CategoryAst| . |Type|) T) ((|CategoryAst| . |Join|) T) ((|CategoryAst| . |BasicType|) T) ((|CategoryAst| . |AbstractSyntaxCategory|) T) ((|CaseAst| . |SpadSyntaxCategory|) T) ((|CaseAst| . |HomotopicTo|) 13685) ((|CaseAst| . |CoercibleTo|) 13640) ((|CaseAst| . |CoercibleFrom|) 13618) ((|CaseAst| . |SetCategory|) T) ((|CaseAst| . |Type|) T) ((|CaseAst| . |Join|) T) ((|CaseAst| . |BasicType|) T) ((|CaseAst| . |AbstractSyntaxCategory|) T) ((|CartesianTensor| . |GradedAlgebra|) 13579) ((|CartesianTensor| . |CoercibleFrom|) 13451) ((|CartesianTensor| . |RetractableTo|) 13435) ((|CartesianTensor| . |SetCategory|) T) ((|CartesianTensor| . |CoercibleTo|) 13409) ((|CartesianTensor| . |Type|) T) ((|CartesianTensor| . |Join|) T) ((|CartesianTensor| . |BasicType|) T) ((|CartesianTensor| . |GradedModule|) 13343) ((|CartesianTensor| . |Eltable|) 13315) ((|CardinalNumber| . |OrderedSet|) T) ((|CardinalNumber| . |CoercibleTo|) 13289) ((|CardinalNumber| . |SetCategory|) T) ((|CardinalNumber| . |BasicType|) T) ((|CardinalNumber| . |Join|) T) ((|CardinalNumber| . |Type|) T) ((|CardinalNumber| . |OrderedType|) T) ((|CardinalNumber| . |AbelianMonoid|) T) ((|CardinalNumber| . |AbelianSemiGroup|) T) ((|CardinalNumber| . |Monoid|) T) ((|CardinalNumber| . |SemiGroup|) T) ((|CardinalNumber| . |RetractableTo|) 13255) ((|CardinalNumber| . |CoercibleFrom|) 13221) ((|CapsuleAst| . |SpadSyntaxCategory|) T) ((|CapsuleAst| . |HomotopicTo|) 13199) ((|CapsuleAst| . |CoercibleTo|) 13154) ((|CapsuleAst| . |CoercibleFrom|) 13132) ((|CapsuleAst| . |SetCategory|) T) ((|CapsuleAst| . |Type|) T) ((|CapsuleAst| . |Join|) T) ((|CapsuleAst| . |BasicType|) T) ((|CapsuleAst| . |AbstractSyntaxCategory|) T) ((|ByteOrder| . |SetCategory|) T) ((|ByteOrder| . |CoercibleTo|) 13106) ((|ByteOrder| . |Type|) T) ((|ByteOrder| . |Join|) T) ((|ByteOrder| . |BasicType|) T) ((|ByteBuffer| . |OneDimensionalArrayAggregate|) 13086) ((|ByteBuffer| . |ShallowlyMutableAggregate|) 13066) ((|ByteBuffer| . |FiniteAggregate|) 13046) ((|ByteBuffer| . |Aggregate|) T) ((|ByteBuffer| . |Join|) T) ((|ByteBuffer| . |Type|) T) ((|ByteBuffer| . |BasicType|) T) ((|ByteBuffer| . |CoercibleTo|) 12965) ((|ByteBuffer| . |Evalable|) NIL) ((|ByteBuffer| . |InnerEvalable|) NIL) ((|ByteBuffer| . |Functorial|) 12945) ((|ByteBuffer| . |SetCategory|) T) ((|ByteBuffer| . |HomogeneousAggregate|) 12925) ((|ByteBuffer| . |LinearAggregate|) 12905) ((|ByteBuffer| . |EltableAggregate|) 12873) ((|ByteBuffer| . |Eltable|) 12798) ((|ByteBuffer| . |IndexedAggregate|) 12766) ((|ByteBuffer| . |ConvertibleTo|) NIL) ((|ByteBuffer| . |Collection|) 12746) ((|ByteBuffer| . |OrderedSet|) T) ((|ByteBuffer| . |OrderedType|) T) ((|ByteBuffer| . |FiniteLinearAggregate|) 12726) ((|Byte| . |OrderedFinite|) T) ((|Byte| . |OrderedType|) T) ((|Byte| . |OrderedSet|) T) ((|Byte| . |SetCategory|) T) ((|Byte| . |CoercibleTo|) 12700) ((|Byte| . |Type|) T) ((|Byte| . |Join|) T) ((|Byte| . |BasicType|) T) ((|Byte| . |Finite|) T) ((|Byte| . |Logic|) T) ((|BinaryTree| . |BinaryTreeCategory|) 12684) ((|BinaryTree| . |ShallowlyMutableAggregate|) 12668) ((|BinaryTree| . |FiniteAggregate|) 12652) ((|BinaryTree| . |RecursiveAggregate|) 12636) ((|BinaryTree| . |Aggregate|) T) ((|BinaryTree| . |Join|) T) ((|BinaryTree| . |Type|) T) ((|BinaryTree| . |BasicType|) 12574) ((|BinaryTree| . |CoercibleTo|) 12476) ((|BinaryTree| . |Evalable|) 12400) ((|BinaryTree| . |InnerEvalable|) 12319) ((|BinaryTree| . |Functorial|) 12303) ((|BinaryTree| . |SetCategory|) 12273) ((|BinaryTree| . |HomogeneousAggregate|) 12257) ((|BinaryTree| . |BinaryRecursiveAggregate|) 12241) ((|BinaryTournament| . |BinaryTreeCategory|) 12225) ((|BinaryTournament| . |ShallowlyMutableAggregate|) 12209) ((|BinaryTournament| . |FiniteAggregate|) 12193) ((|BinaryTournament| . |RecursiveAggregate|) 12177) ((|BinaryTournament| . |Aggregate|) T) ((|BinaryTournament| . |Join|) T) ((|BinaryTournament| . |Type|) T) ((|BinaryTournament| . |BasicType|) 12115) ((|BinaryTournament| . |CoercibleTo|) 12017) ((|BinaryTournament| . |Evalable|) 11941) ((|BinaryTournament| . |InnerEvalable|) 11860) ((|BinaryTournament| . |Functorial|) 11844) ((|BinaryTournament| . |SetCategory|) 11814) ((|BinaryTournament| . |HomogeneousAggregate|) 11798) ((|BinaryTournament| . |BinaryRecursiveAggregate|) 11782) ((|BinarySearchTree| . |BinaryTreeCategory|) 11766) ((|BinarySearchTree| . |ShallowlyMutableAggregate|) 11750) ((|BinarySearchTree| . |FiniteAggregate|) 11734) ((|BinarySearchTree| . |RecursiveAggregate|) 11718) ((|BinarySearchTree| . |Aggregate|) T) ((|BinarySearchTree| . |Join|) T) ((|BinarySearchTree| . |Type|) T) ((|BinarySearchTree| . |BasicType|) 11656) ((|BinarySearchTree| . |CoercibleTo|) 11558) ((|BinarySearchTree| . |Evalable|) 11482) ((|BinarySearchTree| . |InnerEvalable|) 11401) ((|BinarySearchTree| . |Functorial|) 11385) ((|BinarySearchTree| . |SetCategory|) 11355) ((|BinarySearchTree| . |HomogeneousAggregate|) 11339) ((|BinarySearchTree| . |BinaryRecursiveAggregate|) 11323) ((|BalancedPAdicRational| . |QuotientFieldCategory|) 11282) ((|BalancedPAdicRational| . |StepThrough|) NIL) ((|BalancedPAdicRational| . |RetractableTo|) 11241) ((|BalancedPAdicRational| . |CoercibleFrom|) 11137) ((|BalancedPAdicRational| . |ConvertibleTo|) NIL) ((|BalancedPAdicRational| . |RealConstant|) NIL) ((|BalancedPAdicRational| . |PolynomialFactorizationExplicit|) NIL) ((|BalancedPAdicRational| . |Patternable|) 11096) ((|BalancedPAdicRational| . |OrderedRing|) NIL) ((|BalancedPAdicRational| . |OrderedCancellationAbelianMonoid|) NIL) ((|BalancedPAdicRational| . |OrderedAbelianSemiGroup|) NIL) ((|BalancedPAdicRational| . |OrderedType|) NIL) ((|BalancedPAdicRational| . |OrderedSet|) NIL) ((|BalancedPAdicRational| . |OrderedAbelianMonoid|) NIL) ((|BalancedPAdicRational| . |OrderedAbelianGroup|) NIL) ((|BalancedPAdicRational| . |OrderedIntegralDomain|) NIL) ((|BalancedPAdicRational| . |PatternMatchable|) NIL) ((|BalancedPAdicRational| . |FullyPatternMatchable|) 11055) ((|BalancedPAdicRational| . |LinearlyExplicitRingOver|) 11014) ((|BalancedPAdicRational| . |LeftModule|) 10930) ((|BalancedPAdicRational| . |FullyLinearlyExplicitRingOver|) 10889) ((|BalancedPAdicRational| . |Eltable|) 10817) ((|BalancedPAdicRational| . |Evalable|) 10750) ((|BalancedPAdicRational| . |InnerEvalable|) 10617) ((|BalancedPAdicRational| . |Functorial|) 10576) ((|BalancedPAdicRational| . |FullyEvalableOver|) 10535) ((|BalancedPAdicRational| . |DivisionRing|) T) ((|BalancedPAdicRational| . |BiModule|) 10435) ((|BalancedPAdicRational| . |RightLinearSet|) 10351) ((|BalancedPAdicRational| . |RightModule|) 10267) ((|BalancedPAdicRational| . |EntireRing|) T) ((|BalancedPAdicRational| . |Module|) 10183) ((|BalancedPAdicRational| . |LinearSet|) 10099) ((|BalancedPAdicRational| . |LeftLinearSet|) 9995) ((|BalancedPAdicRational| . |Algebra|) 9911) ((|BalancedPAdicRational| . |EuclideanDomain|) T) ((|BalancedPAdicRational| . |GcdDomain|) T) ((|BalancedPAdicRational| . |CommutativeRing|) T) ((|BalancedPAdicRational| . |IntegralDomain|) T) ((|BalancedPAdicRational| . |PrincipalIdealDomain|) T) ((|BalancedPAdicRational| . |UniqueFactorizationDomain|) T) ((|BalancedPAdicRational| . |Field|) T) ((|BalancedPAdicRational| . |DifferentialRing|) NIL) ((|BalancedPAdicRational| . |DifferentialDomain|) NIL) ((|BalancedPAdicRational| . |DifferentialSpace|) NIL) ((|BalancedPAdicRational| . |DifferentialSpaceExtension|) 9870) ((|BalancedPAdicRational| . |PartialDifferentialDomain|) NIL) ((|BalancedPAdicRational| . |PartialDifferentialSpace|) NIL) ((|BalancedPAdicRational| . |PartialDifferentialRing|) NIL) ((|BalancedPAdicRational| . |DifferentialExtension|) 9829) ((|BalancedPAdicRational| . |CharacteristicZero|) T) ((|BalancedPAdicRational| . |CharacteristicNonZero|) NIL) ((|BalancedPAdicRational| . |CancellationAbelianMonoid|) T) ((|BalancedPAdicRational| . |AbelianSemiGroup|) T) ((|BalancedPAdicRational| . |BasicType|) T) ((|BalancedPAdicRational| . |Join|) T) ((|BalancedPAdicRational| . |Type|) T) ((|BalancedPAdicRational| . |CoercibleTo|) 9803) ((|BalancedPAdicRational| . |SetCategory|) T) ((|BalancedPAdicRational| . |AbelianMonoid|) T) ((|BalancedPAdicRational| . |AbelianGroup|) T) ((|BalancedPAdicRational| . |Ring|) T) ((|BalancedPAdicRational| . |Monoid|) T) ((|BalancedPAdicRational| . |SemiRing|) T) ((|BalancedPAdicRational| . |SemiGroup|) T) ((|BalancedPAdicRational| . |Rng|) T) ((|BalancedPAdicInteger| . |PAdicIntegerCategory|) 9787) ((|BalancedPAdicInteger| . |PrincipalIdealDomain|) T) ((|BalancedPAdicInteger| . |IntegralDomain|) T) ((|BalancedPAdicInteger| . |EntireRing|) T) ((|BalancedPAdicInteger| . |CommutativeRing|) T) ((|BalancedPAdicInteger| . |CoercibleFrom|) 9754) ((|BalancedPAdicInteger| . |Module|) 9741) ((|BalancedPAdicInteger| . |LinearSet|) 9728) ((|BalancedPAdicInteger| . |RightModule|) 9715) ((|BalancedPAdicInteger| . |RightLinearSet|) 9702) ((|BalancedPAdicInteger| . |BiModule|) 9687) ((|BalancedPAdicInteger| . |Algebra|) 9674) ((|BalancedPAdicInteger| . |GcdDomain|) T) ((|BalancedPAdicInteger| . |EuclideanDomain|) T) ((|BalancedPAdicInteger| . |Ring|) T) ((|BalancedPAdicInteger| . |Monoid|) T) ((|BalancedPAdicInteger| . |SemiRing|) T) ((|BalancedPAdicInteger| . |SemiGroup|) T) ((|BalancedPAdicInteger| . |Rng|) T) ((|BalancedPAdicInteger| . |AbelianGroup|) T) ((|BalancedPAdicInteger| . |LeftLinearSet|) 9641) ((|BalancedPAdicInteger| . |AbelianMonoid|) T) ((|BalancedPAdicInteger| . |SetCategory|) T) ((|BalancedPAdicInteger| . |CoercibleTo|) 9615) ((|BalancedPAdicInteger| . |Type|) T) ((|BalancedPAdicInteger| . |Join|) T) ((|BalancedPAdicInteger| . |BasicType|) T) ((|BalancedPAdicInteger| . |AbelianSemiGroup|) T) ((|BalancedPAdicInteger| . |CancellationAbelianMonoid|) T) ((|BalancedPAdicInteger| . |LeftModule|) 9602) ((|BalancedPAdicInteger| . |CharacteristicZero|) T) ((|BasicOperator| . |OrderedSet|) T) ((|BasicOperator| . |CoercibleTo|) 9576) ((|BasicOperator| . |SetCategory|) T) ((|BasicOperator| . |BasicType|) T) ((|BasicOperator| . |Join|) T) ((|BasicOperator| . |Type|) T) ((|BasicOperator| . |OrderedType|) T) ((|BasicOperator| . |OperatorCategory|) 9554) ((|Boolean| . |OrderedFinite|) T) ((|Boolean| . |OrderedType|) T) ((|Boolean| . |OrderedSet|) T) ((|Boolean| . |SetCategory|) T) ((|Boolean| . |CoercibleTo|) 9528) ((|Boolean| . |Type|) T) ((|Boolean| . |Join|) T) ((|Boolean| . |BasicType|) T) ((|Boolean| . |Finite|) T) ((|Boolean| . |PropositionalLogic|) T) ((|Boolean| . |Logic|) T) ((|Boolean| . |BooleanLogic|) T) ((|Boolean| . |ConvertibleTo|) 9503) ((|Bits| . |BitAggregate|) T) ((|Bits| . |FiniteLinearAggregate|) 9480) ((|Bits| . |OrderedType|) T) ((|Bits| . |OrderedSet|) T) ((|Bits| . |Collection|) 9457) ((|Bits| . |ConvertibleTo|) 9432) ((|Bits| . |Eltable|) 9354) ((|Bits| . |IndexedAggregate|) 9319) ((|Bits| . |EltableAggregate|) 9284) ((|Bits| . |LinearAggregate|) 9261) ((|Bits| . |HomogeneousAggregate|) 9238) ((|Bits| . |SetCategory|) T) ((|Bits| . |Functorial|) 9215) ((|Bits| . |InnerEvalable|) NIL) ((|Bits| . |Evalable|) NIL) ((|Bits| . |CoercibleTo|) 9189) ((|Bits| . |BasicType|) T) ((|Bits| . |Aggregate|) T) ((|Bits| . |FiniteAggregate|) 9166) ((|Bits| . |ShallowlyMutableAggregate|) 9143) ((|Bits| . |OneDimensionalArrayAggregate|) 9120) ((|Bits| . |Logic|) T) ((|Bits| . |Join|) T) ((|Bits| . |Type|) T) ((|Bits| . |BooleanLogic|) T) ((|BinaryOperation| . |BinaryOperatorCategory|) 9104) ((|BinaryOperation| . |Type|) T) ((|BinaryOperation| . |MappingCategory|) 9078) ((|BinaryOperation| . |SetCategory|) T) ((|BinaryOperation| . |CoercibleTo|) 9052) ((|BinaryOperation| . |Join|) T) ((|BinaryOperation| . |BasicType|) T) ((|Binding| . |CoercibleTo|) 9026) ((|BinaryExpansion| . |QuotientFieldCategory|) 9003) ((|BinaryExpansion| . |StepThrough|) T) ((|BinaryExpansion| . |CoercibleFrom|) 8937) ((|BinaryExpansion| . |RetractableTo|) 8881) ((|BinaryExpansion| . |ConvertibleTo|) 8782) ((|BinaryExpansion| . |RealConstant|) T) ((|BinaryExpansion| . |PolynomialFactorizationExplicit|) NIL) ((|BinaryExpansion| . |Patternable|) 8759) ((|BinaryExpansion| . |OrderedRing|) T) ((|BinaryExpansion| . |OrderedCancellationAbelianMonoid|) T) ((|BinaryExpansion| . |OrderedAbelianSemiGroup|) T) ((|BinaryExpansion| . |OrderedType|) T) ((|BinaryExpansion| . |OrderedSet|) T) ((|BinaryExpansion| . |OrderedAbelianMonoid|) T) ((|BinaryExpansion| . |OrderedAbelianGroup|) T) ((|BinaryExpansion| . |OrderedIntegralDomain|) T) ((|BinaryExpansion| . |PatternMatchable|) 8736) ((|BinaryExpansion| . |FullyPatternMatchable|) 8713) ((|BinaryExpansion| . |LinearlyExplicitRingOver|) 8690) ((|BinaryExpansion| . |FullyLinearlyExplicitRingOver|) 8667) ((|BinaryExpansion| . |Eltable|) NIL) ((|BinaryExpansion| . |Evalable|) NIL) ((|BinaryExpansion| . |InnerEvalable|) NIL) ((|BinaryExpansion| . |Functorial|) 8644) ((|BinaryExpansion| . |FullyEvalableOver|) 8621) ((|BinaryExpansion| . |DivisionRing|) T) ((|BinaryExpansion| . |BiModule|) 8539) ((|BinaryExpansion| . |RightLinearSet|) 8473) ((|BinaryExpansion| . |RightModule|) 8407) ((|BinaryExpansion| . |EntireRing|) T) ((|BinaryExpansion| . |Module|) 8341) ((|BinaryExpansion| . |LinearSet|) 8275) ((|BinaryExpansion| . |LeftModule|) 8209) ((|BinaryExpansion| . |LeftLinearSet|) 8143) ((|BinaryExpansion| . |Algebra|) 8077) ((|BinaryExpansion| . |EuclideanDomain|) T) ((|BinaryExpansion| . |GcdDomain|) T) ((|BinaryExpansion| . |CommutativeRing|) T) ((|BinaryExpansion| . |IntegralDomain|) T) ((|BinaryExpansion| . |PrincipalIdealDomain|) T) ((|BinaryExpansion| . |UniqueFactorizationDomain|) T) ((|BinaryExpansion| . |Field|) T) ((|BinaryExpansion| . |DifferentialRing|) T) ((|BinaryExpansion| . |DifferentialDomain|) 8064) ((|BinaryExpansion| . |DifferentialSpace|) T) ((|BinaryExpansion| . |DifferentialSpaceExtension|) 8041) ((|BinaryExpansion| . |PartialDifferentialDomain|) NIL) ((|BinaryExpansion| . |PartialDifferentialSpace|) NIL) ((|BinaryExpansion| . |PartialDifferentialRing|) NIL) ((|BinaryExpansion| . |DifferentialExtension|) 8018) ((|BinaryExpansion| . |CharacteristicZero|) T) ((|BinaryExpansion| . |CharacteristicNonZero|) NIL) ((|BinaryExpansion| . |CancellationAbelianMonoid|) T) ((|BinaryExpansion| . |AbelianSemiGroup|) T) ((|BinaryExpansion| . |BasicType|) T) ((|BinaryExpansion| . |Join|) T) ((|BinaryExpansion| . |Type|) T) ((|BinaryExpansion| . |CoercibleTo|) 7930) ((|BinaryExpansion| . |SetCategory|) T) ((|BinaryExpansion| . |AbelianMonoid|) T) ((|BinaryExpansion| . |AbelianGroup|) T) ((|BinaryExpansion| . |Ring|) T) ((|BinaryExpansion| . |Monoid|) T) ((|BinaryExpansion| . |SemiRing|) T) ((|BinaryExpansion| . |SemiGroup|) T) ((|BinaryExpansion| . |Rng|) T) ((|BalancedBinaryTree| . |BinaryTreeCategory|) 7914) ((|BalancedBinaryTree| . |ShallowlyMutableAggregate|) 7898) ((|BalancedBinaryTree| . |FiniteAggregate|) 7882) ((|BalancedBinaryTree| . |RecursiveAggregate|) 7866) ((|BalancedBinaryTree| . |Aggregate|) T) ((|BalancedBinaryTree| . |Join|) T) ((|BalancedBinaryTree| . |Type|) T) ((|BalancedBinaryTree| . |BasicType|) 7804) ((|BalancedBinaryTree| . |CoercibleTo|) 7706) ((|BalancedBinaryTree| . |Evalable|) 7630) ((|BalancedBinaryTree| . |InnerEvalable|) 7549) ((|BalancedBinaryTree| . |Functorial|) 7533) ((|BalancedBinaryTree| . |SetCategory|) 7503) ((|BalancedBinaryTree| . |HomogeneousAggregate|) 7487) ((|BalancedBinaryTree| . |BinaryRecursiveAggregate|) 7471) ((|Automorphism| . |Group|) T) ((|Automorphism| . |SemiGroup|) T) ((|Automorphism| . |BasicType|) T) ((|Automorphism| . |Join|) T) ((|Automorphism| . |Type|) T) ((|Automorphism| . |CoercibleTo|) 7445) ((|Automorphism| . |SetCategory|) T) ((|Automorphism| . |Monoid|) T) ((|Automorphism| . |Eltable|) 7424) ((|AttributeAst| . |SpadSyntaxCategory|) T) ((|AttributeAst| . |HomotopicTo|) 7402) ((|AttributeAst| . |CoercibleTo|) 7357) ((|AttributeAst| . |CoercibleFrom|) 7335) ((|AttributeAst| . |SetCategory|) T) ((|AttributeAst| . |Type|) T) ((|AttributeAst| . |Join|) T) ((|AttributeAst| . |BasicType|) T) ((|AttributeAst| . |AbstractSyntaxCategory|) T) ((|ArrayStack| . |StackAggregate|) 7319) ((|ArrayStack| . |FiniteAggregate|) 7303) ((|ArrayStack| . |HomogeneousAggregate|) 7287) ((|ArrayStack| . |SetCategory|) 7257) ((|ArrayStack| . |Functorial|) 7241) ((|ArrayStack| . |InnerEvalable|) 7160) ((|ArrayStack| . |Evalable|) 7084) ((|ArrayStack| . |CoercibleTo|) 6986) ((|ArrayStack| . |BasicType|) 6924) ((|ArrayStack| . |Type|) T) ((|ArrayStack| . |Join|) T) ((|ArrayStack| . |Aggregate|) T) ((|ArrayStack| . |ShallowlyMutableAggregate|) 6908) ((|ArrayStack| . |BagAggregate|) 6892) ((|TwoDimensionalArray| . |TwoDimensionalArrayCategory|) 6840) ((|TwoDimensionalArray| . |ShallowlyMutableAggregate|) 6824) ((|TwoDimensionalArray| . |HomogeneousAggregate|) 6808) ((|TwoDimensionalArray| . |SetCategory|) 6778) ((|TwoDimensionalArray| . |Functorial|) 6762) ((|TwoDimensionalArray| . |InnerEvalable|) 6681) ((|TwoDimensionalArray| . |Evalable|) 6605) ((|TwoDimensionalArray| . |CoercibleTo|) 6507) ((|TwoDimensionalArray| . |BasicType|) 6445) ((|TwoDimensionalArray| . |Type|) T) ((|TwoDimensionalArray| . |Join|) T) ((|TwoDimensionalArray| . |Aggregate|) T) ((|TwoDimensionalArray| . |FiniteAggregate|) 6429) ((|OneDimensionalArray| . |OneDimensionalArrayAggregate|) 6413) ((|OneDimensionalArray| . |ShallowlyMutableAggregate|) 6397) ((|OneDimensionalArray| . |FiniteAggregate|) 6381) ((|OneDimensionalArray| . |Aggregate|) T) ((|OneDimensionalArray| . |Join|) T) ((|OneDimensionalArray| . |Type|) T) ((|OneDimensionalArray| . |BasicType|) 6291) ((|OneDimensionalArray| . |CoercibleTo|) 6165) ((|OneDimensionalArray| . |Evalable|) 6089) ((|OneDimensionalArray| . |InnerEvalable|) 6008) ((|OneDimensionalArray| . |Functorial|) 5992) ((|OneDimensionalArray| . |SetCategory|) 5929) ((|OneDimensionalArray| . |HomogeneousAggregate|) 5913) ((|OneDimensionalArray| . |LinearAggregate|) 5897) ((|OneDimensionalArray| . |EltableAggregate|) 5869) ((|OneDimensionalArray| . |Eltable|) 5798) ((|OneDimensionalArray| . |IndexedAggregate|) 5770) ((|OneDimensionalArray| . |ConvertibleTo|) 5706) ((|OneDimensionalArray| . |Collection|) 5690) ((|OneDimensionalArray| . |OrderedSet|) 5661) ((|OneDimensionalArray| . |OrderedType|) 5632) ((|OneDimensionalArray| . |FiniteLinearAggregate|) 5616) ((|Arity| . |SetCategory|) T) ((|Arity| . |CoercibleTo|) 5590) ((|Arity| . |Type|) T) ((|Arity| . |Join|) T) ((|Arity| . |BasicType|) T) ((|Arity| . |RetractableTo|) 5556) ((|Arity| . |CoercibleFrom|) 5522) ((|Any| . |SetCategory|) T) ((|Any| . |CoercibleTo|) 5496) ((|Any| . |Type|) T) ((|Any| . |Join|) T) ((|Any| . |BasicType|) T) ((|AntiSymm| . |LeftAlgebra|) 5480) ((|AntiSymm| . |CoercibleFrom|) 5444) ((|AntiSymm| . |LeftModule|) 5418) ((|AntiSymm| . |LeftLinearSet|) 5372) ((|AntiSymm| . |Rng|) T) ((|AntiSymm| . |SemiGroup|) T) ((|AntiSymm| . |SemiRing|) T) ((|AntiSymm| . |Monoid|) T) ((|AntiSymm| . |Ring|) T) ((|AntiSymm| . |AbelianGroup|) T) ((|AntiSymm| . |AbelianMonoid|) T) ((|AntiSymm| . |SetCategory|) T) ((|AntiSymm| . |CoercibleTo|) 5346) ((|AntiSymm| . |Type|) T) ((|AntiSymm| . |Join|) T) ((|AntiSymm| . |BasicType|) T) ((|AntiSymm| . |AbelianSemiGroup|) T) ((|AntiSymm| . |CancellationAbelianMonoid|) T) ((|AntiSymm| . |RetractableTo|) 5330) ((|AntiSymm| . |Functorial|) 5314) ((|AnonymousFunction| . |SetCategory|) T) ((|AnonymousFunction| . |CoercibleTo|) 5288) ((|AnonymousFunction| . |Type|) T) ((|AnonymousFunction| . |Join|) T) ((|AnonymousFunction| . |BasicType|) T) ((|AlgebraicNumber| . |ExpressionSpace|) T) ((|AlgebraicNumber| . |BasicType|) T) ((|AlgebraicNumber| . |Join|) T) ((|AlgebraicNumber| . |Type|) T) ((|AlgebraicNumber| . |CoercibleTo|) 5262) ((|AlgebraicNumber| . |SetCategory|) T) ((|AlgebraicNumber| . |CoercibleFrom|) 5109) ((|AlgebraicNumber| . |RetractableTo|) 5037) ((|AlgebraicNumber| . |InnerEvalable|) 4999) ((|AlgebraicNumber| . |Evalable|) 4986) ((|AlgebraicNumber| . |AlgebraicallyClosedField|) T) ((|AlgebraicNumber| . |RadicalCategory|) T) ((|AlgebraicNumber| . |DivisionRing|) T) ((|AlgebraicNumber| . |BiModule|) 4931) ((|AlgebraicNumber| . |RightLinearSet|) 4885) ((|AlgebraicNumber| . |RightModule|) 4839) ((|AlgebraicNumber| . |EntireRing|) T) ((|AlgebraicNumber| . |Module|) 4793) ((|AlgebraicNumber| . |LinearSet|) 4747) ((|AlgebraicNumber| . |LeftModule|) 4681) ((|AlgebraicNumber| . |LeftLinearSet|) 4615) ((|AlgebraicNumber| . |CancellationAbelianMonoid|) T) ((|AlgebraicNumber| . |AbelianSemiGroup|) T) ((|AlgebraicNumber| . |AbelianMonoid|) T) ((|AlgebraicNumber| . |AbelianGroup|) T) ((|AlgebraicNumber| . |Ring|) T) ((|AlgebraicNumber| . |Monoid|) T) ((|AlgebraicNumber| . |SemiRing|) T) ((|AlgebraicNumber| . |SemiGroup|) T) ((|AlgebraicNumber| . |Rng|) T) ((|AlgebraicNumber| . |Algebra|) 4569) ((|AlgebraicNumber| . |EuclideanDomain|) T) ((|AlgebraicNumber| . |GcdDomain|) T) ((|AlgebraicNumber| . |CommutativeRing|) T) ((|AlgebraicNumber| . |IntegralDomain|) T) ((|AlgebraicNumber| . |PrincipalIdealDomain|) T) ((|AlgebraicNumber| . |UniqueFactorizationDomain|) T) ((|AlgebraicNumber| . |Field|) T) ((|AlgebraicNumber| . |LinearlyExplicitRingOver|) 4518) ((|AlgebraicNumber| . |RealConstant|) T) ((|AlgebraicNumber| . |ConvertibleTo|) 4443) ((|AlgebraicNumber| . |CharacteristicZero|) T) ((|AlgebraicNumber| . |DifferentialRing|) T) ((|AlgebraicNumber| . |DifferentialDomain|) 4430) ((|AlgebraicNumber| . |DifferentialSpace|) T) ((|AssociationList| . |AssociationListAggregate|) 4409) ((|AssociationList| . |KeyedDictionary|) 4388) ((|AssociationList| . |EltableAggregate|) 4300) ((|AssociationList| . |Eltable|) 4169) ((|AssociationList| . |HomogeneousAggregate|) 4098) ((|AssociationList| . |Functorial|) 4027) ((|AssociationList| . |InnerEvalable|) 3775) ((|AssociationList| . |Evalable|) 3535) ((|AssociationList| . |IndexedAggregate|) 3447) ((|AssociationList| . |DictionaryOperations|) 3389) ((|AssociationList| . |BagAggregate|) 3331) ((|AssociationList| . |Dictionary|) 3273) ((|AssociationList| . |TableAggregate|) 3252) ((|AssociationList| . |ShallowlyMutableAggregate|) 3181) ((|AssociationList| . |ExtensibleLinearAggregate|) 3123) ((|AssociationList| . |Collection|) 3065) ((|AssociationList| . |Aggregate|) T) ((|AssociationList| . |Join|) T) ((|AssociationList| . |Type|) T) ((|AssociationList| . |BasicType|) T) ((|AssociationList| . |CoercibleTo|) 3039) ((|AssociationList| . |SetCategory|) T) ((|AssociationList| . |ConvertibleTo|) NIL) ((|AssociationList| . |LinearAggregate|) 2981) ((|AssociationList| . |FiniteLinearAggregate|) 2923) ((|AssociationList| . |OrderedType|) NIL) ((|AssociationList| . |OrderedSet|) NIL) ((|AssociationList| . |FiniteAggregate|) 2865) ((|AssociationList| . |StreamAggregate|) 2807) ((|AssociationList| . |RecursiveAggregate|) 2749) ((|AssociationList| . |UnaryRecursiveAggregate|) 2691) ((|AssociationList| . |ListAggregate|) 2633) ((|AlgebraGivenByStructuralConstants| . |FramedNonAssociativeAlgebra|) 2617) ((|AlgebraGivenByStructuralConstants| . |NonAssociativeAlgebra|) 2601) ((|AlgebraGivenByStructuralConstants| . |Monad|) T) ((|AlgebraGivenByStructuralConstants| . |NonAssociativeRng|) T) ((|AlgebraGivenByStructuralConstants| . |BiModule|) 2580) ((|AlgebraGivenByStructuralConstants| . |RightLinearSet|) 2564) ((|AlgebraGivenByStructuralConstants| . |RightModule|) 2548) ((|AlgebraGivenByStructuralConstants| . |AbelianGroup|) T) ((|AlgebraGivenByStructuralConstants| . |LeftLinearSet|) 2477) ((|AlgebraGivenByStructuralConstants| . |AbelianMonoid|) T) ((|AlgebraGivenByStructuralConstants| . |SetCategory|) T) ((|AlgebraGivenByStructuralConstants| . |CoercibleTo|) 2451) ((|AlgebraGivenByStructuralConstants| . |BasicType|) T) ((|AlgebraGivenByStructuralConstants| . |AbelianSemiGroup|) T) ((|AlgebraGivenByStructuralConstants| . |CancellationAbelianMonoid|) T) ((|AlgebraGivenByStructuralConstants| . |LeftModule|) 2400) ((|AlgebraGivenByStructuralConstants| . |LinearSet|) 2384) ((|AlgebraGivenByStructuralConstants| . |Module|) 2368) ((|AlgebraGivenByStructuralConstants| . |FiniteRankNonAssociativeAlgebra|) 2352) ((|AlgebraGivenByStructuralConstants| . |Type|) T) ((|AlgebraGivenByStructuralConstants| . |Join|) T) ((|AlgebraGivenByStructuralConstants| . |Eltable|) 2324) ((|AlgebraicFunctionField| . |FunctionFieldCategory|) 2298) ((|AlgebraicFunctionField| . |CommutativeRing|) T) ((|AlgebraicFunctionField| . |CoercibleFrom|) 2206) ((|AlgebraicFunctionField| . |Rng|) T) ((|AlgebraicFunctionField| . |SemiGroup|) T) ((|AlgebraicFunctionField| . |SemiRing|) T) ((|AlgebraicFunctionField| . |Monoid|) T) ((|AlgebraicFunctionField| . |Ring|) T) ((|AlgebraicFunctionField| . |LeftModule|) 2064) ((|AlgebraicFunctionField| . |LeftLinearSet|) 1972) ((|AlgebraicFunctionField| . |CancellationAbelianMonoid|) T) ((|AlgebraicFunctionField| . |AbelianSemiGroup|) T) ((|AlgebraicFunctionField| . |BasicType|) T) ((|AlgebraicFunctionField| . |Join|) T) ((|AlgebraicFunctionField| . |Type|) T) ((|AlgebraicFunctionField| . |CoercibleTo|) 1946) ((|AlgebraicFunctionField| . |SetCategory|) T) ((|AlgebraicFunctionField| . |AbelianMonoid|) T) ((|AlgebraicFunctionField| . |AbelianGroup|) T) ((|AlgebraicFunctionField| . |RightModule|) 1874) ((|AlgebraicFunctionField| . |RightLinearSet|) 1802) ((|AlgebraicFunctionField| . |BiModule|) 1714) ((|AlgebraicFunctionField| . |ConvertibleTo|) 1698) ((|AlgebraicFunctionField| . |DifferentialExtension|) 1669) ((|AlgebraicFunctionField| . |PartialDifferentialRing|) 1588) ((|AlgebraicFunctionField| . |PartialDifferentialSpace|) 1436) ((|AlgebraicFunctionField| . |PartialDifferentialDomain|) 1282) ((|AlgebraicFunctionField| . |DifferentialSpaceExtension|) 1253) ((|AlgebraicFunctionField| . |DifferentialSpace|) 1152) ((|AlgebraicFunctionField| . |DifferentialDomain|) 1045) ((|AlgebraicFunctionField| . |DifferentialRing|) 997) ((|AlgebraicFunctionField| . |Field|) T) ((|AlgebraicFunctionField| . |UniqueFactorizationDomain|) T) ((|AlgebraicFunctionField| . |PrincipalIdealDomain|) T) ((|AlgebraicFunctionField| . |IntegralDomain|) T) ((|AlgebraicFunctionField| . |Module|) 925) ((|AlgebraicFunctionField| . |LinearSet|) 853) ((|AlgebraicFunctionField| . |Algebra|) 781) ((|AlgebraicFunctionField| . |GcdDomain|) T) ((|AlgebraicFunctionField| . |EuclideanDomain|) T) ((|AlgebraicFunctionField| . |EntireRing|) T) ((|AlgebraicFunctionField| . |DivisionRing|) T) ((|AlgebraicFunctionField| . |Finite|) NIL) ((|AlgebraicFunctionField| . |FiniteFieldCategory|) NIL) ((|AlgebraicFunctionField| . |StepThrough|) NIL) ((|AlgebraicFunctionField| . |CharacteristicNonZero|) 728) ((|AlgebraicFunctionField| . |FieldOfPrimeCharacteristic|) NIL) ((|AlgebraicFunctionField| . |FramedAlgebra|) 694) ((|AlgebraicFunctionField| . |CharacteristicZero|) 644) ((|AlgebraicFunctionField| . |FiniteRankAlgebra|) 610) ((|AlgebraicFunctionField| . |FullyLinearlyExplicitRingOver|) 581) ((|AlgebraicFunctionField| . |LinearlyExplicitRingOver|) 482) ((|AlgebraicFunctionField| . |FullyRetractableTo|) 453) ((|AlgebraicFunctionField| . |RetractableTo|) 283) ((|AlgebraicFunctionField| . |MonogenicAlgebra|) 249) ((|AddAst| . |SpadSyntaxCategory|) T) ((|AddAst| . |HomotopicTo|) 227) ((|AddAst| . |CoercibleTo|) 182) ((|AddAst| . |CoercibleFrom|) 160) ((|AddAst| . |SetCategory|) T) ((|AddAst| . |Type|) T) ((|AddAst| . |Join|) T) ((|AddAst| . |BasicType|) T) ((|AddAst| . |AbstractSyntaxCategory|) T) ((|PlaneAlgebraicCurvePlot| . |PlottablePlaneCurveCategory|) T) ((|PlaneAlgebraicCurvePlot| . |CoercibleTo|) 134) ((|Enumeration| . |EnumerationCategory|) T) ((|Enumeration| . |CoercibleTo|) 108) ((|Enumeration| . |SetCategory|) T) ((|Enumeration| . |BasicType|) T) ((|Enumeration| . |Type|) T) ((|Record| . |RecordCategory|) T) ((|Record| . |CoercibleTo|) 82) ((|Record| . |SetCategory|) T) ((|Record| . |BasicType|) T) ((|Record| . |Type|) T) ((|Union| . |UnionCategory|) T) ((|Union| . |CoercibleTo|) 56) ((|Union| . |SetCategory|) T) ((|Union| . |BasicType|) T) ((|Union| . |Type|) T) ((|Mapping| . |SetCategory|) T) ((|Mapping| . |CoercibleTo|) 30) ((|Mapping| . |Type|) T) ((|Mapping| . |Join|) T) ((|Mapping| . |BasicType|) T))
\ No newline at end of file diff --git a/src/share/algebra/interp.daase b/src/share/algebra/interp.daase index 5d24f455..b7f0f4fb 100644 --- a/src/share/algebra/interp.daase +++ b/src/share/algebra/interp.daase @@ -1,5 +1,5 @@ -(2994629 . 3581079095) +(2991528 . 3662084406) ((|sorted?| ((#1=(|Boolean|) #2=(|Mapping| #1# |#2| |#2|) $) 86 T ELT) ((#1# $) NIL T ELT)) (|sort!| (($ #2# $) 18 T ELT) (#3=($ $) NIL T ELT)) (|setelt| #4=((|#2| $ #5=(|Integer|) |#2|) NIL T ELT) ((|#2| $ #6=(|UniversalSegment| #5#) |#2|) 44 T ELT)) (|reverse!| (#3# 80 T ELT)) (|reduce| ((|#2| #7=(|Mapping| |#2| |#2| |#2|) $ |#2| |#2|) 52 T ELT) ((|#2| #7# $ |#2|) 50 T ELT) ((|#2| #7# $) 49 T ELT)) (|position| ((#5# #8=(|Mapping| #1# |#2|) $) 27 T ELT) ((#5# |#2| $) NIL T ELT) ((#5# |#2| $ #5#) 96 T ELT)) (|merge| (($ #2# $ $) 64 T ELT) (#9=($ $ $) NIL T ELT)) (|members| ((#10=(|List| |#2|) $) 13 T ELT)) (|map!| (#11=($ (|Mapping| |#2| |#2|) $) 37 T ELT)) (|map| (#11# NIL T ELT) (($ #7# $ $) 60 T ELT)) (|insert| (($ |#2| $ #5#) NIL T ELT) (#12=($ $ $ #5#) 67 T ELT)) (|find| (((|Union| |#2| "failed") #8# $) 29 T ELT)) (|every?| (#13=(#1# #8# $) 23 T ELT)) (|elt| #4# ((|#2| $ #5#) NIL T ELT) (#14=($ $ #6#) 66 T ELT)) (|delete| (($ $ #5#) 76 T ELT) (#14# 75 T ELT)) (|count| ((#15=(|NonNegativeInteger|) |#2| $) NIL T ELT) ((#15# #8# $) 34 T ELT)) (|copyInto!| (#12# 69 T ELT)) (|copy| (#3# 68 T ELT)) (|construct| (($ #10#) 73 T ELT)) (|concat| (($ $ |#2|) NIL T ELT) (($ |#2| $) NIL T ELT) (#9# 87 T ELT) (($ (|List| $)) 85 T ELT)) (|coerce| (((|OutputForm|) $) 92 T ELT)) (|any?| (#13# 22 T ELT)) (= (#16=(#1# $ $) 95 T ELT)) (< (#16# 99 T ELT))) (((|OneDimensionalArrayAggregate&| |#1| |#2|) (CATEGORY |package| (SIGNATURE = #1=(#2=(|Boolean|) |#1| |#1|)) (SIGNATURE |coerce| ((|OutputForm|) |#1|)) (SIGNATURE |map!| #3=(|#1| (|Mapping| |#2| |#2|) |#1|)) (SIGNATURE < #1#) (SIGNATURE |sort!| #4=(|#1| |#1|)) (SIGNATURE |sort!| (|#1| #5=(|Mapping| #2# |#2| |#2|) |#1|)) (SIGNATURE |reverse!| #4#) (SIGNATURE |copyInto!| #6=(|#1| |#1| |#1| #7=(|Integer|))) (SIGNATURE |sorted?| (#2# |#1|)) (SIGNATURE |merge| #8=(|#1| |#1| |#1|)) (SIGNATURE |position| (#7# |#2| |#1| #7#)) (SIGNATURE |position| (#7# |#2| |#1|)) (SIGNATURE |position| (#7# #9=(|Mapping| #2# |#2|) |#1|)) (SIGNATURE |sorted?| (#2# #5# |#1|)) (SIGNATURE |merge| (|#1| #5# |#1| |#1|)) (SIGNATURE |any?| #10=(#2# #9# |#1|)) (SIGNATURE |every?| #10#) (SIGNATURE |count| (#11=(|NonNegativeInteger|) #9# |#1|)) (SIGNATURE |members| (#12=(|List| |#2|) |#1|)) (SIGNATURE |reduce| (|#2| #13=(|Mapping| |#2| |#2| |#2|) |#1|)) (SIGNATURE |reduce| (|#2| #13# |#1| |#2|)) (SIGNATURE |find| ((|Union| |#2| "failed") #9# |#1|)) (SIGNATURE |count| (#11# |#2| |#1|)) (SIGNATURE |reduce| (|#2| #13# |#1| |#2| |#2|)) (SIGNATURE |setelt| (|#2| |#1| #14=(|UniversalSegment| #7#) |#2|)) (SIGNATURE |insert| #6#) (SIGNATURE |insert| (|#1| |#2| |#1| #7#)) (SIGNATURE |delete| #15=(|#1| |#1| #14#)) (SIGNATURE |delete| (|#1| |#1| #7#)) (SIGNATURE |map| (|#1| #13# |#1| |#1|)) (SIGNATURE |concat| (|#1| (|List| |#1|))) (SIGNATURE |concat| #8#) (SIGNATURE |concat| (|#1| |#2| |#1|)) (SIGNATURE |concat| (|#1| |#1| |#2|)) (SIGNATURE |elt| #15#) (SIGNATURE |construct| (|#1| #12#)) (SIGNATURE |elt| (|#2| |#1| #7#)) (SIGNATURE |elt| #16=(|#2| |#1| #7# |#2|)) (SIGNATURE |setelt| #16#) (SIGNATURE |map| #3#) (SIGNATURE |copy| #4#)) (|OneDimensionalArrayAggregate| |#2|) (|Type|)) (T |OneDimensionalArrayAggregate&|)) NIL @@ -8,10 +8,10 @@ NIL NIL (|Join| (|FiniteLinearAggregate| |t#1|) (|ShallowlyMutableAggregate| |t#1|)) (((|Aggregate|) . T) ((|BasicType|) OR (|has| |#1| (|SetCategory|)) (|has| |#1| (|OrderedSet|)) (|has| |#1| (|BasicType|))) ((|CoercibleTo| (|OutputForm|)) OR (|has| |#1| (|SetCategory|)) (|has| |#1| (|OrderedSet|)) (|has| |#1| (|CoercibleTo| (|OutputForm|)))) ((|Collection| |#1|) . T) ((|ConvertibleTo| (|InputForm|)) |has| |#1| (|ConvertibleTo| (|InputForm|))) ((|Eltable| #1=(|Integer|) |#1|) . T) ((|Eltable| (|UniversalSegment| (|Integer|)) $) . T) ((|EltableAggregate| #1# |#1|) . T) ((|Evalable| |#1|) AND (|has| |#1| (|Evalable| |#1|)) (|has| |#1| (|SetCategory|))) ((|FiniteAggregate| |#1|) . T) ((|FiniteLinearAggregate| |#1|) . T) ((|Functorial| |#1|) . T) ((|HomogeneousAggregate| |#1|) . T) ((|IndexedAggregate| #1# |#1|) . T) ((|InnerEvalable| |#1| |#1|) AND (|has| |#1| (|Evalable| |#1|)) (|has| |#1| (|SetCategory|))) ((|Join|) . T) ((|LinearAggregate| |#1|) . T) ((|OrderedSet|) |has| |#1| (|OrderedSet|)) ((|OrderedType|) |has| |#1| (|OrderedSet|)) ((|SetCategory|) OR (|has| |#1| (|SetCategory|)) (|has| |#1| (|OrderedSet|))) ((|ShallowlyMutableAggregate| |#1|) . T) ((|Type|) . T)) -((|subtractIfCan| (((|Union| $ "failed") $ $) 12 T ELT)) (|opposite?| (((|Boolean|) $ $) 27 T ELT)) (- (($ $) NIL T ELT) (($ $ $) 9 T ELT)) (* (($ (|PositiveInteger|) $) NIL T ELT) (($ (|NonNegativeInteger|) $) 16 T ELT) (($ (|Integer|) $) 25 T ELT))) -(((|AbelianGroup&| |#1|) (CATEGORY |package| (SIGNATURE - (|#1| |#1| |#1|)) (SIGNATURE - (|#1| |#1|)) (SIGNATURE * (|#1| (|Integer|) |#1|)) (SIGNATURE |subtractIfCan| ((|Union| |#1| "failed") |#1| |#1|)) (SIGNATURE |opposite?| ((|Boolean|) |#1| |#1|)) (SIGNATURE * (|#1| (|NonNegativeInteger|) |#1|)) (SIGNATURE * (|#1| (|PositiveInteger|) |#1|))) (|AbelianGroup|)) (T |AbelianGroup&|)) +((|subtractIfCan| (((|Maybe| $) $ $) 14 T ELT)) (|opposite?| (((|Boolean|) $ $) 29 T ELT)) (- (($ $) NIL T ELT) (($ $ $) 9 T ELT)) (* (($ (|PositiveInteger|) $) NIL T ELT) (($ (|NonNegativeInteger|) $) 18 T ELT) (($ (|Integer|) $) 27 T ELT))) +(((|AbelianGroup&| |#1|) (CATEGORY |package| (SIGNATURE - (|#1| |#1| |#1|)) (SIGNATURE - (|#1| |#1|)) (SIGNATURE * (|#1| (|Integer|) |#1|)) (SIGNATURE |subtractIfCan| ((|Maybe| |#1|) |#1| |#1|)) (SIGNATURE |opposite?| ((|Boolean|) |#1| |#1|)) (SIGNATURE * (|#1| (|NonNegativeInteger|) |#1|)) (SIGNATURE * (|#1| (|PositiveInteger|) |#1|))) (|AbelianGroup|)) (T |AbelianGroup&|)) NIL -((~= (#1=((|Boolean|) $ $) 7 T ELT)) (|zero?| ((#2=(|Boolean|) $) 22 T ELT)) (|subtractIfCan| (((|Union| $ "failed") $ $) 26 T ELT)) (|sample| (#3=($) 23 T CONST)) (|opposite?| ((#2# $ $) 20 T ELT)) (|latex| (((|String|) $) 11 T ELT)) (|hash| (((|SingleInteger|) $) 12 T ELT)) (|coerce| (((|OutputForm|) $) 13 T ELT)) (|before?| (#1# 6 T ELT)) (|Zero| (#3# 24 T CONST)) (= (#1# 8 T ELT)) (- (($ $) 29 T ELT) (($ $ $) 28 T ELT)) (+ (($ $ $) 18 T ELT)) (* (($ (|PositiveInteger|) $) 17 T ELT) (($ (|NonNegativeInteger|) $) 21 T ELT) (($ (|Integer|) $) 30 T ELT))) +((~= (#1=((|Boolean|) $ $) 7 T ELT)) (|zero?| ((#2=(|Boolean|) $) 22 T ELT)) (|subtractIfCan| (((|Maybe| $) $ $) 26 T ELT)) (|sample| (#3=($) 23 T CONST)) (|opposite?| ((#2# $ $) 20 T ELT)) (|latex| (((|String|) $) 11 T ELT)) (|hash| (((|SingleInteger|) $) 12 T ELT)) (|coerce| (((|OutputForm|) $) 13 T ELT)) (|before?| (#1# 6 T ELT)) (|Zero| (#3# 24 T CONST)) (= (#1# 8 T ELT)) (- (($ $) 30 T ELT) (($ $ $) 29 T ELT)) (+ (($ $ $) 18 T ELT)) (* (($ (|PositiveInteger|) $) 17 T ELT) (($ (|NonNegativeInteger|) $) 21 T ELT) (($ (|Integer|) $) 31 T ELT))) (((|AbelianGroup|) (|Category|)) (T |AbelianGroup|)) ((- (*1 *1 *1) (|ofCategory| *1 (|AbelianGroup|))) (- (*1 *1 *1 *1) (|ofCategory| *1 (|AbelianGroup|)))) (|Join| (|CancellationAbelianMonoid|) (|LeftLinearSet| (|Integer|)) (CATEGORY |domain| (SIGNATURE - ($ $)) (SIGNATURE - ($ $ $)))) @@ -35,7 +35,7 @@ NIL ((|zerosOf| (#1=(#2=(|List| $) #3=(|Polynomial| $)) 32 T ELT) (#4=(#2# #5=(|SparseUnivariatePolynomial| $)) 16 T ELT) (#6=(#2# #5# #7=(|Symbol|)) 20 T ELT)) (|zeroOf| (#8=($ #3#) 30 T ELT) (#9=($ #5#) 11 T ELT) (#10=($ #5# #7#) 60 T ELT)) (|rootsOf| (#1# 33 T ELT) (#4# 18 T ELT) (#6# 19 T ELT)) (|rootOf| (#8# 31 T ELT) (#9# 13 T ELT) (#10# NIL T ELT))) (((|AlgebraicallyClosedField&| |#1|) (CATEGORY |package| (SIGNATURE |zerosOf| #1=(#2=(|List| |#1|) #3=(|SparseUnivariatePolynomial| |#1|) #4=(|Symbol|))) (SIGNATURE |zerosOf| #5=(#2# #3#)) (SIGNATURE |zerosOf| #6=(#2# #7=(|Polynomial| |#1|))) (SIGNATURE |zeroOf| #8=(|#1| #3# #4#)) (SIGNATURE |zeroOf| #9=(|#1| #3#)) (SIGNATURE |zeroOf| #10=(|#1| #7#)) (SIGNATURE |rootsOf| #1#) (SIGNATURE |rootsOf| #5#) (SIGNATURE |rootsOf| #6#) (SIGNATURE |rootOf| #8#) (SIGNATURE |rootOf| #9#) (SIGNATURE |rootOf| #10#)) (|AlgebraicallyClosedField|)) (T |AlgebraicallyClosedField&|)) NIL -((~= (#1=((|Boolean|) $ $) 7 T ELT)) (|zerosOf| (((|List| $) (|Polynomial| $)) 98 T ELT) (((|List| $) (|SparseUnivariatePolynomial| $)) 97 T ELT) (((|List| $) (|SparseUnivariatePolynomial| $) (|Symbol|)) 96 T ELT)) (|zeroOf| (($ (|Polynomial| $)) 101 T ELT) (($ (|SparseUnivariatePolynomial| $)) 100 T ELT) (($ (|SparseUnivariatePolynomial| $) (|Symbol|)) 99 T ELT)) (|zero?| ((#2=(|Boolean|) $) 22 T ELT)) (|unitNormal| (((|Record| (|:| |unit| $) (|:| |canonical| $) (|:| |associate| $)) $) 55 T ELT)) (|unitCanonical| (($ $) 54 T ELT)) (|unit?| ((#3=(|Boolean|) $) 52 T ELT)) (|subtractIfCan| (((|Union| $ "failed") $ $) 26 T ELT)) (|squareFreePart| (($ $) 91 T ELT)) (|squareFree| (#4=((|Factored| $) $) 90 T ELT)) (|sqrt| (($ $) 110 T ELT)) (|sizeLess?| (((|Boolean|) $ $) 75 T ELT)) (|sample| (#5=($) 23 T CONST)) (|rootsOf| (((|List| $) (|Polynomial| $)) 104 T ELT) (((|List| $) (|SparseUnivariatePolynomial| $)) 103 T ELT) (((|List| $) (|SparseUnivariatePolynomial| $) (|Symbol|)) 102 T ELT)) (|rootOf| (($ (|Polynomial| $)) 107 T ELT) (($ (|SparseUnivariatePolynomial| $)) 106 T ELT) (($ (|SparseUnivariatePolynomial| $) (|Symbol|)) 105 T ELT)) (|rem| (#6=($ $ $) 71 T ELT)) (|recip| (((|Union| $ "failed") $) 42 T ELT)) (|quo| (#6# 72 T ELT)) (|principalIdeal| (((|Record| (|:| |coef| #7=(|List| $)) (|:| |generator| $)) #7#) 66 T ELT)) (|prime?| (((|Boolean|) $) 89 T ELT)) (|opposite?| ((#2# $ $) 20 T ELT)) (|one?| (((|Boolean|) $) 44 T ELT)) (|nthRoot| (($ $ #8=(|Integer|)) 109 T ELT)) (|multiEuclidean| (((|Union| #9=(|List| $) #10="failed") #9# $) 68 T ELT)) (|lcm| (#11=($ $ $) 60 T ELT) (#12=($ (|List| $)) 59 T ELT)) (|latex| (((|String|) $) 11 T ELT)) (|inv| (($ $) 88 T ELT)) (|hash| (((|SingleInteger|) $) 12 T ELT)) (|gcdPolynomial| ((#13=(|SparseUnivariatePolynomial| $) #13# #13#) 58 T ELT)) (|gcd| (#11# 62 T ELT) (#12# 61 T ELT)) (|factor| (#4# 92 T ELT)) (|extendedEuclidean| (((|Record| #14=(|:| |coef1| $) #15=(|:| |coef2| $) (|:| |generator| $)) $ $) 70 T ELT) (((|Union| (|Record| #14# #15#) #10#) $ $ $) 69 T ELT)) (|exquo| (((|Union| $ "failed") $ $) 56 T ELT)) (|expressIdealMember| (((|Maybe| #7#) #7# $) 65 T ELT)) (|euclideanSize| (((|NonNegativeInteger|) $) 74 T ELT)) (|divide| (((|Record| (|:| |quotient| $) (|:| |remainder| $)) $ $) 73 T ELT)) (|coerce| (((|OutputForm|) $) 13 T ELT) (($ (|Integer|)) 41 T ELT) (($ $) 57 T ELT) (($ #16=(|Fraction| #17=(|Integer|))) 84 T ELT)) (|characteristic| (((|NonNegativeInteger|)) 40 T CONST)) (|before?| (#1# 6 T ELT)) (|associates?| ((#3# $ $) 53 T ELT)) (|annihilate?| (((|Boolean|) $ $) 33 T ELT)) (|Zero| (#5# 24 T CONST)) (|One| (($) 45 T CONST)) (= (#1# 8 T ELT)) (/ (($ $ $) 83 T ELT)) (- (($ $) 29 T ELT) (($ $ $) 28 T ELT)) (+ (($ $ $) 18 T ELT)) (** (($ $ (|PositiveInteger|)) 35 T ELT) (($ $ (|NonNegativeInteger|)) 43 T ELT) (($ $ #17#) 87 T ELT) (($ $ (|Fraction| #8#)) 108 T ELT)) (* (($ (|PositiveInteger|) $) 17 T ELT) (($ (|NonNegativeInteger|) $) 21 T ELT) (($ (|Integer|) . #18=($)) 30 T ELT) (($ $ $) 34 T ELT) (($ $ #16#) 86 T ELT) (($ #16# . #18#) 85 T ELT))) +((~= (#1=((|Boolean|) $ $) 7 T ELT)) (|zerosOf| (((|List| $) (|Polynomial| $)) 99 T ELT) (((|List| $) (|SparseUnivariatePolynomial| $)) 98 T ELT) (((|List| $) (|SparseUnivariatePolynomial| $) (|Symbol|)) 97 T ELT)) (|zeroOf| (($ (|Polynomial| $)) 102 T ELT) (($ (|SparseUnivariatePolynomial| $)) 101 T ELT) (($ (|SparseUnivariatePolynomial| $) (|Symbol|)) 100 T ELT)) (|zero?| ((#2=(|Boolean|) $) 22 T ELT)) (|unitNormal| (((|Record| (|:| |unit| $) (|:| |canonical| $) (|:| |associate| $)) $) 56 T ELT)) (|unitCanonical| (($ $) 55 T ELT)) (|unit?| ((#3=(|Boolean|) $) 53 T ELT)) (|subtractIfCan| (((|Maybe| $) $ $) 26 T ELT)) (|squareFreePart| (($ $) 92 T ELT)) (|squareFree| (#4=((|Factored| $) $) 91 T ELT)) (|sqrt| (($ $) 111 T ELT)) (|sizeLess?| (((|Boolean|) $ $) 76 T ELT)) (|sample| (#5=($) 23 T CONST)) (|rootsOf| (((|List| $) (|Polynomial| $)) 105 T ELT) (((|List| $) (|SparseUnivariatePolynomial| $)) 104 T ELT) (((|List| $) (|SparseUnivariatePolynomial| $) (|Symbol|)) 103 T ELT)) (|rootOf| (($ (|Polynomial| $)) 108 T ELT) (($ (|SparseUnivariatePolynomial| $)) 107 T ELT) (($ (|SparseUnivariatePolynomial| $) (|Symbol|)) 106 T ELT)) (|rem| (#6=($ $ $) 72 T ELT)) (|recip| (((|Union| $ "failed") $) 43 T ELT)) (|quo| (#6# 73 T ELT)) (|principalIdeal| (((|Record| (|:| |coef| #7=(|List| $)) (|:| |generator| $)) #7#) 67 T ELT)) (|prime?| (((|Boolean|) $) 90 T ELT)) (|opposite?| ((#2# $ $) 20 T ELT)) (|one?| (((|Boolean|) $) 45 T ELT)) (|nthRoot| (($ $ #8=(|Integer|)) 110 T ELT)) (|multiEuclidean| (((|Union| #9=(|List| $) #10="failed") #9# $) 69 T ELT)) (|lcm| (#11=($ $ $) 61 T ELT) (#12=($ (|List| $)) 60 T ELT)) (|latex| (((|String|) $) 11 T ELT)) (|inv| (($ $) 89 T ELT)) (|hash| (((|SingleInteger|) $) 12 T ELT)) (|gcdPolynomial| ((#13=(|SparseUnivariatePolynomial| $) #13# #13#) 59 T ELT)) (|gcd| (#11# 63 T ELT) (#12# 62 T ELT)) (|factor| (#4# 93 T ELT)) (|extendedEuclidean| (((|Record| #14=(|:| |coef1| $) #15=(|:| |coef2| $) (|:| |generator| $)) $ $) 71 T ELT) (((|Union| (|Record| #14# #15#) #10#) $ $ $) 70 T ELT)) (|exquo| (((|Union| $ "failed") $ $) 57 T ELT)) (|expressIdealMember| (((|Maybe| #7#) #7# $) 66 T ELT)) (|euclideanSize| (((|NonNegativeInteger|) $) 75 T ELT)) (|divide| (((|Record| (|:| |quotient| $) (|:| |remainder| $)) $ $) 74 T ELT)) (|coerce| (((|OutputForm|) $) 13 T ELT) (($ (|Integer|)) 42 T ELT) (($ $) 58 T ELT) (($ #16=(|Fraction| #17=(|Integer|))) 85 T ELT)) (|characteristic| (((|NonNegativeInteger|)) 41 T CONST)) (|before?| (#1# 6 T ELT)) (|associates?| ((#3# $ $) 54 T ELT)) (|annihilate?| (((|Boolean|) $ $) 34 T ELT)) (|Zero| (#5# 24 T CONST)) (|One| (($) 46 T CONST)) (= (#1# 8 T ELT)) (/ (($ $ $) 84 T ELT)) (- (($ $) 30 T ELT) (($ $ $) 29 T ELT)) (+ (($ $ $) 18 T ELT)) (** (($ $ (|PositiveInteger|)) 36 T ELT) (($ $ (|NonNegativeInteger|)) 44 T ELT) (($ $ #17#) 88 T ELT) (($ $ (|Fraction| #8#)) 109 T ELT)) (* (($ (|PositiveInteger|) $) 17 T ELT) (($ (|NonNegativeInteger|) $) 21 T ELT) (($ (|Integer|) . #18=($)) 31 T ELT) (($ $ $) 35 T ELT) (($ $ #16#) 87 T ELT) (($ #16# . #18#) 86 T ELT))) (((|AlgebraicallyClosedField|) (|Category|)) (T |AlgebraicallyClosedField|)) ((|rootOf| (*1 *1 *2) (AND (|isDomain| *2 (|Polynomial| *1)) (|ofCategory| *1 (|AlgebraicallyClosedField|)))) (|rootOf| (*1 *1 *2) (AND (|isDomain| *2 (|SparseUnivariatePolynomial| *1)) (|ofCategory| *1 (|AlgebraicallyClosedField|)))) (|rootOf| (*1 *1 *2 *3) (AND (|isDomain| *2 (|SparseUnivariatePolynomial| *1)) (|isDomain| *3 (|Symbol|)) (|ofCategory| *1 (|AlgebraicallyClosedField|)))) (|rootsOf| (*1 *2 *3) (AND (|isDomain| *3 (|Polynomial| *1)) (|ofCategory| *1 (|AlgebraicallyClosedField|)) (|isDomain| *2 (|List| *1)))) (|rootsOf| (*1 *2 *3) (AND (|isDomain| *3 (|SparseUnivariatePolynomial| *1)) (|ofCategory| *1 (|AlgebraicallyClosedField|)) (|isDomain| *2 (|List| *1)))) (|rootsOf| (*1 *2 *3 *4) (AND (|isDomain| *3 (|SparseUnivariatePolynomial| *1)) (|isDomain| *4 (|Symbol|)) (|ofCategory| *1 (|AlgebraicallyClosedField|)) (|isDomain| *2 (|List| *1)))) (|zeroOf| (*1 *1 *2) (AND (|isDomain| *2 (|Polynomial| *1)) (|ofCategory| *1 (|AlgebraicallyClosedField|)))) (|zeroOf| (*1 *1 *2) (AND (|isDomain| *2 (|SparseUnivariatePolynomial| *1)) (|ofCategory| *1 (|AlgebraicallyClosedField|)))) (|zeroOf| (*1 *1 *2 *3) (AND (|isDomain| *2 (|SparseUnivariatePolynomial| *1)) (|isDomain| *3 (|Symbol|)) (|ofCategory| *1 (|AlgebraicallyClosedField|)))) (|zerosOf| (*1 *2 *3) (AND (|isDomain| *3 (|Polynomial| *1)) (|ofCategory| *1 (|AlgebraicallyClosedField|)) (|isDomain| *2 (|List| *1)))) (|zerosOf| (*1 *2 *3) (AND (|isDomain| *3 (|SparseUnivariatePolynomial| *1)) (|ofCategory| *1 (|AlgebraicallyClosedField|)) (|isDomain| *2 (|List| *1)))) (|zerosOf| (*1 *2 *3 *4) (AND (|isDomain| *3 (|SparseUnivariatePolynomial| *1)) (|isDomain| *4 (|Symbol|)) (|ofCategory| *1 (|AlgebraicallyClosedField|)) (|isDomain| *2 (|List| *1))))) (|Join| (|Field|) (|RadicalCategory|) (CATEGORY |domain| (SIGNATURE |rootOf| ($ (|Polynomial| $))) (SIGNATURE |rootOf| ($ (|SparseUnivariatePolynomial| $))) (SIGNATURE |rootOf| ($ (|SparseUnivariatePolynomial| $) (|Symbol|))) (SIGNATURE |rootsOf| ((|List| $) (|Polynomial| $))) (SIGNATURE |rootsOf| ((|List| $) (|SparseUnivariatePolynomial| $))) (SIGNATURE |rootsOf| ((|List| $) (|SparseUnivariatePolynomial| $) (|Symbol|))) (SIGNATURE |zeroOf| ($ (|Polynomial| $))) (SIGNATURE |zeroOf| ($ (|SparseUnivariatePolynomial| $))) (SIGNATURE |zeroOf| ($ (|SparseUnivariatePolynomial| $) (|Symbol|))) (SIGNATURE |zerosOf| ((|List| $) (|Polynomial| $))) (SIGNATURE |zerosOf| ((|List| $) (|SparseUnivariatePolynomial| $))) (SIGNATURE |zerosOf| ((|List| $) (|SparseUnivariatePolynomial| $) (|Symbol|))))) @@ -43,7 +43,7 @@ NIL ((|zerosOf| #1=((#2=(|List| $) #3=(|Polynomial| $)) NIL T ELT) #4=((#2# #5=(|SparseUnivariatePolynomial| $)) NIL T ELT) (#6=(#2# #5# #7=(|Symbol|)) 54 T ELT) (#8=(#2# $) 22 T ELT) (#9=(#2# $ #7#) 45 T ELT)) (|zeroOf| #10=(($ #3#) NIL T ELT) #11=(($ #5#) NIL T ELT) (#12=($ #5# #7#) 56 T ELT) (#13=($ $) 20 T ELT) (#14=($ $ #7#) 39 T ELT)) (|rootsOf| #1# #4# (#6# 52 T ELT) (#8# 18 T ELT) (#9# 47 T ELT)) (|rootOf| #10# #11# (#12# NIL T ELT) (#13# 15 T ELT) (#14# 41 T ELT))) (((|AlgebraicallyClosedFunctionSpace&| |#1| |#2|) (CATEGORY |package| (SIGNATURE |zerosOf| #1=(#2=(|List| |#1|) |#1| #3=(|Symbol|))) (SIGNATURE |zeroOf| #4=(|#1| |#1| #3#)) (SIGNATURE |zerosOf| #5=(#2# |#1|)) (SIGNATURE |zeroOf| #6=(|#1| |#1|)) (SIGNATURE |rootsOf| #1#) (SIGNATURE |rootOf| #4#) (SIGNATURE |rootsOf| #5#) (SIGNATURE |rootOf| #6#) (SIGNATURE |zerosOf| #7=(#2# #8=(|SparseUnivariatePolynomial| |#1|) #3#)) (SIGNATURE |zerosOf| #9=(#2# #8#)) (SIGNATURE |zerosOf| #10=(#2# #11=(|Polynomial| |#1|))) (SIGNATURE |zeroOf| #12=(|#1| #8# #3#)) (SIGNATURE |zeroOf| #13=(|#1| #8#)) (SIGNATURE |zeroOf| #14=(|#1| #11#)) (SIGNATURE |rootsOf| #7#) (SIGNATURE |rootsOf| #9#) (SIGNATURE |rootsOf| #10#) (SIGNATURE |rootOf| #12#) (SIGNATURE |rootOf| #13#) (SIGNATURE |rootOf| #14#)) (|AlgebraicallyClosedFunctionSpace| |#2|) (|IntegralDomain|)) (T |AlgebraicallyClosedFunctionSpace&|)) NIL -((~= (#1=((|Boolean|) $ $) 7 T ELT)) (|zerosOf| (#2=(#3=(|List| $) #4=(|Polynomial| $)) 98 T ELT) (#5=(#3# #6=(|SparseUnivariatePolynomial| $)) 97 T ELT) (#7=(#3# #6# #8=(|Symbol|)) 96 T ELT) (((|List| $) $) 148 T ELT) (((|List| $) $ (|Symbol|)) 146 T ELT)) (|zeroOf| (#9=($ #4#) 101 T ELT) (#10=($ #6#) 100 T ELT) (#11=($ #6# #8#) 99 T ELT) (($ $) 149 T ELT) (($ $ (|Symbol|)) 147 T ELT)) (|zero?| ((#12=(|Boolean|) $) 22 T ELT)) (|variables| ((#13=(|List| #14=(|Symbol|)) $) 217 T ELT)) (|univariate| (((|Fraction| (|SparseUnivariatePolynomial| $)) $ #15=(|Kernel| $)) 249 (|has| |#1| . #16=((|IntegralDomain|))) ELT)) (|unitNormal| (((|Record| (|:| |unit| $) (|:| |canonical| $) (|:| |associate| $)) $) 55 T ELT)) (|unitCanonical| (($ $) 54 T ELT)) (|unit?| ((#17=(|Boolean|) $) 52 T ELT)) (|tower| (#18=(#19=(|List| #20=(|Kernel| $)) $) 180 T ELT)) (|subtractIfCan| (((|Union| $ "failed") $ $) 26 T ELT)) (|subst| (($ $ #19# #21=(|List| $)) 170 T ELT) (($ $ (|List| #22=(|Equation| $))) 169 T ELT) (($ $ #22#) 168 T ELT)) (|squareFreePart| (($ $) 91 T ELT)) (|squareFree| (#23=((|Factored| $) $) 90 T ELT)) (|sqrt| (($ $) 110 T ELT)) (|sizeLess?| (((|Boolean|) $ $) 75 T ELT)) (|sample| (#24=($) 23 T CONST)) (|rootsOf| (#2# 104 T ELT) (#5# 103 T ELT) (#7# 102 T ELT) (((|List| $) $) 152 T ELT) (((|List| $) $ (|Symbol|)) 150 T ELT)) (|rootOf| (#9# 107 T ELT) (#10# 106 T ELT) (#11# 105 T ELT) (($ $) 153 T ELT) (($ $ (|Symbol|)) 151 T ELT)) (|retractIfCan| (((|Union| (|Polynomial| |#1|) . #25=("failed")) . #26=($)) 268 (|has| |#1| . #27=((|Ring|))) ELT) (((|Union| (|Fraction| (|Polynomial| |#1|)) . #25#) . #26#) 251 (|has| |#1| . #16#) ELT) (((|Union| |#1| . #25#) . #26#) 213 T ELT) (((|Union| #28=(|Integer|) . #25#) . #26#) 210 (|has| |#1| . #29=((|RetractableTo| #28#))) ELT) (((|Union| #14# . #25#) . #26#) 204 T ELT) (((|Union| #20# . #25#) . #26#) 155 T ELT) (((|Union| #30=(|Fraction| #28#) . #25#) . #26#) 143 (OR (AND (|has| |#1| . #31=((|RetractableTo| #32=(|Integer|)))) (|has| |#1| . #16#)) (|has| |#1| . #33=((|RetractableTo| #30#)))) ELT)) (|retract| (((|Polynomial| |#1|) . #34=($)) 267 (|has| |#1| . #27#) ELT) (((|Fraction| (|Polynomial| |#1|)) . #34#) 250 (|has| |#1| . #16#) ELT) ((|#1| . #34#) 212 T ELT) ((#28# . #34#) 211 (|has| |#1| . #29#) ELT) ((#14# . #34#) 203 T ELT) ((#20# . #34#) 154 T ELT) ((#30# . #34#) 144 (OR (AND (|has| |#1| . #31#) (|has| |#1| . #16#)) (|has| |#1| . #33#)) ELT)) (|rem| (#35=($ $ $) 71 T ELT)) (|reducedSystem| (((|Matrix| |#1|) . #36=(#37=(|Matrix| $))) 256 (|has| |#1| . #27#) ELT) (((|Record| (|:| |mat| (|Matrix| |#1|)) (|:| |vec| (|Vector| |#1|))) . #38=(#37# #39=(|Vector| $))) 255 (|has| |#1| . #27#) ELT) (((|Record| (|:| |mat| (|Matrix| #40=(|Integer|))) (|:| |vec| (|Vector| #40#))) . #38#) 142 (OR (|and| (|has| |#1| . #27#) (|has| |#1| . #41=((|LinearlyExplicitRingOver| #40#)))) (|and| (|has| |#1| . #41#) (|has| |#1| . #27#))) ELT) (((|Matrix| #40#) . #36#) 141 (OR (|and| (|has| |#1| . #27#) (|has| |#1| . #41#)) (|and| (|has| |#1| . #41#) (|has| |#1| . #27#))) ELT)) (|recip| (((|Union| $ "failed") $) 42 T ELT)) (|quo| (#35# 72 T ELT)) (|principalIdeal| (((|Record| (|:| |coef| #42=(|List| $)) (|:| |generator| $)) #42#) 66 T ELT)) (|prime?| (((|Boolean|) $) 89 T ELT)) (|patternMatch| (((|PatternMatchResult| #43=(|Float|) . #44=($)) $ (|Pattern| #43#) (|PatternMatchResult| #43# . #44#)) 209 (|has| |#1| (|PatternMatchable| #43#)) ELT) (((|PatternMatchResult| #45=(|Integer|) . #44#) $ (|Pattern| #45#) (|PatternMatchResult| #45# . #44#)) 208 (|has| |#1| (|PatternMatchable| #45#)) ELT)) (|paren| (#46=($ #21#) 174 T ELT) (#47=($ $) 173 T ELT)) (|opposite?| ((#12# $ $) 20 T ELT)) (|operators| ((#48=(|List| #49=(|BasicOperator|)) $) 181 T ELT)) (|operator| ((#49# #49#) 182 T ELT)) (|one?| (((|Boolean|) $) 44 T ELT)) (|odd?| (#50=(#51=(|Boolean|) $) 202 #52=(|has| $ (|RetractableTo| (|Integer|))) ELT)) (|numerator| (#53=($ $) 234 (|has| |#1| . #27#) ELT)) (|numer| (((|SparseMultivariatePolynomial| |#1| . #54=(#15#)) . #55=($)) 233 (|has| |#1| . #27#) ELT)) (|nthRoot| (($ $ #56=(|Integer|)) 109 T ELT)) (|multiEuclidean| (((|Union| #57=(|List| $) #58="failed") #57# $) 68 T ELT)) (|minPoly| (((|SparseUnivariatePolynomial| $) #20#) 199 #59=(|has| $ (|Ring|)) ELT)) (|map| (($ #60=(|Mapping| $ $) #20#) 188 T ELT)) (|mainKernel| (((|Union| #20# "failed") $) 178 T ELT)) (|leftReducedSystem| (((|Matrix| |#1|) . #61=(#39#)) 258 (|has| |#1| . #27#) ELT) (((|Record| (|:| |mat| (|Matrix| |#1|)) (|:| |vec| (|Vector| |#1|))) . #62=(#39# $)) 257 (|has| |#1| . #27#) ELT) (((|Record| (|:| |mat| (|Matrix| #40#)) (|:| |vec| (|Vector| #40#))) . #62#) 140 (OR (|and| (|has| |#1| . #27#) (|has| |#1| . #41#)) (|and| (|has| |#1| . #41#) (|has| |#1| . #27#))) ELT) (((|Matrix| #40#) . #61#) 139 (OR (|and| (|has| |#1| . #27#) (|has| |#1| . #41#)) (|and| (|has| |#1| . #41#) (|has| |#1| . #27#))) ELT)) (|lcm| (#63=($ $ $) 60 T ELT) (#64=($ (|List| $)) 59 T ELT)) (|latex| (((|String|) $) 11 T ELT)) (|kernels| (#18# 179 T ELT)) (|kernel| (#65=($ #49# #21#) 187 T ELT) (#66=($ #49# $) 186 T ELT)) (|isTimes| (#67=((|Union| #68=(|List| $) #69="failed") $) 228 (|has| |#1| . #70=((|SemiGroup|))) ELT)) 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#14# $ $ $) 221 T ELT) (($ #14# $ $) 220 T ELT) (($ #14# $) 219 T ELT)) (|annihilate?| (((|Boolean|) $ $) 34 T ELT)) (|Zero| (#24# 24 T CONST)) (|One| (($) 46 T CONST)) (D (($ $ (|List| #14#) . #91#) 267 (|has| |#1| . #27#) ELT) (($ $ #14# . #93#) 266 (|has| |#1| . #27#) ELT) (($ $ (|List| #14#)) 265 (|has| |#1| . #27#) ELT) (($ $ #14#) 261 (|has| |#1| . #27#) ELT)) (= (#1# 8 T ELT)) (/ (($ $ $) 84 T ELT) (($ (|SparseMultivariatePolynomial| |#1| . #54#) (|SparseMultivariatePolynomial| |#1| . #54#)) 246 (|has| |#1| . #16#) ELT)) (- (($ $) 30 T ELT) (($ $ $) 29 T ELT)) (+ (($ $ $) 18 T ELT)) (** (($ $ (|PositiveInteger|)) 36 T ELT) (($ $ (|NonNegativeInteger|)) 44 T ELT) (($ $ #100#) 88 T ELT) (($ $ (|Fraction| #56#)) 109 T ELT)) (* (($ (|PositiveInteger|) $) 17 T ELT) (($ (|NonNegativeInteger|) $) 21 T ELT) (($ (|Integer|) . #101=($)) 31 T ELT) (($ $ $) 35 T ELT) (($ $ #99#) 87 T ELT) (($ #99# . #101#) 86 T ELT) (($ $ |#1|) 254 (|has| |#1| (|CommutativeRing|)) ELT) (($ |#1| . #101#) 146 (|has| |#1| . #27#) ELT))) (((|AlgebraicallyClosedFunctionSpace| |#1|) (|Category|) (|IntegralDomain|)) (T |AlgebraicallyClosedFunctionSpace|)) ((|rootOf| (*1 *1 *1) (AND (|ofCategory| *1 (|AlgebraicallyClosedFunctionSpace| *2)) (|ofCategory| *2 (|IntegralDomain|)))) (|rootsOf| (*1 *2 *1) (AND (|ofCategory| *3 (|IntegralDomain|)) (|isDomain| *2 (|List| *1)) (|ofCategory| *1 (|AlgebraicallyClosedFunctionSpace| *3)))) (|rootOf| (*1 *1 *1 *2) (AND (|isDomain| *2 (|Symbol|)) (|ofCategory| *1 (|AlgebraicallyClosedFunctionSpace| *3)) (|ofCategory| *3 (|IntegralDomain|)))) (|rootsOf| (*1 *2 *1 *3) (AND (|isDomain| *3 (|Symbol|)) (|ofCategory| *4 (|IntegralDomain|)) (|isDomain| *2 (|List| *1)) (|ofCategory| *1 (|AlgebraicallyClosedFunctionSpace| *4)))) (|zeroOf| (*1 *1 *1) (AND (|ofCategory| *1 (|AlgebraicallyClosedFunctionSpace| *2)) (|ofCategory| *2 (|IntegralDomain|)))) (|zerosOf| (*1 *2 *1) (AND (|ofCategory| *3 (|IntegralDomain|)) (|isDomain| *2 (|List| *1)) (|ofCategory| *1 (|AlgebraicallyClosedFunctionSpace| *3)))) (|zeroOf| (*1 *1 *1 *2) (AND (|isDomain| *2 (|Symbol|)) (|ofCategory| *1 (|AlgebraicallyClosedFunctionSpace| *3)) (|ofCategory| *3 (|IntegralDomain|)))) (|zerosOf| (*1 *2 *1 *3) (AND (|isDomain| *3 (|Symbol|)) (|ofCategory| *4 (|IntegralDomain|)) (|isDomain| *2 (|List| *1)) (|ofCategory| *1 (|AlgebraicallyClosedFunctionSpace| *4))))) (|Join| (|AlgebraicallyClosedField|) (|FunctionSpace| |t#1|) (CATEGORY |domain| (SIGNATURE |rootOf| ($ $)) (SIGNATURE |rootsOf| ((|List| $) $)) (SIGNATURE |rootOf| ($ $ (|Symbol|))) (SIGNATURE |rootsOf| ((|List| $) $ (|Symbol|))) (SIGNATURE |zeroOf| ($ $)) (SIGNATURE |zerosOf| ((|List| $) $)) (SIGNATURE |zeroOf| ($ $ (|Symbol|))) (SIGNATURE |zerosOf| ((|List| $) $ (|Symbol|))))) @@ -77,7 +77,7 @@ NIL ((|coerce| (((|OutputForm|) $) NIL T ELT) (($ (|Integer|)) NIL T ELT) (($ |#2|) 10 T ELT))) (((|Algebra&| |#1| |#2|) (CATEGORY |package| (SIGNATURE |coerce| (|#1| |#2|)) (SIGNATURE |coerce| (|#1| (|Integer|))) (SIGNATURE |coerce| ((|OutputForm|) |#1|))) (|Algebra| |#2|) (|CommutativeRing|)) (T |Algebra&|)) NIL -((~= (#1=((|Boolean|) $ $) 7 T ELT)) (|zero?| ((#2=(|Boolean|) $) 22 T ELT)) (|subtractIfCan| (((|Union| $ "failed") $ $) 26 T ELT)) (|sample| (#3=($) 23 T CONST)) (|recip| (((|Union| $ "failed") $) 42 T ELT)) (|opposite?| ((#2# $ $) 20 T ELT)) (|one?| (((|Boolean|) $) 44 T ELT)) (|latex| (((|String|) $) 11 T ELT)) (|hash| (((|SingleInteger|) $) 12 T ELT)) (|coerce| (((|OutputForm|) $) 13 T ELT) (($ (|Integer|)) 41 T ELT) (($ |#1|) 52 T ELT)) (|characteristic| (((|NonNegativeInteger|)) 40 T CONST)) (|before?| (#1# 6 T ELT)) (|annihilate?| (((|Boolean|) $ $) 33 T ELT)) (|Zero| (#3# 24 T CONST)) (|One| (($) 45 T CONST)) (= (#1# 8 T ELT)) (- (($ $) 29 T ELT) (($ $ $) 28 T ELT)) (+ (($ $ $) 18 T ELT)) (** (($ $ (|PositiveInteger|)) 35 T ELT) (($ $ (|NonNegativeInteger|)) 43 T ELT)) (* (($ (|PositiveInteger|) $) 17 T ELT) (($ (|NonNegativeInteger|) $) 21 T ELT) (($ (|Integer|) . #4=($)) 30 T ELT) (($ $ $) 34 T ELT) (($ $ |#1|) 54 T ELT) (($ |#1| . #4#) 53 T ELT))) +((~= (#1=((|Boolean|) $ $) 7 T ELT)) (|zero?| ((#2=(|Boolean|) $) 22 T ELT)) (|subtractIfCan| (((|Maybe| $) $ $) 26 T ELT)) (|sample| (#3=($) 23 T CONST)) (|recip| (((|Union| $ "failed") $) 43 T ELT)) (|opposite?| ((#2# $ $) 20 T ELT)) (|one?| (((|Boolean|) $) 45 T ELT)) (|latex| (((|String|) $) 11 T ELT)) (|hash| (((|SingleInteger|) $) 12 T ELT)) (|coerce| (((|OutputForm|) $) 13 T ELT) (($ (|Integer|)) 42 T ELT) (($ |#1|) 53 T ELT)) (|characteristic| (((|NonNegativeInteger|)) 41 T CONST)) (|before?| (#1# 6 T ELT)) (|annihilate?| (((|Boolean|) $ $) 34 T ELT)) (|Zero| (#3# 24 T CONST)) (|One| (($) 46 T CONST)) (= (#1# 8 T ELT)) (- (($ $) 30 T ELT) (($ $ $) 29 T ELT)) (+ (($ $ $) 18 T ELT)) (** (($ $ (|PositiveInteger|)) 36 T ELT) (($ $ (|NonNegativeInteger|)) 44 T ELT)) (* (($ (|PositiveInteger|) $) 17 T ELT) (($ (|NonNegativeInteger|) $) 21 T ELT) (($ (|Integer|) . #4=($)) 31 T ELT) (($ $ $) 35 T ELT) (($ $ |#1|) 55 T ELT) (($ |#1| . #4#) 54 T ELT))) (((|Algebra| |#1|) (|Category|) (|CommutativeRing|)) (T |Algebra|)) NIL (|Join| (|Ring|) (|Module| |t#1|) (|CoercibleFrom| |t#1|)) @@ -85,7 +85,7 @@ NIL ((|split| (#1=(#2=(|Factored| |#1|) |#1|) 41 T ELT)) (|factor| (#1# 30 T ELT) ((#2# |#1| (|List| (|AlgebraicNumber|))) 33 T ELT)) (|doublyTransitive?| (((|Boolean|) |#1|) 59 T ELT))) (((|AlgFactor| |#1|) (CATEGORY |package| (SIGNATURE |factor| (#1=(|Factored| |#1|) |#1| (|List| #2=(|AlgebraicNumber|)))) (SIGNATURE |factor| #3=(#1# |#1|)) (SIGNATURE |split| #3#) (SIGNATURE |doublyTransitive?| ((|Boolean|) |#1|))) (|UnivariatePolynomialCategory| #2#)) (T |AlgFactor|)) ((|doublyTransitive?| #1=(*1 *2 *3) (AND (|isDomain| *2 (|Boolean|)) #2=(|isDomain| *1 (|AlgFactor| *3)) #3=(|ofCategory| *3 (|UnivariatePolynomialCategory| #4=(|AlgebraicNumber|))))) (|split| #1# #5=(AND #6=(|isDomain| *2 (|Factored| *3)) #2# #3#)) (|factor| #1# #5#) (|factor| (*1 *2 *3 *4) (AND (|isDomain| *4 (|List| #4#)) #6# #2# #3#))) -((~= #1=(#2=(#3=(|Boolean|) $ $) NIL T ELT)) (|zero?| #4=(#5=(#3# $) NIL T ELT)) (|yCoordinates| (#6=((|Record| (|:| |num| #7=(|Vector| |#2|)) #8=(|:| |den| |#2|)) $) NIL T ELT)) (|unitNormal| (((|Record| (|:| |unit| $) (|:| |canonical| $) (|:| |associate| $)) $) NIL #9=(|has| #10=(|Fraction| |#2|) #11=(|Field|)) ELT)) (|unitCanonical| #12=(#13=($ $) NIL #9# ELT)) (|unit?| #14=(#5# NIL #9# ELT)) (|traceMatrix| #15=(#16=(#17=(|Matrix| #10#) #18=(|Vector| $)) NIL T ELT) (#19=(#17#) NIL T ELT)) (|trace| #20=((#10# $) NIL T ELT)) (|tableForDiscreteLogarithm| (((|Table| #21=(|PositiveInteger|) #22=(|NonNegativeInteger|)) #23=(|Integer|)) NIL #24=(|has| #10# (|FiniteFieldCategory|)) ELT)) (|subtractIfCan| (#25=(#26=(|Union| $ #27="failed") $ $) NIL T ELT)) (|squareFreePart| #12#) (|squareFree| #28=(((|Factored| $) $) NIL #9# ELT)) (|sizeLess?| #29=(#2# NIL #9# ELT)) (|size| (#30=(#22#) NIL #31=(|has| #10# #32=(|Finite|)) ELT)) (|singularAtInfinity?| #33=(#34=(#3#) NIL T ELT)) (|singular?| #35=(#36=(#3# |#1|) NIL T ELT) #37=(#38=(#3# |#2|) NIL T ELT)) (|sample| (#39=($) NIL T CONST)) (|retractIfCan| (((|Union| #23# . #40=(#27#)) . #41=($)) NIL #42=(|has| #10# (|RetractableTo| #23#)) ELT) (((|Union| #43=(|Fraction| #23#) . #40#) . #41#) NIL #44=(|has| #10# (|RetractableTo| #43#)) ELT) (((|Union| #10# . #40#) . #41#) NIL T ELT)) (|retract| ((#23# . #45=($)) NIL #42# ELT) ((#43# . #45#) NIL #44# ELT) #20#) (|represents| (($ #46=(|Vector| #10#) #18#) NIL T ELT) (#47=($ #46#) 60 T ELT) (#48=($ #7# |#2|) 130 T ELT)) (|representationType| (((|Union| "prime" "polynomial" "normal" "cyclic")) NIL #24# ELT)) (|rem| #49=(#50=($ $ $) NIL #9# ELT)) (|regularRepresentation| ((#17# $ #18#) NIL T ELT) ((#17# $) NIL T ELT)) (|reducedSystem| ((#51=(|Matrix| #23#) . #52=(#53=(|Matrix| $))) NIL #54=(|has| #10# (|LinearlyExplicitRingOver| #23#)) ELT) ((#55=(|Record| (|:| |mat| #51#) (|:| |vec| (|Vector| #23#))) . #56=(#53# #18#)) NIL #54# ELT) ((#57=(|Record| (|:| |mat| #17#) (|:| |vec| #46#)) . #56#) NIL T ELT) ((#17# . #52#) NIL T ELT)) (|reduceBasisAtInfinity| #58=(#59=(#18# #18#) NIL T ELT)) (|reduce| #60=(($ |#3|) NIL T ELT) ((#26# (|Fraction| |#3|)) NIL #9# ELT)) (|recip| ((#26# $) NIL T ELT)) (|rationalPoints| (((|List| (|List| |#1|))) NIL (|has| |#1| #32#) ELT)) (|rationalPoint?| ((#3# |#1| |#1|) NIL T ELT)) (|rank| ((#21#) NIL T ELT)) (|random| (#39# NIL #31# ELT)) (|ramifiedAtInfinity?| #33#) (|ramified?| #35# #37#) (|quo| #49#) (|principalIdeal| (((|Record| (|:| |coef| #61=(|List| $)) #62=(|:| |generator| $)) #61#) NIL #9# ELT)) (|primitivePart| #63=(#13# NIL T ELT)) (|primitiveElement| #64=(#39# NIL #24# ELT)) (|primitive?| (#5# NIL #24# ELT)) (|primeFrobenius| (#65=($ $ #22#) NIL #24# ELT) #66=(#13# NIL #24# ELT)) (|prime?| #14#) (|order| (#67=(#21# $) NIL #24# ELT) (((|OnePointCompletion| #21#) $) NIL #24# ELT)) (|opposite?| #1#) (|one?| #4#) (|numberOfComponents| #68=(#30# NIL T ELT)) (|normalizeAtInfinity| (#59# 105 T ELT)) (|norm| #20#) (|nonSingularModel| (((|List| (|Polynomial| |#1|)) #69=(|Symbol|)) NIL (|has| |#1| #11#) ELT)) (|nextItem| (#70=((|Maybe| $) $) NIL #24# ELT)) (|multiEuclidean| (((|Union| #61# #27#) #61# $) NIL #9# ELT)) (|minimalPolynomial| (#71=(|#3| $) NIL #9# ELT)) (|lookup| (#67# NIL #31# ELT)) (|lift| #72=(#71# NIL T ELT)) (|leftReducedSystem| ((#51# #18#) NIL #54# ELT) ((#55# . #73=(#18# $)) NIL #54# ELT) ((#57# . #73#) NIL T ELT) #15#) (|lcm| #74=(($ #61#) NIL #9# ELT) #49#) (|latex| (((|String|) $) NIL T ELT)) (|knownInfBasis| (((|Void|) #22#) 83 T ELT)) (|inverseIntegralMatrixAtInfinity| (#19# 55 T ELT)) (|inverseIntegralMatrix| (#19# 48 T ELT)) (|inv| #12#) (|integralRepresents| (#48# 131 T ELT)) (|integralMatrixAtInfinity| (#19# 49 T ELT)) (|integralMatrix| (#19# 47 T ELT)) (|integralDerivationMatrix| (((|Record| (|:| |num| (|Matrix| |#2|)) #8#) #75=(|Mapping| |#2| |#2|)) 129 T ELT)) (|integralCoordinates| (#6# 67 T ELT)) (|integralBasisAtInfinity| (#76=(#18#) 46 T ELT)) (|integralBasis| (#76# 45 T ELT)) (|integralAtInfinity?| #4#) (|integral?| #4# ((#3# $ |#1|) NIL T ELT) ((#3# $ |#2|) NIL T ELT)) (|init| (#39# NIL #24# CONST)) (|index| (($ #21#) NIL #31# ELT)) (|hyperelliptic| #77=(((|Union| |#2| #27#)) NIL T ELT)) (|hash| (((|SingleInteger|) $) NIL T ELT)) (|genus| #68#) (|generator| (#39# NIL T ELT)) (|gcdPolynomial| ((#78=(|SparseUnivariatePolynomial| $) #78# #78#) NIL #9# ELT)) (|gcd| #74# #49#) (|factorsOfCyclicGroupSize| (((|List| (|Record| (|:| |factor| #23#) (|:| |exponent| #23#)))) NIL #24# ELT)) (|factor| #28#) (|extendedEuclidean| (((|Union| (|Record| #79=(|:| |coef1| $) #80=(|:| |coef2| $)) #27#) $ $ $) NIL #9# ELT) (((|Record| #79# #80# #62#) $ $) NIL #9# ELT)) (|exquo| (#25# NIL #9# ELT)) (|expressIdealMember| (((|Maybe| #61#) #61# $) NIL #9# ELT)) (|euclideanSize| (#81=(#22# $) NIL #9# ELT)) (|elt| ((|#1| $ |#1| |#1|) NIL T ELT)) (|elliptic| #77#) (|divide| (((|Record| (|:| |quotient| $) (|:| |remainder| $)) $ $) NIL #9# ELT)) (|discriminant| ((#10# #18#) NIL T ELT) ((#10#) 43 T ELT)) (|discreteLog| (#81# NIL #24# ELT) (((|Union| #22# #27#) $ $) NIL #24# ELT)) (|differentiate| #82=(($ $ #83=(|Mapping| #10# #10#)) NIL #9# ELT) #84=(($ $ #83# #22#) NIL #9# ELT) (($ $ #75#) 125 T ELT) #85=(($ $ #86=(|List| #69#) (|List| #22#)) NIL #87=(OR (AND #9# (|has| #10# (|PartialDifferentialRing| #69#))) (AND #9# (|has| #10# (|PartialDifferentialSpace| #69#)))) ELT) #88=(($ $ #69# #22#) NIL #87# ELT) #89=(($ $ #86#) NIL #87# ELT) #90=(($ $ #69#) NIL #87# ELT) #91=(#65# NIL #92=(OR (AND (|has| #10# (|DifferentialRing|)) #9#) (AND (|has| #10# (|DifferentialSpace|)) #9#) #24#) ELT) #93=(#13# NIL #92# ELT)) (|derivationCoordinates| ((#17# #18# #83#) NIL #9# ELT)) (|definingPolynomial| ((|#3|) 54 T ELT)) (|createPrimitiveElement| #64#) (|coordinates| ((#46# $ #18#) NIL T ELT) ((#17# #18# #18#) NIL T ELT) (#94=(#46# $) 61 T ELT) (#16# 106 T ELT)) (|convert| (#94# NIL T ELT) (#47# NIL T ELT) #72# #60#) (|conditionP| (((|Union| #18# #27#) #53#) NIL #24# ELT)) (|complementaryBasis| #58#) (|coerce| (((|OutputForm|) $) NIL T ELT) (($ #23#) NIL T ELT) (($ #10#) NIL T ELT) (($ #43#) NIL (OR #9# #44#) ELT) #12#) (|charthRoot| #66# (#70# NIL (|has| #10# (|CharacteristicNonZero|)) ELT)) (|characteristicPolynomial| #72#) (|characteristic| (#30# NIL T CONST)) (|branchPointAtInfinity?| (#34# 41 T ELT)) (|branchPoint?| (#36# 53 T ELT) (#38# 137 T ELT)) (|before?| #1#) (|basis| (#76# NIL T ELT)) (|associates?| #29#) (|annihilate?| #1#) (|algSplitSimple| (((|Record| (|:| |num| $) #8# (|:| |derivden| |#2|) (|:| |gd| |#2|)) $ #75#) NIL T ELT)) (|absolutelyIrreducible?| #33#) (|Zero| (#39# 17 T CONST)) (|One| (#39# 27 T CONST)) (D #82# #84# #85# #88# #89# #90# #91# #93#) (= #1#) (/ #49#) (- #63# #95=(#50# NIL T ELT)) (+ #95#) (** (($ $ #21#) NIL T ELT) (#65# NIL T ELT) (($ $ #23#) NIL #9# ELT)) (* (($ #21# $) NIL T ELT) (($ #22# $) NIL T ELT) (($ #23# . #96=($)) NIL T ELT) #95# (($ $ #10#) NIL T ELT) (($ #10# . #96#) NIL T ELT) (($ #43# . #96#) NIL #9# ELT) (($ $ #43#) NIL #9# ELT))) +((~= #1=(#2=(#3=(|Boolean|) $ $) NIL T ELT)) (|zero?| #4=(#5=(#3# $) NIL T ELT)) (|yCoordinates| (#6=((|Record| (|:| |num| #7=(|Vector| |#2|)) #8=(|:| |den| |#2|)) $) NIL T ELT)) (|unitNormal| (((|Record| (|:| |unit| $) (|:| |canonical| $) (|:| |associate| $)) $) NIL #9=(|has| #10=(|Fraction| |#2|) #11=(|Field|)) ELT)) (|unitCanonical| #12=(#13=($ $) NIL #9# ELT)) (|unit?| #14=(#5# NIL #9# ELT)) (|traceMatrix| #15=(#16=(#17=(|Matrix| #10#) #18=(|Vector| $)) NIL T ELT) (#19=(#17#) NIL T ELT)) (|trace| #20=((#10# $) NIL T ELT)) (|tableForDiscreteLogarithm| (((|Table| #21=(|PositiveInteger|) #22=(|NonNegativeInteger|)) #23=(|Integer|)) NIL #24=(|has| #10# (|FiniteFieldCategory|)) ELT)) (|subtractIfCan| ((#25=(|Maybe| $) $ $) NIL T ELT)) (|squareFreePart| #12#) (|squareFree| #26=(((|Factored| $) $) NIL #9# ELT)) (|sizeLess?| #27=(#2# NIL #9# ELT)) (|size| (#28=(#22#) NIL #29=(|has| #10# #30=(|Finite|)) ELT)) (|singularAtInfinity?| #31=(#32=(#3#) NIL T ELT)) (|singular?| #33=(#34=(#3# |#1|) NIL T ELT) #35=(#36=(#3# |#2|) NIL T ELT)) (|sample| (#37=($) NIL T CONST)) (|retractIfCan| (((|Union| #23# . #38=(#39="failed")) . #40=($)) NIL #41=(|has| #10# (|RetractableTo| #23#)) ELT) (((|Union| #42=(|Fraction| #23#) . #38#) . #40#) NIL #43=(|has| #10# (|RetractableTo| #42#)) ELT) (((|Union| #10# . #38#) . #40#) NIL T ELT)) (|retract| ((#23# . #44=($)) NIL #41# ELT) ((#42# . #44#) NIL #43# ELT) #20#) (|represents| (($ #45=(|Vector| #10#) #18#) NIL T ELT) (#46=($ #45#) 60 T ELT) (#47=($ #7# |#2|) 130 T ELT)) (|representationType| (((|Union| "prime" "polynomial" "normal" "cyclic")) NIL #24# ELT)) (|rem| #48=(#49=($ $ $) NIL #9# ELT)) (|regularRepresentation| ((#17# $ #18#) NIL T ELT) ((#17# $) NIL T ELT)) (|reducedSystem| ((#50=(|Matrix| #23#) . #51=(#52=(|Matrix| $))) NIL #53=(|has| #10# (|LinearlyExplicitRingOver| #23#)) ELT) ((#54=(|Record| (|:| |mat| #50#) (|:| |vec| (|Vector| #23#))) . #55=(#52# #18#)) NIL #53# ELT) ((#56=(|Record| (|:| |mat| #17#) (|:| |vec| #45#)) . #55#) NIL T ELT) ((#17# . #51#) NIL T ELT)) (|reduceBasisAtInfinity| #57=(#58=(#18# #18#) NIL T ELT)) (|reduce| #59=(($ |#3|) NIL T ELT) ((#60=(|Union| $ #39#) (|Fraction| |#3|)) NIL #9# ELT)) (|recip| ((#60# $) NIL T ELT)) (|rationalPoints| (((|List| (|List| |#1|))) NIL (|has| |#1| #30#) ELT)) (|rationalPoint?| ((#3# |#1| |#1|) NIL T ELT)) (|rank| ((#21#) NIL T ELT)) (|random| (#37# NIL #29# ELT)) (|ramifiedAtInfinity?| #31#) (|ramified?| #33# #35#) (|quo| #48#) (|principalIdeal| (((|Record| (|:| |coef| #61=(|List| $)) #62=(|:| |generator| $)) #61#) NIL #9# ELT)) (|primitivePart| #63=(#13# NIL T ELT)) (|primitiveElement| #64=(#37# NIL #24# ELT)) (|primitive?| (#5# NIL #24# ELT)) (|primeFrobenius| (#65=($ $ #22#) NIL #24# ELT) #66=(#13# NIL #24# ELT)) (|prime?| #14#) (|order| (#67=(#21# $) NIL #24# ELT) (((|OnePointCompletion| #21#) $) NIL #24# ELT)) (|opposite?| #1#) (|one?| #4#) (|numberOfComponents| #68=(#28# NIL T ELT)) (|normalizeAtInfinity| (#58# 105 T ELT)) (|norm| #20#) (|nonSingularModel| (((|List| (|Polynomial| |#1|)) #69=(|Symbol|)) NIL (|has| |#1| #11#) ELT)) (|nextItem| (#70=(#25# $) NIL #24# ELT)) (|multiEuclidean| (((|Union| #61# #39#) #61# $) NIL #9# ELT)) (|minimalPolynomial| (#71=(|#3| $) NIL #9# ELT)) (|lookup| (#67# NIL #29# ELT)) (|lift| #72=(#71# NIL T ELT)) (|leftReducedSystem| ((#50# #18#) NIL #53# ELT) ((#54# . #73=(#18# $)) NIL #53# ELT) ((#56# . #73#) NIL T ELT) #15#) (|lcm| #74=(($ #61#) NIL #9# ELT) #48#) (|latex| (((|String|) $) NIL T ELT)) (|knownInfBasis| (((|Void|) #22#) 83 T ELT)) (|inverseIntegralMatrixAtInfinity| (#19# 55 T ELT)) (|inverseIntegralMatrix| (#19# 48 T ELT)) (|inv| #12#) (|integralRepresents| (#47# 131 T ELT)) (|integralMatrixAtInfinity| (#19# 49 T ELT)) (|integralMatrix| (#19# 47 T ELT)) (|integralDerivationMatrix| (((|Record| (|:| |num| (|Matrix| |#2|)) #8#) #75=(|Mapping| |#2| |#2|)) 129 T ELT)) (|integralCoordinates| (#6# 67 T ELT)) (|integralBasisAtInfinity| (#76=(#18#) 46 T ELT)) (|integralBasis| (#76# 45 T ELT)) (|integralAtInfinity?| #4#) (|integral?| #4# ((#3# $ |#1|) NIL T ELT) ((#3# $ |#2|) NIL T ELT)) (|init| (#37# NIL #24# CONST)) (|index| (($ #21#) NIL #29# ELT)) (|hyperelliptic| #77=(((|Union| |#2| #39#)) NIL T ELT)) (|hash| (((|SingleInteger|) $) NIL T ELT)) (|genus| #68#) (|generator| (#37# NIL T ELT)) (|gcdPolynomial| ((#78=(|SparseUnivariatePolynomial| $) #78# #78#) NIL #9# ELT)) (|gcd| #74# #48#) (|factorsOfCyclicGroupSize| (((|List| (|Record| (|:| |factor| #23#) (|:| |exponent| #23#)))) NIL #24# ELT)) (|factor| #26#) (|extendedEuclidean| (((|Union| (|Record| #79=(|:| |coef1| $) #80=(|:| |coef2| $)) #39#) $ $ $) NIL #9# ELT) (((|Record| #79# #80# #62#) $ $) NIL #9# ELT)) (|exquo| ((#60# $ $) NIL #9# ELT)) (|expressIdealMember| (((|Maybe| #61#) #61# $) NIL #9# ELT)) (|euclideanSize| (#81=(#22# $) NIL #9# ELT)) (|elt| ((|#1| $ |#1| |#1|) NIL T ELT)) (|elliptic| #77#) (|divide| (((|Record| (|:| |quotient| $) (|:| |remainder| $)) $ $) NIL #9# ELT)) (|discriminant| ((#10# #18#) NIL T ELT) ((#10#) 43 T ELT)) (|discreteLog| (#81# NIL #24# ELT) (((|Union| #22# #39#) $ $) NIL #24# ELT)) (|differentiate| #82=(($ $ #83=(|Mapping| #10# #10#)) NIL #9# ELT) #84=(($ $ #83# #22#) NIL #9# ELT) (($ $ #75#) 125 T ELT) #85=(#65# NIL #86=(OR (AND (|has| #10# (|DifferentialRing|)) #9#) (AND (|has| #10# (|DifferentialSpace|)) #9#) #24#) ELT) #87=(#13# NIL #86# ELT) #88=(($ $ #89=(|List| #69#) (|List| #22#)) NIL #90=(OR (AND #9# (|has| #10# (|PartialDifferentialRing| #69#))) (AND #9# (|has| #10# (|PartialDifferentialSpace| #69#)))) ELT) #91=(($ $ #69# #22#) NIL #90# ELT) #92=(($ $ #89#) NIL #90# ELT) #93=(($ $ #69#) NIL #90# ELT)) (|derivationCoordinates| ((#17# #18# #83#) NIL #9# ELT)) (|definingPolynomial| ((|#3|) 54 T ELT)) (|createPrimitiveElement| #64#) (|coordinates| ((#45# $ #18#) NIL T ELT) ((#17# #18# #18#) NIL T ELT) (#94=(#45# $) 61 T ELT) (#16# 106 T ELT)) (|convert| (#94# NIL T ELT) (#46# NIL T ELT) #72# #59#) (|conditionP| (((|Union| #18# #39#) #52#) NIL #24# ELT)) (|complementaryBasis| #57#) (|coerce| (((|OutputForm|) $) NIL T ELT) (($ #23#) NIL T ELT) (($ #10#) NIL T ELT) (($ #42#) NIL (OR #9# #43#) ELT) #12#) (|charthRoot| #66# (#70# NIL (|has| #10# (|CharacteristicNonZero|)) ELT)) (|characteristicPolynomial| #72#) (|characteristic| (#28# NIL T CONST)) (|branchPointAtInfinity?| (#32# 41 T ELT)) (|branchPoint?| (#34# 53 T ELT) (#36# 137 T ELT)) (|before?| #1#) (|basis| (#76# NIL T ELT)) (|associates?| #27#) (|annihilate?| #1#) (|algSplitSimple| (((|Record| (|:| |num| $) #8# (|:| |derivden| |#2|) (|:| |gd| |#2|)) $ #75#) NIL T ELT)) (|absolutelyIrreducible?| #31#) (|Zero| (#37# 17 T CONST)) (|One| (#37# 27 T CONST)) (D #82# #84# #85# #87# #88# #91# #92# #93#) (= #1#) (/ #48#) (- #63# #95=(#49# NIL T ELT)) (+ #95#) (** (($ $ #21#) NIL T ELT) (#65# NIL T ELT) (($ $ #23#) NIL #9# ELT)) (* (($ #21# $) NIL T ELT) (($ #22# $) NIL T ELT) (($ #23# . #96=($)) NIL T ELT) #95# (($ $ #10#) NIL T ELT) (($ #10# . #96#) NIL T ELT) (($ #42# . #96#) NIL #9# ELT) (($ $ #42#) NIL #9# ELT))) (((|AlgebraicFunctionField| |#1| |#2| |#3| |#4|) (|Join| (|FunctionFieldCategory| |#1| |#2| |#3|) (CATEGORY |package| (SIGNATURE |knownInfBasis| ((|Void|) (|NonNegativeInteger|))))) (|Field|) (|UnivariatePolynomialCategory| |#1|) (|UnivariatePolynomialCategory| (|Fraction| |#2|)) |#3|) (T |AlgebraicFunctionField|)) ((|knownInfBasis| (*1 *2 *3) (AND (|isDomain| *3 (|NonNegativeInteger|)) (|ofCategory| *4 (|Field|)) (|ofCategory| *5 (|UnivariatePolynomialCategory| *4)) (|isDomain| *2 (|Void|)) (|isDomain| *1 (|AlgebraicFunctionField| *4 *5 *6 *7)) (|ofCategory| *6 (|UnivariatePolynomialCategory| (|Fraction| *5))) (|ofType| *7 *6)))) ((|rootSplit| (#1=(|#2| |#2|) 47 T ELT)) (|rootSimp| (#1# 136 #2=(AND (|has| |#2| (|FunctionSpace| |#1|)) (|has| |#1| (|Join| (|GcdDomain|) (|RetractableTo| (|Integer|))))) ELT)) (|rootProduct| (#1# 100 #2# ELT)) (|rootPower| (#1# 101 #2# ELT)) (|rootKerSimp| ((|#2| (|BasicOperator|) |#2| (|NonNegativeInteger|)) 80 #2# ELT)) (|ratPoly| (((|SparseUnivariatePolynomial| |#2|) |#2|) 44 T ELT)) (|ratDenom| ((|#2| |#2| (|List| (|Kernel| |#2|))) 18 T ELT) ((|#2| |#2| (|List| |#2|)) 20 T ELT) ((|#2| |#2| |#2|) 21 T ELT) (#1# 16 T ELT))) @@ -97,7 +97,7 @@ NIL ((|weakBiRank| (#1=((|NonNegativeInteger|) |#2|) 70 T ELT)) (|rightRank| (#1# 74 T ELT)) (|radicalOfLeftTraceForm| (#2=(#3=(|List| |#2|)) 37 T ELT)) (|leftRank| (#1# 73 T ELT)) (|doubleRank| (#1# 69 T ELT)) (|biRank| (#1# 72 T ELT)) (|basisOfRightNucloid| (#4=((|List| (|Matrix| |#1|))) 65 T ELT)) (|basisOfRightNucleus| (#2# 60 T ELT)) (|basisOfRightAnnihilator| (#5=(#3# |#2|) 48 T ELT)) (|basisOfNucleus| (#2# 62 T ELT)) (|basisOfMiddleNucleus| (#2# 61 T ELT)) (|basisOfLeftNucloid| (#4# 53 T ELT)) (|basisOfLeftNucleus| (#2# 59 T ELT)) (|basisOfLeftAnnihilator| (#5# 47 T ELT)) (|basisOfCommutingElements| (#2# 55 T ELT)) (|basisOfCentroid| (#4# 66 T ELT)) (|basisOfCenter| (#2# 64 T ELT)) (|basis| ((#6=(|Vector| |#2|) #6#) 99 (|has| |#1| (|EuclideanDomain|)) ELT))) (((|AlgebraPackage| |#1| |#2|) (CATEGORY |package| (SIGNATURE |leftRank| #1=((|NonNegativeInteger|) |#2|)) (SIGNATURE |rightRank| #1#) (SIGNATURE |doubleRank| #1#) (SIGNATURE |weakBiRank| #1#) (SIGNATURE |biRank| #1#) (SIGNATURE |basisOfCommutingElements| #2=(#3=(|List| |#2|))) (SIGNATURE |basisOfLeftAnnihilator| #4=(#3# |#2|)) (SIGNATURE |basisOfRightAnnihilator| #4#) (SIGNATURE |basisOfLeftNucleus| #2#) (SIGNATURE |basisOfRightNucleus| #2#) (SIGNATURE |basisOfMiddleNucleus| #2#) (SIGNATURE |basisOfNucleus| #2#) (SIGNATURE |basisOfCenter| #2#) (SIGNATURE |basisOfLeftNucloid| #5=((|List| (|Matrix| |#1|)))) (SIGNATURE |basisOfRightNucloid| #5#) (SIGNATURE |basisOfCentroid| #5#) (SIGNATURE |radicalOfLeftTraceForm| #2#) (IF (|has| |#1| (|EuclideanDomain|)) (SIGNATURE |basis| (#6=(|Vector| |#2|) #6#)) |%noBranch|)) (|IntegralDomain|) (|FramedNonAssociativeAlgebra| |#1|)) (T |AlgebraPackage|)) ((|basis| (*1 *2 *2) (AND (|isDomain| *2 (|Vector| *4)) #1=(|ofCategory| *4 (|FramedNonAssociativeAlgebra| *3)) (|ofCategory| *3 (|EuclideanDomain|)) #2=(|ofCategory| *3 #3=(|IntegralDomain|)) #4=(|isDomain| *1 (|AlgebraPackage| *3 *4)))) (|radicalOfLeftTraceForm| #5=(*1 *2) #6=(AND #2# (|isDomain| *2 (|List| *4)) #4# #1#)) (|basisOfCentroid| #5# #7=(AND #2# (|isDomain| *2 (|List| (|Matrix| *3))) #4# #1#)) (|basisOfRightNucloid| #5# #7#) (|basisOfLeftNucloid| #5# #7#) (|basisOfCenter| #5# #6#) (|basisOfNucleus| #5# #6#) (|basisOfMiddleNucleus| #5# #6#) (|basisOfRightNucleus| #5# #6#) (|basisOfLeftNucleus| #5# #6#) (|basisOfRightAnnihilator| #8=(*1 *2 *3) #9=(AND #10=(|ofCategory| *4 #3#) (|isDomain| *2 (|List| *3)) #11=(|isDomain| *1 (|AlgebraPackage| *4 *3)) #12=(|ofCategory| *3 (|FramedNonAssociativeAlgebra| *4)))) (|basisOfLeftAnnihilator| #8# #9#) (|basisOfCommutingElements| #5# #6#) (|biRank| #8# #13=(AND #10# (|isDomain| *2 (|NonNegativeInteger|)) #11# #12#)) (|weakBiRank| #8# #13#) (|doubleRank| #8# #13#) (|rightRank| #8# #13#) (|leftRank| #8# #13#)) -((~= #1=((#2=(|Boolean|) $ $) NIL T ELT)) (|zero?| ((#2# $) NIL T ELT)) (|unit| #3=((#4=(|Union| $ #5="failed")) NIL #6=(|has| |#1| (|IntegralDomain|)) ELT)) (|subtractIfCan| ((#4# $ $) NIL T ELT)) (|structuralConstants| ((#7=(|Vector| #8=(|Matrix| |#1|)) #9=(|Vector| $)) NIL T ELT) ((#7#) 24 T ELT)) (|someBasis| (#10=(#9#) 52 T ELT)) (|sample| #11=(($) NIL T CONST)) (|rightUnits| #12=(((|Union| (|Record| (|:| |particular| $) (|:| |basis| (|List| $))) #5#)) NIL #6# ELT)) (|rightUnit| #3#) (|rightTraceMatrix| #13=((#8# #9#) NIL T ELT) #14=((#8#) NIL T ELT)) (|rightTrace| #15=((|#1| $) NIL T ELT)) (|rightRegularRepresentation| #16=((#8# $ #9#) NIL T ELT) #17=((#8# $) NIL T ELT)) (|rightRecip| #18=(#19=(#4# $) NIL #6# ELT)) (|rightRankPolynomial| #20=(((|SparseUnivariatePolynomial| #21=(|Polynomial| |#1|))) NIL (|has| |#1| (|Field|)) ELT)) (|rightPower| #22=(($ $ #23=(|PositiveInteger|)) NIL T ELT)) (|rightNorm| #15#) (|rightMinimalPolynomial| #24=(#25=((|SparseUnivariatePolynomial| |#1|) $) NIL #6# ELT)) (|rightDiscriminant| #26=((|#1| #9#) NIL T ELT) #27=((|#1|) NIL T ELT)) (|rightCharacteristicPolynomial| #28=(#25# NIL T ELT)) (|rightAlternative?| (#29=(#2#) 99 T ELT)) (|represents| (($ #30=(|Vector| |#1|) #9#) NIL T ELT) #31=(#32=($ #30#) NIL T ELT)) (|recip| (#19# 14 #6# ELT)) (|rank| ((#23#) 53 T ELT)) (|powerAssociative?| #33=(#29# NIL T ELT)) (|plenaryPower| #22#) (|opposite?| #1#) (|noncommutativeJordanAlgebra?| #33#) (|lieAlgebra?| #33#) (|lieAdmissible?| (#29# 101 T ELT)) (|leftUnits| #12#) (|leftUnit| #3#) (|leftTraceMatrix| #13# #14#) (|leftTrace| #15#) (|leftRegularRepresentation| #16# #17#) (|leftRecip| #18#) (|leftRankPolynomial| #20#) (|leftPower| #22#) (|leftNorm| #15#) (|leftMinimalPolynomial| #24#) (|leftDiscriminant| #26# #27#) (|leftCharacteristicPolynomial| #28#) (|leftAlternative?| (#29# 98 T ELT)) (|latex| (((|String|) $) NIL T ELT)) (|jordanAlgebra?| (#29# 106 T ELT)) (|jordanAdmissible?| (#29# 105 T ELT)) (|jacobiIdentity?| (#29# 107 T ELT)) (|hash| (((|SingleInteger|) $) NIL T ELT)) (|flexible?| (#29# 100 T ELT)) (|elt| ((|#1| $ #34=(|Integer|)) 55 T ELT)) (|coordinates| ((#30# $ #9#) 48 T ELT) ((#8# #9# #9#) NIL T ELT) (#35=(#30# $) 28 T ELT) #13#) (|convert| (#35# NIL T ELT) #31#) (|conditionsForIdempotents| ((#36=(|List| #21#) #9#) NIL T ELT) ((#36#) NIL T ELT)) (|commutator| #37=(#38=($ $ $) NIL T ELT)) (|commutative?| (#29# 95 T ELT)) (|coerce| (((|OutputForm|) $) 71 T ELT) (#32# 22 T ELT)) (|before?| #1#) (|basis| (#10# 51 T ELT)) (|associatorDependence| (((|List| #30#)) NIL #6# ELT)) (|associator| (($ $ $ $) NIL T ELT)) (|associative?| (#29# 91 T ELT)) (|apply| (($ #8# $) 18 T ELT)) (|antiCommutator| #37#) (|antiCommutative?| (#29# 97 T ELT)) (|antiAssociative?| (#29# 92 T ELT)) (|alternative?| (#29# 90 T ELT)) (|Zero| #11#) (= #1#) (- (($ $) NIL T ELT) #37#) (+ #37#) (** #22#) (* (($ #23# $) NIL T ELT) (($ (|NonNegativeInteger|) $) NIL T ELT) (($ #34# . #39=($)) NIL T ELT) (#38# 80 T ELT) (($ $ |#1|) NIL T ELT) (($ |#1| . #39#) NIL T ELT) (($ (|SquareMatrix| |#2| |#1|) $) 19 T ELT))) +((~= #1=((#2=(|Boolean|) $ $) NIL T ELT)) (|zero?| ((#2# $) NIL T ELT)) (|unit| #3=((#4=(|Union| $ #5="failed")) NIL #6=(|has| |#1| (|IntegralDomain|)) ELT)) (|subtractIfCan| (((|Maybe| $) $ $) NIL T ELT)) (|structuralConstants| ((#7=(|Vector| #8=(|Matrix| |#1|)) #9=(|Vector| $)) NIL T ELT) ((#7#) 24 T ELT)) (|someBasis| (#10=(#9#) 52 T ELT)) (|sample| #11=(($) NIL T CONST)) (|rightUnits| #12=(((|Union| (|Record| (|:| |particular| $) (|:| |basis| (|List| $))) #5#)) NIL #6# ELT)) (|rightUnit| #3#) (|rightTraceMatrix| #13=((#8# #9#) NIL T ELT) #14=((#8#) NIL T ELT)) (|rightTrace| #15=((|#1| $) NIL T ELT)) (|rightRegularRepresentation| #16=((#8# $ #9#) NIL T ELT) #17=((#8# $) NIL T ELT)) (|rightRecip| #18=(#19=(#4# $) NIL #6# ELT)) (|rightRankPolynomial| #20=(((|SparseUnivariatePolynomial| #21=(|Polynomial| |#1|))) NIL (|has| |#1| (|Field|)) ELT)) (|rightPower| #22=(($ $ #23=(|PositiveInteger|)) NIL T ELT)) (|rightNorm| #15#) (|rightMinimalPolynomial| #24=(#25=((|SparseUnivariatePolynomial| |#1|) $) NIL #6# ELT)) (|rightDiscriminant| #26=((|#1| #9#) NIL T ELT) #27=((|#1|) NIL T ELT)) (|rightCharacteristicPolynomial| #28=(#25# NIL T ELT)) (|rightAlternative?| (#29=(#2#) 99 T ELT)) (|represents| (($ #30=(|Vector| |#1|) #9#) NIL T ELT) #31=(#32=($ #30#) NIL T ELT)) (|recip| (#19# 14 #6# ELT)) (|rank| ((#23#) 53 T ELT)) (|powerAssociative?| #33=(#29# NIL T ELT)) (|plenaryPower| #22#) (|opposite?| #1#) (|noncommutativeJordanAlgebra?| #33#) (|lieAlgebra?| #33#) (|lieAdmissible?| (#29# 101 T ELT)) (|leftUnits| #12#) (|leftUnit| #3#) (|leftTraceMatrix| #13# #14#) (|leftTrace| #15#) (|leftRegularRepresentation| #16# #17#) (|leftRecip| #18#) (|leftRankPolynomial| #20#) (|leftPower| #22#) (|leftNorm| #15#) (|leftMinimalPolynomial| #24#) (|leftDiscriminant| #26# #27#) (|leftCharacteristicPolynomial| #28#) (|leftAlternative?| (#29# 98 T ELT)) (|latex| (((|String|) $) NIL T ELT)) (|jordanAlgebra?| (#29# 106 T ELT)) (|jordanAdmissible?| (#29# 105 T ELT)) (|jacobiIdentity?| (#29# 107 T ELT)) (|hash| (((|SingleInteger|) $) NIL T ELT)) (|flexible?| (#29# 100 T ELT)) (|elt| ((|#1| $ #34=(|Integer|)) 55 T ELT)) (|coordinates| ((#30# $ #9#) 48 T ELT) ((#8# #9# #9#) NIL T ELT) (#35=(#30# $) 28 T ELT) #13#) (|convert| (#35# NIL T ELT) #31#) (|conditionsForIdempotents| ((#36=(|List| #21#) #9#) NIL T ELT) ((#36#) NIL T ELT)) (|commutator| #37=(#38=($ $ $) NIL T ELT)) (|commutative?| (#29# 95 T ELT)) (|coerce| (((|OutputForm|) $) 71 T ELT) (#32# 22 T ELT)) (|before?| #1#) (|basis| (#10# 51 T ELT)) (|associatorDependence| (((|List| #30#)) NIL #6# ELT)) (|associator| (($ $ $ $) NIL T ELT)) (|associative?| (#29# 91 T ELT)) (|apply| (($ #8# $) 18 T ELT)) (|antiCommutator| #37#) (|antiCommutative?| (#29# 97 T ELT)) (|antiAssociative?| (#29# 92 T ELT)) (|alternative?| (#29# 90 T ELT)) (|Zero| #11#) (= #1#) (- (($ $) NIL T ELT) #37#) (+ #37#) (** #22#) (* (($ #23# $) NIL T ELT) (($ (|NonNegativeInteger|) $) NIL T ELT) (($ #34# . #39=($)) NIL T ELT) (#38# 80 T ELT) (($ $ |#1|) NIL T ELT) (($ |#1| . #39#) NIL T ELT) (($ (|SquareMatrix| |#2| |#1|) $) 19 T ELT))) (((|AlgebraGivenByStructuralConstants| |#1| |#2| |#3| |#4|) (|Join| (|FramedNonAssociativeAlgebra| |#1|) (|LeftModule| (|SquareMatrix| |#2| |#1|)) (CATEGORY |domain| (SIGNATURE |coerce| ($ (|Vector| |#1|))))) (|Field|) (|PositiveInteger|) (|List| (|Symbol|)) (|Vector| (|Matrix| |#1|))) (T |AlgebraGivenByStructuralConstants|)) ((|coerce| (*1 *1 *2) (AND (|isDomain| *2 (|Vector| *3)) (|ofCategory| *3 (|Field|)) (|ofType| *6 (|Vector| (|Matrix| *3))) (|isDomain| *1 (|AlgebraGivenByStructuralConstants| *3 *4 *5 *6)) (|ofType| *4 (|PositiveInteger|)) (|ofType| *5 (|List| (|Symbol|)))))) ((~= #1=(#2=(#3=(|Boolean|) $ $) NIL (OR #4=(|has| #5=(|Record| (|:| |key| |#1|) (|:| |entry| |#2|)) #6=(|BasicType|)) #7=(|has| |#2| #6#)) ELT)) (|value| #8=(#9=(#5# $) NIL T ELT)) (|third| #8#) (|tail| #10=(#11=($ $) NIL T ELT)) (|table| (#12=($) NIL T ELT) #13=(#14=($ #15=(|List| #5#)) NIL T ELT)) (|swap!| ((#16=(|Void|) $ |#1| |#1|) NIL #17=(|has| $ (|ShallowlyMutableAggregate| |#2|)) ELT) ((#16# $ #18=(|Integer|) #18#) NIL #19=(|has| $ (|ShallowlyMutableAggregate| #5#)) ELT)) (|split!| (#20=($ $ #18#) NIL #19# ELT)) (|sorted?| ((#3# #21=(|Mapping| #3# #5# #5#) $) NIL T ELT) (#22=(#3# $) NIL #23=(|has| #5# #24=(|OrderedSet|)) ELT)) (|sort!| (#25=($ #21# $) NIL #19# ELT) (#11# NIL (AND #19# #23#) ELT)) (|sort| (#25# NIL T ELT) (#11# NIL #23# ELT)) (|size?| #26=((#3# $ #27=(|NonNegativeInteger|)) NIL T ELT)) (|setvalue!| #28=(#29=(#5# $ #5#) NIL #19# ELT)) (|setrest!| (#30=($ $ $) 35 #19# ELT)) (|setlast!| #28#) (|setfirst!| (#29# 37 #19# ELT)) (|setelt| (#31=(|#2| $ |#1| |#2|) 60 #17# ELT) #32=(#33=(#5# $ #18# #5#) NIL #19# ELT) ((#5# $ #34=(|UniversalSegment| #18#) #5#) NIL #19# ELT) ((#5# $ #35="last" #5#) NIL #19# ELT) (($ $ #36="rest" $) NIL #19# ELT) ((#5# $ #37="first" #5#) NIL #19# ELT) ((#5# $ #38="value" #5#) NIL #19# ELT)) (|setchildren!| (($ $ #39=(|List| $)) NIL #19# ELT)) (|select!| #40=(#41=($ #42=(|Mapping| #3# #5#) $) NIL #43=(|has| $ (|FiniteAggregate| #5#)) ELT) #44=(#41# NIL T ELT)) (|select| #40# #40#) (|second| #8#) (|search| (#45=((|Union| |#2| #46="failed") |#1| $) 45 T ELT)) (|sample| (#12# NIL T CONST)) (|reverse!| #47=(#11# NIL #19# ELT)) (|reverse| #10#) (|rest| #48=(($ $ #27#) NIL T ELT) (#11# 31 T ELT)) (|removeDuplicates!| (#11# NIL #4# ELT)) (|removeDuplicates| (#11# NIL #49=(AND #43# #4#) ELT)) (|remove!| (#50=($ #5# $) NIL #43# ELT) #40# (#45# 63 T ELT) #44# (#50# NIL #4# ELT)) (|remove| #51=(#50# NIL #49# ELT) #40# #51# #40#) (|reduce| #52=((#5# #53=(|Mapping| #5# #5# #5#) $ #5# #5#) NIL #4# ELT) #54=((#5# #53# $ #5#) NIL T ELT) #55=((#5# #53# $) NIL T ELT) #52# #54# #55#) (|qsetelt!| (#31# NIL #17# ELT) #32#) (|qelt| #56=((|#2| $ |#1|) NIL T ELT) #57=((#5# $ #18#) NIL T ELT)) (|possiblyInfinite?| #58=(#22# NIL T ELT)) (|position| ((#18# #42# $) NIL T ELT) ((#18# #5# $) NIL #4# ELT) ((#18# #5# $ #18#) NIL #4# ELT)) (|nodes| #59=((#39# $) NIL T ELT)) (|node?| #60=(#2# NIL #4# ELT)) (|new| (($ #27# #5#) NIL T ELT)) (|more?| #26#) (|minIndex| #61=((|#1| $) NIL #62=(|has| |#1| #24#) ELT) (#63=(#18# $) 40 #64=(|has| #18# #24#) ELT)) (|min| #65=(#30# NIL #23# ELT)) (|merge!| #66=(($ #21# $ $) NIL T ELT) #65#) (|merge| #66# #65#) (|members| #67=(#68=(#15# $) 22 T ELT) #67#) (|member?| #69=(#70=(#3# #5# $) NIL #4# ELT) #69#) (|maxIndex| #61# (#63# 42 #64# ELT)) (|max| #65#) (|map!| #71=(($ (|Mapping| #5# #5#) . #72=($)) NIL T ELT) #73=(($ (|Mapping| |#2| |#2|) . #72#) NIL T ELT) #71#) (|map| #71# #73# #71# (($ (|Mapping| |#2| |#2| |#2|) $ $) NIL T ELT) (($ #53# $ $) NIL T ELT) #71#) (|list| (($ #5#) NIL T ELT)) (|less?| #26#) (|leaves| (#68# NIL T ELT)) (|leaf?| #58#) (|latex| (((|String|) $) 51 #74=(OR #75=(|has| #5# #76=(|SetCategory|)) #77=(|has| |#2| #76#)) ELT)) (|last| #48# #8#) (|keys| (#78=((|List| |#1|) $) 24 T ELT)) (|key?| #79=((#3# |#1| $) NIL T ELT)) (|inspect| #8#) (|insert!| (#50# NIL T ELT) #80=(($ #5# $ #18#) NIL T ELT) #81=(#82=($ $ $ #18#) NIL T ELT)) (|insert| #80# #81#) (|indices| (#78# NIL T ELT) (((|List| #18#) $) NIL T ELT)) (|index?| #79# ((#3# #18# $) NIL T ELT)) (|hash| (((|SingleInteger|) $) NIL #74# ELT)) (|first| ((|#2| $) NIL #62# ELT) #48# (#9# 29 T ELT)) (|find| #83=(((|Union| #5# #46#) #42# $) NIL T ELT) #83#) (|fill!| (($ $ |#2|) NIL #17# ELT) (#84=($ $ #5#) NIL #19# ELT)) (|extract!| #8#) (|explicitlyFinite?| #58#) (|every?| #85=((#3# #42# $) NIL T ELT) #85#) (|eval| #86=(($ $ (|List| #87=(|Equation| #5#))) NIL #88=(AND (|has| #5# (|Evalable| #5#)) #75#) ELT) #89=(($ $ #87#) NIL #88# ELT) #90=(($ $ #5# #5#) NIL #88# ELT) #91=(($ $ #15# #15#) NIL #88# ELT) (($ $ #92=(|List| |#2|) #92#) NIL #93=(AND (|has| |#2| (|Evalable| |#2|)) #77#) ELT) (($ $ |#2| |#2|) NIL #93# ELT) (($ $ #94=(|Equation| |#2|)) NIL #93# ELT) (($ $ (|List| #94#)) NIL #93# ELT) #91# #90# #89# #86# #91# #90# #89# #86#) (|eq?| (#2# NIL T ELT)) (|entry?| ((#3# |#2| $) NIL (AND (|has| $ (|FiniteAggregate| |#2|)) #7#) ELT) (#70# NIL #49# ELT)) (|entries| ((#92# $) NIL T ELT) (#68# 21 T ELT)) (|empty?| (#22# 20 T ELT)) (|empty| (#12# 16 T ELT)) (|elt| #56# (#31# NIL T ELT) (#33# NIL T ELT) #57# #95=(($ $ #34#) NIL T ELT) ((#5# $ #35#) NIL T ELT) (($ $ #36#) NIL T ELT) ((#5# $ #37#) NIL T ELT) ((#5# $ #38#) NIL T ELT)) (|distance| ((#18# $ $) NIL T ELT)) (|dictionary| (#12# 14 T ELT) (#14# 15 T ELT)) (|delete!| #96=(#20# NIL T ELT) #95#) (|delete| #96# #95#) (|cyclic?| #58#) (|cycleTail| #10#) (|cycleSplit!| #47#) (|cycleLength| (#97=(#27# $) NIL T ELT)) (|cycleEntry| #10#) (|count| #98=((#27# #5# $) NIL #4# ELT) #99=((#27# #42# $) NIL T ELT) #98# #99#) (|copyInto!| (#82# NIL #19# ELT)) (|copy| #10#) (|convert| ((#100=(|InputForm|) $) NIL (|has| #5# (|ConvertibleTo| #100#)) ELT)) (|construct| #13# #13#) (|concat!| #101=(#84# NIL T ELT) #102=(#30# NIL T ELT)) (|concat| #101# (($ #39#) NIL T ELT) (#50# 33 T ELT) #102#) (|coerce| ((#103=(|OutputForm|) $) NIL (OR (|has| #5# #104=(|CoercibleTo| #103#)) (|has| |#2| #104#)) ELT)) (|children| #59#) (|child?| #60#) (|before?| #1#) (|bag| #13#) (|assoc| (((|Maybe| #5#) |#1| $) 55 T ELT)) (|any?| #85# #85#) (>= #105=(#2# NIL #23# ELT)) (> #105#) (= #1#) (<= #105#) (< #105#) (|#| (#97# 27 T ELT))) @@ -106,18 +106,18 @@ NIL ((|monomial?| (((|Boolean|) $) 12 T ELT)) (|map| (($ (|Mapping| |#2| |#2|) $) 21 T ELT)) (* (($ (|PositiveInteger|) $) NIL T ELT) (($ (|NonNegativeInteger|) $) NIL T ELT) (($ #1=(|Integer|) $) NIL T ELT) (($ $ $) NIL T ELT) (($ $ |#2|) NIL T ELT) (($ |#2| $) NIL T ELT) (($ #2=(|Fraction| #1#) $) 25 T ELT) (($ $ #2#) NIL T ELT))) (((|AbelianMonoidRing&| |#1| |#2| |#3|) (CATEGORY |package| (SIGNATURE * (|#1| |#1| #1=(|Fraction| #2=(|Integer|)))) (SIGNATURE * (|#1| #1# |#1|)) (SIGNATURE |monomial?| ((|Boolean|) |#1|)) (SIGNATURE |map| (|#1| (|Mapping| |#2| |#2|) |#1|)) (SIGNATURE * (|#1| |#2| |#1|)) (SIGNATURE * (|#1| |#1| |#2|)) (SIGNATURE * (|#1| |#1| |#1|)) (SIGNATURE * (|#1| #2# |#1|)) (SIGNATURE * (|#1| (|NonNegativeInteger|) |#1|)) (SIGNATURE * (|#1| (|PositiveInteger|) |#1|))) (|AbelianMonoidRing| |#2| |#3|) (|Ring|) (|OrderedAbelianMonoid|)) (T |AbelianMonoidRing&|)) NIL -((~= (#1=((|Boolean|) $ $) 7 T ELT)) (|zero?| ((#2=(|Boolean|) $) 22 T ELT)) (|unitNormal| (((|Record| (|:| |unit| $) (|:| |canonical| $) (|:| |associate| $)) $) 72 (|has| |#1| . #3=((|IntegralDomain|))) ELT)) (|unitCanonical| (($ $) 73 (|has| |#1| . #3#) ELT)) (|unit?| ((#4=(|Boolean|) $) 75 (|has| |#1| . #3#) ELT)) (|subtractIfCan| (((|Union| $ "failed") $ $) 26 T ELT)) (|sample| (#5=($) 23 T CONST)) (|reductum| (($ $) 81 T ELT)) (|recip| (((|Union| $ "failed") $) 42 T ELT)) (|opposite?| ((#2# $ $) 20 T ELT)) (|one?| (((|Boolean|) $) 44 T ELT)) (|monomial?| (((|Boolean|) $) 83 T ELT)) (|monomial| (($ |#1| |#2|) 82 T ELT)) (|map| (($ (|Mapping| |#1| |#1|) $) 87 T ELT)) (|leadingMonomial| (($ $) 85 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T) ((|AbelianMonoid|) . T) ((|AbelianSemiGroup|) . T) ((|Algebra| #1=(|Fraction| (|Integer|))) |has| |#1| (|Algebra| (|Fraction| (|Integer|)))) ((|Algebra| |#1|) |has| |#1| (|CommutativeRing|)) ((|Algebra| $) |has| |#1| (|IntegralDomain|)) ((|BasicType|) . T) ((|BiModule| #1# #1#) |has| |#1| (|Algebra| (|Fraction| (|Integer|)))) ((|BiModule| |#1| |#1|) . T) ((|BiModule| $ $) OR (|has| |#1| (|IntegralDomain|)) (|has| |#1| (|CommutativeRing|))) ((|CancellationAbelianMonoid|) . T) ((|CharacteristicNonZero|) |has| |#1| (|CharacteristicNonZero|)) ((|CharacteristicZero|) |has| |#1| (|CharacteristicZero|)) ((|CoercibleFrom| #1#) |has| |#1| (|Algebra| (|Fraction| (|Integer|)))) ((|CoercibleFrom| (|Integer|)) . T) ((|CoercibleFrom| |#1|) |has| |#1| (|CommutativeRing|)) ((|CoercibleFrom| $) |has| |#1| (|IntegralDomain|)) ((|CoercibleTo| (|OutputForm|)) . T) ((|CommutativeRing|) OR (|has| |#1| (|IntegralDomain|)) (|has| |#1| (|CommutativeRing|))) ((|EntireRing|) |has| |#1| (|IntegralDomain|)) ((|Functorial| |#1|) . T) ((|IntegralDomain|) |has| |#1| (|IntegralDomain|)) ((|Join|) . T) ((|LeftLinearSet| #1#) |has| |#1| (|Algebra| (|Fraction| (|Integer|)))) ((|LeftLinearSet| (|Integer|)) . T) ((|LeftLinearSet| |#1|) . T) ((|LeftLinearSet| $) . T) ((|LeftModule| #1#) |has| |#1| (|Algebra| (|Fraction| (|Integer|)))) ((|LeftModule| |#1|) . T) ((|LeftModule| $) . T) ((|LinearSet| #1#) |has| |#1| (|Algebra| (|Fraction| (|Integer|)))) ((|LinearSet| |#1|) |has| |#1| (|CommutativeRing|)) ((|LinearSet| $) |has| |#1| (|IntegralDomain|)) ((|Module| #1#) |has| |#1| (|Algebra| (|Fraction| (|Integer|)))) ((|Module| |#1|) |has| |#1| (|CommutativeRing|)) ((|Module| $) |has| |#1| (|IntegralDomain|)) ((|Monoid|) . T) ((|RightLinearSet| #1#) |has| |#1| (|Algebra| (|Fraction| (|Integer|)))) ((|RightLinearSet| |#1|) . T) ((|RightLinearSet| $) OR (|has| |#1| (|IntegralDomain|)) (|has| |#1| (|CommutativeRing|))) ((|RightModule| #1#) |has| |#1| (|Algebra| (|Fraction| (|Integer|)))) ((|RightModule| |#1|) . T) ((|RightModule| $) OR (|has| |#1| (|IntegralDomain|)) (|has| |#1| (|CommutativeRing|))) ((|Ring|) . T) ((|Rng|) . T) ((|SemiGroup|) . T) ((|SemiRing|) . T) ((|SetCategory|) . T) ((|Type|) . T)) -((~= #1=(#2=(#3=(|Boolean|) $ $) NIL T ELT)) (|zerosOf| #4=((#5=(|List| $) #6=(|SparseUnivariatePolynomial| $) #7=(|Symbol|)) NIL T ELT) #8=((#5# #6#) NIL T ELT) #9=((#5# #10=(|Polynomial| $)) NIL T ELT)) (|zeroOf| #11=(($ #6# #7#) NIL T ELT) #12=(($ #6#) NIL T ELT) #13=(($ #10#) NIL T ELT)) (|zero?| (#14=(#3# $) 9 T ELT)) (|unitNormal| (((|Record| (|:| |unit| $) (|:| |canonical| $) (|:| |associate| $)) $) NIL T ELT)) (|unitCanonical| #15=(#16=($ $) NIL T ELT)) (|unit?| #17=(#14# NIL T ELT)) (|tower| #18=((#19=(|List| #20=(|Kernel| $)) $) NIL T ELT)) (|subtractIfCan| #21=((#22=(|Union| $ #23="failed") $ $) NIL T ELT)) (|subst| #24=(($ $ #25=(|Equation| $)) NIL T ELT) #26=(($ $ (|List| #25#)) NIL T ELT) #27=(($ $ #19# #5#) NIL T ELT)) (|squareFreePart| #15#) (|squareFree| #28=(((|Factored| $) $) NIL T ELT)) (|sqrt| #15#) (|sizeLess?| #1#) (|sample| (#29=($) NIL T CONST)) (|rootsOf| #4# #8# #9#) (|rootOf| #11# #12# #13#) (|retractIfCan| #30=(((|Union| #20# . #31=(#23#)) . #32=($)) NIL T ELT) (((|Union| #33=(|Integer|) . #31#) . #32#) NIL T ELT) (((|Union| #34=(|Fraction| #33#) . #31#) . #32#) NIL T ELT)) (|retract| ((#20# . #35=($)) NIL T ELT) ((#33# . #35#) NIL T ELT) ((#34# . #35#) NIL T ELT)) (|rem| #36=(($ $ $) NIL T ELT)) (|reducedSystem| ((#37=(|Record| (|:| |mat| #38=(|Matrix| #33#)) (|:| |vec| (|Vector| #33#))) . #39=(#40=(|Matrix| $) #41=(|Vector| $))) NIL T ELT) ((#38# . #42=(#40#)) NIL T ELT) ((#43=(|Record| (|:| |mat| #44=(|Matrix| #34#)) (|:| |vec| (|Vector| #34#))) . #39#) NIL T ELT) ((#44# . #42#) NIL T ELT)) (|reduce| #15#) (|recip| ((#22# $) NIL T ELT)) (|quo| #36#) (|principalIdeal| (((|Record| (|:| |coef| #5#) #45=(|:| |generator| $)) #5#) NIL T ELT)) (|prime?| #17#) (|paren| #15# #46=(($ #5#) NIL T ELT)) (|opposite?| #1#) (|operators| ((#47=(|List| #48=(|BasicOperator|)) $) NIL T ELT)) (|operator| ((#48# #48#) NIL T ELT)) (|one?| (#14# 11 T ELT)) (|odd?| #49=(#14# NIL (|has| $ (|RetractableTo| #33#)) ELT)) (|numer| #50=((#51=(|SparseMultivariatePolynomial| #33# #20#) $) NIL T ELT)) (|nthRoot| #52=(($ $ #33#) NIL T ELT)) (|norm| ((#6# #6# #20#) NIL T ELT) ((#6# #6# #19#) NIL T ELT) (($ $ #20#) NIL T ELT) (($ $ #19#) NIL T ELT)) (|multiEuclidean| (((|Union| #5# #23#) #5# $) NIL T ELT)) (|minPoly| ((#6# #20#) NIL #53=(|has| $ (|Ring|)) ELT)) (|map| (($ #54=(|Mapping| $ $) #20#) NIL T ELT)) (|mainKernel| #30#) (|leftReducedSystem| ((#37# . #55=(#41# $)) NIL T ELT) ((#38# . #56=(#41#)) NIL T ELT) ((#43# . #55#) NIL T ELT) ((#44# . #56#) NIL T ELT)) (|lcm| #46# #36#) (|latex| (((|String|) $) NIL T ELT)) (|kernels| #18#) (|kernel| #57=(($ #48# $) NIL T ELT) #58=(($ #48# #5#) NIL T ELT)) (|is?| ((#3# $ #48#) NIL T ELT) #59=((#3# $ #7#) NIL T ELT)) (|inv| #15#) (|height| #60=((#61=(|NonNegativeInteger|) $) NIL T ELT)) (|hash| (((|SingleInteger|) $) NIL T ELT)) (|gcdPolynomial| ((#6# #6# #6#) NIL T ELT)) (|gcd| #46# #36#) (|freeOf?| #1# #59#) (|factor| #28#) (|extendedEuclidean| (((|Union| (|Record| #62=(|:| |coef1| $) #63=(|:| |coef2| $)) #23#) $ $ $) NIL T ELT) (((|Record| #62# #63# #45#) $ $) NIL T ELT)) (|exquo| #21#) (|expressIdealMember| (((|Maybe| #5#) #5# $) NIL T ELT)) (|even?| #49#) (|eval| (($ $ #20# $) NIL T ELT) #27# #26# #24# (($ $ $ $) NIL T ELT) (($ $ #5# #5#) NIL T ELT) (($ $ #64=(|List| #7#) #65=(|List| #54#)) NIL T ELT) (($ $ #64# #66=(|List| #67=(|Mapping| $ #5#))) NIL T ELT) (($ $ #7# #67#) NIL T ELT) (($ $ #7# #54#) NIL T ELT) (($ $ #47# #65#) NIL T ELT) (($ $ #47# #66#) NIL T ELT) (($ $ #48# #67#) NIL T ELT) (($ $ #48# #54#) NIL T ELT)) (|euclideanSize| #60#) (|elt| #57# (($ #48# $ $) NIL T ELT) (($ #48# $ $ $) NIL T ELT) (($ #48# $ $ $ $) NIL T ELT) #58#) (|divide| (((|Record| (|:| |quotient| $) (|:| |remainder| $)) $ $) NIL T ELT)) (|distribute| #15# #36#) (|differentiate| #15# #68=(($ $ #61#) NIL T ELT)) (|denom| #50#) (|definingPolynomial| (#16# NIL #53# ELT)) (|convert| ((#69=(|Float|) . #70=($)) NIL T ELT) (((|DoubleFloat|) . #70#) NIL T ELT) (((|Complex| #69#) . #70#) NIL T ELT)) (|coerce| (((|OutputForm|) $) NIL T ELT) (($ #20#) NIL T ELT) (($ #34#) NIL T ELT) #15# (($ #33#) NIL T ELT) (($ #51#) NIL T ELT)) (|characteristic| ((#61#) NIL T CONST)) (|box| #15# #46#) (|belong?| ((#3# #48#) NIL T ELT)) (|before?| #1#) (|associates?| #1#) (|annihilate?| #1#) (|Zero| (#29# 6 T CONST)) (|One| (#29# 10 T CONST)) (D #15# #68#) (= (#2# 13 T ELT)) (/ #36#) (- #36# #15#) (+ #36#) (** #71=(($ $ #34#) NIL T ELT) #52# #68# (($ $ #72=(|PositiveInteger|)) NIL T ELT)) (* (($ #34# . #73=($)) NIL T ELT) #71# #36# (($ #33# . #73#) NIL T ELT) (($ #61# $) NIL T ELT) (($ #72# $) NIL T ELT))) +((~= #1=(#2=(#3=(|Boolean|) $ $) NIL T ELT)) (|zerosOf| #4=((#5=(|List| $) #6=(|SparseUnivariatePolynomial| $) #7=(|Symbol|)) NIL T ELT) #8=((#5# #6#) NIL T ELT) #9=((#5# #10=(|Polynomial| $)) NIL T ELT)) (|zeroOf| #11=(($ #6# #7#) NIL T ELT) #12=(($ #6#) NIL T ELT) #13=(($ #10#) NIL T ELT)) (|zero?| (#14=(#3# $) 9 T ELT)) (|unitNormal| (((|Record| (|:| |unit| $) (|:| |canonical| $) (|:| |associate| $)) $) NIL T ELT)) (|unitCanonical| #15=(#16=($ $) NIL T ELT)) (|unit?| #17=(#14# NIL T ELT)) (|tower| #18=((#19=(|List| #20=(|Kernel| $)) $) NIL T ELT)) (|subtractIfCan| (((|Maybe| $) $ $) NIL T ELT)) (|subst| #21=(($ $ #22=(|Equation| $)) NIL T ELT) #23=(($ $ (|List| #22#)) NIL T ELT) #24=(($ $ #19# #5#) NIL T ELT)) (|squareFreePart| #15#) (|squareFree| #25=(((|Factored| $) $) NIL T ELT)) (|sqrt| #15#) (|sizeLess?| #1#) (|sample| (#26=($) NIL T CONST)) (|rootsOf| #4# #8# #9#) (|rootOf| #11# #12# #13#) (|retractIfCan| #27=(((|Union| #20# . #28=(#29="failed")) . #30=($)) NIL T ELT) (((|Union| #31=(|Integer|) . #28#) . #30#) NIL T ELT) (((|Union| #32=(|Fraction| #31#) . #28#) . #30#) NIL T ELT)) (|retract| ((#20# . #33=($)) NIL T ELT) ((#31# . #33#) NIL T ELT) ((#32# . #33#) NIL T ELT)) (|rem| #34=(($ $ $) NIL T ELT)) (|reducedSystem| ((#35=(|Record| (|:| |mat| #36=(|Matrix| #31#)) (|:| |vec| (|Vector| #31#))) . #37=(#38=(|Matrix| $) 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(|mainKernel| #27#) (|leftReducedSystem| ((#35# . #54=(#39# $)) NIL T ELT) ((#36# . #55=(#39#)) NIL T ELT) ((#41# . #54#) NIL T ELT) ((#42# . #55#) NIL T ELT)) (|lcm| #45# #34#) (|latex| (((|String|) $) NIL T ELT)) (|kernels| #18#) (|kernel| #56=(($ #47# $) NIL T ELT) #57=(($ #47# #5#) NIL T ELT)) (|is?| ((#3# $ #47#) NIL T ELT) #58=((#3# $ #7#) NIL T ELT)) (|inv| #15#) (|height| #59=((#60=(|NonNegativeInteger|) $) NIL T ELT)) (|hash| (((|SingleInteger|) $) NIL T ELT)) (|gcdPolynomial| ((#6# #6# #6#) NIL T ELT)) (|gcd| #45# #34#) (|freeOf?| #1# #58#) (|factor| #25#) (|extendedEuclidean| (((|Union| (|Record| #61=(|:| |coef1| $) #62=(|:| |coef2| $)) #29#) $ $ $) NIL T ELT) (((|Record| #61# #62# #44#) $ $) NIL T ELT)) (|exquo| ((#43# $ $) NIL T ELT)) (|expressIdealMember| (((|Maybe| #5#) #5# $) NIL T ELT)) (|even?| #48#) (|eval| (($ $ #20# $) NIL T ELT) #24# #23# #21# (($ $ $ $) NIL T ELT) (($ $ #5# #5#) NIL T ELT) (($ $ #63=(|List| #7#) #64=(|List| #53#)) NIL T ELT) (($ $ #63# 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CONST)) (D #15# #67#) (= (#2# 13 T ELT)) (/ #34#) (- #34# #15#) (+ #34#) (** #70=(($ $ #32#) NIL T ELT) #51# #67# (($ $ #71=(|PositiveInteger|)) NIL T ELT)) (* (($ #32# . #72=($)) NIL T ELT) #70# #34# (($ #31# . #72#) NIL T ELT) (($ #60# $) NIL T ELT) (($ #71# $) NIL T ELT))) (((|AlgebraicNumber|) (|Join| (|ExpressionSpace|) (|AlgebraicallyClosedField|) (|RetractableTo| #1=(|Integer|)) (|RetractableTo| #2=(|Fraction| #1#)) (|LinearlyExplicitRingOver| #1#) (|RealConstant|) (|LinearlyExplicitRingOver| #2#) (|CharacteristicZero|) (|ConvertibleTo| (|Complex| (|Float|))) (|DifferentialRing|) (|CoercibleFrom| #3=(|SparseMultivariatePolynomial| #1# #4=(|Kernel| $))) (CATEGORY |domain| (SIGNATURE |numer| #5=(#3# $)) (SIGNATURE |denom| #5#) (SIGNATURE |reduce| ($ $)) (SIGNATURE |norm| (#6=(|SparseUnivariatePolynomial| $) #6# #4#)) (SIGNATURE |norm| (#6# #6# #7=(|List| #4#))) (SIGNATURE |norm| ($ $ #4#)) (SIGNATURE |norm| ($ $ #7#))))) (T |AlgebraicNumber|)) ((|numer| #1=(*1 *2 *1) #2=(AND 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(|AnonymousFunction|)))) (|body| #1# (AND (|isDomain| *2 (|Syntax|)) #2#))) -((~= #1=((#2=(|Boolean|) $ $) NIL T ELT)) (|zero?| (#3=(#2# $) 86 T ELT)) (|subtractIfCan| ((#4=(|Union| $ #5="failed") $ $) NIL T ELT)) (|sample| (#6=($) NIL T CONST)) (|retractable?| (#3# 31 T ELT)) (|retractIfCan| (((|Union| |#1| #5#) $) 34 T ELT)) (|retract| (#7=(|#1| $) 35 T ELT)) (|reductum| (#8=($ $) 41 T ELT)) (|recip| ((#4# $) NIL T ELT)) (|opposite?| #1#) (|one?| (#3# NIL T ELT)) (|map| (($ (|Mapping| |#1| |#1|) $) NIL T ELT)) (|leadingCoefficient| (#7# 32 T ELT)) (|leadingBasisTerm| (#8# 75 T ELT)) (|latex| (((|String|) $) NIL T ELT)) (|homogeneous?| (#3# 44 T ELT)) (|hash| (((|SingleInteger|) $) NIL T ELT)) (|generator| (($ #9=(|NonNegativeInteger|)) 73 T ELT)) (|exp| (($ (|List| #10=(|Integer|))) 74 T ELT)) (|degree| ((#9# $) 45 T ELT)) (|coerce| (((|OutputForm|) $) 92 T ELT) (($ #10#) 70 T ELT) (($ |#1|) 68 T ELT)) (|coefficient| ((|#1| $ $) 29 T ELT)) (|characteristic| ((#9#) 72 T CONST)) (|before?| #1#) (|annihilate?| #1#) (|Zero| (#6# 46 T CONST)) (|One| (#6# 17 T CONST)) (= #1#) (- (#8# NIL T ELT) (#11=($ $ $) NIL T ELT)) (+ (#11# 65 T ELT)) (** (($ $ #12=(|PositiveInteger|)) NIL T ELT) (($ $ #9#) NIL T ELT)) (* (($ #12# $) NIL T ELT) (($ #9# $) NIL T ELT) (($ #10# . #13=($)) NIL T ELT) (#11# 66 T ELT) (($ |#1| . #13#) 59 T ELT))) +((~= #1=((#2=(|Boolean|) $ $) NIL T ELT)) (|zero?| (#3=(#2# $) 86 T ELT)) (|subtractIfCan| (((|Maybe| $) $ $) NIL T ELT)) (|sample| (#4=($) NIL T CONST)) (|retractable?| (#3# 31 T ELT)) (|retractIfCan| (((|Union| |#1| #5="failed") $) 34 T ELT)) (|retract| (#6=(|#1| $) 35 T ELT)) (|reductum| (#7=($ $) 41 T ELT)) (|recip| (((|Union| $ #5#) $) NIL T ELT)) (|opposite?| #1#) (|one?| (#3# NIL T ELT)) (|map| (($ (|Mapping| |#1| |#1|) $) NIL T ELT)) (|leadingCoefficient| (#6# 32 T ELT)) (|leadingBasisTerm| (#7# 75 T ELT)) (|latex| (((|String|) $) NIL T ELT)) (|homogeneous?| (#3# 44 T ELT)) (|hash| (((|SingleInteger|) $) NIL T ELT)) (|generator| (($ #8=(|NonNegativeInteger|)) 73 T ELT)) (|exp| (($ (|List| #9=(|Integer|))) 74 T ELT)) (|degree| ((#8# $) 45 T ELT)) (|coerce| (((|OutputForm|) $) 92 T ELT) (($ #9#) 70 T ELT) (($ |#1|) 68 T ELT)) (|coefficient| ((|#1| $ $) 29 T ELT)) (|characteristic| ((#8#) 72 T CONST)) (|before?| #1#) (|annihilate?| #1#) (|Zero| (#4# 46 T CONST)) (|One| (#4# 17 T CONST)) (= #1#) (- (#7# NIL T ELT) (#10=($ $ $) NIL T ELT)) (+ (#10# 65 T ELT)) (** (($ $ #11=(|PositiveInteger|)) NIL T ELT) (($ $ #8#) NIL T ELT)) (* (($ #11# $) NIL T ELT) (($ #8# $) NIL T ELT) (($ #9# . #12=($)) NIL T ELT) (#10# 66 T ELT) (($ |#1| . #12#) 59 T ELT))) (((|AntiSymm| |#1| |#2|) (|Join| (|LeftAlgebra| |#1|) (|RetractableTo| |#1|) (|Functorial| |#1|) (CATEGORY |domain| (SIGNATURE |leadingCoefficient| (|#1| $)) (SIGNATURE |leadingBasisTerm| #1=($ $)) (SIGNATURE |reductum| #1#) (SIGNATURE |coefficient| (|#1| $ $)) (SIGNATURE |generator| ($ #2=(|NonNegativeInteger|))) (SIGNATURE |exp| ($ (|List| (|Integer|)))) (SIGNATURE |homogeneous?| #3=((|Boolean|) $)) (SIGNATURE |retractable?| #3#) (SIGNATURE |degree| (#2# $)))) (|Ring|) (|List| (|Symbol|))) (T |AntiSymm|)) ((|leadingCoefficient| #1=(*1 *2 *1) #2=(AND #3=(|ofCategory| *2 #4=(|Ring|)) #5=(|isDomain| *1 (|AntiSymm| *2 *3)) #6=(|ofType| *3 #7=(|List| (|Symbol|))))) (|leadingBasisTerm| #8=(*1 *1 *1) #9=(AND #5# #3# #6#)) (|reductum| #8# #9#) (|coefficient| (*1 *2 *1 *1) #2#) (|generator| #10=(*1 *1 *2) #11=(AND (|isDomain| *2 (|NonNegativeInteger|)) #12=(|isDomain| *1 (|AntiSymm| *3 *4)) #13=(|ofCategory| *3 #4#) #14=(|ofType| *4 #7#))) (|exp| #10# (AND (|isDomain| *2 (|List| (|Integer|))) #12# #13# #14#)) (|homogeneous?| #1# #15=(AND (|isDomain| *2 (|Boolean|)) #12# #13# #14#)) (|retractable?| #1# #15#) (|degree| #1# #11#)) ((~= #1=(#2=((|Boolean|) $ $) NIL T ELT)) (|obj| ((#3=(|None|) $) 8 T ELT)) (|latex| (((|String|) $) NIL T ELT)) (|hash| (((|SingleInteger|) $) NIL T ELT)) (|dom| ((#4=(|SExpression|) $) 10 T ELT)) (|coerce| (((|OutputForm|) $) 15 T ELT)) (|before?| #1#) (|any| (($ #4# #3#) 16 T ELT)) (= (#2# 12 T ELT))) @@ -179,7 +179,7 @@ NIL NIL (((|AttributeRegistry|) (|Category|)) (T |AttributeRegistry|)) NIL -(|Join| (CATEGORY |package| (ATTRIBUTE (|commutative| "*")) (ATTRIBUTE |unitsKnown|) (ATTRIBUTE |leftUnitary|) (ATTRIBUTE |rightUnitary|) (ATTRIBUTE |noZeroDivisors|) (ATTRIBUTE |canonicalUnitNormal|) (ATTRIBUTE |canonicalsClosed|) (ATTRIBUTE |arbitraryPrecision|) (ATTRIBUTE |partiallyOrderedSet|) (ATTRIBUTE |central|) (ATTRIBUTE |noetherian|) (ATTRIBUTE |additiveValuation|) (ATTRIBUTE |multiplicativeValuation|) (ATTRIBUTE |NullSquare|) (ATTRIBUTE |JacobiIdentity|) (ATTRIBUTE |canonical|))) +(|Join| (CATEGORY |package| (ATTRIBUTE (|commutative| "*")) (ATTRIBUTE |noZeroDivisors|) (ATTRIBUTE |canonicalUnitNormal|) (ATTRIBUTE |partiallyOrderedSet|) (ATTRIBUTE |additiveValuation|) (ATTRIBUTE |multiplicativeValuation|) (ATTRIBUTE |canonical|))) ((~= #1=(#2=(#3=(|Boolean|) $ $) NIL T ELT)) (|sample| (#4=($) NIL T CONST)) (|recip| (((|Union| $ "failed") $) NIL T ELT)) (|one?| ((#3# $) NIL T ELT)) (|morphism| (($ #5=(|Mapping| |#1| |#1|)) 27 T ELT) (($ #5# #5#) 26 T ELT) (($ (|Mapping| |#1| |#1| #6=(|Integer|))) 24 T ELT)) (|latex| (((|String|) $) NIL T ELT)) (|inv| (($ $) 16 T ELT)) (|hash| (((|SingleInteger|) $) NIL T ELT)) (|elt| ((|#1| $ |#1|) 13 T ELT)) (|conjugate| #7=(#8=($ $ $) NIL T ELT)) (|commutator| #7#) (|coerce| (((|OutputForm|) $) 22 T ELT)) (|before?| #1#) (|One| (#4# 8 T CONST)) (= (#2# 10 T ELT)) (/ #7#) (** (($ $ (|PositiveInteger|)) 30 T ELT) (($ $ (|NonNegativeInteger|)) NIL T ELT) (($ $ #6#) 18 T ELT)) (* (#8# 31 T ELT))) (((|Automorphism| |#1|) (|Join| (|Group|) (|Eltable| |#1| |#1|) (CATEGORY |domain| (SIGNATURE |morphism| ($ #1=(|Mapping| |#1| |#1|))) (SIGNATURE |morphism| ($ #1# #1#)) (SIGNATURE |morphism| ($ (|Mapping| |#1| |#1| (|Integer|)))))) (|Ring|)) (T |Automorphism|)) ((|morphism| #1=(*1 *1 *2) #2=(AND (|isDomain| *2 (|Mapping| *3 *3)) #3=(|ofCategory| *3 (|Ring|)) #4=(|isDomain| *1 (|Automorphism| *3)))) (|morphism| (*1 *1 *2 *2) #2#) (|morphism| #1# (AND (|isDomain| *2 (|Mapping| *3 *3 (|Integer|))) #3# #4#))) @@ -208,7 +208,7 @@ NIL ((|bag| (*1 *1 *2) (AND (|isDomain| *2 (|List| *3)) (|ofCategory| *3 (|Type|)) (|ofCategory| *1 (|BagAggregate| *3)))) (|extract!| (*1 *2 *1) (AND (|ofCategory| *1 (|BagAggregate| *2)) (|ofCategory| *2 (|Type|)))) (|insert!| (*1 *1 *2 *1) (AND (|ofCategory| *1 (|BagAggregate| *2)) (|ofCategory| *2 (|Type|)))) (|inspect| (*1 *2 *1) (AND (|ofCategory| *1 (|BagAggregate| *2)) (|ofCategory| *2 (|Type|))))) (|Join| (|HomogeneousAggregate| |t#1|) (|ShallowlyMutableAggregate| |t#1|) (CATEGORY |domain| (SIGNATURE |bag| ($ (|List| |t#1|))) (SIGNATURE |extract!| (|t#1| $)) (SIGNATURE |insert!| ($ |t#1| $)) (SIGNATURE |inspect| (|t#1| $)))) (((|Aggregate|) . T) ((|BasicType|) OR (|has| |#1| (|SetCategory|)) (|has| |#1| (|BasicType|))) ((|CoercibleTo| (|OutputForm|)) OR (|has| |#1| (|SetCategory|)) (|has| |#1| (|CoercibleTo| (|OutputForm|)))) ((|Evalable| |#1|) AND (|has| |#1| (|Evalable| |#1|)) (|has| |#1| (|SetCategory|))) ((|Functorial| |#1|) . T) ((|HomogeneousAggregate| |#1|) . T) ((|InnerEvalable| |#1| |#1|) AND (|has| |#1| (|Evalable| |#1|)) (|has| |#1| (|SetCategory|))) ((|Join|) . T) ((|SetCategory|) |has| |#1| (|SetCategory|)) ((|ShallowlyMutableAggregate| |#1|) . T) ((|Type|) . T)) -((~= #1=(#2=(#3=(|Boolean|) $ $) NIL T ELT)) (|zero?| #4=(#5=(#3# $) NIL T ELT)) (|wholePart| (#6=(#7=(|Integer|) $) NIL #8=(|has| #7# (|EuclideanDomain|)) ELT)) (|unitNormal| (((|Record| (|:| |unit| $) (|:| |canonical| $) (|:| |associate| $)) $) NIL T ELT)) (|unitCanonical| #9=(#10=($ $) NIL T ELT)) (|unit?| #4#) (|subtractIfCan| #11=((#12=(|Union| $ #13="failed") $ $) NIL T ELT)) (|squareFreePolynomial| #14=(((|Factored| #15=(|SparseUnivariatePolynomial| $)) #15#) NIL #16=(|has| #7# (|PolynomialFactorizationExplicit|)) ELT)) (|squareFreePart| #9#) (|squareFree| #17=(((|Factored| $) $) NIL T ELT)) (|solveLinearPolynomialEquation| (((|Union| #18=(|List| #15#) #13#) #18# #15#) NIL #16# ELT)) (|sizeLess?| #1#) (|sign| (#6# NIL #19=(|has| #7# (|OrderedIntegralDomain|)) ELT)) (|sample| #20=(#21=($) NIL T CONST)) (|retractIfCan| (#22=((|Union| #7# . #23=(#13#)) . #24=($)) NIL T ELT) (((|Union| #25=(|Symbol|) . #23#) . #24#) NIL #26=(|has| #7# (|RetractableTo| #25#)) ELT) (((|Union| #27=(|Fraction| #7#) . #23#) . #24#) NIL #28=(|has| #7# (|RetractableTo| #7#)) ELT) (#22# NIL #28# ELT)) (|retract| #29=(#6# NIL T ELT) ((#25# $) NIL #26# ELT) (#30=(#27# $) NIL #28# ELT) (#6# NIL #28# ELT)) (|rem| #31=(#32=($ $ $) NIL T ELT)) (|reducedSystem| (#33=(#34=(|Matrix| #7#) #35=(|Matrix| $)) NIL #36=(|has| #7# (|LinearlyExplicitRingOver| #7#)) ELT) (#37=(#38=(|Record| (|:| |mat| #34#) (|:| |vec| (|Vector| #7#))) #35# #39=(|Vector| $)) NIL #36# ELT) (#37# NIL T ELT) (#33# NIL T ELT)) (|recip| ((#12# $) NIL T ELT)) (|random| (#21# NIL #40=(|has| #7# (|IntegerNumberSystem|)) ELT)) (|quo| #31#) (|principalIdeal| (((|Record| (|:| |coef| #41=(|List| $)) #42=(|:| |generator| $)) #41#) NIL T ELT)) (|prime?| #4#) (|positive?| #43=(#5# NIL #19# ELT)) (|patternMatch| ((#44=(|PatternMatchResult| #7# . #45=($)) $ #46=(|Pattern| #7#) #44#) NIL (|has| #7# (|PatternMatchable| #7#)) ELT) ((#47=(|PatternMatchResult| #48=(|Float|) . #45#) $ #49=(|Pattern| #48#) #47#) NIL (|has| #7# (|PatternMatchable| #48#)) ELT)) (|opposite?| #1#) (|one?| #4#) (|numerator| #9#) (|numer| #29#) (|nextItem| (#50=((|Maybe| $) $) NIL #51=(|has| #7# (|StepThrough|)) ELT)) (|negative?| #43#) (|multiEuclidean| (((|Union| #41# #13#) #41# $) NIL T ELT)) (|min| #52=(#32# NIL #53=(|has| #7# (|OrderedSet|)) ELT)) (|max| #52#) (|map| (($ #54=(|Mapping| #7# #7#) $) NIL T ELT)) (|leftReducedSystem| (#55=(#34# #39#) NIL #36# ELT) (#56=(#38# #39# $) NIL #36# ELT) (#56# NIL T ELT) (#55# NIL T ELT)) (|lcm| #31# #57=(($ #41#) NIL T ELT)) (|latex| (((|String|) $) NIL T ELT)) (|inv| #9#) (|init| (#21# NIL #51# CONST)) (|hash| (((|SingleInteger|) $) NIL T ELT)) (|gcdPolynomial| ((#15# #15# #15#) NIL T ELT)) (|gcd| #31# #57#) (|fractionPart| (#10# NIL #8# ELT) #58=(#30# NIL T ELT)) (|floor| #59=(#6# NIL #40# ELT)) (|factorSquareFreePolynomial| #14#) (|factorPolynomial| #14#) (|factor| #17#) (|extendedEuclidean| (((|Record| #60=(|:| |coef1| $) #61=(|:| |coef2| $) #42#) $ $) NIL T ELT) (((|Union| (|Record| #60# #61#) #13#) $ $ $) NIL T ELT)) (|exquo| #11#) (|expressIdealMember| (((|Maybe| #41#) #41# $) NIL T ELT)) (|eval| (($ $ #62=(|List| #7#) #62#) NIL #63=(|has| #7# (|Evalable| #7#)) ELT) (($ $ #7# #7#) NIL #63# ELT) (($ $ #64=(|Equation| #7#)) NIL #63# ELT) (($ $ (|List| #64#)) NIL #63# ELT) (($ $ #65=(|List| #25#) #62#) NIL #66=(|has| #7# (|InnerEvalable| #25# #7#)) ELT) (($ $ #25# #7#) NIL #66# ELT)) (|euclideanSize| ((#67=(|NonNegativeInteger|) $) NIL T ELT)) (|elt| (#68=($ $ #7#) NIL (|has| #7# (|Eltable| #7# #7#)) ELT)) (|divide| (((|Record| (|:| |quotient| $) (|:| |remainder| $)) $ $) NIL T ELT)) (|differentiate| #69=(($ $ #54#) NIL T ELT) #70=(($ $ #54# #67#) NIL T ELT) #71=(($ $ #25#) NIL #72=(|has| #7# (|PartialDifferentialSpace| #25#)) ELT) #73=(($ $ #65#) NIL #72# ELT) #74=(($ $ #25# #67#) NIL #72# ELT) #75=(($ $ #65# (|List| #67#)) NIL #72# ELT) #76=(#10# NIL #77=(|has| #7# (|DifferentialSpace|)) ELT) #78=(#79=($ $ #67#) NIL #77# ELT)) (|denominator| #9#) (|denom| #29#) (|convert| ((#46# . #80=($)) NIL (|has| #7# (|ConvertibleTo| #46#)) ELT) ((#49# . #80#) NIL (|has| #7# (|ConvertibleTo| #49#)) ELT) ((#81=(|InputForm|) . #80#) NIL (|has| #7# (|ConvertibleTo| #81#)) ELT) ((#48# . #80#) NIL #82=(|has| #7# (|RealConstant|)) ELT) (((|DoubleFloat|) . #80#) NIL #82# ELT)) (|conditionP| (((|Union| #39# #13#) #35#) NIL #83=(AND (|has| $ #84=(|CharacteristicNonZero|)) #16#) ELT)) (|coerce| (((|OutputForm|) $) NIL T ELT) #85=(($ #7#) NIL T ELT) #9# (#86=($ #27#) 8 T ELT) #85# (($ #25#) NIL #26# ELT) #58# (((|RadixExpansion| 2) $) 10 T ELT)) (|charthRoot| (#50# NIL (OR #83# (|has| #7# #84#)) ELT)) (|characteristic| ((#67#) NIL T CONST)) (|ceiling| #59#) (|binary| (#86# 9 T ELT)) (|before?| #1#) (|associates?| #1#) (|annihilate?| #1#) (|abs| (#10# NIL #19# ELT)) (|Zero| #20#) (|One| #20#) (D #69# #70# #71# #73# #74# #75# #76# #78#) (>= #87=(#2# NIL #53# ELT)) (> #87#) (= #1#) (<= #87#) (< #87#) (/ #31# (($ #7# #7#) NIL T ELT)) (- #9# #31#) (+ #31#) (** (($ $ #88=(|PositiveInteger|)) NIL T ELT) (#79# NIL T ELT) #89=(#68# NIL T ELT)) (* (($ #88# $) NIL T ELT) (($ #67# $) NIL T ELT) #90=(($ #7# . #91=($)) NIL T ELT) #31# (($ $ #27#) NIL T ELT) (($ #27# . #91#) NIL T ELT) #90# #89#)) +((~= #1=(#2=(#3=(|Boolean|) $ $) NIL T ELT)) (|zero?| #4=(#5=(#3# $) NIL T ELT)) (|wholePart| (#6=(#7=(|Integer|) $) NIL #8=(|has| #7# (|EuclideanDomain|)) ELT)) (|unitNormal| (((|Record| (|:| |unit| $) (|:| |canonical| $) (|:| |associate| $)) $) NIL T ELT)) (|unitCanonical| #9=(#10=($ $) NIL T ELT)) (|unit?| #4#) (|subtractIfCan| ((#11=(|Maybe| $) $ $) NIL T ELT)) (|squareFreePolynomial| #12=(((|Factored| #13=(|SparseUnivariatePolynomial| $)) #13#) NIL #14=(|has| #7# (|PolynomialFactorizationExplicit|)) ELT)) (|squareFreePart| #9#) (|squareFree| #15=(((|Factored| $) $) NIL T ELT)) (|solveLinearPolynomialEquation| (((|Union| #16=(|List| #13#) #17="failed") #16# #13#) NIL #14# ELT)) (|sizeLess?| #1#) (|sign| (#6# NIL #18=(|has| #7# (|OrderedIntegralDomain|)) ELT)) (|sample| #19=(#20=($) NIL T CONST)) (|retractIfCan| (#21=((|Union| #7# . #22=(#17#)) . #23=($)) NIL T ELT) (((|Union| #24=(|Symbol|) . #22#) . #23#) NIL #25=(|has| #7# (|RetractableTo| #24#)) ELT) (((|Union| #26=(|Fraction| #7#) . #22#) . #23#) NIL #27=(|has| #7# (|RetractableTo| #7#)) ELT) (#21# NIL #27# ELT)) (|retract| #28=(#6# NIL T ELT) ((#24# $) NIL #25# ELT) (#29=(#26# $) NIL #27# ELT) (#6# NIL #27# ELT)) (|rem| #30=(#31=($ $ $) NIL T ELT)) (|reducedSystem| (#32=(#33=(|Matrix| #7#) #34=(|Matrix| $)) NIL #35=(|has| #7# (|LinearlyExplicitRingOver| #7#)) ELT) (#36=(#37=(|Record| (|:| |mat| #33#) (|:| |vec| (|Vector| #7#))) #34# #38=(|Vector| $)) NIL #35# ELT) (#36# NIL T ELT) (#32# NIL T ELT)) (|recip| ((#39=(|Union| $ #17#) $) NIL T ELT)) (|random| (#20# NIL #40=(|has| #7# (|IntegerNumberSystem|)) ELT)) (|quo| #30#) (|principalIdeal| (((|Record| (|:| |coef| #41=(|List| $)) #42=(|:| |generator| $)) #41#) NIL T ELT)) (|prime?| #4#) (|positive?| #43=(#5# NIL #18# ELT)) (|patternMatch| ((#44=(|PatternMatchResult| #7# . #45=($)) $ #46=(|Pattern| #7#) #44#) NIL (|has| #7# (|PatternMatchable| #7#)) ELT) ((#47=(|PatternMatchResult| #48=(|Float|) . #45#) $ #49=(|Pattern| #48#) #47#) NIL (|has| #7# (|PatternMatchable| #48#)) ELT)) (|opposite?| #1#) (|one?| #4#) (|numerator| #9#) (|numer| #28#) (|nextItem| (#50=(#11# $) NIL #51=(|has| #7# (|StepThrough|)) ELT)) (|negative?| #43#) (|multiEuclidean| (((|Union| #41# #17#) #41# $) NIL T ELT)) (|min| #52=(#31# NIL #53=(|has| #7# (|OrderedSet|)) ELT)) (|max| #52#) (|map| (($ #54=(|Mapping| #7# #7#) $) NIL T ELT)) (|leftReducedSystem| (#55=(#33# #38#) NIL #35# ELT) (#56=(#37# #38# $) NIL #35# ELT) (#56# NIL T ELT) (#55# NIL T ELT)) (|lcm| #30# #57=(($ #41#) NIL T ELT)) (|latex| (((|String|) $) NIL T ELT)) (|inv| #9#) (|init| (#20# NIL #51# CONST)) (|hash| (((|SingleInteger|) $) NIL T ELT)) (|gcdPolynomial| ((#13# #13# #13#) NIL T ELT)) (|gcd| #30# #57#) (|fractionPart| (#10# NIL #8# ELT) #58=(#29# NIL T ELT)) (|floor| #59=(#6# NIL #40# ELT)) (|factorSquareFreePolynomial| #12#) (|factorPolynomial| #12#) (|factor| #15#) (|extendedEuclidean| (((|Record| #60=(|:| |coef1| $) #61=(|:| |coef2| $) #42#) $ $) NIL T ELT) (((|Union| (|Record| #60# #61#) #17#) $ $ $) NIL T ELT)) (|exquo| ((#39# $ $) NIL T ELT)) (|expressIdealMember| (((|Maybe| #41#) #41# $) NIL T ELT)) (|eval| (($ $ #62=(|List| #7#) #62#) NIL #63=(|has| #7# (|Evalable| #7#)) ELT) (($ $ #7# #7#) NIL #63# ELT) (($ $ #64=(|Equation| #7#)) NIL #63# ELT) (($ $ (|List| #64#)) NIL #63# ELT) (($ $ #65=(|List| #24#) #62#) NIL #66=(|has| #7# (|InnerEvalable| #24# #7#)) ELT) (($ $ #24# #7#) NIL #66# ELT)) (|euclideanSize| ((#67=(|NonNegativeInteger|) $) NIL T ELT)) (|elt| (#68=($ $ #7#) NIL (|has| #7# (|Eltable| #7# #7#)) ELT)) (|divide| (((|Record| (|:| |quotient| $) (|:| |remainder| $)) $ $) NIL T ELT)) (|differentiate| #69=(($ $ #54#) NIL T ELT) #70=(($ $ #54# #67#) NIL T ELT) #71=(($ $ #24#) NIL #72=(|has| #7# (|PartialDifferentialSpace| #24#)) ELT) #73=(($ $ #65#) NIL #72# ELT) #74=(($ $ #24# #67#) NIL #72# ELT) #75=(($ $ #65# (|List| #67#)) NIL #72# ELT) #76=(#10# NIL #77=(|has| #7# (|DifferentialSpace|)) ELT) #78=(#79=($ $ #67#) NIL #77# ELT)) (|denominator| #9#) (|denom| #28#) (|convert| ((#46# . #80=($)) NIL (|has| #7# (|ConvertibleTo| #46#)) ELT) ((#49# . #80#) NIL (|has| #7# (|ConvertibleTo| #49#)) ELT) ((#81=(|InputForm|) . #80#) NIL (|has| #7# (|ConvertibleTo| #81#)) ELT) ((#48# . #80#) NIL #82=(|has| #7# (|RealConstant|)) ELT) (((|DoubleFloat|) . #80#) NIL #82# ELT)) (|conditionP| (((|Union| #38# #17#) #34#) NIL #83=(AND (|has| $ #84=(|CharacteristicNonZero|)) #14#) ELT)) (|coerce| (((|OutputForm|) $) NIL T ELT) #85=(($ #7#) NIL T ELT) #9# (#86=($ #26#) 8 T ELT) #85# (($ #24#) NIL #25# ELT) #58# (((|RadixExpansion| 2) $) 10 T ELT)) (|charthRoot| (#50# NIL (OR #83# (|has| #7# #84#)) ELT)) (|characteristic| ((#67#) NIL T CONST)) (|ceiling| #59#) (|binary| (#86# 9 T ELT)) (|before?| #1#) (|associates?| #1#) (|annihilate?| #1#) (|abs| (#10# NIL #18# ELT)) (|Zero| #19#) (|One| #19#) (D #69# #70# #71# #73# #74# #75# #76# #78#) (>= #87=(#2# NIL #53# ELT)) (> #87#) (= #1#) (<= #87#) (< #87#) (/ #30# (($ #7# #7#) NIL T ELT)) (- #9# #30#) (+ #30#) (** (($ $ #88=(|PositiveInteger|)) NIL T ELT) (#79# NIL T ELT) #89=(#68# NIL T ELT)) (* (($ #88# $) NIL T ELT) (($ #67# $) NIL T ELT) #90=(($ #7# . #91=($)) NIL T ELT) #30# (($ $ #26#) NIL T ELT) (($ #26# . #91#) NIL T ELT) #90# #89#)) (((|BinaryExpansion|) (|Join| (|QuotientFieldCategory| #1=(|Integer|)) (|CoercibleTo| #2=(|Fraction| #1#)) (|CoercibleTo| (|RadixExpansion| 2)) (CATEGORY |domain| (SIGNATURE |fractionPart| (#2# $)) (SIGNATURE |binary| ($ #2#))))) (T |BinaryExpansion|)) ((|fractionPart| (*1 *2 *1) #1=(AND (|isDomain| *2 (|Fraction| (|Integer|))) (|isDomain| *1 (|BinaryExpansion|)))) (|binary| (*1 *1 *2) #1#)) ((|properties| ((#1=(|List| (|Property|)) $) 14 T ELT)) (|name| ((#2=(|Identifier|) $) 12 T ELT)) (|coerce| (((|OutputForm|) $) 21 T ELT)) (|binding| (($ #2# #1#) 16 T ELT))) @@ -225,10 +225,10 @@ NIL ((~= #1=((#2=(|Boolean|) $ $) NIL T ELT)) (~ #3=(#4=($ $) NIL T ELT)) (|xor| #5=(#6=($ $ $) NIL T ELT)) (|swap!| (((|Void|) $ #7=(|Integer|) #7#) NIL #8=(|has| $ (|ShallowlyMutableAggregate| #2#)) ELT)) (|sorted?| (#9=(#2# $) NIL #10=(|has| #2# #11=(|OrderedSet|)) ELT) #12=((#2# #13=(|Mapping| #2# #2# #2#) $) NIL T ELT)) (|sort!| (#4# NIL (AND #8# #10#) ELT) (#14=($ #13# $) NIL #8# ELT)) (|sort| (#4# NIL #10# ELT) (#14# NIL T ELT)) (|setelt| ((#2# $ #15=(|UniversalSegment| #7#) #2#) NIL #8# ELT) #16=(#17=(#2# $ #7# #2#) NIL #8# ELT)) (|select| #18=(#19=($ #20=(|Mapping| #2# #2#) $) NIL #21=(|has| $ (|FiniteAggregate| #2#)) ELT)) (|sample| (#22=($) NIL T CONST)) (|reverse!| (#4# NIL #8# ELT)) (|reverse| #3#) (|removeDuplicates| (#4# NIL #23=(AND #21# #24=(|has| #2# (|BasicType|))) ELT)) (|remove| #18# (#25=($ #2# $) NIL #23# ELT)) (|reduce| #12# ((#2# #13# $ #2#) NIL T ELT) ((#2# #13# $ #2# #2#) NIL #24# ELT)) (|qsetelt!| #16#) (|qelt| #26=((#2# $ #7#) NIL T ELT)) (|position| ((#7# #2# $ #7#) NIL #24# ELT) ((#7# #2# $) NIL #24# ELT) ((#7# #20# $) NIL T ELT)) (|or| #5#) (|not| #3#) (|nor| #5#) (|new| (#27=($ #28=(|NonNegativeInteger|) #2#) 10 T ELT)) (|nand| #5#) (|minIndex| #29=((#7# $) NIL #30=(|has| #7# #11#) ELT)) (|min| #5#) (|merge| (#6# NIL #10# ELT) #31=(($ #13# $ $) NIL T ELT)) (|members| #32=((#33=(|List| #2#) $) NIL T ELT)) (|member?| (#34=(#2# #2# $) NIL #24# ELT)) (|maxIndex| #29#) (|max| #5#) (|map!| #35=(#19# NIL T ELT)) (|map| #31# #35#) (|latex| (((|String|) $) NIL T ELT)) (|insert| (#36=($ $ $ #7#) NIL T ELT) (($ #2# $ #7#) NIL T ELT)) (|indices| (((|List| #7#) $) NIL T ELT)) (|index?| ((#2# #7# $) NIL T ELT)) (|hash| (((|SingleInteger|) $) NIL T ELT)) (|first| (#9# NIL #30# ELT)) (|find| (((|Union| #2# "failed") #20# $) NIL T ELT)) (|fill!| (#37=($ $ #2#) NIL #8# ELT)) (|every?| #38=((#2# #20# $) NIL T ELT)) (|eval| (($ $ #33# #33#) NIL #39=(AND (|has| #2# (|Evalable| #2#)) (|has| #2# (|SetCategory|))) ELT) (($ $ #2# #2#) NIL #39# ELT) (($ $ #40=(|Equation| #2#)) NIL #39# ELT) (($ $ (|List| #40#)) NIL #39# ELT)) (|eq?| #1#) (|entry?| (#34# NIL #23# ELT)) (|entries| #32#) (|empty?| (#9# NIL T ELT)) (|empty| (#22# NIL T ELT)) (|elt| #41=(($ $ #15#) NIL T ELT) #26# (#17# NIL T ELT)) (|delete| #41# (($ $ #7#) NIL T ELT)) (|count| ((#28# #20# $) NIL T ELT) ((#28# #2# $) NIL #24# ELT)) (|copyInto!| (#36# NIL #8# ELT)) (|copy| #3#) (|convert| ((#42=(|InputForm|) $) NIL (|has| #2# (|ConvertibleTo| #42#)) ELT)) (|construct| (($ #33#) NIL T ELT)) (|concat| (($ (|List| $)) NIL T ELT) #5# (#25# NIL T ELT) (#37# NIL T ELT)) (|coerce| (((|OutputForm|) $) NIL T ELT)) (|bits| (#27# 11 T ELT)) (|before?| #1#) (|any?| #38#) (|and| #5#) (|\\/| #5#) (>= #1#) (> #1#) (= #1#) (<= #1#) (< #1#) (|/\\| #5#) (|#| ((#28# $) NIL T ELT))) (((|Bits|) (|Join| (|BitAggregate|) (CATEGORY |domain| (SIGNATURE |bits| ($ (|NonNegativeInteger|) (|Boolean|)))))) (T |Bits|)) ((|bits| (*1 *1 *2 *3) (AND (|isDomain| *2 (|NonNegativeInteger|)) (|isDomain| *3 (|Boolean|)) (|isDomain| *1 (|Bits|))))) -((~= (#1=((|Boolean|) $ $) 7 T ELT)) (|zero?| ((#2=(|Boolean|) $) 22 T ELT)) (|subtractIfCan| (((|Union| $ "failed") $ $) 26 T ELT)) (|sample| (#3=($) 23 T CONST)) (|opposite?| ((#2# $ $) 20 T ELT)) (|latex| (((|String|) $) 11 T ELT)) (|hash| (((|SingleInteger|) $) 12 T ELT)) (|coerce| (((|OutputForm|) $) 13 T ELT)) (|before?| (#1# 6 T ELT)) (|Zero| (#3# 24 T CONST)) (= (#1# 8 T ELT)) (- (($ $) 29 T ELT) (($ $ $) 28 T ELT)) (+ (($ $ $) 18 T ELT)) (* (($ (|PositiveInteger|) $) 17 T ELT) (($ (|NonNegativeInteger|) $) 21 T ELT) (($ (|Integer|) . #4=($)) 30 T ELT) (($ |#1| . #4#) 33 T ELT) (($ $ |#2|) 37 T ELT))) +((~= (#1=((|Boolean|) $ $) 7 T ELT)) (|zero?| ((#2=(|Boolean|) $) 22 T ELT)) (|subtractIfCan| (((|Maybe| $) $ $) 26 T ELT)) (|sample| (#3=($) 23 T CONST)) (|opposite?| ((#2# $ $) 20 T ELT)) (|latex| (((|String|) $) 11 T ELT)) (|hash| (((|SingleInteger|) $) 12 T ELT)) (|coerce| (((|OutputForm|) $) 13 T ELT)) (|before?| (#1# 6 T ELT)) (|Zero| (#3# 24 T CONST)) (= (#1# 8 T ELT)) (- (($ $) 30 T ELT) (($ $ $) 29 T ELT)) (+ (($ $ $) 18 T ELT)) (* (($ (|PositiveInteger|) $) 17 T ELT) (($ (|NonNegativeInteger|) $) 21 T ELT) (($ (|Integer|) . #4=($)) 31 T ELT) (($ |#1| . #4#) 34 T ELT) (($ $ |#2|) 38 T ELT))) (((|BiModule| |#1| |#2|) (|Category|) (|Ring|) (|Ring|)) (T |BiModule|)) NIL -(|Join| (|LeftModule| |t#1|) (|RightModule| |t#2|) (CATEGORY |package| (ATTRIBUTE |leftUnitary|) (ATTRIBUTE |rightUnitary|))) +(|Join| (|LeftModule| |t#1|) (|RightModule| |t#2|)) (((|AbelianGroup|) . T) ((|AbelianMonoid|) . T) ((|AbelianSemiGroup|) . T) ((|BasicType|) . T) ((|CancellationAbelianMonoid|) . T) ((|CoercibleTo| (|OutputForm|)) . T) ((|Join|) . T) ((|LeftLinearSet| (|Integer|)) . T) ((|LeftLinearSet| |#1|) . T) ((|LeftModule| |#1|) . T) ((|RightLinearSet| |#2|) . T) ((|RightModule| |#2|) . T) ((|SetCategory|) . T) ((|Type|) . T)) ((|or| (#1=($ $ $) 12 T ELT)) (|not| (($ $) 8 T ELT)) (|and| (#1# 10 T ELT))) (((|BooleanLogic&| |#1|) (CATEGORY |package| (SIGNATURE |or| #1=(|#1| |#1| |#1|)) (SIGNATURE |and| #1#) (SIGNATURE |not| (|#1| |#1|))) (|BooleanLogic|)) (T |BooleanLogic&|)) @@ -238,7 +238,7 @@ NIL ((|not| (*1 *1 *1) (|ofCategory| *1 (|BooleanLogic|))) (|and| (*1 *1 *1 *1) (|ofCategory| *1 (|BooleanLogic|))) (|or| (*1 *1 *1 *1) (|ofCategory| *1 (|BooleanLogic|)))) (|Join| (|Logic|) (CATEGORY |domain| (SIGNATURE |not| ($ $)) (SIGNATURE |and| ($ $ $)) (SIGNATURE |or| ($ $ $)))) (((|Join|) . T) ((|Logic|) . T) ((|Type|) . T)) -((~= #1=(#2=((|Boolean|) $ $) NIL T ELT)) (~ (#3=($ $) 9 T ELT)) (|xor| (#4=($ $ $) 14 T ELT)) (|true| (#5=($) 6 T CONST)) (|size| (((|NonNegativeInteger|)) 23 T ELT)) (|random| (#5# 31 T ELT)) (|or| (#4# 12 T ELT)) (|not| (#3# 8 T ELT)) (|nor| (#4# 15 T ELT)) (|nand| (#4# 16 T ELT)) (|min| #6=(#4# NIL T ELT) #7=(#5# NIL T CONST)) (|max| #6# #7#) (|lookup| ((#8=(|PositiveInteger|) $) 29 T ELT)) (|latex| (((|String|) $) NIL T ELT)) (|index| (($ #8#) 27 T ELT)) (|implies| (#4# 19 T ELT)) (|hash| (((|SingleInteger|) $) NIL T ELT)) (|false| (#5# 7 T CONST)) (|equiv| (#4# 20 T ELT)) (|convert| (((|InputForm|) $) 33 T ELT)) (|coerce| (((|OutputForm|) $) 35 T ELT)) (|before?| #1#) (|and| (#4# 10 T ELT)) (|\\/| (#4# 13 T ELT)) (>= #1#) (> #1#) (= (#2# 18 T ELT)) (<= #1#) (< (#2# 21 T ELT)) (|/\\| (#4# 11 T ELT))) +((~= #1=(#2=((|Boolean|) $ $) NIL T ELT)) (~ (#3=($ $) 9 T ELT)) (|xor| (#4=($ $ $) 14 T ELT)) (|true| (#5=($) 6 T CONST)) (|size| (((|NonNegativeInteger|)) 23 T ELT)) (|random| (#5# 32 T ELT)) (|or| (#4# 12 T ELT)) (|not| (#3# 8 T ELT)) (|nor| (#4# 15 T ELT)) (|nand| (#4# 16 T ELT)) (|min| #6=(#4# NIL T ELT) #7=(#5# NIL T CONST)) (|max| #6# #7#) (|lookup| ((#8=(|PositiveInteger|) $) 29 T ELT)) (|latex| (((|String|) $) NIL T ELT)) (|index| (($ #8#) 27 T ELT)) (|implies| (#4# 19 T ELT)) (|hash| (((|SingleInteger|) $) NIL T ELT)) (|false| (#5# 7 T CONST)) (|equiv| (#4# 20 T ELT)) (|convert| (((|InputForm|) $) 34 T ELT)) (|coerce| (((|OutputForm|) $) 36 T ELT)) (|before?| #1#) (|and| (#4# 10 T ELT)) (|\\/| (#4# 13 T ELT)) (>= #1#) (> #1#) (= (#2# 18 T ELT)) (<= #1#) (< (#2# 21 T ELT)) (|/\\| (#4# 11 T ELT))) (((|Boolean|) (|Join| (|OrderedFinite|) (|PropositionalLogic|) (|ConvertibleTo| (|InputForm|)) (CATEGORY |domain| (SIGNATURE |xor| #1=($ $ $)) (SIGNATURE |nand| #1#) (SIGNATURE |nor| #1#)))) (T |Boolean|)) ((|xor| #1=(*1 *1 *1 *1) #2=(|isDomain| *1 (|Boolean|))) (|nand| #1# #2#) (|nor| #1# #2#)) ((~= #1=(#2=(#3=(|Boolean|) $ $) NIL T ELT)) (|weight| ((#4=(|NonNegativeInteger|) $) 92 T ELT) (($ $ #4#) 38 T ELT)) (|unary?| (#5=(#3# $) 42 T ELT)) (|setProperty| (($ $ #6=(|String|) #7=(|None|)) 59 T ELT) (($ $ #8=(|Identifier|) #7#) 34 T ELT)) (|setProperties| (($ $ #9=(|AssociationList| #6# #7#)) 16 T ELT)) (|property| (((|Union| #7# "failed") $ #6#) 27 T ELT) (((|Maybe| #7#) $ #8#) 33 T ELT)) (|properties| ((#9# $) 15 T ELT)) (|operator| (($ #10=(|Symbol|)) 20 T ELT) (($ #10# #4#) 23 T ELT) (($ #10# #11=(|Arity|)) 24 T ELT)) (|nullary?| (#5# 40 T ELT)) (|nary?| (#5# 44 T ELT)) (|name| ((#10# $) 8 T ELT)) (|min| #12=(($ $ $) NIL T ELT)) (|max| #12#) (|latex| ((#6# $) NIL T ELT)) (|is?| ((#3# $ #10#) 11 T ELT)) (|input| (($ $ #13=(|Mapping| #14=(|InputForm|) (|List| #14#))) 65 T ELT) (((|Maybe| #13#) $) 69 T ELT)) (|hash| (((|SingleInteger|) $) NIL T ELT)) (|has?| ((#3# $ #8#) 37 T ELT)) (|equality| (#15=($ $ (|Mapping| #3# $ $)) 46 T ELT)) (|display| (((|Maybe| #16=(|Mapping| #17=(|OutputForm|) (|List| #17#))) $) 67 T ELT) (($ $ #16#) 52 T ELT) (($ $ (|Mapping| #17# #17#)) 54 T ELT)) (|deleteProperty!| (($ $ #6#) 56 T ELT) (#18=($ $ #8#) 57 T ELT)) (|copy| (($ $) 75 T ELT)) (|comparison| (#15# 47 T ELT)) (|coerce| ((#17# $) 61 T ELT)) (|before?| #1#) (|assert| (#18# 35 T ELT)) (|arity| ((#11# $) 70 T ELT)) (>= #1#) (> #1#) (= (#2# 88 T ELT)) (<= #1#) (< (#2# 104 T ELT))) @@ -250,10 +250,10 @@ NIL ((|integerBound| (((|Integer|) |#2|) 41 T ELT))) (((|BoundIntegerRoots| |#1| |#2|) (CATEGORY |package| (SIGNATURE |integerBound| (#1=(|Integer|) |#2|))) (|Join| (|Field|) (|RetractableTo| (|Fraction| #1#))) (|UnivariatePolynomialCategory| |#1|)) (T |BoundIntegerRoots|)) ((|integerBound| (*1 *2 *3) (AND (|ofCategory| *4 (|Join| (|Field|) (|RetractableTo| (|Fraction| *2)))) (|isDomain| *2 (|Integer|)) (|isDomain| *1 (|BoundIntegerRoots| *4 *3)) (|ofCategory| *3 (|UnivariatePolynomialCategory| *4))))) -((~= #1=((#2=(|Boolean|) $ $) NIL T ELT)) (|zero?| #3=((#2# $) NIL T ELT)) (|unitNormal| (((|Record| (|:| |unit| $) (|:| |canonical| $) (|:| |associate| $)) $) NIL T ELT)) (|unitCanonical| #4=(($ $) NIL T ELT)) (|unit?| #3#) (|subtractIfCan| #5=((#6=(|Union| $ #7="failed") $ $) NIL T ELT)) (|sqrt| #8=(($ $ #9=(|Integer|)) NIL T ELT)) (|sizeLess?| #1#) (|sample| #10=(($) NIL T CONST)) (|root| (($ (|SparseUnivariatePolynomial| #9#) #9#) NIL T ELT)) (|rem| #11=(($ $ $) NIL T ELT)) (|recip| ((#6# $) NIL T ELT)) (|quotientByP| #4#) (|quo| #11#) (|principalIdeal| (((|Record| (|:| |coef| #12=(|List| $)) #13=(|:| |generator| $)) #12#) NIL T ELT)) (|order| #14=((#15=(|NonNegativeInteger|) $) NIL T ELT)) (|opposite?| #1#) (|one?| #3#) (|multiEuclidean| (((|Union| #12# #7#) #12# $) NIL T ELT)) (|modulus| ((#9#) NIL T ELT)) (|moduloP| ((#9# $) NIL T ELT)) (|lcm| #11# #16=(($ #12#) NIL T ELT)) (|latex| (((|String|) $) NIL T ELT)) (|hash| (((|SingleInteger|) $) NIL T ELT)) (|gcdPolynomial| ((#17=(|SparseUnivariatePolynomial| $) #17# #17#) NIL T ELT)) (|gcd| #11# #16#) (|extendedEuclidean| (((|Record| #18=(|:| |coef1| $) #19=(|:| |coef2| $) #13#) $ $) NIL T ELT) (((|Union| (|Record| #18# #19#) #7#) $ $ $) NIL T ELT)) (|extend| #8#) (|exquo| #5#) (|expressIdealMember| (((|Maybe| #12#) #12# $) NIL T ELT)) (|euclideanSize| #14#) (|divide| (((|Record| (|:| |quotient| $) (|:| |remainder| $)) $ $) NIL T ELT)) (|digits| (((|Stream| #9#) $) NIL T ELT)) (|complete| #4#) (|coerce| (((|OutputForm|) $) NIL T ELT) (($ #9#) NIL T ELT) #4#) (|characteristic| ((#15#) NIL T CONST)) (|before?| #1#) (|associates?| #1#) (|approximate| ((#9# $ #9#) NIL T ELT)) (|annihilate?| #1#) (|Zero| #10#) (|One| #10#) (= #1#) (- #4# #11#) (+ #11#) (** (($ $ #20=(|PositiveInteger|)) NIL T ELT) (($ $ #15#) NIL T ELT)) (* (($ #20# $) NIL T ELT) (($ #15# $) NIL T ELT) (($ #9# $) NIL T ELT) #11#)) +((~= #1=((#2=(|Boolean|) $ $) NIL T ELT)) (|zero?| #3=((#2# $) NIL T ELT)) (|unitNormal| (((|Record| (|:| |unit| $) (|:| |canonical| $) (|:| |associate| $)) $) NIL T ELT)) (|unitCanonical| #4=(($ $) NIL T ELT)) (|unit?| #3#) (|subtractIfCan| (((|Maybe| $) $ $) NIL T ELT)) (|sqrt| #5=(($ $ #6=(|Integer|)) NIL T ELT)) (|sizeLess?| #1#) (|sample| #7=(($) NIL T CONST)) (|root| (($ (|SparseUnivariatePolynomial| #6#) #6#) NIL T ELT)) (|rem| #8=(($ $ $) NIL T ELT)) (|recip| ((#9=(|Union| $ #10="failed") $) NIL T ELT)) (|quotientByP| #4#) (|quo| #8#) (|principalIdeal| (((|Record| (|:| |coef| #11=(|List| $)) #12=(|:| |generator| $)) #11#) NIL T ELT)) (|order| #13=((#14=(|NonNegativeInteger|) $) NIL T ELT)) (|opposite?| #1#) (|one?| #3#) (|multiEuclidean| (((|Union| #11# #10#) #11# $) NIL T ELT)) (|modulus| ((#6#) NIL T ELT)) (|moduloP| ((#6# $) NIL T ELT)) (|lcm| #8# #15=(($ #11#) NIL T ELT)) (|latex| (((|String|) $) NIL T ELT)) (|hash| (((|SingleInteger|) $) NIL T ELT)) (|gcdPolynomial| ((#16=(|SparseUnivariatePolynomial| $) #16# #16#) NIL T ELT)) (|gcd| #8# #15#) (|extendedEuclidean| (((|Record| #17=(|:| |coef1| $) #18=(|:| |coef2| $) #12#) $ $) NIL T ELT) (((|Union| (|Record| #17# #18#) #10#) $ $ $) NIL T ELT)) (|extend| #5#) (|exquo| ((#9# $ $) NIL T ELT)) (|expressIdealMember| (((|Maybe| #11#) #11# $) NIL T ELT)) (|euclideanSize| #13#) (|divide| (((|Record| (|:| |quotient| $) (|:| |remainder| $)) $ $) NIL T ELT)) (|digits| (((|Stream| #6#) $) NIL T ELT)) (|complete| #4#) (|coerce| (((|OutputForm|) $) NIL T ELT) (($ #6#) NIL T ELT) #4#) (|characteristic| ((#14#) NIL T CONST)) (|before?| #1#) (|associates?| #1#) (|approximate| ((#6# $ #6#) NIL T ELT)) (|annihilate?| #1#) (|Zero| #7#) (|One| #7#) (= #1#) (- #4# #8#) (+ #8#) (** (($ $ #19=(|PositiveInteger|)) NIL T ELT) (($ $ #14#) NIL T ELT)) (* (($ #19# $) NIL T ELT) (($ #14# $) NIL T ELT) (($ #6# $) NIL T ELT) #8#)) (((|BalancedPAdicInteger| |#1|) (|PAdicIntegerCategory| |#1|) (|Integer|)) (T |BalancedPAdicInteger|)) NIL -((~= #1=(#2=(#3=(|Boolean|) $ $) NIL T ELT)) (|zero?| #4=(#5=(#3# $) NIL T ELT)) (|wholePart| (#6=(#7=(|BalancedPAdicInteger| |#1|) $) NIL #8=(|has| #7# (|EuclideanDomain|)) ELT)) (|unitNormal| (((|Record| (|:| |unit| $) (|:| |canonical| $) (|:| |associate| $)) $) NIL T ELT)) (|unitCanonical| #9=(#10=($ $) NIL T ELT)) (|unit?| #4#) (|subtractIfCan| #11=((#12=(|Union| $ #13="failed") $ $) NIL T ELT)) (|squareFreePolynomial| #14=(((|Factored| #15=(|SparseUnivariatePolynomial| $)) #15#) NIL #16=(|has| #7# (|PolynomialFactorizationExplicit|)) ELT)) (|squareFreePart| #9#) (|squareFree| #17=(((|Factored| $) $) NIL T ELT)) (|solveLinearPolynomialEquation| (((|Union| #18=(|List| #15#) #13#) #18# #15#) NIL #16# ELT)) (|sizeLess?| #1#) (|sign| (#19=(#20=(|Integer|) $) NIL #21=(|has| #7# (|OrderedIntegralDomain|)) ELT)) (|sample| #22=(#23=($) NIL T CONST)) (|retractIfCan| (((|Union| #7# . #24=(#13#)) . #25=($)) NIL T ELT) (((|Union| #26=(|Symbol|) . #24#) . #25#) NIL #27=(|has| #7# (|RetractableTo| #26#)) ELT) (((|Union| #28=(|Fraction| #20#) . #24#) . #25#) NIL #29=(|has| #7# (|RetractableTo| #20#)) ELT) (((|Union| #20# . #24#) . #25#) NIL #29# ELT)) (|retract| #30=(#6# NIL T ELT) ((#26# . #31=($)) NIL #27# ELT) ((#28# . #31#) NIL #29# ELT) (#19# NIL #29# ELT)) (|removeZeroes| #9# #32=(($ #20# $) NIL T ELT)) (|rem| #33=(#34=($ $ $) NIL T ELT)) (|reducedSystem| ((#35=(|Matrix| #20#) . #36=(#37=(|Matrix| $))) NIL #38=(|has| #7# (|LinearlyExplicitRingOver| #20#)) ELT) ((#39=(|Record| (|:| |mat| #35#) (|:| |vec| (|Vector| #20#))) . #40=(#37# #41=(|Vector| $))) NIL #38# ELT) ((#42=(|Record| (|:| |mat| #43=(|Matrix| #7#)) (|:| |vec| (|Vector| #7#))) . #40#) NIL T ELT) ((#43# . #36#) NIL T ELT)) (|recip| ((#12# $) NIL T ELT)) (|random| (#23# NIL #44=(|has| #7# (|IntegerNumberSystem|)) ELT)) (|quo| #33#) (|principalIdeal| (((|Record| (|:| |coef| #45=(|List| $)) #46=(|:| |generator| $)) #45#) NIL T ELT)) (|prime?| #4#) (|positive?| #47=(#5# NIL #21# ELT)) (|patternMatch| ((#48=(|PatternMatchResult| #20# . #49=($)) $ #50=(|Pattern| #20#) #48#) NIL (|has| #7# (|PatternMatchable| #20#)) ELT) ((#51=(|PatternMatchResult| #52=(|Float|) . #49#) $ #53=(|Pattern| #52#) #51#) NIL (|has| #7# (|PatternMatchable| #52#)) ELT)) (|opposite?| #1#) (|one?| #4#) (|numerator| #9#) (|numer| #30#) (|nextItem| (#54=((|Maybe| $) $) NIL #55=(|has| #7# (|StepThrough|)) ELT)) (|negative?| #47#) (|multiEuclidean| (((|Union| #45# #13#) #45# $) NIL T ELT)) (|min| #56=(#34# NIL #57=(|has| #7# (|OrderedSet|)) ELT)) (|max| #56#) (|map| (($ #58=(|Mapping| #7# #7#) $) NIL T ELT)) (|leftReducedSystem| ((#35# . #59=(#41#)) NIL #38# ELT) ((#39# . #60=(#41# $)) NIL #38# ELT) ((#42# . #60#) NIL T ELT) ((#43# . #59#) NIL T ELT)) (|lcm| #33# #61=(($ #45#) NIL T ELT)) (|latex| (((|String|) $) NIL T ELT)) (|inv| #9#) (|init| (#23# NIL #55# CONST)) (|hash| (((|SingleInteger|) $) NIL T ELT)) (|gcdPolynomial| ((#15# #15# #15#) NIL T ELT)) (|gcd| #33# #61#) (|fractionPart| (#10# NIL #8# ELT)) (|floor| #62=(#6# NIL #44# ELT)) (|factorSquareFreePolynomial| #14#) (|factorPolynomial| #14#) (|factor| #17#) (|extendedEuclidean| (((|Record| #63=(|:| |coef1| $) #64=(|:| |coef2| $) #46#) $ $) NIL T ELT) (((|Union| (|Record| #63# #64#) #13#) $ $ $) NIL T ELT)) (|exquo| #11#) (|expressIdealMember| (((|Maybe| #45#) #45# $) NIL T ELT)) (|eval| (($ $ #65=(|List| #7#) #65#) NIL #66=(|has| #7# (|Evalable| #7#)) ELT) (($ $ #7# #7#) NIL #66# ELT) (($ $ #67=(|Equation| #7#)) NIL #66# ELT) (($ $ (|List| #67#)) NIL #66# ELT) (($ $ #68=(|List| #26#) #65#) NIL #69=(|has| #7# (|InnerEvalable| #26# #7#)) ELT) (($ $ #26# #7#) NIL #69# ELT)) (|euclideanSize| ((#70=(|NonNegativeInteger|) $) NIL T ELT)) (|elt| (#71=($ $ #7#) NIL (|has| #7# (|Eltable| #7# #7#)) ELT)) (|divide| (((|Record| (|:| |quotient| $) (|:| |remainder| $)) $ $) NIL T ELT)) (|differentiate| #72=(($ $ #58#) NIL T ELT) #73=(($ $ #58# #70#) NIL T ELT) #74=(($ $ #26#) NIL #75=(|has| #7# (|PartialDifferentialSpace| #26#)) ELT) #76=(($ $ #68#) NIL #75# ELT) #77=(($ $ #26# #70#) NIL #75# ELT) #78=(($ $ #68# (|List| #70#)) NIL #75# ELT) #79=(#10# NIL #80=(|has| #7# (|DifferentialSpace|)) ELT) #81=(#82=($ $ #70#) NIL #80# ELT)) (|denominator| #9#) (|denom| #30#) (|convert| ((#50# . #83=($)) NIL (|has| #7# (|ConvertibleTo| #50#)) ELT) ((#53# . #83#) NIL (|has| #7# (|ConvertibleTo| #53#)) ELT) ((#84=(|InputForm|) . #83#) NIL (|has| #7# (|ConvertibleTo| #84#)) ELT) ((#52# . #83#) NIL #85=(|has| #7# (|RealConstant|)) ELT) (((|DoubleFloat|) . #83#) NIL #85# ELT)) (|continuedFraction| (((|ContinuedFraction| #28#) $) NIL T ELT)) (|conditionP| (((|Union| #41# #13#) #37#) NIL #86=(AND (|has| $ #87=(|CharacteristicNonZero|)) #16#) ELT)) (|coerce| (((|OutputForm|) $) NIL T ELT) (($ #20#) NIL T ELT) #9# (($ #28#) NIL T ELT) (($ #7#) NIL T ELT) (($ #26#) NIL #27# ELT)) (|charthRoot| (#54# NIL (OR #86# (|has| #7# #87#)) ELT)) (|characteristic| ((#70#) NIL T CONST)) (|ceiling| #62#) (|before?| #1#) (|associates?| #1#) (|approximate| ((#28# $ #20#) NIL T ELT)) (|annihilate?| #1#) (|abs| (#10# NIL #21# ELT)) (|Zero| #22#) (|One| #22#) (D #72# #73# #74# #76# #77# #78# #79# #81#) (>= #88=(#2# NIL #57# ELT)) (> #88#) (= #1#) (<= #88#) (< #88#) (/ #33# (($ #7# #7#) NIL T ELT)) (- #9# #33#) (+ #33#) (** (($ $ #89=(|PositiveInteger|)) NIL T ELT) (#82# NIL T ELT) (($ $ #20#) NIL T ELT)) (* (($ #89# $) NIL T ELT) (($ #70# $) NIL T ELT) #32# #33# (($ $ #28#) NIL T ELT) (($ #28# . #90=($)) NIL T ELT) (($ #7# . #90#) NIL T ELT) (#71# NIL T ELT))) +((~= #1=(#2=(#3=(|Boolean|) $ $) NIL T ELT)) (|zero?| #4=(#5=(#3# $) NIL T ELT)) (|wholePart| (#6=(#7=(|BalancedPAdicInteger| |#1|) $) NIL #8=(|has| #7# (|EuclideanDomain|)) ELT)) (|unitNormal| (((|Record| (|:| |unit| $) (|:| |canonical| $) (|:| |associate| $)) $) NIL T ELT)) (|unitCanonical| #9=(#10=($ $) NIL T ELT)) (|unit?| #4#) (|subtractIfCan| ((#11=(|Maybe| $) $ $) NIL T ELT)) (|squareFreePolynomial| #12=(((|Factored| #13=(|SparseUnivariatePolynomial| $)) #13#) NIL #14=(|has| #7# (|PolynomialFactorizationExplicit|)) ELT)) (|squareFreePart| #9#) (|squareFree| #15=(((|Factored| $) $) NIL T ELT)) (|solveLinearPolynomialEquation| (((|Union| #16=(|List| #13#) #17="failed") #16# #13#) NIL #14# ELT)) (|sizeLess?| #1#) (|sign| (#18=(#19=(|Integer|) $) NIL #20=(|has| #7# (|OrderedIntegralDomain|)) ELT)) (|sample| #21=(#22=($) NIL T CONST)) (|retractIfCan| (((|Union| #7# . #23=(#17#)) . #24=($)) NIL T ELT) (((|Union| #25=(|Symbol|) . #23#) . #24#) NIL #26=(|has| #7# (|RetractableTo| #25#)) ELT) (((|Union| #27=(|Fraction| #19#) . #23#) . #24#) NIL #28=(|has| #7# (|RetractableTo| #19#)) ELT) (((|Union| #19# . #23#) . #24#) NIL #28# ELT)) (|retract| #29=(#6# NIL T ELT) ((#25# . #30=($)) NIL #26# ELT) ((#27# . #30#) NIL #28# ELT) (#18# NIL #28# ELT)) (|removeZeroes| #9# #31=(($ #19# $) NIL T ELT)) (|rem| #32=(#33=($ $ $) NIL T ELT)) (|reducedSystem| ((#34=(|Matrix| #19#) . #35=(#36=(|Matrix| $))) NIL #37=(|has| #7# (|LinearlyExplicitRingOver| #19#)) ELT) ((#38=(|Record| (|:| |mat| #34#) (|:| |vec| (|Vector| #19#))) . #39=(#36# #40=(|Vector| $))) NIL #37# ELT) ((#41=(|Record| (|:| |mat| #42=(|Matrix| #7#)) (|:| |vec| (|Vector| #7#))) . #39#) NIL T ELT) ((#42# . #35#) NIL T ELT)) (|recip| ((#43=(|Union| $ #17#) $) NIL T ELT)) (|random| (#22# NIL #44=(|has| #7# (|IntegerNumberSystem|)) ELT)) (|quo| #32#) (|principalIdeal| (((|Record| (|:| |coef| #45=(|List| $)) #46=(|:| |generator| $)) #45#) NIL T ELT)) (|prime?| #4#) (|positive?| #47=(#5# NIL #20# ELT)) (|patternMatch| ((#48=(|PatternMatchResult| #19# . #49=($)) $ #50=(|Pattern| #19#) #48#) NIL (|has| #7# (|PatternMatchable| #19#)) ELT) ((#51=(|PatternMatchResult| #52=(|Float|) . #49#) $ #53=(|Pattern| #52#) #51#) NIL (|has| #7# (|PatternMatchable| #52#)) ELT)) (|opposite?| #1#) (|one?| #4#) (|numerator| #9#) (|numer| #29#) (|nextItem| (#54=(#11# $) NIL #55=(|has| #7# (|StepThrough|)) ELT)) (|negative?| #47#) (|multiEuclidean| (((|Union| #45# #17#) #45# $) NIL T ELT)) (|min| #56=(#33# NIL #57=(|has| #7# (|OrderedSet|)) ELT)) (|max| #56#) (|map| (($ #58=(|Mapping| #7# #7#) $) NIL T ELT)) (|leftReducedSystem| ((#34# . #59=(#40#)) NIL #37# ELT) ((#38# . #60=(#40# $)) NIL #37# ELT) ((#41# . #60#) NIL T ELT) ((#42# . #59#) NIL T ELT)) (|lcm| #32# #61=(($ #45#) NIL T ELT)) (|latex| (((|String|) $) NIL T ELT)) (|inv| #9#) (|init| (#22# NIL #55# CONST)) (|hash| (((|SingleInteger|) $) NIL T ELT)) (|gcdPolynomial| ((#13# #13# #13#) NIL T ELT)) (|gcd| #32# #61#) (|fractionPart| (#10# NIL #8# ELT)) (|floor| #62=(#6# NIL #44# ELT)) (|factorSquareFreePolynomial| #12#) (|factorPolynomial| #12#) (|factor| #15#) (|extendedEuclidean| (((|Record| #63=(|:| |coef1| $) #64=(|:| |coef2| $) #46#) $ $) NIL T ELT) (((|Union| (|Record| #63# #64#) #17#) $ $ $) NIL T ELT)) (|exquo| ((#43# $ $) NIL T ELT)) (|expressIdealMember| (((|Maybe| #45#) #45# $) NIL T ELT)) (|eval| (($ $ #65=(|List| #7#) #65#) NIL #66=(|has| #7# (|Evalable| #7#)) ELT) (($ $ #7# #7#) NIL #66# ELT) (($ $ #67=(|Equation| #7#)) NIL #66# ELT) (($ $ (|List| #67#)) NIL #66# ELT) (($ $ #68=(|List| #25#) #65#) NIL #69=(|has| #7# (|InnerEvalable| #25# #7#)) ELT) (($ $ #25# #7#) NIL #69# ELT)) (|euclideanSize| ((#70=(|NonNegativeInteger|) $) NIL T ELT)) (|elt| (#71=($ $ #7#) NIL (|has| #7# (|Eltable| #7# #7#)) ELT)) (|divide| (((|Record| (|:| |quotient| $) (|:| |remainder| $)) $ $) NIL T ELT)) (|differentiate| #72=(($ $ #58#) NIL T ELT) #73=(($ $ #58# #70#) NIL T ELT) #74=(($ $ #25#) NIL #75=(|has| #7# (|PartialDifferentialSpace| #25#)) ELT) #76=(($ $ #68#) NIL #75# ELT) #77=(($ $ #25# #70#) NIL #75# ELT) #78=(($ $ #68# (|List| #70#)) NIL #75# ELT) #79=(#10# NIL #80=(|has| #7# (|DifferentialSpace|)) ELT) #81=(#82=($ $ #70#) NIL #80# ELT)) (|denominator| #9#) (|denom| #29#) (|convert| ((#50# . #83=($)) NIL (|has| #7# (|ConvertibleTo| #50#)) ELT) ((#53# . #83#) NIL (|has| #7# (|ConvertibleTo| #53#)) ELT) ((#84=(|InputForm|) . #83#) NIL (|has| #7# (|ConvertibleTo| #84#)) ELT) ((#52# . #83#) NIL #85=(|has| #7# (|RealConstant|)) ELT) (((|DoubleFloat|) . #83#) NIL #85# ELT)) (|continuedFraction| (((|ContinuedFraction| #27#) $) NIL T ELT)) (|conditionP| (((|Union| #40# #17#) #36#) NIL #86=(AND (|has| $ #87=(|CharacteristicNonZero|)) #14#) ELT)) (|coerce| (((|OutputForm|) $) NIL T ELT) (($ #19#) NIL T ELT) #9# (($ #27#) NIL T ELT) (($ #7#) NIL T ELT) (($ #25#) NIL #26# ELT)) (|charthRoot| (#54# NIL (OR #86# (|has| #7# #87#)) ELT)) (|characteristic| ((#70#) NIL T CONST)) (|ceiling| #62#) (|before?| #1#) (|associates?| #1#) (|approximate| ((#27# $ #19#) NIL T ELT)) (|annihilate?| #1#) (|abs| (#10# NIL #20# ELT)) (|Zero| #21#) (|One| #21#) (D #72# #73# #74# #76# #77# #78# #79# #81#) (>= #88=(#2# NIL #57# ELT)) (> #88#) (= #1#) (<= #88#) (< #88#) (/ #32# (($ #7# #7#) NIL T ELT)) (- #9# #32#) (+ #32#) (** (($ $ #89=(|PositiveInteger|)) NIL T ELT) (#82# NIL T ELT) (($ $ #19#) NIL T ELT)) (* (($ #89# $) NIL T ELT) (($ #70# $) NIL T ELT) #31# #32# (($ $ #27#) NIL T ELT) (($ #27# . #90=($)) NIL T ELT) (($ #7# . #90#) NIL T ELT) (#71# NIL T ELT))) (((|BalancedPAdicRational| |#1|) (|Join| (|QuotientFieldCategory| (|BalancedPAdicInteger| |#1|)) (CATEGORY |domain| (SIGNATURE |approximate| (#1=(|Fraction| #2=(|Integer|)) $ #2#)) (SIGNATURE |continuedFraction| ((|ContinuedFraction| #1#) $)) (SIGNATURE |removeZeroes| ($ $)) (SIGNATURE |removeZeroes| ($ #2# $)))) #2#) (T |BalancedPAdicRational|)) ((|approximate| (*1 *2 *1 *3) (AND (|isDomain| *2 #1=(|Fraction| #2=(|Integer|))) (|isDomain| *1 (|BalancedPAdicRational| *4)) (|ofType| *4 *3) (|isDomain| *3 #2#))) (|continuedFraction| (*1 *2 *1) (AND (|isDomain| *2 (|ContinuedFraction| #1#)) #3=(|isDomain| *1 (|BalancedPAdicRational| *3)) (|ofType| *3 #2#))) (|removeZeroes| (*1 *1 *1) (AND (|isDomain| *1 (|BalancedPAdicRational| *2)) (|ofType| *2 #2#))) (|removeZeroes| (*1 *1 *2 *1) (AND (|isDomain| *2 #2#) #3# (|ofType| *3 *2)))) ((|setelt| ((|#2| $ #1="value" |#2|) NIL T ELT) (($ $ #2="left" $) 59 T ELT) (($ $ #3="right" $) 61 T ELT)) (|nodes| (#4=((|List| $) $) 31 T ELT)) (|node?| (#5=(#6=(|Boolean|) $ $) 36 T ELT)) (|leaves| (((|List| |#2|) $) 25 T ELT)) (|leaf?| (#7=(#6# $) 18 T ELT)) (|elt| ((|#2| $ #1#) NIL T ELT) (($ $ #2#) 10 T ELT) (($ $ #3#) 13 T ELT)) (|cyclic?| (#7# 55 T ELT)) (|coerce| (((|OutputForm|) $) 46 T ELT)) (|children| (#4# 32 T ELT)) (= (#5# 38 T ELT))) @@ -302,10 +302,10 @@ NIL ((~= #1=(#2=((|Boolean|) $ $) NIL T ELT)) (|unknownEndian| (#3=($) 6 T CONST)) (|littleEndian| (#3# 7 T CONST)) (|latex| (((|String|) $) NIL T ELT)) (|hash| (((|SingleInteger|) $) NIL T ELT)) (|coerce| (((|OutputForm|) $) 14 T ELT)) (|bigEndian| (#3# 8 T CONST)) (|before?| #1#) (= (#2# 10 T ELT))) (((|ByteOrder|) (|Join| (|SetCategory|) (CATEGORY |domain| (SIGNATURE |littleEndian| #1=($) |constant|) (SIGNATURE |bigEndian| #1# |constant|) (SIGNATURE |unknownEndian| #1# |constant|)))) (T |ByteOrder|)) ((|littleEndian| #1=(*1 *1) #2=(|isDomain| *1 (|ByteOrder|))) (|bigEndian| #1# #2#) (|unknownEndian| #1# #2#)) -((~= (#1=((|Boolean|) $ $) 7 T ELT)) (|zero?| ((#2=(|Boolean|) $) 22 T ELT)) (|subtractIfCan| (((|Union| $ "failed") $ $) 26 T ELT)) (|sample| (#3=($) 23 T CONST)) (|opposite?| ((#2# $ $) 20 T ELT)) (|latex| (((|String|) $) 11 T ELT)) (|hash| (((|SingleInteger|) $) 12 T ELT)) (|coerce| (((|OutputForm|) $) 13 T ELT)) (|before?| (#1# 6 T ELT)) (|Zero| (#3# 24 T CONST)) (= (#1# 8 T ELT)) (+ (($ $ $) 18 T ELT)) (* (($ (|PositiveInteger|) $) 17 T ELT) (($ (|NonNegativeInteger|) $) 21 T ELT))) +((~= (#1=((|Boolean|) $ $) 7 T ELT)) (|zero?| ((#2=(|Boolean|) $) 22 T ELT)) (|subtractIfCan| (((|Maybe| $) $ $) 26 T ELT)) (|sample| (#3=($) 23 T CONST)) (|opposite?| ((#2# $ $) 20 T ELT)) (|latex| (((|String|) $) 11 T ELT)) (|hash| (((|SingleInteger|) $) 12 T ELT)) (|coerce| (((|OutputForm|) $) 13 T ELT)) (|before?| (#1# 6 T ELT)) (|Zero| (#3# 24 T CONST)) (= (#1# 8 T ELT)) (+ (($ $ $) 18 T ELT)) (* (($ (|PositiveInteger|) $) 17 T ELT) (($ (|NonNegativeInteger|) $) 21 T ELT))) (((|CancellationAbelianMonoid|) (|Category|)) (T |CancellationAbelianMonoid|)) -((|subtractIfCan| (*1 *1 *1 *1) (|partial| |ofCategory| *1 (|CancellationAbelianMonoid|)))) -(|Join| (|AbelianMonoid|) (CATEGORY |domain| (SIGNATURE |subtractIfCan| ((|Union| $ "failed") $ $)))) +((|subtractIfCan| (*1 *2 *1 *1) (AND (|isDomain| *2 (|Maybe| *1)) (|ofCategory| *1 (|CancellationAbelianMonoid|))))) +(|Join| (|AbelianMonoid|) (CATEGORY |domain| (SIGNATURE |subtractIfCan| ((|Maybe| $) $ $)))) (((|AbelianMonoid|) . T) ((|AbelianSemiGroup|) . T) ((|BasicType|) . T) ((|CoercibleTo| (|OutputForm|)) . T) ((|Join|) . T) ((|SetCategory|) . T) ((|Type|) . T)) ((~= (#1=((|Boolean|) $ $) 7 T ELT)) (|setPosition| (((|Void|) $ (|NonNegativeInteger|)) 17 T ELT)) (|position| (((|NonNegativeInteger|) $) 18 T ELT)) (|latex| (((|String|) $) 11 T ELT)) (|hash| (((|SingleInteger|) $) 12 T ELT)) (|coerce| (((|OutputForm|) $) 13 T ELT)) (|before?| (#1# 6 T ELT)) (= (#1# 8 T ELT))) (((|CachableSet|) (|Category|)) (T |CachableSet|)) @@ -349,7 +349,7 @@ NIL ((~= #1=(#2=(#3=(|Boolean|) $ $) NIL T ELT)) (|verticalTab| (#4=($) 30 T CONST)) (|upperCase?| (#5=(#3# $) 42 T ELT)) (|upperCase| (#6=($ $) 52 T ELT)) (|underscore| (#4# 23 T CONST)) (|space| (#4# 21 T CONST)) (|size| ((#7=(|NonNegativeInteger|)) 13 T ELT)) (|random| (#4# 20 T ELT)) (|quote| (#4# 22 T CONST)) (|ord| ((#7# $) 17 T ELT)) (|newline| (#4# 24 T CONST)) (|min| #8=(($ $ $) NIL T ELT) #9=(#4# NIL T CONST)) (|max| #8# #9#) (|lowerCase?| (#5# 44 T ELT)) (|lowerCase| (#6# 53 T ELT)) (|lookup| ((#10=(|PositiveInteger|) $) 18 T ELT)) (|linefeed| (#4# 26 T CONST)) (|latex| ((#11=(|String|) $) 50 T ELT)) (|index| (($ #10#) 16 T ELT)) (|horizontalTab| (#4# 29 T CONST)) (|hexDigit?| (#5# 40 T ELT)) (|hash| (((|SingleInteger|) $) NIL T ELT)) (|formfeed| (#4# 27 T CONST)) (|escape| (#4# 31 T CONST)) (|digit?| (#5# 38 T ELT)) (|coerce| (((|OutputForm|) $) 33 T ELT)) (|char| (($ #7#) 14 T ELT) (($ #11#) 51 T ELT)) (|carriageReturn| (#4# 25 T CONST)) (|before?| #1#) (|backspace| (#4# 28 T CONST)) (|alphanumeric?| (#5# 48 T ELT)) (|alphabetic?| (#5# 46 T ELT)) (>= (#2# 11 T ELT)) (> (#2# 9 T ELT)) (= (#2# 7 T ELT)) (<= (#2# 10 T ELT)) (< (#2# 8 T ELT))) (((|Character|) (|Join| (|OrderedFinite|) (CATEGORY |domain| (SIGNATURE |ord| (#1=(|NonNegativeInteger|) $)) (SIGNATURE |char| ($ #1#)) (SIGNATURE |char| ($ (|String|))) (SIGNATURE |space| #2=($) |constant|) (SIGNATURE |quote| #2# |constant|) (SIGNATURE |underscore| #2# |constant|) (SIGNATURE |newline| #2# |constant|) (SIGNATURE |carriageReturn| #2# |constant|) (SIGNATURE |linefeed| #2# |constant|) (SIGNATURE |formfeed| #2# |constant|) (SIGNATURE |backspace| #2# |constant|) (SIGNATURE |horizontalTab| #2# |constant|) (SIGNATURE |verticalTab| #2# |constant|) (SIGNATURE |escape| #2# |constant|) (SIGNATURE |upperCase| #3=($ $)) (SIGNATURE |lowerCase| #3#) (SIGNATURE |digit?| #4=((|Boolean|) $)) (SIGNATURE |hexDigit?| #4#) (SIGNATURE |alphabetic?| #4#) (SIGNATURE |upperCase?| #4#) (SIGNATURE |lowerCase?| #4#) (SIGNATURE |alphanumeric?| #4#)))) (T |Character|)) ((|ord| #1=(*1 *2 *1) #2=(AND (|isDomain| *2 (|NonNegativeInteger|)) #3=(|isDomain| *1 (|Character|)))) (|char| #4=(*1 *1 *2) #2#) (|char| #4# (AND (|isDomain| *2 (|String|)) #3#)) (|space| #5=(*1 *1) #3#) (|quote| #5# #3#) (|underscore| #5# #3#) (|newline| #5# #3#) (|carriageReturn| #5# #3#) (|linefeed| #5# #3#) (|formfeed| #5# #3#) (|backspace| #5# #3#) (|horizontalTab| #5# #3#) (|verticalTab| #5# #3#) (|escape| #5# #3#) (|upperCase| #6=(*1 *1 *1) #3#) (|lowerCase| #6# #3#) (|digit?| #1# #7=(AND (|isDomain| *2 (|Boolean|)) #3#)) (|hexDigit?| #1# #7#) (|alphabetic?| #1# #7#) (|upperCase?| #1# #7#) (|lowerCase?| #1# #7#) (|alphanumeric?| #1# #7#)) -((~= (#1=((|Boolean|) $ $) 7 T ELT)) (|zero?| ((#2=(|Boolean|) $) 22 T ELT)) (|subtractIfCan| (((|Union| $ "failed") $ $) 26 T ELT)) (|sample| (#3=($) 23 T CONST)) (|recip| (((|Union| $ "failed") $) 42 T ELT)) (|opposite?| ((#2# $ $) 20 T ELT)) (|one?| (((|Boolean|) $) 44 T ELT)) (|latex| (((|String|) $) 11 T ELT)) (|hash| (((|SingleInteger|) $) 12 T ELT)) (|coerce| (((|OutputForm|) $) 13 T ELT) (($ (|Integer|)) 41 T ELT)) (|charthRoot| (((|Maybe| $) $) 47 T ELT)) (|characteristic| (((|NonNegativeInteger|)) 40 T CONST)) (|before?| (#1# 6 T ELT)) (|annihilate?| (((|Boolean|) $ $) 33 T ELT)) (|Zero| (#3# 24 T CONST)) (|One| (($) 45 T CONST)) (= (#1# 8 T ELT)) (- (($ $) 29 T ELT) (($ $ $) 28 T ELT)) (+ (($ $ $) 18 T ELT)) (** (($ $ (|PositiveInteger|)) 35 T ELT) (($ $ (|NonNegativeInteger|)) 43 T ELT)) (* (($ (|PositiveInteger|) $) 17 T ELT) (($ (|NonNegativeInteger|) $) 21 T ELT) (($ (|Integer|) $) 30 T ELT) (($ $ $) 34 T ELT))) +((~= (#1=((|Boolean|) $ $) 7 T ELT)) (|zero?| ((#2=(|Boolean|) $) 22 T ELT)) (|subtractIfCan| (((|Maybe| $) $ $) 26 T ELT)) (|sample| (#3=($) 23 T CONST)) (|recip| (((|Union| $ "failed") $) 43 T ELT)) (|opposite?| ((#2# $ $) 20 T ELT)) (|one?| (((|Boolean|) $) 45 T ELT)) (|latex| (((|String|) $) 11 T ELT)) (|hash| (((|SingleInteger|) $) 12 T ELT)) (|coerce| (((|OutputForm|) $) 13 T ELT) (($ (|Integer|)) 42 T ELT)) (|charthRoot| (((|Maybe| $) $) 48 T ELT)) (|characteristic| (((|NonNegativeInteger|)) 41 T CONST)) (|before?| (#1# 6 T ELT)) (|annihilate?| (((|Boolean|) $ $) 34 T ELT)) (|Zero| (#3# 24 T CONST)) (|One| (($) 46 T CONST)) (= (#1# 8 T ELT)) (- (($ $) 30 T ELT) (($ $ $) 29 T ELT)) (+ (($ $ $) 18 T ELT)) (** (($ $ (|PositiveInteger|)) 36 T ELT) (($ $ (|NonNegativeInteger|)) 44 T ELT)) (* (($ (|PositiveInteger|) $) 17 T ELT) (($ (|NonNegativeInteger|) $) 21 T ELT) (($ (|Integer|) $) 31 T ELT) (($ $ $) 35 T ELT))) (((|CharacteristicNonZero|) (|Category|)) (T |CharacteristicNonZero|)) ((|charthRoot| (*1 *2 *1) (AND (|isDomain| *2 (|Maybe| *1)) (|ofCategory| *1 (|CharacteristicNonZero|))))) (|Join| (|Ring|) (CATEGORY |domain| (SIGNATURE |charthRoot| ((|Maybe| $) $)))) @@ -357,7 +357,7 @@ NIL ((|characteristicPolynomial| ((|#1| (|Matrix| |#1|) |#1|) 19 T ELT))) (((|CharacteristicPolynomialPackage| |#1|) (CATEGORY |package| (SIGNATURE |characteristicPolynomial| (|#1| (|Matrix| |#1|) |#1|))) (|CommutativeRing|)) (T |CharacteristicPolynomialPackage|)) ((|characteristicPolynomial| (*1 *2 *3 *2) (AND (|isDomain| *3 (|Matrix| *2)) (|ofCategory| *2 (|CommutativeRing|)) (|isDomain| *1 (|CharacteristicPolynomialPackage| *2))))) -((~= (#1=((|Boolean|) $ $) 7 T ELT)) (|zero?| ((#2=(|Boolean|) $) 22 T ELT)) (|subtractIfCan| (((|Union| $ "failed") $ $) 26 T ELT)) (|sample| (#3=($) 23 T CONST)) (|recip| (((|Union| $ "failed") $) 42 T ELT)) (|opposite?| ((#2# $ $) 20 T ELT)) (|one?| (((|Boolean|) $) 44 T ELT)) (|latex| (((|String|) $) 11 T ELT)) (|hash| (((|SingleInteger|) $) 12 T ELT)) (|coerce| (((|OutputForm|) $) 13 T ELT) (($ (|Integer|)) 41 T ELT)) (|characteristic| (((|NonNegativeInteger|)) 40 T CONST)) (|before?| (#1# 6 T ELT)) (|annihilate?| (((|Boolean|) $ $) 33 T ELT)) (|Zero| (#3# 24 T CONST)) (|One| (($) 45 T CONST)) (= (#1# 8 T ELT)) (- (($ $) 29 T ELT) (($ $ $) 28 T ELT)) (+ (($ $ $) 18 T ELT)) (** (($ $ (|PositiveInteger|)) 35 T ELT) (($ $ (|NonNegativeInteger|)) 43 T ELT)) (* (($ (|PositiveInteger|) $) 17 T ELT) (($ (|NonNegativeInteger|) $) 21 T ELT) (($ (|Integer|) $) 30 T ELT) (($ $ $) 34 T ELT))) +((~= (#1=((|Boolean|) $ $) 7 T ELT)) (|zero?| ((#2=(|Boolean|) $) 22 T ELT)) (|subtractIfCan| (((|Maybe| $) $ $) 26 T ELT)) (|sample| (#3=($) 23 T CONST)) (|recip| (((|Union| $ "failed") $) 43 T ELT)) (|opposite?| ((#2# $ $) 20 T ELT)) (|one?| (((|Boolean|) $) 45 T ELT)) (|latex| (((|String|) $) 11 T ELT)) (|hash| (((|SingleInteger|) $) 12 T ELT)) (|coerce| (((|OutputForm|) $) 13 T ELT) (($ (|Integer|)) 42 T ELT)) (|characteristic| (((|NonNegativeInteger|)) 41 T CONST)) (|before?| (#1# 6 T ELT)) (|annihilate?| (((|Boolean|) $ $) 34 T ELT)) (|Zero| (#3# 24 T CONST)) (|One| (($) 46 T CONST)) (= (#1# 8 T ELT)) (- (($ $) 30 T ELT) (($ $ $) 29 T ELT)) (+ (($ $ $) 18 T ELT)) (** (($ $ (|PositiveInteger|)) 36 T ELT) (($ $ (|NonNegativeInteger|)) 44 T ELT)) (* (($ (|PositiveInteger|) $) 17 T ELT) (($ (|NonNegativeInteger|) $) 21 T ELT) (($ (|Integer|) $) 31 T ELT) (($ $ $) 35 T ELT))) (((|CharacteristicZero|) (|Category|)) (T |CharacteristicZero|)) NIL (|Join| (|Ring|)) @@ -376,9 +376,9 @@ NIL ((|construct| (*1 *1 *2) (AND (|isDomain| *2 (|List| *3)) (|ofCategory| *3 (|Type|)) (|ofCategory| *1 (|Collection| *3)))) (|remove| (*1 *1 *2 *1) (AND (|isDomain| *2 (|Mapping| (|Boolean|) *3)) (|ofCategory| *1 (|FiniteAggregate| *3)) (|ofCategory| *1 (|Collection| *3)) (|ofCategory| *3 (|Type|)))) (|select| (*1 *1 *2 *1) (AND (|isDomain| *2 (|Mapping| (|Boolean|) *3)) (|ofCategory| *1 (|FiniteAggregate| *3)) (|ofCategory| *1 (|Collection| *3)) (|ofCategory| *3 (|Type|)))) (|remove| (*1 *1 *2 *1) (AND (|ofCategory| *1 (|FiniteAggregate| *2)) (|ofCategory| *1 (|Collection| *2)) (|ofCategory| *2 (|Type|)) (|ofCategory| *2 (|BasicType|)))) (|removeDuplicates| (*1 *1 *1) (AND (|ofCategory| *1 (|FiniteAggregate| *2)) (|ofCategory| *1 (|Collection| *2)) (|ofCategory| *2 (|Type|)) (|ofCategory| *2 (|BasicType|))))) (|Join| (|HomogeneousAggregate| |t#1|) (CATEGORY |domain| (SIGNATURE |construct| ($ (|List| |t#1|))) (IF (|has| $ (|FiniteAggregate| |t#1|)) (PROGN (SIGNATURE |remove| ($ (|Mapping| (|Boolean|) |t#1|) $)) (SIGNATURE |select| ($ (|Mapping| (|Boolean|) |t#1|) $)) (IF (|has| |t#1| (|BasicType|)) (PROGN (SIGNATURE |remove| ($ |t#1| $)) (SIGNATURE |removeDuplicates| ($ $))) |%noBranch|)) |%noBranch|) (IF (|has| |t#1| (|ConvertibleTo| (|InputForm|))) (ATTRIBUTE (|ConvertibleTo| (|InputForm|))) |%noBranch|))) (((|Aggregate|) . T) ((|BasicType|) OR (|has| |#1| (|SetCategory|)) (|has| |#1| (|BasicType|))) ((|CoercibleTo| (|OutputForm|)) OR (|has| |#1| (|SetCategory|)) (|has| |#1| (|CoercibleTo| (|OutputForm|)))) ((|ConvertibleTo| (|InputForm|)) |has| |#1| (|ConvertibleTo| (|InputForm|))) ((|Evalable| |#1|) AND (|has| |#1| (|Evalable| |#1|)) (|has| |#1| (|SetCategory|))) ((|Functorial| |#1|) . T) ((|HomogeneousAggregate| |#1|) . T) ((|InnerEvalable| |#1| |#1|) AND (|has| |#1| (|Evalable| |#1|)) (|has| |#1| (|SetCategory|))) ((|Join|) . T) ((|SetCategory|) |has| |#1| (|SetCategory|)) ((|Type|) . T)) -((~= #1=(#2=(#3=(|Boolean|) $ $) NIL T ELT)) (|zero?| #4=((#3# $) NIL T ELT)) (|subtractIfCan| ((#5=(|Union| $ "failed") $ $) NIL T ELT)) (|sample| (#6=($) NIL T CONST)) (|recip| ((#5# $) 113 T ELT)) (|opposite?| #1#) (|one?| #4#) (|monomial| (($ |#2| #7=(|List| #8=(|PositiveInteger|))) 72 T ELT)) (|latex| (((|String|) $) NIL T ELT)) (|hash| (((|SingleInteger|) $) NIL T ELT)) (|e| (($ #8#) 58 T ELT)) (|dimension| (((|CardinalNumber|)) 23 T ELT)) (|coerce| (((|OutputForm|) $) 88 T ELT) (($ #9=(|Integer|)) 54 T ELT) (($ |#2|) 55 T ELT)) (|coefficient| ((|#2| $ #7#) 75 T ELT)) (|characteristic| ((#10=(|NonNegativeInteger|)) 20 T CONST)) (|before?| #1#) (|annihilate?| #1#) (|Zero| (#6# 48 T CONST)) (|One| (#6# 52 T CONST)) (= (#2# 34 T ELT)) (/ #11=(($ $ |#2|) NIL T ELT)) (- (($ $) 43 T ELT) (#12=($ $ $) 41 T ELT)) (+ (#12# 39 T ELT)) (** (($ $ #8#) NIL T ELT) (($ $ #10#) NIL T ELT)) (* (($ #8# $) NIL T ELT) (($ #10# $) NIL T ELT) (($ #9# $) 45 T ELT) (#12# 64 T ELT) (($ |#2| $) 47 T ELT) #11#)) -(((|CliffordAlgebra| |#1| |#2| |#3|) (|Join| (|Ring|) (|Algebra| |#2|) (|VectorSpace| |#2|) (CATEGORY |domain| (SIGNATURE |e| ($ #1=(|PositiveInteger|))) (SIGNATURE |monomial| ($ |#2| #2=(|List| #1#))) (SIGNATURE |coefficient| (|#2| $ #2#)) (SIGNATURE |recip| ((|Union| $ "failed") $)))) #1# (|Field|) (|QuadraticForm| |#1| |#2|)) (T |CliffordAlgebra|)) -((|recip| (*1 *1 *1) (|partial| AND (|isDomain| *1 (|CliffordAlgebra| *2 *3 *4)) (|ofType| *2 #1=(|PositiveInteger|)) (|ofCategory| *3 #2=(|Field|)) (|ofType| *4 (|QuadraticForm| *2 *3)))) (|e| (*1 *1 *2) (AND (|isDomain| *2 #1#) (|isDomain| *1 (|CliffordAlgebra| *3 *4 *5)) (|ofType| *3 *2) (|ofCategory| *4 #2#) (|ofType| *5 (|QuadraticForm| *3 *4)))) (|monomial| (*1 *1 *2 *3) (AND #3=(|isDomain| *3 (|List| #1#)) #4=(|isDomain| *1 (|CliffordAlgebra| *4 *2 *5)) #5=(|ofType| *4 #1#) #6=(|ofCategory| *2 #2#) #7=(|ofType| *5 (|QuadraticForm| *4 *2)))) (|coefficient| (*1 *2 *1 *3) (AND #3# #6# #4# #5# #7#))) +((~= #1=(#2=(#3=(|Boolean|) $ $) NIL T ELT)) (|zero?| #4=((#3# $) NIL T ELT)) (|subtractIfCan| (((|Maybe| $) $ $) NIL T ELT)) (|sample| (#5=($) NIL T CONST)) (|recip| (((|Union| $ "failed") $) 113 T ELT)) (|opposite?| #1#) (|one?| #4#) (|monomial| (($ |#2| #6=(|List| #7=(|PositiveInteger|))) 72 T ELT)) (|latex| (((|String|) $) NIL T ELT)) (|hash| (((|SingleInteger|) $) NIL T ELT)) (|e| (($ #7#) 58 T ELT)) (|dimension| (((|CardinalNumber|)) 23 T ELT)) (|coerce| (((|OutputForm|) $) 88 T ELT) (($ #8=(|Integer|)) 54 T ELT) (($ |#2|) 55 T ELT)) (|coefficient| ((|#2| $ #6#) 75 T ELT)) (|characteristic| ((#9=(|NonNegativeInteger|)) 20 T CONST)) (|before?| #1#) (|annihilate?| #1#) (|Zero| (#5# 48 T CONST)) (|One| (#5# 52 T CONST)) (= (#2# 34 T ELT)) (/ #10=(($ $ |#2|) NIL T ELT)) (- (($ $) 43 T ELT) (#11=($ $ $) 41 T ELT)) (+ (#11# 39 T ELT)) (** (($ $ #7#) NIL T ELT) (($ $ #9#) NIL T ELT)) (* (($ #7# $) NIL T ELT) (($ #9# $) NIL T ELT) (($ #8# $) 45 T ELT) (#11# 64 T ELT) (($ |#2| $) 47 T ELT) #10#)) +(((|CliffordAlgebra| |#1| |#2| |#3|) (|Join| (|Ring|) (|Algebra| |#2|) (|VectorSpace| |#2|) (CATEGORY |domain| (SIGNATURE |e| ($ #1=(|PositiveInteger|))) (SIGNATURE |monomial| ($ |#2| #2=(|List| #1#))) (SIGNATURE |coefficient| (|#2| $ #2#)))) #1# (|Field|) (|QuadraticForm| |#1| |#2|)) (T |CliffordAlgebra|)) +((|e| (*1 *1 *2) (AND (|isDomain| *2 #1=(|PositiveInteger|)) (|isDomain| *1 (|CliffordAlgebra| *3 *4 *5)) (|ofType| *3 *2) (|ofCategory| *4 #2=(|Field|)) (|ofType| *5 (|QuadraticForm| *3 *4)))) (|monomial| (*1 *1 *2 *3) (AND #3=(|isDomain| *3 (|List| #1#)) #4=(|isDomain| *1 (|CliffordAlgebra| *4 *2 *5)) #5=(|ofType| *4 #1#) #6=(|ofCategory| *2 #2#) #7=(|ofType| *5 (|QuadraticForm| *4 *2)))) (|coefficient| (*1 *2 *1 *3) (AND #3# #6# #4# #5# #7#))) ((|clipWithRanges| ((#1=(|Record| (|:| |brans| #2=(|List| #3=(|List| (|Point| #4=(|DoubleFloat|))))) (|:| |xValues| #5=(|Segment| #4#)) (|:| |yValues| #5#)) #2# #4# #4# #4# #4#) 59 T ELT)) (|clipParametric| (#6=(#1# #7=(|Plot|) #8=(|Fraction| (|Integer|)) #8#) 95 T ELT) (#9=(#1# #7#) 96 T ELT)) (|clip| ((#1# #2#) 99 T ELT) ((#1# #3#) 98 T ELT) (#6# 89 T ELT) (#9# 90 T ELT))) (((|TwoDimensionalPlotClipping|) (CATEGORY |package| (SIGNATURE |clip| #1=(#2=(|Record| (|:| |brans| #3=(|List| #4=(|List| (|Point| #5=(|DoubleFloat|))))) (|:| |xValues| #6=(|Segment| #5#)) (|:| |yValues| #6#)) #7=(|Plot|))) (SIGNATURE |clip| #8=(#2# #7# #9=(|Fraction| (|Integer|)) #9#)) (SIGNATURE |clipParametric| #1#) (SIGNATURE |clipParametric| #8#) (SIGNATURE |clipWithRanges| (#2# #3# #5# #5# #5# #5#)) (SIGNATURE |clip| (#2# #4#)) (SIGNATURE |clip| (#2# #3#)))) (T |TwoDimensionalPlotClipping|)) ((|clip| #1=(*1 *2 *3) (AND #2=(|isDomain| *2 (|Record| (|:| |brans| #3=(|List| #4=(|List| (|Point| #5=(|DoubleFloat|))))) (|:| |xValues| #6=(|Segment| #5#)) (|:| |yValues| #6#))) #7=(|isDomain| *1 (|TwoDimensionalPlotClipping|)) (|isDomain| *3 #3#))) (|clip| #1# (AND #2# #7# (|isDomain| *3 #4#))) (|clipWithRanges| (*1 *2 *3 *4 *4 *4 *4) (AND 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T) ((|MappingCategory| |#1| |#1| |#1|) . T) ((|Type|) . 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(|ComplexCategory| |#2|) (|CommutativeRing|)) (T |ComplexCategory&|)) +((|unitNormal| (((|Record| (|:| |unit| $) (|:| |canonical| $) (|:| |associate| $)) $) 222 T ELT)) (|trace| (#1=(|#2| $) 102 T ELT)) (|tanh| (#2=($ $) 255 T ELT)) (|tan| (#2# 249 T ELT)) (|solveLinearPolynomialEquation| (((|Union| #3=(|List| #4=(|SparseUnivariatePolynomial| $)) #5="failed") #3# #4#) 47 T ELT)) (|sinh| (#2# 253 T ELT)) (|sin| (#2# 247 T ELT)) (|retractIfCan| (((|Union| #6=(|Integer|) #5#) $) NIL T ELT) (#7=((|Union| #8=(|Fraction| #6#) #5#) $) NIL T ELT) (((|Union| |#2| #5#) $) 146 T ELT)) (|retract| ((#6# $) NIL T ELT) (#9=(#8# $) NIL T ELT) (#1# 144 T ELT)) (|rem| (#10=($ $ $) 228 T ELT)) (|reducedSystem| ((#11=(|Matrix| #6#) #12=(|Matrix| $)) NIL T ELT) (((|Record| (|:| |mat| #11#) (|:| |vec| (|Vector| #6#))) #12# #13=(|Vector| $)) NIL T ELT) (((|Record| (|:| |mat| #14=(|Matrix| |#2|)) (|:| |vec| #15=(|Vector| |#2|))) #12# #13#) 160 T ELT) ((#14# #12#) 154 T ELT)) (|reduce| (#16=($ 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ELT) (($ $ #65#) 147 (OR (|and| (|has| |#1| . #18#) (|has| |#1| . #68#)) (|and| (|has| |#1| . #18#) (|has| |#1| . #69#)) (|has| |#1| . #68#)) ELT)) (= (#1# 8 T ELT)) (/ (($ $ $) 141 (|has| |#1| . #18#) ELT)) (- (($ $) 30 T ELT) (($ $ $) 29 T ELT)) (+ (($ $ $) 18 T ELT)) (** (($ $ (|PositiveInteger|)) 36 T ELT) (($ $ (|NonNegativeInteger|)) 44 T ELT) (($ $ (|Fraction| #46#)) 261 (AND (|has| |#1| . #20#) (|has| |#1| . #21#)) ELT) (($ $ $) 259 (|has| |#1| . #10#) ELT) (($ $ #78#) 138 (|has| |#1| . #18#) ELT)) (* (($ (|PositiveInteger|) $) 17 T ELT) (($ (|NonNegativeInteger|) $) 21 T ELT) (($ (|Integer|) . #81=($)) 31 T ELT) (($ $ $) 35 T ELT) (($ $ |#1|) 55 T ELT) (($ |#1| . #81#) 54 T ELT) (($ #77# . #81#) 140 (|has| |#1| . #18#) ELT) (($ $ #77#) 139 (|has| |#1| . #18#) ELT))) (((|ComplexCategory| |#1|) (|Category|) (|CommutativeRing|)) (T |ComplexCategory|)) ((|norm| (*1 *2 *1) (AND (|ofCategory| *1 (|ComplexCategory| *2)) (|ofCategory| *2 (|CommutativeRing|)))) (|imaginary| (*1 *1) (AND (|ofCategory| *1 (|ComplexCategory| *2)) (|ofCategory| *2 (|CommutativeRing|)))) (|conjugate| (*1 *1 *1) (AND (|ofCategory| *1 (|ComplexCategory| *2)) (|ofCategory| *2 (|CommutativeRing|)))) (|complex| (*1 *1 *2 *2) (AND (|ofCategory| *1 (|ComplexCategory| *2)) (|ofCategory| *2 (|CommutativeRing|)))) (|imag| (*1 *2 *1) (AND (|ofCategory| *1 (|ComplexCategory| *2)) (|ofCategory| *2 (|CommutativeRing|)))) (|real| (*1 *2 *1) (AND (|ofCategory| *1 (|ComplexCategory| *2)) (|ofCategory| *2 (|CommutativeRing|)))) (|exquo| (*1 *1 *1 *2) (|partial| AND (|ofCategory| *1 (|ComplexCategory| *2)) (|ofCategory| *2 (|CommutativeRing|)) (|ofCategory| *2 (|IntegralDomain|)))) (|abs| (*1 *1 *1) (AND (|ofCategory| *1 (|ComplexCategory| *2)) (|ofCategory| *2 (|CommutativeRing|)) (|ofCategory| *2 (|RealNumberSystem|)))) (|argument| (*1 *2 *1) (AND (|ofCategory| *1 (|ComplexCategory| *2)) (|ofCategory| *2 (|CommutativeRing|)) (|ofCategory| *2 (|TranscendentalFunctionCategory|)))) (|polarCoordinates| (*1 *2 *1) (AND (|ofCategory| *1 (|ComplexCategory| *3)) (|ofCategory| *3 (|CommutativeRing|)) (|ofCategory| *3 (|RealNumberSystem|)) (|ofCategory| *3 (|TranscendentalFunctionCategory|)) (|isDomain| *2 (|Record| (|:| |r| *3) (|:| |phi| *3))))) (|rational?| (*1 *2 *1) (AND (|ofCategory| *1 (|ComplexCategory| *3)) (|ofCategory| *3 (|CommutativeRing|)) (|ofCategory| *3 (|IntegerNumberSystem|)) (|isDomain| *2 (|Boolean|)))) (|rational| (*1 *2 *1) (AND (|ofCategory| *1 (|ComplexCategory| *3)) (|ofCategory| *3 (|CommutativeRing|)) (|ofCategory| *3 (|IntegerNumberSystem|)) (|isDomain| *2 (|Fraction| (|Integer|))))) (|rationalIfCan| (*1 *2 *1) (|partial| AND (|ofCategory| *1 (|ComplexCategory| *3)) (|ofCategory| *3 (|CommutativeRing|)) (|ofCategory| *3 (|IntegerNumberSystem|)) (|isDomain| *2 (|Fraction| (|Integer|)))))) (|Join| (|MonogenicAlgebra| |t#1| (|SparseUnivariatePolynomial| |t#1|)) (|FullyRetractableTo| |t#1|) (|DifferentialExtension| |t#1|) (|FullyEvalableOver| |t#1|) (|FullyPatternMatchable| |t#1|) (|Patternable| |t#1|) (|FullyLinearlyExplicitRingOver| |t#1|) (|CommutativeRing|) (CATEGORY |domain| (ATTRIBUTE |complex|) (SIGNATURE |imaginary| ($)) (SIGNATURE |conjugate| ($ $)) (SIGNATURE |complex| ($ |t#1| |t#1|)) (SIGNATURE |imag| (|t#1| $)) (SIGNATURE |real| (|t#1| $)) (SIGNATURE |norm| (|t#1| $)) (IF (|has| |t#1| (|IntegralDomain|)) (PROGN (ATTRIBUTE (|IntegralDomain|)) (SIGNATURE |exquo| ((|Union| $ "failed") $ |t#1|))) |%noBranch|) (IF (|has| |t#1| (|EuclideanDomain|)) (ATTRIBUTE (|EuclideanDomain|)) |%noBranch|) (IF (|has| |t#1| (ATTRIBUTE |multiplicativeValuation|)) (ATTRIBUTE |multiplicativeValuation|) |%noBranch|) (IF (|has| |t#1| (ATTRIBUTE |additiveValuation|)) (ATTRIBUTE |additiveValuation|) |%noBranch|) (IF (|has| |t#1| (|Field|)) (ATTRIBUTE (|Field|)) |%noBranch|) (IF (|has| |t#1| (|ConvertibleTo| (|InputForm|))) (ATTRIBUTE (|ConvertibleTo| (|InputForm|))) |%noBranch|) (IF (|has| |t#1| (|CharacteristicZero|)) (ATTRIBUTE (|CharacteristicZero|)) |%noBranch|) (IF (|has| |t#1| (|CharacteristicNonZero|)) (ATTRIBUTE (|CharacteristicNonZero|)) |%noBranch|) (IF (|has| |t#1| (|RealConstant|)) (PROGN (ATTRIBUTE (|ConvertibleTo| (|Complex| (|DoubleFloat|)))) (ATTRIBUTE (|ConvertibleTo| (|Complex| (|Float|))))) |%noBranch|) (IF (|has| |t#1| (|RealNumberSystem|)) (SIGNATURE |abs| ($ $)) |%noBranch|) (IF (|has| |t#1| (|TranscendentalFunctionCategory|)) (PROGN (ATTRIBUTE (|TranscendentalFunctionCategory|)) (SIGNATURE |argument| (|t#1| $)) (IF (|has| |t#1| (|RadicalCategory|)) (ATTRIBUTE (|RadicalCategory|)) |%noBranch|) (IF (|has| |t#1| (|RealNumberSystem|)) (SIGNATURE |polarCoordinates| ((|Record| (|:| |r| |t#1|) (|:| |phi| |t#1|)) $)) |%noBranch|)) |%noBranch|) (IF (|has| |t#1| (|IntegerNumberSystem|)) (PROGN (SIGNATURE |rational?| ((|Boolean|) $)) (SIGNATURE |rational| ((|Fraction| (|Integer|)) $)) (SIGNATURE |rationalIfCan| ((|Union| (|Fraction| (|Integer|)) "failed") $))) |%noBranch|) (IF (|has| |t#1| (|PolynomialFactorizationExplicit|)) (IF (|has| |t#1| (|EuclideanDomain|)) (ATTRIBUTE (|PolynomialFactorizationExplicit|)) |%noBranch|) |%noBranch|))) @@ -439,7 +439,7 @@ NIL ((|macroExpand| ((#1=(|SpadAst|) #1# (|Environment|)) 8 T ELT)) (|elaborateFile| (((|List| #2=(|Maybe| (|Elaboration|))) (|String|)) 81 T ELT)) (|elaborate| ((#2# #1#) 76 T ELT))) (((|CompilerPackage|) (|Join| (|Type|) (CATEGORY |package| (SIGNATURE |macroExpand| (#1=(|SpadAst|) #1# (|Environment|))) (SIGNATURE |elaborate| (#2=(|Maybe| (|Elaboration|)) #1#)) (SIGNATURE |elaborateFile| ((|List| #2#) (|String|)))))) (T |CompilerPackage|)) ((|macroExpand| (*1 *2 *2 *3) (AND (|isDomain| *2 #1=(|SpadAst|)) (|isDomain| *3 (|Environment|)) #2=(|isDomain| *1 (|CompilerPackage|)))) (|elaborate| #3=(*1 *2 *3) (AND (|isDomain| *3 #1#) (|isDomain| *2 #4=(|Maybe| (|Elaboration|))) #2#)) (|elaborateFile| #3# (AND (|isDomain| *3 (|String|)) (|isDomain| *2 (|List| #4#)) #2#))) -((~= #1=(#2=(#3=(|Boolean|) $ $) NIL T ELT)) (|zero?| (#4=(#3# $) 15 T ELT)) (|unitNormal| (((|Record| (|:| |unit| $) (|:| |canonical| $) (|:| |associate| $)) $) NIL #5=(OR #6=(AND #7=(|has| |#1| (|EuclideanDomain|)) #8=(|has| |#1| (|PolynomialFactorizationExplicit|))) #9=(|has| |#1| (|IntegralDomain|))) ELT)) (|unitCanonical| #10=(#11=($ $) NIL #5# ELT)) (|unit?| (#4# NIL #5# ELT)) (|traceMatrix| #12=((#13=(|Matrix| |#1|) #14=(|Vector| $)) NIL T ELT) ((#13#) NIL T ELT)) (|trace| #15=(#16=(|#1| $) NIL T ELT)) (|tanh| #17=(#11# NIL #18=(|has| |#1| (|TranscendentalFunctionCategory|)) ELT)) (|tan| #17#) (|tableForDiscreteLogarithm| (((|Table| #19=(|PositiveInteger|) #20=(|NonNegativeInteger|)) #21=(|Integer|)) NIL #22=(|has| |#1| (|FiniteFieldCategory|)) ELT)) (|subtractIfCan| (#23=(#24=(|Union| $ #25="failed") $ $) NIL T ELT)) (|squareFreePolynomial| #26=(((|Factored| #27=(|SparseUnivariatePolynomial| $)) #27#) NIL #6# ELT)) (|squareFreePart| (#11# NIL #28=(OR #6# #29=(|has| |#1| (|Field|))) ELT)) (|squareFree| #30=(((|Factored| $) $) NIL #28# ELT)) (|sqrt| (#11# NIL #31=(AND (|has| |#1| (|RadicalCategory|)) #18#) ELT)) (|solveLinearPolynomialEquation| (((|Union| #32=(|List| #27#) #25#) #32# #27#) NIL #6# ELT)) (|sizeLess?| (#2# NIL #7# ELT)) (|size| (#33=(#20#) NIL #34=(|has| |#1| (|Finite|)) ELT)) (|sinh| #17#) (|sin| #17#) (|sech| #17#) (|sec| #17#) (|sample| (#35=($) NIL T CONST)) (|retractIfCan| (((|Union| #21# . #36=(#25#)) . #37=($)) NIL #38=(|has| |#1| (|RetractableTo| #21#)) ELT) (#39=((|Union| #40=(|Fraction| #21#) . #36#) . #37#) NIL #41=(|has| |#1| (|RetractableTo| #40#)) ELT) (((|Union| |#1| . #36#) . #37#) NIL T ELT)) (|retract| ((#21# . #42=($)) NIL #38# ELT) (#43=(#40# . #42#) NIL #41# ELT) #15#) (|represents| (($ #44=(|Vector| |#1|) #14#) NIL T ELT) #45=(($ #44#) NIL T ELT)) (|representationType| (((|Union| "prime" "polynomial" "normal" "cyclic")) NIL #22# ELT)) (|rem| #46=(#47=($ $ $) NIL #7# ELT)) (|regularRepresentation| ((#13# $ #14#) NIL T ELT) ((#13# $) NIL T ELT)) (|reducedSystem| ((#48=(|Matrix| #21#) . #49=(#50=(|Matrix| $))) NIL #51=(|has| |#1| (|LinearlyExplicitRingOver| #21#)) ELT) ((#52=(|Record| (|:| |mat| #48#) (|:| |vec| (|Vector| #21#))) . #53=(#50# #14#)) NIL #51# ELT) ((#54=(|Record| (|:| |mat| #13#) (|:| |vec| #44#)) . #53#) NIL T ELT) ((#13# . #49#) NIL T ELT)) (|reduce| #55=(($ #56=(|SparseUnivariatePolynomial| |#1|)) NIL T ELT) ((#24# (|Fraction| #56#)) NIL #29# ELT)) (|recip| ((#24# $) NIL T ELT)) (|real| (#16# 20 T ELT)) (|rationalIfCan| (#39# NIL #57=(|has| |#1| (|IntegerNumberSystem|)) ELT)) (|rational?| (#4# NIL #57# ELT)) (|rational| (#43# NIL #57# ELT)) (|rank| ((#19#) NIL T ELT)) (|random| (#35# NIL #34# ELT)) (|quo| #46#) (|principalIdeal| (((|Record| (|:| |coef| #58=(|List| $)) #59=(|:| |generator| $)) #58#) NIL #7# ELT)) (|primitiveElement| #60=(#35# NIL #22# ELT)) (|primitive?| (#4# NIL #22# ELT)) (|primeFrobenius| (#61=($ $ #20#) NIL #22# ELT) #62=(#11# NIL #22# ELT)) (|prime?| (#4# NIL #28# ELT)) (|polarCoordinates| (((|Record| (|:| |r| |#1|) (|:| |phi| |#1|)) $) NIL (AND #63=(|has| |#1| (|RealNumberSystem|)) #18#) ELT)) (|pi| (#35# NIL #18# ELT)) (|patternMatch| ((#64=(|PatternMatchResult| #21# . #65=($)) $ #66=(|Pattern| #21#) #64#) NIL (|has| |#1| (|PatternMatchable| #21#)) ELT) ((#67=(|PatternMatchResult| #68=(|Float|) . #65#) $ #69=(|Pattern| #68#) #67#) NIL (|has| |#1| (|PatternMatchable| #68#)) ELT)) (|order| (#70=(#19# $) NIL #22# ELT) (((|OnePointCompletion| #19#) $) NIL #22# ELT)) (|opposite?| #1#) (|one?| (#4# 17 T ELT)) (|nthRoot| (#71=($ $ #21#) NIL #31# ELT)) (|norm| (#16# 30 T ELT)) (|nextItem| (#72=((|Maybe| $) $) NIL #22# ELT)) (|multiEuclidean| (((|Union| #58# #25#) #58# $) NIL #7# ELT)) (|minimalPolynomial| (#73=(#56# $) NIL #29# ELT)) (|map| (($ #74=(|Mapping| |#1| |#1|) $) NIL T ELT)) (|lookup| (#70# NIL #34# ELT)) (|log| #17#) (|lift| #75=(#73# NIL T ELT)) (|leftReducedSystem| ((#48# #14#) NIL #51# ELT) ((#52# . #76=(#14# $)) NIL #51# ELT) ((#54# . #76#) NIL T ELT) #12#) (|lcm| #77=(($ #58#) NIL #7# ELT) #46#) (|latex| (((|String|) $) NIL T ELT)) (|inv| (#11# NIL #29# ELT)) (|init| (#35# NIL #22# CONST)) (|index| (($ #19#) NIL #34# ELT)) (|imaginary| #78=(#35# NIL T ELT)) (|imag| (#16# 21 T ELT)) (|hash| (((|SingleInteger|) $) NIL T ELT)) (|generator| #78#) (|gcdPolynomial| ((#27# #27# #27#) NIL #7# ELT)) (|gcd| #77# #46#) (|factorsOfCyclicGroupSize| (((|List| (|Record| (|:| |factor| #21#) (|:| |exponent| #21#)))) NIL #22# ELT)) (|factorSquareFreePolynomial| #26#) (|factorPolynomial| #26#) (|factor| #30#) (|extendedEuclidean| (((|Union| (|Record| #79=(|:| |coef1| $) #80=(|:| |coef2| $)) #25#) $ $ $) NIL #7# ELT) (((|Record| #79# #80# #59#) $ $) NIL #7# ELT)) (|exquo| ((#24# $ |#1|) 28 #9# ELT) (#23# 31 #5# ELT)) (|expressIdealMember| (((|Maybe| #58#) #58# $) NIL #7# ELT)) (|exp| #17#) (|eval| (($ $ #81=(|List| |#1|) #81#) NIL #82=(|has| |#1| (|Evalable| |#1|)) ELT) (($ $ |#1| |#1|) NIL #82# ELT) (($ $ #83=(|Equation| |#1|)) NIL #82# ELT) (($ $ (|List| #83#)) NIL #82# ELT) (($ $ #84=(|List| #85=(|Symbol|)) #81#) NIL #86=(|has| |#1| (|InnerEvalable| #85# |#1|)) ELT) (($ $ #85# |#1|) NIL #86# ELT)) (|euclideanSize| (#87=(#20# $) NIL #7# ELT)) (|elt| (#88=($ $ |#1|) NIL (|has| |#1| (|Eltable| |#1| |#1|)) ELT)) (|divide| (((|Record| (|:| |quotient| $) (|:| |remainder| $)) $ $) NIL #7# ELT)) (|discriminant| ((|#1| #14#) NIL T ELT) ((|#1|) NIL T ELT)) (|discreteLog| (#87# NIL #22# ELT) (((|Union| #20# #25#) $ $) NIL #22# ELT)) (|differentiate| #89=(($ $ #74#) NIL T ELT) #90=(($ $ #74# #20#) NIL T ELT) #91=(($ $ #84# (|List| #20#)) NIL #92=(OR (AND #29# (|has| |#1| (|PartialDifferentialRing| #85#))) (|has| |#1| (|PartialDifferentialSpace| #85#))) ELT) #93=(($ $ #85# #20#) NIL #92# ELT) #94=(($ $ #84#) NIL #92# ELT) #95=(($ $ #85#) NIL #92# ELT) #96=(#61# NIL #97=(OR (AND (|has| |#1| (|DifferentialRing|)) #29#) (|has| |#1| (|DifferentialSpace|))) ELT) #98=(#11# NIL #97# ELT)) (|derivationCoordinates| ((#13# #14# #74#) NIL #29# ELT)) (|definingPolynomial| ((#56#) NIL T ELT)) (|csch| #17#) (|csc| #17#) (|createPrimitiveElement| #60#) (|coth| #17#) (|cot| #17#) (|cosh| #17#) (|cos| #17#) (|coordinates| ((#44# $ #14#) NIL T ELT) ((#13# #14# #14#) NIL T ELT) #99=((#44# $) NIL T ELT) #12#) (|convert| #99# #45# #75# #55# ((#66# . #100=($)) NIL (|has| |#1| (|ConvertibleTo| #66#)) ELT) ((#69# . #100#) NIL (|has| |#1| (|ConvertibleTo| #69#)) ELT) (((|Complex| #68#) . #100#) NIL #101=(|has| |#1| (|RealConstant|)) ELT) (((|Complex| (|DoubleFloat|)) . #100#) NIL #101# ELT) ((#102=(|InputForm|) . #100#) NIL (|has| |#1| (|ConvertibleTo| #102#)) ELT)) (|conjugate| (#11# 29 T ELT)) (|conditionP| (((|Union| #14# #25#) #50#) NIL (OR #103=(AND (|has| $ #104=(|CharacteristicNonZero|)) #7# #8#) #22#) ELT)) (|complex| (($ |#1| |#1|) 19 T ELT)) (|coerce| (((|OutputForm|) $) NIL T ELT) (($ #21#) NIL T ELT) (($ |#1|) 18 T ELT) (($ #40#) NIL (OR #29# #41#) ELT) #10#) (|charthRoot| #62# (#72# NIL (OR #103# (|has| |#1| #104#)) ELT)) (|characteristicPolynomial| #75#) (|characteristic| (#33# NIL T CONST)) (|before?| #1#) (|basis| ((#14#) NIL T ELT)) (|atanh| #17#) (|atan| #17#) (|associates?| (#2# NIL #5# ELT)) (|asinh| #17#) (|asin| #17#) (|asech| #17#) (|asec| #17#) (|argument| (#16# NIL #18# ELT)) (|annihilate?| #1#) (|acsch| #17#) (|acsc| #17#) (|acoth| #17#) (|acot| #17#) (|acosh| #17#) (|acos| #17#) (|abs| (#11# NIL #63# ELT)) (|Zero| (#35# 8 T CONST)) (|One| (#35# 10 T CONST)) (D #89# #90# #91# #93# #94# #95# #96# #98#) (= #1#) (/ (#47# NIL #29# ELT)) (- (#11# NIL T ELT) (#47# NIL T ELT)) (+ (#47# 23 T ELT)) (** (($ $ #19#) NIL T ELT) (#61# NIL T ELT) (#105=($ $ #40#) NIL #31# ELT) (#47# NIL #18# ELT) (#71# NIL #29# ELT)) (* (($ #19# $) NIL T ELT) (($ #20# $) NIL T ELT) (($ #21# . #106=($)) NIL T ELT) (#47# 26 T ELT) (#88# NIL T ELT) (($ |#1| . #106#) NIL T ELT) (($ #40# . #106#) NIL #29# ELT) (#105# NIL #29# ELT))) +((~= #1=(#2=(#3=(|Boolean|) $ $) NIL T ELT)) (|zero?| (#4=(#3# $) 15 T ELT)) (|unitNormal| (((|Record| (|:| |unit| $) (|:| |canonical| $) (|:| |associate| $)) $) NIL #5=(OR #6=(AND #7=(|has| |#1| (|EuclideanDomain|)) #8=(|has| |#1| (|PolynomialFactorizationExplicit|))) #9=(|has| |#1| (|IntegralDomain|))) ELT)) (|unitCanonical| #10=(#11=($ $) NIL #5# ELT)) (|unit?| (#4# NIL #5# ELT)) (|traceMatrix| #12=((#13=(|Matrix| |#1|) #14=(|Vector| $)) NIL T ELT) ((#13#) NIL T ELT)) (|trace| #15=(#16=(|#1| $) NIL T ELT)) (|tanh| #17=(#11# NIL #18=(|has| |#1| (|TranscendentalFunctionCategory|)) ELT)) (|tan| #17#) (|tableForDiscreteLogarithm| (((|Table| #19=(|PositiveInteger|) #20=(|NonNegativeInteger|)) #21=(|Integer|)) NIL #22=(|has| |#1| (|FiniteFieldCategory|)) ELT)) (|subtractIfCan| ((#23=(|Maybe| $) $ $) NIL T ELT)) (|squareFreePolynomial| #24=(((|Factored| #25=(|SparseUnivariatePolynomial| $)) #25#) NIL #6# ELT)) (|squareFreePart| (#11# NIL #26=(OR #6# #27=(|has| |#1| (|Field|))) ELT)) (|squareFree| #28=(((|Factored| $) $) NIL #26# ELT)) (|sqrt| (#11# NIL #29=(AND (|has| |#1| (|RadicalCategory|)) #18#) ELT)) (|solveLinearPolynomialEquation| (((|Union| #30=(|List| #25#) #31="failed") #30# #25#) NIL #6# ELT)) (|sizeLess?| (#2# NIL #7# ELT)) (|size| (#32=(#20#) NIL #33=(|has| |#1| (|Finite|)) ELT)) (|sinh| #17#) (|sin| #17#) (|sech| #17#) (|sec| #17#) (|sample| (#34=($) NIL T CONST)) (|retractIfCan| (((|Union| #21# . #35=(#31#)) . #36=($)) NIL #37=(|has| |#1| (|RetractableTo| #21#)) ELT) (#38=((|Union| #39=(|Fraction| #21#) . #35#) . #36#) NIL #40=(|has| |#1| (|RetractableTo| #39#)) ELT) (((|Union| |#1| . #35#) . #36#) NIL T ELT)) (|retract| ((#21# . #41=($)) NIL #37# ELT) (#42=(#39# . #41#) NIL #40# ELT) #15#) (|represents| (($ #43=(|Vector| |#1|) #14#) NIL T ELT) #44=(($ #43#) NIL T ELT)) (|representationType| (((|Union| "prime" "polynomial" "normal" "cyclic")) NIL #22# ELT)) (|rem| #45=(#46=($ $ $) NIL #7# ELT)) (|regularRepresentation| ((#13# $ #14#) NIL T ELT) ((#13# $) NIL T ELT)) (|reducedSystem| ((#47=(|Matrix| #21#) . #48=(#49=(|Matrix| $))) NIL #50=(|has| |#1| (|LinearlyExplicitRingOver| #21#)) ELT) ((#51=(|Record| (|:| |mat| #47#) (|:| |vec| (|Vector| #21#))) . #52=(#49# #14#)) NIL #50# ELT) ((#53=(|Record| (|:| |mat| #13#) (|:| |vec| #43#)) . #52#) NIL T ELT) ((#13# . #48#) NIL T ELT)) (|reduce| #54=(($ #55=(|SparseUnivariatePolynomial| |#1|)) NIL T ELT) ((#56=(|Union| $ #31#) (|Fraction| #55#)) NIL #27# ELT)) (|recip| ((#56# $) NIL T ELT)) (|real| (#16# 20 T ELT)) (|rationalIfCan| (#38# NIL #57=(|has| |#1| (|IntegerNumberSystem|)) ELT)) (|rational?| (#4# NIL #57# ELT)) (|rational| (#42# NIL #57# ELT)) (|rank| ((#19#) NIL T ELT)) (|random| (#34# NIL #33# ELT)) (|quo| #45#) (|principalIdeal| (((|Record| (|:| |coef| #58=(|List| $)) #59=(|:| |generator| $)) #58#) NIL #7# ELT)) (|primitiveElement| #60=(#34# NIL #22# ELT)) (|primitive?| (#4# NIL #22# ELT)) (|primeFrobenius| (#61=($ $ #20#) NIL #22# ELT) #62=(#11# NIL #22# ELT)) (|prime?| (#4# NIL #26# ELT)) (|polarCoordinates| (((|Record| (|:| |r| |#1|) (|:| |phi| |#1|)) $) NIL (AND #63=(|has| |#1| (|RealNumberSystem|)) #18#) ELT)) (|pi| (#34# NIL #18# ELT)) (|patternMatch| ((#64=(|PatternMatchResult| #21# . #65=($)) $ #66=(|Pattern| #21#) #64#) NIL (|has| |#1| (|PatternMatchable| #21#)) ELT) ((#67=(|PatternMatchResult| #68=(|Float|) . #65#) $ #69=(|Pattern| #68#) #67#) NIL (|has| |#1| (|PatternMatchable| #68#)) ELT)) (|order| (#70=(#19# $) NIL #22# ELT) (((|OnePointCompletion| #19#) $) NIL #22# ELT)) (|opposite?| #1#) (|one?| (#4# 17 T ELT)) (|nthRoot| (#71=($ $ #21#) NIL #29# ELT)) (|norm| (#16# 30 T ELT)) (|nextItem| (#72=(#23# $) NIL #22# ELT)) (|multiEuclidean| (((|Union| #58# #31#) #58# $) NIL #7# ELT)) (|minimalPolynomial| (#73=(#55# $) NIL #27# ELT)) (|map| (($ #74=(|Mapping| |#1| |#1|) $) NIL T ELT)) (|lookup| (#70# NIL #33# ELT)) (|log| #17#) (|lift| #75=(#73# NIL T ELT)) (|leftReducedSystem| ((#47# #14#) NIL #50# ELT) ((#51# . #76=(#14# $)) NIL #50# ELT) ((#53# . #76#) NIL T ELT) #12#) (|lcm| #77=(($ #58#) NIL #7# ELT) #45#) (|latex| (((|String|) $) NIL T ELT)) (|inv| (#11# NIL #27# ELT)) (|init| (#34# NIL #22# CONST)) (|index| (($ #19#) NIL #33# ELT)) (|imaginary| #78=(#34# NIL T ELT)) (|imag| (#16# 21 T ELT)) (|hash| (((|SingleInteger|) $) NIL T ELT)) (|generator| #78#) (|gcdPolynomial| ((#25# #25# #25#) NIL #7# ELT)) (|gcd| #77# #45#) (|factorsOfCyclicGroupSize| (((|List| (|Record| (|:| |factor| #21#) (|:| |exponent| #21#)))) NIL #22# ELT)) (|factorSquareFreePolynomial| #24#) (|factorPolynomial| #24#) (|factor| #28#) (|extendedEuclidean| (((|Union| (|Record| #79=(|:| |coef1| $) #80=(|:| |coef2| $)) #31#) $ $ $) NIL #7# ELT) (((|Record| #79# #80# #59#) $ $) NIL #7# ELT)) (|exquo| ((#56# $ |#1|) 28 #9# ELT) ((#56# $ $) 31 #5# ELT)) (|expressIdealMember| (((|Maybe| #58#) #58# $) NIL #7# ELT)) (|exp| #17#) (|eval| (($ $ #81=(|List| |#1|) #81#) NIL #82=(|has| |#1| (|Evalable| |#1|)) ELT) (($ $ |#1| |#1|) NIL #82# ELT) (($ $ #83=(|Equation| |#1|)) NIL #82# ELT) (($ $ (|List| #83#)) NIL #82# ELT) (($ $ #84=(|List| #85=(|Symbol|)) #81#) NIL #86=(|has| |#1| (|InnerEvalable| #85# |#1|)) ELT) (($ $ #85# |#1|) NIL #86# ELT)) (|euclideanSize| (#87=(#20# $) NIL #7# ELT)) (|elt| (#88=($ $ |#1|) NIL (|has| |#1| (|Eltable| |#1| |#1|)) ELT)) (|divide| (((|Record| (|:| |quotient| $) (|:| |remainder| $)) $ $) NIL #7# ELT)) (|discriminant| ((|#1| #14#) NIL T ELT) ((|#1|) NIL T ELT)) (|discreteLog| (#87# NIL #22# ELT) (((|Union| #20# #31#) $ $) NIL #22# ELT)) (|differentiate| #89=(($ $ #74#) NIL T ELT) #90=(($ $ #74# #20#) NIL T ELT) #91=(#61# NIL #92=(OR (AND (|has| |#1| (|DifferentialRing|)) #27#) (|has| |#1| (|DifferentialSpace|))) ELT) #93=(#11# NIL #92# ELT) #94=(($ $ #84# (|List| #20#)) NIL #95=(OR (AND #27# (|has| |#1| (|PartialDifferentialRing| #85#))) (|has| |#1| (|PartialDifferentialSpace| #85#))) ELT) #96=(($ $ #85# #20#) NIL #95# ELT) #97=(($ $ #84#) NIL #95# ELT) #98=(($ $ #85#) NIL #95# ELT)) (|derivationCoordinates| ((#13# #14# #74#) NIL #27# ELT)) (|definingPolynomial| ((#55#) NIL T ELT)) (|csch| #17#) (|csc| #17#) (|createPrimitiveElement| #60#) (|coth| #17#) (|cot| #17#) (|cosh| #17#) (|cos| #17#) (|coordinates| ((#43# $ #14#) NIL T ELT) ((#13# #14# #14#) NIL T ELT) #99=((#43# $) NIL T ELT) #12#) (|convert| #99# #44# #75# #54# ((#66# . #100=($)) NIL (|has| |#1| (|ConvertibleTo| #66#)) ELT) ((#69# . #100#) NIL (|has| |#1| (|ConvertibleTo| #69#)) ELT) (((|Complex| #68#) . #100#) NIL #101=(|has| |#1| (|RealConstant|)) ELT) (((|Complex| (|DoubleFloat|)) . #100#) NIL #101# ELT) ((#102=(|InputForm|) . #100#) NIL (|has| |#1| (|ConvertibleTo| #102#)) ELT)) (|conjugate| (#11# 29 T ELT)) (|conditionP| (((|Union| #14# #31#) #49#) NIL (OR #103=(AND (|has| $ #104=(|CharacteristicNonZero|)) #7# #8#) #22#) ELT)) (|complex| (($ |#1| |#1|) 19 T ELT)) (|coerce| (((|OutputForm|) $) NIL T ELT) (($ #21#) NIL T ELT) (($ |#1|) 18 T ELT) (($ #39#) NIL (OR #27# #40#) ELT) #10#) (|charthRoot| #62# (#72# NIL (OR #103# (|has| |#1| #104#)) ELT)) (|characteristicPolynomial| #75#) (|characteristic| (#32# NIL T CONST)) (|before?| #1#) (|basis| ((#14#) NIL T ELT)) (|atanh| #17#) (|atan| #17#) (|associates?| (#2# NIL #5# ELT)) (|asinh| #17#) (|asin| #17#) (|asech| #17#) (|asec| #17#) (|argument| (#16# NIL #18# ELT)) (|annihilate?| #1#) (|acsch| #17#) (|acsc| #17#) (|acoth| #17#) (|acot| #17#) (|acosh| #17#) (|acos| #17#) (|abs| (#11# NIL #63# ELT)) (|Zero| (#34# 8 T CONST)) (|One| (#34# 10 T CONST)) (D #89# #90# #91# #93# #94# #96# #97# #98#) (= #1#) (/ (#46# NIL #27# ELT)) (- (#11# NIL T ELT) (#46# NIL T ELT)) (+ (#46# 23 T ELT)) (** (($ $ #19#) NIL T ELT) (#61# NIL T ELT) (#105=($ $ #39#) NIL #29# ELT) (#46# NIL #18# ELT) (#71# NIL #27# ELT)) (* (($ #19# $) NIL T ELT) (($ #20# $) NIL T ELT) (($ #21# . #106=($)) NIL T ELT) (#46# 26 T ELT) (#88# NIL T ELT) (($ |#1| . #106#) NIL T ELT) (($ #39# . #106#) NIL #27# ELT) (#105# NIL #27# ELT))) (((|Complex| |#1|) (|ComplexCategory| |#1|) (|CommutativeRing|)) (T |Complex|)) NIL ((|map| (((|Complex| |#2|) (|Mapping| |#2| |#1|) (|Complex| |#1|)) 14 T ELT))) @@ -451,7 +451,7 @@ NIL ((~= #1=((#2=(|Boolean|) $ $) NIL T ELT)) (|solid?| (#3=(#2# $) 9 T ELT)) (|solid| (#4=(#2# $ #2#) 11 T ELT)) (|new| (($) 13 T ELT)) (|latex| (((|String|) $) NIL T ELT)) (|hash| (((|SingleInteger|) $) NIL T ELT)) (|copy| (($ $) 14 T ELT)) (|coerce| (((|OutputForm|) $) 18 T ELT)) (|closed?| (#3# 8 T ELT)) (|close| (#4# 10 T ELT)) (|before?| #1#) (= #1#)) (((|SubSpaceComponentProperty|) (|Join| (|SetCategory|) (CATEGORY |domain| (SIGNATURE |new| ($)) (SIGNATURE |closed?| #1=(#2=(|Boolean|) $)) (SIGNATURE |solid?| #1#) (SIGNATURE |close| #3=(#2# $ #2#)) (SIGNATURE |solid| #3#) (SIGNATURE |copy| ($ $))))) (T |SubSpaceComponentProperty|)) ((|new| (*1 *1) #1=(|isDomain| *1 (|SubSpaceComponentProperty|))) (|closed?| #2=(*1 *2 *1) #3=(AND (|isDomain| *2 (|Boolean|)) #1#)) (|solid?| #2# #3#) (|close| #4=(*1 *2 *1 *2) #3#) (|solid| #4# #3#) (|copy| (*1 *1 *1) #1#)) -((~= (#1=((|Boolean|) $ $) 7 T ELT)) (|zero?| ((#2=(|Boolean|) $) 22 T ELT)) (|subtractIfCan| (((|Union| $ "failed") $ $) 26 T ELT)) (|sample| (#3=($) 23 T CONST)) (|recip| (((|Union| $ "failed") $) 42 T ELT)) (|opposite?| ((#2# $ $) 20 T ELT)) (|one?| (((|Boolean|) $) 44 T ELT)) (|latex| (((|String|) $) 11 T ELT)) (|hash| (((|SingleInteger|) $) 12 T ELT)) (|coerce| (((|OutputForm|) $) 13 T ELT) (($ (|Integer|)) 41 T ELT)) (|characteristic| (((|NonNegativeInteger|)) 40 T CONST)) (|before?| (#1# 6 T ELT)) (|annihilate?| (((|Boolean|) $ $) 33 T ELT)) (|Zero| (#3# 24 T CONST)) (|One| (($) 45 T CONST)) (= (#1# 8 T ELT)) (- (($ $) 29 T ELT) (($ $ $) 28 T ELT)) (+ (($ $ $) 18 T ELT)) (** (($ $ (|PositiveInteger|)) 35 T ELT) (($ $ (|NonNegativeInteger|)) 43 T ELT)) (* (($ (|PositiveInteger|) $) 17 T ELT) (($ (|NonNegativeInteger|) $) 21 T ELT) (($ (|Integer|) $) 30 T ELT) (($ $ $) 34 T ELT))) +((~= (#1=((|Boolean|) $ $) 7 T ELT)) (|zero?| ((#2=(|Boolean|) $) 22 T ELT)) (|subtractIfCan| (((|Maybe| $) $ $) 26 T ELT)) (|sample| (#3=($) 23 T CONST)) (|recip| (((|Union| $ "failed") $) 43 T ELT)) (|opposite?| ((#2# $ $) 20 T ELT)) (|one?| (((|Boolean|) $) 45 T ELT)) (|latex| (((|String|) $) 11 T ELT)) (|hash| (((|SingleInteger|) $) 12 T ELT)) (|coerce| (((|OutputForm|) $) 13 T ELT) (($ (|Integer|)) 42 T ELT)) (|characteristic| (((|NonNegativeInteger|)) 41 T CONST)) (|before?| (#1# 6 T ELT)) (|annihilate?| (((|Boolean|) $ $) 34 T ELT)) (|Zero| (#3# 24 T CONST)) (|One| (($) 46 T CONST)) (= (#1# 8 T ELT)) (- (($ $) 30 T ELT) (($ $ $) 29 T ELT)) (+ (($ $ $) 18 T ELT)) (** (($ $ (|PositiveInteger|)) 36 T ELT) (($ $ (|NonNegativeInteger|)) 44 T ELT)) (* (($ (|PositiveInteger|) $) 17 T ELT) (($ (|NonNegativeInteger|) $) 21 T ELT) (($ (|Integer|) $) 31 T ELT) (($ $ $) 35 T ELT))) (((|CommutativeRing|) (|Category|)) (T |CommutativeRing|)) NIL (|Join| (|Ring|) (|BiModule| $ $) (CATEGORY |package| (ATTRIBUTE (|commutative| "*")))) @@ -460,7 +460,7 @@ NIL (((|Conduit|) (|Category|)) (T |Conduit|)) ((|close!| (*1 *1 *1) (|ofCategory| *1 (|Conduit|)))) (|Join| (CATEGORY |domain| (SIGNATURE |close!| ($ $)))) -((~= #1=(#2=(#3=(|Boolean|) $ $) NIL T ELT)) (|zero?| #4=((#3# $) NIL T ELT)) (|wholePart| ((|#1| $) 79 T ELT)) (|unitNormal| (((|Record| (|:| |unit| $) (|:| |canonical| $) (|:| |associate| $)) $) NIL T ELT)) (|unitCanonical| #5=(#6=($ $) NIL T ELT)) (|unit?| #4#) (|subtractIfCan| #7=((#8=(|Union| $ #9="failed") $ $) NIL T ELT)) (|squareFreePart| #5#) (|squareFree| #10=(((|Factored| $) $) NIL T ELT)) (|sizeLess?| #1#) (|sample| (#11=($) NIL T CONST)) (|rem| #12=(#13=($ $ $) NIL T ELT)) (|reducedForm| (#6# 21 T ELT)) (|reducedContinuedFraction| (($ |#1| #14=(|Stream| |#1|)) 48 T ELT)) (|recip| ((#8# $) 123 T ELT)) (|quo| #12#) (|principalIdeal| (((|Record| (|:| |coef| #15=(|List| $)) #16=(|:| |generator| $)) #15#) NIL T ELT)) (|prime?| #4#) (|partialQuotients| (#17=(#14# $) 86 T ELT)) (|partialNumerators| (#17# 83 T ELT)) (|partialDenominators| (#17# 84 T ELT)) (|opposite?| #1#) (|one?| #4#) (|numerators| (#17# 93 T ELT)) (|multiEuclidean| (((|Union| #15# #9#) #15# $) NIL T ELT)) (|lcm| #18=(($ #15#) NIL T ELT) #12#) (|latex| (((|String|) $) NIL T ELT)) (|inv| #5#) (|hash| (((|SingleInteger|) $) NIL T ELT)) (|gcdPolynomial| ((#19=(|SparseUnivariatePolynomial| $) #19# #19#) NIL T ELT)) (|gcd| #18# #12#) (|factor| #10#) (|extendedEuclidean| (((|Union| (|Record| #20=(|:| |coef1| $) #21=(|:| |coef2| $)) #9#) $ $ $) NIL T ELT) (((|Record| #20# #21# #16#) $ $) NIL T ELT)) (|extend| (#22=($ $ #23=(|Integer|)) 96 T ELT)) (|exquo| #7#) (|expressIdealMember| (((|Maybe| #15#) #15# $) NIL T ELT)) (|euclideanSize| ((#24=(|NonNegativeInteger|) $) NIL T ELT)) (|divide| (((|Record| (|:| |quotient| $) (|:| |remainder| $)) $ $) NIL T ELT)) (|denominators| (#17# 94 T ELT)) (|convergents| (#25=((|Stream| #26=(|Fraction| |#1|)) $) 14 T ELT)) (|continuedFraction| (#27=($ #26#) 17 T ELT) (($ |#1| #14# #14#) 38 T ELT)) (|complete| (#6# 98 T ELT)) (|coerce| (((|OutputForm|) $) 139 T ELT) (($ #23#) 51 T ELT) (($ |#1|) 52 T ELT) (#27# 36 T ELT) (($ #28=(|Fraction| #23#)) NIL T ELT) #5#) (|characteristic| ((#24#) 67 T CONST)) (|before?| #1#) (|associates?| #1#) (|approximants| (#25# 20 T ELT)) (|annihilate?| #1#) (|Zero| (#11# 103 T CONST)) (|One| (#11# 28 T CONST)) (= (#2# 35 T ELT)) (/ (#13# 121 T ELT)) (- (#6# 112 T ELT) (#13# 109 T ELT)) (+ (#13# 107 T ELT)) (** (($ $ #29=(|PositiveInteger|)) NIL T ELT) (($ $ #24#) NIL T ELT) (#22# NIL T ELT)) (* (($ #29# $) NIL T ELT) (($ #24# $) NIL T ELT) (($ #23# $) 119 T ELT) (#13# 114 T ELT) (($ $ |#1|) NIL T ELT) (($ |#1| $) 116 T ELT) (($ #26# $) 117 T ELT) (($ $ #26#) NIL T ELT) (($ #28# $) NIL T ELT) (($ $ #28#) NIL T ELT))) +((~= #1=(#2=(#3=(|Boolean|) $ $) NIL T ELT)) (|zero?| #4=((#3# $) NIL T ELT)) (|wholePart| ((|#1| $) 79 T ELT)) (|unitNormal| (((|Record| (|:| |unit| $) (|:| |canonical| $) (|:| |associate| $)) $) NIL T ELT)) (|unitCanonical| #5=(#6=($ $) NIL T ELT)) (|unit?| #4#) (|subtractIfCan| (((|Maybe| $) $ $) NIL T ELT)) (|squareFreePart| #5#) (|squareFree| #7=(((|Factored| $) $) NIL T ELT)) (|sizeLess?| #1#) (|sample| (#8=($) NIL T CONST)) (|rem| #9=(#10=($ $ $) NIL T ELT)) (|reducedForm| (#6# 21 T ELT)) (|reducedContinuedFraction| (($ |#1| #11=(|Stream| |#1|)) 48 T ELT)) (|recip| ((#12=(|Union| $ #13="failed") $) 123 T ELT)) (|quo| #9#) (|principalIdeal| (((|Record| (|:| |coef| #14=(|List| $)) #15=(|:| |generator| $)) #14#) NIL T ELT)) (|prime?| #4#) (|partialQuotients| (#16=(#11# $) 86 T ELT)) (|partialNumerators| (#16# 83 T ELT)) (|partialDenominators| (#16# 84 T ELT)) (|opposite?| #1#) (|one?| #4#) (|numerators| (#16# 93 T ELT)) (|multiEuclidean| (((|Union| #14# #13#) #14# $) NIL T ELT)) (|lcm| #17=(($ #14#) NIL T ELT) #9#) (|latex| (((|String|) $) NIL T ELT)) (|inv| #5#) (|hash| (((|SingleInteger|) $) NIL T ELT)) (|gcdPolynomial| ((#18=(|SparseUnivariatePolynomial| $) #18# #18#) NIL T ELT)) (|gcd| #17# #9#) (|factor| #7#) (|extendedEuclidean| (((|Union| (|Record| #19=(|:| |coef1| $) #20=(|:| |coef2| $)) #13#) $ $ $) NIL T ELT) (((|Record| #19# #20# #15#) $ $) NIL T ELT)) (|extend| (#21=($ $ #22=(|Integer|)) 96 T ELT)) (|exquo| ((#12# $ $) NIL T ELT)) (|expressIdealMember| (((|Maybe| #14#) #14# $) NIL T ELT)) (|euclideanSize| ((#23=(|NonNegativeInteger|) $) NIL T ELT)) (|divide| (((|Record| (|:| |quotient| $) (|:| |remainder| $)) $ $) NIL T ELT)) (|denominators| (#16# 94 T ELT)) (|convergents| (#24=((|Stream| #25=(|Fraction| |#1|)) $) 14 T ELT)) (|continuedFraction| (#26=($ #25#) 17 T ELT) (($ |#1| #11# #11#) 38 T ELT)) (|complete| (#6# 98 T ELT)) (|coerce| (((|OutputForm|) $) 139 T ELT) (($ #22#) 51 T ELT) (($ |#1|) 52 T ELT) (#26# 36 T ELT) (($ #27=(|Fraction| #22#)) NIL T ELT) #5#) (|characteristic| ((#23#) 67 T CONST)) (|before?| #1#) (|associates?| #1#) (|approximants| (#24# 20 T ELT)) (|annihilate?| #1#) (|Zero| (#8# 103 T CONST)) (|One| (#8# 28 T CONST)) (= (#2# 35 T ELT)) (/ (#10# 121 T ELT)) (- (#6# 112 T ELT) (#10# 109 T ELT)) (+ (#10# 107 T ELT)) (** (($ $ #28=(|PositiveInteger|)) NIL T ELT) (($ $ #23#) NIL T ELT) (#21# NIL T ELT)) (* (($ #28# $) NIL T ELT) (($ #23# $) NIL T ELT) (($ #22# $) 119 T ELT) (#10# 114 T ELT) (($ $ |#1|) NIL T ELT) (($ |#1| $) 116 T ELT) (($ #25# $) 117 T ELT) (($ $ #25#) NIL T ELT) (($ #27# $) NIL T ELT) (($ $ #27#) NIL T ELT))) (((|ContinuedFraction| |#1|) (|Join| (|Algebra| |#1|) (|Algebra| #1=(|Fraction| |#1|)) (|Field|) (CATEGORY |domain| (SIGNATURE |continuedFraction| ($ #1#)) (SIGNATURE |continuedFraction| ($ |#1| #2=(|Stream| |#1|) #2#)) (SIGNATURE |reducedContinuedFraction| ($ |#1| #2#)) (SIGNATURE |partialNumerators| #3=(#2# $)) (SIGNATURE |partialDenominators| #3#) (SIGNATURE |partialQuotients| #3#) (SIGNATURE |wholePart| (|#1| $)) (SIGNATURE |reducedForm| #4=($ $)) (SIGNATURE |approximants| #5=((|Stream| #1#) $)) (SIGNATURE |convergents| #5#) (SIGNATURE |numerators| #3#) (SIGNATURE |denominators| #3#) (SIGNATURE |extend| ($ $ (|Integer|))) (SIGNATURE |complete| #4#))) (|EuclideanDomain|)) (T |ContinuedFraction|)) ((|continuedFraction| (*1 *1 *2) (AND (|isDomain| *2 #1=(|Fraction| *3)) #2=(|ofCategory| *3 #3=(|EuclideanDomain|)) #4=(|isDomain| *1 (|ContinuedFraction| *3)))) (|continuedFraction| (*1 *1 *2 *3 *3) #5=(AND (|isDomain| *3 (|Stream| *2)) #6=(|ofCategory| *2 #3#) #7=(|isDomain| *1 (|ContinuedFraction| *2)))) (|reducedContinuedFraction| (*1 *1 *2 *3) #5#) (|partialNumerators| #8=(*1 *2 *1) #9=(AND (|isDomain| *2 (|Stream| *3)) #4# #2#)) (|partialDenominators| #8# #9#) (|partialQuotients| #8# #9#) (|wholePart| #8# #10=(AND #7# #6#)) (|reducedForm| #11=(*1 *1 *1) #10#) (|approximants| #8# #12=(AND (|isDomain| *2 (|Stream| #1#)) #4# #2#)) (|convergents| #8# #12#) (|numerators| #8# #9#) (|denominators| #8# #9#) (|extend| (*1 *1 *1 *2) (AND (|isDomain| *2 (|Integer|)) #4# #2#)) (|complete| #11# #10#)) ((|push| (($ #1=(|Binding|) $) 15 T ELT)) (|findBinding| (((|Maybe| #1#) (|Identifier|) $) 14 T ELT)) (|coerce| (((|OutputForm|) $) 18 T ELT)) (|bindings| (((|List| #1#) $) 8 T ELT))) @@ -531,7 +531,7 @@ NIL ((|tracePowMod| (#1=(|#2| |#2| #2=(|NonNegativeInteger|) |#2|) 55 T ELT)) (|trace2PowMod| (#1# 51 T ELT)) (|separateFactors| (((|List| |#2|) #3=(|List| (|Record| (|:| |deg| #2#) (|:| |prod| |#2|)))) 79 T ELT)) (|separateDegrees| ((#3# |#2|) 72 T ELT)) (|irreducible?| ((#4=(|Boolean|) |#2|) 70 T ELT)) (|factorSquareFree| (#5=((|Factored| |#2|) |#2|) 92 T ELT)) (|factor| (#5# 91 T ELT)) (|exptMod| (#1# 49 T ELT)) (|distdfact| (((|Record| (|:| |cont| |#1|) (|:| |factors| (|List| (|Record| (|:| |irr| |#2|) (|:| |pow| (|Integer|)))))) |#2| #4#) 86 T ELT))) (((|DistinctDegreeFactorize| |#1| |#2|) (CATEGORY |package| (SIGNATURE |factor| #1=((|Factored| |#2|) |#2|)) (SIGNATURE |factorSquareFree| #1#) (SIGNATURE |distdfact| ((|Record| (|:| |cont| |#1|) (|:| |factors| (|List| (|Record| (|:| |irr| |#2|) (|:| |pow| (|Integer|)))))) |#2| #2=(|Boolean|))) (SIGNATURE |separateDegrees| (#3=(|List| (|Record| (|:| |deg| #4=(|NonNegativeInteger|)) (|:| |prod| |#2|))) |#2|)) (SIGNATURE |separateFactors| ((|List| |#2|) #3#)) (SIGNATURE |exptMod| #5=(|#2| |#2| #4# |#2|)) (SIGNATURE |trace2PowMod| #5#) (SIGNATURE |tracePowMod| #5#) (SIGNATURE |irreducible?| (#2# |#2|))) (|FiniteFieldCategory|) (|UnivariatePolynomialCategory| |#1|)) (T |DistinctDegreeFactorize|)) ((|irreducible?| #1=(*1 *2 *3) (AND #2=(|ofCategory| *4 #3=(|FiniteFieldCategory|)) (|isDomain| *2 #4=(|Boolean|)) #5=(|isDomain| *1 (|DistinctDegreeFactorize| *4 *3)) #6=(|ofCategory| *3 #7=(|UnivariatePolynomialCategory| *4)))) (|tracePowMod| #8=(*1 *2 *2 *3 *2) #9=(AND (|isDomain| *3 #10=(|NonNegativeInteger|)) #2# (|isDomain| *1 (|DistinctDegreeFactorize| *4 *2)) (|ofCategory| *2 #7#))) (|trace2PowMod| #8# #9#) (|exptMod| #8# #9#) (|separateFactors| #1# (AND (|isDomain| *3 (|List| (|Record| #11=(|:| |deg| #10#) (|:| |prod| *5)))) (|ofCategory| *5 #7#) #2# (|isDomain| *2 (|List| *5)) (|isDomain| *1 (|DistinctDegreeFactorize| *4 *5)))) (|separateDegrees| #1# (AND #2# (|isDomain| *2 (|List| (|Record| #11# (|:| |prod| *3)))) #5# #6#)) (|distdfact| (*1 *2 *3 *4) (AND (|isDomain| *4 #4#) (|ofCategory| *5 #3#) (|isDomain| *2 (|Record| (|:| |cont| *5) (|:| |factors| (|List| (|Record| (|:| |irr| *3) (|:| |pow| (|Integer|))))))) (|isDomain| *1 (|DistinctDegreeFactorize| *5 *3)) (|ofCategory| *3 (|UnivariatePolynomialCategory| *5)))) (|factorSquareFree| #1# #12=(AND #2# (|isDomain| *2 (|Factored| *3)) #5# #6#)) (|factor| #1# #12#)) -((~= #1=(#2=(#3=(|Boolean|) $ $) NIL T ELT)) (|zero?| #4=(#5=(#3# $) NIL T ELT)) (|wholePart| (#6=(#7=(|Integer|) $) NIL #8=(|has| #7# (|EuclideanDomain|)) ELT)) (|unitNormal| (((|Record| (|:| |unit| $) (|:| |canonical| $) (|:| |associate| $)) $) NIL T ELT)) (|unitCanonical| #9=(#10=($ $) NIL T ELT)) (|unit?| #4#) (|subtractIfCan| #11=((#12=(|Union| $ #13="failed") $ $) NIL T ELT)) (|squareFreePolynomial| #14=(((|Factored| #15=(|SparseUnivariatePolynomial| $)) #15#) NIL #16=(|has| #7# (|PolynomialFactorizationExplicit|)) ELT)) (|squareFreePart| #9#) (|squareFree| #17=(((|Factored| $) $) NIL T ELT)) (|solveLinearPolynomialEquation| (((|Union| #18=(|List| #15#) #13#) #18# #15#) NIL #16# ELT)) (|sizeLess?| #1#) (|sign| (#6# NIL #19=(|has| #7# (|OrderedIntegralDomain|)) ELT)) (|sample| #20=(#21=($) NIL T CONST)) (|retractIfCan| (#22=((|Union| #7# . #23=(#13#)) . #24=($)) NIL T ELT) (((|Union| #25=(|Symbol|) . #23#) . #24#) NIL #26=(|has| #7# (|RetractableTo| #25#)) ELT) (((|Union| #27=(|Fraction| #7#) . #23#) . #24#) NIL #28=(|has| #7# (|RetractableTo| #7#)) ELT) (#22# NIL #28# ELT)) (|retract| #29=(#6# NIL T ELT) ((#25# $) NIL #26# ELT) (#30=(#27# $) NIL #28# ELT) (#6# NIL #28# ELT)) (|rem| #31=(#32=($ $ $) NIL T ELT)) (|reducedSystem| (#33=(#34=(|Matrix| #7#) #35=(|Matrix| $)) NIL #36=(|has| #7# (|LinearlyExplicitRingOver| #7#)) ELT) (#37=(#38=(|Record| (|:| |mat| #34#) (|:| |vec| (|Vector| #7#))) #35# #39=(|Vector| $)) NIL #36# ELT) (#37# NIL T ELT) (#33# NIL T ELT)) (|recip| ((#12# $) NIL T ELT)) (|random| (#21# NIL #40=(|has| #7# (|IntegerNumberSystem|)) ELT)) (|quo| #31#) (|principalIdeal| (((|Record| (|:| |coef| #41=(|List| $)) #42=(|:| |generator| $)) #41#) NIL T ELT)) (|prime?| #4#) (|positive?| #43=(#5# NIL #19# ELT)) (|patternMatch| ((#44=(|PatternMatchResult| #7# . #45=($)) $ #46=(|Pattern| #7#) #44#) NIL (|has| #7# (|PatternMatchable| #7#)) ELT) ((#47=(|PatternMatchResult| #48=(|Float|) . #45#) $ #49=(|Pattern| #48#) #47#) NIL (|has| #7# (|PatternMatchable| #48#)) ELT)) (|opposite?| #1#) (|one?| #4#) (|numerator| #9#) (|numer| #29#) (|nextItem| (#50=((|Maybe| $) $) NIL #51=(|has| #7# (|StepThrough|)) ELT)) (|negative?| #43#) (|multiEuclidean| (((|Union| #41# #13#) #41# $) NIL T ELT)) (|min| #52=(#32# NIL #53=(|has| #7# (|OrderedSet|)) ELT)) (|max| #52#) (|map| (($ #54=(|Mapping| #7# #7#) $) NIL T ELT)) (|leftReducedSystem| (#55=(#34# #39#) NIL #36# ELT) (#56=(#38# #39# $) NIL #36# ELT) (#56# NIL T ELT) (#55# NIL T ELT)) (|lcm| #31# #57=(($ #41#) NIL T ELT)) (|latex| (((|String|) $) NIL T ELT)) (|inv| #9#) (|init| (#21# NIL #51# CONST)) (|hash| (((|SingleInteger|) $) NIL T ELT)) (|gcdPolynomial| ((#15# #15# #15#) NIL T ELT)) (|gcd| #31# #57#) (|fractionPart| (#10# NIL #8# ELT) #58=(#30# NIL T ELT)) (|floor| #59=(#6# NIL #40# ELT)) (|factorSquareFreePolynomial| #14#) (|factorPolynomial| #14#) (|factor| #17#) (|extendedEuclidean| (((|Record| #60=(|:| |coef1| $) #61=(|:| |coef2| $) #42#) $ $) NIL T ELT) (((|Union| (|Record| #60# #61#) #13#) $ $ $) NIL T ELT)) (|exquo| #11#) (|expressIdealMember| (((|Maybe| #41#) #41# $) NIL T ELT)) (|eval| (($ $ #62=(|List| #7#) #62#) NIL #63=(|has| #7# (|Evalable| #7#)) ELT) (($ $ #7# #7#) NIL #63# ELT) (($ $ #64=(|Equation| #7#)) NIL #63# ELT) (($ $ (|List| #64#)) NIL #63# ELT) (($ $ #65=(|List| #25#) #62#) NIL #66=(|has| #7# (|InnerEvalable| #25# #7#)) ELT) (($ $ #25# #7#) NIL #66# ELT)) (|euclideanSize| ((#67=(|NonNegativeInteger|) $) NIL T ELT)) (|elt| (#68=($ $ #7#) NIL (|has| #7# (|Eltable| #7# #7#)) ELT)) (|divide| (((|Record| (|:| |quotient| $) (|:| |remainder| $)) $ $) NIL T ELT)) (|differentiate| #69=(($ $ #54#) NIL T ELT) #70=(($ $ #54# #67#) NIL T ELT) #71=(($ $ #25#) NIL #72=(|has| #7# (|PartialDifferentialSpace| #25#)) ELT) #73=(($ $ #65#) NIL #72# ELT) #74=(($ $ #25# #67#) NIL #72# ELT) #75=(($ $ #65# (|List| #67#)) NIL #72# ELT) #76=(#10# NIL #77=(|has| #7# (|DifferentialSpace|)) ELT) #78=(#79=($ $ #67#) NIL #77# ELT)) (|denominator| #9#) (|denom| #29#) (|decimal| (#80=($ #27#) 9 T ELT)) (|convert| ((#46# . #81=($)) NIL (|has| #7# (|ConvertibleTo| #46#)) ELT) ((#49# . #81#) NIL (|has| #7# (|ConvertibleTo| #49#)) ELT) ((#82=(|InputForm|) . #81#) NIL (|has| #7# (|ConvertibleTo| #82#)) ELT) ((#48# . #81#) NIL #83=(|has| #7# (|RealConstant|)) ELT) (((|DoubleFloat|) . #81#) NIL #83# ELT)) (|conditionP| (((|Union| #39# #13#) #35#) NIL #84=(AND (|has| $ #85=(|CharacteristicNonZero|)) #16#) ELT)) (|coerce| (((|OutputForm|) $) NIL T ELT) #86=(($ #7#) NIL T ELT) #9# (#80# 8 T ELT) #86# (($ #25#) NIL #26# ELT) #58# (((|RadixExpansion| 10) $) 10 T ELT)) (|charthRoot| (#50# NIL (OR #84# (|has| #7# #85#)) ELT)) (|characteristic| ((#67#) NIL T CONST)) (|ceiling| #59#) (|before?| #1#) (|associates?| #1#) (|annihilate?| #1#) (|abs| (#10# NIL #19# ELT)) (|Zero| #20#) (|One| #20#) (D #69# #70# #71# #73# #74# #75# #76# #78#) (>= #87=(#2# NIL #53# ELT)) (> #87#) (= #1#) (<= #87#) (< #87#) (/ #31# (($ #7# #7#) NIL T ELT)) (- #9# #31#) (+ #31#) (** (($ $ #88=(|PositiveInteger|)) NIL T ELT) (#79# NIL T ELT) #89=(#68# NIL T ELT)) (* (($ #88# $) NIL T ELT) (($ #67# $) NIL T ELT) #90=(($ #7# . #91=($)) NIL T ELT) #31# (($ $ #27#) NIL T ELT) (($ #27# . #91#) NIL T ELT) #90# #89#)) +((~= #1=(#2=(#3=(|Boolean|) $ $) NIL T ELT)) (|zero?| #4=(#5=(#3# $) NIL T ELT)) (|wholePart| (#6=(#7=(|Integer|) $) NIL #8=(|has| #7# (|EuclideanDomain|)) ELT)) (|unitNormal| (((|Record| (|:| |unit| $) (|:| |canonical| $) (|:| |associate| $)) $) NIL T ELT)) (|unitCanonical| #9=(#10=($ $) NIL T ELT)) (|unit?| #4#) (|subtractIfCan| ((#11=(|Maybe| $) $ $) NIL T ELT)) 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(|:| |mat| #33#) (|:| |vec| (|Vector| #7#))) #34# #38=(|Vector| $)) NIL #35# ELT) (#36# NIL T ELT) (#32# NIL T ELT)) (|recip| ((#39=(|Union| $ #17#) $) NIL T ELT)) (|random| (#20# NIL #40=(|has| #7# (|IntegerNumberSystem|)) ELT)) (|quo| #30#) (|principalIdeal| (((|Record| (|:| |coef| #41=(|List| $)) #42=(|:| |generator| $)) #41#) NIL T ELT)) (|prime?| #4#) (|positive?| #43=(#5# NIL #18# ELT)) (|patternMatch| ((#44=(|PatternMatchResult| #7# . #45=($)) $ #46=(|Pattern| #7#) #44#) NIL (|has| #7# (|PatternMatchable| #7#)) ELT) ((#47=(|PatternMatchResult| #48=(|Float|) . #45#) $ #49=(|Pattern| #48#) #47#) NIL (|has| #7# (|PatternMatchable| #48#)) ELT)) (|opposite?| #1#) (|one?| #4#) (|numerator| #9#) (|numer| #28#) (|nextItem| (#50=(#11# $) NIL #51=(|has| #7# (|StepThrough|)) ELT)) (|negative?| #43#) (|multiEuclidean| (((|Union| #41# #17#) #41# $) NIL T ELT)) (|min| #52=(#31# NIL #53=(|has| #7# (|OrderedSet|)) ELT)) (|max| #52#) (|map| (($ #54=(|Mapping| #7# #7#) $) NIL T ELT)) (|leftReducedSystem| (#55=(#33# #38#) NIL #35# ELT) (#56=(#37# #38# $) NIL #35# ELT) (#56# NIL T ELT) (#55# NIL T ELT)) (|lcm| #30# #57=(($ #41#) NIL T ELT)) (|latex| (((|String|) $) NIL T ELT)) (|inv| #9#) (|init| (#20# NIL #51# CONST)) (|hash| (((|SingleInteger|) $) NIL T ELT)) (|gcdPolynomial| ((#13# #13# #13#) NIL T ELT)) (|gcd| #30# #57#) (|fractionPart| (#10# NIL #8# ELT) #58=(#29# NIL T ELT)) (|floor| #59=(#6# NIL #40# ELT)) (|factorSquareFreePolynomial| #12#) (|factorPolynomial| #12#) (|factor| #15#) (|extendedEuclidean| (((|Record| #60=(|:| |coef1| $) #61=(|:| |coef2| $) #42#) $ $) NIL T ELT) (((|Union| (|Record| #60# #61#) #17#) $ $ $) NIL T ELT)) (|exquo| ((#39# $ $) NIL T ELT)) (|expressIdealMember| (((|Maybe| #41#) #41# $) NIL T ELT)) (|eval| (($ $ #62=(|List| #7#) #62#) NIL #63=(|has| #7# (|Evalable| #7#)) ELT) (($ $ #7# #7#) NIL #63# ELT) (($ $ #64=(|Equation| #7#)) NIL #63# ELT) (($ $ (|List| #64#)) NIL #63# ELT) (($ $ #65=(|List| #24#) #62#) NIL #66=(|has| #7# (|InnerEvalable| #24# #7#)) ELT) (($ $ #24# #7#) NIL #66# ELT)) (|euclideanSize| ((#67=(|NonNegativeInteger|) $) NIL T ELT)) (|elt| (#68=($ $ #7#) NIL (|has| #7# (|Eltable| #7# #7#)) ELT)) (|divide| (((|Record| (|:| |quotient| $) (|:| |remainder| $)) $ $) NIL T ELT)) (|differentiate| #69=(($ $ #54#) NIL T ELT) #70=(($ $ #54# #67#) NIL T ELT) #71=(($ $ #24#) NIL #72=(|has| #7# (|PartialDifferentialSpace| #24#)) ELT) #73=(($ $ #65#) NIL #72# ELT) #74=(($ $ #24# #67#) NIL #72# ELT) #75=(($ $ #65# (|List| #67#)) NIL #72# ELT) #76=(#10# NIL #77=(|has| #7# (|DifferentialSpace|)) ELT) #78=(#79=($ $ #67#) NIL #77# ELT)) (|denominator| #9#) (|denom| #28#) (|decimal| (#80=($ #26#) 9 T ELT)) (|convert| ((#46# . #81=($)) NIL (|has| #7# (|ConvertibleTo| #46#)) ELT) ((#49# . #81#) NIL (|has| #7# (|ConvertibleTo| #49#)) ELT) ((#82=(|InputForm|) . #81#) NIL (|has| #7# (|ConvertibleTo| #82#)) ELT) ((#48# . #81#) NIL #83=(|has| #7# (|RealConstant|)) ELT) (((|DoubleFloat|) . #81#) NIL #83# ELT)) 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#4=(|isDomain| *1 (|DeRhamComplex| *3 *4)) #5=(|ofCategory| *3 #6=(|Join| (|Ring|) (|OrderedSet|))) #7=(|ofType| *4 #8=(|List| (|Symbol|))))) (|leadingBasisTerm| #9=(*1 *1 *1) #10=(AND (|isDomain| *1 (|DeRhamComplex| *2 *3)) (|ofCategory| *2 #6#) (|ofType| *3 #8#))) (|reductum| #9# #10#) (|coefficient| (*1 *2 *1 *1) #2#) (|generator| #11=(*1 *1 *2) (AND (|isDomain| *2 (|NonNegativeInteger|)) #4# #5# #7#)) (|homogeneous?| #1# #12=(AND (|isDomain| *2 (|Boolean|)) #4# #5# #7#)) (|retractable?| #1# #12#) (|degree| #1# (AND (|isDomain| *2 (|Integer|)) #4# #5# #7#)) (|totalDifferential| #11# (AND #3# #5# #4# #7#)) (|exteriorDifferential| #9# #10#)) ((|ignore?| ((#1=(|Boolean|) (|String|)) 26 T ELT)) (|computeInt| (((|Union| #2=(|OrderedCompletion| |#2|) #3="failed") (|Kernel| |#2|) |#2| #2# #2# #1#) 35 T ELT)) (|checkForZero| ((#4=(|Union| #1# #3#) (|SparseUnivariatePolynomial| |#2|) #2# #2# #1#) 83 T ELT) ((#4# (|Polynomial| |#1|) (|Symbol|) #2# #2# #1#) 84 T ELT))) (((|DefiniteIntegrationTools| |#1| |#2|) (CATEGORY |package| (SIGNATURE |ignore?| (#1=(|Boolean|) (|String|))) (SIGNATURE |computeInt| ((|Union| #2=(|OrderedCompletion| |#2|) #3="failed") (|Kernel| |#2|) |#2| #2# #2# #1#)) (SIGNATURE |checkForZero| (#4=(|Union| #1# #3#) (|Polynomial| |#1|) (|Symbol|) #2# #2# #1#)) (SIGNATURE |checkForZero| (#4# (|SparseUnivariatePolynomial| |#2|) #2# #2# #1#))) (|Join| (|GcdDomain|) (|RetractableTo| #5=(|Integer|)) (|LinearlyExplicitRingOver| #5#)) (|Join| (|TranscendentalFunctionCategory|) (|AlgebraicallyClosedFunctionSpace| |#1|))) (T |DefiniteIntegrationTools|)) ((|checkForZero| (*1 *2 *3 *4 *4 *2) (|partial| AND #1=(|isDomain| *2 #2=(|Boolean|)) (|isDomain| *3 (|SparseUnivariatePolynomial| *6)) (|isDomain| *4 (|OrderedCompletion| *6)) (|ofCategory| *6 (|Join| #3=(|TranscendentalFunctionCategory|) (|AlgebraicallyClosedFunctionSpace| *5))) (|ofCategory| *5 #4=(|Join| (|GcdDomain|) (|RetractableTo| #5=(|Integer|)) (|LinearlyExplicitRingOver| #5#))) (|isDomain| *1 (|DefiniteIntegrationTools| *5 *6)))) (|checkForZero| (*1 *2 *3 *4 *5 *5 *2) (|partial| AND #1# (|isDomain| *3 (|Polynomial| *6)) (|isDomain| *4 (|Symbol|)) (|isDomain| *5 (|OrderedCompletion| *7)) #6=(|ofCategory| *6 #4#) (|ofCategory| *7 #7=(|Join| #3# (|AlgebraicallyClosedFunctionSpace| *6))) (|isDomain| *1 (|DefiniteIntegrationTools| *6 *7)))) (|computeInt| (*1 *2 *3 *4 *2 *2 *5) (|partial| AND (|isDomain| *2 (|OrderedCompletion| *4)) (|isDomain| *3 (|Kernel| *4)) (|isDomain| *5 #2#) (|ofCategory| *4 #7#) #6# (|isDomain| *1 (|DefiniteIntegrationTools| *6 *4)))) (|ignore?| (*1 *2 *3) (AND (|isDomain| *3 (|String|)) (|ofCategory| *4 #4#) #1# (|isDomain| *1 (|DefiniteIntegrationTools| *4 *5)) (|ofCategory| *5 (|Join| #3# (|AlgebraicallyClosedFunctionSpace| *4)))))) -((~= #1=(#2=(#3=(|Boolean|) $ $) NIL T ELT)) (|zero?| (#4=(#3# $) 86 T ELT)) (|wholePart| (#5=(#6=(|Integer|) $) 18 T ELT)) (|unitNormal| (((|Record| (|:| |unit| $) (|:| |canonical| $) (|:| |associate| $)) $) NIL T ELT)) (|unitCanonical| #7=(#8=($ $) NIL T ELT)) (|unit?| #9=(#4# NIL T ELT)) (|truncate| #7#) (|tanh| (#8# 73 T ELT)) (|tan| (#8# 61 T ELT)) (|subtractIfCan| #10=((#11=(|Union| $ #12="failed") $ $) NIL T ELT)) (|squareFreePart| #7#) (|squareFree| #13=(((|Factored| $) $) NIL T ELT)) (|sqrt| (#8# 52 T ELT)) (|sizeLess?| #1#) (|sinh| (#8# 71 T ELT)) (|sin| (#8# 59 T ELT)) (|sign| (#5# 83 T ELT)) (|sech| (#8# 76 T ELT)) (|sec| (#8# 63 T ELT)) (|sample| (#14=($) NIL T CONST)) (|round| #7#) (|retractIfCan| (((|Union| #6# . #15=(#12#)) $) 116 T ELT) (((|Union| #16=(|Fraction| #6#) . #15#) $) 113 T ELT)) (|retract| (#5# 114 T ELT) ((#16# $) 111 T ELT)) (|rem| #17=(#18=($ $ $) NIL T ELT)) (|recip| ((#11# $) 91 T ELT)) (|rationalApproximation| ((#16# $ #19=(|NonNegativeInteger|)) 106 T ELT) ((#16# $ #19# #19#) 105 T ELT)) (|quo| #17#) (|principalIdeal| (((|Record| (|:| |coef| #20=(|List| $)) #21=(|:| |generator| $)) #20#) NIL T ELT)) (|prime?| #9#) (|precision| (#22=(#23=(|PositiveInteger|)) 12 T ELT) #24=((#23# #23#) NIL #25=(|has| $ (ATTRIBUTE |arbitraryPrecision|)) ELT)) (|positive?| (#4# 107 T ELT)) (|pi| (#14# 31 T ELT)) (|patternMatch| ((#26=(|PatternMatchResult| #27=(|Float|) $) $ #28=(|Pattern| #27#) #26#) NIL T ELT)) (|order| (#5# 25 T ELT)) (|opposite?| (#2# 141 T ELT)) (|one?| (#4# 87 T ELT)) (|nthRoot| (#29=($ $ #6#) NIL T ELT)) (|norm| #7#) (|negative?| (#4# 85 T ELT)) (|nan?| (#4# 140 T ELT)) (|multiEuclidean| (((|Union| #20# #12#) #20# $) NIL T ELT)) (|min| (#18# 49 T ELT) (#14# 21 #30=(AND (|not| (|has| $ (ATTRIBUTE |arbitraryExponent|))) (|not| #25#)) ELT)) (|max| (#18# 48 T ELT) (#14# 20 #30# ELT)) (|mantissa| (#5# 10 T ELT)) (|log2| (#8# 16 T ELT)) (|log10| (#8# 53 T ELT)) (|log| (#8# 58 T ELT)) (|lcm| #17# #31=(($ #20#) NIL T ELT)) (|latex| (((|String|) $) NIL T ELT)) (|inv| #7#) (|increasePrecision| #32=((#23# #6#) NIL #25# ELT)) (|hash| (((|SingleInteger|) $) 89 T ELT)) (|gcdPolynomial| ((#33=(|SparseUnivariatePolynomial| $) #33# #33#) NIL T ELT)) (|gcd| #17# #31#) (|fractionPart| #7#) (|floor| #7#) (|float| (($ #6# #6#) NIL T ELT) (($ #6# #6# #23#) 98 T ELT)) (|factor| #13#) (|extendedEuclidean| (((|Record| #34=(|:| |coef1| $) #35=(|:| |coef2| $) #21#) $ $) NIL T ELT) (((|Union| (|Record| #34# #35#) #12#) $ $ $) NIL T ELT)) (|exquo| #10#) (|expressIdealMember| (((|Maybe| #20#) #20# $) NIL T ELT)) (|exponent| (#5# 11 T ELT)) (|exp1| (#14# 30 T ELT)) (|exp| (#8# 57 T ELT)) (|euclideanSize| ((#19# $) NIL T ELT)) (|divide| (((|Record| (|:| |quotient| $) (|:| |remainder| $)) $ $) NIL T ELT)) (|digits| (#22# NIL T ELT) #24#) (|differentiate| (#8# 92 T ELT) #36=(($ $ #19#) NIL T ELT)) (|decreasePrecision| #32#) (|csch| (#8# 74 T ELT)) (|csc| (#8# 64 T ELT)) (|coth| (#8# 75 T ELT)) (|cot| (#8# 62 T ELT)) (|cosh| (#8# 72 T ELT)) (|cos| (#8# 60 T ELT)) (|convert| ((#27# $) 102 T ELT) (((|DoubleFloat|) $) 99 T ELT) ((#28# $) NIL T ELT) (((|InputForm|) $) 38 T ELT)) (|coerce| (((|OutputForm|) $) 35 T ELT) #37=(($ #6#) 56 T ELT) #7# #38=(($ #16#) NIL T ELT) #37# #38#) (|characteristic| ((#19#) NIL T CONST)) (|ceiling| #7#) (|bits| (#22# 19 T ELT) #24#) (|before?| #1#) (|base| (#22# 7 T ELT)) (|atanh| (#8# 79 T ELT)) (|atan| (#8# 67 T ELT) (#18# 109 T ELT)) (|associates?| #1#) (|asinh| (#8# 77 T ELT)) (|asin| (#8# 65 T ELT)) (|asech| (#8# 82 T ELT)) (|asec| (#8# 70 T ELT)) (|annihilate?| (#2# 143 T ELT)) (|acsch| (#8# 80 T ELT)) (|acsc| (#8# 68 T ELT)) (|acoth| (#8# 81 T ELT)) (|acot| (#8# 69 T ELT)) (|acosh| (#8# 78 T ELT)) (|acos| (#8# 66 T ELT)) (|abs| (#8# 108 T ELT)) (|Zero| (#14# 27 T CONST)) (|One| (#14# 28 T CONST)) (|Gamma| (#8# 95 T ELT)) (D #7# #36#) (|Beta| (#18# 97 T ELT)) (>= (#2# 42 T ELT)) (> (#2# 40 T ELT)) (= (#2# 50 T ELT)) (<= (#2# 41 T ELT)) (< (#2# 39 T ELT)) (/ (#18# 29 T ELT) (#29# 51 T ELT)) (- (#8# 43 T ELT) (#18# 45 T ELT)) (+ (#18# 44 T ELT)) (** (($ $ #23#) NIL T ELT) #36# (#29# 54 T ELT) (#39=($ $ #16#) 139 T ELT) (#18# 55 T ELT)) (* (($ #23# $) 17 T ELT) (($ #19# $) NIL T ELT) (($ #6# $) 47 T ELT) (#18# 46 T ELT) (#39# NIL T ELT) (($ #16# $) NIL T ELT))) +((~= #1=(#2=(#3=(|Boolean|) $ $) NIL T ELT)) (|zero?| (#4=(#3# $) 86 T ELT)) (|wholePart| (#5=(#6=(|Integer|) $) 18 T ELT)) (|unitNormal| (((|Record| (|:| |unit| $) (|:| |canonical| $) (|:| |associate| $)) $) NIL T ELT)) (|unitCanonical| #7=(#8=($ $) NIL T ELT)) (|unit?| #9=(#4# NIL T ELT)) (|truncate| #7#) (|tanh| (#8# 73 T ELT)) (|tan| (#8# 61 T ELT)) (|subtractIfCan| (((|Maybe| $) $ $) NIL T ELT)) (|squareFreePart| #7#) (|squareFree| #10=(((|Factored| $) $) NIL T ELT)) (|sqrt| (#8# 52 T ELT)) (|sizeLess?| #1#) (|sinh| (#8# 71 T ELT)) (|sin| (#8# 59 T ELT)) (|sign| (#5# 83 T ELT)) (|sech| (#8# 76 T ELT)) (|sec| (#8# 63 T ELT)) (|sample| (#11=($) NIL T CONST)) (|round| #7#) (|retractIfCan| (((|Union| #6# . #12=(#13="failed")) $) 116 T ELT) (((|Union| #14=(|Fraction| #6#) . #12#) $) 113 T ELT)) (|retract| (#5# 114 T ELT) ((#14# $) 111 T ELT)) (|rem| #15=(#16=($ $ $) NIL T ELT)) (|recip| ((#17=(|Union| $ #13#) $) 91 T ELT)) (|rationalApproximation| ((#14# $ #18=(|NonNegativeInteger|)) 106 T ELT) ((#14# $ #18# #18#) 105 T ELT)) (|quo| #15#) (|principalIdeal| (((|Record| (|:| |coef| #19=(|List| $)) #20=(|:| |generator| $)) #19#) NIL T ELT)) (|prime?| #9#) (|precision| (#21=(#22=(|PositiveInteger|)) 12 T ELT) #23=((#22# #22#) NIL #24=(|has| $ (ATTRIBUTE |arbitraryPrecision|)) ELT)) (|positive?| (#4# 107 T ELT)) (|pi| (#11# 31 T ELT)) (|patternMatch| ((#25=(|PatternMatchResult| #26=(|Float|) $) $ #27=(|Pattern| #26#) #25#) NIL T ELT)) (|order| (#5# 25 T ELT)) (|opposite?| (#2# 141 T ELT)) (|one?| (#4# 87 T ELT)) (|nthRoot| (#28=($ $ #6#) NIL T ELT)) (|norm| #7#) (|negative?| (#4# 85 T ELT)) (|nan?| (#4# 140 T ELT)) (|multiEuclidean| (((|Union| #19# #13#) #19# $) NIL T ELT)) (|min| (#16# 49 T ELT) (#11# 21 #29=(AND (|not| (|has| $ (ATTRIBUTE |arbitraryExponent|))) (|not| #24#)) ELT)) (|max| (#16# 48 T ELT) (#11# 20 #29# ELT)) (|mantissa| (#5# 10 T ELT)) (|log2| (#8# 16 T ELT)) (|log10| (#8# 53 T ELT)) (|log| (#8# 58 T ELT)) (|lcm| #15# #30=(($ #19#) NIL T ELT)) (|latex| (((|String|) $) NIL T ELT)) (|inv| #7#) (|increasePrecision| #31=((#22# #6#) NIL #24# ELT)) (|hash| (((|SingleInteger|) $) 89 T ELT)) (|gcdPolynomial| ((#32=(|SparseUnivariatePolynomial| $) #32# #32#) NIL T ELT)) (|gcd| #15# #30#) (|fractionPart| #7#) (|floor| #7#) (|float| (($ #6# #6#) NIL T ELT) (($ #6# #6# #22#) 98 T ELT)) (|factor| #10#) (|extendedEuclidean| (((|Record| #33=(|:| |coef1| $) #34=(|:| |coef2| $) #20#) $ $) NIL T ELT) (((|Union| (|Record| #33# #34#) #13#) $ $ $) NIL T ELT)) (|exquo| ((#17# $ $) NIL T ELT)) (|expressIdealMember| (((|Maybe| #19#) #19# $) NIL T ELT)) (|exponent| (#5# 11 T ELT)) (|exp1| (#11# 30 T ELT)) (|exp| (#8# 57 T ELT)) (|euclideanSize| ((#18# $) NIL T ELT)) (|divide| (((|Record| (|:| |quotient| $) (|:| |remainder| $)) $ $) NIL T ELT)) (|digits| (#21# NIL T ELT) #23#) (|differentiate| (#8# 92 T ELT) #35=(($ $ #18#) NIL T ELT)) (|decreasePrecision| #31#) (|csch| (#8# 74 T ELT)) (|csc| (#8# 64 T ELT)) (|coth| (#8# 75 T ELT)) (|cot| (#8# 62 T ELT)) (|cosh| (#8# 72 T ELT)) (|cos| (#8# 60 T ELT)) (|convert| ((#26# $) 102 T ELT) (((|DoubleFloat|) $) 99 T ELT) ((#27# $) NIL T ELT) (((|InputForm|) $) 38 T ELT)) (|coerce| (((|OutputForm|) $) 35 T ELT) #36=(($ #6#) 56 T ELT) #7# #37=(($ #14#) NIL T ELT) #36# #37#) (|characteristic| ((#18#) NIL T CONST)) (|ceiling| #7#) (|bits| (#21# 19 T ELT) #23#) (|before?| #1#) (|base| (#21# 7 T ELT)) (|atanh| (#8# 79 T ELT)) (|atan| (#8# 67 T ELT) (#16# 109 T ELT)) (|associates?| #1#) (|asinh| (#8# 77 T ELT)) (|asin| (#8# 65 T ELT)) (|asech| (#8# 82 T ELT)) (|asec| (#8# 70 T ELT)) (|annihilate?| (#2# 143 T ELT)) (|acsch| (#8# 80 T ELT)) (|acsc| (#8# 68 T ELT)) (|acoth| (#8# 81 T ELT)) (|acot| (#8# 69 T ELT)) (|acosh| (#8# 78 T ELT)) (|acos| (#8# 66 T ELT)) (|abs| (#8# 108 T ELT)) (|Zero| (#11# 27 T CONST)) (|One| (#11# 28 T CONST)) (|Gamma| (#8# 95 T ELT)) (D #7# #35#) (|Beta| (#16# 97 T ELT)) (>= (#2# 42 T ELT)) (> (#2# 40 T ELT)) (= (#2# 50 T ELT)) (<= (#2# 41 T ELT)) (< (#2# 39 T ELT)) (/ (#16# 29 T ELT) (#28# 51 T ELT)) (- (#8# 43 T ELT) (#16# 45 T ELT)) (+ (#16# 44 T ELT)) (** (($ $ #22#) NIL T ELT) #35# (#28# 54 T ELT) (#38=($ $ #14#) 139 T ELT) (#16# 55 T ELT)) (* (($ #22# $) 17 T ELT) (($ #18# $) NIL T ELT) (($ #6# $) 47 T ELT) (#16# 46 T ELT) (#38# NIL T ELT) (($ #14# $) NIL T ELT))) (((|DoubleFloat|) (|Join| (|FloatingPointSystem|) (|DifferentialRing|) (|TranscendentalFunctionCategory|) (|ConvertibleTo| (|InputForm|)) (CATEGORY |domain| (SIGNATURE / ($ $ #1=(|Integer|))) (SIGNATURE ** #2=($ $ $)) (SIGNATURE |exp1| ($)) (SIGNATURE |log2| #3=($ $)) (SIGNATURE |log10| #3#) (SIGNATURE |atan| #2#) (SIGNATURE |Gamma| #3#) (SIGNATURE |Beta| #2#) (SIGNATURE |rationalApproximation| (#4=(|Fraction| #1#) $ #5=(|NonNegativeInteger|))) (SIGNATURE |rationalApproximation| (#4# $ #5# #5#)) (SIGNATURE |nan?| ((|Boolean|) $))))) (T |DoubleFloat|)) ((** #1=(*1 *1 *1 *1) #2=(|isDomain| *1 (|DoubleFloat|))) (/ (*1 *1 *1 *2) (AND (|isDomain| *2 #3=(|Integer|)) #2#)) (|exp1| (*1 *1) #2#) (|log2| #4=(*1 *1 *1) #2#) (|log10| #4# #2#) (|atan| #1# #2#) (|Gamma| #4# #2#) (|Beta| #1# #2#) (|rationalApproximation| (*1 *2 *1 *3) #5=(AND (|isDomain| *3 (|NonNegativeInteger|)) (|isDomain| *2 (|Fraction| #3#)) #2#)) (|rationalApproximation| (*1 *2 *1 *3 *3) #5#) (|nan?| (*1 *2 *1) (AND (|isDomain| *2 (|Boolean|)) #2#))) ((|polygamma| ((#1=(|Complex| #2=(|DoubleFloat|)) #3=(|NonNegativeInteger|) #1#) 11 T ELT) ((#2# #3# #2#) 12 T ELT)) (|logGamma| (#4=(#1# #1#) 13 T ELT) (#5=(#2# #2#) 14 T ELT)) (|hypergeometric0F1| (#6=(#1# #1# #1#) 19 T ELT) (#7=(#2# #2# #2#) 22 T ELT)) (|digamma| (#4# 27 T ELT) (#5# 26 T ELT)) (|besselY| (#6# 57 T ELT) (#7# 49 T ELT)) (|besselK| (#6# 62 T ELT) (#7# 60 T ELT)) (|besselJ| (#6# 15 T ELT) (#7# 16 T ELT)) (|besselI| (#6# 17 T ELT) (#7# 18 T ELT)) (|airyBi| (#4# 74 T ELT) (#5# 73 T ELT)) (|airyAi| (#5# 68 T ELT) (#4# 72 T ELT)) (|Gamma| (#4# 8 T ELT) (#5# 9 T ELT)) (|Beta| (#6# 35 T ELT) (#7# 31 T ELT))) @@ -572,7 +572,7 @@ NIL NIL (|Join| (|DictionaryOperations| |t#1|)) (((|Aggregate|) . T) ((|BagAggregate| |#1|) . T) ((|BasicType|) OR (|has| |#1| (|SetCategory|)) (|has| |#1| (|BasicType|))) ((|CoercibleTo| (|OutputForm|)) OR (|has| |#1| (|SetCategory|)) (|has| |#1| (|CoercibleTo| (|OutputForm|)))) ((|Collection| |#1|) . T) ((|ConvertibleTo| (|InputForm|)) |has| |#1| (|ConvertibleTo| (|InputForm|))) ((|DictionaryOperations| |#1|) . T) ((|Evalable| |#1|) AND (|has| |#1| (|Evalable| |#1|)) (|has| |#1| (|SetCategory|))) ((|Functorial| |#1|) . T) ((|HomogeneousAggregate| |#1|) . T) ((|InnerEvalable| |#1| |#1|) AND (|has| |#1| (|Evalable| |#1|)) (|has| |#1| (|SetCategory|))) ((|Join|) . T) ((|SetCategory|) |has| |#1| (|SetCategory|)) ((|ShallowlyMutableAggregate| |#1|) . T) ((|Type|) . T)) -((~= (#1=((|Boolean|) $ $) 7 T ELT)) (|zero?| ((#2=(|Boolean|) $) 22 T ELT)) (|subtractIfCan| (((|Union| $ "failed") $ $) 26 T ELT)) (|sample| (#3=($) 23 T CONST)) (|recip| (((|Union| $ "failed") $) 42 T ELT)) (|opposite?| ((#2# $ $) 20 T ELT)) (|one?| (((|Boolean|) $) 44 T ELT)) (|latex| (((|String|) $) 11 T ELT)) (|hash| (((|SingleInteger|) $) 12 T ELT)) (|differentiate| (($ $ (|Mapping| |#1| |#1|) . #4=((|NonNegativeInteger|))) 65 T ELT) (($ $ (|Mapping| |#1| |#1|)) 64 T ELT) (($ $ #5=(|Symbol|)) 63 (|has| |#1| . #6=((|PartialDifferentialSpace| (|Symbol|)))) ELT) (($ $ (|List| #5#)) 61 (|has| |#1| . #6#) ELT) (($ $ #5# . #7=(#8=(|NonNegativeInteger|))) 60 (|has| |#1| . #6#) ELT) (($ $ (|List| #5#) . #9=((|List| #8#))) 59 (|has| |#1| . #6#) ELT) (($ . #10=($)) 55 (|has| |#1| . #11=((|DifferentialSpace|))) ELT) (#12=($ $ (|NonNegativeInteger|)) 53 (|has| |#1| . #11#) ELT)) (|coerce| (((|OutputForm|) $) 13 T ELT) (($ (|Integer|)) 41 T ELT)) (|characteristic| (((|NonNegativeInteger|)) 40 T CONST)) (|before?| (#1# 6 T ELT)) (|annihilate?| (((|Boolean|) $ $) 33 T ELT)) (|Zero| (#3# 24 T CONST)) (|One| (($) 45 T CONST)) (D (($ $ (|Mapping| |#1| |#1|) . #4#) 67 T ELT) (($ $ (|Mapping| |#1| |#1|)) 66 T ELT) (($ $ #5#) 62 (|has| |#1| . #6#) ELT) (($ $ (|List| #5#)) 58 (|has| |#1| . #6#) ELT) (($ $ #5# . #7#) 57 (|has| |#1| . #6#) ELT) (($ $ (|List| #5#) . #9#) 56 (|has| |#1| . #6#) ELT) (($ . #10#) 54 (|has| |#1| . #11#) ELT) (#12# 52 (|has| |#1| . #11#) ELT)) (= (#1# 8 T ELT)) (- (($ $) 29 T ELT) (($ $ $) 28 T ELT)) (+ (($ $ $) 18 T ELT)) (** (($ $ (|PositiveInteger|)) 35 T ELT) (($ $ (|NonNegativeInteger|)) 43 T ELT)) (* (($ (|PositiveInteger|) $) 17 T ELT) (($ (|NonNegativeInteger|) $) 21 T ELT) (($ (|Integer|) $) 30 T ELT) (($ $ $) 34 T ELT))) +((~= (#1=((|Boolean|) $ $) 7 T ELT)) (|zero?| ((#2=(|Boolean|) $) 22 T ELT)) (|subtractIfCan| (((|Maybe| $) $ $) 26 T ELT)) (|sample| (#3=($) 23 T CONST)) (|recip| (((|Union| $ "failed") $) 43 T ELT)) (|opposite?| ((#2# $ $) 20 T ELT)) (|one?| (((|Boolean|) $) 45 T ELT)) (|latex| (((|String|) $) 11 T ELT)) (|hash| (((|SingleInteger|) $) 12 T ELT)) (|differentiate| (($ $ (|Mapping| |#1| |#1|) . #4=((|NonNegativeInteger|))) 66 T ELT) (($ $ (|Mapping| |#1| |#1|)) 65 T ELT) (($ $ #5=(|Symbol|)) 64 (|has| |#1| . #6=((|PartialDifferentialSpace| (|Symbol|)))) ELT) (($ $ (|List| #5#)) 62 (|has| |#1| . #6#) ELT) (($ $ #5# . #7=(#8=(|NonNegativeInteger|))) 61 (|has| |#1| . #6#) ELT) (($ $ (|List| #5#) . #9=((|List| #8#))) 60 (|has| |#1| . #6#) ELT) (($ . #10=($)) 56 (|has| |#1| . #11=((|DifferentialSpace|))) ELT) (#12=($ $ (|NonNegativeInteger|)) 54 (|has| |#1| . #11#) ELT)) (|coerce| (((|OutputForm|) $) 13 T ELT) (($ (|Integer|)) 42 T ELT)) (|characteristic| (((|NonNegativeInteger|)) 41 T CONST)) (|before?| (#1# 6 T ELT)) (|annihilate?| (((|Boolean|) $ $) 34 T ELT)) (|Zero| (#3# 24 T CONST)) (|One| (($) 46 T CONST)) (D (($ $ (|Mapping| |#1| |#1|) . #4#) 68 T ELT) (($ $ (|Mapping| |#1| |#1|)) 67 T ELT) (($ $ #5#) 63 (|has| |#1| . #6#) ELT) (($ $ (|List| #5#)) 59 (|has| |#1| . #6#) ELT) (($ $ #5# . #7#) 58 (|has| |#1| . #6#) ELT) (($ $ (|List| #5#) . #9#) 57 (|has| |#1| . #6#) ELT) (($ . #10#) 55 (|has| |#1| . #11#) ELT) (#12# 53 (|has| |#1| . #11#) ELT)) (= (#1# 8 T ELT)) (- (($ $) 30 T ELT) (($ $ $) 29 T ELT)) (+ (($ $ $) 18 T ELT)) (** (($ $ (|PositiveInteger|)) 36 T ELT) (($ $ (|NonNegativeInteger|)) 44 T ELT)) (* (($ (|PositiveInteger|) $) 17 T ELT) (($ (|NonNegativeInteger|) $) 21 T ELT) (($ (|Integer|) $) 31 T ELT) (($ $ $) 35 T ELT))) (((|DifferentialExtension| |#1|) (|Category|) (|Ring|)) (T |DifferentialExtension|)) NIL (|Join| (|Ring|) (|DifferentialSpaceExtension| |t#1|) (CATEGORY |package| (IF (|has| |t#1| (|DifferentialRing|)) (ATTRIBUTE (|DifferentialRing|)) |%noBranch|) (IF (|has| |t#1| (|PartialDifferentialRing| (|Symbol|))) (ATTRIBUTE (|PartialDifferentialRing| (|Symbol|))) |%noBranch|))) @@ -585,7 +585,7 @@ NIL ((|differentiate| (*1 *2 *1) (AND (|ofCategory| *1 (|DifferentialDomain| *2)) (|ofCategory| *2 (|Type|)))) (D (*1 *2 *1) (AND (|ofCategory| *1 (|DifferentialDomain| *2)) (|ofCategory| *2 (|Type|))))) (|Join| (|Type|) (CATEGORY |domain| (SIGNATURE |differentiate| (|t#1| $)) (SIGNATURE D (|t#1| $)))) (((|Join|) . T) ((|Type|) . T)) -((~= (#1=((|Boolean|) $ $) 7 T ELT)) (|zero?| ((#2=(|Boolean|) $) 22 T ELT)) (|subtractIfCan| (((|Union| $ "failed") $ $) 26 T ELT)) (|sample| (#3=($) 23 T CONST)) (|opposite?| ((#2# $ $) 20 T ELT)) (|latex| (((|String|) $) 11 T ELT)) (|hash| (((|SingleInteger|) $) 12 T ELT)) (|differentiate| (#4=($ $ (|NonNegativeInteger|)) 43 T ELT) (($ . #5=($)) 41 T ELT)) (|coerce| (((|OutputForm|) $) 13 T ELT)) (|before?| (#1# 6 T ELT)) (|Zero| (#3# 24 T CONST)) (D (#4# 44 T ELT) (($ . #5#) 42 T ELT)) (= (#1# 8 T ELT)) (- (($ $) 29 T ELT) (($ $ $) 28 T ELT)) (+ (($ $ $) 18 T ELT)) (* (($ (|PositiveInteger|) $) 17 T ELT) (($ (|NonNegativeInteger|) $) 21 T ELT) (($ (|Integer|) . #6=($)) 30 T ELT) (($ |#1| . #6#) 33 T ELT) (($ $ |#1|) 37 T ELT))) +((~= (#1=((|Boolean|) $ $) 7 T ELT)) (|zero?| ((#2=(|Boolean|) $) 22 T ELT)) (|subtractIfCan| (((|Maybe| $) $ $) 26 T ELT)) (|sample| (#3=($) 23 T CONST)) (|opposite?| ((#2# $ $) 20 T ELT)) (|latex| (((|String|) $) 11 T ELT)) (|hash| (((|SingleInteger|) $) 12 T ELT)) (|differentiate| (#4=($ $ (|NonNegativeInteger|)) 44 T ELT) (($ . #5=($)) 42 T ELT)) (|coerce| (((|OutputForm|) $) 13 T ELT)) (|before?| (#1# 6 T ELT)) (|Zero| (#3# 24 T CONST)) (D (#4# 45 T ELT) (($ . #5#) 43 T ELT)) (= (#1# 8 T ELT)) (- (($ $) 30 T ELT) (($ $ $) 29 T ELT)) (+ (($ $ $) 18 T ELT)) (* (($ (|PositiveInteger|) $) 17 T ELT) (($ (|NonNegativeInteger|) $) 21 T ELT) (($ (|Integer|) . #6=($)) 31 T ELT) (($ |#1| . #6#) 34 T ELT) (($ $ |#1|) 38 T ELT))) (((|DifferentialModule| |#1|) (|Category|) (|Ring|)) (T |DifferentialModule|)) NIL (|Join| (|BiModule| |t#1| |t#1|) (|DifferentialSpace|) (CATEGORY |package| (IF (|has| |t#1| (|CommutativeRing|)) (ATTRIBUTE (|Module| |t#1|)) |%noBranch|))) @@ -598,7 +598,7 @@ NIL ((|differentiate| (*1 *1 *1 *2) (AND (|ofCategory| *1 (|DifferentialSpace|)) (|isDomain| *2 (|NonNegativeInteger|)))) (D (*1 *1 *1 *2) (AND (|ofCategory| *1 (|DifferentialSpace|)) (|isDomain| *2 (|NonNegativeInteger|))))) (|Join| (|DifferentialDomain| $) (CATEGORY |domain| (SIGNATURE |differentiate| ($ $ (|NonNegativeInteger|))) (SIGNATURE D ($ $ (|NonNegativeInteger|))))) (((|DifferentialDomain| $) . T) ((|Join|) . T) ((|Type|) . T)) -((~= (#1=((|Boolean|) $ $) 7 T ELT)) (|zero?| ((#2=(|Boolean|) $) 22 T ELT)) (|subtractIfCan| (((|Union| $ "failed") $ $) 26 T ELT)) (|sample| (#3=($) 23 T CONST)) (|recip| (((|Union| $ "failed") $) 42 T ELT)) (|opposite?| ((#2# $ $) 20 T ELT)) (|one?| (((|Boolean|) $) 44 T ELT)) (|latex| (((|String|) $) 11 T ELT)) (|hash| (((|SingleInteger|) $) 12 T ELT)) (|differentiate| (#4=($ $ (|NonNegativeInteger|)) 50 T ELT) (($ . #5=($)) 48 T ELT)) (|coerce| (((|OutputForm|) $) 13 T ELT) (($ (|Integer|)) 41 T ELT)) (|characteristic| (((|NonNegativeInteger|)) 40 T CONST)) (|before?| (#1# 6 T ELT)) (|annihilate?| (((|Boolean|) $ $) 33 T ELT)) (|Zero| (#3# 24 T CONST)) (|One| (($) 45 T CONST)) (D (#4# 51 T ELT) (($ . #5#) 49 T ELT)) (= (#1# 8 T ELT)) (- (($ $) 29 T ELT) (($ $ $) 28 T ELT)) (+ (($ $ $) 18 T ELT)) (** (($ $ (|PositiveInteger|)) 35 T ELT) (($ $ (|NonNegativeInteger|)) 43 T ELT)) (* (($ (|PositiveInteger|) $) 17 T ELT) (($ (|NonNegativeInteger|) $) 21 T ELT) (($ (|Integer|) $) 30 T ELT) (($ $ $) 34 T ELT))) +((~= (#1=((|Boolean|) $ $) 7 T ELT)) (|zero?| ((#2=(|Boolean|) $) 22 T ELT)) (|subtractIfCan| (((|Maybe| $) $ $) 26 T ELT)) (|sample| (#3=($) 23 T CONST)) (|recip| (((|Union| $ "failed") $) 43 T ELT)) (|opposite?| ((#2# $ $) 20 T ELT)) (|one?| (((|Boolean|) $) 45 T ELT)) (|latex| (((|String|) $) 11 T ELT)) (|hash| (((|SingleInteger|) $) 12 T ELT)) (|differentiate| (#4=($ $ (|NonNegativeInteger|)) 51 T ELT) (($ . #5=($)) 49 T ELT)) (|coerce| (((|OutputForm|) $) 13 T ELT) (($ (|Integer|)) 42 T ELT)) (|characteristic| (((|NonNegativeInteger|)) 41 T CONST)) (|before?| (#1# 6 T ELT)) (|annihilate?| (((|Boolean|) $ $) 34 T ELT)) (|Zero| (#3# 24 T CONST)) (|One| (($) 46 T CONST)) (D (#4# 52 T ELT) (($ . #5#) 50 T ELT)) (= (#1# 8 T ELT)) (- (($ $) 30 T ELT) (($ $ $) 29 T ELT)) (+ (($ $ $) 18 T ELT)) (** (($ $ (|PositiveInteger|)) 36 T ELT) (($ $ (|NonNegativeInteger|)) 44 T ELT)) (* (($ (|PositiveInteger|) $) 17 T ELT) (($ (|NonNegativeInteger|) $) 21 T ELT) (($ (|Integer|) $) 31 T ELT) (($ $ $) 35 T ELT))) (((|DifferentialRing|) (|Category|)) (T |DifferentialRing|)) NIL (|Join| (|Ring|) (|DifferentialSpace|)) @@ -619,15 +619,15 @@ NIL ((|dioSolve| (((|Record| (|:| |varOrder| (|List| (|Symbol|))) (|:| |inhom| (|Union| #1=(|List| (|Vector| (|NonNegativeInteger|))) "failed")) (|:| |hom| #1#)) (|Equation| (|Polynomial| (|Integer|)))) 42 T ELT))) (((|DiophantineSolutionPackage|) (CATEGORY |package| (SIGNATURE |dioSolve| ((|Record| (|:| |varOrder| (|List| (|Symbol|))) (|:| |inhom| (|Union| #1=(|List| (|Vector| (|NonNegativeInteger|))) "failed")) (|:| |hom| #1#)) (|Equation| (|Polynomial| (|Integer|))))))) (T |DiophantineSolutionPackage|)) ((|dioSolve| (*1 *2 *3) (AND (|isDomain| *3 (|Equation| (|Polynomial| (|Integer|)))) (|isDomain| *2 (|Record| (|:| |varOrder| (|List| (|Symbol|))) (|:| |inhom| (|Union| #1=(|List| (|Vector| (|NonNegativeInteger|))) "failed")) (|:| |hom| #1#))) (|isDomain| *1 (|DiophantineSolutionPackage|))))) -((|size| (#1=(#2=(|NonNegativeInteger|)) 56 T ELT)) (|reducedSystem| (((|Record| (|:| |mat| #3=(|Matrix| |#3|)) (|:| |vec| #4=(|Vector| |#3|))) #5=(|Matrix| $) #6=(|Vector| $)) 53 T ELT) ((#3# #5#) 44 T ELT) (((|Record| (|:| |mat| #7=(|Matrix| #8=(|Integer|))) (|:| |vec| (|Vector| #8#))) #5# #6#) NIL T ELT) ((#7# #5#) NIL T ELT)) (|dimension| (((|CardinalNumber|)) 62 T ELT)) (|differentiate| (($ $ #9=(|Mapping| |#3| |#3|)) 18 T ELT) (($ $ #9# #2#) NIL T ELT) (($ $ #10=(|List| #11=(|Symbol|)) (|List| #2#)) NIL T ELT) (($ $ #11# #2#) NIL T ELT) (($ $ #10#) NIL T ELT) (($ $ #11#) NIL T ELT) (($ $ #2#) NIL T ELT) (($ $) NIL T ELT)) (|coerce| ((#4# $) NIL T ELT) (($ |#3|) NIL T ELT) (((|OutputForm|) $) NIL T ELT) (($ #8#) 12 T ELT) (($ (|Fraction| #8#)) NIL T ELT)) (|characteristic| (#1# 15 T CONST)) (/ (($ $ |#3|) 59 T ELT))) -(((|DirectProductCategory&| |#1| |#2| |#3|) (CATEGORY |package| (SIGNATURE |coerce| (|#1| (|Fraction| #1=(|Integer|)))) (SIGNATURE |coerce| (|#1| #1#)) (SIGNATURE |differentiate| (|#1| |#1|)) (SIGNATURE |differentiate| (|#1| |#1| #2=(|NonNegativeInteger|))) (SIGNATURE |differentiate| (|#1| |#1| #3=(|Symbol|))) (SIGNATURE |differentiate| (|#1| |#1| #4=(|List| #3#))) (SIGNATURE |differentiate| (|#1| |#1| #3# #2#)) (SIGNATURE |differentiate| (|#1| |#1| #4# (|List| #2#))) (SIGNATURE |coerce| ((|OutputForm|) |#1|)) (SIGNATURE |characteristic| #5=(#2#) |constant|) (SIGNATURE |reducedSystem| (#6=(|Matrix| #1#) #7=(|Matrix| |#1|))) (SIGNATURE |reducedSystem| ((|Record| (|:| |mat| #6#) (|:| |vec| (|Vector| #1#))) #7# #8=(|Vector| |#1|))) (SIGNATURE |coerce| (|#1| |#3|)) (SIGNATURE |differentiate| (|#1| |#1| #9=(|Mapping| |#3| |#3|) #2#)) (SIGNATURE |differentiate| (|#1| |#1| #9#)) (SIGNATURE |reducedSystem| (#10=(|Matrix| |#3|) #7#)) (SIGNATURE |reducedSystem| ((|Record| (|:| |mat| #10#) (|:| |vec| #11=(|Vector| |#3|))) #7# #8#)) (SIGNATURE |size| #5#) (SIGNATURE / (|#1| |#1| |#3|)) (SIGNATURE |dimension| ((|CardinalNumber|))) (SIGNATURE |coerce| (#11# |#1|))) (|DirectProductCategory| |#2| |#3|) #2# (|Type|)) (T |DirectProductCategory&|)) +((|size| (#1=(#2=(|NonNegativeInteger|)) 56 T ELT)) (|reducedSystem| (((|Record| (|:| |mat| #3=(|Matrix| |#3|)) (|:| |vec| #4=(|Vector| |#3|))) #5=(|Matrix| $) #6=(|Vector| $)) 53 T ELT) ((#3# #5#) 44 T ELT) (((|Record| (|:| |mat| #7=(|Matrix| #8=(|Integer|))) (|:| |vec| (|Vector| #8#))) #5# #6#) NIL T ELT) ((#7# #5#) NIL T ELT)) (|dimension| (((|CardinalNumber|)) 62 T ELT)) (|differentiate| (($ $ #9=(|Mapping| |#3| |#3|)) 18 T ELT) (($ $ #9# #2#) NIL T ELT) (($ $ #2#) NIL T ELT) (($ $) NIL T ELT) (($ $ #10=(|List| #11=(|Symbol|)) (|List| #2#)) NIL T ELT) (($ $ #11# #2#) NIL T ELT) (($ $ #10#) NIL T ELT) (($ $ #11#) NIL T ELT)) (|coerce| ((#4# $) NIL T ELT) (($ |#3|) NIL T ELT) (((|OutputForm|) $) NIL T ELT) (($ #8#) 12 T ELT) (($ (|Fraction| #8#)) NIL T ELT)) (|characteristic| (#1# 15 T CONST)) (/ (($ $ |#3|) 59 T ELT))) +(((|DirectProductCategory&| |#1| |#2| |#3|) (CATEGORY |package| (SIGNATURE |coerce| (|#1| (|Fraction| #1=(|Integer|)))) (SIGNATURE |coerce| (|#1| #1#)) (SIGNATURE |differentiate| (|#1| |#1| #2=(|Symbol|))) (SIGNATURE |differentiate| (|#1| |#1| #3=(|List| #2#))) (SIGNATURE |differentiate| (|#1| |#1| #2# #4=(|NonNegativeInteger|))) (SIGNATURE |differentiate| (|#1| |#1| #3# (|List| #4#))) (SIGNATURE |differentiate| (|#1| |#1|)) (SIGNATURE |differentiate| (|#1| |#1| #4#)) (SIGNATURE |coerce| ((|OutputForm|) |#1|)) (SIGNATURE |characteristic| #5=(#4#) |constant|) (SIGNATURE |reducedSystem| (#6=(|Matrix| #1#) #7=(|Matrix| |#1|))) (SIGNATURE |reducedSystem| ((|Record| (|:| |mat| #6#) (|:| |vec| (|Vector| #1#))) #7# #8=(|Vector| |#1|))) (SIGNATURE |coerce| (|#1| |#3|)) (SIGNATURE |differentiate| (|#1| |#1| #9=(|Mapping| |#3| |#3|) #4#)) (SIGNATURE |differentiate| (|#1| |#1| #9#)) (SIGNATURE |reducedSystem| (#10=(|Matrix| |#3|) #7#)) (SIGNATURE |reducedSystem| ((|Record| (|:| |mat| #10#) (|:| |vec| #11=(|Vector| |#3|))) #7# #8#)) (SIGNATURE |size| #5#) (SIGNATURE / (|#1| |#1| |#3|)) (SIGNATURE |dimension| ((|CardinalNumber|))) (SIGNATURE |coerce| (#11# |#1|))) (|DirectProductCategory| |#2| |#3|) #4# (|Type|)) (T |DirectProductCategory&|)) ((|dimension| #1=(*1 *2) (AND (|ofType| *4 #2=(|NonNegativeInteger|)) #3=(|ofCategory| *5 (|Type|)) (|isDomain| *2 (|CardinalNumber|)) #4=(|isDomain| *1 (|DirectProductCategory&| *3 *4 *5)) #5=(|ofCategory| *3 (|DirectProductCategory| *4 *5)))) (|size| #1# #6=(AND (|ofType| *4 *2) #3# (|isDomain| *2 #2#) #4# #5#)) (|characteristic| #1# #6#)) -((~= (#1=((|Boolean|) $ $) 18 (|has| |#2| . #2=((|BasicType|))) ELT)) (|zero?| ((#3=(|Boolean|) $) 72 (|has| |#2| . #4=((|AbelianMonoid|))) ELT)) (|unitVector| (($ (|PositiveInteger|)) 128 (|has| |#2| (|Ring|)) ELT)) (|swap!| (((|Void|) $ #5=(|Integer|) #5#) 35 (|has| $ (|ShallowlyMutableAggregate| |#2|)) ELT)) (|sup| (($ $ $) 124 (|has| |#2| . #6=((|OrderedAbelianMonoidSup|))) ELT)) (|subtractIfCan| (((|Union| $ "failed") $ $) 75 (|has| |#2| (|CancellationAbelianMonoid|)) ELT)) (|size| (((|NonNegativeInteger|)) 113 (|has| |#2| . #7=((|Finite|))) ELT)) (|setelt| ((|#2| $ #5# |#2|) 47 (|has| $ (|ShallowlyMutableAggregate| |#2|)) ELT)) (|sample| (#8=($) 6 T CONST)) (|retractIfCan| (((|Union| #9=(|Integer|) . #10=("failed")) . #11=($)) 67 (|and| (|has| |#2| . #12=((|RetractableTo| #9#))) (|has| |#2| . #13=((|SetCategory|)))) ELT) (((|Union| #14=(|Fraction| #9#) . #10#) . #11#) 64 (|and| (|has| |#2| . #15=((|RetractableTo| #14#))) (|has| |#2| . #13#)) ELT) (((|Union| |#2| . #10#) . #11#) 61 (|has| |#2| . #13#) ELT)) (|retract| ((#9# . #16=($)) 66 (|and| (|has| |#2| . #12#) (|has| |#2| . #13#)) ELT) ((#14# . #16#) 63 (|and| (|has| |#2| . #15#) (|has| |#2| . #13#)) ELT) ((|#2| . #16#) 62 (|has| |#2| . #13#) ELT)) (|reducedSystem| (((|Matrix| #17=(|Integer|)) . #18=(#19=(|Matrix| $))) 110 (|and| (|has| |#2| . #20=((|LinearlyExplicitRingOver| #17#))) (|has| |#2| . #21=((|Ring|)))) ELT) (((|Record| (|:| |mat| (|Matrix| #17#)) (|:| |vec| (|Vector| #17#))) . #22=(#19# #23=(|Vector| $))) 109 (|and| (|has| |#2| . #20#) (|has| |#2| . #21#)) ELT) (((|Record| (|:| |mat| (|Matrix| |#2|)) (|:| |vec| (|Vector| |#2|))) . #22#) 108 (|has| |#2| . #21#) ELT) (((|Matrix| |#2|) . #18#) 107 (|has| |#2| . #21#) ELT)) (|reduce| ((|#2| (|Mapping| |#2| |#2| |#2|) $ |#2| |#2|) 141 (|has| |#2| . #24=((|BasicType|))) ELT) ((|#2| (|Mapping| |#2| |#2| |#2|) $ |#2|) 137 T ELT) ((|#2| (|Mapping| |#2| |#2| |#2|) $) 136 T ELT)) (|recip| (((|Union| $ "failed") $) 87 (|has| |#2| . #25=((|Ring|))) ELT)) (|random| (($) 116 (|has| |#2| . #7#) ELT)) (|qsetelt!| ((|#2| $ #5# |#2|) 48 (|has| $ (|ShallowlyMutableAggregate| |#2|)) ELT)) (|qelt| ((|#2| $ #5#) 46 T ELT)) (|positive?| (((|Boolean|) $) 123 (|has| |#2| . #6#) ELT)) (|opposite?| ((#3# $ $) 74 (|has| |#2| . #4#) ELT)) (|one?| (((|Boolean|) $) 85 (|has| |#2| . #25#) ELT)) (|minIndex| ((#5# . #26=($)) 38 (|has| #5# . #27=((|OrderedSet|))) ELT)) (|min| (#28=($ $ $) 117 (|has| |#2| . #29=((|OrderedSet|))) ELT)) 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T) ((|BasicType|) OR (|has| |#2| (|SetCategory|)) (|has| |#2| (|Ring|)) (|has| |#2| (|OrderedSet|)) (|has| |#2| (|OrderedAbelianMonoidSup|)) (|has| |#2| (|Monoid|)) (|has| |#2| (|Finite|)) (|has| |#2| (|Field|)) (|has| |#2| (|CommutativeRing|)) (|has| |#2| (|CancellationAbelianMonoid|)) (|has| |#2| (|BasicType|)) (|has| |#2| (|AbelianSemiGroup|)) (|has| |#2| (|AbelianMonoid|)) (|has| |#2| (|AbelianGroup|))) ((|BiModule| |#2| |#2|) OR (|has| |#2| (|Ring|)) (|has| |#2| (|Field|)) (|has| |#2| (|CommutativeRing|))) ((|CancellationAbelianMonoid|) OR (|has| |#2| (|Ring|)) (|has| |#2| (|OrderedAbelianMonoidSup|)) (|has| |#2| (|Field|)) (|has| |#2| (|CommutativeRing|)) (|has| |#2| (|CancellationAbelianMonoid|)) (|has| |#2| (|AbelianGroup|))) ((|CoercibleFrom| #1=(|Fraction| (|Integer|))) AND (|has| |#2| (|RetractableTo| (|Fraction| (|Integer|)))) (|has| |#2| (|SetCategory|))) ((|CoercibleFrom| (|Integer|)) OR (|has| |#2| (|Ring|)) (AND (|has| |#2| (|RetractableTo| (|Integer|))) (|has| |#2| (|SetCategory|)))) ((|CoercibleFrom| |#2|) |has| |#2| (|SetCategory|)) ((|CoercibleTo| (|OutputForm|)) OR (|has| |#2| (|SetCategory|)) (|has| |#2| (|Ring|)) (|has| |#2| (|OrderedSet|)) (|has| |#2| (|OrderedAbelianMonoidSup|)) (|has| |#2| (|Monoid|)) (|has| |#2| (|Finite|)) (|has| |#2| (|Field|)) (|has| |#2| (|CommutativeRing|)) (|has| |#2| (|CoercibleTo| (|OutputForm|))) (|has| |#2| (|CancellationAbelianMonoid|)) (|has| |#2| (|AbelianSemiGroup|)) (|has| |#2| (|AbelianMonoid|)) (|has| |#2| (|AbelianGroup|))) ((|CoercibleTo| (|Vector| |#2|)) . T) ((|DifferentialDomain| $) OR (AND (|has| |#2| (|DifferentialSpace|)) (|has| |#2| (|Ring|))) (AND (|has| |#2| (|DifferentialRing|)) (|has| |#2| (|Ring|)))) ((|DifferentialExtension| |#2|) |has| |#2| (|Ring|)) ((|DifferentialRing|) AND (|has| |#2| (|DifferentialRing|)) (|has| |#2| (|Ring|))) ((|DifferentialSpace|) OR (AND (|has| |#2| (|DifferentialSpace|)) (|has| |#2| (|Ring|))) (AND (|has| |#2| (|DifferentialRing|)) (|has| |#2| (|Ring|)))) ((|DifferentialSpaceExtension| |#2|) |has| |#2| (|Ring|)) ((|Eltable| #2=(|Integer|) |#2|) . T) ((|EltableAggregate| #2# |#2|) . T) ((|Evalable| |#2|) AND (|has| |#2| (|Evalable| |#2|)) (|has| |#2| (|SetCategory|))) ((|Finite|) |has| |#2| (|Finite|)) ((|FiniteAggregate| |#2|) . T) ((|FullyLinearlyExplicitRingOver| |#2|) |has| |#2| (|Ring|)) ((|FullyRetractableTo| |#2|) |has| |#2| (|SetCategory|)) ((|Functorial| |#2|) . T) ((|HomogeneousAggregate| |#2|) . T) ((|IndexedAggregate| #2# |#2|) . T) ((|InnerEvalable| |#2| |#2|) AND (|has| |#2| (|Evalable| |#2|)) (|has| |#2| (|SetCategory|))) ((|Join|) . T) ((|LeftLinearSet| (|Integer|)) OR (|has| |#2| (|Ring|)) (|has| |#2| (|Field|)) (|has| |#2| (|CommutativeRing|)) (|has| |#2| (|AbelianGroup|))) ((|LeftLinearSet| |#2|) OR (|has| |#2| (|Ring|)) (|has| |#2| (|Monoid|)) (|has| |#2| (|Field|)) (|has| |#2| (|CommutativeRing|))) ((|LeftLinearSet| $) |has| |#2| (|Ring|)) ((|LeftModule| #3=(|Integer|)) AND (|has| |#2| (|LinearlyExplicitRingOver| (|Integer|))) (|has| |#2| (|Ring|))) ((|LeftModule| |#2|) OR (|has| |#2| (|Ring|)) (|has| |#2| (|Field|)) (|has| |#2| (|CommutativeRing|))) ((|LeftModule| $) |has| |#2| (|Ring|)) ((|LinearSet| |#2|) OR (|has| |#2| (|Monoid|)) (|has| |#2| (|Field|)) (|has| |#2| (|CommutativeRing|))) ((|LinearlyExplicitRingOver| #3#) AND (|has| |#2| (|LinearlyExplicitRingOver| (|Integer|))) (|has| |#2| (|Ring|))) ((|LinearlyExplicitRingOver| |#2|) |has| |#2| (|Ring|)) ((|Module| |#2|) OR (|has| |#2| (|Field|)) (|has| |#2| (|CommutativeRing|))) ((|Monoid|) |has| |#2| (|Ring|)) ((|OrderedAbelianMonoid|) |has| |#2| (|OrderedAbelianMonoidSup|)) ((|OrderedAbelianMonoidSup|) |has| |#2| (|OrderedAbelianMonoidSup|)) ((|OrderedAbelianSemiGroup|) |has| |#2| (|OrderedAbelianMonoidSup|)) ((|OrderedCancellationAbelianMonoid|) |has| |#2| (|OrderedAbelianMonoidSup|)) ((|OrderedSet|) OR (|has| |#2| (|OrderedSet|)) (|has| |#2| (|OrderedAbelianMonoidSup|))) ((|OrderedType|) OR (|has| |#2| (|OrderedSet|)) (|has| |#2| (|OrderedAbelianMonoidSup|))) ((|PartialDifferentialDomain| $ #4=(|Symbol|)) OR (AND (|has| |#2| (|PartialDifferentialSpace| (|Symbol|))) (|has| |#2| (|Ring|))) (AND (|has| |#2| (|PartialDifferentialRing| (|Symbol|))) (|has| |#2| (|Ring|)))) ((|PartialDifferentialRing| (|Symbol|)) AND (|has| |#2| (|PartialDifferentialRing| (|Symbol|))) (|has| |#2| (|Ring|))) ((|PartialDifferentialSpace| #4#) OR (AND (|has| |#2| (|PartialDifferentialSpace| (|Symbol|))) (|has| |#2| (|Ring|))) (AND (|has| |#2| (|PartialDifferentialRing| (|Symbol|))) (|has| |#2| (|Ring|)))) ((|RetractableTo| #1#) AND (|has| |#2| (|RetractableTo| (|Fraction| (|Integer|)))) (|has| |#2| (|SetCategory|))) ((|RetractableTo| (|Integer|)) AND (|has| |#2| (|RetractableTo| (|Integer|))) (|has| |#2| (|SetCategory|))) ((|RetractableTo| |#2|) |has| |#2| (|SetCategory|)) ((|RightLinearSet| |#2|) OR (|has| |#2| (|Ring|)) (|has| |#2| (|Monoid|)) (|has| |#2| (|Field|)) (|has| |#2| (|CommutativeRing|))) ((|RightModule| |#2|) OR (|has| |#2| (|Ring|)) (|has| |#2| (|Field|)) (|has| |#2| (|CommutativeRing|))) ((|Ring|) |has| |#2| (|Ring|)) ((|Rng|) |has| |#2| (|Ring|)) ((|SemiGroup|) |has| |#2| (|Ring|)) ((|SemiRing|) |has| |#2| (|Ring|)) ((|SetCategory|) OR (|has| |#2| (|SetCategory|)) (|has| |#2| (|Ring|)) (|has| |#2| (|OrderedSet|)) (|has| |#2| (|OrderedAbelianMonoidSup|)) (|has| |#2| (|Monoid|)) (|has| |#2| (|Finite|)) (|has| |#2| (|Field|)) (|has| |#2| (|CommutativeRing|)) (|has| |#2| (|CancellationAbelianMonoid|)) (|has| |#2| (|AbelianSemiGroup|)) (|has| |#2| (|AbelianMonoid|)) (|has| |#2| (|AbelianGroup|))) ((|Type|) . T) ((|VectorSpace| |#2|) |has| |#2| (|Field|))) -((~= #1=(#2=(#3=(|Boolean|) $ $) NIL #4=(|has| |#2| (|BasicType|)) ELT)) (|zero?| (#5=(#3# $) NIL #6=(|has| |#2| (|AbelianMonoid|)) ELT)) (|unitVector| (#7=($ #8=(|PositiveInteger|)) 63 #9=(|has| |#2| (|Ring|)) ELT)) (|swap!| (((|Void|) $ #10=(|Integer|) #10#) NIL #11=(|has| $ (|ShallowlyMutableAggregate| |#2|)) ELT)) (|sup| (#12=($ $ $) 69 #13=(|has| |#2| (|OrderedAbelianMonoidSup|)) ELT)) (|subtractIfCan| ((#14=(|Union| $ #15="failed") $ $) 54 (|has| |#2| (|CancellationAbelianMonoid|)) ELT)) (|size| (#16=(#17=(|NonNegativeInteger|)) NIL #18=(|has| |#2| (|Finite|)) ELT)) (|setelt| #19=(#20=(|#2| $ #10# |#2|) NIL #11# ELT)) (|sample| (#21=($) NIL T CONST)) (|retractIfCan| (((|Union| #10# . #22=(#15#)) . #23=($)) NIL #24=(AND (|has| |#2| (|RetractableTo| #10#)) #25=(|has| |#2| (|SetCategory|))) ELT) (((|Union| #26=(|Fraction| #10#) . #22#) . #23#) NIL #27=(AND (|has| |#2| (|RetractableTo| #26#)) #25#) ELT) ((#28=(|Union| |#2| . #22#) $) 31 #25# ELT)) (|retract| (#29=(#10# . #30=($)) NIL #24# ELT) ((#26# . #30#) NIL #27# ELT) (#31=(|#2| $) 29 #25# ELT)) (|reducedSystem| ((#32=(|Matrix| #10#) . #33=(#34=(|Matrix| $))) NIL #35=(AND (|has| |#2| (|LinearlyExplicitRingOver| #10#)) #9#) ELT) ((#36=(|Record| (|:| |mat| #32#) (|:| |vec| (|Vector| #10#))) . #37=(#34# #38=(|Vector| $))) NIL #35# ELT) ((#39=(|Record| (|:| |mat| #40=(|Matrix| |#2|)) (|:| |vec| #41=(|Vector| |#2|))) . #37#) NIL #9# ELT) ((#40# . #33#) NIL #9# ELT)) (|reduce| ((|#2| #42=(|Mapping| |#2| |#2| |#2|) $ |#2| |#2|) NIL #4# ELT) ((|#2| #42# $ |#2|) NIL T ELT) ((|#2| #42# $) NIL T ELT)) (|recip| ((#14# $) 59 #9# ELT)) (|random| (#21# NIL #18# ELT)) (|qsetelt!| #19#) (|qelt| (#43=(|#2| $ #10#) 57 T ELT)) (|positive?| (#5# NIL #13# ELT)) (|opposite?| (#2# NIL #6# ELT)) (|one?| (#5# NIL #9# ELT)) (|minIndex| (#29# 20 #44=(|has| #10# #45=(|OrderedSet|)) ELT)) (|min| #46=(#12# NIL #47=(|has| |#2| #45#) ELT)) (|members| (#48=(#49=(|List| |#2|) $) 14 T ELT)) (|member?| (#50=(#3# |#2| $) NIL #4# ELT)) (|maxIndex| (#29# NIL #44# ELT)) (|max| #46#) (|map| (($ #51=(|Mapping| |#2| |#2|) $) NIL T ELT)) (|lookup| ((#8# $) NIL #18# ELT)) (|leftReducedSystem| ((#32# . #52=(#38#)) NIL #35# ELT) ((#36# . #53=(#38# $)) NIL #35# ELT) ((#39# . #53#) NIL #9# ELT) ((#40# . #52#) NIL #9# ELT)) (|latex| (((|String|) $) NIL #25# ELT)) (|indices| (((|List| #10#) $) NIL T ELT)) (|index?| ((#3# #10# $) NIL T ELT)) (|index| (#7# NIL #18# ELT)) (|hash| (((|SingleInteger|) $) NIL #25# ELT)) (|first| (#31# NIL #44# ELT)) (|find| ((#28# #54=(|Mapping| #3# |#2|) $) NIL T ELT)) (|fill!| (#55=($ $ |#2|) NIL #11# ELT)) (|every?| (#56=(#3# #54# $) 24 T ELT)) (|eval| (($ $ (|List| #57=(|Equation| |#2|))) NIL #58=(AND (|has| |#2| (|Evalable| |#2|)) #25#) ELT) (($ $ #57#) NIL #58# ELT) (($ $ |#2| |#2|) NIL #58# ELT) (($ $ #49# #49#) NIL #58# ELT)) (|eq?| (#2# NIL T ELT)) (|entry?| (#50# NIL (AND (|has| $ (|FiniteAggregate| |#2|)) #4#) ELT)) (|entries| (#48# NIL T ELT)) (|empty?| (#5# NIL T ELT)) (|empty| (#21# NIL T ELT)) (|elt| (#20# NIL T ELT) (#43# 21 T ELT)) (|dot| ((|#2| $ $) NIL #9# ELT)) (|directProduct| (($ #41#) 18 T ELT)) (|dimension| (((|CardinalNumber|)) NIL #59=(|has| |#2| (|Field|)) ELT)) (|differentiate| #60=(#61=($ $ #17#) NIL #62=(AND (|has| |#2| (|DifferentialSpace|)) #9#) ELT) #63=(#64=($ $) NIL #62# ELT) #65=(($ $ #66=(|List| #67=(|Symbol|)) (|List| #17#)) NIL #68=(AND (|has| |#2| (|PartialDifferentialSpace| #67#)) #9#) ELT) #69=(($ $ #67# #17#) NIL #68# ELT) #70=(($ $ #66#) NIL #68# ELT) #71=(($ $ #67#) NIL #68# ELT) #72=(($ $ #51#) NIL #9# ELT) #73=(($ $ #51# #17#) NIL #9# ELT)) (|count| ((#17# |#2| $) NIL #4# ELT) ((#17# #54# $) NIL T ELT)) (|copy| (#64# NIL T ELT)) (|coerce| ((#41# $) 9 T ELT) (($ #10#) NIL (OR #24# #9#) ELT) (($ #26#) NIL #27# ELT) (($ |#2|) 12 #25# ELT) ((#74=(|OutputForm|) $) NIL (|has| |#2| (|CoercibleTo| #74#)) ELT)) (|characteristic| (#16# NIL #9# CONST)) (|before?| #1#) (|any?| (#56# NIL T ELT)) (|annihilate?| (#2# NIL #9# ELT)) (|Zero| (#21# 37 #6# CONST)) (|One| (#21# 41 #9# CONST)) (D #60# #63# #65# #69# #70# #71# #72# #73#) (>= #75=(#2# NIL #47# ELT)) (> #75#) (= (#2# 28 #4# ELT)) (<= #75#) (< (#2# 67 #47# ELT)) (/ (#55# NIL #59# ELT)) (- (#12# NIL #76=(|has| |#2| (|AbelianGroup|)) ELT) (#64# NIL #76# ELT)) (+ (#12# 35 #77=(|has| |#2| (|AbelianSemiGroup|)) ELT)) (** (#61# NIL #9# ELT) (($ $ #8#) NIL #9# ELT)) (* (#12# 47 #9# ELT) (#55# 45 #78=(|has| |#2| (|Monoid|)) ELT) (($ |#2| $) 46 #78# ELT) (($ #10# $) NIL #76# ELT) (($ #17# $) NIL #6# ELT) (($ #8# $) NIL #77# ELT)) (|#| ((#17# $) NIL T ELT))) +((~= #1=(#2=(#3=(|Boolean|) $ $) NIL #4=(|has| |#2| (|BasicType|)) ELT)) (|zero?| (#5=(#3# $) NIL #6=(|has| |#2| (|AbelianMonoid|)) ELT)) (|unitVector| (#7=($ #8=(|PositiveInteger|)) 71 #9=(|has| |#2| (|Ring|)) ELT)) (|swap!| (((|Void|) $ #10=(|Integer|) #10#) NIL #11=(|has| $ (|ShallowlyMutableAggregate| |#2|)) ELT)) (|sup| (#12=($ $ $) 77 #13=(|has| |#2| (|OrderedAbelianMonoidSup|)) ELT)) (|subtractIfCan| (((|Maybe| $) $ $) 61 (|has| |#2| (|CancellationAbelianMonoid|)) ELT)) (|size| (#14=(#15=(|NonNegativeInteger|)) NIL #16=(|has| |#2| (|Finite|)) ELT)) (|setelt| #17=(#18=(|#2| $ #10# |#2|) NIL #11# ELT)) (|sample| (#19=($) NIL T CONST)) (|retractIfCan| (((|Union| #10# . #20=(#21="failed")) . #22=($)) NIL #23=(AND (|has| |#2| (|RetractableTo| #10#)) #24=(|has| |#2| (|SetCategory|))) ELT) (((|Union| #25=(|Fraction| #10#) . #20#) . #22#) NIL #26=(AND (|has| |#2| (|RetractableTo| #25#)) #24#) ELT) ((#27=(|Union| |#2| . #20#) $) 31 #24# ELT)) (|retract| (#28=(#10# . #29=($)) NIL #23# ELT) ((#25# . #29#) NIL #26# ELT) (#30=(|#2| $) 29 #24# ELT)) (|reducedSystem| ((#31=(|Matrix| #10#) . #32=(#33=(|Matrix| $))) NIL #34=(AND (|has| |#2| (|LinearlyExplicitRingOver| #10#)) #9#) ELT) ((#35=(|Record| (|:| |mat| #31#) (|:| |vec| (|Vector| #10#))) . #36=(#33# #37=(|Vector| $))) NIL #34# ELT) ((#38=(|Record| (|:| |mat| #39=(|Matrix| |#2|)) (|:| |vec| #40=(|Vector| |#2|))) . #36#) NIL #9# ELT) ((#39# . #32#) NIL #9# ELT)) (|reduce| ((|#2| #41=(|Mapping| |#2| |#2| |#2|) $ |#2| |#2|) NIL #4# ELT) ((|#2| #41# $ |#2|) NIL T ELT) ((|#2| #41# $) NIL T ELT)) (|recip| (((|Union| $ #21#) $) 67 #9# ELT)) (|random| (#19# NIL #16# ELT)) (|qsetelt!| #17#) (|qelt| (#42=(|#2| $ #10#) 64 T ELT)) (|positive?| (#5# NIL #13# ELT)) (|opposite?| (#2# NIL #6# ELT)) (|one?| (#5# NIL #9# ELT)) (|minIndex| (#28# 20 #43=(|has| #10# #44=(|OrderedSet|)) ELT)) (|min| #45=(#12# NIL #46=(|has| |#2| #44#) ELT)) (|members| (#47=(#48=(|List| |#2|) $) 14 T ELT)) (|member?| (#49=(#3# |#2| $) NIL #4# ELT)) (|maxIndex| (#28# NIL #43# ELT)) (|max| #45#) (|map| (($ #50=(|Mapping| |#2| |#2|) $) NIL T ELT)) (|lookup| ((#8# $) NIL #16# ELT)) (|leftReducedSystem| ((#31# . #51=(#37#)) NIL #34# ELT) ((#35# . #52=(#37# $)) NIL #34# ELT) ((#38# . #52#) NIL #9# ELT) ((#39# . #51#) NIL #9# ELT)) (|latex| (((|String|) $) NIL #24# ELT)) (|indices| (((|List| #10#) $) NIL T ELT)) (|index?| ((#3# #10# $) NIL T ELT)) (|index| (#7# NIL #16# ELT)) (|hash| (((|SingleInteger|) $) NIL #24# ELT)) (|first| (#30# NIL #43# ELT)) (|find| ((#27# #53=(|Mapping| #3# |#2|) $) NIL T ELT)) (|fill!| (#54=($ $ |#2|) NIL #11# ELT)) (|every?| (#55=(#3# #53# $) 24 T ELT)) (|eval| (($ $ (|List| #56=(|Equation| |#2|))) NIL #57=(AND (|has| |#2| (|Evalable| |#2|)) #24#) ELT) (($ $ #56#) NIL #57# ELT) (($ $ |#2| |#2|) NIL #57# ELT) (($ $ #48# #48#) NIL #57# ELT)) (|eq?| (#2# NIL T ELT)) (|entry?| (#49# NIL (AND (|has| $ (|FiniteAggregate| |#2|)) #4#) ELT)) (|entries| (#47# NIL T ELT)) (|empty?| (#5# NIL T ELT)) (|empty| (#19# NIL T ELT)) (|elt| (#18# NIL T ELT) (#42# 21 T ELT)) (|dot| ((|#2| $ $) NIL #9# ELT)) (|directProduct| (($ #40#) 18 T ELT)) (|dimension| (((|CardinalNumber|)) NIL #58=(|has| |#2| (|Field|)) ELT)) (|differentiate| #59=(#60=($ $ #15#) NIL #61=(AND (|has| |#2| (|DifferentialSpace|)) #9#) ELT) #62=(#63=($ $) NIL #61# ELT) #64=(($ $ #65=(|List| #66=(|Symbol|)) (|List| #15#)) NIL #67=(AND (|has| |#2| (|PartialDifferentialSpace| #66#)) #9#) ELT) #68=(($ $ #66# #15#) NIL #67# ELT) #69=(($ $ #65#) NIL #67# ELT) #70=(($ $ #66#) NIL #67# ELT) #71=(($ $ #50#) NIL #9# ELT) #72=(($ $ #50# #15#) NIL #9# ELT)) (|count| ((#15# |#2| $) NIL #4# ELT) ((#15# #53# $) NIL T ELT)) (|copy| (#63# NIL T ELT)) (|coerce| ((#40# $) 9 T ELT) (($ #10#) NIL (OR #23# #9#) ELT) (($ #25#) NIL #26# ELT) (($ |#2|) 12 #24# ELT) ((#73=(|OutputForm|) $) NIL (|has| |#2| (|CoercibleTo| #73#)) ELT)) (|characteristic| (#14# NIL #9# CONST)) (|before?| #1#) (|any?| (#55# NIL T ELT)) (|annihilate?| (#2# NIL #9# ELT)) (|Zero| (#19# 37 #6# CONST)) (|One| (#19# 41 #9# CONST)) (D #59# #62# #64# #68# #69# #70# #71# #72#) (>= #74=(#2# NIL #46# ELT)) (> #74#) (= (#2# 28 #4# ELT)) (<= #74#) (< (#2# 75 #46# ELT)) (/ (#54# NIL #58# ELT)) (- (#12# NIL #75=(|has| |#2| (|AbelianGroup|)) ELT) (#63# NIL #75# ELT)) (+ (#12# 35 #76=(|has| |#2| (|AbelianSemiGroup|)) ELT)) (** (#60# NIL #9# ELT) (($ $ #8#) NIL #9# ELT)) (* (#12# 47 #9# ELT) (#54# 45 #77=(|has| |#2| (|Monoid|)) ELT) (($ |#2| $) 46 #77# ELT) (($ #10# $) NIL #75# ELT) (($ #15# $) NIL #6# ELT) (($ #8# $) NIL #76# ELT)) (|#| ((#15# $) NIL T ELT))) (((|DirectProduct| |#1| |#2|) (|DirectProductCategory| |#1| |#2|) (|NonNegativeInteger|) (|Type|)) (T |DirectProduct|)) NIL ((|scan| ((#1=(|DirectProduct| |#1| |#3|) #2=(|Mapping| |#3| |#2| |#3|) #3=(|DirectProduct| |#1| |#2|) |#3|) 21 T ELT)) (|reduce| ((|#3| #2# #3# |#3|) 23 T ELT)) (|map| ((#1# (|Mapping| |#3| |#2|) #3#) 18 T ELT))) @@ -639,7 +639,7 @@ NIL ((** (($ $ #1=(|PositiveInteger|)) NIL T ELT) (($ $ #2=(|NonNegativeInteger|)) NIL T ELT) (($ $ #3=(|Integer|)) 18 T ELT)) (* (($ #1# $) NIL T ELT) (($ #2# $) NIL T ELT) (($ #3# $) NIL T ELT) (($ $ $) NIL T ELT) (($ #4=(|Fraction| #3#) $) 25 T ELT) (($ $ #4#) NIL T ELT))) (((|DivisionRing&| |#1|) (CATEGORY |package| (SIGNATURE ** (|#1| |#1| #1=(|Integer|))) (SIGNATURE * (|#1| |#1| #2=(|Fraction| #1#))) (SIGNATURE * (|#1| #2# |#1|)) (SIGNATURE ** (|#1| |#1| #3=(|NonNegativeInteger|))) (SIGNATURE * (|#1| |#1| |#1|)) (SIGNATURE ** (|#1| |#1| #4=(|PositiveInteger|))) (SIGNATURE * (|#1| #1# |#1|)) (SIGNATURE * (|#1| #3# |#1|)) (SIGNATURE * (|#1| #4# |#1|))) (|DivisionRing|)) (T |DivisionRing&|)) NIL -((~= (#1=((|Boolean|) $ $) 7 T ELT)) (|zero?| ((#2=(|Boolean|) $) 22 T ELT)) (|subtractIfCan| (((|Union| $ "failed") $ $) 26 T ELT)) (|sample| (#3=($) 23 T CONST)) (|recip| (((|Union| $ "failed") $) 42 T ELT)) (|opposite?| ((#2# $ $) 20 T ELT)) (|one?| (((|Boolean|) $) 44 T ELT)) (|latex| (((|String|) $) 11 T ELT)) (|inv| (($ $) 55 T ELT)) (|hash| (((|SingleInteger|) $) 12 T ELT)) (|coerce| (((|OutputForm|) $) 13 T ELT) (($ (|Integer|)) 41 T ELT) (($ #4=(|Fraction| (|Integer|))) 59 T ELT)) (|characteristic| (((|NonNegativeInteger|)) 40 T CONST)) (|before?| (#1# 6 T ELT)) (|annihilate?| (((|Boolean|) $ $) 33 T ELT)) (|Zero| (#3# 24 T CONST)) (|One| (($) 45 T CONST)) (= (#1# 8 T ELT)) (- (($ $) 29 T ELT) (($ $ $) 28 T ELT)) (+ (($ $ $) 18 T ELT)) (** (($ $ (|PositiveInteger|)) 35 T ELT) (($ $ (|NonNegativeInteger|)) 43 T ELT) (($ $ (|Integer|)) 56 T ELT)) (* (($ (|PositiveInteger|) $) 17 T ELT) (($ (|NonNegativeInteger|) $) 21 T ELT) (($ (|Integer|) . #5=($)) 30 T ELT) (($ $ $) 34 T ELT) (($ #4# . #5#) 58 T ELT) (($ $ #4#) 57 T ELT))) +((~= (#1=((|Boolean|) $ $) 7 T ELT)) (|zero?| ((#2=(|Boolean|) $) 22 T ELT)) (|subtractIfCan| (((|Maybe| $) $ $) 26 T ELT)) (|sample| (#3=($) 23 T CONST)) (|recip| (((|Union| $ "failed") $) 43 T ELT)) (|opposite?| ((#2# $ $) 20 T ELT)) (|one?| (((|Boolean|) $) 45 T ELT)) (|latex| (((|String|) $) 11 T ELT)) (|inv| (($ $) 56 T ELT)) (|hash| (((|SingleInteger|) $) 12 T ELT)) (|coerce| (((|OutputForm|) $) 13 T ELT) (($ (|Integer|)) 42 T ELT) (($ #4=(|Fraction| (|Integer|))) 60 T ELT)) (|characteristic| (((|NonNegativeInteger|)) 41 T CONST)) (|before?| (#1# 6 T ELT)) (|annihilate?| (((|Boolean|) $ $) 34 T ELT)) (|Zero| (#3# 24 T CONST)) (|One| (($) 46 T CONST)) (= (#1# 8 T ELT)) (- (($ $) 30 T ELT) (($ $ $) 29 T ELT)) (+ (($ $ $) 18 T ELT)) (** (($ $ (|PositiveInteger|)) 36 T ELT) (($ $ (|NonNegativeInteger|)) 44 T ELT) (($ $ (|Integer|)) 57 T ELT)) (* (($ (|PositiveInteger|) $) 17 T ELT) (($ (|NonNegativeInteger|) $) 21 T ELT) (($ (|Integer|) . #5=($)) 31 T ELT) (($ $ $) 35 T ELT) (($ #4# . #5#) 59 T ELT) (($ $ #4#) 58 T ELT))) (((|DivisionRing|) (|Category|)) (T |DivisionRing|)) ((** (*1 *1 *1 *2) (AND (|ofCategory| *1 (|DivisionRing|)) (|isDomain| *2 (|Integer|)))) (|inv| (*1 *1 *1) (|ofCategory| *1 (|DivisionRing|)))) (|Join| (|EntireRing|) (|Algebra| (|Fraction| #1=(|Integer|))) (CATEGORY |domain| (SIGNATURE ** ($ $ #1#)) (SIGNATURE |inv| ($ $)))) @@ -655,12 +655,12 @@ NIL ((|shanksDiscLogAlgorithm| (((|Union| #1=(|NonNegativeInteger|) "failed") |#1| |#1| #1#) 40 T ELT))) (((|DiscreteLogarithmPackage| |#1|) (CATEGORY |package| (SIGNATURE |shanksDiscLogAlgorithm| ((|Union| #1=(|NonNegativeInteger|) "failed") |#1| |#1| #1#))) (|Join| (|Monoid|) (|Finite|) (CATEGORY |package| (SIGNATURE ** (|#1| |#1| (|Integer|)))))) (T |DiscreteLogarithmPackage|)) ((|shanksDiscLogAlgorithm| (*1 *2 *3 *3 *2) (|partial| AND (|isDomain| *2 (|NonNegativeInteger|)) (|ofCategory| *3 (|Join| (|Monoid|) (|Finite|) (CATEGORY |package| (SIGNATURE ** (*3 *3 (|Integer|)))))) (|isDomain| *1 (|DiscreteLogarithmPackage| *3))))) -((~= (#1=((|Boolean|) $ $) 7 T ELT)) (|zero?| ((#2=(|Boolean|) $) 22 T ELT)) (|subtractIfCan| (((|Union| $ "failed") $ $) 26 T ELT)) (|sample| (#3=($) 23 T CONST)) (|opposite?| ((#2# $ $) 20 T ELT)) (|latex| (((|String|) $) 11 T ELT)) (|hash| (((|SingleInteger|) $) 12 T ELT)) (|differentiate| (($ . #4=($)) 60 (|has| |#1| . #5=((|DifferentialSpace|))) ELT) (#6=($ $ (|NonNegativeInteger|)) 58 (|has| |#1| . #5#) ELT) (($ $ #7=(|Symbol|)) 56 (|has| |#1| . #8=((|PartialDifferentialSpace| #7#))) ELT) (($ $ (|List| #7#)) 54 (|has| |#1| . #8#) ELT) (($ $ #7# . #9=(#10=(|NonNegativeInteger|))) 53 (|has| |#1| . #8#) ELT) (($ $ (|List| #7#) . #11=((|List| #10#))) 52 (|has| |#1| . #8#) ELT) (($ $ (|Mapping| |#1| |#1|) . #12=((|NonNegativeInteger|))) 46 T ELT) (($ $ (|Mapping| |#1| |#1|)) 45 T ELT)) (|coerce| (((|OutputForm|) $) 13 T ELT)) (|before?| (#1# 6 T ELT)) (|Zero| (#3# 24 T CONST)) (D (($ . #4#) 59 (|has| |#1| . #5#) ELT) (#6# 57 (|has| |#1| . #5#) ELT) (($ $ #7#) 55 (|has| |#1| . #8#) ELT) (($ $ (|List| #7#)) 51 (|has| |#1| . #8#) ELT) (($ $ #7# . #9#) 50 (|has| |#1| . #8#) ELT) (($ $ (|List| #7#) . #11#) 49 (|has| |#1| . #8#) ELT) (($ $ (|Mapping| |#1| |#1|) . #12#) 48 T ELT) (($ $ (|Mapping| |#1| |#1|)) 47 T ELT)) (= (#1# 8 T ELT)) (- (($ $) 29 T ELT) (($ $ $) 28 T ELT)) (+ (($ $ $) 18 T ELT)) (* (($ (|PositiveInteger|) $) 17 T ELT) (($ (|NonNegativeInteger|) $) 21 T ELT) (($ (|Integer|) . #13=($)) 30 T ELT) (($ |#1| . #13#) 33 T ELT) (($ $ |#1|) 37 T ELT))) +((~= (#1=((|Boolean|) $ $) 7 T ELT)) (|zero?| ((#2=(|Boolean|) $) 22 T ELT)) (|subtractIfCan| (((|Maybe| $) $ $) 26 T ELT)) (|sample| (#3=($) 23 T CONST)) (|opposite?| ((#2# $ $) 20 T ELT)) (|latex| (((|String|) $) 11 T ELT)) (|hash| (((|SingleInteger|) $) 12 T ELT)) (|differentiate| (($ . #4=($)) 61 (|has| |#1| . #5=((|DifferentialSpace|))) ELT) (#6=($ $ (|NonNegativeInteger|)) 59 (|has| |#1| . #5#) ELT) (($ $ #7=(|Symbol|)) 57 (|has| |#1| . #8=((|PartialDifferentialSpace| #7#))) ELT) (($ $ (|List| #7#)) 55 (|has| |#1| . #8#) ELT) (($ $ #7# . #9=(#10=(|NonNegativeInteger|))) 54 (|has| |#1| . #8#) ELT) (($ $ (|List| #7#) . #11=((|List| #10#))) 53 (|has| |#1| . #8#) ELT) (($ $ (|Mapping| |#1| |#1|) . #12=((|NonNegativeInteger|))) 47 T ELT) (($ $ (|Mapping| |#1| |#1|)) 46 T ELT)) (|coerce| (((|OutputForm|) $) 13 T ELT)) (|before?| (#1# 6 T ELT)) (|Zero| (#3# 24 T CONST)) (D (($ . #4#) 60 (|has| |#1| . #5#) ELT) (#6# 58 (|has| |#1| . #5#) ELT) (($ $ #7#) 56 (|has| |#1| . #8#) ELT) (($ $ (|List| #7#)) 52 (|has| |#1| . #8#) ELT) (($ $ #7# . #9#) 51 (|has| |#1| . #8#) ELT) (($ $ (|List| #7#) . #11#) 50 (|has| |#1| . #8#) ELT) (($ $ (|Mapping| |#1| |#1|) . #12#) 49 T ELT) (($ $ (|Mapping| |#1| |#1|)) 48 T ELT)) (= (#1# 8 T ELT)) (- (($ $) 30 T ELT) (($ $ $) 29 T ELT)) (+ (($ $ $) 18 T ELT)) (* (($ (|PositiveInteger|) $) 17 T ELT) (($ (|NonNegativeInteger|) $) 21 T ELT) (($ (|Integer|) . #13=($)) 31 T ELT) (($ |#1| . #13#) 34 T ELT) (($ $ |#1|) 38 T ELT))) (((|DifferentialModuleExtension| |#1|) (|Category|) (|Ring|)) (T |DifferentialModuleExtension|)) NIL (|Join| (|BiModule| |t#1| |t#1|) (|DifferentialSpaceExtension| |t#1|) (CATEGORY |package| (IF (|has| |t#1| (|DifferentialSpace|)) (ATTRIBUTE (|DifferentialModule| |t#1|)) |%noBranch|) (IF (|has| |t#1| (|PartialDifferentialSpace| (|Symbol|))) (ATTRIBUTE (|PartialDifferentialModule| |t#1| (|Symbol|))) |%noBranch|))) (((|AbelianGroup|) . T) ((|AbelianMonoid|) . T) ((|AbelianSemiGroup|) . T) ((|BasicType|) . T) ((|BiModule| |#1| |#1|) . T) ((|CancellationAbelianMonoid|) . T) ((|CoercibleTo| (|OutputForm|)) . T) ((|DifferentialDomain| $) |has| |#1| (|DifferentialSpace|)) ((|DifferentialModule| |#1|) |has| |#1| (|DifferentialSpace|)) ((|DifferentialSpace|) |has| |#1| (|DifferentialSpace|)) ((|DifferentialSpaceExtension| |#1|) . T) ((|Join|) . T) ((|LeftLinearSet| (|Integer|)) . T) ((|LeftLinearSet| |#1|) . T) ((|LeftModule| |#1|) . T) ((|LinearSet| |#1|) OR (AND (|has| |#1| (|CommutativeRing|)) (|has| |#1| (|PartialDifferentialSpace| (|Symbol|)))) (AND (|has| |#1| (|CommutativeRing|)) (|has| |#1| (|DifferentialSpace|)))) ((|Module| |#1|) OR (AND (|has| |#1| (|CommutativeRing|)) (|has| |#1| (|PartialDifferentialSpace| (|Symbol|)))) (AND (|has| |#1| (|CommutativeRing|)) (|has| |#1| (|DifferentialSpace|)))) ((|PartialDifferentialDomain| $ #1=(|Symbol|)) |has| |#1| (|PartialDifferentialSpace| (|Symbol|))) ((|PartialDifferentialModule| |#1| (|Symbol|)) |has| |#1| (|PartialDifferentialSpace| (|Symbol|))) ((|PartialDifferentialSpace| #1#) |has| |#1| (|PartialDifferentialSpace| (|Symbol|))) ((|RightLinearSet| |#1|) . T) ((|RightModule| |#1|) . T) ((|SetCategory|) . T) ((|Type|) . T)) -((~= #1=(#2=(#3=(|Boolean|) $ $) NIL T ELT)) (|zero?| #4=(#5=(#3# $) NIL T ELT)) (|variables| ((#6=(|List| #7=(|OrderedVariableList| |#1|)) $) NIL T ELT)) (|univariate| ((#8=(|SparseUnivariatePolynomial| $) $ #7#) NIL T ELT) ((#9=(|SparseUnivariatePolynomial| |#2|) $) NIL T ELT)) (|unitNormal| (((|Record| (|:| |unit| $) (|:| |canonical| $) (|:| |associate| $)) $) NIL #10=(|has| |#2| (|IntegralDomain|)) ELT)) (|unitCanonical| #11=(#12=($ $) NIL #10# ELT)) (|unit?| (#5# NIL #10# ELT)) (|totalDegree| #13=((#14=(|NonNegativeInteger|) $) NIL T ELT) ((#14# $ #6#) NIL T ELT)) (|subtractIfCan| (#15=(#16=(|Union| $ #17="failed") $ $) NIL T ELT)) (|squareFreePolynomial| #18=(((|Factored| #8#) #8#) NIL #19=(|has| |#2| (|PolynomialFactorizationExplicit|)) ELT)) (|squareFreePart| #20=(#12# NIL #21=(|has| |#2| (|GcdDomain|)) ELT)) (|squareFree| (#22=((|Factored| $) $) NIL #21# ELT)) (|solveLinearPolynomialEquation| (((|Union| #23=(|List| #8#) #17#) #23# #8#) NIL #19# ELT)) (|sample| #24=(($) 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(|mapExponents| (($ (|Mapping| #50# #50#) $) NIL T ELT)) (|map| (($ (|Mapping| |#2| |#2|) $) NIL T ELT)) (|mainVariable| #31#) (|leftReducedSystem| ((#37# . #65=(#43#)) NIL #40# ELT) ((#41# . #66=(#43# $)) NIL #40# ELT) ((#44# . #66#) NIL T ELT) ((#45# . #65#) NIL T ELT)) (|leadingMonomial| #36#) (|leadingCoefficient| #32#) (|lcm| #67=(($ #49#) NIL #21# ELT) #68=(#69=($ $ $) NIL #21# ELT)) (|latex| (((|String|) $) NIL T ELT)) (|isTimes| #70=(((|Union| #49# #17#) $) NIL T ELT)) (|isPlus| #70#) (|isExpt| (((|Union| (|Record| (|:| |var| #7#) (|:| |exponent| #14#)) #17#) $) NIL T ELT)) (|hash| (((|SingleInteger|) $) NIL T ELT)) (|ground?| #4#) (|ground| #32#) (|gcdPolynomial| ((#8# #8# #8#) NIL #21# ELT)) (|gcd| #67# #68#) (|factorSquareFreePolynomial| #18#) (|factorPolynomial| #18#) (|factor| (#22# NIL #19# ELT)) (|exquo| ((#16# $ |#2|) NIL #10# ELT) (#15# NIL #10# ELT)) (|eval| (($ $ (|List| #71=(|Equation| $))) NIL T ELT) (($ $ #71#) NIL T ELT) (($ $ $ $) NIL T ELT) (($ $ #49# #49#) NIL T ELT) (($ $ #7# |#2|) NIL T ELT) (($ $ #6# #72=(|List| |#2|)) NIL T ELT) (($ $ #7# $) NIL T ELT) (($ $ #6# #49#) NIL T ELT)) (|discriminant| (#47# NIL #35# ELT)) (|differentiate| #60# #59# #73=(($ $ #6#) NIL T ELT) #74=(#47# NIL T ELT)) (|degree| #62# #63# #64#) (|convert| ((#54# . #75=($)) NIL (AND (|has| #7# #76=(|ConvertibleTo| #54#)) (|has| |#2| #76#)) ELT) ((#57# . #75#) NIL (AND (|has| #7# #77=(|ConvertibleTo| #57#)) (|has| |#2| #77#)) ELT) ((#78=(|InputForm|) . #75#) NIL (AND (|has| #7# #79=(|ConvertibleTo| #78#)) (|has| |#2| #79#)) ELT)) (|content| (#33# NIL #21# ELT) #46#) (|conditionP| (((|Union| #43# #17#) #39#) NIL #80=(AND (|has| $ #81=(|CharacteristicNonZero|)) #19#) ELT)) (|coerce| (((|OutputForm|) $) NIL T ELT) (($ #28#) NIL T ELT) (($ |#2|) NIL T ELT) (($ #7#) NIL T ELT) (($ #27#) NIL (OR #82=(|has| |#2| (|Algebra| #27#)) #29#) ELT) #11#) (|coefficients| ((#72# $) NIL T ELT)) (|coefficient| ((|#2| $ #50#) NIL T ELT) #59# #60#) (|charthRoot| (((|Maybe| $) $) NIL (OR #80# (|has| |#2| #81#)) ELT)) (|characteristic| ((#14#) NIL T CONST)) (|binomThmExpt| (($ $ $ #14#) NIL #35# ELT)) (|before?| #1#) (|associates?| (#2# NIL #10# ELT)) (|annihilate?| #1#) (|Zero| #24#) (|One| #24#) (D #60# #59# #73# #74#) (= #1#) (/ (#83=($ $ |#2|) NIL (|has| |#2| (|Field|)) ELT)) (- #36# #84=(#69# NIL T ELT)) (+ #84#) (** (($ $ #85=(|PositiveInteger|)) NIL T ELT) (($ $ #14#) NIL T ELT)) (* (($ #85# $) NIL T ELT) (($ #14# $) NIL T ELT) (($ #28# . #86=($)) NIL T ELT) #84# (($ $ #27#) NIL #82# ELT) (($ #27# . #86#) NIL #82# ELT) (($ |#2| . #86#) NIL T ELT) (#83# NIL T ELT))) +((~= #1=(#2=(#3=(|Boolean|) $ $) NIL T ELT)) (|zero?| #4=(#5=(#3# $) NIL T ELT)) (|variables| ((#6=(|List| #7=(|OrderedVariableList| |#1|)) $) NIL T ELT)) (|univariate| ((#8=(|SparseUnivariatePolynomial| $) $ #7#) NIL T ELT) ((#9=(|SparseUnivariatePolynomial| |#2|) $) NIL T ELT)) (|unitNormal| (((|Record| (|:| |unit| $) (|:| |canonical| $) (|:| |associate| $)) $) NIL #10=(|has| |#2| 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. #33#) NIL #29# ELT) ((#7# . #33#) NIL T ELT)) (|resultant| (($ $ $ #7#) NIL #34=(|has| |#2| (|CommutativeRing|)) ELT)) (|reorder| (($ $ (|List| #27#)) NIL T ELT)) (|reductum| #35=(#12# NIL T ELT)) (|reducedSystem| ((#36=(|Matrix| #27#) . #37=(#38=(|Matrix| $))) NIL #39=(|has| |#2| (|LinearlyExplicitRingOver| #27#)) ELT) ((#40=(|Record| (|:| |mat| #36#) (|:| |vec| (|Vector| #27#))) . #41=(#38# #42=(|Vector| $))) NIL #39# ELT) ((#43=(|Record| (|:| |mat| #44=(|Matrix| |#2|)) (|:| |vec| (|Vector| |#2|))) . #41#) NIL T ELT) ((#44# . #37#) NIL T ELT)) (|recip| ((#45=(|Union| $ #22#) $) NIL T ELT)) (|primitivePart| #18# #46=(#47=($ $ #7#) NIL #19# ELT)) (|primitiveMonomials| #48=((#49=(|List| $) $) NIL T ELT)) (|prime?| (#5# NIL #17# ELT)) (|pomopo!| (($ $ |#2| #50=(|DirectProduct| (|#| |#1|) #14#) $) NIL T ELT)) (|patternMatch| ((#51=(|PatternMatchResult| #52=(|Float|) . #53=($)) $ #54=(|Pattern| #52#) #51#) NIL (AND (|has| #7# #55=(|PatternMatchable| #52#)) (|has| |#2| #55#)) ELT) ((#56=(|PatternMatchResult| #27# . #53#) $ #57=(|Pattern| #27#) #56#) NIL (AND (|has| #7# #58=(|PatternMatchable| #27#)) (|has| |#2| #58#)) ELT)) (|opposite?| #1#) (|one?| #4#) (|numberOfMonomials| #13#) (|multivariate| (($ #9# #7#) NIL T ELT) (($ #8# #7#) NIL T ELT)) (|monomials| #48#) (|monomial?| #4#) (|monomial| (($ |#2| #50#) NIL T ELT) #59=(($ $ #7# #14#) NIL T ELT) #60=(($ $ #6# #61=(|List| #14#)) NIL T ELT)) (|monicDivide| (((|Record| (|:| |quotient| $) (|:| |remainder| $)) $ $ #7#) NIL T ELT)) (|minimumDegree| #62=((#50# $) NIL T ELT) #63=((#14# $ #7#) NIL T ELT) #64=((#61# $ #6#) NIL T ELT)) (|mapExponents| (($ (|Mapping| #50# #50#) $) NIL T ELT)) (|map| (($ (|Mapping| |#2| |#2|) $) NIL T ELT)) (|mainVariable| #30#) (|leftReducedSystem| ((#36# . #65=(#42#)) NIL #39# ELT) ((#40# . #66=(#42# $)) NIL #39# ELT) ((#43# . #66#) NIL T ELT) ((#44# . #65#) NIL T ELT)) (|leadingMonomial| #35#) (|leadingCoefficient| #31#) (|lcm| #67=(($ #49#) NIL #19# ELT) #68=(#69=($ $ $) NIL #19# ELT)) (|latex| (((|String|) $) NIL T ELT)) (|isTimes| #70=(((|Union| #49# #22#) $) NIL T ELT)) (|isPlus| #70#) (|isExpt| (((|Union| (|Record| (|:| |var| #7#) (|:| |exponent| #14#)) #22#) $) NIL T ELT)) (|hash| (((|SingleInteger|) $) NIL T ELT)) (|ground?| #4#) (|ground| #31#) (|gcdPolynomial| ((#8# #8# #8#) NIL #19# ELT)) (|gcd| #67# #68#) (|factorSquareFreePolynomial| #16#) (|factorPolynomial| #16#) (|factor| (#20# NIL #17# ELT)) (|exquo| ((#45# $ |#2|) NIL #10# ELT) ((#45# $ $) NIL #10# ELT)) (|eval| (($ $ (|List| #71=(|Equation| $))) NIL T ELT) (($ $ #71#) NIL T ELT) (($ $ $ $) NIL T ELT) (($ $ #49# #49#) NIL T ELT) (($ $ #7# |#2|) NIL T ELT) (($ $ #6# #72=(|List| |#2|)) NIL T ELT) (($ $ #7# $) NIL T ELT) (($ $ #6# #49#) NIL T ELT)) (|discriminant| (#47# NIL #34# ELT)) (|differentiate| #60# #59# #73=(($ $ #6#) NIL T ELT) #74=(#47# NIL T ELT)) (|degree| #62# #63# #64#) (|convert| ((#54# . #75=($)) NIL (AND (|has| #7# #76=(|ConvertibleTo| #54#)) (|has| |#2| #76#)) ELT) ((#57# . #75#) NIL (AND (|has| #7# #77=(|ConvertibleTo| #57#)) (|has| |#2| #77#)) ELT) ((#78=(|InputForm|) . #75#) NIL (AND (|has| #7# #79=(|ConvertibleTo| #78#)) (|has| |#2| #79#)) ELT)) (|content| (#32# NIL #19# ELT) #46#) (|conditionP| (((|Union| #42# #22#) #38#) NIL #80=(AND (|has| $ #81=(|CharacteristicNonZero|)) #17#) ELT)) (|coerce| (((|OutputForm|) $) NIL T ELT) (($ #27#) NIL T ELT) (($ |#2|) NIL T ELT) (($ #7#) NIL T ELT) (($ #26#) NIL (OR #82=(|has| |#2| (|Algebra| #26#)) #28#) ELT) #11#) (|coefficients| ((#72# $) NIL T ELT)) (|coefficient| ((|#2| $ #50#) NIL T ELT) #59# #60#) (|charthRoot| ((#15# $) NIL (OR #80# (|has| |#2| #81#)) ELT)) (|characteristic| ((#14#) NIL T CONST)) (|binomThmExpt| (($ $ $ #14#) NIL #34# ELT)) (|before?| #1#) (|associates?| (#2# NIL #10# ELT)) (|annihilate?| #1#) (|Zero| #23#) (|One| #23#) (D #60# #59# #73# #74#) (= #1#) (/ (#83=($ $ |#2|) NIL (|has| |#2| (|Field|)) ELT)) (- #35# #84=(#69# NIL T ELT)) (+ #84#) (** (($ $ #85=(|PositiveInteger|)) NIL T ELT) (($ $ #14#) NIL T ELT)) (* (($ #85# $) NIL T ELT) (($ #14# $) NIL T ELT) (($ #27# . #86=($)) NIL T ELT) #84# (($ $ #26#) NIL #82# ELT) (($ #26# . #86#) NIL #82# ELT) (($ |#2| . #86#) NIL T ELT) (#83# NIL T ELT))) (((|DistributedMultivariatePolynomial| |#1| |#2|) (|Join| (|PolynomialCategory| |#2| (|DirectProduct| (|#| |#1|) (|NonNegativeInteger|)) (|OrderedVariableList| |#1|)) (CATEGORY |domain| (SIGNATURE |reorder| ($ $ (|List| (|Integer|)))))) (|List| (|Symbol|)) (|Ring|)) (T |DistributedMultivariatePolynomial|)) ((|reorder| (*1 *1 *1 *2) (AND (|isDomain| *2 (|List| (|Integer|))) (|isDomain| *1 (|DistributedMultivariatePolynomial| *3 *4)) (|ofType| *3 (|List| (|Symbol|))) (|ofCategory| *4 (|Ring|))))) ((~= #1=(#2=((|Boolean|) $ $) NIL T ELT)) (|showSummary| (((|Void|) $) 17 T ELT)) (|reify| ((#3=(|ConstructorCall| #4=(|DomainConstructor|)) $) 11 T ELT)) (|reflect| (($ #3#) 12 T ELT)) (|latex| (((|String|) $) NIL T ELT)) (|hash| (((|SingleInteger|) $) NIL T ELT)) (|constructor| ((#4# $) 7 T ELT)) (|coerce| (((|OutputForm|) $) 9 T ELT)) (|before?| #1#) (= (#2# 15 T ELT))) @@ -672,16 +672,16 @@ NIL ((~= #1=(#2=((|Boolean|) $ $) NIL T ELT)) (|latex| (((|String|) $) NIL T ELT)) (|hash| (((|SingleInteger|) $) NIL T ELT)) (|elt| (((|Syntax|) $ #3=(|NonNegativeInteger|)) 14 T ELT)) (|coerce| (((|OutputForm|) $) 20 T ELT)) (|before?| #1#) (= (#2# 17 T ELT)) (|#| ((#3# $) 11 T ELT))) (((|DomainTemplate|) (|Join| (|SetCategory|) (|Eltable| #1=(|NonNegativeInteger|) (|Syntax|)) (CATEGORY |domain| (SIGNATURE |#| (#1# $))))) (T |DomainTemplate|)) ((|#| (*1 *2 *1) (AND (|isDomain| *2 (|NonNegativeInteger|)) (|isDomain| *1 (|DomainTemplate|))))) -((~= #1=(#2=(#3=(|Boolean|) $ $) NIL T ELT)) (|zero?| #4=(#5=(#3# $) NIL T ELT)) (|unitVector| (#6=($ #7=(|PositiveInteger|)) NIL #8=(|has| |#4| (|Ring|)) ELT)) (|swap!| (((|Void|) $ #9=(|Integer|) #9#) NIL #10=(|has| $ (|ShallowlyMutableAggregate| |#4|)) ELT)) (|sup| (#11=($ $ $) NIL #12=(|has| |#4| (|OrderedAbelianMonoidSup|)) ELT)) 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(|isDomain| *2 (|Boolean|)))) (|leader| (*1 *2 *1) (AND (|ofCategory| *1 (|DifferentialPolynomialCategory| *3 *4 *2 *5)) (|ofCategory| *3 (|Ring|)) (|ofCategory| *4 (|OrderedSet|)) (|ofCategory| *5 (|OrderedAbelianMonoidSup|)) (|ofCategory| *2 (|DifferentialVariableCategory| *4)))) (|initial| (*1 *1 *1) (AND (|ofCategory| *1 (|DifferentialPolynomialCategory| *2 *3 *4 *5)) (|ofCategory| *2 (|Ring|)) (|ofCategory| *3 (|OrderedSet|)) (|ofCategory| *4 (|DifferentialVariableCategory| *3)) (|ofCategory| *5 (|OrderedAbelianMonoidSup|)))) (|separant| (*1 *1 *1) (AND (|ofCategory| *1 (|DifferentialPolynomialCategory| *2 *3 *4 *5)) (|ofCategory| *2 (|Ring|)) (|ofCategory| *3 (|OrderedSet|)) (|ofCategory| *4 (|DifferentialVariableCategory| *3)) (|ofCategory| *5 (|OrderedAbelianMonoidSup|)))) (|makeVariable| (*1 *2 *1) (AND (|ofCategory| *3 (|DifferentialRing|)) (|ofCategory| *3 (|Ring|)) (|ofCategory| *4 (|OrderedSet|)) (|ofCategory| *5 (|DifferentialVariableCategory| *4)) (|ofCategory| *6 (|OrderedAbelianMonoidSup|)) (|isDomain| *2 (|Mapping| *1 (|NonNegativeInteger|))) (|ofCategory| *1 (|DifferentialPolynomialCategory| *3 *4 *5 *6))))) (|Join| (|PolynomialCategory| |t#1| |t#4| |t#3|) (|DifferentialExtension| |t#1|) (|RetractableTo| |t#2|) (CATEGORY |domain| (SIGNATURE |makeVariable| ((|Mapping| $ (|NonNegativeInteger|)) |t#2|)) (SIGNATURE |differentialVariables| ((|List| |t#2|) $)) (SIGNATURE |order| ((|NonNegativeInteger|) $ |t#2|)) (SIGNATURE |order| ((|NonNegativeInteger|) $)) (SIGNATURE |degree| ((|NonNegativeInteger|) $ |t#2|)) (SIGNATURE |weights| ((|List| (|NonNegativeInteger|)) $)) (SIGNATURE |weight| ((|NonNegativeInteger|) $)) (SIGNATURE |weights| ((|List| (|NonNegativeInteger|)) $ |t#2|)) (SIGNATURE |weight| ((|NonNegativeInteger|) $ |t#2|)) (SIGNATURE |isobaric?| ((|Boolean|) $)) (SIGNATURE |leader| (|t#3| $)) (SIGNATURE |initial| ($ $)) (SIGNATURE |separant| ($ $)) (IF (|has| |t#1| (|DifferentialRing|)) (PROGN (ATTRIBUTE (|InnerEvalable| |t#2| |t#1|)) (ATTRIBUTE (|InnerEvalable| |t#2| $)) (ATTRIBUTE (|Evalable| $)) (SIGNATURE |makeVariable| ((|Mapping| $ (|NonNegativeInteger|)) $))) |%noBranch|))) @@ -726,7 +726,7 @@ NIL ((|differentiate| (*1 *1 *1 *2) (AND (|isDomain| *2 (|Mapping| *3 *3)) (|ofCategory| *1 (|DifferentialSpaceExtension| *3)) (|ofCategory| *3 (|Type|)))) (|differentiate| (*1 *1 *1 *2 *3) (AND (|isDomain| *2 (|Mapping| *4 *4)) (|isDomain| *3 (|NonNegativeInteger|)) (|ofCategory| *1 (|DifferentialSpaceExtension| *4)) (|ofCategory| *4 (|Type|)))) (D (*1 *1 *1 *2) (AND (|isDomain| *2 (|Mapping| *3 *3)) (|ofCategory| *1 (|DifferentialSpaceExtension| *3)) (|ofCategory| *3 (|Type|)))) (D (*1 *1 *1 *2 *3) (AND (|isDomain| *2 (|Mapping| *4 *4)) (|isDomain| *3 (|NonNegativeInteger|)) (|ofCategory| *1 (|DifferentialSpaceExtension| *4)) (|ofCategory| *4 (|Type|))))) (|Join| (|Type|) (CATEGORY |domain| (SIGNATURE |differentiate| ($ $ (|Mapping| |t#1| |t#1|))) (SIGNATURE |differentiate| ($ $ (|Mapping| |t#1| |t#1|) (|NonNegativeInteger|))) (SIGNATURE D ($ $ (|Mapping| |t#1| |t#1|))) (SIGNATURE D ($ $ (|Mapping| |t#1| |t#1|) (|NonNegativeInteger|))) (IF (|has| |t#1| (|DifferentialSpace|)) (ATTRIBUTE (|DifferentialSpace|)) |%noBranch|) (IF (|has| |t#1| (|PartialDifferentialSpace| (|Symbol|))) (ATTRIBUTE (|PartialDifferentialSpace| (|Symbol|))) |%noBranch|))) (((|DifferentialDomain| $) |has| |#1| (|DifferentialSpace|)) ((|DifferentialSpace|) |has| |#1| (|DifferentialSpace|)) ((|Join|) . T) ((|PartialDifferentialDomain| $ #1=(|Symbol|)) |has| |#1| (|PartialDifferentialSpace| (|Symbol|))) ((|PartialDifferentialSpace| #1#) |has| |#1| (|PartialDifferentialSpace| (|Symbol|))) ((|Type|) . T)) -((~= #1=(#2=(#3=(|Boolean|) $ $) NIL T ELT)) (|zero?| #4=(#5=(#3# $) NIL T ELT)) (|weights| ((#6=(|List| #7=(|NonNegativeInteger|)) $) NIL T ELT) ((#6# $ |#2|) NIL T ELT)) (|weight| #8=(#9=(#7# $) NIL T ELT) #10=((#7# $ |#2|) NIL T ELT)) (|variables| ((#11=(|List| |#3|) $) NIL T ELT)) (|univariate| ((#12=(|SparseUnivariatePolynomial| $) $ |#3|) NIL T ELT) ((#13=(|SparseUnivariatePolynomial| |#1|) $) NIL T ELT)) (|unitNormal| (((|Record| (|:| |unit| $) (|:| |canonical| $) (|:| |associate| $)) $) NIL #14=(|has| |#1| (|IntegralDomain|)) ELT)) (|unitCanonical| #15=(#16=($ $) NIL #14# ELT)) (|unit?| (#5# NIL #14# ELT)) (|totalDegree| #8# ((#7# $ #11#) NIL T ELT)) (|subtractIfCan| (#17=(#18=(|Union| $ #19="failed") $ $) NIL T ELT)) (|squareFreePolynomial| #20=(((|Factored| #12#) #12#) NIL #21=(|has| |#1| (|PolynomialFactorizationExplicit|)) ELT)) (|squareFreePart| #22=(#16# NIL #23=(|has| |#1| (|GcdDomain|)) ELT)) (|squareFree| (#24=((|Factored| $) $) NIL #23# ELT)) (|solveLinearPolynomialEquation| (((|Union| #25=(|List| #12#) #19#) #25# #12#) NIL #21# ELT)) (|separant| #26=(#16# NIL T ELT)) (|sample| #27=(($) NIL T CONST)) (|retractIfCan| (((|Union| |#1| . #28=(#19#)) . #29=($)) NIL T ELT) (((|Union| #30=(|Fraction| #31=(|Integer|)) . #28#) . #29#) NIL #32=(|has| |#1| (|RetractableTo| #30#)) ELT) (((|Union| #31# . #28#) . #29#) NIL #33=(|has| |#1| (|RetractableTo| #31#)) ELT) #34=(((|Union| |#3| . #28#) . #29#) NIL T ELT) (((|Union| |#2| . #28#) . #29#) NIL T ELT) (((|Union| #35=(|SparseMultivariatePolynomial| |#1| |#2|) . #28#) $) 23 T ELT)) (|retract| #36=(#37=(|#1| $) NIL T ELT) ((#30# . #38=($)) NIL #32# ELT) ((#31# . #38#) NIL #33# ELT) #39=((|#3| . #38#) NIL T ELT) ((|#2| . #38#) NIL T ELT) ((#35# . #38#) NIL T ELT)) (|resultant| (($ $ $ |#3|) NIL #40=(|has| |#1| (|CommutativeRing|)) ELT)) (|reductum| #26#) (|reducedSystem| ((#41=(|Matrix| #31#) . #42=(#43=(|Matrix| $))) NIL #44=(|has| |#1| (|LinearlyExplicitRingOver| #31#)) ELT) ((#45=(|Record| (|:| |mat| #41#) (|:| |vec| (|Vector| #31#))) . #46=(#43# #47=(|Vector| $))) NIL #44# ELT) ((#48=(|Record| (|:| |mat| #49=(|Matrix| |#1|)) (|:| |vec| (|Vector| |#1|))) . #46#) NIL T ELT) ((#49# . #42#) NIL T ELT)) (|recip| ((#18# $) NIL T ELT)) (|primitivePart| #22# #50=(#51=($ $ |#3|) NIL #23# ELT)) (|primitiveMonomials| #52=((#53=(|List| $) $) NIL T ELT)) (|prime?| (#5# NIL #21# ELT)) (|pomopo!| (($ $ |#1| #54=(|IndexedExponents| |#3|) $) NIL T ELT)) (|patternMatch| ((#55=(|PatternMatchResult| #56=(|Float|) . #57=($)) $ #58=(|Pattern| #56#) #55#) NIL (AND (|has| |#1| #59=(|PatternMatchable| #56#)) (|has| |#3| #59#)) ELT) ((#60=(|PatternMatchResult| #31# . #57#) $ #61=(|Pattern| #31#) #60#) NIL (AND (|has| |#1| #62=(|PatternMatchable| #31#)) (|has| |#3| #62#)) ELT)) (|order| #10# (#9# 10 T ELT)) (|opposite?| #1#) (|one?| #4#) (|numberOfMonomials| #8#) (|multivariate| (($ #13# |#3|) NIL T ELT) (($ #12# |#3|) NIL T ELT)) (|monomials| #52#) (|monomial?| #4#) (|monomial| (($ |#1| #54#) NIL T ELT) #63=(($ $ |#3| #7#) NIL T ELT) #64=(($ $ #11# #6#) NIL T ELT)) (|monicDivide| (((|Record| (|:| |quotient| $) (|:| |remainder| $)) $ $ |#3|) NIL T ELT)) (|minimumDegree| #65=((#54# $) NIL T ELT) #66=((#7# $ |#3|) NIL T ELT) #67=((#6# $ #11#) NIL T ELT)) (|mapExponents| (($ (|Mapping| #54# #54#) $) NIL T ELT)) (|map| (($ #68=(|Mapping| |#1| |#1|) $) NIL T ELT)) (|makeVariable| ((#69=(|Mapping| $ #7#) |#2|) NIL T ELT) ((#69# $) NIL #70=(|has| |#1| (|DifferentialRing|)) ELT)) (|mainVariable| #34#) (|leftReducedSystem| ((#41# . #71=(#47#)) NIL #44# ELT) ((#45# . #72=(#47# $)) NIL #44# ELT) ((#48# . #72#) NIL T ELT) ((#49# . #71#) NIL T ELT)) (|leadingMonomial| #26#) (|leadingCoefficient| #36#) (|leader| #39#) (|lcm| #73=(($ #53#) NIL #23# ELT) #74=(#75=($ $ $) NIL #23# ELT)) (|latex| (((|String|) $) NIL T ELT)) (|isobaric?| #4#) (|isTimes| #76=(((|Union| #53# #19#) $) NIL T ELT)) (|isPlus| #76#) (|isExpt| (((|Union| (|Record| (|:| |var| |#3|) (|:| |exponent| #7#)) #19#) $) NIL T ELT)) (|initial| #26#) (|hash| (((|SingleInteger|) $) NIL T ELT)) (|ground?| #4#) (|ground| #36#) (|gcdPolynomial| ((#12# #12# #12#) NIL #23# ELT)) (|gcd| #73# #74#) (|factorSquareFreePolynomial| #20#) (|factorPolynomial| #20#) (|factor| (#24# NIL #21# ELT)) (|exquo| ((#18# $ |#1|) NIL #14# ELT) (#17# NIL #14# ELT)) (|eval| (($ $ (|List| #77=(|Equation| $))) NIL T ELT) (($ $ #77#) NIL T ELT) (($ $ $ $) NIL T ELT) (($ $ #53# #53#) NIL T ELT) (($ $ |#3| |#1|) NIL T ELT) (($ $ #11# #78=(|List| |#1|)) NIL T ELT) (($ $ |#3| $) NIL T ELT) (($ $ #11# #53#) NIL T ELT) (($ $ |#2| $) NIL #70# ELT) (($ $ #79=(|List| |#2|) #53#) NIL #70# ELT) (($ $ |#2| |#1|) NIL #70# ELT) (($ $ #79# #78#) NIL #70# ELT)) (|discriminant| (#51# NIL #40# ELT)) (|differentiate| #64# #63# #80=(($ $ #11#) NIL T ELT) #81=(#51# NIL T ELT) #82=(($ $ #68#) NIL T ELT) #83=(($ $ #68# #7#) NIL T ELT) #84=(($ $ #85=(|Symbol|)) NIL #86=(|has| |#1| (|PartialDifferentialSpace| #85#)) ELT) #87=(($ $ #88=(|List| #85#)) NIL #86# ELT) #89=(($ $ #85# #7#) NIL #86# ELT) #90=(($ $ #88# #6#) NIL #86# ELT) #91=(#16# NIL #92=(|has| |#1| (|DifferentialSpace|)) ELT) #93=(#94=($ $ #7#) NIL #92# ELT)) (|differentialVariables| ((#79# $) NIL T ELT)) (|degree| #65# #66# #67# #10#) (|convert| ((#58# . #95=($)) NIL (AND (|has| |#1| #96=(|ConvertibleTo| #58#)) (|has| |#3| #96#)) ELT) ((#61# . #95#) NIL (AND (|has| |#1| #97=(|ConvertibleTo| #61#)) (|has| |#3| #97#)) ELT) ((#98=(|InputForm|) . #95#) NIL (AND (|has| |#1| #99=(|ConvertibleTo| #98#)) (|has| |#3| #99#)) ELT)) (|content| (#37# NIL #23# ELT) #50#) (|conditionP| (((|Union| #47# #19#) #43#) NIL #100=(AND (|has| $ #101=(|CharacteristicNonZero|)) #21#) ELT)) (|coerce| (((|OutputForm|) $) NIL T ELT) (($ #31#) NIL T ELT) (($ |#1|) 26 T ELT) (($ |#3|) 25 T ELT) (($ |#2|) NIL T ELT) (($ #35#) 32 T ELT) (($ #30#) NIL (OR #102=(|has| |#1| (|Algebra| #30#)) #32#) ELT) #15#) (|coefficients| ((#78# $) NIL T ELT)) (|coefficient| ((|#1| $ #54#) NIL T ELT) #63# #64#) (|charthRoot| (((|Maybe| $) $) NIL (OR #100# (|has| |#1| #101#)) ELT)) (|characteristic| ((#7#) NIL T CONST)) (|binomThmExpt| (($ $ $ #7#) NIL #40# ELT)) (|before?| #1#) (|associates?| (#2# NIL #14# ELT)) (|annihilate?| #1#) (|Zero| #27#) (|One| #27#) (D #64# #63# #80# #81# #82# #83# #84# #87# #89# #90# #91# #93#) (= #1#) (/ (#103=($ $ |#1|) NIL (|has| |#1| (|Field|)) ELT)) (- #26# #104=(#75# NIL T ELT)) (+ #104#) (** (($ $ #105=(|PositiveInteger|)) NIL T ELT) (#94# NIL T ELT)) (* (($ #105# $) NIL T ELT) (($ #7# $) NIL T ELT) (($ #31# . #106=($)) NIL T ELT) #104# (($ $ #30#) NIL #102# ELT) (($ #30# . #106#) NIL #102# ELT) (($ |#1| . #106#) NIL T ELT) (#103# NIL T ELT))) +((~= #1=(#2=(#3=(|Boolean|) $ $) NIL T ELT)) (|zero?| #4=(#5=(#3# $) NIL T ELT)) (|weights| ((#6=(|List| #7=(|NonNegativeInteger|)) $) NIL T ELT) ((#6# $ |#2|) NIL T ELT)) (|weight| #8=(#9=(#7# $) NIL T ELT) #10=((#7# $ |#2|) NIL T ELT)) (|variables| ((#11=(|List| |#3|) $) NIL T ELT)) (|univariate| ((#12=(|SparseUnivariatePolynomial| $) $ |#3|) NIL T ELT) ((#13=(|SparseUnivariatePolynomial| |#1|) $) NIL T ELT)) (|unitNormal| (((|Record| (|:| |unit| $) (|:| |canonical| $) (|:| |associate| $)) $) NIL #14=(|has| |#1| (|IntegralDomain|)) ELT)) (|unitCanonical| #15=(#16=($ $) NIL #14# ELT)) (|unit?| (#5# NIL #14# ELT)) (|totalDegree| #8# ((#7# $ #11#) NIL T ELT)) (|subtractIfCan| ((#17=(|Maybe| $) $ $) NIL T ELT)) (|squareFreePolynomial| #18=(((|Factored| #12#) #12#) NIL #19=(|has| |#1| (|PolynomialFactorizationExplicit|)) ELT)) (|squareFreePart| #20=(#16# NIL #21=(|has| |#1| (|GcdDomain|)) ELT)) (|squareFree| (#22=((|Factored| $) $) NIL #21# ELT)) (|solveLinearPolynomialEquation| (((|Union| #23=(|List| #12#) #24="failed") #23# #12#) NIL #19# ELT)) (|separant| #25=(#16# NIL T ELT)) (|sample| #26=(($) NIL T CONST)) (|retractIfCan| (((|Union| |#1| . #27=(#24#)) . #28=($)) NIL T ELT) (((|Union| #29=(|Fraction| #30=(|Integer|)) . #27#) . #28#) NIL #31=(|has| |#1| (|RetractableTo| #29#)) ELT) (((|Union| #30# . #27#) . #28#) NIL #32=(|has| |#1| (|RetractableTo| #30#)) ELT) #33=(((|Union| |#3| . #27#) . #28#) NIL T ELT) (((|Union| |#2| . #27#) . #28#) NIL T ELT) (((|Union| #34=(|SparseMultivariatePolynomial| |#1| |#2|) . #27#) $) 23 T ELT)) (|retract| #35=(#36=(|#1| $) NIL T ELT) ((#29# . #37=($)) NIL #31# ELT) ((#30# . #37#) NIL #32# ELT) #38=((|#3| . #37#) NIL T ELT) ((|#2| . #37#) NIL T ELT) ((#34# . #37#) NIL T ELT)) (|resultant| (($ $ $ |#3|) NIL #39=(|has| |#1| (|CommutativeRing|)) ELT)) (|reductum| #25#) (|reducedSystem| ((#40=(|Matrix| #30#) . #41=(#42=(|Matrix| $))) NIL #43=(|has| |#1| (|LinearlyExplicitRingOver| #30#)) ELT) ((#44=(|Record| (|:| |mat| #40#) (|:| |vec| (|Vector| #30#))) . #45=(#42# #46=(|Vector| $))) NIL #43# ELT) ((#47=(|Record| (|:| |mat| #48=(|Matrix| |#1|)) (|:| |vec| (|Vector| |#1|))) . #45#) NIL T ELT) ((#48# . #41#) NIL T ELT)) (|recip| ((#49=(|Union| $ #24#) $) NIL T ELT)) (|primitivePart| #20# #50=(#51=($ $ |#3|) NIL #21# ELT)) (|primitiveMonomials| #52=((#53=(|List| $) $) NIL T ELT)) (|prime?| (#5# NIL #19# ELT)) (|pomopo!| (($ $ |#1| #54=(|IndexedExponents| |#3|) $) NIL T ELT)) (|patternMatch| ((#55=(|PatternMatchResult| #56=(|Float|) . #57=($)) $ #58=(|Pattern| #56#) #55#) NIL (AND (|has| |#1| #59=(|PatternMatchable| #56#)) (|has| |#3| #59#)) ELT) ((#60=(|PatternMatchResult| #30# . #57#) $ #61=(|Pattern| #30#) #60#) NIL (AND (|has| |#1| #62=(|PatternMatchable| #30#)) (|has| |#3| #62#)) ELT)) (|order| #10# (#9# 10 T ELT)) (|opposite?| #1#) (|one?| #4#) (|numberOfMonomials| #8#) (|multivariate| (($ #13# |#3|) NIL T ELT) (($ #12# |#3|) NIL T ELT)) (|monomials| #52#) (|monomial?| #4#) (|monomial| (($ |#1| #54#) NIL T ELT) #63=(($ $ |#3| #7#) NIL T ELT) #64=(($ $ #11# #6#) NIL T ELT)) (|monicDivide| (((|Record| (|:| |quotient| $) (|:| |remainder| $)) $ $ |#3|) NIL T ELT)) (|minimumDegree| #65=((#54# $) NIL T ELT) #66=((#7# $ |#3|) NIL T ELT) #67=((#6# $ #11#) NIL T ELT)) (|mapExponents| (($ (|Mapping| #54# #54#) $) NIL T ELT)) (|map| (($ #68=(|Mapping| |#1| |#1|) $) NIL T ELT)) (|makeVariable| ((#69=(|Mapping| $ #7#) |#2|) NIL T ELT) ((#69# $) NIL #70=(|has| |#1| (|DifferentialRing|)) ELT)) (|mainVariable| #33#) (|leftReducedSystem| ((#40# . #71=(#46#)) NIL #43# ELT) ((#44# . #72=(#46# $)) NIL #43# ELT) ((#47# . #72#) NIL T ELT) ((#48# . #71#) NIL T ELT)) (|leadingMonomial| #25#) (|leadingCoefficient| #35#) (|leader| #38#) (|lcm| #73=(($ #53#) NIL #21# ELT) #74=(#75=($ $ $) NIL #21# ELT)) (|latex| (((|String|) $) NIL T ELT)) (|isobaric?| #4#) (|isTimes| #76=(((|Union| #53# #24#) $) NIL T ELT)) (|isPlus| #76#) (|isExpt| (((|Union| (|Record| (|:| |var| |#3|) (|:| |exponent| #7#)) #24#) $) NIL T ELT)) (|initial| #25#) (|hash| (((|SingleInteger|) $) NIL T ELT)) (|ground?| #4#) (|ground| #35#) (|gcdPolynomial| ((#12# #12# #12#) NIL #21# ELT)) (|gcd| #73# #74#) (|factorSquareFreePolynomial| #18#) (|factorPolynomial| #18#) (|factor| (#22# NIL #19# ELT)) (|exquo| ((#49# $ |#1|) NIL #14# ELT) ((#49# $ $) NIL #14# ELT)) (|eval| (($ $ (|List| #77=(|Equation| $))) NIL T ELT) (($ $ #77#) NIL T ELT) (($ $ $ $) NIL T ELT) (($ $ #53# #53#) NIL T ELT) (($ $ |#3| |#1|) NIL T ELT) (($ $ #11# #78=(|List| |#1|)) NIL T ELT) (($ $ |#3| $) NIL T ELT) (($ $ #11# #53#) NIL T ELT) (($ $ |#2| $) NIL #70# ELT) (($ $ #79=(|List| |#2|) #53#) NIL #70# ELT) (($ $ |#2| |#1|) NIL #70# ELT) (($ $ #79# #78#) NIL #70# ELT)) (|discriminant| (#51# NIL #39# ELT)) (|differentiate| #64# #63# #80=(($ $ #11#) NIL T ELT) #81=(#51# NIL T ELT) #82=(($ $ #68#) NIL T ELT) #83=(($ $ #68# #7#) NIL T ELT) #84=(($ $ #85=(|Symbol|)) NIL #86=(|has| |#1| (|PartialDifferentialSpace| #85#)) ELT) #87=(($ $ #88=(|List| #85#)) NIL #86# ELT) #89=(($ $ #85# #7#) NIL #86# ELT) #90=(($ $ #88# #6#) NIL #86# ELT) #91=(#16# NIL #92=(|has| |#1| (|DifferentialSpace|)) ELT) #93=(#94=($ $ #7#) NIL #92# ELT)) (|differentialVariables| ((#79# $) NIL T ELT)) (|degree| #65# #66# #67# #10#) (|convert| ((#58# . #95=($)) NIL (AND (|has| |#1| #96=(|ConvertibleTo| #58#)) (|has| |#3| #96#)) ELT) ((#61# . #95#) NIL (AND (|has| |#1| #97=(|ConvertibleTo| #61#)) (|has| |#3| #97#)) ELT) ((#98=(|InputForm|) . #95#) NIL (AND (|has| |#1| #99=(|ConvertibleTo| #98#)) (|has| |#3| #99#)) ELT)) (|content| (#36# NIL #21# ELT) #50#) (|conditionP| (((|Union| #46# #24#) #42#) NIL #100=(AND (|has| $ #101=(|CharacteristicNonZero|)) #19#) ELT)) (|coerce| (((|OutputForm|) $) NIL T ELT) (($ #30#) NIL T ELT) (($ |#1|) 26 T ELT) (($ |#3|) 25 T ELT) (($ |#2|) NIL T ELT) (($ #34#) 32 T ELT) (($ #29#) NIL (OR #102=(|has| |#1| (|Algebra| #29#)) #31#) ELT) #15#) (|coefficients| ((#78# $) NIL T ELT)) (|coefficient| ((|#1| $ #54#) NIL T ELT) #63# #64#) (|charthRoot| ((#17# $) NIL (OR #100# (|has| |#1| #101#)) ELT)) (|characteristic| ((#7#) NIL T CONST)) (|binomThmExpt| (($ $ $ #7#) NIL #39# ELT)) (|before?| #1#) (|associates?| (#2# NIL #14# ELT)) (|annihilate?| #1#) (|Zero| #26#) (|One| #26#) (D #64# #63# #80# #81# #82# #83# #84# #87# #89# #90# #91# #93#) (= #1#) (/ (#103=($ $ |#1|) NIL (|has| |#1| (|Field|)) ELT)) (- #25# #104=(#75# NIL T ELT)) (+ #104#) (** (($ $ #105=(|PositiveInteger|)) NIL T ELT) (#94# NIL T ELT)) (* (($ #105# $) NIL T ELT) (($ #7# $) NIL T ELT) (($ #30# . #106=($)) NIL T ELT) #104# (($ $ #29#) NIL #102# ELT) (($ #29# . #106#) NIL #102# ELT) (($ |#1| . #106#) NIL T ELT) (#103# NIL T ELT))) (((|DifferentialSparseMultivariatePolynomial| |#1| |#2| |#3|) (|Join| (|DifferentialPolynomialCategory| |#1| |#2| |#3| (|IndexedExponents| |#3|)) (|RetractableTo| (|SparseMultivariatePolynomial| |#1| |#2|))) (|Ring|) (|OrderedSet|) (|DifferentialVariableCategory| |#2|)) (T |DifferentialSparseMultivariatePolynomial|)) NIL ((|weight| ((#1=(|NonNegativeInteger|) $) 37 T ELT)) (|retractIfCan| (((|Union| |#2| "failed") $) 22 T ELT)) (|retract| ((|#2| $) 33 T ELT)) (|differentiate| (($ $ #1#) 18 T ELT) (($ $) 14 T ELT)) (|coerce| (((|OutputForm|) $) 32 T ELT) (($ |#2|) 11 T ELT)) (= (#2=((|Boolean|) $ $) 26 T ELT)) (< (#2# 36 T ELT))) @@ -789,13 +789,13 @@ NIL ((|elt| (*1 *2 *1 *3 *2) (AND (|ofCategory| *1 (|EltableAggregate| *3 *2)) (|ofCategory| *3 (|BasicType|)) (|ofCategory| *2 (|Type|)))) (|qelt| (*1 *2 *1 *3) (AND (|ofCategory| *1 (|EltableAggregate| *3 *2)) (|ofCategory| *3 (|BasicType|)) (|ofCategory| *2 (|Type|)))) (|setelt| (*1 *2 *1 *3 *2) (AND (|ofCategory| *1 (|ShallowlyMutableAggregate| *2)) (|ofCategory| *1 (|EltableAggregate| *3 *2)) (|ofCategory| *3 (|BasicType|)) (|ofCategory| *2 (|Type|)))) (|qsetelt!| (*1 *2 *1 *3 *2) (AND (|ofCategory| *1 (|ShallowlyMutableAggregate| *2)) (|ofCategory| *1 (|EltableAggregate| *3 *2)) (|ofCategory| *3 (|BasicType|)) (|ofCategory| *2 (|Type|))))) (|Join| (|Eltable| |t#1| |t#2|) (CATEGORY |domain| (SIGNATURE |elt| (|t#2| $ |t#1| |t#2|)) (SIGNATURE |qelt| (|t#2| $ |t#1|)) (IF (|has| $ (|ShallowlyMutableAggregate| |t#2|)) (PROGN (SIGNATURE |setelt| (|t#2| $ |t#1| |t#2|)) (SIGNATURE |qsetelt!| (|t#2| $ |t#1| |t#2|))) |%noBranch|))) (((|Eltable| |#1| |#2|) . T) ((|Join|) . T) ((|Type|) . T)) -((~= #1=((#2=(|Boolean|) $ $) NIL T ELT)) (|zero?| (#3=(#2# $) 37 T ELT)) (|unitNormal| (((|Record| (|:| |unit| $) (|:| |canonical| $) (|:| |associate| $)) $) 44 T ELT)) (|unitCanonical| (#4=($ $) 41 T ELT)) (|unit?| #5=(#3# NIL T ELT)) (|subtractIfCan| #6=((#7=(|Union| $ #8="failed") $ $) NIL T ELT)) (|sizeLess?| #1#) (|sample| (#9=($) NIL T CONST)) (|rem| (#10=($ $ $) 35 T ELT)) (|reduce| (($ |#2| |#3|) 18 T ELT)) (|recip| ((#7# $) NIL T ELT)) (|quo| #11=(#10# NIL T ELT)) (|principalIdeal| (((|Record| (|:| |coef| #12=(|List| $)) #13=(|:| |generator| $)) #12#) NIL T ELT)) (|opposite?| #1#) (|one?| #5#) (|multiEuclidean| (((|Union| #12# #8#) #12# $) NIL T ELT)) (|modulus| ((|#3| $) NIL T ELT)) (|lcm| #11# #14=(($ #12#) NIL T ELT)) (|latex| (((|String|) $) NIL T ELT)) (|inv| (#4# 19 T ELT)) (|hash| (((|SingleInteger|) $) NIL T ELT)) (|gcdPolynomial| ((#15=(|SparseUnivariatePolynomial| $) #15# #15#) NIL T ELT)) (|gcd| #11# #14#) (|extendedEuclidean| (((|Record| #16=(|:| |coef1| $) #17=(|:| |coef2| $) #13#) $ $) NIL T ELT) (((|Union| (|Record| #16# #17#) #8#) $ $ $) NIL T ELT)) (|exquo| #6#) (|expressIdealMember| (((|Maybe| #12#) #12# $) NIL T ELT)) (|exQuo| #6#) (|euclideanSize| ((#18=(|NonNegativeInteger|) $) 36 T ELT)) (|elt| ((|#2| $ |#2|) 46 T ELT)) (|divide| (((|Record| (|:| |quotient| $) (|:| |remainder| $)) $ $) 23 T ELT)) (|coerce| (((|OutputForm|) $) NIL T ELT) (($ #19=(|Integer|)) NIL T ELT) #20=(#4# NIL T ELT) ((|#2| $) NIL T ELT)) (|characteristic| ((#18#) NIL T CONST)) (|before?| #1#) (|associates?| #1#) (|annihilate?| #1#) (|Zero| (#9# 31 T CONST)) (|One| (#9# 39 T CONST)) (= #1#) (- #20# #11#) (+ #11#) (** (($ $ #21=(|PositiveInteger|)) NIL T ELT) (($ $ #18#) NIL T ELT)) (* (($ #21# $) NIL T ELT) (($ #18# $) NIL T ELT) (($ #19# $) NIL T ELT) (#10# 40 T ELT))) -(((|EuclideanModularRing| |#1| |#2| |#3| |#4| |#5| |#6|) (|Join| (|EuclideanDomain|) (|Eltable| |#2| |#2|) (CATEGORY |domain| (SIGNATURE |modulus| (|#3| $)) (SIGNATURE |coerce| (|#2| $)) (SIGNATURE |reduce| ($ |#2| |#3|)) (SIGNATURE |exQuo| (#1=(|Union| $ #2="failed") $ $)) (SIGNATURE |recip| (#1# $)) (SIGNATURE |inv| ($ $)))) (|CommutativeRing|) (|UnivariatePolynomialCategory| |#1|) (|AbelianMonoid|) (|Mapping| |#2| |#2| |#3|) (|Mapping| (|Union| |#3| #2#) |#3| |#3|) (|Mapping| (|Union| |#2| #2#) |#2| |#2| |#3|)) (T |EuclideanModularRing|)) -((|recip| #1=(*1 *1 *1) #2=(|partial| AND #3=(|ofCategory| *2 #4=(|CommutativeRing|)) #5=(|isDomain| *1 (|EuclideanModularRing| *2 *3 *4 *5 *6 *7)) #6=(|ofCategory| *3 (|UnivariatePolynomialCategory| *2)) #7=(|ofCategory| *4 #8=(|AbelianMonoid|)) #9=(|ofType| *5 (|Mapping| *3 *3 *4)) #10=(|ofType| *6 (|Mapping| #11=(|Union| *4 #12="failed") *4 *4)) #13=(|ofType| *7 (|Mapping| #14=(|Union| *3 #12#) *3 *3 *4)))) (|modulus| #15=(*1 *2 *1) (AND #16=(|ofCategory| *3 #4#) (|ofCategory| *2 #8#) (|isDomain| *1 (|EuclideanModularRing| *3 *4 *2 *5 *6 *7)) (|ofCategory| *4 #17=(|UnivariatePolynomialCategory| *3)) (|ofType| *5 (|Mapping| *4 *4 *2)) (|ofType| *6 (|Mapping| #18=(|Union| *2 #12#) *2 *2)) (|ofType| *7 (|Mapping| #11# *4 *4 *2)))) (|coerce| #15# (AND (|ofCategory| *2 #17#) (|isDomain| *1 (|EuclideanModularRing| *3 *2 *4 *5 *6 *7)) #16# #7# (|ofType| *5 (|Mapping| *2 *2 *4)) #10# (|ofType| *7 (|Mapping| #18# *2 *2 *4)))) (|reduce| (*1 *1 *2 *3) (AND (|ofCategory| *4 #4#) (|isDomain| *1 (|EuclideanModularRing| *4 *2 *3 *5 *6 *7)) (|ofCategory| *2 (|UnivariatePolynomialCategory| *4)) (|ofCategory| *3 #8#) (|ofType| *5 (|Mapping| *2 *2 *3)) (|ofType| *6 (|Mapping| #14# *3 *3)) (|ofType| *7 (|Mapping| #18# *2 *2 *3)))) (|exQuo| (*1 *1 *1 *1) #2#) (|inv| #1# (AND #3# #5# #6# #7# #9# #10# #13#))) +((~= #1=((#2=(|Boolean|) $ $) NIL T ELT)) (|zero?| (#3=(#2# $) 37 T ELT)) (|unitNormal| (((|Record| (|:| |unit| $) (|:| |canonical| $) (|:| |associate| $)) $) 44 T ELT)) (|unitCanonical| (#4=($ $) 41 T ELT)) (|unit?| #5=(#3# NIL T ELT)) (|subtractIfCan| (((|Maybe| $) $ $) NIL T ELT)) (|sizeLess?| #1#) (|sample| (#6=($) NIL T CONST)) (|rem| (#7=($ $ $) 35 T ELT)) (|reduce| (($ |#2| |#3|) 18 T ELT)) (|recip| ((#8=(|Union| $ #9="failed") $) NIL T ELT)) (|quo| #10=(#7# NIL T ELT)) (|principalIdeal| (((|Record| (|:| |coef| #11=(|List| $)) #12=(|:| |generator| $)) #11#) NIL T ELT)) (|opposite?| #1#) (|one?| #5#) (|multiEuclidean| (((|Union| #11# #9#) #11# $) NIL T ELT)) (|modulus| ((|#3| $) NIL T ELT)) (|lcm| #10# #13=(($ #11#) NIL T ELT)) (|latex| (((|String|) $) NIL T ELT)) (|inv| (#4# 19 T ELT)) (|hash| (((|SingleInteger|) $) NIL T ELT)) (|gcdPolynomial| ((#14=(|SparseUnivariatePolynomial| $) #14# #14#) NIL T ELT)) (|gcd| #10# #13#) (|extendedEuclidean| (((|Record| #15=(|:| |coef1| $) #16=(|:| |coef2| $) #12#) $ $) NIL T ELT) (((|Union| (|Record| #15# #16#) #9#) $ $ $) NIL T ELT)) (|exquo| #17=((#8# $ $) NIL T ELT)) (|expressIdealMember| (((|Maybe| #11#) #11# $) NIL T ELT)) (|exQuo| #17#) (|euclideanSize| ((#18=(|NonNegativeInteger|) $) 36 T ELT)) (|elt| ((|#2| $ |#2|) 46 T ELT)) (|divide| (((|Record| (|:| |quotient| $) (|:| |remainder| $)) $ $) 23 T ELT)) (|coerce| (((|OutputForm|) . #19=($)) NIL T ELT) (($ #20=(|Integer|)) NIL T ELT) #21=(#4# NIL T ELT) ((|#2| . #19#) NIL T ELT)) (|characteristic| ((#18#) NIL T CONST)) (|before?| #1#) (|associates?| #1#) (|annihilate?| #1#) (|Zero| (#6# 31 T CONST)) (|One| (#6# 39 T CONST)) (= #1#) (- #21# #10#) (+ #10#) (** (($ $ #22=(|PositiveInteger|)) NIL T ELT) (($ $ #18#) NIL T ELT)) (* (($ #22# $) NIL T ELT) (($ #18# $) NIL T ELT) (($ #20# $) NIL T ELT) (#7# 40 T ELT))) +(((|EuclideanModularRing| |#1| |#2| |#3| |#4| |#5| |#6|) (|Join| (|EuclideanDomain|) (|Eltable| |#2| |#2|) (|CoercibleTo| |#2|) (CATEGORY |domain| (SIGNATURE |modulus| (|#3| $)) (SIGNATURE |reduce| ($ |#2| |#3|)) (SIGNATURE |exQuo| ((|Union| $ #1="failed") $ $)) (SIGNATURE |inv| ($ $)))) (|CommutativeRing|) (|UnivariatePolynomialCategory| |#1|) (|AbelianMonoid|) (|Mapping| |#2| |#2| |#3|) (|Mapping| (|Union| |#3| #1#) |#3| |#3|) (|Mapping| (|Union| |#2| #1#) |#2| |#2| |#3|)) (T |EuclideanModularRing|)) +((|modulus| (*1 *2 *1) (AND (|ofCategory| *3 #1=(|CommutativeRing|)) (|ofCategory| *2 #2=(|AbelianMonoid|)) (|isDomain| *1 (|EuclideanModularRing| *3 *4 *2 *5 *6 *7)) (|ofCategory| *4 (|UnivariatePolynomialCategory| *3)) (|ofType| *5 (|Mapping| *4 *4 *2)) (|ofType| *6 (|Mapping| #3=(|Union| *2 #4="failed") *2 *2)) (|ofType| *7 (|Mapping| #5=(|Union| *4 #4#) *4 *4 *2)))) (|reduce| (*1 *1 *2 *3) (AND (|ofCategory| *4 #1#) (|isDomain| *1 (|EuclideanModularRing| *4 *2 *3 *5 *6 *7)) (|ofCategory| *2 (|UnivariatePolynomialCategory| *4)) (|ofCategory| *3 #2#) (|ofType| *5 (|Mapping| *2 *2 *3)) (|ofType| *6 (|Mapping| #6=(|Union| *3 #4#) *3 *3)) (|ofType| *7 (|Mapping| #3# *2 *2 *3)))) (|exQuo| (*1 *1 *1 *1) (|partial| AND #7=(|ofCategory| *2 #1#) #8=(|isDomain| *1 (|EuclideanModularRing| *2 *3 *4 *5 *6 *7)) #9=(|ofCategory| *3 (|UnivariatePolynomialCategory| *2)) #10=(|ofCategory| *4 #2#) #11=(|ofType| *5 (|Mapping| *3 *3 *4)) #12=(|ofType| *6 (|Mapping| #5# *4 *4)) #13=(|ofType| *7 (|Mapping| #6# *3 *3 *4)))) (|inv| (*1 *1 *1) (AND #7# #8# #9# #10# #11# #12# #13#))) ((|annihilate?| (((|Boolean|) $ $) 10 T ELT))) (((|EntireRing&| |#1|) (CATEGORY |package| (SIGNATURE |annihilate?| ((|Boolean|) |#1| |#1|))) (|EntireRing|)) (T |EntireRing&|)) NIL -((~= (#1=((|Boolean|) $ $) 7 T ELT)) (|zero?| ((#2=(|Boolean|) $) 22 T ELT)) (|subtractIfCan| (((|Union| $ "failed") $ $) 26 T ELT)) (|sample| (#3=($) 23 T CONST)) (|recip| (((|Union| $ "failed") $) 42 T ELT)) (|opposite?| ((#2# $ $) 20 T ELT)) (|one?| (((|Boolean|) $) 44 T ELT)) (|latex| (((|String|) $) 11 T ELT)) (|hash| (((|SingleInteger|) $) 12 T ELT)) (|coerce| (((|OutputForm|) $) 13 T ELT) (($ (|Integer|)) 41 T ELT)) (|characteristic| (((|NonNegativeInteger|)) 40 T CONST)) (|before?| (#1# 6 T ELT)) (|annihilate?| (((|Boolean|) $ $) 33 T ELT)) (|Zero| (#3# 24 T CONST)) (|One| (($) 45 T CONST)) (= (#1# 8 T ELT)) (- (($ $) 29 T ELT) (($ $ $) 28 T ELT)) (+ (($ $ $) 18 T ELT)) (** (($ $ (|PositiveInteger|)) 35 T ELT) (($ $ (|NonNegativeInteger|)) 43 T ELT)) (* (($ (|PositiveInteger|) $) 17 T ELT) (($ (|NonNegativeInteger|) $) 21 T ELT) (($ (|Integer|) $) 30 T ELT) (($ $ $) 34 T ELT))) +((~= (#1=((|Boolean|) $ $) 7 T ELT)) (|zero?| ((#2=(|Boolean|) $) 22 T ELT)) (|subtractIfCan| (((|Maybe| $) $ $) 26 T ELT)) (|sample| (#3=($) 23 T CONST)) (|recip| (((|Union| $ "failed") $) 43 T ELT)) (|opposite?| ((#2# $ $) 20 T ELT)) (|one?| (((|Boolean|) $) 45 T ELT)) (|latex| (((|String|) $) 11 T ELT)) (|hash| (((|SingleInteger|) $) 12 T ELT)) (|coerce| (((|OutputForm|) $) 13 T ELT) (($ (|Integer|)) 42 T ELT)) (|characteristic| (((|NonNegativeInteger|)) 41 T CONST)) (|before?| (#1# 6 T ELT)) (|annihilate?| (((|Boolean|) $ $) 34 T ELT)) (|Zero| (#3# 24 T CONST)) (|One| (($) 46 T CONST)) (= (#1# 8 T ELT)) (- (($ $) 30 T ELT) (($ $ $) 29 T ELT)) (+ (($ $ $) 18 T ELT)) (** (($ $ (|PositiveInteger|)) 36 T ELT) (($ $ (|NonNegativeInteger|)) 44 T ELT)) (* (($ (|PositiveInteger|) $) 17 T ELT) (($ (|NonNegativeInteger|) $) 21 T ELT) (($ (|Integer|) $) 31 T ELT) (($ $ $) 35 T ELT))) (((|EntireRing|) (|Category|)) (T |EntireRing|)) NIL (|Join| (|Ring|) (|BiModule| $ $) (CATEGORY |package| (ATTRIBUTE |noZeroDivisors|))) @@ -806,7 +806,7 @@ NIL ((|generalizedEigenvectors| (((|List| (|Record| #1=(|:| |eigval| #2=(|Union| #3=(|Fraction| #4=(|Polynomial| |#1|)) (|SuchThat| #5=(|Symbol|) #4#))) (|:| |geneigvec| #6=(|List| #7=(|Matrix| #3#))))) #7#) 103 T ELT)) (|generalizedEigenvector| ((#6# #8=(|Record| #1# (|:| |eigmult| #9=(|NonNegativeInteger|)) (|:| |eigvec| #6#)) #7#) 98 T ELT) ((#6# #2# #7# #9# #9#) 42 T ELT)) (|eigenvectors| (((|List| #8#) #7#) 100 T ELT)) (|eigenvector| ((#6# #2# #7#) 76 T ELT)) (|eigenvalues| (((|List| #2#) #7#) 75 T ELT)) (|characteristicPolynomial| ((#4# #7#) 56 T ELT) ((#4# #7# #5#) 57 T ELT))) (((|EigenPackage| |#1|) (CATEGORY |package| (SIGNATURE |characteristicPolynomial| (#1=(|Polynomial| |#1|) #2=(|Matrix| #3=(|Fraction| #1#)) #4=(|Symbol|))) (SIGNATURE |characteristicPolynomial| (#1# #2#)) (SIGNATURE |eigenvalues| ((|List| #5=(|Union| #3# (|SuchThat| #4# #1#))) #2#)) (SIGNATURE |eigenvector| (#6=(|List| #2#) #5# #2#)) (SIGNATURE |generalizedEigenvector| (#6# #5# #2# #7=(|NonNegativeInteger|) #7#)) (SIGNATURE |generalizedEigenvector| (#6# #8=(|Record| #9=(|:| |eigval| #5#) (|:| |eigmult| #7#) (|:| |eigvec| #6#)) #2#)) (SIGNATURE |generalizedEigenvectors| ((|List| (|Record| #9# (|:| |geneigvec| #6#))) #2#)) (SIGNATURE |eigenvectors| ((|List| #8#) #2#))) (|GcdDomain|)) (T |EigenPackage|)) ((|eigenvectors| #1=(*1 *2 *3) (AND #2=(|ofCategory| *4 #3=(|GcdDomain|)) (|isDomain| *2 (|List| (|Record| #4=(|:| |eigval| #5=(|Union| #6=(|Fraction| #7=(|Polynomial| *4)) (|SuchThat| #8=(|Symbol|) #7#))) #9=(|:| |eigmult| #10=(|NonNegativeInteger|)) (|:| |eigvec| #11=(|List| #12=(|Matrix| #6#)))))) #13=(|isDomain| *1 (|EigenPackage| *4)) #14=(|isDomain| *3 #12#))) (|generalizedEigenvectors| #1# (AND #2# (|isDomain| *2 (|List| (|Record| #4# (|:| |geneigvec| #11#)))) #13# #14#)) (|generalizedEigenvector| #15=(*1 *2 *3 *4) (AND (|isDomain| *3 (|Record| (|:| |eigval| #16=(|Union| #17=(|Fraction| #18=(|Polynomial| *5)) (|SuchThat| #8# #18#))) #9# (|:| |eigvec| (|List| *4)))) #19=(|ofCategory| *5 #3#) #20=(|isDomain| *2 (|List| #21=(|Matrix| #17#))) #22=(|isDomain| *1 (|EigenPackage| *5)) #23=(|isDomain| *4 #21#))) (|generalizedEigenvector| (*1 *2 *3 *4 *5 *5) (AND (|isDomain| *3 (|Union| #24=(|Fraction| #25=(|Polynomial| *6)) (|SuchThat| #8# #25#))) (|isDomain| *5 #10#) (|ofCategory| *6 #3#) (|isDomain| *2 (|List| #26=(|Matrix| #24#))) (|isDomain| *1 (|EigenPackage| *6)) (|isDomain| *4 #26#))) (|eigenvector| #15# (AND (|isDomain| *3 #16#) #19# #20# #22# #23#)) (|eigenvalues| #1# (AND #14# #2# (|isDomain| *2 (|List| #5#)) #13#)) (|characteristicPolynomial| #1# (AND #14# (|isDomain| *2 #7#) #13# #2#)) (|characteristicPolynomial| #15# (AND (|isDomain| *3 #21#) (|isDomain| *4 #8#) (|isDomain| *2 #18#) #22# #19#))) -((~= #1=(#2=(#3=(|Boolean|) $ $) NIL #4=(|has| |#1| (|SetCategory|)) ELT)) (|zero?| (#5=(#3# $) NIL #6=(|has| |#1| (|AbelianGroup|)) ELT)) (|swap| (#7=($ $) 12 T ELT)) (|subtractIfCan| ((#8=(|Union| $ "failed") $ $) NIL #6# ELT)) (|subst| (#9=($ $ $) 95 (|has| |#1| (|ExpressionSpace|)) ELT)) (|sample| (#10=($) NIL (OR #6# #11=(|has| |#1| (|Monoid|))) CONST)) (|rightZero| (#7# 51 #6# ELT)) (|rightOne| (#12=(#8# $) 62 #11# ELT)) (|rhs| (#13=(|#1| $) 11 T ELT)) (|recip| (#12# 60 #11# ELT)) (|opposite?| (#2# NIL #6# ELT)) (|one?| (#5# NIL #11# ELT)) (|map| (($ (|Mapping| |#1| |#1|) $) 14 T ELT)) (|lhs| (#13# 10 T ELT)) (|leftZero| (#7# 50 #6# ELT)) (|leftOne| (#12# 61 #11# ELT)) (|latex| (((|String|) $) NIL #4# ELT)) (|inv| (#7# 64 #14=(OR #15=(|has| |#1| (|Field|)) #16=(|has| |#1| (|Group|))) ELT)) (|hash| (((|SingleInteger|) $) NIL #4# ELT)) (|factorAndSplit| ((#17=(|List| $) $) 85 (|has| |#1| (|IntegralDomain|)) ELT)) (|eval| (#9# 24 #18=(AND (|has| |#1| (|Evalable| |#1|)) #4#) ELT) (($ $ #17#) 28 #18# ELT) (($ $ #19=(|Symbol|) |#1|) 17 #20=(|has| |#1| (|InnerEvalable| #19# |#1|)) ELT) (($ $ #21=(|List| #19#) (|List| |#1|)) 21 #20# ELT)) (|equation| (#22=($ |#1| |#1|) 9 T ELT)) (|dimension| (((|CardinalNumber|)) 90 #15# ELT)) (|differentiate| (#23=($ $ #19#) 87 #24=(|has| |#1| (|PartialDifferentialRing| #19#)) ELT) #25=(($ $ #21#) NIL #24# ELT) #26=(($ $ #19# #27=(|NonNegativeInteger|)) NIL #24# ELT) #28=(($ $ #21# (|List| #27#)) NIL #24# ELT)) (|conjugate| #29=(#9# NIL #16# ELT)) (|commutator| #29#) (|coerce| (($ #30=(|Integer|)) NIL #31=(|has| |#1| (|Ring|)) ELT) (#5# 37 #4# ELT) (((|OutputForm|) $) 36 #4# ELT)) (|characteristic| ((#27#) 67 #31# CONST)) (|before?| #1#) (|annihilate?| (#2# NIL #31# ELT)) (|Zero| (#10# 47 #6# CONST)) (|One| (#10# 57 #11# CONST)) (D (#23# NIL #24# ELT) #25# #26# #28#) (= (#22# 8 T ELT) (#2# 32 #4# ELT)) (/ (#32=($ $ |#1|) NIL #15# ELT) (#9# 92 #14# ELT)) (- (#33=($ |#1| $) 45 #6# ELT) (#32# 46 #6# ELT) (#9# 44 #6# ELT) (#7# 43 #6# ELT)) (+ (#33# 40 #34=(|has| |#1| (|AbelianSemiGroup|)) ELT) (#32# 41 #34# ELT) (#9# 39 #34# ELT)) (** (($ $ #30#) NIL #16# ELT) (($ $ #27#) NIL #11# ELT) (($ $ #35=(|PositiveInteger|)) NIL #36=(|has| |#1| (|SemiGroup|)) ELT)) (* (#32# 55 #36# ELT) (#33# 54 #36# ELT) (#9# 53 #36# ELT) (($ #30# $) 70 #6# ELT) (($ #27# $) NIL #6# ELT) (($ #35# $) NIL #34# ELT))) +((~= #1=(#2=(#3=(|Boolean|) $ $) NIL #4=(|has| |#1| (|SetCategory|)) ELT)) (|zero?| (#5=(#3# $) NIL #6=(|has| |#1| (|AbelianGroup|)) ELT)) (|swap| (#7=($ $) 12 T ELT)) (|subtractIfCan| (((|Maybe| $) $ $) NIL #6# ELT)) (|subst| (#8=($ $ $) 95 (|has| |#1| (|ExpressionSpace|)) ELT)) (|sample| (#9=($) NIL (OR #6# #10=(|has| |#1| (|Monoid|))) CONST)) (|rightZero| (#7# 51 #6# ELT)) (|rightOne| (#11=((|Union| $ "failed") $) 62 #10# ELT)) (|rhs| (#12=(|#1| $) 11 T ELT)) (|recip| (#11# 60 #10# ELT)) (|opposite?| (#2# NIL #6# ELT)) (|one?| (#5# NIL #10# ELT)) (|map| (($ (|Mapping| |#1| |#1|) $) 14 T ELT)) (|lhs| (#12# 10 T ELT)) (|leftZero| (#7# 50 #6# ELT)) (|leftOne| (#11# 61 #10# ELT)) (|latex| (((|String|) $) NIL #4# ELT)) (|inv| (#7# 64 #13=(OR #14=(|has| |#1| (|Field|)) #15=(|has| |#1| (|Group|))) ELT)) (|hash| (((|SingleInteger|) $) NIL #4# ELT)) (|factorAndSplit| ((#16=(|List| $) $) 85 (|has| |#1| (|IntegralDomain|)) ELT)) (|eval| (#8# 24 #17=(AND (|has| |#1| (|Evalable| |#1|)) #4#) ELT) (($ $ #16#) 28 #17# ELT) (($ $ #18=(|Symbol|) |#1|) 17 #19=(|has| |#1| (|InnerEvalable| #18# |#1|)) ELT) (($ $ #20=(|List| #18#) (|List| |#1|)) 21 #19# ELT)) (|equation| (#21=($ |#1| |#1|) 9 T ELT)) (|dimension| (((|CardinalNumber|)) 90 #14# ELT)) (|differentiate| (#22=($ $ #18#) 87 #23=(|has| |#1| (|PartialDifferentialRing| #18#)) ELT) #24=(($ $ #20#) NIL #23# ELT) #25=(($ $ #18# #26=(|NonNegativeInteger|)) NIL #23# ELT) #27=(($ $ #20# (|List| #26#)) NIL #23# ELT)) (|conjugate| #28=(#8# NIL #15# ELT)) (|commutator| #28#) (|coerce| (($ #29=(|Integer|)) NIL #30=(|has| |#1| (|Ring|)) ELT) (#5# 37 #4# ELT) (((|OutputForm|) $) 36 #4# ELT)) (|characteristic| ((#26#) 67 #30# CONST)) (|before?| #1#) (|annihilate?| (#2# NIL #30# ELT)) (|Zero| (#9# 47 #6# CONST)) (|One| (#9# 57 #10# CONST)) (D (#22# NIL #23# ELT) #24# #25# #27#) (= (#21# 8 T ELT) (#2# 32 #4# ELT)) (/ (#31=($ $ |#1|) NIL #14# ELT) (#8# 92 #13# ELT)) (- (#32=($ |#1| $) 45 #6# ELT) (#31# 46 #6# ELT) (#8# 44 #6# ELT) (#7# 43 #6# ELT)) (+ (#32# 40 #33=(|has| |#1| (|AbelianSemiGroup|)) ELT) (#31# 41 #33# ELT) (#8# 39 #33# ELT)) (** (($ $ #29#) NIL #15# ELT) (($ $ #26#) NIL #10# ELT) (($ $ #34=(|PositiveInteger|)) NIL #35=(|has| |#1| (|SemiGroup|)) ELT)) (* (#31# 55 #35# ELT) (#32# 54 #35# ELT) (#8# 53 #35# ELT) (($ #29# $) 70 #6# ELT) (($ #26# $) NIL #6# ELT) (($ #34# $) NIL #33# ELT))) (((|Equation| |#1|) (|Join| (|Functorial| |#1|) (CATEGORY |domain| (SIGNATURE = #1=($ |#1| |#1|)) (SIGNATURE |equation| #1#) (SIGNATURE |swap| #2=($ $)) (SIGNATURE |lhs| #3=(|#1| $)) (SIGNATURE |rhs| #3#) (IF (|has| |#1| #4=(|InnerEvalable| #5=(|Symbol|) |#1|)) (ATTRIBUTE #4#) |%noBranch|) (IF (|has| |#1| #6=(|SetCategory|)) (PROGN (ATTRIBUTE #6#) (ATTRIBUTE (|CoercibleTo| (|Boolean|))) (IF (|has| |#1| (|Evalable| |#1|)) (PROGN (SIGNATURE |eval| #7=($ $ $)) (SIGNATURE |eval| ($ $ #8=(|List| $)))) |%noBranch|)) |%noBranch|) (IF (|has| |#1| #9=(|AbelianSemiGroup|)) (PROGN (ATTRIBUTE #9#) (SIGNATURE + #10=($ |#1| $)) (SIGNATURE + #11=($ $ |#1|))) |%noBranch|) (IF (|has| |#1| #12=(|AbelianGroup|)) (PROGN (ATTRIBUTE #12#) (SIGNATURE |leftZero| #2#) (SIGNATURE |rightZero| #2#) (SIGNATURE - #10#) (SIGNATURE - #11#)) |%noBranch|) (IF (|has| |#1| #13=(|SemiGroup|)) (PROGN (ATTRIBUTE #13#) (SIGNATURE * #10#) (SIGNATURE * #11#)) |%noBranch|) (IF (|has| |#1| #14=(|Monoid|)) (PROGN (ATTRIBUTE #14#) #15=(SIGNATURE |leftOne| #16=((|Union| $ "failed") $)) #17=(SIGNATURE |rightOne| #16#)) |%noBranch|) (IF (|has| |#1| #18=(|Group|)) (PROGN (ATTRIBUTE #18#) #15# #17#) |%noBranch|) (IF (|has| |#1| #19=(|Ring|)) (PROGN (ATTRIBUTE #19#) (ATTRIBUTE (|BiModule| |#1| |#1|))) |%noBranch|) (IF (|has| |#1| (|CommutativeRing|)) (ATTRIBUTE (|Module| |#1|)) |%noBranch|) (IF (|has| |#1| (|IntegralDomain|)) (SIGNATURE |factorAndSplit| (#8# $)) |%noBranch|) (IF (|has| |#1| #20=(|PartialDifferentialRing| #5#)) (ATTRIBUTE #20#) |%noBranch|) (IF (|has| |#1| (|Field|)) (PROGN (ATTRIBUTE (|VectorSpace| |#1|)) (SIGNATURE / #7#) (SIGNATURE |inv| #2#)) |%noBranch|) (IF (|has| |#1| (|ExpressionSpace|)) (SIGNATURE |subst| #7#) |%noBranch|))) (|Type|)) (T |Equation|)) ((= #1=(*1 *1 *2 *2) #2=(AND #3=(|isDomain| *1 (|Equation| *2)) #4=(|ofCategory| *2 #5=(|Type|)))) (|equation| #1# #2#) (|swap| #6=(*1 *1 *1) #2#) (|lhs| #7=(*1 *2 *1) #2#) (|rhs| #7# #2#) (|eval| #8=(*1 *1 *1 *1) (AND (|ofCategory| *2 (|Evalable| *2)) (|ofCategory| *2 #9=(|SetCategory|)) #4# #3#)) (|eval| #10=(*1 *1 *1 *2) (AND #11=(|isDomain| *2 (|List| #12=(|Equation| *3))) (|ofCategory| *3 (|Evalable| *3)) (|ofCategory| *3 #9#) #13=(|ofCategory| *3 #5#) #14=(|isDomain| *1 #12#))) (+ #15=(*1 *1 *2 *1) #16=(AND #3# (|ofCategory| *2 (|AbelianSemiGroup|)) #4#)) (+ #10# #16#) (|leftZero| #6# #17=(AND #3# (|ofCategory| *2 (|AbelianGroup|)) #4#)) (|rightZero| #6# #17#) (- #15# #17#) (- #10# #17#) (|leftOne| #6# #18=(|partial| AND #3# (|ofCategory| *2 (|Monoid|)) #4#)) (|rightOne| #6# #18#) (|factorAndSplit| #7# (AND #11# #14# (|ofCategory| *3 (|IntegralDomain|)) #13#)) (|subst| #8# (AND #3# (|ofCategory| *2 (|ExpressionSpace|)) #4#)) (* #10# #19=(AND #3# (|ofCategory| *2 (|SemiGroup|)) #4#)) (* #15# #19#) (/ #8# #20=(OR (AND #3# (|ofCategory| *2 (|Field|)) . #21=(#4#)) (AND #3# (|ofCategory| *2 (|Group|)) . #21#))) (|inv| #6# #20#)) ((|map| (((|Equation| |#2|) (|Mapping| |#2| |#1|) (|Equation| |#1|)) 14 T ELT))) @@ -835,7 +835,7 @@ NIL ((|sizeLess?| (((|Boolean|) $ $) 14 T ELT)) (|rem| (#1=($ $ $) 18 T ELT)) (|quo| (#1# 17 T ELT)) (|principalIdeal| (((|Record| (|:| |coef| #2=(|List| $)) #3=(|:| |generator| $)) #2#) 50 T ELT)) (|multiEuclidean| (((|Union| #2# #4="failed") #2# $) 67 T ELT)) (|gcd| (#1# 25 T ELT) (($ #2#) NIL T ELT)) (|extendedEuclidean| (((|Record| #5=(|:| |coef1| $) #6=(|:| |coef2| $) #3#) $ $) 35 T ELT) (((|Union| (|Record| #5# #6#) #4#) $ $ $) 40 T ELT)) (|exquo| (((|Union| $ #4#) $ $) 21 T ELT)) (|expressIdealMember| (((|Maybe| #2#) #2# $) 55 T ELT))) (((|EuclideanDomain&| |#1|) (CATEGORY |package| (SIGNATURE |multiEuclidean| ((|Union| #1=(|List| |#1|) #2="failed") #1# |#1|)) (SIGNATURE |extendedEuclidean| ((|Union| (|Record| #3=(|:| |coef1| |#1|) #4=(|:| |coef2| |#1|)) #2#) |#1| |#1| |#1|)) (SIGNATURE |extendedEuclidean| ((|Record| #3# #4# #5=(|:| |generator| |#1|)) |#1| |#1|)) (SIGNATURE |rem| #6=(|#1| |#1| |#1|)) (SIGNATURE |quo| #6#) (SIGNATURE |sizeLess?| ((|Boolean|) |#1| |#1|)) (SIGNATURE |expressIdealMember| ((|Maybe| #1#) #1# |#1|)) (SIGNATURE |principalIdeal| ((|Record| (|:| |coef| #1#) #5#) #1#)) (SIGNATURE |gcd| (|#1| #1#)) (SIGNATURE |gcd| #6#) (SIGNATURE |exquo| ((|Union| |#1| #2#) |#1| |#1|))) (|EuclideanDomain|)) (T |EuclideanDomain&|)) NIL -((~= (#1=((|Boolean|) $ $) 7 T ELT)) (|zero?| ((#2=(|Boolean|) $) 22 T ELT)) (|unitNormal| (((|Record| (|:| |unit| $) (|:| |canonical| $) (|:| |associate| $)) $) 55 T ELT)) (|unitCanonical| (($ $) 54 T ELT)) (|unit?| ((#3=(|Boolean|) $) 52 T ELT)) (|subtractIfCan| (((|Union| $ "failed") $ $) 26 T ELT)) (|sizeLess?| (((|Boolean|) $ $) 75 T ELT)) (|sample| (#4=($) 23 T CONST)) (|rem| (($ $ $) 71 T ELT)) (|recip| (((|Union| $ "failed") $) 42 T ELT)) (|quo| (($ $ $) 72 T ELT)) (|principalIdeal| (((|Record| (|:| |coef| #5=(|List| $)) (|:| |generator| $)) #5#) 66 T ELT)) (|opposite?| ((#2# $ $) 20 T ELT)) (|one?| (((|Boolean|) $) 44 T ELT)) (|multiEuclidean| (((|Union| (|List| $) "failed") (|List| $) $) 68 T ELT)) (|lcm| (#6=($ $ $) 60 T ELT) (#7=($ (|List| $)) 59 T ELT)) (|latex| (((|String|) $) 11 T ELT)) (|hash| (((|SingleInteger|) $) 12 T ELT)) (|gcdPolynomial| ((#8=(|SparseUnivariatePolynomial| $) #8# #8#) 58 T ELT)) (|gcd| (#6# 62 T ELT) (#7# 61 T ELT)) (|extendedEuclidean| (((|Record| (|:| |coef1| $) (|:| |coef2| $) (|:| |generator| $)) $ $) 70 T ELT) (((|Union| (|Record| (|:| |coef1| $) (|:| |coef2| $)) "failed") $ $ $) 69 T ELT)) (|exquo| (((|Union| $ "failed") $ $) 56 T ELT)) (|expressIdealMember| (((|Maybe| #5#) #5# $) 65 T ELT)) (|euclideanSize| (((|NonNegativeInteger|) $) 74 T ELT)) (|divide| (((|Record| (|:| |quotient| $) (|:| |remainder| $)) $ $) 73 T ELT)) (|coerce| (((|OutputForm|) $) 13 T ELT) (($ (|Integer|)) 41 T ELT) (($ $) 57 T ELT)) (|characteristic| (((|NonNegativeInteger|)) 40 T CONST)) (|before?| (#1# 6 T ELT)) (|associates?| ((#3# $ $) 53 T ELT)) (|annihilate?| (((|Boolean|) $ $) 33 T ELT)) (|Zero| (#4# 24 T CONST)) (|One| (($) 45 T CONST)) (= (#1# 8 T ELT)) (- (($ $) 29 T ELT) (($ $ $) 28 T ELT)) (+ (($ $ $) 18 T ELT)) (** (($ $ (|PositiveInteger|)) 35 T ELT) (($ $ (|NonNegativeInteger|)) 43 T ELT)) (* (($ (|PositiveInteger|) $) 17 T ELT) (($ (|NonNegativeInteger|) $) 21 T ELT) (($ (|Integer|) $) 30 T ELT) (($ $ $) 34 T ELT))) +((~= (#1=((|Boolean|) $ $) 7 T ELT)) (|zero?| ((#2=(|Boolean|) $) 22 T ELT)) (|unitNormal| (((|Record| (|:| |unit| $) (|:| |canonical| $) (|:| |associate| $)) $) 56 T ELT)) (|unitCanonical| (($ $) 55 T ELT)) (|unit?| ((#3=(|Boolean|) $) 53 T ELT)) (|subtractIfCan| (((|Maybe| $) $ $) 26 T ELT)) (|sizeLess?| (((|Boolean|) $ $) 76 T ELT)) (|sample| (#4=($) 23 T CONST)) (|rem| (($ $ $) 72 T ELT)) (|recip| (((|Union| $ "failed") $) 43 T ELT)) (|quo| (($ $ $) 73 T ELT)) (|principalIdeal| (((|Record| (|:| |coef| #5=(|List| $)) (|:| |generator| $)) #5#) 67 T ELT)) (|opposite?| ((#2# $ $) 20 T ELT)) (|one?| (((|Boolean|) $) 45 T ELT)) (|multiEuclidean| (((|Union| (|List| $) "failed") (|List| $) $) 69 T ELT)) (|lcm| (#6=($ $ $) 61 T ELT) (#7=($ (|List| $)) 60 T ELT)) (|latex| (((|String|) $) 11 T ELT)) (|hash| (((|SingleInteger|) $) 12 T ELT)) (|gcdPolynomial| ((#8=(|SparseUnivariatePolynomial| $) #8# #8#) 59 T ELT)) (|gcd| (#6# 63 T ELT) (#7# 62 T ELT)) (|extendedEuclidean| (((|Record| (|:| |coef1| $) (|:| |coef2| $) (|:| |generator| $)) $ $) 71 T ELT) (((|Union| (|Record| (|:| |coef1| $) (|:| |coef2| $)) "failed") $ $ $) 70 T ELT)) (|exquo| (((|Union| $ "failed") $ $) 57 T ELT)) (|expressIdealMember| (((|Maybe| #5#) #5# $) 66 T ELT)) (|euclideanSize| (((|NonNegativeInteger|) $) 75 T ELT)) (|divide| (((|Record| (|:| |quotient| $) (|:| |remainder| $)) $ $) 74 T ELT)) (|coerce| (((|OutputForm|) $) 13 T ELT) (($ (|Integer|)) 42 T ELT) (($ $) 58 T ELT)) (|characteristic| (((|NonNegativeInteger|)) 41 T CONST)) (|before?| (#1# 6 T ELT)) (|associates?| ((#3# $ $) 54 T ELT)) (|annihilate?| (((|Boolean|) $ $) 34 T ELT)) (|Zero| (#4# 24 T CONST)) (|One| (($) 46 T CONST)) (= (#1# 8 T ELT)) (- (($ $) 30 T ELT) (($ $ $) 29 T ELT)) (+ (($ $ $) 18 T ELT)) (** (($ $ (|PositiveInteger|)) 36 T ELT) (($ $ (|NonNegativeInteger|)) 44 T ELT)) (* (($ (|PositiveInteger|) $) 17 T ELT) (($ (|NonNegativeInteger|) $) 21 T ELT) (($ (|Integer|) $) 31 T ELT) (($ $ $) 35 T ELT))) (((|EuclideanDomain|) (|Category|)) (T |EuclideanDomain|)) ((|sizeLess?| (*1 *2 *1 *1) (AND (|ofCategory| *1 (|EuclideanDomain|)) (|isDomain| *2 (|Boolean|)))) (|euclideanSize| (*1 *2 *1) (AND (|ofCategory| *1 (|EuclideanDomain|)) (|isDomain| *2 (|NonNegativeInteger|)))) (|divide| (*1 *2 *1 *1) (AND (|isDomain| *2 (|Record| (|:| |quotient| *1) (|:| |remainder| *1))) (|ofCategory| *1 (|EuclideanDomain|)))) (|quo| (*1 *1 *1 *1) (|ofCategory| *1 (|EuclideanDomain|))) (|rem| (*1 *1 *1 *1) (|ofCategory| *1 (|EuclideanDomain|))) (|extendedEuclidean| (*1 *2 *1 *1) (AND (|isDomain| *2 (|Record| (|:| |coef1| *1) (|:| |coef2| *1) (|:| |generator| *1))) (|ofCategory| *1 (|EuclideanDomain|)))) (|extendedEuclidean| (*1 *2 *1 *1 *1) (|partial| AND (|isDomain| *2 (|Record| (|:| |coef1| *1) (|:| |coef2| *1))) (|ofCategory| *1 (|EuclideanDomain|)))) (|multiEuclidean| (*1 *2 *2 *1) (|partial| AND (|isDomain| *2 (|List| *1)) (|ofCategory| *1 (|EuclideanDomain|))))) (|Join| (|PrincipalIdealDomain|) (CATEGORY |domain| (SIGNATURE |sizeLess?| ((|Boolean|) $ $)) (SIGNATURE |euclideanSize| ((|NonNegativeInteger|) $)) (SIGNATURE |divide| ((|Record| (|:| |quotient| $) (|:| |remainder| $)) $ $)) (SIGNATURE |quo| ($ $ $)) (SIGNATURE |rem| ($ $ $)) (SIGNATURE |extendedEuclidean| ((|Record| (|:| |coef1| $) (|:| |coef2| $) (|:| |generator| $)) $ $)) (SIGNATURE |extendedEuclidean| ((|Union| (|Record| (|:| |coef1| $) (|:| |coef2| $)) "failed") $ $ $)) (SIGNATURE |multiEuclidean| ((|Union| (|List| $) "failed") (|List| $) $)))) @@ -857,10 +857,10 @@ NIL ((~= #1=(((|Boolean|) $ $) NIL T ELT)) (|level| (((|Integer|) $) 13 T ELT)) (|latex| (((|String|) $) NIL T ELT)) (|hash| (((|SingleInteger|) $) NIL T ELT)) (|expression| (((|SpadAst|) $) 10 T ELT)) (|coerce| (((|OutputForm|) $) 20 T ELT) (($ #2=(|Syntax|)) NIL T ELT) ((#2# $) NIL T ELT)) (|before?| #1#) (= #1#)) (((|ExitAst|) (|Join| (|SpadSyntaxCategory|) (CATEGORY |domain| (SIGNATURE |expression| ((|SpadAst|) $)) (SIGNATURE |level| ((|Integer|) $))))) (T |ExitAst|)) ((|expression| #1=(*1 *2 *1) (AND (|isDomain| *2 (|SpadAst|)) #2=(|isDomain| *1 (|ExitAst|)))) (|level| #1# (AND (|isDomain| *2 (|Integer|)) #2#))) -((~= #1=(#2=(#3=(|Boolean|) $ $) NIL T ELT)) (|zero?| (#4=(#3# $) 60 T ELT)) (|wholePart| (#5=(#6=(|UnivariatePuiseuxSeriesWithExponentialSingularity| |#1| |#2| |#3| |#4|) $) NIL #7=(|has| #6# (|EuclideanDomain|)) ELT)) (|unitNormal| (((|Record| (|:| |unit| $) (|:| |canonical| $) (|:| |associate| $)) $) NIL T ELT)) (|unitCanonical| #8=(#9=($ $) NIL T ELT)) (|unit?| #10=(#4# NIL T ELT)) (|subtractIfCan| #11=((#12=(|Union| $ #13="failed") $ $) NIL T ELT)) (|squareFreePolynomial| #14=(((|Factored| #15=(|SparseUnivariatePolynomial| $)) #15#) NIL #16=(|has| #6# (|PolynomialFactorizationExplicit|)) ELT)) (|squareFreePart| #8#) (|squareFree| #17=(((|Factored| $) $) NIL T ELT)) (|solveLinearPolynomialEquation| (((|Union| #18=(|List| #15#) #13#) #18# #15#) NIL #16# ELT)) (|sizeLess?| #1#) (|sign| (#19=(#20=(|Integer|) $) NIL #21=(|has| #6# (|OrderedIntegralDomain|)) ELT)) (|sample| #22=(#23=($) NIL T CONST)) (|retractIfCan| (((|Union| #6# . #24=(#13#)) . #25=($)) NIL T ELT) (((|Union| #26=(|Symbol|) . #24#) . #25#) NIL #27=(|has| #6# (|RetractableTo| #26#)) ELT) (((|Union| #28=(|Fraction| #20#) . #24#) . #25#) NIL #29=(|has| #6# (|RetractableTo| #20#)) ELT) (((|Union| #20# . #24#) . #25#) NIL #29# ELT) (((|Union| #30=(|UnivariatePuiseuxSeries| |#2| |#3| |#4|) . #24#) $) 26 T ELT)) (|retract| (#5# NIL T ELT) ((#26# . #31=($)) NIL #27# ELT) ((#28# . #31#) NIL #29# ELT) (#19# NIL #29# ELT) ((#30# . #31#) NIL T ELT)) (|rem| #32=(#33=($ $ $) NIL T ELT)) (|reducedSystem| ((#34=(|Matrix| #20#) . #35=(#36=(|Matrix| $))) NIL #37=(|has| #6# (|LinearlyExplicitRingOver| #20#)) ELT) ((#38=(|Record| (|:| |mat| #34#) (|:| |vec| (|Vector| #20#))) . #39=(#36# #40=(|Vector| $))) NIL #37# ELT) ((#41=(|Record| (|:| |mat| #42=(|Matrix| #6#)) (|:| |vec| (|Vector| #6#))) . #39#) NIL T ELT) ((#42# . #35#) NIL T ELT)) (|recip| ((#12# $) NIL T ELT)) (|random| (#23# NIL #43=(|has| #6# (|IntegerNumberSystem|)) ELT)) (|quo| #32#) (|principalIdeal| (((|Record| (|:| |coef| #44=(|List| $)) #45=(|:| |generator| $)) #44#) NIL T ELT)) (|prime?| #10#) (|positive?| #46=(#4# NIL #21# ELT)) (|patternMatch| ((#47=(|PatternMatchResult| #20# . #48=($)) $ #49=(|Pattern| #20#) #47#) NIL (|has| #6# (|PatternMatchable| #20#)) ELT) ((#50=(|PatternMatchResult| #51=(|Float|) . #48#) $ #52=(|Pattern| #51#) #50#) NIL (|has| #6# (|PatternMatchable| #51#)) ELT)) (|opposite?| #1#) (|one?| #10#) (|numerator| #8#) (|numer| (#5# 22 T ELT)) (|nextItem| (#53=((|Maybe| $) $) NIL #54=(|has| #6# (|StepThrough|)) ELT)) (|negative?| #46#) (|multiEuclidean| (((|Union| #44# #13#) #44# $) NIL T ELT)) (|min| #55=(#33# NIL #56=(|has| #6# (|OrderedSet|)) ELT)) (|max| #55#) (|map| (($ #57=(|Mapping| #6# #6#) $) NIL T ELT)) (|limitPlus| (((|Union| (|OrderedCompletion| |#2|) #13#) $) 80 T ELT)) (|leftReducedSystem| ((#34# . #58=(#40#)) NIL #37# ELT) ((#38# . #59=(#40# $)) NIL #37# ELT) ((#41# . #59#) NIL T ELT) ((#42# . #58#) NIL T ELT)) (|lcm| #32# #60=(($ #44#) NIL T ELT)) (|latex| (((|String|) $) NIL T ELT)) (|inv| #8#) (|init| (#23# NIL #54# CONST)) (|hash| (((|SingleInteger|) $) NIL T ELT)) (|gcdPolynomial| ((#15# #15# #15#) NIL T ELT)) (|gcd| #32# #60#) (|fractionPart| (#9# NIL #7# ELT)) (|floor| #61=(#5# NIL #43# ELT)) (|factorSquareFreePolynomial| #14#) (|factorPolynomial| #14#) (|factor| #17#) (|extendedEuclidean| (((|Record| #62=(|:| |coef1| $) #63=(|:| |coef2| $) #45#) $ $) NIL T ELT) (((|Union| (|Record| #62# #63#) #13#) $ $ $) NIL T ELT)) (|exquo| #11#) (|expressIdealMember| (((|Maybe| #44#) #44# $) NIL T ELT)) (|eval| (($ $ #64=(|List| #6#) #64#) NIL #65=(|has| #6# (|Evalable| #6#)) ELT) (($ $ #6# #6#) NIL #65# ELT) (($ $ #66=(|Equation| #6#)) NIL #65# ELT) (($ $ (|List| #66#)) NIL #65# ELT) (($ $ #67=(|List| #26#) #64#) NIL #68=(|has| #6# (|InnerEvalable| #26# #6#)) ELT) (($ $ #26# #6#) NIL #68# ELT)) (|euclideanSize| ((#69=(|NonNegativeInteger|) $) NIL T ELT)) (|elt| (#70=($ $ #6#) NIL (|has| #6# (|Eltable| #6# #6#)) ELT)) (|divide| (((|Record| (|:| |quotient| $) (|:| |remainder| $)) $ $) NIL T ELT)) (|differentiate| #71=(($ $ #57#) NIL T ELT) #72=(($ $ #57# #69#) NIL T ELT) #73=(($ $ #26#) NIL #74=(|has| #6# (|PartialDifferentialSpace| #26#)) ELT) #75=(($ $ #67#) NIL #74# ELT) #76=(($ $ #26# #69#) NIL #74# ELT) #77=(($ $ #67# (|List| #69#)) NIL #74# ELT) #78=(#9# NIL #79=(|has| #6# (|DifferentialSpace|)) ELT) #80=(#81=($ $ #69#) NIL #79# ELT)) (|denominator| #8#) (|denom| (#5# 19 T ELT)) (|convert| ((#49# . #82=($)) NIL (|has| #6# (|ConvertibleTo| #49#)) ELT) ((#52# . #82#) NIL (|has| #6# (|ConvertibleTo| #52#)) ELT) ((#83=(|InputForm|) . #82#) NIL (|has| #6# (|ConvertibleTo| #83#)) ELT) ((#51# . #82#) NIL #84=(|has| #6# (|RealConstant|)) ELT) (((|DoubleFloat|) . #82#) NIL #84# ELT)) (|conditionP| (((|Union| #40# #13#) #36#) NIL #85=(AND (|has| $ #86=(|CharacteristicNonZero|)) #16#) ELT)) (|coerce| (((|OutputForm|) $) NIL T ELT) (($ #20#) NIL T ELT) #8# (($ #28#) NIL T ELT) (($ #6#) 30 T ELT) (($ #26#) NIL #27# ELT) (($ #30#) 37 T ELT)) (|charthRoot| (#53# NIL (OR #85# (|has| #6# #86#)) ELT)) (|characteristic| ((#69#) NIL T CONST)) (|ceiling| #61#) (|before?| #1#) (|associates?| #1#) (|annihilate?| #1#) (|abs| (#9# NIL #21# ELT)) (|Zero| #22#) (|One| #22#) (D #71# #72# #73# #75# #76# #77# #78# #80#) (>= #87=(#2# NIL #56# ELT)) (> #87#) (= #1#) (<= #87#) (< #87#) (/ (#33# 35 T ELT) (($ #6# #6#) 32 T ELT)) (- #8# #32#) (+ #32#) (** (($ $ #88=(|PositiveInteger|)) NIL T ELT) (#81# NIL T ELT) (($ $ #20#) NIL T ELT)) (* (($ #88# $) NIL T ELT) (($ #69# $) NIL T ELT) (($ #20# . #89=($)) NIL T ELT) #32# (($ $ #28#) NIL T ELT) (($ #28# . #89#) NIL T ELT) (($ #6# . #89#) 31 T ELT) (#70# NIL T ELT))) +((~= #1=(#2=(#3=(|Boolean|) $ $) NIL T ELT)) (|zero?| (#4=(#3# $) 60 T ELT)) (|wholePart| (#5=(#6=(|UnivariatePuiseuxSeriesWithExponentialSingularity| |#1| |#2| |#3| |#4|) $) NIL #7=(|has| #6# (|EuclideanDomain|)) ELT)) (|unitNormal| (((|Record| (|:| |unit| $) (|:| |canonical| $) (|:| |associate| $)) $) NIL T ELT)) (|unitCanonical| #8=(#9=($ $) NIL T ELT)) (|unit?| #10=(#4# NIL T ELT)) (|subtractIfCan| ((#11=(|Maybe| $) $ $) NIL T ELT)) (|squareFreePolynomial| #12=(((|Factored| #13=(|SparseUnivariatePolynomial| $)) #13#) NIL #14=(|has| #6# (|PolynomialFactorizationExplicit|)) ELT)) (|squareFreePart| #8#) (|squareFree| #15=(((|Factored| $) $) NIL T ELT)) (|solveLinearPolynomialEquation| (((|Union| #16=(|List| #13#) #17="failed") #16# #13#) NIL #14# ELT)) (|sizeLess?| #1#) (|sign| (#18=(#19=(|Integer|) $) NIL #20=(|has| #6# (|OrderedIntegralDomain|)) ELT)) (|sample| #21=(#22=($) NIL T CONST)) (|retractIfCan| (((|Union| #6# . #23=(#17#)) . #24=($)) NIL T ELT) (((|Union| #25=(|Symbol|) . #23#) . #24#) NIL #26=(|has| #6# (|RetractableTo| #25#)) ELT) (((|Union| #27=(|Fraction| #19#) . #23#) . #24#) NIL #28=(|has| #6# (|RetractableTo| #19#)) ELT) (((|Union| #19# . #23#) . #24#) NIL #28# ELT) (((|Union| #29=(|UnivariatePuiseuxSeries| |#2| |#3| |#4|) . #23#) $) 26 T ELT)) (|retract| (#5# NIL T ELT) ((#25# . #30=($)) NIL #26# ELT) ((#27# . #30#) NIL #28# ELT) (#18# NIL #28# ELT) ((#29# . #30#) NIL T ELT)) (|rem| #31=(#32=($ $ $) NIL T ELT)) (|reducedSystem| ((#33=(|Matrix| #19#) . #34=(#35=(|Matrix| $))) NIL #36=(|has| #6# (|LinearlyExplicitRingOver| #19#)) ELT) ((#37=(|Record| (|:| |mat| #33#) (|:| |vec| (|Vector| #19#))) . #38=(#35# #39=(|Vector| $))) NIL #36# ELT) ((#40=(|Record| (|:| |mat| #41=(|Matrix| #6#)) (|:| |vec| (|Vector| #6#))) . #38#) NIL T ELT) ((#41# . #34#) NIL T ELT)) (|recip| ((#42=(|Union| $ #17#) $) NIL T ELT)) (|random| (#22# NIL #43=(|has| #6# (|IntegerNumberSystem|)) ELT)) (|quo| #31#) (|principalIdeal| (((|Record| (|:| |coef| #44=(|List| $)) #45=(|:| |generator| $)) #44#) NIL T ELT)) (|prime?| #10#) (|positive?| #46=(#4# NIL #20# ELT)) (|patternMatch| ((#47=(|PatternMatchResult| #19# . #48=($)) $ #49=(|Pattern| #19#) #47#) NIL (|has| #6# (|PatternMatchable| #19#)) ELT) ((#50=(|PatternMatchResult| #51=(|Float|) . #48#) $ #52=(|Pattern| #51#) #50#) NIL (|has| #6# (|PatternMatchable| #51#)) ELT)) (|opposite?| #1#) (|one?| #10#) (|numerator| #8#) (|numer| (#5# 22 T ELT)) (|nextItem| (#53=(#11# $) NIL #54=(|has| #6# (|StepThrough|)) ELT)) (|negative?| #46#) (|multiEuclidean| (((|Union| #44# #17#) #44# $) NIL T ELT)) (|min| #55=(#32# NIL #56=(|has| #6# (|OrderedSet|)) ELT)) (|max| #55#) (|map| (($ #57=(|Mapping| #6# #6#) $) NIL T ELT)) (|limitPlus| (((|Union| (|OrderedCompletion| |#2|) #17#) $) 80 T ELT)) (|leftReducedSystem| ((#33# . #58=(#39#)) NIL #36# ELT) ((#37# . #59=(#39# $)) NIL #36# ELT) ((#40# . #59#) NIL T ELT) ((#41# . #58#) NIL T ELT)) (|lcm| #31# #60=(($ #44#) NIL T ELT)) (|latex| (((|String|) $) NIL T ELT)) (|inv| #8#) (|init| (#22# NIL #54# CONST)) (|hash| (((|SingleInteger|) $) NIL T ELT)) (|gcdPolynomial| ((#13# #13# #13#) NIL T ELT)) (|gcd| #31# #60#) (|fractionPart| (#9# NIL #7# ELT)) 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#6#) $) 365 T ELT)) (|univariate| (((|Fraction| #10#) $ #29=(|Kernel| $)) NIL #7# ELT)) (|unitNormal| (((|Record| (|:| |unit| $) (|:| |canonical| $) (|:| |associate| $)) $) NIL #7# ELT)) (|unitCanonical| #16#) (|unit?| #30=(#21# NIL #7# ELT)) (|tower| (#31=(#32=(|List| #29#) $) NIL T ELT)) (|tanh| (#17# 170 #7# ELT)) (|tan| (#17# 146 #7# ELT)) (|summation| (#33=($ $ (|SegmentBinding| $)) 231 #7# ELT) (#15# 227 #7# ELT)) (|subtractIfCan| ((#34=(|Maybe| $) $ $) NIL #35=(OR (|has| |#1| (|AbelianGroup|)) #24#) ELT)) (|subst| #36=(($ $ #37=(|Equation| $)) NIL T ELT) (#38=($ $ (|List| #37#)) 383 T ELT) (#39=($ $ #32# #5#) 438 T ELT)) (|squareFreePolynomial| (#40=((|Factored| #10#) #10#) 305 #41=(AND (|has| |#1| (|GcdDomain|)) #7#) ELT)) (|squareFreePart| #16#) (|squareFree| #42=((#43=(|Factored| $) $) NIL #7# ELT)) (|sqrt| #16#) (|sizeLess?| #44=(#2# NIL #7# ELT)) (|sinh| (#17# 166 #7# ELT)) (|sin| (#17# 142 #7# ELT)) (|simplifyPower| (#45=($ $ #25#) 68 #7# ELT)) (|sech| (#17# 174 #7# ELT)) 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ELT)) (|reducedSystem| ((#65=(|Record| (|:| |mat| #66=(|Matrix| |#1|)) (|:| |vec| (|Vector| |#1|))) #67=(|Matrix| $) #68=(|Vector| $)) 124 #26# ELT) ((#66# #67#) 114 #26# ELT) ((#69=(|Record| (|:| |mat| #70=(|Matrix| #25#)) (|:| |vec| (|Vector| #25#))) #67# #68#) NIL #24# ELT) ((#70# #67#) NIL #24# ELT)) (|reduce| (#17# 95 #7# ELT)) (|recip| ((#71=(|Union| $ #50#) $) NIL #47# ELT)) (|quo| #63#) (|product| (#33# 235 #7# ELT) (#15# 233 #7# ELT)) (|principalIdeal| (((|Record| (|:| |coef| #5#) #72=(|:| |generator| $)) #5#) NIL #7# ELT)) (|prime?| #30#) (|polygamma| (#64# 201 #7# ELT)) (|pi| (#46# 136 #7# ELT)) (|permutation| (#64# 221 #7# ELT)) (|patternMatch| ((#73=(|PatternMatchResult| #25# . #74=($)) $ #75=(|Pattern| #25#) #73#) 389 (|has| |#1| (|PatternMatchable| #25#)) ELT) ((#76=(|PatternMatchResult| #77=(|Float|) . #74#) $ #78=(|Pattern| #77#) #76#) 396 (|has| |#1| (|PatternMatchable| #77#)) ELT)) (|paren| #79=(#17# NIL T ELT) #80=(#81=($ #5#) NIL T ELT)) (|opposite?| (#2# NIL #22# ELT)) (|operators| ((#82=(|List| #83=(|BasicOperator|)) $) NIL T ELT)) (|operator| ((#83# #83#) 275 T ELT)) (|one?| (#21# 27 #47# ELT)) (|odd?| #84=(#21# NIL (|has| $ #55#) ELT)) (|numerator| (#17# 73 #26# ELT)) (|numer| (#85=(#86=(|SparseMultivariatePolynomial| |#1| #29#) $) 90 #26# ELT)) (|number?| (#21# 49 #7# ELT)) (|nthRoot| (#45# NIL #7# ELT)) (|multiEuclidean| ((#87=(|Union| #5# #50#) #5# $) NIL #7# ELT)) (|minPoly| ((#10# #29#) 276 #88=(|has| $ #27#) ELT)) (|map| (($ #89=(|Mapping| $ $) #29#) 434 T ELT)) (|mainKernel| (#48# NIL T ELT)) (|log| (#17# 140 #7# ELT)) (|li| (#17# 246 #7# ELT)) (|leftReducedSystem| ((#65# . #90=(#68# $)) NIL #26# ELT) ((#66# . #91=(#68#)) NIL #26# ELT) ((#69# . #90#) NIL #24# ELT) ((#70# . #91#) NIL #24# ELT)) (|lcm| #92=(#81# NIL #7# ELT) #63#) (|latex| (((|String|) $) NIL T ELT)) (|kernels| (#31# 51 T ELT)) (|kernel| #93=(($ #83# $) NIL T ELT) (#94=($ #83# #5#) 439 T ELT)) (|isTimes| (#95=(#87# $) NIL #47# ELT)) (|isPower| (((|Union| (|Record| (|:| |val| $) #96=(|:| |exponent| #25#)) #50#) $) NIL #26# ELT)) (|isPlus| (#95# 444 #23# ELT)) (|isMult| (((|Union| (|Record| (|:| |coef| #25#) #97=(|:| |var| #29#)) #50#) $) 448 #23# ELT)) (|isExpt| ((#98=(|Union| (|Record| #97# #96#) #50#) $) NIL #47# ELT) ((#98# $ #83#) NIL #26# ELT) ((#98# $ #6#) NIL #26# ELT)) (|is?| ((#3# $ #83#) NIL T ELT) (#99=(#3# $ #6#) 53 T ELT)) (|inv| (#17# NIL #100=(OR #101=(|has| |#1| (|Group|)) #7#) ELT)) (|integral| (#15# 250 #7# ELT) (#33# 252 #7# ELT)) (|height| (#102=(#103=(|NonNegativeInteger|) $) NIL T ELT)) (|hash| (((|SingleInteger|) $) NIL T ELT)) (|ground?| (#21# 45 T ELT)) (|ground| (#62# NIL T ELT)) (|gcdPolynomial| ((#10# #10# #10#) 298 #7# ELT)) (|gcd| #92# #63#) (|freeOf?| #1# (#99# NIL T ELT)) (|factorials| (#15# 225 #7# ELT) (#17# 223 #7# ELT)) (|factorial| (#17# 217 #7# ELT)) (|factorPolynomial| (#40# 303 #41# ELT)) (|factor| #42#) (|extendedEuclidean| (((|Union| (|Record| #104=(|:| |coef1| $) #105=(|:| |coef2| $)) #50#) $ $ $) NIL #7# ELT) (((|Record| #104# #105# #72#) $ $) NIL #7# ELT)) (|exquo| ((#71# $ $) NIL #7# ELT)) (|expressIdealMember| (((|Maybe| #5#) #5# $) NIL #7# ELT)) (|exp| (#17# 138 #7# ELT)) (|even?| #84#) (|eval| (($ $ #29# $) NIL T ELT) (#39# 433 T ELT) (#38# NIL T ELT) #36# (($ $ $ $) NIL T ELT) (($ $ #5# #5#) NIL T ELT) (($ $ #28# #106=(|List| #89#)) NIL T ELT) (($ $ #28# #107=(|List| #108=(|Mapping| $ #5#))) NIL T ELT) (($ $ #6# #108#) NIL T ELT) (($ $ #6# #89#) NIL T ELT) (($ $ #82# #106#) 376 T ELT) (($ $ #82# #107#) NIL T ELT) (($ $ #83# #108#) NIL T ELT) (($ $ #83# #89#) NIL T ELT) (#15# NIL #109=(|has| |#1| (|ConvertibleTo| #110=(|InputForm|))) ELT) (#111=($ $ #28#) NIL #109# ELT) (#17# NIL #109# ELT) (($ $ #83# $ #6#) 363 #109# ELT) (($ $ #82# #5# #6#) 362 #109# ELT) (($ $ #28# #112=(|List| #103#) #106#) NIL #26# ELT) (($ $ #28# #112# #107#) NIL #26# ELT) (($ $ #6# #103# #108#) NIL #26# ELT) (($ $ #6# #103# #89#) NIL #26# ELT)) (|euclideanSize| (#102# NIL #7# ELT)) (|erf| (#17# 238 #7# ELT)) (|elt| #93# (($ #83# $ $) NIL T ELT) (($ #83# $ $ $) NIL T ELT) (($ #83# $ $ $ $) NIL T ELT) (#94# NIL T ELT)) (|divide| (((|Record| (|:| |quotient| $) (|:| |remainder| $)) $ $) NIL #7# ELT)) (|distribute| #79# (#64# NIL T ELT)) (|dilog| (#17# 248 #7# ELT)) (|digamma| (#17# 199 #7# ELT)) (|differentiate| #113=(#15# NIL #26# ELT) #114=(#111# NIL #26# ELT) #115=(($ $ #6# #103#) NIL #26# ELT) #116=(($ $ #28# #112#) NIL #26# ELT)) (|denominator| (#17# 74 #7# ELT)) (|denom| (#85# 92 #7# ELT)) (|definingPolynomial| (#17# 314 #88# ELT)) (|csch| (#17# 176 #7# ELT)) (|csc| (#17# 152 #7# ELT)) (|coth| (#17# 172 #7# ELT)) (|cot| (#17# 148 #7# ELT)) (|cosh| (#17# 168 #7# ELT)) (|cos| (#17# 144 #7# ELT)) (|convert| ((#75# . #117=($)) NIL (|has| |#1| (|ConvertibleTo| #75#)) ELT) ((#78# . #117#) NIL (|has| |#1| (|ConvertibleTo| #78#)) ELT) (($ #43#) NIL #7# ELT) ((#110# $) 360 #109# ELT)) (|conjugate| #118=(#64# NIL #101# ELT)) (|commutator| #118#) (|coerce| (((|OutputForm|) $) 432 T ELT) (($ #29#) 423 T ELT) (($ #6#) 378 T ELT) (($ |#1|) 334 T ELT) #16# (($ #52#) 309 #53# ELT) (($ #86#) 94 #26# ELT) (($ #119=(|Fraction| |#1|)) NIL #7# ELT) (($ #120=(|Polynomial| #119#)) NIL #7# ELT) (($ (|Fraction| #120#)) NIL #7# ELT) (($ #56#) NIL #7# ELT) (($ #57#) NIL #26# ELT) (($ #25#) 36 (OR #54# #26#) ELT) (($ #58#) NIL (OR #7# #60#) ELT)) (|charthRoot| ((#34# $) NIL (|has| |#1| (|CharacteristicNonZero|)) ELT)) (|characteristic| ((#103#) NIL #26# CONST)) (|box| #79# #80#) (|binomial| (#64# 219 #7# ELT)) (|besselY| (#64# 205 #7# ELT)) (|besselK| (#64# 209 #7# ELT)) (|besselJ| (#64# 203 #7# ELT)) (|besselI| (#64# 207 #7# ELT)) (|belong?| ((#3# #83#) 10 T ELT)) (|before?| (#2# 85 T ELT)) (|atanh| (#17# 182 #7# ELT)) (|atan| (#17# 158 #7# ELT)) (|associates?| #44#) (|asinh| (#17# 178 #7# ELT)) (|asin| (#17# 154 #7# ELT)) (|asech| (#17# 186 #7# ELT)) (|asec| (#17# 162 #7# ELT)) (|applyQuote| (($ #6# $) NIL T ELT) (($ #6# $ $) NIL T ELT) (($ #6# $ $ $) NIL T ELT) (($ #6# $ $ $ $) NIL T ELT) (($ #6# #5#) NIL T ELT)) (|annihilate?| (#2# NIL #26# ELT)) (|airyBi| (#17# 213 #7# ELT)) (|airyAi| (#17# 211 #7# ELT)) (|acsch| (#17# 188 #7# ELT)) (|acsc| (#17# 164 #7# ELT)) (|acoth| (#17# 184 #7# ELT)) (|acot| (#17# 160 #7# ELT)) (|acosh| (#17# 180 #7# ELT)) (|acos| (#17# 156 #7# ELT)) (|abs| (#17# 191 #7# ELT)) (|Zero| (#46# 23 #22# CONST)) (|Si| (#17# 242 #7# ELT)) (|One| (#46# 25 #47# CONST)) (|Gamma| (#17# 193 #7# ELT) (#64# 195 #7# ELT)) (|Ei| (#17# 240 #7# ELT)) (D #113# #114# #115# #116#) (|Ci| (#17# 244 #7# ELT)) (|Beta| (#64# 197 #7# ELT)) (= (#2# 87 T ELT)) (/ (($ #86# #86#) 105 #7# ELT) (#64# 44 #100# ELT)) (- (#64# 42 #35# ELT) (#17# 31 #35# ELT)) (+ (#64# 40 #22# ELT)) (** (#64# 65 #7# ELT) (#121=($ $ #58#) 311 #7# ELT) (#45# 79 #100# ELT) (($ $ #103#) 75 #47# ELT) (($ $ #122=(|PositiveInteger|)) 83 #47# ELT)) (* (($ #58# . #123=($)) NIL #7# ELT) (#121# NIL #7# ELT) (($ $ |#1|) NIL (|has| |#1| (|CommutativeRing|)) ELT) (($ |#1| . #123#) NIL #26# ELT) (#64# 38 #47# ELT) (($ #25# $) 34 #35# ELT) (($ #103# $) NIL #22# ELT) (($ #122# $) NIL #22# ELT))) (((|Expression| |#1|) (|Join| (|FunctionSpace| |#1|) (CATEGORY |domain| (IF (|has| |#1| (|IntegralDomain|)) (PROGN (ATTRIBUTE (|AlgebraicallyClosedFunctionSpace| |#1|)) (ATTRIBUTE (|TranscendentalFunctionCategory|)) (ATTRIBUTE (|CombinatorialOpsCategory|)) (ATTRIBUTE (|LiouvillianFunctionCategory|)) (ATTRIBUTE (|SpecialFunctionCategory|)) (SIGNATURE |reduce| ($ $)) (SIGNATURE |number?| ((|Boolean|) $)) (SIGNATURE |simplifyPower| ($ $ #1=(|Integer|))) (IF (|has| |#1| (|GcdDomain|)) (PROGN (SIGNATURE |factorPolynomial| #2=((|Factored| #3=(|SparseUnivariatePolynomial| $)) #3#)) (SIGNATURE |squareFreePolynomial| #2#)) |%noBranch|) (IF (|has| |#1| (|RetractableTo| #1#)) (ATTRIBUTE (|RetractableTo| (|AlgebraicNumber|))) |%noBranch|)) |%noBranch|))) (|SetCategory|)) (T |Expression|)) ((|reduce| (*1 *1 *1) (AND (|isDomain| *1 (|Expression| *2)) (|ofCategory| *2 #1=(|IntegralDomain|)) (|ofCategory| *2 #2=(|SetCategory|)))) (|number?| (*1 *2 *1) (AND (|isDomain| *2 (|Boolean|)) #3=(|isDomain| *1 (|Expression| *3)) #4=(|ofCategory| *3 #1#) #5=(|ofCategory| *3 #2#))) (|simplifyPower| (*1 *1 *1 *2) (AND (|isDomain| *2 (|Integer|)) #3# #4# #5#)) (|factorPolynomial| #6=(*1 *2 *3) #7=(AND (|isDomain| *2 (|Factored| #8=(|SparseUnivariatePolynomial| *1))) (|isDomain| *1 (|Expression| *4)) (|isDomain| *3 #8#) (|ofCategory| *4 (|GcdDomain|)) (|ofCategory| *4 #1#) (|ofCategory| *4 #2#))) (|squareFreePolynomial| #6# #7#)) ((|map| (((|Expression| |#2|) (|Mapping| |#2| |#1|) (|Expression| |#1|)) 13 T ELT))) @@ -875,7 +875,7 @@ NIL ((|tubePlot| ((#1=(|TubePlot| (|Plot3D|)) #2=(|Expression| #3=(|Integer|)) #2# #2# #4=(|Mapping| #5=(|DoubleFloat|) #5#) #6=(|Segment| #5#) #5# #3# #7=(|String|)) 67 T ELT) ((#1# #2# #2# #2# #4# #6# #5# #3#) 68 T ELT) ((#1# #2# #2# #2# #4# #6# #4# #3# #7#) 64 T ELT) ((#1# #2# #2# #2# #4# #6# #4# #3#) 65 T ELT)) (|constantToUnaryFunction| ((#4# #5#) 66 T ELT))) (((|ExpressionTubePlot|) (CATEGORY |package| (SIGNATURE |constantToUnaryFunction| (#1=(|Mapping| #2=(|DoubleFloat|) #2#) #2#)) (SIGNATURE |tubePlot| (#3=(|TubePlot| (|Plot3D|)) #4=(|Expression| #5=(|Integer|)) #4# #4# #1# #6=(|Segment| #2#) #1# #5#)) (SIGNATURE |tubePlot| (#3# #4# #4# #4# #1# #6# #1# #5# #7=(|String|))) (SIGNATURE |tubePlot| (#3# #4# #4# #4# #1# #6# #2# #5#)) (SIGNATURE |tubePlot| (#3# #4# #4# #4# #1# #6# #2# #5# #7#)))) (T |ExpressionTubePlot|)) ((|tubePlot| (*1 *2 *3 *3 *3 *4 *5 *6 *7 *8) (AND #1=(|isDomain| *3 (|Expression| #2=(|Integer|))) #3=(|isDomain| *4 #4=(|Mapping| #5=(|DoubleFloat|) #5#)) #6=(|isDomain| *5 (|Segment| #5#)) #7=(|isDomain| *6 #5#) #8=(|isDomain| *7 #2#) (|isDomain| *8 #9=(|String|)) #10=(|isDomain| *2 (|TubePlot| (|Plot3D|))) #11=(|isDomain| *1 (|ExpressionTubePlot|)))) (|tubePlot| (*1 *2 *3 *3 *3 *4 *5 *6 *7) (AND #1# #3# #6# #7# #8# #10# #11#)) (|tubePlot| (*1 *2 *3 *3 *3 *4 *5 *4 *6 *7) (AND #1# #3# #6# #12=(|isDomain| *6 #2#) (|isDomain| *7 #9#) #10# #11#)) (|tubePlot| (*1 *2 *3 *3 *3 *4 *5 *4 *6) (AND #1# #3# #6# #12# #10# #11#)) (|constantToUnaryFunction| (*1 *2 *3) (AND (|isDomain| *2 #4#) #11# (|isDomain| *3 #5#)))) -((~= #1=(#2=(#3=(|Boolean|) $ $) NIL T ELT)) (|zero?| (#4=(#3# $) 26 T ELT)) (|variables| ((#5=(|List| #6=(|SingletonAsOrderedSet|)) $) NIL T ELT)) (|variable| ((#7=(|Symbol|) $) NIL T ELT)) (|unitNormal| (((|Record| (|:| |unit| $) (|:| |canonical| $) (|:| |associate| $)) $) NIL #8=(|has| |#1| (|IntegralDomain|)) ELT)) (|unitCanonical| #9=(#10=($ $) NIL #8# ELT)) (|unit?| (#4# NIL #8# ELT)) (|truncate| #11=(#12=($ $ #13=(|Fraction| #14=(|Integer|))) NIL T ELT) (($ $ #13# #13#) NIL T ELT)) (|terms| ((#15=(|Stream| (|Record| (|:| |k| #13#) (|:| |c| |#1|))) $) 20 T ELT)) (|tanh| #16=(#10# NIL #17=(|has| |#1| (|Algebra| #13#)) ELT)) (|tan| #16#) (|subtractIfCan| (#18=(#19=(|Union| $ #20="failed") $ $) NIL T ELT)) (|squareFreePart| #21=(#10# NIL #22=(|has| |#1| (|Field|)) ELT)) (|squareFree| #23=(((|Factored| $) $) NIL #22# ELT)) (|sqrt| #16#) (|sizeLess?| (#2# NIL #22# ELT)) (|sinh| #16#) (|sin| #16#) (|series| (($ #24=(|NonNegativeInteger|) #15#) NIL T ELT)) (|sech| #16#) (|sec| #16#) (|sample| #25=(#26=($) NIL T CONST)) (|rem| #27=(#28=($ $ $) NIL #22# ELT)) (|reductum| (#10# 36 T ELT)) (|recip| ((#19# $) NIL T ELT)) (|quo| #27#) (|principalIdeal| (((|Record| (|:| |coef| #29=(|List| $)) #30=(|:| |generator| $)) #29#) NIL #22# ELT)) (|prime?| (#4# NIL #22# ELT)) (|positive?| #31=(#4# NIL T ELT)) (|pole?| #31#) (|pi| (#26# NIL #17# ELT)) (|order| #32=(#33=(#13# $) NIL T ELT) ((#13# $ #13#) 16 T ELT)) (|opposite?| #1#) (|one?| #31#) (|nthRoot| (#34=($ $ #14#) NIL #17# ELT)) (|multiplyExponents| #35=(($ $ #36=(|PositiveInteger|)) NIL T ELT) #11#) (|multiEuclidean| (((|Union| #29# #20#) #29# $) NIL #22# ELT)) (|monomial?| #31#) (|monomial| (($ |#1| #13#) NIL T ELT) (($ $ #6# #13#) NIL T ELT) (($ $ #5# (|List| #13#)) NIL T ELT)) (|min| #37=(#28# NIL T ELT)) (|max| #37#) (|map| (($ (|Mapping| |#1| |#1|) $) NIL T ELT)) (|log| #16#) (|leadingMonomial| #38=(#10# NIL T ELT)) (|leadingCoefficient| #39=((|#1| $) NIL T ELT)) (|lcm| #40=(($ #29#) NIL #22# ELT) #27#) (|latex| (((|String|) $) NIL T ELT)) (|inv| #21#) (|integrate| #16# (#41=($ $ #7#) NIL (OR (AND #17# (|has| |#1| (|AlgebraicallyClosedFunctionSpace| #14#)) (|has| |#1| (|PrimitiveFunctionCategory|)) (|has| |#1| (|TranscendentalFunctionCategory|))) (AND #17# (|has| |#1| (SIGNATURE |integrate| (|#1| |#1| #7#))) (|has| |#1| (SIGNATURE |variables| (#42=(|List| #7#) |#1|))))) ELT)) (|hash| (((|SingleInteger|) $) NIL T ELT)) (|gcdPolynomial| ((#43=(|SparseUnivariatePolynomial| $) #43# #43#) NIL #22# ELT)) (|gcd| #40# #27#) (|factor| #23#) (|extendedEuclidean| (((|Union| (|Record| #44=(|:| |coef1| $) #45=(|:| |coef2| $)) #20#) $ $ $) NIL #22# ELT) (((|Record| #44# #45# #30#) $ $) NIL #22# ELT)) (|extend| #11#) (|exquo| (#18# NIL #8# ELT)) (|expressIdealMember| (((|Maybe| #29#) #29# $) NIL #22# ELT)) (|exponentialOrder| (#33# 17 T ELT)) (|exponential| (($ #46=(|UnivariatePuiseuxSeries| |#1| |#2| |#3|)) 11 T ELT)) (|exponent| ((#46# $) 12 T ELT)) (|exp| #16#) (|eval| (((|Stream| |#1|) $ |#1|) NIL #47=(|has| |#1| (SIGNATURE ** (|#1| |#1| #13#))) ELT)) (|euclideanSize| ((#24# $) NIL #22# ELT)) (|elt| (#48=(|#1| $ #13#) NIL T ELT) (#28# NIL (|has| #13# (|SemiGroup|)) ELT)) (|divide| (((|Record| (|:| |quotient| $) (|:| |remainder| $)) $ $) NIL #22# ELT)) (|differentiate| #49=(#41# NIL #50=(AND (|has| |#1| (|PartialDifferentialRing| #7#)) #51=(|has| |#1| (SIGNATURE * (|#1| #13# |#1|)))) ELT) #52=(($ $ #42#) NIL #50# ELT) #53=(($ $ #7# #24#) NIL #50# ELT) #54=(($ $ #42# (|List| #24#)) NIL #50# ELT) #55=(#10# NIL #51# ELT) #56=(#57=($ $ #24#) NIL #51# ELT)) (|degree| #32#) (|csch| #16#) (|csc| #16#) (|coth| #16#) (|cot| #16#) (|cosh| #16#) (|cos| #16#) (|complete| (#10# 10 T ELT)) (|coerce| (((|OutputForm|) $) 42 T ELT) (($ #14#) NIL T ELT) (($ |#1|) NIL (|has| |#1| (|CommutativeRing|)) ELT) (($ #13#) NIL #17# ELT) #9#) (|coefficient| (#48# 34 T ELT)) (|charthRoot| (((|Maybe| $) $) NIL (|has| |#1| (|CharacteristicNonZero|)) ELT)) (|characteristic| ((#24#) NIL T CONST)) (|center| #39#) (|before?| #1#) (|atanh| #16#) (|atan| #16#) (|associates?| (#2# NIL #8# ELT)) (|asinh| #16#) (|asin| #16#) (|asech| #16#) (|asec| #16#) (|approximate| (#48# NIL (AND #47# (|has| |#1| (SIGNATURE |coerce| (|#1| #7#)))) ELT)) (|annihilate?| #1#) (|acsch| #16#) (|acsc| #16#) (|acoth| #16#) (|acot| #16#) (|acosh| #16#) (|acos| #16#) (|Zero| #25#) (|One| #25#) (D #49# #52# #53# #54# #55# #56#) (>= #1#) (> #1#) (= (#2# 28 T ELT)) (<= #1#) (< (#2# 37 T ELT)) (/ (#58=($ $ |#1|) NIL #22# ELT) #27#) (- #38# #37#) (+ #37#) (** #35# (#57# NIL T ELT) (#34# NIL #22# ELT) (#28# NIL #17# ELT) #59=(#12# NIL #17# ELT)) (* (($ #36# $) NIL T ELT) (($ #24# $) NIL T ELT) (($ #14# . #60=($)) NIL T ELT) #37# (#58# NIL T ELT) (($ |#1| . #60#) NIL T ELT) (($ #13# . #60#) NIL #17# ELT) #59#)) +((~= #1=(#2=(#3=(|Boolean|) $ $) NIL T ELT)) (|zero?| (#4=(#3# $) 26 T ELT)) (|variables| ((#5=(|List| #6=(|SingletonAsOrderedSet|)) $) NIL T ELT)) (|variable| ((#7=(|Symbol|) $) NIL T ELT)) (|unitNormal| (((|Record| (|:| |unit| $) (|:| |canonical| $) (|:| |associate| $)) $) NIL #8=(|has| |#1| (|IntegralDomain|)) ELT)) (|unitCanonical| #9=(#10=($ $) NIL #8# ELT)) (|unit?| (#4# NIL #8# ELT)) (|truncate| #11=(#12=($ $ #13=(|Fraction| #14=(|Integer|))) NIL T ELT) (($ $ #13# #13#) NIL T ELT)) (|terms| ((#15=(|Stream| (|Record| (|:| |k| #13#) (|:| |c| |#1|))) $) 20 T ELT)) (|tanh| #16=(#10# NIL #17=(|has| |#1| (|Algebra| #13#)) ELT)) (|tan| #16#) (|subtractIfCan| ((#18=(|Maybe| $) $ $) NIL T ELT)) (|squareFreePart| #19=(#10# NIL #20=(|has| |#1| (|Field|)) ELT)) (|squareFree| #21=(((|Factored| $) $) NIL #20# ELT)) (|sqrt| #16#) (|sizeLess?| (#2# NIL #20# ELT)) (|sinh| #16#) (|sin| #16#) (|series| (($ #22=(|NonNegativeInteger|) #15#) NIL T ELT)) (|sech| #16#) (|sec| #16#) (|sample| #23=(#24=($) NIL T CONST)) (|rem| #25=(#26=($ $ $) NIL #20# ELT)) (|reductum| (#10# 36 T ELT)) (|recip| ((#27=(|Union| $ #28="failed") $) NIL T ELT)) (|quo| #25#) (|principalIdeal| (((|Record| (|:| |coef| #29=(|List| $)) #30=(|:| |generator| $)) #29#) NIL #20# ELT)) (|prime?| (#4# NIL #20# ELT)) (|positive?| #31=(#4# NIL T ELT)) (|pole?| #31#) (|pi| (#24# NIL #17# ELT)) (|order| #32=(#33=(#13# $) NIL T ELT) ((#13# $ #13#) 16 T ELT)) (|opposite?| #1#) (|one?| #31#) (|nthRoot| (#34=($ $ #14#) NIL #17# ELT)) (|multiplyExponents| #35=(($ $ #36=(|PositiveInteger|)) NIL T ELT) #11#) (|multiEuclidean| (((|Union| #29# #28#) #29# $) NIL #20# ELT)) (|monomial?| #31#) (|monomial| (($ |#1| #13#) NIL T ELT) (($ $ #6# #13#) NIL T ELT) (($ $ #5# (|List| #13#)) NIL T ELT)) (|min| #37=(#26# NIL T ELT)) (|max| #37#) (|map| (($ (|Mapping| |#1| |#1|) $) NIL T ELT)) (|log| #16#) (|leadingMonomial| #38=(#10# NIL T ELT)) (|leadingCoefficient| #39=((|#1| $) NIL T ELT)) (|lcm| #40=(($ #29#) NIL #20# ELT) #25#) (|latex| (((|String|) $) NIL T ELT)) (|inv| #19#) (|integrate| #16# (#41=($ $ #7#) NIL (OR (AND #17# (|has| |#1| (|AlgebraicallyClosedFunctionSpace| #14#)) (|has| |#1| (|PrimitiveFunctionCategory|)) (|has| |#1| (|TranscendentalFunctionCategory|))) (AND #17# (|has| |#1| (SIGNATURE |integrate| (|#1| |#1| #7#))) (|has| |#1| (SIGNATURE |variables| (#42=(|List| #7#) |#1|))))) ELT)) (|hash| (((|SingleInteger|) $) NIL T ELT)) (|gcdPolynomial| ((#43=(|SparseUnivariatePolynomial| $) #43# #43#) NIL #20# ELT)) (|gcd| #40# #25#) (|factor| #21#) (|extendedEuclidean| (((|Union| (|Record| #44=(|:| |coef1| $) #45=(|:| |coef2| $)) #28#) $ $ $) NIL #20# ELT) (((|Record| #44# #45# #30#) $ $) NIL #20# ELT)) (|extend| #11#) (|exquo| ((#27# $ $) NIL #8# ELT)) (|expressIdealMember| (((|Maybe| #29#) #29# $) NIL #20# ELT)) (|exponentialOrder| (#33# 17 T ELT)) (|exponential| (($ #46=(|UnivariatePuiseuxSeries| |#1| |#2| |#3|)) 11 T ELT)) (|exponent| ((#46# $) 12 T ELT)) (|exp| #16#) (|eval| (((|Stream| |#1|) $ |#1|) NIL #47=(|has| |#1| (SIGNATURE ** (|#1| |#1| #13#))) ELT)) (|euclideanSize| ((#22# $) NIL #20# ELT)) (|elt| (#48=(|#1| $ #13#) NIL T ELT) (#26# NIL (|has| #13# (|SemiGroup|)) ELT)) (|divide| (((|Record| (|:| |quotient| $) (|:| |remainder| $)) $ $) NIL #20# ELT)) (|differentiate| #49=(#41# NIL #50=(AND (|has| |#1| (|PartialDifferentialRing| #7#)) #51=(|has| |#1| (SIGNATURE * (|#1| #13# |#1|)))) ELT) #52=(($ $ #42#) NIL #50# ELT) #53=(($ $ #7# #22#) NIL #50# ELT) #54=(($ $ #42# (|List| #22#)) NIL #50# ELT) #55=(#10# NIL #51# ELT) #56=(#57=($ $ #22#) NIL #51# ELT)) (|degree| #32#) (|csch| #16#) (|csc| #16#) (|coth| #16#) (|cot| #16#) (|cosh| #16#) (|cos| #16#) (|complete| (#10# 10 T ELT)) (|coerce| (((|OutputForm|) $) 42 T ELT) (($ #14#) NIL T ELT) (($ |#1|) NIL (|has| |#1| (|CommutativeRing|)) ELT) (($ #13#) NIL #17# ELT) #9#) (|coefficient| (#48# 34 T ELT)) (|charthRoot| ((#18# $) NIL (|has| |#1| (|CharacteristicNonZero|)) ELT)) (|characteristic| ((#22#) NIL T CONST)) (|center| #39#) (|before?| #1#) (|atanh| #16#) (|atan| #16#) (|associates?| (#2# NIL #8# ELT)) (|asinh| #16#) (|asin| #16#) (|asech| #16#) (|asec| #16#) (|approximate| (#48# NIL (AND #47# (|has| |#1| (SIGNATURE |coerce| (|#1| #7#)))) ELT)) (|annihilate?| #1#) (|acsch| #16#) (|acsc| #16#) (|acoth| #16#) (|acot| #16#) (|acosh| #16#) (|acos| #16#) (|Zero| #23#) (|One| #23#) (D #49# #52# #53# #54# #55# #56#) (>= #1#) (> #1#) (= (#2# 28 T ELT)) (<= #1#) (< (#2# 37 T ELT)) (/ (#58=($ $ |#1|) NIL #20# ELT) #25#) (- #38# #37#) (+ #37#) (** #35# (#57# NIL T ELT) (#34# NIL #20# ELT) (#26# NIL #17# ELT) #59=(#12# NIL #17# ELT)) (* (($ #36# $) NIL T ELT) (($ #22# $) NIL T ELT) (($ #14# . #60=($)) NIL T ELT) #37# (#58# NIL T ELT) (($ |#1| . #60#) NIL T ELT) (($ #13# . #60#) NIL #17# ELT) #59#)) (((|ExponentialOfUnivariatePuiseuxSeries| |#1| |#2| |#3|) (|Join| (|UnivariatePuiseuxSeriesCategory| |#1|) (|OrderedAbelianMonoid|) (CATEGORY |domain| (SIGNATURE |exponential| ($ #1=(|UnivariatePuiseuxSeries| |#1| |#2| |#3|))) (SIGNATURE |exponent| (#1# $)) (SIGNATURE |exponentialOrder| ((|Fraction| (|Integer|)) $)))) (|Field|) (|Symbol|) |#1|) (T |ExponentialOfUnivariatePuiseuxSeries|)) ((|exponential| (*1 *1 *2) (AND #1=(|isDomain| *2 (|UnivariatePuiseuxSeries| *3 *4 *5)) #2=(|ofCategory| *3 (|Field|)) #3=(|ofType| *4 (|Symbol|)) #4=(|ofType| *5 *3) #5=(|isDomain| *1 (|ExponentialOfUnivariatePuiseuxSeries| *3 *4 *5)))) (|exponent| #6=(*1 *2 *1) (AND #1# #5# #2# #3# #4#)) (|exponentialOrder| #6# (AND (|isDomain| *2 (|Fraction| (|Integer|))) #5# #2# #3# #4#))) ((|nthRoot| (((|Record| (|:| |exponent| #1=(|NonNegativeInteger|)) (|:| |coef| |#1|) (|:| |radicand| (|List| |#1|))) #2=(|Factored| |#1|) #1#) 35 T ELT)) (|log| (((|List| (|Record| (|:| |coef| #1#) (|:| |logand| |#1|))) #2#) 40 T ELT))) @@ -884,21 +884,21 @@ NIL ((|variables| ((#1=(|List| |#2|) #2=(|SparseUnivariatePolynomial| |#4|)) 45 T ELT)) (|ran| ((|#3| #3=(|Integer|)) 48 T ELT)) (|raisePolynomial| ((#2# #4=(|SparseUnivariatePolynomial| |#3|)) 30 T ELT)) (|normalDeriv| ((#2# #2# #3#) 67 T ELT)) (|lowerPolynomial| ((#4# #2#) 21 T ELT)) (|degree| (((|List| (|NonNegativeInteger|)) #2# #1#) 41 T ELT)) (|completeEval| ((#4# #2# #1# (|List| |#3|)) 35 T ELT))) (((|FactoringUtilities| |#1| |#2| |#3| |#4|) (CATEGORY |package| (SIGNATURE |completeEval| (#1=(|SparseUnivariatePolynomial| |#3|) #2=(|SparseUnivariatePolynomial| |#4|) #3=(|List| |#2|) (|List| |#3|))) (SIGNATURE |degree| ((|List| (|NonNegativeInteger|)) #2# #3#)) (SIGNATURE |variables| (#3# #2#)) (SIGNATURE |lowerPolynomial| (#1# #2#)) (SIGNATURE |raisePolynomial| (#2# #1#)) (SIGNATURE |normalDeriv| (#2# #2# #4=(|Integer|))) (SIGNATURE |ran| (|#3| #4#))) (|OrderedAbelianMonoidSup|) (|OrderedSet|) (|Ring|) (|PolynomialCategory| |#3| |#1| |#2|)) (T |FactoringUtilities|)) ((|ran| #1=(*1 *2 *3) (AND #2=(|isDomain| *3 (|Integer|)) #3=(|ofCategory| *4 #4=(|OrderedAbelianMonoidSup|)) #5=(|ofCategory| *5 #6=(|OrderedSet|)) (|ofCategory| *2 #7=(|Ring|)) (|isDomain| *1 (|FactoringUtilities| *4 *5 *2 *6)) (|ofCategory| *6 (|PolynomialCategory| *2 *4 *5)))) (|normalDeriv| (*1 *2 *2 *3) (AND #8=(|isDomain| *2 #9=(|SparseUnivariatePolynomial| *7)) #2# #10=(|ofCategory| *7 (|PolynomialCategory| *6 *4 *5)) #3# #5# #11=(|ofCategory| *6 #7#) #12=(|isDomain| *1 (|FactoringUtilities| *4 *5 *6 *7)))) (|raisePolynomial| #1# (AND (|isDomain| *3 #13=(|SparseUnivariatePolynomial| *6)) #11# #3# #5# #8# #12# #10#)) (|lowerPolynomial| #1# (AND #14=(|isDomain| *3 #9#) #10# #3# #5# #11# (|isDomain| *2 #13#) #12#)) (|variables| #1# (AND #14# #10# #3# #5# #11# (|isDomain| *2 (|List| *5)) #12#)) (|degree| (*1 *2 *3 *4) (AND (|isDomain| *3 #15=(|SparseUnivariatePolynomial| *8)) (|isDomain| *4 (|List| *6)) (|ofCategory| *6 #6#) (|ofCategory| *8 (|PolynomialCategory| *7 *5 *6)) (|ofCategory| *5 #4#) (|ofCategory| *7 #7#) (|isDomain| *2 (|List| (|NonNegativeInteger|))) (|isDomain| *1 (|FactoringUtilities| *5 *6 *7 *8)))) (|completeEval| (*1 *2 *3 *4 *5) (AND (|isDomain| *3 (|SparseUnivariatePolynomial| *9)) (|isDomain| *4 (|List| *7)) (|isDomain| *5 (|List| *8)) (|ofCategory| *7 #6#) (|ofCategory| *8 #7#) (|ofCategory| *9 (|PolynomialCategory| *8 *6 *7)) (|ofCategory| *6 #4#) (|isDomain| *2 #15#) (|isDomain| *1 (|FactoringUtilities| *6 *7 *8 *9))))) -((~= #1=(#2=(#3=(|Boolean|) $ $) NIL T ELT)) (|zero?| ((#3# $) 19 T ELT)) (|terms| (((|List| (|Record| (|:| |gen| |#1|) (|:| |exp| #4=(|Integer|)))) $) 21 T ELT)) (|subtractIfCan| (((|Union| $ #5="failed") $ $) NIL T ELT)) (|size| ((#6=(|NonNegativeInteger|) $) NIL T ELT)) (|sample| #7=(($) NIL T CONST)) (|retractIfCan| (((|Union| |#1| #5#) $) NIL T ELT)) (|retract| ((|#1| $) NIL T ELT)) (|opposite?| #1#) (|nthFactor| ((|#1| $ #4#) NIL T ELT)) (|nthCoef| ((#4# $ #4#) NIL T ELT)) (|min| #8=(#9=($ $ $) NIL #10=(|has| |#1| (|OrderedSet|)) ELT)) (|max| #8#) (|mapGen| (($ (|Mapping| |#1| |#1|) $) NIL T ELT)) (|mapCoef| (($ (|Mapping| #4# #4#) $) 11 T ELT)) (|latex| (((|String|) $) NIL T ELT)) (|highCommonTerms| (#9# NIL (|has| #4# (|OrderedAbelianMonoid|)) ELT)) (|hash| (((|SingleInteger|) $) NIL T ELT)) (|coerce| (((|OutputForm|) $) NIL T ELT) (($ |#1|) NIL T ELT)) (|coefficient| ((#4# |#1| $) NIL T ELT)) (|before?| #1#) (|Zero| #7#) (>= #11=(#2# NIL #10# ELT)) (> #11#) (= #1#) (<= #11#) (< (#2# 30 #10# ELT)) (- (($ $) 12 T ELT) (#9# 29 T ELT)) (+ (#9# NIL T ELT) (($ |#1| $) NIL T ELT)) (* (($ (|PositiveInteger|) $) NIL T ELT) (($ #6# $) NIL T ELT) (($ #4# $) NIL T ELT) (($ $ #4#) NIL T ELT) (($ #4# |#1|) 28 T ELT))) +((~= #1=(#2=(#3=(|Boolean|) $ $) NIL T ELT)) (|zero?| ((#3# $) 19 T ELT)) (|terms| (((|List| (|Record| (|:| |gen| |#1|) (|:| |exp| #4=(|Integer|)))) $) 21 T ELT)) (|subtractIfCan| (((|Maybe| $) $ $) NIL T ELT)) (|size| ((#5=(|NonNegativeInteger|) $) NIL T ELT)) (|sample| #6=(($) NIL T CONST)) (|retractIfCan| (((|Union| |#1| "failed") $) NIL T ELT)) (|retract| ((|#1| $) NIL T ELT)) (|opposite?| #1#) (|nthFactor| ((|#1| $ #4#) NIL T ELT)) (|nthCoef| ((#4# $ #4#) NIL T ELT)) (|min| #7=(#8=($ $ $) NIL #9=(|has| |#1| (|OrderedSet|)) ELT)) (|max| #7#) (|mapGen| (($ (|Mapping| |#1| |#1|) $) NIL T ELT)) (|mapCoef| (($ (|Mapping| #4# #4#) $) 11 T ELT)) (|latex| (((|String|) $) NIL T ELT)) (|highCommonTerms| (#8# NIL (|has| #4# (|OrderedAbelianMonoid|)) ELT)) (|hash| (((|SingleInteger|) $) NIL T ELT)) (|coerce| (((|OutputForm|) $) NIL T ELT) (($ |#1|) NIL T ELT)) (|coefficient| ((#4# |#1| $) NIL T ELT)) (|before?| #1#) (|Zero| #6#) (>= #10=(#2# NIL #9# ELT)) (> #10#) (= #1#) (<= #10#) (< (#2# 30 #9# ELT)) (- (($ $) 12 T ELT) (#8# 29 T ELT)) (+ (#8# NIL T ELT) (($ |#1| $) NIL T ELT)) (* (($ (|PositiveInteger|) $) NIL T ELT) (($ #5# $) NIL T ELT) (($ #4# $) NIL T ELT) (($ $ #4#) NIL T ELT) (($ #4# |#1|) 28 T ELT))) (((|FreeAbelianGroup| |#1|) (|Join| (|AbelianGroup|) (|Module| #1=(|Integer|)) (|FreeAbelianMonoidCategory| |#1| #1#) (CATEGORY |package| (IF (|has| |#1| #2=(|OrderedSet|)) (ATTRIBUTE #2#) |%noBranch|))) (|SetCategory|)) (T |FreeAbelianGroup|)) NIL -((~= (#1=((|Boolean|) $ $) 7 T ELT)) (|zero?| ((#2=(|Boolean|) $) 22 T ELT)) (|terms| (((|List| (|Record| (|:| |gen| |#1|) (|:| |exp| |#2|))) $) 34 T ELT)) (|subtractIfCan| (((|Union| $ "failed") $ $) 26 T ELT)) (|size| (((|NonNegativeInteger|) $) 35 T ELT)) (|sample| (#3=($) 23 T CONST)) (|retractIfCan| (((|Union| |#1| "failed") $) 39 T ELT)) (|retract| ((|#1| $) 40 T ELT)) (|opposite?| ((#2# $ $) 20 T ELT)) (|nthFactor| ((|#1| $ (|Integer|)) 32 T ELT)) (|nthCoef| ((|#2| $ (|Integer|)) 33 T ELT)) (|mapGen| (($ (|Mapping| |#1| |#1|) $) 29 T ELT)) (|mapCoef| (($ (|Mapping| |#2| |#2|) $) 30 T ELT)) (|latex| (((|String|) $) 11 T ELT)) (|highCommonTerms| (($ $ $) 28 (|has| |#2| (|OrderedAbelianMonoid|)) ELT)) (|hash| (((|SingleInteger|) $) 12 T ELT)) (|coerce| (((|OutputForm|) $) 13 T ELT) (($ |#1|) 38 T ELT)) (|coefficient| ((|#2| |#1| $) 31 T ELT)) (|before?| (#1# 6 T ELT)) (|Zero| (#3# 24 T CONST)) (= (#1# 8 T ELT)) (+ (($ $ $) 18 T ELT) (($ |#1| $) 37 T ELT)) (* (($ (|PositiveInteger|) $) 17 T ELT) (($ (|NonNegativeInteger|) $) 21 T ELT) (($ |#2| |#1|) 36 T ELT))) +((~= (#1=((|Boolean|) $ $) 7 T ELT)) (|zero?| ((#2=(|Boolean|) $) 22 T ELT)) (|terms| (((|List| (|Record| (|:| |gen| |#1|) (|:| |exp| |#2|))) $) 35 T ELT)) (|subtractIfCan| (((|Maybe| $) $ $) 26 T ELT)) (|size| (((|NonNegativeInteger|) $) 36 T ELT)) (|sample| (#3=($) 23 T CONST)) (|retractIfCan| (((|Union| |#1| "failed") $) 40 T ELT)) (|retract| ((|#1| $) 41 T ELT)) (|opposite?| ((#2# $ $) 20 T ELT)) (|nthFactor| ((|#1| $ (|Integer|)) 33 T ELT)) (|nthCoef| ((|#2| $ (|Integer|)) 34 T ELT)) (|mapGen| (($ (|Mapping| |#1| |#1|) $) 30 T ELT)) (|mapCoef| (($ (|Mapping| |#2| |#2|) $) 31 T ELT)) (|latex| (((|String|) $) 11 T ELT)) (|highCommonTerms| (($ $ $) 29 (|has| |#2| (|OrderedAbelianMonoid|)) ELT)) (|hash| (((|SingleInteger|) $) 12 T ELT)) (|coerce| (((|OutputForm|) $) 13 T ELT) (($ |#1|) 39 T ELT)) (|coefficient| ((|#2| |#1| $) 32 T ELT)) (|before?| (#1# 6 T ELT)) (|Zero| (#3# 24 T CONST)) (= (#1# 8 T ELT)) (+ (($ $ $) 18 T ELT) (($ |#1| $) 38 T ELT)) (* (($ (|PositiveInteger|) $) 17 T ELT) (($ (|NonNegativeInteger|) $) 21 T ELT) (($ |#2| |#1|) 37 T ELT))) (((|FreeAbelianMonoidCategory| |#1| |#2|) (|Category|) (|SetCategory|) (|CancellationAbelianMonoid|)) (T |FreeAbelianMonoidCategory|)) ((+ (*1 *1 *2 *1) (AND (|ofCategory| *1 (|FreeAbelianMonoidCategory| *2 *3)) (|ofCategory| *2 (|SetCategory|)) (|ofCategory| *3 (|CancellationAbelianMonoid|)))) (* (*1 *1 *2 *3) (AND (|ofCategory| *1 (|FreeAbelianMonoidCategory| *3 *2)) (|ofCategory| *3 (|SetCategory|)) (|ofCategory| *2 (|CancellationAbelianMonoid|)))) (|size| (*1 *2 *1) (AND (|ofCategory| *1 (|FreeAbelianMonoidCategory| *3 *4)) (|ofCategory| *3 (|SetCategory|)) (|ofCategory| *4 (|CancellationAbelianMonoid|)) (|isDomain| *2 (|NonNegativeInteger|)))) (|terms| (*1 *2 *1) (AND (|ofCategory| *1 (|FreeAbelianMonoidCategory| *3 *4)) (|ofCategory| *3 (|SetCategory|)) (|ofCategory| *4 (|CancellationAbelianMonoid|)) (|isDomain| *2 (|List| (|Record| (|:| |gen| *3) (|:| |exp| *4)))))) (|nthCoef| (*1 *2 *1 *3) (AND (|isDomain| *3 (|Integer|)) (|ofCategory| *1 (|FreeAbelianMonoidCategory| *4 *2)) (|ofCategory| *4 (|SetCategory|)) (|ofCategory| *2 (|CancellationAbelianMonoid|)))) (|nthFactor| (*1 *2 *1 *3) (AND (|isDomain| *3 (|Integer|)) (|ofCategory| *1 (|FreeAbelianMonoidCategory| *2 *4)) (|ofCategory| *4 (|CancellationAbelianMonoid|)) (|ofCategory| *2 (|SetCategory|)))) (|coefficient| (*1 *2 *3 *1) (AND (|ofCategory| *1 (|FreeAbelianMonoidCategory| *3 *2)) (|ofCategory| *3 (|SetCategory|)) (|ofCategory| *2 (|CancellationAbelianMonoid|)))) (|mapCoef| (*1 *1 *2 *1) (AND (|isDomain| *2 (|Mapping| *4 *4)) (|ofCategory| *1 (|FreeAbelianMonoidCategory| *3 *4)) (|ofCategory| *3 (|SetCategory|)) (|ofCategory| *4 (|CancellationAbelianMonoid|)))) (|mapGen| (*1 *1 *2 *1) (AND (|isDomain| *2 (|Mapping| *3 *3)) (|ofCategory| *1 (|FreeAbelianMonoidCategory| *3 *4)) (|ofCategory| *3 (|SetCategory|)) (|ofCategory| *4 (|CancellationAbelianMonoid|)))) (|highCommonTerms| (*1 *1 *1 *1) (AND (|ofCategory| *1 (|FreeAbelianMonoidCategory| *2 *3)) (|ofCategory| *2 (|SetCategory|)) (|ofCategory| *3 (|CancellationAbelianMonoid|)) (|ofCategory| *3 (|OrderedAbelianMonoid|))))) (|Join| (|CancellationAbelianMonoid|) (|RetractableTo| |t#1|) (CATEGORY |domain| (SIGNATURE + ($ |t#1| $)) (SIGNATURE * ($ |t#2| |t#1|)) (SIGNATURE |size| ((|NonNegativeInteger|) $)) (SIGNATURE |terms| ((|List| (|Record| (|:| |gen| |t#1|) (|:| |exp| |t#2|))) $)) (SIGNATURE |nthCoef| (|t#2| $ (|Integer|))) (SIGNATURE |nthFactor| (|t#1| $ (|Integer|))) (SIGNATURE |coefficient| (|t#2| |t#1| $)) (SIGNATURE |mapCoef| ($ (|Mapping| |t#2| |t#2|) $)) (SIGNATURE |mapGen| ($ (|Mapping| |t#1| |t#1|) $)) (IF (|has| |t#2| (|OrderedAbelianMonoid|)) (SIGNATURE |highCommonTerms| ($ $ $)) |%noBranch|))) (((|AbelianMonoid|) . T) ((|AbelianSemiGroup|) . T) ((|BasicType|) . T) ((|CancellationAbelianMonoid|) . T) ((|CoercibleFrom| |#1|) . T) ((|CoercibleTo| (|OutputForm|)) . T) ((|Join|) . T) ((|RetractableTo| |#1|) . T) ((|SetCategory|) . T) ((|Type|) . T)) -((~= #1=((#2=(|Boolean|) $ $) NIL T ELT)) (|zero?| ((#2# $) NIL T ELT)) (|terms| (((|List| (|Record| (|:| |gen| |#1|) (|:| |exp| #3=(|NonNegativeInteger|)))) $) NIL T ELT)) (|subtractIfCan| (((|Union| $ #4="failed") $ $) NIL T ELT)) (|size| ((#3# $) NIL T ELT)) (|sample| #5=(($) NIL T CONST)) (|retractIfCan| (((|Union| |#1| #4#) $) NIL T ELT)) (|retract| ((|#1| $) NIL T ELT)) (|opposite?| #1#) (|nthFactor| ((|#1| $ #6=(|Integer|)) NIL T ELT)) (|nthCoef| ((#3# $ #6#) NIL T ELT)) (|mapGen| (($ (|Mapping| |#1| |#1|) $) NIL T ELT)) (|mapCoef| (($ (|Mapping| #3# #3#) $) NIL T ELT)) (|latex| (((|String|) $) NIL T ELT)) (|highCommonTerms| (#7=($ $ $) NIL (|has| #3# (|OrderedAbelianMonoid|)) ELT)) (|hash| (((|SingleInteger|) $) NIL T ELT)) (|coerce| (((|OutputForm|) $) NIL T ELT) (($ |#1|) NIL T ELT)) (|coefficient| ((#3# |#1| $) NIL T ELT)) (|before?| #1#) (|Zero| #5#) (= #1#) (+ (#7# NIL T ELT) (($ |#1| $) NIL T ELT)) (* (($ (|PositiveInteger|) $) NIL T ELT) (($ #3# $) NIL T ELT) (($ #3# |#1|) NIL T ELT))) +((~= #1=((#2=(|Boolean|) $ $) NIL T ELT)) (|zero?| ((#2# $) NIL T ELT)) (|terms| (((|List| (|Record| (|:| |gen| |#1|) (|:| |exp| #3=(|NonNegativeInteger|)))) $) NIL T ELT)) (|subtractIfCan| (((|Maybe| $) $ $) NIL T ELT)) (|size| ((#3# $) NIL T ELT)) (|sample| #4=(($) NIL T CONST)) (|retractIfCan| (((|Union| |#1| "failed") $) NIL T ELT)) (|retract| ((|#1| $) NIL T ELT)) (|opposite?| #1#) (|nthFactor| ((|#1| $ #5=(|Integer|)) NIL T ELT)) (|nthCoef| ((#3# $ #5#) NIL T ELT)) (|mapGen| (($ (|Mapping| |#1| |#1|) $) NIL T ELT)) (|mapCoef| (($ (|Mapping| #3# #3#) $) NIL T ELT)) (|latex| (((|String|) $) NIL T ELT)) (|highCommonTerms| (#6=($ $ $) NIL (|has| #3# (|OrderedAbelianMonoid|)) ELT)) (|hash| (((|SingleInteger|) $) NIL T ELT)) (|coerce| (((|OutputForm|) $) NIL T ELT) (($ |#1|) NIL T ELT)) (|coefficient| ((#3# |#1| $) NIL T ELT)) (|before?| #1#) (|Zero| #4#) (= #1#) (+ (#6# NIL T ELT) (($ |#1| $) NIL T ELT)) (* (($ (|PositiveInteger|) $) NIL T ELT) (($ #3# $) NIL T ELT) (($ #3# |#1|) NIL T ELT))) (((|FreeAbelianMonoid| |#1|) (|FreeAbelianMonoidCategory| |#1| (|NonNegativeInteger|)) (|SetCategory|)) (T |FreeAbelianMonoid|)) NIL ((|primitivePart| (($ $) 72 T ELT)) (|pomopo!| (($ $ |#2| |#3| $) 14 T ELT)) (|mapExponents| (($ (|Mapping| |#3| |#3|) $) 51 T ELT)) (|ground?| (((|Boolean|) $) 42 T ELT)) (|ground| (#1=(|#2| $) 44 T ELT)) (|exquo| ((#2=(|Union| $ "failed") $ $) NIL T ELT) ((#2# $ |#2|) 64 T ELT)) (|content| (#1# 68 T ELT)) (|coefficients| (((|List| |#2|) $) 56 T ELT)) (|binomThmExpt| (($ $ $ (|NonNegativeInteger|)) 37 T ELT)) (/ (($ $ |#2|) 60 T ELT))) (((|FiniteAbelianMonoidRing&| |#1| |#2| |#3|) (CATEGORY |package| (SIGNATURE |primitivePart| (|#1| |#1|)) (SIGNATURE |content| #1=(|#2| |#1|)) (SIGNATURE |exquo| (#2=(|Union| |#1| "failed") |#1| |#2|)) (SIGNATURE |binomThmExpt| (|#1| |#1| |#1| (|NonNegativeInteger|))) (SIGNATURE |pomopo!| (|#1| |#1| |#2| |#3| |#1|)) (SIGNATURE |mapExponents| (|#1| (|Mapping| |#3| |#3|) |#1|)) (SIGNATURE |coefficients| ((|List| |#2|) |#1|)) (SIGNATURE |ground| #1#) (SIGNATURE |ground?| ((|Boolean|) |#1|)) (SIGNATURE |exquo| (#2# |#1| |#1|)) (SIGNATURE / (|#1| |#1| |#2|))) (|FiniteAbelianMonoidRing| |#2| |#3|) (|Ring|) (|OrderedAbelianMonoid|)) (T |FiniteAbelianMonoidRing&|)) NIL -((~= (#1=((|Boolean|) $ $) 7 T ELT)) (|zero?| ((#2=(|Boolean|) $) 22 T ELT)) (|unitNormal| (((|Record| (|:| |unit| $) (|:| |canonical| $) (|:| |associate| $)) $) 72 (|has| |#1| . #3=((|IntegralDomain|))) ELT)) (|unitCanonical| (($ $) 73 (|has| |#1| . #3#) ELT)) (|unit?| ((#4=(|Boolean|) $) 75 (|has| |#1| . #3#) ELT)) (|subtractIfCan| (((|Union| $ "failed") $ $) 26 T ELT)) (|sample| (#5=($) 23 T CONST)) (|retractIfCan| (((|Union| #6=(|Integer|) . #7=("failed")) . #8=($)) 110 (|has| |#1| . #9=((|RetractableTo| #6#))) ELT) (((|Union| #10=(|Fraction| #6#) . #7#) . #8#) 108 (|has| |#1| . #11=((|RetractableTo| #10#))) ELT) (((|Union| |#1| . #7#) . #8#) 105 T ELT)) (|retract| ((#6# . #12=($)) 109 (|has| |#1| . #9#) ELT) ((#10# . #12#) 107 (|has| |#1| . #11#) ELT) ((|#1| . #12#) 106 T ELT)) (|reductum| (#13=($ $) 81 T ELT)) (|recip| (((|Union| $ "failed") $) 42 T ELT)) (|primitivePart| (($ $) 94 (|has| |#1| (|GcdDomain|)) ELT)) (|pomopo!| (($ $ |#1| |#2| $) 98 T ELT)) (|opposite?| ((#2# $ $) 20 T ELT)) (|one?| (((|Boolean|) $) 44 T ELT)) (|numberOfMonomials| (((|NonNegativeInteger|) $) 101 T ELT)) (|monomial?| (((|Boolean|) $) 83 T ELT)) (|monomial| (($ |#1| |#2|) 82 T ELT)) (|minimumDegree| ((|#2| $) 100 T ELT)) (|mapExponents| (($ (|Mapping| |#2| |#2|) $) 99 T ELT)) (|map| (($ (|Mapping| |#1| |#1|) $) 87 T ELT)) (|leadingMonomial| (#13# 85 T ELT)) (|leadingCoefficient| ((|#1| $) 86 T ELT)) (|latex| (((|String|) $) 11 T ELT)) (|hash| (((|SingleInteger|) $) 12 T ELT)) (|ground?| (((|Boolean|) $) 104 T ELT)) (|ground| ((|#1| $) 103 T ELT)) (|exquo| (((|Union| $ "failed") $ $) 71 (|has| |#1| . #3#) ELT) (((|Union| $ "failed") $ |#1|) 96 (|has| |#1| (|IntegralDomain|)) ELT)) (|degree| ((|#2| $) 84 T ELT)) (|content| ((|#1| $) 95 (|has| |#1| (|GcdDomain|)) ELT)) (|coerce| (((|OutputForm|) $) 13 T ELT) (($ (|Integer|)) 41 T ELT) (($ $) 70 (|has| |#1| . #3#) ELT) (($ |#1|) 68 T ELT) (($ #14=(|Fraction| (|Integer|))) 78 (OR (|has| |#1| . #11#) (|has| |#1| . #15=((|Algebra| #14#)))) ELT)) (|coefficients| (((|List| |#1|) $) 102 T ELT)) (|coefficient| ((|#1| $ |#2|) 80 T ELT)) (|charthRoot| (((|Maybe| $) $) 69 (|has| |#1| (|CharacteristicNonZero|)) ELT)) (|characteristic| (((|NonNegativeInteger|)) 40 T CONST)) (|binomThmExpt| (($ $ $ (|NonNegativeInteger|)) 97 (|has| |#1| (|CommutativeRing|)) ELT)) (|before?| (#1# 6 T ELT)) (|associates?| ((#4# $ $) 74 (|has| |#1| . #3#) ELT)) (|annihilate?| (((|Boolean|) $ $) 33 T ELT)) (|Zero| (#5# 24 T CONST)) (|One| (($) 45 T CONST)) (= (#1# 8 T ELT)) (/ (($ $ |#1|) 79 (|has| |#1| (|Field|)) ELT)) (- (($ $) 29 T ELT) (($ $ $) 28 T ELT)) (+ (($ $ $) 18 T ELT)) (** (($ $ (|PositiveInteger|)) 35 T ELT) (($ $ (|NonNegativeInteger|)) 43 T ELT)) (* (($ (|PositiveInteger|) $) 17 T ELT) (($ (|NonNegativeInteger|) $) 21 T ELT) (($ (|Integer|) . #16=($)) 30 T ELT) (($ $ $) 34 T ELT) (($ $ |#1|) 89 T ELT) (($ |#1| . #16#) 88 T ELT) (($ #14# . #16#) 77 (|has| |#1| . #15#) ELT) (($ $ #14#) 76 (|has| |#1| . #15#) ELT))) +((~= (#1=((|Boolean|) $ $) 7 T ELT)) (|zero?| ((#2=(|Boolean|) $) 22 T ELT)) (|unitNormal| (((|Record| (|:| |unit| $) (|:| |canonical| $) (|:| |associate| $)) $) 73 (|has| |#1| . #3=((|IntegralDomain|))) ELT)) (|unitCanonical| (($ $) 74 (|has| |#1| . #3#) ELT)) (|unit?| ((#4=(|Boolean|) $) 76 (|has| |#1| . #3#) ELT)) (|subtractIfCan| (((|Maybe| $) $ $) 26 T ELT)) (|sample| (#5=($) 23 T CONST)) (|retractIfCan| (((|Union| #6=(|Integer|) . #7=("failed")) . #8=($)) 110 (|has| |#1| . #9=((|RetractableTo| #6#))) ELT) (((|Union| #10=(|Fraction| #6#) . #7#) . #8#) 108 (|has| |#1| . #11=((|RetractableTo| #10#))) ELT) (((|Union| |#1| . #7#) . #8#) 105 T ELT)) (|retract| ((#6# . #12=($)) 109 (|has| |#1| . #9#) ELT) ((#10# . #12#) 107 (|has| |#1| . #11#) ELT) ((|#1| . #12#) 106 T ELT)) (|reductum| (#13=($ $) 82 T ELT)) (|recip| (((|Union| $ "failed") $) 43 T ELT)) (|primitivePart| (($ $) 94 (|has| |#1| (|GcdDomain|)) ELT)) (|pomopo!| (($ $ |#1| |#2| $) 98 T ELT)) (|opposite?| ((#2# $ $) 20 T ELT)) (|one?| (((|Boolean|) $) 45 T ELT)) (|numberOfMonomials| (((|NonNegativeInteger|) $) 101 T ELT)) (|monomial?| (((|Boolean|) $) 84 T ELT)) (|monomial| (($ |#1| |#2|) 83 T ELT)) (|minimumDegree| ((|#2| $) 100 T ELT)) (|mapExponents| (($ (|Mapping| |#2| |#2|) $) 99 T ELT)) (|map| (($ (|Mapping| |#1| |#1|) $) 88 T ELT)) (|leadingMonomial| (#13# 86 T ELT)) (|leadingCoefficient| ((|#1| $) 87 T ELT)) (|latex| (((|String|) $) 11 T ELT)) (|hash| (((|SingleInteger|) $) 12 T ELT)) (|ground?| (((|Boolean|) $) 104 T ELT)) (|ground| ((|#1| $) 103 T ELT)) (|exquo| (((|Union| $ "failed") $ $) 72 (|has| |#1| . #3#) ELT) (((|Union| $ "failed") $ |#1|) 96 (|has| |#1| (|IntegralDomain|)) ELT)) (|degree| ((|#2| $) 85 T ELT)) (|content| ((|#1| $) 95 (|has| |#1| (|GcdDomain|)) ELT)) (|coerce| (((|OutputForm|) $) 13 T ELT) (($ (|Integer|)) 42 T ELT) (($ $) 71 (|has| |#1| . #3#) ELT) (($ |#1|) 69 T ELT) (($ #14=(|Fraction| (|Integer|))) 79 (OR (|has| |#1| . #11#) (|has| |#1| . #15=((|Algebra| #14#)))) ELT)) (|coefficients| (((|List| |#1|) $) 102 T ELT)) (|coefficient| ((|#1| $ |#2|) 81 T ELT)) (|charthRoot| (((|Maybe| $) $) 70 (|has| |#1| (|CharacteristicNonZero|)) ELT)) (|characteristic| (((|NonNegativeInteger|)) 41 T CONST)) (|binomThmExpt| (($ $ $ (|NonNegativeInteger|)) 97 (|has| |#1| (|CommutativeRing|)) ELT)) (|before?| (#1# 6 T ELT)) (|associates?| ((#4# $ $) 75 (|has| |#1| . #3#) ELT)) (|annihilate?| (((|Boolean|) $ $) 34 T ELT)) (|Zero| (#5# 24 T CONST)) (|One| (($) 46 T CONST)) (= (#1# 8 T ELT)) (/ (($ $ |#1|) 80 (|has| |#1| (|Field|)) ELT)) (- (($ $) 30 T ELT) (($ $ $) 29 T ELT)) (+ (($ $ $) 18 T ELT)) (** (($ $ (|PositiveInteger|)) 36 T ELT) (($ $ (|NonNegativeInteger|)) 44 T ELT)) (* (($ (|PositiveInteger|) $) 17 T ELT) (($ (|NonNegativeInteger|) $) 21 T ELT) (($ (|Integer|) . #16=($)) 31 T ELT) (($ $ $) 35 T ELT) (($ $ |#1|) 90 T ELT) (($ |#1| . #16#) 89 T ELT) (($ #14# . #16#) 78 (|has| |#1| . #15#) ELT) (($ $ #14#) 77 (|has| |#1| . #15#) ELT))) (((|FiniteAbelianMonoidRing| |#1| |#2|) (|Category|) (|Ring|) (|OrderedAbelianMonoid|)) (T |FiniteAbelianMonoidRing|)) ((|ground?| (*1 *2 *1) (AND (|ofCategory| *1 (|FiniteAbelianMonoidRing| *3 *4)) (|ofCategory| *3 (|Ring|)) (|ofCategory| *4 (|OrderedAbelianMonoid|)) (|isDomain| *2 (|Boolean|)))) (|ground| (*1 *2 *1) (AND (|ofCategory| *1 (|FiniteAbelianMonoidRing| *2 *3)) (|ofCategory| *3 (|OrderedAbelianMonoid|)) (|ofCategory| *2 (|Ring|)))) (|coefficients| (*1 *2 *1) (AND (|ofCategory| *1 (|FiniteAbelianMonoidRing| *3 *4)) (|ofCategory| *3 (|Ring|)) (|ofCategory| *4 (|OrderedAbelianMonoid|)) (|isDomain| *2 (|List| *3)))) (|numberOfMonomials| (*1 *2 *1) (AND (|ofCategory| *1 (|FiniteAbelianMonoidRing| *3 *4)) (|ofCategory| *3 (|Ring|)) (|ofCategory| *4 (|OrderedAbelianMonoid|)) (|isDomain| *2 (|NonNegativeInteger|)))) (|minimumDegree| (*1 *2 *1) (AND (|ofCategory| *1 (|FiniteAbelianMonoidRing| *3 *2)) (|ofCategory| *3 (|Ring|)) (|ofCategory| *2 (|OrderedAbelianMonoid|)))) (|mapExponents| (*1 *1 *2 *1) (AND (|isDomain| *2 (|Mapping| *4 *4)) (|ofCategory| *1 (|FiniteAbelianMonoidRing| *3 *4)) (|ofCategory| *3 (|Ring|)) (|ofCategory| *4 (|OrderedAbelianMonoid|)))) (|pomopo!| (*1 *1 *1 *2 *3 *1) (AND (|ofCategory| *1 (|FiniteAbelianMonoidRing| *2 *3)) (|ofCategory| *2 (|Ring|)) (|ofCategory| *3 (|OrderedAbelianMonoid|)))) (|binomThmExpt| (*1 *1 *1 *1 *2) (AND (|isDomain| *2 (|NonNegativeInteger|)) (|ofCategory| *1 (|FiniteAbelianMonoidRing| *3 *4)) (|ofCategory| *3 (|Ring|)) (|ofCategory| *4 (|OrderedAbelianMonoid|)) (|ofCategory| *3 (|CommutativeRing|)))) (|exquo| (*1 *1 *1 *2) (|partial| AND (|ofCategory| *1 (|FiniteAbelianMonoidRing| *2 *3)) (|ofCategory| *2 (|Ring|)) (|ofCategory| *3 (|OrderedAbelianMonoid|)) (|ofCategory| *2 (|IntegralDomain|)))) (|content| (*1 *2 *1) (AND (|ofCategory| *1 (|FiniteAbelianMonoidRing| *2 *3)) (|ofCategory| *3 (|OrderedAbelianMonoid|)) (|ofCategory| *2 (|Ring|)) (|ofCategory| *2 (|GcdDomain|)))) (|primitivePart| (*1 *1 *1) (AND (|ofCategory| *1 (|FiniteAbelianMonoidRing| *2 *3)) (|ofCategory| *2 (|Ring|)) (|ofCategory| *3 (|OrderedAbelianMonoid|)) (|ofCategory| *2 (|GcdDomain|))))) (|Join| (|AbelianMonoidRing| |t#1| |t#2|) (|FullyRetractableTo| |t#1|) (CATEGORY |domain| (SIGNATURE |ground?| ((|Boolean|) $)) (SIGNATURE |ground| (|t#1| $)) (SIGNATURE |coefficients| ((|List| |t#1|) $)) (SIGNATURE |numberOfMonomials| ((|NonNegativeInteger|) $)) (SIGNATURE |minimumDegree| (|t#2| $)) (SIGNATURE |mapExponents| ($ (|Mapping| |t#2| |t#2|) $)) (SIGNATURE |pomopo!| ($ $ |t#1| |t#2| $)) (IF (|has| |t#1| (|CommutativeRing|)) (SIGNATURE |binomThmExpt| ($ $ $ (|NonNegativeInteger|))) |%noBranch|) (IF (|has| |t#1| (|IntegralDomain|)) (SIGNATURE |exquo| ((|Union| $ "failed") $ |t#1|)) |%noBranch|) (IF (|has| |t#1| (|GcdDomain|)) (PROGN (SIGNATURE |content| (|t#1| $)) (SIGNATURE |primitivePart| ($ $))) |%noBranch|))) @@ -909,7 +909,7 @@ NIL ((|transcendent?| (#1=((|Boolean|) $) 47 T ELT)) (|transcendenceDegree| (#2=((|NonNegativeInteger|)) 23 T ELT)) (|trace| (#3=(|#2| $) 51 T ELT) (#4=($ $ #5=(|PositiveInteger|)) 123 T ELT)) (|size| (#2# 124 T ELT)) (|represents| (($ #6=(|Vector| |#2|)) 20 T ELT)) (|normal?| (#1# 136 T ELT)) (|norm| (#3# 53 T ELT) (#4# 120 T ELT)) (|minimalPolynomial| (#7=(#8=(|SparseUnivariatePolynomial| |#2|) $) NIL T ELT) (((|SparseUnivariatePolynomial| $) $ #5#) 111 T ELT)) (|linearAssociatedOrder| (#7# 95 T ELT)) (|linearAssociatedLog| (#7# 91 T ELT) (((|Union| #8# "failed") $ $) 88 T ELT)) (|linearAssociatedExp| (($ $ #8#) 58 T ELT)) (|extensionDegree| ((#9=(|OnePointCompletion| #5#)) 30 T ELT) ((#5#) 48 T ELT)) (|dimension| (((|CardinalNumber|)) 27 T ELT)) (|degree| ((#9# $) 32 T ELT) ((#5# $) 139 T ELT)) (|createNormalElement| (($) 130 T ELT)) (|coordinates| ((#6# $) NIL T ELT) (((|Matrix| |#2|) (|Vector| $)) 42 T ELT)) (|charthRoot| (($ $) NIL T ELT) (((|Maybe| $) $) 100 T ELT)) (|algebraic?| (#1# 45 T ELT))) (((|FiniteAlgebraicExtensionField&| |#1| |#2|) (CATEGORY |package| (SIGNATURE |charthRoot| ((|Maybe| |#1|) |#1|)) (SIGNATURE |size| #1=((|NonNegativeInteger|))) (SIGNATURE |charthRoot| (|#1| |#1|)) (SIGNATURE |linearAssociatedLog| ((|Union| #2=(|SparseUnivariatePolynomial| |#2|) "failed") |#1| |#1|)) (SIGNATURE |linearAssociatedLog| #3=(#2# |#1|)) (SIGNATURE |linearAssociatedOrder| #3#) (SIGNATURE |linearAssociatedExp| (|#1| |#1| #2#)) (SIGNATURE |normal?| #4=((|Boolean|) |#1|)) (SIGNATURE |createNormalElement| (|#1|)) (SIGNATURE |trace| #5=(|#1| |#1| #6=(|PositiveInteger|))) (SIGNATURE |norm| #5#) (SIGNATURE |minimalPolynomial| ((|SparseUnivariatePolynomial| |#1|) |#1| #6#)) (SIGNATURE |trace| #7=(|#2| |#1|)) (SIGNATURE |norm| #7#) (SIGNATURE |degree| (#6# |#1|)) (SIGNATURE |extensionDegree| (#6#)) (SIGNATURE |minimalPolynomial| #3#) (SIGNATURE |represents| (|#1| #8=(|Vector| |#2|))) (SIGNATURE |coordinates| ((|Matrix| |#2|) (|Vector| |#1|))) (SIGNATURE |coordinates| (#8# |#1|)) (SIGNATURE |transcendenceDegree| #1#) (SIGNATURE |extensionDegree| (#9=(|OnePointCompletion| #6#))) (SIGNATURE |degree| (#9# |#1|)) (SIGNATURE |transcendent?| #4#) (SIGNATURE |algebraic?| #4#) (SIGNATURE |dimension| ((|CardinalNumber|)))) (|FiniteAlgebraicExtensionField| |#2|) (|Field|)) (T |FiniteAlgebraicExtensionField&|)) ((|dimension| #1=(*1 *2) (AND #2=(|ofCategory| *4 (|Field|)) (|isDomain| *2 (|CardinalNumber|)) #3=(|isDomain| *1 (|FiniteAlgebraicExtensionField&| *3 *4)) #4=(|ofCategory| *3 (|FiniteAlgebraicExtensionField| *4)))) (|extensionDegree| #1# (AND #2# (|isDomain| *2 (|OnePointCompletion| #5=(|PositiveInteger|))) #3# #4#)) (|transcendenceDegree| #1# #6=(AND #2# (|isDomain| *2 (|NonNegativeInteger|)) #3# #4#)) (|extensionDegree| #1# (AND #2# (|isDomain| *2 #5#) #3# #4#)) (|size| #1# #6#)) -((~= (#1=((|Boolean|) $ $) 7 T ELT)) (|zero?| ((#2=(|Boolean|) $) 22 T ELT)) (|unitNormal| (((|Record| (|:| |unit| $) (|:| |canonical| $) (|:| |associate| $)) $) 55 T ELT)) (|unitCanonical| (($ $) 54 T ELT)) (|unit?| ((#3=(|Boolean|) $) 52 T ELT)) (|transcendent?| (#4=((|Boolean|) $) 114 T ELT)) (|transcendenceDegree| ((#5=(|NonNegativeInteger|)) 110 T ELT)) (|trace| ((|#1| $) 162 T ELT) (($ $ (|PositiveInteger|)) 159 (|has| |#1| (|Finite|)) ELT)) (|tableForDiscreteLogarithm| (((|Table| #6=(|PositiveInteger|) #7=(|NonNegativeInteger|)) #8=(|Integer|)) 144 (|has| |#1| . #9=((|Finite|))) ELT)) (|subtractIfCan| (((|Union| $ "failed") $ $) 26 T ELT)) (|squareFreePart| (($ $) 91 T ELT)) (|squareFree| (#10=((|Factored| $) $) 90 T ELT)) (|sizeLess?| (((|Boolean|) $ $) 75 T ELT)) (|size| (((|NonNegativeInteger|)) 134 (|has| |#1| . #9#) ELT)) (|sample| (#11=($) 23 T CONST)) (|retractIfCan| (((|Union| |#1| "failed") $) 121 T ELT)) (|retract| ((|#1| $) 122 T ELT)) (|represents| (($ (|Vector| |#1|)) 168 T ELT)) (|representationType| (((|Union| "prime" "polynomial" "normal" "cyclic")) 150 (|has| |#1| . #9#) ELT)) (|rem| (#12=($ $ $) 71 T ELT)) (|recip| (((|Union| $ "failed") $) 42 T ELT)) (|random| (($) 131 (|has| |#1| . #9#) ELT)) (|quo| (#12# 72 T ELT)) (|principalIdeal| (((|Record| (|:| |coef| #13=(|List| $)) (|:| |generator| $)) #13#) 66 T ELT)) (|primitiveElement| (#14=($) 146 (|has| |#1| . #9#) ELT)) (|primitive?| (((|Boolean|) $) 147 (|has| |#1| . #9#) ELT)) (|primeFrobenius| (($ $ #15=(|NonNegativeInteger|)) 107 (OR (|has| |#1| . #16=((|CharacteristicNonZero|))) (|has| |#1| . #17=((|Finite|)))) ELT) (($ $) 106 (OR (|has| |#1| . #16#) (|has| |#1| . #17#)) ELT)) (|prime?| (((|Boolean|) $) 89 T ELT)) (|order| ((#6# $) 149 (|has| |#1| . #9#) ELT) (((|OnePointCompletion| (|PositiveInteger|)) $) 104 (OR (|has| |#1| . #16#) (|has| |#1| . #17#)) ELT)) (|opposite?| ((#2# $ $) 20 T ELT)) (|one?| (((|Boolean|) $) 44 T ELT)) (|normalElement| (($) 157 (|has| |#1| (|Finite|)) ELT)) (|normal?| (((|Boolean|) $) 156 (|has| |#1| (|Finite|)) ELT)) (|norm| ((|#1| $) 163 T ELT) (($ $ (|PositiveInteger|)) 160 (|has| |#1| (|Finite|)) ELT)) (|nextItem| (((|Maybe| $) $) 135 (|has| |#1| . #9#) ELT)) (|multiEuclidean| (((|Union| #18=(|List| $) #19="failed") #18# $) 68 T ELT)) (|minimalPolynomial| (((|SparseUnivariatePolynomial| |#1|) $) 167 T ELT) (((|SparseUnivariatePolynomial| $) $ (|PositiveInteger|)) 161 (|has| |#1| (|Finite|)) ELT)) (|lookup| ((#20=(|PositiveInteger|) $) 132 (|has| |#1| . #9#) ELT)) (|linearAssociatedOrder| (((|SparseUnivariatePolynomial| |#1|) $) 153 (|has| |#1| (|Finite|)) ELT)) (|linearAssociatedLog| (((|SparseUnivariatePolynomial| |#1|) $) 152 (|has| |#1| (|Finite|)) ELT) (((|Union| (|SparseUnivariatePolynomial| |#1|) "failed") $ $) 151 (|has| |#1| (|Finite|)) ELT)) (|linearAssociatedExp| (($ $ (|SparseUnivariatePolynomial| |#1|)) 154 (|has| |#1| (|Finite|)) ELT)) (|lcm| (#21=($ $ $) 60 T ELT) (#22=($ (|List| $)) 59 T ELT)) (|latex| (((|String|) $) 11 T ELT)) (|inv| (($ $) 88 T ELT)) (|init| (($) 136 (|has| |#1| . #9#) CONST)) (|index| (($ #20#) 133 (|has| |#1| . #9#) ELT)) (|inGroundField?| (#4# 113 T ELT)) (|hash| (((|SingleInteger|) $) 12 T ELT)) (|generator| (($) 155 (|has| |#1| (|Finite|)) ELT)) (|gcdPolynomial| ((#23=(|SparseUnivariatePolynomial| $) #23# #23#) 58 T ELT)) (|gcd| (#21# 62 T ELT) (#22# 61 T ELT)) (|factorsOfCyclicGroupSize| (((|List| (|Record| (|:| |factor| #8#) (|:| |exponent| #8#)))) 143 (|has| |#1| . #9#) ELT)) (|factor| (#10# 92 T ELT)) (|extensionDegree| ((#24=(|OnePointCompletion| (|PositiveInteger|))) 111 T ELT) (((|PositiveInteger|)) 165 T ELT)) (|extendedEuclidean| (((|Record| #25=(|:| |coef1| $) #26=(|:| |coef2| $) (|:| |generator| $)) $ $) 70 T ELT) (((|Union| (|Record| #25# #26#) #19#) $ $ $) 69 T ELT)) (|exquo| (((|Union| $ "failed") $ $) 56 T ELT)) (|expressIdealMember| (((|Maybe| #13#) #13# $) 65 T ELT)) (|euclideanSize| (((|NonNegativeInteger|) $) 74 T ELT)) (|divide| (((|Record| (|:| |quotient| $) (|:| |remainder| $)) $ $) 73 T ELT)) (|discreteLog| ((#7# $) 148 (|has| |#1| . #9#) ELT) (((|Union| #15# "failed") $ $) 105 (OR (|has| |#1| . #16#) (|has| |#1| . #17#)) ELT)) (|dimension| (((|CardinalNumber|)) 119 T ELT)) (|differentiate| (#27=($ $ (|NonNegativeInteger|)) 139 (|has| |#1| . #9#) ELT) (($ . #28=($)) 137 (|has| |#1| . #9#) ELT)) (|degree| ((#24# $) 112 T ELT) (((|PositiveInteger|) $) 164 T ELT)) (|definingPolynomial| (((|SparseUnivariatePolynomial| |#1|)) 166 T ELT)) (|createPrimitiveElement| (#14# 145 (|has| |#1| . #9#) ELT)) (|createNormalElement| (($) 158 (|has| |#1| (|Finite|)) ELT)) (|coordinates| (((|Vector| |#1|) $) 170 T ELT) (((|Matrix| |#1|) (|Vector| $)) 169 T ELT)) (|conditionP| (((|Union| (|Vector| $) "failed") (|Matrix| $)) 142 (|has| |#1| . #9#) ELT)) (|coerce| (((|OutputForm|) $) 13 T ELT) (($ (|Integer|)) 41 T ELT) (($ $) 57 T ELT) (($ #29=(|Fraction| #30=(|Integer|))) 84 T ELT) (($ |#1|) 120 T ELT)) (|charthRoot| (($ $) 141 (|has| |#1| . #9#) ELT) (((|Maybe| $) $) 103 (OR (|has| |#1| . #16#) (|has| |#1| . #17#)) ELT)) (|characteristic| (((|NonNegativeInteger|)) 40 T CONST)) (|before?| (#1# 6 T ELT)) (|basis| (((|Vector| $)) 172 T ELT) (((|Vector| $) (|PositiveInteger|)) 171 T ELT)) (|associates?| ((#3# $ $) 53 T ELT)) (|annihilate?| (((|Boolean|) $ $) 33 T ELT)) (|algebraic?| (#4# 115 T ELT)) (|Zero| (#11# 24 T CONST)) (|One| (($) 45 T CONST)) (|Frobenius| (($ $) 109 (|has| |#1| . #17#) ELT) (($ $ #5#) 108 (|has| |#1| . #17#) ELT)) (D (#27# 140 (|has| |#1| . #9#) ELT) (($ . #28#) 138 (|has| |#1| . #9#) ELT)) (= (#1# 8 T ELT)) (/ (($ $ $) 83 T ELT) (($ $ |#1|) 118 T ELT)) (- (($ $) 29 T ELT) (($ $ $) 28 T ELT)) (+ (($ $ $) 18 T ELT)) (** (($ $ (|PositiveInteger|)) 35 T ELT) (($ $ (|NonNegativeInteger|)) 43 T ELT) (($ $ #30#) 87 T ELT)) (* (($ (|PositiveInteger|) $) 17 T ELT) (($ (|NonNegativeInteger|) $) 21 T ELT) (($ (|Integer|) . #31=($)) 30 T ELT) (($ $ $) 34 T ELT) (($ $ #29#) 86 T ELT) (($ #29# . #31#) 85 T ELT) (($ $ |#1|) 117 T ELT) (($ |#1| . #31#) 116 T ELT))) +((~= (#1=((|Boolean|) $ $) 7 T ELT)) (|zero?| ((#2=(|Boolean|) $) 22 T ELT)) (|unitNormal| (((|Record| (|:| |unit| $) (|:| |canonical| $) (|:| |associate| $)) $) 56 T ELT)) (|unitCanonical| (($ $) 55 T ELT)) (|unit?| ((#3=(|Boolean|) $) 53 T ELT)) (|transcendent?| (#4=((|Boolean|) $) 115 T ELT)) (|transcendenceDegree| ((#5=(|NonNegativeInteger|)) 111 T ELT)) (|trace| ((|#1| $) 162 T ELT) (($ $ (|PositiveInteger|)) 159 (|has| |#1| (|Finite|)) ELT)) (|tableForDiscreteLogarithm| (((|Table| #6=(|PositiveInteger|) #7=(|NonNegativeInteger|)) #8=(|Integer|)) 144 (|has| |#1| . #9=((|Finite|))) ELT)) (|subtractIfCan| (((|Maybe| $) $ $) 26 T ELT)) (|squareFreePart| (($ $) 92 T ELT)) (|squareFree| (#10=((|Factored| $) $) 91 T ELT)) (|sizeLess?| (((|Boolean|) $ $) 76 T ELT)) (|size| (((|NonNegativeInteger|)) 134 (|has| |#1| . #9#) ELT)) (|sample| (#11=($) 23 T CONST)) (|retractIfCan| (((|Union| |#1| "failed") $) 122 T ELT)) (|retract| ((|#1| $) 123 T ELT)) (|represents| (($ (|Vector| |#1|)) 168 T ELT)) (|representationType| (((|Union| "prime" "polynomial" "normal" "cyclic")) 150 (|has| |#1| . #9#) ELT)) (|rem| (#12=($ $ $) 72 T ELT)) (|recip| (((|Union| $ "failed") $) 43 T ELT)) (|random| (($) 131 (|has| |#1| . #9#) ELT)) (|quo| (#12# 73 T ELT)) (|principalIdeal| (((|Record| (|:| |coef| #13=(|List| $)) (|:| |generator| $)) #13#) 67 T ELT)) (|primitiveElement| (#14=($) 146 (|has| |#1| . #9#) ELT)) (|primitive?| (((|Boolean|) $) 147 (|has| |#1| . #9#) ELT)) (|primeFrobenius| (($ $ #15=(|NonNegativeInteger|)) 108 (OR (|has| |#1| . #16=((|CharacteristicNonZero|))) (|has| |#1| . #17=((|Finite|)))) ELT) (($ $) 107 (OR (|has| |#1| . #16#) (|has| |#1| . #17#)) ELT)) (|prime?| (((|Boolean|) $) 90 T ELT)) (|order| ((#6# $) 149 (|has| |#1| . #9#) ELT) (((|OnePointCompletion| (|PositiveInteger|)) $) 105 (OR (|has| |#1| . #16#) (|has| |#1| . #17#)) ELT)) (|opposite?| ((#2# $ $) 20 T ELT)) (|one?| (((|Boolean|) $) 45 T ELT)) 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(#22=($ (|List| $)) 60 T ELT)) (|latex| (((|String|) $) 11 T ELT)) (|inv| (($ $) 89 T ELT)) (|init| (($) 136 (|has| |#1| . #9#) CONST)) (|index| (($ #20#) 133 (|has| |#1| . #9#) ELT)) (|inGroundField?| (#4# 114 T ELT)) (|hash| (((|SingleInteger|) $) 12 T ELT)) (|generator| (($) 155 (|has| |#1| (|Finite|)) ELT)) (|gcdPolynomial| ((#23=(|SparseUnivariatePolynomial| $) #23# #23#) 59 T ELT)) (|gcd| (#21# 63 T ELT) (#22# 62 T ELT)) (|factorsOfCyclicGroupSize| (((|List| (|Record| (|:| |factor| #8#) (|:| |exponent| #8#)))) 143 (|has| |#1| . #9#) ELT)) (|factor| (#10# 93 T ELT)) (|extensionDegree| ((#24=(|OnePointCompletion| (|PositiveInteger|))) 112 T ELT) (((|PositiveInteger|)) 165 T ELT)) (|extendedEuclidean| (((|Record| #25=(|:| |coef1| $) #26=(|:| |coef2| $) (|:| |generator| $)) $ $) 71 T ELT) (((|Union| (|Record| #25# #26#) #19#) $ $ $) 70 T ELT)) (|exquo| (((|Union| $ "failed") $ $) 57 T ELT)) (|expressIdealMember| (((|Maybe| #13#) #13# $) 66 T ELT)) (|euclideanSize| (((|NonNegativeInteger|) $) 75 T ELT)) (|divide| (((|Record| (|:| |quotient| $) (|:| |remainder| $)) $ $) 74 T ELT)) (|discreteLog| ((#7# $) 148 (|has| |#1| . #9#) ELT) (((|Union| #15# "failed") $ $) 106 (OR (|has| |#1| . #16#) (|has| |#1| . #17#)) ELT)) (|dimension| (((|CardinalNumber|)) 120 T ELT)) (|differentiate| (#27=($ $ (|NonNegativeInteger|)) 139 (|has| |#1| . #9#) ELT) (($ . #28=($)) 137 (|has| |#1| . #9#) ELT)) (|degree| ((#24# $) 113 T ELT) (((|PositiveInteger|) $) 164 T ELT)) (|definingPolynomial| (((|SparseUnivariatePolynomial| |#1|)) 166 T ELT)) (|createPrimitiveElement| (#14# 145 (|has| |#1| . #9#) ELT)) (|createNormalElement| (($) 158 (|has| |#1| (|Finite|)) ELT)) (|coordinates| (((|Vector| |#1|) $) 170 T ELT) (((|Matrix| |#1|) (|Vector| $)) 169 T ELT)) (|conditionP| (((|Union| (|Vector| $) "failed") (|Matrix| $)) 142 (|has| |#1| . #9#) ELT)) (|coerce| (((|OutputForm|) $) 13 T ELT) (($ (|Integer|)) 42 T ELT) (($ $) 58 T ELT) (($ #29=(|Fraction| #30=(|Integer|))) 85 T ELT) (($ |#1|) 121 T ELT)) (|charthRoot| (($ $) 141 (|has| |#1| . #9#) ELT) (((|Maybe| $) $) 104 (OR (|has| |#1| . #16#) (|has| |#1| . #17#)) ELT)) (|characteristic| (((|NonNegativeInteger|)) 41 T CONST)) (|before?| (#1# 6 T ELT)) (|basis| (((|Vector| $)) 172 T ELT) (((|Vector| $) (|PositiveInteger|)) 171 T ELT)) (|associates?| ((#3# $ $) 54 T ELT)) (|annihilate?| (((|Boolean|) $ $) 34 T ELT)) (|algebraic?| (#4# 116 T ELT)) (|Zero| (#11# 24 T CONST)) (|One| (($) 46 T CONST)) (|Frobenius| (($ $) 110 (|has| |#1| . #17#) ELT) (($ $ #5#) 109 (|has| |#1| . #17#) ELT)) (D (#27# 140 (|has| |#1| . #9#) ELT) (($ . #28#) 138 (|has| |#1| . #9#) ELT)) (= (#1# 8 T ELT)) (/ (($ $ $) 84 T ELT) (($ $ |#1|) 119 T ELT)) (- (($ $) 30 T ELT) (($ $ $) 29 T ELT)) (+ (($ $ $) 18 T ELT)) (** (($ $ (|PositiveInteger|)) 36 T ELT) (($ $ (|NonNegativeInteger|)) 44 T ELT) (($ $ #30#) 88 T ELT)) (* (($ (|PositiveInteger|) $) 17 T ELT) (($ (|NonNegativeInteger|) $) 21 T ELT) (($ (|Integer|) . #31=($)) 31 T ELT) (($ $ $) 35 T ELT) (($ $ #29#) 87 T ELT) (($ #29# . #31#) 86 T ELT) (($ $ |#1|) 118 T ELT) (($ |#1| . #31#) 117 T ELT))) (((|FiniteAlgebraicExtensionField| |#1|) (|Category|) (|Field|)) (T |FiniteAlgebraicExtensionField|)) ((|basis| (*1 *2) (AND (|ofCategory| *3 (|Field|)) (|isDomain| *2 (|Vector| *1)) (|ofCategory| *1 (|FiniteAlgebraicExtensionField| *3)))) (|basis| (*1 *2 *3) (AND (|isDomain| *3 (|PositiveInteger|)) (|ofCategory| *4 (|Field|)) (|isDomain| *2 (|Vector| *1)) (|ofCategory| *1 (|FiniteAlgebraicExtensionField| *4)))) (|coordinates| (*1 *2 *1) (AND (|ofCategory| *1 (|FiniteAlgebraicExtensionField| *3)) (|ofCategory| *3 (|Field|)) (|isDomain| *2 (|Vector| *3)))) (|coordinates| (*1 *2 *3) (AND (|isDomain| *3 (|Vector| *1)) (|ofCategory| *1 (|FiniteAlgebraicExtensionField| *4)) (|ofCategory| *4 (|Field|)) (|isDomain| *2 (|Matrix| *4)))) (|represents| (*1 *1 *2) (AND (|isDomain| *2 (|Vector| *3)) (|ofCategory| *3 (|Field|)) (|ofCategory| *1 (|FiniteAlgebraicExtensionField| *3)))) (|minimalPolynomial| (*1 *2 *1) (AND (|ofCategory| *1 (|FiniteAlgebraicExtensionField| *3)) (|ofCategory| *3 (|Field|)) (|isDomain| *2 (|SparseUnivariatePolynomial| *3)))) (|definingPolynomial| (*1 *2) (AND (|ofCategory| *1 (|FiniteAlgebraicExtensionField| *3)) (|ofCategory| *3 (|Field|)) (|isDomain| *2 (|SparseUnivariatePolynomial| *3)))) (|extensionDegree| (*1 *2) (AND (|ofCategory| *1 (|FiniteAlgebraicExtensionField| *3)) (|ofCategory| *3 (|Field|)) (|isDomain| *2 (|PositiveInteger|)))) (|degree| (*1 *2 *1) (AND (|ofCategory| *1 (|FiniteAlgebraicExtensionField| *3)) (|ofCategory| *3 (|Field|)) (|isDomain| *2 (|PositiveInteger|)))) (|norm| (*1 *2 *1) (AND (|ofCategory| *1 (|FiniteAlgebraicExtensionField| *2)) (|ofCategory| *2 (|Field|)))) (|trace| (*1 *2 *1) (AND (|ofCategory| *1 (|FiniteAlgebraicExtensionField| *2)) (|ofCategory| *2 (|Field|)))) (|minimalPolynomial| (*1 *2 *1 *3) (AND (|isDomain| *3 (|PositiveInteger|)) (|ofCategory| *4 (|Finite|)) (|ofCategory| *4 (|Field|)) (|isDomain| *2 (|SparseUnivariatePolynomial| *1)) (|ofCategory| *1 (|FiniteAlgebraicExtensionField| *4)))) (|norm| (*1 *1 *1 *2) (AND (|isDomain| *2 (|PositiveInteger|)) (|ofCategory| *1 (|FiniteAlgebraicExtensionField| *3)) (|ofCategory| *3 (|Field|)) (|ofCategory| *3 (|Finite|)))) (|trace| (*1 *1 *1 *2) (AND (|isDomain| *2 (|PositiveInteger|)) (|ofCategory| *1 (|FiniteAlgebraicExtensionField| *3)) (|ofCategory| *3 (|Field|)) (|ofCategory| *3 (|Finite|)))) (|createNormalElement| (*1 *1) (AND (|ofCategory| *1 (|FiniteAlgebraicExtensionField| *2)) (|ofCategory| *2 (|Finite|)) (|ofCategory| *2 (|Field|)))) (|normalElement| (*1 *1) (AND (|ofCategory| *1 (|FiniteAlgebraicExtensionField| *2)) (|ofCategory| *2 (|Finite|)) (|ofCategory| *2 (|Field|)))) (|normal?| (*1 *2 *1) (AND (|ofCategory| *1 (|FiniteAlgebraicExtensionField| *3)) (|ofCategory| *3 (|Field|)) (|ofCategory| *3 (|Finite|)) (|isDomain| *2 (|Boolean|)))) (|generator| (*1 *1) (AND (|ofCategory| *1 (|FiniteAlgebraicExtensionField| *2)) (|ofCategory| *2 (|Finite|)) (|ofCategory| *2 (|Field|)))) (|linearAssociatedExp| (*1 *1 *1 *2) (AND (|isDomain| *2 (|SparseUnivariatePolynomial| *3)) (|ofCategory| *3 (|Finite|)) (|ofCategory| *1 (|FiniteAlgebraicExtensionField| *3)) (|ofCategory| *3 (|Field|)))) (|linearAssociatedOrder| (*1 *2 *1) (AND (|ofCategory| *1 (|FiniteAlgebraicExtensionField| *3)) (|ofCategory| *3 (|Field|)) (|ofCategory| *3 (|Finite|)) (|isDomain| *2 (|SparseUnivariatePolynomial| *3)))) (|linearAssociatedLog| (*1 *2 *1) (AND (|ofCategory| *1 (|FiniteAlgebraicExtensionField| *3)) (|ofCategory| *3 (|Field|)) (|ofCategory| *3 (|Finite|)) (|isDomain| *2 (|SparseUnivariatePolynomial| *3)))) (|linearAssociatedLog| (*1 *2 *1 *1) (|partial| AND (|ofCategory| *1 (|FiniteAlgebraicExtensionField| *3)) (|ofCategory| *3 (|Field|)) (|ofCategory| *3 (|Finite|)) (|isDomain| *2 (|SparseUnivariatePolynomial| *3))))) (|Join| (|ExtensionField| |t#1|) (|RetractableTo| |t#1|) (CATEGORY |domain| (SIGNATURE |basis| ((|Vector| $))) (SIGNATURE |basis| ((|Vector| $) (|PositiveInteger|))) (SIGNATURE |coordinates| ((|Vector| |t#1|) $)) (SIGNATURE |coordinates| ((|Matrix| |t#1|) (|Vector| $))) (SIGNATURE |represents| ($ (|Vector| |t#1|))) (SIGNATURE |minimalPolynomial| ((|SparseUnivariatePolynomial| |t#1|) $)) (SIGNATURE |definingPolynomial| ((|SparseUnivariatePolynomial| |t#1|))) (SIGNATURE |extensionDegree| ((|PositiveInteger|))) (SIGNATURE |degree| ((|PositiveInteger|) $)) (SIGNATURE |norm| (|t#1| $)) (SIGNATURE |trace| (|t#1| $)) (IF (|has| |t#1| (|Finite|)) (PROGN (ATTRIBUTE (|FiniteFieldCategory|)) (SIGNATURE |minimalPolynomial| ((|SparseUnivariatePolynomial| $) $ (|PositiveInteger|))) (SIGNATURE |norm| ($ $ (|PositiveInteger|))) (SIGNATURE |trace| ($ $ (|PositiveInteger|))) (SIGNATURE |createNormalElement| ($)) (SIGNATURE |normalElement| ($)) (SIGNATURE |normal?| ((|Boolean|) $)) (SIGNATURE |generator| ($)) (SIGNATURE |linearAssociatedExp| ($ $ (|SparseUnivariatePolynomial| |t#1|))) (SIGNATURE |linearAssociatedOrder| ((|SparseUnivariatePolynomial| |t#1|) $)) (SIGNATURE |linearAssociatedLog| ((|SparseUnivariatePolynomial| |t#1|) $)) (SIGNATURE |linearAssociatedLog| ((|Union| (|SparseUnivariatePolynomial| |t#1|) "failed") $ $))) |%noBranch|))) @@ -920,7 +920,7 @@ NIL ((~= #1=(#2=((|Boolean|) $ $) NIL T ELT)) (|lookupFunction| (((|Identifier|) $) 20 T ELT)) (|latex| (((|String|) $) NIL T ELT)) (|hash| (((|SingleInteger|) $) NIL T ELT)) (|encodingDirectory| (((|PrimitiveArray| #3=(|NonNegativeInteger|)) $) 18 T ELT)) (|domainTemplate| (((|DomainTemplate|) $) 7 T ELT)) (|coerce| (((|OutputForm|) $) 26 T ELT)) (|categories| (((|PrimitiveArray| (|ConstructorCall| (|CategoryConstructor|))) $) 16 T ELT)) (|before?| #1#) (|attributeData| (((|List| (|Pair| (|Syntax|) #3#)) $) 12 T ELT)) (= (#2# 22 T ELT))) (((|FunctorData|) (|Join| (|SetCategory|) (CATEGORY |domain| (SIGNATURE |domainTemplate| ((|DomainTemplate|) $)) (SIGNATURE |attributeData| ((|List| (|Pair| (|Syntax|) #1=(|NonNegativeInteger|))) $)) (SIGNATURE |encodingDirectory| ((|PrimitiveArray| #1#) $)) (SIGNATURE |categories| ((|PrimitiveArray| (|ConstructorCall| (|CategoryConstructor|))) $)) (SIGNATURE |lookupFunction| ((|Identifier|) $))))) (T |FunctorData|)) ((|domainTemplate| #1=(*1 *2 *1) (AND (|isDomain| *2 (|DomainTemplate|)) #2=(|isDomain| *1 (|FunctorData|)))) (|attributeData| #1# (AND (|isDomain| *2 (|List| (|Pair| (|Syntax|) #3=(|NonNegativeInteger|)))) #2#)) (|encodingDirectory| #1# (AND (|isDomain| *2 (|PrimitiveArray| #3#)) #2#)) (|categories| #1# (AND (|isDomain| *2 (|PrimitiveArray| (|ConstructorCall| (|CategoryConstructor|)))) #2#)) (|lookupFunction| #1# (AND (|isDomain| *2 (|Identifier|)) #2#))) -((~= #1=(#2=(#3=(|Boolean|) $ $) NIL T ELT)) (|zero?| #4=((#3# $) NIL T ELT)) (|subtractIfCan| (((|Union| $ #5="failed") $ $) NIL T ELT)) (|sample| (#6=($) NIL T CONST)) (|reduce| (#7=($ $) 34 T ELT)) (|principal?| #4#) (|opposite?| #1#) (|latex| (((|String|) $) NIL T ELT)) (|lSpaceBasis| (#8=((|Vector| |#4|) $) 133 T ELT)) (|ideal| ((#9=(|FractionalIdeal| |#2| (|Fraction| |#2|) |#3| |#4|) $) 32 T ELT)) (|hash| (((|SingleInteger|) $) NIL T ELT)) (|generator| (((|Union| |#4| #5#) $) 37 T ELT)) (|finiteBasis| (#8# 125 T ELT)) (|divisor| (($ #9#) 42 T ELT) (($ |#4|) 44 T ELT) (($ |#1| |#1|) 46 T ELT) (($ |#1| |#1| #10=(|Integer|)) 48 T ELT) (($ |#4| |#2| |#2| |#2| |#1|) 50 T ELT)) (|decompose| (((|Record| (|:| |id| #9#) (|:| |principalPart| |#4|)) $) 40 T ELT)) (|coerce| (((|OutputForm|) $) 18 T ELT)) (|before?| #1#) (|Zero| (#6# 15 T CONST)) (= (#2# 21 T ELT)) (- (#7# 28 T ELT) (#11=($ $ $) NIL T ELT)) (+ (#11# 26 T ELT)) (* (($ (|PositiveInteger|) $) NIL T ELT) (($ (|NonNegativeInteger|) $) NIL T ELT) (($ #10# $) 24 T ELT))) +((~= #1=(#2=(#3=(|Boolean|) $ $) NIL T ELT)) (|zero?| #4=((#3# $) NIL T ELT)) (|subtractIfCan| (((|Maybe| $) $ $) NIL T ELT)) (|sample| (#5=($) NIL T CONST)) (|reduce| (#6=($ $) 34 T ELT)) (|principal?| #4#) (|opposite?| #1#) (|latex| (((|String|) $) NIL T ELT)) (|lSpaceBasis| (#7=((|Vector| |#4|) $) 133 T ELT)) (|ideal| ((#8=(|FractionalIdeal| |#2| (|Fraction| |#2|) |#3| |#4|) $) 32 T ELT)) (|hash| (((|SingleInteger|) $) NIL T ELT)) (|generator| (((|Union| |#4| "failed") $) 37 T ELT)) (|finiteBasis| (#7# 125 T ELT)) (|divisor| (($ #8#) 42 T ELT) (($ |#4|) 44 T ELT) (($ |#1| |#1|) 46 T ELT) (($ |#1| |#1| #9=(|Integer|)) 48 T ELT) (($ |#4| |#2| |#2| |#2| |#1|) 50 T ELT)) (|decompose| (((|Record| (|:| |id| #8#) (|:| |principalPart| |#4|)) $) 40 T ELT)) (|coerce| (((|OutputForm|) $) 18 T ELT)) (|before?| #1#) (|Zero| (#5# 15 T CONST)) (= (#2# 21 T ELT)) (- (#6# 28 T ELT) (#10=($ $ $) NIL T ELT)) (+ (#10# 26 T ELT)) (* (($ (|PositiveInteger|) $) NIL T ELT) (($ (|NonNegativeInteger|) $) NIL T ELT) (($ #9# $) 24 T ELT))) (((|FiniteDivisor| |#1| |#2| |#3| |#4|) (|Join| (|FiniteDivisorCategory| |#1| |#2| |#3| |#4|) (CATEGORY |domain| (SIGNATURE |finiteBasis| #1=((|Vector| |#4|) $)) (SIGNATURE |lSpaceBasis| #1#))) (|Field|) (|UnivariatePolynomialCategory| |#1|) (|UnivariatePolynomialCategory| (|Fraction| |#2|)) (|FunctionFieldCategory| |#1| |#2| |#3|)) (T |FiniteDivisor|)) ((|finiteBasis| #1=(*1 *2 *1) #2=(AND (|ofCategory| *3 (|Field|)) (|ofCategory| *4 (|UnivariatePolynomialCategory| *3)) (|ofCategory| *5 (|UnivariatePolynomialCategory| (|Fraction| *4))) (|isDomain| *2 (|Vector| *6)) (|isDomain| *1 (|FiniteDivisor| *3 *4 *5 *6)) (|ofCategory| *6 (|FunctionFieldCategory| *3 *4 *5)))) (|lSpaceBasis| #1# #2#)) ((|map| (((|FiniteDivisor| |#5| |#6| |#7| |#8|) (|Mapping| |#5| |#1|) (|FiniteDivisor| |#1| |#2| |#3| |#4|)) 33 T ELT))) @@ -929,7 +929,7 @@ NIL ((|principal?| (((|Boolean|) $) 14 T ELT))) (((|FiniteDivisorCategory&| |#1| |#2| |#3| |#4| |#5|) (CATEGORY |package| (SIGNATURE |principal?| ((|Boolean|) |#1|))) (|FiniteDivisorCategory| |#2| |#3| |#4| |#5|) (|Field|) (|UnivariatePolynomialCategory| |#2|) (|UnivariatePolynomialCategory| (|Fraction| |#3|)) (|FunctionFieldCategory| |#2| |#3| |#4|)) (T |FiniteDivisorCategory&|)) NIL -((~= (#1=((|Boolean|) $ $) 7 T ELT)) (|zero?| ((#2=(|Boolean|) $) 22 T ELT)) (|subtractIfCan| (((|Union| $ "failed") $ $) 26 T ELT)) (|sample| (#3=($) 23 T CONST)) (|reduce| (($ $) 35 T ELT)) (|principal?| (((|Boolean|) $) 34 T ELT)) (|opposite?| ((#2# $ $) 20 T ELT)) (|latex| (((|String|) $) 11 T ELT)) (|ideal| (((|FractionalIdeal| |#2| (|Fraction| |#2|) |#3| |#4|) $) 41 T ELT)) (|hash| (((|SingleInteger|) $) 12 T ELT)) (|generator| (((|Union| |#4| "failed") $) 33 T ELT)) (|divisor| (($ (|FractionalIdeal| |#2| (|Fraction| |#2|) |#3| |#4|)) 40 T ELT) (($ |#4|) 39 T ELT) (($ |#1| |#1|) 38 T ELT) (($ |#1| |#1| (|Integer|)) 37 T ELT) (($ |#4| |#2| |#2| |#2| |#1|) 32 T ELT)) (|decompose| (((|Record| (|:| |id| (|FractionalIdeal| |#2| (|Fraction| |#2|) |#3| |#4|)) (|:| |principalPart| |#4|)) $) 36 T ELT)) (|coerce| (((|OutputForm|) $) 13 T ELT)) (|before?| (#1# 6 T ELT)) (|Zero| (#3# 24 T CONST)) (= (#1# 8 T ELT)) (- (($ $) 29 T ELT) (($ $ $) 28 T ELT)) (+ (($ $ $) 18 T ELT)) (* (($ (|PositiveInteger|) $) 17 T ELT) (($ (|NonNegativeInteger|) $) 21 T ELT) (($ (|Integer|) $) 30 T ELT))) +((~= (#1=((|Boolean|) $ $) 7 T ELT)) (|zero?| ((#2=(|Boolean|) $) 22 T ELT)) (|subtractIfCan| (((|Maybe| $) $ $) 26 T ELT)) (|sample| (#3=($) 23 T CONST)) (|reduce| (($ $) 36 T ELT)) (|principal?| (((|Boolean|) $) 35 T ELT)) (|opposite?| ((#2# $ $) 20 T ELT)) (|latex| (((|String|) $) 11 T ELT)) (|ideal| (((|FractionalIdeal| |#2| (|Fraction| |#2|) |#3| |#4|) $) 42 T ELT)) (|hash| (((|SingleInteger|) $) 12 T ELT)) (|generator| (((|Union| |#4| "failed") $) 34 T ELT)) (|divisor| (($ (|FractionalIdeal| |#2| (|Fraction| |#2|) |#3| |#4|)) 41 T ELT) (($ |#4|) 40 T ELT) (($ |#1| |#1|) 39 T ELT) (($ |#1| |#1| (|Integer|)) 38 T ELT) (($ |#4| |#2| |#2| |#2| |#1|) 33 T ELT)) (|decompose| (((|Record| (|:| |id| (|FractionalIdeal| |#2| (|Fraction| |#2|) |#3| |#4|)) (|:| |principalPart| |#4|)) $) 37 T ELT)) (|coerce| (((|OutputForm|) $) 13 T ELT)) (|before?| (#1# 6 T ELT)) (|Zero| (#3# 24 T CONST)) (= (#1# 8 T ELT)) (- (($ $) 30 T ELT) (($ $ $) 29 T ELT)) (+ (($ $ $) 18 T ELT)) (* (($ (|PositiveInteger|) $) 17 T ELT) (($ (|NonNegativeInteger|) $) 21 T ELT) (($ (|Integer|) $) 31 T ELT))) (((|FiniteDivisorCategory| |#1| |#2| |#3| |#4|) (|Category|) (|Field|) (|UnivariatePolynomialCategory| |t#1|) (|UnivariatePolynomialCategory| (|Fraction| |t#2|)) (|FunctionFieldCategory| |t#1| |t#2| |t#3|)) (T |FiniteDivisorCategory|)) ((|ideal| (*1 *2 *1) (AND (|ofCategory| *1 (|FiniteDivisorCategory| *3 *4 *5 *6)) (|ofCategory| *3 (|Field|)) (|ofCategory| *4 (|UnivariatePolynomialCategory| *3)) (|ofCategory| *5 (|UnivariatePolynomialCategory| (|Fraction| *4))) (|ofCategory| *6 (|FunctionFieldCategory| *3 *4 *5)) (|isDomain| *2 (|FractionalIdeal| *4 (|Fraction| *4) *5 *6)))) (|divisor| (*1 *1 *2) (AND (|isDomain| *2 (|FractionalIdeal| *4 (|Fraction| *4) *5 *6)) (|ofCategory| *4 (|UnivariatePolynomialCategory| *3)) (|ofCategory| *5 (|UnivariatePolynomialCategory| (|Fraction| *4))) (|ofCategory| *6 (|FunctionFieldCategory| *3 *4 *5)) (|ofCategory| *3 (|Field|)) (|ofCategory| *1 (|FiniteDivisorCategory| *3 *4 *5 *6)))) (|divisor| (*1 *1 *2) (AND (|ofCategory| *3 (|Field|)) (|ofCategory| *4 (|UnivariatePolynomialCategory| *3)) (|ofCategory| *5 (|UnivariatePolynomialCategory| (|Fraction| *4))) (|ofCategory| *1 (|FiniteDivisorCategory| *3 *4 *5 *2)) (|ofCategory| *2 (|FunctionFieldCategory| *3 *4 *5)))) (|divisor| (*1 *1 *2 *2) (AND (|ofCategory| *2 (|Field|)) (|ofCategory| *3 (|UnivariatePolynomialCategory| *2)) (|ofCategory| *4 (|UnivariatePolynomialCategory| (|Fraction| *3))) (|ofCategory| *1 (|FiniteDivisorCategory| *2 *3 *4 *5)) (|ofCategory| *5 (|FunctionFieldCategory| *2 *3 *4)))) (|divisor| (*1 *1 *2 *2 *3) (AND (|isDomain| *3 (|Integer|)) (|ofCategory| *2 (|Field|)) (|ofCategory| *4 (|UnivariatePolynomialCategory| *2)) (|ofCategory| *5 (|UnivariatePolynomialCategory| (|Fraction| *4))) (|ofCategory| *1 (|FiniteDivisorCategory| *2 *4 *5 *6)) (|ofCategory| *6 (|FunctionFieldCategory| *2 *4 *5)))) (|decompose| (*1 *2 *1) (AND (|ofCategory| *1 (|FiniteDivisorCategory| *3 *4 *5 *6)) (|ofCategory| *3 (|Field|)) (|ofCategory| *4 (|UnivariatePolynomialCategory| *3)) (|ofCategory| *5 (|UnivariatePolynomialCategory| (|Fraction| *4))) (|ofCategory| *6 (|FunctionFieldCategory| *3 *4 *5)) (|isDomain| *2 (|Record| (|:| |id| (|FractionalIdeal| *4 (|Fraction| *4) *5 *6)) (|:| |principalPart| *6))))) (|reduce| (*1 *1 *1) (AND (|ofCategory| *1 (|FiniteDivisorCategory| *2 *3 *4 *5)) (|ofCategory| *2 (|Field|)) (|ofCategory| *3 (|UnivariatePolynomialCategory| *2)) (|ofCategory| *4 (|UnivariatePolynomialCategory| (|Fraction| *3))) (|ofCategory| *5 (|FunctionFieldCategory| *2 *3 *4)))) (|principal?| (*1 *2 *1) (AND (|ofCategory| *1 (|FiniteDivisorCategory| *3 *4 *5 *6)) (|ofCategory| *3 (|Field|)) (|ofCategory| *4 (|UnivariatePolynomialCategory| *3)) (|ofCategory| *5 (|UnivariatePolynomialCategory| (|Fraction| *4))) (|ofCategory| *6 (|FunctionFieldCategory| *3 *4 *5)) (|isDomain| *2 (|Boolean|)))) (|generator| (*1 *2 *1) (|partial| AND (|ofCategory| *1 (|FiniteDivisorCategory| *3 *4 *5 *2)) (|ofCategory| *3 (|Field|)) (|ofCategory| *4 (|UnivariatePolynomialCategory| *3)) (|ofCategory| *5 (|UnivariatePolynomialCategory| (|Fraction| *4))) (|ofCategory| *2 (|FunctionFieldCategory| *3 *4 *5)))) (|divisor| (*1 *1 *2 *3 *3 *3 *4) (AND (|ofCategory| *4 (|Field|)) (|ofCategory| *3 (|UnivariatePolynomialCategory| *4)) (|ofCategory| *5 (|UnivariatePolynomialCategory| (|Fraction| *3))) (|ofCategory| *1 (|FiniteDivisorCategory| *4 *3 *5 *2)) (|ofCategory| *2 (|FunctionFieldCategory| *4 *3 *5))))) (|Join| (|AbelianGroup|) (CATEGORY |domain| (SIGNATURE |ideal| ((|FractionalIdeal| |t#2| (|Fraction| |t#2|) |t#3| |t#4|) $)) (SIGNATURE |divisor| ($ (|FractionalIdeal| |t#2| (|Fraction| |t#2|) |t#3| |t#4|))) (SIGNATURE |divisor| ($ |t#4|)) (SIGNATURE |divisor| ($ |t#1| |t#1|)) (SIGNATURE |divisor| ($ |t#1| |t#1| (|Integer|))) (SIGNATURE |decompose| ((|Record| (|:| |id| (|FractionalIdeal| |t#2| (|Fraction| |t#2|) |t#3| |t#4|)) (|:| |principalPart| |t#4|)) $)) (SIGNATURE |reduce| ($ $)) (SIGNATURE |principal?| ((|Boolean|) $)) (SIGNATURE |generator| ((|Union| |t#4| "failed") $)) (SIGNATURE |divisor| ($ |t#4| |t#2| |t#2| |t#2| |t#1|)))) @@ -942,13 +942,13 @@ NIL NIL (|Join| (|Functorial| |t#1|) (CATEGORY |domain| (IF (|has| |t#1| (|Eltable| |t#1| |t#1|)) (ATTRIBUTE (|Eltable| |t#1| $)) |%noBranch|) (IF (|has| |t#1| (|Evalable| |t#1|)) (ATTRIBUTE (|Evalable| |t#1|)) |%noBranch|) (IF (|has| |t#1| (|InnerEvalable| (|Symbol|) |t#1|)) (ATTRIBUTE (|InnerEvalable| (|Symbol|) |t#1|)) |%noBranch|))) (((|Eltable| |#1| $) |has| |#1| (|Eltable| |#1| |#1|)) ((|Evalable| |#1|) |has| |#1| (|Evalable| |#1|)) ((|Functorial| |#1|) . T) ((|InnerEvalable| (|Symbol|) |#1|) |has| |#1| (|InnerEvalable| (|Symbol|) |#1|)) ((|InnerEvalable| |#1| |#1|) |has| |#1| (|Evalable| |#1|)) ((|Join|) . T) ((|Type|) . T)) -((~= #1=((#2=(|Boolean|) $ $) NIL T ELT)) (|zero?| #3=(#4=(#2# $) NIL T ELT)) (|unitNormal| (((|Record| (|:| |unit| $) (|:| |canonical| $) (|:| |associate| $)) $) NIL T ELT)) (|unitCanonical| #5=(#6=($ $) NIL T ELT)) (|unit?| #3#) (|transcendent?| #3#) (|transcendenceDegree| (#7=(#8=(|NonNegativeInteger|)) NIL T ELT)) (|trace| #9=((#10=(|PrimeField| |#1|) $) NIL T ELT) #11=(#12=($ $ #13=(|PositiveInteger|)) NIL #14=(|has| #10# (|Finite|)) ELT)) (|tableForDiscreteLogarithm| (((|Table| #13# #8#) #15=(|Integer|)) NIL #14# ELT)) (|subtractIfCan| #16=((#17=(|Union| $ #18="failed") $ $) NIL T ELT)) (|squareFreePart| #5#) (|squareFree| #19=(((|Factored| $) $) NIL T ELT)) (|sizeLess?| #1#) (|size| (#7# NIL #14# ELT)) (|sample| #20=(#21=($) NIL T CONST)) (|retractIfCan| (((|Union| #10# #18#) $) NIL T ELT)) (|retract| #9#) (|represents| (($ #22=(|Vector| #10#)) NIL T ELT)) (|representationType| (((|Union| "prime" "polynomial" "normal" "cyclic")) NIL #14# ELT)) (|rem| #23=(($ $ $) NIL T ELT)) (|recip| ((#17# $) NIL T ELT)) (|random| #24=(#21# NIL #14# ELT)) (|quo| #23#) (|principalIdeal| (((|Record| (|:| |coef| #25=(|List| $)) #26=(|:| |generator| $)) #25#) NIL T ELT)) (|primitiveElement| #24#) (|primitive?| #27=(#4# NIL #14# ELT)) (|primeFrobenius| (#28=($ $ #8#) NIL #29=(OR (|has| #10# (|CharacteristicNonZero|)) #14#) ELT) (#6# NIL #29# ELT)) (|prime?| #3#) (|order| #30=(#31=(#13# $) NIL #14# ELT) (#32=(#33=(|OnePointCompletion| #13#) $) NIL #29# ELT)) (|opposite?| #1#) (|one?| #3#) (|normalElement| #24#) (|normal?| #27#) (|norm| #9# #11#) (|nextItem| (#34=((|Maybe| $) $) NIL #14# ELT)) (|multiEuclidean| (((|Union| #25# #18#) #25# $) NIL T ELT)) (|minimalPolynomial| (#35=(#36=(|SparseUnivariatePolynomial| #10#) $) NIL T ELT) ((#37=(|SparseUnivariatePolynomial| $) $ #13#) NIL #14# ELT)) (|lookup| #30#) (|linearAssociatedOrder| #38=(#35# NIL #14# ELT)) (|linearAssociatedLog| #38# (((|Union| #36# #18#) $ $) NIL #14# ELT)) (|linearAssociatedExp| (($ $ #36#) NIL #14# ELT)) (|lcm| #23# #39=(($ #25#) NIL T ELT)) (|latex| (((|String|) $) NIL T ELT)) (|inv| #5#) (|init| (#21# NIL #14# CONST)) (|index| (($ #13#) NIL #14# ELT)) (|inGroundField?| #3#) (|hash| (((|SingleInteger|) $) NIL T ELT)) (|generator| #24#) (|gcdPolynomial| ((#37# #37# #37#) NIL T ELT)) (|gcd| #23# #39#) (|factorsOfCyclicGroupSize| (((|List| (|Record| (|:| |factor| #15#) (|:| |exponent| #15#)))) NIL #14# ELT)) (|factor| #19#) (|extensionDegree| ((#33#) NIL T ELT) ((#13#) NIL T ELT)) (|extendedEuclidean| (((|Record| #40=(|:| |coef1| $) #41=(|:| |coef2| $) #26#) $ $) NIL T ELT) (((|Union| (|Record| #40# #41#) #18#) $ $ $) NIL T ELT)) (|exquo| #16#) (|expressIdealMember| (((|Maybe| #25#) #25# $) NIL T ELT)) (|euclideanSize| (#42=(#8# $) NIL T ELT)) (|divide| (((|Record| (|:| |quotient| $) (|:| |remainder| $)) $ $) NIL T ELT)) (|discreteLog| (#42# NIL #14# ELT) (((|Union| #8# #18#) $ $) NIL #29# ELT)) (|dimension| (((|CardinalNumber|)) NIL T ELT)) (|differentiate| #43=(#28# NIL #14# ELT) #44=(#6# NIL #14# ELT)) (|degree| (#32# NIL T ELT) (#31# NIL T ELT)) (|definingPolynomial| ((#36#) NIL T ELT)) (|createPrimitiveElement| #24#) (|createNormalElement| #24#) (|coordinates| ((#22# $) NIL T ELT) (((|Matrix| #10#) #45=(|Vector| $)) NIL T ELT)) (|conditionP| (((|Union| #45# #18#) (|Matrix| $)) NIL #14# ELT)) (|coerce| (((|OutputForm|) $) NIL T ELT) (($ #15#) NIL T ELT) #5# (($ #46=(|Fraction| #15#)) NIL T ELT) (($ #10#) NIL T ELT)) (|charthRoot| #44# (#34# NIL #29# ELT)) (|characteristic| (#7# NIL T CONST)) (|before?| #1#) (|basis| ((#45#) NIL T ELT) ((#45# #13#) NIL T ELT)) (|associates?| #1#) (|annihilate?| #1#) (|algebraic?| #3#) (|Zero| #20#) (|One| #20#) (|Frobenius| #44# #43#) (D #43# #44#) (= #1#) (/ #23# #47=(($ $ #10#) NIL T ELT)) (- #5# #23#) (+ #23#) (** (#12# NIL T ELT) (#28# NIL T ELT) (($ $ #15#) NIL T ELT)) (* (($ #13# $) NIL T ELT) (($ #8# $) NIL T ELT) (($ #15# . #48=($)) NIL T ELT) #23# (($ $ #46#) NIL T ELT) (($ #46# . #48#) NIL T ELT) #47# (($ #10# . #48#) NIL T ELT))) +((~= #1=((#2=(|Boolean|) $ $) NIL T ELT)) (|zero?| #3=(#4=(#2# $) NIL T ELT)) (|unitNormal| (((|Record| (|:| |unit| $) (|:| |canonical| $) (|:| |associate| $)) $) NIL T ELT)) (|unitCanonical| #5=(#6=($ $) NIL T ELT)) (|unit?| #3#) (|transcendent?| #3#) (|transcendenceDegree| (#7=(#8=(|NonNegativeInteger|)) NIL T ELT)) (|trace| #9=((#10=(|PrimeField| |#1|) $) NIL T ELT) #11=(#12=($ $ #13=(|PositiveInteger|)) NIL #14=(|has| #10# (|Finite|)) ELT)) (|tableForDiscreteLogarithm| (((|Table| #13# #8#) #15=(|Integer|)) NIL #14# ELT)) (|subtractIfCan| ((#16=(|Maybe| $) $ $) NIL T ELT)) (|squareFreePart| #5#) (|squareFree| #17=(((|Factored| $) $) NIL T ELT)) (|sizeLess?| #1#) (|size| (#7# NIL #14# ELT)) (|sample| #18=(#19=($) NIL T CONST)) (|retractIfCan| (((|Union| #10# #20="failed") $) NIL T ELT)) (|retract| #9#) (|represents| (($ #21=(|Vector| #10#)) NIL T ELT)) (|representationType| (((|Union| "prime" "polynomial" "normal" "cyclic")) NIL #14# ELT)) (|rem| #22=(($ $ $) NIL T ELT)) (|recip| ((#23=(|Union| $ #20#) $) NIL T ELT)) (|random| #24=(#19# NIL #14# ELT)) (|quo| #22#) (|principalIdeal| (((|Record| (|:| |coef| #25=(|List| $)) #26=(|:| |generator| $)) #25#) NIL T ELT)) (|primitiveElement| #24#) (|primitive?| #27=(#4# NIL #14# ELT)) (|primeFrobenius| (#28=($ $ #8#) NIL #29=(OR (|has| #10# (|CharacteristicNonZero|)) #14#) ELT) (#6# NIL #29# ELT)) (|prime?| #3#) (|order| #30=(#31=(#13# $) NIL #14# ELT) (#32=(#33=(|OnePointCompletion| #13#) $) NIL #29# ELT)) (|opposite?| #1#) (|one?| #3#) (|normalElement| #24#) (|normal?| #27#) (|norm| #9# #11#) (|nextItem| (#34=(#16# $) NIL #14# ELT)) (|multiEuclidean| (((|Union| #25# #20#) #25# $) NIL T ELT)) (|minimalPolynomial| (#35=(#36=(|SparseUnivariatePolynomial| #10#) $) NIL T ELT) ((#37=(|SparseUnivariatePolynomial| $) $ #13#) NIL #14# ELT)) (|lookup| #30#) (|linearAssociatedOrder| #38=(#35# NIL #14# ELT)) (|linearAssociatedLog| #38# (((|Union| #36# #20#) $ $) NIL #14# ELT)) (|linearAssociatedExp| (($ $ #36#) NIL #14# ELT)) (|lcm| #22# #39=(($ #25#) NIL T ELT)) (|latex| (((|String|) $) NIL T ELT)) (|inv| #5#) (|init| (#19# NIL #14# CONST)) (|index| (($ #13#) NIL #14# ELT)) (|inGroundField?| #3#) (|hash| (((|SingleInteger|) $) NIL T ELT)) (|generator| #24#) (|gcdPolynomial| ((#37# #37# #37#) NIL T ELT)) (|gcd| #22# #39#) (|factorsOfCyclicGroupSize| (((|List| (|Record| (|:| |factor| #15#) (|:| |exponent| #15#)))) NIL #14# ELT)) (|factor| #17#) (|extensionDegree| ((#33#) NIL T ELT) ((#13#) NIL T ELT)) (|extendedEuclidean| (((|Record| #40=(|:| |coef1| $) #41=(|:| |coef2| $) #26#) $ $) NIL T ELT) (((|Union| (|Record| #40# #41#) #20#) $ $ $) NIL T ELT)) (|exquo| ((#23# $ $) NIL T ELT)) (|expressIdealMember| (((|Maybe| #25#) #25# $) NIL T ELT)) (|euclideanSize| (#42=(#8# $) NIL T ELT)) (|divide| (((|Record| (|:| |quotient| $) (|:| |remainder| $)) $ $) NIL T ELT)) (|discreteLog| (#42# NIL #14# ELT) (((|Union| #8# #20#) $ $) NIL #29# ELT)) (|dimension| (((|CardinalNumber|)) NIL T ELT)) (|differentiate| #43=(#28# NIL #14# ELT) #44=(#6# NIL #14# ELT)) (|degree| (#32# NIL T ELT) (#31# NIL T ELT)) (|definingPolynomial| ((#36#) NIL T ELT)) (|createPrimitiveElement| #24#) (|createNormalElement| #24#) (|coordinates| ((#21# $) NIL T ELT) (((|Matrix| #10#) #45=(|Vector| $)) NIL T ELT)) (|conditionP| (((|Union| #45# #20#) (|Matrix| $)) NIL #14# ELT)) (|coerce| (((|OutputForm|) $) NIL T ELT) (($ #15#) NIL T ELT) #5# (($ #46=(|Fraction| #15#)) NIL T ELT) (($ #10#) NIL T ELT)) (|charthRoot| #44# (#34# NIL #29# ELT)) (|characteristic| (#7# NIL T CONST)) (|before?| #1#) (|basis| ((#45#) NIL T ELT) ((#45# #13#) NIL T ELT)) (|associates?| #1#) (|annihilate?| #1#) (|algebraic?| #3#) (|Zero| #18#) (|One| #18#) (|Frobenius| #44# #43#) (D #43# #44#) (= #1#) (/ #22# #47=(($ $ #10#) NIL T ELT)) (- #5# #22#) (+ #22#) (** (#12# NIL T ELT) (#28# NIL T ELT) (($ $ #15#) NIL T ELT)) (* (($ #13# $) NIL T ELT) (($ #8# $) NIL T ELT) (($ #15# . #48=($)) NIL T ELT) #22# (($ $ #46#) NIL T ELT) (($ #46# . #48#) NIL T ELT) #47# (($ #10# . #48#) NIL T ELT))) (((|FiniteField| |#1| |#2|) (|FiniteAlgebraicExtensionField| (|PrimeField| |#1|)) #1=(|PositiveInteger|) #1#) (T |FiniteField|)) NIL -((|yCoordinates| (((|Record| (|:| |num| #1=(|Vector| |#3|)) #2=(|:| |den| |#3|)) $) 39 T ELT)) (|represents| (($ #3=(|Vector| #4=(|Fraction| |#3|)) #5=(|Vector| $)) NIL T ELT) (($ #3#) NIL T ELT) (($ #1# |#3|) 172 T ELT)) (|reduceBasisAtInfinity| (#6=(#5# #5#) 156 T ELT)) (|rationalPoints| (((|List| (|List| |#2|))) 126 T ELT)) (|rationalPoint?| ((#7=(|Boolean|) |#2| |#2|) 76 T ELT)) (|primitivePart| (#8=($ $) 148 T ELT)) (|numberOfComponents| (#9=(#10=(|NonNegativeInteger|)) 171 T ELT)) (|normalizeAtInfinity| (#6# 219 T ELT)) (|nonSingularModel| (((|List| (|Polynomial| |#2|)) #11=(|Symbol|)) 115 T ELT)) (|integralAtInfinity?| (#12=(#7# $) 168 T ELT)) (|integral?| (#12# 27 T ELT) ((#7# $ |#2|) 31 T ELT) ((#7# $ |#3|) 223 T ELT)) (|hyperelliptic| (#13=((|Union| |#3| "failed")) 52 T ELT)) (|genus| (#9# 183 T ELT)) (|elt| ((|#2| $ |#2| |#2|) 140 T ELT)) (|elliptic| (#13# 71 T ELT)) (|differentiate| (($ $ #14=(|Mapping| #4# #4#)) NIL T ELT) (($ $ #14# #10#) NIL T ELT) (($ $ #15=(|Mapping| |#3| |#3|)) 227 T ELT) (($ $ #16=(|List| #11#) (|List| #10#)) NIL T ELT) (($ $ #11# #10#) NIL T ELT) (($ $ #16#) NIL T ELT) (($ $ #11#) NIL T ELT) (($ $ #10#) NIL T ELT) (#8# NIL T ELT)) (|complementaryBasis| (#6# 162 T ELT)) (|algSplitSimple| (((|Record| (|:| |num| $) #2# (|:| |derivden| |#3|) (|:| |gd| |#3|)) $ #15#) 68 T ELT)) (|absolutelyIrreducible?| ((#7#) 34 T ELT))) -(((|FunctionFieldCategory&| |#1| |#2| |#3| |#4|) (CATEGORY |package| (SIGNATURE |differentiate| #1=(|#1| |#1|)) (SIGNATURE |differentiate| (|#1| |#1| #2=(|NonNegativeInteger|))) (SIGNATURE |differentiate| (|#1| |#1| #3=(|Symbol|))) (SIGNATURE |differentiate| (|#1| |#1| #4=(|List| #3#))) (SIGNATURE |differentiate| (|#1| |#1| #3# #2#)) (SIGNATURE |differentiate| (|#1| |#1| #4# (|List| #2#))) (SIGNATURE |rationalPoints| ((|List| (|List| |#2|)))) (SIGNATURE |nonSingularModel| ((|List| (|Polynomial| |#2|)) #3#)) (SIGNATURE |algSplitSimple| ((|Record| (|:| |num| |#1|) #5=(|:| |den| |#3|) (|:| |derivden| |#3|) (|:| |gd| |#3|)) |#1| #6=(|Mapping| |#3| |#3|))) (SIGNATURE |hyperelliptic| #7=((|Union| |#3| "failed"))) (SIGNATURE |elliptic| #7#) (SIGNATURE |elt| (|#2| |#1| |#2| |#2|)) (SIGNATURE |primitivePart| #1#) (SIGNATURE |differentiate| (|#1| |#1| #6#)) (SIGNATURE |integral?| (#8=(|Boolean|) |#1| |#3|)) (SIGNATURE |integral?| (#8# |#1| |#2|)) (SIGNATURE |represents| (|#1| #9=(|Vector| |#3|) |#3|)) (SIGNATURE |yCoordinates| ((|Record| (|:| |num| #9#) #5#) |#1|)) (SIGNATURE |reduceBasisAtInfinity| #10=(#11=(|Vector| |#1|) #11#)) (SIGNATURE |normalizeAtInfinity| #10#) (SIGNATURE |complementaryBasis| #10#) (SIGNATURE |integral?| #12=(#8# |#1|)) (SIGNATURE |integralAtInfinity?| #12#) (SIGNATURE |rationalPoint?| (#8# |#2| |#2|)) (SIGNATURE |absolutelyIrreducible?| (#8#)) (SIGNATURE |genus| #13=(#2#)) (SIGNATURE |numberOfComponents| #13#) (SIGNATURE |differentiate| (|#1| |#1| #14=(|Mapping| #15=(|Fraction| |#3|) #15#) #2#)) (SIGNATURE |differentiate| (|#1| |#1| #14#)) (SIGNATURE |represents| (|#1| #16=(|Vector| #15#))) (SIGNATURE |represents| (|#1| #16# #11#))) (|FunctionFieldCategory| |#2| |#3| |#4|) (|UniqueFactorizationDomain|) (|UnivariatePolynomialCategory| |#2|) (|UnivariatePolynomialCategory| #15#)) (T |FunctionFieldCategory&|)) +((|yCoordinates| (((|Record| (|:| |num| #1=(|Vector| |#3|)) #2=(|:| |den| |#3|)) $) 39 T ELT)) (|represents| (($ #3=(|Vector| #4=(|Fraction| |#3|)) #5=(|Vector| $)) NIL T ELT) (($ #3#) NIL T ELT) (($ #1# |#3|) 172 T ELT)) (|reduceBasisAtInfinity| (#6=(#5# #5#) 156 T ELT)) (|rationalPoints| (((|List| (|List| |#2|))) 126 T ELT)) (|rationalPoint?| ((#7=(|Boolean|) |#2| |#2|) 76 T ELT)) (|primitivePart| (#8=($ $) 148 T ELT)) (|numberOfComponents| (#9=(#10=(|NonNegativeInteger|)) 171 T ELT)) (|normalizeAtInfinity| (#6# 219 T ELT)) (|nonSingularModel| (((|List| (|Polynomial| |#2|)) #11=(|Symbol|)) 115 T ELT)) (|integralAtInfinity?| (#12=(#7# $) 168 T ELT)) (|integral?| (#12# 27 T ELT) ((#7# $ |#2|) 31 T ELT) ((#7# $ |#3|) 223 T ELT)) (|hyperelliptic| (#13=((|Union| |#3| "failed")) 52 T ELT)) (|genus| (#9# 183 T ELT)) (|elt| ((|#2| $ |#2| |#2|) 140 T ELT)) (|elliptic| (#13# 71 T ELT)) (|differentiate| (($ $ #14=(|Mapping| #4# #4#)) NIL T ELT) (($ $ #14# #10#) NIL T ELT) (($ $ #15=(|Mapping| |#3| |#3|)) 227 T ELT) (($ $ #10#) NIL T ELT) (#8# NIL T ELT) (($ $ #16=(|List| #11#) (|List| #10#)) NIL T ELT) (($ $ #11# #10#) NIL T ELT) (($ $ #16#) NIL T ELT) (($ $ #11#) NIL T ELT)) (|complementaryBasis| (#6# 162 T ELT)) (|algSplitSimple| (((|Record| (|:| |num| $) #2# (|:| |derivden| |#3|) (|:| |gd| |#3|)) $ #15#) 68 T ELT)) (|absolutelyIrreducible?| ((#7#) 34 T ELT))) +(((|FunctionFieldCategory&| |#1| |#2| |#3| |#4|) (CATEGORY |package| (SIGNATURE |differentiate| (|#1| |#1| #1=(|Symbol|))) (SIGNATURE |differentiate| (|#1| |#1| #2=(|List| #1#))) (SIGNATURE |differentiate| (|#1| |#1| #1# #3=(|NonNegativeInteger|))) (SIGNATURE |differentiate| (|#1| |#1| #2# (|List| #3#))) (SIGNATURE |differentiate| #4=(|#1| |#1|)) (SIGNATURE |differentiate| (|#1| |#1| #3#)) (SIGNATURE |rationalPoints| ((|List| (|List| |#2|)))) (SIGNATURE |nonSingularModel| ((|List| (|Polynomial| |#2|)) #1#)) (SIGNATURE |algSplitSimple| ((|Record| (|:| |num| |#1|) #5=(|:| |den| |#3|) (|:| |derivden| |#3|) (|:| |gd| |#3|)) |#1| #6=(|Mapping| |#3| |#3|))) (SIGNATURE |hyperelliptic| #7=((|Union| |#3| "failed"))) (SIGNATURE |elliptic| #7#) (SIGNATURE |elt| (|#2| |#1| |#2| |#2|)) (SIGNATURE |primitivePart| #4#) (SIGNATURE |differentiate| (|#1| |#1| #6#)) (SIGNATURE |integral?| (#8=(|Boolean|) |#1| |#3|)) (SIGNATURE |integral?| (#8# |#1| |#2|)) (SIGNATURE |represents| (|#1| #9=(|Vector| |#3|) |#3|)) (SIGNATURE |yCoordinates| ((|Record| (|:| |num| #9#) #5#) |#1|)) (SIGNATURE |reduceBasisAtInfinity| #10=(#11=(|Vector| |#1|) #11#)) (SIGNATURE |normalizeAtInfinity| #10#) (SIGNATURE |complementaryBasis| #10#) (SIGNATURE |integral?| #12=(#8# |#1|)) (SIGNATURE |integralAtInfinity?| #12#) (SIGNATURE |rationalPoint?| (#8# |#2| |#2|)) (SIGNATURE |absolutelyIrreducible?| (#8#)) (SIGNATURE |genus| #13=(#3#)) (SIGNATURE |numberOfComponents| #13#) (SIGNATURE |differentiate| (|#1| |#1| #14=(|Mapping| #15=(|Fraction| |#3|) #15#) #3#)) (SIGNATURE |differentiate| (|#1| |#1| #14#)) (SIGNATURE |represents| (|#1| #16=(|Vector| #15#))) (SIGNATURE |represents| (|#1| #16# #11#))) (|FunctionFieldCategory| |#2| |#3| |#4|) (|UniqueFactorizationDomain|) (|UnivariatePolynomialCategory| |#2|) (|UnivariatePolynomialCategory| #15#)) (T |FunctionFieldCategory&|)) ((|numberOfComponents| #1=(*1 *2) #2=(AND #3=(|ofCategory| *4 #4=(|UniqueFactorizationDomain|)) #5=(|ofCategory| *5 #6=(|UnivariatePolynomialCategory| *4)) #7=(|ofCategory| *6 (|UnivariatePolynomialCategory| (|Fraction| *5))) (|isDomain| *2 (|NonNegativeInteger|)) #8=(|isDomain| *1 (|FunctionFieldCategory&| *3 *4 *5 *6)) #9=(|ofCategory| *3 (|FunctionFieldCategory| *4 *5 *6)))) (|genus| #1# #2#) (|absolutelyIrreducible?| #1# (AND #3# #5# #7# #10=(|isDomain| *2 (|Boolean|)) #8# #9#)) (|rationalPoint?| (*1 *2 *3 *3) (AND (|ofCategory| *3 #4#) (|ofCategory| *5 (|UnivariatePolynomialCategory| *3)) #7# #10# (|isDomain| *1 (|FunctionFieldCategory&| *4 *3 *5 *6)) (|ofCategory| *4 (|FunctionFieldCategory| *3 *5 *6)))) (|elliptic| #1# #11=(|partial| AND #3# (|ofCategory| *5 (|UnivariatePolynomialCategory| (|Fraction| *2))) (|ofCategory| *2 #6#) (|isDomain| *1 (|FunctionFieldCategory&| *3 *4 *2 *5)) (|ofCategory| *3 (|FunctionFieldCategory| *4 *2 *5)))) (|hyperelliptic| #1# #11#) (|nonSingularModel| (*1 *2 *3) (AND (|isDomain| *3 (|Symbol|)) (|ofCategory| *5 #4#) (|ofCategory| *6 (|UnivariatePolynomialCategory| *5)) (|ofCategory| *7 (|UnivariatePolynomialCategory| (|Fraction| *6))) (|isDomain| *2 (|List| (|Polynomial| *5))) (|isDomain| *1 (|FunctionFieldCategory&| *4 *5 *6 *7)) (|ofCategory| *4 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ELT) (($ (|Integer|) . #57=($)) 31 T ELT) (($ $ $) 35 T ELT) (($ $ (|Fraction| |#2|)) 55 T ELT) (($ (|Fraction| |#2|) . #57#) 54 T ELT) (($ #55# . #57#) 140 (|has| (|Fraction| |#2|) . #3#) ELT) (($ $ #55#) 139 (|has| (|Fraction| |#2|) . #3#) ELT))) (((|FunctionFieldCategory| |#1| |#2| |#3|) (|Category|) (|UniqueFactorizationDomain|) (|UnivariatePolynomialCategory| |t#1|) (|UnivariatePolynomialCategory| (|Fraction| |t#2|))) (T |FunctionFieldCategory|)) ((|numberOfComponents| (*1 *2) (AND (|ofCategory| *1 (|FunctionFieldCategory| *3 *4 *5)) (|ofCategory| *3 (|UniqueFactorizationDomain|)) (|ofCategory| *4 (|UnivariatePolynomialCategory| *3)) (|ofCategory| *5 (|UnivariatePolynomialCategory| (|Fraction| *4))) (|isDomain| *2 (|NonNegativeInteger|)))) (|genus| (*1 *2) (AND (|ofCategory| *1 (|FunctionFieldCategory| *3 *4 *5)) (|ofCategory| *3 (|UniqueFactorizationDomain|)) (|ofCategory| *4 (|UnivariatePolynomialCategory| *3)) (|ofCategory| *5 (|UnivariatePolynomialCategory| (|Fraction| *4))) (|isDomain| *2 (|NonNegativeInteger|)))) (|absolutelyIrreducible?| (*1 *2) (AND (|ofCategory| *1 (|FunctionFieldCategory| *3 *4 *5)) (|ofCategory| *3 (|UniqueFactorizationDomain|)) (|ofCategory| *4 (|UnivariatePolynomialCategory| *3)) (|ofCategory| *5 (|UnivariatePolynomialCategory| (|Fraction| *4))) (|isDomain| *2 (|Boolean|)))) (|rationalPoint?| (*1 *2 *3 *3) (AND (|ofCategory| *1 (|FunctionFieldCategory| *3 *4 *5)) (|ofCategory| *3 (|UniqueFactorizationDomain|)) (|ofCategory| *4 (|UnivariatePolynomialCategory| *3)) (|ofCategory| *5 (|UnivariatePolynomialCategory| (|Fraction| *4))) (|isDomain| *2 (|Boolean|)))) (|branchPointAtInfinity?| (*1 *2) (AND (|ofCategory| *1 (|FunctionFieldCategory| *3 *4 *5)) (|ofCategory| *3 (|UniqueFactorizationDomain|)) (|ofCategory| *4 (|UnivariatePolynomialCategory| *3)) (|ofCategory| *5 (|UnivariatePolynomialCategory| (|Fraction| *4))) (|isDomain| *2 (|Boolean|)))) (|branchPoint?| (*1 *2 *3) (AND (|ofCategory| *1 (|FunctionFieldCategory| *3 *4 *5)) (|ofCategory| *3 (|UniqueFactorizationDomain|)) (|ofCategory| *4 (|UnivariatePolynomialCategory| *3)) (|ofCategory| *5 (|UnivariatePolynomialCategory| (|Fraction| *4))) (|isDomain| *2 (|Boolean|)))) (|branchPoint?| (*1 *2 *3) (AND (|ofCategory| *1 (|FunctionFieldCategory| *4 *3 *5)) (|ofCategory| *4 (|UniqueFactorizationDomain|)) (|ofCategory| *3 (|UnivariatePolynomialCategory| *4)) (|ofCategory| *5 (|UnivariatePolynomialCategory| (|Fraction| *3))) (|isDomain| *2 (|Boolean|)))) (|singularAtInfinity?| (*1 *2) (AND (|ofCategory| *1 (|FunctionFieldCategory| *3 *4 *5)) (|ofCategory| *3 (|UniqueFactorizationDomain|)) (|ofCategory| *4 (|UnivariatePolynomialCategory| *3)) (|ofCategory| *5 (|UnivariatePolynomialCategory| (|Fraction| *4))) (|isDomain| *2 (|Boolean|)))) (|singular?| (*1 *2 *3) (AND (|ofCategory| *1 (|FunctionFieldCategory| *3 *4 *5)) (|ofCategory| *3 (|UniqueFactorizationDomain|)) (|ofCategory| *4 (|UnivariatePolynomialCategory| *3)) (|ofCategory| *5 (|UnivariatePolynomialCategory| (|Fraction| *4))) (|isDomain| *2 (|Boolean|)))) (|singular?| (*1 *2 *3) (AND (|ofCategory| *1 (|FunctionFieldCategory| *4 *3 *5)) (|ofCategory| *4 (|UniqueFactorizationDomain|)) (|ofCategory| *3 (|UnivariatePolynomialCategory| *4)) (|ofCategory| *5 (|UnivariatePolynomialCategory| (|Fraction| *3))) (|isDomain| *2 (|Boolean|)))) (|ramifiedAtInfinity?| (*1 *2) (AND (|ofCategory| *1 (|FunctionFieldCategory| *3 *4 *5)) (|ofCategory| *3 (|UniqueFactorizationDomain|)) (|ofCategory| *4 (|UnivariatePolynomialCategory| *3)) (|ofCategory| *5 (|UnivariatePolynomialCategory| (|Fraction| *4))) (|isDomain| *2 (|Boolean|)))) (|ramified?| (*1 *2 *3) (AND (|ofCategory| *1 (|FunctionFieldCategory| *3 *4 *5)) (|ofCategory| *3 (|UniqueFactorizationDomain|)) (|ofCategory| *4 (|UnivariatePolynomialCategory| *3)) (|ofCategory| *5 (|UnivariatePolynomialCategory| (|Fraction| *4))) (|isDomain| *2 (|Boolean|)))) (|ramified?| (*1 *2 *3) (AND (|ofCategory| *1 (|FunctionFieldCategory| *4 *3 *5)) (|ofCategory| *4 (|UniqueFactorizationDomain|)) (|ofCategory| *3 (|UnivariatePolynomialCategory| *4)) (|ofCategory| *5 (|UnivariatePolynomialCategory| (|Fraction| *3))) (|isDomain| *2 (|Boolean|)))) (|integralBasis| (*1 *2) (AND (|ofCategory| *3 (|UniqueFactorizationDomain|)) (|ofCategory| *4 (|UnivariatePolynomialCategory| *3)) (|ofCategory| *5 (|UnivariatePolynomialCategory| (|Fraction| *4))) (|isDomain| *2 (|Vector| *1)) (|ofCategory| *1 (|FunctionFieldCategory| *3 *4 *5)))) (|integralBasisAtInfinity| (*1 *2) (AND (|ofCategory| *3 (|UniqueFactorizationDomain|)) (|ofCategory| *4 (|UnivariatePolynomialCategory| *3)) (|ofCategory| *5 (|UnivariatePolynomialCategory| (|Fraction| *4))) (|isDomain| *2 (|Vector| *1)) (|ofCategory| *1 (|FunctionFieldCategory| *3 *4 *5)))) (|integralAtInfinity?| (*1 *2 *1) (AND (|ofCategory| *1 (|FunctionFieldCategory| *3 *4 *5)) (|ofCategory| *3 (|UniqueFactorizationDomain|)) (|ofCategory| *4 (|UnivariatePolynomialCategory| *3)) (|ofCategory| *5 (|UnivariatePolynomialCategory| (|Fraction| *4))) (|isDomain| *2 (|Boolean|)))) (|integral?| (*1 *2 *1) (AND (|ofCategory| *1 (|FunctionFieldCategory| *3 *4 *5)) (|ofCategory| *3 (|UniqueFactorizationDomain|)) (|ofCategory| *4 (|UnivariatePolynomialCategory| *3)) (|ofCategory| *5 (|UnivariatePolynomialCategory| (|Fraction| *4))) (|isDomain| *2 (|Boolean|)))) (|complementaryBasis| (*1 *2 *2) (AND (|isDomain| *2 (|Vector| *1)) (|ofCategory| *1 (|FunctionFieldCategory| *3 *4 *5)) (|ofCategory| *3 (|UniqueFactorizationDomain|)) (|ofCategory| *4 (|UnivariatePolynomialCategory| *3)) (|ofCategory| *5 (|UnivariatePolynomialCategory| (|Fraction| *4))))) (|normalizeAtInfinity| (*1 *2 *2) (AND (|isDomain| *2 (|Vector| *1)) (|ofCategory| *1 (|FunctionFieldCategory| *3 *4 *5)) (|ofCategory| *3 (|UniqueFactorizationDomain|)) (|ofCategory| *4 (|UnivariatePolynomialCategory| *3)) (|ofCategory| *5 (|UnivariatePolynomialCategory| (|Fraction| *4))))) (|reduceBasisAtInfinity| (*1 *2 *2) (AND (|isDomain| *2 (|Vector| *1)) (|ofCategory| *1 (|FunctionFieldCategory| *3 *4 *5)) (|ofCategory| *3 (|UniqueFactorizationDomain|)) (|ofCategory| *4 (|UnivariatePolynomialCategory| *3)) (|ofCategory| *5 (|UnivariatePolynomialCategory| (|Fraction| *4))))) (|integralMatrix| (*1 *2) (AND (|ofCategory| *1 (|FunctionFieldCategory| *3 *4 *5)) (|ofCategory| *3 (|UniqueFactorizationDomain|)) (|ofCategory| *4 (|UnivariatePolynomialCategory| *3)) (|ofCategory| *5 (|UnivariatePolynomialCategory| (|Fraction| *4))) (|isDomain| *2 (|Matrix| (|Fraction| *4))))) (|inverseIntegralMatrix| (*1 *2) (AND (|ofCategory| *1 (|FunctionFieldCategory| *3 *4 *5)) (|ofCategory| *3 (|UniqueFactorizationDomain|)) (|ofCategory| *4 (|UnivariatePolynomialCategory| *3)) (|ofCategory| *5 (|UnivariatePolynomialCategory| (|Fraction| *4))) (|isDomain| *2 (|Matrix| (|Fraction| *4))))) (|integralMatrixAtInfinity| (*1 *2) (AND (|ofCategory| *1 (|FunctionFieldCategory| *3 *4 *5)) (|ofCategory| *3 (|UniqueFactorizationDomain|)) (|ofCategory| *4 (|UnivariatePolynomialCategory| *3)) (|ofCategory| *5 (|UnivariatePolynomialCategory| (|Fraction| *4))) (|isDomain| *2 (|Matrix| (|Fraction| *4))))) (|inverseIntegralMatrixAtInfinity| (*1 *2) (AND (|ofCategory| *1 (|FunctionFieldCategory| *3 *4 *5)) (|ofCategory| *3 (|UniqueFactorizationDomain|)) (|ofCategory| *4 (|UnivariatePolynomialCategory| *3)) (|ofCategory| *5 (|UnivariatePolynomialCategory| (|Fraction| *4))) (|isDomain| *2 (|Matrix| (|Fraction| *4))))) (|yCoordinates| (*1 *2 *1) (AND (|ofCategory| *1 (|FunctionFieldCategory| *3 *4 *5)) (|ofCategory| *3 (|UniqueFactorizationDomain|)) (|ofCategory| *4 (|UnivariatePolynomialCategory| *3)) (|ofCategory| *5 (|UnivariatePolynomialCategory| (|Fraction| *4))) (|isDomain| *2 (|Record| (|:| |num| (|Vector| *4)) (|:| |den| *4))))) (|represents| (*1 *1 *2 *3) (AND (|isDomain| *2 (|Vector| *3)) (|ofCategory| *3 (|UnivariatePolynomialCategory| *4)) (|ofCategory| *4 (|UniqueFactorizationDomain|)) (|ofCategory| *1 (|FunctionFieldCategory| *4 *3 *5)) (|ofCategory| *5 (|UnivariatePolynomialCategory| (|Fraction| *3))))) (|integralCoordinates| (*1 *2 *1) (AND (|ofCategory| *1 (|FunctionFieldCategory| *3 *4 *5)) (|ofCategory| *3 (|UniqueFactorizationDomain|)) (|ofCategory| *4 (|UnivariatePolynomialCategory| *3)) (|ofCategory| *5 (|UnivariatePolynomialCategory| (|Fraction| *4))) (|isDomain| *2 (|Record| (|:| |num| (|Vector| *4)) (|:| |den| *4))))) (|integralRepresents| (*1 *1 *2 *3) (AND (|isDomain| *2 (|Vector| *3)) (|ofCategory| *3 (|UnivariatePolynomialCategory| *4)) (|ofCategory| *4 (|UniqueFactorizationDomain|)) (|ofCategory| *1 (|FunctionFieldCategory| *4 *3 *5)) (|ofCategory| *5 (|UnivariatePolynomialCategory| (|Fraction| *3))))) (|integralDerivationMatrix| (*1 *2 *3) (AND (|isDomain| *3 (|Mapping| *5 *5)) (|ofCategory| *1 (|FunctionFieldCategory| *4 *5 *6)) (|ofCategory| *4 (|UniqueFactorizationDomain|)) (|ofCategory| *5 (|UnivariatePolynomialCategory| *4)) (|ofCategory| *6 (|UnivariatePolynomialCategory| (|Fraction| *5))) (|isDomain| *2 (|Record| (|:| |num| (|Matrix| *5)) (|:| |den| *5))))) (|integral?| (*1 *2 *1 *3) (AND (|ofCategory| *1 (|FunctionFieldCategory| *3 *4 *5)) (|ofCategory| *3 (|UniqueFactorizationDomain|)) (|ofCategory| *4 (|UnivariatePolynomialCategory| *3)) (|ofCategory| *5 (|UnivariatePolynomialCategory| (|Fraction| *4))) (|isDomain| *2 (|Boolean|)))) (|integral?| (*1 *2 *1 *3) (AND (|ofCategory| *1 (|FunctionFieldCategory| *4 *3 *5)) (|ofCategory| *4 (|UniqueFactorizationDomain|)) (|ofCategory| *3 (|UnivariatePolynomialCategory| *4)) (|ofCategory| *5 (|UnivariatePolynomialCategory| (|Fraction| *3))) (|isDomain| *2 (|Boolean|)))) (|differentiate| (*1 *1 *1 *2) (AND (|isDomain| *2 (|Mapping| *4 *4)) (|ofCategory| *1 (|FunctionFieldCategory| *3 *4 *5)) (|ofCategory| *3 (|UniqueFactorizationDomain|)) (|ofCategory| *4 (|UnivariatePolynomialCategory| *3)) (|ofCategory| *5 (|UnivariatePolynomialCategory| (|Fraction| *4))))) (|primitivePart| (*1 *1 *1) (AND (|ofCategory| *1 (|FunctionFieldCategory| *2 *3 *4)) (|ofCategory| *2 (|UniqueFactorizationDomain|)) (|ofCategory| *3 (|UnivariatePolynomialCategory| *2)) (|ofCategory| *4 (|UnivariatePolynomialCategory| (|Fraction| *3))))) (|elt| (*1 *2 *1 *2 *2) (AND (|ofCategory| *1 (|FunctionFieldCategory| *2 *3 *4)) (|ofCategory| *2 (|UniqueFactorizationDomain|)) (|ofCategory| *3 (|UnivariatePolynomialCategory| *2)) (|ofCategory| *4 (|UnivariatePolynomialCategory| (|Fraction| *3))))) (|elliptic| (*1 *2) (|partial| AND (|ofCategory| *1 (|FunctionFieldCategory| *3 *2 *4)) (|ofCategory| *3 (|UniqueFactorizationDomain|)) (|ofCategory| *4 (|UnivariatePolynomialCategory| (|Fraction| *2))) (|ofCategory| *2 (|UnivariatePolynomialCategory| *3)))) (|hyperelliptic| (*1 *2) (|partial| AND (|ofCategory| *1 (|FunctionFieldCategory| *3 *2 *4)) (|ofCategory| *3 (|UniqueFactorizationDomain|)) (|ofCategory| *4 (|UnivariatePolynomialCategory| (|Fraction| *2))) (|ofCategory| *2 (|UnivariatePolynomialCategory| *3)))) (|algSplitSimple| (*1 *2 *1 *3) (AND (|isDomain| *3 (|Mapping| *5 *5)) (|ofCategory| *5 (|UnivariatePolynomialCategory| *4)) (|ofCategory| *4 (|UniqueFactorizationDomain|)) (|ofCategory| *6 (|UnivariatePolynomialCategory| (|Fraction| *5))) (|isDomain| *2 (|Record| (|:| |num| *1) (|:| |den| *5) (|:| |derivden| *5) (|:| |gd| *5))) (|ofCategory| *1 (|FunctionFieldCategory| *4 *5 *6)))) (|nonSingularModel| (*1 *2 *3) (AND (|isDomain| *3 (|Symbol|)) (|ofCategory| *1 (|FunctionFieldCategory| *4 *5 *6)) (|ofCategory| *4 (|UniqueFactorizationDomain|)) (|ofCategory| *5 (|UnivariatePolynomialCategory| *4)) (|ofCategory| *6 (|UnivariatePolynomialCategory| (|Fraction| *5))) (|ofCategory| *4 (|Field|)) (|isDomain| *2 (|List| (|Polynomial| *4))))) (|rationalPoints| (*1 *2) (AND (|ofCategory| *1 (|FunctionFieldCategory| *3 *4 *5)) (|ofCategory| *3 (|UniqueFactorizationDomain|)) (|ofCategory| *4 (|UnivariatePolynomialCategory| *3)) (|ofCategory| *5 (|UnivariatePolynomialCategory| (|Fraction| *4))) (|ofCategory| *3 (|Finite|)) (|isDomain| *2 (|List| (|List| *3)))))) (|Join| (|MonogenicAlgebra| (|Fraction| |t#2|) |t#3|) (CATEGORY |domain| (SIGNATURE |numberOfComponents| ((|NonNegativeInteger|))) (SIGNATURE |genus| ((|NonNegativeInteger|))) (SIGNATURE |absolutelyIrreducible?| ((|Boolean|))) (SIGNATURE |rationalPoint?| ((|Boolean|) |t#1| |t#1|)) (SIGNATURE |branchPointAtInfinity?| ((|Boolean|))) (SIGNATURE |branchPoint?| ((|Boolean|) |t#1|)) (SIGNATURE |branchPoint?| ((|Boolean|) |t#2|)) (SIGNATURE |singularAtInfinity?| ((|Boolean|))) (SIGNATURE |singular?| ((|Boolean|) |t#1|)) (SIGNATURE |singular?| ((|Boolean|) |t#2|)) (SIGNATURE |ramifiedAtInfinity?| ((|Boolean|))) (SIGNATURE |ramified?| ((|Boolean|) |t#1|)) (SIGNATURE |ramified?| ((|Boolean|) |t#2|)) (SIGNATURE |integralBasis| ((|Vector| $))) (SIGNATURE |integralBasisAtInfinity| ((|Vector| $))) (SIGNATURE |integralAtInfinity?| ((|Boolean|) $)) (SIGNATURE |integral?| ((|Boolean|) $)) (SIGNATURE |complementaryBasis| ((|Vector| $) (|Vector| $))) (SIGNATURE |normalizeAtInfinity| ((|Vector| $) (|Vector| $))) (SIGNATURE |reduceBasisAtInfinity| ((|Vector| $) (|Vector| $))) (SIGNATURE |integralMatrix| ((|Matrix| (|Fraction| |t#2|)))) (SIGNATURE |inverseIntegralMatrix| ((|Matrix| (|Fraction| |t#2|)))) (SIGNATURE |integralMatrixAtInfinity| ((|Matrix| (|Fraction| |t#2|)))) (SIGNATURE |inverseIntegralMatrixAtInfinity| ((|Matrix| (|Fraction| |t#2|)))) (SIGNATURE |yCoordinates| ((|Record| (|:| |num| (|Vector| |t#2|)) (|:| |den| |t#2|)) $)) (SIGNATURE |represents| ($ (|Vector| |t#2|) |t#2|)) (SIGNATURE |integralCoordinates| ((|Record| (|:| |num| (|Vector| |t#2|)) (|:| |den| |t#2|)) $)) (SIGNATURE |integralRepresents| ($ (|Vector| |t#2|) |t#2|)) (SIGNATURE |integralDerivationMatrix| ((|Record| (|:| |num| (|Matrix| |t#2|)) (|:| |den| |t#2|)) (|Mapping| |t#2| |t#2|))) (SIGNATURE |integral?| ((|Boolean|) $ |t#1|)) (SIGNATURE |integral?| ((|Boolean|) $ |t#2|)) (SIGNATURE |differentiate| ($ $ (|Mapping| |t#2| |t#2|))) (SIGNATURE |primitivePart| ($ $)) (SIGNATURE |elt| (|t#1| $ |t#1| |t#1|)) (SIGNATURE |elliptic| ((|Union| |t#2| "failed"))) (SIGNATURE |hyperelliptic| ((|Union| |t#2| "failed"))) (SIGNATURE |algSplitSimple| ((|Record| (|:| |num| $) (|:| |den| |t#2|) (|:| |derivden| |t#2|) (|:| |gd| |t#2|)) $ (|Mapping| |t#2| |t#2|))) (IF (|has| |t#1| (|Field|)) (SIGNATURE |nonSingularModel| ((|List| (|Polynomial| |t#1|)) (|Symbol|))) |%noBranch|) (IF (|has| |t#1| (|Finite|)) (SIGNATURE |rationalPoints| ((|List| (|List| |t#1|)))) |%noBranch|))) @@ -956,13 +956,13 @@ NIL ((|map| ((|#8| (|Mapping| |#5| |#1|) |#4|) 19 T ELT))) (((|FunctionFieldCategoryFunctions2| |#1| |#2| |#3| |#4| |#5| |#6| |#7| |#8|) (CATEGORY |package| (SIGNATURE |map| (|#8| (|Mapping| |#5| |#1|) |#4|))) #1=(|UniqueFactorizationDomain|) (|UnivariatePolynomialCategory| |#1|) (|UnivariatePolynomialCategory| (|Fraction| |#2|)) (|FunctionFieldCategory| |#1| |#2| |#3|) #1# (|UnivariatePolynomialCategory| |#5|) (|UnivariatePolynomialCategory| (|Fraction| |#6|)) (|FunctionFieldCategory| |#5| |#6| |#7|)) (T |FunctionFieldCategoryFunctions2|)) ((|map| (*1 *2 *3 *4) (AND (|isDomain| *3 (|Mapping| *8 *5)) (|ofCategory| *5 #1=(|UniqueFactorizationDomain|)) (|ofCategory| *8 #1#) (|ofCategory| *6 (|UnivariatePolynomialCategory| *5)) (|ofCategory| *7 (|UnivariatePolynomialCategory| (|Fraction| *6))) (|ofCategory| *9 (|UnivariatePolynomialCategory| *8)) (|ofCategory| *2 (|FunctionFieldCategory| *8 *9 *10)) (|isDomain| *1 (|FunctionFieldCategoryFunctions2| *5 *6 *7 *4 *8 *9 *10 *2)) (|ofCategory| *4 (|FunctionFieldCategory| *5 *6 *7)) (|ofCategory| *10 (|UnivariatePolynomialCategory| (|Fraction| *9)))))) -((~= #1=((#2=(|Boolean|) $ $) NIL T ELT)) (|zero?| #3=(#4=(#2# $) NIL T ELT)) (|unitNormal| (((|Record| (|:| |unit| $) (|:| |canonical| $) (|:| |associate| $)) $) NIL T ELT)) (|unitCanonical| #5=(#6=($ $) NIL T ELT)) (|unit?| #3#) (|transcendent?| #3#) (|transcendenceDegree| (#7=(#8=(|NonNegativeInteger|)) NIL T ELT)) (|trace| #9=((#10=(|PrimeField| |#1|) $) NIL T ELT) #11=(#12=($ $ #13=(|PositiveInteger|)) NIL #14=(|has| #10# (|Finite|)) ELT)) (|tableForDiscreteLogarithm| (((|Table| #13# #8#) #15=(|Integer|)) NIL #14# ELT)) (|subtractIfCan| #16=((#17=(|Union| $ #18="failed") $ $) NIL T ELT)) (|squareFreePart| #5#) (|squareFree| #19=(((|Factored| $) $) NIL T ELT)) (|sizeLess?| #1#) (|size| (#7# NIL #14# ELT)) (|sample| #20=(#21=($) NIL T CONST)) (|retractIfCan| (((|Union| #10# #18#) $) NIL T ELT)) (|retract| #9#) (|represents| (($ #22=(|Vector| #10#)) NIL T ELT)) (|representationType| (((|Union| "prime" "polynomial" "normal" "cyclic")) NIL #14# ELT)) (|rem| #23=(($ $ $) NIL T ELT)) (|recip| ((#17# $) NIL T ELT)) (|random| #24=(#21# NIL #14# ELT)) (|quo| #23#) (|principalIdeal| (((|Record| (|:| |coef| #25=(|List| $)) #26=(|:| |generator| $)) #25#) NIL T ELT)) (|primitiveElement| #24#) (|primitive?| #27=(#4# NIL #14# ELT)) (|primeFrobenius| (#28=($ $ #8#) NIL #29=(OR (|has| #10# (|CharacteristicNonZero|)) #14#) ELT) (#6# NIL #29# ELT)) (|prime?| #3#) (|order| #30=(#31=(#13# $) NIL #14# ELT) (#32=(#33=(|OnePointCompletion| #13#) $) NIL #29# ELT)) (|opposite?| #1#) (|one?| #3#) (|normalElement| #24#) (|normal?| #27#) (|norm| #9# #11#) (|nextItem| (#34=((|Maybe| $) $) NIL #14# ELT)) (|multiEuclidean| (((|Union| #25# #18#) #25# $) NIL T ELT)) (|minimalPolynomial| (#35=(#36=(|SparseUnivariatePolynomial| #10#) $) NIL T ELT) ((#37=(|SparseUnivariatePolynomial| $) $ #13#) NIL #14# ELT)) (|lookup| #30#) (|linearAssociatedOrder| #38=(#35# NIL #14# ELT)) (|linearAssociatedLog| #38# (((|Union| #36# #18#) $ $) NIL #14# ELT)) (|linearAssociatedExp| (($ $ #36#) NIL #14# ELT)) (|lcm| #23# #39=(($ #25#) NIL T ELT)) (|latex| (((|String|) $) NIL T ELT)) (|inv| #5#) (|init| (#21# NIL #14# CONST)) (|index| (($ #13#) NIL #14# ELT)) (|inGroundField?| #3#) (|hash| ((#40=(|SingleInteger|) $) NIL T ELT)) (|getZechTable| (((|PrimitiveArray| #40#)) NIL T ELT)) (|generator| #24#) (|gcdPolynomial| ((#37# #37# #37#) NIL T ELT)) (|gcd| #23# #39#) (|factorsOfCyclicGroupSize| (((|List| (|Record| (|:| |factor| #15#) (|:| |exponent| #15#)))) NIL #14# ELT)) (|factor| #19#) (|extensionDegree| ((#33#) NIL T ELT) ((#13#) NIL T ELT)) (|extendedEuclidean| (((|Record| #41=(|:| |coef1| $) #42=(|:| |coef2| $) #26#) $ $) NIL T ELT) (((|Union| (|Record| #41# #42#) #18#) $ $ $) NIL T ELT)) (|exquo| #16#) (|expressIdealMember| (((|Maybe| #25#) #25# $) NIL T ELT)) (|euclideanSize| (#43=(#8# $) NIL T ELT)) (|divide| (((|Record| (|:| |quotient| $) (|:| |remainder| $)) $ $) NIL T ELT)) (|discreteLog| (#43# NIL #14# ELT) (((|Union| #8# #18#) $ $) NIL #29# ELT)) (|dimension| (((|CardinalNumber|)) NIL T ELT)) (|differentiate| #44=(#28# NIL #14# ELT) #45=(#6# NIL #14# ELT)) (|degree| (#32# NIL T ELT) (#31# NIL T ELT)) (|definingPolynomial| ((#36#) NIL T ELT)) (|createPrimitiveElement| #24#) (|createNormalElement| #24#) (|coordinates| ((#22# $) NIL T ELT) (((|Matrix| #10#) #46=(|Vector| $)) NIL T ELT)) (|conditionP| (((|Union| #46# #18#) (|Matrix| $)) NIL #14# ELT)) (|coerce| (((|OutputForm|) $) NIL T ELT) (($ #15#) NIL T ELT) #5# (($ #47=(|Fraction| #15#)) NIL T ELT) (($ #10#) NIL T ELT)) (|charthRoot| #45# (#34# NIL #29# ELT)) (|characteristic| (#7# NIL T CONST)) (|before?| #1#) (|basis| ((#46#) NIL T ELT) ((#46# #13#) NIL T ELT)) (|associates?| #1#) (|annihilate?| #1#) (|algebraic?| #3#) (|Zero| #20#) (|One| #20#) (|Frobenius| #45# #44#) (D #44# #45#) (= #1#) (/ #23# #48=(($ $ #10#) NIL T ELT)) (- #5# #23#) (+ #23#) (** (#12# NIL T ELT) (#28# NIL T ELT) (($ $ #15#) NIL T ELT)) (* (($ #13# $) NIL T ELT) (($ #8# $) NIL T ELT) (($ #15# . #49=($)) NIL T ELT) #23# (($ $ #47#) NIL T ELT) (($ #47# . #49#) NIL T ELT) #48# (($ #10# . #49#) NIL T ELT))) +((~= #1=((#2=(|Boolean|) $ $) NIL T ELT)) (|zero?| #3=(#4=(#2# $) NIL T ELT)) (|unitNormal| (((|Record| (|:| |unit| $) (|:| |canonical| $) (|:| |associate| $)) $) NIL T ELT)) (|unitCanonical| #5=(#6=($ $) NIL T ELT)) (|unit?| #3#) (|transcendent?| #3#) (|transcendenceDegree| 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#1=(|PositiveInteger|) #1#) (T |FiniteFieldCyclicGroup|)) ((|getZechTable| (*1 *2) (AND (|isDomain| *2 (|PrimitiveArray| (|SingleInteger|))) (|isDomain| *1 (|FiniteFieldCyclicGroup| *3 *4)) (|ofType| *3 #1=(|PositiveInteger|)) (|ofType| *4 #1#)))) -((~= #1=(#2=(#3=(|Boolean|) $ $) NIL T ELT)) (|zero?| (#4=(#3# $) 58 T ELT)) (|unitNormal| (((|Record| (|:| |unit| $) (|:| |canonical| $) (|:| |associate| $)) $) NIL T ELT)) (|unitCanonical| #5=(#6=($ $) NIL T ELT)) (|unit?| #7=(#4# NIL T ELT)) (|transcendent?| #7#) (|transcendenceDegree| (#8=(#9=(|NonNegativeInteger|)) NIL T ELT)) (|trace| #10=(#11=(|#1| $) NIL T ELT) #12=(#13=($ $ #14=(|PositiveInteger|)) NIL #15=(|has| |#1| (|Finite|)) ELT)) (|tableForDiscreteLogarithm| (((|Table| #14# #9#) #16=(|Integer|)) 56 #15# ELT)) (|subtractIfCan| #17=((#18=(|Union| $ #19="failed") $ $) NIL T ELT)) (|squareFreePart| #5#) (|squareFree| #20=(((|Factored| $) $) NIL T ELT)) (|sizeLess?| #1#) (|size| (#8# NIL #15# ELT)) (|sample| (#21=($) NIL T CONST)) 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(#30=(#31=(|OnePointCompletion| #14#) $) NIL #28# ELT)) (|opposite?| #1#) (|one?| (#4# 62 T ELT)) (|normalElement| (#19# 157 #15# ELT)) (|normal?| (#4# NIL #15# ELT)) (|norm| #10# #12#) (|nextItem| (#32=(#17# $) NIL #15# ELT)) (|multiEuclidean| (((|Union| #25# #20#) #25# $) NIL T ELT)) (|minimalPolynomial| (#33=(#34=(|SparseUnivariatePolynomial| |#1|) $) 115 T ELT) ((#35=(|SparseUnivariatePolynomial| $) $ #14#) NIL #15# ELT)) (|lookup| (#29# 165 #15# ELT)) (|linearAssociatedOrder| #36=(#33# NIL #15# ELT)) (|linearAssociatedLog| #36# (((|Union| #34# #20#) $ $) NIL #15# ELT)) (|linearAssociatedExp| (($ $ #34#) NIL #15# ELT)) (|lcm| #22# #37=(($ #25#) NIL T ELT)) (|latex| (((|String|) $) NIL T ELT)) (|inv| (#6# 172 T ELT)) (|init| (#19# NIL #15# CONST)) (|index| (($ #14#) 94 #15# ELT)) (|inGroundField?| (#4# 142 T ELT)) (|hash| ((#38=(|SingleInteger|) $) NIL T ELT)) (|getZechTable| (((|PrimitiveArray| #38#)) 57 T ELT)) (|generator| (#19# 153 #15# ELT)) (|gcdPolynomial| ((#35# #35# #35#) NIL T ELT)) (|gcd| #22# #37#) (|factorsOfCyclicGroupSize| (((|List| (|Record| (|:| |factor| #16#) (|:| |exponent| #16#)))) 117 #15# ELT)) (|factor| #18#) (|extensionDegree| ((#31#) 88 T ELT) ((#14#) 89 T ELT)) (|extendedEuclidean| (((|Record| #39=(|:| |coef1| $) #40=(|:| |coef2| $) #26#) $ $) NIL T ELT) (((|Union| (|Record| #39# #40#) #20#) $ $ $) NIL T ELT)) (|exquo| ((#24# $ $) NIL T ELT)) (|expressIdealMember| (((|Maybe| #25#) #25# $) NIL T ELT)) (|euclideanSize| (#41=(#9# $) NIL T ELT)) (|divide| (((|Record| (|:| |quotient| $) (|:| |remainder| $)) $ $) NIL T ELT)) (|discreteLog| (#41# 156 #15# ELT) (((|Union| #9# #20#) $ $) 149 #28# ELT)) (|dimension| (((|CardinalNumber|)) NIL T ELT)) (|differentiate| #42=(#27# NIL #15# ELT) #43=(#6# NIL #15# ELT)) (|degree| (#30# NIL T ELT) (#29# NIL T ELT)) (|definingPolynomial| ((#34#) 120 T ELT)) (|createPrimitiveElement| (#19# 154 #15# ELT)) (|createNormalElement| (#19# 162 #15# ELT)) (|coordinates| ((#21# $) 76 T ELT) (((|Matrix| |#1|) #44=(|Vector| $)) NIL T ELT)) (|conditionP| (((|Union| #44# #20#) (|Matrix| $)) NIL #15# ELT)) (|coerce| (((|OutputForm|) $) 168 T ELT) (($ #16#) NIL T ELT) #5# (($ #45=(|Fraction| #16#)) NIL T ELT) (($ |#1|) 98 T ELT)) (|charthRoot| #43# (#32# NIL #28# ELT)) (|characteristic| (#8# 150 T CONST)) (|before?| #1#) (|basis| ((#44#) 141 T ELT) ((#44# #14#) 96 T ELT)) (|associates?| #1#) (|annihilate?| #1#) (|algebraic?| #7#) (|Zero| (#19# 66 T CONST)) (|One| (#19# 101 T CONST)) (|Frobenius| (#6# 105 #15# ELT) #42#) (D #42# #43#) (= (#2# 64 T ELT)) (/ (#23# 170 T ELT) (#46=($ $ |#1|) 171 T ELT)) (- (#6# 152 T ELT) #22#) (+ (#23# 84 T ELT)) (** (#13# 174 T ELT) (#27# 175 T ELT) (($ $ #16#) 173 T ELT)) (* (($ #14# $) NIL T ELT) (($ #9# $) NIL T ELT) (($ #16# $) 100 T ELT) (#23# 99 T ELT) (($ $ #45#) NIL T ELT) (($ #45# $) NIL T ELT) (#46# NIL T ELT) (($ |#1| $) 169 T ELT))) (((|FiniteFieldCyclicGroupExtensionByPolynomial| |#1| |#2|) (|Join| (|FiniteAlgebraicExtensionField| |#1|) (CATEGORY |package| (SIGNATURE |getZechTable| ((|PrimitiveArray| (|SingleInteger|)))))) (|FiniteFieldCategory|) (|SparseUnivariatePolynomial| |#1|)) (T |FiniteFieldCyclicGroupExtensionByPolynomial|)) ((|getZechTable| (*1 *2) (AND (|isDomain| *2 (|PrimitiveArray| (|SingleInteger|))) (|isDomain| *1 (|FiniteFieldCyclicGroupExtensionByPolynomial| *3 *4)) (|ofCategory| *3 (|FiniteFieldCategory|)) (|ofType| *4 (|SparseUnivariatePolynomial| *3))))) -((~= #1=((#2=(|Boolean|) $ $) NIL T ELT)) (|zero?| #3=(#4=(#2# $) NIL T ELT)) (|unitNormal| (((|Record| (|:| |unit| $) (|:| |canonical| $) (|:| |associate| $)) $) NIL T ELT)) (|unitCanonical| #5=(#6=($ $) NIL T ELT)) (|unit?| #3#) (|transcendent?| #3#) (|transcendenceDegree| (#7=(#8=(|NonNegativeInteger|)) NIL T ELT)) (|trace| #9=((|#1| $) NIL T ELT) #10=(#11=($ $ #12=(|PositiveInteger|)) NIL #13=(|has| |#1| (|Finite|)) ELT)) (|tableForDiscreteLogarithm| (((|Table| #12# #8#) #14=(|Integer|)) NIL #13# ELT)) (|subtractIfCan| #15=((#16=(|Union| $ #17="failed") $ $) NIL T ELT)) (|squareFreePart| #5#) (|squareFree| #18=(((|Factored| $) $) NIL T ELT)) (|sizeLess?| #1#) (|size| (#7# NIL #13# ELT)) (|sample| #19=(#20=($) NIL T CONST)) (|retractIfCan| (((|Union| |#1| #17#) $) NIL T ELT)) (|retract| #9#) (|represents| (($ #21=(|Vector| |#1|)) NIL T ELT)) (|representationType| (((|Union| "prime" "polynomial" "normal" "cyclic")) NIL #13# ELT)) (|rem| #22=(($ $ $) NIL T ELT)) (|recip| ((#16# $) NIL T ELT)) (|random| #23=(#20# NIL #13# ELT)) (|quo| #22#) (|principalIdeal| (((|Record| (|:| |coef| #24=(|List| $)) #25=(|:| |generator| $)) #24#) NIL T ELT)) (|primitiveElement| #23#) (|primitive?| #26=(#4# NIL #13# ELT)) (|primeFrobenius| (#27=($ $ #8#) NIL #28=(OR (|has| |#1| (|CharacteristicNonZero|)) #13#) ELT) (#6# NIL #28# ELT)) (|prime?| #3#) (|order| #29=(#30=(#12# $) NIL #13# ELT) (#31=(#32=(|OnePointCompletion| #12#) $) NIL #28# ELT)) (|opposite?| #1#) (|one?| #3#) (|normalElement| #23#) (|normal?| #26#) (|norm| #9# #10#) (|nextItem| (#33=((|Maybe| $) $) NIL #13# ELT)) (|multiEuclidean| (((|Union| #24# #17#) #24# $) NIL T ELT)) (|minimalPolynomial| (#34=(#35=(|SparseUnivariatePolynomial| |#1|) $) NIL T ELT) ((#36=(|SparseUnivariatePolynomial| $) $ #12#) NIL #13# ELT)) (|lookup| #29#) (|linearAssociatedOrder| #37=(#34# NIL #13# ELT)) (|linearAssociatedLog| #37# (((|Union| #35# #17#) $ $) NIL #13# ELT)) (|linearAssociatedExp| (($ $ #35#) NIL #13# ELT)) (|lcm| #22# #38=(($ #24#) NIL T ELT)) (|latex| (((|String|) $) NIL T ELT)) (|inv| #5#) (|init| (#20# NIL #13# CONST)) (|index| (($ #12#) NIL #13# ELT)) (|inGroundField?| #3#) (|hash| ((#39=(|SingleInteger|) $) NIL T ELT)) (|getZechTable| (((|PrimitiveArray| #39#)) NIL T ELT)) (|generator| #23#) (|gcdPolynomial| ((#36# #36# #36#) NIL T ELT)) (|gcd| #22# #38#) (|factorsOfCyclicGroupSize| (((|List| (|Record| (|:| |factor| #14#) (|:| |exponent| #14#)))) NIL #13# ELT)) (|factor| #18#) (|extensionDegree| ((#32#) NIL T ELT) ((#12#) NIL T ELT)) (|extendedEuclidean| (((|Record| #40=(|:| |coef1| $) #41=(|:| |coef2| $) #25#) $ $) NIL T ELT) (((|Union| (|Record| #40# #41#) #17#) $ $ $) NIL T ELT)) (|exquo| #15#) (|expressIdealMember| (((|Maybe| #24#) #24# $) NIL T ELT)) (|euclideanSize| (#42=(#8# $) NIL T ELT)) (|divide| (((|Record| (|:| |quotient| $) (|:| |remainder| $)) $ $) NIL T ELT)) (|discreteLog| (#42# NIL #13# ELT) (((|Union| #8# #17#) $ $) NIL #28# ELT)) (|dimension| (((|CardinalNumber|)) NIL T ELT)) (|differentiate| #43=(#27# NIL #13# ELT) #44=(#6# NIL #13# ELT)) (|degree| (#31# NIL T ELT) (#30# NIL T ELT)) (|definingPolynomial| ((#35#) NIL T ELT)) (|createPrimitiveElement| #23#) (|createNormalElement| #23#) (|coordinates| ((#21# $) NIL T ELT) (((|Matrix| |#1|) #45=(|Vector| $)) NIL T ELT)) (|conditionP| (((|Union| #45# #17#) (|Matrix| $)) NIL #13# ELT)) (|coerce| (((|OutputForm|) $) NIL T ELT) (($ #14#) NIL T ELT) #5# (($ #46=(|Fraction| #14#)) NIL T ELT) (($ |#1|) NIL T ELT)) (|charthRoot| #44# (#33# NIL #28# ELT)) (|characteristic| (#7# NIL T CONST)) (|before?| #1#) (|basis| ((#45#) NIL T ELT) ((#45# #12#) NIL T ELT)) (|associates?| #1#) (|annihilate?| #1#) (|algebraic?| #3#) (|Zero| #19#) (|One| #19#) (|Frobenius| #44# #43#) (D #43# #44#) (= #1#) (/ #22# #47=(($ $ |#1|) NIL T ELT)) (- #5# #22#) (+ #22#) (** (#11# NIL T ELT) (#27# NIL T ELT) (($ $ #14#) NIL T ELT)) (* (($ #12# $) NIL T ELT) (($ #8# $) NIL T ELT) (($ #14# . #48=($)) NIL T ELT) #22# (($ $ #46#) NIL T ELT) (($ #46# . #48#) NIL T ELT) #47# (($ |#1| . #48#) NIL T ELT))) +((~= #1=((#2=(|Boolean|) $ $) NIL T ELT)) (|zero?| #3=(#4=(#2# $) NIL T ELT)) (|unitNormal| (((|Record| (|:| |unit| $) (|:| |canonical| $) (|:| |associate| $)) $) NIL T ELT)) (|unitCanonical| #5=(#6=($ $) NIL T ELT)) (|unit?| #3#) (|transcendent?| #3#) (|transcendenceDegree| (#7=(#8=(|NonNegativeInteger|)) NIL T ELT)) (|trace| #9=((|#1| $) NIL T ELT) #10=(#11=($ $ #12=(|PositiveInteger|)) NIL #13=(|has| |#1| (|Finite|)) ELT)) (|tableForDiscreteLogarithm| (((|Table| #12# #8#) #14=(|Integer|)) NIL #13# ELT)) (|subtractIfCan| ((#15=(|Maybe| $) $ $) NIL T ELT)) (|squareFreePart| #5#) (|squareFree| #16=(((|Factored| $) $) NIL T ELT)) (|sizeLess?| #1#) (|size| (#7# NIL #13# ELT)) (|sample| #17=(#18=($) NIL T CONST)) (|retractIfCan| (((|Union| |#1| #19="failed") $) NIL T ELT)) (|retract| #9#) (|represents| (($ #20=(|Vector| |#1|)) NIL T ELT)) (|representationType| (((|Union| "prime" "polynomial" "normal" "cyclic")) NIL #13# ELT)) (|rem| #21=(($ $ $) NIL T ELT)) (|recip| ((#22=(|Union| $ #19#) $) NIL T ELT)) (|random| #23=(#18# NIL #13# ELT)) (|quo| #21#) (|principalIdeal| (((|Record| (|:| |coef| #24=(|List| $)) #25=(|:| |generator| $)) #24#) NIL T ELT)) (|primitiveElement| #23#) (|primitive?| #26=(#4# NIL #13# ELT)) (|primeFrobenius| (#27=($ $ #8#) NIL #28=(OR (|has| |#1| (|CharacteristicNonZero|)) #13#) ELT) (#6# NIL #28# ELT)) (|prime?| #3#) (|order| #29=(#30=(#12# $) NIL #13# ELT) (#31=(#32=(|OnePointCompletion| #12#) $) NIL #28# ELT)) (|opposite?| #1#) (|one?| #3#) (|normalElement| #23#) (|normal?| #26#) (|norm| #9# #10#) (|nextItem| (#33=(#15# $) NIL #13# ELT)) (|multiEuclidean| (((|Union| #24# #19#) #24# $) NIL T ELT)) (|minimalPolynomial| (#34=(#35=(|SparseUnivariatePolynomial| |#1|) $) NIL T ELT) ((#36=(|SparseUnivariatePolynomial| $) $ #12#) NIL #13# ELT)) (|lookup| #29#) (|linearAssociatedOrder| #37=(#34# NIL #13# ELT)) (|linearAssociatedLog| #37# (((|Union| #35# #19#) $ $) NIL #13# ELT)) (|linearAssociatedExp| (($ $ #35#) NIL #13# ELT)) (|lcm| #21# #38=(($ #24#) NIL T ELT)) (|latex| (((|String|) $) NIL T ELT)) (|inv| #5#) (|init| (#18# NIL #13# CONST)) (|index| (($ #12#) NIL #13# ELT)) (|inGroundField?| #3#) (|hash| ((#39=(|SingleInteger|) $) NIL T ELT)) (|getZechTable| (((|PrimitiveArray| #39#)) NIL T ELT)) (|generator| #23#) (|gcdPolynomial| ((#36# #36# #36#) NIL T ELT)) (|gcd| #21# #38#) (|factorsOfCyclicGroupSize| (((|List| (|Record| (|:| |factor| #14#) (|:| |exponent| #14#)))) NIL #13# ELT)) (|factor| #16#) (|extensionDegree| ((#32#) NIL T ELT) ((#12#) NIL T ELT)) (|extendedEuclidean| (((|Record| #40=(|:| |coef1| $) #41=(|:| |coef2| $) #25#) $ $) NIL T ELT) (((|Union| (|Record| #40# #41#) #19#) $ $ $) NIL T ELT)) (|exquo| ((#22# $ $) NIL T ELT)) (|expressIdealMember| (((|Maybe| #24#) #24# $) NIL T ELT)) (|euclideanSize| (#42=(#8# $) NIL T ELT)) (|divide| (((|Record| (|:| |quotient| $) (|:| |remainder| $)) $ $) NIL T ELT)) (|discreteLog| (#42# NIL #13# ELT) (((|Union| #8# #19#) $ $) NIL #28# ELT)) (|dimension| (((|CardinalNumber|)) NIL T ELT)) (|differentiate| #43=(#27# NIL #13# ELT) #44=(#6# NIL #13# ELT)) (|degree| (#31# NIL T ELT) (#30# NIL T ELT)) (|definingPolynomial| ((#35#) NIL T ELT)) (|createPrimitiveElement| #23#) (|createNormalElement| #23#) (|coordinates| ((#20# $) NIL T ELT) (((|Matrix| |#1|) #45=(|Vector| $)) NIL T ELT)) (|conditionP| (((|Union| #45# #19#) (|Matrix| $)) NIL #13# ELT)) (|coerce| (((|OutputForm|) $) NIL T ELT) (($ #14#) NIL T ELT) #5# (($ #46=(|Fraction| #14#)) NIL T ELT) (($ |#1|) NIL T ELT)) (|charthRoot| #44# (#33# NIL #28# ELT)) (|characteristic| (#7# NIL T CONST)) (|before?| #1#) (|basis| ((#45#) NIL T ELT) ((#45# #12#) NIL T ELT)) (|associates?| #1#) (|annihilate?| #1#) (|algebraic?| #3#) (|Zero| #17#) (|One| #17#) (|Frobenius| #44# #43#) (D #43# #44#) (= #1#) (/ #21# #47=(($ $ |#1|) NIL T ELT)) (- #5# #21#) (+ #21#) (** (#11# NIL T ELT) (#27# NIL T ELT) (($ $ #14#) NIL T ELT)) (* (($ #12# $) NIL T ELT) (($ #8# $) NIL T ELT) (($ #14# . #48=($)) NIL T ELT) #21# (($ $ #46#) NIL T ELT) (($ #46# . #48#) NIL T ELT) #47# (($ |#1| . #48#) NIL T ELT))) (((|FiniteFieldCyclicGroupExtension| |#1| |#2|) (|Join| (|FiniteAlgebraicExtensionField| |#1|) (CATEGORY |package| (SIGNATURE |getZechTable| ((|PrimitiveArray| (|SingleInteger|)))))) (|FiniteFieldCategory|) (|PositiveInteger|)) (T |FiniteFieldCyclicGroupExtension|)) ((|getZechTable| (*1 *2) (AND (|isDomain| *2 (|PrimitiveArray| (|SingleInteger|))) (|isDomain| *1 (|FiniteFieldCyclicGroupExtension| *3 *4)) (|ofCategory| *3 (|FiniteFieldCategory|)) (|ofType| *4 (|PositiveInteger|))))) ((|sizeMultiplication| (((|NonNegativeInteger|) #1=(|Vector| (|List| (|Record| (|:| |value| |#1|) (|:| |index| #2=(|SingleInteger|)))))) 61 T ELT)) (|createZechTable| (((|PrimitiveArray| #2#) #3=(|SparseUnivariatePolynomial| |#1|)) 112 T ELT)) (|createMultiplicationTable| ((#1# #3#) 103 T ELT)) (|createMultiplicationMatrix| (((|Matrix| |#1|) #1#) 113 T ELT)) (|createLowComplexityTable| (((|Union| #1# "failed") #4=(|PositiveInteger|)) 13 T ELT)) (|createLowComplexityNormalBasis| (((|Union| #3# #1#) #4#) 18 T ELT))) @@ -974,7 +974,7 @@ NIL ((|primitive?| (((|Boolean|) $) 65 T ELT)) (|order| (((|OnePointCompletion| #1=(|PositiveInteger|)) $) 26 T ELT) ((#1# $) 69 T ELT)) (|nextItem| (#2=((|Maybe| $) $) 21 T ELT)) (|init| (#3=($) 9 T CONST)) (|gcdPolynomial| ((#4=(|SparseUnivariatePolynomial| $) #4# #4#) 120 T ELT)) (|discreteLog| (((|Union| #5=(|NonNegativeInteger|) #6="failed") $ $) 98 T ELT) ((#5# $) 84 T ELT)) (|differentiate| (#7=($ $) 8 T ELT) (($ $ #5#) NIL T ELT)) (|createPrimitiveElement| (#3# 58 T ELT)) (|conditionP| (((|Union| (|Vector| $) #6#) (|Matrix| $)) 41 T ELT)) (|charthRoot| (#2# 50 T ELT) (#7# 47 T ELT))) (((|FiniteFieldCategory&| |#1|) (CATEGORY |package| (SIGNATURE |order| (#1=(|PositiveInteger|) |#1|)) (SIGNATURE |discreteLog| (#2=(|NonNegativeInteger|) |#1|)) (SIGNATURE |primitive?| ((|Boolean|) |#1|)) (SIGNATURE |createPrimitiveElement| #3=(|#1|)) (SIGNATURE |conditionP| ((|Union| (|Vector| |#1|) #4="failed") (|Matrix| |#1|))) (SIGNATURE |charthRoot| #5=(|#1| |#1|)) (SIGNATURE |differentiate| (|#1| |#1| #2#)) (SIGNATURE |differentiate| #5#) (SIGNATURE |init| #3# |constant|) (SIGNATURE |nextItem| #6=((|Maybe| |#1|) |#1|)) (SIGNATURE |discreteLog| ((|Union| #2# #4#) |#1| |#1|)) (SIGNATURE |order| ((|OnePointCompletion| #1#) |#1|)) (SIGNATURE |charthRoot| #6#) (SIGNATURE |gcdPolynomial| (#7=(|SparseUnivariatePolynomial| |#1|) #7# #7#))) (|FiniteFieldCategory|)) (T |FiniteFieldCategory&|)) NIL -((~= (#1=((|Boolean|) $ $) 7 T ELT)) (|zero?| ((#2=(|Boolean|) $) 22 T ELT)) (|unitNormal| (((|Record| (|:| |unit| $) (|:| |canonical| $) (|:| |associate| $)) $) 55 T ELT)) (|unitCanonical| (($ $) 54 T ELT)) (|unit?| ((#3=(|Boolean|) $) 52 T ELT)) (|tableForDiscreteLogarithm| (((|Table| (|PositiveInteger|) (|NonNegativeInteger|)) (|Integer|)) 113 T ELT)) (|subtractIfCan| (((|Union| $ "failed") $ $) 26 T ELT)) (|squareFreePart| (($ $) 91 T ELT)) (|squareFree| (#4=((|Factored| $) $) 90 T ELT)) (|sizeLess?| (((|Boolean|) $ $) 75 T ELT)) (|size| (((|NonNegativeInteger|)) 123 T ELT)) (|sample| (#5=($) 23 T CONST)) (|representationType| (((|Union| "prime" "polynomial" "normal" "cyclic")) 107 T ELT)) (|rem| (#6=($ $ $) 71 T ELT)) (|recip| (((|Union| $ "failed") $) 42 T ELT)) (|random| (($) 126 T ELT)) (|quo| (#6# 72 T ELT)) (|principalIdeal| (((|Record| (|:| |coef| #7=(|List| $)) (|:| |generator| $)) #7#) 66 T ELT)) (|primitiveElement| (($) 111 T ELT)) (|primitive?| (((|Boolean|) $) 110 T ELT)) (|primeFrobenius| (($ $) 97 T ELT) (($ $ #8=(|NonNegativeInteger|)) 96 T ELT)) (|prime?| (((|Boolean|) $) 89 T ELT)) (|order| (((|OnePointCompletion| (|PositiveInteger|)) $) 99 T ELT) (((|PositiveInteger|) $) 108 T ELT)) (|opposite?| ((#2# $ $) 20 T ELT)) (|one?| (((|Boolean|) $) 44 T ELT)) (|nextItem| (((|Maybe| $) $) 122 T ELT)) (|multiEuclidean| (((|Union| #9=(|List| $) #10="failed") #9# $) 68 T ELT)) (|lookup| ((#11=(|PositiveInteger|) $) 125 T ELT)) (|lcm| (#12=($ $ $) 60 T ELT) (#13=($ (|List| $)) 59 T ELT)) (|latex| (((|String|) $) 11 T ELT)) (|inv| (($ $) 88 T ELT)) (|init| (($) 121 T CONST)) (|index| (($ #11#) 124 T ELT)) (|hash| (((|SingleInteger|) $) 12 T ELT)) (|gcdPolynomial| ((#14=(|SparseUnivariatePolynomial| $) #14# #14#) 58 T ELT)) (|gcd| (#12# 62 T ELT) (#13# 61 T ELT)) (|factorsOfCyclicGroupSize| (((|List| (|Record| (|:| |factor| (|Integer|)) (|:| |exponent| (|Integer|))))) 114 T ELT)) (|factor| (#4# 92 T ELT)) (|extendedEuclidean| (((|Record| #15=(|:| |coef1| $) #16=(|:| |coef2| $) (|:| |generator| $)) $ $) 70 T ELT) (((|Union| (|Record| #15# #16#) #10#) $ $ $) 69 T ELT)) (|exquo| (((|Union| $ "failed") $ $) 56 T ELT)) (|expressIdealMember| (((|Maybe| #7#) #7# $) 65 T ELT)) (|euclideanSize| (((|NonNegativeInteger|) $) 74 T ELT)) (|divide| (((|Record| (|:| |quotient| $) (|:| |remainder| $)) $ $) 73 T ELT)) (|discreteLog| (((|Union| #8# "failed") $ $) 98 T ELT) (((|NonNegativeInteger|) $) 109 T ELT)) (|differentiate| (($ . #17=($)) 120 T ELT) (#18=($ $ (|NonNegativeInteger|)) 118 T ELT)) (|createPrimitiveElement| (($) 112 T ELT)) (|conditionP| (((|Union| (|Vector| $) "failed") (|Matrix| $)) 115 T ELT)) (|coerce| (((|OutputForm|) $) 13 T ELT) (($ (|Integer|)) 41 T ELT) (($ $) 57 T ELT) (($ #19=(|Fraction| #20=(|Integer|))) 84 T ELT)) (|charthRoot| (((|Maybe| $) $) 100 T ELT) (($ $) 116 T ELT)) (|characteristic| (((|NonNegativeInteger|)) 40 T CONST)) (|before?| (#1# 6 T ELT)) (|associates?| ((#3# $ $) 53 T ELT)) (|annihilate?| (((|Boolean|) $ $) 33 T ELT)) (|Zero| (#5# 24 T CONST)) (|One| (($) 45 T CONST)) (D (($ . #17#) 119 T ELT) (#18# 117 T ELT)) (= (#1# 8 T ELT)) (/ (($ $ $) 83 T ELT)) (- (($ $) 29 T ELT) (($ $ $) 28 T ELT)) (+ (($ $ $) 18 T ELT)) (** (($ $ (|PositiveInteger|)) 35 T ELT) (($ $ (|NonNegativeInteger|)) 43 T ELT) (($ $ #20#) 87 T ELT)) (* (($ (|PositiveInteger|) $) 17 T ELT) (($ (|NonNegativeInteger|) $) 21 T ELT) (($ (|Integer|) . #21=($)) 30 T ELT) (($ $ $) 34 T ELT) (($ $ #19#) 86 T ELT) (($ #19# . #21#) 85 T ELT))) +((~= (#1=((|Boolean|) $ $) 7 T ELT)) (|zero?| ((#2=(|Boolean|) $) 22 T ELT)) (|unitNormal| (((|Record| (|:| |unit| $) (|:| |canonical| $) (|:| |associate| $)) $) 56 T ELT)) (|unitCanonical| (($ $) 55 T ELT)) (|unit?| ((#3=(|Boolean|) $) 53 T ELT)) (|tableForDiscreteLogarithm| (((|Table| (|PositiveInteger|) (|NonNegativeInteger|)) (|Integer|)) 113 T ELT)) (|subtractIfCan| (((|Maybe| $) $ $) 26 T ELT)) (|squareFreePart| (($ $) 92 T ELT)) (|squareFree| (#4=((|Factored| $) $) 91 T ELT)) (|sizeLess?| (((|Boolean|) $ $) 76 T ELT)) (|size| (((|NonNegativeInteger|)) 123 T ELT)) (|sample| (#5=($) 23 T CONST)) (|representationType| (((|Union| "prime" "polynomial" "normal" "cyclic")) 107 T ELT)) (|rem| (#6=($ $ $) 72 T ELT)) (|recip| (((|Union| $ "failed") $) 43 T ELT)) (|random| (($) 126 T ELT)) (|quo| (#6# 73 T ELT)) (|principalIdeal| (((|Record| (|:| |coef| #7=(|List| $)) (|:| |generator| $)) #7#) 67 T ELT)) (|primitiveElement| (($) 111 T ELT)) (|primitive?| (((|Boolean|) $) 110 T ELT)) (|primeFrobenius| (($ $) 98 T ELT) (($ $ #8=(|NonNegativeInteger|)) 97 T ELT)) (|prime?| (((|Boolean|) $) 90 T ELT)) (|order| (((|OnePointCompletion| (|PositiveInteger|)) $) 100 T ELT) (((|PositiveInteger|) $) 108 T ELT)) (|opposite?| ((#2# $ $) 20 T ELT)) (|one?| (((|Boolean|) $) 45 T ELT)) (|nextItem| (((|Maybe| $) $) 122 T ELT)) (|multiEuclidean| (((|Union| #9=(|List| $) #10="failed") #9# $) 69 T ELT)) (|lookup| ((#11=(|PositiveInteger|) $) 125 T ELT)) (|lcm| (#12=($ $ $) 61 T ELT) (#13=($ (|List| $)) 60 T ELT)) (|latex| (((|String|) $) 11 T ELT)) (|inv| (($ $) 89 T ELT)) (|init| (($) 121 T CONST)) (|index| (($ #11#) 124 T ELT)) (|hash| (((|SingleInteger|) $) 12 T ELT)) (|gcdPolynomial| ((#14=(|SparseUnivariatePolynomial| $) #14# #14#) 59 T ELT)) (|gcd| (#12# 63 T ELT) (#13# 62 T ELT)) (|factorsOfCyclicGroupSize| (((|List| (|Record| (|:| |factor| (|Integer|)) (|:| |exponent| (|Integer|))))) 114 T ELT)) (|factor| (#4# 93 T ELT)) (|extendedEuclidean| (((|Record| #15=(|:| |coef1| $) #16=(|:| |coef2| $) (|:| |generator| $)) $ $) 71 T ELT) (((|Union| (|Record| #15# #16#) #10#) $ $ $) 70 T ELT)) (|exquo| (((|Union| $ "failed") $ $) 57 T ELT)) (|expressIdealMember| (((|Maybe| #7#) #7# $) 66 T ELT)) (|euclideanSize| (((|NonNegativeInteger|) $) 75 T ELT)) (|divide| (((|Record| (|:| |quotient| $) (|:| |remainder| $)) $ $) 74 T ELT)) (|discreteLog| (((|Union| #8# "failed") $ $) 99 T ELT) (((|NonNegativeInteger|) $) 109 T ELT)) (|differentiate| (($ . #17=($)) 120 T ELT) (#18=($ $ (|NonNegativeInteger|)) 118 T ELT)) (|createPrimitiveElement| (($) 112 T ELT)) (|conditionP| (((|Union| (|Vector| $) "failed") (|Matrix| $)) 115 T ELT)) (|coerce| (((|OutputForm|) $) 13 T ELT) (($ (|Integer|)) 42 T ELT) (($ $) 58 T ELT) (($ #19=(|Fraction| #20=(|Integer|))) 85 T ELT)) (|charthRoot| (((|Maybe| $) $) 101 T ELT) (($ $) 116 T ELT)) (|characteristic| (((|NonNegativeInteger|)) 41 T CONST)) (|before?| (#1# 6 T ELT)) (|associates?| ((#3# $ $) 54 T ELT)) (|annihilate?| (((|Boolean|) $ $) 34 T ELT)) (|Zero| (#5# 24 T CONST)) (|One| (($) 46 T CONST)) (D (($ . #17#) 119 T ELT) (#18# 117 T ELT)) (= (#1# 8 T ELT)) (/ (($ $ $) 84 T ELT)) (- (($ $) 30 T ELT) (($ $ $) 29 T ELT)) (+ (($ $ $) 18 T ELT)) (** (($ $ (|PositiveInteger|)) 36 T ELT) (($ $ (|NonNegativeInteger|)) 44 T ELT) (($ $ #20#) 88 T ELT)) (* (($ (|PositiveInteger|) $) 17 T ELT) (($ (|NonNegativeInteger|) $) 21 T ELT) (($ (|Integer|) . #21=($)) 31 T ELT) (($ $ $) 35 T ELT) (($ $ #19#) 87 T ELT) (($ #19# . #21#) 86 T ELT))) (((|FiniteFieldCategory|) (|Category|)) (T |FiniteFieldCategory|)) ((|charthRoot| (*1 *1 *1) (|ofCategory| *1 (|FiniteFieldCategory|))) (|conditionP| (*1 *2 *3) (|partial| AND (|isDomain| *3 (|Matrix| *1)) (|ofCategory| *1 (|FiniteFieldCategory|)) (|isDomain| *2 (|Vector| *1)))) (|factorsOfCyclicGroupSize| (*1 *2) (AND (|ofCategory| *1 (|FiniteFieldCategory|)) (|isDomain| *2 (|List| (|Record| (|:| |factor| (|Integer|)) (|:| |exponent| (|Integer|))))))) (|tableForDiscreteLogarithm| (*1 *2 *3) (AND (|ofCategory| *1 (|FiniteFieldCategory|)) (|isDomain| *3 (|Integer|)) (|isDomain| *2 (|Table| (|PositiveInteger|) (|NonNegativeInteger|))))) (|createPrimitiveElement| (*1 *1) (|ofCategory| *1 (|FiniteFieldCategory|))) (|primitiveElement| (*1 *1) (|ofCategory| *1 (|FiniteFieldCategory|))) (|primitive?| (*1 *2 *1) (AND (|ofCategory| *1 (|FiniteFieldCategory|)) (|isDomain| *2 (|Boolean|)))) (|discreteLog| (*1 *2 *1) (AND (|ofCategory| *1 (|FiniteFieldCategory|)) (|isDomain| *2 (|NonNegativeInteger|)))) (|order| (*1 *2 *1) (AND (|ofCategory| *1 (|FiniteFieldCategory|)) (|isDomain| *2 (|PositiveInteger|)))) (|representationType| (*1 *2) (AND (|ofCategory| *1 (|FiniteFieldCategory|)) (|isDomain| *2 (|Union| "prime" "polynomial" "normal" "cyclic"))))) (|Join| (|FieldOfPrimeCharacteristic|) (|Finite|) (|StepThrough|) (|DifferentialRing|) (CATEGORY |domain| (SIGNATURE |charthRoot| ($ $)) (SIGNATURE |conditionP| ((|Union| (|Vector| $) "failed") (|Matrix| $))) (SIGNATURE |factorsOfCyclicGroupSize| ((|List| (|Record| (|:| |factor| (|Integer|)) (|:| |exponent| (|Integer|)))))) (SIGNATURE |tableForDiscreteLogarithm| ((|Table| (|PositiveInteger|) (|NonNegativeInteger|)) (|Integer|))) (SIGNATURE |createPrimitiveElement| ($)) (SIGNATURE |primitiveElement| ($)) (SIGNATURE |primitive?| ((|Boolean|) $)) (SIGNATURE |discreteLog| ((|NonNegativeInteger|) $)) (SIGNATURE |order| ((|PositiveInteger|) $)) (SIGNATURE |representationType| ((|Union| "prime" "polynomial" "normal" "cyclic"))))) @@ -982,19 +982,19 @@ NIL ((|localIntegralBasis| ((#1=(|Record| (|:| |basis| #2=(|Matrix| |#1|)) (|:| |basisDen| |#1|) (|:| |basisInv| #2#)) |#1|) 55 T ELT)) (|integralBasis| ((#1#) 53 T ELT))) (((|FunctionFieldIntegralBasis| |#1| |#2| |#3|) (CATEGORY |package| (SIGNATURE |integralBasis| (#1=(|Record| (|:| |basis| #2=(|Matrix| |#1|)) (|:| |basisDen| |#1|) (|:| |basisInv| #2#)))) (SIGNATURE |localIntegralBasis| (#1# |#1|))) (|Join| (|EuclideanDomain|) (CATEGORY |domain| (SIGNATURE |squareFree| ((|Factored| $) $)))) (|UnivariatePolynomialCategory| |#1|) (|FramedAlgebra| |#1| |#2|)) (T |FunctionFieldIntegralBasis|)) ((|localIntegralBasis| (*1 *2 *3) #1=(AND (|ofCategory| *3 (|Join| (|EuclideanDomain|) (CATEGORY |domain| (SIGNATURE |squareFree| ((|Factored| $) $))))) (|ofCategory| *4 (|UnivariatePolynomialCategory| *3)) (|isDomain| *2 (|Record| (|:| |basis| #2=(|Matrix| *3)) (|:| |basisDen| *3) (|:| |basisInv| #2#))) (|isDomain| *1 (|FunctionFieldIntegralBasis| *3 *4 *5)) (|ofCategory| *5 (|FramedAlgebra| *3 *4)))) (|integralBasis| (*1 *2) #1#)) -((~= #1=((#2=(|Boolean|) $ $) NIL T ELT)) (|zero?| #3=(#4=(#2# $) NIL T ELT)) (|unitNormal| (((|Record| (|:| |unit| $) (|:| |canonical| $) (|:| |associate| $)) $) NIL T ELT)) (|unitCanonical| #5=(#6=($ $) NIL T ELT)) (|unit?| #3#) (|transcendent?| #3#) (|transcendenceDegree| #7=(#8=(#9=(|NonNegativeInteger|)) NIL T ELT)) (|trace| #10=((#11=(|PrimeField| |#1|) $) NIL T ELT) #12=(#13=($ $ #14=(|PositiveInteger|)) NIL #15=(|has| #11# (|Finite|)) ELT)) (|tableForDiscreteLogarithm| (((|Table| #14# #9#) #16=(|Integer|)) NIL #15# ELT)) (|subtractIfCan| #17=((#18=(|Union| $ #19="failed") $ $) NIL T ELT)) (|squareFreePart| #5#) (|squareFree| #20=(((|Factored| $) $) NIL T ELT)) (|sizeMultiplication| #7#) (|sizeLess?| #1#) (|size| (#8# NIL #15# ELT)) (|sample| #21=(#22=($) NIL T CONST)) (|retractIfCan| (((|Union| #11# #19#) $) NIL T ELT)) (|retract| #10#) (|represents| (($ #23=(|Vector| #11#)) NIL T ELT)) (|representationType| (((|Union| "prime" "polynomial" "normal" "cyclic")) NIL #15# ELT)) (|rem| #24=(($ $ $) NIL T ELT)) (|recip| ((#18# $) NIL T ELT)) (|random| #25=(#22# NIL #15# ELT)) (|quo| #24#) (|principalIdeal| (((|Record| (|:| |coef| #26=(|List| $)) #27=(|:| |generator| $)) #26#) NIL T ELT)) (|primitiveElement| #25#) (|primitive?| #28=(#4# NIL #15# ELT)) (|primeFrobenius| (#29=($ $ #9#) NIL #30=(OR (|has| #11# (|CharacteristicNonZero|)) #15#) ELT) (#6# NIL #30# ELT)) (|prime?| #3#) (|order| #31=(#32=(#14# $) NIL #15# ELT) (#33=(#34=(|OnePointCompletion| #14#) $) NIL #30# ELT)) (|opposite?| #1#) (|one?| #3#) (|normalElement| #25#) (|normal?| #28#) (|norm| #10# #12#) (|nextItem| (#35=((|Maybe| $) $) NIL #15# ELT)) (|multiEuclidean| (((|Union| #26# #19#) #26# $) NIL T ELT)) (|minimalPolynomial| (#36=(#37=(|SparseUnivariatePolynomial| #11#) $) NIL T ELT) ((#38=(|SparseUnivariatePolynomial| $) $ #14#) NIL #15# ELT)) (|lookup| #31#) (|linearAssociatedOrder| #39=(#36# NIL #15# ELT)) (|linearAssociatedLog| #39# (((|Union| #37# #19#) $ $) NIL #15# ELT)) (|linearAssociatedExp| (($ $ #37#) NIL #15# ELT)) (|lcm| #24# #40=(($ #26#) NIL T ELT)) (|latex| (((|String|) $) NIL T ELT)) (|inv| #5#) (|init| (#22# NIL #15# CONST)) (|index| (($ #14#) NIL #15# ELT)) (|inGroundField?| #3#) (|hash| ((#41=(|SingleInteger|) $) NIL T ELT)) (|getMultiplicationTable| (((|Vector| (|List| (|Record| (|:| |value| #11#) (|:| |index| #41#))))) NIL T ELT)) (|getMultiplicationMatrix| ((#42=(|Matrix| #11#)) NIL T ELT)) (|generator| #25#) (|gcdPolynomial| ((#38# #38# #38#) NIL T ELT)) (|gcd| #24# #40#) (|factorsOfCyclicGroupSize| (((|List| (|Record| (|:| |factor| #16#) (|:| |exponent| #16#)))) NIL #15# ELT)) (|factor| #20#) (|extensionDegree| ((#34#) NIL T ELT) ((#14#) NIL T ELT)) (|extendedEuclidean| (((|Record| #43=(|:| |coef1| $) #44=(|:| |coef2| $) #27#) $ $) NIL T ELT) (((|Union| (|Record| #43# #44#) #19#) $ $ $) NIL T ELT)) (|exquo| #17#) (|expressIdealMember| (((|Maybe| #26#) #26# $) NIL T ELT)) (|euclideanSize| (#45=(#9# $) NIL T ELT)) (|divide| (((|Record| (|:| |quotient| $) (|:| |remainder| $)) $ $) NIL T ELT)) (|discreteLog| (#45# NIL #15# ELT) (((|Union| #9# #19#) $ $) NIL #30# ELT)) (|dimension| (((|CardinalNumber|)) NIL T ELT)) (|differentiate| #46=(#29# NIL #15# ELT) #47=(#6# NIL #15# ELT)) (|degree| (#33# NIL T ELT) (#32# NIL T ELT)) (|definingPolynomial| ((#37#) NIL T ELT)) (|createPrimitiveElement| #25#) (|createNormalElement| #25#) (|coordinates| ((#23# $) NIL T ELT) ((#42# #48=(|Vector| $)) NIL T ELT)) (|conditionP| (((|Union| #48# #19#) (|Matrix| $)) NIL #15# ELT)) (|coerce| (((|OutputForm|) $) NIL T ELT) (($ #16#) NIL T ELT) #5# (($ #49=(|Fraction| #16#)) NIL T ELT) (($ #11#) NIL T ELT)) (|charthRoot| #47# (#35# NIL #30# ELT)) (|characteristic| (#8# NIL T CONST)) (|before?| #1#) (|basis| ((#48#) NIL T ELT) ((#48# #14#) NIL T ELT)) (|associates?| #1#) (|annihilate?| #1#) (|algebraic?| #3#) (|Zero| #21#) 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(|extensionDegree| ((#34#) NIL T ELT) ((#14#) NIL T ELT)) (|extendedEuclidean| (((|Record| #43=(|:| |coef1| $) #44=(|:| |coef2| $) #27#) $ $) NIL T ELT) (((|Union| (|Record| #43# #44#) #21#) $ $ $) NIL T ELT)) (|exquo| ((#24# $ $) NIL T ELT)) (|expressIdealMember| (((|Maybe| #26#) #26# $) NIL T ELT)) (|euclideanSize| (#45=(#9# $) NIL T ELT)) (|divide| (((|Record| (|:| |quotient| $) (|:| |remainder| $)) $ $) NIL T ELT)) (|discreteLog| (#45# NIL #15# ELT) (((|Union| #9# #21#) $ $) NIL #30# ELT)) (|dimension| (((|CardinalNumber|)) NIL T ELT)) (|differentiate| #46=(#29# NIL #15# ELT) #47=(#6# NIL #15# ELT)) (|degree| (#33# NIL T ELT) (#32# NIL T ELT)) (|definingPolynomial| ((#37#) NIL T ELT)) (|createPrimitiveElement| #25#) (|createNormalElement| #25#) (|coordinates| ((#22# $) NIL T ELT) ((#42# #48=(|Vector| $)) NIL T ELT)) (|conditionP| (((|Union| #48# #21#) (|Matrix| $)) NIL #15# ELT)) (|coerce| (((|OutputForm|) $) NIL T ELT) (($ #16#) NIL T ELT) #5# (($ #49=(|Fraction| #16#)) NIL T ELT) (($ #11#) NIL T ELT)) (|charthRoot| #47# (#35# NIL #30# ELT)) (|characteristic| (#8# NIL T CONST)) (|before?| #1#) (|basis| ((#48#) NIL T ELT) ((#48# #14#) NIL T ELT)) (|associates?| #1#) (|annihilate?| #1#) (|algebraic?| #3#) (|Zero| #19#) (|One| #19#) (|Frobenius| #47# #46#) (D #46# #47#) (= #1#) (/ #23# #50=(($ $ #11#) NIL T ELT)) (- #5# #23#) (+ #23#) (** (#13# NIL T ELT) (#29# NIL T ELT) (($ $ #16#) NIL T ELT)) (* (($ #14# $) NIL T ELT) (($ #9# $) NIL T ELT) (($ #16# . #51=($)) NIL T ELT) #23# (($ $ #49#) NIL T ELT) (($ #49# . #51#) NIL T ELT) #50# (($ #11# . #51#) NIL T ELT))) (((|FiniteFieldNormalBasis| |#1| |#2|) (|Join| (|FiniteAlgebraicExtensionField| #1=(|PrimeField| |#1|)) (CATEGORY |package| (SIGNATURE |getMultiplicationTable| ((|Vector| (|List| (|Record| (|:| |value| #1#) (|:| |index| (|SingleInteger|))))))) (SIGNATURE |getMultiplicationMatrix| ((|Matrix| #1#))) (SIGNATURE |sizeMultiplication| ((|NonNegativeInteger|))))) #2=(|PositiveInteger|) #2#) (T |FiniteFieldNormalBasis|)) ((|getMultiplicationTable| #1=(*1 *2) (AND (|isDomain| *2 (|Vector| (|List| (|Record| (|:| |value| #2=(|PrimeField| *3)) (|:| |index| (|SingleInteger|)))))) #3=(|isDomain| *1 (|FiniteFieldNormalBasis| *3 *4)) #4=(|ofType| *3 #5=(|PositiveInteger|)) #6=(|ofType| *4 #5#))) (|getMultiplicationMatrix| #1# (AND (|isDomain| *2 (|Matrix| #2#)) #3# #4# #6#)) (|sizeMultiplication| #1# (AND (|isDomain| *2 (|NonNegativeInteger|)) #3# #4# #6#))) -((~= (#1=(#2=(|Boolean|) $ $) 72 T ELT)) (|zero?| (#3=(#2# $) 87 T ELT)) (|unitNormal| (((|Record| (|:| |unit| $) (|:| |canonical| $) (|:| |associate| $)) $) NIL T ELT)) (|unitCanonical| #4=(#5=($ $) NIL T ELT)) (|unit?| #6=(#3# NIL T ELT)) (|transcendent?| #6#) (|transcendenceDegree| (#7=(#8=(|NonNegativeInteger|)) NIL T ELT)) (|trace| (#9=(|#1| $) 105 T ELT) (#10=($ $ #11=(|PositiveInteger|)) 103 #12=(|has| |#1| (|Finite|)) ELT)) (|tableForDiscreteLogarithm| (((|Table| #11# #8#) #13=(|Integer|)) 168 #12# ELT)) (|subtractIfCan| #14=((#15=(|Union| $ #16="failed") $ $) NIL T ELT)) (|squareFreePart| #4#) (|squareFree| #17=(((|Factored| $) $) NIL T ELT)) (|sizeMultiplication| (#7# 102 T ELT)) (|sizeLess?| #18=(#1# NIL T ELT)) (|size| (#7# 185 #12# ELT)) (|sample| (#19=($) NIL T CONST)) (|retractIfCan| (((|Union| |#1| #16#) $) 126 T ELT)) (|retract| (#9# 104 T ELT)) (|represents| (($ #20=(|Vector| |#1|)) 70 T ELT)) (|representationType| (((|Union| "prime" "polynomial" "normal" "cyclic")) 211 #12# ELT)) (|rem| #21=(#22=($ $ $) NIL T ELT)) (|recip| ((#15# $) NIL T ELT)) (|random| (#19# 180 #12# ELT)) (|quo| #21#) (|principalIdeal| (((|Record| (|:| |coef| #23=(|List| $)) #24=(|:| |generator| $)) #23#) NIL T ELT)) (|primitiveElement| (#19# 169 #12# ELT)) (|primitive?| (#3# NIL #12# ELT)) (|primeFrobenius| (#25=($ $ #8#) NIL #26=(OR (|has| |#1| (|CharacteristicNonZero|)) #12#) ELT) (#5# NIL #26# ELT)) (|prime?| #6#) (|order| (#27=(#11# $) NIL #12# ELT) (#28=(#29=(|OnePointCompletion| #11#) $) NIL #26# ELT)) 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(|primitive?| #27=(#4# NIL #14# ELT)) (|primeFrobenius| (#28=($ $ #9#) NIL #29=(OR (|has| |#1| (|CharacteristicNonZero|)) #14#) ELT) (#6# NIL #29# ELT)) (|prime?| #3#) (|order| #30=(#31=(#13# $) NIL #14# ELT) (#32=(#33=(|OnePointCompletion| #13#) $) NIL #29# ELT)) (|opposite?| #1#) (|one?| #3#) (|normalElement| #24#) (|normal?| #27#) (|norm| #10# #11#) (|nextItem| (#34=(#16# $) NIL #14# ELT)) (|multiEuclidean| (((|Union| #25# #20#) #25# $) NIL T ELT)) (|minimalPolynomial| (#35=(#36=(|SparseUnivariatePolynomial| |#1|) $) NIL T ELT) ((#37=(|SparseUnivariatePolynomial| $) $ #13#) NIL #14# ELT)) (|lookup| #30#) (|linearAssociatedOrder| #38=(#35# NIL #14# ELT)) (|linearAssociatedLog| #38# (((|Union| #36# #20#) $ $) NIL #14# ELT)) (|linearAssociatedExp| (($ $ #36#) NIL #14# ELT)) (|lcm| #22# #39=(($ #25#) NIL T ELT)) (|latex| (((|String|) $) NIL T ELT)) (|inv| #5#) (|init| (#19# NIL #14# CONST)) (|index| (($ #13#) NIL #14# ELT)) (|inGroundField?| #3#) (|hash| ((#40=(|SingleInteger|) $) NIL T ELT)) (|getMultiplicationTable| (((|Vector| (|List| (|Record| (|:| |value| |#1|) (|:| |index| #40#))))) NIL T ELT)) (|getMultiplicationMatrix| ((#41=(|Matrix| |#1|)) NIL T ELT)) (|generator| #24#) (|gcdPolynomial| ((#37# #37# #37#) NIL T ELT)) (|gcd| #22# #39#) (|factorsOfCyclicGroupSize| (((|List| (|Record| (|:| |factor| #15#) (|:| |exponent| #15#)))) NIL #14# ELT)) (|factor| #17#) (|extensionDegree| ((#33#) NIL T ELT) ((#13#) NIL T ELT)) (|extendedEuclidean| (((|Record| #42=(|:| |coef1| $) #43=(|:| |coef2| $) #26#) $ $) NIL T ELT) (((|Union| (|Record| #42# #43#) #20#) $ $ $) NIL T ELT)) (|exquo| ((#23# $ $) NIL T ELT)) (|expressIdealMember| (((|Maybe| #25#) #25# $) NIL T ELT)) (|euclideanSize| (#44=(#9# $) NIL T ELT)) (|divide| (((|Record| (|:| |quotient| $) (|:| |remainder| $)) $ $) NIL T ELT)) (|discreteLog| (#44# NIL #14# ELT) (((|Union| #9# #20#) $ $) NIL #29# ELT)) (|dimension| (((|CardinalNumber|)) NIL T ELT)) (|differentiate| #45=(#28# NIL #14# ELT) #46=(#6# NIL #14# ELT)) (|degree| (#32# NIL T ELT) (#31# NIL T ELT)) (|definingPolynomial| ((#36#) NIL T ELT)) (|createPrimitiveElement| #24#) (|createNormalElement| #24#) (|coordinates| ((#21# $) NIL T ELT) ((#41# #47=(|Vector| $)) NIL T ELT)) (|conditionP| (((|Union| #47# #20#) (|Matrix| $)) NIL #14# ELT)) (|coerce| (((|OutputForm|) $) NIL T ELT) (($ #15#) NIL T ELT) #5# (($ #48=(|Fraction| #15#)) NIL T ELT) (($ |#1|) NIL T ELT)) (|charthRoot| #46# (#34# NIL #29# ELT)) (|characteristic| (#8# NIL T CONST)) (|before?| #1#) (|basis| ((#47#) NIL T ELT) ((#47# #13#) NIL T ELT)) (|associates?| #1#) (|annihilate?| #1#) (|algebraic?| #3#) (|Zero| #18#) (|One| #18#) (|Frobenius| #46# #45#) (D #45# #46#) (= #1#) (/ #22# #49=(($ $ |#1|) NIL T ELT)) (- #5# #22#) (+ #22#) (** (#12# NIL T ELT) (#28# NIL T ELT) (($ $ #15#) NIL T ELT)) (* (($ #13# $) NIL T ELT) (($ #9# $) NIL T ELT) (($ #15# . #50=($)) NIL T ELT) #22# (($ $ #48#) NIL T ELT) (($ #48# . #50#) NIL T ELT) #49# (($ |#1| . #50#) NIL T ELT))) (((|FiniteFieldNormalBasisExtension| |#1| |#2|) (|Join| (|FiniteAlgebraicExtensionField| |#1|) (CATEGORY |package| (SIGNATURE |getMultiplicationTable| ((|Vector| (|List| (|Record| (|:| |value| |#1|) (|:| |index| (|SingleInteger|))))))) (SIGNATURE |getMultiplicationMatrix| ((|Matrix| |#1|))) (SIGNATURE |sizeMultiplication| ((|NonNegativeInteger|))))) (|FiniteFieldCategory|) (|PositiveInteger|)) (T |FiniteFieldNormalBasisExtension|)) ((|getMultiplicationTable| #1=(*1 *2) (AND (|isDomain| *2 (|Vector| (|List| (|Record| (|:| |value| *3) (|:| |index| (|SingleInteger|)))))) #2=(|isDomain| *1 (|FiniteFieldNormalBasisExtension| *3 *4)) #3=(|ofCategory| *3 (|FiniteFieldCategory|)) #4=(|ofType| *4 (|PositiveInteger|)))) (|getMultiplicationMatrix| #1# (AND (|isDomain| *2 (|Matrix| *3)) #2# #3# #4#)) (|sizeMultiplication| #1# (AND (|isDomain| *2 (|NonNegativeInteger|)) #2# #3# #4#))) -((~= #1=(#2=(#3=(|Boolean|) $ $) NIL T ELT)) (|zero?| #4=(#5=(#3# $) NIL T ELT)) (|unitNormal| (((|Record| (|:| |unit| $) (|:| |canonical| $) (|:| |associate| $)) $) NIL T ELT)) (|unitCanonical| #6=(#7=($ $) NIL T ELT)) (|unit?| #4#) (|transcendent?| #4#) (|transcendenceDegree| (#8=(#9=(|NonNegativeInteger|)) NIL T ELT)) (|trace| (#10=(|#1| $) NIL T ELT) (#11=($ $ #12=(|PositiveInteger|)) NIL #13=(|has| |#1| (|Finite|)) ELT)) (|tableForDiscreteLogarithm| (((|Table| #12# #9#) #14=(|Integer|)) 130 #13# ELT)) (|subtractIfCan| #15=((#16=(|Union| $ #17="failed") $ $) NIL T ELT)) (|squareFreePart| #6#) (|squareFree| #18=(((|Factored| $) $) NIL T ELT)) (|sizeLess?| #1#) (|size| (#8# 156 #13# ELT)) (|sample| (#19=($) NIL T CONST)) (|retractIfCan| (((|Union| |#1| #17#) $) 104 T ELT)) (|retract| (#10# 101 T ELT)) (|represents| (($ #20=(|Vector| |#1|)) 96 T ELT)) (|representationType| (((|Union| "prime" "polynomial" "normal" "cyclic")) 127 #13# ELT)) (|rem| #21=(#22=($ $ $) NIL T ELT)) (|recip| ((#16# $) NIL T ELT)) (|random| (#19# 93 #13# ELT)) (|quo| #21#) (|principalIdeal| (((|Record| (|:| |coef| #23=(|List| $)) #24=(|:| |generator| $)) #23#) NIL T ELT)) (|primitiveElement| (#19# 52 #13# ELT)) (|primitive?| (#5# NIL #13# ELT)) (|primeFrobenius| (#25=($ $ #9#) NIL #26=(OR (|has| |#1| (|CharacteristicNonZero|)) #13#) ELT) (#7# NIL #26# ELT)) (|prime?| #4#) (|order| (#27=(#12# $) NIL #13# ELT) (#28=(#29=(|OnePointCompletion| #12#) $) NIL #26# ELT)) (|opposite?| #1#) (|one?| #4#) (|normalElement| (#19# 131 #13# ELT)) (|normal?| (#5# 85 #13# ELT)) (|norm| (#10# 48 T ELT) (#11# 53 #13# ELT)) (|nextItem| (#30=((|Maybe| $) $) NIL #13# ELT)) (|multiEuclidean| (((|Union| #23# #17#) #23# $) NIL T ELT)) (|minimalPolynomial| (#31=(#32=(|SparseUnivariatePolynomial| |#1|) $) 76 T ELT) ((#33=(|SparseUnivariatePolynomial| $) $ #12#) NIL #13# ELT)) (|lookup| (#27# 108 #13# ELT)) (|linearAssociatedOrder| #34=(#31# NIL #13# ELT)) (|linearAssociatedLog| #34# (((|Union| #32# #17#) $ $) NIL #13# ELT)) (|linearAssociatedExp| (($ $ #32#) NIL #13# ELT)) (|lcm| #21# #35=(($ #23#) NIL T ELT)) (|latex| (((|String|) $) NIL T ELT)) (|inv| #6#) (|init| (#19# NIL #13# CONST)) (|index| (($ #12#) 106 #13# ELT)) (|inGroundField?| (#5# 158 T ELT)) (|hash| (((|SingleInteger|) $) NIL T ELT)) (|generator| (#19# 45 #13# ELT)) (|gcdPolynomial| ((#33# #33# #33#) NIL T ELT)) (|gcd| #21# #35#) (|factorsOfCyclicGroupSize| (((|List| (|Record| (|:| |factor| #14#) (|:| |exponent| #14#)))) 125 #13# ELT)) (|factor| #18#) (|extensionDegree| ((#29#) NIL T ELT) ((#12#) 155 T ELT)) (|extendedEuclidean| (((|Record| #36=(|:| |coef1| $) #37=(|:| |coef2| $) #24#) $ $) NIL T ELT) (((|Union| (|Record| #36# #37#) #17#) $ $ $) NIL T ELT)) (|exquo| #15#) (|expressIdealMember| (((|Maybe| #23#) #23# $) NIL T ELT)) (|euclideanSize| (#38=(#9# $) NIL T ELT)) (|divide| (((|Record| (|:| |quotient| $) (|:| |remainder| $)) $ $) NIL T ELT)) (|discreteLog| (#38# NIL #13# ELT) (((|Union| #9# #17#) $ $) NIL #26# ELT)) (|dimension| (((|CardinalNumber|)) NIL T ELT)) (|differentiate| #39=(#25# NIL #13# ELT) #40=(#7# NIL #13# ELT)) (|degree| (#28# NIL T ELT) (#27# 68 T ELT)) (|definingPolynomial| ((#32#) 99 T ELT)) (|createPrimitiveElement| (#19# 136 #13# ELT)) (|createNormalElement| (#19# NIL #13# ELT)) (|coordinates| ((#20# $) 64 T ELT) (((|Matrix| |#1|) #41=(|Vector| $)) NIL T ELT)) (|conditionP| (((|Union| #41# #17#) (|Matrix| $)) NIL #13# ELT)) (|coerce| (((|OutputForm|) $) 154 T ELT) (($ #14#) NIL T ELT) #6# (($ #42=(|Fraction| #14#)) NIL T ELT) (($ |#1|) 98 T ELT)) (|charthRoot| #40# (#30# NIL #26# ELT)) (|characteristic| (#8# 160 T CONST)) (|before?| (#2# 162 T ELT)) (|basis| ((#41#) 120 T ELT) ((#41# #12#) 59 T ELT)) (|associates?| #1#) (|annihilate?| #1#) (|algebraic?| #4#) (|Zero| (#19# 122 T CONST)) (|One| (#19# 40 T CONST)) (|Frobenius| (#7# 79 #13# ELT) #39#) (D #39# #40#) (= (#2# 118 T ELT)) (/ (#22# 110 T ELT) (#43=($ $ |#1|) 111 T ELT)) (- (#7# 91 T ELT) (#22# 116 T ELT)) (+ (#22# 114 T ELT)) (** (#11# NIL T ELT) (#25# 54 T ELT) (($ $ #14#) 139 T ELT)) (* (($ #12# $) NIL T ELT) (($ #9# $) NIL T ELT) (($ #14# $) 89 T ELT) (#22# 66 T ELT) (($ $ #42#) NIL T ELT) (($ #42# $) NIL T ELT) (#43# NIL T ELT) (($ |#1| $) 87 T ELT))) +((~= #1=(#2=(#3=(|Boolean|) $ $) NIL T ELT)) (|zero?| #4=(#5=(#3# $) NIL T ELT)) (|unitNormal| (((|Record| (|:| |unit| $) (|:| |canonical| $) (|:| |associate| $)) $) NIL T ELT)) (|unitCanonical| #6=(#7=($ $) NIL T ELT)) (|unit?| #4#) (|transcendent?| #4#) (|transcendenceDegree| (#8=(#9=(|NonNegativeInteger|)) NIL T ELT)) (|trace| (#10=(|#1| $) NIL T ELT) (#11=($ $ #12=(|PositiveInteger|)) NIL #13=(|has| |#1| (|Finite|)) ELT)) (|tableForDiscreteLogarithm| (((|Table| #12# #9#) #14=(|Integer|)) 130 #13# ELT)) (|subtractIfCan| ((#15=(|Maybe| $) $ $) NIL T ELT)) (|squareFreePart| #6#) (|squareFree| #16=(((|Factored| $) $) NIL T ELT)) (|sizeLess?| #1#) (|size| (#8# 156 #13# ELT)) (|sample| (#17=($) NIL T CONST)) (|retractIfCan| (((|Union| |#1| #18="failed") $) 104 T ELT)) (|retract| (#10# 101 T ELT)) (|represents| (($ #19=(|Vector| |#1|)) 96 T ELT)) (|representationType| (((|Union| "prime" "polynomial" "normal" "cyclic")) 127 #13# ELT)) (|rem| #20=(#21=($ $ $) NIL T ELT)) (|recip| ((#22=(|Union| $ #18#) $) NIL T ELT)) (|random| (#17# 93 #13# ELT)) (|quo| #20#) (|principalIdeal| (((|Record| (|:| |coef| #23=(|List| $)) #24=(|:| |generator| $)) #23#) NIL T ELT)) (|primitiveElement| (#17# 52 #13# ELT)) (|primitive?| (#5# NIL #13# ELT)) (|primeFrobenius| (#25=($ $ #9#) NIL #26=(OR (|has| |#1| (|CharacteristicNonZero|)) #13#) ELT) (#7# NIL #26# ELT)) (|prime?| #4#) (|order| (#27=(#12# $) NIL #13# ELT) (#28=(#29=(|OnePointCompletion| #12#) $) NIL #26# ELT)) (|opposite?| #1#) (|one?| #4#) (|normalElement| (#17# 131 #13# ELT)) (|normal?| (#5# 85 #13# ELT)) (|norm| (#10# 48 T ELT) (#11# 53 #13# ELT)) (|nextItem| (#30=(#15# $) NIL #13# ELT)) (|multiEuclidean| (((|Union| #23# #18#) #23# $) NIL T ELT)) (|minimalPolynomial| (#31=(#32=(|SparseUnivariatePolynomial| |#1|) $) 76 T ELT) ((#33=(|SparseUnivariatePolynomial| $) $ #12#) NIL #13# ELT)) (|lookup| (#27# 108 #13# ELT)) (|linearAssociatedOrder| #34=(#31# NIL #13# ELT)) (|linearAssociatedLog| #34# (((|Union| #32# #18#) $ $) NIL #13# ELT)) (|linearAssociatedExp| (($ $ #32#) NIL #13# ELT)) (|lcm| #20# #35=(($ #23#) NIL T ELT)) (|latex| (((|String|) $) NIL T ELT)) (|inv| #6#) (|init| (#17# NIL #13# CONST)) (|index| (($ #12#) 106 #13# ELT)) (|inGroundField?| (#5# 158 T ELT)) (|hash| (((|SingleInteger|) $) NIL T ELT)) (|generator| (#17# 45 #13# ELT)) (|gcdPolynomial| ((#33# #33# #33#) NIL T ELT)) (|gcd| #20# #35#) (|factorsOfCyclicGroupSize| (((|List| (|Record| (|:| |factor| #14#) (|:| |exponent| #14#)))) 125 #13# ELT)) (|factor| #16#) (|extensionDegree| ((#29#) NIL T ELT) ((#12#) 155 T ELT)) (|extendedEuclidean| (((|Record| #36=(|:| |coef1| $) #37=(|:| |coef2| $) #24#) $ $) NIL T ELT) (((|Union| (|Record| #36# #37#) #18#) $ $ $) NIL T ELT)) (|exquo| ((#22# $ $) NIL T ELT)) (|expressIdealMember| (((|Maybe| #23#) #23# $) NIL T ELT)) (|euclideanSize| (#38=(#9# $) NIL T ELT)) (|divide| (((|Record| (|:| |quotient| $) (|:| |remainder| $)) $ $) NIL T ELT)) (|discreteLog| (#38# NIL #13# ELT) (((|Union| #9# #18#) $ $) NIL #26# ELT)) (|dimension| (((|CardinalNumber|)) NIL T ELT)) (|differentiate| #39=(#25# NIL #13# ELT) #40=(#7# NIL #13# ELT)) (|degree| (#28# NIL T ELT) (#27# 68 T ELT)) (|definingPolynomial| ((#32#) 99 T ELT)) (|createPrimitiveElement| (#17# 136 #13# ELT)) (|createNormalElement| (#17# NIL #13# ELT)) (|coordinates| ((#19# $) 64 T ELT) (((|Matrix| |#1|) #41=(|Vector| $)) NIL T ELT)) (|conditionP| (((|Union| #41# #18#) (|Matrix| $)) NIL #13# ELT)) (|coerce| (((|OutputForm|) $) 154 T ELT) (($ #14#) NIL T ELT) #6# (($ #42=(|Fraction| #14#)) NIL T ELT) (($ |#1|) 98 T ELT)) (|charthRoot| #40# (#30# NIL #26# ELT)) (|characteristic| (#8# 160 T CONST)) (|before?| (#2# 162 T ELT)) (|basis| ((#41#) 120 T ELT) ((#41# #12#) 59 T ELT)) (|associates?| #1#) (|annihilate?| #1#) (|algebraic?| #4#) (|Zero| (#17# 122 T CONST)) (|One| (#17# 40 T CONST)) (|Frobenius| (#7# 79 #13# ELT) #39#) (D #39# #40#) (= (#2# 118 T ELT)) (/ (#21# 110 T ELT) (#43=($ $ |#1|) 111 T ELT)) (- (#7# 91 T ELT) (#21# 116 T ELT)) (+ (#21# 114 T ELT)) (** (#11# NIL T ELT) (#25# 54 T ELT) (($ $ #14#) 139 T ELT)) (* (($ #12# $) NIL T ELT) (($ #9# $) NIL T ELT) (($ #14# $) 89 T ELT) (#21# 66 T ELT) (($ $ #42#) NIL T ELT) (($ #42# $) NIL T ELT) (#43# NIL T ELT) (($ |#1| $) 87 T ELT))) (((|FiniteFieldExtensionByPolynomial| |#1| |#2|) (|FiniteAlgebraicExtensionField| |#1|) (|FiniteFieldCategory|) (|SparseUnivariatePolynomial| |#1|)) (T |FiniteFieldExtensionByPolynomial|)) NIL -((|reducedQPowers| (((|PrimitiveArray| #1=(|SparseUnivariatePolynomial| |#1|)) #1#) 49 T ELT)) (|random| ((#1# #2=(|PositiveInteger|) #2#) 159 T ELT) (#3=(#1# #2#) 155 T ELT)) (|primitive?| (#4=((|Boolean|) #1#) 110 T ELT)) (|numberOfPrimitivePoly| (#5=(#2# #2#) 85 T ELT)) (|numberOfNormalPoly| (#5# 94 T ELT)) (|numberOfIrreduciblePoly| (#5# 83 T ELT)) (|normal?| (#4# 114 T ELT)) (|nextPrimitivePoly| (#6=((|Union| #1# "failed") #1#) 139 T ELT)) (|nextPrimitiveNormalPoly| (#6# 144 T ELT)) (|nextNormalPrimitivePoly| (#6# 143 T ELT)) (|nextNormalPoly| (#6# 142 T ELT)) (|nextIrreduciblePoly| (#6# 134 T ELT)) (|leastAffineMultiple| ((#1# #1#) 71 T ELT)) (|createPrimitivePoly| (#3# 149 T ELT)) (|createPrimitiveNormalPoly| (#3# 152 T ELT)) (|createNormalPrimitivePoly| (#3# 151 T ELT)) (|createNormalPoly| (#3# 150 T ELT)) (|createIrreduciblePoly| (#3# 147 T ELT))) +((|reducedQPowers| (((|PrimitiveArray| #1=(|SparseUnivariatePolynomial| |#1|)) #1#) 49 T ELT)) (|random| ((#1# #2=(|PositiveInteger|) #2#) 158 T ELT) (#3=(#1# #2#) 155 T ELT)) (|primitive?| (#4=((|Boolean|) #1#) 110 T ELT)) (|numberOfPrimitivePoly| (#5=(#2# #2#) 85 T ELT)) (|numberOfNormalPoly| (#5# 94 T ELT)) (|numberOfIrreduciblePoly| (#5# 83 T ELT)) (|normal?| (#4# 114 T ELT)) (|nextPrimitivePoly| (#6=((|Union| #1# "failed") #1#) 139 T ELT)) (|nextPrimitiveNormalPoly| (#6# 144 T ELT)) (|nextNormalPrimitivePoly| (#6# 143 T ELT)) (|nextNormalPoly| (#6# 142 T ELT)) (|nextIrreduciblePoly| (#6# 134 T ELT)) (|leastAffineMultiple| ((#1# #1#) 71 T ELT)) (|createPrimitivePoly| (#3# 149 T ELT)) (|createPrimitiveNormalPoly| (#3# 152 T ELT)) (|createNormalPrimitivePoly| (#3# 151 T ELT)) (|createNormalPoly| (#3# 150 T ELT)) (|createIrreduciblePoly| (#3# 147 T ELT))) (((|FiniteFieldPolynomialPackage| |#1|) (CATEGORY |package| (SIGNATURE |primitive?| #1=((|Boolean|) #2=(|SparseUnivariatePolynomial| |#1|))) (SIGNATURE |normal?| #1#) (SIGNATURE |numberOfIrreduciblePoly| #3=(#4=(|PositiveInteger|) #4#)) (SIGNATURE |numberOfPrimitivePoly| #3#) (SIGNATURE |numberOfNormalPoly| #3#) (SIGNATURE |createIrreduciblePoly| #5=(#2# #4#)) (SIGNATURE |createPrimitivePoly| #5#) (SIGNATURE |createNormalPoly| #5#) (SIGNATURE |createNormalPrimitivePoly| #5#) (SIGNATURE |createPrimitiveNormalPoly| #5#) (SIGNATURE |nextIrreduciblePoly| #6=((|Union| #2# "failed") #2#)) (SIGNATURE |nextPrimitivePoly| #6#) (SIGNATURE |nextNormalPoly| #6#) (SIGNATURE |nextNormalPrimitivePoly| #6#) (SIGNATURE |nextPrimitiveNormalPoly| #6#) (SIGNATURE |random| #5#) (SIGNATURE |random| (#2# #4# #4#)) (SIGNATURE |leastAffineMultiple| (#2# #2#)) (SIGNATURE |reducedQPowers| ((|PrimitiveArray| #2#) #2#))) (|FiniteFieldCategory|)) (T |FiniteFieldPolynomialPackage|)) ((|reducedQPowers| #1=(*1 *2 *3) (AND #2=(|ofCategory| *4 #3=(|FiniteFieldCategory|)) (|isDomain| *2 (|PrimitiveArray| #4=(|SparseUnivariatePolynomial| *4))) #5=(|isDomain| *1 (|FiniteFieldPolynomialPackage| *4)) #6=(|isDomain| *3 #4#))) (|leastAffineMultiple| #7=(*1 *2 *2) (AND #8=(|isDomain| *2 (|SparseUnivariatePolynomial| *3)) #9=(|ofCategory| *3 #3#) #10=(|isDomain| *1 (|FiniteFieldPolynomialPackage| *3)))) (|random| (*1 *2 *3 *3) #11=(AND (|isDomain| *3 #12=(|PositiveInteger|)) (|isDomain| *2 #4#) #5# #2#)) (|random| #1# #11#) (|nextPrimitiveNormalPoly| #7# #13=(|partial| AND #8# #9# #10#)) (|nextNormalPrimitivePoly| #7# #13#) (|nextNormalPoly| #7# #13#) (|nextPrimitivePoly| #7# #13#) (|nextIrreduciblePoly| #7# #13#) (|createPrimitiveNormalPoly| #1# #11#) (|createNormalPrimitivePoly| #1# #11#) (|createNormalPoly| #1# #11#) (|createPrimitivePoly| #1# #11#) (|createIrreduciblePoly| #1# #11#) (|numberOfNormalPoly| #7# #14=(AND (|isDomain| *2 #12#) #10# #9#)) (|numberOfPrimitivePoly| #7# #14#) (|numberOfIrreduciblePoly| #7# #14#) (|normal?| #1# #15=(AND #6# #2# (|isDomain| *2 (|Boolean|)) #5#)) (|primitive?| #1# #15#)) ((|rootOfIrreduciblePoly| ((|#1| (|SparseUnivariatePolynomial| |#2|)) 60 T ELT))) @@ -1003,7 +1003,7 @@ NIL ((|solveLinearPolynomialEquation| (((|Union| #1=(|List| |#3|) "failed") #1# |#3|) 40 T ELT))) (((|FiniteFieldSolveLinearPolynomialEquation| |#1| |#2| |#3|) (CATEGORY |package| (SIGNATURE |solveLinearPolynomialEquation| ((|Union| #1=(|List| |#3|) "failed") #1# |#3|))) (|FiniteFieldCategory|) (|UnivariatePolynomialCategory| |#1|) (|UnivariatePolynomialCategory| |#2|)) (T |FiniteFieldSolveLinearPolynomialEquation|)) ((|solveLinearPolynomialEquation| (*1 *2 *2 *3) (|partial| AND (|isDomain| *2 (|List| *3)) (|ofCategory| *3 (|UnivariatePolynomialCategory| *5)) (|ofCategory| *5 (|UnivariatePolynomialCategory| *4)) (|ofCategory| *4 (|FiniteFieldCategory|)) (|isDomain| *1 (|FiniteFieldSolveLinearPolynomialEquation| *4 *5 *3))))) -((~= #1=((#2=(|Boolean|) $ $) NIL T ELT)) (|zero?| #3=(#4=(#2# $) NIL T ELT)) (|unitNormal| (((|Record| (|:| |unit| $) (|:| |canonical| $) (|:| |associate| $)) $) NIL T ELT)) (|unitCanonical| #5=(#6=($ $) NIL T ELT)) (|unit?| #3#) (|transcendent?| #3#) (|transcendenceDegree| (#7=(#8=(|NonNegativeInteger|)) NIL T ELT)) (|trace| #9=((|#1| $) NIL T ELT) #10=(#11=($ $ #12=(|PositiveInteger|)) NIL #13=(|has| |#1| (|Finite|)) ELT)) (|tableForDiscreteLogarithm| (((|Table| #12# #8#) #14=(|Integer|)) NIL #13# ELT)) (|subtractIfCan| #15=((#16=(|Union| $ #17="failed") $ $) NIL T ELT)) (|squareFreePart| #5#) (|squareFree| #18=(((|Factored| $) $) NIL T ELT)) (|sizeLess?| #1#) (|size| (#7# NIL #13# ELT)) (|sample| #19=(#20=($) NIL T CONST)) (|retractIfCan| (((|Union| |#1| #17#) $) NIL T ELT)) (|retract| #9#) (|represents| (($ #21=(|Vector| |#1|)) NIL T ELT)) (|representationType| (((|Union| "prime" "polynomial" "normal" "cyclic")) NIL #13# ELT)) (|rem| #22=(($ $ $) NIL T ELT)) (|recip| ((#16# $) NIL T ELT)) (|random| #23=(#20# NIL #13# ELT)) (|quo| #22#) (|principalIdeal| (((|Record| (|:| |coef| #24=(|List| $)) #25=(|:| |generator| $)) #24#) NIL T ELT)) (|primitiveElement| #23#) (|primitive?| #26=(#4# NIL #13# ELT)) (|primeFrobenius| (#27=($ $ #8#) NIL #28=(OR (|has| |#1| (|CharacteristicNonZero|)) #13#) ELT) (#6# NIL #28# ELT)) (|prime?| #3#) (|order| #29=(#30=(#12# $) NIL #13# ELT) (#31=(#32=(|OnePointCompletion| #12#) $) NIL #28# ELT)) (|opposite?| #1#) (|one?| #3#) (|normalElement| #23#) (|normal?| #26#) (|norm| #9# #10#) (|nextItem| (#33=((|Maybe| $) $) NIL #13# ELT)) (|multiEuclidean| (((|Union| #24# #17#) #24# $) NIL T ELT)) (|minimalPolynomial| (#34=(#35=(|SparseUnivariatePolynomial| |#1|) $) NIL T ELT) ((#36=(|SparseUnivariatePolynomial| $) $ #12#) NIL #13# ELT)) (|lookup| #29#) (|linearAssociatedOrder| #37=(#34# NIL #13# ELT)) (|linearAssociatedLog| #37# (((|Union| #35# #17#) $ $) NIL #13# ELT)) (|linearAssociatedExp| (($ $ #35#) NIL #13# ELT)) (|lcm| #22# #38=(($ #24#) NIL T ELT)) (|latex| (((|String|) $) NIL T ELT)) (|inv| #5#) (|init| (#20# NIL #13# CONST)) (|index| (($ #12#) NIL #13# ELT)) (|inGroundField?| #3#) (|hash| (((|SingleInteger|) $) NIL T ELT)) (|generator| #23#) (|gcdPolynomial| ((#36# #36# #36#) NIL T ELT)) (|gcd| #22# #38#) (|factorsOfCyclicGroupSize| (((|List| (|Record| (|:| |factor| #14#) (|:| |exponent| #14#)))) NIL #13# ELT)) (|factor| #18#) (|extensionDegree| ((#32#) NIL T ELT) ((#12#) NIL T ELT)) (|extendedEuclidean| (((|Record| #39=(|:| |coef1| $) #40=(|:| |coef2| $) #25#) $ $) NIL T ELT) (((|Union| (|Record| #39# #40#) #17#) $ $ $) NIL T ELT)) (|exquo| #15#) (|expressIdealMember| (((|Maybe| #24#) #24# $) NIL T ELT)) (|euclideanSize| (#41=(#8# $) NIL T ELT)) (|divide| (((|Record| (|:| |quotient| $) (|:| |remainder| $)) $ $) NIL T ELT)) (|discreteLog| (#41# NIL #13# ELT) (((|Union| #8# #17#) $ $) NIL #28# ELT)) (|dimension| (((|CardinalNumber|)) NIL T ELT)) (|differentiate| #42=(#27# NIL #13# ELT) #43=(#6# NIL #13# ELT)) (|degree| (#31# NIL T ELT) (#30# NIL T ELT)) (|definingPolynomial| ((#35#) NIL T ELT)) (|createPrimitiveElement| #23#) (|createNormalElement| #23#) (|coordinates| ((#21# $) NIL T ELT) (((|Matrix| |#1|) #44=(|Vector| $)) NIL T ELT)) (|conditionP| (((|Union| #44# #17#) (|Matrix| $)) NIL #13# ELT)) (|coerce| (((|OutputForm|) $) NIL T ELT) (($ #14#) NIL T ELT) #5# (($ #45=(|Fraction| #14#)) NIL T ELT) (($ |#1|) NIL T ELT)) (|charthRoot| #43# (#33# NIL #28# ELT)) (|characteristic| (#7# NIL T CONST)) (|before?| #1#) (|basis| ((#44#) NIL T ELT) ((#44# #12#) NIL T ELT)) (|associates?| #1#) (|annihilate?| #1#) (|algebraic?| #3#) (|Zero| #19#) (|One| #19#) (|Frobenius| #43# #42#) (D #42# #43#) (= #1#) (/ #22# #46=(($ $ |#1|) NIL T ELT)) (- #5# #22#) (+ #22#) (** (#11# NIL T ELT) (#27# NIL T ELT) (($ $ #14#) NIL T ELT)) (* (($ #12# $) NIL T ELT) (($ #8# $) NIL T ELT) (($ #14# . #47=($)) NIL T ELT) #22# (($ $ #45#) NIL T ELT) (($ #45# . #47#) NIL T ELT) #46# (($ |#1| . #47#) NIL T ELT))) +((~= #1=((#2=(|Boolean|) $ $) NIL T ELT)) (|zero?| #3=(#4=(#2# $) NIL T ELT)) (|unitNormal| (((|Record| (|:| |unit| $) (|:| |canonical| $) (|:| |associate| $)) $) NIL T ELT)) (|unitCanonical| #5=(#6=($ $) NIL T ELT)) (|unit?| #3#) (|transcendent?| #3#) (|transcendenceDegree| (#7=(#8=(|NonNegativeInteger|)) NIL T ELT)) (|trace| #9=((|#1| $) NIL T ELT) #10=(#11=($ $ #12=(|PositiveInteger|)) NIL #13=(|has| |#1| (|Finite|)) ELT)) (|tableForDiscreteLogarithm| (((|Table| #12# #8#) #14=(|Integer|)) NIL #13# ELT)) (|subtractIfCan| ((#15=(|Maybe| $) $ $) NIL T ELT)) (|squareFreePart| #5#) (|squareFree| #16=(((|Factored| $) $) NIL T ELT)) (|sizeLess?| #1#) (|size| (#7# NIL #13# ELT)) (|sample| #17=(#18=($) NIL T CONST)) (|retractIfCan| (((|Union| |#1| #19="failed") $) NIL T ELT)) (|retract| #9#) (|represents| (($ #20=(|Vector| |#1|)) NIL T ELT)) (|representationType| (((|Union| "prime" "polynomial" "normal" "cyclic")) NIL #13# ELT)) (|rem| #21=(($ $ $) NIL T ELT)) (|recip| ((#22=(|Union| $ #19#) $) NIL T ELT)) (|random| #23=(#18# NIL #13# ELT)) (|quo| #21#) (|principalIdeal| (((|Record| (|:| |coef| #24=(|List| $)) #25=(|:| |generator| $)) #24#) NIL T ELT)) (|primitiveElement| #23#) (|primitive?| #26=(#4# NIL #13# ELT)) (|primeFrobenius| (#27=($ $ #8#) NIL #28=(OR (|has| |#1| (|CharacteristicNonZero|)) #13#) ELT) (#6# NIL #28# ELT)) (|prime?| #3#) (|order| #29=(#30=(#12# $) NIL #13# ELT) (#31=(#32=(|OnePointCompletion| #12#) $) NIL #28# ELT)) (|opposite?| #1#) (|one?| #3#) (|normalElement| #23#) (|normal?| #26#) (|norm| #9# #10#) (|nextItem| (#33=(#15# $) NIL #13# ELT)) (|multiEuclidean| (((|Union| #24# #19#) #24# $) NIL T ELT)) (|minimalPolynomial| (#34=(#35=(|SparseUnivariatePolynomial| |#1|) $) NIL T ELT) ((#36=(|SparseUnivariatePolynomial| $) $ #12#) NIL #13# ELT)) (|lookup| #29#) (|linearAssociatedOrder| #37=(#34# NIL #13# ELT)) (|linearAssociatedLog| #37# (((|Union| #35# #19#) $ $) NIL #13# ELT)) (|linearAssociatedExp| (($ $ #35#) NIL #13# ELT)) (|lcm| #21# #38=(($ #24#) NIL T ELT)) (|latex| (((|String|) $) NIL T ELT)) (|inv| #5#) (|init| (#18# NIL #13# CONST)) (|index| (($ #12#) NIL #13# ELT)) (|inGroundField?| #3#) (|hash| (((|SingleInteger|) $) NIL T ELT)) (|generator| #23#) (|gcdPolynomial| ((#36# #36# #36#) NIL T ELT)) (|gcd| #21# #38#) (|factorsOfCyclicGroupSize| (((|List| (|Record| (|:| |factor| #14#) (|:| |exponent| #14#)))) NIL #13# ELT)) (|factor| #16#) (|extensionDegree| ((#32#) NIL T ELT) ((#12#) NIL T ELT)) (|extendedEuclidean| (((|Record| #39=(|:| |coef1| $) #40=(|:| |coef2| $) #25#) $ $) NIL T ELT) (((|Union| (|Record| #39# #40#) #19#) $ $ $) NIL T ELT)) (|exquo| ((#22# $ $) NIL T ELT)) (|expressIdealMember| (((|Maybe| #24#) #24# $) NIL T ELT)) (|euclideanSize| (#41=(#8# $) NIL T ELT)) (|divide| (((|Record| (|:| |quotient| $) (|:| |remainder| $)) $ $) NIL T ELT)) (|discreteLog| (#41# NIL #13# ELT) (((|Union| #8# #19#) $ $) NIL #28# ELT)) (|dimension| (((|CardinalNumber|)) NIL T ELT)) (|differentiate| #42=(#27# NIL #13# ELT) #43=(#6# NIL #13# ELT)) (|degree| (#31# NIL T ELT) (#30# NIL T ELT)) (|definingPolynomial| ((#35#) NIL T ELT)) (|createPrimitiveElement| #23#) (|createNormalElement| #23#) (|coordinates| ((#20# $) NIL T ELT) (((|Matrix| |#1|) #44=(|Vector| $)) NIL T ELT)) (|conditionP| (((|Union| #44# #19#) (|Matrix| $)) NIL #13# ELT)) (|coerce| (((|OutputForm|) $) NIL T ELT) (($ #14#) NIL T ELT) #5# (($ #45=(|Fraction| #14#)) NIL T ELT) (($ |#1|) NIL T ELT)) (|charthRoot| #43# (#33# NIL #28# ELT)) (|characteristic| (#7# NIL T CONST)) (|before?| #1#) (|basis| ((#44#) NIL T ELT) ((#44# #12#) NIL T ELT)) (|associates?| #1#) (|annihilate?| #1#) (|algebraic?| #3#) (|Zero| #17#) (|One| #17#) (|Frobenius| #43# #42#) (D #42# #43#) (= #1#) (/ #21# #46=(($ $ |#1|) NIL T ELT)) (- #5# #21#) (+ #21#) (** (#11# NIL T ELT) (#27# NIL T ELT) (($ $ #14#) NIL T ELT)) (* (($ #12# $) NIL T ELT) (($ #8# $) NIL T ELT) (($ #14# . #47=($)) NIL T ELT) #21# (($ $ #45#) NIL T ELT) (($ #45# . #47#) NIL T ELT) #46# (($ |#1| . #47#) NIL T ELT))) (((|FiniteFieldExtension| |#1| |#2|) (|FiniteAlgebraicExtensionField| |#1|) (|FiniteFieldCategory|) (|PositiveInteger|)) (T |FiniteFieldExtension|)) NIL ((|zeroDimensional?| (((|Boolean|) #1=(|List| (|Polynomial| |#1|))) 41 T ELT)) (|groebner| ((#1# #1#) 53 T ELT)) (|fglmIfCan| (((|Union| #1# "failed") #1#) 48 T ELT))) @@ -1015,10 +1015,10 @@ NIL ((|unitNormal| (((|Record| (|:| |unit| $) (|:| |canonical| $) (|:| |associate| $)) $) 13 T ELT)) (|unitCanonical| (#1=($ $) 14 T ELT)) (|squareFree| (#2=((|Factored| $) $) 31 T ELT)) (|prime?| ((#3=(|Boolean|) $) 27 T ELT)) (|inv| (#1# 19 T ELT)) (|gcd| (#4=($ $ $) 22 T ELT) (($ (|List| $)) NIL T ELT)) (|factor| (#2# 32 T ELT)) (|exquo| (((|Union| $ "failed") $ $) 21 T ELT)) (|euclideanSize| (((|NonNegativeInteger|) $) 25 T ELT)) (|divide| (((|Record| (|:| |quotient| $) (|:| |remainder| $)) $ $) 36 T ELT)) (|associates?| ((#3# $ $) 16 T ELT)) (/ (#4# 34 T ELT))) (((|Field&| |#1|) (CATEGORY |package| (SIGNATURE / #1=(|#1| |#1| |#1|)) (SIGNATURE |inv| #2=(|#1| |#1|)) (SIGNATURE |prime?| (#3=(|Boolean|) |#1|)) (SIGNATURE |squareFree| #4=((|Factored| |#1|) |#1|)) (SIGNATURE |factor| #4#) (SIGNATURE |divide| ((|Record| (|:| |quotient| |#1|) (|:| |remainder| |#1|)) |#1| |#1|)) (SIGNATURE |euclideanSize| ((|NonNegativeInteger|) |#1|)) (SIGNATURE |gcd| (|#1| (|List| |#1|))) (SIGNATURE |gcd| #1#) (SIGNATURE |associates?| (#3# |#1| |#1|)) (SIGNATURE |unitCanonical| #2#) (SIGNATURE |unitNormal| ((|Record| (|:| |unit| |#1|) (|:| |canonical| |#1|) (|:| |associate| |#1|)) |#1|)) (SIGNATURE |exquo| ((|Union| |#1| "failed") |#1| |#1|))) (|Field|)) (T |Field&|)) NIL -((~= (#1=((|Boolean|) $ $) 7 T ELT)) (|zero?| ((#2=(|Boolean|) $) 22 T ELT)) (|unitNormal| (((|Record| (|:| |unit| $) (|:| |canonical| $) (|:| |associate| $)) $) 55 T ELT)) (|unitCanonical| (($ $) 54 T ELT)) (|unit?| ((#3=(|Boolean|) $) 52 T ELT)) (|subtractIfCan| (((|Union| $ "failed") $ $) 26 T ELT)) (|squareFreePart| (($ $) 91 T ELT)) (|squareFree| (#4=((|Factored| $) $) 90 T ELT)) (|sizeLess?| (((|Boolean|) $ $) 75 T ELT)) (|sample| (#5=($) 23 T CONST)) (|rem| (#6=($ $ $) 71 T ELT)) (|recip| (((|Union| $ "failed") $) 42 T ELT)) (|quo| (#6# 72 T ELT)) (|principalIdeal| (((|Record| (|:| |coef| #7=(|List| $)) (|:| |generator| $)) #7#) 66 T ELT)) (|prime?| (((|Boolean|) $) 89 T ELT)) (|opposite?| ((#2# $ $) 20 T ELT)) (|one?| (((|Boolean|) $) 44 T ELT)) (|multiEuclidean| (((|Union| #8=(|List| $) #9="failed") #8# $) 68 T ELT)) (|lcm| (#10=($ $ $) 60 T ELT) (#11=($ (|List| $)) 59 T ELT)) (|latex| (((|String|) $) 11 T ELT)) (|inv| (($ $) 88 T ELT)) (|hash| (((|SingleInteger|) $) 12 T ELT)) (|gcdPolynomial| ((#12=(|SparseUnivariatePolynomial| $) #12# #12#) 58 T ELT)) (|gcd| (#10# 62 T ELT) (#11# 61 T ELT)) (|factor| (#4# 92 T ELT)) (|extendedEuclidean| (((|Record| #13=(|:| |coef1| $) #14=(|:| |coef2| $) (|:| |generator| $)) $ $) 70 T ELT) (((|Union| (|Record| #13# #14#) #9#) $ $ $) 69 T ELT)) (|exquo| (((|Union| $ "failed") $ $) 56 T ELT)) (|expressIdealMember| (((|Maybe| #7#) #7# $) 65 T ELT)) (|euclideanSize| (((|NonNegativeInteger|) $) 74 T ELT)) (|divide| (((|Record| (|:| |quotient| $) (|:| |remainder| $)) $ $) 73 T ELT)) (|coerce| (((|OutputForm|) $) 13 T ELT) (($ (|Integer|)) 41 T ELT) (($ $) 57 T ELT) (($ #15=(|Fraction| #16=(|Integer|))) 84 T ELT)) (|characteristic| (((|NonNegativeInteger|)) 40 T CONST)) (|before?| (#1# 6 T ELT)) (|associates?| ((#3# $ $) 53 T ELT)) (|annihilate?| (((|Boolean|) $ $) 33 T ELT)) (|Zero| (#5# 24 T CONST)) (|One| (($) 45 T CONST)) (= (#1# 8 T ELT)) (/ (($ $ $) 83 T ELT)) (- (($ $) 29 T ELT) (($ $ $) 28 T ELT)) (+ (($ $ $) 18 T ELT)) (** (($ $ (|PositiveInteger|)) 35 T ELT) (($ $ (|NonNegativeInteger|)) 43 T ELT) (($ $ #16#) 87 T ELT)) (* (($ (|PositiveInteger|) $) 17 T ELT) (($ (|NonNegativeInteger|) $) 21 T ELT) (($ (|Integer|) . #17=($)) 30 T ELT) (($ $ $) 34 T ELT) (($ $ #15#) 86 T ELT) (($ #15# . #17#) 85 T ELT))) +((~= (#1=((|Boolean|) $ $) 7 T ELT)) (|zero?| ((#2=(|Boolean|) $) 22 T ELT)) (|unitNormal| (((|Record| (|:| |unit| $) (|:| |canonical| $) (|:| |associate| $)) $) 56 T ELT)) (|unitCanonical| (($ $) 55 T ELT)) (|unit?| ((#3=(|Boolean|) $) 53 T ELT)) (|subtractIfCan| (((|Maybe| $) $ $) 26 T ELT)) (|squareFreePart| (($ $) 92 T ELT)) (|squareFree| (#4=((|Factored| $) $) 91 T ELT)) (|sizeLess?| (((|Boolean|) $ $) 76 T ELT)) (|sample| (#5=($) 23 T CONST)) (|rem| (#6=($ $ $) 72 T ELT)) (|recip| (((|Union| $ "failed") $) 43 T ELT)) (|quo| (#6# 73 T ELT)) (|principalIdeal| (((|Record| (|:| |coef| #7=(|List| $)) (|:| |generator| $)) #7#) 67 T ELT)) (|prime?| (((|Boolean|) $) 90 T ELT)) (|opposite?| ((#2# $ $) 20 T ELT)) (|one?| (((|Boolean|) $) 45 T ELT)) (|multiEuclidean| (((|Union| #8=(|List| $) #9="failed") #8# $) 69 T ELT)) (|lcm| (#10=($ $ $) 61 T ELT) (#11=($ (|List| $)) 60 T ELT)) (|latex| (((|String|) $) 11 T ELT)) (|inv| (($ $) 89 T ELT)) (|hash| (((|SingleInteger|) $) 12 T ELT)) (|gcdPolynomial| ((#12=(|SparseUnivariatePolynomial| $) #12# #12#) 59 T ELT)) (|gcd| (#10# 63 T ELT) (#11# 62 T ELT)) (|factor| (#4# 93 T ELT)) (|extendedEuclidean| (((|Record| #13=(|:| |coef1| $) #14=(|:| |coef2| $) (|:| |generator| $)) $ $) 71 T ELT) (((|Union| (|Record| #13# #14#) #9#) $ $ $) 70 T ELT)) (|exquo| (((|Union| $ "failed") $ $) 57 T ELT)) (|expressIdealMember| (((|Maybe| #7#) #7# $) 66 T ELT)) (|euclideanSize| (((|NonNegativeInteger|) $) 75 T ELT)) (|divide| (((|Record| (|:| |quotient| $) (|:| |remainder| $)) $ $) 74 T ELT)) (|coerce| (((|OutputForm|) $) 13 T ELT) (($ (|Integer|)) 42 T ELT) (($ $) 58 T ELT) (($ #15=(|Fraction| #16=(|Integer|))) 85 T ELT)) (|characteristic| (((|NonNegativeInteger|)) 41 T CONST)) (|before?| (#1# 6 T ELT)) (|associates?| ((#3# $ $) 54 T ELT)) (|annihilate?| (((|Boolean|) $ $) 34 T ELT)) (|Zero| (#5# 24 T CONST)) (|One| (($) 46 T CONST)) (= (#1# 8 T ELT)) (/ (($ $ $) 84 T ELT)) (- (($ $) 30 T ELT) (($ $ $) 29 T ELT)) (+ (($ $ $) 18 T ELT)) (** (($ $ (|PositiveInteger|)) 36 T ELT) (($ $ (|NonNegativeInteger|)) 44 T ELT) (($ $ #16#) 88 T ELT)) (* (($ (|PositiveInteger|) $) 17 T ELT) (($ (|NonNegativeInteger|) $) 21 T ELT) (($ (|Integer|) . #17=($)) 31 T ELT) (($ $ $) 35 T ELT) (($ $ #15#) 87 T ELT) (($ #15# . #17#) 86 T ELT))) (((|Field|) (|Category|)) (T |Field|)) ((/ (*1 *1 *1 *1) (|ofCategory| *1 (|Field|)))) -(|Join| (|EuclideanDomain|) (|UniqueFactorizationDomain|) (|DivisionRing|) (CATEGORY |domain| (SIGNATURE / ($ $ $)) (ATTRIBUTE |canonicalUnitNormal|) (ATTRIBUTE |canonicalsClosed|))) +(|Join| (|EuclideanDomain|) (|UniqueFactorizationDomain|) (|DivisionRing|) (CATEGORY |domain| (SIGNATURE / ($ $ $)) (ATTRIBUTE |canonicalUnitNormal|))) (((|AbelianGroup|) . T) ((|AbelianMonoid|) . T) ((|AbelianSemiGroup|) . T) ((|Algebra| #1=(|Fraction| (|Integer|))) . T) ((|Algebra| $) . T) ((|BasicType|) . T) ((|BiModule| #1# #1#) . T) ((|BiModule| $ $) . T) ((|CancellationAbelianMonoid|) . T) ((|CoercibleFrom| #1#) . T) ((|CoercibleFrom| (|Integer|)) . T) ((|CoercibleFrom| $) . T) ((|CoercibleTo| (|OutputForm|)) . T) ((|CommutativeRing|) . T) ((|DivisionRing|) . T) ((|EntireRing|) . T) ((|EuclideanDomain|) . T) ((|GcdDomain|) . T) ((|IntegralDomain|) . T) ((|Join|) . T) ((|LeftLinearSet| #1#) . T) ((|LeftLinearSet| (|Integer|)) . T) ((|LeftLinearSet| $) . T) ((|LeftModule| #1#) . T) ((|LeftModule| $) . T) ((|LinearSet| #1#) . T) ((|LinearSet| $) . T) ((|Module| #1#) . T) ((|Module| $) . T) ((|Monoid|) . T) ((|PrincipalIdealDomain|) . T) ((|RightLinearSet| #1#) . T) ((|RightLinearSet| $) . T) ((|RightModule| #1#) . T) ((|RightModule| $) . T) ((|Ring|) . T) ((|Rng|) . T) ((|SemiGroup|) . T) ((|SemiRing|) . T) ((|SetCategory|) . T) ((|Type|) . T) ((|UniqueFactorizationDomain|) . T)) ((~= #1=(#2=((|Boolean|) $ $) NIL T ELT)) (|write!| ((|#1| $ |#1|) 35 T ELT)) (|reopen!| (($ $ #3=(|String|)) 23 T ELT)) (|readIfCan!| (((|Union| |#1| "failed") $) 34 T ELT)) (|read!| ((|#1| $) 32 T ELT)) (|open| (($ #4=(|FileName|)) 22 T ELT) (($ #4# #3#) 21 T ELT)) (|name| ((#4# $) 25 T ELT)) (|latex| (#5=(#3# $) NIL T ELT)) (|iomode| (#5# 26 T ELT)) (|hash| (((|SingleInteger|) $) NIL T ELT)) (|coerce| (((|OutputForm|) $) 20 T ELT)) (|close!| (($ $) 24 T ELT)) (|before?| #1#) (= (#2# 19 T ELT))) (((|File| |#1|) (|Join| (|FileCategory| (|FileName|) |#1|) (CATEGORY |domain| (SIGNATURE |readIfCan!| ((|Union| |#1| "failed") $)))) (|SetCategory|)) (T |File|)) @@ -1031,10 +1031,10 @@ NIL ((|structuralConstants| (((|Vector| #1=(|Matrix| |#2|)) #2=(|Vector| $)) 67 T ELT)) (|rightTraceMatrix| (#3=(#1# #2#) 139 T ELT)) (|rightTrace| (#4=(|#2| $) 36 T ELT)) (|rightRegularRepresentation| (#5=(#1# $ #2#) 142 T ELT)) (|rightRecip| (#6=((|Union| $ "failed") $) 89 T ELT)) (|rightNorm| (#4# 39 T ELT)) (|rightMinimalPolynomial| (#7=((|SparseUnivariatePolynomial| |#2|) $) 98 T ELT)) (|rightDiscriminant| (#8=(|#2| #2#) 122 T ELT)) (|rightCharacteristicPolynomial| (#7# 32 T ELT)) (|rightAlternative?| (#9=((|Boolean|)) 116 T ELT)) (|represents| (($ #10=(|Vector| |#2|) #2#) 132 T ELT)) (|recip| (#6# 93 T ELT)) (|noncommutativeJordanAlgebra?| (#9# 111 T ELT)) (|lieAlgebra?| (#9# 106 T ELT)) (|lieAdmissible?| (#9# 58 T ELT)) (|leftTraceMatrix| (#3# 137 T ELT)) (|leftTrace| (#4# 35 T ELT)) (|leftRegularRepresentation| (#5# 141 T ELT)) (|leftRecip| (#6# 87 T ELT)) (|leftNorm| (#4# 38 T ELT)) (|leftMinimalPolynomial| (#7# 97 T ELT)) (|leftDiscriminant| (#8# 120 T ELT)) (|leftCharacteristicPolynomial| (#7# 30 T ELT)) (|leftAlternative?| (#9# 115 T ELT)) (|jordanAlgebra?| (#9# 108 T ELT)) (|jordanAdmissible?| (#9# 56 T ELT)) (|jacobiIdentity?| (#9# 103 T ELT)) (|flexible?| (#9# 117 T ELT)) (|coordinates| ((#10# $ #2#) NIL T ELT) ((#1# #2# #2#) 128 T ELT)) (|commutative?| (#9# 113 T ELT)) (|associatorDependence| (((|List| #10#)) 102 T ELT)) (|associative?| (#9# 114 T ELT)) (|antiCommutative?| (#9# 112 T ELT)) (|antiAssociative?| (#9# 51 T ELT)) (|alternative?| (#9# 118 T ELT))) (((|FiniteRankNonAssociativeAlgebra&| |#1| |#2|) (CATEGORY |package| (SIGNATURE |rightMinimalPolynomial| #1=((|SparseUnivariatePolynomial| |#2|) |#1|)) (SIGNATURE |leftMinimalPolynomial| #1#) (SIGNATURE |associatorDependence| ((|List| #2=(|Vector| |#2|)))) (SIGNATURE |rightRecip| #3=((|Union| |#1| "failed") |#1|)) (SIGNATURE |leftRecip| #3#) (SIGNATURE |recip| #3#) (SIGNATURE |lieAlgebra?| #4=((|Boolean|))) (SIGNATURE |jordanAlgebra?| #4#) (SIGNATURE |noncommutativeJordanAlgebra?| #4#) (SIGNATURE |jordanAdmissible?| #4#) (SIGNATURE |lieAdmissible?| #4#) (SIGNATURE |jacobiIdentity?| #4#) (SIGNATURE |alternative?| #4#) (SIGNATURE |flexible?| #4#) (SIGNATURE |rightAlternative?| #4#) (SIGNATURE |leftAlternative?| #4#) (SIGNATURE |antiAssociative?| #4#) (SIGNATURE |associative?| #4#) (SIGNATURE |antiCommutative?| #4#) (SIGNATURE |commutative?| #4#) (SIGNATURE |rightCharacteristicPolynomial| #1#) (SIGNATURE |leftCharacteristicPolynomial| #1#) (SIGNATURE |rightTraceMatrix| #5=(#6=(|Matrix| |#2|) #7=(|Vector| |#1|))) (SIGNATURE |leftTraceMatrix| #5#) (SIGNATURE |rightDiscriminant| #8=(|#2| #7#)) (SIGNATURE |leftDiscriminant| #8#) (SIGNATURE |represents| (|#1| #2# #7#)) (SIGNATURE |coordinates| (#6# #7# #7#)) (SIGNATURE |coordinates| (#2# |#1| #7#)) (SIGNATURE |rightNorm| #9=(|#2| |#1|)) (SIGNATURE |leftNorm| #9#) (SIGNATURE |rightTrace| #9#) (SIGNATURE |leftTrace| #9#) (SIGNATURE |rightRegularRepresentation| #10=(#6# |#1| #7#)) (SIGNATURE |leftRegularRepresentation| #10#) (SIGNATURE |structuralConstants| ((|Vector| #6#) #7#))) (|FiniteRankNonAssociativeAlgebra| |#2|) (|CommutativeRing|)) (T |FiniteRankNonAssociativeAlgebra&|)) ((|commutative?| #1=(*1 *2) #2=(AND #3=(|ofCategory| *4 (|CommutativeRing|)) (|isDomain| *2 (|Boolean|)) #4=(|isDomain| *1 (|FiniteRankNonAssociativeAlgebra&| *3 *4)) #5=(|ofCategory| *3 (|FiniteRankNonAssociativeAlgebra| *4)))) (|antiCommutative?| #1# #2#) (|associative?| #1# #2#) (|antiAssociative?| #1# #2#) (|leftAlternative?| #1# #2#) (|rightAlternative?| #1# #2#) (|flexible?| #1# #2#) (|alternative?| #1# #2#) (|jacobiIdentity?| #1# #2#) (|lieAdmissible?| #1# #2#) (|jordanAdmissible?| #1# #2#) (|noncommutativeJordanAlgebra?| #1# #2#) (|jordanAlgebra?| #1# #2#) (|lieAlgebra?| #1# #2#) (|associatorDependence| #1# (AND #3# (|isDomain| *2 (|List| (|Vector| *4))) #4# #5#))) -((~= (#1=((|Boolean|) $ $) 7 T ELT)) (|zero?| ((#2=(|Boolean|) $) 22 T ELT)) (|unit| (((|Union| $ "failed")) 48 (|has| |#1| (|IntegralDomain|)) ELT)) (|subtractIfCan| (((|Union| $ "failed") $ $) 26 T ELT)) (|structuralConstants| (((|Vector| (|Matrix| |#1|)) (|Vector| $)) 89 T ELT)) (|someBasis| (((|Vector| $)) 92 T ELT)) (|sample| (#3=($) 23 T CONST)) (|rightUnits| (((|Union| (|Record| (|:| |particular| $) (|:| |basis| (|List| $))) "failed")) 51 (|has| |#1| (|IntegralDomain|)) ELT)) (|rightUnit| (((|Union| $ "failed")) 49 (|has| |#1| (|IntegralDomain|)) ELT)) (|rightTraceMatrix| (((|Matrix| |#1|) (|Vector| $)) 76 T ELT)) (|rightTrace| ((|#1| $) 85 T ELT)) (|rightRegularRepresentation| (((|Matrix| |#1|) $ (|Vector| $)) 87 T ELT)) (|rightRecip| (((|Union| $ "failed") $) 56 (|has| |#1| (|IntegralDomain|)) ELT)) (|rightPower| (#4=($ $ (|PositiveInteger|)) 37 T ELT)) (|rightNorm| ((|#1| $) 83 T ELT)) (|rightMinimalPolynomial| (((|SparseUnivariatePolynomial| |#1|) $) 53 (|has| |#1| (|IntegralDomain|)) ELT)) (|rightDiscriminant| ((|#1| (|Vector| $)) 78 T ELT)) (|rightCharacteristicPolynomial| (((|SparseUnivariatePolynomial| |#1|) $) 74 T ELT)) (|rightAlternative?| (((|Boolean|)) 68 T ELT)) (|represents| (($ (|Vector| |#1|) (|Vector| $)) 80 T ELT)) (|recip| (((|Union| $ "failed") $) 58 (|has| |#1| (|IntegralDomain|)) ELT)) (|rank| (((|PositiveInteger|)) 91 T ELT)) (|powerAssociative?| (((|Boolean|)) 65 T ELT)) (|plenaryPower| (($ $ (|PositiveInteger|)) 44 T ELT)) (|opposite?| ((#2# $ $) 20 T ELT)) (|noncommutativeJordanAlgebra?| (((|Boolean|)) 61 T ELT)) (|lieAlgebra?| (((|Boolean|)) 59 T ELT)) (|lieAdmissible?| (((|Boolean|)) 63 T ELT)) (|leftUnits| (((|Union| (|Record| (|:| |particular| $) (|:| |basis| (|List| $))) "failed")) 52 (|has| |#1| (|IntegralDomain|)) ELT)) (|leftUnit| (((|Union| $ "failed")) 50 (|has| |#1| (|IntegralDomain|)) ELT)) (|leftTraceMatrix| (((|Matrix| |#1|) (|Vector| $)) 77 T ELT)) (|leftTrace| ((|#1| $) 86 T ELT)) (|leftRegularRepresentation| (((|Matrix| |#1|) $ (|Vector| $)) 88 T ELT)) (|leftRecip| (((|Union| $ "failed") $) 57 (|has| |#1| (|IntegralDomain|)) ELT)) (|leftPower| (#4# 38 T ELT)) (|leftNorm| ((|#1| $) 84 T ELT)) (|leftMinimalPolynomial| (((|SparseUnivariatePolynomial| |#1|) $) 54 (|has| |#1| (|IntegralDomain|)) ELT)) (|leftDiscriminant| ((|#1| (|Vector| $)) 79 T ELT)) (|leftCharacteristicPolynomial| (((|SparseUnivariatePolynomial| |#1|) $) 75 T ELT)) (|leftAlternative?| (((|Boolean|)) 69 T ELT)) (|latex| (((|String|) $) 11 T ELT)) (|jordanAlgebra?| (((|Boolean|)) 60 T ELT)) (|jordanAdmissible?| (((|Boolean|)) 62 T ELT)) (|jacobiIdentity?| (((|Boolean|)) 64 T ELT)) (|hash| (((|SingleInteger|) $) 12 T ELT)) (|flexible?| (((|Boolean|)) 67 T ELT)) (|coordinates| (((|Vector| |#1|) $ (|Vector| $)) 82 T ELT) (((|Matrix| |#1|) (|Vector| $) (|Vector| $)) 81 T ELT)) (|conditionsForIdempotents| (((|List| (|Polynomial| |#1|)) (|Vector| $)) 90 T ELT)) (|commutator| (#5=($ $ $) 34 T ELT)) (|commutative?| (((|Boolean|)) 73 T ELT)) (|coerce| (((|OutputForm|) $) 13 T ELT)) (|before?| (#1# 6 T ELT)) (|associatorDependence| (((|List| (|Vector| |#1|))) 55 (|has| |#1| (|IntegralDomain|)) ELT)) (|associator| (($ $ $ $) 35 T ELT)) (|associative?| (((|Boolean|)) 71 T ELT)) (|antiCommutator| (#5# 33 T ELT)) (|antiCommutative?| (((|Boolean|)) 72 T ELT)) (|antiAssociative?| (((|Boolean|)) 70 T ELT)) (|alternative?| (((|Boolean|)) 66 T ELT)) (|Zero| (#3# 24 T CONST)) (= (#1# 8 T ELT)) (- (($ $) 29 T ELT) (($ $ $) 28 T ELT)) (+ (($ $ $) 18 T ELT)) (** (#4# 39 T ELT)) (* (($ (|PositiveInteger|) $) 17 T ELT) (($ (|NonNegativeInteger|) $) 21 T ELT) (($ (|Integer|) . #6=($)) 30 T ELT) (($ $ $) 36 T ELT) (($ $ |#1|) 46 T ELT) (($ |#1| . #6#) 45 T ELT))) +((~= (#1=((|Boolean|) $ $) 7 T ELT)) (|zero?| ((#2=(|Boolean|) $) 22 T ELT)) (|unit| (((|Union| $ "failed")) 49 (|has| |#1| (|IntegralDomain|)) ELT)) (|subtractIfCan| (((|Maybe| $) $ $) 26 T ELT)) (|structuralConstants| (((|Vector| (|Matrix| |#1|)) (|Vector| $)) 90 T ELT)) (|someBasis| (((|Vector| $)) 93 T ELT)) (|sample| (#3=($) 23 T CONST)) (|rightUnits| (((|Union| (|Record| (|:| |particular| $) (|:| |basis| (|List| $))) "failed")) 52 (|has| |#1| (|IntegralDomain|)) ELT)) (|rightUnit| (((|Union| $ "failed")) 50 (|has| |#1| (|IntegralDomain|)) ELT)) (|rightTraceMatrix| (((|Matrix| |#1|) (|Vector| $)) 77 T ELT)) (|rightTrace| ((|#1| $) 86 T ELT)) (|rightRegularRepresentation| (((|Matrix| |#1|) $ (|Vector| $)) 88 T ELT)) (|rightRecip| (((|Union| $ "failed") $) 57 (|has| |#1| (|IntegralDomain|)) ELT)) (|rightPower| (#4=($ $ (|PositiveInteger|)) 38 T ELT)) (|rightNorm| ((|#1| $) 84 T ELT)) (|rightMinimalPolynomial| (((|SparseUnivariatePolynomial| |#1|) $) 54 (|has| |#1| (|IntegralDomain|)) ELT)) (|rightDiscriminant| ((|#1| (|Vector| $)) 79 T ELT)) (|rightCharacteristicPolynomial| (((|SparseUnivariatePolynomial| |#1|) $) 75 T ELT)) (|rightAlternative?| (((|Boolean|)) 69 T ELT)) (|represents| (($ (|Vector| |#1|) (|Vector| $)) 81 T ELT)) (|recip| (((|Union| $ "failed") $) 59 (|has| |#1| (|IntegralDomain|)) ELT)) (|rank| (((|PositiveInteger|)) 92 T ELT)) (|powerAssociative?| (((|Boolean|)) 66 T ELT)) (|plenaryPower| (($ $ (|PositiveInteger|)) 45 T ELT)) (|opposite?| ((#2# $ $) 20 T ELT)) (|noncommutativeJordanAlgebra?| (((|Boolean|)) 62 T ELT)) (|lieAlgebra?| (((|Boolean|)) 60 T ELT)) (|lieAdmissible?| (((|Boolean|)) 64 T ELT)) (|leftUnits| (((|Union| (|Record| (|:| |particular| $) (|:| |basis| (|List| $))) "failed")) 53 (|has| |#1| (|IntegralDomain|)) ELT)) (|leftUnit| (((|Union| $ "failed")) 51 (|has| |#1| (|IntegralDomain|)) ELT)) (|leftTraceMatrix| (((|Matrix| |#1|) (|Vector| $)) 78 T ELT)) (|leftTrace| ((|#1| $) 87 T ELT)) (|leftRegularRepresentation| (((|Matrix| |#1|) $ (|Vector| $)) 89 T ELT)) (|leftRecip| (((|Union| $ "failed") $) 58 (|has| |#1| (|IntegralDomain|)) ELT)) (|leftPower| (#4# 39 T ELT)) (|leftNorm| ((|#1| $) 85 T ELT)) (|leftMinimalPolynomial| (((|SparseUnivariatePolynomial| |#1|) $) 55 (|has| |#1| (|IntegralDomain|)) ELT)) (|leftDiscriminant| ((|#1| (|Vector| $)) 80 T ELT)) (|leftCharacteristicPolynomial| (((|SparseUnivariatePolynomial| |#1|) $) 76 T ELT)) (|leftAlternative?| (((|Boolean|)) 70 T ELT)) (|latex| (((|String|) $) 11 T ELT)) (|jordanAlgebra?| (((|Boolean|)) 61 T ELT)) (|jordanAdmissible?| (((|Boolean|)) 63 T ELT)) (|jacobiIdentity?| (((|Boolean|)) 65 T ELT)) (|hash| (((|SingleInteger|) $) 12 T ELT)) (|flexible?| (((|Boolean|)) 68 T ELT)) (|coordinates| (((|Vector| |#1|) $ (|Vector| $)) 83 T ELT) (((|Matrix| |#1|) (|Vector| $) (|Vector| $)) 82 T ELT)) (|conditionsForIdempotents| (((|List| (|Polynomial| |#1|)) (|Vector| $)) 91 T ELT)) (|commutator| (#5=($ $ $) 35 T ELT)) (|commutative?| (((|Boolean|)) 74 T ELT)) (|coerce| (((|OutputForm|) $) 13 T ELT)) (|before?| (#1# 6 T ELT)) (|associatorDependence| (((|List| (|Vector| |#1|))) 56 (|has| |#1| (|IntegralDomain|)) ELT)) (|associator| (($ $ $ $) 36 T ELT)) (|associative?| (((|Boolean|)) 72 T ELT)) (|antiCommutator| (#5# 34 T ELT)) (|antiCommutative?| (((|Boolean|)) 73 T ELT)) (|antiAssociative?| (((|Boolean|)) 71 T ELT)) (|alternative?| (((|Boolean|)) 67 T ELT)) (|Zero| (#3# 24 T CONST)) (= (#1# 8 T ELT)) (- (($ $) 30 T ELT) (($ $ $) 29 T ELT)) (+ (($ $ $) 18 T ELT)) (** (#4# 40 T ELT)) (* (($ (|PositiveInteger|) $) 17 T ELT) (($ (|NonNegativeInteger|) $) 21 T ELT) (($ (|Integer|) . #6=($)) 31 T ELT) (($ $ $) 37 T ELT) (($ $ |#1|) 47 T ELT) (($ |#1| . #6#) 46 T ELT))) (((|FiniteRankNonAssociativeAlgebra| |#1|) (|Category|) (|CommutativeRing|)) (T |FiniteRankNonAssociativeAlgebra|)) ((|someBasis| (*1 *2) (AND (|ofCategory| *3 (|CommutativeRing|)) (|isDomain| *2 (|Vector| *1)) (|ofCategory| *1 (|FiniteRankNonAssociativeAlgebra| *3)))) (|rank| (*1 *2) (AND (|ofCategory| *1 (|FiniteRankNonAssociativeAlgebra| *3)) (|ofCategory| *3 (|CommutativeRing|)) (|isDomain| *2 (|PositiveInteger|)))) (|conditionsForIdempotents| (*1 *2 *3) (AND (|isDomain| *3 (|Vector| *1)) (|ofCategory| *1 (|FiniteRankNonAssociativeAlgebra| *4)) (|ofCategory| *4 (|CommutativeRing|)) (|isDomain| *2 (|List| (|Polynomial| *4))))) (|structuralConstants| (*1 *2 *3) (AND (|isDomain| *3 (|Vector| *1)) (|ofCategory| *1 (|FiniteRankNonAssociativeAlgebra| *4)) (|ofCategory| *4 (|CommutativeRing|)) (|isDomain| *2 (|Vector| (|Matrix| *4))))) (|leftRegularRepresentation| (*1 *2 *1 *3) (AND (|isDomain| *3 (|Vector| *1)) (|ofCategory| *1 (|FiniteRankNonAssociativeAlgebra| *4)) (|ofCategory| *4 (|CommutativeRing|)) (|isDomain| *2 (|Matrix| *4)))) (|rightRegularRepresentation| (*1 *2 *1 *3) (AND (|isDomain| *3 (|Vector| *1)) (|ofCategory| *1 (|FiniteRankNonAssociativeAlgebra| *4)) (|ofCategory| *4 (|CommutativeRing|)) (|isDomain| *2 (|Matrix| *4)))) (|leftTrace| (*1 *2 *1) (AND (|ofCategory| *1 (|FiniteRankNonAssociativeAlgebra| *2)) (|ofCategory| *2 (|CommutativeRing|)))) (|rightTrace| (*1 *2 *1) (AND (|ofCategory| *1 (|FiniteRankNonAssociativeAlgebra| *2)) (|ofCategory| *2 (|CommutativeRing|)))) (|leftNorm| (*1 *2 *1) (AND (|ofCategory| *1 (|FiniteRankNonAssociativeAlgebra| *2)) (|ofCategory| *2 (|CommutativeRing|)))) (|rightNorm| (*1 *2 *1) (AND (|ofCategory| *1 (|FiniteRankNonAssociativeAlgebra| *2)) (|ofCategory| *2 (|CommutativeRing|)))) (|coordinates| (*1 *2 *1 *3) (AND (|isDomain| *3 (|Vector| *1)) (|ofCategory| *1 (|FiniteRankNonAssociativeAlgebra| *4)) (|ofCategory| *4 (|CommutativeRing|)) (|isDomain| *2 (|Vector| *4)))) (|coordinates| (*1 *2 *3 *3) (AND (|isDomain| *3 (|Vector| *1)) (|ofCategory| *1 (|FiniteRankNonAssociativeAlgebra| *4)) (|ofCategory| *4 (|CommutativeRing|)) (|isDomain| *2 (|Matrix| *4)))) (|represents| (*1 *1 *2 *3) (AND (|isDomain| *2 (|Vector| *4)) (|isDomain| *3 (|Vector| *1)) (|ofCategory| *4 (|CommutativeRing|)) (|ofCategory| *1 (|FiniteRankNonAssociativeAlgebra| *4)))) (|leftDiscriminant| (*1 *2 *3) (AND (|isDomain| *3 (|Vector| *1)) (|ofCategory| *1 (|FiniteRankNonAssociativeAlgebra| *2)) (|ofCategory| *2 (|CommutativeRing|)))) (|rightDiscriminant| (*1 *2 *3) (AND (|isDomain| *3 (|Vector| *1)) (|ofCategory| *1 (|FiniteRankNonAssociativeAlgebra| *2)) (|ofCategory| *2 (|CommutativeRing|)))) (|leftTraceMatrix| (*1 *2 *3) (AND (|isDomain| *3 (|Vector| *1)) (|ofCategory| *1 (|FiniteRankNonAssociativeAlgebra| *4)) (|ofCategory| *4 (|CommutativeRing|)) (|isDomain| *2 (|Matrix| *4)))) (|rightTraceMatrix| (*1 *2 *3) (AND (|isDomain| *3 (|Vector| *1)) (|ofCategory| *1 (|FiniteRankNonAssociativeAlgebra| *4)) (|ofCategory| *4 (|CommutativeRing|)) (|isDomain| *2 (|Matrix| *4)))) (|leftCharacteristicPolynomial| (*1 *2 *1) (AND (|ofCategory| *1 (|FiniteRankNonAssociativeAlgebra| *3)) (|ofCategory| *3 (|CommutativeRing|)) (|isDomain| *2 (|SparseUnivariatePolynomial| *3)))) (|rightCharacteristicPolynomial| (*1 *2 *1) (AND (|ofCategory| *1 (|FiniteRankNonAssociativeAlgebra| *3)) (|ofCategory| *3 (|CommutativeRing|)) (|isDomain| *2 (|SparseUnivariatePolynomial| *3)))) (|commutative?| (*1 *2) (AND (|ofCategory| *1 (|FiniteRankNonAssociativeAlgebra| *3)) (|ofCategory| *3 (|CommutativeRing|)) (|isDomain| *2 (|Boolean|)))) (|antiCommutative?| (*1 *2) (AND (|ofCategory| *1 (|FiniteRankNonAssociativeAlgebra| *3)) (|ofCategory| *3 (|CommutativeRing|)) (|isDomain| *2 (|Boolean|)))) (|associative?| (*1 *2) (AND (|ofCategory| *1 (|FiniteRankNonAssociativeAlgebra| *3)) (|ofCategory| *3 (|CommutativeRing|)) (|isDomain| *2 (|Boolean|)))) (|antiAssociative?| (*1 *2) (AND (|ofCategory| *1 (|FiniteRankNonAssociativeAlgebra| *3)) (|ofCategory| *3 (|CommutativeRing|)) (|isDomain| *2 (|Boolean|)))) (|leftAlternative?| (*1 *2) (AND (|ofCategory| *1 (|FiniteRankNonAssociativeAlgebra| *3)) (|ofCategory| *3 (|CommutativeRing|)) (|isDomain| *2 (|Boolean|)))) (|rightAlternative?| (*1 *2) (AND (|ofCategory| *1 (|FiniteRankNonAssociativeAlgebra| *3)) (|ofCategory| *3 (|CommutativeRing|)) (|isDomain| *2 (|Boolean|)))) (|flexible?| (*1 *2) (AND (|ofCategory| *1 (|FiniteRankNonAssociativeAlgebra| *3)) (|ofCategory| *3 (|CommutativeRing|)) (|isDomain| *2 (|Boolean|)))) (|alternative?| (*1 *2) (AND (|ofCategory| *1 (|FiniteRankNonAssociativeAlgebra| *3)) (|ofCategory| *3 (|CommutativeRing|)) (|isDomain| *2 (|Boolean|)))) (|powerAssociative?| (*1 *2) (AND (|ofCategory| *1 (|FiniteRankNonAssociativeAlgebra| *3)) (|ofCategory| *3 (|CommutativeRing|)) (|isDomain| *2 (|Boolean|)))) (|jacobiIdentity?| (*1 *2) (AND (|ofCategory| *1 (|FiniteRankNonAssociativeAlgebra| *3)) (|ofCategory| *3 (|CommutativeRing|)) (|isDomain| *2 (|Boolean|)))) (|lieAdmissible?| (*1 *2) (AND (|ofCategory| *1 (|FiniteRankNonAssociativeAlgebra| *3)) (|ofCategory| *3 (|CommutativeRing|)) (|isDomain| *2 (|Boolean|)))) (|jordanAdmissible?| (*1 *2) (AND (|ofCategory| *1 (|FiniteRankNonAssociativeAlgebra| *3)) (|ofCategory| *3 (|CommutativeRing|)) (|isDomain| *2 (|Boolean|)))) (|noncommutativeJordanAlgebra?| (*1 *2) (AND (|ofCategory| *1 (|FiniteRankNonAssociativeAlgebra| *3)) (|ofCategory| *3 (|CommutativeRing|)) (|isDomain| *2 (|Boolean|)))) (|jordanAlgebra?| (*1 *2) (AND (|ofCategory| *1 (|FiniteRankNonAssociativeAlgebra| *3)) (|ofCategory| *3 (|CommutativeRing|)) (|isDomain| *2 (|Boolean|)))) (|lieAlgebra?| (*1 *2) (AND (|ofCategory| *1 (|FiniteRankNonAssociativeAlgebra| *3)) (|ofCategory| *3 (|CommutativeRing|)) (|isDomain| *2 (|Boolean|)))) (|recip| (*1 *1 *1) (|partial| AND (|ofCategory| *1 (|FiniteRankNonAssociativeAlgebra| *2)) (|ofCategory| *2 (|CommutativeRing|)) (|ofCategory| *2 (|IntegralDomain|)))) (|leftRecip| (*1 *1 *1) (|partial| AND (|ofCategory| *1 (|FiniteRankNonAssociativeAlgebra| *2)) (|ofCategory| *2 (|CommutativeRing|)) (|ofCategory| *2 (|IntegralDomain|)))) (|rightRecip| (*1 *1 *1) (|partial| AND (|ofCategory| *1 (|FiniteRankNonAssociativeAlgebra| *2)) (|ofCategory| *2 (|CommutativeRing|)) (|ofCategory| *2 (|IntegralDomain|)))) (|associatorDependence| (*1 *2) (AND (|ofCategory| *1 (|FiniteRankNonAssociativeAlgebra| *3)) (|ofCategory| *3 (|CommutativeRing|)) (|ofCategory| *3 (|IntegralDomain|)) (|isDomain| *2 (|List| (|Vector| *3))))) (|leftMinimalPolynomial| (*1 *2 *1) (AND (|ofCategory| *1 (|FiniteRankNonAssociativeAlgebra| *3)) (|ofCategory| *3 (|CommutativeRing|)) (|ofCategory| *3 (|IntegralDomain|)) (|isDomain| *2 (|SparseUnivariatePolynomial| *3)))) (|rightMinimalPolynomial| (*1 *2 *1) (AND (|ofCategory| *1 (|FiniteRankNonAssociativeAlgebra| *3)) (|ofCategory| *3 (|CommutativeRing|)) (|ofCategory| *3 (|IntegralDomain|)) (|isDomain| *2 (|SparseUnivariatePolynomial| *3)))) (|leftUnits| (*1 *2) (|partial| AND (|ofCategory| *3 (|IntegralDomain|)) (|ofCategory| *3 (|CommutativeRing|)) (|isDomain| *2 (|Record| (|:| |particular| *1) (|:| |basis| (|List| *1)))) (|ofCategory| *1 (|FiniteRankNonAssociativeAlgebra| *3)))) (|rightUnits| (*1 *2) (|partial| AND (|ofCategory| *3 (|IntegralDomain|)) (|ofCategory| *3 (|CommutativeRing|)) (|isDomain| *2 (|Record| (|:| |particular| *1) (|:| |basis| (|List| *1)))) (|ofCategory| *1 (|FiniteRankNonAssociativeAlgebra| *3)))) (|leftUnit| (*1 *1) (|partial| AND (|ofCategory| *1 (|FiniteRankNonAssociativeAlgebra| *2)) (|ofCategory| *2 (|IntegralDomain|)) (|ofCategory| *2 (|CommutativeRing|)))) (|rightUnit| (*1 *1) (|partial| AND (|ofCategory| *1 (|FiniteRankNonAssociativeAlgebra| *2)) (|ofCategory| *2 (|IntegralDomain|)) (|ofCategory| *2 (|CommutativeRing|)))) (|unit| (*1 *1) (|partial| AND (|ofCategory| *1 (|FiniteRankNonAssociativeAlgebra| *2)) (|ofCategory| *2 (|IntegralDomain|)) (|ofCategory| *2 (|CommutativeRing|))))) -(|Join| (|NonAssociativeAlgebra| |t#1|) (CATEGORY |domain| (SIGNATURE |someBasis| ((|Vector| $))) (SIGNATURE |rank| ((|PositiveInteger|))) (SIGNATURE |conditionsForIdempotents| ((|List| (|Polynomial| |t#1|)) (|Vector| $))) (SIGNATURE |structuralConstants| ((|Vector| (|Matrix| |t#1|)) (|Vector| $))) (SIGNATURE |leftRegularRepresentation| ((|Matrix| |t#1|) $ (|Vector| $))) (SIGNATURE |rightRegularRepresentation| ((|Matrix| |t#1|) $ (|Vector| $))) (SIGNATURE |leftTrace| (|t#1| $)) (SIGNATURE |rightTrace| (|t#1| $)) (SIGNATURE |leftNorm| (|t#1| $)) (SIGNATURE |rightNorm| (|t#1| $)) (SIGNATURE |coordinates| ((|Vector| |t#1|) $ (|Vector| $))) (SIGNATURE |coordinates| ((|Matrix| |t#1|) (|Vector| $) (|Vector| $))) (SIGNATURE |represents| ($ (|Vector| |t#1|) (|Vector| $))) (SIGNATURE |leftDiscriminant| (|t#1| (|Vector| $))) (SIGNATURE |rightDiscriminant| (|t#1| (|Vector| $))) (SIGNATURE |leftTraceMatrix| ((|Matrix| |t#1|) (|Vector| $))) (SIGNATURE |rightTraceMatrix| ((|Matrix| |t#1|) (|Vector| $))) (SIGNATURE |leftCharacteristicPolynomial| ((|SparseUnivariatePolynomial| |t#1|) $)) (SIGNATURE |rightCharacteristicPolynomial| ((|SparseUnivariatePolynomial| |t#1|) $)) (SIGNATURE |commutative?| ((|Boolean|))) (SIGNATURE |antiCommutative?| ((|Boolean|))) (SIGNATURE |associative?| ((|Boolean|))) (SIGNATURE |antiAssociative?| ((|Boolean|))) (SIGNATURE |leftAlternative?| ((|Boolean|))) (SIGNATURE |rightAlternative?| ((|Boolean|))) (SIGNATURE |flexible?| ((|Boolean|))) (SIGNATURE |alternative?| ((|Boolean|))) (SIGNATURE |powerAssociative?| ((|Boolean|))) (SIGNATURE |jacobiIdentity?| ((|Boolean|))) (SIGNATURE |lieAdmissible?| ((|Boolean|))) (SIGNATURE |jordanAdmissible?| ((|Boolean|))) (SIGNATURE |noncommutativeJordanAlgebra?| ((|Boolean|))) (SIGNATURE |jordanAlgebra?| ((|Boolean|))) (SIGNATURE |lieAlgebra?| ((|Boolean|))) (IF (|has| |t#1| (|IntegralDomain|)) (PROGN (SIGNATURE |recip| ((|Union| $ "failed") $)) (SIGNATURE |leftRecip| ((|Union| $ "failed") $)) (SIGNATURE |rightRecip| ((|Union| $ "failed") $)) (SIGNATURE |associatorDependence| ((|List| (|Vector| |t#1|)))) (SIGNATURE |leftMinimalPolynomial| ((|SparseUnivariatePolynomial| |t#1|) $)) (SIGNATURE |rightMinimalPolynomial| ((|SparseUnivariatePolynomial| |t#1|) $)) (SIGNATURE |leftUnits| ((|Union| (|Record| (|:| |particular| $) (|:| |basis| (|List| $))) "failed"))) (SIGNATURE |rightUnits| ((|Union| (|Record| (|:| |particular| $) (|:| |basis| (|List| $))) "failed"))) (SIGNATURE |leftUnit| ((|Union| $ "failed"))) (SIGNATURE |rightUnit| ((|Union| $ "failed"))) (SIGNATURE |unit| ((|Union| $ "failed"))) (ATTRIBUTE |unitsKnown|)) |%noBranch|))) +(|Join| (|NonAssociativeAlgebra| |t#1|) (CATEGORY |domain| (SIGNATURE |someBasis| ((|Vector| $))) (SIGNATURE |rank| ((|PositiveInteger|))) (SIGNATURE |conditionsForIdempotents| ((|List| (|Polynomial| |t#1|)) (|Vector| $))) (SIGNATURE |structuralConstants| ((|Vector| (|Matrix| |t#1|)) (|Vector| $))) (SIGNATURE |leftRegularRepresentation| ((|Matrix| |t#1|) $ (|Vector| $))) (SIGNATURE |rightRegularRepresentation| ((|Matrix| |t#1|) $ (|Vector| $))) (SIGNATURE |leftTrace| (|t#1| $)) (SIGNATURE |rightTrace| (|t#1| $)) (SIGNATURE |leftNorm| (|t#1| $)) (SIGNATURE |rightNorm| (|t#1| $)) (SIGNATURE |coordinates| ((|Vector| |t#1|) $ (|Vector| $))) (SIGNATURE |coordinates| ((|Matrix| |t#1|) (|Vector| $) (|Vector| $))) (SIGNATURE |represents| ($ (|Vector| |t#1|) (|Vector| $))) (SIGNATURE |leftDiscriminant| (|t#1| (|Vector| $))) (SIGNATURE |rightDiscriminant| (|t#1| (|Vector| $))) (SIGNATURE |leftTraceMatrix| ((|Matrix| |t#1|) (|Vector| $))) (SIGNATURE |rightTraceMatrix| ((|Matrix| |t#1|) (|Vector| $))) (SIGNATURE |leftCharacteristicPolynomial| ((|SparseUnivariatePolynomial| |t#1|) $)) (SIGNATURE |rightCharacteristicPolynomial| ((|SparseUnivariatePolynomial| |t#1|) $)) (SIGNATURE |commutative?| ((|Boolean|))) (SIGNATURE |antiCommutative?| ((|Boolean|))) (SIGNATURE |associative?| ((|Boolean|))) (SIGNATURE |antiAssociative?| ((|Boolean|))) (SIGNATURE |leftAlternative?| ((|Boolean|))) (SIGNATURE |rightAlternative?| ((|Boolean|))) (SIGNATURE |flexible?| ((|Boolean|))) (SIGNATURE |alternative?| ((|Boolean|))) (SIGNATURE |powerAssociative?| ((|Boolean|))) (SIGNATURE |jacobiIdentity?| ((|Boolean|))) (SIGNATURE |lieAdmissible?| ((|Boolean|))) (SIGNATURE |jordanAdmissible?| ((|Boolean|))) (SIGNATURE |noncommutativeJordanAlgebra?| ((|Boolean|))) (SIGNATURE |jordanAlgebra?| ((|Boolean|))) (SIGNATURE |lieAlgebra?| ((|Boolean|))) (IF (|has| |t#1| (|IntegralDomain|)) (PROGN (SIGNATURE |recip| ((|Union| $ "failed") $)) (SIGNATURE |leftRecip| ((|Union| $ "failed") $)) (SIGNATURE |rightRecip| ((|Union| $ "failed") $)) (SIGNATURE |associatorDependence| ((|List| (|Vector| |t#1|)))) (SIGNATURE |leftMinimalPolynomial| ((|SparseUnivariatePolynomial| |t#1|) $)) (SIGNATURE |rightMinimalPolynomial| ((|SparseUnivariatePolynomial| |t#1|) $)) (SIGNATURE |leftUnits| ((|Union| (|Record| (|:| |particular| $) (|:| |basis| (|List| $))) "failed"))) (SIGNATURE |rightUnits| ((|Union| (|Record| (|:| |particular| $) (|:| |basis| (|List| $))) "failed"))) (SIGNATURE |leftUnit| ((|Union| $ "failed"))) (SIGNATURE |rightUnit| ((|Union| $ "failed"))) (SIGNATURE |unit| ((|Union| $ "failed")))) |%noBranch|))) (((|AbelianGroup|) . T) ((|AbelianMonoid|) . T) ((|AbelianSemiGroup|) . T) ((|BasicType|) . T) ((|BiModule| |#1| |#1|) . T) ((|CancellationAbelianMonoid|) . T) ((|CoercibleTo| (|OutputForm|)) . T) ((|Join|) . T) ((|LeftLinearSet| (|Integer|)) . T) ((|LeftLinearSet| |#1|) . T) ((|LeftModule| |#1|) . T) ((|LinearSet| |#1|) . T) ((|Module| |#1|) . T) ((|Monad|) . T) ((|NonAssociativeAlgebra| |#1|) . T) ((|NonAssociativeRng|) . T) ((|RightLinearSet| |#1|) . T) ((|RightModule| |#1|) . T) ((|SetCategory|) . T) ((|Type|) . T)) ((|reduce| ((|#2| #1=(|Mapping| |#2| |#2| |#2|) $) NIL T ELT) ((|#2| #1# $ |#2|) NIL T ELT) ((|#2| #1# $ |#2| |#2|) 38 T ELT)) (|member?| ((#2=(|Boolean|) |#2| $) 35 T ELT)) (|find| (((|Union| |#2| "failed") #3=(|Mapping| #2# |#2|) $) 30 T ELT)) (|every?| (#4=(#2# #3# $) 24 T ELT)) (|empty?| ((#2# $) 13 T ELT)) (|count| ((#5=(|NonNegativeInteger|) #3# $) 27 T ELT) ((#5# |#2| $) 33 T ELT)) (|coerce| (((|OutputForm|) $) 46 T ELT)) (|any?| (#4# 21 T ELT)) (= ((#2# $ $) 40 T ELT)) (|#| ((#5# $) 17 T ELT))) (((|FiniteAggregate&| |#1| |#2|) (CATEGORY |package| (SIGNATURE = (#1=(|Boolean|) |#1| |#1|)) (SIGNATURE |coerce| ((|OutputForm|) |#1|)) (SIGNATURE |reduce| (|#2| #2=(|Mapping| |#2| |#2| |#2|) |#1| |#2| |#2|)) (SIGNATURE |member?| (#1# |#2| |#1|)) (SIGNATURE |count| (#3=(|NonNegativeInteger|) |#2| |#1|)) (SIGNATURE |find| ((|Union| |#2| "failed") #4=(|Mapping| #1# |#2|) |#1|)) (SIGNATURE |reduce| (|#2| #2# |#1| |#2|)) (SIGNATURE |reduce| (|#2| #2# |#1|)) (SIGNATURE |count| (#3# #4# |#1|)) (SIGNATURE |every?| #5=(#1# #4# |#1|)) (SIGNATURE |any?| #5#) (SIGNATURE |#| (#3# |#1|)) (SIGNATURE |empty?| (#1# |#1|))) (|FiniteAggregate| |#2|) (|Type|)) (T |FiniteAggregate&|)) @@ -1055,7 +1055,7 @@ NIL ((|traceMatrix| ((#1=(|Matrix| |#2|) #2=(|Vector| $)) 45 T ELT)) (|represents| (($ #3=(|Vector| |#2|) #2#) 39 T ELT)) (|regularRepresentation| ((#1# $ #2#) 47 T ELT)) (|discriminant| ((|#2| #2#) 13 T ELT)) (|coordinates| ((#3# $ #2#) NIL T ELT) ((#1# #2# #2#) 27 T ELT))) (((|FiniteRankAlgebra&| |#1| |#2| |#3|) (CATEGORY |package| (SIGNATURE |traceMatrix| (#1=(|Matrix| |#2|) #2=(|Vector| |#1|))) (SIGNATURE |discriminant| (|#2| #2#)) (SIGNATURE |represents| (|#1| #3=(|Vector| |#2|) #2#)) (SIGNATURE |coordinates| (#1# #2# #2#)) (SIGNATURE |coordinates| (#3# |#1| #2#)) (SIGNATURE |regularRepresentation| (#1# |#1| #2#))) (|FiniteRankAlgebra| |#2| |#3|) (|CommutativeRing|) (|UnivariatePolynomialCategory| |#2|)) (T |FiniteRankAlgebra&|)) NIL -((~= (#1=((|Boolean|) $ $) 7 T ELT)) (|zero?| ((#2=(|Boolean|) $) 22 T ELT)) (|traceMatrix| (((|Matrix| |#1|) (|Vector| $)) 61 T ELT)) (|trace| ((|#1| $) 67 T ELT)) (|subtractIfCan| (((|Union| $ "failed") $ $) 26 T ELT)) (|sample| (#3=($) 23 T CONST)) (|represents| (($ (|Vector| |#1|) (|Vector| $)) 63 T ELT)) (|regularRepresentation| (((|Matrix| |#1|) $ (|Vector| $)) 68 T ELT)) (|recip| (((|Union| $ "failed") $) 42 T ELT)) (|rank| (((|PositiveInteger|)) 69 T ELT)) (|opposite?| ((#2# $ $) 20 T ELT)) (|one?| (((|Boolean|) $) 44 T ELT)) (|norm| ((|#1| $) 66 T ELT)) (|minimalPolynomial| ((|#2| $) 59 (|has| |#1| (|Field|)) ELT)) (|latex| (((|String|) $) 11 T ELT)) (|hash| (((|SingleInteger|) $) 12 T ELT)) (|discriminant| ((|#1| (|Vector| $)) 62 T ELT)) (|coordinates| (((|Vector| |#1|) $ (|Vector| $)) 65 T ELT) (((|Matrix| |#1|) (|Vector| $) (|Vector| $)) 64 T ELT)) (|coerce| (((|OutputForm|) $) 13 T ELT) (($ (|Integer|)) 41 T ELT) (($ |#1|) 52 T ELT)) (|charthRoot| (((|Maybe| $) $) 58 (|has| |#1| (|CharacteristicNonZero|)) ELT)) (|characteristicPolynomial| ((|#2| $) 60 T ELT)) (|characteristic| (((|NonNegativeInteger|)) 40 T CONST)) (|before?| (#1# 6 T ELT)) (|annihilate?| (((|Boolean|) $ $) 33 T ELT)) (|Zero| (#3# 24 T CONST)) (|One| (($) 45 T CONST)) (= (#1# 8 T ELT)) (- (($ $) 29 T ELT) (($ $ $) 28 T ELT)) (+ (($ $ $) 18 T ELT)) (** (($ $ (|PositiveInteger|)) 35 T ELT) (($ $ (|NonNegativeInteger|)) 43 T ELT)) (* (($ (|PositiveInteger|) $) 17 T ELT) (($ (|NonNegativeInteger|) $) 21 T ELT) (($ (|Integer|) . #4=($)) 30 T ELT) (($ $ $) 34 T ELT) (($ $ |#1|) 54 T ELT) (($ |#1| . #4#) 53 T ELT))) +((~= (#1=((|Boolean|) $ $) 7 T ELT)) (|zero?| ((#2=(|Boolean|) $) 22 T ELT)) (|traceMatrix| (((|Matrix| |#1|) (|Vector| $)) 62 T ELT)) (|trace| ((|#1| $) 68 T ELT)) (|subtractIfCan| (((|Maybe| $) $ $) 26 T ELT)) (|sample| (#3=($) 23 T CONST)) (|represents| (($ (|Vector| |#1|) (|Vector| $)) 64 T ELT)) (|regularRepresentation| (((|Matrix| |#1|) $ (|Vector| $)) 69 T ELT)) (|recip| (((|Union| $ "failed") $) 43 T ELT)) (|rank| (((|PositiveInteger|)) 70 T ELT)) (|opposite?| ((#2# $ $) 20 T ELT)) (|one?| (((|Boolean|) $) 45 T ELT)) (|norm| ((|#1| $) 67 T ELT)) (|minimalPolynomial| ((|#2| $) 60 (|has| |#1| (|Field|)) ELT)) (|latex| (((|String|) $) 11 T ELT)) (|hash| (((|SingleInteger|) $) 12 T ELT)) (|discriminant| ((|#1| (|Vector| $)) 63 T ELT)) (|coordinates| (((|Vector| |#1|) $ (|Vector| $)) 66 T ELT) (((|Matrix| |#1|) (|Vector| $) (|Vector| $)) 65 T ELT)) (|coerce| (((|OutputForm|) $) 13 T ELT) (($ (|Integer|)) 42 T ELT) (($ |#1|) 53 T ELT)) (|charthRoot| (((|Maybe| $) $) 59 (|has| |#1| (|CharacteristicNonZero|)) ELT)) (|characteristicPolynomial| ((|#2| $) 61 T ELT)) (|characteristic| (((|NonNegativeInteger|)) 41 T CONST)) (|before?| (#1# 6 T ELT)) (|annihilate?| (((|Boolean|) $ $) 34 T ELT)) (|Zero| (#3# 24 T CONST)) (|One| (($) 46 T CONST)) (= (#1# 8 T ELT)) (- (($ $) 30 T ELT) (($ $ $) 29 T ELT)) (+ (($ $ $) 18 T ELT)) (** (($ $ (|PositiveInteger|)) 36 T ELT) (($ $ (|NonNegativeInteger|)) 44 T ELT)) (* (($ (|PositiveInteger|) $) 17 T ELT) (($ (|NonNegativeInteger|) $) 21 T ELT) (($ (|Integer|) . #4=($)) 31 T ELT) (($ $ $) 35 T ELT) (($ $ |#1|) 55 T ELT) (($ |#1| . #4#) 54 T ELT))) (((|FiniteRankAlgebra| |#1| |#2|) (|Category|) (|CommutativeRing|) (|UnivariatePolynomialCategory| |t#1|)) (T |FiniteRankAlgebra|)) ((|rank| (*1 *2) (AND (|ofCategory| *1 (|FiniteRankAlgebra| *3 *4)) (|ofCategory| *3 (|CommutativeRing|)) (|ofCategory| *4 (|UnivariatePolynomialCategory| *3)) (|isDomain| *2 (|PositiveInteger|)))) (|regularRepresentation| (*1 *2 *1 *3) (AND (|isDomain| *3 (|Vector| *1)) (|ofCategory| *1 (|FiniteRankAlgebra| *4 *5)) (|ofCategory| *4 (|CommutativeRing|)) (|ofCategory| *5 (|UnivariatePolynomialCategory| *4)) (|isDomain| *2 (|Matrix| *4)))) (|trace| (*1 *2 *1) (AND (|ofCategory| *1 (|FiniteRankAlgebra| *2 *3)) (|ofCategory| *3 (|UnivariatePolynomialCategory| *2)) (|ofCategory| *2 (|CommutativeRing|)))) (|norm| (*1 *2 *1) (AND (|ofCategory| *1 (|FiniteRankAlgebra| *2 *3)) (|ofCategory| *3 (|UnivariatePolynomialCategory| *2)) (|ofCategory| *2 (|CommutativeRing|)))) (|coordinates| (*1 *2 *1 *3) (AND (|isDomain| *3 (|Vector| *1)) (|ofCategory| *1 (|FiniteRankAlgebra| *4 *5)) (|ofCategory| *4 (|CommutativeRing|)) (|ofCategory| *5 (|UnivariatePolynomialCategory| *4)) (|isDomain| *2 (|Vector| *4)))) (|coordinates| (*1 *2 *3 *3) (AND (|isDomain| *3 (|Vector| *1)) (|ofCategory| *1 (|FiniteRankAlgebra| *4 *5)) (|ofCategory| *4 (|CommutativeRing|)) (|ofCategory| *5 (|UnivariatePolynomialCategory| *4)) (|isDomain| *2 (|Matrix| *4)))) (|represents| (*1 *1 *2 *3) (AND (|isDomain| *2 (|Vector| *4)) (|isDomain| *3 (|Vector| *1)) (|ofCategory| *4 (|CommutativeRing|)) (|ofCategory| *1 (|FiniteRankAlgebra| *4 *5)) (|ofCategory| *5 (|UnivariatePolynomialCategory| *4)))) (|discriminant| (*1 *2 *3) (AND (|isDomain| *3 (|Vector| *1)) (|ofCategory| *1 (|FiniteRankAlgebra| *2 *4)) (|ofCategory| *4 (|UnivariatePolynomialCategory| *2)) (|ofCategory| *2 (|CommutativeRing|)))) (|traceMatrix| (*1 *2 *3) (AND (|isDomain| *3 (|Vector| *1)) (|ofCategory| *1 (|FiniteRankAlgebra| *4 *5)) (|ofCategory| *4 (|CommutativeRing|)) (|ofCategory| *5 (|UnivariatePolynomialCategory| *4)) (|isDomain| *2 (|Matrix| *4)))) (|characteristicPolynomial| (*1 *2 *1) (AND (|ofCategory| *1 (|FiniteRankAlgebra| *3 *2)) (|ofCategory| *3 (|CommutativeRing|)) (|ofCategory| *2 (|UnivariatePolynomialCategory| *3)))) (|minimalPolynomial| (*1 *2 *1) (AND (|ofCategory| *1 (|FiniteRankAlgebra| *3 *2)) (|ofCategory| *3 (|CommutativeRing|)) (|ofCategory| *3 (|Field|)) (|ofCategory| *2 (|UnivariatePolynomialCategory| *3))))) (|Join| (|Algebra| |t#1|) (CATEGORY |domain| (SIGNATURE |rank| ((|PositiveInteger|))) (SIGNATURE |regularRepresentation| ((|Matrix| |t#1|) $ (|Vector| $))) (SIGNATURE |trace| (|t#1| $)) (SIGNATURE |norm| (|t#1| $)) (SIGNATURE |coordinates| ((|Vector| |t#1|) $ (|Vector| $))) (SIGNATURE |coordinates| ((|Matrix| |t#1|) (|Vector| $) (|Vector| $))) (SIGNATURE |represents| ($ (|Vector| |t#1|) (|Vector| $))) (SIGNATURE |discriminant| (|t#1| (|Vector| $))) (SIGNATURE |traceMatrix| ((|Matrix| |t#1|) (|Vector| $))) (SIGNATURE |characteristicPolynomial| (|t#2| $)) (IF (|has| |t#1| (|Field|)) (SIGNATURE |minimalPolynomial| (|t#2| $)) |%noBranch|) (IF (|has| |t#1| (|CharacteristicZero|)) (ATTRIBUTE (|CharacteristicZero|)) |%noBranch|) (IF (|has| |t#1| (|CharacteristicNonZero|)) (ATTRIBUTE (|CharacteristicNonZero|)) |%noBranch|))) @@ -1071,23 +1071,23 @@ NIL ((|scan| ((|#4| #1=(|Mapping| |#3| |#1| |#3|) |#2| |#3|) 25 T ELT)) (|reduce| ((|#3| #1# |#2| |#3|) 17 T ELT)) (|map| ((|#4| (|Mapping| |#3| |#1|) |#2|) 23 T ELT))) (((|FiniteLinearAggregateFunctions2| |#1| |#2| |#3| |#4|) (CATEGORY |package| (SIGNATURE |map| (|#4| (|Mapping| |#3| |#1|) |#2|)) (SIGNATURE |reduce| (|#3| #1=(|Mapping| |#3| |#1| |#3|) |#2| |#3|)) (SIGNATURE |scan| (|#4| #1# |#2| |#3|))) #2=(|Type|) (|FiniteLinearAggregate| |#1|) #2# (|FiniteLinearAggregate| |#3|)) (T |FiniteLinearAggregateFunctions2|)) ((|scan| (*1 *2 *3 *4 *5) (AND (|isDomain| *3 (|Mapping| *5 *6 *5)) #1=(|ofCategory| *6 #2=(|Type|)) #3=(|ofCategory| *5 #2#) (|ofCategory| *2 #4=(|FiniteLinearAggregate| *5)) (|isDomain| *1 (|FiniteLinearAggregateFunctions2| *6 *4 *5 *2)) (|ofCategory| *4 #5=(|FiniteLinearAggregate| *6)))) (|reduce| (*1 *2 *3 *4 *2) (AND (|isDomain| *3 (|Mapping| *2 *5 *2)) #3# (|ofCategory| *2 #2#) (|isDomain| *1 (|FiniteLinearAggregateFunctions2| *5 *4 *2 *6)) #6=(|ofCategory| *4 #4#) (|ofCategory| *6 (|FiniteLinearAggregate| *2)))) (|map| (*1 *2 *3 *4) (AND (|isDomain| *3 (|Mapping| *6 *5)) #3# #1# (|ofCategory| *2 #5#) (|isDomain| *1 (|FiniteLinearAggregateFunctions2| *5 *4 *6 *2)) #6#))) -((~= (#1=((|Boolean|) $ $) 7 T ELT)) (|zero?| ((#2=(|Boolean|) $) 22 T ELT)) (|varList| (((|List| |#1|) $) 43 T ELT)) (|trunc| (($ $ (|NonNegativeInteger|)) 44 T ELT)) (|subtractIfCan| (((|Union| $ "failed") $ $) 26 T ELT)) (|sample| (#3=($) 23 T CONST)) (|rquo| (((|XRecursivePolynomial| |#1| |#2|) (|XRecursivePolynomial| |#1| |#2|) $) 47 T ELT)) (|opposite?| ((#2# $ $) 20 T ELT)) (|mirror| (($ $) 45 T ELT)) (|lquo| (((|XRecursivePolynomial| |#1| |#2|) (|XRecursivePolynomial| |#1| |#2|) $) 48 T ELT)) (|latex| (((|String|) $) 11 T ELT)) (|hash| (((|SingleInteger|) $) 12 T ELT)) (|eval| (($ $ |#1| $) 42 T ELT) (($ $ (|List| |#1|) (|List| $)) 41 T ELT)) (|degree| (((|NonNegativeInteger|) $) 49 T ELT)) (|construct| (($ $ $) 40 T ELT)) (|coerce| (((|OutputForm|) $) 13 T ELT) (($ |#1|) 52 T ELT) (((|XDistributedPolynomial| |#1| |#2|) $) 51 T ELT) (((|XRecursivePolynomial| |#1| |#2|) $) 50 T ELT)) (|coef| ((|#2| (|XRecursivePolynomial| |#1| |#2|) $) 53 T ELT)) (|before?| (#1# 6 T ELT)) (|Zero| (#3# 24 T CONST)) (|LiePoly| (($ (|LyndonWord| |#1|)) 46 T ELT)) (= (#1# 8 T ELT)) (/ (($ $ |#2|) 39 (|has| |#2| (|Field|)) ELT)) (- (($ $) 29 T ELT) (($ $ $) 28 T ELT)) (+ (($ $ $) 18 T ELT)) (* (($ (|PositiveInteger|) $) 17 T ELT) (($ (|NonNegativeInteger|) $) 21 T ELT) (($ (|Integer|) . #4=($)) 30 T ELT) (($ |#2| . #4#) 33 T ELT) (($ $ |#2|) 37 T ELT))) +((~= (#1=((|Boolean|) $ $) 7 T ELT)) (|zero?| ((#2=(|Boolean|) $) 22 T ELT)) (|varList| (((|List| |#1|) $) 46 T ELT)) (|trunc| (($ $ (|NonNegativeInteger|)) 47 T ELT)) (|subtractIfCan| (((|Maybe| $) $ $) 26 T ELT)) (|sample| (#3=($) 23 T CONST)) (|rquo| (((|XRecursivePolynomial| |#1| |#2|) (|XRecursivePolynomial| |#1| |#2|) $) 50 T ELT)) (|opposite?| ((#2# $ $) 20 T ELT)) (|mirror| (($ $) 48 T ELT)) (|lquo| (((|XRecursivePolynomial| |#1| |#2|) (|XRecursivePolynomial| |#1| |#2|) $) 51 T ELT)) (|latex| (((|String|) $) 11 T ELT)) (|hash| (((|SingleInteger|) $) 12 T ELT)) (|eval| (($ $ |#1| $) 45 T ELT) (($ $ (|List| |#1|) (|List| $)) 44 T ELT)) (|degree| (((|NonNegativeInteger|) $) 52 T ELT)) (|construct| (($ $ $) 41 T ELT)) (|coerce| (((|OutputForm|) . #4=($)) 13 T ELT) (((|XDistributedPolynomial| |#1| |#2|) . #4#) 56 T ELT) (((|XRecursivePolynomial| |#1| |#2|) . #4#) 55 T ELT) (($ |#1|) 53 T ELT)) (|coef| ((|#2| (|XRecursivePolynomial| |#1| |#2|) $) 54 T ELT)) (|before?| (#1# 6 T ELT)) (|Zero| (#3# 24 T CONST)) (|LiePoly| (($ (|LyndonWord| |#1|)) 49 T ELT)) (= (#1# 8 T ELT)) (/ (($ $ |#2|) 40 (|has| |#2| (|Field|)) ELT)) (- (($ $) 30 T ELT) (($ $ $) 29 T ELT)) (+ (($ $ $) 18 T ELT)) (* (($ (|PositiveInteger|) $) 17 T ELT) (($ (|NonNegativeInteger|) $) 21 T ELT) (($ (|Integer|) . #5=($)) 31 T ELT) (($ |#2| . #5#) 34 T ELT) (($ $ |#2|) 38 T ELT))) (((|FreeLieAlgebra| |#1| |#2|) (|Category|) (|OrderedSet|) (|CommutativeRing|)) (T |FreeLieAlgebra|)) -((|coef| (*1 *2 *3 *1) (AND (|isDomain| *3 (|XRecursivePolynomial| *4 *2)) (|ofCategory| *1 (|FreeLieAlgebra| *4 *2)) (|ofCategory| *4 (|OrderedSet|)) (|ofCategory| *2 (|CommutativeRing|)))) (|coerce| (*1 *1 *2) (AND (|ofCategory| *1 (|FreeLieAlgebra| *2 *3)) (|ofCategory| *2 (|OrderedSet|)) (|ofCategory| *3 (|CommutativeRing|)))) (|coerce| (*1 *2 *1) (AND (|ofCategory| *1 (|FreeLieAlgebra| *3 *4)) (|ofCategory| *3 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T)) +((|coef| (*1 *2 *3 *1) (AND (|isDomain| *3 (|XRecursivePolynomial| *4 *2)) (|ofCategory| *1 (|FreeLieAlgebra| *4 *2)) (|ofCategory| *4 (|OrderedSet|)) (|ofCategory| *2 (|CommutativeRing|)))) (|coerce| (*1 *1 *2) (AND (|ofCategory| *1 (|FreeLieAlgebra| *2 *3)) (|ofCategory| *2 (|OrderedSet|)) (|ofCategory| *3 (|CommutativeRing|)))) (|degree| (*1 *2 *1) (AND (|ofCategory| *1 (|FreeLieAlgebra| *3 *4)) (|ofCategory| *3 (|OrderedSet|)) (|ofCategory| *4 (|CommutativeRing|)) (|isDomain| *2 (|NonNegativeInteger|)))) (|lquo| (*1 *2 *2 *1) (AND (|isDomain| *2 (|XRecursivePolynomial| *3 *4)) (|ofCategory| *1 (|FreeLieAlgebra| *3 *4)) (|ofCategory| *3 (|OrderedSet|)) (|ofCategory| *4 (|CommutativeRing|)))) (|rquo| (*1 *2 *2 *1) (AND (|isDomain| *2 (|XRecursivePolynomial| *3 *4)) (|ofCategory| *1 (|FreeLieAlgebra| *3 *4)) (|ofCategory| *3 (|OrderedSet|)) (|ofCategory| *4 (|CommutativeRing|)))) (|LiePoly| (*1 *1 *2) (AND (|isDomain| *2 (|LyndonWord| *3)) (|ofCategory| *3 (|OrderedSet|)) (|ofCategory| *1 (|FreeLieAlgebra| *3 *4)) (|ofCategory| *4 (|CommutativeRing|)))) (|mirror| (*1 *1 *1) (AND (|ofCategory| *1 (|FreeLieAlgebra| *2 *3)) (|ofCategory| *2 (|OrderedSet|)) (|ofCategory| *3 (|CommutativeRing|)))) (|trunc| (*1 *1 *1 *2) (AND (|isDomain| *2 (|NonNegativeInteger|)) (|ofCategory| *1 (|FreeLieAlgebra| *3 *4)) (|ofCategory| *3 (|OrderedSet|)) (|ofCategory| *4 (|CommutativeRing|)))) (|varList| (*1 *2 *1) (AND (|ofCategory| *1 (|FreeLieAlgebra| *3 *4)) (|ofCategory| *3 (|OrderedSet|)) (|ofCategory| *4 (|CommutativeRing|)) (|isDomain| *2 (|List| *3)))) (|eval| (*1 *1 *1 *2 *1) (AND (|ofCategory| *1 (|FreeLieAlgebra| *2 *3)) (|ofCategory| *2 (|OrderedSet|)) (|ofCategory| *3 (|CommutativeRing|)))) (|eval| (*1 *1 *1 *2 *3) (AND (|isDomain| *2 (|List| *4)) (|isDomain| *3 (|List| *1)) (|ofCategory| *1 (|FreeLieAlgebra| *4 *5)) (|ofCategory| *4 (|OrderedSet|)) (|ofCategory| *5 (|CommutativeRing|))))) +(|Join| (|LieAlgebra| |t#2|) (|CoercibleTo| (|XDistributedPolynomial| |t#1| |t#2|)) (|CoercibleTo| (|XRecursivePolynomial| |t#1| |t#2|)) (CATEGORY |domain| (SIGNATURE |coef| (|t#2| (|XRecursivePolynomial| |t#1| |t#2|) $)) (SIGNATURE |coerce| ($ |t#1|)) (SIGNATURE |degree| ((|NonNegativeInteger|) $)) (SIGNATURE |lquo| ((|XRecursivePolynomial| |t#1| |t#2|) (|XRecursivePolynomial| |t#1| |t#2|) $)) (SIGNATURE |rquo| ((|XRecursivePolynomial| |t#1| |t#2|) (|XRecursivePolynomial| |t#1| |t#2|) $)) (SIGNATURE |LiePoly| ($ (|LyndonWord| |t#1|))) (SIGNATURE |mirror| ($ $)) (SIGNATURE |trunc| ($ $ (|NonNegativeInteger|))) (SIGNATURE |varList| ((|List| |t#1|) $)) (SIGNATURE |eval| ($ $ |t#1| $)) (SIGNATURE |eval| ($ $ (|List| |t#1|) (|List| $))))) +(((|AbelianGroup|) . 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((#26=(|PatternMatchResult| #27=(|Float|) $) $ #28=(|Pattern| #27#) #26#) NIL T ELT)) (|outputSpacing| (#29=(#30=(|Void|) #19#) 177 T ELT)) (|outputGeneral| (#31=(#30#) 182 T ELT) (#29# 183 T ELT)) (|outputFloating| (#31# 184 T ELT) (#29# 185 T ELT)) (|outputFixed| (#31# 180 T ELT) (#29# 181 T ELT)) (|order| (#5# 50 T ELT)) (|opposite?| #1#) (|one?| (#4# 21 T ELT)) (|nthRoot| (#11# NIL T ELT)) (|normalize| (#8# 32 T ELT)) (|norm| #7#) (|negative?| (#4# 18 T ELT)) (|multiEuclidean| (((|Union| #20# #14#) #20# $) NIL T ELT)) (|min| #16# #32=(#12# NIL (AND (|not| (|has| $ (ATTRIBUTE |arbitraryExponent|))) (|not| #25#)) ELT)) (|max| #16# #32#) (|mantissa| (#5# 112 T ELT)) (|log2| (#12# 90 T ELT) (#8# 97 T ELT)) (|log10| (#12# 96 T ELT) (#8# 98 T ELT)) (|log| (#8# 84 T ELT)) (|lcm| #16# #33=(($ #20#) NIL T ELT)) (|latex| (#34=((|String|) $) NIL T ELT)) (|inv| (#8# 127 T ELT)) (|increasePrecision| (#35=(#23# #6#) 27 #25# ELT)) (|hash| (((|SingleInteger|) $) NIL T ELT)) (|gcdPolynomial| ((#36=(|SparseUnivariatePolynomial| $) #36# #36#) NIL T ELT)) (|gcd| #16# #33#) (|fractionPart| (#8# 41 T ELT)) (|floor| (#8# 119 T ELT)) (|float| (($ #6# #6#) 115 T ELT) (($ #6# #6# #23#) 116 T ELT)) (|factor| #10#) (|extendedEuclidean| (((|Record| #37=(|:| |coef1| $) #38=(|:| |coef2| $) #21#) $ $) NIL T ELT) (((|Union| (|Record| #37# #38#) #14#) $ $ $) NIL T ELT)) (|exquo| ((#18# $ $) NIL T ELT)) (|expressIdealMember| (((|Maybe| #20#) #20# $) NIL T ELT)) (|exponent| (#5# 113 T ELT)) (|exp1| (#12# 99 T ELT)) (|exp| (#8# 78 T ELT)) (|euclideanSize| ((#19# $) NIL T ELT)) (|divide| (((|Record| (|:| |quotient| $) (|:| |remainder| $)) $ $) NIL T ELT)) (|digits| (#22# 108 T ELT) (#24# 109 #25# ELT)) (|differentiate| (#8# 126 T ELT) #39=(($ $ #19#) NIL T ELT)) (|decreasePrecision| (#35# 31 #25# ELT)) (|csch| #7#) (|csc| #7#) (|coth| #7#) (|cot| #7#) (|cosh| (#8# 80 T ELT)) (|cos| (#8# 71 T ELT)) (|convert| ((#27# $) 202 T ELT) (#40=(#41=(|DoubleFloat|) $) 204 T ELT) ((#28# $) NIL T ELT) (#34# 188 T ELT) (((|InputForm|) $) 200 T ELT) (($ #41#) 209 T ELT)) (|coerce| (((|OutputForm|) $) 192 T ELT) #42=(($ #6#) 214 T ELT) #7# #43=(($ #15#) NIL T ELT) #42# #43# (#40# 205 T ELT)) (|characteristic| ((#19#) NIL T CONST)) (|ceiling| (#8# 121 T ELT)) (|bits| (#22# 42 T ELT) (#24# 62 #25# ELT)) (|before?| #1#) (|base| (#22# 111 T ELT)) (|atanh| (#8# 87 T ELT)) (|atan| (#8# 30 T ELT) (#17# 40 T ELT)) (|associates?| #1#) (|asinh| (#8# 85 T ELT)) (|asin| (#8# 20 T ELT)) (|asech| #7#) (|asec| #7#) (|annihilate?| #1#) (|acsch| #7#) (|acsc| #7#) (|acoth| #7#) (|acot| #7#) (|acosh| (#8# 86 T ELT)) (|acos| (#8# 33 T ELT)) (|abs| (#8# 39 T ELT)) (|Zero| (#12# 17 T CONST)) (|One| (#12# 24 T CONST)) (D #7# #39#) (>= (#2# 189 T ELT)) (> (#2# 26 T ELT)) (= (#2# 37 T ELT)) (<= #1#) (< (#2# 43 T ELT)) (/ (#17# 29 T ELT) (#11# 23 T ELT)) (- (#8# 19 T ELT) (#17# 34 T ELT)) (+ (#17# 54 T ELT)) (** (($ $ #23#) 65 T ELT) #39# (#11# 91 T ELT) (#44=($ $ #15#) 137 T ELT) (#17# 129 T ELT)) (* (($ #23# $) 61 T ELT) (($ #19# $) NIL T ELT) (($ #6# $) 66 T ELT) (#17# 53 T ELT) (#44# NIL T ELT) (($ #15# $) NIL T ELT))) (((|Float|) (|Join| (|FloatingPointSystem|) (|DifferentialRing|) (|ConvertibleTo| (|String|)) (|CoercibleTo| #1=(|DoubleFloat|)) (|TranscendentalFunctionCategory|) (|ConvertibleTo| (|InputForm|)) (|ConvertibleFrom| #1#) (CATEGORY |domain| (SIGNATURE / #2=($ $ #3=(|Integer|))) (SIGNATURE ** #4=($ $ $)) (SIGNATURE |normalize| #5=($ $)) (SIGNATURE |relerror| (#3# $ $)) (SIGNATURE |shift| #2#) (SIGNATURE |rationalApproximation| (#6=(|Fraction| #3#) $ #7=(|NonNegativeInteger|))) (SIGNATURE |rationalApproximation| (#6# $ #7# #7#)) (SIGNATURE |log2| #8=($)) (SIGNATURE |log10| #8#) (SIGNATURE |exp1| #8#) (SIGNATURE |atan| #4#) (SIGNATURE |log2| #5#) (SIGNATURE |log10| #5#) (SIGNATURE |outputFloating| #9=(#10=(|Void|))) (SIGNATURE |outputFloating| #11=(#10# #7#)) (SIGNATURE |outputFixed| #9#) (SIGNATURE |outputFixed| #11#) (SIGNATURE |outputGeneral| #9#) (SIGNATURE |outputGeneral| #11#) (SIGNATURE |outputSpacing| #11#) (ATTRIBUTE |arbitraryPrecision|) (ATTRIBUTE |arbitraryExponent|)))) (T |Float|)) ((** #1=(*1 *1 *1 *1) #2=(|isDomain| *1 (|Float|))) (/ #3=(*1 *1 *1 *2) #4=(AND (|isDomain| *2 #5=(|Integer|)) #2#)) (|normalize| #6=(*1 *1 *1) #2#) (|relerror| (*1 *2 *1 *1) #4#) (|shift| #3# #4#) (|rationalApproximation| (*1 *2 *1 *3) #7=(AND #8=(|isDomain| *3 (|NonNegativeInteger|)) (|isDomain| *2 (|Fraction| #5#)) #2#)) (|rationalApproximation| (*1 *2 *1 *3 *3) #7#) (|log2| #9=(*1 *1) #2#) (|log10| #9# #2#) (|exp1| #9# #2#) (|atan| #1# #2#) (|log2| #6# #2#) (|log10| #6# #2#) (|outputFloating| #10=(*1 *2) #11=(AND #12=(|isDomain| *2 (|Void|)) #2#)) (|outputFloating| #13=(*1 *2 *3) #14=(AND #8# #12# #2#)) (|outputFixed| #10# #11#) (|outputFixed| #13# #14#) (|outputGeneral| #10# #11#) (|outputGeneral| #13# #14#) (|outputSpacing| #13# #14#)) ((|complexSolve| ((#1=(|List| (|Equation| (|Polynomial| #2=(|Complex| |#1|)))) #3=(|Equation| #4=(|Fraction| (|Polynomial| (|Complex| (|Integer|))))) |#1|) 52 T ELT) ((#1# #4# |#1|) 51 T ELT) ((#5=(|List| #1#) (|List| #3#) |#1|) 48 T ELT) ((#5# #6=(|List| #4#) |#1|) 42 T ELT)) (|complexRoots| (((|List| #7=(|List| #2#)) #6# (|List| (|Symbol|)) |#1|) 30 T ELT) ((#7# #4# |#1|) 18 T ELT))) @@ -1096,13 +1096,16 @@ NIL ((|solve| ((#1=(|List| (|Equation| (|Polynomial| |#1|))) #2=(|Equation| #3=(|Fraction| (|Polynomial| (|Integer|)))) |#1|) 47 T ELT) ((#1# #3# |#1|) 46 T ELT) ((#4=(|List| #1#) (|List| #2#) |#1|) 43 T ELT) ((#4# #5=(|List| #3#) |#1|) 37 T ELT)) (|realRoots| ((#6=(|List| |#1|) #3# |#1|) 20 T ELT) (((|List| #6#) #5# (|List| (|Symbol|)) |#1|) 30 T ELT))) (((|FloatingRealPackage| |#1|) (CATEGORY |package| (SIGNATURE |solve| (#1=(|List| #2=(|List| (|Equation| (|Polynomial| |#1|)))) #3=(|List| #4=(|Fraction| (|Polynomial| (|Integer|)))) |#1|)) (SIGNATURE |solve| (#1# (|List| #5=(|Equation| #4#)) |#1|)) (SIGNATURE |solve| (#2# #4# |#1|)) (SIGNATURE |solve| (#2# #5# |#1|)) (SIGNATURE |realRoots| ((|List| #6=(|List| |#1|)) #3# (|List| (|Symbol|)) |#1|)) (SIGNATURE |realRoots| (#6# #4# |#1|))) (|Join| (|OrderedRing|) (|Field|))) (T |FloatingRealPackage|)) ((|realRoots| #1=(*1 *2 *3 *4) (AND #2=(|isDomain| *3 #3=(|Fraction| (|Polynomial| (|Integer|)))) (|isDomain| *2 (|List| *4)) #4=(|isDomain| *1 (|FloatingRealPackage| *4)) #5=(|ofCategory| *4 #6=(|Join| (|OrderedRing|) (|Field|))))) (|realRoots| (*1 *2 *3 *4 *5) (AND #7=(|isDomain| *3 (|List| #3#)) (|isDomain| *4 (|List| (|Symbol|))) (|isDomain| *2 (|List| (|List| *5))) (|isDomain| *1 (|FloatingRealPackage| *5)) (|ofCategory| *5 #6#))) (|solve| #1# (AND (|isDomain| *3 #8=(|Equation| #3#)) #9=(|isDomain| *2 #10=(|List| (|Equation| (|Polynomial| *4)))) #4# #5#)) (|solve| #1# (AND #2# #9# #4# #5#)) (|solve| #1# (AND (|isDomain| *3 (|List| #8#)) #11=(|isDomain| *2 (|List| #10#)) #4# #5#)) (|solve| #1# (AND #7# #11# #4# #5#))) -((~= #1=((#2=(|Boolean|) $ $) NIL T ELT)) (|zero?| ((#2# $) NIL T ELT)) (|terms| ((#3=(|List| (|IndexedProductTerm| |#1| |#2|)) $) NIL T ELT)) (|subtractIfCan| (((|Union| $ "failed") $ $) NIL T ELT)) (|sample| (#4=($) NIL T CONST)) (|reductum| #5=(($ $) NIL T ELT)) (|opposite?| #1#) (|monomial| (($ |#1| |#2|) NIL T ELT)) (|map| (($ (|Mapping| |#1| |#1|) $) NIL T ELT)) (|leadingSupport| ((|#2| $) NIL T ELT)) (|leadingCoefficient| ((|#1| $) NIL T ELT)) (|latex| (((|String|) $) NIL T ELT)) (|hash| (((|SingleInteger|) $) NIL T ELT)) (|convert| (($ #3#) NIL T ELT)) (|coerce| (((|OutputForm|) $) 34 T ELT)) (|before?| #1#) (|Zero| (#4# 12 T CONST)) (= #1#) (- #5# #6=(($ $ $) NIL T ELT)) (+ #6#) (* (($ (|PositiveInteger|) $) NIL T ELT) (($ (|NonNegativeInteger|) $) NIL T ELT) (($ (|Integer|) $) NIL T ELT) (($ |#1| $) 15 T ELT) (($ $ |#1|) 18 T ELT))) +((~= #1=((#2=(|Boolean|) $ $) NIL T ELT)) (|zero?| ((#2# $) NIL T ELT)) (|terms| ((#3=(|List| (|IndexedProductTerm| |#1| |#2|)) $) NIL T ELT)) (|subtractIfCan| (((|Maybe| $) $ $) NIL T ELT)) (|sample| (#4=($) NIL T CONST)) (|reductum| #5=(($ $) NIL T ELT)) (|opposite?| #1#) (|monomial| (($ |#1| |#2|) NIL T ELT)) (|map| (($ (|Mapping| |#1| |#1|) $) NIL T ELT)) (|leadingSupport| ((|#2| $) NIL T ELT)) (|leadingCoefficient| ((|#1| $) NIL T ELT)) (|latex| (((|String|) $) NIL T ELT)) (|hash| (((|SingleInteger|) $) NIL T ELT)) (|convert| (($ #3#) NIL T ELT)) (|coerce| (((|OutputForm|) $) 34 T ELT)) (|before?| #1#) (|Zero| (#4# 12 T CONST)) (= #1#) (- #5# #6=(($ $ $) NIL T ELT)) (+ #6#) (* (($ (|PositiveInteger|) $) NIL T ELT) (($ (|NonNegativeInteger|) $) NIL T ELT) (($ (|Integer|) $) NIL T ELT) (($ |#1| $) 15 T ELT) (($ $ |#1|) 18 T ELT))) (((|FreeModule| |#1| |#2|) (|Join| (|BiModule| |#1| |#1|) (|IndexedDirectProductCategory| |#1| |#2|) (CATEGORY |package| (IF (|has| |#1| (|CommutativeRing|)) (ATTRIBUTE (|Module| |#1|)) |%noBranch|))) (|Ring|) (|OrderedType|)) (T |FreeModule|)) NIL -((~= #1=((#2=(|Boolean|) $ $) NIL T ELT)) (|zero?| #3=((#2# $) NIL T ELT)) (|subtractIfCan| (((|Union| $ #4="failed") $ $) NIL T ELT)) (|sample| (#5=($) NIL T CONST)) (|retractIfCan| (((|Union| |#2| #4#) $) 29 T ELT)) (|retract| (#6=(|#2| $) 31 T ELT)) (|reductum| #7=(($ $) NIL T ELT)) (|opposite?| #1#) (|numberOfMonomials| ((#8=(|NonNegativeInteger|) $) 13 T ELT)) (|monomials| (((|List| $) $) 23 T ELT)) (|monomial?| #3#) (|monom| (#9=($ |#2| |#1|) 21 T ELT)) (|map| (($ (|Mapping| |#1| |#1|) $) NIL T ELT)) (|leadingTerm| ((#10=(|Record| (|:| |k| |#2|) (|:| |c| |#1|)) $) 17 T ELT)) (|leadingMonomial| (#6# 18 T ELT)) (|leadingCoefficient| ((|#1| $) NIL T ELT)) (|latex| (((|String|) $) NIL T ELT)) (|hash| (((|SingleInteger|) $) NIL T ELT)) (|coerce| (((|OutputForm|) $) 50 T ELT) (($ |#2|) 30 T ELT)) (|coefficients| (((|List| |#1|) $) 20 T ELT)) (|coefficient| ((|#1| $ |#2|) 54 T ELT)) (|before?| #1#) (|Zero| (#5# 32 T CONST)) (|ListOfTerms| (((|List| #10#) $) 14 T ELT)) (= #1#) (- #11=(($ $ $) NIL T ELT) #7#) (+ #11#) (* (($ $ |#1|) 36 T ELT) (($ |#1| $) 35 T ELT) (($ (|Integer|) $) NIL T ELT) (($ #8# $) NIL T ELT) (($ (|PositiveInteger|) $) NIL T ELT) (($ |#1| |#2|) 38 T ELT) (#9# 39 T ELT))) +((~= #1=((#2=(|Boolean|) $ $) NIL T ELT)) (|zero?| #3=((#2# $) NIL T ELT)) (|subtractIfCan| (((|Maybe| $) $ $) NIL T ELT)) (|sample| (#4=($) NIL T CONST)) (|retractIfCan| (((|Union| |#2| "failed") $) 29 T ELT)) (|retract| (#5=(|#2| $) 31 T ELT)) (|reductum| #6=(($ $) NIL T ELT)) (|opposite?| #1#) (|numberOfMonomials| ((#7=(|NonNegativeInteger|) $) 13 T ELT)) (|monomials| (((|List| $) $) 23 T ELT)) (|monomial?| #3#) (|monom| (#8=($ |#2| |#1|) 21 T ELT)) (|map| (($ (|Mapping| |#1| |#1|) $) NIL T ELT)) (|leadingTerm| ((#9=(|Record| (|:| |k| |#2|) (|:| |c| |#1|)) $) 17 T ELT)) (|leadingMonomial| (#5# 18 T ELT)) (|leadingCoefficient| ((|#1| $) NIL T ELT)) (|latex| (((|String|) $) NIL T ELT)) (|hash| (((|SingleInteger|) $) NIL T ELT)) (|coerce| (((|OutputForm|) $) 50 T ELT) (($ |#2|) 30 T ELT)) (|coefficients| (((|List| |#1|) $) 20 T ELT)) (|coefficient| ((|#1| $ |#2|) 54 T ELT)) (|before?| #1#) (|Zero| (#4# 32 T CONST)) (|ListOfTerms| (((|List| #9#) $) 14 T ELT)) (= #1#) (- #10=(($ $ $) NIL T ELT) #6#) (+ #10#) (* (($ $ |#1|) 36 T ELT) (($ |#1| $) 35 T ELT) (($ (|Integer|) $) NIL T ELT) (($ #7# $) NIL T ELT) (($ (|PositiveInteger|) $) NIL T ELT) (($ |#1| |#2|) 38 T ELT) (#8# 39 T ELT))) (((|FreeModule1| |#1| |#2|) (|Join| (|FreeModuleCat| |#1| |#2|) (CATEGORY |domain| (SIGNATURE * ($ |#2| |#1|)))) (|Ring|) (|OrderedSet|)) (T |FreeModule1|)) ((* (*1 *1 *2 *3) (AND (|isDomain| *1 (|FreeModule1| *3 *2)) (|ofCategory| *3 (|Ring|)) (|ofCategory| *2 (|OrderedSet|))))) -((~= (#1=((|Boolean|) $ $) 31 T ELT)) (|zero?| ((#2=(|Boolean|) $) 40 T ELT)) (|subtractIfCan| (((|Union| $ "failed") $ $) 43 T ELT)) (|sample| (#3=($) 39 T CONST)) (|retractIfCan| (((|Union| |#2| "failed") $) 28 T ELT)) (|retract| ((|#2| $) 29 T ELT)) (|reductum| (($ $) 15 T ELT)) (|opposite?| ((#2# $ $) 42 T ELT)) (|numberOfMonomials| (((|NonNegativeInteger|) $) 19 T ELT)) (|monomials| (((|List| $) $) 20 T ELT)) (|monomial?| (((|Boolean|) $) 23 T ELT)) (|monom| (($ |#2| |#1|) 24 T ELT)) (|map| (($ (|Mapping| |#1| |#1|) $) 6 T ELT)) (|leadingTerm| (((|Record| (|:| |k| |#2|) (|:| |c| |#1|)) $) 16 T ELT)) (|leadingMonomial| ((|#2| $) 18 T ELT)) (|leadingCoefficient| ((|#1| $) 17 T ELT)) (|latex| (((|String|) $) 35 T ELT)) (|hash| (((|SingleInteger|) $) 34 T ELT)) (|coerce| (((|OutputForm|) $) 33 T ELT) (($ |#2|) 27 T ELT)) (|coefficients| (((|List| |#1|) $) 21 T ELT)) (|coefficient| ((|#1| $ |#2|) 25 T ELT)) (|before?| (#1# 32 T ELT)) (|Zero| (#3# 38 T CONST)) (|ListOfTerms| (((|List| (|Record| (|:| |k| |#2|) (|:| |c| |#1|))) $) 22 T ELT)) (= (#1# 30 T ELT)) (- (($ $ $) 46 T ELT) (($ $) 45 T ELT)) (+ (($ $ $) 36 T ELT)) (* (($ $ |#1|) 48 T ELT) (($ |#1| . #4=($)) 47 T ELT) (($ (|Integer|) . #4#) 44 T ELT) (($ (|NonNegativeInteger|) $) 41 T ELT) (($ (|PositiveInteger|) $) 37 T ELT) (($ |#1| |#2|) 26 T ELT))) +((~= #1=(#2=(#3=(|Boolean|) $ $) NIL T ELT)) (|varList| (((|List| |#1|) $) 15 T ELT)) (|right| (#4=($ $) 19 T ELT)) (|retractable?| ((#3# $) 20 T ELT)) (|retractIfCan| (((|Union| |#1| "failed") $) 23 T ELT)) (|retract| (#5=(|#1| $) 21 T ELT)) (|rest| (#4# 37 T ELT)) (|mirror| (#4# 25 T ELT)) (|min| #6=(#7=($ $ $) NIL T ELT)) (|max| #6#) (|lexico| (#2# 46 T ELT)) (|length| (((|PositiveInteger|) $) 40 T ELT)) (|left| (#4# 18 T ELT)) (|latex| (((|String|) $) NIL T ELT)) (|hash| (((|SingleInteger|) $) NIL T ELT)) (|first| (#5# 36 T ELT)) (|coerce| (((|OutputForm|) $) 32 T ELT) (($ |#1|) 24 T ELT) (((|OrderedFreeMonoid| |#1|) $) 28 T ELT)) (|before?| #1#) (>= #1#) (> #1#) (= (#2# 13 T ELT)) (<= #1#) (< (#2# 44 T ELT)) (* (#7# 35 T ELT))) +(((|FreeMagma| |#1|) (|Join| #1=(|OrderedSet|) (|RetractableTo| |#1|) (|CoercibleTo| (|OrderedFreeMonoid| |#1|)) (CATEGORY |domain| (SIGNATURE * ($ $ $)) (SIGNATURE |first| (|#1| $)) (SIGNATURE |left| #2=($ $)) (SIGNATURE |length| ((|PositiveInteger|) $)) (SIGNATURE |lexico| (#3=(|Boolean|) $ $)) (SIGNATURE |mirror| #2#) (SIGNATURE |rest| #2#) (SIGNATURE |retractable?| (#3# $)) (SIGNATURE |right| #2#) (SIGNATURE |varList| ((|List| |#1|) $)))) #1#) (T |FreeMagma|)) +((* (*1 *1 *1 *1) #1=(AND (|isDomain| *1 (|FreeMagma| *2)) (|ofCategory| *2 #2=(|OrderedSet|)))) (|first| #3=(*1 *2 *1) #1#) (|left| #4=(*1 *1 *1) #1#) (|length| #3# (AND (|isDomain| *2 (|PositiveInteger|)) #5=(|isDomain| *1 (|FreeMagma| *3)) #6=(|ofCategory| *3 #2#))) (|lexico| (*1 *2 *1 *1) #7=(AND (|isDomain| *2 (|Boolean|)) #5# #6#)) (|mirror| #4# #1#) (|rest| #4# #1#) (|retractable?| #3# #7#) (|right| #4# #1#) (|varList| #3# (AND (|isDomain| *2 (|List| *3)) #5# #6#))) +((~= (#1=((|Boolean|) $ $) 31 T ELT)) (|zero?| ((#2=(|Boolean|) $) 40 T ELT)) (|subtractIfCan| (((|Maybe| $) $ $) 43 T ELT)) (|sample| (#3=($) 39 T CONST)) (|retractIfCan| (((|Union| |#2| "failed") $) 28 T ELT)) (|retract| ((|#2| $) 29 T ELT)) (|reductum| (($ $) 15 T ELT)) (|opposite?| ((#2# $ $) 42 T ELT)) (|numberOfMonomials| (((|NonNegativeInteger|) $) 19 T ELT)) (|monomials| (((|List| $) $) 20 T ELT)) (|monomial?| (((|Boolean|) $) 23 T ELT)) (|monom| (($ |#2| |#1|) 24 T ELT)) (|map| (($ (|Mapping| |#1| |#1|) $) 6 T ELT)) (|leadingTerm| (((|Record| (|:| |k| |#2|) (|:| |c| |#1|)) $) 16 T ELT)) (|leadingMonomial| ((|#2| $) 18 T ELT)) (|leadingCoefficient| ((|#1| $) 17 T ELT)) (|latex| (((|String|) $) 35 T ELT)) (|hash| (((|SingleInteger|) $) 34 T ELT)) (|coerce| (((|OutputForm|) $) 33 T ELT) (($ |#2|) 27 T ELT)) (|coefficients| (((|List| |#1|) $) 21 T ELT)) (|coefficient| ((|#1| $ |#2|) 25 T ELT)) (|before?| (#1# 32 T ELT)) (|Zero| (#3# 38 T CONST)) (|ListOfTerms| (((|List| (|Record| (|:| |k| |#2|) (|:| |c| |#1|))) $) 22 T ELT)) (= (#1# 30 T ELT)) (- (($ $ $) 46 T ELT) (($ $) 45 T ELT)) (+ (($ $ $) 36 T ELT)) (* (($ $ |#1|) 48 T ELT) (($ |#1| . #4=($)) 47 T ELT) (($ (|Integer|) . #4#) 44 T ELT) (($ (|NonNegativeInteger|) $) 41 T ELT) (($ (|PositiveInteger|) $) 37 T ELT) (($ |#1| |#2|) 26 T ELT))) (((|FreeModuleCat| |#1| |#2|) (|Category|) (|Ring|) (|SetCategory|)) (T |FreeModuleCat|)) ((* (*1 *1 *2 *3) (AND (|ofCategory| *1 (|FreeModuleCat| *2 *3)) (|ofCategory| *2 (|Ring|)) (|ofCategory| *3 (|SetCategory|)))) (|coefficient| (*1 *2 *1 *3) (AND (|ofCategory| *1 (|FreeModuleCat| *2 *3)) (|ofCategory| *3 (|SetCategory|)) (|ofCategory| *2 (|Ring|)))) (|monom| (*1 *1 *2 *3) (AND (|ofCategory| *1 (|FreeModuleCat| *3 *2)) (|ofCategory| *3 (|Ring|)) (|ofCategory| *2 (|SetCategory|)))) (|monomial?| (*1 *2 *1) (AND (|ofCategory| *1 (|FreeModuleCat| *3 *4)) (|ofCategory| *3 (|Ring|)) (|ofCategory| *4 (|SetCategory|)) (|isDomain| *2 (|Boolean|)))) (|ListOfTerms| (*1 *2 *1) (AND (|ofCategory| *1 (|FreeModuleCat| *3 *4)) (|ofCategory| *3 (|Ring|)) (|ofCategory| *4 (|SetCategory|)) (|isDomain| *2 (|List| (|Record| (|:| |k| *4) (|:| |c| *3)))))) (|coefficients| (*1 *2 *1) (AND (|ofCategory| *1 (|FreeModuleCat| *3 *4)) (|ofCategory| *3 (|Ring|)) (|ofCategory| *4 (|SetCategory|)) (|isDomain| *2 (|List| *3)))) (|monomials| (*1 *2 *1) (AND (|ofCategory| *3 (|Ring|)) (|ofCategory| *4 (|SetCategory|)) (|isDomain| *2 (|List| *1)) (|ofCategory| *1 (|FreeModuleCat| *3 *4)))) (|numberOfMonomials| (*1 *2 *1) (AND (|ofCategory| *1 (|FreeModuleCat| *3 *4)) (|ofCategory| *3 (|Ring|)) (|ofCategory| *4 (|SetCategory|)) (|isDomain| *2 (|NonNegativeInteger|)))) (|leadingMonomial| (*1 *2 *1) (AND (|ofCategory| *1 (|FreeModuleCat| *3 *2)) (|ofCategory| *3 (|Ring|)) (|ofCategory| *2 (|SetCategory|)))) (|leadingCoefficient| (*1 *2 *1) (AND (|ofCategory| *1 (|FreeModuleCat| *2 *3)) (|ofCategory| *3 (|SetCategory|)) (|ofCategory| *2 (|Ring|)))) (|leadingTerm| (*1 *2 *1) (AND (|ofCategory| *1 (|FreeModuleCat| *3 *4)) (|ofCategory| *3 (|Ring|)) (|ofCategory| *4 (|SetCategory|)) (|isDomain| *2 (|Record| (|:| |k| *4) (|:| |c| *3))))) (|reductum| (*1 *1 *1) (AND (|ofCategory| *1 (|FreeModuleCat| *2 *3)) (|ofCategory| *2 (|Ring|)) (|ofCategory| *3 (|SetCategory|))))) (|Join| (|Functorial| |t#1|) (|BiModule| |t#1| |t#1|) (|RetractableTo| |t#2|) (CATEGORY |domain| (SIGNATURE * ($ |t#1| |t#2|)) (SIGNATURE |coefficient| (|t#1| $ |t#2|)) (SIGNATURE |monom| ($ |t#2| |t#1|)) (SIGNATURE |monomial?| ((|Boolean|) $)) (SIGNATURE |ListOfTerms| ((|List| (|Record| (|:| |k| |t#2|) (|:| |c| |t#1|))) $)) (SIGNATURE |coefficients| ((|List| |t#1|) $)) (SIGNATURE |monomials| ((|List| $) $)) (SIGNATURE |numberOfMonomials| ((|NonNegativeInteger|) $)) (SIGNATURE |leadingMonomial| (|t#2| $)) (SIGNATURE |leadingCoefficient| (|t#1| $)) (SIGNATURE |leadingTerm| ((|Record| (|:| |k| |t#2|) (|:| |c| |t#1|)) $)) (SIGNATURE |reductum| ($ $)) (IF (|has| |t#1| (|CommutativeRing|)) (ATTRIBUTE (|Module| |t#1|)) |%noBranch|))) @@ -1123,7 +1126,7 @@ NIL ((|filename| (*1 *1 *2 *2 *2) (AND (|isDomain| *2 (|String|)) (|ofCategory| *1 (|FileNameCategory|)))) (|directory| (*1 *2 *1) (AND (|ofCategory| *1 (|FileNameCategory|)) (|isDomain| *2 (|String|)))) (|name| (*1 *2 *1) (AND (|ofCategory| *1 (|FileNameCategory|)) (|isDomain| *2 (|String|)))) (|extension| (*1 *2 *1) (AND (|ofCategory| *1 (|FileNameCategory|)) (|isDomain| *2 (|String|)))) (|exists?| (*1 *2 *1) (AND (|ofCategory| *1 (|FileNameCategory|)) (|isDomain| *2 (|Boolean|)))) (|readable?| (*1 *2 *1) (AND (|ofCategory| *1 (|FileNameCategory|)) (|isDomain| *2 (|Boolean|)))) (|writable?| (*1 *2 *1) (AND (|ofCategory| *1 (|FileNameCategory|)) (|isDomain| *2 (|Boolean|)))) (|new| (*1 *1 *2 *2 *2) (AND (|isDomain| *2 (|String|)) (|ofCategory| *1 (|FileNameCategory|))))) (|Join| (|SetCategory|) (|HomotopicTo| (|String|)) (CATEGORY |domain| (SIGNATURE |filename| ($ (|String|) (|String|) (|String|))) (SIGNATURE |directory| ((|String|) $)) (SIGNATURE |name| ((|String|) $)) (SIGNATURE |extension| ((|String|) $)) (SIGNATURE |exists?| ((|Boolean|) $)) (SIGNATURE |readable?| ((|Boolean|) $)) (SIGNATURE |writable?| ((|Boolean|) $)) (SIGNATURE |new| ($ (|String|) (|String|) (|String|))))) (((|BasicType|) . T) ((|CoercibleFrom| #1=(|String|)) . T) ((|CoercibleTo| (|OutputForm|)) . T) ((|CoercibleTo| #1#) . T) ((|HomotopicTo| #1#) . T) ((|Join|) . T) ((|SetCategory|) . T) ((|Type|) . T)) -((~= #1=(#2=(#3=(|Boolean|) $ $) NIL T ELT)) (|zero?| ((#3# $) NIL T ELT)) (|subtractIfCan| (((|Union| $ "failed") $ $) NIL T ELT)) (|shallowExpand| (#4=((|OutputForm|) $) 64 T ELT)) (|sample| (#5=($) NIL T CONST)) (|rightPower| #6=(($ $ #7=(|PositiveInteger|)) NIL T ELT)) (|plenaryPower| #6#) (|opposite?| #1#) (|leftPower| #6#) (|latex| (((|String|) $) NIL T ELT)) (|hash| (((|SingleInteger|) $) NIL T ELT)) (|generator| (($ #8=(|NonNegativeInteger|)) 38 T ELT)) (|dimension| ((#8#) 18 T ELT)) (|deepExpand| (#4# 66 T ELT)) (|commutator| #9=(#10=($ $ $) NIL T ELT)) (|coerce| (#4# NIL T ELT)) (|before?| #1#) (|associator| (($ $ $ $) NIL T ELT)) (|antiCommutator| #9#) (|Zero| (#5# 24 T CONST)) (= (#2# 41 T ELT)) (- (($ $) 48 T ELT) (#10# 50 T ELT)) (+ (#10# 51 T ELT)) (** #6#) (* (($ #7# $) NIL T ELT) (($ #8# $) NIL T ELT) (($ (|Integer|) . #11=($)) NIL T ELT) (#10# 52 T ELT) (($ $ |#3|) NIL T ELT) (($ |#3| . #11#) 47 T ELT))) +((~= #1=(#2=(#3=(|Boolean|) $ $) NIL T ELT)) (|zero?| ((#3# $) NIL T ELT)) (|subtractIfCan| (((|Maybe| $) $ $) NIL T ELT)) (|shallowExpand| (#4=((|OutputForm|) $) 64 T ELT)) (|sample| (#5=($) NIL T CONST)) (|rightPower| #6=(($ $ #7=(|PositiveInteger|)) NIL T ELT)) (|plenaryPower| #6#) (|opposite?| #1#) (|leftPower| #6#) (|latex| (((|String|) $) NIL T ELT)) (|hash| (((|SingleInteger|) $) NIL T ELT)) (|generator| (($ #8=(|NonNegativeInteger|)) 38 T ELT)) (|dimension| ((#8#) 18 T ELT)) (|deepExpand| (#4# 66 T ELT)) (|commutator| #9=(#10=($ $ $) NIL T ELT)) (|coerce| (#4# NIL T ELT)) (|before?| #1#) (|associator| (($ $ $ $) NIL T ELT)) (|antiCommutator| #9#) (|Zero| (#5# 24 T CONST)) (= (#2# 41 T ELT)) (- (($ $) 48 T ELT) (#10# 50 T ELT)) (+ (#10# 51 T ELT)) (** #6#) (* (($ #7# $) NIL T ELT) (($ #8# $) NIL T ELT) (($ (|Integer|) . #11=($)) NIL T ELT) (#10# 52 T ELT) (($ $ |#3|) NIL T ELT) (($ |#3| . #11#) 47 T ELT))) (((|FreeNilpotentLie| |#1| |#2| |#3|) (|Join| (|NonAssociativeAlgebra| |#3|) (CATEGORY |domain| (SIGNATURE |dimension| (#1=(|NonNegativeInteger|))) (SIGNATURE |deepExpand| #2=((|OutputForm|) $)) (SIGNATURE |shallowExpand| #2#) (SIGNATURE |generator| ($ #1#)))) #1# #1# (|CommutativeRing|)) (T |FreeNilpotentLie|)) ((|dimension| (*1 *2) #1=(AND (|isDomain| *2 #2=(|NonNegativeInteger|)) #3=(|isDomain| *1 (|FreeNilpotentLie| *3 *4 *5)) (|ofType| *3 *2) (|ofType| *4 *2) #4=(|ofCategory| *5 (|CommutativeRing|)))) (|deepExpand| #5=(*1 *2 *1) #6=(AND (|isDomain| *2 (|OutputForm|)) #3# (|ofType| *3 #2#) (|ofType| *4 #2#) #4#)) (|shallowExpand| #5# #6#) (|generator| (*1 *1 *2) #1#)) ((|order| (((|NonNegativeInteger|) (|FiniteDivisor| |#1| |#2| |#3| |#4|)) 16 T ELT))) @@ -1140,7 +1143,7 @@ NIL ((|primeFrobenius| (($ $) 10 T ELT) (($ $ (|NonNegativeInteger|)) 12 T ELT))) (((|FieldOfPrimeCharacteristic&| |#1|) (CATEGORY |package| (SIGNATURE |primeFrobenius| (|#1| |#1| (|NonNegativeInteger|))) (SIGNATURE |primeFrobenius| (|#1| |#1|))) (|FieldOfPrimeCharacteristic|)) (T |FieldOfPrimeCharacteristic&|)) NIL -((~= (#1=((|Boolean|) $ $) 7 T ELT)) (|zero?| ((#2=(|Boolean|) $) 22 T ELT)) (|unitNormal| (((|Record| (|:| |unit| $) (|:| |canonical| $) (|:| |associate| $)) $) 55 T ELT)) (|unitCanonical| (($ $) 54 T ELT)) (|unit?| ((#3=(|Boolean|) $) 52 T ELT)) (|subtractIfCan| (((|Union| $ "failed") $ $) 26 T ELT)) (|squareFreePart| (($ $) 91 T ELT)) (|squareFree| (#4=((|Factored| $) $) 90 T ELT)) (|sizeLess?| (((|Boolean|) $ $) 75 T ELT)) (|sample| (#5=($) 23 T CONST)) (|rem| (#6=($ $ $) 71 T ELT)) (|recip| (((|Union| $ "failed") $) 42 T ELT)) (|quo| (#6# 72 T ELT)) (|principalIdeal| (((|Record| (|:| |coef| #7=(|List| $)) (|:| |generator| $)) #7#) 66 T ELT)) (|primeFrobenius| (($ $) 97 T ELT) (($ $ (|NonNegativeInteger|)) 96 T ELT)) (|prime?| (((|Boolean|) $) 89 T ELT)) (|order| (((|OnePointCompletion| (|PositiveInteger|)) $) 99 T ELT)) (|opposite?| ((#2# $ $) 20 T ELT)) (|one?| (((|Boolean|) $) 44 T ELT)) (|multiEuclidean| (((|Union| #8=(|List| $) #9="failed") #8# $) 68 T ELT)) (|lcm| (#10=($ $ $) 60 T ELT) (#11=($ (|List| $)) 59 T ELT)) (|latex| (((|String|) $) 11 T ELT)) (|inv| (($ $) 88 T ELT)) (|hash| (((|SingleInteger|) $) 12 T ELT)) (|gcdPolynomial| ((#12=(|SparseUnivariatePolynomial| $) #12# #12#) 58 T ELT)) (|gcd| (#10# 62 T ELT) (#11# 61 T ELT)) (|factor| (#4# 92 T ELT)) (|extendedEuclidean| (((|Record| #13=(|:| |coef1| $) #14=(|:| |coef2| $) (|:| |generator| $)) $ $) 70 T ELT) (((|Union| (|Record| #13# #14#) #9#) $ $ $) 69 T ELT)) (|exquo| (((|Union| $ "failed") $ $) 56 T ELT)) (|expressIdealMember| (((|Maybe| #7#) #7# $) 65 T ELT)) (|euclideanSize| (((|NonNegativeInteger|) $) 74 T ELT)) (|divide| (((|Record| (|:| |quotient| $) (|:| |remainder| $)) $ $) 73 T ELT)) (|discreteLog| (((|Union| (|NonNegativeInteger|) "failed") $ $) 98 T ELT)) (|coerce| (((|OutputForm|) $) 13 T ELT) (($ (|Integer|)) 41 T ELT) (($ $) 57 T ELT) (($ #15=(|Fraction| #16=(|Integer|))) 84 T ELT)) (|charthRoot| (((|Maybe| $) $) 100 T ELT)) (|characteristic| (((|NonNegativeInteger|)) 40 T CONST)) (|before?| (#1# 6 T ELT)) (|associates?| ((#3# $ $) 53 T ELT)) (|annihilate?| (((|Boolean|) $ $) 33 T ELT)) (|Zero| (#5# 24 T CONST)) (|One| (($) 45 T CONST)) (= (#1# 8 T ELT)) (/ (($ $ $) 83 T ELT)) (- (($ $) 29 T ELT) (($ $ $) 28 T ELT)) (+ (($ $ $) 18 T ELT)) (** (($ $ (|PositiveInteger|)) 35 T ELT) (($ $ (|NonNegativeInteger|)) 43 T ELT) (($ $ #16#) 87 T ELT)) (* (($ (|PositiveInteger|) $) 17 T ELT) (($ (|NonNegativeInteger|) $) 21 T ELT) (($ (|Integer|) . #17=($)) 30 T ELT) (($ $ $) 34 T ELT) (($ $ #15#) 86 T ELT) (($ #15# . #17#) 85 T ELT))) +((~= (#1=((|Boolean|) $ $) 7 T ELT)) (|zero?| ((#2=(|Boolean|) $) 22 T ELT)) (|unitNormal| (((|Record| (|:| |unit| $) (|:| |canonical| $) (|:| |associate| $)) $) 56 T ELT)) (|unitCanonical| (($ $) 55 T ELT)) (|unit?| ((#3=(|Boolean|) $) 53 T ELT)) (|subtractIfCan| (((|Maybe| $) $ $) 26 T ELT)) (|squareFreePart| (($ $) 92 T ELT)) (|squareFree| (#4=((|Factored| $) $) 91 T ELT)) (|sizeLess?| (((|Boolean|) $ $) 76 T ELT)) (|sample| (#5=($) 23 T CONST)) (|rem| (#6=($ $ $) 72 T ELT)) (|recip| (((|Union| $ "failed") $) 43 T ELT)) (|quo| (#6# 73 T ELT)) (|principalIdeal| (((|Record| (|:| |coef| #7=(|List| $)) (|:| |generator| $)) #7#) 67 T ELT)) (|primeFrobenius| (($ $) 98 T ELT) (($ $ (|NonNegativeInteger|)) 97 T ELT)) (|prime?| (((|Boolean|) $) 90 T ELT)) (|order| (((|OnePointCompletion| (|PositiveInteger|)) $) 100 T ELT)) (|opposite?| ((#2# $ $) 20 T ELT)) (|one?| (((|Boolean|) $) 45 T ELT)) (|multiEuclidean| (((|Union| #8=(|List| $) #9="failed") #8# $) 69 T ELT)) (|lcm| (#10=($ $ $) 61 T ELT) (#11=($ (|List| $)) 60 T ELT)) (|latex| (((|String|) $) 11 T ELT)) (|inv| (($ $) 89 T ELT)) (|hash| (((|SingleInteger|) $) 12 T ELT)) (|gcdPolynomial| ((#12=(|SparseUnivariatePolynomial| $) #12# #12#) 59 T ELT)) (|gcd| (#10# 63 T ELT) (#11# 62 T ELT)) (|factor| (#4# 93 T ELT)) (|extendedEuclidean| (((|Record| #13=(|:| |coef1| $) #14=(|:| |coef2| $) (|:| |generator| $)) $ $) 71 T ELT) (((|Union| (|Record| #13# #14#) #9#) $ $ $) 70 T ELT)) (|exquo| (((|Union| $ "failed") $ $) 57 T ELT)) (|expressIdealMember| (((|Maybe| #7#) #7# $) 66 T ELT)) (|euclideanSize| (((|NonNegativeInteger|) $) 75 T ELT)) (|divide| (((|Record| (|:| |quotient| $) (|:| |remainder| $)) $ $) 74 T ELT)) (|discreteLog| (((|Union| (|NonNegativeInteger|) "failed") $ $) 99 T ELT)) (|coerce| (((|OutputForm|) $) 13 T ELT) (($ (|Integer|)) 42 T ELT) (($ $) 58 T ELT) (($ #15=(|Fraction| #16=(|Integer|))) 85 T ELT)) (|charthRoot| (((|Maybe| $) $) 101 T ELT)) (|characteristic| (((|NonNegativeInteger|)) 41 T CONST)) (|before?| (#1# 6 T ELT)) (|associates?| ((#3# $ $) 54 T ELT)) (|annihilate?| (((|Boolean|) $ $) 34 T ELT)) (|Zero| (#5# 24 T CONST)) (|One| (($) 46 T CONST)) (= (#1# 8 T ELT)) (/ (($ $ $) 84 T ELT)) (- (($ $) 30 T ELT) (($ $ $) 29 T ELT)) (+ (($ $ $) 18 T ELT)) (** (($ $ (|PositiveInteger|)) 36 T ELT) (($ $ (|NonNegativeInteger|)) 44 T ELT) (($ $ #16#) 88 T ELT)) (* (($ (|PositiveInteger|) $) 17 T ELT) (($ (|NonNegativeInteger|) $) 21 T ELT) (($ (|Integer|) . #17=($)) 31 T ELT) (($ $ $) 35 T ELT) (($ $ #15#) 87 T ELT) (($ #15# . #17#) 86 T ELT))) (((|FieldOfPrimeCharacteristic|) (|Category|)) (T |FieldOfPrimeCharacteristic|)) ((|order| (*1 *2 *1) (AND (|ofCategory| *1 (|FieldOfPrimeCharacteristic|)) (|isDomain| *2 (|OnePointCompletion| (|PositiveInteger|))))) (|discreteLog| (*1 *2 *1 *1) (|partial| AND (|ofCategory| *1 (|FieldOfPrimeCharacteristic|)) (|isDomain| *2 (|NonNegativeInteger|)))) (|primeFrobenius| (*1 *1 *1) (|ofCategory| *1 (|FieldOfPrimeCharacteristic|))) (|primeFrobenius| (*1 *1 *1 *2) (AND (|ofCategory| *1 (|FieldOfPrimeCharacteristic|)) (|isDomain| *2 (|NonNegativeInteger|))))) (|Join| (|Field|) (|CharacteristicNonZero|) (CATEGORY |domain| (SIGNATURE |order| ((|OnePointCompletion| (|PositiveInteger|)) $)) (SIGNATURE |discreteLog| ((|Union| (|NonNegativeInteger|) "failed") $ $)) (SIGNATURE |primeFrobenius| ($ $)) (SIGNATURE |primeFrobenius| ($ $ (|NonNegativeInteger|))))) @@ -1148,18 +1151,18 @@ NIL ((|float| (($ #1=(|Integer|) #1#) 11 T ELT) (($ #1# #1# #2=(|PositiveInteger|)) NIL T ELT)) (|digits| ((#2#) 19 T ELT) ((#2# #2#) NIL T ELT))) (((|FloatingPointSystem&| |#1|) (CATEGORY |package| (SIGNATURE |digits| (#1=(|PositiveInteger|) #1#)) (SIGNATURE |digits| (#1#)) (SIGNATURE |float| (|#1| #2=(|Integer|) #2# #1#)) (SIGNATURE |float| (|#1| #2# #2#))) (|FloatingPointSystem|)) (T |FloatingPointSystem&|)) ((|digits| (*1 *2) #1=(AND (|isDomain| *2 (|PositiveInteger|)) (|isDomain| *1 (|FloatingPointSystem&| *3)) (|ofCategory| *3 (|FloatingPointSystem|)))) (|digits| (*1 *2 *2) #1#)) -((~= (#1=((|Boolean|) $ $) 7 T ELT)) (|zero?| ((#2=(|Boolean|) $) 22 T ELT)) (|wholePart| ((#3=(|Integer|) $) 108 T ELT)) (|unitNormal| (((|Record| (|:| |unit| $) (|:| |canonical| $) (|:| |associate| $)) $) 55 T ELT)) (|unitCanonical| (($ $) 54 T ELT)) (|unit?| ((#4=(|Boolean|) $) 52 T ELT)) (|truncate| (#5=($ $) 106 T ELT)) (|subtractIfCan| (((|Union| $ "failed") $ $) 26 T ELT)) (|squareFreePart| (($ $) 91 T ELT)) (|squareFree| (#6=((|Factored| $) $) 90 T ELT)) (|sqrt| (($ $) 116 T ELT)) (|sizeLess?| (((|Boolean|) $ $) 75 T ELT)) (|sign| (((|Integer|) $) 133 T ELT)) (|sample| (#7=($) 23 T CONST)) (|round| (#5# 105 T ELT)) (|retractIfCan| (((|Union| #3# . #8=("failed")) . #9=($)) 121 T ELT) (((|Union| #10=(|Fraction| #3#) . #8#) . #9#) 118 T ELT)) (|retract| ((#3# . #11=($)) 122 T ELT) ((#10# . #11#) 119 T ELT)) (|rem| (#12=($ $ $) 71 T ELT)) (|recip| (((|Union| $ "failed") $) 42 T ELT)) (|quo| (#12# 72 T ELT)) (|principalIdeal| (((|Record| (|:| |coef| #13=(|List| $)) (|:| |generator| $)) #13#) 66 T ELT)) (|prime?| (((|Boolean|) $) 89 T ELT)) (|precision| (((|PositiveInteger|)) 149 T ELT) (((|PositiveInteger|) (|PositiveInteger|)) 146 (|has| $ (ATTRIBUTE |arbitraryPrecision|)) ELT)) (|positive?| (((|Boolean|) $) 131 T ELT)) (|patternMatch| (((|PatternMatchResult| #14=(|Float|) . #15=($)) $ (|Pattern| #14#) (|PatternMatchResult| #14# . #15#)) 112 T ELT)) (|order| (((|Integer|) $) 155 T ELT)) (|opposite?| ((#2# $ $) 20 T ELT)) (|one?| (((|Boolean|) $) 44 T ELT)) (|nthRoot| (($ $ #16=(|Integer|)) 115 T ELT)) (|norm| (#5# 111 T ELT)) (|negative?| (((|Boolean|) $) 132 T ELT)) (|multiEuclidean| (((|Union| #17=(|List| $) #18="failed") #17# $) 68 T ELT)) (|min| (#19=($ $ $) 125 T ELT) (($) 143 (AND (|not| (|has| $ (ATTRIBUTE |arbitraryPrecision|))) (|not| (|has| $ (ATTRIBUTE |arbitraryExponent|)))) ELT)) (|max| (#19# 126 T ELT) (($) 142 (AND (|not| (|has| $ (ATTRIBUTE |arbitraryPrecision|))) (|not| (|has| $ (ATTRIBUTE |arbitraryExponent|)))) ELT)) (|mantissa| (((|Integer|) $) 152 T ELT)) (|lcm| (#20=($ $ $) 60 T ELT) (#21=($ (|List| $)) 59 T ELT)) (|latex| (((|String|) $) 11 T ELT)) (|inv| (($ $) 88 T ELT)) (|increasePrecision| (((|PositiveInteger|) (|Integer|)) 145 (|has| $ (ATTRIBUTE |arbitraryPrecision|)) ELT)) (|hash| (((|SingleInteger|) $) 12 T ELT)) (|gcdPolynomial| ((#22=(|SparseUnivariatePolynomial| $) #22# #22#) 58 T ELT)) (|gcd| (#20# 62 T ELT) (#21# 61 T ELT)) 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(|RealConstant|)) ELT) (((|DoubleFloat|) . #76#) NIL #78# ELT)) (|conditionP| (((|Union| #36# #12#) #32#) 112 #79=(AND (|has| $ #80=(|CharacteristicNonZero|)) #15#) ELT)) (|coerce| (((|OutputForm|) $) NIL T ELT) (($ #19#) NIL T ELT) #7# (($ #26#) NIL T ELT) (($ |#1|) 10 T ELT) (($ #23#) NIL #25# ELT)) (|charthRoot| (#48# 92 (OR #79# (|has| |#1| #80#)) ELT)) (|characteristic| ((#63#) 93 T CONST)) (|ceiling| (#5# 24 #39# ELT)) (|before?| #1#) (|associates?| #1#) (|annihilate?| #1#) (|abs| (#8# NIL #20# ELT)) (|Zero| (#21# 28 T CONST)) (|One| (#21# 8 T CONST)) (D (#65# NIL T ELT) #66# #67# #69# #70# #71# #72# #74#) (>= #81=(#2# NIL #51# ELT)) (> #81#) (= (#2# 48 T ELT)) (<= #81#) (< #81#) (/ (#29# 123 T ELT) (($ |#1| |#1|) 34 T ELT)) (- (#8# 23 T ELT) (#29# 37 T ELT)) (+ (#29# 35 T ELT)) (** (($ $ #82=(|PositiveInteger|)) NIL T ELT) (#75# NIL T ELT) (($ $ #19#) 122 T ELT)) (* (($ #82# $) NIL T ELT) (($ #63# $) NIL T ELT) (($ #19# $) 42 T ELT) (#29# 39 T ELT) (($ $ #26#) NIL T ELT) (($ #26# $) NIL T ELT) (($ |#1| $) 43 T ELT) (#64# 70 T ELT))) +((~= #1=(#2=(#3=(|Boolean|) $ $) NIL T ELT)) (|zero?| (#4=(#3# $) 13 T ELT)) (|wholePart| (#5=(|#1| $) 21 #6=(|has| |#1| (|EuclideanDomain|)) ELT)) (|unitNormal| (((|Record| (|:| |unit| $) (|:| |canonical| $) (|:| |associate| $)) $) NIL T ELT)) (|unitCanonical| #7=(#8=($ $) NIL T ELT)) (|unit?| #9=(#4# NIL T ELT)) (|subtractIfCan| ((#10=(|Maybe| $) $ $) NIL T ELT)) (|squareFreePolynomial| (#11=((|Factored| #12=(|SparseUnivariatePolynomial| $)) #12#) NIL #13=(|has| |#1| (|PolynomialFactorizationExplicit|)) ELT)) (|squareFreePart| #7#) (|squareFree| #14=(((|Factored| $) $) NIL T ELT)) (|solveLinearPolynomialEquation| (((|Union| #15=(|List| #12#) #16="failed") #15# #12#) NIL #13# ELT)) (|sizeLess?| #1#) (|sign| (#17=(#18=(|Integer|) $) NIL #19=(|has| |#1| (|OrderedIntegralDomain|)) ELT)) (|sample| (#20=($) NIL T CONST)) (|retractIfCan| (((|Union| |#1| . #21=(#16#)) $) 17 T ELT) (((|Union| #22=(|Symbol|) . #21#) . #23=($)) NIL #24=(|has| |#1| (|RetractableTo| #22#)) ELT) (((|Union| #25=(|Fraction| #18#) . #21#) $) 54 #26=(|has| |#1| (|RetractableTo| #18#)) ELT) (((|Union| #18# . #21#) . #23#) NIL #26# ELT)) (|retract| (#5# 15 T ELT) ((#22# $) NIL #24# ELT) ((#25# $) 51 #26# ELT) (#17# NIL #26# ELT)) (|rem| #27=(#28=($ $ $) NIL T ELT)) (|reducedSystem| ((#29=(|Matrix| #18#) . #30=(#31=(|Matrix| $))) NIL #32=(|has| |#1| (|LinearlyExplicitRingOver| #18#)) ELT) ((#33=(|Record| (|:| |mat| #29#) (|:| |vec| (|Vector| #18#))) . #34=(#31# #35=(|Vector| $))) NIL #32# ELT) ((#36=(|Record| (|:| |mat| #37=(|Matrix| |#1|)) (|:| |vec| (|Vector| |#1|))) . #34#) NIL T ELT) ((#37# . #30#) NIL T ELT)) (|recip| ((#38=(|Union| $ #16#) $) 32 T ELT)) (|random| (#20# NIL #39=(|has| |#1| (|IntegerNumberSystem|)) ELT)) (|quo| #27#) (|principalIdeal| (((|Record| (|:| |coef| #40=(|List| $)) #41=(|:| |generator| $)) #40#) NIL T ELT)) (|prime?| #9#) (|positive?| (#4# NIL #19# ELT)) (|patternMatch| ((#42=(|PatternMatchResult| #18# . #43=($)) $ #44=(|Pattern| #18#) #42#) NIL (|has| |#1| (|PatternMatchable| #18#)) ELT) ((#45=(|PatternMatchResult| #46=(|Float|) . #43#) $ #47=(|Pattern| #46#) #45#) NIL (|has| |#1| (|PatternMatchable| #46#)) ELT)) (|opposite?| #1#) (|one?| (#4# 38 T ELT)) (|numerator| #7#) (|numer| (#5# 55 T ELT)) (|nextItem| (#48=(#10# $) NIL #49=(|has| |#1| (|StepThrough|)) ELT)) (|negative?| (#4# 22 #19# ELT)) (|multiEuclidean| (((|Union| #40# #16#) #40# $) NIL T ELT)) (|min| #50=(#28# NIL #51=(|has| |#1| (|OrderedSet|)) ELT)) (|max| #50#) (|map| (($ #52=(|Mapping| |#1| |#1|) $) NIL T ELT)) (|leftReducedSystem| ((#29# . #53=(#35#)) NIL #32# ELT) ((#33# . #54=(#35# $)) NIL #32# ELT) ((#36# . #54#) NIL T ELT) ((#37# . #53#) NIL T ELT)) (|lcm| #27# #55=(($ #40#) NIL T ELT)) (|latex| (((|String|) $) NIL T ELT)) (|inv| #7#) (|init| (#20# NIL #49# CONST)) (|hash| (((|SingleInteger|) $) NIL T ELT)) (|gcdPolynomial| ((#12# #12# #12#) 82 T ELT)) (|gcd| #27# #55#) (|fractionPart| (#8# NIL #6# ELT)) (|floor| (#5# 26 #39# ELT)) (|factorSquareFreePolynomial| (#11# 133 #13# ELT)) (|factorPolynomial| (#11# 128 #13# ELT)) (|factor| #14#) (|extendedEuclidean| (((|Record| #56=(|:| |coef1| $) #57=(|:| |coef2| $) #41#) $ $) NIL T ELT) (((|Union| (|Record| #56# #57#) #16#) $ $ $) NIL T ELT)) (|exquo| ((#38# $ $) NIL T ELT)) (|expressIdealMember| (((|Maybe| #40#) #40# $) NIL T ELT)) (|eval| (($ $ #58=(|List| |#1|) #58#) NIL #59=(|has| |#1| (|Evalable| |#1|)) ELT) (($ $ |#1| |#1|) NIL #59# ELT) (($ $ #60=(|Equation| |#1|)) NIL #59# ELT) (($ $ (|List| #60#)) NIL #59# ELT) (($ $ #61=(|List| #22#) #58#) NIL #62=(|has| |#1| (|InnerEvalable| #22# |#1|)) ELT) (($ $ #22# |#1|) NIL #62# ELT)) (|euclideanSize| ((#63=(|NonNegativeInteger|) $) NIL T ELT)) (|elt| (#64=($ $ |#1|) NIL (|has| |#1| (|Eltable| |#1| |#1|)) ELT)) (|divide| (((|Record| (|:| |quotient| $) (|:| |remainder| $)) $ $) NIL T ELT)) (|differentiate| (#65=($ $ #52#) 45 T ELT) #66=(($ $ #52# #63#) NIL T ELT) #67=(($ $ #22#) NIL #68=(|has| |#1| (|PartialDifferentialSpace| #22#)) ELT) #69=(($ $ #61#) NIL #68# ELT) #70=(($ $ #22# #63#) NIL #68# ELT) #71=(($ $ #61# (|List| #63#)) NIL #68# ELT) #72=(#8# NIL #73=(|has| |#1| (|DifferentialSpace|)) ELT) #74=(#75=($ $ #63#) NIL #73# ELT)) (|denominator| #7#) (|denom| (#5# 57 T ELT)) (|convert| ((#44# . #76=($)) NIL (|has| |#1| (|ConvertibleTo| #44#)) ELT) ((#47# . #76#) NIL (|has| |#1| (|ConvertibleTo| #47#)) ELT) ((#77=(|InputForm|) . #76#) NIL (|has| |#1| (|ConvertibleTo| #77#)) ELT) ((#46# . #76#) NIL #78=(|has| |#1| (|RealConstant|)) ELT) (((|DoubleFloat|) . #76#) NIL #78# ELT)) (|conditionP| (((|Union| #35# #16#) #31#) 112 #79=(AND (|has| $ #80=(|CharacteristicNonZero|)) #13#) ELT)) (|coerce| (((|OutputForm|) $) NIL T ELT) (($ #18#) NIL T ELT) #7# (($ #25#) NIL T ELT) (($ |#1|) 10 T ELT) (($ #22#) NIL #24# ELT)) (|charthRoot| (#48# 92 (OR #79# (|has| |#1| #80#)) ELT)) (|characteristic| ((#63#) 93 T CONST)) (|ceiling| (#5# 24 #39# ELT)) (|before?| #1#) (|associates?| #1#) (|annihilate?| #1#) (|abs| (#8# NIL #19# ELT)) (|Zero| (#20# 28 T CONST)) (|One| (#20# 8 T CONST)) (D (#65# NIL T ELT) #66# #67# #69# #70# #71# #72# #74#) (>= #81=(#2# NIL #51# ELT)) (> #81#) (= (#2# 48 T ELT)) (<= #81#) (< #81#) (/ (#28# 123 T ELT) (($ |#1| |#1|) 34 T ELT)) (- (#8# 23 T ELT) (#28# 37 T ELT)) (+ (#28# 35 T ELT)) (** (($ $ #82=(|PositiveInteger|)) NIL T ELT) (#75# NIL T ELT) (($ $ #18#) 122 T ELT)) (* (($ #82# $) NIL T ELT) (($ #63# $) NIL T ELT) (($ #18# $) 42 T ELT) (#28# 39 T ELT) (($ $ #25#) NIL T ELT) (($ #25# $) NIL T ELT) (($ |#1| $) 43 T ELT) (#64# 70 T ELT))) (((|Fraction| |#1|) (|Join| (|QuotientFieldCategory| |#1|) (CATEGORY |package| (IF (|has| |#1| #1=(ATTRIBUTE |canonical|)) (IF (|has| |#1| (|GcdDomain|)) (IF (|has| |#1| (ATTRIBUTE |canonicalUnitNormal|)) #1# |%noBranch|) |%noBranch|) |%noBranch|))) (|IntegralDomain|)) (T |Fraction|)) NIL ((|map| (((|Fraction| |#2|) (|Mapping| |#2| |#1|) (|Fraction| |#1|)) 13 T ELT))) @@ -1168,7 +1171,7 @@ NIL ((|traceMatrix| (#1=(#2=(|Matrix| |#2|) #3=(|Vector| $)) NIL T ELT) ((#2#) 18 T ELT)) (|represents| (($ #4=(|Vector| |#2|) #3#) NIL T ELT) (#5=($ #4#) 24 T ELT)) (|regularRepresentation| ((#2# $ #3#) NIL T ELT) ((#2# $) 40 T ELT)) (|minimalPolynomial| (#6=(|#3| $) 69 T ELT)) (|discriminant| ((|#2| #3#) NIL T ELT) ((|#2|) 20 T ELT)) (|coordinates| ((#4# $ #3#) NIL T ELT) ((#2# #3# #3#) NIL T ELT) (#7=(#4# $) 22 T ELT) (#1# 38 T ELT)) (|convert| (#7# 11 T ELT) (#5# 13 T ELT)) (|characteristicPolynomial| (#6# 55 T ELT))) (((|FramedAlgebra&| |#1| |#2| |#3|) (CATEGORY |package| (SIGNATURE |regularRepresentation| (#1=(|Matrix| |#2|) |#1|)) (SIGNATURE |discriminant| (|#2|)) (SIGNATURE |traceMatrix| (#1#)) (SIGNATURE |convert| #2=(|#1| #3=(|Vector| |#2|))) (SIGNATURE |convert| #4=(#3# |#1|)) (SIGNATURE |represents| #2#) (SIGNATURE |coordinates| #5=(#1# #6=(|Vector| |#1|))) (SIGNATURE |coordinates| #4#) (SIGNATURE |minimalPolynomial| #7=(|#3| |#1|)) (SIGNATURE |characteristicPolynomial| #7#) (SIGNATURE |traceMatrix| #5#) (SIGNATURE |discriminant| (|#2| #6#)) (SIGNATURE |represents| (|#1| #3# #6#)) (SIGNATURE |coordinates| (#1# #6# #6#)) (SIGNATURE |coordinates| (#3# |#1| #6#)) (SIGNATURE |regularRepresentation| (#1# |#1| #6#))) (|FramedAlgebra| |#2| |#3|) (|CommutativeRing|) (|UnivariatePolynomialCategory| |#2|)) (T |FramedAlgebra&|)) ((|traceMatrix| #1=(*1 *2) (AND (|ofCategory| *4 #2=(|CommutativeRing|)) (|ofCategory| *5 (|UnivariatePolynomialCategory| *4)) (|isDomain| *2 (|Matrix| *4)) (|isDomain| *1 (|FramedAlgebra&| *3 *4 *5)) (|ofCategory| *3 (|FramedAlgebra| *4 *5)))) (|discriminant| #1# (AND (|ofCategory| *4 (|UnivariatePolynomialCategory| *2)) (|ofCategory| *2 #2#) (|isDomain| *1 (|FramedAlgebra&| *3 *2 *4)) (|ofCategory| *3 (|FramedAlgebra| *2 *4))))) -((~= (#1=((|Boolean|) $ $) 7 T ELT)) (|zero?| ((#2=(|Boolean|) $) 22 T ELT)) (|traceMatrix| (((|Matrix| |#1|) #3=(|Vector| $)) 61 T ELT) (((|Matrix| |#1|)) 77 T ELT)) (|trace| ((|#1| . #4=($)) 67 T ELT)) (|subtractIfCan| (((|Union| $ "failed") $ $) 26 T ELT)) (|sample| (#5=($) 23 T CONST)) (|represents| (($ (|Vector| |#1|) #3#) 63 T ELT) (($ (|Vector| |#1|)) 80 T ELT)) (|regularRepresentation| (((|Matrix| |#1|) $ #3#) 68 T ELT) (((|Matrix| |#1|) $) 75 T ELT)) (|recip| (((|Union| $ "failed") $) 42 T ELT)) (|rank| (((|PositiveInteger|)) 69 T ELT)) (|opposite?| ((#2# $ $) 20 T ELT)) (|one?| (((|Boolean|) $) 44 T ELT)) (|norm| ((|#1| . #4#) 66 T ELT)) (|minimalPolynomial| ((|#2| . #6=($)) 59 (|has| |#1| (|Field|)) ELT)) (|latex| (((|String|) $) 11 T ELT)) (|hash| (((|SingleInteger|) $) 12 T ELT)) (|discriminant| ((|#1| #3#) 62 T ELT) ((|#1|) 76 T ELT)) (|coordinates| (((|Vector| |#1|) $ #3#) 65 T ELT) (((|Matrix| |#1|) #3# #3#) 64 T ELT) (((|Vector| |#1|) $) 82 T ELT) (((|Matrix| |#1|) (|Vector| $)) 81 T ELT)) (|convert| (((|Vector| |#1|) $) 79 T ELT) (($ (|Vector| |#1|)) 78 T ELT)) (|coerce| (((|OutputForm|) $) 13 T ELT) (($ (|Integer|)) 41 T ELT) (($ |#1|) 52 T ELT)) (|charthRoot| (((|Maybe| $) $) 58 (|has| |#1| (|CharacteristicNonZero|)) ELT)) (|characteristicPolynomial| ((|#2| . #6#) 60 T ELT)) (|characteristic| (((|NonNegativeInteger|)) 40 T CONST)) (|before?| (#1# 6 T ELT)) (|basis| (((|Vector| $)) 83 T ELT)) (|annihilate?| (((|Boolean|) $ $) 33 T ELT)) (|Zero| (#5# 24 T CONST)) (|One| (($) 45 T CONST)) (= (#1# 8 T ELT)) (- (($ $) 29 T ELT) (($ $ $) 28 T ELT)) (+ (($ $ $) 18 T ELT)) (** (($ $ (|PositiveInteger|)) 35 T ELT) (($ $ (|NonNegativeInteger|)) 43 T ELT)) (* (($ (|PositiveInteger|) $) 17 T ELT) (($ (|NonNegativeInteger|) $) 21 T ELT) (($ (|Integer|) . #7=($)) 30 T ELT) (($ $ $) 34 T ELT) (($ $ |#1|) 54 T ELT) (($ |#1| . #7#) 53 T ELT))) +((~= (#1=((|Boolean|) $ $) 7 T ELT)) (|zero?| ((#2=(|Boolean|) $) 22 T ELT)) (|traceMatrix| (((|Matrix| |#1|) #3=(|Vector| $)) 62 T ELT) (((|Matrix| |#1|)) 77 T ELT)) (|trace| ((|#1| . #4=($)) 68 T ELT)) (|subtractIfCan| (((|Maybe| $) $ $) 26 T ELT)) (|sample| (#5=($) 23 T CONST)) (|represents| (($ (|Vector| |#1|) #3#) 64 T ELT) (($ (|Vector| |#1|)) 80 T ELT)) (|regularRepresentation| (((|Matrix| |#1|) $ #3#) 69 T ELT) (((|Matrix| |#1|) $) 75 T ELT)) (|recip| (((|Union| $ "failed") $) 43 T ELT)) (|rank| (((|PositiveInteger|)) 70 T ELT)) (|opposite?| ((#2# $ $) 20 T ELT)) (|one?| (((|Boolean|) $) 45 T ELT)) (|norm| ((|#1| . #4#) 67 T ELT)) (|minimalPolynomial| ((|#2| . #6=($)) 60 (|has| |#1| (|Field|)) ELT)) (|latex| (((|String|) $) 11 T ELT)) (|hash| (((|SingleInteger|) $) 12 T ELT)) (|discriminant| ((|#1| #3#) 63 T ELT) ((|#1|) 76 T ELT)) (|coordinates| (((|Vector| |#1|) $ #3#) 66 T ELT) (((|Matrix| |#1|) #3# #3#) 65 T ELT) (((|Vector| |#1|) $) 82 T ELT) (((|Matrix| |#1|) (|Vector| $)) 81 T ELT)) (|convert| (((|Vector| |#1|) $) 79 T ELT) (($ (|Vector| |#1|)) 78 T ELT)) (|coerce| (((|OutputForm|) $) 13 T ELT) (($ (|Integer|)) 42 T ELT) (($ |#1|) 53 T ELT)) (|charthRoot| (((|Maybe| $) $) 59 (|has| |#1| (|CharacteristicNonZero|)) ELT)) (|characteristicPolynomial| ((|#2| . #6#) 61 T ELT)) (|characteristic| (((|NonNegativeInteger|)) 41 T CONST)) (|before?| (#1# 6 T ELT)) (|basis| (((|Vector| $)) 83 T ELT)) (|annihilate?| (((|Boolean|) $ $) 34 T ELT)) (|Zero| (#5# 24 T CONST)) (|One| (($) 46 T CONST)) (= (#1# 8 T ELT)) (- (($ $) 30 T ELT) (($ $ $) 29 T ELT)) (+ (($ $ $) 18 T ELT)) (** (($ $ (|PositiveInteger|)) 36 T ELT) (($ $ (|NonNegativeInteger|)) 44 T ELT)) (* (($ (|PositiveInteger|) $) 17 T ELT) (($ (|NonNegativeInteger|) $) 21 T ELT) (($ (|Integer|) . #7=($)) 31 T ELT) (($ $ $) 35 T ELT) (($ $ |#1|) 55 T ELT) (($ |#1| . #7#) 54 T ELT))) (((|FramedAlgebra| |#1| |#2|) (|Category|) (|CommutativeRing|) (|UnivariatePolynomialCategory| |t#1|)) (T |FramedAlgebra|)) ((|basis| (*1 *2) (AND (|ofCategory| *3 (|CommutativeRing|)) (|ofCategory| *4 (|UnivariatePolynomialCategory| *3)) (|isDomain| *2 (|Vector| *1)) (|ofCategory| *1 (|FramedAlgebra| *3 *4)))) (|coordinates| (*1 *2 *1) (AND (|ofCategory| *1 (|FramedAlgebra| *3 *4)) (|ofCategory| *3 (|CommutativeRing|)) (|ofCategory| *4 (|UnivariatePolynomialCategory| *3)) (|isDomain| *2 (|Vector| *3)))) (|coordinates| (*1 *2 *3) (AND (|isDomain| *3 (|Vector| *1)) (|ofCategory| *1 (|FramedAlgebra| *4 *5)) (|ofCategory| *4 (|CommutativeRing|)) (|ofCategory| *5 (|UnivariatePolynomialCategory| *4)) (|isDomain| *2 (|Matrix| *4)))) (|represents| (*1 *1 *2) (AND (|isDomain| *2 (|Vector| *3)) (|ofCategory| *3 (|CommutativeRing|)) (|ofCategory| *1 (|FramedAlgebra| *3 *4)) (|ofCategory| *4 (|UnivariatePolynomialCategory| *3)))) (|convert| (*1 *2 *1) (AND (|ofCategory| *1 (|FramedAlgebra| *3 *4)) (|ofCategory| *3 (|CommutativeRing|)) (|ofCategory| *4 (|UnivariatePolynomialCategory| *3)) (|isDomain| *2 (|Vector| *3)))) (|convert| (*1 *1 *2) (AND (|isDomain| *2 (|Vector| *3)) (|ofCategory| *3 (|CommutativeRing|)) (|ofCategory| *1 (|FramedAlgebra| *3 *4)) (|ofCategory| *4 (|UnivariatePolynomialCategory| *3)))) (|traceMatrix| (*1 *2) (AND (|ofCategory| *1 (|FramedAlgebra| *3 *4)) (|ofCategory| *3 (|CommutativeRing|)) (|ofCategory| *4 (|UnivariatePolynomialCategory| *3)) (|isDomain| *2 (|Matrix| *3)))) (|discriminant| (*1 *2) (AND (|ofCategory| *1 (|FramedAlgebra| *2 *3)) (|ofCategory| *3 (|UnivariatePolynomialCategory| *2)) (|ofCategory| *2 (|CommutativeRing|)))) (|regularRepresentation| (*1 *2 *1) (AND (|ofCategory| *1 (|FramedAlgebra| *3 *4)) (|ofCategory| *3 (|CommutativeRing|)) (|ofCategory| *4 (|UnivariatePolynomialCategory| *3)) (|isDomain| *2 (|Matrix| *3))))) (|Join| (|FiniteRankAlgebra| |t#1| |t#2|) (CATEGORY |domain| (SIGNATURE |basis| ((|Vector| $))) (SIGNATURE |coordinates| ((|Vector| |t#1|) $)) (SIGNATURE |coordinates| ((|Matrix| |t#1|) (|Vector| $))) (SIGNATURE |represents| ($ (|Vector| |t#1|))) (SIGNATURE |convert| ((|Vector| |t#1|) $)) (SIGNATURE |convert| ($ (|Vector| |t#1|))) (SIGNATURE |traceMatrix| ((|Matrix| |t#1|))) (SIGNATURE |discriminant| (|t#1|)) (SIGNATURE |regularRepresentation| ((|Matrix| |t#1|) $)))) @@ -1181,7 +1184,7 @@ NIL NIL (|Join| (|RetractableTo| |t#1|) (CATEGORY |package| (IF (|has| |t#1| (|RetractableTo| (|Integer|))) (ATTRIBUTE (|RetractableTo| (|Integer|))) |%noBranch|) (IF (|has| |t#1| (|RetractableTo| (|Fraction| (|Integer|)))) (ATTRIBUTE (|RetractableTo| (|Fraction| (|Integer|)))) |%noBranch|))) (((|CoercibleFrom| #1=(|Fraction| (|Integer|))) |has| |#1| (|RetractableTo| (|Fraction| (|Integer|)))) ((|CoercibleFrom| #2=(|Integer|)) |has| |#1| (|RetractableTo| (|Integer|))) ((|CoercibleFrom| |#1|) . T) ((|RetractableTo| #1#) |has| |#1| (|RetractableTo| (|Fraction| (|Integer|)))) ((|RetractableTo| #2#) |has| |#1| (|RetractableTo| (|Integer|))) ((|RetractableTo| |#1|) . T)) -((~= #1=(#2=(#3=(|Boolean|) $ $) NIL T ELT)) (|sample| (#4=($) NIL T CONST)) (|recip| (((|Union| $ "failed") $) NIL T ELT)) (|randomLC| ((|#4| #5=(|NonNegativeInteger|) #6=(|Vector| |#4|)) 55 T ELT)) (|one?| ((#3# $) NIL T ELT)) (|numer| (#7=(#6# $) 15 T ELT)) (|norm| ((|#2| $) 53 T ELT)) (|minimize| (#8=($ $) 156 T ELT)) (|latex| (((|String|) $) NIL T ELT)) (|inv| (#8# 103 T ELT)) (|ideal| (($ #6#) 102 T ELT)) (|hash| (((|SingleInteger|) $) NIL T ELT)) (|denom| ((|#1| $) 16 T ELT)) (|conjugate| #9=(#10=($ $ $) NIL T ELT)) (|commutator| #9#) (|coerce| (((|OutputForm|) $) 147 T ELT)) (|before?| #1#) (|basis| (#7# 140 T ELT)) (|One| (#4# 11 T CONST)) (= (#2# 39 T ELT)) (/ #9#) (** (($ $ (|PositiveInteger|)) NIL T ELT) (($ $ #5#) NIL T ELT) (($ $ (|Integer|)) 133 T ELT)) (* (#10# 130 T ELT))) +((~= #1=(#2=(#3=(|Boolean|) $ $) NIL T ELT)) (|sample| (#4=($) NIL T CONST)) (|recip| (((|Union| $ "failed") $) NIL T ELT)) (|randomLC| ((|#4| #5=(|NonNegativeInteger|) #6=(|Vector| |#4|)) 55 T ELT)) (|one?| ((#3# $) NIL T ELT)) (|numer| (#7=(#6# $) 15 T ELT)) (|norm| ((|#2| $) 53 T ELT)) (|minimize| (#8=($ $) 155 T ELT)) (|latex| (((|String|) $) NIL T ELT)) (|inv| (#8# 103 T ELT)) (|ideal| (($ #6#) 102 T ELT)) (|hash| (((|SingleInteger|) $) NIL T ELT)) (|denom| ((|#1| $) 16 T ELT)) (|conjugate| #9=(#10=($ $ $) NIL T ELT)) (|commutator| #9#) (|coerce| (((|OutputForm|) $) 147 T ELT)) (|before?| #1#) (|basis| (#7# 140 T ELT)) (|One| (#4# 11 T CONST)) (= (#2# 39 T ELT)) (/ #9#) (** (($ $ (|PositiveInteger|)) NIL T ELT) (($ $ #5#) NIL T ELT) (($ $ (|Integer|)) 133 T ELT)) (* (#10# 130 T ELT))) (((|FractionalIdeal| |#1| |#2| |#3| |#4|) (|Join| (|Group|) (CATEGORY |domain| (SIGNATURE |ideal| ($ #1=(|Vector| |#4|))) (SIGNATURE |basis| #2=(#1# $)) (SIGNATURE |norm| (|#2| $)) (SIGNATURE |numer| #2#) (SIGNATURE |denom| (|#1| $)) (SIGNATURE |minimize| ($ $)) (SIGNATURE |randomLC| (|#4| (|NonNegativeInteger|) #1#)))) (|EuclideanDomain|) (|QuotientFieldCategory| |#1|) (|UnivariatePolynomialCategory| |#2|) (|Join| (|FramedAlgebra| |#2| |#3|) (|RetractableTo| |#2|))) (T |FractionalIdeal|)) ((|ideal| (*1 *1 *2) (AND #1=(|isDomain| *2 (|Vector| *6)) #2=(|ofCategory| *6 (|Join| (|FramedAlgebra| *4 *5) (|RetractableTo| *4))) #3=(|ofCategory| *4 #4=(|QuotientFieldCategory| *3)) #5=(|ofCategory| *5 (|UnivariatePolynomialCategory| *4)) #6=(|ofCategory| *3 #7=(|EuclideanDomain|)) #8=(|isDomain| *1 (|FractionalIdeal| *3 *4 *5 *6)))) (|basis| #9=(*1 *2 *1) #10=(AND #6# #3# #5# #1# #8# #2#)) (|norm| #9# (AND (|ofCategory| *4 (|UnivariatePolynomialCategory| *2)) (|ofCategory| *2 #4#) (|isDomain| *1 (|FractionalIdeal| *3 *2 *4 *5)) #6# (|ofCategory| *5 (|Join| (|FramedAlgebra| *2 *4) (|RetractableTo| *2))))) (|numer| #9# #10#) (|denom| #9# (AND #11=(|ofCategory| *3 (|QuotientFieldCategory| *2)) #12=(|ofCategory| *4 (|UnivariatePolynomialCategory| *3)) #13=(|ofCategory| *2 #7#) #14=(|isDomain| *1 (|FractionalIdeal| *2 *3 *4 *5)) #15=(|ofCategory| *5 (|Join| (|FramedAlgebra| *3 *4) (|RetractableTo| *3))))) (|minimize| (*1 *1 *1) (AND #13# #11# #12# #14# #15#)) (|randomLC| (*1 *2 *3 *4) (AND (|isDomain| *3 (|NonNegativeInteger|)) (|isDomain| *4 (|Vector| *2)) (|ofCategory| *5 #7#) (|ofCategory| *6 (|QuotientFieldCategory| *5)) (|ofCategory| *2 (|Join| (|FramedAlgebra| *6 *7) (|RetractableTo| *6))) (|isDomain| *1 (|FractionalIdeal| *5 *6 *7 *2)) (|ofCategory| *7 (|UnivariatePolynomialCategory| *6))))) ((|map| (((|FractionalIdeal| |#5| |#6| |#7| |#8|) (|Mapping| |#5| |#1|) (|FractionalIdeal| |#1| |#2| |#3| |#4|)) 35 T ELT))) @@ -1196,7 +1199,7 @@ NIL ((|unit| (#1=((|Union| $ #2="failed")) 99 T ELT)) (|structuralConstants| ((#3=(|Vector| #4=(|Matrix| |#2|)) #5=(|Vector| $)) NIL T ELT) ((#3#) 104 T ELT)) (|rightUnits| (#6=((|Union| (|Record| (|:| |particular| $) (|:| |basis| (|List| $))) #2#)) 97 T ELT)) (|rightUnit| (#1# 96 T ELT)) (|rightTraceMatrix| #7=(#8=(#4# #5#) NIL T ELT) (#9=(#4#) 115 T ELT)) (|rightRegularRepresentation| #10=((#4# $ #5#) NIL T ELT) (#11=(#4# $) 123 T ELT)) (|rightRankPolynomial| (#12=((|SparseUnivariatePolynomial| #13=(|Polynomial| |#2|))) 64 T ELT)) (|rightDiscriminant| #14=((|#2| #5#) NIL T ELT) (#15=(|#2|) 119 T ELT)) (|represents| (($ #16=(|Vector| |#2|) #5#) NIL T ELT) (#17=($ #16#) 125 T ELT)) (|leftUnits| (#6# 95 T ELT)) (|leftUnit| (#1# 87 T ELT)) (|leftTraceMatrix| #7# (#9# 113 T ELT)) (|leftRegularRepresentation| #10# (#11# 121 T ELT)) (|leftRankPolynomial| (#12# 63 T ELT)) (|leftDiscriminant| #14# (#15# 117 T ELT)) (|coordinates| ((#16# $ #5#) NIL T ELT) ((#4# #5# #5#) NIL T ELT) (#18=(#16# $) 124 T ELT) (#8# 133 T ELT)) (|convert| (#18# 109 T ELT) (#17# 111 T ELT)) (|conditionsForIdempotents| ((#19=(|List| #13#) #5#) NIL T ELT) ((#19#) 107 T ELT)) (|apply| (($ #4# $) 103 T ELT))) (((|FramedNonAssociativeAlgebra&| |#1| |#2|) (CATEGORY |package| (SIGNATURE |apply| (|#1| #1=(|Matrix| |#2|) |#1|)) (SIGNATURE |rightRankPolynomial| #2=((|SparseUnivariatePolynomial| #3=(|Polynomial| |#2|)))) (SIGNATURE |leftRankPolynomial| #2#) (SIGNATURE |rightRegularRepresentation| #4=(#1# |#1|)) (SIGNATURE |leftRegularRepresentation| #4#) (SIGNATURE |rightTraceMatrix| #5=(#1#)) (SIGNATURE |leftTraceMatrix| #5#) (SIGNATURE |rightDiscriminant| #6=(|#2|)) (SIGNATURE |leftDiscriminant| #6#) (SIGNATURE |convert| #7=(|#1| #8=(|Vector| |#2|))) (SIGNATURE |convert| #9=(#8# |#1|)) (SIGNATURE |represents| #7#) (SIGNATURE |conditionsForIdempotents| (#10=(|List| #3#))) (SIGNATURE |structuralConstants| (#11=(|Vector| #1#))) (SIGNATURE |coordinates| #12=(#1# #13=(|Vector| |#1|))) (SIGNATURE |coordinates| #9#) (SIGNATURE |unit| #14=((|Union| |#1| #15="failed"))) (SIGNATURE |rightUnit| #14#) (SIGNATURE |leftUnit| #14#) (SIGNATURE |rightUnits| #16=((|Union| (|Record| (|:| |particular| |#1|) (|:| |basis| (|List| |#1|))) #15#))) (SIGNATURE |leftUnits| #16#) (SIGNATURE |rightTraceMatrix| #12#) (SIGNATURE |leftTraceMatrix| #12#) (SIGNATURE |rightDiscriminant| #17=(|#2| #13#)) (SIGNATURE |leftDiscriminant| #17#) (SIGNATURE |represents| (|#1| #8# #13#)) (SIGNATURE |coordinates| (#1# #13# #13#)) (SIGNATURE |coordinates| (#8# |#1| #13#)) (SIGNATURE |rightRegularRepresentation| #18=(#1# |#1| #13#)) (SIGNATURE |leftRegularRepresentation| #18#) (SIGNATURE |structuralConstants| (#11# #13#)) (SIGNATURE |conditionsForIdempotents| (#10# #13#))) (|FramedNonAssociativeAlgebra| |#2|) (|CommutativeRing|)) (T |FramedNonAssociativeAlgebra&|)) ((|structuralConstants| #1=(*1 *2) (AND #2=(|ofCategory| *4 #3=(|CommutativeRing|)) (|isDomain| *2 (|Vector| #4=(|Matrix| *4))) #5=(|isDomain| *1 (|FramedNonAssociativeAlgebra&| *3 *4)) #6=(|ofCategory| *3 (|FramedNonAssociativeAlgebra| *4)))) (|conditionsForIdempotents| #1# (AND #2# (|isDomain| *2 (|List| #7=(|Polynomial| *4))) #5# #6#)) (|leftDiscriminant| #1# #8=(AND (|ofCategory| *2 #3#) (|isDomain| *1 (|FramedNonAssociativeAlgebra&| *3 *2)) (|ofCategory| *3 (|FramedNonAssociativeAlgebra| *2)))) (|rightDiscriminant| #1# #8#) (|leftTraceMatrix| #1# #9=(AND #2# (|isDomain| *2 #4#) #5# #6#)) (|rightTraceMatrix| #1# #9#) (|leftRankPolynomial| #1# #10=(AND #2# (|isDomain| *2 (|SparseUnivariatePolynomial| #7#)) #5# #6#)) (|rightRankPolynomial| #1# #10#)) -((~= (#1=((|Boolean|) $ $) 7 T ELT)) (|zero?| ((#2=(|Boolean|) $) 22 T ELT)) (|unit| (#3=(#4=(|Union| $ #5="failed")) 48 (|has| |#1| . #6=((|IntegralDomain|))) ELT)) (|subtractIfCan| (((|Union| $ "failed") $ $) 26 T ELT)) (|structuralConstants| (((|Vector| (|Matrix| |#1|)) #7=(|Vector| $)) 89 T ELT) (((|Vector| (|Matrix| |#1|))) 115 T ELT)) (|someBasis| ((#7#) 92 T ELT)) (|sample| (#8=($) 23 T CONST)) (|rightUnits| (#9=((|Union| (|Record| (|:| |particular| $) (|:| |basis| (|List| $))) #5#)) 51 (|has| |#1| . #6#) ELT)) (|rightUnit| (#3# 49 (|has| |#1| . #6#) ELT)) (|rightTraceMatrix| (((|Matrix| |#1|) . #10=(#7#)) 76 T ELT) (((|Matrix| |#1|)) 107 T ELT)) (|rightTrace| ((|#1| . #11=($)) 85 T ELT)) (|rightRegularRepresentation| (((|Matrix| |#1|) . #12=($ #7#)) 87 T ELT) (((|Matrix| |#1|) $) 105 T ELT)) (|rightRecip| (#13=(#4# $) 56 (|has| |#1| . #6#) ELT)) (|rightRankPolynomial| (((|SparseUnivariatePolynomial| (|Polynomial| |#1|))) 103 (|has| |#1| (|Field|)) ELT)) (|rightPower| (#14=($ $ (|PositiveInteger|)) 37 T ELT)) (|rightNorm| ((|#1| . #11#) 83 T ELT)) (|rightMinimalPolynomial| (((|SparseUnivariatePolynomial| |#1|) . #15=($)) 53 (|has| |#1| . #6#) ELT)) (|rightDiscriminant| ((|#1| . #16=(#7#)) 78 T ELT) ((|#1|) 109 T ELT)) (|rightCharacteristicPolynomial| (((|SparseUnivariatePolynomial| |#1|) . #15#) 74 T ELT)) (|rightAlternative?| (#17=((|Boolean|)) 68 T ELT)) (|represents| (($ (|Vector| |#1|) #7#) 80 T ELT) (($ (|Vector| |#1|)) 113 T ELT)) (|recip| (#13# 58 (|has| |#1| . #6#) ELT)) (|rank| (((|PositiveInteger|)) 91 T ELT)) (|powerAssociative?| (#17# 65 T ELT)) (|plenaryPower| (($ $ (|PositiveInteger|)) 44 T ELT)) (|opposite?| ((#2# $ $) 20 T ELT)) (|noncommutativeJordanAlgebra?| (#17# 61 T ELT)) (|lieAlgebra?| (#17# 59 T ELT)) (|lieAdmissible?| (#17# 63 T ELT)) (|leftUnits| (#9# 52 (|has| |#1| . #6#) ELT)) (|leftUnit| (#3# 50 (|has| |#1| . #6#) ELT)) (|leftTraceMatrix| (((|Matrix| |#1|) . #10#) 77 T ELT) (((|Matrix| |#1|)) 108 T ELT)) (|leftTrace| ((|#1| . #11#) 86 T ELT)) (|leftRegularRepresentation| (((|Matrix| |#1|) . #12#) 88 T ELT) (((|Matrix| |#1|) $) 106 T ELT)) (|leftRecip| (#13# 57 (|has| |#1| . #6#) ELT)) (|leftRankPolynomial| (((|SparseUnivariatePolynomial| (|Polynomial| |#1|))) 104 (|has| |#1| (|Field|)) ELT)) (|leftPower| (#14# 38 T ELT)) (|leftNorm| ((|#1| . #11#) 84 T ELT)) (|leftMinimalPolynomial| (((|SparseUnivariatePolynomial| |#1|) . #15#) 54 (|has| |#1| . #6#) ELT)) (|leftDiscriminant| ((|#1| . #16#) 79 T ELT) ((|#1|) 110 T ELT)) (|leftCharacteristicPolynomial| (((|SparseUnivariatePolynomial| |#1|) . #15#) 75 T ELT)) (|leftAlternative?| (#17# 69 T ELT)) (|latex| (((|String|) $) 11 T ELT)) (|jordanAlgebra?| (#17# 60 T ELT)) (|jordanAdmissible?| (#17# 62 T ELT)) (|jacobiIdentity?| (#17# 64 T ELT)) (|hash| (((|SingleInteger|) $) 12 T ELT)) (|flexible?| (#17# 67 T ELT)) (|elt| ((|#1| $ (|Integer|)) 119 T ELT)) (|coordinates| (((|Vector| |#1|) $ #7#) 82 T ELT) (((|Matrix| |#1|) #7# #7#) 81 T ELT) (((|Vector| |#1|) $) 117 T ELT) (((|Matrix| |#1|) (|Vector| $)) 116 T ELT)) (|convert| (((|Vector| |#1|) $) 112 T ELT) (($ (|Vector| |#1|)) 111 T ELT)) (|conditionsForIdempotents| (((|List| (|Polynomial| |#1|)) #7#) 90 T ELT) (((|List| (|Polynomial| |#1|))) 114 T ELT)) (|commutator| (#18=($ $ $) 34 T ELT)) (|commutative?| (#17# 73 T ELT)) (|coerce| (((|OutputForm|) $) 13 T ELT)) (|before?| (#1# 6 T ELT)) (|basis| (((|Vector| $)) 118 T ELT)) (|associatorDependence| (((|List| (|Vector| |#1|))) 55 (|has| |#1| . #6#) ELT)) (|associator| (($ $ $ $) 35 T ELT)) (|associative?| (#17# 71 T ELT)) (|apply| (($ (|Matrix| |#1|) $) 102 T ELT)) (|antiCommutator| (#18# 33 T ELT)) (|antiCommutative?| (#17# 72 T ELT)) (|antiAssociative?| (#17# 70 T ELT)) (|alternative?| (#17# 66 T ELT)) (|Zero| (#8# 24 T CONST)) (= (#1# 8 T ELT)) (- (($ $) 29 T ELT) (($ $ $) 28 T ELT)) (+ (($ $ $) 18 T ELT)) (** (#14# 39 T ELT)) (* (($ (|PositiveInteger|) $) 17 T ELT) (($ (|NonNegativeInteger|) $) 21 T ELT) (($ (|Integer|) . #19=($)) 30 T ELT) (($ $ $) 36 T ELT) (($ $ |#1|) 46 T ELT) (($ |#1| . #19#) 45 T ELT))) +((~= (#1=((|Boolean|) $ $) 7 T ELT)) (|zero?| ((#2=(|Boolean|) $) 22 T ELT)) (|unit| (#3=(#4=(|Union| $ #5="failed")) 49 (|has| |#1| . #6=((|IntegralDomain|))) ELT)) (|subtractIfCan| (((|Maybe| $) $ $) 26 T ELT)) (|structuralConstants| (((|Vector| (|Matrix| |#1|)) #7=(|Vector| $)) 90 T ELT) (((|Vector| (|Matrix| |#1|))) 116 T ELT)) (|someBasis| ((#7#) 93 T ELT)) (|sample| (#8=($) 23 T CONST)) (|rightUnits| (#9=((|Union| (|Record| (|:| |particular| $) (|:| |basis| (|List| $))) #5#)) 52 (|has| |#1| . #6#) ELT)) (|rightUnit| (#3# 50 (|has| |#1| . #6#) ELT)) (|rightTraceMatrix| (((|Matrix| |#1|) . #10=(#7#)) 77 T ELT) (((|Matrix| |#1|)) 108 T ELT)) (|rightTrace| ((|#1| . #11=($)) 86 T ELT)) (|rightRegularRepresentation| (((|Matrix| |#1|) . #12=($ #7#)) 88 T ELT) (((|Matrix| |#1|) $) 106 T ELT)) (|rightRecip| (#13=(#4# $) 57 (|has| |#1| . #6#) ELT)) (|rightRankPolynomial| (((|SparseUnivariatePolynomial| (|Polynomial| |#1|))) 104 (|has| |#1| (|Field|)) ELT)) (|rightPower| (#14=($ $ (|PositiveInteger|)) 38 T ELT)) (|rightNorm| ((|#1| . #11#) 84 T ELT)) (|rightMinimalPolynomial| (((|SparseUnivariatePolynomial| |#1|) . #15=($)) 54 (|has| |#1| . #6#) ELT)) (|rightDiscriminant| ((|#1| . #16=(#7#)) 79 T ELT) ((|#1|) 110 T ELT)) (|rightCharacteristicPolynomial| (((|SparseUnivariatePolynomial| |#1|) . #15#) 75 T ELT)) (|rightAlternative?| (#17=((|Boolean|)) 69 T ELT)) (|represents| (($ (|Vector| |#1|) #7#) 81 T ELT) (($ (|Vector| |#1|)) 114 T ELT)) (|recip| (#13# 59 (|has| |#1| . #6#) ELT)) (|rank| (((|PositiveInteger|)) 92 T ELT)) (|powerAssociative?| (#17# 66 T ELT)) (|plenaryPower| (($ $ (|PositiveInteger|)) 45 T ELT)) (|opposite?| ((#2# $ $) 20 T ELT)) (|noncommutativeJordanAlgebra?| (#17# 62 T ELT)) (|lieAlgebra?| (#17# 60 T ELT)) (|lieAdmissible?| (#17# 64 T ELT)) (|leftUnits| (#9# 53 (|has| |#1| . #6#) ELT)) (|leftUnit| (#3# 51 (|has| |#1| . #6#) ELT)) (|leftTraceMatrix| (((|Matrix| |#1|) . #10#) 78 T ELT) (((|Matrix| |#1|)) 109 T ELT)) (|leftTrace| ((|#1| . #11#) 87 T ELT)) (|leftRegularRepresentation| (((|Matrix| |#1|) . #12#) 89 T ELT) (((|Matrix| |#1|) $) 107 T ELT)) (|leftRecip| (#13# 58 (|has| |#1| . #6#) ELT)) (|leftRankPolynomial| (((|SparseUnivariatePolynomial| (|Polynomial| |#1|))) 105 (|has| |#1| (|Field|)) ELT)) (|leftPower| (#14# 39 T ELT)) (|leftNorm| ((|#1| . #11#) 85 T ELT)) (|leftMinimalPolynomial| (((|SparseUnivariatePolynomial| |#1|) . #15#) 55 (|has| |#1| . #6#) ELT)) (|leftDiscriminant| ((|#1| . #16#) 80 T ELT) ((|#1|) 111 T ELT)) (|leftCharacteristicPolynomial| (((|SparseUnivariatePolynomial| |#1|) . #15#) 76 T ELT)) (|leftAlternative?| (#17# 70 T ELT)) (|latex| (((|String|) $) 11 T ELT)) (|jordanAlgebra?| (#17# 61 T ELT)) (|jordanAdmissible?| (#17# 63 T ELT)) (|jacobiIdentity?| (#17# 65 T ELT)) (|hash| (((|SingleInteger|) $) 12 T ELT)) (|flexible?| (#17# 68 T ELT)) (|elt| ((|#1| $ (|Integer|)) 120 T ELT)) (|coordinates| (((|Vector| |#1|) $ #7#) 83 T ELT) (((|Matrix| |#1|) #7# #7#) 82 T ELT) (((|Vector| |#1|) $) 118 T ELT) (((|Matrix| |#1|) (|Vector| $)) 117 T ELT)) (|convert| (((|Vector| |#1|) $) 113 T ELT) (($ (|Vector| |#1|)) 112 T ELT)) (|conditionsForIdempotents| (((|List| (|Polynomial| |#1|)) #7#) 91 T ELT) (((|List| (|Polynomial| |#1|))) 115 T ELT)) (|commutator| (#18=($ $ $) 35 T ELT)) (|commutative?| (#17# 74 T ELT)) (|coerce| (((|OutputForm|) $) 13 T ELT)) (|before?| (#1# 6 T ELT)) (|basis| (((|Vector| $)) 119 T ELT)) (|associatorDependence| (((|List| (|Vector| |#1|))) 56 (|has| |#1| . #6#) ELT)) (|associator| (($ $ $ $) 36 T ELT)) (|associative?| (#17# 72 T ELT)) (|apply| (($ (|Matrix| |#1|) $) 103 T ELT)) (|antiCommutator| (#18# 34 T ELT)) (|antiCommutative?| (#17# 73 T ELT)) (|antiAssociative?| (#17# 71 T ELT)) (|alternative?| (#17# 67 T ELT)) (|Zero| (#8# 24 T CONST)) (= (#1# 8 T ELT)) (- (($ $) 30 T ELT) (($ $ $) 29 T ELT)) (+ (($ $ $) 18 T ELT)) (** (#14# 40 T ELT)) (* (($ (|PositiveInteger|) $) 17 T ELT) (($ (|NonNegativeInteger|) $) 21 T ELT) (($ (|Integer|) . #19=($)) 31 T ELT) (($ $ $) 37 T ELT) (($ $ |#1|) 47 T ELT) (($ |#1| . #19#) 46 T ELT))) (((|FramedNonAssociativeAlgebra| |#1|) (|Category|) (|CommutativeRing|)) (T |FramedNonAssociativeAlgebra|)) ((|basis| (*1 *2) (AND (|ofCategory| *3 (|CommutativeRing|)) (|isDomain| *2 (|Vector| *1)) (|ofCategory| *1 (|FramedNonAssociativeAlgebra| *3)))) (|coordinates| (*1 *2 *1) (AND (|ofCategory| *1 (|FramedNonAssociativeAlgebra| *3)) (|ofCategory| *3 (|CommutativeRing|)) (|isDomain| *2 (|Vector| *3)))) (|coordinates| (*1 *2 *3) (AND (|isDomain| *3 (|Vector| *1)) (|ofCategory| *1 (|FramedNonAssociativeAlgebra| *4)) (|ofCategory| *4 (|CommutativeRing|)) (|isDomain| *2 (|Matrix| *4)))) (|structuralConstants| (*1 *2) (AND (|ofCategory| *1 (|FramedNonAssociativeAlgebra| *3)) (|ofCategory| *3 (|CommutativeRing|)) (|isDomain| *2 (|Vector| (|Matrix| *3))))) (|conditionsForIdempotents| (*1 *2) (AND (|ofCategory| *1 (|FramedNonAssociativeAlgebra| *3)) (|ofCategory| *3 (|CommutativeRing|)) (|isDomain| *2 (|List| (|Polynomial| *3))))) (|represents| (*1 *1 *2) (AND (|isDomain| *2 (|Vector| *3)) (|ofCategory| *3 (|CommutativeRing|)) (|ofCategory| *1 (|FramedNonAssociativeAlgebra| *3)))) (|convert| (*1 *2 *1) (AND (|ofCategory| *1 (|FramedNonAssociativeAlgebra| *3)) (|ofCategory| *3 (|CommutativeRing|)) (|isDomain| *2 (|Vector| *3)))) (|convert| (*1 *1 *2) (AND (|isDomain| *2 (|Vector| *3)) (|ofCategory| *3 (|CommutativeRing|)) (|ofCategory| *1 (|FramedNonAssociativeAlgebra| *3)))) (|leftDiscriminant| (*1 *2) (AND (|ofCategory| *1 (|FramedNonAssociativeAlgebra| *2)) (|ofCategory| *2 (|CommutativeRing|)))) (|rightDiscriminant| (*1 *2) (AND (|ofCategory| *1 (|FramedNonAssociativeAlgebra| *2)) (|ofCategory| *2 (|CommutativeRing|)))) (|leftTraceMatrix| (*1 *2) (AND (|ofCategory| *1 (|FramedNonAssociativeAlgebra| *3)) (|ofCategory| *3 (|CommutativeRing|)) (|isDomain| *2 (|Matrix| *3)))) (|rightTraceMatrix| (*1 *2) (AND (|ofCategory| *1 (|FramedNonAssociativeAlgebra| *3)) (|ofCategory| *3 (|CommutativeRing|)) (|isDomain| *2 (|Matrix| *3)))) (|leftRegularRepresentation| (*1 *2 *1) (AND (|ofCategory| *1 (|FramedNonAssociativeAlgebra| *3)) (|ofCategory| *3 (|CommutativeRing|)) (|isDomain| *2 (|Matrix| *3)))) (|rightRegularRepresentation| (*1 *2 *1) (AND (|ofCategory| *1 (|FramedNonAssociativeAlgebra| *3)) (|ofCategory| *3 (|CommutativeRing|)) (|isDomain| *2 (|Matrix| *3)))) (|leftRankPolynomial| (*1 *2) (AND (|ofCategory| *1 (|FramedNonAssociativeAlgebra| *3)) (|ofCategory| *3 (|CommutativeRing|)) (|ofCategory| *3 (|Field|)) (|isDomain| *2 (|SparseUnivariatePolynomial| (|Polynomial| *3))))) (|rightRankPolynomial| (*1 *2) (AND (|ofCategory| *1 (|FramedNonAssociativeAlgebra| *3)) (|ofCategory| *3 (|CommutativeRing|)) 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(SIGNATURE |rightRegularRepresentation| ((|Matrix| |t#1|) $)) (IF (|has| |t#1| (|Field|)) (PROGN (SIGNATURE |leftRankPolynomial| ((|SparseUnivariatePolynomial| (|Polynomial| |t#1|)))) (SIGNATURE |rightRankPolynomial| ((|SparseUnivariatePolynomial| (|Polynomial| |t#1|))))) |%noBranch|) (SIGNATURE |apply| ($ (|Matrix| |t#1|) $)))) @@ -1207,7 +1210,7 @@ NIL ((|variables| ((#1=(|List| #2=(|Symbol|)) $) 81 T ELT)) (|univariate| (((|Fraction| (|SparseUnivariatePolynomial| $)) $ #3=(|Kernel| $)) 313 T ELT)) (|subst| #4=(($ $ #5=(|Equation| $)) NIL T ELT) #6=(($ $ (|List| #5#)) NIL T ELT) (#7=($ $ #8=(|List| #3#) #9=(|List| $)) 277 T ELT)) (|retractIfCan| (#10=((|Union| #3# #11="failed") $) NIL T ELT) (((|Union| #2# #11#) $) 84 T ELT) (((|Union| #12=(|Integer|) #11#) $) NIL T ELT) (((|Union| |#2| #11#) $) 273 T ELT) (((|Union| #13=(|Fraction| #14=(|Polynomial| |#2|)) #11#) $) 363 T ELT) (((|Union| #14# #11#) $) 275 T ELT) (((|Union| #15=(|Fraction| #12#) #11#) $) NIL T ELT)) (|retract| ((#3# 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(((|Union| (|Polynomial| |#1|) . #15#) . #16#) 137 (|has| |#1| . #21=((|Ring|))) ELT) (((|Union| #22=(|Fraction| #18#) . #15#) . #16#) 111 (OR (AND (|has| |#1| . #23=((|RetractableTo| (|Integer|)))) (|has| |#1| . #24=((|IntegralDomain|)))) (|has| |#1| . #25=((|RetractableTo| #22#)))) ELT)) (|retract| ((#8# . #26=($)) 68 T ELT) ((#17# . #26#) 236 T ELT) ((#18# . #26#) 228 (|has| |#1| . #19#) ELT) ((|#1| . #26#) 227 T ELT) (((|Fraction| (|Polynomial| |#1|)) . #26#) 189 (|has| |#1| . #20#) ELT) (((|Polynomial| |#1|) . #26#) 138 (|has| |#1| . #21#) ELT) ((#22# . #26#) 112 (OR (AND (|has| |#1| . #23#) (|has| |#1| . #24#)) (|has| |#1| . #25#)) ELT)) (|rem| (#27=($ $ $) 177 (|has| |#1| . #4#) ELT)) (|reducedSystem| (((|Matrix| #28=(|Integer|)) . #29=(#30=(|Matrix| $))) 155 (|and| (|has| |#1| . #31=((|LinearlyExplicitRingOver| #28#))) (|has| |#1| . #32=((|Ring|)))) ELT) (((|Record| (|:| |mat| (|Matrix| #28#)) (|:| |vec| (|Vector| #28#))) . #33=(#30# #34=(|Vector| $))) 154 (|and| (|has| |#1| . #31#) (|has| |#1| . #32#)) ELT) (((|Record| (|:| |mat| (|Matrix| |#1|)) (|:| |vec| (|Vector| |#1|))) . #33#) 153 (|has| |#1| . #32#) ELT) (((|Matrix| |#1|) . #29#) 152 (|has| |#1| . #32#) ELT)) (|recip| (((|Union| $ "failed") $) 119 (|has| |#1| . #14#) ELT)) (|quo| (#27# 176 (|has| |#1| . #4#) ELT)) (|principalIdeal| (((|Record| (|:| |coef| #35=(|List| $)) (|:| |generator| $)) #35#) 171 (|has| |#1| . #4#) ELT)) (|prime?| (((|Boolean|) $) 184 (|has| |#1| . #4#) ELT)) (|patternMatch| (((|PatternMatchResult| #36=(|Integer|) . #37=($)) $ (|Pattern| #36#) (|PatternMatchResult| #36# . #37#)) 231 (|has| |#1| (|PatternMatchable| #36#)) ELT) (((|PatternMatchResult| #38=(|Float|) . #37#) $ (|Pattern| #38#) (|PatternMatchResult| #38# . #37#)) 230 (|has| |#1| (|PatternMatchable| #38#)) ELT)) (|paren| (#39=($ $) 49 T ELT) (#40=($ #11#) 48 T ELT)) (|opposite?| ((#2# $ $) 131 (|has| |#1| . #3#) ELT)) (|operators| ((#41=(|List| #42=(|BasicOperator|)) $) 41 T ELT)) (|operator| ((#42# #42#) 40 T ELT)) 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*1) (AND (|ofCategory| *1 (|FunctionSpace| *2)) (|ofCategory| *2 (|SetCategory|)))) (|variables| (*1 *2 *1) (AND (|ofCategory| *1 (|FunctionSpace| *3)) (|ofCategory| *3 (|SetCategory|)) (|isDomain| *2 (|List| (|Symbol|))))) (|applyQuote| (*1 *1 *2 *1) (AND (|isDomain| *2 (|Symbol|)) (|ofCategory| *1 (|FunctionSpace| *3)) (|ofCategory| *3 (|SetCategory|)))) (|applyQuote| (*1 *1 *2 *1 *1) (AND (|isDomain| *2 (|Symbol|)) (|ofCategory| *1 (|FunctionSpace| *3)) (|ofCategory| *3 (|SetCategory|)))) (|applyQuote| (*1 *1 *2 *1 *1 *1) (AND (|isDomain| *2 (|Symbol|)) (|ofCategory| *1 (|FunctionSpace| *3)) (|ofCategory| *3 (|SetCategory|)))) (|applyQuote| (*1 *1 *2 *1 *1 *1 *1) (AND (|isDomain| *2 (|Symbol|)) (|ofCategory| *1 (|FunctionSpace| *3)) (|ofCategory| *3 (|SetCategory|)))) (|applyQuote| (*1 *1 *2 *3) (AND (|isDomain| *2 (|Symbol|)) (|isDomain| *3 (|List| *1)) (|ofCategory| *1 (|FunctionSpace| *4)) (|ofCategory| *4 (|SetCategory|)))) (|eval| (*1 *1 *1 *2) (AND (|isDomain| *2 (|Symbol|)) 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|t#1| (|Kernel| $)))) (SIGNATURE |coerce| ($ (|Fraction| |t#1|))) (SIGNATURE |coerce| ($ (|Polynomial| (|Fraction| |t#1|)))) (SIGNATURE |coerce| ($ (|Fraction| (|Polynomial| (|Fraction| |t#1|))))) (SIGNATURE |univariate| ((|Fraction| (|SparseUnivariatePolynomial| $)) $ (|Kernel| $))) (IF (|has| |t#1| (|RetractableTo| (|Integer|))) (ATTRIBUTE (|RetractableTo| (|Fraction| (|Integer|)))) |%noBranch|)) |%noBranch|))) @@ -1221,7 +1224,7 @@ NIL ((|localAbs| ((|#2| |#2|) 105 T ELT)) (|exprToUPS| (#1=((|Union| (|:| |%series| |#4|) (|:| |%problem| (|Record| (|:| |func| #2=(|String|)) (|:| |prob| #2#)))) |#2| (|Boolean|) #2#) 52 T ELT)) (|exprToGenUPS| (#1# 169 T ELT))) (((|FunctionSpaceToUnivariatePowerSeries| |#1| |#2| |#3| |#4| |#5| |#6|) (CATEGORY |package| (SIGNATURE |exprToUPS| #1=((|Union| (|:| |%series| |#4|) (|:| |%problem| (|Record| (|:| |func| #2=(|String|)) (|:| |prob| #2#)))) |#2| (|Boolean|) #2#)) (SIGNATURE |exprToGenUPS| #1#) (SIGNATURE |localAbs| (|#2| |#2|))) (|Join| (|GcdDomain|) (|RetractableTo| #3=(|Integer|)) (|LinearlyExplicitRingOver| #3#)) (|Join| (|AlgebraicallyClosedField|) #4=(|TranscendentalFunctionCategory|) (|FunctionSpace| |#1|) (CATEGORY |domain| (SIGNATURE |coerce| ($ |#3|)))) (|OrderedRing|) (|Join| (|UnivariatePowerSeriesCategory| |#2| |#3|) (|Field|) #4# (CATEGORY |domain| (SIGNATURE |differentiate| #5=($ $)) (SIGNATURE |integrate| #5#))) (|PartialTranscendentalFunctions| |#4|) (|Symbol|)) (T |FunctionSpaceToUnivariatePowerSeries|)) ((|localAbs| (*1 *2 *2) (AND (|ofCategory| *3 #1=(|Join| (|GcdDomain|) (|RetractableTo| #2=(|Integer|)) (|LinearlyExplicitRingOver| #2#))) (|ofCategory| *2 (|Join| #3=(|AlgebraicallyClosedField|) #4=(|TranscendentalFunctionCategory|) (|FunctionSpace| *3) (CATEGORY |domain| (SIGNATURE |coerce| ($ *4))))) (|ofCategory| *4 #5=(|OrderedRing|)) (|ofCategory| *5 (|Join| (|UnivariatePowerSeriesCategory| *2 *4) #6=(|Field|) #4# #7=(CATEGORY |domain| (SIGNATURE |differentiate| #8=($ $)) (SIGNATURE |integrate| #8#)))) (|isDomain| *1 (|FunctionSpaceToUnivariatePowerSeries| *3 *2 *4 *5 *6 *7)) (|ofCategory| *6 (|PartialTranscendentalFunctions| *5)) (|ofType| *7 #9=(|Symbol|)))) (|exprToGenUPS| #10=(*1 *2 *3 *4 *5) #11=(AND (|isDomain| *4 (|Boolean|)) (|ofCategory| *6 #1#) (|ofCategory| *3 (|Join| #3# #4# (|FunctionSpace| *6) (CATEGORY |domain| (SIGNATURE |coerce| ($ *7))))) (|ofCategory| *7 #5#) (|ofCategory| *8 (|Join| (|UnivariatePowerSeriesCategory| *3 *7) #6# #4# #7#)) (|isDomain| *2 (|Union| (|:| |%series| *8) (|:| |%problem| (|Record| (|:| |func| #12=(|String|)) (|:| |prob| #12#))))) (|isDomain| *1 (|FunctionSpaceToUnivariatePowerSeries| *6 *3 *7 *8 *9 *10)) (|isDomain| *5 #12#) (|ofCategory| *9 (|PartialTranscendentalFunctions| *8)) (|ofType| *10 #9#))) (|exprToUPS| #10# #11#)) -((|universe| (#1=($) 51 T ELT)) (|union| (($ |#2| $) NIL T ELT) #2=(($ $ |#2|) NIL T ELT) (#3=($ $ $) 47 T ELT)) (|symmetricDifference| (#3# 46 T ELT)) (|subset?| (#4=(#5=(|Boolean|) $ $) 35 T ELT)) (|size| ((#6=(|NonNegativeInteger|)) 55 T ELT)) (|set| (#7=($ (|List| |#2|)) 23 T ELT) #8=(#1# NIL T ELT)) (|random| (#1# 66 T ELT)) (|part?| (#4# 15 T ELT)) (|min| (#9=(|#2| $) 77 T ELT)) (|max| (#9# 75 T ELT)) (|lookup| ((#10=(|PositiveInteger|) $) 70 T ELT)) (|intersect| (#3# 42 T ELT)) (|index| (($ #10#) 60 T ELT)) (|difference| #2# (#3# 45 T ELT)) (|count| ((#6# |#2| $) 31 T ELT) ((#6# (|Mapping| #5# |#2|) $) NIL T ELT)) (|construct| (#7# 27 T ELT)) (|complement| (($ $) 53 T ELT)) (|coerce| (((|OutputForm|) $) 40 T ELT)) (|cardinality| ((#6# $) 24 T ELT)) (|brace| (#7# 22 T ELT) #8#) (= (#4# 19 T ELT))) +((|universe| (#1=($) 51 T ELT)) (|union| (($ |#2| $) NIL T ELT) #2=(($ $ |#2|) NIL T ELT) (#3=($ $ $) 47 T ELT)) (|symmetricDifference| (#3# 46 T ELT)) (|subset?| (#4=(#5=(|Boolean|) $ $) 35 T ELT)) (|size| ((#6=(|NonNegativeInteger|)) 55 T ELT)) (|set| (#7=($ (|List| |#2|)) 23 T ELT) #8=(#1# NIL T ELT)) (|random| (#1# 65 T ELT)) (|part?| (#4# 15 T ELT)) (|min| (#9=(|#2| $) 76 T ELT)) (|max| (#9# 74 T ELT)) (|lookup| ((#10=(|PositiveInteger|) $) 69 T ELT)) (|intersect| (#3# 42 T ELT)) (|index| (($ #10#) 60 T ELT)) (|difference| #2# (#3# 45 T ELT)) (|count| ((#6# |#2| $) 31 T ELT) ((#6# (|Mapping| #5# |#2|) $) NIL T ELT)) (|construct| (#7# 27 T ELT)) (|complement| (($ $) 53 T ELT)) (|coerce| (((|OutputForm|) $) 40 T ELT)) (|cardinality| ((#6# $) 24 T ELT)) (|brace| (#7# 22 T ELT) #8#) (= (#4# 19 T ELT))) (((|FiniteSetAggregate&| |#1| |#2|) (CATEGORY |package| (SIGNATURE |size| (#1=(|NonNegativeInteger|))) (SIGNATURE |index| (|#1| #2=(|PositiveInteger|))) (SIGNATURE |lookup| (#2# |#1|)) (SIGNATURE |random| #3=(|#1|)) (SIGNATURE |min| #4=(|#2| |#1|)) (SIGNATURE |max| #4#) (SIGNATURE |universe| #3#) (SIGNATURE |complement| (|#1| |#1|)) (SIGNATURE |cardinality| (#1# |#1|)) (SIGNATURE |count| (#1# (|Mapping| #5=(|Boolean|) |#2|) |#1|)) (SIGNATURE |count| (#1# |#2| |#1|)) (SIGNATURE = #6=(#5# |#1| |#1|)) (SIGNATURE |coerce| ((|OutputForm|) |#1|)) (SIGNATURE |part?| #6#) (SIGNATURE |brace| #3#) (SIGNATURE |brace| #7=(|#1| (|List| |#2|))) (SIGNATURE |set| #3#) (SIGNATURE |set| #7#) (SIGNATURE |intersect| #8=(|#1| |#1| |#1|)) (SIGNATURE |difference| #8#) (SIGNATURE |difference| #9=(|#1| |#1| |#2|)) (SIGNATURE |symmetricDifference| #8#) (SIGNATURE |subset?| #6#) (SIGNATURE |union| #8#) (SIGNATURE |union| #9#) (SIGNATURE |union| (|#1| |#2| |#1|)) (SIGNATURE |construct| #7#)) (|FiniteSetAggregate| |#2|) (|SetCategory|)) (T |FiniteSetAggregate&|)) ((|size| (*1 *2) (AND (|ofCategory| *4 (|SetCategory|)) (|isDomain| *2 (|NonNegativeInteger|)) (|isDomain| *1 (|FiniteSetAggregate&| *3 *4)) (|ofCategory| *3 (|FiniteSetAggregate| *4))))) ((~= (#1=((|Boolean|) $ $) 18 T ELT)) (|universe| (($) 61 (|has| |#1| (|Finite|)) ELT)) (|union| (($ |#1| $) 87 T ELT) (($ $ |#1|) 86 T ELT) (#2=($ $ $) 85 T ELT)) (|symmetricDifference| (#2# 83 T ELT)) (|subset?| (#3=((|Boolean|) $ $) 84 T ELT)) (|size| (((|NonNegativeInteger|)) 55 (|has| |#1| . #4=((|Finite|))) ELT)) (|set| (($ (|List| |#1|)) 79 T ELT) (#5=($) 78 T ELT)) (|select!| (($ (|Mapping| #6=(|Boolean|) |#1|) . #7=($)) 42 (|has| $ (|FiniteAggregate| |#1|)) ELT)) (|select| (($ (|Mapping| #8=(|Boolean|) |#1|) . #9=($)) 49 (|has| $ (|FiniteAggregate| |#1|)) ELT)) (|sample| (#10=($) 6 T CONST)) (|removeDuplicates| (($ $) 51 (AND (|has| |#1| . #11=((|BasicType|))) (|has| $ (|FiniteAggregate| |#1|))) ELT)) (|remove!| (($ |#1| $) 44 (|has| $ (|FiniteAggregate| |#1|)) ELT) (($ (|Mapping| #6# |#1|) . #7#) 43 (|has| $ (|FiniteAggregate| |#1|)) ELT)) (|remove| (($ |#1| $) 50 (AND (|has| |#1| . #11#) (|has| $ (|FiniteAggregate| |#1|))) ELT) (($ (|Mapping| #8# |#1|) . #9#) 48 (|has| $ (|FiniteAggregate| |#1|)) ELT)) (|reduce| ((|#1| (|Mapping| |#1| |#1| |#1|) $ |#1| |#1|) 74 (|has| |#1| . #12=((|BasicType|))) ELT) ((|#1| (|Mapping| |#1| |#1| |#1|) $ |#1|) 70 T ELT) ((|#1| (|Mapping| |#1| |#1| |#1|) $) 69 T ELT)) (|random| (($) 58 (|has| |#1| . #4#) ELT)) (|part?| (#3# 75 T ELT)) (|min| ((|#1| $) 59 (|has| |#1| (|OrderedSet|)) ELT)) (|members| (((|List| |#1|) $) 68 T ELT)) (|member?| ((#13=(|Boolean|) |#1| $) 73 (|has| |#1| . #12#) ELT)) (|max| ((|#1| $) 60 (|has| |#1| (|OrderedSet|)) ELT)) (|map!| (($ (|Mapping| |#1| |#1|) $) 39 T ELT)) (|map| (($ (|Mapping| |#1| |#1|) $) 26 T ELT)) (|lookup| ((#14=(|PositiveInteger|) $) 57 (|has| |#1| . #4#) ELT)) (|latex| (((|String|) $) 21 T ELT)) (|intersect| (#2# 80 T ELT)) (|inspect| ((|#1| . #15=($)) 35 T ELT)) (|insert!| (($ |#1| $) 36 T ELT)) (|index| (($ #14#) 56 (|has| |#1| . #4#) ELT)) (|hash| (((|SingleInteger|) $) 20 T ELT)) (|find| (((|Union| |#1| "failed") (|Mapping| #13# |#1|) $) 71 T ELT)) (|extract!| ((|#1| . #15#) 37 T ELT)) (|every?| ((#13# (|Mapping| #13# |#1|) . #16=($)) 66 T ELT)) (|eval| (($ $ (|List| (|Equation| |#1|))) 25 (AND (|has| |#1| (|Evalable| |#1|)) (|has| |#1| . #17=((|SetCategory|)))) ELT) (($ $ (|Equation| |#1|)) 24 (AND (|has| |#1| (|Evalable| |#1|)) (|has| |#1| . #17#)) ELT) (($ $ |#1| |#1|) 23 (AND (|has| |#1| (|Evalable| |#1|)) (|has| |#1| . #17#)) ELT) (($ $ (|List| |#1|) (|List| |#1|)) 22 (AND (|has| |#1| (|Evalable| |#1|)) (|has| |#1| . #17#)) ELT)) (|eq?| ((#18=(|Boolean|) $ $) 10 T ELT)) (|empty?| ((#18# $) 7 T ELT)) (|empty| (#10# 8 T ELT)) (|difference| (($ $ |#1|) 82 T ELT) (#2# 81 T ELT)) (|dictionary| (($) 46 T ELT) (($ (|List| |#1|)) 45 T ELT)) (|count| ((#19=(|NonNegativeInteger|) |#1| $) 72 (|has| |#1| . #12#) ELT) ((#19# (|Mapping| #13# |#1|) $) 67 T ELT)) (|copy| (($ $) 9 T ELT)) (|convert| ((#20=(|InputForm|) $) 52 (|has| |#1| (|ConvertibleTo| #20#)) ELT)) (|construct| (($ (|List| |#1|)) 47 T ELT)) (|complement| (($ $) 62 (|has| |#1| (|Finite|)) ELT)) (|coerce| (((|OutputForm|) $) 16 T ELT)) (|cardinality| (((|NonNegativeInteger|) $) 63 T ELT)) (|brace| (($ (|List| |#1|)) 77 T ELT) (#5# 76 T ELT)) (|before?| (#1# 19 T ELT)) (|bag| (($ (|List| |#1|)) 38 T ELT)) (|any?| ((#13# (|Mapping| #13# |#1|) . #16#) 65 T ELT)) (= (#1# 17 T ELT)) (|#| ((#19# $) 64 T ELT))) @@ -1235,7 +1238,7 @@ NIL ((|internalIntegrate0| (#1=((|IntegrationResult| |#2|) |#2| #2=(|Symbol|)) 36 T ELT)) (|internalIntegrate| (#1# 21 T ELT)) (|complexIntegrate| ((|#2| |#2| #2#) 26 T ELT))) (((|FunctionSpaceComplexIntegration| |#1| |#2|) (CATEGORY |package| (SIGNATURE |internalIntegrate| #1=((|IntegrationResult| |#2|) |#2| #2=(|Symbol|))) (SIGNATURE |internalIntegrate0| #1#) (SIGNATURE |complexIntegrate| (|#2| |#2| #2#))) (|Join| (|EuclideanDomain|) (|CharacteristicZero|) (|RetractableTo| #3=(|Integer|)) (|LinearlyExplicitRingOver| #3#)) (|Join| (|TranscendentalFunctionCategory|) (|AlgebraicallyClosedFunctionSpace| |#1|))) (T |FunctionSpaceComplexIntegration|)) ((|complexIntegrate| (*1 *2 *2 *3) (AND (|isDomain| *3 #1=(|Symbol|)) (|ofCategory| *4 #2=(|Join| (|EuclideanDomain|) (|CharacteristicZero|) (|RetractableTo| #3=(|Integer|)) (|LinearlyExplicitRingOver| #3#))) (|isDomain| *1 (|FunctionSpaceComplexIntegration| *4 *2)) (|ofCategory| *2 (|Join| #4=(|TranscendentalFunctionCategory|) (|AlgebraicallyClosedFunctionSpace| *4))))) (|internalIntegrate0| #5=(*1 *2 *3 *4) #6=(AND (|isDomain| *4 #1#) (|ofCategory| *5 #2#) (|isDomain| *2 (|IntegrationResult| *3)) (|isDomain| *1 (|FunctionSpaceComplexIntegration| *5 *3)) (|ofCategory| *3 (|Join| #4# (|AlgebraicallyClosedFunctionSpace| *5))))) (|internalIntegrate| #5# #6#)) -((~= #1=((#2=(|Boolean|) $ $) NIL T ELT)) (|zero?| #3=((#2# $) NIL T ELT)) (|subtractIfCan| ((#4=(|Union| $ "failed") $ $) NIL T ELT)) (|sample| (#5=($) NIL T CONST)) (|recip| ((#4# $) NIL T ELT)) (|opposite?| #1#) (|one?| #3#) (|makeSin| (#6=($ |#2| |#1|) 37 T ELT)) (|makeCos| (#6# 35 T ELT)) (|latex| (((|String|) $) NIL T ELT)) (|hash| (((|SingleInteger|) $) NIL T ELT)) (|coerce| (((|OutputForm|) $) NIL T ELT) (($ #7=(|Integer|)) NIL T ELT) (($ |#1|) NIL T ELT) (($ (|FourierComponent| |#2|)) 25 T ELT)) (|characteristic| ((#8=(|NonNegativeInteger|)) NIL T CONST)) (|before?| #1#) (|annihilate?| #1#) (|Zero| (#5# 10 T CONST)) (|One| (#5# 16 T CONST)) (= #1#) (- (($ $) NIL T ELT) (#9=($ $ $) NIL T ELT)) (+ (#9# 36 T ELT)) (** (($ $ #10=(|PositiveInteger|)) NIL T ELT) (($ $ #8#) NIL T ELT)) (* (($ #10# $) NIL T ELT) (($ #8# $) NIL T ELT) (($ #7# . #11=($)) NIL T ELT) (#9# 40 T ELT) (($ $ |#1|) NIL T ELT) (($ |#1| . #11#) NIL T ELT))) +((~= #1=((#2=(|Boolean|) $ $) NIL T ELT)) (|zero?| #3=((#2# $) NIL T ELT)) (|subtractIfCan| (((|Maybe| $) $ $) NIL T ELT)) (|sample| (#4=($) NIL T CONST)) (|recip| (((|Union| $ "failed") $) NIL T ELT)) (|opposite?| #1#) (|one?| #3#) (|makeSin| (#5=($ |#2| |#1|) 37 T ELT)) (|makeCos| (#5# 35 T ELT)) (|latex| (((|String|) $) NIL T ELT)) (|hash| (((|SingleInteger|) $) NIL T ELT)) (|coerce| (((|OutputForm|) $) NIL T ELT) (($ #6=(|Integer|)) NIL T ELT) (($ |#1|) NIL T ELT) (($ (|FourierComponent| |#2|)) 25 T ELT)) (|characteristic| ((#7=(|NonNegativeInteger|)) NIL T CONST)) (|before?| #1#) (|annihilate?| #1#) (|Zero| (#4# 10 T CONST)) (|One| (#4# 16 T CONST)) (= #1#) (- (($ $) NIL T ELT) (#8=($ $ $) NIL T ELT)) (+ (#8# 36 T ELT)) (** (($ $ #9=(|PositiveInteger|)) NIL T ELT) (($ $ #7#) NIL T ELT)) (* (($ #9# $) NIL T ELT) (($ #7# $) NIL T ELT) (($ #6# . #10=($)) NIL T ELT) (#8# 40 T ELT) (($ $ |#1|) NIL T ELT) (($ |#1| . #10#) NIL T ELT))) (((|FourierSeries| |#1| |#2|) (|Join| (|Algebra| |#1|) (CATEGORY |domain| (IF (|has| |#2| #1=(ATTRIBUTE |canonical|)) (IF (|has| |#1| #1#) #1# |%noBranch|) |%noBranch|) (SIGNATURE |coerce| ($ |#1|)) (SIGNATURE |coerce| ($ (|FourierComponent| |#2|))) (SIGNATURE |makeSin| #2=($ |#2| |#1|)) (SIGNATURE |makeCos| #2#))) (|Join| (|CommutativeRing|) (|Algebra| (|Fraction| (|Integer|)))) (|Join| (|OrderedSet|) (|AbelianGroup|))) (T |FourierSeries|)) ((|coerce| #1=(*1 *1 *2) (AND (|isDomain| *1 (|FourierSeries| *2 *3)) (|ofCategory| *2 #2=(|Join| (|CommutativeRing|) (|Algebra| (|Fraction| (|Integer|))))) (|ofCategory| *3 #3=(|Join| (|OrderedSet|) (|AbelianGroup|))))) (|coerce| #1# (AND (|isDomain| *2 (|FourierComponent| *4)) (|ofCategory| *4 #3#) (|isDomain| *1 (|FourierSeries| *3 *4)) #4=(|ofCategory| *3 #2#))) (|makeSin| #5=(*1 *1 *2 *3) #6=(AND (|isDomain| *1 (|FourierSeries| *3 *2)) #4# (|ofCategory| *2 #3#))) (|makeCos| #5# #6#)) ((|integrate| (((|Union| |#2| (|List| |#2|)) |#2| (|Symbol|)) 115 T ELT))) @@ -1250,9 +1253,9 @@ NIL ((|newReduc| (((|Void|)) 18 T ELT)) (|bringDown| (((|SparseUnivariatePolynomial| #1=(|Fraction| (|Integer|))) |#2| (|Kernel| |#2|)) 40 T ELT) ((#1# |#2|) 27 T ELT))) (((|FunctionSpaceReduce| |#1| |#2|) (CATEGORY |package| (SIGNATURE |bringDown| (#1=(|Fraction| #2=(|Integer|)) |#2|)) (SIGNATURE |bringDown| ((|SparseUnivariatePolynomial| #1#) |#2| (|Kernel| |#2|))) (SIGNATURE |newReduc| ((|Void|)))) (|Join| (|IntegralDomain|) (|RetractableTo| #2#)) (|FunctionSpace| |#1|)) (T |FunctionSpaceReduce|)) ((|newReduc| (*1 *2) (AND (|ofCategory| *3 #1=(|Join| (|IntegralDomain|) (|RetractableTo| #2=(|Integer|)))) (|isDomain| *2 (|Void|)) (|isDomain| *1 (|FunctionSpaceReduce| *3 *4)) (|ofCategory| *4 (|FunctionSpace| *3)))) (|bringDown| (*1 *2 *3 *4) (AND (|isDomain| *4 (|Kernel| *3)) (|ofCategory| *3 (|FunctionSpace| *5)) (|ofCategory| *5 #1#) (|isDomain| *2 (|SparseUnivariatePolynomial| #3=(|Fraction| #2#))) (|isDomain| *1 (|FunctionSpaceReduce| *5 *3)))) (|bringDown| (*1 *2 *3) (AND (|ofCategory| *4 #1#) (|isDomain| *2 #3#) (|isDomain| *1 (|FunctionSpaceReduce| *4 *3)) (|ofCategory| *3 (|FunctionSpace| *4))))) -((|real?| (#1=(#2=(|Boolean|) $) 33 T ELT)) (|logical?| (#1# 35 T ELT)) (|integer?| (#1# 36 T ELT)) (|doubleComplex?| (#1# 39 T ELT)) (|double?| (#1# 34 T ELT)) (|complex?| (#1# 38 T ELT)) (|coerce| (((|OutputForm|) $) 20 T ELT) (($ (|String|)) 32 T ELT) (($ #3=(|Symbol|)) 30 T ELT) ((#3# $) 24 T ELT) (((|SExpression|) $) 23 T ELT)) (|character?| (#1# 37 T ELT)) (= ((#2# $ $) 17 T ELT))) -(((|FortranScalarType|) (|Join| (|CoercibleTo| (|OutputForm|)) (CATEGORY |domain| (SIGNATURE |coerce| ($ (|String|))) (SIGNATURE |coerce| ($ #1=(|Symbol|))) (SIGNATURE |coerce| (#1# $)) (SIGNATURE |coerce| ((|SExpression|) $)) (SIGNATURE |real?| #2=(#3=(|Boolean|) $)) (SIGNATURE |double?| #2#) (SIGNATURE |integer?| #2#) (SIGNATURE |complex?| #2#) (SIGNATURE |doubleComplex?| #2#) (SIGNATURE |character?| #2#) (SIGNATURE |logical?| #2#) (SIGNATURE = (#3# $ $))))) (T |FortranScalarType|)) -((|coerce| #1=(*1 *1 *2) (AND (|isDomain| *2 (|String|)) #2=(|isDomain| *1 (|FortranScalarType|)))) (|coerce| #1# #3=(AND (|isDomain| *2 (|Symbol|)) #2#)) (|coerce| #4=(*1 *2 *1) #3#) (|coerce| #4# (AND (|isDomain| *2 (|SExpression|)) #2#)) (|real?| #4# #5=(AND (|isDomain| *2 (|Boolean|)) #2#)) (|double?| #4# #5#) (|integer?| #4# #5#) (|complex?| #4# #5#) (|doubleComplex?| #4# #5#) (|character?| #4# #5#) (|logical?| #4# #5#) (= (*1 *2 *1 *1) #5#)) +((|real?| (#1=(#2=(|Boolean|) $) 33 T ELT)) (|logical?| (#1# 35 T ELT)) (|integer?| (#1# 36 T ELT)) (|doubleComplex?| (#1# 39 T ELT)) (|double?| (#1# 34 T ELT)) (|complex?| (#1# 38 T ELT)) (|coerce| (((|OutputForm|) $) 20 T ELT) ((#3=(|Symbol|) $) 24 T ELT) (((|SExpression|) $) 23 T ELT) (($ (|String|)) 32 T ELT) (($ #3#) 30 T ELT)) (|character?| (#1# 37 T ELT)) (= ((#2# $ $) 17 T ELT))) +(((|FortranScalarType|) (|Join| (|CoercibleTo| (|OutputForm|)) (|CoercibleTo| #1=(|Symbol|)) (|CoercibleTo| (|SExpression|)) (CATEGORY |domain| (SIGNATURE |coerce| ($ (|String|))) (SIGNATURE |coerce| ($ #1#)) (SIGNATURE |real?| #2=(#3=(|Boolean|) $)) (SIGNATURE |double?| #2#) (SIGNATURE |integer?| #2#) (SIGNATURE |complex?| #2#) (SIGNATURE |doubleComplex?| #2#) (SIGNATURE |character?| #2#) (SIGNATURE |logical?| #2#) (SIGNATURE = (#3# $ $))))) (T |FortranScalarType|)) +((|coerce| #1=(*1 *1 *2) (AND (|isDomain| *2 (|String|)) #2=(|isDomain| *1 (|FortranScalarType|)))) (|coerce| #1# (AND (|isDomain| *2 (|Symbol|)) #2#)) (|real?| #3=(*1 *2 *1) #4=(AND (|isDomain| *2 (|Boolean|)) #2#)) (|double?| #3# #4#) (|integer?| #3# #4#) (|complex?| #3# #4#) (|doubleComplex?| #3# #4#) (|character?| #3# #4#) (|logical?| #3# #4#) (= (*1 *2 *1 *1) #4#)) ((|qfactor| (((|Union| (|Factored| #1=(|SparseUnivariatePolynomial| (|Fraction| (|Integer|)))) #2="failed") |#3|) 71 T ELT)) (|ffactor| (((|Factored| |#3|) |#3|) 34 T ELT)) (|anfactor| (((|Union| (|Factored| #3=(|SparseUnivariatePolynomial| #4=(|AlgebraicNumber|))) #2#) |#3|) 29 (|has| |#2| (|RetractableTo| #4#)) ELT)) (|UP2ifCan| (((|Union| (|:| |overq| #1#) (|:| |overan| #3#) (|:| |failed| (|Boolean|))) |#3|) 37 T ELT))) (((|FunctionSpaceUnivariatePolynomialFactor| |#1| |#2| |#3|) (CATEGORY |package| (SIGNATURE |ffactor| ((|Factored| |#3|) |#3|)) (SIGNATURE |qfactor| ((|Union| (|Factored| #1=(|SparseUnivariatePolynomial| (|Fraction| #2=(|Integer|)))) #3="failed") |#3|)) (SIGNATURE |UP2ifCan| ((|Union| (|:| |overq| #1#) (|:| |overan| #4=(|SparseUnivariatePolynomial| #5=(|AlgebraicNumber|))) (|:| |failed| (|Boolean|))) |#3|)) (IF (|has| |#2| (|RetractableTo| #5#)) (SIGNATURE |anfactor| ((|Union| (|Factored| #4#) #3#) |#3|)) |%noBranch|)) (|Join| (|IntegralDomain|) (|RetractableTo| #2#)) (|FunctionSpace| |#1|) (|UnivariatePolynomialCategory| |#2|)) (T |FunctionSpaceUnivariatePolynomialFactor|)) ((|anfactor| #1=(*1 *2 *3) (|partial| AND (|ofCategory| *5 (|RetractableTo| #2=(|AlgebraicNumber|))) #3=(|ofCategory| *4 (|Join| (|IntegralDomain|) (|RetractableTo| #4=(|Integer|)))) #5=(|ofCategory| *5 (|FunctionSpace| *4)) (|isDomain| *2 (|Factored| #6=(|SparseUnivariatePolynomial| #2#))) #7=(|isDomain| *1 (|FunctionSpaceUnivariatePolynomialFactor| *4 *5 *3)) #8=(|ofCategory| *3 (|UnivariatePolynomialCategory| *5)))) (|UP2ifCan| #1# (AND #3# #5# (|isDomain| *2 (|Union| (|:| |overq| #9=(|SparseUnivariatePolynomial| (|Fraction| #4#))) (|:| |overan| #6#) (|:| |failed| (|Boolean|)))) #7# #8#)) (|qfactor| #1# (|partial| AND #3# #5# (|isDomain| *2 (|Factored| #9#)) #7# #8#)) (|ffactor| #1# (AND #3# #5# (|isDomain| *2 (|Factored| *3)) #7# #8#))) @@ -1270,7 +1273,7 @@ NIL ((~= #1=(#2=((|Boolean|) $ $) NIL T ELT)) (|signature| (((|Signature|) $) 7 T ELT)) (|latex| (((|String|) $) NIL T ELT)) (|hash| (((|SingleInteger|) $) NIL T ELT)) (|coerce| (((|OutputForm|) $) 13 T ELT)) (|before?| #1#) (= (#2# 9 T ELT))) (((|FunctionDescriptor|) (|Join| (|SetCategory|) (CATEGORY |domain| (SIGNATURE |signature| ((|Signature|) $))))) (T |FunctionDescriptor|)) ((|signature| (*1 *2 *1) (AND (|isDomain| *2 (|Signature|)) (|isDomain| *1 (|FunctionDescriptor|))))) -((|useSingleFactorBound?| (#1=(#2=(|Boolean|)) 18 T ELT)) (|useSingleFactorBound| (#3=(#2# #2#) 19 T ELT)) (|useEisensteinCriterion?| (#1# 14 T ELT)) (|useEisensteinCriterion| (#3# 15 T ELT)) (|tryFunctionalDecomposition?| (#1# 16 T ELT)) (|tryFunctionalDecomposition| (#3# 17 T ELT)) (|stopMusserTrials| (#4=(#5=(|PositiveInteger|) #5#) 22 T ELT) (#6=(#5#) 21 T ELT)) (|numberOfFactors| ((#7=(|NonNegativeInteger|) #8=(|List| (|Record| (|:| |factor| |#1|) (|:| |degree| #9=(|Integer|))))) 52 T ELT)) (|musserTrials| (#4# 24 T ELT) (#6# 23 T ELT)) (|modularFactor| (((|Record| (|:| |prime| #9#) (|:| |factors| (|List| |#1|))) |#1|) 94 T ELT)) (|makeFR| ((#10=(|Factored| |#1|) #11=(|Record| (|:| |contp| #9#) (|:| |factors| (|List| (|Record| (|:| |irr| |#1|) (|:| |pow| #9#)))))) 176 T ELT)) (|henselFact| ((#11# |#1| #2#) 209 T ELT)) (|factorSquareFree| (#12=(#10# |#1| #7# #7#) 224 T ELT) (#13=(#10# |#1| #14=(|List| #7#) #7#) 221 T ELT) (#15=(#10# |#1| #14#) 223 T ELT) (#16=(#10# |#1| #7#) 222 T ELT) (#17=(#10# |#1|) 220 T ELT)) (|factorOfDegree| ((#18=(|Union| |#1| "failed") #5# |#1| #14# #7# #2#) 226 T ELT) ((#18# #5# |#1| #14# #7#) 227 T ELT) ((#18# #5# |#1| #14#) 229 T ELT) ((#18# #5# |#1| #7#) 228 T ELT) ((#18# #5# |#1|) 230 T ELT)) (|factor| (#12# 219 T ELT) (#13# 215 T ELT) (#15# 217 T ELT) (#16# 216 T ELT) (#17# 214 T ELT)) (|eisensteinIrreducible?| ((#2# |#1|) 43 T ELT)) (|degreePartition| (((|Multiset| #7#) #8#) 99 T ELT)) (|btwFact| ((#11# |#1| #2# (|Set| #7#) #7#) 213 T ELT))) +((|useSingleFactorBound?| (#1=(#2=(|Boolean|)) 18 T ELT)) (|useSingleFactorBound| (#3=(#2# #2#) 19 T ELT)) (|useEisensteinCriterion?| (#1# 14 T ELT)) (|useEisensteinCriterion| (#3# 15 T ELT)) (|tryFunctionalDecomposition?| (#1# 16 T ELT)) (|tryFunctionalDecomposition| (#3# 17 T ELT)) (|stopMusserTrials| (#4=(#5=(|PositiveInteger|) #5#) 22 T ELT) (#6=(#5#) 21 T ELT)) (|numberOfFactors| ((#7=(|NonNegativeInteger|) #8=(|List| (|Record| (|:| |factor| |#1|) (|:| |degree| #9=(|Integer|))))) 52 T ELT)) (|musserTrials| (#4# 24 T ELT) (#6# 23 T ELT)) (|modularFactor| (((|Record| (|:| |prime| #9#) (|:| |factors| (|List| |#1|))) |#1|) 94 T ELT)) (|makeFR| ((#10=(|Factored| |#1|) #11=(|Record| (|:| |contp| #9#) (|:| |factors| (|List| (|Record| (|:| |irr| |#1|) (|:| |pow| #9#)))))) 179 T ELT)) (|henselFact| ((#11# |#1| #2#) 212 T ELT)) (|factorSquareFree| (#12=(#10# |#1| #7# #7#) 227 T ELT) (#13=(#10# |#1| #14=(|List| #7#) #7#) 224 T ELT) (#15=(#10# |#1| #14#) 226 T ELT) (#16=(#10# |#1| #7#) 225 T ELT) (#17=(#10# |#1|) 223 T ELT)) (|factorOfDegree| ((#18=(|Union| |#1| "failed") #5# |#1| #14# #7# #2#) 229 T ELT) ((#18# #5# |#1| #14# #7#) 230 T ELT) ((#18# #5# |#1| #14#) 232 T ELT) ((#18# #5# |#1| #7#) 231 T ELT) ((#18# #5# |#1|) 233 T ELT)) (|factor| (#12# 222 T ELT) (#13# 218 T ELT) (#15# 220 T ELT) (#16# 219 T ELT) (#17# 217 T ELT)) (|eisensteinIrreducible?| ((#2# |#1|) 43 T ELT)) (|degreePartition| (((|Multiset| #7#) #8#) 99 T ELT)) (|btwFact| ((#11# |#1| #2# (|Set| #7#) #7#) 216 T ELT))) (((|GaloisGroupFactorizer| |#1|) (CATEGORY |package| (SIGNATURE |makeFR| (#1=(|Factored| |#1|) #2=(|Record| (|:| |contp| #3=(|Integer|)) (|:| |factors| (|List| (|Record| (|:| |irr| |#1|) (|:| |pow| #3#))))))) (SIGNATURE |degreePartition| ((|Multiset| #4=(|NonNegativeInteger|)) #5=(|List| (|Record| (|:| |factor| |#1|) (|:| |degree| #3#))))) (SIGNATURE |musserTrials| #6=(#7=(|PositiveInteger|))) (SIGNATURE |musserTrials| #8=(#7# #7#)) (SIGNATURE |stopMusserTrials| #6#) (SIGNATURE |stopMusserTrials| #8#) (SIGNATURE |numberOfFactors| (#4# #5#)) (SIGNATURE |modularFactor| ((|Record| (|:| |prime| #3#) (|:| |factors| (|List| |#1|))) |#1|)) (SIGNATURE |useSingleFactorBound?| #9=(#10=(|Boolean|))) (SIGNATURE |useSingleFactorBound| #11=(#10# #10#)) (SIGNATURE |useEisensteinCriterion?| #9#) (SIGNATURE |useEisensteinCriterion| #11#) (SIGNATURE |eisensteinIrreducible?| (#10# |#1|)) (SIGNATURE |tryFunctionalDecomposition?| #9#) (SIGNATURE |tryFunctionalDecomposition| #11#) (SIGNATURE |factor| #12=(#1# |#1|)) (SIGNATURE |factor| #13=(#1# |#1| #4#)) (SIGNATURE |factor| #14=(#1# |#1| #15=(|List| #4#))) (SIGNATURE |factor| #16=(#1# |#1| #15# #4#)) (SIGNATURE |factor| #17=(#1# |#1| #4# #4#)) (SIGNATURE |factorSquareFree| #12#) (SIGNATURE |factorSquareFree| #13#) (SIGNATURE |factorSquareFree| #14#) (SIGNATURE |factorSquareFree| #16#) (SIGNATURE |factorSquareFree| #17#) (SIGNATURE |factorOfDegree| (#18=(|Union| |#1| "failed") #7# |#1|)) (SIGNATURE |factorOfDegree| (#18# #7# |#1| #4#)) (SIGNATURE |factorOfDegree| (#18# #7# |#1| #15#)) (SIGNATURE |factorOfDegree| (#18# #7# |#1| #15# #4#)) (SIGNATURE |factorOfDegree| (#18# #7# |#1| #15# #4# #10#)) (SIGNATURE |henselFact| (#2# |#1| #10#)) (SIGNATURE |btwFact| (#2# |#1| #10# (|Set| #4#) #4#))) (|UnivariatePolynomialCategory| #3#)) (T |GaloisGroupFactorizer|)) ((|btwFact| (*1 *2 *3 *4 *5 *6) (AND #1=(|isDomain| *4 #2=(|Boolean|)) (|isDomain| *5 (|Set| #3=(|NonNegativeInteger|))) (|isDomain| *6 #3#) #4=(|isDomain| *2 (|Record| #5=(|:| |contp| #6=(|Integer|)) (|:| |factors| (|List| (|Record| (|:| |irr| *3) #7=(|:| |pow| #6#)))))) #8=(|isDomain| *1 (|GaloisGroupFactorizer| *3)) #9=(|ofCategory| *3 #10=(|UnivariatePolynomialCategory| #6#)))) (|henselFact| #11=(*1 *2 *3 *4) (AND #1# #4# #8# #9#)) (|factorOfDegree| (*1 *2 *3 *2 *4 *5 *6) (|partial| AND #12=(|isDomain| *3 #13=(|PositiveInteger|)) #14=(|isDomain| *4 (|List| #3#)) #15=(|isDomain| *5 #3#) (|isDomain| *6 #2#) #16=(|isDomain| *1 (|GaloisGroupFactorizer| *2)) #17=(|ofCategory| *2 #10#))) (|factorOfDegree| (*1 *2 *3 *2 *4 *5) (|partial| AND #12# #14# #15# #16# #17#)) (|factorOfDegree| #18=(*1 *2 *3 *2 *4) (|partial| AND #12# #14# #16# #17#)) (|factorOfDegree| #18# (|partial| AND #12# #19=(|isDomain| *4 #3#) #16# #17#)) (|factorOfDegree| (*1 *2 *3 *2) (|partial| AND #12# #16# #17#)) (|factorSquareFree| #20=(*1 *2 *3 *4 *4) #21=(AND #19# #22=(|isDomain| *2 (|Factored| *3)) #8# #9#)) (|factorSquareFree| #23=(*1 *2 *3 *4 *5) #24=(AND #14# #15# #22# #8# #9#)) (|factorSquareFree| #11# #25=(AND #14# #22# #8# #9#)) (|factorSquareFree| #11# #21#) (|factorSquareFree| #26=(*1 *2 *3) #27=(AND #22# #8# #9#)) (|factor| #20# #21#) (|factor| #23# #24#) (|factor| #11# #25#) (|factor| #11# #21#) (|factor| #26# #27#) (|tryFunctionalDecomposition| #28=(*1 *2 *2) #29=(AND (|isDomain| *2 #2#) #8# #9#)) (|tryFunctionalDecomposition?| #30=(*1 *2) #29#) (|eisensteinIrreducible?| #26# #29#) (|useEisensteinCriterion| #28# #29#) (|useEisensteinCriterion?| #30# #29#) (|useSingleFactorBound| #28# #29#) (|useSingleFactorBound?| #30# #29#) (|modularFactor| #26# (AND (|isDomain| *2 (|Record| (|:| |prime| #6#) (|:| |factors| (|List| *3)))) #8# #9#)) (|numberOfFactors| #26# (AND #31=(|isDomain| *3 (|List| (|Record| (|:| |factor| *4) (|:| |degree| #6#)))) #32=(|ofCategory| *4 #10#) (|isDomain| *2 #3#) #33=(|isDomain| *1 (|GaloisGroupFactorizer| *4)))) (|stopMusserTrials| #28# #34=(AND (|isDomain| *2 #13#) #8# #9#)) (|stopMusserTrials| #30# #34#) (|musserTrials| #28# #34#) (|musserTrials| #30# #34#) (|degreePartition| #26# (AND #31# #32# (|isDomain| *2 (|Multiset| #3#)) #33#)) (|makeFR| #26# (AND (|isDomain| *3 (|Record| #5# (|:| |factors| (|List| (|Record| (|:| |irr| *4) #7#))))) #32# (|isDomain| *2 (|Factored| *4)) #33#))) ((|singleFactorBound| (#1=(#2=(|Integer|) |#2|) 52 T ELT) ((#2# |#2| (|NonNegativeInteger|)) 51 T ELT)) (|rootBound| (#1# 64 T ELT)) (|quadraticNorm| (#3=(|#3| |#2|) 26 T ELT)) (|norm| (#4=(|#3| |#2| (|PositiveInteger|)) 15 T ELT)) (|length| (#3# 16 T ELT)) (|infinityNorm| (#3# 9 T ELT)) (|height| (#3# 10 T ELT)) (|bombieriNorm| (#4# 71 T ELT) (#3# 34 T ELT)) (|beauzamyBound| (#1# 66 T ELT))) @@ -1288,27 +1291,27 @@ NIL ((|normalForm| ((|#4| |#4| #1=(|List| |#4|)) 20 (|has| |#1| (|Field|)) ELT)) (|groebner| ((#1# #1# #2=(|String|) #2#) 46 T ELT) ((#1# #1# #2#) 45 T ELT) ((#1# #1#) 34 T ELT))) (((|GroebnerPackage| |#1| |#2| |#3| |#4|) (CATEGORY |package| (SIGNATURE |groebner| (#1=(|List| |#4|) #1#)) (SIGNATURE |groebner| (#1# #1# #2=(|String|))) (SIGNATURE |groebner| (#1# #1# #2# #2#)) (IF (|has| |#1| (|Field|)) (SIGNATURE |normalForm| (|#4| |#4| #1#)) |%noBranch|)) (|GcdDomain|) (|OrderedAbelianMonoidSup|) (|OrderedSet|) (|PolynomialCategory| |#1| |#2| |#3|)) (T |GroebnerPackage|)) ((|normalForm| #1=(*1 *2 *2 *3) (AND (|isDomain| *3 (|List| *2)) (|ofCategory| *2 #2=(|PolynomialCategory| *4 *5 *6)) (|ofCategory| *4 (|Field|)) #3=(|ofCategory| *4 #4=(|GcdDomain|)) #5=(|ofCategory| *5 #6=(|OrderedAbelianMonoidSup|)) #7=(|ofCategory| *6 #8=(|OrderedSet|)) (|isDomain| *1 (|GroebnerPackage| *4 *5 *6 *2)))) (|groebner| (*1 *2 *2 *3 *3) #9=(AND (|isDomain| *2 (|List| *7)) (|isDomain| *3 (|String|)) (|ofCategory| *7 #2#) #3# #5# #7# (|isDomain| *1 (|GroebnerPackage| *4 *5 *6 *7)))) (|groebner| #1# #9#) (|groebner| (*1 *2 *2) (AND (|isDomain| *2 (|List| *6)) (|ofCategory| *6 (|PolynomialCategory| *3 *4 *5)) (|ofCategory| *3 #4#) (|ofCategory| *4 #6#) (|ofCategory| *5 #8#) (|isDomain| *1 (|GroebnerPackage| *3 *4 *5 *6))))) -((|euclideanNormalForm| ((|#4| |#4| #1=(|List| |#4|)) 82 T ELT)) (|euclideanGroebner| ((#1# #1# #2=(|String|) #2#) 22 T ELT) ((#1# #1# #2#) 21 T ELT) ((#1# #1#) 13 T ELT))) +((|euclideanNormalForm| ((|#4| |#4| #1=(|List| |#4|)) 87 T ELT)) (|euclideanGroebner| ((#1# #1# #2=(|String|) #2#) 22 T ELT) ((#1# #1# #2#) 21 T ELT) ((#1# #1#) 13 T ELT))) (((|EuclideanGroebnerBasisPackage| |#1| |#2| |#3| |#4|) (CATEGORY |package| (SIGNATURE |euclideanNormalForm| (|#4| |#4| #1=(|List| |#4|))) (SIGNATURE |euclideanGroebner| (#1# #1#)) (SIGNATURE |euclideanGroebner| (#1# #1# #2=(|String|))) (SIGNATURE |euclideanGroebner| (#1# #1# #2# #2#))) (|EuclideanDomain|) (|OrderedAbelianMonoidSup|) (|OrderedSet|) (|PolynomialCategory| |#1| |#2| |#3|)) (T |EuclideanGroebnerBasisPackage|)) ((|euclideanGroebner| (*1 *2 *2 *3 *3) #1=(AND (|isDomain| *2 (|List| *7)) (|isDomain| *3 (|String|)) (|ofCategory| *7 #2=(|PolynomialCategory| *4 *5 *6)) #3=(|ofCategory| *4 #4=(|EuclideanDomain|)) #5=(|ofCategory| *5 #6=(|OrderedAbelianMonoidSup|)) #7=(|ofCategory| *6 #8=(|OrderedSet|)) (|isDomain| *1 (|EuclideanGroebnerBasisPackage| *4 *5 *6 *7)))) (|euclideanGroebner| #9=(*1 *2 *2 *3) #1#) (|euclideanGroebner| (*1 *2 *2) (AND (|isDomain| *2 (|List| *6)) (|ofCategory| *6 (|PolynomialCategory| *3 *4 *5)) (|ofCategory| *3 #4#) (|ofCategory| *4 #6#) (|ofCategory| *5 #8#) (|isDomain| *1 (|EuclideanGroebnerBasisPackage| *3 *4 *5 *6)))) (|euclideanNormalForm| #9# (AND (|isDomain| *3 (|List| *2)) (|ofCategory| *2 #2#) #3# #5# #7# (|isDomain| *1 (|EuclideanGroebnerBasisPackage| *4 *5 *6 *2))))) ((|groebnerFactorize| (#1=(#2=(|List| #3=(|List| |#4|)) #3# #4=(|Boolean|)) 90 T ELT) (#5=(#2# #3#) 89 T ELT) ((#2# #3# #3# #4#) 83 T ELT) ((#2# #3# #3#) 84 T ELT)) (|factorGroebnerBasis| (#1# 56 T ELT) (#5# 78 T ELT))) (((|GroebnerFactorizationPackage| |#1| |#2| |#3| |#4|) (CATEGORY |package| (SIGNATURE |factorGroebnerBasis| #1=(#2=(|List| #3=(|List| |#4|)) #3#)) (SIGNATURE |factorGroebnerBasis| #4=(#2# #3# #5=(|Boolean|))) (SIGNATURE |groebnerFactorize| (#2# #3# #3#)) (SIGNATURE |groebnerFactorize| (#2# #3# #3# #5#)) (SIGNATURE |groebnerFactorize| #1#) (SIGNATURE |groebnerFactorize| #4#)) (|Join| (|EuclideanDomain|) (|CharacteristicZero|)) (|OrderedAbelianMonoidSup|) (|OrderedSet|) (|PolynomialCategory| |#1| |#2| |#3|)) (T |GroebnerFactorizationPackage|)) ((|groebnerFactorize| #1=(*1 *2 *3 *4) #2=(AND (|isDomain| *4 (|Boolean|)) (|ofCategory| *5 #3=(|Join| (|EuclideanDomain|) (|CharacteristicZero|))) (|ofCategory| *6 #4=(|OrderedAbelianMonoidSup|)) (|ofCategory| *7 #5=(|OrderedSet|)) (|ofCategory| *8 (|PolynomialCategory| *5 *6 *7)) (|isDomain| *2 (|List| #6=(|List| *8))) (|isDomain| *1 (|GroebnerFactorizationPackage| *5 *6 *7 *8)) (|isDomain| *3 #6#))) (|groebnerFactorize| #7=(*1 *2 *3) #8=(AND (|ofCategory| *4 #3#) (|ofCategory| *5 #4#) (|ofCategory| *6 #5#) (|ofCategory| *7 (|PolynomialCategory| *4 *5 *6)) (|isDomain| *2 (|List| #9=(|List| *7))) (|isDomain| *1 (|GroebnerFactorizationPackage| *4 *5 *6 *7)) (|isDomain| *3 #9#))) (|groebnerFactorize| (*1 *2 *3 *3 *4) #2#) (|groebnerFactorize| (*1 *2 *3 *3) #8#) (|factorGroebnerBasis| #1# #2#) (|factorGroebnerBasis| #7# #8#)) -((|virtualDegree| ((#1=(|NonNegativeInteger|) |#4|) 12 T ELT)) (|updatF| ((#2=(|List| #3=(|Record| #4=(|:| |totdeg| #1#) (|:| |pol| |#4|))) |#4| #1# #2#) 39 T ELT)) (|updatD| ((#5=(|List| #6=(|Record| (|:| |lcmfij| |#2|) #4# (|:| |poli| |#4|) (|:| |polj| |#4|))) #5# #5#) 49 T ELT)) (|sPol| ((|#4| #6#) 52 T ELT)) (|redPol| (#7=(|#4| |#4| #8=(|List| |#4|)) 54 T ELT)) (|redPo| (((|Record| (|:| |poly| |#4|) (|:| |mult| |#1|)) |#4| #8#) 96 T ELT)) (|prinshINFO| ((#9=(|Void|) |#4|) 59 T ELT)) (|prinpolINFO| ((#9# #8#) 69 T ELT)) (|prindINFO| ((#10=(|Integer|) #6# |#4| |#4| #10# #10# #10#) 66 T ELT)) (|prinb| ((#9# #10#) 110 T ELT)) (|minGbasis| ((#8# #8#) 104 T ELT)) (|makeCrit| ((#6# #3# |#4| #1#) 31 T ELT)) (|lepol| ((#10# |#4|) 109 T ELT)) (|hMonic| ((|#4| |#4|) 37 T ELT)) (|gbasis| ((#8# #8# #10# #10#) 74 T ELT)) (|fprindINFO| ((#10# #6# |#4| |#4| #10# #10# #10# #10#) 123 T ELT)) (|critpOrder| ((#11=(|Boolean|) #6# #6#) 20 T ELT)) (|critT| ((#11# #6#) 78 T ELT)) (|critMonD1| ((#5# |#2| #5#) 76 T ELT)) (|critMTonD1| ((#5# #5#) 47 T ELT)) (|critM| ((#11# |#2| |#2|) 75 T ELT)) (|critBonD| ((#5# |#4| #5#) 48 T ELT)) (|critB| ((#11# |#2| |#2| |#2| |#2|) 80 T ELT)) (|credPol| (#7# 97 T ELT))) +((|virtualDegree| ((#1=(|NonNegativeInteger|) |#4|) 12 T ELT)) (|updatF| ((#2=(|List| #3=(|Record| #4=(|:| |totdeg| #1#) (|:| |pol| |#4|))) |#4| #1# #2#) 41 T ELT)) (|updatD| ((#5=(|List| #6=(|Record| (|:| |lcmfij| |#2|) #4# (|:| |poli| |#4|) (|:| |polj| |#4|))) #5# #5#) 51 T ELT)) (|sPol| ((|#4| #6#) 54 T ELT)) (|redPol| (#7=(|#4| |#4| #8=(|List| |#4|)) 56 T ELT)) (|redPo| (((|Record| (|:| |poly| |#4|) (|:| |mult| |#1|)) |#4| #8#) 101 T ELT)) (|prinshINFO| ((#9=(|Void|) |#4|) 61 T ELT)) (|prinpolINFO| ((#9# #8#) 71 T ELT)) (|prindINFO| ((#10=(|Integer|) #6# |#4| |#4| #10# #10# #10#) 68 T ELT)) (|prinb| ((#9# #10#) 115 T ELT)) (|minGbasis| ((#8# #8#) 109 T ELT)) (|makeCrit| ((#6# #3# |#4| #1#) 33 T ELT)) (|lepol| ((#10# |#4|) 114 T ELT)) (|hMonic| ((|#4| |#4|) 39 T ELT)) (|gbasis| ((#8# #8# #10# #10#) 76 T ELT)) (|fprindINFO| ((#10# #6# |#4| |#4| #10# #10# #10# #10#) 128 T ELT)) (|critpOrder| ((#11=(|Boolean|) #6# #6#) 20 T ELT)) (|critT| ((#11# #6#) 80 T ELT)) (|critMonD1| ((#5# |#2| #5#) 78 T ELT)) (|critMTonD1| ((#5# #5#) 49 T ELT)) (|critM| ((#11# |#2| |#2|) 77 T ELT)) (|critBonD| ((#5# |#4| #5#) 50 T ELT)) (|critB| ((#11# |#2| |#2| |#2| |#2|) 82 T ELT)) (|credPol| (#7# 102 T ELT))) (((|GroebnerInternalPackage| |#1| |#2| |#3| |#4|) (CATEGORY |package| (SIGNATURE |credPol| #1=(|#4| |#4| #2=(|List| |#4|))) (SIGNATURE |redPol| #1#) (SIGNATURE |gbasis| (#2# #2# #3=(|Integer|) #3#)) (SIGNATURE |critT| (#4=(|Boolean|) #5=(|Record| (|:| |lcmfij| |#2|) #6=(|:| |totdeg| #7=(|NonNegativeInteger|)) (|:| |poli| |#4|) (|:| |polj| |#4|)))) (SIGNATURE |critM| (#4# |#2| |#2|)) (SIGNATURE |critB| (#4# |#2| |#2| |#2| |#2|)) (SIGNATURE |critBonD| (#8=(|List| #5#) |#4| #8#)) (SIGNATURE |critMTonD1| (#8# #8#)) (SIGNATURE |critMonD1| (#8# |#2| #8#)) (SIGNATURE |redPo| ((|Record| (|:| |poly| |#4|) (|:| |mult| |#1|)) |#4| #2#)) (SIGNATURE |hMonic| (|#4| |#4|)) (SIGNATURE |updatF| (#9=(|List| #10=(|Record| #6# (|:| |pol| |#4|))) |#4| #7# #9#)) (SIGNATURE |sPol| (|#4| #5#)) (SIGNATURE |updatD| (#8# #8# #8#)) (SIGNATURE |minGbasis| (#2# #2#)) (SIGNATURE |lepol| (#3# |#4|)) (SIGNATURE |prinshINFO| (#11=(|Void|) |#4|)) (SIGNATURE |prindINFO| (#3# #5# |#4| |#4| #3# #3# #3#)) (SIGNATURE |fprindINFO| (#3# #5# |#4| |#4| #3# #3# #3# #3#)) (SIGNATURE |prinpolINFO| (#11# #2#)) (SIGNATURE |prinb| (#11# #3#)) (SIGNATURE |critpOrder| (#4# #5# #5#)) (SIGNATURE |makeCrit| (#5# #10# |#4| #7#)) (SIGNATURE |virtualDegree| (#7# |#4|))) (|GcdDomain|) (|OrderedAbelianMonoidSup|) (|OrderedSet|) (|PolynomialCategory| |#1| |#2| |#3|)) (T |GroebnerInternalPackage|)) ((|virtualDegree| #1=(*1 *2 *3) (AND #2=(|ofCategory| *4 #3=(|GcdDomain|)) #4=(|ofCategory| *5 #5=(|OrderedAbelianMonoidSup|)) #6=(|ofCategory| *6 #7=(|OrderedSet|)) (|isDomain| *2 #8=(|NonNegativeInteger|)) #9=(|isDomain| *1 (|GroebnerInternalPackage| *4 *5 *6 *3)) #10=(|ofCategory| *3 #11=(|PolynomialCategory| *4 *5 *6)))) (|makeCrit| (*1 *2 *3 *4 *5) (AND (|isDomain| *3 (|Record| #12=(|:| |totdeg| #8#) (|:| |pol| *4))) (|isDomain| *5 #8#) (|ofCategory| *4 (|PolynomialCategory| *6 *7 *8)) (|ofCategory| *6 #3#) (|ofCategory| *7 #5#) (|ofCategory| *8 #7#) (|isDomain| *2 (|Record| (|:| |lcmfij| *7) (|:| |totdeg| *5) #13=(|:| |poli| *4) #14=(|:| |polj| *4))) (|isDomain| *1 (|GroebnerInternalPackage| *6 *7 *8 *4)))) (|critpOrder| #15=(*1 *2 *3 *3) #16=(AND (|isDomain| *3 (|Record| #17=(|:| |lcmfij| *5) #12# (|:| |poli| *7) (|:| |polj| *7))) #4# #18=(|ofCategory| *7 #11#) #2# #6# #19=(|isDomain| *2 (|Boolean|)) #20=(|isDomain| *1 (|GroebnerInternalPackage| *4 *5 *6 *7)))) (|prinb| #1# (AND #21=(|isDomain| *3 #22=(|Integer|)) #2# #4# #6# #23=(|isDomain| *2 (|Void|)) #20# #18#)) (|prinpolINFO| #1# (AND (|isDomain| *3 #24=(|List| *7)) #18# #2# #4# #6# #23# #20#)) (|fprindINFO| (*1 *2 *3 *4 *4 *2 *2 *2 *2) #25=(AND #26=(|isDomain| *2 #22#) (|isDomain| *3 (|Record| (|:| |lcmfij| *6) #12# #13# #14#)) #27=(|ofCategory| *6 #5#) (|ofCategory| *4 #28=(|PolynomialCategory| *5 *6 *7)) #29=(|ofCategory| *5 #3#) #30=(|ofCategory| *7 #7#) (|isDomain| *1 (|GroebnerInternalPackage| *5 *6 *7 *4)))) (|prindINFO| (*1 *2 *3 *4 *4 *2 *2 *2) #25#) (|prinshINFO| #1# (AND #2# #4# #6# #23# #9# #10#)) (|lepol| #1# (AND #2# #4# #6# #26# #9# #10#)) (|minGbasis| #31=(*1 *2 *2) (AND (|isDomain| *2 (|List| *6)) #32=(|ofCategory| *6 #33=(|PolynomialCategory| *3 *4 *5)) #34=(|ofCategory| *3 #3#) #35=(|ofCategory| *4 #5#) #36=(|ofCategory| *5 #7#) #37=(|isDomain| *1 (|GroebnerInternalPackage| *3 *4 *5 *6)))) (|updatD| (*1 *2 *2 *2) #38=(AND (|isDomain| *2 (|List| (|Record| (|:| |lcmfij| *4) #12# #39=(|:| |poli| *6) #40=(|:| |polj| *6)))) #35# #32# #34# #36# #37#)) (|sPol| #1# (AND (|isDomain| *3 (|Record| #17# #12# (|:| |poli| *2) (|:| |polj| *2))) #4# #41=(|ofCategory| *2 #11#) #42=(|isDomain| *1 (|GroebnerInternalPackage| *4 *5 *6 *2)) #2# #6#)) (|updatF| (*1 *2 *3 *4 *2) (AND (|isDomain| *2 (|List| (|Record| #12# (|:| |pol| *3)))) (|isDomain| *4 #8#) #43=(|ofCategory| *3 #28#) #29# #27# #30# #44=(|isDomain| *1 (|GroebnerInternalPackage| *5 *6 *7 *3)))) (|hMonic| #31# (AND #34# #35# #36# (|isDomain| *1 (|GroebnerInternalPackage| *3 *4 *5 *2)) (|ofCategory| *2 #33#))) (|redPo| (*1 *2 *3 *4) (AND (|isDomain| *4 (|List| *3)) #43# #29# #27# #30# (|isDomain| *2 (|Record| (|:| |poly| *3) (|:| |mult| *5))) #44#)) (|critMonD1| #45=(*1 *2 *3 *2) (AND (|isDomain| *2 (|List| (|Record| (|:| |lcmfij| *3) #12# #39# #40#))) #46=(|ofCategory| *3 #5#) #47=(|ofCategory| *6 (|PolynomialCategory| *4 *3 *5)) #2# #36# #48=(|isDomain| *1 (|GroebnerInternalPackage| *4 *3 *5 *6)))) (|critMTonD1| #31# #38#) (|critBonD| #45# (AND (|isDomain| *2 (|List| (|Record| #17# #12# (|:| |poli| *3) (|:| |polj| *3)))) #4# #10# #2# #6# #9#)) (|critB| (*1 *2 *3 *3 *3 *3) #49=(AND #2# #46# #36# #19# #48# #47#)) (|critM| #15# #49#) (|critT| #1# #16#) (|gbasis| (*1 *2 *2 *3 *3) (AND (|isDomain| *2 #24#) #21# #18# #2# #4# #6# #20#)) (|redPol| #50=(*1 *2 *2 *3) #51=(AND (|isDomain| *3 (|List| *2)) #41# #2# #4# #6# #42#)) (|credPol| #50# #51#)) ((|lcm| (#1=($ $ $) 14 T ELT) (#2=($ (|List| $)) 21 T ELT)) (|gcdPolynomial| ((#3=(|SparseUnivariatePolynomial| $) #3# #3#) 45 T ELT)) (|gcd| (#1# NIL T ELT) (#2# 22 T ELT))) (((|GcdDomain&| |#1|) (CATEGORY |package| (SIGNATURE |gcdPolynomial| (#1=(|SparseUnivariatePolynomial| |#1|) #1# #1#)) (SIGNATURE |lcm| #2=(|#1| (|List| |#1|))) (SIGNATURE |lcm| #3=(|#1| |#1| |#1|)) (SIGNATURE |gcd| #2#) (SIGNATURE |gcd| #3#)) (|GcdDomain|)) (T |GcdDomain&|)) NIL -((~= (#1=((|Boolean|) $ $) 7 T ELT)) (|zero?| ((#2=(|Boolean|) $) 22 T ELT)) (|unitNormal| (((|Record| (|:| |unit| $) (|:| |canonical| $) (|:| |associate| $)) $) 55 T ELT)) (|unitCanonical| (($ $) 54 T ELT)) (|unit?| ((#3=(|Boolean|) $) 52 T ELT)) (|subtractIfCan| (((|Union| $ "failed") $ $) 26 T ELT)) (|sample| (#4=($) 23 T CONST)) (|recip| (((|Union| $ "failed") $) 42 T ELT)) (|opposite?| ((#2# $ $) 20 T ELT)) (|one?| (((|Boolean|) $) 44 T ELT)) (|lcm| (($ $ $) 60 T ELT) (($ (|List| $)) 59 T ELT)) (|latex| (((|String|) $) 11 T ELT)) (|hash| (((|SingleInteger|) $) 12 T ELT)) (|gcdPolynomial| (((|SparseUnivariatePolynomial| $) (|SparseUnivariatePolynomial| $) (|SparseUnivariatePolynomial| $)) 58 T ELT)) (|gcd| (($ $ $) 62 T ELT) (($ (|List| $)) 61 T ELT)) (|exquo| (((|Union| $ "failed") $ $) 56 T ELT)) (|coerce| (((|OutputForm|) $) 13 T ELT) (($ (|Integer|)) 41 T ELT) (($ $) 57 T ELT)) (|characteristic| (((|NonNegativeInteger|)) 40 T CONST)) (|before?| (#1# 6 T ELT)) (|associates?| ((#3# $ $) 53 T ELT)) (|annihilate?| (((|Boolean|) $ $) 33 T ELT)) (|Zero| (#4# 24 T CONST)) (|One| (($) 45 T CONST)) (= (#1# 8 T ELT)) (- (($ $) 29 T ELT) (($ $ $) 28 T ELT)) (+ (($ $ $) 18 T ELT)) (** (($ $ (|PositiveInteger|)) 35 T ELT) (($ $ (|NonNegativeInteger|)) 43 T ELT)) (* (($ (|PositiveInteger|) $) 17 T ELT) (($ (|NonNegativeInteger|) $) 21 T ELT) (($ (|Integer|) $) 30 T ELT) (($ $ $) 34 T ELT))) +((~= (#1=((|Boolean|) $ $) 7 T ELT)) (|zero?| ((#2=(|Boolean|) $) 22 T ELT)) (|unitNormal| (((|Record| (|:| |unit| $) (|:| |canonical| $) (|:| |associate| $)) $) 56 T ELT)) (|unitCanonical| (($ $) 55 T ELT)) (|unit?| ((#3=(|Boolean|) $) 53 T ELT)) (|subtractIfCan| (((|Maybe| $) $ $) 26 T ELT)) (|sample| (#4=($) 23 T CONST)) (|recip| (((|Union| $ "failed") $) 43 T ELT)) (|opposite?| ((#2# $ $) 20 T ELT)) (|one?| (((|Boolean|) $) 45 T ELT)) (|lcm| (($ $ $) 61 T ELT) (($ (|List| $)) 60 T ELT)) (|latex| (((|String|) $) 11 T ELT)) (|hash| (((|SingleInteger|) $) 12 T ELT)) (|gcdPolynomial| (((|SparseUnivariatePolynomial| $) (|SparseUnivariatePolynomial| $) (|SparseUnivariatePolynomial| $)) 59 T ELT)) (|gcd| (($ $ $) 63 T ELT) (($ (|List| $)) 62 T ELT)) (|exquo| (((|Union| $ "failed") $ $) 57 T ELT)) (|coerce| (((|OutputForm|) $) 13 T ELT) (($ (|Integer|)) 42 T ELT) (($ $) 58 T ELT)) (|characteristic| (((|NonNegativeInteger|)) 41 T CONST)) (|before?| (#1# 6 T ELT)) (|associates?| ((#3# $ $) 54 T ELT)) (|annihilate?| (((|Boolean|) $ $) 34 T ELT)) (|Zero| (#4# 24 T CONST)) (|One| (($) 46 T CONST)) (= (#1# 8 T ELT)) (- (($ $) 30 T ELT) (($ $ $) 29 T ELT)) (+ (($ $ $) 18 T ELT)) (** (($ $ (|PositiveInteger|)) 36 T ELT) (($ $ (|NonNegativeInteger|)) 44 T ELT)) (* (($ (|PositiveInteger|) $) 17 T ELT) (($ (|NonNegativeInteger|) $) 21 T ELT) (($ (|Integer|) $) 31 T ELT) (($ $ $) 35 T ELT))) (((|GcdDomain|) (|Category|)) (T |GcdDomain|)) ((|gcd| (*1 *1 *1 *1) (|ofCategory| *1 (|GcdDomain|))) (|gcd| (*1 *1 *2) (AND (|isDomain| *2 (|List| *1)) (|ofCategory| *1 (|GcdDomain|)))) (|lcm| (*1 *1 *1 *1) (|ofCategory| *1 (|GcdDomain|))) (|lcm| (*1 *1 *2) (AND (|isDomain| *2 (|List| *1)) (|ofCategory| *1 (|GcdDomain|)))) (|gcdPolynomial| (*1 *2 *2 *2) (AND (|isDomain| *2 (|SparseUnivariatePolynomial| *1)) (|ofCategory| *1 (|GcdDomain|))))) (|Join| (|IntegralDomain|) (CATEGORY |domain| (SIGNATURE |gcd| ($ $ $)) (SIGNATURE |gcd| ($ (|List| $))) (SIGNATURE |lcm| ($ $ $)) (SIGNATURE |lcm| ($ (|List| $))) (SIGNATURE |gcdPolynomial| ((|SparseUnivariatePolynomial| $) (|SparseUnivariatePolynomial| $) (|SparseUnivariatePolynomial| $))))) (((|AbelianGroup|) . T) ((|AbelianMonoid|) . T) ((|AbelianSemiGroup|) . T) ((|Algebra| $) . T) ((|BasicType|) . T) ((|BiModule| $ $) . T) ((|CancellationAbelianMonoid|) . T) ((|CoercibleFrom| (|Integer|)) . T) ((|CoercibleFrom| $) . T) ((|CoercibleTo| (|OutputForm|)) . T) ((|CommutativeRing|) . T) ((|EntireRing|) . T) ((|IntegralDomain|) . T) ((|Join|) . T) ((|LeftLinearSet| (|Integer|)) . T) ((|LeftLinearSet| $) . T) ((|LeftModule| $) . T) ((|LinearSet| $) . T) ((|Module| $) . T) ((|Monoid|) . T) ((|RightLinearSet| $) . T) ((|RightModule| $) . T) ((|Ring|) . T) ((|Rng|) . T) ((|SemiGroup|) . T) ((|SemiRing|) . T) ((|SetCategory|) . T) ((|Type|) . T)) -((~= #1=((#2=(|Boolean|) $ $) NIL T ELT)) (|zero?| ((#2# $) NIL T ELT)) (|unit| #3=((#4=(|Union| $ #5="failed")) NIL #6=(|has| #7=(|Fraction| #8=(|Polynomial| |#1|)) #9=(|IntegralDomain|)) ELT)) (|subtractIfCan| ((#4# $ $) NIL T ELT)) (|structuralConstants| ((#10=(|Vector| #11=(|Matrix| #7#)) #12=(|Vector| $)) NIL T ELT) ((#10#) NIL T ELT)) (|someBasis| (#13=(#12#) NIL T ELT)) (|sample| #14=(#15=($) NIL T CONST)) (|rightUnits| #16=(((|Union| (|Record| (|:| |particular| $) (|:| |basis| (|List| $))) #5#)) NIL T ELT)) (|rightUnit| #3#) (|rightTraceMatrix| #17=((#11# #12#) NIL T ELT) #18=((#11#) NIL T ELT)) (|rightTrace| #19=(#20=(#7# $) NIL T ELT)) (|rightRegularRepresentation| #21=((#11# $ #12#) NIL T ELT) #22=((#11# $) NIL T ELT)) (|rightRecip| #23=((#4# $) NIL #6# ELT)) (|rightRankPolynomial| #24=(((|SparseUnivariatePolynomial| #25=(|Polynomial| #7#))) NIL (|has| #7# (|Field|)) ELT) (#26=(#27=(|SparseUnivariatePolynomial| #7#)) 89 #28=(|has| |#1| #9#) ELT)) (|rightPower| #29=(($ $ #30=(|PositiveInteger|)) NIL T ELT)) (|rightNorm| #19#) (|rightMinimalPolynomial| (#31=(#27# $) 87 #6# ELT)) (|rightDiscriminant| #32=((#7# #12#) NIL T ELT) #33=(#34=(#7#) NIL T ELT)) (|rightCharacteristicPolynomial| #35=(#31# NIL T ELT)) (|rightAlternative?| #36=((#2#) NIL T ELT)) (|represents| (($ #37=(|Vector| #7#) #12#) 111 T ELT) #38=(#39=($ #37#) NIL T ELT)) (|recip| #23#) (|rank| ((#30#) NIL T ELT)) (|powerAssociative?| #36#) (|plenaryPower| #29#) (|opposite?| #1#) (|noncommutativeJordanAlgebra?| #36#) (|lieAlgebra?| #36#) (|lieAdmissible?| #36#) (|leftUnits| #16#) (|leftUnit| #3#) (|leftTraceMatrix| #17# #18#) (|leftTrace| #19#) (|leftRegularRepresentation| #21# #22#) (|leftRecip| #23#) (|leftRankPolynomial| #24# (#26# 88 #28# ELT)) (|leftPower| #29#) (|leftNorm| #19#) (|leftMinimalPolynomial| (#31# 84 #6# ELT)) (|leftDiscriminant| #32# #33#) (|leftCharacteristicPolynomial| #35#) (|leftAlternative?| #36#) (|latex| (((|String|) $) NIL T ELT)) (|jordanAlgebra?| #36#) (|jordanAdmissible?| #36#) (|jacobiIdentity?| #36#) (|hash| (((|SingleInteger|) $) NIL T ELT)) (|genericRightTraceForm| (#40=(#7# $ $) 75 #28# ELT)) (|genericRightTrace| (#20# 74 #28# ELT)) (|genericRightNorm| (#20# 101 #28# ELT)) (|genericRightMinimalPolynomial| (#31# 93 #28# ELT)) (|genericRightDiscriminant| (#34# 76 #28# ELT)) (|genericLeftTraceForm| (#40# 64 #28# ELT)) (|genericLeftTrace| (#20# 63 #28# ELT)) (|genericLeftNorm| (#20# 100 #28# ELT)) (|genericLeftMinimalPolynomial| (#31# 92 #28# ELT)) (|genericLeftDiscriminant| (#34# 73 #28# ELT)) (|generic| (#15# 107 T ELT) (($ #41=(|Symbol|)) 115 T ELT) (($ #42=(|Vector| #41#)) 114 T ELT) (($ #12#) 102 T ELT) (($ #41# #12#) 113 T ELT) (($ #42# #12#) 112 T ELT)) (|flexible?| #36#) (|elt| ((#7# $ #43=(|Integer|)) NIL T ELT)) (|coordinates| ((#37# $ #12#) 104 T ELT) ((#11# #12# #12#) NIL T ELT) (#44=(#37# $) 44 T ELT) #17#) (|convert| (#44# NIL T ELT) (#39# 41 T ELT)) (|conditionsForIdempotents| ((#45=(|List| #25#) #12#) NIL T ELT) ((#45#) NIL T ELT) ((#46=(|List| #8#) #12#) 105 #28# ELT) ((#46#) 106 #28# ELT)) (|commutator| #47=(#48=($ $ $) NIL T ELT)) (|commutative?| #36#) (|coerce| (((|OutputForm|) $) NIL T ELT) #38#) (|before?| #1#) (|basis| (#13# 66 T ELT)) (|associatorDependence| (((|List| #37#)) NIL #6# ELT)) (|associator| (($ $ $ $) NIL T ELT)) (|associative?| #36#) (|apply| (($ #11# $) NIL T ELT)) (|antiCommutator| #47#) (|antiCommutative?| #36#) (|antiAssociative?| #36#) (|alternative?| #36#) (|Zero| #14#) (= #1#) (- (($ $) NIL T ELT) (#48# 103 T ELT)) (+ #47#) (** #29#) (* (($ #30# $) NIL T ELT) (($ (|NonNegativeInteger|) $) NIL T ELT) (($ #43# . #49=($)) NIL T ELT) (#48# 62 T ELT) (($ $ #7#) NIL T ELT) (($ #7# . #49#) NIL T ELT) (($ (|SquareMatrix| |#2| #7#) . #49#) NIL T ELT))) +((~= #1=((#2=(|Boolean|) $ $) NIL T ELT)) (|zero?| ((#2# $) NIL T ELT)) (|unit| #3=((#4=(|Union| $ #5="failed")) NIL #6=(|has| #7=(|Fraction| #8=(|Polynomial| |#1|)) #9=(|IntegralDomain|)) ELT)) (|subtractIfCan| (((|Maybe| $) $ $) NIL T ELT)) (|structuralConstants| ((#10=(|Vector| #11=(|Matrix| #7#)) #12=(|Vector| $)) NIL T ELT) ((#10#) NIL T ELT)) (|someBasis| (#13=(#12#) NIL T ELT)) (|sample| #14=(#15=($) NIL T CONST)) (|rightUnits| #16=(((|Union| (|Record| (|:| |particular| $) (|:| |basis| (|List| $))) #5#)) NIL T ELT)) (|rightUnit| #3#) (|rightTraceMatrix| #17=((#11# #12#) NIL T ELT) #18=((#11#) NIL T ELT)) (|rightTrace| #19=(#20=(#7# $) NIL T ELT)) (|rightRegularRepresentation| #21=((#11# $ #12#) NIL T ELT) #22=((#11# $) NIL T ELT)) (|rightRecip| #23=((#4# $) NIL #6# ELT)) (|rightRankPolynomial| #24=(((|SparseUnivariatePolynomial| #25=(|Polynomial| #7#))) NIL (|has| #7# (|Field|)) ELT) (#26=(#27=(|SparseUnivariatePolynomial| #7#)) 89 #28=(|has| |#1| #9#) ELT)) (|rightPower| #29=(($ $ #30=(|PositiveInteger|)) NIL T ELT)) (|rightNorm| #19#) (|rightMinimalPolynomial| (#31=(#27# $) 87 #6# ELT)) (|rightDiscriminant| #32=((#7# #12#) NIL T ELT) #33=(#34=(#7#) NIL T ELT)) (|rightCharacteristicPolynomial| #35=(#31# NIL T ELT)) (|rightAlternative?| #36=((#2#) NIL T ELT)) (|represents| (($ #37=(|Vector| #7#) #12#) 111 T ELT) #38=(#39=($ #37#) NIL T ELT)) (|recip| #23#) (|rank| ((#30#) NIL T ELT)) (|powerAssociative?| #36#) (|plenaryPower| #29#) (|opposite?| #1#) (|noncommutativeJordanAlgebra?| #36#) (|lieAlgebra?| #36#) (|lieAdmissible?| #36#) (|leftUnits| #16#) (|leftUnit| #3#) (|leftTraceMatrix| #17# #18#) (|leftTrace| #19#) (|leftRegularRepresentation| #21# #22#) (|leftRecip| #23#) (|leftRankPolynomial| #24# (#26# 88 #28# ELT)) (|leftPower| #29#) (|leftNorm| #19#) (|leftMinimalPolynomial| (#31# 84 #6# ELT)) (|leftDiscriminant| #32# #33#) (|leftCharacteristicPolynomial| #35#) (|leftAlternative?| #36#) (|latex| (((|String|) $) NIL T ELT)) (|jordanAlgebra?| #36#) (|jordanAdmissible?| #36#) (|jacobiIdentity?| #36#) (|hash| (((|SingleInteger|) $) NIL T ELT)) (|genericRightTraceForm| (#40=(#7# $ $) 75 #28# ELT)) (|genericRightTrace| (#20# 74 #28# ELT)) (|genericRightNorm| (#20# 101 #28# ELT)) (|genericRightMinimalPolynomial| (#31# 93 #28# ELT)) (|genericRightDiscriminant| (#34# 76 #28# ELT)) (|genericLeftTraceForm| (#40# 64 #28# ELT)) (|genericLeftTrace| (#20# 63 #28# ELT)) (|genericLeftNorm| (#20# 100 #28# ELT)) (|genericLeftMinimalPolynomial| (#31# 92 #28# ELT)) (|genericLeftDiscriminant| (#34# 73 #28# ELT)) (|generic| (#15# 107 T ELT) (($ #41=(|Symbol|)) 115 T ELT) (($ #42=(|Vector| #41#)) 114 T ELT) (($ #12#) 102 T ELT) (($ #41# #12#) 113 T ELT) (($ #42# #12#) 112 T ELT)) (|flexible?| #36#) (|elt| ((#7# $ #43=(|Integer|)) NIL T ELT)) (|coordinates| ((#37# $ #12#) 104 T ELT) ((#11# #12# #12#) NIL T ELT) (#44=(#37# $) 44 T ELT) #17#) (|convert| (#44# NIL T ELT) (#39# 41 T ELT)) (|conditionsForIdempotents| ((#45=(|List| #25#) #12#) NIL T ELT) ((#45#) NIL T ELT) ((#46=(|List| #8#) #12#) 105 #28# ELT) ((#46#) 106 #28# ELT)) (|commutator| #47=(#48=($ $ $) NIL T ELT)) (|commutative?| #36#) (|coerce| (((|OutputForm|) $) NIL T ELT) #38#) (|before?| #1#) (|basis| (#13# 66 T ELT)) (|associatorDependence| (((|List| #37#)) NIL #6# ELT)) (|associator| (($ $ $ $) NIL T ELT)) (|associative?| #36#) (|apply| (($ #11# $) NIL T ELT)) (|antiCommutator| #47#) (|antiCommutative?| #36#) (|antiAssociative?| #36#) (|alternative?| #36#) (|Zero| #14#) (= #1#) (- (($ $) NIL T ELT) (#48# 103 T ELT)) (+ #47#) (** #29#) (* (($ #30# $) NIL T ELT) (($ (|NonNegativeInteger|) $) NIL T ELT) (($ #43# . #49=($)) NIL T ELT) (#48# 62 T ELT) (($ $ #7#) NIL T ELT) (($ #7# . #49#) NIL T ELT) (($ (|SquareMatrix| |#2| #7#) . #49#) NIL T ELT))) (((|GenericNonAssociativeAlgebra| |#1| |#2| |#3| |#4|) (|Join| (|FramedNonAssociativeAlgebra| #1=(|Fraction| #2=(|Polynomial| |#1|))) (|LeftModule| (|SquareMatrix| |#2| #1#)) (CATEGORY |domain| (SIGNATURE |coerce| ($ (|Vector| #1#))) (SIGNATURE |leftUnits| #3=((|Union| (|Record| (|:| |particular| $) (|:| |basis| (|List| $))) "failed"))) (SIGNATURE |rightUnits| #3#) (SIGNATURE |generic| ($)) (SIGNATURE |generic| ($ #4=(|Symbol|))) (SIGNATURE |generic| ($ #5=(|Vector| #4#))) (SIGNATURE |generic| ($ #6=(|Vector| $))) (SIGNATURE |generic| ($ #4# #6#)) (SIGNATURE |generic| ($ #5# #6#)) (IF (|has| |#1| (|IntegralDomain|)) (PROGN (SIGNATURE |leftRankPolynomial| #7=(#8=(|SparseUnivariatePolynomial| #1#))) (SIGNATURE |genericLeftMinimalPolynomial| #9=(#8# $)) (SIGNATURE |genericLeftTrace| #10=(#1# $)) (SIGNATURE |genericLeftNorm| #10#) (SIGNATURE |rightRankPolynomial| #7#) (SIGNATURE |genericRightMinimalPolynomial| #9#) (SIGNATURE |genericRightTrace| #10#) (SIGNATURE |genericRightNorm| #10#) (SIGNATURE |genericLeftTraceForm| #11=(#1# $ $)) (SIGNATURE |genericLeftDiscriminant| #12=(#1#)) (SIGNATURE |genericRightTraceForm| #11#) (SIGNATURE |genericRightDiscriminant| #12#) (SIGNATURE |conditionsForIdempotents| (#13=(|List| #2#) #6#)) (SIGNATURE |conditionsForIdempotents| (#13#))) |%noBranch|))) (|CommutativeRing|) (|PositiveInteger|) (|List| #4#) (|Vector| (|Matrix| |#1|))) (T |GenericNonAssociativeAlgebra|)) ((|coerce| #1=(*1 *1 *2) (AND (|isDomain| *2 (|Vector| #2=(|Fraction| #3=(|Polynomial| *3)))) #4=(|ofCategory| *3 #5=(|CommutativeRing|)) #6=(|ofType| *6 (|Vector| (|Matrix| *3))) #7=(|isDomain| *1 #8=(|GenericNonAssociativeAlgebra| *3 *4 *5 *6)) #9=(|ofType| *4 #10=(|PositiveInteger|)) #11=(|ofType| *5 #12=(|List| #13=(|Symbol|))))) (|leftUnits| #14=(*1 *2) #15=(|partial| AND (|isDomain| *2 (|Record| (|:| |particular| #8#) (|:| |basis| (|List| #8#)))) #7# #4# #9# #11# #6#)) (|rightUnits| #14# #15#) (|generic| (*1 *1) (AND (|isDomain| *1 (|GenericNonAssociativeAlgebra| *2 *3 *4 *5)) (|ofCategory| *2 #5#) (|ofType| *3 #10#) (|ofType| *4 #12#) (|ofType| *5 (|Vector| (|Matrix| *2))))) (|generic| #1# (AND #16=(|isDomain| *2 #13#) #7# #4# #9# (|ofType| *5 #17=(|List| *2)) #6#)) (|generic| #1# (AND #18=(|isDomain| *2 (|Vector| #13#)) #7# #4# #9# #11# #6#)) (|generic| #1# (AND (|isDomain| *2 (|Vector| #8#)) #7# #4# #9# #11# #6#)) (|generic| #19=(*1 *1 *2 *3) (AND #16# #20=(|isDomain| *3 (|Vector| #21=(|GenericNonAssociativeAlgebra| *4 *5 *6 *7))) #22=(|isDomain| *1 #21#) #23=(|ofCategory| *4 #5#) #24=(|ofType| *5 #10#) (|ofType| *6 #17#) #25=(|ofType| *7 (|Vector| (|Matrix| *4))))) (|generic| #19# (AND #18# #20# #22# #23# #24# #26=(|ofType| *6 #12#) #25#)) (|leftRankPolynomial| #14# #27=(AND (|isDomain| *2 (|SparseUnivariatePolynomial| #2#)) #7# #28=(|ofCategory| *3 #29=(|IntegralDomain|)) #4# #9# #11# #6#)) (|genericLeftMinimalPolynomial| #30=(*1 *2 *1) #27#) (|genericLeftTrace| #30# #31=(AND (|isDomain| *2 #2#) #7# #28# #4# #9# #11# #6#)) (|genericLeftNorm| #30# #31#) (|rightRankPolynomial| #14# #27#) (|genericRightMinimalPolynomial| #30# #27#) (|genericRightTrace| #30# #31#) (|genericRightNorm| #30# #31#) (|genericLeftTraceForm| #32=(*1 *2 *1 *1) #31#) (|genericLeftDiscriminant| #14# #31#) (|genericRightTraceForm| #32# #31#) (|genericRightDiscriminant| #14# #31#) (|conditionsForIdempotents| (*1 *2 *3) (AND #20# (|isDomain| *2 (|List| (|Polynomial| *4))) #22# (|ofCategory| *4 #29#) #23# #24# #26# #25#)) (|conditionsForIdempotents| #14# (AND (|isDomain| *2 (|List| #3#)) #7# #28# #4# #9# #11# #6#))) -((~= #1=(#2=(#3=(|Boolean|) $ $) NIL T ELT)) (|zero?| (#4=(#3# $) 19 T ELT)) (|variables| ((#5=(|List| #6=(|OrderedVariableList| |#1|)) $) 88 T ELT)) (|univariate| ((#7=(|SparseUnivariatePolynomial| $) $ #6#) 53 T ELT) ((#8=(|SparseUnivariatePolynomial| |#2|) $) 140 T ELT)) (|unitNormal| (((|Record| (|:| |unit| $) (|:| |canonical| $) (|:| |associate| $)) $) NIL #9=(|has| |#2| (|IntegralDomain|)) ELT)) (|unitCanonical| #10=(#11=($ $) NIL #9# ELT)) (|unit?| (#4# NIL #9# ELT)) (|totalDegree| (#12=(#13=(|NonNegativeInteger|) $) 28 T ELT) ((#13# $ #5#) NIL T ELT)) (|subtractIfCan| (#14=(#15=(|Union| $ #16="failed") $ $) NIL T ELT)) (|squareFreePolynomial| #17=(((|Factored| #7#) #7#) NIL #18=(|has| |#2| (|PolynomialFactorizationExplicit|)) ELT)) (|squareFreePart| #19=(#11# NIL #20=(|has| |#2| (|GcdDomain|)) ELT)) (|squareFree| (#21=((|Factored| $) $) NIL #20# ELT)) (|solveLinearPolynomialEquation| (((|Union| #22=(|List| #7#) #16#) #22# #7#) NIL #18# ELT)) (|sample| (#23=($) NIL T CONST)) (|retractIfCan| (((|Union| |#2| . #24=(#16#)) $) 51 T ELT) (((|Union| #25=(|Fraction| #26=(|Integer|)) . #24#) . #27=($)) NIL #28=(|has| |#2| (|RetractableTo| #25#)) ELT) (((|Union| #26# . #24#) . #27#) NIL #29=(|has| |#2| (|RetractableTo| #26#)) ELT) (#30=((|Union| #6# . #24#) . #27#) NIL T ELT)) (|retract| (#31=(|#2| $) 49 T ELT) ((#25# . #32=($)) NIL #28# ELT) ((#26# . #32#) NIL #29# ELT) ((#6# . #32#) NIL T ELT)) (|resultant| (($ $ $ #6#) NIL #33=(|has| |#2| (|CommutativeRing|)) ELT)) (|reorder| (($ $ (|List| #26#)) 95 T ELT)) (|reductum| (#11# 81 T ELT)) (|reducedSystem| ((#34=(|Matrix| #26#) . #35=(#36=(|Matrix| $))) NIL #37=(|has| |#2| (|LinearlyExplicitRingOver| #26#)) ELT) ((#38=(|Record| (|:| |mat| #34#) (|:| |vec| (|Vector| #26#))) . #39=(#36# #40=(|Vector| $))) NIL #37# ELT) ((#41=(|Record| (|:| |mat| #42=(|Matrix| |#2|)) (|:| |vec| (|Vector| |#2|))) . #39#) NIL T ELT) ((#42# . #35#) NIL T ELT)) (|recip| ((#15# $) NIL T ELT)) (|primitivePart| #19# #43=(#44=($ $ #6#) NIL #20# ELT)) (|primitiveMonomials| #45=((#46=(|List| $) $) NIL T ELT)) (|prime?| (#4# NIL #18# ELT)) (|pomopo!| (($ $ |#2| |#3| $) NIL T ELT)) (|patternMatch| ((#47=(|PatternMatchResult| #48=(|Float|) . #49=($)) $ #50=(|Pattern| #48#) #47#) NIL (AND (|has| #6# #51=(|PatternMatchable| #48#)) (|has| |#2| #51#)) ELT) ((#52=(|PatternMatchResult| #26# . #49#) $ #53=(|Pattern| #26#) #52#) NIL (AND (|has| #6# #54=(|PatternMatchable| #26#)) (|has| |#2| #54#)) ELT)) (|opposite?| #1#) (|one?| (#4# NIL T ELT)) (|numberOfMonomials| (#12# 66 T ELT)) (|multivariate| (($ #8# #6#) 145 T ELT) (($ #7# #6#) 59 T ELT)) (|monomials| #45#) (|monomial?| (#4# 69 T ELT)) (|monomial| (($ |#2| |#3|) 36 T ELT) (#55=($ $ #6# #13#) 38 T ELT) #56=(($ $ #5# #57=(|List| #13#)) NIL T ELT)) (|monicDivide| (((|Record| (|:| |quotient| $) (|:| |remainder| $)) $ $ #6#) NIL T ELT)) (|minimumDegree| (#58=(|#3| $) NIL T ELT) (#59=(#13# $ #6#) 57 T ELT) (#60=(#57# $ #5#) 64 T ELT)) (|mapExponents| (($ (|Mapping| |#3| |#3|) $) NIL T ELT)) (|map| (($ (|Mapping| |#2| |#2|) $) NIL T ELT)) (|mainVariable| (#30# 46 T ELT)) (|leftReducedSystem| ((#34# . #61=(#40#)) NIL #37# ELT) ((#38# . #62=(#40# $)) NIL #37# ELT) ((#41# . #62#) NIL T ELT) ((#42# . #61#) NIL T ELT)) (|leadingMonomial| #63=(#11# NIL T ELT)) (|leadingCoefficient| (#31# 48 T ELT)) (|lcm| #64=(($ #46#) NIL #20# ELT) (#65=($ $ $) NIL #20# ELT)) (|latex| (((|String|) $) NIL T ELT)) (|isTimes| #66=(((|Union| #46# #16#) $) NIL T ELT)) (|isPlus| #66#) (|isExpt| (((|Union| (|Record| (|:| |var| #6#) (|:| |exponent| #13#)) #16#) $) NIL T ELT)) (|hash| (((|SingleInteger|) $) NIL T ELT)) (|ground?| (#4# 47 T ELT)) (|ground| (#31# 138 T ELT)) (|gcdPolynomial| ((#7# #7# #7#) NIL #20# ELT)) (|gcd| #64# (#65# 151 #20# ELT)) (|factorSquareFreePolynomial| #17#) (|factorPolynomial| #17#) (|factor| (#21# NIL #18# ELT)) (|exquo| ((#15# $ |#2|) NIL #9# ELT) (#14# NIL #9# ELT)) (|eval| (($ $ (|List| #67=(|Equation| $))) NIL T ELT) (($ $ #67#) NIL T ELT) (($ $ $ $) NIL T ELT) (($ $ #46# #46#) NIL T ELT) (($ $ #6# |#2|) 102 T ELT) (($ $ #5# #68=(|List| |#2|)) 108 T ELT) (($ $ #6# $) 100 T ELT) (($ $ #5# #46#) 126 T ELT)) (|discriminant| (#44# NIL #33# ELT)) (|differentiate| #56# #69=(#55# NIL T ELT) #70=(($ $ #5#) NIL T ELT) (#44# 60 T ELT)) (|degree| (#58# 80 T ELT) (#59# 43 T ELT) (#60# 63 T ELT)) (|convert| ((#50# . #71=($)) NIL (AND (|has| #6# #72=(|ConvertibleTo| #50#)) (|has| |#2| #72#)) ELT) ((#53# . #71#) NIL (AND (|has| #6# #73=(|ConvertibleTo| #53#)) (|has| |#2| #73#)) ELT) ((#74=(|InputForm|) . #71#) NIL (AND (|has| #6# #75=(|ConvertibleTo| #74#)) (|has| |#2| #75#)) ELT)) (|content| (#31# 147 #20# ELT) #43#) (|conditionP| (((|Union| #40# #16#) #36#) NIL #76=(AND (|has| $ #77=(|CharacteristicNonZero|)) #18#) ELT)) (|coerce| (((|OutputForm|) $) 175 T ELT) (($ #26#) NIL T ELT) (($ |#2|) 101 T ELT) (($ #6#) 40 T ELT) (($ #25#) NIL (OR #78=(|has| |#2| (|Algebra| #25#)) #28#) ELT) #10#) (|coefficients| ((#68# $) NIL T ELT)) (|coefficient| ((|#2| $ |#3|) NIL T ELT) #69# #56#) (|charthRoot| (((|Maybe| $) $) NIL (OR #76# (|has| |#2| #77#)) ELT)) (|characteristic| ((#13#) NIL T CONST)) (|binomThmExpt| (($ $ $ #13#) NIL #33# ELT)) (|before?| #1#) (|associates?| (#2# NIL #9# ELT)) (|annihilate?| #1#) (|Zero| (#23# 24 T CONST)) (|One| (#23# 32 T CONST)) (D #56# #69# #70# (#44# NIL T ELT)) (= #1#) (/ (#79=($ $ |#2|) 77 (|has| |#2| (|Field|)) ELT)) (- #63# (#65# NIL T ELT)) (+ (#65# 133 T ELT)) (** (($ $ #80=(|PositiveInteger|)) NIL T ELT) (($ $ #13#) 131 T ELT)) (* (($ #80# $) NIL T ELT) (($ #13# $) NIL T ELT) (($ #26# . #81=($)) NIL T ELT) (#65# 37 T ELT) (($ $ #25#) NIL #78# ELT) (($ #25# . #81#) NIL #78# ELT) (($ |#2| . #81#) 76 T ELT) (#79# NIL T ELT))) +((~= #1=(#2=(#3=(|Boolean|) $ $) NIL T ELT)) (|zero?| (#4=(#3# $) 19 T ELT)) (|variables| ((#5=(|List| #6=(|OrderedVariableList| |#1|)) $) 88 T ELT)) (|univariate| ((#7=(|SparseUnivariatePolynomial| $) $ #6#) 53 T ELT) ((#8=(|SparseUnivariatePolynomial| |#2|) $) 140 T ELT)) (|unitNormal| (((|Record| (|:| |unit| $) (|:| |canonical| $) (|:| |associate| $)) $) NIL #9=(|has| |#2| (|IntegralDomain|)) ELT)) (|unitCanonical| #10=(#11=($ $) NIL #9# ELT)) (|unit?| (#4# NIL #9# ELT)) (|totalDegree| (#12=(#13=(|NonNegativeInteger|) $) 28 T ELT) ((#13# $ #5#) NIL T ELT)) (|subtractIfCan| ((#14=(|Maybe| $) $ $) NIL T ELT)) (|squareFreePolynomial| #15=(((|Factored| #7#) #7#) NIL #16=(|has| |#2| (|PolynomialFactorizationExplicit|)) ELT)) (|squareFreePart| #17=(#11# NIL #18=(|has| |#2| (|GcdDomain|)) ELT)) (|squareFree| (#19=((|Factored| $) $) NIL #18# ELT)) (|solveLinearPolynomialEquation| (((|Union| #20=(|List| #7#) #21="failed") #20# #7#) NIL #16# ELT)) (|sample| (#22=($) NIL T CONST)) (|retractIfCan| (((|Union| |#2| . #23=(#21#)) $) 51 T ELT) (((|Union| #24=(|Fraction| #25=(|Integer|)) . #23#) . #26=($)) NIL #27=(|has| |#2| (|RetractableTo| #24#)) ELT) (((|Union| #25# . #23#) . #26#) NIL #28=(|has| |#2| (|RetractableTo| #25#)) ELT) (#29=((|Union| #6# . #23#) . #26#) NIL T ELT)) (|retract| (#30=(|#2| $) 49 T ELT) ((#24# . #31=($)) NIL #27# ELT) ((#25# . #31#) NIL #28# ELT) ((#6# . #31#) NIL T ELT)) (|resultant| (($ $ $ #6#) NIL #32=(|has| |#2| (|CommutativeRing|)) ELT)) (|reorder| (($ $ (|List| #25#)) 95 T ELT)) (|reductum| (#11# 81 T ELT)) (|reducedSystem| ((#33=(|Matrix| #25#) . #34=(#35=(|Matrix| $))) NIL #36=(|has| |#2| (|LinearlyExplicitRingOver| #25#)) ELT) ((#37=(|Record| (|:| |mat| #33#) (|:| |vec| (|Vector| #25#))) . #38=(#35# #39=(|Vector| $))) NIL #36# ELT) ((#40=(|Record| (|:| |mat| #41=(|Matrix| |#2|)) (|:| |vec| (|Vector| |#2|))) . #38#) NIL T ELT) ((#41# . #34#) NIL T ELT)) (|recip| ((#42=(|Union| $ #21#) $) NIL T ELT)) (|primitivePart| #17# #43=(#44=($ $ #6#) NIL #18# ELT)) (|primitiveMonomials| #45=((#46=(|List| $) $) NIL T ELT)) (|prime?| (#4# NIL #16# ELT)) (|pomopo!| (($ $ |#2| |#3| $) NIL T ELT)) (|patternMatch| ((#47=(|PatternMatchResult| #48=(|Float|) . #49=($)) $ #50=(|Pattern| #48#) #47#) NIL (AND (|has| #6# #51=(|PatternMatchable| #48#)) (|has| |#2| #51#)) ELT) ((#52=(|PatternMatchResult| #25# . #49#) $ #53=(|Pattern| #25#) #52#) NIL (AND (|has| #6# #54=(|PatternMatchable| #25#)) (|has| |#2| #54#)) ELT)) (|opposite?| #1#) (|one?| (#4# NIL T ELT)) (|numberOfMonomials| (#12# 66 T ELT)) (|multivariate| (($ #8# #6#) 145 T ELT) (($ #7# #6#) 59 T ELT)) (|monomials| #45#) (|monomial?| (#4# 69 T ELT)) (|monomial| (($ |#2| |#3|) 36 T ELT) (#55=($ $ #6# #13#) 38 T ELT) #56=(($ $ #5# #57=(|List| #13#)) NIL T ELT)) (|monicDivide| (((|Record| (|:| |quotient| $) (|:| |remainder| $)) $ $ #6#) NIL T ELT)) (|minimumDegree| (#58=(|#3| $) NIL T ELT) (#59=(#13# $ #6#) 57 T ELT) (#60=(#57# $ #5#) 64 T ELT)) (|mapExponents| (($ (|Mapping| |#3| |#3|) $) NIL T ELT)) (|map| (($ (|Mapping| |#2| |#2|) $) NIL T ELT)) (|mainVariable| (#29# 46 T ELT)) (|leftReducedSystem| ((#33# . #61=(#39#)) NIL #36# ELT) ((#37# . #62=(#39# $)) NIL #36# ELT) ((#40# . #62#) NIL T ELT) ((#41# . #61#) NIL T ELT)) (|leadingMonomial| #63=(#11# NIL T ELT)) (|leadingCoefficient| (#30# 48 T ELT)) (|lcm| #64=(($ #46#) NIL #18# ELT) (#65=($ $ $) NIL #18# ELT)) (|latex| (((|String|) $) NIL T ELT)) (|isTimes| #66=(((|Union| #46# #21#) $) NIL T ELT)) (|isPlus| #66#) (|isExpt| (((|Union| (|Record| (|:| |var| #6#) (|:| |exponent| #13#)) #21#) $) NIL T ELT)) (|hash| (((|SingleInteger|) $) NIL T ELT)) (|ground?| (#4# 47 T ELT)) (|ground| (#30# 138 T ELT)) (|gcdPolynomial| ((#7# #7# #7#) NIL #18# ELT)) (|gcd| #64# (#65# 151 #18# ELT)) (|factorSquareFreePolynomial| #15#) (|factorPolynomial| #15#) (|factor| (#19# NIL #16# ELT)) (|exquo| ((#42# $ |#2|) NIL #9# ELT) ((#42# $ $) NIL #9# ELT)) (|eval| (($ $ (|List| #67=(|Equation| $))) NIL T ELT) (($ $ #67#) NIL T ELT) (($ $ $ $) NIL T ELT) (($ $ #46# #46#) NIL T ELT) (($ $ #6# |#2|) 102 T ELT) (($ $ #5# #68=(|List| |#2|)) 108 T ELT) (($ $ #6# $) 100 T ELT) (($ $ #5# #46#) 126 T ELT)) (|discriminant| (#44# NIL #32# ELT)) (|differentiate| #56# #69=(#55# NIL T ELT) #70=(($ $ #5#) NIL T ELT) (#44# 60 T ELT)) (|degree| (#58# 80 T ELT) (#59# 43 T ELT) (#60# 63 T ELT)) (|convert| ((#50# . #71=($)) NIL (AND (|has| #6# #72=(|ConvertibleTo| #50#)) (|has| |#2| #72#)) ELT) ((#53# . #71#) NIL (AND (|has| #6# #73=(|ConvertibleTo| #53#)) (|has| |#2| #73#)) ELT) ((#74=(|InputForm|) . #71#) NIL (AND (|has| #6# #75=(|ConvertibleTo| #74#)) (|has| |#2| #75#)) ELT)) (|content| (#30# 147 #18# ELT) #43#) (|conditionP| (((|Union| #39# #21#) #35#) NIL #76=(AND (|has| $ #77=(|CharacteristicNonZero|)) #16#) ELT)) (|coerce| (((|OutputForm|) $) 175 T ELT) (($ #25#) NIL T ELT) (($ |#2|) 101 T ELT) (($ #6#) 40 T ELT) (($ #24#) NIL (OR #78=(|has| |#2| (|Algebra| #24#)) #27#) ELT) #10#) (|coefficients| ((#68# $) NIL T ELT)) (|coefficient| ((|#2| $ |#3|) NIL T ELT) #69# #56#) (|charthRoot| ((#14# $) NIL (OR #76# (|has| |#2| #77#)) ELT)) (|characteristic| ((#13#) NIL T CONST)) (|binomThmExpt| (($ $ $ #13#) NIL #32# ELT)) (|before?| #1#) (|associates?| (#2# NIL #9# ELT)) (|annihilate?| #1#) (|Zero| (#22# 24 T CONST)) (|One| (#22# 32 T CONST)) (D #56# #69# #70# (#44# NIL T ELT)) (= #1#) (/ (#79=($ $ |#2|) 77 (|has| |#2| (|Field|)) ELT)) (- #63# (#65# NIL T ELT)) (+ (#65# 133 T ELT)) (** (($ $ #80=(|PositiveInteger|)) NIL T ELT) (($ $ #13#) 131 T ELT)) (* (($ #80# $) NIL T ELT) (($ #13# $) NIL T ELT) (($ #25# . #81=($)) NIL T ELT) (#65# 37 T ELT) (($ $ #24#) NIL #78# ELT) (($ #24# . #81#) NIL #78# ELT) (($ |#2| . #81#) 76 T ELT) (#79# NIL T ELT))) (((|GeneralDistributedMultivariatePolynomial| |#1| |#2| |#3|) (|Join| (|PolynomialCategory| |#2| |#3| (|OrderedVariableList| |#1|)) (CATEGORY |domain| (SIGNATURE |reorder| ($ $ (|List| (|Integer|)))))) (|List| (|Symbol|)) (|Ring|) (|DirectProductCategory| (|#| |#1|) (|NonNegativeInteger|))) (T |GeneralDistributedMultivariatePolynomial|)) ((|reorder| (*1 *1 *1 *2) (AND (|isDomain| *2 (|List| (|Integer|))) (|ofType| *3 (|List| (|Symbol|))) (|isDomain| *1 (|GeneralDistributedMultivariatePolynomial| *3 *4 *5)) (|ofCategory| *4 (|Ring|)) (|ofCategory| *5 (|DirectProductCategory| (|#| *3) (|NonNegativeInteger|)))))) ((|testModulus| (((|Boolean|) |#1| #1=(|List| |#2|)) 90 T ELT)) (|tablePow| (((|Union| #2=(|Vector| #1#) #3="failed") #4=(|NonNegativeInteger|) |#1| #1#) 99 T ELT)) (|solveid| (((|Union| #1# #3#) |#2| |#1| #2#) 101 T ELT)) (|reduction| ((|#2| |#2| |#1|) 35 T ELT)) (|compBound| ((#4# |#2| #1#) 26 T ELT))) @@ -1329,7 +1332,7 @@ NIL ((|reduction| ((|#2| |#2| |#1|) 15 T ELT)) (|completeHensel| ((#1=(|List| |#2|) |#2| #1# |#1| #2=(|PositiveInteger|)) 82 T ELT)) (|HenselLift| (((|Record| (|:| |plist| #1#) (|:| |modulo| |#1|)) |#2| #1# |#1| #2#) 71 T ELT))) (((|GeneralHenselPackage| |#1| |#2|) (CATEGORY |package| (SIGNATURE |HenselLift| ((|Record| (|:| |plist| #1=(|List| |#2|)) (|:| |modulo| |#1|)) |#2| #1# |#1| #2=(|PositiveInteger|))) (SIGNATURE |completeHensel| (#1# |#2| #1# |#1| #2#)) (SIGNATURE |reduction| (|#2| |#2| |#1|))) (|EuclideanDomain|) (|UnivariatePolynomialCategory| |#1|)) (T |GeneralHenselPackage|)) ((|reduction| (*1 *2 *2 *3) (AND (|ofCategory| *3 #1=(|EuclideanDomain|)) (|isDomain| *1 (|GeneralHenselPackage| *3 *2)) (|ofCategory| *2 (|UnivariatePolynomialCategory| *3)))) (|completeHensel| (*1 *2 *3 *2 *4 *5) (AND (|isDomain| *2 #2=(|List| *3)) (|isDomain| *5 #3=(|PositiveInteger|)) (|ofCategory| *3 (|UnivariatePolynomialCategory| *4)) (|ofCategory| *4 #1#) (|isDomain| *1 (|GeneralHenselPackage| *4 *3)))) (|HenselLift| (*1 *2 *3 *4 *5 *6) (AND (|isDomain| *6 #3#) (|ofCategory| *5 #1#) (|ofCategory| *3 (|UnivariatePolynomialCategory| *5)) (|isDomain| *2 (|Record| (|:| |plist| #2#) (|:| |modulo| *5))) (|isDomain| *1 (|GeneralHenselPackage| *5 *3)) (|isDomain| *4 #2#)))) -((~= #1=((#2=(|Boolean|) $ $) NIL T ELT)) (|zero?| ((#2# $) 28 T ELT)) (|unitVector| (($ |#3|) 25 T ELT)) (|subtractIfCan| (((|Union| $ "failed") $ $) NIL T ELT)) (|sample| (#3=($) NIL T CONST)) (|reductum| (#4=($ $) 32 T ELT)) (|opposite?| #1#) (|multMonom| (($ |#2| |#4| $) 33 T ELT)) (|monomial| (($ |#2| #5=(|ModuleMonomial| |#3| |#4| |#5|)) 24 T ELT)) (|leadingMonomial| ((#5# $) 15 T ELT)) (|leadingIndex| ((|#3| $) 19 T ELT)) (|leadingExponent| ((|#4| $) 17 T ELT)) (|leadingCoefficient| ((|#2| $) 29 T ELT)) (|latex| (((|String|) $) NIL T ELT)) (|hash| (((|SingleInteger|) $) NIL T ELT)) (|coerce| (((|OutputForm|) $) NIL T ELT)) (|build| (($ |#2| |#3| |#4|) 26 T ELT)) (|before?| #1#) (|Zero| (#3# 36 T CONST)) (= #1#) (- (#4# NIL T ELT) (#6=($ $ $) NIL T ELT)) (+ (#6# 34 T ELT)) (* (($ (|PositiveInteger|) $) NIL T ELT) (($ (|NonNegativeInteger|) $) NIL T ELT) (($ (|Integer|) . #7=($)) NIL T ELT) (($ |#6| $) 40 T ELT) (($ $ |#6|) NIL T ELT) (($ $ |#2|) NIL T ELT) (($ |#2| . #7#) NIL T ELT))) +((~= #1=((#2=(|Boolean|) $ $) NIL T ELT)) (|zero?| ((#2# $) 28 T ELT)) (|unitVector| (($ |#3|) 25 T ELT)) (|subtractIfCan| (((|Maybe| $) $ $) NIL T ELT)) (|sample| (#3=($) NIL T CONST)) (|reductum| (#4=($ $) 32 T ELT)) (|opposite?| #1#) (|multMonom| (($ |#2| |#4| $) 33 T ELT)) (|monomial| (($ |#2| #5=(|ModuleMonomial| |#3| |#4| |#5|)) 24 T ELT)) (|leadingMonomial| ((#5# $) 15 T ELT)) (|leadingIndex| ((|#3| $) 19 T ELT)) (|leadingExponent| ((|#4| $) 17 T ELT)) (|leadingCoefficient| ((|#2| $) 29 T ELT)) (|latex| (((|String|) $) NIL T ELT)) (|hash| (((|SingleInteger|) $) NIL T ELT)) (|coerce| (((|OutputForm|) $) NIL T ELT)) (|build| (($ |#2| |#3| |#4|) 26 T ELT)) (|before?| #1#) (|Zero| (#3# 36 T CONST)) (= #1#) (- (#4# NIL T ELT) (#6=($ $ $) NIL T ELT)) (+ (#6# 34 T ELT)) (* (($ (|PositiveInteger|) $) NIL T ELT) (($ (|NonNegativeInteger|) $) NIL T ELT) (($ (|Integer|) . #7=($)) NIL T ELT) (($ |#6| $) 40 T ELT) (($ $ |#6|) NIL T ELT) (($ $ |#2|) NIL T ELT) (($ |#2| . #7#) NIL T ELT))) (((|GeneralModulePolynomial| |#1| |#2| |#3| |#4| |#5| |#6|) (|Join| (|Module| |#6|) (|Module| |#2|) (CATEGORY |domain| (SIGNATURE |leadingCoefficient| (|#2| $)) (SIGNATURE |leadingMonomial| (#1=(|ModuleMonomial| |#3| |#4| |#5|) $)) (SIGNATURE |leadingExponent| (|#4| $)) (SIGNATURE |leadingIndex| (|#3| $)) (SIGNATURE |reductum| ($ $)) (SIGNATURE |monomial| ($ |#2| #1#)) (SIGNATURE |unitVector| ($ |#3|)) (SIGNATURE |build| ($ |#2| |#3| |#4|)) (SIGNATURE |multMonom| ($ |#2| |#4| $)) (SIGNATURE * ($ |#6| $)))) (|List| (|Symbol|)) (|CommutativeRing|) (|OrderedSet|) (|DirectProductCategory| (|#| |#1|) (|NonNegativeInteger|)) (|Mapping| (|Boolean|) #2=(|Record| (|:| |index| |#3|) (|:| |exponent| |#4|)) #2#) (|PolynomialCategory| |#2| |#4| (|OrderedVariableList| |#1|))) (T |GeneralModulePolynomial|)) ((* (*1 *1 *2 *1) (AND #1=(|ofType| *3 #2=(|List| (|Symbol|))) #3=(|ofCategory| *4 #4=(|CommutativeRing|)) #5=(|ofCategory| *6 #6=(|DirectProductCategory| (|#| *3) #7=(|NonNegativeInteger|))) #8=(|ofType| *7 (|Mapping| #9=(|Boolean|) #10=(|Record| #11=(|:| |index| *5) (|:| |exponent| *6)) #10#)) (|isDomain| *1 (|GeneralModulePolynomial| *3 *4 *5 *6 *7 *2)) #12=(|ofCategory| *5 #13=(|OrderedSet|)) (|ofCategory| *2 #14=(|PolynomialCategory| *4 *6 #15=(|OrderedVariableList| *3))))) (|leadingCoefficient| #16=(*1 *2 *1) (AND #1# #17=(|ofCategory| *5 #6#) #18=(|ofType| *6 (|Mapping| #9# #19=(|Record| (|:| |index| *4) #20=(|:| |exponent| *5)) #19#)) #21=(|ofCategory| *2 #4#) (|isDomain| *1 (|GeneralModulePolynomial| *3 *2 *4 *5 *6 *7)) #22=(|ofCategory| *4 #13#) (|ofCategory| *7 (|PolynomialCategory| *2 *5 #15#)))) (|leadingMonomial| #16# (AND #1# #3# #5# #8# (|isDomain| *2 #23=(|ModuleMonomial| *5 *6 *7)) (|isDomain| *1 (|GeneralModulePolynomial| *3 *4 *5 *6 *7 *8)) #12# (|ofCategory| *8 #14#))) (|leadingExponent| #16# (AND #1# #3# (|ofType| *6 (|Mapping| #9# #24=(|Record| #11# (|:| |exponent| *2)) #24#)) (|ofCategory| *2 #6#) (|isDomain| *1 (|GeneralModulePolynomial| *3 *4 *5 *2 *6 *7)) #12# (|ofCategory| *7 (|PolynomialCategory| *4 *2 #15#)))) (|leadingIndex| #16# (AND #1# #3# #17# #25=(|ofType| *6 (|Mapping| #9# #26=(|Record| (|:| |index| *2) #20#) #26#)) #27=(|ofCategory| *2 #13#) #28=(|isDomain| *1 (|GeneralModulePolynomial| *3 *4 *2 *5 *6 *7)) #29=(|ofCategory| *7 (|PolynomialCategory| *4 *5 #15#)))) (|reductum| (*1 *1 *1) (AND (|ofType| *2 #2#) (|ofCategory| *3 #4#) (|ofCategory| *5 (|DirectProductCategory| (|#| *2) #7#)) #18# (|isDomain| *1 (|GeneralModulePolynomial| *2 *3 *4 *5 *6 *7)) #22# (|ofCategory| *7 (|PolynomialCategory| *3 *5 (|OrderedVariableList| *2))))) (|monomial| (*1 *1 *2 *3) (AND (|isDomain| *3 #23#) #12# (|ofCategory| *6 #30=(|DirectProductCategory| (|#| *4) #7#)) #8# #31=(|ofType| *4 #2#) #21# (|isDomain| *1 (|GeneralModulePolynomial| *4 *2 *5 *6 *7 *8)) (|ofCategory| *8 (|PolynomialCategory| *2 *6 #32=(|OrderedVariableList| *4))))) (|unitVector| (*1 *1 *2) (AND #1# #3# #17# #25# #28# #27# #29#)) (|build| (*1 *1 *2 *3 *4) (AND (|ofType| *5 #2#) #21# (|ofCategory| *4 (|DirectProductCategory| (|#| *5) #7#)) (|ofType| *6 (|Mapping| #9# #33=(|Record| (|:| |index| *3) (|:| |exponent| *4)) #33#)) (|isDomain| *1 (|GeneralModulePolynomial| *5 *2 *3 *4 *6 *7)) (|ofCategory| *3 #13#) (|ofCategory| *7 (|PolynomialCategory| *2 *4 (|OrderedVariableList| *5))))) (|multMonom| (*1 *1 *2 *3 *1) (AND #31# #21# (|ofCategory| *3 #30#) (|ofType| *6 (|Mapping| #9# #34=(|Record| #11# (|:| |exponent| *3)) #34#)) (|isDomain| *1 (|GeneralModulePolynomial| *4 *2 *5 *3 *6 *7)) #12# (|ofCategory| *7 (|PolynomialCategory| *2 *3 #32#))))) ((|GospersMethod| (((|Union| |#5| "failed") |#5| |#2| (|Mapping| |#2|)) 39 T ELT))) @@ -1353,8 +1356,8 @@ NIL (((|GraphicsDefaults|) (CATEGORY |package| (SIGNATURE |clipPointsDefault| #1=(#2=(|Boolean|))) (SIGNATURE |drawToScale| #1#) (SIGNATURE |clipPointsDefault| #3=(#2# #2#)) (SIGNATURE |drawToScale| #3#) (SIGNATURE |adaptive| #1#) (SIGNATURE |maxPoints| #4=(#5=(|Integer|))) (SIGNATURE |minPoints| #4#) (SIGNATURE |screenResolution| #4#) (SIGNATURE |adaptive| #3#) (SIGNATURE |maxPoints| #6=(#5# #5#)) (SIGNATURE |minPoints| #6#) (SIGNATURE |screenResolution| #6#))) (T |GraphicsDefaults|)) ((|screenResolution| #1=(*1 *2 *2) #2=(AND (|isDomain| *2 (|Integer|)) #3=(|isDomain| *1 (|GraphicsDefaults|)))) (|minPoints| #1# #2#) (|maxPoints| #1# #2#) (|adaptive| #1# #4=(AND (|isDomain| *2 (|Boolean|)) #3#)) (|screenResolution| #5=(*1 *2) #2#) (|minPoints| #5# #2#) (|maxPoints| #5# #2#) (|adaptive| #5# #4#) (|drawToScale| #1# #4#) (|clipPointsDefault| #1# #4#) (|drawToScale| #5# #4#) (|clipPointsDefault| #5# #4#)) ((~= #1=(((|Boolean|) $ $) NIL T ELT)) (|units| ((#2=(|List| #3=(|Float|)) $) 34 T ELT) ((#2# $ #2#) 145 T ELT)) (|ranges| ((#4=(|List| (|Segment| #3#)) $) 16 T ELT) ((#4# $ #4#) 142 T ELT)) (|putColorInfo| ((#5=(|List| #6=(|List| #7=(|Point| #8=(|DoubleFloat|)))) #5# #9=(|List| #10=(|Palette|))) 58 T ELT)) (|pointLists| ((#5# $) 137 T ELT)) (|point| ((#11=(|Void|) $ #7# #10#) 162 T ELT)) (|makeGraphImage| (($ $) 136 T ELT) (#12=($ #5#) 148 T ELT) (($ #5# #9# #9# #13=(|List| #14=(|PositiveInteger|))) 147 T ELT) (($ #5# #9# #9# #13# (|List| (|DrawOption|))) 149 T ELT)) (|latex| (((|String|) $) NIL T ELT)) (|key| (((|Integer|) $) 110 T ELT)) (|hash| (((|SingleInteger|) $) NIL T ELT)) (|graphImage| (($) 146 T ELT)) (|figureUnits| (((|List| #8#) #5#) 89 T ELT)) (|component| ((#11# $ #6# #10# #10# #14#) 154 T ELT) (#15=(#11# $ #7#) 156 T ELT) ((#11# $ #7# #10# #10# #14#) 155 T ELT)) (|coerce| (((|OutputForm|) $) 168 T ELT) (#12# 163 T ELT)) (|before?| #1#) (|appendPoint| (#15# 161 T ELT)) (= #1#)) -(((|GraphImage|) (|Join| (|SetCategory|) (CATEGORY |domain| (SIGNATURE |graphImage| ($)) (SIGNATURE |makeGraphImage| ($ $)) (SIGNATURE |makeGraphImage| #1=($ #2=(|List| #3=(|List| #4=(|Point| #5=(|DoubleFloat|)))))) (SIGNATURE |makeGraphImage| ($ #2# #6=(|List| #7=(|Palette|)) #6# #8=(|List| #9=(|PositiveInteger|)))) (SIGNATURE |makeGraphImage| ($ #2# #6# #6# #8# (|List| (|DrawOption|)))) (SIGNATURE |pointLists| (#2# $)) (SIGNATURE |key| ((|Integer|) $)) (SIGNATURE |ranges| (#10=(|List| (|Segment| #11=(|Float|))) $)) (SIGNATURE |ranges| (#10# $ #10#)) (SIGNATURE |units| (#12=(|List| #11#) $)) (SIGNATURE |units| (#12# $ #12#)) (SIGNATURE |component| (#13=(|Void|) $ #3# #7# #7# #9#)) (SIGNATURE |component| #14=(#13# $ #4#)) (SIGNATURE |component| (#13# $ #4# #7# #7# #9#)) (SIGNATURE |appendPoint| #14#) (SIGNATURE |point| (#13# $ #4# #7#)) (SIGNATURE |coerce| #1#) (SIGNATURE |coerce| ((|OutputForm|) $)) (SIGNATURE |putColorInfo| (#2# #2# #6#)) (SIGNATURE |figureUnits| ((|List| #5#) #2#))))) (T |GraphImage|)) -((|coerce| #1=(*1 *2 *1) (AND (|isDomain| *2 (|OutputForm|)) #2=(|isDomain| *1 (|GraphImage|)))) (|graphImage| (*1 *1) #2#) (|makeGraphImage| (*1 *1 *1) #2#) (|makeGraphImage| #3=(*1 *1 *2) #4=(AND #5=(|isDomain| *2 #6=(|List| #7=(|List| #8=(|Point| #9=(|DoubleFloat|))))) #2#)) (|makeGraphImage| (*1 *1 *2 *3 *3 *4) (AND #5# #10=(|isDomain| *3 (|List| #11=(|Palette|))) #12=(|isDomain| *4 (|List| #13=(|PositiveInteger|))) #2#)) (|makeGraphImage| (*1 *1 *2 *3 *3 *4 *5) (AND #5# #10# #12# (|isDomain| *5 (|List| (|DrawOption|))) #2#)) (|pointLists| #1# #4#) (|key| #1# (AND (|isDomain| *2 (|Integer|)) #2#)) (|ranges| #1# #14=(AND (|isDomain| *2 (|List| (|Segment| #15=(|Float|)))) #2#)) (|ranges| #16=(*1 *2 *1 *2) #14#) (|units| #1# #17=(AND (|isDomain| *2 (|List| #15#)) #2#)) (|units| #16# #17#) (|component| #18=(*1 *2 *1 *3 *4 *4 *5) (AND (|isDomain| *3 #7#) #19=(|isDomain| *4 #11#) #20=(|isDomain| *5 #13#) #21=(|isDomain| *2 (|Void|)) #2#)) (|component| #22=(*1 *2 *1 *3) #23=(AND #24=(|isDomain| *3 #8#) #21# #2#)) (|component| #18# (AND #24# #19# #20# #21# #2#)) (|appendPoint| #22# #23#) (|point| (*1 *2 *1 *3 *4) (AND #24# #19# #21# #2#)) (|coerce| #3# #4#) (|putColorInfo| (*1 *2 *2 *3) (AND #5# #10# #2#)) (|figureUnits| (*1 *2 *3) (AND (|isDomain| *3 #6#) (|isDomain| *2 (|List| #9#)) #2#))) +(((|GraphImage|) (|Join| (|SetCategory|) (CATEGORY |domain| (SIGNATURE |graphImage| ($)) (SIGNATURE |makeGraphImage| ($ $)) (SIGNATURE |makeGraphImage| #1=($ #2=(|List| #3=(|List| #4=(|Point| #5=(|DoubleFloat|)))))) (SIGNATURE |makeGraphImage| ($ #2# #6=(|List| #7=(|Palette|)) #6# #8=(|List| #9=(|PositiveInteger|)))) (SIGNATURE |makeGraphImage| ($ #2# #6# #6# #8# (|List| (|DrawOption|)))) (SIGNATURE |pointLists| (#2# $)) (SIGNATURE |key| ((|Integer|) $)) (SIGNATURE |ranges| (#10=(|List| (|Segment| #11=(|Float|))) $)) (SIGNATURE |ranges| (#10# $ #10#)) (SIGNATURE |units| (#12=(|List| #11#) $)) (SIGNATURE |units| (#12# $ #12#)) (SIGNATURE |component| (#13=(|Void|) $ #3# #7# #7# #9#)) (SIGNATURE |component| #14=(#13# $ #4#)) (SIGNATURE |component| (#13# $ #4# #7# #7# #9#)) (SIGNATURE |appendPoint| #14#) (SIGNATURE |point| (#13# $ #4# #7#)) (SIGNATURE |coerce| #1#) (SIGNATURE |putColorInfo| (#2# #2# #6#)) (SIGNATURE |figureUnits| ((|List| #5#) #2#))))) (T |GraphImage|)) +((|graphImage| (*1 *1) #1=(|isDomain| *1 (|GraphImage|))) (|makeGraphImage| (*1 *1 *1) #1#) (|makeGraphImage| #2=(*1 *1 *2) #3=(AND #4=(|isDomain| *2 #5=(|List| #6=(|List| #7=(|Point| #8=(|DoubleFloat|))))) #1#)) (|makeGraphImage| (*1 *1 *2 *3 *3 *4) (AND #4# #9=(|isDomain| *3 (|List| #10=(|Palette|))) #11=(|isDomain| *4 (|List| #12=(|PositiveInteger|))) #1#)) (|makeGraphImage| (*1 *1 *2 *3 *3 *4 *5) (AND #4# #9# #11# (|isDomain| *5 (|List| (|DrawOption|))) #1#)) (|pointLists| #13=(*1 *2 *1) #3#) (|key| #13# (AND (|isDomain| *2 (|Integer|)) #1#)) (|ranges| #13# #14=(AND (|isDomain| *2 (|List| (|Segment| #15=(|Float|)))) #1#)) (|ranges| #16=(*1 *2 *1 *2) #14#) (|units| #13# #17=(AND (|isDomain| *2 (|List| #15#)) #1#)) (|units| #16# #17#) (|component| #18=(*1 *2 *1 *3 *4 *4 *5) (AND (|isDomain| *3 #6#) #19=(|isDomain| *4 #10#) #20=(|isDomain| *5 #12#) #21=(|isDomain| *2 (|Void|)) #1#)) (|component| #22=(*1 *2 *1 *3) #23=(AND #24=(|isDomain| *3 #7#) #21# #1#)) (|component| #18# (AND #24# #19# #20# #21# #1#)) (|appendPoint| #22# #23#) (|point| (*1 *2 *1 *3 *4) (AND #24# #19# #21# #1#)) (|coerce| #2# #3#) (|putColorInfo| (*1 *2 *2 *3) (AND #4# #9# #1#)) (|figureUnits| (*1 *2 *3) (AND (|isDomain| *3 #5#) (|isDomain| *2 (|List| #8#)) #1#))) ((- (($ $) NIL T ELT) (($ $ $) 11 T ELT))) (((|GradedModule&| |#1| |#2| |#3|) (CATEGORY |package| (SIGNATURE - (|#1| |#1| |#1|)) (SIGNATURE - (|#1| |#1|))) (|GradedModule| |#2| |#3|) (|CommutativeRing|) (|AbelianMonoid|)) (T |GradedModule&|)) NIL @@ -1363,7 +1366,7 @@ NIL ((|degree| (*1 *2 *1) (AND (|ofCategory| *1 (|GradedModule| *3 *2)) (|ofCategory| *3 (|CommutativeRing|)) (|ofCategory| *2 (|AbelianMonoid|)))) (|Zero| (*1 *1) (AND (|ofCategory| *1 (|GradedModule| *2 *3)) (|ofCategory| *2 (|CommutativeRing|)) (|ofCategory| *3 (|AbelianMonoid|)))) (* (*1 *1 *2 *1) (AND (|ofCategory| *1 (|GradedModule| *2 *3)) (|ofCategory| *2 (|CommutativeRing|)) (|ofCategory| *3 (|AbelianMonoid|)))) (* (*1 *1 *1 *2) (AND (|ofCategory| *1 (|GradedModule| *2 *3)) (|ofCategory| *2 (|CommutativeRing|)) (|ofCategory| *3 (|AbelianMonoid|)))) (- (*1 *1 *1) (AND (|ofCategory| *1 (|GradedModule| *2 *3)) (|ofCategory| *2 (|CommutativeRing|)) (|ofCategory| *3 (|AbelianMonoid|)))) (+ (*1 *1 *1 *1) (AND (|ofCategory| *1 (|GradedModule| *2 *3)) (|ofCategory| *2 (|CommutativeRing|)) (|ofCategory| *3 (|AbelianMonoid|)))) (- (*1 *1 *1 *1) (AND (|ofCategory| *1 (|GradedModule| *2 *3)) (|ofCategory| *2 (|CommutativeRing|)) (|ofCategory| *3 (|AbelianMonoid|))))) (|Join| (|SetCategory|) (CATEGORY |domain| (SIGNATURE |degree| (|t#2| $)) (SIGNATURE |Zero| ($) |constant|) (SIGNATURE * ($ |t#1| $)) (SIGNATURE * ($ $ |t#1|)) (SIGNATURE - ($ $)) (SIGNATURE + ($ $ $)) (SIGNATURE - ($ $ $)))) (((|BasicType|) . T) ((|CoercibleTo| (|OutputForm|)) . T) ((|Join|) . T) ((|SetCategory|) . T) ((|Type|) . T)) -((|testDim| (((|Union| #1=(|List| (|HomogeneousDistributedMultivariatePolynomial| |#1| |#2|)) "failed") #1# #2=(|List| (|OrderedVariableList| |#1|))) 135 T ELT)) (|groebSolve| (((|List| #3=(|List| (|DistributedMultivariatePolynomial| |#1| |#2|))) #3# #2#) 132 T ELT)) (|genericPosition| (((|Record| (|:| |dpolys| #3#) (|:| |coords| (|List| (|Integer|)))) #3# #2#) 87 T ELT))) +((|testDim| (((|Union| #1=(|List| (|HomogeneousDistributedMultivariatePolynomial| |#1| |#2|)) "failed") #1# #2=(|List| (|OrderedVariableList| |#1|))) 134 T ELT)) (|groebSolve| (((|List| #3=(|List| (|DistributedMultivariatePolynomial| |#1| |#2|))) #3# #2#) 131 T ELT)) (|genericPosition| (((|Record| (|:| |dpolys| #3#) (|:| |coords| (|List| (|Integer|)))) #3# #2#) 86 T ELT))) (((|GroebnerSolve| |#1| |#2| |#3|) (CATEGORY |package| (SIGNATURE |groebSolve| ((|List| #1=(|List| (|DistributedMultivariatePolynomial| |#1| |#2|))) #1# #2=(|List| (|OrderedVariableList| |#1|)))) (SIGNATURE |testDim| ((|Union| #3=(|List| (|HomogeneousDistributedMultivariatePolynomial| |#1| |#2|)) "failed") #3# #2#)) (SIGNATURE |genericPosition| ((|Record| (|:| |dpolys| #1#) (|:| |coords| (|List| (|Integer|)))) #1# #2#))) (|List| (|Symbol|)) #4=(|GcdDomain|) #4#) (T |GroebnerSolve|)) ((|genericPosition| #1=(*1 *2 *3 *4) (AND #2=(|isDomain| *4 (|List| (|OrderedVariableList| *5))) #3=(|ofType| *5 #4=(|List| (|Symbol|))) #5=(|ofCategory| *6 #6=(|GcdDomain|)) (|isDomain| *2 (|Record| (|:| |dpolys| #7=(|List| (|DistributedMultivariatePolynomial| *5 *6))) (|:| |coords| (|List| (|Integer|))))) #8=(|isDomain| *1 (|GroebnerSolve| *5 *6 *7)) #9=(|isDomain| *3 #7#) #10=(|ofCategory| *7 #6#))) (|testDim| (*1 *2 *2 *3) (|partial| AND (|isDomain| *2 (|List| (|HomogeneousDistributedMultivariatePolynomial| *4 *5))) (|isDomain| *3 (|List| (|OrderedVariableList| *4))) (|ofType| *4 #4#) (|ofCategory| *5 #6#) (|isDomain| *1 (|GroebnerSolve| *4 *5 *6)) #5#)) (|groebSolve| #1# (AND #2# #3# #5# (|isDomain| *2 (|List| #7#)) #8# #9# #10#))) ((|recip| (((|Union| $ "failed") $) 11 T ELT)) (|conjugate| (#1=($ $ $) 22 T ELT)) (|commutator| (#1# 23 T ELT)) (/ (#1# 9 T ELT)) (** (($ $ (|PositiveInteger|)) NIL T ELT) (($ $ (|NonNegativeInteger|)) NIL T ELT) (($ $ (|Integer|)) 21 T ELT))) @@ -1372,9 +1375,9 @@ NIL ((~= (#1=((|Boolean|) $ $) 7 T ELT)) (|sample| (#2=($) 23 T CONST)) (|recip| (((|Union| $ "failed") $) 20 T ELT)) (|one?| (((|Boolean|) $) 22 T ELT)) (|latex| (((|String|) $) 11 T ELT)) (|inv| (($ $) 30 T ELT)) (|hash| (((|SingleInteger|) $) 12 T ELT)) (|conjugate| (($ $ $) 27 T ELT)) (|commutator| (($ $ $) 26 T ELT)) (|coerce| (((|OutputForm|) $) 13 T ELT)) (|before?| (#1# 6 T ELT)) (|One| (#2# 24 T CONST)) (= (#1# 8 T ELT)) (/ (($ $ $) 29 T ELT)) (** (($ $ (|PositiveInteger|)) 17 T ELT) (($ $ (|NonNegativeInteger|)) 21 T ELT) (($ $ (|Integer|)) 28 T ELT)) (* (($ $ $) 18 T ELT))) (((|Group|) (|Category|)) (T |Group|)) ((|inv| (*1 *1 *1) (|ofCategory| *1 (|Group|))) (/ (*1 *1 *1 *1) (|ofCategory| *1 (|Group|))) (** (*1 *1 *1 *2) (AND (|ofCategory| *1 (|Group|)) (|isDomain| *2 (|Integer|)))) (|conjugate| (*1 *1 *1 *1) (|ofCategory| *1 (|Group|))) (|commutator| (*1 *1 *1 *1) (|ofCategory| *1 (|Group|)))) -(|Join| (|Monoid|) (CATEGORY |domain| (SIGNATURE |inv| ($ $)) (SIGNATURE / ($ $ $)) (SIGNATURE ** ($ $ (|Integer|))) (ATTRIBUTE |unitsKnown|) (SIGNATURE |conjugate| ($ $ $)) (SIGNATURE |commutator| ($ $ $)))) +(|Join| (|Monoid|) (CATEGORY |domain| (SIGNATURE |inv| ($ $)) (SIGNATURE / ($ $ $)) (SIGNATURE ** ($ $ (|Integer|))) (SIGNATURE |conjugate| ($ $ $)) (SIGNATURE |commutator| ($ $ $)))) (((|BasicType|) . T) ((|CoercibleTo| (|OutputForm|)) . T) ((|Join|) . T) ((|Monoid|) . T) ((|SemiGroup|) . T) ((|SetCategory|) . T) ((|Type|) . T)) -((~= #1=(#2=(#3=(|Boolean|) $ $) NIL T ELT)) (|zero?| #4=(#5=(#3# $) NIL T ELT)) (|variables| ((#6=(|List| #7=(|SingletonAsOrderedSet|)) $) NIL T ELT)) (|variable| ((#8=(|Symbol|) $) 18 T ELT)) (|unitNormal| (((|Record| (|:| |unit| $) (|:| |canonical| $) (|:| |associate| $)) $) NIL #9=(|has| |#1| (|IntegralDomain|)) ELT)) (|unitCanonical| #10=(#11=($ $) NIL #9# ELT)) (|unit?| (#5# NIL #9# ELT)) (|truncate| #12=(#13=($ $ #14=(|Fraction| #15=(|Integer|))) NIL T ELT) (($ $ #14# #14#) NIL T ELT)) (|terms| ((#16=(|Stream| (|Record| (|:| |k| #14#) (|:| |c| |#1|))) $) NIL T ELT)) (|tanh| #17=(#11# NIL #18=(|has| |#1| (|Algebra| #14#)) ELT)) (|tan| #17#) (|subtractIfCan| (#19=(#20=(|Union| $ #21="failed") $ $) NIL T ELT)) (|squareFreePart| #22=(#11# NIL #23=(|has| |#1| (|Field|)) ELT)) (|squareFree| #24=(((|Factored| $) $) NIL #23# ELT)) (|sqrt| #17#) (|sizeLess?| (#2# NIL #23# ELT)) (|sinh| #17#) (|sin| #17#) (|series| (($ #25=(|NonNegativeInteger|) #16#) NIL T ELT)) (|sech| #17#) (|sec| #17#) (|sample| #26=(#27=($) NIL T CONST)) (|rem| #28=(#29=($ $ $) NIL #23# ELT)) (|reductum| #30=(#11# NIL T ELT)) (|recip| ((#20# $) NIL T ELT)) (|quo| #28#) (|principalIdeal| (((|Record| (|:| |coef| #31=(|List| $)) #32=(|:| |generator| $)) #31#) NIL #23# ELT)) (|prime?| (#5# NIL #23# ELT)) (|pole?| #4#) (|pi| (#27# NIL #18# ELT)) (|order| #33=((#14# $) NIL T ELT) ((#14# $ #14#) NIL T ELT)) (|opposite?| #1#) (|one?| #4#) (|nthRoot| (#34=($ $ #15#) NIL #18# ELT)) (|multiplyExponents| #35=(($ $ #36=(|PositiveInteger|)) NIL T ELT) #12#) (|multiEuclidean| (((|Union| #31# #21#) #31# $) NIL #23# ELT)) (|monomial?| #4#) (|monomial| (($ |#1| #14#) NIL T ELT) (($ $ #7# #14#) NIL T ELT) (($ $ #6# (|List| #14#)) NIL T ELT)) (|map| (($ (|Mapping| |#1| |#1|) $) 25 T ELT)) (|log| #17#) (|leadingMonomial| #30#) (|leadingCoefficient| (#37=(|#1| $) NIL T ELT)) (|lcm| #38=(($ #31#) NIL #23# ELT) #28#) (|latex| (((|String|) $) NIL T ELT)) (|inv| #22#) (|integrate| (#11# 29 #18# ELT) (#39=($ $ #8#) 35 (OR (AND #18# (|has| |#1| (|AlgebraicallyClosedFunctionSpace| #15#)) (|has| |#1| (|PrimitiveFunctionCategory|)) (|has| |#1| (|TranscendentalFunctionCategory|))) (AND #18# (|has| |#1| (SIGNATURE |integrate| (|#1| |#1| #8#))) (|has| |#1| (SIGNATURE |variables| (#40=(|List| #8#) |#1|))))) ELT) (#41=($ $ #42=(|Variable| |#2|)) 30 #18# ELT)) (|hash| (((|SingleInteger|) $) NIL T ELT)) (|gcdPolynomial| ((#43=(|SparseUnivariatePolynomial| $) #43# #43#) NIL #23# ELT)) (|gcd| #38# #28#) (|factor| #24#) (|extendedEuclidean| (((|Union| (|Record| #44=(|:| |coef1| $) #45=(|:| |coef2| $)) #21#) $ $ $) NIL #23# ELT) (((|Record| #44# #45# #32#) $ $) NIL #23# ELT)) (|extend| #12#) (|exquo| (#19# NIL #9# ELT)) (|expressIdealMember| (((|Maybe| #31#) #31# $) NIL #23# ELT)) (|exp| #17#) (|eval| (((|Stream| |#1|) $ |#1|) NIL #46=(|has| |#1| (SIGNATURE ** (|#1| |#1| #14#))) ELT)) (|euclideanSize| ((#25# $) NIL #23# ELT)) (|elt| #47=(#48=(|#1| $ #14#) NIL T ELT) (#29# NIL (|has| #14# (|SemiGroup|)) ELT)) (|divide| (((|Record| (|:| |quotient| $) (|:| |remainder| $)) $ $) NIL #23# ELT)) (|differentiate| (#39# 28 #49=(AND (|has| |#1| (|PartialDifferentialRing| #8#)) #50=(|has| |#1| (SIGNATURE * (|#1| #14# |#1|)))) ELT) #51=(($ $ #40#) NIL #49# ELT) #52=(($ $ #8# #25#) NIL #49# ELT) #53=(($ $ #40# (|List| #25#)) NIL #49# ELT) (#11# 14 #50# ELT) #54=(#55=($ $ #25#) NIL #50# ELT) (#41# 16 T ELT)) (|degree| #33#) (|csch| #17#) (|csc| #17#) (|coth| #17#) (|cot| #17#) (|cosh| #17#) (|cos| #17#) (|complete| #30#) (|coerce| (((|OutputForm|) $) NIL T ELT) (($ #15#) NIL T ELT) (($ |#1|) NIL (|has| |#1| (|CommutativeRing|)) ELT) (($ #42#) NIL T ELT) (($ (|UnivariatePuiseuxSeries| |#1| |#2| |#3|)) 9 T ELT) (($ #14#) NIL #18# ELT) #10#) (|coefficient| #47#) (|charthRoot| (((|Maybe| $) $) NIL (|has| |#1| (|CharacteristicNonZero|)) ELT)) (|characteristic| ((#25#) NIL T CONST)) (|center| (#37# 21 T ELT)) (|before?| #1#) (|atanh| #17#) (|atan| #17#) (|associates?| (#2# NIL #9# ELT)) (|asinh| #17#) (|asin| #17#) (|asech| #17#) (|asec| #17#) (|approximate| (#48# NIL (AND #46# (|has| |#1| (SIGNATURE |coerce| (|#1| #8#)))) ELT)) (|annihilate?| #1#) (|acsch| #17#) (|acsc| #17#) (|acoth| #17#) (|acot| #17#) (|acosh| #17#) (|acos| #17#) (|Zero| #26#) (|One| #26#) (D (#39# NIL #49# ELT) #51# #52# #53# (#11# NIL #50# ELT) #54# (#41# NIL T ELT)) (= #1#) (/ (#56=($ $ |#1|) NIL #23# ELT) #28#) (- #30# (#29# 27 T ELT)) (+ #57=(#29# NIL T ELT)) (** #35# (#55# NIL T ELT) (#34# NIL #23# ELT) (#29# NIL #18# ELT) #58=(#13# NIL #18# ELT)) (* (($ #36# $) NIL T ELT) (($ #25# $) NIL T ELT) (($ #15# . #59=($)) NIL T ELT) #57# (#56# NIL T ELT) (($ |#1| . #59#) 26 T ELT) (($ #14# . #59#) NIL #18# ELT) #58#)) +((~= #1=(#2=(#3=(|Boolean|) $ $) NIL T ELT)) (|zero?| #4=(#5=(#3# $) NIL T ELT)) (|variables| ((#6=(|List| #7=(|SingletonAsOrderedSet|)) $) NIL T ELT)) (|variable| ((#8=(|Symbol|) $) 18 T ELT)) (|unitNormal| (((|Record| (|:| |unit| $) (|:| |canonical| $) (|:| |associate| $)) $) NIL #9=(|has| |#1| (|IntegralDomain|)) ELT)) (|unitCanonical| #10=(#11=($ $) NIL #9# ELT)) (|unit?| (#5# NIL #9# ELT)) (|truncate| #12=(#13=($ $ #14=(|Fraction| #15=(|Integer|))) NIL T ELT) (($ $ #14# #14#) NIL T ELT)) (|terms| ((#16=(|Stream| (|Record| (|:| |k| #14#) (|:| |c| |#1|))) $) NIL T ELT)) (|tanh| #17=(#11# NIL #18=(|has| |#1| (|Algebra| #14#)) ELT)) (|tan| #17#) (|subtractIfCan| ((#19=(|Maybe| $) $ $) NIL T ELT)) (|squareFreePart| #20=(#11# NIL #21=(|has| |#1| (|Field|)) ELT)) (|squareFree| #22=(((|Factored| $) $) NIL #21# ELT)) (|sqrt| #17#) (|sizeLess?| (#2# NIL #21# ELT)) (|sinh| #17#) (|sin| #17#) (|series| (($ #23=(|NonNegativeInteger|) #16#) NIL T ELT)) (|sech| #17#) (|sec| #17#) (|sample| #24=(#25=($) NIL T CONST)) (|rem| #26=(#27=($ $ $) NIL #21# ELT)) (|reductum| #28=(#11# NIL T ELT)) (|recip| ((#29=(|Union| $ #30="failed") $) NIL T ELT)) (|quo| #26#) (|principalIdeal| (((|Record| (|:| |coef| #31=(|List| $)) #32=(|:| |generator| $)) #31#) NIL #21# ELT)) (|prime?| (#5# NIL #21# ELT)) (|pole?| #4#) (|pi| (#25# NIL #18# ELT)) (|order| #33=((#14# $) NIL T ELT) ((#14# $ #14#) NIL T ELT)) (|opposite?| #1#) (|one?| #4#) (|nthRoot| (#34=($ $ #15#) NIL #18# ELT)) (|multiplyExponents| #35=(($ $ #36=(|PositiveInteger|)) NIL T ELT) #12#) (|multiEuclidean| (((|Union| #31# #30#) #31# $) NIL #21# ELT)) (|monomial?| #4#) (|monomial| (($ |#1| #14#) NIL T ELT) (($ $ #7# #14#) NIL T ELT) (($ $ #6# (|List| #14#)) NIL T ELT)) (|map| (($ (|Mapping| |#1| |#1|) $) 25 T ELT)) (|log| #17#) (|leadingMonomial| #28#) (|leadingCoefficient| (#37=(|#1| $) NIL T ELT)) (|lcm| #38=(($ #31#) NIL #21# ELT) #26#) (|latex| (((|String|) $) NIL T ELT)) (|inv| #20#) (|integrate| (#11# 29 #18# ELT) (#39=($ $ #8#) 35 (OR (AND #18# (|has| |#1| (|AlgebraicallyClosedFunctionSpace| #15#)) (|has| |#1| (|PrimitiveFunctionCategory|)) (|has| |#1| (|TranscendentalFunctionCategory|))) (AND #18# (|has| |#1| (SIGNATURE |integrate| (|#1| |#1| #8#))) (|has| |#1| (SIGNATURE |variables| (#40=(|List| #8#) |#1|))))) ELT) (#41=($ $ #42=(|Variable| |#2|)) 30 #18# ELT)) (|hash| (((|SingleInteger|) $) NIL T ELT)) (|gcdPolynomial| ((#43=(|SparseUnivariatePolynomial| $) #43# #43#) NIL #21# ELT)) (|gcd| #38# #26#) (|factor| #22#) (|extendedEuclidean| (((|Union| (|Record| #44=(|:| |coef1| $) #45=(|:| |coef2| $)) #30#) $ $ $) NIL #21# ELT) (((|Record| #44# #45# #32#) $ $) NIL #21# ELT)) (|extend| #12#) (|exquo| ((#29# $ $) NIL #9# ELT)) (|expressIdealMember| (((|Maybe| #31#) #31# $) NIL #21# ELT)) (|exp| #17#) (|eval| (((|Stream| |#1|) $ |#1|) NIL #46=(|has| |#1| (SIGNATURE ** (|#1| |#1| #14#))) ELT)) (|euclideanSize| ((#23# $) NIL #21# ELT)) (|elt| #47=(#48=(|#1| $ #14#) NIL T ELT) (#27# NIL (|has| #14# (|SemiGroup|)) ELT)) (|divide| (((|Record| (|:| |quotient| $) (|:| |remainder| $)) $ $) NIL #21# ELT)) (|differentiate| (#39# 28 #49=(AND (|has| |#1| (|PartialDifferentialRing| #8#)) #50=(|has| |#1| (SIGNATURE * (|#1| #14# |#1|)))) ELT) #51=(($ $ #40#) NIL #49# ELT) #52=(($ $ #8# #23#) NIL #49# ELT) #53=(($ $ #40# (|List| #23#)) NIL #49# ELT) (#11# 14 #50# ELT) #54=(#55=($ $ #23#) NIL #50# ELT) (#41# 16 T ELT)) (|degree| #33#) (|csch| #17#) (|csc| #17#) (|coth| #17#) (|cot| #17#) (|cosh| #17#) (|cos| #17#) (|complete| #28#) (|coerce| (((|OutputForm|) $) NIL T ELT) (($ #15#) NIL T ELT) (($ |#1|) NIL (|has| |#1| (|CommutativeRing|)) ELT) (($ #42#) NIL T ELT) (($ (|UnivariatePuiseuxSeries| |#1| |#2| |#3|)) 9 T ELT) (($ #14#) NIL #18# ELT) #10#) (|coefficient| #47#) (|charthRoot| ((#19# $) NIL (|has| |#1| (|CharacteristicNonZero|)) ELT)) (|characteristic| ((#23#) NIL T CONST)) (|center| (#37# 21 T ELT)) (|before?| #1#) (|atanh| #17#) (|atan| #17#) (|associates?| (#2# NIL #9# ELT)) (|asinh| #17#) (|asin| #17#) (|asech| #17#) (|asec| #17#) (|approximate| (#48# NIL (AND #46# (|has| |#1| (SIGNATURE |coerce| (|#1| #8#)))) ELT)) (|annihilate?| #1#) (|acsch| #17#) (|acsc| #17#) (|acoth| #17#) (|acot| #17#) (|acosh| #17#) (|acos| #17#) (|Zero| #24#) (|One| #24#) (D (#39# NIL #49# ELT) #51# #52# #53# (#11# NIL #50# ELT) #54# (#41# NIL T ELT)) (= #1#) (/ (#56=($ $ |#1|) NIL #21# ELT) #26#) (- #28# (#27# 27 T ELT)) (+ #57=(#27# NIL T ELT)) (** #35# (#55# NIL T ELT) (#34# NIL #21# ELT) (#27# NIL #18# ELT) #58=(#13# NIL #18# ELT)) (* (($ #36# $) NIL T ELT) (($ #23# $) NIL T ELT) (($ #15# . #59=($)) NIL T ELT) #57# (#56# NIL T ELT) (($ |#1| . #59#) 26 T ELT) (($ #14# . #59#) NIL #18# ELT) #58#)) (((|GeneralUnivariatePowerSeries| |#1| |#2| |#3|) (|Join| (|UnivariatePuiseuxSeriesCategory| |#1|) (|PartialDifferentialDomain| $ #1=(|Variable| |#2|)) (CATEGORY |domain| (SIGNATURE |coerce| ($ #1#)) (SIGNATURE |coerce| ($ (|UnivariatePuiseuxSeries| |#1| |#2| |#3|))) (IF (|has| |#1| (|Algebra| (|Fraction| (|Integer|)))) (SIGNATURE |integrate| ($ $ #1#)) |%noBranch|))) (|Ring|) (|Symbol|) |#1|) (T |GeneralUnivariatePowerSeries|)) ((|coerce| #1=(*1 *1 *2) (AND #2=(|isDomain| *2 (|Variable| *4)) #3=(|ofType| *4 (|Symbol|)) #4=(|isDomain| *1 (|GeneralUnivariatePowerSeries| *3 *4 *5)) #5=(|ofCategory| *3 (|Ring|)) #6=(|ofType| *5 *3))) (|coerce| #1# (AND (|isDomain| *2 (|UnivariatePuiseuxSeries| *3 *4 *5)) #5# #3# #6# #4#)) (|integrate| (*1 *1 *1 *2) (AND #2# #3# #4# (|ofCategory| *3 (|Algebra| (|Fraction| (|Integer|)))) #5# #6#))) ((~= #1=(#2=(#3=(|Boolean|) $ $) NIL (OR #4=(|has| #5=(|Record| (|:| |key| |#1|) (|:| |entry| |#2|)) #6=(|BasicType|)) #7=(|has| |#2| #6#)) ELT)) (|table| #8=(#9=($) NIL T ELT) #10=(($ #11=(|List| #5#)) NIL T ELT)) (|swap!| (((|Void|) $ |#1| |#1|) NIL #12=(|has| $ (|ShallowlyMutableAggregate| |#2|)) ELT)) (|setelt| (#13=(|#2| $ |#1| |#2|) 18 #12# ELT)) (|select!| #14=(($ #15=(|Mapping| #3# #5#) $) NIL #16=(|has| $ (|FiniteAggregate| #5#)) ELT)) (|select| #14#) (|search| (#17=((|Union| |#2| #18="failed") |#1| $) 19 T ELT)) (|sample| (#9# NIL T CONST)) (|removeDuplicates| (#19=($ $) NIL #20=(AND #16# #4#) ELT)) (|remove!| (#21=($ #5# $) NIL #16# ELT) #14# (#17# 16 T ELT)) (|remove| (#21# NIL #20# ELT) #14#) (|reduce| ((#5# #22=(|Mapping| #5# #5# #5#) $ #5# #5#) NIL #4# ELT) ((#5# #22# $ #5#) NIL T ELT) ((#5# #22# $) NIL T ELT)) (|qsetelt!| (#13# NIL #12# ELT)) (|qelt| (#23=(|#2| $ |#1|) NIL T ELT)) (|minIndex| #24=((|#1| $) NIL #25=(|has| |#1| (|OrderedSet|)) ELT)) (|members| ((#11# $) NIL T ELT)) (|member?| ((#3# #5# $) NIL #4# ELT)) (|maxIndex| #24#) (|map!| #26=(($ (|Mapping| #5# #5#) . #27=($)) NIL T ELT) #28=(($ (|Mapping| |#2| |#2|) . #27#) NIL T ELT)) (|map| #26# #28# #26# (($ (|Mapping| |#2| |#2| |#2|) $ $) NIL T ELT)) (|latex| (((|String|) $) NIL #29=(OR #30=(|has| #5# #31=(|SetCategory|)) #32=(|has| |#2| #31#)) ELT)) (|keys| #33=(((|List| |#1|) $) NIL T ELT)) (|key?| #34=((#3# |#1| $) NIL T ELT)) (|inspect| #35=((#5# $) NIL T ELT)) (|insert!| (#21# NIL T ELT)) (|indices| #33#) (|index?| #34#) (|hash| (((|SingleInteger|) $) NIL #29# ELT)) (|first| ((|#2| $) NIL #25# ELT)) (|find| (((|Union| #5# #18#) #15# $) NIL T ELT)) (|fill!| (($ $ |#2|) NIL #12# ELT)) (|extract!| #35#) (|every?| #36=((#3# #15# $) NIL T ELT)) (|eval| #37=(($ $ (|List| #38=(|Equation| #5#))) NIL #39=(AND (|has| #5# (|Evalable| #5#)) #30#) ELT) #40=(($ $ #38#) NIL #39# ELT) #41=(($ $ #5# #5#) NIL #39# ELT) #42=(($ $ #11# #11#) NIL #39# ELT) (($ $ #43=(|List| |#2|) #43#) NIL #44=(AND (|has| |#2| (|Evalable| |#2|)) #32#) ELT) (($ $ |#2| |#2|) NIL #44# ELT) (($ $ #45=(|Equation| |#2|)) NIL #44# ELT) (($ $ (|List| #45#)) NIL #44# ELT) #42# #41# #40# #37#) (|eq?| (#2# NIL T ELT)) (|entry?| ((#3# |#2| $) NIL (AND (|has| $ (|FiniteAggregate| |#2|)) #7#) ELT)) (|entries| ((#43# $) NIL T ELT)) (|empty?| ((#3# $) NIL T ELT)) (|empty| #8#) (|elt| (#23# 13 T ELT) (#13# NIL T ELT)) (|dictionary| #8# #10#) (|count| ((#46=(|NonNegativeInteger|) #5# $) NIL #4# ELT) ((#46# #15# $) NIL T ELT)) (|copy| (#19# NIL T ELT)) (|convert| ((#47=(|InputForm|) $) NIL (|has| #5# (|ConvertibleTo| #47#)) ELT)) (|construct| #10#) (|coerce| ((#48=(|OutputForm|) $) NIL (OR (|has| #5# #49=(|CoercibleTo| #48#)) (|has| |#2| #49#)) ELT)) (|before?| #1#) (|bag| #10#) (|any?| #36#) (= #1#) (|#| ((#46# $) NIL T ELT))) @@ -1383,7 +1386,7 @@ NIL ((~= #1=(#2=(#3=(|Boolean|) $ $) NIL T ELT)) (|zeroSetSplitIntoTriangularSystems| (((|List| (|Record| (|:| |close| $) #4=(|:| |open| #5=(|List| |#4|)))) #5#) NIL T ELT)) (|zeroSetSplit| (((|List| $) #5#) NIL T ELT)) (|variables| #6=(((|List| |#3|) $) NIL T ELT)) (|trivialIdeal?| #7=(#8=(#3# $) NIL T ELT)) (|triangular?| #9=(#8# NIL #10=(|has| |#1| (|IntegralDomain|)) ELT)) (|stronglyReduced?| #11=(#12=(#3# |#4| $) NIL T ELT) #7#) (|stronglyReduce| #13=((|#4| |#4| $) NIL T ELT)) (|sort| (((|Record| (|:| |under| $) (|:| |floor| $) (|:| |upper| $)) $ |#3|) NIL T ELT)) (|select| #14=(($ #15=(|Mapping| #3# |#4|) $) NIL #16=(|has| $ (|FiniteAggregate| |#4|)) ELT) ((#17=(|Union| |#4| #18="failed") $ |#3|) NIL T ELT)) (|sample| (#19=($) NIL T CONST)) (|roughUnitIdeal?| (#8# 28 #10# ELT)) (|roughSubIdeal?| #20=(#2# NIL #10# ELT)) (|roughEqualIdeals?| #20#) (|roughBase?| #9#) (|rewriteSetWithReduction| ((#5# #5# $ #21=(|Mapping| |#4| |#4| |#4|) #22=(|Mapping| #3# |#4| |#4|)) NIL T ELT)) (|rewriteIdealWithRemainder| #23=((#5# #5# $) NIL #10# ELT)) (|rewriteIdealWithHeadRemainder| #23#) (|retractIfCan| ((#24=(|Union| $ #18#) #5#) NIL T ELT)) (|retract| (#25=($ #5#) NIL T ELT)) (|rest| ((#24# $) 44 T ELT)) (|removeZero| #13#) (|removeDuplicates| (#26=($ $) NIL #27=(AND #16# #28=(|has| |#4| (|BasicType|))) ELT)) (|remove| (($ |#4| $) NIL #27# ELT) #14#) (|remainder| (((|Record| (|:| |rnum| |#1|) (|:| |polnum| |#4|) #29=(|:| |den| |#1|)) |#4| $) NIL #10# ELT)) (|reduced?| ((#3# |#4| $ #22#) NIL T ELT)) (|reduceByQuasiMonic| #13#) (|reduce| ((|#4| #21# $ |#4| |#4|) NIL #28# ELT) ((|#4| #21# $ |#4|) NIL T ELT) ((|#4| #21# $) NIL T ELT) ((|#4| |#4| $ #21# #22#) NIL T ELT)) (|quasiComponent| (((|Record| (|:| |close| #5#) #4#) $) NIL T ELT)) (|normalized?| #11# #7#) (|mvar| ((|#3| $) 37 T ELT)) (|members| (#30=(#5# $) 18 T ELT)) (|member?| (#12# 26 #28# ELT)) (|map!| (#31=($ (|Mapping| |#4| |#4|) $) 24 T ELT)) (|map| (#31# 22 T ELT)) (|mainVariables| #6#) (|mainVariable?| #32=((#3# |#3| $) NIL T ELT)) (|latex| (((|String|) $) NIL T ELT)) (|last| (#33=(#17# $) 41 T ELT)) (|initials| (#30# NIL T ELT)) (|initiallyReduced?| #11# #7#) (|initiallyReduce| #13#) (|infRittWu?| #1#) (|headRemainder| (((|Record| (|:| |num| |#4|) #29#) |#4| $) NIL #10# ELT)) (|headReduced?| #11# #7#) (|headReduce| #13#) (|hash| (((|SingleInteger|) $) NIL T ELT)) (|first| (#33# 39 T ELT)) (|find| ((#17# #15# $) NIL T ELT)) (|extendIfCan| ((#24# $ |#4|) 54 T ELT)) (|extend| (($ $ |#4|) NIL T ELT)) (|every?| #34=((#3# #15# $) NIL T ELT)) (|eval| (($ $ #5# #5#) NIL #35=(AND (|has| |#4| (|Evalable| |#4|)) (|has| |#4| (|SetCategory|))) ELT) (($ $ |#4| |#4|) NIL #35# ELT) (($ $ #36=(|Equation| |#4|)) NIL #35# ELT) (($ $ (|List| #36#)) NIL #35# ELT)) (|eq?| #1#) (|empty?| (#8# 17 T ELT)) (|empty| (#19# 14 T ELT)) (|degree| #37=(#38=(#39=(|NonNegativeInteger|) $) NIL T ELT)) (|count| ((#39# |#4| $) NIL #28# ELT) ((#39# #15# $) NIL T ELT)) (|copy| (#26# 13 T ELT)) (|convert| ((#40=(|InputForm|) $) NIL (|has| |#4| (|ConvertibleTo| #40#)) ELT)) (|construct| (#25# 21 T ELT)) (|collectUpper| (#41=($ $ |#3|) 48 T ELT)) (|collectUnder| (#41# 50 T ELT)) (|collectQuasiMonic| (#26# NIL T ELT)) (|collect| (#41# NIL T ELT)) (|coerce| (((|OutputForm|) $) 34 T ELT) (#30# 45 T ELT)) (|coHeight| (#38# NIL (|has| |#3| (|Finite|)) ELT)) (|before?| #1#) (|basicSet| ((#42=(|Union| (|Record| (|:| |bas| $) (|:| |top| #5#)) #18#) #5# #22#) NIL T ELT) ((#42# #5# #15# #22#) NIL T ELT)) (|autoReduced?| ((#3# $ (|Mapping| #3# |#4| #5#)) NIL T ELT)) (|any?| #34#) (|algebraicVariables| #6#) (|algebraic?| #32#) (= #1#) (|#| #37#)) (((|GeneralTriangularSet| |#1| |#2| |#3| |#4|) (|TriangularSetCategory| |#1| |#2| |#3| |#4|) (|IntegralDomain|) (|OrderedAbelianMonoidSup|) (|OrderedSet|) (|RecursivePolynomialCategory| |#1| |#2| |#3|)) (T |GeneralTriangularSet|)) NIL -((~= #1=((#2=(|Boolean|) $ $) NIL T ELT)) (|zero?| #3=((#2# $) NIL T ELT)) (|unitNormal| (((|Record| (|:| |unit| $) (|:| |canonical| $) (|:| |associate| $)) $) NIL T ELT)) (|unitCanonical| #4=(($ $) NIL T ELT)) (|unit?| #3#) (|subtractIfCan| #5=((#6=(|Union| $ #7="failed") $ $) NIL T ELT)) (|squareFreePart| #4#) (|squareFree| #8=(((|Factored| $) $) NIL T ELT)) (|sizeLess?| #1#) (|sample| (#9=($) NIL T CONST)) (|retractIfCan| (((|Union| #10=(|Integer|) . #11=(#7#)) . #12=($)) NIL T ELT) (((|Union| #13=(|Fraction| #10#) . #11#) . #12#) NIL T ELT)) (|retract| ((#10# . #14=($)) NIL T ELT) ((#13# . #14#) NIL T ELT)) (|rem| #15=(($ $ $) NIL T ELT)) (|recip| ((#6# $) NIL T ELT)) (|quo| #15#) (|principalIdeal| (((|Record| (|:| |coef| #16=(|List| $)) #17=(|:| |generator| $)) #16#) NIL T ELT)) (|prime?| #3#) (|pi| (#9# 17 T ELT)) (|opposite?| #1#) (|one?| #3#) (|multiEuclidean| (((|Union| #16# #7#) #16# $) NIL T ELT)) (|lcm| #15# #18=(($ #16#) NIL T ELT)) (|latex| (((|String|) $) NIL T ELT)) (|inv| #4#) (|hash| (((|SingleInteger|) $) NIL T ELT)) (|gcdPolynomial| ((#19=(|SparseUnivariatePolynomial| $) #19# #19#) NIL T ELT)) (|gcd| #15# #18#) (|factor| #8#) (|extendedEuclidean| (((|Record| #20=(|:| |coef1| $) #21=(|:| |coef2| $) #17#) $ $) NIL T ELT) (((|Union| (|Record| #20# #21#) #7#) $ $ $) NIL T ELT)) (|exquo| #5#) (|expressIdealMember| (((|Maybe| #16#) #16# $) NIL T ELT)) (|euclideanSize| ((#22=(|NonNegativeInteger|) $) NIL T ELT)) (|divide| (((|Record| (|:| |quotient| $) (|:| |remainder| $)) $ $) NIL T ELT)) (|convert| (#23=((|Float|) $) 21 T ELT) (#24=((|DoubleFloat|) $) 24 T ELT) (((|Fraction| (|SparseUnivariatePolynomial| #10#)) $) 18 T ELT) (((|InputForm|) $) 53 T ELT)) (|coerce| (((|OutputForm|) $) 51 T ELT) (($ #10#) NIL T ELT) #4# (($ #13#) NIL T ELT) (#24# 23 T ELT) (#23# 20 T ELT)) (|characteristic| ((#22#) NIL T CONST)) (|before?| #1#) (|associates?| #1#) (|annihilate?| #1#) (|Zero| (#9# 37 T CONST)) (|One| (#9# 8 T CONST)) (= #1#) (/ #15#) (- #4# #15#) (+ #15#) (** (($ $ #25=(|PositiveInteger|)) NIL T ELT) (($ $ #22#) NIL T ELT) (($ $ #10#) NIL T ELT)) (* (($ #25# $) NIL T ELT) (($ #22# $) NIL T ELT) (($ #10# . #26=($)) NIL T ELT) #15# (($ $ #13#) NIL T ELT) (($ #13# . #26#) NIL T ELT))) +((~= #1=((#2=(|Boolean|) $ $) NIL T ELT)) (|zero?| #3=((#2# $) NIL T ELT)) (|unitNormal| (((|Record| (|:| |unit| $) (|:| |canonical| $) (|:| |associate| $)) $) NIL T ELT)) (|unitCanonical| #4=(($ $) NIL T ELT)) (|unit?| #3#) (|subtractIfCan| (((|Maybe| $) $ $) NIL T ELT)) (|squareFreePart| #4#) (|squareFree| #5=(((|Factored| $) $) NIL T ELT)) (|sizeLess?| #1#) (|sample| (#6=($) NIL T CONST)) (|retractIfCan| (((|Union| #7=(|Integer|) . #8=(#9="failed")) . #10=($)) NIL T ELT) (((|Union| #11=(|Fraction| #7#) . #8#) . #10#) NIL T ELT)) (|retract| ((#7# . #12=($)) NIL T ELT) ((#11# . #12#) NIL T ELT)) (|rem| #13=(($ $ $) NIL T ELT)) (|recip| ((#14=(|Union| $ #9#) $) NIL T ELT)) (|quo| #13#) (|principalIdeal| (((|Record| (|:| |coef| #15=(|List| $)) #16=(|:| |generator| $)) #15#) NIL T ELT)) (|prime?| #3#) (|pi| (#6# 17 T ELT)) (|opposite?| #1#) (|one?| #3#) (|multiEuclidean| (((|Union| #15# #9#) #15# $) NIL T ELT)) (|lcm| #13# #17=(($ #15#) NIL T ELT)) (|latex| (((|String|) $) NIL T ELT)) (|inv| #4#) (|hash| (((|SingleInteger|) $) NIL T ELT)) (|gcdPolynomial| ((#18=(|SparseUnivariatePolynomial| $) #18# #18#) NIL T ELT)) (|gcd| #13# #17#) (|factor| #5#) (|extendedEuclidean| (((|Record| #19=(|:| |coef1| $) #20=(|:| |coef2| $) #16#) $ $) NIL T ELT) (((|Union| (|Record| #19# #20#) #9#) $ $ $) NIL T ELT)) (|exquo| ((#14# $ $) NIL T ELT)) (|expressIdealMember| (((|Maybe| #15#) #15# $) NIL T ELT)) (|euclideanSize| ((#21=(|NonNegativeInteger|) $) NIL T ELT)) (|divide| (((|Record| (|:| |quotient| $) (|:| |remainder| $)) $ $) NIL T ELT)) (|convert| (#22=((|Float|) $) 21 T ELT) (#23=((|DoubleFloat|) $) 24 T ELT) (((|Fraction| (|SparseUnivariatePolynomial| #7#)) $) 18 T ELT) (((|InputForm|) $) 53 T ELT)) (|coerce| (((|OutputForm|) $) 51 T ELT) (($ #7#) NIL T ELT) #4# (($ #11#) NIL T ELT) (#23# 23 T ELT) (#22# 20 T ELT)) (|characteristic| ((#21#) NIL T CONST)) (|before?| #1#) (|associates?| #1#) (|annihilate?| #1#) (|Zero| (#6# 37 T CONST)) (|One| (#6# 8 T CONST)) (= #1#) (/ #13#) (- #4# #13#) (+ #13#) (** (($ $ #24=(|PositiveInteger|)) NIL T ELT) (($ $ #21#) NIL T ELT) (($ $ #7#) NIL T ELT)) (* (($ #24# $) NIL T ELT) (($ #21# $) NIL T ELT) (($ #7# . #25=($)) NIL T ELT) #13# (($ $ #11#) NIL T ELT) (($ #11# . #25#) NIL T ELT))) (((|Pi|) (|Join| (|Field|) (|CharacteristicZero|) (|RetractableTo| #1=(|Integer|)) (|RetractableTo| (|Fraction| #1#)) (|RealConstant|) (|CoercibleTo| (|DoubleFloat|)) (|CoercibleTo| (|Float|)) (|ConvertibleTo| (|Fraction| (|SparseUnivariatePolynomial| #1#))) (|ConvertibleTo| (|InputForm|)) (CATEGORY |domain| (SIGNATURE |pi| ($))))) (T |Pi|)) ((|pi| (*1 *1) (|isDomain| *1 (|Pi|)))) ((~= #1=(((|Boolean|) $ $) NIL T ELT)) (|rhs| (#2=((|SpadAst|) $) 12 T ELT)) (|lhs| (#2# 10 T ELT)) (|latex| (((|String|) $) NIL T ELT)) (|hash| (((|SingleInteger|) $) NIL T ELT)) (|coerce| (((|OutputForm|) $) 18 T ELT) (($ #3=(|Syntax|)) NIL T ELT) ((#3# $) NIL T ELT)) (|before?| #1#) (= #1#)) @@ -1395,10 +1398,10 @@ NIL ((|lfunc| ((#1=(|Integer|) #1# #1#) 19 T ELT)) (|inHallBasis?| (((|Boolean|) #1# #1# #1# #1#) 28 T ELT)) (|generate| (((|Vector| (|List| #1#)) #2=(|NonNegativeInteger|) #2#) 42 T ELT))) (((|HallBasis|) (CATEGORY |package| (SIGNATURE |lfunc| (#1=(|Integer|) #1# #1#)) (SIGNATURE |inHallBasis?| ((|Boolean|) #1# #1# #1# #1#)) (SIGNATURE |generate| ((|Vector| (|List| #1#)) #2=(|NonNegativeInteger|) #2#)))) (T |HallBasis|)) ((|generate| (*1 *2 *3 *3) (AND (|isDomain| *3 (|NonNegativeInteger|)) (|isDomain| *2 (|Vector| (|List| #1=(|Integer|)))) #2=(|isDomain| *1 (|HallBasis|)))) (|inHallBasis?| (*1 *2 *3 *3 *3 *3) (AND (|isDomain| *3 #1#) (|isDomain| *2 (|Boolean|)) #2#)) (|lfunc| (*1 *2 *2 *2) (AND (|isDomain| *2 #1#) #2#))) -((~= #1=(#2=(#3=(|Boolean|) $ $) NIL T ELT)) (|zero?| #4=(#5=(#3# $) NIL T ELT)) (|variables| ((#6=(|List| #7=(|OrderedVariableList| |#1|)) $) NIL T ELT)) (|univariate| ((#8=(|SparseUnivariatePolynomial| $) $ #7#) NIL T ELT) ((#9=(|SparseUnivariatePolynomial| |#2|) $) NIL T ELT)) (|unitNormal| (((|Record| (|:| |unit| $) (|:| |canonical| $) (|:| |associate| $)) $) NIL #10=(|has| |#2| (|IntegralDomain|)) ELT)) (|unitCanonical| #11=(#12=($ $) NIL #10# ELT)) (|unit?| (#5# NIL #10# ELT)) (|totalDegree| #13=((#14=(|NonNegativeInteger|) $) NIL T ELT) ((#14# $ #6#) NIL T ELT)) (|subtractIfCan| (#15=(#16=(|Union| $ #17="failed") $ $) NIL T ELT)) (|squareFreePolynomial| #18=(((|Factored| #8#) #8#) NIL #19=(|has| |#2| (|PolynomialFactorizationExplicit|)) ELT)) (|squareFreePart| #20=(#12# NIL #21=(|has| |#2| (|GcdDomain|)) ELT)) (|squareFree| (#22=((|Factored| $) $) NIL #21# ELT)) (|solveLinearPolynomialEquation| (((|Union| #23=(|List| #8#) #17#) #23# #8#) NIL #19# ELT)) (|sample| #24=(($) NIL T CONST)) (|retractIfCan| (((|Union| |#2| . #25=(#17#)) . #26=($)) NIL T ELT) (((|Union| #27=(|Fraction| #28=(|Integer|)) . #25#) . #26#) NIL #29=(|has| |#2| (|RetractableTo| #27#)) ELT) (((|Union| #28# . #25#) . #26#) NIL #30=(|has| |#2| (|RetractableTo| #28#)) ELT) #31=(((|Union| #7# . #25#) . #26#) NIL T ELT)) (|retract| #32=(#33=(|#2| . #34=($)) NIL T ELT) ((#27# . #34#) NIL #29# ELT) ((#28# . #34#) NIL #30# ELT) ((#7# . #34#) NIL T ELT)) (|resultant| (($ $ $ #7#) NIL #35=(|has| |#2| (|CommutativeRing|)) ELT)) (|reorder| (($ $ (|List| #28#)) NIL T ELT)) (|reductum| #36=(#12# NIL T ELT)) (|reducedSystem| ((#37=(|Matrix| #28#) . #38=(#39=(|Matrix| $))) NIL #40=(|has| |#2| (|LinearlyExplicitRingOver| #28#)) ELT) ((#41=(|Record| (|:| |mat| #37#) (|:| |vec| (|Vector| #28#))) . #42=(#39# #43=(|Vector| $))) NIL #40# ELT) ((#44=(|Record| (|:| |mat| #45=(|Matrix| |#2|)) (|:| |vec| (|Vector| |#2|))) . #42#) NIL T ELT) ((#45# . #38#) NIL T ELT)) (|recip| ((#16# $) NIL T ELT)) (|primitivePart| #20# #46=(#47=($ $ #7#) NIL #21# ELT)) (|primitiveMonomials| #48=((#49=(|List| $) $) NIL T ELT)) (|prime?| (#5# NIL #19# ELT)) (|pomopo!| (($ $ |#2| #50=(|HomogeneousDirectProduct| (|#| |#1|) #14#) $) NIL T ELT)) (|patternMatch| ((#51=(|PatternMatchResult| #52=(|Float|) . #53=($)) $ #54=(|Pattern| #52#) #51#) NIL (AND (|has| #7# #55=(|PatternMatchable| #52#)) (|has| |#2| #55#)) ELT) ((#56=(|PatternMatchResult| #28# . #53#) $ #57=(|Pattern| #28#) #56#) NIL (AND (|has| #7# #58=(|PatternMatchable| #28#)) (|has| |#2| #58#)) ELT)) (|opposite?| #1#) (|one?| #4#) (|numberOfMonomials| #13#) (|multivariate| (($ #9# #7#) NIL T ELT) (($ #8# #7#) NIL T ELT)) (|monomials| #48#) (|monomial?| #4#) (|monomial| (($ |#2| #50#) NIL T ELT) #59=(($ $ #7# #14#) NIL T ELT) #60=(($ $ #6# #61=(|List| #14#)) NIL T ELT)) (|monicDivide| (((|Record| (|:| |quotient| $) (|:| |remainder| $)) $ $ #7#) NIL T ELT)) (|minimumDegree| #62=((#50# $) NIL T ELT) #63=((#14# $ #7#) NIL T ELT) #64=((#61# $ #6#) NIL T ELT)) (|mapExponents| (($ (|Mapping| #50# #50#) $) NIL T ELT)) (|map| (($ (|Mapping| |#2| |#2|) $) NIL T ELT)) (|mainVariable| #31#) (|leftReducedSystem| ((#37# . #65=(#43#)) NIL #40# ELT) ((#41# . #66=(#43# $)) NIL #40# ELT) ((#44# . #66#) NIL T ELT) ((#45# . #65#) NIL T ELT)) (|leadingMonomial| #36#) (|leadingCoefficient| #32#) (|lcm| #67=(($ #49#) NIL #21# ELT) #68=(#69=($ $ $) NIL #21# ELT)) (|latex| (((|String|) $) NIL T ELT)) (|isTimes| #70=(((|Union| #49# #17#) $) NIL T ELT)) (|isPlus| #70#) (|isExpt| (((|Union| (|Record| (|:| |var| #7#) (|:| |exponent| #14#)) #17#) $) NIL T ELT)) (|hash| (((|SingleInteger|) $) NIL T ELT)) (|ground?| #4#) (|ground| #32#) (|gcdPolynomial| ((#8# #8# #8#) NIL #21# ELT)) (|gcd| #67# #68#) (|factorSquareFreePolynomial| #18#) (|factorPolynomial| #18#) (|factor| (#22# NIL #19# ELT)) (|exquo| ((#16# $ |#2|) NIL #10# ELT) (#15# NIL #10# ELT)) (|eval| (($ $ (|List| #71=(|Equation| $))) NIL T ELT) (($ $ #71#) NIL T ELT) (($ $ $ $) NIL T ELT) (($ $ #49# #49#) NIL T ELT) (($ $ #7# |#2|) NIL T ELT) (($ $ #6# #72=(|List| |#2|)) NIL T ELT) (($ $ #7# $) NIL T ELT) (($ $ #6# #49#) NIL T ELT)) (|discriminant| (#47# NIL #35# ELT)) (|differentiate| #60# #59# #73=(($ $ #6#) NIL T ELT) #74=(#47# NIL T ELT)) (|degree| #62# #63# #64#) (|convert| ((#54# . #75=($)) NIL (AND (|has| #7# #76=(|ConvertibleTo| #54#)) (|has| |#2| #76#)) ELT) ((#57# . #75#) NIL (AND (|has| #7# #77=(|ConvertibleTo| #57#)) (|has| |#2| #77#)) ELT) ((#78=(|InputForm|) . #75#) NIL (AND (|has| #7# #79=(|ConvertibleTo| #78#)) (|has| |#2| #79#)) ELT)) (|content| (#33# NIL #21# ELT) #46#) (|conditionP| (((|Union| #43# #17#) #39#) NIL #80=(AND (|has| $ #81=(|CharacteristicNonZero|)) #19#) ELT)) (|coerce| (((|OutputForm|) $) NIL T ELT) (($ #28#) NIL T ELT) (($ |#2|) NIL T ELT) (($ #7#) NIL T ELT) (($ #27#) NIL (OR #82=(|has| |#2| (|Algebra| #27#)) #29#) ELT) #11#) (|coefficients| ((#72# $) NIL T ELT)) (|coefficient| ((|#2| $ #50#) NIL T ELT) #59# #60#) (|charthRoot| (((|Maybe| $) $) NIL (OR #80# (|has| |#2| #81#)) ELT)) (|characteristic| ((#14#) NIL T CONST)) (|binomThmExpt| (($ $ $ #14#) NIL #35# ELT)) (|before?| #1#) (|associates?| (#2# NIL #10# ELT)) (|annihilate?| #1#) (|Zero| #24#) (|One| #24#) (D #60# #59# #73# #74#) (= #1#) (/ (#83=($ $ |#2|) NIL (|has| |#2| (|Field|)) ELT)) (- #36# #84=(#69# NIL T ELT)) (+ #84#) (** (($ $ #85=(|PositiveInteger|)) NIL T ELT) (($ $ #14#) NIL T ELT)) (* (($ #85# $) NIL T ELT) (($ #14# $) NIL T ELT) (($ #28# . #86=($)) NIL T ELT) #84# (($ $ #27#) NIL #82# ELT) (($ #27# . #86#) NIL #82# ELT) (($ |#2| . #86#) NIL T ELT) (#83# NIL T ELT))) +((~= #1=(#2=(#3=(|Boolean|) $ $) NIL T ELT)) (|zero?| #4=(#5=(#3# $) NIL T ELT)) (|variables| ((#6=(|List| #7=(|OrderedVariableList| |#1|)) $) NIL T ELT)) (|univariate| ((#8=(|SparseUnivariatePolynomial| $) $ #7#) NIL T ELT) ((#9=(|SparseUnivariatePolynomial| |#2|) $) NIL T ELT)) (|unitNormal| (((|Record| (|:| |unit| $) (|:| |canonical| $) (|:| |associate| $)) $) NIL #10=(|has| |#2| (|IntegralDomain|)) ELT)) (|unitCanonical| #11=(#12=($ $) NIL #10# ELT)) (|unit?| (#5# NIL #10# ELT)) (|totalDegree| #13=((#14=(|NonNegativeInteger|) $) NIL T ELT) ((#14# $ #6#) NIL T ELT)) (|subtractIfCan| ((#15=(|Maybe| $) $ $) NIL T ELT)) (|squareFreePolynomial| #16=(((|Factored| #8#) #8#) NIL #17=(|has| |#2| (|PolynomialFactorizationExplicit|)) ELT)) (|squareFreePart| #18=(#12# NIL #19=(|has| |#2| (|GcdDomain|)) ELT)) (|squareFree| (#20=((|Factored| $) $) NIL #19# ELT)) (|solveLinearPolynomialEquation| (((|Union| #21=(|List| #8#) #22="failed") #21# #8#) NIL #17# ELT)) (|sample| #23=(($) NIL T CONST)) (|retractIfCan| (((|Union| |#2| . #24=(#22#)) . #25=($)) NIL T ELT) (((|Union| #26=(|Fraction| #27=(|Integer|)) . #24#) . #25#) NIL #28=(|has| |#2| (|RetractableTo| #26#)) ELT) (((|Union| #27# . #24#) . #25#) NIL #29=(|has| |#2| (|RetractableTo| #27#)) ELT) #30=(((|Union| #7# . #24#) . #25#) NIL T ELT)) (|retract| #31=(#32=(|#2| . #33=($)) NIL T ELT) ((#26# . #33#) NIL #28# ELT) ((#27# . #33#) NIL #29# ELT) ((#7# . #33#) NIL T ELT)) (|resultant| (($ $ $ #7#) NIL #34=(|has| |#2| (|CommutativeRing|)) ELT)) (|reorder| (($ $ (|List| #27#)) NIL T ELT)) (|reductum| #35=(#12# NIL T ELT)) (|reducedSystem| ((#36=(|Matrix| #27#) . #37=(#38=(|Matrix| $))) NIL #39=(|has| |#2| (|LinearlyExplicitRingOver| #27#)) ELT) ((#40=(|Record| (|:| |mat| #36#) (|:| |vec| (|Vector| #27#))) . #41=(#38# #42=(|Vector| $))) NIL #39# ELT) ((#43=(|Record| (|:| |mat| #44=(|Matrix| |#2|)) (|:| |vec| (|Vector| |#2|))) . #41#) NIL T ELT) ((#44# . #37#) NIL T ELT)) (|recip| ((#45=(|Union| $ #22#) $) NIL T ELT)) (|primitivePart| #18# #46=(#47=($ $ #7#) NIL #19# ELT)) (|primitiveMonomials| #48=((#49=(|List| $) $) NIL T ELT)) (|prime?| (#5# NIL #17# ELT)) (|pomopo!| (($ $ |#2| #50=(|HomogeneousDirectProduct| (|#| |#1|) #14#) $) NIL T ELT)) (|patternMatch| ((#51=(|PatternMatchResult| #52=(|Float|) . #53=($)) $ #54=(|Pattern| #52#) #51#) NIL (AND (|has| #7# #55=(|PatternMatchable| #52#)) (|has| |#2| #55#)) ELT) ((#56=(|PatternMatchResult| #27# . #53#) $ #57=(|Pattern| #27#) #56#) NIL (AND (|has| #7# #58=(|PatternMatchable| #27#)) (|has| |#2| #58#)) ELT)) (|opposite?| #1#) (|one?| #4#) (|numberOfMonomials| #13#) (|multivariate| (($ #9# #7#) NIL T ELT) (($ #8# #7#) NIL T ELT)) (|monomials| #48#) (|monomial?| #4#) (|monomial| (($ |#2| #50#) NIL T ELT) #59=(($ $ #7# #14#) NIL T ELT) #60=(($ $ #6# #61=(|List| #14#)) NIL T ELT)) (|monicDivide| (((|Record| (|:| |quotient| $) (|:| |remainder| $)) $ $ #7#) NIL T ELT)) (|minimumDegree| #62=((#50# $) NIL T ELT) #63=((#14# $ #7#) NIL T ELT) #64=((#61# $ #6#) NIL T ELT)) (|mapExponents| (($ (|Mapping| #50# #50#) $) NIL T ELT)) (|map| (($ (|Mapping| |#2| |#2|) $) NIL T ELT)) (|mainVariable| #30#) (|leftReducedSystem| ((#36# . #65=(#42#)) NIL #39# ELT) ((#40# . #66=(#42# $)) NIL #39# ELT) ((#43# . #66#) NIL T ELT) ((#44# . #65#) NIL T ELT)) (|leadingMonomial| #35#) (|leadingCoefficient| #31#) (|lcm| #67=(($ #49#) NIL #19# ELT) #68=(#69=($ $ $) NIL #19# ELT)) (|latex| (((|String|) $) NIL T ELT)) (|isTimes| #70=(((|Union| #49# #22#) $) NIL T ELT)) 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ELT) #84# (($ $ #26#) NIL #82# ELT) (($ #26# . #86#) NIL #82# ELT) (($ |#2| . #86#) NIL T ELT) (#83# NIL T ELT))) (((|HomogeneousDistributedMultivariatePolynomial| |#1| |#2|) (|Join| (|PolynomialCategory| |#2| (|HomogeneousDirectProduct| (|#| |#1|) (|NonNegativeInteger|)) (|OrderedVariableList| |#1|)) (CATEGORY |domain| (SIGNATURE |reorder| ($ $ (|List| (|Integer|)))))) (|List| (|Symbol|)) (|Ring|)) (T |HomogeneousDistributedMultivariatePolynomial|)) ((|reorder| (*1 *1 *1 *2) (AND (|isDomain| *2 (|List| (|Integer|))) (|isDomain| *1 (|HomogeneousDistributedMultivariatePolynomial| *3 *4)) (|ofType| *3 (|List| (|Symbol|))) (|ofCategory| *4 (|Ring|))))) -((~= #1=(#2=(#3=(|Boolean|) $ $) NIL #4=(|has| |#2| (|BasicType|)) ELT)) (|zero?| (#5=(#3# $) NIL #6=(|has| |#2| (|AbelianMonoid|)) ELT)) (|unitVector| (#7=($ #8=(|PositiveInteger|)) NIL #9=(|has| |#2| (|Ring|)) ELT)) (|swap!| (((|Void|) $ #10=(|Integer|) #10#) NIL #11=(|has| $ (|ShallowlyMutableAggregate| |#2|)) ELT)) (|sup| (#12=($ $ $) 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(|:| |mat| #40=(|Matrix| |#2|)) (|:| |vec| #41=(|Vector| |#2|))) . #37#) NIL #9# ELT) ((#40# . #33#) NIL #9# ELT)) (|reduce| ((|#2| #42=(|Mapping| |#2| |#2| |#2|) $ |#2| |#2|) NIL #4# ELT) ((|#2| #42# $ |#2|) NIL T ELT) ((|#2| #42# $) NIL T ELT)) (|recip| ((#14# $) NIL #9# ELT)) (|random| (#21# NIL #18# ELT)) (|qsetelt!| #19#) (|qelt| (#43=(|#2| $ #10#) 11 T ELT)) (|positive?| (#5# NIL #13# ELT)) (|opposite?| (#2# NIL #6# ELT)) (|one?| (#5# NIL #9# ELT)) (|minIndex| #44=(#29# NIL #45=(|has| #10# #46=(|OrderedSet|)) ELT)) (|min| #47=(#12# NIL #48=(|has| |#2| #46#) ELT)) (|members| #49=((#50=(|List| |#2|) $) NIL T ELT)) (|member?| (#51=(#3# |#2| $) NIL #4# ELT)) (|maxIndex| #44#) (|max| #47#) (|map| (($ #52=(|Mapping| |#2| |#2|) $) NIL T ELT)) (|lookup| ((#8# $) NIL #18# ELT)) (|leftReducedSystem| ((#32# . #53=(#38#)) NIL #35# ELT) ((#36# . #54=(#38# $)) NIL #35# ELT) ((#39# . #54#) NIL #9# ELT) ((#40# . #53#) NIL #9# ELT)) (|latex| (((|String|) $) NIL #25# ELT)) (|indices| (((|List| #10#) $) NIL T ELT)) (|index?| ((#3# #10# $) NIL T ELT)) (|index| (#7# NIL #18# ELT)) (|hash| (((|SingleInteger|) $) NIL #25# ELT)) (|first| (#31# NIL #45# ELT)) (|find| ((#28# #55=(|Mapping| #3# |#2|) $) NIL T ELT)) (|fill!| (#56=($ $ |#2|) NIL #11# ELT)) (|every?| #57=((#3# #55# $) NIL T ELT)) (|eval| (($ $ (|List| #58=(|Equation| |#2|))) NIL #59=(AND (|has| |#2| (|Evalable| |#2|)) #25#) ELT) (($ $ #58#) NIL #59# ELT) (($ $ |#2| |#2|) NIL #59# ELT) (($ $ #50# #50#) NIL #59# ELT)) (|eq?| (#2# NIL T ELT)) (|entry?| (#51# NIL (AND (|has| $ (|FiniteAggregate| |#2|)) #4#) ELT)) (|entries| #49#) (|empty?| (#5# NIL T ELT)) (|empty| (#21# NIL T ELT)) (|elt| (#20# NIL T ELT) (#43# NIL T ELT)) (|dot| ((|#2| $ $) NIL #9# ELT)) (|directProduct| (($ #41#) NIL T ELT)) (|dimension| (((|CardinalNumber|)) NIL #60=(|has| |#2| (|Field|)) ELT)) (|differentiate| #61=(#62=($ $ #17#) NIL #63=(AND (|has| |#2| (|DifferentialSpace|)) #9#) ELT) #64=(#65=($ $) NIL #63# ELT) #66=(($ $ #67=(|List| #68=(|Symbol|)) 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NIL #9# ELT)) (* (#12# NIL #9# ELT) (#56# NIL #80=(|has| |#2| (|Monoid|)) ELT) (($ |#2| . #81=($)) NIL #80# ELT) (($ #10# . #81#) NIL #78# ELT) (($ #17# $) NIL #6# ELT) (($ #8# $) NIL #79# ELT)) (|#| ((#17# $) NIL T ELT))) +((~= #1=(#2=(#3=(|Boolean|) $ $) NIL #4=(|has| |#2| (|BasicType|)) ELT)) (|zero?| (#5=(#3# $) NIL #6=(|has| |#2| (|AbelianMonoid|)) ELT)) (|unitVector| (#7=($ #8=(|PositiveInteger|)) NIL #9=(|has| |#2| (|Ring|)) ELT)) (|swap!| (((|Void|) $ #10=(|Integer|) #10#) NIL #11=(|has| $ (|ShallowlyMutableAggregate| |#2|)) ELT)) (|sup| (#12=($ $ $) NIL #13=(|has| |#2| (|OrderedAbelianMonoidSup|)) ELT)) (|subtractIfCan| (((|Maybe| $) $ $) NIL (|has| |#2| (|CancellationAbelianMonoid|)) ELT)) (|size| (#14=(#15=(|NonNegativeInteger|)) NIL #16=(|has| |#2| (|Finite|)) ELT)) (|setelt| #17=(#18=(|#2| $ #10# |#2|) NIL #11# ELT)) (|sample| (#19=($) NIL T CONST)) (|retractIfCan| (((|Union| #10# . #20=(#21="failed")) . #22=($)) NIL #23=(AND (|has| |#2| (|RetractableTo| #10#)) #24=(|has| |#2| (|SetCategory|))) ELT) (((|Union| #25=(|Fraction| #10#) . #20#) . #22#) NIL #26=(AND (|has| |#2| (|RetractableTo| #25#)) #24#) ELT) ((#27=(|Union| |#2| . #20#) . #22#) NIL #24# ELT)) (|retract| (#28=(#10# . #29=($)) NIL #23# ELT) ((#25# . #29#) NIL #26# ELT) (#30=(|#2| . #29#) NIL #24# ELT)) (|reducedSystem| ((#31=(|Matrix| #10#) . #32=(#33=(|Matrix| $))) NIL #34=(AND (|has| |#2| (|LinearlyExplicitRingOver| #10#)) #9#) ELT) ((#35=(|Record| (|:| |mat| #31#) (|:| |vec| (|Vector| #10#))) . #36=(#33# #37=(|Vector| $))) NIL #34# ELT) ((#38=(|Record| (|:| |mat| #39=(|Matrix| |#2|)) (|:| |vec| #40=(|Vector| |#2|))) . #36#) NIL #9# ELT) ((#39# . #32#) NIL #9# ELT)) (|reduce| ((|#2| #41=(|Mapping| |#2| |#2| |#2|) $ |#2| |#2|) NIL #4# ELT) ((|#2| #41# $ |#2|) NIL T ELT) ((|#2| #41# $) NIL T ELT)) (|recip| (((|Union| $ #21#) $) NIL #9# ELT)) (|random| (#19# NIL #16# ELT)) (|qsetelt!| #17#) (|qelt| (#42=(|#2| $ #10#) 11 T ELT)) (|positive?| (#5# NIL #13# ELT)) (|opposite?| (#2# NIL #6# ELT)) (|one?| (#5# NIL #9# ELT)) (|minIndex| #43=(#28# NIL #44=(|has| #10# #45=(|OrderedSet|)) ELT)) (|min| #46=(#12# NIL #47=(|has| |#2| #45#) ELT)) (|members| #48=((#49=(|List| |#2|) $) NIL T ELT)) (|member?| (#50=(#3# |#2| $) NIL #4# ELT)) (|maxIndex| #43#) (|max| #46#) (|map| (($ #51=(|Mapping| |#2| |#2|) $) NIL T ELT)) (|lookup| ((#8# $) NIL #16# ELT)) (|leftReducedSystem| ((#31# . #52=(#37#)) NIL #34# ELT) ((#35# . #53=(#37# $)) NIL #34# ELT) ((#38# . #53#) NIL #9# ELT) ((#39# . #52#) NIL #9# ELT)) (|latex| (((|String|) $) NIL #24# ELT)) (|indices| (((|List| #10#) $) NIL T ELT)) (|index?| ((#3# #10# $) NIL T ELT)) (|index| (#7# NIL #16# ELT)) (|hash| (((|SingleInteger|) $) NIL #24# ELT)) (|first| (#30# NIL #44# ELT)) (|find| ((#27# #54=(|Mapping| #3# |#2|) $) NIL T ELT)) (|fill!| (#55=($ $ |#2|) NIL #11# ELT)) (|every?| #56=((#3# #54# $) NIL T ELT)) (|eval| (($ $ (|List| #57=(|Equation| |#2|))) NIL #58=(AND (|has| |#2| (|Evalable| |#2|)) #24#) ELT) (($ $ #57#) NIL #58# ELT) (($ $ |#2| |#2|) NIL #58# ELT) (($ $ #49# #49#) NIL #58# ELT)) (|eq?| (#2# NIL T ELT)) (|entry?| (#50# NIL (AND (|has| $ (|FiniteAggregate| |#2|)) #4#) ELT)) (|entries| #48#) (|empty?| (#5# NIL T ELT)) (|empty| (#19# NIL T ELT)) (|elt| (#18# NIL T ELT) (#42# NIL T ELT)) (|dot| ((|#2| $ $) NIL #9# ELT)) (|directProduct| (($ #40#) NIL T ELT)) (|dimension| (((|CardinalNumber|)) NIL #59=(|has| |#2| (|Field|)) ELT)) (|differentiate| #60=(#61=($ $ #15#) NIL #62=(AND (|has| |#2| (|DifferentialSpace|)) #9#) ELT) #63=(#64=($ $) NIL #62# ELT) #65=(($ $ #66=(|List| #67=(|Symbol|)) (|List| #15#)) NIL #68=(AND (|has| |#2| (|PartialDifferentialSpace| #67#)) #9#) ELT) #69=(($ $ #67# #15#) NIL #68# ELT) #70=(($ $ #66#) NIL #68# ELT) #71=(($ $ #67#) NIL #68# ELT) #72=(($ $ #51#) NIL #9# ELT) #73=(($ $ #51# #15#) NIL #9# ELT)) (|count| ((#15# |#2| $) NIL #4# ELT) ((#15# #54# $) NIL T ELT)) (|copy| (#64# NIL T ELT)) (|coerce| ((#40# . #74=($)) NIL T ELT) (($ #10#) NIL (OR #23# #9#) ELT) (($ #25#) NIL #26# ELT) (($ |#2|) NIL #24# ELT) ((#75=(|OutputForm|) . #74#) NIL (|has| |#2| (|CoercibleTo| #75#)) ELT)) (|characteristic| (#14# NIL #9# CONST)) (|before?| #1#) (|any?| #56#) (|annihilate?| (#2# NIL #9# ELT)) (|Zero| (#19# NIL #6# CONST)) (|One| (#19# NIL #9# CONST)) (D #60# #63# #65# #69# #70# #71# #72# #73#) (>= #76=(#2# NIL #47# ELT)) (> #76#) (= #1#) (<= #76#) (< (#2# 17 #47# ELT)) (/ (#55# NIL #59# ELT)) (- (#12# NIL #77=(|has| |#2| (|AbelianGroup|)) ELT) (#64# NIL #77# ELT)) (+ (#12# NIL #78=(|has| |#2| (|AbelianSemiGroup|)) ELT)) (** (#61# NIL #9# ELT) (($ $ #8#) NIL #9# ELT)) (* (#12# NIL #9# ELT) (#55# NIL #79=(|has| |#2| (|Monoid|)) ELT) (($ |#2| . #80=($)) NIL #79# ELT) (($ #10# . #80#) NIL #77# ELT) (($ #15# $) NIL #6# ELT) (($ #8# $) NIL #78# ELT)) (|#| ((#15# $) NIL T ELT))) (((|HomogeneousDirectProduct| |#1| |#2|) (|DirectProductCategory| |#1| |#2|) (|NonNegativeInteger|) (|OrderedAbelianMonoidSup|)) (T |HomogeneousDirectProduct|)) NIL ((~= #1=(((|Boolean|) $ $) NIL T ELT)) (|parameters| ((#2=(|List| (|ParameterAst|)) $) 16 T ELT)) (|name| ((#3=(|Identifier|) $) 14 T ELT)) (|latex| (((|String|) $) NIL T ELT)) (|headAst| (($ #3# #2#) 12 T ELT)) (|hash| (((|SingleInteger|) $) NIL T ELT)) (|coerce| (((|OutputForm|) $) 23 T ELT) (($ #4=(|Syntax|)) NIL T ELT) ((#4# $) NIL T ELT)) (|before?| #1#) (= #1#)) @@ -1407,13 +1410,13 @@ NIL ((~= #1=(#2=(#3=(|Boolean|) $ $) NIL #4=(|has| |#1| (|BasicType|)) ELT)) (|sample| (#5=($) NIL T CONST)) (|reduce| ((|#1| #6=(|Mapping| |#1| |#1| |#1|) $ |#1| |#1|) NIL #4# ELT) ((|#1| #6# $ |#1|) NIL T ELT) ((|#1| #6# $) NIL T ELT)) (|merge!| (#7=($ $ $) 48 T ELT)) (|merge| (#7# 47 T ELT)) (|members| ((#8=(|List| |#1|) $) NIL T ELT)) (|member?| ((#3# |#1| $) NIL #4# ELT)) (|max| (#9=(|#1| $) 40 T ELT)) (|map!| #10=(($ (|Mapping| |#1| |#1|) $) NIL T ELT)) (|map| #10#) (|latex| (((|String|) $) NIL #11=(|has| |#1| (|SetCategory|)) ELT)) (|inspect| (#9# 41 T ELT)) (|insert!| (($ |#1| $) 18 T ELT)) (|heap| (#12=($ #8#) 19 T ELT)) (|hash| (((|SingleInteger|) $) NIL #11# ELT)) (|find| (((|Union| |#1| "failed") #13=(|Mapping| #3# |#1|) $) NIL T ELT)) (|extract!| (#9# 34 T ELT)) (|every?| #14=((#3# #13# $) NIL T ELT)) (|eval| (($ $ (|List| #15=(|Equation| |#1|))) NIL #16=(AND (|has| |#1| (|Evalable| |#1|)) #11#) ELT) (($ $ #15#) NIL #16# ELT) (($ $ |#1| |#1|) NIL #16# ELT) (($ $ #8# #8#) NIL #16# ELT)) (|eq?| (#2# NIL T ELT)) (|empty?| ((#3# $) NIL T ELT)) (|empty| (#5# 11 T ELT)) (|count| ((#17=(|NonNegativeInteger|) |#1| $) NIL #4# ELT) ((#17# #13# $) NIL T ELT)) (|copy| (($ $) NIL T ELT)) (|coerce| ((#18=(|OutputForm|) $) NIL (|has| |#1| (|CoercibleTo| #18#)) ELT)) (|before?| #1#) (|bag| (#12# 45 T ELT)) (|any?| #14#) (= #1#) (|#| ((#17# $) 29 T ELT))) (((|Heap| |#1|) (|Join| (|PriorityQueueAggregate| |#1|) (CATEGORY |domain| (SIGNATURE |heap| ($ (|List| |#1|))))) (|OrderedSet|)) (T |Heap|)) ((|heap| (*1 *1 *2) (AND (|isDomain| *2 (|List| *3)) (|ofCategory| *3 (|OrderedSet|)) (|isDomain| *1 (|Heap| *3))))) -((~= #1=(#2=(#3=(|Boolean|) $ $) NIL T ELT)) (|zero?| #4=((#3# $) NIL T ELT)) (|subtractIfCan| (((|Union| $ #5="failed") $ $) NIL T ELT)) (|sample| (#6=($) NIL T CONST)) (|reduce| (#7=($ $) 71 T ELT)) (|principal?| #4#) (|opposite?| #1#) (|latex| (((|String|) $) NIL T ELT)) (|ideal| ((#8=(|FractionalIdeal| |#2| (|Fraction| |#2|) |#3| |#4|) $) 45 T ELT)) (|hash| (((|SingleInteger|) $) NIL T ELT)) (|generator| (((|Union| |#4| #5#) $) 117 T ELT)) (|divisor| (($ #8#) 80 T ELT) (($ |#4|) 31 T ELT) (($ |#1| |#1|) 127 T ELT) (($ |#1| |#1| #9=(|Integer|)) NIL T ELT) (($ |#4| |#2| |#2| |#2| |#1|) 140 T ELT)) (|decompose| (((|Record| (|:| |id| #8#) (|:| |principalPart| |#4|)) $) 47 T ELT)) (|coerce| (((|OutputForm|) $) 110 T ELT)) (|before?| #1#) (|Zero| (#6# 32 T CONST)) (= (#2# 121 T ELT)) (- (#7# 76 T ELT) (#10=($ $ $) NIL T ELT)) (+ (#10# 72 T ELT)) (* (($ (|PositiveInteger|) $) NIL T ELT) (($ (|NonNegativeInteger|) $) NIL T ELT) (($ #9# $) 77 T ELT))) +((~= #1=(#2=(#3=(|Boolean|) $ $) NIL T ELT)) (|zero?| #4=((#3# $) NIL T ELT)) (|subtractIfCan| (((|Maybe| $) $ $) NIL T ELT)) (|sample| (#5=($) NIL T CONST)) (|reduce| (#6=($ $) 71 T ELT)) (|principal?| #4#) (|opposite?| #1#) (|latex| (((|String|) $) NIL T ELT)) (|ideal| ((#7=(|FractionalIdeal| |#2| (|Fraction| |#2|) |#3| |#4|) $) 45 T ELT)) (|hash| (((|SingleInteger|) $) NIL T ELT)) (|generator| (((|Union| |#4| "failed") $) 117 T ELT)) (|divisor| (($ #7#) 80 T ELT) (($ |#4|) 31 T ELT) (($ |#1| |#1|) 127 T ELT) (($ |#1| |#1| #8=(|Integer|)) NIL T ELT) (($ |#4| |#2| |#2| |#2| |#1|) 140 T ELT)) (|decompose| (((|Record| (|:| |id| #7#) (|:| |principalPart| |#4|)) $) 47 T ELT)) (|coerce| (((|OutputForm|) $) 110 T ELT)) (|before?| #1#) (|Zero| (#5# 32 T CONST)) (= (#2# 121 T ELT)) (- (#6# 76 T ELT) (#9=($ $ $) NIL T ELT)) (+ (#9# 72 T ELT)) (* (($ (|PositiveInteger|) $) NIL T ELT) (($ (|NonNegativeInteger|) $) NIL T ELT) (($ #8# $) 77 T ELT))) (((|HyperellipticFiniteDivisor| |#1| |#2| |#3| |#4|) (|FiniteDivisorCategory| |#1| |#2| |#3| |#4|) (|Field|) (|UnivariatePolynomialCategory| |#1|) (|UnivariatePolynomialCategory| (|Fraction| |#2|)) (|FunctionFieldCategory| |#1| |#2| |#3|)) (T |HyperellipticFiniteDivisor|)) NIL ((|lintgcd| ((#1=(|Integer|) #2=(|List| #1#)) 53 T ELT)) (|gcdprim| (#3=(|#1| #4=(|List| |#1|)) 94 T ELT)) (|gcdcofactprim| (#5=(#4# #4#) 95 T ELT)) (|gcdcofact| (#5# 97 T ELT)) (|gcd| (#3# 96 T ELT)) (|content| ((#2# #4#) 56 T ELT))) (((|HeuGcd| |#1|) (CATEGORY |package| (SIGNATURE |gcd| #1=(|#1| #2=(|List| |#1|))) (SIGNATURE |gcdprim| #1#) (SIGNATURE |gcdcofact| #3=(#2# #2#)) (SIGNATURE |gcdcofactprim| #3#) (SIGNATURE |content| (#4=(|List| #5=(|Integer|)) #2#)) (SIGNATURE |lintgcd| (#5# #4#))) (|UnivariatePolynomialCategory| #5#)) (T |HeuGcd|)) ((|lintgcd| #1=(*1 *2 *3) (AND (|isDomain| *3 #2=(|List| #3=(|Integer|))) (|isDomain| *2 #3#) #4=(|isDomain| *1 (|HeuGcd| *4)) (|ofCategory| *4 (|UnivariatePolynomialCategory| *2)))) (|content| #1# (AND (|isDomain| *3 (|List| *4)) (|ofCategory| *4 #5=(|UnivariatePolynomialCategory| #3#)) (|isDomain| *2 #2#) #4#)) (|gcdcofactprim| #6=(*1 *2 *2) #7=(AND (|isDomain| *2 (|List| *3)) (|ofCategory| *3 #5#) (|isDomain| *1 (|HeuGcd| *3)))) (|gcdcofact| #6# #7#) (|gcdprim| #1# #8=(AND (|isDomain| *3 (|List| *2)) (|isDomain| *1 (|HeuGcd| *2)) (|ofCategory| *2 #5#))) (|gcd| #1# #8#)) -((~= #1=(#2=(#3=(|Boolean|) $ $) NIL T ELT)) (|zero?| #4=(#5=(#3# $) NIL T ELT)) (|wholePart| (#6=(#7=(|Integer|) $) NIL #8=(|has| #7# (|EuclideanDomain|)) ELT)) (|unitNormal| (((|Record| (|:| |unit| $) (|:| |canonical| $) (|:| |associate| $)) $) NIL T ELT)) (|unitCanonical| #9=(#10=($ $) NIL T ELT)) (|unit?| #4#) (|subtractIfCan| #11=((#12=(|Union| $ #13="failed") $ $) NIL T ELT)) (|squareFreePolynomial| #14=(((|Factored| #15=(|SparseUnivariatePolynomial| $)) #15#) NIL #16=(|has| #7# (|PolynomialFactorizationExplicit|)) ELT)) (|squareFreePart| #9#) (|squareFree| #17=(((|Factored| $) $) NIL T ELT)) (|solveLinearPolynomialEquation| (((|Union| #18=(|List| #15#) #13#) #18# #15#) NIL #16# ELT)) (|sizeLess?| #1#) (|sign| (#6# NIL #19=(|has| #7# (|OrderedIntegralDomain|)) ELT)) (|sample| #20=(#21=($) NIL T CONST)) (|retractIfCan| (#22=((|Union| #7# . #23=(#13#)) . #24=($)) NIL T ELT) (((|Union| #25=(|Symbol|) . #23#) . #24#) NIL #26=(|has| #7# (|RetractableTo| #25#)) ELT) (((|Union| #27=(|Fraction| #7#) . #23#) . #24#) NIL #28=(|has| #7# (|RetractableTo| #7#)) ELT) (#22# NIL #28# ELT)) (|retract| #29=(#6# NIL T ELT) ((#25# $) NIL #26# ELT) (#30=(#27# $) NIL #28# ELT) (#6# NIL #28# ELT)) (|rem| #31=(#32=($ $ $) NIL T ELT)) (|reducedSystem| (#33=(#34=(|Matrix| #7#) #35=(|Matrix| $)) NIL #36=(|has| #7# (|LinearlyExplicitRingOver| #7#)) ELT) (#37=(#38=(|Record| (|:| |mat| #34#) (|:| |vec| (|Vector| #7#))) #35# #39=(|Vector| $)) NIL #36# ELT) (#37# NIL T ELT) (#33# NIL T ELT)) (|recip| ((#12# $) NIL T ELT)) (|random| (#21# NIL #40=(|has| #7# (|IntegerNumberSystem|)) ELT)) (|quo| #31#) (|principalIdeal| (((|Record| (|:| |coef| #41=(|List| $)) #42=(|:| |generator| $)) #41#) NIL T ELT)) (|prime?| #4#) (|positive?| #43=(#5# NIL #19# ELT)) (|patternMatch| ((#44=(|PatternMatchResult| #7# . #45=($)) $ #46=(|Pattern| #7#) #44#) NIL (|has| #7# (|PatternMatchable| #7#)) ELT) ((#47=(|PatternMatchResult| #48=(|Float|) . #45#) $ #49=(|Pattern| #48#) #47#) NIL (|has| #7# (|PatternMatchable| #48#)) ELT)) (|opposite?| #1#) (|one?| #4#) (|numerator| #9#) (|numer| #29#) (|nextItem| (#50=((|Maybe| $) $) NIL #51=(|has| #7# (|StepThrough|)) ELT)) (|negative?| #43#) (|multiEuclidean| (((|Union| #41# #13#) #41# $) NIL T ELT)) (|min| #52=(#32# NIL #53=(|has| #7# (|OrderedSet|)) ELT)) (|max| #52#) (|map| (($ #54=(|Mapping| #7# #7#) $) NIL T ELT)) (|leftReducedSystem| (#55=(#34# #39#) NIL #36# ELT) (#56=(#38# #39# $) NIL #36# ELT) (#56# NIL T ELT) (#55# NIL T ELT)) (|lcm| #31# #57=(($ #41#) NIL T ELT)) (|latex| (((|String|) $) NIL T ELT)) (|inv| #9#) (|init| (#21# NIL #51# CONST)) (|hex| (#58=($ #27#) 9 T ELT)) (|hash| (((|SingleInteger|) $) NIL T ELT)) (|gcdPolynomial| ((#15# #15# #15#) NIL T ELT)) (|gcd| #31# #57#) (|fractionPart| (#10# NIL #8# ELT) #59=(#30# NIL T ELT)) (|floor| #60=(#6# NIL #40# ELT)) (|factorSquareFreePolynomial| #14#) (|factorPolynomial| #14#) (|factor| #17#) (|extendedEuclidean| (((|Record| #61=(|:| |coef1| $) #62=(|:| |coef2| $) #42#) $ $) NIL T ELT) (((|Union| (|Record| #61# #62#) #13#) $ $ $) NIL T ELT)) (|exquo| #11#) (|expressIdealMember| (((|Maybe| #41#) #41# $) NIL T ELT)) (|eval| (($ $ #63=(|List| #7#) #63#) NIL #64=(|has| #7# (|Evalable| #7#)) ELT) (($ $ #7# #7#) NIL #64# ELT) (($ $ #65=(|Equation| #7#)) NIL #64# ELT) (($ $ (|List| #65#)) NIL #64# ELT) (($ $ #66=(|List| #25#) #63#) NIL #67=(|has| #7# (|InnerEvalable| #25# #7#)) ELT) (($ $ #25# #7#) NIL #67# ELT)) (|euclideanSize| ((#68=(|NonNegativeInteger|) $) NIL T ELT)) (|elt| (#69=($ $ #7#) NIL (|has| #7# (|Eltable| #7# #7#)) ELT)) (|divide| (((|Record| (|:| |quotient| $) (|:| |remainder| $)) $ $) NIL T ELT)) (|differentiate| #70=(($ $ #54#) NIL T ELT) #71=(($ $ #54# #68#) NIL T ELT) #72=(($ $ #25#) NIL #73=(|has| #7# (|PartialDifferentialSpace| #25#)) ELT) #74=(($ $ #66#) NIL #73# ELT) #75=(($ $ #25# #68#) NIL #73# ELT) #76=(($ $ #66# (|List| #68#)) NIL #73# ELT) #77=(#10# NIL #78=(|has| #7# (|DifferentialSpace|)) ELT) #79=(#80=($ $ #68#) NIL #78# ELT)) (|denominator| #9#) (|denom| #29#) (|convert| ((#46# . #81=($)) NIL (|has| #7# (|ConvertibleTo| #46#)) ELT) ((#49# . #81#) NIL (|has| #7# (|ConvertibleTo| #49#)) ELT) ((#82=(|InputForm|) . #81#) NIL (|has| #7# (|ConvertibleTo| #82#)) ELT) ((#48# . #81#) NIL #83=(|has| #7# (|RealConstant|)) ELT) (((|DoubleFloat|) . #81#) NIL #83# ELT)) (|conditionP| (((|Union| #39# #13#) #35#) NIL #84=(AND (|has| $ #85=(|CharacteristicNonZero|)) #16#) ELT)) (|coerce| (((|OutputForm|) $) NIL T ELT) #86=(($ #7#) NIL T ELT) #9# (#58# 8 T ELT) #86# (($ #25#) NIL #26# ELT) #59# (((|RadixExpansion| 16) $) 10 T ELT)) (|charthRoot| (#50# NIL (OR #84# (|has| #7# #85#)) ELT)) (|characteristic| ((#68#) NIL T CONST)) (|ceiling| #60#) (|before?| #1#) (|associates?| #1#) (|annihilate?| #1#) (|abs| (#10# NIL #19# ELT)) (|Zero| #20#) (|One| #20#) (D #70# #71# #72# #74# #75# #76# #77# #79#) (>= #87=(#2# NIL #53# ELT)) (> #87#) (= #1#) (<= #87#) (< #87#) (/ #31# (($ #7# #7#) NIL T ELT)) (- #9# #31#) (+ #31#) (** (($ $ #88=(|PositiveInteger|)) NIL T ELT) (#80# NIL T ELT) #89=(#69# NIL T ELT)) (* (($ #88# $) NIL T ELT) (($ #68# $) NIL T ELT) #90=(($ #7# . #91=($)) NIL T ELT) #31# (($ $ #27#) NIL T ELT) (($ #27# . #91#) NIL T ELT) #90# #89#)) +((~= #1=(#2=(#3=(|Boolean|) $ $) NIL T ELT)) (|zero?| #4=(#5=(#3# $) NIL T ELT)) (|wholePart| (#6=(#7=(|Integer|) $) NIL #8=(|has| #7# (|EuclideanDomain|)) ELT)) (|unitNormal| (((|Record| (|:| |unit| $) (|:| |canonical| $) (|:| |associate| $)) $) NIL T ELT)) (|unitCanonical| #9=(#10=($ $) NIL T ELT)) (|unit?| #4#) (|subtractIfCan| ((#11=(|Maybe| $) $ $) NIL T ELT)) (|squareFreePolynomial| #12=(((|Factored| #13=(|SparseUnivariatePolynomial| $)) #13#) NIL #14=(|has| #7# (|PolynomialFactorizationExplicit|)) ELT)) (|squareFreePart| #9#) (|squareFree| #15=(((|Factored| $) $) NIL T ELT)) (|solveLinearPolynomialEquation| (((|Union| #16=(|List| #13#) #17="failed") #16# #13#) NIL #14# ELT)) (|sizeLess?| #1#) (|sign| (#6# NIL #18=(|has| #7# (|OrderedIntegralDomain|)) ELT)) (|sample| #19=(#20=($) NIL T CONST)) (|retractIfCan| (#21=((|Union| #7# . #22=(#17#)) . #23=($)) NIL T ELT) (((|Union| #24=(|Symbol|) . #22#) . #23#) NIL #25=(|has| #7# (|RetractableTo| #24#)) ELT) (((|Union| #26=(|Fraction| #7#) . #22#) . #23#) NIL #27=(|has| #7# (|RetractableTo| #7#)) ELT) (#21# NIL #27# ELT)) (|retract| #28=(#6# NIL T ELT) ((#24# $) NIL #25# ELT) (#29=(#26# $) NIL #27# ELT) (#6# NIL #27# ELT)) (|rem| #30=(#31=($ $ $) NIL T ELT)) (|reducedSystem| (#32=(#33=(|Matrix| #7#) #34=(|Matrix| $)) NIL #35=(|has| #7# (|LinearlyExplicitRingOver| #7#)) ELT) (#36=(#37=(|Record| (|:| |mat| #33#) (|:| |vec| (|Vector| #7#))) #34# #38=(|Vector| $)) NIL #35# ELT) (#36# NIL T ELT) (#32# NIL T ELT)) (|recip| ((#39=(|Union| $ #17#) $) NIL T ELT)) (|random| (#20# NIL #40=(|has| #7# (|IntegerNumberSystem|)) ELT)) (|quo| #30#) (|principalIdeal| (((|Record| (|:| |coef| #41=(|List| $)) #42=(|:| |generator| $)) #41#) NIL T ELT)) (|prime?| #4#) (|positive?| #43=(#5# NIL #18# ELT)) (|patternMatch| ((#44=(|PatternMatchResult| #7# . #45=($)) $ #46=(|Pattern| #7#) #44#) NIL (|has| #7# (|PatternMatchable| #7#)) ELT) ((#47=(|PatternMatchResult| #48=(|Float|) . #45#) $ #49=(|Pattern| #48#) #47#) NIL (|has| #7# (|PatternMatchable| #48#)) ELT)) (|opposite?| #1#) (|one?| #4#) (|numerator| #9#) (|numer| #28#) (|nextItem| (#50=(#11# $) NIL #51=(|has| #7# (|StepThrough|)) ELT)) (|negative?| #43#) (|multiEuclidean| (((|Union| #41# #17#) #41# $) NIL T ELT)) (|min| #52=(#31# NIL #53=(|has| #7# (|OrderedSet|)) ELT)) (|max| #52#) (|map| (($ #54=(|Mapping| #7# #7#) $) NIL T ELT)) (|leftReducedSystem| (#55=(#33# #38#) NIL #35# ELT) (#56=(#37# #38# $) NIL #35# ELT) (#56# NIL T ELT) (#55# NIL T ELT)) (|lcm| #30# #57=(($ #41#) NIL T ELT)) (|latex| (((|String|) $) NIL T ELT)) (|inv| #9#) (|init| (#20# NIL #51# CONST)) (|hex| (#58=($ #26#) 9 T ELT)) (|hash| (((|SingleInteger|) $) NIL T ELT)) (|gcdPolynomial| ((#13# #13# #13#) NIL T ELT)) (|gcd| #30# #57#) (|fractionPart| (#10# NIL #8# ELT) #59=(#29# NIL T ELT)) (|floor| #60=(#6# NIL #40# ELT)) (|factorSquareFreePolynomial| #12#) (|factorPolynomial| #12#) (|factor| #15#) (|extendedEuclidean| (((|Record| #61=(|:| |coef1| $) #62=(|:| |coef2| $) #42#) $ $) NIL T ELT) (((|Union| (|Record| #61# #62#) #17#) $ $ $) NIL T ELT)) (|exquo| ((#39# $ $) NIL T ELT)) (|expressIdealMember| (((|Maybe| #41#) #41# $) NIL T ELT)) (|eval| (($ $ #63=(|List| #7#) #63#) NIL #64=(|has| #7# (|Evalable| #7#)) ELT) (($ $ #7# #7#) NIL #64# ELT) (($ $ #65=(|Equation| #7#)) NIL #64# ELT) (($ $ (|List| #65#)) NIL #64# ELT) (($ $ #66=(|List| #24#) #63#) NIL #67=(|has| #7# (|InnerEvalable| #24# #7#)) ELT) (($ $ #24# #7#) NIL #67# ELT)) (|euclideanSize| ((#68=(|NonNegativeInteger|) $) NIL T ELT)) (|elt| (#69=($ $ #7#) NIL (|has| #7# (|Eltable| #7# #7#)) ELT)) (|divide| (((|Record| (|:| |quotient| $) (|:| |remainder| $)) $ $) NIL T ELT)) (|differentiate| #70=(($ $ #54#) NIL T ELT) #71=(($ $ #54# #68#) NIL T ELT) #72=(($ $ #24#) NIL #73=(|has| #7# (|PartialDifferentialSpace| #24#)) ELT) #74=(($ $ #66#) NIL #73# ELT) #75=(($ $ #24# #68#) NIL #73# ELT) #76=(($ $ #66# (|List| #68#)) NIL #73# ELT) #77=(#10# NIL #78=(|has| #7# (|DifferentialSpace|)) ELT) #79=(#80=($ $ #68#) NIL #78# ELT)) (|denominator| #9#) (|denom| #28#) (|convert| ((#46# . #81=($)) NIL (|has| #7# (|ConvertibleTo| #46#)) ELT) ((#49# . #81#) NIL (|has| #7# (|ConvertibleTo| #49#)) ELT) ((#82=(|InputForm|) . #81#) NIL (|has| #7# (|ConvertibleTo| #82#)) ELT) ((#48# . #81#) NIL #83=(|has| #7# (|RealConstant|)) ELT) (((|DoubleFloat|) . #81#) NIL #83# ELT)) (|conditionP| (((|Union| #38# #17#) #34#) NIL #84=(AND (|has| $ #85=(|CharacteristicNonZero|)) #14#) ELT)) 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($ #2#))))) (T |HexadecimalExpansion|)) ((|fractionPart| (*1 *2 *1) #1=(AND (|isDomain| *2 (|Fraction| (|Integer|))) (|isDomain| *1 (|HexadecimalExpansion|)))) (|hex| (*1 *1 *2) #1#)) ((|eval| (($ $ (|List| #1=(|Equation| |#2|))) 13 T ELT) (($ $ #1#) NIL T ELT) (($ $ |#2| |#2|) NIL T ELT) (($ $ #2=(|List| |#2|) #2#) NIL T ELT))) @@ -1442,7 +1445,7 @@ NIL ((|factor| (((|Factored| |#4|) |#4| (|Mapping| (|Factored| |#2|) |#2|)) 54 T ELT))) (((|InnerAlgFactor| |#1| |#2| |#3| |#4|) (CATEGORY |package| (SIGNATURE |factor| ((|Factored| |#4|) |#4| (|Mapping| (|Factored| |#2|) |#2|)))) #1=(|Field|) (|UnivariatePolynomialCategory| |#1|) (|Join| #1# (|CharacteristicZero|) (|MonogenicAlgebra| |#1| |#2|)) (|UnivariatePolynomialCategory| |#3|)) (T |InnerAlgFactor|)) ((|factor| (*1 *2 *3 *4) (AND (|isDomain| *4 (|Mapping| (|Factored| *6) *6)) (|ofCategory| *6 (|UnivariatePolynomialCategory| *5)) (|ofCategory| *5 #1=(|Field|)) (|ofCategory| *7 (|Join| #1# (|CharacteristicZero|) (|MonogenicAlgebra| *5 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NIL T ELT)) (|operator| ((#49# #49#) NIL T ELT)) (|one?| (#14# 42 T ELT)) (|odd?| #50=(#14# NIL (|has| $ (|RetractableTo| #33#)) ELT)) (|numer| (#51=(#52=(|SparseMultivariatePolynomial| #33# #20#) $) 37 T ELT)) (|nthRoot| (#53=($ $ #33#) NIL T ELT)) (|norm| ((#6# #6# #20#) 86 T ELT) ((#6# #6# #19#) 61 T ELT) (($ $ #20#) 75 T ELT) (($ $ #19#) 76 T ELT)) (|multiEuclidean| (((|Union| #5# #23#) #5# $) NIL T ELT)) (|minPoly| ((#6# #20#) 73 #54=(|has| $ (|Ring|)) ELT)) (|map| (($ #55=(|Mapping| $ $) #20#) NIL T ELT)) (|mainKernel| #30#) (|leftReducedSystem| ((#38# . #56=(#42# $)) NIL T ELT) ((#39# . #57=(#42#)) NIL T ELT) ((#44# . #56#) NIL T ELT) ((#45# . #57#) NIL T ELT)) (|lcm| #47# #36#) (|latex| (((|String|) $) NIL T ELT)) (|kernels| (#18# NIL T ELT)) (|kernel| #58=(($ #49# $) NIL T ELT) #59=(($ #49# #5#) NIL T ELT)) (|is?| ((#3# $ #49#) NIL T ELT) #60=((#3# $ #7#) NIL T ELT)) (|inv| #15#) (|height| #61=((#62=(|NonNegativeInteger|) $) NIL T ELT)) (|hash| (((|SingleInteger|) $) NIL T 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|reduce| ($ $)) (SIGNATURE |trueEqual| ((|Boolean|) $ $)) (SIGNATURE |norm| (#6=(|SparseUnivariatePolynomial| $) #6# #4#)) (SIGNATURE |norm| (#6# #6# #7=(|List| #4#))) (SIGNATURE |norm| ($ $ #4#)) (SIGNATURE |norm| ($ $ #7#))))) (T |InnerAlgebraicNumber|)) ((|numer| #1=(*1 *2 *1) #2=(AND (|isDomain| *2 (|SparseMultivariatePolynomial| (|Integer|) #3=(|Kernel| #4=(|InnerAlgebraicNumber|)))) #5=(|isDomain| *1 #4#))) (|denom| #1# #2#) (|reduce| (*1 *1 *1) #5#) (|trueEqual| (*1 *2 *1 *1) (AND (|isDomain| *2 (|Boolean|)) #5#)) (|norm| #6=(*1 *2 *2 *3) (AND #7=(|isDomain| *2 (|SparseUnivariatePolynomial| #4#)) (|isDomain| *3 #3#) #5#)) (|norm| #6# (AND #7# (|isDomain| *3 #8=(|List| #3#)) #5#)) (|norm| #9=(*1 *1 *1 *2) (AND (|isDomain| *2 #3#) #5#)) (|norm| #9# (AND (|isDomain| *2 #8#) #5#))) ((~= #1=(#2=(#3=(|Boolean|) $ $) NIL #4=(|has| |#1| (|BasicType|)) ELT)) (|swap!| (((|Void|) $ #5=(|Integer|) #5#) NIL #6=(|has| $ (|ShallowlyMutableAggregate| |#1|)) ELT)) (|sorted?| ((#3# #7=(|Mapping| #3# |#1| |#1|) $) NIL T ELT) (#8=(#3# $) NIL #9=(|has| |#1| #10=(|OrderedSet|)) ELT)) (|sort!| (#11=($ #7# $) NIL #6# ELT) (#12=($ $) NIL (AND #6# #9#) ELT)) (|sort| (#11# NIL T ELT) (#12# NIL #9# ELT)) (|setelt| (#13=(|#1| $ #5# |#1|) 19 #6# ELT) ((|#1| $ #14=(|UniversalSegment| #5#) |#1|) NIL #6# ELT)) (|select| #15=(($ #16=(|Mapping| #3# |#1|) $) NIL #17=(|has| $ (|FiniteAggregate| |#1|)) ELT)) (|sample| (#18=($) NIL T CONST)) (|reverse!| (#12# NIL #6# ELT)) (|reverse| #19=(#12# NIL T ELT)) (|removeDuplicates| (#12# NIL #20=(AND #17# #4#) ELT)) (|remove| (#21=($ |#1| $) NIL #20# ELT) #15#) (|reduce| ((|#1| #22=(|Mapping| |#1| |#1| |#1|) $ |#1| |#1|) NIL #4# ELT) ((|#1| #22# $ |#1|) NIL T ELT) ((|#1| #22# $) NIL T ELT)) (|qsetelt!| (#13# 14 #6# ELT)) (|qelt| (#23=(|#1| $ #5#) 13 T ELT)) (|position| ((#5# #16# $) NIL T ELT) ((#5# |#1| $) NIL #4# ELT) ((#5# |#1| $ #5#) NIL #4# ELT)) (|new| (($ #24=(|NonNegativeInteger|) |#1|) NIL T ELT)) (|minIndex| (#25=(#5# $) 9 #26=(|has| #5# #10#) ELT)) (|min| #27=(#28=($ $ $) NIL #9# ELT)) (|merge| (($ #7# $ $) NIL T ELT) #27#) (|members| #29=((#30=(|List| |#1|) $) NIL T ELT)) (|member?| (#31=(#3# |#1| $) NIL #4# ELT)) (|maxIndex| (#25# 16 #26# ELT)) (|max| #27#) (|map!| #32=(($ (|Mapping| |#1| |#1|) $) NIL T ELT)) (|map| #32# (($ #22# $ $) NIL T ELT)) (|latex| (((|String|) $) NIL #33=(|has| |#1| (|SetCategory|)) ELT)) (|insert| (($ |#1| $ #5#) NIL T ELT) (#34=($ $ $ #5#) NIL T ELT)) (|indices| (((|List| #5#) $) NIL T ELT)) (|index?| ((#3# #5# $) NIL T ELT)) (|hash| (((|SingleInteger|) $) NIL #33# ELT)) (|first| ((|#1| $) NIL #26# ELT)) (|find| (((|Union| |#1| "failed") #16# $) NIL T ELT)) (|fill!| (#35=($ $ |#1|) NIL #6# ELT)) (|every?| #36=((#3# #16# $) NIL T ELT)) (|eval| (($ $ (|List| #37=(|Equation| |#1|))) NIL #38=(AND (|has| |#1| (|Evalable| |#1|)) #33#) ELT) (($ $ #37#) NIL #38# ELT) (($ $ |#1| |#1|) NIL #38# ELT) (($ $ #30# #30#) NIL #38# ELT)) (|eq?| (#2# NIL T ELT)) (|entry?| (#31# NIL #20# ELT)) (|entries| #29#) (|empty?| (#8# NIL T ELT)) (|empty| (#18# NIL T ELT)) (|elt| (#13# NIL T ELT) (#23# 18 T ELT) #39=(($ $ #14#) NIL T ELT)) (|delete| (($ $ #5#) NIL T ELT) #39#) (|count| ((#24# |#1| $) NIL #4# ELT) ((#24# #16# $) NIL T ELT)) (|copyInto!| (#34# NIL #6# ELT)) (|copy| #19#) (|convert| ((#40=(|InputForm|) $) NIL (|has| |#1| (|ConvertibleTo| #40#)) ELT)) (|construct| (($ #30#) NIL T ELT)) (|concat| (#35# NIL T ELT) (#21# NIL T ELT) (#28# NIL T ELT) (($ (|List| $)) NIL T ELT)) (|coerce| ((#41=(|OutputForm|) $) NIL (|has| |#1| (|CoercibleTo| #41#)) ELT)) (|before?| #1#) (|any?| #36#) (>= #42=(#2# NIL #9# ELT)) (> #42#) (= #1#) (<= #42#) (< #42#) (|#| ((#24# $) NIL T ELT))) @@ -1472,7 +1475,7 @@ NIL ((~= #1=(#2=(#3=(|Boolean|) $ $) NIL T ELT)) (|zeroDim?| ((#3# $ #4=(|List| |#3|)) 127 T ELT) (#5=(#3# $) 128 T ELT)) (|zero?| (#5# 178 T ELT)) (|saturate| (#6=($ $ |#4|) 117 T ELT) (($ $ |#4| #4#) 122 T ELT)) (|relationsIdeal| (((|SuchThat| (|List| #7=(|Polynomial| |#1|)) (|List| (|Equation| #7#))) #8=(|List| |#4|)) 171 (|has| |#3| (|ConvertibleTo| (|Symbol|))) ELT)) (|quotient| (#9=($ $ $) 107 T ELT) (#6# 105 T ELT)) (|one?| (#5# 177 T ELT)) (|leadingIdeal| (#10=($ $) 132 T ELT)) (|latex| (((|String|) $) NIL T ELT)) (|intersect| (#9# 99 T ELT) (($ (|List| $)) 101 T ELT)) (|inRadical?| (#11=(#3# |#4| $) 130 T ELT)) (|in?| (#2# 82 T ELT)) (|ideal| (#12=($ #8#) 106 T ELT)) (|hash| (((|SingleInteger|) $) NIL T ELT)) (|groebnerIdeal| (#12# 175 T ELT)) (|groebner?| (#5# 176 T ELT)) (|groebner| (#10# 85 T ELT)) (|generators| ((#8# $) 73 T ELT)) (|generalPosition| ((#13=(|Record| (|:| |mval| #14=(|Matrix| |#1|)) (|:| |invmval| #14#) (|:| |genIdeal| $)) $ #4#) NIL T ELT)) (|element?| (#11# 89 T ELT)) (|dimension| ((#15=(|Integer|) $ #4#) 134 T ELT) ((#15# $) 135 T ELT)) (|coerce| (((|OutputForm|) $) 174 T ELT) (#12# 102 T ELT)) (|before?| #1#) (|backOldPos| (($ #13#) NIL T ELT)) (= (#2# 84 T ELT)) (+ (#9# 109 T ELT)) (** (($ $ (|NonNegativeInteger|)) 115 T ELT)) (* (#9# 113 T ELT))) (((|PolynomialIdeals| |#1| |#2| |#3| |#4|) (|Join| (|SetCategory|) (CATEGORY |package| (SIGNATURE * #1=($ $ $)) (SIGNATURE ** ($ $ (|NonNegativeInteger|))) (SIGNATURE + #1#) (SIGNATURE |one?| #2=(#3=(|Boolean|) $)) (SIGNATURE |zero?| #2#) (SIGNATURE |element?| #4=(#3# |#4| $)) (SIGNATURE |in?| (#3# $ $)) (SIGNATURE |inRadical?| #4#) (SIGNATURE |zeroDim?| (#3# $ #5=(|List| |#3|))) (SIGNATURE |zeroDim?| #2#) (SIGNATURE |intersect| #1#) (SIGNATURE |intersect| ($ (|List| $))) (SIGNATURE |quotient| #1#) (SIGNATURE |quotient| #6=($ $ |#4|)) (SIGNATURE |groebner| #7=($ $)) (SIGNATURE |generalPosition| (#8=(|Record| (|:| |mval| #9=(|Matrix| |#1|)) (|:| |invmval| #9#) (|:| |genIdeal| $)) $ #5#)) (SIGNATURE |backOldPos| ($ #8#)) (SIGNATURE |dimension| (#10=(|Integer|) $ #5#)) (SIGNATURE |dimension| (#10# $)) (SIGNATURE |leadingIdeal| #7#) (SIGNATURE |ideal| #11=($ #12=(|List| |#4|))) (SIGNATURE |groebnerIdeal| #11#) (SIGNATURE |groebner?| #2#) (SIGNATURE |generators| (#12# $)) (SIGNATURE |coerce| #11#) (SIGNATURE |saturate| #6#) (SIGNATURE |saturate| ($ $ |#4| #5#)) (IF (|has| |#3| (|ConvertibleTo| (|Symbol|))) (SIGNATURE |relationsIdeal| ((|SuchThat| (|List| #13=(|Polynomial| |#1|)) (|List| (|Equation| #13#))) #12#)) |%noBranch|))) (|Field|) (|OrderedAbelianMonoidSup|) (|OrderedSet|) (|PolynomialCategory| |#1| |#2| |#3|)) (T |PolynomialIdeals|)) ((* #1=(*1 *1 *1 *1) #2=(AND (|ofCategory| *2 #3=(|Field|)) (|ofCategory| *3 #4=(|OrderedAbelianMonoidSup|)) (|ofCategory| *4 #5=(|OrderedSet|)) (|isDomain| *1 (|PolynomialIdeals| *2 *3 *4 *5)) (|ofCategory| *5 (|PolynomialCategory| *2 *3 *4)))) (** #6=(*1 *1 *1 *2) (AND (|isDomain| *2 (|NonNegativeInteger|)) #7=(|ofCategory| *3 #3#) #8=(|ofCategory| *4 #4#) #9=(|ofCategory| *5 #5#) #10=(|isDomain| *1 #11=(|PolynomialIdeals| *3 *4 *5 *6)) #12=(|ofCategory| *6 #13=(|PolynomialCategory| *3 *4 *5)))) (+ #1# #2#) (|one?| #14=(*1 *2 *1) #15=(AND #7# #8# #9# #16=(|isDomain| *2 (|Boolean|)) #10# #12#)) (|zero?| #14# #15#) (|element?| #17=(*1 *2 *3 *1) #18=(AND #19=(|ofCategory| *4 #3#) #20=(|ofCategory| *5 #4#) #21=(|ofCategory| *6 #5#) #16# (|isDomain| *1 (|PolynomialIdeals| *4 *5 *6 *3)) (|ofCategory| *3 #22=(|PolynomialCategory| *4 *5 *6)))) (|in?| (*1 *2 *1 *1) #15#) (|inRadical?| #17# #18#) (|zeroDim?| #23=(*1 *2 *1 *3) (AND #24=(|isDomain| *3 #25=(|List| *6)) #21# #19# #20# #16# #26=(|isDomain| *1 #27=(|PolynomialIdeals| *4 *5 *6 *7)) #28=(|ofCategory| *7 #22#))) (|zeroDim?| #14# #15#) (|intersect| #1# #2#) (|intersect| #29=(*1 *1 *2) (AND (|isDomain| *2 (|List| #11#)) #7# #8# #9# #10# #12#)) (|quotient| #1# #2#) (|quotient| #6# #30=(AND #7# #8# #9# (|isDomain| *1 (|PolynomialIdeals| *3 *4 *5 *2)) (|ofCategory| *2 #13#))) (|groebner| #31=(*1 *1 *1) #2#) (|generalPosition| #23# (AND #24# #21# #19# #20# (|isDomain| *2 (|Record| (|:| |mval| #32=(|Matrix| *4)) (|:| |invmval| #32#) (|:| |genIdeal| #27#))) #26# #28#)) (|backOldPos| #29# (AND (|isDomain| *2 (|Record| (|:| |mval| #33=(|Matrix| *3)) (|:| |invmval| #33#) (|:| |genIdeal| #11#))) #7# #8# #9# #10# #12#)) (|dimension| #23# (AND #24# #21# #19# #20# #34=(|isDomain| *2 (|Integer|)) #26# #28#)) (|dimension| #14# (AND #7# #8# #9# #34# #10# #12#)) (|leadingIdeal| #31# #2#) (|ideal| #29# #35=(AND #36=(|isDomain| *2 #25#) #12# #7# #8# #9# #10#)) (|groebnerIdeal| #29# #35#) (|groebner?| #14# #15#) (|generators| #14# (AND #7# #8# #9# #36# #10# #12#)) (|coerce| #29# #35#) (|saturate| #6# #30#) (|saturate| (*1 *1 *1 *2 *3) (AND #24# #21# #19# #20# (|isDomain| *1 (|PolynomialIdeals| *4 *5 *6 *2)) (|ofCategory| *2 #22#))) (|relationsIdeal| (*1 *2 *3) (AND (|isDomain| *3 (|List| *7)) #28# (|ofCategory| *6 (|ConvertibleTo| (|Symbol|))) #19# #20# #21# (|isDomain| *2 (|SuchThat| (|List| #37=(|Polynomial| *4)) (|List| (|Equation| #37#)))) #26#))) -((|zeroDimPrime?| (#1=((|Boolean|) #2=(|PolynomialIdeals| #3=(|Fraction| (|Integer|)) (|DirectProduct| |#2| (|NonNegativeInteger|)) #4=(|OrderedVariableList| |#1|) (|DistributedMultivariatePolynomial| |#1| #3#))) 178 T ELT)) (|zeroDimPrimary?| (#1# 179 T ELT)) (|radical| ((#2# #2#) 129 T ELT)) (|prime?| (#1# NIL T ELT)) (|primaryDecomp| (((|List| #2#) #2#) 181 T ELT)) (|contract| ((#2# #2# (|List| #4#)) 197 T ELT))) +((|zeroDimPrime?| (#1=((|Boolean|) #2=(|PolynomialIdeals| #3=(|Fraction| (|Integer|)) (|DirectProduct| |#2| (|NonNegativeInteger|)) #4=(|OrderedVariableList| |#1|) (|DistributedMultivariatePolynomial| |#1| #3#))) 182 T ELT)) (|zeroDimPrimary?| (#1# 183 T ELT)) (|radical| ((#2# #2#) 128 T ELT)) (|prime?| (#1# NIL T ELT)) (|primaryDecomp| (((|List| #2#) #2#) 185 T ELT)) (|contract| ((#2# #2# (|List| #4#)) 201 T ELT))) (((|IdealDecompositionPackage| |#1| |#2|) (CATEGORY |package| (SIGNATURE |zeroDimPrime?| #1=((|Boolean|) #2=(|PolynomialIdeals| #3=(|Fraction| (|Integer|)) (|DirectProduct| |#2| #4=(|NonNegativeInteger|)) #5=(|OrderedVariableList| |#1|) (|DistributedMultivariatePolynomial| |#1| #3#)))) (SIGNATURE |zeroDimPrimary?| #1#) (SIGNATURE |prime?| #1#) (SIGNATURE |radical| (#2# #2#)) (SIGNATURE |primaryDecomp| ((|List| #2#) #2#)) (SIGNATURE |contract| (#2# #2# (|List| #5#)))) (|List| (|Symbol|)) #4#) (T |IdealDecompositionPackage|)) ((|contract| (*1 *2 *2 *3) (AND (|isDomain| *2 #1=(|PolynomialIdeals| #2=(|Fraction| (|Integer|)) (|DirectProduct| *5 #3=(|NonNegativeInteger|)) #4=(|OrderedVariableList| *4) (|DistributedMultivariatePolynomial| *4 #2#))) (|isDomain| *3 (|List| #4#)) #5=(|ofType| *4 #6=(|List| (|Symbol|))) #7=(|ofType| *5 #3#) #8=(|isDomain| *1 (|IdealDecompositionPackage| *4 *5)))) (|primaryDecomp| #9=(*1 *2 *3) (AND #5# #7# (|isDomain| *2 (|List| #1#)) #8# #10=(|isDomain| *3 #1#))) (|radical| (*1 *2 *2) (AND (|isDomain| *2 (|PolynomialIdeals| #2# (|DirectProduct| *4 #3#) (|OrderedVariableList| *3) (|DistributedMultivariatePolynomial| *3 #2#))) (|ofType| *3 #6#) (|ofType| *4 #3#) (|isDomain| *1 (|IdealDecompositionPackage| *3 *4)))) (|prime?| #9# #11=(AND #10# #5# #7# (|isDomain| *2 (|Boolean|)) #8#)) (|zeroDimPrimary?| #9# #11#) (|zeroDimPrime?| #9# #11#)) ((|elt| ((|#1| $ |#1| |#1|) 6 T ELT))) @@ -1483,7 +1486,7 @@ NIL ((~= #1=(#2=((|Boolean|) $ $) NIL T ELT)) (|latex| (((|String|) $) NIL T ELT)) (|hash| (((|SingleInteger|) $) NIL T ELT)) (|gensym| (($) 6 T ELT)) (|coerce| (((|OutputForm|) $) 10 T ELT)) (|before?| #1#) (= (#2# 8 T ELT))) (((|Identifier|) (|Join| (|SetCategory|) (CATEGORY |domain| (SIGNATURE |gensym| ($))))) (T |Identifier|)) ((|gensym| (*1 *1) (|isDomain| *1 (|Identifier|)))) -((~= #1=((#2=(|Boolean|) $ $) NIL T ELT)) (|zero?| ((#2# $) NIL T ELT)) (|terms| ((#3=(|List| (|IndexedProductTerm| |#1| |#2|)) $) 10 T ELT)) (|subtractIfCan| (((|Union| $ "failed") $ $) NIL T ELT)) (|sample| (#4=($) NIL T CONST)) (|reductum| (#5=($ $) NIL T ELT)) (|opposite?| #1#) (|monomial| (($ |#1| |#2|) NIL T ELT)) (|map| (($ (|Mapping| |#1| |#1|) $) NIL T ELT)) (|leadingSupport| ((|#2| $) NIL T ELT)) (|leadingCoefficient| ((|#1| $) NIL T ELT)) (|latex| (((|String|) $) NIL T ELT)) (|hash| (((|SingleInteger|) $) NIL T ELT)) (|convert| (($ #3#) 15 T ELT)) (|coerce| (((|OutputForm|) $) NIL T ELT)) (|before?| #1#) (|Zero| (#4# 20 T CONST)) (= #1#) (- (#5# 16 T ELT) (#6=($ $ $) 36 T ELT)) (+ (#6# NIL T ELT)) (* (($ (|PositiveInteger|) $) NIL T ELT) (($ (|NonNegativeInteger|) $) NIL T ELT) (($ (|Integer|) $) 25 T ELT))) +((~= #1=((#2=(|Boolean|) $ $) NIL T ELT)) (|zero?| ((#2# $) NIL T ELT)) (|terms| ((#3=(|List| (|IndexedProductTerm| |#1| |#2|)) $) 10 T ELT)) (|subtractIfCan| (((|Maybe| $) $ $) NIL T ELT)) (|sample| (#4=($) NIL T CONST)) (|reductum| (#5=($ $) NIL T ELT)) (|opposite?| #1#) (|monomial| (($ |#1| |#2|) NIL T ELT)) (|map| (($ (|Mapping| |#1| |#1|) $) NIL T ELT)) (|leadingSupport| ((|#2| $) NIL T ELT)) (|leadingCoefficient| ((|#1| $) NIL T ELT)) (|latex| (((|String|) $) NIL T ELT)) (|hash| (((|SingleInteger|) $) NIL T ELT)) (|convert| (($ #3#) 15 T ELT)) (|coerce| (((|OutputForm|) $) NIL T ELT)) (|before?| #1#) (|Zero| (#4# 20 T CONST)) (= #1#) (- (#5# 16 T ELT) (#6=($ $ $) 36 T ELT)) (+ (#6# NIL T ELT)) (* (($ (|PositiveInteger|) $) NIL T ELT) (($ (|NonNegativeInteger|) $) NIL T ELT) (($ (|Integer|) $) 25 T ELT))) (((|IndexedDirectProductAbelianGroup| |#1| |#2|) (|Join| #1=(|AbelianGroup|) (|IndexedDirectProductCategory| |#1| |#2|)) #1# (|OrderedType|)) (T |IndexedDirectProductAbelianGroup|)) NIL ((~= #1=(#2=(#3=(|Boolean|) $ $) NIL T ELT)) (|zero?| ((#3# $) 16 T ELT)) (|terms| ((#4=(|List| (|IndexedProductTerm| |#1| |#2|)) $) 13 T ELT)) (|sample| (#5=($) NIL T CONST)) (|reductum| (($ $) 39 T ELT)) (|opposite?| (#2# 44 T ELT)) (|monomial| (($ |#1| |#2|) 36 T ELT)) (|map| (($ (|Mapping| |#1| |#1|) $) 38 T ELT)) (|leadingSupport| ((|#2| $) NIL T ELT)) (|leadingCoefficient| ((|#1| $) 41 T ELT)) (|latex| (((|String|) $) NIL T ELT)) (|hash| (((|SingleInteger|) $) NIL T ELT)) (|convert| (($ #4#) 11 T ELT)) (|coerce| (((|OutputForm|) $) NIL T ELT)) (|before?| #1#) (|Zero| (#5# 12 T CONST)) (= #1#) (+ (($ $ $) 30 T ELT)) (* (($ (|PositiveInteger|) $) NIL T ELT) (($ (|NonNegativeInteger|) $) 35 T ELT))) @@ -1500,7 +1503,7 @@ NIL ((~= #1=(#2=(#3=(|Boolean|) $ $) NIL T ELT)) (|zero?| #4=((#3# $) NIL T ELT)) (|terms| ((#5=(|List| (|IndexedProductTerm| |#1| |#2|)) $) 10 T ELT)) (|sample| #6=(($) NIL T CONST)) (|reductum| (($ $) NIL T ELT)) (|positive?| #4#) (|opposite?| #1#) (|monomial| (($ |#1| |#2|) NIL T ELT)) (|min| #7=(($ $ $) NIL T ELT)) (|max| #7#) (|map| (($ (|Mapping| |#1| |#1|) $) NIL T ELT)) (|leadingSupport| ((|#2| $) NIL T ELT)) (|leadingCoefficient| ((|#1| $) NIL T ELT)) (|latex| (((|String|) $) NIL T ELT)) (|hash| (((|SingleInteger|) $) NIL T ELT)) (|convert| (($ #5#) NIL T ELT)) (|coerce| (((|OutputForm|) $) NIL T ELT)) (|before?| #1#) (|Zero| #6#) (>= #1#) (> #1#) (= #1#) (<= #1#) (< (#2# 21 T ELT)) (+ #7#) (* (($ (|PositiveInteger|) $) NIL T ELT) (($ (|NonNegativeInteger|) $) NIL T ELT))) (((|IndexedDirectProductOrderedAbelianMonoid| |#1| |#2|) (|Join| #1=(|OrderedAbelianMonoid|) (|IndexedDirectProductCategory| |#1| |#2|)) #1# (|OrderedType|)) (T |IndexedDirectProductOrderedAbelianMonoid|)) NIL -((~= #1=((#2=(|Boolean|) $ $) NIL T ELT)) (|zero?| #3=((#2# $) NIL T ELT)) (|terms| ((#4=(|List| (|IndexedProductTerm| |#1| |#2|)) $) NIL T ELT)) (|sup| (#5=($ $ $) 24 T ELT)) (|subtractIfCan| (((|Union| $ "failed") $ $) 20 T ELT)) (|sample| #6=(($) NIL T CONST)) (|reductum| (($ $) NIL T ELT)) (|positive?| #3#) (|opposite?| #1#) (|monomial| (($ |#1| |#2|) NIL T ELT)) (|min| #7=(#5# NIL T ELT)) (|max| #7#) (|map| (($ (|Mapping| |#1| |#1|) $) NIL T ELT)) (|leadingSupport| ((|#2| $) NIL T ELT)) (|leadingCoefficient| ((|#1| $) NIL T ELT)) (|latex| (((|String|) $) NIL T ELT)) (|hash| (((|SingleInteger|) $) NIL T ELT)) (|convert| (($ #4#) NIL T ELT)) (|coerce| (((|OutputForm|) $) NIL T ELT)) (|before?| #1#) (|Zero| #6#) (>= #1#) (> #1#) (= #1#) (<= #1#) (< #1#) (+ #7#) (* (($ (|PositiveInteger|) $) NIL T ELT) (($ (|NonNegativeInteger|) $) NIL T ELT))) +((~= #1=((#2=(|Boolean|) $ $) NIL T ELT)) (|zero?| #3=((#2# $) NIL T ELT)) (|terms| ((#4=(|List| (|IndexedProductTerm| |#1| |#2|)) $) NIL T ELT)) (|sup| (#5=($ $ $) 33 T ELT)) (|subtractIfCan| (((|Maybe| $) $ $) 23 T ELT)) (|sample| #6=(($) NIL T CONST)) (|reductum| (($ $) NIL T ELT)) (|positive?| #3#) (|opposite?| #1#) (|monomial| (($ |#1| |#2|) NIL T ELT)) (|min| #7=(#5# NIL T ELT)) (|max| #7#) (|map| (($ (|Mapping| |#1| |#1|) $) NIL T ELT)) (|leadingSupport| ((|#2| $) NIL T ELT)) (|leadingCoefficient| ((|#1| $) NIL T ELT)) (|latex| (((|String|) $) NIL T ELT)) (|hash| (((|SingleInteger|) $) NIL T ELT)) (|convert| (($ #4#) NIL T ELT)) (|coerce| (((|OutputForm|) $) NIL T ELT)) (|before?| #1#) (|Zero| #6#) (>= #1#) (> #1#) (= #1#) (<= #1#) (< #1#) (+ #7#) (* (($ (|PositiveInteger|) $) NIL T ELT) (($ (|NonNegativeInteger|) $) NIL T ELT))) (((|IndexedDirectProductOrderedAbelianMonoidSup| |#1| |#2|) (|Join| #1=(|OrderedAbelianMonoidSup|) (|IndexedDirectProductCategory| |#1| |#2|)) #1# (|OrderedSet|)) (T |IndexedDirectProductOrderedAbelianMonoidSup|)) NIL ((~= #1=(((|Boolean|) $ $) NIL T ELT)) (|term| (($ |#2| |#1|) 9 T ELT)) (|index| ((|#2| $) 11 T ELT)) (|coerce| (((|Pair| |#2| |#1|) $) 14 T ELT)) (|coefficient| ((|#1| $) 13 T ELT)) (|before?| #1#) (= #1#)) @@ -1513,7 +1516,7 @@ NIL (((|InnerEvalable| |#1| |#2|) (|Category|) (|SetCategory|) (|Type|)) (T |InnerEvalable|)) ((|eval| (*1 *1 *1 *2 *3) (AND (|isDomain| *2 (|List| *4)) (|isDomain| *3 (|List| *5)) (|ofCategory| *1 (|InnerEvalable| *4 *5)) (|ofCategory| *4 (|SetCategory|)) (|ofCategory| *5 (|Type|)))) (|eval| (*1 *1 *1 *2 *3) (AND (|ofCategory| *1 (|InnerEvalable| *2 *3)) (|ofCategory| *2 (|SetCategory|)) (|ofCategory| *3 (|Type|))))) (|Join| (CATEGORY |domain| (SIGNATURE |eval| ($ $ |t#1| |t#2|)) (SIGNATURE |eval| ($ $ (|List| |t#1|) (|List| |t#2|))))) -((~= #1=(#2=(#3=(|Boolean|) $ $) NIL T ELT)) (|zero?| ((#3# $) 17 T ELT)) (|terms| (((|List| (|Record| (|:| |gen| |#1|) (|:| |exp| |#2|))) $) 19 T ELT)) (|subtractIfCan| (((|Union| $ #4="failed") $ $) NIL T ELT)) (|size| ((#5=(|NonNegativeInteger|) $) NIL T ELT)) (|sample| (#6=($) NIL T CONST)) (|retractIfCan| (((|Union| |#1| #4#) $) NIL T ELT)) (|retract| ((|#1| $) NIL T ELT)) (|opposite?| #1#) (|nthFactor| ((|#1| $ #7=(|Integer|)) 24 T ELT)) (|nthCoef| ((|#2| $ #7#) 22 T ELT)) (|mapGen| (($ (|Mapping| |#1| |#1|) $) 48 T ELT)) (|mapCoef| (($ (|Mapping| |#2| |#2|) $) 45 T ELT)) (|latex| (((|String|) $) NIL T ELT)) (|highCommonTerms| (#8=($ $ $) 55 (|has| |#2| (|OrderedAbelianMonoid|)) ELT)) (|hash| (((|SingleInteger|) $) NIL T ELT)) (|coerce| (((|OutputForm|) $) 44 T ELT) (($ |#1|) NIL T ELT)) (|coefficient| ((|#2| |#1| $) 51 T ELT)) (|before?| #1#) (|Zero| (#6# 11 T CONST)) (= (#2# 30 T ELT)) (+ (#8# 28 T ELT) (($ |#1| $) 26 T ELT)) (* (($ (|PositiveInteger|) $) NIL T ELT) (($ #5# $) 37 T ELT) (($ |#2| |#1|) 32 T ELT))) +((~= #1=(#2=(#3=(|Boolean|) $ $) NIL T ELT)) (|zero?| ((#3# $) 17 T ELT)) (|terms| (((|List| (|Record| (|:| |gen| |#1|) (|:| |exp| |#2|))) $) 19 T ELT)) (|subtractIfCan| (((|Maybe| $) $ $) NIL T ELT)) (|size| ((#4=(|NonNegativeInteger|) $) NIL T ELT)) (|sample| (#5=($) NIL T CONST)) (|retractIfCan| (((|Union| |#1| "failed") $) NIL T ELT)) (|retract| ((|#1| $) NIL T ELT)) (|opposite?| #1#) (|nthFactor| ((|#1| $ #6=(|Integer|)) 24 T ELT)) (|nthCoef| ((|#2| $ #6#) 22 T ELT)) (|mapGen| (($ (|Mapping| |#1| |#1|) $) 48 T ELT)) (|mapCoef| (($ (|Mapping| |#2| |#2|) $) 45 T ELT)) (|latex| (((|String|) $) NIL T ELT)) (|highCommonTerms| (#7=($ $ $) 55 (|has| |#2| (|OrderedAbelianMonoid|)) ELT)) (|hash| (((|SingleInteger|) $) NIL T ELT)) (|coerce| (((|OutputForm|) $) 44 T ELT) (($ |#1|) NIL T ELT)) (|coefficient| ((|#2| |#1| $) 51 T ELT)) (|before?| #1#) (|Zero| (#5# 11 T CONST)) (= (#2# 30 T ELT)) (+ (#7# 28 T ELT) (($ |#1| $) 26 T ELT)) (* (($ (|PositiveInteger|) $) NIL T ELT) (($ #4# $) 37 T ELT) (($ |#2| |#1|) 32 T ELT))) (((|InnerFreeAbelianMonoid| |#1| |#2| |#3|) (|FreeAbelianMonoidCategory| |#1| |#2|) (|SetCategory|) (|CancellationAbelianMonoid|) |#2|) (T |InnerFreeAbelianMonoid|)) NIL ((~= #1=(#2=(#3=(|Boolean|) $ $) NIL #4=(|has| |#1| (|BasicType|)) ELT)) (|swap!| (((|Void|) $ #5=(|Integer|) #5#) NIL #6=(|has| $ (|ShallowlyMutableAggregate| |#1|)) ELT)) (|sorted?| ((#3# #7=(|Mapping| #3# |#1| |#1|) $) NIL T ELT) (#8=(#3# $) NIL #9=(|has| |#1| #10=(|OrderedSet|)) ELT)) (|sort!| (#11=($ #7# $) NIL #6# ELT) (#12=($ $) NIL (AND #6# #9#) ELT)) (|sort| (#11# NIL T ELT) (#12# NIL #9# ELT)) (|shrinkable| ((#3# #3#) 32 T ELT)) (|setelt| (#13=(|#1| $ #5# |#1|) 42 #6# ELT) ((|#1| $ #14=(|UniversalSegment| #5#) |#1|) NIL #6# ELT)) (|select!| (#15=($ #16=(|Mapping| #3# |#1|) $) 79 T ELT)) (|select| #17=(#15# NIL #18=(|has| $ (|FiniteAggregate| |#1|)) ELT)) (|sample| (#19=($) NIL T CONST)) (|reverse!| (#12# NIL #6# ELT)) (|reverse| (#12# NIL T ELT)) (|removeDuplicates!| (#12# 83 #4# ELT)) (|removeDuplicates| (#12# NIL #20=(AND #18# #4#) ELT)) (|remove!| (#21=($ |#1| $) NIL #4# ELT) (#15# 66 T ELT)) (|remove| (#21# NIL #20# ELT) #17#) (|reduce| ((|#1| #22=(|Mapping| |#1| |#1| |#1|) $ |#1| |#1|) NIL #4# ELT) ((|#1| #22# $ |#1|) NIL T ELT) ((|#1| #22# $) NIL T ELT)) (|qsetelt!| (#13# NIL #6# ELT)) (|qelt| (#23=(|#1| $ #5#) NIL T ELT)) (|position| ((#5# #16# $) NIL T ELT) ((#5# |#1| $) NIL #4# ELT) ((#5# |#1| $ #5#) NIL #4# ELT)) (|physicalLength!| (#24=($ $ #5#) 19 T ELT)) (|physicalLength| (#25=(#26=(|NonNegativeInteger|) $) 13 T ELT)) (|new| (($ #26# |#1|) 31 T ELT)) (|minIndex| (#27=(#5# $) 29 #28=(|has| #5# #10#) ELT)) (|min| #29=(#30=($ $ $) NIL #9# ELT)) (|merge!| #29# (#31=($ #7# $ $) 57 T ELT)) (|merge| (#31# 58 T ELT) #29#) (|members| #32=((#33=(|List| |#1|) $) NIL T ELT)) (|member?| (#34=(#3# |#1| $) NIL #4# ELT)) (|maxIndex| (#27# 28 #28# ELT)) (|max| #29#) (|map!| #35=(($ (|Mapping| |#1| |#1|) $) NIL T ELT)) (|map| #35# (($ #22# $ $) NIL T ELT)) (|latex| (((|String|) $) NIL #36=(|has| |#1| (|SetCategory|)) ELT)) (|insert!| (#37=($ $ $ #5#) 75 T ELT) (#38=($ |#1| $ #5#) 59 T ELT)) (|insert| (#38# NIL T ELT) (#37# NIL T ELT)) (|indices| (((|List| #5#) $) NIL T ELT)) (|index?| ((#3# #5# $) NIL T ELT)) (|hash| (((|SingleInteger|) $) NIL #36# ELT)) (|flexibleArray| (#39=($ #33#) 43 T ELT)) (|first| ((|#1| $) NIL #28# ELT)) (|find| (((|Union| |#1| "failed") #16# $) NIL T ELT)) (|fill!| (#40=($ $ |#1|) 24 #6# ELT)) (|every?| #41=((#3# #16# $) NIL T ELT)) (|eval| (($ $ (|List| #42=(|Equation| |#1|))) NIL #43=(AND (|has| |#1| (|Evalable| |#1|)) #36#) ELT) (($ $ #42#) NIL #43# ELT) (($ $ |#1| |#1|) NIL #43# ELT) (($ $ #33# #33#) NIL #43# ELT)) (|eq?| (#2# 62 T ELT)) (|entry?| (#34# NIL #20# ELT)) (|entries| #32#) (|empty?| (#8# NIL T ELT)) (|empty| (#19# 21 T ELT)) (|elt| (#13# NIL T ELT) (#23# 55 T ELT) #44=(#45=($ $ #14#) NIL T ELT)) (|delete!| (#45# 73 T ELT) (#24# 67 T ELT)) (|delete| (#24# NIL T ELT) #44#) (|count| ((#26# |#1| $) NIL #4# ELT) ((#26# #16# $) NIL T ELT)) (|copyInto!| (#37# 63 #6# ELT)) (|copy| (#12# 53 T ELT)) (|convert| ((#46=(|InputForm|) $) NIL (|has| |#1| (|ConvertibleTo| #46#)) ELT)) (|construct| (#39# NIL T ELT)) (|concat!| (#30# 64 T ELT) (#40# 61 T ELT)) (|concat| (#40# NIL T ELT) (#21# 60 T ELT) (#30# NIL T ELT) (($ (|List| $)) NIL T ELT)) (|coerce| ((#47=(|OutputForm|) $) NIL (|has| |#1| (|CoercibleTo| #47#)) ELT)) (|before?| #1#) (|any?| #41#) (>= #48=(#2# NIL #9# ELT)) (> #48#) (= #1#) (<= #48#) (< #48#) (|#| (#25# 22 T ELT))) @@ -1522,7 +1525,7 @@ NIL ((~= #1=(((|Boolean|) $ $) NIL T ELT)) (|thenBranch| (#2=((|SpadAst|) $) 12 T ELT)) (|latex| (((|String|) $) NIL T ELT)) (|hash| (((|SingleInteger|) $) NIL T ELT)) (|elseBranch| (#2# 14 T ELT)) (|condition| (#2# 10 T ELT)) (|coerce| (((|OutputForm|) $) 20 T ELT) (($ #3=(|Syntax|)) NIL T ELT) ((#3# $) NIL T ELT)) (|before?| #1#) (= #1#)) (((|IfAst|) (|Join| (|SpadSyntaxCategory|) (CATEGORY |domain| (SIGNATURE |condition| #1=((|SpadAst|) $)) (SIGNATURE |thenBranch| #1#) (SIGNATURE |elseBranch| #1#)))) (T |IfAst|)) ((|condition| #1=(*1 *2 *1) #2=(AND (|isDomain| *2 (|SpadAst|)) (|isDomain| *1 (|IfAst|)))) (|thenBranch| #1# #2#) (|elseBranch| #1# #2#)) -((~= #1=((#2=(|Boolean|) $ $) NIL T ELT)) (|zero?| #3=(#4=(#2# $) NIL T ELT)) (|unitNormal| (((|Record| (|:| |unit| $) (|:| |canonical| $) (|:| |associate| $)) $) NIL T ELT)) (|unitCanonical| #5=(#6=($ $) NIL T ELT)) (|unit?| #3#) (|transcendent?| #3#) (|transcendenceDegree| (#7=(#8=(|NonNegativeInteger|)) NIL T ELT)) (|trace| #9=((#10=(|InnerPrimeField| |#1|) $) NIL T ELT) #11=(#12=($ $ #13=(|PositiveInteger|)) NIL #14=(|has| #10# (|Finite|)) ELT)) (|tableForDiscreteLogarithm| (((|Table| #13# #8#) #15=(|Integer|)) NIL #14# ELT)) (|subtractIfCan| #16=((#17=(|Union| $ #18="failed") $ $) NIL T ELT)) (|squareFreePart| #5#) (|squareFree| #19=(((|Factored| $) $) NIL T ELT)) (|sizeLess?| #1#) (|size| (#7# NIL #14# ELT)) (|sample| #20=(#21=($) NIL T CONST)) (|retractIfCan| (((|Union| #10# #18#) $) NIL T ELT)) (|retract| #9#) (|represents| (($ #22=(|Vector| #10#)) NIL T ELT)) (|representationType| (((|Union| "prime" "polynomial" "normal" "cyclic")) NIL #14# ELT)) (|rem| #23=(($ $ $) NIL T ELT)) (|recip| ((#17# $) NIL T ELT)) (|random| #24=(#21# NIL #14# ELT)) (|quo| #23#) (|principalIdeal| (((|Record| (|:| |coef| #25=(|List| $)) #26=(|:| |generator| $)) #25#) NIL T ELT)) (|primitiveElement| #24#) (|primitive?| #27=(#4# NIL #14# ELT)) (|primeFrobenius| (#28=($ $ #8#) NIL #29=(OR (|has| #10# (|CharacteristicNonZero|)) #14#) ELT) (#6# NIL #29# ELT)) (|prime?| #3#) (|order| #30=(#31=(#13# $) NIL #14# ELT) (#32=(#33=(|OnePointCompletion| #13#) $) NIL #29# ELT)) (|opposite?| #1#) (|one?| #3#) (|normalElement| #24#) (|normal?| #27#) (|norm| #9# #11#) (|nextItem| (#34=((|Maybe| $) $) NIL #14# ELT)) (|multiEuclidean| (((|Union| #25# #18#) #25# $) NIL T ELT)) (|minimalPolynomial| (#35=(#36=(|SparseUnivariatePolynomial| #10#) $) NIL T ELT) ((#37=(|SparseUnivariatePolynomial| $) $ #13#) NIL #14# ELT)) (|lookup| #30#) (|linearAssociatedOrder| #38=(#35# NIL #14# ELT)) (|linearAssociatedLog| #38# (((|Union| #36# #18#) $ $) NIL #14# ELT)) (|linearAssociatedExp| (($ $ #36#) NIL #14# ELT)) (|lcm| #23# #39=(($ #25#) NIL T ELT)) (|latex| (((|String|) $) NIL T ELT)) (|inv| #5#) (|init| (#21# NIL #14# CONST)) (|index| (($ #13#) NIL #14# ELT)) (|inGroundField?| #3#) (|hash| (((|SingleInteger|) $) NIL T ELT)) (|generator| #24#) (|gcdPolynomial| ((#37# #37# #37#) NIL T ELT)) (|gcd| #23# #39#) (|factorsOfCyclicGroupSize| (((|List| (|Record| (|:| |factor| #15#) (|:| |exponent| #15#)))) NIL #14# ELT)) (|factor| #19#) (|extensionDegree| ((#33#) NIL T ELT) ((#13#) NIL T ELT)) (|extendedEuclidean| (((|Record| #40=(|:| |coef1| $) #41=(|:| |coef2| $) #26#) $ $) NIL T ELT) (((|Union| (|Record| #40# #41#) #18#) $ $ $) NIL T ELT)) (|exquo| #16#) (|expressIdealMember| (((|Maybe| #25#) #25# $) NIL T ELT)) (|euclideanSize| (#42=(#8# $) NIL T ELT)) (|divide| (((|Record| (|:| |quotient| $) (|:| |remainder| $)) $ $) NIL T ELT)) (|discreteLog| (#42# NIL #14# ELT) (((|Union| #8# #18#) $ $) NIL #29# ELT)) (|dimension| (((|CardinalNumber|)) NIL T ELT)) (|differentiate| #43=(#28# NIL #14# ELT) #44=(#6# NIL #14# ELT)) (|degree| (#32# NIL T ELT) (#31# NIL T ELT)) (|definingPolynomial| ((#36#) NIL T ELT)) (|createPrimitiveElement| #24#) (|createNormalElement| #24#) (|coordinates| ((#22# $) NIL T ELT) (((|Matrix| #10#) #45=(|Vector| $)) NIL T ELT)) (|conditionP| (((|Union| #45# #18#) (|Matrix| $)) NIL #14# ELT)) (|coerce| (((|OutputForm|) $) NIL T ELT) (($ #15#) NIL T ELT) #5# (($ #46=(|Fraction| #15#)) NIL T ELT) (($ #10#) NIL T ELT)) (|charthRoot| #44# (#34# NIL #29# ELT)) (|characteristic| (#7# NIL T CONST)) (|before?| #1#) (|basis| ((#45#) NIL T ELT) ((#45# #13#) NIL T ELT)) (|associates?| #1#) (|annihilate?| #1#) (|algebraic?| #3#) (|Zero| #20#) (|One| #20#) (|Frobenius| #44# #43#) (D #43# #44#) (= #1#) (/ #23# #47=(($ $ #10#) NIL T ELT)) (- #5# #23#) (+ #23#) (** (#12# NIL T ELT) (#28# NIL T ELT) (($ $ #15#) NIL T ELT)) (* (($ #13# $) NIL T ELT) (($ #8# $) NIL T ELT) (($ #15# . #48=($)) NIL T ELT) #23# (($ $ #46#) NIL T ELT) (($ #46# . #48#) NIL T ELT) #47# (($ #10# . #48#) NIL T ELT))) +((~= #1=((#2=(|Boolean|) $ $) NIL T ELT)) (|zero?| #3=(#4=(#2# $) NIL T ELT)) (|unitNormal| (((|Record| (|:| |unit| $) (|:| |canonical| $) (|:| |associate| $)) $) NIL T ELT)) (|unitCanonical| #5=(#6=($ $) NIL T ELT)) (|unit?| #3#) (|transcendent?| #3#) (|transcendenceDegree| (#7=(#8=(|NonNegativeInteger|)) NIL T ELT)) (|trace| #9=((#10=(|InnerPrimeField| |#1|) $) NIL T ELT) #11=(#12=($ $ #13=(|PositiveInteger|)) NIL #14=(|has| #10# (|Finite|)) ELT)) (|tableForDiscreteLogarithm| (((|Table| #13# #8#) #15=(|Integer|)) NIL #14# ELT)) (|subtractIfCan| ((#16=(|Maybe| $) $ $) NIL T ELT)) (|squareFreePart| #5#) (|squareFree| #17=(((|Factored| $) $) NIL T ELT)) (|sizeLess?| #1#) (|size| (#7# NIL #14# ELT)) (|sample| #18=(#19=($) NIL T CONST)) (|retractIfCan| (((|Union| #10# #20="failed") $) NIL T ELT)) (|retract| #9#) (|represents| (($ #21=(|Vector| #10#)) NIL T ELT)) (|representationType| (((|Union| "prime" "polynomial" "normal" "cyclic")) NIL #14# ELT)) (|rem| #22=(($ $ $) NIL T ELT)) (|recip| ((#23=(|Union| $ #20#) $) NIL T ELT)) (|random| #24=(#19# NIL #14# ELT)) (|quo| #22#) (|principalIdeal| (((|Record| (|:| |coef| #25=(|List| $)) #26=(|:| |generator| $)) #25#) NIL T ELT)) (|primitiveElement| #24#) (|primitive?| #27=(#4# NIL #14# ELT)) (|primeFrobenius| (#28=($ $ #8#) NIL #29=(OR (|has| #10# (|CharacteristicNonZero|)) #14#) ELT) (#6# NIL #29# ELT)) (|prime?| #3#) (|order| #30=(#31=(#13# $) NIL #14# ELT) (#32=(#33=(|OnePointCompletion| #13#) $) NIL #29# ELT)) (|opposite?| #1#) (|one?| #3#) (|normalElement| #24#) (|normal?| #27#) (|norm| #9# #11#) (|nextItem| (#34=(#16# $) NIL #14# ELT)) (|multiEuclidean| (((|Union| #25# #20#) #25# $) NIL T ELT)) (|minimalPolynomial| (#35=(#36=(|SparseUnivariatePolynomial| #10#) $) NIL T ELT) ((#37=(|SparseUnivariatePolynomial| $) $ #13#) NIL #14# ELT)) (|lookup| #30#) (|linearAssociatedOrder| #38=(#35# NIL #14# ELT)) (|linearAssociatedLog| #38# (((|Union| #36# #20#) $ $) NIL #14# ELT)) (|linearAssociatedExp| (($ $ #36#) NIL #14# ELT)) (|lcm| #22# #39=(($ #25#) NIL T ELT)) (|latex| (((|String|) $) NIL T ELT)) (|inv| #5#) (|init| (#19# NIL #14# CONST)) (|index| (($ #13#) NIL #14# ELT)) (|inGroundField?| #3#) (|hash| (((|SingleInteger|) $) NIL T ELT)) (|generator| #24#) (|gcdPolynomial| ((#37# #37# #37#) NIL T ELT)) (|gcd| #22# #39#) (|factorsOfCyclicGroupSize| (((|List| (|Record| (|:| |factor| #15#) (|:| |exponent| #15#)))) NIL #14# ELT)) (|factor| #17#) (|extensionDegree| ((#33#) NIL T ELT) ((#13#) NIL T ELT)) (|extendedEuclidean| (((|Record| #40=(|:| |coef1| $) #41=(|:| |coef2| $) #26#) $ $) NIL T ELT) (((|Union| (|Record| #40# #41#) #20#) $ $ $) NIL T ELT)) (|exquo| ((#23# $ $) NIL T ELT)) (|expressIdealMember| (((|Maybe| #25#) #25# $) NIL T ELT)) (|euclideanSize| (#42=(#8# $) NIL T ELT)) (|divide| (((|Record| (|:| |quotient| $) (|:| |remainder| $)) $ $) NIL T ELT)) (|discreteLog| (#42# NIL #14# ELT) (((|Union| #8# #20#) $ $) NIL #29# ELT)) (|dimension| (((|CardinalNumber|)) NIL T ELT)) (|differentiate| #43=(#28# NIL #14# ELT) #44=(#6# NIL #14# ELT)) (|degree| (#32# NIL T ELT) (#31# NIL T ELT)) (|definingPolynomial| ((#36#) NIL T ELT)) (|createPrimitiveElement| #24#) (|createNormalElement| #24#) (|coordinates| ((#21# $) NIL T ELT) (((|Matrix| #10#) #45=(|Vector| $)) NIL T ELT)) (|conditionP| (((|Union| #45# #20#) (|Matrix| $)) NIL #14# ELT)) (|coerce| (((|OutputForm|) $) NIL T ELT) (($ #15#) NIL T ELT) #5# (($ #46=(|Fraction| #15#)) NIL T ELT) (($ #10#) NIL T ELT)) (|charthRoot| #44# (#34# NIL #29# ELT)) (|characteristic| (#7# NIL T CONST)) (|before?| #1#) (|basis| ((#45#) NIL T ELT) ((#45# #13#) NIL T ELT)) (|associates?| #1#) (|annihilate?| #1#) (|algebraic?| #3#) (|Zero| #18#) (|One| #18#) (|Frobenius| #44# #43#) (D #43# #44#) (= #1#) (/ #22# #47=(($ $ #10#) NIL T ELT)) (- #5# #22#) (+ #22#) (** (#12# NIL T ELT) (#28# NIL T ELT) (($ $ #15#) NIL T ELT)) (* (($ #13# $) NIL T ELT) (($ #8# $) NIL T ELT) (($ #15# . #48=($)) NIL T ELT) #22# (($ $ #46#) NIL T ELT) (($ #46# . #48#) NIL T ELT) #47# (($ #10# . #48#) NIL T ELT))) (((|InnerFiniteField| |#1| |#2|) (|FiniteAlgebraicExtensionField| (|InnerPrimeField| |#1|)) #1=(|PositiveInteger|) #1#) (T |InnerFiniteField|)) NIL ((|rowEchelon| (#1=(|#4| |#4|) 38 T ELT)) (|rank| (#2=((|NonNegativeInteger|) |#4|) 45 T ELT)) (|nullity| (#2# 46 T ELT)) (|nullSpace| (((|List| |#3|) |#4|) 57 (|has| |#3| (|ShallowlyMutableAggregate| |#1|)) ELT)) (|inverse| (((|Union| |#4| "failed") |#4|) 69 T ELT)) (|generalizedInverse| (#1# 61 T ELT)) (|determinant| ((|#1| |#4|) 60 T ELT))) @@ -1554,7 +1557,7 @@ NIL ((|incrementBy| ((#1=(|Mapping| |#1| |#1|) |#1|) 11 T ELT)) (|increment| ((#1#) 10 T ELT))) (((|IncrementingMaps| |#1|) (CATEGORY |package| (SIGNATURE |increment| (#1=(|Mapping| |#1| |#1|))) (SIGNATURE |incrementBy| (#1# |#1|))) (|Join| (|Monoid|) (|AbelianSemiGroup|))) (T |IncrementingMaps|)) ((|incrementBy| (*1 *2 *3) #1=(AND (|isDomain| *2 (|Mapping| *3 *3)) (|isDomain| *1 (|IncrementingMaps| *3)) (|ofCategory| *3 (|Join| (|Monoid|) (|AbelianSemiGroup|))))) (|increment| (*1 *2) #1#)) -((~= #1=((#2=(|Boolean|) $ $) NIL T ELT)) (|zero?| #3=((#2# $) NIL T ELT)) (|terms| ((#4=(|List| (|IndexedProductTerm| #5=(|NonNegativeInteger|) |#1|)) $) NIL T ELT)) (|sup| #6=(($ $ $) NIL T ELT)) (|subtractIfCan| (((|Union| $ "failed") $ $) NIL T ELT)) (|sample| #7=(($) NIL T CONST)) (|reductum| (($ $) NIL T ELT)) (|positive?| #3#) (|opposite?| #1#) (|monomial| (($ #5# |#1|) NIL T ELT)) (|min| #6#) (|max| #6#) (|map| (($ (|Mapping| #5# #5#) $) NIL T ELT)) (|leadingSupport| ((|#1| $) NIL T ELT)) (|leadingCoefficient| ((#5# $) NIL T ELT)) (|latex| (((|String|) $) NIL T ELT)) (|hash| (((|SingleInteger|) $) NIL T ELT)) (|convert| (($ #4#) NIL T ELT)) (|coerce| (((|OutputForm|) $) 28 T ELT)) (|before?| #1#) (|Zero| #7#) (>= #1#) (> #1#) (= #1#) (<= #1#) (< #1#) (+ #6#) (* (($ (|PositiveInteger|) $) NIL T ELT) (($ #5# $) NIL T ELT))) +((~= #1=((#2=(|Boolean|) $ $) NIL T ELT)) (|zero?| #3=((#2# $) NIL T ELT)) (|terms| ((#4=(|List| (|IndexedProductTerm| #5=(|NonNegativeInteger|) |#1|)) $) NIL T ELT)) (|sup| #6=(($ $ $) NIL T ELT)) (|subtractIfCan| (((|Maybe| $) $ $) NIL T ELT)) (|sample| #7=(($) NIL T CONST)) (|reductum| (($ $) NIL T ELT)) (|positive?| #3#) (|opposite?| #1#) (|monomial| (($ #5# |#1|) NIL T ELT)) (|min| #6#) (|max| #6#) (|map| (($ (|Mapping| #5# #5#) $) NIL T ELT)) (|leadingSupport| ((|#1| $) NIL T ELT)) (|leadingCoefficient| ((#5# $) NIL T ELT)) (|latex| (((|String|) $) NIL T ELT)) (|hash| (((|SingleInteger|) $) NIL T ELT)) (|convert| (($ #4#) NIL T ELT)) (|coerce| (((|OutputForm|) $) 28 T ELT)) (|before?| #1#) (|Zero| #7#) (>= #1#) (> #1#) (= #1#) (<= #1#) (< #1#) (+ #6#) (* (($ (|PositiveInteger|) $) NIL T ELT) (($ #5# $) NIL T ELT))) (((|IndexedExponents| |#1|) (|Join| (|OrderedAbelianMonoidSup|) (|IndexedDirectProductCategory| (|NonNegativeInteger|) |#1|)) (|OrderedSet|)) (T |IndexedExponents|)) NIL ((|solve1| (((|List| |#2|) #1=(|SparseUnivariatePolynomial| |#1|) |#3|) 98 T ELT)) (|innerEigenvectors| (((|List| (|Record| (|:| |outval| |#2|) (|:| |outmult| (|Integer|)) (|:| |outvect| (|List| (|Matrix| |#2|))))) #2=(|Matrix| |#1|) |#3| (|Mapping| (|Factored| #1#) #1#)) 114 T ELT)) (|charpol| ((#1# #2#) 110 T ELT))) @@ -1596,13 +1599,13 @@ NIL ((|symmetricRemainder| (#1=($ $ $) 87 T ELT)) (|squareFree| (#2=((|Factored| $) $) 50 T ELT)) (|retractIfCan| (((|Union| #3=(|Integer|) #4="failed") $) 62 T ELT)) (|retract| (#5=(#3# $) 40 T ELT)) (|rationalIfCan| (((|Union| #6=(|Fraction| #3#) #4#) $) 80 T ELT)) (|rational?| (#7=(#8=(|Boolean|) $) 24 T ELT)) (|rational| ((#6# $) 78 T ELT)) (|prime?| (#7# 53 T ELT)) (|powmod| (($ $ $ $) 94 T ELT)) (|permutation| (#1# 60 T ELT)) (|patternMatch| ((#9=(|PatternMatchResult| #3# $) $ #10=(|Pattern| #3#) #9#) 75 T ELT)) (|nextItem| (((|Maybe| $) $) 70 T ELT)) (|mask| (#11=($ $) 22 T ELT)) (|invmod| (#1# 92 T ELT)) (|init| (($) 63 T CONST)) (|factorial| (#11# 56 T ELT)) (|factor| (#2# 48 T ELT)) (|even?| (#7# 15 T ELT)) (|euclideanSize| ((#12=(|NonNegativeInteger|) $) 30 T ELT)) (|differentiate| (#11# 11 T ELT) (($ $ #12#) NIL T ELT)) (|copy| (#11# 16 T ELT)) (|convert| (#5# NIL T ELT) (((|InputForm|) $) 39 T ELT) ((#10# $) 43 T ELT) (((|Float|) $) 33 T ELT) (((|DoubleFloat|) $) 36 T ELT)) (|characteristic| ((#12#) 9 T CONST)) (|bit?| ((#8# $ $) 19 T ELT)) (|binomial| (#1# 58 T ELT))) (((|IntegerNumberSystem&| |#1|) (CATEGORY |package| (SIGNATURE |invmod| #1=(|#1| |#1| |#1|)) (SIGNATURE |powmod| (|#1| |#1| |#1| |#1|)) (SIGNATURE |mask| #2=(|#1| |#1|)) (SIGNATURE |copy| #2#) (SIGNATURE |rationalIfCan| ((|Union| #3=(|Fraction| #4=(|Integer|)) #5="failed") |#1|)) (SIGNATURE |rational| (#3# |#1|)) (SIGNATURE |rational?| #6=(#7=(|Boolean|) |#1|)) (SIGNATURE |symmetricRemainder| #1#) (SIGNATURE |bit?| (#7# |#1| |#1|)) (SIGNATURE |even?| #6#) (SIGNATURE |init| (|#1|) |constant|) (SIGNATURE |nextItem| ((|Maybe| |#1|) |#1|)) (SIGNATURE |convert| ((|DoubleFloat|) |#1|)) (SIGNATURE |convert| ((|Float|) |#1|)) (SIGNATURE |permutation| #1#) (SIGNATURE |factorial| #2#) (SIGNATURE |binomial| #1#) (SIGNATURE |patternMatch| (#8=(|PatternMatchResult| #4# |#1|) |#1| #9=(|Pattern| #4#) #8#)) (SIGNATURE |convert| (#9# |#1|)) (SIGNATURE |convert| ((|InputForm|) |#1|)) (SIGNATURE |retractIfCan| ((|Union| #4# #5#) |#1|)) (SIGNATURE |retract| #10=(#4# |#1|)) (SIGNATURE |convert| #10#) (SIGNATURE |differentiate| (|#1| |#1| #11=(|NonNegativeInteger|))) (SIGNATURE |differentiate| #2#) (SIGNATURE |euclideanSize| (#11# |#1|)) (SIGNATURE |factor| #12=((|Factored| |#1|) |#1|)) (SIGNATURE |squareFree| #12#) (SIGNATURE |prime?| #6#) (SIGNATURE |characteristic| (#11#) |constant|)) (|IntegerNumberSystem|)) (T |IntegerNumberSystem&|)) ((|characteristic| (*1 *2) (AND (|isDomain| *2 (|NonNegativeInteger|)) (|isDomain| *1 (|IntegerNumberSystem&| *3)) (|ofCategory| *3 (|IntegerNumberSystem|))))) -((~= (#1=((|Boolean|) $ $) 7 T ELT)) (|zero?| ((#2=(|Boolean|) $) 22 T ELT)) (|unitNormal| (((|Record| (|:| |unit| $) (|:| |canonical| $) (|:| |associate| $)) $) 55 T ELT)) (|unitCanonical| (($ $) 54 T ELT)) (|unit?| ((#3=(|Boolean|) $) 52 T ELT)) (|symmetricRemainder| (($ $ $) 102 T ELT)) (|subtractIfCan| (((|Union| $ "failed") $ $) 26 T ELT)) (|submod| (($ $ $ $) 91 T ELT)) (|squareFreePart| (($ $) 66 T ELT)) (|squareFree| (#4=((|Factored| $) $) 67 T ELT)) (|sizeLess?| (((|Boolean|) $ $) 145 T ELT)) (|sign| (((|Integer|) $) 134 T ELT)) (|shift| (($ $ $) 105 T ELT)) (|sample| (#5=($) 23 T CONST)) (|retractIfCan| (((|Union| #6=(|Integer|) "failed") $) 126 T ELT)) (|retract| ((#6# $) 127 T ELT)) (|rem| (#7=($ $ $) 149 T ELT)) (|reducedSystem| (((|Record| (|:| |mat| (|Matrix| #8=(|Integer|))) (|:| |vec| (|Vector| #8#))) #9=(|Matrix| $) #10=(|Vector| $)) 124 T ELT) (((|Matrix| #8#) #9#) 123 T ELT)) (|recip| (((|Union| $ "failed") $) 42 T ELT)) (|rationalIfCan| (((|Union| (|Fraction| (|Integer|)) "failed") $) 99 T ELT)) (|rational?| (((|Boolean|) $) 101 T ELT)) (|rational| (((|Fraction| (|Integer|)) $) 100 T ELT)) (|random| (($) 98 T ELT) (($ $) 97 T ELT)) (|quo| (#7# 148 T ELT)) (|principalIdeal| (((|Record| (|:| |coef| #11=(|List| $)) (|:| |generator| $)) #11#) 143 T ELT)) (|prime?| (((|Boolean|) $) 68 T ELT)) (|powmod| (($ $ $ $) 89 T ELT)) (|positiveRemainder| (($ $ $) 103 T ELT)) (|positive?| (((|Boolean|) $) 136 T ELT)) (|permutation| (#12=($ $ $) 114 T ELT)) (|patternMatch| (((|PatternMatchResult| #13=(|Integer|) . #14=($)) $ (|Pattern| #13#) (|PatternMatchResult| #13# . #14#)) 117 T ELT)) (|opposite?| ((#2# $ $) 20 T ELT)) (|one?| (((|Boolean|) $) 44 T ELT)) (|odd?| (((|Boolean|) $) 109 T ELT)) (|nextItem| (((|Maybe| $) $) 111 T ELT)) (|negative?| (((|Boolean|) $) 135 T ELT)) (|multiEuclidean| (((|Union| #15=(|List| $) #16="failed") #15# $) 152 T ELT)) (|mulmod| (($ $ $ $) 90 T ELT)) (|min| (#17=($ $ $) 142 T ELT)) (|max| (#17# 141 T ELT)) (|mask| (($ $) 93 T ELT)) (|length| (($ $) 106 T ELT)) (|leftReducedSystem| (((|Record| (|:| |mat| (|Matrix| #8#)) (|:| |vec| (|Vector| #8#))) #10# $) 122 T ELT) (((|Matrix| #8#) #10#) 121 T ELT)) (|lcm| (#18=($ $ $) 60 T ELT) (#19=($ (|List| $)) 59 T ELT)) (|latex| (((|String|) $) 11 T ELT)) (|invmod| (($ $ $) 88 T ELT)) (|init| (($) 110 T CONST)) (|inc| (($ $) 95 T ELT)) (|hash| (((|SingleInteger|) $) 12 T ELT)) (|gcdPolynomial| ((#20=(|SparseUnivariatePolynomial| $) #20# #20#) 58 T ELT)) (|gcd| (#18# 62 T ELT) (#19# 61 T ELT)) (|factorial| (($ $) 115 T ELT)) (|factor| (#4# 65 T ELT)) (|extendedEuclidean| (((|Union| (|Record| #21=(|:| |coef1| $) #22=(|:| |coef2| $)) #16#) $ $ $) 151 T ELT) (((|Record| #21# #22# (|:| |generator| $)) $ $) 150 T ELT)) (|exquo| (((|Union| $ "failed") $ $) 56 T ELT)) (|expressIdealMember| (((|Maybe| #11#) #11# $) 144 T ELT)) (|even?| (((|Boolean|) $) 108 T ELT)) (|euclideanSize| (((|NonNegativeInteger|) $) 146 T ELT)) (|divide| (((|Record| (|:| |quotient| $) (|:| |remainder| $)) $ $) 147 T ELT)) (|differentiate| (($ . #23=($)) 132 T ELT) (#24=($ $ (|NonNegativeInteger|)) 130 T ELT)) (|dec| (($ $) 94 T ELT)) (|copy| (($ $) 96 T ELT)) (|convert| (((|Integer|) . #25=($)) 128 T ELT) (((|InputForm|) . #25#) 119 T ELT) (((|Pattern| (|Integer|)) . #25#) 118 T ELT) (((|Float|) . #25#) 113 T ELT) (((|DoubleFloat|) . #25#) 112 T ELT)) (|coerce| (((|OutputForm|) $) 13 T ELT) (($ (|Integer|)) 41 T ELT) (($ $) 57 T ELT) (($ #6#) 125 T ELT)) (|characteristic| (((|NonNegativeInteger|)) 40 T CONST)) (|bit?| (((|Boolean|) $ $) 104 T ELT)) (|binomial| (#12# 116 T ELT)) (|before?| (#1# 6 T ELT)) (|base| (($) 107 T ELT)) (|associates?| ((#3# $ $) 53 T ELT)) (|annihilate?| (((|Boolean|) $ $) 33 T ELT)) (|addmod| (($ $ $ $) 92 T ELT)) (|abs| (($ $) 133 T ELT)) (|Zero| (#5# 24 T CONST)) (|One| (($) 45 T CONST)) (D (($ . #23#) 131 T ELT) (#24# 129 T ELT)) (>= (#26=((|Boolean|) $ $) 140 T ELT)) (> (#26# 138 T ELT)) (= (#1# 8 T ELT)) (<= (#26# 139 T ELT)) (< (#26# 137 T ELT)) (- (($ $) 29 T ELT) (($ $ $) 28 T ELT)) (+ (($ $ $) 18 T ELT)) (** (($ $ (|PositiveInteger|)) 35 T ELT) (($ $ (|NonNegativeInteger|)) 43 T ELT)) (* (($ (|PositiveInteger|) $) 17 T ELT) (($ (|NonNegativeInteger|) $) 21 T ELT) (($ (|Integer|) . #27=($)) 30 T ELT) (($ $ $) 34 T ELT) (($ #8# . #27#) 120 T ELT))) +((~= (#1=((|Boolean|) $ $) 7 T ELT)) (|zero?| ((#2=(|Boolean|) $) 22 T ELT)) (|unitNormal| (((|Record| (|:| |unit| $) (|:| |canonical| $) (|:| |associate| $)) $) 56 T ELT)) (|unitCanonical| (($ $) 55 T ELT)) (|unit?| ((#3=(|Boolean|) $) 53 T ELT)) (|symmetricRemainder| (($ $ $) 103 T ELT)) (|subtractIfCan| (((|Maybe| $) $ $) 26 T ELT)) (|submod| (($ $ $ $) 92 T ELT)) (|squareFreePart| (($ $) 67 T ELT)) (|squareFree| (#4=((|Factored| $) $) 68 T ELT)) (|sizeLess?| (((|Boolean|) $ $) 146 T ELT)) (|sign| (((|Integer|) $) 135 T ELT)) (|shift| (($ $ $) 106 T ELT)) (|sample| (#5=($) 23 T CONST)) (|retractIfCan| (((|Union| #6=(|Integer|) "failed") $) 127 T ELT)) (|retract| ((#6# $) 128 T ELT)) (|rem| (#7=($ $ $) 150 T ELT)) (|reducedSystem| (((|Record| (|:| |mat| (|Matrix| #8=(|Integer|))) (|:| |vec| (|Vector| #8#))) #9=(|Matrix| $) #10=(|Vector| $)) 125 T ELT) (((|Matrix| #8#) #9#) 124 T ELT)) (|recip| (((|Union| $ "failed") $) 43 T ELT)) (|rationalIfCan| (((|Union| (|Fraction| (|Integer|)) "failed") $) 100 T ELT)) (|rational?| (((|Boolean|) $) 102 T ELT)) (|rational| (((|Fraction| (|Integer|)) $) 101 T ELT)) (|random| (($) 99 T ELT) (($ $) 98 T ELT)) (|quo| (#7# 149 T ELT)) (|principalIdeal| (((|Record| (|:| |coef| #11=(|List| $)) (|:| |generator| $)) #11#) 144 T ELT)) (|prime?| (((|Boolean|) $) 69 T ELT)) (|powmod| (($ $ $ $) 90 T ELT)) (|positiveRemainder| (($ $ $) 104 T ELT)) (|positive?| (((|Boolean|) $) 137 T ELT)) (|permutation| (#12=($ $ $) 115 T ELT)) (|patternMatch| (((|PatternMatchResult| #13=(|Integer|) . #14=($)) $ (|Pattern| #13#) (|PatternMatchResult| #13# . #14#)) 118 T ELT)) (|opposite?| ((#2# $ $) 20 T ELT)) (|one?| (((|Boolean|) $) 45 T ELT)) (|odd?| (((|Boolean|) $) 110 T ELT)) (|nextItem| (((|Maybe| $) $) 112 T ELT)) (|negative?| (((|Boolean|) $) 136 T ELT)) (|multiEuclidean| (((|Union| #15=(|List| $) #16="failed") #15# $) 153 T ELT)) (|mulmod| (($ $ $ $) 91 T ELT)) (|min| (#17=($ $ $) 143 T ELT)) (|max| (#17# 142 T ELT)) (|mask| (($ $) 94 T ELT)) (|length| (($ $) 107 T ELT)) (|leftReducedSystem| (((|Record| (|:| |mat| (|Matrix| #8#)) (|:| |vec| (|Vector| #8#))) #10# $) 123 T ELT) (((|Matrix| #8#) #10#) 122 T ELT)) (|lcm| (#18=($ $ $) 61 T ELT) (#19=($ (|List| $)) 60 T ELT)) (|latex| (((|String|) $) 11 T ELT)) (|invmod| (($ $ $) 89 T ELT)) (|init| (($) 111 T CONST)) (|inc| (($ $) 96 T ELT)) (|hash| (((|SingleInteger|) $) 12 T ELT)) (|gcdPolynomial| ((#20=(|SparseUnivariatePolynomial| $) #20# #20#) 59 T ELT)) (|gcd| (#18# 63 T ELT) (#19# 62 T ELT)) (|factorial| (($ $) 116 T ELT)) (|factor| (#4# 66 T ELT)) (|extendedEuclidean| (((|Union| (|Record| #21=(|:| |coef1| $) #22=(|:| |coef2| $)) #16#) $ $ $) 152 T ELT) (((|Record| #21# #22# (|:| |generator| $)) $ $) 151 T ELT)) (|exquo| 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(SIGNATURE |symmetricRemainder| #6#) (SIGNATURE |rational?| #2#) (SIGNATURE |rational| (#7=(|Fraction| #1#) $)) (SIGNATURE |rationalIfCan| ((|Union| #7# "failed") $)) (SIGNATURE |random| #4#) (SIGNATURE |random| #5#) (SIGNATURE |copy| #5#) (SIGNATURE |inc| #5#) (SIGNATURE |dec| #5#) (SIGNATURE |mask| #5#) (SIGNATURE |addmod| #8=($ $ $ $)) (SIGNATURE |submod| #8#) (SIGNATURE |mulmod| #8#) (SIGNATURE |powmod| #8#) (SIGNATURE |invmod| #6#) (ATTRIBUTE |canonicalUnitNormal|))) (((|AbelianGroup|) . T) ((|AbelianMonoid|) . T) ((|AbelianSemiGroup|) . T) ((|Algebra| $) . T) ((|BasicType|) . T) ((|BiModule| $ $) . T) ((|CancellationAbelianMonoid|) . T) ((|CharacteristicZero|) . T) ((|CoercibleFrom| (|Integer|)) . T) ((|CoercibleFrom| $) . T) ((|CoercibleTo| (|OutputForm|)) . T) ((|CombinatorialFunctionCategory|) . T) ((|CommutativeRing|) . T) ((|ConvertibleTo| (|DoubleFloat|)) . T) ((|ConvertibleTo| (|Float|)) . T) ((|ConvertibleTo| (|InputForm|)) . T) ((|ConvertibleTo| #1=(|Integer|)) . T) ((|ConvertibleTo| (|Pattern| #1#)) . T) ((|DifferentialDomain| $) . T) ((|DifferentialRing|) . T) ((|DifferentialSpace|) . T) ((|EntireRing|) . T) ((|EuclideanDomain|) . T) ((|GcdDomain|) . T) ((|IntegralDomain|) . T) ((|Join|) . T) ((|LeftLinearSet| (|Integer|)) . T) ((|LeftLinearSet| $) . T) ((|LeftModule| #1#) . T) ((|LeftModule| $) . T) ((|LinearSet| $) . T) ((|LinearlyExplicitRingOver| #1#) . T) ((|Module| $) . T) ((|Monoid|) . T) ((|OrderedAbelianGroup|) . T) ((|OrderedAbelianMonoid|) . 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T)) -((~= #1=(#2=(#3=(|Boolean|) $ $) NIL T ELT)) (|zero?| (#4=(#3# $) 8 T ELT)) (|unitNormal| (((|Record| (|:| |unit| $) (|:| |canonical| $) (|:| |associate| $)) $) 77 T ELT)) (|unitCanonical| (#5=($ $) 78 T ELT)) (|unit?| #6=(#4# NIL T ELT)) (|symmetricRemainder| #7=(#8=($ $ $) NIL T ELT)) (|subtractIfCan| (#9=(#10=(|Union| $ #11="failed") $ $) NIL T ELT)) (|submod| (#12=($ $ $ $) 31 T ELT)) (|squareFreePart| #13=(#5# NIL T ELT)) (|squareFree| (#14=((|Factored| $) $) NIL T ELT)) (|sizeLess?| #1#) (|sign| #15=(#16=(#17=(|Integer|) $) NIL T ELT)) (|shift| (#8# 71 T ELT)) (|sample| #18=(#19=($) NIL T CONST)) (|retractIfCan| (((|Union| #17# #11#) $) NIL T ELT)) (|retract| #15#) (|rem| (#8# 45 T ELT)) (|reducedSystem| ((#20=(|Record| (|:| |mat| #21=(|Matrix| #17#)) (|:| |vec| (|Vector| #17#))) #22=(|Matrix| $) #23=(|Vector| $)) 53 T ELT) ((#21# #22#) 49 T ELT)) (|recip| ((#10# $) 74 T ELT)) (|rationalIfCan| (((|Union| #24=(|Fraction| #17#) #11#) $) NIL T ELT)) (|rational?| #6#) (|rational| ((#24# $) NIL T ELT)) (|random| (#19# 55 T ELT) (#5# 56 T ELT)) (|quo| (#8# 70 T ELT)) (|principalIdeal| (((|Record| (|:| |coef| #25=(|List| $)) #26=(|:| |generator| $)) #25#) NIL T ELT)) (|prime?| #6#) (|powmod| (#12# NIL T ELT)) (|positiveRemainder| (#8# 46 T ELT)) (|positive?| (#4# 22 T ELT)) (|permutation| #7#) (|patternMatch| ((#27=(|PatternMatchResult| #17# $) $ #28=(|Pattern| #17#) #27#) NIL T ELT)) (|opposite?| (#2# 110 T ELT)) (|one?| (#4# 9 T ELT)) (|odd?| (#4# 64 T ELT)) (|nextItem| (((|Maybe| $) $) NIL T ELT)) (|negative?| (#4# 21 T ELT)) (|multiEuclidean| (((|Union| #25# #11#) #25# $) NIL T ELT)) (|mulmod| (#12# 32 T ELT)) (|min| (#8# 67 T ELT)) (|max| (#8# 66 T ELT)) (|mask| #13#) (|length| (#5# 29 T ELT)) (|leftReducedSystem| ((#20# #23# $) NIL T ELT) ((#21# #23#) NIL T ELT)) (|lcm| #7# #29=(($ #25#) NIL T ELT)) (|latex| (((|String|) $) 44 T ELT)) (|invmod| #7#) (|init| #18#) (|inc| (#5# 15 T ELT)) (|hash| (((|SingleInteger|) $) 19 T ELT)) (|gcdPolynomial| ((#30=(|SparseUnivariatePolynomial| $) #30# #30#) 109 T ELT)) (|gcd| (#8# 75 T ELT) #29#) (|factorial| #13#) (|factor| (#14# 95 T ELT)) (|extendedEuclidean| (((|Union| (|Record| #31=(|:| |coef1| $) #32=(|:| |coef2| $)) #11#) $ $ $) NIL T ELT) (((|Record| #31# #32# #26#) $ $) NIL T ELT)) (|exquo| (#9# 93 T ELT)) (|expressIdealMember| (((|Maybe| #25#) #25# $) NIL T ELT)) (|even?| (#4# 65 T ELT)) (|euclideanSize| ((#33=(|NonNegativeInteger|) $) NIL T ELT)) (|divide| (((|Record| (|:| |quotient| $) (|:| |remainder| $)) $ $) 69 T ELT)) (|differentiate| #13# #34=(#35=($ $ #33#) NIL T ELT)) (|dec| (#5# 17 T ELT)) (|copy| (#5# 13 T ELT)) (|convert| (#16# 28 T ELT) (((|InputForm|) $) 41 T ELT) ((#28# $) NIL T ELT) (((|Float|) $) 35 T ELT) (((|DoubleFloat|) $) 38 T ELT)) (|coerce| (((|OutputForm|) $) 26 T ELT) #36=(($ #17#) 27 T ELT) #13# #36#) (|characteristic| ((#33#) NIL T CONST)) (|bit?| #1#) (|binomial| #7#) (|before?| #1#) (|base| (#19# 12 T ELT)) (|associates?| #1#) (|annihilate?| (#2# 112 T ELT)) (|addmod| (#12# 30 T ELT)) (|abs| (#5# 54 T ELT)) (|Zero| (#19# 10 T CONST)) (|One| (#19# 11 T CONST)) (D #13# #34#) (>= (#2# 59 T ELT)) (> (#2# 57 T ELT)) (= (#2# 7 T ELT)) (<= (#2# 58 T ELT)) (< (#2# 20 T ELT)) (- (#5# 42 T ELT) (#8# 16 T ELT)) (+ (#8# 14 T ELT)) (** (($ $ #37=(|PositiveInteger|)) NIL T ELT) (#35# 63 T ELT)) (* (($ #37# $) NIL T ELT) (($ #33# $) NIL T ELT) #38=(($ #17# $) 61 T ELT) (#8# 60 T ELT) #38#)) -(((|Integer|) (|Join| (|IntegerNumberSystem|) (CATEGORY |package| (ATTRIBUTE |canonical|) (ATTRIBUTE |canonicalsClosed|) (ATTRIBUTE |noetherian|)))) (T |Integer|)) +((~= #1=(#2=(#3=(|Boolean|) $ $) NIL T ELT)) (|zero?| (#4=(#3# $) 10 T ELT)) (|unitNormal| (((|Record| (|:| |unit| $) (|:| |canonical| $) (|:| |associate| $)) $) 76 T ELT)) (|unitCanonical| (#5=($ $) 77 T ELT)) (|unit?| #6=(#4# NIL T ELT)) (|symmetricRemainder| #7=(#8=($ $ $) NIL T ELT)) (|subtractIfCan| ((#9=(|Maybe| $) $ $) NIL T ELT)) (|submod| (#10=($ $ $ $) 29 T ELT)) (|squareFreePart| #11=(#5# NIL T ELT)) (|squareFree| (#12=((|Factored| $) $) NIL T ELT)) (|sizeLess?| #1#) (|sign| #13=(#14=(#15=(|Integer|) $) NIL T ELT)) (|shift| (#8# 71 T ELT)) (|sample| #16=(#17=($) NIL T CONST)) (|retractIfCan| (((|Union| #15# #18="failed") $) NIL T ELT)) (|retract| #13#) (|rem| (#8# 43 T ELT)) (|reducedSystem| ((#19=(|Record| (|:| |mat| #20=(|Matrix| #15#)) (|:| |vec| (|Vector| #15#))) #21=(|Matrix| $) #22=(|Vector| $)) 53 T ELT) ((#20# #21#) 49 T ELT)) (|recip| ((#23=(|Union| $ #18#) $) 73 T ELT)) (|rationalIfCan| (((|Union| #24=(|Fraction| #15#) #18#) $) NIL T ELT)) (|rational?| #6#) (|rational| ((#24# $) NIL T ELT)) (|random| (#17# 55 T ELT) (#5# 56 T ELT)) (|quo| (#8# 70 T ELT)) (|principalIdeal| (((|Record| (|:| |coef| #25=(|List| $)) #26=(|:| |generator| $)) #25#) NIL T ELT)) (|prime?| #6#) (|powmod| (#10# NIL T ELT)) (|positiveRemainder| (#8# 46 T ELT)) (|positive?| (#4# 20 T ELT)) (|permutation| #7#) (|patternMatch| ((#27=(|PatternMatchResult| #15# $) $ #28=(|Pattern| #15#) #27#) NIL T ELT)) (|opposite?| (#2# 109 T ELT)) (|one?| (#4# 11 T ELT)) (|odd?| (#4# 64 T ELT)) (|nextItem| ((#9# $) NIL T ELT)) (|negative?| (#4# 19 T ELT)) (|multiEuclidean| (((|Union| #25# #18#) #25# $) NIL T ELT)) (|mulmod| (#10# 30 T ELT)) (|min| (#8# 67 T ELT)) (|max| (#8# 66 T ELT)) (|mask| #11#) (|length| (#5# 27 T ELT)) (|leftReducedSystem| ((#19# #22# $) NIL T ELT) ((#20# #22#) NIL T ELT)) (|lcm| #7# #29=(($ #25#) NIL T ELT)) (|latex| (((|String|) $) 42 T ELT)) (|invmod| #7#) (|init| #16#) (|inc| (#5# 14 T ELT)) (|hash| (((|SingleInteger|) $) 17 T ELT)) (|gcdPolynomial| ((#30=(|SparseUnivariatePolynomial| $) #30# #30#) 108 T ELT)) (|gcd| (#8# 74 T ELT) #29#) (|factorial| #11#) (|factor| (#12# 94 T ELT)) (|extendedEuclidean| (((|Union| (|Record| #31=(|:| |coef1| $) #32=(|:| |coef2| $)) #18#) $ $ $) NIL T ELT) (((|Record| #31# #32# #26#) $ $) NIL T ELT)) (|exquo| ((#23# $ $) 92 T ELT)) (|expressIdealMember| (((|Maybe| #25#) #25# $) NIL T ELT)) (|even?| (#4# 65 T ELT)) (|euclideanSize| ((#33=(|NonNegativeInteger|) $) NIL T ELT)) (|divide| (((|Record| (|:| |quotient| $) (|:| |remainder| $)) $ $) 69 T ELT)) (|differentiate| #11# #34=(#35=($ $ #33#) NIL T ELT)) (|dec| (#5# 15 T ELT)) (|copy| (#5# 13 T ELT)) (|convert| (#14# 26 T ELT) (((|InputForm|) $) 39 T ELT) ((#28# $) NIL T ELT) (((|Float|) $) 33 T ELT) (((|DoubleFloat|) $) 36 T ELT)) (|coerce| (((|OutputForm|) $) 24 T ELT) #36=(($ #15#) 25 T ELT) #11# #36#) (|characteristic| ((#33#) NIL T CONST)) (|bit?| #1#) (|binomial| #7#) (|before?| #1#) (|base| (#17# 12 T ELT)) (|associates?| #1#) (|annihilate?| (#2# 111 T ELT)) (|addmod| (#10# 28 T ELT)) (|abs| (#5# 54 T ELT)) (|Zero| (#17# 6 T CONST)) (|One| (#17# 7 T CONST)) (D #11# #34#) (>= (#2# 59 T ELT)) (> (#2# 57 T ELT)) (= (#2# 9 T ELT)) (<= (#2# 58 T ELT)) (< (#2# 18 T ELT)) (- (#5# 40 T ELT) (#8# 44 T ELT)) (+ (#8# 45 T ELT)) (** (($ $ #37=(|PositiveInteger|)) NIL T ELT) (#35# 63 T ELT)) (* (($ #37# $) NIL T ELT) (($ #33# $) NIL T ELT) #38=(($ #15# $) 61 T ELT) (#8# 60 T ELT) #38#)) +(((|Integer|) (|Join| (|IntegerNumberSystem|) (CATEGORY |package| (ATTRIBUTE |canonical|)))) (T |Integer|)) NIL ((~= #1=(((|Boolean|) $ $) NIL T ELT)) (|size| (((|NonNegativeInteger|)) NIL T ELT)) (|sample| #2=(#3=($) NIL T CONST)) (|random| (#3# NIL T ELT)) (|min| #4=(($ $ $) NIL T ELT) #2#) (|max| #4# #2#) (|lookup| ((#5=(|PositiveInteger|) $) NIL T ELT)) (|latex| (((|String|) $) NIL T ELT)) (|index| (($ #5#) NIL T ELT)) (|hash| (((|SingleInteger|) $) NIL T ELT)) (|coerce| (((|OutputForm|) $) NIL T ELT)) (|before?| #1#) (>= #1#) (> #1#) (= #1#) (<= #1#) (< #1#)) (((|Int16|) (|Join| (|OrderedFinite|) (CATEGORY |domain| (SIGNATURE |sample| ($) |constant|)))) (T |Int16|)) @@ -1632,7 +1635,7 @@ NIL ((|bitTruth| (((|Boolean|) #1=(|Integer|) #1#) 12 T ELT)) (|bitLength| ((#1# #1#) 7 T ELT)) (|bitCoef| ((#1# #1# #1#) 10 T ELT))) (((|IntegerBits|) (CATEGORY |package| (SIGNATURE |bitLength| (#1=(|Integer|) #1#)) (SIGNATURE |bitCoef| (#1# #1# #1#)) (SIGNATURE |bitTruth| ((|Boolean|) #1# #1#)))) (T |IntegerBits|)) ((|bitTruth| (*1 *2 *3 *3) (AND (|isDomain| *3 #1=(|Integer|)) (|isDomain| *2 (|Boolean|)) #2=(|isDomain| *1 (|IntegerBits|)))) (|bitCoef| (*1 *2 *2 *2) #3=(AND (|isDomain| *2 #1#) #2#)) (|bitLength| (*1 *2 *2) #3#)) -((~= (#1=((|Boolean|) $ $) 7 T ELT)) (|zero?| ((#2=(|Boolean|) $) 22 T ELT)) (|width| ((|#1| $) 77 T ELT)) (|unitNormal| (((|Record| (|:| |unit| $) (|:| |canonical| $) (|:| |associate| $)) $) 55 T ELT)) (|unitCanonical| (($ $) 54 T ELT)) (|unit?| ((#3=(|Boolean|) $) 52 T ELT)) (|tanh| (#4=($ $) 107 T ELT)) (|tan| (#5=($ $) 90 T ELT)) (|sup| ((|#1| $) 78 T ELT)) (|subtractIfCan| (((|Union| $ "failed") $ $) 26 T ELT)) (|sqrt| (($ $) 89 T ELT)) (|sinh| (#4# 106 T ELT)) (|sin| (#5# 91 T ELT)) (|sech| (#4# 105 T ELT)) (|sec| (#5# 92 T ELT)) (|sample| (#6=($) 23 T CONST)) (|retractIfCan| (((|Union| #7=(|Integer|) "failed") $) 85 T ELT)) (|retract| ((#7# $) 86 T ELT)) (|recip| (((|Union| $ "failed") $) 42 T ELT)) (|qinterval| (($ |#1| |#1|) 82 T ELT)) (|positive?| (((|Boolean|) $) 76 T ELT)) (|pi| (($) 117 T ELT)) (|opposite?| ((#2# $ $) 20 T ELT)) (|one?| (((|Boolean|) $) 44 T ELT)) (|nthRoot| (($ $ #8=(|Integer|)) 88 T ELT)) (|negative?| (((|Boolean|) $) 75 T ELT)) (|min| (#9=($ $ $) 118 T ELT)) (|max| (#9# 119 T ELT)) (|log| (#10=($ $) 114 T ELT)) (|lcm| (#11=($ $ $) 60 T ELT) (#12=($ (|List| $)) 59 T ELT)) (|latex| (((|String|) $) 11 T ELT)) (|interval| (($ |#1| |#1|) 83 T ELT) (($ |#1|) 81 T ELT) (($ (|Fraction| (|Integer|))) 80 T ELT)) (|inf| ((|#1| $) 79 T ELT)) (|hash| (((|SingleInteger|) $) 12 T ELT)) (|gcdPolynomial| ((#13=(|SparseUnivariatePolynomial| $) #13# #13#) 58 T ELT)) (|gcd| (#11# 62 T ELT) (#12# 61 T ELT)) (|exquo| (((|Union| $ "failed") $ $) 56 T ELT)) (|exp| (#10# 115 T ELT)) (|csch| (#4# 104 T ELT)) (|csc| (#5# 93 T ELT)) (|coth| (#4# 103 T ELT)) (|cot| (#5# 94 T ELT)) (|cosh| (#4# 102 T ELT)) (|cos| (#5# 95 T ELT)) (|contains?| (((|Boolean|) $ |#1|) 74 T ELT)) (|coerce| (((|OutputForm|) $) 13 T ELT) (($ (|Integer|)) 41 T ELT) (($ $) 57 T ELT) (($ #7#) 84 T ELT)) (|characteristic| (((|NonNegativeInteger|)) 40 T CONST)) (|before?| (#1# 6 T ELT)) (|atanh| (#14=($ $) 113 T ELT)) (|atan| (#15=($ $) 101 T ELT)) (|associates?| ((#3# $ $) 53 T ELT)) (|asinh| (#14# 112 T ELT)) (|asin| (#15# 100 T ELT)) (|asech| (#14# 111 T ELT)) (|asec| (#15# 99 T ELT)) (|annihilate?| (((|Boolean|) $ $) 33 T ELT)) (|acsch| (#14# 110 T ELT)) (|acsc| (#15# 98 T ELT)) (|acoth| (#14# 109 T ELT)) (|acot| (#15# 97 T ELT)) (|acosh| (#14# 108 T ELT)) (|acos| (#15# 96 T ELT)) (|Zero| (#6# 24 T CONST)) (|One| (($) 45 T CONST)) (>= (#16=((|Boolean|) $ $) 120 T ELT)) (> (#16# 122 T ELT)) (= (#1# 8 T ELT)) (<= (#16# 121 T ELT)) (< (#16# 123 T ELT)) (- (($ $) 29 T ELT) (($ $ $) 28 T ELT)) (+ (($ $ $) 18 T ELT)) (** (($ $ (|PositiveInteger|)) 35 T ELT) (($ $ (|NonNegativeInteger|)) 43 T ELT) (($ $ $) 116 T ELT) (($ $ (|Fraction| #8#)) 87 T ELT)) (* (($ (|PositiveInteger|) $) 17 T ELT) (($ (|NonNegativeInteger|) $) 21 T ELT) (($ (|Integer|) $) 30 T ELT) (($ $ $) 34 T ELT))) +((~= (#1=((|Boolean|) $ $) 7 T ELT)) (|zero?| ((#2=(|Boolean|) $) 22 T ELT)) (|width| ((|#1| $) 78 T ELT)) (|unitNormal| (((|Record| (|:| |unit| $) (|:| |canonical| $) (|:| |associate| $)) $) 56 T ELT)) (|unitCanonical| (($ $) 55 T ELT)) (|unit?| ((#3=(|Boolean|) $) 53 T ELT)) (|tanh| (#4=($ $) 108 T ELT)) (|tan| (#5=($ $) 91 T ELT)) (|sup| ((|#1| $) 79 T ELT)) (|subtractIfCan| (((|Maybe| $) $ $) 26 T ELT)) (|sqrt| (($ $) 90 T ELT)) (|sinh| (#4# 107 T ELT)) (|sin| (#5# 92 T ELT)) (|sech| (#4# 106 T ELT)) (|sec| (#5# 93 T ELT)) (|sample| (#6=($) 23 T CONST)) (|retractIfCan| (((|Union| #7=(|Integer|) "failed") $) 86 T ELT)) (|retract| ((#7# $) 87 T ELT)) (|recip| (((|Union| $ "failed") $) 43 T ELT)) (|qinterval| (($ |#1| |#1|) 83 T ELT)) (|positive?| (((|Boolean|) $) 77 T ELT)) (|pi| (($) 118 T ELT)) (|opposite?| ((#2# $ $) 20 T ELT)) (|one?| (((|Boolean|) $) 45 T ELT)) (|nthRoot| (($ $ #8=(|Integer|)) 89 T ELT)) (|negative?| (((|Boolean|) $) 76 T ELT)) (|min| (#9=($ $ $) 119 T ELT)) (|max| (#9# 120 T ELT)) (|log| (#10=($ $) 115 T ELT)) (|lcm| (#11=($ $ $) 61 T ELT) (#12=($ (|List| $)) 60 T ELT)) (|latex| (((|String|) $) 11 T ELT)) (|interval| (($ |#1| |#1|) 84 T ELT) (($ |#1|) 82 T ELT) (($ (|Fraction| (|Integer|))) 81 T ELT)) (|inf| ((|#1| $) 80 T ELT)) (|hash| (((|SingleInteger|) $) 12 T ELT)) (|gcdPolynomial| ((#13=(|SparseUnivariatePolynomial| $) #13# #13#) 59 T ELT)) (|gcd| (#11# 63 T ELT) (#12# 62 T ELT)) (|exquo| (((|Union| $ "failed") $ $) 57 T ELT)) (|exp| (#10# 116 T ELT)) (|csch| (#4# 105 T ELT)) (|csc| (#5# 94 T ELT)) (|coth| (#4# 104 T ELT)) (|cot| (#5# 95 T ELT)) (|cosh| (#4# 103 T ELT)) (|cos| (#5# 96 T ELT)) (|contains?| (((|Boolean|) $ |#1|) 75 T ELT)) (|coerce| (((|OutputForm|) $) 13 T ELT) (($ (|Integer|)) 42 T ELT) (($ $) 58 T ELT) (($ #7#) 85 T ELT)) (|characteristic| (((|NonNegativeInteger|)) 41 T CONST)) (|before?| (#1# 6 T ELT)) (|atanh| (#14=($ $) 114 T ELT)) (|atan| (#15=($ $) 102 T ELT)) (|associates?| ((#3# $ $) 54 T ELT)) (|asinh| (#14# 113 T ELT)) (|asin| (#15# 101 T ELT)) (|asech| (#14# 112 T ELT)) (|asec| (#15# 100 T ELT)) (|annihilate?| (((|Boolean|) $ $) 34 T ELT)) (|acsch| (#14# 111 T ELT)) (|acsc| (#15# 99 T ELT)) (|acoth| (#14# 110 T ELT)) (|acot| (#15# 98 T ELT)) (|acosh| (#14# 109 T ELT)) (|acos| (#15# 97 T ELT)) (|Zero| (#6# 24 T CONST)) (|One| (($) 46 T CONST)) (>= (#16=((|Boolean|) $ $) 121 T ELT)) (> (#16# 123 T ELT)) (= (#1# 8 T ELT)) (<= (#16# 122 T ELT)) (< (#16# 124 T ELT)) (- (($ $) 30 T ELT) (($ $ $) 29 T ELT)) (+ (($ $ $) 18 T ELT)) (** (($ $ (|PositiveInteger|)) 36 T ELT) (($ $ (|NonNegativeInteger|)) 44 T ELT) (($ $ $) 117 T ELT) (($ $ (|Fraction| #8#)) 88 T ELT)) (* (($ (|PositiveInteger|) $) 17 T ELT) (($ (|NonNegativeInteger|) $) 21 T ELT) (($ (|Integer|) $) 31 T ELT) (($ $ $) 35 T ELT))) (((|IntervalCategory| |#1|) (|Category|) (|Join| (|FloatingPointSystem|) (|TranscendentalFunctionCategory|))) (T |IntervalCategory|)) ((|interval| (*1 *1 *2 *2) (AND (|ofCategory| *1 (|IntervalCategory| *2)) (|ofCategory| *2 (|Join| (|FloatingPointSystem|) (|TranscendentalFunctionCategory|))))) (|qinterval| (*1 *1 *2 *2) (AND (|ofCategory| *1 (|IntervalCategory| *2)) (|ofCategory| *2 (|Join| (|FloatingPointSystem|) (|TranscendentalFunctionCategory|))))) (|interval| (*1 *1 *2) (AND (|ofCategory| *1 (|IntervalCategory| *2)) (|ofCategory| *2 (|Join| (|FloatingPointSystem|) (|TranscendentalFunctionCategory|))))) (|interval| (*1 *1 *2) (AND (|isDomain| *2 (|Fraction| (|Integer|))) (|ofCategory| *1 (|IntervalCategory| *3)) (|ofCategory| *3 (|Join| (|FloatingPointSystem|) (|TranscendentalFunctionCategory|))))) (|inf| (*1 *2 *1) (AND (|ofCategory| *1 (|IntervalCategory| *2)) (|ofCategory| *2 (|Join| (|FloatingPointSystem|) (|TranscendentalFunctionCategory|))))) (|sup| (*1 *2 *1) (AND (|ofCategory| *1 (|IntervalCategory| *2)) (|ofCategory| *2 (|Join| (|FloatingPointSystem|) (|TranscendentalFunctionCategory|))))) (|width| (*1 *2 *1) (AND (|ofCategory| *1 (|IntervalCategory| *2)) (|ofCategory| *2 (|Join| (|FloatingPointSystem|) (|TranscendentalFunctionCategory|))))) (|positive?| (*1 *2 *1) (AND (|ofCategory| *1 (|IntervalCategory| *3)) (|ofCategory| *3 (|Join| (|FloatingPointSystem|) (|TranscendentalFunctionCategory|))) (|isDomain| *2 (|Boolean|)))) (|negative?| (*1 *2 *1) (AND (|ofCategory| *1 (|IntervalCategory| *3)) (|ofCategory| *3 (|Join| (|FloatingPointSystem|) (|TranscendentalFunctionCategory|))) (|isDomain| *2 (|Boolean|)))) (|contains?| (*1 *2 *1 *3) (AND (|ofCategory| *1 (|IntervalCategory| *3)) (|ofCategory| *3 (|Join| (|FloatingPointSystem|) (|TranscendentalFunctionCategory|))) (|isDomain| *2 (|Boolean|))))) (|Join| (|GcdDomain|) (|OrderedSet|) (|TranscendentalFunctionCategory|) (|RadicalCategory|) (|RetractableTo| (|Integer|)) (CATEGORY |domain| (ATTRIBUTE |approximate|) (SIGNATURE |interval| ($ |t#1| |t#1|)) (SIGNATURE |qinterval| ($ |t#1| |t#1|)) (SIGNATURE |interval| ($ |t#1|)) (SIGNATURE |interval| ($ (|Fraction| (|Integer|)))) (SIGNATURE |inf| (|t#1| $)) (SIGNATURE |sup| (|t#1| $)) (SIGNATURE |width| (|t#1| $)) (SIGNATURE |positive?| ((|Boolean|) $)) (SIGNATURE |negative?| ((|Boolean|) $)) (SIGNATURE |contains?| ((|Boolean|) $ |t#1|)))) @@ -1640,7 +1643,7 @@ NIL ((|unitNormal| (((|Record| (|:| |unit| $) (|:| |canonical| $) (|:| |associate| $)) $) 9 T ELT)) (|unitCanonical| (($ $) 11 T ELT)) (|unit?| ((#1=(|Boolean|) $) 20 T ELT)) (|recip| (((|Union| $ "failed") $) 16 T ELT)) (|associates?| ((#1# $ $) 22 T ELT))) (((|IntegralDomain&| |#1|) (CATEGORY |package| (SIGNATURE |unit?| (#1=(|Boolean|) |#1|)) (SIGNATURE |associates?| (#1# |#1| |#1|)) (SIGNATURE |unitCanonical| (|#1| |#1|)) (SIGNATURE |unitNormal| ((|Record| (|:| |unit| |#1|) (|:| |canonical| |#1|) (|:| |associate| |#1|)) |#1|)) (SIGNATURE |recip| ((|Union| |#1| "failed") |#1|))) (|IntegralDomain|)) (T |IntegralDomain&|)) NIL -((~= (#1=((|Boolean|) $ $) 7 T ELT)) (|zero?| ((#2=(|Boolean|) $) 22 T ELT)) (|unitNormal| (((|Record| (|:| |unit| $) (|:| |canonical| $) (|:| |associate| $)) $) 55 T ELT)) (|unitCanonical| (($ $) 54 T ELT)) (|unit?| (((|Boolean|) $) 52 T ELT)) (|subtractIfCan| (((|Union| $ "failed") $ $) 26 T ELT)) (|sample| (#3=($) 23 T CONST)) (|recip| (((|Union| $ "failed") $) 42 T ELT)) (|opposite?| ((#2# $ $) 20 T ELT)) (|one?| (((|Boolean|) $) 44 T ELT)) (|latex| (((|String|) $) 11 T ELT)) (|hash| (((|SingleInteger|) $) 12 T ELT)) (|exquo| (((|Union| $ "failed") $ $) 56 T ELT)) (|coerce| (((|OutputForm|) $) 13 T ELT) (($ (|Integer|)) 41 T ELT) (($ $) 57 T ELT)) (|characteristic| (((|NonNegativeInteger|)) 40 T CONST)) (|before?| (#1# 6 T ELT)) (|associates?| (((|Boolean|) $ $) 53 T ELT)) (|annihilate?| (((|Boolean|) $ $) 33 T ELT)) (|Zero| (#3# 24 T CONST)) (|One| (($) 45 T CONST)) (= (#1# 8 T ELT)) (- (($ $) 29 T ELT) (($ $ $) 28 T ELT)) (+ (($ $ $) 18 T ELT)) (** (($ $ (|PositiveInteger|)) 35 T ELT) (($ $ (|NonNegativeInteger|)) 43 T ELT)) (* (($ (|PositiveInteger|) $) 17 T ELT) (($ (|NonNegativeInteger|) $) 21 T ELT) (($ (|Integer|) $) 30 T ELT) (($ $ $) 34 T ELT))) +((~= (#1=((|Boolean|) $ $) 7 T ELT)) (|zero?| ((#2=(|Boolean|) $) 22 T ELT)) (|unitNormal| (((|Record| (|:| |unit| $) (|:| |canonical| $) (|:| |associate| $)) $) 56 T ELT)) (|unitCanonical| (($ $) 55 T ELT)) (|unit?| (((|Boolean|) $) 53 T ELT)) (|subtractIfCan| (((|Maybe| $) $ $) 26 T ELT)) (|sample| (#3=($) 23 T CONST)) (|recip| (((|Union| $ "failed") $) 43 T ELT)) (|opposite?| ((#2# $ $) 20 T ELT)) (|one?| (((|Boolean|) $) 45 T ELT)) (|latex| (((|String|) $) 11 T ELT)) (|hash| (((|SingleInteger|) $) 12 T ELT)) (|exquo| (((|Union| $ "failed") $ $) 57 T ELT)) (|coerce| (((|OutputForm|) $) 13 T ELT) (($ (|Integer|)) 42 T ELT) (($ $) 58 T ELT)) (|characteristic| (((|NonNegativeInteger|)) 41 T CONST)) (|before?| (#1# 6 T ELT)) (|associates?| (((|Boolean|) $ $) 54 T ELT)) (|annihilate?| (((|Boolean|) $ $) 34 T ELT)) (|Zero| (#3# 24 T CONST)) (|One| (($) 46 T CONST)) (= (#1# 8 T ELT)) (- (($ $) 30 T ELT) (($ $ $) 29 T ELT)) (+ (($ $ $) 18 T ELT)) (** (($ $ (|PositiveInteger|)) 36 T ELT) (($ $ (|NonNegativeInteger|)) 44 T ELT)) (* (($ (|PositiveInteger|) $) 17 T ELT) (($ (|NonNegativeInteger|) $) 21 T ELT) (($ (|Integer|) $) 31 T ELT) (($ $ $) 35 T ELT))) (((|IntegralDomain|) (|Category|)) (T |IntegralDomain|)) ((|exquo| (*1 *1 *1 *1) (|partial| |ofCategory| *1 (|IntegralDomain|))) (|unitNormal| (*1 *2 *1) (AND (|isDomain| *2 (|Record| (|:| |unit| *1) (|:| |canonical| *1) (|:| |associate| *1))) (|ofCategory| *1 (|IntegralDomain|)))) (|unitCanonical| (*1 *1 *1) (|ofCategory| *1 (|IntegralDomain|))) (|associates?| (*1 *2 *1 *1) (AND (|ofCategory| *1 (|IntegralDomain|)) (|isDomain| *2 (|Boolean|)))) (|unit?| (*1 *2 *1) (AND (|ofCategory| *1 (|IntegralDomain|)) (|isDomain| *2 (|Boolean|))))) (|Join| (|CommutativeRing|) (|Algebra| $) (|EntireRing|) (CATEGORY |domain| (SIGNATURE |exquo| ((|Union| $ "failed") $ $)) (SIGNATURE |unitNormal| ((|Record| (|:| |unit| $) (|:| |canonical| $) (|:| |associate| $)) $)) (SIGNATURE |unitCanonical| ($ $)) (SIGNATURE |associates?| ((|Boolean|) $ $)) (SIGNATURE |unit?| ((|Boolean|) $)))) @@ -1678,7 +1681,7 @@ NIL ((|limitedIntegrate| (((|Union| (|Record| (|:| |mainpart| #1=(|Fraction| (|Polynomial| |#1|))) (|:| |limitedlogs| (|List| (|Record| #2=(|:| |coeff| #1#) (|:| |logand| #1#))))) #3="failed") #1# #4=(|Symbol|) (|List| #1#)) 48 T ELT)) (|internalIntegrate| (((|IntegrationResult| #1#) #1# #4#) 28 T ELT)) (|infieldIntegrate| (((|Union| #1# #3#) #1# #4#) 23 T ELT)) (|extendedIntegrate| (((|Union| (|Record| (|:| |ratpart| #1#) #2#) #3#) #1# #4# #1#) 35 T ELT))) (((|RationalFunctionIntegration| |#1|) (CATEGORY |package| (SIGNATURE |internalIntegrate| ((|IntegrationResult| #1=(|Fraction| (|Polynomial| |#1|))) #1# #2=(|Symbol|))) (SIGNATURE |infieldIntegrate| ((|Union| #1# #3="failed") #1# #2#)) (SIGNATURE |limitedIntegrate| ((|Union| (|Record| (|:| |mainpart| #1#) (|:| |limitedlogs| (|List| (|Record| #4=(|:| |coeff| #1#) (|:| |logand| #1#))))) #3#) #1# #2# (|List| #1#))) (SIGNATURE |extendedIntegrate| ((|Union| (|Record| (|:| |ratpart| #1#) #4#) #3#) #1# #2# #1#))) (|Join| (|IntegralDomain|) (|RetractableTo| (|Integer|)) (|CharacteristicZero|))) (T |RationalFunctionIntegration|)) ((|extendedIntegrate| (*1 *2 *3 *4 *3) (|partial| AND #1=(|isDomain| *4 #2=(|Symbol|)) #3=(|ofCategory| *5 #4=(|Join| (|IntegralDomain|) (|RetractableTo| (|Integer|)) (|CharacteristicZero|))) (|isDomain| *2 (|Record| (|:| |ratpart| #5=(|Fraction| (|Polynomial| *5))) (|:| |coeff| #5#))) #6=(|isDomain| *1 (|RationalFunctionIntegration| *5)) #7=(|isDomain| *3 #5#))) (|limitedIntegrate| (*1 *2 *3 *4 *5) (|partial| AND #1# (|isDomain| *5 (|List| #8=(|Fraction| (|Polynomial| *6)))) (|isDomain| *3 #8#) (|ofCategory| *6 #4#) (|isDomain| *2 (|Record| (|:| |mainpart| *3) (|:| |limitedlogs| (|List| (|Record| (|:| |coeff| *3) (|:| |logand| *3)))))) (|isDomain| *1 (|RationalFunctionIntegration| *6)))) (|infieldIntegrate| (*1 *2 *2 *3) (|partial| AND (|isDomain| *2 (|Fraction| (|Polynomial| *4))) (|isDomain| *3 #2#) (|ofCategory| *4 #4#) (|isDomain| *1 (|RationalFunctionIntegration| *4)))) (|internalIntegrate| (*1 *2 *3 *4) (AND #1# #3# (|isDomain| *2 (|IntegrationResult| #5#)) #6# #7#))) -((~= (#1=(#2=(|Boolean|) $ $) 77 T ELT)) (|zero?| (#3=(#2# $) 49 T ELT)) (|width| (#4=(|#1| $) 39 T ELT)) (|unitNormal| (((|Record| (|:| |unit| $) (|:| |canonical| $) (|:| |associate| $)) $) NIL T ELT)) (|unitCanonical| #5=(#6=($ $) NIL T ELT)) (|unit?| (#3# 81 T ELT)) (|tanh| (#6# 142 T ELT)) (|tan| (#6# 120 T ELT)) (|sup| (#4# 37 T ELT)) (|subtractIfCan| (#7=(#8=(|Union| $ #9="failed") $ $) NIL T ELT)) (|sqrt| #5#) (|sinh| (#6# 144 T ELT)) (|sin| (#6# 116 T ELT)) (|sech| (#6# 146 T ELT)) (|sec| (#6# 124 T ELT)) (|sample| (#10=($) NIL T CONST)) (|retractIfCan| (((|Union| #11=(|Integer|) #9#) $) 95 T ELT)) (|retract| ((#11# $) 97 T ELT)) (|recip| ((#8# $) 80 T ELT)) (|qinterval| (#12=($ |#1| |#1|) 35 T ELT)) (|positive?| (#3# 44 T ELT)) (|pi| (#10# 106 T ELT)) (|opposite?| #13=(#1# NIL T ELT)) (|one?| (#3# 56 T ELT)) (|nthRoot| (($ $ #11#) NIL T ELT)) (|negative?| (#3# 46 T ELT)) (|min| #14=(#15=($ $ $) NIL T ELT)) (|max| #14#) (|log| (#6# 108 T ELT)) (|lcm| #14# #16=(($ (|List| $)) NIL T ELT)) (|latex| (((|String|) $) NIL T ELT)) (|interval| (#12# 29 T ELT) (($ |#1|) 34 T ELT) (($ #17=(|Fraction| #11#)) 94 T ELT)) (|inf| (#4# 36 T ELT)) (|hash| (((|SingleInteger|) $) NIL T ELT)) (|gcdPolynomial| ((#18=(|SparseUnivariatePolynomial| $) #18# #18#) NIL T ELT)) (|gcd| (#15# 83 T ELT) #16#) (|exquo| (#7# 82 T ELT)) (|exp| (#6# 110 T ELT)) (|csch| (#6# 150 T ELT)) (|csc| (#6# 122 T ELT)) (|coth| (#6# 152 T ELT)) (|cot| (#6# 126 T ELT)) (|cosh| (#6# 148 T ELT)) (|cos| (#6# 118 T ELT)) (|contains?| ((#2# $ |#1|) 42 T ELT)) (|coerce| (((|OutputForm|) $) 102 T ELT) #19=(($ #11#) 85 T ELT) #5# #19#) (|characteristic| ((#20=(|NonNegativeInteger|)) 104 T CONST)) (|before?| #13#) (|atanh| (#6# 164 T ELT)) (|atan| (#6# 132 T ELT)) (|associates?| #13#) (|asinh| (#6# 162 T ELT)) (|asin| (#6# 128 T ELT)) (|asech| (#6# 160 T ELT)) (|asec| (#6# 140 T ELT)) (|annihilate?| #13#) (|acsch| (#6# 158 T ELT)) (|acsc| (#6# 138 T ELT)) (|acoth| (#6# 156 T ELT)) (|acot| (#6# 134 T ELT)) (|acosh| (#6# 154 T ELT)) (|acos| (#6# 130 T ELT)) (|Zero| (#10# 30 T CONST)) (|One| (#10# 10 T CONST)) (>= #13#) (> #13#) (= (#1# 50 T ELT)) (<= #13#) (< (#1# 48 T ELT)) (- (#6# 54 T ELT) (#15# 55 T ELT)) (+ (#15# 53 T ELT)) (** (($ $ #21=(|PositiveInteger|)) 73 T ELT) (($ $ #20#) NIL T ELT) (#15# 112 T ELT) (($ $ #17#) 166 T ELT)) (* (($ #21# $) 67 T ELT) (($ #20# $) NIL T ELT) (($ #11# $) 66 T ELT) (#15# 62 T ELT))) +((~= (#1=(#2=(|Boolean|) $ $) 77 T ELT)) (|zero?| (#3=(#2# $) 49 T ELT)) (|width| (#4=(|#1| $) 39 T ELT)) (|unitNormal| (((|Record| (|:| |unit| $) (|:| |canonical| $) (|:| |associate| $)) $) NIL T ELT)) (|unitCanonical| #5=(#6=($ $) NIL T ELT)) (|unit?| 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#20=(|PositiveInteger|)) 73 T ELT) (($ $ #19#) NIL T ELT) (#14# 112 T ELT) (($ $ #16#) 166 T ELT)) (* (($ #20# $) 67 T ELT) (($ #19# $) NIL T ELT) (($ #8# $) 66 T ELT) (#14# 62 T ELT))) (((|Interval| |#1|) (|IntervalCategory| |#1|) (|Join| (|FloatingPointSystem|) (|TranscendentalFunctionCategory|))) (T |Interval|)) NIL ((|solveLinearPolynomialEquation| (((|Union| #1=(|List| #2=(|SparseUnivariatePolynomial| (|Integer|))) "failed") #1# #2#) 27 T ELT))) @@ -1707,16 +1710,16 @@ NIL ((~= #1=(#2=((|Boolean|) $ $) NIL T ELT)) (|resolve| (((|Maybe| $) (|Hostname|)) 23 T ELT)) (|latex| ((#3=(|String|) $) NIL T ELT)) (|ip4Address| (($ #3#) 16 T ELT)) (|hash| (((|SingleInteger|) $) NIL T ELT)) (|coerce| (((|OutputForm|) $) 33 T ELT)) (|bytes| (((|DataArray| 4 (|Byte|)) $) 24 T ELT)) (|before?| #1#) (= (#2# 26 T ELT))) (((|IP4Address|) (|Join| (|SetCategory|) (CATEGORY |domain| (SIGNATURE |ip4Address| ($ (|String|))) (SIGNATURE |bytes| ((|DataArray| 4 (|Byte|)) $)) (SIGNATURE |resolve| ((|Maybe| 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(|multiEuclidean| (((|Union| #26# #18#) #26# $) NIL T ELT)) (|minimalPolynomial| ((#34=(|SparseUnivariatePolynomial| $) $ #13#) NIL #14# ELT) (#35=(#34# $) 104 T ELT)) (|lookup| (#32# 67 T ELT)) (|linearAssociatedOrder| #36=(#35# NIL #14# ELT)) (|linearAssociatedLog| (((|Union| #34# #18#) $ $) NIL #14# ELT) #36#) (|linearAssociatedExp| (($ $ #34#) NIL #14# ELT)) (|lcm| #24# #37=(($ #26#) NIL T ELT)) (|latex| (((|String|) $) NIL T ELT)) (|inv| #5#) (|init| #20#) (|index| (($ #13#) 60 T ELT)) (|inGroundField?| (#4# 87 T ELT)) (|hash| (((|SingleInteger|) $) NIL T ELT)) (|generator| (#21# 28 #14# ELT)) (|gcdPolynomial| ((#34# #34# #34#) NIL T ELT)) (|gcd| #24# #37#) (|factorsOfCyclicGroupSize| (((|List| (|Record| (|:| |factor| #15#) (|:| |exponent| #15#)))) 54 T ELT)) (|factor| #19#) (|extensionDegree| ((#13#) 86 T ELT) ((#31#) NIL T ELT)) (|extendedEuclidean| (((|Record| #38=(|:| |coef1| $) #39=(|:| |coef2| $) #27#) $ $) NIL T ELT) (((|Union| (|Record| #38# #39#) #18#) $ $ $) NIL T ELT)) 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27 T CONST)) (|Frobenius| (#29# NIL #14# ELT) (#6# NIL #14# ELT)) (D #5# #28#) (= #1#) (/ #24#) (- #5# #24#) (+ #24#) (** (#12# NIL T ELT) #28# (($ $ #15#) 34 T ELT)) (* (($ #13# $) NIL T ELT) (($ #10# $) NIL T ELT) (($ #15# . #43=($)) NIL T ELT) (#25# 81 T ELT) (($ $ #42#) NIL T ELT) (($ #42# . #43#) NIL T ELT))) +((~= #1=(#2=(#3=(|Boolean|) $ $) NIL T ELT)) (|zero?| (#4=(#3# $) 30 T ELT)) (|unitNormal| (((|Record| (|:| |unit| $) (|:| |canonical| $) (|:| |associate| $)) $) NIL T ELT)) (|unitCanonical| #5=(#6=($ $) NIL T ELT)) (|unit?| #7=(#4# NIL T ELT)) (|transcendent?| #7#) (|transcendenceDegree| #8=(#9=(#10=(|NonNegativeInteger|)) NIL T ELT)) (|trace| #11=(#12=($ $ #13=(|PositiveInteger|)) NIL #14=(|has| $ (|Finite|)) ELT) #5#) (|tableForDiscreteLogarithm| (((|Table| #13# #10#) #15=(|Integer|)) 59 T ELT)) (|subtractIfCan| ((#16=(|Maybe| $) $ $) NIL T ELT)) (|squareFreePart| #5#) (|squareFree| #17=(((|Factored| $) $) NIL T ELT)) (|sizeLess?| #1#) (|size| #8#) (|sample| #18=(#19=($) NIL T CONST)) (|retractIfCan| (#20=(#21=(|Union| $ #22="failed") $) 95 T ELT)) (|retract| (#6# 94 T ELT)) (|represents| (($ #23=(|Vector| $)) 93 T ELT)) (|representationType| (((|Union| "prime" "polynomial" "normal" "cyclic")) 56 T ELT)) (|rem| #24=(#25=($ $ $) NIL T ELT)) (|recip| (#20# 47 T ELT)) (|random| (#19# NIL T ELT)) (|quo| #24#) (|principalIdeal| (((|Record| (|:| |coef| #26=(|List| $)) #27=(|:| |generator| $)) #26#) NIL T ELT)) (|primitiveElement| (#19# 61 T ELT)) (|primitive?| #7#) (|primeFrobenius| #5# #28=(#29=($ $ #10#) NIL T ELT)) (|prime?| #7#) (|order| #30=((#31=(|OnePointCompletion| #13#) $) NIL T ELT) (#32=(#13# $) NIL T ELT)) (|opposite?| #1#) (|one?| #7#) (|normalElement| (#19# 49 #14# ELT)) (|normal?| (#4# NIL #14# ELT)) (|norm| #11# #5#) (|nextItem| #33=((#16# $) NIL T ELT)) (|multiEuclidean| (((|Union| #26# #22#) #26# $) NIL T ELT)) (|minimalPolynomial| ((#34=(|SparseUnivariatePolynomial| $) $ #13#) NIL #14# ELT) (#35=(#34# $) 104 T ELT)) (|lookup| (#32# 67 T ELT)) (|linearAssociatedOrder| #36=(#35# NIL #14# ELT)) (|linearAssociatedLog| (((|Union| #34# #22#) $ $) NIL #14# ELT) #36#) (|linearAssociatedExp| (($ $ #34#) NIL #14# ELT)) (|lcm| #24# #37=(($ #26#) NIL T ELT)) (|latex| (((|String|) $) NIL T ELT)) (|inv| #5#) (|init| #18#) (|index| (($ #13#) 60 T ELT)) (|inGroundField?| (#4# 87 T ELT)) (|hash| (((|SingleInteger|) $) NIL T ELT)) (|generator| (#19# 28 #14# ELT)) (|gcdPolynomial| ((#34# #34# #34#) NIL T ELT)) (|gcd| #24# #37#) (|factorsOfCyclicGroupSize| (((|List| (|Record| (|:| |factor| #15#) (|:| |exponent| #15#)))) 54 T ELT)) (|factor| #17#) (|extensionDegree| ((#13#) 86 T ELT) ((#31#) NIL T ELT)) (|extendedEuclidean| (((|Record| #38=(|:| |coef1| $) #39=(|:| |coef2| $) #27#) $ $) NIL T ELT) (((|Union| (|Record| #38# #39#) #22#) $ $ $) NIL T ELT)) (|exquo| ((#21# $ $) NIL T ELT)) (|expressIdealMember| (((|Maybe| #26#) #26# $) NIL T ELT)) (|euclideanSize| #40=((#10# $) NIL T ELT)) (|divide| (((|Record| (|:| |quotient| $) (|:| |remainder| $)) $ $) NIL T ELT)) (|discreteLog| (((|Union| #10# #22#) $ $) NIL T ELT) #40#) (|dimension| (((|CardinalNumber|)) NIL T ELT)) (|differentiate| #5# #28#) (|degree| (#32# 85 T ELT) #30#) (|definingPolynomial| ((#34#) 102 T ELT)) (|createPrimitiveElement| (#19# 66 T ELT)) (|createNormalElement| (#19# 50 #14# ELT)) (|coordinates| ((#41=(|Matrix| $) #23#) NIL T ELT) ((#23# $) 91 T ELT)) (|convert| ((#15# $) 42 T ELT)) (|conditionP| (((|Union| #23# #22#) #41#) NIL T ELT)) (|coerce| (((|OutputForm|) $) NIL T ELT) (($ #15#) 45 T ELT) #5# (($ #42=(|Fraction| #15#)) NIL T ELT)) (|charthRoot| #33# (#6# 105 T ELT)) (|characteristic| (#9# 51 T CONST)) (|before?| (#2# 107 T ELT)) (|basis| ((#23# #13#) 97 T ELT) ((#23#) 96 T ELT)) (|associates?| #1#) (|annihilate?| #1#) (|algebraic?| #7#) (|Zero| (#19# 31 T CONST)) (|One| (#19# 27 T CONST)) (|Frobenius| (#29# NIL #14# ELT) (#6# NIL #14# ELT)) (D #5# #28#) (= #1#) (/ #24#) (- #5# #24#) (+ #24#) (** (#12# NIL T ELT) #28# (($ $ #15#) 34 T ELT)) (* (($ #13# $) NIL T ELT) (($ #10# $) NIL T ELT) (($ #15# . #43=($)) NIL T ELT) (#25# 81 T ELT) (($ $ #42#) NIL T ELT) (($ #42# . #43#) NIL T ELT))) (((|InnerPrimeField| |#1|) (|Join| (|FiniteFieldCategory|) (|FiniteAlgebraicExtensionField| $) (|ConvertibleTo| (|Integer|))) (|PositiveInteger|)) (T |InnerPrimeField|)) NIL ((|iprint| (((|Void|) (|String|)) 10 T ELT))) (((|InternalPrintPackage|) (CATEGORY |package| (SIGNATURE |iprint| ((|Void|) (|String|))))) (T |InternalPrintPackage|)) ((|iprint| (*1 *2 *3) (AND (|isDomain| *3 (|String|)) (|isDomain| *2 (|Void|)) (|isDomain| *1 (|InternalPrintPackage|))))) -((~= #1=((#2=(|Boolean|) $ $) NIL T ELT)) (|zero?| (#3=(#2# $) NIL T ELT)) (|subtractIfCan| (((|Union| $ #4="failed") $ $) NIL T ELT)) (|sample| (#5=($) NIL T CONST)) (|retractIfCan| (((|Union| |#1| #4#) $) 77 T ELT)) (|retract| (#6=(|#1| $) NIL T ELT)) (|ratpart| (#6# 30 T ELT)) (|opposite?| #1#) (|notelem| ((#7=(|List| (|Record| (|:| |integrand| |#1|) (|:| |intvar| |#1|))) $) 32 T ELT)) (|mkAnswer| (($ |#1| #8=(|List| (|Record| (|:| |scalar| #9=(|Fraction| #10=(|Integer|))) (|:| |coeff| #11=(|SparseUnivariatePolynomial| |#1|)) (|:| |logand| #11#))) #7#) 28 T ELT)) (|logpart| ((#8# $) 31 T ELT)) (|latex| (((|String|) $) NIL T ELT)) (|integral| (($ |#1| |#1|) 38 T ELT) (($ |#1| #12=(|Symbol|)) 49 (|has| |#1| (|RetractableTo| #12#)) ELT)) (|hash| (((|SingleInteger|) $) NIL T ELT)) (|elem?| (#3# 35 T ELT)) (|differentiate| ((|#1| $ (|Mapping| |#1| |#1|)) 89 T ELT) ((|#1| $ #12#) 90 (|has| |#1| (|PartialDifferentialRing| #12#)) ELT)) (|coerce| (((|OutputForm|) $) 113 T ELT) (($ |#1|) 29 T ELT)) (|before?| #1#) (|Zero| (#5# 18 T CONST)) (= #1#) (- (($ $) 17 T ELT) (#13=($ $ $) NIL T ELT)) (+ (#13# 86 T ELT)) (* (($ (|PositiveInteger|) $) NIL T ELT) (($ (|NonNegativeInteger|) $) NIL T ELT) (($ #10# $) 16 T ELT) (($ #9# $) 41 T ELT) (($ $ #9#) NIL T ELT))) +((~= #1=((#2=(|Boolean|) $ $) NIL T ELT)) (|zero?| (#3=(#2# $) NIL T ELT)) (|subtractIfCan| (((|Maybe| $) $ $) NIL T ELT)) (|sample| (#4=($) NIL T CONST)) (|retractIfCan| (((|Union| |#1| "failed") $) 77 T ELT)) (|retract| (#5=(|#1| $) NIL T ELT)) (|ratpart| (#5# 30 T ELT)) (|opposite?| #1#) (|notelem| ((#6=(|List| (|Record| (|:| |integrand| |#1|) (|:| |intvar| |#1|))) $) 32 T ELT)) (|mkAnswer| (($ |#1| #7=(|List| (|Record| (|:| |scalar| #8=(|Fraction| #9=(|Integer|))) (|:| |coeff| #10=(|SparseUnivariatePolynomial| |#1|)) (|:| |logand| #10#))) #6#) 28 T ELT)) (|logpart| ((#7# $) 31 T ELT)) (|latex| (((|String|) $) NIL T ELT)) (|integral| (($ |#1| |#1|) 38 T ELT) (($ |#1| #11=(|Symbol|)) 49 (|has| |#1| (|RetractableTo| #11#)) ELT)) (|hash| (((|SingleInteger|) $) NIL T ELT)) (|elem?| (#3# 35 T ELT)) (|differentiate| ((|#1| $ (|Mapping| |#1| |#1|)) 89 T ELT) ((|#1| $ #11#) 90 (|has| |#1| (|PartialDifferentialRing| #11#)) ELT)) (|coerce| (((|OutputForm|) $) 113 T ELT) (($ |#1|) 29 T ELT)) (|before?| #1#) (|Zero| (#4# 18 T CONST)) (= #1#) (- (($ $) 17 T ELT) (#12=($ $ $) NIL T ELT)) (+ (#12# 86 T ELT)) (* (($ (|PositiveInteger|) $) NIL T ELT) (($ (|NonNegativeInteger|) $) NIL T ELT) (($ #9# $) 16 T ELT) (($ #8# $) 41 T ELT) (($ $ #8#) NIL T ELT))) (((|IntegrationResult| |#1|) (|Join| (|Module| #1=(|Fraction| (|Integer|))) (|RetractableTo| |#1|) (CATEGORY |domain| (SIGNATURE |mkAnswer| ($ |#1| #2=(|List| (|Record| (|:| |scalar| #1#) (|:| |coeff| #3=(|SparseUnivariatePolynomial| |#1|)) (|:| |logand| #3#))) #4=(|List| (|Record| (|:| |integrand| |#1|) (|:| |intvar| |#1|))))) (SIGNATURE |ratpart| (|#1| $)) (SIGNATURE |logpart| (#2# $)) (SIGNATURE |notelem| (#4# $)) (SIGNATURE |elem?| ((|Boolean|) $)) (SIGNATURE |integral| ($ |#1| |#1|)) (SIGNATURE |differentiate| (|#1| $ (|Mapping| |#1| |#1|))) (IF (|has| |#1| (|PartialDifferentialRing| #5=(|Symbol|))) (SIGNATURE |differentiate| (|#1| $ #5#)) |%noBranch|) (IF (|has| |#1| (|RetractableTo| #5#)) (SIGNATURE |integral| ($ |#1| #5#)) |%noBranch|))) (|Field|)) (T |IntegrationResult|)) ((|mkAnswer| (*1 *1 *2 *3 *4) (AND (|isDomain| *3 (|List| (|Record| #1=(|:| |scalar| (|Fraction| (|Integer|))) (|:| |coeff| #2=(|SparseUnivariatePolynomial| *2)) (|:| |logand| #2#)))) (|isDomain| *4 (|List| (|Record| (|:| |integrand| *2) (|:| |intvar| *2)))) #3=(|ofCategory| *2 #4=(|Field|)) #5=(|isDomain| *1 (|IntegrationResult| *2)))) (|ratpart| #6=(*1 *2 *1) #7=(AND #5# #3#)) (|logpart| #6# (AND (|isDomain| *2 (|List| (|Record| #1# (|:| |coeff| #8=(|SparseUnivariatePolynomial| *3)) (|:| |logand| #8#)))) #9=(|isDomain| *1 (|IntegrationResult| *3)) #10=(|ofCategory| *3 #4#))) (|notelem| #6# (AND (|isDomain| *2 (|List| (|Record| (|:| |integrand| *3) (|:| |intvar| *3)))) #9# #10#)) (|elem?| #6# (AND (|isDomain| *2 (|Boolean|)) #9# #10#)) (|integral| (*1 *1 *2 *2) #7#) (|differentiate| #11=(*1 *2 *1 *3) (AND (|isDomain| *3 (|Mapping| *2 *2)) #5# #3#)) (|differentiate| #11# (AND #3# (|ofCategory| *2 (|PartialDifferentialRing| *3)) #5# #12=(|isDomain| *3 (|Symbol|)))) (|integral| (*1 *1 *2 *3) (AND #12# #5# (|ofCategory| *2 (|RetractableTo| *3)) #3#))) ((|map| (((|Union| (|Record| (|:| |mainpart| |#2|) (|:| |limitedlogs| (|List| (|Record| #1=(|:| |coeff| |#2|) (|:| |logand| |#2|))))) #2="failed") #3=(|Mapping| |#2| |#1|) (|Union| (|Record| (|:| |mainpart| |#1|) (|:| |limitedlogs| (|List| (|Record| #4=(|:| |coeff| |#1|) (|:| |logand| |#1|))))) #2#)) 44 T ELT) (((|Union| |#2| #2#) #3# (|Union| |#1| #2#)) 11 T ELT) (((|Union| (|Record| (|:| |ratpart| |#2|) #1#) #2#) #3# (|Union| (|Record| (|:| |ratpart| |#1|) #4#) #2#)) 35 T ELT) (((|IntegrationResult| |#2|) #3# (|IntegrationResult| |#1|)) 30 T ELT))) @@ -1749,10 +1752,10 @@ NIL ((|sum| ((#1=(|Record| (|:| |num| |#4|) (|:| |den| (|Integer|))) |#4| |#2|) 23 T ELT) ((#1# |#4| |#2| (|Segment| |#4|)) 32 T ELT))) (((|InnerPolySum| |#1| |#2| |#3| |#4|) (CATEGORY |package| (SIGNATURE |sum| (#1=(|Record| (|:| |num| |#4|) (|:| |den| (|Integer|))) |#4| |#2| (|Segment| |#4|))) (SIGNATURE |sum| (#1# |#4| |#2|))) (|OrderedAbelianMonoidSup|) (|OrderedSet|) (|IntegralDomain|) (|PolynomialCategory| |#3| |#1| |#2|)) (T |InnerPolySum|)) ((|sum| (*1 *2 *3 *4) (AND (|ofCategory| *5 #1=(|OrderedAbelianMonoidSup|)) #2=(|ofCategory| *4 (|OrderedSet|)) (|ofCategory| *6 #3=(|IntegralDomain|)) #4=(|isDomain| *2 (|Record| (|:| |num| *3) (|:| |den| (|Integer|)))) (|isDomain| *1 (|InnerPolySum| *5 *4 *6 *3)) (|ofCategory| *3 (|PolynomialCategory| *6 *5 *4)))) (|sum| (*1 *2 *3 *4 *5) (AND (|isDomain| *5 (|Segment| *3)) (|ofCategory| *3 (|PolynomialCategory| *7 *6 *4)) (|ofCategory| *6 #1#) #2# (|ofCategory| *7 #3#) #4# (|isDomain| *1 (|InnerPolySum| *6 *4 *7 *3))))) -((~= #1=(#2=(#3=(|Boolean|) $ $) NIL T ELT)) (|zero?| (#4=(#3# $) 71 T ELT)) (|variables| ((#5=(|List| #6=(|SingletonAsOrderedSet|)) $) NIL T ELT)) (|variable| ((#7=(|Symbol|) $) NIL T ELT)) (|unitNormal| (((|Record| (|:| |unit| $) (|:| |canonical| $) (|:| |associate| $)) $) NIL #8=(|has| |#1| (|IntegralDomain|)) ELT)) (|unitCanonical| #9=(#10=($ $) NIL #8# ELT)) (|unit?| (#4# NIL #8# ELT)) (|truncate| (#11=($ $ #12=(|Integer|)) 58 T ELT) (($ $ #12# #12#) 59 T ELT)) (|terms| (#13=(#14=(|Stream| (|Record| (|:| |k| #12#) (|:| |c| |#1|))) $) 65 T ELT)) (|taylorQuoByVar| (#10# 109 T ELT)) (|subtractIfCan| (#15=(#16=(|Union| $ "failed") $ $) NIL T ELT)) (|seriesToOutputForm| ((#17=(|OutputForm|) #14# #18=(|Reference| (|OrderedCompletion| #12#)) #7# |#1| #19=(|Fraction| #12#)) 232 T ELT)) (|series| (($ #14#) 36 T ELT)) (|sample| (#20=($) NIL T CONST)) (|reductum| #21=(#10# NIL T ELT)) (|recip| ((#16# $) NIL T ELT)) (|pole?| #22=(#4# NIL T ELT)) (|order| (#23=(#12# $) 63 T ELT) ((#12# $ #12#) 64 T ELT)) (|opposite?| #1#) (|one?| #22#) (|multiplyExponents| (#24=($ $ #25=(|PositiveInteger|)) 83 T ELT)) (|multiplyCoefficients| (($ (|Mapping| |#1| #12#) $) 80 T ELT)) (|monomial?| (#4# 26 T ELT)) (|monomial| (($ |#1| #12#) 22 T ELT) (($ $ #6# #12#) NIL T ELT) (($ $ #5# (|List| #12#)) NIL T ELT)) (|map| (($ (|Mapping| |#1| |#1|) $) 75 T ELT)) (|makeSeries| (($ #18# #14#) 13 T ELT)) (|leadingMonomial| #21#) (|leadingCoefficient| #26=((|#1| $) NIL T ELT)) (|latex| (((|String|) $) NIL T ELT)) (|integrate| (#10# 120 #27=(|has| |#1| (|Algebra| #19#)) ELT)) (|iExquo| ((#16# $ $ #3#) 108 T ELT)) (|iCompose| (#28=($ $ $) 116 T ELT)) (|hash| (((|SingleInteger|) $) NIL T ELT)) (|getStream| (#13# 15 T ELT)) (|getRef| ((#18# $) 14 T ELT)) (|extend| (#11# 47 T ELT)) (|exquo| (#15# NIL #8# ELT)) (|eval| (((|Stream| |#1|) $ |#1|) NIL #29=(|has| |#1| (SIGNATURE ** (|#1| |#1| #12#))) ELT)) (|elt| (#30=(|#1| $ #12#) 62 T ELT) (#28# NIL (|has| #12# (|SemiGroup|)) ELT)) (|differentiate| #31=(($ $ #7#) NIL #32=(AND (|has| |#1| (|PartialDifferentialRing| #7#)) #33=(|has| |#1| (SIGNATURE * (|#1| #12# |#1|)))) ELT) #34=(($ $ #35=(|List| #7#)) NIL #32# ELT) #36=(($ $ #7# #37=(|NonNegativeInteger|)) NIL #32# ELT) #38=(($ $ #35# (|List| #37#)) NIL #32# ELT) (#10# 77 #33# ELT) #39=(#40=($ $ #37#) NIL #33# ELT)) (|degree| (#23# NIL T ELT)) (|complete| (#10# 48 T ELT)) (|coerce| ((#17# $) NIL T ELT) (($ #12#) 29 T ELT) (($ #19#) NIL #27# ELT) #9# (($ |#1|) 28 (|has| |#1| (|CommutativeRing|)) ELT)) (|coefficient| (#30# 61 T ELT)) (|charthRoot| (((|Maybe| $) $) NIL (|has| |#1| (|CharacteristicNonZero|)) ELT)) (|characteristic| ((#37#) 39 T CONST)) (|center| #26#) (|cTanh| (#10# 192 #27# ELT)) (|cTan| (#10# 167 #27# ELT)) (|cSinh| (#10# 189 #27# ELT)) (|cSin| (#10# 164 #27# ELT)) (|cSech| (#10# 194 #27# ELT)) (|cSec| (#10# 170 #27# ELT)) (|cRationalPower| (#41=($ $ #19#) 157 #27# ELT)) (|cPower| (#42=($ $ |#1|) 128 #27# ELT)) (|cLog| (#10# 161 #27# ELT)) (|cExp| (#10# 159 #27# ELT)) (|cCsch| (#10# 195 #27# ELT)) (|cCsc| (#10# 171 #27# ELT)) (|cCoth| (#10# 193 #27# ELT)) (|cCot| (#10# 169 #27# ELT)) (|cCosh| (#10# 190 #27# ELT)) (|cCos| (#10# 165 #27# ELT)) (|cAtanh| (#10# 200 #27# ELT)) (|cAtan| (#10# 180 #27# ELT)) (|cAsinh| (#10# 197 #27# ELT)) (|cAsin| (#10# 176 #27# ELT)) (|cAsech| (#10# 204 #27# ELT)) (|cAsec| (#10# 184 #27# ELT)) (|cAcsch| (#10# 206 #27# ELT)) (|cAcsc| (#10# 186 #27# ELT)) (|cAcoth| (#10# 202 #27# ELT)) (|cAcot| (#10# 182 #27# ELT)) (|cAcosh| (#10# 199 #27# ELT)) (|cAcos| (#10# 178 #27# ELT)) (|before?| #1#) (|associates?| (#2# NIL #8# ELT)) (|approximate| (#30# NIL (AND #29# (|has| |#1| (SIGNATURE |coerce| (|#1| #7#)))) ELT)) (|annihilate?| #1#) (|Zero| (#20# 30 T CONST)) (|One| (#20# 40 T CONST)) (D #31# #34# #36# #38# (#10# NIL #33# ELT) #39#) (= (#2# 73 T ELT)) (/ (#42# NIL (|has| |#1| (|Field|)) ELT)) (- (#10# 91 T ELT) (#28# 72 T ELT)) (+ (#28# 88 T ELT)) (** (#24# NIL T ELT) (#40# 111 T ELT)) (* (($ #25# $) 98 T ELT) (($ #37# $) 96 T ELT) (($ #12# $) 93 T ELT) (#28# 104 T ELT) (#42# NIL T ELT) (($ |#1| . #43=($)) 123 T ELT) (($ #19# . #43#) NIL #27# ELT) (#41# NIL #27# ELT))) +((~= #1=(#2=(#3=(|Boolean|) $ $) NIL T ELT)) (|zero?| (#4=(#3# $) 71 T ELT)) (|variables| ((#5=(|List| #6=(|SingletonAsOrderedSet|)) $) NIL T ELT)) (|variable| ((#7=(|Symbol|) $) NIL T ELT)) (|unitNormal| (((|Record| (|:| |unit| $) (|:| |canonical| $) (|:| |associate| $)) $) NIL #8=(|has| |#1| (|IntegralDomain|)) ELT)) (|unitCanonical| #9=(#10=($ $) NIL #8# ELT)) (|unit?| (#4# NIL #8# ELT)) (|truncate| (#11=($ $ #12=(|Integer|)) 58 T ELT) (($ $ #12# #12#) 59 T ELT)) (|terms| (#13=(#14=(|Stream| (|Record| (|:| |k| #12#) (|:| |c| |#1|))) $) 65 T ELT)) (|taylorQuoByVar| (#10# 109 T ELT)) (|subtractIfCan| ((#15=(|Maybe| $) $ $) NIL T ELT)) (|seriesToOutputForm| ((#16=(|OutputForm|) #14# #17=(|Reference| (|OrderedCompletion| #12#)) #7# |#1| #18=(|Fraction| #12#)) 232 T ELT)) (|series| (($ #14#) 36 T ELT)) (|sample| (#19=($) NIL T CONST)) (|reductum| #20=(#10# NIL T ELT)) (|recip| ((#21=(|Union| $ "failed") $) NIL T ELT)) (|pole?| #22=(#4# NIL T ELT)) (|order| (#23=(#12# $) 63 T ELT) ((#12# $ #12#) 64 T ELT)) (|opposite?| #1#) (|one?| #22#) (|multiplyExponents| (#24=($ $ #25=(|PositiveInteger|)) 83 T ELT)) (|multiplyCoefficients| (($ (|Mapping| |#1| #12#) $) 80 T ELT)) (|monomial?| (#4# 26 T ELT)) (|monomial| (($ |#1| #12#) 22 T ELT) (($ $ #6# #12#) NIL T ELT) (($ $ #5# (|List| #12#)) NIL T ELT)) (|map| (($ (|Mapping| |#1| |#1|) $) 75 T ELT)) (|makeSeries| (($ #17# #14#) 13 T ELT)) (|leadingMonomial| #20#) (|leadingCoefficient| #26=((|#1| $) NIL T ELT)) (|latex| (((|String|) $) NIL T ELT)) (|integrate| (#10# 120 #27=(|has| |#1| (|Algebra| #18#)) ELT)) (|iExquo| ((#21# $ $ #3#) 108 T ELT)) (|iCompose| (#28=($ $ $) 116 T ELT)) (|hash| (((|SingleInteger|) $) NIL T ELT)) (|getStream| (#13# 15 T ELT)) (|getRef| ((#17# $) 14 T ELT)) (|extend| (#11# 47 T ELT)) (|exquo| ((#21# $ $) NIL #8# ELT)) (|eval| (((|Stream| |#1|) $ |#1|) NIL #29=(|has| |#1| (SIGNATURE ** (|#1| |#1| #12#))) ELT)) (|elt| (#30=(|#1| $ #12#) 62 T ELT) (#28# NIL (|has| #12# (|SemiGroup|)) ELT)) (|differentiate| #31=(($ $ #7#) NIL #32=(AND (|has| |#1| (|PartialDifferentialRing| #7#)) #33=(|has| |#1| (SIGNATURE * (|#1| #12# |#1|)))) ELT) #34=(($ $ #35=(|List| #7#)) NIL #32# ELT) #36=(($ $ #7# #37=(|NonNegativeInteger|)) NIL #32# ELT) #38=(($ $ #35# (|List| #37#)) NIL #32# ELT) (#10# 77 #33# ELT) #39=(#40=($ $ #37#) NIL #33# ELT)) (|degree| (#23# NIL T ELT)) (|complete| (#10# 48 T ELT)) (|coerce| ((#16# $) NIL T ELT) (($ #12#) 29 T ELT) (($ #18#) NIL #27# ELT) #9# (($ |#1|) 28 (|has| |#1| (|CommutativeRing|)) ELT)) (|coefficient| (#30# 61 T ELT)) (|charthRoot| ((#15# $) NIL (|has| |#1| (|CharacteristicNonZero|)) ELT)) (|characteristic| ((#37#) 39 T CONST)) (|center| #26#) (|cTanh| (#10# 192 #27# ELT)) (|cTan| (#10# 167 #27# ELT)) (|cSinh| (#10# 189 #27# ELT)) (|cSin| (#10# 164 #27# ELT)) (|cSech| (#10# 194 #27# ELT)) (|cSec| (#10# 170 #27# ELT)) (|cRationalPower| (#41=($ $ #18#) 157 #27# ELT)) (|cPower| (#42=($ $ |#1|) 128 #27# ELT)) (|cLog| (#10# 161 #27# ELT)) (|cExp| (#10# 159 #27# ELT)) (|cCsch| (#10# 195 #27# ELT)) (|cCsc| (#10# 171 #27# ELT)) (|cCoth| (#10# 193 #27# ELT)) (|cCot| (#10# 169 #27# ELT)) (|cCosh| (#10# 190 #27# ELT)) (|cCos| (#10# 165 #27# ELT)) (|cAtanh| (#10# 200 #27# ELT)) (|cAtan| (#10# 180 #27# ELT)) (|cAsinh| 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#1=(|Integer|)) (CATEGORY |domain| (SIGNATURE |makeSeries| ($ #2=(|Reference| (|OrderedCompletion| #1#)) #3=(|Stream| (|Record| (|:| |k| #1#) (|:| |c| |#1|))))) (SIGNATURE |getRef| (#2# $)) (SIGNATURE |getStream| (#3# $)) (SIGNATURE |series| ($ #3#)) (SIGNATURE |monomial?| (#4=(|Boolean|) $)) (SIGNATURE |multiplyCoefficients| ($ (|Mapping| |#1| #1#) $)) (SIGNATURE |iExquo| ((|Union| $ "failed") $ $ #4#)) (SIGNATURE |taylorQuoByVar| #5=($ $)) (SIGNATURE |iCompose| ($ $ $)) (SIGNATURE |seriesToOutputForm| ((|OutputForm|) #3# #2# (|Symbol|) |#1| #6=(|Fraction| #1#))) (IF (|has| |#1| (|Algebra| #6#)) (PROGN (SIGNATURE |integrate| #5#) (SIGNATURE |cPower| ($ $ |#1|)) (SIGNATURE |cRationalPower| ($ $ #6#)) (SIGNATURE |cExp| #5#) (SIGNATURE |cLog| #5#) (SIGNATURE |cSin| #5#) (SIGNATURE |cCos| #5#) (SIGNATURE |cTan| #5#) (SIGNATURE |cCot| #5#) (SIGNATURE |cSec| #5#) (SIGNATURE |cCsc| #5#) (SIGNATURE |cAsin| #5#) (SIGNATURE |cAcos| #5#) (SIGNATURE |cAtan| #5#) (SIGNATURE |cAcot| #5#) (SIGNATURE 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(*1 *1 *2 *1) (AND (|isDomain| *2 (|Mapping| *3 #8#)) #4# #3#)) (|iExquo| (*1 *1 *1 *1 *2) (|partial| AND #2# #3# #4#)) (|taylorQuoByVar| #11=(*1 *1 *1) #12=(AND #13=(|isDomain| *1 (|InnerSparseUnivariatePowerSeries| *2)) #14=(|ofCategory| *2 #5#))) (|iCompose| (*1 *1 *1 *1) #12#) (|seriesToOutputForm| (*1 *2 *3 *4 *5 *6 *7) (AND (|isDomain| *3 (|Stream| (|Record| #9# (|:| |c| *6)))) (|isDomain| *4 #7#) (|isDomain| *5 (|Symbol|)) (|isDomain| *7 #15=(|Fraction| #8#)) (|ofCategory| *6 #5#) (|isDomain| *2 (|OutputForm|)) (|isDomain| *1 (|InnerSparseUnivariatePowerSeries| *6)))) (|integrate| #11# #16=(AND #13# (|ofCategory| *2 (|Algebra| #15#)) #14#)) (|cPower| #17=(*1 *1 *1 *2) #16#) (|cRationalPower| #17# (AND (|isDomain| *2 #15#) #3# (|ofCategory| *3 (|Algebra| *2)) #4#)) (|cExp| #11# #16#) (|cLog| #11# #16#) (|cSin| #11# #16#) (|cCos| #11# #16#) (|cTan| #11# #16#) (|cCot| #11# #16#) (|cSec| #11# #16#) (|cCsc| #11# #16#) (|cAsin| #11# #16#) (|cAcos| #11# #16#) (|cAtan| #11# #16#) (|cAcot| #11# #16#) (|cAsec| #11# #16#) (|cAcsc| #11# #16#) (|cSinh| #11# #16#) (|cCosh| #11# #16#) (|cTanh| #11# #16#) (|cCoth| #11# #16#) (|cSech| #11# #16#) (|cCsch| #11# #16#) (|cAsinh| #11# #16#) (|cAcosh| #11# #16#) (|cAtanh| #11# #16#) (|cAcoth| #11# #16#) (|cAsech| #11# #16#) (|cAcsch| #11# #16#)) -((~= #1=(#2=(#3=(|Boolean|) $ $) NIL T ELT)) (|zero?| (#4=(#3# $) 62 T ELT)) (|unitNormal| (((|Record| (|:| |unit| $) (|:| |canonical| $) (|:| |associate| $)) $) NIL #5=(|has| |#1| (|IntegralDomain|)) ELT)) (|unitCanonical| #6=(#7=($ $) NIL #5# ELT)) (|unit?| (#4# NIL #5# ELT)) (|subtractIfCan| (#8=(#9=(|Union| $ "failed") $ $) NIL T ELT)) (|series| (($ #10=(|Stream| |#1|)) 9 T ELT)) (|sample| (#11=($) NIL T CONST)) (|recip| ((#9# $) 44 T ELT)) (|pole?| (#4# 56 T ELT)) (|order| ((#12=(|NonNegativeInteger|) $) 61 T ELT) ((#12# $ #12#) 60 T ELT)) (|opposite?| #1#) (|one?| (#4# NIL T ELT)) (|latex| (((|String|) $) NIL T ELT)) (|hash| (((|SingleInteger|) $) NIL T ELT)) (|exquo| (#8# 46 #5# ELT)) (|coerce| (((|OutputForm|) $) NIL T ELT) (($ #13=(|Integer|)) NIL T ELT) #6#) (|coefficients| ((#10# $) 25 T ELT)) (|characteristic| ((#12#) 55 T CONST)) (|before?| #1#) (|associates?| (#2# NIL #5# ELT)) (|annihilate?| #1#) (|Zero| (#11# 10 T CONST)) (|One| (#11# 14 T CONST)) (= (#2# 24 T ELT)) (- (#7# 32 T ELT) (#14=($ $ $) 16 T ELT)) (+ (#14# 27 T ELT)) (** (($ $ #15=(|PositiveInteger|)) NIL T ELT) (($ $ #12#) 53 T ELT)) (* (($ #15# $) NIL T ELT) (($ #12# $) NIL T ELT) (($ #13# $) 36 T ELT) (#14# 30 T ELT) (($ $ |#1|) 40 T ELT) (($ |#1| $) 39 T ELT) (($ $ #13#) 38 T ELT))) +((~= #1=(#2=(#3=(|Boolean|) $ $) NIL T ELT)) (|zero?| (#4=(#3# $) 62 T ELT)) (|unitNormal| (((|Record| (|:| |unit| $) (|:| |canonical| $) (|:| |associate| $)) $) NIL #5=(|has| |#1| (|IntegralDomain|)) ELT)) (|unitCanonical| #6=(#7=($ $) NIL #5# ELT)) (|unit?| (#4# NIL #5# ELT)) (|subtractIfCan| (((|Maybe| $) $ $) NIL T ELT)) (|series| (($ #8=(|Stream| |#1|)) 9 T ELT)) (|sample| (#9=($) NIL T CONST)) (|recip| ((#10=(|Union| $ "failed") $) 44 T ELT)) (|pole?| (#4# 56 T ELT)) (|order| ((#11=(|NonNegativeInteger|) $) 61 T ELT) ((#11# $ #11#) 60 T ELT)) (|opposite?| #1#) (|one?| (#4# NIL T ELT)) (|latex| (((|String|) $) NIL T ELT)) (|hash| (((|SingleInteger|) $) NIL T ELT)) (|exquo| ((#10# $ $) 46 #5# ELT)) (|coerce| (((|OutputForm|) $) NIL T ELT) (($ #12=(|Integer|)) NIL T ELT) #6#) (|coefficients| ((#8# $) 25 T ELT)) (|characteristic| ((#11#) 55 T CONST)) (|before?| #1#) (|associates?| (#2# NIL #5# ELT)) (|annihilate?| #1#) (|Zero| (#9# 10 T CONST)) (|One| (#9# 14 T CONST)) (= (#2# 24 T ELT)) (- (#7# 32 T ELT) (#13=($ $ $) 16 T ELT)) (+ (#13# 27 T ELT)) (** (($ $ #14=(|PositiveInteger|)) NIL T ELT) (($ $ #11#) 53 T ELT)) (* (($ #14# $) NIL T ELT) (($ #11# $) NIL T ELT) (($ #12# $) 36 T ELT) (#13# 30 T ELT) (($ $ |#1|) 40 T ELT) (($ |#1| $) 39 T ELT) (($ $ #12#) 38 T ELT))) (((|InnerTaylorSeries| |#1|) (|Join| #1=(|Ring|) (|BiModule| |#1| |#1|) (CATEGORY |domain| (SIGNATURE |coefficients| (#2=(|Stream| |#1|) $)) (SIGNATURE |series| ($ #2#)) (SIGNATURE |pole?| ((|Boolean|) $)) (SIGNATURE |order| (#3=(|NonNegativeInteger|) $)) (SIGNATURE |order| (#3# $ #3#)) (SIGNATURE * ($ $ (|Integer|))) (IF (|has| |#1| #4=(|IntegralDomain|)) (ATTRIBUTE #4#) |%noBranch|))) #1#) (T |InnerTaylorSeries|)) ((|coefficients| #1=(*1 *2 *1) (AND #2=(|isDomain| *2 (|Stream| *3)) #3=(|isDomain| *1 (|InnerTaylorSeries| *3)) #4=(|ofCategory| *3 (|Ring|)))) (|series| (*1 *1 *2) (AND #2# #4# #3#)) (|pole?| #1# (AND (|isDomain| *2 (|Boolean|)) #3# #4#)) (|order| #1# #5=(AND (|isDomain| *2 (|NonNegativeInteger|)) #3# #4#)) (|order| (*1 *2 *1 *2) #5#) (* (*1 *1 *1 *2) (AND (|isDomain| *2 (|Integer|)) #3# #4#))) ((~= #1=(((|Boolean|) $ $) NIL T ELT)) (|voidMode| (#2=($) 8 T CONST)) (|noValueMode| (#2# 7 T CONST)) (|mappingMode| (($ $ (|List| $)) 16 T ELT)) (|latex| (((|String|) $) NIL T ELT)) (|jokerMode| (#2# 6 T CONST)) (|hash| (((|SingleInteger|) $) NIL T ELT)) (|coerce| (((|OutputForm|) . #3=($)) NIL T ELT) (($ #4=(|Syntax|)) 15 T ELT) ((#4# . #3#) 10 T ELT)) (|categoryMode| (#2# NIL T CONST)) (|before?| #1#) (= #1#)) @@ -1781,7 +1784,7 @@ NIL ((~= #1=(((|Boolean|) $ $) NIL T ELT)) (|latex| (((|String|) $) NIL T ELT)) (|hash| (((|SingleInteger|) $) NIL T ELT)) (|coerce| (((|OutputForm|) . #2=($)) NIL T ELT) (($ #3=(|Syntax|)) NIL T ELT) ((#3# . #2#) NIL T ELT) ((#4=(|TypeAst|) $) 15 T ELT) (($ #5=(|List| #4#)) 14 T ELT)) (|categories| ((#5# $) 12 T ELT)) (|before?| #1#) (= #1#)) (((|JoinAst|) (|Join| (|SpadSyntaxCategory|) (|CoercibleTo| #1=(|TypeAst|)) (CATEGORY |domain| (SIGNATURE |coerce| ($ #2=(|List| #1#))) (SIGNATURE |categories| (#2# $))))) (T |JoinAst|)) ((|coerce| (*1 *1 *2) #1=(AND (|isDomain| *2 (|List| (|TypeAst|))) (|isDomain| *1 (|JoinAst|)))) (|categories| (*1 *2 *1) #1#)) -((~= #1=((#2=(|Boolean|) $ $) NIL T ELT)) (|zero?| ((#2# $) NIL T ELT)) (|unit| #3=((#4=(|Union| $ #5="failed")) NIL #6=(OR (AND #7=(|has| |#2| (|FiniteRankNonAssociativeAlgebra| |#1|)) #8=(|has| |#1| (|IntegralDomain|))) (AND #9=(|has| |#2| (|FramedNonAssociativeAlgebra| |#1|)) #8#)) ELT)) (|subtractIfCan| ((#4# $ $) NIL T ELT)) (|structuralConstants| ((#10=(|Vector| #11=(|Matrix| |#1|))) NIL #9# ELT) ((#10# #12=(|Vector| $)) NIL #7# ELT)) (|someBasis| (#13=(#12#) NIL #7# ELT)) (|sample| #14=(($) NIL T CONST)) (|rightUnits| #15=(((|Union| (|Record| (|:| |particular| $) (|:| |basis| (|List| $))) #5#)) NIL #6# ELT)) (|rightUnit| #3#) (|rightTraceMatrix| #16=((#11#) NIL #9# ELT) #17=(#18=(#11# #12#) NIL #7# ELT)) (|rightTrace| #19=((|#1| $) NIL #7# ELT)) (|rightRegularRepresentation| #20=((#11# $) NIL #9# ELT) #21=((#11# $ #12#) NIL #7# ELT)) (|rightRecip| #22=((#4# $) NIL #6# ELT)) (|rightRankPolynomial| #23=(((|SparseUnivariatePolynomial| #24=(|Polynomial| |#1|))) NIL (AND #9# (|has| |#1| (|Field|))) ELT)) (|rightPower| #25=(#26=($ $ #27=(|PositiveInteger|)) NIL T ELT)) (|rightNorm| #19#) (|rightMinimalPolynomial| #28=(#29=((|SparseUnivariatePolynomial| |#1|) $) NIL #6# ELT)) (|rightDiscriminant| #30=((|#1|) NIL #9# ELT) #31=((|#1| #12#) NIL #7# ELT)) (|rightCharacteristicPolynomial| #32=(#29# NIL #7# ELT)) (|rightAlternative?| #33=((#2#) NIL #7# ELT)) (|represents| #34=(($ #35=(|Vector| |#1|)) NIL #9# ELT) (($ #35# #12#) NIL #7# ELT)) (|recip| #22#) (|rank| ((#27#) NIL #7# ELT)) (|powerAssociative?| #33#) (|plenaryPower| #25#) (|opposite?| #1#) (|noncommutativeJordanAlgebra?| #33#) (|lieAlgebra?| #33#) (|lieAdmissible?| #33#) (|leftUnits| #15#) (|leftUnit| #3#) (|leftTraceMatrix| #16# #17#) (|leftTrace| #19#) (|leftRegularRepresentation| #20# #21#) (|leftRecip| #22#) (|leftRankPolynomial| #23#) (|leftPower| #25#) (|leftNorm| #19#) (|leftMinimalPolynomial| #28#) (|leftDiscriminant| #30# #31#) (|leftCharacteristicPolynomial| #32#) (|leftAlternative?| #33#) (|latex| (((|String|) $) NIL T ELT)) (|jordanAlgebra?| #33#) (|jordanAdmissible?| #33#) (|jacobiIdentity?| #33#) (|hash| (((|SingleInteger|) $) NIL T ELT)) (|flexible?| #33#) (|elt| ((|#1| $ #36=(|Integer|)) NIL #9# ELT)) (|coordinates| (#18# NIL #9# ELT) #37=((#35# $) NIL #9# ELT) ((#11# #12# #12#) NIL #7# ELT) ((#35# $ #12#) NIL #7# ELT)) (|convert| #34# #37#) (|conditionsForIdempotents| ((#38=(|List| #24#)) NIL #9# ELT) ((#38# #12#) NIL #7# ELT)) (|commutator| #39=(#40=($ $ $) NIL T ELT)) (|commutative?| #33#) (|coerce| (((|OutputForm|) $) NIL T ELT) ((|#2| $) 21 T ELT) (($ |#2|) 22 T ELT)) (|before?| #1#) (|basis| (#13# NIL #9# ELT)) (|associatorDependence| (((|List| #35#)) NIL #6# ELT)) (|associator| (($ $ $ $) NIL T ELT)) (|associative?| #33#) (|apply| (($ #11# $) NIL #9# ELT)) (|antiCommutator| #39#) (|antiCommutative?| #33#) (|antiAssociative?| #33#) (|alternative?| #33#) (|Zero| #14#) (= #1#) (- (($ $) NIL T ELT) #39#) (+ #39#) (** (#26# 24 T ELT)) (* (($ #27# $) NIL T ELT) (($ (|NonNegativeInteger|) $) NIL T ELT) (($ #36# . #41=($)) NIL T ELT) (#40# 20 T ELT) (($ $ |#1|) NIL T ELT) (($ |#1| . #41#) NIL T ELT))) +((~= #1=((#2=(|Boolean|) $ $) NIL T ELT)) (|zero?| ((#2# $) NIL T ELT)) (|unit| #3=((#4=(|Union| $ #5="failed")) NIL #6=(OR (AND #7=(|has| |#2| (|FiniteRankNonAssociativeAlgebra| |#1|)) #8=(|has| |#1| (|IntegralDomain|))) (AND #9=(|has| |#2| (|FramedNonAssociativeAlgebra| |#1|)) #8#)) ELT)) (|subtractIfCan| (((|Maybe| $) $ $) NIL T ELT)) (|structuralConstants| ((#10=(|Vector| #11=(|Matrix| |#1|))) NIL #9# ELT) ((#10# #12=(|Vector| $)) NIL #7# ELT)) (|someBasis| (#13=(#12#) NIL #7# ELT)) (|sample| #14=(($) NIL T CONST)) (|rightUnits| #15=(((|Union| (|Record| (|:| |particular| $) (|:| |basis| (|List| $))) #5#)) NIL #6# ELT)) (|rightUnit| #3#) (|rightTraceMatrix| #16=((#11#) NIL #9# ELT) #17=(#18=(#11# #12#) NIL #7# ELT)) (|rightTrace| #19=((|#1| $) NIL #7# ELT)) (|rightRegularRepresentation| #20=((#11# $) NIL #9# ELT) #21=((#11# $ #12#) NIL #7# ELT)) (|rightRecip| #22=((#4# $) NIL #6# ELT)) (|rightRankPolynomial| #23=(((|SparseUnivariatePolynomial| #24=(|Polynomial| |#1|))) NIL (AND #9# (|has| |#1| (|Field|))) ELT)) (|rightPower| #25=(#26=($ $ #27=(|PositiveInteger|)) NIL T ELT)) (|rightNorm| #19#) (|rightMinimalPolynomial| #28=(#29=((|SparseUnivariatePolynomial| |#1|) $) NIL #6# ELT)) (|rightDiscriminant| #30=((|#1|) NIL #9# ELT) #31=((|#1| #12#) NIL #7# ELT)) (|rightCharacteristicPolynomial| #32=(#29# NIL #7# ELT)) (|rightAlternative?| #33=((#2#) NIL #7# ELT)) (|represents| #34=(($ #35=(|Vector| |#1|)) NIL #9# ELT) (($ #35# #12#) NIL #7# ELT)) (|recip| #22#) (|rank| ((#27#) NIL #7# ELT)) (|powerAssociative?| #33#) (|plenaryPower| #25#) (|opposite?| #1#) (|noncommutativeJordanAlgebra?| #33#) (|lieAlgebra?| #33#) (|lieAdmissible?| #33#) (|leftUnits| #15#) (|leftUnit| #3#) (|leftTraceMatrix| #16# #17#) (|leftTrace| #19#) (|leftRegularRepresentation| #20# #21#) (|leftRecip| #22#) (|leftRankPolynomial| #23#) (|leftPower| #25#) (|leftNorm| #19#) (|leftMinimalPolynomial| #28#) (|leftDiscriminant| #30# #31#) (|leftCharacteristicPolynomial| #32#) (|leftAlternative?| #33#) (|latex| (((|String|) $) NIL T ELT)) (|jordanAlgebra?| #33#) (|jordanAdmissible?| #33#) (|jacobiIdentity?| #33#) (|hash| (((|SingleInteger|) $) NIL T ELT)) (|flexible?| #33#) (|elt| ((|#1| $ #36=(|Integer|)) NIL #9# ELT)) (|coordinates| (#18# NIL #9# ELT) #37=((#35# $) NIL #9# ELT) ((#11# #12# #12#) NIL #7# ELT) ((#35# $ #12#) NIL #7# ELT)) (|convert| #34# #37#) (|conditionsForIdempotents| ((#38=(|List| #24#)) NIL #9# ELT) ((#38# #12#) NIL #7# ELT)) (|commutator| #39=(#40=($ $ $) NIL T ELT)) (|commutative?| #33#) (|coerce| (((|OutputForm|) $) NIL T ELT) ((|#2| $) 21 T ELT) (($ |#2|) 22 T ELT)) (|before?| #1#) (|basis| (#13# NIL #9# ELT)) (|associatorDependence| (((|List| #35#)) NIL #6# ELT)) (|associator| (($ $ $ $) NIL T ELT)) (|associative?| #33#) (|apply| (($ #11# $) NIL #9# ELT)) (|antiCommutator| #39#) (|antiCommutative?| #33#) (|antiAssociative?| #33#) (|alternative?| #33#) (|Zero| #14#) (= #1#) (- (($ $) NIL T ELT) #39#) (+ #39#) (** (#26# 24 T ELT)) (* (($ #27# $) NIL T ELT) (($ (|NonNegativeInteger|) $) NIL T ELT) (($ #36# . #41=($)) NIL T ELT) (#40# 20 T ELT) (($ $ |#1|) NIL T ELT) (($ |#1| . #41#) NIL T ELT))) (((|AssociatedJordanAlgebra| |#1| |#2|) (|Join| #1=(|NonAssociativeAlgebra| |#1|) (|CoercibleTo| |#2|) (CATEGORY |domain| (SIGNATURE |coerce| ($ |#2|)) (IF (|has| |#2| #2=(|FramedNonAssociativeAlgebra| |#1|)) (ATTRIBUTE #2#) |%noBranch|) (IF (|has| |#2| #3=(|FiniteRankNonAssociativeAlgebra| |#1|)) (ATTRIBUTE #3#) |%noBranch|))) (|CommutativeRing|) #1#) (T |AssociatedJordanAlgebra|)) ((|coerce| (*1 *1 *2) (AND (|ofCategory| *3 (|CommutativeRing|)) (|isDomain| *1 (|AssociatedJordanAlgebra| *3 *2)) (|ofCategory| *2 (|NonAssociativeAlgebra| *3))))) ((~= #1=(((|Boolean|) $ $) NIL T ELT)) (|latex| (((|String|) $) NIL T ELT)) (|hash| (((|SingleInteger|) $) NIL T ELT)) (|coerce| (((|OutputForm|) $) NIL T ELT) (($ #2=(|Byte|)) 6 T ELT) ((#2# $) 7 T ELT)) (|before?| #1#) (= #1#)) @@ -1802,7 +1805,7 @@ NIL ((~= #1=(((|Boolean|) $ $) NIL T ELT)) (|latex| (((|String|) $) NIL T ELT)) (|hash| (((|SingleInteger|) $) NIL T ELT)) (|coerce| (((|OutputForm|) $) 19 T ELT) (($ #2=(|JVMBytecode|)) 12 T ELT) ((#2# $) 11 T ELT) (($ #3=(|Byte|)) NIL T ELT) ((#3# $) 14 T ELT)) (|before?| #1#) (= #1#)) (((|JVMOpcode|) (|Join| (|SetCategory|) (|HomotopicTo| (|JVMBytecode|)) (|HomotopicTo| (|Byte|)))) (T |JVMOpcode|)) NIL -((~= #1=(#2=(#3=(|Boolean|) $ $) NIL T ELT)) (|write!| ((#4=(|Record| (|:| |key| #5=(|String|)) (|:| |entry| |#1|)) $ #4#) 40 T ELT)) (|table| #6=(($ #7=(|List| #4#)) NIL T ELT) #8=(#9=($) NIL T ELT)) (|swap!| (((|Void|) $ #5# #5#) NIL #10=(|has| $ (|ShallowlyMutableAggregate| |#1|)) ELT)) (|setelt| (#11=(|#1| $ #5# |#1|) 50 #10# ELT)) (|select!| #12=(($ #13=(|Mapping| #3# #4#) $) NIL #14=(|has| $ (|FiniteAggregate| #4#)) ELT)) (|select| #12#) (|search| (#15=((|Union| |#1| #16="failed") #5# $) 53 T ELT)) (|sample| (#9# NIL T CONST)) (|reopen!| (($ $ #5#) 25 T ELT)) (|removeDuplicates| (#17=($ $) NIL #18=(AND #14# #19=(|has| #4# #20=(|BasicType|))) ELT)) (|remove!| (#15# 54 T ELT) #12# (#21=($ #4# $) NIL #14# ELT)) (|remove| #12# (#21# NIL #18# ELT)) (|reduce| ((#4# #22=(|Mapping| #4# #4# #4#) $) NIL T ELT) ((#4# #22# $ #4#) NIL T ELT) ((#4# #22# $ #4# #4#) NIL #19# ELT)) (|read!| (#23=(#4# $) 39 T ELT)) (|qsetelt!| (#11# NIL #10# ELT)) (|qelt| (#24=(|#1| $ #5#) NIL T ELT)) (|pack!| (#17# 55 T ELT)) (|open| (($ #25=(|FileName|)) 23 T ELT) (($ #25# #5#) 22 T ELT)) (|name| ((#25# $) 41 T ELT)) (|minIndex| #26=(#27=(#5# $) NIL #28=(|has| #5# (|OrderedSet|)) ELT)) (|members| ((#7# $) NIL T ELT)) (|member?| ((#3# #4# $) NIL #19# ELT)) (|maxIndex| #26#) (|map!| #29=(($ (|Mapping| |#1| |#1|) . #30=($)) NIL T ELT) #31=(($ (|Mapping| #4# #4#) . #30#) NIL T ELT)) (|map| (($ (|Mapping| |#1| |#1| |#1|) $ $) NIL T ELT) #29# #31#) (|latex| (#27# NIL T ELT)) (|keys| (#32=((|List| #5#) $) 46 T ELT)) (|key?| #33=((#3# #5# $) NIL T ELT)) (|iomode| (#27# 42 T ELT)) (|inspect| #34=(#23# NIL T ELT)) (|insert!| (#21# NIL T ELT)) (|indices| (#32# NIL T ELT)) (|index?| #33#) (|hash| (((|SingleInteger|) $) NIL T ELT)) (|first| ((|#1| $) NIL #28# ELT)) (|find| (((|Union| #4# #16#) #13# $) NIL T ELT)) (|fill!| (($ $ |#1|) NIL #10# ELT)) (|extract!| #34#) (|every?| #35=((#3# #13# $) NIL T ELT)) (|eval| (($ $ (|List| #36=(|Equation| |#1|))) NIL #37=(AND (|has| |#1| (|Evalable| |#1|)) (|has| |#1| #38=(|SetCategory|))) ELT) (($ $ #36#) NIL #37# ELT) (($ $ |#1| |#1|) NIL #37# ELT) (($ $ #39=(|List| |#1|) #39#) NIL #37# ELT) (($ $ #7# #7#) NIL #40=(AND (|has| #4# (|Evalable| #4#)) (|has| #4# #38#)) ELT) (($ $ #4# #4#) NIL #40# ELT) (($ $ #41=(|Equation| #4#)) NIL #40# ELT) (($ $ (|List| #41#)) NIL #40# ELT)) (|eq?| #1#) (|entry?| ((#3# |#1| $) NIL (AND (|has| $ (|FiniteAggregate| |#1|)) (|has| |#1| #20#)) ELT)) (|entries| ((#39# $) NIL T ELT)) (|empty?| ((#3# $) NIL T ELT)) (|empty| (#9# 44 T ELT)) (|elt| (#11# NIL T ELT) (#24# 49 T ELT)) (|dictionary| #6# #8#) (|count| ((#42=(|NonNegativeInteger|) #13# $) NIL T ELT) ((#42# #4# $) NIL #19# ELT)) (|copy| (#17# NIL T ELT)) (|convert| ((#43=(|InputForm|) $) NIL (|has| #4# (|ConvertibleTo| #43#)) ELT)) (|construct| #6#) (|coerce| (((|OutputForm|) $) 21 T ELT)) (|close!| (#17# 26 T ELT)) (|before?| #1#) (|bag| #6#) (|any?| #35#) (= (#2# 20 T ELT)) (|#| ((#42# $) 48 T ELT))) +((~= #1=(#2=(#3=(|Boolean|) $ $) NIL T ELT)) (|write!| ((#4=(|Record| (|:| |key| #5=(|String|)) (|:| |entry| |#1|)) $ #4#) 39 T ELT)) (|table| #6=(($ #7=(|List| #4#)) NIL T ELT) #8=(#9=($) NIL T ELT)) (|swap!| (((|Void|) $ #5# #5#) NIL #10=(|has| $ (|ShallowlyMutableAggregate| |#1|)) ELT)) (|setelt| (#11=(|#1| $ #5# |#1|) 49 #10# ELT)) (|select!| #12=(($ #13=(|Mapping| #3# #4#) $) NIL #14=(|has| $ (|FiniteAggregate| #4#)) ELT)) (|select| #12#) (|search| (#15=((|Union| |#1| #16="failed") #5# $) 52 T ELT)) (|sample| (#9# NIL T CONST)) (|reopen!| (($ $ #5#) 25 T ELT)) (|removeDuplicates| (#17=($ $) NIL #18=(AND #14# #19=(|has| #4# #20=(|BasicType|))) ELT)) (|remove!| (#15# 53 T ELT) #12# (#21=($ #4# $) NIL #14# ELT)) (|remove| #12# (#21# NIL #18# ELT)) (|reduce| ((#4# #22=(|Mapping| #4# #4# #4#) $) NIL T ELT) ((#4# #22# $ #4#) NIL T ELT) ((#4# #22# $ #4# #4#) NIL #19# ELT)) (|read!| (#23=(#4# $) 38 T ELT)) (|qsetelt!| (#11# NIL #10# ELT)) (|qelt| (#24=(|#1| $ #5#) NIL T ELT)) (|pack!| (#17# 54 T ELT)) (|open| (($ #25=(|FileName|)) 23 T ELT) (($ #25# #5#) 22 T ELT)) (|name| ((#25# $) 40 T ELT)) (|minIndex| #26=(#27=(#5# $) NIL #28=(|has| #5# (|OrderedSet|)) ELT)) (|members| ((#7# $) NIL T ELT)) (|member?| ((#3# #4# $) NIL #19# ELT)) (|maxIndex| #26#) (|map!| #29=(($ (|Mapping| |#1| |#1|) . #30=($)) NIL T ELT) #31=(($ (|Mapping| #4# #4#) . #30#) NIL T ELT)) (|map| (($ (|Mapping| |#1| |#1| |#1|) $ $) NIL T ELT) #29# #31#) (|latex| (#27# NIL T ELT)) (|keys| (#32=((|List| #5#) $) 45 T ELT)) (|key?| #33=((#3# #5# $) NIL T ELT)) (|iomode| (#27# 41 T ELT)) (|inspect| #34=(#23# NIL T ELT)) (|insert!| (#21# NIL T ELT)) (|indices| (#32# NIL T ELT)) (|index?| #33#) (|hash| (((|SingleInteger|) $) NIL T ELT)) (|first| ((|#1| $) NIL #28# ELT)) (|find| (((|Union| #4# #16#) #13# $) NIL T ELT)) (|fill!| (($ $ |#1|) NIL #10# ELT)) (|extract!| #34#) (|every?| #35=((#3# #13# $) NIL T ELT)) (|eval| (($ $ (|List| #36=(|Equation| |#1|))) NIL #37=(AND (|has| |#1| (|Evalable| |#1|)) (|has| |#1| #38=(|SetCategory|))) ELT) (($ $ #36#) NIL #37# ELT) (($ $ |#1| |#1|) NIL #37# ELT) (($ $ #39=(|List| |#1|) #39#) NIL #37# ELT) (($ $ #7# #7#) NIL #40=(AND (|has| #4# (|Evalable| #4#)) (|has| #4# #38#)) ELT) (($ $ #4# #4#) NIL #40# ELT) (($ $ #41=(|Equation| #4#)) NIL #40# ELT) (($ $ (|List| #41#)) NIL #40# ELT)) (|eq?| #1#) (|entry?| ((#3# |#1| $) NIL (AND (|has| $ (|FiniteAggregate| |#1|)) (|has| |#1| #20#)) ELT)) (|entries| ((#39# $) NIL T ELT)) (|empty?| ((#3# $) NIL T ELT)) (|empty| (#9# 43 T ELT)) (|elt| (#11# NIL T ELT) (#24# 48 T ELT)) (|dictionary| #6# #8#) (|count| ((#42=(|NonNegativeInteger|) #13# $) NIL T ELT) ((#42# #4# $) NIL #19# ELT)) (|copy| (#17# NIL T ELT)) (|convert| ((#43=(|InputForm|) $) NIL (|has| #4# (|ConvertibleTo| #43#)) ELT)) (|construct| #6#) (|coerce| (((|OutputForm|) $) 21 T ELT)) (|close!| (#17# 26 T ELT)) (|before?| #1#) (|bag| #6#) (|any?| #35#) (= (#2# 20 T ELT)) (|#| ((#42# $) 47 T ELT))) (((|KeyedAccessFile| |#1|) (|Join| (|FileCategory| (|FileName|) (|Record| (|:| |key| #1=(|String|)) (|:| |entry| |#1|))) (|TableAggregate| #1# |#1|) (CATEGORY |domain| (SIGNATURE |pack!| ($ $)))) (|SetCategory|)) (T |KeyedAccessFile|)) ((|pack!| (*1 *1 *1) (AND (|isDomain| *1 (|KeyedAccessFile| *2)) (|ofCategory| *2 (|SetCategory|))))) ((|keys| (((|List| |#2|) $) 19 T ELT)) (|key?| (((|Boolean|) |#2| $) 12 T ELT)) (|elt| ((|#3| $ |#2|) 20 T ELT) ((|#3| $ |#2| |#3|) 21 T ELT))) @@ -1841,13 +1844,13 @@ NIL (((|ConvertibleFrom| |#1|) (|Category|) (|Type|)) (T |ConvertibleFrom|)) ((|convert| (*1 *1 *2) (AND (|ofCategory| *1 (|ConvertibleFrom| *2)) (|ofCategory| *2 (|Type|))))) (|Join| (CATEGORY |domain| (SIGNATURE |convert| ($ |t#1|)))) -((~= #1=(#2=(#3=(|Boolean|) $ $) NIL T ELT)) (|zero?| #4=(#5=(#3# $) NIL T ELT)) (|subtractIfCan| ((#6=(|Union| $ "failed") $ $) NIL T ELT)) (|sign| ((#7=(|Integer|) $) NIL #8=(|has| |#1| (|OrderedRing|)) ELT)) (|sample| #9=(#10=($) NIL T CONST)) (|recip| ((#6# $) NIL T ELT)) (|positive?| #11=(#5# NIL #8# ELT)) (|opposite?| #1#) (|one?| #4#) (|numer| ((|#1| $) 13 T ELT)) (|negative?| #11#) (|min| #12=(#13=($ $ $) NIL #8# ELT)) (|max| #12#) (|latex| (((|String|) $) NIL T ELT)) (|hash| (((|SingleInteger|) $) NIL T ELT)) (|denom| ((|#3| $) 15 T ELT)) (|coerce| (((|OutputForm|) $) NIL T ELT) (($ #7#) NIL T ELT) (($ |#2|) NIL T ELT)) (|characteristic| ((#14=(|NonNegativeInteger|)) 20 T CONST)) (|before?| #1#) (|annihilate?| #1#) (|abs| (#15=($ $) NIL #8# ELT)) (|Zero| #9#) (|One| (#10# 12 T CONST)) (>= #16=(#2# NIL #8# ELT)) (> #16#) (= #1#) (<= #16#) (< #16#) (/ (($ $ |#3|) NIL T ELT) (($ |#1| |#3|) 11 T ELT)) (- (#15# NIL T ELT) #17=(#13# NIL T ELT)) (+ #17#) (** (($ $ #18=(|PositiveInteger|)) NIL T ELT) (($ $ #14#) NIL T ELT)) (* (($ #18# $) NIL T ELT) (($ #14# $) NIL T ELT) (($ #7# . #19=($)) NIL T ELT) (#13# 17 T ELT) (($ $ |#2|) NIL T ELT) (($ |#2| . #19#) NIL T ELT))) +((~= #1=(#2=(#3=(|Boolean|) $ $) NIL T ELT)) (|zero?| #4=(#5=(#3# $) NIL T ELT)) (|subtractIfCan| (((|Maybe| $) $ $) NIL T ELT)) (|sign| ((#6=(|Integer|) $) NIL #7=(|has| |#1| (|OrderedRing|)) ELT)) (|sample| #8=(#9=($) NIL T CONST)) (|recip| (((|Union| $ "failed") $) NIL T ELT)) (|positive?| #10=(#5# NIL #7# ELT)) (|opposite?| #1#) (|one?| #4#) (|numer| ((|#1| $) 13 T ELT)) (|negative?| #10#) (|min| #11=(#12=($ $ $) NIL #7# ELT)) (|max| #11#) (|latex| (((|String|) $) NIL T ELT)) (|hash| (((|SingleInteger|) $) NIL T ELT)) (|denom| ((|#3| $) 15 T ELT)) (|coerce| (((|OutputForm|) $) NIL T ELT) (($ #6#) NIL T ELT) (($ |#2|) NIL T ELT)) (|characteristic| ((#13=(|NonNegativeInteger|)) 20 T CONST)) (|before?| #1#) (|annihilate?| #1#) (|abs| (#14=($ $) NIL #7# ELT)) (|Zero| #8#) (|One| (#9# 12 T CONST)) (>= #15=(#2# NIL #7# ELT)) (> #15#) (= #1#) (<= #15#) (< #15#) (/ (($ $ |#3|) NIL T ELT) (($ |#1| |#3|) 11 T ELT)) (- (#14# NIL T ELT) #16=(#12# NIL T ELT)) (+ #16#) (** (($ $ #17=(|PositiveInteger|)) NIL T ELT) (($ $ #13#) NIL T ELT)) (* (($ #17# $) NIL T ELT) (($ #13# $) NIL T ELT) (($ #6# . #18=($)) NIL T ELT) (#12# 17 T ELT) (($ $ |#2|) NIL T ELT) (($ |#2| . #18#) NIL T ELT))) (((|LocalAlgebra| |#1| |#2| |#3|) (|Join| #1=(|Algebra| |#2|) (CATEGORY |domain| (IF (|has| |#1| #2=(|OrderedRing|)) (ATTRIBUTE #2#) |%noBranch|) (SIGNATURE / ($ $ |#3|)) (SIGNATURE / ($ |#1| |#3|)) (SIGNATURE |numer| (|#1| $)) (SIGNATURE |denom| (|#3| $)))) #1# (|CommutativeRing|) (|SubsetCategory| (|Monoid|) |#2|)) (T |LocalAlgebra|)) ((/ (*1 *1 *1 *2) (AND #1=(|ofCategory| *4 #2=(|CommutativeRing|)) #3=(|isDomain| *1 (|LocalAlgebra| *3 *4 *2)) #4=(|ofCategory| *3 #5=(|Algebra| *4)) #6=(|ofCategory| *2 #7=(|SubsetCategory| #8=(|Monoid|) *4)))) (/ (*1 *1 *2 *3) (AND #1# (|isDomain| *1 (|LocalAlgebra| *2 *4 *3)) (|ofCategory| *2 #5#) (|ofCategory| *3 #7#))) (|numer| #9=(*1 *2 *1) (AND (|ofCategory| *3 #2#) (|ofCategory| *2 (|Algebra| *3)) (|isDomain| *1 (|LocalAlgebra| *2 *3 *4)) (|ofCategory| *4 (|SubsetCategory| #8# *3)))) (|denom| #9# (AND #1# #6# #3# #4#))) ((|coerce| (((|OutputForm|) $) NIL T ELT) (($ (|Integer|)) NIL T ELT) (($ |#2|) 10 T ELT))) (((|LeftAlgebra&| |#1| |#2|) (CATEGORY |package| (SIGNATURE |coerce| (|#1| |#2|)) (SIGNATURE |coerce| (|#1| (|Integer|))) (SIGNATURE |coerce| ((|OutputForm|) |#1|))) (|LeftAlgebra| |#2|) (|Ring|)) (T |LeftAlgebra&|)) NIL -((~= (#1=((|Boolean|) $ $) 7 T ELT)) (|zero?| ((#2=(|Boolean|) $) 22 T ELT)) (|subtractIfCan| (((|Union| $ "failed") $ $) 26 T ELT)) (|sample| (#3=($) 23 T CONST)) (|recip| (((|Union| $ "failed") $) 42 T ELT)) (|opposite?| ((#2# $ $) 20 T ELT)) (|one?| (((|Boolean|) $) 44 T ELT)) (|latex| (((|String|) $) 11 T ELT)) (|hash| (((|SingleInteger|) $) 12 T ELT)) (|coerce| (((|OutputForm|) $) 13 T ELT) (($ (|Integer|)) 41 T ELT) (($ |#1|) 49 T ELT)) (|characteristic| (((|NonNegativeInteger|)) 40 T CONST)) (|before?| (#1# 6 T ELT)) (|annihilate?| (((|Boolean|) $ $) 33 T ELT)) (|Zero| (#3# 24 T CONST)) (|One| (($) 45 T CONST)) (= (#1# 8 T ELT)) (- (($ $) 29 T ELT) (($ $ $) 28 T ELT)) (+ (($ $ $) 18 T ELT)) (** (($ $ (|PositiveInteger|)) 35 T ELT) (($ $ (|NonNegativeInteger|)) 43 T ELT)) (* (($ (|PositiveInteger|) $) 17 T ELT) (($ (|NonNegativeInteger|) $) 21 T ELT) (($ (|Integer|) . #4=($)) 30 T ELT) (($ $ $) 34 T ELT) (($ |#1| . #4#) 50 T ELT))) +((~= (#1=((|Boolean|) $ $) 7 T ELT)) (|zero?| ((#2=(|Boolean|) $) 22 T ELT)) (|subtractIfCan| (((|Maybe| $) $ $) 26 T ELT)) (|sample| (#3=($) 23 T CONST)) (|recip| (((|Union| $ "failed") $) 43 T ELT)) (|opposite?| ((#2# $ $) 20 T ELT)) (|one?| (((|Boolean|) $) 45 T ELT)) (|latex| (((|String|) $) 11 T ELT)) (|hash| (((|SingleInteger|) $) 12 T ELT)) (|coerce| (((|OutputForm|) $) 13 T ELT) (($ (|Integer|)) 42 T ELT) (($ |#1|) 50 T ELT)) (|characteristic| (((|NonNegativeInteger|)) 41 T CONST)) (|before?| (#1# 6 T ELT)) (|annihilate?| (((|Boolean|) $ $) 34 T ELT)) (|Zero| (#3# 24 T CONST)) (|One| (($) 46 T CONST)) (= (#1# 8 T ELT)) (- (($ $) 30 T ELT) (($ $ $) 29 T ELT)) (+ (($ $ $) 18 T ELT)) (** (($ $ (|PositiveInteger|)) 36 T ELT) (($ $ (|NonNegativeInteger|)) 44 T ELT)) (* (($ (|PositiveInteger|) $) 17 T ELT) (($ (|NonNegativeInteger|) $) 21 T ELT) (($ (|Integer|) . #4=($)) 31 T ELT) (($ $ $) 35 T ELT) (($ |#1| . #4#) 51 T ELT))) (((|LeftAlgebra| |#1|) (|Category|) (|Ring|)) (T |LeftAlgebra|)) ((|coerce| (*1 *1 *2) (AND (|ofCategory| *1 (|LeftAlgebra| *2)) (|ofCategory| *2 (|Ring|))))) (|Join| (|Ring|) (|LeftModule| |t#1|) (CATEGORY |domain| (SIGNATURE |coerce| ($ |t#1|)))) @@ -1855,7 +1858,7 @@ NIL ((|laplace| ((|#2| |#2| #1=(|Symbol|) #1#) 16 T ELT))) (((|LaplaceTransform| |#1| |#2|) (CATEGORY |package| (SIGNATURE |laplace| (|#2| |#2| #1=(|Symbol|) #1#))) (|Join| (|EuclideanDomain|) (|CharacteristicZero|) (|RetractableTo| #2=(|Integer|)) (|LinearlyExplicitRingOver| #2#)) (|Join| (|TranscendentalFunctionCategory|) (|PrimitiveFunctionCategory|) (|AlgebraicallyClosedFunctionSpace| |#1|))) (T |LaplaceTransform|)) ((|laplace| (*1 *2 *2 *3 *3) (AND (|isDomain| *3 (|Symbol|)) (|ofCategory| *4 (|Join| (|EuclideanDomain|) (|CharacteristicZero|) (|RetractableTo| #1=(|Integer|)) (|LinearlyExplicitRingOver| #1#))) (|isDomain| *1 (|LaplaceTransform| *4 *2)) (|ofCategory| *2 (|Join| (|TranscendentalFunctionCategory|) (|PrimitiveFunctionCategory|) (|AlgebraicallyClosedFunctionSpace| *4)))))) -((~= (#1=(#2=(|Boolean|) $ $) 64 T ELT)) (|zero?| (#3=(#2# $) 58 T ELT)) (|unitNormal| (((|Record| (|:| |unit| $) (|:| |canonical| $) (|:| |associate| $)) $) NIL T ELT)) (|unitCanonical| #4=(#5=($ $) NIL T ELT)) (|unit?| #6=(#3# NIL T ELT)) (|trailingCoefficient| (#7=(|#1| $) 55 T ELT)) (|subtractIfCan| (#8=(#9=(|Union| $ #10="failed") $ $) NIL T ELT)) (|sizeLess?| (#1# NIL #11=(|has| |#1| (|Field|)) ELT)) (|separate| (((|Record| (|:| |polyPart| $) (|:| |fracPart| #12=(|Fraction| |#2|))) #12#) 111 #11# ELT)) (|sample| (#13=($) NIL T CONST)) (|retractIfCan| (((|Union| #14=(|Integer|) . #15=(#10#)) . #16=($)) NIL #17=(|has| |#1| (|RetractableTo| #14#)) ELT) (((|Union| #18=(|Fraction| #14#) . #15#) . #16#) NIL #19=(|has| |#1| (|RetractableTo| #18#)) ELT) (((|Union| |#1| . #15#) $) 99 T ELT) (((|Union| |#2| . #15#) $) 95 T ELT)) (|retract| (#20=(#14# $) NIL #17# ELT) ((#18# . #21=($)) NIL #19# ELT) (#7# NIL T ELT) ((|#2| . #21#) NIL T ELT)) (|rem| #22=(#23=($ $ $) NIL #11# ELT)) (|reductum| (#5# 27 T ELT)) (|recip| ((#9# $) 88 T ELT)) (|quo| #22#) (|principalIdeal| (((|Record| (|:| |coef| #24=(|List| $)) #25=(|:| |generator| $)) #24#) NIL #11# ELT)) (|order| (#20# 22 T ELT)) (|opposite?| #26=(#1# NIL T ELT)) (|one?| #6#) (|multiEuclidean| (((|Union| #24# #10#) #24# $) NIL #11# ELT)) (|monomial?| (#3# 40 T ELT)) (|monomial| (($ |#1| #14#) 24 T ELT)) (|leadingCoefficient| (#7# 57 T ELT)) (|lcm| #27=(($ #24#) NIL #11# ELT) #22#) (|latex| (((|String|) $) NIL T ELT)) (|hash| (((|SingleInteger|) $) NIL T ELT)) (|gcdPolynomial| ((#28=(|SparseUnivariatePolynomial| $) #28# #28#) NIL #11# ELT)) (|gcd| #27# (#23# 101 #11# ELT)) (|extendedEuclidean| (((|Union| (|Record| #29=(|:| |coef1| $) #30=(|:| |coef2| $)) #10#) $ $ $) 116 #11# ELT) (((|Record| #29# #30# #25#) $ $) NIL #11# ELT)) (|exquo| (#8# 93 T ELT)) (|expressIdealMember| (((|Maybe| #24#) #24# $) NIL #11# ELT)) (|euclideanSize| ((#31=(|NonNegativeInteger|) $) 115 #11# ELT)) (|divide| (((|Record| (|:| |quotient| $) (|:| |remainder| $)) $ $) 114 #11# ELT)) (|differentiate| #32=(($ $ #33=(|Mapping| |#2| |#2|) #31#) NIL T ELT) (#34=($ $ #33#) 75 T ELT) #35=(#5# NIL #36=(|has| |#2| (|DifferentialSpace|)) ELT) #37=(#38=($ $ #31#) NIL #36# ELT) #39=(($ $ #40=(|Symbol|)) NIL #41=(|has| |#2| (|PartialDifferentialSpace| #40#)) ELT) #42=(($ $ #43=(|List| #40#)) NIL #41# ELT) #44=(($ $ #40# #31#) NIL #41# ELT) #45=(($ $ #43# (|List| #31#)) NIL #41# ELT)) (|degree| (#20# 38 T ELT)) (|convert| ((#12# $) 47 T ELT)) (|coerce| (((|OutputForm|) $) 69 T ELT) (($ #14#) 35 T ELT) #4# (($ #18#) NIL #19# ELT) (($ |#1|) 34 T ELT) (($ |#2|) 25 T ELT)) (|coefficient| ((|#1| $ #14#) 72 T ELT)) (|charthRoot| (((|Maybe| $) $) NIL (|has| |#1| (|CharacteristicNonZero|)) ELT)) (|characteristic| ((#31#) 32 T CONST)) (|before?| #26#) (|associates?| #26#) (|annihilate?| #26#) (|Zero| (#13# 9 T CONST)) (|One| (#13# 14 T CONST)) (D #32# (#34# NIL T ELT) #35# #37# #39# #42# #44# #45#) (= (#1# 21 T ELT)) (- (#5# 51 T ELT) (#23# NIL T ELT)) (+ (#23# 90 T ELT)) (** (($ $ #46=(|PositiveInteger|)) NIL T ELT) (#38# NIL T ELT)) (* (($ #46# $) NIL T ELT) (($ #31# $) NIL T ELT) (($ #14# $) 29 T ELT) (#23# 49 T ELT))) +((~= (#1=(#2=(|Boolean|) $ $) 64 T ELT)) (|zero?| (#3=(#2# $) 58 T ELT)) (|unitNormal| (((|Record| (|:| |unit| $) (|:| |canonical| $) (|:| |associate| $)) $) NIL T ELT)) (|unitCanonical| #4=(#5=($ $) NIL T ELT)) (|unit?| #6=(#3# NIL T ELT)) (|trailingCoefficient| (#7=(|#1| $) 55 T ELT)) (|subtractIfCan| ((#8=(|Maybe| $) $ $) NIL T ELT)) (|sizeLess?| (#1# NIL #9=(|has| |#1| (|Field|)) ELT)) (|separate| (((|Record| (|:| |polyPart| $) (|:| |fracPart| #10=(|Fraction| |#2|))) #10#) 111 #9# ELT)) (|sample| (#11=($) NIL T CONST)) (|retractIfCan| (((|Union| #12=(|Integer|) . #13=(#14="failed")) . #15=($)) NIL #16=(|has| |#1| (|RetractableTo| #12#)) ELT) (((|Union| #17=(|Fraction| #12#) . #13#) . #15#) NIL #18=(|has| |#1| (|RetractableTo| #17#)) ELT) (((|Union| |#1| . #13#) $) 99 T ELT) (((|Union| |#2| . #13#) $) 95 T ELT)) (|retract| (#19=(#12# $) NIL #16# ELT) ((#17# . #20=($)) NIL #18# ELT) (#7# NIL T ELT) ((|#2| . #20#) NIL T ELT)) (|rem| #21=(#22=($ $ $) NIL #9# ELT)) (|reductum| (#5# 27 T ELT)) (|recip| ((#23=(|Union| $ #14#) $) 88 T ELT)) (|quo| #21#) (|principalIdeal| (((|Record| (|:| |coef| #24=(|List| $)) #25=(|:| |generator| $)) #24#) NIL #9# ELT)) (|order| (#19# 22 T ELT)) (|opposite?| #26=(#1# NIL T ELT)) (|one?| #6#) (|multiEuclidean| (((|Union| #24# #14#) #24# $) NIL #9# ELT)) (|monomial?| (#3# 40 T ELT)) (|monomial| (($ |#1| #12#) 24 T ELT)) (|leadingCoefficient| (#7# 57 T ELT)) (|lcm| #27=(($ #24#) NIL #9# ELT) #21#) (|latex| (((|String|) $) NIL T ELT)) (|hash| (((|SingleInteger|) $) NIL T ELT)) (|gcdPolynomial| ((#28=(|SparseUnivariatePolynomial| $) #28# #28#) NIL #9# ELT)) (|gcd| #27# (#22# 101 #9# ELT)) (|extendedEuclidean| (((|Union| (|Record| #29=(|:| |coef1| $) #30=(|:| |coef2| $)) #14#) $ $ $) 116 #9# ELT) (((|Record| #29# #30# #25#) $ $) NIL #9# ELT)) (|exquo| ((#23# $ $) 93 T ELT)) (|expressIdealMember| (((|Maybe| #24#) #24# $) NIL #9# ELT)) (|euclideanSize| ((#31=(|NonNegativeInteger|) $) 115 #9# ELT)) (|divide| (((|Record| (|:| |quotient| $) (|:| |remainder| $)) $ $) 114 #9# ELT)) (|differentiate| #32=(($ $ #33=(|Mapping| |#2| |#2|) #31#) NIL T ELT) (#34=($ $ #33#) 75 T ELT) #35=(#5# NIL #36=(|has| |#2| (|DifferentialSpace|)) ELT) #37=(#38=($ $ #31#) NIL #36# ELT) #39=(($ $ #40=(|Symbol|)) NIL #41=(|has| |#2| (|PartialDifferentialSpace| #40#)) ELT) #42=(($ $ #43=(|List| #40#)) NIL #41# ELT) #44=(($ $ #40# #31#) NIL #41# ELT) #45=(($ $ #43# (|List| #31#)) NIL #41# ELT)) (|degree| (#19# 38 T ELT)) (|convert| ((#10# $) 47 T ELT)) (|coerce| (((|OutputForm|) $) 69 T ELT) (($ #12#) 35 T ELT) #4# (($ #17#) NIL #18# ELT) (($ |#1|) 34 T ELT) (($ |#2|) 25 T ELT)) (|coefficient| ((|#1| $ #12#) 72 T ELT)) (|charthRoot| ((#8# $) NIL (|has| |#1| (|CharacteristicNonZero|)) ELT)) (|characteristic| ((#31#) 32 T CONST)) (|before?| #26#) (|associates?| #26#) (|annihilate?| #26#) (|Zero| (#11# 9 T CONST)) (|One| (#11# 14 T CONST)) (D #32# (#34# NIL T ELT) #35# #37# #39# #42# #44# #45#) (= (#1# 21 T ELT)) (- (#5# 51 T ELT) (#22# NIL T ELT)) (+ (#22# 90 T ELT)) (** (($ $ #46=(|PositiveInteger|)) NIL T ELT) (#38# NIL T ELT)) (* (($ #46# $) NIL T ELT) (($ #31# $) NIL T ELT) (($ #12# $) 29 T ELT) (#22# 49 T ELT))) (((|LaurentPolynomial| |#1| |#2|) (|Join| (|DifferentialExtension| |#2|) #1=(|IntegralDomain|) (|ConvertibleTo| #2=(|Fraction| |#2|)) (|FullyRetractableTo| |#1|) (|RetractableTo| |#2|) (CATEGORY |domain| (SIGNATURE |monomial?| ((|Boolean|) $)) (SIGNATURE |degree| #3=(#4=(|Integer|) $)) (SIGNATURE |order| #3#) (SIGNATURE |reductum| ($ $)) (SIGNATURE |leadingCoefficient| #5=(|#1| $)) (SIGNATURE |trailingCoefficient| #5#) (SIGNATURE |coefficient| (|#1| $ #4#)) (SIGNATURE |monomial| ($ |#1| #4#)) (IF (|has| |#1| #6=(|CharacteristicZero|)) (ATTRIBUTE #6#) |%noBranch|) (IF (|has| |#1| #7=(|CharacteristicNonZero|)) (ATTRIBUTE #7#) |%noBranch|) (IF (|has| |#1| (|Field|)) (PROGN (ATTRIBUTE (|EuclideanDomain|)) (SIGNATURE |separate| ((|Record| (|:| |polyPart| $) (|:| |fracPart| #2#)) #2#))) |%noBranch|))) #1# (|UnivariatePolynomialCategory| |#1|)) (T |LaurentPolynomial|)) ((|monomial?| #1=(*1 *2 *1) (AND #2=(|ofCategory| *3 #3=(|IntegralDomain|)) (|isDomain| *2 (|Boolean|)) #4=(|isDomain| *1 (|LaurentPolynomial| *3 *4)) #5=(|ofCategory| *4 (|UnivariatePolynomialCategory| *3)))) (|degree| #1# #6=(AND #2# (|isDomain| *2 #7=(|Integer|)) #4# #5#)) (|order| #1# #6#) (|reductum| (*1 *1 *1) #8=(AND #9=(|ofCategory| *2 #3#) (|isDomain| *1 (|LaurentPolynomial| *2 *3)) (|ofCategory| *3 #10=(|UnivariatePolynomialCategory| *2)))) (|leadingCoefficient| #1# #8#) (|trailingCoefficient| #1# #8#) (|coefficient| (*1 *2 *1 *3) #11=(AND (|isDomain| *3 #7#) #9# (|isDomain| *1 (|LaurentPolynomial| *2 *4)) (|ofCategory| *4 #10#))) (|monomial| (*1 *1 *2 *3) #11#) (|separate| (*1 *2 *3) (AND (|ofCategory| *4 (|Field|)) (|ofCategory| *4 #3#) (|ofCategory| *5 (|UnivariatePolynomialCategory| *4)) (|isDomain| *2 (|Record| (|:| |polyPart| #12=(|LaurentPolynomial| *4 *5)) (|:| |fracPart| #13=(|Fraction| *5)))) (|isDomain| *1 #12#) (|isDomain| *3 #13#)))) ((|zeroSetSplit| (((|List| |#6|) (|List| |#4|) (|Boolean|)) 54 T ELT)) (|normalizeIfCan| ((|#6| |#6|) 48 T ELT))) @@ -1868,8 +1871,8 @@ NIL (((|LetAst|) (|Join| (|SpadSyntaxCategory|) (CATEGORY |domain| (SIGNATURE |lhs| #1=((|SpadAst|) $)) (SIGNATURE |rhs| #1#)))) (T |LetAst|)) ((|lhs| #1=(*1 *2 *1) #2=(AND (|isDomain| *2 (|SpadAst|)) (|isDomain| *1 (|LetAst|)))) (|rhs| #1# #2#)) ((~= #1=(#2=(#3=(|Boolean|) $ $) NIL T ELT)) (|varList| ((#4=(|List| |#1|) $) NIL T ELT)) (|sample| (#5=($) NIL T CONST)) (|recip| (((|Union| $ "failed") $) NIL T ELT)) (|one?| ((#3# $) NIL T ELT)) (|mirror| (#6=($ $) 77 T ELT)) (|log| ((#7=(|LiePolynomial| |#1| |#2|) $) 60 T ELT)) (|latex| (((|String|) $) NIL T ELT)) (|inv| (#6# 81 T ELT)) (|identification| (((|List| (|Equation| |#2|)) $ $) 42 T ELT)) (|hash| (((|SingleInteger|) $) NIL T ELT)) (|exp| (($ #7#) 56 T ELT)) (|conjugate| #8=(#9=($ $ $) NIL T ELT)) (|commutator| #8#) (|coerce| (((|OutputForm|) $) 66 T ELT) (((|XDistributedPolynomial| |#1| |#2|) $) NIL T ELT) (((|XPBWPolynomial| |#1| |#2|) $) 74 T ELT)) (|before?| #1#) (|One| (#5# 61 T CONST)) (|LyndonCoordinates| (((|List| (|Record| (|:| |k| (|LyndonWord| |#1|)) #10=(|:| |c| |#2|))) $) 41 T ELT)) (|LyndonBasis| (((|List| #7#) #4#) 73 T ELT)) (|ListOfTerms| (((|List| (|Record| (|:| |k| (|PoincareBirkhoffWittLyndonBasis| |#1|)) #10#)) $) 46 T ELT)) (= (#2# 62 T ELT)) (/ #8#) (** (($ $ (|PositiveInteger|)) NIL T ELT) (($ $ (|NonNegativeInteger|)) NIL T ELT) (($ $ (|Integer|)) NIL T ELT)) (* (#9# 52 T ELT))) -(((|LieExponentials| |#1| |#2| |#3|) (|Join| (|Group|) (CATEGORY |domain| (SIGNATURE |exp| ($ #1=(|LiePolynomial| |#1| |#2|))) (SIGNATURE |log| (#1# $)) (SIGNATURE |ListOfTerms| ((|List| (|Record| (|:| |k| (|PoincareBirkhoffWittLyndonBasis| |#1|)) #2=(|:| |c| |#2|))) $)) (SIGNATURE |coerce| ((|XDistributedPolynomial| |#1| |#2|) $)) (SIGNATURE |coerce| ((|XPBWPolynomial| |#1| |#2|) $)) (SIGNATURE |mirror| ($ $)) (SIGNATURE |varList| (#3=(|List| |#1|) $)) (SIGNATURE |LyndonBasis| ((|List| #1#) #3#)) (SIGNATURE |LyndonCoordinates| ((|List| (|Record| (|:| |k| (|LyndonWord| |#1|)) #2#)) $)) (SIGNATURE |identification| ((|List| (|Equation| |#2|)) $ $)))) (|OrderedSet|) (|Join| (|CommutativeRing|) (|Module| (|Fraction| (|Integer|)))) (|PositiveInteger|)) (T |LieExponentials|)) -((|exp| (*1 *1 *2) (AND #1=(|isDomain| *2 (|LiePolynomial| *3 *4)) #2=(|ofCategory| *3 #3=(|OrderedSet|)) #4=(|ofCategory| *4 #5=(|Join| (|CommutativeRing|) (|Module| (|Fraction| (|Integer|))))) #6=(|isDomain| *1 (|LieExponentials| *3 *4 *5)) #7=(|ofType| *5 #8=(|PositiveInteger|)))) (|log| #9=(*1 *2 *1) (AND #1# #6# #2# #4# #7#)) (|ListOfTerms| #9# (AND (|isDomain| *2 (|List| (|Record| (|:| |k| (|PoincareBirkhoffWittLyndonBasis| *3)) #10=(|:| |c| *4)))) #6# #2# #4# #7#)) (|coerce| #9# (AND (|isDomain| *2 (|XDistributedPolynomial| *3 *4)) #6# #2# #4# #7#)) (|coerce| #9# (AND (|isDomain| *2 (|XPBWPolynomial| *3 *4)) #6# #2# #4# #7#)) (|mirror| (*1 *1 *1) (AND (|isDomain| *1 (|LieExponentials| *2 *3 *4)) (|ofCategory| *2 #3#) (|ofCategory| *3 #5#) (|ofType| *4 #8#))) (|varList| #9# (AND (|isDomain| *2 (|List| *3)) #6# #2# #4# #7#)) (|LyndonBasis| (*1 *2 *3) (AND (|isDomain| *3 (|List| *4)) (|ofCategory| *4 #3#) (|isDomain| *2 (|List| (|LiePolynomial| *4 *5))) (|isDomain| *1 (|LieExponentials| *4 *5 *6)) (|ofCategory| *5 #5#) (|ofType| *6 #8#))) (|LyndonCoordinates| #9# (AND (|isDomain| *2 (|List| (|Record| (|:| |k| (|LyndonWord| *3)) #10#))) #6# #2# #4# #7#)) (|identification| (*1 *2 *1 *1) (AND (|isDomain| *2 (|List| (|Equation| *4))) #6# #2# #4# #7#))) +(((|LieExponentials| |#1| |#2| |#3|) (|Join| (|Group|) (|CoercibleTo| (|XDistributedPolynomial| |#1| |#2|)) (|CoercibleTo| (|XPBWPolynomial| |#1| |#2|)) (CATEGORY |domain| (SIGNATURE |exp| ($ #1=(|LiePolynomial| |#1| |#2|))) (SIGNATURE |log| (#1# $)) (SIGNATURE |ListOfTerms| ((|List| (|Record| (|:| |k| (|PoincareBirkhoffWittLyndonBasis| |#1|)) #2=(|:| |c| |#2|))) $)) (SIGNATURE |mirror| ($ $)) (SIGNATURE |varList| (#3=(|List| |#1|) $)) (SIGNATURE |LyndonBasis| ((|List| #1#) #3#)) (SIGNATURE |LyndonCoordinates| ((|List| (|Record| (|:| |k| (|LyndonWord| |#1|)) #2#)) $)) (SIGNATURE |identification| ((|List| (|Equation| |#2|)) $ $)))) (|OrderedSet|) (|Join| (|CommutativeRing|) (|Module| (|Fraction| (|Integer|)))) (|PositiveInteger|)) (T |LieExponentials|)) +((|exp| (*1 *1 *2) (AND #1=(|isDomain| *2 (|LiePolynomial| *3 *4)) #2=(|ofCategory| *3 #3=(|OrderedSet|)) #4=(|ofCategory| *4 #5=(|Join| (|CommutativeRing|) (|Module| (|Fraction| (|Integer|))))) #6=(|isDomain| *1 (|LieExponentials| *3 *4 *5)) #7=(|ofType| *5 #8=(|PositiveInteger|)))) (|log| #9=(*1 *2 *1) (AND #1# #6# #2# #4# #7#)) (|ListOfTerms| #9# (AND (|isDomain| *2 (|List| (|Record| (|:| |k| (|PoincareBirkhoffWittLyndonBasis| *3)) #10=(|:| |c| *4)))) #6# #2# #4# #7#)) (|mirror| (*1 *1 *1) (AND (|isDomain| *1 (|LieExponentials| *2 *3 *4)) (|ofCategory| *2 #3#) (|ofCategory| *3 #5#) (|ofType| *4 #8#))) (|varList| #9# (AND (|isDomain| *2 (|List| *3)) #6# #2# #4# #7#)) (|LyndonBasis| (*1 *2 *3) (AND (|isDomain| *3 (|List| *4)) (|ofCategory| *4 #3#) (|isDomain| *2 (|List| (|LiePolynomial| *4 *5))) (|isDomain| *1 (|LieExponentials| *4 *5 *6)) (|ofCategory| *5 #5#) (|ofType| *6 #8#))) (|LyndonCoordinates| #9# (AND (|isDomain| *2 (|List| (|Record| (|:| |k| (|LyndonWord| *3)) #10#))) #6# #2# #4# #7#)) (|identification| (*1 *2 *1 *1) (AND (|isDomain| *2 (|List| (|Equation| *4))) #6# #2# #4# #7#))) ((|zeroSetSplit| (#1=((|List| (|SquareFreeRegularTriangularSet| |#1| (|IndexedExponents| #2=(|OrderedVariableList| |#2|)) #2# #3=(|NewSparseMultivariatePolynomial| |#1| #2#))) #4=(|List| #3#) #5=(|Boolean|)) 103 T ELT) (#6=((|List| (|RegularChain| |#1| |#2|)) #4# #5#) 77 T ELT)) (|zeroDimensional?| ((#5# #4#) 26 T ELT)) (|squareFreeLexTriangular| (#1# 102 T ELT)) (|lexTriangular| (#6# 76 T ELT)) (|groebner| ((#4# #4#) 30 T ELT)) (|fglmIfCan| (((|Union| #4# "failed") #4#) 29 T ELT))) (((|LexTriangularPackage| |#1| |#2|) (CATEGORY |package| (SIGNATURE |zeroDimensional?| (#1=(|Boolean|) #2=(|List| #3=(|NewSparseMultivariatePolynomial| |#1| #4=(|OrderedVariableList| |#2|))))) (SIGNATURE |fglmIfCan| ((|Union| #2# "failed") #2#)) (SIGNATURE |groebner| (#2# #2#)) (SIGNATURE |lexTriangular| #5=((|List| (|RegularChain| |#1| |#2|)) #2# #1#)) (SIGNATURE |squareFreeLexTriangular| #6=((|List| (|SquareFreeRegularTriangularSet| |#1| (|IndexedExponents| #4#) #4# #3#)) #2# #1#)) (SIGNATURE |zeroSetSplit| #5#) (SIGNATURE |zeroSetSplit| #6#)) (|GcdDomain|) (|List| (|Symbol|))) (T |LexTriangularPackage|)) ((|zeroSetSplit| #1=(*1 *2 *3 *4) #2=(AND #3=(|isDomain| *3 (|List| #4=(|NewSparseMultivariatePolynomial| *5 #5=(|OrderedVariableList| *6)))) #6=(|isDomain| *4 #7=(|Boolean|)) #8=(|ofCategory| *5 #9=(|GcdDomain|)) #10=(|ofType| *6 #11=(|List| (|Symbol|))) (|isDomain| *2 (|List| (|SquareFreeRegularTriangularSet| *5 (|IndexedExponents| #5#) #5# #4#))) #12=(|isDomain| *1 (|LexTriangularPackage| *5 *6)))) (|zeroSetSplit| #1# #13=(AND #3# #6# #8# #10# (|isDomain| *2 (|List| (|RegularChain| *5 *6))) #12#)) (|squareFreeLexTriangular| #1# #2#) (|lexTriangular| #1# #13#) (|groebner| #14=(*1 *2 *2) (AND #15=(|isDomain| *2 (|List| (|NewSparseMultivariatePolynomial| *3 (|OrderedVariableList| *4)))) #16=(|ofCategory| *3 #9#) #17=(|ofType| *4 #11#) #18=(|isDomain| *1 (|LexTriangularPackage| *3 *4)))) (|fglmIfCan| #14# (|partial| AND #15# #16# #17# #18#)) (|zeroDimensional?| (*1 *2 *3) (AND (|isDomain| *3 (|List| (|NewSparseMultivariatePolynomial| *4 (|OrderedVariableList| *5)))) (|ofCategory| *4 #9#) (|ofType| *5 #11#) (|isDomain| *2 #7#) (|isDomain| *1 (|LexTriangularPackage| *4 *5))))) @@ -1881,22 +1884,22 @@ NIL ((|Ei| (*1 *1 *1) (|ofCategory| *1 (|LiouvillianFunctionCategory|))) (|Si| (*1 *1 *1) (|ofCategory| *1 (|LiouvillianFunctionCategory|))) (|Ci| (*1 *1 *1) (|ofCategory| *1 (|LiouvillianFunctionCategory|))) (|li| (*1 *1 *1) (|ofCategory| *1 (|LiouvillianFunctionCategory|))) (|dilog| (*1 *1 *1) (|ofCategory| *1 (|LiouvillianFunctionCategory|))) (|erf| (*1 *1 *1) (|ofCategory| *1 (|LiouvillianFunctionCategory|)))) (|Join| (|PrimitiveFunctionCategory|) (|TranscendentalFunctionCategory|) (CATEGORY |domain| (SIGNATURE |Ei| ($ $)) (SIGNATURE |Si| ($ $)) (SIGNATURE |Ci| ($ $)) (SIGNATURE |li| ($ $)) (SIGNATURE |dilog| ($ $)) (SIGNATURE |erf| ($ $)))) (((|ArcHyperbolicFunctionCategory|) . T) ((|ArcTrigonometricFunctionCategory|) . T) ((|ElementaryFunctionCategory|) . T) ((|HyperbolicFunctionCategory|) . T) ((|PrimitiveFunctionCategory|) . T) ((|TranscendentalFunctionCategory|) . T) ((|TrigonometricFunctionCategory|) . T)) -((|transform| ((#1=(|HomogeneousDistributedMultivariatePolynomial| |#1| |#2|) #2=(|DistributedMultivariatePolynomial| |#1| |#2|)) 65 T ELT)) (|totolex| ((#3=(|List| #2#) #4=(|List| #1#)) 90 T ELT)) (|minPol| ((#1# #4# #5=(|OrderedVariableList| |#1|)) 92 T ELT) ((#1# #4# #4# #5#) 91 T ELT)) (|linGenPos| (((|Record| (|:| |gblist| #3#) (|:| |gvlist| #6=(|List| (|Integer|)))) #4#) 136 T ELT)) (|intcompBasis| ((#4# #5# #4# #4#) 105 T ELT)) (|groebgen| (((|Record| (|:| |glbase| #3#) (|:| |glval| #6#)) #3#) 147 T ELT)) (|coord| (((|Vector| |#2|) #1# #4#) 70 T ELT)) (|computeBasis| ((#4# #4#) 47 T ELT)) (|choosemon| ((#2# #2# #3#) 61 T ELT)) (|anticoord| ((#2# (|List| |#2|) #2# #3#) 113 T ELT))) +((|transform| ((#1=(|HomogeneousDistributedMultivariatePolynomial| |#1| |#2|) #2=(|DistributedMultivariatePolynomial| |#1| |#2|)) 65 T ELT)) (|totolex| ((#3=(|List| #2#) #4=(|List| #1#)) 90 T ELT)) (|minPol| ((#1# #4# #5=(|OrderedVariableList| |#1|)) 92 T ELT) ((#1# #4# #4# #5#) 91 T ELT)) (|linGenPos| (((|Record| (|:| |gblist| #3#) (|:| |gvlist| #6=(|List| (|Integer|)))) #4#) 135 T ELT)) (|intcompBasis| ((#4# #5# #4# #4#) 105 T ELT)) (|groebgen| (((|Record| (|:| |glbase| #3#) (|:| |glval| #6#)) #3#) 146 T ELT)) (|coord| (((|Vector| |#2|) #1# #4#) 70 T ELT)) (|computeBasis| ((#4# #4#) 47 T ELT)) (|choosemon| ((#2# #2# #3#) 61 T ELT)) (|anticoord| ((#2# (|List| |#2|) #2# #3#) 113 T ELT))) (((|LinGroebnerPackage| |#1| |#2|) (CATEGORY |package| (SIGNATURE |linGenPos| ((|Record| (|:| |gblist| #1=(|List| #2=(|DistributedMultivariatePolynomial| |#1| |#2|))) (|:| |gvlist| #3=(|List| (|Integer|)))) #4=(|List| #5=(|HomogeneousDistributedMultivariatePolynomial| |#1| |#2|)))) (SIGNATURE |groebgen| ((|Record| (|:| |glbase| #1#) (|:| |glval| #3#)) #1#)) (SIGNATURE |totolex| (#1# #4#)) (SIGNATURE |minPol| (#5# #4# #4# #6=(|OrderedVariableList| |#1|))) (SIGNATURE |minPol| (#5# #4# #6#)) (SIGNATURE |computeBasis| (#4# #4#)) (SIGNATURE |coord| ((|Vector| |#2|) #5# #4#)) (SIGNATURE |anticoord| (#2# (|List| |#2|) #2# #1#)) (SIGNATURE |intcompBasis| (#4# #6# #4# #4#)) (SIGNATURE |choosemon| (#2# #2# #1#)) (SIGNATURE |transform| (#5# #2#))) (|List| (|Symbol|)) (|GcdDomain|)) (T |LinGroebnerPackage|)) ((|transform| #1=(*1 *2 *3) (AND (|isDomain| *3 #2=(|DistributedMultivariatePolynomial| *4 *5)) #3=(|ofType| *4 #4=(|List| (|Symbol|))) #5=(|ofCategory| *5 #6=(|GcdDomain|)) (|isDomain| *2 #7=(|HomogeneousDistributedMultivariatePolynomial| *4 *5)) #8=(|isDomain| *1 (|LinGroebnerPackage| *4 *5)))) (|choosemon| (*1 *2 *2 *3) (AND #9=(|isDomain| *3 #10=(|List| #2#)) (|isDomain| *2 #2#) #3# #5# #8#)) (|intcompBasis| (*1 *2 *3 *2 *2) (AND (|isDomain| *2 #11=(|List| #7#)) (|isDomain| *3 (|OrderedVariableList| *4)) #3# #5# #8#)) (|anticoord| (*1 *2 *3 *2 *4) (AND (|isDomain| *3 (|List| *6)) (|isDomain| *4 (|List| #12=(|DistributedMultivariatePolynomial| *5 *6))) #13=(|ofCategory| *6 #6#) (|isDomain| *2 #12#) #14=(|ofType| *5 #4#) #15=(|isDomain| *1 (|LinGroebnerPackage| *5 *6)))) (|coord| #16=(*1 *2 *3 *4) (AND (|isDomain| *4 #17=(|List| #18=(|HomogeneousDistributedMultivariatePolynomial| *5 *6))) (|isDomain| *3 #18#) #14# #13# (|isDomain| *2 (|Vector| *6)) #15#)) (|computeBasis| (*1 *2 *2) (AND (|isDomain| *2 (|List| (|HomogeneousDistributedMultivariatePolynomial| *3 *4))) (|ofType| *3 #4#) (|ofCategory| *4 #6#) (|isDomain| *1 (|LinGroebnerPackage| *3 *4)))) (|minPol| #16# #19=(AND (|isDomain| *3 #17#) (|isDomain| *4 (|OrderedVariableList| *5)) #14# (|isDomain| *2 #18#) #15# #13#)) (|minPol| (*1 *2 *3 *3 *4) #19#) (|totolex| #1# (AND #20=(|isDomain| *3 #11#) #3# #5# (|isDomain| *2 #10#) #8#)) (|groebgen| #1# (AND #3# #5# (|isDomain| *2 (|Record| (|:| |glbase| #10#) (|:| |glval| #21=(|List| (|Integer|))))) #8# #9#)) (|linGenPos| #1# (AND #20# #3# #5# (|isDomain| *2 (|Record| (|:| |gblist| #10#) (|:| |gvlist| #21#))) #8#))) ((~= #1=(#2=(#3=(|Boolean|) $ $) NIL (OR #4=(|has| #5=(|Any|) #6=(|BasicType|)) #7=(|has| #8=(|Record| (|:| |key| #9=(|String|)) (|:| |entry| #5#)) #6#)) ELT)) (|table| #10=(#11=($) NIL T ELT) #12=(($ #13=(|List| #8#)) NIL T ELT)) (|swap!| (((|Void|) $ #9# #9#) NIL #14=(|has| $ (|ShallowlyMutableAggregate| #5#)) ELT)) (|setelt| #15=(#16=(#5# $ #9# #5#) NIL #14# ELT) ((#5# $ #17=(|Symbol|) #5#) 16 T ELT)) (|select!| #18=(($ #19=(|Mapping| #3# #8#) $) NIL #20=(|has| $ (|FiniteAggregate| #8#)) ELT)) (|select| #18#) (|search| #21=(((|Union| #5# #22="failed") #9# $) NIL T ELT)) (|sample| (#11# NIL T CONST)) (|removeDuplicates| (#23=($ $) NIL #24=(AND #20# #7#) ELT)) (|remove!| (#25=($ #8# $) NIL #20# ELT) #18# #21#) (|remove| (#25# NIL #24# ELT) #18#) (|reduce| ((#8# #26=(|Mapping| #8# #8# #8#) $ #8# #8#) NIL #7# ELT) ((#8# #26# $ #8#) NIL T ELT) ((#8# #26# $) NIL T ELT)) (|qsetelt!| #15#) (|qelt| #27=((#5# $ #9#) NIL T ELT)) (|pack!| #28=(#23# NIL T ELT)) (|minIndex| #29=(#30=(#9# $) NIL #31=(|has| #9# (|OrderedSet|)) ELT)) (|members| ((#13# $) NIL T ELT)) (|member?| ((#3# #8# $) NIL #7# ELT)) (|maxIndex| #29#) (|map!| #32=(($ (|Mapping| #8# #8#) . #33=($)) NIL T ELT) #34=(($ (|Mapping| #5# #5#) . #33#) NIL T ELT)) (|map| #32# #34# #32# (($ (|Mapping| #5# #5# #5#) $ $) NIL T ELT)) (|library| (($ (|FileName|)) 8 T ELT)) (|latex| (#30# NIL #35=(OR #36=(|has| #5# #37=(|SetCategory|)) #38=(|has| #8# #37#)) ELT)) (|keys| #39=(((|List| #9#) $) NIL T ELT)) (|key?| #40=((#3# #9# $) NIL T ELT)) (|inspect| #41=((#8# $) NIL T ELT)) (|insert!| (#25# NIL T ELT)) (|indices| #39#) (|index?| #40#) (|hash| (((|SingleInteger|) $) NIL #35# ELT)) (|first| ((#5# $) NIL #31# ELT)) (|find| (((|Union| #8# #22#) #19# $) NIL T ELT)) (|fill!| (($ $ #5#) NIL #14# ELT)) (|extract!| #41#) (|every?| #42=((#3# #19# $) NIL T ELT)) (|eval| #43=(($ $ (|List| #44=(|Equation| #8#))) NIL #45=(AND (|has| #8# (|Evalable| #8#)) #38#) ELT) #46=(($ $ #44#) NIL #45# ELT) #47=(($ $ #8# #8#) NIL #45# ELT) #48=(($ $ #13# #13#) NIL #45# ELT) (($ $ #49=(|List| #5#) #49#) NIL #50=(AND (|has| #5# (|Evalable| #5#)) #36#) ELT) (($ $ #5# #5#) NIL #50# ELT) (($ $ #51=(|Equation| #5#)) NIL #50# ELT) (($ $ (|List| #51#)) NIL #50# ELT) #48# #47# #46# #43#) (|eq?| (#2# NIL T ELT)) (|entry?| ((#3# #5# $) NIL (AND (|has| $ (|FiniteAggregate| #5#)) #4#) ELT)) (|entries| ((#49# $) NIL T ELT)) (|empty?| ((#3# $) NIL T ELT)) (|empty| #10#) (|elt| #27# (#16# NIL T ELT) ((#5# $ #17#) 14 T ELT)) (|dictionary| #10# #12#) (|count| ((#52=(|NonNegativeInteger|) #8# $) NIL #7# ELT) ((#52# #19# $) NIL T ELT)) (|copy| #28#) (|convert| ((#53=(|InputForm|) $) NIL (|has| #8# (|ConvertibleTo| #53#)) ELT)) (|construct| #12#) (|coerce| ((#54=(|OutputForm|) $) NIL (OR (|has| #8# #55=(|CoercibleTo| #54#)) (|has| #5# #55#)) ELT)) (|before?| #1#) (|bag| #12#) (|any?| #42#) (= #1#) (|#| ((#52# $) NIL T ELT))) (((|Library|) (|Join| (|TableAggregate| (|String|) #1=(|Any|)) (|Eltable| #2=(|Symbol|) #1#) (CATEGORY |domain| (SIGNATURE |library| ($ (|FileName|))) (SIGNATURE |pack!| ($ $)) (SIGNATURE |setelt| (#1# $ #2# #1#))))) (T |Library|)) ((|library| (*1 *1 *2) (AND (|isDomain| *2 (|FileName|)) #1=(|isDomain| *1 (|Library|)))) (|pack!| (*1 *1 *1) #1#) (|setelt| (*1 *2 *1 *3 *2) (AND (|isDomain| *2 (|Any|)) (|isDomain| *3 (|Symbol|)) #1#))) -((~= #1=((#2=(|Boolean|) $ $) NIL T ELT)) (|zero?| ((#2# $) NIL T ELT)) (|unit| #3=((#4=(|Union| $ #5="failed")) NIL #6=(OR (AND #7=(|has| |#2| (|FiniteRankNonAssociativeAlgebra| |#1|)) #8=(|has| |#1| (|IntegralDomain|))) (AND #9=(|has| |#2| (|FramedNonAssociativeAlgebra| |#1|)) #8#)) ELT)) (|subtractIfCan| ((#4# $ $) NIL T ELT)) (|structuralConstants| ((#10=(|Vector| #11=(|Matrix| |#1|))) NIL #9# ELT) ((#10# #12=(|Vector| $)) NIL #7# ELT)) (|someBasis| (#13=(#12#) NIL #7# ELT)) (|sample| (#14=($) NIL T CONST)) (|rightUnits| #15=(((|Union| (|Record| (|:| |particular| $) (|:| |basis| (|List| $))) #5#)) NIL #6# ELT)) (|rightUnit| #3#) (|rightTraceMatrix| #16=((#11#) NIL #9# ELT) #17=(#18=(#11# #12#) NIL #7# ELT)) (|rightTrace| #19=((|#1| $) NIL #7# ELT)) (|rightRegularRepresentation| #20=((#11# $) NIL #9# ELT) #21=((#11# $ #12#) NIL #7# ELT)) (|rightRecip| #22=((#4# $) NIL #6# ELT)) (|rightRankPolynomial| #23=(((|SparseUnivariatePolynomial| #24=(|Polynomial| |#1|))) NIL (AND #9# (|has| |#1| (|Field|))) ELT)) (|rightPower| #25=(#26=($ $ #27=(|PositiveInteger|)) NIL T ELT)) (|rightNorm| #19#) (|rightMinimalPolynomial| #28=(#29=((|SparseUnivariatePolynomial| |#1|) $) NIL #6# ELT)) (|rightDiscriminant| #30=((|#1|) NIL #9# ELT) #31=((|#1| #12#) NIL #7# ELT)) (|rightCharacteristicPolynomial| #32=(#29# NIL #7# ELT)) (|rightAlternative?| #33=((#2#) NIL #7# ELT)) (|represents| #34=(($ #35=(|Vector| |#1|)) NIL #9# ELT) (($ #35# #12#) NIL #7# ELT)) (|recip| #22#) (|rank| ((#27#) NIL #7# ELT)) (|powerAssociative?| #33#) (|plenaryPower| #25#) (|opposite?| #1#) (|noncommutativeJordanAlgebra?| #33#) (|lieAlgebra?| #33#) (|lieAdmissible?| #33#) (|leftUnits| #15#) (|leftUnit| #3#) (|leftTraceMatrix| #16# #17#) (|leftTrace| #19#) (|leftRegularRepresentation| #20# #21#) (|leftRecip| #22#) (|leftRankPolynomial| #23#) (|leftPower| #25#) (|leftNorm| #19#) (|leftMinimalPolynomial| #28#) (|leftDiscriminant| #30# #31#) (|leftCharacteristicPolynomial| #32#) (|leftAlternative?| #33#) (|latex| (((|String|) $) NIL T ELT)) (|jordanAlgebra?| #33#) (|jordanAdmissible?| #33#) (|jacobiIdentity?| #33#) (|hash| (((|SingleInteger|) $) NIL T ELT)) (|flexible?| #33#) (|elt| ((|#1| $ #36=(|Integer|)) NIL #9# ELT)) (|coordinates| (#18# NIL #9# ELT) #37=((#35# $) NIL #9# ELT) ((#11# #12# #12#) NIL #7# ELT) ((#35# $ #12#) NIL #7# ELT)) (|convert| #34# #37#) (|conditionsForIdempotents| ((#38=(|List| #24#)) NIL #9# ELT) ((#38# #12#) NIL #7# ELT)) (|commutator| #39=(#40=($ $ $) NIL T ELT)) (|commutative?| #33#) (|coerce| (((|OutputForm|) $) NIL T ELT) ((|#2| $) 11 T ELT) (($ |#2|) 12 T ELT)) (|before?| #1#) (|basis| (#13# NIL #9# ELT)) (|associatorDependence| (((|List| #35#)) NIL #6# ELT)) (|associator| (($ $ $ $) NIL T ELT)) (|associative?| #33#) (|apply| (($ #11# $) NIL #9# ELT)) (|antiCommutator| #39#) (|antiCommutative?| #33#) (|antiAssociative?| #33#) (|alternative?| #33#) (|Zero| (#14# 18 T CONST)) (= #1#) (- (($ $) NIL T ELT) #39#) (+ #39#) (** (#26# 19 T ELT)) (* (($ #27# $) NIL T ELT) (($ (|NonNegativeInteger|) $) NIL T ELT) (($ #36# . #41=($)) NIL T ELT) (#40# 10 T ELT) (($ $ |#1|) NIL T ELT) (($ |#1| . #41#) NIL T ELT))) +((~= #1=((#2=(|Boolean|) $ $) NIL T ELT)) (|zero?| ((#2# $) NIL T ELT)) (|unit| #3=((#4=(|Union| $ #5="failed")) NIL #6=(OR (AND #7=(|has| |#2| (|FiniteRankNonAssociativeAlgebra| |#1|)) #8=(|has| |#1| (|IntegralDomain|))) (AND #9=(|has| |#2| (|FramedNonAssociativeAlgebra| |#1|)) #8#)) ELT)) (|subtractIfCan| (((|Maybe| $) $ $) NIL T ELT)) (|structuralConstants| ((#10=(|Vector| #11=(|Matrix| |#1|))) NIL #9# ELT) ((#10# #12=(|Vector| $)) NIL #7# ELT)) (|someBasis| (#13=(#12#) NIL #7# ELT)) (|sample| (#14=($) NIL T CONST)) (|rightUnits| #15=(((|Union| (|Record| (|:| |particular| $) (|:| |basis| (|List| $))) #5#)) NIL #6# ELT)) (|rightUnit| #3#) (|rightTraceMatrix| #16=((#11#) NIL #9# ELT) #17=(#18=(#11# #12#) NIL #7# ELT)) (|rightTrace| #19=((|#1| $) NIL #7# ELT)) (|rightRegularRepresentation| #20=((#11# $) NIL #9# ELT) #21=((#11# $ #12#) NIL #7# ELT)) (|rightRecip| #22=((#4# $) NIL #6# ELT)) (|rightRankPolynomial| #23=(((|SparseUnivariatePolynomial| #24=(|Polynomial| |#1|))) NIL (AND #9# (|has| |#1| (|Field|))) ELT)) (|rightPower| #25=(#26=($ $ #27=(|PositiveInteger|)) NIL T ELT)) (|rightNorm| #19#) (|rightMinimalPolynomial| #28=(#29=((|SparseUnivariatePolynomial| |#1|) $) NIL #6# ELT)) (|rightDiscriminant| #30=((|#1|) NIL #9# ELT) #31=((|#1| #12#) NIL #7# ELT)) (|rightCharacteristicPolynomial| #32=(#29# NIL #7# ELT)) (|rightAlternative?| #33=((#2#) NIL #7# ELT)) (|represents| #34=(($ #35=(|Vector| |#1|)) NIL #9# ELT) (($ #35# #12#) NIL #7# ELT)) (|recip| #22#) (|rank| ((#27#) NIL #7# ELT)) (|powerAssociative?| #33#) (|plenaryPower| #25#) (|opposite?| #1#) (|noncommutativeJordanAlgebra?| #33#) (|lieAlgebra?| #33#) (|lieAdmissible?| #33#) (|leftUnits| #15#) (|leftUnit| #3#) (|leftTraceMatrix| #16# #17#) (|leftTrace| #19#) (|leftRegularRepresentation| #20# #21#) (|leftRecip| #22#) (|leftRankPolynomial| #23#) (|leftPower| #25#) (|leftNorm| #19#) (|leftMinimalPolynomial| #28#) (|leftDiscriminant| #30# #31#) (|leftCharacteristicPolynomial| #32#) (|leftAlternative?| #33#) (|latex| (((|String|) $) NIL T ELT)) (|jordanAlgebra?| #33#) (|jordanAdmissible?| #33#) (|jacobiIdentity?| #33#) (|hash| (((|SingleInteger|) $) NIL T ELT)) (|flexible?| #33#) (|elt| ((|#1| $ #36=(|Integer|)) NIL #9# ELT)) (|coordinates| (#18# NIL #9# ELT) #37=((#35# $) NIL #9# ELT) ((#11# #12# #12#) NIL #7# ELT) ((#35# $ #12#) NIL #7# ELT)) (|convert| #34# #37#) (|conditionsForIdempotents| ((#38=(|List| #24#)) NIL #9# ELT) ((#38# #12#) NIL #7# ELT)) (|commutator| #39=(#40=($ $ $) NIL T ELT)) (|commutative?| #33#) (|coerce| (((|OutputForm|) $) NIL T ELT) ((|#2| $) 11 T ELT) (($ |#2|) 12 T ELT)) (|before?| #1#) (|basis| (#13# NIL #9# ELT)) (|associatorDependence| (((|List| #35#)) NIL #6# ELT)) (|associator| (($ $ $ $) NIL T ELT)) (|associative?| #33#) (|apply| (($ #11# $) NIL #9# ELT)) (|antiCommutator| #39#) (|antiCommutative?| #33#) (|antiAssociative?| #33#) (|alternative?| #33#) (|Zero| (#14# 18 T CONST)) (= #1#) (- (($ $) NIL T ELT) #39#) (+ #39#) (** (#26# 19 T ELT)) (* (($ #27# $) NIL T ELT) (($ (|NonNegativeInteger|) $) NIL T ELT) (($ #36# . #41=($)) NIL T ELT) (#40# 10 T ELT) (($ $ |#1|) NIL T ELT) (($ |#1| . #41#) NIL T ELT))) (((|AssociatedLieAlgebra| |#1| |#2|) (|Join| #1=(|NonAssociativeAlgebra| |#1|) (|CoercibleTo| |#2|) (CATEGORY |domain| (SIGNATURE |coerce| ($ |#2|)) (IF (|has| |#2| #2=(|FramedNonAssociativeAlgebra| |#1|)) (ATTRIBUTE #2#) |%noBranch|) (IF (|has| |#2| #3=(|FiniteRankNonAssociativeAlgebra| |#1|)) (ATTRIBUTE #3#) |%noBranch|))) (|CommutativeRing|) #1#) (T |AssociatedLieAlgebra|)) ((|coerce| (*1 *1 *2) (AND (|ofCategory| *3 (|CommutativeRing|)) (|isDomain| *1 (|AssociatedLieAlgebra| *3 *2)) (|ofCategory| *2 (|NonAssociativeAlgebra| *3))))) ((/ (($ $ |#2|) 10 T ELT))) (((|LieAlgebra&| |#1| |#2|) (CATEGORY |package| (SIGNATURE / (|#1| |#1| |#2|))) (|LieAlgebra| |#2|) (|CommutativeRing|)) (T |LieAlgebra&|)) NIL -((~= (#1=((|Boolean|) $ $) 7 T ELT)) (|zero?| ((#2=(|Boolean|) $) 22 T ELT)) (|subtractIfCan| (((|Union| $ "failed") $ $) 26 T ELT)) (|sample| (#3=($) 23 T CONST)) (|opposite?| ((#2# $ $) 20 T ELT)) (|latex| (((|String|) $) 11 T ELT)) (|hash| (((|SingleInteger|) $) 12 T ELT)) (|construct| (($ $ $) 40 T ELT)) (|coerce| (((|OutputForm|) $) 13 T ELT)) (|before?| (#1# 6 T ELT)) (|Zero| (#3# 24 T CONST)) (= (#1# 8 T ELT)) (/ (($ $ |#1|) 39 (|has| |#1| (|Field|)) ELT)) (- (($ $) 29 T ELT) (($ $ $) 28 T ELT)) (+ (($ $ $) 18 T ELT)) (* (($ (|PositiveInteger|) $) 17 T ELT) (($ (|NonNegativeInteger|) $) 21 T ELT) (($ (|Integer|) . #4=($)) 30 T ELT) (($ |#1| . #4#) 33 T ELT) (($ $ |#1|) 37 T ELT))) +((~= (#1=((|Boolean|) $ $) 7 T ELT)) (|zero?| ((#2=(|Boolean|) $) 22 T ELT)) (|subtractIfCan| (((|Maybe| $) $ $) 26 T ELT)) (|sample| (#3=($) 23 T CONST)) (|opposite?| ((#2# $ $) 20 T ELT)) (|latex| (((|String|) $) 11 T ELT)) (|hash| (((|SingleInteger|) $) 12 T ELT)) (|construct| (($ $ $) 41 T ELT)) (|coerce| (((|OutputForm|) $) 13 T ELT)) (|before?| (#1# 6 T ELT)) (|Zero| (#3# 24 T CONST)) (= (#1# 8 T ELT)) (/ (($ $ |#1|) 40 (|has| |#1| (|Field|)) ELT)) (- (($ $) 30 T ELT) (($ $ $) 29 T ELT)) (+ (($ $ $) 18 T ELT)) (* (($ (|PositiveInteger|) $) 17 T ELT) (($ (|NonNegativeInteger|) $) 21 T ELT) (($ (|Integer|) . #4=($)) 31 T ELT) (($ |#1| . #4#) 34 T ELT) (($ $ |#1|) 38 T ELT))) (((|LieAlgebra| |#1|) (|Category|) (|CommutativeRing|)) (T |LieAlgebra|)) ((|construct| (*1 *1 *1 *1) (AND (|ofCategory| *1 (|LieAlgebra| *2)) (|ofCategory| *2 (|CommutativeRing|)))) (/ (*1 *1 *1 *2) (AND (|ofCategory| *1 (|LieAlgebra| *2)) (|ofCategory| *2 (|CommutativeRing|)) (|ofCategory| *2 (|Field|))))) -(|Join| (|Module| |t#1|) (CATEGORY |domain| (ATTRIBUTE |NullSquare|) (ATTRIBUTE |JacobiIdentity|) (SIGNATURE |construct| ($ $ $)) (IF (|has| |t#1| (|Field|)) (SIGNATURE / ($ $ |t#1|)) |%noBranch|))) +(|Join| (|Module| |t#1|) (CATEGORY |domain| (SIGNATURE |construct| ($ $ $)) (IF (|has| |t#1| (|Field|)) (SIGNATURE / ($ $ |t#1|)) |%noBranch|))) (((|AbelianGroup|) . T) ((|AbelianMonoid|) . T) ((|AbelianSemiGroup|) . T) ((|BasicType|) . T) ((|BiModule| |#1| |#1|) . T) ((|CancellationAbelianMonoid|) . T) ((|CoercibleTo| (|OutputForm|)) . T) ((|Join|) . T) ((|LeftLinearSet| (|Integer|)) . T) ((|LeftLinearSet| |#1|) . T) ((|LeftModule| |#1|) . T) ((|LinearSet| |#1|) . T) ((|Module| |#1|) . T) ((|RightLinearSet| |#1|) . T) ((|RightModule| |#1|) . T) ((|SetCategory|) . T) ((|Type|) . T)) ((|limit| ((#1=(|Union| #2=(|OrderedCompletion| |#2|) #3="failed") |#2| (|Equation| |#2|) (|String|)) 105 T ELT) (((|Union| #2# (|Record| (|:| |leftHandLimit| #1#) (|:| |rightHandLimit| #1#)) #3#) |#2| (|Equation| #2#)) 130 T ELT)) (|complexLimit| (((|Union| #4=(|OnePointCompletion| |#2|) #3#) |#2| (|Equation| #4#)) 135 T ELT))) (((|PowerSeriesLimitPackage| |#1| |#2|) (CATEGORY |package| (SIGNATURE |limit| ((|Union| #1=(|OrderedCompletion| |#2|) (|Record| (|:| |leftHandLimit| #2=(|Union| #1# #3="failed")) (|:| |rightHandLimit| #2#)) #3#) |#2| (|Equation| #1#))) (SIGNATURE |complexLimit| ((|Union| #4=(|OnePointCompletion| |#2|) #3#) |#2| (|Equation| #4#))) (SIGNATURE |limit| (#2# |#2| (|Equation| |#2|) (|String|)))) (|Join| (|GcdDomain|) (|RetractableTo| #5=(|Integer|)) (|LinearlyExplicitRingOver| #5#)) (|Join| (|AlgebraicallyClosedField|) (|TranscendentalFunctionCategory|) (|FunctionSpace| |#1|))) (T |PowerSeriesLimitPackage|)) @@ -1910,15 +1913,15 @@ NIL ((|solveLinear| (((|Union| (|Vector| (|Fraction| |#1|)) #1="failed") #2=(|Vector| |#2|) |#2|) 64 (|not| #3=(|has| |#1| (|Field|))) ELT) ((#4=(|Union| (|Vector| |#1|) #1#) #2# |#2|) 49 #3# ELT)) (|linearlyDependent?| (((|Boolean|) #2#) 33 T ELT)) (|linearDependence| ((#4# #2#) 40 T ELT))) (((|LinearDependence| |#1| |#2|) (CATEGORY |package| (SIGNATURE |linearlyDependent?| ((|Boolean|) #1=(|Vector| |#2|))) (SIGNATURE |linearDependence| (#2=(|Union| (|Vector| |#1|) #3="failed") #1#)) (IF (|has| |#1| (|Field|)) (SIGNATURE |solveLinear| (#2# #1# |#2|)) (SIGNATURE |solveLinear| ((|Union| (|Vector| (|Fraction| |#1|)) #3#) #1# |#2|)))) (|IntegralDomain|) (|Join| (|Ring|) (|LinearlyExplicitRingOver| |#1|))) (T |LinearDependence|)) ((|solveLinear| #1=(*1 *2 *3 *4) (|partial| AND #2=(|isDomain| *3 #3=(|Vector| *4)) #4=(|ofCategory| *4 (|Join| #5=(|Ring|) (|LinearlyExplicitRingOver| *5))) (|not| #6=(|ofCategory| *5 (|Field|))) #7=(|ofCategory| *5 #8=(|IntegralDomain|)) (|isDomain| *2 (|Vector| (|Fraction| *5))) #9=(|isDomain| *1 (|LinearDependence| *5 *4)))) (|solveLinear| #1# (|partial| AND #2# #4# #6# #7# (|isDomain| *2 #10=(|Vector| *5)) #9#)) (|linearDependence| #11=(*1 *2 *3) (|partial| AND #12=(|isDomain| *3 #10#) #13=(|ofCategory| *5 (|Join| #5# (|LinearlyExplicitRingOver| *4))) #14=(|ofCategory| *4 #8#) (|isDomain| *2 #3#) #15=(|isDomain| *1 (|LinearDependence| *4 *5)))) (|linearlyDependent?| #11# (AND #12# #13# #14# (|isDomain| *2 (|Boolean|)) #15#))) -((~= #1=((#2=(|Boolean|) $ $) NIL T ELT)) (|zero?| ((#2# $) NIL T ELT)) (|terms| ((#3=(|List| (|IndexedProductTerm| |#1| #4=(|LinearBasis| |#2|))) $) NIL T ELT)) (|subtractIfCan| (((|Union| $ "failed") $ $) NIL T ELT)) (|sample| (#5=($) NIL T CONST)) (|reductum| #6=(($ $) NIL T ELT)) (|opposite?| #1#) (|monomial| (($ |#1| #4#) NIL T ELT)) (|map| (($ (|Mapping| |#1| |#1|) $) NIL T ELT)) (|linearElement| (($ (|List| |#1|)) 25 T ELT)) (|leadingSupport| ((#4# $) NIL T ELT)) (|leadingCoefficient| ((|#1| $) NIL T ELT)) (|latex| (((|String|) $) NIL T ELT)) (|hash| (((|SingleInteger|) $) NIL T ELT)) (|dimension| (((|CardinalNumber|)) 16 T ELT)) (|coordinates| (((|Vector| |#1|) $) 44 T ELT)) (|convert| (($ #3#) NIL T ELT)) (|coerce| (((|OutputForm|) $) NIL T ELT) (($ #4#) 11 T ELT)) (|before?| #1#) (|Zero| (#5# 20 T CONST)) (= #1#) (/ #7=(($ $ |#1|) NIL T ELT)) (- #6# (#8=($ $ $) NIL T ELT)) (+ (#8# 17 T ELT)) (* (($ (|PositiveInteger|) $) NIL T ELT) (($ (|NonNegativeInteger|) $) NIL T ELT) (($ (|Integer|) . #9=($)) NIL T ELT) (($ |#1| . #9#) NIL T ELT) #7#)) +((~= #1=((#2=(|Boolean|) $ $) NIL T ELT)) (|zero?| ((#2# $) NIL T ELT)) (|terms| ((#3=(|List| (|IndexedProductTerm| |#1| #4=(|LinearBasis| |#2|))) $) NIL T ELT)) (|subtractIfCan| (((|Maybe| $) $ $) NIL T ELT)) (|sample| (#5=($) NIL T CONST)) (|reductum| #6=(($ $) NIL T ELT)) (|opposite?| #1#) (|monomial| (($ |#1| #4#) NIL T ELT)) (|map| (($ (|Mapping| |#1| |#1|) $) NIL T ELT)) (|linearElement| (($ (|List| |#1|)) 25 T ELT)) (|leadingSupport| ((#4# $) NIL T ELT)) (|leadingCoefficient| ((|#1| $) NIL T ELT)) (|latex| (((|String|) $) NIL T ELT)) (|hash| (((|SingleInteger|) $) NIL T ELT)) (|dimension| (((|CardinalNumber|)) 16 T ELT)) (|coordinates| (((|Vector| |#1|) $) 44 T ELT)) (|convert| (($ #3#) NIL T ELT)) (|coerce| (((|OutputForm|) $) NIL T ELT) (($ #4#) 11 T ELT)) (|before?| #1#) (|Zero| (#5# 20 T CONST)) (= #1#) (/ #7=(($ $ |#1|) NIL T ELT)) (- #6# (#8=($ $ $) NIL T ELT)) (+ (#8# 17 T ELT)) (* (($ (|PositiveInteger|) $) NIL T ELT) (($ (|NonNegativeInteger|) $) NIL T ELT) (($ (|Integer|) . #9=($)) NIL T ELT) (($ |#1| . #9#) NIL T ELT) #7#)) (((|LinearElement| |#1| |#2|) (|Join| (|VectorSpace| |#1|) (|CoercibleFrom| #1=(|LinearBasis| |#2|)) (|IndexedDirectProductCategory| |#1| #1#) (CATEGORY |domain| (SIGNATURE |linearElement| ($ (|List| |#1|))) (SIGNATURE |coordinates| ((|Vector| |#1|) $)))) (|Field|) (|List| (|Symbol|))) (T |LinearElement|)) ((|linearElement| (*1 *1 *2) (AND (|isDomain| *2 (|List| *3)) #1=(|ofCategory| *3 (|Field|)) #2=(|isDomain| *1 (|LinearElement| *3 *4)) #3=(|ofType| *4 (|List| (|Symbol|))))) (|coordinates| (*1 *2 *1) (AND (|isDomain| *2 (|Vector| *3)) #2# #1# #3#))) -((~= (#1=((|Boolean|) $ $) 7 T ELT)) (|zero?| ((#2=(|Boolean|) $) 22 T ELT)) (|subtractIfCan| (((|Union| $ "failed") $ $) 26 T ELT)) (|sample| (#3=($) 23 T CONST)) (|reducedSystem| (((|Matrix| |#1|) (|Matrix| $)) 36 T ELT) (((|Record| (|:| |mat| (|Matrix| |#1|)) (|:| |vec| (|Vector| |#1|))) (|Matrix| $) (|Vector| $)) 35 T ELT)) (|opposite?| ((#2# $ $) 20 T ELT)) (|leftReducedSystem| (((|Matrix| |#1|) (|Vector| $)) 38 T ELT) (((|Record| (|:| |mat| (|Matrix| |#1|)) (|:| |vec| (|Vector| |#1|))) (|Vector| $) $) 37 T ELT)) (|latex| (((|String|) $) 11 T ELT)) (|hash| (((|SingleInteger|) $) 12 T ELT)) (|coerce| (((|OutputForm|) $) 13 T ELT)) (|before?| (#1# 6 T ELT)) (|Zero| (#3# 24 T CONST)) (= (#1# 8 T ELT)) (- (($ $) 29 T ELT) (($ $ $) 28 T ELT)) (+ (($ $ $) 18 T ELT)) (* (($ (|PositiveInteger|) $) 17 T ELT) (($ (|NonNegativeInteger|) $) 21 T ELT) (($ (|Integer|) . #4=($)) 30 T ELT) (($ |#1| . #4#) 33 T ELT))) +((~= (#1=((|Boolean|) $ $) 7 T ELT)) (|zero?| ((#2=(|Boolean|) $) 22 T ELT)) (|subtractIfCan| (((|Maybe| $) $ $) 26 T ELT)) (|sample| (#3=($) 23 T CONST)) (|reducedSystem| (((|Matrix| |#1|) (|Matrix| $)) 37 T ELT) (((|Record| (|:| |mat| (|Matrix| |#1|)) (|:| |vec| (|Vector| |#1|))) (|Matrix| $) (|Vector| $)) 36 T ELT)) (|opposite?| ((#2# $ $) 20 T ELT)) (|leftReducedSystem| (((|Matrix| |#1|) (|Vector| $)) 39 T ELT) (((|Record| (|:| |mat| (|Matrix| |#1|)) (|:| |vec| (|Vector| |#1|))) (|Vector| $) $) 38 T ELT)) (|latex| (((|String|) $) 11 T ELT)) (|hash| (((|SingleInteger|) $) 12 T ELT)) (|coerce| (((|OutputForm|) $) 13 T ELT)) (|before?| (#1# 6 T ELT)) (|Zero| (#3# 24 T CONST)) (= (#1# 8 T ELT)) (- (($ $) 30 T ELT) (($ $ $) 29 T ELT)) (+ (($ $ $) 18 T ELT)) (* (($ (|PositiveInteger|) $) 17 T ELT) (($ (|NonNegativeInteger|) $) 21 T ELT) (($ (|Integer|) . #4=($)) 31 T ELT) (($ |#1| . #4#) 34 T ELT))) (((|LinearlyExplicitRingOver| |#1|) (|Category|) (|Ring|)) (T |LinearlyExplicitRingOver|)) ((|leftReducedSystem| (*1 *2 *3) (AND (|isDomain| *3 (|Vector| *1)) (|ofCategory| *1 (|LinearlyExplicitRingOver| *4)) (|ofCategory| *4 (|Ring|)) (|isDomain| *2 (|Matrix| *4)))) (|leftReducedSystem| (*1 *2 *3 *1) (AND (|isDomain| *3 (|Vector| *1)) (|ofCategory| *1 (|LinearlyExplicitRingOver| *4)) (|ofCategory| *4 (|Ring|)) (|isDomain| *2 (|Record| (|:| |mat| (|Matrix| *4)) (|:| |vec| (|Vector| *4)))))) (|reducedSystem| (*1 *2 *3) (AND (|isDomain| *3 (|Matrix| *1)) (|ofCategory| *1 (|LinearlyExplicitRingOver| *4)) (|ofCategory| *4 (|Ring|)) (|isDomain| *2 (|Matrix| *4)))) (|reducedSystem| (*1 *2 *3 *4) (AND (|isDomain| *3 (|Matrix| *1)) (|isDomain| *4 (|Vector| *1)) (|ofCategory| *1 (|LinearlyExplicitRingOver| *5)) (|ofCategory| *5 (|Ring|)) (|isDomain| *2 (|Record| (|:| |mat| (|Matrix| *5)) (|:| |vec| (|Vector| *5))))))) (|Join| (|LeftModule| |t#1|) (CATEGORY |domain| (SIGNATURE |leftReducedSystem| ((|Matrix| |t#1|) (|Vector| $))) (SIGNATURE |leftReducedSystem| ((|Record| (|:| |mat| (|Matrix| |t#1|)) (|:| |vec| (|Vector| |t#1|))) (|Vector| $) $)) (SIGNATURE |reducedSystem| ((|Matrix| |t#1|) (|Matrix| $))) (SIGNATURE |reducedSystem| ((|Record| (|:| |mat| (|Matrix| |t#1|)) (|:| |vec| (|Vector| |t#1|))) (|Matrix| $) (|Vector| $))))) (((|AbelianGroup|) . T) ((|AbelianMonoid|) . T) ((|AbelianSemiGroup|) . T) ((|BasicType|) . T) ((|CancellationAbelianMonoid|) . T) ((|CoercibleTo| (|OutputForm|)) . T) ((|Join|) . T) ((|LeftLinearSet| (|Integer|)) . T) ((|LeftLinearSet| |#1|) . T) ((|LeftModule| |#1|) . T) ((|SetCategory|) . T) ((|Type|) . T)) -((~= #1=((#2=(|Boolean|) $ $) NIL T ELT)) (|zero?| ((#2# $) NIL T ELT)) (|subtractIfCan| (((|Union| $ "failed") $ $) NIL T ELT)) (|sample| (#3=($) NIL T CONST)) (|opposite?| #1#) (|linearForm| (($ (|List| |#1|)) 23 T ELT)) (|latex| (((|String|) $) NIL T ELT)) (|hash| (((|SingleInteger|) $) NIL T ELT)) (|elt| ((|#1| $ (|LinearElement| |#1| |#2|)) 46 T ELT)) (|dimension| (((|CardinalNumber|)) 13 T ELT)) (|coordinates| (((|Vector| |#1|) $) 42 T ELT)) (|coerce| (((|OutputForm|) $) NIL T ELT)) (|before?| #1#) (|Zero| (#3# 18 T CONST)) (= #1#) (/ #4=(($ $ |#1|) NIL T ELT)) (- (($ $) NIL T ELT) (#5=($ $ $) NIL T ELT)) (+ (#5# 14 T ELT)) (* (($ (|PositiveInteger|) $) NIL T ELT) (($ (|NonNegativeInteger|) $) NIL T ELT) (($ (|Integer|) . #6=($)) NIL T ELT) (($ |#1| . #6#) NIL T ELT) #4#)) +((~= #1=((#2=(|Boolean|) $ $) NIL T ELT)) (|zero?| ((#2# $) NIL T ELT)) (|subtractIfCan| (((|Maybe| $) $ $) NIL T ELT)) (|sample| (#3=($) NIL T CONST)) (|opposite?| #1#) (|linearForm| (($ (|List| |#1|)) 23 T ELT)) (|latex| (((|String|) $) NIL T ELT)) (|hash| (((|SingleInteger|) $) NIL T ELT)) (|elt| ((|#1| $ (|LinearElement| |#1| |#2|)) 46 T ELT)) (|dimension| (((|CardinalNumber|)) 13 T ELT)) (|coordinates| (((|Vector| |#1|) $) 42 T ELT)) (|coerce| (((|OutputForm|) $) NIL T ELT)) (|before?| #1#) (|Zero| (#3# 18 T CONST)) (= #1#) (/ #4=(($ $ |#1|) NIL T ELT)) (- (($ $) NIL T ELT) (#5=($ $ $) NIL T ELT)) (+ (#5# 14 T ELT)) (* (($ (|PositiveInteger|) $) NIL T ELT) (($ (|NonNegativeInteger|) $) NIL T ELT) (($ (|Integer|) . #6=($)) NIL T ELT) (($ |#1| . #6#) NIL T ELT) #4#)) (((|LinearForm| |#1| |#2|) (|Join| (|VectorSpace| |#1|) (|Eltable| (|LinearElement| |#1| |#2|) |#1|) (CATEGORY |domain| (SIGNATURE |linearForm| ($ (|List| |#1|))) (SIGNATURE |coordinates| ((|Vector| |#1|) $)))) (|Field|) (|List| (|Symbol|))) (T |LinearForm|)) ((|linearForm| (*1 *1 *2) (AND (|isDomain| *2 (|List| *3)) #1=(|ofCategory| *3 (|Field|)) #2=(|isDomain| *1 (|LinearForm| *3 *4)) #3=(|ofType| *4 (|List| (|Symbol|))))) (|coordinates| (*1 *2 *1) (AND (|isDomain| *2 (|Vector| *3)) #2# #1# #3#))) ((~= (#1=((|Boolean|) $ $) 7 T ELT)) (|latex| (((|String|) $) 11 T ELT)) (|hash| (((|SingleInteger|) $) 12 T ELT)) (|coerce| (((|OutputForm|) $) 13 T ELT)) (|before?| (#1# 6 T ELT)) (= (#1# 8 T ELT)) (* (($ |#1| $) 17 T ELT) (($ $ |#1|) 20 T ELT))) @@ -1949,7 +1952,7 @@ NIL ((~= #1=(#2=(#3=(|Boolean|) $ $) NIL #4=(|has| |#1| (|BasicType|)) ELT)) (|substitute| (($ |#1| |#1| $) 45 T ELT)) (|select!| (#5=($ #6=(|Mapping| #3# |#1|) $) 61 #7=(|has| $ (|FiniteAggregate| |#1|)) ELT)) (|select| #8=(#5# NIL #7# ELT)) (|sample| (#9=($) NIL T CONST)) (|removeDuplicates!| (#10=($ $) 47 T ELT)) (|removeDuplicates| (#10# NIL #11=(AND #7# #4#) ELT)) (|remove!| (#12=($ |#1| $) 58 #7# ELT) (#5# 60 #7# ELT)) (|remove| (#12# NIL #11# ELT) #8#) (|reduce| ((|#1| #13=(|Mapping| |#1| |#1| |#1|) $ |#1| |#1|) NIL #4# ELT) ((|#1| #13# $ |#1|) NIL T ELT) ((|#1| #13# $) NIL T ELT)) (|members| ((#14=(|List| |#1|) $) 9 T ELT)) (|member?| ((#3# |#1| $) NIL #4# ELT)) (|map!| (#15=($ (|Mapping| |#1| |#1|) $) 41 T ELT)) (|map| (#15# 39 T ELT)) (|latex| (((|String|) $) NIL #16=(|has| |#1| (|SetCategory|)) ELT)) (|inspect| (#17=(|#1| $) 49 T ELT)) (|insert!| (#12# 30 T ELT) (($ |#1| $ #18=(|NonNegativeInteger|)) 44 T ELT)) (|hash| (((|SingleInteger|) $) NIL #16# ELT)) (|find| (((|Union| |#1| "failed") #6# $) NIL T ELT)) (|extract!| (#17# 52 T ELT)) (|every?| #19=((#3# #6# $) NIL T ELT)) (|eval| (($ $ (|List| #20=(|Equation| |#1|))) NIL #21=(AND (|has| |#1| (|Evalable| |#1|)) #16#) ELT) (($ $ #20#) NIL #21# ELT) (($ $ |#1| |#1|) NIL #21# ELT) (($ $ #14# #14#) NIL #21# ELT)) (|eq?| (#2# NIL T ELT)) (|empty?| (#22=(#3# $) 23 T ELT)) (|empty| (#9# 29 T ELT)) (|duplicates?| (#22# 56 T ELT)) (|duplicates| (((|List| (|Record| (|:| |entry| |#1|) (|:| |count| #18#))) $) 69 T ELT)) (|dictionary| (#9# 26 T ELT) (#23=($ #14#) 19 T ELT)) (|count| ((#18# |#1| $) 65 #4# ELT) ((#18# #6# $) NIL T ELT)) (|copy| (#10# 20 T ELT)) (|convert| ((#24=(|InputForm|) $) 36 (|has| |#1| (|ConvertibleTo| #24#)) ELT)) (|construct| (#23# NIL T ELT)) (|coerce| ((#25=(|OutputForm|) $) 14 (|has| |#1| (|CoercibleTo| #25#)) ELT)) (|before?| #1#) (|bag| (#23# 24 T ELT)) (|any?| #19#) (= (#2# 71 #4# ELT)) (|#| ((#18# $) 17 T ELT))) (((|ListMultiDictionary| |#1|) (|Join| (|MultiDictionary| |#1|) (|FiniteAggregate| |#1|) (CATEGORY |domain| (SIGNATURE |duplicates?| ((|Boolean|) $)) (SIGNATURE |substitute| ($ |#1| |#1| $)))) (|SetCategory|)) (T |ListMultiDictionary|)) ((|duplicates?| (*1 *2 *1) (AND (|isDomain| *2 (|Boolean|)) (|isDomain| *1 (|ListMultiDictionary| *3)) (|ofCategory| *3 #1=(|SetCategory|)))) (|substitute| (*1 *1 *2 *2 *1) (AND (|isDomain| *1 (|ListMultiDictionary| *2)) (|ofCategory| *2 #1#)))) -((~= (#1=((|Boolean|) $ $) 7 T ELT)) (|zero?| ((#2=(|Boolean|) $) 22 T ELT)) (|subtractIfCan| (((|Union| $ "failed") $ $) 26 T ELT)) (|sample| (#3=($) 23 T CONST)) (|opposite?| ((#2# $ $) 20 T ELT)) (|latex| (((|String|) $) 11 T ELT)) (|hash| (((|SingleInteger|) $) 12 T ELT)) (|coerce| (((|OutputForm|) $) 13 T ELT)) (|before?| (#1# 6 T ELT)) (|Zero| (#3# 24 T CONST)) (= (#1# 8 T ELT)) (- (($ $) 29 T ELT) (($ $ $) 28 T ELT)) (+ (($ $ $) 18 T ELT)) (* (($ (|PositiveInteger|) $) 17 T ELT) (($ (|NonNegativeInteger|) $) 21 T ELT) (($ (|Integer|) . #4=($)) 30 T ELT) (($ |#1| . #4#) 33 T ELT))) +((~= (#1=((|Boolean|) $ $) 7 T ELT)) (|zero?| ((#2=(|Boolean|) $) 22 T ELT)) (|subtractIfCan| (((|Maybe| $) $ $) 26 T ELT)) (|sample| (#3=($) 23 T CONST)) (|opposite?| ((#2# $ $) 20 T ELT)) (|latex| (((|String|) $) 11 T ELT)) (|hash| (((|SingleInteger|) $) 12 T ELT)) (|coerce| (((|OutputForm|) $) 13 T ELT)) (|before?| (#1# 6 T ELT)) (|Zero| (#3# 24 T CONST)) (= (#1# 8 T ELT)) (- (($ $) 30 T ELT) (($ $ $) 29 T ELT)) (+ (($ $ $) 18 T ELT)) (* (($ (|PositiveInteger|) $) 17 T ELT) (($ (|NonNegativeInteger|) $) 21 T ELT) (($ (|Integer|) . #4=($)) 31 T ELT) (($ |#1| . #4#) 34 T ELT))) (((|LeftModule| |#1|) (|Category|) (|Rng|)) (T |LeftModule|)) NIL (|Join| (|AbelianGroup|) (|LeftLinearSet| |t#1|)) @@ -1965,25 +1968,25 @@ NIL ((|new| (*1 *1 *2 *3) (AND (|isDomain| *2 (|NonNegativeInteger|)) (|ofCategory| *1 (|LinearAggregate| *3)) (|ofCategory| *3 (|Type|)))) (|concat| (*1 *1 *1 *2) (AND (|ofCategory| *1 (|LinearAggregate| *2)) (|ofCategory| *2 (|Type|)))) (|concat| (*1 *1 *2 *1) (AND (|ofCategory| *1 (|LinearAggregate| *2)) (|ofCategory| *2 (|Type|)))) (|concat| (*1 *1 *1 *1) (AND (|ofCategory| *1 (|LinearAggregate| *2)) (|ofCategory| *2 (|Type|)))) (|concat| (*1 *1 *2) (AND (|isDomain| *2 (|List| *1)) (|ofCategory| *1 (|LinearAggregate| *3)) (|ofCategory| *3 (|Type|)))) (|map| (*1 *1 *2 *1 *1) (AND (|isDomain| *2 (|Mapping| *3 *3 *3)) (|ofCategory| *1 (|LinearAggregate| *3)) (|ofCategory| *3 (|Type|)))) (|delete| (*1 *1 *1 *2) (AND (|isDomain| *2 (|Integer|)) (|ofCategory| *1 (|LinearAggregate| *3)) (|ofCategory| *3 (|Type|)))) (|delete| (*1 *1 *1 *2) (AND (|isDomain| *2 (|UniversalSegment| (|Integer|))) (|ofCategory| *1 (|LinearAggregate| *3)) (|ofCategory| *3 (|Type|)))) (|insert| (*1 *1 *2 *1 *3) (AND (|isDomain| *3 (|Integer|)) (|ofCategory| *1 (|LinearAggregate| *2)) (|ofCategory| *2 (|Type|)))) (|insert| (*1 *1 *1 *1 *2) (AND (|isDomain| *2 (|Integer|)) (|ofCategory| *1 (|LinearAggregate| *3)) (|ofCategory| *3 (|Type|)))) (|setelt| (*1 *2 *1 *3 *2) (AND (|isDomain| *3 (|UniversalSegment| (|Integer|))) (|ofCategory| *1 (|ShallowlyMutableAggregate| *2)) (|ofCategory| *1 (|LinearAggregate| *2)) (|ofCategory| *2 (|Type|))))) (|Join| (|IndexedAggregate| (|Integer|) |t#1|) (|Collection| |t#1|) (|Eltable| (|UniversalSegment| (|Integer|)) $) (CATEGORY |domain| (SIGNATURE |new| ($ (|NonNegativeInteger|) |t#1|)) (SIGNATURE |concat| ($ $ |t#1|)) (SIGNATURE |concat| ($ |t#1| $)) (SIGNATURE |concat| ($ $ $)) (SIGNATURE |concat| ($ (|List| $))) (SIGNATURE |map| ($ (|Mapping| |t#1| |t#1| |t#1|) $ $)) (SIGNATURE |delete| ($ $ (|Integer|))) (SIGNATURE |delete| ($ $ (|UniversalSegment| (|Integer|)))) (SIGNATURE |insert| ($ |t#1| $ (|Integer|))) (SIGNATURE |insert| ($ $ $ (|Integer|))) (IF (|has| $ (|ShallowlyMutableAggregate| |t#1|)) (SIGNATURE |setelt| (|t#1| $ (|UniversalSegment| (|Integer|)) |t#1|)) |%noBranch|))) (((|Aggregate|) . T) ((|BasicType|) OR (|has| |#1| (|SetCategory|)) (|has| |#1| (|BasicType|))) ((|CoercibleTo| (|OutputForm|)) OR (|has| |#1| (|SetCategory|)) (|has| |#1| (|CoercibleTo| (|OutputForm|)))) ((|Collection| |#1|) . T) ((|ConvertibleTo| (|InputForm|)) |has| |#1| (|ConvertibleTo| (|InputForm|))) ((|Eltable| #1=(|Integer|) |#1|) . T) ((|Eltable| (|UniversalSegment| (|Integer|)) $) . T) ((|EltableAggregate| #1# |#1|) . T) ((|Evalable| |#1|) AND (|has| |#1| (|Evalable| |#1|)) (|has| |#1| (|SetCategory|))) ((|Functorial| |#1|) . T) ((|HomogeneousAggregate| |#1|) . T) ((|IndexedAggregate| #1# |#1|) . T) ((|InnerEvalable| |#1| |#1|) AND (|has| |#1| (|Evalable| |#1|)) (|has| |#1| (|SetCategory|))) ((|Join|) . T) ((|SetCategory|) |has| |#1| (|SetCategory|)) ((|Type|) . T)) -((~= #1=(#2=(#3=(|Boolean|) $ $) NIL T ELT)) (|zero?| (#4=(#3# $) 15 T ELT)) (|subtractIfCan| (((|Union| $ "failed") $ $) NIL T ELT)) (|sign| ((#5=(|Integer|) $) NIL #6=(|has| |#1| (|OrderedAbelianGroup|)) ELT)) (|sample| (#7=($) NIL T CONST)) (|positive?| #8=(#4# NIL #6# ELT)) (|opposite?| #1#) (|numer| ((|#1| $) 23 T ELT)) (|negative?| #8#) (|min| #9=(#10=($ $ $) NIL #6# ELT)) (|max| #9#) (|latex| (((|String|) $) 48 T ELT)) (|hash| (((|SingleInteger|) $) NIL T ELT)) (|denom| ((|#3| $) 24 T ELT)) (|coerce| (((|OutputForm|) $) 43 T ELT)) (|before?| (#2# 22 T ELT)) (|abs| (#11=($ $) NIL #6# ELT)) (|Zero| (#7# 10 T CONST)) (>= #12=(#2# NIL #6# ELT)) (> #12#) (= (#2# 20 T ELT)) (<= #12#) (< (#2# 26 #6# ELT)) (/ (($ $ |#3|) 36 T ELT) (($ |#1| |#3|) 37 T ELT)) (- (#11# 17 T ELT) (#10# NIL T ELT)) (+ (#10# 29 T ELT)) (* (($ (|PositiveInteger|) $) NIL T ELT) (($ (|NonNegativeInteger|) $) NIL T ELT) (($ #5# $) 32 T ELT) (($ |#2| $) 34 T ELT) (($ $ |#2|) NIL T ELT))) +((~= #1=(#2=(#3=(|Boolean|) $ $) NIL T ELT)) (|zero?| (#4=(#3# $) 15 T ELT)) (|subtractIfCan| (((|Maybe| $) $ $) NIL T ELT)) (|sign| ((#5=(|Integer|) $) NIL #6=(|has| |#1| (|OrderedAbelianGroup|)) ELT)) (|sample| (#7=($) NIL T CONST)) (|positive?| #8=(#4# NIL #6# ELT)) (|opposite?| #1#) (|numer| ((|#1| $) 23 T ELT)) (|negative?| #8#) (|min| #9=(#10=($ $ $) NIL #6# ELT)) (|max| #9#) (|latex| (((|String|) $) 48 T ELT)) (|hash| (((|SingleInteger|) $) NIL T ELT)) (|denom| ((|#3| $) 24 T ELT)) (|coerce| (((|OutputForm|) $) 43 T ELT)) (|before?| (#2# 22 T ELT)) (|abs| (#11=($ $) NIL #6# ELT)) (|Zero| (#7# 10 T CONST)) (>= #12=(#2# NIL #6# ELT)) (> #12#) (= (#2# 20 T ELT)) (<= #12#) (< (#2# 26 #6# ELT)) (/ (($ $ |#3|) 36 T ELT) (($ |#1| |#3|) 37 T ELT)) (- (#11# 17 T ELT) (#10# NIL T ELT)) (+ (#10# 29 T ELT)) (* (($ (|PositiveInteger|) $) NIL T ELT) (($ (|NonNegativeInteger|) $) NIL T ELT) (($ #5# $) 32 T ELT) (($ |#2| $) 34 T ELT) (($ $ |#2|) NIL T ELT))) (((|Localize| |#1| |#2| |#3|) (|Join| #1=(|Module| |#2|) (CATEGORY |domain| (IF (|has| |#1| #2=(|OrderedAbelianGroup|)) (ATTRIBUTE #2#) |%noBranch|) (SIGNATURE / ($ $ |#3|)) (SIGNATURE / ($ |#1| |#3|)) (SIGNATURE |numer| (|#1| $)) (SIGNATURE |denom| (|#3| $)))) #1# (|CommutativeRing|) (|SubsetCategory| (|Monoid|) |#2|)) (T |Localize|)) ((/ (*1 *1 *1 *2) (AND #1=(|ofCategory| *4 #2=(|CommutativeRing|)) #3=(|isDomain| *1 (|Localize| *3 *4 *2)) #4=(|ofCategory| *3 #5=(|Module| *4)) #6=(|ofCategory| *2 #7=(|SubsetCategory| #8=(|Monoid|) *4)))) (/ (*1 *1 *2 *3) (AND #1# (|isDomain| *1 (|Localize| *2 *4 *3)) (|ofCategory| *2 #5#) (|ofCategory| *3 #7#))) (|numer| #9=(*1 *2 *1) (AND (|ofCategory| *3 #2#) (|ofCategory| *2 (|Module| *3)) (|isDomain| *1 (|Localize| *2 *3 *4)) (|ofCategory| *4 (|SubsetCategory| #8# *3)))) (|denom| #9# (AND #1# #6# #3# #4#))) ((|solve| (((|Union| |#2| #1="failed") |#3| |#2| #2=(|Symbol|) |#2| #3=(|List| |#2|)) 174 T ELT) (((|Union| (|Record| (|:| |particular| |#2|) (|:| |basis| #3#)) #1#) |#3| |#2| #2#) 44 T ELT))) (((|ElementaryFunctionLODESolver| |#1| |#2| |#3|) (CATEGORY |package| (SIGNATURE |solve| ((|Union| (|Record| (|:| |particular| |#2|) (|:| |basis| #1=(|List| |#2|))) #2="failed") |#3| |#2| #3=(|Symbol|))) (SIGNATURE |solve| ((|Union| |#2| #2#) |#3| |#2| #3# |#2| #1#))) (|Join| (|EuclideanDomain|) (|RetractableTo| #4=(|Integer|)) (|LinearlyExplicitRingOver| #4#) (|CharacteristicZero|)) (|Join| (|AlgebraicallyClosedFunctionSpace| |#1|) (|TranscendentalFunctionCategory|) (|PrimitiveFunctionCategory|)) (|LinearOrdinaryDifferentialOperatorCategory| |#2|)) (T |ElementaryFunctionLODESolver|)) ((|solve| (*1 *2 *3 *2 *4 *2 *5) (|partial| AND (|isDomain| *4 #1=(|Symbol|)) (|isDomain| *5 (|List| *2)) (|ofCategory| *2 #2=(|Join| (|AlgebraicallyClosedFunctionSpace| *6) (|TranscendentalFunctionCategory|) (|PrimitiveFunctionCategory|))) #3=(|ofCategory| *6 (|Join| (|EuclideanDomain|) (|RetractableTo| #4=(|Integer|)) (|LinearlyExplicitRingOver| #4#) (|CharacteristicZero|))) (|isDomain| *1 (|ElementaryFunctionLODESolver| *6 *2 *3)) (|ofCategory| *3 (|LinearOrdinaryDifferentialOperatorCategory| *2)))) (|solve| (*1 *2 *3 *4 *5) (|partial| AND (|isDomain| *5 #1#) #3# (|ofCategory| *4 #2#) (|isDomain| *2 (|Record| (|:| |particular| *4) (|:| |basis| (|List| *4)))) (|isDomain| *1 (|ElementaryFunctionLODESolver| *6 *4 *3)) (|ofCategory| *3 (|LinearOrdinaryDifferentialOperatorCategory| *4))))) -((~= #1=((#2=(|Boolean|) $ $) NIL T ELT)) (|zero?| #3=((#2# $) NIL T ELT)) (|symmetricSquare| (#4=($ $) NIL #5=(|has| |#1| (|Field|)) ELT)) (|symmetricProduct| (#6=($ $ $) 28 #5# ELT)) (|symmetricPower| (#7=($ $ #8=(|NonNegativeInteger|)) 31 #5# ELT)) (|subtractIfCan| (#9=(#10=(|Union| $ #11="failed") $ $) NIL T ELT)) (|sample| (#12=($) NIL T CONST)) (|rightRemainder| #13=(#6# NIL #5# ELT)) (|rightQuotient| #13#) (|rightLcm| #13#) (|rightGcd| #13#) (|rightExtendedGcd| #14=(((|Record| (|:| |coef1| $) (|:| |coef2| $) (|:| |generator| $)) $ $) NIL #5# ELT)) (|rightExactQuotient| #15=(#9# NIL #5# ELT)) (|rightDivide| #16=(#17=((|Record| (|:| |quotient| $) (|:| |remainder| $)) $ $) NIL #5# ELT)) (|retractIfCan| (((|Union| #18=(|Integer|) . #19=(#11#)) . #20=($)) NIL #21=(|has| |#1| (|RetractableTo| #18#)) ELT) (((|Union| #22=(|Fraction| #18#) . #19#) . #20#) NIL #23=(|has| |#1| (|RetractableTo| #22#)) ELT) (((|Union| |#1| . #19#) . #20#) NIL T ELT)) (|retract| ((#18# . #24=($)) NIL #21# ELT) ((#22# . #24#) NIL #23# ELT) #25=(#26=(|#1| . #24#) NIL T ELT)) (|reductum| #27=(#4# NIL T ELT)) (|recip| ((#10# $) NIL T ELT)) (|primitivePart| (#4# NIL #28=(|has| |#1| (|GcdDomain|)) ELT)) (|opposite?| #1#) (|one?| #3#) (|monomial| (($ |#1| #8#) NIL T ELT)) (|monicRightDivide| #29=(#17# NIL #30=(|has| |#1| (|IntegralDomain|)) ELT)) (|monicLeftDivide| #29#) (|minimumDegree| #31=((#8# $) NIL T ELT)) (|leftRemainder| #13#) (|leftQuotient| #13#) (|leftLcm| #13#) (|leftGcd| #13#) (|leftExtendedGcd| #14#) (|leftExactQuotient| #15#) (|leftDivide| #16#) (|leadingCoefficient| #25#) (|latex| (((|String|) $) NIL T ELT)) (|hash| (((|SingleInteger|) $) NIL T ELT)) (|exquo| ((#10# $ |#1|) NIL #30# ELT)) (|elt| ((|#1| $ |#1|) 24 T ELT)) (|directSum| (#6# 33 #5# ELT)) (|degree| #31#) (|content| (#26# NIL #28# ELT)) (|coerce| (((|OutputForm|) $) 20 T ELT) (($ #18#) NIL T ELT) (($ #22#) NIL #23# ELT) (($ |#1|) NIL T ELT)) (|coefficients| (((|List| |#1|) $) NIL T ELT)) (|coefficient| ((|#1| $ #8#) NIL T ELT)) (|characteristic| ((#8#) NIL T CONST)) (|before?| #1#) (|apply| ((|#1| $ |#1| |#1|) 23 T ELT)) (|annihilate?| #1#) (|adjoint| #27#) (|Zero| (#12# 21 T CONST)) (|One| (#12# 8 T CONST)) (D (#12# NIL T ELT)) (= #1#) (- #27# #32=(#6# NIL T ELT)) (+ #32#) (** (($ $ #33=(|PositiveInteger|)) NIL T ELT) (#7# NIL T ELT)) (* (($ #33# $) NIL T ELT) (($ #8# $) NIL T ELT) (($ #18# . #34=($)) NIL T ELT) #32# (($ $ |#1|) NIL T ELT) (($ |#1| . #34#) NIL T ELT))) +((~= #1=((#2=(|Boolean|) $ $) NIL T ELT)) (|zero?| #3=((#2# $) NIL T ELT)) (|symmetricSquare| (#4=($ $) NIL #5=(|has| |#1| (|Field|)) ELT)) (|symmetricProduct| (#6=($ $ $) 28 #5# ELT)) (|symmetricPower| (#7=($ $ #8=(|NonNegativeInteger|)) 31 #5# ELT)) (|subtractIfCan| (((|Maybe| $) $ $) NIL T ELT)) (|sample| (#9=($) NIL T CONST)) (|rightRemainder| #10=(#6# NIL #5# ELT)) (|rightQuotient| #10#) (|rightLcm| #10#) (|rightGcd| #10#) (|rightExtendedGcd| #11=(((|Record| (|:| |coef1| $) (|:| |coef2| $) (|:| |generator| $)) $ $) NIL #5# ELT)) (|rightExactQuotient| #12=((#13=(|Union| $ #14="failed") $ $) NIL #5# ELT)) (|rightDivide| #15=(#16=((|Record| (|:| |quotient| $) (|:| |remainder| $)) $ $) NIL #5# ELT)) (|retractIfCan| (((|Union| #17=(|Integer|) . #18=(#14#)) . #19=($)) NIL #20=(|has| |#1| (|RetractableTo| #17#)) ELT) (((|Union| #21=(|Fraction| #17#) . #18#) . #19#) NIL #22=(|has| |#1| (|RetractableTo| #21#)) ELT) (((|Union| |#1| . #18#) . #19#) NIL T ELT)) (|retract| ((#17# . #23=($)) NIL #20# ELT) ((#21# . #23#) NIL #22# ELT) #24=(#25=(|#1| . #23#) NIL T ELT)) (|reductum| #26=(#4# NIL T ELT)) (|recip| ((#13# $) NIL T ELT)) (|primitivePart| (#4# NIL #27=(|has| |#1| (|GcdDomain|)) ELT)) (|opposite?| #1#) (|one?| #3#) (|monomial| (($ |#1| #8#) NIL T ELT)) (|monicRightDivide| #28=(#16# NIL #29=(|has| |#1| (|IntegralDomain|)) ELT)) (|monicLeftDivide| #28#) (|minimumDegree| #30=((#8# $) NIL T ELT)) (|leftRemainder| #10#) (|leftQuotient| #10#) (|leftLcm| #10#) (|leftGcd| #10#) (|leftExtendedGcd| #11#) (|leftExactQuotient| #12#) (|leftDivide| #15#) (|leadingCoefficient| #24#) (|latex| (((|String|) $) NIL T ELT)) (|hash| (((|SingleInteger|) $) NIL T ELT)) (|exquo| ((#13# $ |#1|) NIL #29# ELT)) (|elt| ((|#1| $ |#1|) 24 T ELT)) (|directSum| (#6# 33 #5# ELT)) (|degree| #30#) (|content| (#25# NIL #27# ELT)) (|coerce| (((|OutputForm|) $) 20 T ELT) (($ #17#) NIL T ELT) (($ #21#) NIL #22# ELT) (($ |#1|) NIL T ELT)) (|coefficients| (((|List| |#1|) $) NIL T ELT)) (|coefficient| ((|#1| $ #8#) NIL T ELT)) (|characteristic| ((#8#) NIL T CONST)) (|before?| #1#) (|apply| ((|#1| $ |#1| |#1|) 23 T ELT)) (|annihilate?| #1#) (|adjoint| #26#) (|Zero| (#9# 21 T CONST)) (|One| (#9# 8 T CONST)) (D (#9# NIL T ELT)) (= #1#) (- #26# #31=(#6# NIL T ELT)) (+ #31#) (** (($ $ #32=(|PositiveInteger|)) NIL T ELT) (#7# NIL T ELT)) (* (($ #32# $) NIL T ELT) (($ #8# $) NIL T ELT) (($ #17# . #33=($)) NIL T ELT) #31# (($ $ |#1|) NIL T ELT) (($ |#1| . #33#) NIL T ELT))) (((|LinearOrdinaryDifferentialOperator| |#1| |#2|) (|LinearOrdinaryDifferentialOperatorCategory| |#1|) (|Ring|) (|Mapping| |#1| |#1|)) (T |LinearOrdinaryDifferentialOperator|)) NIL -((~= #1=((#2=(|Boolean|) $ $) NIL T ELT)) (|zero?| #3=((#2# $) NIL T ELT)) (|symmetricSquare| (#4=($ $) NIL #5=(|has| |#1| (|Field|)) ELT)) (|symmetricProduct| #6=(#7=($ $ $) NIL #5# ELT)) (|symmetricPower| (#8=($ $ #9=(|NonNegativeInteger|)) NIL #5# ELT)) (|subtractIfCan| (#10=(#11=(|Union| $ #12="failed") $ $) NIL T ELT)) (|sample| #13=(#14=($) NIL T CONST)) (|rightRemainder| #6#) (|rightQuotient| #6#) (|rightLcm| #6#) (|rightGcd| #6#) (|rightExtendedGcd| #15=(((|Record| (|:| |coef1| $) (|:| |coef2| $) (|:| |generator| $)) $ $) NIL #5# ELT)) (|rightExactQuotient| #16=(#10# NIL #5# ELT)) (|rightDivide| #17=(#18=((|Record| (|:| |quotient| $) (|:| |remainder| $)) $ $) NIL #5# ELT)) (|retractIfCan| (((|Union| #19=(|Integer|) . #20=(#12#)) . #21=($)) NIL #22=(|has| |#1| (|RetractableTo| #19#)) ELT) (((|Union| #23=(|Fraction| #19#) . #20#) . #21#) NIL #24=(|has| |#1| (|RetractableTo| #23#)) ELT) (((|Union| |#1| . #20#) . #21#) NIL T ELT)) (|retract| ((#19# . #25=($)) NIL #22# ELT) ((#23# . #25#) NIL #24# ELT) #26=(#27=(|#1| . #25#) NIL T ELT)) (|reductum| #28=(#4# NIL T ELT)) (|recip| ((#11# $) NIL T ELT)) (|primitivePart| (#4# NIL #29=(|has| |#1| (|GcdDomain|)) ELT)) (|opposite?| #1#) (|one?| #3#) (|monomial| (($ |#1| #9#) NIL T ELT)) (|monicRightDivide| #30=(#18# NIL #31=(|has| |#1| (|IntegralDomain|)) ELT)) (|monicLeftDivide| #30#) (|minimumDegree| #32=((#9# $) NIL T ELT)) (|leftRemainder| #6#) (|leftQuotient| #6#) (|leftLcm| #6#) (|leftGcd| #6#) (|leftExtendedGcd| #15#) (|leftExactQuotient| #16#) (|leftDivide| #17#) (|leadingCoefficient| #26#) (|latex| (((|String|) $) NIL T ELT)) (|hash| (((|SingleInteger|) $) NIL T ELT)) (|exquo| ((#11# $ |#1|) NIL #31# ELT)) (|elt| ((|#1| $ |#1|) NIL T ELT)) (|directSum| #6#) (|degree| #32#) (|content| (#27# NIL #29# ELT)) (|coerce| (((|OutputForm|) $) NIL T ELT) (($ #19#) NIL T ELT) (($ #23#) NIL #24# ELT) (($ |#1|) NIL T ELT)) (|coefficients| (((|List| |#1|) $) NIL T ELT)) (|coefficient| ((|#1| $ #9#) NIL T ELT)) (|characteristic| ((#9#) NIL T CONST)) (|before?| #1#) (|apply| ((|#1| $ |#1| |#1|) NIL T ELT)) (|annihilate?| #1#) (|adjoint| #28#) (|Zero| #13#) (|One| #13#) (D (#14# NIL T ELT)) (= #1#) (- #28# #33=(#7# NIL T ELT)) (+ #33#) (** (($ $ #34=(|PositiveInteger|)) NIL T ELT) (#8# NIL T ELT)) (* (($ #34# $) NIL T ELT) (($ #9# $) NIL T ELT) (($ #19# . #35=($)) NIL T ELT) #33# (($ $ |#1|) NIL T ELT) (($ |#1| . #35#) NIL T ELT))) +((~= #1=((#2=(|Boolean|) $ $) NIL T ELT)) (|zero?| #3=((#2# $) NIL T ELT)) (|symmetricSquare| (#4=($ $) NIL #5=(|has| |#1| (|Field|)) ELT)) (|symmetricProduct| #6=(#7=($ $ $) NIL #5# ELT)) (|symmetricPower| (#8=($ $ #9=(|NonNegativeInteger|)) NIL #5# ELT)) (|subtractIfCan| (((|Maybe| $) $ $) NIL T ELT)) (|sample| #10=(#11=($) NIL T CONST)) (|rightRemainder| #6#) (|rightQuotient| #6#) (|rightLcm| #6#) (|rightGcd| #6#) (|rightExtendedGcd| #12=(((|Record| (|:| |coef1| $) (|:| |coef2| $) (|:| |generator| $)) $ $) NIL #5# ELT)) (|rightExactQuotient| #13=((#14=(|Union| $ #15="failed") $ $) NIL #5# ELT)) (|rightDivide| #16=(#17=((|Record| (|:| |quotient| $) (|:| |remainder| $)) $ $) NIL #5# ELT)) (|retractIfCan| (((|Union| #18=(|Integer|) . #19=(#15#)) . #20=($)) NIL #21=(|has| |#1| (|RetractableTo| #18#)) ELT) (((|Union| #22=(|Fraction| #18#) . #19#) . #20#) NIL #23=(|has| |#1| (|RetractableTo| #22#)) ELT) (((|Union| |#1| . #19#) . #20#) NIL T ELT)) (|retract| ((#18# . #24=($)) NIL #21# ELT) ((#22# . #24#) NIL #23# ELT) #25=(#26=(|#1| . #24#) NIL T ELT)) (|reductum| #27=(#4# NIL T ELT)) (|recip| ((#14# $) NIL T ELT)) (|primitivePart| (#4# NIL #28=(|has| |#1| (|GcdDomain|)) ELT)) (|opposite?| #1#) (|one?| #3#) (|monomial| (($ |#1| #9#) NIL T ELT)) (|monicRightDivide| #29=(#17# NIL #30=(|has| |#1| (|IntegralDomain|)) ELT)) (|monicLeftDivide| #29#) (|minimumDegree| #31=((#9# $) NIL T ELT)) (|leftRemainder| #6#) (|leftQuotient| #6#) (|leftLcm| #6#) (|leftGcd| #6#) (|leftExtendedGcd| #12#) (|leftExactQuotient| #13#) (|leftDivide| #16#) (|leadingCoefficient| #25#) (|latex| (((|String|) $) NIL T ELT)) (|hash| (((|SingleInteger|) $) NIL T ELT)) (|exquo| ((#14# $ |#1|) NIL #30# ELT)) (|elt| ((|#1| $ |#1|) NIL T ELT)) (|directSum| #6#) (|degree| #31#) (|content| (#26# NIL #28# ELT)) (|coerce| (((|OutputForm|) $) NIL T ELT) (($ #18#) NIL T ELT) (($ #22#) NIL #23# ELT) (($ |#1|) NIL T ELT)) (|coefficients| (((|List| |#1|) $) NIL T ELT)) (|coefficient| ((|#1| $ #9#) NIL T ELT)) (|characteristic| ((#9#) NIL T CONST)) (|before?| #1#) (|apply| ((|#1| $ |#1| |#1|) NIL T ELT)) (|annihilate?| #1#) (|adjoint| #27#) (|Zero| #10#) (|One| #10#) (D (#11# NIL T ELT)) (= #1#) (- #27# #32=(#7# NIL T ELT)) (+ #32#) (** (($ $ #33=(|PositiveInteger|)) NIL T ELT) (#8# NIL T ELT)) (* (($ #33# $) NIL T ELT) (($ #9# $) NIL T ELT) (($ #18# . #34=($)) NIL T ELT) #32# (($ $ |#1|) NIL T ELT) (($ |#1| . #34#) NIL T ELT))) (((|LinearOrdinaryDifferentialOperator1| |#1|) (|LinearOrdinaryDifferentialOperatorCategory| |#1|) (|DifferentialRing|)) (T |LinearOrdinaryDifferentialOperator1|)) NIL -((~= #1=((#2=(|Boolean|) $ $) NIL T ELT)) (|zero?| #3=((#2# $) NIL T ELT)) (|symmetricSquare| (#4=($ $) NIL #5=(|has| |#1| (|Field|)) ELT)) (|symmetricProduct| #6=(#7=($ $ $) NIL #5# ELT)) (|symmetricPower| (#8=($ $ #9=(|NonNegativeInteger|)) NIL #5# ELT)) (|subtractIfCan| (#10=(#11=(|Union| $ #12="failed") $ $) NIL T ELT)) (|sample| #13=(#14=($) NIL T CONST)) (|rightRemainder| #6#) (|rightQuotient| #6#) (|rightLcm| #6#) (|rightGcd| #6#) (|rightExtendedGcd| #15=(((|Record| (|:| |coef1| $) (|:| |coef2| $) (|:| |generator| $)) $ $) NIL #5# ELT)) (|rightExactQuotient| #16=(#10# NIL #5# ELT)) (|rightDivide| #17=(#18=((|Record| (|:| |quotient| $) (|:| |remainder| $)) $ $) NIL #5# ELT)) (|retractIfCan| (((|Union| #19=(|Integer|) . #20=(#12#)) . #21=($)) NIL #22=(|has| |#1| (|RetractableTo| #19#)) ELT) (((|Union| #23=(|Fraction| #19#) . #20#) . #21#) NIL #24=(|has| |#1| (|RetractableTo| #23#)) ELT) (((|Union| |#1| . #20#) . #21#) NIL T ELT)) (|retract| ((#19# . #25=($)) NIL #22# ELT) ((#23# . #25#) NIL #24# ELT) #26=(#27=(|#1| . #25#) NIL T ELT)) (|reductum| #28=(#4# NIL T ELT)) (|recip| ((#11# $) NIL T ELT)) (|primitivePart| (#4# NIL #29=(|has| |#1| (|GcdDomain|)) ELT)) (|opposite?| #1#) (|one?| #3#) (|monomial| (($ |#1| #9#) NIL T ELT)) (|monicRightDivide| #30=(#18# NIL #31=(|has| |#1| (|IntegralDomain|)) ELT)) (|monicLeftDivide| #30#) (|minimumDegree| #32=((#9# $) NIL T ELT)) (|leftRemainder| #6#) (|leftQuotient| #6#) (|leftLcm| #6#) (|leftGcd| #6#) (|leftExtendedGcd| #15#) (|leftExactQuotient| #16#) (|leftDivide| #17#) (|leadingCoefficient| #26#) (|latex| (((|String|) $) NIL T ELT)) (|hash| (((|SingleInteger|) $) NIL T ELT)) (|exquo| ((#11# $ |#1|) NIL #31# ELT)) (|elt| ((|#1| $ |#1|) NIL T ELT) ((|#2| $ |#2|) 13 T ELT)) (|directSum| #6#) (|degree| #32#) (|content| (#27# NIL #29# ELT)) (|coerce| (((|OutputForm|) $) NIL T ELT) (($ #19#) NIL T ELT) (($ #23#) NIL #24# ELT) (($ |#1|) NIL T ELT)) (|coefficients| (((|List| |#1|) $) NIL T ELT)) (|coefficient| ((|#1| $ #9#) NIL T ELT)) (|characteristic| ((#9#) NIL T CONST)) (|before?| #1#) (|apply| ((|#1| $ |#1| |#1|) NIL T ELT)) (|annihilate?| #1#) (|adjoint| #28#) (|Zero| #13#) (|One| #13#) (D (#14# NIL T ELT)) (= #1#) (- #28# #33=(#7# NIL T ELT)) (+ #33#) (** (($ $ #34=(|PositiveInteger|)) NIL T ELT) (#8# NIL T ELT)) (* (($ #34# $) NIL T ELT) (($ #9# $) NIL T ELT) (($ #19# . #35=($)) NIL T ELT) #33# (($ $ |#1|) NIL T ELT) (($ |#1| . #35#) NIL T ELT))) +((~= #1=((#2=(|Boolean|) $ $) NIL T ELT)) (|zero?| #3=((#2# $) NIL T ELT)) (|symmetricSquare| (#4=($ $) NIL #5=(|has| |#1| (|Field|)) ELT)) (|symmetricProduct| #6=(#7=($ $ $) NIL #5# ELT)) (|symmetricPower| (#8=($ $ #9=(|NonNegativeInteger|)) NIL #5# ELT)) (|subtractIfCan| (((|Maybe| $) $ $) NIL T ELT)) (|sample| #10=(#11=($) NIL T CONST)) (|rightRemainder| #6#) (|rightQuotient| #6#) (|rightLcm| #6#) (|rightGcd| #6#) (|rightExtendedGcd| #12=(((|Record| (|:| |coef1| $) (|:| |coef2| $) (|:| |generator| $)) $ $) NIL #5# ELT)) (|rightExactQuotient| #13=((#14=(|Union| $ #15="failed") $ $) NIL #5# ELT)) (|rightDivide| #16=(#17=((|Record| (|:| |quotient| $) (|:| |remainder| $)) $ $) NIL #5# ELT)) (|retractIfCan| (((|Union| #18=(|Integer|) . #19=(#15#)) . #20=($)) NIL #21=(|has| |#1| (|RetractableTo| #18#)) ELT) (((|Union| #22=(|Fraction| #18#) . #19#) . #20#) NIL #23=(|has| |#1| (|RetractableTo| #22#)) ELT) (((|Union| |#1| . #19#) . #20#) NIL T ELT)) (|retract| ((#18# . #24=($)) NIL #21# ELT) ((#22# . #24#) NIL #23# ELT) #25=(#26=(|#1| . #24#) NIL T ELT)) (|reductum| #27=(#4# NIL T ELT)) (|recip| ((#14# $) NIL T ELT)) (|primitivePart| (#4# NIL #28=(|has| |#1| (|GcdDomain|)) ELT)) (|opposite?| #1#) (|one?| #3#) (|monomial| (($ |#1| #9#) NIL T ELT)) (|monicRightDivide| #29=(#17# NIL #30=(|has| |#1| (|IntegralDomain|)) ELT)) (|monicLeftDivide| #29#) (|minimumDegree| #31=((#9# $) NIL T ELT)) (|leftRemainder| #6#) (|leftQuotient| #6#) (|leftLcm| #6#) (|leftGcd| #6#) (|leftExtendedGcd| #12#) (|leftExactQuotient| #13#) (|leftDivide| #16#) (|leadingCoefficient| #25#) (|latex| (((|String|) $) NIL T ELT)) (|hash| (((|SingleInteger|) $) NIL T ELT)) (|exquo| ((#14# $ |#1|) NIL #30# ELT)) (|elt| ((|#1| $ |#1|) NIL T ELT) ((|#2| $ |#2|) 13 T ELT)) (|directSum| #6#) (|degree| #31#) (|content| (#26# NIL #28# ELT)) (|coerce| (((|OutputForm|) $) NIL T ELT) (($ #18#) NIL T ELT) (($ #22#) NIL #23# ELT) (($ |#1|) NIL T ELT)) (|coefficients| (((|List| |#1|) $) NIL T ELT)) (|coefficient| ((|#1| $ #9#) NIL T ELT)) (|characteristic| ((#9#) NIL T CONST)) (|before?| #1#) (|apply| ((|#1| $ |#1| |#1|) NIL T ELT)) (|annihilate?| #1#) (|adjoint| #27#) (|Zero| #10#) (|One| #10#) (D (#11# NIL T ELT)) (= #1#) (- #27# #32=(#7# NIL T ELT)) (+ #32#) (** (($ $ #33=(|PositiveInteger|)) NIL T ELT) (#8# NIL T ELT)) (* (($ #33# $) NIL T ELT) (($ #9# $) NIL T ELT) (($ #18# . #34=($)) NIL T ELT) #32# (($ $ |#1|) NIL T ELT) (($ |#1| . #34#) NIL T ELT))) (((|LinearOrdinaryDifferentialOperator2| |#1| |#2|) (|Join| (|LinearOrdinaryDifferentialOperatorCategory| |#1|) (|Eltable| |#2| |#2|)) (|DifferentialRing|) (|Join| (|LeftModule| |#1|) (CATEGORY |domain| (SIGNATURE |differentiate| ($ $))))) (T |LinearOrdinaryDifferentialOperator2|)) NIL ((|symmetricSquare| (#1=($ $) 29 T ELT)) (|adjoint| (#1# 27 T ELT)) (D (($) 13 T ELT))) (((|LinearOrdinaryDifferentialOperatorCategory&| |#1| |#2|) (CATEGORY |package| (SIGNATURE |symmetricSquare| #1=(|#1| |#1|)) (SIGNATURE |adjoint| #1#) (SIGNATURE D (|#1|))) (|LinearOrdinaryDifferentialOperatorCategory| |#2|) (|Ring|)) (T |LinearOrdinaryDifferentialOperatorCategory&|)) NIL -((~= (#1=((|Boolean|) $ $) 7 T ELT)) (|zero?| ((#2=(|Boolean|) $) 22 T ELT)) (|symmetricSquare| (($ $) 96 (|has| |#1| (|Field|)) ELT)) (|symmetricProduct| (($ $ $) 98 (|has| |#1| (|Field|)) ELT)) (|symmetricPower| (($ $ (|NonNegativeInteger|)) 97 (|has| |#1| (|Field|)) ELT)) (|subtractIfCan| (((|Union| $ "failed") $ $) 26 T ELT)) (|sample| (#3=($) 23 T CONST)) (|rightRemainder| (#4=($ $ $) 58 (|has| |#1| . #5=((|Field|))) ELT)) (|rightQuotient| (#4# 59 (|has| |#1| . #5#) ELT)) (|rightLcm| (#4# 61 (|has| |#1| . #5#) ELT)) (|rightGcd| (#4# 56 (|has| |#1| . #5#) ELT)) (|rightExtendedGcd| (#6=((|Record| (|:| |coef1| $) (|:| |coef2| $) (|:| |generator| $)) $ $) 55 (|has| |#1| . #5#) ELT)) (|rightExactQuotient| (#7=(#8=(|Union| $ "failed") $ $) 57 (|has| |#1| . #5#) ELT)) (|rightDivide| (#9=((|Record| (|:| |quotient| $) (|:| |remainder| $)) $ $) 60 (|has| |#1| . #5#) ELT)) (|retractIfCan| (((|Union| #10=(|Integer|) . #11=("failed")) . #12=($)) 88 (|has| |#1| . #13=((|RetractableTo| #10#))) ELT) (((|Union| #14=(|Fraction| #10#) . #11#) . #12#) 85 (|has| |#1| . #15=((|RetractableTo| #14#))) ELT) (((|Union| |#1| . #11#) . #12#) 82 T ELT)) (|retract| ((#10# . #16=($)) 87 (|has| |#1| . #13#) ELT) ((#14# . #16#) 84 (|has| |#1| . #15#) ELT) ((|#1| . #16#) 83 T ELT)) (|reductum| (#17=($ $) 77 T ELT)) (|recip| (((|Union| $ "failed") $) 42 T ELT)) (|primitivePart| (#17# 68 (|has| |#1| . #18=((|GcdDomain|))) ELT)) (|opposite?| ((#2# $ $) 20 T ELT)) (|one?| (((|Boolean|) $) 44 T ELT)) (|monomial| (($ |#1| #19=(|NonNegativeInteger|)) 75 T ELT)) (|monicRightDivide| (#9# 70 (|has| |#1| . #20=((|IntegralDomain|))) ELT)) (|monicLeftDivide| (#9# 71 (|has| |#1| . #20#) ELT)) (|minimumDegree| (#21=(#19# $) 79 T ELT)) (|leftRemainder| (#4# 65 (|has| |#1| . #5#) ELT)) (|leftQuotient| (#4# 66 (|has| |#1| . #5#) ELT)) (|leftLcm| (#4# 54 (|has| |#1| . #5#) ELT)) (|leftGcd| (#4# 63 (|has| |#1| . #5#) ELT)) (|leftExtendedGcd| (#6# 62 (|has| |#1| . #5#) ELT)) (|leftExactQuotient| (#7# 64 (|has| |#1| . #5#) ELT)) (|leftDivide| (#9# 67 (|has| |#1| . #5#) ELT)) (|leadingCoefficient| ((|#1| . #22=($)) 78 T ELT)) (|latex| (((|String|) $) 11 T ELT)) (|hash| (((|SingleInteger|) $) 12 T ELT)) (|exquo| ((#8# $ |#1|) 72 (|has| |#1| . #20#) ELT)) (|elt| ((|#1| $ |#1|) 101 T ELT)) (|directSum| (($ $ $) 95 (|has| |#1| (|Field|)) ELT)) (|degree| (#21# 80 T ELT)) (|content| ((|#1| . #22#) 69 (|has| |#1| . #18#) ELT)) (|coerce| (((|OutputForm|) $) 13 T ELT) (($ (|Integer|)) 41 T ELT) (($ #14#) 86 (|has| |#1| . #15#) ELT) (($ |#1|) 81 T ELT)) (|coefficients| (((|List| |#1|) $) 74 T ELT)) (|coefficient| ((|#1| $ #19#) 76 T ELT)) (|characteristic| (((|NonNegativeInteger|)) 40 T CONST)) (|before?| (#1# 6 T ELT)) (|apply| ((|#1| $ |#1| |#1|) 73 T ELT)) (|annihilate?| (((|Boolean|) $ $) 33 T ELT)) (|adjoint| (($ $) 99 T ELT)) (|Zero| (#3# 24 T CONST)) (|One| (($) 45 T CONST)) (D (($) 100 T ELT)) (= (#1# 8 T ELT)) (- (($ $) 29 T ELT) (($ $ $) 28 T ELT)) (+ (($ $ $) 18 T ELT)) (** (($ $ (|PositiveInteger|)) 35 T ELT) (($ $ (|NonNegativeInteger|)) 43 T ELT)) (* (($ (|PositiveInteger|) $) 17 T ELT) (($ (|NonNegativeInteger|) $) 21 T ELT) (($ (|Integer|) . #23=($)) 30 T ELT) (($ $ $) 34 T ELT) (($ $ |#1|) 90 T ELT) (($ |#1| . #23#) 89 T ELT))) +((~= (#1=((|Boolean|) $ $) 7 T ELT)) (|zero?| ((#2=(|Boolean|) $) 22 T ELT)) (|symmetricSquare| (($ $) 97 (|has| |#1| (|Field|)) ELT)) (|symmetricProduct| (($ $ $) 99 (|has| |#1| (|Field|)) ELT)) (|symmetricPower| (($ $ (|NonNegativeInteger|)) 98 (|has| |#1| (|Field|)) ELT)) (|subtractIfCan| (((|Maybe| $) $ $) 26 T ELT)) (|sample| (#3=($) 23 T CONST)) (|rightRemainder| (#4=($ $ $) 59 (|has| |#1| . #5=((|Field|))) ELT)) (|rightQuotient| (#4# 60 (|has| |#1| . #5#) ELT)) (|rightLcm| (#4# 62 (|has| |#1| . #5#) ELT)) (|rightGcd| (#4# 57 (|has| |#1| . #5#) ELT)) (|rightExtendedGcd| (#6=((|Record| (|:| |coef1| $) (|:| |coef2| $) (|:| |generator| $)) $ $) 56 (|has| |#1| . #5#) ELT)) (|rightExactQuotient| (#7=(#8=(|Union| $ "failed") $ $) 58 (|has| |#1| . #5#) ELT)) (|rightDivide| (#9=((|Record| (|:| |quotient| $) (|:| |remainder| $)) $ $) 61 (|has| |#1| . #5#) ELT)) (|retractIfCan| (((|Union| #10=(|Integer|) . #11=("failed")) . #12=($)) 89 (|has| |#1| . #13=((|RetractableTo| #10#))) ELT) (((|Union| #14=(|Fraction| #10#) . #11#) . #12#) 86 (|has| |#1| . #15=((|RetractableTo| #14#))) ELT) (((|Union| |#1| . #11#) . #12#) 83 T ELT)) (|retract| ((#10# . #16=($)) 88 (|has| |#1| . #13#) ELT) ((#14# . #16#) 85 (|has| |#1| . #15#) ELT) ((|#1| . #16#) 84 T ELT)) (|reductum| (#17=($ $) 78 T ELT)) (|recip| (((|Union| $ "failed") $) 43 T ELT)) (|primitivePart| (#17# 69 (|has| |#1| . #18=((|GcdDomain|))) ELT)) (|opposite?| ((#2# $ $) 20 T ELT)) (|one?| (((|Boolean|) $) 45 T ELT)) (|monomial| (($ |#1| #19=(|NonNegativeInteger|)) 76 T ELT)) (|monicRightDivide| (#9# 71 (|has| |#1| . #20=((|IntegralDomain|))) ELT)) (|monicLeftDivide| (#9# 72 (|has| |#1| . #20#) ELT)) (|minimumDegree| (#21=(#19# $) 80 T ELT)) (|leftRemainder| (#4# 66 (|has| |#1| . #5#) ELT)) (|leftQuotient| (#4# 67 (|has| |#1| . #5#) ELT)) (|leftLcm| (#4# 55 (|has| |#1| . #5#) ELT)) (|leftGcd| (#4# 64 (|has| |#1| . #5#) ELT)) (|leftExtendedGcd| (#6# 63 (|has| |#1| . #5#) ELT)) (|leftExactQuotient| (#7# 65 (|has| |#1| . #5#) ELT)) (|leftDivide| (#9# 68 (|has| |#1| . #5#) ELT)) (|leadingCoefficient| ((|#1| . #22=($)) 79 T ELT)) (|latex| (((|String|) $) 11 T ELT)) (|hash| (((|SingleInteger|) $) 12 T ELT)) (|exquo| ((#8# $ |#1|) 73 (|has| |#1| . #20#) ELT)) (|elt| ((|#1| $ |#1|) 102 T ELT)) (|directSum| (($ $ $) 96 (|has| |#1| (|Field|)) ELT)) (|degree| (#21# 81 T ELT)) (|content| ((|#1| . #22#) 70 (|has| |#1| . #18#) ELT)) (|coerce| (((|OutputForm|) $) 13 T ELT) (($ (|Integer|)) 42 T ELT) (($ #14#) 87 (|has| |#1| . #15#) ELT) (($ |#1|) 82 T ELT)) (|coefficients| (((|List| |#1|) $) 75 T ELT)) (|coefficient| ((|#1| $ #19#) 77 T ELT)) (|characteristic| (((|NonNegativeInteger|)) 41 T CONST)) (|before?| (#1# 6 T ELT)) (|apply| ((|#1| $ |#1| |#1|) 74 T ELT)) (|annihilate?| (((|Boolean|) $ $) 34 T ELT)) (|adjoint| (($ $) 100 T ELT)) (|Zero| (#3# 24 T CONST)) (|One| (($) 46 T CONST)) (D (($) 101 T ELT)) (= (#1# 8 T ELT)) (- (($ $) 30 T ELT) (($ $ $) 29 T ELT)) (+ (($ $ $) 18 T ELT)) (** (($ $ (|PositiveInteger|)) 36 T ELT) (($ $ (|NonNegativeInteger|)) 44 T ELT)) (* (($ (|PositiveInteger|) $) 17 T ELT) (($ (|NonNegativeInteger|) $) 21 T ELT) (($ (|Integer|) . #23=($)) 31 T ELT) (($ $ $) 35 T ELT) (($ $ |#1|) 91 T ELT) (($ |#1| . #23#) 90 T ELT))) (((|LinearOrdinaryDifferentialOperatorCategory| |#1|) (|Category|) (|Ring|)) (T |LinearOrdinaryDifferentialOperatorCategory|)) ((D (*1 *1) (AND (|ofCategory| *1 (|LinearOrdinaryDifferentialOperatorCategory| *2)) (|ofCategory| *2 (|Ring|)))) (|adjoint| (*1 *1 *1) (AND (|ofCategory| *1 (|LinearOrdinaryDifferentialOperatorCategory| *2)) (|ofCategory| *2 (|Ring|)))) (|symmetricProduct| (*1 *1 *1 *1) (AND (|ofCategory| *1 (|LinearOrdinaryDifferentialOperatorCategory| *2)) (|ofCategory| *2 (|Ring|)) (|ofCategory| *2 (|Field|)))) (|symmetricPower| (*1 *1 *1 *2) (AND (|isDomain| *2 (|NonNegativeInteger|)) (|ofCategory| *1 (|LinearOrdinaryDifferentialOperatorCategory| *3)) (|ofCategory| *3 (|Ring|)) (|ofCategory| *3 (|Field|)))) (|symmetricSquare| (*1 *1 *1) (AND (|ofCategory| *1 (|LinearOrdinaryDifferentialOperatorCategory| *2)) (|ofCategory| *2 (|Ring|)) (|ofCategory| *2 (|Field|)))) (|directSum| (*1 *1 *1 *1) (AND (|ofCategory| *1 (|LinearOrdinaryDifferentialOperatorCategory| *2)) (|ofCategory| *2 (|Ring|)) (|ofCategory| *2 (|Field|))))) (|Join| (|UnivariateSkewPolynomialCategory| |t#1|) (|Eltable| |t#1| |t#1|) (CATEGORY |domain| (SIGNATURE D ($)) (SIGNATURE |adjoint| ($ $)) (IF (|has| |t#1| (|Field|)) (PROGN (SIGNATURE |symmetricProduct| ($ $ $)) (SIGNATURE |symmetricPower| ($ $ (|NonNegativeInteger|))) (SIGNATURE |symmetricSquare| ($ $)) (SIGNATURE |directSum| ($ $ $))) |%noBranch|))) @@ -2005,7 +2008,7 @@ NIL ((|solveLinearPolynomialEquationByFractions| (((|Union| #1=(|List| #2=(|SparseUnivariatePolynomial| |#1|)) "failed") #1# #2#) 33 T ELT))) (((|LinearPolynomialEquationByFractions| |#1|) (CATEGORY |package| (SIGNATURE |solveLinearPolynomialEquationByFractions| ((|Union| #1=(|List| #2=(|SparseUnivariatePolynomial| |#1|)) "failed") #1# #2#))) (|PolynomialFactorizationExplicit|)) (T |LinearPolynomialEquationByFractions|)) ((|solveLinearPolynomialEquationByFractions| (*1 *2 *2 *3) (|partial| AND (|isDomain| *2 (|List| #1=(|SparseUnivariatePolynomial| *4))) (|isDomain| *3 #1#) (|ofCategory| *4 (|PolynomialFactorizationExplicit|)) (|isDomain| *1 (|LinearPolynomialEquationByFractions| *4))))) -((~= #1=(#2=(#3=(|Boolean|) $ $) NIL T ELT)) (|zero?| #4=((#3# $) NIL T ELT)) (|varList| ((#5=(|List| |#1|) $) 85 T ELT)) (|trunc| (($ $ #6=(|NonNegativeInteger|)) 95 T ELT)) (|subtractIfCan| ((#7=(|Union| $ #8="failed") $ $) NIL T ELT)) (|sample| (#9=($) NIL T CONST)) (|rquo| (#10=(#11=(|XRecursivePolynomial| |#1| |#2|) #11# $) 50 T ELT)) (|retractIfCan| (((|Union| #12=(|LyndonWord| |#1|) #8#) $) NIL T ELT)) (|retract| #13=((#12# $) NIL T ELT)) (|reductum| (#14=($ $) 94 T ELT)) (|opposite?| #1#) (|numberOfMonomials| (#15=(#6# $) NIL T ELT)) (|monomials| ((#16=(|List| $) $) NIL T ELT)) (|monomial?| #4#) (|monom| (($ #12# |#2|) 70 T ELT)) (|mirror| (#14# 90 T ELT)) (|map| (($ (|Mapping| |#2| |#2|) $) NIL T ELT)) (|lquo| (#10# 49 T ELT)) (|leadingTerm| ((#17=(|Record| (|:| |k| #12#) (|:| |c| |#2|)) $) NIL T ELT)) (|leadingMonomial| #13#) (|leadingCoefficient| ((|#2| $) NIL T ELT)) (|latex| (((|String|) $) NIL T ELT)) (|hash| (((|SingleInteger|) $) NIL T ELT)) (|eval| (($ $ |#1| $) 32 T ELT) (($ $ #5# #16#) 34 T ELT)) (|degree| (#15# 92 T ELT)) (|construct| (#18=($ $ $) 20 T ELT) (($ #12# #12#) 79 T ELT) (($ #12# $) 77 T ELT) (($ $ #12#) 78 T ELT)) (|coerce| (((|OutputForm|) $) NIL T ELT) (($ |#1|) 76 T ELT) ((#19=(|XDistributedPolynomial| |#1| |#2|) $) 60 T ELT) ((#11# $) 43 T ELT) (#20=($ #12#) 27 T ELT)) (|coefficients| (((|List| |#2|) $) NIL T ELT)) (|coefficient| ((|#2| $ #12#) NIL T ELT)) (|coef| ((|#2| #11# $) 45 T ELT)) (|before?| #1#) (|Zero| (#9# 23 T CONST)) (|ListOfTerms| (((|List| #17#) $) NIL T ELT)) (|LiePolyIfCan| ((#7# #19#) 62 T ELT)) (|LiePoly| (#20# 14 T ELT)) (= (#2# 46 T ELT)) (/ (#21=($ $ |#2|) NIL (|has| |#2| (|Field|)) ELT)) (- (#14# 68 T ELT) (#18# NIL T ELT)) (+ (#18# 31 T ELT)) (* (($ (|PositiveInteger|) $) NIL T ELT) (($ #6# $) NIL T ELT) (($ (|Integer|) . #22=($)) NIL T ELT) (($ |#2| . #22#) 30 T ELT) (#21# NIL T ELT) (($ |#2| #12#) NIL T ELT))) +((~= #1=(#2=(#3=(|Boolean|) $ $) NIL T ELT)) (|zero?| #4=((#3# $) NIL T ELT)) (|varList| ((#5=(|List| |#1|) $) 85 T ELT)) (|trunc| (($ $ #6=(|NonNegativeInteger|)) 95 T ELT)) (|subtractIfCan| (((|Maybe| $) $ $) NIL T ELT)) (|sample| (#7=($) NIL T CONST)) (|rquo| (#8=(#9=(|XRecursivePolynomial| |#1| |#2|) #9# $) 50 T ELT)) (|retractIfCan| (((|Union| #10=(|LyndonWord| |#1|) #11="failed") $) NIL T ELT)) (|retract| #12=((#10# $) NIL T ELT)) (|reductum| (#13=($ $) 94 T ELT)) (|opposite?| #1#) (|numberOfMonomials| (#14=(#6# $) NIL T ELT)) (|monomials| ((#15=(|List| $) $) NIL T ELT)) (|monomial?| #4#) (|monom| (($ #10# |#2|) 70 T ELT)) (|mirror| (#13# 90 T ELT)) (|map| (($ (|Mapping| |#2| |#2|) $) NIL T ELT)) (|lquo| (#8# 49 T ELT)) (|leadingTerm| ((#16=(|Record| (|:| |k| #10#) (|:| |c| |#2|)) $) NIL T ELT)) (|leadingMonomial| #12#) (|leadingCoefficient| ((|#2| $) NIL T ELT)) (|latex| (((|String|) $) NIL T ELT)) (|hash| (((|SingleInteger|) $) NIL T ELT)) (|eval| (($ $ |#1| $) 32 T ELT) (($ $ #5# #15#) 34 T ELT)) (|degree| (#14# 92 T ELT)) (|construct| (#17=($ $ $) 20 T ELT) (($ #10# #10#) 79 T ELT) (($ #10# $) 77 T ELT) (($ $ #10#) 78 T ELT)) (|coerce| (((|OutputForm|) $) NIL T ELT) ((#18=(|XDistributedPolynomial| |#1| |#2|) $) 60 T ELT) ((#9# $) 43 T ELT) (($ |#1|) 76 T ELT) (#19=($ #10#) 27 T ELT)) (|coefficients| (((|List| |#2|) $) NIL T ELT)) (|coefficient| ((|#2| $ #10#) NIL T ELT)) (|coef| ((|#2| #9# $) 45 T ELT)) (|before?| #1#) (|Zero| (#7# 23 T CONST)) (|ListOfTerms| (((|List| #16#) $) NIL T ELT)) (|LiePolyIfCan| (((|Union| $ #11#) #18#) 62 T ELT)) (|LiePoly| (#19# 14 T ELT)) (= (#2# 46 T ELT)) (/ (#20=($ $ |#2|) NIL (|has| |#2| (|Field|)) ELT)) (- (#13# 68 T ELT) (#17# NIL T ELT)) (+ (#17# 31 T ELT)) (* (($ (|PositiveInteger|) $) NIL T ELT) (($ #6# $) NIL T ELT) (($ (|Integer|) . #21=($)) NIL T ELT) (($ |#2| . #21#) 30 T ELT) (#20# NIL T ELT) (($ |#2| #10#) NIL T ELT))) (((|LiePolynomial| |#1| |#2|) (|Join| (|FreeLieAlgebra| |#1| |#2|) (|FreeModuleCat| |#2| #1=(|LyndonWord| |#1|)) (CATEGORY |domain| (SIGNATURE |LiePolyIfCan| ((|Union| $ "failed") (|XDistributedPolynomial| |#1| |#2|))) (SIGNATURE |construct| ($ #1# #1#)) (SIGNATURE |construct| ($ #1# $)) (SIGNATURE |construct| ($ $ #1#)))) (|OrderedSet|) (|CommutativeRing|)) (T |LiePolynomial|)) ((|LiePolyIfCan| (*1 *1 *2) (|partial| AND (|isDomain| *2 (|XDistributedPolynomial| *3 *4)) #1=(|ofCategory| *3 (|OrderedSet|)) #2=(|ofCategory| *4 (|CommutativeRing|)) #3=(|isDomain| *1 (|LiePolynomial| *3 *4)))) (|construct| (*1 *1 *2 *2) #4=(AND (|isDomain| *2 (|LyndonWord| *3)) #1# #3# #2#)) (|construct| (*1 *1 *2 *1) #4#) (|construct| (*1 *1 *1 *2) #4#)) ((|sorted?| ((#1=(|Boolean|) $) NIL T ELT) ((#1# #2=(|Mapping| #1# |#2| |#2|) $) 59 T ELT)) (|sort!| (#3=($ $) NIL T ELT) (($ #2# $) 12 T ELT)) (|select!| (#4=($ #5=(|Mapping| #1# |#2|) $) 29 T ELT)) (|reverse!| (#3# 65 T ELT)) (|removeDuplicates!| (#3# 74 T ELT)) (|remove!| (($ |#2| $) NIL T ELT) (#4# 43 T ELT)) (|reduce| ((|#2| #6=(|Mapping| |#2| |#2| |#2|) $) 21 T ELT) ((|#2| #6# $ |#2|) 60 T ELT) ((|#2| #6# $ |#2| |#2|) 62 T ELT)) (|position| ((#7=(|Integer|) |#2| $ #7#) 71 T ELT) ((#7# |#2| $) NIL T ELT) ((#7# #5# $) 54 T ELT)) (|new| (($ (|NonNegativeInteger|) |#2|) 63 T ELT)) (|merge!| #8=(($ $ $) NIL T ELT) (#9=($ #2# $ $) 31 T ELT)) (|merge| #8# (#9# 24 T ELT)) (|map| (($ (|Mapping| |#2| |#2|) $) NIL T ELT) (($ #6# $ $) 64 T ELT)) (|list| (($ |#2|) 15 T ELT)) (|insert!| (#10=($ $ $ #7#) 42 T ELT) (($ |#2| $ #7#) 40 T ELT)) (|find| (((|Union| |#2| "failed") #5# $) 53 T ELT)) (|delete!| (($ $ (|UniversalSegment| #7#)) 51 T ELT) (($ $ #7#) 44 T ELT)) (|copyInto!| (#10# 70 T ELT)) (|copy| (#3# 68 T ELT)) (< ((#1# $ $) 76 T ELT))) @@ -2025,15 +2028,15 @@ NIL ((|linSolve| (((|Record| (|:| |particular| (|Union| #1=(|Vector| (|Fraction| |#4|)) "failed")) (|:| |basis| (|List| #1#))) (|List| |#4|) (|List| |#3|)) 51 T ELT))) (((|LinearSystemPolynomialPackage| |#1| |#2| |#3| |#4|) (CATEGORY |package| (SIGNATURE |linSolve| ((|Record| (|:| |particular| (|Union| #1=(|Vector| (|Fraction| |#4|)) "failed")) (|:| |basis| (|List| #1#))) (|List| |#4|) (|List| |#3|)))) (|IntegralDomain|) (|OrderedAbelianMonoidSup|) (|OrderedSet|) (|PolynomialCategory| |#1| |#2| |#3|)) (T |LinearSystemPolynomialPackage|)) ((|linSolve| (*1 *2 *3 *4) (AND (|isDomain| *3 (|List| *8)) (|isDomain| *4 (|List| *7)) (|ofCategory| *7 (|OrderedSet|)) (|ofCategory| *8 (|PolynomialCategory| *5 *6 *7)) (|ofCategory| *5 (|IntegralDomain|)) (|ofCategory| *6 (|OrderedAbelianMonoidSup|)) (|isDomain| *2 (|Record| (|:| |particular| (|Union| #1=(|Vector| (|Fraction| *8)) "failed")) (|:| |basis| (|List| #1#)))) (|isDomain| *1 (|LinearSystemPolynomialPackage| *5 *6 *7 *8))))) -((~= #1=((#2=(|Boolean|) $ $) NIL T ELT)) (|zero?| #3=((#2# $) NIL T ELT)) (|unit| #4=((#5=(|Union| $ #6="failed")) NIL #7=(|has| |#2| (|IntegralDomain|)) ELT)) (|trace| #8=(#9=(|#2| $) NIL T ELT)) (|symmetric?| #3#) (|subtractIfCan| ((#5# $ $) NIL T ELT)) (|structuralConstants| ((#10=(|Vector| #11=(|Matrix| |#2|))) NIL T ELT) ((#10# #12=(|Vector| $)) NIL T ELT)) (|square?| #3#) (|someBasis| (#13=(#12#) 41 T ELT)) (|scalarMatrix| #14=(($ |#2|) NIL T ELT)) (|sample| #15=(#16=($) NIL T CONST)) (|rowEchelon| (#17=($ $) NIL (|has| |#2| (|EuclideanDomain|)) ELT)) (|row| #18=((#19=(|DirectProduct| |#1| |#2|) $ #20=(|Integer|)) NIL T ELT)) (|rightUnits| #21=(((|Union| (|Record| (|:| |particular| $) (|:| |basis| (|List| $))) #6#)) NIL #7# ELT)) (|rightUnit| #4#) (|rightTraceMatrix| #22=((#11#) NIL T ELT) #23=((#11# #12#) NIL T ELT)) (|rightTrace| #8#) (|rightRegularRepresentation| #24=((#11# $) NIL T ELT) #25=((#11# $ #12#) NIL T ELT)) (|rightRecip| #26=(#27=(#5# $) NIL #7# ELT)) (|rightRankPolynomial| #28=(((|SparseUnivariatePolynomial| #29=(|Polynomial| |#2|))) NIL #30=(|has| |#2| (|Field|)) ELT)) (|rightPower| #31=(($ $ #32=(|PositiveInteger|)) NIL T ELT)) (|rightNorm| #8#) (|rightMinimalPolynomial| #33=(#34=((|SparseUnivariatePolynomial| |#2|) $) NIL #7# ELT)) (|rightDiscriminant| #35=((|#2|) NIL T ELT) #36=((|#2| #12#) NIL T ELT)) (|rightCharacteristicPolynomial| #37=(#34# NIL T ELT)) (|rightAlternative?| #38=((#2#) NIL T ELT)) (|retractIfCan| (((|Union| #20# . #39=(#6#)) . #40=($)) NIL #41=(|has| |#2| (|RetractableTo| #20#)) ELT) (((|Union| #42=(|Fraction| #20#) . #39#) . #40#) NIL #43=(|has| |#2| (|RetractableTo| #42#)) ELT) ((#44=(|Union| |#2| . #39#) . #40#) NIL T ELT)) (|retract| (#45=(#20# . #46=($)) NIL #41# ELT) ((#42# . #46#) NIL #43# ELT) #8#) (|represents| #47=(($ #48=(|Vector| |#2|)) NIL T ELT) (($ #48# #12#) NIL T ELT)) (|reducedSystem| ((#49=(|Matrix| #20#) . #50=(#51=(|Matrix| $))) NIL #52=(|has| |#2| (|LinearlyExplicitRingOver| #20#)) ELT) ((#53=(|Record| (|:| |mat| #49#) (|:| |vec| (|Vector| #20#))) . #54=(#51# #12#)) NIL #52# ELT) ((#55=(|Record| (|:| |mat| #11#) (|:| |vec| #48#)) . #54#) NIL T ELT) ((#11# . #50#) NIL T ELT)) (|reduce| ((|#2| #56=(|Mapping| |#2| |#2| |#2|) $) NIL T ELT) ((|#2| #56# $ |#2|) NIL T ELT) ((|#2| #56# $ |#2| |#2|) NIL #57=(|has| |#2| (|BasicType|)) ELT)) (|recip| (#27# NIL T ELT)) (|rank| #58=(#59=(#60=(|NonNegativeInteger|) $) NIL #7# ELT) ((#32#) 42 T ELT)) (|qelt| (#61=(|#2| $ #20# #20#) NIL T ELT)) (|powerAssociative?| #38#) (|plenaryPower| #31#) (|opposite?| #1#) (|one?| #3#) (|nullity| #58#) (|nullSpace| (((|List| #19#) $) NIL #7# ELT)) (|nrows| #62=(#59# NIL T ELT)) (|noncommutativeJordanAlgebra?| #38#) (|ncols| #62#) (|minordet| #63=(#9# NIL (|has| |#2| (ATTRIBUTE (|commutative| "*"))) ELT)) (|minRowIndex| #64=(#45# NIL T ELT)) (|minColIndex| #64#) (|members| ((#65=(|List| |#2|) $) NIL T ELT)) (|member?| ((#2# |#2| $) NIL #57# ELT)) (|maxRowIndex| #64#) (|maxColIndex| #64#) (|matrix| (($ #66=(|List| #65#)) NIL T ELT)) (|map| (($ #56# $ $) NIL T ELT) (($ #67=(|Mapping| |#2| |#2|) $) NIL T ELT)) (|listOfLists| ((#66# $) NIL T ELT)) (|lieAlgebra?| #38#) (|lieAdmissible?| #38#) (|leftUnits| #21#) (|leftUnit| #4#) (|leftTraceMatrix| #22# #23#) (|leftTrace| #8#) (|leftRegularRepresentation| #24# #25#) (|leftReducedSystem| ((#49# #12#) NIL #52# ELT) ((#53# . #68=(#12# $)) NIL #52# ELT) ((#55# . #68#) NIL T ELT) #23#) (|leftRecip| #26#) (|leftRankPolynomial| #28#) (|leftPower| #31#) (|leftNorm| #8#) (|leftMinimalPolynomial| #33#) (|leftDiscriminant| #35# #36#) (|leftCharacteristicPolynomial| #37#) (|leftAlternative?| #38#) (|latex| (((|String|) $) NIL T ELT)) (|jordanAlgebra?| #38#) (|jordanAdmissible?| #38#) (|jacobiIdentity?| #38#) (|inverse| (#27# NIL #30# ELT)) (|hash| (((|SingleInteger|) $) NIL T ELT)) (|flexible?| #38#) (|find| ((#44# #69=(|Mapping| #2# |#2|) $) NIL T ELT)) (|exquo| ((#5# $ |#2|) NIL #7# ELT)) (|every?| #70=((#2# #69# $) NIL T ELT)) (|eval| (($ $ (|List| #71=(|Equation| |#2|))) NIL #72=(AND (|has| |#2| (|Evalable| |#2|)) (|has| |#2| (|SetCategory|))) ELT) (($ $ #71#) NIL #72# ELT) (($ $ |#2| |#2|) NIL #72# ELT) (($ $ #65# #65#) NIL #72# ELT)) (|eq?| #1#) (|empty?| #3#) (|empty| (#16# NIL T ELT)) (|elt| ((|#2| $ #20# #20# |#2|) NIL T ELT) (#61# 27 T ELT) ((|#2| $ #20#) NIL T ELT)) (|differentiate| #73=(($ $ #67# #60#) NIL T ELT) #74=(($ $ #67#) NIL T ELT) #75=(#17# NIL #76=(|has| |#2| (|DifferentialSpace|)) ELT) #77=(#78=($ $ #60#) NIL #76# ELT) #79=(($ $ #80=(|Symbol|)) NIL #81=(|has| |#2| (|PartialDifferentialSpace| #80#)) ELT) #82=(($ $ #83=(|List| #80#)) NIL #81# ELT) #84=(($ $ #80# #60#) NIL #81# ELT) #85=(($ $ #83# (|List| #60#)) NIL #81# ELT)) (|diagonalProduct| #8#) (|diagonalMatrix| (($ #65#) NIL T ELT)) (|diagonal?| #3#) (|diagonal| ((#19# $) NIL T ELT)) (|determinant| #63#) (|count| ((#60# #69# $) NIL T ELT) ((#60# |#2| $) NIL #57# ELT)) (|copy| #86=(#17# NIL T ELT)) (|coordinates| #23# #87=((#48# $) NIL T ELT) ((#11# #12# #12#) NIL T ELT) ((#48# $ #12#) 30 T ELT)) (|convert| #47# #87#) (|conditionsForIdempotents| ((#88=(|List| #29#)) NIL T ELT) ((#88# #12#) NIL T ELT)) (|commutator| #89=(($ $ $) NIL T ELT)) (|commutative?| #38#) (|column| #18#) (|coerce| (((|OutputForm|) $) NIL T ELT) (($ #20#) NIL T ELT) (($ #42#) NIL #43# ELT) #14# #24#) (|characteristic| ((#60#) NIL T CONST)) (|before?| #1#) (|basis| (#13# 40 T ELT)) (|associatorDependence| (((|List| #48#)) NIL #7# ELT)) (|associator| (($ $ $ $) NIL T ELT)) (|associative?| #38#) (|apply| (($ #11# $) NIL T ELT)) (|any?| #70#) (|antisymmetric?| #3#) (|antiCommutator| #89#) (|antiCommutative?| #38#) (|antiAssociative?| #38#) (|annihilate?| #1#) (|alternative?| #38#) (|Zero| #15#) (|One| #15#) (D #73# #74# #75# #77# #79# #82# #84# #85#) (= #1#) (/ (#90=($ $ |#2|) NIL #30# ELT)) (- #86# #89#) (+ #89#) (** #31# (#78# NIL T ELT) (($ $ #20#) NIL #30# ELT)) (* (($ #32# $) NIL T ELT) (($ #60# $) NIL T ELT) (($ #20# . #91=($)) NIL T ELT) #89# (#90# NIL T ELT) (($ |#2| . #91#) NIL T ELT) ((#19# $ #19#) NIL T ELT) ((#19# #19# $) NIL T ELT)) (|#| #62#)) +((~= #1=((#2=(|Boolean|) $ $) NIL T ELT)) (|zero?| #3=((#2# $) NIL T ELT)) (|unit| #4=((#5=(|Union| $ #6="failed")) NIL #7=(|has| |#2| (|IntegralDomain|)) ELT)) (|trace| #8=(#9=(|#2| $) NIL T ELT)) (|symmetric?| #3#) (|subtractIfCan| (((|Maybe| $) $ $) NIL T ELT)) (|structuralConstants| ((#10=(|Vector| #11=(|Matrix| |#2|))) NIL T ELT) ((#10# #12=(|Vector| $)) NIL T ELT)) (|square?| #3#) (|someBasis| (#13=(#12#) 41 T ELT)) (|scalarMatrix| #14=(($ |#2|) NIL T ELT)) (|sample| #15=(#16=($) NIL T CONST)) (|rowEchelon| (#17=($ $) NIL (|has| |#2| (|EuclideanDomain|)) ELT)) (|row| #18=((#19=(|DirectProduct| |#1| |#2|) $ #20=(|Integer|)) NIL T ELT)) (|rightUnits| #21=(((|Union| (|Record| (|:| |particular| $) (|:| |basis| (|List| $))) #6#)) NIL #7# ELT)) (|rightUnit| #4#) (|rightTraceMatrix| #22=((#11#) NIL T ELT) #23=((#11# #12#) NIL T ELT)) (|rightTrace| #8#) (|rightRegularRepresentation| #24=((#11# $) NIL T ELT) #25=((#11# $ #12#) NIL T ELT)) (|rightRecip| #26=(#27=(#5# $) NIL #7# ELT)) (|rightRankPolynomial| #28=(((|SparseUnivariatePolynomial| #29=(|Polynomial| |#2|))) NIL #30=(|has| |#2| (|Field|)) ELT)) (|rightPower| #31=(($ $ #32=(|PositiveInteger|)) NIL T ELT)) (|rightNorm| #8#) (|rightMinimalPolynomial| #33=(#34=((|SparseUnivariatePolynomial| |#2|) $) NIL #7# ELT)) (|rightDiscriminant| #35=((|#2|) NIL T ELT) #36=((|#2| #12#) NIL T ELT)) (|rightCharacteristicPolynomial| #37=(#34# NIL T ELT)) (|rightAlternative?| #38=((#2#) NIL T ELT)) (|retractIfCan| (((|Union| #20# . #39=(#6#)) . #40=($)) NIL #41=(|has| |#2| (|RetractableTo| #20#)) ELT) (((|Union| #42=(|Fraction| #20#) . #39#) . #40#) NIL #43=(|has| |#2| (|RetractableTo| #42#)) ELT) ((#44=(|Union| |#2| . #39#) . #40#) NIL T ELT)) (|retract| (#45=(#20# . #46=($)) NIL #41# ELT) ((#42# . #46#) NIL #43# ELT) #8#) (|represents| #47=(($ #48=(|Vector| |#2|)) NIL T ELT) (($ #48# #12#) NIL T ELT)) (|reducedSystem| ((#49=(|Matrix| #20#) . #50=(#51=(|Matrix| $))) NIL #52=(|has| |#2| (|LinearlyExplicitRingOver| #20#)) ELT) ((#53=(|Record| (|:| |mat| #49#) (|:| |vec| (|Vector| #20#))) . #54=(#51# #12#)) NIL #52# ELT) ((#55=(|Record| (|:| |mat| #11#) (|:| |vec| #48#)) . #54#) NIL T ELT) ((#11# . #50#) NIL T ELT)) (|reduce| ((|#2| #56=(|Mapping| |#2| |#2| |#2|) $) NIL T ELT) ((|#2| #56# $ |#2|) NIL T ELT) ((|#2| #56# $ |#2| |#2|) NIL #57=(|has| |#2| (|BasicType|)) ELT)) (|recip| (#27# NIL T ELT)) (|rank| #58=(#59=(#60=(|NonNegativeInteger|) $) NIL #7# ELT) ((#32#) 42 T ELT)) (|qelt| (#61=(|#2| $ #20# #20#) NIL T ELT)) (|powerAssociative?| #38#) (|plenaryPower| #31#) (|opposite?| #1#) (|one?| #3#) (|nullity| #58#) (|nullSpace| (((|List| #19#) $) NIL #7# ELT)) (|nrows| #62=(#59# NIL T ELT)) (|noncommutativeJordanAlgebra?| #38#) (|ncols| #62#) (|minordet| #63=(#9# NIL (|has| |#2| (ATTRIBUTE (|commutative| "*"))) ELT)) (|minRowIndex| #64=(#45# NIL T ELT)) (|minColIndex| #64#) (|members| ((#65=(|List| |#2|) $) NIL T ELT)) (|member?| ((#2# |#2| $) NIL #57# ELT)) (|maxRowIndex| #64#) (|maxColIndex| #64#) (|matrix| (($ #66=(|List| #65#)) NIL T ELT)) (|map| (($ #56# $ $) NIL T ELT) (($ #67=(|Mapping| |#2| |#2|) $) NIL T ELT)) (|listOfLists| ((#66# $) NIL T ELT)) (|lieAlgebra?| #38#) (|lieAdmissible?| #38#) (|leftUnits| #21#) (|leftUnit| #4#) (|leftTraceMatrix| #22# #23#) (|leftTrace| #8#) (|leftRegularRepresentation| #24# #25#) (|leftReducedSystem| ((#49# #12#) NIL #52# ELT) ((#53# . #68=(#12# $)) NIL #52# ELT) ((#55# . #68#) NIL T ELT) #23#) (|leftRecip| #26#) (|leftRankPolynomial| #28#) (|leftPower| #31#) (|leftNorm| #8#) (|leftMinimalPolynomial| #33#) (|leftDiscriminant| #35# #36#) (|leftCharacteristicPolynomial| #37#) (|leftAlternative?| #38#) (|latex| (((|String|) $) NIL T ELT)) (|jordanAlgebra?| #38#) (|jordanAdmissible?| #38#) (|jacobiIdentity?| #38#) (|inverse| (#27# NIL #30# ELT)) (|hash| (((|SingleInteger|) $) NIL T ELT)) (|flexible?| #38#) (|find| ((#44# #69=(|Mapping| #2# |#2|) $) NIL T ELT)) (|exquo| ((#5# $ |#2|) NIL #7# ELT)) (|every?| #70=((#2# #69# $) NIL T ELT)) (|eval| (($ $ (|List| #71=(|Equation| |#2|))) NIL #72=(AND (|has| |#2| (|Evalable| |#2|)) (|has| |#2| (|SetCategory|))) ELT) (($ $ #71#) NIL #72# ELT) (($ $ |#2| |#2|) NIL #72# ELT) (($ $ #65# #65#) NIL #72# ELT)) (|eq?| #1#) (|empty?| #3#) (|empty| (#16# NIL T ELT)) (|elt| ((|#2| $ #20# #20# |#2|) NIL T ELT) (#61# 27 T ELT) ((|#2| $ #20#) NIL T ELT)) (|differentiate| #73=(($ $ #67# #60#) NIL T ELT) #74=(($ $ #67#) NIL T ELT) #75=(#17# NIL #76=(|has| |#2| (|DifferentialSpace|)) ELT) #77=(#78=($ $ #60#) NIL #76# ELT) #79=(($ $ #80=(|Symbol|)) NIL #81=(|has| |#2| (|PartialDifferentialSpace| #80#)) ELT) #82=(($ $ #83=(|List| #80#)) NIL #81# ELT) #84=(($ $ #80# #60#) NIL #81# ELT) #85=(($ $ #83# (|List| #60#)) NIL #81# ELT)) (|diagonalProduct| #8#) (|diagonalMatrix| (($ #65#) NIL T ELT)) (|diagonal?| #3#) (|diagonal| ((#19# $) NIL T ELT)) (|determinant| #63#) (|count| ((#60# #69# $) NIL T ELT) ((#60# |#2| $) NIL #57# ELT)) (|copy| #86=(#17# NIL T ELT)) (|coordinates| #23# #87=((#48# $) NIL T ELT) ((#11# #12# #12#) NIL T ELT) ((#48# $ #12#) 30 T ELT)) (|convert| #47# #87#) (|conditionsForIdempotents| ((#88=(|List| #29#)) NIL T ELT) ((#88# #12#) NIL T ELT)) (|commutator| #89=(($ $ $) NIL T ELT)) (|commutative?| #38#) (|column| #18#) (|coerce| (((|OutputForm|) $) NIL T ELT) (($ #20#) NIL T ELT) (($ #42#) NIL #43# ELT) #14# #24#) (|characteristic| ((#60#) NIL T CONST)) (|before?| #1#) (|basis| (#13# 40 T ELT)) (|associatorDependence| (((|List| #48#)) NIL #7# ELT)) (|associator| (($ $ $ $) NIL T ELT)) (|associative?| #38#) (|apply| (($ #11# $) NIL T ELT)) (|any?| #70#) (|antisymmetric?| #3#) (|antiCommutator| #89#) (|antiCommutative?| #38#) (|antiAssociative?| #38#) (|annihilate?| #1#) (|alternative?| #38#) (|Zero| #15#) (|One| #15#) (D #73# #74# #75# #77# #79# #82# #84# #85#) (= #1#) (/ (#90=($ $ |#2|) NIL #30# ELT)) (- #86# #89#) (+ #89#) (** #31# (#78# NIL T ELT) (($ $ #20#) NIL #30# ELT)) (* (($ #32# $) NIL T ELT) (($ #60# $) NIL T ELT) (($ #20# . #91=($)) NIL T ELT) #89# (#90# NIL T ELT) (($ |#2| . #91#) NIL T ELT) ((#19# $ #19#) NIL T ELT) ((#19# #19# $) NIL T ELT)) (|#| #62#)) (((|LieSquareMatrix| |#1| |#2|) (|Join| (|SquareMatrixCategory| |#1| |#2| #1=(|DirectProduct| |#1| |#2|) #1#) (|CoercibleTo| (|Matrix| |#2|)) (|FramedNonAssociativeAlgebra| |#2|)) (|PositiveInteger|) (|CommutativeRing|)) (T |LieSquareMatrix|)) NIL ((~= #1=(((|Boolean|) $ $) NIL T ELT)) (|latex| (((|String|) $) NIL T ELT)) (|hash| (((|SingleInteger|) $) NIL T ELT)) (|elements| (((|List| (|SpadAst|)) $) 12 T ELT)) (|coerce| (((|OutputForm|) $) 18 T ELT) (($ #2=(|Syntax|)) NIL T ELT) ((#2# $) NIL T ELT)) (|before?| #1#) (= #1#)) (((|ConstructAst|) (|Join| (|SpadSyntaxCategory|) (CATEGORY |domain| (SIGNATURE |elements| ((|List| (|SpadAst|)) $))))) (T |ConstructAst|)) ((|elements| (*1 *2 *1) (AND (|isDomain| *2 (|List| (|SpadAst|))) (|isDomain| *1 (|ConstructAst|))))) -((~= #1=(#2=(#3=(|Boolean|) $ $) NIL T ELT)) (|varList| ((#4=(|List| |#1|) $) NIL T ELT)) (|right| (#5=($ $) 62 T ELT)) (|retractable?| ((#3# $) NIL T ELT)) (|retractIfCan| (((|Union| |#1| #6="failed") $) NIL T ELT)) (|retract| ((|#1| $) NIL T ELT)) (|min| #7=(($ $ $) NIL T ELT)) (|max| #7#) (|lyndonIfCan| (((|Union| $ #6#) #8=(|OrderedFreeMonoid| |#1|)) 28 T ELT)) (|lyndon?| ((#3# #8#) 18 T ELT)) (|lyndon| (($ #8#) 29 T ELT)) (|lexico| (#2# 36 T ELT)) (|length| ((#9=(|PositiveInteger|) $) 43 T ELT)) (|left| (#5# NIL T ELT)) (|latex| (((|String|) $) NIL T ELT)) (|hash| (((|SingleInteger|) $) NIL T ELT)) (|factor| ((#10=(|List| $) #8#) 20 T ELT)) (|coerce| (((|OutputForm|) $) 51 T ELT) (($ |#1|) 40 T ELT) ((#8# $) 47 T ELT) (((|Magma| |#1|) $) 52 T ELT)) (|before?| #1#) (|LyndonWordsList1| (((|OneDimensionalArray| #10#) #4# #9#) 67 T ELT)) (|LyndonWordsList| ((#10# #4# #9#) 70 T ELT)) (>= #1#) (> #1#) (= (#2# 63 T ELT)) (<= #1#) (< (#2# 46 T ELT))) -(((|LyndonWord| |#1|) (|Join| #1=(|OrderedSet|) (|RetractableTo| |#1|) (CATEGORY |domain| (SIGNATURE |retractable?| (#2=(|Boolean|) $)) (SIGNATURE |left| #3=($ $)) (SIGNATURE |right| #3#) (SIGNATURE |length| (#4=(|PositiveInteger|) $)) (SIGNATURE |lexico| (#2# $ $)) (SIGNATURE |coerce| (#5=(|OrderedFreeMonoid| |#1|) $)) (SIGNATURE |coerce| ((|Magma| |#1|) $)) (SIGNATURE |factor| (#6=(|List| $) #5#)) (SIGNATURE |lyndon?| (#2# #5#)) (SIGNATURE |lyndon| ($ #5#)) (SIGNATURE |lyndonIfCan| ((|Union| $ "failed") #5#)) (SIGNATURE |varList| (#7=(|List| |#1|) $)) (SIGNATURE |LyndonWordsList1| ((|OneDimensionalArray| #6#) #7# #4#)) (SIGNATURE |LyndonWordsList| (#6# #7# #4#)))) #1#) (T |LyndonWord|)) -((|retractable?| #1=(*1 *2 *1) #2=(AND #3=(|isDomain| *2 (|Boolean|)) #4=(|isDomain| *1 (|LyndonWord| *3)) #5=(|ofCategory| *3 #6=(|OrderedSet|)))) (|left| #7=(*1 *1 *1) #8=(AND (|isDomain| *1 (|LyndonWord| *2)) (|ofCategory| *2 #6#))) (|right| #7# #8#) (|length| #1# (AND (|isDomain| *2 #9=(|PositiveInteger|)) #4# #5#)) (|lexico| (*1 *2 *1 *1) #2#) (|coerce| #1# (AND #10=(|isDomain| *2 (|OrderedFreeMonoid| *3)) #4# #5#)) (|coerce| #1# (AND (|isDomain| *2 (|Magma| *3)) #4# #5#)) (|factor| #11=(*1 *2 *3) (AND #12=(|isDomain| *3 (|OrderedFreeMonoid| *4)) #13=(|ofCategory| *4 #6#) (|isDomain| *2 (|List| #14=(|LyndonWord| *4))) #15=(|isDomain| *1 #14#))) (|lyndon?| #11# (AND #12# #13# #3# #15#)) (|lyndon| #16=(*1 *1 *2) (AND #10# #5# #4#)) (|lyndonIfCan| #16# (|partial| AND #10# #5# #4#)) (|varList| #1# (AND (|isDomain| *2 (|List| *3)) #4# #5#)) (|LyndonWordsList1| #17=(*1 *2 *3 *4) (AND #18=(|isDomain| *3 (|List| *5)) #19=(|isDomain| *4 #9#) #20=(|ofCategory| *5 #6#) (|isDomain| *2 (|OneDimensionalArray| #21=(|List| #22=(|LyndonWord| *5)))) #23=(|isDomain| *1 #22#))) (|LyndonWordsList| #17# (AND #18# #19# #20# (|isDomain| *2 #21#) #23#))) +((~= #1=(#2=(#3=(|Boolean|) $ $) NIL T ELT)) (|varList| ((#4=(|List| |#1|) $) NIL T ELT)) (|right| (#5=($ $) 62 T ELT)) (|retractable?| ((#3# $) NIL T ELT)) (|retractIfCan| (((|Union| |#1| #6="failed") $) NIL T ELT)) (|retract| ((|#1| $) NIL T ELT)) (|min| #7=(($ $ $) NIL T ELT)) (|max| #7#) (|lyndonIfCan| (((|Union| $ #6#) #8=(|OrderedFreeMonoid| |#1|)) 28 T ELT)) (|lyndon?| ((#3# #8#) 18 T ELT)) (|lyndon| (($ #8#) 29 T ELT)) (|lexico| (#2# 36 T ELT)) (|length| ((#9=(|PositiveInteger|) $) 43 T ELT)) (|left| (#5# NIL T ELT)) (|latex| (((|String|) $) NIL T ELT)) (|hash| (((|SingleInteger|) $) NIL T ELT)) (|factor| ((#10=(|List| $) #8#) 20 T ELT)) (|coerce| (((|OutputForm|) $) 51 T ELT) (($ |#1|) 40 T ELT) ((#8# $) 47 T ELT) (((|FreeMagma| |#1|) $) 52 T ELT)) (|before?| #1#) (|LyndonWordsList1| (((|OneDimensionalArray| #10#) #4# #9#) 67 T ELT)) (|LyndonWordsList| ((#10# #4# #9#) 70 T ELT)) (>= #1#) (> #1#) (= (#2# 63 T ELT)) (<= #1#) (< (#2# 46 T ELT))) +(((|LyndonWord| |#1|) (|Join| #1=(|OrderedSet|) (|RetractableTo| |#1|) (|CoercibleTo| #2=(|OrderedFreeMonoid| |#1|)) (|CoercibleTo| (|FreeMagma| |#1|)) (CATEGORY |domain| (SIGNATURE |retractable?| (#3=(|Boolean|) $)) (SIGNATURE |left| #4=($ $)) (SIGNATURE |right| #4#) (SIGNATURE |length| (#5=(|PositiveInteger|) $)) (SIGNATURE |lexico| (#3# $ $)) (SIGNATURE |factor| (#6=(|List| $) #2#)) (SIGNATURE |lyndon?| (#3# #2#)) (SIGNATURE |lyndon| ($ #2#)) (SIGNATURE |lyndonIfCan| ((|Union| $ "failed") #2#)) (SIGNATURE |varList| (#7=(|List| |#1|) $)) (SIGNATURE |LyndonWordsList1| ((|OneDimensionalArray| #6#) #7# #5#)) (SIGNATURE |LyndonWordsList| (#6# #7# #5#)))) #1#) (T |LyndonWord|)) +((|retractable?| #1=(*1 *2 *1) #2=(AND #3=(|isDomain| *2 (|Boolean|)) #4=(|isDomain| *1 (|LyndonWord| *3)) #5=(|ofCategory| *3 #6=(|OrderedSet|)))) (|left| #7=(*1 *1 *1) #8=(AND (|isDomain| *1 (|LyndonWord| *2)) (|ofCategory| *2 #6#))) (|right| #7# #8#) (|length| #1# (AND (|isDomain| *2 #9=(|PositiveInteger|)) #4# #5#)) (|lexico| (*1 *2 *1 *1) #2#) (|factor| #10=(*1 *2 *3) (AND #11=(|isDomain| *3 (|OrderedFreeMonoid| *4)) #12=(|ofCategory| *4 #6#) (|isDomain| *2 (|List| #13=(|LyndonWord| *4))) #14=(|isDomain| *1 #13#))) (|lyndon?| #10# (AND #11# #12# #3# #14#)) (|lyndon| #15=(*1 *1 *2) (AND #16=(|isDomain| *2 (|OrderedFreeMonoid| *3)) #5# #4#)) (|lyndonIfCan| #15# (|partial| AND #16# #5# #4#)) (|varList| #1# (AND (|isDomain| *2 (|List| *3)) #4# #5#)) (|LyndonWordsList1| #17=(*1 *2 *3 *4) (AND #18=(|isDomain| *3 (|List| *5)) #19=(|isDomain| *4 #9#) #20=(|ofCategory| *5 #6#) (|isDomain| *2 (|OneDimensionalArray| #21=(|List| #22=(|LyndonWord| *5)))) #23=(|isDomain| *1 #22#))) (|LyndonWordsList| #17# (AND #18# #19# #20# (|isDomain| *2 #21#) #23#))) ((|value| (#1=(|#2| $) 96 T ELT)) (|tail| (#2=($ $) 117 T ELT)) (|size?| (#3=(#4=(|Boolean|) $ #5=(|NonNegativeInteger|)) 35 T ELT)) (|rest| (#2# 105 T ELT) (#6=($ $ #5#) 108 T ELT)) (|possiblyInfinite?| (#7=(#4# $) 118 T ELT)) (|nodes| (#8=((|List| $) $) 92 T ELT)) (|node?| (#9=(#4# $ $) 88 T ELT)) (|more?| (#3# 33 T ELT)) (|minIndex| (#10=(#11=(|Integer|) $) 62 T ELT)) (|maxIndex| (#10# 61 T ELT)) (|less?| (#3# 31 T ELT)) (|leaf?| (#7# 94 T ELT)) (|last| (#1# 109 T ELT) (#6# 113 T ELT)) (|insert| (($ $ $ #11#) 79 T ELT) (($ |#2| $ #11#) 78 T ELT)) (|indices| (((|List| #11#) $) 60 T ELT)) (|index?| ((#4# #11# $) 55 T ELT)) (|first| (#1# NIL T ELT) (#6# 104 T ELT)) (|extend| (#12=($ $ #11#) 121 T ELT)) (|explicitlyFinite?| (#7# 120 T ELT)) (|entries| ((#13=(|List| |#2|) $) 42 T ELT)) (|elt| ((|#2| $ "value") NIL T ELT) ((|#2| $ "first") 103 T ELT) (($ $ "rest") 107 T ELT) ((|#2| $ "last") 116 T ELT) (#14=($ $ (|UniversalSegment| #11#)) 75 T ELT) ((|#2| $ #11#) 53 T ELT) ((|#2| $ #11# |#2|) 54 T ELT)) (|distance| ((#11# $ $) 87 T ELT)) (|delete| (#14# 74 T ELT) (#12# 68 T ELT)) (|cyclic?| (#7# 83 T ELT)) (|cycleTail| (#2# 101 T ELT)) (|cycleLength| ((#5# $) 100 T ELT)) (|cycleEntry| (#2# 99 T ELT)) (|construct| (($ #13#) 49 T ELT)) (|complete| (#2# 122 T ELT)) (|children| (#8# 86 T ELT)) (|child?| (#9# 85 T ELT)) (= (#9# 20 T ELT))) (((|LazyStreamAggregate&| |#1| |#2|) (CATEGORY |package| (SIGNATURE = #1=(#2=(|Boolean|) |#1| |#1|)) (SIGNATURE |complete| #3=(|#1| |#1|)) (SIGNATURE |extend| #4=(|#1| |#1| #5=(|Integer|))) (SIGNATURE |size?| #6=(#2# |#1| #7=(|NonNegativeInteger|))) (SIGNATURE |more?| #6#) (SIGNATURE |less?| #6#) (SIGNATURE |possiblyInfinite?| #8=(#2# |#1|)) (SIGNATURE |explicitlyFinite?| #8#) (SIGNATURE |elt| (|#2| |#1| #5# |#2|)) (SIGNATURE |elt| (|#2| |#1| #5#)) (SIGNATURE |entries| (#9=(|List| |#2|) |#1|)) (SIGNATURE |index?| (#2# #5# |#1|)) (SIGNATURE |indices| ((|List| #5#) |#1|)) (SIGNATURE |maxIndex| #10=(#5# |#1|)) (SIGNATURE |minIndex| #10#) (SIGNATURE |construct| (|#1| #9#)) (SIGNATURE |elt| #11=(|#1| |#1| (|UniversalSegment| #5#))) (SIGNATURE |delete| #4#) (SIGNATURE |delete| #11#) (SIGNATURE |insert| (|#1| |#2| |#1| #5#)) (SIGNATURE |insert| (|#1| |#1| |#1| #5#)) (SIGNATURE |cycleTail| #3#) (SIGNATURE |cycleLength| (#7# |#1|)) (SIGNATURE |cycleEntry| #3#) (SIGNATURE |tail| #3#) (SIGNATURE |last| #12=(|#1| |#1| #7#)) (SIGNATURE |elt| (|#2| |#1| "last")) (SIGNATURE |last| #13=(|#2| |#1|)) (SIGNATURE |rest| #12#) (SIGNATURE |elt| (|#1| |#1| "rest")) (SIGNATURE |rest| #3#) (SIGNATURE |first| #12#) (SIGNATURE |elt| (|#2| |#1| "first")) (SIGNATURE |first| #13#) (SIGNATURE |node?| #1#) (SIGNATURE |child?| #1#) (SIGNATURE |distance| (#5# |#1| |#1|)) (SIGNATURE |cyclic?| #8#) (SIGNATURE |elt| (|#2| |#1| "value")) (SIGNATURE |value| #13#) (SIGNATURE |leaf?| #8#) (SIGNATURE |nodes| #14=((|List| |#1|) |#1|)) (SIGNATURE |children| #14#)) (|LazyStreamAggregate| |#2|) (|Type|)) (T |LazyStreamAggregate&|)) NIL @@ -2045,9 +2048,6 @@ NIL ((~= #1=(((|Boolean|) $ $) NIL T ELT)) (|latex| (((|String|) $) NIL T ELT)) (|head| (((|HeadAst|) $) 15 T ELT)) (|hash| (((|SingleInteger|) $) NIL T ELT)) (|coerce| (((|OutputForm|) $) 24 T ELT) (($ #2=(|Syntax|)) NIL T ELT) ((#2# $) NIL T ELT)) (|body| (((|SpadAst|) $) 17 T ELT)) (|before?| #1#) (= #1#)) (((|MacroAst|) (|Join| (|SpadSyntaxCategory|) (CATEGORY |domain| (SIGNATURE |head| ((|HeadAst|) $)) (SIGNATURE |body| ((|SpadAst|) $))))) (T |MacroAst|)) ((|head| #1=(*1 *2 *1) (AND (|isDomain| *2 (|HeadAst|)) #2=(|isDomain| *1 (|MacroAst|)))) (|body| #1# (AND (|isDomain| *2 (|SpadAst|)) #2#))) -((~= #1=(#2=(#3=(|Boolean|) $ $) NIL T ELT)) (|varList| (((|List| |#1|) $) 15 T ELT)) (|right| (#4=($ $) 19 T ELT)) (|retractable?| ((#3# $) 20 T ELT)) (|retractIfCan| (((|Union| |#1| "failed") $) 23 T ELT)) (|retract| (#5=(|#1| $) 21 T ELT)) (|rest| (#4# 37 T ELT)) (|mirror| (#4# 25 T ELT)) (|min| #6=(#7=($ $ $) NIL T ELT)) (|max| #6#) (|lexico| (#2# 46 T ELT)) (|length| (((|PositiveInteger|) $) 40 T ELT)) (|left| (#4# 18 T ELT)) (|latex| (((|String|) $) NIL T ELT)) (|hash| (((|SingleInteger|) $) NIL T ELT)) (|first| (#5# 36 T ELT)) (|coerce| (((|OutputForm|) $) 32 T ELT) (($ |#1|) 24 T ELT) (((|OrderedFreeMonoid| |#1|) $) 28 T ELT)) (|before?| #1#) (>= #1#) (> #1#) (= (#2# 13 T ELT)) (<= #1#) (< (#2# 44 T ELT)) (* (#7# 35 T ELT))) -(((|Magma| |#1|) (|Join| #1=(|OrderedSet|) (|RetractableTo| |#1|) (CATEGORY |domain| (SIGNATURE * ($ $ $)) (SIGNATURE |coerce| ((|OrderedFreeMonoid| |#1|) $)) (SIGNATURE |first| (|#1| $)) (SIGNATURE |left| #2=($ $)) (SIGNATURE |length| ((|PositiveInteger|) $)) (SIGNATURE |lexico| (#3=(|Boolean|) $ $)) (SIGNATURE |mirror| #2#) (SIGNATURE |rest| #2#) (SIGNATURE |retractable?| (#3# $)) (SIGNATURE |right| #2#) (SIGNATURE |varList| ((|List| |#1|) $)))) #1#) (T |Magma|)) -((* (*1 *1 *1 *1) #1=(AND (|isDomain| *1 (|Magma| *2)) (|ofCategory| *2 #2=(|OrderedSet|)))) (|coerce| #3=(*1 *2 *1) (AND (|isDomain| *2 (|OrderedFreeMonoid| *3)) #4=(|isDomain| *1 (|Magma| *3)) #5=(|ofCategory| *3 #2#))) (|first| #3# #1#) (|left| #6=(*1 *1 *1) #1#) (|length| #3# (AND (|isDomain| *2 (|PositiveInteger|)) #4# #5#)) (|lexico| (*1 *2 *1 *1) #7=(AND (|isDomain| *2 (|Boolean|)) #4# #5#)) (|mirror| #6# #1#) (|rest| #6# #1#) (|retractable?| #3# #7#) (|right| #6# #1#) (|varList| #3# (AND (|isDomain| *2 (|List| *3)) #4# #5#))) ((|recur| ((|#1| (|Mapping| |#1| #1=(|NonNegativeInteger|) |#1|) #1# |#1|) 11 T ELT)) (|iter| ((|#1| (|Mapping| |#1| |#1|) #1# |#1|) 9 T ELT))) (((|MappingPackageInternalHacks1| |#1|) (CATEGORY |package| (SIGNATURE |iter| (|#1| (|Mapping| |#1| |#1|) #1=(|NonNegativeInteger|) |#1|)) (SIGNATURE |recur| (|#1| (|Mapping| |#1| #1# |#1|) #1# |#1|))) (|SetCategory|)) (T |MappingPackageInternalHacks1|)) ((|recur| #1=(*1 *2 *3 *4 *2) (AND (|isDomain| *3 (|Mapping| *2 #2=(|NonNegativeInteger|) *2)) #3=(|isDomain| *4 #2#) #4=(|ofCategory| *2 (|SetCategory|)) #5=(|isDomain| *1 (|MappingPackageInternalHacks1| *2)))) (|iter| #1# (AND (|isDomain| *3 (|Mapping| *2 *2)) #3# #4# #5#))) @@ -2089,9 +2089,9 @@ NIL ((|times!| (#1=(#2=(|Matrix| |#1|) #2# #2# #2#) 37 T ELT)) (|rightScalarTimes!| ((#2# #2# #2# |#1|) 32 T ELT)) (|power!| ((#2# #2# #2# #2# #2# #3=(|NonNegativeInteger|)) 43 T ELT)) (|plus!| (#1# 25 T ELT)) (|minus!| (#1# 29 T ELT) (#4=(#2# #2# #2#) 27 T ELT)) (|leftScalarTimes!| ((#2# #2# |#1| #2#) 31 T ELT)) (|copy!| (#4# 23 T ELT)) (** ((#2# #2# #3#) 46 T ELT))) (((|StorageEfficientMatrixOperations| |#1|) (CATEGORY |package| (SIGNATURE |copy!| #1=(#2=(|Matrix| |#1|) #2# #2#)) (SIGNATURE |plus!| #3=(#2# #2# #2# #2#)) (SIGNATURE |minus!| #1#) (SIGNATURE |minus!| #3#) (SIGNATURE |leftScalarTimes!| (#2# #2# |#1| #2#)) (SIGNATURE |rightScalarTimes!| (#2# #2# #2# |#1|)) (SIGNATURE |times!| #3#) (SIGNATURE |power!| (#2# #2# #2# #2# #2# #4=(|NonNegativeInteger|))) (SIGNATURE ** (#2# #2# #4#))) (|Ring|)) (T |StorageEfficientMatrixOperations|)) ((** (*1 *2 *2 *3) #1=(AND (|isDomain| *2 (|Matrix| *4)) (|isDomain| *3 (|NonNegativeInteger|)) (|ofCategory| *4 #2=(|Ring|)) (|isDomain| *1 (|StorageEfficientMatrixOperations| *4)))) (|power!| (*1 *2 *2 *2 *2 *2 *3) #1#) (|times!| #3=(*1 *2 *2 *2 *2) #4=(AND (|isDomain| *2 (|Matrix| *3)) (|ofCategory| *3 #2#) (|isDomain| *1 (|StorageEfficientMatrixOperations| *3)))) (|rightScalarTimes!| (*1 *2 *2 *2 *3) #4#) (|leftScalarTimes!| (*1 *2 *2 *3 *2) #4#) (|minus!| #3# #4#) (|minus!| #5=(*1 *2 *2 *2) #4#) (|plus!| #3# #4#) (|copy!| #5# #4#)) -((|retractIfCan| (((|Union| |#1| "failed") $) 18 T ELT)) (|retract| (#1=(|#1| $) NIL T ELT)) (|nothing| (($) 7 T CONST)) (|just| (#2=($ |#1|) 8 T ELT)) (|coerce| (#2# 16 T ELT) (((|OutputForm|) $) 23 T ELT)) (|case| ((#3=(|Boolean|) $ (|[\|\|]| |#1|)) 14 T ELT) ((#3# $ (|[\|\|]| |nothing|)) 11 T ELT)) (|autoCoerce| (#1# 15 T ELT))) -(((|Maybe| |#1|) (|Join| (|UnionType|) (|RetractableTo| |#1|) #1=(|CoercibleTo| (|OutputForm|)) (CATEGORY |domain| (SIGNATURE |just| ($ |#1|)) (SIGNATURE |case| (#2=(|Boolean|) $ (|[\|\|]| |#1|))) (SIGNATURE |case| (#2# $ (|[\|\|]| |nothing|))) (SIGNATURE |autoCoerce| (|#1| $)) (SIGNATURE |nothing| ($) |constant|))) #1#) (T |Maybe|)) -((|just| (*1 *1 *2) #1=(AND (|isDomain| *1 (|Maybe| *2)) (|ofCategory| *2 #2=(|CoercibleTo| (|OutputForm|))))) (|case| #3=(*1 *2 *1 *3) (AND (|isDomain| *3 (|[\|\|]| *4)) #4=(|ofCategory| *4 #2#) #5=(|isDomain| *2 (|Boolean|)) #6=(|isDomain| *1 (|Maybe| *4)))) (|case| #3# (AND (|isDomain| *3 (|[\|\|]| |nothing|)) #5# #6# #4#)) (|autoCoerce| (*1 *2 *1) #1#) (|nothing| (*1 *1) #1#)) +((|retractIfCan| (((|Union| |#1| "failed") $) 18 T ELT)) (|retract| (#1=(|#1| $) NIL T ELT)) (|nothing| (($) 7 T CONST)) (|just| (#2=($ |#1|) 8 T ELT)) (|coerce| (#2# 16 T ELT) ((#3=(|OutputForm|) $) 23 (|has| |#1| (|CoercibleTo| #3#)) ELT)) (|case| ((#4=(|Boolean|) $ (|[\|\|]| |#1|)) 14 T ELT) ((#4# $ (|[\|\|]| |nothing|)) 11 T ELT)) (|autoCoerce| (#1# 15 T ELT))) +(((|Maybe| |#1|) (|Join| (|UnionType|) (|RetractableTo| |#1|) (CATEGORY |domain| (SIGNATURE |just| ($ |#1|)) (SIGNATURE |case| (#1=(|Boolean|) $ (|[\|\|]| |#1|))) (SIGNATURE |case| (#1# $ (|[\|\|]| |nothing|))) (SIGNATURE |autoCoerce| (|#1| $)) (SIGNATURE |nothing| ($) |constant|) (IF (|has| |#1| #2=(|CoercibleTo| (|OutputForm|))) (ATTRIBUTE #2#) |%noBranch|))) (|Type|)) (T |Maybe|)) +((|just| (*1 *1 *2) #1=(AND (|isDomain| *1 (|Maybe| *2)) (|ofCategory| *2 #2=(|Type|)))) (|case| #3=(*1 *2 *1 *3) (AND (|isDomain| *3 (|[\|\|]| *4)) #4=(|ofCategory| *4 #2#) #5=(|isDomain| *2 (|Boolean|)) #6=(|isDomain| *1 (|Maybe| *4)))) (|case| #3# (AND (|isDomain| *3 (|[\|\|]| |nothing|)) #5# #6# #4#)) (|autoCoerce| (*1 *2 *1) #1#) (|nothing| (*1 *1) #1#)) ((|splitDenominator| (((|Record| (|:| |num| #1=(|Matrix| |#1|)) (|:| |den| |#1|)) #2=(|Matrix| |#2|)) 20 T ELT)) (|commonDenominator| ((|#1| #2#) 9 T ELT)) (|clearDenominator| ((#1# #2#) 18 T ELT))) (((|MatrixCommonDenominator| |#1| |#2|) (CATEGORY |package| (SIGNATURE |commonDenominator| (|#1| #1=(|Matrix| |#2|))) (SIGNATURE |clearDenominator| (#2=(|Matrix| |#1|) #1#)) (SIGNATURE |splitDenominator| ((|Record| (|:| |num| #2#) (|:| |den| |#1|)) #1#))) (|IntegralDomain|) (|QuotientFieldCategory| |#1|)) (T |MatrixCommonDenominator|)) ((|splitDenominator| #1=(*1 *2 *3) (AND #2=(|isDomain| *3 (|Matrix| *5)) #3=(|ofCategory| *5 (|QuotientFieldCategory| *4)) #4=(|ofCategory| *4 #5=(|IntegralDomain|)) (|isDomain| *2 (|Record| (|:| |num| #6=(|Matrix| *4)) (|:| |den| *4))) #7=(|isDomain| *1 (|MatrixCommonDenominator| *4 *5)))) (|clearDenominator| #1# (AND #2# #3# #4# (|isDomain| *2 #6#) #7#)) (|commonDenominator| #1# (AND (|isDomain| *3 #6#) (|ofCategory| *4 (|QuotientFieldCategory| *2)) (|ofCategory| *2 #5#) (|isDomain| *1 (|MatrixCommonDenominator| *2 *4))))) @@ -2109,7 +2109,7 @@ NIL ((|factor| (((|Factored| #1=(|SparseUnivariatePolynomial| |#4|)) #1#) 87 T ELT) (((|Factored| |#4|) |#4|) 270 T ELT))) (((|MultFiniteFactorize| |#1| |#2| |#3| |#4|) (CATEGORY |package| (SIGNATURE |factor| ((|Factored| |#4|) |#4|)) (SIGNATURE |factor| ((|Factored| #1=(|SparseUnivariatePolynomial| |#4|)) #1#))) (|OrderedSet|) (|OrderedAbelianMonoidSup|) (|FiniteFieldCategory|) (|PolynomialCategory| |#3| |#2| |#1|)) (T |MultFiniteFactorize|)) ((|factor| #1=(*1 *2 *3) (AND #2=(|ofCategory| *4 (|OrderedSet|)) #3=(|ofCategory| *5 (|OrderedAbelianMonoidSup|)) #4=(|ofCategory| *6 (|FiniteFieldCategory|)) (|ofCategory| *7 #5=(|PolynomialCategory| *6 *5 *4)) (|isDomain| *2 (|Factored| #6=(|SparseUnivariatePolynomial| *7))) (|isDomain| *1 (|MultFiniteFactorize| *4 *5 *6 *7)) (|isDomain| *3 #6#))) (|factor| #1# (AND #2# #3# #4# (|isDomain| *2 (|Factored| *3)) (|isDomain| *1 (|MultFiniteFactorize| *4 *5 *6 *3)) (|ofCategory| *3 #5#)))) -((|rowEchelonLocal| ((#1=(|Matrix| |#1|) #1# |#1| |#1|) 85 T ELT)) (|rowEchelon| (#2=(#1# #1# |#1|) 66 T ELT)) (|rowEchLocal| (#2# 86 T ELT)) (|rowEch| ((#1# #1#) 67 T ELT)) (|normalizedDivide| (((|Record| (|:| |quotient| |#1|) (|:| |remainder| |#1|)) |#1| |#1|) 84 T ELT))) +((|rowEchelonLocal| ((#1=(|Matrix| |#1|) #1# |#1| |#1|) 84 T ELT)) (|rowEchelon| (#2=(#1# #1# |#1|) 65 T ELT)) (|rowEchLocal| (#2# 85 T ELT)) (|rowEch| ((#1# #1#) 66 T ELT)) (|normalizedDivide| (((|Record| (|:| |quotient| |#1|) (|:| |remainder| |#1|)) |#1| |#1|) 83 T ELT))) (((|ModularHermitianRowReduction| |#1|) (CATEGORY |package| (SIGNATURE |rowEch| (#1=(|Matrix| |#1|) #1#)) (SIGNATURE |rowEchelon| #2=(#1# #1# |#1|)) (SIGNATURE |rowEchLocal| #2#) (SIGNATURE |rowEchelonLocal| (#1# #1# |#1| |#1|)) (SIGNATURE |normalizedDivide| ((|Record| (|:| |quotient| |#1|) (|:| |remainder| |#1|)) |#1| |#1|))) (|EuclideanDomain|)) (T |ModularHermitianRowReduction|)) ((|normalizedDivide| (*1 *2 *3 *3) (AND (|isDomain| *2 (|Record| (|:| |quotient| *3) (|:| |remainder| *3))) #1=(|isDomain| *1 (|ModularHermitianRowReduction| *3)) #2=(|ofCategory| *3 (|EuclideanDomain|)))) (|rowEchelonLocal| (*1 *2 *2 *3 *3) #3=(AND (|isDomain| *2 (|Matrix| *3)) #2# #1#)) (|rowEchLocal| #4=(*1 *2 *2 *3) #3#) (|rowEchelon| #4# #3#) (|rowEch| (*1 *2 *2) #3#)) ((|compiledFunction| ((#1=(|Mapping| |#4| |#2| |#3|) |#1| #2=(|Symbol|) #2#) 19 T ELT)) (|binaryFunction| ((#1# #2#) 12 T ELT))) @@ -2130,7 +2130,7 @@ NIL ((|lifting1| ((#1=(|Union| #2=(|List| #3=(|SparseUnivariatePolynomial| |#4|)) "failed") #3# #4=(|List| |#2|) #2# #5=(|List| |#3|) #6=(|List| |#4|) (|List| (|List| (|Record| (|:| |expt| #7=(|NonNegativeInteger|)) (|:| |pcoef| |#4|)))) #8=(|List| #7#) #9=(|Vector| #10=(|List| (|SparseUnivariatePolynomial| |#3|))) |#3|) 92 T ELT)) (|lifting| ((#1# #3# #4# #10# #5# #6# #8# |#3|) 110 T ELT)) (|corrPoly| ((#1# #3# #4# #5# #8# #2# #9# |#3|) 48 T ELT))) (((|MultivariateLifting| |#1| |#2| |#3| |#4|) (CATEGORY |package| (SIGNATURE |corrPoly| (#1=(|Union| #2=(|List| #3=(|SparseUnivariatePolynomial| |#4|)) "failed") #3# #4=(|List| |#2|) #5=(|List| |#3|) #6=(|List| #7=(|NonNegativeInteger|)) #2# #8=(|Vector| #9=(|List| (|SparseUnivariatePolynomial| |#3|))) |#3|)) (SIGNATURE |lifting| (#1# #3# #4# #9# #5# #10=(|List| |#4|) #6# |#3|)) (SIGNATURE |lifting1| (#1# #3# #4# #2# #5# #10# (|List| (|List| (|Record| (|:| |expt| #7#) (|:| |pcoef| |#4|)))) #6# #8# |#3|))) (|OrderedAbelianMonoidSup|) (|OrderedSet|) (|EuclideanDomain|) (|PolynomialCategory| |#3| |#1| |#2|)) (T |MultivariateLifting|)) ((|lifting1| (*1 *2 *3 *4 *2 *5 *6 *7 *8 *9 *10) (|partial| AND (|isDomain| *2 (|List| #1=(|SparseUnivariatePolynomial| *13))) (|isDomain| *3 #1#) (|isDomain| *4 #2=(|List| *12)) (|isDomain| *5 #3=(|List| *10)) (|isDomain| *6 (|List| *13)) (|isDomain| *7 (|List| (|List| (|Record| (|:| |expt| #4=(|NonNegativeInteger|)) (|:| |pcoef| *13))))) #5=(|isDomain| *8 #6=(|List| #4#)) (|isDomain| *9 (|Vector| (|List| (|SparseUnivariatePolynomial| *10)))) (|ofCategory| *12 #7=(|OrderedSet|)) (|ofCategory| *10 #8=(|EuclideanDomain|)) (|ofCategory| *13 (|PolynomialCategory| *10 *11 *12)) (|ofCategory| *11 #9=(|OrderedAbelianMonoidSup|)) (|isDomain| *1 (|MultivariateLifting| *11 *12 *10 *13)))) (|lifting| (*1 *2 *3 *4 *5 *6 *7 *8 *9) (|partial| AND (|isDomain| *4 (|List| *11)) (|isDomain| *5 (|List| (|SparseUnivariatePolynomial| *9))) (|isDomain| *6 (|List| *9)) (|isDomain| *7 #2#) #5# (|ofCategory| *11 #7#) (|ofCategory| *9 #8#) (|ofCategory| *12 (|PolynomialCategory| *9 *10 *11)) (|ofCategory| *10 #9#) (|isDomain| *2 (|List| #10=(|SparseUnivariatePolynomial| *12))) (|isDomain| *1 (|MultivariateLifting| *10 *11 *9 *12)) (|isDomain| *3 #10#))) (|corrPoly| (*1 *2 *3 *4 *5 *6 *2 *7 *8) (|partial| AND (|isDomain| *2 (|List| #11=(|SparseUnivariatePolynomial| *11))) (|isDomain| *3 #11#) (|isDomain| *4 #3#) (|isDomain| *5 (|List| *8)) (|isDomain| *6 #6#) (|isDomain| *7 (|Vector| (|List| (|SparseUnivariatePolynomial| *8)))) (|ofCategory| *10 #7#) (|ofCategory| *8 #8#) (|ofCategory| *11 (|PolynomialCategory| *8 *9 *10)) (|ofCategory| *9 #9#) (|isDomain| *1 (|MultivariateLifting| *9 *10 *8 *11))))) -((~= (#1=((|Boolean|) $ $) 7 T ELT)) (|zero?| ((#2=(|Boolean|) $) 22 T ELT)) (|subtractIfCan| (((|Union| $ "failed") $ $) 26 T ELT)) (|sample| (#3=($) 23 T CONST)) (|reductum| (($ $) 56 T ELT)) (|recip| (((|Union| $ "failed") $) 42 T ELT)) (|opposite?| ((#2# $ $) 20 T ELT)) (|one?| (((|Boolean|) $) 44 T ELT)) (|monomial| (($ |#1| (|NonNegativeInteger|)) 54 T ELT)) (|minimumDegree| (((|NonNegativeInteger|) $) 58 T ELT)) (|leadingCoefficient| ((|#1| $) 57 T ELT)) (|latex| (((|String|) $) 11 T ELT)) (|hash| (((|SingleInteger|) $) 12 T ELT)) (|degree| (((|NonNegativeInteger|) $) 59 T ELT)) (|coerce| (((|OutputForm|) $) 13 T ELT) (($ (|Integer|)) 41 T ELT) (($ |#1|) 53 (|has| |#1| (|CommutativeRing|)) ELT)) (|coefficient| ((|#1| $ (|NonNegativeInteger|)) 55 T ELT)) (|characteristic| (((|NonNegativeInteger|)) 40 T CONST)) (|before?| (#1# 6 T ELT)) (|annihilate?| (((|Boolean|) $ $) 33 T ELT)) (|Zero| (#3# 24 T CONST)) (|One| (($) 45 T CONST)) (= (#1# 8 T ELT)) (- (($ $) 29 T ELT) (($ $ $) 28 T ELT)) (+ (($ $ $) 18 T ELT)) (** (($ $ (|PositiveInteger|)) 35 T ELT) (($ $ (|NonNegativeInteger|)) 43 T ELT)) (* (($ (|PositiveInteger|) $) 17 T ELT) (($ (|NonNegativeInteger|) $) 21 T ELT) (($ (|Integer|) . #4=($)) 30 T ELT) (($ $ $) 34 T ELT) (($ $ |#1|) 61 T ELT) (($ |#1| . #4#) 60 T ELT))) +((~= (#1=((|Boolean|) $ $) 7 T ELT)) (|zero?| ((#2=(|Boolean|) $) 22 T ELT)) (|subtractIfCan| (((|Maybe| $) $ $) 26 T ELT)) (|sample| (#3=($) 23 T CONST)) (|reductum| (($ $) 57 T ELT)) (|recip| (((|Union| $ "failed") $) 43 T ELT)) (|opposite?| ((#2# $ $) 20 T ELT)) (|one?| (((|Boolean|) $) 45 T ELT)) (|monomial| (($ |#1| (|NonNegativeInteger|)) 55 T ELT)) (|minimumDegree| (((|NonNegativeInteger|) $) 59 T ELT)) (|leadingCoefficient| ((|#1| $) 58 T ELT)) (|latex| (((|String|) $) 11 T ELT)) (|hash| (((|SingleInteger|) $) 12 T ELT)) (|degree| (((|NonNegativeInteger|) $) 60 T ELT)) (|coerce| (((|OutputForm|) $) 13 T ELT) (($ (|Integer|)) 42 T ELT) (($ |#1|) 54 (|has| |#1| (|CommutativeRing|)) ELT)) (|coefficient| ((|#1| $ (|NonNegativeInteger|)) 56 T ELT)) (|characteristic| (((|NonNegativeInteger|)) 41 T CONST)) (|before?| (#1# 6 T ELT)) (|annihilate?| (((|Boolean|) $ $) 34 T ELT)) (|Zero| (#3# 24 T CONST)) (|One| (($) 46 T CONST)) (= (#1# 8 T ELT)) (- (($ $) 30 T ELT) (($ $ $) 29 T ELT)) (+ (($ $ $) 18 T ELT)) (** (($ $ (|PositiveInteger|)) 36 T ELT) (($ $ (|NonNegativeInteger|)) 44 T ELT)) (* (($ (|PositiveInteger|) $) 17 T ELT) (($ (|NonNegativeInteger|) $) 21 T ELT) (($ (|Integer|) . #4=($)) 31 T ELT) (($ $ $) 35 T ELT) (($ $ |#1|) 62 T ELT) (($ |#1| . #4#) 61 T ELT))) (((|MonogenicLinearOperator| |#1|) (|Category|) (|Ring|)) (T |MonogenicLinearOperator|)) ((|degree| (*1 *2 *1) (AND (|ofCategory| *1 (|MonogenicLinearOperator| *3)) (|ofCategory| *3 (|Ring|)) (|isDomain| *2 (|NonNegativeInteger|)))) (|minimumDegree| (*1 *2 *1) (AND (|ofCategory| *1 (|MonogenicLinearOperator| *3)) (|ofCategory| *3 (|Ring|)) (|isDomain| *2 (|NonNegativeInteger|)))) (|leadingCoefficient| (*1 *2 *1) (AND (|ofCategory| *1 (|MonogenicLinearOperator| *2)) (|ofCategory| *2 (|Ring|)))) (|reductum| (*1 *1 *1) (AND (|ofCategory| *1 (|MonogenicLinearOperator| *2)) (|ofCategory| *2 (|Ring|)))) (|coefficient| (*1 *2 *1 *3) (AND (|isDomain| *3 (|NonNegativeInteger|)) (|ofCategory| *1 (|MonogenicLinearOperator| *2)) (|ofCategory| *2 (|Ring|)))) (|monomial| (*1 *1 *2 *3) (AND (|isDomain| *3 (|NonNegativeInteger|)) (|ofCategory| *1 (|MonogenicLinearOperator| *2)) (|ofCategory| *2 (|Ring|))))) (|Join| (|Ring|) (|BiModule| |t#1| |t#1|) (CATEGORY |domain| (IF (|has| |t#1| (|CommutativeRing|)) (ATTRIBUTE (|Algebra| |t#1|)) |%noBranch|) (SIGNATURE |degree| ((|NonNegativeInteger|) $)) (SIGNATURE |minimumDegree| ((|NonNegativeInteger|) $)) (SIGNATURE |leadingCoefficient| (|t#1| $)) (SIGNATURE |reductum| ($ $)) (SIGNATURE |coefficient| (|t#1| $ (|NonNegativeInteger|))) (SIGNATURE |monomial| ($ |t#1| (|NonNegativeInteger|))))) @@ -2141,25 +2141,25 @@ NIL ((~= #1=(((|Boolean|) $ $) NIL T ELT)) (|latex| ((#2=(|String|) $) NIL T ELT)) (|hash| (((|SingleInteger|) $) NIL T ELT)) (|exprex| (#3=(#2# #4=(|OutputForm|)) 36 T ELT)) (|display| (((|Void|) #2#) 29 T ELT)) (|coerceS| (#3# 26 T ELT)) (|coerceL| (#3# 27 T ELT)) (|coerce| ((#4# $) NIL T ELT) (#3# 25 T ELT)) (|before?| #1#) (= #1#)) (((|MathMLFormat|) (|Join| (|SetCategory|) (CATEGORY |package| (SIGNATURE |coerce| #1=(#2=(|String|) (|OutputForm|))) (SIGNATURE |coerceS| #1#) (SIGNATURE |coerceL| #1#) (SIGNATURE |exprex| #1#) (SIGNATURE |display| ((|Void|) #2#))))) (T |MathMLFormat|)) ((|coerce| #1=(*1 *2 *3) #2=(AND (|isDomain| *3 (|OutputForm|)) (|isDomain| *2 #3=(|String|)) #4=(|isDomain| *1 (|MathMLFormat|)))) (|coerceS| #1# #2#) (|coerceL| #1# #2#) (|exprex| #1# #2#) (|display| #1# (AND (|isDomain| *3 #3#) (|isDomain| *2 (|Void|)) #4#))) -((~= #1=((#2=(|Boolean|) $ $) NIL T ELT)) (|zero?| #3=((#2# $) NIL T ELT)) (|unitNormal| (((|Record| (|:| |unit| $) (|:| |canonical| $) (|:| |associate| $)) $) NIL T ELT)) (|unitCanonical| #4=(($ $) NIL T ELT)) (|unit?| #3#) (|subtractIfCan| #5=((#6=(|Union| $ #7="failed") $ $) NIL T ELT)) (|squareFreePart| #4#) (|squareFree| #8=(((|Factored| $) $) NIL T ELT)) (|sizeLess?| #1#) (|sample| #9=(($) NIL T CONST)) (|rem| #10=(($ $ $) NIL T ELT)) (|reduce| (($ |#1| |#2|) NIL T ELT)) (|recip| ((#6# $) NIL T ELT)) (|quo| #10#) (|principalIdeal| (((|Record| (|:| |coef| #11=(|List| $)) #12=(|:| |generator| $)) #11#) NIL T ELT)) (|prime?| #3#) (|opposite?| #1#) (|one?| #3#) (|multiEuclidean| (((|Union| #11# #7#) #11# $) NIL T ELT)) (|modulus| ((|#2| $) NIL T ELT)) (|lcm| #10# #13=(($ #11#) NIL T ELT)) (|latex| (((|String|) $) NIL T ELT)) (|inv| #4#) (|hash| (((|SingleInteger|) $) NIL T ELT)) (|gcdPolynomial| ((#14=(|SparseUnivariatePolynomial| $) #14# #14#) NIL T ELT)) (|gcd| #10# #13#) (|factor| #8#) (|extendedEuclidean| (((|Record| #15=(|:| |coef1| $) #16=(|:| |coef2| $) #12#) $ $) NIL T ELT) (((|Union| (|Record| #15# #16#) #7#) $ $ $) NIL T ELT)) (|exquo| #5#) (|expressIdealMember| (((|Maybe| #11#) #11# $) NIL T ELT)) (|exQuo| #5#) (|euclideanSize| ((#17=(|NonNegativeInteger|) $) NIL T ELT)) (|divide| (((|Record| (|:| |quotient| $) (|:| |remainder| $)) $ $) NIL T ELT)) (|coerce| (((|OutputForm|) $) NIL T ELT) (($ #18=(|Integer|)) NIL T ELT) #4# (($ #19=(|Fraction| #18#)) NIL T ELT) ((|#1| $) NIL T ELT)) (|characteristic| ((#17#) NIL T CONST)) (|before?| #1#) (|associates?| #1#) (|annihilate?| #1#) (|Zero| #9#) (|One| #9#) (= #1#) (/ #10#) (- #4# #10#) (+ #10#) (** (($ $ #20=(|PositiveInteger|)) NIL T ELT) (($ $ #17#) NIL T ELT) (($ $ #18#) NIL T ELT)) (* (($ #20# $) NIL T ELT) (($ #17# $) NIL T ELT) (($ #18# . #21=($)) NIL T ELT) #10# (($ $ #19#) NIL T ELT) (($ #19# . #21#) NIL T ELT))) -(((|ModularField| |#1| |#2| |#3| |#4| |#5|) (|Join| (|Field|) (CATEGORY |domain| (SIGNATURE |modulus| (|#2| $)) (SIGNATURE |coerce| (|#1| $)) (SIGNATURE |reduce| ($ |#1| |#2|)) (SIGNATURE |exQuo| ((|Union| $ #1="failed") $ $)))) (|CommutativeRing|) (|AbelianMonoid|) (|Mapping| |#1| |#1| |#2|) (|Mapping| (|Union| |#2| #1#) |#2| |#2|) (|Mapping| (|Union| |#1| #1#) |#1| |#1| |#2|)) (T |ModularField|)) -((|modulus| #1=(*1 *2 *1) (AND (|ofCategory| *2 #2=(|AbelianMonoid|)) (|isDomain| *1 (|ModularField| *3 *2 *4 *5 *6)) (|ofCategory| *3 #3=(|CommutativeRing|)) (|ofType| *4 (|Mapping| *3 *3 *2)) (|ofType| *5 (|Mapping| #4=(|Union| *2 #5="failed") *2 *2)) (|ofType| *6 (|Mapping| #6=(|Union| *3 #5#) *3 *3 *2)))) (|coerce| #1# (AND #7=(|ofCategory| *2 #3#) #8=(|isDomain| *1 (|ModularField| *2 *3 *4 *5 *6)) #9=(|ofCategory| *3 #2#) #10=(|ofType| *4 (|Mapping| *2 *2 *3)) #11=(|ofType| *5 (|Mapping| #6# *3 *3)) #12=(|ofType| *6 (|Mapping| #4# *2 *2 *3)))) (|reduce| (*1 *1 *2 *3) (AND #8# #7# #9# #10# #11# #12#)) (|exQuo| (*1 *1 *1 *1) (|partial| AND #8# #7# #9# #10# #11# #12#))) -((~= #1=(#2=(#3=(|Boolean|) $ $) NIL T ELT)) (|zero?| (#4=(#3# $) 37 T ELT)) (|vectorise| ((#5=(|Vector| |#1|) $ #6=(|NonNegativeInteger|)) NIL T ELT)) (|variables| ((#7=(|List| #8=(|SingletonAsOrderedSet|)) $) NIL T ELT)) (|unmakeSUP| (($ #9=(|SparseUnivariatePolynomial| |#1|)) NIL T ELT)) (|univariate| ((#10=(|SparseUnivariatePolynomial| $) $ #8#) NIL T ELT) #11=((#9# $) NIL T ELT)) (|unitNormal| (((|Record| (|:| |unit| $) (|:| |canonical| $) (|:| |associate| $)) $) NIL #12=(|has| |#1| (|IntegralDomain|)) ELT)) (|unitCanonical| #13=(#14=($ $) NIL #12# ELT)) (|unit?| (#4# NIL #12# ELT)) (|totalDegree| #15=(#16=(#6# $) NIL T ELT) ((#6# $ #7#) NIL T ELT)) (|subtractIfCan| (#17=(#18=(|Union| $ #19="failed") $ $) NIL T ELT)) (|subResultantGcd| #20=(#21=($ $ $) NIL #12# ELT)) (|squareFreePolynomial| #22=(((|Factored| #10#) #10#) NIL #23=(|has| |#1| (|PolynomialFactorizationExplicit|)) ELT)) (|squareFreePart| #24=(#14# NIL #25=(|has| |#1| (|GcdDomain|)) ELT)) (|squareFree| (#26=((|Factored| $) $) NIL #25# ELT)) (|solveLinearPolynomialEquation| (((|Union| #27=(|List| #10#) #19#) #27# #10#) NIL #23# ELT)) (|sizeLess?| (#2# NIL #28=(|has| |#1| (|Field|)) ELT)) (|size| (#29=(#6#) 55 #30=(|has| |#1| (|Finite|)) ELT)) (|shiftRight| #31=(#32=($ $ #6#) NIL T ELT)) (|shiftLeft| 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((#53=(|Record| (|:| |mat| #54=(|Matrix| |#1|)) (|:| |vec| #5#)) . #51#) NIL T ELT) ((#54# . #47#) NIL T ELT)) (|reduce| (#55=($ |#2|) 49 T ELT)) (|recip| ((#18# $) 98 T ELT)) (|random| (#33# 59 #30# ELT)) (|quo| #45#) (|pseudoRemainder| #56=(#21# NIL T ELT)) (|pseudoQuotient| #20#) (|pseudoDivide| (((|Record| (|:| |coef| |#1|) #57=(|:| |quotient| $) #58=(|:| |remainder| $)) $ $) NIL #12# ELT)) (|principalIdeal| (((|Record| (|:| |coef| #59=(|List| $)) #60=(|:| |generator| $)) #59#) NIL #28# ELT)) (|primitivePart| #24# #61=(#62=($ $ #8#) NIL #25# ELT)) (|primitiveMonomials| #63=((#59# $) NIL T ELT)) (|prime?| (#4# NIL #23# ELT)) (|pow| (#64=((|PrimitiveArray| $)) 89 T ELT)) (|pomopo!| (($ $ |#1| #6# $) NIL T ELT)) (|patternMatch| ((#65=(|PatternMatchResult| #66=(|Float|) . #67=($)) $ #68=(|Pattern| #66#) #65#) NIL (AND (|has| #8# #69=(|PatternMatchable| #66#)) (|has| |#1| #69#)) ELT) ((#70=(|PatternMatchResult| #37# . #67#) $ #71=(|Pattern| #37#) #70#) NIL (AND (|has| #8# 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((#46# . #86=(#52#)) NIL #49# ELT) ((#50# . #87=(#52# $)) NIL #49# ELT) ((#53# . #87#) NIL T ELT) ((#54# . #86#) NIL T ELT)) (|leadingMonomial| #88=(#14# NIL T ELT)) (|leadingCoefficient| (#42# 35 T ELT)) (|lcm| #89=(($ #59#) NIL #25# ELT) #90=(#21# NIL #25# ELT)) (|latex| (((|String|) $) NIL T ELT)) (|karatsubaDivide| ((#80# $ #6#) NIL T ELT)) (|isTimes| #91=((#76# $) NIL T ELT)) (|isPlus| #91#) (|isExpt| (((|Union| (|Record| (|:| |var| #8#) (|:| |exponent| #6#)) #19#) $) NIL T ELT)) (|integrate| (#14# NIL #92=(|has| |#1| (|Algebra| #36#)) ELT)) (|init| (#33# NIL #75# CONST)) (|index| (($ #85#) NIL #30# ELT)) (|hash| (((|SingleInteger|) $) NIL T ELT)) (|ground?| #73#) (|ground| #41#) (|gcdPolynomial| ((#10# #10# #10#) NIL #25# ELT)) (|gcd| #89# #90#) (|frobenius| (#14# 88 (|has| |#1| (|FiniteFieldCategory|)) ELT)) (|factorSquareFreePolynomial| #22#) (|factorPolynomial| #22#) (|factor| (#26# NIL #23# ELT)) (|extendedEuclidean| (((|Union| (|Record| #93=(|:| |coef1| $) #94=(|:| |coef2| $)) #19#) $ $ $) NIL #28# ELT) (((|Record| #93# #94# #60#) $ $) NIL #28# ELT)) (|exquo| ((#18# $ |#1|) NIL #12# ELT) (#17# 97 #12# ELT)) (|expressIdealMember| (((|Maybe| #59#) #59# $) NIL #28# ELT)) (|eval| (($ $ (|List| #95=(|Equation| $))) NIL T ELT) (($ $ #95#) NIL T ELT) (($ $ $ $) NIL T ELT) (($ $ #59# #59#) NIL T ELT) (($ $ #8# |#1|) NIL T ELT) (($ $ #7# #96=(|List| |#1|)) NIL T ELT) (($ $ #8# $) NIL T ELT) (($ $ #7# #59#) NIL T ELT)) (|euclideanSize| (#16# NIL #28# ELT)) (|elt| ((|#1| $ |#1|) NIL T ELT) #56# ((#97=(|Fraction| $) #97# #97#) NIL #12# ELT) ((|#1| #97# |#1|) NIL #28# ELT) ((#97# $ #97#) NIL #12# ELT)) (|divideExponents| ((#18# $ #6#) NIL T ELT)) (|divide| (#81# 99 #28# ELT)) (|discriminant| (#62# NIL #44# ELT) (#42# NIL #44# ELT)) (|differentiate| #78# #77# #98=(($ $ #7#) NIL T ELT) #99=(#62# NIL T ELT) #88# #31# #100=(($ $ #84#) NIL T ELT) #101=(($ $ #84# #6#) NIL T ELT) (($ $ #84# $) NIL T ELT) #102=(($ $ #103=(|Symbol|)) NIL #104=(|has| |#1| 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(|subtractIfCan| (((|Maybe| $) $ $) NIL T ELT)) (|squareFreePart| #4#) (|squareFree| #5=(((|Factored| $) $) NIL T ELT)) (|sizeLess?| #1#) (|sample| #6=(($) NIL T CONST)) (|rem| #7=(($ $ $) NIL T ELT)) (|reduce| (($ |#1| |#2|) NIL T ELT)) (|recip| ((#8=(|Union| $ #9="failed") $) NIL T ELT)) (|quo| #7#) (|principalIdeal| (((|Record| (|:| |coef| #10=(|List| $)) #11=(|:| |generator| $)) #10#) NIL T ELT)) (|prime?| #3#) (|opposite?| #1#) (|one?| #3#) (|multiEuclidean| (((|Union| #10# #9#) #10# $) NIL T ELT)) (|modulus| ((|#2| $) NIL T ELT)) (|lcm| #7# #12=(($ #10#) NIL T ELT)) (|latex| (((|String|) $) NIL T ELT)) (|inv| #4#) (|hash| (((|SingleInteger|) $) NIL T ELT)) (|gcdPolynomial| ((#13=(|SparseUnivariatePolynomial| $) #13# #13#) NIL T ELT)) (|gcd| #7# #12#) (|factor| #5#) (|extendedEuclidean| (((|Record| #14=(|:| |coef1| $) #15=(|:| |coef2| $) #11#) $ $) NIL T ELT) (((|Union| (|Record| #14# #15#) #9#) $ $ $) NIL T ELT)) (|exquo| #16=((#8# $ $) NIL T ELT)) (|expressIdealMember| (((|Maybe| #10#) #10# $) NIL T ELT)) (|exQuo| #16#) (|euclideanSize| ((#17=(|NonNegativeInteger|) $) NIL T ELT)) (|divide| (((|Record| (|:| |quotient| $) (|:| |remainder| $)) $ $) NIL T ELT)) (|coerce| (((|OutputForm|) . #18=($)) NIL T ELT) (($ #19=(|Integer|)) NIL T ELT) #4# (($ #20=(|Fraction| #19#)) NIL T ELT) ((|#1| . #18#) NIL T ELT)) (|characteristic| ((#17#) NIL T CONST)) (|before?| #1#) (|associates?| #1#) (|annihilate?| #1#) (|Zero| #6#) (|One| #6#) (= #1#) (/ #7#) (- #4# #7#) (+ #7#) (** (($ $ #21=(|PositiveInteger|)) NIL T ELT) (($ $ #17#) NIL T ELT) (($ $ #19#) NIL T ELT)) (* (($ #21# $) NIL T ELT) (($ #17# $) NIL T ELT) (($ #19# . #22=($)) NIL T ELT) #7# (($ $ #20#) NIL T ELT) (($ #20# . #22#) NIL T ELT))) +(((|ModularField| |#1| |#2| |#3| |#4| |#5|) (|Join| (|Field|) (|CoercibleTo| |#1|) (CATEGORY |domain| (SIGNATURE |modulus| (|#2| $)) (SIGNATURE |reduce| ($ |#1| |#2|)) (SIGNATURE |exQuo| ((|Union| $ #1="failed") $ $)))) (|CommutativeRing|) (|AbelianMonoid|) (|Mapping| |#1| |#1| |#2|) (|Mapping| (|Union| |#2| #1#) |#2| |#2|) (|Mapping| (|Union| |#1| #1#) |#1| |#1| |#2|)) (T |ModularField|)) +((|modulus| (*1 *2 *1) (AND (|ofCategory| *2 #1=(|AbelianMonoid|)) (|isDomain| *1 (|ModularField| *3 *2 *4 *5 *6)) (|ofCategory| *3 #2=(|CommutativeRing|)) (|ofType| *4 (|Mapping| *3 *3 *2)) (|ofType| *5 (|Mapping| #3=(|Union| *2 #4="failed") *2 *2)) (|ofType| *6 (|Mapping| #5=(|Union| *3 #4#) *3 *3 *2)))) (|reduce| (*1 *1 *2 *3) (AND #6=(|isDomain| *1 (|ModularField| *2 *3 *4 *5 *6)) #7=(|ofCategory| *2 #2#) #8=(|ofCategory| *3 #1#) #9=(|ofType| *4 (|Mapping| *2 *2 *3)) #10=(|ofType| *5 (|Mapping| #5# *3 *3)) #11=(|ofType| *6 (|Mapping| #3# *2 *2 *3)))) (|exQuo| (*1 *1 *1 *1) (|partial| AND #6# #7# #8# #9# #10# #11#))) +((~= #1=(#2=(#3=(|Boolean|) $ $) NIL T ELT)) (|zero?| (#4=(#3# $) 37 T ELT)) (|vectorise| ((#5=(|Vector| |#1|) $ #6=(|NonNegativeInteger|)) NIL T ELT)) (|variables| ((#7=(|List| #8=(|SingletonAsOrderedSet|)) $) NIL T ELT)) (|unmakeSUP| (($ #9=(|SparseUnivariatePolynomial| |#1|)) NIL T ELT)) (|univariate| ((#10=(|SparseUnivariatePolynomial| $) $ #8#) NIL T ELT) #11=((#9# $) NIL T ELT)) (|unitNormal| (((|Record| (|:| |unit| $) (|:| |canonical| $) (|:| |associate| $)) $) NIL #12=(|has| |#1| (|IntegralDomain|)) ELT)) (|unitCanonical| #13=(#14=($ $) NIL #12# ELT)) (|unit?| (#4# NIL #12# ELT)) (|totalDegree| #15=(#16=(#6# $) NIL T ELT) ((#6# $ #7#) NIL T ELT)) (|subtractIfCan| ((#17=(|Maybe| $) $ $) NIL T ELT)) (|subResultantGcd| #18=(#19=($ $ $) NIL #12# ELT)) (|squareFreePolynomial| #20=(((|Factored| #10#) #10#) NIL #21=(|has| |#1| (|PolynomialFactorizationExplicit|)) ELT)) (|squareFreePart| #22=(#14# NIL #23=(|has| |#1| (|GcdDomain|)) ELT)) (|squareFree| (#24=((|Factored| $) $) NIL #23# ELT)) (|solveLinearPolynomialEquation| (((|Union| #25=(|List| #10#) #26="failed") #25# #10#) NIL #21# ELT)) (|sizeLess?| (#2# NIL #27=(|has| |#1| (|Field|)) ELT)) (|size| (#28=(#6#) 55 #29=(|has| |#1| (|Finite|)) ELT)) (|shiftRight| #30=(#31=($ $ #6#) NIL T ELT)) (|shiftLeft| #30#) (|setPoly| ((|#2| |#2|) 51 T ELT)) (|separate| (((|Record| (|:| |primePart| $) (|:| |commonPart| $)) $ $) NIL #23# ELT)) (|sample| (#32=($) NIL T CONST)) (|retractIfCan| (((|Union| |#1| . #33=(#26#)) . #34=($)) NIL T ELT) (((|Union| #35=(|Fraction| #36=(|Integer|)) . #33#) . #34#) NIL #37=(|has| |#1| (|RetractableTo| #35#)) ELT) (((|Union| #36# . #33#) . #34#) NIL #38=(|has| |#1| (|RetractableTo| #36#)) ELT) #39=(((|Union| #8# . #33#) . #34#) NIL T ELT)) (|retract| #40=(#41=(|#1| . #42=($)) NIL T ELT) ((#35# . #42#) NIL #37# ELT) ((#36# . #42#) NIL #38# ELT) ((#8# . #42#) NIL T ELT)) (|resultant| (($ $ $ #8#) NIL #43=(|has| |#1| (|CommutativeRing|)) ELT) ((|#1| $ $) NIL #43# ELT)) (|rem| #44=(#19# NIL #27# ELT)) (|reductum| (#14# 72 T ELT)) (|reducedSystem| ((#45=(|Matrix| #36#) . #46=(#47=(|Matrix| $))) NIL #48=(|has| |#1| (|LinearlyExplicitRingOver| #36#)) ELT) ((#49=(|Record| (|:| |mat| #45#) (|:| |vec| (|Vector| #36#))) . #50=(#47# 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ELT) (($ $ #10#) NIL T ELT)) (* (($ #12# $) NIL T ELT) (($ #10# $) NIL T ELT) (($ #9# $) 21 T ELT) (#11# 20 T ELT))) -(((|ModularRing| |#1| |#2| |#3| |#4| |#5|) (|Join| (|Ring|) (CATEGORY |domain| (SIGNATURE |modulus| (|#2| $)) (SIGNATURE |coerce| (|#1| $)) (SIGNATURE |reduce| ($ |#1| |#2|)) (SIGNATURE |exQuo| (#1=(|Union| $ #2="failed") $ $)) (SIGNATURE |recip| (#1# $)) (SIGNATURE |inv| ($ $)))) (|CommutativeRing|) (|AbelianMonoid|) (|Mapping| |#1| |#1| |#2|) (|Mapping| (|Union| |#2| #2#) |#2| |#2|) (|Mapping| (|Union| |#1| #2#) |#1| |#1| |#2|)) (T |ModularRing|)) -((|recip| #1=(*1 *1 *1) #2=(|partial| AND #3=(|isDomain| *1 (|ModularRing| *2 *3 *4 *5 *6)) #4=(|ofCategory| *2 #5=(|CommutativeRing|)) #6=(|ofCategory| *3 #7=(|AbelianMonoid|)) #8=(|ofType| *4 (|Mapping| *2 *2 *3)) #9=(|ofType| *5 (|Mapping| #10=(|Union| *3 #11="failed") *3 *3)) #12=(|ofType| *6 (|Mapping| #13=(|Union| *2 #11#) *2 *2 *3)))) (|modulus| #14=(*1 *2 *1) (AND (|ofCategory| *2 #7#) (|isDomain| *1 (|ModularRing| *3 *2 *4 *5 *6)) (|ofCategory| *3 #5#) (|ofType| *4 (|Mapping| *3 *3 *2)) (|ofType| *5 (|Mapping| #13# *2 *2)) (|ofType| *6 (|Mapping| #10# *3 *3 *2)))) (|coerce| #14# (AND #4# #3# #6# #8# #9# #12#)) (|reduce| (*1 *1 *2 *3) #15=(AND #3# #4# #6# #8# #9# #12#)) (|exQuo| (*1 *1 *1 *1) #2#) (|inv| #1# #15#)) +((~= #1=(#2=(#3=(|Boolean|) $ $) NIL T ELT)) (|zero?| (#4=(#3# $) 33 T ELT)) (|subtractIfCan| (((|Maybe| $) $ $) NIL T ELT)) (|sample| (#5=($) NIL T CONST)) (|reduce| (($ |#1| |#2|) 25 T ELT)) (|recip| ((#6=(|Union| $ "failed") $) 51 T ELT)) (|opposite?| #1#) (|one?| (#4# 35 T ELT)) (|modulus| ((|#2| $) 12 T ELT)) (|latex| (((|String|) $) NIL T ELT)) (|inv| (#7=($ $) 52 T ELT)) (|hash| (((|SingleInteger|) $) NIL T ELT)) (|exQuo| ((#6# $ $) 50 T ELT)) (|coerce| (((|OutputForm|) $) 24 T ELT) (($ #8=(|Integer|)) 19 T ELT) ((|#1| $) 13 T ELT)) (|characteristic| ((#9=(|NonNegativeInteger|)) 28 T CONST)) (|before?| #1#) (|annihilate?| #1#) (|Zero| (#5# 16 T CONST)) (|One| (#5# 30 T CONST)) (= (#2# 41 T ELT)) (- (#7# 46 T ELT) (#10=($ $ $) 40 T ELT)) (+ (#10# 43 T ELT)) (** (($ $ #11=(|PositiveInteger|)) NIL T ELT) (($ $ #9#) NIL T ELT)) (* (($ #11# $) NIL T ELT) (($ #9# $) NIL T ELT) (($ #8# $) 21 T ELT) (#10# 20 T ELT))) +(((|ModularRing| |#1| |#2| |#3| |#4| |#5|) (|Join| (|Ring|) (|CoercibleTo| |#1|) (CATEGORY |domain| (SIGNATURE |modulus| (|#2| $)) (SIGNATURE |reduce| ($ |#1| |#2|)) (SIGNATURE |exQuo| ((|Union| $ #1="failed") $ $)) (SIGNATURE |inv| ($ $)))) (|CommutativeRing|) (|AbelianMonoid|) (|Mapping| |#1| |#1| |#2|) (|Mapping| (|Union| |#2| #1#) |#2| |#2|) (|Mapping| (|Union| |#1| #1#) |#1| |#1| |#2|)) (T |ModularRing|)) +((|modulus| (*1 *2 *1) (AND (|ofCategory| *2 #1=(|AbelianMonoid|)) (|isDomain| *1 (|ModularRing| *3 *2 *4 *5 *6)) (|ofCategory| *3 #2=(|CommutativeRing|)) (|ofType| *4 (|Mapping| *3 *3 *2)) (|ofType| *5 (|Mapping| #3=(|Union| *2 #4="failed") *2 *2)) (|ofType| *6 (|Mapping| #5=(|Union| *3 #4#) *3 *3 *2)))) (|reduce| (*1 *1 *2 *3) #6=(AND #7=(|isDomain| *1 (|ModularRing| *2 *3 *4 *5 *6)) #8=(|ofCategory| *2 #2#) #9=(|ofCategory| *3 #1#) #10=(|ofType| *4 (|Mapping| *2 *2 *3)) #11=(|ofType| *5 (|Mapping| #5# *3 *3)) #12=(|ofType| *6 (|Mapping| #3# *2 *2 *3)))) (|exQuo| (*1 *1 *1 *1) (|partial| AND #7# #8# #9# #10# #11# #12#)) (|inv| (*1 *1 *1) #6#)) ((* (($ (|PositiveInteger|) $) NIL T ELT) (($ (|NonNegativeInteger|) $) NIL T ELT) (($ (|Integer|) $) NIL T ELT) (($ |#2| $) NIL T ELT) (($ $ |#2|) 9 T ELT))) (((|Module&| |#1| |#2|) (CATEGORY |package| (SIGNATURE * (|#1| |#1| |#2|)) (SIGNATURE * (|#1| |#2| |#1|)) (SIGNATURE * (|#1| (|Integer|) |#1|)) (SIGNATURE * (|#1| (|NonNegativeInteger|) |#1|)) (SIGNATURE * (|#1| (|PositiveInteger|) |#1|))) (|Module| |#2|) (|CommutativeRing|)) (T |Module&|)) NIL -((~= (#1=((|Boolean|) $ $) 7 T ELT)) (|zero?| ((#2=(|Boolean|) $) 22 T ELT)) (|subtractIfCan| (((|Union| $ "failed") $ $) 26 T ELT)) (|sample| (#3=($) 23 T CONST)) (|opposite?| ((#2# $ $) 20 T ELT)) (|latex| (((|String|) $) 11 T ELT)) (|hash| (((|SingleInteger|) $) 12 T ELT)) (|coerce| (((|OutputForm|) $) 13 T ELT)) (|before?| (#1# 6 T ELT)) (|Zero| (#3# 24 T CONST)) (= (#1# 8 T ELT)) (- (($ $) 29 T ELT) (($ $ $) 28 T ELT)) (+ (($ $ $) 18 T ELT)) (* (($ (|PositiveInteger|) $) 17 T ELT) (($ (|NonNegativeInteger|) $) 21 T ELT) (($ (|Integer|) . #4=($)) 30 T ELT) (($ |#1| . #4#) 33 T ELT) (($ $ |#1|) 37 T ELT))) +((~= (#1=((|Boolean|) $ $) 7 T ELT)) (|zero?| ((#2=(|Boolean|) $) 22 T ELT)) (|subtractIfCan| (((|Maybe| $) $ $) 26 T ELT)) (|sample| (#3=($) 23 T CONST)) (|opposite?| ((#2# $ $) 20 T ELT)) (|latex| (((|String|) $) 11 T ELT)) (|hash| (((|SingleInteger|) $) 12 T ELT)) (|coerce| (((|OutputForm|) $) 13 T ELT)) (|before?| (#1# 6 T ELT)) (|Zero| (#3# 24 T CONST)) (= (#1# 8 T ELT)) (- (($ $) 30 T ELT) (($ $ $) 29 T ELT)) (+ (($ $ $) 18 T ELT)) (* (($ (|PositiveInteger|) $) 17 T ELT) (($ (|NonNegativeInteger|) $) 21 T ELT) (($ (|Integer|) . #4=($)) 31 T ELT) (($ |#1| . #4#) 34 T ELT) (($ $ |#1|) 38 T ELT))) (((|Module| |#1|) (|Category|) (|CommutativeRing|)) (T |Module|)) NIL (|Join| (|BiModule| |t#1| |t#1|) (|LinearSet| |t#1|)) @@ -2183,10 +2183,10 @@ NIL ((|One| (*1 *1) (|ofCategory| *1 (|MonadWithUnit|))) (|one?| (*1 *2 *1) (AND (|ofCategory| *1 (|MonadWithUnit|)) (|isDomain| *2 (|Boolean|)))) (|rightPower| (*1 *1 *1 *2) (AND (|ofCategory| *1 (|MonadWithUnit|)) (|isDomain| *2 (|NonNegativeInteger|)))) (|leftPower| (*1 *1 *1 *2) (AND (|ofCategory| *1 (|MonadWithUnit|)) (|isDomain| *2 (|NonNegativeInteger|)))) (** (*1 *1 *1 *2) (AND (|ofCategory| *1 (|MonadWithUnit|)) (|isDomain| *2 (|NonNegativeInteger|)))) (|recip| (*1 *1 *1) (|partial| |ofCategory| *1 (|MonadWithUnit|))) (|leftRecip| (*1 *1 *1) (|partial| |ofCategory| *1 (|MonadWithUnit|))) (|rightRecip| (*1 *1 *1) (|partial| |ofCategory| *1 (|MonadWithUnit|)))) (|Join| (|Monad|) (CATEGORY |domain| (SIGNATURE |One| ($) |constant|) (SIGNATURE |one?| ((|Boolean|) $)) (SIGNATURE |rightPower| ($ $ (|NonNegativeInteger|))) (SIGNATURE 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T) ((|CoercibleTo| (|OutputForm|)) . T) ((|Join|) . T) ((|Monad|) . T) ((|SetCategory|) . T) ((|Type|) . 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(SIGNATURE |retract| (#12# |#1|)) (SIGNATURE |retractIfCan| ((|Union| #12# #8#) |#1|)) (SIGNATURE |convert| #13=(|#3| |#1|)) (SIGNATURE |convert| (|#1| #14=(|Vector| |#2|))) (SIGNATURE |convert| (#14# |#1|)) (SIGNATURE |basis| (#6#)) (SIGNATURE |characteristicPolynomial| #13#) (SIGNATURE |norm| #10#) (SIGNATURE |recip| (#7# |#1|))) (|MonogenicAlgebra| |#2| |#3|) (|CommutativeRing|) (|UnivariatePolynomialCategory| |#2|)) (T |MonogenicAlgebra&|)) +((|size| ((#1=(|NonNegativeInteger|)) 39 T ELT)) (|retractIfCan| (((|Union| #2=(|Integer|) #3="failed") $) NIL T ELT) (((|Union| #4=(|Fraction| #2#) #3#) $) NIL T ELT) (((|Union| |#2| #3#) $) 26 T ELT)) (|retract| ((#2# $) NIL T ELT) ((#4# $) NIL T ELT) (#5=(|#2| $) 23 T ELT)) (|reduce| (#6=($ |#3|) NIL T ELT) ((#7=(|Union| $ #3#) (|Fraction| |#3|)) 49 T ELT)) (|recip| ((#7# $) 69 T ELT)) (|random| (#8=($) 43 T ELT)) (|norm| (#5# 21 T ELT)) (|generator| (#8# 18 T ELT)) (|differentiate| (($ $ #9=(|Mapping| |#2| |#2|)) 57 T ELT) (($ $ #9# #1#) 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(SIGNATURE |derivationCoordinates| ((|Matrix| |#2|) #6=(|Vector| |#1|) #5#)) (SIGNATURE |reduce| (#7=(|Union| |#1| #8="failed") (|Fraction| |#3|))) (SIGNATURE |convert| #9=(|#1| |#3|)) (SIGNATURE |reduce| #9#) (SIGNATURE |generator| #4#) (SIGNATURE |retractIfCan| ((|Union| |#2| #8#) |#1|)) (SIGNATURE |retract| #10=(|#2| |#1|)) (SIGNATURE |retract| (#11=(|Fraction| #12=(|Integer|)) |#1|)) (SIGNATURE |retractIfCan| ((|Union| #11# #8#) |#1|)) (SIGNATURE |retract| (#12# |#1|)) (SIGNATURE |retractIfCan| ((|Union| #12# #8#) |#1|)) (SIGNATURE |convert| #13=(|#3| |#1|)) (SIGNATURE |convert| (|#1| #14=(|Vector| |#2|))) (SIGNATURE |convert| (#14# |#1|)) (SIGNATURE |basis| (#6#)) (SIGNATURE |characteristicPolynomial| #13#) (SIGNATURE |norm| #10#) (SIGNATURE |recip| (#7# |#1|))) (|MonogenicAlgebra| |#2| |#3|) (|CommutativeRing|) (|UnivariatePolynomialCategory| |#2|)) (T |MonogenicAlgebra&|)) ((|size| (*1 *2) (AND (|ofCategory| *4 (|CommutativeRing|)) (|ofCategory| *5 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#3#) ELT)) (|size| (((|NonNegativeInteger|)) 108 (|has| |#1| . #12=((|Finite|))) ELT)) (|sample| (#13=($) 23 T CONST)) (|retractIfCan| (((|Union| #14=(|Integer|) . #15=("failed")) . #16=($)) 194 (|has| |#1| . #17=((|RetractableTo| #14#))) ELT) (((|Union| #18=(|Fraction| #14#) . #15#) . #16#) 192 (|has| |#1| . #19=((|RetractableTo| #18#))) ELT) (((|Union| |#1| . #15#) . #16#) 189 T ELT)) (|retract| ((#14# . #20=($)) 193 (|has| |#1| . #17#) ELT) ((#18# . #20#) 191 (|has| |#1| . #19#) ELT) ((|#1| . #20#) 190 T ELT)) (|represents| (($ (|Vector| |#1|) #5#) 63 T ELT) (($ (|Vector| |#1|)) 80 T ELT)) (|representationType| (((|Union| "prime" "polynomial" "normal" "cyclic")) 173 (|has| |#1| . #10#) ELT)) (|rem| (#21=($ $ $) 129 (|has| |#1| . #3#) ELT)) (|regularRepresentation| (((|Matrix| |#1|) $ #5#) 68 T ELT) (((|Matrix| |#1|) $) 75 T ELT)) (|reducedSystem| (((|Matrix| #22=(|Integer|)) . #23=(#24=(|Matrix| $))) 186 (|has| |#1| . #25=((|LinearlyExplicitRingOver| #22#))) ELT) (((|Record| (|:| |mat| (|Matrix| #22#)) (|:| |vec| (|Vector| #22#))) . #26=(#24# #27=(|Vector| $))) 185 (|has| |#1| . #25#) ELT) (((|Record| (|:| |mat| (|Matrix| |#1|)) (|:| |vec| (|Vector| |#1|))) . #26#) 184 T ELT) (((|Matrix| |#1|) . #23#) 183 T ELT)) (|reduce| (($ |#2|) 178 T ELT) (((|Union| $ "failed") (|Fraction| |#2|)) 175 (|has| |#1| (|Field|)) ELT)) (|recip| (((|Union| $ "failed") $) 42 T ELT)) (|rank| (((|PositiveInteger|)) 69 T ELT)) (|random| (($) 111 (|has| |#1| . #12#) ELT)) (|quo| (#21# 128 (|has| |#1| . #3#) ELT)) (|principalIdeal| (((|Record| (|:| |coef| #28=(|List| $)) (|:| |generator| $)) #28#) 123 (|has| |#1| . #3#) ELT)) (|primitiveElement| (#29=($) 169 (|has| |#1| . #10#) ELT)) (|primitive?| (((|Boolean|) $) 170 (|has| |#1| . #10#) ELT)) (|primeFrobenius| (($ $ #30=(|NonNegativeInteger|)) 161 (|has| |#1| . #10#) ELT) (($ $) 160 (|has| |#1| . #10#) ELT)) (|prime?| (((|Boolean|) $) 136 (|has| |#1| . #3#) ELT)) (|order| ((#7# $) 172 (|has| |#1| . #10#) ELT) (((|OnePointCompletion| 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(((|Maybe| $) $ $) 26 T ELT)) (|squareFreePart| (($ $) 134 (|has| |#1| . #3#) ELT)) (|squareFree| (#11=((|Factored| $) $) 135 (|has| |#1| . #3#) ELT)) (|sizeLess?| (((|Boolean|) $ $) 125 (|has| |#1| . #3#) ELT)) (|size| (((|NonNegativeInteger|)) 108 (|has| |#1| . #12=((|Finite|))) ELT)) (|sample| (#13=($) 23 T CONST)) (|retractIfCan| (((|Union| #14=(|Integer|) . #15=("failed")) . #16=($)) 194 (|has| |#1| . #17=((|RetractableTo| #14#))) ELT) (((|Union| #18=(|Fraction| #14#) . #15#) . #16#) 192 (|has| |#1| . #19=((|RetractableTo| #18#))) ELT) (((|Union| |#1| . #15#) . #16#) 189 T ELT)) (|retract| ((#14# . #20=($)) 193 (|has| |#1| . #17#) ELT) ((#18# . #20#) 191 (|has| |#1| . #19#) ELT) ((|#1| . #20#) 190 T ELT)) (|represents| (($ (|Vector| |#1|) #5#) 64 T ELT) (($ (|Vector| |#1|)) 80 T ELT)) (|representationType| (((|Union| "prime" "polynomial" "normal" "cyclic")) 173 (|has| |#1| . #10#) ELT)) (|rem| (#21=($ $ $) 129 (|has| |#1| . #3#) ELT)) (|regularRepresentation| (((|Matrix| |#1|) $ #5#) 69 T ELT) (((|Matrix| |#1|) $) 75 T ELT)) (|reducedSystem| (((|Matrix| #22=(|Integer|)) . #23=(#24=(|Matrix| $))) 186 (|has| |#1| . #25=((|LinearlyExplicitRingOver| #22#))) ELT) (((|Record| (|:| |mat| (|Matrix| #22#)) (|:| |vec| (|Vector| #22#))) . #26=(#24# #27=(|Vector| $))) 185 (|has| |#1| . #25#) ELT) (((|Record| (|:| |mat| (|Matrix| |#1|)) (|:| |vec| (|Vector| |#1|))) . #26#) 184 T ELT) (((|Matrix| |#1|) . #23#) 183 T ELT)) (|reduce| (($ |#2|) 178 T ELT) (((|Union| $ "failed") (|Fraction| |#2|)) 175 (|has| |#1| (|Field|)) ELT)) (|recip| (((|Union| $ "failed") $) 43 T ELT)) (|rank| (((|PositiveInteger|)) 70 T ELT)) (|random| (($) 111 (|has| |#1| . #12#) ELT)) (|quo| (#21# 128 (|has| |#1| . #3#) ELT)) (|principalIdeal| (((|Record| (|:| |coef| #28=(|List| $)) (|:| |generator| $)) #28#) 123 (|has| |#1| . #3#) ELT)) (|primitiveElement| (#29=($) 169 (|has| |#1| . #10#) ELT)) (|primitive?| (((|Boolean|) $) 170 (|has| |#1| . #10#) ELT)) (|primeFrobenius| (($ $ 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#46#) 146 (|and| (|has| |#1| . #49#) (|has| |#1| . #44#)) ELT) (($ $ (|Mapping| |#1| |#1|)) 145 (|has| |#1| . #44#) ELT) (($ $ (|Mapping| |#1| |#1|) . #51=((|NonNegativeInteger|))) 144 (|has| |#1| . #44#) ELT)) (|derivationCoordinates| (((|Matrix| |#1|) (|Vector| $) (|Mapping| |#1| |#1|)) 174 (|has| |#1| (|Field|)) ELT)) (|definingPolynomial| ((|#2|) 179 T ELT)) (|createPrimitiveElement| (#29# 168 (|has| |#1| . #10#) ELT)) (|coordinates| (((|Vector| |#1|) $ #5#) 66 T ELT) (((|Matrix| |#1|) #5# #5#) 65 T ELT) (((|Vector| |#1|) . #52=($)) 82 T ELT) (((|Matrix| |#1|) #53=(|Vector| $)) 81 T ELT)) (|convert| (((|Vector| |#1|) . #52#) 79 T ELT) (($ (|Vector| |#1|)) 78 T ELT) ((|#2| $) 195 T ELT) (($ |#2|) 177 T ELT)) (|conditionP| (((|Union| (|Vector| $) "failed") (|Matrix| $)) 165 (|has| |#1| . #10#) ELT)) (|coerce| (((|OutputForm|) $) 13 T ELT) (($ (|Integer|)) 42 T ELT) (($ |#1|) 53 T ELT) (($ $) 112 (|has| |#1| . #3#) ELT) (($ #18#) 107 (OR (|has| |#1| . #3#) (|has| |#1| . #19#)) ELT)) 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|#1| |#1|) . #51#) 142 (|has| |#1| . #44#) ELT)) (= (#1# 8 T ELT)) (/ (($ $ $) 141 (|has| |#1| . #3#) ELT)) (- (($ $) 30 T ELT) (($ $ $) 29 T ELT)) (+ (($ $ $) 18 T ELT)) (** (($ $ (|PositiveInteger|)) 36 T ELT) (($ $ (|NonNegativeInteger|)) 44 T ELT) (($ $ #54=(|Integer|)) 138 (|has| |#1| . #3#) ELT)) (* (($ (|PositiveInteger|) $) 17 T ELT) (($ (|NonNegativeInteger|) $) 21 T ELT) (($ (|Integer|) . #55=($)) 31 T ELT) (($ $ $) 35 T ELT) (($ $ |#1|) 55 T ELT) (($ |#1| . #55#) 54 T ELT) (($ #56=(|Fraction| #54#) . #55#) 140 (|has| |#1| . #3#) ELT) (($ $ #56#) 139 (|has| |#1| . #3#) ELT))) (((|MonogenicAlgebra| |#1| |#2|) (|Category|) (|CommutativeRing|) (|UnivariatePolynomialCategory| |t#1|)) (T |MonogenicAlgebra|)) ((|generator| (*1 *1) (AND (|ofCategory| *2 (|CommutativeRing|)) (|ofCategory| *1 (|MonogenicAlgebra| *2 *3)) (|ofCategory| *3 (|UnivariatePolynomialCategory| *2)))) (|definingPolynomial| (*1 *2) (AND (|ofCategory| *1 (|MonogenicAlgebra| *3 *2)) (|ofCategory| *3 (|CommutativeRing|)) (|ofCategory| *2 (|UnivariatePolynomialCategory| *3)))) (|reduce| (*1 *1 *2) (AND (|ofCategory| *3 (|CommutativeRing|)) (|ofCategory| *1 (|MonogenicAlgebra| *3 *2)) (|ofCategory| *2 (|UnivariatePolynomialCategory| *3)))) (|convert| (*1 *1 *2) (AND (|ofCategory| *3 (|CommutativeRing|)) (|ofCategory| *1 (|MonogenicAlgebra| *3 *2)) (|ofCategory| *2 (|UnivariatePolynomialCategory| *3)))) (|lift| (*1 *2 *1) (AND (|ofCategory| *1 (|MonogenicAlgebra| *3 *2)) (|ofCategory| *3 (|CommutativeRing|)) (|ofCategory| *2 (|UnivariatePolynomialCategory| *3)))) (|reduce| (*1 *1 *2) (|partial| AND (|isDomain| *2 (|Fraction| *4)) (|ofCategory| *4 (|UnivariatePolynomialCategory| *3)) (|ofCategory| *3 (|Field|)) (|ofCategory| *3 (|CommutativeRing|)) (|ofCategory| *1 (|MonogenicAlgebra| *3 *4)))) (|derivationCoordinates| (*1 *2 *3 *4) (AND (|isDomain| *3 (|Vector| *1)) (|isDomain| *4 (|Mapping| *5 *5)) (|ofCategory| *5 (|Field|)) (|ofCategory| *1 (|MonogenicAlgebra| *5 *6)) (|ofCategory| *5 (|CommutativeRing|)) (|ofCategory| *6 (|UnivariatePolynomialCategory| *5)) (|isDomain| *2 (|Matrix| *5))))) (|Join| (|FramedAlgebra| |t#1| |t#2|) (|CommutativeRing|) (|ConvertibleTo| |t#2|) (|FullyRetractableTo| |t#1|) (|FullyLinearlyExplicitRingOver| |t#1|) (CATEGORY |domain| (SIGNATURE |generator| ($)) (SIGNATURE |definingPolynomial| (|t#2|)) (SIGNATURE |reduce| ($ |t#2|)) (SIGNATURE |convert| ($ |t#2|)) (SIGNATURE |lift| (|t#2| $)) (IF (|has| |t#1| (|Finite|)) (ATTRIBUTE (|Finite|)) |%noBranch|) (IF (|has| |t#1| (|Field|)) (PROGN (ATTRIBUTE (|Field|)) (ATTRIBUTE (|DifferentialExtension| |t#1|)) (SIGNATURE |reduce| ((|Union| $ "failed") (|Fraction| |t#2|))) (SIGNATURE |derivationCoordinates| ((|Matrix| |t#1|) (|Vector| $) (|Mapping| |t#1| |t#1|)))) |%noBranch|) (IF (|has| |t#1| (|FiniteFieldCategory|)) (ATTRIBUTE (|FiniteFieldCategory|)) |%noBranch|))) @@ -2219,7 +2219,7 @@ NIL ((|factor| (((|Factored| |#4|) |#4|) 42 T ELT))) (((|MPolyCatPolyFactorizer| |#1| |#2| |#3| |#4|) (CATEGORY |package| (SIGNATURE |factor| ((|Factored| |#4|) |#4|))) (|OrderedAbelianMonoidSup|) (|Join| (|OrderedSet|) (CATEGORY |domain| (SIGNATURE |convert| (#1=(|Symbol|) $)) (SIGNATURE |variable| ((|Union| $ "failed") #1#)))) (|EuclideanDomain|) (|PolynomialCategory| (|Polynomial| |#3|) |#1| |#2|)) (T |MPolyCatPolyFactorizer|)) ((|factor| (*1 *2 *3) (AND (|ofCategory| *4 (|OrderedAbelianMonoidSup|)) (|ofCategory| *5 (|Join| (|OrderedSet|) (CATEGORY |domain| (SIGNATURE |convert| (#1=(|Symbol|) $)) (SIGNATURE |variable| ((|Union| $ "failed") #1#))))) (|ofCategory| *6 (|EuclideanDomain|)) (|isDomain| *2 (|Factored| *3)) (|isDomain| *1 (|MPolyCatPolyFactorizer| *4 *5 *6 *3)) (|ofCategory| *3 (|PolynomialCategory| (|Polynomial| *6) *4 *5))))) -((~= #1=(#2=(#3=(|Boolean|) $ $) NIL T ELT)) (|zero?| #4=(#5=(#3# $) NIL T ELT)) (|variables| ((#6=(|List| #7=(|OrderedVariableList| |#1|)) $) NIL T ELT)) (|univariate| ((#8=(|SparseUnivariatePolynomial| $) $ #7#) NIL T ELT) ((#9=(|SparseUnivariatePolynomial| |#2|) $) NIL T ELT)) (|unitNormal| (((|Record| (|:| |unit| $) (|:| |canonical| $) (|:| |associate| $)) $) NIL #10=(|has| |#2| (|IntegralDomain|)) ELT)) (|unitCanonical| #11=(#12=($ $) NIL #10# ELT)) (|unit?| (#5# NIL #10# ELT)) (|totalDegree| #13=((#14=(|NonNegativeInteger|) $) NIL T ELT) ((#14# $ #6#) NIL T ELT)) (|subtractIfCan| (#15=(#16=(|Union| $ #17="failed") $ $) NIL T ELT)) (|squareFreePolynomial| #18=(((|Factored| #8#) #8#) NIL #19=(|has| |#2| (|PolynomialFactorizationExplicit|)) ELT)) (|squareFreePart| #20=(#12# NIL #21=(|has| |#2| (|GcdDomain|)) ELT)) (|squareFree| (#22=((|Factored| $) $) NIL #21# ELT)) (|solveLinearPolynomialEquation| (((|Union| #23=(|List| #8#) #17#) #23# #8#) NIL #19# ELT)) (|sample| #24=(($) NIL T CONST)) (|retractIfCan| (((|Union| |#2| . #25=(#17#)) . #26=($)) NIL T ELT) (((|Union| #27=(|Fraction| #28=(|Integer|)) . #25#) . #26#) NIL #29=(|has| |#2| (|RetractableTo| #27#)) ELT) (((|Union| #28# . #25#) . #26#) NIL #30=(|has| |#2| (|RetractableTo| #28#)) ELT) #31=(((|Union| #7# . #25#) . #26#) NIL T ELT)) (|retract| #32=(#33=(|#2| . #34=($)) NIL T ELT) ((#27# . #34#) NIL #29# ELT) ((#28# . #34#) NIL #30# ELT) ((#7# . #34#) NIL T ELT)) (|resultant| (($ $ $ #7#) NIL #35=(|has| |#2| (|CommutativeRing|)) ELT)) (|reductum| #36=(#12# NIL T ELT)) (|reducedSystem| ((#37=(|Matrix| #28#) . #38=(#39=(|Matrix| $))) NIL #40=(|has| |#2| (|LinearlyExplicitRingOver| #28#)) ELT) ((#41=(|Record| (|:| |mat| #37#) (|:| |vec| (|Vector| #28#))) . #42=(#39# #43=(|Vector| $))) NIL #40# ELT) ((#44=(|Record| (|:| |mat| #45=(|Matrix| |#2|)) (|:| |vec| (|Vector| |#2|))) . #42#) NIL T ELT) ((#45# . #38#) NIL T ELT)) (|recip| ((#16# $) NIL T ELT)) (|primitivePart| #20# #46=(#47=($ $ #7#) NIL #21# ELT)) (|primitiveMonomials| #48=((#49=(|List| $) $) NIL T ELT)) (|prime?| (#5# NIL #19# ELT)) (|pomopo!| (($ $ |#2| #50=(|IndexedExponents| #7#) $) NIL T ELT)) (|patternMatch| ((#51=(|PatternMatchResult| #52=(|Float|) . #53=($)) $ #54=(|Pattern| #52#) #51#) NIL (AND (|has| #7# #55=(|PatternMatchable| #52#)) (|has| |#2| #55#)) ELT) ((#56=(|PatternMatchResult| #28# . #53#) $ #57=(|Pattern| #28#) #56#) NIL (AND (|has| #7# #58=(|PatternMatchable| #28#)) (|has| |#2| #58#)) ELT)) (|opposite?| #1#) (|one?| #4#) (|numberOfMonomials| #13#) (|multivariate| (($ #9# #7#) NIL T ELT) (($ #8# #7#) NIL T ELT)) (|monomials| #48#) (|monomial?| #4#) (|monomial| (($ |#2| #50#) NIL T ELT) #59=(($ $ #7# #14#) NIL T ELT) #60=(($ $ #6# #61=(|List| #14#)) NIL T ELT)) (|monicDivide| (((|Record| (|:| |quotient| $) (|:| |remainder| $)) $ $ #7#) NIL T ELT)) (|minimumDegree| #62=((#50# $) NIL T ELT) #63=((#14# $ #7#) NIL T ELT) #64=((#61# $ #6#) NIL T ELT)) (|mapExponents| (($ (|Mapping| #50# #50#) $) NIL T ELT)) (|map| (($ (|Mapping| |#2| |#2|) $) NIL T ELT)) (|mainVariable| #31#) (|leftReducedSystem| ((#37# . #65=(#43#)) NIL #40# ELT) ((#41# . #66=(#43# $)) NIL #40# ELT) ((#44# . #66#) NIL T ELT) ((#45# . #65#) NIL T ELT)) (|leadingMonomial| #36#) (|leadingCoefficient| #32#) (|lcm| #67=(($ #49#) NIL #21# ELT) #68=(#69=($ $ $) NIL #21# ELT)) (|latex| (((|String|) $) NIL T ELT)) (|isTimes| #70=(((|Union| #49# #17#) $) NIL T ELT)) (|isPlus| #70#) (|isExpt| (((|Union| (|Record| (|:| |var| #7#) (|:| |exponent| #14#)) #17#) $) NIL T ELT)) (|hash| (((|SingleInteger|) $) NIL T ELT)) (|ground?| #4#) (|ground| #32#) (|gcdPolynomial| ((#8# #8# #8#) NIL #21# ELT)) (|gcd| #67# #68#) (|factorSquareFreePolynomial| #18#) (|factorPolynomial| #18#) (|factor| (#22# NIL #19# ELT)) (|exquo| ((#16# $ |#2|) NIL #10# ELT) (#15# NIL #10# ELT)) (|eval| (($ $ (|List| #71=(|Equation| $))) NIL T ELT) (($ $ #71#) NIL T ELT) (($ $ $ $) NIL T ELT) (($ $ #49# #49#) NIL T ELT) (($ $ #7# |#2|) NIL T ELT) (($ $ #6# #72=(|List| |#2|)) NIL T ELT) (($ $ #7# $) NIL T ELT) (($ $ #6# #49#) NIL T ELT)) (|discriminant| (#47# NIL #35# ELT)) (|differentiate| #60# #59# #73=(($ $ #6#) NIL T ELT) #74=(#47# NIL T ELT)) (|degree| #62# #63# #64#) (|convert| ((#54# . #75=($)) NIL (AND (|has| #7# #76=(|ConvertibleTo| #54#)) (|has| |#2| #76#)) ELT) ((#57# . #75#) NIL (AND (|has| #7# #77=(|ConvertibleTo| #57#)) (|has| |#2| #77#)) ELT) ((#78=(|InputForm|) . #75#) NIL (AND (|has| #7# #79=(|ConvertibleTo| #78#)) (|has| |#2| #79#)) ELT)) (|content| (#33# NIL #21# ELT) #46#) (|conditionP| (((|Union| #43# #17#) #39#) NIL #80=(AND (|has| $ #81=(|CharacteristicNonZero|)) #19#) ELT)) (|coerce| (((|OutputForm|) $) NIL T ELT) (($ #28#) NIL T ELT) (($ |#2|) NIL T ELT) (($ #7#) NIL T ELT) #11# (($ #27#) NIL (OR #82=(|has| |#2| (|Algebra| #27#)) #29#) ELT)) (|coefficients| ((#72# $) NIL T ELT)) (|coefficient| ((|#2| $ #50#) NIL T ELT) #59# #60#) (|charthRoot| (((|Maybe| $) $) NIL (OR #80# (|has| |#2| #81#)) ELT)) (|characteristic| ((#14#) NIL T CONST)) (|binomThmExpt| (($ $ $ #14#) NIL #35# ELT)) (|before?| #1#) (|associates?| (#2# NIL #10# ELT)) (|annihilate?| #1#) (|Zero| #24#) (|One| #24#) (D #60# #59# #73# #74#) (= #1#) (/ (#83=($ $ |#2|) NIL (|has| |#2| (|Field|)) ELT)) (- #36# #84=(#69# NIL T ELT)) (+ #84#) (** (($ $ #85=(|PositiveInteger|)) NIL T ELT) (($ $ #14#) NIL T ELT)) (* (($ #85# $) NIL T ELT) (($ #14# $) NIL T ELT) (($ #28# . #86=($)) NIL T ELT) #84# (($ $ #27#) NIL #82# ELT) (($ #27# . #86#) NIL #82# ELT) (($ |#2| . #86#) NIL T ELT) (#83# NIL T ELT))) +((~= #1=(#2=(#3=(|Boolean|) $ $) NIL T ELT)) (|zero?| #4=(#5=(#3# $) NIL T ELT)) (|variables| ((#6=(|List| #7=(|OrderedVariableList| |#1|)) $) NIL T ELT)) (|univariate| ((#8=(|SparseUnivariatePolynomial| $) $ #7#) NIL T ELT) ((#9=(|SparseUnivariatePolynomial| |#2|) $) NIL T ELT)) (|unitNormal| (((|Record| (|:| |unit| $) (|:| |canonical| $) (|:| |associate| $)) $) NIL #10=(|has| |#2| (|IntegralDomain|)) ELT)) (|unitCanonical| #11=(#12=($ $) NIL #10# ELT)) (|unit?| (#5# NIL #10# ELT)) (|totalDegree| #13=((#14=(|NonNegativeInteger|) $) NIL T ELT) ((#14# $ #6#) NIL T ELT)) (|subtractIfCan| ((#15=(|Maybe| $) $ $) NIL T ELT)) (|squareFreePolynomial| #16=(((|Factored| #8#) #8#) NIL #17=(|has| |#2| (|PolynomialFactorizationExplicit|)) ELT)) (|squareFreePart| #18=(#12# NIL #19=(|has| |#2| (|GcdDomain|)) ELT)) (|squareFree| (#20=((|Factored| $) $) NIL #19# ELT)) (|solveLinearPolynomialEquation| (((|Union| #21=(|List| #8#) #22="failed") #21# #8#) NIL #17# ELT)) (|sample| #23=(($) NIL T CONST)) (|retractIfCan| (((|Union| |#2| . #24=(#22#)) . #25=($)) NIL T ELT) (((|Union| #26=(|Fraction| #27=(|Integer|)) . #24#) . #25#) NIL #28=(|has| |#2| (|RetractableTo| #26#)) ELT) (((|Union| #27# . #24#) . #25#) NIL #29=(|has| |#2| (|RetractableTo| #27#)) ELT) #30=(((|Union| #7# . #24#) . #25#) NIL T ELT)) (|retract| #31=(#32=(|#2| . #33=($)) NIL T ELT) ((#26# . #33#) NIL #28# ELT) ((#27# . #33#) NIL #29# ELT) ((#7# . #33#) NIL T ELT)) (|resultant| (($ $ $ #7#) NIL #34=(|has| |#2| (|CommutativeRing|)) ELT)) (|reductum| #35=(#12# NIL T ELT)) (|reducedSystem| ((#36=(|Matrix| #27#) . #37=(#38=(|Matrix| $))) NIL #39=(|has| |#2| (|LinearlyExplicitRingOver| #27#)) ELT) ((#40=(|Record| (|:| |mat| #36#) (|:| |vec| (|Vector| #27#))) . #41=(#38# #42=(|Vector| $))) NIL #39# ELT) ((#43=(|Record| (|:| |mat| #44=(|Matrix| |#2|)) (|:| |vec| (|Vector| |#2|))) . #41#) NIL T ELT) ((#44# . #37#) NIL T ELT)) (|recip| ((#45=(|Union| $ #22#) $) NIL T ELT)) (|primitivePart| #18# #46=(#47=($ $ #7#) NIL #19# ELT)) (|primitiveMonomials| #48=((#49=(|List| $) $) NIL T ELT)) (|prime?| (#5# NIL #17# ELT)) (|pomopo!| (($ $ |#2| #50=(|IndexedExponents| #7#) $) NIL T ELT)) (|patternMatch| ((#51=(|PatternMatchResult| #52=(|Float|) . #53=($)) $ #54=(|Pattern| #52#) #51#) NIL (AND (|has| #7# #55=(|PatternMatchable| #52#)) (|has| |#2| #55#)) ELT) ((#56=(|PatternMatchResult| #27# . #53#) $ #57=(|Pattern| #27#) #56#) NIL (AND (|has| #7# #58=(|PatternMatchable| #27#)) (|has| |#2| #58#)) ELT)) (|opposite?| #1#) (|one?| #4#) (|numberOfMonomials| #13#) (|multivariate| (($ #9# #7#) NIL T ELT) (($ #8# #7#) NIL T ELT)) (|monomials| #48#) (|monomial?| #4#) (|monomial| (($ |#2| #50#) NIL T ELT) #59=(($ $ #7# #14#) NIL T ELT) #60=(($ $ #6# #61=(|List| #14#)) NIL T ELT)) (|monicDivide| (((|Record| (|:| |quotient| $) (|:| |remainder| $)) $ $ #7#) NIL T ELT)) (|minimumDegree| #62=((#50# $) NIL T ELT) #63=((#14# $ #7#) NIL T ELT) #64=((#61# $ #6#) NIL T ELT)) (|mapExponents| (($ (|Mapping| #50# #50#) $) NIL T ELT)) (|map| (($ (|Mapping| |#2| |#2|) $) NIL T ELT)) (|mainVariable| #30#) (|leftReducedSystem| ((#36# . #65=(#42#)) NIL #39# ELT) ((#40# . #66=(#42# $)) NIL #39# ELT) ((#43# . #66#) NIL T ELT) ((#44# . #65#) NIL T ELT)) (|leadingMonomial| #35#) (|leadingCoefficient| #31#) (|lcm| #67=(($ #49#) NIL #19# ELT) #68=(#69=($ $ $) NIL #19# ELT)) (|latex| (((|String|) $) NIL T ELT)) (|isTimes| #70=(((|Union| #49# #22#) $) NIL T ELT)) (|isPlus| #70#) (|isExpt| (((|Union| (|Record| (|:| |var| #7#) (|:| |exponent| #14#)) #22#) $) NIL T ELT)) (|hash| (((|SingleInteger|) $) NIL T ELT)) (|ground?| #4#) (|ground| #31#) (|gcdPolynomial| ((#8# #8# #8#) NIL #19# ELT)) (|gcd| #67# #68#) (|factorSquareFreePolynomial| #16#) (|factorPolynomial| #16#) (|factor| (#20# NIL #17# ELT)) (|exquo| ((#45# $ |#2|) NIL #10# ELT) ((#45# $ $) NIL #10# ELT)) (|eval| (($ $ (|List| #71=(|Equation| $))) NIL T ELT) (($ $ #71#) NIL T ELT) (($ $ $ $) NIL T ELT) (($ $ #49# #49#) NIL T ELT) (($ $ #7# |#2|) NIL T ELT) (($ $ #6# #72=(|List| |#2|)) NIL T ELT) (($ $ #7# $) NIL T ELT) (($ $ #6# #49#) NIL T ELT)) (|discriminant| (#47# NIL #34# ELT)) (|differentiate| #60# #59# #73=(($ $ #6#) NIL T ELT) #74=(#47# NIL T ELT)) (|degree| #62# #63# #64#) (|convert| ((#54# . #75=($)) NIL (AND (|has| #7# #76=(|ConvertibleTo| #54#)) (|has| |#2| #76#)) ELT) ((#57# . #75#) NIL (AND (|has| #7# #77=(|ConvertibleTo| #57#)) (|has| |#2| #77#)) ELT) ((#78=(|InputForm|) . #75#) NIL (AND (|has| #7# #79=(|ConvertibleTo| #78#)) (|has| |#2| #79#)) ELT)) (|content| (#32# NIL #19# ELT) #46#) (|conditionP| (((|Union| #42# #22#) #38#) NIL #80=(AND (|has| $ #81=(|CharacteristicNonZero|)) #17#) ELT)) (|coerce| (((|OutputForm|) $) NIL T ELT) (($ #27#) NIL T ELT) (($ |#2|) NIL T ELT) (($ #7#) NIL T ELT) #11# (($ #26#) NIL (OR #82=(|has| |#2| (|Algebra| #26#)) #28#) ELT)) (|coefficients| ((#72# $) NIL T ELT)) (|coefficient| ((|#2| $ #50#) NIL T ELT) #59# #60#) (|charthRoot| ((#15# $) NIL (OR #80# (|has| |#2| #81#)) ELT)) (|characteristic| ((#14#) NIL T CONST)) (|binomThmExpt| (($ $ $ #14#) NIL #34# ELT)) (|before?| #1#) (|associates?| (#2# NIL #10# ELT)) (|annihilate?| #1#) (|Zero| #23#) (|One| #23#) (D #60# #59# #73# #74#) (= #1#) (/ (#83=($ $ |#2|) NIL (|has| |#2| (|Field|)) ELT)) (- #35# #84=(#69# NIL T ELT)) (+ #84#) (** (($ $ #85=(|PositiveInteger|)) NIL T ELT) (($ $ #14#) NIL T ELT)) (* (($ #85# $) NIL T ELT) (($ #14# $) NIL T ELT) (($ #27# . #86=($)) NIL T ELT) #84# (($ $ #26#) NIL #82# ELT) (($ #26# . #86#) NIL #82# ELT) (($ |#2| . #86#) NIL T ELT) (#83# NIL T ELT))) (((|MultivariatePolynomial| |#1| |#2|) (|PolynomialCategory| |#2| (|IndexedExponents| #1=(|OrderedVariableList| |#1|)) #1#) (|List| (|Symbol|)) (|Ring|)) (T |MultivariatePolynomial|)) NIL ((|totalfract| (((|Record| (|:| |sup| #1=(|Polynomial| |#3|)) (|:| |inf| #1#)) |#4|) 14 T ELT)) (|pushup| (#2=(|#4| |#4| |#2|) 33 T ELT)) (|pushuconst| ((|#4| (|Fraction| #1#) |#2|) 62 T ELT)) (|pushucoef| ((|#4| (|SparseUnivariatePolynomial| #1#) |#2|) 74 T ELT)) (|pushdterm| ((|#4| (|SparseUnivariatePolynomial| |#4|) |#2|) 49 T ELT)) (|pushdown| (#2# 52 T ELT)) (|factor| (((|Factored| |#4|) |#4|) 40 T ELT))) @@ -2231,7 +2231,7 @@ NIL ((|map| (((|MonoidRing| |#2| |#3|) (|Mapping| |#2| |#1|) (|MonoidRing| |#1| |#3|)) 18 T ELT))) (((|MonoidRingFunctions2| |#1| |#2| |#3|) (CATEGORY |package| (SIGNATURE |map| ((|MonoidRing| |#2| |#3|) (|Mapping| |#2| |#1|) (|MonoidRing| |#1| |#3|)))) #1=(|Ring|) #1# (|Monoid|)) (T |MonoidRingFunctions2|)) ((|map| (*1 *2 *3 *4) (AND (|isDomain| *3 (|Mapping| *6 *5)) (|isDomain| *4 (|MonoidRing| *5 *7)) (|ofCategory| *5 #1=(|Ring|)) (|ofCategory| *6 #1#) (|ofCategory| *7 (|Monoid|)) (|isDomain| *2 (|MonoidRing| *6 *7)) (|isDomain| *1 (|MonoidRingFunctions2| *5 *6 *7))))) -((~= #1=(#2=(#3=(|Boolean|) $ $) NIL T ELT)) (|zero?| (#4=(#3# $) 36 T ELT)) (|terms| ((#5=(|List| (|Record| (|:| |coef| |#1|) (|:| |monom| |#2|))) $) 37 T ELT)) (|subtractIfCan| ((#6=(|Union| $ #7="failed") $ $) NIL T ELT)) (|size| (#8=(#9=(|NonNegativeInteger|)) 22 #10=(AND (|has| |#2| #11=(|Finite|)) (|has| |#1| #11#)) ELT)) (|sample| (#12=($) NIL T CONST)) (|retractIfCan| (((|Union| |#2| . #13=(#7#)) $) 76 T ELT) (((|Union| |#1| . #13#) $) 79 T ELT)) (|retract| (#14=(|#2| $) NIL T ELT) (#15=(|#1| $) NIL T ELT)) (|reductum| (#16=($ $) 99 #17=(|has| |#2| (|OrderedSet|)) ELT)) (|recip| ((#6# $) 83 T ELT)) (|random| (#12# 48 #10# ELT)) (|opposite?| #1#) (|one?| #18=(#4# NIL T ELT)) (|numberOfMonomials| ((#9# $) 70 T ELT)) (|monomials| (((|List| $) $) 52 T ELT)) (|monomial?| #18#) (|monomial| (($ |#1| |#2|) 17 T ELT)) (|map| (($ (|Mapping| |#1| |#1|) $) 68 T ELT)) (|lookup| ((#19=(|PositiveInteger|) $) 43 #10# ELT)) (|leadingMonomial| (#14# 98 #17# ELT)) (|leadingCoefficient| (#15# 97 #17# ELT)) (|latex| (((|String|) $) NIL T ELT)) (|index| (($ #19#) 35 #10# ELT)) (|hash| (((|SingleInteger|) $) NIL T ELT)) (|coerce| (((|OutputForm|) $) 96 T ELT) (($ #20=(|Integer|)) 59 T ELT) (($ |#2|) 55 T ELT) (($ |#1|) 56 T ELT) (($ #5#) 11 T ELT)) (|coefficients| (((|List| |#1|) $) 54 T ELT)) (|coefficient| ((|#1| $ |#2|) 114 T ELT)) (|charthRoot| (((|Maybe| $) $) NIL (|has| |#1| (|CharacteristicNonZero|)) ELT)) (|characteristic| (#8# NIL T CONST)) (|before?| #1#) (|annihilate?| #1#) (|Zero| (#12# 12 T CONST)) (|One| (#12# 44 T CONST)) (= (#2# 104 T ELT)) (- (#16# 61 T ELT) (#21=($ $ $) NIL T ELT)) (+ (#21# 33 T ELT)) (** (($ $ #19#) NIL T ELT) (($ $ #9#) NIL T ELT)) (* (($ #19# $) NIL T ELT) (($ #9# $) NIL T ELT) (($ #20# $) 66 T ELT) (#21# 117 T ELT) (($ |#1| $) 63 #22=(|has| |#1| (|CommutativeRing|)) ELT) (($ $ |#1|) NIL #22# ELT))) +((~= #1=(#2=(#3=(|Boolean|) $ $) NIL T ELT)) (|zero?| (#4=(#3# $) 36 T ELT)) (|terms| ((#5=(|List| (|Record| (|:| |coef| |#1|) (|:| |monom| |#2|))) $) 37 T ELT)) (|subtractIfCan| ((#6=(|Maybe| $) $ $) NIL T ELT)) (|size| (#7=(#8=(|NonNegativeInteger|)) 22 #9=(AND (|has| |#2| #10=(|Finite|)) (|has| |#1| #10#)) ELT)) (|sample| (#11=($) NIL T CONST)) (|retractIfCan| (((|Union| |#2| . #12=(#13="failed")) $) 76 T ELT) (((|Union| |#1| . #12#) $) 79 T ELT)) (|retract| (#14=(|#2| $) NIL T ELT) (#15=(|#1| $) NIL T ELT)) (|reductum| (#16=($ $) 99 #17=(|has| |#2| (|OrderedSet|)) ELT)) (|recip| (((|Union| $ #13#) $) 83 T ELT)) (|random| (#11# 48 #9# ELT)) (|opposite?| #1#) (|one?| #18=(#4# NIL T ELT)) (|numberOfMonomials| ((#8# $) 70 T ELT)) (|monomials| (((|List| $) $) 52 T ELT)) (|monomial?| #18#) (|monomial| (($ |#1| |#2|) 17 T ELT)) (|map| (($ (|Mapping| |#1| |#1|) $) 68 T ELT)) (|lookup| ((#19=(|PositiveInteger|) $) 43 #9# ELT)) (|leadingMonomial| (#14# 98 #17# ELT)) (|leadingCoefficient| (#15# 97 #17# ELT)) (|latex| (((|String|) $) NIL T ELT)) (|index| (($ #19#) 35 #9# ELT)) (|hash| (((|SingleInteger|) $) NIL T ELT)) (|coerce| (((|OutputForm|) $) 96 T ELT) (($ #20=(|Integer|)) 59 T ELT) (($ |#2|) 55 T ELT) (($ |#1|) 56 T ELT) (($ #5#) 11 T ELT)) (|coefficients| (((|List| |#1|) $) 54 T ELT)) (|coefficient| ((|#1| $ |#2|) 114 T ELT)) (|charthRoot| ((#6# $) NIL (|has| |#1| (|CharacteristicNonZero|)) ELT)) (|characteristic| (#7# NIL T CONST)) (|before?| #1#) (|annihilate?| #1#) (|Zero| (#11# 12 T CONST)) (|One| (#11# 44 T CONST)) (= (#2# 104 T ELT)) (- (#16# 61 T ELT) (#21=($ $ $) NIL T ELT)) (+ (#21# 33 T ELT)) (** (($ $ #19#) NIL T ELT) (($ $ #8#) NIL T ELT)) (* (($ #19# $) NIL T ELT) (($ #8# $) NIL T ELT) (($ #20# $) 66 T ELT) (#21# 117 T ELT) (($ |#1| $) 63 #22=(|has| |#1| (|CommutativeRing|)) ELT) (($ $ |#1|) NIL #22# ELT))) (((|MonoidRing| |#1| |#2|) (|Join| #1=(|Ring|) (|RetractableTo| |#2|) (|RetractableTo| |#1|) (|Functorial| |#1|) (CATEGORY |domain| (SIGNATURE |monomial| ($ |#1| |#2|)) (SIGNATURE |coefficient| (|#1| $ |#2|)) (SIGNATURE |coerce| ($ #2=(|List| (|Record| (|:| |coef| |#1|) (|:| |monom| |#2|))))) (SIGNATURE |terms| (#2# $)) (SIGNATURE |monomial?| ((|Boolean|) $)) (SIGNATURE |coefficients| ((|List| |#1|) $)) (SIGNATURE |monomials| ((|List| $) $)) (SIGNATURE |numberOfMonomials| ((|NonNegativeInteger|) $)) (IF (|has| |#1| #3=(|CharacteristicZero|)) (ATTRIBUTE #3#) |%noBranch|) (IF (|has| |#1| #4=(|CharacteristicNonZero|)) (ATTRIBUTE #4#) |%noBranch|) (IF (|has| |#1| (|CommutativeRing|)) (ATTRIBUTE (|Algebra| |#1|)) |%noBranch|) (IF (|has| |#1| #5=(|Finite|)) (IF (|has| |#2| #5#) (ATTRIBUTE #5#) |%noBranch|) |%noBranch|) (IF (|has| |#2| (|OrderedSet|)) (PROGN (SIGNATURE |leadingMonomial| (|#2| $)) (SIGNATURE |leadingCoefficient| (|#1| $)) (SIGNATURE |reductum| ($ $))) |%noBranch|))) #1# (|Monoid|)) (T |MonoidRing|)) ((|monomial| (*1 *1 *2 *3) (AND #1=(|isDomain| *1 (|MonoidRing| *2 *3)) #2=(|ofCategory| *2 #3=(|Ring|)) #4=(|ofCategory| *3 #5=(|Monoid|)))) (|coefficient| (*1 *2 *1 *3) (AND #2# #1# #4#)) (|coerce| (*1 *1 *2) (AND #6=(|isDomain| *2 (|List| (|Record| (|:| |coef| *3) (|:| |monom| *4)))) #7=(|ofCategory| *3 #3#) #8=(|ofCategory| *4 #5#) #9=(|isDomain| *1 #10=(|MonoidRing| *3 *4)))) (|terms| #11=(*1 *2 *1) (AND #6# #9# #7# #8#)) (|monomial?| #11# (AND (|isDomain| *2 (|Boolean|)) #9# #7# #8#)) (|coefficients| #11# (AND (|isDomain| *2 (|List| *3)) #9# #7# #8#)) (|monomials| #11# (AND (|isDomain| *2 (|List| #10#)) #9# #7# #8#)) (|numberOfMonomials| #11# (AND (|isDomain| *2 (|NonNegativeInteger|)) #9# #7# #8#)) (|leadingMonomial| #11# (AND (|ofCategory| *2 #5#) (|ofCategory| *2 #12=(|OrderedSet|)) (|isDomain| *1 (|MonoidRing| *3 *2)) #7#)) (|leadingCoefficient| #11# (AND #2# #1# #13=(|ofCategory| *3 #12#) #4#)) (|reductum| (*1 *1 *1) (AND #1# #13# #2# #4#))) ((~= #1=(#2=(#3=(|Boolean|) $ $) NIL T ELT)) (|unique| (#4=(#5=(|List| |#1|) $) 38 T ELT)) (|union| (#6=($ |#1| $) NIL T ELT) #7=(($ $ |#1|) NIL T ELT) (#8=($ $ $) 95 T ELT)) (|symmetricDifference| (#8# 99 T ELT)) (|subset?| (#2# 107 T ELT)) (|set| (#9=($ #5#) 26 T ELT) (#10=($) 17 T ELT)) (|select!| (#11=($ #12=(|Mapping| #3# |#1|) $) 86 #13=(|has| $ (|FiniteAggregate| |#1|)) ELT)) (|select| #14=(#11# NIL #13# ELT)) (|sample| (#10# NIL T CONST)) (|removeDuplicates!| (#15=($ $) 88 T ELT)) (|removeDuplicates| (#15# NIL #16=(AND #13# #17=(|has| |#1| (|BasicType|))) ELT)) (|remove!| (#6# 71 #13# ELT) (#11# 80 #13# ELT) (#18=($ |#1| $ #19=(|Integer|)) 78 T ELT) (#20=($ #12# $ #19#) 81 T ELT)) (|remove| (#6# NIL #16# ELT) #14# (#18# 83 T ELT) (#20# 84 T ELT)) (|reduce| ((|#1| #21=(|Mapping| |#1| |#1| |#1|) $ |#1| |#1|) NIL #17# ELT) ((|#1| #21# $ |#1|) NIL T ELT) ((|#1| #21# $) NIL T ELT)) (|part?| (#2# 106 T ELT)) (|multiset| (#10# 15 T ELT) (($ |#1|) 28 T ELT) (#9# 23 T ELT)) (|members| (#4# 32 T ELT)) (|member?| ((#3# |#1| $) 66 #17# ELT)) (|map!| (#22=($ (|Mapping| |#1| |#1|) $) 91 T ELT)) (|map| (#22# 92 T ELT)) (|latex| (((|String|) $) NIL T ELT)) (|intersect| (#8# 97 T ELT)) (|inspect| (#23=(|#1| $) 63 T ELT)) (|insert!| (#6# 64 T ELT) (($ |#1| $ #24=(|NonNegativeInteger|)) 89 T ELT)) (|hash| (((|SingleInteger|) $) NIL T ELT)) (|find| (((|Union| |#1| "failed") #12# $) NIL T ELT)) (|extract!| (#23# 62 T ELT)) (|every?| #25=((#3# #12# $) NIL T ELT)) (|eval| (($ $ (|List| #26=(|Equation| |#1|))) NIL #27=(AND (|has| |#1| (|Evalable| |#1|)) (|has| |#1| (|SetCategory|))) ELT) (($ $ #26#) NIL #27# ELT) (($ $ |#1| |#1|) NIL #27# ELT) (($ $ #5# #5#) NIL #27# ELT)) (|eq?| #1#) (|empty?| ((#3# $) 57 T ELT)) (|empty| (#10# 14 T ELT)) (|duplicates| (((|List| (|Record| (|:| |entry| |#1|) (|:| |count| #24#))) $) 56 T ELT)) (|difference| #7# (#8# 98 T ELT)) (|dictionary| (#10# 16 T ELT) (#9# 25 T ELT)) (|count| ((#24# |#1| $) 69 #17# ELT) ((#24# #12# $) NIL T ELT)) (|copy| (#15# 82 T ELT)) (|convert| ((#28=(|InputForm|) $) 36 (|has| |#1| (|ConvertibleTo| #28#)) ELT)) (|construct| (#9# 22 T ELT)) (|coerce| (((|OutputForm|) $) 50 T ELT)) (|brace| (#9# 27 T ELT) (#10# 18 T ELT)) (|before?| #1#) (|bag| (#9# 24 T ELT)) (|any?| #25#) (= (#2# 103 T ELT)) (|#| ((#24# $) 68 T ELT))) @@ -2248,7 +2248,7 @@ NIL ((|mergeDifference| ((#1=(|List| |#1|) #1# #1#) 15 T ELT))) (((|MergeThing| |#1|) (CATEGORY |package| (SIGNATURE |mergeDifference| (#1=(|List| |#1|) #1# #1#))) (|OrderedSet|)) (T |MergeThing|)) ((|mergeDifference| (*1 *2 *2 *2) (AND (|isDomain| *2 (|List| *3)) (|ofCategory| *3 (|OrderedSet|)) (|isDomain| *1 (|MergeThing| *3))))) -((~= (#1=((|Boolean|) $ $) 7 T ELT)) (|zero?| ((#2=(|Boolean|) $) 22 T ELT)) (|variables| (((|List| |#2|) $) 160 T ELT)) (|unitNormal| (((|Record| (|:| |unit| $) (|:| |canonical| $) (|:| |associate| $)) $) 153 (|has| |#1| . #3=((|IntegralDomain|))) ELT)) (|unitCanonical| (($ $) 152 (|has| |#1| . #3#) ELT)) (|unit?| ((#4=(|Boolean|) $) 150 (|has| |#1| . #3#) ELT)) (|tanh| (#5=($ $) 109 (|has| |#1| . #6=((|Algebra| (|Fraction| (|Integer|))))) ELT)) (|tan| (#7=($ $) 92 (|has| |#1| . #6#) ELT)) (|subtractIfCan| (((|Union| $ "failed") $ $) 26 T ELT)) (|sqrt| (($ $) 91 (|has| |#1| . #8=((|Algebra| (|Fraction| (|Integer|))))) ELT)) (|sinh| (#5# 108 (|has| |#1| . #6#) ELT)) (|sin| (#7# 93 (|has| |#1| . #6#) ELT)) (|sech| (#5# 107 (|has| |#1| . #6#) ELT)) (|sec| (#7# 94 (|has| |#1| . #6#) ELT)) (|sample| (#9=($) 23 T CONST)) (|reductum| (#10=($ $) 144 T ELT)) (|recip| (((|Union| $ "failed") $) 42 T ELT)) (|polynomial| (((|Polynomial| |#1|) $ (|NonNegativeInteger|)) 122 T ELT) (((|Polynomial| |#1|) $ (|NonNegativeInteger|) (|NonNegativeInteger|)) 121 T ELT)) (|pole?| (((|Boolean|) $) 161 T ELT)) (|pi| (($) 119 (|has| |#1| . #6#) ELT)) (|order| (((|NonNegativeInteger|) $ |#2|) 124 T ELT) (((|NonNegativeInteger|) $ |#2| (|NonNegativeInteger|)) 123 T ELT)) (|opposite?| ((#2# $ $) 20 T ELT)) (|one?| (((|Boolean|) $) 44 T ELT)) (|nthRoot| (($ $ #11=(|Integer|)) 90 (|has| |#1| . #8#) ELT)) (|monomial?| (((|Boolean|) $) 142 T ELT)) (|monomial| (($ $ (|List| |#2|) (|List| (|IndexedExponents| |#2|))) 159 T ELT) (($ $ |#2| (|IndexedExponents| |#2|)) 158 T ELT) (($ |#1| (|IndexedExponents| |#2|)) 143 T ELT) (($ $ |#2| (|NonNegativeInteger|)) 126 T ELT) (($ $ (|List| |#2|) (|List| (|NonNegativeInteger|))) 125 T ELT)) (|map| (($ (|Mapping| |#1| |#1|) $) 138 T ELT)) (|log| (#12=($ $) 116 (|has| |#1| . #6#) ELT)) (|leadingMonomial| (#10# 140 T ELT)) (|leadingCoefficient| ((|#1| $) 139 T ELT)) (|latex| (((|String|) $) 11 T ELT)) (|integrate| (($ $ |#2|) 120 (|has| |#1| (|Algebra| (|Fraction| (|Integer|)))) ELT)) (|hash| (((|SingleInteger|) $) 12 T ELT)) (|extend| (($ $ (|NonNegativeInteger|)) 127 T ELT)) (|exquo| (((|Union| $ "failed") $ $) 154 (|has| |#1| . #3#) ELT)) (|exp| (#12# 117 (|has| |#1| . #6#) ELT)) (|eval| (($ $ |#2| $) 135 T ELT) (($ $ (|List| |#2|) (|List| $)) 134 T ELT) (($ $ (|List| (|Equation| $))) 133 T ELT) (($ $ (|Equation| $)) 132 T ELT) (($ $ $ $) 131 T ELT) (($ $ (|List| $) (|List| $)) 130 T ELT)) (|differentiate| (($ $ (|List| |#2|) . #13=((|List| #14=(|NonNegativeInteger|)))) 52 T ELT) (($ $ |#2| . #15=(#14#)) 51 T ELT) (($ $ (|List| |#2|)) 50 T ELT) (($ $ |#2|) 48 T ELT)) (|degree| (((|IndexedExponents| |#2|) $) 141 T ELT)) (|csch| (#5# 106 (|has| |#1| . #6#) ELT)) (|csc| (#7# 95 (|has| |#1| . #6#) ELT)) (|coth| (#5# 105 (|has| |#1| . #6#) ELT)) (|cot| (#7# 96 (|has| |#1| . #6#) ELT)) (|cosh| (#5# 104 (|has| |#1| . #6#) ELT)) (|cos| (#7# 97 (|has| |#1| . #6#) ELT)) (|complete| (($ $) 162 T ELT)) (|coerce| (((|OutputForm|) $) 13 T ELT) (($ (|Integer|)) 41 T ELT) (($ |#1|) 157 (|has| |#1| (|CommutativeRing|)) ELT) (($ $) 155 (|has| |#1| . #3#) ELT) (($ #16=(|Fraction| (|Integer|))) 147 (|has| |#1| . #17=((|Algebra| #16#))) ELT)) (|coefficient| ((|#1| $ (|IndexedExponents| |#2|)) 145 T ELT) (($ $ |#2| (|NonNegativeInteger|)) 129 T ELT) (($ $ (|List| |#2|) (|List| (|NonNegativeInteger|))) 128 T ELT)) (|charthRoot| (((|Maybe| $) $) 156 (|has| |#1| (|CharacteristicNonZero|)) ELT)) (|characteristic| (((|NonNegativeInteger|)) 40 T CONST)) (|before?| (#1# 6 T ELT)) (|atanh| (#18=($ $) 115 (|has| |#1| . #6#) ELT)) (|atan| (#19=($ $) 103 (|has| |#1| . #6#) ELT)) (|associates?| ((#4# $ $) 151 (|has| |#1| . #3#) ELT)) (|asinh| (#18# 114 (|has| |#1| . #6#) ELT)) (|asin| (#19# 102 (|has| |#1| . #6#) ELT)) (|asech| (#18# 113 (|has| |#1| . #6#) ELT)) (|asec| (#19# 101 (|has| |#1| . #6#) ELT)) (|annihilate?| (((|Boolean|) $ $) 33 T ELT)) (|acsch| (#18# 112 (|has| |#1| . #6#) ELT)) (|acsc| (#19# 100 (|has| |#1| . #6#) ELT)) (|acoth| (#18# 111 (|has| |#1| . #6#) ELT)) (|acot| (#19# 99 (|has| |#1| . #6#) ELT)) (|acosh| (#18# 110 (|has| |#1| . #6#) ELT)) (|acos| (#19# 98 (|has| |#1| . #6#) ELT)) (|Zero| (#9# 24 T CONST)) (|One| (($) 45 T CONST)) (D (($ $ (|List| |#2|) . #13#) 55 T ELT) (($ $ |#2| . #15#) 54 T ELT) (($ $ (|List| |#2|)) 53 T ELT) (($ $ |#2|) 49 T ELT)) (= (#1# 8 T ELT)) (/ (($ $ |#1|) 146 (|has| |#1| (|Field|)) ELT)) (- (($ $) 29 T ELT) (($ $ $) 28 T ELT)) (+ (($ $ $) 18 T ELT)) (** (($ $ (|PositiveInteger|)) 35 T ELT) (($ $ (|NonNegativeInteger|)) 43 T ELT) (($ $ $) 118 (|has| |#1| . #6#) ELT) (($ $ (|Fraction| #11#)) 89 (|has| |#1| . #8#) ELT)) (* (($ (|PositiveInteger|) $) 17 T ELT) (($ (|NonNegativeInteger|) $) 21 T ELT) (($ (|Integer|) . #20=($)) 30 T ELT) (($ $ $) 34 T ELT) (($ $ #16#) 149 (|has| |#1| . #17#) ELT) (($ #16# . #20#) 148 (|has| |#1| . #17#) ELT) (($ |#1| . #20#) 137 T ELT) (($ $ |#1|) 136 T ELT))) +((~= (#1=((|Boolean|) $ $) 7 T ELT)) (|zero?| ((#2=(|Boolean|) $) 22 T ELT)) (|variables| (((|List| |#2|) $) 161 T ELT)) (|unitNormal| (((|Record| (|:| |unit| $) (|:| |canonical| $) (|:| |associate| $)) $) 154 (|has| |#1| . #3=((|IntegralDomain|))) ELT)) (|unitCanonical| (($ $) 153 (|has| |#1| . #3#) ELT)) (|unit?| ((#4=(|Boolean|) $) 151 (|has| |#1| . #3#) ELT)) (|tanh| (#5=($ $) 110 (|has| |#1| . #6=((|Algebra| (|Fraction| (|Integer|))))) ELT)) (|tan| (#7=($ $) 93 (|has| |#1| . #6#) ELT)) (|subtractIfCan| (((|Maybe| $) $ $) 26 T ELT)) (|sqrt| (($ $) 92 (|has| |#1| . #8=((|Algebra| (|Fraction| (|Integer|))))) ELT)) (|sinh| (#5# 109 (|has| |#1| . #6#) ELT)) (|sin| (#7# 94 (|has| |#1| . #6#) ELT)) (|sech| (#5# 108 (|has| |#1| . #6#) ELT)) (|sec| (#7# 95 (|has| |#1| . #6#) ELT)) (|sample| (#9=($) 23 T CONST)) (|reductum| (#10=($ $) 145 T ELT)) (|recip| (((|Union| $ "failed") $) 43 T ELT)) (|polynomial| (((|Polynomial| |#1|) $ (|NonNegativeInteger|)) 123 T ELT) (((|Polynomial| |#1|) $ (|NonNegativeInteger|) (|NonNegativeInteger|)) 122 T ELT)) (|pole?| (((|Boolean|) $) 162 T ELT)) (|pi| (($) 120 (|has| |#1| . #6#) ELT)) (|order| (((|NonNegativeInteger|) $ |#2|) 125 T ELT) (((|NonNegativeInteger|) $ |#2| (|NonNegativeInteger|)) 124 T ELT)) (|opposite?| ((#2# $ $) 20 T ELT)) (|one?| (((|Boolean|) $) 45 T ELT)) (|nthRoot| (($ $ #11=(|Integer|)) 91 (|has| |#1| . #8#) ELT)) (|monomial?| (((|Boolean|) $) 143 T ELT)) (|monomial| (($ $ (|List| |#2|) (|List| (|IndexedExponents| |#2|))) 160 T ELT) (($ $ |#2| (|IndexedExponents| |#2|)) 159 T ELT) (($ |#1| (|IndexedExponents| |#2|)) 144 T ELT) (($ $ |#2| (|NonNegativeInteger|)) 127 T ELT) (($ $ (|List| |#2|) (|List| (|NonNegativeInteger|))) 126 T ELT)) (|map| (($ (|Mapping| |#1| |#1|) $) 139 T ELT)) (|log| (#12=($ $) 117 (|has| |#1| . #6#) ELT)) (|leadingMonomial| (#10# 141 T ELT)) (|leadingCoefficient| ((|#1| $) 140 T ELT)) (|latex| (((|String|) $) 11 T ELT)) (|integrate| (($ $ |#2|) 121 (|has| |#1| (|Algebra| (|Fraction| (|Integer|)))) ELT)) (|hash| (((|SingleInteger|) $) 12 T ELT)) (|extend| (($ $ (|NonNegativeInteger|)) 128 T ELT)) (|exquo| (((|Union| $ "failed") $ $) 155 (|has| |#1| . #3#) ELT)) (|exp| (#12# 118 (|has| |#1| . #6#) ELT)) (|eval| (($ $ |#2| $) 136 T ELT) (($ $ (|List| |#2|) (|List| $)) 135 T ELT) (($ $ (|List| (|Equation| $))) 134 T ELT) (($ $ (|Equation| $)) 133 T ELT) (($ $ $ $) 132 T ELT) (($ $ (|List| $) (|List| $)) 131 T ELT)) (|differentiate| (($ $ (|List| |#2|) . #13=((|List| #14=(|NonNegativeInteger|)))) 53 T ELT) (($ $ |#2| . #15=(#14#)) 52 T ELT) (($ $ (|List| |#2|)) 51 T ELT) (($ $ |#2|) 49 T ELT)) (|degree| (((|IndexedExponents| |#2|) $) 142 T ELT)) (|csch| (#5# 107 (|has| |#1| . #6#) ELT)) (|csc| (#7# 96 (|has| |#1| . #6#) ELT)) (|coth| (#5# 106 (|has| |#1| . #6#) ELT)) (|cot| (#7# 97 (|has| |#1| . #6#) ELT)) (|cosh| (#5# 105 (|has| |#1| . #6#) ELT)) (|cos| (#7# 98 (|has| |#1| . #6#) ELT)) (|complete| (($ $) 163 T ELT)) (|coerce| (((|OutputForm|) $) 13 T ELT) (($ (|Integer|)) 42 T ELT) (($ |#1|) 158 (|has| |#1| (|CommutativeRing|)) ELT) (($ $) 156 (|has| |#1| . #3#) ELT) (($ #16=(|Fraction| (|Integer|))) 148 (|has| |#1| . #17=((|Algebra| #16#))) ELT)) (|coefficient| ((|#1| $ (|IndexedExponents| |#2|)) 146 T ELT) (($ $ |#2| (|NonNegativeInteger|)) 130 T ELT) (($ $ (|List| |#2|) (|List| (|NonNegativeInteger|))) 129 T ELT)) (|charthRoot| (((|Maybe| $) $) 157 (|has| |#1| (|CharacteristicNonZero|)) ELT)) (|characteristic| (((|NonNegativeInteger|)) 41 T CONST)) (|before?| (#1# 6 T ELT)) (|atanh| (#18=($ $) 116 (|has| |#1| . #6#) ELT)) (|atan| (#19=($ $) 104 (|has| |#1| . #6#) ELT)) (|associates?| ((#4# $ $) 152 (|has| |#1| . #3#) ELT)) (|asinh| (#18# 115 (|has| |#1| . #6#) ELT)) (|asin| (#19# 103 (|has| |#1| . #6#) ELT)) (|asech| (#18# 114 (|has| |#1| . #6#) ELT)) (|asec| (#19# 102 (|has| |#1| . #6#) ELT)) (|annihilate?| (((|Boolean|) $ $) 34 T ELT)) (|acsch| (#18# 113 (|has| |#1| . #6#) ELT)) (|acsc| (#19# 101 (|has| |#1| . #6#) ELT)) (|acoth| (#18# 112 (|has| |#1| . #6#) ELT)) (|acot| (#19# 100 (|has| |#1| . #6#) ELT)) (|acosh| (#18# 111 (|has| |#1| . #6#) ELT)) (|acos| (#19# 99 (|has| |#1| . #6#) ELT)) (|Zero| (#9# 24 T CONST)) (|One| (($) 46 T CONST)) (D (($ $ (|List| |#2|) . #13#) 56 T ELT) (($ $ |#2| . #15#) 55 T ELT) (($ $ (|List| |#2|)) 54 T ELT) (($ $ |#2|) 50 T ELT)) (= (#1# 8 T ELT)) (/ (($ $ |#1|) 147 (|has| |#1| (|Field|)) ELT)) (- (($ $) 30 T ELT) (($ $ $) 29 T ELT)) (+ (($ $ $) 18 T ELT)) (** (($ $ (|PositiveInteger|)) 36 T ELT) (($ $ (|NonNegativeInteger|)) 44 T ELT) (($ $ $) 119 (|has| |#1| . #6#) ELT) (($ $ (|Fraction| #11#)) 90 (|has| |#1| . #8#) ELT)) (* (($ (|PositiveInteger|) $) 17 T ELT) (($ (|NonNegativeInteger|) $) 21 T ELT) (($ (|Integer|) . #20=($)) 31 T ELT) (($ $ $) 35 T ELT) (($ $ #16#) 150 (|has| |#1| . #17#) ELT) (($ #16# . #20#) 149 (|has| |#1| . #17#) ELT) (($ |#1| . #20#) 138 T ELT) (($ $ |#1|) 137 T ELT))) (((|MultivariateTaylorSeriesCategory| |#1| |#2|) (|Category|) (|Ring|) (|OrderedSet|)) (T |MultivariateTaylorSeriesCategory|)) ((|coefficient| (*1 *1 *1 *2 *3) (AND (|isDomain| *3 (|NonNegativeInteger|)) (|ofCategory| *1 (|MultivariateTaylorSeriesCategory| *4 *2)) (|ofCategory| *4 (|Ring|)) (|ofCategory| *2 (|OrderedSet|)))) (|coefficient| (*1 *1 *1 *2 *3) (AND (|isDomain| *2 (|List| *5)) (|isDomain| *3 (|List| (|NonNegativeInteger|))) (|ofCategory| *1 (|MultivariateTaylorSeriesCategory| *4 *5)) (|ofCategory| *4 (|Ring|)) (|ofCategory| *5 (|OrderedSet|)))) (|extend| (*1 *1 *1 *2) (AND (|isDomain| *2 (|NonNegativeInteger|)) (|ofCategory| *1 (|MultivariateTaylorSeriesCategory| *3 *4)) (|ofCategory| *3 (|Ring|)) (|ofCategory| *4 (|OrderedSet|)))) (|monomial| (*1 *1 *1 *2 *3) (AND (|isDomain| *3 (|NonNegativeInteger|)) (|ofCategory| *1 (|MultivariateTaylorSeriesCategory| *4 *2)) (|ofCategory| *4 (|Ring|)) (|ofCategory| *2 (|OrderedSet|)))) (|monomial| (*1 *1 *1 *2 *3) (AND (|isDomain| *2 (|List| *5)) (|isDomain| *3 (|List| (|NonNegativeInteger|))) (|ofCategory| *1 (|MultivariateTaylorSeriesCategory| *4 *5)) (|ofCategory| *4 (|Ring|)) (|ofCategory| *5 (|OrderedSet|)))) (|order| (*1 *2 *1 *3) (AND (|ofCategory| *1 (|MultivariateTaylorSeriesCategory| *4 *3)) (|ofCategory| *4 (|Ring|)) (|ofCategory| *3 (|OrderedSet|)) (|isDomain| *2 (|NonNegativeInteger|)))) (|order| (*1 *2 *1 *3 *2) (AND (|isDomain| *2 (|NonNegativeInteger|)) (|ofCategory| *1 (|MultivariateTaylorSeriesCategory| *4 *3)) (|ofCategory| *4 (|Ring|)) (|ofCategory| *3 (|OrderedSet|)))) (|polynomial| (*1 *2 *1 *3) (AND (|isDomain| *3 (|NonNegativeInteger|)) (|ofCategory| *1 (|MultivariateTaylorSeriesCategory| *4 *5)) (|ofCategory| *4 (|Ring|)) (|ofCategory| *5 (|OrderedSet|)) (|isDomain| *2 (|Polynomial| *4)))) (|polynomial| (*1 *2 *1 *3 *3) (AND (|isDomain| *3 (|NonNegativeInteger|)) (|ofCategory| *1 (|MultivariateTaylorSeriesCategory| *4 *5)) (|ofCategory| *4 (|Ring|)) (|ofCategory| *5 (|OrderedSet|)) (|isDomain| *2 (|Polynomial| *4)))) (|integrate| (*1 *1 *1 *2) (AND (|ofCategory| *1 (|MultivariateTaylorSeriesCategory| *3 *2)) (|ofCategory| *3 (|Ring|)) (|ofCategory| *2 (|OrderedSet|)) (|ofCategory| *3 (|Algebra| (|Fraction| (|Integer|))))))) (|Join| (|PartialDifferentialRing| |t#2|) (|PowerSeriesCategory| |t#1| (|IndexedExponents| |t#2|) |t#2|) (|InnerEvalable| |t#2| $) (|Evalable| $) (CATEGORY |domain| (SIGNATURE |coefficient| ($ $ |t#2| (|NonNegativeInteger|))) (SIGNATURE |coefficient| ($ $ (|List| |t#2|) (|List| (|NonNegativeInteger|)))) (SIGNATURE |extend| ($ $ (|NonNegativeInteger|))) (SIGNATURE |monomial| ($ $ |t#2| (|NonNegativeInteger|))) (SIGNATURE |monomial| ($ $ (|List| |t#2|) (|List| (|NonNegativeInteger|)))) (SIGNATURE |order| ((|NonNegativeInteger|) $ |t#2|)) (SIGNATURE |order| ((|NonNegativeInteger|) $ |t#2| (|NonNegativeInteger|))) (SIGNATURE |polynomial| ((|Polynomial| |t#1|) $ (|NonNegativeInteger|))) (SIGNATURE |polynomial| ((|Polynomial| |t#1|) $ (|NonNegativeInteger|) (|NonNegativeInteger|))) (IF (|has| |t#1| (|Algebra| (|Fraction| (|Integer|)))) (PROGN (SIGNATURE |integrate| ($ $ |t#2|)) (ATTRIBUTE (|RadicalCategory|)) (ATTRIBUTE (|TranscendentalFunctionCategory|))) |%noBranch|))) @@ -2262,7 +2262,7 @@ NIL ((|plenaryPower| (($ $ (|PositiveInteger|)) 17 T ELT))) (((|NonAssociativeAlgebra&| |#1| |#2|) (CATEGORY |package| (SIGNATURE |plenaryPower| (|#1| |#1| (|PositiveInteger|)))) (|NonAssociativeAlgebra| |#2|) (|CommutativeRing|)) (T |NonAssociativeAlgebra&|)) NIL -((~= (#1=((|Boolean|) $ $) 7 T ELT)) (|zero?| ((#2=(|Boolean|) $) 22 T ELT)) (|subtractIfCan| (((|Union| $ "failed") $ $) 26 T ELT)) (|sample| (#3=($) 23 T CONST)) (|rightPower| (#4=($ $ (|PositiveInteger|)) 37 T ELT)) (|plenaryPower| (($ $ (|PositiveInteger|)) 44 T ELT)) (|opposite?| ((#2# $ $) 20 T ELT)) (|leftPower| (#4# 38 T ELT)) (|latex| (((|String|) $) 11 T ELT)) (|hash| (((|SingleInteger|) $) 12 T ELT)) (|commutator| (#5=($ $ $) 34 T ELT)) (|coerce| (((|OutputForm|) $) 13 T ELT)) (|before?| (#1# 6 T ELT)) (|associator| (($ $ $ $) 35 T ELT)) (|antiCommutator| (#5# 33 T ELT)) (|Zero| (#3# 24 T CONST)) (= (#1# 8 T ELT)) (- (($ $) 29 T ELT) (($ $ $) 28 T ELT)) (+ (($ $ $) 18 T ELT)) (** (#4# 39 T ELT)) (* (($ (|PositiveInteger|) $) 17 T ELT) (($ (|NonNegativeInteger|) $) 21 T ELT) (($ (|Integer|) . #6=($)) 30 T ELT) (($ $ $) 36 T ELT) (($ $ |#1|) 46 T ELT) (($ |#1| . #6#) 45 T ELT))) +((~= (#1=((|Boolean|) $ $) 7 T ELT)) (|zero?| ((#2=(|Boolean|) $) 22 T ELT)) (|subtractIfCan| (((|Maybe| $) $ $) 26 T ELT)) (|sample| (#3=($) 23 T CONST)) (|rightPower| (#4=($ $ (|PositiveInteger|)) 38 T ELT)) (|plenaryPower| (($ $ (|PositiveInteger|)) 45 T ELT)) (|opposite?| ((#2# $ $) 20 T ELT)) (|leftPower| (#4# 39 T ELT)) (|latex| (((|String|) $) 11 T ELT)) (|hash| (((|SingleInteger|) $) 12 T ELT)) (|commutator| (#5=($ $ $) 35 T ELT)) (|coerce| (((|OutputForm|) $) 13 T ELT)) (|before?| (#1# 6 T ELT)) (|associator| (($ $ $ $) 36 T ELT)) (|antiCommutator| (#5# 34 T ELT)) (|Zero| (#3# 24 T CONST)) (= (#1# 8 T ELT)) (- (($ $) 30 T ELT) (($ $ $) 29 T ELT)) (+ (($ $ $) 18 T ELT)) (** (#4# 40 T ELT)) (* (($ (|PositiveInteger|) $) 17 T ELT) (($ (|NonNegativeInteger|) $) 21 T ELT) (($ (|Integer|) . #6=($)) 31 T ELT) (($ $ $) 37 T ELT) (($ $ |#1|) 47 T ELT) (($ |#1| . #6#) 46 T ELT))) (((|NonAssociativeAlgebra| |#1|) (|Category|) (|CommutativeRing|)) (T |NonAssociativeAlgebra|)) ((|plenaryPower| (*1 *1 *1 *2) (AND (|isDomain| *2 (|PositiveInteger|)) (|ofCategory| *1 (|NonAssociativeAlgebra| *3)) (|ofCategory| *3 (|CommutativeRing|))))) (|Join| (|NonAssociativeRng|) (|Module| |t#1|) (CATEGORY |domain| (SIGNATURE |plenaryPower| ($ $ (|PositiveInteger|))))) @@ -2270,7 +2270,7 @@ NIL ((|commutator| (#1=($ $ $) 10 T ELT)) (|associator| (($ $ $ $) 9 T ELT)) (|antiCommutator| (#1# 12 T ELT))) (((|NonAssociativeRng&| |#1|) (CATEGORY |package| (SIGNATURE |antiCommutator| #1=(|#1| |#1| |#1|)) (SIGNATURE |commutator| #1#) (SIGNATURE |associator| (|#1| |#1| |#1| |#1|))) (|NonAssociativeRng|)) (T |NonAssociativeRng&|)) NIL -((~= (#1=((|Boolean|) $ $) 7 T ELT)) (|zero?| ((#2=(|Boolean|) $) 22 T ELT)) (|subtractIfCan| (((|Union| $ "failed") $ $) 26 T ELT)) (|sample| (#3=($) 23 T CONST)) (|rightPower| (#4=($ $ (|PositiveInteger|)) 37 T ELT)) (|opposite?| ((#2# $ $) 20 T ELT)) (|leftPower| (#4# 38 T ELT)) (|latex| (((|String|) $) 11 T ELT)) (|hash| (((|SingleInteger|) $) 12 T ELT)) (|commutator| (($ $ $) 34 T ELT)) (|coerce| (((|OutputForm|) $) 13 T ELT)) (|before?| (#1# 6 T ELT)) (|associator| (($ $ $ $) 35 T ELT)) (|antiCommutator| (($ $ $) 33 T ELT)) (|Zero| (#3# 24 T CONST)) (= (#1# 8 T ELT)) (- (($ $) 29 T ELT) (($ $ $) 28 T ELT)) (+ (($ $ $) 18 T ELT)) (** (#4# 39 T ELT)) (* (($ (|PositiveInteger|) $) 17 T ELT) (($ (|NonNegativeInteger|) $) 21 T ELT) (($ (|Integer|) $) 30 T ELT) (($ $ $) 36 T ELT))) +((~= (#1=((|Boolean|) $ $) 7 T ELT)) (|zero?| ((#2=(|Boolean|) $) 22 T ELT)) (|subtractIfCan| (((|Maybe| $) $ $) 26 T ELT)) (|sample| (#3=($) 23 T CONST)) (|rightPower| (#4=($ $ (|PositiveInteger|)) 38 T ELT)) (|opposite?| ((#2# $ $) 20 T ELT)) (|leftPower| (#4# 39 T ELT)) (|latex| (((|String|) $) 11 T ELT)) (|hash| (((|SingleInteger|) $) 12 T ELT)) (|commutator| (($ $ $) 35 T ELT)) (|coerce| (((|OutputForm|) $) 13 T ELT)) (|before?| (#1# 6 T ELT)) (|associator| (($ $ $ $) 36 T ELT)) (|antiCommutator| (($ $ $) 34 T ELT)) (|Zero| (#3# 24 T CONST)) (= (#1# 8 T ELT)) (- (($ $) 30 T ELT) (($ $ $) 29 T ELT)) (+ (($ $ $) 18 T ELT)) (** (#4# 40 T ELT)) (* (($ (|PositiveInteger|) $) 17 T ELT) (($ (|NonNegativeInteger|) $) 21 T ELT) (($ (|Integer|) $) 31 T ELT) (($ $ $) 37 T ELT))) (((|NonAssociativeRng|) (|Category|)) (T |NonAssociativeRng|)) ((|associator| (*1 *1 *1 *1 *1) (|ofCategory| *1 (|NonAssociativeRng|))) (|commutator| (*1 *1 *1 *1) (|ofCategory| *1 (|NonAssociativeRng|))) (|antiCommutator| (*1 *1 *1 *1) (|ofCategory| *1 (|NonAssociativeRng|)))) (|Join| (|AbelianGroup|) (|Monad|) (CATEGORY |domain| (SIGNATURE |associator| ($ $ $ $)) (SIGNATURE |commutator| ($ $ $)) (SIGNATURE |antiCommutator| ($ $ $)))) @@ -2278,7 +2278,7 @@ NIL ((|coerce| (((|OutputForm|) $) NIL T ELT) (($ (|Integer|)) 10 T ELT))) (((|NonAssociativeRing&| |#1|) (CATEGORY |package| (SIGNATURE |coerce| (|#1| (|Integer|))) (SIGNATURE |coerce| ((|OutputForm|) |#1|))) (|NonAssociativeRing|)) (T |NonAssociativeRing&|)) NIL -((~= (#1=((|Boolean|) $ $) 7 T ELT)) (|zero?| ((#2=(|Boolean|) $) 22 T ELT)) (|subtractIfCan| (((|Union| $ "failed") $ $) 26 T ELT)) (|sample| (#3=($) 23 T CONST)) (|rightRecip| (#4=((|Union| $ "failed") $) 49 T ELT)) (|rightPower| (#5=($ $ (|PositiveInteger|)) 37 T ELT) (#6=($ $ (|NonNegativeInteger|)) 44 T ELT)) (|recip| (#4# 47 T ELT)) (|opposite?| ((#2# $ $) 20 T ELT)) (|one?| (((|Boolean|) $) 43 T ELT)) (|leftRecip| (#4# 48 T ELT)) (|leftPower| (#5# 38 T ELT) (#6# 45 T ELT)) (|latex| (((|String|) $) 11 T ELT)) (|hash| (((|SingleInteger|) $) 12 T ELT)) (|commutator| (#7=($ $ $) 34 T ELT)) (|coerce| (((|OutputForm|) $) 13 T ELT) (($ (|Integer|)) 40 T ELT)) (|characteristic| (((|NonNegativeInteger|)) 41 T CONST)) (|before?| (#1# 6 T ELT)) (|associator| (($ $ $ $) 35 T ELT)) (|antiCommutator| (#7# 33 T ELT)) (|Zero| (#3# 24 T CONST)) (|One| (($) 42 T CONST)) (= (#1# 8 T ELT)) (- (($ $) 29 T ELT) (($ $ $) 28 T ELT)) (+ (($ $ $) 18 T ELT)) (** (#5# 39 T ELT) (#6# 46 T ELT)) (* (($ (|PositiveInteger|) $) 17 T ELT) (($ (|NonNegativeInteger|) $) 21 T ELT) (($ (|Integer|) $) 30 T ELT) (($ $ $) 36 T ELT))) +((~= (#1=((|Boolean|) $ $) 7 T ELT)) (|zero?| ((#2=(|Boolean|) $) 22 T ELT)) (|subtractIfCan| (((|Maybe| $) $ $) 26 T ELT)) (|sample| (#3=($) 23 T CONST)) (|rightRecip| (#4=((|Union| $ "failed") $) 50 T ELT)) (|rightPower| (#5=($ $ (|PositiveInteger|)) 38 T ELT) (#6=($ $ (|NonNegativeInteger|)) 45 T ELT)) (|recip| (#4# 48 T ELT)) (|opposite?| ((#2# $ $) 20 T ELT)) (|one?| (((|Boolean|) $) 44 T ELT)) (|leftRecip| (#4# 49 T ELT)) (|leftPower| (#5# 39 T ELT) (#6# 46 T ELT)) (|latex| (((|String|) $) 11 T ELT)) (|hash| (((|SingleInteger|) $) 12 T ELT)) (|commutator| (#7=($ $ $) 35 T ELT)) (|coerce| (((|OutputForm|) $) 13 T ELT) (($ (|Integer|)) 41 T ELT)) (|characteristic| (((|NonNegativeInteger|)) 42 T CONST)) (|before?| (#1# 6 T ELT)) (|associator| (($ $ $ $) 36 T ELT)) (|antiCommutator| (#7# 34 T ELT)) (|Zero| (#3# 24 T CONST)) (|One| (($) 43 T CONST)) (= (#1# 8 T ELT)) (- (($ $) 30 T ELT) (($ $ $) 29 T ELT)) (+ (($ $ $) 18 T ELT)) (** (#5# 40 T ELT) (#6# 47 T ELT)) (* (($ (|PositiveInteger|) $) 17 T ELT) (($ (|NonNegativeInteger|) $) 21 T ELT) (($ (|Integer|) $) 31 T ELT) (($ $ $) 37 T ELT))) (((|NonAssociativeRing|) (|Category|)) (T |NonAssociativeRing|)) ((|characteristic| (*1 *2) (AND (|ofCategory| *1 (|NonAssociativeRing|)) (|isDomain| *2 (|NonNegativeInteger|)))) (|coerce| (*1 *1 *2) (AND (|isDomain| *2 (|Integer|)) (|ofCategory| *1 (|NonAssociativeRing|))))) (|Join| (|NonAssociativeRng|) (|MonadWithUnit|) (CATEGORY |domain| (SIGNATURE |characteristic| ((|NonNegativeInteger|)) |constant|) (SIGNATURE |coerce| ($ (|Integer|))))) @@ -2303,7 +2303,7 @@ NIL ((|solveInField| (#1=(#2=(|List| (|List| (|Equation| (|Fraction| #3=(|Polynomial| |#1|))))) #4=(|List| #3#)) 19 T ELT) (#5=(#2# #4# (|List| (|Symbol|))) 18 T ELT)) (|solve| (#1# 21 T ELT) (#5# 20 T ELT))) (((|NonLinearSolvePackage| |#1|) (CATEGORY |package| (SIGNATURE |solveInField| #1=(#2=(|List| (|List| (|Equation| (|Fraction| #3=(|Polynomial| |#1|))))) #4=(|List| #3#) (|List| (|Symbol|)))) (SIGNATURE |solveInField| #5=(#2# #4#)) (SIGNATURE |solve| #1#) (SIGNATURE |solve| #5#)) (|IntegralDomain|)) (T |NonLinearSolvePackage|)) ((|solve| #1=(*1 *2 *3) #2=(AND (|isDomain| *3 (|List| #3=(|Polynomial| *4))) (|ofCategory| *4 #4=(|IntegralDomain|)) (|isDomain| *2 (|List| (|List| (|Equation| (|Fraction| #3#))))) (|isDomain| *1 (|NonLinearSolvePackage| *4)))) (|solve| #5=(*1 *2 *3 *4) #6=(AND (|isDomain| *3 (|List| #7=(|Polynomial| *5))) (|isDomain| *4 (|List| (|Symbol|))) (|ofCategory| *5 #4#) (|isDomain| *2 (|List| (|List| (|Equation| (|Fraction| #7#))))) (|isDomain| *1 (|NonLinearSolvePackage| *5)))) (|solveInField| #1# #2#) (|solveInField| #5# #6#)) -((~= #1=((#2=(|Boolean|) $ $) NIL T ELT)) (|zero?| #3=((#2# $) NIL T ELT)) (|sup| (#4=($ $ $) 10 T ELT)) (|subtractIfCan| (#5=(#6=(|Union| $ "failed") $ $) 15 T ELT)) (|shift| (($ $ (|Integer|)) 11 T ELT)) (|sample| #7=(#8=($) NIL T CONST)) (|rem| #9=(#4# NIL T ELT)) (|recip| ((#6# $) NIL T ELT)) (|random| (($ $) NIL T ELT)) (|quo| #9#) (|positive?| #3#) (|opposite?| #1#) (|one?| #3#) (|min| #9#) (|max| #9#) (|latex| (((|String|) $) NIL T ELT)) (|hash| (((|SingleInteger|) $) NIL T ELT)) (|gcd| #9#) (|exquo| (#5# NIL T ELT)) (|divide| (((|Record| (|:| |quotient| $) (|:| |remainder| $)) $ $) NIL T ELT)) (|coerce| (((|OutputForm|) $) NIL T ELT)) (|before?| #1#) (|Zero| (#8# 6 T CONST)) (|One| #7#) (>= #1#) (> #1#) (= #1#) (<= #1#) (< #1#) (+ #9#) (** (($ $ #10=(|NonNegativeInteger|)) NIL T ELT) (($ $ #11=(|PositiveInteger|)) NIL T ELT)) (* (($ #11# $) NIL T ELT) (($ #10# $) NIL T ELT) #9#)) +((~= #1=((#2=(|Boolean|) $ $) NIL T ELT)) (|zero?| #3=((#2# $) NIL T ELT)) (|sup| (#4=($ $ $) 10 T ELT)) (|subtractIfCan| (((|Maybe| $) $ $) 18 T ELT)) (|shift| (($ $ (|Integer|)) 11 T ELT)) (|sample| #5=(#6=($) NIL T CONST)) (|rem| #7=(#4# NIL T ELT)) (|recip| ((#8=(|Union| $ "failed") $) NIL T ELT)) (|random| (($ $) NIL T ELT)) (|quo| #7#) (|positive?| #3#) (|opposite?| #1#) (|one?| #3#) (|min| #7#) (|max| #7#) (|latex| (((|String|) $) NIL T ELT)) (|hash| (((|SingleInteger|) $) NIL T ELT)) (|gcd| #7#) (|exquo| ((#8# $ $) NIL T ELT)) (|divide| (((|Record| (|:| |quotient| $) (|:| |remainder| $)) $ $) NIL T ELT)) (|coerce| (((|OutputForm|) $) NIL T ELT)) (|before?| #1#) (|Zero| (#6# 6 T CONST)) (|One| #5#) (>= #1#) (> #1#) (= #1#) (<= #1#) (< #1#) (+ #7#) (** (($ $ #9=(|NonNegativeInteger|)) NIL T ELT) (($ $ #10=(|PositiveInteger|)) NIL T ELT)) (* (($ #10# $) NIL T ELT) (($ #9# $) NIL T ELT) #7#)) (((|NonNegativeInteger|) (|Join| (|OrderedAbelianMonoidSup|) (|Monoid|) (CATEGORY |domain| (SIGNATURE |quo| #1=($ $ $)) (SIGNATURE |rem| #1#) (SIGNATURE |gcd| #1#) (SIGNATURE |divide| ((|Record| (|:| |quotient| $) (|:| |remainder| $)) $ $)) (SIGNATURE |exquo| ((|Union| $ "failed") $ $)) (SIGNATURE |shift| ($ $ (|Integer|))) (SIGNATURE |random| ($ $)) (ATTRIBUTE (|commutative| "*"))))) (T |NonNegativeInteger|)) ((|quo| #1=(*1 *1 *1 *1) #2=(|isDomain| *1 #3=(|NonNegativeInteger|))) (|rem| #1# #2#) (|gcd| #1# #2#) (|divide| (*1 *2 *1 *1) (AND (|isDomain| *2 (|Record| (|:| |quotient| #3#) (|:| |remainder| #3#))) #2#)) (|exquo| #1# (|partial| |isDomain| *1 #3#)) (|shift| (*1 *1 *1 *2) (AND (|isDomain| *2 (|Integer|)) #2#)) (|random| (*1 *1 *1) #2#)) ((|Integer|) (|%not| (|%ilt| |#1| 0))) @@ -2331,10 +2331,10 @@ NIL ((|realEigenvectors| (((|List| (|Record| (|:| |outval| |#1|) (|:| |outmult| #1=(|Integer|)) (|:| |outvect| (|List| (|Matrix| |#1|))))) #2=(|Matrix| #3=(|Fraction| #1#)) |#1|) 31 T ELT)) (|realEigenvalues| (((|List| |#1|) #2# |#1|) 21 T ELT)) (|characteristicPolynomial| ((#4=(|Polynomial| #3#) #2# (|Symbol|)) 18 T ELT) ((#4# #2#) 17 T ELT))) (((|NumericRealEigenPackage| |#1|) (CATEGORY |package| (SIGNATURE |characteristicPolynomial| (#1=(|Polynomial| #2=(|Fraction| #3=(|Integer|))) #4=(|Matrix| #2#))) (SIGNATURE |characteristicPolynomial| (#1# #4# (|Symbol|))) (SIGNATURE |realEigenvalues| ((|List| |#1|) #4# |#1|)) (SIGNATURE |realEigenvectors| ((|List| (|Record| (|:| |outval| |#1|) (|:| |outmult| #3#) (|:| |outvect| (|List| (|Matrix| |#1|))))) #4# |#1|))) (|Join| (|Field|) (|OrderedRing|))) (T |NumericRealEigenPackage|)) ((|realEigenvectors| #1=(*1 *2 *3 *4) (AND #2=(|isDomain| *3 (|Matrix| #3=(|Fraction| #4=(|Integer|)))) (|isDomain| *2 (|List| (|Record| (|:| |outval| *4) (|:| |outmult| #4#) (|:| |outvect| (|List| (|Matrix| *4)))))) #5=(|isDomain| *1 (|NumericRealEigenPackage| *4)) #6=(|ofCategory| *4 #7=(|Join| (|Field|) (|OrderedRing|))))) (|realEigenvalues| #1# (AND #2# (|isDomain| *2 (|List| *4)) #5# #6#)) (|characteristicPolynomial| #1# (AND #2# (|isDomain| *4 (|Symbol|)) #8=(|isDomain| *2 (|Polynomial| #3#)) (|isDomain| *1 (|NumericRealEigenPackage| *5)) (|ofCategory| *5 #7#))) (|characteristicPolynomial| (*1 *2 *3) (AND #2# #8# #5# #6#))) -((~= #1=(#2=(#3=(|Boolean|) $ $) NIL T ELT)) (|zero?| (#4=(#3# $) 36 T ELT)) (|variables| ((#5=(|List| |#2|) $) NIL T ELT)) (|univariate| ((#6=(|SparseUnivariatePolynomial| $) $ |#2|) NIL T ELT) ((#7=(|SparseUnivariatePolynomial| |#1|) $) NIL T ELT)) (|unitNormal| (((|Record| (|:| |unit| $) (|:| |canonical| $) (|:| |associate| $)) $) NIL #8=(|has| |#1| (|IntegralDomain|)) ELT)) (|unitCanonical| #9=(#10=($ $) NIL #8# ELT)) (|unit?| (#4# NIL #8# ELT)) (|totalDegree| #11=(#12=(#13=(|NonNegativeInteger|) $) NIL T ELT) ((#13# $ #5#) NIL T ELT)) (|tail| (#10# 30 T ELT)) (|supRittWu?| #1#) (|subtractIfCan| (#14=(#15=(|Union| $ #16="failed") $ $) NIL T ELT)) (|subResultantGcd| (#17=($ $ $) 110 #8# ELT)) (|subResultantChain| ((#18=(|List| $) $ $) 123 #8# ELT)) (|squareFreePolynomial| #19=(((|Factored| #6#) #6#) NIL #20=(|has| |#1| (|PolynomialFactorizationExplicit|)) ELT)) (|squareFreePart| #21=(#10# NIL #22=(|has| |#1| (|GcdDomain|)) ELT)) (|squareFree| (#23=((|Factored| $) $) NIL #22# ELT)) (|solveLinearPolynomialEquation| (((|Union| #24=(|List| #6#) #16#) #24# #6#) NIL #20# ELT)) (|sample| (#25=($) NIL T CONST)) (|retractIfCan| (((|Union| |#1| . #26=(#16#)) . #27=($)) NIL T ELT) (((|Union| #28=(|Fraction| #29=(|Integer|)) . #26#) . #27#) NIL #30=(|has| |#1| (|RetractableTo| #28#)) ELT) (((|Union| #29# . #26#) . #27#) NIL #31=(|has| |#1| (|RetractableTo| #29#)) ELT) #32=(((|Union| |#2| . #26#) . #27#) NIL T ELT) ((#15# #33=(|Polynomial| #28#)) NIL #34=(AND #35=(|has| |#1| (|Algebra| #28#)) #36=(|has| |#2| (|ConvertibleTo| (|Symbol|)))) ELT) ((#15# #37=(|Polynomial| #29#)) NIL #38=(OR (AND #39=(|has| |#1| (|Algebra| #29#)) #36# #40=(|not| #35#)) #34#) ELT) ((#15# #41=(|Polynomial| |#1|)) NIL #42=(OR (AND #36# #40# (|not| #39#)) (AND #39# #36# #40# (|not| (|has| |#1| (|IntegerNumberSystem|)))) (AND #35# #36# (|not| (|has| |#1| (|QuotientFieldCategory| #29#))))) ELT) (((|Union| #43=(|SparseMultivariatePolynomial| |#1| |#2|) . #26#) $) 21 T ELT)) (|retract| #44=(#45=(|#1| . #46=($)) NIL T ELT) ((#28# . #46#) NIL #30# ELT) ((#29# . #46#) NIL #31# ELT) (#47=(|#2| . #46#) NIL T ELT) #48=(($ #33#) NIL #34# ELT) #49=(($ #37#) NIL #38# ELT) (#50=($ #41#) NIL #42# ELT) (#51=(#43# . #46#) NIL T ELT)) (|resultant| (#52=($ $ $ |#2|) NIL #53=(|has| |#1| (|CommutativeRing|)) ELT) (#17# 121 #8# ELT)) (|reductum| #54=(#10# NIL T ELT) #55=(#56=($ $ |#2|) NIL T ELT)) (|reducedSystem| ((#57=(|Matrix| #29#) . #58=(#59=(|Matrix| $))) NIL #60=(|has| |#1| (|LinearlyExplicitRingOver| #29#)) ELT) ((#61=(|Record| (|:| |mat| #57#) (|:| |vec| (|Vector| #29#))) . #62=(#59# #63=(|Vector| $))) NIL #60# ELT) ((#64=(|Record| (|:| |mat| #65=(|Matrix| |#1|)) (|:| |vec| (|Vector| |#1|))) . #62#) NIL T ELT) ((#65# . #58#) NIL T ELT)) (|reduced?| #1# #66=((#3# $ #18#) NIL T ELT)) (|recip| ((#15# $) NIL T ELT)) (|quasiMonic?| #67=(#4# NIL T ELT)) (|pseudoDivide| ((#68=(|Record| #69=(|:| |quotient| $) #70=(|:| |remainder| $)) $ $) 81 T ELT)) (|primitivePart!| (#10# 136 #22# ELT)) (|primitivePart| #21# #71=(#56# NIL #22# ELT)) (|primitiveMonomials| #72=(#73=(#18# $) NIL T ELT)) (|prime?| (#4# NIL #20# ELT)) (|primPartElseUnitCanonical!| #9#) (|primPartElseUnitCanonical| #9#) (|prem| (#17# 76 T ELT) #74=(#52# NIL T ELT)) (|pquo| (#17# 79 T ELT) #74#) (|pomopo!| (($ $ |#1| #75=(|IndexedExponents| |#2|) $) NIL T ELT)) (|patternMatch| ((#76=(|PatternMatchResult| #77=(|Float|) . #78=($)) $ #79=(|Pattern| #77#) #76#) NIL (AND (|has| |#1| #80=(|PatternMatchable| #77#)) (|has| |#2| #80#)) ELT) ((#81=(|PatternMatchResult| #29# . #78#) $ #82=(|Pattern| #29#) #81#) NIL (AND (|has| |#1| #83=(|PatternMatchable| #29#)) (|has| |#2| #83#)) ELT)) (|opposite?| #1#) (|one?| (#4# 57 T ELT)) (|numberOfMonomials| #11#) (|normalized?| #1# #66#) (|nextsubResultant2| (($ $ $ $ $) 107 #8# ELT)) (|mvar| (#47# 22 T ELT)) (|multivariate| (($ #7# |#2|) NIL T ELT) (($ #6# |#2|) NIL T ELT)) (|monomials| #72#) (|monomial?| #67#) (|monomial| (($ |#1| #75#) NIL T ELT) (#84=($ $ |#2| #13#) 38 T ELT) #85=(($ $ #5# #86=(|List| #13#)) NIL T ELT)) (|monicModulo| (#17# 63 T ELT)) (|monicDivide| ((#68# $ $ |#2|) NIL T ELT)) (|monic?| #67#) (|minimumDegree| #87=((#75# $) NIL T ELT) (#88=(#13# $ |#2|) NIL T ELT) #89=((#86# $ #5#) NIL T ELT)) (|mdeg| (#12# 23 T ELT)) (|mapExponents| (($ (|Mapping| #75# #75#) $) NIL T ELT)) (|map| (($ (|Mapping| |#1| |#1|) $) NIL T ELT)) (|mainVariable| #32#) (|mainSquareFreePart| #21#) (|mainPrimitivePart| #21#) (|mainMonomials| #72#) (|mainMonomial| (#10# 39 T ELT)) (|mainContent| #21#) (|mainCoefficients| (#73# 43 T ELT)) (|leftReducedSystem| ((#57# . #90=(#63#)) NIL #60# ELT) ((#61# . #91=(#63# $)) NIL #60# ELT) ((#64# . #91#) NIL T ELT) ((#65# . #90#) NIL T ELT)) (|leastMonomial| (#10# 41 T ELT)) (|leadingMonomial| #54#) (|leadingCoefficient| #44# (#56# 48 T ELT)) (|lcm| #92=(($ #18#) NIL #22# ELT) #93=(#17# NIL #22# ELT)) (|lazyResidueClass| (((|Record| (|:| |polnum| $) (|:| |polden| $) (|:| |power| #13#)) $ $) 96 T ELT)) (|lazyPseudoDivide| ((#94=(|Record| #95=(|:| |coef| $) #96=(|:| |gap| #13#) #69# #70#) $ $) 78 T ELT) ((#94# $ $ |#2|) NIL T ELT)) (|lazyPremWithDefault| ((#97=(|Record| #95# #96# #70#) $ $) NIL T ELT) ((#97# $ $ |#2|) NIL T ELT)) (|lazyPrem| (#17# 83 T ELT) #74#) (|lazyPquo| (#17# 86 T ELT) #74#) (|latex| (#98=((|String|) $) NIL T ELT)) (|lastSubResultant| (#17# 125 #8# ELT)) (|iteratedInitials| (#73# 32 T ELT)) (|isTimes| #99=(((|Union| #18# #16#) $) NIL T ELT)) (|isPlus| #99#) (|isExpt| (((|Union| (|Record| (|:| |var| |#2|) (|:| |exponent| #13#)) #16#) $) NIL T ELT)) (|initiallyReduced?| #1# #66#) (|initiallyReduce| #100=(#17# NIL T ELT)) (|init| (#10# 24 T ELT)) (|infRittWu?| #1#) (|headReduced?| #1# #66#) (|headReduce| #100#) (|head| (#10# 26 T ELT)) (|hash| (((|SingleInteger|) $) NIL T ELT)) (|halfExtendedSubResultantGcd2| (((|Record| #101=(|:| |gcd| $) #102=(|:| |coef2| $)) $ $) 116 #8# ELT)) (|halfExtendedSubResultantGcd1| (((|Record| #101# #103=(|:| |coef1| $)) $ $) 113 #8# ELT)) (|ground?| (#4# 56 T ELT)) (|ground| (#45# 58 T ELT)) (|gcdPolynomial| ((#6# #6# #6#) NIL #22# ELT)) (|gcd| ((|#1| |#1| $) 133 #22# ELT) #92# #93#) (|factorSquareFreePolynomial| #19#) (|factorPolynomial| #19#) (|factor| (#23# NIL #20# ELT)) (|extendedSubResultantGcd| (((|Record| #101# #103# #102#) $ $) 119 #8# ELT)) (|exquo| ((#15# $ |#1|) NIL #8# ELT) (#14# 98 #8# ELT)) (|exactQuotient!| (#104=($ $ |#1|) 129 #8# ELT) #105=(#17# NIL #8# ELT)) (|exactQuotient| (#104# 128 #8# ELT) #105#) (|eval| (($ $ (|List| #106=(|Equation| $))) NIL T ELT) (($ $ #106#) NIL T ELT) (($ $ $ $) NIL T ELT) (($ $ #18# #18#) NIL T ELT) (($ $ |#2| |#1|) NIL T ELT) (($ $ #5# #107=(|List| |#1|)) NIL T ELT) (($ $ |#2| $) NIL T ELT) (($ $ #5# #18#) NIL T ELT)) (|discriminant| (#56# NIL #53# ELT)) (|differentiate| #85# #108=(#84# NIL T ELT) #109=(($ $ #5#) NIL T ELT) #55#) (|degree| #87# (#88# 45 T ELT) #89#) (|deepestTail| #54#) (|deepestInitial| (#10# 35 T ELT)) (|convert| ((#79# . #110=($)) NIL (AND (|has| |#1| #111=(|ConvertibleTo| #79#)) (|has| |#2| #111#)) ELT) ((#82# . #110#) NIL (AND (|has| |#1| #112=(|ConvertibleTo| #82#)) (|has| |#2| #112#)) ELT) ((#113=(|InputForm|) . #110#) NIL (AND (|has| |#1| #114=(|ConvertibleTo| #113#)) (|has| |#2| #114#)) ELT) #48# #49# (#50# NIL #36# ELT) (#98# NIL (AND #31# #36#) ELT) #115=((#41# . #110#) NIL #36# ELT)) (|content| (#45# 132 #22# ELT) #71#) (|conditionP| (((|Union| #63# #16#) #59#) NIL #116=(AND (|has| $ #117=(|CharacteristicNonZero|)) #20#) ELT)) (|coerce| (((|OutputForm|) $) NIL T ELT) (($ #29#) NIL T ELT) (($ |#1|) NIL T ELT) (($ |#2|) NIL T ELT) #115# (#51# 18 T ELT) (($ #43#) 19 T ELT) (($ #28#) NIL (OR #35# #30#) ELT) #9#) (|coefficients| ((#107# $) NIL T ELT)) (|coefficient| ((|#1| $ #75#) NIL T ELT) (#84# 47 T ELT) #85#) (|charthRoot| (((|Maybe| $) $) NIL (OR #116# (|has| |#1| #117#)) ELT)) (|characteristic| ((#13#) NIL T CONST)) (|binomThmExpt| (#118=($ $ $ #13#) NIL #53# ELT)) (|before?| #1#) (|associates?| (#2# NIL #8# ELT)) (|annihilate?| #1#) (|Zero| (#25# 13 T CONST)) (|RittWuCompare| (((|Union| #3# #16#) $ $) NIL T ELT)) (|One| (#25# 37 T CONST)) (|LazardQuotient2| (($ $ $ $ #13#) 105 #8# ELT)) (|LazardQuotient| (#118# 104 #8# ELT)) (D #85# #108# #109# #55#) (= #1#) (/ (#104# NIL (|has| |#1| (|Field|)) ELT)) (- #54# (#17# 75 T ELT)) (+ (#17# 85 T ELT)) (** (($ $ #119=(|PositiveInteger|)) NIL T ELT) (($ $ #13#) 70 T ELT)) (* (($ #119# $) NIL T ELT) (($ #13# $) NIL T ELT) (($ #29# . #120=($)) NIL T ELT) (#17# 62 T ELT) (($ $ #28#) NIL #35# ELT) (($ #28# . #120#) NIL #35# ELT) (($ |#1| . #120#) 61 T ELT) (#104# NIL T ELT))) +((~= #1=(#2=(#3=(|Boolean|) $ $) NIL T ELT)) (|zero?| (#4=(#3# $) 36 T ELT)) (|variables| ((#5=(|List| |#2|) $) NIL T ELT)) (|univariate| ((#6=(|SparseUnivariatePolynomial| $) $ |#2|) NIL T ELT) ((#7=(|SparseUnivariatePolynomial| |#1|) $) NIL T ELT)) (|unitNormal| (((|Record| (|:| |unit| $) (|:| |canonical| $) (|:| |associate| $)) $) NIL #8=(|has| |#1| (|IntegralDomain|)) ELT)) (|unitCanonical| #9=(#10=($ $) NIL #8# ELT)) (|unit?| (#4# NIL #8# ELT)) (|totalDegree| #11=(#12=(#13=(|NonNegativeInteger|) $) NIL T ELT) ((#13# $ #5#) NIL T ELT)) (|tail| (#10# 30 T ELT)) (|supRittWu?| #1#) (|subtractIfCan| ((#14=(|Maybe| $) $ $) NIL T ELT)) (|subResultantGcd| (#15=($ $ $) 110 #8# ELT)) (|subResultantChain| ((#16=(|List| $) $ $) 123 #8# ELT)) (|squareFreePolynomial| #17=(((|Factored| #6#) #6#) NIL #18=(|has| |#1| (|PolynomialFactorizationExplicit|)) ELT)) (|squareFreePart| #19=(#10# NIL #20=(|has| |#1| (|GcdDomain|)) ELT)) (|squareFree| (#21=((|Factored| $) $) NIL #20# ELT)) (|solveLinearPolynomialEquation| (((|Union| #22=(|List| #6#) #23="failed") #22# #6#) NIL #18# ELT)) (|sample| (#24=($) NIL T CONST)) (|retractIfCan| (((|Union| |#1| . #25=(#23#)) . #26=($)) NIL T ELT) (((|Union| #27=(|Fraction| #28=(|Integer|)) . #25#) . #26#) NIL #29=(|has| |#1| (|RetractableTo| #27#)) ELT) (((|Union| #28# . #25#) . #26#) NIL #30=(|has| |#1| (|RetractableTo| #28#)) ELT) #31=(((|Union| |#2| . #25#) . #26#) NIL T ELT) ((#32=(|Union| $ #23#) #33=(|Polynomial| #27#)) NIL #34=(AND #35=(|has| |#1| (|Algebra| #27#)) #36=(|has| |#2| (|ConvertibleTo| (|Symbol|)))) ELT) ((#32# #37=(|Polynomial| #28#)) NIL #38=(OR (AND #39=(|has| |#1| (|Algebra| #28#)) #36# #40=(|not| #35#)) #34#) ELT) ((#32# #41=(|Polynomial| |#1|)) NIL #42=(OR (AND #36# #40# (|not| #39#)) (AND #39# #36# #40# (|not| (|has| |#1| (|IntegerNumberSystem|)))) (AND #35# #36# (|not| (|has| |#1| (|QuotientFieldCategory| #28#))))) ELT) (((|Union| #43=(|SparseMultivariatePolynomial| |#1| |#2|) . #25#) $) 21 T ELT)) (|retract| #44=(#45=(|#1| . #46=($)) NIL T ELT) ((#27# . #46#) NIL #29# ELT) ((#28# . #46#) NIL #30# ELT) (#47=(|#2| . #46#) NIL T ELT) #48=(($ #33#) NIL #34# ELT) #49=(($ #37#) NIL #38# ELT) (#50=($ #41#) NIL #42# ELT) (#51=(#43# . #46#) NIL T ELT)) (|resultant| (#52=($ $ $ |#2|) NIL #53=(|has| |#1| (|CommutativeRing|)) ELT) (#15# 121 #8# ELT)) (|reductum| #54=(#10# NIL T ELT) #55=(#56=($ $ |#2|) NIL T ELT)) (|reducedSystem| ((#57=(|Matrix| #28#) . #58=(#59=(|Matrix| $))) NIL #60=(|has| |#1| (|LinearlyExplicitRingOver| #28#)) ELT) ((#61=(|Record| (|:| |mat| #57#) (|:| |vec| (|Vector| #28#))) . #62=(#59# #63=(|Vector| $))) NIL #60# ELT) ((#64=(|Record| (|:| |mat| #65=(|Matrix| |#1|)) (|:| |vec| (|Vector| |#1|))) . #62#) NIL T ELT) ((#65# . #58#) NIL T ELT)) (|reduced?| #1# #66=((#3# $ #16#) NIL T ELT)) (|recip| ((#32# $) NIL T ELT)) (|quasiMonic?| #67=(#4# NIL T ELT)) (|pseudoDivide| ((#68=(|Record| #69=(|:| |quotient| $) #70=(|:| |remainder| $)) $ $) 81 T ELT)) (|primitivePart!| (#10# 136 #20# ELT)) (|primitivePart| #19# #71=(#56# NIL #20# ELT)) (|primitiveMonomials| #72=(#73=(#16# $) NIL T ELT)) (|prime?| (#4# NIL #18# ELT)) (|primPartElseUnitCanonical!| #9#) (|primPartElseUnitCanonical| #9#) (|prem| (#15# 76 T ELT) #74=(#52# NIL T ELT)) (|pquo| (#15# 79 T ELT) #74#) (|pomopo!| (($ $ |#1| #75=(|IndexedExponents| |#2|) $) NIL T ELT)) (|patternMatch| ((#76=(|PatternMatchResult| #77=(|Float|) . #78=($)) $ #79=(|Pattern| #77#) #76#) NIL (AND (|has| |#1| #80=(|PatternMatchable| #77#)) (|has| |#2| #80#)) ELT) ((#81=(|PatternMatchResult| #28# . #78#) $ #82=(|Pattern| #28#) #81#) NIL (AND (|has| |#1| #83=(|PatternMatchable| #28#)) (|has| |#2| #83#)) ELT)) (|opposite?| #1#) (|one?| (#4# 57 T ELT)) (|numberOfMonomials| #11#) (|normalized?| #1# #66#) (|nextsubResultant2| (($ $ $ $ $) 107 #8# ELT)) (|mvar| (#47# 22 T ELT)) (|multivariate| (($ #7# |#2|) NIL T ELT) (($ #6# |#2|) NIL T ELT)) (|monomials| #72#) (|monomial?| #67#) (|monomial| (($ |#1| #75#) NIL T ELT) (#84=($ $ |#2| #13#) 38 T ELT) #85=(($ $ #5# #86=(|List| #13#)) NIL T ELT)) (|monicModulo| (#15# 63 T ELT)) (|monicDivide| ((#68# $ $ |#2|) NIL T ELT)) (|monic?| #67#) (|minimumDegree| #87=((#75# $) NIL T ELT) (#88=(#13# $ |#2|) NIL T ELT) #89=((#86# $ #5#) NIL T ELT)) (|mdeg| (#12# 23 T ELT)) (|mapExponents| (($ (|Mapping| #75# #75#) $) NIL T ELT)) (|map| (($ (|Mapping| |#1| |#1|) $) NIL T ELT)) (|mainVariable| #31#) (|mainSquareFreePart| #19#) (|mainPrimitivePart| #19#) (|mainMonomials| #72#) (|mainMonomial| (#10# 39 T ELT)) (|mainContent| #19#) (|mainCoefficients| (#73# 43 T ELT)) (|leftReducedSystem| ((#57# . #90=(#63#)) NIL #60# ELT) ((#61# . #91=(#63# $)) NIL #60# ELT) ((#64# . #91#) NIL T ELT) ((#65# . #90#) NIL T ELT)) (|leastMonomial| (#10# 41 T ELT)) (|leadingMonomial| #54#) (|leadingCoefficient| #44# (#56# 48 T ELT)) (|lcm| #92=(($ #16#) NIL #20# ELT) #93=(#15# NIL #20# ELT)) (|lazyResidueClass| (((|Record| (|:| |polnum| $) (|:| |polden| $) (|:| |power| #13#)) $ $) 96 T ELT)) (|lazyPseudoDivide| ((#94=(|Record| #95=(|:| |coef| $) #96=(|:| |gap| #13#) #69# #70#) $ $) 78 T ELT) ((#94# $ $ |#2|) NIL T ELT)) (|lazyPremWithDefault| ((#97=(|Record| #95# #96# #70#) $ $) NIL T ELT) ((#97# $ $ |#2|) NIL T ELT)) (|lazyPrem| (#15# 83 T ELT) #74#) (|lazyPquo| (#15# 86 T ELT) #74#) (|latex| (#98=((|String|) $) NIL T ELT)) (|lastSubResultant| (#15# 125 #8# ELT)) (|iteratedInitials| (#73# 32 T ELT)) (|isTimes| #99=(((|Union| #16# #23#) $) NIL T ELT)) (|isPlus| #99#) (|isExpt| (((|Union| (|Record| (|:| |var| |#2|) (|:| |exponent| #13#)) #23#) $) NIL T ELT)) (|initiallyReduced?| #1# #66#) (|initiallyReduce| #100=(#15# NIL T ELT)) (|init| (#10# 24 T ELT)) (|infRittWu?| #1#) (|headReduced?| #1# #66#) (|headReduce| #100#) (|head| (#10# 26 T ELT)) (|hash| (((|SingleInteger|) $) NIL T ELT)) (|halfExtendedSubResultantGcd2| (((|Record| #101=(|:| |gcd| $) #102=(|:| |coef2| $)) $ $) 116 #8# ELT)) (|halfExtendedSubResultantGcd1| (((|Record| #101# #103=(|:| |coef1| $)) $ $) 113 #8# ELT)) (|ground?| (#4# 56 T ELT)) (|ground| (#45# 58 T ELT)) (|gcdPolynomial| ((#6# #6# #6#) NIL #20# ELT)) (|gcd| ((|#1| |#1| $) 133 #20# ELT) #92# #93#) (|factorSquareFreePolynomial| #17#) (|factorPolynomial| #17#) (|factor| (#21# NIL #18# ELT)) (|extendedSubResultantGcd| (((|Record| #101# #103# #102#) $ $) 119 #8# ELT)) (|exquo| ((#32# $ |#1|) NIL #8# ELT) ((#32# $ $) 98 #8# ELT)) (|exactQuotient!| (#104=($ $ |#1|) 129 #8# ELT) #105=(#15# NIL #8# ELT)) (|exactQuotient| (#104# 128 #8# ELT) #105#) (|eval| (($ $ (|List| #106=(|Equation| $))) NIL T ELT) (($ $ #106#) NIL T ELT) (($ $ $ $) NIL T ELT) (($ $ #16# #16#) NIL T ELT) (($ $ |#2| |#1|) NIL T ELT) (($ $ #5# #107=(|List| |#1|)) NIL T ELT) (($ $ |#2| $) NIL T ELT) (($ $ #5# #16#) NIL T ELT)) (|discriminant| (#56# NIL #53# ELT)) (|differentiate| #85# #108=(#84# NIL T ELT) #109=(($ $ #5#) NIL T ELT) #55#) (|degree| #87# (#88# 45 T ELT) #89#) (|deepestTail| #54#) (|deepestInitial| (#10# 35 T ELT)) (|convert| ((#79# . #110=($)) NIL (AND (|has| |#1| #111=(|ConvertibleTo| #79#)) (|has| |#2| #111#)) ELT) ((#82# . #110#) NIL (AND (|has| |#1| #112=(|ConvertibleTo| #82#)) (|has| |#2| #112#)) ELT) ((#113=(|InputForm|) . #110#) NIL (AND (|has| |#1| #114=(|ConvertibleTo| #113#)) (|has| |#2| #114#)) ELT) #48# #49# (#50# NIL #36# ELT) (#98# NIL (AND #30# #36#) ELT) #115=((#41# . #110#) NIL #36# ELT)) (|content| (#45# 132 #20# ELT) #71#) (|conditionP| (((|Union| #63# #23#) #59#) NIL #116=(AND (|has| $ #117=(|CharacteristicNonZero|)) #18#) ELT)) (|coerce| (((|OutputForm|) $) NIL T ELT) (($ #28#) NIL T ELT) (($ |#1|) NIL T ELT) (($ |#2|) NIL T ELT) #115# (#51# 18 T ELT) (($ #43#) 19 T ELT) (($ #27#) NIL (OR #35# #29#) ELT) #9#) (|coefficients| ((#107# $) NIL T ELT)) (|coefficient| ((|#1| $ #75#) NIL T ELT) (#84# 47 T ELT) #85#) (|charthRoot| ((#14# $) NIL (OR #116# (|has| |#1| #117#)) ELT)) (|characteristic| ((#13#) NIL T CONST)) (|binomThmExpt| (#118=($ $ $ #13#) NIL #53# ELT)) (|before?| #1#) (|associates?| (#2# NIL #8# ELT)) (|annihilate?| #1#) (|Zero| (#24# 13 T CONST)) (|RittWuCompare| (((|Union| #3# #23#) $ $) NIL T ELT)) (|One| (#24# 37 T CONST)) (|LazardQuotient2| (($ $ $ $ #13#) 105 #8# ELT)) (|LazardQuotient| (#118# 104 #8# ELT)) (D #85# #108# #109# #55#) (= #1#) (/ (#104# NIL (|has| |#1| (|Field|)) ELT)) (- #54# (#15# 75 T ELT)) (+ (#15# 85 T ELT)) (** (($ $ #119=(|PositiveInteger|)) NIL T ELT) (($ $ #13#) 70 T ELT)) (* (($ #119# $) NIL T ELT) (($ #13# $) NIL T ELT) (($ #28# . #120=($)) NIL T ELT) (#15# 62 T ELT) (($ $ #27#) NIL #35# ELT) (($ #27# . #120#) NIL #35# ELT) (($ |#1| . #120#) 61 T ELT) (#104# NIL T ELT))) (((|NewSparseMultivariatePolynomial| |#1| |#2|) (|Join| (|RecursivePolynomialCategory| |#1| (|IndexedExponents| |#2|) |#2|) (|CoercibleTo| #1=(|SparseMultivariatePolynomial| |#1| |#2|)) (|RetractableTo| #1#)) (|Ring|) (|OrderedSet|)) (T |NewSparseMultivariatePolynomial|)) NIL -((~= #1=(#2=(#3=(|Boolean|) $ $) NIL T ELT)) (|zero?| (#4=(#3# $) 12 T ELT)) (|vectorise| ((#5=(|Vector| |#1|) $ #6=(|NonNegativeInteger|)) NIL T ELT)) (|variables| ((#7=(|List| #8=(|SingletonAsOrderedSet|)) $) NIL T ELT)) (|unmakeSUP| (#9=($ #10=(|SparseUnivariatePolynomial| |#1|)) NIL T ELT)) (|univariate| ((#11=(|SparseUnivariatePolynomial| $) $ #8#) NIL T ELT) #12=(#13=(#10# $) NIL T ELT)) (|unitNormal| (((|Record| (|:| |unit| $) (|:| |canonical| $) (|:| |associate| $)) $) NIL #14=(|has| |#1| (|IntegralDomain|)) ELT)) (|unitCanonical| #15=(#16=($ $) NIL #14# ELT)) (|unit?| (#4# NIL #14# ELT)) (|totalDegree| #17=(#18=(#6# $) NIL T ELT) ((#6# $ #7#) NIL T ELT)) (|subtractIfCan| (#19=(#20=(|Union| $ #21="failed") $ $) NIL T ELT)) (|subResultantsChain| ((#22=(|List| $) $ $) 54 #14# ELT)) (|subResultantGcd| (#23=($ $ $) 50 #14# ELT)) (|squareFreePolynomial| #24=(((|Factored| #11#) #11#) NIL #25=(|has| |#1| (|PolynomialFactorizationExplicit|)) ELT)) (|squareFreePart| #26=(#16# NIL #27=(|has| |#1| (|GcdDomain|)) ELT)) (|squareFree| (#28=((|Factored| $) $) NIL #27# ELT)) (|solveLinearPolynomialEquation| (((|Union| #29=(|List| #11#) #21#) #29# #11#) NIL #25# ELT)) (|sizeLess?| (#2# NIL #30=(|has| |#1| (|Field|)) ELT)) (|shiftRight| #31=(($ $ #6#) NIL T ELT)) (|shiftLeft| #31#) (|separate| (((|Record| (|:| |primePart| $) (|:| |commonPart| $)) $ $) NIL #27# ELT)) (|sample| (#32=($) NIL T CONST)) (|retractIfCan| (((|Union| |#1| . #33=(#21#)) . #34=($)) NIL T ELT) (((|Union| #35=(|Fraction| #36=(|Integer|)) . #33#) . #34#) NIL #37=(|has| |#1| (|RetractableTo| #35#)) ELT) (((|Union| #36# . #33#) . #34#) NIL #38=(|has| |#1| (|RetractableTo| #36#)) ELT) #39=(((|Union| #8# . #33#) . #34#) NIL T ELT) (((|Union| #10# . #33#) $) 10 T ELT)) (|retract| #40=(#41=(|#1| . #42=($)) NIL T ELT) ((#35# . #42#) NIL #37# ELT) ((#36# . #42#) NIL #38# ELT) ((#8# . #42#) NIL T ELT) #12#) (|resultant| (($ $ $ #8#) NIL #43=(|has| |#1| (|CommutativeRing|)) ELT) ((|#1| $ $) 58 #43# ELT)) (|rem| #44=(#23# NIL #30# ELT)) (|reductum| #45=(#16# NIL T ELT)) (|reducedSystem| ((#46=(|Matrix| #36#) . #47=(#48=(|Matrix| $))) NIL #49=(|has| |#1| (|LinearlyExplicitRingOver| #36#)) ELT) ((#50=(|Record| (|:| |mat| #46#) (|:| |vec| (|Vector| #36#))) . #51=(#48# #52=(|Vector| $))) NIL #49# ELT) ((#53=(|Record| (|:| |mat| #54=(|Matrix| |#1|)) (|:| |vec| #5#)) . #51#) NIL T ELT) ((#54# . #47#) NIL T ELT)) (|recip| ((#20# $) NIL T ELT)) (|quo| #44#) (|pseudoRemainder| #55=(#23# NIL T ELT)) (|pseudoQuotient| (#23# 87 #14# ELT)) (|pseudoDivide| (((|Record| #56=(|:| |coef| |#1|) #57=(|:| |quotient| $) #58=(|:| |remainder| $)) $ $) 86 #14# ELT)) (|principalIdeal| (((|Record| (|:| |coef| #22#) #59=(|:| |generator| $)) #22#) NIL #30# ELT)) (|primitivePart| #26# #60=(#61=($ $ #8#) NIL #27# ELT)) (|primitiveMonomials| #62=((#22# $) NIL T ELT)) (|prime?| (#4# NIL #25# ELT)) (|pomopo!| (($ $ |#1| #6# $) NIL T ELT)) (|patternMatch| ((#63=(|PatternMatchResult| #64=(|Float|) . #65=($)) $ #66=(|Pattern| #64#) #63#) NIL (AND (|has| #8# #67=(|PatternMatchable| #64#)) (|has| |#1| #67#)) ELT) ((#68=(|PatternMatchResult| #36# . #65#) $ #69=(|Pattern| #36#) #68#) NIL (AND (|has| #8# #70=(|PatternMatchable| #36#)) (|has| |#1| #70#)) ELT)) (|order| ((#6# $ $) NIL #14# ELT)) (|opposite?| #1#) (|one?| #71=(#4# NIL T ELT)) (|numberOfMonomials| #17#) (|nextItem| (#72=((|Maybe| $) $) NIL #73=(|has| |#1| (|StepThrough|)) ELT)) (|multivariate| (($ #10# #8#) NIL T ELT) (($ #11# #8#) NIL T ELT)) (|multiplyExponents| #31#) (|multiEuclidean| ((#74=(|Union| #22# #21#) #22# $) NIL #30# ELT)) (|monomials| #62#) (|monomial?| #71#) (|monomial| (($ |#1| #6#) NIL T ELT) #75=(($ $ #8# #6#) NIL T ELT) #76=(($ $ #7# #77=(|List| #6#)) NIL T ELT)) (|monicModulo| (#23# 27 T ELT)) (|monicDivide| ((#78=(|Record| #57# #58#) $ $ #8#) NIL T ELT) (#79=(#78# $ $) NIL T ELT)) (|minimumDegree| #17# #80=((#6# $ #8#) NIL T ELT) #81=((#77# $ #7#) NIL T ELT)) (|mapExponents| (($ (|Mapping| #6# #6#) $) NIL T ELT)) (|map| (($ #82=(|Mapping| |#1| |#1|) $) NIL T ELT)) (|makeSUP| #12#) (|mainVariable| #39#) (|leftReducedSystem| ((#46# . #83=(#52#)) NIL #49# ELT) ((#50# . #84=(#52# $)) NIL #49# ELT) ((#53# . #84#) NIL T ELT) ((#54# . #83#) NIL T ELT)) (|leadingMonomial| #45#) (|leadingCoefficient| #40#) (|lcm| #85=(($ #22#) NIL #27# ELT) #86=(#23# NIL #27# ELT)) (|lazyResidueClass| (((|Record| (|:| |polnum| $) (|:| |polden| |#1|) (|:| |power| #6#)) $ $) 37 T ELT)) (|lazyPseudoRemainder| (#23# 41 T ELT)) (|lazyPseudoQuotient| (#23# 47 T ELT)) (|lazyPseudoDivide| (((|Record| #56# (|:| |gap| #6#) #57# #58#) $ $) 46 T ELT)) (|latex| (((|String|) $) NIL T ELT)) (|lastSubResultant| (#23# 56 #14# ELT)) (|karatsubaDivide| ((#78# $ #6#) NIL T ELT)) (|isTimes| #87=((#74# $) NIL T ELT)) (|isPlus| #87#) (|isExpt| (((|Union| (|Record| (|:| |var| #8#) (|:| |exponent| #6#)) #21#) $) NIL T ELT)) (|integrate| (#16# NIL #88=(|has| |#1| (|Algebra| #35#)) ELT)) (|init| (#32# NIL #73# CONST)) (|hash| (((|SingleInteger|) $) NIL T ELT)) (|halfExtendedSubResultantGcd2| (((|Record| #89=(|:| |gcd| $) #90=(|:| |coef2| $)) $ $) 82 #14# ELT)) (|halfExtendedSubResultantGcd1| (((|Record| #89# #91=(|:| |coef1| $)) $ $) 78 #14# ELT)) (|halfExtendedResultant2| (((|Record| #92=(|:| |resultant| |#1|) #90#) $ $) 70 #14# ELT)) (|halfExtendedResultant1| (((|Record| #92# #91#) $ $) 66 #14# ELT)) (|ground?| (#4# 13 T ELT)) (|ground| #40#) (|gcdPolynomial| ((#11# #11# #11#) NIL #27# ELT)) (|gcd| #85# #86#) (|fmecg| (($ $ #6# |#1| $) 26 T ELT)) (|factorSquareFreePolynomial| #24#) (|factorPolynomial| #24#) (|factor| (#28# NIL #25# ELT)) (|extendedSubResultantGcd| (((|Record| #89# #91# #90#) $ $) 74 #14# ELT)) (|extendedResultant| (((|Record| #92# #91# #90#) $ $) 62 #14# ELT)) (|extendedEuclidean| (((|Union| (|Record| #91# #90#) #21#) $ $ $) NIL #30# ELT) (((|Record| #91# #90# #59#) $ $) NIL #30# ELT)) (|exquo| ((#20# $ |#1|) NIL #14# ELT) #93=(#19# NIL #14# ELT)) (|expressIdealMember| (((|Maybe| #22#) #22# $) NIL #30# ELT)) (|eval| (($ $ (|List| #94=(|Equation| $))) NIL T ELT) (($ $ #94#) NIL T ELT) (($ $ $ $) NIL T ELT) (($ $ #22# #22#) NIL T ELT) (($ $ #8# |#1|) NIL T ELT) (($ $ #7# #95=(|List| |#1|)) NIL T ELT) (($ $ #8# $) NIL T ELT) (($ $ #7# #22#) NIL T ELT)) (|euclideanSize| (#18# NIL #30# ELT)) (|elt| ((|#1| $ |#1|) NIL T ELT) #55# ((#96=(|Fraction| $) #96# #96#) NIL #14# ELT) ((|#1| #96# |#1|) NIL #30# ELT) ((#96# $ #96#) NIL #14# ELT)) (|divideExponents| ((#20# $ #6#) NIL T ELT)) (|divide| (#79# NIL #30# ELT)) (|discriminant| (#61# NIL #43# ELT) (#41# NIL #43# ELT)) (|differentiate| #76# #75# #97=(($ $ #7#) NIL T ELT) #98=(#61# NIL T ELT) #45# #31# #99=(($ $ #82#) NIL T ELT) #100=(($ $ #82# #6#) NIL T ELT) (($ $ #82# $) NIL T ELT) #101=(($ $ #102=(|Symbol|)) NIL #103=(|has| |#1| (|PartialDifferentialSpace| #102#)) ELT) #104=(($ $ #105=(|List| #102#)) NIL #103# ELT) #106=(($ $ #102# #6#) NIL #103# ELT) #107=(($ $ #105# #77#) NIL #103# ELT)) (|degree| #17# #80# #81#) (|convert| ((#66# . #108=($)) NIL (AND (|has| #8# #109=(|ConvertibleTo| #66#)) (|has| |#1| #109#)) ELT) ((#69# . #108#) NIL (AND (|has| #8# #110=(|ConvertibleTo| #69#)) (|has| |#1| #110#)) ELT) ((#111=(|InputForm|) . #108#) NIL (AND (|has| #8# #112=(|ConvertibleTo| #111#)) (|has| |#1| #112#)) ELT)) (|content| (#41# NIL #27# ELT) #60#) (|conditionP| (((|Union| #52# #21#) #48#) NIL #113=(AND (|has| $ #114=(|CharacteristicNonZero|)) #25#) ELT)) (|composite| #93# (((|Union| #96# #21#) #96# $) NIL #14# ELT)) (|coerce| (((|OutputForm|) $) NIL T ELT) (($ #36#) NIL T ELT) (($ |#1|) NIL T ELT) (($ #8#) NIL T ELT) (#13# 7 T ELT) (#9# 8 T ELT) (($ #35#) NIL (OR #88# #37#) ELT) #15#) (|coefficients| ((#95# $) NIL T ELT)) (|coefficient| ((|#1| $ #6#) NIL T ELT) #75# #76#) (|charthRoot| (#72# NIL (OR #113# (|has| |#1| #114#)) ELT)) (|characteristic| ((#6#) NIL T CONST)) (|binomThmExpt| (($ $ $ #6#) NIL #43# ELT)) (|before?| #1#) (|associates?| (#2# NIL #14# ELT)) (|annihilate?| #1#) (|Zero| (#32# 28 T CONST)) (|One| (#32# 32 T CONST)) (D #76# #75# #97# #98# #45# #31# #99# #100# #101# #104# #106# #107#) (= #1#) (/ (#115=($ $ |#1|) NIL #30# ELT)) (- (#16# 40 T ELT) #55#) (+ #55#) (** (($ $ #116=(|PositiveInteger|)) NIL T ELT) #31#) (* (($ #116# $) NIL T ELT) (($ #6# $) NIL T ELT) (($ #36# . #117=($)) NIL T ELT) #55# (($ $ #35#) NIL #88# ELT) (($ #35# . #117#) NIL #88# ELT) (($ |#1| . #117#) 31 T ELT) (#115# NIL T ELT))) +((~= #1=(#2=(#3=(|Boolean|) $ $) NIL T ELT)) (|zero?| (#4=(#3# $) 12 T ELT)) (|vectorise| ((#5=(|Vector| |#1|) $ #6=(|NonNegativeInteger|)) NIL T ELT)) (|variables| ((#7=(|List| #8=(|SingletonAsOrderedSet|)) $) NIL T ELT)) (|unmakeSUP| (#9=($ #10=(|SparseUnivariatePolynomial| |#1|)) NIL T ELT)) (|univariate| ((#11=(|SparseUnivariatePolynomial| $) $ #8#) NIL T ELT) #12=(#13=(#10# $) NIL T ELT)) (|unitNormal| (((|Record| (|:| |unit| $) (|:| |canonical| $) (|:| |associate| $)) $) NIL #14=(|has| |#1| (|IntegralDomain|)) ELT)) (|unitCanonical| #15=(#16=($ $) NIL #14# ELT)) (|unit?| (#4# NIL #14# ELT)) (|totalDegree| #17=(#18=(#6# $) NIL T ELT) ((#6# $ #7#) NIL T ELT)) (|subtractIfCan| ((#19=(|Maybe| $) $ $) NIL T ELT)) (|subResultantsChain| ((#20=(|List| $) $ $) 58 #14# ELT)) (|subResultantGcd| (#21=($ $ $) 54 #14# ELT)) (|squareFreePolynomial| #22=(((|Factored| #11#) #11#) NIL #23=(|has| |#1| (|PolynomialFactorizationExplicit|)) ELT)) (|squareFreePart| #24=(#16# NIL #25=(|has| |#1| (|GcdDomain|)) ELT)) (|squareFree| (#26=((|Factored| $) $) NIL #25# ELT)) (|solveLinearPolynomialEquation| (((|Union| #27=(|List| #11#) #28="failed") #27# #11#) NIL #23# ELT)) (|sizeLess?| (#2# NIL #29=(|has| |#1| (|Field|)) ELT)) (|shiftRight| #30=(($ $ #6#) NIL T ELT)) (|shiftLeft| #30#) (|separate| (((|Record| (|:| |primePart| $) (|:| |commonPart| $)) $ $) NIL #25# ELT)) (|sample| (#31=($) NIL T CONST)) (|retractIfCan| (((|Union| |#1| . #32=(#28#)) . #33=($)) NIL T ELT) (((|Union| #34=(|Fraction| #35=(|Integer|)) . #32#) . #33#) NIL #36=(|has| |#1| (|RetractableTo| #34#)) ELT) (((|Union| #35# . #32#) . #33#) NIL #37=(|has| |#1| (|RetractableTo| #35#)) ELT) #38=(((|Union| #8# . #32#) . #33#) NIL T ELT) (((|Union| #10# . #32#) $) 10 T ELT)) (|retract| #39=(#40=(|#1| . #41=($)) NIL T ELT) ((#34# . #41#) NIL #36# ELT) ((#35# . #41#) NIL #37# ELT) ((#8# . #41#) NIL T ELT) #12#) (|resultant| (($ $ $ #8#) NIL #42=(|has| |#1| (|CommutativeRing|)) ELT) ((|#1| $ $) 62 #42# ELT)) (|rem| #43=(#21# NIL #29# ELT)) (|reductum| #44=(#16# NIL T ELT)) (|reducedSystem| ((#45=(|Matrix| #35#) . #46=(#47=(|Matrix| $))) NIL #48=(|has| |#1| (|LinearlyExplicitRingOver| #35#)) ELT) ((#49=(|Record| (|:| |mat| #45#) (|:| |vec| (|Vector| #35#))) . #50=(#47# #51=(|Vector| $))) NIL #48# ELT) ((#52=(|Record| (|:| |mat| #53=(|Matrix| |#1|)) (|:| |vec| #5#)) . #50#) NIL T ELT) ((#53# . #46#) NIL T ELT)) (|recip| ((#54=(|Union| $ #28#) $) NIL T ELT)) (|quo| #43#) (|pseudoRemainder| #55=(#21# NIL T ELT)) (|pseudoQuotient| (#21# 91 #14# ELT)) (|pseudoDivide| (((|Record| #56=(|:| |coef| |#1|) #57=(|:| |quotient| $) #58=(|:| |remainder| $)) $ $) 90 #14# ELT)) (|principalIdeal| (((|Record| (|:| |coef| #20#) #59=(|:| |generator| $)) #20#) NIL #29# ELT)) (|primitivePart| #24# #60=(#61=($ $ #8#) NIL #25# ELT)) (|primitiveMonomials| #62=((#20# $) NIL T ELT)) (|prime?| (#4# NIL #23# ELT)) (|pomopo!| (($ $ |#1| #6# $) NIL T ELT)) (|patternMatch| ((#63=(|PatternMatchResult| #64=(|Float|) . #65=($)) $ #66=(|Pattern| #64#) #63#) NIL (AND (|has| #8# #67=(|PatternMatchable| #64#)) (|has| |#1| #67#)) ELT) ((#68=(|PatternMatchResult| #35# . #65#) $ #69=(|Pattern| #35#) #68#) NIL (AND (|has| #8# #70=(|PatternMatchable| #35#)) (|has| |#1| #70#)) ELT)) (|order| ((#6# $ $) NIL #14# ELT)) (|opposite?| #1#) (|one?| #71=(#4# NIL T ELT)) (|numberOfMonomials| #17#) (|nextItem| (#72=(#19# $) NIL #73=(|has| |#1| (|StepThrough|)) ELT)) (|multivariate| (($ #10# #8#) NIL T ELT) (($ #11# #8#) NIL T ELT)) (|multiplyExponents| #30#) (|multiEuclidean| ((#74=(|Union| #20# #28#) #20# $) NIL #29# ELT)) (|monomials| #62#) (|monomial?| #71#) (|monomial| (($ |#1| #6#) NIL T ELT) #75=(($ $ #8# #6#) NIL T ELT) #76=(($ $ #7# #77=(|List| #6#)) NIL T ELT)) (|monicModulo| (#21# 31 T ELT)) (|monicDivide| ((#78=(|Record| #57# #58#) $ $ #8#) NIL T ELT) (#79=(#78# $ $) NIL T ELT)) (|minimumDegree| #17# #80=((#6# $ #8#) NIL T ELT) #81=((#77# $ #7#) NIL T ELT)) (|mapExponents| (($ (|Mapping| #6# #6#) $) NIL T ELT)) (|map| (($ #82=(|Mapping| |#1| |#1|) $) NIL T ELT)) (|makeSUP| #12#) (|mainVariable| #38#) (|leftReducedSystem| ((#45# . #83=(#51#)) NIL #48# ELT) ((#49# . #84=(#51# $)) NIL #48# ELT) ((#52# . #84#) NIL T ELT) ((#53# . #83#) NIL T ELT)) (|leadingMonomial| #44#) (|leadingCoefficient| #39#) (|lcm| #85=(($ #20#) NIL #25# ELT) #86=(#21# NIL #25# ELT)) (|lazyResidueClass| (((|Record| (|:| |polnum| $) (|:| |polden| |#1|) (|:| |power| #6#)) $ $) 41 T ELT)) (|lazyPseudoRemainder| (#21# 45 T ELT)) (|lazyPseudoQuotient| (#21# 51 T ELT)) (|lazyPseudoDivide| (((|Record| #56# (|:| |gap| #6#) #57# #58#) $ $) 50 T ELT)) (|latex| (((|String|) $) NIL T ELT)) (|lastSubResultant| (#21# 60 #14# ELT)) (|karatsubaDivide| ((#78# $ #6#) NIL T ELT)) (|isTimes| #87=((#74# $) NIL T ELT)) (|isPlus| #87#) (|isExpt| (((|Union| (|Record| (|:| |var| #8#) (|:| |exponent| #6#)) #28#) $) NIL T ELT)) (|integrate| (#16# NIL #88=(|has| |#1| (|Algebra| #34#)) ELT)) (|init| (#31# NIL #73# CONST)) (|hash| (((|SingleInteger|) $) NIL T ELT)) (|halfExtendedSubResultantGcd2| (((|Record| #89=(|:| |gcd| $) #90=(|:| |coef2| $)) $ $) 86 #14# ELT)) (|halfExtendedSubResultantGcd1| (((|Record| #89# #91=(|:| |coef1| $)) $ $) 82 #14# ELT)) (|halfExtendedResultant2| (((|Record| #92=(|:| |resultant| |#1|) #90#) $ $) 74 #14# ELT)) (|halfExtendedResultant1| (((|Record| #92# #91#) $ $) 70 #14# ELT)) (|ground?| (#4# 13 T ELT)) (|ground| #39#) (|gcdPolynomial| ((#11# #11# #11#) NIL #25# ELT)) (|gcd| #85# #86#) (|fmecg| (($ $ #6# |#1| $) 30 T ELT)) (|factorSquareFreePolynomial| #22#) (|factorPolynomial| #22#) (|factor| (#26# NIL #23# ELT)) (|extendedSubResultantGcd| (((|Record| #89# #91# #90#) $ $) 78 #14# ELT)) (|extendedResultant| (((|Record| #92# #91# #90#) $ $) 66 #14# ELT)) (|extendedEuclidean| (((|Union| (|Record| #91# #90#) #28#) $ $ $) NIL #29# ELT) (((|Record| #91# #90# #59#) $ $) NIL #29# ELT)) (|exquo| ((#54# $ |#1|) NIL #14# ELT) #93=((#54# $ $) NIL #14# ELT)) (|expressIdealMember| (((|Maybe| #20#) #20# $) NIL #29# ELT)) (|eval| (($ $ (|List| #94=(|Equation| $))) NIL T ELT) (($ $ #94#) NIL T ELT) (($ $ $ $) NIL T ELT) (($ $ #20# #20#) NIL T ELT) (($ $ #8# |#1|) NIL T ELT) (($ $ #7# #95=(|List| |#1|)) NIL T ELT) (($ $ #8# $) NIL T ELT) (($ $ #7# #20#) NIL T ELT)) (|euclideanSize| (#18# NIL #29# ELT)) (|elt| ((|#1| $ |#1|) NIL T ELT) #55# ((#96=(|Fraction| $) #96# #96#) NIL #14# ELT) ((|#1| #96# |#1|) NIL #29# ELT) ((#96# $ #96#) NIL #14# ELT)) (|divideExponents| ((#54# $ #6#) NIL T ELT)) (|divide| (#79# NIL #29# ELT)) (|discriminant| (#61# NIL #42# ELT) (#40# NIL #42# ELT)) (|differentiate| #76# #75# #97=(($ $ #7#) NIL T ELT) #98=(#61# NIL T ELT) #44# #30# #99=(($ $ #82#) NIL T ELT) #100=(($ $ #82# #6#) NIL T ELT) (($ $ #82# $) NIL T ELT) #101=(($ $ #102=(|Symbol|)) NIL #103=(|has| |#1| (|PartialDifferentialSpace| #102#)) ELT) #104=(($ $ #105=(|List| #102#)) NIL #103# ELT) #106=(($ $ #102# #6#) NIL #103# ELT) #107=(($ $ #105# #77#) NIL #103# ELT)) (|degree| #17# #80# #81#) (|convert| ((#66# . #108=($)) NIL (AND (|has| #8# #109=(|ConvertibleTo| #66#)) (|has| |#1| #109#)) ELT) ((#69# . #108#) NIL (AND (|has| #8# #110=(|ConvertibleTo| #69#)) (|has| |#1| #110#)) ELT) ((#111=(|InputForm|) . #108#) NIL (AND (|has| #8# #112=(|ConvertibleTo| #111#)) (|has| |#1| #112#)) ELT)) (|content| (#40# NIL #25# ELT) #60#) (|conditionP| (((|Union| #51# #28#) #47#) NIL #113=(AND (|has| $ #114=(|CharacteristicNonZero|)) #23#) ELT)) (|composite| #93# (((|Union| #96# #28#) #96# $) NIL #14# ELT)) (|coerce| (((|OutputForm|) $) NIL T ELT) (($ #35#) NIL T ELT) (($ |#1|) NIL T ELT) (($ #8#) NIL T ELT) (#13# 7 T ELT) (#9# 8 T ELT) (($ #34#) NIL (OR #88# #36#) ELT) #15#) (|coefficients| ((#95# $) NIL T ELT)) (|coefficient| ((|#1| $ #6#) NIL T ELT) #75# #76#) (|charthRoot| (#72# NIL (OR #113# (|has| |#1| #114#)) ELT)) (|characteristic| ((#6#) NIL T CONST)) (|binomThmExpt| (($ $ $ #6#) NIL #42# ELT)) (|before?| #1#) (|associates?| (#2# NIL #14# ELT)) (|annihilate?| #1#) (|Zero| (#31# 32 T CONST)) (|One| (#31# 36 T CONST)) (D #76# #75# #97# #98# #44# #30# #99# #100# #101# #104# #106# #107#) (= #1#) (/ (#115=($ $ |#1|) NIL #29# ELT)) (- (#16# 44 T ELT) #55#) (+ #55#) (** (($ $ #116=(|PositiveInteger|)) NIL T ELT) #30#) (* (($ #116# $) NIL T ELT) (($ #6# $) NIL T ELT) (($ #35# . #117=($)) NIL T ELT) #55# (($ $ #34#) NIL #88# ELT) (($ #34# . #117#) NIL #88# ELT) (($ |#1| . #117#) 35 T ELT) (#115# NIL T ELT))) (((|NewSparseUnivariatePolynomial| |#1|) (|Join| (|UnivariatePolynomialCategory| |#1|) (|CoercibleTo| #1=(|SparseUnivariatePolynomial| |#1|)) (|RetractableTo| #1#) (CATEGORY |domain| (SIGNATURE |fmecg| ($ $ #2=(|NonNegativeInteger|) |#1| $)) (SIGNATURE |monicModulo| #3=($ $ $)) (SIGNATURE |lazyResidueClass| ((|Record| (|:| |polnum| $) (|:| |polden| |#1|) (|:| |power| #2#)) $ $)) (SIGNATURE |lazyPseudoRemainder| #3#) (SIGNATURE |lazyPseudoDivide| ((|Record| (|:| |coef| |#1|) (|:| |gap| #2#) (|:| |quotient| $) (|:| |remainder| $)) $ $)) (SIGNATURE |lazyPseudoQuotient| #3#) (IF (|has| |#1| (|IntegralDomain|)) (PROGN (SIGNATURE |subResultantsChain| ((|List| $) $ $)) (SIGNATURE |lastSubResultant| #3#) (SIGNATURE |extendedSubResultantGcd| ((|Record| #4=(|:| |gcd| $) #5=(|:| |coef1| $) #6=(|:| |coef2| $)) $ $)) (SIGNATURE |halfExtendedSubResultantGcd1| ((|Record| #4# #5#) $ $)) (SIGNATURE |halfExtendedSubResultantGcd2| ((|Record| #4# #6#) $ $)) (SIGNATURE |extendedResultant| ((|Record| #7=(|:| |resultant| |#1|) #5# #6#) $ $)) (SIGNATURE |halfExtendedResultant1| ((|Record| #7# #5#) $ $)) (SIGNATURE |halfExtendedResultant2| ((|Record| #7# #6#) $ $))) |%noBranch|))) (|Ring|)) (T |NewSparseUnivariatePolynomial|)) ((|fmecg| (*1 *1 *1 *2 *3 *1) (AND (|isDomain| *2 #1=(|NonNegativeInteger|)) #2=(|isDomain| *1 #3=(|NewSparseUnivariatePolynomial| *3)) #4=(|ofCategory| *3 #5=(|Ring|)))) (|monicModulo| #6=(*1 *1 *1 *1) #7=(AND #8=(|isDomain| *1 (|NewSparseUnivariatePolynomial| *2)) #9=(|ofCategory| *2 #5#))) (|lazyResidueClass| #10=(*1 *2 *1 *1) (AND (|isDomain| *2 (|Record| (|:| |polnum| #3#) (|:| |polden| *3) (|:| |power| #1#))) #2# #4#)) (|lazyPseudoRemainder| #6# #7#) (|lazyPseudoDivide| #10# (AND (|isDomain| *2 (|Record| (|:| |coef| *3) (|:| |gap| #1#) (|:| |quotient| #3#) (|:| |remainder| #3#))) #2# #4#)) (|lazyPseudoQuotient| #6# #7#) (|subResultantsChain| #10# (AND (|isDomain| *2 (|List| #3#)) #2# #11=(|ofCategory| *3 #12=(|IntegralDomain|)) #4#)) (|lastSubResultant| #6# (AND #8# (|ofCategory| *2 #12#) #9#)) (|extendedSubResultantGcd| #10# (AND (|isDomain| *2 (|Record| #13=(|:| |gcd| #3#) #14=(|:| |coef1| #3#) #15=(|:| |coef2| #3#))) #2# #11# #4#)) (|halfExtendedSubResultantGcd1| #10# (AND (|isDomain| *2 (|Record| #13# #14#)) #2# #11# #4#)) (|halfExtendedSubResultantGcd2| #10# (AND (|isDomain| *2 (|Record| #13# #15#)) #2# #11# #4#)) (|extendedResultant| #10# (AND (|isDomain| *2 (|Record| #16=(|:| |resultant| *3) #14# #15#)) #2# #11# #4#)) (|halfExtendedResultant1| #10# (AND (|isDomain| *2 (|Record| #16# #14#)) #2# #11# #4#)) (|halfExtendedResultant2| #10# (AND (|isDomain| *2 (|Record| #16# #15#)) #2# #11# #4#))) ((|map| (((|NewSparseUnivariatePolynomial| |#2|) (|Mapping| |#2| |#1|) (|NewSparseUnivariatePolynomial| |#1|)) 13 T ELT))) @@ -2366,7 +2366,7 @@ NIL ((|sign| (((|Integer|) $) 17 T ELT)) (|negative?| (((|Boolean|) $) 10 T ELT)) (|abs| (($ $) 19 T ELT))) (((|OrderedAbelianGroup&| |#1|) (CATEGORY |package| (SIGNATURE |abs| (|#1| |#1|)) (SIGNATURE |sign| ((|Integer|) |#1|)) (SIGNATURE |negative?| ((|Boolean|) |#1|))) (|OrderedAbelianGroup|)) (T |OrderedAbelianGroup&|)) NIL -((~= (#1=((|Boolean|) $ $) 7 T ELT)) (|zero?| ((#2=(|Boolean|) $) 31 T ELT)) (|subtractIfCan| (((|Union| $ "failed") $ $) 35 T ELT)) (|sign| (((|Integer|) $) 38 T ELT)) (|sample| (#3=($) 30 T CONST)) (|positive?| (((|Boolean|) $) 28 T ELT)) (|opposite?| ((#2# $ $) 33 T ELT)) (|negative?| (((|Boolean|) $) 39 T ELT)) (|min| (#4=($ $ $) 23 T ELT)) (|max| (#4# 22 T ELT)) (|latex| (((|String|) $) 11 T ELT)) (|hash| (((|SingleInteger|) $) 12 T ELT)) (|coerce| (((|OutputForm|) $) 13 T ELT)) (|before?| (#1# 6 T ELT)) (|abs| (($ $) 37 T ELT)) (|Zero| (#3# 29 T CONST)) (>= (#5=((|Boolean|) $ $) 21 T ELT)) (> (#5# 19 T ELT)) (= (#1# 8 T ELT)) (<= (#5# 20 T ELT)) (< (#5# 18 T ELT)) (- (($ $ $) 42 T ELT) (($ $) 41 T ELT)) (+ (($ $ $) 25 T ELT)) (* (($ (|PositiveInteger|) $) 26 T ELT) (($ (|NonNegativeInteger|) $) 32 T ELT) (($ (|Integer|) $) 40 T ELT))) +((~= (#1=((|Boolean|) $ $) 7 T ELT)) (|zero?| ((#2=(|Boolean|) $) 31 T ELT)) (|subtractIfCan| (((|Maybe| $) $ $) 35 T ELT)) (|sign| (((|Integer|) $) 39 T ELT)) (|sample| (#3=($) 30 T CONST)) (|positive?| (((|Boolean|) $) 28 T ELT)) (|opposite?| ((#2# $ $) 33 T ELT)) (|negative?| (((|Boolean|) $) 40 T ELT)) (|min| (#4=($ $ $) 23 T ELT)) (|max| (#4# 22 T ELT)) (|latex| (((|String|) $) 11 T ELT)) (|hash| (((|SingleInteger|) $) 12 T ELT)) (|coerce| (((|OutputForm|) $) 13 T ELT)) (|before?| (#1# 6 T ELT)) (|abs| (($ $) 38 T ELT)) (|Zero| (#3# 29 T CONST)) (>= (#5=((|Boolean|) $ $) 21 T ELT)) (> (#5# 19 T ELT)) (= (#1# 8 T ELT)) (<= (#5# 20 T ELT)) (< (#5# 18 T ELT)) (- (($ $ $) 43 T ELT) (($ $) 42 T ELT)) (+ (($ $ $) 25 T ELT)) (* (($ (|PositiveInteger|) $) 26 T ELT) (($ (|NonNegativeInteger|) $) 32 T ELT) (($ (|Integer|) $) 41 T ELT))) (((|OrderedAbelianGroup|) (|Category|)) (T |OrderedAbelianGroup|)) ((|negative?| (*1 *2 *1) (AND (|ofCategory| *1 (|OrderedAbelianGroup|)) (|isDomain| *2 (|Boolean|)))) (|sign| (*1 *2 *1) (AND (|ofCategory| *1 (|OrderedAbelianGroup|)) (|isDomain| *2 (|Integer|)))) (|abs| (*1 *1 *1) (|ofCategory| *1 (|OrderedAbelianGroup|)))) (|Join| (|OrderedCancellationAbelianMonoid|) (|AbelianGroup|) (CATEGORY |domain| (SIGNATURE |negative?| ((|Boolean|) $)) (SIGNATURE |sign| ((|Integer|) $)) (SIGNATURE |abs| ($ $)))) @@ -2379,7 +2379,7 @@ NIL ((|positive?| (*1 *2 *1) (AND (|ofCategory| *1 (|OrderedAbelianMonoid|)) (|isDomain| *2 (|Boolean|))))) (|Join| (|OrderedAbelianSemiGroup|) (|AbelianMonoid|) (CATEGORY |domain| (SIGNATURE |positive?| ((|Boolean|) $)))) (((|AbelianMonoid|) . T) ((|AbelianSemiGroup|) . T) ((|BasicType|) . T) ((|CoercibleTo| (|OutputForm|)) . T) ((|Join|) . T) ((|OrderedAbelianSemiGroup|) . T) ((|OrderedSet|) . T) ((|OrderedType|) . T) ((|SetCategory|) . T) ((|Type|) . T)) -((~= (#1=((|Boolean|) $ $) 7 T ELT)) (|zero?| ((#2=(|Boolean|) $) 31 T ELT)) (|sup| (($ $ $) 36 T ELT)) (|subtractIfCan| (((|Union| $ "failed") $ $) 35 T ELT)) (|sample| (#3=($) 30 T CONST)) (|positive?| (((|Boolean|) $) 28 T ELT)) (|opposite?| ((#2# $ $) 33 T ELT)) (|min| (#4=($ $ $) 23 T ELT)) (|max| (#4# 22 T ELT)) (|latex| (((|String|) $) 11 T ELT)) (|hash| (((|SingleInteger|) $) 12 T ELT)) (|coerce| (((|OutputForm|) $) 13 T ELT)) (|before?| (#1# 6 T ELT)) (|Zero| (#3# 29 T CONST)) (>= (#5=((|Boolean|) $ $) 21 T ELT)) (> (#5# 19 T ELT)) (= (#1# 8 T ELT)) (<= (#5# 20 T ELT)) (< (#5# 18 T ELT)) (+ (($ $ $) 25 T ELT)) (* (($ (|PositiveInteger|) $) 26 T ELT) (($ (|NonNegativeInteger|) $) 32 T ELT))) +((~= (#1=((|Boolean|) $ $) 7 T ELT)) (|zero?| ((#2=(|Boolean|) $) 31 T ELT)) (|sup| (($ $ $) 37 T ELT)) (|subtractIfCan| (((|Maybe| $) $ $) 35 T ELT)) (|sample| (#3=($) 30 T CONST)) (|positive?| (((|Boolean|) $) 28 T ELT)) (|opposite?| ((#2# $ $) 33 T ELT)) (|min| (#4=($ $ $) 23 T ELT)) (|max| (#4# 22 T ELT)) (|latex| (((|String|) $) 11 T ELT)) (|hash| (((|SingleInteger|) $) 12 T ELT)) (|coerce| (((|OutputForm|) $) 13 T ELT)) (|before?| (#1# 6 T ELT)) (|Zero| (#3# 29 T CONST)) (>= (#5=((|Boolean|) $ $) 21 T ELT)) (> (#5# 19 T ELT)) (= (#1# 8 T ELT)) (<= (#5# 20 T ELT)) (< (#5# 18 T ELT)) (+ (($ $ $) 25 T ELT)) (* (($ (|PositiveInteger|) $) 26 T ELT) (($ (|NonNegativeInteger|) $) 32 T ELT))) (((|OrderedAbelianMonoidSup|) (|Category|)) (T |OrderedAbelianMonoidSup|)) ((|sup| (*1 *1 *1 *1) (|ofCategory| *1 (|OrderedAbelianMonoidSup|)))) (|Join| (|OrderedCancellationAbelianMonoid|) (CATEGORY |domain| (SIGNATURE |sup| ($ $ $)))) @@ -2392,17 +2392,17 @@ NIL ((|zero?| (#1=(#2=(|Boolean|) $) 42 T ELT)) (|retractIfCan| (((|Union| #3=(|Integer|) #4="failed") $) NIL T ELT) (#5=((|Union| #6=(|Fraction| #3#) #4#) $) NIL T ELT) (((|Union| |#2| #4#) $) 45 T ELT)) (|retract| ((#3# $) NIL T ELT) (#7=(#6# $) NIL T ELT) (#8=(|#2| $) 43 T ELT)) (|rationalIfCan| (#5# 78 T ELT)) (|rational?| (#1# 72 T ELT)) (|rational| (#7# 76 T ELT)) (|norm| (#8# 26 T ELT)) (|map| (($ (|Mapping| |#2| |#2|) $) 23 T ELT)) (|inv| (#9=($ $) 58 T ELT)) (|convert| (((|InputForm|) $) 67 T ELT)) (|conjugate| (#9# 21 T ELT)) (|coerce| (((|OutputForm|) $) 53 T ELT) (($ #3#) 40 T ELT) (($ |#2|) 38 T ELT) (($ #6#) NIL T ELT)) (|characteristic| ((#10=(|NonNegativeInteger|)) 10 T CONST)) (|abs| (#8# 71 T ELT)) (= (#11=(#2# $ $) 30 T ELT)) (< (#11# 69 T ELT)) (- (#9# 32 T ELT) #12=(#13=($ $ $) NIL T ELT)) (+ (#13# 31 T ELT)) (* (($ (|PositiveInteger|) $) NIL T ELT) (($ #10# $) NIL T ELT) (($ #3# $) 36 T ELT) #12# (($ $ |#2|) NIL T ELT) (($ |#2| $) 33 T ELT))) (((|OctonionCategory&| |#1| |#2|) (CATEGORY |package| (SIGNATURE < #1=(#2=(|Boolean|) |#1| |#1|)) (SIGNATURE |convert| ((|InputForm|) |#1|)) (SIGNATURE |inv| #3=(|#1| |#1|)) (SIGNATURE |rationalIfCan| #4=((|Union| #5=(|Fraction| #6=(|Integer|)) #7="failed") |#1|)) (SIGNATURE |rational| #8=(#5# |#1|)) (SIGNATURE |rational?| #9=(#2# |#1|)) (SIGNATURE |abs| #10=(|#2| |#1|)) (SIGNATURE |norm| #10#) (SIGNATURE |conjugate| #3#) (SIGNATURE |map| (|#1| (|Mapping| |#2| |#2|) |#1|)) (SIGNATURE |retractIfCan| ((|Union| |#2| #7#) |#1|)) (SIGNATURE |retract| #10#) (SIGNATURE |retract| #8#) (SIGNATURE |retractIfCan| #4#) (SIGNATURE |coerce| (|#1| #5#)) (SIGNATURE |retract| (#6# |#1|)) (SIGNATURE |retractIfCan| ((|Union| #6# #7#) |#1|)) (SIGNATURE |coerce| (|#1| |#2|)) (SIGNATURE * (|#1| |#2| |#1|)) (SIGNATURE * (|#1| |#1| |#2|)) (SIGNATURE |characteristic| (#11=(|NonNegativeInteger|)) |constant|) (SIGNATURE |coerce| (|#1| #6#)) (SIGNATURE * #12=(|#1| |#1| |#1|)) (SIGNATURE - #12#) (SIGNATURE - #3#) (SIGNATURE * (|#1| #6# |#1|)) (SIGNATURE * (|#1| #11# |#1|)) (SIGNATURE |zero?| #9#) (SIGNATURE * (|#1| (|PositiveInteger|) |#1|)) (SIGNATURE + #12#) (SIGNATURE |coerce| ((|OutputForm|) |#1|)) (SIGNATURE = #1#)) (|OctonionCategory| |#2|) (|CommutativeRing|)) (T |OctonionCategory&|)) ((|characteristic| (*1 *2) (AND (|ofCategory| *4 (|CommutativeRing|)) (|isDomain| *2 (|NonNegativeInteger|)) (|isDomain| *1 (|OctonionCategory&| *3 *4)) (|ofCategory| *3 (|OctonionCategory| *4))))) -((~= (#1=((|Boolean|) $ $) 7 T ELT)) (|zero?| ((#2=(|Boolean|) $) 22 T ELT)) (|subtractIfCan| (((|Union| $ "failed") $ $) 26 T ELT)) (|size| (((|NonNegativeInteger|)) 67 (|has| |#1| . #3=((|Finite|))) ELT)) (|sample| (#4=($) 23 T CONST)) (|retractIfCan| (((|Union| #5=(|Integer|) . #6=("failed")) . #7=($)) 109 (|has| |#1| . #8=((|RetractableTo| #5#))) ELT) (((|Union| #9=(|Fraction| #5#) . #6#) . #7#) 106 (|has| |#1| . #10=((|RetractableTo| #9#))) ELT) (((|Union| |#1| . #6#) . #7#) 103 T ELT)) (|retract| ((#5# . #11=($)) 108 (|has| |#1| . #8#) ELT) ((#9# . #11#) 105 (|has| |#1| . #10#) ELT) ((|#1| . #11#) 104 T ELT)) (|recip| (((|Union| $ "failed") $) 42 T ELT)) (|real| ((|#1| $) 93 T ELT)) (|rationalIfCan| (((|Union| (|Fraction| (|Integer|)) "failed") $) 80 (|has| |#1| (|IntegerNumberSystem|)) ELT)) (|rational?| (((|Boolean|) $) 82 (|has| |#1| (|IntegerNumberSystem|)) ELT)) (|rational| (((|Fraction| (|Integer|)) $) 81 (|has| |#1| (|IntegerNumberSystem|)) ELT)) (|random| (($) 70 (|has| |#1| . #3#) ELT)) (|opposite?| ((#2# $ $) 20 T ELT)) (|one?| (((|Boolean|) $) 44 T ELT)) (|octon| (($ |#1| |#1| |#1| |#1| |#1| |#1| |#1| |#1|) 84 T ELT)) (|norm| ((|#1| $) 85 T ELT)) (|min| (#12=($ $ $) 71 (|has| |#1| . #13=((|OrderedSet|))) ELT)) (|max| (#12# 72 (|has| |#1| . #13#) ELT)) (|map| (($ (|Mapping| |#1| |#1|) $) 95 T ELT)) (|lookup| ((#14=(|PositiveInteger|) $) 69 (|has| |#1| . #3#) ELT)) (|latex| (((|String|) $) 11 T ELT)) (|inv| (($ $) 79 (|has| |#1| (|Field|)) ELT)) (|index| (($ #14#) 68 (|has| |#1| . #3#) ELT)) (|imagk| ((|#1| $) 90 T ELT)) (|imagj| ((|#1| $) 91 T ELT)) (|imagi| ((|#1| $) 92 T ELT)) (|imagK| ((|#1| $) 86 T ELT)) (|imagJ| ((|#1| $) 87 T ELT)) (|imagI| ((|#1| $) 88 T ELT)) (|imagE| ((|#1| $) 89 T ELT)) (|hash| (((|SingleInteger|) $) 12 T ELT)) (|eval| (($ $ (|List| |#1|) (|List| |#1|)) 101 (|has| |#1| (|Evalable| |#1|)) ELT) (($ $ |#1| |#1|) 100 (|has| |#1| (|Evalable| |#1|)) ELT) (($ $ (|Equation| |#1|)) 99 (|has| |#1| (|Evalable| |#1|)) ELT) (($ $ (|List| (|Equation| |#1|))) 98 (|has| |#1| (|Evalable| |#1|)) ELT) (($ $ (|List| #15=(|Symbol|)) (|List| |#1|)) 97 (|has| |#1| (|InnerEvalable| #15# |#1|)) ELT) (($ $ #15# |#1|) 96 (|has| |#1| (|InnerEvalable| #15# |#1|)) ELT)) (|elt| (($ $ |#1|) 102 (|has| |#1| (|Eltable| |#1| |#1|)) ELT)) (|convert| (((|InputForm|) $) 77 (|has| |#1| (|ConvertibleTo| (|InputForm|))) ELT)) (|conjugate| (($ $) 94 T ELT)) (|coerce| (((|OutputForm|) $) 13 T ELT) (($ (|Integer|)) 41 T ELT) (($ |#1|) 52 T ELT) (($ #9#) 107 (|has| |#1| . #10#) ELT)) (|charthRoot| (((|Maybe| $) $) 78 (|has| |#1| (|CharacteristicNonZero|)) ELT)) (|characteristic| (((|NonNegativeInteger|)) 40 T CONST)) (|before?| (#1# 6 T ELT)) (|annihilate?| (((|Boolean|) $ $) 33 T ELT)) (|abs| ((|#1| $) 83 (|has| |#1| (|RealNumberSystem|)) ELT)) (|Zero| (#4# 24 T CONST)) (|One| (($) 45 T CONST)) (>= (#16=((|Boolean|) $ $) 73 (|has| |#1| . #13#) ELT)) (> (#16# 75 (|has| |#1| . #13#) ELT)) (= (#1# 8 T ELT)) (<= (#16# 74 (|has| |#1| . #13#) ELT)) (< (#16# 76 (|has| |#1| . #13#) ELT)) (- (($ $) 29 T ELT) (($ $ $) 28 T ELT)) (+ (($ $ $) 18 T ELT)) (** (($ $ (|PositiveInteger|)) 35 T ELT) (($ $ (|NonNegativeInteger|)) 43 T ELT)) (* (($ (|PositiveInteger|) $) 17 T ELT) (($ (|NonNegativeInteger|) $) 21 T ELT) (($ (|Integer|) . #17=($)) 30 T ELT) (($ $ $) 34 T ELT) (($ $ |#1|) 54 T ELT) (($ |#1| . #17#) 53 T ELT))) +((~= (#1=((|Boolean|) $ $) 7 T ELT)) (|zero?| ((#2=(|Boolean|) $) 22 T ELT)) (|subtractIfCan| (((|Maybe| $) $ $) 26 T ELT)) (|size| (((|NonNegativeInteger|)) 68 (|has| |#1| . #3=((|Finite|))) ELT)) (|sample| (#4=($) 23 T CONST)) (|retractIfCan| (((|Union| #5=(|Integer|) . #6=("failed")) . #7=($)) 110 (|has| |#1| . #8=((|RetractableTo| #5#))) ELT) (((|Union| #9=(|Fraction| #5#) . #6#) . #7#) 107 (|has| |#1| . #10=((|RetractableTo| #9#))) ELT) (((|Union| |#1| . #6#) . #7#) 104 T ELT)) (|retract| ((#5# . #11=($)) 109 (|has| |#1| . #8#) ELT) ((#9# . #11#) 106 (|has| |#1| . #10#) ELT) ((|#1| . #11#) 105 T ELT)) (|recip| (((|Union| $ "failed") $) 43 T ELT)) (|real| ((|#1| $) 94 T ELT)) (|rationalIfCan| (((|Union| (|Fraction| (|Integer|)) "failed") $) 81 (|has| |#1| (|IntegerNumberSystem|)) ELT)) (|rational?| (((|Boolean|) $) 83 (|has| |#1| (|IntegerNumberSystem|)) ELT)) (|rational| (((|Fraction| (|Integer|)) $) 82 (|has| |#1| (|IntegerNumberSystem|)) ELT)) (|random| (($) 71 (|has| |#1| . #3#) ELT)) (|opposite?| ((#2# $ $) 20 T ELT)) (|one?| (((|Boolean|) $) 45 T ELT)) (|octon| (($ |#1| |#1| |#1| |#1| |#1| |#1| |#1| |#1|) 85 T ELT)) (|norm| ((|#1| $) 86 T ELT)) (|min| (#12=($ $ $) 72 (|has| |#1| . #13=((|OrderedSet|))) ELT)) (|max| (#12# 73 (|has| |#1| . #13#) ELT)) (|map| (($ (|Mapping| |#1| |#1|) $) 96 T ELT)) (|lookup| ((#14=(|PositiveInteger|) $) 70 (|has| |#1| . #3#) ELT)) (|latex| (((|String|) $) 11 T ELT)) (|inv| (($ $) 80 (|has| |#1| (|Field|)) ELT)) (|index| (($ #14#) 69 (|has| |#1| . #3#) ELT)) (|imagk| ((|#1| $) 91 T ELT)) (|imagj| ((|#1| $) 92 T ELT)) (|imagi| ((|#1| $) 93 T ELT)) (|imagK| ((|#1| $) 87 T ELT)) (|imagJ| ((|#1| $) 88 T ELT)) (|imagI| ((|#1| $) 89 T ELT)) (|imagE| ((|#1| $) 90 T ELT)) (|hash| (((|SingleInteger|) $) 12 T ELT)) (|eval| (($ $ (|List| |#1|) (|List| |#1|)) 102 (|has| |#1| (|Evalable| |#1|)) ELT) (($ $ |#1| |#1|) 101 (|has| |#1| (|Evalable| |#1|)) ELT) (($ $ (|Equation| |#1|)) 100 (|has| |#1| (|Evalable| |#1|)) ELT) (($ $ (|List| (|Equation| |#1|))) 99 (|has| |#1| (|Evalable| |#1|)) ELT) (($ $ (|List| #15=(|Symbol|)) (|List| |#1|)) 98 (|has| |#1| (|InnerEvalable| #15# |#1|)) ELT) (($ $ #15# |#1|) 97 (|has| |#1| (|InnerEvalable| #15# |#1|)) ELT)) (|elt| (($ $ |#1|) 103 (|has| |#1| (|Eltable| |#1| |#1|)) ELT)) (|convert| (((|InputForm|) $) 78 (|has| |#1| (|ConvertibleTo| (|InputForm|))) ELT)) (|conjugate| (($ $) 95 T ELT)) (|coerce| (((|OutputForm|) $) 13 T ELT) (($ (|Integer|)) 42 T ELT) (($ |#1|) 53 T ELT) (($ #9#) 108 (|has| |#1| . #10#) ELT)) (|charthRoot| (((|Maybe| $) $) 79 (|has| |#1| (|CharacteristicNonZero|)) ELT)) (|characteristic| (((|NonNegativeInteger|)) 41 T CONST)) (|before?| (#1# 6 T ELT)) (|annihilate?| (((|Boolean|) $ $) 34 T ELT)) (|abs| ((|#1| $) 84 (|has| |#1| (|RealNumberSystem|)) ELT)) (|Zero| (#4# 24 T CONST)) (|One| (($) 46 T CONST)) (>= (#16=((|Boolean|) $ $) 74 (|has| |#1| . #13#) ELT)) (> (#16# 76 (|has| |#1| . #13#) ELT)) (= (#1# 8 T ELT)) (<= (#16# 75 (|has| |#1| . #13#) ELT)) (< (#16# 77 (|has| |#1| . #13#) ELT)) (- (($ $) 30 T ELT) (($ $ $) 29 T ELT)) (+ (($ $ $) 18 T ELT)) (** (($ $ (|PositiveInteger|)) 36 T ELT) (($ $ (|NonNegativeInteger|)) 44 T ELT)) (* (($ (|PositiveInteger|) $) 17 T ELT) (($ (|NonNegativeInteger|) $) 21 T ELT) (($ (|Integer|) . #17=($)) 31 T ELT) (($ $ $) 35 T ELT) (($ $ |#1|) 55 T ELT) (($ |#1| . #17#) 54 T ELT))) (((|OctonionCategory| |#1|) (|Category|) (|CommutativeRing|)) (T |OctonionCategory|)) ((|conjugate| (*1 *1 *1) (AND (|ofCategory| *1 (|OctonionCategory| *2)) (|ofCategory| *2 (|CommutativeRing|)))) (|real| (*1 *2 *1) (AND (|ofCategory| *1 (|OctonionCategory| *2)) (|ofCategory| *2 (|CommutativeRing|)))) (|imagi| (*1 *2 *1) (AND (|ofCategory| *1 (|OctonionCategory| *2)) (|ofCategory| *2 (|CommutativeRing|)))) (|imagj| (*1 *2 *1) (AND (|ofCategory| *1 (|OctonionCategory| *2)) (|ofCategory| *2 (|CommutativeRing|)))) (|imagk| (*1 *2 *1) (AND (|ofCategory| *1 (|OctonionCategory| *2)) (|ofCategory| *2 (|CommutativeRing|)))) (|imagE| (*1 *2 *1) (AND (|ofCategory| *1 (|OctonionCategory| *2)) (|ofCategory| *2 (|CommutativeRing|)))) (|imagI| (*1 *2 *1) (AND (|ofCategory| *1 (|OctonionCategory| *2)) (|ofCategory| *2 (|CommutativeRing|)))) (|imagJ| (*1 *2 *1) (AND (|ofCategory| *1 (|OctonionCategory| *2)) (|ofCategory| *2 (|CommutativeRing|)))) (|imagK| (*1 *2 *1) (AND (|ofCategory| *1 (|OctonionCategory| *2)) (|ofCategory| *2 (|CommutativeRing|)))) (|norm| (*1 *2 *1) (AND (|ofCategory| *1 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(|Algebra| #31#)) #33#) ELT) #16#) (|coefficients| ((#79# $) NIL T ELT)) (|coefficient| ((|#1| $ #55#) NIL T ELT) #64# #65#) (|charthRoot| (((|Maybe| $) $) NIL (OR #99# (|has| |#1| #100#)) ELT)) (|characteristic| ((#7#) NIL T CONST)) (|binomThmExpt| (($ $ $ #7#) NIL #41# ELT)) (|before?| #1#) (|associates?| (#2# NIL #15# ELT)) (|annihilate?| #1#) (|Zero| #28#) (|One| #28#) (D #65# #64# #81# #82# #83# #84# #85# #87# #88# #89# #90# #92#) (= #1#) (/ (#102=($ $ |#1|) NIL (|has| |#1| (|Field|)) ELT)) (- #27# #103=(#76# NIL T ELT)) (+ #103#) (** (($ $ #104=(|PositiveInteger|)) NIL T ELT) (#93# NIL T ELT)) (* (($ #104# $) NIL T ELT) (($ #7# $) NIL T ELT) (($ #32# . #105=($)) NIL T ELT) #103# (($ $ #31#) NIL #101# ELT) (($ #31# . #105#) NIL #101# ELT) (($ |#1| . #105#) NIL T ELT) (#102# NIL T ELT))) +((~= #1=(#2=(#3=(|Boolean|) $ $) NIL T ELT)) (|zero?| #4=(#5=(#3# $) NIL T ELT)) (|weights| ((#6=(|List| #7=(|NonNegativeInteger|)) $) NIL T ELT) ((#6# $ #8=(|Symbol|)) NIL T ELT)) (|weight| #9=((#7# $) NIL T ELT) #10=((#7# $ #8#) NIL T ELT)) (|variables| ((#11=(|List| #12=(|OrderlyDifferentialVariable| #8#)) $) NIL T ELT)) (|univariate| ((#13=(|SparseUnivariatePolynomial| $) $ #12#) NIL T ELT) ((#14=(|SparseUnivariatePolynomial| |#1|) $) NIL T ELT)) (|unitNormal| (((|Record| (|:| |unit| $) (|:| |canonical| $) (|:| |associate| $)) $) NIL #15=(|has| |#1| (|IntegralDomain|)) ELT)) (|unitCanonical| #16=(#17=($ $) NIL #15# ELT)) (|unit?| (#5# NIL #15# ELT)) (|totalDegree| #9# ((#7# $ #11#) NIL T ELT)) (|subtractIfCan| ((#18=(|Maybe| $) $ $) NIL T ELT)) (|squareFreePolynomial| #19=(((|Factored| #13#) #13#) NIL #20=(|has| |#1| (|PolynomialFactorizationExplicit|)) ELT)) (|squareFreePart| #21=(#17# NIL #22=(|has| |#1| (|GcdDomain|)) ELT)) (|squareFree| (#23=((|Factored| $) $) NIL #22# ELT)) (|solveLinearPolynomialEquation| (((|Union| #24=(|List| #13#) #25="failed") #24# #13#) NIL #20# ELT)) (|separant| #26=(#17# NIL T ELT)) (|sample| #27=(($) NIL T CONST)) (|retractIfCan| (((|Union| |#1| . #28=(#25#)) . #29=($)) NIL T ELT) (((|Union| #30=(|Fraction| #31=(|Integer|)) . #28#) . #29#) NIL #32=(|has| |#1| (|RetractableTo| #30#)) ELT) (((|Union| #31# . #28#) . #29#) NIL #33=(|has| |#1| (|RetractableTo| #31#)) ELT) #34=(((|Union| #12# . #28#) . #29#) NIL T ELT) (((|Union| #8# . #28#) . #29#) NIL T ELT) (((|Union| #35=(|SparseMultivariatePolynomial| |#1| #8#) . #28#) . #29#) NIL T ELT)) (|retract| #36=(#37=(|#1| . #38=($)) NIL T ELT) ((#30# . #38#) NIL #32# ELT) ((#31# . #38#) NIL #33# ELT) #39=((#12# . #38#) NIL T ELT) ((#8# . #38#) NIL T ELT) ((#35# . #38#) NIL T ELT)) (|resultant| (($ $ $ #12#) NIL #40=(|has| |#1| (|CommutativeRing|)) ELT)) (|reductum| #26#) (|reducedSystem| ((#41=(|Matrix| #31#) . #42=(#43=(|Matrix| $))) NIL #44=(|has| |#1| (|LinearlyExplicitRingOver| #31#)) ELT) ((#45=(|Record| (|:| |mat| #41#) (|:| |vec| (|Vector| #31#))) . #46=(#43# #47=(|Vector| $))) NIL #44# ELT) ((#48=(|Record| (|:| |mat| #49=(|Matrix| |#1|)) (|:| |vec| (|Vector| |#1|))) . #46#) NIL T ELT) ((#49# . #42#) NIL T ELT)) (|recip| ((#50=(|Union| $ #25#) $) NIL T ELT)) (|primitivePart| #21# #51=(#52=($ $ #12#) NIL #22# ELT)) (|primitiveMonomials| #53=((#54=(|List| $) $) NIL T ELT)) (|prime?| (#5# NIL #20# ELT)) (|pomopo!| (($ $ |#1| #55=(|IndexedExponents| #12#) $) NIL T ELT)) (|patternMatch| ((#56=(|PatternMatchResult| #57=(|Float|) . #58=($)) $ #59=(|Pattern| #57#) #56#) NIL (AND (|has| #12# #60=(|PatternMatchable| #57#)) (|has| |#1| #60#)) ELT) ((#61=(|PatternMatchResult| #31# . #58#) $ #62=(|Pattern| #31#) #61#) NIL (AND (|has| #12# #63=(|PatternMatchable| #31#)) (|has| |#1| #63#)) ELT)) (|order| #10# #9#) (|opposite?| #1#) (|one?| #4#) (|numberOfMonomials| #9#) (|multivariate| (($ #14# #12#) NIL T ELT) (($ #13# #12#) NIL T ELT)) (|monomials| #53#) (|monomial?| #4#) (|monomial| (($ |#1| #55#) NIL T ELT) #64=(($ $ #12# #7#) NIL T ELT) #65=(($ $ #11# #6#) NIL T ELT)) (|monicDivide| (((|Record| (|:| |quotient| $) (|:| |remainder| $)) $ $ #12#) NIL T ELT)) (|minimumDegree| #66=((#55# $) NIL T ELT) #67=((#7# $ #12#) NIL T ELT) #68=((#6# $ #11#) NIL T ELT)) (|mapExponents| (($ (|Mapping| #55# #55#) $) NIL T ELT)) (|map| (($ #69=(|Mapping| |#1| |#1|) $) NIL T ELT)) (|makeVariable| ((#70=(|Mapping| $ #7#) #8#) NIL T ELT) ((#70# $) NIL #71=(|has| |#1| (|DifferentialRing|)) ELT)) (|mainVariable| #34#) (|leftReducedSystem| ((#41# . #72=(#47#)) NIL #44# ELT) ((#45# . #73=(#47# $)) NIL #44# ELT) ((#48# . #73#) NIL T ELT) ((#49# . #72#) NIL T ELT)) (|leadingMonomial| #26#) (|leadingCoefficient| #36#) (|leader| #39#) (|lcm| #74=(($ #54#) NIL #22# ELT) #75=(#76=($ $ $) NIL #22# ELT)) (|latex| (((|String|) $) NIL T ELT)) (|isobaric?| #4#) (|isTimes| #77=(((|Union| #54# #25#) $) NIL T ELT)) (|isPlus| #77#) (|isExpt| (((|Union| (|Record| (|:| |var| #12#) (|:| |exponent| #7#)) #25#) $) NIL T ELT)) (|initial| #26#) (|hash| (((|SingleInteger|) $) NIL T ELT)) (|ground?| #4#) (|ground| #36#) (|gcdPolynomial| ((#13# #13# #13#) NIL #22# ELT)) (|gcd| #74# #75#) (|factorSquareFreePolynomial| #19#) (|factorPolynomial| #19#) (|factor| (#23# NIL #20# ELT)) (|exquo| ((#50# $ |#1|) NIL #15# ELT) ((#50# $ $) NIL #15# ELT)) (|eval| (($ $ (|List| #78=(|Equation| $))) NIL T ELT) (($ $ #78#) NIL T ELT) (($ $ $ $) NIL T ELT) (($ $ #54# #54#) NIL T ELT) (($ $ #12# |#1|) NIL T ELT) (($ $ #11# #79=(|List| |#1|)) NIL T ELT) (($ $ #12# $) NIL T ELT) (($ $ #11# #54#) NIL T ELT) (($ $ #8# $) NIL #71# ELT) (($ $ #80=(|List| #8#) #54#) NIL #71# ELT) (($ $ #8# |#1|) NIL #71# ELT) (($ $ #80# #79#) NIL #71# ELT)) (|discriminant| (#52# NIL #40# ELT)) (|differentiate| #65# #64# #81=(($ $ #11#) NIL T ELT) #82=(#52# NIL T ELT) #83=(($ $ #69#) NIL T ELT) #84=(($ $ #69# #7#) NIL T ELT) #85=(($ $ #8#) NIL #86=(|has| |#1| (|PartialDifferentialSpace| #8#)) ELT) #87=(($ $ #80#) NIL #86# ELT) #88=(($ $ #8# #7#) NIL #86# ELT) #89=(($ $ #80# #6#) NIL #86# ELT) #90=(#17# NIL #91=(|has| |#1| (|DifferentialSpace|)) ELT) #92=(#93=($ $ #7#) NIL #91# ELT)) (|differentialVariables| ((#80# $) NIL T ELT)) (|degree| #66# #67# #68# #10#) (|convert| ((#59# . #94=($)) NIL (AND (|has| #12# #95=(|ConvertibleTo| #59#)) (|has| |#1| #95#)) ELT) ((#62# . #94#) NIL (AND (|has| #12# #96=(|ConvertibleTo| #62#)) (|has| |#1| #96#)) ELT) ((#97=(|InputForm|) . #94#) NIL (AND (|has| #12# #98=(|ConvertibleTo| #97#)) (|has| |#1| #98#)) ELT)) (|content| (#37# NIL #22# ELT) #51#) (|conditionP| (((|Union| #47# #25#) #43#) NIL #99=(AND (|has| $ #100=(|CharacteristicNonZero|)) #20#) ELT)) (|coerce| (((|OutputForm|) $) NIL T ELT) (($ #31#) NIL T ELT) (($ |#1|) NIL T ELT) (($ #12#) NIL T ELT) (($ #8#) NIL T ELT) (($ #35#) NIL T ELT) (($ #30#) NIL (OR #101=(|has| |#1| (|Algebra| #30#)) #32#) ELT) #16#) (|coefficients| ((#79# $) NIL T ELT)) (|coefficient| ((|#1| $ #55#) NIL T ELT) #64# #65#) (|charthRoot| ((#18# $) NIL (OR #99# (|has| |#1| #100#)) ELT)) (|characteristic| ((#7#) NIL T CONST)) (|binomThmExpt| (($ $ $ #7#) NIL #40# ELT)) (|before?| #1#) (|associates?| (#2# NIL #15# ELT)) (|annihilate?| #1#) (|Zero| #27#) (|One| #27#) (D #65# #64# #81# #82# #83# #84# #85# #87# #88# #89# #90# #92#) (= #1#) (/ (#102=($ $ |#1|) NIL (|has| |#1| (|Field|)) ELT)) (- #26# #103=(#76# NIL T ELT)) (+ #103#) (** (($ $ #104=(|PositiveInteger|)) NIL T ELT) (#93# NIL T ELT)) (* (($ #104# $) NIL T ELT) (($ #7# $) NIL T ELT) (($ #31# . #105=($)) NIL T ELT) #103# (($ $ #30#) NIL #101# ELT) (($ #30# . #105#) NIL #101# ELT) (($ |#1| . #105#) NIL T ELT) (#102# NIL T ELT))) (((|OrderlyDifferentialPolynomial| |#1|) (|Join| (|DifferentialPolynomialCategory| |#1| #1=(|Symbol|) #2=(|OrderlyDifferentialVariable| #1#) (|IndexedExponents| #2#)) (|RetractableTo| (|SparseMultivariatePolynomial| |#1| #1#))) (|Ring|)) (T |OrderlyDifferentialPolynomial|)) NIL -((~= #1=(#2=(#3=(|Boolean|) $ $) NIL T ELT)) (|zero?| #4=(#5=(#3# $) NIL T ELT)) (|unitNormal| (((|Record| (|:| |unit| $) (|:| |canonical| $) (|:| |associate| $)) $) NIL #6=(|has| |#2| (|Field|)) ELT)) (|unitCanonical| #7=(#8=($ $) NIL #6# ELT)) (|unit?| #9=(#5# NIL #6# ELT)) (|subtractIfCan| (#10=(#11=(|Union| $ #12="failed") $ $) NIL T ELT)) (|squareFreePart| #7#) (|squareFree| #13=(((|Factored| $) $) NIL #6# ELT)) (|sizeLess?| #14=(#2# NIL #6# ELT)) (|sample| #15=(($) NIL T CONST)) (|rem| #16=(#17=($ $ $) NIL #6# ELT)) (|recip| ((#11# $) NIL T ELT)) (|quo| #16#) (|principalIdeal| (((|Record| (|:| |coef| #18=(|List| $)) #19=(|:| |generator| $)) #18#) NIL #6# ELT)) (|prime?| #9#) (|opposite?| #1#) (|one?| #4#) (|multiEuclidean| (((|Union| #18# #12#) #18# $) NIL #6# ELT)) (|lcm| #20=(($ #18#) NIL #6# ELT) #16#) (|latex| (((|String|) $) NIL T ELT)) (|inv| (#8# 20 #6# ELT)) (|hash| (((|SingleInteger|) $) NIL T ELT)) (|gcdPolynomial| ((#21=(|SparseUnivariatePolynomial| $) #21# #21#) NIL #6# ELT)) (|gcd| #20# #16#) (|factor| #13#) (|extendedEuclidean| (((|Union| (|Record| #22=(|:| |coef1| $) #23=(|:| |coef2| $)) #12#) $ $ $) NIL #6# ELT) (((|Record| #22# #23# #19#) $ $) NIL #6# ELT)) (|exquo| (#10# NIL #6# ELT)) (|expressIdealMember| (((|Maybe| #18#) #18# $) NIL #6# ELT)) (|euclideanSize| ((#24=(|NonNegativeInteger|) $) NIL #6# ELT)) (|divide| (((|Record| (|:| |quotient| $) (|:| |remainder| $)) $ $) NIL #6# ELT)) (|differentiate| (#8# 13 T ELT) #25=(($ $ #24#) NIL T ELT)) (|coerce| (((|OutputForm|) $) NIL T ELT) (($ #26=(|Integer|)) NIL T ELT) (($ |#2|) 10 T ELT) ((|#2| $) 11 T ELT) (($ #27=(|Fraction| #26#)) NIL #6# ELT) #7#) (|characteristic| ((#24#) NIL T CONST)) (|before?| #1#) (|associates?| #14#) (|annihilate?| #1#) (|Zero| #15#) (|One| #15#) (D #28=(#8# NIL T ELT) #25#) (= #1#) (/ (#17# 15 #6# ELT)) (- #28# #29=(#17# NIL T ELT)) (+ #29#) (** #25# (($ $ #30=(|PositiveInteger|)) NIL T ELT) (($ $ #26#) 18 #6# ELT)) (* (($ #30# $) NIL T ELT) (($ #24# $) NIL T ELT) (($ #26# . #31=($)) NIL T ELT) #29# #29# (($ #27# . #31#) NIL #6# ELT) (($ $ #27#) NIL #6# ELT))) +((~= #1=(#2=(#3=(|Boolean|) $ $) NIL T ELT)) (|zero?| #4=(#5=(#3# $) NIL T ELT)) (|unitNormal| (((|Record| (|:| |unit| $) (|:| |canonical| $) (|:| |associate| $)) $) NIL #6=(|has| |#2| (|Field|)) ELT)) (|unitCanonical| #7=(#8=($ $) NIL #6# ELT)) (|unit?| #9=(#5# NIL #6# ELT)) (|subtractIfCan| (((|Maybe| $) $ $) NIL T ELT)) (|squareFreePart| #7#) (|squareFree| #10=(((|Factored| $) $) NIL #6# ELT)) (|sizeLess?| #11=(#2# NIL #6# ELT)) (|sample| #12=(($) NIL T CONST)) (|rem| #13=(#14=($ $ $) NIL #6# ELT)) (|recip| ((#15=(|Union| $ #16="failed") $) NIL T ELT)) (|quo| #13#) (|principalIdeal| (((|Record| (|:| |coef| #17=(|List| $)) #18=(|:| |generator| $)) #17#) NIL #6# ELT)) (|prime?| #9#) (|opposite?| #1#) (|one?| #4#) (|multiEuclidean| (((|Union| #17# #16#) #17# $) NIL #6# ELT)) (|lcm| #19=(($ #17#) NIL #6# ELT) #13#) (|latex| (((|String|) $) NIL T ELT)) (|inv| (#8# 20 #6# ELT)) (|hash| (((|SingleInteger|) $) NIL T ELT)) (|gcdPolynomial| ((#20=(|SparseUnivariatePolynomial| $) #20# #20#) NIL #6# ELT)) (|gcd| #19# #13#) (|factor| #10#) (|extendedEuclidean| (((|Union| (|Record| #21=(|:| |coef1| $) #22=(|:| |coef2| $)) #16#) $ $ $) NIL #6# ELT) (((|Record| #21# #22# #18#) $ $) NIL #6# ELT)) (|exquo| ((#15# $ $) NIL #6# ELT)) (|expressIdealMember| (((|Maybe| #17#) #17# $) NIL #6# ELT)) (|euclideanSize| ((#23=(|NonNegativeInteger|) $) NIL #6# ELT)) (|divide| (((|Record| (|:| |quotient| $) (|:| |remainder| $)) $ $) NIL #6# ELT)) (|differentiate| (#8# 13 T ELT) #24=(($ $ #23#) NIL T ELT)) (|coerce| (((|OutputForm|) $) NIL T ELT) (($ #25=(|Integer|)) NIL T ELT) (($ |#2|) 10 T ELT) ((|#2| $) 11 T ELT) (($ #26=(|Fraction| #25#)) NIL #6# ELT) #7#) (|characteristic| ((#23#) NIL T CONST)) (|before?| #1#) (|associates?| #11#) (|annihilate?| #1#) (|Zero| #12#) (|One| #12#) (D #27=(#8# NIL T ELT) #24#) (= #1#) (/ (#14# 15 #6# ELT)) (- #27# #28=(#14# NIL T ELT)) (+ #28#) (** #24# (($ $ #29=(|PositiveInteger|)) NIL T ELT) (($ $ #25#) 18 #6# ELT)) (* (($ #29# $) NIL T ELT) (($ #23# $) NIL T ELT) (($ #25# . #30=($)) NIL T ELT) #28# #28# (($ #26# . #30#) NIL #6# ELT) (($ $ #26#) NIL #6# ELT))) (((|OrdinaryDifferentialRing| |#1| |#2| |#3|) (|Join| (|BiModule| $ $) (|DifferentialRing|) (|HomotopicTo| |#2|) (CATEGORY |package| (IF (|has| |#2| #1=(|Field|)) (ATTRIBUTE #1#) |%noBranch|))) (|SetCategory|) (|PartialDifferentialRing| |#1|) |#1|) (T |OrdinaryDifferentialRing|)) NIL ((~= #1=(((|Boolean|) $ $) NIL T ELT)) (|weight| (#2=(#3=(|NonNegativeInteger|) $) NIL T ELT)) (|variable| (#4=(|#1| $) 10 T ELT)) (|retractIfCan| (((|Union| |#1| "failed") $) NIL T ELT)) (|retract| (#4# NIL T ELT)) (|order| (#2# 11 T ELT)) (|min| #5=(($ $ $) NIL T ELT)) (|max| #5#) (|makeVariable| (($ |#1| #3#) 9 T ELT)) (|latex| (((|String|) $) NIL T ELT)) (|hash| (((|SingleInteger|) $) NIL T ELT)) (|differentiate| #6=(($ $ #3#) NIL T ELT) #7=(($ $) NIL T ELT)) (|coerce| (((|OutputForm|) $) NIL T ELT) (($ |#1|) NIL T ELT)) (|before?| #1#) (D #6# #7#) (>= #1#) (> #1#) (= #1#) (<= #1#) (< #1#)) @@ -2456,12 +2456,12 @@ NIL ((~= #1=(#2=(#3=(|Boolean|) $ $) NIL T ELT)) (|varList| (((|List| |#1|) $) 39 T ELT)) (|size| (#4=(#5=(|NonNegativeInteger|) $) NIL T ELT)) (|sample| (#6=($) NIL T CONST)) (|rquo| #7=((#8=(|Union| $ #9="failed") $ $) NIL T ELT) (#10=(#8# $ |#1|) 29 T ELT)) (|retractIfCan| (((|Union| |#1| #9#) $) NIL T ELT)) (|retract| (#11=(|#1| $) NIL T ELT)) (|rest| (#12=($ $) 43 T ELT)) (|recip| ((#8# $) NIL T ELT)) (|overlap| (((|Record| #13=(|:| |lm| $) (|:| |mm| $) #14=(|:| |rm| $)) $ $) NIL T ELT)) (|one?| ((#3# $) NIL T ELT)) (|nthFactor| ((|#1| $ #15=(|Integer|)) NIL T ELT)) (|nthExpon| ((#5# $ #15#) NIL T ELT)) (|mirror| (#12# 55 T ELT)) (|min| #16=(($ $ $) NIL T ELT)) (|max| #16#) (|mapGen| (($ (|Mapping| |#1| |#1|) $) NIL T ELT)) (|mapExpon| (($ (|Mapping| #5# #5#) $) NIL T ELT)) (|lquo| #7# (#10# 26 T ELT)) (|lexico| (#2# 52 T ELT)) (|length| (#4# 35 T ELT)) (|latex| (((|String|) $) NIL T ELT)) (|hcrf| #16#) (|hclf| #16#) (|hash| (((|SingleInteger|) $) NIL T ELT)) (|first| (#11# 42 T ELT)) (|factors| (((|List| (|Record| (|:| |gen| |#1|) (|:| |exp| #5#))) $) NIL T ELT)) (|divide| #17=(((|Union| (|Record| #13# #14#) #9#) $ $) NIL T ELT)) (|div| #17#) (|coerce| (((|OutputForm|) $) NIL T ELT) (($ |#1|) NIL T ELT)) (|before?| #1#) (|One| (#6# 7 T CONST)) (>= #1#) (> #1#) (= #1#) (<= #1#) (< (#2# 54 T ELT)) (** (($ $ (|PositiveInteger|)) NIL T ELT) (($ $ #5#) NIL T ELT) (($ |#1| #5#) NIL T ELT)) (* #16# (($ |#1| $) NIL T ELT) (($ $ |#1|) NIL T ELT))) (((|OrderedFreeMonoid| |#1|) (|Join| (|FreeMonoidCategory| |#1|) (|OrderedMonoid|) (CATEGORY |domain| (SIGNATURE |first| (|#1| $)) (SIGNATURE |rest| #1=($ $)) (SIGNATURE |mirror| #1#) (SIGNATURE |lexico| ((|Boolean|) $ $)) (SIGNATURE |lquo| #2=((|Union| $ #3="failed") $ |#1|)) (SIGNATURE |rquo| #2#) (SIGNATURE |div| ((|Union| (|Record| (|:| |lm| $) (|:| |rm| $)) #3#) $ $)) (SIGNATURE |length| ((|NonNegativeInteger|) $)) (SIGNATURE |varList| ((|List| |#1|) $)))) (|OrderedSet|)) (T |OrderedFreeMonoid|)) ((|first| #1=(*1 *2 *1) #2=(AND #3=(|isDomain| *1 (|OrderedFreeMonoid| *2)) #4=(|ofCategory| *2 #5=(|OrderedSet|)))) (|rest| #6=(*1 *1 *1) #2#) (|mirror| #6# #2#) (|lexico| #7=(*1 *2 *1 *1) (AND (|isDomain| *2 (|Boolean|)) #8=(|isDomain| *1 #9=(|OrderedFreeMonoid| *3)) #10=(|ofCategory| *3 #5#))) (|lquo| #11=(*1 *1 *1 *2) #12=(|partial| AND #3# #4#)) (|rquo| #11# #12#) (|div| #7# (|partial| AND (|isDomain| *2 (|Record| (|:| |lm| #9#) (|:| |rm| #9#))) #8# #10#)) (|length| #1# (AND (|isDomain| *2 (|NonNegativeInteger|)) #8# #10#)) (|varList| #1# (AND (|isDomain| *2 (|List| *3)) #8# #10#))) -((~= (#1=((|Boolean|) $ $) 7 T ELT)) (|zero?| ((#2=(|Boolean|) $) 22 T ELT)) (|unitNormal| (((|Record| (|:| |unit| $) (|:| |canonical| $) (|:| |associate| $)) $) 55 T ELT)) (|unitCanonical| (($ $) 54 T ELT)) (|unit?| ((#3=(|Boolean|) $) 52 T ELT)) (|subtractIfCan| (((|Union| $ "failed") $ $) 26 T ELT)) (|sign| (((|Integer|) $) 69 T ELT)) (|sample| (#4=($) 23 T CONST)) (|recip| (((|Union| $ "failed") $) 42 T ELT)) (|positive?| (((|Boolean|) $) 67 T ELT)) (|opposite?| ((#2# $ $) 20 T ELT)) (|one?| (((|Boolean|) $) 44 T ELT)) (|negative?| (((|Boolean|) $) 68 T ELT)) (|min| (#5=($ $ $) 61 T ELT)) (|max| (#5# 62 T ELT)) (|latex| (((|String|) $) 11 T ELT)) (|hash| (((|SingleInteger|) $) 12 T ELT)) (|exquo| (((|Union| $ "failed") $ $) 56 T ELT)) (|coerce| (((|OutputForm|) $) 13 T ELT) (($ (|Integer|)) 41 T ELT) (($ $) 57 T ELT)) (|characteristic| (((|NonNegativeInteger|)) 40 T CONST)) (|before?| (#1# 6 T ELT)) (|associates?| ((#3# $ $) 53 T ELT)) (|annihilate?| (((|Boolean|) $ $) 33 T ELT)) (|abs| (($ $) 70 T ELT)) (|Zero| (#4# 24 T CONST)) (|One| (($) 45 T CONST)) (>= (#6=((|Boolean|) $ $) 63 T ELT)) (> (#6# 65 T ELT)) (= (#1# 8 T ELT)) (<= (#6# 64 T ELT)) (< (#6# 66 T ELT)) (- (($ $) 29 T ELT) (($ $ $) 28 T ELT)) (+ (($ $ $) 18 T ELT)) (** (($ $ (|PositiveInteger|)) 35 T ELT) (($ $ (|NonNegativeInteger|)) 43 T ELT)) (* (($ (|PositiveInteger|) $) 17 T ELT) (($ (|NonNegativeInteger|) $) 21 T ELT) (($ (|Integer|) $) 30 T ELT) (($ $ $) 34 T ELT))) +((~= (#1=((|Boolean|) $ $) 7 T ELT)) (|zero?| ((#2=(|Boolean|) $) 22 T ELT)) (|unitNormal| (((|Record| (|:| |unit| $) (|:| |canonical| $) (|:| |associate| $)) $) 56 T ELT)) (|unitCanonical| (($ $) 55 T ELT)) (|unit?| ((#3=(|Boolean|) $) 53 T ELT)) (|subtractIfCan| (((|Maybe| $) $ $) 26 T ELT)) (|sign| (((|Integer|) $) 70 T ELT)) (|sample| (#4=($) 23 T CONST)) (|recip| (((|Union| $ "failed") $) 43 T ELT)) (|positive?| (((|Boolean|) $) 68 T ELT)) (|opposite?| ((#2# $ $) 20 T ELT)) (|one?| (((|Boolean|) $) 45 T ELT)) (|negative?| (((|Boolean|) $) 69 T ELT)) (|min| (#5=($ $ $) 62 T ELT)) (|max| (#5# 63 T ELT)) (|latex| (((|String|) $) 11 T ELT)) (|hash| (((|SingleInteger|) $) 12 T ELT)) (|exquo| (((|Union| $ "failed") $ $) 57 T ELT)) (|coerce| (((|OutputForm|) $) 13 T ELT) (($ (|Integer|)) 42 T ELT) (($ $) 58 T ELT)) (|characteristic| (((|NonNegativeInteger|)) 41 T CONST)) (|before?| (#1# 6 T ELT)) (|associates?| ((#3# $ $) 54 T ELT)) (|annihilate?| (((|Boolean|) $ $) 34 T ELT)) (|abs| (($ $) 71 T ELT)) (|Zero| (#4# 24 T CONST)) (|One| (($) 46 T CONST)) (>= (#6=((|Boolean|) $ $) 64 T ELT)) (> (#6# 66 T ELT)) (= (#1# 8 T ELT)) (<= (#6# 65 T ELT)) (< (#6# 67 T ELT)) (- (($ $) 30 T ELT) (($ $ $) 29 T ELT)) (+ (($ $ $) 18 T ELT)) (** (($ $ (|PositiveInteger|)) 36 T ELT) (($ $ (|NonNegativeInteger|)) 44 T ELT)) (* (($ (|PositiveInteger|) $) 17 T ELT) (($ (|NonNegativeInteger|) $) 21 T ELT) (($ (|Integer|) $) 31 T ELT) (($ $ $) 35 T ELT))) (((|OrderedIntegralDomain|) (|Category|)) (T |OrderedIntegralDomain|)) NIL (|Join| (|IntegralDomain|) (|OrderedRing|)) (((|AbelianGroup|) . T) ((|AbelianMonoid|) . T) ((|AbelianSemiGroup|) . T) ((|Algebra| $) . T) ((|BasicType|) . T) ((|BiModule| $ $) . T) ((|CancellationAbelianMonoid|) . T) ((|CharacteristicZero|) . T) ((|CoercibleFrom| (|Integer|)) . T) ((|CoercibleFrom| $) . T) ((|CoercibleTo| (|OutputForm|)) . T) ((|CommutativeRing|) . T) ((|EntireRing|) . T) ((|IntegralDomain|) . T) ((|Join|) . T) ((|LeftLinearSet| (|Integer|)) . T) ((|LeftLinearSet| $) . T) ((|LeftModule| $) . T) ((|LinearSet| $) . T) ((|Module| $) . T) ((|Monoid|) . T) ((|OrderedAbelianGroup|) . T) ((|OrderedAbelianMonoid|) . T) ((|OrderedAbelianSemiGroup|) . T) ((|OrderedCancellationAbelianMonoid|) . T) ((|OrderedRing|) . T) ((|OrderedSet|) . T) ((|OrderedType|) . T) ((|RightLinearSet| $) . T) ((|RightModule| $) . T) ((|Ring|) . T) ((|Rng|) . T) ((|SemiGroup|) . T) ((|SemiRing|) . T) ((|SetCategory|) . T) ((|Type|) . T)) -((~= #1=((#2=(|Boolean|) $ $) NIL T ELT)) (|zero?| #3=((#2# $) NIL T ELT)) (|subtractIfCan| ((#4=(|Union| $ "failed") $ $) NIL T ELT)) (|sample| #5=(($) NIL T CONST)) (|reductum| #6=(#7=($ $) NIL T ELT)) (|recip| ((#4# $) NIL T ELT)) (|po| ((|#1| $) 10 T ELT)) (|opposite?| #1#) (|op| (($ |#1|) 9 T ELT)) (|one?| #3#) (|monomial| (($ |#2| #8=(|NonNegativeInteger|)) NIL T ELT)) (|minimumDegree| #9=((#8# $) NIL T ELT)) (|leadingCoefficient| ((|#2| $) NIL T ELT)) (|latex| (((|String|) $) NIL T ELT)) (|hash| (((|SingleInteger|) $) NIL T ELT)) (|differentiate| #10=(#7# NIL #11=(|has| |#1| (|DifferentialRing|)) ELT) #12=(#13=($ $ #8#) NIL #11# ELT)) (|degree| #9#) (|coerce| (((|OutputForm|) $) 17 T ELT) (($ #14=(|Integer|)) NIL T ELT) (($ |#2|) NIL (|has| |#2| (|CommutativeRing|)) ELT)) (|coefficient| ((|#2| $ #8#) NIL T ELT)) (|characteristic| ((#8#) NIL T CONST)) (|before?| #1#) (|annihilate?| #1#) (|Zero| #5#) (|One| #5#) (D #10# #12#) (= #1#) (- #6# #15=(#16=($ $ $) NIL T ELT)) (+ #15#) (** (($ $ #17=(|PositiveInteger|)) NIL T ELT) (#13# NIL T ELT)) (* (($ #17# $) NIL T ELT) (($ #8# $) NIL T ELT) (($ #14# . #18=($)) NIL T ELT) (#16# 12 T ELT) (($ $ |#2|) NIL T ELT) (($ |#2| . #18#) NIL T ELT))) +((~= #1=((#2=(|Boolean|) $ $) NIL T ELT)) (|zero?| #3=((#2# $) NIL T ELT)) (|subtractIfCan| (((|Maybe| $) $ $) NIL T ELT)) (|sample| #4=(($) NIL T CONST)) (|reductum| #5=(#6=($ $) NIL T ELT)) (|recip| (((|Union| $ "failed") $) NIL T ELT)) (|po| ((|#1| $) 10 T ELT)) (|opposite?| #1#) (|op| (($ |#1|) 9 T ELT)) (|one?| #3#) (|monomial| (($ |#2| #7=(|NonNegativeInteger|)) NIL T ELT)) (|minimumDegree| #8=((#7# $) NIL T ELT)) (|leadingCoefficient| ((|#2| $) NIL T ELT)) (|latex| (((|String|) $) NIL T ELT)) (|hash| (((|SingleInteger|) $) NIL T ELT)) (|differentiate| #9=(#6# NIL #10=(|has| |#1| (|DifferentialRing|)) ELT) #11=(#12=($ $ #7#) NIL #10# ELT)) (|degree| #8#) (|coerce| (((|OutputForm|) $) 17 T ELT) (($ #13=(|Integer|)) NIL T ELT) (($ |#2|) NIL (|has| |#2| (|CommutativeRing|)) ELT)) (|coefficient| ((|#2| $ #7#) NIL T ELT)) (|characteristic| ((#7#) NIL T CONST)) (|before?| #1#) (|annihilate?| #1#) (|Zero| #4#) (|One| #4#) (D #9# #11#) (= #1#) (- #5# #14=(#15=($ $ $) NIL T ELT)) (+ #14#) (** (($ $ #16=(|PositiveInteger|)) NIL T ELT) (#12# NIL T ELT)) (* (($ #16# $) NIL T ELT) (($ #7# $) NIL T ELT) (($ #13# . #17=($)) NIL T ELT) (#15# 12 T ELT) (($ $ |#2|) NIL T ELT) (($ |#2| . #17#) NIL T ELT))) (((|OppositeMonogenicLinearOperator| |#1| |#2|) (|Join| #1=(|MonogenicLinearOperator| |#2|) (CATEGORY |domain| (IF (|has| |#1| #2=(|DifferentialRing|)) (ATTRIBUTE #2#) |%noBranch|) (SIGNATURE |op| ($ |#1|)) (SIGNATURE |po| (|#1| $)))) #1# (|Ring|)) (T |OppositeMonogenicLinearOperator|)) ((|op| (*1 *1 *2) (AND #1=(|ofCategory| *3 (|Ring|)) #2=(|isDomain| *1 (|OppositeMonogenicLinearOperator| *2 *3)) #3=(|ofCategory| *2 (|MonogenicLinearOperator| *3)))) (|po| (*1 *2 *1) (AND #3# #2# #1#))) ((~= (#1=((|Boolean|) $ $) 18 T ELT)) (|union| (($ |#1| $) 71 T ELT) (($ $ |#1|) 70 T ELT) (#2=($ $ $) 69 T ELT)) (|symmetricDifference| (#2# 67 T ELT)) (|subset?| (#3=((|Boolean|) $ $) 68 T ELT)) (|set| (($ (|List| |#1|)) 63 T ELT) (#4=($) 62 T ELT)) (|select!| (($ (|Mapping| #5=(|Boolean|) |#1|) . #6=($)) 42 (|has| $ (|FiniteAggregate| |#1|)) ELT)) (|select| (($ (|Mapping| #7=(|Boolean|) |#1|) . #8=($)) 49 (|has| $ (|FiniteAggregate| |#1|)) ELT)) (|sample| (#9=($) 6 T CONST)) (|removeDuplicates!| (($ $) 55 T ELT)) (|removeDuplicates| (($ $) 51 (AND (|has| |#1| . #10=((|BasicType|))) (|has| $ (|FiniteAggregate| |#1|))) ELT)) (|remove!| (($ |#1| $) 44 (|has| $ (|FiniteAggregate| |#1|)) ELT) (($ (|Mapping| #5# |#1|) . #6#) 43 (|has| $ (|FiniteAggregate| |#1|)) ELT)) (|remove| (($ |#1| $) 50 (AND (|has| |#1| . #10#) (|has| $ (|FiniteAggregate| |#1|))) ELT) (($ (|Mapping| #7# |#1|) . #8#) 48 (|has| $ (|FiniteAggregate| |#1|)) ELT)) (|reduce| ((|#1| (|Mapping| |#1| |#1| |#1|) $) 80 T ELT) ((|#1| (|Mapping| |#1| |#1| |#1|) $ |#1|) 79 T ELT) ((|#1| (|Mapping| |#1| |#1| |#1|) $ |#1| |#1|) 75 (|has| |#1| . #11=((|BasicType|))) ELT)) (|part?| (#3# 59 T ELT)) (|min| ((|#1| $) 74 T ELT)) (|merge!| (#12=($ $ $) 88 T ELT)) (|merge| (#12# 87 T ELT)) (|members| (((|List| |#1|) $) 81 T ELT)) (|member?| ((#13=(|Boolean|) |#1| $) 76 (|has| |#1| . #11#) ELT)) (|max| ((|#1| $) 86 T ELT)) (|map!| (($ (|Mapping| |#1| |#1|) $) 39 T ELT)) (|map| (($ (|Mapping| |#1| |#1|) $) 26 T ELT)) (|latex| (((|String|) $) 21 T ELT)) (|intersect| (#2# 64 T ELT)) (|inspect| ((|#1| . #14=($)) 35 T ELT)) (|insert!| (($ |#1| $) 36 T ELT) (($ |#1| $ #15=(|NonNegativeInteger|)) 56 T ELT)) (|hash| (((|SingleInteger|) $) 20 T ELT)) (|find| (((|Union| |#1| "failed") (|Mapping| #13# |#1|) $) 78 T ELT)) (|extract!| ((|#1| . #14#) 37 T ELT)) (|every?| ((#13# (|Mapping| #13# |#1|) . #16=($)) 83 T ELT)) (|eval| (($ $ (|List| (|Equation| |#1|))) 25 (AND (|has| |#1| (|Evalable| |#1|)) (|has| |#1| . #17=((|SetCategory|)))) ELT) (($ $ (|Equation| |#1|)) 24 (AND (|has| |#1| (|Evalable| |#1|)) (|has| |#1| . #17#)) ELT) (($ $ |#1| |#1|) 23 (AND (|has| |#1| (|Evalable| |#1|)) (|has| |#1| . #17#)) ELT) (($ $ (|List| |#1|) (|List| |#1|)) 22 (AND (|has| |#1| (|Evalable| |#1|)) (|has| |#1| . #17#)) ELT)) (|eq?| ((#18=(|Boolean|) $ $) 10 T ELT)) (|empty?| ((#18# $) 7 T ELT)) (|empty| (#9# 8 T ELT)) (|duplicates| (((|List| (|Record| (|:| |entry| |#1|) (|:| |count| #15#))) $) 54 T ELT)) (|difference| (($ $ |#1|) 66 T ELT) (#2# 65 T ELT)) (|dictionary| (($) 46 T ELT) (($ (|List| |#1|)) 45 T ELT)) (|count| ((#19=(|NonNegativeInteger|) (|Mapping| #13# |#1|) $) 82 T ELT) ((#19# |#1| $) 77 (|has| |#1| . #11#) ELT)) (|copy| (($ $) 9 T ELT)) (|convert| ((#20=(|InputForm|) $) 52 (|has| |#1| (|ConvertibleTo| #20#)) ELT)) (|construct| (($ (|List| |#1|)) 47 T ELT)) (|coerce| (((|OutputForm|) $) 16 T ELT)) (|brace| (($ (|List| |#1|)) 61 T ELT) (#4# 60 T ELT)) (|before?| (#1# 19 T ELT)) (|bag| (($ (|List| |#1|)) 38 T ELT)) (|any?| ((#13# (|Mapping| #13# |#1|) . #16#) 84 T ELT)) (= (#1# 17 T ELT)) (|#| ((#19# $) 85 T ELT))) @@ -2469,13 +2469,13 @@ NIL ((|min| (*1 *2 *1) (AND (|ofCategory| *1 (|OrderedMultisetAggregate| *2)) (|ofCategory| *2 (|OrderedSet|))))) (|Join| (|MultisetAggregate| |t#1|) (|PriorityQueueAggregate| |t#1|) (CATEGORY |domain| (SIGNATURE |min| (|t#1| $)))) (((|Aggregate|) . T) ((|BagAggregate| |#1|) . T) ((|BasicType|) . T) ((|CoercibleTo| (|OutputForm|)) . T) ((|Collection| |#1|) . T) ((|ConvertibleTo| (|InputForm|)) |has| |#1| (|ConvertibleTo| (|InputForm|))) ((|DictionaryOperations| |#1|) . T) ((|Evalable| |#1|) AND (|has| |#1| (|Evalable| |#1|)) (|has| |#1| (|SetCategory|))) ((|FiniteAggregate| |#1|) . T) ((|Functorial| |#1|) . T) ((|HomogeneousAggregate| |#1|) . T) ((|InnerEvalable| |#1| |#1|) AND (|has| |#1| (|Evalable| |#1|)) (|has| |#1| (|SetCategory|))) ((|Join|) . T) ((|MultiDictionary| |#1|) . T) ((|MultisetAggregate| |#1|) . T) ((|PriorityQueueAggregate| |#1|) . T) ((|SetAggregate| |#1|) . T) ((|SetCategory|) . T) ((|ShallowlyMutableAggregate| |#1|) . T) ((|Type|) . T)) -((~= (#1=(#2=(|Boolean|) $ $) NIL T ELT)) (|zero?| (#3=(#2# $) NIL #4=(|has| |#1| (|AbelianGroup|)) ELT)) (|subtractIfCan| ((#5=(|Union| $ #6="failed") $ $) NIL #4# ELT)) (|sign| (#7=(#8=(|Integer|) $) NIL #9=(|has| |#1| (|OrderedRing|)) ELT)) (|sample| (#10=($) NIL #4# CONST)) (|retractIfCan| (((|Union| #8# . #11=(#6#)) $) NIL #12=(|has| |#1| (|RetractableTo| #8#)) ELT) (#13=((|Union| #14=(|Fraction| #8#) #6#) $) NIL #15=(|has| |#1| (|RetractableTo| #14#)) ELT) (((|Union| |#1| . #11#) $) 15 T ELT)) (|retract| (#7# NIL #12# ELT) (#16=(#14# $) NIL #15# ELT) ((|#1| $) 9 T ELT)) (|recip| ((#5# $) 42 #9# ELT)) (|rationalIfCan| (#13# 51 #17=(|has| |#1| (|IntegerNumberSystem|)) ELT)) (|rational?| (#3# 46 #17# ELT)) (|rational| (#16# 48 #17# ELT)) (|positive?| #18=(#3# NIL #9# ELT)) (|opposite?| (#1# NIL #4# ELT)) (|one?| #18#) (|negative?| #18#) (|min| #19=(#20=($ $ $) NIL #9# ELT)) (|max| #19#) (|latex| (((|String|) $) NIL T ELT)) (|infinity| (#10# 13 T ELT)) (|infinite?| (#3# 12 T ELT)) (|hash| (((|SingleInteger|) $) NIL T ELT)) (|finite?| (#3# 11 T ELT)) (|coerce| (((|OutputForm|) $) 18 T ELT) (($ #14#) NIL #15# ELT) (($ |#1|) 8 T ELT) (($ #8#) NIL (OR #9# #12#) ELT)) (|characteristic| ((#21=(|NonNegativeInteger|)) 36 #9# CONST)) (|before?| (#1# 53 T ELT)) (|annihilate?| #22=(#1# NIL #9# ELT)) (|abs| (#23=($ $) NIL #9# ELT)) (|Zero| (#10# 23 #4# CONST)) (|One| (#10# 33 #9# CONST)) (>= #22#) (> #22#) (= (#1# 21 T ELT)) (<= #22#) (< (#1# 45 #9# ELT)) (- (#20# NIL #4# ELT) (#23# 29 #4# ELT)) (+ (#20# 31 #4# ELT)) (** (($ $ #24=(|PositiveInteger|)) NIL #9# ELT) (($ $ #21#) NIL #9# ELT)) (* (#20# 39 #9# ELT) (($ #8# $) 27 #4# ELT) (($ #21# $) NIL #4# ELT) (($ #24# $) NIL #4# ELT))) +((~= (#1=(#2=(|Boolean|) $ $) NIL T ELT)) (|zero?| (#3=(#2# $) NIL #4=(|has| |#1| (|AbelianGroup|)) ELT)) (|subtractIfCan| (((|Maybe| $) $ $) NIL #4# ELT)) (|sign| (#5=(#6=(|Integer|) $) NIL #7=(|has| |#1| (|OrderedRing|)) ELT)) (|sample| (#8=($) NIL #4# CONST)) (|retractIfCan| (((|Union| #6# . #9=(#10="failed")) $) NIL #11=(|has| |#1| (|RetractableTo| #6#)) ELT) (#12=((|Union| #13=(|Fraction| #6#) #10#) $) NIL #14=(|has| |#1| (|RetractableTo| #13#)) ELT) (((|Union| |#1| . #9#) $) 15 T ELT)) (|retract| (#5# NIL #11# ELT) (#15=(#13# $) NIL #14# ELT) ((|#1| $) 9 T ELT)) (|recip| (((|Union| $ #10#) $) 42 #7# ELT)) (|rationalIfCan| (#12# 51 #16=(|has| |#1| (|IntegerNumberSystem|)) ELT)) (|rational?| (#3# 46 #16# ELT)) (|rational| (#15# 48 #16# ELT)) (|positive?| #17=(#3# NIL #7# ELT)) (|opposite?| (#1# NIL #4# ELT)) (|one?| #17#) (|negative?| #17#) (|min| #18=(#19=($ $ $) NIL #7# ELT)) (|max| #18#) (|latex| (((|String|) $) NIL T ELT)) (|infinity| (#8# 13 T ELT)) (|infinite?| (#3# 12 T ELT)) (|hash| (((|SingleInteger|) $) NIL T ELT)) (|finite?| (#3# 11 T ELT)) (|coerce| (((|OutputForm|) $) 18 T ELT) (($ #13#) NIL #14# ELT) (($ |#1|) 8 T ELT) (($ #6#) NIL (OR #7# #11#) ELT)) (|characteristic| ((#20=(|NonNegativeInteger|)) 36 #7# CONST)) (|before?| (#1# 53 T ELT)) (|annihilate?| #21=(#1# NIL #7# ELT)) (|abs| (#22=($ $) NIL #7# ELT)) (|Zero| (#8# 23 #4# CONST)) (|One| (#8# 33 #7# CONST)) (>= #21#) (> #21#) (= (#1# 21 T ELT)) (<= #21#) (< (#1# 45 #7# ELT)) (- (#19# NIL #4# ELT) (#22# 29 #4# ELT)) (+ (#19# 31 #4# ELT)) (** (($ $ #23=(|PositiveInteger|)) NIL #7# ELT) (($ $ #20#) NIL #7# ELT)) (* (#19# 39 #7# ELT) (($ #6# $) 27 #4# ELT) (($ #20# $) NIL #4# ELT) (($ #23# $) NIL #4# ELT))) (((|OnePointCompletion| |#1|) (|Join| #1=(|SetCategory|) (|FullyRetractableTo| |#1|) (CATEGORY |domain| (SIGNATURE |infinity| ($)) (SIGNATURE |finite?| #2=((|Boolean|) $)) (SIGNATURE |infinite?| #2#) (IF (|has| |#1| #3=(|AbelianGroup|)) (ATTRIBUTE #3#) |%noBranch|) (IF (|has| |#1| #4=(|OrderedRing|)) (ATTRIBUTE #4#) |%noBranch|) (IF (|has| |#1| (|IntegerNumberSystem|)) (PROGN (SIGNATURE |rational?| #2#) (SIGNATURE |rational| (#5=(|Fraction| (|Integer|)) $)) (SIGNATURE |rationalIfCan| ((|Union| #5# "failed") $))) |%noBranch|))) #1#) (T |OnePointCompletion|)) ((|infinity| (*1 *1) (AND (|isDomain| *1 (|OnePointCompletion| *2)) (|ofCategory| *2 #1=(|SetCategory|)))) (|finite?| #2=(*1 *2 *1) #3=(AND #4=(|isDomain| *2 (|Boolean|)) #5=(|isDomain| *1 (|OnePointCompletion| *3)) #6=(|ofCategory| *3 #1#))) (|infinite?| #2# #3#) (|rational?| #2# (AND #4# #5# #7=(|ofCategory| *3 (|IntegerNumberSystem|)) #6#)) (|rational| #2# (AND #8=(|isDomain| *2 (|Fraction| (|Integer|))) #5# #7# #6#)) (|rationalIfCan| #2# (|partial| AND #8# #5# #7# #6#))) ((|map| ((#1=(|OnePointCompletion| |#2|) #2=(|Mapping| |#2| |#1|) #3=(|OnePointCompletion| |#1|) #1#) 12 T ELT) ((#1# #2# #3#) 13 T ELT))) (((|OnePointCompletionFunctions2| |#1| |#2|) (CATEGORY |package| (SIGNATURE |map| (#1=(|OnePointCompletion| |#2|) #2=(|Mapping| |#2| |#1|) #3=(|OnePointCompletion| |#1|))) (SIGNATURE |map| (#1# #2# #3# #1#))) #4=(|SetCategory|) #4#) (T |OnePointCompletionFunctions2|)) ((|map| (*1 *2 *3 *4 *2) (AND #1=(|isDomain| *2 (|OnePointCompletion| *6)) #2=(|isDomain| *3 (|Mapping| *6 *5)) #3=(|isDomain| *4 (|OnePointCompletion| *5)) #4=(|ofCategory| *5 #5=(|SetCategory|)) #6=(|ofCategory| *6 #5#) #7=(|isDomain| *1 (|OnePointCompletionFunctions2| *5 *6)))) (|map| (*1 *2 *3 *4) (AND #2# #3# #4# #6# #1# #7#))) -((~= #1=((#2=(|Boolean|) $ $) NIL T ELT)) (|zero?| #3=((#2# $) NIL T ELT)) (|subtractIfCan| ((#4=(|Union| $ #5="failed") $ $) NIL T ELT)) (|sample| #6=(($) NIL T CONST)) (|retractIfCan| (((|Union| |#1| . #7=(#5#)) . #8=($)) NIL T ELT) (((|Union| #9=(|BasicOperator|) . #7#) . #8#) NIL T ELT)) (|retract| ((|#1| . #10=($)) NIL T ELT) ((#9# . #10#) NIL T ELT)) (|recip| ((#4# $) NIL T ELT)) (|opposite?| #1#) (|opeval| ((|#1| #9# |#1|) NIL T ELT)) (|one?| #3#) (|makeop| (($ |#1| (|FreeGroup| #9#)) NIL T ELT)) (|latex| (((|String|) $) NIL T ELT)) (|hash| (((|SingleInteger|) $) NIL T ELT)) (|evaluateInverse| #11=(($ $ (|Mapping| |#1| |#1|)) NIL T ELT)) (|evaluate| #11#) (|elt| ((|#1| $ |#1|) NIL T ELT)) (|conjug| ((|#1| |#1|) NIL #12=(|has| |#1| (|CommutativeRing|)) ELT)) (|coerce| (((|OutputForm|) $) NIL T ELT) (($ #13=(|Integer|)) NIL T ELT) (($ |#1|) NIL T ELT) (($ #9#) NIL T ELT)) (|charthRoot| (((|Maybe| $) $) NIL (|has| |#1| (|CharacteristicNonZero|)) ELT)) (|characteristic| ((#14=(|NonNegativeInteger|)) NIL T CONST)) (|before?| #1#) (|annihilate?| #1#) (|adjoint| (#15=($ $) NIL #12# ELT) (#16=($ $ $) NIL #12# ELT)) (|Zero| #6#) (|One| #6#) (= #1#) (- (#15# NIL T ELT) #17=(#16# NIL T ELT)) (+ #17#) (** (($ $ #18=(|PositiveInteger|)) NIL T ELT) (($ $ #14#) NIL T ELT) (($ #9# #13#) NIL T ELT) (($ $ #13#) NIL T ELT)) (* (($ #18# $) NIL T ELT) (($ #14# $) NIL T ELT) (($ #13# . #19=($)) NIL T ELT) #17# (($ |#1| . #19#) NIL #12# ELT) (($ $ |#1|) NIL #12# ELT))) +((~= #1=((#2=(|Boolean|) $ $) NIL T ELT)) (|zero?| #3=((#2# $) NIL T ELT)) (|subtractIfCan| ((#4=(|Maybe| $) $ $) NIL T ELT)) (|sample| #5=(($) NIL T CONST)) (|retractIfCan| (((|Union| |#1| . #6=(#7="failed")) . #8=($)) NIL T ELT) (((|Union| #9=(|BasicOperator|) . #6#) . #8#) NIL T ELT)) (|retract| ((|#1| . #10=($)) NIL T ELT) ((#9# . #10#) NIL T ELT)) (|recip| (((|Union| $ #7#) $) NIL T ELT)) (|opposite?| #1#) (|opeval| ((|#1| #9# |#1|) NIL T ELT)) (|one?| #3#) (|makeop| (($ |#1| (|FreeGroup| #9#)) NIL T ELT)) (|latex| (((|String|) $) NIL T ELT)) (|hash| (((|SingleInteger|) $) NIL T ELT)) (|evaluateInverse| #11=(($ $ (|Mapping| |#1| |#1|)) NIL T ELT)) (|evaluate| #11#) (|elt| ((|#1| $ |#1|) NIL T ELT)) (|conjug| ((|#1| |#1|) NIL #12=(|has| |#1| (|CommutativeRing|)) ELT)) (|coerce| (((|OutputForm|) $) NIL T ELT) (($ #13=(|Integer|)) NIL T ELT) (($ |#1|) NIL T ELT) (($ #9#) NIL T ELT)) (|charthRoot| ((#4# $) NIL (|has| |#1| (|CharacteristicNonZero|)) ELT)) (|characteristic| ((#14=(|NonNegativeInteger|)) NIL T CONST)) (|before?| #1#) (|annihilate?| #1#) (|adjoint| (#15=($ $) NIL #12# ELT) (#16=($ $ $) NIL #12# ELT)) (|Zero| #5#) (|One| #5#) (= #1#) (- (#15# NIL T ELT) #17=(#16# NIL T ELT)) (+ #17#) (** (($ $ #18=(|PositiveInteger|)) NIL T ELT) (($ $ #14#) NIL T ELT) (($ #9# #13#) NIL T ELT) (($ $ #13#) NIL T ELT)) (* (($ #18# $) NIL T ELT) (($ #14# $) NIL T ELT) (($ #13# . #19=($)) NIL T ELT) #17# (($ |#1| . #19#) NIL #12# ELT) (($ $ |#1|) NIL #12# ELT))) (((|Operator| |#1|) (|Join| #1=(|Ring|) (|RetractableTo| |#1|) (|RetractableTo| #2=(|BasicOperator|)) (|Eltable| |#1| |#1|) (CATEGORY |domain| (IF (|has| |#1| #3=(|CharacteristicZero|)) (ATTRIBUTE #3#) |%noBranch|) (IF (|has| |#1| #4=(|CharacteristicNonZero|)) (ATTRIBUTE #4#) |%noBranch|) (IF (|has| |#1| (|CommutativeRing|)) (PROGN (ATTRIBUTE (|Algebra| |#1|)) (SIGNATURE |adjoint| ($ $)) (SIGNATURE |adjoint| ($ $ $)) (SIGNATURE |conjug| (|#1| |#1|))) |%noBranch|) (SIGNATURE |evaluate| #5=($ $ (|Mapping| |#1| |#1|))) (SIGNATURE |evaluateInverse| #5#) (SIGNATURE ** ($ #2# #6=(|Integer|))) (SIGNATURE ** ($ $ #6#)) (SIGNATURE |opeval| (|#1| #2# |#1|)) (SIGNATURE |makeop| ($ |#1| (|FreeGroup| #2#))))) #1#) (T |Operator|)) ((|adjoint| (*1 *1 *1) #1=(AND #2=(|isDomain| *1 (|Operator| *2)) (|ofCategory| *2 (|CommutativeRing|)) #3=(|ofCategory| *2 #4=(|Ring|)))) (|adjoint| (*1 *1 *1 *1) #1#) (|conjug| (*1 *2 *2) #1#) (|evaluate| #5=(*1 *1 *1 *2) #6=(AND (|isDomain| *2 (|Mapping| *3 *3)) #7=(|ofCategory| *3 #4#) #8=(|isDomain| *1 (|Operator| *3)))) (|evaluateInverse| #5# #6#) (** #9=(*1 *1 *2 *3) (AND (|isDomain| *2 #10=(|BasicOperator|)) (|isDomain| *3 #11=(|Integer|)) (|isDomain| *1 (|Operator| *4)) (|ofCategory| *4 #4#))) (** #5# (AND (|isDomain| *2 #11#) #8# #7#)) (|opeval| (*1 *2 *3 *2) (AND (|isDomain| *3 #10#) #2# #3#)) (|makeop| #9# (AND (|isDomain| *3 (|FreeGroup| #10#)) #2# #3#))) ((|is?| (((|Boolean|) $ |#2|) 14 T ELT)) (|coerce| (((|OutputForm|) $) 11 T ELT))) @@ -2492,7 +2492,7 @@ NIL ((~= #1=(#2=(#3=(|Boolean|) $ $) NIL T ELT)) (|signature| ((#4=(|Signature|) $) 10 T ELT)) (|name| ((#5=(|Identifier|) $) 9 T ELT)) (|latex| (((|String|) $) NIL T ELT)) (|is?| ((#3# $ #5#) NIL T ELT)) (|hash| (((|SingleInteger|) $) NIL T ELT)) (|construct| (($ #5# #4#) 8 T ELT)) (|coerce| (((|OutputForm|) $) 25 T ELT)) (|before?| #1#) (|arity| (((|Arity|) $) 20 T ELT)) (= (#2# 12 T ELT))) (((|OperatorSignature|) (|Join| (|OperatorCategory| #1=(|Identifier|)) (CATEGORY |domain| (SIGNATURE |signature| (#2=(|Signature|) $)) (SIGNATURE |construct| ($ #1# #2#))))) (T |OperatorSignature|)) ((|signature| (*1 *2 *1) (AND (|isDomain| *2 #1=(|Signature|)) #2=(|isDomain| *1 (|OperatorSignature|)))) (|construct| (*1 *1 *2 *3) (AND (|isDomain| *2 (|Identifier|)) (|isDomain| *3 #1#) #2#))) -((~= #1=(#2=(#3=(|Boolean|) $ $) NIL T ELT)) (|zero?| (#4=(#3# $) NIL #5=(|has| |#1| (|AbelianGroup|)) ELT)) (|whatInfinity| (#6=((|SingleInteger|) $) 31 T ELT)) (|subtractIfCan| ((#7=(|Union| $ #8="failed") $ $) NIL #5# ELT)) (|sign| (#9=(#10=(|Integer|) $) NIL #11=(|has| |#1| (|OrderedRing|)) ELT)) (|sample| (#12=($) NIL #5# CONST)) (|retractIfCan| (((|Union| #10# . #13=(#8#)) $) NIL #14=(|has| |#1| (|RetractableTo| #10#)) ELT) (#15=((|Union| #16=(|Fraction| #10#) #8#) $) NIL #17=(|has| |#1| (|RetractableTo| #16#)) ELT) (((|Union| |#1| . #13#) $) 18 T ELT)) (|retract| (#9# NIL #14# ELT) (#18=(#16# $) NIL #17# ELT) ((|#1| $) 9 T ELT)) (|recip| ((#7# $) 57 #11# ELT)) (|rationalIfCan| (#15# 65 #19=(|has| |#1| (|IntegerNumberSystem|)) ELT)) (|rational?| (#4# 60 #19# ELT)) (|rational| (#18# 63 #19# ELT)) (|positive?| #20=(#4# NIL #11# ELT)) (|plusInfinity| (#12# 14 T ELT)) (|opposite?| (#2# NIL #5# ELT)) (|one?| #20#) (|negative?| #20#) (|minusInfinity| (#12# 16 T ELT)) (|min| #21=(#22=($ $ $) NIL #11# ELT)) (|max| #21#) (|latex| (((|String|) $) NIL T ELT)) (|infinite?| (#4# 12 T ELT)) (|hash| (#6# NIL T ELT)) (|finite?| (#4# 11 T ELT)) (|coerce| (((|OutputForm|) $) 24 T ELT) (($ #16#) NIL #17# ELT) (($ |#1|) 8 T ELT) (($ #10#) NIL (OR #11# #14#) ELT)) (|characteristic| ((#23=(|NonNegativeInteger|)) 50 #11# CONST)) (|before?| #1#) (|annihilate?| #24=(#2# NIL #11# ELT)) (|abs| (#25=($ $) NIL #11# ELT)) (|Zero| (#12# 37 #5# CONST)) (|One| (#12# 47 #11# CONST)) (>= #24#) (> #24#) (= (#2# 35 T ELT)) (<= #24#) (< (#2# 59 #11# ELT)) (- (#22# NIL #5# ELT) (#25# 43 #5# ELT)) (+ (#22# 45 #5# ELT)) (** (($ $ #26=(|PositiveInteger|)) NIL #11# ELT) (($ $ #23#) NIL #11# ELT)) (* (#22# 54 #11# ELT) (($ #10# $) 41 #5# ELT) (($ #23# $) NIL #5# ELT) (($ #26# $) NIL #5# ELT))) +((~= #1=(#2=(#3=(|Boolean|) $ $) NIL T ELT)) (|zero?| (#4=(#3# $) NIL #5=(|has| |#1| (|AbelianGroup|)) ELT)) (|whatInfinity| (#6=((|SingleInteger|) $) 31 T ELT)) (|subtractIfCan| (((|Maybe| $) $ $) NIL #5# ELT)) (|sign| (#7=(#8=(|Integer|) $) NIL #9=(|has| |#1| (|OrderedRing|)) ELT)) (|sample| (#10=($) NIL #5# CONST)) (|retractIfCan| (((|Union| #8# . #11=(#12="failed")) $) NIL #13=(|has| |#1| (|RetractableTo| #8#)) ELT) (#14=((|Union| #15=(|Fraction| #8#) #12#) $) NIL #16=(|has| |#1| (|RetractableTo| #15#)) ELT) (((|Union| |#1| . #11#) $) 18 T ELT)) (|retract| (#7# NIL #13# ELT) (#17=(#15# $) NIL #16# ELT) ((|#1| $) 9 T ELT)) (|recip| (((|Union| $ #12#) $) 57 #9# ELT)) (|rationalIfCan| (#14# 65 #18=(|has| |#1| (|IntegerNumberSystem|)) ELT)) (|rational?| (#4# 60 #18# ELT)) (|rational| (#17# 63 #18# ELT)) (|positive?| #19=(#4# NIL #9# ELT)) (|plusInfinity| (#10# 14 T ELT)) (|opposite?| (#2# NIL #5# ELT)) (|one?| #19#) (|negative?| #19#) (|minusInfinity| (#10# 16 T ELT)) (|min| #20=(#21=($ $ $) NIL #9# ELT)) (|max| #20#) (|latex| (((|String|) $) NIL T ELT)) (|infinite?| (#4# 12 T ELT)) (|hash| (#6# NIL T ELT)) (|finite?| (#4# 11 T ELT)) (|coerce| (((|OutputForm|) $) 24 T ELT) (($ #15#) NIL #16# ELT) (($ |#1|) 8 T ELT) (($ #8#) NIL (OR #9# #13#) ELT)) (|characteristic| ((#22=(|NonNegativeInteger|)) 50 #9# CONST)) (|before?| #1#) (|annihilate?| #23=(#2# NIL #9# ELT)) (|abs| (#24=($ $) NIL #9# ELT)) (|Zero| (#10# 37 #5# CONST)) (|One| (#10# 47 #9# CONST)) (>= #23#) (> #23#) (= (#2# 35 T ELT)) (<= #23#) (< (#2# 59 #9# ELT)) (- (#21# NIL #5# ELT) (#24# 43 #5# ELT)) (+ (#21# 45 #5# ELT)) (** (($ $ #25=(|PositiveInteger|)) NIL #9# ELT) (($ $ #22#) NIL #9# ELT)) (* (#21# 54 #9# ELT) (($ #8# $) 41 #5# ELT) (($ #22# $) NIL #5# ELT) (($ #25# $) NIL #5# ELT))) (((|OrderedCompletion| |#1|) (|Join| #1=(|SetCategory|) (|FullyRetractableTo| |#1|) (CATEGORY |domain| (SIGNATURE |plusInfinity| #2=($)) (SIGNATURE |minusInfinity| #2#) (SIGNATURE |finite?| #3=((|Boolean|) $)) (SIGNATURE |infinite?| #3#) (SIGNATURE |whatInfinity| ((|SingleInteger|) $)) (IF (|has| |#1| #4=(|AbelianGroup|)) (ATTRIBUTE #4#) |%noBranch|) (IF (|has| |#1| #5=(|OrderedRing|)) (ATTRIBUTE #5#) |%noBranch|) (IF (|has| |#1| (|IntegerNumberSystem|)) (PROGN (SIGNATURE |rational?| #3#) (SIGNATURE |rational| (#6=(|Fraction| (|Integer|)) $)) (SIGNATURE |rationalIfCan| ((|Union| #6# "failed") $))) |%noBranch|))) #1#) (T |OrderedCompletion|)) ((|plusInfinity| #1=(*1 *1) #2=(AND (|isDomain| *1 (|OrderedCompletion| *2)) (|ofCategory| *2 #3=(|SetCategory|)))) (|minusInfinity| #1# #2#) (|finite?| #4=(*1 *2 *1) #5=(AND #6=(|isDomain| *2 (|Boolean|)) #7=(|isDomain| *1 (|OrderedCompletion| *3)) #8=(|ofCategory| *3 #3#))) (|infinite?| #4# #5#) (|whatInfinity| #4# (AND (|isDomain| *2 (|SingleInteger|)) #7# #8#)) (|rational?| #4# (AND #6# #7# #9=(|ofCategory| *3 (|IntegerNumberSystem|)) #8#)) (|rational| #4# (AND #10=(|isDomain| *2 (|Fraction| (|Integer|))) #7# #9# #8#)) (|rationalIfCan| #4# (|partial| AND #10# #7# #9# #8#))) ((|map| ((#1=(|OrderedCompletion| |#2|) #2=(|Mapping| |#2| |#1|) #3=(|OrderedCompletion| |#1|) #1# #1#) 13 T ELT) ((#1# #2# #3#) 14 T ELT))) @@ -2511,7 +2511,7 @@ NIL NIL (|Join| (|OrderedSemiGroup|) (|Monoid|)) (((|BasicType|) . T) ((|CoercibleTo| (|OutputForm|)) . T) ((|Join|) . T) ((|Monoid|) . T) ((|OrderedSemiGroup|) . T) ((|OrderedSet|) . T) ((|OrderedType|) . T) ((|SemiGroup|) . T) ((|SetCategory|) . T) ((|Type|) . T)) -((~= (#1=((|Boolean|) $ $) 7 T ELT)) (|zero?| ((#2=(|Boolean|) $) 31 T ELT)) (|subtractIfCan| (((|Union| $ "failed") $ $) 35 T ELT)) (|sign| (((|Integer|) $) 38 T ELT)) (|sample| (#3=($) 30 T CONST)) (|recip| (((|Union| $ "failed") $) 55 T ELT)) (|positive?| (((|Boolean|) $) 28 T ELT)) (|opposite?| ((#2# $ $) 33 T ELT)) (|one?| (((|Boolean|) $) 53 T ELT)) (|negative?| (((|Boolean|) $) 39 T ELT)) (|min| (#4=($ $ $) 23 T ELT)) (|max| (#4# 22 T ELT)) (|latex| (((|String|) $) 11 T ELT)) (|hash| (((|SingleInteger|) $) 12 T ELT)) (|coerce| (((|OutputForm|) $) 13 T ELT) (($ (|Integer|)) 56 T ELT)) (|characteristic| (((|NonNegativeInteger|)) 57 T CONST)) (|before?| (#1# 6 T ELT)) (|annihilate?| (((|Boolean|) $ $) 51 T ELT)) (|abs| (($ $) 37 T ELT)) (|Zero| (#3# 29 T CONST)) (|One| (($) 52 T CONST)) (>= (#5=((|Boolean|) $ $) 21 T ELT)) (> (#5# 19 T ELT)) (= (#1# 8 T ELT)) (<= (#5# 20 T ELT)) (< (#5# 18 T ELT)) (- (($ $ $) 42 T ELT) (($ $) 41 T ELT)) (+ (($ $ $) 25 T ELT)) (** (($ $ (|NonNegativeInteger|)) 54 T ELT) (($ $ (|PositiveInteger|)) 49 T ELT)) (* (($ (|PositiveInteger|) $) 26 T ELT) (($ (|NonNegativeInteger|) $) 32 T ELT) (($ (|Integer|) $) 40 T ELT) (($ $ $) 50 T ELT))) +((~= (#1=((|Boolean|) $ $) 7 T ELT)) (|zero?| ((#2=(|Boolean|) $) 31 T ELT)) (|subtractIfCan| (((|Maybe| $) $ $) 35 T ELT)) (|sign| (((|Integer|) $) 39 T ELT)) (|sample| (#3=($) 30 T CONST)) (|recip| (((|Union| $ "failed") $) 56 T ELT)) (|positive?| (((|Boolean|) $) 28 T ELT)) (|opposite?| ((#2# $ $) 33 T ELT)) (|one?| (((|Boolean|) $) 54 T ELT)) (|negative?| (((|Boolean|) $) 40 T ELT)) (|min| (#4=($ $ $) 23 T ELT)) (|max| (#4# 22 T ELT)) (|latex| (((|String|) $) 11 T ELT)) (|hash| (((|SingleInteger|) $) 12 T ELT)) (|coerce| (((|OutputForm|) $) 13 T ELT) (($ (|Integer|)) 57 T ELT)) (|characteristic| (((|NonNegativeInteger|)) 58 T CONST)) (|before?| (#1# 6 T ELT)) (|annihilate?| (((|Boolean|) $ $) 52 T ELT)) (|abs| (($ $) 38 T ELT)) (|Zero| (#3# 29 T CONST)) (|One| (($) 53 T CONST)) (>= (#5=((|Boolean|) $ $) 21 T ELT)) (> (#5# 19 T ELT)) (= (#1# 8 T ELT)) (<= (#5# 20 T ELT)) (< (#5# 18 T ELT)) (- (($ $ $) 43 T ELT) (($ $) 42 T ELT)) (+ (($ $ $) 25 T ELT)) (** (($ $ (|NonNegativeInteger|)) 55 T ELT) (($ $ (|PositiveInteger|)) 50 T ELT)) (* (($ (|PositiveInteger|) $) 26 T ELT) (($ (|NonNegativeInteger|) $) 32 T ELT) (($ (|Integer|) $) 41 T ELT) (($ $ $) 51 T ELT))) (((|OrderedRing|) (|Category|)) (T |OrderedRing|)) NIL (|Join| (|OrderedAbelianGroup|) (|CharacteristicZero|) (|Monoid|)) @@ -2535,18 +2535,18 @@ NIL ((|rightRemainder| (#1=($ $ $) 49 T ELT)) (|rightQuotient| (#1# 48 T ELT)) (|rightLcm| (#1# 46 T ELT)) (|rightGcd| (#1# 55 T ELT)) (|rightExtendedGcd| (#2=((|Record| (|:| |coef1| $) (|:| |coef2| $) (|:| |generator| $)) $ $) 50 T ELT)) (|rightExactQuotient| (#3=(#4=(|Union| $ #5="failed") $ $) 53 T ELT)) (|retractIfCan| (((|Union| #6=(|Integer|) #5#) $) NIL T ELT) (((|Union| #7=(|Fraction| #6#) #5#) $) NIL T ELT) (((|Union| |#2| #5#) $) 29 T ELT)) (|primitivePart| (($ $) 39 T ELT)) (|leftRemainder| (#1# 43 T ELT)) (|leftQuotient| (#1# 42 T ELT)) (|leftLcm| (#1# 51 T ELT)) (|leftGcd| (#1# 57 T ELT)) (|leftExtendedGcd| (#2# 45 T ELT)) (|leftExactQuotient| (#3# 52 T ELT)) (|exquo| ((#4# $ |#2|) 32 T ELT)) (|content| ((|#2| $) 36 T ELT)) (|coerce| (((|OutputForm|) $) NIL T ELT) (($ #6#) NIL T ELT) (($ #7#) NIL T ELT) (($ |#2|) 13 T ELT)) (|coefficients| (((|List| |#2|) $) 21 T ELT)) (* (($ (|PositiveInteger|) $) NIL T ELT) (($ (|NonNegativeInteger|) $) NIL T ELT) (($ #6# $) NIL T ELT) (#1# NIL T ELT) (($ $ |#2|) NIL T ELT) (($ |#2| $) 25 T ELT))) (((|UnivariateSkewPolynomialCategory&| |#1| |#2|) (CATEGORY |package| (SIGNATURE |leftLcm| #1=(|#1| |#1| |#1|)) (SIGNATURE |rightExtendedGcd| #2=((|Record| (|:| |coef1| |#1|) (|:| |coef2| |#1|) (|:| |generator| |#1|)) |#1| |#1|)) (SIGNATURE |rightGcd| #1#) (SIGNATURE |rightExactQuotient| #3=(#4=(|Union| |#1| #5="failed") |#1| |#1|)) (SIGNATURE |rightRemainder| #1#) (SIGNATURE |rightQuotient| #1#) (SIGNATURE |rightLcm| #1#) (SIGNATURE |leftExtendedGcd| #2#) (SIGNATURE |leftGcd| #1#) (SIGNATURE |leftExactQuotient| #3#) (SIGNATURE |leftRemainder| #1#) (SIGNATURE |leftQuotient| #1#) (SIGNATURE |primitivePart| (|#1| |#1|)) (SIGNATURE |content| (|#2| |#1|)) (SIGNATURE |exquo| (#4# |#1| |#2|)) (SIGNATURE |coefficients| ((|List| |#2|) |#1|)) (SIGNATURE |coerce| (|#1| |#2|)) (SIGNATURE |retractIfCan| ((|Union| |#2| #5#) |#1|)) (SIGNATURE |retractIfCan| ((|Union| #6=(|Fraction| #7=(|Integer|)) #5#) |#1|)) (SIGNATURE |coerce| (|#1| #6#)) (SIGNATURE |retractIfCan| ((|Union| #7# #5#) |#1|)) (SIGNATURE * (|#1| |#2| |#1|)) (SIGNATURE * (|#1| |#1| |#2|)) (SIGNATURE |coerce| (|#1| #7#)) (SIGNATURE * #1#) (SIGNATURE * (|#1| #7# |#1|)) (SIGNATURE * (|#1| (|NonNegativeInteger|) |#1|)) (SIGNATURE * (|#1| (|PositiveInteger|) |#1|)) (SIGNATURE |coerce| ((|OutputForm|) |#1|))) (|UnivariateSkewPolynomialCategory| |#2|) (|Ring|)) (T |UnivariateSkewPolynomialCategory&|)) NIL -((~= (#1=((|Boolean|) $ $) 7 T ELT)) (|zero?| ((#2=(|Boolean|) $) 22 T ELT)) (|subtractIfCan| (((|Union| $ "failed") $ $) 26 T ELT)) (|sample| (#3=($) 23 T CONST)) (|rightRemainder| (($ $ $) 58 (|has| |#1| (|Field|)) ELT)) (|rightQuotient| (($ $ $) 59 (|has| |#1| (|Field|)) ELT)) (|rightLcm| (($ $ $) 61 (|has| |#1| (|Field|)) ELT)) (|rightGcd| (($ $ $) 56 (|has| |#1| (|Field|)) ELT)) (|rightExtendedGcd| (((|Record| (|:| |coef1| $) (|:| |coef2| $) (|:| |generator| $)) $ $) 55 (|has| |#1| (|Field|)) ELT)) (|rightExactQuotient| (((|Union| $ "failed") $ $) 57 (|has| |#1| (|Field|)) ELT)) (|rightDivide| (((|Record| (|:| |quotient| $) (|:| |remainder| $)) $ $) 60 (|has| |#1| (|Field|)) ELT)) (|retractIfCan| (((|Union| #4=(|Integer|) . #5=("failed")) . #6=($)) 88 (|has| |#1| . #7=((|RetractableTo| #4#))) ELT) (((|Union| #8=(|Fraction| #4#) . #5#) . #6#) 85 (|has| |#1| . #9=((|RetractableTo| #8#))) ELT) (((|Union| |#1| . #5#) . #6#) 82 T ELT)) (|retract| ((#4# . #10=($)) 87 (|has| |#1| . #7#) ELT) ((#8# . #10#) 84 (|has| |#1| . #9#) ELT) ((|#1| . #10#) 83 T ELT)) (|reductum| (($ $) 77 T ELT)) (|recip| (((|Union| $ "failed") $) 42 T ELT)) (|primitivePart| (($ $) 68 (|has| |#1| (|GcdDomain|)) ELT)) (|opposite?| ((#2# $ $) 20 T ELT)) (|one?| (((|Boolean|) $) 44 T ELT)) (|monomial| (($ |#1| (|NonNegativeInteger|)) 75 T ELT)) (|monicRightDivide| (((|Record| (|:| |quotient| $) (|:| |remainder| $)) $ $) 70 (|has| |#1| (|IntegralDomain|)) ELT)) (|monicLeftDivide| (((|Record| (|:| |quotient| $) (|:| |remainder| $)) $ $) 71 (|has| |#1| (|IntegralDomain|)) ELT)) (|minimumDegree| (((|NonNegativeInteger|) $) 79 T ELT)) (|leftRemainder| (($ $ $) 65 (|has| |#1| (|Field|)) ELT)) (|leftQuotient| (($ $ $) 66 (|has| |#1| (|Field|)) ELT)) (|leftLcm| (($ $ $) 54 (|has| |#1| (|Field|)) ELT)) (|leftGcd| (($ $ $) 63 (|has| |#1| (|Field|)) ELT)) (|leftExtendedGcd| (((|Record| (|:| |coef1| $) (|:| |coef2| $) (|:| |generator| $)) $ $) 62 (|has| |#1| (|Field|)) ELT)) (|leftExactQuotient| (((|Union| $ "failed") $ $) 64 (|has| |#1| (|Field|)) ELT)) (|leftDivide| (((|Record| (|:| |quotient| $) (|:| |remainder| $)) $ $) 67 (|has| |#1| (|Field|)) ELT)) (|leadingCoefficient| ((|#1| $) 78 T ELT)) (|latex| (((|String|) $) 11 T ELT)) (|hash| (((|SingleInteger|) $) 12 T ELT)) (|exquo| (((|Union| $ "failed") $ |#1|) 72 (|has| |#1| (|IntegralDomain|)) ELT)) (|degree| (((|NonNegativeInteger|) $) 80 T ELT)) (|content| ((|#1| $) 69 (|has| |#1| (|GcdDomain|)) ELT)) (|coerce| (((|OutputForm|) $) 13 T ELT) (($ (|Integer|)) 41 T ELT) (($ #8#) 86 (|has| |#1| . #9#) ELT) (($ |#1|) 81 T ELT)) (|coefficients| (((|List| |#1|) $) 74 T ELT)) (|coefficient| ((|#1| $ (|NonNegativeInteger|)) 76 T ELT)) (|characteristic| (((|NonNegativeInteger|)) 40 T CONST)) (|before?| (#1# 6 T ELT)) (|apply| ((|#1| $ |#1| |#1|) 73 T ELT)) (|annihilate?| (((|Boolean|) $ $) 33 T ELT)) (|Zero| (#3# 24 T CONST)) (|One| (($) 45 T CONST)) (= (#1# 8 T ELT)) (- (($ $) 29 T ELT) (($ $ $) 28 T ELT)) (+ (($ $ $) 18 T ELT)) (** (($ $ (|PositiveInteger|)) 35 T ELT) (($ $ (|NonNegativeInteger|)) 43 T ELT)) (* (($ (|PositiveInteger|) $) 17 T ELT) (($ (|NonNegativeInteger|) $) 21 T ELT) (($ (|Integer|) . #11=($)) 30 T ELT) (($ $ $) 34 T ELT) (($ $ |#1|) 90 T ELT) (($ |#1| . #11#) 89 T ELT))) +((~= (#1=((|Boolean|) $ $) 7 T ELT)) (|zero?| ((#2=(|Boolean|) $) 22 T ELT)) (|subtractIfCan| (((|Maybe| $) $ $) 26 T ELT)) (|sample| (#3=($) 23 T CONST)) (|rightRemainder| (($ $ $) 59 (|has| |#1| (|Field|)) ELT)) (|rightQuotient| (($ $ $) 60 (|has| |#1| (|Field|)) ELT)) (|rightLcm| (($ $ $) 62 (|has| |#1| (|Field|)) ELT)) (|rightGcd| (($ $ $) 57 (|has| |#1| (|Field|)) ELT)) (|rightExtendedGcd| (((|Record| (|:| |coef1| $) (|:| |coef2| $) (|:| |generator| $)) $ $) 56 (|has| |#1| (|Field|)) ELT)) (|rightExactQuotient| (((|Union| $ "failed") $ $) 58 (|has| |#1| (|Field|)) ELT)) (|rightDivide| (((|Record| (|:| |quotient| $) (|:| |remainder| $)) $ $) 61 (|has| |#1| (|Field|)) ELT)) (|retractIfCan| (((|Union| #4=(|Integer|) . #5=("failed")) . #6=($)) 89 (|has| |#1| . #7=((|RetractableTo| #4#))) ELT) (((|Union| #8=(|Fraction| #4#) . #5#) . #6#) 86 (|has| |#1| . #9=((|RetractableTo| #8#))) ELT) (((|Union| |#1| . #5#) . #6#) 83 T ELT)) (|retract| ((#4# . #10=($)) 88 (|has| |#1| . #7#) ELT) ((#8# . #10#) 85 (|has| |#1| . #9#) ELT) ((|#1| . #10#) 84 T ELT)) (|reductum| (($ $) 78 T ELT)) (|recip| (((|Union| $ "failed") $) 43 T ELT)) (|primitivePart| (($ $) 69 (|has| |#1| (|GcdDomain|)) ELT)) (|opposite?| ((#2# $ $) 20 T ELT)) (|one?| (((|Boolean|) $) 45 T ELT)) (|monomial| (($ |#1| (|NonNegativeInteger|)) 76 T ELT)) (|monicRightDivide| (((|Record| (|:| |quotient| $) (|:| |remainder| $)) $ $) 71 (|has| |#1| (|IntegralDomain|)) ELT)) (|monicLeftDivide| (((|Record| (|:| |quotient| $) (|:| |remainder| $)) $ $) 72 (|has| |#1| (|IntegralDomain|)) ELT)) (|minimumDegree| (((|NonNegativeInteger|) $) 80 T ELT)) (|leftRemainder| (($ $ $) 66 (|has| |#1| (|Field|)) ELT)) (|leftQuotient| (($ $ $) 67 (|has| |#1| (|Field|)) ELT)) (|leftLcm| (($ $ $) 55 (|has| |#1| (|Field|)) ELT)) (|leftGcd| (($ $ $) 64 (|has| |#1| (|Field|)) ELT)) (|leftExtendedGcd| (((|Record| (|:| |coef1| $) (|:| |coef2| $) (|:| |generator| $)) $ $) 63 (|has| |#1| (|Field|)) ELT)) (|leftExactQuotient| (((|Union| $ "failed") $ $) 65 (|has| |#1| (|Field|)) ELT)) (|leftDivide| (((|Record| (|:| |quotient| $) (|:| |remainder| $)) $ $) 68 (|has| |#1| (|Field|)) ELT)) (|leadingCoefficient| ((|#1| $) 79 T ELT)) (|latex| (((|String|) $) 11 T ELT)) (|hash| (((|SingleInteger|) $) 12 T ELT)) (|exquo| (((|Union| $ "failed") $ |#1|) 73 (|has| |#1| (|IntegralDomain|)) ELT)) (|degree| (((|NonNegativeInteger|) $) 81 T ELT)) (|content| ((|#1| $) 70 (|has| |#1| (|GcdDomain|)) ELT)) (|coerce| (((|OutputForm|) $) 13 T ELT) (($ (|Integer|)) 42 T ELT) (($ #8#) 87 (|has| |#1| . #9#) ELT) (($ |#1|) 82 T ELT)) (|coefficients| (((|List| |#1|) $) 75 T ELT)) (|coefficient| ((|#1| $ (|NonNegativeInteger|)) 77 T ELT)) (|characteristic| (((|NonNegativeInteger|)) 41 T CONST)) (|before?| (#1# 6 T ELT)) (|apply| ((|#1| $ |#1| |#1|) 74 T ELT)) (|annihilate?| (((|Boolean|) $ $) 34 T ELT)) (|Zero| (#3# 24 T CONST)) (|One| (($) 46 T CONST)) (= (#1# 8 T ELT)) (- (($ $) 30 T ELT) (($ $ $) 29 T ELT)) (+ (($ $ $) 18 T ELT)) (** (($ $ (|PositiveInteger|)) 36 T ELT) (($ $ (|NonNegativeInteger|)) 44 T ELT)) (* (($ (|PositiveInteger|) $) 17 T ELT) (($ (|NonNegativeInteger|) $) 21 T ELT) (($ (|Integer|) . #11=($)) 31 T ELT) (($ $ $) 35 T ELT) (($ $ |#1|) 91 T ELT) (($ |#1| . #11#) 90 T ELT))) (((|UnivariateSkewPolynomialCategory| |#1|) (|Category|) (|Ring|)) (T |UnivariateSkewPolynomialCategory|)) ((|degree| (*1 *2 *1) (AND (|ofCategory| *1 (|UnivariateSkewPolynomialCategory| *3)) (|ofCategory| *3 (|Ring|)) (|isDomain| *2 (|NonNegativeInteger|)))) (|minimumDegree| (*1 *2 *1) (AND (|ofCategory| *1 (|UnivariateSkewPolynomialCategory| *3)) (|ofCategory| *3 (|Ring|)) (|isDomain| *2 (|NonNegativeInteger|)))) (|leadingCoefficient| (*1 *2 *1) (AND (|ofCategory| *1 (|UnivariateSkewPolynomialCategory| *2)) (|ofCategory| *2 (|Ring|)))) (|reductum| (*1 *1 *1) (AND (|ofCategory| *1 (|UnivariateSkewPolynomialCategory| *2)) (|ofCategory| *2 (|Ring|)))) (|coefficient| (*1 *2 *1 *3) (AND (|isDomain| *3 (|NonNegativeInteger|)) (|ofCategory| *1 (|UnivariateSkewPolynomialCategory| *2)) (|ofCategory| *2 (|Ring|)))) (|monomial| (*1 *1 *2 *3) (AND (|isDomain| *3 (|NonNegativeInteger|)) (|ofCategory| *1 (|UnivariateSkewPolynomialCategory| *2)) (|ofCategory| *2 (|Ring|)))) (|coefficients| (*1 *2 *1) (AND (|ofCategory| *1 (|UnivariateSkewPolynomialCategory| *3)) (|ofCategory| *3 (|Ring|)) (|isDomain| *2 (|List| *3)))) (|apply| (*1 *2 *1 *2 *2) (AND (|ofCategory| *1 (|UnivariateSkewPolynomialCategory| *2)) (|ofCategory| *2 (|Ring|)))) (|exquo| (*1 *1 *1 *2) (|partial| AND (|ofCategory| *1 (|UnivariateSkewPolynomialCategory| *2)) (|ofCategory| *2 (|Ring|)) (|ofCategory| *2 (|IntegralDomain|)))) (|monicLeftDivide| (*1 *2 *1 *1) (AND (|ofCategory| *3 (|IntegralDomain|)) (|ofCategory| *3 (|Ring|)) (|isDomain| *2 (|Record| (|:| |quotient| *1) (|:| |remainder| *1))) (|ofCategory| *1 (|UnivariateSkewPolynomialCategory| *3)))) (|monicRightDivide| (*1 *2 *1 *1) (AND (|ofCategory| *3 (|IntegralDomain|)) (|ofCategory| *3 (|Ring|)) (|isDomain| *2 (|Record| (|:| |quotient| *1) (|:| |remainder| *1))) (|ofCategory| *1 (|UnivariateSkewPolynomialCategory| *3)))) (|content| (*1 *2 *1) (AND (|ofCategory| *1 (|UnivariateSkewPolynomialCategory| *2)) (|ofCategory| *2 (|Ring|)) (|ofCategory| *2 (|GcdDomain|)))) (|primitivePart| (*1 *1 *1) (AND (|ofCategory| *1 (|UnivariateSkewPolynomialCategory| *2)) (|ofCategory| *2 (|Ring|)) (|ofCategory| *2 (|GcdDomain|)))) (|leftDivide| (*1 *2 *1 *1) (AND (|ofCategory| *3 (|Field|)) (|ofCategory| *3 (|Ring|)) (|isDomain| *2 (|Record| (|:| |quotient| *1) (|:| |remainder| *1))) (|ofCategory| *1 (|UnivariateSkewPolynomialCategory| *3)))) (|leftQuotient| (*1 *1 *1 *1) (AND (|ofCategory| *1 (|UnivariateSkewPolynomialCategory| *2)) (|ofCategory| *2 (|Ring|)) (|ofCategory| *2 (|Field|)))) (|leftRemainder| (*1 *1 *1 *1) (AND (|ofCategory| *1 (|UnivariateSkewPolynomialCategory| *2)) (|ofCategory| *2 (|Ring|)) (|ofCategory| *2 (|Field|)))) (|leftExactQuotient| (*1 *1 *1 *1) (|partial| AND (|ofCategory| *1 (|UnivariateSkewPolynomialCategory| *2)) (|ofCategory| *2 (|Ring|)) (|ofCategory| *2 (|Field|)))) (|leftGcd| (*1 *1 *1 *1) (AND (|ofCategory| *1 (|UnivariateSkewPolynomialCategory| *2)) (|ofCategory| *2 (|Ring|)) (|ofCategory| *2 (|Field|)))) (|leftExtendedGcd| (*1 *2 *1 *1) (AND (|ofCategory| *3 (|Field|)) (|ofCategory| *3 (|Ring|)) (|isDomain| *2 (|Record| (|:| |coef1| *1) (|:| |coef2| *1) (|:| |generator| *1))) (|ofCategory| *1 (|UnivariateSkewPolynomialCategory| *3)))) (|rightLcm| (*1 *1 *1 *1) (AND (|ofCategory| *1 (|UnivariateSkewPolynomialCategory| *2)) (|ofCategory| *2 (|Ring|)) (|ofCategory| *2 (|Field|)))) (|rightDivide| (*1 *2 *1 *1) (AND (|ofCategory| *3 (|Field|)) (|ofCategory| *3 (|Ring|)) (|isDomain| *2 (|Record| (|:| |quotient| *1) (|:| |remainder| *1))) (|ofCategory| *1 (|UnivariateSkewPolynomialCategory| *3)))) (|rightQuotient| (*1 *1 *1 *1) (AND (|ofCategory| *1 (|UnivariateSkewPolynomialCategory| *2)) (|ofCategory| *2 (|Ring|)) (|ofCategory| *2 (|Field|)))) (|rightRemainder| (*1 *1 *1 *1) (AND (|ofCategory| *1 (|UnivariateSkewPolynomialCategory| *2)) (|ofCategory| *2 (|Ring|)) (|ofCategory| *2 (|Field|)))) (|rightExactQuotient| (*1 *1 *1 *1) (|partial| AND (|ofCategory| *1 (|UnivariateSkewPolynomialCategory| *2)) (|ofCategory| *2 (|Ring|)) (|ofCategory| *2 (|Field|)))) (|rightGcd| (*1 *1 *1 *1) (AND (|ofCategory| *1 (|UnivariateSkewPolynomialCategory| *2)) (|ofCategory| *2 (|Ring|)) (|ofCategory| *2 (|Field|)))) (|rightExtendedGcd| (*1 *2 *1 *1) (AND (|ofCategory| *3 (|Field|)) (|ofCategory| *3 (|Ring|)) (|isDomain| *2 (|Record| (|:| |coef1| *1) (|:| |coef2| *1) (|:| |generator| *1))) (|ofCategory| *1 (|UnivariateSkewPolynomialCategory| *3)))) (|leftLcm| (*1 *1 *1 *1) (AND (|ofCategory| *1 (|UnivariateSkewPolynomialCategory| *2)) (|ofCategory| *2 (|Ring|)) (|ofCategory| *2 (|Field|))))) (|Join| (|Ring|) (|BiModule| |t#1| |t#1|) (|FullyRetractableTo| |t#1|) (CATEGORY |domain| (SIGNATURE |degree| ((|NonNegativeInteger|) $)) (SIGNATURE |minimumDegree| ((|NonNegativeInteger|) $)) (SIGNATURE |leadingCoefficient| (|t#1| $)) (SIGNATURE |reductum| ($ $)) (SIGNATURE |coefficient| (|t#1| $ (|NonNegativeInteger|))) (SIGNATURE |monomial| ($ |t#1| (|NonNegativeInteger|))) (SIGNATURE |coefficients| ((|List| |t#1|) $)) (SIGNATURE |apply| (|t#1| $ |t#1| |t#1|)) (IF (|has| |t#1| (|CommutativeRing|)) (ATTRIBUTE (|Algebra| |t#1|)) |%noBranch|) (IF (|has| |t#1| (|IntegralDomain|)) (PROGN (SIGNATURE |exquo| ((|Union| $ "failed") $ |t#1|)) (SIGNATURE |monicLeftDivide| ((|Record| (|:| |quotient| $) (|:| |remainder| $)) $ $)) (SIGNATURE |monicRightDivide| ((|Record| (|:| |quotient| $) (|:| |remainder| $)) $ $))) |%noBranch|) (IF (|has| |t#1| (|GcdDomain|)) (PROGN (SIGNATURE |content| (|t#1| $)) (SIGNATURE |primitivePart| ($ $))) |%noBranch|) (IF (|has| |t#1| (|Field|)) (PROGN (SIGNATURE |leftDivide| ((|Record| (|:| |quotient| $) (|:| |remainder| $)) $ $)) (SIGNATURE |leftQuotient| ($ $ $)) (SIGNATURE |leftRemainder| ($ $ $)) (SIGNATURE |leftExactQuotient| ((|Union| $ "failed") $ $)) (SIGNATURE |leftGcd| ($ $ $)) (SIGNATURE |leftExtendedGcd| ((|Record| (|:| |coef1| $) (|:| |coef2| $) (|:| |generator| $)) $ $)) (SIGNATURE |rightLcm| ($ $ $)) (SIGNATURE |rightDivide| ((|Record| (|:| |quotient| $) (|:| |remainder| $)) $ $)) (SIGNATURE |rightQuotient| ($ $ $)) (SIGNATURE |rightRemainder| ($ $ $)) (SIGNATURE |rightExactQuotient| ((|Union| $ "failed") $ $)) (SIGNATURE |rightGcd| ($ $ $)) (SIGNATURE |rightExtendedGcd| ((|Record| (|:| |coef1| $) (|:| |coef2| $) (|:| |generator| $)) $ $)) (SIGNATURE |leftLcm| ($ $ $))) |%noBranch|))) (((|AbelianGroup|) . T) ((|AbelianMonoid|) . T) ((|AbelianSemiGroup|) . T) ((|Algebra| |#1|) |has| |#1| (|CommutativeRing|)) ((|BasicType|) . T) ((|BiModule| |#1| |#1|) . T) ((|CancellationAbelianMonoid|) . T) ((|CoercibleFrom| #1=(|Fraction| (|Integer|))) |has| |#1| (|RetractableTo| (|Fraction| (|Integer|)))) ((|CoercibleFrom| (|Integer|)) . T) ((|CoercibleFrom| |#1|) . T) ((|CoercibleTo| (|OutputForm|)) . T) ((|FullyRetractableTo| |#1|) . T) ((|Join|) . T) ((|LeftLinearSet| (|Integer|)) . T) ((|LeftLinearSet| |#1|) . T) ((|LeftLinearSet| $) . T) ((|LeftModule| |#1|) . T) ((|LeftModule| $) . T) ((|LinearSet| |#1|) |has| |#1| (|CommutativeRing|)) ((|Module| |#1|) |has| |#1| (|CommutativeRing|)) ((|Monoid|) . T) ((|RetractableTo| #1#) |has| |#1| (|RetractableTo| (|Fraction| (|Integer|)))) ((|RetractableTo| (|Integer|)) |has| |#1| (|RetractableTo| (|Integer|))) ((|RetractableTo| |#1|) . T) ((|RightLinearSet| |#1|) . T) ((|RightModule| |#1|) . T) ((|Ring|) . T) ((|Rng|) . T) ((|SemiGroup|) . T) ((|SemiRing|) . T) ((|SetCategory|) . T) ((|Type|) . T)) -((|times| ((|#2| |#2| |#2| #1=(|Automorphism| |#1|) #2=(|Mapping| |#1| |#1|)) 20 T ELT)) (|rightDivide| (#3=((|Record| (|:| |quotient| |#2|) (|:| |remainder| |#2|)) |#2| |#2| #1#) 46 #4=(|has| |#1| (|Field|)) ELT)) (|monicRightDivide| (#3# 43 #5=(|has| |#1| (|IntegralDomain|)) ELT)) (|monicLeftDivide| (#3# 42 #5# ELT)) (|leftDivide| (#3# 45 #4# ELT)) (|apply| ((|#1| |#2| |#1| |#1| #1# #2#) 33 T ELT))) +((|times| ((|#2| |#2| |#2| #1=(|Automorphism| |#1|) #2=(|Mapping| |#1| |#1|)) 20 T ELT)) (|rightDivide| (#3=((|Record| (|:| |quotient| |#2|) (|:| |remainder| |#2|)) |#2| |#2| #1#) 51 #4=(|has| |#1| (|Field|)) ELT)) (|monicRightDivide| (#3# 48 #5=(|has| |#1| (|IntegralDomain|)) ELT)) (|monicLeftDivide| (#3# 47 #5# ELT)) (|leftDivide| (#3# 50 #4# ELT)) (|apply| ((|#1| |#2| |#1| |#1| #1# #2#) 37 T ELT))) (((|UnivariateSkewPolynomialCategoryOps| |#1| |#2|) (CATEGORY |package| (SIGNATURE |times| (|#2| |#2| |#2| #1=(|Automorphism| |#1|) #2=(|Mapping| |#1| |#1|))) (SIGNATURE |apply| (|#1| |#2| |#1| |#1| #1# #2#)) (IF (|has| |#1| (|IntegralDomain|)) (PROGN (SIGNATURE |monicLeftDivide| #3=((|Record| (|:| |quotient| |#2|) (|:| |remainder| |#2|)) |#2| |#2| #1#)) (SIGNATURE |monicRightDivide| #3#)) |%noBranch|) (IF (|has| |#1| (|Field|)) (PROGN (SIGNATURE |leftDivide| #3#) (SIGNATURE |rightDivide| #3#)) |%noBranch|)) (|Ring|) (|UnivariateSkewPolynomialCategory| |#1|)) (T |UnivariateSkewPolynomialCategoryOps|)) ((|rightDivide| #1=(*1 *2 *3 *3 *4) #2=(AND #3=(|isDomain| *4 #4=(|Automorphism| *5)) (|ofCategory| *5 (|Field|)) #5=(|ofCategory| *5 #6=(|Ring|)) #7=(|isDomain| *2 (|Record| (|:| |quotient| *3) (|:| |remainder| *3))) #8=(|isDomain| *1 (|UnivariateSkewPolynomialCategoryOps| *5 *3)) #9=(|ofCategory| *3 #10=(|UnivariateSkewPolynomialCategory| *5)))) (|leftDivide| #1# #2#) (|monicRightDivide| #1# #11=(AND #3# (|ofCategory| *5 (|IntegralDomain|)) #5# #7# #8# #9#)) (|monicLeftDivide| #1# #11#) (|apply| (*1 *2 *3 *2 *2 *4 *5) (AND (|isDomain| *4 (|Automorphism| *2)) (|isDomain| *5 (|Mapping| *2 *2)) (|ofCategory| *2 #6#) (|isDomain| *1 (|UnivariateSkewPolynomialCategoryOps| *2 *3)) (|ofCategory| *3 (|UnivariateSkewPolynomialCategory| *2)))) (|times| (*1 *2 *2 *2 *3 *4) (AND (|isDomain| *3 #4#) (|isDomain| *4 (|Mapping| *5 *5)) #5# (|isDomain| *1 (|UnivariateSkewPolynomialCategoryOps| *5 *2)) (|ofCategory| *2 #10#)))) -((~= #1=((#2=(|Boolean|) $ $) NIL T ELT)) (|zero?| #3=((#2# $) NIL T ELT)) (|subtractIfCan| (#4=(#5=(|Union| $ #6="failed") $ $) NIL T ELT)) (|sample| #7=(#8=($) NIL T CONST)) (|rightRemainder| #9=(#10=($ $ $) NIL #11=(|has| |#1| (|Field|)) ELT)) (|rightQuotient| #9#) (|rightLcm| #9#) (|rightGcd| #9#) (|rightExtendedGcd| #12=(((|Record| (|:| |coef1| $) (|:| |coef2| $) (|:| |generator| $)) $ $) NIL #11# ELT)) (|rightExactQuotient| #13=(#4# NIL #11# ELT)) (|rightDivide| (#14=((|Record| (|:| |quotient| $) (|:| |remainder| $)) $ $) 34 #11# ELT)) (|retractIfCan| (((|Union| #15=(|Integer|) . #16=(#6#)) . #17=($)) NIL #18=(|has| |#1| (|RetractableTo| #15#)) ELT) (((|Union| #19=(|Fraction| #15#) . #16#) . #17#) NIL #20=(|has| |#1| (|RetractableTo| #19#)) ELT) (((|Union| |#1| . #16#) . #17#) NIL T ELT)) (|retract| ((#15# . #21=($)) NIL #18# ELT) ((#19# . #21#) NIL #20# ELT) #22=(#23=(|#1| . #21#) NIL T ELT)) (|reductum| #24=(#25=($ $) NIL T ELT)) (|recip| ((#5# $) NIL T ELT)) (|primitivePart| (#25# NIL #26=(|has| |#1| (|GcdDomain|)) ELT)) (|outputForm| ((#27=(|OutputForm|) $ #27#) NIL T ELT)) (|opposite?| #1#) (|one?| #3#) (|monomial| (($ |#1| #28=(|NonNegativeInteger|)) NIL T ELT)) (|monicRightDivide| (#14# 30 #29=(|has| |#1| (|IntegralDomain|)) ELT)) (|monicLeftDivide| (#14# 28 #29# ELT)) (|minimumDegree| #30=((#28# $) NIL T ELT)) (|leftRemainder| #9#) (|leftQuotient| #9#) (|leftLcm| #9#) (|leftGcd| #9#) (|leftExtendedGcd| #12#) (|leftExactQuotient| #13#) (|leftDivide| (#14# 32 #11# ELT)) (|leadingCoefficient| #22#) (|latex| (((|String|) $) NIL T ELT)) (|hash| (((|SingleInteger|) $) NIL T ELT)) (|exquo| ((#5# $ |#1|) NIL #29# ELT)) (|degree| #30#) (|content| (#23# NIL #26# ELT)) (|coerce| ((#27# $) NIL T ELT) (($ #15#) NIL T ELT) (($ #19#) NIL #20# ELT) (($ |#1|) NIL T ELT)) (|coefficients| (((|List| |#1|) $) NIL T ELT)) (|coefficient| ((|#1| $ #28#) NIL T ELT)) (|characteristic| ((#28#) NIL T CONST)) (|before?| #1#) (|apply| ((|#1| $ |#1| |#1|) 15 T ELT)) (|annihilate?| #1#) (|Zero| #7#) (|One| (#8# 23 T CONST)) (= #1#) (- #24# #31=(#10# NIL T ELT)) (+ #31#) (** (($ $ #32=(|PositiveInteger|)) 19 T ELT) (($ $ #28#) 24 T ELT)) (* (($ #32# $) NIL T ELT) (($ #28# $) NIL T ELT) (($ #15# . #33=($)) NIL T ELT) (#10# 13 T ELT) (($ $ |#1|) NIL T ELT) (($ |#1| . #33#) NIL T ELT))) +((~= #1=((#2=(|Boolean|) $ $) NIL T ELT)) (|zero?| #3=((#2# $) NIL T ELT)) (|subtractIfCan| (((|Maybe| $) $ $) NIL T ELT)) (|sample| #4=(#5=($) NIL T CONST)) (|rightRemainder| #6=(#7=($ $ $) NIL #8=(|has| |#1| (|Field|)) ELT)) (|rightQuotient| #6#) (|rightLcm| #6#) (|rightGcd| #6#) (|rightExtendedGcd| #9=(((|Record| (|:| |coef1| $) (|:| |coef2| $) (|:| |generator| $)) $ $) NIL #8# ELT)) (|rightExactQuotient| #10=((#11=(|Union| $ #12="failed") $ $) NIL #8# ELT)) (|rightDivide| (#13=((|Record| (|:| |quotient| $) (|:| |remainder| $)) $ $) 34 #8# ELT)) (|retractIfCan| (((|Union| #14=(|Integer|) . #15=(#12#)) . #16=($)) NIL #17=(|has| |#1| (|RetractableTo| #14#)) ELT) (((|Union| #18=(|Fraction| #14#) . #15#) . #16#) NIL #19=(|has| |#1| (|RetractableTo| #18#)) ELT) (((|Union| |#1| . #15#) . #16#) NIL T ELT)) (|retract| ((#14# . #20=($)) NIL #17# ELT) ((#18# . #20#) NIL #19# ELT) #21=(#22=(|#1| . #20#) NIL T ELT)) (|reductum| #23=(#24=($ $) NIL T ELT)) (|recip| ((#11# $) NIL T ELT)) (|primitivePart| (#24# NIL #25=(|has| |#1| (|GcdDomain|)) ELT)) (|outputForm| ((#26=(|OutputForm|) $ #26#) NIL T ELT)) (|opposite?| #1#) (|one?| #3#) (|monomial| (($ |#1| #27=(|NonNegativeInteger|)) NIL T ELT)) (|monicRightDivide| (#13# 30 #28=(|has| |#1| (|IntegralDomain|)) ELT)) (|monicLeftDivide| (#13# 28 #28# ELT)) (|minimumDegree| #29=((#27# $) NIL T ELT)) (|leftRemainder| #6#) (|leftQuotient| #6#) (|leftLcm| #6#) (|leftGcd| #6#) (|leftExtendedGcd| #9#) (|leftExactQuotient| #10#) (|leftDivide| (#13# 32 #8# ELT)) (|leadingCoefficient| #21#) (|latex| (((|String|) $) NIL T ELT)) (|hash| (((|SingleInteger|) $) NIL T ELT)) (|exquo| ((#11# $ |#1|) NIL #28# ELT)) (|degree| #29#) (|content| (#22# NIL #25# ELT)) (|coerce| ((#26# $) NIL T ELT) (($ #14#) NIL T ELT) (($ #18#) NIL #19# ELT) (($ |#1|) NIL T ELT)) (|coefficients| (((|List| |#1|) $) NIL T ELT)) (|coefficient| ((|#1| $ #27#) NIL T ELT)) (|characteristic| ((#27#) NIL T CONST)) (|before?| #1#) (|apply| ((|#1| $ |#1| |#1|) 15 T ELT)) (|annihilate?| #1#) (|Zero| #4#) (|One| (#5# 23 T CONST)) (= #1#) (- #23# #30=(#7# NIL T ELT)) (+ #30#) (** (($ $ #31=(|PositiveInteger|)) 19 T ELT) (($ $ #27#) 24 T ELT)) (* (($ #31# $) NIL T ELT) (($ #27# $) NIL T ELT) (($ #14# . #32=($)) NIL T ELT) (#7# 13 T ELT) (($ $ |#1|) NIL T ELT) (($ |#1| . #32#) NIL T ELT))) (((|SparseUnivariateSkewPolynomial| |#1| |#2| |#3|) (|Join| (|UnivariateSkewPolynomialCategory| |#1|) (CATEGORY |domain| (SIGNATURE |outputForm| (#1=(|OutputForm|) $ #1#)))) (|Ring|) (|Automorphism| |#1|) (|Mapping| |#1| |#1|)) (T |SparseUnivariateSkewPolynomial|)) ((|outputForm| (*1 *2 *1 *2) (AND (|isDomain| *2 (|OutputForm|)) (|isDomain| *1 (|SparseUnivariateSkewPolynomial| *3 *4 *5)) (|ofCategory| *3 (|Ring|)) (|ofType| *4 (|Automorphism| *3)) (|ofType| *5 (|Mapping| *3 *3))))) -((~= #1=((#2=(|Boolean|) $ $) NIL T ELT)) (|zero?| #3=((#2# $) NIL T ELT)) (|subtractIfCan| (#4=(#5=(|Union| $ #6="failed") $ $) NIL T ELT)) (|sample| #7=(#8=($) NIL T CONST)) (|rightRemainder| #9=(#10=($ $ $) NIL #11=(|has| |#2| (|Field|)) ELT)) (|rightQuotient| #9#) (|rightLcm| #9#) (|rightGcd| #9#) (|rightExtendedGcd| #12=(((|Record| (|:| |coef1| $) (|:| |coef2| $) (|:| |generator| $)) $ $) NIL #11# ELT)) (|rightExactQuotient| #13=(#4# NIL #11# ELT)) (|rightDivide| #14=(#15=((|Record| (|:| |quotient| $) (|:| |remainder| $)) $ $) NIL #11# ELT)) (|retractIfCan| (((|Union| #16=(|Integer|) . #17=(#6#)) . #18=($)) NIL #19=(|has| |#2| (|RetractableTo| #16#)) ELT) (((|Union| #20=(|Fraction| #16#) . #17#) . #18#) NIL #21=(|has| |#2| (|RetractableTo| #20#)) ELT) (((|Union| |#2| . #17#) . #18#) NIL T ELT)) (|retract| ((#16# . #22=($)) NIL #19# ELT) ((#20# . #22#) NIL #21# ELT) #23=(#24=(|#2| . #22#) NIL T ELT)) (|reductum| #25=(#26=($ $) NIL T ELT)) (|recip| ((#5# $) NIL T ELT)) (|primitivePart| (#26# NIL #27=(|has| |#2| (|GcdDomain|)) ELT)) (|opposite?| #1#) (|one?| #3#) (|monomial| (($ |#2| #28=(|NonNegativeInteger|)) 17 T ELT)) (|monicRightDivide| #29=(#15# NIL #30=(|has| |#2| (|IntegralDomain|)) ELT)) (|monicLeftDivide| #29#) (|minimumDegree| #31=((#28# $) NIL T ELT)) (|leftRemainder| #9#) (|leftQuotient| #9#) (|leftLcm| #9#) (|leftGcd| #9#) (|leftExtendedGcd| #12#) (|leftExactQuotient| #13#) (|leftDivide| #14#) (|leadingCoefficient| #23#) (|latex| (((|String|) $) NIL T ELT)) (|hash| (((|SingleInteger|) $) NIL T ELT)) (|exquo| ((#5# $ |#2|) NIL #30# ELT)) (|degree| #31#) (|content| (#24# NIL #27# ELT)) (|coerce| (((|OutputForm|) $) 24 T ELT) (($ #16#) NIL T ELT) (($ #20#) NIL #21# ELT) (($ |#2|) NIL T ELT) (($ (|Variable| |#1|)) 19 T ELT)) (|coefficients| (((|List| |#2|) $) NIL T ELT)) (|coefficient| ((|#2| $ #28#) NIL T ELT)) (|characteristic| ((#28#) NIL T CONST)) (|before?| #1#) (|apply| ((|#2| $ |#2| |#2|) NIL T ELT)) (|annihilate?| #1#) (|Zero| #7#) (|One| (#8# 13 T CONST)) (= #1#) (- #25# #32=(#10# NIL T ELT)) (+ #32#) (** (($ $ #33=(|PositiveInteger|)) NIL T ELT) (($ $ #28#) NIL T ELT)) (* (($ #33# $) NIL T ELT) (($ #28# $) NIL T ELT) (($ #16# . #34=($)) NIL T ELT) #32# (($ $ |#2|) NIL T ELT) (($ |#2| . #34#) NIL T ELT))) +((~= #1=((#2=(|Boolean|) $ $) NIL T ELT)) (|zero?| #3=((#2# $) NIL T ELT)) (|subtractIfCan| (((|Maybe| $) $ $) NIL T ELT)) (|sample| #4=(#5=($) NIL T CONST)) (|rightRemainder| #6=(#7=($ $ $) NIL #8=(|has| |#2| (|Field|)) ELT)) (|rightQuotient| #6#) (|rightLcm| #6#) (|rightGcd| #6#) (|rightExtendedGcd| #9=(((|Record| (|:| |coef1| $) (|:| |coef2| $) (|:| |generator| $)) $ $) NIL #8# ELT)) (|rightExactQuotient| #10=((#11=(|Union| $ #12="failed") $ $) NIL #8# ELT)) (|rightDivide| #13=(#14=((|Record| (|:| |quotient| $) (|:| |remainder| $)) $ $) NIL #8# ELT)) (|retractIfCan| (((|Union| #15=(|Integer|) . #16=(#12#)) . #17=($)) NIL #18=(|has| |#2| (|RetractableTo| #15#)) ELT) (((|Union| #19=(|Fraction| #15#) . #16#) . #17#) NIL #20=(|has| |#2| (|RetractableTo| #19#)) ELT) (((|Union| |#2| . #16#) . #17#) NIL T ELT)) (|retract| ((#15# . #21=($)) NIL #18# ELT) ((#19# . #21#) NIL #20# ELT) #22=(#23=(|#2| . #21#) NIL T ELT)) (|reductum| #24=(#25=($ $) NIL T ELT)) (|recip| ((#11# $) NIL T ELT)) (|primitivePart| (#25# NIL #26=(|has| |#2| (|GcdDomain|)) ELT)) (|opposite?| #1#) (|one?| #3#) (|monomial| (($ |#2| #27=(|NonNegativeInteger|)) 17 T ELT)) (|monicRightDivide| #28=(#14# NIL #29=(|has| |#2| (|IntegralDomain|)) ELT)) (|monicLeftDivide| #28#) (|minimumDegree| #30=((#27# $) NIL T ELT)) (|leftRemainder| #6#) (|leftQuotient| #6#) (|leftLcm| #6#) (|leftGcd| #6#) (|leftExtendedGcd| #9#) (|leftExactQuotient| #10#) (|leftDivide| #13#) (|leadingCoefficient| #22#) (|latex| (((|String|) $) NIL T ELT)) (|hash| (((|SingleInteger|) $) NIL T ELT)) (|exquo| ((#11# $ |#2|) NIL #29# ELT)) (|degree| #30#) (|content| (#23# NIL #26# ELT)) (|coerce| (((|OutputForm|) $) 24 T ELT) (($ #15#) NIL T ELT) (($ #19#) NIL #20# ELT) (($ |#2|) NIL T ELT) (($ (|Variable| |#1|)) 19 T ELT)) (|coefficients| (((|List| |#2|) $) NIL T ELT)) (|coefficient| ((|#2| $ #27#) NIL T ELT)) (|characteristic| ((#27#) NIL T CONST)) (|before?| #1#) (|apply| ((|#2| $ |#2| |#2|) NIL T ELT)) (|annihilate?| #1#) (|Zero| #4#) (|One| (#5# 13 T CONST)) (= #1#) (- #24# #31=(#7# NIL T ELT)) (+ #31#) (** (($ $ #32=(|PositiveInteger|)) NIL T ELT) (($ $ #27#) NIL T ELT)) (* (($ #32# $) NIL T ELT) (($ #27# $) NIL T ELT) (($ #15# . #33=($)) NIL T ELT) #31# (($ $ |#2|) NIL T ELT) (($ |#2| . #33#) NIL T ELT))) (((|UnivariateSkewPolynomial| |#1| |#2| |#3| |#4|) (|Join| (|UnivariateSkewPolynomialCategory| |#2|) (|CoercibleFrom| (|Variable| |#1|))) (|Symbol|) (|Ring|) (|Automorphism| |#2|) (|Mapping| |#2| |#2|)) (T |UnivariateSkewPolynomial|)) NIL ((|legendreP| (#1=(|#1| #2=(|NonNegativeInteger|) |#1|) 45 (|has| |#1| (|Algebra| (|Fraction| (|Integer|)))) ELT)) (|laguerreL| ((|#1| #2# #2# |#1|) 36 T ELT) (#1# 24 T ELT)) (|hermiteH| (#1# 40 T ELT)) (|chebyshevU| (#1# 38 T ELT)) (|chebyshevT| (#1# 37 T ELT))) @@ -2583,7 +2583,7 @@ NIL ((~= #1=(#2=((|Boolean|) $ $) NIL T ELT)) (|name| (((|Identifier|) $) 12 T ELT)) (|members| (((|List| (|FunctionDescriptor|)) $) 14 T ELT)) (|latex| (((|String|) $) NIL T ELT)) (|hash| (((|SingleInteger|) $) NIL T ELT)) (|coerce| (((|OutputForm|) $) 22 T ELT)) (|before?| #1#) (= (#2# 17 T ELT))) (((|OverloadSet|) (|Join| (|SetCategory|) (CATEGORY |domain| (SIGNATURE |name| ((|Identifier|) $)) (SIGNATURE |members| ((|List| (|FunctionDescriptor|)) $))))) (T |OverloadSet|)) ((|name| #1=(*1 *2 *1) (AND (|isDomain| *2 (|Identifier|)) #2=(|isDomain| *1 (|OverloadSet|)))) (|members| #1# (AND (|isDomain| *2 (|List| (|FunctionDescriptor|))) #2#))) -((~= #1=((#2=(|Boolean|) $ $) NIL T ELT)) (|zero?| #3=((#2# $) NIL T ELT)) (|subtractIfCan| (#4=(#5=(|Union| $ "failed") $ $) NIL T ELT)) (|sample| #6=(($) NIL T CONST)) (|recip| ((#5# $) NIL T ELT)) (|opposite?| #1#) (|one?| #3#) (|latex| (((|String|) $) NIL T ELT)) (|hash| (((|SingleInteger|) $) NIL T ELT)) (|coerce| (((|OutputForm|) . #7=($)) NIL T ELT) (($ #8=(|Integer|)) NIL T ELT) (($ #9=(|Polynomial| |#1|)) NIL T ELT) ((#9# . #7#) NIL T ELT) (($ |#1|) NIL #10=(|has| |#1| (|CommutativeRing|)) ELT)) (|characteristic| ((#11=(|NonNegativeInteger|)) NIL T CONST)) (|changeWeightLevel| (((|Void|) #11#) NIL T ELT)) (|before?| #1#) (|annihilate?| #1#) (|Zero| #6#) (|One| #6#) (= #1#) (/ (#4# NIL (|has| |#1| (|Field|)) ELT)) (- (($ $) NIL T ELT) #12=(($ $ $) NIL T ELT)) (+ #12#) (** (($ $ #13=(|PositiveInteger|)) NIL T ELT) (($ $ #11#) NIL T ELT)) (* (($ #13# $) NIL T ELT) (($ #11# $) NIL T ELT) (($ #8# . #14=($)) NIL T ELT) #12# (($ |#1| . #14#) NIL #10# ELT) (($ $ |#1|) NIL #10# ELT))) +((~= #1=((#2=(|Boolean|) $ $) NIL T ELT)) (|zero?| #3=((#2# $) NIL T ELT)) (|subtractIfCan| (((|Maybe| $) $ $) NIL T ELT)) (|sample| #4=(($) NIL T CONST)) (|recip| ((#5=(|Union| $ "failed") $) NIL T ELT)) (|opposite?| #1#) (|one?| #3#) (|latex| (((|String|) $) NIL T ELT)) (|hash| (((|SingleInteger|) $) NIL T ELT)) (|coerce| (((|OutputForm|) . #6=($)) NIL T ELT) (($ #7=(|Integer|)) NIL T ELT) (($ #8=(|Polynomial| |#1|)) NIL T ELT) ((#8# . #6#) NIL T ELT) (($ |#1|) NIL #9=(|has| |#1| (|CommutativeRing|)) ELT)) (|characteristic| ((#10=(|NonNegativeInteger|)) NIL T CONST)) (|changeWeightLevel| (((|Void|) #10#) NIL T ELT)) (|before?| #1#) (|annihilate?| #1#) (|Zero| #4#) (|One| #4#) (= #1#) (/ ((#5# $ $) NIL (|has| |#1| (|Field|)) ELT)) (- (($ $) NIL T ELT) #11=(($ $ $) NIL T ELT)) (+ #11#) (** (($ $ #12=(|PositiveInteger|)) NIL T ELT) (($ $ #10#) NIL T ELT)) (* (($ #12# $) NIL T ELT) (($ #10# $) NIL T ELT) (($ #7# . #13=($)) NIL T ELT) #11# (($ |#1| . #13#) NIL #9# ELT) (($ $ |#1|) NIL #9# ELT))) (((|OrdinaryWeightedPolynomials| |#1| |#2| |#3| |#4|) (|Join| #1=(|Ring|) (|HomotopicTo| (|Polynomial| |#1|)) (CATEGORY |domain| (IF (|has| |#1| (|CommutativeRing|)) (ATTRIBUTE (|Algebra| |#1|)) |%noBranch|) (IF (|has| |#1| (|Field|)) (SIGNATURE / ((|Union| $ "failed") $ $)) |%noBranch|) (SIGNATURE |changeWeightLevel| ((|Void|) #2=(|NonNegativeInteger|))))) #1# (|List| (|Symbol|)) (|List| #2#) #2#) (T |OrdinaryWeightedPolynomials|)) ((/ (*1 *1 *1 *1) (|partial| AND (|isDomain| *1 (|OrdinaryWeightedPolynomials| *2 *3 *4 *5)) (|ofCategory| *2 (|Field|)) (|ofCategory| *2 #1=(|Ring|)) (|ofType| *3 #2=(|List| (|Symbol|))) (|ofType| *4 (|List| #3=(|NonNegativeInteger|))) (|ofType| *5 #3#))) (|changeWeightLevel| (*1 *2 *3) (AND (|isDomain| *3 #3#) (|isDomain| *2 (|Void|)) (|isDomain| *1 (|OrdinaryWeightedPolynomials| *4 *5 *6 *7)) (|ofCategory| *4 #1#) (|ofType| *5 #2#) (|ofType| *6 (|List| *3)) (|ofType| *7 *3)))) ((|padecf| (((|Union| (|ContinuedFraction| |#3|) #1="failed") #2=(|NonNegativeInteger|) #2# |#2| |#2|) 38 T ELT)) (|pade| (((|Union| (|Fraction| |#3|) #1#) #2# #2# |#2| |#2|) 29 T ELT))) @@ -2592,18 +2592,18 @@ NIL ((|pade| ((#1=(|Union| (|Fraction| (|UnivariatePolynomial| |#2| |#1|)) "failed") #2=(|NonNegativeInteger|) #2# #3=(|UnivariateTaylorSeries| |#1| |#2| |#3|)) 30 T ELT) ((#1# #2# #2# #3# #3#) 28 T ELT))) (((|PadeApproximantPackage| |#1| |#2| |#3|) (CATEGORY |package| (SIGNATURE |pade| (#1=(|Union| (|Fraction| (|UnivariatePolynomial| |#2| |#1|)) "failed") #2=(|NonNegativeInteger|) #2# #3=(|UnivariateTaylorSeries| |#1| |#2| |#3|) #3#)) (SIGNATURE |pade| (#1# #2# #2# #3#))) (|Field|) (|Symbol|) |#1|) (T |PadeApproximantPackage|)) ((|pade| (*1 *2 *3 *3 *4) #1=(|partial| AND (|isDomain| *3 (|NonNegativeInteger|)) (|isDomain| *4 (|UnivariateTaylorSeries| *5 *6 *7)) (|ofCategory| *5 (|Field|)) (|ofType| *6 (|Symbol|)) (|ofType| *7 *5) (|isDomain| *2 (|Fraction| (|UnivariatePolynomial| *6 *5))) (|isDomain| *1 (|PadeApproximantPackage| *5 *6 *7)))) (|pade| (*1 *2 *3 *3 *4 *4) #1#)) -((~= #1=((#2=(|Boolean|) $ $) NIL T ELT)) (|zero?| #3=((#2# $) NIL T ELT)) (|unitNormal| (((|Record| (|:| |unit| $) (|:| |canonical| $) (|:| |associate| $)) $) NIL T ELT)) (|unitCanonical| #4=(($ $) NIL T ELT)) (|unit?| #3#) (|subtractIfCan| #5=((#6=(|Union| $ #7="failed") $ $) NIL T ELT)) (|sqrt| #8=(($ $ #9=(|Integer|)) NIL T ELT)) (|sizeLess?| #1#) (|sample| #10=(($) NIL T CONST)) (|root| (($ (|SparseUnivariatePolynomial| #9#) #9#) NIL T ELT)) (|rem| #11=(($ $ $) NIL T ELT)) (|recip| ((#6# $) NIL T ELT)) (|quotientByP| #4#) (|quo| #11#) (|principalIdeal| (((|Record| (|:| |coef| #12=(|List| $)) #13=(|:| |generator| $)) #12#) NIL T ELT)) (|order| #14=((#15=(|NonNegativeInteger|) $) NIL T ELT)) (|opposite?| #1#) (|one?| #3#) (|multiEuclidean| (((|Union| #12# #7#) #12# $) NIL T ELT)) (|modulus| ((#9#) NIL T ELT)) (|moduloP| ((#9# $) NIL T ELT)) (|lcm| #11# #16=(($ #12#) NIL T ELT)) (|latex| (((|String|) $) NIL T ELT)) (|hash| (((|SingleInteger|) $) NIL T ELT)) (|gcdPolynomial| ((#17=(|SparseUnivariatePolynomial| $) #17# #17#) NIL T ELT)) (|gcd| #11# #16#) (|extendedEuclidean| (((|Record| #18=(|:| |coef1| $) #19=(|:| |coef2| $) #13#) $ $) NIL T ELT) (((|Union| (|Record| #18# #19#) #7#) $ $ $) NIL T ELT)) (|extend| #8#) (|exquo| #5#) (|expressIdealMember| (((|Maybe| #12#) #12# $) NIL T ELT)) (|euclideanSize| #14#) (|divide| (((|Record| (|:| |quotient| $) (|:| |remainder| $)) $ $) NIL T ELT)) (|digits| (((|Stream| #9#) $) NIL T ELT)) (|complete| #4#) (|coerce| (((|OutputForm|) $) NIL T ELT) (($ #9#) NIL T ELT) #4#) (|characteristic| ((#15#) NIL T CONST)) (|before?| #1#) (|associates?| #1#) (|approximate| ((#9# $ #9#) NIL T ELT)) (|annihilate?| #1#) (|Zero| #10#) (|One| #10#) (= #1#) (- #4# #11#) (+ #11#) (** (($ $ #20=(|PositiveInteger|)) NIL T ELT) (($ $ #15#) NIL T ELT)) (* (($ #20# $) NIL T ELT) (($ #15# $) NIL T ELT) (($ #9# $) NIL T ELT) #11#)) +((~= #1=((#2=(|Boolean|) $ $) NIL T ELT)) (|zero?| #3=((#2# $) NIL T ELT)) (|unitNormal| (((|Record| (|:| |unit| $) (|:| |canonical| $) (|:| |associate| $)) $) NIL T ELT)) (|unitCanonical| #4=(($ $) NIL T ELT)) (|unit?| #3#) (|subtractIfCan| (((|Maybe| $) $ $) NIL T ELT)) (|sqrt| #5=(($ $ #6=(|Integer|)) NIL T ELT)) (|sizeLess?| #1#) (|sample| #7=(($) NIL T CONST)) (|root| (($ (|SparseUnivariatePolynomial| #6#) #6#) NIL T ELT)) (|rem| #8=(($ $ $) NIL T ELT)) (|recip| ((#9=(|Union| $ #10="failed") $) NIL T ELT)) (|quotientByP| #4#) (|quo| #8#) (|principalIdeal| (((|Record| (|:| |coef| #11=(|List| $)) #12=(|:| |generator| $)) #11#) NIL T ELT)) (|order| #13=((#14=(|NonNegativeInteger|) $) NIL T ELT)) (|opposite?| #1#) (|one?| #3#) (|multiEuclidean| (((|Union| #11# #10#) #11# $) NIL T ELT)) (|modulus| ((#6#) NIL T ELT)) (|moduloP| ((#6# $) NIL T ELT)) (|lcm| #8# #15=(($ #11#) NIL T ELT)) (|latex| (((|String|) $) NIL T ELT)) (|hash| (((|SingleInteger|) $) NIL T ELT)) (|gcdPolynomial| ((#16=(|SparseUnivariatePolynomial| $) #16# #16#) NIL T ELT)) (|gcd| #8# #15#) (|extendedEuclidean| (((|Record| #17=(|:| |coef1| $) #18=(|:| |coef2| $) #12#) $ $) NIL T ELT) (((|Union| (|Record| #17# #18#) #10#) $ $ $) NIL T ELT)) (|extend| #5#) (|exquo| ((#9# $ $) NIL T ELT)) (|expressIdealMember| (((|Maybe| #11#) #11# $) NIL T ELT)) (|euclideanSize| #13#) (|divide| (((|Record| (|:| |quotient| $) (|:| |remainder| $)) $ $) NIL T ELT)) (|digits| (((|Stream| #6#) $) NIL T ELT)) (|complete| #4#) (|coerce| (((|OutputForm|) $) NIL T ELT) (($ #6#) NIL T ELT) #4#) (|characteristic| ((#14#) NIL T CONST)) (|before?| #1#) (|associates?| #1#) (|approximate| ((#6# $ #6#) NIL T ELT)) (|annihilate?| #1#) (|Zero| #7#) (|One| #7#) (= #1#) (- #4# #8#) (+ #8#) (** (($ $ #19=(|PositiveInteger|)) NIL T ELT) (($ $ #14#) NIL T ELT)) (* (($ #19# $) NIL T ELT) (($ #14# $) NIL T ELT) (($ #6# $) NIL T ELT) #8#)) (((|PAdicInteger| |#1|) (|PAdicIntegerCategory| |#1|) (|Integer|)) (T |PAdicInteger|)) NIL -((~= (#1=((|Boolean|) $ $) 7 T ELT)) (|zero?| ((#2=(|Boolean|) $) 22 T ELT)) (|unitNormal| (((|Record| (|:| |unit| $) (|:| |canonical| $) (|:| |associate| $)) $) 55 T ELT)) (|unitCanonical| (($ $) 54 T ELT)) (|unit?| ((#3=(|Boolean|) $) 52 T ELT)) (|subtractIfCan| (((|Union| $ "failed") $ $) 26 T ELT)) (|sqrt| (($ $ (|Integer|)) 78 T ELT)) (|sizeLess?| (((|Boolean|) $ $) 75 T ELT)) (|sample| (#4=($) 23 T CONST)) (|root| (($ (|SparseUnivariatePolynomial| (|Integer|)) (|Integer|)) 77 T ELT)) (|rem| (#5=($ $ $) 71 T ELT)) (|recip| (((|Union| $ "failed") $) 42 T ELT)) (|quotientByP| (($ $) 80 T ELT)) (|quo| (#5# 72 T ELT)) (|principalIdeal| (((|Record| (|:| |coef| #6=(|List| $)) (|:| |generator| $)) #6#) 66 T ELT)) (|order| (((|NonNegativeInteger|) $) 85 T ELT)) (|opposite?| ((#2# $ $) 20 T ELT)) (|one?| (((|Boolean|) $) 44 T ELT)) (|multiEuclidean| (((|Union| #7=(|List| $) #8="failed") #7# $) 68 T ELT)) (|modulus| (((|Integer|)) 82 T ELT)) (|moduloP| (((|Integer|) $) 81 T ELT)) (|lcm| (#9=($ $ $) 60 T ELT) (#10=($ (|List| $)) 59 T ELT)) (|latex| (((|String|) $) 11 T ELT)) (|hash| (((|SingleInteger|) $) 12 T ELT)) (|gcdPolynomial| ((#11=(|SparseUnivariatePolynomial| $) #11# #11#) 58 T ELT)) (|gcd| (#9# 62 T ELT) (#10# 61 T ELT)) (|extendedEuclidean| (((|Record| #12=(|:| |coef1| $) #13=(|:| |coef2| $) (|:| |generator| $)) $ $) 70 T ELT) (((|Union| (|Record| #12# #13#) #8#) $ $ $) 69 T ELT)) (|extend| (($ $ (|Integer|)) 84 T ELT)) (|exquo| (((|Union| $ "failed") $ $) 56 T ELT)) (|expressIdealMember| (((|Maybe| #6#) #6# $) 65 T ELT)) (|euclideanSize| (((|NonNegativeInteger|) $) 74 T ELT)) (|divide| (((|Record| (|:| |quotient| $) (|:| |remainder| $)) $ $) 73 T ELT)) (|digits| (((|Stream| (|Integer|)) $) 86 T ELT)) (|complete| (($ $) 83 T ELT)) (|coerce| (((|OutputForm|) $) 13 T ELT) (($ (|Integer|)) 41 T ELT) (($ $) 57 T ELT)) (|characteristic| (((|NonNegativeInteger|)) 40 T CONST)) (|before?| (#1# 6 T ELT)) (|associates?| ((#3# $ $) 53 T ELT)) (|approximate| (((|Integer|) $ (|Integer|)) 79 T ELT)) (|annihilate?| (((|Boolean|) $ $) 33 T ELT)) (|Zero| (#4# 24 T CONST)) (|One| (($) 45 T CONST)) (= (#1# 8 T ELT)) (- (($ $) 29 T ELT) (($ $ $) 28 T ELT)) (+ (($ $ $) 18 T ELT)) (** (($ $ (|PositiveInteger|)) 35 T ELT) (($ $ (|NonNegativeInteger|)) 43 T ELT)) (* (($ (|PositiveInteger|) $) 17 T ELT) (($ (|NonNegativeInteger|) $) 21 T ELT) (($ (|Integer|) $) 30 T ELT) (($ $ $) 34 T ELT))) +((~= (#1=((|Boolean|) $ $) 7 T ELT)) (|zero?| ((#2=(|Boolean|) $) 22 T ELT)) (|unitNormal| (((|Record| (|:| |unit| $) (|:| |canonical| $) (|:| |associate| $)) $) 56 T ELT)) (|unitCanonical| (($ $) 55 T ELT)) (|unit?| ((#3=(|Boolean|) $) 53 T ELT)) (|subtractIfCan| (((|Maybe| $) $ $) 26 T ELT)) (|sqrt| (($ $ (|Integer|)) 79 T ELT)) (|sizeLess?| (((|Boolean|) $ $) 76 T ELT)) (|sample| (#4=($) 23 T CONST)) (|root| (($ (|SparseUnivariatePolynomial| (|Integer|)) (|Integer|)) 78 T ELT)) (|rem| (#5=($ $ $) 72 T ELT)) (|recip| (((|Union| $ "failed") $) 43 T ELT)) (|quotientByP| (($ $) 81 T ELT)) (|quo| (#5# 73 T ELT)) (|principalIdeal| (((|Record| (|:| |coef| #6=(|List| $)) (|:| |generator| $)) #6#) 67 T ELT)) (|order| (((|NonNegativeInteger|) $) 86 T ELT)) (|opposite?| ((#2# $ $) 20 T ELT)) (|one?| (((|Boolean|) $) 45 T ELT)) (|multiEuclidean| (((|Union| #7=(|List| $) #8="failed") #7# $) 69 T ELT)) (|modulus| (((|Integer|)) 83 T ELT)) (|moduloP| (((|Integer|) $) 82 T ELT)) (|lcm| (#9=($ $ $) 61 T ELT) (#10=($ (|List| $)) 60 T ELT)) (|latex| (((|String|) $) 11 T ELT)) (|hash| (((|SingleInteger|) $) 12 T ELT)) (|gcdPolynomial| ((#11=(|SparseUnivariatePolynomial| $) #11# #11#) 59 T ELT)) (|gcd| (#9# 63 T ELT) (#10# 62 T ELT)) (|extendedEuclidean| (((|Record| #12=(|:| |coef1| $) #13=(|:| |coef2| $) (|:| |generator| $)) $ $) 71 T ELT) (((|Union| (|Record| #12# #13#) #8#) $ $ $) 70 T ELT)) (|extend| (($ $ (|Integer|)) 85 T ELT)) (|exquo| (((|Union| $ "failed") $ $) 57 T ELT)) (|expressIdealMember| (((|Maybe| #6#) #6# $) 66 T ELT)) (|euclideanSize| (((|NonNegativeInteger|) $) 75 T ELT)) (|divide| (((|Record| (|:| |quotient| $) (|:| |remainder| $)) $ $) 74 T ELT)) (|digits| (((|Stream| (|Integer|)) $) 87 T ELT)) (|complete| (($ $) 84 T ELT)) (|coerce| (((|OutputForm|) $) 13 T ELT) (($ (|Integer|)) 42 T ELT) (($ $) 58 T ELT)) (|characteristic| (((|NonNegativeInteger|)) 41 T CONST)) (|before?| (#1# 6 T ELT)) (|associates?| ((#3# $ $) 54 T ELT)) (|approximate| (((|Integer|) $ (|Integer|)) 80 T ELT)) (|annihilate?| (((|Boolean|) $ $) 34 T ELT)) (|Zero| (#4# 24 T CONST)) (|One| (($) 46 T CONST)) (= (#1# 8 T ELT)) (- (($ $) 30 T ELT) (($ $ $) 29 T ELT)) (+ (($ $ $) 18 T ELT)) (** (($ $ (|PositiveInteger|)) 36 T ELT) (($ $ (|NonNegativeInteger|)) 44 T ELT)) (* (($ (|PositiveInteger|) $) 17 T ELT) (($ (|NonNegativeInteger|) $) 21 T ELT) (($ (|Integer|) $) 31 T ELT) (($ $ $) 35 T ELT))) (((|PAdicIntegerCategory| |#1|) (|Category|) (|Integer|)) (T |PAdicIntegerCategory|)) ((|digits| (*1 *2 *1) (AND (|ofCategory| *1 (|PAdicIntegerCategory| *3)) (|isDomain| *2 (|Stream| (|Integer|))))) (|order| (*1 *2 *1) (AND (|ofCategory| *1 (|PAdicIntegerCategory| *3)) (|isDomain| *2 (|NonNegativeInteger|)))) (|extend| (*1 *1 *1 *2) (AND (|ofCategory| *1 (|PAdicIntegerCategory| *3)) (|isDomain| *2 (|Integer|)))) (|complete| (*1 *1 *1) (|ofCategory| *1 (|PAdicIntegerCategory| *2))) (|modulus| (*1 *2) (AND (|ofCategory| *1 (|PAdicIntegerCategory| *3)) (|isDomain| *2 (|Integer|)))) (|moduloP| (*1 *2 *1) (AND (|ofCategory| *1 (|PAdicIntegerCategory| *3)) (|isDomain| *2 (|Integer|)))) (|quotientByP| (*1 *1 *1) (|ofCategory| *1 (|PAdicIntegerCategory| *2))) (|approximate| (*1 *2 *1 *2) (AND (|ofCategory| *1 (|PAdicIntegerCategory| *3)) (|isDomain| *2 (|Integer|)))) (|sqrt| (*1 *1 *1 *2) (AND (|ofCategory| *1 (|PAdicIntegerCategory| *3)) (|isDomain| *2 (|Integer|)))) (|root| (*1 *1 *2 *3) 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#25# ELT) ((#26# . #29#) NIL #27# ELT) (#18# NIL #27# ELT)) (|removeZeroes| (#9# 35 T ELT) (#30=($ #19# $) 38 T ELT)) (|rem| #31=(#32=($ $ $) NIL T ELT)) (|reducedSystem| ((#33=(|Matrix| #19#) . #34=(#35=(|Matrix| $))) NIL #36=(|has| |#2| (|LinearlyExplicitRingOver| #19#)) ELT) ((#37=(|Record| (|:| |mat| #33#) (|:| |vec| (|Vector| #19#))) . #38=(#35# #39=(|Vector| $))) NIL #36# ELT) ((#40=(|Record| (|:| |mat| #41=(|Matrix| |#2|)) (|:| |vec| (|Vector| |#2|))) . #38#) NIL T ELT) ((#41# . #34#) NIL T ELT)) (|recip| ((#11# $) 64 T ELT)) (|random| (#21# NIL #42=(|has| |#2| (|IntegerNumberSystem|)) ELT)) (|quo| #31#) (|principalIdeal| (((|Record| (|:| |coef| #43=(|List| $)) #44=(|:| |generator| $)) #43#) NIL T ELT)) (|prime?| #4#) (|positive?| #45=(#5# NIL #20# ELT)) (|patternMatch| ((#46=(|PatternMatchResult| #19# . #47=($)) $ #48=(|Pattern| #19#) #46#) NIL (|has| |#2| (|PatternMatchable| #19#)) ELT) ((#49=(|PatternMatchResult| #50=(|Float|) . #47#) $ #51=(|Pattern| #50#) #49#) NIL (|has| 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ELT) (((|Union| (|Record| #61# #62#) #12#) $ $ $) NIL T ELT)) (|exquo| #10#) (|expressIdealMember| (((|Maybe| #43#) #43# $) NIL T ELT)) (|eval| (($ $ #63=(|List| |#2|) #63#) NIL #64=(|has| |#2| (|Evalable| |#2|)) ELT) (($ $ |#2| |#2|) NIL #64# ELT) (($ $ #65=(|Equation| |#2|)) NIL #64# ELT) (($ $ (|List| #65#)) NIL #64# ELT) (($ $ #66=(|List| #24#) #63#) NIL #67=(|has| |#2| (|InnerEvalable| #24# |#2|)) ELT) (($ $ #24# |#2|) NIL #67# ELT)) (|euclideanSize| ((#68=(|NonNegativeInteger|) $) NIL T ELT)) (|elt| (#69=($ $ |#2|) NIL (|has| |#2| (|Eltable| |#2| |#2|)) ELT)) (|divide| (((|Record| (|:| |quotient| $) (|:| |remainder| $)) $ $) NIL T ELT)) (|differentiate| #70=(($ $ #56#) NIL T ELT) #71=(($ $ #56# #68#) NIL T ELT) #72=(($ $ #24#) NIL #73=(|has| |#2| (|PartialDifferentialSpace| #24#)) ELT) #74=(($ $ #66#) NIL #73# ELT) #75=(($ $ #24# #68#) NIL #73# ELT) #76=(($ $ #66# (|List| #68#)) NIL #73# ELT) #77=(#9# NIL #78=(|has| |#2| (|DifferentialSpace|)) ELT) #79=(#80=($ $ #68#) NIL #78# ELT)) (|denominator| #8#) (|denom| #28#) (|convert| ((#48# . #81=($)) NIL (|has| |#2| (|ConvertibleTo| #48#)) ELT) ((#51# . #81#) NIL (|has| |#2| (|ConvertibleTo| #51#)) ELT) ((#82=(|InputForm|) . #81#) NIL (|has| |#2| (|ConvertibleTo| #82#)) ELT) ((#50# . #81#) NIL #83=(|has| |#2| (|RealConstant|)) ELT) (((|DoubleFloat|) . #81#) NIL #83# ELT)) (|continuedFraction| (((|ContinuedFraction| #26#) $) 78 T ELT)) (|conditionP| (((|Union| #39# #12#) #35#) NIL #84=(AND (|has| $ #85=(|CharacteristicNonZero|)) #15#) ELT)) (|coerce| (((|OutputForm|) $) 105 T ELT) (($ #19#) 20 T ELT) #8# (($ #26#) 25 T ELT) (($ |#2|) 19 T ELT) (($ #24#) NIL #25# ELT)) (|charthRoot| (#52# NIL (OR #84# (|has| |#2| #85#)) ELT)) (|characteristic| ((#68#) NIL T CONST)) (|ceiling| #60#) (|before?| #1#) (|associates?| #1#) (|approximate| ((#26# $ #19#) 71 T ELT)) (|annihilate?| #1#) (|abs| (#9# NIL #20# ELT)) (|Zero| (#21# 15 T CONST)) (|One| (#21# 17 T CONST)) (D #70# #71# #72# #74# #75# #76# #77# #79#) (>= #86=(#2# NIL #55# ELT)) (> #86#) (= (#2# 46 T ELT)) (<= #86#) (< #86#) (/ (#32# 24 T ELT) (($ |#2| |#2|) 65 T ELT)) (- (#9# 50 T ELT) (#32# 52 T ELT)) (+ (#32# 48 T ELT)) (** (($ $ #87=(|PositiveInteger|)) NIL T ELT) (#80# NIL T ELT) (($ $ #19#) 61 T ELT)) (* (($ #87# $) NIL T ELT) (($ #68# $) NIL T ELT) (#30# 53 T ELT) (#32# 55 T ELT) (($ $ #26#) NIL T ELT) (($ #26# $) NIL T ELT) (($ |#2| $) 66 T ELT) (#69# NIL T ELT))) +((~= #1=(#2=(#3=(|Boolean|) $ $) NIL T ELT)) (|zero?| #4=(#5=(#3# $) NIL T ELT)) (|wholePart| (#6=(|#2| $) NIL #7=(|has| |#2| (|EuclideanDomain|)) ELT)) (|unitNormal| (((|Record| (|:| |unit| $) (|:| |canonical| $) (|:| |associate| $)) $) NIL T ELT)) (|unitCanonical| #8=(#9=($ $) NIL T ELT)) (|unit?| #4#) (|subtractIfCan| ((#10=(|Maybe| $) $ $) NIL T ELT)) (|squareFreePolynomial| #11=(((|Factored| #12=(|SparseUnivariatePolynomial| $)) #12#) NIL #13=(|has| |#2| (|PolynomialFactorizationExplicit|)) ELT)) (|squareFreePart| #8#) (|squareFree| #14=(((|Factored| $) $) NIL T ELT)) (|solveLinearPolynomialEquation| (((|Union| #15=(|List| #12#) #16="failed") #15# #12#) NIL #13# ELT)) (|sizeLess?| #1#) (|sign| (#17=(#18=(|Integer|) $) NIL #19=(|has| |#2| (|OrderedIntegralDomain|)) ELT)) (|sample| (#20=($) NIL T CONST)) (|retractIfCan| (((|Union| |#2| . #21=(#16#)) . #22=($)) NIL T ELT) (((|Union| #23=(|Symbol|) . #21#) . #22#) NIL #24=(|has| |#2| (|RetractableTo| #23#)) ELT) (((|Union| #25=(|Fraction| #18#) . #21#) . #22#) NIL #26=(|has| |#2| (|RetractableTo| #18#)) ELT) (((|Union| #18# . #21#) . #22#) NIL #26# ELT)) (|retract| #27=(#6# NIL T ELT) ((#23# . #28=($)) NIL #24# ELT) ((#25# . #28#) NIL #26# ELT) (#17# NIL #26# ELT)) (|removeZeroes| (#9# 35 T ELT) (#29=($ #18# $) 38 T ELT)) (|rem| #30=(#31=($ $ $) NIL T ELT)) (|reducedSystem| ((#32=(|Matrix| #18#) . #33=(#34=(|Matrix| $))) NIL #35=(|has| |#2| (|LinearlyExplicitRingOver| #18#)) ELT) ((#36=(|Record| (|:| |mat| #32#) (|:| |vec| (|Vector| #18#))) . #37=(#34# #38=(|Vector| $))) NIL #35# ELT) ((#39=(|Record| (|:| |mat| #40=(|Matrix| |#2|)) (|:| |vec| (|Vector| |#2|))) . #37#) NIL T ELT) ((#40# . #33#) NIL T ELT)) (|recip| ((#41=(|Union| $ #16#) $) 64 T ELT)) (|random| (#20# NIL #42=(|has| |#2| (|IntegerNumberSystem|)) ELT)) (|quo| #30#) (|principalIdeal| (((|Record| (|:| |coef| #43=(|List| $)) #44=(|:| |generator| $)) #43#) NIL T ELT)) (|prime?| #4#) (|positive?| #45=(#5# NIL #19# ELT)) (|patternMatch| ((#46=(|PatternMatchResult| #18# . #47=($)) $ #48=(|Pattern| #18#) #46#) NIL (|has| |#2| (|PatternMatchable| #18#)) ELT) ((#49=(|PatternMatchResult| #50=(|Float|) . #47#) $ #51=(|Pattern| #50#) #49#) NIL (|has| |#2| (|PatternMatchable| #50#)) ELT)) (|opposite?| #1#) (|one?| #4#) (|numerator| #8#) (|numer| #27#) (|nextItem| (#52=(#10# $) NIL #53=(|has| |#2| (|StepThrough|)) ELT)) (|negative?| #45#) (|multiEuclidean| (((|Union| #43# #16#) #43# $) NIL T ELT)) (|min| #54=(#31# NIL #55=(|has| |#2| (|OrderedSet|)) ELT)) (|max| #54#) (|map| (($ #56=(|Mapping| |#2| |#2|) $) NIL T ELT)) (|leftReducedSystem| ((#32# . #57=(#38#)) NIL #35# ELT) ((#36# . #58=(#38# $)) NIL #35# ELT) ((#39# . #58#) NIL T ELT) ((#40# . #57#) NIL T ELT)) (|lcm| #30# #59=(($ #43#) NIL T ELT)) (|latex| (((|String|) $) NIL T ELT)) (|inv| (#9# 60 T ELT)) (|init| (#20# NIL #53# CONST)) (|hash| (((|SingleInteger|) $) NIL T ELT)) (|gcdPolynomial| ((#12# #12# #12#) NIL T ELT)) (|gcd| #30# #59#) (|fractionPart| (#9# NIL #7# ELT)) (|floor| #60=(#6# NIL #42# ELT)) (|factorSquareFreePolynomial| #11#) (|factorPolynomial| #11#) (|factor| #14#) (|extendedEuclidean| (((|Record| #61=(|:| |coef1| $) #62=(|:| |coef2| $) #44#) $ $) NIL T ELT) (((|Union| (|Record| #61# #62#) #16#) $ $ $) NIL T ELT)) (|exquo| ((#41# $ $) NIL T ELT)) (|expressIdealMember| (((|Maybe| #43#) #43# $) NIL T ELT)) (|eval| (($ $ #63=(|List| |#2|) #63#) NIL #64=(|has| |#2| (|Evalable| |#2|)) ELT) (($ $ |#2| |#2|) NIL #64# ELT) (($ $ #65=(|Equation| |#2|)) NIL #64# ELT) (($ $ (|List| #65#)) NIL #64# ELT) (($ $ #66=(|List| #23#) #63#) NIL #67=(|has| |#2| (|InnerEvalable| #23# |#2|)) ELT) (($ $ #23# |#2|) NIL #67# ELT)) (|euclideanSize| ((#68=(|NonNegativeInteger|) $) NIL T ELT)) (|elt| (#69=($ $ |#2|) NIL (|has| |#2| (|Eltable| |#2| |#2|)) ELT)) (|divide| (((|Record| (|:| |quotient| $) (|:| |remainder| $)) $ $) NIL T ELT)) (|differentiate| #70=(($ $ #56#) NIL T ELT) #71=(($ $ #56# #68#) NIL T ELT) #72=(($ $ #23#) NIL #73=(|has| |#2| (|PartialDifferentialSpace| #23#)) ELT) #74=(($ $ #66#) NIL #73# ELT) #75=(($ $ #23# #68#) NIL #73# ELT) #76=(($ $ #66# (|List| #68#)) NIL #73# ELT) #77=(#9# NIL #78=(|has| |#2| (|DifferentialSpace|)) ELT) #79=(#80=($ $ #68#) NIL #78# ELT)) (|denominator| #8#) (|denom| #27#) (|convert| ((#48# . #81=($)) NIL (|has| |#2| (|ConvertibleTo| #48#)) ELT) ((#51# . #81#) NIL (|has| |#2| (|ConvertibleTo| #51#)) ELT) ((#82=(|InputForm|) . #81#) NIL (|has| |#2| (|ConvertibleTo| #82#)) ELT) ((#50# . #81#) NIL #83=(|has| |#2| (|RealConstant|)) ELT) (((|DoubleFloat|) . #81#) NIL #83# ELT)) (|continuedFraction| (((|ContinuedFraction| #25#) $) 78 T ELT)) (|conditionP| (((|Union| #38# #16#) #34#) NIL #84=(AND (|has| $ #85=(|CharacteristicNonZero|)) #13#) ELT)) (|coerce| (((|OutputForm|) $) 105 T ELT) (($ #18#) 20 T ELT) #8# (($ #25#) 25 T ELT) (($ |#2|) 19 T ELT) (($ #23#) NIL #24# ELT)) (|charthRoot| (#52# NIL (OR #84# (|has| |#2| #85#)) ELT)) (|characteristic| ((#68#) NIL T CONST)) (|ceiling| #60#) (|before?| #1#) (|associates?| #1#) (|approximate| ((#25# $ #18#) 71 T ELT)) (|annihilate?| #1#) (|abs| (#9# NIL #19# ELT)) (|Zero| (#20# 15 T CONST)) (|One| (#20# 17 T CONST)) (D #70# #71# #72# #74# #75# #76# #77# #79#) (>= #86=(#2# NIL #55# ELT)) (> #86#) (= (#2# 46 T ELT)) (<= #86#) (< #86#) (/ (#31# 24 T ELT) (($ |#2| |#2|) 65 T ELT)) (- (#9# 50 T ELT) (#31# 52 T ELT)) (+ (#31# 48 T ELT)) (** (($ $ #87=(|PositiveInteger|)) NIL T ELT) (#80# NIL T ELT) (($ $ #18#) 61 T ELT)) (* (($ #87# $) NIL T ELT) (($ #68# $) NIL T ELT) (#29# 53 T ELT) (#31# 55 T ELT) (($ $ #25#) NIL T ELT) (($ #25# $) NIL T ELT) (($ |#2| $) 66 T ELT) (#69# NIL T ELT))) (((|PAdicRationalConstructor| |#1| |#2|) (|Join| (|QuotientFieldCategory| |#2|) (CATEGORY |domain| (SIGNATURE |approximate| (#1=(|Fraction| #2=(|Integer|)) $ #2#)) (SIGNATURE |continuedFraction| ((|ContinuedFraction| #1#) $)) (SIGNATURE |removeZeroes| ($ $)) (SIGNATURE |removeZeroes| ($ #2# $)))) #2# (|PAdicIntegerCategory| |#1|)) (T |PAdicRationalConstructor|)) ((|approximate| (*1 *2 *1 *3) (AND (|ofType| *4 *3) (|isDomain| *2 #1=(|Fraction| #2=(|Integer|))) (|isDomain| *1 (|PAdicRationalConstructor| *4 *5)) (|isDomain| *3 #2#) (|ofCategory| *5 (|PAdicIntegerCategory| *4)))) (|continuedFraction| (*1 *2 *1) (AND (|ofType| *3 #2#) (|isDomain| *2 (|ContinuedFraction| #1#)) #3=(|isDomain| *1 (|PAdicRationalConstructor| *3 *4)) #4=(|ofCategory| *4 (|PAdicIntegerCategory| *3)))) (|removeZeroes| (*1 *1 *1) (AND (|ofType| *2 #2#) (|isDomain| *1 (|PAdicRationalConstructor| *2 *3)) (|ofCategory| *3 (|PAdicIntegerCategory| *2)))) (|removeZeroes| (*1 *1 *2 *1) (AND (|isDomain| *2 #2#) (|ofType| *3 *2) #3# #4#))) ((~= #1=(#2=((|Boolean|) $ $) NIL #3=(AND (|has| |#1| #4=(|SetCategory|)) (|has| |#2| #4#)) ELT)) (|second| ((|#2| $) 12 T ELT)) (|pair| (#5=($ |#1| |#2|) 9 T ELT)) (|latex| (((|String|) $) NIL #3# ELT)) (|hash| (((|SingleInteger|) $) NIL #3# ELT)) (|first| ((|#1| $) 11 T ELT)) (|construct| (#5# 10 T ELT)) (|coerce| ((#6=(|OutputForm|) $) 18 (OR (AND (|has| |#1| #7=(|CoercibleTo| #6#)) (|has| |#2| #7#)) #3#) ELT)) (|before?| #1#) (= (#2# 23 #3# ELT))) @@ -2674,8 +2674,8 @@ NIL (((|PatternFunctions2| |#1| |#2|) (CATEGORY |package| (SIGNATURE |map| ((|Pattern| |#2|) (|Mapping| |#2| |#1|) (|Pattern| |#1|)))) #1=(|SetCategory|) #1#) (T |PatternFunctions2|)) ((|map| (*1 *2 *3 *4) (AND (|isDomain| *3 (|Mapping| *6 *5)) (|isDomain| *4 (|Pattern| *5)) (|ofCategory| *5 #1=(|SetCategory|)) (|ofCategory| *6 #1#) (|isDomain| *2 (|Pattern| *6)) (|isDomain| *1 (|PatternFunctions2| *5 *6))))) ((~= #1=(#2=(#3=(|Boolean|) $ $) NIL T ELT)) (|varList| (((|List| |#1|) $) 20 T ELT)) (|retractable?| ((#3# $) 49 T ELT)) (|retractIfCan| (((|Union| #4=(|LyndonWord| |#1|) "failed") $) 55 T ELT)) (|retract| (#5=(#4# $) 53 T ELT)) (|rest| (($ $) 24 T ELT)) (|min| #6=(($ $ $) NIL T ELT)) (|max| #6#) (|length| (((|NonNegativeInteger|) $) 60 T ELT)) (|latex| (((|String|) $) NIL T ELT)) (|hash| (((|SingleInteger|) $) NIL T ELT)) (|first| (#5# 22 T ELT)) (|coerce| (((|OutputForm|) $) 47 T ELT) (($ #4#) 27 T ELT) (((|OrderedFreeMonoid| |#1|) $) 36 T ELT) (($ |#1|) 26 T ELT)) (|before?| #1#) (|One| (($) 11 T CONST)) (|ListOfTerms| (((|List| #4#) $) 28 T ELT)) (>= #1#) (> #1#) (= (#2# 14 T ELT)) (<= #1#) (< (#2# 66 T ELT))) -(((|PoincareBirkhoffWittLyndonBasis| |#1|) (|Join| #1=(|OrderedSet|) (|RetractableTo| #2=(|LyndonWord| |#1|)) (CATEGORY |domain| (SIGNATURE |One| ($) |constant|) (SIGNATURE |coerce| ((|OrderedFreeMonoid| |#1|) $)) (SIGNATURE |coerce| ($ |#1|)) (SIGNATURE |first| (#2# $)) (SIGNATURE |length| ((|NonNegativeInteger|) $)) (SIGNATURE |ListOfTerms| ((|List| #2#) $)) (SIGNATURE |rest| ($ $)) (SIGNATURE |retractable?| ((|Boolean|) $)) (SIGNATURE |varList| ((|List| |#1|) $)))) #1#) (T |PoincareBirkhoffWittLyndonBasis|)) -((|One| (*1 *1) #1=(AND (|isDomain| *1 (|PoincareBirkhoffWittLyndonBasis| *2)) (|ofCategory| *2 #2=(|OrderedSet|)))) (|coerce| #3=(*1 *2 *1) (AND (|isDomain| *2 (|OrderedFreeMonoid| *3)) #4=(|isDomain| *1 (|PoincareBirkhoffWittLyndonBasis| *3)) #5=(|ofCategory| *3 #2#))) (|coerce| (*1 *1 *2) #1#) (|first| #3# (AND (|isDomain| *2 #6=(|LyndonWord| *3)) #4# #5#)) (|length| #3# (AND (|isDomain| *2 (|NonNegativeInteger|)) #4# #5#)) (|ListOfTerms| #3# (AND (|isDomain| *2 (|List| #6#)) #4# #5#)) (|rest| (*1 *1 *1) #1#) (|retractable?| #3# (AND (|isDomain| *2 (|Boolean|)) #4# #5#)) (|varList| #3# (AND (|isDomain| *2 (|List| *3)) #4# #5#))) +(((|PoincareBirkhoffWittLyndonBasis| |#1|) (|Join| #1=(|OrderedSet|) (|RetractableTo| #2=(|LyndonWord| |#1|)) (|CoercibleTo| (|OrderedFreeMonoid| |#1|)) (CATEGORY |domain| (SIGNATURE |One| ($) |constant|) (SIGNATURE |coerce| ($ |#1|)) (SIGNATURE |first| (#2# $)) (SIGNATURE |length| ((|NonNegativeInteger|) $)) (SIGNATURE |ListOfTerms| ((|List| #2#) $)) (SIGNATURE |rest| ($ $)) (SIGNATURE |retractable?| ((|Boolean|) $)) (SIGNATURE |varList| ((|List| |#1|) $)))) #1#) (T |PoincareBirkhoffWittLyndonBasis|)) +((|One| (*1 *1) #1=(AND (|isDomain| *1 (|PoincareBirkhoffWittLyndonBasis| *2)) (|ofCategory| *2 #2=(|OrderedSet|)))) (|coerce| (*1 *1 *2) #1#) (|first| #3=(*1 *2 *1) (AND (|isDomain| *2 #4=(|LyndonWord| *3)) #5=(|isDomain| *1 (|PoincareBirkhoffWittLyndonBasis| *3)) #6=(|ofCategory| *3 #2#))) (|length| #3# (AND (|isDomain| *2 (|NonNegativeInteger|)) #5# #6#)) (|ListOfTerms| #3# (AND (|isDomain| *2 (|List| #4#)) #5# #6#)) (|rest| (*1 *1 *1) #1#) (|retractable?| #3# (AND (|isDomain| *2 (|Boolean|)) #5# #6#)) (|varList| #3# (AND (|isDomain| *2 (|List| *3)) #5# #6#))) ((|compose| ((|#1| |#1| |#1|) 19 T ELT))) (((|PolynomialComposition| |#1| |#2|) (CATEGORY |package| (SIGNATURE |compose| (|#1| |#1| |#1|))) (|UnivariatePolynomialCategory| |#2|) (|Ring|)) (T |PolynomialComposition|)) ((|compose| (*1 *2 *2 *2) (AND (|ofCategory| *3 (|Ring|)) (|isDomain| *1 (|PolynomialComposition| *2 *3)) (|ofCategory| *2 (|UnivariatePolynomialCategory| *3))))) @@ -2690,12 +2690,12 @@ NIL ((|rightFactorCandidate| ((|#1| |#1| #1=(|NonNegativeInteger|)) 26 T ELT)) (|leftFactor| (((|Union| |#1| #2="failed") |#1| |#1|) 23 T ELT)) (|decompose| (((|Union| (|Record| (|:| |left| |#1|) (|:| |right| |#1|)) #2#) |#1| #1# #1#) 29 T ELT) (((|List| |#1|) |#1|) 38 T ELT))) (((|PolynomialDecomposition| |#1| |#2|) (CATEGORY |package| (SIGNATURE |decompose| ((|List| |#1|) |#1|)) (SIGNATURE |decompose| ((|Union| (|Record| (|:| |left| |#1|) (|:| |right| |#1|)) #1="failed") |#1| #2=(|NonNegativeInteger|) #2#)) (SIGNATURE |leftFactor| ((|Union| |#1| #1#) |#1| |#1|)) (SIGNATURE |rightFactorCandidate| (|#1| |#1| #2#))) (|UnivariatePolynomialCategory| |#2|) (|Field|)) (T |PolynomialDecomposition|)) ((|rightFactorCandidate| (*1 *2 *2 *3) (AND (|isDomain| *3 #1=(|NonNegativeInteger|)) #2=(|ofCategory| *4 #3=(|Field|)) (|isDomain| *1 (|PolynomialDecomposition| *2 *4)) (|ofCategory| *2 #4=(|UnivariatePolynomialCategory| *4)))) (|leftFactor| (*1 *2 *2 *2) (|partial| AND (|ofCategory| *3 #3#) (|isDomain| *1 (|PolynomialDecomposition| *2 *3)) (|ofCategory| *2 (|UnivariatePolynomialCategory| *3)))) (|decompose| (*1 *2 *3 *4 *4) (|partial| AND (|isDomain| *4 #1#) (|ofCategory| *5 #3#) (|isDomain| *2 (|Record| (|:| |left| *3) (|:| |right| *3))) (|isDomain| *1 (|PolynomialDecomposition| *3 *5)) (|ofCategory| *3 (|UnivariatePolynomialCategory| *5)))) (|decompose| (*1 *2 *3) (AND #2# (|isDomain| *2 (|List| *3)) (|isDomain| *1 (|PolynomialDecomposition| *3 *4)) (|ofCategory| *3 #4#)))) -((~= (#1=((|Boolean|) $ $) 7 T ELT)) (|zero?| ((#2=(|Boolean|) $) 22 T ELT)) (|subtractIfCan| (((|Union| $ "failed") $ $) 26 T ELT)) (|sample| (#3=($) 23 T CONST)) (|opposite?| ((#2# $ $) 20 T ELT)) (|latex| (((|String|) $) 11 T ELT)) (|hash| (((|SingleInteger|) $) 12 T ELT)) (|differentiate| (($ $ (|List| |#2|) . #4=((|List| #5=(|NonNegativeInteger|)))) 45 T ELT) (($ $ |#2| . #6=(#5#)) 44 T ELT) (($ $ (|List| |#2|)) 43 T ELT) (($ $ |#2|) 41 T ELT)) (|coerce| (((|OutputForm|) $) 13 T ELT)) (|before?| (#1# 6 T ELT)) (|Zero| (#3# 24 T CONST)) (D (($ $ (|List| |#2|) . #4#) 48 T ELT) (($ $ |#2| . #6#) 47 T ELT) (($ $ (|List| |#2|)) 46 T ELT) (($ $ |#2|) 42 T ELT)) (= (#1# 8 T ELT)) (- (($ $) 29 T ELT) (($ $ $) 28 T ELT)) (+ (($ $ $) 18 T ELT)) (* (($ (|PositiveInteger|) $) 17 T ELT) (($ (|NonNegativeInteger|) $) 21 T ELT) (($ (|Integer|) . #7=($)) 30 T ELT) (($ |#1| . #7#) 33 T ELT) (($ $ |#1|) 37 T ELT))) +((~= (#1=((|Boolean|) $ $) 7 T ELT)) (|zero?| ((#2=(|Boolean|) $) 22 T ELT)) (|subtractIfCan| (((|Maybe| $) $ $) 26 T ELT)) (|sample| (#3=($) 23 T CONST)) (|opposite?| ((#2# $ $) 20 T ELT)) (|latex| (((|String|) $) 11 T ELT)) (|hash| (((|SingleInteger|) $) 12 T ELT)) (|differentiate| (($ $ (|List| |#2|) . #4=((|List| #5=(|NonNegativeInteger|)))) 46 T ELT) (($ $ |#2| . #6=(#5#)) 45 T ELT) (($ $ (|List| |#2|)) 44 T ELT) (($ $ |#2|) 42 T ELT)) (|coerce| (((|OutputForm|) $) 13 T ELT)) (|before?| (#1# 6 T ELT)) (|Zero| (#3# 24 T CONST)) (D (($ $ (|List| |#2|) . #4#) 49 T ELT) (($ $ |#2| . #6#) 48 T ELT) (($ $ (|List| |#2|)) 47 T ELT) (($ $ |#2|) 43 T ELT)) (= (#1# 8 T ELT)) (- (($ $) 30 T ELT) (($ $ $) 29 T ELT)) (+ (($ $ $) 18 T ELT)) (* (($ (|PositiveInteger|) $) 17 T ELT) (($ (|NonNegativeInteger|) $) 21 T ELT) (($ (|Integer|) . #7=($)) 31 T ELT) (($ |#1| . #7#) 34 T ELT) (($ $ |#1|) 38 T ELT))) (((|PartialDifferentialModule| |#1| |#2|) (|Category|) (|Ring|) (|BasicType|)) (T |PartialDifferentialModule|)) NIL (|Join| (|BiModule| |t#1| |t#1|) (|PartialDifferentialSpace| |t#2|) (CATEGORY |package| (IF (|has| |t#1| (|CommutativeRing|)) (ATTRIBUTE (|Module| |t#1|)) |%noBranch|))) (((|AbelianGroup|) . T) ((|AbelianMonoid|) . T) ((|AbelianSemiGroup|) . T) ((|BasicType|) . T) ((|BiModule| |#1| |#1|) . T) ((|CancellationAbelianMonoid|) . T) ((|CoercibleTo| (|OutputForm|)) . T) ((|Join|) . T) ((|LeftLinearSet| (|Integer|)) . T) ((|LeftLinearSet| |#1|) . T) ((|LeftModule| |#1|) . T) ((|LinearSet| |#1|) |has| |#1| (|CommutativeRing|)) ((|Module| |#1|) |has| |#1| (|CommutativeRing|)) ((|PartialDifferentialDomain| $ |#2|) . T) ((|PartialDifferentialSpace| |#2|) . T) ((|RightLinearSet| |#1|) . T) ((|RightModule| |#1|) . T) ((|SetCategory|) . T) ((|Type|) . T)) -((~= (#1=((|Boolean|) $ $) 7 T ELT)) (|zero?| ((#2=(|Boolean|) $) 22 T ELT)) (|subtractIfCan| (((|Union| $ "failed") $ $) 26 T ELT)) (|sample| (#3=($) 23 T CONST)) (|recip| (((|Union| $ "failed") $) 42 T ELT)) (|opposite?| ((#2# $ $) 20 T ELT)) (|one?| (((|Boolean|) $) 44 T ELT)) (|latex| (((|String|) $) 11 T ELT)) (|hash| (((|SingleInteger|) $) 12 T ELT)) (|differentiate| (($ $ (|List| |#1|) . #4=((|List| #5=(|NonNegativeInteger|)))) 52 T ELT) (($ $ |#1| . #6=(#5#)) 51 T ELT) (($ $ (|List| |#1|)) 50 T ELT) (($ $ |#1|) 48 T ELT)) (|coerce| (((|OutputForm|) $) 13 T ELT) (($ (|Integer|)) 41 T ELT)) (|characteristic| (((|NonNegativeInteger|)) 40 T CONST)) (|before?| (#1# 6 T ELT)) (|annihilate?| (((|Boolean|) $ $) 33 T ELT)) (|Zero| (#3# 24 T CONST)) (|One| (($) 45 T CONST)) (D (($ $ (|List| |#1|) . #4#) 55 T ELT) (($ $ |#1| . #6#) 54 T ELT) (($ $ (|List| |#1|)) 53 T ELT) (($ $ |#1|) 49 T ELT)) (= (#1# 8 T ELT)) (- (($ $) 29 T ELT) (($ $ $) 28 T ELT)) (+ (($ $ $) 18 T ELT)) (** (($ $ (|PositiveInteger|)) 35 T ELT) (($ $ (|NonNegativeInteger|)) 43 T ELT)) (* (($ (|PositiveInteger|) $) 17 T ELT) (($ (|NonNegativeInteger|) $) 21 T ELT) (($ (|Integer|) $) 30 T ELT) (($ $ $) 34 T ELT))) +((~= (#1=((|Boolean|) $ $) 7 T ELT)) (|zero?| ((#2=(|Boolean|) $) 22 T ELT)) (|subtractIfCan| (((|Maybe| $) $ $) 26 T ELT)) (|sample| (#3=($) 23 T CONST)) (|recip| (((|Union| $ "failed") $) 43 T ELT)) (|opposite?| ((#2# $ $) 20 T ELT)) (|one?| (((|Boolean|) $) 45 T ELT)) (|latex| (((|String|) $) 11 T ELT)) (|hash| (((|SingleInteger|) $) 12 T ELT)) (|differentiate| (($ $ (|List| |#1|) . #4=((|List| #5=(|NonNegativeInteger|)))) 53 T ELT) (($ $ |#1| . #6=(#5#)) 52 T ELT) (($ $ (|List| |#1|)) 51 T ELT) (($ $ |#1|) 49 T ELT)) (|coerce| (((|OutputForm|) $) 13 T ELT) (($ (|Integer|)) 42 T ELT)) (|characteristic| (((|NonNegativeInteger|)) 41 T CONST)) (|before?| (#1# 6 T ELT)) (|annihilate?| (((|Boolean|) $ $) 34 T ELT)) (|Zero| (#3# 24 T CONST)) (|One| (($) 46 T CONST)) (D (($ $ (|List| |#1|) . #4#) 56 T ELT) (($ $ |#1| . #6#) 55 T ELT) (($ $ (|List| |#1|)) 54 T ELT) (($ $ |#1|) 50 T ELT)) (= (#1# 8 T ELT)) (- (($ $) 30 T ELT) (($ $ $) 29 T ELT)) (+ (($ $ $) 18 T ELT)) (** (($ $ (|PositiveInteger|)) 36 T ELT) (($ $ (|NonNegativeInteger|)) 44 T ELT)) (* (($ (|PositiveInteger|) $) 17 T ELT) (($ (|NonNegativeInteger|) $) 21 T ELT) (($ (|Integer|) $) 31 T ELT) (($ $ $) 35 T ELT))) (((|PartialDifferentialRing| |#1|) (|Category|) (|BasicType|)) (T |PartialDifferentialRing|)) NIL (|Join| (|Ring|) (|PartialDifferentialSpace| |t#1|)) @@ -2722,22 +2722,22 @@ NIL ((|cycle| (*1 *1 *2) (AND (|isDomain| *2 (|List| *3)) (|ofCategory| *3 (|SetCategory|)) (|ofCategory| *1 (|PermutationCategory| *3)))) (|cycles| (*1 *1 *2) (AND (|isDomain| *2 (|List| (|List| *3))) (|ofCategory| *3 (|SetCategory|)) (|ofCategory| *1 (|PermutationCategory| *3)))) (|support| (*1 *2 *1) (AND (|ofCategory| *1 (|PermutationCategory| *3)) (|ofCategory| *3 (|SetCategory|)) (|isDomain| *2 (|Set| *3)))) (|orbit| (*1 *2 *1 *3) (AND (|ofCategory| *1 (|PermutationCategory| *3)) (|ofCategory| *3 (|SetCategory|)) (|isDomain| *2 (|Set| *3)))) (< (*1 *2 *1 *1) (AND (|ofCategory| *1 (|PermutationCategory| *3)) (|ofCategory| *3 (|SetCategory|)) (|isDomain| *2 (|Boolean|))))) (|Join| (|Group|) (|Eltable| |t#1| |t#1|) (CATEGORY |domain| (SIGNATURE |cycle| ($ (|List| |t#1|))) (SIGNATURE |cycles| ($ (|List| (|List| |t#1|)))) (SIGNATURE |support| ((|Set| |t#1|) $)) (SIGNATURE |orbit| ((|Set| |t#1|) $ |t#1|)) (SIGNATURE < ((|Boolean|) $ $)) (IF (|has| |t#1| (|OrderedSet|)) (ATTRIBUTE (|OrderedSet|)) |%noBranch|) (IF (|has| |t#1| (|Finite|)) (ATTRIBUTE (|OrderedSet|)) |%noBranch|))) (((|BasicType|) . T) ((|CoercibleTo| (|OutputForm|)) . T) ((|Eltable| |#1| |#1|) . T) ((|Group|) . T) ((|Join|) . T) ((|Monoid|) . T) ((|OrderedSet|) OR (|has| |#1| (|OrderedSet|)) (|has| |#1| (|Finite|))) ((|OrderedType|) OR (|has| |#1| (|OrderedSet|)) (|has| |#1| (|Finite|))) ((|SemiGroup|) . T) ((|SetCategory|) . T) ((|Type|) . T)) -((~= #1=(#2=(#3=(|Boolean|) $ $) NIL T ELT)) (|wordsForStrongGenerators| (((|List| #4=(|List| #5=(|NonNegativeInteger|))) $) 163 T ELT)) (|wordInStrongGenerators| (#6=(#4# #7=(|Permutation| |#1|) $) 191 T ELT)) (|wordInGenerators| (#6# 192 T ELT)) (|support| ((#8=(|Set| |#1|) $) 155 T ELT)) (|strongGenerators| (#9=(#10=(|List| #7#) $) 152 T ELT)) (|random| ((#7# $ #11=(|Integer|)) 157 T ELT) ((#7# $) 158 T ELT)) (|permutationGroup| (#12=($ #10#) 165 T ELT)) (|order| (#13=(#5# $) 159 T ELT)) (|orbits| ((#14=(|Set| #8#) $) 189 T ELT)) (|orbit| ((#8# $ |#1|) 180 T ELT) ((#14# $ #8#) 201 T ELT) (((|Set| #15=(|List| |#1|)) $ #15#) 204 T ELT)) (|member?| ((#3# #7# $) 140 T ELT)) (|latex| (((|String|) $) NIL T ELT)) (|initializeGroupForWordProblem| ((#16=(|Void|) $) 145 T ELT) ((#16# $ #11# #11#) 205 T ELT)) (|hash| (((|SingleInteger|) $) NIL T ELT)) (|generators| (#9# 146 T ELT)) (|elt| ((#7# $ #5#) 153 T ELT)) (|degree| (#13# 160 T ELT)) (|coerce| (((|OutputForm|) $) 177 T ELT) (#9# 28 T ELT) (#12# 164 T ELT)) (|before?| #1#) (|base| ((#15# $) 162 T ELT)) (= (#2# 198 T ELT)) (<= (#2# 195 T ELT)) (< (#2# 194 T ELT))) -(((|PermutationGroup| |#1|) (|Join| #1=(|SetCategory|) (CATEGORY |domain| (SIGNATURE |coerce| #2=(#3=(|List| #4=(|Permutation| |#1|)) $)) (SIGNATURE |generators| #2#) (SIGNATURE |elt| (#4# $ #5=(|NonNegativeInteger|))) (SIGNATURE |random| (#4# $ #6=(|Integer|))) (SIGNATURE |random| (#4# $)) (SIGNATURE |order| #7=(#5# $)) (SIGNATURE |degree| #7#) (SIGNATURE |base| (#8=(|List| |#1|) $)) (SIGNATURE |strongGenerators| #2#) (SIGNATURE |wordsForStrongGenerators| ((|List| #9=(|List| #5#)) $)) (SIGNATURE |coerce| #10=($ #3#)) (SIGNATURE |permutationGroup| #10#) (SIGNATURE |orbit| (#11=(|Set| |#1|) $ |#1|)) (SIGNATURE |orbits| (#12=(|Set| #11#) $)) (SIGNATURE |orbit| (#12# $ #11#)) (SIGNATURE |orbit| ((|Set| #8#) $ #8#)) (SIGNATURE |member?| (#13=(|Boolean|) #4# $)) (SIGNATURE |wordInStrongGenerators| #14=(#9# #4# $)) (SIGNATURE |wordInGenerators| #14#) (SIGNATURE |support| (#11# $)) (SIGNATURE < #15=(#13# $ $)) (SIGNATURE <= #15#) (SIGNATURE |initializeGroupForWordProblem| (#16=(|Void|) $)) (SIGNATURE |initializeGroupForWordProblem| (#16# $ #6# #6#)))) #1#) (T |PermutationGroup|)) -((|coerce| #1=(*1 *2 *1) #2=(AND #3=(|isDomain| *2 (|List| #4=(|Permutation| *3))) #5=(|isDomain| *1 (|PermutationGroup| *3)) #6=(|ofCategory| *3 #7=(|SetCategory|)))) (|generators| #1# #2#) (|elt| #8=(*1 *2 *1 *3) (AND (|isDomain| *3 #9=(|NonNegativeInteger|)) #10=(|isDomain| *2 #11=(|Permutation| *4)) #12=(|isDomain| *1 (|PermutationGroup| *4)) #13=(|ofCategory| *4 #7#))) (|random| #8# (AND #14=(|isDomain| *3 (|Integer|)) #10# #12# #13#)) (|random| #1# (AND (|isDomain| *2 #4#) #5# #6#)) (|order| #1# #15=(AND (|isDomain| *2 #9#) #5# #6#)) (|degree| #1# #15#) (|base| #1# (AND (|isDomain| *2 (|List| *3)) #5# #6#)) (|strongGenerators| #1# #2#) (|wordsForStrongGenerators| #1# (AND (|isDomain| *2 (|List| #16=(|List| #9#))) #5# #6#)) (|coerce| #17=(*1 *1 *2) #18=(AND #3# #6# #5#)) (|permutationGroup| #17# #18#) (|orbit| #8# #19=(AND (|isDomain| *2 #20=(|Set| *3)) #5# #6#)) (|orbits| #1# (AND (|isDomain| *2 (|Set| #20#)) #5# #6#)) (|orbit| #8# (AND #13# (|isDomain| *2 (|Set| #21=(|Set| *4))) #12# (|isDomain| *3 #21#))) (|orbit| #8# (AND #13# (|isDomain| *2 (|Set| #22=(|List| *4))) #12# (|isDomain| *3 #22#))) (|member?| #23=(*1 *2 *3 *1) (AND #24=(|isDomain| *3 #11#) #13# #25=(|isDomain| *2 (|Boolean|)) #12#)) (|wordInStrongGenerators| #23# #26=(AND #24# #13# (|isDomain| *2 #16#) #12#)) (|wordInGenerators| #23# #26#) (|support| #1# #19#) (< #27=(*1 *2 *1 *1) #28=(AND #25# #5# #6#)) (<= #27# #28#) (|initializeGroupForWordProblem| #1# (AND #29=(|isDomain| *2 (|Void|)) #5# #6#)) (|initializeGroupForWordProblem| (*1 *2 *1 *3 *3) (AND #14# #29# #12# #13#))) -((~= #1=((#2=(|Boolean|) $ $) NIL T ELT)) (|zero?| #3=(#4=(#2# $) NIL T ELT)) (|unitNormal| (((|Record| (|:| |unit| $) (|:| |canonical| $) (|:| |associate| $)) $) NIL T ELT)) (|unitCanonical| #5=(#6=($ $) NIL T ELT)) (|unit?| #3#) (|transcendent?| #3#) (|transcendenceDegree| #7=(#8=(#9=(|NonNegativeInteger|)) NIL T ELT)) (|trace| #10=(#11=($ $ #12=(|PositiveInteger|)) NIL #13=(|has| $ (|Finite|)) ELT) #5#) (|tableForDiscreteLogarithm| (((|Table| #12# #9#) #14=(|Integer|)) NIL T ELT)) (|subtractIfCan| #15=((#16=(|Union| $ #17="failed") $ $) NIL T ELT)) (|squareFreePart| #5#) (|squareFree| #18=(((|Factored| $) $) NIL T ELT)) (|sizeLess?| #1#) (|size| #7#) (|sample| #19=(#20=($) NIL T CONST)) (|retractIfCan| #21=((#16# $) NIL T ELT)) (|retract| #5#) (|represents| (($ #22=(|Vector| $)) NIL T ELT)) (|representationType| (((|Union| "prime" "polynomial" "normal" "cyclic")) NIL T ELT)) (|rem| #23=(($ $ $) NIL T ELT)) (|recip| #21#) (|random| #24=(#20# NIL T ELT)) (|quo| #23#) (|principalIdeal| (((|Record| (|:| |coef| #25=(|List| $)) #26=(|:| |generator| $)) #25#) NIL T ELT)) (|primitiveElement| #24#) (|primitive?| #3#) (|primeFrobenius| #5# #27=(#28=($ $ #9#) NIL T ELT)) (|prime?| 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(|PositiveInteger|)) (T |PrimeField|)) NIL ((|solveLinearPolynomialEquationByRecursion| ((#1=(|Union| #2=(|List| #3=(|SparseUnivariatePolynomial| |#4|)) "failed") #2# #3#) 164 T ELT)) (|randomR| ((|#1|) 101 T ELT)) (|factorSquareFreeByRecursion| (#4=(#5=(|Factored| #3#) #3#) 173 T ELT)) (|factorSFBRlcUnit| ((#5# (|List| |#3|) #3#) 83 T ELT)) (|factorByRecursion| (#4# 183 T ELT)) (|bivariateSLPEBR| ((#1# #2# #3# |#3|) 117 T ELT))) (((|PolynomialFactorizationByRecursion| |#1| |#2| |#3| |#4|) (CATEGORY |package| (SIGNATURE |solveLinearPolynomialEquationByRecursion| (#1=(|Union| #2=(|List| #3=(|SparseUnivariatePolynomial| |#4|)) "failed") #2# #3#)) (SIGNATURE |factorByRecursion| #4=(#5=(|Factored| #3#) #3#)) (SIGNATURE |factorSquareFreeByRecursion| #4#) (SIGNATURE |randomR| (|#1|)) (SIGNATURE |bivariateSLPEBR| (#1# #2# #3# |#3|)) (SIGNATURE |factorSFBRlcUnit| (#5# (|List| |#3|) #3#))) (|PolynomialFactorizationExplicit|) (|OrderedAbelianMonoidSup|) (|OrderedSet|) (|PolynomialCategory| |#1| |#2| |#3|)) (T |PolynomialFactorizationByRecursion|)) ((|factorSFBRlcUnit| (*1 *2 *3 *4) (AND (|isDomain| *3 (|List| *7)) (|ofCategory| *7 #1=(|OrderedSet|)) #2=(|ofCategory| *5 #3=(|PolynomialFactorizationExplicit|)) #4=(|ofCategory| *6 #5=(|OrderedAbelianMonoidSup|)) (|ofCategory| *8 (|PolynomialCategory| *5 *6 *7)) (|isDomain| *2 (|Factored| #6=(|SparseUnivariatePolynomial| *8))) (|isDomain| *1 (|PolynomialFactorizationByRecursion| *5 *6 *7 *8)) (|isDomain| *4 #6#))) (|bivariateSLPEBR| (*1 *2 *2 *3 *4) (|partial| AND #7=(|isDomain| *2 (|List| #8=(|SparseUnivariatePolynomial| *7))) #9=(|isDomain| *3 #8#) (|ofCategory| *7 (|PolynomialCategory| *5 *6 *4)) #2# #4# #10=(|ofCategory| *4 #1#) (|isDomain| *1 (|PolynomialFactorizationByRecursion| *5 *6 *4 *7)))) (|randomR| (*1 *2) (AND (|ofCategory| *3 #5#) #10# (|ofCategory| *2 #3#) (|isDomain| *1 (|PolynomialFactorizationByRecursion| *2 *3 *4 *5)) (|ofCategory| *5 (|PolynomialCategory| *2 *3 *4)))) (|factorSquareFreeByRecursion| #11=(*1 *2 *3) #12=(AND #13=(|ofCategory| *4 #3#) #14=(|ofCategory| *5 #5#) #15=(|ofCategory| *6 #1#) #16=(|ofCategory| *7 (|PolynomialCategory| *4 *5 *6)) (|isDomain| *2 (|Factored| #8#)) #17=(|isDomain| *1 (|PolynomialFactorizationByRecursion| *4 *5 *6 *7)) #9#)) (|factorByRecursion| #11# #12#) (|solveLinearPolynomialEquationByRecursion| (*1 *2 *2 *3) (|partial| AND #7# #9# #16# #13# #14# #15# #17#))) -((|solveLinearPolynomialEquationByRecursion| (((|Union| #1=(|List| #2=(|SparseUnivariatePolynomial| |#2|)) "failed") #1# #2#) 39 T ELT)) (|randomR| ((|#1|) 71 T ELT)) (|factorSquareFreeByRecursion| (#3=((|Factored| #2#) #2#) 125 T ELT)) (|factorSFBRlcUnit| (#3# 109 T ELT)) (|factorByRecursion| (#3# 136 T ELT))) +((|solveLinearPolynomialEquationByRecursion| (((|Union| #1=(|List| #2=(|SparseUnivariatePolynomial| |#2|)) "failed") #1# #2#) 39 T ELT)) (|randomR| ((|#1|) 71 T ELT)) (|factorSquareFreeByRecursion| (#3=((|Factored| #2#) #2#) 124 T ELT)) (|factorSFBRlcUnit| (#3# 109 T ELT)) (|factorByRecursion| (#3# 135 T ELT))) (((|PolynomialFactorizationByRecursionUnivariate| |#1| |#2|) (CATEGORY |package| (SIGNATURE |solveLinearPolynomialEquationByRecursion| ((|Union| #1=(|List| #2=(|SparseUnivariatePolynomial| |#2|)) "failed") #1# #2#)) (SIGNATURE |factorByRecursion| #3=((|Factored| #2#) #2#)) (SIGNATURE |factorSquareFreeByRecursion| #3#) (SIGNATURE |randomR| (|#1|)) (SIGNATURE |factorSFBRlcUnit| #3#)) (|PolynomialFactorizationExplicit|) (|UnivariatePolynomialCategory| |#1|)) (T |PolynomialFactorizationByRecursionUnivariate|)) ((|factorSFBRlcUnit| #1=(*1 *2 *3) #2=(AND #3=(|ofCategory| *4 #4=(|PolynomialFactorizationExplicit|)) #5=(|ofCategory| *5 (|UnivariatePolynomialCategory| *4)) (|isDomain| *2 (|Factored| #6=(|SparseUnivariatePolynomial| *5))) #7=(|isDomain| *1 (|PolynomialFactorizationByRecursionUnivariate| *4 *5)) #8=(|isDomain| *3 #6#))) (|randomR| (*1 *2) (AND (|ofCategory| *2 #4#) (|isDomain| *1 (|PolynomialFactorizationByRecursionUnivariate| *2 *3)) (|ofCategory| *3 (|UnivariatePolynomialCategory| *2)))) (|factorSquareFreeByRecursion| #1# #2#) (|factorByRecursion| #1# #2#) (|solveLinearPolynomialEquationByRecursion| (*1 *2 *2 *3) (|partial| AND (|isDomain| *2 (|List| #6#)) #8# #5# #3# #7#))) ((|solveLinearPolynomialEquation| (((|Union| #1=(|List| #2=(|SparseUnivariatePolynomial| $)) "failed") #1# #2#) 46 T ELT)) (|gcdPolynomial| ((#2# #2# #2#) 18 T ELT)) (|charthRoot| (((|Maybe| $) $) 40 T ELT))) (((|PolynomialFactorizationExplicit&| |#1|) (CATEGORY |package| (SIGNATURE |charthRoot| ((|Maybe| |#1|) |#1|)) (SIGNATURE |solveLinearPolynomialEquation| ((|Union| #1=(|List| #2=(|SparseUnivariatePolynomial| |#1|)) "failed") #1# #2#)) (SIGNATURE |gcdPolynomial| (#2# #2# #2#))) (|PolynomialFactorizationExplicit|)) (T |PolynomialFactorizationExplicit&|)) NIL -((~= (#1=((|Boolean|) $ $) 7 T ELT)) (|zero?| ((#2=(|Boolean|) $) 22 T ELT)) (|unitNormal| (((|Record| (|:| |unit| $) (|:| |canonical| $) (|:| |associate| $)) $) 55 T ELT)) (|unitCanonical| (($ $) 54 T ELT)) (|unit?| ((#3=(|Boolean|) $) 52 T ELT)) (|subtractIfCan| (((|Union| $ "failed") $ $) 26 T ELT)) (|squareFreePolynomial| (((|Factored| (|SparseUnivariatePolynomial| $)) (|SparseUnivariatePolynomial| $)) 75 T ELT)) (|squareFreePart| (($ $) 66 T ELT)) (|squareFree| (#4=((|Factored| $) $) 67 T ELT)) (|solveLinearPolynomialEquation| (((|Union| (|List| (|SparseUnivariatePolynomial| $)) "failed") (|List| (|SparseUnivariatePolynomial| $)) (|SparseUnivariatePolynomial| $)) 72 T ELT)) (|sample| (#5=($) 23 T CONST)) (|recip| (((|Union| $ "failed") $) 42 T ELT)) (|prime?| (((|Boolean|) $) 68 T ELT)) (|opposite?| ((#2# $ $) 20 T ELT)) (|one?| (((|Boolean|) $) 44 T ELT)) (|lcm| (#6=($ $ $) 60 T ELT) (#7=($ (|List| $)) 59 T ELT)) (|latex| (((|String|) $) 11 T ELT)) (|hash| (((|SingleInteger|) $) 12 T ELT)) (|gcdPolynomial| ((#8=(|SparseUnivariatePolynomial| $) #8# #8#) 58 T ELT)) (|gcd| (#6# 62 T ELT) (#7# 61 T ELT)) (|factorSquareFreePolynomial| (((|Factored| (|SparseUnivariatePolynomial| $)) (|SparseUnivariatePolynomial| $)) 73 T ELT)) (|factorPolynomial| (((|Factored| (|SparseUnivariatePolynomial| $)) (|SparseUnivariatePolynomial| $)) 74 T ELT)) (|factor| (#4# 65 T ELT)) (|exquo| (((|Union| $ "failed") $ $) 56 T ELT)) (|conditionP| (((|Union| (|Vector| $) "failed") (|Matrix| $)) 71 (|has| $ (|CharacteristicNonZero|)) ELT)) (|coerce| (((|OutputForm|) $) 13 T ELT) (($ (|Integer|)) 41 T ELT) (($ $) 57 T ELT)) (|charthRoot| (((|Maybe| $) $) 70 (|has| $ (|CharacteristicNonZero|)) ELT)) (|characteristic| (((|NonNegativeInteger|)) 40 T CONST)) (|before?| (#1# 6 T ELT)) (|associates?| ((#3# $ $) 53 T ELT)) (|annihilate?| (((|Boolean|) $ $) 33 T ELT)) (|Zero| (#5# 24 T CONST)) (|One| (($) 45 T CONST)) (= (#1# 8 T ELT)) (- (($ $) 29 T ELT) (($ $ $) 28 T ELT)) (+ (($ $ $) 18 T ELT)) (** (($ $ (|PositiveInteger|)) 35 T ELT) (($ $ (|NonNegativeInteger|)) 43 T ELT)) (* (($ (|PositiveInteger|) $) 17 T ELT) (($ (|NonNegativeInteger|) $) 21 T ELT) (($ (|Integer|) $) 30 T ELT) (($ $ $) 34 T ELT))) +((~= (#1=((|Boolean|) $ $) 7 T ELT)) (|zero?| ((#2=(|Boolean|) $) 22 T ELT)) (|unitNormal| (((|Record| (|:| |unit| $) (|:| |canonical| $) (|:| |associate| $)) $) 56 T ELT)) (|unitCanonical| (($ $) 55 T ELT)) (|unit?| ((#3=(|Boolean|) $) 53 T ELT)) (|subtractIfCan| (((|Maybe| $) $ $) 26 T ELT)) (|squareFreePolynomial| (((|Factored| (|SparseUnivariatePolynomial| $)) (|SparseUnivariatePolynomial| $)) 76 T ELT)) (|squareFreePart| (($ $) 67 T ELT)) (|squareFree| (#4=((|Factored| $) $) 68 T ELT)) (|solveLinearPolynomialEquation| (((|Union| (|List| (|SparseUnivariatePolynomial| $)) "failed") (|List| (|SparseUnivariatePolynomial| $)) (|SparseUnivariatePolynomial| $)) 73 T ELT)) (|sample| (#5=($) 23 T CONST)) (|recip| (((|Union| $ "failed") $) 43 T ELT)) (|prime?| (((|Boolean|) $) 69 T ELT)) (|opposite?| ((#2# $ $) 20 T ELT)) (|one?| (((|Boolean|) $) 45 T ELT)) (|lcm| (#6=($ $ $) 61 T ELT) (#7=($ (|List| $)) 60 T ELT)) (|latex| (((|String|) $) 11 T ELT)) (|hash| (((|SingleInteger|) $) 12 T ELT)) (|gcdPolynomial| ((#8=(|SparseUnivariatePolynomial| $) #8# #8#) 59 T ELT)) (|gcd| (#6# 63 T ELT) (#7# 62 T ELT)) (|factorSquareFreePolynomial| (((|Factored| (|SparseUnivariatePolynomial| $)) (|SparseUnivariatePolynomial| $)) 74 T ELT)) (|factorPolynomial| (((|Factored| (|SparseUnivariatePolynomial| $)) (|SparseUnivariatePolynomial| $)) 75 T ELT)) (|factor| (#4# 66 T ELT)) (|exquo| (((|Union| $ "failed") $ $) 57 T ELT)) (|conditionP| (((|Union| (|Vector| $) "failed") (|Matrix| $)) 72 (|has| $ (|CharacteristicNonZero|)) ELT)) (|coerce| (((|OutputForm|) $) 13 T ELT) (($ (|Integer|)) 42 T ELT) (($ $) 58 T ELT)) (|charthRoot| (((|Maybe| $) $) 71 (|has| $ (|CharacteristicNonZero|)) ELT)) (|characteristic| (((|NonNegativeInteger|)) 41 T CONST)) (|before?| (#1# 6 T ELT)) (|associates?| ((#3# $ $) 54 T ELT)) (|annihilate?| (((|Boolean|) $ $) 34 T ELT)) (|Zero| (#5# 24 T CONST)) (|One| (($) 46 T CONST)) (= (#1# 8 T ELT)) (- (($ $) 30 T ELT) (($ $ $) 29 T ELT)) (+ (($ $ $) 18 T ELT)) (** (($ $ (|PositiveInteger|)) 36 T ELT) (($ $ (|NonNegativeInteger|)) 44 T ELT)) (* (($ (|PositiveInteger|) $) 17 T ELT) (($ (|NonNegativeInteger|) $) 21 T ELT) (($ (|Integer|) $) 31 T ELT) (($ $ $) 35 T ELT))) (((|PolynomialFactorizationExplicit|) (|Category|)) (T |PolynomialFactorizationExplicit|)) ((|gcdPolynomial| (*1 *2 *2 *2) (AND (|isDomain| *2 (|SparseUnivariatePolynomial| *1)) (|ofCategory| *1 (|PolynomialFactorizationExplicit|)))) (|squareFreePolynomial| (*1 *2 *3) (AND (|ofCategory| *1 (|PolynomialFactorizationExplicit|)) (|isDomain| *2 (|Factored| (|SparseUnivariatePolynomial| *1))) (|isDomain| *3 (|SparseUnivariatePolynomial| *1)))) (|factorPolynomial| (*1 *2 *3) (AND (|ofCategory| *1 (|PolynomialFactorizationExplicit|)) (|isDomain| *2 (|Factored| (|SparseUnivariatePolynomial| *1))) (|isDomain| *3 (|SparseUnivariatePolynomial| *1)))) (|factorSquareFreePolynomial| (*1 *2 *3) (AND (|ofCategory| *1 (|PolynomialFactorizationExplicit|)) (|isDomain| *2 (|Factored| (|SparseUnivariatePolynomial| *1))) (|isDomain| *3 (|SparseUnivariatePolynomial| *1)))) (|solveLinearPolynomialEquation| (*1 *2 *2 *3) (|partial| AND (|isDomain| *2 (|List| (|SparseUnivariatePolynomial| *1))) (|isDomain| *3 (|SparseUnivariatePolynomial| *1)) (|ofCategory| *1 (|PolynomialFactorizationExplicit|)))) (|conditionP| (*1 *2 *3) (|partial| AND (|isDomain| *3 (|Matrix| *1)) (|ofCategory| *1 (|CharacteristicNonZero|)) (|ofCategory| *1 (|PolynomialFactorizationExplicit|)) (|isDomain| *2 (|Vector| *1)))) (|charthRoot| (*1 *2 *1) (AND (|isDomain| *2 (|Maybe| *1)) (|ofCategory| *1 (|CharacteristicNonZero|)) (|ofCategory| *1 (|PolynomialFactorizationExplicit|))))) (|Join| (|UniqueFactorizationDomain|) (CATEGORY |domain| (SIGNATURE |squareFreePolynomial| ((|Factored| (|SparseUnivariatePolynomial| $)) (|SparseUnivariatePolynomial| $))) (SIGNATURE |factorPolynomial| ((|Factored| (|SparseUnivariatePolynomial| $)) (|SparseUnivariatePolynomial| $))) (SIGNATURE |factorSquareFreePolynomial| ((|Factored| (|SparseUnivariatePolynomial| $)) (|SparseUnivariatePolynomial| $))) (SIGNATURE |gcdPolynomial| ((|SparseUnivariatePolynomial| $) (|SparseUnivariatePolynomial| $) (|SparseUnivariatePolynomial| $))) (SIGNATURE |solveLinearPolynomialEquation| ((|Union| (|List| (|SparseUnivariatePolynomial| $)) "failed") (|List| (|SparseUnivariatePolynomial| $)) (|SparseUnivariatePolynomial| $))) (IF (|has| $ (|CharacteristicNonZero|)) (PROGN (SIGNATURE |conditionP| ((|Union| (|Vector| $) "failed") (|Matrix| $))) (SIGNATURE |charthRoot| ((|Maybe| $) $))) |%noBranch|))) @@ -2751,9 +2751,9 @@ NIL ((|polyred| ((|#2| |#2|) 26 T ELT)) (|mix| ((#1=(|Integer|) (|List| #2=(|Record| (|:| |den| #1#) (|:| |gcdnum| #1#)))) 15 T ELT)) (|getGoodPrime| (((|PositiveInteger|) #1#) 38 T ELT)) (|doubleDisc| (#3=(#1# |#2|) 45 T ELT)) (|badNum| (#3# 21 T ELT) ((#2# |#1|) 20 T ELT))) (((|PointsOfFiniteOrderTools| |#1| |#2|) (CATEGORY |package| (SIGNATURE |getGoodPrime| ((|PositiveInteger|) #1=(|Integer|))) (SIGNATURE |badNum| (#2=(|Record| (|:| |den| #1#) (|:| |gcdnum| #1#)) |#1|)) (SIGNATURE |badNum| #3=(#1# |#2|)) (SIGNATURE |mix| (#1# (|List| #2#))) (SIGNATURE |doubleDisc| #3#) (SIGNATURE |polyred| (|#2| |#2|))) (|UnivariatePolynomialCategory| (|Fraction| #1#)) (|UnivariatePolynomialCategory| (|Fraction| |#1|))) (T |PointsOfFiniteOrderTools|)) ((|polyred| (*1 *2 *2) (AND #1=(|ofCategory| *3 (|UnivariatePolynomialCategory| (|Fraction| #2=(|Integer|)))) (|isDomain| *1 (|PointsOfFiniteOrderTools| *3 *2)) (|ofCategory| *2 #3=(|UnivariatePolynomialCategory| (|Fraction| *3))))) (|doubleDisc| #4=(*1 *2 *3) #5=(AND #6=(|ofCategory| *4 (|UnivariatePolynomialCategory| (|Fraction| *2))) #7=(|isDomain| *2 #2#) (|isDomain| *1 (|PointsOfFiniteOrderTools| *4 *3)) (|ofCategory| *3 #8=(|UnivariatePolynomialCategory| (|Fraction| *4))))) (|mix| #4# (AND (|isDomain| *3 (|List| #9=(|Record| (|:| |den| #2#) (|:| |gcdnum| #2#)))) #6# #7# #10=(|isDomain| *1 (|PointsOfFiniteOrderTools| *4 *5)) #11=(|ofCategory| *5 #8#))) (|badNum| #4# #5#) (|badNum| #4# (AND #1# (|isDomain| *2 #9#) (|isDomain| *1 (|PointsOfFiniteOrderTools| *3 *4)) #12=(|ofCategory| *4 #3#))) (|getGoodPrime| #4# (AND (|isDomain| *3 #2#) #12# (|isDomain| *2 (|PositiveInteger|)) #10# #11#))) -((~= #1=(#2=(#3=(|Boolean|) $ $) NIL T ELT)) (|zero?| #4=((#3# $) NIL T ELT)) (|wholePart| (#5=(|#1| $) 99 T ELT)) (|unitNormal| (((|Record| (|:| |unit| $) (|:| |canonical| $) (|:| |associate| $)) $) NIL T ELT)) (|unitCanonical| #6=(#7=($ $) NIL T ELT)) (|unit?| #4#) (|subtractIfCan| (#8=(#9=(|Union| $ #10="failed") $ $) NIL T ELT)) (|squareFreePart| #6#) (|squareFree| #11=(((|Factored| $) $) NIL T ELT)) (|sizeLess?| #1#) (|sample| (#12=($) NIL T CONST)) (|rem| #13=(#14=($ $ $) NIL T ELT)) (|recip| ((#9# $) 93 T ELT)) (|quo| #13#) (|principalIdeal| (((|Record| (|:| |coef| #15=(|List| $)) #16=(|:| |generator| $)) #15#) NIL T ELT)) (|prime?| #4#) (|partialFraction| (($ |#1| #17=(|Factored| |#1|)) 91 T ELT)) (|padicallyExpand| (((|SparseUnivariatePolynomial| |#1|) |#1| |#1|) 52 T ELT)) (|padicFraction| (#7# 60 T ELT)) (|opposite?| #1#) (|one?| #4#) (|numberOfFractionalTerms| ((#18=(|Integer|) $) 96 T ELT)) (|nthFractionalTerm| (#19=($ $ #18#) 98 T ELT)) (|multiEuclidean| (((|Union| #15# #10#) #15# $) NIL T ELT)) (|lcm| #13# #20=(($ #15#) NIL T ELT)) (|latex| (((|String|) $) NIL T ELT)) (|inv| #6#) (|hash| (((|SingleInteger|) $) NIL T ELT)) (|gcdPolynomial| ((#21=(|SparseUnivariatePolynomial| $) #21# #21#) NIL T ELT)) (|gcd| #13# #20#) (|firstNumer| (#5# 95 T ELT)) (|firstDenom| ((#17# $) 94 T ELT)) (|factor| #11#) (|extendedEuclidean| (((|Record| #22=(|:| |coef1| $) #23=(|:| |coef2| $) #16#) $ $) NIL T ELT) (((|Union| (|Record| #22# #23#) #10#) $ $ $) NIL T ELT)) (|exquo| (#8# 92 T ELT)) (|expressIdealMember| (((|Maybe| #15#) #15# $) NIL T ELT)) (|euclideanSize| ((#24=(|NonNegativeInteger|) $) NIL T ELT)) (|divide| (((|Record| (|:| |quotient| $) (|:| |remainder| $)) $ $) NIL T ELT)) (|compactFraction| (#7# 49 T ELT)) (|coerce| (((|OutputForm|) $) 123 T ELT) (($ #18#) 72 T ELT) #6# (($ #25=(|Fraction| #18#)) NIL T ELT) (($ |#1|) 40 T ELT) (((|Fraction| |#1|) $) 77 T ELT) (($ (|Fraction| #17#)) 85 T ELT)) (|characteristic| ((#24#) 70 T CONST)) (|before?| #1#) (|associates?| #1#) (|annihilate?| #1#) (|Zero| (#12# 24 T CONST)) (|One| (#12# 12 T CONST)) (= (#2# 86 T ELT)) (/ #13#) (- (#7# 107 T ELT) #13#) (+ (#14# 48 T ELT)) (** (($ $ #26=(|PositiveInteger|)) NIL T ELT) (($ $ #24#) NIL T ELT) (#19# NIL T ELT)) (* (($ #26# $) NIL T ELT) (($ #24# $) NIL T ELT) (($ #18# $) 109 T ELT) (#14# 47 T ELT) (($ $ #25#) NIL T ELT) (($ #25# $) NIL T ELT) (($ |#1| $) 108 T ELT) (($ $ |#1|) NIL T ELT))) -(((|PartialFraction| |#1|) (|Join| (|Field|) (|Algebra| |#1|) (CATEGORY |domain| (SIGNATURE |coerce| ((|Fraction| |#1|) $)) (SIGNATURE |coerce| ($ (|Fraction| #1=(|Factored| |#1|)))) (SIGNATURE |compactFraction| #2=($ $)) (SIGNATURE |firstDenom| (#1# $)) (SIGNATURE |firstNumer| #3=(|#1| $)) (SIGNATURE |nthFractionalTerm| ($ $ #4=(|Integer|))) (SIGNATURE |numberOfFractionalTerms| (#4# $)) (SIGNATURE |padicallyExpand| ((|SparseUnivariatePolynomial| |#1|) |#1| |#1|)) (SIGNATURE |padicFraction| #2#) (SIGNATURE |partialFraction| ($ |#1| #1#)) (SIGNATURE |wholePart| #3#))) (|EuclideanDomain|)) (T |PartialFraction|)) -((|coerce| #1=(*1 *2 *1) (AND (|isDomain| *2 (|Fraction| *3)) #2=(|isDomain| *1 (|PartialFraction| *3)) #3=(|ofCategory| *3 #4=(|EuclideanDomain|)))) (|coerce| (*1 *1 *2) (AND (|isDomain| *2 (|Fraction| #5=(|Factored| *3))) #3# #2#)) (|compactFraction| #6=(*1 *1 *1) #7=(AND #8=(|isDomain| *1 (|PartialFraction| *2)) #9=(|ofCategory| *2 #4#))) (|firstDenom| #1# (AND (|isDomain| *2 #5#) #2# #3#)) (|firstNumer| #1# #7#) (|nthFractionalTerm| (*1 *1 *1 *2) #10=(AND (|isDomain| *2 (|Integer|)) #2# #3#)) (|numberOfFractionalTerms| #1# #10#) (|padicallyExpand| (*1 *2 *3 *3) (AND (|isDomain| *2 (|SparseUnivariatePolynomial| *3)) #2# #3#)) (|padicFraction| #6# #7#) (|partialFraction| (*1 *1 *2 *3) (AND (|isDomain| *3 (|Factored| *2)) #9# #8#)) (|wholePart| #1# #7#)) +((~= #1=(#2=(#3=(|Boolean|) $ $) NIL T ELT)) (|zero?| #4=((#3# $) NIL T ELT)) (|wholePart| (#5=(|#1| $) 99 T ELT)) (|unitNormal| (((|Record| (|:| |unit| $) (|:| |canonical| $) (|:| |associate| $)) $) NIL T ELT)) (|unitCanonical| #6=(#7=($ $) NIL T ELT)) (|unit?| #4#) (|subtractIfCan| (((|Maybe| $) $ $) NIL T ELT)) (|squareFreePart| #6#) (|squareFree| #8=(((|Factored| $) $) NIL T ELT)) (|sizeLess?| #1#) (|sample| (#9=($) NIL T CONST)) (|rem| #10=(#11=($ $ $) NIL T ELT)) (|recip| ((#12=(|Union| $ #13="failed") $) 93 T ELT)) (|quo| #10#) (|principalIdeal| (((|Record| (|:| |coef| #14=(|List| $)) #15=(|:| |generator| $)) #14#) NIL T ELT)) (|prime?| #4#) (|partialFraction| (($ |#1| #16=(|Factored| |#1|)) 91 T ELT)) (|padicallyExpand| (((|SparseUnivariatePolynomial| |#1|) |#1| |#1|) 52 T ELT)) (|padicFraction| (#7# 60 T ELT)) (|opposite?| #1#) (|one?| #4#) (|numberOfFractionalTerms| ((#17=(|Integer|) $) 96 T ELT)) (|nthFractionalTerm| (#18=($ $ #17#) 98 T ELT)) (|multiEuclidean| (((|Union| #14# #13#) #14# $) NIL T ELT)) (|lcm| #10# #19=(($ #14#) NIL T ELT)) (|latex| (((|String|) $) NIL T ELT)) (|inv| #6#) (|hash| (((|SingleInteger|) $) NIL T ELT)) (|gcdPolynomial| ((#20=(|SparseUnivariatePolynomial| $) #20# #20#) NIL T ELT)) (|gcd| #10# #19#) (|firstNumer| (#5# 95 T ELT)) (|firstDenom| ((#16# $) 94 T ELT)) (|factor| #8#) (|extendedEuclidean| (((|Record| #21=(|:| |coef1| $) #22=(|:| |coef2| $) #15#) $ $) NIL T ELT) (((|Union| (|Record| #21# #22#) #13#) $ $ $) NIL T ELT)) (|exquo| ((#12# $ $) 92 T ELT)) (|expressIdealMember| (((|Maybe| #14#) #14# $) NIL T ELT)) (|euclideanSize| ((#23=(|NonNegativeInteger|) $) NIL T ELT)) (|divide| (((|Record| (|:| |quotient| $) (|:| |remainder| $)) $ $) NIL T ELT)) (|compactFraction| (#7# 49 T ELT)) (|coerce| (((|OutputForm|) $) 123 T ELT) (($ #17#) 72 T ELT) #6# (($ #24=(|Fraction| #17#)) NIL T ELT) (($ |#1|) 40 T ELT) (((|Fraction| |#1|) $) 77 T ELT) (($ (|Fraction| #16#)) 85 T ELT)) (|characteristic| ((#23#) 70 T CONST)) (|before?| #1#) (|associates?| #1#) (|annihilate?| #1#) (|Zero| (#9# 24 T CONST)) (|One| (#9# 12 T CONST)) (= (#2# 86 T ELT)) (/ #10#) (- (#7# 107 T ELT) #10#) (+ (#11# 48 T ELT)) (** (($ $ #25=(|PositiveInteger|)) NIL T ELT) (($ $ #23#) NIL T ELT) (#18# NIL T ELT)) (* (($ #25# $) NIL T ELT) (($ #23# $) NIL T ELT) (($ #17# $) 109 T ELT) (#11# 47 T ELT) (($ $ #24#) NIL T ELT) (($ #24# $) NIL T ELT) (($ |#1| $) 108 T ELT) (($ $ |#1|) NIL T ELT))) +(((|PartialFraction| |#1|) (|Join| (|Field|) (|Algebra| |#1|) (|CoercibleTo| (|Fraction| |#1|)) (CATEGORY |domain| (SIGNATURE |coerce| ($ (|Fraction| #1=(|Factored| |#1|)))) (SIGNATURE |compactFraction| #2=($ $)) (SIGNATURE |firstDenom| (#1# $)) (SIGNATURE |firstNumer| #3=(|#1| $)) (SIGNATURE |nthFractionalTerm| ($ $ #4=(|Integer|))) (SIGNATURE |numberOfFractionalTerms| (#4# $)) (SIGNATURE |padicallyExpand| ((|SparseUnivariatePolynomial| |#1|) |#1| |#1|)) (SIGNATURE |padicFraction| #2#) (SIGNATURE |partialFraction| ($ |#1| #1#)) (SIGNATURE |wholePart| #3#))) (|EuclideanDomain|)) (T |PartialFraction|)) +((|coerce| (*1 *1 *2) (AND (|isDomain| *2 (|Fraction| #1=(|Factored| *3))) #2=(|ofCategory| *3 #3=(|EuclideanDomain|)) #4=(|isDomain| *1 (|PartialFraction| *3)))) (|compactFraction| #5=(*1 *1 *1) #6=(AND #7=(|isDomain| *1 (|PartialFraction| *2)) #8=(|ofCategory| *2 #3#))) (|firstDenom| #9=(*1 *2 *1) (AND (|isDomain| *2 #1#) #4# #2#)) (|firstNumer| #9# #6#) (|nthFractionalTerm| (*1 *1 *1 *2) #10=(AND (|isDomain| *2 (|Integer|)) #4# #2#)) (|numberOfFractionalTerms| #9# #10#) (|padicallyExpand| (*1 *2 *3 *3) (AND (|isDomain| *2 (|SparseUnivariatePolynomial| *3)) #4# #2#)) (|padicFraction| #5# #6#) (|partialFraction| (*1 *1 *2 *3) (AND (|isDomain| *3 (|Factored| *2)) #8# #7#)) (|wholePart| #9# #6#)) ((|partialFraction| ((#1=(|Any|) #2=(|Polynomial| |#1|) (|Factored| #2#) #3=(|Symbol|)) 17 T ELT) ((#1# (|Fraction| #2#) #3#) 18 T ELT))) (((|PartialFractionPackage| |#1|) (CATEGORY |package| (SIGNATURE |partialFraction| (#1=(|Any|) (|Fraction| #2=(|Polynomial| |#1|)) #3=(|Symbol|))) (SIGNATURE |partialFraction| (#1# #2# (|Factored| #2#) #3#))) (|Join| (|EuclideanDomain|) (|CharacteristicZero|))) (T |PartialFractionPackage|)) ((|partialFraction| (*1 *2 *3 *4 *5) (AND (|isDomain| *4 (|Factored| #1=(|Polynomial| *6))) (|isDomain| *5 #2=(|Symbol|)) (|isDomain| *3 #1#) (|ofCategory| *6 #3=(|Join| (|EuclideanDomain|) (|CharacteristicZero|))) #4=(|isDomain| *2 (|Any|)) (|isDomain| *1 (|PartialFractionPackage| *6)))) (|partialFraction| (*1 *2 *3 *4) (AND (|isDomain| *3 (|Fraction| (|Polynomial| *5))) (|isDomain| *4 #2#) (|ofCategory| *5 #3#) #4# (|isDomain| *1 (|PartialFractionPackage| *5))))) @@ -2773,7 +2773,7 @@ NIL ((|coerce| (((|Expression| |#1|) (|Pi|)) 16 T ELT))) (((|PiCoercions| |#1|) (CATEGORY |package| (SIGNATURE |coerce| ((|Expression| |#1|) (|Pi|)))) (|IntegralDomain|)) (T |PiCoercions|)) ((|coerce| (*1 *2 *3) (AND (|isDomain| *3 (|Pi|)) (|isDomain| *2 (|Expression| *4)) (|isDomain| *1 (|PiCoercions| *4)) (|ofCategory| *4 (|IntegralDomain|))))) -((~= (#1=((|Boolean|) $ $) 7 T ELT)) (|zero?| ((#2=(|Boolean|) $) 22 T ELT)) (|unitNormal| (((|Record| (|:| |unit| $) (|:| |canonical| $) (|:| |associate| $)) $) 55 T ELT)) (|unitCanonical| (($ $) 54 T ELT)) (|unit?| ((#3=(|Boolean|) $) 52 T ELT)) (|subtractIfCan| (((|Union| $ "failed") $ $) 26 T ELT)) (|sample| (#4=($) 23 T CONST)) (|recip| (((|Union| $ "failed") $) 42 T ELT)) (|principalIdeal| (((|Record| (|:| |coef| (|List| $)) (|:| |generator| $)) (|List| $)) 66 T ELT)) (|opposite?| ((#2# $ $) 20 T ELT)) (|one?| (((|Boolean|) $) 44 T ELT)) (|lcm| (#5=($ $ $) 60 T ELT) (#6=($ (|List| $)) 59 T ELT)) (|latex| (((|String|) $) 11 T ELT)) (|hash| (((|SingleInteger|) $) 12 T ELT)) (|gcdPolynomial| ((#7=(|SparseUnivariatePolynomial| $) #7# #7#) 58 T ELT)) (|gcd| (#5# 62 T ELT) (#6# 61 T ELT)) (|exquo| (((|Union| $ "failed") $ $) 56 T ELT)) (|expressIdealMember| (((|Maybe| (|List| $)) (|List| $) $) 65 T ELT)) (|coerce| (((|OutputForm|) $) 13 T ELT) (($ (|Integer|)) 41 T ELT) (($ $) 57 T ELT)) (|characteristic| (((|NonNegativeInteger|)) 40 T CONST)) (|before?| (#1# 6 T ELT)) (|associates?| ((#3# $ $) 53 T ELT)) (|annihilate?| (((|Boolean|) $ $) 33 T ELT)) (|Zero| (#4# 24 T CONST)) (|One| (($) 45 T CONST)) (= (#1# 8 T ELT)) (- (($ $) 29 T ELT) (($ $ $) 28 T ELT)) (+ (($ $ $) 18 T ELT)) (** (($ $ (|PositiveInteger|)) 35 T ELT) (($ $ (|NonNegativeInteger|)) 43 T ELT)) (* (($ (|PositiveInteger|) $) 17 T ELT) (($ (|NonNegativeInteger|) $) 21 T ELT) (($ (|Integer|) $) 30 T ELT) (($ $ $) 34 T ELT))) +((~= (#1=((|Boolean|) $ $) 7 T ELT)) (|zero?| ((#2=(|Boolean|) $) 22 T ELT)) (|unitNormal| (((|Record| (|:| |unit| $) (|:| |canonical| $) (|:| |associate| $)) $) 56 T ELT)) (|unitCanonical| (($ $) 55 T ELT)) (|unit?| ((#3=(|Boolean|) $) 53 T ELT)) (|subtractIfCan| (((|Maybe| $) $ $) 26 T ELT)) (|sample| (#4=($) 23 T CONST)) (|recip| (((|Union| $ "failed") $) 43 T ELT)) (|principalIdeal| (((|Record| (|:| |coef| (|List| $)) (|:| |generator| $)) (|List| $)) 67 T ELT)) (|opposite?| ((#2# $ $) 20 T ELT)) (|one?| (((|Boolean|) $) 45 T ELT)) (|lcm| (#5=($ $ $) 61 T ELT) (#6=($ (|List| $)) 60 T ELT)) (|latex| (((|String|) $) 11 T ELT)) (|hash| (((|SingleInteger|) $) 12 T ELT)) (|gcdPolynomial| ((#7=(|SparseUnivariatePolynomial| $) #7# #7#) 59 T ELT)) (|gcd| (#5# 63 T ELT) (#6# 62 T ELT)) (|exquo| (((|Union| $ "failed") $ $) 57 T ELT)) (|expressIdealMember| (((|Maybe| (|List| $)) (|List| $) $) 66 T ELT)) (|coerce| (((|OutputForm|) $) 13 T ELT) (($ (|Integer|)) 42 T ELT) (($ $) 58 T ELT)) (|characteristic| (((|NonNegativeInteger|)) 41 T CONST)) (|before?| (#1# 6 T ELT)) (|associates?| ((#3# $ $) 54 T ELT)) (|annihilate?| (((|Boolean|) $ $) 34 T ELT)) (|Zero| (#4# 24 T CONST)) (|One| (($) 46 T CONST)) (= (#1# 8 T ELT)) (- (($ $) 30 T ELT) (($ $ $) 29 T ELT)) (+ (($ $ $) 18 T ELT)) (** (($ $ (|PositiveInteger|)) 36 T ELT) (($ $ (|NonNegativeInteger|)) 44 T ELT)) (* (($ (|PositiveInteger|) $) 17 T ELT) (($ (|NonNegativeInteger|) $) 21 T ELT) (($ (|Integer|) $) 31 T ELT) (($ $ $) 35 T ELT))) (((|PrincipalIdealDomain|) (|Category|)) (T |PrincipalIdealDomain|)) ((|principalIdeal| (*1 *2 *3) (AND (|ofCategory| *1 (|PrincipalIdealDomain|)) (|isDomain| *2 (|Record| (|:| |coef| (|List| *1)) (|:| |generator| *1))) (|isDomain| *3 (|List| *1)))) (|expressIdealMember| (*1 *2 *3 *1) (AND (|ofCategory| *1 (|PrincipalIdealDomain|)) (|isDomain| *2 (|Maybe| (|List| *1))) (|isDomain| *3 (|List| *1))))) (|Join| (|GcdDomain|) (CATEGORY |domain| (SIGNATURE |principalIdeal| ((|Record| (|:| |coef| (|List| $)) (|:| |generator| $)) (|List| $))) (SIGNATURE |expressIdealMember| ((|Maybe| (|List| $)) (|List| $) $)))) @@ -2850,7 +2850,7 @@ NIL ((|sylvesterSequence| ((#1=(|List| |#2|) |#2| |#2|) 10 T ELT)) (|sturmVariationsOf| ((#2=(|NonNegativeInteger|) #3=(|List| |#1|)) 47 #4=(|has| |#1| (|OrderedRing|)) ELT)) (|sturmSequence| ((#1# |#2|) 11 T ELT)) (|lazyVariations| ((#2# #3# #5=(|Integer|) #5#) 45 #4# ELT)) (|boundOfCauchy| ((|#1| |#2|) 37 #4# ELT))) (((|RealPolynomialUtilitiesPackage| |#1| |#2|) (CATEGORY |package| (SIGNATURE |sylvesterSequence| (#1=(|List| |#2|) |#2| |#2|)) (SIGNATURE |sturmSequence| (#1# |#2|)) (IF (|has| |#1| (|OrderedRing|)) (PROGN (SIGNATURE |boundOfCauchy| (|#1| |#2|)) (SIGNATURE |sturmVariationsOf| (#2=(|NonNegativeInteger|) #3=(|List| |#1|))) (SIGNATURE |lazyVariations| (#2# #3# #4=(|Integer|) #4#))) |%noBranch|)) (|Field|) (|UnivariatePolynomialCategory| |#1|)) (T |RealPolynomialUtilitiesPackage|)) ((|lazyVariations| (*1 *2 *3 *4 *4) (AND (|isDomain| *3 (|List| *5)) (|isDomain| *4 (|Integer|)) (|ofCategory| *5 #1=(|OrderedRing|)) (|ofCategory| *5 #2=(|Field|)) #3=(|isDomain| *2 (|NonNegativeInteger|)) (|isDomain| *1 (|RealPolynomialUtilitiesPackage| *5 *6)) (|ofCategory| *6 (|UnivariatePolynomialCategory| *5)))) (|sturmVariationsOf| #4=(*1 *2 *3) (AND (|isDomain| *3 (|List| *4)) (|ofCategory| *4 #1#) #5=(|ofCategory| *4 #2#) #3# (|isDomain| *1 (|RealPolynomialUtilitiesPackage| *4 *5)) (|ofCategory| *5 #6=(|UnivariatePolynomialCategory| *4)))) (|boundOfCauchy| #4# (AND (|ofCategory| *2 #2#) (|ofCategory| *2 #1#) (|isDomain| *1 (|RealPolynomialUtilitiesPackage| *2 *3)) (|ofCategory| *3 (|UnivariatePolynomialCategory| *2)))) (|sturmSequence| #4# #7=(AND #5# (|isDomain| *2 (|List| *3)) (|isDomain| *1 (|RealPolynomialUtilitiesPackage| *4 *3)) (|ofCategory| *3 #6#))) (|sylvesterSequence| (*1 *2 *3 *3) #7#)) -((~= #1=(#2=(#3=(|Boolean|) $ $) NIL T ELT)) (|zero?| #4=(#5=(#3# $) NIL T ELT)) (|variables| ((#6=(|List| #7=(|Symbol|)) $) 16 T ELT)) (|univariate| ((#8=(|SparseUnivariatePolynomial| $) $ #7#) 21 T ELT) ((#9=(|SparseUnivariatePolynomial| |#1|) $) NIL T ELT)) (|unitNormal| (((|Record| (|:| |unit| $) (|:| |canonical| $) (|:| |associate| $)) $) NIL #10=(|has| |#1| (|IntegralDomain|)) ELT)) (|unitCanonical| #11=(#12=($ $) NIL #10# ELT)) (|unit?| (#5# NIL #10# ELT)) (|totalDegree| #13=((#14=(|NonNegativeInteger|) $) NIL T ELT) ((#14# $ #6#) NIL T ELT)) (|subtractIfCan| (#15=(#16=(|Union| $ #17="failed") $ $) NIL T ELT)) (|squareFreePolynomial| #18=(((|Factored| #8#) #8#) NIL #19=(|has| |#1| (|PolynomialFactorizationExplicit|)) ELT)) (|squareFreePart| #20=(#12# NIL #21=(|has| |#1| (|GcdDomain|)) ELT)) (|squareFree| (#22=((|Factored| $) $) NIL #21# ELT)) (|solveLinearPolynomialEquation| (((|Union| #23=(|List| #8#) #17#) #23# #8#) NIL #19# ELT)) (|sample| #24=(($) NIL T CONST)) (|retractIfCan| (((|Union| |#1| . #25=(#17#)) . #26=($)) 8 T ELT) (((|Union| #27=(|Fraction| #28=(|Integer|)) . #25#) . #26#) NIL #29=(|has| |#1| (|RetractableTo| #27#)) ELT) (((|Union| #28# . #25#) . #26#) NIL #30=(|has| |#1| (|RetractableTo| #28#)) ELT) (#31=((|Union| #7# . #25#) . #26#) NIL T ELT)) (|retract| #32=(#33=(|#1| . #34=($)) NIL T ELT) ((#27# . #34#) NIL #29# ELT) ((#28# . #34#) NIL #30# ELT) ((#7# . #34#) NIL T ELT)) (|resultant| (($ $ $ #7#) NIL #35=(|has| |#1| (|CommutativeRing|)) ELT)) (|reductum| #36=(#12# NIL T ELT)) (|reducedSystem| ((#37=(|Matrix| #28#) . #38=(#39=(|Matrix| $))) NIL #40=(|has| |#1| (|LinearlyExplicitRingOver| #28#)) ELT) ((#41=(|Record| (|:| |mat| #37#) (|:| |vec| (|Vector| #28#))) . #42=(#39# #43=(|Vector| $))) NIL #40# ELT) ((#44=(|Record| (|:| |mat| #45=(|Matrix| |#1|)) (|:| |vec| (|Vector| |#1|))) . #42#) NIL T ELT) ((#45# . #38#) NIL T ELT)) (|recip| ((#16# $) NIL T ELT)) (|primitivePart| #20# #46=(#47=($ $ #7#) NIL #21# ELT)) (|primitiveMonomials| #48=((#49=(|List| $) $) NIL T ELT)) (|prime?| (#5# NIL #19# ELT)) (|pomopo!| (($ $ |#1| #50=(|IndexedExponents| #7#) $) NIL T ELT)) (|patternMatch| ((#51=(|PatternMatchResult| #52=(|Float|) . #53=($)) $ #54=(|Pattern| #52#) #51#) NIL (AND (|has| #7# #55=(|PatternMatchable| #52#)) (|has| |#1| #55#)) ELT) ((#56=(|PatternMatchResult| #28# . #53#) $ #57=(|Pattern| #28#) #56#) NIL (AND (|has| #7# #58=(|PatternMatchable| #28#)) (|has| |#1| #58#)) ELT)) (|opposite?| #1#) (|one?| #4#) (|numberOfMonomials| #13#) (|multivariate| (($ #9# #7#) NIL T ELT) (($ #8# #7#) NIL T ELT)) (|monomials| #48#) (|monomial?| #4#) (|monomial| (($ |#1| #50#) NIL T ELT) #59=(($ $ #7# #14#) NIL T ELT) #60=(($ $ #6# #61=(|List| #14#)) NIL T ELT)) (|monicDivide| (((|Record| (|:| |quotient| $) (|:| |remainder| $)) $ $ #7#) NIL T ELT)) (|minimumDegree| #62=((#50# $) NIL T ELT) #63=((#14# $ #7#) NIL T ELT) #64=((#61# $ #6#) NIL T ELT)) (|mapExponents| (($ (|Mapping| #50# #50#) $) NIL T ELT)) (|map| (($ (|Mapping| |#1| |#1|) $) NIL T ELT)) (|mainVariable| (#31# 19 T ELT)) (|leftReducedSystem| ((#37# . #65=(#43#)) NIL #40# ELT) ((#41# . #66=(#43# $)) NIL #40# ELT) ((#44# . #66#) NIL T ELT) ((#45# . #65#) NIL T ELT)) (|leadingMonomial| #36#) (|leadingCoefficient| #32#) (|lcm| #67=(($ #49#) NIL #21# ELT) #68=(#69=($ $ $) NIL #21# ELT)) (|latex| (((|String|) $) NIL T ELT)) (|isTimes| #70=(((|Union| #49# #17#) $) NIL T ELT)) (|isPlus| #70#) (|isExpt| (((|Union| (|Record| (|:| |var| #7#) (|:| |exponent| #14#)) #17#) $) NIL T ELT)) (|integrate| (#47# 29 #71=(|has| |#1| (|Algebra| #27#)) ELT)) (|hash| (((|SingleInteger|) $) NIL T ELT)) (|ground?| #4#) (|ground| #32#) (|gcdPolynomial| ((#8# #8# #8#) NIL #21# ELT)) (|gcd| #67# #68#) (|factorSquareFreePolynomial| #18#) (|factorPolynomial| #18#) (|factor| (#22# NIL #19# ELT)) (|exquo| ((#16# $ |#1|) NIL #10# ELT) (#15# NIL #10# ELT)) (|eval| (($ $ (|List| #72=(|Equation| $))) NIL T ELT) (($ $ #72#) NIL T ELT) (($ $ $ $) NIL T ELT) (($ $ #49# #49#) NIL T ELT) (($ $ #7# |#1|) NIL T ELT) (($ $ #6# #73=(|List| |#1|)) NIL T ELT) (($ $ #7# $) NIL T ELT) (($ $ #6# #49#) NIL T ELT)) (|discriminant| (#47# NIL #35# ELT)) (|differentiate| #60# #59# #74=(($ $ #6#) NIL T ELT) #75=(#47# NIL T ELT)) (|degree| #62# #63# #64#) (|convert| ((#54# . #76=($)) NIL (AND (|has| #7# #77=(|ConvertibleTo| #54#)) (|has| |#1| #77#)) ELT) ((#57# . #76#) NIL (AND (|has| #7# #78=(|ConvertibleTo| #57#)) (|has| |#1| #78#)) ELT) ((#79=(|InputForm|) . #76#) NIL (AND (|has| #7# #80=(|ConvertibleTo| #79#)) (|has| |#1| #80#)) ELT)) (|content| (#33# NIL #21# ELT) #46#) (|conditionP| (((|Union| #43# #17#) #39#) NIL #81=(AND (|has| $ #82=(|CharacteristicNonZero|)) #19#) ELT)) (|coerce| (((|OutputForm|) $) 25 T ELT) (($ #28#) NIL T ELT) (($ |#1|) NIL T ELT) (($ #7#) 27 T ELT) (($ #27#) NIL (OR #71# #29#) ELT) #11#) (|coefficients| ((#73# $) NIL T ELT)) (|coefficient| ((|#1| $ #50#) NIL T ELT) #59# #60#) (|charthRoot| (((|Maybe| $) $) NIL (OR #81# (|has| |#1| #82#)) ELT)) (|characteristic| ((#14#) NIL T CONST)) (|binomThmExpt| (($ $ $ #14#) NIL #35# ELT)) (|before?| #1#) (|associates?| (#2# NIL #10# ELT)) (|annihilate?| #1#) (|Zero| #24#) (|One| #24#) (D #60# #59# #74# #75#) (= #1#) (/ (#83=($ $ |#1|) NIL (|has| |#1| (|Field|)) ELT)) (- #36# #84=(#69# NIL T ELT)) (+ #84#) (** (($ $ #85=(|PositiveInteger|)) NIL T ELT) (($ $ #14#) NIL T ELT)) (* (($ #85# $) NIL T ELT) (($ #14# $) NIL T ELT) (($ #28# . #86=($)) NIL T ELT) #84# (($ $ #27#) NIL #71# ELT) (($ #27# . #86#) NIL #71# ELT) (($ |#1| . #86#) NIL T ELT) (#83# NIL T ELT))) +((~= #1=(#2=(#3=(|Boolean|) $ $) NIL T ELT)) (|zero?| #4=(#5=(#3# $) NIL T ELT)) (|variables| ((#6=(|List| #7=(|Symbol|)) $) 16 T ELT)) (|univariate| ((#8=(|SparseUnivariatePolynomial| $) $ #7#) 21 T ELT) ((#9=(|SparseUnivariatePolynomial| |#1|) $) NIL T ELT)) (|unitNormal| (((|Record| (|:| |unit| $) (|:| |canonical| $) (|:| |associate| $)) $) NIL #10=(|has| |#1| (|IntegralDomain|)) ELT)) (|unitCanonical| #11=(#12=($ $) NIL #10# ELT)) (|unit?| (#5# NIL #10# ELT)) (|totalDegree| #13=((#14=(|NonNegativeInteger|) $) NIL T ELT) ((#14# $ #6#) NIL T ELT)) (|subtractIfCan| ((#15=(|Maybe| $) $ $) NIL T ELT)) (|squareFreePolynomial| #16=(((|Factored| #8#) #8#) NIL #17=(|has| |#1| (|PolynomialFactorizationExplicit|)) ELT)) (|squareFreePart| #18=(#12# NIL #19=(|has| |#1| (|GcdDomain|)) ELT)) (|squareFree| (#20=((|Factored| $) $) NIL #19# ELT)) (|solveLinearPolynomialEquation| (((|Union| #21=(|List| #8#) #22="failed") #21# #8#) NIL #17# ELT)) (|sample| #23=(($) NIL T CONST)) (|retractIfCan| (((|Union| |#1| . #24=(#22#)) . #25=($)) 8 T ELT) (((|Union| #26=(|Fraction| #27=(|Integer|)) . #24#) . #25#) NIL #28=(|has| |#1| (|RetractableTo| #26#)) ELT) (((|Union| #27# . #24#) . #25#) NIL #29=(|has| |#1| (|RetractableTo| #27#)) ELT) (#30=((|Union| #7# . #24#) . #25#) NIL T ELT)) (|retract| #31=(#32=(|#1| . #33=($)) NIL T ELT) ((#26# . #33#) NIL #28# ELT) ((#27# . #33#) NIL #29# ELT) ((#7# . #33#) NIL T ELT)) (|resultant| (($ $ $ #7#) NIL #34=(|has| |#1| (|CommutativeRing|)) ELT)) (|reductum| #35=(#12# NIL T ELT)) (|reducedSystem| ((#36=(|Matrix| #27#) . #37=(#38=(|Matrix| $))) NIL #39=(|has| |#1| (|LinearlyExplicitRingOver| #27#)) ELT) ((#40=(|Record| (|:| |mat| #36#) (|:| |vec| (|Vector| #27#))) . #41=(#38# #42=(|Vector| $))) NIL #39# ELT) ((#43=(|Record| (|:| |mat| #44=(|Matrix| |#1|)) (|:| |vec| (|Vector| |#1|))) . #41#) NIL T ELT) ((#44# . #37#) NIL T ELT)) (|recip| ((#45=(|Union| $ #22#) $) NIL T ELT)) (|primitivePart| #18# #46=(#47=($ $ #7#) NIL #19# ELT)) (|primitiveMonomials| #48=((#49=(|List| $) $) NIL T ELT)) (|prime?| (#5# NIL #17# ELT)) (|pomopo!| (($ $ |#1| #50=(|IndexedExponents| #7#) $) NIL T ELT)) (|patternMatch| ((#51=(|PatternMatchResult| #52=(|Float|) . #53=($)) $ #54=(|Pattern| #52#) #51#) NIL (AND (|has| #7# #55=(|PatternMatchable| #52#)) (|has| |#1| #55#)) ELT) ((#56=(|PatternMatchResult| #27# . #53#) $ #57=(|Pattern| #27#) #56#) NIL (AND (|has| #7# #58=(|PatternMatchable| #27#)) (|has| |#1| #58#)) ELT)) (|opposite?| #1#) (|one?| #4#) (|numberOfMonomials| #13#) (|multivariate| (($ #9# #7#) NIL T ELT) (($ #8# #7#) NIL T ELT)) (|monomials| #48#) (|monomial?| #4#) (|monomial| (($ |#1| #50#) NIL T ELT) #59=(($ $ #7# #14#) NIL T ELT) #60=(($ $ #6# #61=(|List| #14#)) NIL T ELT)) (|monicDivide| (((|Record| (|:| |quotient| $) (|:| |remainder| $)) $ $ #7#) NIL T ELT)) (|minimumDegree| #62=((#50# $) NIL T ELT) #63=((#14# $ #7#) NIL T ELT) #64=((#61# $ #6#) NIL T ELT)) (|mapExponents| (($ (|Mapping| #50# #50#) $) NIL T ELT)) (|map| (($ (|Mapping| |#1| |#1|) $) NIL T ELT)) (|mainVariable| (#30# 19 T ELT)) (|leftReducedSystem| ((#36# . #65=(#42#)) NIL #39# ELT) ((#40# . #66=(#42# $)) NIL #39# ELT) ((#43# . #66#) NIL T ELT) ((#44# . #65#) NIL T ELT)) (|leadingMonomial| #35#) (|leadingCoefficient| #31#) (|lcm| #67=(($ #49#) NIL #19# ELT) #68=(#69=($ $ $) NIL #19# ELT)) (|latex| (((|String|) $) NIL T ELT)) (|isTimes| #70=(((|Union| #49# #22#) $) NIL T ELT)) (|isPlus| #70#) (|isExpt| (((|Union| (|Record| (|:| |var| #7#) (|:| |exponent| #14#)) #22#) $) NIL T ELT)) (|integrate| (#47# 29 #71=(|has| |#1| (|Algebra| #26#)) ELT)) (|hash| (((|SingleInteger|) $) NIL T ELT)) (|ground?| #4#) (|ground| #31#) (|gcdPolynomial| ((#8# #8# #8#) NIL #19# ELT)) (|gcd| #67# #68#) (|factorSquareFreePolynomial| #16#) (|factorPolynomial| #16#) (|factor| (#20# NIL #17# ELT)) (|exquo| ((#45# $ |#1|) NIL #10# 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(|OrderedSet|)) (|isDomain| *2 (|NonNegativeInteger|)))) (|minimumDegree| (*1 *2 *1 *3) (AND (|isDomain| *3 (|List| *6)) (|ofCategory| *1 (|PolynomialCategory| *4 *5 *6)) (|ofCategory| *4 (|Ring|)) (|ofCategory| *5 (|OrderedAbelianMonoidSup|)) (|ofCategory| *6 (|OrderedSet|)) (|isDomain| *2 (|List| (|NonNegativeInteger|))))) (|monicDivide| (*1 *2 *1 *1 *3) (AND (|ofCategory| *4 (|Ring|)) (|ofCategory| *5 (|OrderedAbelianMonoidSup|)) (|ofCategory| *3 (|OrderedSet|)) (|isDomain| *2 (|Record| (|:| |quotient| *1) (|:| |remainder| *1))) (|ofCategory| *1 (|PolynomialCategory| *4 *5 *3)))) (|monomial| (*1 *1 *1 *2 *3) (AND (|isDomain| *3 (|NonNegativeInteger|)) (|ofCategory| *1 (|PolynomialCategory| *4 *5 *2)) (|ofCategory| *4 (|Ring|)) (|ofCategory| *5 (|OrderedAbelianMonoidSup|)) (|ofCategory| *2 (|OrderedSet|)))) (|monomial| (*1 *1 *1 *2 *3) (AND (|isDomain| *2 (|List| *6)) (|isDomain| *3 (|List| (|NonNegativeInteger|))) (|ofCategory| *1 (|PolynomialCategory| *4 *5 *6)) (|ofCategory| *4 (|Ring|)) (|ofCategory| *5 (|OrderedAbelianMonoidSup|)) (|ofCategory| *6 (|OrderedSet|)))) (|multivariate| (*1 *1 *2 *3) (AND (|isDomain| *2 (|SparseUnivariatePolynomial| *4)) (|ofCategory| *4 (|Ring|)) (|ofCategory| *1 (|PolynomialCategory| *4 *5 *3)) (|ofCategory| *5 (|OrderedAbelianMonoidSup|)) (|ofCategory| *3 (|OrderedSet|)))) (|multivariate| (*1 *1 *2 *3) (AND (|isDomain| *2 (|SparseUnivariatePolynomial| *1)) (|ofCategory| *1 (|PolynomialCategory| *4 *5 *3)) (|ofCategory| *4 (|Ring|)) (|ofCategory| *5 (|OrderedAbelianMonoidSup|)) (|ofCategory| *3 (|OrderedSet|)))) (|isPlus| (*1 *2 *1) (|partial| AND (|ofCategory| *3 (|Ring|)) (|ofCategory| *4 (|OrderedAbelianMonoidSup|)) (|ofCategory| *5 (|OrderedSet|)) (|isDomain| *2 (|List| *1)) (|ofCategory| *1 (|PolynomialCategory| *3 *4 *5)))) (|isTimes| (*1 *2 *1) (|partial| AND (|ofCategory| *3 (|Ring|)) (|ofCategory| *4 (|OrderedAbelianMonoidSup|)) (|ofCategory| *5 (|OrderedSet|)) (|isDomain| *2 (|List| *1)) (|ofCategory| *1 (|PolynomialCategory| *3 *4 *5)))) (|isExpt| (*1 *2 *1) (|partial| AND (|ofCategory| *1 (|PolynomialCategory| *3 *4 *5)) (|ofCategory| *3 (|Ring|)) (|ofCategory| *4 (|OrderedAbelianMonoidSup|)) (|ofCategory| *5 (|OrderedSet|)) (|isDomain| *2 (|Record| (|:| |var| *5) (|:| |exponent| (|NonNegativeInteger|)))))) (|totalDegree| (*1 *2 *1) (AND (|ofCategory| *1 (|PolynomialCategory| *3 *4 *5)) (|ofCategory| *3 (|Ring|)) (|ofCategory| *4 (|OrderedAbelianMonoidSup|)) (|ofCategory| *5 (|OrderedSet|)) (|isDomain| *2 (|NonNegativeInteger|)))) (|totalDegree| (*1 *2 *1 *3) (AND (|isDomain| *3 (|List| *6)) (|ofCategory| *1 (|PolynomialCategory| *4 *5 *6)) (|ofCategory| *4 (|Ring|)) (|ofCategory| *5 (|OrderedAbelianMonoidSup|)) (|ofCategory| *6 (|OrderedSet|)) (|isDomain| *2 (|NonNegativeInteger|)))) (|variables| (*1 *2 *1) (AND (|ofCategory| *1 (|PolynomialCategory| *3 *4 *5)) (|ofCategory| *3 (|Ring|)) (|ofCategory| *4 (|OrderedAbelianMonoidSup|)) (|ofCategory| *5 (|OrderedSet|)) (|isDomain| *2 (|List| *5)))) (|primitiveMonomials| (*1 *2 *1) (AND (|ofCategory| *3 (|Ring|)) (|ofCategory| *4 (|OrderedAbelianMonoidSup|)) (|ofCategory| *5 (|OrderedSet|)) (|isDomain| *2 (|List| *1)) (|ofCategory| *1 (|PolynomialCategory| *3 *4 *5)))) (|resultant| (*1 *1 *1 *1 *2) (AND (|ofCategory| *1 (|PolynomialCategory| *3 *4 *2)) (|ofCategory| *3 (|Ring|)) (|ofCategory| *4 (|OrderedAbelianMonoidSup|)) (|ofCategory| *2 (|OrderedSet|)) (|ofCategory| *3 (|CommutativeRing|)))) (|discriminant| (*1 *1 *1 *2) (AND (|ofCategory| *1 (|PolynomialCategory| *3 *4 *2)) (|ofCategory| *3 (|Ring|)) (|ofCategory| *4 (|OrderedAbelianMonoidSup|)) (|ofCategory| *2 (|OrderedSet|)) (|ofCategory| *3 (|CommutativeRing|)))) (|content| (*1 *1 *1 *2) (AND (|ofCategory| *1 (|PolynomialCategory| *3 *4 *2)) (|ofCategory| *3 (|Ring|)) (|ofCategory| *4 (|OrderedAbelianMonoidSup|)) (|ofCategory| *2 (|OrderedSet|)) (|ofCategory| *3 (|GcdDomain|)))) (|primitivePart| (*1 *1 *1 *2) (AND (|ofCategory| *1 (|PolynomialCategory| *3 *4 *2)) (|ofCategory| *3 (|Ring|)) (|ofCategory| *4 (|OrderedAbelianMonoidSup|)) (|ofCategory| *2 (|OrderedSet|)) (|ofCategory| *3 (|GcdDomain|)))) (|squareFreePart| (*1 *1 *1) (AND (|ofCategory| *1 (|PolynomialCategory| *2 *3 *4)) (|ofCategory| *2 (|Ring|)) (|ofCategory| *3 (|OrderedAbelianMonoidSup|)) (|ofCategory| *4 (|OrderedSet|)) (|ofCategory| *2 (|GcdDomain|)))) (|squareFree| (*1 *2 *1) (AND (|ofCategory| *3 (|GcdDomain|)) (|ofCategory| *3 (|Ring|)) (|ofCategory| *4 (|OrderedAbelianMonoidSup|)) (|ofCategory| *5 (|OrderedSet|)) (|isDomain| *2 (|Factored| *1)) (|ofCategory| *1 (|PolynomialCategory| *3 *4 *5))))) (|Join| (|PartialDifferentialRing| |t#3|) (|FiniteAbelianMonoidRing| |t#1| |t#2|) (|Evalable| $) (|InnerEvalable| |t#3| |t#1|) (|InnerEvalable| |t#3| $) (|RetractableTo| |t#3|) (|FullyLinearlyExplicitRingOver| |t#1|) (CATEGORY |domain| (SIGNATURE |degree| ((|NonNegativeInteger|) $ |t#3|)) (SIGNATURE |degree| ((|List| (|NonNegativeInteger|)) $ (|List| |t#3|))) (SIGNATURE |coefficient| ($ $ |t#3| (|NonNegativeInteger|))) (SIGNATURE |coefficient| ($ $ (|List| |t#3|) (|List| (|NonNegativeInteger|)))) (SIGNATURE |monomials| ((|List| $) $)) (SIGNATURE |univariate| ((|SparseUnivariatePolynomial| $) $ |t#3|)) (SIGNATURE |univariate| ((|SparseUnivariatePolynomial| |t#1|) $)) (SIGNATURE |mainVariable| ((|Union| |t#3| "failed") $)) (SIGNATURE |minimumDegree| ((|NonNegativeInteger|) $ |t#3|)) (SIGNATURE |minimumDegree| ((|List| (|NonNegativeInteger|)) $ (|List| |t#3|))) (SIGNATURE |monicDivide| ((|Record| (|:| |quotient| $) (|:| |remainder| $)) $ $ |t#3|)) (SIGNATURE |monomial| ($ $ |t#3| (|NonNegativeInteger|))) (SIGNATURE |monomial| ($ $ (|List| |t#3|) (|List| (|NonNegativeInteger|)))) (SIGNATURE |multivariate| ($ (|SparseUnivariatePolynomial| |t#1|) |t#3|)) (SIGNATURE |multivariate| ($ (|SparseUnivariatePolynomial| $) |t#3|)) (SIGNATURE |isPlus| ((|Union| (|List| $) "failed") $)) (SIGNATURE |isTimes| ((|Union| (|List| $) "failed") $)) (SIGNATURE |isExpt| ((|Union| (|Record| (|:| |var| |t#3|) (|:| |exponent| (|NonNegativeInteger|))) "failed") $)) (SIGNATURE |totalDegree| ((|NonNegativeInteger|) $)) (SIGNATURE |totalDegree| ((|NonNegativeInteger|) $ (|List| |t#3|))) (SIGNATURE |variables| ((|List| |t#3|) $)) (SIGNATURE |primitiveMonomials| ((|List| $) $)) (IF (|has| |t#1| (|ConvertibleTo| (|InputForm|))) (IF (|has| |t#3| (|ConvertibleTo| (|InputForm|))) (ATTRIBUTE (|ConvertibleTo| (|InputForm|))) |%noBranch|) |%noBranch|) (IF (|has| |t#1| (|ConvertibleTo| (|Pattern| (|Integer|)))) (IF (|has| |t#3| (|ConvertibleTo| (|Pattern| (|Integer|)))) (ATTRIBUTE (|ConvertibleTo| (|Pattern| (|Integer|)))) |%noBranch|) |%noBranch|) (IF (|has| |t#1| (|ConvertibleTo| (|Pattern| (|Float|)))) (IF (|has| |t#3| (|ConvertibleTo| (|Pattern| (|Float|)))) (ATTRIBUTE (|ConvertibleTo| (|Pattern| (|Float|)))) |%noBranch|) |%noBranch|) (IF (|has| |t#1| (|PatternMatchable| (|Integer|))) (IF (|has| |t#3| (|PatternMatchable| (|Integer|))) (ATTRIBUTE (|PatternMatchable| (|Integer|))) |%noBranch|) |%noBranch|) (IF (|has| |t#1| (|PatternMatchable| (|Float|))) (IF (|has| |t#3| (|PatternMatchable| (|Float|))) (ATTRIBUTE (|PatternMatchable| (|Float|))) |%noBranch|) |%noBranch|) (IF (|has| |t#1| (|CommutativeRing|)) (PROGN (SIGNATURE |resultant| ($ $ $ |t#3|)) (SIGNATURE |discriminant| ($ $ |t#3|))) |%noBranch|) (IF (|has| |t#1| (|GcdDomain|)) (PROGN (ATTRIBUTE (|GcdDomain|)) (SIGNATURE |content| ($ $ |t#3|)) (SIGNATURE |primitivePart| ($ $)) (SIGNATURE |primitivePart| ($ $ |t#3|)) (SIGNATURE |squareFree| ((|Factored| $) $)) (SIGNATURE |squareFreePart| ($ $))) |%noBranch|) (IF (|has| |t#1| (ATTRIBUTE |canonicalUnitNormal|)) (ATTRIBUTE |canonicalUnitNormal|) |%noBranch|) (IF (|has| |t#1| (|PolynomialFactorizationExplicit|)) (ATTRIBUTE (|PolynomialFactorizationExplicit|)) |%noBranch|))) @@ -2884,7 +2884,7 @@ NIL ((|listBranches| (*1 *2 *1) (AND (|ofCategory| *1 (|PlottablePlaneCurveCategory|)) (|isDomain| *2 (|List| (|List| (|Point| (|DoubleFloat|))))))) (|xRange| (*1 *2 *1) (AND (|ofCategory| *1 (|PlottablePlaneCurveCategory|)) (|isDomain| *2 (|Segment| (|DoubleFloat|))))) (|yRange| (*1 *2 *1) (AND (|ofCategory| *1 (|PlottablePlaneCurveCategory|)) (|isDomain| *2 (|Segment| (|DoubleFloat|)))))) (|Join| (|CoercibleTo| (|OutputForm|)) (CATEGORY |domain| (SIGNATURE |listBranches| ((|List| (|List| (|Point| (|DoubleFloat|)))) $)) (SIGNATURE |xRange| ((|Segment| (|DoubleFloat|)) $)) (SIGNATURE |yRange| ((|Segment| (|DoubleFloat|)) $)))) (((|CoercibleTo| (|OutputForm|)) . T)) -((~= #1=(#2=(#3=(|Boolean|) $ $) NIL T ELT)) (|zero?| #4=(#5=(#3# $) NIL T ELT)) (|unitNormal| (((|Record| (|:| |unit| $) (|:| |canonical| $) (|:| |associate| $)) $) 80 #6=(|has| |#1| (|IntegralDomain|)) ELT)) (|unitCanonical| (#7=($ $) 81 #6# ELT)) (|unit?| (#5# NIL #6# ELT)) (|subtractIfCan| (#8=(#9=(|Union| $ #10="failed") $ $) NIL T ELT)) (|sample| (#11=($) NIL T CONST)) (|retractIfCan| (((|Union| #12=(|Integer|) . #13=(#10#)) . #14=($)) NIL #15=(|has| |#1| (|RetractableTo| #12#)) ELT) (((|Union| #16=(|Fraction| #12#) . #13#) . #14#) NIL #17=(|has| |#1| (|RetractableTo| #16#)) ELT) (((|Union| |#1| . #13#) $) 35 T ELT)) (|retract| ((#12# . #18=($)) NIL #15# ELT) ((#16# . #18#) NIL #17# ELT) #19=(#20=(|#1| . #18#) NIL T ELT)) (|reductum| (#7# 32 T ELT)) (|recip| ((#9# $) 43 T ELT)) (|primitivePart| (#7# NIL #21=(|has| |#1| (|GcdDomain|)) ELT)) (|pomopo!| (($ $ |#1| |#2| $) 64 T ELT)) (|opposite?| #1#) (|one?| #4#) (|numberOfMonomials| ((#22=(|NonNegativeInteger|) $) 18 T ELT)) (|monomial?| #4#) (|monomial| (($ |#1| |#2|) NIL T ELT)) (|minimumDegree| (#23=(|#2| $) 25 T ELT)) (|mapExponents| (($ (|Mapping| |#2| |#2|) $) NIL T ELT)) (|map| (($ (|Mapping| |#1| |#1|) $) NIL T ELT)) (|leadingMonomial| (#7# 29 T ELT)) (|leadingCoefficient| (#20# 27 T ELT)) (|latex| (((|String|) $) NIL T ELT)) (|hash| (((|SingleInteger|) $) NIL T ELT)) (|ground?| (#5# 52 T ELT)) (|ground| #19#) (|fmecg| (($ $ |#2| |#1| $) 90 (AND (|has| |#2| (|CancellationAbelianMonoid|)) #6#) ELT)) (|exquo| (#8# 92 #6# ELT) ((#9# $ |#1|) 87 #6# ELT)) (|degree| (#23# 23 T ELT)) (|content| (#20# NIL #21# ELT)) (|coerce| (((|OutputForm|) $) NIL T ELT) (($ #12#) 47 T ELT) (#7# NIL #6# ELT) (($ |#1|) 42 T ELT) (($ #16#) NIL (OR #24=(|has| |#1| (|Algebra| #16#)) #17#) ELT)) (|coefficients| (((|List| |#1|) $) NIL T ELT)) (|coefficient| ((|#1| $ |#2|) 38 T ELT)) (|charthRoot| (((|Maybe| $) $) NIL (|has| |#1| (|CharacteristicNonZero|)) ELT)) (|characteristic| ((#22#) 15 T CONST)) (|binomThmExpt| (($ $ $ #22#) 76 (|has| |#1| (|CommutativeRing|)) ELT)) (|before?| #1#) (|associates?| (#2# 86 #6# ELT)) (|annihilate?| #1#) (|Zero| (#11# 28 T CONST)) (|One| (#11# 12 T CONST)) (= (#2# 85 T ELT)) (/ (#25=($ $ |#1|) 93 (|has| |#1| (|Field|)) ELT)) (- (#7# NIL T ELT) #26=(#27=($ $ $) NIL T ELT)) (+ #26#) (** (($ $ #28=(|PositiveInteger|)) 71 T ELT) (($ $ #22#) 69 T ELT)) (* (($ #28# $) NIL T ELT) (($ #22# $) NIL T ELT) (($ #12# . #29=($)) NIL T ELT) (#27# 68 T ELT) (#25# 66 T ELT) (($ |#1| . #29#) 65 T ELT) (($ #16# . #29#) NIL #24# ELT) (($ $ #16#) NIL #24# ELT))) +((~= #1=(#2=(#3=(|Boolean|) $ $) NIL T ELT)) (|zero?| #4=(#5=(#3# $) NIL T ELT)) (|unitNormal| (((|Record| (|:| |unit| $) (|:| |canonical| $) (|:| |associate| $)) $) 80 #6=(|has| |#1| (|IntegralDomain|)) ELT)) (|unitCanonical| (#7=($ $) 81 #6# ELT)) (|unit?| (#5# NIL #6# ELT)) (|subtractIfCan| ((#8=(|Maybe| $) $ $) NIL T ELT)) (|sample| (#9=($) NIL T CONST)) (|retractIfCan| (((|Union| #10=(|Integer|) . #11=(#12="failed")) . #13=($)) NIL #14=(|has| |#1| (|RetractableTo| #10#)) ELT) (((|Union| #15=(|Fraction| #10#) . #11#) . #13#) NIL #16=(|has| |#1| (|RetractableTo| #15#)) ELT) (((|Union| |#1| . #11#) $) 35 T ELT)) (|retract| ((#10# . #17=($)) NIL #14# ELT) ((#15# . #17#) NIL #16# ELT) #18=(#19=(|#1| . #17#) NIL T ELT)) (|reductum| (#7# 32 T ELT)) (|recip| ((#20=(|Union| $ #12#) $) 43 T ELT)) (|primitivePart| (#7# NIL #21=(|has| |#1| (|GcdDomain|)) ELT)) (|pomopo!| (($ $ |#1| |#2| $) 64 T ELT)) (|opposite?| #1#) (|one?| #4#) (|numberOfMonomials| ((#22=(|NonNegativeInteger|) $) 18 T ELT)) (|monomial?| #4#) (|monomial| (($ |#1| |#2|) NIL T ELT)) (|minimumDegree| (#23=(|#2| $) 25 T ELT)) (|mapExponents| (($ (|Mapping| |#2| |#2|) $) NIL T ELT)) (|map| (($ (|Mapping| |#1| |#1|) $) NIL T ELT)) (|leadingMonomial| (#7# 29 T ELT)) (|leadingCoefficient| (#19# 27 T ELT)) (|latex| (((|String|) $) NIL T ELT)) (|hash| (((|SingleInteger|) $) NIL T ELT)) (|ground?| (#5# 52 T ELT)) (|ground| #18#) (|fmecg| (($ $ |#2| |#1| $) 90 (AND (|has| |#2| (|CancellationAbelianMonoid|)) #6#) ELT)) (|exquo| ((#20# $ $) 97 #6# ELT) ((#20# $ |#1|) 87 #6# ELT)) (|degree| (#23# 23 T ELT)) (|content| (#19# NIL #21# ELT)) (|coerce| (((|OutputForm|) $) NIL T ELT) (($ #10#) 47 T ELT) (#7# NIL #6# ELT) (($ |#1|) 42 T ELT) (($ #15#) NIL (OR #24=(|has| |#1| (|Algebra| #15#)) #16#) ELT)) (|coefficients| (((|List| |#1|) $) NIL T ELT)) (|coefficient| ((|#1| $ |#2|) 38 T ELT)) (|charthRoot| ((#8# $) NIL (|has| |#1| (|CharacteristicNonZero|)) ELT)) (|characteristic| ((#22#) 15 T CONST)) (|binomThmExpt| (($ $ $ #22#) 76 (|has| |#1| (|CommutativeRing|)) ELT)) (|before?| #1#) (|associates?| (#2# 86 #6# ELT)) (|annihilate?| #1#) (|Zero| (#9# 28 T CONST)) (|One| (#9# 12 T CONST)) (= (#2# 85 T ELT)) (/ (#25=($ $ |#1|) 98 (|has| |#1| (|Field|)) ELT)) (- (#7# NIL T ELT) #26=(#27=($ $ $) NIL T ELT)) (+ #26#) (** (($ $ #28=(|PositiveInteger|)) 71 T ELT) (($ $ #22#) 69 T ELT)) (* (($ #28# $) NIL T ELT) (($ #22# $) NIL T ELT) (($ #10# . #29=($)) NIL T ELT) (#27# 68 T ELT) (#25# 66 T ELT) (($ |#1| . #29#) 65 T ELT) (($ #15# . #29#) NIL #24# ELT) (($ $ #15#) NIL #24# ELT))) (((|PolynomialRing| |#1| |#2|) (|Join| (|FiniteAbelianMonoidRing| |#1| |#2|) (CATEGORY |domain| (IF (|has| |#1| (|IntegralDomain|)) (IF (|has| |#2| (|CancellationAbelianMonoid|)) (SIGNATURE |fmecg| ($ $ |#2| |#1| $)) |%noBranch|) |%noBranch|) (IF (|has| |#1| #1=(ATTRIBUTE |canonicalUnitNormal|)) #1# |%noBranch|))) (|Ring|) (|OrderedAbelianMonoid|)) (T |PolynomialRing|)) ((|fmecg| (*1 *1 *1 *2 *3 *1) (AND (|isDomain| *1 (|PolynomialRing| *3 *2)) (|ofCategory| *2 (|CancellationAbelianMonoid|)) (|ofCategory| *3 (|IntegralDomain|)) (|ofCategory| *3 (|Ring|)) (|ofCategory| *2 (|OrderedAbelianMonoid|))))) ((|firstUncouplingMatrix| (((|Union| (|Matrix| |#1|) "failed") |#2| (|PositiveInteger|)) 18 T ELT))) @@ -2909,7 +2909,7 @@ NIL ((|print| (((|Void|) (|OutputForm|)) 9 T ELT))) (((|PrintPackage|) (CATEGORY |package| (SIGNATURE |print| ((|Void|) (|OutputForm|))))) (T |PrintPackage|)) ((|print| (*1 *2 *3) (AND (|isDomain| *3 (|OutputForm|)) (|isDomain| *2 (|Void|)) (|isDomain| *1 (|PrintPackage|))))) -((~= #1=(#2=(#3=(|Boolean|) $ $) NIL T ELT)) (|zero?| (#4=(#3# $) NIL #5=(OR #6=(AND (|has| |#1| #7=(|AbelianGroup|)) (|has| |#2| #7#)) #8=(AND (|has| |#1| #9=(|AbelianMonoid|)) (|has| |#2| #9#)) #10=(AND (|has| |#1| #11=(|CancellationAbelianMonoid|)) (|has| |#2| #11#)) #12=(AND (|has| |#1| #13=(|OrderedAbelianMonoidSup|)) (|has| |#2| #13#))) ELT)) (|sup| (#14=($ $ $) 65 #12# ELT)) (|subtractIfCan| ((#15=(|Union| $ "failed") $ $) 52 (OR #6# #10# #12#) ELT)) (|size| ((#16=(|NonNegativeInteger|)) 36 #17=(AND (|has| |#1| #18=(|Finite|)) (|has| |#2| #18#)) ELT)) (|selectsecond| ((|#2| $) 22 T ELT)) (|selectfirst| ((|#1| $) 21 T ELT)) (|sample| (#19=($) NIL (OR #6# #8# #10# #20=(AND (|has| |#1| #21=(|Group|)) (|has| |#2| #21#)) #22=(AND (|has| |#1| #23=(|Monoid|)) (|has| |#2| #23#)) #12#) CONST)) (|recip| ((#15# $) NIL #24=(OR #20# #22#) ELT)) (|random| (#19# NIL #17# ELT)) (|positive?| (#4# NIL #12# ELT)) (|opposite?| (#2# NIL #5# ELT)) (|one?| (#4# NIL #24# ELT)) (|min| #25=(#14# NIL #26=(OR #12# (AND (|has| |#1| #27=(|OrderedSet|)) (|has| |#2| #27#))) ELT)) (|max| #25#) (|makeprod| (($ |#1| |#2|) 20 T ELT)) (|lookup| ((#28=(|PositiveInteger|) $) NIL #17# ELT)) (|latex| (((|String|) $) NIL T ELT)) (|inv| (#29=($ $) 39 #20# ELT)) (|index| (($ #28#) NIL #17# ELT)) (|hash| (((|SingleInteger|) $) NIL T ELT)) (|conjugate| #30=(#14# NIL #20# ELT)) (|commutator| #30#) (|coerce| (((|OutputForm|) $) 14 T ELT)) (|before?| #1#) (|Zero| (#19# 42 #5# CONST)) (|One| (#19# 25 #24# CONST)) (>= #31=(#2# NIL #26# ELT)) (> #31#) (= (#2# 19 T ELT)) (<= #31#) (< (#2# 69 #26# ELT)) (/ #30#) (- (#14# 58 #6# ELT) (#29# 55 #6# ELT)) (+ (#14# 45 #5# ELT)) (** (($ $ #32=(|Integer|)) NIL #20# ELT) (($ $ #16#) 32 #24# ELT) (($ $ #28#) NIL #24# ELT)) (* (($ #32# $) 62 #6# ELT) (($ #16# $) 48 #5# ELT) (($ #28# $) NIL #5# ELT) (#14# 28 #24# ELT))) +((~= #1=(#2=(#3=(|Boolean|) $ $) NIL T ELT)) (|zero?| (#4=(#3# $) NIL #5=(OR #6=(AND (|has| |#1| #7=(|AbelianGroup|)) (|has| |#2| #7#)) #8=(AND (|has| |#1| #9=(|AbelianMonoid|)) (|has| |#2| #9#)) #10=(AND (|has| |#1| #11=(|CancellationAbelianMonoid|)) (|has| |#2| #11#)) #12=(AND (|has| |#1| #13=(|OrderedAbelianMonoidSup|)) (|has| |#2| #13#))) ELT)) (|sup| (#14=($ $ $) 75 #12# ELT)) (|subtractIfCan| (((|Maybe| $) $ $) 62 (OR #6# #10# #12#) ELT)) (|size| ((#15=(|NonNegativeInteger|)) 36 #16=(AND (|has| |#1| #17=(|Finite|)) (|has| |#2| #17#)) ELT)) (|selectsecond| ((|#2| $) 22 T ELT)) (|selectfirst| ((|#1| $) 21 T ELT)) (|sample| (#18=($) NIL (OR #6# #8# #10# #19=(AND (|has| |#1| #20=(|Group|)) (|has| |#2| #20#)) #21=(AND (|has| |#1| #22=(|Monoid|)) (|has| |#2| #22#)) #12#) CONST)) (|recip| (((|Union| $ "failed") $) NIL #23=(OR #19# #21#) ELT)) (|random| (#18# NIL #16# ELT)) (|positive?| (#4# NIL #12# ELT)) (|opposite?| (#2# NIL #5# ELT)) (|one?| (#4# NIL #23# ELT)) (|min| #24=(#14# NIL #25=(OR #12# (AND (|has| |#1| #26=(|OrderedSet|)) (|has| |#2| #26#))) ELT)) (|max| #24#) (|makeprod| (($ |#1| |#2|) 20 T ELT)) (|lookup| ((#27=(|PositiveInteger|) $) NIL #16# ELT)) (|latex| (((|String|) $) NIL T ELT)) (|inv| (#28=($ $) 39 #19# ELT)) (|index| (($ #27#) NIL #16# ELT)) (|hash| (((|SingleInteger|) $) NIL T ELT)) (|conjugate| #29=(#14# NIL #19# ELT)) (|commutator| #29#) (|coerce| (((|OutputForm|) $) 14 T ELT)) (|before?| #1#) (|Zero| (#18# 42 #5# CONST)) (|One| (#18# 25 #23# CONST)) (>= #30=(#2# NIL #25# ELT)) (> #30#) (= (#2# 19 T ELT)) (<= #30#) (< (#2# 79 #25# ELT)) (/ #29#) (- (#14# 68 #6# ELT) (#28# 65 #6# ELT)) (+ (#14# 45 #5# ELT)) (** (($ $ #31=(|Integer|)) NIL #19# ELT) (($ $ #15#) 32 #23# ELT) (($ $ #27#) NIL #23# ELT)) (* (($ #31# $) 72 #6# ELT) (($ #15# $) 48 #5# ELT) (($ #27# $) NIL #5# ELT) (#14# 28 #23# ELT))) (((|Product| |#1| |#2|) (|Join| #1=(|SetCategory|) (CATEGORY |domain| (IF (|has| |#1| #2=(|Finite|)) (IF (|has| |#2| #2#) (ATTRIBUTE #2#) |%noBranch|) |%noBranch|) (IF (|has| |#1| #3=(|Monoid|)) (IF (|has| |#2| #3#) (ATTRIBUTE #3#) |%noBranch|) |%noBranch|) (IF (|has| |#1| #4=(|AbelianMonoid|)) (IF (|has| |#2| #4#) (ATTRIBUTE #4#) |%noBranch|) |%noBranch|) (IF (|has| |#1| #5=(|CancellationAbelianMonoid|)) (IF (|has| |#2| #5#) (ATTRIBUTE #5#) |%noBranch|) |%noBranch|) (IF (|has| |#1| #6=(|Group|)) (IF (|has| |#2| #6#) (ATTRIBUTE #6#) |%noBranch|) |%noBranch|) (IF (|has| |#1| #7=(|AbelianGroup|)) (IF (|has| |#2| #7#) (ATTRIBUTE #7#) |%noBranch|) |%noBranch|) (IF (|has| |#1| #8=(|OrderedAbelianMonoidSup|)) (IF (|has| |#2| #8#) (ATTRIBUTE #8#) |%noBranch|) |%noBranch|) (IF (|has| |#1| #9=(|OrderedSet|)) (IF (|has| |#2| #9#) (ATTRIBUTE #9#) |%noBranch|) |%noBranch|) (SIGNATURE |makeprod| ($ |#1| |#2|)) (SIGNATURE |selectfirst| (|#1| $)) (SIGNATURE |selectsecond| (|#2| $)))) #1# #1#) (T |Product|)) ((|makeprod| (*1 *1 *2 *3) (AND #1=(|isDomain| *1 (|Product| *2 *3)) #2=(|ofCategory| *2 #3=(|SetCategory|)) #4=(|ofCategory| *3 #3#))) (|selectfirst| #5=(*1 *2 *1) (AND #2# #1# #4#)) (|selectsecond| #5# (AND #2# (|isDomain| *1 (|Product| *3 *2)) #4#))) ((|value| ((#1=(|SExpression|) $) 13 T ELT)) (|property| (($ #2=(|Identifier|) #1#) 15 T ELT)) (|name| ((#2# $) 11 T ELT)) (|coerce| (((|OutputForm|) $) 25 T ELT))) @@ -2940,13 +2940,13 @@ NIL ((~= #1=(((|Boolean|) $ $) NIL T ELT)) (|target| (((|TypeAst|) $) 14 T ELT)) (|latex| (((|String|) $) NIL T ELT)) (|hash| (((|SingleInteger|) $) NIL T ELT)) (|expression| (((|SpadAst|) $) 11 T ELT)) (|coerce| (((|OutputForm|) $) 21 T ELT) (($ #2=(|Syntax|)) NIL T ELT) ((#2# $) NIL T ELT)) (|before?| #1#) (= #1#)) (((|PretendAst|) (|Join| (|SpadSyntaxCategory|) (CATEGORY |domain| (SIGNATURE |expression| ((|SpadAst|) $)) (SIGNATURE |target| ((|TypeAst|) $))))) (T |PretendAst|)) ((|expression| #1=(*1 *2 *1) (AND (|isDomain| *2 (|SpadAst|)) #2=(|isDomain| *1 (|PretendAst|)))) (|target| #1# (AND (|isDomain| *2 (|TypeAst|)) #2#))) -((~= #1=(#2=(#3=(|Boolean|) $ $) NIL T ELT)) (|zero?| (#4=(#3# $) 40 T ELT)) (|subtractIfCan| (((|Union| $ "failed") $ $) 54 T ELT)) (|sample| (#5=($) NIL T CONST)) (|powers| (((|List| (|Pair| #6=(|PositiveInteger|) #6#)) $) 64 T ELT)) (|positive?| (#4# NIL T ELT)) (|pdct| ((#6# $) 91 T ELT)) (|parts| (#7=(#8=(|List| #6#) $) 17 T ELT)) (|partitions| (((|Stream| $) #9=(|NonNegativeInteger|)) 39 T ELT)) (|partition| (($ #8#) 16 T ELT)) (|opposite?| #1#) (|min| #10=(#11=($ $ $) NIL T ELT)) (|max| #10#) (|latex| (((|String|) $) NIL T ELT)) (|hash| (((|SingleInteger|) $) NIL T ELT)) (|conjugate| (($ $) 67 T ELT)) (|coerce| (((|OutputForm|) $) 87 T ELT) (#7# 11 T ELT)) (|before?| #1#) (|Zero| (#5# 10 T CONST)) (>= #1#) (> #1#) (= (#2# 44 T ELT)) (<= #1#) (< (#2# 42 T ELT)) (+ (#11# 46 T ELT)) (* (($ #6# $) NIL T ELT) (($ #9# $) 49 T ELT)) (|#| ((#9# $) 22 T ELT))) +((~= #1=(#2=(#3=(|Boolean|) $ $) NIL T ELT)) (|zero?| (#4=(#3# $) 40 T ELT)) (|subtractIfCan| (((|Maybe| $) $ $) 62 T ELT)) (|sample| (#5=($) NIL T CONST)) (|powers| (((|List| (|Pair| #6=(|PositiveInteger|) #6#)) $) 72 T ELT)) (|positive?| (#4# NIL T ELT)) (|pdct| ((#6# $) 99 T ELT)) (|parts| (#7=(#8=(|List| #6#) $) 17 T ELT)) (|partitions| (((|Stream| $) #9=(|NonNegativeInteger|)) 39 T ELT)) (|partition| (($ #8#) 16 T ELT)) (|opposite?| #1#) (|min| #10=(#11=($ $ $) NIL T ELT)) (|max| #10#) (|latex| (((|String|) $) NIL T ELT)) (|hash| (((|SingleInteger|) $) NIL T ELT)) (|conjugate| (($ $) 75 T ELT)) (|coerce| (((|OutputForm|) $) 95 T ELT) (#7# 11 T ELT)) (|before?| #1#) (|Zero| (#5# 10 T CONST)) (>= #1#) (> #1#) (= (#2# 44 T ELT)) (<= #1#) (< (#2# 42 T ELT)) (+ (#11# 46 T ELT)) (* (($ #6# $) NIL T ELT) (($ #9# $) 51 T ELT)) (|#| ((#9# $) 22 T ELT))) (((|Partition|) (|Join| (|OrderedCancellationAbelianMonoid|) (|CoercibleTo| #1=(|List| #2=(|PositiveInteger|))) (CATEGORY |domain| (SIGNATURE |partition| ($ #1#)) (SIGNATURE |parts| (#1# $)) (SIGNATURE |#| (#3=(|NonNegativeInteger|) $)) (SIGNATURE |partitions| ((|Stream| $) #3#)) (SIGNATURE |powers| ((|List| (|Pair| #2# #2#)) $)) (SIGNATURE |pdct| (#2# $)) (SIGNATURE |conjugate| ($ $))))) (T |Partition|)) ((|partition| (*1 *1 *2) #1=(AND (|isDomain| *2 (|List| #2=(|PositiveInteger|))) #3=(|isDomain| *1 #4=(|Partition|)))) (|parts| #5=(*1 *2 *1) #1#) (|#| #5# (AND (|isDomain| *2 #6=(|NonNegativeInteger|)) #3#)) (|partitions| (*1 *2 *3) (AND (|isDomain| *3 #6#) (|isDomain| *2 (|Stream| #4#)) #3#)) (|powers| #5# (AND (|isDomain| *2 (|List| (|Pair| #2# #2#))) #3#)) (|pdct| #5# (AND (|isDomain| *2 #2#) #3#)) (|conjugate| (*1 *1 *1) #3#)) ((/ (#1=($ $ |#2|) 31 T ELT)) (- (($ $) 23 T ELT) #2=(($ $ $) NIL T ELT)) (* (($ (|PositiveInteger|) $) NIL T ELT) (($ (|NonNegativeInteger|) $) NIL T ELT) (($ #3=(|Integer|) $) 17 T ELT) #2# (#1# 21 T ELT) (($ |#2| $) 20 T ELT) (($ #4=(|Fraction| #3#) $) 27 T ELT) (($ $ #4#) 29 T ELT))) (((|PowerSeriesCategory&| |#1| |#2| |#3| |#4|) (CATEGORY |package| (SIGNATURE * (|#1| |#1| #1=(|Fraction| #2=(|Integer|)))) (SIGNATURE * (|#1| #1# |#1|)) (SIGNATURE / #3=(|#1| |#1| |#2|)) (SIGNATURE * (|#1| |#2| |#1|)) (SIGNATURE * #3#) (SIGNATURE * #4=(|#1| |#1| |#1|)) (SIGNATURE - #4#) (SIGNATURE - (|#1| |#1|)) (SIGNATURE * (|#1| #2# |#1|)) (SIGNATURE * (|#1| (|NonNegativeInteger|) |#1|)) (SIGNATURE * (|#1| (|PositiveInteger|) |#1|))) (|PowerSeriesCategory| |#2| |#3| |#4|) (|Ring|) (|OrderedAbelianMonoid|) (|OrderedSet|)) (T |PowerSeriesCategory&|)) NIL -((~= (#1=((|Boolean|) $ $) 7 T ELT)) (|zero?| ((#2=(|Boolean|) $) 22 T ELT)) (|variables| (((|List| |#3|) $) 96 T ELT)) (|unitNormal| (((|Record| (|:| |unit| $) (|:| |canonical| $) (|:| |associate| $)) $) 72 (|has| |#1| . #3=((|IntegralDomain|))) ELT)) (|unitCanonical| (($ $) 73 (|has| |#1| . #3#) ELT)) (|unit?| ((#4=(|Boolean|) $) 75 (|has| |#1| . #3#) ELT)) (|subtractIfCan| (((|Union| $ "failed") $ $) 26 T ELT)) (|sample| (#5=($) 23 T CONST)) (|reductum| (#6=($ $) 81 T ELT)) (|recip| (((|Union| $ "failed") $) 42 T ELT)) (|pole?| (((|Boolean|) $) 95 T ELT)) (|opposite?| ((#2# $ $) 20 T ELT)) (|one?| (((|Boolean|) $) 44 T ELT)) (|monomial?| (((|Boolean|) $) 83 T ELT)) (|monomial| (($ |#1| |#2|) 82 T ELT) (($ $ |#3| |#2|) 98 T ELT) (($ $ (|List| |#3|) (|List| |#2|)) 97 T ELT)) (|map| (($ (|Mapping| |#1| |#1|) $) 87 T ELT)) (|leadingMonomial| (#6# 85 T ELT)) (|leadingCoefficient| ((|#1| $) 86 T ELT)) (|latex| (((|String|) $) 11 T ELT)) (|hash| (((|SingleInteger|) $) 12 T ELT)) (|exquo| (((|Union| $ "failed") $ $) 71 (|has| |#1| . #3#) ELT)) (|degree| ((|#2| $) 84 T ELT)) (|complete| (($ $) 94 T ELT)) (|coerce| (((|OutputForm|) $) 13 T ELT) (($ (|Integer|)) 41 T ELT) (($ #7=(|Fraction| (|Integer|))) 78 (|has| |#1| . #8=((|Algebra| #7#))) ELT) (($ $) 70 (|has| |#1| . #3#) ELT) (($ |#1|) 68 (|has| |#1| (|CommutativeRing|)) ELT)) (|coefficient| ((|#1| $ |#2|) 80 T ELT)) (|charthRoot| (((|Maybe| $) $) 69 (|has| |#1| (|CharacteristicNonZero|)) ELT)) (|characteristic| (((|NonNegativeInteger|)) 40 T CONST)) (|before?| (#1# 6 T ELT)) (|associates?| ((#4# $ $) 74 (|has| |#1| . #3#) ELT)) (|annihilate?| (((|Boolean|) $ $) 33 T ELT)) (|Zero| (#5# 24 T CONST)) (|One| (($) 45 T CONST)) (= (#1# 8 T ELT)) (/ (($ $ |#1|) 79 (|has| |#1| (|Field|)) ELT)) (- (($ $) 29 T ELT) (($ $ $) 28 T ELT)) (+ (($ $ $) 18 T ELT)) (** (($ $ (|PositiveInteger|)) 35 T ELT) (($ $ (|NonNegativeInteger|)) 43 T ELT)) (* (($ (|PositiveInteger|) $) 17 T ELT) (($ (|NonNegativeInteger|) $) 21 T ELT) (($ (|Integer|) . #9=($)) 30 T ELT) (($ $ $) 34 T ELT) (($ $ |#1|) 89 T ELT) (($ |#1| . #9#) 88 T ELT) (($ #7# . #9#) 77 (|has| |#1| . #8#) ELT) (($ $ #7#) 76 (|has| |#1| . #8#) ELT))) +((~= (#1=((|Boolean|) $ $) 7 T ELT)) (|zero?| ((#2=(|Boolean|) $) 22 T ELT)) (|variables| (((|List| |#3|) $) 96 T ELT)) (|unitNormal| (((|Record| (|:| |unit| $) (|:| |canonical| $) (|:| |associate| $)) $) 73 (|has| |#1| . #3=((|IntegralDomain|))) ELT)) (|unitCanonical| (($ $) 74 (|has| |#1| . #3#) ELT)) (|unit?| ((#4=(|Boolean|) $) 76 (|has| |#1| . #3#) ELT)) (|subtractIfCan| (((|Maybe| $) $ $) 26 T ELT)) (|sample| (#5=($) 23 T CONST)) (|reductum| (#6=($ $) 82 T ELT)) (|recip| (((|Union| $ "failed") $) 43 T ELT)) (|pole?| (((|Boolean|) $) 95 T ELT)) (|opposite?| ((#2# $ $) 20 T ELT)) (|one?| (((|Boolean|) $) 45 T ELT)) (|monomial?| (((|Boolean|) $) 84 T ELT)) (|monomial| (($ |#1| |#2|) 83 T ELT) (($ $ |#3| |#2|) 98 T ELT) (($ $ (|List| |#3|) (|List| |#2|)) 97 T ELT)) (|map| (($ (|Mapping| |#1| |#1|) $) 88 T ELT)) (|leadingMonomial| (#6# 86 T ELT)) (|leadingCoefficient| ((|#1| $) 87 T ELT)) (|latex| (((|String|) $) 11 T ELT)) (|hash| (((|SingleInteger|) $) 12 T ELT)) (|exquo| (((|Union| $ "failed") $ $) 72 (|has| |#1| . #3#) ELT)) (|degree| ((|#2| $) 85 T ELT)) (|complete| (($ $) 94 T ELT)) (|coerce| (((|OutputForm|) $) 13 T ELT) (($ (|Integer|)) 42 T ELT) (($ #7=(|Fraction| (|Integer|))) 79 (|has| |#1| . #8=((|Algebra| #7#))) ELT) (($ $) 71 (|has| |#1| . #3#) ELT) (($ |#1|) 69 (|has| |#1| (|CommutativeRing|)) ELT)) (|coefficient| ((|#1| $ |#2|) 81 T ELT)) (|charthRoot| (((|Maybe| $) $) 70 (|has| |#1| (|CharacteristicNonZero|)) ELT)) (|characteristic| (((|NonNegativeInteger|)) 41 T CONST)) (|before?| (#1# 6 T ELT)) (|associates?| ((#4# $ $) 75 (|has| |#1| . #3#) ELT)) (|annihilate?| (((|Boolean|) $ $) 34 T ELT)) (|Zero| (#5# 24 T CONST)) (|One| (($) 46 T CONST)) (= (#1# 8 T ELT)) (/ (($ $ |#1|) 80 (|has| |#1| (|Field|)) ELT)) (- (($ $) 30 T ELT) (($ $ $) 29 T ELT)) (+ (($ $ $) 18 T ELT)) (** (($ $ (|PositiveInteger|)) 36 T ELT) (($ $ (|NonNegativeInteger|)) 44 T ELT)) (* (($ (|PositiveInteger|) $) 17 T ELT) (($ (|NonNegativeInteger|) $) 21 T ELT) (($ (|Integer|) . #9=($)) 31 T ELT) (($ $ $) 35 T ELT) (($ $ |#1|) 90 T ELT) (($ |#1| . #9#) 89 T ELT) (($ #7# . #9#) 78 (|has| |#1| . #8#) ELT) (($ $ #7#) 77 (|has| |#1| . #8#) ELT))) (((|PowerSeriesCategory| |#1| |#2| |#3|) (|Category|) (|Ring|) (|OrderedAbelianMonoid|) (|OrderedSet|)) (T |PowerSeriesCategory|)) ((|leadingCoefficient| (*1 *2 *1) (AND (|ofCategory| *1 (|PowerSeriesCategory| *2 *3 *4)) (|ofCategory| *3 (|OrderedAbelianMonoid|)) (|ofCategory| *4 (|OrderedSet|)) (|ofCategory| *2 (|Ring|)))) (|leadingMonomial| (*1 *1 *1) (AND (|ofCategory| *1 (|PowerSeriesCategory| *2 *3 *4)) (|ofCategory| *2 (|Ring|)) (|ofCategory| *3 (|OrderedAbelianMonoid|)) (|ofCategory| *4 (|OrderedSet|)))) (|degree| (*1 *2 *1) (AND (|ofCategory| *1 (|PowerSeriesCategory| *3 *2 *4)) (|ofCategory| *3 (|Ring|)) (|ofCategory| *4 (|OrderedSet|)) (|ofCategory| *2 (|OrderedAbelianMonoid|)))) (|monomial| (*1 *1 *1 *2 *3) (AND (|ofCategory| *1 (|PowerSeriesCategory| *4 *3 *2)) (|ofCategory| *4 (|Ring|)) (|ofCategory| *3 (|OrderedAbelianMonoid|)) (|ofCategory| *2 (|OrderedSet|)))) (|monomial| (*1 *1 *1 *2 *3) (AND (|isDomain| *2 (|List| *6)) (|isDomain| *3 (|List| *5)) (|ofCategory| *1 (|PowerSeriesCategory| *4 *5 *6)) (|ofCategory| *4 (|Ring|)) (|ofCategory| *5 (|OrderedAbelianMonoid|)) (|ofCategory| *6 (|OrderedSet|)))) (|variables| (*1 *2 *1) (AND (|ofCategory| *1 (|PowerSeriesCategory| *3 *4 *5)) (|ofCategory| *3 (|Ring|)) (|ofCategory| *4 (|OrderedAbelianMonoid|)) (|ofCategory| *5 (|OrderedSet|)) (|isDomain| *2 (|List| *5)))) (|pole?| (*1 *2 *1) (AND (|ofCategory| *1 (|PowerSeriesCategory| *3 *4 *5)) (|ofCategory| *3 (|Ring|)) (|ofCategory| *4 (|OrderedAbelianMonoid|)) (|ofCategory| *5 (|OrderedSet|)) (|isDomain| *2 (|Boolean|)))) (|complete| (*1 *1 *1) (AND (|ofCategory| *1 (|PowerSeriesCategory| *2 *3 *4)) (|ofCategory| *2 (|Ring|)) (|ofCategory| *3 (|OrderedAbelianMonoid|)) (|ofCategory| *4 (|OrderedSet|))))) (|Join| (|AbelianMonoidRing| |t#1| |t#2|) (CATEGORY |domain| (SIGNATURE |monomial| ($ $ |t#3| |t#2|)) (SIGNATURE |monomial| ($ $ (|List| |t#3|) (|List| |t#2|))) (SIGNATURE |leadingMonomial| ($ $)) (SIGNATURE |leadingCoefficient| (|t#1| $)) (SIGNATURE |degree| (|t#2| $)) (SIGNATURE |variables| ((|List| |t#3|) $)) (SIGNATURE |pole?| ((|Boolean|) $)) (SIGNATURE |complete| ($ $)))) @@ -2956,7 +2956,7 @@ NIL ((|listBranches| (*1 *2 *1) (AND (|ofCategory| *1 (|PlottableSpaceCurveCategory|)) (|isDomain| *2 (|List| (|List| (|Point| (|DoubleFloat|))))))) (|xRange| (*1 *2 *1) (AND (|ofCategory| *1 (|PlottableSpaceCurveCategory|)) (|isDomain| *2 (|Segment| (|DoubleFloat|))))) (|yRange| (*1 *2 *1) (AND (|ofCategory| *1 (|PlottableSpaceCurveCategory|)) (|isDomain| *2 (|Segment| (|DoubleFloat|))))) (|zRange| (*1 *2 *1) (AND (|ofCategory| *1 (|PlottableSpaceCurveCategory|)) (|isDomain| *2 (|Segment| (|DoubleFloat|)))))) (|Join| (|CoercibleTo| (|OutputForm|)) (CATEGORY |domain| (SIGNATURE |listBranches| ((|List| (|List| (|Point| (|DoubleFloat|)))) $)) (SIGNATURE |xRange| ((|Segment| (|DoubleFloat|)) $)) (SIGNATURE |yRange| ((|Segment| (|DoubleFloat|)) $)) (SIGNATURE |zRange| ((|Segment| (|DoubleFloat|)) $)))) (((|CoercibleTo| (|OutputForm|)) . T)) -((|variables| (#1=((|List| |#4|) $) 23 T ELT)) (|trivialIdeal?| (#2=(#3=(|Boolean|) $) 55 T ELT)) (|triangular?| (#2# 54 T ELT)) (|sort| (((|Record| (|:| |under| $) (|:| |floor| $) (|:| |upper| $)) $ |#4|) 42 T ELT)) (|roughUnitIdeal?| (#2# 56 T ELT)) (|roughSubIdeal?| (#4=(#3# $ $) 62 T ELT)) (|roughEqualIdeals?| (#4# 65 T ELT)) (|roughBase?| (#2# 60 T ELT)) (|rewriteIdealWithRemainder| (#5=(#6=(|List| |#5|) #6# $) 98 T ELT)) (|rewriteIdealWithHeadRemainder| (#5# 95 T ELT)) (|remainder| (((|Record| (|:| |rnum| |#2|) (|:| |polnum| |#5|) #7=(|:| |den| |#2|)) |#5| $) 88 T ELT)) (|mainVariables| (#1# 27 T ELT)) (|mainVariable?| ((#3# |#4| $) 34 T ELT)) (|headRemainder| (((|Record| (|:| |num| |#5|) #7#) |#5| $) 81 T ELT)) (|collectUpper| (#8=($ $ |#4|) 39 T ELT)) (|collectUnder| (#8# 38 T ELT)) (|collect| (#8# 40 T ELT)) (= (#4# 46 T ELT))) +((|variables| (#1=((|List| |#4|) $) 23 T ELT)) (|trivialIdeal?| (#2=(#3=(|Boolean|) $) 55 T ELT)) (|triangular?| (#2# 54 T ELT)) (|sort| (((|Record| (|:| |under| $) (|:| |floor| $) (|:| |upper| $)) $ |#4|) 42 T ELT)) (|roughUnitIdeal?| (#2# 56 T ELT)) (|roughSubIdeal?| (#4=(#3# $ $) 62 T ELT)) (|roughEqualIdeals?| (#4# 65 T ELT)) (|roughBase?| (#2# 60 T ELT)) (|rewriteIdealWithRemainder| (#5=(#6=(|List| |#5|) #6# $) 103 T ELT)) (|rewriteIdealWithHeadRemainder| (#5# 100 T ELT)) (|remainder| (((|Record| (|:| |rnum| |#2|) (|:| |polnum| |#5|) #7=(|:| |den| |#2|)) |#5| $) 93 T ELT)) (|mainVariables| (#1# 27 T ELT)) (|mainVariable?| ((#3# |#4| $) 34 T ELT)) (|headRemainder| (((|Record| (|:| |num| |#5|) #7#) |#5| $) 86 T ELT)) (|collectUpper| (#8=($ $ |#4|) 39 T ELT)) (|collectUnder| (#8# 38 T ELT)) (|collect| (#8# 40 T ELT)) (= (#4# 46 T ELT))) (((|PolynomialSetCategory&| |#1| |#2| |#3| |#4| |#5|) (CATEGORY |package| (SIGNATURE |triangular?| #1=(#2=(|Boolean|) |#1|)) (SIGNATURE |rewriteIdealWithRemainder| #3=(#4=(|List| |#5|) #4# |#1|)) (SIGNATURE |rewriteIdealWithHeadRemainder| #3#) (SIGNATURE |remainder| ((|Record| (|:| |rnum| |#2|) (|:| |polnum| |#5|) #5=(|:| |den| |#2|)) |#5| |#1|)) (SIGNATURE |headRemainder| ((|Record| (|:| |num| |#5|) #5#) |#5| |#1|)) (SIGNATURE |roughUnitIdeal?| #1#) (SIGNATURE |roughEqualIdeals?| #6=(#2# |#1| |#1|)) (SIGNATURE |roughSubIdeal?| #6#) (SIGNATURE |roughBase?| #1#) (SIGNATURE |trivialIdeal?| #1#) (SIGNATURE |sort| ((|Record| (|:| |under| |#1|) (|:| |floor| |#1|) (|:| |upper| |#1|)) |#1| |#4|)) (SIGNATURE |collectUpper| #7=(|#1| |#1| |#4|)) (SIGNATURE |collect| #7#) (SIGNATURE |collectUnder| #7#) (SIGNATURE |mainVariable?| (#2# |#4| |#1|)) (SIGNATURE |mainVariables| #8=((|List| |#4|) |#1|)) (SIGNATURE |variables| #8#) (SIGNATURE = #6#)) (|PolynomialSetCategory| |#2| |#3| |#4| |#5|) (|Ring|) (|OrderedAbelianMonoidSup|) (|OrderedSet|) (|RecursivePolynomialCategory| |#2| |#3| |#4|)) (T |PolynomialSetCategory&|)) NIL ((~= (#1=((|Boolean|) $ $) 7 T ELT)) (|variables| (((|List| |#3|) $) 39 T ELT)) (|trivialIdeal?| (((|Boolean|) $) 32 T ELT)) (|triangular?| (((|Boolean|) $) 23 (|has| |#1| (|IntegralDomain|)) ELT)) (|sort| (((|Record| (|:| |under| $) (|:| |floor| $) (|:| |upper| $)) $ |#3|) 33 T ELT)) (|select| (($ (|Mapping| #2=(|Boolean|) |#4|) . #3=($)) 67 (|has| $ (|FiniteAggregate| |#4|)) ELT)) (|sample| (#4=($) 59 T CONST)) (|roughUnitIdeal?| (((|Boolean|) $) 28 (|has| |#1| (|IntegralDomain|)) ELT)) (|roughSubIdeal?| (((|Boolean|) $ $) 30 (|has| |#1| (|IntegralDomain|)) ELT)) (|roughEqualIdeals?| (((|Boolean|) $ $) 29 (|has| |#1| (|IntegralDomain|)) ELT)) (|roughBase?| (((|Boolean|) $) 31 (|has| |#1| (|IntegralDomain|)) ELT)) (|rewriteIdealWithRemainder| (((|List| |#4|) (|List| |#4|) $) 24 (|has| |#1| (|IntegralDomain|)) ELT)) (|rewriteIdealWithHeadRemainder| (((|List| |#4|) (|List| |#4|) $) 25 (|has| |#1| (|IntegralDomain|)) ELT)) (|retractIfCan| (((|Union| $ "failed") (|List| |#4|)) 42 T ELT)) (|retract| (($ (|List| |#4|)) 41 T ELT)) (|removeDuplicates| (($ $) 69 (AND (|has| |#4| . #5=((|BasicType|))) (|has| $ (|FiniteAggregate| |#4|))) ELT)) (|remove| (($ |#4| $) 68 (AND (|has| |#4| . #5#) (|has| $ (|FiniteAggregate| |#4|))) ELT) (($ (|Mapping| #2# |#4|) . #3#) 66 (|has| $ (|FiniteAggregate| |#4|)) ELT)) (|remainder| (((|Record| (|:| |rnum| |#1|) (|:| |polnum| |#4|) (|:| |den| |#1|)) |#4| $) 26 (|has| |#1| (|IntegralDomain|)) ELT)) (|reduce| ((|#4| (|Mapping| |#4| |#4| |#4|) $ |#4| |#4|) 54 (|has| |#4| . #6=((|BasicType|))) ELT) ((|#4| (|Mapping| |#4| |#4| |#4|) $ |#4|) 50 T ELT) ((|#4| (|Mapping| |#4| |#4| |#4|) $) 49 T ELT)) (|mvar| ((|#3| $) 40 T ELT)) (|members| (((|List| |#4|) $) 48 T ELT)) (|member?| ((#7=(|Boolean|) |#4| $) 53 (|has| |#4| . #6#) ELT)) (|map| (($ (|Mapping| |#4| |#4|) $) 60 T ELT)) (|mainVariables| (((|List| |#3|) $) 38 T ELT)) (|mainVariable?| (((|Boolean|) |#3| $) 37 T ELT)) (|latex| (((|String|) $) 11 T ELT)) (|headRemainder| (((|Record| (|:| |num| |#4|) (|:| |den| |#1|)) |#4| $) 27 (|has| |#1| (|IntegralDomain|)) ELT)) (|hash| (((|SingleInteger|) $) 12 T ELT)) (|find| (((|Union| |#4| "failed") (|Mapping| #7# |#4|) $) 51 T ELT)) (|every?| ((#7# (|Mapping| #7# |#4|) . #8=($)) 46 T ELT)) (|eval| (($ $ (|List| |#4|) (|List| |#4|)) 64 (AND (|has| |#4| (|Evalable| |#4|)) (|has| |#4| . #9=((|SetCategory|)))) ELT) (($ $ |#4| |#4|) 63 (AND (|has| |#4| (|Evalable| |#4|)) (|has| |#4| . #9#)) ELT) (($ $ (|Equation| |#4|)) 62 (AND (|has| |#4| (|Evalable| |#4|)) (|has| |#4| . #9#)) ELT) (($ $ (|List| (|Equation| |#4|))) 61 (AND (|has| |#4| (|Evalable| |#4|)) (|has| |#4| . #9#)) ELT)) (|eq?| ((#10=(|Boolean|) $ $) 55 T ELT)) (|empty?| ((#10# $) 58 T ELT)) (|empty| (#4# 57 T ELT)) (|count| ((#11=(|NonNegativeInteger|) |#4| $) 52 (|has| |#4| . #6#) ELT) ((#11# (|Mapping| #7# |#4|) $) 47 T ELT)) (|copy| (($ $) 56 T ELT)) (|convert| ((#12=(|InputForm|) $) 70 (|has| |#4| (|ConvertibleTo| #12#)) ELT)) (|construct| (($ (|List| |#4|)) 65 T ELT)) (|collectUpper| (($ $ |#3|) 34 T ELT)) (|collectUnder| (($ $ |#3|) 36 T ELT)) (|collect| (($ $ |#3|) 35 T ELT)) (|coerce| (((|OutputForm|) . #13=($)) 13 T ELT) (((|List| |#4|) . #13#) 43 T ELT)) (|before?| (#1# 6 T ELT)) (|any?| ((#7# (|Mapping| #7# |#4|) . #8#) 45 T ELT)) (= (#1# 8 T ELT)) (|#| ((#11# $) 44 T ELT))) @@ -3009,7 +3009,7 @@ NIL ((|retractIfCan| (((|Union| |#2| #1="failed") $) NIL T ELT) (((|Union| #2=(|Symbol|) #1#) $) 72 T ELT) (((|Union| #3=(|Fraction| #4=(|Integer|)) #1#) $) NIL T ELT) (((|Union| #4# #1#) $) 102 T ELT)) (|retract| ((|#2| $) NIL T ELT) ((#2# $) 67 T ELT) ((#3# $) NIL T ELT) ((#4# $) 99 T ELT)) (|reducedSystem| ((#5=(|Matrix| #4#) #6=(|Matrix| $)) NIL T ELT) (((|Record| (|:| |mat| #5#) (|:| |vec| (|Vector| #4#))) #6# #7=(|Vector| $)) NIL T ELT) (((|Record| (|:| |mat| #8=(|Matrix| |#2|)) (|:| |vec| (|Vector| |#2|))) #6# #7#) 121 T ELT) ((#8# #6#) 35 T ELT)) (|random| (#9=($) 105 T ELT)) (|patternMatch| ((#10=(|PatternMatchResult| #4# $) $ #11=(|Pattern| #4#) #10#) 82 T ELT) ((#12=(|PatternMatchResult| #13=(|Float|) $) $ #14=(|Pattern| #13#) #12#) 91 T ELT)) (|numerator| (#15=($ $) 10 T ELT)) (|nextItem| (((|Maybe| $) $) 27 T ELT)) (|map| (($ #16=(|Mapping| |#2| |#2|) $) 29 T ELT)) (|init| (#9# 16 T CONST)) (|fractionPart| (#15# 61 T ELT)) (|differentiate| (($ $ #16#) 43 T ELT) (($ $ #16# #17=(|NonNegativeInteger|)) NIL T ELT) (($ $ #2#) NIL T ELT) (($ $ #18=(|List| #2#)) NIL T ELT) (($ $ #2# #17#) NIL T ELT) (($ $ #18# (|List| #17#)) NIL T ELT) #19=(#15# NIL T ELT) (($ $ #17#) NIL T ELT)) (|denominator| (#15# 12 T ELT)) (|convert| ((#11# $) 77 T ELT) ((#14# $) 86 T ELT) (((|InputForm|) $) 47 T ELT) ((#13# $) 51 T ELT) (((|DoubleFloat|) $) 55 T ELT)) (|coerce| (((|OutputForm|) $) NIL T ELT) (($ #4#) NIL T ELT) #19# (($ #3#) 97 T ELT) (($ |#2|) NIL T ELT) (($ #2#) 64 T ELT)) (|characteristic| ((#17#) 38 T CONST)) (< (((|Boolean|) $ $) 57 T ELT))) (((|QuotientFieldCategory&| |#1| |#2|) (CATEGORY |package| (SIGNATURE < ((|Boolean|) |#1| |#1|)) (SIGNATURE |differentiate| (|#1| |#1| #1=(|NonNegativeInteger|))) (SIGNATURE |differentiate| #2=(|#1| |#1|)) (SIGNATURE |differentiate| (|#1| |#1| 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*4 (|IntegralDomain|)) (|isDomain| *2 (|NonNegativeInteger|)) (|isDomain| *1 (|QuotientFieldCategory&| *3 *4)) (|ofCategory| *3 (|QuotientFieldCategory| *4))))) -((~= (#1=((|Boolean|) $ $) 7 T ELT)) (|zero?| ((#2=(|Boolean|) $) 22 T ELT)) (|wholePart| ((|#1| $) 173 (|has| |#1| (|EuclideanDomain|)) ELT)) (|unitNormal| (((|Record| (|:| |unit| $) (|:| |canonical| $) (|:| |associate| $)) $) 55 T ELT)) (|unitCanonical| (($ $) 54 T ELT)) (|unit?| ((#3=(|Boolean|) $) 52 T ELT)) (|subtractIfCan| (((|Union| $ "failed") $ $) 26 T ELT)) (|squareFreePolynomial| (#4=((|Factored| #5=(|SparseUnivariatePolynomial| $)) #5#) 164 (|has| |#1| . #6=((|PolynomialFactorizationExplicit|))) ELT)) (|squareFreePart| (($ $) 91 T ELT)) (|squareFree| (#7=((|Factored| $) $) 90 T ELT)) (|solveLinearPolynomialEquation| (((|Union| #8=(|List| #5#) #9="failed") #8# #5#) 167 (|has| |#1| . #6#) ELT)) (|sizeLess?| (((|Boolean|) $ $) 75 T ELT)) (|sign| (((|Integer|) $) 154 (|has| |#1| . #10=((|OrderedIntegralDomain|))) ELT)) 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. #23#) 185 T ELT)) (|recip| (((|Union| $ "failed") $) 42 T ELT)) (|random| (($) 171 (|has| |#1| (|IntegerNumberSystem|)) ELT)) (|quo| (#21# 72 T ELT)) (|principalIdeal| (((|Record| (|:| |coef| #28=(|List| $)) (|:| |generator| $)) #28#) 66 T ELT)) (|prime?| (((|Boolean|) $) 89 T ELT)) (|positive?| (((|Boolean|) $) 156 (|has| |#1| . #10#) ELT)) (|patternMatch| (((|PatternMatchResult| #29=(|Integer|) . #30=($)) $ (|Pattern| #29#) (|PatternMatchResult| #29# . #30#)) 180 (|has| |#1| (|PatternMatchable| #29#)) ELT) (((|PatternMatchResult| #31=(|Float|) . #30#) $ (|Pattern| #31#) (|PatternMatchResult| #31# . #30#)) 179 (|has| |#1| (|PatternMatchable| #31#)) ELT)) (|opposite?| ((#2# $ $) 20 T ELT)) (|one?| (((|Boolean|) $) 44 T ELT)) (|numerator| (($ $) 175 T ELT)) (|numer| ((|#1| $) 177 T ELT)) (|nextItem| (((|Maybe| $) $) 142 (|has| |#1| . #32=((|StepThrough|))) ELT)) (|negative?| (((|Boolean|) $) 155 (|has| |#1| . #10#) ELT)) (|multiEuclidean| (((|Union| #33=(|List| $) #34="failed") #33# 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|associate| $)) $) 56 T ELT)) (|unitCanonical| (($ $) 55 T ELT)) (|unit?| ((#3=(|Boolean|) $) 53 T ELT)) (|subtractIfCan| (((|Maybe| $) $ $) 26 T ELT)) (|squareFreePolynomial| (#4=((|Factored| #5=(|SparseUnivariatePolynomial| $)) #5#) 165 (|has| |#1| . #6=((|PolynomialFactorizationExplicit|))) ELT)) (|squareFreePart| (($ $) 92 T ELT)) (|squareFree| (#7=((|Factored| $) $) 91 T ELT)) (|solveLinearPolynomialEquation| (((|Union| #8=(|List| #5#) #9="failed") #8# #5#) 168 (|has| |#1| . #6#) ELT)) (|sizeLess?| (((|Boolean|) $ $) 76 T ELT)) (|sign| (((|Integer|) $) 155 (|has| |#1| . #10=((|OrderedIntegralDomain|))) ELT)) (|sample| (#11=($) 23 T CONST)) (|retractIfCan| (((|Union| |#1| . #12=("failed")) . #13=($)) 204 T ELT) (((|Union| #14=(|Symbol|) . #12#) . #13#) 163 (|has| |#1| . #15=((|RetractableTo| (|Symbol|)))) ELT) (((|Union| #16=(|Fraction| (|Integer|)) . #12#) . #13#) 146 (|has| |#1| . #17=((|RetractableTo| (|Integer|)))) ELT) (((|Union| #18=(|Integer|) . #12#) . #13#) 144 (|has| |#1| . #19=((|RetractableTo| (|Integer|)))) ELT)) (|retract| ((|#1| . #20=($)) 205 T ELT) ((#14# . #20#) 164 (|has| |#1| . #15#) ELT) ((#16# . #20#) 147 (|has| |#1| . #17#) ELT) ((#18# . #20#) 145 (|has| |#1| . #19#) ELT)) (|rem| (#21=($ $ $) 72 T ELT)) (|reducedSystem| (((|Matrix| #22=(|Integer|)) . #23=(#24=(|Matrix| $))) 189 (|has| |#1| . #25=((|LinearlyExplicitRingOver| #22#))) ELT) (((|Record| (|:| |mat| (|Matrix| #22#)) (|:| |vec| (|Vector| #22#))) . #26=(#24# #27=(|Vector| $))) 188 (|has| |#1| . #25#) ELT) (((|Record| (|:| |mat| (|Matrix| |#1|)) (|:| |vec| (|Vector| |#1|))) . #26#) 187 T ELT) (((|Matrix| |#1|) . #23#) 186 T ELT)) (|recip| (((|Union| $ "failed") $) 43 T ELT)) (|random| (($) 172 (|has| |#1| (|IntegerNumberSystem|)) ELT)) (|quo| (#21# 73 T ELT)) (|principalIdeal| (((|Record| (|:| |coef| #28=(|List| $)) (|:| |generator| $)) #28#) 67 T ELT)) (|prime?| (((|Boolean|) $) 90 T ELT)) (|positive?| (((|Boolean|) $) 157 (|has| |#1| . #10#) ELT)) (|patternMatch| 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ELT)) (|eval| (($ $ (|List| |#1|) (|List| |#1|)) 202 (|has| |#1| (|Evalable| |#1|)) ELT) (($ $ |#1| |#1|) 201 (|has| |#1| (|Evalable| |#1|)) ELT) (($ $ (|Equation| |#1|)) 200 (|has| |#1| (|Evalable| |#1|)) ELT) (($ $ (|List| (|Equation| |#1|))) 199 (|has| |#1| (|Evalable| |#1|)) ELT) (($ $ (|List| #44=(|Symbol|)) (|List| |#1|)) 198 (|has| |#1| (|InnerEvalable| #44# |#1|)) ELT) (($ $ #44# |#1|) 197 (|has| |#1| (|InnerEvalable| #44# |#1|)) ELT)) (|euclideanSize| (((|NonNegativeInteger|) $) 75 T ELT)) (|elt| (($ $ |#1|) 203 (|has| |#1| (|Eltable| |#1| |#1|)) ELT)) (|divide| (((|Record| (|:| |quotient| $) (|:| |remainder| $)) $ $) 74 T ELT)) (|differentiate| (($ $ (|Mapping| |#1| |#1|)) 195 T ELT) (($ $ (|Mapping| |#1| |#1|) . #45=((|NonNegativeInteger|))) 194 T ELT) (($ . #46=($)) 141 (|has| |#1| . #47=((|DifferentialSpace|))) ELT) (#48=($ $ (|NonNegativeInteger|)) 139 (|has| |#1| . #47#) ELT) (($ $ #49=(|Symbol|)) 137 (|has| |#1| . #50=((|PartialDifferentialSpace| (|Symbol|)))) ELT) (($ 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(OR (|has| |#1| (|CharacteristicNonZero|)) (|and| #58# (|has| |#1| . #6#))) ELT)) (|characteristic| (((|NonNegativeInteger|)) 41 T CONST)) (|ceiling| ((|#1| $) 171 (|has| |#1| (|IntegerNumberSystem|)) ELT)) (|before?| (#1# 6 T ELT)) (|associates?| ((#3# $ $) 54 T ELT)) (|annihilate?| (((|Boolean|) $ $) 34 T ELT)) (|abs| (($ $) 154 (|has| |#1| . #10#) ELT)) (|Zero| (#11# 24 T CONST)) (|One| (($) 46 T CONST)) (D (($ $ (|Mapping| |#1| |#1|)) 193 T ELT) (($ $ (|Mapping| |#1| |#1|) . #45#) 192 T ELT) (($ . #46#) 140 (|has| |#1| . #47#) ELT) (#48# 138 (|has| |#1| . #47#) ELT) (($ $ #49#) 136 (|has| |#1| . #50#) ELT) (($ $ (|List| #49#)) 132 (|has| |#1| . #50#) ELT) (($ $ #49# . #51#) 131 (|has| |#1| . #50#) ELT) (($ $ (|List| #49#) . #53#) 130 (|has| |#1| . #50#) ELT)) (>= (#61=((|Boolean|) $ $) 150 (|has| |#1| . #36#) ELT)) (> (#61# 152 (|has| |#1| . #36#) ELT)) (= (#1# 8 T ELT)) (<= (#61# 151 (|has| |#1| . #36#) ELT)) (< (#61# 153 (|has| |#1| . #36#) ELT)) (/ (($ $ $) 84 T ELT) (($ |#1| |#1|) 179 T ELT)) (- (($ $) 30 T ELT) (($ $ $) 29 T ELT)) (+ (($ $ $) 18 T ELT)) (** (($ $ (|PositiveInteger|)) 36 T ELT) (($ $ (|NonNegativeInteger|)) 44 T ELT) (($ $ #60#) 88 T ELT)) (* (($ (|PositiveInteger|) $) 17 T ELT) (($ (|NonNegativeInteger|) $) 21 T ELT) (($ (|Integer|) . #62=($)) 31 T ELT) (($ $ $) 35 T ELT) (($ $ #59#) 87 T ELT) (($ #59# . #62#) 86 T ELT) (($ |#1| . #62#) 207 T ELT) (($ $ |#1|) 206 T ELT))) (((|QuotientFieldCategory| |#1|) (|Category|) (|IntegralDomain|)) (T |QuotientFieldCategory|)) ((/ (*1 *1 *2 *2) (AND (|ofCategory| *1 (|QuotientFieldCategory| *2)) (|ofCategory| *2 (|IntegralDomain|)))) (|numer| (*1 *2 *1) (AND (|ofCategory| *1 (|QuotientFieldCategory| *2)) (|ofCategory| *2 (|IntegralDomain|)))) (|denom| (*1 *2 *1) (AND (|ofCategory| *1 (|QuotientFieldCategory| *2)) (|ofCategory| *2 (|IntegralDomain|)))) (|numerator| (*1 *1 *1) (AND (|ofCategory| *1 (|QuotientFieldCategory| *2)) (|ofCategory| *2 (|IntegralDomain|)))) (|denominator| (*1 *1 *1) (AND 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(|FullyLinearlyExplicitRingOver| |t#1|) (|Patternable| |t#1|) (|FullyPatternMatchable| |t#1|) (CATEGORY |domain| (SIGNATURE / ($ |t#1| |t#1|)) (SIGNATURE |numer| (|t#1| $)) (SIGNATURE |denom| (|t#1| $)) (SIGNATURE |numerator| ($ $)) (SIGNATURE |denominator| ($ $)) (IF (|has| |t#1| (|StepThrough|)) (ATTRIBUTE (|StepThrough|)) |%noBranch|) (IF (|has| |t#1| (|RetractableTo| (|Integer|))) (PROGN (ATTRIBUTE (|RetractableTo| (|Integer|))) (ATTRIBUTE (|RetractableTo| (|Fraction| (|Integer|))))) |%noBranch|) (IF (|has| |t#1| (|OrderedSet|)) (ATTRIBUTE (|OrderedSet|)) |%noBranch|) (IF (|has| |t#1| (|OrderedIntegralDomain|)) (ATTRIBUTE (|OrderedIntegralDomain|)) |%noBranch|) (IF (|has| |t#1| (|RealConstant|)) (ATTRIBUTE (|RealConstant|)) |%noBranch|) (IF (|has| |t#1| (|ConvertibleTo| (|InputForm|))) (ATTRIBUTE (|ConvertibleTo| (|InputForm|))) |%noBranch|) (IF (|has| |t#1| (|CharacteristicZero|)) (ATTRIBUTE (|CharacteristicZero|)) |%noBranch|) (IF (|has| |t#1| (|CharacteristicNonZero|)) (ATTRIBUTE (|CharacteristicNonZero|)) |%noBranch|) (IF (|has| |t#1| (|RetractableTo| (|Symbol|))) (ATTRIBUTE (|RetractableTo| (|Symbol|))) |%noBranch|) (IF (|has| |t#1| (|EuclideanDomain|)) (PROGN (SIGNATURE |wholePart| (|t#1| $)) (SIGNATURE |fractionPart| ($ $))) |%noBranch|) (IF (|has| |t#1| (|IntegerNumberSystem|)) (PROGN (SIGNATURE |random| ($)) (SIGNATURE |ceiling| (|t#1| $)) (SIGNATURE |floor| (|t#1| $))) |%noBranch|) (IF (|has| |t#1| (|PolynomialFactorizationExplicit|)) (ATTRIBUTE (|PolynomialFactorizationExplicit|)) |%noBranch|))) @@ -3017,7 +3017,7 @@ NIL ((|map| ((|#4| (|Mapping| |#2| |#1|) |#3|) 14 T ELT))) (((|QuotientFieldCategoryFunctions2| |#1| |#2| |#3| |#4|) (CATEGORY |package| (SIGNATURE |map| (|#4| (|Mapping| |#2| |#1|) |#3|))) #1=(|IntegralDomain|) #1# (|QuotientFieldCategory| |#1|) (|QuotientFieldCategory| |#2|)) (T |QuotientFieldCategoryFunctions2|)) ((|map| (*1 *2 *3 *4) (AND (|isDomain| *3 (|Mapping| *6 *5)) (|ofCategory| *5 #1=(|IntegralDomain|)) (|ofCategory| *6 #1#) (|ofCategory| *2 (|QuotientFieldCategory| *6)) (|isDomain| *1 (|QuotientFieldCategoryFunctions2| *5 *6 *4 *2)) (|ofCategory| *4 (|QuotientFieldCategory| *5))))) -((~= #1=((#2=(|Boolean|) $ $) NIL T ELT)) (|zero?| ((#2# $) NIL T ELT)) (|subtractIfCan| (((|Union| $ "failed") $ $) NIL T ELT)) (|sample| #3=(($) NIL T CONST)) (|quadraticForm| (($ #4=(|SquareMatrix| |#1| |#2|)) 11 T ELT)) (|opposite?| #1#) (|matrix| ((#4# $) 12 T ELT)) (|latex| (((|String|) $) NIL T ELT)) (|hash| (((|SingleInteger|) $) NIL T ELT)) (|elt| ((|#2| $ (|DirectProduct| |#1| |#2|)) 16 T ELT)) (|coerce| (((|OutputForm|) $) NIL T ELT)) (|before?| #1#) (|Zero| #3#) (= #1#) (- (($ $) NIL T ELT) #5=(($ $ $) NIL T ELT)) (+ #5#) (* (($ (|PositiveInteger|) $) NIL T ELT) (($ (|NonNegativeInteger|) $) NIL T ELT) (($ (|Integer|) $) NIL T ELT))) +((~= #1=((#2=(|Boolean|) $ $) NIL T ELT)) (|zero?| ((#2# $) NIL T ELT)) (|subtractIfCan| (((|Maybe| $) $ $) NIL T ELT)) (|sample| #3=(($) NIL T CONST)) (|quadraticForm| (($ #4=(|SquareMatrix| |#1| |#2|)) 11 T ELT)) (|opposite?| #1#) (|matrix| ((#4# $) 12 T ELT)) (|latex| (((|String|) $) NIL T ELT)) (|hash| (((|SingleInteger|) $) NIL T ELT)) (|elt| ((|#2| $ (|DirectProduct| |#1| |#2|)) 16 T ELT)) (|coerce| (((|OutputForm|) $) NIL T ELT)) (|before?| #1#) (|Zero| #3#) (= #1#) (- (($ $) NIL T ELT) #5=(($ $ $) NIL T ELT)) (+ #5#) (* (($ (|PositiveInteger|) $) NIL T ELT) (($ (|NonNegativeInteger|) $) NIL T ELT) (($ (|Integer|) $) NIL T ELT))) (((|QuadraticForm| |#1| |#2|) (|Join| (|AbelianGroup|) (|Eltable| (|DirectProduct| |#1| |#2|) |#2|) (CATEGORY |domain| (SIGNATURE |quadraticForm| ($ #1=(|SquareMatrix| |#1| |#2|))) (SIGNATURE |matrix| (#1# $)))) (|PositiveInteger|) (|Field|)) (T |QuadraticForm|)) ((|quadraticForm| (*1 *1 *2) (AND #1=(|isDomain| *2 (|SquareMatrix| *3 *4)) #2=(|ofType| *3 (|PositiveInteger|)) #3=(|ofCategory| *4 (|Field|)) #4=(|isDomain| *1 (|QuadraticForm| *3 *4)))) (|matrix| (*1 *2 *1) (AND #1# #4# #2# #3#))) ((~= #1=(((|Boolean|) $ $) NIL T ELT)) (|latex| (((|String|) $) NIL T ELT)) (|hash| (((|SingleInteger|) $) NIL T ELT)) (|expression| (((|SpadAst|) $) 10 T ELT)) (|coerce| (((|OutputForm|) $) 16 T ELT) (($ #2=(|Syntax|)) NIL T ELT) ((#2# $) NIL T ELT)) (|before?| #1#) (= #1#)) @@ -3028,13 +3028,13 @@ NIL ((|enqueue!| (*1 *2 *2 *1) (AND (|ofCategory| *1 (|QueueAggregate| *2)) (|ofCategory| *2 (|Type|)))) (|dequeue!| (*1 *2 *1) (AND (|ofCategory| *1 (|QueueAggregate| *2)) (|ofCategory| *2 (|Type|)))) (|rotate!| (*1 *1 *1) (AND (|ofCategory| *1 (|QueueAggregate| *2)) (|ofCategory| *2 (|Type|)))) (|length| (*1 *2 *1) (AND (|ofCategory| *1 (|QueueAggregate| *3)) (|ofCategory| *3 (|Type|)) (|isDomain| *2 (|NonNegativeInteger|)))) (|front| (*1 *2 *1) (AND (|ofCategory| *1 (|QueueAggregate| *2)) (|ofCategory| *2 (|Type|)))) (|back| (*1 *2 *1) (AND (|ofCategory| *1 (|QueueAggregate| *2)) (|ofCategory| *2 (|Type|))))) (|Join| (|BagAggregate| |t#1|) (|FiniteAggregate| |t#1|) (CATEGORY |domain| (SIGNATURE |enqueue!| (|t#1| |t#1| $)) (SIGNATURE |dequeue!| (|t#1| $)) (SIGNATURE |rotate!| ($ $)) (SIGNATURE |length| ((|NonNegativeInteger|) $)) (SIGNATURE |front| (|t#1| $)) (SIGNATURE |back| (|t#1| $)))) (((|Aggregate|) . T) ((|BagAggregate| |#1|) . T) ((|BasicType|) OR (|has| |#1| (|SetCategory|)) (|has| |#1| (|BasicType|))) ((|CoercibleTo| (|OutputForm|)) OR (|has| |#1| (|SetCategory|)) (|has| |#1| (|CoercibleTo| (|OutputForm|)))) ((|Evalable| |#1|) AND (|has| |#1| (|Evalable| |#1|)) (|has| |#1| (|SetCategory|))) ((|FiniteAggregate| |#1|) . T) ((|Functorial| |#1|) . T) ((|HomogeneousAggregate| |#1|) . T) ((|InnerEvalable| |#1| |#1|) AND (|has| |#1| (|Evalable| |#1|)) (|has| |#1| (|SetCategory|))) ((|Join|) . T) ((|SetCategory|) |has| |#1| (|SetCategory|)) ((|ShallowlyMutableAggregate| |#1|) . T) ((|Type|) . T)) -((~= #1=(#2=(#3=(|Boolean|) $ $) NIL T ELT)) (|zero?| #4=(#5=(#3# $) NIL T ELT)) (|subtractIfCan| ((#6=(|Union| $ #7="failed") $ $) NIL T ELT)) (|sample| (#8=($) NIL T CONST)) (|retractIfCan| (((|Union| #9=(|Integer|) . #10=(#7#)) . #11=($)) NIL #12=(|has| |#1| (|RetractableTo| #9#)) ELT) (#13=((|Union| #14=(|Fraction| #9#) . #10#) . #11#) NIL #15=(|has| |#1| (|RetractableTo| #14#)) ELT) (((|Union| |#1| . #10#) . #11#) NIL T ELT)) (|retract| ((#9# . #16=($)) NIL #12# ELT) (#17=(#14# . #16#) NIL #15# ELT) #18=(#19=(|#1| . #16#) NIL T ELT)) (|reducedSystem| ((#20=(|Matrix| #9#) . #21=(#22=(|Matrix| $))) NIL #23=(|has| |#1| (|LinearlyExplicitRingOver| #9#)) ELT) ((#24=(|Record| (|:| |mat| #20#) (|:| |vec| (|Vector| #9#))) . #25=(#22# #26=(|Vector| $))) NIL #23# ELT) ((#27=(|Record| (|:| |mat| #28=(|Matrix| |#1|)) (|:| |vec| (|Vector| |#1|))) . #25#) NIL T ELT) ((#28# . #21#) NIL T ELT)) (|recip| ((#6# $) NIL T ELT)) (|real| (#19# 12 T ELT)) (|rationalIfCan| (#13# NIL #29=(|has| |#1| (|IntegerNumberSystem|)) ELT)) (|rational?| (#5# NIL #29# ELT)) (|rational| (#17# NIL #29# ELT)) (|quatern| (($ |#1| |#1| |#1| |#1|) 16 T ELT)) (|opposite?| #1#) (|one?| #4#) (|norm| #18#) (|min| #30=(#31=($ $ $) NIL #32=(|has| |#1| (|OrderedSet|)) ELT)) (|max| #30#) (|map| (($ #33=(|Mapping| |#1| |#1|) $) NIL T ELT)) (|leftReducedSystem| ((#20# . #34=(#26#)) NIL #23# ELT) ((#24# . #35=(#26# $)) NIL #23# ELT) ((#27# . #35#) NIL T ELT) ((#28# . #34#) NIL T ELT)) (|latex| (((|String|) $) NIL T ELT)) (|inv| (#36=($ $) NIL #37=(|has| |#1| (|Field|)) ELT)) (|imagK| (#19# 15 T ELT)) (|imagJ| (#19# 14 T ELT)) (|imagI| (#19# 13 T ELT)) (|hash| (((|SingleInteger|) $) NIL T ELT)) (|eval| (($ $ #38=(|List| |#1|) #38#) NIL #39=(|has| |#1| (|Evalable| |#1|)) ELT) (($ $ |#1| |#1|) NIL #39# ELT) (($ $ #40=(|Equation| |#1|)) NIL #39# ELT) (($ $ (|List| #40#)) NIL #39# ELT) (($ $ #41=(|List| #42=(|Symbol|)) #38#) NIL #43=(|has| |#1| (|InnerEvalable| #42# |#1|)) ELT) (($ $ #42# |#1|) NIL #43# ELT)) (|elt| (#44=($ $ |#1|) NIL (|has| |#1| (|Eltable| |#1| |#1|)) ELT)) (|differentiate| #45=(($ $ #33#) NIL T ELT) #46=(($ $ #33# #47=(|NonNegativeInteger|)) NIL T ELT) #48=(#36# NIL #49=(|has| |#1| (|DifferentialSpace|)) ELT) #50=(#51=($ $ #47#) NIL #49# ELT) #52=(($ $ #42#) NIL #53=(|has| |#1| (|PartialDifferentialSpace| #42#)) ELT) #54=(($ $ #41#) NIL #53# ELT) #55=(($ $ #42# #47#) NIL #53# ELT) #56=(($ $ #41# (|List| #47#)) NIL #53# ELT)) (|convert| ((#57=(|InputForm|) $) NIL (|has| |#1| (|ConvertibleTo| #57#)) ELT)) (|conjugate| #58=(#36# NIL T ELT)) (|coerce| (((|OutputForm|) $) NIL T ELT) (($ #9#) NIL T ELT) (($ |#1|) NIL T ELT) (($ #14#) NIL (OR #37# #15#) ELT)) (|charthRoot| (((|Maybe| $) $) NIL (|has| |#1| (|CharacteristicNonZero|)) ELT)) (|characteristic| ((#47#) NIL T CONST)) (|before?| #1#) (|annihilate?| #1#) (|abs| (#19# NIL (|has| |#1| (|RealNumberSystem|)) ELT)) (|Zero| (#8# 8 T CONST)) (|One| (#8# 10 T CONST)) (D #45# #46# #48# #50# #52# #54# #55# #56#) (>= #59=(#2# NIL #32# ELT)) (> #59#) (= #1#) (<= #59#) (< #59#) (- #58# #60=(#31# NIL T ELT)) (+ #60#) (** (($ $ #61=(|PositiveInteger|)) NIL T ELT) (#51# NIL T ELT) (($ $ #9#) NIL #37# ELT)) (* (($ #61# $) NIL T ELT) (($ #47# $) NIL T ELT) (($ #9# . #62=($)) NIL T ELT) (#31# 20 T ELT) (#44# NIL T ELT) (($ |#1| . #62#) NIL T ELT) (($ $ #14#) NIL #37# ELT) (($ #14# . #62#) NIL #37# ELT))) +((~= #1=(#2=(#3=(|Boolean|) $ $) NIL T ELT)) (|zero?| #4=(#5=(#3# $) NIL T ELT)) (|subtractIfCan| ((#6=(|Maybe| $) $ $) NIL T ELT)) (|sample| (#7=($) NIL T CONST)) (|retractIfCan| (((|Union| #8=(|Integer|) . #9=(#10="failed")) . #11=($)) NIL #12=(|has| |#1| (|RetractableTo| #8#)) ELT) (#13=((|Union| #14=(|Fraction| #8#) . #9#) . #11#) NIL #15=(|has| |#1| (|RetractableTo| #14#)) ELT) (((|Union| |#1| . #9#) . #11#) NIL T ELT)) (|retract| ((#8# . #16=($)) NIL #12# ELT) (#17=(#14# . #16#) NIL #15# ELT) #18=(#19=(|#1| . #16#) NIL T ELT)) (|reducedSystem| ((#20=(|Matrix| #8#) . #21=(#22=(|Matrix| $))) NIL #23=(|has| |#1| (|LinearlyExplicitRingOver| #8#)) ELT) ((#24=(|Record| (|:| |mat| #20#) (|:| |vec| (|Vector| #8#))) . #25=(#22# #26=(|Vector| $))) NIL #23# ELT) ((#27=(|Record| (|:| |mat| #28=(|Matrix| |#1|)) (|:| |vec| (|Vector| |#1|))) . #25#) NIL T ELT) ((#28# . #21#) NIL T ELT)) (|recip| (((|Union| $ #10#) $) NIL T ELT)) (|real| (#19# 12 T ELT)) (|rationalIfCan| (#13# NIL #29=(|has| |#1| (|IntegerNumberSystem|)) ELT)) (|rational?| (#5# NIL #29# ELT)) (|rational| (#17# NIL #29# ELT)) (|quatern| (($ |#1| |#1| |#1| |#1|) 16 T ELT)) (|opposite?| #1#) (|one?| #4#) (|norm| #18#) (|min| #30=(#31=($ $ $) NIL #32=(|has| |#1| (|OrderedSet|)) ELT)) (|max| #30#) (|map| (($ #33=(|Mapping| |#1| |#1|) $) NIL T ELT)) (|leftReducedSystem| ((#20# . #34=(#26#)) NIL #23# ELT) ((#24# . #35=(#26# $)) NIL #23# ELT) ((#27# . #35#) NIL T ELT) ((#28# . #34#) NIL T ELT)) (|latex| (((|String|) $) NIL T ELT)) (|inv| (#36=($ $) NIL #37=(|has| |#1| (|Field|)) ELT)) (|imagK| (#19# 15 T ELT)) (|imagJ| (#19# 14 T ELT)) (|imagI| (#19# 13 T ELT)) (|hash| (((|SingleInteger|) $) NIL T ELT)) (|eval| (($ $ #38=(|List| |#1|) #38#) NIL #39=(|has| |#1| (|Evalable| |#1|)) ELT) (($ $ |#1| |#1|) NIL #39# ELT) (($ $ #40=(|Equation| |#1|)) NIL #39# ELT) (($ $ (|List| #40#)) NIL #39# ELT) (($ $ #41=(|List| #42=(|Symbol|)) #38#) NIL #43=(|has| |#1| (|InnerEvalable| #42# |#1|)) ELT) (($ $ #42# |#1|) NIL #43# ELT)) (|elt| (#44=($ $ |#1|) NIL (|has| |#1| (|Eltable| |#1| |#1|)) ELT)) (|differentiate| #45=(($ $ #33#) NIL T ELT) #46=(($ $ #33# #47=(|NonNegativeInteger|)) NIL T ELT) #48=(#36# NIL #49=(|has| |#1| (|DifferentialSpace|)) ELT) #50=(#51=($ $ #47#) NIL #49# ELT) #52=(($ $ #42#) NIL #53=(|has| |#1| (|PartialDifferentialSpace| #42#)) ELT) #54=(($ $ #41#) NIL #53# ELT) #55=(($ $ #42# #47#) NIL #53# ELT) #56=(($ $ #41# (|List| #47#)) NIL #53# ELT)) (|convert| ((#57=(|InputForm|) $) NIL (|has| |#1| (|ConvertibleTo| #57#)) ELT)) (|conjugate| #58=(#36# NIL T ELT)) (|coerce| (((|OutputForm|) $) NIL T ELT) (($ #8#) NIL T ELT) (($ |#1|) NIL T ELT) (($ #14#) NIL (OR #37# #15#) ELT)) (|charthRoot| ((#6# $) NIL (|has| |#1| (|CharacteristicNonZero|)) ELT)) (|characteristic| ((#47#) NIL T CONST)) (|before?| #1#) (|annihilate?| #1#) (|abs| (#19# NIL (|has| |#1| (|RealNumberSystem|)) ELT)) (|Zero| (#7# 8 T CONST)) (|One| (#7# 10 T CONST)) (D #45# #46# #48# #50# #52# #54# #55# #56#) (>= #59=(#2# NIL #32# ELT)) (> #59#) (= #1#) (<= #59#) (< #59#) (- #58# #60=(#31# NIL T ELT)) (+ #60#) (** (($ $ #61=(|PositiveInteger|)) NIL T ELT) (#51# NIL T ELT) (($ $ #8#) NIL #37# ELT)) (* (($ #61# $) NIL T ELT) (($ #47# $) NIL T ELT) (($ #8# . #62=($)) NIL T ELT) (#31# 20 T ELT) (#44# NIL T ELT) (($ |#1| . #62#) NIL T ELT) (($ $ #14#) NIL #37# ELT) (($ #14# . #62#) NIL #37# ELT))) (((|Quaternion| |#1|) (|QuaternionCategory| |#1|) (|CommutativeRing|)) (T |Quaternion|)) NIL ((|zero?| (#1=(#2=(|Boolean|) $) 43 T ELT)) (|retractIfCan| (((|Union| #3=(|Integer|) #4="failed") $) NIL T ELT) (#5=((|Union| #6=(|Fraction| #3#) #4#) $) NIL T ELT) (((|Union| |#2| #4#) $) 46 T ELT)) (|retract| ((#3# $) NIL T ELT) (#7=(#6# $) NIL T ELT) (#8=(|#2| $) 44 T ELT)) (|rationalIfCan| (#5# 78 T ELT)) (|rational?| (#1# 72 T ELT)) (|rational| (#7# 76 T ELT)) (|one?| (#1# 42 T ELT)) (|norm| (#8# 22 T ELT)) (|map| (($ #9=(|Mapping| |#2| |#2|) $) 19 T ELT)) (|inv| (#10=($ $) 58 T ELT)) (|differentiate| (($ $ #9#) 35 T ELT) (($ $ #9# #11=(|NonNegativeInteger|)) NIL T ELT) (($ $ #12=(|Symbol|)) NIL T ELT) (($ $ #13=(|List| #12#)) NIL T ELT) (($ $ #12# #11#) NIL T ELT) (($ $ #13# (|List| #11#)) NIL T ELT) (#10# NIL T ELT) (($ $ #11#) NIL T ELT)) (|convert| (((|InputForm|) $) 67 T ELT)) (|conjugate| (#10# 17 T ELT)) (|coerce| (((|OutputForm|) $) 53 T ELT) (($ #3#) 39 T ELT) (($ |#2|) 37 T ELT) (($ #6#) NIL T ELT)) (|characteristic| ((#11#) 10 T CONST)) (|abs| (#8# 71 T ELT)) (= (#14=(#2# $ $) 26 T ELT)) (< (#14# 69 T ELT)) (- (#10# 30 T ELT) (#15=($ $ $) 29 T ELT)) (+ (#15# 27 T ELT)) (* (($ (|PositiveInteger|) $) NIL T ELT) (($ #11# $) NIL T ELT) (($ #3# $) 34 T ELT) (#15# NIL T ELT) (($ $ |#2|) NIL T ELT) (($ |#2| $) 31 T ELT) (($ $ #6#) NIL T ELT) (($ #6# $) NIL T ELT))) (((|QuaternionCategory&| |#1| |#2|) (CATEGORY |package| (SIGNATURE |coerce| (|#1| #1=(|Fraction| #2=(|Integer|)))) (SIGNATURE |differentiate| (|#1| |#1| #3=(|NonNegativeInteger|))) (SIGNATURE |differentiate| #4=(|#1| |#1|)) (SIGNATURE |differentiate| (|#1| |#1| #5=(|List| #6=(|Symbol|)) (|List| #3#))) (SIGNATURE |differentiate| (|#1| |#1| #6# #3#)) (SIGNATURE |differentiate| (|#1| |#1| #5#)) (SIGNATURE |differentiate| (|#1| |#1| #6#)) (SIGNATURE < #7=(#8=(|Boolean|) |#1| |#1|)) (SIGNATURE * (|#1| #1# |#1|)) (SIGNATURE * (|#1| |#1| #1#)) (SIGNATURE |inv| #4#) (SIGNATURE |convert| ((|InputForm|) |#1|)) (SIGNATURE |rationalIfCan| #9=((|Union| #1# #10="failed") |#1|)) (SIGNATURE |rational| #11=(#1# |#1|)) (SIGNATURE |rational?| #12=(#8# |#1|)) (SIGNATURE |abs| #13=(|#2| |#1|)) (SIGNATURE |norm| #13#) (SIGNATURE |conjugate| #4#) (SIGNATURE |map| (|#1| #14=(|Mapping| |#2| |#2|) |#1|)) (SIGNATURE |differentiate| (|#1| |#1| #14# #3#)) (SIGNATURE |differentiate| (|#1| |#1| #14#)) (SIGNATURE |retractIfCan| ((|Union| |#2| #10#) |#1|)) (SIGNATURE |retract| #13#) (SIGNATURE |retract| #11#) (SIGNATURE |retractIfCan| #9#) (SIGNATURE |retract| (#2# |#1|)) (SIGNATURE |retractIfCan| ((|Union| #2# #10#) |#1|)) (SIGNATURE |coerce| (|#1| |#2|)) (SIGNATURE * (|#1| |#2| |#1|)) (SIGNATURE * (|#1| |#1| |#2|)) (SIGNATURE |characteristic| (#3#) |constant|) (SIGNATURE |coerce| (|#1| #2#)) (SIGNATURE |one?| #12#) (SIGNATURE * #15=(|#1| |#1| |#1|)) (SIGNATURE - #15#) (SIGNATURE - #4#) (SIGNATURE * (|#1| #2# |#1|)) (SIGNATURE * (|#1| #3# |#1|)) (SIGNATURE |zero?| #12#) (SIGNATURE * (|#1| (|PositiveInteger|) |#1|)) (SIGNATURE + #15#) (SIGNATURE |coerce| ((|OutputForm|) |#1|)) (SIGNATURE = #7#)) (|QuaternionCategory| |#2|) (|CommutativeRing|)) (T |QuaternionCategory&|)) ((|characteristic| (*1 *2) (AND (|ofCategory| *4 (|CommutativeRing|)) (|isDomain| *2 (|NonNegativeInteger|)) (|isDomain| *1 (|QuaternionCategory&| *3 *4)) (|ofCategory| *3 (|QuaternionCategory| *4))))) -((~= (#1=((|Boolean|) $ $) 7 T ELT)) (|zero?| ((#2=(|Boolean|) $) 22 T ELT)) (|subtractIfCan| (((|Union| $ "failed") $ $) 26 T ELT)) (|sample| (#3=($) 23 T CONST)) (|retractIfCan| (((|Union| #4=(|Integer|) . #5=("failed")) . #6=($)) 143 (|has| |#1| . #7=((|RetractableTo| #4#))) ELT) (((|Union| #8=(|Fraction| #4#) . #5#) . #6#) 141 (|has| |#1| . #9=((|RetractableTo| #8#))) ELT) (((|Union| |#1| . #5#) . #6#) 138 T ELT)) (|retract| ((#4# . #10=($)) 142 (|has| |#1| . #7#) ELT) ((#8# . #10#) 140 (|has| |#1| . #9#) ELT) ((|#1| . #10#) 139 T ELT)) (|reducedSystem| (((|Matrix| #11=(|Integer|)) . #12=(#13=(|Matrix| $))) 123 (|has| |#1| . #14=((|LinearlyExplicitRingOver| #11#))) ELT) (((|Record| (|:| |mat| (|Matrix| #11#)) (|:| |vec| (|Vector| #11#))) . #15=(#13# #16=(|Vector| $))) 122 (|has| |#1| . #14#) ELT) (((|Record| (|:| |mat| (|Matrix| |#1|)) (|:| |vec| (|Vector| |#1|))) . #15#) 121 T ELT) (((|Matrix| |#1|) . #12#) 120 T ELT)) (|recip| (((|Union| $ "failed") $) 42 T ELT)) (|real| ((|#1| $) 111 T ELT)) (|rationalIfCan| (((|Union| (|Fraction| (|Integer|)) "failed") $) 107 (|has| |#1| (|IntegerNumberSystem|)) ELT)) (|rational?| (((|Boolean|) $) 109 (|has| |#1| (|IntegerNumberSystem|)) ELT)) (|rational| (((|Fraction| (|Integer|)) $) 108 (|has| |#1| (|IntegerNumberSystem|)) ELT)) (|quatern| (($ |#1| |#1| |#1| |#1|) 112 T ELT)) (|opposite?| ((#2# $ $) 20 T ELT)) (|one?| (((|Boolean|) $) 44 T ELT)) (|norm| ((|#1| $) 113 T ELT)) (|min| (#17=($ $ $) 95 (|has| |#1| . #18=((|OrderedSet|))) ELT)) (|max| (#17# 96 (|has| |#1| . #18#) ELT)) (|map| (($ (|Mapping| |#1| |#1|) $) 126 T ELT)) (|leftReducedSystem| (((|Matrix| #11#) . #19=(#16#)) 125 (|has| |#1| . #14#) ELT) (((|Record| (|:| |mat| (|Matrix| #11#)) (|:| |vec| (|Vector| #11#))) . #20=(#16# $)) 124 (|has| |#1| . #14#) ELT) (((|Record| (|:| |mat| (|Matrix| |#1|)) (|:| |vec| (|Vector| |#1|))) . #20#) 119 T ELT) 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22 T ELT)) (|subtractIfCan| (((|Maybe| $) $ $) 26 T ELT)) (|sample| (#3=($) 23 T CONST)) (|retractIfCan| (((|Union| #4=(|Integer|) . #5=("failed")) . #6=($)) 144 (|has| |#1| . #7=((|RetractableTo| #4#))) ELT) (((|Union| #8=(|Fraction| #4#) . #5#) . #6#) 142 (|has| |#1| . #9=((|RetractableTo| #8#))) ELT) (((|Union| |#1| . #5#) . #6#) 139 T ELT)) (|retract| ((#4# . #10=($)) 143 (|has| |#1| . #7#) ELT) ((#8# . #10#) 141 (|has| |#1| . #9#) ELT) ((|#1| . #10#) 140 T ELT)) (|reducedSystem| (((|Matrix| #11=(|Integer|)) . #12=(#13=(|Matrix| $))) 124 (|has| |#1| . #14=((|LinearlyExplicitRingOver| #11#))) ELT) (((|Record| (|:| |mat| (|Matrix| #11#)) (|:| |vec| (|Vector| #11#))) . #15=(#13# #16=(|Vector| $))) 123 (|has| |#1| . #14#) ELT) (((|Record| (|:| |mat| (|Matrix| |#1|)) (|:| |vec| (|Vector| |#1|))) . #15#) 122 T ELT) (((|Matrix| |#1|) . #12#) 121 T ELT)) (|recip| (((|Union| $ "failed") $) 43 T ELT)) (|real| ((|#1| $) 112 T ELT)) (|rationalIfCan| (((|Union| (|Fraction| (|Integer|)) 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ELT)) (|imagI| ((|#1| $) 117 T ELT)) (|hash| (((|SingleInteger|) $) 12 T ELT)) (|eval| (($ $ (|List| |#1|) (|List| |#1|)) 133 (|has| |#1| (|Evalable| |#1|)) ELT) (($ $ |#1| |#1|) 132 (|has| |#1| (|Evalable| |#1|)) ELT) (($ $ (|Equation| |#1|)) 131 (|has| |#1| (|Evalable| |#1|)) ELT) (($ $ (|List| (|Equation| |#1|))) 130 (|has| |#1| (|Evalable| |#1|)) ELT) (($ $ (|List| #22=(|Symbol|)) (|List| |#1|)) 129 (|has| |#1| (|InnerEvalable| #22# |#1|)) ELT) (($ $ #22# |#1|) 128 (|has| |#1| (|InnerEvalable| #22# |#1|)) ELT)) (|elt| (($ $ |#1|) 134 (|has| |#1| (|Eltable| |#1| |#1|)) ELT)) (|differentiate| (($ $ (|Mapping| |#1| |#1|)) 138 T ELT) (($ $ (|Mapping| |#1| |#1|) . #23=((|NonNegativeInteger|))) 137 T ELT) (($ . #24=($)) 95 (|has| |#1| . #25=((|DifferentialSpace|))) ELT) (#26=($ $ (|NonNegativeInteger|)) 93 (|has| |#1| . #25#) ELT) (($ $ #27=(|Symbol|)) 91 (|has| |#1| . #28=((|PartialDifferentialSpace| (|Symbol|)))) ELT) (($ $ (|List| #27#)) 89 (|has| |#1| . #28#) ELT) (($ $ #27# . #29=(#30=(|NonNegativeInteger|))) 88 (|has| |#1| . #28#) ELT) (($ $ (|List| #27#) . #31=((|List| #30#))) 87 (|has| |#1| . #28#) ELT)) (|convert| (((|InputForm|) $) 106 (|has| |#1| (|ConvertibleTo| (|InputForm|))) ELT)) (|conjugate| (($ $) 118 T ELT)) (|coerce| (((|OutputForm|) $) 13 T ELT) (($ (|Integer|)) 42 T ELT) (($ |#1|) 53 T ELT) (($ #8#) 83 (OR (|has| |#1| . #21#) (|has| |#1| . #9#)) ELT)) (|charthRoot| (((|Maybe| $) $) 107 (|has| |#1| (|CharacteristicNonZero|)) ELT)) (|characteristic| (((|NonNegativeInteger|)) 41 T CONST)) (|before?| (#1# 6 T ELT)) (|annihilate?| (((|Boolean|) $ $) 34 T ELT)) (|abs| ((|#1| $) 111 (|has| |#1| (|RealNumberSystem|)) ELT)) (|Zero| (#3# 24 T CONST)) (|One| (($) 46 T CONST)) (D (($ $ (|Mapping| |#1| |#1|)) 136 T ELT) (($ $ (|Mapping| |#1| |#1|) . #23#) 135 T ELT) (($ . #24#) 94 (|has| |#1| . #25#) ELT) (#26# 92 (|has| |#1| . #25#) ELT) (($ $ #27#) 90 (|has| |#1| . #28#) ELT) (($ $ (|List| #27#)) 86 (|has| |#1| . #28#) ELT) (($ $ #27# . #29#) 85 (|has| |#1| . #28#) ELT) (($ $ (|List| #27#) . #31#) 84 (|has| |#1| . #28#) ELT)) (>= (#32=((|Boolean|) $ $) 98 (|has| |#1| . #18#) ELT)) (> (#32# 100 (|has| |#1| . #18#) ELT)) (= (#1# 8 T ELT)) (<= (#32# 99 (|has| |#1| . #18#) ELT)) (< (#32# 101 (|has| |#1| . #18#) ELT)) (- (($ $) 30 T ELT) (($ $ $) 29 T ELT)) (+ (($ $ $) 18 T ELT)) (** (($ $ (|PositiveInteger|)) 36 T ELT) (($ $ (|NonNegativeInteger|)) 44 T ELT) (($ $ #33=(|Integer|)) 104 (|has| |#1| . #21#) ELT)) (* (($ (|PositiveInteger|) $) 17 T ELT) (($ (|NonNegativeInteger|) $) 21 T ELT) (($ (|Integer|) . #34=($)) 31 T ELT) (($ $ $) 35 T ELT) (($ $ |#1|) 55 T ELT) (($ |#1| . #34#) 54 T ELT) (($ $ #35=(|Fraction| #33#)) 103 (|has| |#1| . #21#) ELT) (($ #35# . #34#) 102 (|has| |#1| . #21#) ELT))) (((|QuaternionCategory| |#1|) (|Category|) (|CommutativeRing|)) (T |QuaternionCategory|)) ((|conjugate| (*1 *1 *1) (AND (|ofCategory| *1 (|QuaternionCategory| *2)) (|ofCategory| *2 (|CommutativeRing|)))) (|imagI| (*1 *2 *1) (AND (|ofCategory| *1 (|QuaternionCategory| *2)) (|ofCategory| *2 (|CommutativeRing|)))) (|imagJ| (*1 *2 *1) (AND (|ofCategory| *1 (|QuaternionCategory| *2)) (|ofCategory| *2 (|CommutativeRing|)))) (|imagK| (*1 *2 *1) (AND (|ofCategory| *1 (|QuaternionCategory| *2)) (|ofCategory| *2 (|CommutativeRing|)))) (|norm| (*1 *2 *1) (AND (|ofCategory| *1 (|QuaternionCategory| *2)) (|ofCategory| *2 (|CommutativeRing|)))) (|quatern| (*1 *1 *2 *2 *2 *2) (AND (|ofCategory| *1 (|QuaternionCategory| *2)) (|ofCategory| *2 (|CommutativeRing|)))) (|real| (*1 *2 *1) (AND (|ofCategory| *1 (|QuaternionCategory| *2)) (|ofCategory| *2 (|CommutativeRing|)))) (|abs| (*1 *2 *1) (AND (|ofCategory| *1 (|QuaternionCategory| *2)) (|ofCategory| *2 (|CommutativeRing|)) (|ofCategory| *2 (|RealNumberSystem|)))) (|rational?| (*1 *2 *1) (AND (|ofCategory| *1 (|QuaternionCategory| *3)) (|ofCategory| *3 (|CommutativeRing|)) (|ofCategory| *3 (|IntegerNumberSystem|)) (|isDomain| *2 (|Boolean|)))) (|rational| (*1 *2 *1) (AND (|ofCategory| *1 (|QuaternionCategory| *3)) (|ofCategory| *3 (|CommutativeRing|)) (|ofCategory| *3 (|IntegerNumberSystem|)) (|isDomain| *2 (|Fraction| (|Integer|))))) (|rationalIfCan| (*1 *2 *1) (|partial| AND (|ofCategory| *1 (|QuaternionCategory| *3)) (|ofCategory| *3 (|CommutativeRing|)) (|ofCategory| *3 (|IntegerNumberSystem|)) (|isDomain| *2 (|Fraction| (|Integer|)))))) (|Join| (|Algebra| |t#1|) (|FullyRetractableTo| |t#1|) (|DifferentialExtension| |t#1|) (|FullyEvalableOver| |t#1|) (|FullyLinearlyExplicitRingOver| |t#1|) (CATEGORY |domain| (SIGNATURE |conjugate| ($ $)) (SIGNATURE |imagI| (|t#1| $)) (SIGNATURE |imagJ| (|t#1| $)) (SIGNATURE |imagK| (|t#1| $)) (SIGNATURE |norm| (|t#1| $)) (SIGNATURE |quatern| ($ |t#1| |t#1| |t#1| |t#1|)) (SIGNATURE |real| (|t#1| $)) (IF (|has| |t#1| (|EntireRing|)) (ATTRIBUTE (|EntireRing|)) |%noBranch|) (IF (|has| |t#1| (|OrderedSet|)) (ATTRIBUTE (|OrderedSet|)) |%noBranch|) (IF (|has| |t#1| (|Field|)) (ATTRIBUTE (|DivisionRing|)) |%noBranch|) (IF (|has| |t#1| (|ConvertibleTo| (|InputForm|))) (ATTRIBUTE (|ConvertibleTo| (|InputForm|))) |%noBranch|) (IF (|has| |t#1| (|CharacteristicZero|)) (ATTRIBUTE (|CharacteristicZero|)) |%noBranch|) (IF (|has| |t#1| (|CharacteristicNonZero|)) (ATTRIBUTE (|CharacteristicNonZero|)) |%noBranch|) (IF (|has| |t#1| (|RealNumberSystem|)) (SIGNATURE |abs| (|t#1| $)) |%noBranch|) (IF (|has| |t#1| (|IntegerNumberSystem|)) (PROGN (SIGNATURE |rational?| ((|Boolean|) $)) (SIGNATURE |rational| ((|Fraction| (|Integer|)) $)) (SIGNATURE |rationalIfCan| ((|Union| (|Fraction| (|Integer|)) "failed") $))) |%noBranch|))) @@ -3052,10 +3052,10 @@ NIL (((|RadicalCategory|) (|Category|)) (T |RadicalCategory|)) ((** (*1 *1 *1 *2) (AND (|ofCategory| *1 (|RadicalCategory|)) (|isDomain| *2 (|Fraction| (|Integer|))))) (|nthRoot| (*1 *1 *1 *2) (AND (|ofCategory| *1 (|RadicalCategory|)) (|isDomain| *2 (|Integer|)))) (|sqrt| (*1 *1 *1) (|ofCategory| *1 (|RadicalCategory|)))) (|Join| (CATEGORY |domain| (SIGNATURE |sqrt| ($ $)) (SIGNATURE |nthRoot| ($ $ (|Integer|))) (SIGNATURE ** ($ $ (|Fraction| (|Integer|)))))) -((~= #1=(#2=(#3=(|Boolean|) $ $) NIL T ELT)) (|zero?| #4=(#5=(#3# $) NIL T ELT)) (|yCoordinates| (#6=((|Record| (|:| |num| #7=(|Vector| |#2|)) #8=(|:| |den| |#2|)) $) NIL T ELT)) (|unitNormal| (((|Record| (|:| |unit| $) (|:| |canonical| $) (|:| |associate| $)) $) NIL #9=(|has| #10=(|Fraction| |#2|) #11=(|Field|)) ELT)) (|unitCanonical| #12=(#13=($ $) NIL #9# ELT)) (|unit?| #14=(#5# NIL #9# ELT)) (|traceMatrix| #15=((#16=(|Matrix| #10#) #17=(|Vector| $)) NIL T ELT) (#18=(#16#) NIL T ELT)) (|trace| #19=((#10# $) NIL T ELT)) (|tableForDiscreteLogarithm| (((|Table| #20=(|PositiveInteger|) #21=(|NonNegativeInteger|)) #22=(|Integer|)) NIL #23=(|has| #10# (|FiniteFieldCategory|)) ELT)) (|subtractIfCan| (#24=(#25=(|Union| $ #26="failed") $ $) NIL T ELT)) (|squareFreePart| #12#) (|squareFree| #27=(((|Factored| $) $) NIL #9# ELT)) (|sizeLess?| #28=(#2# NIL #9# ELT)) (|size| (#29=(#21#) NIL #30=(|has| #10# 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#54=(#51# #17#)) NIL #52# ELT) ((#55=(|Record| (|:| |mat| #16#) (|:| |vec| #44#)) . #54#) NIL T ELT) ((#16# . #50#) NIL T ELT)) (|reduceBasisAtInfinity| #56=((#17# #17#) NIL T ELT)) (|reduce| (#57=($ |#3|) 73 T ELT) ((#25# (|Fraction| |#3|)) NIL #9# ELT)) (|recip| ((#25# $) NIL T ELT)) (|rationalPoints| (((|List| (|List| |#1|))) NIL (|has| |#1| #31#) ELT)) (|rationalPoint?| ((#3# |#1| |#1|) NIL T ELT)) (|rank| ((#20#) NIL T ELT)) (|random| (#37# NIL #30# ELT)) (|ramifiedAtInfinity?| #32#) (|ramified?| (#34# 61 T ELT) (#35# 164 T ELT)) (|quo| #47#) (|principalIdeal| (((|Record| (|:| |coef| #58=(|List| $)) #59=(|:| |generator| $)) #58#) NIL #9# ELT)) (|primitivePart| #60=(#13# NIL T ELT)) (|primitiveElement| #61=(#37# NIL #23# ELT)) (|primitive?| (#5# NIL #23# ELT)) (|primeFrobenius| (#62=($ $ #21#) NIL #23# ELT) #63=(#13# NIL #23# ELT)) (|prime?| #14#) (|order| (#64=(#20# $) NIL #23# ELT) (((|OnePointCompletion| #20#) $) NIL #23# ELT)) (|opposite?| #1#) (|one?| #4#) (|numberOfComponents| #65=(#29# NIL T ELT)) (|normalizeAtInfinity| #56#) (|norm| #19#) (|nonSingularModel| (((|List| (|Polynomial| |#1|)) #66=(|Symbol|)) NIL (|has| |#1| #11#) ELT)) (|nextItem| (#67=((|Maybe| $) $) NIL #23# ELT)) (|multiEuclidean| (((|Union| #58# #26#) #58# $) NIL #9# ELT)) (|minimalPolynomial| (#68=(|#3| $) NIL #9# ELT)) (|lookup| (#64# NIL #30# ELT)) (|lift| #69=(#68# NIL T ELT)) (|leftReducedSystem| ((#49# #17#) NIL #52# ELT) ((#53# . #70=(#17# $)) NIL #52# ELT) ((#55# . #70#) NIL T ELT) #15#) (|lcm| #71=(($ #58#) NIL #9# ELT) #47#) (|latex| (((|String|) $) NIL T ELT)) (|inverseIntegralMatrixAtInfinity| (#18# 57 T ELT)) (|inverseIntegralMatrix| (#18# 56 T ELT)) (|inv| #12#) (|integralRepresents| (#46# 80 T ELT)) (|integralMatrixAtInfinity| (#18# 55 T ELT)) (|integralMatrix| (#18# 54 T ELT)) (|integralDerivationMatrix| (((|Record| (|:| |num| (|Matrix| |#2|)) #8#) #72=(|Mapping| |#2| |#2|)) 95 T ELT)) (|integralCoordinates| (#6# 86 T ELT)) (|integralBasisAtInfinity| (#73=(#17#) 51 T ELT)) (|integralBasis| (#73# 50 T ELT)) (|integralAtInfinity?| #4#) (|integral?| #4# ((#3# $ |#1|) NIL T ELT) ((#3# $ |#2|) NIL T ELT)) (|init| (#37# NIL #23# CONST)) (|index| (($ #20#) NIL #30# ELT)) (|hyperelliptic| (#74=((|Union| |#2| #26#)) 70 T ELT)) (|hash| (((|SingleInteger|) $) NIL T ELT)) (|genus| #65#) (|generator| (#37# NIL T ELT)) (|gcdPolynomial| ((#75=(|SparseUnivariatePolynomial| $) #75# #75#) NIL #9# ELT)) (|gcd| #71# #47#) (|factorsOfCyclicGroupSize| (((|List| (|Record| (|:| |factor| #22#) (|:| |exponent| #22#)))) NIL #23# ELT)) (|factor| #27#) (|extendedEuclidean| (((|Union| (|Record| #76=(|:| |coef1| $) #77=(|:| |coef2| $)) #26#) $ $ $) NIL #9# ELT) (((|Record| #76# #77# #59#) $ $) NIL #9# ELT)) (|exquo| (#24# NIL #9# ELT)) (|expressIdealMember| (((|Maybe| #58#) #58# $) NIL #9# ELT)) (|euclideanSize| (#78=(#21# $) NIL #9# ELT)) (|elt| ((|#1| $ |#1| |#1|) NIL T ELT)) (|elliptic| (#74# 68 T ELT)) (|divide| (((|Record| (|:| |quotient| $) (|:| |remainder| $)) $ $) NIL #9# ELT)) (|discriminant| ((#10# #17#) NIL T ELT) ((#10#) 47 T ELT)) (|discreteLog| (#78# NIL #23# ELT) (((|Union| #21# #26#) $ $) NIL #23# ELT)) (|differentiate| #79=(($ $ #80=(|Mapping| #10# #10#)) NIL #9# ELT) #81=(($ $ #80# #21#) NIL #9# ELT) (($ $ #72#) NIL T ELT) #82=(($ $ #83=(|List| #66#) (|List| #21#)) NIL #84=(OR (AND #9# (|has| #10# (|PartialDifferentialRing| #66#))) (AND #9# (|has| #10# (|PartialDifferentialSpace| #66#)))) ELT) #85=(($ $ #66# #21#) NIL #84# ELT) #86=(($ $ #83#) NIL #84# ELT) #87=(($ $ #66#) NIL #84# ELT) #88=(#62# NIL #89=(OR (AND (|has| #10# (|DifferentialRing|)) #9#) (AND (|has| #10# (|DifferentialSpace|)) #9#) #23#) ELT) #90=(#13# NIL #89# ELT)) (|derivationCoordinates| ((#16# #17# #80#) NIL #9# ELT)) (|definingPolynomial| ((|#3|) 58 T ELT)) (|createPrimitiveElement| #61#) (|coordinates| ((#44# $ #17#) NIL T ELT) ((#16# #17# #17#) NIL T ELT) (#91=(#44# $) 81 T ELT) #15#) (|convert| (#91# NIL T ELT) (#45# NIL T ELT) #69# (#57# NIL T ELT)) (|conditionP| (((|Union| #17# #26#) #51#) NIL #23# ELT)) (|complementaryBasis| #56#) (|coerce| (((|OutputForm|) $) NIL T ELT) (($ #22#) NIL T ELT) (($ #10#) NIL T ELT) (($ #41#) NIL (OR #9# #42#) ELT) #12#) (|charthRoot| #63# (#67# NIL (|has| #10# (|CharacteristicNonZero|)) ELT)) (|characteristicPolynomial| #69#) (|characteristic| (#29# NIL T CONST)) (|branchPointAtInfinity?| (#33# 65 T ELT)) (|branchPoint?| (#34# 167 T ELT) (#35# 168 T ELT)) (|before?| #1#) (|basis| (#73# NIL T ELT)) (|associates?| #28#) (|annihilate?| #1#) (|algSplitSimple| (((|Record| (|:| |num| $) #8# (|:| |derivden| |#2|) (|:| |gd| |#2|)) $ #72#) NIL T ELT)) (|absolutelyIrreducible?| #32#) (|Zero| #36#) (|One| #36#) (D #79# #81# #82# #85# #86# #87# #88# #90#) (= #1#) (/ #47#) (- #60# #92=(#48# NIL T ELT)) (+ #92#) (** (($ $ #20#) NIL T ELT) (#62# NIL T ELT) (($ $ #22#) NIL #9# ELT)) (* (($ #20# $) NIL T ELT) (($ #21# $) NIL T ELT) (($ #22# . #93=($)) NIL T ELT) #92# (($ $ #10#) NIL T ELT) (($ #10# . #93#) NIL T ELT) (($ #41# . #93#) NIL #9# ELT) (($ $ #41#) NIL #9# ELT))) +((~= #1=(#2=(#3=(|Boolean|) $ $) NIL T ELT)) (|zero?| #4=(#5=(#3# $) NIL T ELT)) (|yCoordinates| (#6=((|Record| (|:| |num| #7=(|Vector| |#2|)) #8=(|:| |den| |#2|)) $) NIL T ELT)) (|unitNormal| (((|Record| (|:| |unit| $) (|:| |canonical| $) (|:| |associate| $)) $) NIL #9=(|has| #10=(|Fraction| |#2|) #11=(|Field|)) ELT)) (|unitCanonical| #12=(#13=($ $) NIL #9# ELT)) (|unit?| #14=(#5# NIL #9# ELT)) (|traceMatrix| #15=((#16=(|Matrix| #10#) #17=(|Vector| $)) NIL T ELT) (#18=(#16#) NIL T ELT)) (|trace| #19=((#10# $) NIL T ELT)) (|tableForDiscreteLogarithm| (((|Table| #20=(|PositiveInteger|) #21=(|NonNegativeInteger|)) #22=(|Integer|)) NIL #23=(|has| #10# (|FiniteFieldCategory|)) ELT)) (|subtractIfCan| ((#24=(|Maybe| $) $ $) NIL T ELT)) (|squareFreePart| #12#) (|squareFree| #25=(((|Factored| $) $) NIL #9# ELT)) (|sizeLess?| #26=(#2# NIL #9# ELT)) (|size| (#27=(#21#) NIL #28=(|has| #10# #29=(|Finite|)) ELT)) (|singularAtInfinity?| #30=(#31=(#3#) NIL T ELT)) (|singular?| (#32=(#3# |#1|) 162 T ELT) (#33=(#3# |#2|) 166 T ELT)) (|sample| #34=(#35=($) NIL T CONST)) (|retractIfCan| (((|Union| #22# . #36=(#37="failed")) . #38=($)) NIL #39=(|has| #10# (|RetractableTo| #22#)) ELT) (((|Union| #40=(|Fraction| #22#) . #36#) . #38#) NIL #41=(|has| #10# (|RetractableTo| #40#)) ELT) (((|Union| #10# . #36#) . #38#) NIL T ELT)) (|retract| ((#22# . #42=($)) NIL #39# ELT) ((#40# . #42#) NIL #41# ELT) #19#) (|represents| (($ #43=(|Vector| #10#) #17#) NIL T ELT) (#44=($ #43#) 79 T ELT) (#45=($ #7# |#2|) NIL T ELT)) (|representationType| (((|Union| "prime" "polynomial" "normal" "cyclic")) NIL #23# ELT)) (|rem| #46=(#47=($ $ $) NIL #9# ELT)) (|regularRepresentation| ((#16# $ #17#) NIL T ELT) ((#16# $) NIL T ELT)) (|reducedSystem| ((#48=(|Matrix| #22#) . #49=(#50=(|Matrix| $))) NIL #51=(|has| #10# (|LinearlyExplicitRingOver| #22#)) ELT) ((#52=(|Record| (|:| |mat| #48#) (|:| |vec| (|Vector| #22#))) . #53=(#50# #17#)) NIL #51# ELT) ((#54=(|Record| (|:| |mat| #16#) (|:| |vec| #43#)) . #53#) NIL T ELT) ((#16# . #49#) NIL T ELT)) (|reduceBasisAtInfinity| #55=((#17# #17#) NIL T ELT)) (|reduce| (#56=($ |#3|) 73 T ELT) ((#57=(|Union| $ #37#) (|Fraction| |#3|)) NIL #9# ELT)) (|recip| ((#57# $) NIL T ELT)) (|rationalPoints| (((|List| (|List| |#1|))) NIL (|has| |#1| #29#) ELT)) (|rationalPoint?| ((#3# |#1| |#1|) NIL T ELT)) (|rank| ((#20#) NIL T ELT)) (|random| (#35# NIL #28# ELT)) (|ramifiedAtInfinity?| #30#) (|ramified?| (#32# 61 T ELT) (#33# 164 T ELT)) (|quo| #46#) (|principalIdeal| (((|Record| (|:| |coef| #58=(|List| $)) #59=(|:| |generator| $)) #58#) NIL #9# ELT)) (|primitivePart| #60=(#13# NIL T ELT)) (|primitiveElement| #61=(#35# NIL #23# ELT)) (|primitive?| (#5# NIL #23# ELT)) (|primeFrobenius| (#62=($ $ #21#) NIL #23# ELT) #63=(#13# NIL #23# ELT)) (|prime?| #14#) (|order| (#64=(#20# $) NIL #23# ELT) (((|OnePointCompletion| #20#) $) NIL #23# ELT)) (|opposite?| #1#) (|one?| #4#) (|numberOfComponents| #65=(#27# NIL T ELT)) (|normalizeAtInfinity| #55#) (|norm| #19#) (|nonSingularModel| (((|List| (|Polynomial| |#1|)) #66=(|Symbol|)) NIL (|has| |#1| #11#) ELT)) (|nextItem| (#67=(#24# $) NIL #23# ELT)) (|multiEuclidean| (((|Union| #58# #37#) #58# $) NIL #9# ELT)) (|minimalPolynomial| (#68=(|#3| $) NIL #9# ELT)) (|lookup| (#64# NIL #28# ELT)) (|lift| #69=(#68# NIL T ELT)) (|leftReducedSystem| ((#48# #17#) NIL #51# ELT) ((#52# . #70=(#17# $)) NIL #51# ELT) ((#54# . #70#) NIL T ELT) #15#) (|lcm| #71=(($ #58#) NIL #9# ELT) #46#) (|latex| (((|String|) $) NIL T ELT)) (|inverseIntegralMatrixAtInfinity| (#18# 57 T ELT)) (|inverseIntegralMatrix| (#18# 56 T ELT)) (|inv| #12#) (|integralRepresents| (#45# 80 T ELT)) (|integralMatrixAtInfinity| (#18# 55 T ELT)) (|integralMatrix| (#18# 54 T ELT)) (|integralDerivationMatrix| (((|Record| (|:| |num| (|Matrix| |#2|)) #8#) #72=(|Mapping| |#2| |#2|)) 95 T ELT)) (|integralCoordinates| (#6# 86 T ELT)) (|integralBasisAtInfinity| (#73=(#17#) 51 T ELT)) (|integralBasis| (#73# 50 T ELT)) (|integralAtInfinity?| #4#) (|integral?| #4# ((#3# $ |#1|) NIL T ELT) ((#3# $ |#2|) NIL T ELT)) (|init| (#35# NIL #23# CONST)) (|index| (($ #20#) NIL #28# ELT)) (|hyperelliptic| (#74=((|Union| |#2| #37#)) 70 T ELT)) (|hash| (((|SingleInteger|) $) NIL T ELT)) (|genus| #65#) (|generator| (#35# NIL T ELT)) (|gcdPolynomial| ((#75=(|SparseUnivariatePolynomial| $) #75# #75#) NIL #9# ELT)) (|gcd| #71# #46#) (|factorsOfCyclicGroupSize| (((|List| (|Record| (|:| |factor| #22#) (|:| |exponent| #22#)))) NIL #23# ELT)) (|factor| #25#) (|extendedEuclidean| (((|Union| (|Record| #76=(|:| |coef1| $) #77=(|:| |coef2| $)) #37#) $ $ $) NIL #9# ELT) (((|Record| #76# #77# #59#) $ $) NIL #9# ELT)) (|exquo| ((#57# $ $) NIL #9# ELT)) (|expressIdealMember| (((|Maybe| #58#) #58# $) NIL #9# ELT)) (|euclideanSize| (#78=(#21# $) NIL #9# ELT)) (|elt| ((|#1| $ |#1| |#1|) NIL T ELT)) (|elliptic| (#74# 68 T ELT)) (|divide| (((|Record| (|:| |quotient| $) (|:| |remainder| $)) $ $) NIL #9# ELT)) (|discriminant| ((#10# #17#) NIL T ELT) ((#10#) 47 T ELT)) (|discreteLog| (#78# NIL #23# ELT) (((|Union| #21# #37#) $ $) NIL #23# ELT)) (|differentiate| #79=(($ $ #80=(|Mapping| #10# #10#)) NIL #9# ELT) #81=(($ $ #80# #21#) NIL #9# ELT) (($ $ #72#) NIL T ELT) #82=(#62# NIL #83=(OR (AND (|has| #10# (|DifferentialRing|)) #9#) (AND (|has| #10# (|DifferentialSpace|)) #9#) #23#) ELT) #84=(#13# NIL #83# ELT) #85=(($ $ #86=(|List| #66#) (|List| #21#)) NIL #87=(OR (AND #9# (|has| #10# (|PartialDifferentialRing| #66#))) (AND #9# (|has| #10# (|PartialDifferentialSpace| #66#)))) ELT) #88=(($ $ #66# #21#) NIL #87# ELT) #89=(($ $ #86#) NIL #87# ELT) #90=(($ $ #66#) NIL #87# ELT)) (|derivationCoordinates| ((#16# #17# #80#) NIL #9# ELT)) (|definingPolynomial| ((|#3|) 58 T ELT)) (|createPrimitiveElement| #61#) (|coordinates| ((#43# $ #17#) NIL T ELT) ((#16# #17# #17#) NIL T ELT) (#91=(#43# $) 81 T ELT) #15#) (|convert| (#91# NIL T ELT) (#44# NIL T ELT) #69# (#56# NIL T ELT)) (|conditionP| (((|Union| #17# #37#) #50#) NIL #23# ELT)) (|complementaryBasis| #55#) (|coerce| (((|OutputForm|) $) NIL T ELT) (($ #22#) NIL T ELT) (($ #10#) NIL T ELT) (($ #40#) NIL (OR #9# #41#) ELT) #12#) (|charthRoot| #63# (#67# NIL (|has| #10# (|CharacteristicNonZero|)) ELT)) (|characteristicPolynomial| #69#) (|characteristic| (#27# NIL T CONST)) (|branchPointAtInfinity?| (#31# 65 T ELT)) (|branchPoint?| (#32# 167 T ELT) (#33# 168 T ELT)) (|before?| #1#) (|basis| (#73# NIL T ELT)) (|associates?| #26#) (|annihilate?| #1#) (|algSplitSimple| (((|Record| (|:| |num| $) #8# (|:| |derivden| |#2|) (|:| |gd| |#2|)) $ #72#) NIL T ELT)) (|absolutelyIrreducible?| #30#) (|Zero| #34#) (|One| #34#) (D #79# #81# #82# #84# #85# #88# #89# #90#) (= #1#) (/ #46#) (- #60# #92=(#47# NIL T ELT)) (+ #92#) (** (($ $ #20#) NIL T ELT) (#62# NIL T ELT) (($ $ #22#) NIL #9# ELT)) (* (($ #20# $) NIL T ELT) (($ #21# $) NIL T ELT) (($ #22# . #93=($)) NIL T ELT) #92# (($ $ #10#) NIL T ELT) (($ #10# . #93#) NIL T ELT) (($ #40# . #93#) NIL #9# ELT) (($ $ #40#) NIL #9# ELT))) (((|RadicalFunctionField| |#1| |#2| |#3| |#4| |#5|) (|FunctionFieldCategory| |#1| |#2| |#3|) (|UniqueFactorizationDomain|) (|UnivariatePolynomialCategory| |#1|) (|UnivariatePolynomialCategory| #1=(|Fraction| |#2|)) #1# (|NonNegativeInteger|)) (T |RadicalFunctionField|)) NIL -((~= #1=(#2=(#3=(|Boolean|) $ $) NIL T ELT)) (|zero?| #4=(#5=(#3# $) NIL T ELT)) (|wholeRagits| (#6=(#7=(|List| #8=(|Integer|)) $) 73 T ELT)) (|wholeRadix| (($ #7#) 81 T ELT)) (|wholePart| (#9=(#8# $) 48 #10=(|has| #8# (|EuclideanDomain|)) ELT)) (|unitNormal| (((|Record| (|:| |unit| $) (|:| |canonical| $) (|:| |associate| $)) $) NIL T ELT)) (|unitCanonical| #11=(#12=($ $) NIL T ELT)) (|unit?| #4#) (|subtractIfCan| #13=((#14=(|Union| $ #15="failed") $ $) NIL T ELT)) (|squareFreePolynomial| #16=(((|Factored| #17=(|SparseUnivariatePolynomial| $)) #17#) NIL #18=(|has| #8# (|PolynomialFactorizationExplicit|)) ELT)) (|squareFreePart| #11#) (|squareFree| #19=(((|Factored| $) $) NIL T ELT)) (|solveLinearPolynomialEquation| (((|Union| #20=(|List| #17#) #15#) #20# #17#) NIL #18# ELT)) (|sizeLess?| #1#) (|sign| (#9# NIL #21=(|has| #8# (|OrderedIntegralDomain|)) ELT)) (|sample| (#22=($) NIL T CONST)) (|retractIfCan| (#23=((|Union| #8# . #24=(#15#)) $) 60 T ELT) (((|Union| #25=(|Symbol|) . #24#) $) NIL #26=(|has| #8# (|RetractableTo| #25#)) ELT) (((|Union| #27=(|Fraction| #8#) . #24#) $) 57 #28=(|has| #8# (|RetractableTo| #8#)) ELT) (#23# 60 #28# ELT)) (|retract| (#9# NIL T ELT) ((#25# $) NIL #26# ELT) (#29=(#27# $) NIL #28# ELT) (#9# NIL #28# ELT)) (|rem| #30=(#31=($ $ $) NIL T ELT)) (|reducedSystem| (#32=(#33=(|Matrix| #8#) #34=(|Matrix| $)) NIL #35=(|has| #8# (|LinearlyExplicitRingOver| #8#)) ELT) (#36=(#37=(|Record| (|:| |mat| #33#) (|:| |vec| (|Vector| #8#))) #34# #38=(|Vector| $)) NIL #35# ELT) (#36# NIL T ELT) (#32# NIL T ELT)) (|recip| ((#14# $) NIL T ELT)) (|random| (#22# NIL #39=(|has| #8# (|IntegerNumberSystem|)) ELT)) (|quo| #30#) (|principalIdeal| (((|Record| (|:| |coef| #40=(|List| $)) #41=(|:| |generator| $)) #40#) NIL T ELT)) (|prime?| #4#) (|prefixRagits| (#6# 79 T ELT)) (|positive?| #42=(#5# NIL #21# ELT)) (|patternMatch| ((#43=(|PatternMatchResult| #8# . #44=($)) $ #45=(|Pattern| #8#) #43#) NIL (|has| #8# (|PatternMatchable| #8#)) ELT) ((#46=(|PatternMatchResult| #47=(|Float|) . #44#) $ #48=(|Pattern| #47#) #46#) NIL (|has| #8# (|PatternMatchable| #47#)) ELT)) (|opposite?| #1#) (|one?| #4#) (|numerator| #11#) (|numer| (#9# 45 T ELT)) (|nextItem| (#49=((|Maybe| $) $) NIL #50=(|has| #8# (|StepThrough|)) ELT)) (|negative?| #42#) (|multiEuclidean| (((|Union| #40# #15#) #40# $) NIL T ELT)) (|min| #51=(#31# NIL #52=(|has| #8# (|OrderedSet|)) ELT)) (|max| #51#) (|map| (($ #53=(|Mapping| #8# #8#) $) NIL T ELT)) (|leftReducedSystem| (#54=(#33# #38#) NIL #35# ELT) (#55=(#37# #38# $) NIL #35# ELT) (#55# NIL T ELT) (#54# NIL T ELT)) (|lcm| #30# #56=(($ #40#) NIL T ELT)) (|latex| (((|String|) $) NIL T ELT)) (|inv| #11#) (|init| (#22# NIL #50# CONST)) (|hash| (((|SingleInteger|) $) NIL T ELT)) (|gcdPolynomial| ((#17# #17# #17#) NIL T ELT)) (|gcd| #30# #56#) (|fractionPart| (#12# NIL #10# ELT) (#29# 50 T ELT)) (|fractRagits| (((|Stream| #8#) $) 78 T ELT)) (|fractRadix| (($ #7# #7#) 82 T ELT)) (|floor| (#9# 64 #39# ELT)) (|factorSquareFreePolynomial| #16#) (|factorPolynomial| #16#) (|factor| #19#) (|extendedEuclidean| (((|Record| #57=(|:| |coef1| $) #58=(|:| |coef2| $) #41#) $ $) NIL T ELT) (((|Union| (|Record| #57# #58#) #15#) $ $ $) NIL T ELT)) (|exquo| #13#) (|expressIdealMember| (((|Maybe| #40#) #40# $) NIL T ELT)) (|eval| (($ $ #7# #7#) NIL #59=(|has| #8# (|Evalable| #8#)) ELT) (($ $ #8# #8#) NIL #59# ELT) (($ $ #60=(|Equation| #8#)) NIL #59# ELT) (($ $ (|List| #60#)) NIL #59# ELT) (($ $ #61=(|List| #25#) #7#) NIL #62=(|has| #8# (|InnerEvalable| #25# #8#)) ELT) (($ $ #25# #8#) NIL #62# ELT)) (|euclideanSize| ((#63=(|NonNegativeInteger|) $) NIL T ELT)) (|elt| (#64=($ $ #8#) NIL (|has| #8# (|Eltable| #8# #8#)) ELT)) (|divide| (((|Record| (|:| |quotient| $) (|:| |remainder| $)) $ $) NIL T ELT)) (|differentiate| #65=(($ $ #53#) NIL T ELT) #66=(($ $ #53# #63#) NIL T ELT) #67=(($ $ #25#) NIL #68=(|has| #8# (|PartialDifferentialSpace| #25#)) ELT) #69=(($ $ #61#) NIL #68# ELT) #70=(($ $ #25# #63#) NIL #68# ELT) #71=(($ $ #61# (|List| #63#)) NIL #68# ELT) (#12# 15 #72=(|has| #8# (|DifferentialSpace|)) ELT) #73=(#74=($ $ #63#) NIL #72# ELT)) (|denominator| #11#) (|denom| (#9# 47 T ELT)) (|cycleRagits| (#6# 80 T ELT)) (|convert| ((#45# . #75=($)) NIL (|has| #8# (|ConvertibleTo| #45#)) ELT) ((#48# . #75#) NIL (|has| #8# (|ConvertibleTo| #48#)) ELT) ((#76=(|InputForm|) . #75#) NIL (|has| #8# (|ConvertibleTo| #76#)) ELT) ((#47# . #75#) NIL #77=(|has| #8# (|RealConstant|)) ELT) (((|DoubleFloat|) . #75#) NIL #77# ELT)) (|conditionP| (((|Union| #38# #15#) #34#) NIL #78=(AND (|has| $ #79=(|CharacteristicNonZero|)) #18#) ELT)) (|coerce| (((|OutputForm|) $) 108 T ELT) #80=(($ #8#) 51 T ELT) #11# (($ #27#) 27 T ELT) #80# (($ #25#) NIL #26# ELT) (#29# 25 T ELT)) (|charthRoot| (#49# NIL (OR #78# (|has| #8# #79#)) ELT)) (|characteristic| ((#63#) 13 T CONST)) (|ceiling| (#9# 62 #39# ELT)) (|before?| #1#) (|associates?| #1#) (|annihilate?| #1#) (|abs| (#12# NIL #21# ELT)) (|Zero| (#22# 14 T CONST)) (|One| (#22# 17 T CONST)) (D #65# #66# #67# #69# #70# #71# (#12# NIL #72# ELT) #73#) (>= #81=(#2# NIL #52# ELT)) (> #81#) (= (#2# 21 T ELT)) (<= #81#) (< (#2# 40 #52# ELT)) (/ (#31# 36 T ELT) (($ #8# #8#) 38 T ELT)) (- (#12# 23 T ELT) (#31# 30 T ELT)) (+ (#31# 28 T ELT)) (** (($ $ #82=(|PositiveInteger|)) NIL T ELT) (#74# NIL T ELT) #83=(#64# NIL T ELT)) (* (($ #82# $) NIL T ELT) (($ #63# $) NIL T ELT) #84=(($ #8# $) 32 T ELT) (#31# 34 T ELT) (($ $ #27#) NIL T ELT) (($ #27# $) NIL T ELT) #84# #83#)) +((~= #1=(#2=(#3=(|Boolean|) $ $) NIL T ELT)) (|zero?| #4=(#5=(#3# $) NIL T ELT)) (|wholeRagits| (#6=(#7=(|List| #8=(|Integer|)) $) 73 T ELT)) (|wholeRadix| (($ #7#) 81 T ELT)) 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((#24# $) NIL #25# ELT) (#28=(#26# $) NIL #27# ELT) (#9# NIL #27# ELT)) (|rem| #29=(#30=($ $ $) NIL T ELT)) (|reducedSystem| (#31=(#32=(|Matrix| #8#) #33=(|Matrix| $)) NIL #34=(|has| #8# (|LinearlyExplicitRingOver| #8#)) ELT) (#35=(#36=(|Record| (|:| |mat| #32#) (|:| |vec| (|Vector| #8#))) #33# #37=(|Vector| $)) NIL #34# ELT) (#35# NIL T ELT) (#31# NIL T ELT)) (|recip| ((#38=(|Union| $ #19#) $) NIL T ELT)) (|random| (#21# NIL #39=(|has| #8# (|IntegerNumberSystem|)) ELT)) (|quo| #29#) (|principalIdeal| (((|Record| (|:| |coef| #40=(|List| $)) #41=(|:| |generator| $)) #40#) NIL T ELT)) (|prime?| #4#) (|prefixRagits| (#6# 79 T ELT)) (|positive?| #42=(#5# NIL #20# ELT)) (|patternMatch| ((#43=(|PatternMatchResult| #8# . #44=($)) $ #45=(|Pattern| #8#) #43#) NIL (|has| #8# (|PatternMatchable| #8#)) ELT) ((#46=(|PatternMatchResult| #47=(|Float|) . #44#) $ #48=(|Pattern| #47#) #46#) NIL (|has| #8# (|PatternMatchable| #47#)) ELT)) (|opposite?| #1#) (|one?| #4#) (|numerator| #11#) (|numer| (#9# 45 T ELT)) (|nextItem| (#49=(#13# $) NIL #50=(|has| #8# (|StepThrough|)) ELT)) (|negative?| #42#) (|multiEuclidean| (((|Union| #40# #19#) #40# $) NIL T ELT)) (|min| #51=(#30# NIL #52=(|has| #8# (|OrderedSet|)) ELT)) (|max| #51#) (|map| (($ #53=(|Mapping| #8# #8#) $) NIL T ELT)) (|leftReducedSystem| (#54=(#32# #37#) NIL #34# ELT) (#55=(#36# #37# $) NIL #34# ELT) (#55# NIL T ELT) (#54# NIL T ELT)) (|lcm| #29# #56=(($ #40#) NIL T ELT)) (|latex| (((|String|) $) NIL T ELT)) (|inv| #11#) (|init| (#21# NIL #50# CONST)) (|hash| (((|SingleInteger|) $) NIL T ELT)) (|gcdPolynomial| ((#15# #15# #15#) NIL T ELT)) (|gcd| #29# #56#) (|fractionPart| (#12# NIL #10# ELT) (#28# 50 T ELT)) (|fractRagits| (((|Stream| #8#) $) 78 T ELT)) (|fractRadix| (($ #7# #7#) 82 T ELT)) (|floor| (#9# 64 #39# ELT)) (|factorSquareFreePolynomial| #14#) (|factorPolynomial| #14#) (|factor| #17#) (|extendedEuclidean| (((|Record| #57=(|:| |coef1| $) #58=(|:| |coef2| $) #41#) $ $) NIL T ELT) (((|Union| (|Record| #57# #58#) #19#) $ $ $) NIL T ELT)) (|exquo| ((#38# $ $) NIL T ELT)) (|expressIdealMember| (((|Maybe| #40#) #40# $) NIL T ELT)) (|eval| (($ $ #7# #7#) NIL #59=(|has| #8# (|Evalable| #8#)) ELT) (($ $ #8# #8#) NIL #59# ELT) (($ $ #60=(|Equation| #8#)) NIL #59# ELT) (($ $ (|List| #60#)) NIL #59# ELT) (($ $ #61=(|List| #24#) #7#) NIL #62=(|has| #8# (|InnerEvalable| #24# #8#)) ELT) (($ $ #24# #8#) NIL #62# ELT)) (|euclideanSize| ((#63=(|NonNegativeInteger|) $) NIL T ELT)) (|elt| (#64=($ $ #8#) NIL (|has| #8# (|Eltable| #8# #8#)) ELT)) (|divide| (((|Record| (|:| |quotient| $) (|:| |remainder| $)) $ $) NIL T ELT)) (|differentiate| #65=(($ $ #53#) NIL T ELT) #66=(($ $ #53# #63#) NIL T ELT) #67=(($ $ #24#) NIL #68=(|has| #8# (|PartialDifferentialSpace| #24#)) ELT) #69=(($ $ #61#) NIL #68# ELT) #70=(($ $ #24# #63#) NIL #68# ELT) #71=(($ $ #61# (|List| #63#)) NIL #68# ELT) (#12# 15 #72=(|has| #8# (|DifferentialSpace|)) ELT) #73=(#74=($ $ #63#) NIL #72# ELT)) (|denominator| #11#) (|denom| (#9# 47 T ELT)) (|cycleRagits| (#6# 80 T ELT)) (|convert| ((#45# . #75=($)) NIL (|has| #8# (|ConvertibleTo| #45#)) ELT) ((#48# . #75#) NIL (|has| #8# (|ConvertibleTo| #48#)) ELT) ((#76=(|InputForm|) . #75#) NIL (|has| #8# (|ConvertibleTo| #76#)) ELT) ((#47# . #75#) NIL #77=(|has| #8# (|RealConstant|)) ELT) (((|DoubleFloat|) . #75#) NIL #77# ELT)) (|conditionP| (((|Union| #37# #19#) #33#) NIL #78=(AND (|has| $ #79=(|CharacteristicNonZero|)) #16#) ELT)) (|coerce| (((|OutputForm|) $) 108 T ELT) #80=(($ #8#) 51 T ELT) #11# (($ #26#) 27 T ELT) #80# (($ #24#) NIL #25# ELT) (#28# 25 T ELT)) (|charthRoot| (#49# NIL (OR #78# (|has| #8# #79#)) ELT)) (|characteristic| ((#63#) 13 T CONST)) (|ceiling| (#9# 62 #39# ELT)) (|before?| #1#) (|associates?| #1#) (|annihilate?| #1#) (|abs| (#12# NIL #20# ELT)) (|Zero| (#21# 14 T CONST)) (|One| (#21# 17 T CONST)) (D #65# #66# #67# #69# #70# #71# (#12# NIL #72# ELT) #73#) (>= #81=(#2# NIL #52# ELT)) (> #81#) (= (#2# 21 T ELT)) (<= #81#) (< (#2# 40 #52# ELT)) (/ (#30# 36 T ELT) (($ #8# #8#) 38 T ELT)) (- (#12# 23 T ELT) (#30# 30 T ELT)) (+ (#30# 28 T ELT)) (** (($ $ #82=(|PositiveInteger|)) NIL T ELT) (#74# NIL T ELT) #83=(#64# NIL T ELT)) (* (($ #82# $) NIL T ELT) (($ #63# $) NIL T ELT) #84=(($ #8# $) 32 T ELT) (#30# 34 T ELT) (($ $ #26#) NIL T ELT) (($ #26# $) NIL T ELT) #84# #83#)) (((|RadixExpansion| |#1|) (|Join| (|QuotientFieldCategory| #1=(|Integer|)) (|CoercibleTo| #2=(|Fraction| #1#)) (CATEGORY |domain| (SIGNATURE |fractionPart| (#2# $)) (SIGNATURE |wholeRagits| #3=(#4=(|List| #1#) $)) (SIGNATURE |fractRagits| ((|Stream| #1#) $)) (SIGNATURE |prefixRagits| #3#) (SIGNATURE |cycleRagits| #3#) (SIGNATURE |wholeRadix| ($ #4#)) (SIGNATURE |fractRadix| ($ #4# #4#)))) #1#) (T |RadixExpansion|)) ((|fractionPart| #1=(*1 *2 *1) (AND (|isDomain| *2 (|Fraction| #2=(|Integer|))) #3=(|isDomain| *1 (|RadixExpansion| *3)) #4=(|ofType| *3 #2#))) (|wholeRagits| #1# #5=(AND (|isDomain| *2 (|List| #2#)) #3# #4#)) (|fractRagits| #1# (AND (|isDomain| *2 (|Stream| #2#)) #3# #4#)) (|prefixRagits| #1# #5#) (|cycleRagits| #1# #5#) (|wholeRadix| (*1 *1 *2) #5#) (|fractRadix| (*1 *1 *2 *2) #5#)) ((|radix| (((|Any|) (|Fraction| #1=(|Integer|)) #1#) 9 T ELT))) @@ -3081,7 +3081,7 @@ NIL ((|sqrt| (($ $) 9 T ELT) (#1=($ $ #2=(|PositiveInteger|)) 49 T ELT) (($ #3=(|Fraction| #4=(|Integer|))) 13 T ELT) (($ #4#) 15 T ELT)) (|rootOf| ((#5=(|Union| $ "failed") #6=(|SparseUnivariatePolynomial| $) #2# (|OutputForm|)) 24 T ELT) ((#5# #6# #2#) 32 T ELT)) (|nthRoot| (#7=($ $ #4#) 58 T ELT)) (|characteristic| ((#8=(|NonNegativeInteger|)) 18 T CONST)) (|allRootsOf| ((#9=(|List| $) #6#) NIL T ELT) ((#9# (|SparseUnivariatePolynomial| #3#)) 63 T ELT) ((#9# (|SparseUnivariatePolynomial| #4#)) 68 T ELT) ((#9# (|Polynomial| $)) 72 T ELT) ((#9# (|Polynomial| #3#)) 76 T ELT) ((#9# (|Polynomial| #4#)) 80 T ELT)) (** (#1# NIL T ELT) (($ $ #8#) NIL T ELT) (#7# NIL T ELT) (($ $ #3#) 53 T ELT))) (((|RealClosedField&| |#1|) (CATEGORY |package| (SIGNATURE |sqrt| (|#1| 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(|Integer|)) 41 T ELT) (($ #26=(|Fraction| #27=(|Integer|))) 138 T ELT) (($ $) 109 T ELT) (($ #9#) 102 T ELT) (($ #28=(|Integer|)) 101 T ELT) (($ #29=(|Fraction| (|Integer|))) 98 T ELT)) (|characteristic| (((|NonNegativeInteger|)) 40 T CONST)) (|before?| (#1# 6 T ELT)) (|associates?| ((#3# $ $) 113 T ELT)) (|approximate| (((|Fraction| (|Integer|)) $ $) 76 T ELT)) (|annihilate?| (((|Boolean|) $ $) 33 T ELT)) (|allRootsOf| (((|List| $) (|SparseUnivariatePolynomial| $)) 87 T ELT) (((|List| $) (|SparseUnivariatePolynomial| (|Fraction| (|Integer|)))) 86 T ELT) (((|List| $) (|SparseUnivariatePolynomial| (|Integer|))) 85 T ELT) (((|List| $) (|Polynomial| $)) 84 T ELT) (((|List| $) (|Polynomial| (|Fraction| (|Integer|)))) 83 T ELT) (((|List| $) (|Polynomial| (|Integer|))) 82 T ELT)) (|abs| (($ $) 149 T ELT)) (|Zero| (#5# 24 T CONST)) (|One| (($) 45 T CONST)) (>= (#30=((|Boolean|) $ $) 142 T ELT)) (> (#30# 144 T ELT)) (= (#1# 8 T ELT)) (<= (#30# 143 T ELT)) (< (#30# 145 T ELT)) (/ (($ $ $) 139 T ELT)) (- (($ $) 29 T ELT) (($ $ $) 28 T ELT)) (+ (($ $ $) 18 T ELT)) (** (($ $ (|PositiveInteger|)) 35 T ELT) (($ $ (|NonNegativeInteger|)) 43 T ELT) (($ $ #27#) 135 T ELT) (($ $ (|Fraction| #17#)) 93 T ELT)) (* (($ (|PositiveInteger|) $) 17 T ELT) (($ (|NonNegativeInteger|) $) 21 T ELT) (($ (|Integer|) . #31=($)) 30 T ELT) (($ $ $) 34 T ELT) (($ #26# . #31#) 137 T ELT) (($ $ #26#) 136 T ELT) (($ #28# . #31#) 100 T ELT) (($ $ #28#) 99 T ELT) (($ #29# . #31#) 97 T ELT) (($ $ #29#) 96 T ELT))) +((~= (#1=((|Boolean|) $ $) 7 T ELT)) (|zero?| ((#2=(|Boolean|) $) 22 T ELT)) (|unitNormal| (((|Record| (|:| |unit| $) (|:| |canonical| $) (|:| |associate| $)) $) 112 T ELT)) (|unitCanonical| (($ $) 113 T ELT)) (|unit?| ((#3=(|Boolean|) $) 115 T ELT)) (|subtractIfCan| (((|Maybe| $) $ $) 26 T ELT)) (|squareFreePart| (($ $) 132 T ELT)) (|squareFree| (#4=((|Factored| $) $) 133 T ELT)) (|sqrt| (($ $) 96 T ELT) (($ $ (|PositiveInteger|)) 82 T ELT) (($ (|Fraction| (|Integer|))) 81 T ELT) (($ (|Integer|)) 80 T ELT)) (|sizeLess?| (((|Boolean|) $ $) 123 T ELT)) (|sign| (((|Integer|) $) 149 T ELT)) (|sample| (#5=($) 23 T CONST)) (|rootOf| (((|Union| $ "failed") (|SparseUnivariatePolynomial| $) (|PositiveInteger|) (|OutputForm|)) 90 T ELT) (((|Union| $ "failed") (|SparseUnivariatePolynomial| $) (|PositiveInteger|)) 89 T ELT)) (|retractIfCan| (((|Union| #6=(|Integer|) . #7=("failed")) . #8=($)) 109 (|has| #9=(|Fraction| (|Integer|)) . #10=((|RetractableTo| #11=(|Integer|)))) ELT) (((|Union| #12=(|Fraction| #6#) . #7#) . #8#) 107 (|has| #9# . #13=((|RetractableTo| (|Fraction| #11#)))) ELT) (((|Union| #9# . #7#) . #8#) 104 T ELT)) (|retract| ((#6# . #14=($)) 108 (|has| #9# . #10#) ELT) ((#12# . #14#) 106 (|has| #9# . #13#) ELT) ((#9# . #14#) 105 T ELT)) (|rename!| (($ $ (|OutputForm|)) 79 T ELT)) (|rename| (($ $ (|OutputForm|)) 78 T ELT)) (|rem| (#15=($ $ $) 127 T ELT)) (|recip| (((|Union| $ "failed") $) 43 T ELT)) (|quo| (#15# 126 T ELT)) (|principalIdeal| (((|Record| (|:| |coef| #16=(|List| $)) (|:| |generator| $)) #16#) 121 T ELT)) (|prime?| (((|Boolean|) $) 134 T ELT)) (|positive?| (((|Boolean|) $) 147 T ELT)) (|opposite?| ((#2# $ $) 20 T ELT)) (|one?| (((|Boolean|) $) 45 T ELT)) (|nthRoot| (($ $ #17=(|Integer|)) 95 T ELT)) (|negative?| (((|Boolean|) $) 148 T ELT)) (|multiEuclidean| (((|Union| #18=(|List| $) #19="failed") #18# $) 130 T ELT)) (|min| (#20=($ $ $) 141 T ELT)) (|max| (#20# 142 T ELT)) (|mainValue| (((|Union| (|SparseUnivariatePolynomial| $) "failed") $) 91 T ELT)) (|mainForm| (((|Union| (|OutputForm|) "failed") $) 93 T ELT)) (|mainDefiningPolynomial| (((|Union| (|SparseUnivariatePolynomial| $) "failed") $) 92 T ELT)) (|lcm| (#21=($ (|List| $)) 119 T ELT) (#22=($ $ $) 118 T ELT)) (|latex| (((|String|) $) 11 T ELT)) (|inv| (($ $) 135 T ELT)) (|hash| (((|SingleInteger|) $) 12 T ELT)) (|gcdPolynomial| ((#23=(|SparseUnivariatePolynomial| $) #23# #23#) 120 T ELT)) (|gcd| (#21# 117 T ELT) (#22# 116 T ELT)) (|factor| (#4# 131 T ELT)) (|extendedEuclidean| (((|Union| (|Record| #24=(|:| |coef1| $) #25=(|:| |coef2| $)) #19#) $ $ $) 129 T ELT) (((|Record| #24# #25# (|:| |generator| $)) $ $) 128 T ELT)) (|exquo| (((|Union| $ "failed") $ $) 111 T ELT)) (|expressIdealMember| (((|Maybe| #16#) #16# $) 122 T ELT)) (|euclideanSize| (((|NonNegativeInteger|) $) 124 T ELT)) (|divide| (((|Record| (|:| |quotient| $) (|:| |remainder| $)) $ $) 125 T ELT)) (|coerce| (((|OutputForm|) $) 13 T ELT) (($ (|Integer|)) 42 T ELT) (($ #26=(|Fraction| #27=(|Integer|))) 139 T ELT) (($ $) 110 T ELT) (($ #9#) 103 T ELT) (($ #28=(|Integer|)) 102 T ELT) (($ #29=(|Fraction| (|Integer|))) 99 T ELT)) (|characteristic| (((|NonNegativeInteger|)) 41 T CONST)) (|before?| (#1# 6 T ELT)) (|associates?| ((#3# $ $) 114 T ELT)) (|approximate| (((|Fraction| (|Integer|)) $ $) 77 T ELT)) (|annihilate?| (((|Boolean|) $ $) 34 T ELT)) (|allRootsOf| (((|List| $) (|SparseUnivariatePolynomial| $)) 88 T ELT) (((|List| $) (|SparseUnivariatePolynomial| (|Fraction| (|Integer|)))) 87 T ELT) (((|List| $) (|SparseUnivariatePolynomial| (|Integer|))) 86 T ELT) (((|List| $) (|Polynomial| $)) 85 T ELT) (((|List| $) (|Polynomial| (|Fraction| (|Integer|)))) 84 T ELT) (((|List| $) (|Polynomial| (|Integer|))) 83 T ELT)) (|abs| (($ $) 150 T ELT)) (|Zero| (#5# 24 T CONST)) (|One| (($) 46 T CONST)) (>= (#30=((|Boolean|) $ $) 143 T ELT)) (> (#30# 145 T ELT)) (= (#1# 8 T ELT)) (<= (#30# 144 T ELT)) (< (#30# 146 T ELT)) (/ (($ $ $) 140 T ELT)) (- (($ $) 30 T ELT) (($ $ $) 29 T ELT)) (+ (($ $ $) 18 T ELT)) (** (($ $ (|PositiveInteger|)) 36 T ELT) (($ $ (|NonNegativeInteger|)) 44 T ELT) (($ $ #27#) 136 T ELT) (($ $ (|Fraction| #17#)) 94 T ELT)) (* (($ (|PositiveInteger|) $) 17 T ELT) (($ (|NonNegativeInteger|) $) 21 T ELT) (($ (|Integer|) . #31=($)) 31 T ELT) (($ $ $) 35 T ELT) (($ #26# . #31#) 138 T ELT) (($ $ #26#) 137 T ELT) (($ #28# . #31#) 101 T ELT) (($ $ #28#) 100 T ELT) (($ #29# . #31#) 98 T ELT) (($ $ #29#) 97 T ELT))) (((|RealClosedField|) (|Category|)) (T |RealClosedField|)) ((|sqrt| (*1 *1 *1) (|ofCategory| *1 (|RealClosedField|))) (|mainForm| (*1 *2 *1) (|partial| AND (|ofCategory| *1 (|RealClosedField|)) (|isDomain| *2 (|OutputForm|)))) (|mainDefiningPolynomial| (*1 *2 *1) (|partial| AND (|isDomain| *2 (|SparseUnivariatePolynomial| *1)) (|ofCategory| *1 (|RealClosedField|)))) (|mainValue| (*1 *2 *1) (|partial| AND (|isDomain| *2 (|SparseUnivariatePolynomial| *1)) (|ofCategory| *1 (|RealClosedField|)))) (|rootOf| (*1 *1 *2 *3 *4) (|partial| AND (|isDomain| *2 (|SparseUnivariatePolynomial| *1)) (|isDomain| *3 (|PositiveInteger|)) (|isDomain| *4 (|OutputForm|)) (|ofCategory| *1 (|RealClosedField|)))) (|rootOf| (*1 *1 *2 *3) (|partial| AND (|isDomain| *2 (|SparseUnivariatePolynomial| *1)) (|isDomain| *3 (|PositiveInteger|)) (|ofCategory| *1 (|RealClosedField|)))) (|allRootsOf| (*1 *2 *3) (AND (|isDomain| *3 (|SparseUnivariatePolynomial| *1)) (|ofCategory| *1 (|RealClosedField|)) (|isDomain| *2 (|List| *1)))) (|allRootsOf| (*1 *2 *3) (AND (|isDomain| *3 (|SparseUnivariatePolynomial| (|Fraction| (|Integer|)))) (|isDomain| *2 (|List| *1)) (|ofCategory| *1 (|RealClosedField|)))) (|allRootsOf| (*1 *2 *3) (AND (|isDomain| *3 (|SparseUnivariatePolynomial| (|Integer|))) (|isDomain| *2 (|List| *1)) (|ofCategory| *1 (|RealClosedField|)))) (|allRootsOf| (*1 *2 *3) (AND (|isDomain| *3 (|Polynomial| *1)) (|ofCategory| *1 (|RealClosedField|)) (|isDomain| *2 (|List| *1)))) (|allRootsOf| (*1 *2 *3) (AND (|isDomain| *3 (|Polynomial| (|Fraction| (|Integer|)))) (|isDomain| *2 (|List| *1)) (|ofCategory| *1 (|RealClosedField|)))) (|allRootsOf| (*1 *2 *3) (AND (|isDomain| *3 (|Polynomial| (|Integer|))) (|isDomain| *2 (|List| *1)) (|ofCategory| *1 (|RealClosedField|)))) (|sqrt| (*1 *1 *1 *2) (AND (|ofCategory| *1 (|RealClosedField|)) (|isDomain| *2 (|PositiveInteger|)))) (|sqrt| (*1 *1 *2) (AND (|isDomain| *2 (|Fraction| (|Integer|))) (|ofCategory| *1 (|RealClosedField|)))) (|sqrt| (*1 *1 *2) (AND (|isDomain| *2 (|Integer|)) (|ofCategory| *1 (|RealClosedField|)))) (|rename!| (*1 *1 *1 *2) (AND (|ofCategory| *1 (|RealClosedField|)) (|isDomain| *2 (|OutputForm|)))) (|rename| (*1 *1 *1 *2) (AND (|ofCategory| *1 (|RealClosedField|)) (|isDomain| *2 (|OutputForm|)))) (|approximate| (*1 *2 *1 *1) (AND (|ofCategory| *1 (|RealClosedField|)) (|isDomain| *2 (|Fraction| (|Integer|)))))) (|Join| (|CharacteristicZero|) (|OrderedRing|) (|CommutativeRing|) (|Field|) (|FullyRetractableTo| (|Fraction| (|Integer|))) (|Algebra| (|Integer|)) (|Algebra| (|Fraction| (|Integer|))) (|RadicalCategory|) (CATEGORY |domain| (SIGNATURE |mainForm| ((|Union| (|OutputForm|) "failed") $)) (SIGNATURE |mainDefiningPolynomial| ((|Union| (|SparseUnivariatePolynomial| $) "failed") $)) (SIGNATURE |mainValue| ((|Union| (|SparseUnivariatePolynomial| $) "failed") $)) (SIGNATURE |rootOf| ((|Union| $ "failed") (|SparseUnivariatePolynomial| $) (|PositiveInteger|) (|OutputForm|))) (SIGNATURE |rootOf| ((|Union| $ "failed") (|SparseUnivariatePolynomial| $) (|PositiveInteger|))) (SIGNATURE |allRootsOf| ((|List| $) (|SparseUnivariatePolynomial| $))) (SIGNATURE |allRootsOf| ((|List| $) (|SparseUnivariatePolynomial| (|Fraction| (|Integer|))))) (SIGNATURE |allRootsOf| ((|List| $) (|SparseUnivariatePolynomial| (|Integer|)))) (SIGNATURE |allRootsOf| ((|List| $) (|Polynomial| $))) (SIGNATURE |allRootsOf| ((|List| $) (|Polynomial| (|Fraction| (|Integer|))))) (SIGNATURE |allRootsOf| ((|List| $) (|Polynomial| (|Integer|)))) (SIGNATURE |sqrt| ($ $ (|PositiveInteger|))) (SIGNATURE |sqrt| ($ $)) (SIGNATURE |sqrt| ($ (|Fraction| (|Integer|)))) (SIGNATURE |sqrt| ($ (|Integer|))) (SIGNATURE |rename!| ($ $ (|OutputForm|))) (SIGNATURE |rename| ($ $ (|OutputForm|))) (SIGNATURE |approximate| ((|Fraction| (|Integer|)) $ $)))) @@ -3121,7 +3121,7 @@ NIL ((|solve| ((#1=(|List| #2=(|Float|)) #3=(|Polynomial| #4=(|Integer|)) #2#) 28 T ELT) ((#1# (|Polynomial| (|Fraction| #4#)) #2#) 27 T ELT)) (|realSolve| (((|List| #1#) (|List| #3#) (|List| (|Symbol|)) #2#) 37 T ELT))) (((|RealSolvePackage|) (CATEGORY |package| (SIGNATURE |solve| (#1=(|List| #2=(|Float|)) (|Polynomial| (|Fraction| #3=(|Integer|))) #2#)) (SIGNATURE |solve| (#1# #4=(|Polynomial| #3#) #2#)) (SIGNATURE |realSolve| ((|List| #1#) (|List| #4#) (|List| (|Symbol|)) #2#)))) (T |RealSolvePackage|)) ((|realSolve| (*1 *2 *3 *4 *5) (AND (|isDomain| *3 (|List| #1=(|Polynomial| #2=(|Integer|)))) (|isDomain| *4 (|List| (|Symbol|))) (|isDomain| *2 (|List| #3=(|List| #4=(|Float|)))) #5=(|isDomain| *1 (|RealSolvePackage|)) (|isDomain| *5 #4#))) (|solve| #6=(*1 *2 *3 *4) (AND (|isDomain| *3 #1#) #7=(|isDomain| *2 #3#) #5# #8=(|isDomain| *4 #4#))) (|solve| #6# (AND (|isDomain| *3 (|Polynomial| (|Fraction| #2#))) #7# #5# #8#))) -((~= #1=(#2=(#3=(|Boolean|) $ $) NIL T ELT)) (|zero?| (#4=(#3# $) 75 T ELT)) (|unitNormal| (((|Record| (|:| |unit| $) (|:| |canonical| $) (|:| |associate| $)) $) NIL T ELT)) (|unitCanonical| #5=(#6=($ $) NIL T ELT)) (|unit?| #7=(#4# NIL T ELT)) (|subtractIfCan| #8=((#9=(|Union| $ #10="failed") $ $) NIL T ELT)) (|squareFreePart| #5#) (|squareFree| #11=(((|Factored| $) $) NIL T ELT)) (|sqrt| #5# #12=(($ $ #13=(|PositiveInteger|)) NIL T ELT) #14=(($ #15=(|Fraction| #16=(|Integer|))) NIL T ELT) #17=(($ #16#) NIL T ELT)) (|sizeLess?| #1#) (|sign| (#18=(#16# $) 70 T ELT)) (|sample| (#19=($) NIL T CONST)) (|rootOf| ((#9# #20=(|SparseUnivariatePolynomial| $) #13# #21=(|OutputForm|)) NIL T ELT) ((#9# #20# #13#) 55 T ELT)) (|retractIfCan| (#22=((|Union| #15# . #23=(#10#)) . #24=($)) NIL #25=(|has| #15# (|RetractableTo| #15#)) ELT) (#22# NIL T ELT) (((|Union| |#1| . #23#) $) 115 T ELT) (((|Union| #16# . #23#) . #24#) NIL #26=(OR (|has| #15# #27=(|RetractableTo| #16#)) (|has| |#1| #27#)) ELT)) (|retract| (#28=(#15# $) 17 #25# ELT) (#28# 17 T ELT) ((|#1| $) 116 T ELT) (#18# NIL #26# ELT)) (|rename!| (#29=($ $ #21#) 47 T ELT)) (|rename| (#29# 48 T ELT)) (|rem| #30=(#31=($ $ $) NIL T ELT)) (|relativeApprox| (#32=(#15# $ $) 21 T ELT)) (|recip| ((#9# $) 88 T ELT)) (|quo| #30#) (|principalIdeal| (((|Record| (|:| |coef| #33=(|List| $)) #34=(|:| |generator| $)) #33#) NIL T ELT)) (|prime?| #7#) (|positive?| (#4# 66 T ELT)) (|opposite?| #1#) (|one?| #7#) (|nthRoot| #35=(($ $ #16#) NIL T ELT)) (|negative?| (#4# 69 T ELT)) (|multiEuclidean| (((|Union| #33# #10#) #33# $) NIL T ELT)) (|min| #30#) (|max| #30#) (|mainValue| (#36=((|Union| #20# #10#) $) 83 T ELT)) (|mainForm| (((|Union| #21# #10#) $) 82 T ELT)) (|mainDefiningPolynomial| (#36# 80 T ELT)) (|mainCharacterization| (((|Union| #37=(|RightOpenIntervalRootCharacterization| $ #20#) #10#) $) 78 T ELT)) (|lcm| #38=(($ #33#) NIL T ELT) #30#) (|latex| (((|String|) $) NIL T ELT)) (|inv| (#6# 89 T ELT)) (|hash| (((|SingleInteger|) $) NIL T ELT)) (|gcdPolynomial| ((#20# #20# #20#) NIL T ELT)) (|gcd| #38# #30#) (|factor| #11#) (|extendedEuclidean| (((|Union| (|Record| #39=(|:| |coef1| $) #40=(|:| |coef2| $)) #10#) $ $ $) NIL T ELT) (((|Record| #39# #40# #34#) $ $) NIL T ELT)) (|exquo| #8#) (|expressIdealMember| (((|Maybe| #33#) #33# $) NIL T ELT)) (|euclideanSize| ((#41=(|NonNegativeInteger|) $) NIL T ELT)) (|divide| (((|Record| (|:| |quotient| $) (|:| |remainder| $)) $ $) NIL T ELT)) (|coerce| ((#21# $) 87 T ELT) #17# #14# (#6# 63 T ELT) #14# #17# #14# (($ |#1|) 118 T ELT)) (|characteristic| ((#41#) NIL T CONST)) (|before?| #1#) (|associates?| #1#) (|approximate| (#32# 27 T ELT)) (|annihilate?| #1#) (|allRootsOf| ((#33# #20#) 61 T ELT) ((#33# (|SparseUnivariatePolynomial| #15#)) NIL T ELT) ((#33# (|SparseUnivariatePolynomial| #16#)) NIL T ELT) ((#33# (|Polynomial| $)) NIL T ELT) ((#33# (|Polynomial| #15#)) NIL T ELT) ((#33# (|Polynomial| #16#)) NIL T ELT)) (|algebraicOf| (($ #37# #21#) 46 T ELT)) (|abs| (#6# 22 T ELT)) (|Zero| (#19# 32 T CONST)) (|One| (#19# 39 T CONST)) (>= #1#) (> #1#) (= (#2# 76 T ELT)) (<= #1#) (< (#2# 24 T ELT)) (/ (#31# 37 T ELT)) (- (#6# 38 T ELT) (#31# 74 T ELT)) (+ (#31# 111 T ELT)) (** #12# (($ $ #41#) NIL T ELT) #35# #42=(($ $ #15#) NIL T ELT)) (* (($ #13# $) NIL T ELT) (($ #41# $) NIL T ELT) #43=(($ #16# $) 71 T ELT) (#31# 103 T ELT) #44=(($ #15# $) NIL T ELT) #42# #43# #35# #44# #42# (($ |#1| $) 101 T ELT) (($ $ |#1|) NIL T ELT))) +((~= #1=(#2=(#3=(|Boolean|) $ $) NIL T ELT)) (|zero?| (#4=(#3# $) 75 T ELT)) (|unitNormal| (((|Record| (|:| |unit| $) (|:| |canonical| $) (|:| |associate| $)) $) NIL T ELT)) (|unitCanonical| #5=(#6=($ $) NIL T ELT)) (|unit?| #7=(#4# NIL T ELT)) (|subtractIfCan| (((|Maybe| $) $ $) NIL T ELT)) (|squareFreePart| #5#) (|squareFree| #8=(((|Factored| $) $) NIL T ELT)) (|sqrt| #5# #9=(($ $ #10=(|PositiveInteger|)) NIL T ELT) #11=(($ #12=(|Fraction| #13=(|Integer|))) NIL T ELT) #14=(($ #13#) NIL T ELT)) (|sizeLess?| #1#) (|sign| (#15=(#13# $) 70 T ELT)) (|sample| (#16=($) NIL T CONST)) (|rootOf| ((#17=(|Union| $ #18="failed") #19=(|SparseUnivariatePolynomial| $) #10# #20=(|OutputForm|)) NIL T ELT) ((#17# #19# #10#) 55 T ELT)) (|retractIfCan| (#21=((|Union| #12# . #22=(#18#)) . #23=($)) NIL #24=(|has| #12# (|RetractableTo| #12#)) ELT) (#21# NIL T ELT) (((|Union| |#1| . #22#) $) 115 T ELT) (((|Union| #13# . #22#) . #23#) NIL #25=(OR (|has| #12# #26=(|RetractableTo| #13#)) (|has| |#1| #26#)) ELT)) (|retract| (#27=(#12# $) 17 #24# ELT) (#27# 17 T ELT) ((|#1| $) 116 T ELT) (#15# NIL #25# ELT)) (|rename!| (#28=($ $ #20#) 47 T ELT)) (|rename| (#28# 48 T ELT)) (|rem| #29=(#30=($ $ $) NIL T ELT)) (|relativeApprox| (#31=(#12# $ $) 21 T ELT)) (|recip| ((#17# $) 88 T ELT)) (|quo| #29#) (|principalIdeal| (((|Record| (|:| |coef| #32=(|List| $)) #33=(|:| |generator| $)) #32#) NIL T ELT)) (|prime?| #7#) (|positive?| (#4# 66 T ELT)) (|opposite?| #1#) (|one?| #7#) (|nthRoot| #34=(($ $ #13#) NIL T ELT)) (|negative?| (#4# 69 T ELT)) (|multiEuclidean| (((|Union| #32# #18#) #32# $) NIL T ELT)) (|min| #29#) (|max| #29#) (|mainValue| (#35=((|Union| #19# #18#) $) 83 T ELT)) (|mainForm| (((|Union| #20# #18#) $) 82 T ELT)) (|mainDefiningPolynomial| (#35# 80 T ELT)) (|mainCharacterization| (((|Union| #36=(|RightOpenIntervalRootCharacterization| $ #19#) #18#) $) 78 T ELT)) (|lcm| #37=(($ #32#) NIL T ELT) #29#) (|latex| (((|String|) $) NIL T ELT)) (|inv| (#6# 89 T ELT)) (|hash| (((|SingleInteger|) $) NIL T ELT)) (|gcdPolynomial| ((#19# #19# #19#) NIL T ELT)) (|gcd| #37# #29#) (|factor| #8#) (|extendedEuclidean| (((|Union| (|Record| #38=(|:| |coef1| $) #39=(|:| |coef2| $)) #18#) $ $ $) NIL T ELT) (((|Record| #38# #39# #33#) $ $) NIL T ELT)) (|exquo| ((#17# $ $) NIL T ELT)) (|expressIdealMember| (((|Maybe| #32#) #32# $) NIL T ELT)) (|euclideanSize| ((#40=(|NonNegativeInteger|) $) NIL T ELT)) (|divide| (((|Record| (|:| |quotient| $) (|:| |remainder| $)) $ $) NIL T ELT)) (|coerce| ((#20# $) 87 T ELT) #14# #11# (#6# 63 T ELT) #11# #14# #11# (($ |#1|) 118 T ELT)) (|characteristic| ((#40#) NIL T CONST)) (|before?| #1#) (|associates?| #1#) (|approximate| (#31# 27 T ELT)) (|annihilate?| #1#) (|allRootsOf| ((#32# #19#) 61 T ELT) ((#32# (|SparseUnivariatePolynomial| #12#)) NIL T ELT) ((#32# (|SparseUnivariatePolynomial| #13#)) NIL T ELT) ((#32# (|Polynomial| $)) NIL T ELT) ((#32# (|Polynomial| #12#)) NIL T ELT) ((#32# (|Polynomial| #13#)) NIL T ELT)) (|algebraicOf| (($ #36# #20#) 46 T ELT)) (|abs| (#6# 22 T ELT)) (|Zero| (#16# 32 T CONST)) (|One| (#16# 39 T CONST)) (>= #1#) (> #1#) (= (#2# 76 T ELT)) (<= #1#) (< (#2# 24 T ELT)) (/ (#30# 37 T ELT)) (- (#6# 38 T ELT) (#30# 74 T ELT)) (+ (#30# 111 T ELT)) (** #9# (($ $ #40#) NIL T ELT) #34# #41=(($ $ #12#) NIL T ELT)) (* (($ #10# $) NIL T ELT) (($ #40# $) NIL T ELT) #42=(($ #13# $) 71 T ELT) (#30# 103 T ELT) #43=(($ #12# $) NIL T ELT) #41# #42# #34# #43# #41# (($ |#1| $) 101 T ELT) (($ $ |#1|) NIL T ELT))) (((|RealClosure| |#1|) (|Join| (|RealClosedField|) (|FullyRetractableTo| |#1|) (|Algebra| |#1|) (CATEGORY |domain| (SIGNATURE |algebraicOf| ($ #1=(|RightOpenIntervalRootCharacterization| $ (|SparseUnivariatePolynomial| $)) (|OutputForm|))) (SIGNATURE |mainCharacterization| ((|Union| #1# "failed") $)) (SIGNATURE |relativeApprox| ((|Fraction| (|Integer|)) $ $)))) (|Join| (|OrderedRing|) (|Field|) (|RealConstant|))) (T |RealClosure|)) ((|algebraicOf| (*1 *1 *2 *3) (AND (|isDomain| *2 (|RightOpenIntervalRootCharacterization| #1=(|RealClosure| *4) (|SparseUnivariatePolynomial| #1#))) (|isDomain| *3 (|OutputForm|)) (|isDomain| *1 #1#) (|ofCategory| *4 #2=(|Join| (|OrderedRing|) (|Field|) (|RealConstant|))))) (|mainCharacterization| (*1 *2 *1) (|partial| AND (|isDomain| *2 (|RightOpenIntervalRootCharacterization| #3=(|RealClosure| *3) (|SparseUnivariatePolynomial| #3#))) #4=(|isDomain| *1 #3#) #5=(|ofCategory| *3 #2#))) (|relativeApprox| (*1 *2 *1 *1) (AND (|isDomain| *2 (|Fraction| (|Integer|))) #4# #5#))) ((|ReduceOrder| (((|Record| (|:| |eq| |#2|) (|:| |op| #1=(|List| |#1|))) |#2| #1#) 32 T ELT) ((|#2| |#2| |#1|) 27 T ELT))) @@ -3139,7 +3139,7 @@ NIL ((|tensorProduct| ((#1=(|List| #2=(|Matrix| |#1|)) #1#) 69 T ELT) ((#2# #2#) 68 T ELT) ((#1# #1# #1#) 67 T ELT) ((#2# #2# #2#) 64 T ELT)) (|symmetricTensors| (#3=(#1# #1# #4=(|PositiveInteger|)) 62 T ELT) (#5=(#2# #2# #4#) 61 T ELT)) (|permutationRepresentation| ((#6=(|List| #7=(|Matrix| #8=(|Integer|))) (|List| #9=(|List| #8#))) 80 T ELT) ((#6# (|List| #10=(|Permutation| #8#)) #8#) 79 T ELT) ((#7# #9#) 76 T ELT) ((#7# #10# #8#) 74 T ELT)) (|createGenericMatrix| (((|Matrix| (|Polynomial| |#1|)) (|NonNegativeInteger|)) 94 T ELT)) (|antisymmetricTensors| (#3# 48 #11=(|has| |#1| (ATTRIBUTE (|commutative| "*"))) ELT) (#5# 46 #11# ELT))) (((|RepresentationPackage1| |#1|) (CATEGORY |package| (IF #1=(|has| |#1| (ATTRIBUTE (|commutative| "*"))) (SIGNATURE |antisymmetricTensors| #2=(#3=(|Matrix| |#1|) #3# #4=(|PositiveInteger|))) |%noBranch|) (IF #1# (SIGNATURE |antisymmetricTensors| #5=(#6=(|List| #3#) #6# #4#)) |%noBranch|) (SIGNATURE |createGenericMatrix| ((|Matrix| (|Polynomial| |#1|)) (|NonNegativeInteger|))) (SIGNATURE |symmetricTensors| #2#) (SIGNATURE |symmetricTensors| #5#) (SIGNATURE |tensorProduct| (#3# #3# #3#)) (SIGNATURE |tensorProduct| (#6# #6# #6#)) (SIGNATURE |tensorProduct| (#3# #3#)) (SIGNATURE |tensorProduct| (#6# #6#)) (SIGNATURE |permutationRepresentation| (#7=(|Matrix| #8=(|Integer|)) #9=(|Permutation| #8#) #8#)) (SIGNATURE |permutationRepresentation| (#7# #10=(|List| #8#))) (SIGNATURE |permutationRepresentation| (#11=(|List| #7#) (|List| #9#) #8#)) (SIGNATURE |permutationRepresentation| (#11# (|List| #10#)))) (|Ring|)) (T |RepresentationPackage1|)) ((|permutationRepresentation| #1=(*1 *2 *3) (AND (|isDomain| *3 (|List| #2=(|List| #3=(|Integer|)))) (|isDomain| *2 (|List| #4=(|Matrix| #3#))) #5=(|isDomain| *1 (|RepresentationPackage1| *4)) #6=(|ofCategory| *4 #7=(|Ring|)))) (|permutationRepresentation| #8=(*1 *2 *3 *4) (AND (|isDomain| *3 (|List| #9=(|Permutation| #3#))) #10=(|isDomain| *4 #3#) #11=(|isDomain| *2 (|List| #12=(|Matrix| *4))) #13=(|isDomain| *1 (|RepresentationPackage1| *5)) #14=(|ofCategory| *5 #7#))) (|permutationRepresentation| #1# (AND (|isDomain| *3 #2#) (|isDomain| *2 #4#) #5# #6#)) (|permutationRepresentation| #8# (AND (|isDomain| *3 #9#) #10# #15=(|isDomain| *2 #12#) #13# #14#)) (|tensorProduct| #16=(*1 *2 *2) #17=(AND (|isDomain| *2 (|List| #18=(|Matrix| *3))) #19=(|ofCategory| *3 #7#) #20=(|isDomain| *1 (|RepresentationPackage1| *3)))) (|tensorProduct| #16# #21=(AND (|isDomain| *2 #18#) #19# #20#)) (|tensorProduct| #22=(*1 *2 *2 *2) #17#) (|tensorProduct| #22# #21#) (|symmetricTensors| #23=(*1 *2 *2 *3) (AND #11# #24=(|isDomain| *3 (|PositiveInteger|)) #6# #5#)) (|symmetricTensors| #23# (AND #15# #24# #6# #5#)) (|createGenericMatrix| #1# (AND (|isDomain| *3 (|NonNegativeInteger|)) (|isDomain| *2 (|Matrix| (|Polynomial| *4))) #5# #6#)) (|antisymmetricTensors| #23# (AND #11# #24# #25=(|has| *4 (ATTRIBUTE (|commutative| "*"))) #6# #5#)) (|antisymmetricTensors| #23# (AND #15# #24# #25# #6# #5#))) -((|standardBasisOfCyclicSubmodule| ((#1=(|Matrix| |#1|) #2=(|List| #1#) #3=(|Vector| |#1|)) 69 #4=(|has| |#1| (|EuclideanDomain|)) ELT)) (|split| ((#5=(|List| #2#) #2# #6=(|Vector| #3#)) 107 #7=(|has| |#1| (|Field|)) ELT) ((#5# #2# #3#) 104 #7# ELT)) (|scanOneDimSubspaces| ((#3# (|List| #3#) #8=(|Integer|)) 113 #9=(AND #7# (|has| |#1| (|Finite|))) ELT)) (|meatAxe| ((#5# #2# (|PositiveInteger|)) 119 #9# ELT) ((#5# #2# #10=(|Boolean|)) 118 #9# ELT) ((#5# #2#) 117 #9# ELT) ((#5# #2# #10# #8# #8#) 116 #9# ELT)) (|isAbsolutelyIrreducible?| ((#10# #2#) 101 #7# ELT) ((#10# #2# #8#) 100 #7# ELT)) (|cyclicSubmodule| ((#6# #2# #3#) 66 #4# ELT)) (|createRandomElement| ((#1# #2# #1#) 46 T ELT)) (|completeEchelonBasis| ((#1# #6#) 39 T ELT)) (|areEquivalent?| ((#1# #2# #2# #8#) 93 #7# ELT) ((#1# #2# #2#) 92 #7# ELT) ((#1# #2# #2# #10# #8#) 91 #7# ELT))) +((|standardBasisOfCyclicSubmodule| ((#1=(|Matrix| |#1|) #2=(|List| #1#) #3=(|Vector| |#1|)) 68 #4=(|has| |#1| (|EuclideanDomain|)) ELT)) (|split| ((#5=(|List| #2#) #2# #6=(|Vector| #3#)) 106 #7=(|has| |#1| (|Field|)) ELT) ((#5# #2# #3#) 103 #7# ELT)) (|scanOneDimSubspaces| ((#3# (|List| #3#) #8=(|Integer|)) 112 #9=(AND #7# (|has| |#1| (|Finite|))) ELT)) (|meatAxe| ((#5# #2# (|PositiveInteger|)) 118 #9# ELT) ((#5# #2# #10=(|Boolean|)) 117 #9# ELT) ((#5# #2#) 116 #9# ELT) ((#5# #2# #10# #8# #8#) 115 #9# ELT)) (|isAbsolutelyIrreducible?| ((#10# #2#) 100 #7# ELT) ((#10# #2# #8#) 99 #7# ELT)) (|cyclicSubmodule| ((#6# #2# #3#) 65 #4# ELT)) (|createRandomElement| ((#1# #2# #1#) 45 T ELT)) (|completeEchelonBasis| ((#1# #6#) 39 T ELT)) (|areEquivalent?| ((#1# #2# #2# #8#) 92 #7# ELT) ((#1# #2# #2#) 91 #7# ELT) ((#1# #2# #2# #10# #8#) 90 #7# ELT))) (((|RepresentationPackage2| |#1|) (CATEGORY |package| (SIGNATURE |completeEchelonBasis| (#1=(|Matrix| |#1|) #2=(|Vector| #3=(|Vector| |#1|)))) (SIGNATURE |createRandomElement| (#1# #4=(|List| #1#) #1#)) (IF (|has| |#1| (|EuclideanDomain|)) (PROGN (SIGNATURE |cyclicSubmodule| (#2# #4# #3#)) (SIGNATURE |standardBasisOfCyclicSubmodule| (#1# #4# #3#))) |%noBranch|) (IF #5=(|has| |#1| (|Field|)) (PROGN (SIGNATURE |areEquivalent?| (#1# #4# #4# #6=(|Boolean|) #7=(|Integer|))) (SIGNATURE |areEquivalent?| (#1# #4# #4#)) (SIGNATURE |areEquivalent?| (#1# #4# #4# #7#)) (SIGNATURE |isAbsolutelyIrreducible?| (#6# #4# #7#)) (SIGNATURE |isAbsolutelyIrreducible?| (#6# #4#)) (SIGNATURE |split| (#8=(|List| #4#) #4# #3#)) (SIGNATURE |split| (#8# #4# #2#))) |%noBranch|) (IF (|has| |#1| (|Finite|)) (IF #5# (PROGN (SIGNATURE |meatAxe| (#8# #4# #6# #7# #7#)) (SIGNATURE |meatAxe| (#8# #4#)) (SIGNATURE |meatAxe| (#8# #4# #6#)) (SIGNATURE |meatAxe| (#8# #4# (|PositiveInteger|))) (SIGNATURE |scanOneDimSubspaces| (#3# (|List| #3#) #7#))) |%noBranch|) |%noBranch|)) (|Ring|)) (T |RepresentationPackage2|)) ((|scanOneDimSubspaces| #1=(*1 *2 *3 *4) (AND (|isDomain| *3 (|List| #2=(|Vector| *5))) #3=(|isDomain| *4 #4=(|Integer|)) (|isDomain| *2 #2#) #5=(|isDomain| *1 (|RepresentationPackage2| *5)) #6=(|ofCategory| *5 #7=(|Field|)) #8=(|ofCategory| *5 #9=(|Finite|)) #10=(|ofCategory| *5 #11=(|Ring|)))) (|meatAxe| #1# (AND (|isDomain| *4 (|PositiveInteger|)) #6# #8# #10# #12=(|isDomain| *2 (|List| #13=(|List| #14=(|Matrix| *5)))) #5# #15=(|isDomain| *3 #13#))) (|meatAxe| #1# (AND #16=(|isDomain| *4 #17=(|Boolean|)) #6# #8# #10# #12# #5# #15#)) (|meatAxe| #18=(*1 *2 *3) (AND #19=(|ofCategory| *4 #7#) (|ofCategory| *4 #9#) #20=(|ofCategory| *4 #11#) (|isDomain| *2 (|List| #21=(|List| #22=(|Matrix| *4)))) #23=(|isDomain| *1 (|RepresentationPackage2| *4)) #24=(|isDomain| *3 #21#))) (|meatAxe| (*1 *2 *3 *4 *5 *5) (AND #16# #25=(|isDomain| *5 #4#) #26=(|ofCategory| *6 #7#) (|ofCategory| *6 #9#) #27=(|ofCategory| *6 #11#) (|isDomain| *2 (|List| #28=(|List| #29=(|Matrix| *6)))) #30=(|isDomain| *1 (|RepresentationPackage2| *6)) #31=(|isDomain| *3 #28#))) (|split| #1# (AND (|isDomain| *4 #32=(|Vector| #2#)) #6# #10# #12# #5# #15#)) (|split| #1# (AND #33=(|isDomain| *4 #2#) #6# #10# #12# #5# #15#)) (|isAbsolutelyIrreducible?| #18# (AND #24# #19# #20# #34=(|isDomain| *2 #17#) #23#)) (|isAbsolutelyIrreducible?| #1# (AND #15# #3# #6# #10# #34# #5#)) (|areEquivalent?| (*1 *2 *3 *3 *4) (AND #15# #3# #35=(|isDomain| *2 #14#) #5# #6# #10#)) (|areEquivalent?| (*1 *2 *3 *3) (AND #24# #36=(|isDomain| *2 #22#) #23# #19# #20#)) (|areEquivalent?| (*1 *2 *3 *3 *4 *5) (AND #31# #16# #25# (|isDomain| *2 #29#) #30# #26# #27#)) (|standardBasisOfCyclicSubmodule| #1# (AND #15# #33# #37=(|ofCategory| *5 (|EuclideanDomain|)) #10# #35# #5#)) (|cyclicSubmodule| #1# (AND #15# #37# #10# (|isDomain| *2 #32#) #5# #33#)) (|createRandomElement| (*1 *2 *3 *2) (AND #24# #36# #20# #23#)) (|completeEchelonBasis| #18# (AND (|isDomain| *3 (|Vector| (|Vector| *4))) #20# #36# #23#))) ((|double| ((|#1| (|PositiveInteger|) |#1|) 18 T ELT))) @@ -3151,7 +3151,7 @@ NIL ((|coerce| ((|#1| (|Exit|)) 11 T ELT) (((|Void|) |#1|) 9 T ELT))) (((|ResolveLatticeCompletion| |#1|) (CATEGORY |package| (SIGNATURE |coerce| ((|Void|) |#1|)) (SIGNATURE |coerce| (|#1| (|Exit|)))) (|Type|)) (T |ResolveLatticeCompletion|)) ((|coerce| #1=(*1 *2 *3) (AND (|isDomain| *3 (|Exit|)) (|isDomain| *1 (|ResolveLatticeCompletion| *2)) (|ofCategory| *2 #2=(|Type|)))) (|coerce| #1# (AND (|isDomain| *2 (|Void|)) (|isDomain| *1 (|ResolveLatticeCompletion| *3)) (|ofCategory| *3 #2#)))) -((~= #1=(#2=(#3=(|Boolean|) $ $) NIL T ELT)) (|zero?| #4=((#3# $) NIL T ELT)) (|subtractIfCan| ((#5=(|Union| $ "failed") $ $) NIL T ELT)) (|sample| (#6=($) NIL T CONST)) (|reduce| (#7=($ |#4|) 24 T ELT)) (|recip| ((#5# $) NIL T ELT)) (|opposite?| #1#) (|one?| #4#) (|lift| ((|#4| $) 26 T ELT)) (|latex| (((|String|) $) NIL T ELT)) (|hash| (((|SingleInteger|) $) NIL T ELT)) (|coerce| (((|OutputForm|) $) 45 T ELT) (($ #8=(|Integer|)) NIL T ELT) (($ |#1|) NIL T ELT) (#7# 25 T ELT)) (|characteristic| ((#9=(|NonNegativeInteger|)) 42 T CONST)) (|before?| #1#) (|annihilate?| #1#) (|Zero| (#6# 21 T CONST)) (|One| (#6# 22 T CONST)) (= (#2# 39 T ELT)) (- (($ $) 30 T ELT) (#10=($ $ $) NIL T ELT)) (+ (#10# 28 T ELT)) (** (($ $ #11=(|PositiveInteger|)) NIL T ELT) (($ $ #9#) NIL T ELT)) (* (($ #11# $) NIL T ELT) (($ #9# $) NIL T ELT) (($ #8# $) 35 T ELT) (#10# 32 T ELT) (($ |#1| $) 37 T ELT) (($ $ |#1|) NIL T ELT))) +((~= #1=(#2=(#3=(|Boolean|) $ $) NIL T ELT)) (|zero?| #4=((#3# $) NIL T ELT)) (|subtractIfCan| (((|Maybe| $) $ $) NIL T ELT)) (|sample| (#5=($) NIL T CONST)) (|reduce| (#6=($ |#4|) 24 T ELT)) (|recip| (((|Union| $ "failed") $) NIL T ELT)) (|opposite?| #1#) (|one?| #4#) (|lift| ((|#4| $) 26 T ELT)) (|latex| (((|String|) $) NIL T ELT)) (|hash| (((|SingleInteger|) $) NIL T ELT)) (|coerce| (((|OutputForm|) $) 45 T ELT) (($ #7=(|Integer|)) NIL T ELT) (($ |#1|) NIL T ELT) (#6# 25 T ELT)) (|characteristic| ((#8=(|NonNegativeInteger|)) 42 T CONST)) (|before?| #1#) (|annihilate?| #1#) (|Zero| (#5# 21 T CONST)) (|One| (#5# 22 T CONST)) (= (#2# 39 T ELT)) (- (($ $) 30 T ELT) (#9=($ $ $) NIL T ELT)) (+ (#9# 28 T ELT)) (** (($ $ #10=(|PositiveInteger|)) NIL T ELT) (($ $ #8#) NIL T ELT)) (* (($ #10# $) NIL T ELT) (($ #8# $) NIL T ELT) (($ #7# $) 35 T ELT) (#9# 32 T ELT) (($ |#1| $) 37 T ELT) (($ $ |#1|) NIL T ELT))) (((|ResidueRing| |#1| |#2| |#3| |#4| |#5|) (|Join| (|CommutativeRing|) (|Algebra| |#1|) (CATEGORY |domain| (SIGNATURE |reduce| #1=($ |#4|)) (SIGNATURE |coerce| #1#) (SIGNATURE |lift| (|#4| $)))) (|Field|) (|OrderedAbelianMonoidSup|) (|OrderedSet|) (|PolynomialCategory| |#1| |#2| |#3|) (|List| |#4|)) (T |ResidueRing|)) ((|reduce| #1=(*1 *1 *2) #2=(AND #3=(|ofCategory| *3 (|Field|)) #4=(|ofCategory| *4 (|OrderedAbelianMonoidSup|)) #5=(|ofCategory| *5 (|OrderedSet|)) #6=(|isDomain| *1 (|ResidueRing| *3 *4 *5 *2 *6)) #7=(|ofCategory| *2 (|PolynomialCategory| *3 *4 *5)) #8=(|ofType| *6 (|List| *2)))) (|coerce| #1# #2#) (|lift| (*1 *2 *1) (AND #7# #6# #3# #4# #5# #8#))) ((~= #1=(((|Boolean|) $ $) NIL T ELT)) (|latex| (((|String|) $) NIL T ELT)) (|hash| (((|SingleInteger|) $) NIL T ELT)) (|expression| (((|SpadAst|) $) 11 T ELT)) (|coerce| (((|OutputForm|) $) 17 T ELT) (($ #2=(|Syntax|)) NIL T ELT) ((#2# $) NIL T ELT)) (|before?| #1#) (= #1#)) @@ -3199,10 +3199,10 @@ NIL ((|coerce| (((|OutputForm|) $) NIL T ELT) (($ (|Integer|)) 10 T ELT))) (((|Ring&| |#1|) (CATEGORY |package| (SIGNATURE |coerce| (|#1| (|Integer|))) (SIGNATURE |coerce| ((|OutputForm|) |#1|))) (|Ring|)) (T |Ring&|)) NIL -((~= (#1=((|Boolean|) $ $) 7 T ELT)) (|zero?| ((#2=(|Boolean|) $) 22 T ELT)) (|subtractIfCan| (((|Union| $ "failed") $ $) 26 T ELT)) (|sample| (#3=($) 23 T CONST)) (|recip| (((|Union| $ "failed") $) 42 T ELT)) (|opposite?| ((#2# $ $) 20 T ELT)) (|one?| (((|Boolean|) $) 44 T ELT)) (|latex| (((|String|) $) 11 T ELT)) (|hash| (((|SingleInteger|) $) 12 T ELT)) (|coerce| (((|OutputForm|) $) 13 T ELT) (($ (|Integer|)) 41 T ELT)) (|characteristic| (((|NonNegativeInteger|)) 40 T CONST)) (|before?| (#1# 6 T ELT)) (|annihilate?| (((|Boolean|) $ $) 33 T ELT)) (|Zero| (#3# 24 T CONST)) (|One| (($) 45 T CONST)) (= (#1# 8 T ELT)) (- (($ $) 29 T ELT) (($ $ $) 28 T ELT)) (+ (($ $ $) 18 T ELT)) (** (($ $ (|PositiveInteger|)) 35 T ELT) (($ $ (|NonNegativeInteger|)) 43 T ELT)) (* (($ (|PositiveInteger|) $) 17 T ELT) (($ (|NonNegativeInteger|) $) 21 T ELT) (($ (|Integer|) $) 30 T ELT) (($ $ $) 34 T ELT))) +((~= (#1=((|Boolean|) $ $) 7 T ELT)) (|zero?| ((#2=(|Boolean|) $) 22 T ELT)) (|subtractIfCan| (((|Maybe| $) $ $) 26 T ELT)) (|sample| (#3=($) 23 T CONST)) (|recip| (((|Union| $ "failed") $) 43 T ELT)) (|opposite?| ((#2# $ $) 20 T ELT)) (|one?| (((|Boolean|) $) 45 T ELT)) (|latex| (((|String|) $) 11 T ELT)) (|hash| (((|SingleInteger|) $) 12 T ELT)) (|coerce| (((|OutputForm|) $) 13 T ELT) (($ (|Integer|)) 42 T ELT)) (|characteristic| (((|NonNegativeInteger|)) 41 T CONST)) (|before?| (#1# 6 T ELT)) (|annihilate?| (((|Boolean|) $ $) 34 T ELT)) (|Zero| (#3# 24 T CONST)) (|One| (($) 46 T CONST)) (= (#1# 8 T ELT)) (- (($ $) 30 T ELT) (($ $ $) 29 T ELT)) (+ (($ $ $) 18 T ELT)) (** (($ $ (|PositiveInteger|)) 36 T ELT) (($ $ (|NonNegativeInteger|)) 44 T ELT)) (* (($ (|PositiveInteger|) $) 17 T ELT) (($ (|NonNegativeInteger|) $) 21 T ELT) (($ (|Integer|) $) 31 T ELT) (($ $ $) 35 T ELT))) (((|Ring|) (|Category|)) (T |Ring|)) ((|characteristic| (*1 *2) (AND (|ofCategory| *1 (|Ring|)) (|isDomain| *2 (|NonNegativeInteger|))))) -(|Join| (|Rng|) (|SemiRing|) (|LeftModule| $) (|CoercibleFrom| (|Integer|)) (CATEGORY |package| (SIGNATURE |characteristic| ((|NonNegativeInteger|)) |constant|) (ATTRIBUTE |unitsKnown|))) +(|Join| (|Rng|) (|SemiRing|) (|LeftModule| $) (|CoercibleFrom| (|Integer|)) (CATEGORY |package| (SIGNATURE |characteristic| ((|NonNegativeInteger|)) |constant|))) (((|AbelianGroup|) . T) ((|AbelianMonoid|) . T) ((|AbelianSemiGroup|) . T) ((|BasicType|) . T) ((|CancellationAbelianMonoid|) . T) ((|CoercibleFrom| (|Integer|)) . T) ((|CoercibleTo| (|OutputForm|)) . T) ((|Join|) . T) ((|LeftLinearSet| (|Integer|)) . T) ((|LeftLinearSet| $) . T) ((|LeftModule| $) . T) ((|Monoid|) . T) ((|Rng|) . T) ((|SemiGroup|) . T) ((|SemiRing|) . T) ((|SetCategory|) . T) ((|Type|) . T)) ((|interpolate| (((|Fraction| (|Polynomial| |#2|)) #1=(|List| |#2|) #1# #2=(|NonNegativeInteger|) #2#) 55 T ELT))) (((|RationalInterpolation| |#1| |#2|) (CATEGORY |package| (SIGNATURE |interpolate| ((|Fraction| (|Polynomial| |#2|)) #1=(|List| |#2|) #1# #2=(|NonNegativeInteger|) #2#))) (|Symbol|) (|Field|)) (T |RationalInterpolation|)) @@ -3215,18 +3215,18 @@ NIL ((|symmetric?| (#1=((|Boolean|) $) 38 T ELT)) (|square?| (#1# 17 T ELT)) (|nrows| (#2=((|NonNegativeInteger|) $) 13 T ELT)) (|ncols| (#2# 14 T ELT)) (|diagonal?| (#1# 30 T ELT)) (|antisymmetric?| (#1# 40 T ELT))) (((|RectangularMatrixCategory&| |#1| |#2| |#3| |#4| |#5| |#6|) (CATEGORY |package| (SIGNATURE |ncols| #1=(#2=(|NonNegativeInteger|) |#1|)) (SIGNATURE |nrows| #1#) (SIGNATURE |antisymmetric?| #3=((|Boolean|) |#1|)) (SIGNATURE |symmetric?| #3#) (SIGNATURE |diagonal?| #3#) (SIGNATURE |square?| #3#)) (|RectangularMatrixCategory| |#2| |#3| |#4| |#5| |#6|) #2# #2# (|Ring|) (|DirectProductCategory| |#3| |#4|) (|DirectProductCategory| |#2| |#4|)) (T |RectangularMatrixCategory&|)) NIL -((~= (#1=((|Boolean|) $ $) 7 T ELT)) (|zero?| ((#2=(|Boolean|) $) 22 T ELT)) (|symmetric?| (((|Boolean|) $) 63 T ELT)) (|subtractIfCan| (((|Union| $ "failed") $ $) 26 T ELT)) (|square?| (((|Boolean|) $) 65 T ELT)) (|sample| (#3=($) 23 T CONST)) (|rowEchelon| (($ $) 46 (|has| |#3| (|EuclideanDomain|)) ELT)) (|row| ((|#4| $ (|Integer|)) 51 T ELT)) (|reduce| ((|#3| (|Mapping| |#3| |#3| |#3|) $ |#3| |#3|) 86 (|has| |#3| . #4=((|BasicType|))) ELT) ((|#3| (|Mapping| |#3| |#3| |#3|) $ |#3|) 82 T ELT) ((|#3| (|Mapping| |#3| |#3| |#3|) $) 81 T ELT)) (|rank| (((|NonNegativeInteger|) $) 45 (|has| |#3| (|IntegralDomain|)) ELT)) (|qelt| ((|#3| $ (|Integer|) (|Integer|)) 53 T ELT)) (|opposite?| ((#2# $ $) 20 T ELT)) (|nullity| (((|NonNegativeInteger|) $) 44 (|has| |#3| (|IntegralDomain|)) ELT)) (|nullSpace| (((|List| |#5|) $) 43 (|has| |#3| (|IntegralDomain|)) ELT)) (|nrows| (((|NonNegativeInteger|) $) 57 T ELT)) (|ncols| (((|NonNegativeInteger|) $) 56 T ELT)) (|minRowIndex| (((|Integer|) $) 61 T ELT)) (|minColIndex| (((|Integer|) $) 59 T ELT)) (|members| (((|List| |#3|) $) 80 T ELT)) (|member?| ((#5=(|Boolean|) |#3| $) 85 (|has| |#3| . #4#) ELT)) (|maxRowIndex| (((|Integer|) $) 60 T ELT)) (|maxColIndex| (((|Integer|) $) 58 T ELT)) (|matrix| (($ (|List| (|List| |#3|))) 66 T ELT)) (|map| (($ (|Mapping| |#3| |#3|) $) 71 T ELT) (($ (|Mapping| |#3| |#3| |#3|) $ $) 49 T ELT)) (|listOfLists| (((|List| (|List| |#3|)) $) 55 T ELT)) (|latex| (((|String|) $) 11 T ELT)) (|hash| (((|SingleInteger|) $) 12 T ELT)) (|find| (((|Union| |#3| "failed") (|Mapping| #5# |#3|) $) 83 T ELT)) (|exquo| (((|Union| $ "failed") $ |#3|) 48 (|has| |#3| (|IntegralDomain|)) ELT)) (|every?| ((#5# (|Mapping| #5# |#3|) . #6=($)) 78 T ELT)) (|eval| (($ $ (|List| |#3|) (|List| |#3|)) 75 (AND (|has| |#3| (|Evalable| |#3|)) (|has| |#3| . #7=((|SetCategory|)))) ELT) (($ $ |#3| |#3|) 74 (AND (|has| |#3| (|Evalable| |#3|)) (|has| |#3| . #7#)) ELT) (($ $ (|Equation| |#3|)) 73 (AND (|has| |#3| (|Evalable| |#3|)) (|has| |#3| . #7#)) ELT) (($ $ (|List| (|Equation| |#3|))) 72 (AND (|has| |#3| (|Evalable| |#3|)) (|has| |#3| . #7#)) ELT)) (|eq?| ((#8=(|Boolean|) $ $) 67 T ELT)) (|empty?| ((#8# $) 70 T ELT)) (|empty| (($) 69 T ELT)) (|elt| ((|#3| $ (|Integer|) (|Integer|)) 54 T ELT) ((|#3| $ (|Integer|) (|Integer|) |#3|) 52 T ELT)) (|diagonal?| (((|Boolean|) $) 64 T ELT)) (|count| ((#9=(|NonNegativeInteger|) |#3| $) 84 (|has| |#3| . #4#) ELT) ((#9# (|Mapping| #5# |#3|) $) 79 T ELT)) (|copy| (($ $) 68 T ELT)) (|column| ((|#5| $ (|Integer|)) 50 T ELT)) (|coerce| (((|OutputForm|) $) 13 T ELT)) (|before?| (#1# 6 T ELT)) (|any?| ((#5# (|Mapping| #5# |#3|) . #6#) 77 T ELT)) (|antisymmetric?| (((|Boolean|) $) 62 T ELT)) (|Zero| (#3# 24 T CONST)) (= (#1# 8 T ELT)) (/ (($ $ |#3|) 47 (|has| |#3| (|Field|)) ELT)) (- (($ $) 29 T ELT) (($ $ $) 28 T ELT)) (+ (($ $ $) 18 T ELT)) (* (($ (|PositiveInteger|) $) 17 T ELT) (($ (|NonNegativeInteger|) $) 21 T ELT) (($ (|Integer|) . #10=($)) 30 T ELT) (($ |#3| . #10#) 33 T ELT) (($ $ |#3|) 37 T ELT)) (|#| ((#9# $) 76 T ELT))) +((~= (#1=((|Boolean|) $ $) 7 T ELT)) (|zero?| ((#2=(|Boolean|) $) 22 T ELT)) (|symmetric?| (((|Boolean|) $) 64 T ELT)) (|subtractIfCan| (((|Maybe| $) $ $) 26 T ELT)) (|square?| (((|Boolean|) $) 66 T ELT)) (|sample| (#3=($) 23 T CONST)) (|rowEchelon| (($ $) 47 (|has| |#3| (|EuclideanDomain|)) ELT)) (|row| ((|#4| $ (|Integer|)) 52 T ELT)) (|reduce| ((|#3| (|Mapping| |#3| |#3| |#3|) $ |#3| |#3|) 87 (|has| |#3| . #4=((|BasicType|))) ELT) ((|#3| (|Mapping| |#3| |#3| |#3|) $ |#3|) 83 T ELT) ((|#3| (|Mapping| |#3| |#3| |#3|) $) 82 T ELT)) (|rank| (((|NonNegativeInteger|) $) 46 (|has| |#3| (|IntegralDomain|)) ELT)) (|qelt| ((|#3| $ (|Integer|) (|Integer|)) 54 T ELT)) (|opposite?| ((#2# $ $) 20 T ELT)) (|nullity| (((|NonNegativeInteger|) $) 45 (|has| |#3| (|IntegralDomain|)) ELT)) (|nullSpace| (((|List| |#5|) $) 44 (|has| |#3| (|IntegralDomain|)) ELT)) (|nrows| (((|NonNegativeInteger|) $) 58 T ELT)) (|ncols| (((|NonNegativeInteger|) $) 57 T ELT)) (|minRowIndex| (((|Integer|) $) 62 T ELT)) (|minColIndex| (((|Integer|) $) 60 T ELT)) (|members| (((|List| |#3|) $) 81 T ELT)) (|member?| ((#5=(|Boolean|) |#3| $) 86 (|has| |#3| . #4#) ELT)) (|maxRowIndex| (((|Integer|) $) 61 T ELT)) (|maxColIndex| (((|Integer|) $) 59 T ELT)) (|matrix| (($ (|List| (|List| |#3|))) 67 T ELT)) (|map| (($ (|Mapping| |#3| |#3|) $) 72 T ELT) (($ (|Mapping| |#3| |#3| |#3|) $ $) 50 T ELT)) (|listOfLists| (((|List| (|List| |#3|)) $) 56 T ELT)) (|latex| (((|String|) $) 11 T ELT)) (|hash| (((|SingleInteger|) $) 12 T ELT)) (|find| (((|Union| |#3| "failed") (|Mapping| #5# |#3|) $) 84 T ELT)) (|exquo| (((|Union| $ "failed") $ |#3|) 49 (|has| |#3| (|IntegralDomain|)) ELT)) (|every?| ((#5# (|Mapping| #5# |#3|) . #6=($)) 79 T ELT)) (|eval| (($ $ (|List| |#3|) (|List| |#3|)) 76 (AND (|has| |#3| (|Evalable| |#3|)) (|has| |#3| . #7=((|SetCategory|)))) ELT) (($ $ |#3| |#3|) 75 (AND (|has| |#3| (|Evalable| |#3|)) (|has| |#3| . #7#)) ELT) (($ $ (|Equation| |#3|)) 74 (AND (|has| |#3| (|Evalable| |#3|)) (|has| |#3| . #7#)) ELT) (($ $ (|List| (|Equation| |#3|))) 73 (AND (|has| |#3| (|Evalable| |#3|)) (|has| |#3| . #7#)) ELT)) (|eq?| ((#8=(|Boolean|) $ $) 68 T ELT)) (|empty?| ((#8# $) 71 T ELT)) (|empty| (($) 70 T ELT)) (|elt| ((|#3| $ (|Integer|) (|Integer|)) 55 T ELT) ((|#3| $ (|Integer|) (|Integer|) |#3|) 53 T ELT)) (|diagonal?| (((|Boolean|) $) 65 T ELT)) (|count| ((#9=(|NonNegativeInteger|) |#3| $) 85 (|has| |#3| . #4#) ELT) ((#9# (|Mapping| #5# |#3|) $) 80 T ELT)) (|copy| (($ $) 69 T ELT)) (|column| ((|#5| $ (|Integer|)) 51 T ELT)) (|coerce| (((|OutputForm|) $) 13 T ELT)) (|before?| (#1# 6 T ELT)) (|any?| ((#5# (|Mapping| #5# |#3|) . #6#) 78 T ELT)) (|antisymmetric?| (((|Boolean|) $) 63 T ELT)) (|Zero| (#3# 24 T CONST)) (= (#1# 8 T ELT)) (/ (($ $ |#3|) 48 (|has| |#3| (|Field|)) ELT)) (- (($ $) 30 T ELT) (($ $ $) 29 T ELT)) (+ (($ $ $) 18 T ELT)) (* (($ (|PositiveInteger|) $) 17 T ELT) (($ (|NonNegativeInteger|) $) 21 T ELT) (($ (|Integer|) . #10=($)) 31 T ELT) (($ |#3| . #10#) 34 T ELT) (($ $ |#3|) 38 T ELT)) (|#| ((#9# $) 77 T ELT))) (((|RectangularMatrixCategory| |#1| |#2| |#3| |#4| |#5|) (|Category|) #1=(|NonNegativeInteger|) #1# (|Ring|) (|DirectProductCategory| |t#2| |t#3|) (|DirectProductCategory| |t#1| |t#3|)) (T |RectangularMatrixCategory|)) ((|matrix| (*1 *1 *2) (AND (|isDomain| *2 (|List| (|List| *5))) (|ofCategory| *5 (|Ring|)) (|ofCategory| *1 (|RectangularMatrixCategory| *3 *4 *5 *6 *7)) (|ofCategory| *6 (|DirectProductCategory| *4 *5)) (|ofCategory| *7 (|DirectProductCategory| *3 *5)))) (|square?| (*1 *2 *1) (AND (|ofCategory| *1 (|RectangularMatrixCategory| *3 *4 *5 *6 *7)) (|ofCategory| *5 (|Ring|)) (|ofCategory| *6 (|DirectProductCategory| *4 *5)) (|ofCategory| *7 (|DirectProductCategory| *3 *5)) (|isDomain| *2 (|Boolean|)))) (|diagonal?| (*1 *2 *1) (AND (|ofCategory| *1 (|RectangularMatrixCategory| *3 *4 *5 *6 *7)) (|ofCategory| *5 (|Ring|)) (|ofCategory| *6 (|DirectProductCategory| *4 *5)) (|ofCategory| *7 (|DirectProductCategory| *3 *5)) (|isDomain| *2 (|Boolean|)))) (|symmetric?| (*1 *2 *1) (AND (|ofCategory| *1 (|RectangularMatrixCategory| *3 *4 *5 *6 *7)) (|ofCategory| *5 (|Ring|)) (|ofCategory| *6 (|DirectProductCategory| *4 *5)) (|ofCategory| *7 (|DirectProductCategory| *3 *5)) (|isDomain| *2 (|Boolean|)))) (|antisymmetric?| (*1 *2 *1) (AND (|ofCategory| *1 (|RectangularMatrixCategory| *3 *4 *5 *6 *7)) (|ofCategory| *5 (|Ring|)) (|ofCategory| *6 (|DirectProductCategory| *4 *5)) (|ofCategory| *7 (|DirectProductCategory| *3 *5)) (|isDomain| *2 (|Boolean|)))) (|minRowIndex| (*1 *2 *1) (AND (|ofCategory| *1 (|RectangularMatrixCategory| *3 *4 *5 *6 *7)) (|ofCategory| *5 (|Ring|)) (|ofCategory| *6 (|DirectProductCategory| *4 *5)) (|ofCategory| *7 (|DirectProductCategory| *3 *5)) (|isDomain| *2 (|Integer|)))) (|maxRowIndex| (*1 *2 *1) (AND (|ofCategory| *1 (|RectangularMatrixCategory| *3 *4 *5 *6 *7)) (|ofCategory| *5 (|Ring|)) (|ofCategory| *6 (|DirectProductCategory| *4 *5)) (|ofCategory| *7 (|DirectProductCategory| *3 *5)) (|isDomain| *2 (|Integer|)))) (|minColIndex| (*1 *2 *1) (AND (|ofCategory| *1 (|RectangularMatrixCategory| *3 *4 *5 *6 *7)) (|ofCategory| *5 (|Ring|)) (|ofCategory| *6 (|DirectProductCategory| *4 *5)) (|ofCategory| *7 (|DirectProductCategory| *3 *5)) (|isDomain| *2 (|Integer|)))) (|maxColIndex| (*1 *2 *1) (AND (|ofCategory| *1 (|RectangularMatrixCategory| *3 *4 *5 *6 *7)) (|ofCategory| *5 (|Ring|)) (|ofCategory| *6 (|DirectProductCategory| *4 *5)) (|ofCategory| *7 (|DirectProductCategory| *3 *5)) (|isDomain| *2 (|Integer|)))) (|nrows| (*1 *2 *1) (AND (|ofCategory| *1 (|RectangularMatrixCategory| *3 *4 *5 *6 *7)) (|ofCategory| *5 (|Ring|)) (|ofCategory| *6 (|DirectProductCategory| *4 *5)) (|ofCategory| *7 (|DirectProductCategory| *3 *5)) (|isDomain| *2 (|NonNegativeInteger|)))) (|ncols| (*1 *2 *1) (AND (|ofCategory| *1 (|RectangularMatrixCategory| *3 *4 *5 *6 *7)) (|ofCategory| *5 (|Ring|)) (|ofCategory| *6 (|DirectProductCategory| *4 *5)) (|ofCategory| *7 (|DirectProductCategory| *3 *5)) (|isDomain| *2 (|NonNegativeInteger|)))) (|listOfLists| (*1 *2 *1) (AND (|ofCategory| *1 (|RectangularMatrixCategory| *3 *4 *5 *6 *7)) (|ofCategory| *5 (|Ring|)) (|ofCategory| *6 (|DirectProductCategory| *4 *5)) (|ofCategory| *7 (|DirectProductCategory| *3 *5)) (|isDomain| *2 (|List| (|List| *5))))) (|elt| (*1 *2 *1 *3 *3) (AND (|isDomain| *3 (|Integer|)) (|ofCategory| *1 (|RectangularMatrixCategory| *4 *5 *2 *6 *7)) (|ofCategory| *6 (|DirectProductCategory| *5 *2)) (|ofCategory| *7 (|DirectProductCategory| *4 *2)) (|ofCategory| *2 (|Ring|)))) (|qelt| (*1 *2 *1 *3 *3) (AND (|isDomain| *3 (|Integer|)) (|ofCategory| *1 (|RectangularMatrixCategory| *4 *5 *2 *6 *7)) (|ofCategory| *6 (|DirectProductCategory| *5 *2)) (|ofCategory| *7 (|DirectProductCategory| *4 *2)) (|ofCategory| *2 (|Ring|)))) (|elt| (*1 *2 *1 *3 *3 *2) (AND (|isDomain| *3 (|Integer|)) (|ofCategory| *1 (|RectangularMatrixCategory| *4 *5 *2 *6 *7)) (|ofCategory| *2 (|Ring|)) (|ofCategory| *6 (|DirectProductCategory| *5 *2)) (|ofCategory| *7 (|DirectProductCategory| *4 *2)))) (|row| (*1 *2 *1 *3) (AND (|isDomain| *3 (|Integer|)) (|ofCategory| *1 (|RectangularMatrixCategory| *4 *5 *6 *2 *7)) (|ofCategory| *6 (|Ring|)) (|ofCategory| *7 (|DirectProductCategory| *4 *6)) (|ofCategory| *2 (|DirectProductCategory| *5 *6)))) (|column| (*1 *2 *1 *3) (AND (|isDomain| *3 (|Integer|)) (|ofCategory| *1 (|RectangularMatrixCategory| *4 *5 *6 *7 *2)) (|ofCategory| *6 (|Ring|)) (|ofCategory| *7 (|DirectProductCategory| *5 *6)) (|ofCategory| *2 (|DirectProductCategory| *4 *6)))) (|map| (*1 *1 *2 *1 *1) (AND (|isDomain| *2 (|Mapping| *5 *5 *5)) (|ofCategory| *1 (|RectangularMatrixCategory| *3 *4 *5 *6 *7)) (|ofCategory| *5 (|Ring|)) (|ofCategory| *6 (|DirectProductCategory| *4 *5)) (|ofCategory| *7 (|DirectProductCategory| *3 *5)))) (|exquo| (*1 *1 *1 *2) (|partial| AND (|ofCategory| *1 (|RectangularMatrixCategory| *3 *4 *2 *5 *6)) (|ofCategory| *2 (|Ring|)) (|ofCategory| *5 (|DirectProductCategory| *4 *2)) (|ofCategory| *6 (|DirectProductCategory| *3 *2)) (|ofCategory| *2 (|IntegralDomain|)))) (/ (*1 *1 *1 *2) (AND (|ofCategory| *1 (|RectangularMatrixCategory| *3 *4 *2 *5 *6)) (|ofCategory| *2 (|Ring|)) (|ofCategory| *5 (|DirectProductCategory| *4 *2)) (|ofCategory| *6 (|DirectProductCategory| *3 *2)) (|ofCategory| *2 (|Field|)))) (|rowEchelon| (*1 *1 *1) (AND (|ofCategory| *1 (|RectangularMatrixCategory| *2 *3 *4 *5 *6)) (|ofCategory| *4 (|Ring|)) (|ofCategory| *5 (|DirectProductCategory| *3 *4)) (|ofCategory| *6 (|DirectProductCategory| *2 *4)) (|ofCategory| *4 (|EuclideanDomain|)))) (|rank| (*1 *2 *1) (AND (|ofCategory| *1 (|RectangularMatrixCategory| *3 *4 *5 *6 *7)) (|ofCategory| *5 (|Ring|)) (|ofCategory| *6 (|DirectProductCategory| *4 *5)) (|ofCategory| *7 (|DirectProductCategory| *3 *5)) (|ofCategory| *5 (|IntegralDomain|)) (|isDomain| *2 (|NonNegativeInteger|)))) (|nullity| (*1 *2 *1) (AND (|ofCategory| *1 (|RectangularMatrixCategory| *3 *4 *5 *6 *7)) (|ofCategory| *5 (|Ring|)) (|ofCategory| *6 (|DirectProductCategory| *4 *5)) (|ofCategory| *7 (|DirectProductCategory| *3 *5)) (|ofCategory| *5 (|IntegralDomain|)) (|isDomain| *2 (|NonNegativeInteger|)))) (|nullSpace| (*1 *2 *1) (AND (|ofCategory| *1 (|RectangularMatrixCategory| *3 *4 *5 *6 *7)) (|ofCategory| *5 (|Ring|)) (|ofCategory| *6 (|DirectProductCategory| *4 *5)) (|ofCategory| *7 (|DirectProductCategory| *3 *5)) (|ofCategory| *5 (|IntegralDomain|)) (|isDomain| *2 (|List| *7))))) (|Join| (|BiModule| |t#3| |t#3|) (|FiniteAggregate| |t#3|) (CATEGORY |domain| (IF (|has| |t#3| (|CommutativeRing|)) (ATTRIBUTE (|Module| |t#3|)) |%noBranch|) (SIGNATURE |matrix| ($ (|List| (|List| |t#3|)))) (SIGNATURE |square?| ((|Boolean|) $)) (SIGNATURE |diagonal?| ((|Boolean|) $)) (SIGNATURE |symmetric?| ((|Boolean|) $)) (SIGNATURE |antisymmetric?| ((|Boolean|) $)) (SIGNATURE |minRowIndex| ((|Integer|) $)) (SIGNATURE |maxRowIndex| ((|Integer|) $)) (SIGNATURE |minColIndex| ((|Integer|) $)) (SIGNATURE |maxColIndex| ((|Integer|) $)) (SIGNATURE |nrows| ((|NonNegativeInteger|) $)) (SIGNATURE |ncols| ((|NonNegativeInteger|) $)) (SIGNATURE |listOfLists| ((|List| (|List| |t#3|)) $)) (SIGNATURE |elt| (|t#3| $ (|Integer|) (|Integer|))) (SIGNATURE |qelt| (|t#3| $ (|Integer|) (|Integer|))) (SIGNATURE |elt| (|t#3| $ (|Integer|) (|Integer|) |t#3|)) (SIGNATURE |row| (|t#4| $ (|Integer|))) (SIGNATURE |column| (|t#5| $ (|Integer|))) (SIGNATURE |map| ($ (|Mapping| |t#3| |t#3| |t#3|) $ $)) (IF (|has| |t#3| (|IntegralDomain|)) (SIGNATURE |exquo| ((|Union| $ "failed") $ |t#3|)) |%noBranch|) (IF (|has| |t#3| (|Field|)) (SIGNATURE / ($ $ |t#3|)) |%noBranch|) (IF (|has| |t#3| (|EuclideanDomain|)) (SIGNATURE |rowEchelon| ($ $)) |%noBranch|) (IF (|has| |t#3| (|IntegralDomain|)) (PROGN (SIGNATURE |rank| ((|NonNegativeInteger|) $)) (SIGNATURE |nullity| ((|NonNegativeInteger|) $)) (SIGNATURE |nullSpace| ((|List| |t#5|) $))) |%noBranch|))) (((|AbelianGroup|) . T) ((|AbelianMonoid|) . T) ((|AbelianSemiGroup|) . T) ((|Aggregate|) . T) ((|BasicType|) . T) ((|BiModule| |#3| |#3|) . T) ((|CancellationAbelianMonoid|) . T) ((|CoercibleTo| (|OutputForm|)) . T) ((|Evalable| |#3|) AND (|has| |#3| (|Evalable| |#3|)) (|has| |#3| (|SetCategory|))) ((|FiniteAggregate| |#3|) . T) ((|Functorial| |#3|) . T) ((|HomogeneousAggregate| |#3|) . T) ((|InnerEvalable| |#3| |#3|) AND (|has| |#3| (|Evalable| |#3|)) (|has| |#3| (|SetCategory|))) ((|Join|) . T) ((|LeftLinearSet| (|Integer|)) . T) ((|LeftLinearSet| |#3|) . T) ((|LeftModule| |#3|) . T) ((|LinearSet| |#3|) |has| |#3| (|CommutativeRing|)) ((|Module| |#3|) |has| |#3| (|CommutativeRing|)) ((|RightLinearSet| |#3|) . T) ((|RightModule| |#3|) . T) ((|SetCategory|) . T) ((|Type|) . T)) -((~= #1=((#2=(|Boolean|) $ $) NIL T ELT)) (|zero?| #3=((#2# $) NIL T ELT)) (|symmetric?| #3#) (|subtractIfCan| ((#4=(|Union| $ #5="failed") $ $) NIL T ELT)) (|square?| #3#) (|sample| (#6=($) NIL T CONST)) (|rowEchelon| (#7=($ $) 46 (|has| |#3| (|EuclideanDomain|)) ELT)) (|row| (((|DirectProduct| |#2| |#3|) $ #8=(|Integer|)) 35 T ELT)) (|reduce| ((|#3| #9=(|Mapping| |#3| |#3| |#3|) $ |#3| |#3|) NIL #10=(|has| |#3| (|BasicType|)) ELT) ((|#3| #9# $ |#3|) NIL T ELT) ((|#3| #9# $) NIL T ELT)) (|rectangularMatrix| (($ #11=(|Matrix| |#3|)) 44 T ELT)) (|rank| (#12=(#13=(|NonNegativeInteger|) $) 48 #14=(|has| |#3| (|IntegralDomain|)) ELT)) (|qelt| #15=((|#3| $ #8# #8#) NIL T ELT)) (|opposite?| #1#) (|nullity| (#12# 50 #14# ELT)) (|nullSpace| (((|List| #16=(|DirectProduct| |#1| |#3|)) $) 54 #14# ELT)) (|nrows| #17=(#12# NIL T ELT)) (|ncols| #17#) (|minRowIndex| #18=((#8# $) NIL T ELT)) (|minColIndex| #18#) (|members| ((#19=(|List| |#3|) $) NIL T ELT)) (|member?| ((#2# |#3| $) NIL #10# ELT)) (|maxRowIndex| #18#) (|maxColIndex| #18#) (|matrix| (($ #20=(|List| #19#)) 30 T ELT)) (|map| (($ (|Mapping| |#3| |#3|) $) NIL T ELT) (($ #9# $ $) NIL T ELT)) (|listOfLists| ((#20# $) NIL T ELT)) (|latex| (((|String|) $) NIL T ELT)) (|hash| (((|SingleInteger|) $) NIL T ELT)) (|find| (((|Union| |#3| #5#) #21=(|Mapping| #2# |#3|) $) NIL T ELT)) (|exquo| ((#4# $ |#3|) NIL #14# ELT)) (|every?| #22=((#2# #21# $) NIL T ELT)) (|eval| (($ $ #19# #19#) NIL #23=(AND (|has| |#3| (|Evalable| |#3|)) (|has| |#3| (|SetCategory|))) ELT) (($ $ |#3| |#3|) NIL #23# ELT) (($ $ #24=(|Equation| |#3|)) NIL #23# ELT) (($ $ (|List| #24#)) NIL #23# ELT)) (|eq?| #1#) (|empty?| #3#) (|empty| (#6# NIL T ELT)) (|elt| #15# ((|#3| $ #8# #8# |#3|) NIL T ELT)) (|dimension| (((|CardinalNumber|)) 58 #25=(|has| |#3| (|Field|)) ELT)) (|diagonal?| #3#) (|count| ((#13# |#3| $) NIL #10# ELT) ((#13# #21# $) NIL T ELT)) (|copy| #26=(#7# NIL T ELT)) (|convert| ((#27=(|InputForm|) $) 65 (|has| |#3| (|ConvertibleTo| #27#)) ELT)) (|column| ((#16# $ #8#) 39 T ELT)) (|coerce| (((|OutputForm|) $) 18 T ELT) ((#11# $) 41 T ELT)) (|before?| #1#) (|any?| #22#) (|antisymmetric?| #3#) (|Zero| (#6# 15 T CONST)) (= #1#) (/ (#28=($ $ |#3|) NIL #25# ELT)) (- #26# #29=(($ $ $) NIL T ELT)) (+ #29#) (* (($ (|PositiveInteger|) $) NIL T ELT) (($ #13# $) NIL T ELT) (($ #8# . #30=($)) NIL T ELT) (($ |#3| . #30#) NIL T ELT) (#28# NIL T ELT)) (|#| #17#)) +((~= #1=((#2=(|Boolean|) $ $) NIL T ELT)) (|zero?| #3=((#2# $) NIL T ELT)) (|symmetric?| #3#) (|subtractIfCan| (((|Maybe| $) $ $) NIL T ELT)) (|square?| #3#) (|sample| (#4=($) NIL T CONST)) (|rowEchelon| (#5=($ $) 46 (|has| |#3| (|EuclideanDomain|)) ELT)) (|row| (((|DirectProduct| |#2| |#3|) $ #6=(|Integer|)) 35 T ELT)) (|reduce| ((|#3| #7=(|Mapping| |#3| |#3| |#3|) $ |#3| |#3|) NIL #8=(|has| |#3| (|BasicType|)) ELT) ((|#3| #7# $ |#3|) NIL T ELT) ((|#3| #7# $) NIL T ELT)) (|rectangularMatrix| (($ #9=(|Matrix| |#3|)) 44 T ELT)) (|rank| (#10=(#11=(|NonNegativeInteger|) $) 48 #12=(|has| |#3| (|IntegralDomain|)) ELT)) (|qelt| #13=((|#3| $ #6# #6#) NIL T ELT)) (|opposite?| #1#) (|nullity| (#10# 50 #12# ELT)) (|nullSpace| (((|List| #14=(|DirectProduct| |#1| |#3|)) $) 54 #12# ELT)) (|nrows| #15=(#10# NIL T ELT)) (|ncols| #15#) (|minRowIndex| #16=((#6# $) NIL T ELT)) (|minColIndex| #16#) (|members| ((#17=(|List| |#3|) $) NIL T ELT)) (|member?| ((#2# |#3| $) NIL #8# ELT)) (|maxRowIndex| #16#) (|maxColIndex| #16#) (|matrix| (($ #18=(|List| #17#)) 30 T ELT)) (|map| (($ (|Mapping| |#3| |#3|) $) NIL T ELT) (($ #7# $ $) NIL T ELT)) (|listOfLists| ((#18# $) NIL T ELT)) (|latex| (((|String|) $) NIL T ELT)) (|hash| (((|SingleInteger|) $) NIL T ELT)) (|find| (((|Union| |#3| #19="failed") #20=(|Mapping| #2# |#3|) $) NIL T ELT)) (|exquo| (((|Union| $ #19#) $ |#3|) NIL #12# ELT)) (|every?| #21=((#2# #20# $) NIL T ELT)) (|eval| (($ $ #17# #17#) NIL #22=(AND (|has| |#3| (|Evalable| |#3|)) (|has| |#3| (|SetCategory|))) ELT) (($ $ |#3| |#3|) NIL #22# ELT) (($ $ #23=(|Equation| |#3|)) NIL #22# ELT) (($ $ (|List| #23#)) NIL #22# ELT)) (|eq?| #1#) (|empty?| #3#) (|empty| (#4# NIL T ELT)) (|elt| #13# ((|#3| $ #6# #6# |#3|) NIL T ELT)) (|dimension| (((|CardinalNumber|)) 58 #24=(|has| |#3| (|Field|)) ELT)) (|diagonal?| #3#) (|count| ((#11# |#3| $) NIL #8# ELT) ((#11# #20# $) NIL T ELT)) (|copy| #25=(#5# NIL T ELT)) (|convert| ((#26=(|InputForm|) $) 65 (|has| |#3| (|ConvertibleTo| #26#)) ELT)) (|column| ((#14# $ #6#) 39 T ELT)) (|coerce| (((|OutputForm|) $) 18 T ELT) ((#9# $) 41 T ELT)) (|before?| #1#) (|any?| #21#) (|antisymmetric?| #3#) (|Zero| (#4# 15 T CONST)) (= #1#) (/ (#27=($ $ |#3|) NIL #24# ELT)) (- #25# #28=(($ $ $) NIL T ELT)) (+ #28#) (* (($ (|PositiveInteger|) $) NIL T ELT) (($ #11# $) NIL T ELT) (($ #6# . #29=($)) NIL T ELT) (($ |#3| . #29#) NIL T ELT) (#27# NIL T ELT)) (|#| #15#)) (((|RectangularMatrix| |#1| |#2| |#3|) (|Join| (|RectangularMatrixCategory| |#1| |#2| |#3| (|DirectProduct| |#2| |#3|) (|DirectProduct| |#1| |#3|)) (|CoercibleTo| #1=(|Matrix| |#3|)) (CATEGORY |domain| (IF (|has| |#3| (|Field|)) (ATTRIBUTE (|VectorSpace| |#3|)) |%noBranch|) (IF (|has| |#3| #2=(|ConvertibleTo| (|InputForm|))) (ATTRIBUTE #2#) |%noBranch|) (SIGNATURE |rectangularMatrix| ($ #1#)))) #3=(|NonNegativeInteger|) #3# (|Ring|)) (T |RectangularMatrix|)) ((|rectangularMatrix| (*1 *1 *2) (AND (|isDomain| *2 (|Matrix| *5)) (|ofCategory| *5 (|Ring|)) (|isDomain| *1 (|RectangularMatrix| *3 *4 *5)) (|ofType| *3 #1=(|NonNegativeInteger|)) (|ofType| *4 #1#)))) ((|reduce| ((|#7| (|Mapping| |#7| |#3| |#7|) |#6| |#7|) 36 T ELT)) (|map| ((|#10| (|Mapping| |#7| |#3|) |#6|) 34 T ELT))) (((|RectangularMatrixCategoryFunctions2| |#1| |#2| |#3| |#4| |#5| |#6| |#7| |#8| |#9| |#10|) (CATEGORY |package| (SIGNATURE |map| (|#10| (|Mapping| |#7| |#3|) |#6|)) (SIGNATURE |reduce| (|#7| (|Mapping| |#7| |#3| |#7|) |#6| |#7|))) #1=(|NonNegativeInteger|) #1# #2=(|Ring|) (|DirectProductCategory| |#2| |#3|) (|DirectProductCategory| |#1| |#3|) (|RectangularMatrixCategory| |#1| |#2| |#3| |#4| |#5|) #2# (|DirectProductCategory| |#2| |#7|) (|DirectProductCategory| |#1| |#7|) (|RectangularMatrixCategory| |#1| |#2| |#7| |#8| |#9|)) (T |RectangularMatrixCategoryFunctions2|)) ((|reduce| (*1 *2 *3 *4 *2) (AND (|isDomain| *3 (|Mapping| *2 *7 *2)) #1=(|ofCategory| *7 #2=(|Ring|)) (|ofCategory| *2 #2#) #3=(|ofType| *5 #4=(|NonNegativeInteger|)) #5=(|ofType| *6 #4#) #6=(|ofCategory| *8 (|DirectProductCategory| *6 *7)) #7=(|ofCategory| *9 (|DirectProductCategory| *5 *7)) (|ofCategory| *10 (|DirectProductCategory| *6 *2)) (|ofCategory| *11 (|DirectProductCategory| *5 *2)) (|isDomain| *1 (|RectangularMatrixCategoryFunctions2| *5 *6 *7 *8 *9 *4 *2 *10 *11 *12)) #8=(|ofCategory| *4 (|RectangularMatrixCategory| *5 *6 *7 *8 *9)) (|ofCategory| *12 (|RectangularMatrixCategory| *5 *6 *2 *10 *11)))) (|map| (*1 *2 *3 *4) (AND (|isDomain| *3 (|Mapping| *10 *7)) #1# (|ofCategory| *10 #2#) #3# #5# #6# #7# (|ofCategory| *2 (|RectangularMatrixCategory| *5 *6 *10 *11 *12)) (|isDomain| *1 (|RectangularMatrixCategoryFunctions2| *5 *6 *7 *8 *9 *4 *10 *11 *12 *2)) #8# (|ofCategory| *11 (|DirectProductCategory| *6 *10)) (|ofCategory| *12 (|DirectProductCategory| *5 *10))))) -((~= (#1=((|Boolean|) $ $) 7 T ELT)) (|zero?| ((#2=(|Boolean|) $) 22 T ELT)) (|subtractIfCan| (((|Union| $ "failed") $ $) 26 T ELT)) (|sample| (#3=($) 23 T CONST)) (|opposite?| ((#2# $ $) 20 T ELT)) (|latex| (((|String|) $) 11 T ELT)) (|hash| (((|SingleInteger|) $) 12 T ELT)) (|coerce| (((|OutputForm|) $) 13 T ELT)) (|before?| (#1# 6 T ELT)) (|Zero| (#3# 24 T CONST)) (= (#1# 8 T ELT)) (- (($ $) 29 T ELT) (($ $ $) 28 T ELT)) (+ (($ $ $) 18 T ELT)) (* (($ (|PositiveInteger|) $) 17 T ELT) (($ (|NonNegativeInteger|) $) 21 T ELT) (($ (|Integer|) $) 30 T ELT) (($ $ |#1|) 33 T ELT))) +((~= (#1=((|Boolean|) $ $) 7 T ELT)) (|zero?| ((#2=(|Boolean|) $) 22 T ELT)) (|subtractIfCan| (((|Maybe| $) $ $) 26 T ELT)) (|sample| (#3=($) 23 T CONST)) (|opposite?| ((#2# $ $) 20 T ELT)) (|latex| (((|String|) $) 11 T ELT)) (|hash| (((|SingleInteger|) $) 12 T ELT)) (|coerce| (((|OutputForm|) $) 13 T ELT)) (|before?| (#1# 6 T ELT)) (|Zero| (#3# 24 T CONST)) (= (#1# 8 T ELT)) (- (($ $) 30 T ELT) (($ $ $) 29 T ELT)) (+ (($ $ $) 18 T ELT)) (* (($ (|PositiveInteger|) $) 17 T ELT) (($ (|NonNegativeInteger|) $) 21 T ELT) (($ (|Integer|) $) 31 T ELT) (($ $ |#1|) 34 T ELT))) (((|RightModule| |#1|) (|Category|) (|Rng|)) (T |RightModule|)) NIL (|Join| (|AbelianGroup|) (|RightLinearSet| |t#1|)) @@ -3234,7 +3234,7 @@ NIL ((|annihilate?| (((|Boolean|) $ $) 10 T ELT))) (((|Rng&| |#1|) (CATEGORY |package| (SIGNATURE |annihilate?| ((|Boolean|) |#1| |#1|))) (|Rng|)) (T |Rng&|)) NIL -((~= (#1=((|Boolean|) $ $) 7 T ELT)) (|zero?| ((#2=(|Boolean|) $) 22 T ELT)) (|subtractIfCan| (((|Union| $ "failed") $ $) 26 T ELT)) (|sample| (#3=($) 23 T CONST)) (|opposite?| ((#2# $ $) 20 T ELT)) (|latex| (((|String|) $) 11 T ELT)) (|hash| (((|SingleInteger|) $) 12 T ELT)) (|coerce| (((|OutputForm|) $) 13 T ELT)) (|before?| (#1# 6 T ELT)) (|annihilate?| (((|Boolean|) $ $) 33 T ELT)) (|Zero| (#3# 24 T CONST)) (= (#1# 8 T ELT)) (- (($ $) 29 T ELT) (($ $ $) 28 T ELT)) (+ (($ $ $) 18 T ELT)) (** (($ $ (|PositiveInteger|)) 35 T ELT)) (* (($ (|PositiveInteger|) $) 17 T ELT) (($ (|NonNegativeInteger|) $) 21 T ELT) (($ (|Integer|) $) 30 T ELT) (($ $ $) 34 T ELT))) +((~= (#1=((|Boolean|) $ $) 7 T ELT)) (|zero?| ((#2=(|Boolean|) $) 22 T ELT)) (|subtractIfCan| (((|Maybe| $) $ $) 26 T ELT)) (|sample| (#3=($) 23 T CONST)) (|opposite?| ((#2# $ $) 20 T ELT)) (|latex| (((|String|) $) 11 T ELT)) (|hash| (((|SingleInteger|) $) 12 T ELT)) (|coerce| (((|OutputForm|) $) 13 T ELT)) (|before?| (#1# 6 T ELT)) (|annihilate?| (((|Boolean|) $ $) 34 T ELT)) (|Zero| (#3# 24 T CONST)) (= (#1# 8 T ELT)) (- (($ $) 30 T ELT) (($ $ $) 29 T ELT)) (+ (($ $ $) 18 T ELT)) (** (($ $ (|PositiveInteger|)) 36 T ELT)) (* (($ (|PositiveInteger|) $) 17 T ELT) (($ (|NonNegativeInteger|) $) 21 T ELT) (($ (|Integer|) $) 31 T ELT) (($ $ $) 35 T ELT))) (((|Rng|) (|Category|)) (T |Rng|)) ((|annihilate?| (*1 *2 *1 *1) (AND (|ofCategory| *1 (|Rng|)) (|isDomain| *2 (|Boolean|))))) (|Join| (|AbelianGroup|) (|SemiGroup|) (CATEGORY |domain| (SIGNATURE |annihilate?| ((|Boolean|) $ $)))) @@ -3245,7 +3245,7 @@ NIL ((|truncate| (#1=($ $) 17 T ELT)) (|round| (#1# 25 T ELT)) (|patternMatch| ((#2=(|PatternMatchResult| #3=(|Float|) $) $ #4=(|Pattern| #3#) #2#) 54 T ELT)) (|norm| (#1# 27 T ELT)) (|fractionPart| (#1# 12 T ELT)) (|floor| (#1# 40 T ELT)) (|convert| ((#3# $) NIL T ELT) (((|DoubleFloat|) $) NIL T ELT) ((#4# $) 36 T ELT)) (|coerce| (((|OutputForm|) $) NIL T ELT) #5=(($ #6=(|Integer|)) NIL T ELT) (#1# NIL T ELT) #7=(($ (|Fraction| #6#)) 31 T ELT) #5# #7#) (|characteristic| (((|NonNegativeInteger|)) 9 T CONST)) (|ceiling| (#1# 44 T ELT))) (((|RealNumberSystem&| |#1|) (CATEGORY |package| (SIGNATURE |round| #1=(|#1| |#1|)) (SIGNATURE |truncate| #1#) (SIGNATURE |fractionPart| #1#) (SIGNATURE |floor| #1#) (SIGNATURE |ceiling| #1#) (SIGNATURE |norm| #1#) (SIGNATURE |patternMatch| (#2=(|PatternMatchResult| #3=(|Float|) |#1|) |#1| #4=(|Pattern| #3#) #2#)) (SIGNATURE |convert| (#4# |#1|)) #5=(SIGNATURE |coerce| (|#1| (|Fraction| #6=(|Integer|)))) #7=(SIGNATURE |coerce| (|#1| #6#)) (SIGNATURE |convert| ((|DoubleFloat|) |#1|)) (SIGNATURE |convert| (#3# |#1|)) #5# (SIGNATURE |coerce| #1#) (SIGNATURE |characteristic| ((|NonNegativeInteger|)) |constant|) #7# (SIGNATURE |coerce| ((|OutputForm|) |#1|))) (|RealNumberSystem|)) (T |RealNumberSystem&|)) ((|characteristic| (*1 *2) (AND (|isDomain| *2 (|NonNegativeInteger|)) (|isDomain| *1 (|RealNumberSystem&| *3)) (|ofCategory| *3 (|RealNumberSystem|))))) -((~= (#1=((|Boolean|) $ $) 7 T ELT)) (|zero?| ((#2=(|Boolean|) $) 22 T ELT)) (|wholePart| (((|Integer|) $) 108 T ELT)) (|unitNormal| (((|Record| (|:| |unit| $) (|:| |canonical| $) (|:| |associate| $)) $) 55 T ELT)) (|unitCanonical| (($ $) 54 T ELT)) (|unit?| ((#3=(|Boolean|) $) 52 T ELT)) (|truncate| (($ $) 106 T ELT)) (|subtractIfCan| (((|Union| $ "failed") $ $) 26 T ELT)) (|squareFreePart| (($ $) 91 T ELT)) (|squareFree| (#4=((|Factored| $) $) 90 T ELT)) (|sqrt| (($ $) 116 T ELT)) (|sizeLess?| (((|Boolean|) $ $) 75 T ELT)) (|sign| (((|Integer|) $) 133 T ELT)) (|sample| (#5=($) 23 T CONST)) (|round| (($ $) 105 T ELT)) (|retractIfCan| (((|Union| #6=(|Integer|) . #7=("failed")) . #8=($)) 121 T ELT) (((|Union| #9=(|Fraction| (|Integer|)) . #7#) . #8#) 118 T ELT)) (|retract| ((#6# . #10=($)) 122 T ELT) ((#9# . #10#) 119 T ELT)) (|rem| (#11=($ $ $) 71 T ELT)) (|recip| (((|Union| $ "failed") $) 42 T ELT)) (|quo| (#11# 72 T ELT)) (|principalIdeal| (((|Record| (|:| |coef| #12=(|List| $)) (|:| |generator| $)) #12#) 66 T ELT)) (|prime?| (((|Boolean|) $) 89 T ELT)) (|positive?| (((|Boolean|) $) 131 T ELT)) (|patternMatch| (((|PatternMatchResult| #13=(|Float|) . #14=($)) $ (|Pattern| #13#) (|PatternMatchResult| #13# . #14#)) 112 T ELT)) (|opposite?| ((#2# $ $) 20 T ELT)) (|one?| (((|Boolean|) $) 44 T ELT)) (|nthRoot| (($ $ #15=(|Integer|)) 115 T ELT)) (|norm| (($ $) 111 T ELT)) (|negative?| (((|Boolean|) $) 132 T ELT)) (|multiEuclidean| (((|Union| #16=(|List| $) #17="failed") #16# $) 68 T ELT)) (|min| (#18=($ $ $) 125 T ELT)) (|max| (#18# 126 T ELT)) (|lcm| (#19=($ $ $) 60 T ELT) (#20=($ (|List| $)) 59 T ELT)) (|latex| (((|String|) $) 11 T ELT)) (|inv| (($ $) 88 T ELT)) (|hash| (((|SingleInteger|) $) 12 T ELT)) (|gcdPolynomial| ((#21=(|SparseUnivariatePolynomial| $) #21# #21#) 58 T ELT)) (|gcd| (#19# 62 T ELT) (#20# 61 T ELT)) (|fractionPart| (($ $) 107 T ELT)) (|floor| (($ $) 109 T ELT)) (|factor| (#4# 92 T ELT)) (|extendedEuclidean| (((|Record| #22=(|:| |coef1| $) #23=(|:| |coef2| $) (|:| |generator| $)) $ $) 70 T ELT) (((|Union| (|Record| #22# #23#) #17#) $ $ $) 69 T ELT)) (|exquo| (((|Union| $ "failed") $ $) 56 T ELT)) (|expressIdealMember| (((|Maybe| #12#) #12# $) 65 T ELT)) (|euclideanSize| (((|NonNegativeInteger|) $) 74 T ELT)) (|divide| (((|Record| (|:| |quotient| $) (|:| |remainder| $)) $ $) 73 T ELT)) (|convert| (((|Float|) . #24=($)) 124 T ELT) (((|DoubleFloat|) . #24#) 123 T ELT) (((|Pattern| (|Float|)) . #24#) 113 T ELT)) (|coerce| (((|OutputForm|) $) 13 T ELT) (($ (|Integer|)) 41 T ELT) (($ $) 57 T ELT) (($ #25=(|Fraction| #26=(|Integer|))) 84 T ELT) (($ #6#) 120 T ELT) (($ #9#) 117 T ELT)) (|characteristic| (((|NonNegativeInteger|)) 40 T CONST)) (|ceiling| (($ $) 110 T ELT)) (|before?| (#1# 6 T ELT)) (|associates?| ((#3# $ $) 53 T ELT)) (|annihilate?| (((|Boolean|) $ $) 33 T ELT)) (|abs| (($ $) 134 T ELT)) (|Zero| (#5# 24 T CONST)) (|One| (($) 45 T CONST)) (>= (#27=((|Boolean|) $ $) 127 T ELT)) (> (#27# 129 T ELT)) (= (#1# 8 T ELT)) (<= (#27# 128 T ELT)) (< (#27# 130 T ELT)) (/ (($ $ $) 83 T ELT)) (- (($ $) 29 T ELT) (($ $ $) 28 T ELT)) (+ (($ $ $) 18 T ELT)) (** (($ $ (|PositiveInteger|)) 35 T ELT) (($ $ (|NonNegativeInteger|)) 43 T ELT) (($ $ #26#) 87 T ELT) (($ $ (|Fraction| #15#)) 114 T ELT)) (* (($ (|PositiveInteger|) $) 17 T ELT) (($ (|NonNegativeInteger|) $) 21 T ELT) (($ (|Integer|) . #28=($)) 30 T ELT) (($ $ $) 34 T ELT) (($ $ #25#) 86 T ELT) (($ #25# . #28#) 85 T ELT))) +((~= (#1=((|Boolean|) $ $) 7 T ELT)) (|zero?| ((#2=(|Boolean|) $) 22 T ELT)) (|wholePart| (((|Integer|) $) 109 T ELT)) (|unitNormal| (((|Record| (|:| |unit| $) (|:| |canonical| $) (|:| |associate| $)) $) 56 T ELT)) (|unitCanonical| (($ $) 55 T ELT)) (|unit?| ((#3=(|Boolean|) $) 53 T ELT)) (|truncate| (($ $) 107 T ELT)) (|subtractIfCan| (((|Maybe| $) $ $) 26 T ELT)) (|squareFreePart| (($ $) 92 T ELT)) (|squareFree| (#4=((|Factored| $) $) 91 T ELT)) (|sqrt| (($ $) 117 T ELT)) (|sizeLess?| (((|Boolean|) $ $) 76 T ELT)) (|sign| (((|Integer|) $) 134 T ELT)) (|sample| (#5=($) 23 T CONST)) (|round| (($ $) 106 T ELT)) (|retractIfCan| (((|Union| #6=(|Integer|) . #7=("failed")) . #8=($)) 122 T ELT) (((|Union| #9=(|Fraction| (|Integer|)) . #7#) . #8#) 119 T ELT)) (|retract| ((#6# . #10=($)) 123 T ELT) ((#9# . #10#) 120 T ELT)) (|rem| (#11=($ $ $) 72 T ELT)) (|recip| (((|Union| $ "failed") $) 43 T ELT)) (|quo| (#11# 73 T ELT)) (|principalIdeal| (((|Record| (|:| |coef| #12=(|List| $)) (|:| |generator| $)) #12#) 67 T ELT)) (|prime?| (((|Boolean|) $) 90 T ELT)) (|positive?| (((|Boolean|) $) 132 T ELT)) (|patternMatch| (((|PatternMatchResult| #13=(|Float|) . #14=($)) $ (|Pattern| #13#) (|PatternMatchResult| #13# . #14#)) 113 T ELT)) (|opposite?| ((#2# $ $) 20 T ELT)) (|one?| (((|Boolean|) $) 45 T ELT)) (|nthRoot| (($ $ #15=(|Integer|)) 116 T ELT)) (|norm| (($ $) 112 T ELT)) (|negative?| (((|Boolean|) $) 133 T ELT)) (|multiEuclidean| (((|Union| #16=(|List| $) #17="failed") #16# $) 69 T ELT)) (|min| (#18=($ $ $) 126 T ELT)) (|max| (#18# 127 T ELT)) (|lcm| (#19=($ $ $) 61 T ELT) (#20=($ (|List| $)) 60 T ELT)) (|latex| (((|String|) $) 11 T ELT)) (|inv| (($ $) 89 T ELT)) (|hash| (((|SingleInteger|) $) 12 T ELT)) (|gcdPolynomial| ((#21=(|SparseUnivariatePolynomial| $) #21# #21#) 59 T ELT)) (|gcd| (#19# 63 T ELT) (#20# 62 T ELT)) (|fractionPart| (($ $) 108 T ELT)) (|floor| (($ $) 110 T ELT)) (|factor| (#4# 93 T ELT)) (|extendedEuclidean| (((|Record| #22=(|:| |coef1| $) #23=(|:| |coef2| $) (|:| |generator| $)) $ $) 71 T ELT) (((|Union| (|Record| #22# #23#) #17#) $ $ $) 70 T ELT)) (|exquo| (((|Union| $ "failed") $ $) 57 T ELT)) (|expressIdealMember| (((|Maybe| #12#) #12# $) 66 T ELT)) (|euclideanSize| (((|NonNegativeInteger|) $) 75 T ELT)) (|divide| (((|Record| (|:| |quotient| $) (|:| |remainder| $)) $ $) 74 T ELT)) (|convert| (((|Float|) . #24=($)) 125 T ELT) (((|DoubleFloat|) . #24#) 124 T ELT) (((|Pattern| (|Float|)) . #24#) 114 T ELT)) (|coerce| (((|OutputForm|) $) 13 T ELT) (($ (|Integer|)) 42 T ELT) (($ $) 58 T ELT) (($ #25=(|Fraction| #26=(|Integer|))) 85 T ELT) (($ #6#) 121 T ELT) (($ #9#) 118 T ELT)) (|characteristic| (((|NonNegativeInteger|)) 41 T CONST)) (|ceiling| (($ $) 111 T ELT)) (|before?| (#1# 6 T ELT)) (|associates?| ((#3# $ $) 54 T ELT)) (|annihilate?| (((|Boolean|) $ $) 34 T ELT)) (|abs| (($ $) 135 T ELT)) (|Zero| (#5# 24 T CONST)) (|One| (($) 46 T CONST)) (>= (#27=((|Boolean|) $ $) 128 T ELT)) (> (#27# 130 T ELT)) (= (#1# 8 T ELT)) (<= (#27# 129 T ELT)) (< (#27# 131 T ELT)) (/ (($ $ $) 84 T ELT)) (- (($ $) 30 T ELT) (($ $ $) 29 T ELT)) (+ (($ $ $) 18 T ELT)) (** (($ $ (|PositiveInteger|)) 36 T ELT) (($ $ (|NonNegativeInteger|)) 44 T ELT) (($ $ #26#) 88 T ELT) (($ $ (|Fraction| #15#)) 115 T ELT)) (* (($ (|PositiveInteger|) $) 17 T ELT) (($ (|NonNegativeInteger|) $) 21 T ELT) (($ (|Integer|) . #28=($)) 31 T ELT) (($ $ $) 35 T ELT) (($ $ #25#) 87 T ELT) (($ #25# . #28#) 86 T ELT))) (((|RealNumberSystem|) (|Category|)) (T |RealNumberSystem|)) ((|norm| (*1 *1 *1) (|ofCategory| *1 (|RealNumberSystem|))) (|ceiling| (*1 *1 *1) (|ofCategory| *1 (|RealNumberSystem|))) (|floor| (*1 *1 *1) (|ofCategory| *1 (|RealNumberSystem|))) (|wholePart| (*1 *2 *1) (AND (|ofCategory| *1 (|RealNumberSystem|)) (|isDomain| *2 (|Integer|)))) (|fractionPart| (*1 *1 *1) (|ofCategory| *1 (|RealNumberSystem|))) (|truncate| (*1 *1 *1) (|ofCategory| *1 (|RealNumberSystem|))) (|round| (*1 *1 *1) (|ofCategory| *1 (|RealNumberSystem|)))) (|Join| (|Field|) (|OrderedRing|) (|RealConstant|) (|RetractableTo| #1=(|Integer|)) (|RetractableTo| (|Fraction| #1#)) (|RadicalCategory|) (|ConvertibleTo| (|Pattern| #2=(|Float|))) (|PatternMatchable| #2#) (|CharacteristicZero|) (CATEGORY |domain| (SIGNATURE |norm| #3=($ $)) (SIGNATURE |ceiling| #3#) (SIGNATURE |floor| #3#) (SIGNATURE |wholePart| (#1# $)) (SIGNATURE |fractionPart| #3#) (SIGNATURE |truncate| #3#) (SIGNATURE |round| #3#))) @@ -3253,13 +3253,13 @@ NIL ((~= #1=(#2=(#3=(|Boolean|) $ $) NIL T ELT)) (|zero?| (#4=(#3# |#2| $) 26 T ELT)) (|size| (#5=(|#1| $) 10 T ELT)) (|sign| (((|Integer|) |#2| $) 119 T ELT)) (|rootOf| (((|Union| $ #6="failed") |#2| (|PositiveInteger|)) 76 T ELT)) (|right| (#5# 31 T ELT)) (|relativeApprox| (#7=(|#1| |#2| $ |#1|) 40 T ELT)) (|refine| (($ $) 28 T ELT)) (|recip| (((|Union| |#2| #6#) |#2| $) 113 T ELT)) (|positive?| #8=(#4# NIL T ELT)) (|negative?| #8#) (|mightHaveRoots| (#4# 27 T ELT)) (|middle| (#5# 120 T ELT)) (|left| (#5# 30 T ELT)) (|latex| (((|String|) $) NIL T ELT)) (|hash| (((|SingleInteger|) $) NIL T ELT)) (|definingPolynomial| ((|#2| $) 104 T ELT)) (|coerce| (((|OutputForm|) $) 95 T ELT)) (|before?| #1#) (|approximate| (#7# 41 T ELT)) (|allRootsOf| (((|List| $) |#2|) 78 T ELT)) (= (#2# 99 T ELT))) (((|RightOpenIntervalRootCharacterization| |#1| |#2|) (|Join| (|RealRootCharacterizationCategory| |#1| |#2|) (CATEGORY |domain| (SIGNATURE |left| #1=(|#1| $)) (SIGNATURE |right| #1#) (SIGNATURE |size| #1#) (SIGNATURE |middle| #1#) (SIGNATURE |refine| ($ $)) (SIGNATURE |mightHaveRoots| ((|Boolean|) |#2| $)) (SIGNATURE |relativeApprox| (|#1| |#2| $ |#1|)))) (|Join| (|OrderedRing|) (|Field|)) (|UnivariatePolynomialCategory| |#1|)) (T |RightOpenIntervalRootCharacterization|)) ((|relativeApprox| (*1 *2 *3 *1 *2) #1=(AND (|ofCategory| *2 #2=(|Join| (|OrderedRing|) (|Field|))) (|isDomain| *1 (|RightOpenIntervalRootCharacterization| *2 *3)) (|ofCategory| *3 (|UnivariatePolynomialCategory| *2)))) (|left| #3=(*1 *2 *1) #1#) (|right| #3# #1#) (|size| #3# #1#) (|middle| #3# #1#) (|refine| (*1 *1 *1) #1#) (|mightHaveRoots| (*1 *2 *3 *1) (AND (|ofCategory| *4 #2#) (|isDomain| *2 (|Boolean|)) (|isDomain| *1 (|RightOpenIntervalRootCharacterization| *4 *3)) (|ofCategory| *3 (|UnivariatePolynomialCategory| *4))))) -((~= #1=((#2=(|Boolean|) $ $) NIL T ELT)) (|zero?| #3=((#2# $) NIL T ELT)) (|unitNormal| (((|Record| (|:| |unit| $) (|:| |canonical| $) (|:| |associate| $)) $) NIL T ELT)) (|unitCanonical| #4=(#5=($ $) NIL T ELT)) (|unit?| #3#) (|symmetricRemainder| #6=(($ $ $) NIL T ELT)) (|subtractIfCan| #7=((#8=(|Union| $ #9="failed") $ $) NIL T ELT)) (|submod| #10=(($ $ $ $) NIL T ELT)) (|squareFreePart| #4#) (|squareFree| #11=(((|Factored| $) $) NIL T ELT)) (|sizeLess?| #1#) (|sign| #12=(#13=(#14=(|Integer|) $) NIL T ELT)) (|shift| #6#) (|sample| #15=(#16=($) NIL T CONST)) (|roman| (#17=($ (|Symbol|)) 10 T ELT) (#18=($ #14#) 7 T ELT)) (|retractIfCan| (((|Union| #14# #9#) $) NIL T ELT)) (|retract| #12#) (|rem| #6#) (|reducedSystem| ((#19=(|Record| (|:| |mat| #20=(|Matrix| #14#)) (|:| |vec| (|Vector| #14#))) #21=(|Matrix| $) #22=(|Vector| $)) NIL T ELT) ((#20# #21#) NIL T ELT)) (|recip| ((#8# $) NIL T ELT)) (|rationalIfCan| (((|Union| #23=(|Fraction| #14#) #9#) $) NIL T ELT)) (|rational?| #3#) (|rational| ((#23# $) NIL T ELT)) (|random| #24=(#16# NIL T ELT) #4#) (|quo| #6#) (|principalIdeal| (((|Record| (|:| |coef| #25=(|List| $)) #26=(|:| |generator| $)) #25#) NIL T ELT)) (|prime?| #3#) (|powmod| #10#) (|positiveRemainder| #6#) (|positive?| #3#) (|permutation| #6#) (|patternMatch| ((#27=(|PatternMatchResult| #14# $) $ #28=(|Pattern| #14#) #27#) NIL T ELT)) (|opposite?| #1#) (|one?| #3#) (|odd?| #3#) (|nextItem| (((|Maybe| $) $) NIL T ELT)) (|negative?| #3#) (|multiEuclidean| (((|Union| #25# #9#) #25# $) NIL T ELT)) (|mulmod| #10#) (|min| #6#) (|max| #6#) (|mask| #4#) (|length| #4#) (|leftReducedSystem| ((#19# #22# $) NIL T ELT) ((#20# #22#) NIL T ELT)) (|lcm| #6# #29=(($ #25#) NIL T ELT)) (|latex| (((|String|) $) NIL T ELT)) (|invmod| #6#) (|init| #15#) (|inc| #4#) (|hash| (((|SingleInteger|) $) NIL T ELT)) (|gcdPolynomial| ((#30=(|SparseUnivariatePolynomial| $) #30# #30#) NIL T ELT)) (|gcd| #6# #29#) (|factorial| #4#) (|factor| #11#) (|extendedEuclidean| (((|Union| (|Record| #31=(|:| |coef1| $) #32=(|:| |coef2| $)) #9#) $ $ $) NIL T ELT) (((|Record| #31# #32# #26#) $ $) NIL T ELT)) (|exquo| #7#) (|expressIdealMember| (((|Maybe| #25#) #25# $) NIL T ELT)) (|even?| #3#) (|euclideanSize| ((#33=(|NonNegativeInteger|) $) NIL T ELT)) (|divide| (((|Record| (|:| |quotient| $) (|:| |remainder| $)) $ $) NIL T ELT)) (|differentiate| #4# #34=(($ $ #33#) NIL T ELT)) (|dec| #4#) (|copy| #4#) (|convert| (#13# 16 T ELT) (((|InputForm|) . #35=($)) NIL T ELT) ((#28# . #35#) NIL T ELT) (((|Float|) . #35#) NIL T ELT) (((|DoubleFloat|) . #35#) NIL T ELT) (#17# 9 T ELT)) (|coerce| (((|OutputForm|) $) 23 T ELT) #36=(#18# 6 T ELT) #4# #36#) (|characteristic| ((#33#) NIL T CONST)) (|bit?| #1#) (|binomial| #6#) (|before?| #1#) (|base| #24#) (|associates?| #1#) (|annihilate?| #1#) (|addmod| #10#) (|abs| #4#) (|Zero| #15#) (|One| #15#) (D #4# #34#) (>= #1#) (> #1#) (= #1#) (<= #1#) (< #1#) (- (#5# 22 T ELT) #6#) (+ #6#) (** (($ $ #37=(|PositiveInteger|)) NIL T ELT) #34#) (* (($ #37# $) NIL T ELT) (($ #33# $) NIL T ELT) #38=(($ #14# $) NIL T ELT) #6# #38#)) -(((|RomanNumeral|) (|Join| (|IntegerNumberSystem|) (|ConvertibleFrom| #1=(|Symbol|)) (CATEGORY |domain| (ATTRIBUTE |canonical|) (ATTRIBUTE |canonicalsClosed|) (ATTRIBUTE |noetherian|) (SIGNATURE |roman| ($ #1#)) (SIGNATURE |roman| ($ (|Integer|)))))) (T |RomanNumeral|)) +((~= #1=((#2=(|Boolean|) $ $) NIL T ELT)) (|zero?| #3=((#2# $) NIL T ELT)) (|unitNormal| (((|Record| (|:| |unit| $) (|:| |canonical| $) (|:| |associate| $)) $) NIL T ELT)) (|unitCanonical| #4=(#5=($ $) NIL T ELT)) (|unit?| #3#) (|symmetricRemainder| #6=(($ $ $) NIL T ELT)) (|subtractIfCan| ((#7=(|Maybe| $) $ $) NIL T ELT)) (|submod| #8=(($ $ $ $) NIL T ELT)) (|squareFreePart| #4#) (|squareFree| #9=(((|Factored| $) $) NIL T ELT)) (|sizeLess?| #1#) (|sign| #10=(#11=(#12=(|Integer|) $) NIL T ELT)) (|shift| #6#) (|sample| #13=(#14=($) NIL T CONST)) (|roman| (#15=($ (|Symbol|)) 10 T ELT) (#16=($ #12#) 7 T ELT)) (|retractIfCan| (((|Union| #12# #17="failed") $) NIL T ELT)) (|retract| #10#) (|rem| #6#) (|reducedSystem| ((#18=(|Record| (|:| |mat| #19=(|Matrix| #12#)) (|:| |vec| (|Vector| #12#))) #20=(|Matrix| $) #21=(|Vector| $)) NIL T ELT) ((#19# #20#) NIL T ELT)) (|recip| ((#22=(|Union| $ #17#) $) NIL T ELT)) (|rationalIfCan| (((|Union| #23=(|Fraction| #12#) #17#) $) NIL T ELT)) (|rational?| #3#) (|rational| ((#23# $) NIL T ELT)) (|random| #24=(#14# NIL T ELT) #4#) (|quo| #6#) (|principalIdeal| (((|Record| (|:| |coef| #25=(|List| $)) #26=(|:| |generator| $)) #25#) NIL T ELT)) (|prime?| #3#) (|powmod| #8#) (|positiveRemainder| #6#) (|positive?| #3#) (|permutation| #6#) (|patternMatch| ((#27=(|PatternMatchResult| #12# $) $ #28=(|Pattern| #12#) #27#) NIL T ELT)) (|opposite?| #1#) (|one?| #3#) (|odd?| #3#) (|nextItem| ((#7# $) NIL T ELT)) (|negative?| #3#) (|multiEuclidean| (((|Union| #25# #17#) #25# $) NIL T ELT)) (|mulmod| #8#) (|min| #6#) (|max| #6#) (|mask| #4#) (|length| #4#) (|leftReducedSystem| ((#18# #21# $) NIL T ELT) ((#19# #21#) NIL T ELT)) (|lcm| #6# #29=(($ #25#) NIL T ELT)) (|latex| (((|String|) $) NIL T ELT)) (|invmod| #6#) (|init| #13#) (|inc| #4#) (|hash| (((|SingleInteger|) $) NIL T ELT)) (|gcdPolynomial| ((#30=(|SparseUnivariatePolynomial| $) #30# #30#) NIL T ELT)) (|gcd| #6# #29#) (|factorial| #4#) (|factor| #9#) (|extendedEuclidean| (((|Union| (|Record| #31=(|:| |coef1| $) #32=(|:| |coef2| $)) #17#) $ $ $) NIL T ELT) (((|Record| #31# #32# #26#) $ $) NIL T ELT)) (|exquo| ((#22# $ $) NIL T ELT)) (|expressIdealMember| (((|Maybe| #25#) #25# $) NIL T ELT)) (|even?| #3#) (|euclideanSize| ((#33=(|NonNegativeInteger|) $) NIL T ELT)) (|divide| (((|Record| (|:| |quotient| $) (|:| |remainder| $)) $ $) NIL T ELT)) (|differentiate| #4# #34=(($ $ #33#) NIL T ELT)) (|dec| #4#) (|copy| #4#) (|convert| (#11# 16 T ELT) (((|InputForm|) . #35=($)) NIL T ELT) ((#28# . #35#) NIL T ELT) (((|Float|) . #35#) NIL T ELT) (((|DoubleFloat|) . #35#) NIL T ELT) (#15# 9 T ELT)) (|coerce| (((|OutputForm|) $) 23 T ELT) #36=(#16# 6 T ELT) #4# #36#) (|characteristic| ((#33#) NIL T CONST)) (|bit?| #1#) (|binomial| #6#) (|before?| #1#) (|base| #24#) (|associates?| #1#) (|annihilate?| #1#) (|addmod| #8#) (|abs| #4#) (|Zero| #13#) (|One| #13#) (D #4# #34#) (>= #1#) (> #1#) (= #1#) (<= #1#) (< #1#) (- (#5# 22 T ELT) #6#) (+ #6#) (** (($ $ #37=(|PositiveInteger|)) NIL T ELT) #34#) (* (($ #37# $) NIL T ELT) (($ #33# $) NIL T ELT) #38=(($ #12# $) NIL T ELT) #6# #38#)) +(((|RomanNumeral|) (|Join| (|IntegerNumberSystem|) (|ConvertibleFrom| #1=(|Symbol|)) (CATEGORY |domain| (ATTRIBUTE 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#55=(|ConvertibleTo| #53#)) (|has| |#1| #55#)) ELT) ((#56=(|Pattern| #36#) . #54#) 96 (AND (|has| |#3| #57=(|ConvertibleTo| #56#)) (|has| |#1| #57#)) ELT) ((#58=(|InputForm|) . #54#) 95 (AND (|has| |#3| #59=(|ConvertibleTo| #58#)) (|has| |#1| #59#)) ELT) (($ (|Polynomial| (|Fraction| (|Integer|)))) 252 (AND (|has| |#1| (|Algebra| (|Fraction| (|Integer|)))) (|has| |#3| (|ConvertibleTo| (|Symbol|)))) ELT) (($ (|Polynomial| (|Integer|))) 249 (OR (AND (|not| (|has| |#1| (|Algebra| (|Fraction| (|Integer|))))) (|has| |#1| (|Algebra| (|Integer|))) (|has| |#3| (|ConvertibleTo| (|Symbol|)))) (AND (|has| |#1| (|Algebra| (|Fraction| (|Integer|)))) (|has| |#3| (|ConvertibleTo| (|Symbol|))))) ELT) (($ (|Polynomial| |#1|)) 246 (|has| |#3| (|ConvertibleTo| (|Symbol|))) ELT) (((|String|) . #54#) 224 (AND (|has| |#1| (|RetractableTo| (|Integer|))) (|has| |#3| (|ConvertibleTo| (|Symbol|)))) ELT) (((|Polynomial| |#1|) . #54#) 223 (|has| |#3| (|ConvertibleTo| (|Symbol|))) ELT)) (|content| ((|#1| . #48#) 194 (|has| |#1| . #30#) ELT) (($ $ |#3|) 121 (|has| |#1| . #10#) ELT)) (|conditionP| (((|Union| (|Vector| $) #13#) (|Matrix| $)) 119 (|and| #60=(|has| $ (|CharacteristicNonZero|)) (|has| |#1| . #9#)) ELT)) (|coerce| (((|OutputForm|) . #61=($)) 13 T ELT) (($ (|Integer|)) 42 T ELT) (($ |#1|) 184 T ELT) (($ |#3|) 154 T ELT) (((|Polynomial| |#1|) . #61#) 222 (|has| |#3| (|ConvertibleTo| (|Symbol|))) ELT) (($ #17#) 93 (OR (|has| |#1| . #19#) (|has| |#1| . #62=((|Algebra| #63=(|Fraction| (|Integer|)))))) ELT) (($ $) 100 (|has| |#1| . #4#) ELT)) (|coefficients| (((|List| |#1|) $) 187 T ELT)) (|coefficient| ((|#1| $ |#2|) 174 T ELT) (($ $ |#3| . #39#) 143 T ELT) (($ $ (|List| |#3|) . #40#) 142 T ELT)) (|charthRoot| (((|Maybe| $) $) 94 (OR (|and| #60# (|has| |#1| . #9#)) (|has| |#1| (|CharacteristicNonZero|))) ELT)) (|characteristic| (((|NonNegativeInteger|)) 41 T CONST)) (|binomThmExpt| (($ $ $ #38#) 192 (|has| |#1| (|CommutativeRing|)) ELT)) (|before?| (#1# 6 T ELT)) (|associates?| ((#5# $ $) 104 (|has| |#1| . #4#) ELT)) (|annihilate?| (((|Boolean|) $ $) 34 T ELT)) (|Zero| (#14# 24 T CONST)) (|RittWuCompare| (((|Union| (|Boolean|) "failed") $ $) 282 T ELT)) (|One| (($) 46 T CONST)) (|LazardQuotient2| (($ $ $ $ (|NonNegativeInteger|)) 231 (|has| |#1| (|IntegralDomain|)) ELT)) (|LazardQuotient| (($ $ $ (|NonNegativeInteger|)) 232 (|has| |#1| (|IntegralDomain|)) ELT)) (D (($ $ (|List| |#3|) . #50#) 56 T ELT) (($ $ |#3| . #52#) 55 T ELT) (($ $ (|List| |#3|)) 54 T ELT) (($ $ |#3|) 50 T ELT)) (= (#1# 8 T ELT)) (/ (($ $ |#1|) 175 (|has| |#1| (|Field|)) ELT)) (- (($ $) 30 T ELT) (($ $ $) 29 T ELT)) (+ (($ $ $) 18 T ELT)) (** (($ $ (|PositiveInteger|)) 36 T ELT) (($ $ (|NonNegativeInteger|)) 44 T ELT)) (* (($ (|PositiveInteger|) $) 17 T ELT) (($ (|NonNegativeInteger|) $) 21 T ELT) (($ (|Integer|) . #64=($)) 31 T ELT) (($ $ $) 35 T ELT) (($ $ #63#) 177 (|has| |#1| . #62#) ELT) (($ #63# . #64#) 176 (|has| |#1| . #62#) ELT) (($ |#1| . #64#) 166 T ELT) (($ $ |#1|) 165 T ELT))) (((|RecursivePolynomialCategory| |#1| |#2| |#3|) (|Category|) (|Ring|) (|OrderedAbelianMonoidSup|) (|OrderedSet|)) (T |RecursivePolynomialCategory|)) ((|mvar| (*1 *2 *1) (AND (|ofCategory| *1 (|RecursivePolynomialCategory| *3 *4 *2)) (|ofCategory| *3 (|Ring|)) (|ofCategory| *4 (|OrderedAbelianMonoidSup|)) (|ofCategory| *2 (|OrderedSet|)))) (|mdeg| (*1 *2 *1) (AND (|ofCategory| *1 (|RecursivePolynomialCategory| *3 *4 *5)) (|ofCategory| *3 (|Ring|)) (|ofCategory| *4 (|OrderedAbelianMonoidSup|)) (|ofCategory| *5 (|OrderedSet|)) (|isDomain| *2 (|NonNegativeInteger|)))) (|init| (*1 *1 *1) (AND (|ofCategory| *1 (|RecursivePolynomialCategory| *2 *3 *4)) (|ofCategory| *2 (|Ring|)) (|ofCategory| *3 (|OrderedAbelianMonoidSup|)) (|ofCategory| *4 (|OrderedSet|)))) (|head| (*1 *1 *1) (AND (|ofCategory| *1 (|RecursivePolynomialCategory| *2 *3 *4)) (|ofCategory| *2 (|Ring|)) (|ofCategory| *3 (|OrderedAbelianMonoidSup|)) (|ofCategory| *4 (|OrderedSet|)))) (|tail| (*1 *1 *1) (AND (|ofCategory| *1 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(*1 *1 *1 *2) (AND (|ofCategory| *1 (|RecursivePolynomialCategory| *3 *4 *2)) (|ofCategory| *3 (|Ring|)) (|ofCategory| *4 (|OrderedAbelianMonoidSup|)) (|ofCategory| *2 (|OrderedSet|)))) (|monic?| (*1 *2 *1) (AND (|ofCategory| *1 (|RecursivePolynomialCategory| *3 *4 *5)) (|ofCategory| *3 (|Ring|)) (|ofCategory| *4 (|OrderedAbelianMonoidSup|)) (|ofCategory| *5 (|OrderedSet|)) (|isDomain| *2 (|Boolean|)))) (|quasiMonic?| (*1 *2 *1) (AND (|ofCategory| *1 (|RecursivePolynomialCategory| *3 *4 *5)) (|ofCategory| *3 (|Ring|)) (|ofCategory| *4 (|OrderedAbelianMonoidSup|)) (|ofCategory| *5 (|OrderedSet|)) (|isDomain| *2 (|Boolean|)))) (|mainMonomial| (*1 *1 *1) (AND (|ofCategory| *1 (|RecursivePolynomialCategory| *2 *3 *4)) (|ofCategory| *2 (|Ring|)) (|ofCategory| *3 (|OrderedAbelianMonoidSup|)) (|ofCategory| *4 (|OrderedSet|)))) (|leastMonomial| (*1 *1 *1) (AND (|ofCategory| *1 (|RecursivePolynomialCategory| *2 *3 *4)) (|ofCategory| *2 (|Ring|)) (|ofCategory| *3 (|OrderedAbelianMonoidSup|)) (|ofCategory| *4 (|OrderedSet|)))) (|mainCoefficients| (*1 *2 *1) (AND (|ofCategory| *3 (|Ring|)) (|ofCategory| *4 (|OrderedAbelianMonoidSup|)) (|ofCategory| *5 (|OrderedSet|)) (|isDomain| *2 (|List| *1)) (|ofCategory| *1 (|RecursivePolynomialCategory| *3 *4 *5)))) (|mainMonomials| (*1 *2 *1) (AND (|ofCategory| *3 (|Ring|)) (|ofCategory| *4 (|OrderedAbelianMonoidSup|)) (|ofCategory| *5 (|OrderedSet|)) (|isDomain| *2 (|List| *1)) (|ofCategory| *1 (|RecursivePolynomialCategory| *3 *4 *5)))) (|RittWuCompare| (*1 *2 *1 *1) (|partial| AND (|ofCategory| *1 (|RecursivePolynomialCategory| *3 *4 *5)) (|ofCategory| *3 (|Ring|)) (|ofCategory| *4 (|OrderedAbelianMonoidSup|)) (|ofCategory| *5 (|OrderedSet|)) (|isDomain| *2 (|Boolean|)))) (|infRittWu?| (*1 *2 *1 *1) (AND (|ofCategory| *1 (|RecursivePolynomialCategory| *3 *4 *5)) (|ofCategory| *3 (|Ring|)) (|ofCategory| *4 (|OrderedAbelianMonoidSup|)) (|ofCategory| *5 (|OrderedSet|)) (|isDomain| *2 (|Boolean|)))) (|supRittWu?| (*1 *2 *1 *1) (AND (|ofCategory| *1 (|RecursivePolynomialCategory| *3 *4 *5)) (|ofCategory| *3 (|Ring|)) (|ofCategory| *4 (|OrderedAbelianMonoidSup|)) (|ofCategory| *5 (|OrderedSet|)) (|isDomain| *2 (|Boolean|)))) (|reduced?| (*1 *2 *1 *1) (AND (|ofCategory| *1 (|RecursivePolynomialCategory| *3 *4 *5)) (|ofCategory| *3 (|Ring|)) (|ofCategory| *4 (|OrderedAbelianMonoidSup|)) (|ofCategory| *5 (|OrderedSet|)) (|isDomain| *2 (|Boolean|)))) (|reduced?| (*1 *2 *1 *3) (AND (|isDomain| *3 (|List| *1)) (|ofCategory| *1 (|RecursivePolynomialCategory| *4 *5 *6)) (|ofCategory| *4 (|Ring|)) (|ofCategory| *5 (|OrderedAbelianMonoidSup|)) (|ofCategory| *6 (|OrderedSet|)) (|isDomain| *2 (|Boolean|)))) (|headReduced?| (*1 *2 *1 *1) (AND (|ofCategory| *1 (|RecursivePolynomialCategory| *3 *4 *5)) (|ofCategory| *3 (|Ring|)) (|ofCategory| *4 (|OrderedAbelianMonoidSup|)) (|ofCategory| *5 (|OrderedSet|)) (|isDomain| *2 (|Boolean|)))) (|headReduced?| (*1 *2 *1 *3) (AND (|isDomain| *3 (|List| *1)) (|ofCategory| *1 (|RecursivePolynomialCategory| *4 *5 *6)) (|ofCategory| *4 (|Ring|)) (|ofCategory| *5 (|OrderedAbelianMonoidSup|)) (|ofCategory| *6 (|OrderedSet|)) (|isDomain| *2 (|Boolean|)))) (|initiallyReduced?| (*1 *2 *1 *1) (AND (|ofCategory| *1 (|RecursivePolynomialCategory| *3 *4 *5)) (|ofCategory| *3 (|Ring|)) (|ofCategory| *4 (|OrderedAbelianMonoidSup|)) (|ofCategory| *5 (|OrderedSet|)) (|isDomain| *2 (|Boolean|)))) (|initiallyReduced?| (*1 *2 *1 *3) (AND (|isDomain| *3 (|List| *1)) (|ofCategory| *1 (|RecursivePolynomialCategory| *4 *5 *6)) (|ofCategory| *4 (|Ring|)) (|ofCategory| *5 (|OrderedAbelianMonoidSup|)) (|ofCategory| *6 (|OrderedSet|)) (|isDomain| *2 (|Boolean|)))) (|normalized?| (*1 *2 *1 *1) (AND (|ofCategory| *1 (|RecursivePolynomialCategory| *3 *4 *5)) (|ofCategory| *3 (|Ring|)) (|ofCategory| *4 (|OrderedAbelianMonoidSup|)) (|ofCategory| *5 (|OrderedSet|)) (|isDomain| *2 (|Boolean|)))) (|normalized?| (*1 *2 *1 *3) (AND (|isDomain| *3 (|List| *1)) (|ofCategory| *1 (|RecursivePolynomialCategory| *4 *5 *6)) (|ofCategory| *4 (|Ring|)) (|ofCategory| *5 (|OrderedAbelianMonoidSup|)) (|ofCategory| *6 (|OrderedSet|)) (|isDomain| *2 (|Boolean|)))) (|prem| (*1 *1 *1 *1) (AND (|ofCategory| *1 (|RecursivePolynomialCategory| *2 *3 *4)) (|ofCategory| *2 (|Ring|)) (|ofCategory| *3 (|OrderedAbelianMonoidSup|)) (|ofCategory| *4 (|OrderedSet|)))) (|pquo| (*1 *1 *1 *1) (AND (|ofCategory| *1 (|RecursivePolynomialCategory| *2 *3 *4)) (|ofCategory| *2 (|Ring|)) (|ofCategory| *3 (|OrderedAbelianMonoidSup|)) (|ofCategory| *4 (|OrderedSet|)))) (|prem| (*1 *1 *1 *1 *2) (AND (|ofCategory| *1 (|RecursivePolynomialCategory| *3 *4 *2)) (|ofCategory| *3 (|Ring|)) (|ofCategory| *4 (|OrderedAbelianMonoidSup|)) (|ofCategory| *2 (|OrderedSet|)))) (|pquo| (*1 *1 *1 *1 *2) (AND (|ofCategory| *1 (|RecursivePolynomialCategory| *3 *4 *2)) (|ofCategory| *3 (|Ring|)) (|ofCategory| *4 (|OrderedAbelianMonoidSup|)) (|ofCategory| *2 (|OrderedSet|)))) (|lazyPrem| (*1 *1 *1 *1) (AND (|ofCategory| *1 (|RecursivePolynomialCategory| *2 *3 *4)) (|ofCategory| *2 (|Ring|)) (|ofCategory| *3 (|OrderedAbelianMonoidSup|)) (|ofCategory| *4 (|OrderedSet|)))) (|lazyPquo| (*1 *1 *1 *1) (AND (|ofCategory| *1 (|RecursivePolynomialCategory| *2 *3 *4)) (|ofCategory| *2 (|Ring|)) (|ofCategory| *3 (|OrderedAbelianMonoidSup|)) (|ofCategory| *4 (|OrderedSet|)))) (|lazyPrem| (*1 *1 *1 *1 *2) (AND (|ofCategory| *1 (|RecursivePolynomialCategory| *3 *4 *2)) (|ofCategory| *3 (|Ring|)) (|ofCategory| *4 (|OrderedAbelianMonoidSup|)) (|ofCategory| *2 (|OrderedSet|)))) (|lazyPquo| (*1 *1 *1 *1 *2) (AND (|ofCategory| *1 (|RecursivePolynomialCategory| *3 *4 *2)) (|ofCategory| *3 (|Ring|)) (|ofCategory| *4 (|OrderedAbelianMonoidSup|)) (|ofCategory| *2 (|OrderedSet|)))) (|lazyPremWithDefault| (*1 *2 *1 *1) (AND (|ofCategory| *3 (|Ring|)) (|ofCategory| *4 (|OrderedAbelianMonoidSup|)) (|ofCategory| *5 (|OrderedSet|)) (|isDomain| *2 (|Record| (|:| |coef| *1) (|:| |gap| (|NonNegativeInteger|)) (|:| |remainder| *1))) (|ofCategory| *1 (|RecursivePolynomialCategory| *3 *4 *5)))) (|lazyPremWithDefault| (*1 *2 *1 *1 *3) (AND (|ofCategory| *4 (|Ring|)) (|ofCategory| *5 (|OrderedAbelianMonoidSup|)) (|ofCategory| *3 (|OrderedSet|)) (|isDomain| *2 (|Record| (|:| |coef| *1) (|:| |gap| (|NonNegativeInteger|)) (|:| |remainder| *1))) (|ofCategory| *1 (|RecursivePolynomialCategory| *4 *5 *3)))) (|lazyPseudoDivide| (*1 *2 *1 *1) (AND (|ofCategory| *3 (|Ring|)) (|ofCategory| *4 (|OrderedAbelianMonoidSup|)) (|ofCategory| *5 (|OrderedSet|)) (|isDomain| *2 (|Record| (|:| |coef| *1) (|:| |gap| (|NonNegativeInteger|)) (|:| |quotient| *1) (|:| |remainder| *1))) (|ofCategory| *1 (|RecursivePolynomialCategory| *3 *4 *5)))) (|lazyPseudoDivide| (*1 *2 *1 *1 *3) (AND (|ofCategory| *4 (|Ring|)) (|ofCategory| *5 (|OrderedAbelianMonoidSup|)) (|ofCategory| *3 (|OrderedSet|)) (|isDomain| *2 (|Record| (|:| |coef| *1) (|:| |gap| (|NonNegativeInteger|)) (|:| |quotient| *1) (|:| |remainder| *1))) (|ofCategory| *1 (|RecursivePolynomialCategory| *4 *5 *3)))) (|pseudoDivide| (*1 *2 *1 *1) (AND (|ofCategory| *3 (|Ring|)) (|ofCategory| *4 (|OrderedAbelianMonoidSup|)) (|ofCategory| *5 (|OrderedSet|)) (|isDomain| *2 (|Record| (|:| |quotient| *1) (|:| |remainder| *1))) (|ofCategory| *1 (|RecursivePolynomialCategory| *3 *4 *5)))) (|monicModulo| (*1 *1 *1 *1) (AND (|ofCategory| *1 (|RecursivePolynomialCategory| *2 *3 *4)) (|ofCategory| *2 (|Ring|)) (|ofCategory| *3 (|OrderedAbelianMonoidSup|)) (|ofCategory| *4 (|OrderedSet|)))) (|lazyResidueClass| (*1 *2 *1 *1) (AND (|ofCategory| *3 (|Ring|)) (|ofCategory| *4 (|OrderedAbelianMonoidSup|)) (|ofCategory| *5 (|OrderedSet|)) (|isDomain| *2 (|Record| (|:| |polnum| *1) (|:| |polden| *1) (|:| |power| (|NonNegativeInteger|)))) (|ofCategory| *1 (|RecursivePolynomialCategory| *3 *4 *5)))) (|headReduce| (*1 *1 *1 *1) (AND (|ofCategory| *1 (|RecursivePolynomialCategory| *2 *3 *4)) (|ofCategory| *2 (|Ring|)) (|ofCategory| *3 (|OrderedAbelianMonoidSup|)) (|ofCategory| *4 (|OrderedSet|)))) (|initiallyReduce| (*1 *1 *1 *1) (AND (|ofCategory| *1 (|RecursivePolynomialCategory| *2 *3 *4)) (|ofCategory| *2 (|Ring|)) (|ofCategory| *3 (|OrderedAbelianMonoidSup|)) (|ofCategory| *4 (|OrderedSet|)))) (|retractIfCan| (*1 *1 *2) (|partial| AND (|isDomain| *2 (|Polynomial| (|Fraction| (|Integer|)))) (|ofCategory| *1 (|RecursivePolynomialCategory| *3 *4 *5)) (|ofCategory| *3 (|Algebra| (|Fraction| (|Integer|)))) (|ofCategory| *5 (|ConvertibleTo| (|Symbol|))) (|ofCategory| *3 (|Ring|)) (|ofCategory| *4 (|OrderedAbelianMonoidSup|)) (|ofCategory| *5 (|OrderedSet|)))) (|retract| (*1 *1 *2) (AND (|isDomain| *2 (|Polynomial| (|Fraction| (|Integer|)))) (|ofCategory| *1 (|RecursivePolynomialCategory| *3 *4 *5)) (|ofCategory| *3 (|Algebra| (|Fraction| (|Integer|)))) (|ofCategory| *5 (|ConvertibleTo| (|Symbol|))) (|ofCategory| *3 (|Ring|)) (|ofCategory| *4 (|OrderedAbelianMonoidSup|)) (|ofCategory| *5 (|OrderedSet|)))) (|convert| (*1 *1 *2) (AND (|isDomain| *2 (|Polynomial| (|Fraction| (|Integer|)))) (|ofCategory| *1 (|RecursivePolynomialCategory| *3 *4 *5)) (|ofCategory| *3 (|Algebra| (|Fraction| (|Integer|)))) (|ofCategory| *5 (|ConvertibleTo| (|Symbol|))) (|ofCategory| *3 (|Ring|)) (|ofCategory| *4 (|OrderedAbelianMonoidSup|)) (|ofCategory| *5 (|OrderedSet|)))) (|retractIfCan| (*1 *1 *2) (|partial| OR (AND #1=(|isDomain| *2 (|Polynomial| (|Integer|))) #2=(|ofCategory| *1 (|RecursivePolynomialCategory| *3 *4 *5)) (AND (|not| (|ofCategory| *3 (|Algebra| (|Fraction| (|Integer|))))) (|ofCategory| *3 (|Algebra| (|Integer|))) (|ofCategory| *5 (|ConvertibleTo| (|Symbol|)))) . #3=((|ofCategory| *3 (|Ring|)) (|ofCategory| *4 (|OrderedAbelianMonoidSup|)) (|ofCategory| *5 (|OrderedSet|)))) (AND #1# #2# (AND (|ofCategory| *3 (|Algebra| (|Fraction| (|Integer|)))) (|ofCategory| *5 (|ConvertibleTo| (|Symbol|)))) . #3#))) (|retract| (*1 *1 *2) (OR (AND #4=(|isDomain| *2 (|Polynomial| (|Integer|))) #5=(|ofCategory| *1 (|RecursivePolynomialCategory| *3 *4 *5)) (AND (|not| (|ofCategory| *3 (|Algebra| (|Fraction| (|Integer|))))) (|ofCategory| *3 (|Algebra| (|Integer|))) (|ofCategory| *5 (|ConvertibleTo| (|Symbol|)))) . #6=((|ofCategory| *3 (|Ring|)) (|ofCategory| *4 (|OrderedAbelianMonoidSup|)) (|ofCategory| *5 (|OrderedSet|)))) (AND #4# #5# (AND (|ofCategory| *3 (|Algebra| (|Fraction| (|Integer|)))) (|ofCategory| *5 (|ConvertibleTo| (|Symbol|)))) . #6#))) (|convert| (*1 *1 *2) (OR (AND #7=(|isDomain| *2 (|Polynomial| (|Integer|))) #8=(|ofCategory| *1 (|RecursivePolynomialCategory| *3 *4 *5)) (AND (|not| (|ofCategory| *3 (|Algebra| (|Fraction| (|Integer|))))) (|ofCategory| *3 (|Algebra| (|Integer|))) (|ofCategory| *5 (|ConvertibleTo| (|Symbol|)))) . #9=((|ofCategory| *3 (|Ring|)) (|ofCategory| *4 (|OrderedAbelianMonoidSup|)) (|ofCategory| *5 (|OrderedSet|)))) (AND #7# #8# (AND (|ofCategory| *3 (|Algebra| (|Fraction| (|Integer|)))) (|ofCategory| *5 (|ConvertibleTo| (|Symbol|)))) . #9#))) (|retractIfCan| (*1 *1 *2) (|partial| OR (AND #10=(|isDomain| *2 (|Polynomial| *3)) (AND (|not| (|ofCategory| *3 (|Algebra| (|Fraction| (|Integer|))))) (|not| (|ofCategory| *3 (|Algebra| (|Integer|)))) (|ofCategory| *5 (|ConvertibleTo| (|Symbol|)))) . #11=((|ofCategory| *3 (|Ring|)) (|ofCategory| *1 (|RecursivePolynomialCategory| *3 *4 *5)) (|ofCategory| *4 (|OrderedAbelianMonoidSup|)) (|ofCategory| *5 (|OrderedSet|)))) (AND #10# (AND (|not| (|ofCategory| *3 (|IntegerNumberSystem|))) (|not| (|ofCategory| *3 (|Algebra| (|Fraction| (|Integer|))))) (|ofCategory| *3 (|Algebra| (|Integer|))) (|ofCategory| *5 (|ConvertibleTo| (|Symbol|)))) . #11#) (AND #10# (AND (|not| (|ofCategory| *3 (|QuotientFieldCategory| (|Integer|)))) (|ofCategory| *3 (|Algebra| (|Fraction| (|Integer|)))) (|ofCategory| *5 (|ConvertibleTo| (|Symbol|)))) . #11#))) (|retract| (*1 *1 *2) (OR (AND #12=(|isDomain| *2 (|Polynomial| *3)) (AND (|not| (|ofCategory| *3 (|Algebra| (|Fraction| (|Integer|))))) (|not| (|ofCategory| *3 (|Algebra| (|Integer|)))) (|ofCategory| *5 (|ConvertibleTo| (|Symbol|)))) . #13=((|ofCategory| *3 (|Ring|)) (|ofCategory| *1 (|RecursivePolynomialCategory| *3 *4 *5)) (|ofCategory| *4 (|OrderedAbelianMonoidSup|)) (|ofCategory| *5 (|OrderedSet|)))) (AND #12# (AND (|not| (|ofCategory| *3 (|IntegerNumberSystem|))) (|not| (|ofCategory| *3 (|Algebra| (|Fraction| (|Integer|))))) (|ofCategory| *3 (|Algebra| (|Integer|))) (|ofCategory| *5 (|ConvertibleTo| (|Symbol|)))) . #13#) (AND #12# (AND (|not| (|ofCategory| *3 (|QuotientFieldCategory| (|Integer|)))) (|ofCategory| *3 (|Algebra| (|Fraction| (|Integer|)))) (|ofCategory| *5 (|ConvertibleTo| (|Symbol|)))) . #13#))) (|convert| (*1 *1 *2) (AND (|isDomain| *2 (|Polynomial| *3)) (|ofCategory| *3 (|Ring|)) (|ofCategory| *1 (|RecursivePolynomialCategory| *3 *4 *5)) (|ofCategory| *5 (|ConvertibleTo| (|Symbol|))) (|ofCategory| *4 (|OrderedAbelianMonoidSup|)) (|ofCategory| *5 (|OrderedSet|)))) (|primPartElseUnitCanonical| (*1 *1 *1) (AND (|ofCategory| *1 (|RecursivePolynomialCategory| *2 *3 *4)) (|ofCategory| *2 (|Ring|)) (|ofCategory| *3 (|OrderedAbelianMonoidSup|)) (|ofCategory| *4 (|OrderedSet|)) (|ofCategory| *2 (|IntegralDomain|)))) (|primPartElseUnitCanonical!| (*1 *1 *1) (AND (|ofCategory| *1 (|RecursivePolynomialCategory| *2 *3 *4)) (|ofCategory| *2 (|Ring|)) (|ofCategory| *3 (|OrderedAbelianMonoidSup|)) (|ofCategory| *4 (|OrderedSet|)) (|ofCategory| *2 (|IntegralDomain|)))) (|exactQuotient| (*1 *1 *1 *2) (AND (|ofCategory| *1 (|RecursivePolynomialCategory| *2 *3 *4)) (|ofCategory| *2 (|Ring|)) (|ofCategory| *3 (|OrderedAbelianMonoidSup|)) (|ofCategory| *4 (|OrderedSet|)) (|ofCategory| *2 (|IntegralDomain|)))) (|exactQuotient!| (*1 *1 *1 *2) (AND (|ofCategory| *1 (|RecursivePolynomialCategory| *2 *3 *4)) (|ofCategory| *2 (|Ring|)) (|ofCategory| *3 (|OrderedAbelianMonoidSup|)) (|ofCategory| *4 (|OrderedSet|)) (|ofCategory| *2 (|IntegralDomain|)))) (|exactQuotient| (*1 *1 *1 *1) (AND (|ofCategory| *1 (|RecursivePolynomialCategory| *2 *3 *4)) (|ofCategory| *2 (|Ring|)) (|ofCategory| *3 (|OrderedAbelianMonoidSup|)) (|ofCategory| *4 (|OrderedSet|)) (|ofCategory| *2 (|IntegralDomain|)))) (|exactQuotient!| (*1 *1 *1 *1) (AND (|ofCategory| *1 (|RecursivePolynomialCategory| *2 *3 *4)) (|ofCategory| *2 (|Ring|)) (|ofCategory| *3 (|OrderedAbelianMonoidSup|)) (|ofCategory| *4 (|OrderedSet|)) (|ofCategory| *2 (|IntegralDomain|)))) (|subResultantGcd| (*1 *1 *1 *1) (AND (|ofCategory| *1 (|RecursivePolynomialCategory| *2 *3 *4)) (|ofCategory| *2 (|Ring|)) (|ofCategory| *3 (|OrderedAbelianMonoidSup|)) (|ofCategory| *4 (|OrderedSet|)) (|ofCategory| *2 (|IntegralDomain|)))) (|extendedSubResultantGcd| (*1 *2 *1 *1) (AND (|ofCategory| *3 (|IntegralDomain|)) (|ofCategory| *3 (|Ring|)) (|ofCategory| *4 (|OrderedAbelianMonoidSup|)) (|ofCategory| *5 (|OrderedSet|)) (|isDomain| *2 (|Record| (|:| |gcd| *1) (|:| |coef1| *1) (|:| |coef2| *1))) (|ofCategory| *1 (|RecursivePolynomialCategory| *3 *4 *5)))) (|halfExtendedSubResultantGcd1| (*1 *2 *1 *1) (AND (|ofCategory| *3 (|IntegralDomain|)) (|ofCategory| *3 (|Ring|)) (|ofCategory| *4 (|OrderedAbelianMonoidSup|)) (|ofCategory| *5 (|OrderedSet|)) (|isDomain| *2 (|Record| (|:| |gcd| *1) (|:| |coef1| *1))) (|ofCategory| *1 (|RecursivePolynomialCategory| *3 *4 *5)))) (|halfExtendedSubResultantGcd2| (*1 *2 *1 *1) (AND (|ofCategory| *3 (|IntegralDomain|)) (|ofCategory| *3 (|Ring|)) (|ofCategory| *4 (|OrderedAbelianMonoidSup|)) (|ofCategory| *5 (|OrderedSet|)) (|isDomain| *2 (|Record| (|:| |gcd| *1) (|:| |coef2| *1))) (|ofCategory| *1 (|RecursivePolynomialCategory| *3 *4 *5)))) (|resultant| (*1 *1 *1 *1) (AND (|ofCategory| *1 (|RecursivePolynomialCategory| *2 *3 *4)) (|ofCategory| *2 (|Ring|)) (|ofCategory| *3 (|OrderedAbelianMonoidSup|)) (|ofCategory| *4 (|OrderedSet|)) (|ofCategory| *2 (|IntegralDomain|)))) (|subResultantChain| (*1 *2 *1 *1) (AND (|ofCategory| *3 (|IntegralDomain|)) (|ofCategory| *3 (|Ring|)) (|ofCategory| *4 (|OrderedAbelianMonoidSup|)) (|ofCategory| *5 (|OrderedSet|)) (|isDomain| *2 (|List| *1)) (|ofCategory| *1 (|RecursivePolynomialCategory| *3 *4 *5)))) (|lastSubResultant| (*1 *1 *1 *1) (AND (|ofCategory| *1 (|RecursivePolynomialCategory| *2 *3 *4)) (|ofCategory| *2 (|Ring|)) (|ofCategory| *3 (|OrderedAbelianMonoidSup|)) (|ofCategory| *4 (|OrderedSet|)) (|ofCategory| *2 (|IntegralDomain|)))) (|LazardQuotient| (*1 *1 *1 *1 *2) (AND (|isDomain| *2 (|NonNegativeInteger|)) (|ofCategory| *1 (|RecursivePolynomialCategory| *3 *4 *5)) (|ofCategory| *3 (|Ring|)) (|ofCategory| *4 (|OrderedAbelianMonoidSup|)) (|ofCategory| *5 (|OrderedSet|)) (|ofCategory| *3 (|IntegralDomain|)))) (|LazardQuotient2| (*1 *1 *1 *1 *1 *2) (AND (|isDomain| *2 (|NonNegativeInteger|)) (|ofCategory| *1 (|RecursivePolynomialCategory| *3 *4 *5)) (|ofCategory| *3 (|Ring|)) (|ofCategory| *4 (|OrderedAbelianMonoidSup|)) (|ofCategory| *5 (|OrderedSet|)) (|ofCategory| *3 (|IntegralDomain|)))) (|nextsubResultant2| (*1 *1 *1 *1 *1 *1) (AND (|ofCategory| *1 (|RecursivePolynomialCategory| *2 *3 *4)) (|ofCategory| *2 (|Ring|)) (|ofCategory| *3 (|OrderedAbelianMonoidSup|)) (|ofCategory| *4 (|OrderedSet|)) (|ofCategory| *2 (|IntegralDomain|)))) (|gcd| (*1 *2 *2 *1) (AND (|ofCategory| *1 (|RecursivePolynomialCategory| *2 *3 *4)) (|ofCategory| *2 (|Ring|)) (|ofCategory| *3 (|OrderedAbelianMonoidSup|)) (|ofCategory| *4 (|OrderedSet|)) (|ofCategory| *2 (|GcdDomain|)))) (|primitivePart!| (*1 *1 *1) (AND (|ofCategory| *1 (|RecursivePolynomialCategory| *2 *3 *4)) (|ofCategory| *2 (|Ring|)) (|ofCategory| *3 (|OrderedAbelianMonoidSup|)) (|ofCategory| *4 (|OrderedSet|)) (|ofCategory| *2 (|GcdDomain|)))) (|mainContent| (*1 *1 *1) (AND (|ofCategory| *1 (|RecursivePolynomialCategory| *2 *3 *4)) (|ofCategory| *2 (|Ring|)) (|ofCategory| *3 (|OrderedAbelianMonoidSup|)) (|ofCategory| *4 (|OrderedSet|)) (|ofCategory| *2 (|GcdDomain|)))) (|mainPrimitivePart| (*1 *1 *1) (AND (|ofCategory| *1 (|RecursivePolynomialCategory| *2 *3 *4)) (|ofCategory| *2 (|Ring|)) (|ofCategory| *3 (|OrderedAbelianMonoidSup|)) (|ofCategory| *4 (|OrderedSet|)) (|ofCategory| *2 (|GcdDomain|)))) (|mainSquareFreePart| (*1 *1 *1) (AND (|ofCategory| *1 (|RecursivePolynomialCategory| *2 *3 *4)) (|ofCategory| *2 (|Ring|)) (|ofCategory| *3 (|OrderedAbelianMonoidSup|)) (|ofCategory| *4 (|OrderedSet|)) (|ofCategory| *2 (|GcdDomain|))))) (|Join| (|PolynomialCategory| |t#1| |t#2| |t#3|) (CATEGORY |domain| (SIGNATURE |mvar| (|t#3| $)) (SIGNATURE |mdeg| ((|NonNegativeInteger|) $)) (SIGNATURE |init| ($ $)) (SIGNATURE |head| ($ $)) (SIGNATURE |tail| ($ $)) (SIGNATURE |deepestTail| ($ $)) (SIGNATURE |iteratedInitials| ((|List| $) $)) (SIGNATURE |deepestInitial| ($ $)) (SIGNATURE |leadingCoefficient| ($ $ |t#3|)) (SIGNATURE |reductum| ($ $ |t#3|)) (SIGNATURE |monic?| ((|Boolean|) $)) (SIGNATURE |quasiMonic?| ((|Boolean|) $)) (SIGNATURE |mainMonomial| ($ $)) (SIGNATURE |leastMonomial| ($ $)) (SIGNATURE |mainCoefficients| ((|List| $) $)) (SIGNATURE |mainMonomials| ((|List| $) $)) (SIGNATURE |RittWuCompare| ((|Union| (|Boolean|) "failed") $ $)) (SIGNATURE |infRittWu?| ((|Boolean|) $ $)) (SIGNATURE |supRittWu?| ((|Boolean|) $ $)) (SIGNATURE |reduced?| ((|Boolean|) $ $)) (SIGNATURE |reduced?| ((|Boolean|) $ (|List| $))) (SIGNATURE |headReduced?| ((|Boolean|) $ $)) (SIGNATURE |headReduced?| ((|Boolean|) $ (|List| $))) (SIGNATURE |initiallyReduced?| ((|Boolean|) $ $)) (SIGNATURE |initiallyReduced?| ((|Boolean|) $ (|List| $))) (SIGNATURE |normalized?| ((|Boolean|) $ $)) (SIGNATURE |normalized?| ((|Boolean|) $ (|List| $))) (SIGNATURE |prem| ($ $ $)) (SIGNATURE |pquo| ($ $ $)) (SIGNATURE |prem| ($ $ $ |t#3|)) (SIGNATURE |pquo| ($ $ $ |t#3|)) (SIGNATURE |lazyPrem| ($ $ $)) (SIGNATURE |lazyPquo| ($ $ $)) (SIGNATURE |lazyPrem| ($ $ $ |t#3|)) (SIGNATURE |lazyPquo| ($ $ $ |t#3|)) (SIGNATURE |lazyPremWithDefault| ((|Record| (|:| |coef| $) (|:| |gap| (|NonNegativeInteger|)) (|:| |remainder| $)) $ $)) (SIGNATURE |lazyPremWithDefault| ((|Record| (|:| |coef| $) (|:| |gap| (|NonNegativeInteger|)) (|:| |remainder| $)) $ $ |t#3|)) (SIGNATURE |lazyPseudoDivide| ((|Record| (|:| |coef| $) (|:| |gap| (|NonNegativeInteger|)) (|:| |quotient| $) (|:| |remainder| $)) $ $)) (SIGNATURE |lazyPseudoDivide| ((|Record| (|:| |coef| $) (|:| |gap| (|NonNegativeInteger|)) (|:| |quotient| $) (|:| |remainder| $)) $ $ |t#3|)) (SIGNATURE |pseudoDivide| ((|Record| (|:| |quotient| $) (|:| |remainder| $)) $ $)) (SIGNATURE |monicModulo| ($ $ $)) (SIGNATURE |lazyResidueClass| ((|Record| (|:| |polnum| $) (|:| |polden| $) (|:| |power| (|NonNegativeInteger|))) $ $)) (SIGNATURE |headReduce| ($ $ $)) (SIGNATURE |initiallyReduce| ($ $ $)) (IF (|has| |t#3| (|ConvertibleTo| (|Symbol|))) (PROGN (ATTRIBUTE (|CoercibleTo| (|Polynomial| |t#1|))) (ATTRIBUTE (|ConvertibleTo| (|Polynomial| |t#1|))) (IF (|has| |t#1| (|Algebra| (|Fraction| (|Integer|)))) (PROGN (SIGNATURE |retractIfCan| ((|Union| $ "failed") (|Polynomial| (|Fraction| (|Integer|))))) (SIGNATURE |retract| ($ (|Polynomial| (|Fraction| (|Integer|))))) (SIGNATURE |convert| ($ (|Polynomial| (|Fraction| (|Integer|))))) (SIGNATURE |retractIfCan| ((|Union| $ "failed") (|Polynomial| (|Integer|)))) (SIGNATURE |retract| ($ (|Polynomial| (|Integer|)))) (SIGNATURE |convert| ($ (|Polynomial| (|Integer|)))) (IF (|has| |t#1| (|QuotientFieldCategory| (|Integer|))) |%noBranch| (PROGN (SIGNATURE |retractIfCan| ((|Union| $ "failed") (|Polynomial| |t#1|))) (SIGNATURE |retract| ($ (|Polynomial| |t#1|)))))) |%noBranch|) (IF (|has| |t#1| (|Algebra| (|Integer|))) (IF (|has| |t#1| (|Algebra| (|Fraction| (|Integer|)))) |%noBranch| (PROGN (SIGNATURE |retractIfCan| ((|Union| $ "failed") (|Polynomial| (|Integer|)))) (SIGNATURE |retract| ($ (|Polynomial| (|Integer|)))) (SIGNATURE |convert| ($ (|Polynomial| (|Integer|)))) (IF (|has| |t#1| (|IntegerNumberSystem|)) |%noBranch| (PROGN (SIGNATURE |retractIfCan| ((|Union| $ "failed") (|Polynomial| |t#1|))) (SIGNATURE |retract| ($ (|Polynomial| |t#1|))))))) |%noBranch|) (IF (|has| |t#1| (|Algebra| (|Integer|))) |%noBranch| (IF (|has| |t#1| (|Algebra| (|Fraction| (|Integer|)))) |%noBranch| (PROGN (SIGNATURE |retractIfCan| ((|Union| $ "failed") (|Polynomial| |t#1|))) (SIGNATURE |retract| ($ (|Polynomial| |t#1|)))))) (SIGNATURE |convert| ($ (|Polynomial| |t#1|))) (IF (|has| |t#1| (|RetractableTo| (|Integer|))) (ATTRIBUTE (|ConvertibleTo| (|String|))) |%noBranch|)) |%noBranch|) (IF (|has| |t#1| (|IntegralDomain|)) (PROGN (SIGNATURE |primPartElseUnitCanonical| ($ $)) (SIGNATURE |primPartElseUnitCanonical!| ($ $)) (SIGNATURE |exactQuotient| ($ $ |t#1|)) (SIGNATURE |exactQuotient!| ($ $ |t#1|)) (SIGNATURE |exactQuotient| ($ $ $)) (SIGNATURE |exactQuotient!| ($ $ $)) (SIGNATURE |subResultantGcd| ($ $ $)) (SIGNATURE |extendedSubResultantGcd| ((|Record| (|:| |gcd| $) (|:| |coef1| $) (|:| |coef2| $)) $ $)) (SIGNATURE |halfExtendedSubResultantGcd1| ((|Record| (|:| |gcd| $) (|:| |coef1| $)) $ $)) (SIGNATURE |halfExtendedSubResultantGcd2| ((|Record| (|:| |gcd| $) (|:| |coef2| $)) $ $)) (SIGNATURE |resultant| ($ $ $)) (SIGNATURE |subResultantChain| ((|List| $) $ $)) (SIGNATURE |lastSubResultant| ($ $ $)) (SIGNATURE |LazardQuotient| ($ $ $ (|NonNegativeInteger|))) (SIGNATURE |LazardQuotient2| ($ $ $ $ (|NonNegativeInteger|))) (SIGNATURE |nextsubResultant2| ($ $ $ $ $))) |%noBranch|) (IF (|has| |t#1| (|GcdDomain|)) (PROGN (SIGNATURE |gcd| (|t#1| |t#1| $)) (SIGNATURE |primitivePart!| ($ $)) (SIGNATURE |mainContent| ($ $)) (SIGNATURE |mainPrimitivePart| ($ $)) (SIGNATURE |mainSquareFreePart| ($ $))) |%noBranch|))) @@ -3278,7 +3278,7 @@ NIL ((|upDateBranches| ((#1=(|List| #2=(|Record| (|:| |val| #3=(|List| |#4|)) (|:| |tower| |#5|))) #3# #4=(|List| |#5|) #1# #5=(|Record| (|:| |done| #4#) (|:| |todo| #1#)) #6=(|NonNegativeInteger|)) 114 T ELT)) (|transcendentalDecompose| (#7=(#5# |#4| |#5|) 64 T ELT) (#8=(#5# |#4| |#5| #6#) 63 T ELT)) (|printInfo| (((|Void|) #1# #6#) 99 T ELT)) (|numberOfVariables| (#9=(#6# #3# #4#) 30 T ELT)) (|internalDecompose| (#7# 66 T ELT) (#8# 65 T ELT) ((#5# |#4| |#5| #6# #10=(|Boolean|)) 67 T ELT)) (|decompose| ((#4# #3# #4# #10# #10# #10# #10# #10#) 86 T ELT) ((#4# #3# #4# #10# #10#) 87 T ELT)) (|convert| (((|String|) #2#) 92 T ELT)) (|algebraicDecompose| ((#5# |#4| |#5| #10#) 62 T ELT)) (|KrullNumber| (#9# 21 T ELT))) (((|RegularSetDecompositionPackage| |#1| |#2| |#3| |#4| |#5|) (CATEGORY |package| (SIGNATURE |KrullNumber| #1=(#2=(|NonNegativeInteger|) #3=(|List| |#4|) #4=(|List| |#5|))) (SIGNATURE |numberOfVariables| #1#) (SIGNATURE |algebraicDecompose| (#5=(|Record| (|:| |done| #4#) (|:| |todo| #6=(|List| #7=(|Record| (|:| |val| #3#) (|:| |tower| |#5|))))) |#4| |#5| #8=(|Boolean|))) (SIGNATURE |transcendentalDecompose| #9=(#5# |#4| |#5| #2#)) (SIGNATURE |transcendentalDecompose| #10=(#5# |#4| |#5|)) (SIGNATURE |internalDecompose| (#5# |#4| |#5| #2# #8#)) (SIGNATURE |internalDecompose| #9#) (SIGNATURE |internalDecompose| #10#) (SIGNATURE |decompose| (#4# #3# #4# #8# #8#)) (SIGNATURE |decompose| (#4# #3# #4# #8# #8# #8# #8# #8#)) (SIGNATURE |upDateBranches| (#6# #3# #4# #6# #5# #2#)) (SIGNATURE |convert| ((|String|) #7#)) (SIGNATURE |printInfo| ((|Void|) #6# #2#))) (|GcdDomain|) (|OrderedAbelianMonoidSup|) (|OrderedSet|) (|RecursivePolynomialCategory| |#1| |#2| |#3|) (|RegularTriangularSetCategory| |#1| |#2| |#3| |#4|)) (T |RegularSetDecompositionPackage|)) ((|printInfo| #1=(*1 *2 *3 *4) (AND (|isDomain| *3 (|List| (|Record| (|:| |val| #2=(|List| *8)) (|:| |tower| *9)))) (|isDomain| *4 #3=(|NonNegativeInteger|)) #4=(|ofCategory| *8 #5=(|RecursivePolynomialCategory| *5 *6 *7)) #6=(|ofCategory| *9 (|RegularTriangularSetCategory| *5 *6 *7 *8)) #7=(|ofCategory| *5 #8=(|GcdDomain|)) #9=(|ofCategory| *6 #10=(|OrderedAbelianMonoidSup|)) #11=(|ofCategory| *7 #12=(|OrderedSet|)) (|isDomain| *2 (|Void|)) #13=(|isDomain| *1 (|RegularSetDecompositionPackage| *5 *6 *7 *8 *9)))) (|convert| (*1 *2 *3) (AND (|isDomain| *3 (|Record| (|:| |val| (|List| *7)) (|:| |tower| *8))) (|ofCategory| *7 (|RecursivePolynomialCategory| *4 *5 *6)) (|ofCategory| *8 (|RegularTriangularSetCategory| *4 *5 *6 *7)) (|ofCategory| *4 #8#) (|ofCategory| *5 #10#) (|ofCategory| *6 #12#) (|isDomain| *2 (|String|)) (|isDomain| *1 (|RegularSetDecompositionPackage| *4 *5 *6 *7 *8)))) (|upDateBranches| (*1 *2 *3 *4 *2 *5 *6) (AND (|isDomain| *5 (|Record| (|:| |done| #14=(|List| *11)) (|:| |todo| (|List| (|Record| (|:| |val| *3) #15=(|:| |tower| *11)))))) (|isDomain| *6 #3#) (|isDomain| *2 (|List| (|Record| (|:| |val| #16=(|List| *10)) #15#))) (|isDomain| *3 #16#) (|isDomain| *4 #14#) (|ofCategory| *10 #17=(|RecursivePolynomialCategory| *7 *8 *9)) (|ofCategory| *11 (|RegularTriangularSetCategory| *7 *8 *9 *10)) #18=(|ofCategory| *7 #8#) #19=(|ofCategory| *8 #10#) #20=(|ofCategory| *9 #12#) (|isDomain| *1 (|RegularSetDecompositionPackage| *7 *8 *9 *10 *11)))) (|decompose| (*1 *2 *3 *2 *4 *4 *4 *4 *4) #21=(AND (|isDomain| *2 #22=(|List| *9)) #23=(|isDomain| *3 #2#) (|isDomain| *4 #24=(|Boolean|)) #4# #6# #7# #9# #11# #13#)) (|decompose| (*1 *2 *3 *2 *4 *4) #21#) (|internalDecompose| #1# #25=(AND #7# #9# #11# (|ofCategory| *3 #5#) #26=(|isDomain| *2 (|Record| (|:| |done| (|List| *4)) (|:| |todo| (|List| (|Record| (|:| |val| (|List| *3)) (|:| |tower| *4)))))) (|isDomain| *1 (|RegularSetDecompositionPackage| *5 *6 *7 *3 *4)) (|ofCategory| *4 (|RegularTriangularSetCategory| *5 *6 *7 *3)))) (|internalDecompose| #27=(*1 *2 *3 *4 *5) #28=(AND #29=(|isDomain| *5 #3#) #30=(|ofCategory| *6 #8#) #31=(|ofCategory| *7 #10#) #32=(|ofCategory| *8 #12#) #33=(|ofCategory| *3 (|RecursivePolynomialCategory| *6 *7 *8)) #26# #34=(|isDomain| *1 (|RegularSetDecompositionPackage| *6 *7 *8 *3 *4)) #35=(|ofCategory| *4 (|RegularTriangularSetCategory| *6 *7 *8 *3)))) (|internalDecompose| (*1 *2 *3 *4 *5 *6) (AND #29# (|isDomain| *6 #24#) #18# #19# #20# (|ofCategory| *3 #17#) #26# (|isDomain| *1 (|RegularSetDecompositionPackage| *7 *8 *9 *3 *4)) (|ofCategory| *4 (|RegularTriangularSetCategory| *7 *8 *9 *3)))) (|transcendentalDecompose| #1# #25#) (|transcendentalDecompose| #27# #28#) (|algebraicDecompose| #27# (AND (|isDomain| *5 #24#) #30# #31# #32# #33# #26# #34# #35#)) (|numberOfVariables| #1# #36=(AND #23# (|isDomain| *4 #22#) #4# #6# #7# #9# #11# (|isDomain| *2 #3#) #13#)) (|KrullNumber| #1# #36#)) -((|purelyTranscendental?| (#1=(#2=(|Boolean|) |#5| $) 26 T ELT)) (|purelyAlgebraicLeadingMonomial?| (#1# 29 T ELT)) (|purelyAlgebraic?| (#1# 18 T ELT) ((#2# $) 52 T ELT)) (|intersect| #3=((#4=(|List| $) |#5| $) NIL T ELT) (#5=(#4# #6=(|List| |#5|) $) 94 T ELT) (#7=(#4# #6# #4#) 92 T ELT) (#8=(#4# |#5| #4#) 95 T ELT)) (|extend| (($ $ |#5|) NIL T ELT) #3# (#8# 73 T ELT) (#5# 75 T ELT) (#7# 77 T ELT)) (|augment| #3# (#8# 64 T ELT) (#5# 69 T ELT) (#7# 71 T ELT)) (|algebraicCoefficients?| (#1# 32 T ELT))) +((|purelyTranscendental?| (#1=(#2=(|Boolean|) |#5| $) 26 T ELT)) (|purelyAlgebraicLeadingMonomial?| (#1# 29 T ELT)) (|purelyAlgebraic?| (#1# 18 T ELT) ((#2# $) 54 T ELT)) (|intersect| #3=((#4=(|List| $) |#5| $) NIL T ELT) (#5=(#4# #6=(|List| |#5|) $) 96 T ELT) (#7=(#4# #6# #4#) 94 T ELT) (#8=(#4# |#5| #4#) 97 T ELT)) (|extend| (($ $ |#5|) NIL T ELT) #3# (#8# 75 T ELT) (#5# 77 T ELT) (#7# 79 T ELT)) (|augment| #3# (#8# 66 T ELT) (#5# 71 T ELT) (#7# 73 T ELT)) (|algebraicCoefficients?| (#1# 32 T ELT))) (((|RegularTriangularSetCategory&| |#1| |#2| |#3| |#4| |#5|) (CATEGORY |package| (SIGNATURE |extend| #1=(#2=(|List| |#1|) #3=(|List| |#5|) #2#)) (SIGNATURE |extend| #4=(#2# #3# |#1|)) (SIGNATURE |extend| #5=(#2# |#5| #2#)) (SIGNATURE |extend| #6=(#2# |#5| |#1|)) (SIGNATURE |augment| #1#) (SIGNATURE |augment| #4#) (SIGNATURE |augment| #5#) (SIGNATURE |augment| #6#) (SIGNATURE |intersect| #5#) (SIGNATURE |intersect| #1#) (SIGNATURE |intersect| #4#) (SIGNATURE |intersect| #6#) (SIGNATURE |purelyAlgebraicLeadingMonomial?| #7=(#8=(|Boolean|) |#5| |#1|)) (SIGNATURE |purelyAlgebraic?| (#8# |#1|)) (SIGNATURE |algebraicCoefficients?| #7#) (SIGNATURE |purelyTranscendental?| #7#) (SIGNATURE |purelyAlgebraic?| #7#) (SIGNATURE |extend| (|#1| |#1| |#5|))) (|RegularTriangularSetCategory| |#2| |#3| |#4| |#5|) (|GcdDomain|) (|OrderedAbelianMonoidSup|) (|OrderedSet|) (|RecursivePolynomialCategory| |#2| |#3| |#4|)) (T |RegularTriangularSetCategory&|)) NIL ((~= (#1=((|Boolean|) $ $) 7 T ELT)) (|zeroSetSplitIntoTriangularSystems| (((|List| (|Record| (|:| |close| $) (|:| |open| (|List| |#4|)))) (|List| |#4|)) 91 T ELT)) (|zeroSetSplit| (((|List| $) (|List| |#4|)) 92 T ELT) (((|List| $) (|List| |#4|) (|Boolean|)) 120 T ELT)) (|variables| (((|List| |#3|) . #2=($)) 39 T ELT)) (|trivialIdeal?| (#3=(#4=(|Boolean|) $) 32 T ELT)) (|triangular?| (#3# 23 (|has| |#1| . #5=((|IntegralDomain|))) ELT)) (|stronglyReduced?| ((#6=(|Boolean|) |#4| . #7=($)) 107 T ELT) (#8=(#6# $) 103 T ELT)) (|stronglyReduce| ((|#4| |#4| . #9=($)) 98 T ELT)) (|squareFreePart| (((|List| (|Record| (|:| |val| |#4|) (|:| |tower| $))) |#4| $) 135 T ELT)) (|sort| (((|Record| (|:| |under| $) (|:| |floor| $) (|:| |upper| $)) $ |#3|) 33 T ELT)) (|select| (($ (|Mapping| #10=(|Boolean|) |#4|) . #11=($)) 67 (|has| $ (|FiniteAggregate| |#4|)) ELT) (((|Union| |#4| . #12=(#13="failed")) $ |#3|) 85 T ELT)) (|sample| (#14=($) 59 T CONST)) (|roughUnitIdeal?| (#3# 28 (|has| |#1| . #5#) ELT)) (|roughSubIdeal?| (#15=(#4# $ $) 30 (|has| |#1| . #5#) ELT)) (|roughEqualIdeals?| (#15# 29 (|has| |#1| . #5#) ELT)) (|roughBase?| (#3# 31 (|has| |#1| . #5#) ELT)) (|rewriteSetWithReduction| (((|List| |#4|) (|List| |#4|) $ (|Mapping| |#4| |#4| |#4|) (|Mapping| #6# |#4| |#4|)) 99 T ELT)) (|rewriteIdealWithRemainder| (((|List| |#4|) (|List| |#4|) . #16=($)) 24 (|has| |#1| . #5#) ELT)) (|rewriteIdealWithHeadRemainder| (((|List| |#4|) (|List| |#4|) . #16#) 25 (|has| |#1| . #5#) ELT)) (|retractIfCan| (((|Union| $ "failed") (|List| |#4|)) 42 T ELT)) (|retract| (($ (|List| |#4|)) 41 T ELT)) (|rest| ((#17=(|Union| $ #13#) $) 88 T ELT)) (|removeZero| ((|#4| |#4| . #9#) 95 T ELT)) (|removeDuplicates| (($ $) 69 (AND (|has| |#4| . #18=((|BasicType|))) (|has| $ (|FiniteAggregate| |#4|))) ELT)) (|remove| (($ |#4| $) 68 (AND (|has| |#4| . #18#) (|has| $ (|FiniteAggregate| |#4|))) ELT) (($ (|Mapping| #10# |#4|) . #11#) 66 (|has| $ (|FiniteAggregate| |#4|)) ELT)) (|remainder| (((|Record| (|:| |rnum| |#1|) (|:| |polnum| |#4|) (|:| |den| |#1|)) |#4| $) 26 (|has| |#1| . #5#) ELT)) (|reduced?| ((#6# |#4| $ (|Mapping| #6# |#4| |#4|)) 108 T ELT)) (|reduceByQuasiMonic| ((|#4| |#4| . #9#) 93 T ELT)) (|reduce| ((|#4| (|Mapping| |#4| |#4| |#4|) $ |#4| |#4|) 54 (|has| |#4| . #19=((|BasicType|))) ELT) ((|#4| (|Mapping| |#4| |#4| |#4|) $ |#4|) 50 T ELT) ((|#4| (|Mapping| |#4| |#4| |#4|) $) 49 T ELT) ((|#4| |#4| $ (|Mapping| |#4| |#4| |#4|) (|Mapping| #6# |#4| |#4|)) 100 T ELT)) (|quasiComponent| (((|Record| (|:| |close| (|List| |#4|)) (|:| |open| (|List| |#4|))) $) 111 T ELT)) (|purelyTranscendental?| (((|Boolean|) |#4| $) 145 T ELT)) (|purelyAlgebraicLeadingMonomial?| (((|Boolean|) |#4| $) 142 T ELT)) (|purelyAlgebraic?| (((|Boolean|) |#4| $) 146 T ELT) (((|Boolean|) $) 143 T ELT)) (|normalized?| ((#6# |#4| . #7#) 110 T ELT) (#8# 109 T ELT)) (|mvar| ((|#3| $) 40 T ELT)) (|members| (((|List| |#4|) $) 48 T ELT)) (|member?| ((#20=(|Boolean|) |#4| $) 53 (|has| |#4| . #19#) ELT)) (|map!| (($ (|Mapping| |#4| |#4|) $) 117 T ELT)) (|map| (($ (|Mapping| |#4| |#4|) $) 60 T ELT)) (|mainVariables| (((|List| |#3|) . #2#) 38 T ELT)) (|mainVariable?| ((#4# |#3| $) 37 T ELT)) (|latex| (((|String|) $) 11 T ELT)) (|lastSubResultantElseSplit| (((|Union| |#4| (|List| $)) |#4| |#4| $) 137 T ELT)) (|lastSubResultant| (((|List| (|Record| (|:| |val| |#4|) (|:| |tower| $))) |#4| |#4| $) 136 T ELT)) (|last| (((|Union| |#4| . #12#) . #21=($)) 89 T ELT)) (|invertibleSet| (((|List| $) |#4| $) 138 T ELT)) (|invertibleElseSplit?| (((|Union| (|Boolean|) (|List| $)) |#4| $) 141 T ELT)) (|invertible?| (((|List| (|Record| (|:| |val| (|Boolean|)) (|:| |tower| $))) |#4| $) 140 T ELT) (((|Boolean|) |#4| $) 139 T ELT)) (|intersect| (((|List| $) |#4| $) 134 T ELT) (((|List| $) (|List| |#4|) $) 133 T ELT) (((|List| $) (|List| |#4|) (|List| $)) 132 T ELT) (((|List| $) |#4| (|List| $)) 131 T ELT)) (|internalAugment| (($ |#4| $) 126 T ELT) (($ (|List| |#4|) $) 125 T ELT)) (|initials| (((|List| |#4|) $) 113 T ELT)) (|initiallyReduced?| ((#6# |#4| . #7#) 105 T ELT) (#8# 101 T ELT)) (|initiallyReduce| ((|#4| |#4| . #9#) 96 T ELT)) (|infRittWu?| ((#6# $ $) 116 T ELT)) (|headRemainder| (((|Record| (|:| |num| |#4|) (|:| |den| |#1|)) |#4| $) 27 (|has| |#1| . #5#) ELT)) (|headReduced?| ((#6# |#4| . #7#) 106 T ELT) (#8# 102 T ELT)) (|headReduce| ((|#4| |#4| . #9#) 97 T ELT)) (|hash| (((|SingleInteger|) $) 12 T ELT)) (|first| (((|Union| |#4| . #12#) . #21#) 90 T ELT)) (|find| (((|Union| |#4| "failed") (|Mapping| #20# |#4|) $) 51 T ELT)) (|extendIfCan| ((#17# $ |#4|) 84 T ELT)) (|extend| (($ $ |#4|) 83 T ELT) (((|List| $) |#4| $) 124 T ELT) (((|List| $) |#4| (|List| $)) 123 T ELT) (((|List| $) (|List| |#4|) $) 122 T ELT) (((|List| $) (|List| |#4|) (|List| $)) 121 T ELT)) (|every?| ((#20# (|Mapping| #20# |#4|) . #22=($)) 46 T ELT)) (|eval| (($ $ (|List| |#4|) (|List| |#4|)) 64 (AND (|has| |#4| (|Evalable| |#4|)) (|has| |#4| . #23=((|SetCategory|)))) ELT) (($ $ |#4| |#4|) 63 (AND (|has| |#4| (|Evalable| |#4|)) (|has| |#4| . #23#)) ELT) (($ $ (|Equation| |#4|)) 62 (AND (|has| |#4| (|Evalable| |#4|)) (|has| |#4| . #23#)) ELT) (($ $ (|List| (|Equation| |#4|))) 61 (AND (|has| |#4| (|Evalable| |#4|)) (|has| |#4| . #23#)) ELT)) (|eq?| ((#24=(|Boolean|) $ $) 55 T ELT)) (|empty?| ((#24# $) 58 T ELT)) (|empty| (#14# 57 T ELT)) (|degree| (#25=((|NonNegativeInteger|) $) 112 T ELT)) (|count| ((#26=(|NonNegativeInteger|) |#4| $) 52 (|has| |#4| . #19#) ELT) ((#26# (|Mapping| #20# |#4|) $) 47 T ELT)) (|copy| (($ $) 56 T ELT)) (|convert| ((#27=(|InputForm|) $) 70 (|has| |#4| (|ConvertibleTo| #27#)) ELT)) (|construct| (($ (|List| |#4|)) 65 T ELT)) (|collectUpper| (($ $ |#3|) 34 T ELT)) (|collectUnder| (($ $ |#3|) 36 T ELT)) (|collectQuasiMonic| (($ $) 94 T ELT)) (|collect| (($ $ |#3|) 35 T ELT)) (|coerce| (((|OutputForm|) . #28=($)) 13 T ELT) (((|List| |#4|) . #28#) 43 T ELT)) (|coHeight| (#25# 82 (|has| |#3| (|Finite|)) ELT)) (|before?| (#1# 6 T ELT)) (|basicSet| (((|Union| (|Record| #29=(|:| |bas| $) (|:| |top| (|List| |#4|))) . #30=(#13#)) (|List| |#4|) (|Mapping| #6# |#4| |#4|)) 115 T ELT) (((|Union| (|Record| #29# (|:| |top| (|List| |#4|))) . #30#) (|List| |#4|) (|Mapping| #6# |#4|) (|Mapping| #6# |#4| |#4|)) 114 T ELT)) (|autoReduced?| ((#6# $ (|Mapping| #6# |#4| (|List| |#4|))) 104 T ELT)) (|augment| (((|List| $) |#4| $) 130 T ELT) (((|List| $) |#4| (|List| $)) 129 T ELT) (((|List| $) (|List| |#4|) $) 128 T ELT) (((|List| $) (|List| |#4|) (|List| $)) 127 T ELT)) (|any?| ((#20# (|Mapping| #20# |#4|) . #22#) 45 T ELT)) (|algebraicVariables| (((|List| |#3|) $) 87 T ELT)) (|algebraicCoefficients?| (((|Boolean|) |#4| $) 144 T ELT)) (|algebraic?| ((#6# |#3| $) 86 T ELT)) (= (#1# 8 T ELT)) (|#| ((#26# $) 44 T ELT))) @@ -3307,7 +3307,7 @@ NIL ((|rur| ((#1=(|List| (|Record| (|:| |complexRoots| (|SparseUnivariatePolynomial| |#1|)) (|:| |coordinates| #2=(|List| (|Polynomial| |#1|))))) #2# #3=(|Boolean|) #3#) 88 T ELT) ((#1# #2#) 92 T ELT) ((#1# #2# #3#) 90 T ELT))) (((|RationalUnivariateRepresentationPackage| |#1| |#2|) (CATEGORY |package| (SIGNATURE |rur| (#1=(|List| (|Record| (|:| |complexRoots| (|SparseUnivariatePolynomial| |#1|)) (|:| |coordinates| #2=(|List| (|Polynomial| |#1|))))) #2# #3=(|Boolean|))) (SIGNATURE |rur| (#1# #2#)) (SIGNATURE |rur| (#1# #2# #3# #3#))) (|Join| (|EuclideanDomain|) (|CharacteristicZero|)) (|List| (|Symbol|))) (T |RationalUnivariateRepresentationPackage|)) ((|rur| (*1 *2 *3 *4 *4) #1=(AND (|isDomain| *4 (|Boolean|)) (|ofCategory| *5 #2=(|Join| (|EuclideanDomain|) (|CharacteristicZero|))) (|isDomain| *2 (|List| (|Record| (|:| |complexRoots| (|SparseUnivariatePolynomial| *5)) (|:| |coordinates| #3=(|List| (|Polynomial| *5)))))) (|isDomain| *1 (|RationalUnivariateRepresentationPackage| *5 *6)) (|isDomain| *3 #3#) (|ofType| *6 #4=(|List| (|Symbol|))))) (|rur| (*1 *2 *3) (AND (|ofCategory| *4 #2#) (|isDomain| *2 (|List| (|Record| (|:| |complexRoots| (|SparseUnivariatePolynomial| *4)) (|:| |coordinates| #5=(|List| (|Polynomial| *4)))))) (|isDomain| *1 (|RationalUnivariateRepresentationPackage| *4 *5)) (|isDomain| *3 #5#) (|ofType| *5 #4#))) (|rur| (*1 *2 *3 *4) #1#)) -((~= #1=(#2=(#3=(|Boolean|) $ $) NIL T ELT)) (|zero?| (#4=(#3# $) 132 T ELT)) (|unitNormal| (((|Record| (|:| |unit| $) (|:| |canonical| $) (|:| |associate| $)) $) NIL #5=(|has| |#1| (|Field|)) ELT)) (|unitCanonical| #6=(#7=($ $) NIL #5# ELT)) (|unit?| #8=(#4# NIL #5# ELT)) (|traceMatrix| #9=(#10=(#11=(|Matrix| |#1|) #12=(|Vector| $)) NIL T ELT) ((#11#) 117 T ELT)) (|trace| (#13=(|#1| $) 121 T ELT)) (|tableForDiscreteLogarithm| (((|Table| #14=(|PositiveInteger|) #15=(|NonNegativeInteger|)) #16=(|Integer|)) NIL #17=(|has| |#1| (|FiniteFieldCategory|)) ELT)) (|subtractIfCan| (#18=(#19=(|Union| $ #20="failed") $ $) NIL T ELT)) (|squareFreePart| #6#) (|squareFree| #21=(((|Factored| $) $) NIL #5# ELT)) (|sizeLess?| #22=(#2# NIL #5# ELT)) (|size| (#23=(#15#) 43 #24=(|has| |#1| (|Finite|)) ELT)) (|sample| (#25=($) NIL T CONST)) (|retractIfCan| (((|Union| #16# . #26=(#20#)) . #27=($)) NIL #28=(|has| |#1| (|RetractableTo| #16#)) ELT) (((|Union| #29=(|Fraction| #16#) . #26#) . #27#) NIL #30=(|has| |#1| (|RetractableTo| #29#)) ELT) (((|Union| |#1| . #26#) . #27#) NIL T ELT)) (|retract| ((#16# . #31=($)) NIL #28# ELT) ((#29# . #31#) NIL #30# ELT) #32=(#13# NIL T ELT)) (|represents| (($ #33=(|Vector| |#1|) #12#) NIL T ELT) (#34=($ #33#) 46 T ELT)) (|representationType| (((|Union| "prime" "polynomial" "normal" "cyclic")) NIL #17# ELT)) (|rem| #35=(#36=($ $ $) NIL #5# ELT)) (|regularRepresentation| ((#11# $ #12#) NIL T ELT) ((#11# $) NIL T ELT)) (|reducedSystem| ((#37=(|Matrix| #16#) #38=(|Matrix| $)) NIL #39=(|has| |#1| (|LinearlyExplicitRingOver| #16#)) ELT) ((#40=(|Record| (|:| |mat| #37#) (|:| |vec| (|Vector| #16#))) #38# #12#) NIL #39# ELT) ((#41=(|Record| (|:| |mat| #11#) (|:| |vec| #33#)) #38# #12#) 109 T ELT) ((#11# #38#) 104 T ELT)) (|reduce| (#42=($ |#2|) 62 T ELT) ((#19# (|Fraction| |#2|)) NIL #5# ELT)) (|recip| ((#19# $) NIL T ELT)) (|rank| ((#14#) 80 T ELT)) (|random| (#25# 47 #24# ELT)) (|quo| #35#) (|principalIdeal| (((|Record| (|:| |coef| #43=(|List| $)) #44=(|:| |generator| $)) #43#) NIL #5# ELT)) (|primitiveElement| #45=(#25# NIL #17# ELT)) (|primitive?| (#4# NIL #17# ELT)) (|primeFrobenius| (#46=($ $ #15#) NIL #17# ELT) #47=(#7# NIL #17# ELT)) (|prime?| #8#) (|order| (#48=(#14# $) NIL #17# ELT) (((|OnePointCompletion| #14#) $) NIL #17# ELT)) (|opposite?| #1#) (|one?| (#4# NIL T ELT)) (|norm| #32#) (|nextItem| (#49=((|Maybe| $) $) NIL #17# ELT)) (|multiEuclidean| (((|Union| #43# #20#) #43# $) NIL #5# ELT)) (|minimalPolynomial| (#50=(|#2| $) 87 #5# ELT)) (|lookup| (#48# 140 #24# ELT)) (|lift| (#50# 59 T ELT)) (|leftReducedSystem| ((#37# #12#) NIL #39# ELT) ((#40# . #51=(#12# $)) NIL #39# ELT) ((#41# . #51#) NIL T ELT) #9#) (|lcm| #52=(($ #43#) NIL #5# ELT) #35#) (|latex| (((|String|) $) NIL T ELT)) (|inv| #6#) (|init| (#25# NIL #17# CONST)) (|index| (($ #14#) 131 #24# ELT)) (|hash| (((|SingleInteger|) $) NIL T ELT)) (|generator| (#25# 123 T ELT)) (|gcdPolynomial| ((#53=(|SparseUnivariatePolynomial| $) #53# #53#) NIL #5# ELT)) (|gcd| #52# #35#) (|factorsOfCyclicGroupSize| (((|List| (|Record| (|:| |factor| #16#) (|:| |exponent| #16#)))) NIL #17# ELT)) (|factor| #21#) (|extendedEuclidean| (((|Union| (|Record| #54=(|:| |coef1| $) #55=(|:| |coef2| $)) #20#) $ $ $) NIL #5# ELT) (((|Record| #54# #55# #44#) $ $) NIL #5# ELT)) (|exquo| (#18# NIL #5# ELT)) (|expressIdealMember| (((|Maybe| #43#) #43# $) NIL #5# ELT)) (|euclideanSize| (#56=(#15# $) NIL #5# ELT)) (|divide| (((|Record| (|:| |quotient| $) (|:| |remainder| $)) $ $) NIL #5# ELT)) (|discriminant| ((|#1| #12#) NIL T ELT) ((|#1|) 113 T ELT)) (|discreteLog| (#56# NIL #17# ELT) (((|Union| #15# #20#) $ $) NIL #17# ELT)) (|differentiate| #57=(#46# NIL #58=(OR (AND (|has| |#1| (|DifferentialSpace|)) #5#) #17#) ELT) #59=(#7# NIL #58# ELT) #60=(($ $ #61=(|List| #62=(|Symbol|)) (|List| #15#)) NIL #63=(AND #5# (|has| |#1| (|PartialDifferentialSpace| #62#))) ELT) #64=(($ $ #62# #15#) NIL #63# ELT) #65=(($ $ #61#) NIL #63# ELT) #66=(($ $ #62#) NIL #63# ELT) #67=(($ $ #68=(|Mapping| |#1| |#1|)) NIL #5# ELT) #69=(($ $ #68# #15#) NIL #5# ELT)) (|derivationCoordinates| ((#11# #12# #68#) NIL #5# ELT)) (|definingPolynomial| ((|#2|) 77 T ELT)) (|createPrimitiveElement| #45#) (|coordinates| ((#33# $ #12#) 92 T ELT) ((#11# #12# #12#) NIL T ELT) (#70=(#33# $) 72 T ELT) (#10# 88 T ELT)) (|convert| (#70# NIL T ELT) (#34# NIL T ELT) (#50# NIL T ELT) (#42# NIL T ELT)) (|conditionP| (((|Union| #12# #20#) #38#) NIL #17# ELT)) (|coerce| (((|OutputForm|) $) 58 T ELT) (($ #16#) 53 T ELT) (($ |#1|) 55 T ELT) #6# (($ #29#) NIL (OR #5# #30#) ELT)) (|charthRoot| #47# (#49# NIL (|has| |#1| (|CharacteristicNonZero|)) ELT)) (|characteristicPolynomial| (#50# 85 T ELT)) (|characteristic| (#23# 79 T CONST)) (|before?| #1#) (|basis| ((#12#) 84 T ELT)) (|associates?| #22#) (|annihilate?| #1#) (|Zero| (#25# 32 T CONST)) (|One| (#25# 19 T CONST)) (D #57# #59# #60# #64# #65# #66# #67# #69#) (= (#2# 64 T ELT)) (/ #35#) (- (#7# 68 T ELT) (#36# NIL T ELT)) (+ (#36# 66 T ELT)) (** (($ $ #14#) NIL T ELT) (#46# NIL T ELT) (($ $ #16#) NIL #5# ELT)) (* (($ #14# $) NIL T ELT) (($ #15# $) NIL T ELT) (($ #16# $) 51 T ELT) (#36# 70 T ELT) (($ $ |#1|) NIL T ELT) (($ |#1| $) 48 T ELT) (($ #29# $) NIL #5# ELT) (($ $ #29#) NIL #5# ELT))) +((~= #1=(#2=(#3=(|Boolean|) $ $) NIL T ELT)) (|zero?| (#4=(#3# $) 135 T ELT)) (|unitNormal| (((|Record| (|:| |unit| $) (|:| |canonical| $) (|:| |associate| $)) $) NIL #5=(|has| |#1| (|Field|)) ELT)) (|unitCanonical| #6=(#7=($ $) NIL #5# ELT)) (|unit?| #8=(#4# NIL #5# ELT)) (|traceMatrix| #9=(#10=(#11=(|Matrix| |#1|) #12=(|Vector| $)) NIL T ELT) ((#11#) 120 T ELT)) (|trace| (#13=(|#1| $) 124 T ELT)) (|tableForDiscreteLogarithm| (((|Table| #14=(|PositiveInteger|) #15=(|NonNegativeInteger|)) #16=(|Integer|)) NIL #17=(|has| |#1| (|FiniteFieldCategory|)) ELT)) (|subtractIfCan| ((#18=(|Maybe| $) $ $) NIL T ELT)) (|squareFreePart| #6#) (|squareFree| #19=(((|Factored| $) $) NIL #5# ELT)) (|sizeLess?| #20=(#2# NIL #5# ELT)) (|size| (#21=(#15#) 46 #22=(|has| |#1| (|Finite|)) ELT)) (|sample| (#23=($) NIL T CONST)) (|retractIfCan| (((|Union| #16# . #24=(#25="failed")) . #26=($)) NIL #27=(|has| |#1| (|RetractableTo| #16#)) ELT) (((|Union| #28=(|Fraction| #16#) . #24#) . #26#) NIL #29=(|has| |#1| (|RetractableTo| #28#)) ELT) (((|Union| |#1| . #24#) . #26#) NIL T ELT)) (|retract| ((#16# . #30=($)) NIL #27# ELT) ((#28# . #30#) NIL #29# ELT) #31=(#13# NIL T ELT)) (|represents| (($ #32=(|Vector| |#1|) #12#) NIL T ELT) (#33=($ #32#) 49 T ELT)) (|representationType| (((|Union| "prime" "polynomial" "normal" "cyclic")) NIL #17# ELT)) (|rem| #34=(#35=($ $ $) NIL #5# ELT)) (|regularRepresentation| ((#11# $ #12#) NIL T ELT) ((#11# $) NIL T ELT)) (|reducedSystem| ((#36=(|Matrix| #16#) #37=(|Matrix| $)) NIL #38=(|has| |#1| (|LinearlyExplicitRingOver| #16#)) ELT) ((#39=(|Record| (|:| |mat| #36#) (|:| |vec| (|Vector| #16#))) #37# #12#) NIL #38# ELT) ((#40=(|Record| (|:| |mat| #11#) (|:| |vec| #32#)) #37# #12#) 112 T ELT) ((#11# #37#) 107 T ELT)) (|reduce| (#41=($ |#2|) 65 T ELT) ((#42=(|Union| $ #25#) (|Fraction| |#2|)) NIL #5# ELT)) (|recip| ((#42# $) NIL T ELT)) (|rank| ((#14#) 83 T ELT)) (|random| (#23# 50 #22# ELT)) (|quo| #34#) (|principalIdeal| (((|Record| (|:| |coef| #43=(|List| $)) #44=(|:| |generator| $)) #43#) NIL #5# ELT)) (|primitiveElement| #45=(#23# NIL #17# ELT)) (|primitive?| (#4# NIL #17# ELT)) (|primeFrobenius| (#46=($ $ #15#) NIL #17# ELT) #47=(#7# NIL #17# ELT)) (|prime?| #8#) (|order| (#48=(#14# $) NIL #17# ELT) (((|OnePointCompletion| #14#) $) NIL #17# ELT)) (|opposite?| #1#) (|one?| (#4# NIL T ELT)) (|norm| #31#) (|nextItem| (#49=(#18# $) NIL #17# ELT)) (|multiEuclidean| (((|Union| #43# #25#) #43# $) NIL #5# ELT)) (|minimalPolynomial| (#50=(|#2| $) 90 #5# ELT)) (|lookup| (#48# 143 #22# ELT)) (|lift| (#50# 62 T ELT)) (|leftReducedSystem| ((#36# #12#) NIL #38# ELT) ((#39# . #51=(#12# $)) NIL #38# ELT) ((#40# . #51#) NIL T ELT) #9#) (|lcm| #52=(($ #43#) NIL #5# ELT) #34#) (|latex| (((|String|) $) NIL T ELT)) (|inv| #6#) (|init| (#23# NIL #17# CONST)) (|index| (($ #14#) 134 #22# ELT)) (|hash| (((|SingleInteger|) $) NIL T ELT)) (|generator| (#23# 126 T ELT)) (|gcdPolynomial| ((#53=(|SparseUnivariatePolynomial| $) #53# #53#) NIL #5# ELT)) (|gcd| #52# #34#) (|factorsOfCyclicGroupSize| (((|List| (|Record| (|:| |factor| #16#) (|:| |exponent| #16#)))) NIL #17# ELT)) (|factor| #19#) (|extendedEuclidean| (((|Union| (|Record| #54=(|:| |coef1| $) #55=(|:| |coef2| $)) #25#) $ $ $) NIL #5# ELT) (((|Record| #54# #55# #44#) $ $) NIL #5# ELT)) (|exquo| ((#42# $ $) NIL #5# ELT)) (|expressIdealMember| (((|Maybe| #43#) #43# $) NIL #5# ELT)) (|euclideanSize| (#56=(#15# $) NIL #5# ELT)) (|divide| (((|Record| (|:| |quotient| $) (|:| |remainder| $)) $ $) NIL #5# ELT)) (|discriminant| ((|#1| #12#) NIL T ELT) ((|#1|) 116 T ELT)) (|discreteLog| (#56# NIL #17# ELT) (((|Union| #15# #25#) $ $) NIL #17# ELT)) (|differentiate| #57=(#46# NIL #58=(OR (AND (|has| |#1| (|DifferentialSpace|)) #5#) #17#) ELT) #59=(#7# NIL #58# ELT) #60=(($ $ #61=(|List| #62=(|Symbol|)) (|List| #15#)) NIL #63=(AND #5# (|has| |#1| (|PartialDifferentialSpace| #62#))) ELT) #64=(($ $ #62# #15#) NIL #63# ELT) #65=(($ $ #61#) NIL #63# ELT) #66=(($ $ #62#) NIL #63# ELT) #67=(($ $ #68=(|Mapping| |#1| |#1|)) NIL #5# ELT) #69=(($ $ #68# #15#) NIL #5# ELT)) (|derivationCoordinates| ((#11# #12# #68#) NIL #5# ELT)) (|definingPolynomial| ((|#2|) 80 T ELT)) (|createPrimitiveElement| #45#) (|coordinates| ((#32# $ #12#) 95 T ELT) ((#11# #12# #12#) NIL T ELT) (#70=(#32# $) 75 T ELT) (#10# 91 T ELT)) (|convert| (#70# NIL T ELT) (#33# NIL T ELT) (#50# NIL T ELT) (#41# NIL T ELT)) (|conditionP| (((|Union| #12# #25#) #37#) NIL #17# ELT)) (|coerce| (((|OutputForm|) $) 61 T ELT) (($ #16#) 56 T ELT) (($ |#1|) 58 T ELT) #6# (($ #28#) NIL (OR #5# #29#) ELT)) (|charthRoot| #47# (#49# NIL (|has| |#1| (|CharacteristicNonZero|)) ELT)) (|characteristicPolynomial| (#50# 88 T ELT)) (|characteristic| (#21# 82 T CONST)) (|before?| #1#) (|basis| ((#12#) 87 T ELT)) (|associates?| #20#) (|annihilate?| #1#) (|Zero| (#23# 35 T CONST)) (|One| (#23# 19 T CONST)) (D #57# #59# #60# #64# #65# #66# #67# #69#) (= (#2# 67 T ELT)) (/ #34#) (- (#7# 71 T ELT) (#35# NIL T ELT)) (+ (#35# 69 T ELT)) (** (($ $ #14#) NIL T ELT) (#46# NIL T ELT) (($ $ #16#) NIL #5# ELT)) (* (($ #14# $) NIL T ELT) (($ #15# $) NIL T ELT) (($ #16# $) 54 T ELT) (#35# 73 T ELT) (($ $ |#1|) NIL T ELT) (($ |#1| $) 51 T ELT) (($ #28# $) NIL #5# ELT) (($ $ #28#) NIL #5# ELT))) (((|SimpleAlgebraicExtension| |#1| |#2| |#3|) (|MonogenicAlgebra| |#1| |#2|) (|CommutativeRing|) (|UnivariatePolynomialCategory| |#1|) |#2|) (T |SimpleAlgebraicExtension|)) NIL ((|factor| (((|Factored| |#3|) |#3|) 18 T ELT))) @@ -3333,7 +3333,7 @@ NIL ((|structuralConstants| (((|Vector| #1=(|Matrix| |#1|)) #2=(|List| #1#)) 45 T ELT) (((|Vector| #3=(|Matrix| #4=(|Polynomial| |#1|))) #5=(|List| (|Symbol|)) #3#) 75 T ELT) (((|Vector| #6=(|Matrix| (|Fraction| #4#))) #5# #6#) 92 T ELT)) (|coordinates| (((|Vector| |#1|) #1# #2#) 39 T ELT))) (((|StructuralConstantsPackage| |#1|) (CATEGORY |package| (SIGNATURE |structuralConstants| ((|Vector| #1=(|Matrix| (|Fraction| #2=(|Polynomial| |#1|)))) #3=(|List| (|Symbol|)) #1#)) (SIGNATURE |structuralConstants| ((|Vector| #4=(|Matrix| #2#)) #3# #4#)) (SIGNATURE |structuralConstants| ((|Vector| #5=(|Matrix| |#1|)) #6=(|List| #5#))) (SIGNATURE |coordinates| ((|Vector| |#1|) #5# #6#))) (|Field|)) (T |StructuralConstantsPackage|)) ((|coordinates| #1=(*1 *2 *3 *4) (AND (|isDomain| *4 (|List| #2=(|Matrix| *5))) (|isDomain| *3 #2#) #3=(|ofCategory| *5 #4=(|Field|)) (|isDomain| *2 (|Vector| *5)) #5=(|isDomain| *1 (|StructuralConstantsPackage| *5)))) (|structuralConstants| (*1 *2 *3) (AND (|isDomain| *3 (|List| #6=(|Matrix| *4))) (|ofCategory| *4 #4#) (|isDomain| *2 (|Vector| #6#)) (|isDomain| *1 (|StructuralConstantsPackage| *4)))) (|structuralConstants| #1# (AND #7=(|isDomain| *3 (|List| (|Symbol|))) #3# (|isDomain| *2 (|Vector| #8=(|Matrix| #9=(|Polynomial| *5)))) #5# (|isDomain| *4 #8#))) (|structuralConstants| #1# (AND #7# #3# (|isDomain| *2 (|Vector| #10=(|Matrix| (|Fraction| #9#)))) #5# (|isDomain| *4 #10#)))) -((~= #1=(#2=(#3=(|Boolean|) $ $) NIL T ELT)) (|zero?| #4=(#5=(#3# $) NIL T ELT)) (|weights| ((#6=(|List| #7=(|NonNegativeInteger|)) $) NIL T ELT) ((#6# $ #8=(|Symbol|)) NIL T ELT)) (|weight| #9=((#7# $) NIL T ELT) #10=((#7# $ #8#) NIL T ELT)) (|variables| ((#11=(|List| #12=(|SequentialDifferentialVariable| #8#)) $) NIL T ELT)) (|univariate| ((#13=(|SparseUnivariatePolynomial| $) $ #12#) NIL T ELT) ((#14=(|SparseUnivariatePolynomial| |#1|) $) NIL T ELT)) (|unitNormal| (((|Record| (|:| |unit| $) (|:| |canonical| $) (|:| |associate| $)) $) NIL #15=(|has| |#1| (|IntegralDomain|)) ELT)) (|unitCanonical| #16=(#17=($ $) NIL #15# ELT)) (|unit?| (#5# NIL #15# ELT)) (|totalDegree| #9# ((#7# $ #11#) NIL T ELT)) (|subtractIfCan| (#18=(#19=(|Union| $ #20="failed") $ $) NIL T ELT)) (|squareFreePolynomial| #21=(((|Factored| #13#) #13#) NIL #22=(|has| |#1| (|PolynomialFactorizationExplicit|)) ELT)) (|squareFreePart| #23=(#17# NIL #24=(|has| |#1| (|GcdDomain|)) ELT)) (|squareFree| (#25=((|Factored| $) $) NIL #24# ELT)) (|solveLinearPolynomialEquation| (((|Union| #26=(|List| #13#) #20#) #26# #13#) NIL #22# ELT)) (|separant| #27=(#17# NIL T ELT)) (|sample| #28=(($) NIL T CONST)) (|retractIfCan| (((|Union| |#1| . #29=(#20#)) . #30=($)) NIL T ELT) (((|Union| #31=(|Fraction| #32=(|Integer|)) . #29#) . #30#) NIL #33=(|has| |#1| (|RetractableTo| #31#)) ELT) (((|Union| #32# . #29#) . #30#) NIL #34=(|has| |#1| (|RetractableTo| #32#)) ELT) #35=(((|Union| #12# . #29#) . #30#) NIL T ELT) (((|Union| #8# . #29#) . #30#) NIL T ELT) (((|Union| #36=(|SparseMultivariatePolynomial| |#1| #8#) . #29#) . #30#) NIL T ELT)) (|retract| #37=(#38=(|#1| . #39=($)) NIL T ELT) ((#31# . #39#) NIL #33# ELT) ((#32# . #39#) NIL #34# ELT) #40=((#12# . #39#) NIL T ELT) ((#8# . #39#) NIL T ELT) ((#36# . #39#) NIL T ELT)) (|resultant| (($ $ $ #12#) NIL #41=(|has| |#1| (|CommutativeRing|)) ELT)) (|reductum| #27#) (|reducedSystem| ((#42=(|Matrix| #32#) . #43=(#44=(|Matrix| $))) NIL #45=(|has| |#1| (|LinearlyExplicitRingOver| #32#)) ELT) ((#46=(|Record| (|:| |mat| #42#) (|:| |vec| (|Vector| #32#))) . #47=(#44# #48=(|Vector| $))) NIL #45# ELT) ((#49=(|Record| (|:| |mat| #50=(|Matrix| |#1|)) (|:| |vec| (|Vector| |#1|))) . #47#) NIL T ELT) ((#50# . #43#) NIL T ELT)) (|recip| ((#19# $) NIL T ELT)) (|primitivePart| #23# #51=(#52=($ $ #12#) NIL #24# ELT)) (|primitiveMonomials| #53=((#54=(|List| $) $) NIL T ELT)) (|prime?| (#5# NIL #22# ELT)) (|pomopo!| (($ $ |#1| #55=(|IndexedExponents| #12#) $) NIL T ELT)) (|patternMatch| ((#56=(|PatternMatchResult| #57=(|Float|) . #58=($)) $ #59=(|Pattern| #57#) #56#) NIL (AND (|has| #12# #60=(|PatternMatchable| #57#)) (|has| |#1| #60#)) ELT) ((#61=(|PatternMatchResult| #32# . #58#) $ #62=(|Pattern| #32#) #61#) NIL (AND (|has| #12# #63=(|PatternMatchable| #32#)) (|has| |#1| #63#)) ELT)) (|order| #10# #9#) (|opposite?| #1#) (|one?| #4#) (|numberOfMonomials| #9#) (|multivariate| (($ #14# #12#) NIL T ELT) (($ #13# #12#) NIL T ELT)) (|monomials| #53#) (|monomial?| #4#) (|monomial| (($ |#1| #55#) NIL T ELT) #64=(($ $ #12# #7#) NIL T ELT) #65=(($ $ #11# #6#) NIL T ELT)) (|monicDivide| (((|Record| (|:| |quotient| $) (|:| |remainder| $)) $ $ #12#) NIL T ELT)) (|minimumDegree| #66=((#55# $) NIL T ELT) #67=((#7# $ #12#) NIL T ELT) #68=((#6# $ #11#) NIL T ELT)) (|mapExponents| (($ (|Mapping| #55# #55#) $) NIL T ELT)) (|map| (($ #69=(|Mapping| |#1| |#1|) $) NIL T ELT)) (|makeVariable| ((#70=(|Mapping| $ #7#) #8#) NIL T ELT) ((#70# $) NIL #71=(|has| |#1| (|DifferentialRing|)) ELT)) (|mainVariable| #35#) (|leftReducedSystem| ((#42# . #72=(#48#)) NIL #45# ELT) ((#46# . #73=(#48# $)) NIL #45# ELT) ((#49# . #73#) NIL T ELT) ((#50# . #72#) NIL T ELT)) (|leadingMonomial| #27#) (|leadingCoefficient| #37#) (|leader| #40#) (|lcm| #74=(($ #54#) NIL #24# ELT) #75=(#76=($ $ $) NIL #24# ELT)) (|latex| (((|String|) $) NIL T ELT)) (|isobaric?| #4#) (|isTimes| #77=(((|Union| #54# #20#) $) NIL T ELT)) (|isPlus| #77#) (|isExpt| (((|Union| (|Record| (|:| |var| #12#) (|:| |exponent| #7#)) #20#) $) NIL T ELT)) (|initial| #27#) (|hash| (((|SingleInteger|) $) NIL T ELT)) (|ground?| #4#) (|ground| #37#) (|gcdPolynomial| ((#13# #13# #13#) NIL #24# ELT)) (|gcd| #74# #75#) (|factorSquareFreePolynomial| #21#) (|factorPolynomial| #21#) (|factor| (#25# NIL #22# ELT)) (|exquo| ((#19# $ |#1|) NIL #15# ELT) (#18# NIL #15# ELT)) (|eval| (($ $ (|List| #78=(|Equation| $))) NIL T ELT) (($ $ #78#) NIL T ELT) (($ $ $ $) NIL T ELT) (($ $ #54# #54#) NIL T ELT) (($ $ #12# |#1|) NIL T ELT) (($ $ #11# #79=(|List| |#1|)) NIL T ELT) (($ $ #12# $) NIL T ELT) (($ $ #11# #54#) NIL T ELT) (($ $ #8# $) NIL #71# ELT) (($ $ #80=(|List| #8#) #54#) NIL #71# ELT) (($ $ #8# |#1|) NIL #71# ELT) (($ $ #80# #79#) NIL #71# ELT)) (|discriminant| (#52# NIL #41# ELT)) (|differentiate| #65# #64# #81=(($ $ #11#) NIL T ELT) #82=(#52# NIL T ELT) #83=(($ $ #69#) NIL T ELT) #84=(($ $ #69# #7#) NIL T ELT) #85=(($ $ #8#) NIL #86=(|has| |#1| (|PartialDifferentialSpace| #8#)) ELT) #87=(($ $ #80#) NIL #86# ELT) #88=(($ $ #8# #7#) NIL #86# ELT) #89=(($ $ #80# #6#) NIL #86# ELT) #90=(#17# NIL #91=(|has| |#1| (|DifferentialSpace|)) ELT) #92=(#93=($ $ #7#) NIL #91# ELT)) (|differentialVariables| ((#80# $) NIL T ELT)) (|degree| #66# #67# #68# #10#) (|convert| ((#59# . #94=($)) NIL (AND (|has| #12# #95=(|ConvertibleTo| #59#)) (|has| |#1| #95#)) ELT) ((#62# . #94#) NIL (AND (|has| #12# #96=(|ConvertibleTo| #62#)) (|has| |#1| #96#)) ELT) ((#97=(|InputForm|) . #94#) NIL (AND (|has| #12# #98=(|ConvertibleTo| #97#)) (|has| |#1| #98#)) ELT)) (|content| (#38# NIL #24# ELT) #51#) (|conditionP| (((|Union| #48# #20#) #44#) NIL #99=(AND (|has| $ #100=(|CharacteristicNonZero|)) #22#) ELT)) (|coerce| (((|OutputForm|) $) NIL T ELT) (($ #32#) NIL T ELT) (($ |#1|) NIL T ELT) (($ #12#) NIL T ELT) (($ #8#) NIL T ELT) (($ #36#) NIL T ELT) (($ #31#) NIL (OR #101=(|has| |#1| (|Algebra| #31#)) #33#) ELT) #16#) (|coefficients| ((#79# $) NIL T ELT)) (|coefficient| ((|#1| $ #55#) NIL T ELT) #64# #65#) (|charthRoot| (((|Maybe| $) $) NIL (OR #99# (|has| |#1| #100#)) ELT)) (|characteristic| ((#7#) NIL T CONST)) (|binomThmExpt| (($ $ $ #7#) NIL #41# ELT)) (|before?| #1#) (|associates?| (#2# NIL #15# ELT)) (|annihilate?| #1#) (|Zero| #28#) (|One| #28#) (D #65# #64# #81# #82# #83# #84# #85# #87# #88# #89# #90# #92#) (= #1#) (/ (#102=($ $ |#1|) NIL (|has| |#1| (|Field|)) ELT)) (- #27# #103=(#76# NIL T ELT)) (+ #103#) (** (($ $ #104=(|PositiveInteger|)) NIL T ELT) (#93# NIL T ELT)) (* (($ #104# $) NIL T ELT) (($ #7# $) NIL T ELT) (($ #32# . #105=($)) NIL T ELT) #103# (($ $ #31#) NIL #101# ELT) (($ #31# . #105#) NIL #101# ELT) (($ |#1| . #105#) NIL T ELT) (#102# NIL T ELT))) +((~= #1=(#2=(#3=(|Boolean|) $ $) NIL T ELT)) (|zero?| #4=(#5=(#3# $) NIL T ELT)) (|weights| ((#6=(|List| #7=(|NonNegativeInteger|)) $) NIL T ELT) ((#6# $ #8=(|Symbol|)) NIL T ELT)) (|weight| #9=((#7# $) NIL T ELT) #10=((#7# $ #8#) NIL T ELT)) (|variables| ((#11=(|List| #12=(|SequentialDifferentialVariable| #8#)) $) NIL T ELT)) (|univariate| ((#13=(|SparseUnivariatePolynomial| $) $ #12#) NIL T ELT) ((#14=(|SparseUnivariatePolynomial| |#1|) $) NIL T ELT)) (|unitNormal| (((|Record| (|:| |unit| $) (|:| |canonical| $) (|:| |associate| $)) $) NIL #15=(|has| |#1| (|IntegralDomain|)) ELT)) (|unitCanonical| #16=(#17=($ $) NIL #15# ELT)) (|unit?| (#5# NIL #15# ELT)) (|totalDegree| #9# ((#7# $ #11#) NIL T ELT)) (|subtractIfCan| ((#18=(|Maybe| $) $ $) NIL T ELT)) (|squareFreePolynomial| #19=(((|Factored| #13#) #13#) NIL #20=(|has| |#1| (|PolynomialFactorizationExplicit|)) ELT)) (|squareFreePart| #21=(#17# NIL #22=(|has| |#1| (|GcdDomain|)) ELT)) (|squareFree| (#23=((|Factored| $) $) NIL #22# ELT)) (|solveLinearPolynomialEquation| (((|Union| #24=(|List| #13#) #25="failed") #24# #13#) NIL #20# ELT)) (|separant| #26=(#17# NIL T ELT)) (|sample| #27=(($) NIL T CONST)) (|retractIfCan| (((|Union| |#1| . #28=(#25#)) . #29=($)) NIL T ELT) (((|Union| #30=(|Fraction| #31=(|Integer|)) . #28#) . #29#) NIL #32=(|has| |#1| (|RetractableTo| #30#)) ELT) (((|Union| #31# . #28#) . #29#) NIL #33=(|has| |#1| (|RetractableTo| #31#)) ELT) #34=(((|Union| #12# . #28#) . #29#) NIL T ELT) (((|Union| #8# . #28#) . #29#) NIL T ELT) (((|Union| #35=(|SparseMultivariatePolynomial| |#1| #8#) . #28#) . #29#) NIL T ELT)) (|retract| #36=(#37=(|#1| . #38=($)) NIL T ELT) ((#30# . #38#) NIL #32# ELT) ((#31# . #38#) NIL #33# ELT) #39=((#12# . #38#) NIL T ELT) ((#8# . #38#) NIL T ELT) ((#35# . #38#) NIL T ELT)) (|resultant| (($ $ $ #12#) NIL #40=(|has| |#1| (|CommutativeRing|)) ELT)) (|reductum| #26#) (|reducedSystem| ((#41=(|Matrix| #31#) . #42=(#43=(|Matrix| $))) NIL #44=(|has| |#1| (|LinearlyExplicitRingOver| #31#)) ELT) ((#45=(|Record| (|:| |mat| #41#) (|:| |vec| (|Vector| #31#))) . #46=(#43# #47=(|Vector| $))) NIL #44# ELT) ((#48=(|Record| (|:| |mat| #49=(|Matrix| |#1|)) (|:| |vec| (|Vector| |#1|))) . #46#) NIL T ELT) ((#49# . #42#) NIL T ELT)) (|recip| ((#50=(|Union| $ #25#) $) NIL T ELT)) (|primitivePart| #21# #51=(#52=($ $ #12#) NIL #22# ELT)) (|primitiveMonomials| #53=((#54=(|List| $) $) NIL T ELT)) (|prime?| (#5# NIL #20# ELT)) (|pomopo!| (($ $ |#1| #55=(|IndexedExponents| #12#) $) NIL T ELT)) (|patternMatch| ((#56=(|PatternMatchResult| #57=(|Float|) . #58=($)) $ #59=(|Pattern| #57#) #56#) NIL (AND (|has| #12# #60=(|PatternMatchable| #57#)) (|has| |#1| #60#)) ELT) ((#61=(|PatternMatchResult| #31# . #58#) $ #62=(|Pattern| #31#) #61#) NIL (AND (|has| #12# #63=(|PatternMatchable| #31#)) (|has| |#1| #63#)) ELT)) (|order| #10# #9#) (|opposite?| #1#) (|one?| #4#) (|numberOfMonomials| #9#) (|multivariate| (($ #14# #12#) NIL T ELT) (($ #13# #12#) NIL T ELT)) (|monomials| #53#) (|monomial?| #4#) (|monomial| (($ |#1| #55#) NIL T ELT) #64=(($ $ #12# #7#) NIL T ELT) #65=(($ $ #11# #6#) NIL T ELT)) (|monicDivide| (((|Record| (|:| |quotient| $) (|:| |remainder| $)) $ $ #12#) NIL T ELT)) (|minimumDegree| #66=((#55# $) NIL T ELT) #67=((#7# $ #12#) NIL T ELT) #68=((#6# $ #11#) NIL T ELT)) (|mapExponents| (($ (|Mapping| #55# #55#) $) NIL T ELT)) (|map| (($ #69=(|Mapping| |#1| |#1|) $) NIL T ELT)) (|makeVariable| ((#70=(|Mapping| $ #7#) #8#) NIL T ELT) ((#70# $) NIL #71=(|has| |#1| (|DifferentialRing|)) ELT)) (|mainVariable| #34#) (|leftReducedSystem| ((#41# . #72=(#47#)) NIL #44# ELT) ((#45# . #73=(#47# $)) NIL #44# ELT) ((#48# . #73#) NIL T ELT) ((#49# . #72#) NIL T ELT)) (|leadingMonomial| #26#) (|leadingCoefficient| #36#) (|leader| #39#) (|lcm| #74=(($ #54#) NIL #22# ELT) #75=(#76=($ $ $) NIL #22# ELT)) (|latex| (((|String|) $) NIL T ELT)) (|isobaric?| #4#) (|isTimes| #77=(((|Union| #54# #25#) $) NIL T ELT)) (|isPlus| #77#) (|isExpt| (((|Union| (|Record| (|:| |var| #12#) (|:| |exponent| #7#)) #25#) $) NIL T ELT)) (|initial| #26#) (|hash| (((|SingleInteger|) $) NIL T ELT)) (|ground?| #4#) (|ground| #36#) (|gcdPolynomial| ((#13# #13# #13#) NIL #22# ELT)) (|gcd| #74# #75#) (|factorSquareFreePolynomial| #19#) (|factorPolynomial| #19#) (|factor| (#23# NIL #20# ELT)) (|exquo| ((#50# $ |#1|) NIL #15# ELT) ((#50# $ $) NIL #15# ELT)) (|eval| (($ $ (|List| #78=(|Equation| $))) NIL T ELT) (($ $ #78#) NIL T ELT) (($ $ $ $) NIL T ELT) (($ $ #54# #54#) NIL T ELT) (($ $ #12# |#1|) NIL T ELT) (($ $ #11# #79=(|List| |#1|)) NIL T ELT) (($ $ #12# $) NIL T ELT) (($ $ #11# #54#) NIL T ELT) (($ $ #8# $) NIL #71# ELT) (($ $ #80=(|List| #8#) #54#) NIL #71# ELT) (($ $ #8# |#1|) NIL #71# ELT) (($ $ #80# #79#) NIL #71# ELT)) (|discriminant| (#52# NIL #40# ELT)) (|differentiate| #65# #64# #81=(($ $ #11#) NIL T ELT) #82=(#52# NIL T ELT) #83=(($ $ #69#) NIL T ELT) #84=(($ $ #69# #7#) NIL T ELT) #85=(($ $ #8#) NIL #86=(|has| |#1| (|PartialDifferentialSpace| #8#)) ELT) #87=(($ $ #80#) NIL #86# ELT) #88=(($ $ #8# #7#) NIL #86# ELT) #89=(($ $ #80# #6#) NIL #86# ELT) #90=(#17# NIL #91=(|has| |#1| (|DifferentialSpace|)) ELT) #92=(#93=($ $ #7#) NIL #91# ELT)) (|differentialVariables| ((#80# $) NIL T ELT)) (|degree| #66# #67# #68# #10#) (|convert| ((#59# . #94=($)) NIL (AND (|has| #12# #95=(|ConvertibleTo| #59#)) (|has| |#1| #95#)) ELT) ((#62# . #94#) NIL (AND (|has| #12# #96=(|ConvertibleTo| #62#)) (|has| |#1| #96#)) ELT) ((#97=(|InputForm|) . #94#) NIL (AND (|has| #12# #98=(|ConvertibleTo| #97#)) (|has| |#1| #98#)) ELT)) (|content| (#37# NIL #22# ELT) #51#) (|conditionP| (((|Union| #47# #25#) #43#) NIL #99=(AND (|has| $ #100=(|CharacteristicNonZero|)) #20#) ELT)) (|coerce| (((|OutputForm|) $) NIL T ELT) (($ #31#) NIL T ELT) (($ |#1|) NIL T ELT) (($ #12#) NIL T ELT) (($ #8#) NIL T ELT) (($ #35#) NIL T ELT) (($ #30#) NIL (OR #101=(|has| |#1| (|Algebra| #30#)) #32#) ELT) #16#) (|coefficients| ((#79# $) NIL T ELT)) (|coefficient| ((|#1| $ #55#) NIL T ELT) #64# #65#) (|charthRoot| ((#18# $) NIL (OR #99# (|has| |#1| #100#)) ELT)) (|characteristic| ((#7#) NIL T CONST)) (|binomThmExpt| (($ $ $ #7#) NIL #40# ELT)) (|before?| #1#) (|associates?| (#2# NIL #15# ELT)) (|annihilate?| #1#) (|Zero| #27#) (|One| #27#) (D #65# #64# #81# #82# #83# #84# #85# #87# #88# #89# #90# #92#) (= #1#) (/ (#102=($ $ |#1|) NIL (|has| |#1| (|Field|)) ELT)) (- #26# #103=(#76# NIL T ELT)) (+ #103#) (** (($ $ #104=(|PositiveInteger|)) NIL T ELT) (#93# NIL T ELT)) (* (($ #104# $) NIL T ELT) (($ #7# $) NIL T ELT) (($ #31# . #105=($)) NIL T ELT) #103# (($ $ #30#) NIL #101# ELT) (($ #30# . #105#) NIL #101# ELT) (($ |#1| . #105#) NIL T ELT) (#102# NIL T ELT))) (((|SequentialDifferentialPolynomial| |#1|) (|Join| (|DifferentialPolynomialCategory| |#1| #1=(|Symbol|) #2=(|SequentialDifferentialVariable| #1#) (|IndexedExponents| #2#)) (|RetractableTo| (|SparseMultivariatePolynomial| |#1| #1#))) (|Ring|)) (T |SequentialDifferentialPolynomial|)) NIL ((~= #1=(#2=((|Boolean|) $ $) NIL T ELT)) (|weight| (#3=(#4=(|NonNegativeInteger|) $) NIL T ELT)) (|variable| (#5=(|#1| $) 10 T ELT)) (|retractIfCan| (((|Union| |#1| "failed") $) NIL T ELT)) (|retract| (#5# NIL T ELT)) (|order| (#3# 11 T ELT)) (|min| #6=(($ $ $) NIL T ELT)) (|max| #6#) (|makeVariable| (($ |#1| #4#) 9 T ELT)) (|latex| (((|String|) $) NIL T ELT)) (|hash| (((|SingleInteger|) $) NIL T ELT)) (|differentiate| #7=(($ $ #4#) NIL T ELT) #8=(($ $) NIL T ELT)) (|coerce| (((|OutputForm|) $) NIL T ELT) (($ |#1|) NIL T ELT)) (|before?| #1#) (D #7# #8#) (>= #1#) (> #1#) (= #1#) (<= #1#) (< (#2# 16 T ELT))) @@ -3386,7 +3386,7 @@ NIL ((|hash| #1=(*1 *2 *1) (AND #2=(|ofCategory| *1 (|SetCategory|)) (|isDomain| *2 (|SingleInteger|)))) (|latex| #1# (AND #2# (|isDomain| *2 (|String|))))) (|Join| (|BasicType|) (|CoercibleTo| (|OutputForm|)) (CATEGORY |domain| (SIGNATURE |hash| ((|SingleInteger|) $)) (SIGNATURE |latex| ((|String|) $)))) (((|BasicType|) . T) ((|CoercibleTo| (|OutputForm|)) . T) ((|Join|) . T) ((|Type|) . T)) -((~= #1=(#2=(#3=(|Boolean|) $ $) NIL T ELT)) (|size| ((#4=(|NonNegativeInteger|)) 36 T ELT)) (|setOfMinN| (($ #5=(|List| #6=(|PositiveInteger|))) 70 T ELT)) (|replaceKthElement| ((#7=(|Union| $ "failed") $ #6# #6#) 81 T ELT)) (|random| (($) 40 T ELT)) (|member?| ((#3# #6# $) 42 T ELT)) (|lookup| ((#6# $) 64 T ELT)) (|latex| (((|String|) $) NIL T ELT)) (|index| (($ #6#) 39 T ELT)) (|incrementKthElement| ((#7# $ #6#) 77 T ELT)) (|hash| (((|SingleInteger|) $) NIL T ELT)) (|enumerate| (((|Vector| $)) 47 T ELT)) (|elements| ((#5# $) 27 T ELT)) (|delta| ((#4# $ #6# #6#) 78 T ELT)) (|coerce| (((|OutputForm|) $) 32 T ELT)) (|before?| #1#) (= (#2# 24 T ELT))) +((~= #1=(#2=(#3=(|Boolean|) $ $) NIL T ELT)) (|size| ((#4=(|NonNegativeInteger|)) 35 T ELT)) (|setOfMinN| (($ #5=(|List| #6=(|PositiveInteger|))) 69 T ELT)) (|replaceKthElement| ((#7=(|Union| $ "failed") $ #6# #6#) 80 T ELT)) (|random| (($) 39 T ELT)) (|member?| ((#3# #6# $) 41 T ELT)) (|lookup| ((#6# $) 63 T ELT)) (|latex| (((|String|) $) NIL T ELT)) (|index| (($ #6#) 38 T ELT)) (|incrementKthElement| ((#7# $ #6#) 76 T ELT)) (|hash| (((|SingleInteger|) $) NIL T ELT)) (|enumerate| (((|Vector| $)) 46 T ELT)) (|elements| ((#5# $) 27 T ELT)) (|delta| ((#4# $ #6# #6#) 77 T ELT)) (|coerce| (((|OutputForm|) $) 32 T ELT)) (|before?| #1#) (= (#2# 24 T ELT))) (((|SetOfMIntegersInOneToN| |#1| |#2|) (|Join| (|Finite|) (CATEGORY |domain| (SIGNATURE |incrementKthElement| (#1=(|Union| $ "failed") $ #2=(|PositiveInteger|))) (SIGNATURE |replaceKthElement| (#1# $ #2# #2#)) (SIGNATURE |elements| (#3=(|List| #2#) $)) (SIGNATURE |setOfMinN| ($ #3#)) (SIGNATURE |enumerate| ((|Vector| $))) (SIGNATURE |member?| ((|Boolean|) #2# $)) (SIGNATURE |delta| ((|NonNegativeInteger|) $ #2# #2#)))) #2# #2#) (T |SetOfMIntegersInOneToN|)) ((|incrementKthElement| (*1 *1 *1 *2) #1=(|partial| AND (|isDomain| *2 #2=(|PositiveInteger|)) #3=(|isDomain| *1 #4=(|SetOfMIntegersInOneToN| *3 *4)) (|ofType| *3 *2) (|ofType| *4 *2))) (|replaceKthElement| (*1 *1 *1 *2 *2) #1#) (|elements| (*1 *2 *1) #5=(AND (|isDomain| *2 (|List| #2#)) #3# #6=(|ofType| *3 #2#) #7=(|ofType| *4 #2#))) (|setOfMinN| (*1 *1 *2) #5#) (|enumerate| (*1 *2) (AND (|isDomain| *2 (|Vector| #4#)) #3# #6# #7#)) (|member?| (*1 *2 *3 *1) (AND #8=(|isDomain| *3 #2#) (|isDomain| *2 (|Boolean|)) #9=(|isDomain| *1 (|SetOfMIntegersInOneToN| *4 *5)) #10=(|ofType| *4 *3) #11=(|ofType| *5 *3))) (|delta| (*1 *2 *1 *3 *3) (AND #8# (|isDomain| *2 (|NonNegativeInteger|)) #9# #10# #11#))) ((~= #1=((#2=(|Boolean|) $ $) NIL T ELT)) (|symbol?| #3=((#2# $) NIL T ELT)) (|symbol| ((#4=(|Symbol|) $) NIL T ELT)) (|string?| #3#) (|string| #5=((#6=(|String|) $) NIL T ELT)) (|pair?| #3#) (|null?| #3#) (|list?| #3#) (|latex| #5#) (|integer?| #3#) (|integer| #7=((#8=(|Integer|) $) NIL T ELT)) (|hash| (((|SingleInteger|) $) NIL T ELT)) (|float?| #3#) (|float| ((#9=(|DoubleFloat|) $) NIL T ELT)) (|expr| #10=((#11=(|OutputForm|) $) NIL T ELT)) (|eq| #1#) (|elt| (($ $ #8#) NIL T ELT) (($ $ (|List| #8#)) NIL T ELT)) (|destruct| ((#12=(|List| $) $) NIL T ELT)) (|convert| (($ #6#) NIL T ELT) (($ #4#) NIL T ELT) (($ #8#) NIL T ELT) (($ #9#) NIL T ELT) (($ #11#) NIL T ELT) (($ #12#) NIL T ELT)) (|coerce| #10#) (|cdr| #13=(($ $) NIL T ELT)) (|car| #13#) (|before?| #1#) (|atom?| #3#) (= #1#) (|#| #7#)) @@ -3430,7 +3430,7 @@ NIL ((* (*1 *1 *1 *1) (|ofCategory| *1 (|SemiGroup|))) (** (*1 *1 *1 *2) (AND (|ofCategory| *1 (|SemiGroup|)) (|isDomain| *2 (|PositiveInteger|))))) (|Join| (|SetCategory|) (CATEGORY |domain| (SIGNATURE * ($ $ $)) (SIGNATURE ** ($ $ (|PositiveInteger|))))) (((|BasicType|) . T) ((|CoercibleTo| (|OutputForm|)) . T) ((|Join|) . T) ((|SetCategory|) . T) ((|Type|) . T)) -((~= #1=(#2=(#3=(|Boolean|) $ $) NIL #4=(|has| |#3| (|BasicType|)) ELT)) (|zero?| (#5=(#3# $) NIL #6=(|has| |#3| (|AbelianMonoid|)) ELT)) (|unitVector| (#7=($ #8=(|PositiveInteger|)) NIL #9=(|has| |#3| (|Ring|)) ELT)) (|swap!| (((|Void|) $ #10=(|Integer|) #10#) NIL #11=(|has| $ (|ShallowlyMutableAggregate| |#3|)) ELT)) (|sup| (#12=($ $ $) NIL #13=(|has| |#3| (|OrderedAbelianMonoidSup|)) ELT)) (|subtractIfCan| ((#14=(|Union| $ #15="failed") $ $) NIL (|has| |#3| (|CancellationAbelianMonoid|)) ELT)) (|size| (#16=(#17=(|NonNegativeInteger|)) NIL #18=(|has| |#3| (|Finite|)) ELT)) (|setelt| #19=(#20=(|#3| $ #10# |#3|) NIL #11# ELT)) (|sample| (#21=($) NIL T CONST)) (|retractIfCan| (((|Union| #10# . #22=(#15#)) . #23=($)) NIL #24=(AND (|has| |#3| (|RetractableTo| #10#)) #25=(|has| |#3| (|SetCategory|))) ELT) (((|Union| #26=(|Fraction| #10#) . #22#) . #23#) NIL #27=(AND (|has| |#3| (|RetractableTo| #26#)) #25#) ELT) ((#28=(|Union| |#3| . #22#) . #23#) NIL #25# ELT)) (|retract| (#29=(#10# . #30=($)) NIL #24# ELT) ((#26# . #30#) NIL #27# ELT) (#31=(|#3| . #30#) NIL #25# ELT)) (|reducedSystem| ((#32=(|Matrix| #10#) . #33=(#34=(|Matrix| $))) NIL #35=(AND (|has| |#3| (|LinearlyExplicitRingOver| #10#)) #9#) ELT) ((#36=(|Record| (|:| |mat| #32#) (|:| |vec| (|Vector| #10#))) . #37=(#34# #38=(|Vector| $))) NIL #35# ELT) ((#39=(|Record| (|:| |mat| #40=(|Matrix| |#3|)) (|:| |vec| #41=(|Vector| |#3|))) . #37#) NIL #9# ELT) ((#40# . #33#) NIL #9# ELT)) (|reduce| ((|#3| #42=(|Mapping| |#3| |#3| |#3|) $ |#3| |#3|) NIL #4# ELT) ((|#3| #42# $ |#3|) NIL T ELT) ((|#3| #42# $) NIL T ELT)) (|recip| ((#14# $) NIL #9# ELT)) (|random| (#21# NIL #18# ELT)) (|qsetelt!| #19#) (|qelt| (#43=(|#3| $ #10#) 12 T ELT)) (|positive?| (#5# NIL #13# ELT)) (|opposite?| (#2# NIL #6# ELT)) (|one?| (#5# NIL #9# ELT)) (|minIndex| #44=(#29# NIL #45=(|has| #10# #46=(|OrderedSet|)) ELT)) (|min| #47=(#12# NIL #48=(|has| |#3| #46#) ELT)) (|members| #49=((#50=(|List| |#3|) $) NIL T ELT)) (|member?| (#51=(#3# |#3| $) NIL #4# ELT)) (|maxIndex| #44#) (|max| #47#) (|map| (($ #52=(|Mapping| |#3| |#3|) $) NIL T ELT)) (|lookup| ((#8# $) NIL #18# ELT)) (|leftReducedSystem| ((#32# . #53=(#38#)) NIL #35# ELT) ((#36# . #54=(#38# $)) NIL #35# ELT) ((#39# . #54#) NIL #9# ELT) ((#40# . #53#) NIL #9# ELT)) (|latex| (((|String|) $) NIL #25# ELT)) (|indices| (((|List| #10#) $) NIL T ELT)) (|index?| ((#3# #10# $) NIL T ELT)) (|index| (#7# NIL #18# ELT)) (|hash| (((|SingleInteger|) $) NIL #25# ELT)) (|first| (#31# NIL #45# ELT)) (|find| ((#28# #55=(|Mapping| #3# |#3|) $) NIL T ELT)) (|fill!| (#56=($ $ |#3|) NIL #11# ELT)) (|every?| #57=((#3# #55# $) NIL T ELT)) (|eval| (($ $ (|List| #58=(|Equation| |#3|))) NIL #59=(AND (|has| |#3| (|Evalable| |#3|)) #25#) ELT) (($ $ #58#) NIL #59# ELT) (($ $ |#3| |#3|) NIL #59# ELT) (($ $ #50# #50#) NIL #59# ELT)) (|eq?| (#2# NIL T ELT)) (|entry?| (#51# NIL (AND (|has| $ (|FiniteAggregate| |#3|)) #4#) ELT)) (|entries| #49#) (|empty?| (#5# NIL T ELT)) (|empty| (#21# NIL T ELT)) (|elt| (#20# NIL T ELT) (#43# NIL T ELT)) (|dot| ((|#3| $ $) NIL #9# ELT)) (|directProduct| (($ #41#) NIL T ELT)) (|dimension| (((|CardinalNumber|)) NIL #60=(|has| |#3| (|Field|)) ELT)) (|differentiate| #61=(#62=($ $ #17#) NIL #63=(AND (|has| |#3| (|DifferentialSpace|)) #9#) ELT) #64=(#65=($ $) NIL #63# ELT) #66=(($ $ #67=(|List| #68=(|Symbol|)) (|List| #17#)) NIL #69=(AND (|has| |#3| (|PartialDifferentialSpace| #68#)) #9#) ELT) #70=(($ $ #68# #17#) NIL #69# ELT) #71=(($ $ #67#) NIL #69# ELT) #72=(($ $ #68#) NIL #69# ELT) #73=(($ $ #52#) NIL #9# ELT) #74=(($ $ #52# #17#) NIL #9# ELT)) (|count| ((#17# |#3| $) NIL #4# ELT) ((#17# #55# $) NIL T ELT)) (|copy| (#65# NIL T ELT)) (|coerce| ((#41# . #75=($)) NIL T ELT) (($ #10#) NIL (OR #24# #9#) ELT) (($ #26#) NIL #27# ELT) (($ |#3|) NIL #25# ELT) ((#76=(|OutputForm|) . #75#) NIL (|has| |#3| (|CoercibleTo| #76#)) ELT)) (|characteristic| (#16# NIL #9# CONST)) (|before?| #1#) (|any?| #57#) (|annihilate?| (#2# NIL #9# ELT)) (|Zero| (#21# NIL #6# CONST)) (|One| (#21# NIL #9# CONST)) (D #61# #64# #66# #70# #71# #72# #73# #74#) (>= #77=(#2# NIL #48# ELT)) (> #77#) (= #1#) (<= #77#) (< (#2# 24 #48# ELT)) (/ (#56# NIL #60# ELT)) (- (#12# NIL #78=(|has| |#3| (|AbelianGroup|)) ELT) (#65# NIL #78# ELT)) (+ (#12# NIL #79=(|has| |#3| (|AbelianSemiGroup|)) ELT)) (** (#62# NIL #9# ELT) (($ $ #8#) NIL #9# ELT)) (* (#12# NIL #9# ELT) (#56# NIL #80=(|has| |#3| (|Monoid|)) ELT) (($ |#3| . #81=($)) NIL #80# ELT) (($ #10# . #81#) NIL #78# ELT) (($ #17# $) NIL #6# ELT) (($ #8# $) NIL #79# ELT)) (|#| ((#17# $) NIL T ELT))) +((~= #1=(#2=(#3=(|Boolean|) $ $) NIL #4=(|has| |#3| (|BasicType|)) ELT)) (|zero?| (#5=(#3# $) NIL #6=(|has| |#3| (|AbelianMonoid|)) ELT)) (|unitVector| (#7=($ #8=(|PositiveInteger|)) NIL #9=(|has| |#3| (|Ring|)) ELT)) (|swap!| (((|Void|) $ #10=(|Integer|) #10#) NIL #11=(|has| $ (|ShallowlyMutableAggregate| |#3|)) ELT)) (|sup| (#12=($ $ $) NIL #13=(|has| |#3| (|OrderedAbelianMonoidSup|)) ELT)) (|subtractIfCan| (((|Maybe| $) $ $) NIL (|has| |#3| (|CancellationAbelianMonoid|)) ELT)) (|size| (#14=(#15=(|NonNegativeInteger|)) NIL #16=(|has| |#3| (|Finite|)) ELT)) (|setelt| #17=(#18=(|#3| $ #10# |#3|) NIL #11# ELT)) (|sample| (#19=($) NIL T CONST)) (|retractIfCan| (((|Union| #10# . #20=(#21="failed")) . #22=($)) NIL #23=(AND (|has| |#3| (|RetractableTo| #10#)) #24=(|has| |#3| (|SetCategory|))) ELT) (((|Union| #25=(|Fraction| #10#) . #20#) . #22#) NIL #26=(AND (|has| |#3| (|RetractableTo| #25#)) #24#) ELT) ((#27=(|Union| |#3| . #20#) . #22#) NIL #24# ELT)) (|retract| (#28=(#10# . #29=($)) NIL #23# ELT) ((#25# . #29#) NIL #26# ELT) (#30=(|#3| . #29#) NIL #24# ELT)) (|reducedSystem| ((#31=(|Matrix| #10#) . #32=(#33=(|Matrix| $))) NIL #34=(AND (|has| |#3| (|LinearlyExplicitRingOver| #10#)) #9#) ELT) ((#35=(|Record| (|:| |mat| #31#) (|:| |vec| (|Vector| #10#))) . #36=(#33# #37=(|Vector| $))) NIL #34# ELT) ((#38=(|Record| (|:| |mat| #39=(|Matrix| |#3|)) (|:| |vec| #40=(|Vector| |#3|))) . #36#) NIL #9# ELT) ((#39# . #32#) NIL #9# ELT)) (|reduce| ((|#3| #41=(|Mapping| |#3| |#3| |#3|) $ |#3| |#3|) NIL #4# ELT) ((|#3| #41# $ |#3|) NIL T ELT) ((|#3| #41# $) NIL T ELT)) (|recip| (((|Union| $ #21#) $) NIL #9# ELT)) (|random| (#19# NIL #16# ELT)) (|qsetelt!| #17#) (|qelt| (#42=(|#3| $ #10#) 12 T ELT)) (|positive?| (#5# NIL #13# ELT)) (|opposite?| (#2# NIL #6# ELT)) (|one?| (#5# NIL #9# ELT)) (|minIndex| #43=(#28# NIL #44=(|has| #10# #45=(|OrderedSet|)) ELT)) (|min| #46=(#12# NIL #47=(|has| |#3| #45#) ELT)) (|members| #48=((#49=(|List| |#3|) $) NIL T ELT)) (|member?| (#50=(#3# |#3| $) NIL #4# ELT)) (|maxIndex| #43#) (|max| #46#) (|map| (($ #51=(|Mapping| |#3| |#3|) $) NIL T ELT)) (|lookup| ((#8# $) NIL #16# ELT)) (|leftReducedSystem| ((#31# . #52=(#37#)) NIL #34# ELT) ((#35# . #53=(#37# $)) NIL #34# ELT) ((#38# . #53#) NIL #9# ELT) ((#39# . #52#) NIL #9# ELT)) (|latex| (((|String|) $) NIL #24# ELT)) (|indices| (((|List| #10#) $) NIL T ELT)) (|index?| ((#3# #10# $) NIL T ELT)) (|index| (#7# NIL #16# ELT)) (|hash| (((|SingleInteger|) $) NIL #24# ELT)) (|first| (#30# NIL #44# ELT)) (|find| ((#27# #54=(|Mapping| #3# |#3|) $) NIL T ELT)) (|fill!| (#55=($ $ |#3|) NIL #11# ELT)) (|every?| #56=((#3# #54# $) NIL T ELT)) (|eval| (($ $ (|List| #57=(|Equation| |#3|))) NIL #58=(AND (|has| |#3| (|Evalable| |#3|)) #24#) ELT) (($ $ #57#) NIL #58# ELT) (($ $ |#3| |#3|) NIL #58# ELT) (($ $ #49# #49#) NIL #58# ELT)) (|eq?| (#2# NIL T ELT)) (|entry?| (#50# NIL (AND (|has| $ (|FiniteAggregate| |#3|)) #4#) ELT)) (|entries| #48#) (|empty?| (#5# NIL T ELT)) (|empty| (#19# NIL T ELT)) (|elt| (#18# NIL T ELT) (#42# NIL T ELT)) (|dot| ((|#3| $ $) NIL #9# ELT)) (|directProduct| (($ #40#) NIL T ELT)) (|dimension| (((|CardinalNumber|)) NIL #59=(|has| |#3| (|Field|)) ELT)) (|differentiate| #60=(#61=($ $ #15#) NIL #62=(AND (|has| |#3| (|DifferentialSpace|)) #9#) ELT) #63=(#64=($ $) NIL #62# ELT) #65=(($ $ #66=(|List| #67=(|Symbol|)) (|List| #15#)) NIL #68=(AND (|has| |#3| (|PartialDifferentialSpace| #67#)) #9#) ELT) #69=(($ $ #67# #15#) NIL #68# ELT) #70=(($ $ #66#) NIL #68# ELT) #71=(($ $ #67#) NIL #68# ELT) #72=(($ $ #51#) NIL #9# ELT) #73=(($ $ #51# #15#) NIL #9# ELT)) (|count| ((#15# |#3| $) NIL #4# ELT) ((#15# #54# $) NIL T ELT)) (|copy| (#64# NIL T ELT)) (|coerce| ((#40# . #74=($)) NIL T ELT) (($ #10#) NIL (OR #23# #9#) ELT) (($ #25#) NIL #26# ELT) (($ |#3|) NIL #24# ELT) ((#75=(|OutputForm|) . #74#) NIL (|has| |#3| (|CoercibleTo| #75#)) ELT)) (|characteristic| (#14# NIL #9# CONST)) (|before?| #1#) (|any?| #56#) (|annihilate?| (#2# NIL #9# ELT)) (|Zero| (#19# NIL #6# CONST)) (|One| (#19# NIL #9# CONST)) (D #60# #63# #65# #69# #70# #71# #72# #73#) (>= #76=(#2# NIL #47# ELT)) (> #76#) (= #1#) (<= #76#) (< (#2# 24 #47# ELT)) (/ (#55# NIL #59# ELT)) (- (#12# NIL #77=(|has| |#3| (|AbelianGroup|)) ELT) (#64# NIL #77# ELT)) (+ (#12# NIL #78=(|has| |#3| (|AbelianSemiGroup|)) ELT)) (** (#61# NIL #9# ELT) (($ $ #8#) NIL #9# ELT)) (* (#12# NIL #9# ELT) (#55# NIL #79=(|has| |#3| (|Monoid|)) ELT) (($ |#3| . #80=($)) NIL #79# ELT) (($ #10# . #80#) NIL #77# ELT) (($ #15# $) NIL #6# ELT) (($ #8# $) NIL #78# ELT)) (|#| ((#15# $) NIL T ELT))) (((|SplitHomogeneousDirectProduct| |#1| |#2| |#3|) (|DirectProductCategory| |#1| |#3|) #1=(|NonNegativeInteger|) #1# (|OrderedAbelianMonoidSup|)) (T |SplitHomogeneousDirectProduct|)) NIL ((|subresultantSequence| (#1=((|List| #2=(|UnivariatePolynomial| |#2| |#1|)) #2# #2#) 50 T ELT)) (|countRealRootsMultiple| (#3=(#4=(|Integer|) #2#) 95 #5=(|has| |#1| (|GcdDomain|)) ELT)) (|countRealRoots| (#3# 79 T ELT)) (|SturmHabichtSequence| (#1# 58 T ELT)) (|SturmHabichtMultiple| (#6=(#4# #2# #2#) 81 #5# ELT)) (|SturmHabichtCoefficients| (((|List| |#1|) #2# #2#) 61 T ELT)) (|SturmHabicht| (#6# 78 T ELT))) @@ -3451,8 +3451,8 @@ NIL ((|simplify| (((|Expression| (|Integer|)) (|AlgebraicNumber|)) 12 T ELT))) (((|SimplifyAlgebraicNumberConvertPackage|) (CATEGORY |package| (SIGNATURE |simplify| ((|Expression| (|Integer|)) (|AlgebraicNumber|))))) (T |SimplifyAlgebraicNumberConvertPackage|)) ((|simplify| (*1 *2 *3) (AND (|isDomain| *3 (|AlgebraicNumber|)) (|isDomain| *2 (|Expression| (|Integer|))) (|isDomain| *1 (|SimplifyAlgebraicNumberConvertPackage|))))) -((~= #1=(#2=(#3=(|Boolean|) $ $) NIL T ELT)) (~ (#4=($ $) 22 T ELT)) (|zero?| (#5=(#3# $) 49 T ELT)) (|xor| (#6=($ $ $) 28 T ELT)) (|unitNormal| (((|Record| (|:| |unit| $) (|:| |canonical| $) (|:| |associate| $)) $) 75 T ELT)) (|unitCanonical| #7=(#4# NIL T ELT)) (|unit?| #8=(#5# NIL T ELT)) (|symmetricRemainder| #9=(#6# NIL T ELT)) (|subtractIfCan| #10=((#11=(|Union| $ #12="failed") $ $) NIL T ELT)) (|submod| (#13=($ $ $ $) 59 T ELT)) (|squareFreePart| #7#) (|squareFree| #14=(((|Factored| $) $) NIL T ELT)) (|sizeLess?| #1#) (|size| (#15=(#16=(|NonNegativeInteger|)) 61 T ELT)) (|sign| #17=(#18=(#19=(|Integer|) $) NIL T ELT)) (|shift| (#6# 56 T ELT)) (|sample| #20=(#21=($) NIL T CONST)) (|retractIfCan| (((|Union| #19# #12#) $) NIL T ELT)) (|retract| #17#) (|rem| (#6# 42 T ELT)) (|reducedSystem| ((#22=(|Record| (|:| |mat| #23=(|Matrix| #19#)) (|:| |vec| (|Vector| #19#))) #24=(|Matrix| $) #25=(|Vector| $)) 70 T ELT) ((#23# #24#) 8 T ELT)) (|recip| ((#11# $) NIL T ELT)) (|rationalIfCan| (((|Union| #26=(|Fraction| #19#) #12#) $) NIL T ELT)) (|rational?| #8#) (|rational| ((#26# $) NIL T ELT)) (|random| (#21# 73 T ELT) (#4# 72 T ELT)) (|quo| (#6# 41 T ELT)) (|principalIdeal| (((|Record| (|:| |coef| #27=(|List| $)) #28=(|:| |generator| $)) #27#) NIL T ELT)) (|prime?| #8#) (|powmod| (#13# NIL T ELT)) (|positiveRemainder| (#6# 71 T ELT)) (|positive?| (#5# 76 T ELT)) (|permutation| #9#) (|patternMatch| ((#29=(|PatternMatchResult| #19# $) $ #30=(|Pattern| #19#) #29#) NIL T ELT)) (|or| (#6# 27 T ELT)) (|opposite?| #1#) (|one?| (#5# 50 T ELT)) (|odd?| (#5# 47 T ELT)) (|not| (#4# 23 T ELT)) (|nextItem| (((|Maybe| $) $) NIL T ELT)) (|negative?| (#5# 60 T ELT)) (|multiEuclidean| (((|Union| #27# #12#) #27# $) NIL T ELT)) (|mulmod| (#13# 57 T ELT)) (|min| (#6# 52 T ELT) (#21# 19 T CONST)) (|max| (#6# 51 T ELT) (#21# 18 T CONST)) (|mask| #7#) (|lookup| ((#31=(|PositiveInteger|) $) 66 T ELT)) (|length| (#4# 55 T ELT)) (|leftReducedSystem| ((#22# #25# $) NIL T ELT) ((#23# #25#) NIL T ELT)) (|lcm| #9# #32=(($ #27#) NIL T ELT)) (|latex| (((|String|) $) NIL T ELT)) (|invmod| #9#) (|init| #20#) (|index| (($ #31#) 65 T ELT)) (|inc| (#4# 33 T ELT)) (|hash| (((|SingleInteger|) $) 54 T ELT)) (|gcdPolynomial| ((#33=(|SparseUnivariatePolynomial| $) #33# #33#) NIL T ELT)) (|gcd| (#6# 45 T ELT) #32#) (|factorial| #7#) (|factor| #14#) (|extendedEuclidean| (((|Union| (|Record| #34=(|:| |coef1| $) #35=(|:| |coef2| $)) #12#) $ $ $) NIL T ELT) (((|Record| #34# #35# #28#) $ $) NIL T ELT)) (|exquo| #10#) (|expressIdealMember| (((|Maybe| #27#) #27# $) NIL T ELT)) (|even?| (#5# 48 T ELT)) (|euclideanSize| ((#16# $) NIL T ELT)) (|divide| (((|Record| (|:| |quotient| $) (|:| |remainder| $)) $ $) 44 T ELT)) (|differentiate| #7# #36=(#37=($ $ #16#) NIL T ELT)) (|dec| (#4# 34 T ELT)) (|copy| #7#) (|convert| (#18# 12 T ELT) (((|InputForm|) . #38=($)) NIL T ELT) ((#30# . #38#) NIL T ELT) (((|Float|) . #38#) NIL T ELT) (((|DoubleFloat|) . #38#) NIL T ELT)) (|coerce| (((|OutputForm|) $) 11 T ELT) #39=(($ #19#) 13 T ELT) #7# #39#) (|characteristic| (#15# NIL T CONST)) (|bit?| #1#) (|binomial| #9#) (|before?| #1#) (|base| (#21# 17 T ELT)) (|associates?| #1#) (|annihilate?| #1#) (|and| (#6# 26 T ELT)) (|addmod| (#13# 58 T ELT)) (|abs| (#4# 46 T ELT)) (|\\/| (#6# 25 T ELT)) (|Zero| (#21# 15 T CONST)) (|One| (#21# 16 T CONST)) (D #7# #36#) (>= (#2# 32 T ELT)) (> (#2# 30 T ELT)) (= (#2# 21 T ELT)) (<= (#2# 31 T ELT)) (< (#2# 29 T ELT)) (|/\\| (#6# 24 T ELT)) (- (#4# 35 T ELT) (#6# 37 T ELT)) (+ (#6# 36 T ELT)) (** (($ $ #31#) NIL T ELT) (#37# 40 T ELT)) (* (($ #31# $) NIL T ELT) (($ #16# $) NIL T ELT) #40=(($ #19# $) 14 T ELT) (#6# 38 T ELT) #40#)) -(((|SingleInteger|) (|Join| (|IntegerNumberSystem|) (|OrderedFinite|) (|BooleanLogic|) (CATEGORY |domain| (ATTRIBUTE |canonical|) (ATTRIBUTE |canonicalsClosed|) (ATTRIBUTE |noetherian|) (SIGNATURE |xor| ($ $ $))))) (T |SingleInteger|)) +((~= #1=(#2=(#3=(|Boolean|) $ $) NIL T ELT)) (~ (#4=($ $) 22 T ELT)) (|zero?| (#5=(#3# $) 49 T ELT)) (|xor| (#6=($ $ $) 28 T ELT)) (|unitNormal| (((|Record| (|:| |unit| $) (|:| |canonical| $) (|:| |associate| $)) $) 75 T ELT)) (|unitCanonical| #7=(#4# NIL T ELT)) (|unit?| #8=(#5# NIL T ELT)) (|symmetricRemainder| #9=(#6# NIL T ELT)) (|subtractIfCan| ((#10=(|Maybe| $) $ $) NIL T ELT)) (|submod| (#11=($ $ $ $) 59 T ELT)) (|squareFreePart| #7#) (|squareFree| #12=(((|Factored| $) $) NIL T ELT)) (|sizeLess?| #1#) (|size| (#13=(#14=(|NonNegativeInteger|)) 61 T ELT)) (|sign| #15=(#16=(#17=(|Integer|) $) NIL T ELT)) (|shift| (#6# 56 T ELT)) (|sample| #18=(#19=($) NIL T CONST)) (|retractIfCan| (((|Union| #17# #20="failed") $) NIL T ELT)) (|retract| #15#) (|rem| (#6# 42 T ELT)) (|reducedSystem| ((#21=(|Record| (|:| |mat| #22=(|Matrix| #17#)) (|:| |vec| (|Vector| #17#))) #23=(|Matrix| $) #24=(|Vector| $)) 70 T ELT) ((#22# #23#) 8 T ELT)) (|recip| ((#25=(|Union| $ #20#) $) NIL T ELT)) (|rationalIfCan| (((|Union| #26=(|Fraction| #17#) #20#) $) NIL T ELT)) (|rational?| #8#) (|rational| ((#26# $) NIL T ELT)) (|random| (#19# 73 T ELT) (#4# 72 T ELT)) (|quo| (#6# 41 T ELT)) (|principalIdeal| (((|Record| (|:| |coef| #27=(|List| $)) #28=(|:| |generator| $)) #27#) NIL T ELT)) (|prime?| #8#) (|powmod| (#11# NIL T ELT)) (|positiveRemainder| (#6# 71 T ELT)) (|positive?| (#5# 76 T ELT)) (|permutation| #9#) (|patternMatch| ((#29=(|PatternMatchResult| #17# $) $ #30=(|Pattern| #17#) #29#) NIL T ELT)) (|or| (#6# 27 T ELT)) (|opposite?| #1#) (|one?| (#5# 50 T ELT)) (|odd?| (#5# 47 T ELT)) (|not| (#4# 23 T ELT)) (|nextItem| ((#10# $) NIL T ELT)) (|negative?| (#5# 60 T ELT)) (|multiEuclidean| (((|Union| #27# #20#) #27# $) NIL T ELT)) (|mulmod| (#11# 57 T ELT)) (|min| (#6# 52 T ELT) (#19# 19 T CONST)) (|max| (#6# 51 T ELT) (#19# 18 T CONST)) (|mask| #7#) (|lookup| ((#31=(|PositiveInteger|) $) 66 T ELT)) (|length| (#4# 55 T ELT)) (|leftReducedSystem| ((#21# #24# $) NIL T ELT) ((#22# #24#) NIL T ELT)) (|lcm| #9# #32=(($ #27#) NIL T ELT)) (|latex| (((|String|) $) NIL T ELT)) (|invmod| #9#) (|init| #18#) (|index| (($ #31#) 65 T ELT)) (|inc| (#4# 33 T ELT)) (|hash| (((|SingleInteger|) $) 54 T ELT)) (|gcdPolynomial| ((#33=(|SparseUnivariatePolynomial| $) #33# #33#) NIL T ELT)) (|gcd| (#6# 45 T ELT) #32#) (|factorial| #7#) (|factor| #12#) (|extendedEuclidean| (((|Union| (|Record| #34=(|:| |coef1| $) #35=(|:| |coef2| $)) #20#) $ $ $) NIL T ELT) (((|Record| #34# #35# #28#) $ $) NIL T ELT)) (|exquo| ((#25# $ $) NIL T ELT)) (|expressIdealMember| (((|Maybe| #27#) #27# $) NIL T ELT)) (|even?| (#5# 48 T ELT)) (|euclideanSize| ((#14# $) NIL T ELT)) (|divide| (((|Record| (|:| |quotient| $) (|:| |remainder| $)) $ $) 44 T ELT)) (|differentiate| #7# #36=(#37=($ $ #14#) NIL T ELT)) (|dec| (#4# 34 T ELT)) (|copy| #7#) (|convert| (#16# 12 T ELT) (((|InputForm|) . #38=($)) NIL T ELT) ((#30# . #38#) NIL T ELT) (((|Float|) . #38#) NIL T ELT) (((|DoubleFloat|) . #38#) NIL T ELT)) (|coerce| (((|OutputForm|) $) 11 T ELT) #39=(($ #17#) 13 T ELT) #7# #39#) (|characteristic| (#13# NIL T CONST)) (|bit?| #1#) (|binomial| #9#) (|before?| #1#) (|base| (#19# 17 T ELT)) (|associates?| #1#) (|annihilate?| #1#) (|and| (#6# 26 T ELT)) (|addmod| (#11# 58 T ELT)) (|abs| (#4# 46 T ELT)) (|\\/| (#6# 25 T ELT)) (|Zero| (#19# 15 T CONST)) (|One| (#19# 16 T CONST)) (D #7# #36#) (>= (#2# 32 T ELT)) (> (#2# 30 T ELT)) (= (#2# 21 T ELT)) (<= (#2# 31 T ELT)) (< (#2# 29 T ELT)) (|/\\| (#6# 24 T ELT)) (- (#4# 35 T ELT) (#6# 37 T ELT)) (+ (#6# 36 T ELT)) (** (($ $ #31#) NIL T ELT) (#37# 40 T ELT)) (* (($ #31# $) NIL T ELT) (($ #14# $) NIL T ELT) #40=(($ #17# $) 14 T ELT) (#6# 38 T ELT) #40#)) +(((|SingleInteger|) (|Join| (|IntegerNumberSystem|) (|OrderedFinite|) (|BooleanLogic|) (CATEGORY |domain| (ATTRIBUTE |canonical|) (SIGNATURE |xor| ($ $ $))))) (T |SingleInteger|)) ((|xor| (*1 *1 *1 *1) (|isDomain| *1 (|SingleInteger|)))) ((|Integer|) (|%ismall?| |#1|)) ((~= (#1=((|Boolean|) $ $) 18 (|has| |#1| . #2=((|BasicType|))) ELT)) (|top| ((|#1| $) 42 T ELT)) (|sample| (#3=($) 6 T CONST)) (|reduce| ((|#1| (|Mapping| |#1| |#1| |#1|) $ |#1| |#1|) 55 (|has| |#1| . #4=((|BasicType|))) ELT) ((|#1| (|Mapping| |#1| |#1| |#1|) $ |#1|) 51 T ELT) ((|#1| (|Mapping| |#1| |#1| |#1|) $) 50 T ELT)) (|push!| ((|#1| |#1| $) 44 T ELT)) (|pop!| ((|#1| $) 43 T ELT)) (|members| (((|List| |#1|) $) 49 T ELT)) (|member?| ((#5=(|Boolean|) |#1| $) 54 (|has| |#1| . #4#) ELT)) (|map!| (($ (|Mapping| |#1| |#1|) $) 39 T ELT)) (|map| (($ (|Mapping| |#1| |#1|) $) 26 T ELT)) (|latex| (((|String|) $) 21 (|has| |#1| . #6=((|SetCategory|))) ELT)) (|inspect| ((|#1| . #7=($)) 35 T ELT)) (|insert!| (($ |#1| $) 36 T ELT)) (|hash| (((|SingleInteger|) $) 20 (|has| |#1| . #6#) ELT)) (|find| (((|Union| |#1| "failed") (|Mapping| #5# |#1|) $) 52 T ELT)) (|extract!| ((|#1| . #7#) 37 T ELT)) (|every?| ((#5# (|Mapping| #5# |#1|) . #8=($)) 47 T ELT)) (|eval| (($ $ (|List| (|Equation| |#1|))) 25 (AND (|has| |#1| (|Evalable| |#1|)) (|has| |#1| . #6#)) ELT) (($ $ (|Equation| |#1|)) 24 (AND (|has| |#1| (|Evalable| |#1|)) (|has| |#1| . #6#)) ELT) (($ $ |#1| |#1|) 23 (AND (|has| |#1| (|Evalable| |#1|)) (|has| |#1| . #6#)) ELT) (($ $ (|List| |#1|) (|List| |#1|)) 22 (AND (|has| |#1| (|Evalable| |#1|)) (|has| |#1| . #6#)) ELT)) (|eq?| ((#9=(|Boolean|) $ $) 10 T ELT)) (|empty?| ((#9# $) 7 T ELT)) (|empty| (#3# 8 T ELT)) (|depth| (((|NonNegativeInteger|) $) 41 T ELT)) (|count| ((#10=(|NonNegativeInteger|) |#1| $) 53 (|has| |#1| . #4#) ELT) ((#10# (|Mapping| #5# |#1|) $) 48 T ELT)) (|copy| (($ $) 9 T ELT)) (|coerce| (((|OutputForm|) $) 16 (|has| |#1| (|CoercibleTo| (|OutputForm|))) ELT)) (|before?| (#1# 19 (|has| |#1| . #2#) ELT)) (|bag| (($ (|List| |#1|)) 38 T ELT)) (|any?| ((#5# (|Mapping| #5# |#1|) . #8#) 46 T ELT)) (= (#1# 17 (|has| |#1| . #2#) ELT)) (|#| ((#10# $) 45 T ELT))) @@ -3468,7 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((|Union| |#3| #11="failed") |#1|)) (SIGNATURE |retract| #6#) (SIGNATURE |retract| (#12=(|Fraction| #5#) |#1|)) (SIGNATURE |retractIfCan| ((|Union| #12# #11#) |#1|)) (SIGNATURE |coerce| (|#1| #12#)) (SIGNATURE |retract| (#5# |#1|)) (SIGNATURE |retractIfCan| ((|Union| #5# #11#) |#1|)) (SIGNATURE |differentiate| (|#1| |#1| #13=(|Mapping| |#3| |#3|))) (SIGNATURE |differentiate| (|#1| |#1| #13# #3#)) (SIGNATURE |coerce| (|#1| #5#)) (SIGNATURE ** #4#) (SIGNATURE ** (|#1| |#1| (|PositiveInteger|))) (SIGNATURE |coerce| ((|OutputForm|) |#1|))) (|SquareMatrixCategory| |#2| |#3| |#4| |#5|) #3# (|Ring|) #14=(|DirectProductCategory| |#2| |#3|) #14#) (T |SquareMatrixCategory&|)) NIL -((~= (#1=((|Boolean|) $ $) 7 T ELT)) (|zero?| ((#2=(|Boolean|) $) 22 T ELT)) (|trace| ((|#2| $) 91 T ELT)) (|symmetric?| (#3=((|Boolean|) $) 134 T ELT)) (|subtractIfCan| (((|Union| $ "failed") $ $) 26 T ELT)) (|square?| (#3# 132 T ELT)) (|scalarMatrix| (($ |#2|) 94 T ELT)) (|sample| (#4=($) 23 T CONST)) (|rowEchelon| (($ $) 151 (|has| |#2| (|EuclideanDomain|)) ELT)) (|row| ((|#3| $ #5=(|Integer|)) 146 T ELT)) (|retractIfCan| (((|Union| #6=(|Integer|) . #7=("failed")) . #8=($)) 110 (|has| |#2| . #9=((|RetractableTo| #6#))) ELT) (((|Union| #10=(|Fraction| #6#) . #7#) . #8#) 107 (|has| |#2| . #11=((|RetractableTo| #10#))) ELT) (((|Union| |#2| . #7#) . #8#) 104 T ELT)) (|retract| ((#6# . #12=($)) 109 (|has| |#2| . #9#) ELT) ((#10# . #12#) 106 (|has| |#2| . #11#) ELT) ((|#2| . #12#) 105 T ELT)) (|reducedSystem| (((|Matrix| #13=(|Integer|)) . #14=(#15=(|Matrix| $))) 100 (|has| |#2| . #16=((|LinearlyExplicitRingOver| #13#))) ELT) (((|Record| (|:| |mat| (|Matrix| #13#)) (|:| |vec| (|Vector| #13#))) . #17=(#15# #18=(|Vector| $))) 99 (|has| |#2| . #16#) ELT) (((|Record| (|:| |mat| (|Matrix| |#2|)) (|:| |vec| (|Vector| |#2|))) . #17#) 98 T ELT) (((|Matrix| |#2|) . #14#) 97 T ELT)) (|reduce| ((|#2| (|Mapping| |#2| |#2| |#2|) $) 116 T ELT) ((|#2| (|Mapping| |#2| |#2| |#2|) $ |#2|) 115 T ELT) ((|#2| (|Mapping| 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|#2|)) $) 142 T ELT)) (|leftReducedSystem| (((|Matrix| #13#) . #26=(#18#)) 102 (|has| |#2| . #16#) ELT) (((|Record| (|:| |mat| (|Matrix| #13#)) (|:| |vec| (|Vector| #13#))) . #27=(#18# $)) 101 (|has| |#2| . #16#) ELT) (((|Record| (|:| |mat| (|Matrix| |#2|)) (|:| |vec| (|Vector| |#2|))) . #27#) 96 T ELT) (((|Matrix| |#2|) . #26#) 95 T ELT)) (|latex| (((|String|) $) 11 T ELT)) (|inverse| (((|Union| $ "failed") $) 85 (|has| |#2| (|Field|)) ELT)) (|hash| (((|SingleInteger|) $) 12 T ELT)) (|find| (((|Union| |#2| "failed") (|Mapping| #25# |#2|) $) 114 T ELT)) (|exquo| (((|Union| $ "failed") $ |#2|) 149 (|has| |#2| . #21#) ELT)) (|every?| ((#25# (|Mapping| #25# |#2|) . #28=($)) 119 T ELT)) (|eval| (($ $ (|List| (|Equation| |#2|))) 125 (AND (|has| |#2| (|Evalable| |#2|)) (|has| |#2| . #29=((|SetCategory|)))) ELT) (($ $ (|Equation| |#2|)) 124 (AND (|has| |#2| (|Evalable| |#2|)) (|has| |#2| . #29#)) ELT) (($ $ |#2| |#2|) 123 (AND (|has| |#2| (|Evalable| |#2|)) (|has| |#2| . #29#)) ELT) (($ $ 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(ATTRIBUTE (|commutative| #23#))) ELT)) (|count| ((#40=(|NonNegativeInteger|) (|Mapping| #25# |#2|) $) 118 T ELT) ((#40# |#2| $) 113 (|has| |#2| . #19#) ELT)) (|copy| (($ $) 129 T ELT)) (|column| ((|#4| $ #5#) 147 T ELT)) (|coerce| (((|OutputForm|) $) 13 T ELT) (($ (|Integer|)) 41 T ELT) (($ #10#) 108 (|has| |#2| . #11#) ELT) (($ |#2|) 103 T ELT)) (|characteristic| (((|NonNegativeInteger|)) 40 T CONST)) (|before?| (#1# 6 T ELT)) (|any?| ((#25# (|Mapping| #25# |#2|) . #28#) 120 T ELT)) (|antisymmetric?| (#3# 135 T ELT)) (|annihilate?| (((|Boolean|) $ $) 33 T ELT)) (|Zero| (#4# 24 T CONST)) (|One| (($) 45 T CONST)) (D (($ $ (|Mapping| |#2| |#2|) . #31#) 67 T ELT) (($ $ (|Mapping| |#2| |#2|)) 66 T ELT) (($ . #32#) 54 (|has| |#2| . #33#) ELT) (#34# 52 (|has| |#2| . #33#) ELT) (($ $ #35#) 62 (|has| |#2| . #36#) ELT) (($ $ (|List| #35#)) 58 (|has| |#2| . #36#) ELT) (($ $ #35# . #37#) 57 (|has| |#2| . #36#) ELT) (($ $ (|List| #35#) . #39#) 56 (|has| |#2| . #36#) ELT)) (= (#1# 8 T ELT)) (/ (($ $ |#2|) 150 (|has| |#2| (|Field|)) ELT)) (- (($ $) 29 T ELT) (($ $ $) 28 T ELT)) (+ (($ $ $) 18 T ELT)) (** (($ $ (|PositiveInteger|)) 35 T ELT) (($ $ (|NonNegativeInteger|)) 43 T ELT) (($ $ (|Integer|)) 84 (|has| |#2| (|Field|)) ELT)) (* (($ (|PositiveInteger|) $) 17 T ELT) (($ (|NonNegativeInteger|) $) 21 T ELT) (($ (|Integer|) . #41=($)) 30 T ELT) (($ $ $) 34 T ELT) (($ $ |#2|) 156 T ELT) (($ |#2| . #41#) 155 T ELT) ((|#4| $ |#4|) 89 T ELT) ((|#3| |#3| $) 88 T ELT)) (|#| ((#40# $) 121 T ELT))) +((~= (#1=((|Boolean|) $ $) 7 T ELT)) (|zero?| ((#2=(|Boolean|) $) 22 T ELT)) (|trace| ((|#2| $) 92 T ELT)) (|symmetric?| (#3=((|Boolean|) $) 135 T ELT)) (|subtractIfCan| (((|Maybe| $) $ $) 26 T ELT)) (|square?| (#3# 133 T ELT)) (|scalarMatrix| (($ |#2|) 95 T ELT)) (|sample| (#4=($) 23 T CONST)) (|rowEchelon| (($ $) 152 (|has| |#2| (|EuclideanDomain|)) ELT)) (|row| ((|#3| $ #5=(|Integer|)) 147 T ELT)) (|retractIfCan| (((|Union| #6=(|Integer|) . #7=("failed")) . #8=($)) 111 (|has| |#2| . #9=((|RetractableTo| #6#))) ELT) (((|Union| #10=(|Fraction| #6#) . #7#) . #8#) 108 (|has| |#2| . #11=((|RetractableTo| #10#))) ELT) (((|Union| |#2| . #7#) . #8#) 105 T ELT)) (|retract| ((#6# . #12=($)) 110 (|has| |#2| . #9#) ELT) ((#10# . #12#) 107 (|has| |#2| . #11#) ELT) ((|#2| . #12#) 106 T ELT)) (|reducedSystem| (((|Matrix| #13=(|Integer|)) . #14=(#15=(|Matrix| $))) 101 (|has| |#2| . #16=((|LinearlyExplicitRingOver| #13#))) ELT) (((|Record| (|:| |mat| (|Matrix| #13#)) (|:| |vec| (|Vector| #13#))) . #17=(#15# #18=(|Vector| $))) 100 (|has| |#2| . #16#) ELT) (((|Record| (|:| |mat| (|Matrix| |#2|)) (|:| |vec| (|Vector| |#2|))) . #17#) 99 T ELT) (((|Matrix| |#2|) . #14#) 98 T ELT)) (|reduce| ((|#2| (|Mapping| |#2| |#2| |#2|) $) 117 T ELT) ((|#2| (|Mapping| |#2| |#2| |#2|) $ |#2|) 116 T ELT) ((|#2| (|Mapping| |#2| |#2| |#2|) $ |#2| |#2|) 112 (|has| |#2| . #19=((|BasicType|))) ELT)) (|recip| (((|Union| $ "failed") $) 43 T ELT)) (|rank| (#20=((|NonNegativeInteger|) $) 153 (|has| |#2| . #21=((|IntegralDomain|))) ELT)) (|qelt| ((|#2| . #22=($ #5# #5#)) 145 T ELT)) (|opposite?| ((#2# $ $) 20 T ELT)) (|one?| (((|Boolean|) $) 45 T ELT)) (|nullity| (#20# 154 (|has| |#2| . #21#) ELT)) (|nullSpace| (((|List| |#4|) $) 155 (|has| |#2| . #21#) ELT)) (|nrows| (#20# 141 T ELT)) (|ncols| (#20# 142 T ELT)) (|minordet| ((|#2| $) 87 (|has| |#2| (ATTRIBUTE (|commutative| #23="*"))) ELT)) (|minRowIndex| (#24=(#5# $) 137 T ELT)) (|minColIndex| (#24# 139 T ELT)) (|members| (((|List| |#2|) $) 118 T ELT)) (|member?| ((#25=(|Boolean|) |#2| $) 113 (|has| |#2| . #19#) ELT)) (|maxRowIndex| (#24# 138 T ELT)) (|maxColIndex| (#24# 140 T ELT)) (|matrix| (($ (|List| (|List| |#2|))) 132 T ELT)) (|map| (($ (|Mapping| |#2| |#2| |#2|) $ $) 149 T ELT) (($ (|Mapping| |#2| |#2|) $) 127 T ELT)) (|listOfLists| (((|List| (|List| |#2|)) $) 143 T ELT)) (|leftReducedSystem| (((|Matrix| #13#) . #26=(#18#)) 103 (|has| |#2| . #16#) ELT) (((|Record| (|:| |mat| (|Matrix| #13#)) (|:| |vec| (|Vector| #13#))) . #27=(#18# $)) 102 (|has| |#2| . #16#) ELT) (((|Record| (|:| |mat| (|Matrix| |#2|)) (|:| |vec| (|Vector| |#2|))) . #27#) 97 T ELT) (((|Matrix| |#2|) . #26#) 96 T ELT)) (|latex| (((|String|) $) 11 T ELT)) (|inverse| (((|Union| $ "failed") $) 86 (|has| |#2| (|Field|)) ELT)) (|hash| (((|SingleInteger|) $) 12 T ELT)) (|find| (((|Union| |#2| "failed") (|Mapping| #25# |#2|) $) 115 T ELT)) (|exquo| (((|Union| $ "failed") $ |#2|) 150 (|has| |#2| . #21#) ELT)) (|every?| ((#25# (|Mapping| #25# |#2|) . #28=($)) 120 T ELT)) (|eval| (($ $ (|List| (|Equation| |#2|))) 126 (AND (|has| |#2| (|Evalable| |#2|)) (|has| |#2| . #29=((|SetCategory|)))) ELT) (($ $ (|Equation| |#2|)) 125 (AND (|has| |#2| (|Evalable| |#2|)) (|has| |#2| . #29#)) ELT) (($ $ |#2| |#2|) 124 (AND (|has| |#2| (|Evalable| |#2|)) (|has| |#2| . #29#)) ELT) (($ $ (|List| |#2|) (|List| |#2|)) 123 (AND (|has| |#2| (|Evalable| |#2|)) (|has| |#2| . #29#)) ELT)) (|eq?| ((#30=(|Boolean|) $ $) 131 T ELT)) (|empty?| ((#30# $) 128 T ELT)) (|empty| (($) 129 T ELT)) (|elt| ((|#2| $ #5# #5# |#2|) 146 T ELT) ((|#2| . #22#) 144 T ELT)) (|differentiate| (($ $ (|Mapping| |#2| |#2|) . #31=((|NonNegativeInteger|))) 66 T ELT) (($ $ (|Mapping| |#2| |#2|)) 65 T ELT) (($ . #32=($)) 56 (|has| |#2| . #33=((|DifferentialSpace|))) ELT) (#34=($ $ (|NonNegativeInteger|)) 54 (|has| |#2| . #33#) ELT) (($ $ #35=(|Symbol|)) 64 (|has| |#2| . #36=((|PartialDifferentialSpace| (|Symbol|)))) ELT) (($ $ (|List| #35#)) 62 (|has| |#2| . #36#) ELT) (($ $ #35# . #37=(#38=(|NonNegativeInteger|))) 61 (|has| |#2| . #36#) ELT) (($ $ (|List| #35#) . #39=((|List| #38#))) 60 (|has| |#2| . #36#) ELT)) (|diagonalProduct| ((|#2| $) 91 T ELT)) (|diagonalMatrix| (($ (|List| |#2|)) 94 T ELT)) (|diagonal?| (#3# 134 T ELT)) (|diagonal| ((|#3| $) 93 T ELT)) (|determinant| ((|#2| $) 88 (|has| |#2| (ATTRIBUTE (|commutative| #23#))) ELT)) (|count| ((#40=(|NonNegativeInteger|) (|Mapping| #25# |#2|) $) 119 T ELT) ((#40# |#2| $) 114 (|has| |#2| . #19#) ELT)) (|copy| (($ $) 130 T ELT)) (|column| ((|#4| $ #5#) 148 T ELT)) (|coerce| (((|OutputForm|) $) 13 T ELT) (($ (|Integer|)) 42 T ELT) (($ #10#) 109 (|has| |#2| . #11#) ELT) (($ |#2|) 104 T ELT)) (|characteristic| (((|NonNegativeInteger|)) 41 T CONST)) (|before?| (#1# 6 T ELT)) (|any?| ((#25# (|Mapping| #25# |#2|) . #28#) 121 T ELT)) (|antisymmetric?| (#3# 136 T ELT)) (|annihilate?| (((|Boolean|) $ $) 34 T ELT)) (|Zero| (#4# 24 T CONST)) (|One| (($) 46 T CONST)) (D (($ $ (|Mapping| |#2| |#2|) . #31#) 68 T ELT) (($ $ (|Mapping| |#2| |#2|)) 67 T ELT) (($ . #32#) 55 (|has| |#2| . #33#) ELT) (#34# 53 (|has| |#2| . #33#) ELT) (($ $ #35#) 63 (|has| |#2| . #36#) ELT) (($ $ (|List| #35#)) 59 (|has| |#2| . #36#) ELT) (($ $ #35# . #37#) 58 (|has| |#2| . #36#) ELT) (($ $ (|List| #35#) . #39#) 57 (|has| |#2| . #36#) ELT)) (= (#1# 8 T ELT)) (/ (($ $ |#2|) 151 (|has| |#2| (|Field|)) ELT)) (- (($ $) 30 T ELT) (($ $ $) 29 T ELT)) (+ (($ $ $) 18 T ELT)) (** (($ $ (|PositiveInteger|)) 36 T ELT) (($ $ (|NonNegativeInteger|)) 44 T ELT) (($ $ (|Integer|)) 85 (|has| |#2| (|Field|)) ELT)) (* (($ (|PositiveInteger|) $) 17 T ELT) (($ (|NonNegativeInteger|) $) 21 T ELT) (($ (|Integer|) . #41=($)) 31 T ELT) (($ $ $) 35 T ELT) (($ $ |#2|) 157 T ELT) (($ |#2| . #41#) 156 T ELT) ((|#4| $ |#4|) 90 T ELT) ((|#3| |#3| $) 89 T ELT)) (|#| ((#40# $) 122 T ELT))) (((|SquareMatrixCategory| |#1| |#2| |#3| |#4|) (|Category|) (|NonNegativeInteger|) (|Ring|) (|DirectProductCategory| |t#1| |t#2|) (|DirectProductCategory| |t#1| |t#2|)) (T |SquareMatrixCategory|)) ((|scalarMatrix| (*1 *1 *2) (AND (|ofCategory| *2 (|Ring|)) (|ofCategory| *1 (|SquareMatrixCategory| *3 *2 *4 *5)) (|ofCategory| *4 (|DirectProductCategory| *3 *2)) (|ofCategory| *5 (|DirectProductCategory| *3 *2)))) (|diagonalMatrix| (*1 *1 *2) (AND (|isDomain| *2 (|List| *4)) (|ofCategory| *4 (|Ring|)) (|ofCategory| *1 (|SquareMatrixCategory| *3 *4 *5 *6)) (|ofCategory| *5 (|DirectProductCategory| *3 *4)) (|ofCategory| *6 (|DirectProductCategory| *3 *4)))) (|diagonal| (*1 *2 *1) (AND (|ofCategory| *1 (|SquareMatrixCategory| *3 *4 *2 *5)) (|ofCategory| *4 (|Ring|)) (|ofCategory| *5 (|DirectProductCategory| *3 *4)) (|ofCategory| *2 (|DirectProductCategory| *3 *4)))) (|trace| (*1 *2 *1) (AND (|ofCategory| *1 (|SquareMatrixCategory| *3 *2 *4 *5)) (|ofCategory| *4 (|DirectProductCategory| *3 *2)) (|ofCategory| *5 (|DirectProductCategory| *3 *2)) (|ofCategory| *2 (|Ring|)))) (|diagonalProduct| (*1 *2 *1) (AND (|ofCategory| *1 (|SquareMatrixCategory| *3 *2 *4 *5)) (|ofCategory| *4 (|DirectProductCategory| *3 *2)) (|ofCategory| *5 (|DirectProductCategory| *3 *2)) (|ofCategory| *2 (|Ring|)))) (* (*1 *2 *1 *2) (AND (|ofCategory| *1 (|SquareMatrixCategory| *3 *4 *5 *2)) (|ofCategory| *4 (|Ring|)) (|ofCategory| *5 (|DirectProductCategory| *3 *4)) (|ofCategory| *2 (|DirectProductCategory| *3 *4)))) (* (*1 *2 *2 *1) (AND (|ofCategory| *1 (|SquareMatrixCategory| *3 *4 *2 *5)) (|ofCategory| *4 (|Ring|)) (|ofCategory| *2 (|DirectProductCategory| *3 *4)) (|ofCategory| *5 (|DirectProductCategory| *3 *4)))) (|determinant| (*1 *2 *1) (AND (|ofCategory| *1 (|SquareMatrixCategory| *3 *2 *4 *5)) (|ofCategory| *4 (|DirectProductCategory| *3 *2)) (|ofCategory| *5 (|DirectProductCategory| *3 *2)) (|has| *2 (ATTRIBUTE (|commutative| #1="*"))) (|ofCategory| *2 (|Ring|)))) (|minordet| (*1 *2 *1) (AND (|ofCategory| *1 (|SquareMatrixCategory| *3 *2 *4 *5)) (|ofCategory| *4 (|DirectProductCategory| *3 *2)) (|ofCategory| *5 (|DirectProductCategory| *3 *2)) (|has| *2 (ATTRIBUTE (|commutative| #1#))) (|ofCategory| *2 (|Ring|)))) (|inverse| (*1 *1 *1) (|partial| AND (|ofCategory| *1 (|SquareMatrixCategory| *2 *3 *4 *5)) (|ofCategory| *3 (|Ring|)) (|ofCategory| *4 (|DirectProductCategory| *2 *3)) (|ofCategory| *5 (|DirectProductCategory| *2 *3)) (|ofCategory| *3 (|Field|)))) (** (*1 *1 *1 *2) (AND (|isDomain| *2 (|Integer|)) (|ofCategory| *1 (|SquareMatrixCategory| *3 *4 *5 *6)) (|ofCategory| *4 (|Ring|)) (|ofCategory| *5 (|DirectProductCategory| *3 *4)) (|ofCategory| *6 (|DirectProductCategory| *3 *4)) (|ofCategory| *4 (|Field|))))) (|Join| (|DifferentialExtension| |t#2|) (|BiModule| |t#2| |t#2|) (|RectangularMatrixCategory| |t#1| |t#1| |t#2| |t#3| |t#4|) (|FullyRetractableTo| |t#2|) (|FullyLinearlyExplicitRingOver| |t#2|) (CATEGORY |domain| (IF (|has| |t#2| (|CommutativeRing|)) (ATTRIBUTE (|Module| |t#2|)) |%noBranch|) (SIGNATURE |scalarMatrix| ($ |t#2|)) (SIGNATURE |diagonalMatrix| ($ (|List| |t#2|))) (SIGNATURE |diagonal| (|t#3| $)) (SIGNATURE |trace| (|t#2| $)) (SIGNATURE |diagonalProduct| (|t#2| $)) (SIGNATURE * (|t#4| $ |t#4|)) (SIGNATURE * (|t#3| |t#3| $)) (IF (|has| |t#2| (ATTRIBUTE (|commutative| "*"))) (PROGN (ATTRIBUTE (|Algebra| |t#2|)) (SIGNATURE |determinant| (|t#2| $)) (SIGNATURE |minordet| (|t#2| $))) |%noBranch|) (IF (|has| |t#2| (|Field|)) (PROGN (SIGNATURE |inverse| ((|Union| $ "failed") $)) (SIGNATURE ** ($ $ (|Integer|)))) |%noBranch|))) @@ -3476,10 +3476,10 @@ NIL ((|smith| (#1=(|#4| |#4|) 81 T ELT)) (|hermite| (#1# 76 T ELT)) (|diophantineSystem| (((|Record| (|:| |particular| (|Union| |#3| "failed")) (|:| |basis| (|List| |#3|))) |#4| |#3|) 91 T ELT)) (|completeSmith| (((|Record| (|:| |Smith| |#4|) (|:| |leftEqMat| |#4|) (|:| |rightEqMat| |#4|)) |#4|) 80 T ELT)) (|completeHermite| (((|Record| (|:| |Hermite| |#4|) (|:| |eqMat| |#4|)) |#4|) 78 T ELT))) (((|SmithNormalForm| |#1| |#2| |#3| |#4|) (CATEGORY |package| (SIGNATURE |hermite| #1=(|#4| |#4|)) (SIGNATURE |completeHermite| ((|Record| (|:| |Hermite| |#4|) (|:| |eqMat| |#4|)) |#4|)) (SIGNATURE |smith| #1#) (SIGNATURE |completeSmith| ((|Record| (|:| |Smith| |#4|) (|:| |leftEqMat| |#4|) (|:| |rightEqMat| |#4|)) |#4|)) (SIGNATURE |diophantineSystem| ((|Record| (|:| |particular| (|Union| |#3| "failed")) (|:| |basis| (|List| |#3|))) |#4| |#3|))) (|EuclideanDomain|) #2=(|FiniteLinearAggregate| |#1|) #2# (|MatrixCategory| |#1| |#2| |#3|)) (T |SmithNormalForm|)) ((|diophantineSystem| (*1 *2 *3 *4) (AND (|ofCategory| *5 #1=(|EuclideanDomain|)) (|ofCategory| *6 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(|SparseMultivariateTaylorSeries| *3 *4 *2)) (|ofCategory| *2 (|PolynomialCategory| *3 (|IndexedExponents| *4) *4)))) (* (*1 *1 *2 *1) #9#) (|csubst| (*1 *2 *3 *4) (AND (|isDomain| *3 (|List| *6)) (|isDomain| *4 (|List| #10=(|Stream| *7))) (|ofCategory| *6 #3#) (|ofCategory| *7 (|PolynomialCategory| *5 (|IndexedExponents| *6) *6)) (|ofCategory| *5 #2#) (|isDomain| *2 (|Mapping| #10# *7)) (|isDomain| *1 (|SparseMultivariateTaylorSeries| *5 *6 *7)))) (|integrate| (*1 *1 *1 *2 *3) (AND (|ofCategory| *3 #11=(|Algebra| (|Fraction| (|Integer|)))) #5# #6# #7# #8#)) (|fintegrate| (*1 *1 *2 *3 *4) (AND (|isDomain| *2 (|Mapping| #12=(|SparseMultivariateTaylorSeries| *4 *3 *5))) (|ofCategory| *4 #11#) #1# (|ofCategory| *3 #3#) (|isDomain| *1 #12#) (|ofCategory| *5 (|PolynomialCategory| *4 (|IndexedExponents| *3) *3))))) ((~= (#1=((|Boolean|) $ $) 7 T ELT)) (|zeroSetSplitIntoTriangularSystems| (((|List| (|Record| (|:| |close| $) (|:| |open| (|List| |#4|)))) (|List| |#4|)) 91 T ELT)) (|zeroSetSplit| (((|List| $) (|List| |#4|)) 92 T ELT) ((#2=(|List| $) (|List| |#4|) #3=(|Boolean|)) 120 T ELT)) (|variables| (((|List| |#3|) . #4=($)) 39 T ELT)) (|trivialIdeal?| (#5=(#6=(|Boolean|) $) 32 T ELT)) (|triangular?| (#5# 23 (|has| |#1| . #7=((|IntegralDomain|))) ELT)) (|stronglyReduced?| ((#8=(|Boolean|) |#4| . #9=($)) 107 T ELT) (#10=(#8# $) 103 T ELT)) (|stronglyReduce| ((|#4| |#4| . #11=($)) 98 T ELT)) (|squareFreePart| (((|List| (|Record| (|:| |val| |#4|) . #12=(#13=(|:| |tower| $)))) |#4| $) 135 T ELT)) (|sort| (((|Record| (|:| |under| $) (|:| |floor| $) (|:| |upper| $)) $ |#3|) 33 T ELT)) (|select| (($ (|Mapping| #14=(|Boolean|) |#4|) . #15=($)) 67 (|has| $ (|FiniteAggregate| |#4|)) ELT) (((|Union| |#4| . #16=(#17="failed")) $ |#3|) 85 T ELT)) (|sample| (#18=($) 59 T CONST)) (|roughUnitIdeal?| (#5# 28 (|has| |#1| . #7#) ELT)) (|roughSubIdeal?| (#19=(#6# $ $) 30 (|has| |#1| . #7#) ELT)) (|roughEqualIdeals?| (#19# 29 (|has| |#1| . #7#) ELT)) (|roughBase?| (#5# 31 (|has| 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(|reduceByQuasiMonic| ((|#4| |#4| . #11#) 93 T ELT)) (|reduce| ((|#4| (|Mapping| |#4| |#4| |#4|) $ |#4| |#4|) 54 (|has| |#4| . #23=((|BasicType|))) ELT) ((|#4| (|Mapping| |#4| |#4| |#4|) $ |#4|) 50 T ELT) ((|#4| (|Mapping| |#4| |#4| |#4|) $) 49 T ELT) ((|#4| |#4| $ (|Mapping| |#4| |#4| |#4|) (|Mapping| #8# |#4| |#4|)) 100 T ELT)) (|quasiComponent| (((|Record| (|:| |close| (|List| |#4|)) (|:| |open| (|List| |#4|))) $) 111 T ELT)) (|purelyTranscendental?| ((#3# |#4| . #24=($)) 145 T ELT)) (|purelyAlgebraicLeadingMonomial?| ((#3# |#4| . #24#) 142 T ELT)) (|purelyAlgebraic?| ((#3# |#4| . #24#) 146 T ELT) ((#3# $) 143 T ELT)) (|normalized?| ((#8# |#4| . #9#) 110 T ELT) (#10# 109 T ELT)) (|mvar| ((|#3| $) 40 T ELT)) (|members| (((|List| |#4|) $) 48 T ELT)) (|member?| ((#25=(|Boolean|) |#4| $) 53 (|has| |#4| . #23#) ELT)) (|map!| (($ (|Mapping| |#4| |#4|) $) 117 T ELT)) (|map| (($ (|Mapping| |#4| |#4|) $) 60 T ELT)) (|mainVariables| (((|List| |#3|) . #4#) 38 T ELT)) (|mainVariable?| ((#6# |#3| $) 37 T ELT)) (|latex| (((|String|) $) 11 T ELT)) (|lastSubResultantElseSplit| (((|Union| |#4| #2#) |#4| |#4| $) 137 T ELT)) (|lastSubResultant| (((|List| (|Record| (|:| |val| |#4|) . #12#)) |#4| |#4| $) 136 T ELT)) (|last| (((|Union| |#4| . #16#) . #26=($)) 89 T ELT)) (|invertibleSet| ((#2# |#4| . #27=($)) 138 T ELT)) (|invertibleElseSplit?| (((|Union| #3# #2#) |#4| $) 141 T ELT)) (|invertible?| (((|List| (|Record| (|:| |val| #3#) #13#)) |#4| $) 140 T ELT) ((#3# |#4| . #24#) 139 T ELT)) (|intersect| ((#2# |#4| . #27#) 134 T ELT) ((#2# (|List| |#4|) . #28=($)) 133 T ELT) ((#2# (|List| |#4|) . #29=(#2#)) 132 T ELT) ((#2# |#4| . #30=(#2#)) 131 T ELT)) (|internalAugment| (($ |#4| $) 126 T ELT) (($ (|List| |#4|) $) 125 T ELT)) (|initials| (((|List| |#4|) $) 113 T ELT)) (|initiallyReduced?| ((#8# |#4| . #9#) 105 T ELT) (#10# 101 T ELT)) (|initiallyReduce| ((|#4| |#4| . #11#) 96 T ELT)) (|infRittWu?| ((#8# $ $) 116 T ELT)) (|headRemainder| (((|Record| (|:| |num| |#4|) (|:| |den| |#1|)) 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((#33=(|Boolean|) $ $) 55 T ELT)) (|empty?| ((#33# $) 58 T ELT)) (|empty| (#18# 57 T ELT)) (|degree| (#34=((|NonNegativeInteger|) $) 112 T ELT)) (|count| ((#35=(|NonNegativeInteger|) |#4| $) 52 (|has| |#4| . #23#) ELT) ((#35# (|Mapping| #25# |#4|) $) 47 T ELT)) (|copy| (($ $) 56 T ELT)) (|convert| ((#36=(|InputForm|) $) 70 (|has| |#4| (|ConvertibleTo| #36#)) ELT)) (|construct| (($ (|List| |#4|)) 65 T ELT)) (|collectUpper| (($ $ |#3|) 34 T ELT)) (|collectUnder| (($ $ |#3|) 36 T ELT)) (|collectQuasiMonic| (($ $) 94 T ELT)) (|collect| (($ $ |#3|) 35 T ELT)) (|coerce| (((|OutputForm|) . #37=($)) 13 T ELT) (((|List| |#4|) . #37#) 43 T ELT)) (|coHeight| (#34# 82 (|has| |#3| (|Finite|)) ELT)) (|before?| (#1# 6 T ELT)) (|basicSet| (((|Union| (|Record| #38=(|:| |bas| $) (|:| |top| (|List| |#4|))) . #39=(#17#)) (|List| |#4|) (|Mapping| #8# |#4| |#4|)) 115 T ELT) (((|Union| (|Record| #38# (|:| |top| (|List| |#4|))) . #39#) (|List| |#4|) (|Mapping| #8# |#4|) (|Mapping| #8# |#4| |#4|)) 114 T ELT)) 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NIL T ELT) #38#) (|differentiate| #52=(($ $ #44# #36#) NIL T ELT) #53=(($ $ #44#) NIL T ELT) #54=(#5# NIL #55=(|has| |#2| (|DifferentialSpace|)) ELT) #56=(#57=($ $ #36#) NIL #55# ELT) #58=(($ $ #59=(|Symbol|)) NIL #60=(|has| |#2| (|PartialDifferentialSpace| #59#)) ELT) #61=(($ $ #62=(|List| #59#)) NIL #60# ELT) #63=(($ $ #59# #36#) NIL #60# ELT) #64=(($ $ #62# (|List| #36#)) NIL #60# ELT)) (|diagonalProduct| #6#) (|diagonalMatrix| (($ #42#) 48 T ELT)) (|diagonal?| #3#) (|diagonal| ((#14# $) NIL T ELT)) (|determinant| (#7# 62 #40# ELT)) (|count| ((#36# #48# $) NIL T ELT) ((#36# |#2| $) NIL #33# ELT)) (|copy| #4#) (|convert| ((#65=(|InputForm|) $) 87 (|has| |#2| (|ConvertibleTo| #65#)) ELT)) (|column| (#13# 42 T ELT)) (|coerce| (((|OutputForm|) $) 45 T ELT) (($ #15#) NIL T ELT) (($ #19#) NIL #20# ELT) (#11# NIL T ELT) ((#10# $) 50 T ELT)) (|characteristic| ((#36#) 21 T CONST)) (|before?| #1#) (|any?| #49#) (|antisymmetric?| #3#) (|annihilate?| #1#) (|Zero| (#12# 15 T CONST)) (|One| (#12# 19 T CONST)) (D #52# #53# #54# #56# #58# #61# #63# #64#) (= #1#) (/ (#66=($ $ |#2|) NIL #47# ELT)) (- #4# #67=(($ $ $) NIL T ELT)) (+ #67#) (** (($ $ #68=(|PositiveInteger|)) NIL T ELT) (#57# 60 T ELT) (($ $ #15#) 79 #47# ELT)) (* (($ #68# $) NIL T ELT) (($ #36# $) NIL T ELT) (($ #15# . #69=($)) NIL T ELT) #67# (#66# NIL T ELT) (($ |#2| . #69#) NIL T ELT) ((#14# $ #14#) 56 T ELT) ((#14# #14# $) 58 T ELT)) (|#| #39#)) -(((|SquareMatrix| |#1| |#2|) (|Join| (|SquareMatrixCategory| |#1| |#2| #1=(|DirectProduct| |#1| |#2|) #1#) (|CoercibleTo| #2=(|Matrix| |#2|)) (CATEGORY |domain| (SIGNATURE |new| ($ |#2|)) (SIGNATURE |transpose| ($ $)) (SIGNATURE |squareMatrix| ($ #2#)) (IF #3=(|has| |#2| (ATTRIBUTE (|commutative| "*"))) (ATTRIBUTE |central|) |%noBranch|) (IF #3# (IF (|has| |#2| #4=(ATTRIBUTE |unitsKnown|)) #4# |%noBranch|) |%noBranch|) (IF (|has| |#2| #5=(|ConvertibleTo| (|InputForm|))) (ATTRIBUTE #5#) |%noBranch|))) (|NonNegativeInteger|) (|Ring|)) (T |SquareMatrix|)) +((~= #1=((#2=(|Boolean|) $ $) NIL T ELT)) (|zero?| #3=((#2# $) NIL T ELT)) (|transpose| #4=(#5=($ $) NIL T ELT)) (|trace| #6=(#7=(|#2| $) NIL T ELT)) (|symmetric?| #3#) (|subtractIfCan| (((|Maybe| $) $ $) NIL T ELT)) (|squareMatrix| (($ #8=(|Matrix| |#2|)) 53 T ELT)) (|square?| #3#) (|scalarMatrix| (#9=($ |#2|) 14 T ELT)) (|sample| (#10=($) NIL T CONST)) (|rowEchelon| (#5# 66 (|has| |#2| (|EuclideanDomain|)) ELT)) (|row| (#11=(#12=(|DirectProduct| |#1| |#2|) $ #13=(|Integer|)) 40 T ELT)) (|retractIfCan| (((|Union| #13# . #14=(#15="failed")) . #16=($)) NIL #17=(|has| |#2| (|RetractableTo| #13#)) ELT) (((|Union| #18=(|Fraction| #13#) . #14#) . #16#) NIL #19=(|has| |#2| (|RetractableTo| #18#)) ELT) ((#20=(|Union| |#2| . #14#) . #16#) NIL T ELT)) (|retract| (#21=(#13# . #22=($)) NIL #17# ELT) ((#18# . #22#) NIL #19# ELT) #6#) (|reducedSystem| ((#23=(|Matrix| #13#) . #24=(#25=(|Matrix| $))) NIL #26=(|has| |#2| (|LinearlyExplicitRingOver| #13#)) ELT) ((#27=(|Record| (|:| |mat| #23#) (|:| |vec| (|Vector| #13#))) . #28=(#25# #29=(|Vector| $))) NIL #26# ELT) ((#30=(|Record| (|:| |mat| #8#) (|:| |vec| (|Vector| |#2|))) . #28#) NIL T ELT) ((#8# . #24#) NIL T ELT)) (|reduce| ((|#2| #31=(|Mapping| |#2| |#2| |#2|) $) NIL T ELT) ((|#2| #31# $ |#2|) NIL T ELT) ((|#2| #31# $ |#2| |#2|) NIL #32=(|has| |#2| (|BasicType|)) ELT)) (|recip| (#33=(#34=(|Union| $ #15#) $) 80 T ELT)) (|rank| (#35=(#36=(|NonNegativeInteger|) $) 68 #37=(|has| |#2| (|IntegralDomain|)) ELT)) (|qelt| #38=((|#2| $ #13# #13#) NIL T ELT)) (|opposite?| #1#) (|one?| #3#) (|nullity| (#35# 70 #37# ELT)) (|nullSpace| (((|List| #12#) $) 74 #37# ELT)) (|nrows| #39=(#35# NIL T ELT)) (|new| (#9# 23 T ELT)) (|ncols| #39#) (|minordet| (#7# 64 #40=(|has| |#2| (ATTRIBUTE (|commutative| "*"))) ELT)) (|minRowIndex| #41=(#21# NIL T ELT)) (|minColIndex| #41#) (|members| ((#42=(|List| |#2|) $) NIL T ELT)) (|member?| ((#2# |#2| $) NIL #32# ELT)) (|maxRowIndex| #41#) (|maxColIndex| #41#) (|matrix| (($ #43=(|List| #42#)) 35 T ELT)) (|map| (($ #31# $ $) NIL T ELT) (($ #44=(|Mapping| |#2| |#2|) $) NIL T ELT)) (|listOfLists| ((#43# $) NIL T ELT)) (|leftReducedSystem| ((#23# . #45=(#29#)) NIL #26# ELT) ((#27# . #46=(#29# $)) NIL #26# ELT) ((#30# . #46#) NIL T ELT) ((#8# . #45#) NIL T ELT)) (|latex| (((|String|) $) NIL T ELT)) (|inverse| (#33# 77 #47=(|has| |#2| (|Field|)) ELT)) (|hash| (((|SingleInteger|) $) NIL T ELT)) (|find| ((#20# #48=(|Mapping| #2# |#2|) $) NIL T ELT)) (|exquo| ((#34# $ |#2|) NIL #37# ELT)) (|every?| #49=((#2# #48# $) NIL T ELT)) (|eval| (($ $ (|List| #50=(|Equation| |#2|))) NIL #51=(AND (|has| |#2| (|Evalable| |#2|)) (|has| |#2| (|SetCategory|))) ELT) (($ $ #50#) NIL #51# ELT) (($ $ |#2| |#2|) NIL #51# ELT) (($ $ #42# #42#) NIL #51# ELT)) (|eq?| #1#) (|empty?| #3#) (|empty| (#10# NIL T ELT)) (|elt| ((|#2| $ #13# #13# |#2|) NIL T ELT) #38#) (|differentiate| #52=(($ $ #44# #36#) NIL T ELT) #53=(($ $ #44#) NIL T ELT) #54=(#5# NIL #55=(|has| |#2| (|DifferentialSpace|)) ELT) #56=(#57=($ $ #36#) NIL #55# ELT) #58=(($ $ #59=(|Symbol|)) NIL #60=(|has| |#2| (|PartialDifferentialSpace| #59#)) ELT) #61=(($ $ #62=(|List| #59#)) NIL #60# ELT) #63=(($ $ #59# #36#) NIL #60# ELT) #64=(($ $ #62# (|List| #36#)) NIL #60# ELT)) (|diagonalProduct| #6#) (|diagonalMatrix| (($ #42#) 48 T ELT)) (|diagonal?| #3#) (|diagonal| ((#12# $) NIL T ELT)) (|determinant| (#7# 62 #40# ELT)) (|count| ((#36# #48# $) NIL T ELT) ((#36# |#2| $) NIL #32# ELT)) (|copy| #4#) (|convert| ((#65=(|InputForm|) $) 87 (|has| |#2| (|ConvertibleTo| #65#)) ELT)) (|column| (#11# 42 T ELT)) (|coerce| (((|OutputForm|) $) 45 T ELT) (($ #13#) NIL T ELT) (($ #18#) NIL #19# ELT) (#9# NIL T ELT) ((#8# $) 50 T ELT)) (|characteristic| ((#36#) 21 T CONST)) (|before?| #1#) (|any?| #49#) (|antisymmetric?| #3#) (|annihilate?| #1#) (|Zero| (#10# 15 T CONST)) (|One| (#10# 19 T CONST)) (D #52# #53# #54# #56# #58# #61# #63# #64#) (= #1#) (/ (#66=($ $ |#2|) NIL #47# ELT)) (- #4# #67=(($ $ $) NIL T ELT)) (+ #67#) (** (($ $ #68=(|PositiveInteger|)) NIL T ELT) (#57# 60 T ELT) (($ $ #13#) 79 #47# ELT)) (* (($ #68# $) NIL T ELT) (($ #36# $) NIL T ELT) (($ #13# . #69=($)) NIL T ELT) #67# (#66# NIL T ELT) (($ |#2| . #69#) NIL T ELT) ((#12# $ #12#) 56 T ELT) ((#12# #12# $) 58 T ELT)) (|#| #39#)) +(((|SquareMatrix| |#1| |#2|) (|Join| (|SquareMatrixCategory| |#1| |#2| #1=(|DirectProduct| |#1| |#2|) #1#) (|CoercibleTo| #2=(|Matrix| |#2|)) (CATEGORY |domain| (SIGNATURE |new| ($ |#2|)) (SIGNATURE |transpose| ($ $)) (SIGNATURE |squareMatrix| ($ #2#)) (IF (|has| |#2| #3=(|ConvertibleTo| (|InputForm|))) (ATTRIBUTE #3#) |%noBranch|))) (|NonNegativeInteger|) (|Ring|)) (T |SquareMatrix|)) ((|new| #1=(*1 *1 *2) (AND (|isDomain| *1 (|SquareMatrix| *3 *2)) #2=(|ofType| *3 #3=(|NonNegativeInteger|)) (|ofCategory| *2 #4=(|Ring|)))) (|transpose| (*1 *1 *1) (AND (|isDomain| *1 (|SquareMatrix| *2 *3)) (|ofType| *2 #3#) (|ofCategory| *3 #4#))) (|squareMatrix| #1# (AND (|isDomain| *2 (|Matrix| *4)) (|ofCategory| *4 #4#) (|isDomain| *1 (|SquareMatrix| *3 *4)) #2#))) ((|upperCase| (#1=($ $) 19 T ELT)) (|trim| (($ $ #2=(|Character|)) 10 T ELT) (($ $ (|CharacterClass|)) 14 T ELT)) (|prefix?| (((|Boolean|) $ $) 24 T ELT)) (|lowerCase| (#1# 17 T ELT)) (|elt| ((#2# $ #3=(|Integer|) #2#) NIL T ELT) ((#2# $ #3#) NIL T ELT) (($ $ (|UniversalSegment| #3#)) NIL T ELT) (($ $ $) 31 T ELT)) (|coerce| (($ #2#) 29 T ELT) (((|OutputForm|) $) NIL T ELT))) (((|StringAggregate&| |#1|) (CATEGORY |package| (SIGNATURE |coerce| ((|OutputForm|) |#1|)) (SIGNATURE |elt| (|#1| |#1| |#1|)) (SIGNATURE |trim| (|#1| |#1| (|CharacterClass|))) (SIGNATURE |trim| (|#1| |#1| #1=(|Character|))) (SIGNATURE |coerce| (|#1| #1#)) (SIGNATURE |prefix?| ((|Boolean|) |#1| |#1|)) (SIGNATURE |upperCase| #2=(|#1| |#1|)) (SIGNATURE |lowerCase| #2#) (SIGNATURE |elt| (|#1| |#1| (|UniversalSegment| #3=(|Integer|)))) (SIGNATURE |elt| (#1# |#1| #3#)) (SIGNATURE |elt| (#1# |#1| #3# #1#))) (|StringAggregate|)) (T |StringAggregate&|)) @@ -3620,7 +3620,7 @@ NIL ((~= #1=(((|Boolean|) $ $) NIL T ELT)) (|predicate| (((|SpadAst|) $) 10 T ELT)) (|latex| (((|String|) $) NIL T ELT)) (|hash| (((|SingleInteger|) $) NIL T ELT)) (|coerce| (((|OutputForm|) $) 16 T ELT) (($ #2=(|Syntax|)) NIL T ELT) ((#2# $) NIL T ELT)) (|before?| #1#) (= #1#)) (((|SuchThatAst|) (|Join| (|SpadSyntaxCategory|) (CATEGORY |domain| (SIGNATURE |predicate| ((|SpadAst|) $))))) (T |SuchThatAst|)) ((|predicate| (*1 *2 *1) (AND (|isDomain| *2 (|SpadAst|)) (|isDomain| *1 (|SuchThatAst|))))) -((~= #1=(#2=(#3=(|Boolean|) $ $) NIL T ELT)) (|zero?| #4=(#5=(#3# $) NIL T ELT)) (|wholePart| (#6=(#7=(|SparseUnivariateTaylorSeries| |#1| |#2| |#3|) $) NIL #8=(AND (|has| #7# (|EuclideanDomain|)) #9=(|has| |#1| (|Field|))) ELT)) (|variables| ((#10=(|List| #11=(|SingletonAsOrderedSet|)) $) NIL T ELT)) (|variable| (#12=(#13=(|Symbol|) $) 11 T ELT)) (|unitNormal| (((|Record| (|:| |unit| $) (|:| |canonical| $) (|:| |associate| $)) $) NIL #14=(OR #15=(AND #16=(|has| #7# (|PolynomialFactorizationExplicit|)) #9#) #17=(AND (|has| #7# (|OrderedIntegralDomain|)) #9#) #18=(|has| |#1| (|IntegralDomain|))) ELT)) (|unitCanonical| #19=(#20=($ $) NIL #14# ELT)) (|unit?| (#5# NIL #14# ELT)) (|truncate| (#21=($ $ #22=(|Integer|)) NIL T ELT) (($ $ #22# #22#) 75 T ELT)) (|terms| ((#23=(|Stream| (|Record| (|:| |k| #22#) (|:| |c| |#1|))) $) NIL T ELT)) (|taylorRep| (#6# 42 T ELT)) (|taylorIfCan| (#24=((|Union| #7# #25="failed") $) 32 T ELT)) (|taylor| (#6# 33 T ELT)) (|tanh| (#20# 116 #26=(|has| |#1| (|Algebra| #27=(|Fraction| #22#))) ELT)) (|tan| (#20# 92 #26# ELT)) (|subtractIfCan| (#28=(#29=(|Union| $ #25#) $ $) NIL T ELT)) (|squareFreePolynomial| #30=(((|Factored| #31=(|SparseUnivariatePolynomial| $)) #31#) NIL #15# ELT)) (|squareFreePart| #32=(#20# NIL #9# ELT)) (|squareFree| #33=(((|Factored| $) $) NIL #9# ELT)) (|sqrt| (#20# NIL #26# ELT)) (|solveLinearPolynomialEquation| (((|Union| #34=(|List| #31#) #25#) #34# #31#) NIL #15# ELT)) (|sizeLess?| (#2# NIL #9# ELT)) (|sinh| (#20# 112 #26# ELT)) (|sin| (#20# 88 #26# ELT)) (|sign| (#35=(#22# $) NIL #17# ELT)) (|series| (($ #23#) NIL T ELT)) (|sech| (#20# 120 #26# ELT)) (|sec| (#20# 96 #26# ELT)) (|sample| (#36=($) NIL T CONST)) (|retractIfCan| (#24# 34 T ELT) (((|Union| #13# . #37=(#25#)) . #38=($)) NIL #39=(AND (|has| #7# (|RetractableTo| #13#)) #9#) ELT) (((|Union| #27# . #37#) . #38#) NIL #40=(AND (|has| #7# (|RetractableTo| #22#)) #9#) ELT) (((|Union| #22# . #37#) . #38#) NIL #40# ELT)) (|retract| (#6# 140 T ELT) (#12# NIL #39# ELT) ((#27# $) NIL #40# ELT) (#35# NIL #40# ELT)) (|removeZeroes| (#20# 37 T ELT) (#41=($ #22# $) 38 T ELT)) (|rem| #42=(#43=($ $ $) NIL #9# ELT)) (|reductum| #44=(#20# NIL T ELT)) (|reducedSystem| ((#45=(|Matrix| #7#) . #46=(#47=(|Matrix| $))) NIL #9# ELT) ((#48=(|Record| (|:| |mat| #45#) (|:| |vec| (|Vector| #7#))) . #49=(#47# #50=(|Vector| $))) NIL #9# ELT) ((#51=(|Record| (|:| |mat| #52=(|Matrix| #22#)) (|:| |vec| (|Vector| #22#))) . #49#) NIL #53=(AND (|has| #7# (|LinearlyExplicitRingOver| #22#)) #9#) ELT) ((#52# . #46#) NIL #53# ELT)) (|recip| ((#29# $) 54 T ELT)) (|rationalFunction| ((#54=(|Fraction| (|Polynomial| |#1|)) $ #22#) 74 #18# ELT) ((#54# $ #22# #22#) 76 #18# ELT)) (|random| (#36# NIL #55=(AND (|has| #7# (|IntegerNumberSystem|)) #9#) ELT)) (|quo| #42#) (|principalIdeal| (((|Record| (|:| |coef| #56=(|List| $)) #57=(|:| |generator| $)) #56#) NIL #9# ELT)) (|prime?| (#5# NIL #9# ELT)) (|positive?| #58=(#5# NIL #17# ELT)) (|pole?| (#5# 28 T ELT)) (|pi| (#36# NIL #26# ELT)) (|patternMatch| ((#59=(|PatternMatchResult| #60=(|Float|) . #61=($)) $ #62=(|Pattern| #60#) #59#) NIL (AND (|has| #7# (|PatternMatchable| #60#)) #9#) ELT) ((#63=(|PatternMatchResult| #22# . #61#) $ #64=(|Pattern| #22#) #63#) NIL (AND (|has| #7# (|PatternMatchable| #22#)) #9#) ELT)) (|order| (#35# NIL T ELT) ((#22# $ #22#) 26 T ELT)) (|opposite?| #1#) (|one?| #4#) (|numerator| #32#) (|numer| (#6# 44 #9# ELT)) (|nthRoot| (#21# NIL #26# ELT)) (|nextItem| (#65=((|Maybe| $) $) NIL #66=(AND (|has| #7# (|StepThrough|)) #9#) ELT)) (|negative?| #58#) (|multiplyExponents| #67=(($ $ #68=(|PositiveInteger|)) NIL T ELT)) (|multiplyCoefficients| (($ (|Mapping| |#1| #22#) $) NIL T ELT)) (|multiEuclidean| (((|Union| #56# #25#) #56# $) NIL #9# ELT)) (|monomial?| #4#) (|monomial| (($ |#1| #22#) 19 T ELT) (($ $ #11# #22#) NIL T ELT) (($ $ #10# (|List| #22#)) NIL T ELT)) (|min| #69=(#43# NIL #70=(OR #17# (AND (|has| #7# (|OrderedSet|)) #9#)) ELT)) (|max| #69#) (|map| (($ (|Mapping| |#1| |#1|) . #71=($)) NIL T ELT) (($ #72=(|Mapping| #7# #7#) . #71#) NIL #9# ELT)) (|log| (#20# 81 #26# ELT)) (|leftReducedSystem| ((#45# . #73=(#50#)) NIL #9# ELT) ((#48# . #74=(#50# $)) NIL #9# ELT) ((#51# . #74#) NIL #53# ELT) ((#52# . #73#) NIL #53# ELT)) (|leadingMonomial| #44#) (|leadingCoefficient| (#75=(|#1| $) NIL T ELT)) (|lcm| #76=(($ #56#) NIL #9# ELT) #42#) (|laurent| (($ #22# #7#) 36 T ELT)) (|latex| (((|String|) $) NIL T ELT)) (|inv| #32#) (|integrate| (#20# 79 #26# ELT) (#77=($ $ #13#) NIL (OR (AND #26# (|has| |#1| (|AlgebraicallyClosedFunctionSpace| #22#)) (|has| |#1| (|PrimitiveFunctionCategory|)) (|has| |#1| (|TranscendentalFunctionCategory|))) (AND #26# (|has| |#1| (SIGNATURE |integrate| (|#1| |#1| #13#))) (|has| |#1| (SIGNATURE |variables| (#78=(|List| #13#) |#1|))))) ELT) (#79=($ $ #80=(|Variable| |#2|)) 80 #26# ELT)) (|init| (#36# NIL #66# CONST)) (|hash| (((|SingleInteger|) $) NIL T ELT)) (|gcdPolynomial| ((#31# #31# #31#) NIL #9# ELT)) (|gcd| #76# #42#) (|fractionPart| (#20# NIL #8# ELT)) (|floor| #81=(#6# NIL #55# ELT)) (|factorSquareFreePolynomial| #30#) (|factorPolynomial| #30#) (|factor| #33#) (|extendedEuclidean| (((|Union| (|Record| #82=(|:| |coef1| $) #83=(|:| |coef2| $)) #25#) $ $ $) NIL #9# ELT) (((|Record| #82# #83# #57#) $ $) NIL #9# ELT)) (|extend| (#21# 158 T ELT)) (|exquo| (#28# 55 #14# ELT)) (|expressIdealMember| (((|Maybe| #56#) #56# $) NIL #9# ELT)) (|exp| (#20# 82 #26# ELT)) (|eval| (((|Stream| |#1|) $ |#1|) NIL #84=(|has| |#1| (SIGNATURE ** (|#1| |#1| #22#))) ELT) (($ 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(|sinh| (#20# 112 #26# ELT)) (|sin| (#20# 88 #26# ELT)) (|sign| (#34=(#22# $) NIL #17# ELT)) (|series| (($ #23#) NIL T ELT)) (|sech| (#20# 120 #26# ELT)) (|sec| (#20# 96 #26# ELT)) (|sample| (#35=($) NIL T CONST)) (|retractIfCan| (#24# 34 T ELT) (((|Union| #13# . #36=(#25#)) . #37=($)) NIL #38=(AND (|has| #7# (|RetractableTo| #13#)) #9#) ELT) (((|Union| #27# . #36#) . #37#) NIL #39=(AND (|has| #7# (|RetractableTo| #22#)) #9#) ELT) (((|Union| #22# . #36#) . #37#) NIL #39# ELT)) (|retract| (#6# 140 T ELT) (#12# NIL #38# ELT) ((#27# $) NIL #39# ELT) (#34# NIL #39# ELT)) (|removeZeroes| (#20# 37 T ELT) (#40=($ #22# $) 38 T ELT)) (|rem| #41=(#42=($ $ $) NIL #9# ELT)) (|reductum| #43=(#20# NIL T ELT)) (|reducedSystem| ((#44=(|Matrix| #7#) . #45=(#46=(|Matrix| $))) NIL #9# ELT) ((#47=(|Record| (|:| |mat| #44#) (|:| |vec| (|Vector| #7#))) . #48=(#46# #49=(|Vector| $))) NIL #9# ELT) ((#50=(|Record| (|:| |mat| #51=(|Matrix| #22#)) (|:| |vec| (|Vector| #22#))) . #48#) NIL #52=(AND (|has| #7# (|LinearlyExplicitRingOver| #22#)) #9#) ELT) ((#51# . #45#) NIL #52# ELT)) (|recip| ((#53=(|Union| $ #25#) $) 54 T ELT)) (|rationalFunction| ((#54=(|Fraction| (|Polynomial| |#1|)) $ #22#) 74 #18# ELT) ((#54# $ #22# #22#) 76 #18# ELT)) (|random| (#35# NIL #55=(AND (|has| #7# (|IntegerNumberSystem|)) #9#) ELT)) (|quo| #41#) (|principalIdeal| (((|Record| (|:| |coef| #56=(|List| $)) #57=(|:| |generator| $)) #56#) NIL #9# ELT)) (|prime?| (#5# NIL #9# ELT)) (|positive?| #58=(#5# NIL #17# ELT)) (|pole?| (#5# 28 T ELT)) (|pi| (#35# NIL #26# ELT)) (|patternMatch| ((#59=(|PatternMatchResult| #60=(|Float|) . #61=($)) $ #62=(|Pattern| #60#) #59#) NIL (AND (|has| #7# (|PatternMatchable| #60#)) #9#) ELT) ((#63=(|PatternMatchResult| #22# . #61#) $ #64=(|Pattern| #22#) #63#) NIL (AND (|has| #7# (|PatternMatchable| #22#)) #9#) ELT)) (|order| (#34# NIL T ELT) ((#22# $ #22#) 26 T ELT)) (|opposite?| #1#) (|one?| #4#) (|numerator| #31#) (|numer| (#6# 44 #9# ELT)) (|nthRoot| (#21# NIL #26# ELT)) (|nextItem| (#65=(#28# $) NIL #66=(AND (|has| #7# (|StepThrough|)) #9#) ELT)) (|negative?| #58#) (|multiplyExponents| #67=(($ $ #68=(|PositiveInteger|)) NIL T ELT)) (|multiplyCoefficients| (($ (|Mapping| |#1| #22#) $) NIL T ELT)) (|multiEuclidean| (((|Union| #56# #25#) #56# $) NIL #9# ELT)) (|monomial?| #4#) (|monomial| (($ |#1| #22#) 19 T ELT) (($ $ #11# #22#) NIL T ELT) (($ $ #10# (|List| #22#)) NIL T ELT)) (|min| #69=(#42# NIL #70=(OR #17# (AND (|has| #7# (|OrderedSet|)) #9#)) ELT)) (|max| #69#) (|map| (($ (|Mapping| |#1| |#1|) . #71=($)) NIL T ELT) (($ #72=(|Mapping| #7# #7#) . #71#) NIL #9# ELT)) (|log| (#20# 81 #26# ELT)) (|leftReducedSystem| ((#44# . #73=(#49#)) NIL #9# ELT) ((#47# . #74=(#49# $)) NIL #9# ELT) ((#50# . #74#) NIL #52# ELT) ((#51# . #73#) NIL #52# ELT)) (|leadingMonomial| #43#) (|leadingCoefficient| (#75=(|#1| $) NIL T ELT)) (|lcm| #76=(($ #56#) NIL #9# ELT) #41#) (|laurent| (($ #22# #7#) 36 T ELT)) (|latex| (((|String|) $) NIL T ELT)) (|inv| #31#) (|integrate| (#20# 79 #26# ELT) (#77=($ $ #13#) NIL (OR (AND #26# (|has| |#1| (|AlgebraicallyClosedFunctionSpace| #22#)) (|has| |#1| (|PrimitiveFunctionCategory|)) (|has| |#1| (|TranscendentalFunctionCategory|))) (AND #26# (|has| |#1| (SIGNATURE |integrate| (|#1| |#1| #13#))) (|has| |#1| (SIGNATURE |variables| (#78=(|List| #13#) |#1|))))) ELT) (#79=($ $ #80=(|Variable| |#2|)) 80 #26# ELT)) (|init| (#35# NIL #66# CONST)) (|hash| (((|SingleInteger|) $) NIL T ELT)) (|gcdPolynomial| ((#30# #30# #30#) NIL #9# ELT)) (|gcd| #76# #41#) (|fractionPart| (#20# NIL #8# ELT)) (|floor| #81=(#6# NIL #55# ELT)) (|factorSquareFreePolynomial| #29#) (|factorPolynomial| #29#) (|factor| #32#) (|extendedEuclidean| (((|Union| (|Record| #82=(|:| |coef1| $) #83=(|:| |coef2| $)) #25#) $ $ $) NIL #9# ELT) (((|Record| #82# #83# #57#) $ $) NIL #9# ELT)) (|extend| (#21# 158 T ELT)) (|exquo| ((#53# $ $) 55 #14# ELT)) (|expressIdealMember| (((|Maybe| #56#) #56# $) NIL #9# ELT)) (|exp| (#20# 82 #26# ELT)) (|eval| (((|Stream| |#1|) $ |#1|) NIL #84=(|has| |#1| (SIGNATURE ** (|#1| |#1| #22#))) ELT) (($ $ #13# #7#) NIL #85=(AND (|has| #7# (|InnerEvalable| #13# #7#)) #9#) ELT) (($ $ #78# #86=(|List| #7#)) NIL #85# ELT) (($ $ (|List| #87=(|Equation| #7#))) NIL #88=(AND (|has| #7# (|Evalable| #7#)) #9#) ELT) (($ $ #87#) NIL #88# ELT) (($ $ #7# #7#) NIL #88# ELT) (($ $ #86# #86#) NIL #88# ELT)) (|euclideanSize| ((#89=(|NonNegativeInteger|) $) NIL #9# ELT)) (|elt| (#90=(|#1| $ #22#) NIL T ELT) (#42# 61 (|has| #22# (|SemiGroup|)) ELT) (#91=($ $ #7#) NIL (AND (|has| #7# (|Eltable| #7# #7#)) #9#) ELT)) (|divide| (((|Record| (|:| |quotient| $) (|:| |remainder| $)) $ $) NIL #9# ELT)) (|differentiate| #92=(($ $ #72# #89#) NIL #9# ELT) #93=(($ $ #72#) NIL #9# ELT) (#79# 57 T ELT) (#20# 56 #94=(OR (AND (|has| #7# (|DifferentialRing|)) #9#) (AND (|has| #7# (|DifferentialSpace|)) #9#) #95=(|has| |#1| (SIGNATURE * (|#1| #22# |#1|)))) ELT) #96=(#97=($ $ #89#) NIL #94# ELT) #98=(#77# NIL #99=(OR (AND (|has| #7# #100=(|PartialDifferentialRing| #13#)) #9#) (AND (|has| #7# (|PartialDifferentialSpace| #13#)) #9#) (AND (|has| |#1| #100#) #95#)) ELT) #101=(($ $ #78#) NIL #99# ELT) #102=(($ $ #13# #89#) NIL #99# ELT) #103=(($ $ #78# (|List| #89#)) NIL #99# ELT)) (|denominator| #31#) (|denom| (#6# 46 #9# ELT)) (|degree| (#34# 43 T ELT)) (|csch| (#20# 122 #26# ELT)) (|csc| (#20# 98 #26# ELT)) (|coth| (#20# 118 #26# ELT)) (|cot| (#20# 94 #26# ELT)) (|cosh| (#20# 114 #26# ELT)) (|cos| (#20# 90 #26# ELT)) (|convert| ((#104=(|InputForm|) . #105=($)) NIL (AND (|has| #7# (|ConvertibleTo| #104#)) #9#) ELT) ((#60# . #105#) NIL #106=(AND (|has| #7# (|RealConstant|)) #9#) ELT) (((|DoubleFloat|) . #105#) NIL #106# ELT) ((#62# . #105#) NIL (AND (|has| #7# (|ConvertibleTo| #62#)) #9#) ELT) ((#64# . #105#) NIL (AND (|has| #7# (|ConvertibleTo| #64#)) #9#) ELT)) (|conditionP| (((|Union| #49# #25#) #46#) NIL #107=(AND (|has| $ #108=(|CharacteristicNonZero|)) #16# #9#) ELT)) (|complete| #43#) (|coerce| (((|OutputForm|) $) 162 T ELT) (($ #22#) NIL T ELT) (($ |#1|) NIL (|has| |#1| (|CommutativeRing|)) ELT) (($ #7#) 30 T ELT) (($ #80#) 25 T ELT) (($ #13#) NIL #38# ELT) #19# (($ #27#) NIL (OR #39# #26#) ELT)) (|coefficient| (#90# 77 T ELT)) (|charthRoot| (#65# NIL (OR #107# (AND (|has| #7# #108#) #9#) (|has| |#1| #108#)) ELT)) (|characteristic| ((#89#) NIL T CONST)) (|center| (#75# 12 T ELT)) (|ceiling| #81#) (|before?| #1#) (|atanh| (#20# 128 #26# ELT)) (|atan| (#20# 104 #26# ELT)) (|associates?| (#2# NIL #14# ELT)) (|asinh| (#20# 124 #26# ELT)) (|asin| (#20# 100 #26# ELT)) (|asech| (#20# 132 #26# ELT)) (|asec| (#20# 108 #26# ELT)) (|approximate| (#90# NIL (AND #84# (|has| |#1| (SIGNATURE |coerce| (|#1| #13#)))) ELT)) (|annihilate?| #1#) (|acsch| (#20# 134 #26# ELT)) (|acsc| (#20# 110 #26# ELT)) (|acoth| (#20# 130 #26# ELT)) (|acot| (#20# 106 #26# ELT)) (|acosh| (#20# 126 #26# ELT)) (|acos| (#20# 102 #26# ELT)) (|abs| (#20# NIL #17# ELT)) (|Zero| (#35# 21 T CONST)) (|One| (#35# 16 T CONST)) (D #92# #93# (#79# NIL T ELT) (#20# NIL #94# ELT) #96# #98# #101# #102# #103#) (>= #109=(#2# NIL #70# ELT)) (> #109#) (= #1#) (<= #109#) (< #109#) (/ (#110=($ $ |#1|) NIL #9# ELT) (#42# 49 #9# ELT) (($ #7# #7#) 50 #9# ELT)) (- #43# (#42# NIL T ELT)) (+ (#42# 23 T ELT)) (** #67# (#97# 60 T ELT) (#21# NIL #9# ELT) (#42# 83 #26# ELT) (#111=($ $ #27#) 137 #26# ELT)) (* (($ #68# $) NIL T ELT) (($ #89# $) NIL T ELT) (#40# NIL T ELT) (#42# 35 T ELT) (#110# NIL T ELT) (($ |#1| . #112=($)) NIL T ELT) (#91# 48 #9# ELT) (($ #7# $) 47 #9# ELT) (($ #27# . #112#) NIL #26# ELT) (#111# NIL #26# ELT))) (((|SparseUnivariateLaurentSeries| |#1| |#2| |#3|) (|Join| (|UnivariateLaurentSeriesConstructorCategory| |#1| (|SparseUnivariateTaylorSeries| |#1| |#2| |#3|)) (|PartialDifferentialDomain| $ #1=(|Variable| |#2|)) (CATEGORY |domain| (SIGNATURE |coerce| ($ #1#)) (IF (|has| |#1| (|Algebra| (|Fraction| (|Integer|)))) (SIGNATURE |integrate| ($ $ #1#)) |%noBranch|))) (|Ring|) (|Symbol|) |#1|) (T |SparseUnivariateLaurentSeries|)) ((|coerce| (*1 *1 *2) (AND #1=(|isDomain| *2 (|Variable| *4)) #2=(|ofType| *4 (|Symbol|)) #3=(|isDomain| *1 (|SparseUnivariateLaurentSeries| *3 *4 *5)) #4=(|ofCategory| *3 (|Ring|)) #5=(|ofType| *5 *3))) (|integrate| (*1 *1 *1 *2) (AND #1# #2# #3# (|ofCategory| *3 (|Algebra| (|Fraction| (|Integer|)))) #4# #5#))) ((|sum| ((|#2| |#2| (|SegmentBinding| |#2|)) 26 T ELT) ((|#2| |#2| (|Symbol|)) 28 T ELT))) @@ -3629,7 +3629,7 @@ NIL ((|sum| ((#1=(|Union| #2=(|Fraction| #3=(|Polynomial| |#1|)) (|Expression| |#1|)) #2# (|SegmentBinding| #2#)) 31 T ELT) ((#2# #3# (|SegmentBinding| #3#)) 44 T ELT) ((#1# #2# #4=(|Symbol|)) 33 T ELT) ((#2# #3# #4#) 36 T ELT))) (((|RationalFunctionSum| |#1|) (CATEGORY |package| (SIGNATURE |sum| (#1=(|Fraction| #2=(|Polynomial| |#1|)) #2# #3=(|Symbol|))) (SIGNATURE |sum| (#4=(|Union| #1# (|Expression| |#1|)) #1# #3#)) (SIGNATURE |sum| (#1# #2# (|SegmentBinding| #2#))) (SIGNATURE |sum| (#4# #1# (|SegmentBinding| #1#)))) (|Join| (|IntegralDomain|) (|RetractableTo| (|Integer|)))) (T |RationalFunctionSum|)) ((|sum| #1=(*1 *2 *3 *4) (AND (|isDomain| *4 (|SegmentBinding| #2=(|Fraction| #3=(|Polynomial| *5)))) #4=(|isDomain| *3 #2#) #5=(|ofCategory| *5 (|Join| (|IntegralDomain|) (|RetractableTo| (|Integer|)))) (|isDomain| *2 (|Union| *3 #6=(|Expression| *5))) #7=(|isDomain| *1 (|RationalFunctionSum| *5)))) (|sum| #1# (AND (|isDomain| *4 (|SegmentBinding| #3#)) #8=(|isDomain| *3 #3#) #5# (|isDomain| *2 (|Fraction| *3)) #7#)) (|sum| #1# (AND #9=(|isDomain| *4 (|Symbol|)) #5# (|isDomain| *2 (|Union| #2# #6#)) #7# #4#)) (|sum| #1# (AND #9# #5# (|isDomain| *2 #2#) #7# #8#))) -((~= (#1=(#2=(|Boolean|) $ $) 172 T ELT)) (|zero?| (#3=(#2# $) 44 T ELT)) (|vectorise| ((#4=(|Vector| |#1|) $ #5=(|NonNegativeInteger|)) NIL T ELT)) (|variables| ((#6=(|List| #7=(|SingletonAsOrderedSet|)) $) NIL T ELT)) (|unmakeSUP| (($ #8=(|SparseUnivariatePolynomial| |#1|)) NIL T ELT)) (|univariate| ((#9=(|SparseUnivariatePolynomial| $) $ #7#) 83 T ELT) (#10=(#8# $) 72 T ELT)) (|unitNormal| (((|Record| (|:| |unit| $) (|:| |canonical| $) (|:| |associate| $)) $) NIL #11=(|has| |#1| (|IntegralDomain|)) ELT)) (|unitCanonical| (#12=($ $) 166 #11# ELT)) (|unit?| (#3# NIL #11# ELT)) (|totalDegree| #13=(#14=(#5# $) NIL T ELT) ((#5# $ #6#) NIL T ELT)) (|subtractIfCan| (#15=(#16=(|Union| $ #17="failed") $ $) NIL T ELT)) (|subResultantGcd| (#18=($ $ $) 160 #11# ELT)) (|squareFreePolynomial| (#19=((|Factored| #9#) #9#) 97 #20=(|has| |#1| (|PolynomialFactorizationExplicit|)) ELT)) (|squareFreePart| (#12# NIL #21=(|has| |#1| (|GcdDomain|)) ELT)) (|squareFree| (#22=((|Factored| $) $) NIL #21# ELT)) (|solveLinearPolynomialEquation| (((|Union| #23=(|List| #9#) #17#) #23# #9#) 117 #20# ELT)) (|sizeLess?| (#1# NIL #24=(|has| |#1| (|Field|)) ELT)) (|shiftRight| (#25=($ $ #5#) 62 T ELT)) (|shiftLeft| (#25# 64 T ELT)) (|separate| (((|Record| (|:| |primePart| $) (|:| |commonPart| $)) $ $) NIL #21# ELT)) (|sample| (#26=($) NIL T CONST)) (|retractIfCan| (((|Union| |#1| . #27=(#17#)) . #28=($)) NIL T ELT) (((|Union| #29=(|Fraction| #30=(|Integer|)) . #27#) . #28#) NIL #31=(|has| |#1| (|RetractableTo| #29#)) ELT) (((|Union| #30# . #27#) . #28#) NIL #32=(|has| |#1| (|RetractableTo| #30#)) ELT) #33=(((|Union| #7# . #27#) . #28#) NIL T ELT)) (|retract| #34=(#35=(|#1| . #36=($)) NIL T ELT) ((#29# . #36#) NIL #31# ELT) ((#30# . #36#) NIL #32# ELT) ((#7# . #36#) NIL T ELT)) (|resultant| (($ $ $ #7#) NIL #37=(|has| |#1| (|CommutativeRing|)) ELT) ((|#1| $ $) 162 #37# ELT)) (|rem| #38=(#18# NIL #24# ELT)) (|reductum| (#12# 81 T ELT)) (|reducedSystem| ((#39=(|Matrix| #30#) . #40=(#41=(|Matrix| $))) NIL #42=(|has| |#1| (|LinearlyExplicitRingOver| #30#)) ELT) ((#43=(|Record| (|:| |mat| #39#) (|:| |vec| (|Vector| #30#))) . #44=(#41# #45=(|Vector| $))) NIL #42# ELT) ((#46=(|Record| (|:| |mat| #47=(|Matrix| |#1|)) (|:| |vec| #4#)) . #44#) NIL T ELT) ((#47# . #40#) NIL T ELT)) (|recip| ((#16# $) NIL T ELT)) (|quo| #38#) (|pseudoRemainder| (#18# 133 T ELT)) (|pseudoQuotient| (#18# NIL #11# ELT)) (|pseudoDivide| (((|Record| (|:| |coef| |#1|) #48=(|:| |quotient| $) #49=(|:| |remainder| $)) $ $) NIL #11# ELT)) (|principalIdeal| (((|Record| (|:| |coef| #50=(|List| $)) #51=(|:| |generator| $)) #50#) NIL #24# ELT)) (|primitivePart| (#12# 167 #21# ELT) #52=(#53=($ $ #7#) NIL #21# ELT)) (|primitiveMonomials| #54=((#50# $) NIL T ELT)) (|prime?| (#3# NIL #20# ELT)) (|pomopo!| (($ $ |#1| #5# $) 70 T ELT)) (|patternMatch| ((#55=(|PatternMatchResult| #56=(|Float|) . #57=($)) $ #58=(|Pattern| #56#) #55#) NIL (AND (|has| #7# #59=(|PatternMatchable| #56#)) (|has| |#1| #59#)) ELT) ((#60=(|PatternMatchResult| #30# . #57#) $ #61=(|Pattern| #30#) #60#) NIL (AND (|has| #7# #62=(|PatternMatchable| #30#)) (|has| |#1| #62#)) ELT)) (|outputForm| ((#63=(|OutputForm|) $ #63#) 150 T ELT)) (|order| ((#5# $ $) NIL #11# ELT)) (|opposite?| #64=(#1# NIL T ELT)) (|one?| (#3# 49 T ELT)) (|numberOfMonomials| #13#) (|nextItem| (#65=((|Maybe| $) $) NIL #66=(|has| |#1| (|StepThrough|)) ELT)) (|multivariate| (($ #8# #7#) 74 T ELT) (($ #9# #7#) 91 T ELT)) (|multiplyExponents| (#25# 52 T ELT)) (|multiEuclidean| ((#67=(|Union| #50# #17#) #50# $) NIL #24# ELT)) (|monomials| #54#) (|monomial?| (#3# NIL T ELT)) (|monomial| (($ |#1| #5#) 89 T ELT) #68=(($ $ #7# #5#) NIL T ELT) #69=(($ $ #6# #70=(|List| #5#)) NIL T ELT)) (|monicDivide| ((#71=(|Record| #48# #49#) $ $ #7#) NIL T ELT) (#72=(#71# $ $) 155 T ELT)) (|minimumDegree| #13# #73=((#5# $ #7#) NIL T ELT) #74=((#70# $ #6#) NIL T ELT)) (|mapExponents| (($ (|Mapping| #5# #5#) $) NIL T ELT)) (|map| (($ #75=(|Mapping| |#1| |#1|) $) NIL T ELT)) (|makeSUP| (#10# NIL T ELT)) (|mainVariable| #33#) (|leftReducedSystem| ((#39# . #76=(#45#)) NIL #42# ELT) ((#43# . #77=(#45# $)) NIL #42# ELT) ((#46# . #77#) NIL T ELT) ((#47# . #76#) NIL T ELT)) (|leadingMonomial| #78=(#12# NIL T ELT)) (|leadingCoefficient| (#35# 77 T ELT)) (|lcm| #79=(($ #50#) NIL #21# ELT) (#18# NIL #21# ELT)) (|latex| (((|String|) $) NIL T ELT)) (|karatsubaDivide| ((#71# $ #5#) 61 T ELT)) (|isTimes| #80=((#67# $) NIL T ELT)) (|isPlus| #80#) (|isExpt| (((|Union| (|Record| (|:| |var| #7#) (|:| |exponent| #5#)) #17#) $) NIL T ELT)) (|integrate| (#12# NIL #81=(|has| |#1| (|Algebra| #29#)) ELT)) (|init| (#26# NIL #66# CONST)) (|hash| (((|SingleInteger|) $) NIL T ELT)) (|ground?| (#3# 51 T ELT)) (|ground| #34#) (|gcdPolynomial| ((#9# #9# #9#) 105 #21# ELT)) (|gcd| #79# (#18# 169 #21# ELT)) (|fmecg| (($ $ #5# |#1| $) 125 T ELT)) (|factorSquareFreePolynomial| (#19# 103 #20# ELT)) (|factorPolynomial| (#19# 102 #20# ELT)) (|factor| (#22# 110 #20# ELT)) (|extendedEuclidean| (((|Union| (|Record| #82=(|:| |coef1| $) #83=(|:| |coef2| $)) #17#) $ $ $) NIL #24# ELT) (((|Record| #82# #83# #51#) $ $) NIL #24# ELT)) (|exquo| ((#16# $ |#1|) 165 #11# ELT) (#15# 126 #11# ELT)) (|expressIdealMember| (((|Maybe| #50#) #50# $) NIL #24# ELT)) (|eval| (($ $ (|List| #84=(|Equation| $))) NIL T ELT) (($ $ #84#) NIL T ELT) (($ $ $ $) NIL T ELT) (($ $ #50# #50#) NIL T ELT) (($ $ #7# |#1|) NIL T ELT) (($ $ #6# #85=(|List| |#1|)) NIL T ELT) (($ $ #7# $) NIL T ELT) (($ $ #6# #50#) NIL T ELT)) (|euclideanSize| (#14# NIL #24# ELT)) (|elt| ((|#1| $ |#1|) 152 T ELT) (#18# 153 T ELT) ((#86=(|Fraction| $) #86# #86#) NIL #11# ELT) ((|#1| #86# |#1|) NIL #24# ELT) ((#86# $ #86#) NIL #11# ELT)) (|divideExponents| ((#16# $ #5#) 55 T ELT)) (|divide| (#72# 173 #24# ELT)) (|discriminant| (#53# NIL #37# ELT) (#35# 158 #37# ELT)) (|differentiate| #69# #68# #87=(($ $ #6#) NIL T ELT) #88=(#53# NIL T ELT) #78# #89=(#25# NIL T ELT) #90=(($ $ #75#) NIL T ELT) #91=(($ $ #75# #5#) NIL T ELT) (($ $ #75# $) NIL T ELT) #92=(($ $ #93=(|Symbol|)) NIL #94=(|has| |#1| (|PartialDifferentialSpace| #93#)) ELT) #95=(($ $ #96=(|List| #93#)) NIL #94# ELT) #97=(($ $ #93# #5#) NIL #94# ELT) #98=(($ $ #96# #70#) NIL #94# ELT)) (|degree| (#14# 79 T ELT) #73# #74#) (|convert| ((#58# . #99=($)) NIL (AND (|has| #7# #100=(|ConvertibleTo| #58#)) (|has| |#1| #100#)) ELT) ((#61# . #99#) NIL (AND (|has| #7# #101=(|ConvertibleTo| #61#)) (|has| |#1| #101#)) ELT) ((#102=(|InputForm|) . #99#) NIL (AND (|has| #7# #103=(|ConvertibleTo| #102#)) (|has| |#1| #103#)) ELT)) (|content| (#35# 164 #21# ELT) #52#) (|conditionP| (((|Union| #45# #17#) #41#) NIL #104=(AND (|has| $ #105=(|CharacteristicNonZero|)) #20#) ELT)) (|composite| (#15# NIL #11# ELT) (((|Union| #86# #17#) #86# $) NIL #11# ELT)) (|coerce| ((#63# $) 151 T ELT) (($ #30#) NIL T ELT) (($ |#1|) 78 T ELT) (($ #7#) NIL T ELT) (($ #29#) NIL (OR #81# #31#) ELT) (#12# NIL #11# ELT)) (|coefficients| ((#85# $) NIL T ELT)) (|coefficient| ((|#1| $ #5#) NIL T ELT) #68# #69#) (|charthRoot| (#65# NIL (OR #104# (|has| |#1| #105#)) ELT)) (|characteristic| ((#5#) NIL T CONST)) (|binomThmExpt| (($ $ $ #5#) 42 #37# ELT)) (|before?| #64#) (|associates?| (#1# NIL #11# ELT)) (|annihilate?| #64#) (|Zero| (#26# 18 T CONST)) (|One| (#26# 20 T CONST)) (D #69# #68# #87# #88# #78# #89# #90# #91# #92# #95# #97# #98#) (= (#1# 122 T ELT)) (/ (#106=($ $ |#1|) 174 #24# ELT)) (- #78# (#18# NIL T ELT)) (+ (#18# 92 T ELT)) (** (($ $ #107=(|PositiveInteger|)) 14 T ELT) (#25# 12 T ELT)) (* (($ #107# $) NIL T ELT) (($ #5# $) NIL T ELT) (($ #30# . #108=($)) NIL T ELT) (#18# 40 T ELT) (($ $ #29#) NIL #81# ELT) (($ #29# . #108#) NIL #81# ELT) (($ |#1| . #108#) 131 T ELT) (#106# NIL T ELT))) +((~= (#1=(#2=(|Boolean|) $ $) 177 T ELT)) (|zero?| (#3=(#2# $) 44 T ELT)) (|vectorise| ((#4=(|Vector| |#1|) $ #5=(|NonNegativeInteger|)) NIL T ELT)) (|variables| ((#6=(|List| #7=(|SingletonAsOrderedSet|)) $) NIL T ELT)) (|unmakeSUP| (($ #8=(|SparseUnivariatePolynomial| |#1|)) NIL T ELT)) (|univariate| ((#9=(|SparseUnivariatePolynomial| $) $ #7#) 86 T ELT) (#10=(#8# $) 75 T ELT)) (|unitNormal| (((|Record| (|:| |unit| $) (|:| |canonical| $) (|:| |associate| $)) $) NIL #11=(|has| |#1| (|IntegralDomain|)) ELT)) (|unitCanonical| (#12=($ $) 171 #11# ELT)) (|unit?| (#3# NIL #11# ELT)) (|totalDegree| #13=(#14=(#5# $) NIL T ELT) ((#5# $ #6#) NIL T ELT)) (|subtractIfCan| ((#15=(|Maybe| $) $ $) NIL T ELT)) (|subResultantGcd| (#16=($ $ $) 165 #11# ELT)) (|squareFreePolynomial| (#17=((|Factored| #9#) #9#) 100 #18=(|has| |#1| (|PolynomialFactorizationExplicit|)) ELT)) (|squareFreePart| (#12# NIL #19=(|has| |#1| (|GcdDomain|)) ELT)) (|squareFree| (#20=((|Factored| $) $) NIL #19# ELT)) (|solveLinearPolynomialEquation| (((|Union| #21=(|List| #9#) #22="failed") #21# #9#) 120 #18# ELT)) (|sizeLess?| (#1# NIL #23=(|has| |#1| (|Field|)) ELT)) (|shiftRight| (#24=($ $ #5#) 65 T ELT)) (|shiftLeft| (#24# 67 T ELT)) (|separate| (((|Record| (|:| |primePart| $) (|:| |commonPart| $)) $ $) NIL #19# ELT)) (|sample| (#25=($) NIL T CONST)) (|retractIfCan| (((|Union| |#1| . #26=(#22#)) . #27=($)) NIL T ELT) (((|Union| #28=(|Fraction| #29=(|Integer|)) . #26#) . #27#) NIL #30=(|has| |#1| (|RetractableTo| #28#)) ELT) (((|Union| #29# . #26#) . #27#) NIL #31=(|has| |#1| (|RetractableTo| #29#)) ELT) #32=(((|Union| #7# . #26#) . #27#) NIL T ELT)) (|retract| #33=(#34=(|#1| . #35=($)) NIL T ELT) ((#28# . #35#) NIL #30# ELT) ((#29# . #35#) NIL #31# ELT) ((#7# . #35#) NIL T ELT)) (|resultant| (($ $ $ #7#) NIL #36=(|has| |#1| (|CommutativeRing|)) ELT) ((|#1| $ $) 167 #36# ELT)) (|rem| #37=(#16# NIL #23# ELT)) (|reductum| (#12# 84 T ELT)) (|reducedSystem| ((#38=(|Matrix| #29#) . #39=(#40=(|Matrix| $))) NIL #41=(|has| |#1| (|LinearlyExplicitRingOver| #29#)) ELT) ((#42=(|Record| (|:| |mat| #38#) (|:| |vec| (|Vector| #29#))) . #43=(#40# #44=(|Vector| $))) NIL #41# ELT) ((#45=(|Record| (|:| |mat| #46=(|Matrix| |#1|)) (|:| |vec| #4#)) . #43#) NIL T ELT) ((#46# . #39#) NIL T ELT)) (|recip| ((#47=(|Union| $ #22#) $) NIL T ELT)) (|quo| #37#) (|pseudoRemainder| (#16# 138 T ELT)) (|pseudoQuotient| (#16# NIL #11# ELT)) (|pseudoDivide| (((|Record| (|:| |coef| |#1|) #48=(|:| |quotient| $) #49=(|:| |remainder| $)) $ $) NIL #11# ELT)) (|principalIdeal| (((|Record| (|:| |coef| #50=(|List| $)) #51=(|:| |generator| $)) #50#) NIL #23# ELT)) (|primitivePart| (#12# 172 #19# ELT) #52=(#53=($ $ #7#) NIL #19# ELT)) (|primitiveMonomials| #54=((#50# $) NIL T ELT)) (|prime?| (#3# NIL #18# ELT)) (|pomopo!| (($ $ |#1| #5# $) 73 T ELT)) (|patternMatch| ((#55=(|PatternMatchResult| #56=(|Float|) . #57=($)) $ #58=(|Pattern| #56#) #55#) NIL (AND (|has| #7# #59=(|PatternMatchable| #56#)) (|has| |#1| #59#)) ELT) ((#60=(|PatternMatchResult| #29# . #57#) $ #61=(|Pattern| #29#) #60#) NIL (AND (|has| #7# #62=(|PatternMatchable| #29#)) (|has| |#1| #62#)) ELT)) (|outputForm| ((#63=(|OutputForm|) $ #63#) 155 T ELT)) (|order| ((#5# $ $) NIL #11# ELT)) (|opposite?| #64=(#1# NIL T ELT)) (|one?| (#3# 49 T ELT)) (|numberOfMonomials| #13#) (|nextItem| (#65=(#15# $) NIL #66=(|has| |#1| (|StepThrough|)) ELT)) (|multivariate| (($ #8# #7#) 77 T ELT) (($ #9# #7#) 94 T ELT)) (|multiplyExponents| (#24# 52 T ELT)) (|multiEuclidean| ((#67=(|Union| #50# #22#) #50# $) NIL #23# ELT)) (|monomials| #54#) (|monomial?| (#3# NIL T ELT)) (|monomial| (($ |#1| #5#) 92 T ELT) #68=(($ $ #7# #5#) NIL T ELT) #69=(($ $ #6# #70=(|List| #5#)) NIL T ELT)) (|monicDivide| ((#71=(|Record| #48# #49#) $ $ #7#) NIL T ELT) (#72=(#71# $ $) 160 T ELT)) (|minimumDegree| #13# #73=((#5# $ #7#) NIL T ELT) #74=((#70# $ #6#) NIL T ELT)) (|mapExponents| (($ (|Mapping| #5# #5#) $) NIL T ELT)) (|map| (($ #75=(|Mapping| |#1| |#1|) $) NIL T ELT)) (|makeSUP| (#10# NIL T ELT)) (|mainVariable| #32#) (|leftReducedSystem| ((#38# . #76=(#44#)) NIL #41# ELT) ((#42# . #77=(#44# $)) NIL #41# ELT) ((#45# . #77#) NIL T ELT) ((#46# . #76#) NIL T ELT)) (|leadingMonomial| #78=(#12# NIL T ELT)) (|leadingCoefficient| (#34# 80 T ELT)) (|lcm| #79=(($ #50#) NIL #19# ELT) (#16# NIL #19# ELT)) (|latex| (((|String|) $) NIL T ELT)) (|karatsubaDivide| ((#71# $ #5#) 64 T ELT)) (|isTimes| #80=((#67# $) NIL T ELT)) (|isPlus| #80#) (|isExpt| (((|Union| (|Record| (|:| |var| #7#) (|:| |exponent| #5#)) #22#) $) NIL T ELT)) (|integrate| (#12# NIL #81=(|has| |#1| (|Algebra| #28#)) ELT)) (|init| (#25# NIL #66# CONST)) (|hash| (((|SingleInteger|) $) NIL T ELT)) (|ground?| (#3# 51 T ELT)) (|ground| #33#) (|gcdPolynomial| ((#9# #9# #9#) 108 #19# ELT)) (|gcd| #79# (#16# 174 #19# ELT)) (|fmecg| (($ $ #5# |#1| $) 130 T ELT)) (|factorSquareFreePolynomial| (#17# 106 #18# ELT)) (|factorPolynomial| (#17# 105 #18# ELT)) (|factor| (#20# 113 #18# ELT)) (|extendedEuclidean| (((|Union| (|Record| #82=(|:| |coef1| $) #83=(|:| |coef2| $)) #22#) $ $ $) NIL #23# ELT) (((|Record| #82# #83# #51#) $ $) NIL #23# ELT)) (|exquo| ((#47# $ |#1|) 170 #11# ELT) (#84=(#47# $ $) 131 #11# ELT)) (|expressIdealMember| (((|Maybe| #50#) #50# $) NIL #23# ELT)) (|eval| (($ $ (|List| #85=(|Equation| $))) NIL T ELT) (($ $ #85#) NIL T ELT) (($ $ $ $) NIL T ELT) (($ $ #50# #50#) NIL T ELT) (($ $ #7# |#1|) NIL T ELT) (($ $ #6# #86=(|List| |#1|)) NIL T ELT) (($ $ #7# $) NIL T ELT) (($ $ #6# #50#) NIL T ELT)) (|euclideanSize| (#14# NIL #23# ELT)) (|elt| ((|#1| $ |#1|) 157 T ELT) (#16# 158 T ELT) ((#87=(|Fraction| $) #87# #87#) NIL #11# ELT) ((|#1| #87# |#1|) NIL #23# ELT) ((#87# $ #87#) NIL #11# ELT)) (|divideExponents| ((#47# $ #5#) 55 T ELT)) (|divide| (#72# 178 #23# ELT)) (|discriminant| (#53# NIL #36# ELT) (#34# 163 #36# ELT)) (|differentiate| #69# #68# #88=(($ $ #6#) NIL T ELT) #89=(#53# NIL T ELT) #78# #90=(#24# NIL T ELT) #91=(($ $ #75#) NIL T ELT) #92=(($ $ #75# #5#) NIL T ELT) (($ $ #75# $) NIL T ELT) #93=(($ $ #94=(|Symbol|)) NIL #95=(|has| |#1| (|PartialDifferentialSpace| #94#)) ELT) #96=(($ $ #97=(|List| #94#)) NIL #95# ELT) #98=(($ $ #94# #5#) NIL #95# ELT) #99=(($ $ #97# #70#) NIL #95# ELT)) (|degree| (#14# 82 T ELT) #73# #74#) (|convert| ((#58# . #100=($)) NIL (AND (|has| #7# #101=(|ConvertibleTo| #58#)) (|has| |#1| #101#)) ELT) ((#61# . #100#) NIL (AND (|has| #7# #102=(|ConvertibleTo| #61#)) (|has| |#1| #102#)) ELT) ((#103=(|InputForm|) . #100#) NIL (AND (|has| #7# #104=(|ConvertibleTo| #103#)) (|has| |#1| #104#)) ELT)) (|content| (#34# 169 #19# ELT) #52#) (|conditionP| (((|Union| #44# #22#) #40#) NIL #105=(AND (|has| $ #106=(|CharacteristicNonZero|)) #18#) ELT)) (|composite| (#84# NIL #11# ELT) (((|Union| #87# #22#) #87# $) NIL #11# ELT)) (|coerce| ((#63# $) 156 T ELT) (($ #29#) NIL T ELT) (($ |#1|) 81 T ELT) (($ #7#) NIL T ELT) (($ #28#) NIL (OR #81# #30#) ELT) (#12# NIL #11# ELT)) (|coefficients| ((#86# $) NIL T ELT)) (|coefficient| ((|#1| $ #5#) NIL T ELT) #68# #69#) (|charthRoot| (#65# NIL (OR #105# (|has| |#1| #106#)) ELT)) (|characteristic| ((#5#) NIL T CONST)) (|binomThmExpt| (($ $ $ #5#) 42 #36# ELT)) (|before?| #64#) (|associates?| (#1# NIL #11# ELT)) (|annihilate?| #64#) (|Zero| (#25# 18 T CONST)) (|One| (#25# 20 T CONST)) (D #69# #68# #88# #89# #78# #90# #91# #92# #93# #96# #98# #99#) (= (#1# 125 T ELT)) (/ (#107=($ $ |#1|) 179 #23# ELT)) (- #78# (#16# NIL T ELT)) (+ (#16# 95 T ELT)) (** (($ $ #108=(|PositiveInteger|)) 14 T ELT) (#24# 12 T ELT)) (* (($ #108# $) NIL T ELT) (($ #5# $) NIL T ELT) (($ #29# . #109=($)) NIL T ELT) (#16# 40 T ELT) (($ $ #28#) NIL #81# ELT) (($ #28# . #109#) NIL #81# ELT) (($ |#1| . #109#) 136 T ELT) (#107# NIL T ELT))) (((|SparseUnivariatePolynomial| |#1|) (|Join| (|UnivariatePolynomialCategory| |#1|) (CATEGORY |domain| (SIGNATURE |outputForm| (#1=(|OutputForm|) $ #1#)) (SIGNATURE |fmecg| ($ $ (|NonNegativeInteger|) |#1| $)))) (|Ring|)) (T |SparseUnivariatePolynomial|)) ((|outputForm| (*1 *2 *1 *2) (AND (|isDomain| *2 (|OutputForm|)) #1=(|isDomain| *1 (|SparseUnivariatePolynomial| *3)) #2=(|ofCategory| *3 (|Ring|)))) (|fmecg| (*1 *1 *1 *2 *3 *1) (AND (|isDomain| *2 (|NonNegativeInteger|)) #1# #2#))) ((|map| (((|SparseUnivariatePolynomial| |#2|) (|Mapping| |#2| |#1|) (|SparseUnivariatePolynomial| |#1|)) 13 T ELT))) @@ -3638,10 +3638,10 @@ NIL ((|squareFree| (#1=((|Factored| #2=(|SparseUnivariatePolynomial| (|Fraction| |#4|))) #2#) 51 T ELT)) (|factor| (#1# 52 T ELT))) (((|SupFractionFactorizer| |#1| |#2| |#3| |#4|) (CATEGORY |package| (SIGNATURE |factor| #1=((|Factored| #2=(|SparseUnivariatePolynomial| (|Fraction| |#4|))) #2#)) (SIGNATURE |squareFree| #1#)) (|OrderedAbelianMonoidSup|) (|OrderedSet|) (|GcdDomain|) (|PolynomialCategory| |#3| |#1| |#2|)) (T |SupFractionFactorizer|)) ((|squareFree| #1=(*1 *2 *3) #2=(AND (|ofCategory| *4 (|OrderedAbelianMonoidSup|)) (|ofCategory| *5 (|OrderedSet|)) (|ofCategory| *6 (|GcdDomain|)) (|ofCategory| *7 (|PolynomialCategory| *6 *4 *5)) (|isDomain| *2 (|Factored| #3=(|SparseUnivariatePolynomial| (|Fraction| *7)))) (|isDomain| *1 (|SupFractionFactorizer| *4 *5 *6 *7)) (|isDomain| *3 #3#))) (|factor| #1# #2#)) -((~= #1=(#2=(#3=(|Boolean|) $ $) NIL T ELT)) (|zero?| #4=(#5=(#3# $) NIL T ELT)) (|variables| ((#6=(|List| #7=(|SingletonAsOrderedSet|)) $) NIL T ELT)) (|variable| ((#8=(|Symbol|) $) 11 T ELT)) (|unitNormal| (((|Record| (|:| |unit| $) (|:| |canonical| $) (|:| |associate| $)) $) NIL #9=(|has| |#1| (|IntegralDomain|)) ELT)) (|unitCanonical| #10=(#11=($ $) NIL #9# ELT)) (|unit?| (#5# NIL #9# ELT)) (|truncate| #12=(#13=($ $ #14=(|Fraction| #15=(|Integer|))) NIL T ELT) (($ $ #14# #14#) NIL T ELT)) (|terms| ((#16=(|Stream| (|Record| (|:| |k| #14#) (|:| |c| |#1|))) $) NIL T ELT)) (|tanh| #17=(#11# NIL #18=(|has| |#1| (|Algebra| #14#)) ELT)) (|tan| #17#) (|subtractIfCan| (#19=(#20=(|Union| $ #21="failed") $ $) NIL T ELT)) (|squareFreePart| #22=(#11# NIL #23=(|has| |#1| (|Field|)) ELT)) (|squareFree| #24=(((|Factored| $) $) NIL #23# ELT)) (|sqrt| #17#) (|sizeLess?| (#2# NIL #23# ELT)) (|sinh| #17#) (|sin| #17#) (|series| (($ #25=(|NonNegativeInteger|) #16#) NIL T ELT)) (|sech| #17#) (|sec| #17#) (|sample| (#26=($) NIL T CONST)) (|retractIfCan| (#27=((|Union| #28=(|SparseUnivariateLaurentSeries| |#1| |#2| |#3|) . #29=(#21#)) $) 33 T ELT) (((|Union| #30=(|SparseUnivariateTaylorSeries| |#1| |#2| |#3|) . #29#) $) 36 T ELT)) (|retract| #31=(#32=(#28# . #33=($)) NIL T ELT) ((#30# . #33#) NIL T ELT)) (|rem| #34=(#35=($ $ $) NIL #23# ELT)) (|reductum| #36=(#11# NIL T ELT)) (|recip| ((#20# $) NIL T ELT)) (|rationalPower| (#37=(#14# $) 59 T ELT)) (|quo| #34#) (|puiseux| (($ #14# #28#) NIL T ELT)) (|principalIdeal| (((|Record| (|:| |coef| #38=(|List| $)) #39=(|:| |generator| $)) #38#) NIL #23# ELT)) (|prime?| (#5# NIL #23# ELT)) (|pole?| #4#) (|pi| (#26# NIL #18# ELT)) (|order| #40=(#37# NIL T ELT) ((#14# $ #14#) NIL T ELT)) (|opposite?| #1#) (|one?| #4#) (|nthRoot| (#41=($ $ #15#) NIL #18# ELT)) (|multiplyExponents| #42=(($ $ #43=(|PositiveInteger|)) NIL T ELT) #12#) (|multiEuclidean| (((|Union| #38# #21#) #38# $) NIL #23# ELT)) (|monomial?| #4#) (|monomial| (($ |#1| #14#) 20 T ELT) (($ $ #7# #14#) NIL T ELT) (($ $ #6# (|List| #14#)) NIL T ELT)) (|map| (($ (|Mapping| |#1| |#1|) $) NIL T ELT)) (|log| #17#) (|leadingMonomial| #36#) (|leadingCoefficient| (#44=(|#1| $) NIL T ELT)) (|lcm| #45=(($ #38#) NIL #23# ELT) #34#) (|laurentRep| (#32# 41 T ELT)) (|laurentIfCan| (#27# NIL T ELT)) (|laurent| #31#) (|latex| (((|String|) $) NIL T ELT)) (|inv| #22#) (|integrate| (#11# 39 #18# ELT) (#46=($ $ #8#) NIL (OR (AND #18# (|has| |#1| (|AlgebraicallyClosedFunctionSpace| #15#)) (|has| |#1| (|PrimitiveFunctionCategory|)) (|has| |#1| (|TranscendentalFunctionCategory|))) (AND #18# (|has| |#1| (SIGNATURE |integrate| (|#1| |#1| #8#))) (|has| |#1| (SIGNATURE |variables| (#47=(|List| #8#) |#1|))))) ELT) (#48=($ $ #49=(|Variable| |#2|)) 40 #18# ELT)) (|hash| (((|SingleInteger|) $) NIL T ELT)) (|gcdPolynomial| ((#50=(|SparseUnivariatePolynomial| $) #50# #50#) NIL #23# ELT)) (|gcd| #45# #34#) (|factor| #24#) (|extendedEuclidean| (((|Union| (|Record| #51=(|:| |coef1| $) #52=(|:| |coef2| $)) #21#) $ $ $) NIL #23# ELT) (((|Record| #51# #52# #39#) $ $) NIL #23# ELT)) (|extend| #12#) (|exquo| (#19# NIL #9# ELT)) (|expressIdealMember| (((|Maybe| #38#) #38# $) NIL #23# ELT)) (|exp| #17#) (|eval| (((|Stream| |#1|) $ |#1|) NIL #53=(|has| |#1| (SIGNATURE ** (|#1| |#1| #14#))) ELT)) (|euclideanSize| ((#25# $) NIL #23# ELT)) (|elt| #54=(#55=(|#1| $ #14#) NIL T ELT) (#35# NIL (|has| #14# (|SemiGroup|)) ELT)) (|divide| (((|Record| (|:| |quotient| $) (|:| |remainder| $)) $ $) NIL #23# ELT)) (|differentiate| #56=(#46# NIL #57=(AND (|has| |#1| (|PartialDifferentialRing| #8#)) #58=(|has| |#1| (SIGNATURE * (|#1| #14# |#1|)))) ELT) #59=(($ $ #47#) NIL #57# ELT) #60=(($ $ #8# #25#) NIL #57# ELT) #61=(($ $ #47# (|List| #25#)) NIL #57# ELT) (#11# 37 #58# ELT) #62=(#63=($ $ #25#) NIL #58# ELT) (#48# 38 T ELT)) (|degree| #40#) (|csch| #17#) (|csc| #17#) (|coth| #17#) (|cot| #17#) (|cosh| #17#) (|cos| #17#) (|complete| #36#) (|coerce| (((|OutputForm|) $) 62 T ELT) (($ #15#) NIL T ELT) (($ |#1|) NIL (|has| |#1| (|CommutativeRing|)) ELT) (($ #28#) 30 T ELT) (($ #30#) 31 T ELT) (($ #49#) 26 T ELT) (($ #14#) NIL #18# ELT) #10#) (|coefficient| #54#) (|charthRoot| (((|Maybe| $) $) NIL (|has| |#1| (|CharacteristicNonZero|)) ELT)) (|characteristic| ((#25#) NIL T CONST)) (|center| (#44# 12 T ELT)) (|before?| #1#) (|atanh| #17#) (|atan| #17#) (|associates?| (#2# NIL #9# ELT)) (|asinh| #17#) (|asin| #17#) (|asech| #17#) (|asec| #17#) (|approximate| (#55# NIL (AND #53# (|has| |#1| (SIGNATURE |coerce| (|#1| #8#)))) ELT)) (|annihilate?| #1#) (|acsch| #17#) (|acsc| #17#) (|acoth| #17#) (|acot| #17#) (|acosh| #17#) (|acos| #17#) (|Zero| (#26# 22 T CONST)) (|One| (#26# 16 T CONST)) (D #56# #59# #60# #61# (#11# NIL #58# ELT) #62# (#48# NIL T ELT)) (= #1#) (/ (#64=($ $ |#1|) NIL #23# ELT) #34#) (- #36# #65=(#35# NIL T ELT)) (+ (#35# 24 T ELT)) (** #42# (#63# NIL T ELT) (#41# NIL #23# ELT) (#35# NIL #18# ELT) #66=(#13# NIL #18# ELT)) (* (($ #43# $) NIL T ELT) (($ #25# $) NIL T ELT) (($ #15# . #67=($)) NIL T ELT) #65# (#64# NIL T ELT) (($ |#1| . #67#) NIL T ELT) (($ #14# . #67#) NIL #18# ELT) #66#)) +((~= #1=(#2=(#3=(|Boolean|) $ $) NIL T ELT)) (|zero?| #4=(#5=(#3# $) NIL T ELT)) (|variables| ((#6=(|List| #7=(|SingletonAsOrderedSet|)) $) NIL T ELT)) (|variable| ((#8=(|Symbol|) $) 11 T ELT)) (|unitNormal| (((|Record| (|:| |unit| $) (|:| |canonical| $) (|:| |associate| $)) $) NIL #9=(|has| |#1| (|IntegralDomain|)) ELT)) (|unitCanonical| #10=(#11=($ $) NIL #9# ELT)) (|unit?| (#5# NIL #9# ELT)) (|truncate| #12=(#13=($ $ #14=(|Fraction| #15=(|Integer|))) NIL T ELT) (($ $ #14# #14#) NIL T ELT)) (|terms| ((#16=(|Stream| (|Record| (|:| |k| #14#) (|:| |c| |#1|))) $) NIL T ELT)) (|tanh| #17=(#11# NIL #18=(|has| |#1| (|Algebra| #14#)) ELT)) (|tan| #17#) (|subtractIfCan| ((#19=(|Maybe| $) $ $) NIL T ELT)) (|squareFreePart| #20=(#11# NIL #21=(|has| |#1| (|Field|)) ELT)) (|squareFree| #22=(((|Factored| $) $) NIL #21# ELT)) (|sqrt| #17#) (|sizeLess?| (#2# NIL #21# ELT)) (|sinh| #17#) (|sin| #17#) (|series| (($ #23=(|NonNegativeInteger|) #16#) NIL T ELT)) (|sech| #17#) (|sec| #17#) (|sample| (#24=($) NIL T CONST)) (|retractIfCan| (#25=((|Union| #26=(|SparseUnivariateLaurentSeries| |#1| |#2| |#3|) . #27=(#28="failed")) $) 33 T ELT) (((|Union| #29=(|SparseUnivariateTaylorSeries| |#1| |#2| |#3|) . #27#) $) 36 T ELT)) (|retract| #30=(#31=(#26# . #32=($)) NIL T ELT) ((#29# . #32#) NIL T ELT)) (|rem| #33=(#34=($ $ $) NIL #21# ELT)) (|reductum| #35=(#11# NIL T ELT)) (|recip| ((#36=(|Union| $ #28#) $) NIL T ELT)) (|rationalPower| (#37=(#14# $) 59 T ELT)) (|quo| #33#) (|puiseux| (($ #14# #26#) NIL T ELT)) (|principalIdeal| (((|Record| (|:| |coef| #38=(|List| $)) #39=(|:| |generator| $)) #38#) NIL #21# ELT)) (|prime?| (#5# NIL #21# ELT)) (|pole?| #4#) (|pi| (#24# NIL #18# ELT)) (|order| #40=(#37# NIL T ELT) ((#14# $ #14#) NIL T ELT)) (|opposite?| #1#) (|one?| #4#) (|nthRoot| (#41=($ $ #15#) NIL #18# ELT)) (|multiplyExponents| #42=(($ $ #43=(|PositiveInteger|)) NIL T ELT) #12#) (|multiEuclidean| (((|Union| #38# #28#) #38# $) NIL #21# ELT)) (|monomial?| #4#) (|monomial| (($ |#1| #14#) 20 T ELT) (($ $ #7# #14#) NIL T ELT) (($ $ #6# (|List| #14#)) NIL T ELT)) (|map| (($ (|Mapping| |#1| |#1|) $) NIL T ELT)) (|log| #17#) (|leadingMonomial| #35#) (|leadingCoefficient| (#44=(|#1| $) NIL T ELT)) (|lcm| #45=(($ #38#) NIL #21# ELT) #33#) (|laurentRep| (#31# 41 T ELT)) (|laurentIfCan| (#25# NIL T ELT)) (|laurent| #30#) (|latex| (((|String|) $) NIL T ELT)) (|inv| #20#) (|integrate| (#11# 39 #18# ELT) (#46=($ $ #8#) NIL (OR (AND #18# (|has| |#1| (|AlgebraicallyClosedFunctionSpace| #15#)) (|has| |#1| (|PrimitiveFunctionCategory|)) (|has| |#1| (|TranscendentalFunctionCategory|))) (AND #18# (|has| |#1| (SIGNATURE |integrate| (|#1| |#1| #8#))) (|has| |#1| (SIGNATURE |variables| (#47=(|List| #8#) |#1|))))) ELT) (#48=($ $ #49=(|Variable| |#2|)) 40 #18# ELT)) (|hash| (((|SingleInteger|) $) NIL T ELT)) (|gcdPolynomial| ((#50=(|SparseUnivariatePolynomial| $) #50# #50#) NIL #21# ELT)) (|gcd| #45# #33#) (|factor| #22#) (|extendedEuclidean| (((|Union| (|Record| #51=(|:| |coef1| $) #52=(|:| |coef2| $)) #28#) $ $ $) NIL #21# ELT) (((|Record| #51# #52# #39#) $ $) NIL #21# ELT)) (|extend| #12#) (|exquo| ((#36# $ $) NIL #9# ELT)) (|expressIdealMember| (((|Maybe| #38#) #38# $) NIL #21# ELT)) (|exp| #17#) (|eval| (((|Stream| |#1|) $ |#1|) NIL #53=(|has| |#1| (SIGNATURE ** (|#1| |#1| #14#))) ELT)) (|euclideanSize| ((#23# $) NIL #21# ELT)) (|elt| #54=(#55=(|#1| $ #14#) NIL T ELT) (#34# NIL (|has| #14# (|SemiGroup|)) ELT)) (|divide| (((|Record| (|:| |quotient| $) (|:| |remainder| $)) $ $) NIL #21# ELT)) (|differentiate| #56=(#46# NIL #57=(AND (|has| |#1| (|PartialDifferentialRing| #8#)) #58=(|has| |#1| (SIGNATURE * (|#1| #14# |#1|)))) ELT) #59=(($ $ #47#) NIL #57# ELT) #60=(($ $ #8# #23#) NIL #57# ELT) #61=(($ $ #47# (|List| #23#)) NIL #57# ELT) (#11# 37 #58# ELT) #62=(#63=($ $ #23#) NIL #58# ELT) (#48# 38 T ELT)) (|degree| #40#) (|csch| #17#) (|csc| #17#) (|coth| #17#) (|cot| #17#) (|cosh| #17#) (|cos| #17#) (|complete| #35#) (|coerce| (((|OutputForm|) $) 62 T ELT) (($ #15#) NIL T ELT) (($ |#1|) NIL (|has| |#1| (|CommutativeRing|)) ELT) (($ #26#) 30 T ELT) (($ #29#) 31 T ELT) (($ #49#) 26 T ELT) (($ #14#) NIL #18# ELT) #10#) (|coefficient| #54#) (|charthRoot| ((#19# $) NIL (|has| |#1| (|CharacteristicNonZero|)) ELT)) (|characteristic| ((#23#) NIL T CONST)) (|center| (#44# 12 T ELT)) (|before?| #1#) (|atanh| #17#) (|atan| #17#) (|associates?| (#2# NIL #9# ELT)) (|asinh| #17#) (|asin| #17#) (|asech| #17#) (|asec| #17#) (|approximate| (#55# NIL (AND #53# (|has| |#1| (SIGNATURE |coerce| (|#1| #8#)))) ELT)) (|annihilate?| #1#) (|acsch| #17#) (|acsc| #17#) (|acoth| #17#) (|acot| #17#) (|acosh| #17#) (|acos| #17#) (|Zero| (#24# 22 T CONST)) (|One| (#24# 16 T CONST)) (D #56# #59# #60# #61# (#11# NIL #58# ELT) #62# (#48# NIL T ELT)) (= #1#) (/ (#64=($ $ |#1|) NIL #21# ELT) #33#) (- #35# #65=(#34# NIL T ELT)) (+ (#34# 24 T ELT)) (** #42# (#63# NIL T ELT) (#41# NIL #21# ELT) (#34# NIL #18# ELT) #66=(#13# NIL #18# ELT)) (* (($ #43# $) NIL T ELT) (($ #23# $) NIL T ELT) (($ #15# . #67=($)) NIL T ELT) #65# (#64# NIL T ELT) (($ |#1| . #67#) NIL T ELT) (($ #14# . #67#) NIL #18# ELT) #66#)) (((|SparseUnivariatePuiseuxSeries| |#1| |#2| |#3|) (|Join| (|UnivariatePuiseuxSeriesConstructorCategory| |#1| (|SparseUnivariateLaurentSeries| |#1| |#2| |#3|)) (|PartialDifferentialDomain| $ #1=(|Variable| |#2|)) (|RetractableTo| (|SparseUnivariateTaylorSeries| 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T ELT) (#36=($ $ $) 132 (|has| #9# (|SemiGroup|)) ELT)) (|differentiate| #37=(#30# NIL #38=(AND (|has| |#1| (|PartialDifferentialRing| #7#)) #39=(|has| |#1| (SIGNATURE * (|#1| #9# |#1|)))) ELT) #40=(($ $ #31#) NIL #38# ELT) #41=(($ $ #7# #9#) NIL #38# ELT) #42=(($ $ #31# #28#) NIL #38# ELT) (#12# 29 #39# ELT) #43=(#13# NIL #39# ELT) (#32# 31 T ELT)) (|degree| (#24# NIL T ELT)) (|csch| (#12# 179 #15# ELT)) (|csc| (#12# 155 #15# ELT)) (|coth| (#12# 175 #15# ELT)) (|cot| (#12# 151 #15# ELT)) (|cosh| (#12# 171 #15# ELT)) (|cos| (#12# 147 #15# ELT)) (|complete| #22#) (|coerce| (((|OutputForm|) $) 206 T ELT) (($ #17#) NIL T ELT) (($ #16#) NIL #15# ELT) #11# (($ |#1|) 130 (|has| |#1| (|CommutativeRing|)) ELT) (($ #8#) 55 T ELT) (($ #33#) 36 T ELT)) (|coefficients| ((#20# $) 101 T ELT)) (|coefficient| (#35# 121 T ELT)) (|charthRoot| (((|Maybe| $) $) NIL (|has| |#1| (|CharacteristicNonZero|)) ELT)) (|characteristic| ((#9#) NIL T CONST)) (|center| (#29# 58 T ELT)) (|before?| #1#) (|atanh| (#12# 185 #15# ELT)) (|atan| (#12# 161 #15# ELT)) (|associates?| (#2# NIL #10# ELT)) (|asinh| (#12# 181 #15# ELT)) (|asin| (#12# 157 #15# ELT)) (|asech| (#12# 189 #15# ELT)) (|asec| (#12# 165 #15# ELT)) (|approximate| (#35# NIL (AND #34# (|has| |#1| (SIGNATURE |coerce| (|#1| #7#)))) ELT)) (|annihilate?| #1#) (|acsch| (#12# 191 #15# ELT)) (|acsc| (#12# 167 #15# ELT)) (|acoth| (#12# 187 #15# ELT)) (|acot| (#12# 163 #15# ELT)) (|acosh| (#12# 183 #15# ELT)) (|acos| (#12# 159 #15# ELT)) (|Zero| (#21# 17 T CONST)) (|One| (#21# 20 T CONST)) (D #37# #40# #41# #42# (#12# NIL #39# ELT) #43# (#32# NIL T ELT)) (= #1#) (/ (#44=($ $ |#1|) NIL #45=(|has| |#1| (|Field|)) ELT)) (- #22# (#36# 198 T ELT)) (+ (#36# 35 T ELT)) (** #26# (#13# NIL T ELT) (#44# 203 #45# ELT) (#36# 138 #15# ELT) (#46=($ $ #16#) 141 #15# ELT)) (* (($ #27# $) NIL T ELT) (($ #9# $) NIL T ELT) (($ #17# . #47=($)) NIL T ELT) (#36# 136 T ELT) (#44# NIL T ELT) (($ |#1| . #47#) NIL T ELT) (($ #16# . #47#) NIL #15# ELT) (#46# NIL #15# ELT))) 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(|coth| (#12# 175 #15# ELT)) (|cot| (#12# 151 #15# ELT)) (|cosh| (#12# 171 #15# ELT)) (|cos| (#12# 147 #15# ELT)) (|complete| #21#) (|coerce| (((|OutputForm|) $) 206 T ELT) (($ #17#) NIL T ELT) (($ #16#) NIL #15# ELT) #11# (($ |#1|) 130 (|has| |#1| (|CommutativeRing|)) ELT) (($ #8#) 55 T ELT) (($ #33#) 36 T ELT)) (|coefficients| ((#19# $) 101 T ELT)) (|coefficient| (#35# 121 T ELT)) (|charthRoot| ((#18# $) NIL (|has| |#1| (|CharacteristicNonZero|)) ELT)) (|characteristic| ((#9#) NIL T CONST)) (|center| (#29# 58 T ELT)) (|before?| #1#) (|atanh| (#12# 185 #15# ELT)) (|atan| (#12# 161 #15# ELT)) (|associates?| (#2# NIL #10# ELT)) (|asinh| (#12# 181 #15# ELT)) (|asin| (#12# 157 #15# ELT)) (|asech| (#12# 189 #15# ELT)) (|asec| (#12# 165 #15# ELT)) (|approximate| (#35# NIL (AND #34# (|has| |#1| (SIGNATURE |coerce| (|#1| #7#)))) ELT)) (|annihilate?| #1#) (|acsch| (#12# 191 #15# ELT)) (|acsc| (#12# 167 #15# ELT)) (|acoth| (#12# 187 #15# ELT)) (|acot| (#12# 163 #15# ELT)) (|acosh| (#12# 183 #15# ELT)) (|acos| (#12# 159 #15# ELT)) (|Zero| (#20# 17 T CONST)) (|One| (#20# 20 T CONST)) (D #37# #40# #41# #42# (#12# NIL #39# ELT) #43# (#32# NIL T ELT)) (= #1#) (/ (#44=($ $ |#1|) NIL #45=(|has| |#1| (|Field|)) ELT)) (- #21# (#36# 198 T ELT)) (+ (#36# 35 T ELT)) (** #26# (#13# NIL T ELT) (#44# 203 #45# ELT) (#36# 138 #15# ELT) (#46=($ $ #16#) 141 #15# ELT)) (* (($ #27# $) NIL T ELT) (($ #9# $) NIL T ELT) (($ #17# . #47=($)) NIL T ELT) (#36# 136 T ELT) (#44# NIL T ELT) (($ |#1| . #47#) NIL T ELT) (($ #16# . #47#) NIL #15# ELT) (#46# NIL #15# ELT))) (((|SparseUnivariateTaylorSeries| |#1| |#2| |#3|) (|Join| (|UnivariateTaylorSeriesCategory| |#1|) (|PartialDifferentialDomain| $ #1=(|Variable| |#2|)) (CATEGORY |domain| (SIGNATURE |coerce| ($ #2=(|UnivariatePolynomial| |#2| |#1|))) (SIGNATURE |univariatePolynomial| (#2# $ (|NonNegativeInteger|))) (SIGNATURE |coerce| ($ #1#)) (IF (|has| |#1| (|Algebra| (|Fraction| (|Integer|)))) (SIGNATURE |integrate| ($ $ #1#)) |%noBranch|))) (|Ring|) (|Symbol|) |#1|) (T |SparseUnivariateTaylorSeries|)) ((|coerce| #1=(*1 *1 *2) (AND (|isDomain| *2 (|UnivariatePolynomial| *4 *3)) #2=(|ofCategory| *3 #3=(|Ring|)) #4=(|ofType| *4 #5=(|Symbol|)) #6=(|ofType| *5 *3) #7=(|isDomain| *1 (|SparseUnivariateTaylorSeries| *3 *4 *5)))) (|univariatePolynomial| (*1 *2 *1 *3) (AND (|isDomain| *3 (|NonNegativeInteger|)) (|isDomain| *2 (|UnivariatePolynomial| *5 *4)) (|isDomain| *1 (|SparseUnivariateTaylorSeries| *4 *5 *6)) (|ofCategory| *4 #3#) (|ofType| *5 #5#) (|ofType| *6 *4))) (|coerce| #1# (AND #8=(|isDomain| *2 (|Variable| *4)) #4# #7# #2# #6#)) (|integrate| (*1 *1 *1 *2) (AND #8# #4# #7# (|ofCategory| *3 (|Algebra| (|Fraction| (|Integer|)))) #2# #6#))) ((~= #1=(#2=(#3=(|Boolean|) $ $) NIL T ELT)) (|superscript| (#4=($ $ #5=(|List| #6=(|OutputForm|))) 48 T ELT)) (|subscript| (#4# 46 T ELT)) (|string| (#7=(#8=(|String|) $) 88 T ELT)) (|scripts| ((#9=(|Record| (|:| |sub| #5#) (|:| |sup| #5#) (|:| |presup| #5#) (|:| |presub| #5#) (|:| |args| #5#)) $) 95 T ELT)) (|scripted?| ((#3# $) 86 T ELT)) (|script| (($ $ (|List| #5#)) 45 T ELT) (($ $ #9#) 85 T ELT)) (|sample| (#10=($) 151 T CONST)) (|retractIfCan| (((|Union| #11=(|Identifier|) "failed") $) 155 T ELT)) (|retract| ((#11# $) NIL T ELT)) (|resetNew| (((|Void|)) 123 T ELT)) (|patternMatch| ((#12=(|PatternMatchResult| #13=(|Integer|) . #14=($)) $ #15=(|Pattern| #13#) #12#) 55 T ELT) ((#16=(|PatternMatchResult| #17=(|Float|) . #14#) $ #18=(|Pattern| #17#) #16#) 62 T ELT)) (|new| (#10# 109 T ELT) (#19=($ $) 118 T ELT)) (|name| (#19# 87 T ELT)) (|min| #20=(($ $ $) NIL T ELT)) (|max| #20#) (|list| (((|List| $) $) 124 T ELT)) (|latex| (#7# 101 T ELT)) (|hash| (((|SingleInteger|) $) NIL T ELT)) (|elt| (#4# 47 T ELT)) (|convert| (((|InputForm|) $) 33 T ELT) (((|Symbol|) $) 34 T ELT) ((#15# $) 66 T ELT) ((#18# $) 64 T ELT)) (|coerce| ((#6# $) 41 T ELT) (($ #8#) 35 T ELT) (($ #11#) 153 T ELT)) (|before?| #1#) (|argscript| (#4# 49 T ELT)) (>= #1#) (> #1#) (= (#2# 37 T ELT)) (<= #1#) (< (#2# 38 T ELT))) @@ -3650,15 +3650,15 @@ NIL ((|symFunc| ((#1=(|Vector| |#1|) |#1| (|PositiveInteger|)) 18 T ELT) ((#1# (|List| |#1|)) 25 T ELT))) (((|SymmetricFunctions| |#1|) (CATEGORY |package| (SIGNATURE |symFunc| (#1=(|Vector| |#1|) (|List| |#1|))) (SIGNATURE |symFunc| (#1# |#1| (|PositiveInteger|)))) (|Ring|)) (T |SymmetricFunctions|)) ((|symFunc| (*1 *2 *3 *4) (AND (|isDomain| *4 (|PositiveInteger|)) (|isDomain| *2 (|Vector| *3)) (|isDomain| *1 (|SymmetricFunctions| *3)) (|ofCategory| *3 #1=(|Ring|)))) (|symFunc| (*1 *2 *3) (AND (|isDomain| *3 (|List| *4)) (|ofCategory| *4 #1#) (|isDomain| *2 (|Vector| *4)) (|isDomain| *1 (|SymmetricFunctions| *4))))) -((~= #1=(#2=(#3=(|Boolean|) $ $) NIL T ELT)) (|zero?| #4=(#5=(#3# $) NIL T ELT)) (|unitNormal| (((|Record| (|:| |unit| $) (|:| |canonical| $) (|:| |associate| $)) $) NIL #6=(|has| |#1| (|IntegralDomain|)) ELT)) (|unitCanonical| #7=(#8=($ $) NIL #6# ELT)) (|unit?| (#5# NIL #6# ELT)) (|subtractIfCan| (#9=(#10=(|Union| $ #11="failed") $ $) NIL T ELT)) (|sample| #12=(#13=($) NIL T CONST)) (|retractIfCan| (((|Union| #14=(|Integer|) . #15=(#11#)) . #16=($)) NIL #17=(|has| |#1| (|RetractableTo| #14#)) ELT) (((|Union| #18=(|Fraction| #14#) . #15#) . #16#) NIL #19=(|has| |#1| (|RetractableTo| #18#)) ELT) (((|Union| |#1| . #15#) . #16#) NIL T ELT)) (|retract| ((#14# . #20=($)) NIL #17# ELT) ((#18# . #20#) NIL #19# ELT) #21=(#22=(|#1| . #20#) NIL T ELT)) (|reductum| #23=(#8# NIL T ELT)) (|recip| ((#10# $) NIL T ELT)) (|primitivePart| (#8# NIL #24=(|has| |#1| (|GcdDomain|)) ELT)) (|pomopo!| (($ $ |#1| #25=(|Partition|) $) NIL T ELT)) (|opposite?| #1#) (|one?| (#5# 18 T ELT)) (|numberOfMonomials| ((#26=(|NonNegativeInteger|) $) NIL T ELT)) (|monomial?| #4#) (|monomial| (($ |#1| #25#) NIL T ELT)) (|minimumDegree| #27=((#25# $) NIL T ELT)) (|mapExponents| (($ (|Mapping| #25# #25#) $) NIL T ELT)) (|map| (($ (|Mapping| |#1| |#1|) $) NIL T ELT)) (|leadingMonomial| #23#) (|leadingCoefficient| #21#) (|latex| (((|String|) $) NIL T ELT)) (|hash| (((|SingleInteger|) $) NIL T ELT)) (|ground?| #4#) (|ground| #21#) (|fmecg| (($ $ #25# |#1| $) NIL (AND (|has| #25# (|CancellationAbelianMonoid|)) #6#) ELT)) (|exquo| (#9# NIL #6# ELT) ((#10# $ |#1|) NIL #6# ELT)) (|degree| #27#) (|content| (#22# NIL #24# ELT)) (|coerce| (((|OutputForm|) $) NIL T ELT) (($ #14#) NIL T ELT) #7# (($ |#1|) NIL T ELT) (($ #18#) NIL (OR #28=(|has| |#1| (|Algebra| #18#)) #19#) ELT)) (|coefficients| (((|List| |#1|) $) NIL T ELT)) (|coefficient| ((|#1| $ #25#) NIL T ELT)) (|charthRoot| (((|Maybe| $) $) NIL (|has| |#1| (|CharacteristicNonZero|)) ELT)) (|characteristic| ((#26#) NIL T CONST)) (|binomThmExpt| (($ $ $ #26#) NIL (|has| |#1| (|CommutativeRing|)) ELT)) (|before?| #1#) (|associates?| (#2# NIL #6# ELT)) (|annihilate?| #1#) (|Zero| (#13# 13 T CONST)) (|One| #12#) (= #1#) (/ (#29=($ $ |#1|) NIL (|has| |#1| (|Field|)) ELT)) (- #23# (#30=($ $ $) NIL T ELT)) (+ (#30# 22 T ELT)) (** (($ $ #31=(|PositiveInteger|)) NIL T ELT) (($ $ #26#) NIL T ELT)) (* (($ #31# $) NIL T ELT) (($ #26# $) NIL T ELT) (($ #14# . #32=($)) NIL T ELT) (#30# 23 T ELT) (#29# NIL T ELT) (($ |#1| . #32#) 17 T ELT) (($ #18# . #32#) NIL #28# ELT) (($ $ #18#) NIL #28# ELT))) +((~= #1=(#2=(#3=(|Boolean|) $ $) NIL T ELT)) (|zero?| #4=(#5=(#3# $) NIL T ELT)) (|unitNormal| (((|Record| (|:| |unit| $) (|:| |canonical| $) (|:| |associate| $)) $) NIL #6=(|has| |#1| (|IntegralDomain|)) ELT)) (|unitCanonical| #7=(#8=($ $) NIL #6# ELT)) (|unit?| (#5# NIL #6# ELT)) (|subtractIfCan| ((#9=(|Maybe| $) $ $) NIL T ELT)) (|sample| #10=(#11=($) NIL T CONST)) (|retractIfCan| (((|Union| #12=(|Integer|) . #13=(#14="failed")) . #15=($)) NIL #16=(|has| |#1| (|RetractableTo| #12#)) ELT) (((|Union| #17=(|Fraction| #12#) . #13#) . #15#) NIL #18=(|has| |#1| (|RetractableTo| #17#)) ELT) (((|Union| |#1| . #13#) . #15#) NIL T ELT)) (|retract| ((#12# . #19=($)) NIL #16# ELT) ((#17# . #19#) NIL #18# ELT) #20=(#21=(|#1| . #19#) NIL T ELT)) (|reductum| #22=(#8# NIL T ELT)) (|recip| ((#23=(|Union| $ #14#) $) NIL T ELT)) (|primitivePart| (#8# NIL #24=(|has| |#1| (|GcdDomain|)) ELT)) (|pomopo!| (($ $ |#1| #25=(|Partition|) $) NIL T ELT)) (|opposite?| #1#) (|one?| (#5# 18 T ELT)) (|numberOfMonomials| ((#26=(|NonNegativeInteger|) $) NIL T ELT)) (|monomial?| #4#) (|monomial| (($ |#1| #25#) NIL T ELT)) (|minimumDegree| #27=((#25# $) NIL T ELT)) (|mapExponents| (($ (|Mapping| #25# #25#) $) NIL T ELT)) (|map| (($ (|Mapping| |#1| |#1|) $) NIL T ELT)) (|leadingMonomial| #22#) (|leadingCoefficient| #20#) (|latex| (((|String|) $) NIL T ELT)) (|hash| (((|SingleInteger|) $) NIL T ELT)) (|ground?| #4#) (|ground| #20#) (|fmecg| (($ $ #25# |#1| $) NIL (AND (|has| #25# (|CancellationAbelianMonoid|)) #6#) ELT)) (|exquo| ((#23# $ $) NIL #6# ELT) ((#23# $ |#1|) NIL #6# ELT)) (|degree| #27#) (|content| (#21# NIL #24# ELT)) (|coerce| (((|OutputForm|) $) NIL T ELT) (($ #12#) NIL T ELT) #7# (($ |#1|) NIL T ELT) (($ #17#) NIL (OR #28=(|has| |#1| (|Algebra| #17#)) #18#) ELT)) (|coefficients| (((|List| |#1|) $) NIL T ELT)) (|coefficient| ((|#1| $ #25#) NIL T ELT)) (|charthRoot| ((#9# $) NIL (|has| |#1| (|CharacteristicNonZero|)) ELT)) (|characteristic| ((#26#) NIL T CONST)) (|binomThmExpt| (($ $ $ #26#) NIL (|has| |#1| (|CommutativeRing|)) ELT)) (|before?| #1#) (|associates?| (#2# NIL #6# ELT)) (|annihilate?| #1#) (|Zero| (#11# 13 T CONST)) (|One| #10#) (= #1#) (/ (#29=($ $ |#1|) NIL (|has| |#1| (|Field|)) ELT)) (- #22# (#30=($ $ $) NIL T ELT)) (+ (#30# 22 T ELT)) (** (($ $ #31=(|PositiveInteger|)) NIL T ELT) (($ $ #26#) NIL T ELT)) (* (($ #31# $) NIL T ELT) (($ #26# $) NIL T ELT) (($ #12# . #32=($)) NIL T ELT) (#30# 23 T ELT) (#29# NIL T ELT) (($ |#1| . #32#) 17 T ELT) (($ #17# . #32#) NIL #28# ELT) (($ $ #17#) NIL #28# ELT))) (((|SymmetricPolynomial| |#1|) (|Join| (|FiniteAbelianMonoidRing| |#1| #1=(|Partition|)) (CATEGORY |domain| (IF (|has| |#1| (|IntegralDomain|)) (IF (|has| #1# (|CancellationAbelianMonoid|)) (SIGNATURE |fmecg| ($ $ #1# |#1| $)) |%noBranch|) |%noBranch|) (IF (|has| |#1| #2=(ATTRIBUTE |canonicalUnitNormal|)) #2# |%noBranch|))) (|Ring|)) (T |SymmetricPolynomial|)) ((|fmecg| (*1 *1 *1 *2 *3 *1) (AND (|isDomain| *2 (|Partition|)) (|ofCategory| *2 (|CancellationAbelianMonoid|)) (|isDomain| *1 (|SymmetricPolynomial| *3)) (|ofCategory| *3 (|IntegralDomain|)) (|ofCategory| *3 (|Ring|))))) ((|symbolTableOf| (((|SymbolTable|) #1=(|Symbol|) $) 26 T ELT)) (|showTheSymbolTable| (#2=($) 30 T ELT)) (|returnTypeOf| ((#3=(|Union| (|:| |fst| (|FortranScalarType|)) (|:| |void| "void")) #1# $) 23 T ELT)) (|returnType!| ((#4=(|Void|) #1# #3# $) 42 T ELT) ((#4# #1# #3#) 43 T ELT) ((#4# #3#) 44 T ELT)) (|printTypes| (#5=(#4# #1#) 59 T ELT)) (|printHeader| ((#4# #1# $) 56 T ELT) (#5# 57 T ELT) (#6=(#4#) 58 T ELT)) (|newSubProgram| (#5# 38 T ELT)) (|endSubProgram| (#7=(#1#) 37 T ELT)) (|empty| (#2# 35 T ELT)) (|declare!| ((#8=(|FortranType|) #1# #8# #1# $) 46 T ELT) ((#8# #9=(|List| #1#) #8# #1# $) 50 T ELT) ((#8# #1# #8#) 47 T ELT) ((#8# #1# #8# #1#) 51 T ELT)) (|currentSubProgram| (#7# 36 T ELT)) (|coerce| (((|OutputForm|) $) 29 T ELT)) (|clearTheSymbolTable| (#6# 31 T ELT) (#5# 34 T ELT)) (|argumentListOf| ((#9# #1# $) 25 T ELT)) (|argumentList!| ((#4# #1# #9# $) 39 T ELT) ((#4# #1# #9#) 40 T ELT) ((#4# #9#) 41 T ELT))) (((|TheSymbolTable|) (|Join| (|CoercibleTo| (|OutputForm|)) (CATEGORY |domain| (SIGNATURE |showTheSymbolTable| #1=($)) (SIGNATURE |clearTheSymbolTable| #2=(#3=(|Void|))) (SIGNATURE |clearTheSymbolTable| #4=(#3# #5=(|Symbol|))) (SIGNATURE |declare!| (#6=(|FortranType|) #5# #6# #5# $)) (SIGNATURE |declare!| (#6# #7=(|List| #5#) #6# #5# $)) (SIGNATURE |declare!| (#6# #5# #6#)) (SIGNATURE |declare!| (#6# #5# #6# #5#)) (SIGNATURE |newSubProgram| #4#) (SIGNATURE |currentSubProgram| #8=(#5#)) (SIGNATURE |endSubProgram| #8#) (SIGNATURE |argumentList!| (#3# #5# #7# $)) (SIGNATURE |argumentList!| (#3# #5# #7#)) (SIGNATURE |argumentList!| (#3# #7#)) (SIGNATURE |returnType!| (#3# #5# #9=(|Union| (|:| |fst| (|FortranScalarType|)) (|:| |void| "void")) $)) (SIGNATURE |returnType!| (#3# #5# #9#)) (SIGNATURE |returnType!| (#3# #9#)) (SIGNATURE |printHeader| (#3# #5# $)) (SIGNATURE |printHeader| #4#) (SIGNATURE |printHeader| #2#) (SIGNATURE |printTypes| #4#) (SIGNATURE |empty| #1#) (SIGNATURE |returnTypeOf| (#9# #5# $)) (SIGNATURE |argumentListOf| (#7# #5# $)) (SIGNATURE |symbolTableOf| ((|SymbolTable|) #5# $))))) (T |TheSymbolTable|)) ((|showTheSymbolTable| #1=(*1 *1) #2=(|isDomain| *1 (|TheSymbolTable|))) (|clearTheSymbolTable| #3=(*1 *2) #4=(AND #5=(|isDomain| *2 (|Void|)) #2#)) (|clearTheSymbolTable| #6=(*1 *2 *3) #7=(AND #8=(|isDomain| *3 #9=(|Symbol|)) #5# #2#)) (|declare!| (*1 *2 *3 *2 *3 *1) #10=(AND #11=(|isDomain| *2 (|FortranType|)) #8# #2#)) (|declare!| (*1 *2 *3 *2 *4 *1) (AND #11# #12=(|isDomain| *3 #13=(|List| #9#)) (|isDomain| *4 #9#) #2#)) (|declare!| (*1 *2 *3 *2) #10#) (|declare!| (*1 *2 *3 *2 *3) #10#) (|newSubProgram| #6# #7#) (|currentSubProgram| #3# #14=(AND (|isDomain| *2 #9#) #2#)) (|endSubProgram| #3# #14#) (|argumentList!| #15=(*1 *2 *3 *4 *1) #16=(AND (|isDomain| *4 #13#) #8# #5# #2#)) (|argumentList!| #17=(*1 *2 *3 *4) #16#) (|argumentList!| #6# (AND #12# #5# #2#)) (|returnType!| #15# #18=(AND #8# (|isDomain| *4 #19=(|Union| (|:| |fst| (|FortranScalarType|)) (|:| |void| "void"))) #5# #2#)) (|returnType!| #17# #18#) (|returnType!| #6# (AND (|isDomain| *3 #19#) #5# #2#)) (|printHeader| #20=(*1 *2 *3 *1) #7#) (|printHeader| #6# #7#) (|printHeader| #3# #4#) (|printTypes| #6# #7#) (|empty| #1# #2#) (|returnTypeOf| #20# (AND #8# (|isDomain| *2 #19#) #2#)) (|argumentListOf| #20# (AND (|isDomain| *2 #13#) #2# #8#)) (|symbolTableOf| #20# (AND #8# (|isDomain| *2 (|SymbolTable|)) #2#))) ((|typeLists| (((|List| #1=(|List| (|Union| (|:| |name| #2=(|Symbol|)) (|:| |bounds| (|List| (|Union| (|:| S #2#) (|:| P (|Polynomial| (|Integer|))))))))) $) 66 T ELT)) (|typeList| ((#1# (|FortranScalarType|) $) 47 T ELT)) (|symbolTable| (($ (|List| (|Record| (|:| |key| #2#) (|:| |entry| #3=(|FortranType|))))) 17 T ELT)) (|printTypes| (((|Void|) $) 73 T ELT)) (|parametersOf| (#4=(#5=(|List| #2#) $) 22 T ELT)) (|newTypeLists| (((|SExpression|) $) 60 T ELT)) (|fortranTypeOf| ((#3# #2# $) 27 T ELT)) (|externalList| (#4# 30 T ELT)) (|empty| (($) 19 T ELT)) (|declare!| ((#3# #5# #3# $) 25 T ELT) ((#3# #2# #3# $) 24 T ELT)) (|coerce| (((|OutputForm|) $) 12 T ELT) (((|Table| #2# #3#) $) 13 T ELT))) -(((|SymbolTable|) (|Join| (|CoercibleTo| (|OutputForm|)) (CATEGORY |domain| (SIGNATURE |coerce| ((|Table| #1=(|Symbol|) #2=(|FortranType|)) $)) (SIGNATURE |empty| ($)) (SIGNATURE |declare!| (#2# #3=(|List| #1#) #2# $)) (SIGNATURE |declare!| (#2# #1# #2# $)) (SIGNATURE |fortranTypeOf| (#2# #1# $)) (SIGNATURE |parametersOf| #4=(#3# $)) (SIGNATURE |typeList| (#5=(|List| (|Union| (|:| |name| #1#) (|:| |bounds| (|List| (|Union| (|:| S #1#) (|:| P (|Polynomial| (|Integer|)))))))) (|FortranScalarType|) $)) (SIGNATURE |externalList| #4#) (SIGNATURE |typeLists| ((|List| #5#) $)) (SIGNATURE |newTypeLists| ((|SExpression|) $)) (SIGNATURE |printTypes| ((|Void|) $)) (SIGNATURE |symbolTable| ($ (|List| (|Record| (|:| |key| #1#) (|:| |entry| #2#)))))))) (T |SymbolTable|)) -((|coerce| #1=(*1 *2 *1) (AND (|isDomain| *2 (|Table| #2=(|Symbol|) #3=(|FortranType|))) #4=(|isDomain| *1 (|SymbolTable|)))) (|empty| (*1 *1) #4#) (|declare!| #5=(*1 *2 *3 *2 *1) (AND #6=(|isDomain| *2 #3#) (|isDomain| *3 #7=(|List| #2#)) #4#)) (|declare!| #5# (AND #6# #8=(|isDomain| *3 #2#) #4#)) (|fortranTypeOf| #9=(*1 *2 *3 *1) (AND #8# #6# #4#)) (|parametersOf| #1# #10=(AND (|isDomain| *2 #7#) #4#)) (|typeList| #9# (AND (|isDomain| *3 (|FortranScalarType|)) (|isDomain| *2 #11=(|List| (|Union| (|:| |name| #2#) (|:| |bounds| (|List| (|Union| (|:| S #2#) (|:| P (|Polynomial| (|Integer|))))))))) #4#)) (|externalList| #1# #10#) (|typeLists| #1# (AND (|isDomain| *2 (|List| #11#)) #4#)) (|newTypeLists| #1# (AND (|isDomain| *2 (|SExpression|)) #4#)) (|printTypes| #1# (AND (|isDomain| *2 (|Void|)) #4#)) (|symbolTable| (*1 *1 *2) (AND (|isDomain| *2 (|List| (|Record| (|:| |key| #2#) (|:| |entry| #3#)))) #4#))) +(((|SymbolTable|) (|Join| (|CoercibleTo| (|OutputForm|)) (|CoercibleTo| (|Table| #1=(|Symbol|) #2=(|FortranType|))) (CATEGORY |domain| (SIGNATURE |empty| ($)) (SIGNATURE |declare!| (#2# #3=(|List| #1#) #2# $)) (SIGNATURE |declare!| (#2# #1# #2# $)) (SIGNATURE |fortranTypeOf| (#2# #1# $)) (SIGNATURE |parametersOf| #4=(#3# $)) (SIGNATURE |typeList| (#5=(|List| (|Union| (|:| |name| #1#) (|:| |bounds| (|List| (|Union| (|:| S #1#) (|:| P (|Polynomial| (|Integer|)))))))) (|FortranScalarType|) $)) (SIGNATURE |externalList| #4#) (SIGNATURE |typeLists| ((|List| #5#) $)) (SIGNATURE |newTypeLists| ((|SExpression|) $)) (SIGNATURE |printTypes| ((|Void|) $)) (SIGNATURE |symbolTable| ($ (|List| (|Record| (|:| |key| #1#) (|:| |entry| #2#)))))))) (T |SymbolTable|)) +((|empty| (*1 *1) #1=(|isDomain| *1 (|SymbolTable|))) (|declare!| #2=(*1 *2 *3 *2 *1) (AND #3=(|isDomain| *2 #4=(|FortranType|)) (|isDomain| *3 #5=(|List| #6=(|Symbol|))) #1#)) (|declare!| #2# (AND #3# #7=(|isDomain| *3 #6#) #1#)) (|fortranTypeOf| #8=(*1 *2 *3 *1) (AND #7# #3# #1#)) (|parametersOf| #9=(*1 *2 *1) #10=(AND (|isDomain| *2 #5#) #1#)) (|typeList| #8# (AND (|isDomain| *3 (|FortranScalarType|)) (|isDomain| *2 #11=(|List| (|Union| (|:| |name| #6#) (|:| |bounds| (|List| (|Union| (|:| S #6#) (|:| P (|Polynomial| (|Integer|))))))))) #1#)) (|externalList| #9# #10#) (|typeLists| #9# (AND (|isDomain| *2 (|List| #11#)) #1#)) (|newTypeLists| #9# (AND (|isDomain| *2 (|SExpression|)) #1#)) (|printTypes| #9# (AND (|isDomain| *2 (|Void|)) #1#)) (|symbolTable| (*1 *1 *2) (AND (|isDomain| *2 (|List| (|Record| (|:| |key| #6#) (|:| |entry| #4#)))) #1#))) ((~= #1=(#2=(#3=(|Boolean|) $ $) NIL T ELT)) (|retractIfCan| (((|Union| #4=(|Integer|) . #5=("failed")) $) 29 T ELT) (((|Union| #6=(|DoubleFloat|) . #5#) $) 35 T ELT) (((|Union| #7=(|Identifier|) . #5#) $) 43 T ELT) (((|Union| #8=(|String|) . #5#) $) 47 T ELT)) (|retract| (#9=(#4# $) 30 T ELT) (#10=(#6# $) 36 T ELT) (#11=(#7# $) 40 T ELT) (#12=(#8# $) 48 T ELT)) (|nil?| (#13=(#3# $) 53 T ELT)) (|latex| (#12# NIL T ELT)) (|hash| (((|SingleInteger|) $) NIL T ELT)) (|getOperator| (((|Union| #4# #6# #7# #8# $) $) 56 T ELT)) (|getOperands| ((#14=(|List| $) $) 58 T ELT)) (|convert| ((#15=(|SExpression|) $) 24 T ELT) (($ #15#) 25 T ELT)) (|compound?| (#13# 57 T ELT)) (|coerce| (((|OutputForm|) $) 23 T ELT) (($ #4#) 26 T ELT) (($ #6#) 32 T ELT) (($ #7#) 38 T ELT) (($ #8#) 44 T ELT) (((|InputForm|) $) 60 T ELT) (#9# 31 T ELT) (#10# 37 T ELT) (#11# 41 T ELT) (#12# 49 T ELT)) (|case| ((#3# $ (|[\|\|]| #4#)) 10 T ELT) ((#3# $ (|[\|\|]| #6#)) 13 T ELT) ((#3# $ (|[\|\|]| #7#)) 19 T ELT) ((#3# $ (|[\|\|]| #8#)) 16 T ELT)) (|buildSyntax| (($ #7# #14#) 51 T ELT) (($ $ #14#) 52 T ELT)) (|before?| #1#) (|autoCoerce| (#9# 27 T ELT) (#10# 33 T ELT) (#11# 39 T ELT) (#12# 45 T ELT)) (= (#2# 7 T ELT))) (((|Syntax|) (|Join| (|UnionType|) (|SetCategory|) (|RetractableTo| #1=(|Integer|)) (|RetractableTo| #2=(|DoubleFloat|)) (|RetractableTo| #3=(|Identifier|)) (|RetractableTo| #4=(|String|)) (|CoercibleTo| (|InputForm|)) (CATEGORY |domain| (SIGNATURE |convert| (#5=(|SExpression|) $)) (SIGNATURE |convert| ($ #5#)) (SIGNATURE |coerce| #6=(#1# $)) (SIGNATURE |autoCoerce| #6#) (SIGNATURE |coerce| #7=(#2# $)) (SIGNATURE |autoCoerce| #7#) (SIGNATURE |coerce| #8=(#3# $)) (SIGNATURE |autoCoerce| #8#) (SIGNATURE |coerce| #9=(#4# $)) (SIGNATURE |autoCoerce| #9#) (SIGNATURE |buildSyntax| ($ #3# #10=(|List| $))) (SIGNATURE |buildSyntax| ($ $ #10#)) (SIGNATURE |nil?| #11=(#12=(|Boolean|) $)) (SIGNATURE |getOperator| ((|Union| #1# #2# #3# #4# $) $)) (SIGNATURE |getOperands| (#10# $)) (SIGNATURE |compound?| #11#) (SIGNATURE |case| (#12# $ (|[\|\|]| #1#))) (SIGNATURE |case| (#12# $ (|[\|\|]| #2#))) (SIGNATURE |case| (#12# $ (|[\|\|]| #3#))) (SIGNATURE |case| (#12# $ (|[\|\|]| #4#)))))) (T |Syntax|)) ((|convert| #1=(*1 *2 *1) #2=(AND (|isDomain| *2 (|SExpression|)) #3=(|isDomain| *1 #4=(|Syntax|)))) (|convert| (*1 *1 *2) #2#) (|coerce| #1# #5=(AND (|isDomain| *2 #6=(|Integer|)) #3#)) (|autoCoerce| #1# #5#) (|coerce| #1# #7=(AND (|isDomain| *2 #8=(|DoubleFloat|)) #3#)) (|autoCoerce| #1# #7#) (|coerce| #1# #9=(AND #10=(|isDomain| *2 #11=(|Identifier|)) #3#)) (|autoCoerce| #1# #9#) (|coerce| #1# #12=(AND (|isDomain| *2 #13=(|String|)) #3#)) (|autoCoerce| #1# #12#) (|buildSyntax| (*1 *1 *2 *3) (AND #10# (|isDomain| *3 #14=(|List| #4#)) #3#)) (|buildSyntax| (*1 *1 *1 *2) #15=(AND (|isDomain| *2 #14#) #3#)) (|nil?| #1# #16=(AND #17=(|isDomain| *2 (|Boolean|)) #3#)) (|getOperator| #1# (AND (|isDomain| *2 (|Union| #6# #8# #11# #13# #4#)) #3#)) (|getOperands| #1# #15#) (|compound?| #1# #16#) (|case| #18=(*1 *2 *1 *3) (AND (|isDomain| *3 (|[\|\|]| #6#)) #17# #3#)) (|case| #18# (AND (|isDomain| *3 (|[\|\|]| #8#)) #17# #3#)) (|case| #18# (AND (|isDomain| *3 (|[\|\|]| #11#)) #17# #3#)) (|case| #18# (AND (|isDomain| *3 (|[\|\|]| #13#)) #17# #3#))) @@ -3686,8 +3686,8 @@ NIL (((|Table| |#1| |#2|) (|TableAggregate| |#1| |#2|) #1=(|SetCategory|) #1#) (T |Table|)) NIL ((|tableau| (($ #1=(|List| (|List| |#1|))) 10 T ELT)) (|listOfLists| ((#1# $) 11 T ELT)) (|coerce| (((|OutputForm|) $) 33 T ELT))) -(((|Tableau| |#1|) (CATEGORY |domain| (SIGNATURE |tableau| ($ #1=(|List| (|List| |#1|)))) (SIGNATURE |listOfLists| (#1# $)) (SIGNATURE |coerce| ((|OutputForm|) $))) (|SetCategory|)) (T |Tableau|)) -((|coerce| #1=(*1 *2 *1) (AND (|isDomain| *2 (|OutputForm|)) #2=(|isDomain| *1 (|Tableau| *3)) #3=(|ofCategory| *3 (|SetCategory|)))) (|listOfLists| #1# (AND #4=(|isDomain| *2 (|List| (|List| *3))) #2# #3#)) (|tableau| (*1 *1 *2) (AND #4# #3# #2#))) +(((|Tableau| |#1|) (|Join| (|CoercibleTo| (|OutputForm|)) (CATEGORY |domain| (SIGNATURE |tableau| ($ #1=(|List| (|List| |#1|)))) (SIGNATURE |listOfLists| (#1# $)))) (|SetCategory|)) (T |Tableau|)) +((|tableau| (*1 *1 *2) (AND #1=(|isDomain| *2 (|List| (|List| *3))) #2=(|ofCategory| *3 (|SetCategory|)) #3=(|isDomain| *1 (|Tableau| *3)))) (|listOfLists| (*1 *2 *1) (AND #1# #3# #2#))) ((~= #1=((#2=(|Boolean|) $ $) NIL T ELT)) (|operator| (($ |#1| #3=(|Arity|)) 11 T ELT)) (|name| ((|#1| $) 13 T ELT)) (|latex| (((|String|) $) NIL T ELT)) (|is?| ((#2# $ |#1|) NIL T ELT)) (|hash| (((|SingleInteger|) $) NIL T ELT)) (|coerce| (((|OutputForm|) $) NIL T ELT)) (|before?| #1#) (|arity| ((#3# $) 15 T ELT)) (= #1#)) (((|TermAlgebraOperator| |#1|) (|Join| (|OperatorCategory| |#1|) (CATEGORY |domain| (SIGNATURE |operator| ($ |#1| (|Arity|))))) (|SetCategory|)) (T |TermAlgebraOperator|)) ((|operator| (*1 *1 *2 *3) (AND (|isDomain| *3 (|Arity|)) (|isDomain| *1 (|TermAlgebraOperator| *2)) (|ofCategory| *2 (|SetCategory|))))) @@ -3711,7 +3711,7 @@ NIL ((|coerce| (((|TexFormat|) |#1|) 11 T ELT))) (((|TexFormat1| |#1|) (CATEGORY |package| (SIGNATURE |coerce| ((|TexFormat|) |#1|))) (|SetCategory|)) (T |TexFormat1|)) ((|coerce| (*1 *2 *3) (AND (|isDomain| *2 (|TexFormat|)) (|isDomain| *1 (|TexFormat1| *3)) (|ofCategory| *3 (|SetCategory|))))) -((~= #1=((#2=(|Boolean|) $ $) NIL T ELT)) (|writeLine!| (#3=(#4=(|String|) $ #4#) 21 T ELT) (#5=(#4# $) 20 T ELT)) (|write!| (#3# 19 T ELT)) (|reopen!| (($ $ #4#) NIL T ELT)) (|readLineIfCan!| (#6=((|Union| #4# "failed") $) 11 T ELT)) (|readLine!| (#5# 8 T ELT)) (|readIfCan!| (#6# 12 T ELT)) (|read!| (#5# 9 T ELT)) (|open| (($ #7=(|FileName|)) NIL T ELT) (($ #7# #4#) NIL T ELT)) (|name| ((#7# $) NIL T ELT)) (|latex| #8=(#5# NIL T ELT)) (|iomode| #8#) (|hash| (((|SingleInteger|) $) NIL T ELT)) (|endOfFile?| ((#2# $) 25 T ELT)) (|coerce| (((|OutputForm|) $) NIL T ELT)) (|close!| (($ $) NIL T ELT)) (|before?| #1#) (= #1#)) +((~= #1=((#2=(|Boolean|) $ $) NIL T ELT)) (|writeLine!| (#3=(#4=(|String|) $ #4#) 21 T ELT) (#5=(#4# $) 20 T ELT)) (|write!| (#3# 19 T ELT)) (|reopen!| (($ $ #4#) NIL T ELT)) (|readLineIfCan!| (#6=((|Union| #4# "failed") $) 11 T ELT)) (|readLine!| (#5# 8 T ELT)) (|readIfCan!| (#6# 12 T ELT)) (|read!| (#5# 9 T ELT)) (|open| (($ #7=(|FileName|)) NIL T ELT) (($ #7# #4#) NIL T ELT)) (|name| ((#7# $) NIL T ELT)) (|latex| #8=(#5# NIL T ELT)) (|iomode| #8#) (|hash| (((|SingleInteger|) $) NIL T ELT)) (|endOfFile?| ((#2# $) 24 T ELT)) (|coerce| (((|OutputForm|) $) NIL T ELT)) (|close!| (($ $) NIL T ELT)) (|before?| #1#) (= #1#)) (((|TextFile|) (|Join| (|FileCategory| (|FileName|) #1=(|String|)) (CATEGORY |domain| (SIGNATURE |writeLine!| (#1# $ #1#)) (SIGNATURE |writeLine!| #2=(#1# $)) (SIGNATURE |readLine!| #2#) (SIGNATURE |readLineIfCan!| #3=((|Union| #1# "failed") $)) (SIGNATURE |readIfCan!| #3#) (SIGNATURE |endOfFile?| ((|Boolean|) $))))) (T |TextFile|)) ((|writeLine!| (*1 *2 *1 *2) #1=(AND #2=(|isDomain| *2 (|String|)) #3=(|isDomain| *1 (|TextFile|)))) (|writeLine!| #4=(*1 *2 *1) #1#) (|readLine!| #4# #1#) (|readLineIfCan!| #4# #5=(|partial| AND #2# #3#)) (|readIfCan!| #4# #5#) (|endOfFile?| #4# (AND (|isDomain| *2 (|Boolean|)) #3#))) ((|sign| (#1=((|Union| #2=(|Integer|) "failed") |#1|) 19 T ELT)) (|nonQsign| (#1# 14 T ELT)) (|direction| ((#2# (|String|)) 33 T ELT))) @@ -3747,10 +3747,10 @@ NIL ((|tanh2trigh| (#1=(|#2| |#2|) 148 T ELT)) (|tanh2coth| (#1# 145 T ELT)) (|tan2trig| (#1# 136 T ELT)) (|tan2cot| (#1# 133 T ELT)) (|sinh2csch| (#1# 141 T ELT)) (|sin2csc| (#1# 129 T ELT)) (|simplifyLog| (#1# 44 T ELT)) (|simplifyExp| (#1# 105 T ELT)) (|simplify| (#1# 88 T ELT)) (|sech2cosh| (#1# 143 T ELT)) (|sec2cos| (#1# 131 T ELT)) (|removeSinhSq| (#1# 153 T ELT)) (|removeSinSq| (#1# 151 T ELT)) (|removeCoshSq| (#1# 152 T ELT)) (|removeCosSq| (#1# 150 T ELT)) (|htrigs| (#1# 163 T ELT)) (|expandTrigProducts| (#1# 30 (AND (|has| |#2| #2=(|ConvertibleTo| (|Pattern| |#1|))) (|has| |#2| #3=(|PatternMatchable| |#1|)) (|has| |#1| #2#) (|has| |#1| #3#)) ELT)) (|expandPower| (#1# 89 T ELT)) (|expandLog| (#1# 154 T ELT)) (|expand| (#1# 155 T ELT)) (|csch2sinh| (#1# 142 T ELT)) (|csc2sin| (#1# 130 T ELT)) (|coth2trigh| (#1# 149 T ELT)) (|coth2tanh| (#1# 147 T ELT)) (|cot2trig| (#1# 137 T ELT)) (|cot2tan| (#1# 135 T ELT)) (|cosh2sech| (#1# 139 T ELT)) (|cos2sec| (#1# 127 T ELT))) (((|TranscendentalManipulations| |#1| |#2|) (CATEGORY |package| (SIGNATURE |expand| #1=(|#2| |#2|)) (SIGNATURE |simplify| #1#) (SIGNATURE |htrigs| #1#) (SIGNATURE |simplifyExp| #1#) (SIGNATURE |simplifyLog| #1#) (SIGNATURE |expandPower| #1#) (SIGNATURE |expandLog| #1#) (SIGNATURE |cos2sec| #1#) (SIGNATURE |cosh2sech| #1#) (SIGNATURE |cot2trig| #1#) (SIGNATURE |coth2trigh| #1#) (SIGNATURE |csc2sin| #1#) (SIGNATURE |csch2sinh| #1#) (SIGNATURE |sec2cos| #1#) (SIGNATURE |sech2cosh| #1#) (SIGNATURE |sin2csc| #1#) (SIGNATURE |sinh2csch| #1#) (SIGNATURE |tan2trig| #1#) (SIGNATURE |tanh2trigh| #1#) (SIGNATURE |tan2cot| #1#) (SIGNATURE |tanh2coth| #1#) (SIGNATURE |cot2tan| #1#) (SIGNATURE |coth2tanh| #1#) (SIGNATURE |removeCosSq| #1#) (SIGNATURE |removeSinSq| #1#) (SIGNATURE |removeCoshSq| #1#) (SIGNATURE |removeSinhSq| #1#) (IF (|has| |#1| #2=(|PatternMatchable| |#1|)) (IF (|has| |#1| #3=(|ConvertibleTo| (|Pattern| |#1|))) (IF (|has| |#2| #3#) (IF (|has| |#2| #2#) (SIGNATURE |expandTrigProducts| #1#) |%noBranch|) |%noBranch|) |%noBranch|) |%noBranch|)) (|GcdDomain|) (|Join| (|FunctionSpace| |#1|) (|TranscendentalFunctionCategory|))) (T |TranscendentalManipulations|)) ((|expandTrigProducts| #1=(*1 *2 *2) (AND (|ofCategory| *3 #2=(|ConvertibleTo| (|Pattern| *3))) (|ofCategory| *3 #3=(|PatternMatchable| *3)) #4=(|ofCategory| *3 (|GcdDomain|)) #5=(|isDomain| *1 (|TranscendentalManipulations| *3 *2)) (|ofCategory| *2 #2#) (|ofCategory| *2 #3#) #6=(|ofCategory| *2 (|Join| (|FunctionSpace| *3) (|TranscendentalFunctionCategory|))))) (|removeSinhSq| #1# #7=(AND #4# #5# #6#)) (|removeCoshSq| #1# #7#) (|removeSinSq| #1# #7#) (|removeCosSq| #1# #7#) (|coth2tanh| #1# #7#) (|cot2tan| #1# #7#) (|tanh2coth| #1# #7#) (|tan2cot| #1# #7#) (|tanh2trigh| #1# #7#) (|tan2trig| #1# #7#) (|sinh2csch| #1# #7#) (|sin2csc| #1# #7#) (|sech2cosh| #1# #7#) (|sec2cos| #1# #7#) (|csch2sinh| #1# #7#) (|csc2sin| #1# #7#) (|coth2trigh| #1# #7#) (|cot2trig| #1# #7#) (|cosh2sech| #1# #7#) (|cos2sec| #1# #7#) (|expandLog| #1# #7#) (|expandPower| #1# #7#) (|simplifyLog| #1# #7#) (|simplifyExp| #1# #7#) (|htrigs| #1# #7#) (|simplify| #1# #7#) (|expand| #1# #7#)) -((~= #1=(#2=(#3=(|Boolean|) $ $) NIL T ELT)) (|zero?| #4=(#5=(#3# $) NIL T ELT)) (|variables| ((#6=(|List| #7=(|Symbol|)) $) NIL T ELT)) (|unitNormal| (((|Record| (|:| |unit| $) (|:| |canonical| $) (|:| |associate| $)) $) NIL #8=(|has| |#1| (|IntegralDomain|)) ELT)) (|unitCanonical| #9=(#10=($ $) NIL #8# ELT)) (|unit?| (#5# NIL #8# ELT)) (|tanh| #11=(#10# NIL #12=(|has| |#1| (|Algebra| #13=(|Fraction| #14=(|Integer|)))) ELT)) (|tan| #11#) (|subtractIfCan| (#15=(#16=(|Union| $ "failed") $ $) NIL T ELT)) (|sqrt| #11#) (|sinh| #11#) (|sin| #11#) (|sech| #11#) (|sec| #11#) (|sample| #17=(#18=($) NIL T CONST)) (|reductum| #19=(#10# NIL T ELT)) (|recip| ((#16# $) NIL T ELT)) (|polynomial| (#20=(#21=(|Polynomial| |#1|) $ #22=(|NonNegativeInteger|)) 18 T ELT) ((#21# $ #22# #22#) NIL T ELT)) (|pole?| #4#) (|pi| (#18# NIL #12# ELT)) (|order| ((#22# $ #7#) NIL T ELT) ((#22# $ #7# #22#) NIL T ELT)) (|opposite?| #1#) (|one?| #4#) (|nthRoot| (($ $ #14#) NIL #12# ELT)) (|monomial?| #4#) (|monomial| (($ $ #6# (|List| #23=(|IndexedExponents| #7#))) NIL T ELT) (($ $ #7# #23#) NIL T ELT) (($ |#1| #23#) NIL T ELT) #24=(($ $ #7# #22#) NIL T ELT) #25=(($ $ #6# (|List| #22#)) NIL T ELT)) (|map| (($ (|Mapping| |#1| |#1|) $) NIL T ELT)) (|log| #11#) (|leadingMonomial| #19#) (|leadingCoefficient| ((|#1| $) NIL T ELT)) (|latex| (((|String|) $) NIL T ELT)) (|integrate| (#26=($ $ #7#) NIL #12# ELT) (($ $ #7# |#1|) NIL #12# ELT)) (|hash| (((|SingleInteger|) $) NIL T ELT)) (|fintegrate| (($ (|Mapping| $) #7# |#1|) NIL #12# ELT)) (|extend| #27=(($ $ #22#) NIL T ELT)) (|exquo| (#15# NIL #8# ELT)) (|exp| #11#) (|eval| (($ $ #7# $) NIL T ELT) (($ $ #6# #28=(|List| $)) NIL T ELT) (($ $ (|List| #29=(|Equation| $))) NIL T ELT) (($ $ #29#) NIL T ELT) (($ $ $ $) NIL T ELT) (($ $ #28# #28#) NIL T ELT)) (|differentiate| #25# #24# #30=(($ $ #6#) NIL T ELT) #31=(#26# NIL T ELT)) (|degree| ((#23# $) NIL T ELT)) (|csch| #11#) (|csc| #11#) (|coth| #11#) (|cot| #11#) (|cosh| #11#) (|cos| #11#) (|complete| #19#) (|coerce| (((|OutputForm|) $) NIL T ELT) (($ #14#) NIL T ELT) (($ |#1|) NIL (|has| |#1| (|CommutativeRing|)) ELT) #9# (($ #13#) NIL #12# ELT) (($ #7#) NIL T ELT) (($ #21#) NIL T ELT)) (|coefficient| ((|#1| $ #23#) NIL T ELT) #24# #25# (#20# NIL T ELT)) (|charthRoot| (((|Maybe| $) $) NIL (|has| |#1| (|CharacteristicNonZero|)) ELT)) (|characteristic| ((#22#) NIL T CONST)) (|before?| #1#) (|atanh| #11#) (|atan| #11#) (|associates?| (#2# NIL #8# ELT)) (|asinh| #11#) (|asin| #11#) (|asech| #11#) (|asec| #11#) (|annihilate?| #1#) (|acsch| #11#) (|acsc| #11#) (|acoth| #11#) (|acot| #11#) (|acosh| #11#) (|acos| #11#) (|Zero| #17#) (|One| #17#) (D #25# #24# #30# #31#) (= #1#) (/ (#32=($ $ |#1|) NIL (|has| |#1| (|Field|)) ELT)) (- #19# #33=(#34=($ $ $) NIL T ELT)) (+ #33#) (** (($ $ #35=(|PositiveInteger|)) NIL T ELT) #27# (#34# NIL #12# ELT) #36=(($ $ #13#) NIL #12# ELT)) (* (($ #35# $) NIL T ELT) (($ #22# $) NIL T ELT) (($ #14# . #37=($)) NIL T ELT) #33# #36# (($ #13# . #37#) NIL #12# ELT) (($ |#1| . #37#) NIL T ELT) (#32# NIL T ELT))) +((~= #1=(#2=(#3=(|Boolean|) $ $) NIL T ELT)) (|zero?| #4=(#5=(#3# $) NIL T ELT)) (|variables| ((#6=(|List| #7=(|Symbol|)) $) NIL T ELT)) (|unitNormal| (((|Record| (|:| |unit| $) (|:| |canonical| $) (|:| |associate| $)) $) NIL #8=(|has| |#1| (|IntegralDomain|)) ELT)) (|unitCanonical| #9=(#10=($ $) NIL #8# ELT)) (|unit?| (#5# NIL #8# ELT)) (|tanh| #11=(#10# NIL #12=(|has| |#1| (|Algebra| #13=(|Fraction| #14=(|Integer|)))) ELT)) (|tan| #11#) (|subtractIfCan| ((#15=(|Maybe| $) $ $) NIL T ELT)) (|sqrt| #11#) (|sinh| #11#) (|sin| #11#) (|sech| #11#) (|sec| #11#) (|sample| #16=(#17=($) NIL T CONST)) (|reductum| #18=(#10# NIL T ELT)) (|recip| ((#19=(|Union| $ "failed") $) NIL T ELT)) (|polynomial| (#20=(#21=(|Polynomial| |#1|) $ #22=(|NonNegativeInteger|)) 18 T ELT) ((#21# $ #22# #22#) NIL T ELT)) (|pole?| #4#) (|pi| (#17# NIL #12# ELT)) (|order| ((#22# $ #7#) NIL T ELT) ((#22# $ #7# #22#) NIL T ELT)) (|opposite?| #1#) (|one?| #4#) (|nthRoot| (($ $ #14#) NIL #12# ELT)) (|monomial?| #4#) (|monomial| (($ $ #6# (|List| #23=(|IndexedExponents| #7#))) NIL T ELT) (($ $ #7# #23#) NIL T ELT) (($ |#1| #23#) NIL T ELT) #24=(($ $ #7# #22#) NIL T ELT) #25=(($ $ #6# (|List| #22#)) NIL T ELT)) (|map| (($ (|Mapping| |#1| |#1|) $) NIL T ELT)) (|log| #11#) (|leadingMonomial| #18#) (|leadingCoefficient| ((|#1| $) NIL T ELT)) (|latex| (((|String|) $) NIL T ELT)) (|integrate| (#26=($ $ #7#) NIL #12# ELT) (($ $ #7# |#1|) NIL #12# ELT)) (|hash| (((|SingleInteger|) $) NIL T ELT)) (|fintegrate| (($ (|Mapping| $) #7# |#1|) NIL #12# ELT)) (|extend| #27=(($ $ #22#) NIL T ELT)) (|exquo| ((#19# $ $) NIL #8# ELT)) (|exp| #11#) (|eval| (($ $ #7# $) NIL T ELT) (($ $ #6# #28=(|List| $)) NIL T ELT) (($ $ (|List| #29=(|Equation| $))) NIL T ELT) (($ $ #29#) NIL T ELT) (($ $ $ $) NIL T ELT) (($ $ #28# #28#) NIL T ELT)) (|differentiate| #25# #24# #30=(($ $ #6#) NIL T ELT) #31=(#26# NIL T ELT)) (|degree| ((#23# $) NIL T ELT)) (|csch| #11#) (|csc| #11#) (|coth| #11#) (|cot| #11#) (|cosh| #11#) (|cos| #11#) (|complete| #18#) (|coerce| (((|OutputForm|) $) NIL T ELT) (($ #14#) NIL T ELT) (($ |#1|) NIL (|has| |#1| (|CommutativeRing|)) ELT) #9# (($ #13#) NIL #12# ELT) (($ #7#) NIL T ELT) (($ #21#) NIL T ELT)) (|coefficient| ((|#1| $ #23#) NIL T ELT) #24# #25# (#20# NIL T ELT)) (|charthRoot| ((#15# $) NIL (|has| |#1| (|CharacteristicNonZero|)) ELT)) (|characteristic| ((#22#) NIL T CONST)) (|before?| #1#) (|atanh| #11#) (|atan| #11#) (|associates?| (#2# NIL #8# ELT)) (|asinh| #11#) (|asin| #11#) (|asech| #11#) (|asec| #11#) (|annihilate?| #1#) (|acsch| #11#) (|acsc| #11#) (|acoth| #11#) (|acot| #11#) (|acosh| #11#) (|acos| #11#) (|Zero| #16#) (|One| #16#) (D #25# #24# #30# #31#) (= #1#) (/ (#32=($ $ |#1|) NIL (|has| |#1| (|Field|)) ELT)) (- #18# #33=(#34=($ $ $) NIL T ELT)) (+ #33#) (** (($ $ #35=(|PositiveInteger|)) NIL T ELT) #27# (#34# NIL #12# ELT) #36=(($ $ #13#) NIL #12# ELT)) (* (($ #35# $) NIL T ELT) (($ #22# $) NIL T ELT) (($ #14# . #37=($)) NIL T ELT) #33# #36# (($ #13# . #37#) NIL #12# ELT) (($ |#1| . #37#) NIL T ELT) (#32# NIL T ELT))) (((|TaylorSeries| |#1|) (|Join| (|MultivariateTaylorSeriesCategory| |#1| #1=(|Symbol|)) (CATEGORY |domain| (SIGNATURE |coefficient| (#2=(|Polynomial| |#1|) $ (|NonNegativeInteger|))) (SIGNATURE |coerce| ($ #1#)) (SIGNATURE |coerce| ($ #2#)) (IF (|has| |#1| (|Algebra| (|Fraction| (|Integer|)))) (PROGN (SIGNATURE |integrate| ($ $ #1# |#1|)) (SIGNATURE |fintegrate| ($ (|Mapping| $) #1# |#1|))) |%noBranch|))) (|Ring|)) (T |TaylorSeries|)) ((|coefficient| (*1 *2 *1 *3) (AND (|isDomain| *3 (|NonNegativeInteger|)) (|isDomain| *2 (|Polynomial| *4)) #1=(|isDomain| *1 #2=(|TaylorSeries| *4)) #3=(|ofCategory| *4 #4=(|Ring|)))) (|coerce| #5=(*1 *1 *2) (AND #6=(|isDomain| *2 #7=(|Symbol|)) #8=(|isDomain| *1 (|TaylorSeries| *3)) #9=(|ofCategory| *3 #4#))) (|coerce| #5# (AND (|isDomain| *2 (|Polynomial| *3)) #9# #8#)) (|integrate| (*1 *1 *1 *2 *3) (AND #6# #8# (|ofCategory| *3 #10=(|Algebra| (|Fraction| (|Integer|)))) #9#)) (|fintegrate| (*1 *1 *2 *3 *4) (AND (|isDomain| *2 (|Mapping| #2#)) (|isDomain| *3 #7#) #1# (|ofCategory| *4 #10#) #3#))) -((|stronglyReduced?| (#1=(#2=(|Boolean|) |#5| $) 68 T ELT) (#3=(#2# $) 109 T ELT)) (|stronglyReduce| (#4=(|#5| |#5| $) 83 T ELT)) (|select| (($ #5=(|Mapping| #2# |#5|) $) NIL T ELT) ((#6=(|Union| |#5| #7="failed") $ |#4|) 126 T ELT)) (|rewriteSetWithReduction| ((#8=(|List| |#5|) #8# $ #9=(|Mapping| |#5| |#5| |#5|) #10=(|Mapping| #2# |#5| |#5|)) 81 T ELT)) (|retractIfCan| ((#11=(|Union| $ #7#) #8#) 134 T ELT)) (|rest| ((#11# $) 119 T ELT)) (|removeZero| (#4# 101 T ELT)) (|reduced?| ((#2# |#5| $ #10#) 36 T ELT)) (|reduceByQuasiMonic| (#4# 105 T ELT)) (|reduce| ((|#5| #9# $ |#5| |#5|) NIL T ELT) ((|#5| #9# $ |#5|) NIL T ELT) ((|#5| #9# $) NIL T ELT) ((|#5| |#5| $ #9# #10#) 77 T ELT)) (|quasiComponent| (((|Record| (|:| |close| #8#) (|:| |open| #8#)) $) 63 T ELT)) (|normalized?| (#1# 66 T ELT) (#3# 110 T ELT)) (|mvar| ((|#4| $) 115 T ELT)) (|last| (#12=(#6# $) 117 T ELT)) (|initials| (#13=(#8# $) 55 T ELT)) (|initiallyReduced?| (#1# 75 T ELT) (#3# 114 T ELT)) (|initiallyReduce| (#4# 89 T ELT)) (|infRittWu?| (#14=(#2# $ $) 29 T ELT)) (|headReduced?| (#1# 71 T ELT) (#3# 112 T ELT)) (|headReduce| (#4# 86 T ELT)) (|first| (#12# 116 T ELT)) (|extend| (($ $ |#5|) 135 T ELT)) (|degree| (#15=((|NonNegativeInteger|) $) 60 T ELT)) (|construct| (($ #8#) 132 T ELT)) (|collectUpper| (#16=($ $ |#4|) 130 T ELT)) (|collectUnder| (#16# 128 T ELT)) (|collectQuasiMonic| (($ $) 127 T ELT)) (|coerce| (((|OutputForm|) $) NIL T ELT) (#13# 120 T ELT)) (|coHeight| (#15# 139 T ELT)) (|basicSet| ((#17=(|Union| (|Record| (|:| |bas| $) (|:| |top| #8#)) #7#) #8# #10#) 49 T ELT) ((#17# #8# #5# #10#) 51 T ELT)) (|autoReduced?| ((#2# $ (|Mapping| #2# |#5| #8#)) 107 T ELT)) (|algebraicVariables| (((|List| |#4|) $) 122 T ELT)) (|algebraic?| ((#2# |#4| $) 125 T ELT)) (= (#14# 20 T ELT))) +((|stronglyReduced?| (#1=(#2=(|Boolean|) |#5| $) 68 T ELT) (#3=(#2# $) 109 T ELT)) (|stronglyReduce| (#4=(|#5| |#5| $) 83 T ELT)) (|select| (($ #5=(|Mapping| #2# |#5|) $) NIL T ELT) ((#6=(|Union| |#5| #7="failed") $ |#4|) 126 T ELT)) (|rewriteSetWithReduction| ((#8=(|List| |#5|) #8# $ #9=(|Mapping| |#5| |#5| |#5|) #10=(|Mapping| #2# |#5| |#5|)) 81 T ELT)) (|retractIfCan| ((#11=(|Union| $ #7#) #8#) 134 T ELT)) (|rest| ((#11# $) 119 T ELT)) (|removeZero| (#4# 101 T ELT)) (|reduced?| ((#2# |#5| $ #10#) 36 T ELT)) (|reduceByQuasiMonic| (#4# 105 T ELT)) (|reduce| ((|#5| #9# $ |#5| |#5|) NIL T ELT) ((|#5| #9# $ |#5|) NIL T ELT) ((|#5| #9# $) NIL T ELT) ((|#5| |#5| $ #9# #10#) 77 T ELT)) (|quasiComponent| (((|Record| (|:| |close| #8#) (|:| |open| #8#)) $) 63 T ELT)) (|normalized?| (#1# 66 T ELT) (#3# 110 T ELT)) (|mvar| ((|#4| $) 115 T ELT)) (|last| (#12=(#6# $) 117 T ELT)) (|initials| (#13=(#8# $) 55 T ELT)) (|initiallyReduced?| (#1# 75 T ELT) (#3# 114 T ELT)) (|initiallyReduce| (#4# 89 T ELT)) (|infRittWu?| (#14=(#2# $ $) 29 T ELT)) (|headReduced?| (#1# 71 T ELT) (#3# 112 T ELT)) (|headReduce| (#4# 86 T ELT)) (|first| (#12# 116 T ELT)) (|extend| (($ $ |#5|) 135 T ELT)) (|degree| (#15=((|NonNegativeInteger|) $) 60 T ELT)) (|construct| (($ #8#) 132 T ELT)) (|collectUpper| (#16=($ $ |#4|) 130 T ELT)) (|collectUnder| (#16# 128 T ELT)) (|collectQuasiMonic| (($ $) 127 T ELT)) (|coerce| (((|OutputForm|) $) NIL T ELT) (#13# 120 T ELT)) (|coHeight| (#15# 142 T ELT)) (|basicSet| ((#17=(|Union| (|Record| (|:| |bas| $) (|:| |top| #8#)) #7#) #8# #10#) 49 T ELT) ((#17# #8# #5# #10#) 51 T ELT)) (|autoReduced?| ((#2# $ (|Mapping| #2# |#5| #8#)) 107 T ELT)) (|algebraicVariables| (((|List| |#4|) $) 122 T ELT)) (|algebraic?| ((#2# |#4| $) 125 T ELT)) (= (#14# 20 T ELT))) (((|TriangularSetCategory&| |#1| |#2| |#3| |#4| |#5|) (CATEGORY |package| (SIGNATURE |coHeight| #1=((|NonNegativeInteger|) |#1|)) (SIGNATURE |extend| (|#1| |#1| |#5|)) (SIGNATURE |select| (#2=(|Union| |#5| #3="failed") |#1| |#4|)) (SIGNATURE |algebraic?| (#4=(|Boolean|) |#4| |#1|)) (SIGNATURE |algebraicVariables| ((|List| |#4|) |#1|)) (SIGNATURE |rest| (#5=(|Union| |#1| #3#) |#1|)) (SIGNATURE |last| #6=(#2# |#1|)) (SIGNATURE |first| #6#) (SIGNATURE |reduceByQuasiMonic| #7=(|#5| |#5| |#1|)) (SIGNATURE |collectQuasiMonic| (|#1| |#1|)) (SIGNATURE |removeZero| #7#) (SIGNATURE |initiallyReduce| #7#) (SIGNATURE |headReduce| #7#) (SIGNATURE |stronglyReduce| #7#) (SIGNATURE |rewriteSetWithReduction| (#8=(|List| |#5|) #8# |#1| #9=(|Mapping| |#5| |#5| |#5|) #10=(|Mapping| #4# |#5| |#5|))) (SIGNATURE |reduce| (|#5| |#5| |#1| #9# #10#)) (SIGNATURE |initiallyReduced?| #11=(#4# |#1|)) (SIGNATURE |headReduced?| #11#) (SIGNATURE |stronglyReduced?| #11#) (SIGNATURE |autoReduced?| (#4# |#1| (|Mapping| #4# |#5| #8#))) (SIGNATURE |initiallyReduced?| #12=(#4# |#5| |#1|)) (SIGNATURE |headReduced?| #12#) (SIGNATURE |stronglyReduced?| #12#) (SIGNATURE |reduced?| (#4# |#5| |#1| #10#)) (SIGNATURE |normalized?| #11#) (SIGNATURE |normalized?| #12#) (SIGNATURE |quasiComponent| ((|Record| (|:| |close| #8#) (|:| |open| #8#)) |#1|)) (SIGNATURE |degree| #1#) (SIGNATURE |initials| #13=(#8# |#1|)) (SIGNATURE |basicSet| (#14=(|Union| (|Record| (|:| |bas| |#1|) (|:| |top| #8#)) #3#) #8# #15=(|Mapping| #4# |#5|) #10#)) (SIGNATURE |basicSet| (#14# #8# #10#)) (SIGNATURE |infRittWu?| #16=(#4# |#1| |#1|)) (SIGNATURE |collectUpper| #17=(|#1| |#1| |#4|)) (SIGNATURE |collectUnder| #17#) (SIGNATURE |mvar| (|#4| |#1|)) (SIGNATURE |retractIfCan| (#5# #8#)) (SIGNATURE |coerce| #13#) (SIGNATURE |reduce| (|#5| #9# |#1|)) (SIGNATURE |reduce| (|#5| #9# |#1| |#5|)) (SIGNATURE |reduce| (|#5| #9# |#1| |#5| |#5|)) (SIGNATURE |construct| (|#1| #8#)) (SIGNATURE |select| (|#1| #15# |#1|)) (SIGNATURE |coerce| ((|OutputForm|) |#1|)) (SIGNATURE = #16#)) (|TriangularSetCategory| |#2| |#3| |#4| |#5|) (|IntegralDomain|) (|OrderedAbelianMonoidSup|) (|OrderedSet|) (|RecursivePolynomialCategory| |#2| |#3| |#4|)) (T |TriangularSetCategory&|)) NIL ((~= (#1=((|Boolean|) $ $) 7 T ELT)) (|zeroSetSplitIntoTriangularSystems| (((|List| (|Record| (|:| |close| $) (|:| |open| (|List| |#4|)))) (|List| |#4|)) 91 T ELT)) (|zeroSetSplit| (((|List| $) (|List| |#4|)) 92 T ELT)) (|variables| (((|List| |#3|) . #2=($)) 39 T ELT)) (|trivialIdeal?| (#3=(#4=(|Boolean|) $) 32 T ELT)) (|triangular?| (#3# 23 (|has| |#1| . #5=((|IntegralDomain|))) ELT)) (|stronglyReduced?| (((|Boolean|) |#4| $) 107 T ELT) (((|Boolean|) $) 103 T ELT)) (|stronglyReduce| ((|#4| |#4| $) 98 T ELT)) (|sort| (((|Record| (|:| |under| $) (|:| |floor| $) (|:| |upper| $)) $ |#3|) 33 T ELT)) (|select| (($ (|Mapping| #6=(|Boolean|) |#4|) . #7=($)) 67 (|has| $ (|FiniteAggregate| |#4|)) ELT) (((|Union| |#4| "failed") $ |#3|) 85 T ELT)) (|sample| (#8=($) 59 T CONST)) (|roughUnitIdeal?| (#3# 28 (|has| |#1| . #5#) ELT)) (|roughSubIdeal?| (#9=(#4# $ $) 30 (|has| |#1| . #5#) ELT)) (|roughEqualIdeals?| (#9# 29 (|has| |#1| . #5#) ELT)) (|roughBase?| (#3# 31 (|has| |#1| . #5#) ELT)) (|rewriteSetWithReduction| (((|List| |#4|) (|List| |#4|) $ (|Mapping| |#4| |#4| |#4|) (|Mapping| (|Boolean|) |#4| |#4|)) 99 T ELT)) (|rewriteIdealWithRemainder| (((|List| |#4|) (|List| |#4|) . #10=($)) 24 (|has| |#1| . #5#) ELT)) (|rewriteIdealWithHeadRemainder| (((|List| |#4|) (|List| |#4|) . #10#) 25 (|has| |#1| . #5#) ELT)) (|retractIfCan| (((|Union| $ "failed") (|List| |#4|)) 42 T ELT)) (|retract| (($ (|List| |#4|)) 41 T ELT)) (|rest| (((|Union| $ "failed") $) 88 T ELT)) (|removeZero| ((|#4| |#4| $) 95 T ELT)) (|removeDuplicates| (($ $) 69 (AND (|has| |#4| . #11=((|BasicType|))) (|has| $ (|FiniteAggregate| |#4|))) ELT)) (|remove| (($ |#4| $) 68 (AND (|has| |#4| . #11#) (|has| $ (|FiniteAggregate| |#4|))) ELT) (($ (|Mapping| #6# |#4|) . #7#) 66 (|has| $ (|FiniteAggregate| |#4|)) ELT)) (|remainder| (((|Record| (|:| |rnum| |#1|) (|:| |polnum| |#4|) (|:| |den| |#1|)) |#4| $) 26 (|has| |#1| . #5#) ELT)) (|reduced?| (((|Boolean|) |#4| $ (|Mapping| (|Boolean|) |#4| |#4|)) 108 T ELT)) (|reduceByQuasiMonic| ((|#4| |#4| $) 93 T ELT)) (|reduce| ((|#4| (|Mapping| |#4| |#4| |#4|) $ |#4| |#4|) 54 (|has| |#4| . #12=((|BasicType|))) ELT) ((|#4| (|Mapping| |#4| |#4| |#4|) $ |#4|) 50 T ELT) ((|#4| (|Mapping| |#4| |#4| |#4|) $) 49 T ELT) ((|#4| |#4| $ (|Mapping| |#4| |#4| |#4|) (|Mapping| (|Boolean|) |#4| |#4|)) 100 T ELT)) (|quasiComponent| (((|Record| (|:| |close| (|List| |#4|)) (|:| |open| (|List| |#4|))) $) 111 T ELT)) (|normalized?| (((|Boolean|) |#4| $) 110 T ELT) (((|Boolean|) $) 109 T ELT)) (|mvar| ((|#3| $) 40 T ELT)) (|members| (((|List| |#4|) $) 48 T ELT)) (|member?| ((#13=(|Boolean|) |#4| $) 53 (|has| |#4| . #12#) ELT)) (|map!| (($ (|Mapping| |#4| |#4|) $) 117 T ELT)) (|map| (($ (|Mapping| |#4| |#4|) $) 60 T ELT)) (|mainVariables| (((|List| |#3|) . #2#) 38 T ELT)) (|mainVariable?| ((#4# |#3| $) 37 T ELT)) (|latex| (((|String|) $) 11 T ELT)) (|last| (((|Union| |#4| "failed") $) 89 T ELT)) (|initials| (((|List| |#4|) $) 113 T ELT)) (|initiallyReduced?| (((|Boolean|) |#4| $) 105 T ELT) (((|Boolean|) $) 101 T ELT)) (|initiallyReduce| ((|#4| |#4| $) 96 T ELT)) (|infRittWu?| (((|Boolean|) $ $) 116 T ELT)) (|headRemainder| (((|Record| (|:| |num| |#4|) (|:| |den| |#1|)) |#4| $) 27 (|has| |#1| . #5#) ELT)) (|headReduced?| (((|Boolean|) |#4| $) 106 T ELT) (((|Boolean|) $) 102 T ELT)) (|headReduce| ((|#4| |#4| $) 97 T ELT)) (|hash| (((|SingleInteger|) $) 12 T ELT)) (|first| (((|Union| |#4| "failed") $) 90 T ELT)) (|find| (((|Union| |#4| "failed") (|Mapping| #13# |#4|) $) 51 T ELT)) (|extendIfCan| (((|Union| $ "failed") $ |#4|) 84 T ELT)) (|extend| (($ $ |#4|) 83 T ELT)) (|every?| ((#13# (|Mapping| #13# |#4|) . #14=($)) 46 T ELT)) (|eval| (($ $ (|List| |#4|) (|List| |#4|)) 64 (AND (|has| |#4| (|Evalable| |#4|)) (|has| |#4| . #15=((|SetCategory|)))) ELT) (($ $ |#4| |#4|) 63 (AND (|has| |#4| (|Evalable| |#4|)) (|has| |#4| . #15#)) ELT) (($ $ (|Equation| |#4|)) 62 (AND (|has| |#4| (|Evalable| |#4|)) (|has| |#4| . #15#)) ELT) (($ $ (|List| (|Equation| |#4|))) 61 (AND (|has| |#4| (|Evalable| |#4|)) (|has| |#4| . #15#)) ELT)) (|eq?| ((#16=(|Boolean|) $ $) 55 T ELT)) (|empty?| ((#16# $) 58 T ELT)) (|empty| (#8# 57 T ELT)) (|degree| (((|NonNegativeInteger|) $) 112 T ELT)) (|count| ((#17=(|NonNegativeInteger|) |#4| $) 52 (|has| |#4| . #12#) ELT) ((#17# (|Mapping| #13# |#4|) $) 47 T ELT)) (|copy| (($ $) 56 T ELT)) (|convert| ((#18=(|InputForm|) $) 70 (|has| |#4| (|ConvertibleTo| #18#)) ELT)) (|construct| (($ (|List| |#4|)) 65 T ELT)) (|collectUpper| (($ $ |#3|) 34 T ELT)) (|collectUnder| (($ $ |#3|) 36 T ELT)) (|collectQuasiMonic| (($ $) 94 T ELT)) (|collect| (($ $ |#3|) 35 T ELT)) (|coerce| (((|OutputForm|) . #19=($)) 13 T ELT) (((|List| |#4|) . #19#) 43 T ELT)) (|coHeight| (((|NonNegativeInteger|) $) 82 (|has| |#3| (|Finite|)) ELT)) (|before?| (#1# 6 T ELT)) (|basicSet| (((|Union| (|Record| (|:| |bas| $) (|:| |top| (|List| |#4|))) "failed") (|List| |#4|) (|Mapping| (|Boolean|) |#4| |#4|)) 115 T ELT) (((|Union| (|Record| (|:| |bas| $) (|:| |top| (|List| |#4|))) "failed") (|List| |#4|) (|Mapping| (|Boolean|) |#4|) (|Mapping| (|Boolean|) |#4| |#4|)) 114 T ELT)) (|autoReduced?| (((|Boolean|) $ (|Mapping| (|Boolean|) |#4| (|List| |#4|))) 104 T ELT)) (|any?| ((#13# (|Mapping| #13# |#4|) . #14#) 45 T ELT)) (|algebraicVariables| (((|List| |#3|) $) 87 T ELT)) (|algebraic?| (((|Boolean|) |#3| $) 86 T ELT)) (= (#1# 8 T ELT)) (|#| ((#17# $) 44 T ELT))) @@ -3787,7 +3787,7 @@ NIL ((|squareFreePart| (($ $) 17 T ELT)) (|prime?| (((|Boolean|) $) 27 T ELT))) (((|UniqueFactorizationDomain&| |#1|) (CATEGORY |package| (SIGNATURE |squareFreePart| (|#1| |#1|)) (SIGNATURE |prime?| ((|Boolean|) |#1|))) (|UniqueFactorizationDomain|)) (T |UniqueFactorizationDomain&|)) NIL -((~= (#1=((|Boolean|) $ $) 7 T ELT)) (|zero?| ((#2=(|Boolean|) $) 22 T ELT)) (|unitNormal| (((|Record| (|:| |unit| $) (|:| |canonical| $) (|:| |associate| $)) $) 55 T ELT)) (|unitCanonical| (($ $) 54 T ELT)) (|unit?| ((#3=(|Boolean|) $) 52 T ELT)) (|subtractIfCan| (((|Union| $ "failed") $ $) 26 T ELT)) (|squareFreePart| (($ $) 66 T ELT)) (|squareFree| (((|Factored| $) $) 67 T ELT)) (|sample| (#4=($) 23 T CONST)) (|recip| (((|Union| $ "failed") $) 42 T ELT)) (|prime?| (((|Boolean|) $) 68 T ELT)) (|opposite?| ((#2# $ $) 20 T ELT)) (|one?| (((|Boolean|) $) 44 T ELT)) (|lcm| (#5=($ $ $) 60 T ELT) (#6=($ (|List| $)) 59 T ELT)) (|latex| (((|String|) $) 11 T ELT)) (|hash| (((|SingleInteger|) $) 12 T ELT)) (|gcdPolynomial| ((#7=(|SparseUnivariatePolynomial| $) #7# #7#) 58 T ELT)) (|gcd| (#5# 62 T ELT) (#6# 61 T ELT)) (|factor| (((|Factored| $) $) 65 T ELT)) (|exquo| (((|Union| $ "failed") $ $) 56 T ELT)) (|coerce| (((|OutputForm|) $) 13 T ELT) (($ (|Integer|)) 41 T ELT) (($ $) 57 T ELT)) (|characteristic| (((|NonNegativeInteger|)) 40 T CONST)) (|before?| (#1# 6 T ELT)) (|associates?| ((#3# $ $) 53 T ELT)) (|annihilate?| (((|Boolean|) $ $) 33 T ELT)) (|Zero| (#4# 24 T CONST)) (|One| (($) 45 T CONST)) (= (#1# 8 T ELT)) (- (($ $) 29 T ELT) (($ $ $) 28 T ELT)) (+ (($ $ $) 18 T ELT)) (** (($ $ (|PositiveInteger|)) 35 T ELT) (($ $ (|NonNegativeInteger|)) 43 T ELT)) (* (($ (|PositiveInteger|) $) 17 T ELT) (($ (|NonNegativeInteger|) $) 21 T ELT) (($ (|Integer|) $) 30 T ELT) (($ $ $) 34 T ELT))) +((~= (#1=((|Boolean|) $ $) 7 T ELT)) (|zero?| ((#2=(|Boolean|) $) 22 T ELT)) (|unitNormal| (((|Record| (|:| |unit| $) (|:| |canonical| $) (|:| |associate| $)) $) 56 T ELT)) (|unitCanonical| (($ $) 55 T ELT)) (|unit?| ((#3=(|Boolean|) $) 53 T ELT)) (|subtractIfCan| (((|Maybe| $) $ $) 26 T ELT)) (|squareFreePart| (($ $) 67 T ELT)) (|squareFree| (((|Factored| $) $) 68 T ELT)) (|sample| (#4=($) 23 T CONST)) (|recip| (((|Union| $ "failed") $) 43 T ELT)) (|prime?| (((|Boolean|) $) 69 T ELT)) (|opposite?| ((#2# $ $) 20 T ELT)) (|one?| (((|Boolean|) $) 45 T ELT)) (|lcm| (#5=($ $ $) 61 T ELT) (#6=($ (|List| $)) 60 T ELT)) (|latex| (((|String|) $) 11 T ELT)) (|hash| (((|SingleInteger|) $) 12 T ELT)) (|gcdPolynomial| ((#7=(|SparseUnivariatePolynomial| $) #7# #7#) 59 T ELT)) (|gcd| (#5# 63 T ELT) (#6# 62 T ELT)) (|factor| (((|Factored| $) $) 66 T ELT)) (|exquo| (((|Union| $ "failed") $ $) 57 T ELT)) (|coerce| (((|OutputForm|) $) 13 T ELT) (($ (|Integer|)) 42 T ELT) (($ $) 58 T ELT)) (|characteristic| (((|NonNegativeInteger|)) 41 T CONST)) (|before?| (#1# 6 T ELT)) (|associates?| ((#3# $ $) 54 T ELT)) (|annihilate?| (((|Boolean|) $ $) 34 T ELT)) (|Zero| (#4# 24 T CONST)) (|One| (($) 46 T CONST)) (= (#1# 8 T ELT)) (- (($ $) 30 T ELT) (($ $ $) 29 T ELT)) (+ (($ $ $) 18 T ELT)) (** (($ $ (|PositiveInteger|)) 36 T ELT) (($ $ (|NonNegativeInteger|)) 44 T ELT)) (* (($ (|PositiveInteger|) $) 17 T ELT) (($ (|NonNegativeInteger|) $) 21 T ELT) (($ (|Integer|) $) 31 T ELT) (($ $ $) 35 T ELT))) (((|UniqueFactorizationDomain|) (|Category|)) (T |UniqueFactorizationDomain|)) ((|prime?| (*1 *2 *1) (AND (|ofCategory| *1 (|UniqueFactorizationDomain|)) (|isDomain| *2 (|Boolean|)))) (|squareFree| (*1 *2 *1) (AND (|isDomain| *2 (|Factored| *1)) (|ofCategory| *1 (|UniqueFactorizationDomain|)))) (|squareFreePart| (*1 *1 *1) (|ofCategory| *1 (|UniqueFactorizationDomain|))) (|factor| (*1 *2 *1) (AND (|isDomain| *2 (|Factored| *1)) (|ofCategory| *1 (|UniqueFactorizationDomain|))))) (|Join| (|GcdDomain|) (CATEGORY |domain| (SIGNATURE |prime?| ((|Boolean|) $)) (SIGNATURE |squareFree| ((|Factored| $) $)) (SIGNATURE |squareFreePart| ($ $)) (SIGNATURE |factor| ((|Factored| $) $)))) @@ -3808,13 +3808,13 @@ NIL (((|UInt8|) (|Join| (|OrderedFinite|) (|Logic|) (CATEGORY |domain| (SIGNATURE |bitand| #1=($ $ $)) (SIGNATURE |bitior| #1#) (SIGNATURE |sample| ($) |constant|)))) (T |UInt8|)) ((|bitand| #1=(*1 *1 *1 *1) #2=(|isDomain| *1 (|UInt8|))) (|bitior| #1# #2#) (|sample| (*1 *1) #2#)) ((|NonNegativeInteger|) (|%not| (|%ilt| 8 (|%ilength| |#1|)))) -((~= #1=(#2=(#3=(|Boolean|) $ $) NIL T ELT)) (|zero?| #4=(#5=(#3# $) NIL T ELT)) (|wholePart| (#6=(#7=(|UnivariateTaylorSeries| |#1| |#2| |#3|) $) NIL #8=(AND (|has| #7# (|EuclideanDomain|)) #9=(|has| |#1| (|Field|))) ELT)) (|variables| ((#10=(|List| #11=(|SingletonAsOrderedSet|)) $) NIL T ELT)) (|variable| (#12=(#13=(|Symbol|) $) 10 T ELT)) (|unitNormal| (((|Record| (|:| |unit| $) (|:| |canonical| $) (|:| |associate| $)) $) NIL #14=(OR #15=(AND (|has| #7# (|OrderedIntegralDomain|)) #9#) #16=(AND #17=(|has| #7# (|PolynomialFactorizationExplicit|)) #9#) #18=(|has| |#1| (|IntegralDomain|))) ELT)) (|unitCanonical| #19=(#20=($ $) NIL #14# ELT)) (|unit?| (#5# NIL #14# ELT)) (|truncate| #21=(#22=($ $ #23=(|Integer|)) NIL T ELT) (($ $ #23# #23#) NIL T ELT)) (|terms| ((#24=(|Stream| (|Record| (|:| |k| #23#) (|:| |c| |#1|))) $) NIL T ELT)) (|taylorRep| #25=(#6# NIL T ELT)) (|taylorIfCan| #26=(((|Union| #7# #27="failed") $) NIL T ELT)) (|taylor| #25#) (|tanh| #28=(#20# NIL #29=(|has| |#1| (|Algebra| #30=(|Fraction| #23#))) ELT)) (|tan| #28#) (|subtractIfCan| (#31=(#32=(|Union| $ #27#) $ $) NIL T ELT)) (|squareFreePolynomial| #33=(((|Factored| #34=(|SparseUnivariatePolynomial| $)) #34#) NIL #16# ELT)) (|squareFreePart| #35=(#20# NIL #9# ELT)) (|squareFree| #36=(((|Factored| $) $) NIL #9# ELT)) (|sqrt| #28#) (|solveLinearPolynomialEquation| (((|Union| #37=(|List| #34#) #27#) #37# #34#) NIL #16# ELT)) (|sizeLess?| (#2# NIL #9# ELT)) (|sinh| #28#) (|sin| #28#) (|sign| (#38=(#23# $) NIL #15# ELT)) (|series| (($ #24#) NIL T ELT)) (|sech| #28#) (|sec| #28#) (|sample| (#39=($) NIL T CONST)) (|retractIfCan| #26# (((|Union| #13# . #40=(#27#)) . #41=($)) NIL #42=(AND (|has| #7# (|RetractableTo| #13#)) #9#) ELT) (((|Union| #30# . #40#) . #41#) NIL #43=(AND (|has| #7# (|RetractableTo| #23#)) #9#) ELT) (((|Union| #23# . #40#) . #41#) NIL #43# ELT)) (|retract| #25# (#12# NIL #42# ELT) ((#30# $) NIL #43# ELT) (#38# NIL #43# ELT)) (|removeZeroes| #44=(#20# NIL T ELT) #45=(($ #23# $) NIL T ELT)) (|rem| #46=(#47=($ $ $) NIL #9# ELT)) (|reductum| #44#) (|reducedSystem| ((#48=(|Matrix| #7#) . #49=(#50=(|Matrix| $))) NIL #9# ELT) ((#51=(|Record| (|:| |mat| #48#) (|:| |vec| (|Vector| #7#))) . #52=(#50# #53=(|Vector| $))) NIL #9# ELT) ((#54=(|Record| (|:| |mat| #55=(|Matrix| #23#)) (|:| |vec| (|Vector| #23#))) . #52#) NIL #56=(AND (|has| #7# (|LinearlyExplicitRingOver| #23#)) #9#) ELT) ((#55# . #49#) NIL #56# ELT)) (|recip| ((#32# $) NIL T ELT)) (|rationalFunction| ((#57=(|Fraction| (|Polynomial| |#1|)) $ #23#) NIL #18# ELT) ((#57# $ #23# #23#) NIL #18# ELT)) (|random| (#39# NIL #58=(AND (|has| #7# (|IntegerNumberSystem|)) #9#) ELT)) (|quo| #46#) (|principalIdeal| (((|Record| (|:| |coef| #59=(|List| $)) #60=(|:| |generator| $)) #59#) NIL #9# ELT)) (|prime?| (#5# NIL #9# ELT)) (|positive?| #61=(#5# NIL #15# ELT)) (|pole?| #4#) (|pi| (#39# NIL #29# ELT)) (|patternMatch| ((#62=(|PatternMatchResult| #63=(|Float|) . #64=($)) $ #65=(|Pattern| #63#) #62#) NIL (AND (|has| #7# (|PatternMatchable| #63#)) #9#) ELT) ((#66=(|PatternMatchResult| #23# . #64#) $ #67=(|Pattern| #23#) #66#) NIL (AND (|has| #7# (|PatternMatchable| #23#)) #9#) ELT)) (|order| #68=(#38# NIL T ELT) ((#23# $ #23#) NIL T ELT)) (|opposite?| #1#) (|one?| #4#) (|numerator| #35#) (|numer| #69=(#6# NIL #9# ELT)) (|nthRoot| (#22# NIL #29# ELT)) (|nextItem| (#70=((|Maybe| $) $) NIL #71=(AND (|has| #7# (|StepThrough|)) #9#) ELT)) (|negative?| #61#) (|multiplyExponents| #72=(($ $ #73=(|PositiveInteger|)) NIL T ELT)) (|multiplyCoefficients| (($ (|Mapping| |#1| #23#) $) NIL T ELT)) (|multiEuclidean| (((|Union| #59# #27#) #59# $) NIL #9# ELT)) (|monomial?| #4#) (|monomial| (($ |#1| #23#) 18 T ELT) (($ $ #11# #23#) NIL T ELT) (($ $ #10# (|List| #23#)) NIL T ELT)) (|min| #74=(#47# NIL #75=(OR #15# (AND (|has| #7# (|OrderedSet|)) #9#)) ELT)) (|max| #74#) (|map| (($ (|Mapping| |#1| |#1|) . #76=($)) NIL T ELT) (($ #77=(|Mapping| #7# #7#) . #76#) NIL #9# ELT)) (|log| #28#) (|leftReducedSystem| ((#48# . #78=(#53#)) NIL #9# ELT) ((#51# . #79=(#53# $)) NIL #9# ELT) ((#54# . #79#) NIL #56# ELT) ((#55# . #78#) NIL #56# ELT)) (|leadingMonomial| #44#) (|leadingCoefficient| (#80=(|#1| $) NIL T ELT)) (|lcm| #81=(($ #59#) NIL #9# ELT) #46#) (|laurent| (($ #23# #7#) NIL T ELT)) (|latex| (((|String|) $) NIL T ELT)) (|inv| #35#) (|integrate| (#20# 27 #29# ELT) (#82=($ $ #13#) NIL (OR (AND #29# (|has| |#1| (|AlgebraicallyClosedFunctionSpace| #23#)) (|has| |#1| (|PrimitiveFunctionCategory|)) (|has| |#1| (|TranscendentalFunctionCategory|))) (AND #29# (|has| |#1| (SIGNATURE |integrate| (|#1| |#1| #13#))) (|has| |#1| (SIGNATURE |variables| (#83=(|List| #13#) |#1|))))) ELT) (#84=($ $ #85=(|Variable| |#2|)) 28 #29# ELT)) (|init| (#39# NIL #71# CONST)) (|hash| (((|SingleInteger|) $) NIL T ELT)) (|gcdPolynomial| ((#34# #34# #34#) NIL #9# ELT)) (|gcd| #81# #46#) (|fractionPart| (#20# NIL #8# ELT)) (|floor| #86=(#6# NIL #58# ELT)) (|factorSquareFreePolynomial| #33#) (|factorPolynomial| #33#) (|factor| #36#) (|extendedEuclidean| (((|Union| (|Record| #87=(|:| |coef1| $) #88=(|:| |coef2| $)) #27#) $ $ $) NIL #9# ELT) (((|Record| #87# #88# #60#) $ $) NIL #9# ELT)) (|extend| #21#) (|exquo| (#31# NIL #14# ELT)) (|expressIdealMember| (((|Maybe| #59#) #59# $) NIL #9# ELT)) (|exp| #28#) (|eval| (((|Stream| |#1|) $ |#1|) NIL #89=(|has| |#1| (SIGNATURE ** (|#1| |#1| #23#))) ELT) (($ $ #13# #7#) NIL #90=(AND (|has| #7# (|InnerEvalable| #13# #7#)) #9#) ELT) (($ $ #83# #91=(|List| #7#)) NIL #90# ELT) (($ $ (|List| #92=(|Equation| #7#))) NIL #93=(AND (|has| #7# (|Evalable| #7#)) #9#) ELT) (($ $ #92#) NIL #93# ELT) (($ $ #7# #7#) NIL #93# ELT) (($ $ #91# #91#) NIL #93# ELT)) (|euclideanSize| ((#94=(|NonNegativeInteger|) $) NIL #9# ELT)) (|elt| #95=(#96=(|#1| $ #23#) NIL T ELT) (#47# NIL (|has| #23# (|SemiGroup|)) ELT) (#97=($ $ #7#) NIL (AND (|has| #7# (|Eltable| #7# #7#)) #9#) ELT)) (|divide| (((|Record| (|:| |quotient| $) (|:| |remainder| $)) $ $) NIL #9# ELT)) (|differentiate| #98=(($ $ #77# #94#) NIL #9# ELT) #99=(($ $ #77#) NIL #9# ELT) (#84# 26 T ELT) (#20# 25 #100=(OR (AND (|has| #7# (|DifferentialRing|)) #9#) (AND (|has| #7# (|DifferentialSpace|)) #9#) #101=(|has| |#1| (SIGNATURE * (|#1| #23# |#1|)))) ELT) #102=(#103=($ $ #94#) NIL #100# ELT) #104=(#82# NIL #105=(OR (AND (|has| #7# #106=(|PartialDifferentialRing| #13#)) #9#) (AND (|has| #7# (|PartialDifferentialSpace| #13#)) #9#) (AND (|has| |#1| #106#) #101#)) ELT) #107=(($ $ #83#) NIL #105# ELT) #108=(($ $ #13# #94#) NIL #105# ELT) #109=(($ $ #83# (|List| #94#)) NIL #105# ELT)) (|denominator| #35#) (|denom| #69#) (|degree| #68#) (|csch| #28#) (|csc| #28#) (|coth| #28#) (|cot| #28#) (|cosh| #28#) (|cos| #28#) (|convert| ((#110=(|InputForm|) . #111=($)) NIL (AND (|has| #7# (|ConvertibleTo| #110#)) #9#) ELT) ((#63# . #111#) NIL #112=(AND (|has| #7# (|RealConstant|)) #9#) ELT) (((|DoubleFloat|) . #111#) NIL #112# ELT) ((#65# . #111#) NIL (AND (|has| #7# (|ConvertibleTo| #65#)) #9#) ELT) ((#67# . #111#) NIL (AND (|has| #7# (|ConvertibleTo| #67#)) #9#) ELT)) (|conditionP| (((|Union| #53# #27#) #50#) NIL #113=(AND (|has| $ #114=(|CharacteristicNonZero|)) #17# #9#) ELT)) (|complete| #44#) (|coerce| (((|OutputForm|) $) NIL T ELT) (($ #23#) NIL T ELT) (($ |#1|) NIL (|has| |#1| (|CommutativeRing|)) ELT) (($ #7#) NIL T ELT) (($ #85#) 24 T ELT) (($ #13#) NIL #42# ELT) #19# (($ #30#) NIL (OR #43# #29#) ELT)) (|coefficient| #95#) (|charthRoot| (#70# NIL (OR #113# (AND (|has| #7# #114#) #9#) (|has| |#1| #114#)) ELT)) (|characteristic| ((#94#) NIL T CONST)) (|center| (#80# 11 T ELT)) (|ceiling| #86#) (|before?| #1#) (|atanh| #28#) (|atan| #28#) (|associates?| (#2# NIL #14# ELT)) (|asinh| #28#) (|asin| #28#) (|asech| #28#) (|asec| #28#) (|approximate| (#96# NIL (AND #89# (|has| |#1| (SIGNATURE |coerce| (|#1| #13#)))) ELT)) (|annihilate?| #1#) (|acsch| #28#) (|acsc| #28#) (|acoth| #28#) (|acot| #28#) (|acosh| #28#) (|acos| #28#) (|abs| (#20# NIL #15# ELT)) (|Zero| (#39# 20 T CONST)) (|One| (#39# 15 T CONST)) (D #98# #99# (#84# NIL T ELT) (#20# NIL #100# ELT) #102# #104# #107# #108# #109#) (>= #115=(#2# NIL #75# ELT)) (> #115#) (= #1#) (<= #115#) (< #115#) (/ (#116=($ $ |#1|) NIL #9# ELT) #46# (($ #7# #7#) NIL #9# ELT)) (- #44# #117=(#47# NIL T ELT)) (+ (#47# 22 T ELT)) (** #72# (#103# NIL T ELT) (#22# NIL #9# ELT) (#47# NIL #29# ELT) #118=(($ $ #30#) NIL #29# ELT)) (* (($ #73# $) NIL T ELT) (($ #94# $) NIL T ELT) #45# #117# (#116# NIL T ELT) (($ |#1| . #119=($)) NIL T ELT) (#97# NIL #9# ELT) (($ #7# . #119#) NIL #9# ELT) (($ #30# . #119#) NIL #29# ELT) #118#)) +((~= #1=(#2=(#3=(|Boolean|) $ $) NIL T ELT)) (|zero?| #4=(#5=(#3# $) NIL T ELT)) (|wholePart| (#6=(#7=(|UnivariateTaylorSeries| |#1| |#2| |#3|) $) NIL #8=(AND (|has| #7# (|EuclideanDomain|)) #9=(|has| |#1| (|Field|))) ELT)) (|variables| ((#10=(|List| #11=(|SingletonAsOrderedSet|)) $) NIL T ELT)) (|variable| (#12=(#13=(|Symbol|) $) 10 T ELT)) (|unitNormal| (((|Record| (|:| |unit| $) (|:| |canonical| $) (|:| |associate| $)) $) NIL #14=(OR #15=(AND (|has| #7# (|OrderedIntegralDomain|)) #9#) #16=(AND #17=(|has| #7# (|PolynomialFactorizationExplicit|)) #9#) #18=(|has| |#1| (|IntegralDomain|))) ELT)) (|unitCanonical| #19=(#20=($ $) NIL #14# ELT)) (|unit?| (#5# NIL #14# ELT)) (|truncate| #21=(#22=($ $ #23=(|Integer|)) NIL T ELT) (($ $ #23# #23#) NIL T ELT)) (|terms| ((#24=(|Stream| (|Record| (|:| |k| #23#) (|:| |c| |#1|))) $) NIL T ELT)) (|taylorRep| #25=(#6# NIL T ELT)) (|taylorIfCan| #26=(((|Union| #7# #27="failed") $) NIL T ELT)) (|taylor| #25#) (|tanh| #28=(#20# NIL #29=(|has| |#1| (|Algebra| #30=(|Fraction| #23#))) ELT)) (|tan| #28#) (|subtractIfCan| ((#31=(|Maybe| $) $ $) NIL T ELT)) (|squareFreePolynomial| #32=(((|Factored| #33=(|SparseUnivariatePolynomial| $)) #33#) NIL #16# ELT)) (|squareFreePart| #34=(#20# NIL #9# ELT)) (|squareFree| #35=(((|Factored| $) $) NIL #9# ELT)) (|sqrt| #28#) (|solveLinearPolynomialEquation| (((|Union| #36=(|List| #33#) #27#) #36# #33#) NIL #16# ELT)) (|sizeLess?| (#2# NIL #9# ELT)) (|sinh| #28#) (|sin| #28#) (|sign| (#37=(#23# $) NIL #15# ELT)) (|series| (($ #24#) NIL T ELT)) (|sech| #28#) (|sec| #28#) (|sample| (#38=($) NIL T CONST)) (|retractIfCan| #26# (((|Union| #13# . #39=(#27#)) . #40=($)) NIL #41=(AND (|has| #7# (|RetractableTo| #13#)) #9#) ELT) (((|Union| #30# . #39#) . #40#) NIL #42=(AND (|has| #7# (|RetractableTo| #23#)) #9#) ELT) (((|Union| #23# . #39#) . #40#) NIL #42# ELT)) (|retract| #25# (#12# NIL #41# ELT) ((#30# $) NIL #42# ELT) (#37# NIL #42# ELT)) (|removeZeroes| #43=(#20# NIL T ELT) #44=(($ #23# $) NIL T ELT)) (|rem| #45=(#46=($ $ $) NIL #9# ELT)) (|reductum| #43#) (|reducedSystem| ((#47=(|Matrix| #7#) . #48=(#49=(|Matrix| $))) NIL #9# ELT) ((#50=(|Record| (|:| |mat| #47#) (|:| |vec| (|Vector| #7#))) . #51=(#49# #52=(|Vector| $))) NIL #9# ELT) ((#53=(|Record| (|:| |mat| #54=(|Matrix| #23#)) (|:| |vec| (|Vector| #23#))) . #51#) NIL #55=(AND (|has| #7# (|LinearlyExplicitRingOver| #23#)) #9#) ELT) ((#54# . #48#) NIL #55# ELT)) (|recip| 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|#1| . #11#) ELT) (($ $ $) 173 (|has| |#1| . #9#) ELT) (($ $ (|Fraction| #18#)) 144 (|has| |#1| . #13#) ELT)) (* (($ (|PositiveInteger|) $) 17 T ELT) (($ (|NonNegativeInteger|) $) 21 T ELT) (($ (|Integer|) . #38=($)) 31 T ELT) (($ $ $) 35 T ELT) (($ $ |#1|) 90 T ELT) (($ |#1| . #38#) 89 T ELT) (($ #33# . #38#) 78 (|has| |#1| . #35#) ELT) (($ $ #33#) 77 (|has| |#1| . #35#) ELT))) (((|UnivariateLaurentSeriesCategory| |#1|) (|Category|) (|Ring|)) (T |UnivariateLaurentSeriesCategory|)) ((|series| (*1 *1 *2) (AND (|isDomain| *2 (|Stream| (|Record| (|:| |k| (|Integer|)) (|:| |c| *3)))) (|ofCategory| *3 (|Ring|)) (|ofCategory| *1 (|UnivariateLaurentSeriesCategory| *3)))) (|multiplyCoefficients| (*1 *1 *2 *1) (AND (|isDomain| *2 (|Mapping| *3 (|Integer|))) (|ofCategory| *1 (|UnivariateLaurentSeriesCategory| *3)) (|ofCategory| *3 (|Ring|)))) (|rationalFunction| (*1 *2 *1 *3) (AND (|isDomain| *3 (|Integer|)) (|ofCategory| *1 (|UnivariateLaurentSeriesCategory| *4)) (|ofCategory| *4 (|Ring|)) 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(SIGNATURE |integrate| ($ $ (|Symbol|))) |%noBranch|) |%noBranch|) |%noBranch|) (ATTRIBUTE (|RadicalCategory|)) (ATTRIBUTE (|TranscendentalFunctionCategory|))) |%noBranch|) (IF (|has| |t#1| (|Field|)) (ATTRIBUTE (|Field|)) |%noBranch|))) @@ -3822,12 +3822,12 @@ NIL ((|zero?| (((|Boolean|) $) 12 T ELT)) (|retractIfCan| (((|Union| |#3| #1="failed") $) 17 T ELT) (((|Union| #2=(|Symbol|) #1#) $) NIL T ELT) (((|Union| #3=(|Fraction| #4=(|Integer|)) #1#) $) NIL T ELT) (((|Union| #4# #1#) $) NIL T ELT)) (|retract| ((|#3| $) 14 T ELT) ((#2# $) NIL T ELT) ((#3# $) NIL T ELT) ((#4# $) NIL T ELT))) (((|UnivariateLaurentSeriesConstructorCategory&| |#1| |#2| |#3|) (CATEGORY |package| (SIGNATURE |retractIfCan| ((|Union| #1=(|Integer|) #2="failed") |#1|)) (SIGNATURE |retract| (#1# |#1|)) (SIGNATURE |retractIfCan| ((|Union| #3=(|Fraction| #1#) #2#) |#1|)) (SIGNATURE |retract| (#3# |#1|)) (SIGNATURE |retractIfCan| ((|Union| #4=(|Symbol|) #2#) |#1|)) (SIGNATURE |retract| (#4# |#1|)) (SIGNATURE 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$) 303 T ELT)) (|taylorIfCan| (((|Union| |#2| "failed") $) 299 T ELT)) (|taylor| ((|#2| $) 300 T ELT)) (|tanh| (#11=($ $) 164 (|has| |#1| . #12=((|Algebra| (|Fraction| #10#)))) ELT)) (|tan| (#13=($ $) 147 (|has| |#1| . #12#) ELT)) (|subtractIfCan| (((|Union| $ "failed") $ $) 26 T ELT)) (|squareFreePolynomial| (#14=((|Factored| #15=(|SparseUnivariatePolynomial| $)) #15#) 276 (|and| (|has| |#2| . #16=((|PolynomialFactorizationExplicit|))) (|has| |#1| . #5#)) ELT)) (|squareFreePart| (($ $) 191 (|has| |#1| . #17=((|Field|))) ELT)) (|squareFree| (#18=((|Factored| $) $) 192 (|has| |#1| . #17#) ELT)) (|sqrt| (($ $) 146 (|has| |#1| . #12#) ELT)) (|solveLinearPolynomialEquation| (((|Union| #19=(|List| #15#) #20="failed") #19# #15#) 273 (|and| (|has| |#2| . #16#) (|has| |#1| . #5#)) ELT)) (|sizeLess?| (((|Boolean|) $ $) 182 (|has| |#1| . #17#) ELT)) (|sinh| (#11# 163 (|has| |#1| . #12#) ELT)) (|sin| (#13# 148 (|has| |#1| . #12#) ELT)) (|sign| (((|Integer|) $) 285 (|and| (|has| |#2| . #21=((|OrderedIntegralDomain|))) (|has| |#1| . #5#)) ELT)) (|series| (($ (|Stream| (|Record| (|:| |k| #10#) (|:| |c| |#1|)))) 202 T ELT)) (|sech| (#11# 162 (|has| |#1| . #12#) ELT)) (|sec| (#13# 149 (|has| |#1| . #12#) ELT)) (|sample| (#22=($) 23 T CONST)) (|retractIfCan| (((|Union| |#2| . #23=("failed")) . #24=($)) 306 T ELT) (((|Union| #25=(|Integer|) . #23#) . #24#) 296 (|and| (|has| |#2| . #26=((|RetractableTo| #25#))) (|has| |#1| . #5#)) ELT) (((|Union| #27=(|Fraction| #25#) . #23#) . #24#) 294 (|and| (|has| |#2| . #26#) (|has| |#1| . #5#)) ELT) (((|Union| #28=(|Symbol|) . #23#) . #24#) 278 (|and| (|has| |#2| . #29=((|RetractableTo| #28#))) (|has| |#1| . #5#)) ELT)) (|retract| ((|#2| . #30=($)) 307 T ELT) ((#25# . #30#) 295 (|and| (|has| |#2| . #26#) (|has| |#1| . #5#)) ELT) ((#27# . #30#) 293 (|and| (|has| |#2| . #26#) (|has| |#1| . #5#)) ELT) ((#28# . #30#) 277 (|and| (|has| |#2| . #29#) (|has| |#1| . #5#)) ELT)) (|removeZeroes| (($ $) 302 T ELT) (($ (|Integer|) $) 301 T ELT)) (|rem| (#31=($ $ $) 186 (|has| |#1| . #17#) ELT)) (|reductum| (#32=($ $) 81 T ELT)) (|reducedSystem| (((|Matrix| |#2|) . #33=(#34=(|Matrix| $))) 255 (|has| |#1| . #5#) ELT) (((|Record| (|:| |mat| (|Matrix| |#2|)) (|:| |vec| (|Vector| |#2|))) . #35=(#34# #36=(|Vector| $))) 254 (|has| |#1| . #5#) ELT) (((|Record| (|:| |mat| (|Matrix| #37=(|Integer|))) (|:| |vec| (|Vector| #37#))) . #35#) 253 (|and| (|has| |#2| . #38=((|LinearlyExplicitRingOver| #37#))) (|has| |#1| . #5#)) ELT) (((|Matrix| #37#) . #33#) 252 (|and| (|has| |#2| . #38#) (|has| |#1| . #5#)) ELT)) (|recip| (((|Union| $ "failed") $) 42 T ELT)) (|rationalFunction| (((|Fraction| (|Polynomial| |#1|)) $ #10#) 200 (|has| |#1| . #39=((|IntegralDomain|))) ELT) (((|Fraction| (|Polynomial| |#1|)) $ #10# #10#) 199 (|has| |#1| . #39#) ELT)) (|random| (($) 269 (|and| (|has| |#2| . #40=((|IntegerNumberSystem|))) (|has| |#1| . #5#)) ELT)) (|quo| (#31# 185 (|has| |#1| . #17#) ELT)) (|principalIdeal| (((|Record| (|:| |coef| #41=(|List| $)) (|:| |generator| $)) #41#) 180 (|has| |#1| . #17#) ELT)) (|prime?| (((|Boolean|) $) 193 (|has| |#1| . #17#) ELT)) (|positive?| (((|Boolean|) $) 283 (|and| (|has| |#2| . #21#) (|has| |#1| . #5#)) ELT)) (|pole?| (((|Boolean|) $) 95 T ELT)) (|pi| (($) 174 (|has| |#1| . #12#) ELT)) (|patternMatch| (((|PatternMatchResult| #42=(|Float|) . #43=($)) $ (|Pattern| #42#) (|PatternMatchResult| #42# . #43#)) 261 (|and| (|has| |#2| (|PatternMatchable| #42#)) (|has| |#1| . #5#)) ELT) (((|PatternMatchResult| #44=(|Integer|) . #43#) $ (|Pattern| #44#) (|PatternMatchResult| #44# . #43#)) 260 (|and| (|has| |#2| (|PatternMatchable| #44#)) (|has| |#1| . #5#)) ELT)) (|order| ((#10# $) 127 T ELT) ((#10# $ #10#) 126 T ELT)) (|opposite?| ((#2# $ $) 20 T ELT)) (|one?| (((|Boolean|) $) 44 T ELT)) (|numerator| (#45=($ $) 265 (|has| |#1| . #5#) ELT)) (|numer| ((|#2| . #3#) 263 (|has| |#1| . #5#) ELT)) (|nthRoot| (($ $ #46=(|Integer|)) 145 (|has| |#1| . #12#) ELT)) (|nextItem| (((|Maybe| $) $) 297 (|and| (|has| |#2| . #47=((|StepThrough|))) (|has| |#1| . #5#)) ELT)) (|negative?| (((|Boolean|) $) 284 (|and| (|has| |#2| . #21#) (|has| |#1| . #5#)) ELT)) (|multiplyExponents| (($ $ (|PositiveInteger|)) 128 T ELT)) (|multiplyCoefficients| (($ (|Mapping| |#1| #10#) $) 201 T ELT)) (|multiEuclidean| (((|Union| #48=(|List| $) #49="failed") #48# $) 189 (|has| |#1| . #17#) ELT)) (|monomial?| (((|Boolean|) $) 83 T ELT)) (|monomial| (($ |#1| #10#) 82 T ELT) (($ $ #6# #10#) 98 T ELT) (($ $ (|List| #6#) (|List| #10#)) 97 T ELT)) (|min| (#50=($ $ $) 292 (|and| (|has| |#2| . #51=((|OrderedSet|))) (|has| |#1| . #5#)) ELT)) (|max| (#50# 291 (|and| (|has| |#2| . #51#) (|has| |#1| . #5#)) ELT)) (|map| (($ (|Mapping| |#1| |#1|) . #52=($)) 87 T ELT) (($ (|Mapping| |#2| |#2|) . #52#) 245 (|has| |#1| . #5#) ELT)) (|log| (#53=($ $) 171 (|has| |#1| . #12#) ELT)) (|leftReducedSystem| (((|Matrix| |#2|) . #54=(#36#)) 257 (|has| |#1| . #5#) ELT) (((|Record| (|:| |mat| (|Matrix| |#2|)) (|:| |vec| (|Vector| |#2|))) . #55=(#36# $)) 256 (|has| |#1| . #5#) ELT) (((|Record| (|:| |mat| (|Matrix| #37#)) (|:| |vec| (|Vector| #37#))) . #55#) 251 (|and| (|has| |#2| . #38#) (|has| |#1| . #5#)) ELT) (((|Matrix| #37#) . #54#) 250 (|and| (|has| |#2| . #38#) (|has| |#1| . #5#)) ELT)) (|leadingMonomial| (#32# 85 T ELT)) (|leadingCoefficient| ((|#1| $) 86 T ELT)) (|lcm| (#56=($ (|List| $)) 178 (|has| |#1| . #17#) ELT) (#57=($ $ $) 177 (|has| |#1| . #17#) ELT)) (|laurent| (($ (|Integer|) |#2|) 304 T ELT)) (|latex| (((|String|) $) 11 T ELT)) (|inv| (($ $) 194 (|has| |#1| . #17#) ELT)) (|integrate| (($ $) 198 (|has| |#1| . #12#) ELT) (($ $ #58=(|Symbol|)) 197 (OR (AND (|has| |#1| (|AlgebraicallyClosedFunctionSpace| #10#)) (|has| |#1| (|PrimitiveFunctionCategory|)) (|has| |#1| (|TranscendentalFunctionCategory|)) (|has| |#1| . #12#)) (AND (|has| |#1| (SIGNATURE |variables| ((|List| #58#) |#1|))) (|has| |#1| (SIGNATURE |integrate| (|#1| |#1| #58#))) (|has| |#1| . #12#))) ELT)) (|init| (($) 298 (|and| (|has| |#2| . #47#) (|has| |#1| . #5#)) CONST)) (|hash| (((|SingleInteger|) $) 12 T ELT)) (|gcdPolynomial| ((#59=(|SparseUnivariatePolynomial| $) #59# #59#) 179 (|has| |#1| . #17#) ELT)) (|gcd| (#56# 176 (|has| |#1| . #17#) ELT) (#57# 175 (|has| |#1| . #17#) ELT)) (|fractionPart| (#45# 268 (|and| (|has| |#2| . #4#) (|has| |#1| . #5#)) ELT)) (|floor| ((|#2| . #3#) 271 (|and| (|has| |#2| . #40#) (|has| |#1| . #5#)) ELT)) (|factorSquareFreePolynomial| (#14# 274 (|and| (|has| |#2| . #16#) (|has| |#1| . #5#)) ELT)) (|factorPolynomial| (#14# 275 (|and| (|has| |#2| . #16#) (|has| |#1| . #5#)) ELT)) (|factor| (#18# 190 (|has| |#1| . #17#) ELT)) (|extendedEuclidean| (((|Union| (|Record| #60=(|:| |coef1| $) #61=(|:| |coef2| $)) #49#) $ $ $) 188 (|has| |#1| . #17#) ELT) (((|Record| #60# #61# (|:| |generator| $)) $ $) 187 (|has| |#1| . #17#) ELT)) (|extend| (($ $ #10#) 122 T ELT)) (|exquo| (((|Union| $ "failed") $ $) 71 (|has| |#1| . #8#) ELT)) (|expressIdealMember| (((|Maybe| #41#) #41# $) 181 (|has| |#1| . #17#) ELT)) (|exp| (#53# 172 (|has| |#1| . #12#) ELT)) (|eval| (((|Stream| |#1|) $ |#1|) 121 (|has| |#1| (SIGNATURE ** (|#1| |#1| #10#))) ELT) (($ $ #62=(|Symbol|) |#2|) 244 (|and| (|has| |#2| (|InnerEvalable| #62# |#2|)) (|has| |#1| . #5#)) ELT) (($ $ (|List| #62#) (|List| |#2|)) 243 (|and| (|has| |#2| (|InnerEvalable| #62# |#2|)) (|has| |#1| . #5#)) ELT) (($ $ (|List| (|Equation| |#2|))) 242 (|and| (|has| |#2| (|Evalable| |#2|)) (|has| |#1| . #5#)) ELT) (($ $ (|Equation| |#2|)) 241 (|and| (|has| |#2| (|Evalable| |#2|)) (|has| |#1| . #5#)) ELT) (($ $ |#2| |#2|) 240 (|and| (|has| |#2| (|Evalable| |#2|)) (|has| |#1| . #5#)) ELT) (($ $ (|List| |#2|) (|List| |#2|)) 239 (|and| (|has| |#2| (|Evalable| |#2|)) (|has| |#1| . #5#)) ELT)) (|euclideanSize| (((|NonNegativeInteger|) $) 183 (|has| |#1| . #17#) ELT)) (|elt| ((|#1| $ #10#) 132 T ELT) (($ $ $) 108 (|has| #10# (|SemiGroup|)) ELT) (($ $ |#2|) 238 (|and| (|has| |#2| (|Eltable| |#2| |#2|)) (|has| |#1| . #5#)) ELT)) (|divide| (((|Record| (|:| |quotient| $) (|:| |remainder| $)) $ $) 184 (|has| |#1| . #17#) ELT)) (|differentiate| (($ $ (|Mapping| |#2| |#2|) . #63=((|NonNegativeInteger|))) 247 (|has| |#1| . #5#) ELT) (($ $ (|Mapping| |#2| |#2|)) 246 (|has| |#1| . #5#) ELT) (($ . #64=($)) 112 (OR (|and| (|has| |#2| . #65=((|DifferentialSpace|))) (|has| |#1| . #5#)) (|has| |#1| (SIGNATURE * (|#1| #10# |#1|)))) ELT) (#66=($ $ (|NonNegativeInteger|)) 110 (OR (|and| (|has| |#2| . #65#) (|has| |#1| . #5#)) (|has| |#1| (SIGNATURE * (|#1| #10# |#1|)))) ELT) (($ $ #7#) 120 (OR (|and| (|has| |#2| . #67=((|PartialDifferentialSpace| (|Symbol|)))) (|has| |#1| . #5#)) (AND (|has| |#1| . #68=((|PartialDifferentialRing| #7#))) (|has| |#1| (SIGNATURE * (|#1| #10# |#1|))))) ELT) (($ $ (|List| #7#)) 118 (OR (|and| (|has| |#2| . #67#) (|has| |#1| . #5#)) (AND (|has| |#1| . #68#) (|has| |#1| (SIGNATURE * (|#1| #10# |#1|))))) ELT) (($ $ #7# . #69=(#70=(|NonNegativeInteger|))) 117 (OR (|and| (|has| |#2| . #67#) (|has| |#1| . #5#)) (AND (|has| |#1| . #68#) (|has| |#1| (SIGNATURE * (|#1| #10# |#1|))))) ELT) (($ $ (|List| #7#) . #71=((|List| #70#))) 116 (OR (|and| (|has| |#2| . #67#) (|has| |#1| . #5#)) (AND (|has| |#1| . #68#) (|has| |#1| (SIGNATURE * (|#1| #10# |#1|))))) ELT)) (|denominator| (#45# 266 (|has| |#1| . #5#) ELT)) (|denom| ((|#2| . #3#) 264 (|has| |#1| . #5#) ELT)) (|degree| ((#10# $) 84 T ELT)) (|csch| (#11# 161 (|has| |#1| . #12#) ELT)) (|csc| (#13# 150 (|has| |#1| . #12#) ELT)) (|coth| (#11# 160 (|has| |#1| . #12#) ELT)) (|cot| (#13# 151 (|has| |#1| . #12#) ELT)) (|cosh| (#11# 159 (|has| |#1| . #12#) ELT)) (|cos| (#13# 152 (|has| |#1| . #12#) ELT)) (|convert| (((|DoubleFloat|) . #72=($)) 282 (|and| (|has| |#2| . #73=((|RealConstant|))) (|has| |#1| . #5#)) ELT) (((|Float|) . #72#) 281 (|and| (|has| |#2| . #73#) (|has| |#1| . #5#)) ELT) ((#74=(|InputForm|) . #72#) 280 (|and| (|has| |#2| (|ConvertibleTo| #74#)) (|has| |#1| . #5#)) ELT) ((#75=(|Pattern| (|Float|)) . #72#) 259 (|and| (|has| |#2| (|ConvertibleTo| #75#)) (|has| |#1| . #5#)) ELT) ((#76=(|Pattern| (|Integer|)) . #72#) 258 (|and| (|has| |#2| (|ConvertibleTo| #76#)) (|has| |#1| . #5#)) ELT)) (|conditionP| (((|Union| (|Vector| $) #20#) (|Matrix| $)) 272 (|and| (|and| #77=(|has| $ (|CharacteristicNonZero|)) (|has| |#2| . #16#)) (|has| |#1| . #5#)) ELT)) (|complete| (($ $) 94 T ELT)) (|coerce| (((|OutputForm|) $) 13 T ELT) (($ (|Integer|)) 41 T ELT) (($ |#1|) 68 (|has| |#1| (|CommutativeRing|)) ELT) (($ |#2|) 305 T ELT) (($ #28#) 279 (|and| (|has| |#2| . #29#) (|has| |#1| . #5#)) ELT) (($ #78=(|Fraction| #79=(|Integer|))) 78 (|has| |#1| . #80=((|Algebra| (|Fraction| (|Integer|))))) ELT) (($ $) 70 (|has| |#1| . #8#) ELT)) (|coefficient| ((|#1| $ #10#) 80 T ELT)) (|charthRoot| (((|Maybe| $) $) 69 (OR (|and| (OR (|has| |#2| (|CharacteristicNonZero|)) (|and| #77# (|has| |#2| . #16#))) (|has| |#1| . #5#)) (|has| |#1| (|CharacteristicNonZero|))) ELT)) (|characteristic| (((|NonNegativeInteger|)) 40 T CONST)) (|center| ((|#1| $) 129 T ELT)) 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75 (|has| |#1| . #8#) ELT)) (|asinh| (#81# 169 (|has| |#1| . #12#) ELT)) (|asin| (#82# 157 (|has| |#1| . #12#) ELT)) (|asech| (#81# 168 (|has| |#1| . #12#) ELT)) (|asec| (#82# 156 (|has| |#1| . #12#) ELT)) (|approximate| ((|#1| $ #10#) 123 (AND (|has| |#1| (SIGNATURE ** (|#1| |#1| #10#))) (|has| |#1| (SIGNATURE |coerce| (|#1| #7#)))) ELT)) (|annihilate?| (((|Boolean|) $ $) 34 T ELT)) (|acsch| (#81# 167 (|has| |#1| . #12#) ELT)) (|acsc| (#82# 155 (|has| |#1| . #12#) ELT)) (|acoth| (#81# 166 (|has| |#1| . #12#) ELT)) (|acot| (#82# 154 (|has| |#1| . #12#) ELT)) (|acosh| (#81# 165 (|has| |#1| . #12#) ELT)) (|acos| (#82# 153 (|has| |#1| . #12#) ELT)) (|abs| (($ $) 286 (|and| (|has| |#2| . #21#) (|has| |#1| . #5#)) ELT)) (|Zero| (#22# 24 T CONST)) (|One| (($) 46 T CONST)) (D (($ $ (|Mapping| |#2| |#2|) . #63#) 249 (|has| |#1| . #5#) ELT) (($ $ (|Mapping| |#2| |#2|)) 248 (|has| |#1| . #5#) ELT) (($ . #64#) 111 (OR (|and| (|has| |#2| . #65#) (|has| |#1| . #5#)) (|has| |#1| (SIGNATURE * (|#1| #10# |#1|)))) ELT) (#66# 109 (OR (|and| (|has| |#2| . #65#) (|has| |#1| . #5#)) (|has| |#1| (SIGNATURE * (|#1| #10# |#1|)))) ELT) (($ $ #7#) 119 (OR (|and| (|has| |#2| . #67#) (|has| |#1| . #5#)) (AND (|has| |#1| . #68#) (|has| |#1| (SIGNATURE * (|#1| #10# |#1|))))) ELT) (($ $ (|List| #7#)) 115 (OR (|and| (|has| |#2| . #67#) (|has| |#1| . #5#)) (AND (|has| |#1| . #68#) (|has| |#1| (SIGNATURE * (|#1| #10# |#1|))))) ELT) (($ $ #7# . #69#) 114 (OR (|and| (|has| |#2| . #67#) (|has| |#1| . #5#)) (AND (|has| |#1| . #68#) (|has| |#1| (SIGNATURE * (|#1| #10# |#1|))))) ELT) (($ $ (|List| #7#) . #71#) 113 (OR (|and| (|has| |#2| . #67#) (|has| |#1| . #5#)) (AND (|has| |#1| . #68#) (|has| |#1| (SIGNATURE * (|#1| #10# |#1|))))) ELT)) (>= (#83=((|Boolean|) $ $) 290 (|and| (|has| |#2| . #51#) (|has| |#1| . #5#)) ELT)) (> (#83# 288 (|and| (|has| |#2| . #51#) (|has| |#1| . #5#)) ELT)) (= (#1# 8 T ELT)) (<= (#83# 289 (|and| (|has| |#2| . #51#) (|has| |#1| . #5#)) ELT)) (< (#83# 287 (|and| (|has| |#2| . #51#) (|has| |#1| . #5#)) ELT)) (/ (($ $ |#1|) 80 (|has| |#1| (|Field|)) ELT) (($ $ $) 196 (|has| |#1| . #17#) ELT) (($ |#2| |#2|) 262 (|has| |#1| . #5#) ELT)) (- (($ $) 30 T ELT) (($ $ $) 29 T ELT)) (+ (($ $ $) 18 T ELT)) (** (($ $ (|PositiveInteger|)) 36 T ELT) (($ $ (|NonNegativeInteger|)) 44 T ELT) (($ $ #79#) 195 (|has| |#1| . #17#) ELT) (($ $ $) 173 (|has| |#1| . #12#) ELT) (($ $ (|Fraction| #46#)) 144 (|has| |#1| . #12#) ELT)) (* (($ (|PositiveInteger|) $) 17 T ELT) (($ (|NonNegativeInteger|) $) 21 T ELT) (($ (|Integer|) . #84=($)) 31 T ELT) (($ $ $) 35 T ELT) (($ $ |#1|) 90 T ELT) (($ |#1| . #84#) 89 T ELT) (($ $ |#2|) 237 (|has| |#1| . #5#) ELT) (($ |#2| . #84#) 236 (|has| |#1| . #5#) ELT) (($ #78# . #84#) 78 (|has| |#1| . #80#) ELT) (($ $ #78#) 77 (|has| |#1| . #80#) ELT))) (((|UnivariateLaurentSeriesConstructorCategory| |#1| |#2|) (|Category|) (|Ring|) (|UnivariateTaylorSeriesCategory| |t#1|)) (T |UnivariateLaurentSeriesConstructorCategory|)) ((|degree| (*1 *2 *1) (AND (|ofCategory| *1 (|UnivariateLaurentSeriesConstructorCategory| *3 *4)) (|ofCategory| *3 (|Ring|)) (|ofCategory| *4 (|UnivariateTaylorSeriesCategory| *3)) (|isDomain| *2 (|Integer|)))) (|laurent| (*1 *1 *2 *3) (AND (|isDomain| *2 (|Integer|)) (|ofCategory| *4 (|Ring|)) (|ofCategory| *1 (|UnivariateLaurentSeriesConstructorCategory| *4 *3)) (|ofCategory| *3 (|UnivariateTaylorSeriesCategory| *4)))) (|taylorRep| (*1 *2 *1) (AND (|ofCategory| *1 (|UnivariateLaurentSeriesConstructorCategory| *3 *2)) (|ofCategory| *3 (|Ring|)) (|ofCategory| *2 (|UnivariateTaylorSeriesCategory| *3)))) (|removeZeroes| (*1 *1 *1) (AND (|ofCategory| *1 (|UnivariateLaurentSeriesConstructorCategory| *2 *3)) (|ofCategory| *2 (|Ring|)) (|ofCategory| *3 (|UnivariateTaylorSeriesCategory| *2)))) (|removeZeroes| (*1 *1 *2 *1) (AND (|isDomain| *2 (|Integer|)) (|ofCategory| *1 (|UnivariateLaurentSeriesConstructorCategory| *3 *4)) (|ofCategory| *3 (|Ring|)) (|ofCategory| *4 (|UnivariateTaylorSeriesCategory| *3)))) (|taylor| (*1 *2 *1) (AND (|ofCategory| *1 (|UnivariateLaurentSeriesConstructorCategory| *3 *2)) (|ofCategory| *3 (|Ring|)) (|ofCategory| *2 (|UnivariateTaylorSeriesCategory| *3)))) (|taylorIfCan| (*1 *2 *1) (|partial| AND (|ofCategory| *1 (|UnivariateLaurentSeriesConstructorCategory| *3 *2)) (|ofCategory| *3 (|Ring|)) (|ofCategory| *2 (|UnivariateTaylorSeriesCategory| *3))))) (|Join| (|UnivariateLaurentSeriesCategory| |t#1|) (|RetractableTo| |t#2|) (|CoercibleFrom| |t#2|) (CATEGORY |domain| (SIGNATURE |laurent| ($ (|Integer|) |t#2|)) (SIGNATURE |degree| ((|Integer|) $)) (SIGNATURE |taylorRep| (|t#2| $)) (SIGNATURE |removeZeroes| ($ $)) (SIGNATURE |removeZeroes| ($ (|Integer|) $)) (SIGNATURE |taylor| (|t#2| $)) (SIGNATURE |taylorIfCan| ((|Union| |t#2| "failed") $)) (IF (|has| |t#1| (|Field|)) (ATTRIBUTE (|QuotientFieldCategory| |t#2|)) |%noBranch|))) (((|AbelianGroup|) . T) ((|AbelianMonoid|) . T) ((|AbelianMonoidRing| |#1| #1=(|Integer|)) . T) ((|AbelianSemiGroup|) . T) ((|Algebra| #2=(|Fraction| (|Integer|))) OR (|has| |#1| (|Field|)) (|has| |#1| (|Algebra| (|Fraction| (|Integer|))))) ((|Algebra| |#1|) |has| |#1| (|CommutativeRing|)) ((|Algebra| |#2|) |has| |#1| (|Field|)) ((|Algebra| $) OR (|has| |#1| (|IntegralDomain|)) (|has| |#1| (|Field|))) ((|ArcHyperbolicFunctionCategory|) |has| |#1| (|Algebra| (|Fraction| (|Integer|)))) ((|ArcTrigonometricFunctionCategory|) |has| |#1| (|Algebra| (|Fraction| (|Integer|)))) ((|BasicType|) . T) ((|BiModule| #2# #2#) OR (|has| |#1| (|Field|)) (|has| |#1| (|Algebra| (|Fraction| (|Integer|))))) ((|BiModule| |#1| |#1|) . T) ((|BiModule| |#2| |#2|) |has| |#1| (|Field|)) ((|BiModule| $ $) OR (|has| |#1| (|IntegralDomain|)) (|has| |#1| (|Field|)) (|has| |#1| (|CommutativeRing|))) ((|CancellationAbelianMonoid|) . T) ((|CharacteristicNonZero|) OR (AND (|has| |#1| (|Field|)) (|has| |#2| (|CharacteristicNonZero|))) (|has| |#1| (|CharacteristicNonZero|))) ((|CharacteristicZero|) OR (AND (|has| |#1| (|Field|)) (|has| |#2| (|OrderedIntegralDomain|))) (AND (|has| |#1| (|Field|)) (|has| |#2| (|CharacteristicZero|))) (|has| |#1| (|CharacteristicZero|))) ((|CoercibleFrom| #2#) OR (|has| |#1| (|Field|)) (|has| |#1| (|Algebra| (|Fraction| (|Integer|))))) ((|CoercibleFrom| (|Integer|)) . T) ((|CoercibleFrom| #3=(|Symbol|)) AND (|has| |#1| (|Field|)) (|has| |#2| (|RetractableTo| (|Symbol|)))) ((|CoercibleFrom| |#1|) |has| |#1| (|CommutativeRing|)) ((|CoercibleFrom| |#2|) . T) ((|CoercibleFrom| $) OR (|has| |#1| (|IntegralDomain|)) (|has| |#1| (|Field|))) ((|CoercibleTo| (|OutputForm|)) . T) ((|CommutativeRing|) OR (|has| |#1| (|IntegralDomain|)) (|has| |#1| (|Field|)) (|has| |#1| (|CommutativeRing|))) ((|ConvertibleTo| (|DoubleFloat|)) AND (|has| |#1| (|Field|)) (|has| |#2| (|RealConstant|))) ((|ConvertibleTo| (|Float|)) AND (|has| |#1| (|Field|)) (|has| |#2| (|RealConstant|))) ((|ConvertibleTo| (|InputForm|)) AND (|has| |#1| (|Field|)) (|has| |#2| (|ConvertibleTo| (|InputForm|)))) ((|ConvertibleTo| (|Pattern| (|Float|))) AND (|has| |#1| (|Field|)) (|has| |#2| (|ConvertibleTo| (|Pattern| (|Float|))))) ((|ConvertibleTo| (|Pattern| (|Integer|))) AND (|has| |#1| (|Field|)) (|has| |#2| (|ConvertibleTo| (|Pattern| (|Integer|))))) ((|DifferentialDomain| $) OR (|has| |#1| (SIGNATURE * (|#1| (|Integer|) |#1|))) (AND (|has| |#1| (|Field|)) (|has| |#2| (|DifferentialSpace|))) (AND (|has| |#1| (|Field|)) (|has| |#2| (|DifferentialRing|)))) ((|DifferentialExtension| |#2|) |has| |#1| (|Field|)) ((|DifferentialRing|) OR (|has| |#1| (SIGNATURE * (|#1| (|Integer|) |#1|))) (AND (|has| |#1| (|Field|)) (|has| |#2| (|DifferentialRing|)))) ((|DifferentialSpace|) OR (|has| |#1| (SIGNATURE * (|#1| (|Integer|) |#1|))) (AND (|has| |#1| (|Field|)) (|has| |#2| (|DifferentialSpace|))) (AND (|has| |#1| (|Field|)) (|has| |#2| (|DifferentialRing|)))) ((|DifferentialSpaceExtension| |#2|) |has| |#1| (|Field|)) ((|DivisionRing|) |has| |#1| (|Field|)) ((|ElementaryFunctionCategory|) |has| |#1| (|Algebra| (|Fraction| (|Integer|)))) ((|Eltable| #1# |#1|) . T) ((|Eltable| |#2| $) AND (|has| |#1| (|Field|)) (|has| |#2| (|Eltable| |#2| |#2|))) ((|Eltable| $ $) |has| (|Integer|) (|SemiGroup|)) ((|EntireRing|) OR (|has| |#1| (|IntegralDomain|)) (|has| |#1| (|Field|))) ((|EuclideanDomain|) |has| |#1| (|Field|)) ((|Evalable| |#2|) AND (|has| |#1| (|Field|)) (|has| |#2| (|Evalable| |#2|))) ((|Field|) |has| |#1| (|Field|)) ((|FullyEvalableOver| |#2|) |has| |#1| (|Field|)) ((|FullyLinearlyExplicitRingOver| |#2|) |has| |#1| (|Field|)) ((|FullyPatternMatchable| |#2|) |has| |#1| (|Field|)) ((|Functorial| |#1|) . T) ((|Functorial| |#2|) |has| |#1| (|Field|)) ((|GcdDomain|) |has| |#1| (|Field|)) ((|HyperbolicFunctionCategory|) |has| |#1| (|Algebra| (|Fraction| (|Integer|)))) ((|InnerEvalable| (|Symbol|) |#2|) AND (|has| |#1| (|Field|)) (|has| |#2| (|InnerEvalable| (|Symbol|) |#2|))) ((|InnerEvalable| |#2| |#2|) AND (|has| |#1| (|Field|)) (|has| |#2| (|Evalable| |#2|))) ((|IntegralDomain|) OR (|has| |#1| (|IntegralDomain|)) (|has| |#1| (|Field|))) ((|Join|) . T) ((|LeftLinearSet| #2#) OR (|has| |#1| (|Field|)) (|has| |#1| (|Algebra| (|Fraction| (|Integer|))))) ((|LeftLinearSet| (|Integer|)) . T) ((|LeftLinearSet| |#1|) . T) ((|LeftLinearSet| |#2|) |has| |#1| (|Field|)) ((|LeftLinearSet| $) . T) ((|LeftModule| #2#) OR (|has| |#1| (|Field|)) (|has| |#1| (|Algebra| (|Fraction| (|Integer|))))) ((|LeftModule| #4=(|Integer|)) AND (|has| |#1| (|Field|)) (|has| |#2| (|LinearlyExplicitRingOver| (|Integer|)))) ((|LeftModule| |#1|) . T) ((|LeftModule| |#2|) |has| |#1| (|Field|)) ((|LeftModule| $) . T) ((|LinearSet| #2#) OR (|has| |#1| (|Field|)) (|has| |#1| (|Algebra| (|Fraction| (|Integer|))))) ((|LinearSet| |#1|) |has| |#1| (|CommutativeRing|)) ((|LinearSet| |#2|) |has| |#1| (|Field|)) ((|LinearSet| $) OR (|has| |#1| (|IntegralDomain|)) (|has| |#1| (|Field|))) ((|LinearlyExplicitRingOver| #4#) AND (|has| |#1| (|Field|)) (|has| |#2| (|LinearlyExplicitRingOver| (|Integer|)))) ((|LinearlyExplicitRingOver| |#2|) |has| |#1| (|Field|)) ((|Module| #2#) OR (|has| |#1| (|Field|)) (|has| |#1| (|Algebra| (|Fraction| (|Integer|))))) ((|Module| |#1|) |has| |#1| (|CommutativeRing|)) ((|Module| |#2|) |has| |#1| (|Field|)) ((|Module| $) OR (|has| |#1| (|IntegralDomain|)) (|has| |#1| (|Field|))) ((|Monoid|) . T) ((|OrderedAbelianGroup|) AND (|has| |#1| (|Field|)) (|has| |#2| (|OrderedIntegralDomain|))) ((|OrderedAbelianMonoid|) AND (|has| |#1| (|Field|)) (|has| |#2| (|OrderedIntegralDomain|))) ((|OrderedAbelianSemiGroup|) AND (|has| |#1| (|Field|)) (|has| |#2| (|OrderedIntegralDomain|))) ((|OrderedCancellationAbelianMonoid|) AND (|has| |#1| (|Field|)) (|has| |#2| (|OrderedIntegralDomain|))) ((|OrderedIntegralDomain|) AND (|has| |#1| (|Field|)) (|has| |#2| (|OrderedIntegralDomain|))) ((|OrderedRing|) AND (|has| |#1| (|Field|)) (|has| |#2| (|OrderedIntegralDomain|))) ((|OrderedSet|) OR (AND (|has| |#1| (|Field|)) (|has| |#2| (|OrderedSet|))) (AND (|has| |#1| (|Field|)) (|has| |#2| (|OrderedIntegralDomain|)))) ((|OrderedType|) OR (AND (|has| |#1| (|Field|)) (|has| |#2| (|OrderedSet|))) (AND (|has| |#1| (|Field|)) (|has| |#2| (|OrderedIntegralDomain|)))) ((|PartialDifferentialDomain| $ #5=(|Symbol|)) OR (AND (|has| |#1| (|PartialDifferentialRing| (|Symbol|))) (|has| |#1| (SIGNATURE * (|#1| (|Integer|) |#1|)))) (AND (|has| |#1| (|Field|)) (|has| |#2| (|PartialDifferentialSpace| (|Symbol|)))) (AND (|has| |#1| (|Field|)) (|has| |#2| (|PartialDifferentialRing| (|Symbol|))))) ((|PartialDifferentialRing| (|Symbol|)) OR (AND (|has| |#1| (|PartialDifferentialRing| (|Symbol|))) (|has| |#1| (SIGNATURE * (|#1| (|Integer|) |#1|)))) (AND (|has| |#1| (|Field|)) (|has| |#2| (|PartialDifferentialRing| (|Symbol|))))) ((|PartialDifferentialSpace| #5#) OR (AND (|has| |#1| (|PartialDifferentialRing| (|Symbol|))) (|has| |#1| (SIGNATURE * (|#1| (|Integer|) |#1|)))) (AND (|has| |#1| (|Field|)) (|has| |#2| (|PartialDifferentialSpace| (|Symbol|)))) (AND (|has| |#1| (|Field|)) (|has| |#2| (|PartialDifferentialRing| (|Symbol|))))) ((|PatternMatchable| (|Float|)) AND (|has| |#1| (|Field|)) (|has| |#2| (|PatternMatchable| (|Float|)))) ((|PatternMatchable| (|Integer|)) AND (|has| |#1| (|Field|)) (|has| |#2| (|PatternMatchable| (|Integer|)))) ((|Patternable| |#2|) |has| |#1| (|Field|)) ((|PolynomialFactorizationExplicit|) AND (|has| |#1| (|Field|)) (|has| |#2| (|PolynomialFactorizationExplicit|))) ((|PowerSeriesCategory| |#1| #1# (|SingletonAsOrderedSet|)) . T) ((|PrincipalIdealDomain|) |has| |#1| (|Field|)) ((|QuotientFieldCategory| |#2|) |has| |#1| (|Field|)) ((|RadicalCategory|) |has| |#1| (|Algebra| (|Fraction| (|Integer|)))) ((|RealConstant|) AND (|has| |#1| (|Field|)) (|has| |#2| (|RealConstant|))) ((|RetractableTo| (|Fraction| (|Integer|))) AND (|has| |#1| (|Field|)) (|has| |#2| (|RetractableTo| (|Integer|)))) ((|RetractableTo| (|Integer|)) AND (|has| |#1| (|Field|)) (|has| |#2| (|RetractableTo| (|Integer|)))) ((|RetractableTo| #3#) AND (|has| |#1| (|Field|)) (|has| |#2| (|RetractableTo| (|Symbol|)))) ((|RetractableTo| |#2|) . T) ((|RightLinearSet| #2#) OR (|has| |#1| (|Field|)) (|has| |#1| (|Algebra| (|Fraction| (|Integer|))))) ((|RightLinearSet| |#1|) . T) ((|RightLinearSet| |#2|) |has| |#1| (|Field|)) ((|RightLinearSet| $) OR (|has| |#1| (|IntegralDomain|)) (|has| |#1| (|Field|)) (|has| |#1| (|CommutativeRing|))) ((|RightModule| #2#) OR (|has| |#1| (|Field|)) (|has| |#1| (|Algebra| (|Fraction| (|Integer|))))) ((|RightModule| |#1|) . T) ((|RightModule| |#2|) |has| |#1| (|Field|)) ((|RightModule| $) OR (|has| |#1| (|IntegralDomain|)) (|has| |#1| (|Field|)) (|has| |#1| (|CommutativeRing|))) ((|Ring|) . T) ((|Rng|) . T) ((|SemiGroup|) . T) ((|SemiRing|) . T) ((|SetCategory|) . T) ((|StepThrough|) AND (|has| |#1| (|Field|)) (|has| |#2| (|StepThrough|))) ((|TranscendentalFunctionCategory|) |has| |#1| (|Algebra| (|Fraction| (|Integer|)))) ((|TrigonometricFunctionCategory|) |has| |#1| (|Algebra| (|Fraction| (|Integer|)))) ((|Type|) . T) ((|UniqueFactorizationDomain|) |has| |#1| (|Field|)) ((|UnivariateLaurentSeriesCategory| |#1|) . T) ((|UnivariatePowerSeriesCategory| |#1| #1#) . T)) -((~= #1=(#2=(#3=(|Boolean|) $ $) NIL T ELT)) (|zero?| (#4=(#3# $) 83 T ELT)) (|wholePart| (#5=(|#2| $) NIL #6=(AND #7=(|has| |#1| (|Field|)) (|has| |#2| (|EuclideanDomain|))) ELT)) (|variables| ((#8=(|List| #9=(|SingletonAsOrderedSet|)) $) NIL T ELT)) (|variable| (#10=(#11=(|Symbol|) $) 102 T ELT)) (|unitNormal| (((|Record| (|:| |unit| $) (|:| |canonical| $) (|:| |associate| $)) $) NIL #12=(|has| |#1| (|IntegralDomain|)) ELT)) (|unitCanonical| #13=(#14=($ $) NIL #12# ELT)) (|unit?| (#4# NIL #12# ELT)) (|truncate| (#15=($ $ #16=(|Integer|)) 111 T ELT) (($ $ #16# #16#) 114 T ELT)) (|terms| ((#17=(|Stream| (|Record| (|:| |k| #16#) (|:| |c| |#1|))) $) 51 T ELT)) (|taylorRep| (#5# 11 T ELT)) (|taylorIfCan| (#18=((|Union| |#2| #19="failed") $) 35 T ELT)) (|taylor| (#5# 36 T ELT)) (|tanh| (#14# 208 #20=(|has| |#1| (|Algebra| #21=(|Fraction| #16#))) ELT)) (|tan| (#14# 184 #20# ELT)) (|subtractIfCan| (#22=(#23=(|Union| $ #19#) $ $) NIL T ELT)) (|squareFreePolynomial| #24=(((|Factored| 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$)) NIL #7# ELT) ((#47# . #71#) NIL #49# ELT) ((#48# . #70#) NIL #49# ELT)) (|leadingMonomial| #40#) (|leadingCoefficient| (#72=(|#1| $) NIL T ELT)) (|lcm| #73=(($ #53#) NIL #7# ELT) #38#) (|laurent| (($ #16# |#2|) 10 T ELT)) (|latex| (((|String|) $) NIL T ELT)) (|inv| (#14# 161 #7# ELT)) (|integrate| (#14# 230 #20# ELT) (#74=($ $ #11#) 235 (OR (AND #20# (|has| |#1| (|AlgebraicallyClosedFunctionSpace| #16#)) (|has| |#1| (|PrimitiveFunctionCategory|)) (|has| |#1| (|TranscendentalFunctionCategory|))) (AND #20# (|has| |#1| (SIGNATURE |integrate| (|#1| |#1| #11#))) (|has| |#1| (SIGNATURE |variables| (#75=(|List| #11#) |#1|))))) ELT)) (|init| (#32# NIL #64# CONST)) (|hash| (((|SingleInteger|) $) NIL T ELT)) (|gcdPolynomial| ((#24# #24# #24#) NIL #7# ELT)) (|gcd| #73# #38#) (|fractionPart| (#14# NIL #6# ELT)) (|floor| #76=(#5# NIL #52# ELT)) (|factorSquareFreePolynomial| #23#) (|factorPolynomial| #23#) (|factor| #28#) (|extendedEuclidean| (((|Union| (|Record| #77=(|:| |coef1| $) #78=(|:| 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#7# ELT) (#14# 151 #89=(OR (AND #7# (|has| |#2| (|DifferentialSpace|))) #90=(|has| |#1| (SIGNATURE * (|#1| #16# |#1|)))) ELT) #91=(#92=($ $ #84#) NIL #89# ELT) (#74# 155 #93=(OR (AND (|has| |#1| (|PartialDifferentialRing| #11#)) #90#) (AND #7# (|has| |#2| (|PartialDifferentialSpace| #11#)))) ELT) #94=(($ $ #75#) NIL #93# ELT) #95=(($ $ #11# #84#) NIL #93# ELT) #96=(($ $ #75# (|List| #84#)) NIL #93# ELT)) (|denominator| #27#) (|denom| (#5# 168 #7# ELT)) (|degree| (#30# 12 T ELT)) (|csch| (#14# 214 #20# ELT)) (|csc| (#14# 190 #20# ELT)) (|coth| (#14# 210 #20# ELT)) (|cot| (#14# 186 #20# ELT)) (|cosh| (#14# 206 #20# ELT)) (|cos| (#14# 182 #20# ELT)) (|convert| (((|DoubleFloat|) . #97=($)) NIL #98=(AND #7# (|has| |#2| (|RealConstant|))) ELT) ((#57# . #97#) NIL #98# ELT) ((#99=(|InputForm|) . #97#) NIL (AND #7# (|has| |#2| (|ConvertibleTo| #99#))) ELT) ((#59# . #97#) NIL (AND #7# (|has| |#2| (|ConvertibleTo| #59#))) ELT) ((#61# . #97#) NIL (AND #7# (|has| |#2| (|ConvertibleTo| #61#))) ELT)) (|conditionP| (((|Union| #46# #19#) #43#) NIL #100=(AND (|has| $ #101=(|CharacteristicNonZero|)) #7# #26#) ELT)) (|complete| (#14# 138 T ELT)) (|coerce| (((|OutputForm|) $) 268 T ELT) (($ #16#) 24 T ELT) (($ |#1|) 22 (|has| |#1| (|CommutativeRing|)) ELT) (($ |#2|) 21 T ELT) (($ #11#) NIL #36# ELT) (($ #21#) 171 #20# ELT) #13#) (|coefficient| (#85# 87 T ELT)) (|charthRoot| (#63# NIL (OR #100# (|has| |#1| #101#) (AND #7# (|has| |#2| #101#))) ELT)) (|characteristic| ((#84#) 157 T CONST)) (|center| (#72# 104 T ELT)) (|ceiling| #76#) (|before?| #1#) (|atanh| (#14# 220 #20# ELT)) (|atan| (#14# 196 #20# ELT)) (|associates?| (#2# NIL #12# ELT)) (|asinh| (#14# 216 #20# ELT)) (|asin| (#14# 192 #20# ELT)) (|asech| (#14# 224 #20# ELT)) (|asec| (#14# 200 #20# ELT)) (|approximate| (#85# 136 (AND #79# (|has| |#1| (SIGNATURE |coerce| (|#1| #11#)))) ELT)) (|annihilate?| #1#) (|acsch| (#14# 226 #20# ELT)) (|acsc| (#14# 202 #20# ELT)) (|acoth| (#14# 222 #20# ELT)) (|acot| (#14# 198 #20# ELT)) (|acosh| (#14# 218 #20# ELT)) (|acos| (#14# 194 #20# ELT)) (|abs| (#14# NIL #31# ELT)) (|Zero| (#32# 13 T CONST)) (|One| (#32# 18 T CONST)) (D #87# #88# (#14# NIL #89# ELT) #91# (#74# NIL #93# ELT) #94# #95# #96#) (>= #102=(#2# NIL #68# ELT)) (> #102#) (= (#2# 74 T ELT)) (<= #102#) (< #102#) (/ (#103=($ $ |#1|) NIL #7# ELT) (#39# 165 #7# ELT) (($ |#2| |#2|) 166 #7# ELT)) (- (#14# 229 T ELT) (#39# 80 T ELT)) (+ (#39# 78 T ELT)) (** (#65# NIL T ELT) (#92# 86 T ELT) (#15# 162 #7# ELT) (#39# NIL #20# ELT) (#104=($ $ #21#) 174 #20# ELT)) (* (($ #66# $) NIL T ELT) (($ #84# $) NIL T ELT) (#37# NIL T ELT) (#39# 81 T ELT) (#103# NIL T ELT) (($ |#1| . #105=($)) 154 T ELT) (#86# 164 #7# ELT) (($ |#2| $) 163 #7# ELT) (($ #21# . #105#) NIL #20# ELT) (#104# NIL #20# ELT))) (((|UnivariateLaurentSeriesConstructor| |#1| |#2|) (|UnivariateLaurentSeriesConstructorCategory| |#1| |#2|) (|Ring|) (|UnivariateTaylorSeriesCategory| |#1|)) (T |UnivariateLaurentSeriesConstructor|)) NIL ((|henselFact| (((|Record| (|:| |contp| #1=(|Integer|)) (|:| |factors| (|List| (|Record| (|:| |irr| |#1|) (|:| |pow| #1#))))) |#1| (|Boolean|)) 13 T ELT)) (|factorSquareFree| (#2=((|Factored| |#1|) |#1|) 26 T ELT)) (|factor| (#2# 24 T ELT))) @@ -3839,7 +3839,7 @@ NIL ((|map| (((|Stream| |#2|) #1=(|Mapping| |#2| |#1|) #2=(|UniversalSegment| |#1|)) 23 (|has| |#1| (|OrderedRing|)) ELT) (((|UniversalSegment| |#2|) #1# #2#) 17 T ELT))) (((|UniversalSegmentFunctions2| |#1| |#2|) (CATEGORY |package| (SIGNATURE |map| ((|UniversalSegment| |#2|) #1=(|Mapping| |#2| |#1|) #2=(|UniversalSegment| |#1|))) (IF (|has| |#1| (|OrderedRing|)) (SIGNATURE |map| ((|Stream| |#2|) #1# #2#)) |%noBranch|)) #3=(|Type|) #3#) (T |UniversalSegmentFunctions2|)) ((|map| #1=(*1 *2 *3 *4) (AND #2=(|isDomain| *3 (|Mapping| *6 *5)) #3=(|isDomain| *4 (|UniversalSegment| *5)) (|ofCategory| *5 (|OrderedRing|)) #4=(|ofCategory| *5 #5=(|Type|)) #6=(|ofCategory| *6 #5#) (|isDomain| *2 (|Stream| *6)) #7=(|isDomain| *1 (|UniversalSegmentFunctions2| *5 *6)))) (|map| #1# (AND #2# #3# #4# #6# (|isDomain| *2 (|UniversalSegment| *6)) #7#))) -((~= #1=(#2=(#3=(|Boolean|) $ $) NIL T ELT)) (|zero?| #4=(#5=(#3# $) NIL T ELT)) (|vectorise| ((#6=(|Vector| |#2|) $ #7=(|NonNegativeInteger|)) NIL T ELT)) (|variables| ((#8=(|List| #9=(|SingletonAsOrderedSet|)) $) NIL T ELT)) (|unmakeSUP| (($ #10=(|SparseUnivariatePolynomial| |#2|)) NIL T ELT)) (|univariate| ((#11=(|SparseUnivariatePolynomial| $) $ #9#) NIL T ELT) #12=((#10# $) NIL T ELT)) (|unitNormal| (((|Record| (|:| |unit| $) (|:| |canonical| $) (|:| |associate| $)) $) NIL #13=(|has| |#2| (|IntegralDomain|)) ELT)) (|unitCanonical| #14=(#15=($ $) NIL #13# ELT)) (|unit?| (#5# NIL #13# ELT)) (|totalDegree| #16=(#17=(#7# $) NIL T ELT) ((#7# $ #8#) NIL T ELT)) (|subtractIfCan| (#18=(#19=(|Union| $ #20="failed") $ $) NIL T ELT)) (|subResultantGcd| #21=(#22=($ $ $) NIL #13# ELT)) (|squareFreePolynomial| #23=(((|Factored| #11#) #11#) NIL #24=(|has| |#2| (|PolynomialFactorizationExplicit|)) ELT)) (|squareFreePart| #25=(#15# NIL #26=(|has| |#2| (|GcdDomain|)) ELT)) (|squareFree| (#27=((|Factored| $) $) NIL #26# ELT)) (|solveLinearPolynomialEquation| (((|Union| #28=(|List| #11#) #20#) #28# #11#) NIL #24# ELT)) (|sizeLess?| (#2# NIL #29=(|has| |#2| (|Field|)) ELT)) (|shiftRight| #30=(($ $ #7#) NIL T ELT)) (|shiftLeft| #30#) (|separate| (((|Record| (|:| |primePart| $) (|:| |commonPart| $)) $ $) NIL #26# ELT)) (|sample| #31=(#32=($) NIL T CONST)) (|retractIfCan| (((|Union| |#2| . #33=(#20#)) . #34=($)) NIL T ELT) (((|Union| #35=(|Fraction| #36=(|Integer|)) . #33#) . #34#) NIL #37=(|has| |#2| (|RetractableTo| #35#)) ELT) (((|Union| #36# . #33#) . #34#) NIL #38=(|has| |#2| (|RetractableTo| #36#)) ELT) #39=(((|Union| #9# . #33#) . #34#) NIL T ELT)) (|retract| #40=(#41=(|#2| . #42=($)) NIL T ELT) ((#35# . #42#) NIL #37# ELT) ((#36# . #42#) NIL #38# ELT) ((#9# . #42#) NIL T ELT)) (|resultant| (($ $ $ #9#) NIL #43=(|has| |#2| (|CommutativeRing|)) ELT) ((|#2| $ $) NIL #43# ELT)) (|rem| #44=(#22# NIL #29# ELT)) (|reductum| #45=(#15# NIL T ELT)) (|reducedSystem| ((#46=(|Matrix| #36#) . #47=(#48=(|Matrix| $))) NIL #49=(|has| |#2| (|LinearlyExplicitRingOver| #36#)) ELT) ((#50=(|Record| (|:| |mat| #46#) (|:| |vec| (|Vector| #36#))) . #51=(#48# #52=(|Vector| $))) NIL #49# ELT) ((#53=(|Record| (|:| |mat| #54=(|Matrix| |#2|)) (|:| |vec| #6#)) . #51#) NIL T ELT) ((#54# . #47#) NIL T ELT)) (|recip| ((#19# $) NIL T ELT)) (|quo| #44#) (|pseudoRemainder| #55=(#22# NIL T ELT)) (|pseudoQuotient| #21#) (|pseudoDivide| (((|Record| (|:| |coef| |#2|) #56=(|:| |quotient| $) #57=(|:| |remainder| $)) $ $) NIL #13# ELT)) (|principalIdeal| (((|Record| (|:| |coef| #58=(|List| $)) #59=(|:| |generator| $)) #58#) NIL #29# ELT)) (|primitivePart| #25# #60=(#61=($ $ #9#) NIL #26# ELT)) (|primitiveMonomials| #62=((#58# $) NIL T ELT)) (|prime?| (#5# NIL #24# ELT)) (|pomopo!| (($ $ |#2| #7# $) NIL T ELT)) (|patternMatch| ((#63=(|PatternMatchResult| #64=(|Float|) . #65=($)) $ #66=(|Pattern| #64#) #63#) NIL (AND (|has| #9# #67=(|PatternMatchable| #64#)) (|has| |#2| #67#)) ELT) ((#68=(|PatternMatchResult| #36# . #65#) $ #69=(|Pattern| #36#) #68#) NIL (AND (|has| #9# #70=(|PatternMatchable| #36#)) (|has| |#2| #70#)) ELT)) (|order| ((#7# $ $) NIL #13# ELT)) (|opposite?| #1#) (|one?| #4#) (|numberOfMonomials| #16#) (|nextItem| (#71=((|Maybe| $) $) NIL #72=(|has| |#2| (|StepThrough|)) ELT)) (|multivariate| (($ #10# #9#) NIL T ELT) (($ #11# #9#) NIL T ELT)) (|multiplyExponents| #30#) (|multiEuclidean| ((#73=(|Union| #58# #20#) #58# $) NIL #29# ELT)) (|monomials| #62#) (|monomial?| #4#) (|monomial| (($ |#2| #7#) 18 T ELT) #74=(($ $ #9# #7#) NIL T ELT) #75=(($ $ #8# #76=(|List| #7#)) NIL T ELT)) (|monicDivide| ((#77=(|Record| #56# #57#) $ $ #9#) NIL T ELT) (#78=(#77# $ $) NIL T ELT)) (|minimumDegree| #16# #79=((#7# $ #9#) NIL T ELT) #80=((#76# $ #8#) NIL T ELT)) (|mapExponents| (($ (|Mapping| #7# #7#) $) NIL T ELT)) (|map| (($ #81=(|Mapping| |#2| |#2|) $) NIL T ELT)) (|makeSUP| #12#) (|mainVariable| #39#) (|leftReducedSystem| ((#46# . #82=(#52#)) NIL #49# ELT) ((#50# . #83=(#52# $)) NIL #49# ELT) ((#53# . #83#) NIL T ELT) ((#54# . #82#) NIL T ELT)) (|leadingMonomial| #45#) (|leadingCoefficient| #40#) (|lcm| #84=(($ #58#) NIL #26# ELT) #85=(#22# NIL #26# ELT)) (|latex| (((|String|) $) NIL T ELT)) (|karatsubaDivide| ((#77# $ #7#) NIL T ELT)) (|isTimes| #86=((#73# $) NIL T ELT)) (|isPlus| #86#) (|isExpt| (((|Union| (|Record| (|:| |var| #9#) (|:| |exponent| #7#)) #20#) $) NIL T ELT)) (|integrate| (#15# NIL #87=(|has| |#2| (|Algebra| #35#)) ELT)) (|init| (#32# NIL #72# CONST)) (|hash| (((|SingleInteger|) $) NIL T ELT)) (|ground?| #4#) (|ground| #40#) (|gcdPolynomial| ((#11# #11# #11#) NIL #26# ELT)) (|gcd| #84# #85#) (|fmecg| (($ $ #7# |#2| $) NIL T ELT)) (|factorSquareFreePolynomial| #23#) (|factorPolynomial| #23#) (|factor| (#27# NIL #24# ELT)) (|extendedEuclidean| (((|Union| (|Record| #88=(|:| |coef1| $) #89=(|:| |coef2| $)) #20#) $ $ $) NIL #29# ELT) (((|Record| #88# #89# #59#) $ $) NIL #29# ELT)) (|exquo| ((#19# $ |#2|) NIL #13# ELT) #90=(#18# NIL #13# ELT)) (|expressIdealMember| (((|Maybe| #58#) #58# $) NIL #29# ELT)) (|eval| (($ $ (|List| #91=(|Equation| $))) NIL T ELT) (($ $ #91#) NIL T ELT) (($ $ $ $) NIL T ELT) (($ $ #58# #58#) NIL T ELT) (($ $ #9# |#2|) NIL T ELT) (($ $ #8# #92=(|List| |#2|)) NIL T ELT) (($ $ #9# $) NIL T ELT) (($ $ #8# #58#) NIL T ELT)) (|euclideanSize| (#17# NIL #29# ELT)) (|elt| ((|#2| $ |#2|) NIL T ELT) #55# ((#93=(|Fraction| $) #93# #93#) NIL #13# ELT) ((|#2| #93# |#2|) NIL #29# ELT) ((#93# $ #93#) NIL #13# ELT)) (|divideExponents| ((#19# $ #7#) NIL T ELT)) (|divide| (#78# NIL #29# ELT)) (|discriminant| (#61# NIL #43# ELT) (#41# NIL #43# ELT)) (|differentiate| #75# #74# #94=(($ $ #8#) NIL T ELT) #95=(#61# NIL T ELT) #45# #30# #96=(($ $ #81#) NIL T ELT) #97=(($ $ #81# #7#) NIL T ELT) (($ $ #81# $) NIL T ELT) #98=(($ $ #99=(|Symbol|)) NIL #100=(|has| |#2| (|PartialDifferentialSpace| #99#)) ELT) #101=(($ $ #102=(|List| #99#)) NIL #100# ELT) #103=(($ $ #99# #7#) NIL #100# ELT) #104=(($ $ #102# #76#) NIL #100# ELT)) (|degree| #16# #79# #80#) (|convert| ((#66# . #105=($)) NIL (AND (|has| #9# #106=(|ConvertibleTo| #66#)) (|has| |#2| #106#)) ELT) ((#69# . #105#) NIL (AND (|has| #9# #107=(|ConvertibleTo| #69#)) (|has| |#2| #107#)) ELT) ((#108=(|InputForm|) . #105#) NIL (AND (|has| #9# #109=(|ConvertibleTo| #108#)) (|has| |#2| #109#)) ELT)) (|content| (#41# NIL #26# ELT) #60#) (|conditionP| (((|Union| #52# #20#) #48#) NIL #110=(AND (|has| $ #111=(|CharacteristicNonZero|)) #24#) ELT)) (|composite| #90# (((|Union| #93# #20#) #93# $) NIL #13# ELT)) (|coerce| (((|OutputForm|) $) 13 T ELT) (($ #36#) NIL T ELT) (($ |#2|) NIL T ELT) (($ #9#) NIL T ELT) (($ (|Variable| |#1|)) 20 T ELT) (($ #35#) NIL (OR #87# #37#) ELT) #14#) (|coefficients| ((#92# $) NIL T ELT)) (|coefficient| ((|#2| $ #7#) NIL T ELT) #74# #75#) (|charthRoot| (#71# NIL (OR #110# (|has| |#2| #111#)) ELT)) (|characteristic| ((#7#) NIL T CONST)) (|binomThmExpt| (($ $ $ #7#) NIL #43# ELT)) (|before?| #1#) (|associates?| (#2# NIL #13# ELT)) (|annihilate?| #1#) (|Zero| #31#) (|One| (#32# 14 T CONST)) (D #75# #74# #94# #95# #45# #30# #96# #97# #98# #101# #103# #104#) (= #1#) (/ (#112=($ $ |#2|) NIL #29# ELT)) (- #45# #55#) (+ #55#) (** (($ $ #113=(|PositiveInteger|)) NIL T ELT) #30#) (* (($ #113# $) NIL T ELT) (($ #7# $) NIL T ELT) (($ #36# . #114=($)) NIL T ELT) #55# (($ $ #35#) NIL #87# ELT) (($ #35# . #114#) NIL #87# ELT) (($ |#2| . #114#) NIL T ELT) (#112# NIL T ELT))) +((~= #1=(#2=(#3=(|Boolean|) $ $) NIL T ELT)) (|zero?| #4=(#5=(#3# $) NIL T ELT)) (|vectorise| ((#6=(|Vector| |#2|) $ #7=(|NonNegativeInteger|)) NIL T ELT)) (|variables| ((#8=(|List| #9=(|SingletonAsOrderedSet|)) $) NIL T ELT)) (|unmakeSUP| (($ #10=(|SparseUnivariatePolynomial| |#2|)) NIL T ELT)) (|univariate| ((#11=(|SparseUnivariatePolynomial| $) $ #9#) NIL T ELT) #12=((#10# $) NIL T ELT)) (|unitNormal| (((|Record| (|:| |unit| $) (|:| |canonical| $) (|:| |associate| $)) $) NIL #13=(|has| |#2| (|IntegralDomain|)) ELT)) (|unitCanonical| #14=(#15=($ $) NIL #13# ELT)) (|unit?| (#5# NIL #13# ELT)) (|totalDegree| #16=(#17=(#7# $) NIL T ELT) ((#7# $ #8#) NIL T ELT)) (|subtractIfCan| ((#18=(|Maybe| $) $ $) NIL T ELT)) (|subResultantGcd| #19=(#20=($ $ $) NIL #13# ELT)) (|squareFreePolynomial| #21=(((|Factored| #11#) #11#) NIL #22=(|has| |#2| (|PolynomialFactorizationExplicit|)) ELT)) (|squareFreePart| #23=(#15# NIL #24=(|has| |#2| (|GcdDomain|)) ELT)) (|squareFree| (#25=((|Factored| $) $) NIL #24# ELT)) (|solveLinearPolynomialEquation| (((|Union| #26=(|List| #11#) #27="failed") #26# #11#) NIL #22# ELT)) (|sizeLess?| (#2# NIL #28=(|has| |#2| (|Field|)) ELT)) (|shiftRight| #29=(($ $ #7#) NIL T ELT)) (|shiftLeft| #29#) (|separate| (((|Record| (|:| |primePart| $) (|:| |commonPart| $)) $ $) NIL #24# ELT)) (|sample| #30=(#31=($) NIL T CONST)) (|retractIfCan| (((|Union| |#2| . #32=(#27#)) . #33=($)) NIL T ELT) (((|Union| #34=(|Fraction| #35=(|Integer|)) . #32#) . #33#) NIL #36=(|has| |#2| (|RetractableTo| #34#)) ELT) (((|Union| #35# . #32#) . #33#) NIL #37=(|has| |#2| (|RetractableTo| #35#)) ELT) #38=(((|Union| #9# . #32#) . #33#) NIL T ELT)) (|retract| #39=(#40=(|#2| . #41=($)) NIL T ELT) ((#34# . #41#) NIL #36# ELT) ((#35# . #41#) NIL #37# ELT) ((#9# . #41#) NIL T ELT)) (|resultant| (($ $ $ #9#) NIL #42=(|has| |#2| (|CommutativeRing|)) ELT) ((|#2| $ $) NIL #42# ELT)) (|rem| #43=(#20# NIL #28# ELT)) (|reductum| #44=(#15# NIL T ELT)) (|reducedSystem| ((#45=(|Matrix| #35#) . #46=(#47=(|Matrix| $))) NIL #48=(|has| |#2| (|LinearlyExplicitRingOver| #35#)) ELT) ((#49=(|Record| (|:| |mat| #45#) (|:| |vec| (|Vector| #35#))) . #50=(#47# #51=(|Vector| $))) NIL #48# ELT) ((#52=(|Record| (|:| |mat| #53=(|Matrix| |#2|)) (|:| |vec| #6#)) . #50#) NIL T ELT) ((#53# . #46#) NIL T ELT)) (|recip| ((#54=(|Union| $ #27#) $) NIL T ELT)) (|quo| #43#) (|pseudoRemainder| #55=(#20# NIL T ELT)) (|pseudoQuotient| #19#) (|pseudoDivide| (((|Record| (|:| |coef| |#2|) #56=(|:| |quotient| $) #57=(|:| |remainder| $)) $ $) NIL #13# ELT)) (|principalIdeal| (((|Record| (|:| |coef| #58=(|List| $)) #59=(|:| |generator| $)) #58#) NIL #28# ELT)) (|primitivePart| #23# #60=(#61=($ $ #9#) NIL #24# ELT)) (|primitiveMonomials| #62=((#58# $) NIL T ELT)) (|prime?| (#5# NIL #22# ELT)) (|pomopo!| (($ $ |#2| #7# $) NIL T ELT)) (|patternMatch| ((#63=(|PatternMatchResult| #64=(|Float|) . #65=($)) $ #66=(|Pattern| #64#) #63#) NIL (AND (|has| #9# #67=(|PatternMatchable| #64#)) (|has| |#2| #67#)) ELT) ((#68=(|PatternMatchResult| #35# . #65#) $ #69=(|Pattern| #35#) #68#) NIL (AND (|has| #9# #70=(|PatternMatchable| #35#)) (|has| |#2| #70#)) ELT)) (|order| ((#7# $ $) NIL #13# ELT)) (|opposite?| #1#) (|one?| #4#) (|numberOfMonomials| #16#) (|nextItem| (#71=(#18# $) NIL #72=(|has| |#2| (|StepThrough|)) ELT)) (|multivariate| (($ #10# #9#) NIL T ELT) (($ #11# #9#) NIL T ELT)) (|multiplyExponents| #29#) (|multiEuclidean| ((#73=(|Union| #58# #27#) #58# $) NIL #28# ELT)) (|monomials| #62#) (|monomial?| #4#) (|monomial| (($ |#2| #7#) 18 T ELT) #74=(($ $ #9# #7#) NIL T ELT) #75=(($ $ #8# #76=(|List| #7#)) NIL T ELT)) (|monicDivide| ((#77=(|Record| #56# #57#) $ $ #9#) NIL T ELT) (#78=(#77# $ $) NIL T ELT)) (|minimumDegree| #16# #79=((#7# $ #9#) NIL T ELT) #80=((#76# $ #8#) NIL T ELT)) (|mapExponents| (($ (|Mapping| #7# #7#) $) NIL T ELT)) (|map| (($ #81=(|Mapping| |#2| |#2|) $) NIL T ELT)) (|makeSUP| #12#) (|mainVariable| #38#) (|leftReducedSystem| ((#45# . #82=(#51#)) NIL #48# ELT) ((#49# . #83=(#51# $)) NIL #48# ELT) ((#52# . #83#) NIL T ELT) ((#53# . #82#) NIL T ELT)) (|leadingMonomial| #44#) (|leadingCoefficient| #39#) (|lcm| #84=(($ #58#) NIL #24# ELT) #85=(#20# NIL #24# ELT)) (|latex| (((|String|) $) NIL T ELT)) (|karatsubaDivide| ((#77# $ #7#) NIL T ELT)) (|isTimes| #86=((#73# $) NIL T ELT)) (|isPlus| #86#) (|isExpt| (((|Union| (|Record| (|:| |var| #9#) (|:| |exponent| #7#)) #27#) $) NIL T ELT)) (|integrate| (#15# NIL #87=(|has| |#2| (|Algebra| #34#)) ELT)) (|init| (#31# NIL #72# CONST)) (|hash| (((|SingleInteger|) $) NIL T ELT)) (|ground?| #4#) (|ground| #39#) (|gcdPolynomial| ((#11# #11# #11#) NIL #24# ELT)) (|gcd| #84# #85#) (|fmecg| (($ $ #7# |#2| $) NIL T ELT)) (|factorSquareFreePolynomial| #21#) (|factorPolynomial| #21#) (|factor| (#25# NIL #22# ELT)) (|extendedEuclidean| (((|Union| (|Record| #88=(|:| |coef1| $) #89=(|:| |coef2| $)) #27#) $ $ $) NIL #28# ELT) (((|Record| #88# #89# #59#) $ $) NIL #28# ELT)) (|exquo| ((#54# $ |#2|) NIL #13# ELT) #90=((#54# $ $) NIL #13# ELT)) (|expressIdealMember| (((|Maybe| #58#) #58# $) NIL #28# ELT)) (|eval| (($ $ (|List| #91=(|Equation| $))) NIL T ELT) (($ $ #91#) NIL T ELT) (($ $ $ $) NIL T ELT) (($ $ #58# #58#) NIL T ELT) (($ $ #9# |#2|) NIL T ELT) (($ $ #8# #92=(|List| |#2|)) NIL T ELT) (($ $ #9# $) NIL T ELT) (($ $ #8# #58#) NIL T ELT)) (|euclideanSize| (#17# NIL #28# ELT)) (|elt| ((|#2| $ |#2|) NIL T ELT) #55# ((#93=(|Fraction| $) #93# #93#) NIL #13# ELT) ((|#2| #93# |#2|) NIL #28# ELT) ((#93# $ #93#) NIL #13# ELT)) (|divideExponents| ((#54# $ #7#) NIL T ELT)) (|divide| (#78# NIL #28# ELT)) (|discriminant| (#61# NIL #42# ELT) (#40# NIL #42# ELT)) (|differentiate| #75# #74# #94=(($ $ #8#) NIL T ELT) #95=(#61# NIL T ELT) #44# #29# #96=(($ $ #81#) NIL T ELT) #97=(($ $ #81# #7#) NIL T ELT) (($ $ #81# $) NIL T ELT) #98=(($ $ #99=(|Symbol|)) NIL #100=(|has| |#2| (|PartialDifferentialSpace| #99#)) ELT) #101=(($ $ #102=(|List| #99#)) NIL #100# ELT) #103=(($ $ #99# #7#) NIL #100# ELT) #104=(($ $ #102# #76#) NIL #100# ELT)) (|degree| #16# #79# #80#) (|convert| ((#66# . #105=($)) NIL (AND (|has| #9# #106=(|ConvertibleTo| #66#)) (|has| |#2| #106#)) ELT) ((#69# . #105#) NIL (AND (|has| #9# #107=(|ConvertibleTo| #69#)) (|has| |#2| #107#)) ELT) ((#108=(|InputForm|) . #105#) NIL (AND (|has| #9# #109=(|ConvertibleTo| #108#)) (|has| |#2| #109#)) ELT)) (|content| (#40# NIL #24# ELT) #60#) (|conditionP| (((|Union| #51# #27#) #47#) NIL #110=(AND (|has| $ #111=(|CharacteristicNonZero|)) #22#) ELT)) (|composite| #90# (((|Union| #93# #27#) #93# $) NIL #13# ELT)) (|coerce| (((|OutputForm|) $) 13 T ELT) (($ #35#) NIL T ELT) (($ |#2|) NIL T ELT) (($ #9#) NIL T ELT) (($ (|Variable| |#1|)) 20 T ELT) (($ #34#) NIL (OR #87# #36#) ELT) #14#) (|coefficients| ((#92# $) NIL T ELT)) (|coefficient| ((|#2| $ #7#) NIL T ELT) #74# #75#) (|charthRoot| (#71# NIL (OR #110# (|has| |#2| #111#)) ELT)) (|characteristic| ((#7#) NIL T CONST)) (|binomThmExpt| (($ $ $ #7#) NIL #42# ELT)) (|before?| #1#) (|associates?| (#2# NIL #13# ELT)) (|annihilate?| #1#) (|Zero| #30#) (|One| (#31# 14 T CONST)) (D #75# #74# #94# #95# #44# #29# #96# #97# #98# #101# #103# #104#) (= #1#) (/ (#112=($ $ |#2|) NIL #28# ELT)) (- #44# #55#) (+ #55#) (** (($ $ #113=(|PositiveInteger|)) NIL T ELT) #29#) (* (($ #113# $) NIL T ELT) (($ #7# $) NIL T ELT) (($ #35# . #114=($)) NIL T ELT) #55# (($ $ #34#) NIL #87# ELT) (($ #34# . #114#) NIL #87# ELT) (($ |#2| . #114#) NIL T ELT) (#112# NIL T ELT))) (((|UnivariatePolynomial| |#1| |#2|) (|Join| (|UnivariatePolynomialCategory| |#2|) (|CoercibleFrom| (|Variable| |#1|)) (CATEGORY |domain| (SIGNATURE |fmecg| ($ $ (|NonNegativeInteger|) |#2| $)))) (|Symbol|) (|Ring|)) (T |UnivariatePolynomial|)) ((|fmecg| (*1 *1 *1 *2 *3 *1) (AND (|isDomain| *2 (|NonNegativeInteger|)) (|isDomain| *1 (|UnivariatePolynomial| *4 *3)) (|ofType| *4 (|Symbol|)) (|ofCategory| *3 (|Ring|))))) ((|map| (((|UnivariatePolynomial| |#3| |#4|) (|Mapping| |#4| |#2|) (|UnivariatePolynomial| |#1| |#2|)) 15 T ELT))) @@ -3848,19 +3848,19 @@ NIL ((|splitDenominator| (((|Record| (|:| |num| |#3|) (|:| |den| |#1|)) |#3|) 21 T ELT)) (|commonDenominator| ((|#1| |#3|) 13 T ELT)) (|clearDenominator| ((|#3| |#3|) 19 T ELT))) (((|UnivariatePolynomialCommonDenominator| |#1| |#2| |#3|) (CATEGORY |package| (SIGNATURE |commonDenominator| (|#1| |#3|)) (SIGNATURE |clearDenominator| (|#3| |#3|)) (SIGNATURE |splitDenominator| ((|Record| (|:| |num| |#3|) (|:| |den| |#1|)) |#3|))) (|IntegralDomain|) (|QuotientFieldCategory| |#1|) (|UnivariatePolynomialCategory| |#2|)) (T |UnivariatePolynomialCommonDenominator|)) ((|splitDenominator| #1=(*1 *2 *3) (AND (|ofCategory| *4 #2=(|IntegralDomain|)) (|ofCategory| *5 (|QuotientFieldCategory| *4)) (|isDomain| *2 (|Record| (|:| |num| *3) (|:| |den| *4))) (|isDomain| *1 (|UnivariatePolynomialCommonDenominator| *4 *5 *3)) (|ofCategory| *3 (|UnivariatePolynomialCategory| *5)))) (|clearDenominator| (*1 *2 *2) (AND (|ofCategory| *3 #2#) (|ofCategory| *4 (|QuotientFieldCategory| *3)) (|isDomain| *1 (|UnivariatePolynomialCommonDenominator| *3 *4 *2)) (|ofCategory| *2 #3=(|UnivariatePolynomialCategory| *4)))) (|commonDenominator| #1# (AND (|ofCategory| *4 (|QuotientFieldCategory| *2)) (|ofCategory| *2 #2#) (|isDomain| *1 (|UnivariatePolynomialCommonDenominator| *2 *4 *3)) (|ofCategory| *3 #3#)))) -((|rightFactorIfCan| ((#1=(|Union| |#2| #2="failed") |#2| #3=(|NonNegativeInteger|) |#1|) 35 T ELT)) (|monicRightFactorIfCan| ((#1# |#2| #3#) 36 T ELT)) (|monicDecomposeIfCan| (((|Union| (|Record| (|:| |left| |#2|) (|:| |right| |#2|)) #2#) |#2|) 50 T ELT)) (|monicCompleteDecompose| (((|List| |#2|) |#2|) 52 T ELT)) (|leftFactorIfCan| ((#1# |#2| |#2|) 46 T ELT))) +((|rightFactorIfCan| ((#1=(|Union| |#2| #2="failed") |#2| #3=(|NonNegativeInteger|) |#1|) 38 T ELT)) (|monicRightFactorIfCan| ((#1# |#2| #3#) 39 T ELT)) (|monicDecomposeIfCan| (((|Union| (|Record| (|:| |left| |#2|) (|:| |right| |#2|)) #2#) |#2|) 53 T ELT)) (|monicCompleteDecompose| (((|List| |#2|) |#2|) 55 T ELT)) (|leftFactorIfCan| ((#1# |#2| |#2|) 49 T ELT))) (((|UnivariatePolynomialDecompositionPackage| |#1| |#2|) (CATEGORY |package| (SIGNATURE |monicRightFactorIfCan| (#1=(|Union| |#2| #2="failed") |#2| #3=(|NonNegativeInteger|))) (SIGNATURE |rightFactorIfCan| (#1# |#2| #3# |#1|)) (SIGNATURE |leftFactorIfCan| (#1# |#2| |#2|)) (SIGNATURE |monicDecomposeIfCan| ((|Union| (|Record| (|:| |left| |#2|) (|:| |right| |#2|)) #2#) |#2|)) (SIGNATURE |monicCompleteDecompose| ((|List| |#2|) |#2|))) (|Join| (|IntegralDomain|) (|CharacteristicZero|)) (|UnivariatePolynomialCategory| |#1|)) (T |UnivariatePolynomialDecompositionPackage|)) ((|monicCompleteDecompose| #1=(*1 *2 *3) (AND #2=(|ofCategory| *4 #3=(|Join| (|IntegralDomain|) (|CharacteristicZero|))) (|isDomain| *2 (|List| *3)) #4=(|isDomain| *1 (|UnivariatePolynomialDecompositionPackage| *4 *3)) #5=(|ofCategory| *3 #6=(|UnivariatePolynomialCategory| *4)))) (|monicDecomposeIfCan| #1# (|partial| AND #2# (|isDomain| *2 (|Record| (|:| |left| *3) (|:| |right| *3))) #4# #5#)) (|leftFactorIfCan| (*1 *2 *2 *2) (|partial| AND (|ofCategory| *3 #3#) (|isDomain| *1 (|UnivariatePolynomialDecompositionPackage| *3 *2)) (|ofCategory| *2 (|UnivariatePolynomialCategory| *3)))) (|rightFactorIfCan| (*1 *2 *2 *3 *4) #7=(|partial| AND (|isDomain| *3 (|NonNegativeInteger|)) #2# (|isDomain| *1 (|UnivariatePolynomialDecompositionPackage| *4 *2)) (|ofCategory| *2 #6#))) (|monicRightFactorIfCan| (*1 *2 *2 *3) #7#)) -((|divideIfCan| (((|Union| (|Record| (|:| |quotient| |#2|) (|:| |remainder| |#2|)) "failed") |#2| |#2|) 30 T ELT))) +((|divideIfCan| (((|Union| (|Record| (|:| |quotient| |#2|) (|:| |remainder| |#2|)) "failed") |#2| |#2|) 35 T ELT))) (((|UnivariatePolynomialDivisionPackage| |#1| |#2|) (CATEGORY |package| (SIGNATURE |divideIfCan| ((|Union| (|Record| (|:| |quotient| |#2|) (|:| |remainder| |#2|)) "failed") |#2| |#2|))) (|IntegralDomain|) (|UnivariatePolynomialCategory| |#1|)) (T |UnivariatePolynomialDivisionPackage|)) ((|divideIfCan| (*1 *2 *3 *3) (|partial| AND (|ofCategory| *4 (|IntegralDomain|)) (|isDomain| *2 (|Record| (|:| |quotient| *3) (|:| |remainder| *3))) (|isDomain| *1 (|UnivariatePolynomialDivisionPackage| *4 *3)) (|ofCategory| *3 (|UnivariatePolynomialCategory| *4))))) -((|noKaratsuba| (#1=(|#2| |#2| |#2|) 22 T ELT)) (|karatsubaOnce| (#1# 36 T ELT)) (|karatsuba| ((|#2| |#2| |#2| #2=(|NonNegativeInteger|) #2#) 44 T ELT))) +((|noKaratsuba| (#1=(|#2| |#2| |#2|) 22 T ELT)) (|karatsubaOnce| (#1# 36 T ELT)) (|karatsuba| ((|#2| |#2| |#2| #2=(|NonNegativeInteger|) #2#) 46 T ELT))) (((|UnivariatePolynomialMultiplicationPackage| |#1| |#2|) (CATEGORY |package| (SIGNATURE |noKaratsuba| #1=(|#2| |#2| |#2|)) (SIGNATURE |karatsubaOnce| #1#) (SIGNATURE |karatsuba| (|#2| |#2| |#2| #2=(|NonNegativeInteger|) #2#))) (|Ring|) (|UnivariatePolynomialCategory| |#1|)) (T |UnivariatePolynomialMultiplicationPackage|)) ((|karatsuba| (*1 *2 *2 *2 *3 *3) (AND (|isDomain| *3 (|NonNegativeInteger|)) (|ofCategory| *4 #1=(|Ring|)) (|isDomain| *1 (|UnivariatePolynomialMultiplicationPackage| *4 *2)) (|ofCategory| *2 (|UnivariatePolynomialCategory| *4)))) (|karatsubaOnce| #2=(*1 *2 *2 *2) #3=(AND (|ofCategory| *3 #1#) (|isDomain| *1 (|UnivariatePolynomialMultiplicationPackage| *3 *2)) (|ofCategory| *2 (|UnivariatePolynomialCategory| *3)))) (|noKaratsuba| #2# #3#)) ((|vectorise| (((|Vector| |#2|) $ #1=(|NonNegativeInteger|)) 129 T ELT)) (|variables| ((#2=(|List| #3=(|SingletonAsOrderedSet|)) $) 16 T ELT)) (|unmakeSUP| (($ #4=(|SparseUnivariatePolynomial| |#2|)) 80 T ELT)) (|totalDegree| #5=(#6=(#1# $) NIL T ELT) ((#1# $ #2#) 21 T ELT)) (|squareFreePolynomial| (#7=((|Factored| #8=(|SparseUnivariatePolynomial| $)) #8#) 217 T ELT)) (|squareFreePart| (#9=($ $) 207 T ELT)) (|squareFree| (#10=((|Factored| $) $) 205 T ELT)) (|solveLinearPolynomialEquation| (((|Union| #11=(|List| #8#) #12="failed") #11# #8#) 95 T ELT)) (|shiftRight| (#13=($ $ #1#) 84 T ELT)) (|shiftLeft| (#13# 86 T ELT)) (|separate| (((|Record| (|:| |primePart| $) (|:| |commonPart| $)) $ $) 157 T ELT)) (|retractIfCan| (((|Union| |#2| #12#) $) 132 T ELT) (((|Union| #14=(|Fraction| #15=(|Integer|)) #12#) $) NIL T ELT) (((|Union| #15# #12#) $) NIL T ELT) (#16=((|Union| #3# #12#) $) NIL T ELT)) (|retract| (#17=(|#2| $) 130 T ELT) ((#14# $) NIL T ELT) ((#15# $) NIL T ELT) ((#3# $) NIL T ELT)) (|pseudoQuotient| (#18=($ $ $) 182 T ELT)) (|pseudoDivide| (((|Record| (|:| |coef| |#2|) #19=(|:| |quotient| $) #20=(|:| |remainder| $)) $ $) 185 T ELT)) (|order| ((#1# $ $) 202 T ELT)) (|nextItem| (((|Maybe| $) $) 149 T ELT)) (|monomial| (($ |#2| #1#) NIL T ELT) (#21=($ $ #3# #1#) 59 T ELT) #22=(($ $ #2# #23=(|List| #1#)) NIL T ELT)) (|minimumDegree| #5# (#24=(#1# $ #3#) 54 T ELT) (#25=(#23# $ #2#) 55 T ELT)) (|makeSUP| ((#4# $) 72 T ELT)) (|mainVariable| (#16# 52 T ELT)) (|karatsubaDivide| ((#26=(|Record| #19# #20#) $ #1#) 83 T ELT)) (|integrate| (#9# 232 T ELT)) (|init| (($) 134 T CONST)) (|gcdPolynomial| ((#8# #8# #8#) 214 T ELT)) (|factorSquareFreePolynomial| (#7# 101 T ELT)) (|factorPolynomial| (#7# 99 T ELT)) (|factor| (#10# 120 T ELT)) (|eval| (($ $ (|List| #27=(|Equation| $))) 51 T ELT) (($ $ #27#) NIL T ELT) (($ $ $ $) NIL T ELT) (($ $ #28=(|List| $) #28#) NIL T ELT) (($ $ #3# |#2|) 39 T ELT) (($ $ #2# (|List| |#2|)) 36 T ELT) (($ $ #3# $) 32 T ELT) (($ $ #2# #28#) 30 T ELT)) (|euclideanSize| (#6# 220 T ELT)) (|elt| ((|#2| $ |#2|) NIL T ELT) (#18# NIL T ELT) 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*1 *1) (AND (|ofCategory| *3 (|IntegralDomain|)) (|ofCategory| *3 (|Ring|)) (|isDomain| *2 (|Record| (|:| |coef| *3) (|:| |quotient| *1) (|:| |remainder| *1))) (|ofCategory| *1 (|UnivariatePolynomialCategory| *3)))) (|separate| (*1 *2 *1 *1) (AND (|ofCategory| *3 (|GcdDomain|)) (|ofCategory| *3 (|Ring|)) (|isDomain| *2 (|Record| (|:| |primePart| *1) (|:| |commonPart| *1))) (|ofCategory| *1 (|UnivariatePolynomialCategory| *3)))) (|elt| (*1 *2 *3 *2) (AND (|isDomain| *3 (|Fraction| *1)) (|ofCategory| *1 (|UnivariatePolynomialCategory| *2)) (|ofCategory| *2 (|Ring|)) (|ofCategory| *2 (|Field|)))) (|integrate| (*1 *1 *1) (AND (|ofCategory| *1 (|UnivariatePolynomialCategory| *2)) (|ofCategory| *2 (|Ring|)) (|ofCategory| *2 (|Algebra| (|Fraction| (|Integer|))))))) (|Join| (|PolynomialCategory| |t#1| (|NonNegativeInteger|) (|SingletonAsOrderedSet|)) (|Eltable| |t#1| |t#1|) (|Eltable| $ $) (|DifferentialRing|) (|DifferentialExtension| |t#1|) (CATEGORY |domain| (SIGNATURE |vectorise| ((|Vector| |t#1|) $ (|NonNegativeInteger|))) (SIGNATURE |makeSUP| ((|SparseUnivariatePolynomial| |t#1|) $)) (SIGNATURE |unmakeSUP| ($ (|SparseUnivariatePolynomial| |t#1|))) (SIGNATURE |multiplyExponents| ($ $ (|NonNegativeInteger|))) (SIGNATURE |divideExponents| ((|Union| $ "failed") $ (|NonNegativeInteger|))) (SIGNATURE |monicDivide| ((|Record| (|:| |quotient| $) (|:| |remainder| $)) $ $)) (SIGNATURE |karatsubaDivide| ((|Record| (|:| |quotient| $) (|:| |remainder| $)) $ (|NonNegativeInteger|))) (SIGNATURE |shiftRight| ($ $ (|NonNegativeInteger|))) (SIGNATURE |shiftLeft| ($ $ (|NonNegativeInteger|))) (SIGNATURE |pseudoRemainder| ($ $ $)) (SIGNATURE |differentiate| ($ $ (|Mapping| |t#1| |t#1|) $)) (IF (|has| |t#1| (|StepThrough|)) (ATTRIBUTE (|StepThrough|)) |%noBranch|) (IF (|has| |t#1| (|CommutativeRing|)) (PROGN (SIGNATURE |discriminant| (|t#1| $)) (SIGNATURE |resultant| (|t#1| $ $))) |%noBranch|) (IF (|has| |t#1| (|IntegralDomain|)) (PROGN (ATTRIBUTE (|Eltable| (|Fraction| $) (|Fraction| $))) (SIGNATURE |elt| ((|Fraction| $) (|Fraction| $) (|Fraction| $))) (SIGNATURE |order| ((|NonNegativeInteger|) $ $)) (SIGNATURE |subResultantGcd| ($ $ $)) (SIGNATURE |composite| ((|Union| $ "failed") $ $)) (SIGNATURE |composite| ((|Union| (|Fraction| $) "failed") (|Fraction| $) $)) (SIGNATURE |pseudoQuotient| ($ $ $)) (SIGNATURE |pseudoDivide| ((|Record| (|:| |coef| |t#1|) (|:| |quotient| $) (|:| |remainder| $)) $ $))) |%noBranch|) (IF (|has| |t#1| (|GcdDomain|)) (SIGNATURE |separate| ((|Record| (|:| |primePart| $) (|:| |commonPart| $)) $ $)) |%noBranch|) (IF (|has| |t#1| (|Field|)) (PROGN (ATTRIBUTE (|EuclideanDomain|)) (ATTRIBUTE |additiveValuation|) (SIGNATURE |elt| (|t#1| (|Fraction| $) |t#1|))) |%noBranch|) (IF (|has| |t#1| (|Algebra| (|Fraction| (|Integer|)))) (SIGNATURE |integrate| ($ $)) |%noBranch|))) @@ -3871,7 +3871,7 @@ NIL ((|variables| ((#1=(|List| #2=(|SingletonAsOrderedSet|)) $) 34 T ELT)) (|reductum| (#3=($ $) 31 T ELT)) (|monomial| (($ |#2| |#3|) NIL T ELT) (($ $ #2# |#3|) 28 T ELT) (($ $ #1# (|List| |#3|)) 27 T ELT)) (|leadingMonomial| (#3# 14 T ELT)) (|leadingCoefficient| ((|#2| $) 12 T ELT)) (|degree| ((|#3| $) 10 T ELT))) (((|UnivariatePowerSeriesCategory&| |#1| |#2| |#3|) (CATEGORY |package| (SIGNATURE |variables| (#1=(|List| #2=(|SingletonAsOrderedSet|)) |#1|)) (SIGNATURE |monomial| (|#1| |#1| #1# (|List| |#3|))) (SIGNATURE |monomial| (|#1| |#1| #2# |#3|)) (SIGNATURE |reductum| #3=(|#1| |#1|)) (SIGNATURE |monomial| (|#1| |#2| |#3|)) (SIGNATURE |degree| (|#3| |#1|)) (SIGNATURE |leadingMonomial| #3#) (SIGNATURE |leadingCoefficient| (|#2| |#1|))) (|UnivariatePowerSeriesCategory| |#2| |#3|) (|Ring|) (|OrderedAbelianMonoid|)) (T |UnivariatePowerSeriesCategory&|)) NIL -((~= (#1=((|Boolean|) $ $) 7 T ELT)) (|zero?| ((#2=(|Boolean|) $) 22 T ELT)) (|variables| (((|List| #3=(|SingletonAsOrderedSet|)) $) 96 T ELT)) (|variable| (((|Symbol|) $) 130 T ELT)) (|unitNormal| (((|Record| (|:| |unit| $) (|:| |canonical| $) (|:| |associate| $)) $) 72 (|has| |#1| . #4=((|IntegralDomain|))) ELT)) (|unitCanonical| (($ $) 73 (|has| |#1| . #4#) ELT)) (|unit?| ((#5=(|Boolean|) $) 75 (|has| |#1| . #4#) ELT)) (|truncate| (($ $ |#2|) 125 T ELT) (($ $ |#2| |#2|) 124 T ELT)) (|terms| (((|Stream| (|Record| (|:| |k| |#2|) (|:| |c| |#1|))) $) 131 T ELT)) (|subtractIfCan| (((|Union| $ "failed") $ $) 26 T ELT)) (|sample| (#6=($) 23 T CONST)) (|reductum| (#7=($ $) 81 T ELT)) (|recip| (((|Union| $ "failed") $) 42 T ELT)) (|pole?| (((|Boolean|) $) 95 T ELT)) (|order| ((|#2| $) 127 T ELT) ((|#2| $ |#2|) 126 T ELT)) (|opposite?| ((#2# $ $) 20 T ELT)) (|one?| (((|Boolean|) $) 44 T ELT)) (|multiplyExponents| (($ $ (|PositiveInteger|)) 128 T ELT)) (|monomial?| (((|Boolean|) $) 83 T ELT)) (|monomial| (($ |#1| |#2|) 82 T ELT) (($ $ #3# |#2|) 98 T ELT) (($ $ (|List| #3#) (|List| |#2|)) 97 T ELT)) (|map| (($ (|Mapping| |#1| |#1|) $) 87 T ELT)) (|leadingMonomial| (#7# 85 T ELT)) (|leadingCoefficient| ((|#1| $) 86 T ELT)) (|latex| (((|String|) $) 11 T ELT)) (|hash| (((|SingleInteger|) $) 12 T ELT)) (|extend| (($ $ |#2|) 122 T ELT)) (|exquo| (((|Union| $ "failed") $ $) 71 (|has| |#1| . #4#) ELT)) (|eval| (((|Stream| |#1|) $ |#1|) 121 (|has| |#1| (SIGNATURE ** (|#1| |#1| |#2|))) ELT)) (|elt| ((|#1| $ |#2|) 132 T ELT) (($ $ $) 108 (|has| |#2| (|SemiGroup|)) ELT)) (|differentiate| (($ $ #8=(|Symbol|)) 120 (AND (|has| |#1| . #9=((|PartialDifferentialRing| (|Symbol|)))) (|has| |#1| (SIGNATURE * (|#1| |#2| |#1|)))) ELT) (($ $ (|List| #8#)) 118 (AND (|has| |#1| . #9#) (|has| |#1| (SIGNATURE * (|#1| |#2| |#1|)))) ELT) (($ $ #8# . #10=(#11=(|NonNegativeInteger|))) 117 (AND (|has| |#1| . #9#) (|has| |#1| (SIGNATURE * (|#1| |#2| |#1|)))) ELT) (($ $ (|List| #8#) . #12=((|List| #11#))) 116 (AND (|has| |#1| . #9#) (|has| |#1| (SIGNATURE * (|#1| |#2| |#1|)))) ELT) (($ . #13=($)) 112 (|has| |#1| (SIGNATURE * (|#1| |#2| |#1|))) ELT) (#14=($ $ (|NonNegativeInteger|)) 110 (|has| |#1| (SIGNATURE * (|#1| |#2| |#1|))) ELT)) (|degree| ((|#2| $) 84 T ELT)) (|complete| (($ $) 94 T ELT)) (|coerce| (((|OutputForm|) $) 13 T ELT) (($ (|Integer|)) 41 T ELT) (($ #15=(|Fraction| (|Integer|))) 78 (|has| |#1| . #16=((|Algebra| #15#))) ELT) (($ $) 70 (|has| |#1| . #4#) ELT) (($ |#1|) 68 (|has| |#1| (|CommutativeRing|)) ELT)) (|coefficient| ((|#1| $ |#2|) 80 T ELT)) (|charthRoot| (((|Maybe| $) $) 69 (|has| |#1| (|CharacteristicNonZero|)) ELT)) (|characteristic| (((|NonNegativeInteger|)) 40 T CONST)) (|center| ((|#1| $) 129 T ELT)) (|before?| (#1# 6 T ELT)) (|associates?| ((#5# $ $) 74 (|has| |#1| . #4#) ELT)) (|approximate| ((|#1| $ |#2|) 123 (AND (|has| |#1| (SIGNATURE ** (|#1| |#1| |#2|))) (|has| |#1| (SIGNATURE |coerce| (|#1| (|Symbol|))))) ELT)) (|annihilate?| (((|Boolean|) $ $) 33 T ELT)) (|Zero| (#6# 24 T CONST)) (|One| (($) 45 T CONST)) (D (($ $ #8#) 119 (AND (|has| |#1| . #9#) (|has| |#1| (SIGNATURE * (|#1| |#2| |#1|)))) ELT) (($ $ (|List| #8#)) 115 (AND (|has| |#1| . #9#) (|has| |#1| (SIGNATURE * (|#1| |#2| |#1|)))) ELT) (($ $ #8# . #10#) 114 (AND (|has| |#1| . #9#) (|has| |#1| (SIGNATURE * (|#1| |#2| |#1|)))) ELT) (($ $ (|List| #8#) . #12#) 113 (AND (|has| |#1| . #9#) (|has| |#1| (SIGNATURE * (|#1| |#2| |#1|)))) ELT) (($ . #13#) 111 (|has| |#1| (SIGNATURE * (|#1| |#2| |#1|))) ELT) (#14# 109 (|has| |#1| (SIGNATURE * (|#1| |#2| |#1|))) ELT)) (= (#1# 8 T ELT)) (/ (($ $ |#1|) 79 (|has| |#1| (|Field|)) ELT)) (- (($ $) 29 T ELT) (($ $ $) 28 T ELT)) (+ (($ $ $) 18 T ELT)) (** (($ $ (|PositiveInteger|)) 35 T ELT) (($ $ (|NonNegativeInteger|)) 43 T ELT)) (* (($ (|PositiveInteger|) $) 17 T ELT) (($ (|NonNegativeInteger|) $) 21 T ELT) (($ (|Integer|) . #17=($)) 30 T ELT) (($ $ $) 34 T ELT) (($ $ |#1|) 89 T ELT) (($ |#1| . #17#) 88 T ELT) (($ #15# . #17#) 77 (|has| |#1| . #16#) ELT) (($ $ #15#) 76 (|has| |#1| . #16#) ELT))) +((~= (#1=((|Boolean|) $ $) 7 T ELT)) (|zero?| ((#2=(|Boolean|) $) 22 T ELT)) (|variables| (((|List| #3=(|SingletonAsOrderedSet|)) $) 96 T ELT)) (|variable| (((|Symbol|) $) 130 T ELT)) (|unitNormal| (((|Record| (|:| |unit| $) (|:| |canonical| $) (|:| |associate| $)) $) 73 (|has| |#1| . #4=((|IntegralDomain|))) ELT)) (|unitCanonical| (($ $) 74 (|has| |#1| . #4#) ELT)) (|unit?| ((#5=(|Boolean|) $) 76 (|has| |#1| . #4#) ELT)) (|truncate| (($ $ |#2|) 125 T ELT) (($ $ |#2| |#2|) 124 T ELT)) (|terms| (((|Stream| (|Record| (|:| |k| |#2|) (|:| |c| |#1|))) $) 131 T ELT)) (|subtractIfCan| (((|Maybe| $) $ $) 26 T ELT)) (|sample| (#6=($) 23 T CONST)) (|reductum| (#7=($ $) 82 T ELT)) (|recip| (((|Union| $ "failed") $) 43 T ELT)) (|pole?| (((|Boolean|) $) 95 T ELT)) (|order| ((|#2| $) 127 T ELT) ((|#2| $ |#2|) 126 T ELT)) (|opposite?| ((#2# $ $) 20 T ELT)) (|one?| (((|Boolean|) $) 45 T ELT)) (|multiplyExponents| (($ $ (|PositiveInteger|)) 128 T ELT)) (|monomial?| (((|Boolean|) $) 84 T ELT)) (|monomial| (($ |#1| |#2|) 83 T ELT) (($ $ #3# |#2|) 98 T ELT) (($ $ (|List| #3#) (|List| |#2|)) 97 T ELT)) (|map| (($ (|Mapping| |#1| |#1|) $) 88 T ELT)) (|leadingMonomial| (#7# 86 T ELT)) (|leadingCoefficient| ((|#1| $) 87 T ELT)) (|latex| (((|String|) $) 11 T ELT)) (|hash| (((|SingleInteger|) $) 12 T ELT)) (|extend| (($ $ |#2|) 122 T ELT)) (|exquo| (((|Union| $ "failed") $ $) 72 (|has| |#1| . #4#) ELT)) (|eval| (((|Stream| |#1|) $ |#1|) 121 (|has| |#1| (SIGNATURE ** (|#1| |#1| |#2|))) ELT)) (|elt| ((|#1| $ |#2|) 132 T ELT) (($ $ $) 108 (|has| |#2| (|SemiGroup|)) ELT)) (|differentiate| (($ $ #8=(|Symbol|)) 120 (AND (|has| |#1| . #9=((|PartialDifferentialRing| (|Symbol|)))) (|has| |#1| (SIGNATURE * (|#1| |#2| |#1|)))) ELT) (($ $ (|List| #8#)) 118 (AND (|has| |#1| . #9#) (|has| |#1| (SIGNATURE * (|#1| |#2| |#1|)))) ELT) (($ $ #8# . #10=(#11=(|NonNegativeInteger|))) 117 (AND (|has| |#1| . #9#) (|has| |#1| (SIGNATURE * (|#1| |#2| |#1|)))) ELT) (($ $ (|List| #8#) . #12=((|List| #11#))) 116 (AND (|has| |#1| . #9#) (|has| |#1| (SIGNATURE * (|#1| |#2| |#1|)))) ELT) (($ . #13=($)) 112 (|has| |#1| (SIGNATURE * (|#1| |#2| |#1|))) ELT) (#14=($ $ (|NonNegativeInteger|)) 110 (|has| |#1| (SIGNATURE * (|#1| |#2| |#1|))) ELT)) (|degree| ((|#2| $) 85 T ELT)) (|complete| (($ $) 94 T ELT)) (|coerce| (((|OutputForm|) $) 13 T ELT) (($ (|Integer|)) 42 T ELT) (($ #15=(|Fraction| (|Integer|))) 79 (|has| |#1| . #16=((|Algebra| #15#))) ELT) (($ $) 71 (|has| |#1| . #4#) ELT) (($ |#1|) 69 (|has| |#1| (|CommutativeRing|)) ELT)) (|coefficient| ((|#1| $ |#2|) 81 T ELT)) (|charthRoot| (((|Maybe| $) $) 70 (|has| |#1| (|CharacteristicNonZero|)) ELT)) (|characteristic| (((|NonNegativeInteger|)) 41 T CONST)) (|center| ((|#1| $) 129 T ELT)) (|before?| (#1# 6 T ELT)) (|associates?| ((#5# $ $) 75 (|has| |#1| . #4#) ELT)) (|approximate| ((|#1| $ |#2|) 123 (AND (|has| |#1| (SIGNATURE ** (|#1| |#1| |#2|))) (|has| |#1| (SIGNATURE |coerce| (|#1| (|Symbol|))))) ELT)) (|annihilate?| (((|Boolean|) $ $) 34 T ELT)) (|Zero| (#6# 24 T CONST)) (|One| (($) 46 T CONST)) (D (($ $ #8#) 119 (AND (|has| |#1| . #9#) (|has| |#1| (SIGNATURE * (|#1| |#2| |#1|)))) ELT) (($ $ (|List| #8#)) 115 (AND (|has| |#1| . #9#) (|has| |#1| (SIGNATURE * (|#1| |#2| |#1|)))) ELT) (($ $ #8# . #10#) 114 (AND (|has| |#1| . #9#) (|has| |#1| (SIGNATURE * (|#1| |#2| |#1|)))) ELT) (($ $ (|List| #8#) . #12#) 113 (AND (|has| |#1| . #9#) (|has| |#1| (SIGNATURE * (|#1| |#2| |#1|)))) ELT) (($ . #13#) 111 (|has| |#1| (SIGNATURE * (|#1| |#2| |#1|))) ELT) (#14# 109 (|has| |#1| (SIGNATURE * (|#1| |#2| |#1|))) ELT)) (= (#1# 8 T ELT)) (/ (($ $ |#1|) 80 (|has| |#1| (|Field|)) ELT)) (- (($ $) 30 T ELT) (($ $ $) 29 T ELT)) (+ (($ $ $) 18 T ELT)) (** (($ $ (|PositiveInteger|)) 36 T ELT) (($ $ (|NonNegativeInteger|)) 44 T ELT)) (* (($ (|PositiveInteger|) $) 17 T ELT) (($ (|NonNegativeInteger|) $) 21 T ELT) (($ (|Integer|) . #17=($)) 31 T ELT) (($ $ $) 35 T ELT) (($ $ |#1|) 90 T ELT) (($ |#1| . #17#) 89 T ELT) (($ #15# . #17#) 78 (|has| |#1| . #16#) ELT) (($ $ #15#) 77 (|has| |#1| . #16#) ELT))) (((|UnivariatePowerSeriesCategory| |#1| |#2|) (|Category|) (|Ring|) (|OrderedAbelianMonoid|)) (T |UnivariatePowerSeriesCategory|)) ((|terms| (*1 *2 *1) (AND (|ofCategory| *1 (|UnivariatePowerSeriesCategory| *3 *4)) (|ofCategory| *3 (|Ring|)) (|ofCategory| *4 (|OrderedAbelianMonoid|)) (|isDomain| *2 (|Stream| (|Record| (|:| |k| *4) (|:| |c| *3)))))) (|variable| (*1 *2 *1) (AND (|ofCategory| *1 (|UnivariatePowerSeriesCategory| *3 *4)) (|ofCategory| *3 (|Ring|)) (|ofCategory| *4 (|OrderedAbelianMonoid|)) (|isDomain| *2 (|Symbol|)))) (|center| (*1 *2 *1) (AND (|ofCategory| *1 (|UnivariatePowerSeriesCategory| *2 *3)) (|ofCategory| *3 (|OrderedAbelianMonoid|)) (|ofCategory| *2 (|Ring|)))) (|multiplyExponents| (*1 *1 *1 *2) (AND (|isDomain| *2 (|PositiveInteger|)) (|ofCategory| *1 (|UnivariatePowerSeriesCategory| *3 *4)) (|ofCategory| *3 (|Ring|)) (|ofCategory| *4 (|OrderedAbelianMonoid|)))) (|order| (*1 *2 *1) (AND (|ofCategory| *1 (|UnivariatePowerSeriesCategory| *3 *2)) (|ofCategory| *3 (|Ring|)) (|ofCategory| *2 (|OrderedAbelianMonoid|)))) (|order| (*1 *2 *1 *2) (AND (|ofCategory| *1 (|UnivariatePowerSeriesCategory| *3 *2)) (|ofCategory| *3 (|Ring|)) (|ofCategory| *2 (|OrderedAbelianMonoid|)))) (|truncate| (*1 *1 *1 *2) (AND (|ofCategory| *1 (|UnivariatePowerSeriesCategory| *3 *2)) (|ofCategory| *3 (|Ring|)) (|ofCategory| *2 (|OrderedAbelianMonoid|)))) (|truncate| (*1 *1 *1 *2 *2) (AND (|ofCategory| *1 (|UnivariatePowerSeriesCategory| *3 *2)) (|ofCategory| *3 (|Ring|)) (|ofCategory| *2 (|OrderedAbelianMonoid|)))) (|approximate| (*1 *2 *1 *3) (AND (|ofCategory| *1 (|UnivariatePowerSeriesCategory| *2 *3)) (|ofCategory| *3 (|OrderedAbelianMonoid|)) (|has| *2 (SIGNATURE ** (*2 *2 *3))) (|has| *2 (SIGNATURE |coerce| (*2 (|Symbol|)))) (|ofCategory| *2 (|Ring|)))) (|extend| (*1 *1 *1 *2) (AND (|ofCategory| *1 (|UnivariatePowerSeriesCategory| *3 *2)) (|ofCategory| *3 (|Ring|)) (|ofCategory| *2 (|OrderedAbelianMonoid|)))) (|eval| (*1 *2 *1 *3) (AND (|ofCategory| *1 (|UnivariatePowerSeriesCategory| *3 *4)) (|ofCategory| *3 (|Ring|)) (|ofCategory| *4 (|OrderedAbelianMonoid|)) (|has| *3 (SIGNATURE ** (*3 *3 *4))) (|isDomain| *2 (|Stream| *3))))) (|Join| (|PowerSeriesCategory| |t#1| |t#2| (|SingletonAsOrderedSet|)) (|Eltable| |t#2| |t#1|) (CATEGORY |domain| (SIGNATURE |terms| ((|Stream| (|Record| (|:| |k| |t#2|) (|:| |c| |t#1|))) $)) (SIGNATURE |variable| ((|Symbol|) $)) (SIGNATURE |center| (|t#1| $)) (SIGNATURE |multiplyExponents| ($ $ (|PositiveInteger|))) (SIGNATURE |order| (|t#2| $)) (SIGNATURE |order| (|t#2| $ |t#2|)) (SIGNATURE |truncate| ($ $ |t#2|)) (SIGNATURE |truncate| ($ $ |t#2| |t#2|)) (IF (|has| |t#1| (SIGNATURE |coerce| (|t#1| (|Symbol|)))) (IF (|has| |t#1| (SIGNATURE ** (|t#1| |t#1| |t#2|))) (SIGNATURE |approximate| (|t#1| $ |t#2|)) |%noBranch|) |%noBranch|) (SIGNATURE |extend| ($ $ |t#2|)) (IF (|has| |t#2| (|SemiGroup|)) (ATTRIBUTE (|Eltable| $ $)) |%noBranch|) (IF (|has| |t#1| (SIGNATURE * (|t#1| |t#2| |t#1|))) (PROGN (ATTRIBUTE (|DifferentialRing|)) (IF (|has| |t#1| (|PartialDifferentialRing| (|Symbol|))) (ATTRIBUTE (|PartialDifferentialRing| (|Symbol|))) |%noBranch|)) |%noBranch|) (IF (|has| |t#1| (SIGNATURE ** (|t#1| |t#1| |t#2|))) (SIGNATURE |eval| ((|Stream| |t#1|) $ |t#1|)) |%noBranch|))) @@ -3879,13 +3879,13 @@ NIL ((|squareFreePart| ((|#2| |#2|) 12 T ELT)) (|squareFree| (((|Factored| |#2|) |#2|) 14 T ELT)) (|BumInSepFFE| ((#1=(|Record| (|:| |flg| (|Union| "nil" "sqfr" "irred" "prime")) (|:| |fctr| |#2|) (|:| |xpnt| (|Integer|))) #1#) 30 T ELT))) (((|UnivariatePolynomialSquareFree| |#1| |#2|) (CATEGORY |package| (SIGNATURE |squareFree| ((|Factored| |#2|) |#2|)) (SIGNATURE |squareFreePart| (|#2| |#2|)) (SIGNATURE |BumInSepFFE| (#1=(|Record| (|:| |flg| (|Union| "nil" "sqfr" "irred" "prime")) (|:| |fctr| |#2|) (|:| |xpnt| (|Integer|))) #1#))) #2=(|IntegralDomain|) (|Join| (|UnivariatePolynomialCategory| |#1|) #2# (CATEGORY |domain| (SIGNATURE |gcd| ($ $ $))))) (T |UnivariatePolynomialSquareFree|)) ((|BumInSepFFE| #1=(*1 *2 *2) (AND (|isDomain| *2 (|Record| (|:| |flg| (|Union| "nil" "sqfr" "irred" "prime")) (|:| |fctr| *4) (|:| |xpnt| (|Integer|)))) (|ofCategory| *4 #2=(|Join| (|UnivariatePolynomialCategory| *3) #3=(|IntegralDomain|) #4=(CATEGORY |domain| (SIGNATURE |gcd| ($ $ $))))) #5=(|ofCategory| *3 #3#) (|isDomain| *1 (|UnivariatePolynomialSquareFree| *3 *4)))) (|squareFreePart| #1# (AND #5# (|isDomain| *1 (|UnivariatePolynomialSquareFree| *3 *2)) (|ofCategory| *2 #2#))) (|squareFree| (*1 *2 *3) (AND (|ofCategory| *4 #3#) (|isDomain| *2 (|Factored| *3)) (|isDomain| *1 (|UnivariatePolynomialSquareFree| *4 *3)) (|ofCategory| *3 (|Join| (|UnivariatePolynomialCategory| *4) #3# #4#))))) -((~= #1=(#2=(#3=(|Boolean|) $ $) NIL T ELT)) (|zero?| #4=(#5=(#3# $) NIL T ELT)) (|variables| ((#6=(|List| #7=(|SingletonAsOrderedSet|)) $) NIL T ELT)) (|variable| ((#8=(|Symbol|) $) 11 T ELT)) (|unitNormal| (((|Record| (|:| |unit| $) (|:| |canonical| $) (|:| |associate| $)) $) NIL #9=(|has| |#1| (|IntegralDomain|)) ELT)) (|unitCanonical| #10=(#11=($ $) NIL #9# ELT)) (|unit?| (#5# NIL #9# ELT)) (|truncate| #12=(#13=($ $ #14=(|Fraction| #15=(|Integer|))) NIL T ELT) (($ $ #14# #14#) NIL T ELT)) (|terms| ((#16=(|Stream| (|Record| (|:| |k| #14#) (|:| |c| |#1|))) $) NIL T ELT)) (|tanh| #17=(#11# NIL #18=(|has| |#1| (|Algebra| #14#)) ELT)) (|tan| #17#) (|subtractIfCan| (#19=(#20=(|Union| $ #21="failed") $ $) NIL T ELT)) (|squareFreePart| #22=(#11# NIL #23=(|has| |#1| (|Field|)) ELT)) (|squareFree| #24=(((|Factored| $) $) NIL #23# ELT)) (|sqrt| #17#) (|sizeLess?| (#2# NIL #23# ELT)) (|sinh| #17#) (|sin| #17#) (|series| (($ #25=(|NonNegativeInteger|) #16#) NIL T ELT)) (|sech| #17#) (|sec| #17#) (|sample| (#26=($) NIL T CONST)) (|retractIfCan| (#27=((|Union| #28=(|UnivariateLaurentSeries| |#1| |#2| |#3|) . #29=(#21#)) $) 19 T ELT) (((|Union| #30=(|UnivariateTaylorSeries| |#1| |#2| |#3|) . #29#) $) 22 T ELT)) (|retract| #31=(#32=(#28# . #33=($)) NIL T ELT) ((#30# . #33#) NIL T ELT)) (|rem| #34=(#35=($ $ $) NIL #23# ELT)) (|reductum| #36=(#11# NIL T ELT)) (|recip| ((#20# $) NIL T ELT)) (|rationalPower| (#37=(#14# $) 68 T ELT)) (|quo| #34#) (|puiseux| (($ #14# #28#) NIL T ELT)) (|principalIdeal| (((|Record| (|:| |coef| #38=(|List| $)) #39=(|:| |generator| $)) #38#) NIL #23# ELT)) (|prime?| (#5# NIL #23# ELT)) (|pole?| #4#) (|pi| (#26# NIL #18# ELT)) (|order| #40=(#37# NIL T ELT) ((#14# $ #14#) NIL T ELT)) (|opposite?| #1#) (|one?| #4#) (|nthRoot| (#41=($ $ #15#) NIL #18# ELT)) (|multiplyExponents| #42=(($ $ #43=(|PositiveInteger|)) NIL T ELT) #12#) (|multiEuclidean| (((|Union| #38# #21#) #38# $) NIL #23# ELT)) (|monomial?| #4#) (|monomial| (($ |#1| #14#) 30 T ELT) (($ $ #7# #14#) NIL T ELT) (($ $ #6# (|List| #14#)) NIL T ELT)) (|map| (($ (|Mapping| |#1| |#1|) $) NIL T ELT)) (|log| #17#) (|leadingMonomial| #36#) (|leadingCoefficient| (#44=(|#1| $) NIL T ELT)) (|lcm| #45=(($ #38#) NIL #23# ELT) #34#) (|laurentRep| (#32# 71 T ELT)) (|laurentIfCan| (#27# NIL T ELT)) (|laurent| #31#) (|latex| (((|String|) $) NIL T ELT)) (|inv| #22#) (|integrate| (#11# 39 #18# ELT) (#46=($ $ #8#) NIL (OR (AND #18# (|has| |#1| (|AlgebraicallyClosedFunctionSpace| #15#)) (|has| |#1| (|PrimitiveFunctionCategory|)) (|has| |#1| (|TranscendentalFunctionCategory|))) (AND #18# (|has| |#1| (SIGNATURE |integrate| (|#1| |#1| #8#))) (|has| |#1| (SIGNATURE |variables| (#47=(|List| #8#) |#1|))))) ELT) (#48=($ $ #49=(|Variable| |#2|)) 40 #18# ELT)) (|hash| (((|SingleInteger|) $) NIL T ELT)) (|gcdPolynomial| ((#50=(|SparseUnivariatePolynomial| $) #50# #50#) NIL #23# ELT)) (|gcd| #45# #34#) (|factor| #24#) (|extendedEuclidean| (((|Union| (|Record| #51=(|:| |coef1| $) #52=(|:| |coef2| $)) #21#) $ $ $) NIL #23# ELT) (((|Record| #51# #52# #39#) $ $) NIL #23# ELT)) (|extend| #12#) (|exquo| (#19# NIL #9# ELT)) (|expressIdealMember| (((|Maybe| #38#) #38# $) NIL #23# ELT)) (|exp| #17#) (|eval| (((|Stream| |#1|) $ |#1|) NIL #53=(|has| |#1| (SIGNATURE ** (|#1| |#1| #14#))) ELT)) (|euclideanSize| ((#25# $) NIL #23# ELT)) (|elt| #54=(#55=(|#1| $ #14#) NIL T ELT) (#35# NIL (|has| #14# (|SemiGroup|)) ELT)) (|divide| (((|Record| (|:| |quotient| $) (|:| |remainder| $)) $ $) NIL #23# ELT)) (|differentiate| #56=(#46# NIL #57=(AND (|has| |#1| (|PartialDifferentialRing| #8#)) #58=(|has| |#1| (SIGNATURE * (|#1| #14# |#1|)))) ELT) #59=(($ $ #47#) NIL #57# ELT) #60=(($ $ #8# #25#) NIL #57# ELT) #61=(($ $ #47# (|List| #25#)) NIL #57# ELT) (#11# 37 #58# ELT) #62=(#63=($ $ #25#) NIL #58# ELT) (#48# 38 T ELT)) (|degree| #40#) (|csch| #17#) (|csc| #17#) (|coth| #17#) (|cot| #17#) (|cosh| #17#) (|cos| #17#) (|complete| #36#) (|coerce| (((|OutputForm|) $) 107 T ELT) (($ #15#) NIL T ELT) (($ |#1|) NIL (|has| |#1| (|CommutativeRing|)) ELT) (($ #28#) 16 T ELT) (($ #30#) 17 T ELT) (($ #49#) 36 T ELT) (($ #14#) NIL #18# ELT) #10#) (|coefficient| #54#) (|charthRoot| (((|Maybe| $) $) NIL (|has| |#1| (|CharacteristicNonZero|)) ELT)) (|characteristic| ((#25#) NIL T CONST)) (|center| (#44# 12 T ELT)) (|before?| #1#) (|atanh| #17#) (|atan| #17#) (|associates?| (#2# NIL #9# ELT)) (|asinh| #17#) (|asin| #17#) (|asech| #17#) (|asec| #17#) (|approximate| (#55# 73 (AND #53# (|has| |#1| (SIGNATURE |coerce| (|#1| #8#)))) ELT)) (|annihilate?| #1#) (|acsch| #17#) (|acsc| #17#) (|acoth| #17#) (|acot| #17#) (|acosh| #17#) (|acos| #17#) (|Zero| (#26# 32 T CONST)) (|One| (#26# 26 T CONST)) (D #56# #59# #60# #61# (#11# NIL #58# ELT) #62# (#48# NIL T ELT)) (= #1#) (/ (#64=($ $ |#1|) NIL #23# ELT) #34#) (- #36# #65=(#35# NIL T ELT)) (+ (#35# 34 T ELT)) (** #42# (#63# NIL T ELT) (#41# NIL #23# ELT) (#35# NIL #18# ELT) #66=(#13# NIL #18# ELT)) (* (($ #43# $) NIL T ELT) (($ #25# $) NIL T ELT) (($ #15# . #67=($)) NIL T ELT) #65# (#64# NIL T ELT) (($ |#1| . #67#) NIL T ELT) (($ #14# . #67#) NIL #18# ELT) #66#)) +((~= #1=(#2=(#3=(|Boolean|) $ $) NIL T ELT)) (|zero?| #4=(#5=(#3# $) NIL T ELT)) (|variables| ((#6=(|List| #7=(|SingletonAsOrderedSet|)) $) NIL T ELT)) (|variable| ((#8=(|Symbol|) $) 11 T ELT)) (|unitNormal| (((|Record| (|:| |unit| $) (|:| |canonical| $) (|:| |associate| $)) $) NIL #9=(|has| |#1| (|IntegralDomain|)) ELT)) (|unitCanonical| #10=(#11=($ $) NIL #9# ELT)) (|unit?| (#5# NIL #9# ELT)) (|truncate| #12=(#13=($ $ #14=(|Fraction| #15=(|Integer|))) NIL T ELT) (($ $ #14# #14#) NIL T ELT)) (|terms| ((#16=(|Stream| (|Record| (|:| |k| #14#) (|:| |c| |#1|))) $) NIL T ELT)) (|tanh| #17=(#11# NIL #18=(|has| |#1| (|Algebra| #14#)) ELT)) (|tan| #17#) (|subtractIfCan| ((#19=(|Maybe| $) $ $) NIL T ELT)) (|squareFreePart| #20=(#11# NIL #21=(|has| |#1| (|Field|)) ELT)) (|squareFree| #22=(((|Factored| $) $) NIL #21# ELT)) (|sqrt| #17#) (|sizeLess?| (#2# NIL #21# ELT)) (|sinh| #17#) (|sin| #17#) (|series| (($ #23=(|NonNegativeInteger|) #16#) NIL T ELT)) (|sech| #17#) (|sec| #17#) (|sample| (#24=($) NIL T CONST)) (|retractIfCan| (#25=((|Union| #26=(|UnivariateLaurentSeries| |#1| |#2| |#3|) . #27=(#28="failed")) $) 19 T ELT) (((|Union| #29=(|UnivariateTaylorSeries| |#1| |#2| |#3|) . #27#) $) 22 T ELT)) (|retract| #30=(#31=(#26# . #32=($)) NIL T ELT) ((#29# . #32#) NIL T ELT)) (|rem| #33=(#34=($ $ $) NIL #21# ELT)) (|reductum| #35=(#11# NIL T ELT)) (|recip| ((#36=(|Union| $ #28#) $) NIL T ELT)) (|rationalPower| (#37=(#14# $) 68 T ELT)) (|quo| #33#) (|puiseux| (($ #14# #26#) NIL T ELT)) (|principalIdeal| (((|Record| (|:| |coef| #38=(|List| $)) #39=(|:| |generator| $)) #38#) NIL #21# ELT)) (|prime?| (#5# NIL #21# ELT)) (|pole?| #4#) (|pi| (#24# NIL #18# ELT)) (|order| #40=(#37# NIL T ELT) ((#14# $ #14#) NIL T ELT)) (|opposite?| #1#) (|one?| #4#) (|nthRoot| (#41=($ $ #15#) NIL #18# ELT)) (|multiplyExponents| #42=(($ $ #43=(|PositiveInteger|)) NIL T ELT) #12#) (|multiEuclidean| (((|Union| #38# #28#) #38# $) NIL #21# ELT)) (|monomial?| #4#) (|monomial| (($ |#1| #14#) 30 T ELT) (($ $ #7# #14#) NIL T ELT) (($ $ #6# (|List| #14#)) NIL T ELT)) (|map| (($ (|Mapping| |#1| |#1|) $) NIL T ELT)) (|log| #17#) (|leadingMonomial| #35#) (|leadingCoefficient| (#44=(|#1| $) NIL T ELT)) (|lcm| #45=(($ #38#) NIL #21# ELT) #33#) (|laurentRep| (#31# 71 T ELT)) (|laurentIfCan| (#25# NIL T ELT)) (|laurent| #30#) (|latex| (((|String|) $) NIL T ELT)) (|inv| #20#) (|integrate| (#11# 39 #18# ELT) (#46=($ $ #8#) NIL (OR (AND #18# (|has| |#1| (|AlgebraicallyClosedFunctionSpace| #15#)) (|has| |#1| (|PrimitiveFunctionCategory|)) (|has| |#1| (|TranscendentalFunctionCategory|))) (AND #18# (|has| |#1| (SIGNATURE |integrate| (|#1| |#1| #8#))) (|has| |#1| (SIGNATURE |variables| (#47=(|List| #8#) |#1|))))) ELT) (#48=($ $ #49=(|Variable| |#2|)) 40 #18# ELT)) (|hash| (((|SingleInteger|) $) NIL T ELT)) (|gcdPolynomial| ((#50=(|SparseUnivariatePolynomial| $) #50# #50#) NIL #21# ELT)) (|gcd| #45# #33#) (|factor| #22#) (|extendedEuclidean| (((|Union| (|Record| #51=(|:| |coef1| $) #52=(|:| |coef2| $)) #28#) $ $ $) NIL #21# ELT) (((|Record| #51# #52# #39#) $ $) NIL #21# ELT)) (|extend| #12#) (|exquo| ((#36# $ $) NIL #9# ELT)) (|expressIdealMember| (((|Maybe| #38#) #38# $) NIL #21# ELT)) (|exp| #17#) (|eval| (((|Stream| |#1|) $ |#1|) NIL #53=(|has| |#1| (SIGNATURE ** (|#1| |#1| #14#))) ELT)) (|euclideanSize| ((#23# $) NIL #21# ELT)) (|elt| #54=(#55=(|#1| $ #14#) NIL T ELT) (#34# NIL (|has| #14# (|SemiGroup|)) ELT)) (|divide| (((|Record| (|:| |quotient| $) (|:| |remainder| $)) $ $) NIL #21# ELT)) (|differentiate| #56=(#46# NIL #57=(AND (|has| |#1| (|PartialDifferentialRing| #8#)) #58=(|has| |#1| (SIGNATURE * (|#1| #14# |#1|)))) ELT) #59=(($ $ #47#) NIL #57# ELT) #60=(($ $ #8# #23#) NIL #57# ELT) #61=(($ $ #47# (|List| #23#)) NIL #57# ELT) (#11# 37 #58# ELT) #62=(#63=($ $ #23#) NIL #58# ELT) (#48# 38 T ELT)) (|degree| #40#) (|csch| #17#) (|csc| #17#) (|coth| #17#) (|cot| #17#) (|cosh| #17#) (|cos| #17#) (|complete| #35#) (|coerce| (((|OutputForm|) $) 107 T ELT) (($ #15#) NIL T ELT) (($ |#1|) NIL (|has| |#1| (|CommutativeRing|)) ELT) (($ #26#) 16 T ELT) (($ #29#) 17 T ELT) (($ #49#) 36 T ELT) (($ #14#) NIL #18# ELT) #10#) (|coefficient| #54#) (|charthRoot| ((#19# $) NIL (|has| |#1| (|CharacteristicNonZero|)) ELT)) (|characteristic| ((#23#) NIL T CONST)) (|center| (#44# 12 T ELT)) (|before?| #1#) (|atanh| #17#) (|atan| #17#) (|associates?| (#2# NIL #9# ELT)) (|asinh| #17#) (|asin| #17#) (|asech| #17#) (|asec| #17#) (|approximate| (#55# 73 (AND #53# (|has| |#1| (SIGNATURE |coerce| (|#1| #8#)))) ELT)) (|annihilate?| #1#) (|acsch| #17#) (|acsc| #17#) (|acoth| #17#) (|acot| #17#) (|acosh| #17#) (|acos| #17#) (|Zero| (#24# 32 T CONST)) (|One| (#24# 26 T CONST)) (D #56# #59# #60# #61# (#11# NIL #58# ELT) #62# (#48# NIL T ELT)) (= #1#) (/ (#64=($ $ |#1|) NIL #21# ELT) #33#) (- #35# #65=(#34# NIL T ELT)) (+ (#34# 34 T ELT)) (** #42# (#63# NIL T ELT) (#41# NIL #21# ELT) (#34# NIL #18# ELT) #66=(#13# NIL #18# ELT)) (* (($ #43# $) NIL T ELT) (($ #23# $) NIL T ELT) (($ #15# . #67=($)) NIL T ELT) #65# (#64# NIL T ELT) (($ |#1| . #67#) NIL T ELT) (($ #14# . #67#) NIL #18# ELT) #66#)) (((|UnivariatePuiseuxSeries| |#1| |#2| |#3|) (|Join| (|UnivariatePuiseuxSeriesConstructorCategory| |#1| (|UnivariateLaurentSeries| |#1| |#2| |#3|)) (|PartialDifferentialDomain| $ #1=(|Variable| |#2|)) (|RetractableTo| (|UnivariateTaylorSeries| |#1| |#2| |#3|)) (|CoercibleFrom| #1#) (CATEGORY |domain| (IF (|has| |#1| (|Algebra| (|Fraction| (|Integer|)))) (SIGNATURE |integrate| ($ $ #1#)) |%noBranch|))) (|Ring|) (|Symbol|) |#1|) (T |UnivariatePuiseuxSeries|)) ((|integrate| (*1 *1 *1 *2) (AND (|isDomain| *2 (|Variable| *4)) (|ofType| *4 (|Symbol|)) (|isDomain| *1 (|UnivariatePuiseuxSeries| *3 *4 *5)) (|ofCategory| *3 (|Algebra| (|Fraction| (|Integer|)))) (|ofCategory| *3 (|Ring|)) (|ofType| *5 *3)))) ((|map| (((|UnivariatePuiseuxSeries| |#2| |#4| |#6|) (|Mapping| |#2| |#1|) (|UnivariatePuiseuxSeries| |#1| |#3| |#5|)) 24 T ELT))) (((|UnivariatePuiseuxSeriesFunctions2| |#1| |#2| |#3| |#4| |#5| |#6|) (CATEGORY |package| (SIGNATURE |map| ((|UnivariatePuiseuxSeries| |#2| |#4| |#6|) (|Mapping| |#2| |#1|) (|UnivariatePuiseuxSeries| |#1| |#3| |#5|)))) #1=(|Ring|) #1# #2=(|Symbol|) #2# |#1| |#2|) (T |UnivariatePuiseuxSeriesFunctions2|)) ((|map| (*1 *2 *3 *4) (AND (|isDomain| *3 (|Mapping| *6 *5)) (|isDomain| *4 (|UnivariatePuiseuxSeries| *5 *7 *9)) (|ofCategory| *5 #1=(|Ring|)) (|ofCategory| *6 #1#) (|ofType| *7 #2=(|Symbol|)) (|ofType| *9 *5) (|ofType| *10 *6) (|isDomain| *2 (|UnivariatePuiseuxSeries| *6 *8 *10)) (|isDomain| *1 (|UnivariatePuiseuxSeriesFunctions2| *5 *6 *7 *8 *9 *10)) (|ofType| *8 #2#)))) -((~= (#1=((|Boolean|) $ $) 7 T ELT)) (|zero?| ((#2=(|Boolean|) $) 22 T ELT)) (|variables| (((|List| #3=(|SingletonAsOrderedSet|)) $) 96 T ELT)) (|variable| ((#4=(|Symbol|) $) 130 T ELT)) (|unitNormal| (((|Record| (|:| |unit| $) (|:| |canonical| $) (|:| |associate| $)) $) 72 (|has| |#1| . #5=((|IntegralDomain|))) ELT)) (|unitCanonical| (($ $) 73 (|has| |#1| . #5#) ELT)) (|unit?| ((#6=(|Boolean|) $) 75 (|has| |#1| . #5#) ELT)) (|truncate| (($ $ #7=(|Fraction| (|Integer|))) 125 T ELT) (($ $ #7# #7#) 124 T ELT)) (|terms| (((|Stream| (|Record| (|:| |k| #7#) (|:| |c| |#1|))) $) 131 T ELT)) (|tanh| (#8=($ $) 164 (|has| |#1| . #9=((|Algebra| (|Fraction| (|Integer|))))) ELT)) (|tan| (#10=($ $) 147 (|has| |#1| . #9#) ELT)) 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ELT)) (|before?| (#1# 6 T ELT)) (|atanh| (#37=($ $) 170 (|has| |#1| . #10#) ELT)) (|atan| (#38=($ $) 158 (|has| |#1| . #10#) ELT)) (|associates?| ((#6# $ $) 75 (|has| |#1| . #5#) ELT)) (|asinh| (#37# 169 (|has| |#1| . #10#) ELT)) (|asin| (#38# 157 (|has| |#1| . #10#) ELT)) (|asech| (#37# 168 (|has| |#1| . #10#) ELT)) (|asec| (#38# 156 (|has| |#1| . #10#) ELT)) (|approximate| ((|#1| $ #7#) 123 (AND (|has| |#1| (SIGNATURE ** (|#1| |#1| #7#))) (|has| |#1| (SIGNATURE |coerce| (|#1| #4#)))) ELT)) (|annihilate?| (((|Boolean|) $ $) 34 T ELT)) (|acsch| (#37# 167 (|has| |#1| . #10#) ELT)) (|acsc| (#38# 155 (|has| |#1| . #10#) ELT)) (|acoth| (#37# 166 (|has| |#1| . #10#) ELT)) (|acot| (#38# 154 (|has| |#1| . #10#) ELT)) (|acosh| (#37# 165 (|has| |#1| . #10#) ELT)) (|acos| (#38# 153 (|has| |#1| . #10#) ELT)) (|Zero| (#14# 24 T CONST)) (|One| (($) 46 T CONST)) (D (($ $ #4#) 119 (AND (|has| |#1| . #28#) (|has| |#1| (SIGNATURE * (|#1| #7# |#1|)))) ELT) (($ $ (|List| #4#)) 115 (AND (|has| |#1| . 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#34#) 77 (|has| |#1| . #36#) ELT))) (((|UnivariatePuiseuxSeriesConstructorCategory| |#1| |#2|) (|Category|) (|Ring|) (|UnivariateLaurentSeriesCategory| |t#1|)) (T |UnivariatePuiseuxSeriesConstructorCategory|)) ((|degree| (*1 *2 *1) (AND (|ofCategory| *1 (|UnivariatePuiseuxSeriesConstructorCategory| *3 *4)) (|ofCategory| *3 (|Ring|)) (|ofCategory| *4 (|UnivariateLaurentSeriesCategory| *3)) (|isDomain| *2 (|Fraction| (|Integer|))))) (|puiseux| (*1 *1 *2 *3) (AND (|isDomain| *2 (|Fraction| (|Integer|))) (|ofCategory| *4 (|Ring|)) (|ofCategory| *1 (|UnivariatePuiseuxSeriesConstructorCategory| *4 *3)) (|ofCategory| *3 (|UnivariateLaurentSeriesCategory| *4)))) (|rationalPower| (*1 *2 *1) (AND (|ofCategory| *1 (|UnivariatePuiseuxSeriesConstructorCategory| *3 *4)) (|ofCategory| *3 (|Ring|)) (|ofCategory| *4 (|UnivariateLaurentSeriesCategory| *3)) (|isDomain| *2 (|Fraction| (|Integer|))))) (|laurentRep| (*1 *2 *1) (AND (|ofCategory| *1 (|UnivariatePuiseuxSeriesConstructorCategory| *3 *2)) (|ofCategory| *3 (|Ring|)) (|ofCategory| *2 (|UnivariateLaurentSeriesCategory| *3)))) (|laurent| (*1 *2 *1) (AND (|ofCategory| *1 (|UnivariatePuiseuxSeriesConstructorCategory| *3 *2)) (|ofCategory| *3 (|Ring|)) (|ofCategory| *2 (|UnivariateLaurentSeriesCategory| *3)))) (|laurentIfCan| (*1 *2 *1) (|partial| AND (|ofCategory| *1 (|UnivariatePuiseuxSeriesConstructorCategory| *3 *2)) (|ofCategory| *3 (|Ring|)) (|ofCategory| *2 (|UnivariateLaurentSeriesCategory| *3))))) (|Join| (|UnivariatePuiseuxSeriesCategory| |t#1|) (|RetractableTo| |t#2|) (|CoercibleFrom| |t#2|) (CATEGORY |domain| (SIGNATURE |puiseux| ($ (|Fraction| (|Integer|)) |t#2|)) (SIGNATURE |rationalPower| ((|Fraction| (|Integer|)) $)) (SIGNATURE |laurentRep| (|t#2| $)) (SIGNATURE |degree| ((|Fraction| (|Integer|)) $)) (SIGNATURE |laurent| (|t#2| $)) (SIGNATURE |laurentIfCan| ((|Union| |t#2| "failed") $)))) (((|AbelianGroup|) . T) ((|AbelianMonoid|) . T) ((|AbelianMonoidRing| |#1| #1=(|Fraction| (|Integer|))) . T) ((|AbelianSemiGroup|) . T) ((|Algebra| #2=(|Fraction| (|Integer|))) OR (|has| |#1| (|Field|)) (|has| |#1| (|Algebra| (|Fraction| (|Integer|))))) ((|Algebra| |#1|) |has| |#1| (|CommutativeRing|)) ((|Algebra| $) OR (|has| |#1| (|IntegralDomain|)) (|has| |#1| (|Field|))) ((|ArcHyperbolicFunctionCategory|) |has| |#1| (|Algebra| (|Fraction| (|Integer|)))) ((|ArcTrigonometricFunctionCategory|) |has| |#1| (|Algebra| (|Fraction| (|Integer|)))) ((|BasicType|) . T) ((|BiModule| #2# #2#) OR (|has| |#1| (|Field|)) (|has| |#1| (|Algebra| (|Fraction| (|Integer|))))) ((|BiModule| |#1| |#1|) . T) ((|BiModule| $ $) OR (|has| |#1| (|IntegralDomain|)) (|has| |#1| (|Field|)) (|has| |#1| (|CommutativeRing|))) ((|CancellationAbelianMonoid|) . T) ((|CharacteristicNonZero|) |has| |#1| (|CharacteristicNonZero|)) ((|CharacteristicZero|) |has| |#1| (|CharacteristicZero|)) ((|CoercibleFrom| #2#) OR (|has| |#1| (|Field|)) (|has| |#1| (|Algebra| (|Fraction| (|Integer|))))) ((|CoercibleFrom| (|Integer|)) . T) ((|CoercibleFrom| |#1|) |has| |#1| (|CommutativeRing|)) ((|CoercibleFrom| |#2|) . T) ((|CoercibleFrom| $) OR (|has| |#1| (|IntegralDomain|)) (|has| |#1| (|Field|))) ((|CoercibleTo| (|OutputForm|)) . T) ((|CommutativeRing|) OR (|has| |#1| (|IntegralDomain|)) (|has| |#1| (|Field|)) (|has| |#1| (|CommutativeRing|))) ((|DifferentialDomain| $) |has| |#1| (SIGNATURE * (|#1| (|Fraction| (|Integer|)) |#1|))) ((|DifferentialRing|) |has| |#1| (SIGNATURE * (|#1| (|Fraction| (|Integer|)) |#1|))) ((|DifferentialSpace|) |has| |#1| (SIGNATURE * (|#1| (|Fraction| (|Integer|)) |#1|))) ((|DivisionRing|) |has| |#1| (|Field|)) ((|ElementaryFunctionCategory|) |has| |#1| (|Algebra| (|Fraction| (|Integer|)))) ((|Eltable| #1# |#1|) . T) ((|Eltable| $ $) |has| (|Fraction| (|Integer|)) (|SemiGroup|)) ((|EntireRing|) OR (|has| |#1| (|IntegralDomain|)) (|has| |#1| (|Field|))) ((|EuclideanDomain|) |has| |#1| (|Field|)) ((|Field|) |has| |#1| (|Field|)) ((|Functorial| |#1|) . T) ((|GcdDomain|) |has| |#1| (|Field|)) ((|HyperbolicFunctionCategory|) |has| |#1| (|Algebra| (|Fraction| (|Integer|)))) ((|IntegralDomain|) OR (|has| |#1| (|IntegralDomain|)) (|has| |#1| (|Field|))) ((|Join|) . T) ((|LeftLinearSet| #2#) OR (|has| |#1| (|Field|)) (|has| |#1| (|Algebra| (|Fraction| (|Integer|))))) ((|LeftLinearSet| (|Integer|)) . T) ((|LeftLinearSet| |#1|) . T) ((|LeftLinearSet| $) . T) ((|LeftModule| #2#) OR (|has| |#1| (|Field|)) (|has| |#1| (|Algebra| (|Fraction| (|Integer|))))) ((|LeftModule| |#1|) . T) ((|LeftModule| $) . T) ((|LinearSet| #2#) OR (|has| |#1| (|Field|)) (|has| |#1| (|Algebra| (|Fraction| (|Integer|))))) ((|LinearSet| |#1|) |has| |#1| (|CommutativeRing|)) ((|LinearSet| $) OR (|has| |#1| (|IntegralDomain|)) (|has| |#1| (|Field|))) ((|Module| #2#) OR (|has| |#1| (|Field|)) (|has| |#1| (|Algebra| (|Fraction| (|Integer|))))) ((|Module| |#1|) |has| |#1| (|CommutativeRing|)) ((|Module| $) OR (|has| |#1| (|IntegralDomain|)) (|has| |#1| (|Field|))) ((|Monoid|) . T) ((|PartialDifferentialDomain| $ #3=(|Symbol|)) AND (|has| |#1| (|PartialDifferentialRing| (|Symbol|))) (|has| |#1| (SIGNATURE * (|#1| (|Fraction| (|Integer|)) |#1|)))) ((|PartialDifferentialRing| #3#) AND (|has| |#1| (|PartialDifferentialRing| (|Symbol|))) (|has| |#1| (SIGNATURE * (|#1| (|Fraction| (|Integer|)) |#1|)))) ((|PartialDifferentialSpace| #3#) AND (|has| |#1| (|PartialDifferentialRing| (|Symbol|))) (|has| |#1| (SIGNATURE * (|#1| (|Fraction| (|Integer|)) |#1|)))) ((|PowerSeriesCategory| |#1| #1# (|SingletonAsOrderedSet|)) . T) ((|PrincipalIdealDomain|) |has| |#1| (|Field|)) ((|RadicalCategory|) |has| |#1| (|Algebra| (|Fraction| (|Integer|)))) ((|RetractableTo| |#2|) . T) ((|RightLinearSet| #2#) OR (|has| |#1| (|Field|)) (|has| |#1| (|Algebra| (|Fraction| (|Integer|))))) ((|RightLinearSet| |#1|) . T) ((|RightLinearSet| $) OR (|has| |#1| (|IntegralDomain|)) (|has| |#1| (|Field|)) (|has| |#1| (|CommutativeRing|))) ((|RightModule| #2#) OR (|has| |#1| (|Field|)) (|has| |#1| (|Algebra| (|Fraction| (|Integer|))))) ((|RightModule| |#1|) . T) ((|RightModule| $) OR (|has| |#1| (|IntegralDomain|)) (|has| |#1| (|Field|)) (|has| |#1| (|CommutativeRing|))) ((|Ring|) . T) ((|Rng|) . T) ((|SemiGroup|) . T) ((|SemiRing|) . T) ((|SetCategory|) . T) ((|TranscendentalFunctionCategory|) |has| |#1| (|Algebra| (|Fraction| (|Integer|)))) ((|TrigonometricFunctionCategory|) |has| |#1| (|Algebra| (|Fraction| (|Integer|)))) ((|Type|) . T) ((|UniqueFactorizationDomain|) |has| |#1| (|Field|)) ((|UnivariatePowerSeriesCategory| |#1| #1#) . T) ((|UnivariatePuiseuxSeriesCategory| |#1|) . T)) -((~= #1=(#2=(#3=(|Boolean|) $ $) NIL T ELT)) (|zero?| #4=(#5=(#3# $) NIL T ELT)) (|variables| ((#6=(|List| #7=(|SingletonAsOrderedSet|)) $) NIL T ELT)) (|variable| ((#8=(|Symbol|) $) 104 T ELT)) (|unitNormal| (((|Record| (|:| |unit| $) (|:| |canonical| $) (|:| |associate| $)) $) NIL #9=(|has| |#1| (|IntegralDomain|)) ELT)) (|unitCanonical| #10=(#11=($ $) NIL #9# ELT)) (|unit?| (#5# NIL #9# ELT)) (|truncate| (#12=($ $ #13=(|Fraction| #14=(|Integer|))) 116 T ELT) (($ $ #13# #13#) 118 T ELT)) (|terms| ((#15=(|Stream| (|Record| (|:| |k| #13#) (|:| |c| |#1|))) $) 54 T ELT)) (|tanh| (#11# 192 #16=(|has| |#1| (|Algebra| #13#)) ELT)) (|tan| (#11# 168 #16# ELT)) (|subtractIfCan| (#17=(#18=(|Union| $ #19="failed") $ $) NIL T ELT)) (|squareFreePart| (#11# NIL #20=(|has| |#1| (|Field|)) ELT)) (|squareFree| #21=(((|Factored| $) $) NIL #20# ELT)) (|sqrt| (#11# NIL #16# ELT)) (|sizeLess?| (#2# NIL #20# ELT)) (|sinh| (#11# 188 #16# ELT)) (|sin| (#11# 164 #16# ELT)) (|series| (($ #22=(|NonNegativeInteger|) #15#) 65 T ELT)) (|sech| (#11# 196 #16# ELT)) (|sec| (#11# 172 #16# ELT)) (|sample| (#23=($) NIL T CONST)) (|retractIfCan| (#24=((|Union| |#2| #19#) $) NIL T ELT)) (|retract| (#25=(|#2| $) NIL T ELT)) (|rem| #26=(#27=($ $ $) NIL #20# ELT)) (|reductum| #28=(#11# NIL T ELT)) (|recip| ((#18# $) 85 T ELT)) (|rationalPower| (#29=(#13# $) 13 T ELT)) (|quo| #26#) (|puiseux| (($ #13# |#2|) 11 T ELT)) (|principalIdeal| (((|Record| (|:| |coef| #30=(|List| $)) #31=(|:| |generator| $)) #30#) NIL #20# ELT)) (|prime?| (#5# NIL #20# ELT)) (|pole?| (#5# 74 T ELT)) (|pi| (#23# NIL #16# ELT)) (|order| (#29# 113 T ELT) ((#13# $ #13#) 114 T ELT)) (|opposite?| #1#) (|one?| #4#) (|nthRoot| (#32=($ $ #14#) NIL #16# ELT)) (|multiplyExponents| (#33=($ $ #34=(|PositiveInteger|)) 130 T ELT) (#12# 128 T ELT)) (|multiEuclidean| (((|Union| #30# #19#) #30# $) NIL #20# ELT)) (|monomial?| #4#) (|monomial| (($ |#1| #13#) 33 T ELT) (($ $ #7# #13#) NIL T ELT) (($ $ #6# (|List| #13#)) NIL T 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NIL #20# ELT)) (|extend| (#12# 122 T ELT)) (|exquo| (#17# NIL #9# ELT)) (|expressIdealMember| (((|Maybe| #30#) #30# $) NIL #20# ELT)) (|exp| (#11# 160 #16# ELT)) (|eval| (((|Stream| |#1|) $ |#1|) 98 #42=(|has| |#1| (SIGNATURE ** (|#1| |#1| #13#))) ELT)) (|euclideanSize| ((#22# $) NIL #20# ELT)) (|elt| (#43=(|#1| $ #13#) 108 T ELT) (#27# 94 (|has| #13# (|SemiGroup|)) ELT)) (|divide| (((|Record| (|:| |quotient| $) (|:| |remainder| $)) $ $) NIL #20# ELT)) (|differentiate| (#37# 138 #44=(AND (|has| |#1| (|PartialDifferentialRing| #8#)) #45=(|has| |#1| (SIGNATURE * (|#1| #13# |#1|)))) ELT) #46=(($ $ #38#) NIL #44# ELT) #47=(($ $ #8# #22#) NIL #44# ELT) #48=(($ $ #38# (|List| #22#)) NIL #44# ELT) (#11# 134 #45# ELT) #49=(#50=($ $ #22#) NIL #45# ELT)) (|degree| (#29# 16 T ELT)) (|csch| (#11# 198 #16# ELT)) (|csc| (#11# 174 #16# ELT)) (|coth| (#11# 194 #16# ELT)) (|cot| (#11# 170 #16# ELT)) (|cosh| (#11# 190 #16# ELT)) (|cos| (#11# 166 #16# ELT)) (|complete| (#11# 120 T ELT)) (|coerce| 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(|RetractableTo| #4#) (|LinearlyExplicitRingOver| #4#) (|GcdDomain|)) (|Join| (|AlgebraicallyClosedField|) (|TranscendentalFunctionCategory|) (|FunctionSpace| |#1|)) (|Symbol|) |#2|) (T |UnivariatePuiseuxSeriesWithExponentialSingularity|)) ((|limitPlus| #1=(*1 *2 *1) (|partial| AND #2=(|ofCategory| *3 (|Join| (|RetractableTo| #3=(|Integer|)) (|LinearlyExplicitRingOver| #3#) (|GcdDomain|))) (|isDomain| *2 (|OrderedCompletion| *4)) #4=(|isDomain| *1 (|UnivariatePuiseuxSeriesWithExponentialSingularity| *3 *4 *5 *6)) #5=(|ofCategory| *4 (|Join| (|AlgebraicallyClosedField|) (|TranscendentalFunctionCategory|) (|FunctionSpace| *3))) #6=(|ofType| *5 (|Symbol|)) #7=(|ofType| *6 *4))) (|dominantTerm| #1# (|partial| AND #2# (|isDomain| *2 (|Record| (|:| |%term| (|Record| (|:| |%coef| (|UnivariatePuiseuxSeries| *4 *5 *6)) (|:| |%expon| (|ExponentialOfUnivariatePuiseuxSeries| *4 *5 *6)) (|:| |%expTerms| (|List| (|Record| (|:| |k| (|Fraction| #3#)) (|:| |c| *4)))))) (|:| |%type| (|String|)))) #4# #5# #6# #7#))) ((|value| (#1=(|#2| $) 34 T ELT)) (|third| (#1# 18 T ELT)) (|tail| (#2=($ $) 43 T ELT)) (|split!| (($ $ (|Integer|)) 78 T ELT)) (|setvalue!| (#3=(|#2| $ |#2|) 75 T ELT)) (|setlast!| (#3# 71 T ELT)) (|setelt| ((|#2| $ #4="value" |#2|) NIL T ELT) ((|#2| $ #5="first" |#2|) 64 T ELT) (($ $ #6="rest" $) 68 T ELT) ((|#2| $ #7="last" |#2|) 66 T ELT)) (|setchildren!| (($ $ #8=(|List| $)) 74 T ELT)) (|second| (#1# 17 T ELT)) (|rest| (#2# NIL T ELT) (#9=($ $ #10=(|NonNegativeInteger|)) 51 T ELT)) (|nodes| (#11=(#8# $) 31 T ELT)) (|node?| (#12=(#13=(|Boolean|) $ $) 62 T ELT)) (|leaf?| (#14=(#13# $) 33 T ELT)) (|last| (#1# 25 T ELT) (#9# 57 T ELT)) (|elt| ((|#2| $ #4#) NIL T ELT) ((|#2| $ #5#) 10 T ELT) (($ $ #6#) 16 T ELT) ((|#2| $ #7#) 13 T ELT)) (|cyclic?| (#14# 23 T ELT)) (|cycleTail| (#2# 46 T ELT)) (|cycleSplit!| (#2# 79 T ELT)) (|cycleLength| ((#10# $) 50 T ELT)) (|cycleEntry| (#2# 49 T ELT)) (|concat| (($ $ $) 70 T ELT) (($ |#2| $) NIL T ELT)) (|children| (#11# 32 T ELT)) (= (#12# 60 T ELT))) @@ -3912,7 +3912,7 @@ NIL ((|concat| (*1 *1 *1 *1) (AND (|ofCategory| *1 (|UnaryRecursiveAggregate| *2)) (|ofCategory| *2 (|Type|)))) (|concat| (*1 *1 *2 *1) (AND (|ofCategory| *1 (|UnaryRecursiveAggregate| *2)) (|ofCategory| *2 (|Type|)))) (|first| (*1 *2 *1) (AND (|ofCategory| *1 (|UnaryRecursiveAggregate| *2)) (|ofCategory| *2 (|Type|)))) (|elt| (*1 *2 *1 *3) (AND (|isDomain| *3 "first") (|ofCategory| *1 (|UnaryRecursiveAggregate| *2)) (|ofCategory| *2 (|Type|)))) (|first| (*1 *1 *1 *2) (AND (|isDomain| *2 (|NonNegativeInteger|)) (|ofCategory| *1 (|UnaryRecursiveAggregate| *3)) (|ofCategory| *3 (|Type|)))) (|rest| (*1 *1 *1) (AND (|ofCategory| *1 (|UnaryRecursiveAggregate| *2)) (|ofCategory| *2 (|Type|)))) (|elt| (*1 *1 *1 *2) (AND (|isDomain| *2 "rest") (|ofCategory| *1 (|UnaryRecursiveAggregate| *3)) (|ofCategory| *3 (|Type|)))) (|rest| (*1 *1 *1 *2) (AND (|isDomain| *2 (|NonNegativeInteger|)) (|ofCategory| *1 (|UnaryRecursiveAggregate| *3)) (|ofCategory| *3 (|Type|)))) (|last| (*1 *2 *1) (AND (|ofCategory| *1 (|UnaryRecursiveAggregate| *2)) (|ofCategory| *2 (|Type|)))) (|elt| (*1 *2 *1 *3) (AND (|isDomain| *3 "last") (|ofCategory| *1 (|UnaryRecursiveAggregate| *2)) (|ofCategory| *2 (|Type|)))) (|last| (*1 *1 *1 *2) (AND (|isDomain| *2 (|NonNegativeInteger|)) (|ofCategory| *1 (|UnaryRecursiveAggregate| *3)) (|ofCategory| *3 (|Type|)))) (|tail| (*1 *1 *1) (AND (|ofCategory| *1 (|UnaryRecursiveAggregate| *2)) (|ofCategory| *2 (|Type|)))) (|second| (*1 *2 *1) (AND (|ofCategory| *1 (|UnaryRecursiveAggregate| *2)) (|ofCategory| *2 (|Type|)))) (|third| (*1 *2 *1) (AND (|ofCategory| *1 (|UnaryRecursiveAggregate| *2)) (|ofCategory| *2 (|Type|)))) (|cycleEntry| (*1 *1 *1) (AND (|ofCategory| *1 (|UnaryRecursiveAggregate| *2)) (|ofCategory| *2 (|Type|)))) (|cycleLength| (*1 *2 *1) (AND (|ofCategory| *1 (|UnaryRecursiveAggregate| *3)) (|ofCategory| *3 (|Type|)) (|isDomain| *2 (|NonNegativeInteger|)))) (|cycleTail| (*1 *1 *1) (AND (|ofCategory| *1 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(|NonNegativeInteger|))) (SIGNATURE |rest| ($ $)) (SIGNATURE |elt| ($ $ "rest")) (SIGNATURE |rest| ($ $ (|NonNegativeInteger|))) (SIGNATURE |last| (|t#1| $)) (SIGNATURE |elt| (|t#1| $ "last")) (SIGNATURE |last| ($ $ (|NonNegativeInteger|))) (SIGNATURE |tail| ($ $)) (SIGNATURE |second| (|t#1| $)) (SIGNATURE |third| (|t#1| $)) (SIGNATURE |cycleEntry| ($ $)) (SIGNATURE |cycleLength| ((|NonNegativeInteger|) $)) (SIGNATURE |cycleTail| ($ $)) (IF (|has| $ (|ShallowlyMutableAggregate| |t#1|)) (PROGN (SIGNATURE |concat!| ($ $ $)) (SIGNATURE |concat!| ($ $ |t#1|)) (SIGNATURE |cycleSplit!| ($ $)) (SIGNATURE |setfirst!| (|t#1| $ |t#1|)) (SIGNATURE |setelt| (|t#1| $ "first" |t#1|)) (SIGNATURE |setrest!| ($ $ $)) (SIGNATURE |setelt| ($ $ "rest" $)) (SIGNATURE |setlast!| (|t#1| $ |t#1|)) (SIGNATURE |setelt| (|t#1| $ "last" |t#1|)) (SIGNATURE |split!| ($ $ (|Integer|)))) |%noBranch|))) (((|Aggregate|) . T) ((|BasicType|) OR (|has| |#1| (|SetCategory|)) (|has| |#1| (|BasicType|))) ((|CoercibleTo| (|OutputForm|)) OR (|has| |#1| (|SetCategory|)) (|has| |#1| (|CoercibleTo| (|OutputForm|)))) ((|Evalable| |#1|) AND (|has| |#1| (|Evalable| |#1|)) (|has| |#1| (|SetCategory|))) ((|Functorial| |#1|) . T) ((|HomogeneousAggregate| |#1|) . T) ((|InnerEvalable| |#1| |#1|) AND (|has| |#1| (|Evalable| |#1|)) (|has| |#1| (|SetCategory|))) ((|Join|) . T) ((|RecursiveAggregate| |#1|) . T) ((|SetCategory|) |has| |#1| (|SetCategory|)) ((|Type|) . T)) -((~= #1=(#2=(#3=(|Boolean|) $ $) NIL T ELT)) (|zero?| #4=(#5=(#3# $) NIL T ELT)) (|variables| ((#6=(|List| #7=(|SingletonAsOrderedSet|)) $) NIL T ELT)) (|variable| ((#8=(|Symbol|) $) 87 T ELT)) (|univariatePolynomial| ((#9=(|UnivariatePolynomial| |#2| |#1|) $ #10=(|NonNegativeInteger|)) 70 T ELT)) (|unitNormal| (((|Record| (|:| |unit| $) (|:| |canonical| $) (|:| |associate| $)) $) NIL #11=(|has| |#1| (|IntegralDomain|)) ELT)) (|unitCanonical| #12=(#13=($ $) NIL #11# ELT)) (|unit?| (#5# 139 #11# ELT)) (|truncate| (#14=($ $ #10#) 125 T ELT) (($ $ #10# #10#) 127 T ELT)) (|terms| ((#15=(|Stream| (|Record| (|:| |k| #10#) (|:| |c| |#1|))) $) 42 T ELT)) (|tanh| #16=(#13# NIL #17=(|has| |#1| (|Algebra| #18=(|Fraction| #19=(|Integer|)))) ELT)) (|tan| #16#) (|subtractIfCan| (#20=(#21=(|Union| $ "failed") $ $) NIL T ELT)) (|sqrt| #16#) (|sinh| #16#) (|sin| #16#) (|series| (($ #15#) 49 T ELT) (($ #22=(|Stream| |#1|)) NIL T ELT)) (|sech| #16#) (|sec| #16#) (|sample| (#23=($) NIL T CONST)) 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NIL #40# ELT) (#34# 101 T ELT)) (|degree| #26#) (|csch| #16#) (|csc| #16#) (|coth| #16#) (|cot| #16#) (|cosh| #16#) (|cos| #16#) (|complete| (#13# 123 T ELT)) (|coerce| (((|OutputForm|) $) NIL T ELT) (($ #19#) 26 T ELT) (($ #18#) 145 #17# ELT) #12# (($ |#1|) 25 (|has| |#1| (|CommutativeRing|)) ELT) (($ #9#) 78 T ELT) (($ #35#) 22 T ELT)) (|coefficients| ((#22# $) NIL T ELT)) (|coefficient| (#37# 92 T ELT)) (|charthRoot| (((|Maybe| $) $) NIL (|has| |#1| (|CharacteristicNonZero|)) ELT)) (|characteristic| ((#10#) NIL T CONST)) (|center| (#31# 88 T ELT)) (|before?| #1#) (|atanh| #16#) (|atan| #16#) (|associates?| (#2# NIL #11# ELT)) (|asinh| #16#) (|asin| #16#) (|asech| #16#) (|asec| #16#) (|approximate| (#37# 86 (AND #36# (|has| |#1| (SIGNATURE |coerce| (|#1| #8#)))) ELT)) (|annihilate?| #1#) (|acsch| #16#) (|acsc| #16#) (|acoth| #16#) (|acot| #16#) (|acosh| #16#) (|acos| #16#) (|Zero| (#23# 18 T CONST)) (|One| (#23# 13 T CONST)) (D (#32# NIL #39# ELT) #41# #42# #43# (#13# NIL #40# ELT) #44# (#34# NIL T ELT)) (= #1#) (/ (#45=($ $ |#1|) NIL #46=(|has| |#1| (|Field|)) ELT)) (- #24# (#38# 105 T ELT)) (+ (#38# 20 T ELT)) (** (#28# NIL T ELT) (#14# NIL T ELT) (#45# 142 #46# ELT) (#38# NIL #17# ELT) #47=(($ $ #18#) NIL #17# ELT)) (* (($ #29# $) NIL T ELT) (($ #10# $) NIL T ELT) (($ #19# . #48=($)) NIL T ELT) (#38# NIL T ELT) (#45# NIL T ELT) (($ |#1| . #48#) 104 T ELT) (($ #18# . #48#) NIL #17# ELT) #47#)) +((~= #1=(#2=(#3=(|Boolean|) $ $) NIL T ELT)) (|zero?| #4=(#5=(#3# $) NIL T ELT)) (|variables| ((#6=(|List| #7=(|SingletonAsOrderedSet|)) $) NIL T ELT)) (|variable| ((#8=(|Symbol|) $) 87 T ELT)) (|univariatePolynomial| ((#9=(|UnivariatePolynomial| |#2| |#1|) $ #10=(|NonNegativeInteger|)) 70 T ELT)) (|unitNormal| (((|Record| (|:| |unit| $) (|:| |canonical| $) (|:| |associate| $)) $) NIL #11=(|has| |#1| (|IntegralDomain|)) ELT)) (|unitCanonical| #12=(#13=($ $) NIL #11# ELT)) (|unit?| (#5# 139 #11# ELT)) (|truncate| (#14=($ $ #10#) 125 T ELT) (($ $ #10# #10#) 127 T ELT)) (|terms| ((#15=(|Stream| (|Record| (|:| |k| #10#) (|:| |c| |#1|))) $) 42 T ELT)) (|tanh| #16=(#13# NIL #17=(|has| |#1| (|Algebra| #18=(|Fraction| #19=(|Integer|)))) ELT)) (|tan| #16#) (|subtractIfCan| ((#20=(|Maybe| $) $ $) NIL T ELT)) (|sqrt| #16#) (|sinh| #16#) (|sin| #16#) (|series| (($ #15#) 49 T ELT) (($ #21=(|Stream| |#1|)) NIL T ELT)) (|sech| #16#) (|sec| #16#) (|sample| (#22=($) NIL T CONST)) (|revert| (#13# 131 T ELT)) (|reductum| #23=(#13# NIL T ELT)) (|recip| ((#24=(|Union| $ "failed") $) NIL T ELT)) (|quoByVar| (#13# 137 T ELT)) (|polynomial| ((#25=(|Polynomial| |#1|) $ #10#) 60 T ELT) ((#25# $ #10# #10#) 62 T ELT)) (|pole?| #4#) (|pi| (#22# NIL #17# ELT)) (|order| #26=((#10# $) NIL T ELT) ((#10# $ #10#) NIL T ELT)) (|opposite?| #1#) (|one?| #4#) (|oddlambert| (#13# 115 T ELT)) (|nthRoot| (($ $ #19#) NIL #17# ELT)) (|multisect| (#27=($ #19# #19# $) 133 T ELT)) (|multiplyExponents| (#28=($ $ #29=(|PositiveInteger|)) 136 T ELT)) (|multiplyCoefficients| (($ (|Mapping| |#1| #19#) $) 109 T ELT)) (|monomial?| #4#) (|monomial| (($ |#1| #10#) 16 T ELT) (($ $ #7# #10#) NIL T ELT) (($ $ #6# #30=(|List| #10#)) NIL T ELT)) (|map| (($ (|Mapping| |#1| |#1|) $) 96 T ELT)) (|log| #16#) (|leadingMonomial| #23#) (|leadingCoefficient| (#31=(|#1| $) NIL T ELT)) (|latex| (((|String|) $) NIL T ELT)) (|lambert| (#13# 113 T ELT)) (|lagrange| (#13# 111 T ELT)) (|invmultisect| (#27# 135 T ELT)) (|integrate| (#13# 147 #17# ELT) (#32=($ $ #8#) 153 (OR (AND #17# (|has| |#1| (|AlgebraicallyClosedFunctionSpace| #19#)) (|has| |#1| (|PrimitiveFunctionCategory|)) (|has| |#1| (|TranscendentalFunctionCategory|))) (AND #17# (|has| |#1| (SIGNATURE |integrate| (|#1| |#1| #8#))) (|has| |#1| (SIGNATURE |variables| (#33=(|List| #8#) |#1|))))) ELT) (#34=($ $ #35=(|Variable| |#2|)) 148 #17# ELT)) (|hash| (((|SingleInteger|) $) NIL T ELT)) (|generalLambert| (($ $ #19# #19#) 119 T ELT)) (|extend| (#14# 121 T ELT)) (|exquo| ((#24# $ $) NIL #11# ELT)) (|exp| #16#) (|evenlambert| (#13# 117 T ELT)) (|eval| ((#21# $ |#1|) 98 #36=(|has| |#1| (SIGNATURE ** (|#1| |#1| #10#))) ELT)) (|elt| (#37=(|#1| $ #10#) 93 T ELT) (#38=($ $ $) 129 (|has| #10# (|SemiGroup|)) ELT)) (|differentiate| (#32# 106 #39=(AND (|has| |#1| (|PartialDifferentialRing| #8#)) #40=(|has| |#1| (SIGNATURE * (|#1| #10# |#1|)))) ELT) #41=(($ $ #33#) NIL #39# ELT) #42=(($ $ #8# #10#) NIL #39# ELT) #43=(($ $ #33# #30#) NIL #39# ELT) (#13# 100 #40# ELT) #44=(#14# NIL #40# ELT) (#34# 101 T ELT)) (|degree| #26#) (|csch| #16#) (|csc| #16#) (|coth| #16#) (|cot| #16#) (|cosh| #16#) (|cos| #16#) (|complete| (#13# 123 T ELT)) (|coerce| (((|OutputForm|) $) NIL T ELT) (($ #19#) 26 T ELT) (($ #18#) 145 #17# ELT) #12# (($ |#1|) 25 (|has| |#1| (|CommutativeRing|)) ELT) (($ #9#) 78 T ELT) (($ #35#) 22 T ELT)) (|coefficients| ((#21# $) NIL T ELT)) (|coefficient| (#37# 92 T ELT)) (|charthRoot| ((#20# $) NIL (|has| |#1| (|CharacteristicNonZero|)) ELT)) (|characteristic| ((#10#) NIL T CONST)) (|center| (#31# 88 T ELT)) (|before?| #1#) (|atanh| #16#) (|atan| #16#) (|associates?| (#2# NIL #11# ELT)) (|asinh| #16#) (|asin| #16#) (|asech| #16#) (|asec| #16#) (|approximate| (#37# 86 (AND #36# (|has| |#1| (SIGNATURE |coerce| (|#1| #8#)))) ELT)) (|annihilate?| #1#) (|acsch| #16#) (|acsc| #16#) (|acoth| #16#) (|acot| #16#) (|acosh| #16#) (|acos| #16#) (|Zero| (#22# 18 T CONST)) (|One| (#22# 13 T CONST)) (D (#32# NIL #39# ELT) #41# #42# #43# (#13# NIL #40# ELT) #44# (#34# NIL T ELT)) (= #1#) (/ (#45=($ $ |#1|) NIL #46=(|has| |#1| (|Field|)) ELT)) (- #23# (#38# 105 T ELT)) (+ (#38# 20 T ELT)) (** (#28# NIL T ELT) (#14# NIL T ELT) (#45# 142 #46# ELT) (#38# NIL #17# ELT) #47=(($ $ #18#) NIL #17# ELT)) (* (($ #29# $) NIL T ELT) (($ #10# $) NIL T ELT) (($ #19# . #48=($)) NIL T ELT) (#38# NIL T ELT) (#45# NIL T ELT) (($ |#1| . #48#) 104 T ELT) (($ #18# . #48#) NIL #17# ELT) #47#)) (((|UnivariateTaylorSeries| |#1| |#2| |#3|) (|Join| (|UnivariateTaylorSeriesCategory| |#1|) (|PartialDifferentialDomain| $ #1=(|Variable| |#2|)) 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(|PrimitiveFunctionCategory|)) (IF (|has| |t#1| (|AlgebraicallyClosedFunctionSpace| (|Integer|))) (SIGNATURE |integrate| ($ $ (|Symbol|))) |%noBranch|) |%noBranch|) |%noBranch|) (ATTRIBUTE (|RadicalCategory|)) (ATTRIBUTE (|TranscendentalFunctionCategory|))) |%noBranch|))) @@ -3937,8 +3937,8 @@ NIL NIL (|Join| (CATEGORY |package| (ATTRIBUTE |nil|))) ((~= #1=(#2=((|Boolean|) $ $) NIL T ELT)) (|variable| ((#3=(|Symbol|)) 12 T ELT)) (|latex| (((|String|) $) 18 T ELT)) (|hash| (((|SingleInteger|) $) NIL T ELT)) (|coerce| (((|OutputForm|) $) 11 T ELT) ((#3# $) 8 T ELT)) (|before?| #1#) (= (#2# 15 T ELT))) -(((|Variable| |#1|) (|Join| (|SetCategory|) (|CoercibleTo| #1=(|Symbol|)) (CATEGORY |domain| (SIGNATURE |coerce| (#1# $)) (SIGNATURE |variable| (#1#)))) #1#) (T |Variable|)) -((|coerce| (*1 *2 *1) #1=(AND (|isDomain| *2 (|Symbol|)) (|isDomain| *1 (|Variable| *3)) (|ofType| *3 *2))) (|variable| (*1 *2) #1#)) +(((|Variable| |#1|) (|Join| (|SetCategory|) (|CoercibleTo| #1=(|Symbol|)) (CATEGORY |package| (SIGNATURE |variable| (#1#)))) #1#) (T |Variable|)) +((|variable| (*1 *2) (AND (|isDomain| *2 (|Symbol|)) (|isDomain| *1 (|Variable| *3)) (|ofType| *3 *2)))) ((|zero| (($ (|NonNegativeInteger|)) 19 T ELT)) (|outerProduct| (((|Matrix| |#2|) $ $) 41 T ELT)) (|magnitude| (#1=(|#2| $) 51 T ELT)) (|length| (#1# 50 T ELT)) (|dot| ((|#2| $ $) 36 T ELT)) (|cross| (#2=($ $ $) 47 T ELT)) (- (($ $) 23 T ELT) (#2# 29 T ELT)) (+ (#2# 15 T ELT)) (* (($ (|Integer|) $) 26 T ELT) (($ |#2| $) 32 T ELT) (($ $ |#2|) 31 T ELT))) (((|VectorCategory&| |#1| |#2|) (CATEGORY |package| (SIGNATURE |magnitude| #1=(|#2| |#1|)) (SIGNATURE |length| #1#) (SIGNATURE |cross| #2=(|#1| |#1| |#1|)) (SIGNATURE |outerProduct| ((|Matrix| |#2|) |#1| |#1|)) (SIGNATURE |dot| (|#2| |#1| |#1|)) (SIGNATURE * (|#1| |#1| |#2|)) (SIGNATURE * (|#1| |#2| |#1|)) (SIGNATURE * (|#1| (|Integer|) |#1|)) (SIGNATURE - #2#) (SIGNATURE - (|#1| |#1|)) (SIGNATURE |zero| (|#1| (|NonNegativeInteger|))) (SIGNATURE + #2#)) 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|phi| #5#) (|:| |scale| #5#) (|:| |scaleX| #5#) (|:| |scaleY| #5#) (|:| |scaleZ| #5#) (|:| |deltaX| #5#) (|:| |deltaY| #5#)) $)) (SIGNATURE |viewpoint| (#8# $ #12#)) (SIGNATURE |viewpoint| (#8# $ #13=(|Integer|) #13# #2# #2# #2#)) (SIGNATURE |viewpoint| #14=(#8# $ #2# #2#)) (SIGNATURE |viewpoint| #15=(#8# $ #2# #2# #2#)) (SIGNATURE |controlPanel| #11#) (SIGNATURE |axes| #11#) (SIGNATURE |diagonals| #11#) (SIGNATURE |outlineRender| #11#) (SIGNATURE |drawStyle| #11#) (SIGNATURE |rotate| #14#) (SIGNATURE |rotate| (#8# $ #13# #13#)) (SIGNATURE |zoom| #16=(#8# $ #2#)) (SIGNATURE |zoom| #15#) (SIGNATURE |translate| #14#) (SIGNATURE |perspective| #11#) (SIGNATURE |eyeDistance| #16#) (SIGNATURE |hitherPlane| #16#) (SIGNATURE |showRegion| #11#) (SIGNATURE |showClipRegion| #11#) (SIGNATURE |clipSurface| #11#) (SIGNATURE |lighting| #15#) (SIGNATURE |intensity| #16#) (SIGNATURE |reset| #17=(#8# $)) (SIGNATURE |colorDef| (#8# $ #18=(|Color|) #18#)) (SIGNATURE |write| (#6# $ #6#)) (SIGNATURE |write| 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(|Point| #8#)) #16=(|isDomain| *2 (|Void|)) #4#)) (|options| #12# #17=(AND (|isDomain| *2 #11#) #4#)) (|options| #14# #17#) (|move| #18=(*1 *2 *1 *3 *3) (AND #15# #16# #4#)) (|resize| #18# (AND (|isDomain| *3 #19=(|PositiveInteger|)) #16# #4#)) (|title| #20=(*1 *2 *1 *3) #21=(AND #9# #16# #4#)) (|dimensions| (*1 *2 *1 *3 *3 *4 *4) (AND #15# (|isDomain| *4 #19#) #16# #4#)) (|viewpoint| (*1 *2 *1 *3 *3 *3 *3 *3) #22=(AND (|isDomain| *3 #3#) #16# #4#)) (|viewpoint| #12# (AND (|isDomain| *2 #23=(|Record| (|:| |theta| #8#) (|:| |phi| #8#) (|:| |scale| #8#) (|:| |scaleX| #8#) (|:| |scaleY| #8#) (|:| |scaleZ| #8#) (|:| |deltaX| #8#) (|:| |deltaY| #8#))) #4#)) (|viewpoint| #20# (AND (|isDomain| *3 #23#) #16# #4#)) (|viewpoint| (*1 *2 *1 *3 *3 *4 *4 *4) (AND #24=(|isDomain| *3 #25=(|Integer|)) (|isDomain| *4 #3#) #16# #4#)) (|viewpoint| #18# #22#) (|viewpoint| #26=(*1 *2 *1 *3 *3 *3) #22#) (|controlPanel| #20# #21#) (|axes| #20# #21#) (|diagonals| #20# #21#) (|outlineRender| #20# #21#) (|drawStyle| #20# #21#) (|rotate| #18# #22#) (|rotate| #18# (AND #24# #16# #4#)) (|zoom| #20# #22#) (|zoom| #26# #22#) (|translate| #18# #22#) (|perspective| #20# #21#) (|eyeDistance| #20# #22#) (|hitherPlane| #20# #22#) (|showRegion| #20# #21#) (|showClipRegion| #20# #21#) (|clipSurface| #20# #21#) (|lighting| #26# #22#) (|intensity| #20# #22#) (|reset| #12# #27=(AND #16# #4#)) (|colorDef| #18# (AND (|isDomain| *3 (|Color|)) #16# #4#)) (|write| (*1 *2 *1 *2) #28=(AND #29=(|isDomain| *2 #10#) #4#)) (|write| (*1 *2 *1 *2 *2) #28#) (|write| (*1 *2 *1 *2 *3) (AND (|isDomain| *3 (|List| #10#)) #29# #4#)) (|close| #12# #27#) (|key| #12# (AND (|isDomain| *2 #25#) #4#))) @@ -3971,7 +3971,7 @@ NIL ((/ (($ $ |#2|) 10 T ELT))) (((|VectorSpace&| |#1| |#2|) (CATEGORY |package| (SIGNATURE / (|#1| |#1| |#2|))) (|VectorSpace| |#2|) (|Field|)) (T |VectorSpace&|)) NIL -((~= (#1=((|Boolean|) $ $) 7 T ELT)) (|zero?| ((#2=(|Boolean|) $) 22 T ELT)) (|subtractIfCan| (((|Union| $ "failed") $ $) 26 T ELT)) (|sample| (#3=($) 23 T CONST)) (|opposite?| ((#2# $ $) 20 T ELT)) (|latex| (((|String|) $) 11 T ELT)) (|hash| (((|SingleInteger|) $) 12 T ELT)) (|dimension| (((|CardinalNumber|)) 39 T ELT)) (|coerce| (((|OutputForm|) $) 13 T ELT)) (|before?| (#1# 6 T ELT)) (|Zero| (#3# 24 T CONST)) (= (#1# 8 T ELT)) (/ (($ $ |#1|) 40 T ELT)) (- (($ $) 29 T ELT) (($ $ $) 28 T ELT)) (+ (($ $ $) 18 T ELT)) (* (($ (|PositiveInteger|) $) 17 T ELT) (($ (|NonNegativeInteger|) $) 21 T ELT) (($ (|Integer|) . #4=($)) 30 T ELT) (($ |#1| . #4#) 33 T ELT) (($ $ |#1|) 37 T ELT))) +((~= (#1=((|Boolean|) $ $) 7 T ELT)) (|zero?| ((#2=(|Boolean|) $) 22 T ELT)) (|subtractIfCan| (((|Maybe| $) $ $) 26 T ELT)) (|sample| (#3=($) 23 T CONST)) (|opposite?| ((#2# $ $) 20 T ELT)) (|latex| (((|String|) $) 11 T ELT)) (|hash| (((|SingleInteger|) $) 12 T ELT)) (|dimension| (((|CardinalNumber|)) 40 T ELT)) (|coerce| (((|OutputForm|) $) 13 T ELT)) (|before?| (#1# 6 T ELT)) (|Zero| (#3# 24 T CONST)) (= (#1# 8 T ELT)) (/ (($ $ |#1|) 41 T ELT)) (- (($ $) 30 T ELT) (($ $ $) 29 T ELT)) (+ (($ $ $) 18 T ELT)) (* (($ (|PositiveInteger|) $) 17 T ELT) (($ (|NonNegativeInteger|) $) 21 T ELT) (($ (|Integer|) . #4=($)) 31 T ELT) (($ |#1| . #4#) 34 T ELT) (($ $ |#1|) 38 T ELT))) (((|VectorSpace| |#1|) (|Category|) (|Field|)) (T |VectorSpace|)) ((/ (*1 *1 *1 *2) (AND (|ofCategory| *1 (|VectorSpace| *2)) (|ofCategory| *2 (|Field|)))) (|dimension| (*1 *2) (AND (|ofCategory| *1 (|VectorSpace| *3)) (|ofCategory| *3 (|Field|)) (|isDomain| *2 (|CardinalNumber|))))) (|Join| (|Module| |t#1|) (CATEGORY |domain| (SIGNATURE / ($ $ |t#1|)) (SIGNATURE |dimension| ((|CardinalNumber|))))) @@ -3988,18 +3988,18 @@ NIL ((~= #1=(((|Boolean|) $ $) NIL T ELT)) (|latex| (((|String|) $) NIL T ELT)) (|hash| (((|SingleInteger|) $) NIL T ELT)) (|condition| (((|SpadAst|) $) 11 T ELT)) (|coerce| (((|OutputForm|) $) 17 T ELT) (($ #2=(|Syntax|)) NIL T ELT) ((#2# $) NIL T ELT)) (|before?| #1#) (= #1#)) (((|WhileAst|) (|Join| (|SpadSyntaxCategory|) (CATEGORY |domain| (SIGNATURE |condition| ((|SpadAst|) $))))) (T |WhileAst|)) ((|condition| (*1 *2 *1) (AND (|isDomain| *2 (|SpadAst|)) (|isDomain| *1 (|WhileAst|))))) -((~= #1=(#2=(#3=(|Boolean|) $ $) NIL T ELT)) (|zero?| (#4=(#3# $) 59 T ELT)) (|subtractIfCan| (#5=(#6=(|Union| $ "failed") $ $) NIL T ELT)) (|sample| (#7=($) NIL T CONST)) (|recip| ((#6# $) NIL T ELT)) (|opposite?| #1#) (|one?| (#4# NIL T ELT)) (|latex| (((|String|) $) NIL T ELT)) (|hash| (((|SingleInteger|) $) NIL T ELT)) (|coerce| (((|OutputForm|) $) 82 T ELT) (($ #8=(|Integer|)) NIL T ELT) (($ |#4|) 66 T ELT) ((|#4| $) 71 T ELT) (($ |#1|) NIL #9=(|has| |#1| (|CommutativeRing|)) ELT)) (|characteristic| ((#10=(|NonNegativeInteger|)) NIL T CONST)) (|changeWeightLevel| (((|Void|) #10#) 16 T ELT)) (|before?| #1#) (|annihilate?| #1#) (|Zero| (#7# 36 T CONST)) (|One| (#7# 85 T CONST)) (= (#2# 88 T ELT)) (/ (#5# NIL (|has| |#1| (|Field|)) ELT)) (- (($ $) 90 T ELT) (#11=($ $ $) NIL T ELT)) (+ (#11# 64 T ELT)) (** (($ $ #12=(|PositiveInteger|)) NIL T ELT) (($ $ #10#) NIL T ELT)) (* (($ #12# $) NIL T ELT) (($ #10# $) NIL T ELT) (($ #8# . #13=($)) NIL T ELT) (#11# 92 T ELT) (($ |#1| . #13#) NIL #9# ELT) (($ $ |#1|) NIL #9# ELT))) +((~= #1=(#2=(#3=(|Boolean|) $ $) NIL T ELT)) (|zero?| (#4=(#3# $) 59 T ELT)) (|subtractIfCan| (((|Maybe| $) $ $) NIL T ELT)) (|sample| (#5=($) NIL T CONST)) (|recip| ((#6=(|Union| $ "failed") $) NIL T ELT)) (|opposite?| #1#) (|one?| (#4# NIL T ELT)) (|latex| (((|String|) $) NIL T ELT)) (|hash| (((|SingleInteger|) $) NIL T ELT)) (|coerce| (((|OutputForm|) $) 82 T ELT) (($ #7=(|Integer|)) NIL T ELT) (($ |#4|) 66 T ELT) ((|#4| $) 71 T ELT) (($ |#1|) NIL #8=(|has| |#1| (|CommutativeRing|)) ELT)) (|characteristic| ((#9=(|NonNegativeInteger|)) NIL T CONST)) (|changeWeightLevel| (((|Void|) #9#) 16 T ELT)) (|before?| #1#) (|annihilate?| #1#) (|Zero| (#5# 36 T CONST)) (|One| (#5# 85 T CONST)) (= (#2# 88 T ELT)) (/ ((#6# $ $) NIL (|has| |#1| (|Field|)) ELT)) (- (($ $) 90 T ELT) (#10=($ $ $) NIL T ELT)) (+ (#10# 64 T ELT)) (** (($ $ #11=(|PositiveInteger|)) NIL T ELT) (($ $ #9#) NIL T ELT)) (* (($ #11# $) NIL T ELT) (($ #9# $) NIL T ELT) (($ #7# . #12=($)) NIL T ELT) (#10# 92 T ELT) (($ |#1| . #12#) NIL #8# ELT) (($ $ |#1|) NIL #8# ELT))) (((|WeightedPolynomials| |#1| |#2| |#3| |#4| |#5| |#6| |#7|) (|Join| #1=(|Ring|) (|HomotopicTo| |#4|) (CATEGORY |domain| (IF (|has| |#1| (|CommutativeRing|)) (ATTRIBUTE (|Algebra| |#1|)) |%noBranch|) (IF (|has| |#1| (|Field|)) (SIGNATURE / ((|Union| $ "failed") $ $)) |%noBranch|) (SIGNATURE |changeWeightLevel| ((|Void|) #2=(|NonNegativeInteger|))))) #1# (|OrderedSet|) (|OrderedAbelianMonoidSup|) (|PolynomialCategory| |#1| |#3| |#2|) (|List| |#2|) (|List| #2#) #2#) (T |WeightedPolynomials|)) ((/ (*1 *1 *1 *1) (|partial| AND (|ofCategory| *2 (|Field|)) (|ofCategory| *2 #1=(|Ring|)) (|ofCategory| *3 #2=(|OrderedSet|)) (|ofCategory| *4 #3=(|OrderedAbelianMonoidSup|)) (|ofType| *6 #4=(|List| *3)) (|isDomain| *1 (|WeightedPolynomials| *2 *3 *4 *5 *6 *7 *8)) (|ofCategory| *5 (|PolynomialCategory| *2 *4 *3)) (|ofType| *7 (|List| #5=(|NonNegativeInteger|))) (|ofType| *8 #5#))) (|changeWeightLevel| (*1 *2 *3) (AND (|isDomain| *3 #5#) (|ofCategory| *4 #1#) (|ofCategory| *5 #2#) (|ofCategory| *6 #3#) (|ofType| *8 (|List| *5)) (|isDomain| *2 (|Void|)) (|isDomain| *1 (|WeightedPolynomials| *4 *5 *6 *7 *8 *9 *10)) (|ofCategory| *7 (|PolynomialCategory| *4 *6 *5)) (|ofType| *9 #4#) (|ofType| *10 *3)))) ((~= #1=(#2=(#3=(|Boolean|) $ $) NIL T ELT)) (|zeroSetSplitIntoTriangularSystems| (((|List| (|Record| (|:| |close| $) #4=(|:| |open| #5=(|List| |#4|)))) #5#) NIL T ELT)) (|zeroSetSplit| (#6=(#7=(|List| $) #5#) 95 T ELT)) (|variables| #8=(((|List| |#3|) $) NIL T ELT)) (|trivialIdeal?| #9=(#10=(#3# $) NIL T ELT)) (|triangular?| #11=(#10# NIL #12=(|has| |#1| (|IntegralDomain|)) ELT)) (|stronglyReduced?| #13=(#14=(#3# |#4| $) NIL T ELT) #9#) (|stronglyReduce| #15=(#16=(|#4| |#4| $) NIL T ELT)) (|sort| (((|Record| (|:| |under| $) (|:| |floor| $) (|:| |upper| $)) $ |#3|) NIL T ELT)) (|select| #17=(($ #18=(|Mapping| #3# |#4|) $) NIL #19=(|has| $ (|FiniteAggregate| |#4|)) ELT) ((#20=(|Union| |#4| #21="failed") $ |#3|) NIL T ELT)) (|sample| (#22=($) NIL T CONST)) (|roughUnitIdeal?| #11#) (|roughSubIdeal?| #23=(#2# NIL #12# ELT)) (|roughEqualIdeals?| #23#) (|roughBase?| #11#) (|rewriteSetWithReduction| ((#5# #5# $ #24=(|Mapping| |#4| |#4| |#4|) #25=(|Mapping| #3# |#4| |#4|)) 31 T ELT)) (|rewriteIdealWithRemainder| (#26=(#5# #5# $) 28 #12# ELT)) (|rewriteIdealWithHeadRemainder| (#26# NIL #12# ELT)) (|retractIfCan| (#27=(#28=(|Union| $ #21#) #5#) NIL T ELT)) (|retract| #29=(($ #5#) NIL T ELT)) (|rest| ((#28# $) 77 T ELT)) (|removeZero| (#16# 82 T ELT)) (|removeDuplicates| (#30=($ $) NIL #31=(AND #19# #32=(|has| |#4| (|BasicType|))) ELT)) (|remove| (($ |#4| $) NIL #31# ELT) #17#) (|remainder| (((|Record| (|:| |rnum| |#1|) (|:| |polnum| |#4|) #33=(|:| |den| |#1|)) |#4| $) NIL #12# ELT)) (|reduced?| ((#3# |#4| $ #25#) NIL T ELT)) (|reduceByQuasiMonic| #15#) (|reduce| ((|#4| #24# $ |#4| |#4|) NIL #32# ELT) ((|#4| #24# $ |#4|) NIL T ELT) ((|#4| #24# $) NIL T ELT) ((|#4| |#4| $ #24# #25#) NIL T ELT)) (|quasiComponent| (((|Record| (|:| |close| #5#) #4#) $) NIL T ELT)) (|normalized?| #13# #9#) (|mvar| ((|#3| $) 83 T ELT)) (|members| (#34=(#5# $) 32 T ELT)) (|member?| (#14# NIL #32# ELT)) (|medialSet| (#35=(#28# #5# #25# #24#) 35 T ELT) (#27# 38 T ELT)) (|map!| #36=(($ (|Mapping| |#4| |#4|) $) NIL T ELT)) (|map| #36#) (|mainVariables| #8#) (|mainVariable?| #37=((#3# |#3| $) NIL T ELT)) (|latex| (((|String|) $) NIL T ELT)) (|last| (#38=(#20# $) NIL T ELT)) (|initials| (#34# 53 T ELT)) (|initiallyReduced?| #13# #9#) (|initiallyReduce| (#16# 81 T ELT)) (|infRittWu?| (#2# 92 T ELT)) (|headRemainder| (((|Record| (|:| |num| |#4|) #33#) |#4| $) NIL #12# ELT)) (|headReduced?| #13# #9#) (|headReduce| #15#) (|hash| (((|SingleInteger|) $) NIL T ELT)) (|first| (#38# 76 T ELT)) (|find| ((#20# #18# $) NIL T ELT)) (|extendIfCan| ((#28# $ |#4|) NIL T ELT)) (|extend| (($ $ |#4|) NIL T ELT)) (|every?| #39=((#3# #18# $) NIL T ELT)) (|eval| (($ $ #5# #5#) NIL #40=(AND (|has| |#4| (|Evalable| |#4|)) (|has| |#4| (|SetCategory|))) ELT) (($ $ |#4| |#4|) NIL #40# ELT) (($ $ #41=(|Equation| |#4|)) NIL #40# ELT) (($ $ (|List| #41#)) NIL #40# ELT)) (|eq?| #1#) (|empty?| (#10# 74 T ELT)) (|empty| (#22# 45 T ELT)) (|degree| #42=(#43=(#44=(|NonNegativeInteger|) $) NIL T ELT)) (|count| ((#44# |#4| $) NIL #32# ELT) ((#44# #18# $) NIL T ELT)) (|copy| #45=(#30# NIL T ELT)) (|convert| ((#46=(|InputForm|) $) NIL (|has| |#4| (|ConvertibleTo| #46#)) ELT)) (|construct| #29#) (|collectUpper| #47=(($ $ |#3|) NIL T ELT)) (|collectUnder| #47#) (|collectQuasiMonic| #45#) (|collect| #47#) (|coerce| (((|OutputForm|) $) NIL T ELT) (#34# 62 T ELT)) (|coHeight| (#43# NIL (|has| |#3| (|Finite|)) ELT)) (|characteristicSet| (#35# 43 T ELT) (#27# 44 T ELT)) (|characteristicSerie| ((#7# #5# #25# #24#) 72 T ELT) (#6# 73 T ELT)) (|before?| #1#) (|basicSet| ((#48=(|Union| (|Record| (|:| |bas| $) (|:| |top| #5#)) #21#) #5# #25#) 27 T ELT) ((#48# #5# #18# #25#) NIL T ELT)) (|autoReduced?| ((#3# $ (|Mapping| #3# |#4| #5#)) NIL T ELT)) (|any?| #39#) (|algebraicVariables| #8#) (|algebraic?| #37#) (= #1#) (|#| #42#)) (((|WuWenTsunTriangularSet| |#1| |#2| |#3| |#4|) (|Join| (|TriangularSetCategory| |#1| |#2| |#3| |#4|) (CATEGORY |domain| (SIGNATURE |medialSet| #1=(#2=(|Union| $ "failed") #3=(|List| |#4|) #4=(|Mapping| (|Boolean|) |#4| |#4|) #5=(|Mapping| |#4| |#4| |#4|))) (SIGNATURE |medialSet| #6=(#2# #3#)) (SIGNATURE |characteristicSet| #1#) (SIGNATURE |characteristicSet| #6#) (SIGNATURE |characteristicSerie| (#7=(|List| $) #3# #4# #5#)) (SIGNATURE |characteristicSerie| (#7# #3#)))) (|IntegralDomain|) (|OrderedAbelianMonoidSup|) (|OrderedSet|) (|RecursivePolynomialCategory| |#1| |#2| |#3|)) (T |WuWenTsunTriangularSet|)) ((|medialSet| #1=(*1 *1 *2 *3 *4) #2=(|partial| AND (|isDomain| *2 (|List| *8)) (|isDomain| *3 (|Mapping| #3=(|Boolean|) *8 *8)) (|isDomain| *4 (|Mapping| *8 *8 *8)) (|ofCategory| *8 (|RecursivePolynomialCategory| *5 *6 *7)) (|ofCategory| *5 #4=(|IntegralDomain|)) (|ofCategory| *6 #5=(|OrderedAbelianMonoidSup|)) (|ofCategory| *7 #6=(|OrderedSet|)) (|isDomain| *1 (|WuWenTsunTriangularSet| *5 *6 *7 *8)))) (|medialSet| #7=(*1 *1 *2) #8=(|partial| AND (|isDomain| *2 (|List| *6)) (|ofCategory| *6 (|RecursivePolynomialCategory| *3 *4 *5)) (|ofCategory| *3 #4#) (|ofCategory| *4 #5#) (|ofCategory| *5 #6#) (|isDomain| *1 (|WuWenTsunTriangularSet| *3 *4 *5 *6)))) (|characteristicSet| #1# #2#) (|characteristicSet| #7# #8#) (|characteristicSerie| (*1 *2 *3 *4 *5) (AND (|isDomain| *3 (|List| *9)) (|isDomain| *4 (|Mapping| #3# *9 *9)) (|isDomain| *5 (|Mapping| *9 *9 *9)) (|ofCategory| *9 (|RecursivePolynomialCategory| *6 *7 *8)) (|ofCategory| *6 #4#) (|ofCategory| *7 #5#) (|ofCategory| *8 #6#) (|isDomain| *2 (|List| #9=(|WuWenTsunTriangularSet| *6 *7 *8 *9))) (|isDomain| *1 #9#))) (|characteristicSerie| (*1 *2 *3) (AND (|isDomain| *3 (|List| *7)) (|ofCategory| *7 (|RecursivePolynomialCategory| *4 *5 *6)) (|ofCategory| *4 #4#) (|ofCategory| *5 #5#) (|ofCategory| *6 #6#) (|isDomain| *2 (|List| #10=(|WuWenTsunTriangularSet| *4 *5 *6 *7))) (|isDomain| *1 #10#)))) -((~= (#1=((|Boolean|) $ $) 7 T ELT)) (|zero?| ((#2=(|Boolean|) $) 22 T ELT)) (|subtractIfCan| (((|Union| $ "failed") $ $) 26 T ELT)) (|sample| (#3=($) 23 T CONST)) (|recip| (((|Union| $ "failed") $) 42 T ELT)) (|opposite?| ((#2# $ $) 20 T ELT)) (|one?| (((|Boolean|) $) 44 T ELT)) (|latex| (((|String|) $) 11 T ELT)) (|hash| (((|SingleInteger|) $) 12 T ELT)) (|coerce| (((|OutputForm|) $) 13 T ELT) (($ (|Integer|)) 41 T ELT) (($ |#1|) 53 T ELT)) (|characteristic| (((|NonNegativeInteger|)) 40 T CONST)) (|before?| (#1# 6 T ELT)) (|annihilate?| (((|Boolean|) $ $) 33 T ELT)) (|Zero| (#3# 24 T CONST)) (|One| (($) 45 T CONST)) (= (#1# 8 T ELT)) (- (($ $) 29 T ELT) (($ $ $) 28 T ELT)) (+ (($ $ $) 18 T ELT)) (** (($ $ (|PositiveInteger|)) 35 T ELT) (($ $ (|NonNegativeInteger|)) 43 T ELT)) (* (($ (|PositiveInteger|) $) 17 T ELT) (($ (|NonNegativeInteger|) $) 21 T ELT) (($ (|Integer|) . #4=($)) 30 T ELT) (($ $ $) 34 T ELT) (($ $ |#1|) 55 T ELT) (($ |#1| . #4#) 54 T ELT))) +((~= (#1=((|Boolean|) $ $) 7 T ELT)) (|zero?| ((#2=(|Boolean|) $) 22 T ELT)) (|subtractIfCan| (((|Maybe| $) $ $) 26 T ELT)) (|sample| (#3=($) 23 T CONST)) (|recip| (((|Union| $ "failed") $) 43 T ELT)) (|opposite?| ((#2# $ $) 20 T ELT)) (|one?| (((|Boolean|) $) 45 T ELT)) (|latex| (((|String|) $) 11 T ELT)) (|hash| (((|SingleInteger|) $) 12 T ELT)) (|coerce| (((|OutputForm|) $) 13 T ELT) (($ (|Integer|)) 42 T ELT) (($ |#1|) 54 T ELT)) (|characteristic| (((|NonNegativeInteger|)) 41 T CONST)) (|before?| (#1# 6 T ELT)) (|annihilate?| (((|Boolean|) $ $) 34 T ELT)) (|Zero| (#3# 24 T CONST)) (|One| (($) 46 T CONST)) (= (#1# 8 T ELT)) (- (($ $) 30 T ELT) (($ $ $) 29 T ELT)) (+ (($ $ $) 18 T ELT)) (** (($ $ (|PositiveInteger|)) 36 T ELT) (($ $ (|NonNegativeInteger|)) 44 T ELT)) (* (($ (|PositiveInteger|) $) 17 T ELT) (($ (|NonNegativeInteger|) $) 21 T ELT) (($ (|Integer|) . #4=($)) 31 T ELT) (($ $ $) 35 T ELT) (($ $ |#1|) 56 T ELT) (($ |#1| . #4#) 55 T ELT))) (((|XAlgebra| |#1|) (|Category|) (|Ring|)) (T |XAlgebra|)) NIL (|Join| (|Ring|) (|BiModule| |t#1| |t#1|) (|CoercibleFrom| |t#1|) (CATEGORY |package| (IF (|has| |t#1| (|CommutativeRing|)) (ATTRIBUTE (|Algebra| |t#1|)) |%noBranch|))) (((|AbelianGroup|) . T) ((|AbelianMonoid|) . T) ((|AbelianSemiGroup|) . T) ((|Algebra| |#1|) |has| |#1| (|CommutativeRing|)) ((|BasicType|) . T) ((|BiModule| |#1| |#1|) . T) ((|CancellationAbelianMonoid|) . T) ((|CoercibleFrom| (|Integer|)) . T) ((|CoercibleFrom| |#1|) . T) ((|CoercibleTo| (|OutputForm|)) . T) ((|Join|) . T) ((|LeftLinearSet| (|Integer|)) . T) ((|LeftLinearSet| |#1|) . T) ((|LeftLinearSet| $) . T) ((|LeftModule| |#1|) . T) ((|LeftModule| $) . T) ((|LinearSet| |#1|) |has| |#1| (|CommutativeRing|)) ((|Module| |#1|) |has| |#1| (|CommutativeRing|)) ((|Monoid|) . T) ((|RightLinearSet| |#1|) . T) ((|RightModule| |#1|) . T) ((|Ring|) . T) ((|Rng|) . T) ((|SemiGroup|) . T) ((|SemiRing|) . T) ((|SetCategory|) . T) ((|Type|) . T)) -((~= (#1=(#2=(|Boolean|) $ $) 69 T ELT)) (|zero?| #3=(#4=(#2# $) NIL T ELT)) (|varList| (((|List| |#1|) $) 54 T ELT)) (|trunc| (#5=($ $ #6=(|NonNegativeInteger|)) 47 T ELT)) (|subtractIfCan| ((#7=(|Union| $ #8="failed") $ $) NIL T ELT)) (|sh| (#5# 25 #9=(|has| |#2| (|CommutativeRing|)) ELT) (#10=($ $ $) 26 #9# ELT)) (|sample| (#11=($) NIL T CONST)) (|rquo| (#10# 72 T ELT) (#12=($ $ #13=(|OrderedFreeMonoid| |#1|)) 58 T ELT) (#14=($ $ |#1|) 62 T ELT)) (|retractIfCan| (((|Union| #13# #8#) $) NIL T ELT)) (|retract| #15=(#16=(#13# $) NIL T ELT)) (|reductum| (#17=($ $) 40 T ELT)) (|recip| ((#7# $) NIL T ELT)) (|quasiRegular?| #3#) (|quasiRegular| #18=(#17# NIL T ELT)) (|opposite?| #19=(#1# NIL T ELT)) (|one?| #3#) (|numberOfMonomials| (#20=(#6# $) NIL T ELT)) (|monomials| (((|List| $) $) NIL T ELT)) (|monomial?| #3#) (|monom| (($ #13# |#2|) 39 T ELT)) (|mirror| (#17# 41 T ELT)) (|mindegTerm| (#21=(#22=(|Record| (|:| |k| #13#) (|:| |c| |#2|)) $) 13 T ELT)) (|mindeg| #15#) (|maxdeg| (#16# 42 T ELT)) (|map| (($ (|Mapping| |#2| |#2|) $) NIL T ELT)) (|lquo| (#10# 71 T ELT) (#12# 60 T ELT) (#14# 64 T ELT)) (|leadingTerm| (#21# NIL T ELT)) (|leadingMonomial| (#16# 36 T ELT)) (|leadingCoefficient| (#23=(|#2| $) 38 T ELT)) (|latex| (((|String|) $) NIL T ELT)) (|hash| (((|SingleInteger|) $) NIL T ELT)) (|degree| (#20# 44 T ELT)) (|constant?| (#4# 48 T ELT)) (|constant| (#23# NIL T ELT)) (|coerce| (((|OutputForm|) $) NIL T ELT) (($ #13#) 31 T ELT) (($ |#1|) 32 T ELT) (($ |#2|) NIL T ELT) (($ #24=(|Integer|)) NIL T ELT)) (|coefficients| (((|List| |#2|) $) NIL T ELT)) (|coefficient| #25=((|#2| $ #13#) NIL T ELT)) (|coef| ((|#2| $ $) 78 T ELT) #25#) (|characteristic| ((#6#) NIL T CONST)) (|before?| #19#) (|annihilate?| #19#) (|Zero| (#11# 14 T CONST)) (|One| (#11# 20 T CONST)) (|ListOfTerms| (((|List| #22#) $) NIL T ELT)) (= (#1# 45 T ELT)) (- #26=(#10# NIL T ELT) #18#) (+ (#10# 29 T ELT)) (** (#5# NIL T ELT) (($ $ #27=(|PositiveInteger|)) NIL T ELT)) (* (($ $ |#2|) 70 T ELT) (($ |#2| . #28=($)) 28 T ELT) (($ #24# . #28#) NIL T ELT) (($ #6# $) NIL T ELT) (($ #27# $) NIL T ELT) (($ |#2| #13#) NIL T ELT) (($ |#1| $) 34 T ELT) #26#)) +((~= (#1=(#2=(|Boolean|) $ $) 69 T ELT)) (|zero?| #3=(#4=(#2# $) NIL T ELT)) (|varList| (((|List| |#1|) $) 54 T ELT)) (|trunc| (#5=($ $ #6=(|NonNegativeInteger|)) 47 T ELT)) (|subtractIfCan| (((|Maybe| $) $ $) NIL T ELT)) (|sh| (#5# 25 #7=(|has| |#2| (|CommutativeRing|)) ELT) (#8=($ $ $) 26 #7# ELT)) (|sample| (#9=($) NIL T CONST)) (|rquo| (#8# 72 T ELT) (#10=($ $ #11=(|OrderedFreeMonoid| |#1|)) 58 T ELT) (#12=($ $ |#1|) 62 T ELT)) (|retractIfCan| (((|Union| #11# #13="failed") $) NIL T ELT)) (|retract| #14=(#15=(#11# $) NIL T ELT)) (|reductum| (#16=($ $) 40 T ELT)) (|recip| (((|Union| $ #13#) $) NIL T ELT)) (|quasiRegular?| #3#) (|quasiRegular| #17=(#16# NIL T ELT)) (|opposite?| #18=(#1# NIL T ELT)) (|one?| #3#) (|numberOfMonomials| (#19=(#6# $) NIL T ELT)) (|monomials| (((|List| $) $) NIL T ELT)) (|monomial?| #3#) (|monom| (($ #11# |#2|) 39 T ELT)) (|mirror| (#16# 41 T ELT)) (|mindegTerm| (#20=(#21=(|Record| (|:| |k| #11#) (|:| |c| |#2|)) $) 13 T ELT)) (|mindeg| #14#) (|maxdeg| (#15# 42 T ELT)) (|map| (($ (|Mapping| |#2| |#2|) $) NIL T ELT)) (|lquo| (#8# 71 T ELT) (#10# 60 T ELT) (#12# 64 T ELT)) (|leadingTerm| (#20# NIL T ELT)) (|leadingMonomial| (#15# 36 T ELT)) (|leadingCoefficient| (#22=(|#2| $) 38 T ELT)) (|latex| (((|String|) $) NIL T ELT)) (|hash| (((|SingleInteger|) $) NIL T ELT)) (|degree| (#19# 44 T ELT)) (|constant?| (#4# 48 T ELT)) (|constant| (#22# NIL T ELT)) (|coerce| (((|OutputForm|) $) NIL T ELT) (($ #11#) 31 T ELT) (($ |#1|) 32 T ELT) (($ |#2|) NIL T ELT) (($ #23=(|Integer|)) NIL T ELT)) (|coefficients| (((|List| |#2|) $) NIL T ELT)) (|coefficient| #24=((|#2| $ #11#) NIL T ELT)) (|coef| ((|#2| $ $) 78 T ELT) #24#) (|characteristic| ((#6#) NIL T CONST)) (|before?| #18#) (|annihilate?| #18#) (|Zero| (#9# 14 T CONST)) (|One| (#9# 20 T CONST)) (|ListOfTerms| (((|List| #21#) $) NIL T ELT)) (= (#1# 45 T ELT)) (- #25=(#8# NIL T ELT) #17#) (+ (#8# 29 T ELT)) (** (#5# NIL T ELT) (($ $ #26=(|PositiveInteger|)) NIL T ELT)) (* (($ $ |#2|) 70 T ELT) (($ |#2| . #27=($)) 28 T ELT) (($ #23# . #27#) NIL T ELT) (($ #6# $) NIL T ELT) (($ #26# $) NIL T ELT) (($ |#2| #11#) NIL T ELT) (($ |#1| $) 34 T ELT) #25#)) (((|XDistributedPolynomial| |#1| |#2|) (|Join| (|FreeModuleCat| |#2| (|OrderedFreeMonoid| |#1|)) (|XPolynomialsCat| |#1| |#2|)) (|OrderedSet|) (|Ring|)) (T |XDistributedPolynomial|)) NIL ((|log| (#1=(|#3| |#3| #2=(|NonNegativeInteger|)) 28 T ELT)) (|exp| (#1# 34 T ELT)) (|Hausdorff| ((|#3| |#3| |#3| #2#) 35 T ELT))) @@ -4008,31 +4008,31 @@ NIL ((|transcendent?| (#1=((|Boolean|) $) 15 T ELT)) (|algebraic?| (#1# 14 T ELT)) (|Frobenius| (($ $) 19 T ELT) (($ $ (|NonNegativeInteger|)) 21 T ELT))) (((|ExtensionField&| |#1| |#2|) (CATEGORY |package| (SIGNATURE |Frobenius| (|#1| |#1| (|NonNegativeInteger|))) (SIGNATURE |Frobenius| (|#1| |#1|)) (SIGNATURE |transcendent?| #1=((|Boolean|) |#1|)) (SIGNATURE |algebraic?| #1#)) (|ExtensionField| |#2|) (|Field|)) (T |ExtensionField&|)) NIL -((~= (#1=((|Boolean|) $ $) 7 T ELT)) (|zero?| ((#2=(|Boolean|) $) 22 T ELT)) (|unitNormal| (((|Record| (|:| |unit| $) (|:| |canonical| $) (|:| |associate| $)) $) 55 T ELT)) (|unitCanonical| (($ $) 54 T ELT)) (|unit?| ((#3=(|Boolean|) $) 52 T ELT)) (|transcendent?| (((|Boolean|) $) 114 T ELT)) (|transcendenceDegree| (((|NonNegativeInteger|)) 110 T ELT)) (|subtractIfCan| (((|Union| $ "failed") $ $) 26 T ELT)) (|squareFreePart| (($ $) 91 T ELT)) (|squareFree| (#4=((|Factored| $) $) 90 T ELT)) (|sizeLess?| (((|Boolean|) $ $) 75 T ELT)) (|sample| (#5=($) 23 T CONST)) (|retractIfCan| (((|Union| |#1| "failed") $) 121 T ELT)) (|retract| ((|#1| $) 122 T ELT)) (|rem| (#6=($ $ $) 71 T ELT)) (|recip| (((|Union| $ "failed") $) 42 T ELT)) (|quo| (#6# 72 T ELT)) (|principalIdeal| (((|Record| (|:| |coef| #7=(|List| $)) (|:| |generator| $)) #7#) 66 T ELT)) (|primeFrobenius| (($ $ #8=(|NonNegativeInteger|)) 107 (OR (|has| |#1| . #9=((|CharacteristicNonZero|))) (|has| |#1| . #10=((|Finite|)))) ELT) (($ $) 106 (OR (|has| |#1| . #9#) (|has| |#1| . #10#)) ELT)) (|prime?| (((|Boolean|) $) 89 T ELT)) (|order| (((|OnePointCompletion| (|PositiveInteger|)) $) 104 (OR (|has| |#1| . #9#) (|has| |#1| . #10#)) ELT)) (|opposite?| ((#2# $ $) 20 T ELT)) (|one?| (((|Boolean|) $) 44 T ELT)) (|multiEuclidean| (((|Union| #11=(|List| $) #12="failed") #11# $) 68 T ELT)) (|lcm| (#13=($ $ $) 60 T ELT) (#14=($ (|List| $)) 59 T ELT)) (|latex| (((|String|) $) 11 T ELT)) (|inv| (($ $) 88 T ELT)) (|inGroundField?| (((|Boolean|) $) 113 T ELT)) (|hash| (((|SingleInteger|) $) 12 T ELT)) (|gcdPolynomial| ((#15=(|SparseUnivariatePolynomial| $) #15# #15#) 58 T ELT)) (|gcd| (#13# 62 T ELT) (#14# 61 T ELT)) (|factor| (#4# 92 T ELT)) (|extensionDegree| (((|OnePointCompletion| (|PositiveInteger|))) 111 T ELT)) (|extendedEuclidean| (((|Record| #16=(|:| |coef1| $) #17=(|:| |coef2| $) (|:| |generator| $)) $ $) 70 T ELT) (((|Union| (|Record| #16# #17#) #12#) $ $ $) 69 T ELT)) (|exquo| (((|Union| $ "failed") $ $) 56 T ELT)) (|expressIdealMember| (((|Maybe| #7#) #7# $) 65 T ELT)) (|euclideanSize| (((|NonNegativeInteger|) $) 74 T ELT)) (|divide| (((|Record| (|:| |quotient| $) (|:| |remainder| $)) $ $) 73 T ELT)) (|discreteLog| (((|Union| #8# "failed") $ $) 105 (OR (|has| |#1| . #9#) (|has| |#1| . #10#)) ELT)) (|dimension| (((|CardinalNumber|)) 119 T ELT)) (|degree| (((|OnePointCompletion| (|PositiveInteger|)) $) 112 T ELT)) (|coerce| (((|OutputForm|) $) 13 T ELT) (($ (|Integer|)) 41 T ELT) (($ $) 57 T ELT) (($ #18=(|Fraction| #19=(|Integer|))) 84 T ELT) (($ |#1|) 120 T ELT)) (|charthRoot| (((|Maybe| $) $) 103 (OR (|has| |#1| . #9#) (|has| |#1| . #10#)) ELT)) (|characteristic| (((|NonNegativeInteger|)) 40 T CONST)) (|before?| (#1# 6 T ELT)) (|associates?| ((#3# $ $) 53 T ELT)) (|annihilate?| (((|Boolean|) $ $) 33 T ELT)) (|algebraic?| (((|Boolean|) $) 115 T ELT)) (|Zero| (#5# 24 T CONST)) (|One| (($) 45 T CONST)) (|Frobenius| (($ $) 109 (|has| |#1| (|Finite|)) ELT) (($ $ (|NonNegativeInteger|)) 108 (|has| |#1| (|Finite|)) ELT)) (= (#1# 8 T ELT)) (/ (($ $ $) 83 T ELT) (($ $ |#1|) 118 T ELT)) (- (($ $) 29 T ELT) (($ $ $) 28 T ELT)) (+ (($ $ $) 18 T ELT)) (** (($ $ (|PositiveInteger|)) 35 T ELT) (($ $ (|NonNegativeInteger|)) 43 T ELT) (($ $ #19#) 87 T ELT)) (* (($ (|PositiveInteger|) $) 17 T ELT) (($ (|NonNegativeInteger|) $) 21 T ELT) (($ (|Integer|) . #20=($)) 30 T ELT) (($ $ $) 34 T ELT) (($ $ #18#) 86 T ELT) (($ #18# . #20#) 85 T ELT) (($ $ |#1|) 117 T ELT) (($ |#1| . #20#) 116 T ELT))) +((~= (#1=((|Boolean|) $ $) 7 T ELT)) (|zero?| ((#2=(|Boolean|) $) 22 T ELT)) (|unitNormal| (((|Record| (|:| |unit| $) (|:| |canonical| $) (|:| |associate| $)) $) 56 T ELT)) (|unitCanonical| (($ $) 55 T ELT)) (|unit?| ((#3=(|Boolean|) $) 53 T ELT)) (|transcendent?| (((|Boolean|) $) 115 T ELT)) (|transcendenceDegree| (((|NonNegativeInteger|)) 111 T ELT)) (|subtractIfCan| (((|Maybe| $) $ $) 26 T ELT)) (|squareFreePart| (($ $) 92 T ELT)) (|squareFree| (#4=((|Factored| $) $) 91 T ELT)) (|sizeLess?| (((|Boolean|) $ $) 76 T ELT)) (|sample| (#5=($) 23 T CONST)) (|retractIfCan| (((|Union| |#1| "failed") $) 122 T ELT)) (|retract| ((|#1| $) 123 T ELT)) (|rem| (#6=($ $ $) 72 T ELT)) (|recip| (((|Union| $ "failed") $) 43 T ELT)) (|quo| (#6# 73 T ELT)) (|principalIdeal| (((|Record| (|:| |coef| #7=(|List| $)) (|:| |generator| $)) #7#) 67 T ELT)) (|primeFrobenius| (($ $ #8=(|NonNegativeInteger|)) 108 (OR (|has| |#1| . #9=((|CharacteristicNonZero|))) (|has| |#1| . #10=((|Finite|)))) ELT) (($ $) 107 (OR (|has| |#1| . #9#) (|has| |#1| . #10#)) ELT)) (|prime?| (((|Boolean|) $) 90 T ELT)) (|order| (((|OnePointCompletion| (|PositiveInteger|)) $) 105 (OR (|has| |#1| . #9#) (|has| |#1| . #10#)) ELT)) (|opposite?| ((#2# $ $) 20 T ELT)) (|one?| (((|Boolean|) $) 45 T ELT)) (|multiEuclidean| (((|Union| #11=(|List| $) #12="failed") #11# $) 69 T ELT)) (|lcm| (#13=($ $ $) 61 T ELT) (#14=($ (|List| $)) 60 T ELT)) (|latex| (((|String|) $) 11 T ELT)) (|inv| (($ $) 89 T ELT)) (|inGroundField?| (((|Boolean|) $) 114 T ELT)) (|hash| (((|SingleInteger|) $) 12 T ELT)) (|gcdPolynomial| ((#15=(|SparseUnivariatePolynomial| $) #15# #15#) 59 T ELT)) (|gcd| (#13# 63 T ELT) (#14# 62 T ELT)) (|factor| (#4# 93 T ELT)) (|extensionDegree| (((|OnePointCompletion| (|PositiveInteger|))) 112 T ELT)) (|extendedEuclidean| (((|Record| #16=(|:| |coef1| $) #17=(|:| |coef2| $) (|:| |generator| $)) $ $) 71 T ELT) (((|Union| (|Record| #16# #17#) #12#) $ $ $) 70 T ELT)) (|exquo| (((|Union| $ "failed") $ $) 57 T ELT)) (|expressIdealMember| (((|Maybe| #7#) #7# $) 66 T ELT)) (|euclideanSize| (((|NonNegativeInteger|) $) 75 T ELT)) (|divide| (((|Record| (|:| |quotient| $) (|:| |remainder| $)) $ $) 74 T ELT)) (|discreteLog| (((|Union| #8# "failed") $ $) 106 (OR (|has| |#1| . #9#) (|has| |#1| . #10#)) ELT)) (|dimension| (((|CardinalNumber|)) 120 T ELT)) (|degree| (((|OnePointCompletion| (|PositiveInteger|)) $) 113 T ELT)) (|coerce| (((|OutputForm|) $) 13 T ELT) (($ (|Integer|)) 42 T ELT) (($ $) 58 T ELT) (($ #18=(|Fraction| #19=(|Integer|))) 85 T ELT) (($ |#1|) 121 T ELT)) (|charthRoot| (((|Maybe| $) $) 104 (OR (|has| |#1| . #9#) (|has| |#1| . #10#)) ELT)) (|characteristic| (((|NonNegativeInteger|)) 41 T CONST)) (|before?| (#1# 6 T ELT)) (|associates?| ((#3# $ $) 54 T ELT)) (|annihilate?| (((|Boolean|) $ $) 34 T ELT)) (|algebraic?| (((|Boolean|) $) 116 T ELT)) (|Zero| (#5# 24 T CONST)) (|One| (($) 46 T CONST)) (|Frobenius| (($ $) 110 (|has| |#1| (|Finite|)) ELT) (($ $ (|NonNegativeInteger|)) 109 (|has| |#1| (|Finite|)) ELT)) (= (#1# 8 T ELT)) (/ (($ $ $) 84 T ELT) (($ $ |#1|) 119 T ELT)) (- (($ $) 30 T ELT) (($ $ $) 29 T ELT)) (+ (($ $ $) 18 T ELT)) (** (($ $ (|PositiveInteger|)) 36 T ELT) (($ $ (|NonNegativeInteger|)) 44 T ELT) (($ $ #19#) 88 T ELT)) (* (($ (|PositiveInteger|) $) 17 T ELT) (($ (|NonNegativeInteger|) $) 21 T ELT) (($ (|Integer|) . #20=($)) 31 T ELT) (($ $ $) 35 T ELT) (($ $ #18#) 87 T ELT) (($ #18# . #20#) 86 T ELT) (($ $ |#1|) 118 T ELT) (($ |#1| . #20#) 117 T ELT))) (((|ExtensionField| |#1|) (|Category|) (|Field|)) (T |ExtensionField|)) ((|algebraic?| (*1 *2 *1) (AND (|ofCategory| *1 (|ExtensionField| *3)) (|ofCategory| *3 (|Field|)) (|isDomain| *2 (|Boolean|)))) (|transcendent?| (*1 *2 *1) (AND (|ofCategory| *1 (|ExtensionField| *3)) (|ofCategory| *3 (|Field|)) (|isDomain| *2 (|Boolean|)))) (|inGroundField?| (*1 *2 *1) (AND (|ofCategory| *1 (|ExtensionField| *3)) (|ofCategory| *3 (|Field|)) (|isDomain| *2 (|Boolean|)))) (|degree| (*1 *2 *1) (AND (|ofCategory| *1 (|ExtensionField| *3)) (|ofCategory| *3 (|Field|)) (|isDomain| *2 (|OnePointCompletion| (|PositiveInteger|))))) (|extensionDegree| (*1 *2) (AND (|ofCategory| *1 (|ExtensionField| *3)) (|ofCategory| *3 (|Field|)) (|isDomain| *2 (|OnePointCompletion| (|PositiveInteger|))))) (|transcendenceDegree| (*1 *2) (AND (|ofCategory| *1 (|ExtensionField| *3)) (|ofCategory| *3 (|Field|)) (|isDomain| *2 (|NonNegativeInteger|)))) (|Frobenius| (*1 *1 *1) (AND (|ofCategory| *1 (|ExtensionField| *2)) (|ofCategory| *2 (|Field|)) (|ofCategory| *2 (|Finite|)))) (|Frobenius| (*1 *1 *1 *2) (AND (|isDomain| *2 (|NonNegativeInteger|)) (|ofCategory| *1 (|ExtensionField| *3)) (|ofCategory| *3 (|Field|)) (|ofCategory| *3 (|Finite|))))) (|Join| (|Field|) (|RetractableTo| |t#1|) (|VectorSpace| |t#1|) (CATEGORY |domain| (IF (|has| |t#1| (|CharacteristicZero|)) (ATTRIBUTE (|CharacteristicZero|)) |%noBranch|) (IF (|has| |t#1| (|CharacteristicNonZero|)) (ATTRIBUTE (|FieldOfPrimeCharacteristic|)) |%noBranch|) (SIGNATURE |algebraic?| ((|Boolean|) $)) (SIGNATURE |transcendent?| ((|Boolean|) $)) (SIGNATURE |inGroundField?| ((|Boolean|) $)) (SIGNATURE |degree| ((|OnePointCompletion| (|PositiveInteger|)) $)) (SIGNATURE |extensionDegree| ((|OnePointCompletion| (|PositiveInteger|)))) (SIGNATURE |transcendenceDegree| ((|NonNegativeInteger|))) (IF (|has| |t#1| (|Finite|)) (PROGN (ATTRIBUTE (|FieldOfPrimeCharacteristic|)) (SIGNATURE |Frobenius| ($ $)) (SIGNATURE |Frobenius| ($ $ (|NonNegativeInteger|)))) |%noBranch|))) (((|AbelianGroup|) . T) ((|AbelianMonoid|) . T) ((|AbelianSemiGroup|) . T) ((|Algebra| #1=(|Fraction| (|Integer|))) . T) ((|Algebra| $) . T) ((|BasicType|) . T) ((|BiModule| #1# #1#) . T) ((|BiModule| |#1| |#1|) . T) ((|BiModule| $ $) . T) ((|CancellationAbelianMonoid|) . T) ((|CharacteristicNonZero|) OR (|has| |#1| (|Finite|)) (|has| |#1| (|CharacteristicNonZero|))) ((|CharacteristicZero|) |has| |#1| (|CharacteristicZero|)) ((|CoercibleFrom| #1#) . T) ((|CoercibleFrom| (|Integer|)) . T) ((|CoercibleFrom| |#1|) . T) ((|CoercibleFrom| $) . T) ((|CoercibleTo| (|OutputForm|)) . T) ((|CommutativeRing|) . T) ((|DivisionRing|) . T) ((|EntireRing|) . T) ((|EuclideanDomain|) . T) ((|Field|) . T) ((|FieldOfPrimeCharacteristic|) OR (|has| |#1| (|Finite|)) (|has| |#1| (|CharacteristicNonZero|))) ((|GcdDomain|) . T) ((|IntegralDomain|) . T) ((|Join|) . T) ((|LeftLinearSet| #1#) . T) ((|LeftLinearSet| (|Integer|)) . T) ((|LeftLinearSet| |#1|) . T) ((|LeftLinearSet| $) . T) ((|LeftModule| #1#) . T) ((|LeftModule| |#1|) . T) ((|LeftModule| $) . T) ((|LinearSet| #1#) . T) ((|LinearSet| |#1|) . T) ((|LinearSet| $) . T) ((|Module| #1#) . T) ((|Module| |#1|) . T) ((|Module| $) . T) ((|Monoid|) . T) ((|PrincipalIdealDomain|) . T) ((|RetractableTo| |#1|) . T) ((|RightLinearSet| #1#) . T) ((|RightLinearSet| |#1|) . T) ((|RightLinearSet| $) . T) ((|RightModule| #1#) . T) ((|RightModule| |#1|) . T) ((|RightModule| $) . T) ((|Ring|) . T) ((|Rng|) . T) ((|SemiGroup|) . T) ((|SemiRing|) . T) ((|SetCategory|) . T) ((|Type|) . T) ((|UniqueFactorizationDomain|) . T) ((|VectorSpace| |#1|) . T)) -((~= (#1=((|Boolean|) $ $) 7 T ELT)) (|zero?| ((#2=(|Boolean|) $) 22 T ELT)) (|varList| (((|List| |#1|) $) 56 T ELT)) (|subtractIfCan| (((|Union| $ "failed") $ $) 26 T ELT)) (|sh| (($ $ $) 58 (|has| |#2| (|CommutativeRing|)) ELT) (($ $ (|NonNegativeInteger|)) 57 (|has| |#2| (|CommutativeRing|)) ELT)) (|sample| (#3=($) 23 T CONST)) (|rquo| (($ $ |#1|) 69 T ELT) (($ $ (|OrderedFreeMonoid| |#1|)) 68 T ELT) (($ $ $) 67 T ELT)) (|retractIfCan| (((|Union| (|OrderedFreeMonoid| |#1|) "failed") $) 79 T ELT)) (|retract| (((|OrderedFreeMonoid| |#1|) $) 80 T ELT)) (|recip| (((|Union| $ "failed") $) 42 T ELT)) (|quasiRegular?| (((|Boolean|) $) 60 T ELT)) (|quasiRegular| (($ $) 59 T ELT)) (|opposite?| ((#2# $ $) 20 T ELT)) (|one?| (((|Boolean|) $) 44 T ELT)) (|monomial?| (((|Boolean|) $) 65 T ELT)) (|monom| (($ (|OrderedFreeMonoid| |#1|) |#2|) 66 T ELT)) (|mirror| (($ $) 64 T ELT)) (|mindegTerm| (((|Record| (|:| |k| (|OrderedFreeMonoid| |#1|)) (|:| |c| |#2|)) $) 75 T ELT)) (|mindeg| 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(((|OutputForm|) $) 66 T ELT) (($ #17=(|Integer|)) 47 T ELT) (($ |#1|) 42 T ELT) (($ |#2|) NIL T ELT)) (|coefficients| (((|List| |#1|) $) NIL T ELT)) (|coefficient| (#18=(|#1| $ |#2|) NIL T ELT)) (|coef| (#18# 29 T ELT)) (|characteristic| ((#14#) 14 T CONST)) (|before?| #1#) (|annihilate?| #1#) (|Zero| (#8# 30 T CONST)) (|One| (#8# 11 T CONST)) (|ListOfTerms| (((|List| #15#) $) NIL T ELT)) (= (#2# 31 T ELT)) (/ (#19=($ $ |#1|) 68 (|has| |#1| (|Field|)) ELT)) (- #11# (#20=($ $ $) NIL T ELT)) (+ (#20# 51 T ELT)) (** (($ $ #21=(|PositiveInteger|)) NIL T ELT) (($ $ #14#) 53 T ELT)) (* (($ #21# $) NIL T ELT) (($ #14# $) NIL T ELT) (($ #17# . #22=($)) NIL T ELT) (#20# 52 T ELT) (($ |#1| . #22#) 48 T ELT) (#19# NIL T ELT) (($ |#1| |#2|) NIL T ELT)) (|#| (#13# 18 T ELT))) -(((|XPolynomialRing| |#1| |#2|) (|Join| #1=(|Ring|) (|XAlgebra| |#1|) (|FreeModuleCat| |#1| |#2|) (|CoercibleFrom| |#2|) (|Functorial| |#1|) (CATEGORY |domain| (SIGNATURE * #2=($ $ |#1|)) (SIGNATURE |#| ((|NonNegativeInteger|) $)) (SIGNATURE |maxdeg| #3=(|#2| $)) (SIGNATURE |mindeg| #3#) (SIGNATURE |reductum| #4=($ $)) (SIGNATURE |coef| (|#1| $ |#2|)) (SIGNATURE |constant?| #5=((|Boolean|) $)) (SIGNATURE |constant| (|#1| $)) (SIGNATURE |quasiRegular?| #5#) (SIGNATURE |quasiRegular| #4#) (IF (|has| |#1| (|Field|)) (SIGNATURE / #2#) |%noBranch|) (IF (|has| |#1| #6=(ATTRIBUTE |noZeroDivisors|)) #6# |%noBranch|) (IF (|has| |#1| #7=(ATTRIBUTE |unitsKnown|)) #7# |%noBranch|) (IF (|has| |#1| #8=(ATTRIBUTE |canonicalUnitNormal|)) #8# |%noBranch|))) #1# (|OrderedMonoid|)) (T |XPolynomialRing|)) +((~= #1=(#2=(#3=(|Boolean|) $ $) NIL T ELT)) (|zero?| #4=(#5=(#3# $) NIL T ELT)) (|subtractIfCan| (((|Maybe| $) $ $) NIL T ELT)) (|sample| (#6=($) NIL T CONST)) (|retractIfCan| (((|Union| |#2| #7="failed") $) NIL T ELT)) (|retract| #8=(#9=(|#2| $) NIL T ELT)) (|reductum| #10=(#11=($ $) NIL T ELT)) (|recip| (((|Union| $ #7#) $) 43 T ELT)) (|quasiRegular?| (#5# 37 T ELT)) (|quasiRegular| (#11# 38 T ELT)) (|opposite?| #1#) (|one?| #4#) (|numberOfMonomials| (#12=(#13=(|NonNegativeInteger|) $) NIL T ELT)) (|monomials| (((|List| $) $) NIL T ELT)) (|monomial?| #4#) (|monom| (($ |#2| |#1|) NIL T ELT)) (|mindeg| (#9# 25 T ELT)) (|maxdeg| (#9# 23 T ELT)) (|map| (($ (|Mapping| |#1| |#1|) $) NIL T ELT)) (|leadingTerm| ((#14=(|Record| (|:| |k| |#2|) (|:| |c| |#1|)) $) NIL T ELT)) (|leadingMonomial| #8#) (|leadingCoefficient| (#15=(|#1| $) NIL T ELT)) (|latex| (((|String|) $) NIL T ELT)) (|hash| (((|SingleInteger|) $) NIL T ELT)) (|constant?| (#5# 33 T ELT)) (|constant| (#15# 34 T ELT)) (|coerce| (((|OutputForm|) $) 66 T ELT) (($ #16=(|Integer|)) 47 T ELT) (($ |#1|) 42 T ELT) (($ |#2|) NIL T ELT)) (|coefficients| (((|List| |#1|) $) NIL T ELT)) (|coefficient| (#17=(|#1| $ |#2|) NIL T ELT)) (|coef| (#17# 29 T ELT)) (|characteristic| ((#13#) 14 T CONST)) (|before?| #1#) (|annihilate?| #1#) (|Zero| (#6# 30 T CONST)) (|One| (#6# 11 T CONST)) (|ListOfTerms| (((|List| #14#) $) NIL T ELT)) (= (#2# 31 T ELT)) (/ (#18=($ $ |#1|) 68 (|has| |#1| (|Field|)) ELT)) (- #10# (#19=($ $ $) NIL T ELT)) (+ (#19# 51 T ELT)) (** (($ $ #20=(|PositiveInteger|)) NIL T ELT) (($ $ #13#) 53 T ELT)) (* (($ #20# $) NIL T ELT) (($ #13# $) NIL T ELT) (($ #16# . #21=($)) NIL T ELT) (#19# 52 T ELT) (($ |#1| . #21#) 48 T ELT) (#18# NIL T ELT) (($ |#1| |#2|) NIL T ELT)) (|#| (#12# 18 T ELT))) +(((|XPolynomialRing| |#1| |#2|) (|Join| #1=(|Ring|) (|XAlgebra| |#1|) (|FreeModuleCat| |#1| |#2|) (|CoercibleFrom| |#2|) (|Functorial| |#1|) (CATEGORY |domain| (SIGNATURE * #2=($ $ |#1|)) (SIGNATURE |#| ((|NonNegativeInteger|) $)) (SIGNATURE |maxdeg| #3=(|#2| $)) (SIGNATURE |mindeg| #3#) (SIGNATURE |reductum| #4=($ $)) (SIGNATURE |coef| (|#1| $ |#2|)) (SIGNATURE |constant?| #5=((|Boolean|) $)) (SIGNATURE |constant| (|#1| $)) (SIGNATURE |quasiRegular?| #5#) (SIGNATURE |quasiRegular| #4#) (IF (|has| |#1| (|Field|)) (SIGNATURE / #2#) |%noBranch|) (IF (|has| |#1| #6=(ATTRIBUTE |noZeroDivisors|)) #6# |%noBranch|) (IF (|has| |#1| #7=(ATTRIBUTE |canonicalUnitNormal|)) #7# |%noBranch|))) #1# (|OrderedMonoid|)) (T |XPolynomialRing|)) ((* #1=(*1 *1 *1 *2) #2=(AND #3=(|isDomain| *1 (|XPolynomialRing| *2 *3)) #4=(|ofCategory| *2 #5=(|Ring|)) #6=(|ofCategory| *3 #7=(|OrderedMonoid|)))) (|reductum| #8=(*1 *1 *1) #2#) (|#| #9=(*1 *2 *1) (AND (|isDomain| *2 (|NonNegativeInteger|)) #10=(|isDomain| *1 (|XPolynomialRing| *3 *4)) #11=(|ofCategory| *3 #5#) #12=(|ofCategory| *4 #7#))) (|maxdeg| #9# #13=(AND (|ofCategory| *2 #7#) (|isDomain| *1 (|XPolynomialRing| *3 *2)) #11#)) (|mindeg| #9# #13#) (|coef| (*1 *2 *1 *3) #14=(AND #4# #3# #6#)) (|constant?| #9# #15=(AND (|isDomain| *2 (|Boolean|)) #10# #11# #12#)) (|constant| #9# #14#) (|quasiRegular?| #9# #15#) (|quasiRegular| #8# #2#) (/ #1# (AND #3# (|ofCategory| *2 (|Field|)) #4# #6#))) -((~= (#1=(#2=(|Boolean|) $ $) 27 T ELT)) (|zero?| #3=(#4=(#2# $) NIL T ELT)) (|varList| (((|List| |#1|) $) 132 T ELT)) (|unexpand| (($ #5=(|XDistributedPolynomial| |#1| |#2|)) 50 T ELT)) (|trunc| (#6=($ $ #7=(|NonNegativeInteger|)) 38 T ELT)) (|subtractIfCan| ((#8=(|Union| $ #9="failed") $ $) NIL T ELT)) (|sh| (#10=($ $ $) 54 #11=(|has| |#2| (|CommutativeRing|)) ELT) (#6# 52 #11# ELT)) (|sample| (#12=($) NIL T CONST)) (|rquo| (#13=($ $ |#1|) 114 T ELT) (#14=($ $ #15=(|OrderedFreeMonoid| |#1|)) 115 T ELT) (#10# 26 T ELT)) (|retractIfCan| (((|Union| #15# #9#) $) NIL T ELT)) (|retract| (#16=(#15# $) NIL T ELT)) (|recip| ((#8# $) 122 T ELT)) (|quasiRegular?| (#4# 117 T ELT)) (|quasiRegular| (#17=($ $) 118 T ELT)) (|opposite?| #18=(#1# NIL T ELT)) (|one?| #3#) (|monomial?| #3#) (|monom| (($ #15# |#2|) 20 T ELT)) (|mirror| (#17# NIL T ELT)) (|mindegTerm| (((|Record| (|:| |k| #15#) (|:| |c| |#2|)) $) NIL T ELT)) (|mindeg| (#16# 123 T ELT)) (|maxdeg| (#16# 126 T ELT)) (|map| (($ (|Mapping| |#2| |#2|) $) 131 T ELT)) (|lquo| (#13# 112 T ELT) (#14# 113 T ELT) (#10# 62 T ELT)) (|latex| (((|String|) $) NIL T ELT)) (|hash| (((|SingleInteger|) $) NIL T ELT)) (|expand| ((#5# $) 94 T ELT)) (|degree| ((#7# $) 129 T ELT)) (|constant?| (#4# 81 T ELT)) (|constant| ((|#2| $) 32 T ELT)) (|coerce| (((|OutputForm|) $) 73 T ELT) (($ #19=(|Integer|)) 87 T ELT) (($ |#2|) 85 T ELT) (($ #15#) 18 T ELT) (($ |#1|) 84 T ELT)) (|coef| ((|#2| $ #15#) 116 T ELT) ((|#2| $ $) 28 T ELT)) (|characteristic| ((#7#) 120 T CONST)) (|before?| #18#) (|annihilate?| #18#) (|Zero| (#12# 15 T CONST)) (|RemainderList| (((|List| (|Record| (|:| |k| |#1|) (|:| |c| $))) $) 59 T ELT)) (|One| (#12# 33 T CONST)) (= (#1# 14 T ELT)) (- (#17# 98 T ELT) (#10# 101 T ELT)) (+ (#10# 61 T ELT)) (** (($ $ #20=(|PositiveInteger|)) NIL T ELT) (#6# 55 T ELT)) (* (($ #20# $) NIL T ELT) (($ #7# $) 53 T ELT) (($ #19# $) 106 T ELT) (#10# 22 T ELT) (($ |#2| $) 19 T ELT) (($ $ |#2|) 21 T ELT) (($ |#1| $) 92 T ELT))) +((~= (#1=(#2=(|Boolean|) $ $) 27 T ELT)) (|zero?| #3=(#4=(#2# $) NIL T ELT)) (|varList| (((|List| |#1|) $) 132 T ELT)) (|unexpand| (($ #5=(|XDistributedPolynomial| |#1| |#2|)) 50 T ELT)) (|trunc| (#6=($ $ #7=(|NonNegativeInteger|)) 38 T ELT)) (|subtractIfCan| (((|Maybe| $) $ $) NIL T ELT)) (|sh| (#8=($ $ $) 54 #9=(|has| |#2| (|CommutativeRing|)) ELT) (#6# 52 #9# ELT)) (|sample| (#10=($) NIL T CONST)) (|rquo| (#11=($ $ |#1|) 114 T ELT) (#12=($ $ #13=(|OrderedFreeMonoid| |#1|)) 115 T ELT) (#8# 26 T ELT)) (|retractIfCan| (((|Union| #13# #14="failed") $) NIL T ELT)) (|retract| (#15=(#13# $) NIL T ELT)) (|recip| (((|Union| $ #14#) $) 122 T ELT)) (|quasiRegular?| (#4# 117 T ELT)) (|quasiRegular| (#16=($ $) 118 T ELT)) (|opposite?| #17=(#1# NIL T ELT)) (|one?| #3#) (|monomial?| #3#) (|monom| (($ #13# |#2|) 20 T ELT)) (|mirror| (#16# NIL T ELT)) (|mindegTerm| (((|Record| (|:| |k| #13#) (|:| |c| |#2|)) $) NIL T ELT)) (|mindeg| (#15# 123 T ELT)) (|maxdeg| (#15# 126 T ELT)) (|map| (($ (|Mapping| |#2| |#2|) $) 131 T ELT)) (|lquo| (#11# 112 T ELT) (#12# 113 T ELT) (#8# 62 T ELT)) (|latex| (((|String|) $) NIL T ELT)) (|hash| (((|SingleInteger|) $) NIL T ELT)) (|expand| ((#5# $) 94 T ELT)) (|degree| ((#7# $) 129 T ELT)) (|constant?| (#4# 81 T ELT)) (|constant| ((|#2| $) 32 T ELT)) (|coerce| (((|OutputForm|) $) 73 T ELT) (($ #18=(|Integer|)) 87 T ELT) (($ |#2|) 85 T ELT) (($ #13#) 18 T ELT) (($ |#1|) 84 T ELT)) (|coef| ((|#2| $ #13#) 116 T ELT) ((|#2| $ $) 28 T ELT)) (|characteristic| ((#7#) 120 T CONST)) (|before?| #17#) (|annihilate?| #17#) (|Zero| (#10# 15 T CONST)) (|RemainderList| (((|List| (|Record| (|:| |k| |#1|) (|:| |c| $))) $) 59 T ELT)) (|One| (#10# 33 T CONST)) (= (#1# 14 T ELT)) (- (#16# 98 T ELT) (#8# 101 T ELT)) (+ (#8# 61 T ELT)) (** (($ $ #19=(|PositiveInteger|)) NIL T ELT) (#6# 55 T ELT)) (* (($ #19# $) NIL T ELT) (($ #7# $) 53 T ELT) (($ #18# $) 106 T ELT) (#8# 22 T ELT) (($ |#2| $) 19 T ELT) (($ $ |#2|) 21 T ELT) (($ |#1| $) 92 T ELT))) (((|XRecursivePolynomial| |#1| |#2|) (|Join| (|XPolynomialsCat| |#1| |#2|) (CATEGORY |domain| (SIGNATURE |expand| (#1=(|XDistributedPolynomial| |#1| |#2|) $)) (SIGNATURE |unexpand| ($ #1#)) (SIGNATURE |RemainderList| ((|List| (|Record| (|:| |k| |#1|) (|:| |c| $))) $)))) (|OrderedSet|) (|Ring|)) (T |XRecursivePolynomial|)) ((|expand| #1=(*1 *2 *1) (AND #2=(|isDomain| *2 (|XDistributedPolynomial| *3 *4)) #3=(|isDomain| *1 #4=(|XRecursivePolynomial| *3 *4)) #5=(|ofCategory| *3 (|OrderedSet|)) #6=(|ofCategory| *4 (|Ring|)))) (|unexpand| (*1 *1 *2) (AND #2# #5# #6# #3#)) (|RemainderList| #1# (AND (|isDomain| *2 (|List| (|Record| (|:| |k| *3) (|:| |c| #4#)))) #3# #5# #6#))) ((~= #1=(#2=((|Boolean|) $ $) NIL T ELT)) (|youngDiagram| (($ (|List| (|PositiveInteger|))) 11 T ELT)) (|shape| (#3=(#4=(|Partition|) $) 12 T ELT)) (|latex| (((|String|) $) NIL T ELT)) (|hash| (((|SingleInteger|) $) NIL T ELT)) (|coerce| (((|OutputForm|) $) 25 T ELT) (($ #4#) 14 T ELT) (#3# 13 T ELT)) (|before?| #1#) (= (#2# 17 T ELT))) @@ -4047,7 +4047,7 @@ NIL ((|solveLinearlyOverQ| (((|Union| (|Vector| (|Fraction| #1=(|Integer|))) #2="failed") #3=(|Vector| |#1|) |#1|) 21 T ELT)) (|linearlyDependentOverZ?| (((|Boolean|) #3#) 12 T ELT)) (|linearDependenceOverZ| (((|Union| (|Vector| #1#) #2#) #3#) 16 T ELT))) (((|IntegerLinearDependence| |#1|) (CATEGORY |package| (SIGNATURE |linearlyDependentOverZ?| ((|Boolean|) #1=(|Vector| |#1|))) (SIGNATURE |linearDependenceOverZ| ((|Union| (|Vector| #2=(|Integer|)) #3="failed") #1#)) (SIGNATURE |solveLinearlyOverQ| ((|Union| (|Vector| (|Fraction| #2#)) #3#) #1# |#1|))) (|Join| (|Ring|) (|LinearlyExplicitRingOver| #2#))) (T |IntegerLinearDependence|)) ((|solveLinearlyOverQ| (*1 *2 *3 *4) (|partial| AND #1=(|isDomain| *3 (|Vector| *4)) #2=(|ofCategory| *4 (|Join| (|Ring|) (|LinearlyExplicitRingOver| #3=(|Integer|)))) (|isDomain| *2 (|Vector| (|Fraction| #3#))) #4=(|isDomain| *1 (|IntegerLinearDependence| *4)))) (|linearDependenceOverZ| #5=(*1 *2 *3) (|partial| AND #1# #2# (|isDomain| *2 (|Vector| #3#)) #4#)) (|linearlyDependentOverZ?| #5# (AND #1# #2# (|isDomain| *2 (|Boolean|)) #4#))) -((~= #1=(#2=(#3=(|Boolean|) $ $) NIL T ELT)) (|zero?| (#4=(#3# $) 12 T ELT)) (|subtractIfCan| ((#5=(|Union| $ "failed") $ $) NIL T ELT)) (|size| (#6=(#7=(|NonNegativeInteger|)) 9 T ELT)) (|sample| (#8=($) NIL T CONST)) (|recip| ((#5# $) 57 T ELT)) (|random| (#8# 46 T ELT)) (|opposite?| #1#) (|one?| (#4# 38 T ELT)) (|nextItem| (((|Maybe| $) $) 36 T ELT)) (|lookup| ((#9=(|PositiveInteger|) $) 14 T ELT)) (|latex| (((|String|) $) NIL T ELT)) (|init| (#8# 26 T CONST)) (|index| (($ #9#) 47 T ELT)) (|hash| (((|SingleInteger|) $) NIL T ELT)) (|convert| ((#10=(|Integer|) $) 16 T ELT)) (|coerce| (((|OutputForm|) $) 21 T ELT) (($ #10#) 18 T ELT)) (|characteristic| (#6# 10 T CONST)) (|before?| (#2# 59 T ELT)) (|annihilate?| #1#) (|Zero| (#8# 23 T CONST)) (|One| (#8# 25 T CONST)) (= (#2# 31 T ELT)) (- (($ $) 50 T ELT) (#11=($ $ $) 44 T ELT)) (+ (#11# 29 T ELT)) (** (($ $ #9#) NIL T ELT) (($ $ #7#) 52 T ELT)) (* (($ #9# $) NIL T ELT) (($ #7# $) NIL T ELT) (($ #10# $) 41 T ELT) (#11# 40 T ELT))) +((~= #1=(#2=(#3=(|Boolean|) $ $) NIL T ELT)) (|zero?| (#4=(#3# $) 12 T ELT)) (|subtractIfCan| ((#5=(|Maybe| $) $ $) NIL T ELT)) (|size| (#6=(#7=(|NonNegativeInteger|)) 9 T ELT)) (|sample| (#8=($) NIL T CONST)) (|recip| (((|Union| $ "failed") $) 57 T ELT)) (|random| (#8# 46 T ELT)) (|opposite?| #1#) (|one?| (#4# 38 T ELT)) (|nextItem| ((#5# $) 36 T ELT)) (|lookup| ((#9=(|PositiveInteger|) $) 14 T ELT)) (|latex| (((|String|) $) NIL T ELT)) (|init| (#8# 26 T CONST)) (|index| (($ #9#) 47 T ELT)) (|hash| (((|SingleInteger|) $) NIL T ELT)) (|convert| ((#10=(|Integer|) $) 16 T ELT)) (|coerce| (((|OutputForm|) $) 21 T ELT) (($ #10#) 18 T ELT)) (|characteristic| (#6# 10 T CONST)) (|before?| (#2# 59 T ELT)) (|annihilate?| #1#) (|Zero| (#8# 23 T CONST)) (|One| (#8# 25 T CONST)) (= (#2# 31 T ELT)) (- (($ $) 50 T ELT) (#11=($ $ $) 44 T ELT)) (+ (#11# 29 T ELT)) (** (($ $ #9#) NIL T ELT) (($ $ #7#) 52 T ELT)) (* (($ #9# $) NIL T ELT) (($ #7# $) NIL T ELT) (($ #10# $) 41 T ELT) (#11# 40 T ELT))) (((|IntegerMod| |#1|) (|Join| (|CommutativeRing|) (|Finite|) (|ConvertibleTo| (|Integer|)) (|StepThrough|)) (|PositiveInteger|)) (T |IntegerMod|)) NIL NIL @@ -4062,4 +4062,4 @@ NIL NIL NIL NIL -((|Union| 2994614 2994619 2994624 NIL NIL NIL (NIL) |domain| NIL NIL NIL) (|Record| 2994599 2994604 2994609 NIL NIL NIL (NIL) |domain| NIL NIL NIL) (|Mapping| 2994584 2994589 2994594 NIL NIL NIL (NIL) |domain| NIL NIL NIL) (|Enumeration| 2994569 2994574 2994579 NIL NIL NIL (NIL) |domain| NIL NIL NIL) (|IntegerMod| 2993419 2994416 2994564 "ZMOD" NIL ZMOD (NIL NIL) |domain| NIL NIL NIL) (|IntegerLinearDependence| 2992336 2992589 2992976 "ZLINDEP" NIL ZLINDEP (NIL T) |package| NIL NIL NIL) (|ZeroDimensionalSolvePackage| 2987126 2988309 2989937 "ZDSOLVE" NIL ZDSOLVE (NIL T NIL NIL) |package| NIL NIL NIL) (|ParadoxicalCombinatorsForStreams| 2986384 2986504 2986739 "YSTREAM" NIL YSTREAM (NIL T) |package| NIL NIL NIL) (|YoungDiagram| 2985658 2985998 2986205 "YDIAGRAM" NIL YDIAGRAM (NIL) |domain| NIL NIL NIL) (|XRecursivePolynomial| 2983002 2984979 2985304 "XRPOLY" NIL XRPOLY (NIL T T) |domain| NIL NIL NIL) (|XPolynomialRing| 2979727 2981499 2982297 "XPR" NIL XPR (NIL T T) |domain| NIL NIL NIL) (|XPolynomialsCat| 2975772 2977990 2978084 "XPOLYC" 2978604 XPOLYC (NIL T T) |category| NIL 2978813 NIL) (|XPolynomial| 2973354 2975168 2975462 "XPOLY" NIL XPOLY (NIL T) |domain| NIL NIL NIL) (|XPBWPolynomial| 2969403 2972097 2972725 "XPBWPOLY" NIL XPBWPOLY (NIL T T) |domain| NIL NIL NIL) (|XFreeAlgebra| 2961633 2963731 2963819 "XFALG" 2967322 XFALG (NIL T T) |category| NIL 2968522 NIL) (|ExtensionField| 2954543 2958032 2958105 "XF" 2959258 XF (NIL T) |category| NIL 2960041 NIL) (|ExtensionField&| 2954100 2954252 2954538 "XF-" NIL XF- (NIL T T) |package| NIL NIL NIL) (|XExponentialPackage| 2953327 2953459 2953775 "XEXPPKG" NIL XEXPPKG (NIL T T T) |package| NIL NIL NIL) (|XDistributedPolynomial| 2950988 2953138 2953322 "XDPOLY" NIL XDPOLY (NIL T T) |domain| NIL NIL NIL) (|XAlgebra| 2949029 2950004 2950064 "XALG" 2950069 XALG (NIL T) |category| NIL 2950239 NIL) 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\ No newline at end of file diff --git a/src/share/algebra/operation.daase b/src/share/algebra/operation.daase index 6bf1fe21..fa861702 100644 --- a/src/share/algebra/operation.daase +++ b/src/share/algebra/operation.daase @@ -1,5 +1,5 @@ -(1293668 . 3581079093) +(1288378 . 3662084403) (((*1 *2 *3 *4) (|partial| AND (|isDomain| *3 (|Vector| *4)) (|ofCategory| *4 (|Join| (|Ring|) (|LinearlyExplicitRingOver| (|Integer|)))) @@ -509,6 +509,8 @@ ((*1 *1 *2 *3) (AND (|isDomain| *1 (|FreeModule1| *3 *2)) (|ofCategory| *3 (|Ring|)) (|ofCategory| *2 (|OrderedSet|)))) + ((*1 *1 *1 *1) + (AND (|isDomain| *1 (|FreeMagma| *2)) (|ofCategory| *2 (|OrderedSet|)))) ((*1 *1 *2 *3) (AND (|ofCategory| *1 (|FreeModuleCat| *2 *3)) (|ofCategory| *2 (|Ring|)) (|ofCategory| *3 (|SetCategory|)))) @@ -552,8 +554,6 @@ (|ofCategory| *3 (|Ring|)))) ((*1 *1 *2 *1) (AND (|ofCategory| *1 (|LeftLinearSet| *2)) (|ofCategory| *2 (|SemiGroup|)))) - ((*1 *1 *1 *1) - (AND (|isDomain| *1 (|Magma| *2)) (|ofCategory| *2 (|OrderedSet|)))) ((*1 *2 *3 *4) (AND (|isDomain| *3 (|Mapping| *7 *6)) (|isDomain| *4 (|Mapping| *6 *5)) (|ofCategory| *5 (|SetCategory|)) (|ofCategory| *6 (|SetCategory|)) @@ -980,13 +980,6 @@ (|isDomain| *1 (|DrawNumericHack| *4)))) ((*1 *1 *2) (AND (|isDomain| *2 (|List| (|Integer|))) (|isDomain| *1 (|ExtAlgBasis|)))) - ((*1 *2 *1) - (AND (|ofCategory| *2 (|UnivariatePolynomialCategory| *3)) - (|isDomain| *1 (|EuclideanModularRing| *3 *2 *4 *5 *6 *7)) - (|ofCategory| *3 (|CommutativeRing|)) - (|ofCategory| *4 (|AbelianMonoid|)) (|ofType| *5 (|Mapping| *2 *2 *4)) - (|ofType| *6 (|Mapping| (|Union| *4 "failed") *4 *4)) - (|ofType| *7 (|Mapping| (|Union| *2 "failed") *2 *2 *4)))) ((*1 *1 *2) (AND (|isDomain| *2 (|UnivariatePuiseuxSeries| *4 *5 *6)) (|ofCategory| *4 @@ -1009,14 +1002,6 @@ (|ofCategory| *2 (|FiniteAlgebraicExtensionField| *4)) (|isDomain| *1 (|FiniteFieldHomomorphisms| *2 *4 *3)) (|ofCategory| *3 (|FiniteAlgebraicExtensionField| *4)))) - ((*1 *2 *1) - (AND (|ofCategory| *1 (|FreeLieAlgebra| *3 *4)) - (|ofCategory| *3 (|OrderedSet|)) (|ofCategory| *4 (|CommutativeRing|)) - (|isDomain| *2 (|XRecursivePolynomial| *3 *4)))) - ((*1 *2 *1) - (AND (|ofCategory| *1 (|FreeLieAlgebra| *3 *4)) - (|ofCategory| *3 (|OrderedSet|)) (|ofCategory| *4 (|CommutativeRing|)) - (|isDomain| *2 (|XDistributedPolynomial| *3 *4)))) ((*1 *1 *2) (AND (|ofCategory| *1 (|FreeLieAlgebra| *2 *3)) (|ofCategory| *2 (|OrderedSet|)) (|ofCategory| *3 (|CommutativeRing|)))) @@ -1049,10 +1034,6 @@ (|Join| (|CommutativeRing|) (|Algebra| (|Fraction| (|Integer|))))) (|ofCategory| *3 (|Join| (|OrderedSet|) (|AbelianGroup|))))) - ((*1 *2 *1) - (AND (|isDomain| *2 (|SExpression|)) (|isDomain| *1 (|FortranScalarType|)))) - ((*1 *2 *1) - (AND (|isDomain| *2 (|Symbol|)) (|isDomain| *1 (|FortranScalarType|)))) ((*1 *1 *2) (AND (|isDomain| *2 (|Symbol|)) (|isDomain| *1 (|FortranScalarType|)))) ((*1 *1 *2) @@ -1068,8 +1049,6 @@ ((*1 *1 *2) (AND (|isDomain| *2 (|List| (|List| (|Point| (|DoubleFloat|))))) (|isDomain| *1 (|GraphImage|)))) - ((*1 *2 *1) - (AND (|isDomain| *2 (|OutputForm|)) (|isDomain| *1 (|GraphImage|)))) ((*1 *1 *2) (AND (|isDomain| *2 (|UnivariatePuiseuxSeries| *3 *4 *5)) (|ofCategory| *3 (|Ring|)) (|ofType| *4 (|Symbol|)) (|ofType| *5 *3) @@ -1099,35 +1078,10 @@ (AND (|ofCategory| *1 (|CoercibleFrom| *2)) (|ofCategory| *2 (|Type|)))) ((*1 *1 *2) (AND (|ofCategory| *1 (|LeftAlgebra| *2)) (|ofCategory| *2 (|Ring|)))) - ((*1 *2 *1) - (AND (|isDomain| *2 (|XPBWPolynomial| *3 *4)) - (|isDomain| *1 (|LieExponentials| *3 *4 *5)) - (|ofCategory| *3 (|OrderedSet|)) - (|ofCategory| *4 - (|Join| (|CommutativeRing|) - (|Module| (|Fraction| (|Integer|))))) - (|ofType| *5 (|PositiveInteger|)))) - ((*1 *2 *1) - (AND (|isDomain| *2 (|XDistributedPolynomial| *3 *4)) - (|isDomain| *1 (|LieExponentials| *3 *4 *5)) - (|ofCategory| *3 (|OrderedSet|)) - (|ofCategory| *4 - (|Join| (|CommutativeRing|) - (|Module| (|Fraction| (|Integer|))))) - (|ofType| *5 (|PositiveInteger|)))) ((*1 *1 *2) (AND (|ofCategory| *3 (|CommutativeRing|)) (|isDomain| *1 (|AssociatedLieAlgebra| *3 *2)) (|ofCategory| *2 (|NonAssociativeAlgebra| *3)))) - ((*1 *2 *1) - (AND (|isDomain| *2 (|Magma| *3)) (|isDomain| *1 (|LyndonWord| *3)) - (|ofCategory| *3 (|OrderedSet|)))) - ((*1 *2 *1) - (AND (|isDomain| *2 (|OrderedFreeMonoid| *3)) - (|isDomain| *1 (|LyndonWord| *3)) (|ofCategory| *3 (|OrderedSet|)))) - ((*1 *2 *1) - (AND (|isDomain| *2 (|OrderedFreeMonoid| *3)) (|isDomain| *1 (|Magma| *3)) - (|ofCategory| *3 (|OrderedSet|)))) ((*1 *1 *2) (AND (|isDomain| *2 (|Signature|)) (|isDomain| *1 (|MappingAst|)))) ((*1 *2 *3) @@ -1140,18 +1094,6 @@ ((*1 *2 *3) (AND (|isDomain| *3 (|OutputForm|)) (|isDomain| *2 (|String|)) (|isDomain| *1 (|MathMLFormat|)))) - ((*1 *2 *1) - (AND (|ofCategory| *2 (|CommutativeRing|)) - (|isDomain| *1 (|ModularField| *2 *3 *4 *5 *6)) - (|ofCategory| *3 (|AbelianMonoid|)) (|ofType| *4 (|Mapping| *2 *2 *3)) - (|ofType| *5 (|Mapping| (|Union| *3 "failed") *3 *3)) - (|ofType| *6 (|Mapping| (|Union| *2 "failed") *2 *2 *3)))) - ((*1 *2 *1) - (AND (|ofCategory| *2 (|CommutativeRing|)) - (|isDomain| *1 (|ModularRing| *2 *3 *4 *5 *6)) - (|ofCategory| *3 (|AbelianMonoid|)) (|ofType| *4 (|Mapping| *2 *2 *3)) - (|ofType| *5 (|Mapping| (|Union| *3 "failed") *3 *3)) - (|ofType| *6 (|Mapping| (|Union| *2 "failed") *2 *2 *3)))) ((*1 *1 *2) (AND (|isDomain| *2 (|List| (|Record| (|:| |coef| *3) (|:| |monom| *4)))) (|ofCategory| *3 (|Ring|)) (|ofCategory| *4 (|Monoid|)) @@ -1173,10 +1115,6 @@ ((*1 *1 *2) (AND (|isDomain| *1 (|PoincareBirkhoffWittLyndonBasis| *2)) (|ofCategory| *2 (|OrderedSet|)))) - ((*1 *2 *1) - (AND (|isDomain| *2 (|OrderedFreeMonoid| *3)) - (|isDomain| *1 (|PoincareBirkhoffWittLyndonBasis| *3)) - (|ofCategory| *3 (|OrderedSet|)))) ((*1 *1 *2) (AND (|isDomain| *2 (|List| *3)) (|ofCategory| *3 (|SetCategory|)) (|isDomain| *1 (|Permutation| *3)))) @@ -1184,20 +1122,9 @@ (AND (|isDomain| *2 (|List| (|List| *3))) (|ofCategory| *3 (|SetCategory|)) (|isDomain| *1 (|Permutation| *3)))) ((*1 *1 *2) - (AND (|isDomain| *2 (|List| (|Permutation| *3))) - (|ofCategory| *3 (|SetCategory|)) - (|isDomain| *1 (|PermutationGroup| *3)))) - ((*1 *2 *1) - (AND (|isDomain| *2 (|List| (|Permutation| *3))) - (|isDomain| *1 (|PermutationGroup| *3)) - (|ofCategory| *3 (|SetCategory|)))) - ((*1 *1 *2) (AND (|isDomain| *2 (|Fraction| (|Factored| *3))) (|ofCategory| *3 (|EuclideanDomain|)) (|isDomain| *1 (|PartialFraction| *3)))) - ((*1 *2 *1) - (AND (|isDomain| *2 (|Fraction| *3)) (|isDomain| *1 (|PartialFraction| *3)) - (|ofCategory| *3 (|EuclideanDomain|)))) ((*1 *2 *3) (AND (|isDomain| *3 (|Pi|)) (|isDomain| *2 (|Expression| *4)) (|isDomain| *1 (|PiCoercions| *4)) @@ -1227,9 +1154,6 @@ (AND (|ofCategory| *3 (|Ring|)) (|ofCategory| *2 (|OrderedSet|)) (|isDomain| *1 (|SparseMultivariateTaylorSeries| *3 *2 *4)) (|ofCategory| *4 (|PolynomialCategory| *3 (|IndexedExponents| *2) *2)))) - ((*1 *2 *1) - (AND (|ofCategory| *1 (|ThreeSpaceCategory| *3)) (|ofCategory| *3 (|Ring|)) - (|isDomain| *2 (|OutputForm|)))) ((*1 *1 *2) (AND (|isDomain| *2 (|Character|)) (|ofCategory| *1 (|StringAggregate|)))) ((*1 *2 *3) @@ -1248,16 +1172,10 @@ (AND (|isDomain| *2 (|UnivariatePolynomial| *4 *3)) (|ofCategory| *3 (|Ring|)) (|ofType| *4 (|Symbol|)) (|ofType| *5 *3) (|isDomain| *1 (|SparseUnivariateTaylorSeries| *3 *4 *5)))) - ((*1 *2 *1) - (AND (|isDomain| *2 (|Table| (|Symbol|) (|FortranType|))) - (|isDomain| *1 (|SymbolTable|)))) ((*1 *2 *1) (AND (|isDomain| *2 (|String|)) (|isDomain| *1 (|Syntax|)))) ((*1 *2 *1) (AND (|isDomain| *2 (|Identifier|)) (|isDomain| *1 (|Syntax|)))) ((*1 *2 *1) (AND (|isDomain| *2 (|DoubleFloat|)) (|isDomain| *1 (|Syntax|)))) ((*1 *2 *1) (AND (|isDomain| *2 (|Integer|)) (|isDomain| *1 (|Syntax|)))) - ((*1 *2 *1) - (AND (|isDomain| *2 (|OutputForm|)) (|isDomain| *1 (|Tableau| *3)) - (|ofCategory| *3 (|SetCategory|)))) ((*1 *2 *3) (AND (|isDomain| *2 (|TexFormat|)) (|isDomain| *1 (|TexFormat1| *3)) (|ofCategory| *3 (|SetCategory|)))) @@ -1282,27 +1200,13 @@ (AND (|isDomain| *2 (|UnivariatePolynomial| *4 *3)) (|ofCategory| *3 (|Ring|)) (|ofType| *4 (|Symbol|)) (|ofType| *5 *3) (|isDomain| *1 (|UnivariateTaylorSeries| *3 *4 *5)))) - ((*1 *2 *1) - (AND (|isDomain| *2 (|Symbol|)) (|isDomain| *1 (|Variable| *3)) - (|ofType| *3 *2))) ((*1 *2 *3) (AND (|isDomain| *3 (|GraphImage|)) (|isDomain| *2 (|TwoDimensionalViewport|)) (|isDomain| *1 (|ViewportPackage|)))) - ((*1 *2 *1) - (AND (|isDomain| *2 (|OutputForm|)) - (|isDomain| *1 (|TwoDimensionalViewport|)))) ((*1 *1 *2) (AND (|ofCategory| *1 (|XFreeAlgebra| *2 *3)) (|ofCategory| *2 (|OrderedSet|)) (|ofCategory| *3 (|Ring|)))) - ((*1 *2 *1) - (AND (|isDomain| *2 (|XRecursivePolynomial| *3 *4)) - (|isDomain| *1 (|XPBWPolynomial| *3 *4)) - (|ofCategory| *3 (|OrderedSet|)) (|ofCategory| *4 (|CommutativeRing|)))) - ((*1 *2 *1) - (AND (|isDomain| *2 (|XDistributedPolynomial| *3 *4)) - (|isDomain| *1 (|XPBWPolynomial| *3 *4)) - (|ofCategory| *3 (|OrderedSet|)) (|ofCategory| *4 (|CommutativeRing|)))) ((*1 *1 *2) (AND (|isDomain| *2 (|LiePolynomial| *3 *4)) (|ofCategory| *3 (|OrderedSet|)) (|ofCategory| *4 (|CommutativeRing|)) @@ -1519,6 +1423,8 @@ (AND (|ofCategory| *1 (|FreeLieAlgebra| *2 *3)) (|ofCategory| *2 (|OrderedSet|)) (|ofCategory| *3 (|CommutativeRing|)))) ((*1 *1 *1) + (AND (|isDomain| *1 (|FreeMagma| *2)) (|ofCategory| *2 (|OrderedSet|)))) + ((*1 *1 *1) (AND (|isDomain| *1 (|LieExponentials| *2 *3 *4)) (|ofCategory| *2 (|OrderedSet|)) (|ofCategory| *3 @@ -1526,8 +1432,6 @@ (|Module| (|Fraction| (|Integer|))))) (|ofType| *4 (|PositiveInteger|)))) ((*1 *1 *1) - (AND (|isDomain| *1 (|Magma| *2)) (|ofCategory| *2 (|OrderedSet|)))) - ((*1 *1 *1) (AND (|isDomain| *1 (|OrderedFreeMonoid| *2)) (|ofCategory| *2 (|OrderedSet|)))) ((*1 *1 *1) @@ -1547,6 +1451,9 @@ (|ofCategory| *3 (|OrderedSet|)) (|ofCategory| *4 (|CommutativeRing|)) (|isDomain| *2 (|List| *3)))) ((*1 *2 *1) + (AND (|isDomain| *2 (|List| *3)) (|isDomain| *1 (|FreeMagma| *3)) + (|ofCategory| *3 (|OrderedSet|)))) + ((*1 *2 *1) (AND (|isDomain| *2 (|List| *3)) (|isDomain| *1 (|LieExponentials| *3 *4 *5)) (|ofCategory| *3 (|OrderedSet|)) (|ofCategory| *4 @@ -1557,9 +1464,6 @@ (AND (|isDomain| *2 (|List| *3)) (|isDomain| *1 (|LyndonWord| *3)) (|ofCategory| *3 (|OrderedSet|)))) ((*1 *2 *1) - (AND (|isDomain| *2 (|List| *3)) (|isDomain| *1 (|Magma| *3)) - (|ofCategory| *3 (|OrderedSet|)))) - ((*1 *2 *1) (AND (|isDomain| *2 (|List| *3)) (|isDomain| *1 (|OrderedFreeMonoid| *3)) (|ofCategory| *3 (|OrderedSet|)))) ((*1 *2 *1) @@ -3066,7 +2970,10 @@ ((*1 *1 *1 *1) (AND (|ofCategory| *1 (|VectorCategory| *2)) (|ofCategory| *2 (|Type|)) (|ofCategory| *2 (|Ring|))))) -(((*1 *2 *3) +(((*1 *2 *1) + (AND (|isDomain| *2 (|PositiveInteger|)) (|isDomain| *1 (|FreeMagma| *3)) + (|ofCategory| *3 (|OrderedSet|)))) + ((*1 *2 *3) (AND (|ofCategory| *4 (|Ring|)) (|ofCategory| *2 (|Join| (|FloatingPointSystem|) (|RetractableTo| *4) @@ -3079,9 +2986,6 @@ (AND (|isDomain| *2 (|PositiveInteger|)) (|isDomain| *1 (|LyndonWord| *3)) (|ofCategory| *3 (|OrderedSet|)))) ((*1 *2 *1) - (AND (|isDomain| *2 (|PositiveInteger|)) (|isDomain| *1 (|Magma| *3)) - (|ofCategory| *3 (|OrderedSet|)))) - ((*1 *2 *1) (AND (|isDomain| *2 (|NonNegativeInteger|)) (|isDomain| *1 (|OrderedFreeMonoid| *3)) (|ofCategory| *3 (|OrderedSet|)))) @@ -3838,12 +3742,12 @@ (AND (|ofCategory| *1 (|UnaryRecursiveAggregate| *2)) (|ofCategory| *2 (|Type|))))) (((*1 *2 *1) + (AND (|isDomain| *1 (|FreeMagma| *2)) (|ofCategory| *2 (|OrderedSet|)))) + ((*1 *2 *1) (AND (|ofCategory| *1 (|IndexedAggregate| *3 *2)) (|ofCategory| *3 (|BasicType|)) (|ofCategory| *3 (|OrderedSet|)) (|ofCategory| *2 (|Type|)))) ((*1 *2 *1) - (AND (|isDomain| *1 (|Magma| *2)) (|ofCategory| *2 (|OrderedSet|)))) - ((*1 *2 *1) (AND (|isDomain| *1 (|OrderedFreeMonoid| *2)) (|ofCategory| *2 (|OrderedSet|)))) ((*1 *2 *1) @@ -4031,7 +3935,7 @@ (AND (|isDomain| *3 "first") (|ofCategory| *1 (|UnaryRecursiveAggregate| *2)) (|ofCategory| *2 (|Type|))))) (((*1 *1 *1) - (AND (|isDomain| *1 (|Magma| *2)) (|ofCategory| *2 (|OrderedSet|)))) + (AND (|isDomain| *1 (|FreeMagma| *2)) (|ofCategory| *2 (|OrderedSet|)))) ((*1 *1 *1) (AND (|isDomain| *1 (|OrderedFreeMonoid| *2)) (|ofCategory| *2 (|OrderedSet|)))) @@ -7151,6 +7055,9 @@ ((*1 *1 *2 *3) (AND (|isDomain| *3 (|Arity|)) (|isDomain| *1 (|TermAlgebraOperator| *2)) (|ofCategory| *2 (|SetCategory|))))) +(((*1 *1 *2) + (AND (|isDomain| *2 (|List| (|List| *3))) (|ofCategory| *3 (|SetCategory|)) + (|isDomain| *1 (|Tableau| *3))))) (((*1 *2 *1) (AND (|ofCategory| *1 (|MatrixCategory| *3 *4 *5)) (|ofCategory| *3 (|Ring|)) (|ofCategory| *4 (|FiniteLinearAggregate| *3)) @@ -7165,9 +7072,6 @@ ((*1 *2 *1) (AND (|isDomain| *2 (|List| (|List| *3))) (|isDomain| *1 (|Tableau| *3)) (|ofCategory| *3 (|SetCategory|))))) -(((*1 *1 *2) - (AND (|isDomain| *2 (|List| (|List| *3))) (|ofCategory| *3 (|SetCategory|)) - (|isDomain| *1 (|Tableau| *3))))) (((*1 *2 *3) (AND (|ofCategory| *4 (|OrderedSet|)) (|isDomain| *2 @@ -7631,9 +7535,7 @@ (|isDomain| *2 (|List| (|Equation| (|Fraction| (|Polynomial| *4))))) (|isDomain| *1 (|SystemSolvePackage| *4)) (|isDomain| *3 (|Equation| (|Fraction| (|Polynomial| *4))))))) -(((*1 *2 *1) - (AND (|isDomain| *1 (|Maybe| *2)) - (|ofCategory| *2 (|CoercibleTo| (|OutputForm|))))) +(((*1 *2 *1) (AND (|isDomain| *1 (|Maybe| *2)) (|ofCategory| *2 (|Type|)))) ((*1 *2 *1) (AND (|isDomain| *2 (|String|)) (|isDomain| *1 (|ParameterAst|)))) ((*1 *2 *1) (AND (|isDomain| *2 (|Identifier|)) (|isDomain| *1 (|ParameterAst|)))) @@ -7738,11 +7640,9 @@ (|isDomain| *1 (|KleeneTrivalentLogic|)))) ((*1 *2 *1 *3) (AND (|isDomain| *3 (|[\|\|]| |nothing|)) (|isDomain| *2 (|Boolean|)) - (|isDomain| *1 (|Maybe| *4)) - (|ofCategory| *4 (|CoercibleTo| (|OutputForm|))))) + (|isDomain| *1 (|Maybe| *4)) (|ofCategory| *4 (|Type|)))) ((*1 *2 *1 *3) - (AND (|isDomain| *3 (|[\|\|]| *4)) - (|ofCategory| *4 (|CoercibleTo| (|OutputForm|))) + (AND (|isDomain| *3 (|[\|\|]| *4)) (|ofCategory| *4 (|Type|)) (|isDomain| *2 (|Boolean|)) (|isDomain| *1 (|Maybe| *4)))) ((*1 *2 *1 *3) (AND (|isDomain| *3 (|[\|\|]| (|String|))) (|isDomain| *2 (|Boolean|)) @@ -8995,26 +8895,9 @@ (|isDomain| *1 (|StreamTaylorSeriesOperations| *4)) (|ofCategory| *4 (|Ring|)) (|isDomain| *3 (|Integer|))))) (((*1 *1 *1) - (|partial| AND (|isDomain| *1 (|CliffordAlgebra| *2 *3 *4)) - (|ofType| *2 (|PositiveInteger|)) (|ofCategory| *3 (|Field|)) - (|ofType| *4 (|QuadraticForm| *2 *3)))) - ((*1 *1 *1) - (|partial| AND (|ofCategory| *2 (|CommutativeRing|)) - (|isDomain| *1 (|EuclideanModularRing| *2 *3 *4 *5 *6 *7)) - (|ofCategory| *3 (|UnivariatePolynomialCategory| *2)) - (|ofCategory| *4 (|AbelianMonoid|)) (|ofType| *5 (|Mapping| *3 *3 *4)) - (|ofType| *6 (|Mapping| (|Union| *4 "failed") *4 *4)) - (|ofType| *7 (|Mapping| (|Union| *3 "failed") *3 *3 *4)))) - ((*1 *1 *1) (|partial| AND (|ofCategory| *1 (|FiniteRankNonAssociativeAlgebra| *2)) (|ofCategory| *2 (|CommutativeRing|)) (|ofCategory| *2 (|IntegralDomain|)))) ((*1 *1 *1) - (|partial| AND (|isDomain| *1 (|ModularRing| *2 *3 *4 *5 *6)) - (|ofCategory| *2 (|CommutativeRing|)) (|ofCategory| *3 (|AbelianMonoid|)) - (|ofType| *4 (|Mapping| *2 *2 *3)) - (|ofType| *5 (|Mapping| (|Union| *3 "failed") *3 *3)) - (|ofType| *6 (|Mapping| (|Union| *2 "failed") *2 *2 *3)))) - ((*1 *1 *1) (AND (|isDomain| *1 (|MoebiusTransform| *2)) (|ofCategory| *2 (|Field|)))) ((*1 *1) (AND (|isDomain| *1 (|MoebiusTransform| *2)) (|ofCategory| *2 (|Field|)))) @@ -12622,9 +12505,9 @@ (AND (|ofCategory| *1 (|BinaryRecursiveAggregate| *2)) (|ofCategory| *2 (|Type|)))) ((*1 *1 *1) - (AND (|isDomain| *1 (|LyndonWord| *2)) (|ofCategory| *2 (|OrderedSet|)))) + (AND (|isDomain| *1 (|FreeMagma| *2)) (|ofCategory| *2 (|OrderedSet|)))) ((*1 *1 *1) - (AND (|isDomain| *1 (|Magma| *2)) (|ofCategory| *2 (|OrderedSet|)))) + (AND (|isDomain| *1 (|LyndonWord| *2)) (|ofCategory| *2 (|OrderedSet|)))) ((*1 *1 *1) (|isDomain| *1 (|OutputForm|))) ((*1 *1 *1 *2) (AND (|isDomain| *2 (|Integer|)) (|isDomain| *1 (|OutputForm|)))) @@ -12636,9 +12519,9 @@ (AND (|ofCategory| *1 (|BinaryRecursiveAggregate| *2)) (|ofCategory| *2 (|Type|)))) ((*1 *1 *1) - (AND (|isDomain| *1 (|LyndonWord| *2)) (|ofCategory| *2 (|OrderedSet|)))) + (AND (|isDomain| *1 (|FreeMagma| *2)) (|ofCategory| *2 (|OrderedSet|)))) ((*1 *1 *1) - (AND (|isDomain| *1 (|Magma| *2)) (|ofCategory| *2 (|OrderedSet|)))) + (AND (|isDomain| *1 (|LyndonWord| *2)) (|ofCategory| *2 (|OrderedSet|)))) ((*1 *1 *1) (|isDomain| *1 (|OutputForm|))) ((*1 *1 *1 *2) (AND (|isDomain| *2 (|Integer|)) (|isDomain| *1 (|OutputForm|)))) @@ -17101,10 +16984,10 @@ (|ofCategory| *3 (|Join| (|Ring|) (|OrderedSet|))) (|ofType| *4 (|List| (|Symbol|))))) ((*1 *2 *1) - (AND (|isDomain| *2 (|Boolean|)) (|isDomain| *1 (|LyndonWord| *3)) + (AND (|isDomain| *2 (|Boolean|)) (|isDomain| *1 (|FreeMagma| *3)) (|ofCategory| *3 (|OrderedSet|)))) ((*1 *2 *1) - (AND (|isDomain| *2 (|Boolean|)) (|isDomain| *1 (|Magma| *3)) + (AND (|isDomain| *2 (|Boolean|)) (|isDomain| *1 (|LyndonWord| *3)) (|ofCategory| *3 (|OrderedSet|)))) ((*1 *2 *1) (AND (|isDomain| *2 (|Boolean|)) @@ -17900,10 +17783,10 @@ (|isDomain| *1 (|OppositeMonogenicLinearOperator| *2 *3)) (|ofCategory| *3 (|Ring|))))) (((*1 *2 *1 *1) - (AND (|isDomain| *2 (|Boolean|)) (|isDomain| *1 (|LyndonWord| *3)) + (AND (|isDomain| *2 (|Boolean|)) (|isDomain| *1 (|FreeMagma| *3)) (|ofCategory| *3 (|OrderedSet|)))) ((*1 *2 *1 *1) - (AND (|isDomain| *2 (|Boolean|)) (|isDomain| *1 (|Magma| *3)) + (AND (|isDomain| *2 (|Boolean|)) (|isDomain| *1 (|LyndonWord| *3)) (|ofCategory| *3 (|OrderedSet|)))) ((*1 *2 *1 *1) (AND (|isDomain| *2 (|Boolean|)) (|isDomain| *1 (|OrderedFreeMonoid| *3)) @@ -19523,12 +19406,8 @@ (|isDomain| *2 (|List| (|Record| (|:| |entry| *3) (|:| |count| (|NonNegativeInteger|)))))))) -(((*1 *1 *2) - (AND (|isDomain| *1 (|Maybe| *2)) - (|ofCategory| *2 (|CoercibleTo| (|OutputForm|)))))) -(((*1 *1) - (AND (|isDomain| *1 (|Maybe| *2)) - (|ofCategory| *2 (|CoercibleTo| (|OutputForm|)))))) +(((*1 *1 *2) (AND (|isDomain| *1 (|Maybe| *2)) (|ofCategory| *2 (|Type|))))) +(((*1 *1) (AND (|isDomain| *1 (|Maybe| *2)) (|ofCategory| *2 (|Type|))))) (((*1 *2 *2 *2 *2 *2 *3) (AND (|isDomain| *2 (|Matrix| *4)) (|isDomain| *3 (|NonNegativeInteger|)) (|ofCategory| *4 (|Ring|)) @@ -26641,7 +26520,9 @@ (((*1 *2 *1 *3) (AND (|ofCategory| *1 (|CachableSet|)) (|isDomain| *3 (|NonNegativeInteger|)) (|isDomain| *2 (|Void|))))) -(((*1 *1 *1 *1) (|partial| |ofCategory| *1 (|CancellationAbelianMonoid|)))) +(((*1 *2 *1 *1) + (AND (|isDomain| *2 (|Maybe| *1)) + (|ofCategory| *1 (|CancellationAbelianMonoid|))))) (((*1 *1) (|isDomain| *1 (|ByteOrder|)))) (((*1 *1) (|isDomain| *1 (|ByteOrder|)))) (((*1 *1) (|isDomain| *1 (|ByteOrder|)))) @@ -27292,1034 +27173,1033 @@ (|ofCategory| *1 (|AlgebraicallyClosedFunctionSpace| *3))))) (((*1 *2 *1 *1) (AND (|ofCategory| *1 (|AbelianMonoid|)) (|isDomain| *2 (|Boolean|))))) -((|opposite?| . 1293577) (|zerosOf| . 1292730) (|zeroOf| . 1292044) - (|rootsOf| . 1291197) (|makeSketch| . 1290980) (|inrootof| . 1290762) - (|droot| . 1290545) (|iroot| . 1290310) (|eq?| . 1290223) (|assoc| . 1289992) - (|doublyTransitive?| . 1289829) (|knownInfBasis| . 1289485) - (|rootSplit| . 1288478) (|ratDenom| . 1284366) (|ratPoly| . 1283302) - (|rootPower| . 1282171) (|rootProduct| . 1281040) (|rootSimp| . 1279909) - (|rootKerSimp| . 1278692) (|leftRank| . 1278477) (|rightRank| . 1278262) - (|doubleRank| . 1278047) (|weakBiRank| . 1277832) (|biRank| . 1277617) - (|basisOfCommutingElements| . 1277423) (|basisOfLeftAnnihilator| . 1277226) - (|basisOfRightAnnihilator| . 1277029) (|basisOfLeftNucleus| . 1276835) - (|basisOfRightNucleus| . 1276641) (|basisOfMiddleNucleus| . 1276447) - (|basisOfNucleus| . 1276253) (|basisOfCenter| . 1276059) - (|basisOfLeftNucloid| . 1275847) (|basisOfRightNucloid| . 1275635) - (|basisOfCentroid| . 1275423) (|radicalOfLeftTraceForm| . 1275229) - (|obj| . 1275158) (|dom| . 1275080) (|any| . 1274965) (|applyRules| . 1273974) - (|localUnquote| . 1273518) (|arbitrary| . 1273479) (|setColumn!| . 1273213) - (|setRow!| . 1272947) (|oneDimensionalArray| . 1272677) - (|associatedSystem| . 1272304) (|uncouplingMatrices| . 1272030) - (|associatedEquations| . 1271568) (|arrayStack| . 1271441) - (|morphism| . 1271046) (|balancedFactorisation| . 1270521) - (|before?| . 1270434) (|mapDown!| . 1270117) (|mapUp!| . 1269802) - (|setleaves!| . 1269664) (|balancedBinaryTree| . 1269508) - (|sylvesterMatrix| . 1269184) (|bezoutMatrix| . 1268860) - (|bezoutResultant| . 1268479) (|bezoutDiscriminant| . 1268101) - (|inspect| . 1268012) (|extract!| . 1267923) (|bag| . 1267799) - (|binding| . 1267668) (|binaryOperation| . 1267534) - (|setProperties| . 1267410) (|setProperty| . 1267162) - (|deleteProperty!| . 1266984) (|has?| . 1266857) (|comparison| . 1266724) - (|equality| . 1266591) (|nary?| . 1266505) (|unary?| . 1266419) - (|nullary?| . 1266333) (|properties| . 1266124) (|derivative| . 1265513) - (|constantOperator| . 1265360) (|constantOpIfCan| . 1265205) - (|integerBound| . 1264970) (|setright!| . 1264801) (|setleft!| . 1264632) - (|brillhartIrreducible?| . 1264311) (|brillhartTrials| . 1263960) - (|noLinearFactor?| . 1263800) (|insertRoot!| . 1263693) - (|binarySearchTree| . 1263561) (|nor| . 1263462) (|nand| . 1263363) - (|node| . 1263248) (|binaryTournament| . 1263116) (|binaryTree| . 1262928) - (|byte| . 1262840) (|setLength!| . 1262743) (|capacity| . 1262649) - (|byteBuffer| . 1262555) (|unknownEndian| . 1262512) (|bigEndian| . 1262469) - (|littleEndian| . 1262426) (|subtractIfCan| . 1262349) - (|setPosition| . 1262217) (|generalizedContinuumHypothesisAssumed| . 1262130) - (|generalizedContinuumHypothesisAssumed?| . 1262048) (|countable?| . 1261961) - (|Aleph| . 1261856) (|unravel| . 1261644) (|ravel| . 1261432) - (|leviCivitaSymbol| . 1261251) (|kroneckerDelta| . 1261070) - (|reindex| . 1260839) (|parents| . 1260710) (|principalAncestors| . 1260581) - (|exportedOperators| . 1260474) (|alphanumeric| . 1260426) - (|alphabetic| . 1260378) (|hexDigit| . 1260330) (|digit| . 1260282) - (|charClass| . 1260093) (|alphanumeric?| . 1260013) (|lowerCase?| . 1259933) - (|upperCase?| . 1259853) (|alphabetic?| . 1259773) (|hexDigit?| . 1259693) - (|digit?| . 1259613) (|escape| . 1259570) (|verticalTab| . 1259527) - (|horizontalTab| . 1259484) (|backspace| . 1259441) (|formfeed| . 1259398) - (|linefeed| . 1259355) (|carriageReturn| . 1259312) (|newline| . 1259269) - (|underscore| . 1259226) (|char| . 1259056) (|ord| . 1258963) - (|mkIntegral| . 1258624) (|radPoly| . 1258250) (|rootPoly| . 1257779) - (|goodPoint| . 1257516) (|chvar| . 1257054) (|removeDuplicates| . 1256880) - (|e| . 1256678) (|clipParametric| . 1255979) (|clipWithRanges| . 1255618) - (|numberOfHues| . 1255537) (|yellow| . 1255498) (|iifact| . 1255336) - (|iibinom| . 1255146) (|iiperm| . 1254956) (|iipow| . 1254766) - (|iidsum| . 1254576) (|iidprod| . 1254386) (|ipow| . 1254196) - (|factorial| . 1253845) (|multinomial| . 1253689) (|permutation| . 1253329) - (|stirling1| . 1253201) (|stirling2| . 1253073) (|summation| . 1252450) - (|factorials| . 1251931) (|mkcomm| . 1251802) - (|commutativeOperation| . 1251658) (|polarCoordinates| . 1251380) - (|complex| . 1251267) (|imaginary| . 1251160) (|elaborateFile| . 1251008) - (|elaborate| . 1250871) (|macroExpand| . 1250741) (|solid| . 1250633) - (|solid?| . 1250528) (|denominators| . 1250388) (|numerators| . 1250248) - (|convergents| . 1250088) (|approximants| . 1249928) (|reducedForm| . 1249818) - (|partialQuotients| . 1249678) (|partialDenominators| . 1249538) - (|partialNumerators| . 1249398) (|reducedContinuedFraction| . 1249255) - (|push| . 1249174) (|bindings| . 1249085) (|cartesian| . 1248835) - (|polar| . 1248585) (|cylindrical| . 1248335) (|spherical| . 1248085) - (|parabolic| . 1247835) (|parabolicCylindrical| . 1247585) - (|paraboloidal| . 1247335) (|ellipticCylindrical| . 1247060) - (|prolateSpheroidal| . 1246785) (|oblateSpheroidal| . 1246510) - (|bipolar| . 1246235) (|bipolarCylindrical| . 1245960) (|toroidal| . 1245685) - (|conical| . 1245407) (|modTree| . 1245273) (|multiEuclideanTree| . 1245139) - (|complexZeros| . 1244346) (|divisorCascade| . 1243694) (|graeffe| . 1243485) - (|pleskenSplit| . 1242947) (|reciprocalPolynomial| . 1242738) - (|rootRadius| . 1242319) (|schwerpunkt| . 1242084) (|setErrorBound| . 1241875) - (|startPolynomial| . 1241575) (|cycleElt| . 1241419) - (|computeCycleLength| . 1241226) (|computeCycleEntry| . 1241076) - (|findConstructor| . 1240940) (|arguments| . 1240785) (|operations| . 1240671) - (|dualSignature| . 1240561) (|kind| . 1240362) (|package| . 1240313) - (|domain| . 1240264) (|category| . 1240215) (|coerceP| . 1239986) - (|powerSum| . 1239811) (|elementary| . 1239633) (|alternating| . 1239455) - (|cyclic| . 1239280) (|dihedral| . 1239105) (|cap| . 1238922) - (|cup| . 1238787) (|wreath| . 1238652) (|SFunction| . 1238468) - (|skewSFunction| . 1238289) (|cyclotomicDecomposition| . 1238107) - (|cyclotomicFactorization| . 1237921) (|qsetelt| . 1237734) - (|doubleResultant| . 1237388) (|distdfact| . 1236975) - (|separateDegrees| . 1236689) (|trace2PowMod| . 1236453) - (|tracePowMod| . 1236217) (|irreducible?| . 1236005) (|decimal| . 1235896) - (|innerint| . 1235069) (|exteriorDifferential| . 1234906) - (|totalDifferential| . 1234702) (|homogeneous?| . 1234358) - (|leadingBasisTerm| . 1234070) (|ignore?| . 1233598) (|computeInt| . 1233092) - (|checkForZero| . 1232031) (|nan?| . 1231949) (|logGamma| . 1231717) - (|hypergeometric0F1| . 1231479) (|rotatez| . 1231308) (|rotatey| . 1231137) - (|rotatex| . 1230966) (|identity| . 1230798) (|dictionary| . 1230553) - (|dioSolve| . 1230118) (|directProduct| . 1229980) (|newLine| . 1229899) - (|copies| . 1229775) (|say| . 1229532) (|sayLength| . 1229283) - (|setnext!| . 1229117) (|setprevious!| . 1228951) (|next| . 1228846) - (|previous| . 1228741) (|datalist| . 1228617) - (|shanksDiscLogAlgorithm| . 1228311) (|showSummary| . 1228237) - (|reflect| . 1228121) (|reify| . 1228005) (|constructor| . 1227715) - (|functorData| . 1227621) (|separant| . 1227351) (|initial| . 1227081) - (|leader| . 1226811) (|isobaric?| . 1226506) (|weights| . 1225855) - (|differentialVariables| . 1225550) (|extractBottom!| . 1225457) - (|extractTop!| . 1225364) (|insertBottom!| . 1225268) (|insertTop!| . 1225172) - (|bottom!| . 1225079) (|top!| . 1224986) (|dequeue| . 1224648) - (|makeObject| . 1219580) (|recolor| . 1219281) (|drawComplex| . 1218999) - (|drawComplexVectorField| . 1218748) (|setRealSteps| . 1218666) - (|setImagSteps| . 1218584) (|setClipValue| . 1218496) (|draw| . 1209296) - (|option?| . 1209136) (|range| . 1208905) (|colorFunction| . 1208478) - (|curveColor| . 1208320) (|pointColor| . 1208162) (|clip| . 1206600) - (|clipBoolean| . 1206457) (|style| . 1206237) (|toScale| . 1206015) - (|pointColorPalette| . 1205872) (|curveColorPalette| . 1205729) - (|var1Steps| . 1205482) (|var2Steps| . 1205235) (|space| . 1204921) - (|tubePoints| . 1204674) (|tubeRadius| . 1204456) (|option| . 1204112) - (|weight| . 1203110) (|makeVariable| . 1202239) (|Nul| . 1202144) - (|exponents| . 1202051) (|iisqrt2| . 1201866) (|iisqrt3| . 1201681) - (|iiexp| . 1201493) (|iilog| . 1201305) (|iisin| . 1201117) - (|iicos| . 1200929) (|iitan| . 1200741) (|iicot| . 1200553) - (|iisec| . 1200365) (|iicsc| . 1200177) (|iiasin| . 1199989) - (|iiacos| . 1199801) (|iiatan| . 1199613) (|iiacot| . 1199425) - (|iiasec| . 1199237) (|iiacsc| . 1199049) (|iisinh| . 1198861) - (|iicosh| . 1198673) (|iitanh| . 1198485) (|iicoth| . 1198297) - (|iisech| . 1198109) (|iicsch| . 1197921) (|iiasinh| . 1197733) - (|iiacosh| . 1197545) (|iiatanh| . 1197357) (|iiacoth| . 1197169) - (|iiasech| . 1196981) (|iiacsch| . 1196793) (|specialTrigs| . 1196517) - (|localReal?| . 1196301) (|rischNormalize| . 1195670) - (|realElementary| . 1194746) (|validExponential| . 1194229) - (|rootNormalize| . 1193732) (|tanQ| . 1193224) (|callForm?| . 1193131) - (|getIdentifier| . 1193022) (|variable?| . 1192929) (|getConstant| . 1192819) - (|type| . 1192727) (|environment| . 1192639) (|typeForm| . 1192546) - (|irForm| . 1192436) (|elaboration| . 1192244) (|select!| . 1191872) - (|delete!| . 1191559) (|sn| . 1191368) (|cn| . 1191177) (|dn| . 1190986) - (|sncndn| . 1190719) (|qsetelt!| . 1190253) (|categoryFrame| . 1190208) - (|interactiveEnv| . 1190163) (|currentEnv| . 1190118) - (|putProperties| . 1189980) (|getProperties| . 1189845) - (|putProperty| . 1189710) (|getProperty| . 1189568) (|scopes| . 1189477) - (|eigenvalues| . 1189163) (|eigenvector| . 1188812) - (|generalizedEigenvector| . 1187949) (|generalizedEigenvectors| . 1187484) - (|eigenvectors| . 1186988) (|factorAndSplit| . 1186820) (|rightOne| . 1186695) - (|leftOne| . 1186570) (|rightZero| . 1186445) (|leftZero| . 1186320) - (|swap| . 1185996) (|error| . 1185479) (|minPoly| . 1184998) - (|freeOf?| . 1184780) (|operators| . 1184668) (|tower| . 1184560) - (|kernels| . 1184452) (|mainKernel| . 1184347) (|distribute| . 1184238) - (|subst| . 1183761) (|multiEuclidean| . 1183655) - (|extendedEuclidean| . 1183358) (|euclideanSize| . 1183250) - (|sizeLess?| . 1183157) (|simplifyPower| . 1182990) (|number?| . 1182826) - (|seriesSolve| . 1178827) (|constantToUnaryFunction| . 1178674) - (|tubePlot| . 1177295) (|exponentialOrder| . 1177080) - (|completeEval| . 1176645) (|lowerPolynomial| . 1176279) - (|raisePolynomial| . 1175913) (|normalDeriv| . 1175566) (|ran| . 1175279) - (|highCommonTerms| . 1175052) (|mapCoef| . 1174834) (|nthCoef| . 1174622) - (|binomThmExpt| . 1174372) (|pomopo!| . 1174210) (|mapExponents| . 1174013) - (|linearAssociatedLog| . 1173610) (|linearAssociatedOrder| . 1173410) - (|linearAssociatedExp| . 1173200) (|createNormalElement| . 1173060) - (|sin?| . 1172928) (|lookupFunction| . 1172841) - (|encodingDirectory| . 1172720) (|attributeData| . 1172589) - (|domainTemplate| . 1172498) (|lSpaceBasis| . 1172161) - (|finiteBasis| . 1171824) (|principal?| . 1171479) (|divisor| . 1169820) - (|rationalPoints| . 1169115) (|nonSingularModel| . 1168325) - (|algSplitSimple| . 1167890) (|hyperelliptic| . 1167310) - (|elliptic| . 1166457) (|integralDerivationMatrix| . 1166074) - (|integralRepresents| . 1165767) (|integralCoordinates| . 1165425) - (|yCoordinates| . 1165083) (|inverseIntegralMatrixAtInfinity| . 1164769) - (|integralMatrixAtInfinity| . 1164455) (|inverseIntegralMatrix| . 1164141) - (|integralMatrix| . 1163827) (|reduceBasisAtInfinity| . 1163523) - (|normalizeAtInfinity| . 1163219) (|complementaryBasis| . 1162915) - (|integral?| . 1162007) (|integralAtInfinity?| . 1161705) - (|integralBasisAtInfinity| . 1161404) (|ramified?| . 1160802) - (|ramifiedAtInfinity?| . 1160503) (|singular?| . 1159901) - (|singularAtInfinity?| . 1159602) (|branchPoint?| . 1159000) - (|branchPointAtInfinity?| . 1158701) (|rationalPoint?| . 1158031) - (|absolutelyIrreducible?| . 1157373) (|genus| . 1156693) - (|getZechTable| . 1156008) (|createZechTable| . 1155774) - (|createMultiplicationTable| . 1155480) - (|createMultiplicationMatrix| . 1155226) - (|createLowComplexityTable| . 1154956) - (|createLowComplexityNormalBasis| . 1154558) (|representationType| . 1154423) - (|createPrimitiveElement| . 1154368) (|tableForDiscreteLogarithm| . 1154198) - (|factorsOfCyclicGroupSize| . 1154019) (|sizeMultiplication| . 1152931) - (|getMultiplicationMatrix| . 1152119) (|getMultiplicationTable| . 1151251) - (|primitive?| . 1150949) (|numberOfIrreduciblePoly| . 1150781) - (|numberOfPrimitivePoly| . 1150613) (|numberOfNormalPoly| . 1150445) - (|createIrreduciblePoly| . 1150220) (|createPrimitivePoly| . 1149995) - (|createNormalPoly| . 1149770) (|createNormalPrimitivePoly| . 1149545) - (|createPrimitiveNormalPoly| . 1149320) (|nextIrreduciblePoly| . 1149136) - (|nextPrimitivePoly| . 1148952) (|nextNormalPoly| . 1148768) - (|nextNormalPrimitivePoly| . 1148584) (|nextPrimitiveNormalPoly| . 1148400) - (|leastAffineMultiple| . 1148218) (|reducedQPowers| . 1147960) - (|rootOfIrreduciblePoly| . 1147354) (|write!| . 1147211) (|read!| . 1147071) - (|iomode| . 1146897) (|close!| . 1146713) (|reopen!| . 1146543) - (|open| . 1146235) (|rightUnit| . 1146069) (|leftUnit| . 1145903) - (|rightMinimalPolynomial| . 1145676) (|leftMinimalPolynomial| . 1145449) - (|associatorDependence| . 1145003) (|lieAlgebra?| . 1144637) - (|jordanAlgebra?| . 1144271) (|noncommutativeJordanAlgebra?| . 1143905) - (|jordanAdmissible?| . 1143539) (|lieAdmissible?| . 1143173) - (|jacobiIdentity?| . 1142807) (|powerAssociative?| . 1142656) - (|alternative?| . 1142290) (|flexible?| . 1141924) - (|rightAlternative?| . 1141558) (|leftAlternative?| . 1141192) - (|antiAssociative?| . 1140826) (|associative?| . 1140460) - (|antiCommutative?| . 1140094) (|commutative?| . 1139728) - (|rightCharacteristicPolynomial| . 1139545) - (|leftCharacteristicPolynomial| . 1139362) (|rightNorm| . 1139236) - (|leftNorm| . 1139110) (|rightTrace| . 1138984) (|leftTrace| . 1138858) - (|someBasis| . 1138705) (|find| . 1138554) (|count| . 1138192) - (|every?| . 1138012) (|any?| . 1137832) (|sort!| . 1137419) - (|copyInto!| . 1137215) (|sorted?| . 1136855) (|LiePoly| . 1136669) - (|quickSort| . 1136364) (|heapSort| . 1136059) (|shellSort| . 1135754) - (|outputSpacing| . 1135633) (|outputGeneral| . 1135444) - (|outputFixed| . 1135255) (|outputFloating| . 1135066) (|exp1| . 1134985) - (|log10| . 1134861) (|log2| . 1134737) (|rationalApproximation| . 1134151) - (|relerror| . 1134072) (|complexSolve| . 1132903) (|complexRoots| . 1132344) - (|realRoots| . 1131840) (|leadingTerm| . 1131646) (|overlap| . 1131458) - (|hcrf| . 1131346) (|hclf| . 1131234) (|writable?| . 1131143) - (|readable?| . 1131052) (|exists?| . 1130961) (|extension| . 1130871) - (|directory| . 1130781) (|filename| . 1130685) (|shallowExpand| . 1130444) - (|deepExpand| . 1130203) (|fracPart| . 1129844) (|polyPart| . 1129637) - (|fullPartialFraction| . 1129391) (|primeFrobenius| . 1129206) - (|discreteLog| . 1128968) (|decreasePrecision| . 1128780) - (|increasePrecision| . 1128592) (|precision| . 1128328) (|bits| . 1127940) - (|mantissa| . 1127846) (|unitNormalize| . 1127753) (|unit| . 1127408) - (|flagFactor| . 1127212) (|sqfrFactor| . 1127081) (|primeFactor| . 1126950) - (|nthFlag| . 1126757) (|nthExponent| . 1126626) - (|irreducibleFactor| . 1126495) (|factors| . 1125922) (|nilFactor| . 1125791) - (|regularRepresentation| . 1125331) (|traceMatrix| . 1124622) - (|randomLC| . 1124232) (|minimize| . 1123900) (|module| . 1123164) - (|rightRegularRepresentation| . 1122818) - (|leftRegularRepresentation| . 1122472) (|rightTraceMatrix| . 1121923) - (|leftTraceMatrix| . 1121374) (|rightDiscriminant| . 1120915) - (|leftDiscriminant| . 1120456) (|represents| . 1119219) - (|mergeFactors| . 1119067) (|isMult| . 1118830) (|applyQuote| . 1118115) - (|ground| . 1117860) (|ground?| . 1117542) (|exprToXXP| . 1116752) - (|exprToUPS| . 1115475) (|exprToGenUPS| . 1114198) (|localAbs| . 1112791) - (|universe| . 1112656) (|complement| . 1112518) (|cardinality| . 1112363) - (|internalIntegrate0| . 1111810) (|makeCos| . 1111536) (|makeSin| . 1111262) - (|iiGamma| . 1111096) (|iiabs| . 1110930) (|bringDown| . 1110362) - (|newReduc| . 1110146) (|logical?| . 1110056) (|character?| . 1109966) - (|doubleComplex?| . 1109876) (|complex?| . 1109786) (|double?| . 1109696) - (|ffactor| . 1109390) (|qfactor| . 1109014) (|UP2ifCan| . 1108529) - (|anfactor| . 1108102) (|fortranCharacter| . 1108057) - (|fortranDoubleComplex| . 1108012) (|fortranComplex| . 1107967) - (|fortranLogical| . 1107922) (|fortranInteger| . 1107877) - (|fortranDouble| . 1107832) (|fortranReal| . 1107787) (|external?| . 1107705) - (|dimensionsOf| . 1107590) (|scalarTypeOf| . 1107444) (|makeFR| . 1106831) - (|musserTrials| . 1106472) (|stopMusserTrials| . 1106113) - (|numberOfFactors| . 1105708) (|modularFactor| . 1105482) - (|useSingleFactorBound?| . 1105318) (|useSingleFactorBound| . 1105151) - (|useEisensteinCriterion?| . 1104987) (|useEisensteinCriterion| . 1104820) - (|eisensteinIrreducible?| . 1104653) (|tryFunctionalDecomposition?| . 1104489) - (|tryFunctionalDecomposition| . 1104322) (|btwFact| . 1103831) - (|beauzamyBound| . 1103387) (|bombieriNorm| . 1102518) (|rootBound| . 1102074) - (|singleFactorBound| . 1101139) (|quadraticNorm| . 1100723) - (|infinityNorm| . 1100307) (|scaleRoots| . 1100128) (|shiftRoots| . 1099949) - (|degreePartition| . 1099396) (|factorOfDegree| . 1097889) - (|factorsOfDegree| . 1097607) (|pascalTriangle| . 1097435) - (|rangePascalTriangle| . 1097158) (|sizePascalTriangle| . 1097020) - (|fillPascalTriangle| . 1096896) (|safeCeiling| . 1096724) - (|safeFloor| . 1096552) (|safetyMargin| . 1096177) (|sumSquares| . 1096025) - (|euclideanNormalForm| . 1095706) (|euclideanGroebner| . 1094699) - (|factorGroebnerBasis| . 1093881) (|groebnerFactorize| . 1092241) - (|credPol| . 1091934) (|redPol| . 1091627) (|gbasis| . 1091289) - (|critT| . 1090869) (|critM| . 1090569) (|critB| . 1090263) - (|critBonD| . 1089856) (|critMTonD1| . 1089452) (|critMonD1| . 1089045) - (|redPo| . 1088672) (|hMonic| . 1088403) (|updatF| . 1088003) - (|sPol| . 1087614) (|updatD| . 1087207) (|minGbasis| . 1086903) - (|lepol| . 1086606) (|prinshINFO| . 1086312) (|prindINFO| . 1085852) - (|fprindINFO| . 1085389) (|prinpolINFO| . 1085060) (|prinb| . 1084738) - (|critpOrder| . 1084315) (|makeCrit| . 1083808) (|virtualDegree| . 1083500) - (|lcm| . 1083369) (|conditionsForIdempotents| . 1081998) - (|genericRightDiscriminant| . 1081652) (|genericRightTraceForm| . 1081300) - (|genericLeftDiscriminant| . 1080954) (|genericLeftTraceForm| . 1080602) - (|genericRightNorm| . 1080253) (|genericRightTrace| . 1079904) - (|genericRightMinimalPolynomial| . 1079540) (|rightRankPolynomial| . 1078711) - (|genericLeftNorm| . 1078362) (|genericLeftTrace| . 1078013) - (|genericLeftMinimalPolynomial| . 1077649) (|leftRankPolynomial| . 1076820) - (|generic| . 1074956) (|rightUnits| . 1074327) (|leftUnits| . 1073698) - (|compBound| . 1073446) (|tablePow| . 1073158) (|solveid| . 1072912) - (|testModulus| . 1072678) (|HenselLift| . 1072336) - (|completeHensel| . 1072079) (|multMonom| . 1071494) (|build| . 1070909) - (|leadingIndex| . 1070330) (|leadingExponent| . 1069751) - (|GospersMethod| . 1069163) (|nextSubsetGray| . 1069014) - (|firstSubsetGray| . 1068861) (|clipPointsDefault| . 1068688) - (|drawToScale| . 1068515) (|adaptive| . 1068122) (|figureUnits| . 1067952) - (|putColorInfo| . 1067790) (|appendPoint| . 1067658) (|component| . 1067097) - (|ranges| . 1066604) (|pointLists| . 1066482) (|makeGraphImage| . 1065822) - (|graphImage| . 1065778) (|groebSolve| . 1065368) (|testDim| . 1065042) - (|genericPosition| . 1064561) (|lfunc| . 1064476) (|inHallBasis?| . 1064350) - (|reorder| . 1063586) (|parameters| . 1063385) (|headAst| . 1063250) - (|heap| . 1063130) (|gcdprim| . 1062978) (|gcdcofact| . 1062819) - (|gcdcofactprim| . 1062660) (|lintgcd| . 1062473) (|hex| . 1062360) - (|host| . 1062282) (|trueEqual| . 1062186) (|factorList| . 1061554) - (|listConjugateBases| . 1060943) (|matrixGcd| . 1060481) - (|divideIfCan!| . 1060027) (|leastPower| . 1059598) (|idealiser| . 1058757) - (|idealiserMatrix| . 1058337) (|moduleSum| . 1057848) - (|mapUnivariate| . 1057112) (|mapUnivariateIfCan| . 1056734) - (|mapMatrixIfCan| . 1056312) (|mapBivariate| . 1055904) - (|fullDisplay| . 1054990) (|relationsIdeal| . 1054512) (|saturate| . 1053961) - (|groebner?| . 1053675) (|groebnerIdeal| . 1053382) (|ideal| . 1052367) - (|leadingIdeal| . 1052109) (|backOldPos| . 1051712) - (|generalPosition| . 1051256) (|quotient| . 1050736) (|zeroDim?| . 1050128) - (|inRadical?| . 1049839) (|in?| . 1049550) (|element?| . 1049261) - (|zeroDimPrime?| . 1048676) (|zeroDimPrimary?| . 1048091) - (|radical| . 1047537) (|primaryDecomp| . 1046502) (|contract| . 1045473) - (|gensym| . 1045429) (|leadingSupport| . 1045275) (|combineWithIf| . 1045012) - (|term| . 1044867) (|shrinkable| . 1044580) (|physicalLength!| . 1044296) - (|physicalLength| . 1043987) (|flexibleArray| . 1043700) - (|elseBranch| . 1043624) (|thenBranch| . 1043548) - (|generalizedInverse| . 1043262) (|imports| . 1043171) (|sequence| . 1043095) - (|readBytes!| . 1042952) (|readUInt32!| . 1042845) (|readInt32!| . 1042739) - (|readUInt16!| . 1042632) (|readInt16!| . 1042526) (|readUInt8!| . 1042420) - (|readInt8!| . 1042315) (|readByte!| . 1042210) (|setFieldInfo| . 1041948) - (|pol| . 1041734) (|xn| . 1041504) (|dAndcExp| . 1041254) (|repSq| . 1041048) - (|expPot| . 1040844) (|qPot| . 1040649) (|lookup| . 1040362) - (|normal?| . 1039786) (|basis| . 1037944) (|normalElement| . 1037606) - (|minimalPolynomial| . 1036777) (|position!| . 1036680) (|eof?| . 1036592) - (|inputBinaryFile| . 1036418) (|increment| . 1036250) - (|incrementBy| . 1036079) (|charpol| . 1035784) (|solve1| . 1035488) - (|innerEigenvectors| . 1034930) (|compile| . 1034800) (|declare| . 1034673) - (|parseString| . 1034594) (|unparse| . 1034515) (|flatten| . 1034469) - (|lambda| . 1034376) (|binary| . 1034174) (|packageCall| . 1034016) - (|interpret| . 1033811) (|innerSolve1| . 1033219) (|innerSolve| . 1032863) - (|makeEq| . 1032509) (|modularGcdPrimitive| . 1032217) - (|modularGcd| . 1031925) (|reduction| . 1031318) (|signAround| . 1030543) - (|invmod| . 1030482) (|powmod| . 1030418) (|mulmod| . 1030354) - (|submod| . 1030290) (|addmod| . 1030226) (|mask| . 1030168) (|dec| . 1030110) - (|inc| . 1030052) (|symmetricRemainder| . 1029991) - (|positiveRemainder| . 1029930) (|bit?| . 1029833) (|algint| . 1029360) - (|algintegrate| . 1028757) (|palgintegrate| . 1028154) - (|palginfieldint| . 1027684) (|bitLength| . 1027602) (|bitCoef| . 1027515) - (|bitTruth| . 1027393) (|contains?| . 1027146) (|inf| . 1026937) - (|qinterval| . 1026725) (|interval| . 1026051) (|unit?| . 1025962) - (|associates?| . 1025870) (|unitCanonical| . 1025817) (|unitNormal| . 1025661) - (|lfextendedint| . 1025090) (|lflimitedint| . 1024395) - (|lfinfieldint| . 1023893) (|lfintegrate| . 1023317) (|lfextlimint| . 1022671) - (|BasicMethod| . 1022508) (|PollardSmallFactor| . 1022378) - (|palgint0| . 1021046) (|palgextint0| . 1019732) (|palglimint0| . 1018170) - (|palgRDE0| . 1016844) (|palgLODE0| . 1015200) (|chineseRemainder| . 1014131) - (|divisors| . 1013979) (|eulerPhi| . 1013871) (|fibonacci| . 1013763) - (|harmonic| . 1013607) (|jacobi| . 1013496) (|moebiusMu| . 1013388) - (|numberOfDivisors| . 1013280) (|sumOfDivisors| . 1013172) - (|sumOfKthPowerDivisors| . 1013022) (|HermiteIntegrate| . 1012178) - (|palgint| . 1011578) (|palgextint| . 1010983) (|palglimint| . 1010264) - (|palgRDE| . 1009659) (|palgLODE| . 1008872) (|splitConstant| . 1008325) - (|pmComplexintegrate| . 1007629) (|pmintegrate| . 1006263) - (|infieldint| . 1005956) (|extendedint| . 1005556) (|limitedint| . 1005040) - (|integerIfCan| . 1004891) (|internalIntegrate| . 1003942) - (|infieldIntegrate| . 1003630) (|limitedIntegrate| . 1003094) - (|extendedIntegrate| . 1002663) (|varselect| . 1002440) (|kmax| . 1002217) - (|ksec| . 1001954) (|vark| . 1001696) (|removeConstantTerm| . 1001468) - (|mkPrim| . 1001189) (|intPatternMatch| . 1000413) (|primintegrate| . 999907) - (|expintegrate| . 999378) (|tanintegrate| . 998901) - (|primextendedint| . 998344) (|expextendedint| . 997764) - (|primlimitedint| . 997099) (|explimitedint| . 996415) - (|primextintfrac| . 996076) (|primlimintfrac| . 995621) - (|primintfldpoly| . 995329) (|expintfldpoly| . 994977) - (|monomialIntegrate| . 994569) (|monomialIntPoly| . 994281) - (|inverseLaplace| . 993695) (|inputOutputBinaryFile| . 993509) - (|closed| . 993469) (|bothWays| . 993429) (|input| . 993121) - (|resolve| . 992989) (|bytes| . 992886) (|ip4Address| . 992806) - (|iprint| . 992682) (|elem?| . 992554) (|notelem| . 992380) - (|logpart| . 992069) (|ratpart| . 991976) (|mkAnswer| . 991581) - (|irDef| . 991429) (|irCtor| . 991280) (|irVar| . 991131) - (|perfectNthPower?| . 990945) (|perfectNthRoot| . 990589) - (|approxNthRoot| . 990431) (|perfectSquare?| . 990294) - (|perfectSqrt| . 990179) (|approxSqrt| . 990070) - (|generateIrredPoly| . 989849) (|complexExpand| . 989034) - (|complexIntegrate| . 988112) - (|dimensionOfIrreducibleRepresentation| . 987950) - (|irreducibleRepresentation| . 987333) (|checkRur| . 986829) - (|cAcsch| . 986653) (|cAsech| . 986477) (|cAcoth| . 986301) - (|cAtanh| . 986125) (|cAcosh| . 985949) (|cAsinh| . 985773) (|cCsch| . 985597) - (|cSech| . 985421) (|cCoth| . 985245) (|cTanh| . 985069) (|cCosh| . 984893) - (|cSinh| . 984717) (|cAcsc| . 984541) (|cAsec| . 984365) (|cAcot| . 984189) - (|cAtan| . 984013) (|cAcos| . 983837) (|cAsin| . 983661) (|cCsc| . 983485) - (|cSec| . 983309) (|cCot| . 983133) (|cTan| . 982957) (|cCos| . 982781) - (|cSin| . 982605) (|cLog| . 982429) (|cExp| . 982253) - (|cRationalPower| . 982055) (|cPower| . 981876) - (|seriesToOutputForm| . 981493) (|iCompose| . 981376) - (|taylorQuoByVar| . 981262) (|iExquo| . 981105) (|getStream| . 980911) - (|getRef| . 980726) (|makeSeries| . 980458) (|mappingMode| . 980341) - (|categoryMode| . 980291) (|voidMode| . 980241) (|noValueMode| . 980191) - (|jokerMode| . 980141) (GF2FG . 979613) (FG2F . 979123) (F2FG . 978633) - (|explogs2trigs| . 978112) (|trigs2explogs| . 977527) (|swap!| . 977296) - (|fill!| . 976874) (|minIndex| . 976706) (|maxIndex| . 976538) - (|entry?| . 976285) (|indices| . 976115) (|index?| . 975942) - (|entries| . 975772) (|categories| . 975540) (|jvmInterface| . 975488) - (|jvmSuper| . 975436) (|jvmNameAndTypeConstantTag| . 975388) - (|jvmInterfaceMethodConstantTag| . 975340) - (|jvmMethodrefConstantTag| . 975292) (|jvmFieldrefConstantTag| . 975244) - (|jvmStringConstantTag| . 975196) (|jvmClassConstantTag| . 975148) - (|jvmDoubleConstantTag| . 975100) (|jvmLongConstantTag| . 975052) - (|jvmFloatConstantTag| . 975004) (|jvmIntegerConstantTag| . 974956) - (|jvmUTF8ConstantTag| . 974908) (|jvmTransient| . 974860) - (|jvmVolatile| . 974812) (|jvmStrict| . 974763) (|jvmAbstract| . 974664) - (|jvmNative| . 974615) (|jvmSynchronized| . 974566) (|jvmFinal| . 974421) - (|jvmStatic| . 974326) (|jvmProtected| . 974231) (|jvmPrivate| . 974136) - (|jvmPublic| . 973991) (|search| . 973839) (|keys| . 973661) (|key?| . 973480) - (|symbolIfCan| . 973352) (|kernel| . 972787) (|argument| . 972394) - (|constantKernel| . 972222) (|constantIfCan| . 972041) (|kovacic| . 971085) - (|unknown| . 971031) (|laplace| . 970479) (|trailingCoefficient| . 970306) - (|normalizeIfCan| . 969851) (|polCase| . 969467) (|distFact| . 968724) - (|identification| . 968383) (|LyndonCoordinates| . 968030) - (|LyndonBasis| . 967656) (|zeroDimensional?| . 967164) (|fglmIfCan| . 966723) - (|groebner| . 965086) (|lexTriangular| . 964760) - (|squareFreeLexTriangular| . 963963) (|belong?| . 962175) (|erf| . 961837) - (|dilog| . 961499) (|li| . 961161) (|Ci| . 960823) (|Si| . 960485) - (|Ei| . 960147) (|linGenPos| . 959771) (|groebgen| . 959390) - (|totolex| . 959090) (|minPol| . 958387) (|computeBasis| . 958159) - (|coord| . 957482) (|anticoord| . 957149) (|intcompBasis| . 956869) - (|choosemon| . 956581) (|transform| . 956294) (|pack!| . 956148) - (|library| . 956069) (|complexLimit| . 954930) (|limit| . 952104) - (|linearlyDependent?| . 951853) (|linearDependence| . 951602) - (|solveLinear| . 951016) (|linearElement| . 950848) (|reducedSystem| . 950403) - (|leftReducedSystem| . 949988) (|linearForm| . 949830) - (|setDifference| . 949707) (|setIntersection| . 949584) (|setUnion| . 949461) - (|append| . 949381) (|null| . 949267) (|nil| . 949193) (|substitute| . 949079) - (|duplicates?| . 948943) (|mapGen| . 948238) (|mapExpon| . 947696) - (|commutativeEquality| . 947497) (|plus| . 947154) (|leftMult| . 946983) - (|rightMult| . 946812) (|makeUnit| . 946647) (|reverse!| . 946227) - (|reverse| . 945782) (|nthFactor| . 944979) (|nthExpon| . 944469) - (|makeMulti| . 944235) (|makeTerm| . 944064) (|listOfMonoms| . 943823) - (|insert| . 943559) (|delete| . 943280) (|symmetricSquare| . 943126) - (|factor1| . 942514) (|symmetricProduct| . 942120) (|symmetricPower| . 941634) - (|directSum| . 941240) (|\\/| . 941193) (|/\\| . 941146) (~ . 941102) - (|solveLinearPolynomialEquationByFractions| . 940834) - (|hasSolution?| . 940129) (|linSolve| . 939608) (|LyndonWordsList| . 939386) - (|LyndonWordsList1| . 939140) (|lyndonIfCan| . 938995) (|lyndon| . 938856) - (|lyndon?| . 938682) (|numberOfComputedEntries| . 938540) (|rst| . 938437) - (|frst| . 938334) (|lazyEvaluate| . 938231) (|lazy?| . 938100) - (|explicitlyEmpty?| . 937969) (|explicitEntries?| . 937838) (|iter| . 937635) - (|arg1| . 937478) (|arg2| . 937321) (|comp| . 937042) (|mappingAst| . 936912) - (|nullary| . 936777) (|fixedPoint| . 936417) (|id| . 936313) - (|recur| . 935921) (|const| . 935739) (|curry| . 935523) (|diag| . 935304) - (|curryRight| . 935038) (|curryLeft| . 934772) (|constantRight| . 934509) - (|constantLeft| . 934246) (|twist| . 933980) (|setsubMatrix!| . 933731) - (|subMatrix| . 933479) (|swapColumns!| . 933233) (|swapRows!| . 932987) - (|vertConcat| . 932779) (|horizConcat| . 932571) (|squareTop| . 932366) - (|elRow1!| . 932041) (|elRow2!| . 931713) (|elColumn2!| . 931385) - (|fractionFreeGauss!| . 931050) (|invertIfCan| . 930725) (|copy!| . 930578) - (|plus!| . 930428) (|minus!| . 930133) (|leftScalarTimes!| . 929983) - (|rightScalarTimes!| . 929833) (|times!| . 929683) (|power!| . 929481) - (|nothing| . 929375) (|just| . 929266) (|duplicates| . 929046) - (|removeDuplicates!| . 928801) (|linears| . 928623) (|ddFact| . 928366) - (|separateFactors| . 927775) (|exptMod| . 927357) (|meshPar2Var| . 926215) - (|meshFun2Var| . 925751) (|meshPar1Var| . 925384) (|ptFunc| . 925003) - (|rowEch| . 924852) (|rowEchLocal| . 924698) (|rowEchelonLocal| . 924541) - (|normalizedDivide| . 923930) (|binaryFunction| . 923624) - (|makeFloatFunction| . 923131) (|function| . 922366) (|makeRecord| . 922173) - (|unaryFunction| . 921908) (|compiledFunction| . 921330) (|corrPoly| . 920744) - (|lifting| . 920134) (|lifting1| . 919384) (|exprex| . 919262) - (|coerceL| . 919140) (|coerceS| . 919018) (|frobenius| . 918822) - (|computePowers| . 918610) (|pow| . 918398) (|An| . 918214) - (|UnVectorise| . 918030) (|Vectorise| . 917846) (|setPoly| . 917699) - (|index| . 916947) (|exponent| . 916187) (|exQuo| . 915173) - (|moebius| . 915072) (|rightRecip| . 914843) (|leftRecip| . 914614) - (|leftPower| . 914416) (|rightPower| . 914218) - (|derivationCoordinates| . 913904) (|generator| . 912721) (|one?| . 912198) - (|monoidOperation| . 912056) (|neutralValue| . 911945) - (|splitSquarefree| . 911609) (|normalDenom| . 911364) (|reshape| . 910553) - (|totalfract| . 909928) (|pushdterm| . 909345) (|pushucoef| . 908747) - (|pushuconst| . 908259) (|numberOfMonomials| . 907714) (|unique| . 907589) - (|multiset| . 907291) (|systemCommand| . 907169) (|mergeDifference| . 907040) - (|squareFreePrim| . 906734) (|compdegd| . 906304) (|univcase| . 905995) - (|consnewpol| . 905418) (|nsqfree| . 904726) (|intChoose| . 903930) - (|coefChoose| . 903593) (|myDegree| . 903127) (|normDeriv2| . 902765) - (|plenaryPower| . 902603) (|antiCommutator| . 902544) (|commutator| . 902440) - (|associator| . 902378) (|complexEigenvalues| . 902123) - (|complexEigenvectors| . 901727) (|isConnected?| . 901589) - (|connectTo| . 901214) (|shift| . 900801) (|normalizedAssociate| . 900450) - (|normalize| . 899062) (|outputArgs| . 898646) (|normInvertible?| . 898203) - (|normFactors| . 897816) (|npcoef| . 896977) (|listexp| . 896607) - (|characteristicPolynomial| . 894460) (|realEigenvalues| . 894232) - (|realEigenvectors| . 893875) (|halfExtendedResultant2| . 893605) - (|halfExtendedResultant1| . 893335) (|extendedResultant| . 893030) - (|subResultantsChain| . 892810) (|lazyPseudoQuotient| . 892696) - (|lazyPseudoRemainder| . 892582) (|bernoulliB| . 892344) (|eulerE| . 892106) - (|numeric| . 890387) (|complexNumeric| . 886345) (|numericIfCan| . 884912) - (|complexNumericIfCan| . 881711) (|FormatArabic| . 881583) - (|ScanArabic| . 881455) (|FormatRoman| . 881327) (|ScanRoman| . 881199) - (|ScanFloatIgnoreSpaces| . 881081) (|ScanFloatIgnoreSpacesIfCan| . 880957) - (|rk4| . 880339) (|rk4a| . 880026) (|rk4qc| . 879159) (|rk4f| . 878852) - (|aromberg| . 878510) (|asimpson| . 878168) (|atrapezoidal| . 877826) - (|romberg| . 877487) (|simpson| . 877148) (|trapezoidal| . 876809) - (|rombergo| . 876470) (|simpsono| . 876131) (|trapezoidalo| . 875792) - (|sup| . 875520) (|inv| . 874246) (|imagE| . 874135) (|imagk| . 874024) - (|imagj| . 873913) (|imagi| . 873802) (|octon| . 873534) - (|constDsolve| . 872818) (|expint| . 872271) (|diff| . 871686) - (|algDsolve| . 871002) (|denomLODE| . 869989) (|indicialEquations| . 867805) - (|indicialEquation| . 866805) (|denomRicDE| . 866304) - (|leadingCoefficientRicDE| . 865740) (|constantCoefficientRicDE| . 865109) - (|changeVar| . 864149) (|ratDsolve| . 861861) - (|indicialEquationAtInfinity| . 861037) (|reduceLODE| . 860572) - (|singRicDE| . 859060) (|polyRicDE| . 857632) (|ricDsolve| . 853334) - (|triangulate| . 852488) (|solveInField| . 851379) - (|wronskianMatrix| . 850878) (|variationOfParameters| . 850643) - (|lexico| . 850258) (|po| . 850086) (|op| . 849914) (|infinity| . 849704) - (|makeop| . 849372) (|opeval| . 849068) (|evaluateInverse| . 848771) - (|evaluate| . 847699) (|conjug| . 847393) (|adjoint| . 846250) - (|arity| . 846117) (|getDatabase| . 845980) (|whatInfinity| . 845833) - (|infinite?| . 845566) (|finite?| . 845214) (|minusInfinity| . 845006) - (|plusInfinity| . 844798) (|pureLex| . 844575) (|totalLex| . 844352) - (|reverseLex| . 844129) (|min| . 843599) (|leftLcm| . 843279) - (|rightExtendedGcd| . 843035) (|rightGcd| . 842888) - (|rightExactQuotient| . 842735) (|rightRemainder| . 842588) - (|rightQuotient| . 842441) (|rightLcm| . 842294) (|leftExtendedGcd| . 842050) - (|leftGcd| . 841730) (|leftExactQuotient| . 841402) (|leftRemainder| . 841082) - (|leftQuotient| . 840762) (|times| . 840491) (|apply| . 839674) - (|monicLeftDivide| . 839099) (|monicRightDivide| . 838524) - (|leftDivide| . 837719) (|rightDivide| . 837162) (|hermiteH| . 836991) - (|laguerreL| . 836648) (|legendreP| . 836415) (|outputList| . 836292) - (|writeBytes!| . 836148) (|writeUInt8!| . 836012) (|writeInt8!| . 835878) - (|writeByte!| . 835744) (|isOpen?| . 835477) (|outputBinaryFile| . 835301) - (|not| . 835205) (|or| . 835103) (|and| . 835001) (|quo| . 834840) - (|rem| . 834679) (|div| . 834429) (>= . 834292) (> . 834155) (~= . 834020) - (|blankSeparate| . 833925) (|semicolonSeparate| . 833830) - (|commaSeparate| . 833735) (|pile| . 833640) (|paren| . 833360) - (|bracket| . 833220) (|prod| . 833074) (|overlabel| . 833024) - (|overbar| . 832977) (|prime| . 832835) (|quote| . 832747) - (|supersub| . 832649) (|presuper| . 832599) (|presub| . 832549) - (|super| . 832499) (|sub| . 832449) (|rarrow| . 832399) (|assign| . 832349) - (|slash| . 832299) (|over| . 832249) (|zag| . 832199) (|box| . 832012) - (|label| . 831962) (|infix?| . 831881) (|postfix| . 831831) (|infix| . 831682) - (|prefix| . 831584) (|vconcat| . 831441) (|hconcat| . 831298) - (|rspace| . 831212) (|vspace| . 831131) (|hspace| . 831050) - (|superHeight| . 830969) (|subHeight| . 830888) (|height| . 829942) - (|width| . 829578) (|doubleFloatFormat| . 829498) (|messagePrint| . 829384) - (|message| . 829304) (|members| . 829068) (|padecf| . 828749) - (|pade| . 827790) (|root| . 827523) (|quotientByP| . 827461) - (|moduloP| . 827356) (|modulus| . 826080) (|digits| . 825389) - (|continuedFraction| . 824380) (|pair| . 824261) (|light| . 824185) - (|pastel| . 824109) (|bright| . 823813) (|dim| . 823737) (|dark| . 823661) - (|getSyntaxFormsFromFile| . 823540) (|surface| . 823442) - (|coordinate| . 823017) (|conjugates| . 822884) (|shuffle| . 822712) - (|shufflein| . 822540) (|sequences| . 822201) (|permutations| . 822041) - (|lists| . 821785) (|makeResult| . 821481) (|is?| . 820263) (|Is| . 818895) - (|addMatchRestricted| . 818704) (|insertMatch| . 818516) (|addMatch| . 818328) - (|getMatch| . 818141) (|failed| . 817801) (|failed?| . 817399) - (|optpair| . 817257) (|getBadValues| . 817128) (|resetBadValues| . 817039) - (|hasTopPredicate?| . 816915) (|topPredicate| . 816736) - (|setTopPredicate| . 816574) (|patternVariable| . 816414) - (|withPredicates| . 816282) (|setPredicates| . 816150) (|predicates| . 816021) - (|hasPredicate?| . 815897) (|optional?| . 815773) (|multiple?| . 815649) - (|generic?| . 815525) (|quoted?| . 815401) (|inR?| . 815277) - (|isList| . 815135) (|isQuotient| . 814957) (|isOp| . 814562) - (|Zero| . 814240) (|satisfy?| . 813581) (|addBadValue| . 813290) - (|badValues| . 813088) (|retractable?| . 812204) (|ListOfTerms| . 811453) - (|One| . 810976) (|leftFactor| . 810801) (|rightFactorCandidate| . 810589) - (D . 809257) (|ptree| . 809070) (|coerceImages| . 808942) - (|fixedPoints| . 808786) (|odd?| . 808423) (|even?| . 808060) - (|numberOfCycles| . 807921) (|cyclePartition| . 807791) - (|coerceListOfPairs| . 807654) (|coercePreimagesImages| . 807517) - (|listRepresentation| . 807332) (|permanent| . 807016) (|cycles| . 806869) - (|cycle| . 806731) (|initializeGroupForWordProblem| . 806432) (<= . 806161) - (< . 805751) (|support| . 805484) (|wordInGenerators| . 805286) - (|wordInStrongGenerators| . 805088) (|orbits| . 804941) (|orbit| . 804330) - (|permutationGroup| . 804174) (|wordsForStrongGenerators| . 804005) - (|strongGenerators| . 803849) (|base| . 803484) (|generators| . 803044) - (|bivariateSLPEBR| . 802627) - (|solveLinearPolynomialEquationByRecursion| . 801878) - (|factorByRecursion| . 801107) (|factorSquareFreeByRecursion| . 800336) - (|randomR| . 799535) (|factorSFBRlcUnit| . 798733) (|charthRoot| . 798417) - (|conditionP| . 798079) (|solveLinearPolynomialEquation| . 797041) - (|factorSquareFreePolynomial| . 796836) (|factorPolynomial| . 796331) - (|squareFreePolynomial| . 795826) (|gcdPolynomial| . 795221) - (|torsion?| . 794239) (|torsionIfCan| . 793225) (|getGoodPrime| . 792924) - (|badNum| . 792356) (|mix| . 792018) (|doubleDisc| . 791760) - (|polyred| . 791533) (|padicFraction| . 791425) (|padicallyExpand| . 791257) - (|numberOfFractionalTerms| . 791121) (|nthFractionalTerm| . 790982) - (|firstNumer| . 790874) (|firstDenom| . 790734) (|compactFraction| . 790626) - (|partialFraction| . 789926) (|gcdPrimitive| . 789037) - (|symmetricGroup| . 788702) (|alternatingGroup| . 788367) - (|abelianGroup| . 788190) (|cyclicGroup| . 787855) (|dihedralGroup| . 787520) - (|mathieu11| . 787231) (|mathieu12| . 786942) (|mathieu22| . 786653) - (|mathieu23| . 786364) (|mathieu24| . 786075) (|janko2| . 785786) - (|rubiksGroup| . 785664) (|youngGroup| . 785335) (|lexGroebner| . 785147) - (|totalGroebner| . 784959) (|expressIdealMember| . 784816) - (|principalIdeal| . 784634) (|LagrangeInterpolation| . 784423) - (|psolve| . 775850) (|wrregime| . 775020) (|rdregime| . 774134) - (|bsolve| . 772882) (|dmp2rfi| . 771591) (|se2rfi| . 771138) - (|pr2dmp| . 770750) (|hasoln| . 770238) (|ParCondList| . 769412) - (|redpps| . 768854) (|B1solve| . 768030) (|factorset| . 767648) - (|maxrank| . 766946) (|minrank| . 766244) (|minset| . 765853) - (|nextSublist| . 765415) (|overset?| . 764958) (|ParCond| . 764370) - (|redmat| . 763955) (|regime| . 762848) (|sqfree| . 762501) - (|inconsistent?| . 761654) (|debug| . 761579) (|numFunEvals| . 761507) - (|setAdaptive| . 761432) (|adaptive?| . 761360) - (|setScreenResolution| . 761285) (|screenResolution| . 761042) - (|setMaxPoints| . 760967) (|maxPoints| . 760724) (|setMinPoints| . 760649) - (|minPoints| . 760406) (|parametric?| . 760331) (|plotPolar| . 759649) - (|debug3D| . 759572) (|numFunEvals3D| . 759498) (|setAdaptive3D| . 759421) - (|adaptive3D?| . 759347) (|setScreenResolution3D| . 759270) - (|screenResolution3D| . 759196) (|setMaxPoints3D| . 759119) - (|maxPoints3D| . 759045) (|setMinPoints3D| . 758968) (|minPoints3D| . 758894) - (|tValues| . 758786) (|tRange| . 758600) (|plot| . 756598) - (|pointPlot| . 755893) (|calcRanges| . 755712) (|assert| . 755244) - (|optional| . 754941) (|multiple| . 754638) (|fixPredicate| . 754303) - (|patternMatch| . 749580) (|patternMatchTimes| . 749061) - (|bernoulli| . 748717) (|chebyshevT| . 748371) (|chebyshevU| . 748025) - (|cyclotomic| . 747503) (|euler| . 747207) (|fixedDivisor| . 747030) - (|laguerre| . 746853) (|legendre| . 746554) (|dmpToHdmp| . 746282) - (|hdmpToDmp| . 746010) (|pToHdmp| . 745771) (|hdmpToP| . 745532) - (|dmpToP| . 745304) (|pToDmp| . 745076) (|sylvesterSequence| . 744868) - (|sturmSequence| . 744663) (|boundOfCauchy| . 744452) - (|sturmVariationsOf| . 744167) (|lazyVariations| . 743841) - (|content| . 743082) (|primitiveMonomials| . 742860) (|totalDegree| . 742344) - (|minimumDegree| . 741368) (|monomials| . 740811) (|isPlus| . 739731) - (|isTimes| . 738658) (|isExpt| . 736827) (|isPower| . 735853) - (|rroot| . 735150) (|qroot| . 734399) (|froot| . 733657) (|nthr| . 732945) - (|port| . 732856) (|firstUncouplingMatrix| . 732582) (|integral| . 731472) - (|primitiveElement| . 729201) (|nextPrime| . 729084) (|prevPrime| . 728967) - (|primes| . 728819) (|print| . 728623) (|selectsecond| . 728490) - (|selectfirst| . 728357) (|makeprod| . 728221) (|property| . 727839) - (|disjunction| . 727727) (|conjunction| . 727615) (|isEquiv| . 727429) - (|isImplies| . 727243) (|isOr| . 727057) (|isAnd| . 726871) (|isNot| . 726701) - (|isAtom| . 726563) (|atoms| . 726112) (|dual| . 725680) (|equiv| . 725620) - (|implies| . 725560) (|false| . 725506) (|true| . 725452) (|merge!| . 725028) - (|max| . 724500) (|resultantEuclidean| . 724221) - (|semiResultantEuclidean2| . 723967) (|semiResultantEuclidean1| . 723713) - (|indiceSubResultant| . 723482) (|indiceSubResultantEuclidean| . 723151) - (|semiIndiceSubResultantEuclidean| . 722845) (|degreeSubResultant| . 722614) - (|degreeSubResultantEuclidean| . 722283) - (|semiDegreeSubResultantEuclidean| . 721977) - (|lastSubResultantEuclidean| . 721695) - (|semiLastSubResultantEuclidean| . 721438) - (|subResultantGcdEuclidean| . 721165) - (|semiSubResultantGcdEuclidean2| . 720917) - (|semiSubResultantGcdEuclidean1| . 720669) (|discriminantEuclidean| . 720390) - (|semiDiscriminantEuclidean| . 720136) (|chainSubResultants| . 719926) - (|schema| . 719689) (|resultantReduit| . 719475) - (|resultantReduitEuclidean| . 719140) - (|semiResultantReduitEuclidean| . 718848) (|divide| . 718099) - (|Lazard| . 717868) (|Lazard2| . 717634) (|nextsousResultant2| . 717446) - (|resultantnaif| . 717264) (|resultantEuclideannaif| . 716985) - (|semiResultantEuclideannaif| . 716731) (|pdct| . 716641) (|powers| . 716507) - (|partitions| . 716366) (|parts| . 716260) (|partition| . 716031) - (|complete| . 715394) (|pole?| . 715049) (|monomial| . 711798) - (|leadingMonomial| . 710546) (|zRange| . 710421) (|yRange| . 710173) - (|xRange| . 709925) (|listBranches| . 709645) (|triangular?| . 709307) - (|rewriteIdealWithRemainder| . 708959) - (|rewriteIdealWithHeadRemainder| . 708611) (|remainder| . 708207) - (|headRemainder| . 707830) (|roughUnitIdeal?| . 707492) - (|roughEqualIdeals?| . 707151) (|roughSubIdeal?| . 706810) - (|roughBase?| . 706472) (|trivialIdeal?| . 706171) (|sort| . 705372) - (|collectUpper| . 705103) (|collect| . 704834) (|collectUnder| . 704565) - (|mainVariable?| . 704261) (|mainVariables| . 703960) - (|removeSquaresIfCan| . 703636) (|unprotectedRemoveRedundantFactors| . 703316) - (|removeRedundantFactors| . 701642) (|certainlySubVariety?| . 701287) - (|possiblyNewVariety?| . 700895) (|probablyZeroDim?| . 700543) - (|selectPolynomials| . 700072) (|selectOrPolynomials| . 699592) - (|selectAndPolynomials| . 699112) (|quasiMonicPolynomials| . 698694) - (|univariate?| . 698377) (|univariatePolynomials| . 697959) - (|linear?| . 697642) (|linearPolynomials| . 697224) (|bivariate?| . 696907) - (|bivariatePolynomials| . 696489) - (|removeRoughlyRedundantFactorsInPols| . 695806) - (|removeRoughlyRedundantFactorsInPol| . 695479) (|interReduce| . 695155) - (|roughBasicSet| . 694720) (|crushedSet| . 694396) - (|rewriteSetByReducingWithParticularGenerators| . 693923) - (|rewriteIdealWithQuasiMonicGenerators| . 693496) - (|squareFreeFactors| . 693147) (|univariatePolynomialsGcds| . 692406) - (|removeRoughlyRedundantFactorsInContents| . 692047) - (|removeRedundantFactorsInContents| . 691688) - (|removeRedundantFactorsInPols| . 691329) (|irreducibleFactors| . 690912) - (|lazyIrreducibleFactors| . 690495) - (|removeIrreducibleRedundantFactors| . 690075) (|normalForm| . 689429) - (|changeBase| . 689208) (|companionBlocks| . 688936) (|xCoord| . 688813) - (|yCoord| . 688690) (|zCoord| . 688567) (|rCoord| . 688444) - (|thetaCoord| . 688321) (|phiCoord| . 688198) (|color| . 688001) - (|hue| . 687730) (|shade| . 687531) (|nthRootIfCan| . 687340) - (|expIfCan| . 687194) (|logIfCan| . 687048) (|sinIfCan| . 686902) - (|cosIfCan| . 686756) (|tanIfCan| . 686610) (|cotIfCan| . 686464) - (|secIfCan| . 686318) (|cscIfCan| . 686172) (|asinIfCan| . 686026) - (|acosIfCan| . 685880) (|atanIfCan| . 685734) (|acotIfCan| . 685588) - (|asecIfCan| . 685442) (|acscIfCan| . 685296) (|sinhIfCan| . 685150) - (|coshIfCan| . 685004) (|tanhIfCan| . 684858) (|cothIfCan| . 684712) - (|sechIfCan| . 684566) (|cschIfCan| . 684420) (|asinhIfCan| . 684274) - (|acoshIfCan| . 684128) (|atanhIfCan| . 683982) (|acothIfCan| . 683836) - (|asechIfCan| . 683690) (|acschIfCan| . 683544) (|pushdown| . 681931) - (|pushup| . 680318) (|reducedDiscriminant| . 680003) - (|idealSimplify| . 679747) (|definingInequation| . 679491) - (|definingEquations| . 679200) (|setStatus| . 678887) - (|quasiAlgebraicSet| . 678593) (|radicalSimplify| . 678065) - (|random| . 676734) (|denominator| . 676480) (|numerator| . 676236) - (|denom| . 674775) (|numer| . 673294) (|quadraticForm| . 673122) - (|back| . 673031) (|front| . 672940) (|rotate!| . 672849) - (|dequeue!| . 672758) (|enqueue!| . 672664) (|quatern| . 672542) - (|imagK| . 672320) (|imagJ| . 672098) (|imagI| . 671876) - (|conjugate| . 671337) (|queue| . 671215) (|nthRoot| . 670789) - (|fractRadix| . 670654) (|wholeRadix| . 670522) (|cycleRagits| . 670390) - (|prefixRagits| . 670258) (|fractRagits| . 670124) (|wholeRagits| . 669992) - (|radix| . 669830) (|randnum| . 669653) (|reseed| . 669530) (|seed| . 669442) - (|rational| . 667959) (|rational?| . 666607) (|rationalIfCan| . 665124) - (|setvalue!| . 664968) (|setchildren!| . 664777) (|node?| . 664612) - (|child?| . 664447) (|distance| . 664314) (|leaves| . 664184) - (|nodes| . 664054) (|rename| . 663958) (|rename!| . 663862) - (|mainValue| . 663737) (|mainDefiningPolynomial| . 663612) - (|mainForm| . 663506) (|sqrt| . 662992) (|rischDE| . 661915) - (|rischDEsys| . 661059) (|monomRDE| . 660590) (|baseRDE| . 660197) - (|polyRDE| . 659583) (|monomRDEsys| . 659076) (|baseRDEsys| . 658708) - (|weighted| . 658483) (|rdHack1| . 658227) (|midpoint| . 657958) - (|midpoints| . 657633) (|realZeros| . 655068) - (|mainCharacterization| . 654710) (|algebraicOf| . 654328) - (|ReduceOrder| . 653878) (|setref| . 653791) (|deref| . 653709) - (|ref| . 653627) (= . 653197) (|radicalEigenvectors| . 652804) - (|radicalEigenvector| . 652543) (|radicalEigenvalues| . 652346) - (|eigenMatrix| . 652142) (|normalise| . 652017) (|gramschmidt| . 651883) - (|orthonormalBasis| . 651675) (|antisymmetricTensors| . 651215) - (|createGenericMatrix| . 651013) (|symmetricTensors| . 650646) - (|tensorProduct| . 650092) (|permutationRepresentation| . 649228) - (|completeEchelonBasis| . 649046) (|createRandomElement| . 648863) - (|cyclicSubmodule| . 648587) (|standardBasisOfCyclicSubmodule| . 648329) - (|areEquivalent?| . 647593) (|isAbsolutelyIrreducible?| . 647145) - (|meatAxe| . 645933) (|scanOneDimSubspaces| . 645651) (|double| . 645399) - (|expt| . 645147) (|lift| . 643261) (|solveRetract| . 642884) - (|variables| . 640774) (|mainVariable| . 639885) (|univariate| . 636631) - (|multivariate| . 634617) (|uniform01| . 634525) (|normal01| . 634433) - (|exponential1| . 634341) (|chiSquare1| . 634200) (|normal| . 634057) - (|exponential| . 633692) (|chiSquare| . 633532) (F . 633369) (|t| . 633209) - (|factorFraction| . 632969) (|componentUpperBound| . 632866) (|blue| . 632723) - (|green| . 632580) (|red| . 632437) (|whitePoint| . 632334) - (|uniform| . 631857) (|binomial| . 631262) (|poisson| . 631111) - (|geometric| . 630960) (|ridHack1| . 630845) (|interpolate| . 630115) - (|nullSpace| . 628165) (|nullity| . 626838) (|rank| . 624009) - (|rowEchelon| . 622183) (|column| . 621649) (|row| . 621115) (|qelt| . 620264) - (|ncols| . 619714) (|nrows| . 619164) (|maxColIndex| . 618636) - (|minColIndex| . 618108) (|maxRowIndex| . 617580) (|minRowIndex| . 617052) - (|antisymmetric?| . 616544) (|symmetric?| . 616036) (|diagonal?| . 615528) - (|square?| . 615020) (|matrix| . 613898) (|rectangularMatrix| . 613675) - (|annihilate?| . 613596) (|characteristic| . 611709) (|round| . 611654) - (|fractionPart| . 610983) (|wholePart| . 610520) (|floor| . 610303) - (|ceiling| . 610086) (|norm| . 606222) (|mightHaveRoots| . 605975) - (|refine| . 604073) (|middle| . 603864) (|size| . 601861) (|right| . 601244) - (|left| . 600627) (|roman| . 600462) (|mainSquareFreePart| . 600227) - (|mainPrimitivePart| . 599992) (|mainContent| . 599757) - (|primitivePart!| . 599522) (|gcd| . 597232) (|nextsubResultant2| . 596983) - (|LazardQuotient2| . 596688) (|LazardQuotient| . 596396) - (|subResultantChain| . 596118) (|halfExtendedSubResultantGcd2| . 595536) - (|halfExtendedSubResultantGcd1| . 594954) (|extendedSubResultantGcd| . 594329) - (|exactQuotient!| . 593845) (|exactQuotient| . 593361) - (|primPartElseUnitCanonical!| . 593121) (|primPartElseUnitCanonical| . 592881) - (|retract| . 590344) (|retractIfCan| . 587356) (|lazyResidueClass| . 586751) - (|monicModulo| . 586433) (|lazyPseudoDivide| . 585413) - (|lazyPremWithDefault| . 584736) (|lazyPquo| . 584323) (|lazyPrem| . 583910) - (|pquo| . 583497) (|prem| . 583084) (|supRittWu?| . 582850) - (|RittWuCompare| . 582614) (|mainMonomials| . 582383) - (|mainCoefficients| . 582152) (|leastMonomial| . 581949) - (|mainMonomial| . 581746) (|quasiMonic?| . 581515) (|monic?| . 581082) - (|leadingCoefficient| . 578801) (|deepestInitial| . 578598) - (|iteratedInitials| . 578367) (|deepestTail| . 578164) (|head| . 577697) - (|mdeg| . 577448) (|mvar| . 576981) (|iterators| . 576800) - (|relativeApprox| . 576190) (|rootOf| . 574652) (|allRootsOf| . 573527) - (|definingPolynomial| . 572475) (|positive?| . 571896) (|negative?| . 571318) - (|zero?| . 570630) (|augment| . 569288) (|lastSubResultant| . 568352) - (|lastSubResultantElseSplit| . 568013) (|invertibleSet| . 567690) - (|invertible?| . 566989) (|invertibleElseSplit?| . 566644) - (|purelyAlgebraicLeadingMonomial?| . 566321) - (|algebraicCoefficients?| . 565998) (|purelyTranscendental?| . 565675) - (|purelyAlgebraic?| . 565034) (|prepareSubResAlgo| . 564578) - (|internalLastSubResultant| . 563578) (|integralLastSubResultant| . 563139) - (|toseLastSubResultant| . 562700) (|toseInvertible?| . 561853) - (|toseInvertibleSet| . 561457) (|toseSquareFreePart| . 561021) - (|expression| . 560544) (|quotedOperators| . 560083) (|pattern| . 559658) - (|suchThat| . 557441) (|rule| . 556562) (|rules| . 556091) - (|ruleset| . 555620) (|rur| . 553705) (|create| . 553650) - (|clearCache| . 553528) (|cache| . 553403) (|enterInCache| . 553110) - (|currentCategoryFrame| . 553071) (|currentScope| . 553032) - (|pushNewContour| . 552953) (|findBinding| . 552695) (|contours| . 552608) - (|structuralConstants| . 551263) (|coordinates| . 548591) (|bounds| . 548499) - (|equation| . 547965) (|incr| . 547838) (|high| . 547746) (|low| . 547654) - (|hi| . 547562) (|lo| . 547470) (BY . 547340) (|body| . 546420) - (|union| . 545767) (|subset?| . 545633) (|symmetricDifference| . 545527) - (|difference| . 545317) (|intersect| . 543291) (|set| . 543062) - (|brace| . 542695) (|part?| . 542561) (|latex| . 542476) (|hash| . 542384) - (|delta| . 542175) (|member?| . 541658) (|enumerate| . 541446) - (|setOfMinN| . 541246) (|elements| . 540954) (|replaceKthElement| . 540789) - (|incrementKthElement| . 540627) (|cdr| . 540355) (|car| . 540083) - (|expr| . 539811) (|float| . 539303) (|integer| . 538893) (|symbol| . 538621) - (|destruct| . 538101) (|float?| . 537801) (|integer?| . 537266) - (|symbol?| . 536844) (|string?| . 536544) (|list?| . 536244) - (|pair?| . 535944) (|atom?| . 535644) (|null?| . 535344) (|eq| . 534955) - (|startTable!| . 534119) (|stopTable!| . 533355) - (|supDimElseRittWu?| . 532573) (|algebraicSort| . 531797) - (|moreAlgebraic?| . 531015) (|subTriSet?| . 530233) (|subPolSet?| . 529395) - (|internalSubPolSet?| . 528557) (|internalInfRittWu?| . 527719) - (|internalSubQuasiComponent?| . 526965) (|subQuasiComponent?| . 525333) - (|removeSuperfluousQuasiComponents| . 524557) (|subCase?| . 523639) - (|removeSuperfluousCases| . 522807) (|prepareDecompose| . 521601) - (|branchIfCan| . 520567) (|startTableGcd!| . 519705) - (|stopTableGcd!| . 518915) (|startTableInvSet!| . 518053) - (|stopTableInvSet!| . 517263) (|stosePrepareSubResAlgo| . 516789) - (|stoseInternalLastSubResultant| . 515757) - (|stoseIntegralLastSubResultant| . 515300) (|stoseLastSubResultant| . 514843) - (|stoseInvertible?sqfreg| . 514372) (|stoseInvertibleSetsqfreg| . 513958) - (|stoseInvertible?reg| . 513487) (|stoseInvertibleSetreg| . 513073) - (|stoseInvertible?| . 512190) (|stoseInvertibleSet| . 511776) - (|stoseSquareFreePart| . 511322) (|coleman| . 511146) - (|inverseColeman| . 510970) (|listYoungTableaus| . 510783) - (|makeYoungTableau| . 510558) (|nextColeman| . 510382) - (|nextLatticePermutation| . 510172) (|nextPartition| . 509815) - (|numberOfImproperPartitions| . 509697) (|subSet| . 509532) - (|unrankImproperPartitions0| . 509367) (|unrankImproperPartitions1| . 509202) - (|semiGroupOperation| . 509060) (|subresultantSequence| . 508794) - (|SturmHabichtSequence| . 508528) (|SturmHabichtCoefficients| . 508290) - (|SturmHabicht| . 508052) (|countRealRoots| . 507817) - (|SturmHabichtMultiple| . 507540) (|countRealRootsMultiple| . 507266) - (|source| . 507086) (|target| . 506691) (|signature| . 506212) - (|signatureAst| . 506084) (|xor| . 505934) (|depth| . 505664) (|top| . 505573) - (|pop!| . 505482) (|push!| . 505388) (|map!| . 505235) (|minordet| . 504423) - (|determinant| . 503327) (|diagonalProduct| . 502685) (|trace| . 501784) - (|diagonal| . 501557) (|diagonalMatrix| . 500710) (|scalarMatrix| . 500231) - (|hermite| . 499778) (|completeHermite| . 499430) (|smith| . 499152) - (|completeSmith| . 498772) (|diophantineSystem| . 498364) (|csubst| . 498006) - (|particularSolution| . 496836) (|mapSolve| . 496293) (|linear| . 495610) - (|quadratic| . 494924) (|cubic| . 494235) (|quartic| . 493543) - (|aLinear| . 493230) (|aQuadratic| . 492914) (|aCubic| . 492595) - (|aQuartic| . 492273) (|radicalSolve| . 489909) (|radicalRoots| . 489314) - (|contractSolve| . 488571) (|decomposeFunc| . 488365) (|unvectorise| . 487879) - (|bubbleSort!| . 487197) (|insertionSort!| . 486515) (|check| . 485989) - (|objects| . 485640) (|lprop| . 485483) (|llprop| . 485317) (|lllp| . 485159) - (|lllip| . 484991) (|lp| . 484851) (|mesh?| . 484721) (|mesh| . 483315) - (|polygon?| . 483185) (|polygon| . 482626) (|closedCurve?| . 482496) - (|closedCurve| . 481937) (|curve?| . 481807) (|curve| . 481053) - (|point?| . 480923) (|enterPointData| . 480734) (|composites| . 480604) - (|components| . 480474) (|numberOfComposites| . 480333) - (|numberOfComponents| . 479514) (|create3Space| . 479288) (|parse| . 479163) - (|outputAsFortran| . 478744) (|outputAsScript| . 478481) - (|outputAsTex| . 478218) (|abs| . 477470) (|Beta| . 476792) - (|digamma| . 476336) (|polygamma| . 475783) (|Gamma| . 475051) - (|besselJ| . 474583) (|besselY| . 474115) (|besselI| . 473647) - (|besselK| . 473179) (|airyAi| . 472723) (|airyBi| . 472267) - (|subNode?| . 471988) (|infLex?| . 471658) (|setEmpty!| . 471466) - (|setStatus!| . 471243) (|setCondition!| . 471048) (|setValue!| . 470853) - (|copy| . 470271) (|status| . 469768) (|value| . 469238) (|empty?| . 468649) - (|splitNodeOf!| . 468087) (|remove!| . 466722) (|remove| . 465664) - (|subNodeOf?| . 465338) (|nodeOf?| . 465068) (|result| . 464801) - (|conditions| . 464581) (|updateStatus!| . 464389) - (|extractSplittingLeaf| . 464195) (|squareMatrix| . 464024) - (|transpose| . 463095) (|rightTrim| . 462895) (|leftTrim| . 462695) - (|trim| . 462495) (|split| . 460265) (|position| . 459306) - (|replace| . 459182) (|match?| . 459049) (|match| . 457596) - (|substring?| . 457465) (|suffix?| . 457372) (|prefix?| . 457279) - (|upperCase!| . 457225) (|upperCase| . 457081) (|lowerCase!| . 457027) - (|lowerCase| . 456883) (|KrullNumber| . 455931) (|numberOfVariables| . 454979) - (|algebraicDecompose| . 453767) (|transcendentalDecompose| . 451323) - (|internalDecompose| . 447540) (|decompose| . 444306) - (|upDateBranches| . 442872) (|printInfo| . 441868) (|preprocess| . 440802) - (|internalZeroSetSplit| . 439952) (|internalAugment| . 438547) - (|stack| . 438432) (|size?| . 438256) (|possiblyInfinite?| . 438129) - (|explicitlyFinite?| . 438002) (|nextItem| . 437915) (|init| . 437667) - (|step| . 437589) (|upperBound| . 437499) (|lowerBound| . 437421) - (|iterationVar| . 437263) (|infiniteProduct| . 436280) - (|evenInfiniteProduct| . 435297) (|oddInfiniteProduct| . 434314) - (|generalInfiniteProduct| . 433208) (|filterUntil| . 432935) - (|filterWhile| . 432662) (|generate| . 432134) (|showAll?| . 431987) - (|showAllElements| . 431834) (|output| . 431228) (|cons| . 431068) - (|delay| . 430938) (|findCycle| . 430674) (|repeating?| . 430486) - (|repeating| . 430370) (|exquo| . 428793) (|recip| . 426694) - (|integers| . 426510) (|oddintegers| . 426326) (|int| . 425490) - (|mapmult| . 425347) (|deriv| . 425207) (|gderiv| . 425014) - (|compose| . 424703) (|addiag| . 424515) (|lazyIntegrate| . 424261) - (|nlde| . 424011) (|powern| . 423787) (|mapdiv| . 423609) - (|lazyGintegrate| . 423336) (|power| . 423158) (|sincos| . 422903) - (|sinhcosh| . 422638) (|asin| . 421350) (|acos| . 420062) (|atan| . 418682) - (|acot| . 417394) (|asec| . 416106) (|acsc| . 414818) (|sinh| . 413536) - (|cosh| . 412254) (|tanh| . 410972) (|coth| . 409690) (|sech| . 408408) - (|csch| . 407126) (|asinh| . 405841) (|acosh| . 404556) (|atanh| . 403271) - (|acoth| . 401986) (|asech| . 400701) (|acsch| . 399416) - (|subresultantVector| . 399193) (|primitivePart| . 397918) - (|pointData| . 397753) (|parent| . 397626) (|level| . 397377) - (|extractProperty| . 397197) (|extractClosed| . 397042) - (|extractIndex| . 396869) (|extractPoint| . 396713) (|traverse| . 396528) - (|defineProperty| . 396287) (|closeComponent| . 396071) - (|modifyPoint| . 395416) (|addPointLast| . 395205) (|addPoint2| . 395046) - (|addPoint| . 394394) (|merge| . 393450) (|deepCopy| . 393323) - (|shallowCopy| . 393196) (|numberOfChildren| . 393023) (|children| . 392717) - (|child| . 392541) (|birth| . 392414) (|internal?| . 392259) - (|root?| . 392104) (|leaf?| . 391821) (|rhs| . 390815) (|lhs| . 389809) - (|construct| . 384954) (|predicate| . 384657) (|sum| . 381477) - (|outputForm| . 380476) (|list| . 380301) (|string| . 379678) - (|argscript| . 379584) (|superscript| . 379490) (|subscript| . 379396) - (|script| . 378954) (|scripts| . 378527) (|scripted?| . 378450) - (|name| . 377366) (|resetNew| . 377295) (|symFunc| . 376963) - (|symbolTableOf| . 376835) (|argumentListOf| . 376703) - (|returnTypeOf| . 376512) (|printHeader| . 376198) (|returnType!| . 375596) - (|argumentList!| . 375156) (|endSubProgram| . 375075) - (|currentSubProgram| . 374994) (|newSubProgram| . 374876) - (|clearTheSymbolTable| . 374681) (|showTheSymbolTable| . 374633) - (|symbolTable| . 374478) (|printTypes| . 374283) (|newTypeLists| . 374195) - (|typeLists| . 373876) (|externalList| . 373784) (|typeList| . 373411) - (|parametersOf| . 373319) (|fortranTypeOf| . 373194) (|declare!| . 372376) - (|empty| . 371682) (|case| . 365564) (|compound?| . 365487) - (|getOperands| . 365274) (|getOperator| . 365015) (|nil?| . 364938) - (|buildSyntax| . 364722) (|autoCoerce| . 361212) (|solve| . 344140) - (|triangularSystems| . 343869) (|loadNativeModule| . 343759) - (|nativeModuleExtension| . 343686) (|hostByteOrder| . 343610) - (|hostPlatform| . 343537) (|rootDirectory| . 343464) (|bumprow| . 343144) - (|bumptab| . 342901) (|bumptab1| . 342714) (|untab| . 342518) - (|bat1| . 342318) (|bat| . 342131) (|tab1| . 341931) (|tab| . 341760) - (|lex| . 341620) (|slex| . 341452) (|inverse| . 339623) (|maxrow| . 339285) - (|mr| . 338937) (|tableau| . 338804) (|listOfLists| . 338147) - (|operator| . 335804) (|tanSum| . 335676) (|tanAn| . 335480) - (|tanNa| . 335349) (|table| . 334995) (|initTable!| . 334813) - (|printInfo!| . 334598) (|startStats!| . 334386) (|printStats!| . 334204) - (|clearTable!| . 334022) (|usingTable?| . 333837) (|printingInfo?| . 333652) - (|makingStats?| . 333467) (|extractIfCan| . 333305) (|insert!| . 332365) - (|setPrologue!| . 332272) (|setTex!| . 332179) (|setEpilogue!| . 332086) - (|prologue| . 331996) (|new| . 330595) (|tex| . 330505) (|epilogue| . 330415) - (|display| . 329244) (|endOfFile?| . 329165) (|readIfCan!| . 328978) - (|readLineIfCan!| . 328888) (|readLine!| . 328810) (|writeLine!| . 328653) - (|sign| . 325825) (|nonQsign| . 325697) (|direction| . 325548) - (|createThreeSpace| . 325434) (|pi| . 325151) (|cyclicParents| . 325021) - (|cyclicEqual?| . 324897) (|cyclicEntries| . 324767) (|cyclicCopy| . 324681) - (|tree| . 324345) (|cyclic?| . 324096) (|cos| . 322709) (|cot| . 321424) - (|csc| . 320139) (|sec| . 318854) (|sin| . 317467) (|tan| . 316182) - (|complexNormalize| . 314493) (|complexElementary| . 312804) - (|trigs| . 312027) (|real| . 310885) (|imag| . 309963) (|real?| . 309036) - (|complexForm| . 308176) (|UpTriBddDenomInv| . 307885) - (|LowTriBddDenomInv| . 307594) (|simplify| . 306649) (|htrigs| . 306392) - (|simplifyExp| . 306135) (|simplifyLog| . 305878) (|expandPower| . 305621) - (|expandLog| . 305364) (|cos2sec| . 305107) (|cosh2sech| . 304850) - (|cot2trig| . 304593) (|coth2trigh| . 304336) (|csc2sin| . 304079) - (|csch2sinh| . 303822) (|sec2cos| . 303565) (|sech2cosh| . 303308) - (|sin2csc| . 303051) (|sinh2csch| . 302794) (|tan2trig| . 302537) - (|tanh2trigh| . 302280) (|tan2cot| . 302023) (|tanh2coth| . 301766) - (|cot2tan| . 301509) (|coth2tanh| . 301252) (|removeCosSq| . 300995) - (|removeSinSq| . 300738) (|removeCoshSq| . 300481) (|removeSinhSq| . 300224) - (|expandTrigProducts| . 299753) (|fintegrate| . 299135) - (|coefficient| . 295891) (|coHeight| . 295533) (|extendIfCan| . 295253) - (|algebraicVariables| . 294935) (|zeroSetSplitIntoTriangularSystems| . 294524) - (|zeroSetSplit| . 290117) (|reduceByQuasiMonic| . 289831) - (|collectQuasiMonic| . 289548) (|removeZero| . 289262) - (|initiallyReduce| . 288772) (|headReduce| . 288282) - (|stronglyReduce| . 287996) (|rewriteSetWithReduction| . 287579) - (|autoReduced?| . 287196) (|initiallyReduced?| . 286060) - (|headReduced?| . 284924) (|stronglyReduced?| . 284287) (|reduced?| . 283411) - (|normalized?| . 282275) (|quasiComponent| . 281899) (|initials| . 281581) - (|basicSet| . 280676) (|infRittWu?| . 279287) (|getCurve| . 279174) - (|listLoops| . 278994) (|closed?| . 278750) (|open?| . 278609) - (|setClosed| . 278465) (|tube| . 278028) (|point| . 276933) - (|unitVector| . 276073) (|cosSinInfo| . 275923) (|loopPoints| . 275690) - (|select| . 274804) (|generalTwoFactor| . 274481) (|generalSqFr| . 274158) - (|twoFactor| . 273804) (|setOrder| . 273453) (|getOrder| . 273263) - (|less?| . 272734) (|userOrdered?| . 272587) (|largest| . 272200) - (|more?| . 271840) (|setVariableOrder| . 271559) (|getVariableOrder| . 271374) - (|resetVariableOrder| . 271273) (|prime?| . 270294) (|sample| . 269419) - (|bitior| . 269086) (|bitand| . 268753) (|rationalFunction| . 268264) - (|taylorIfCan| . 268067) (|taylor| . 262903) (|removeZeroes| . 261729) - (|taylorRep| . 261537) (|factor| . 248774) (|factorSquareFree| . 247031) - (|henselFact| . 246265) (|hasHi| . 246139) (|segment| . 245694) - (SEGMENT . 245417) (|fmecg| . 244422) (|commonDenominator| . 243461) - (|clearDenominator| . 242470) (|splitDenominator| . 240648) - (|monicRightFactorIfCan| . 240373) (|rightFactorIfCan| . 240095) - (|leftFactorIfCan| . 239859) (|monicDecomposeIfCan| . 239563) - (|monicCompleteDecompose| . 239300) (|divideIfCan| . 239033) - (|noKaratsuba| . 238843) (|karatsubaOnce| . 238653) (|karatsuba| . 238418) - (|separate| . 237642) (|pseudoDivide| . 236833) (|pseudoQuotient| . 236681) - (|composite| . 236204) (|subResultantGcd| . 235631) (|resultant| . 234821) - (|discriminant| . 233295) (|differentiate| . 231204) - (|pseudoRemainder| . 231089) (|shiftLeft| . 230928) (|shiftRight| . 230767) - (|karatsubaDivide| . 230538) (|monicDivide| . 230075) - (|divideExponents| . 229912) (|unmakeSUP| . 229743) (|makeSUP| . 229574) - (|vectorise| . 229383) (|eval| . 222403) (|extend| . 219915) - (|approximate| . 218659) (|truncate| . 218281) (|order| . 213533) - (|center| . 212959) (|terms| . 212073) (|squareFreePart| . 211087) - (|BumInSepFFE| . 210650) (|multiplyExponents| . 210122) - (|laurentIfCan| . 209924) (|laurent| . 205744) (|laurentRep| . 205551) - (|rationalPower| . 205310) (|puiseux| . 201129) (|dominantTerm| . 200139) - (|limitPlus| . 199022) (|split!| . 198819) (|setlast!| . 198651) - (|setrest!| . 198363) (|setelt| . 196130) (|setfirst!| . 195962) - (|cycleSplit!| . 195797) (|concat!| . 195079) (|cycleTail| . 194972) - (|cycleLength| . 194826) (|cycleEntry| . 194719) (|third| . 194612) - (|second| . 194391) (|tail| . 193980) (|last| . 193261) (|rest| . 192421) - (|elt| . 184870) (|first| . 183702) (|concat| . 182913) - (|invmultisect| . 182541) (|multisect| . 182169) (|revert| . 181879) - (|generalLambert| . 181507) (|evenlambert| . 181217) (|oddlambert| . 180927) - (|lambert| . 180637) (|lagrange| . 180347) (|univariatePolynomial| . 179833) - (|integrate| . 168294) (** . 162445) (|polynomial| . 161567) - (|multiplyCoefficients| . 161076) (|quoByVar| . 160962) - (|coefficients| . 160053) (|series| . 152618) (|stFunc1| . 152307) - (|stFunc2| . 151979) (|stFuncN| . 151650) (|fixedPointExquo| . 151440) - (|ode1| . 151189) (|ode2| . 150932) (|ode| . 150644) (|mpsode| . 150305) - (UP2UTS . 150004) (UTS2UP . 149661) (LODO2FUN . 149310) (RF2UTS . 148933) - (|variable| . 148017) (|magnitude| . 147854) (|length| . 146391) - (|cross| . 146064) (|outerProduct| . 145906) (|dot| . 145362) (- . 143102) - (|zero| . 142670) (+ . 140351) (|vector| . 140235) (|scan| . 138036) - (|reduce| . 131196) (|map| . 106269) (|graphCurves| . 105619) - (|drawCurves| . 105087) (|update| . 104915) (|show| . 104747) - (|scale| . 104219) (|connect| . 104051) (|region| . 103883) - (|points| . 103715) (|units| . 103046) (|getGraph| . 102902) - (|putGraph| . 102730) (|graphs| . 102419) (|graphStates| . 101878) - (|graphState| . 101609) (|makeViewport2D| . 101404) (|viewport2D| . 101348) - (|getPickedPoints| . 101223) (|key| . 100947) (|close| . 100657) - (|write| . 99967) (|colorDef| . 99834) (|reset| . 99650) (|intensity| . 99520) - (|lighting| . 99384) (|clipSurface| . 99253) (|showClipRegion| . 99122) - (|showRegion| . 98991) (|hitherPlane| . 98861) (|eyeDistance| . 98731) - (|perspective| . 98600) (|translate| . 98124) (|zoom| . 97567) - (|rotate| . 97301) (|drawStyle| . 97170) (|outlineRender| . 97039) - (|diagonals| . 96908) (|axes| . 96444) (|controlPanel| . 96186) - (|viewpoint| . 93999) (|dimensions| . 93613) (|title| . 93137) - (|resize| . 92855) (|move| . 92567) (|options| . 92107) - (|modifyPointData| . 91738) (|subspace| . 91235) (|makeViewport3D| . 90845) - (|viewport3D| . 90787) (|viewDeltaYDefault| . 90602) - (|viewDeltaXDefault| . 90417) (|viewZoomDefault| . 90232) - (|viewPhiDefault| . 90047) (|viewThetaDefault| . 89862) - (|pointColorDefault| . 89683) (|lineColorDefault| . 89504) - (|axesColorDefault| . 89325) (|unitsColorDefault| . 89146) - (|pointSizeDefault| . 88937) (|viewPosDefault| . 88704) - (|viewSizeDefault| . 88477) (|viewDefaults| . 88391) - (|viewWriteDefault| . 88182) (|viewWriteAvailable| . 88078) - (|var1StepsDefault| . 87869) (|var2StepsDefault| . 87660) - (|tubePointsDefault| . 87451) (|tubeRadiusDefault| . 87224) (|void| . 87186) - (|dimension| . 85682) (|crest| . 85430) (|cfirst| . 85178) - (|sts2stst| . 84928) (|clikeUniv| . 84660) (|weierstrass| . 84430) - (|qqq| . 84144) (|integralBasis| . 82082) (|localIntegralBasis| . 80335) - (|qualifier| . 80256) (|mainExpression| . 80177) (|condition| . 79834) - (|changeWeightLevel| . 79145) (|characteristicSerie| . 78268) - (|characteristicSet| . 77561) (|medialSet| . 76854) (|Hausdorff| . 76559) - (|Frobenius| . 75906) (|transcendenceDegree| . 75559) - (|extensionDegree| . 74811) (|inGroundField?| . 74684) - (|transcendent?| . 74557) (|algebraic?| . 74111) (|varList| . 72924) - (|sh| . 72520) (|mirror| . 71770) (|monomial?| . 70774) (|monom| . 70280) - (|rquo| . 69403) (|lquo| . 68526) (|mindegTerm| . 68304) (|log| . 65893) - (|exp| . 63580) (|product| . 62424) (|LiePolyIfCan| . 62034) - (|coerce| . 45955) (|trunc| . 45579) (|degree| . 41157) (/ . 37324) - (|quasiRegular| . 37058) (|quasiRegular?| . 36729) (|constant| . 35944) - (|constant?| . 35402) (|coef| . 34749) (|mindeg| . 34435) (|maxdeg| . 34118) - (|#| . 33308) (|reductum| . 31131) (* . 23431) (|RemainderList| . 23017) +((|opposite?| . 1288287) (|zerosOf| . 1287440) (|zeroOf| . 1286754) + (|rootsOf| . 1285907) (|makeSketch| . 1285690) (|inrootof| . 1285472) + (|droot| . 1285255) (|iroot| . 1285020) (|eq?| . 1284933) (|assoc| . 1284702) + (|doublyTransitive?| . 1284539) (|knownInfBasis| . 1284195) + (|rootSplit| . 1283188) (|ratDenom| . 1279076) (|ratPoly| . 1278012) + (|rootPower| . 1276881) (|rootProduct| . 1275750) (|rootSimp| . 1274619) + (|rootKerSimp| . 1273402) (|leftRank| . 1273187) (|rightRank| . 1272972) + (|doubleRank| . 1272757) (|weakBiRank| . 1272542) (|biRank| . 1272327) + (|basisOfCommutingElements| . 1272133) (|basisOfLeftAnnihilator| . 1271936) + (|basisOfRightAnnihilator| . 1271739) (|basisOfLeftNucleus| . 1271545) + (|basisOfRightNucleus| . 1271351) (|basisOfMiddleNucleus| . 1271157) + (|basisOfNucleus| . 1270963) (|basisOfCenter| . 1270769) + (|basisOfLeftNucloid| . 1270557) (|basisOfRightNucloid| . 1270345) + (|basisOfCentroid| . 1270133) (|radicalOfLeftTraceForm| . 1269939) + (|obj| . 1269868) (|dom| . 1269790) (|any| . 1269675) (|applyRules| . 1268684) + (|localUnquote| . 1268228) (|arbitrary| . 1268189) (|setColumn!| . 1267923) + (|setRow!| . 1267657) (|oneDimensionalArray| . 1267387) + (|associatedSystem| . 1267014) (|uncouplingMatrices| . 1266740) + (|associatedEquations| . 1266278) (|arrayStack| . 1266151) + (|morphism| . 1265756) (|balancedFactorisation| . 1265231) + (|before?| . 1265144) (|mapDown!| . 1264827) (|mapUp!| . 1264512) + (|setleaves!| . 1264374) (|balancedBinaryTree| . 1264218) + (|sylvesterMatrix| . 1263894) (|bezoutMatrix| . 1263570) + (|bezoutResultant| . 1263189) (|bezoutDiscriminant| . 1262811) + (|inspect| . 1262722) (|extract!| . 1262633) (|bag| . 1262509) + (|binding| . 1262378) (|binaryOperation| . 1262244) + (|setProperties| . 1262120) (|setProperty| . 1261872) + (|deleteProperty!| . 1261694) (|has?| . 1261567) (|comparison| . 1261434) + (|equality| . 1261301) (|nary?| . 1261215) (|unary?| . 1261129) + (|nullary?| . 1261043) (|properties| . 1260834) (|derivative| . 1260223) + (|constantOperator| . 1260070) (|constantOpIfCan| . 1259915) + (|integerBound| . 1259680) (|setright!| . 1259511) (|setleft!| . 1259342) + (|brillhartIrreducible?| . 1259021) (|brillhartTrials| . 1258670) + (|noLinearFactor?| . 1258510) (|insertRoot!| . 1258403) + (|binarySearchTree| . 1258271) (|nor| . 1258172) (|nand| . 1258073) + (|node| . 1257958) (|binaryTournament| . 1257826) (|binaryTree| . 1257638) + (|byte| . 1257550) (|setLength!| . 1257453) (|capacity| . 1257359) + (|byteBuffer| . 1257265) (|unknownEndian| . 1257222) (|bigEndian| . 1257179) + (|littleEndian| . 1257136) (|subtractIfCan| . 1257025) + (|setPosition| . 1256893) (|generalizedContinuumHypothesisAssumed| . 1256806) + (|generalizedContinuumHypothesisAssumed?| . 1256724) (|countable?| . 1256637) + (|Aleph| . 1256532) (|unravel| . 1256320) (|ravel| . 1256108) + (|leviCivitaSymbol| . 1255927) (|kroneckerDelta| . 1255746) + (|reindex| . 1255515) (|parents| . 1255386) (|principalAncestors| . 1255257) + (|exportedOperators| . 1255150) (|alphanumeric| . 1255102) + (|alphabetic| . 1255054) (|hexDigit| . 1255006) (|digit| . 1254958) + (|charClass| . 1254769) (|alphanumeric?| . 1254689) (|lowerCase?| . 1254609) + (|upperCase?| . 1254529) (|alphabetic?| . 1254449) (|hexDigit?| . 1254369) + (|digit?| . 1254289) (|escape| . 1254246) (|verticalTab| . 1254203) + (|horizontalTab| . 1254160) (|backspace| . 1254117) (|formfeed| . 1254074) + (|linefeed| . 1254031) (|carriageReturn| . 1253988) (|newline| . 1253945) + (|underscore| . 1253902) (|char| . 1253732) (|ord| . 1253639) + (|mkIntegral| . 1253300) (|radPoly| . 1252926) (|rootPoly| . 1252455) + (|goodPoint| . 1252192) (|chvar| . 1251730) (|removeDuplicates| . 1251556) + (|e| . 1251354) (|clipParametric| . 1250655) (|clipWithRanges| . 1250294) + (|numberOfHues| . 1250213) (|yellow| . 1250174) (|iifact| . 1250012) + (|iibinom| . 1249822) (|iiperm| . 1249632) (|iipow| . 1249442) + (|iidsum| . 1249252) (|iidprod| . 1249062) (|ipow| . 1248872) + (|factorial| . 1248521) (|multinomial| . 1248365) (|permutation| . 1248005) + (|stirling1| . 1247877) (|stirling2| . 1247749) (|summation| . 1247126) + (|factorials| . 1246607) (|mkcomm| . 1246478) + (|commutativeOperation| . 1246334) (|polarCoordinates| . 1246056) + (|complex| . 1245943) (|imaginary| . 1245836) (|elaborateFile| . 1245684) + (|elaborate| . 1245547) (|macroExpand| . 1245417) (|solid| . 1245309) + (|solid?| . 1245204) (|denominators| . 1245064) (|numerators| . 1244924) + (|convergents| . 1244764) (|approximants| . 1244604) (|reducedForm| . 1244494) + (|partialQuotients| . 1244354) (|partialDenominators| . 1244214) + (|partialNumerators| . 1244074) (|reducedContinuedFraction| . 1243931) + (|push| . 1243850) (|bindings| . 1243761) (|cartesian| . 1243511) + (|polar| . 1243261) (|cylindrical| . 1243011) (|spherical| . 1242761) + (|parabolic| . 1242511) (|parabolicCylindrical| . 1242261) + (|paraboloidal| . 1242011) (|ellipticCylindrical| . 1241736) + (|prolateSpheroidal| . 1241461) (|oblateSpheroidal| . 1241186) + (|bipolar| . 1240911) (|bipolarCylindrical| . 1240636) (|toroidal| . 1240361) + (|conical| . 1240083) (|modTree| . 1239949) (|multiEuclideanTree| . 1239815) + (|complexZeros| . 1239022) (|divisorCascade| . 1238370) (|graeffe| . 1238161) + (|pleskenSplit| . 1237623) (|reciprocalPolynomial| . 1237414) + (|rootRadius| . 1236995) (|schwerpunkt| . 1236760) (|setErrorBound| . 1236551) + (|startPolynomial| . 1236251) (|cycleElt| . 1236095) + (|computeCycleLength| . 1235902) (|computeCycleEntry| . 1235752) + (|findConstructor| . 1235616) (|arguments| . 1235461) (|operations| . 1235347) + (|dualSignature| . 1235237) (|kind| . 1235038) (|package| . 1234989) + (|domain| . 1234940) (|category| . 1234891) (|coerceP| . 1234662) + (|powerSum| . 1234487) (|elementary| . 1234309) (|alternating| . 1234131) + (|cyclic| . 1233956) (|dihedral| . 1233781) (|cap| . 1233598) + (|cup| . 1233463) (|wreath| . 1233328) (|SFunction| . 1233144) + (|skewSFunction| . 1232965) (|cyclotomicDecomposition| . 1232783) + (|cyclotomicFactorization| . 1232597) (|qsetelt| . 1232410) + (|doubleResultant| . 1232064) (|distdfact| . 1231651) + (|separateDegrees| . 1231365) (|trace2PowMod| . 1231129) + (|tracePowMod| . 1230893) (|irreducible?| . 1230681) (|decimal| . 1230572) + (|innerint| . 1229745) (|exteriorDifferential| . 1229582) + (|totalDifferential| . 1229378) (|homogeneous?| . 1229034) + (|leadingBasisTerm| . 1228746) (|ignore?| . 1228274) (|computeInt| . 1227768) + (|checkForZero| . 1226707) (|nan?| . 1226625) (|logGamma| . 1226393) + (|hypergeometric0F1| . 1226155) (|rotatez| . 1225984) (|rotatey| . 1225813) + (|rotatex| . 1225642) (|identity| . 1225474) (|dictionary| . 1225229) + (|dioSolve| . 1224794) (|directProduct| . 1224656) (|newLine| . 1224575) + (|copies| . 1224451) (|say| . 1224208) (|sayLength| . 1223959) + (|setnext!| . 1223793) (|setprevious!| . 1223627) (|next| . 1223522) + (|previous| . 1223417) (|datalist| . 1223293) + (|shanksDiscLogAlgorithm| . 1222987) (|showSummary| . 1222913) + (|reflect| . 1222797) (|reify| . 1222681) (|constructor| . 1222391) + (|functorData| . 1222297) (|separant| . 1222027) (|initial| . 1221757) + (|leader| . 1221487) (|isobaric?| . 1221182) (|weights| . 1220531) + (|differentialVariables| . 1220226) (|extractBottom!| . 1220133) + (|extractTop!| . 1220040) (|insertBottom!| . 1219944) (|insertTop!| . 1219848) + (|bottom!| . 1219755) (|top!| . 1219662) (|dequeue| . 1219324) + (|makeObject| . 1214256) (|recolor| . 1213957) (|drawComplex| . 1213675) + (|drawComplexVectorField| . 1213424) (|setRealSteps| . 1213342) + (|setImagSteps| . 1213260) (|setClipValue| . 1213172) (|draw| . 1203972) + (|option?| . 1203812) (|range| . 1203581) (|colorFunction| . 1203154) + (|curveColor| . 1202996) (|pointColor| . 1202838) (|clip| . 1201276) + (|clipBoolean| . 1201133) (|style| . 1200913) (|toScale| . 1200691) + (|pointColorPalette| . 1200548) (|curveColorPalette| . 1200405) + (|var1Steps| . 1200158) (|var2Steps| . 1199911) (|space| . 1199597) + (|tubePoints| . 1199350) (|tubeRadius| . 1199132) (|option| . 1198788) + (|weight| . 1197786) (|makeVariable| . 1196915) (|Nul| . 1196820) + (|exponents| . 1196727) (|iisqrt2| . 1196542) (|iisqrt3| . 1196357) + (|iiexp| . 1196169) (|iilog| . 1195981) (|iisin| . 1195793) + (|iicos| . 1195605) (|iitan| . 1195417) (|iicot| . 1195229) + (|iisec| . 1195041) (|iicsc| . 1194853) (|iiasin| . 1194665) + (|iiacos| . 1194477) (|iiatan| . 1194289) (|iiacot| . 1194101) + (|iiasec| . 1193913) (|iiacsc| . 1193725) (|iisinh| . 1193537) + (|iicosh| . 1193349) (|iitanh| . 1193161) (|iicoth| . 1192973) + (|iisech| . 1192785) (|iicsch| . 1192597) (|iiasinh| . 1192409) + (|iiacosh| . 1192221) (|iiatanh| . 1192033) (|iiacoth| . 1191845) + (|iiasech| . 1191657) (|iiacsch| . 1191469) (|specialTrigs| . 1191193) + (|localReal?| . 1190977) (|rischNormalize| . 1190346) + (|realElementary| . 1189422) (|validExponential| . 1188905) + (|rootNormalize| . 1188408) (|tanQ| . 1187900) (|callForm?| . 1187807) + (|getIdentifier| . 1187698) (|variable?| . 1187605) (|getConstant| . 1187495) + (|type| . 1187403) (|environment| . 1187315) (|typeForm| . 1187222) + (|irForm| . 1187112) (|elaboration| . 1186920) (|select!| . 1186548) + (|delete!| . 1186235) (|sn| . 1186044) (|cn| . 1185853) (|dn| . 1185662) + (|sncndn| . 1185395) (|qsetelt!| . 1184929) (|categoryFrame| . 1184884) + (|interactiveEnv| . 1184839) (|currentEnv| . 1184794) + (|putProperties| . 1184656) (|getProperties| . 1184521) + (|putProperty| . 1184386) (|getProperty| . 1184244) (|scopes| . 1184153) + (|eigenvalues| . 1183839) (|eigenvector| . 1183488) + (|generalizedEigenvector| . 1182625) (|generalizedEigenvectors| . 1182160) + (|eigenvectors| . 1181664) (|factorAndSplit| . 1181496) (|rightOne| . 1181371) + (|leftOne| . 1181246) (|rightZero| . 1181121) (|leftZero| . 1180996) + (|swap| . 1180672) (|error| . 1180155) (|minPoly| . 1179674) + (|freeOf?| . 1179456) (|operators| . 1179344) (|tower| . 1179236) + (|kernels| . 1179128) (|mainKernel| . 1179023) (|distribute| . 1178914) + (|subst| . 1178437) (|multiEuclidean| . 1178331) + (|extendedEuclidean| . 1178034) (|euclideanSize| . 1177926) + (|sizeLess?| . 1177833) (|simplifyPower| . 1177666) (|number?| . 1177502) + (|seriesSolve| . 1173503) (|constantToUnaryFunction| . 1173350) + (|tubePlot| . 1171971) (|exponentialOrder| . 1171756) + (|completeEval| . 1171321) (|lowerPolynomial| . 1170955) + (|raisePolynomial| . 1170589) (|normalDeriv| . 1170242) (|ran| . 1169955) + (|highCommonTerms| . 1169728) (|mapCoef| . 1169510) (|nthCoef| . 1169298) + (|binomThmExpt| . 1169048) (|pomopo!| . 1168886) (|mapExponents| . 1168689) + (|linearAssociatedLog| . 1168286) (|linearAssociatedOrder| . 1168086) + (|linearAssociatedExp| . 1167876) (|createNormalElement| . 1167736) + (|sin?| . 1167604) (|lookupFunction| . 1167517) + (|encodingDirectory| . 1167396) (|attributeData| . 1167265) + (|domainTemplate| . 1167174) (|lSpaceBasis| . 1166837) + (|finiteBasis| . 1166500) (|principal?| . 1166155) (|divisor| . 1164496) + (|rationalPoints| . 1163791) (|nonSingularModel| . 1163001) + (|algSplitSimple| . 1162566) (|hyperelliptic| . 1161986) + (|elliptic| . 1161133) (|integralDerivationMatrix| . 1160750) + (|integralRepresents| . 1160443) (|integralCoordinates| . 1160101) + (|yCoordinates| . 1159759) (|inverseIntegralMatrixAtInfinity| . 1159445) + (|integralMatrixAtInfinity| . 1159131) (|inverseIntegralMatrix| . 1158817) + (|integralMatrix| . 1158503) (|reduceBasisAtInfinity| . 1158199) + (|normalizeAtInfinity| . 1157895) (|complementaryBasis| . 1157591) + (|integral?| . 1156683) (|integralAtInfinity?| . 1156381) + (|integralBasisAtInfinity| . 1156080) (|ramified?| . 1155478) + (|ramifiedAtInfinity?| . 1155179) (|singular?| . 1154577) + (|singularAtInfinity?| . 1154278) (|branchPoint?| . 1153676) + (|branchPointAtInfinity?| . 1153377) (|rationalPoint?| . 1152707) + (|absolutelyIrreducible?| . 1152049) (|genus| . 1151369) + (|getZechTable| . 1150684) (|createZechTable| . 1150450) + (|createMultiplicationTable| . 1150156) + (|createMultiplicationMatrix| . 1149902) + (|createLowComplexityTable| . 1149632) + (|createLowComplexityNormalBasis| . 1149234) (|representationType| . 1149099) + (|createPrimitiveElement| . 1149044) (|tableForDiscreteLogarithm| . 1148874) + (|factorsOfCyclicGroupSize| . 1148695) (|sizeMultiplication| . 1147607) + (|getMultiplicationMatrix| . 1146795) (|getMultiplicationTable| . 1145927) + (|primitive?| . 1145625) (|numberOfIrreduciblePoly| . 1145457) + (|numberOfPrimitivePoly| . 1145289) (|numberOfNormalPoly| . 1145121) + (|createIrreduciblePoly| . 1144896) (|createPrimitivePoly| . 1144671) + (|createNormalPoly| . 1144446) (|createNormalPrimitivePoly| . 1144221) + (|createPrimitiveNormalPoly| . 1143996) (|nextIrreduciblePoly| . 1143812) + (|nextPrimitivePoly| . 1143628) (|nextNormalPoly| . 1143444) + (|nextNormalPrimitivePoly| . 1143260) (|nextPrimitiveNormalPoly| . 1143076) + (|leastAffineMultiple| . 1142894) (|reducedQPowers| . 1142636) + (|rootOfIrreduciblePoly| . 1142030) (|write!| . 1141887) (|read!| . 1141747) + (|iomode| . 1141573) (|close!| . 1141389) (|reopen!| . 1141219) + (|open| . 1140911) (|rightUnit| . 1140745) (|leftUnit| . 1140579) + (|rightMinimalPolynomial| . 1140352) (|leftMinimalPolynomial| . 1140125) + (|associatorDependence| . 1139679) (|lieAlgebra?| . 1139313) + (|jordanAlgebra?| . 1138947) (|noncommutativeJordanAlgebra?| . 1138581) + (|jordanAdmissible?| . 1138215) (|lieAdmissible?| . 1137849) + (|jacobiIdentity?| . 1137483) (|powerAssociative?| . 1137332) + (|alternative?| . 1136966) (|flexible?| . 1136600) + (|rightAlternative?| . 1136234) (|leftAlternative?| . 1135868) + (|antiAssociative?| . 1135502) (|associative?| . 1135136) + (|antiCommutative?| . 1134770) (|commutative?| . 1134404) + (|rightCharacteristicPolynomial| . 1134221) + (|leftCharacteristicPolynomial| . 1134038) (|rightNorm| . 1133912) + (|leftNorm| . 1133786) (|rightTrace| . 1133660) (|leftTrace| . 1133534) + (|someBasis| . 1133381) (|find| . 1133230) (|count| . 1132868) + (|every?| . 1132688) (|any?| . 1132508) (|sort!| . 1132095) + (|copyInto!| . 1131891) (|sorted?| . 1131531) (|LiePoly| . 1131345) + (|quickSort| . 1131040) (|heapSort| . 1130735) (|shellSort| . 1130430) + (|outputSpacing| . 1130309) (|outputGeneral| . 1130120) + (|outputFixed| . 1129931) (|outputFloating| . 1129742) (|exp1| . 1129661) + (|log10| . 1129537) (|log2| . 1129413) (|rationalApproximation| . 1128827) + (|relerror| . 1128748) (|complexSolve| . 1127579) (|complexRoots| . 1127020) + (|realRoots| . 1126516) (|leadingTerm| . 1126322) (|overlap| . 1126134) + (|hcrf| . 1126022) (|hclf| . 1125910) (|writable?| . 1125819) + (|readable?| . 1125728) (|exists?| . 1125637) (|extension| . 1125547) + (|directory| . 1125457) (|filename| . 1125361) (|shallowExpand| . 1125120) + (|deepExpand| . 1124879) (|fracPart| . 1124520) (|polyPart| . 1124313) + (|fullPartialFraction| . 1124067) (|primeFrobenius| . 1123882) + (|discreteLog| . 1123644) (|decreasePrecision| . 1123456) + (|increasePrecision| . 1123268) (|precision| . 1123004) (|bits| . 1122616) + (|mantissa| . 1122522) (|unitNormalize| . 1122429) (|unit| . 1122084) + (|flagFactor| . 1121888) (|sqfrFactor| . 1121757) (|primeFactor| . 1121626) + (|nthFlag| . 1121433) (|nthExponent| . 1121302) + (|irreducibleFactor| . 1121171) (|factors| . 1120598) (|nilFactor| . 1120467) + (|regularRepresentation| . 1120007) (|traceMatrix| . 1119298) + (|randomLC| . 1118908) (|minimize| . 1118576) (|module| . 1117840) + (|rightRegularRepresentation| . 1117494) + (|leftRegularRepresentation| . 1117148) (|rightTraceMatrix| . 1116599) + (|leftTraceMatrix| . 1116050) (|rightDiscriminant| . 1115591) + (|leftDiscriminant| . 1115132) (|represents| . 1113895) + (|mergeFactors| . 1113743) (|isMult| . 1113506) (|applyQuote| . 1112791) + (|ground| . 1112536) (|ground?| . 1112218) (|exprToXXP| . 1111428) + (|exprToUPS| . 1110151) (|exprToGenUPS| . 1108874) (|localAbs| . 1107467) + (|universe| . 1107332) (|complement| . 1107194) (|cardinality| . 1107039) + (|internalIntegrate0| . 1106486) (|makeCos| . 1106212) (|makeSin| . 1105938) + (|iiGamma| . 1105772) (|iiabs| . 1105606) (|bringDown| . 1105038) + (|newReduc| . 1104822) (|logical?| . 1104732) (|character?| . 1104642) + (|doubleComplex?| . 1104552) (|complex?| . 1104462) (|double?| . 1104372) + (|ffactor| . 1104066) (|qfactor| . 1103690) (|UP2ifCan| . 1103205) + (|anfactor| . 1102778) (|fortranCharacter| . 1102733) + (|fortranDoubleComplex| . 1102688) (|fortranComplex| . 1102643) + (|fortranLogical| . 1102598) (|fortranInteger| . 1102553) + (|fortranDouble| . 1102508) (|fortranReal| . 1102463) (|external?| . 1102381) + (|dimensionsOf| . 1102266) (|scalarTypeOf| . 1102120) (|makeFR| . 1101507) + (|musserTrials| . 1101148) (|stopMusserTrials| . 1100789) + (|numberOfFactors| . 1100384) (|modularFactor| . 1100158) + (|useSingleFactorBound?| . 1099994) (|useSingleFactorBound| . 1099827) + (|useEisensteinCriterion?| . 1099663) (|useEisensteinCriterion| . 1099496) + (|eisensteinIrreducible?| . 1099329) (|tryFunctionalDecomposition?| . 1099165) + (|tryFunctionalDecomposition| . 1098998) (|btwFact| . 1098507) + (|beauzamyBound| . 1098063) (|bombieriNorm| . 1097194) (|rootBound| . 1096750) + (|singleFactorBound| . 1095815) (|quadraticNorm| . 1095399) + (|infinityNorm| . 1094983) (|scaleRoots| . 1094804) (|shiftRoots| . 1094625) + (|degreePartition| . 1094072) (|factorOfDegree| . 1092565) + (|factorsOfDegree| . 1092283) (|pascalTriangle| . 1092111) + (|rangePascalTriangle| . 1091834) (|sizePascalTriangle| . 1091696) + (|fillPascalTriangle| . 1091572) (|safeCeiling| . 1091400) + (|safeFloor| . 1091228) (|safetyMargin| . 1090853) (|sumSquares| . 1090701) + (|euclideanNormalForm| . 1090382) (|euclideanGroebner| . 1089375) + (|factorGroebnerBasis| . 1088557) (|groebnerFactorize| . 1086917) + (|credPol| . 1086610) (|redPol| . 1086303) (|gbasis| . 1085965) + (|critT| . 1085545) (|critM| . 1085245) (|critB| . 1084939) + (|critBonD| . 1084532) (|critMTonD1| . 1084128) (|critMonD1| . 1083721) + (|redPo| . 1083348) (|hMonic| . 1083079) (|updatF| . 1082679) + (|sPol| . 1082290) (|updatD| . 1081883) (|minGbasis| . 1081579) + (|lepol| . 1081282) (|prinshINFO| . 1080988) (|prindINFO| . 1080528) + (|fprindINFO| . 1080065) (|prinpolINFO| . 1079736) (|prinb| . 1079414) + (|critpOrder| . 1078991) (|makeCrit| . 1078484) (|virtualDegree| . 1078176) + (|lcm| . 1078045) (|conditionsForIdempotents| . 1076674) + (|genericRightDiscriminant| . 1076328) (|genericRightTraceForm| . 1075976) + (|genericLeftDiscriminant| . 1075630) (|genericLeftTraceForm| . 1075278) + (|genericRightNorm| . 1074929) (|genericRightTrace| . 1074580) + (|genericRightMinimalPolynomial| . 1074216) (|rightRankPolynomial| . 1073387) + (|genericLeftNorm| . 1073038) (|genericLeftTrace| . 1072689) + (|genericLeftMinimalPolynomial| . 1072325) (|leftRankPolynomial| . 1071496) + (|generic| . 1069632) (|rightUnits| . 1069003) (|leftUnits| . 1068374) + (|compBound| . 1068122) (|tablePow| . 1067834) (|solveid| . 1067588) + (|testModulus| . 1067354) (|HenselLift| . 1067012) + (|completeHensel| . 1066755) (|multMonom| . 1066170) (|build| . 1065585) + (|leadingIndex| . 1065006) (|leadingExponent| . 1064427) + (|GospersMethod| . 1063839) (|nextSubsetGray| . 1063690) + (|firstSubsetGray| . 1063537) (|clipPointsDefault| . 1063364) + (|drawToScale| . 1063191) (|adaptive| . 1062798) (|figureUnits| . 1062628) + (|putColorInfo| . 1062466) (|appendPoint| . 1062334) (|component| . 1061773) + (|ranges| . 1061280) (|pointLists| . 1061158) (|makeGraphImage| . 1060498) + (|graphImage| . 1060454) (|groebSolve| . 1060044) (|testDim| . 1059718) + (|genericPosition| . 1059237) (|lfunc| . 1059152) (|inHallBasis?| . 1059026) + (|reorder| . 1058262) (|parameters| . 1058061) (|headAst| . 1057926) + (|heap| . 1057806) (|gcdprim| . 1057654) (|gcdcofact| . 1057495) + (|gcdcofactprim| . 1057336) (|lintgcd| . 1057149) (|hex| . 1057036) + (|host| . 1056958) (|trueEqual| . 1056862) (|factorList| . 1056230) + (|listConjugateBases| . 1055619) (|matrixGcd| . 1055157) + (|divideIfCan!| . 1054703) (|leastPower| . 1054274) (|idealiser| . 1053433) + (|idealiserMatrix| . 1053013) (|moduleSum| . 1052524) + (|mapUnivariate| . 1051788) (|mapUnivariateIfCan| . 1051410) + (|mapMatrixIfCan| . 1050988) (|mapBivariate| . 1050580) + (|fullDisplay| . 1049666) (|relationsIdeal| . 1049188) (|saturate| . 1048637) + (|groebner?| . 1048351) (|groebnerIdeal| . 1048058) (|ideal| . 1047043) + (|leadingIdeal| . 1046785) (|backOldPos| . 1046388) + (|generalPosition| . 1045932) (|quotient| . 1045412) (|zeroDim?| . 1044804) + (|inRadical?| . 1044515) (|in?| . 1044226) (|element?| . 1043937) + (|zeroDimPrime?| . 1043352) (|zeroDimPrimary?| . 1042767) + (|radical| . 1042213) (|primaryDecomp| . 1041178) (|contract| . 1040149) + (|gensym| . 1040105) (|leadingSupport| . 1039951) (|combineWithIf| . 1039688) + (|term| . 1039543) (|shrinkable| . 1039256) (|physicalLength!| . 1038972) + (|physicalLength| . 1038663) (|flexibleArray| . 1038376) + (|elseBranch| . 1038300) (|thenBranch| . 1038224) + (|generalizedInverse| . 1037938) (|imports| . 1037847) (|sequence| . 1037771) + (|readBytes!| . 1037628) (|readUInt32!| . 1037521) (|readInt32!| . 1037415) + (|readUInt16!| . 1037308) (|readInt16!| . 1037202) (|readUInt8!| . 1037096) + (|readInt8!| . 1036991) (|readByte!| . 1036886) (|setFieldInfo| . 1036624) + (|pol| . 1036410) (|xn| . 1036180) (|dAndcExp| . 1035930) (|repSq| . 1035724) + (|expPot| . 1035520) (|qPot| . 1035325) (|lookup| . 1035038) + (|normal?| . 1034462) (|basis| . 1032620) (|normalElement| . 1032282) + (|minimalPolynomial| . 1031453) (|position!| . 1031356) (|eof?| . 1031268) + (|inputBinaryFile| . 1031094) (|increment| . 1030926) + (|incrementBy| . 1030755) (|charpol| . 1030460) (|solve1| . 1030164) + (|innerEigenvectors| . 1029606) (|compile| . 1029476) (|declare| . 1029349) + (|parseString| . 1029270) (|unparse| . 1029191) (|flatten| . 1029145) + (|lambda| . 1029052) (|binary| . 1028850) (|packageCall| . 1028692) + (|interpret| . 1028487) (|innerSolve1| . 1027895) (|innerSolve| . 1027539) + (|makeEq| . 1027185) (|modularGcdPrimitive| . 1026893) + (|modularGcd| . 1026601) (|reduction| . 1025994) (|signAround| . 1025219) + (|invmod| . 1025158) (|powmod| . 1025094) (|mulmod| . 1025030) + (|submod| . 1024966) (|addmod| . 1024902) (|mask| . 1024844) (|dec| . 1024786) + (|inc| . 1024728) (|symmetricRemainder| . 1024667) + (|positiveRemainder| . 1024606) (|bit?| . 1024509) (|algint| . 1024036) + (|algintegrate| . 1023433) (|palgintegrate| . 1022830) + (|palginfieldint| . 1022360) (|bitLength| . 1022278) (|bitCoef| . 1022191) + (|bitTruth| . 1022069) (|contains?| . 1021822) (|inf| . 1021613) + (|qinterval| . 1021401) (|interval| . 1020727) (|unit?| . 1020638) + (|associates?| . 1020546) (|unitCanonical| . 1020493) (|unitNormal| . 1020337) + (|lfextendedint| . 1019766) (|lflimitedint| . 1019071) + (|lfinfieldint| . 1018569) (|lfintegrate| . 1017993) (|lfextlimint| . 1017347) + (|BasicMethod| . 1017184) (|PollardSmallFactor| . 1017054) + (|palgint0| . 1015722) (|palgextint0| . 1014408) (|palglimint0| . 1012846) + (|palgRDE0| . 1011520) (|palgLODE0| . 1009876) (|chineseRemainder| . 1008807) + (|divisors| . 1008655) (|eulerPhi| . 1008547) (|fibonacci| . 1008439) + (|harmonic| . 1008283) (|jacobi| . 1008172) (|moebiusMu| . 1008064) + (|numberOfDivisors| . 1007956) (|sumOfDivisors| . 1007848) + (|sumOfKthPowerDivisors| . 1007698) (|HermiteIntegrate| . 1006854) + (|palgint| . 1006254) (|palgextint| . 1005659) (|palglimint| . 1004940) + (|palgRDE| . 1004335) (|palgLODE| . 1003548) (|splitConstant| . 1003001) + (|pmComplexintegrate| . 1002305) (|pmintegrate| . 1000939) + (|infieldint| . 1000632) (|extendedint| . 1000232) (|limitedint| . 999716) + (|integerIfCan| . 999567) (|internalIntegrate| . 998618) + (|infieldIntegrate| . 998306) (|limitedIntegrate| . 997770) + (|extendedIntegrate| . 997339) (|varselect| . 997116) (|kmax| . 996893) + (|ksec| . 996630) (|vark| . 996372) (|removeConstantTerm| . 996144) + (|mkPrim| . 995865) (|intPatternMatch| . 995089) (|primintegrate| . 994583) + (|expintegrate| . 994054) (|tanintegrate| . 993577) + (|primextendedint| . 993020) (|expextendedint| . 992440) + (|primlimitedint| . 991775) (|explimitedint| . 991091) + (|primextintfrac| . 990752) (|primlimintfrac| . 990297) + (|primintfldpoly| . 990005) (|expintfldpoly| . 989653) + (|monomialIntegrate| . 989245) (|monomialIntPoly| . 988957) + (|inverseLaplace| . 988371) (|inputOutputBinaryFile| . 988185) + (|closed| . 988145) (|bothWays| . 988105) (|input| . 987797) + (|resolve| . 987665) (|bytes| . 987562) (|ip4Address| . 987482) + (|iprint| . 987358) (|elem?| . 987230) (|notelem| . 987056) + (|logpart| . 986745) (|ratpart| . 986652) (|mkAnswer| . 986257) + (|irDef| . 986105) (|irCtor| . 985956) (|irVar| . 985807) + (|perfectNthPower?| . 985621) (|perfectNthRoot| . 985265) + (|approxNthRoot| . 985107) (|perfectSquare?| . 984970) + (|perfectSqrt| . 984855) (|approxSqrt| . 984746) + (|generateIrredPoly| . 984525) (|complexExpand| . 983710) + (|complexIntegrate| . 982788) + (|dimensionOfIrreducibleRepresentation| . 982626) + (|irreducibleRepresentation| . 982009) (|checkRur| . 981505) + (|cAcsch| . 981329) (|cAsech| . 981153) (|cAcoth| . 980977) + (|cAtanh| . 980801) (|cAcosh| . 980625) (|cAsinh| . 980449) (|cCsch| . 980273) + (|cSech| . 980097) (|cCoth| . 979921) (|cTanh| . 979745) (|cCosh| . 979569) + (|cSinh| . 979393) (|cAcsc| . 979217) (|cAsec| . 979041) (|cAcot| . 978865) + (|cAtan| . 978689) (|cAcos| . 978513) (|cAsin| . 978337) (|cCsc| . 978161) + (|cSec| . 977985) (|cCot| . 977809) (|cTan| . 977633) (|cCos| . 977457) + (|cSin| . 977281) (|cLog| . 977105) (|cExp| . 976929) + (|cRationalPower| . 976731) (|cPower| . 976552) + (|seriesToOutputForm| . 976169) (|iCompose| . 976052) + (|taylorQuoByVar| . 975938) (|iExquo| . 975781) (|getStream| . 975587) + (|getRef| . 975402) (|makeSeries| . 975134) (|mappingMode| . 975017) + (|categoryMode| . 974967) (|voidMode| . 974917) (|noValueMode| . 974867) + (|jokerMode| . 974817) (GF2FG . 974289) (FG2F . 973799) (F2FG . 973309) + (|explogs2trigs| . 972788) (|trigs2explogs| . 972203) (|swap!| . 971972) + (|fill!| . 971550) (|minIndex| . 971382) (|maxIndex| . 971214) + (|entry?| . 970961) (|indices| . 970791) (|index?| . 970618) + (|entries| . 970448) (|categories| . 970216) (|jvmInterface| . 970164) + (|jvmSuper| . 970112) (|jvmNameAndTypeConstantTag| . 970064) + (|jvmInterfaceMethodConstantTag| . 970016) + (|jvmMethodrefConstantTag| . 969968) (|jvmFieldrefConstantTag| . 969920) + (|jvmStringConstantTag| . 969872) (|jvmClassConstantTag| . 969824) + (|jvmDoubleConstantTag| . 969776) (|jvmLongConstantTag| . 969728) + (|jvmFloatConstantTag| . 969680) (|jvmIntegerConstantTag| . 969632) + (|jvmUTF8ConstantTag| . 969584) (|jvmTransient| . 969536) + (|jvmVolatile| . 969488) (|jvmStrict| . 969439) (|jvmAbstract| . 969340) + (|jvmNative| . 969291) (|jvmSynchronized| . 969242) (|jvmFinal| . 969097) + (|jvmStatic| . 969002) (|jvmProtected| . 968907) (|jvmPrivate| . 968812) + (|jvmPublic| . 968667) (|search| . 968515) (|keys| . 968337) (|key?| . 968156) + (|symbolIfCan| . 968028) (|kernel| . 967463) (|argument| . 967070) + (|constantKernel| . 966898) (|constantIfCan| . 966717) (|kovacic| . 965761) + (|unknown| . 965707) (|laplace| . 965155) (|trailingCoefficient| . 964982) + (|normalizeIfCan| . 964527) (|polCase| . 964143) (|distFact| . 963400) + (|identification| . 963059) (|LyndonCoordinates| . 962706) + (|LyndonBasis| . 962332) (|zeroDimensional?| . 961840) (|fglmIfCan| . 961399) + (|groebner| . 959762) (|lexTriangular| . 959436) + (|squareFreeLexTriangular| . 958639) (|belong?| . 956851) (|erf| . 956513) + (|dilog| . 956175) (|li| . 955837) (|Ci| . 955499) (|Si| . 955161) + (|Ei| . 954823) (|linGenPos| . 954447) (|groebgen| . 954066) + (|totolex| . 953766) (|minPol| . 953063) (|computeBasis| . 952835) + (|coord| . 952158) (|anticoord| . 951825) (|intcompBasis| . 951545) + (|choosemon| . 951257) (|transform| . 950970) (|pack!| . 950824) + (|library| . 950745) (|complexLimit| . 949606) (|limit| . 946780) + (|linearlyDependent?| . 946529) (|linearDependence| . 946278) + (|solveLinear| . 945692) (|linearElement| . 945524) (|reducedSystem| . 945079) + (|leftReducedSystem| . 944664) (|linearForm| . 944506) + (|setDifference| . 944383) (|setIntersection| . 944260) (|setUnion| . 944137) + (|append| . 944057) (|null| . 943943) (|nil| . 943869) (|substitute| . 943755) + (|duplicates?| . 943619) (|mapGen| . 942914) (|mapExpon| . 942372) + (|commutativeEquality| . 942173) (|plus| . 941830) (|leftMult| . 941659) + (|rightMult| . 941488) (|makeUnit| . 941323) (|reverse!| . 940903) + (|reverse| . 940458) (|nthFactor| . 939655) (|nthExpon| . 939145) + (|makeMulti| . 938911) (|makeTerm| . 938740) (|listOfMonoms| . 938499) + (|insert| . 938235) (|delete| . 937956) (|symmetricSquare| . 937802) + (|factor1| . 937190) (|symmetricProduct| . 936796) (|symmetricPower| . 936310) + (|directSum| . 935916) (|\\/| . 935869) (|/\\| . 935822) (~ . 935778) + (|solveLinearPolynomialEquationByFractions| . 935510) + (|hasSolution?| . 934805) (|linSolve| . 934284) (|LyndonWordsList| . 934062) + (|LyndonWordsList1| . 933816) (|lyndonIfCan| . 933671) (|lyndon| . 933532) + (|lyndon?| . 933358) (|numberOfComputedEntries| . 933216) (|rst| . 933113) + (|frst| . 933010) (|lazyEvaluate| . 932907) (|lazy?| . 932776) + (|explicitlyEmpty?| . 932645) (|explicitEntries?| . 932514) (|iter| . 932311) + (|arg1| . 932154) (|arg2| . 931997) (|comp| . 931718) (|mappingAst| . 931588) + (|nullary| . 931453) (|fixedPoint| . 931093) (|id| . 930989) + (|recur| . 930597) (|const| . 930415) (|curry| . 930199) (|diag| . 929980) + (|curryRight| . 929714) (|curryLeft| . 929448) (|constantRight| . 929185) + (|constantLeft| . 928922) (|twist| . 928656) (|setsubMatrix!| . 928407) + (|subMatrix| . 928155) (|swapColumns!| . 927909) (|swapRows!| . 927663) + (|vertConcat| . 927455) (|horizConcat| . 927247) (|squareTop| . 927042) + (|elRow1!| . 926717) (|elRow2!| . 926389) (|elColumn2!| . 926061) + (|fractionFreeGauss!| . 925726) (|invertIfCan| . 925401) (|copy!| . 925254) + (|plus!| . 925104) (|minus!| . 924809) (|leftScalarTimes!| . 924659) + (|rightScalarTimes!| . 924509) (|times!| . 924359) (|power!| . 924157) + (|nothing| . 924082) (|just| . 924004) (|duplicates| . 923784) + (|removeDuplicates!| . 923539) (|linears| . 923361) (|ddFact| . 923104) + (|separateFactors| . 922513) (|exptMod| . 922095) (|meshPar2Var| . 920953) + (|meshFun2Var| . 920489) (|meshPar1Var| . 920122) (|ptFunc| . 919741) + (|rowEch| . 919590) (|rowEchLocal| . 919436) (|rowEchelonLocal| . 919279) + (|normalizedDivide| . 918668) (|binaryFunction| . 918362) + (|makeFloatFunction| . 917869) (|function| . 917104) (|makeRecord| . 916911) + (|unaryFunction| . 916646) (|compiledFunction| . 916068) (|corrPoly| . 915482) + (|lifting| . 914872) (|lifting1| . 914122) (|exprex| . 914000) + (|coerceL| . 913878) (|coerceS| . 913756) (|frobenius| . 913560) + (|computePowers| . 913348) (|pow| . 913136) (|An| . 912952) + (|UnVectorise| . 912768) (|Vectorise| . 912584) (|setPoly| . 912437) + (|index| . 911685) (|exponent| . 910925) (|exQuo| . 909911) + (|moebius| . 909810) (|rightRecip| . 909581) (|leftRecip| . 909352) + (|leftPower| . 909154) (|rightPower| . 908956) + (|derivationCoordinates| . 908642) (|generator| . 907459) (|one?| . 906936) + (|monoidOperation| . 906794) (|neutralValue| . 906683) + (|splitSquarefree| . 906347) (|normalDenom| . 906102) (|reshape| . 905291) + (|totalfract| . 904666) (|pushdterm| . 904083) (|pushucoef| . 903485) + (|pushuconst| . 902997) (|numberOfMonomials| . 902452) (|unique| . 902327) + (|multiset| . 902029) (|systemCommand| . 901907) (|mergeDifference| . 901778) + (|squareFreePrim| . 901472) (|compdegd| . 901042) (|univcase| . 900733) + (|consnewpol| . 900156) (|nsqfree| . 899464) (|intChoose| . 898668) + (|coefChoose| . 898331) (|myDegree| . 897865) (|normDeriv2| . 897503) + (|plenaryPower| . 897341) (|antiCommutator| . 897282) (|commutator| . 897178) + (|associator| . 897116) (|complexEigenvalues| . 896861) + (|complexEigenvectors| . 896465) (|isConnected?| . 896327) + (|connectTo| . 895952) (|shift| . 895539) (|normalizedAssociate| . 895188) + (|normalize| . 893800) (|outputArgs| . 893384) (|normInvertible?| . 892941) + (|normFactors| . 892554) (|npcoef| . 891715) (|listexp| . 891345) + (|characteristicPolynomial| . 889198) (|realEigenvalues| . 888970) + (|realEigenvectors| . 888613) (|halfExtendedResultant2| . 888343) + (|halfExtendedResultant1| . 888073) (|extendedResultant| . 887768) + (|subResultantsChain| . 887548) (|lazyPseudoQuotient| . 887434) + (|lazyPseudoRemainder| . 887320) (|bernoulliB| . 887082) (|eulerE| . 886844) + (|numeric| . 885125) (|complexNumeric| . 881083) (|numericIfCan| . 879650) + (|complexNumericIfCan| . 876449) (|FormatArabic| . 876321) + (|ScanArabic| . 876193) (|FormatRoman| . 876065) (|ScanRoman| . 875937) + (|ScanFloatIgnoreSpaces| . 875819) (|ScanFloatIgnoreSpacesIfCan| . 875695) + (|rk4| . 875077) (|rk4a| . 874764) (|rk4qc| . 873897) (|rk4f| . 873590) + (|aromberg| . 873248) (|asimpson| . 872906) (|atrapezoidal| . 872564) + (|romberg| . 872225) (|simpson| . 871886) (|trapezoidal| . 871547) + (|rombergo| . 871208) (|simpsono| . 870869) (|trapezoidalo| . 870530) + (|sup| . 870258) (|inv| . 868984) (|imagE| . 868873) (|imagk| . 868762) + (|imagj| . 868651) (|imagi| . 868540) (|octon| . 868272) + (|constDsolve| . 867556) (|expint| . 867009) (|diff| . 866424) + (|algDsolve| . 865740) (|denomLODE| . 864727) (|indicialEquations| . 862543) + (|indicialEquation| . 861543) (|denomRicDE| . 861042) + (|leadingCoefficientRicDE| . 860478) (|constantCoefficientRicDE| . 859847) + (|changeVar| . 858887) (|ratDsolve| . 856599) + (|indicialEquationAtInfinity| . 855775) (|reduceLODE| . 855310) + (|singRicDE| . 853798) (|polyRicDE| . 852370) (|ricDsolve| . 848072) + (|triangulate| . 847226) (|solveInField| . 846117) + (|wronskianMatrix| . 845616) (|variationOfParameters| . 845381) + (|lexico| . 844992) (|po| . 844820) (|op| . 844648) (|infinity| . 844438) + (|makeop| . 844106) (|opeval| . 843802) (|evaluateInverse| . 843505) + (|evaluate| . 842433) (|conjug| . 842127) (|adjoint| . 840984) + (|arity| . 840851) (|getDatabase| . 840714) (|whatInfinity| . 840567) + (|infinite?| . 840300) (|finite?| . 839948) (|minusInfinity| . 839740) + (|plusInfinity| . 839532) (|pureLex| . 839309) (|totalLex| . 839086) + (|reverseLex| . 838863) (|min| . 838333) (|leftLcm| . 838013) + (|rightExtendedGcd| . 837769) (|rightGcd| . 837622) + (|rightExactQuotient| . 837469) (|rightRemainder| . 837322) + (|rightQuotient| . 837175) (|rightLcm| . 837028) (|leftExtendedGcd| . 836784) + (|leftGcd| . 836464) (|leftExactQuotient| . 836136) (|leftRemainder| . 835816) + (|leftQuotient| . 835496) (|times| . 835225) (|apply| . 834408) + (|monicLeftDivide| . 833833) (|monicRightDivide| . 833258) + (|leftDivide| . 832453) (|rightDivide| . 831896) (|hermiteH| . 831725) + (|laguerreL| . 831382) (|legendreP| . 831149) (|outputList| . 831026) + (|writeBytes!| . 830882) (|writeUInt8!| . 830746) (|writeInt8!| . 830612) + (|writeByte!| . 830478) (|isOpen?| . 830211) (|outputBinaryFile| . 830035) + (|not| . 829939) (|or| . 829837) (|and| . 829735) (|quo| . 829574) + (|rem| . 829413) (|div| . 829163) (>= . 829026) (> . 828889) (~= . 828754) + (|blankSeparate| . 828659) (|semicolonSeparate| . 828564) + (|commaSeparate| . 828469) (|pile| . 828374) (|paren| . 828094) + (|bracket| . 827954) (|prod| . 827808) (|overlabel| . 827758) + (|overbar| . 827711) (|prime| . 827569) (|quote| . 827481) + (|supersub| . 827383) (|presuper| . 827333) (|presub| . 827283) + (|super| . 827233) (|sub| . 827183) (|rarrow| . 827133) (|assign| . 827083) + (|slash| . 827033) (|over| . 826983) (|zag| . 826933) (|box| . 826746) + (|label| . 826696) (|infix?| . 826615) (|postfix| . 826565) (|infix| . 826416) + (|prefix| . 826318) (|vconcat| . 826175) (|hconcat| . 826032) + (|rspace| . 825946) (|vspace| . 825865) (|hspace| . 825784) + (|superHeight| . 825703) (|subHeight| . 825622) (|height| . 824676) + (|width| . 824312) (|doubleFloatFormat| . 824232) (|messagePrint| . 824118) + (|message| . 824038) (|members| . 823802) (|padecf| . 823483) + (|pade| . 822524) (|root| . 822257) (|quotientByP| . 822195) + (|moduloP| . 822090) (|modulus| . 820814) (|digits| . 820123) + (|continuedFraction| . 819114) (|pair| . 818995) (|light| . 818919) + (|pastel| . 818843) (|bright| . 818547) (|dim| . 818471) (|dark| . 818395) + (|getSyntaxFormsFromFile| . 818274) (|surface| . 818176) + (|coordinate| . 817751) (|conjugates| . 817618) (|shuffle| . 817446) + (|shufflein| . 817274) (|sequences| . 816935) (|permutations| . 816775) + (|lists| . 816519) (|makeResult| . 816215) (|is?| . 814997) (|Is| . 813629) + (|addMatchRestricted| . 813438) (|insertMatch| . 813250) (|addMatch| . 813062) + (|getMatch| . 812875) (|failed| . 812535) (|failed?| . 812133) + (|optpair| . 811991) (|getBadValues| . 811862) (|resetBadValues| . 811773) + (|hasTopPredicate?| . 811649) (|topPredicate| . 811470) + (|setTopPredicate| . 811308) (|patternVariable| . 811148) + (|withPredicates| . 811016) (|setPredicates| . 810884) (|predicates| . 810755) + (|hasPredicate?| . 810631) (|optional?| . 810507) (|multiple?| . 810383) + (|generic?| . 810259) (|quoted?| . 810135) (|inR?| . 810011) + (|isList| . 809869) (|isQuotient| . 809691) (|isOp| . 809296) + (|Zero| . 808974) (|satisfy?| . 808315) (|addBadValue| . 808024) + (|badValues| . 807822) (|retractable?| . 806934) (|ListOfTerms| . 806183) + (|One| . 805706) (|leftFactor| . 805531) (|rightFactorCandidate| . 805319) + (D . 803987) (|ptree| . 803800) (|coerceImages| . 803672) + (|fixedPoints| . 803516) (|odd?| . 803153) (|even?| . 802790) + (|numberOfCycles| . 802651) (|cyclePartition| . 802521) + (|coerceListOfPairs| . 802384) (|coercePreimagesImages| . 802247) + (|listRepresentation| . 802062) (|permanent| . 801746) (|cycles| . 801599) + (|cycle| . 801461) (|initializeGroupForWordProblem| . 801162) (<= . 800891) + (< . 800481) (|support| . 800214) (|wordInGenerators| . 800016) + (|wordInStrongGenerators| . 799818) (|orbits| . 799671) (|orbit| . 799060) + (|permutationGroup| . 798904) (|wordsForStrongGenerators| . 798735) + (|strongGenerators| . 798579) (|base| . 798214) (|generators| . 797774) + (|bivariateSLPEBR| . 797357) + (|solveLinearPolynomialEquationByRecursion| . 796608) + (|factorByRecursion| . 795837) (|factorSquareFreeByRecursion| . 795066) + (|randomR| . 794265) (|factorSFBRlcUnit| . 793463) (|charthRoot| . 793147) + (|conditionP| . 792809) (|solveLinearPolynomialEquation| . 791771) + (|factorSquareFreePolynomial| . 791566) (|factorPolynomial| . 791061) + (|squareFreePolynomial| . 790556) (|gcdPolynomial| . 789951) + (|torsion?| . 788969) (|torsionIfCan| . 787955) (|getGoodPrime| . 787654) + (|badNum| . 787086) (|mix| . 786748) (|doubleDisc| . 786490) + (|polyred| . 786263) (|padicFraction| . 786155) (|padicallyExpand| . 785987) + (|numberOfFractionalTerms| . 785851) (|nthFractionalTerm| . 785712) + (|firstNumer| . 785604) (|firstDenom| . 785464) (|compactFraction| . 785356) + (|partialFraction| . 784656) (|gcdPrimitive| . 783767) + (|symmetricGroup| . 783432) (|alternatingGroup| . 783097) + (|abelianGroup| . 782920) (|cyclicGroup| . 782585) (|dihedralGroup| . 782250) + (|mathieu11| . 781961) (|mathieu12| . 781672) (|mathieu22| . 781383) + (|mathieu23| . 781094) (|mathieu24| . 780805) (|janko2| . 780516) + (|rubiksGroup| . 780394) (|youngGroup| . 780065) (|lexGroebner| . 779877) + (|totalGroebner| . 779689) (|expressIdealMember| . 779546) + (|principalIdeal| . 779364) (|LagrangeInterpolation| . 779153) + (|psolve| . 770580) (|wrregime| . 769750) (|rdregime| . 768864) + (|bsolve| . 767612) (|dmp2rfi| . 766321) (|se2rfi| . 765868) + (|pr2dmp| . 765480) (|hasoln| . 764968) (|ParCondList| . 764142) + (|redpps| . 763584) (|B1solve| . 762760) (|factorset| . 762378) + (|maxrank| . 761676) (|minrank| . 760974) (|minset| . 760583) + (|nextSublist| . 760145) (|overset?| . 759688) (|ParCond| . 759100) + (|redmat| . 758685) (|regime| . 757578) (|sqfree| . 757231) + (|inconsistent?| . 756384) (|debug| . 756309) (|numFunEvals| . 756237) + (|setAdaptive| . 756162) (|adaptive?| . 756090) + (|setScreenResolution| . 756015) (|screenResolution| . 755772) + (|setMaxPoints| . 755697) (|maxPoints| . 755454) (|setMinPoints| . 755379) + (|minPoints| . 755136) (|parametric?| . 755061) (|plotPolar| . 754379) + (|debug3D| . 754302) (|numFunEvals3D| . 754228) (|setAdaptive3D| . 754151) + (|adaptive3D?| . 754077) (|setScreenResolution3D| . 754000) + (|screenResolution3D| . 753926) (|setMaxPoints3D| . 753849) + (|maxPoints3D| . 753775) (|setMinPoints3D| . 753698) (|minPoints3D| . 753624) + (|tValues| . 753516) (|tRange| . 753330) (|plot| . 751328) + (|pointPlot| . 750623) (|calcRanges| . 750442) (|assert| . 749974) + (|optional| . 749671) (|multiple| . 749368) (|fixPredicate| . 749033) + (|patternMatch| . 744310) (|patternMatchTimes| . 743791) + (|bernoulli| . 743447) (|chebyshevT| . 743101) (|chebyshevU| . 742755) + (|cyclotomic| . 742233) (|euler| . 741937) (|fixedDivisor| . 741760) + (|laguerre| . 741583) (|legendre| . 741284) (|dmpToHdmp| . 741012) + (|hdmpToDmp| . 740740) (|pToHdmp| . 740501) (|hdmpToP| . 740262) + (|dmpToP| . 740034) (|pToDmp| . 739806) (|sylvesterSequence| . 739598) + (|sturmSequence| . 739393) (|boundOfCauchy| . 739182) + (|sturmVariationsOf| . 738897) (|lazyVariations| . 738571) + (|content| . 737812) (|primitiveMonomials| . 737590) (|totalDegree| . 737074) + (|minimumDegree| . 736098) (|monomials| . 735541) (|isPlus| . 734461) + (|isTimes| . 733388) (|isExpt| . 731557) (|isPower| . 730583) + (|rroot| . 729880) (|qroot| . 729129) (|froot| . 728387) (|nthr| . 727675) + (|port| . 727586) (|firstUncouplingMatrix| . 727312) (|integral| . 726202) + (|primitiveElement| . 723931) (|nextPrime| . 723814) (|prevPrime| . 723697) + (|primes| . 723549) (|print| . 723353) (|selectsecond| . 723220) + (|selectfirst| . 723087) (|makeprod| . 722951) (|property| . 722569) + (|disjunction| . 722457) (|conjunction| . 722345) (|isEquiv| . 722159) + (|isImplies| . 721973) (|isOr| . 721787) (|isAnd| . 721601) (|isNot| . 721431) + (|isAtom| . 721293) (|atoms| . 720842) (|dual| . 720410) (|equiv| . 720350) + (|implies| . 720290) (|false| . 720236) (|true| . 720182) (|merge!| . 719758) + (|max| . 719230) (|resultantEuclidean| . 718951) + (|semiResultantEuclidean2| . 718697) (|semiResultantEuclidean1| . 718443) + (|indiceSubResultant| . 718212) (|indiceSubResultantEuclidean| . 717881) + (|semiIndiceSubResultantEuclidean| . 717575) (|degreeSubResultant| . 717344) + (|degreeSubResultantEuclidean| . 717013) + (|semiDegreeSubResultantEuclidean| . 716707) + (|lastSubResultantEuclidean| . 716425) + (|semiLastSubResultantEuclidean| . 716168) + (|subResultantGcdEuclidean| . 715895) + (|semiSubResultantGcdEuclidean2| . 715647) + (|semiSubResultantGcdEuclidean1| . 715399) (|discriminantEuclidean| . 715120) + (|semiDiscriminantEuclidean| . 714866) (|chainSubResultants| . 714656) + (|schema| . 714419) (|resultantReduit| . 714205) + (|resultantReduitEuclidean| . 713870) + (|semiResultantReduitEuclidean| . 713578) (|divide| . 712829) + (|Lazard| . 712598) (|Lazard2| . 712364) (|nextsousResultant2| . 712176) + (|resultantnaif| . 711994) (|resultantEuclideannaif| . 711715) + (|semiResultantEuclideannaif| . 711461) (|pdct| . 711371) (|powers| . 711237) + (|partitions| . 711096) (|parts| . 710990) (|partition| . 710761) + (|complete| . 710124) (|pole?| . 709779) (|monomial| . 706528) + (|leadingMonomial| . 705276) (|zRange| . 705151) (|yRange| . 704903) + (|xRange| . 704655) (|listBranches| . 704375) (|triangular?| . 704037) + (|rewriteIdealWithRemainder| . 703689) + (|rewriteIdealWithHeadRemainder| . 703341) (|remainder| . 702937) + (|headRemainder| . 702560) (|roughUnitIdeal?| . 702222) + (|roughEqualIdeals?| . 701881) (|roughSubIdeal?| . 701540) + (|roughBase?| . 701202) (|trivialIdeal?| . 700901) (|sort| . 700102) + (|collectUpper| . 699833) (|collect| . 699564) (|collectUnder| . 699295) + (|mainVariable?| . 698991) (|mainVariables| . 698690) + (|removeSquaresIfCan| . 698366) (|unprotectedRemoveRedundantFactors| . 698046) + (|removeRedundantFactors| . 696372) (|certainlySubVariety?| . 696017) + (|possiblyNewVariety?| . 695625) (|probablyZeroDim?| . 695273) + (|selectPolynomials| . 694802) (|selectOrPolynomials| . 694322) + (|selectAndPolynomials| . 693842) (|quasiMonicPolynomials| . 693424) + (|univariate?| . 693107) (|univariatePolynomials| . 692689) + (|linear?| . 692372) (|linearPolynomials| . 691954) (|bivariate?| . 691637) + (|bivariatePolynomials| . 691219) + (|removeRoughlyRedundantFactorsInPols| . 690536) + (|removeRoughlyRedundantFactorsInPol| . 690209) (|interReduce| . 689885) + (|roughBasicSet| . 689450) (|crushedSet| . 689126) + (|rewriteSetByReducingWithParticularGenerators| . 688653) + (|rewriteIdealWithQuasiMonicGenerators| . 688226) + (|squareFreeFactors| . 687877) (|univariatePolynomialsGcds| . 687136) + (|removeRoughlyRedundantFactorsInContents| . 686777) + (|removeRedundantFactorsInContents| . 686418) + (|removeRedundantFactorsInPols| . 686059) (|irreducibleFactors| . 685642) + (|lazyIrreducibleFactors| . 685225) + (|removeIrreducibleRedundantFactors| . 684805) (|normalForm| . 684159) + (|changeBase| . 683938) (|companionBlocks| . 683666) (|xCoord| . 683543) + (|yCoord| . 683420) (|zCoord| . 683297) (|rCoord| . 683174) + (|thetaCoord| . 683051) (|phiCoord| . 682928) (|color| . 682731) + (|hue| . 682460) (|shade| . 682261) (|nthRootIfCan| . 682070) + (|expIfCan| . 681924) (|logIfCan| . 681778) (|sinIfCan| . 681632) + (|cosIfCan| . 681486) (|tanIfCan| . 681340) (|cotIfCan| . 681194) + (|secIfCan| . 681048) (|cscIfCan| . 680902) (|asinIfCan| . 680756) + (|acosIfCan| . 680610) (|atanIfCan| . 680464) (|acotIfCan| . 680318) + (|asecIfCan| . 680172) (|acscIfCan| . 680026) (|sinhIfCan| . 679880) + (|coshIfCan| . 679734) (|tanhIfCan| . 679588) (|cothIfCan| . 679442) + (|sechIfCan| . 679296) (|cschIfCan| . 679150) (|asinhIfCan| . 679004) + (|acoshIfCan| . 678858) (|atanhIfCan| . 678712) (|acothIfCan| . 678566) + (|asechIfCan| . 678420) (|acschIfCan| . 678274) (|pushdown| . 676661) + (|pushup| . 675048) (|reducedDiscriminant| . 674733) + (|idealSimplify| . 674477) (|definingInequation| . 674221) + (|definingEquations| . 673930) (|setStatus| . 673617) + (|quasiAlgebraicSet| . 673323) (|radicalSimplify| . 672795) + (|random| . 671464) (|denominator| . 671210) (|numerator| . 670966) + (|denom| . 669505) (|numer| . 668024) (|quadraticForm| . 667852) + (|back| . 667761) (|front| . 667670) (|rotate!| . 667579) + (|dequeue!| . 667488) (|enqueue!| . 667394) (|quatern| . 667272) + (|imagK| . 667050) (|imagJ| . 666828) (|imagI| . 666606) + (|conjugate| . 666067) (|queue| . 665945) (|nthRoot| . 665519) + (|fractRadix| . 665384) (|wholeRadix| . 665252) (|cycleRagits| . 665120) + (|prefixRagits| . 664988) (|fractRagits| . 664854) (|wholeRagits| . 664722) + (|radix| . 664560) (|randnum| . 664383) (|reseed| . 664260) (|seed| . 664172) + (|rational| . 662689) (|rational?| . 661337) (|rationalIfCan| . 659854) + (|setvalue!| . 659698) (|setchildren!| . 659507) (|node?| . 659342) + (|child?| . 659177) (|distance| . 659044) (|leaves| . 658914) + (|nodes| . 658784) (|rename| . 658688) (|rename!| . 658592) + (|mainValue| . 658467) (|mainDefiningPolynomial| . 658342) + (|mainForm| . 658236) (|sqrt| . 657722) (|rischDE| . 656645) + (|rischDEsys| . 655789) (|monomRDE| . 655320) (|baseRDE| . 654927) + (|polyRDE| . 654313) (|monomRDEsys| . 653806) (|baseRDEsys| . 653438) + (|weighted| . 653213) (|rdHack1| . 652957) (|midpoint| . 652688) + (|midpoints| . 652363) (|realZeros| . 649798) + (|mainCharacterization| . 649440) (|algebraicOf| . 649058) + (|ReduceOrder| . 648608) (|setref| . 648521) (|deref| . 648439) + (|ref| . 648357) (= . 647927) (|radicalEigenvectors| . 647534) + (|radicalEigenvector| . 647273) (|radicalEigenvalues| . 647076) + (|eigenMatrix| . 646872) (|normalise| . 646747) (|gramschmidt| . 646613) + (|orthonormalBasis| . 646405) (|antisymmetricTensors| . 645945) + (|createGenericMatrix| . 645743) (|symmetricTensors| . 645376) + (|tensorProduct| . 644822) (|permutationRepresentation| . 643958) + (|completeEchelonBasis| . 643776) (|createRandomElement| . 643593) + (|cyclicSubmodule| . 643317) (|standardBasisOfCyclicSubmodule| . 643059) + (|areEquivalent?| . 642323) (|isAbsolutelyIrreducible?| . 641875) + (|meatAxe| . 640663) (|scanOneDimSubspaces| . 640381) (|double| . 640129) + (|expt| . 639877) (|lift| . 637991) (|solveRetract| . 637614) + (|variables| . 635504) (|mainVariable| . 634615) (|univariate| . 631361) + (|multivariate| . 629347) (|uniform01| . 629255) (|normal01| . 629163) + (|exponential1| . 629071) (|chiSquare1| . 628930) (|normal| . 628787) + (|exponential| . 628422) (|chiSquare| . 628262) (F . 628099) (|t| . 627939) + (|factorFraction| . 627699) (|componentUpperBound| . 627596) (|blue| . 627453) + (|green| . 627310) (|red| . 627167) (|whitePoint| . 627064) + (|uniform| . 626587) (|binomial| . 625992) (|poisson| . 625841) + (|geometric| . 625690) (|ridHack1| . 625575) (|interpolate| . 624845) + (|nullSpace| . 622895) (|nullity| . 621568) (|rank| . 618739) + (|rowEchelon| . 616913) (|column| . 616379) (|row| . 615845) (|qelt| . 614994) + (|ncols| . 614444) (|nrows| . 613894) (|maxColIndex| . 613366) + (|minColIndex| . 612838) (|maxRowIndex| . 612310) (|minRowIndex| . 611782) + (|antisymmetric?| . 611274) (|symmetric?| . 610766) (|diagonal?| . 610258) + (|square?| . 609750) (|matrix| . 608628) (|rectangularMatrix| . 608405) + (|annihilate?| . 608326) (|characteristic| . 606439) (|round| . 606384) + (|fractionPart| . 605713) (|wholePart| . 605250) (|floor| . 605033) + (|ceiling| . 604816) (|norm| . 600952) (|mightHaveRoots| . 600705) + (|refine| . 598803) (|middle| . 598594) (|size| . 596591) (|right| . 595970) + (|left| . 595349) (|roman| . 595184) (|mainSquareFreePart| . 594949) + (|mainPrimitivePart| . 594714) (|mainContent| . 594479) + (|primitivePart!| . 594244) (|gcd| . 591954) (|nextsubResultant2| . 591705) + (|LazardQuotient2| . 591410) (|LazardQuotient| . 591118) + (|subResultantChain| . 590840) (|halfExtendedSubResultantGcd2| . 590258) + (|halfExtendedSubResultantGcd1| . 589676) (|extendedSubResultantGcd| . 589051) + (|exactQuotient!| . 588567) (|exactQuotient| . 588083) + (|primPartElseUnitCanonical!| . 587843) (|primPartElseUnitCanonical| . 587603) + (|retract| . 585066) (|retractIfCan| . 582078) (|lazyResidueClass| . 581473) + (|monicModulo| . 581155) (|lazyPseudoDivide| . 580135) + (|lazyPremWithDefault| . 579458) (|lazyPquo| . 579045) (|lazyPrem| . 578632) + (|pquo| . 578219) (|prem| . 577806) (|supRittWu?| . 577572) + (|RittWuCompare| . 577336) (|mainMonomials| . 577105) + (|mainCoefficients| . 576874) (|leastMonomial| . 576671) + (|mainMonomial| . 576468) (|quasiMonic?| . 576237) (|monic?| . 575804) + (|leadingCoefficient| . 573523) (|deepestInitial| . 573320) + (|iteratedInitials| . 573089) (|deepestTail| . 572886) (|head| . 572419) + (|mdeg| . 572170) (|mvar| . 571703) (|iterators| . 571522) + (|relativeApprox| . 570912) (|rootOf| . 569374) (|allRootsOf| . 568249) + (|definingPolynomial| . 567197) (|positive?| . 566618) (|negative?| . 566040) + (|zero?| . 565352) (|augment| . 564010) (|lastSubResultant| . 563074) + (|lastSubResultantElseSplit| . 562735) (|invertibleSet| . 562412) + (|invertible?| . 561711) (|invertibleElseSplit?| . 561366) + (|purelyAlgebraicLeadingMonomial?| . 561043) + (|algebraicCoefficients?| . 560720) (|purelyTranscendental?| . 560397) + (|purelyAlgebraic?| . 559756) (|prepareSubResAlgo| . 559300) + (|internalLastSubResultant| . 558300) (|integralLastSubResultant| . 557861) + (|toseLastSubResultant| . 557422) (|toseInvertible?| . 556575) + (|toseInvertibleSet| . 556179) (|toseSquareFreePart| . 555743) + (|expression| . 555266) (|quotedOperators| . 554805) (|pattern| . 554380) + (|suchThat| . 552163) (|rule| . 551284) (|rules| . 550813) + (|ruleset| . 550342) (|rur| . 548427) (|create| . 548372) + (|clearCache| . 548250) (|cache| . 548125) (|enterInCache| . 547832) + (|currentCategoryFrame| . 547793) (|currentScope| . 547754) + (|pushNewContour| . 547675) (|findBinding| . 547417) (|contours| . 547330) + (|structuralConstants| . 545985) (|coordinates| . 543313) (|bounds| . 543221) + (|equation| . 542687) (|incr| . 542560) (|high| . 542468) (|low| . 542376) + (|hi| . 542284) (|lo| . 542192) (BY . 542062) (|body| . 541142) + (|union| . 540489) (|subset?| . 540355) (|symmetricDifference| . 540249) + (|difference| . 540039) (|intersect| . 538013) (|set| . 537784) + (|brace| . 537417) (|part?| . 537283) (|latex| . 537198) (|hash| . 537106) + (|delta| . 536897) (|member?| . 536380) (|enumerate| . 536168) + (|setOfMinN| . 535968) (|elements| . 535676) (|replaceKthElement| . 535511) + (|incrementKthElement| . 535349) (|cdr| . 535077) (|car| . 534805) + (|expr| . 534533) (|float| . 534025) (|integer| . 533615) (|symbol| . 533343) + (|destruct| . 532823) (|float?| . 532523) (|integer?| . 531988) + (|symbol?| . 531566) (|string?| . 531266) (|list?| . 530966) + (|pair?| . 530666) (|atom?| . 530366) (|null?| . 530066) (|eq| . 529677) + (|startTable!| . 528841) (|stopTable!| . 528077) + (|supDimElseRittWu?| . 527295) (|algebraicSort| . 526519) + (|moreAlgebraic?| . 525737) (|subTriSet?| . 524955) (|subPolSet?| . 524117) + (|internalSubPolSet?| . 523279) (|internalInfRittWu?| . 522441) + (|internalSubQuasiComponent?| . 521687) (|subQuasiComponent?| . 520055) + (|removeSuperfluousQuasiComponents| . 519279) (|subCase?| . 518361) + (|removeSuperfluousCases| . 517529) (|prepareDecompose| . 516323) + (|branchIfCan| . 515289) (|startTableGcd!| . 514427) + (|stopTableGcd!| . 513637) (|startTableInvSet!| . 512775) + (|stopTableInvSet!| . 511985) (|stosePrepareSubResAlgo| . 511511) + (|stoseInternalLastSubResultant| . 510479) + (|stoseIntegralLastSubResultant| . 510022) (|stoseLastSubResultant| . 509565) + (|stoseInvertible?sqfreg| . 509094) (|stoseInvertibleSetsqfreg| . 508680) + (|stoseInvertible?reg| . 508209) (|stoseInvertibleSetreg| . 507795) + (|stoseInvertible?| . 506912) (|stoseInvertibleSet| . 506498) + (|stoseSquareFreePart| . 506044) (|coleman| . 505868) + (|inverseColeman| . 505692) (|listYoungTableaus| . 505505) + (|makeYoungTableau| . 505280) (|nextColeman| . 505104) + (|nextLatticePermutation| . 504894) (|nextPartition| . 504537) + (|numberOfImproperPartitions| . 504419) (|subSet| . 504254) + (|unrankImproperPartitions0| . 504089) (|unrankImproperPartitions1| . 503924) + (|semiGroupOperation| . 503782) (|subresultantSequence| . 503516) + (|SturmHabichtSequence| . 503250) (|SturmHabichtCoefficients| . 503012) + (|SturmHabicht| . 502774) (|countRealRoots| . 502539) + (|SturmHabichtMultiple| . 502262) (|countRealRootsMultiple| . 501988) + (|source| . 501808) (|target| . 501413) (|signature| . 500934) + (|signatureAst| . 500806) (|xor| . 500656) (|depth| . 500386) (|top| . 500295) + (|pop!| . 500204) (|push!| . 500110) (|map!| . 499957) (|minordet| . 499145) + (|determinant| . 498049) (|diagonalProduct| . 497407) (|trace| . 496506) + (|diagonal| . 496279) (|diagonalMatrix| . 495432) (|scalarMatrix| . 494953) + (|hermite| . 494500) (|completeHermite| . 494152) (|smith| . 493874) + (|completeSmith| . 493494) (|diophantineSystem| . 493086) (|csubst| . 492728) + (|particularSolution| . 491558) (|mapSolve| . 491015) (|linear| . 490332) + (|quadratic| . 489646) (|cubic| . 488957) (|quartic| . 488265) + (|aLinear| . 487952) (|aQuadratic| . 487636) (|aCubic| . 487317) + (|aQuartic| . 486995) (|radicalSolve| . 484631) (|radicalRoots| . 484036) + (|contractSolve| . 483293) (|decomposeFunc| . 483087) (|unvectorise| . 482601) + (|bubbleSort!| . 481919) (|insertionSort!| . 481237) (|check| . 480711) + (|objects| . 480362) (|lprop| . 480205) (|llprop| . 480039) (|lllp| . 479881) + (|lllip| . 479713) (|lp| . 479573) (|mesh?| . 479443) (|mesh| . 478037) + (|polygon?| . 477907) (|polygon| . 477348) (|closedCurve?| . 477218) + (|closedCurve| . 476659) (|curve?| . 476529) (|curve| . 475775) + (|point?| . 475645) (|enterPointData| . 475456) (|composites| . 475326) + (|components| . 475196) (|numberOfComposites| . 475055) + (|numberOfComponents| . 474236) (|create3Space| . 474010) (|parse| . 473885) + (|outputAsFortran| . 473466) (|outputAsScript| . 473203) + (|outputAsTex| . 472940) (|abs| . 472192) (|Beta| . 471514) + (|digamma| . 471058) (|polygamma| . 470505) (|Gamma| . 469773) + (|besselJ| . 469305) (|besselY| . 468837) (|besselI| . 468369) + (|besselK| . 467901) (|airyAi| . 467445) (|airyBi| . 466989) + (|subNode?| . 466710) (|infLex?| . 466380) (|setEmpty!| . 466188) + (|setStatus!| . 465965) (|setCondition!| . 465770) (|setValue!| . 465575) + (|copy| . 464993) (|status| . 464490) (|value| . 463960) (|empty?| . 463371) + (|splitNodeOf!| . 462809) (|remove!| . 461444) (|remove| . 460386) + (|subNodeOf?| . 460060) (|nodeOf?| . 459790) (|result| . 459523) + (|conditions| . 459303) (|updateStatus!| . 459111) + (|extractSplittingLeaf| . 458917) (|squareMatrix| . 458746) + (|transpose| . 457817) (|rightTrim| . 457617) (|leftTrim| . 457417) + (|trim| . 457217) (|split| . 454987) (|position| . 454028) + (|replace| . 453904) (|match?| . 453771) (|match| . 452318) + (|substring?| . 452187) (|suffix?| . 452094) (|prefix?| . 452001) + (|upperCase!| . 451947) (|upperCase| . 451803) (|lowerCase!| . 451749) + (|lowerCase| . 451605) (|KrullNumber| . 450653) (|numberOfVariables| . 449701) + (|algebraicDecompose| . 448489) (|transcendentalDecompose| . 446045) + (|internalDecompose| . 442262) (|decompose| . 439028) + (|upDateBranches| . 437594) (|printInfo| . 436590) (|preprocess| . 435524) + (|internalZeroSetSplit| . 434674) (|internalAugment| . 433269) + (|stack| . 433154) (|size?| . 432978) (|possiblyInfinite?| . 432851) + (|explicitlyFinite?| . 432724) (|nextItem| . 432637) (|init| . 432389) + (|step| . 432311) (|upperBound| . 432221) (|lowerBound| . 432143) + (|iterationVar| . 431985) (|infiniteProduct| . 431002) + (|evenInfiniteProduct| . 430019) (|oddInfiniteProduct| . 429036) + (|generalInfiniteProduct| . 427930) (|filterUntil| . 427657) + (|filterWhile| . 427384) (|generate| . 426856) (|showAll?| . 426709) + (|showAllElements| . 426556) (|output| . 425950) (|cons| . 425790) + (|delay| . 425660) (|findCycle| . 425396) (|repeating?| . 425208) + (|repeating| . 425092) (|exquo| . 423515) (|recip| . 422290) + (|integers| . 422106) (|oddintegers| . 421922) (|int| . 421086) + (|mapmult| . 420943) (|deriv| . 420803) (|gderiv| . 420610) + (|compose| . 420299) (|addiag| . 420111) (|lazyIntegrate| . 419857) + (|nlde| . 419607) (|powern| . 419383) (|mapdiv| . 419205) + (|lazyGintegrate| . 418932) (|power| . 418754) (|sincos| . 418499) + (|sinhcosh| . 418234) (|asin| . 416946) (|acos| . 415658) (|atan| . 414278) + (|acot| . 412990) (|asec| . 411702) (|acsc| . 410414) (|sinh| . 409132) + (|cosh| . 407850) (|tanh| . 406568) (|coth| . 405286) (|sech| . 404004) + (|csch| . 402722) (|asinh| . 401437) (|acosh| . 400152) (|atanh| . 398867) + (|acoth| . 397582) (|asech| . 396297) (|acsch| . 395012) + (|subresultantVector| . 394789) (|primitivePart| . 393514) + (|pointData| . 393349) (|parent| . 393222) (|level| . 392973) + (|extractProperty| . 392793) (|extractClosed| . 392638) + (|extractIndex| . 392465) (|extractPoint| . 392309) (|traverse| . 392124) + (|defineProperty| . 391883) (|closeComponent| . 391667) + (|modifyPoint| . 391012) (|addPointLast| . 390801) (|addPoint2| . 390642) + (|addPoint| . 389990) (|merge| . 389046) (|deepCopy| . 388919) + (|shallowCopy| . 388792) (|numberOfChildren| . 388619) (|children| . 388313) + (|child| . 388137) (|birth| . 388010) (|internal?| . 387855) + (|root?| . 387700) (|leaf?| . 387417) (|rhs| . 386411) (|lhs| . 385405) + (|construct| . 380550) (|predicate| . 380253) (|sum| . 377073) + (|outputForm| . 376072) (|list| . 375897) (|string| . 375274) + (|argscript| . 375180) (|superscript| . 375086) (|subscript| . 374992) + (|script| . 374550) (|scripts| . 374123) (|scripted?| . 374046) + (|name| . 372962) (|resetNew| . 372891) (|symFunc| . 372559) + (|symbolTableOf| . 372431) (|argumentListOf| . 372299) + (|returnTypeOf| . 372108) (|printHeader| . 371794) (|returnType!| . 371192) + (|argumentList!| . 370752) (|endSubProgram| . 370671) + (|currentSubProgram| . 370590) (|newSubProgram| . 370472) + (|clearTheSymbolTable| . 370277) (|showTheSymbolTable| . 370229) + (|symbolTable| . 370074) (|printTypes| . 369879) (|newTypeLists| . 369791) + (|typeLists| . 369472) (|externalList| . 369380) (|typeList| . 369007) + (|parametersOf| . 368915) (|fortranTypeOf| . 368790) (|declare!| . 367972) + (|empty| . 367278) (|case| . 361218) (|compound?| . 361141) + (|getOperands| . 360928) (|getOperator| . 360669) (|nil?| . 360592) + (|buildSyntax| . 360376) (|autoCoerce| . 356897) (|solve| . 339825) + (|triangularSystems| . 339554) (|loadNativeModule| . 339444) + (|nativeModuleExtension| . 339371) (|hostByteOrder| . 339295) + (|hostPlatform| . 339222) (|rootDirectory| . 339149) (|bumprow| . 338829) + (|bumptab| . 338586) (|bumptab1| . 338399) (|untab| . 338203) + (|bat1| . 338003) (|bat| . 337816) (|tab1| . 337616) (|tab| . 337445) + (|lex| . 337305) (|slex| . 337137) (|inverse| . 335308) (|maxrow| . 334970) + (|mr| . 334622) (|listOfLists| . 333965) (|tableau| . 333832) + (|operator| . 331489) (|tanSum| . 331361) (|tanAn| . 331165) + (|tanNa| . 331034) (|table| . 330680) (|initTable!| . 330498) + (|printInfo!| . 330283) (|startStats!| . 330071) (|printStats!| . 329889) + (|clearTable!| . 329707) (|usingTable?| . 329522) (|printingInfo?| . 329337) + (|makingStats?| . 329152) (|extractIfCan| . 328990) (|insert!| . 328050) + (|setPrologue!| . 327957) (|setTex!| . 327864) (|setEpilogue!| . 327771) + (|prologue| . 327681) (|new| . 326280) (|tex| . 326190) (|epilogue| . 326100) + (|display| . 324929) (|endOfFile?| . 324850) (|readIfCan!| . 324663) + (|readLineIfCan!| . 324573) (|readLine!| . 324495) (|writeLine!| . 324338) + (|sign| . 321510) (|nonQsign| . 321382) (|direction| . 321233) + (|createThreeSpace| . 321119) (|pi| . 320836) (|cyclicParents| . 320706) + (|cyclicEqual?| . 320582) (|cyclicEntries| . 320452) (|cyclicCopy| . 320366) + (|tree| . 320030) (|cyclic?| . 319781) (|cos| . 318394) (|cot| . 317109) + (|csc| . 315824) (|sec| . 314539) (|sin| . 313152) (|tan| . 311867) + (|complexNormalize| . 310178) (|complexElementary| . 308489) + (|trigs| . 307712) (|real| . 306570) (|imag| . 305648) (|real?| . 304721) + (|complexForm| . 303861) (|UpTriBddDenomInv| . 303570) + (|LowTriBddDenomInv| . 303279) (|simplify| . 302334) (|htrigs| . 302077) + (|simplifyExp| . 301820) (|simplifyLog| . 301563) (|expandPower| . 301306) + (|expandLog| . 301049) (|cos2sec| . 300792) (|cosh2sech| . 300535) + (|cot2trig| . 300278) (|coth2trigh| . 300021) (|csc2sin| . 299764) + (|csch2sinh| . 299507) (|sec2cos| . 299250) (|sech2cosh| . 298993) + (|sin2csc| . 298736) (|sinh2csch| . 298479) (|tan2trig| . 298222) + (|tanh2trigh| . 297965) (|tan2cot| . 297708) (|tanh2coth| . 297451) + (|cot2tan| . 297194) (|coth2tanh| . 296937) (|removeCosSq| . 296680) + (|removeSinSq| . 296423) (|removeCoshSq| . 296166) (|removeSinhSq| . 295909) + (|expandTrigProducts| . 295438) (|fintegrate| . 294820) + (|coefficient| . 291576) (|coHeight| . 291218) (|extendIfCan| . 290938) + (|algebraicVariables| . 290620) (|zeroSetSplitIntoTriangularSystems| . 290209) + (|zeroSetSplit| . 285802) (|reduceByQuasiMonic| . 285516) + (|collectQuasiMonic| . 285233) (|removeZero| . 284947) + (|initiallyReduce| . 284457) (|headReduce| . 283967) + (|stronglyReduce| . 283681) (|rewriteSetWithReduction| . 283264) + (|autoReduced?| . 282881) (|initiallyReduced?| . 281745) + (|headReduced?| . 280609) (|stronglyReduced?| . 279972) (|reduced?| . 279096) + (|normalized?| . 277960) (|quasiComponent| . 277584) (|initials| . 277266) + (|basicSet| . 276361) (|infRittWu?| . 274972) (|getCurve| . 274859) + (|listLoops| . 274679) (|closed?| . 274435) (|open?| . 274294) + (|setClosed| . 274150) (|tube| . 273713) (|point| . 272618) + (|unitVector| . 271758) (|cosSinInfo| . 271608) (|loopPoints| . 271375) + (|select| . 270489) (|generalTwoFactor| . 270166) (|generalSqFr| . 269843) + (|twoFactor| . 269489) (|setOrder| . 269138) (|getOrder| . 268948) + (|less?| . 268419) (|userOrdered?| . 268272) (|largest| . 267885) + (|more?| . 267525) (|setVariableOrder| . 267244) (|getVariableOrder| . 267059) + (|resetVariableOrder| . 266958) (|prime?| . 265979) (|sample| . 265104) + (|bitior| . 264771) (|bitand| . 264438) (|rationalFunction| . 263949) + (|taylorIfCan| . 263752) (|taylor| . 258588) (|removeZeroes| . 257414) + (|taylorRep| . 257222) (|factor| . 244459) (|factorSquareFree| . 242716) + (|henselFact| . 241950) (|hasHi| . 241824) (|segment| . 241379) + (SEGMENT . 241102) (|fmecg| . 240107) (|commonDenominator| . 239146) + (|clearDenominator| . 238155) (|splitDenominator| . 236333) + (|monicRightFactorIfCan| . 236058) (|rightFactorIfCan| . 235780) + (|leftFactorIfCan| . 235544) (|monicDecomposeIfCan| . 235248) + (|monicCompleteDecompose| . 234985) (|divideIfCan| . 234718) + (|noKaratsuba| . 234528) (|karatsubaOnce| . 234338) (|karatsuba| . 234103) + (|separate| . 233327) (|pseudoDivide| . 232518) (|pseudoQuotient| . 232366) + (|composite| . 231889) (|subResultantGcd| . 231316) (|resultant| . 230506) + (|discriminant| . 228980) (|differentiate| . 226889) + (|pseudoRemainder| . 226774) (|shiftLeft| . 226613) (|shiftRight| . 226452) + (|karatsubaDivide| . 226223) (|monicDivide| . 225760) + (|divideExponents| . 225597) (|unmakeSUP| . 225428) (|makeSUP| . 225259) + (|vectorise| . 225068) (|eval| . 218088) (|extend| . 215600) + (|approximate| . 214344) (|truncate| . 213966) (|order| . 209218) + (|center| . 208644) (|terms| . 207758) (|squareFreePart| . 206772) + (|BumInSepFFE| . 206335) (|multiplyExponents| . 205807) + (|laurentIfCan| . 205609) (|laurent| . 201429) (|laurentRep| . 201236) + (|rationalPower| . 200995) (|puiseux| . 196814) (|dominantTerm| . 195824) + (|limitPlus| . 194707) (|split!| . 194504) (|setlast!| . 194336) + (|setrest!| . 194048) (|setelt| . 191815) (|setfirst!| . 191647) + (|cycleSplit!| . 191482) (|concat!| . 190764) (|cycleTail| . 190657) + (|cycleLength| . 190511) (|cycleEntry| . 190404) (|third| . 190297) + (|second| . 190076) (|tail| . 189665) (|last| . 188946) (|rest| . 188102) + (|elt| . 180551) (|first| . 179379) (|concat| . 178590) + (|invmultisect| . 178218) (|multisect| . 177846) (|revert| . 177556) + (|generalLambert| . 177184) (|evenlambert| . 176894) (|oddlambert| . 176604) + (|lambert| . 176314) (|lagrange| . 176024) (|univariatePolynomial| . 175510) + (|integrate| . 163971) (** . 158122) (|polynomial| . 157244) + (|multiplyCoefficients| . 156753) (|quoByVar| . 156639) + (|coefficients| . 155730) (|series| . 148295) (|stFunc1| . 147984) + (|stFunc2| . 147656) (|stFuncN| . 147327) (|fixedPointExquo| . 147117) + (|ode1| . 146866) (|ode2| . 146609) (|ode| . 146321) (|mpsode| . 145982) + (UP2UTS . 145681) (UTS2UP . 145338) (LODO2FUN . 144987) (RF2UTS . 144610) + (|variable| . 143694) (|magnitude| . 143531) (|length| . 142064) + (|cross| . 141737) (|outerProduct| . 141579) (|dot| . 141035) (- . 138775) + (|zero| . 138343) (+ . 136024) (|vector| . 135908) (|scan| . 133709) + (|reduce| . 126869) (|map| . 101942) (|graphCurves| . 101292) + (|drawCurves| . 100760) (|update| . 100588) (|show| . 100420) + (|scale| . 99892) (|connect| . 99724) (|region| . 99556) (|points| . 99388) + (|units| . 98719) (|getGraph| . 98575) (|putGraph| . 98403) (|graphs| . 98092) + (|graphStates| . 97551) (|graphState| . 97282) (|makeViewport2D| . 97077) + (|viewport2D| . 97021) (|getPickedPoints| . 96896) (|key| . 96620) + (|close| . 96330) (|write| . 95640) (|colorDef| . 95507) (|reset| . 95323) + (|intensity| . 95193) (|lighting| . 95057) (|clipSurface| . 94926) + (|showClipRegion| . 94795) (|showRegion| . 94664) (|hitherPlane| . 94534) + (|eyeDistance| . 94404) (|perspective| . 94273) (|translate| . 93797) + (|zoom| . 93240) (|rotate| . 92974) (|drawStyle| . 92843) + (|outlineRender| . 92712) (|diagonals| . 92581) (|axes| . 92117) + (|controlPanel| . 91859) (|viewpoint| . 89672) (|dimensions| . 89286) + (|title| . 88810) (|resize| . 88528) (|move| . 88240) (|options| . 87780) + (|modifyPointData| . 87411) (|subspace| . 86908) (|makeViewport3D| . 86518) + (|viewport3D| . 86460) (|viewDeltaYDefault| . 86275) + (|viewDeltaXDefault| . 86090) (|viewZoomDefault| . 85905) + (|viewPhiDefault| . 85720) (|viewThetaDefault| . 85535) + (|pointColorDefault| . 85356) (|lineColorDefault| . 85177) + (|axesColorDefault| . 84998) (|unitsColorDefault| . 84819) + (|pointSizeDefault| . 84610) (|viewPosDefault| . 84377) + (|viewSizeDefault| . 84150) (|viewDefaults| . 84064) + (|viewWriteDefault| . 83855) (|viewWriteAvailable| . 83751) + (|var1StepsDefault| . 83542) (|var2StepsDefault| . 83333) + (|tubePointsDefault| . 83124) (|tubeRadiusDefault| . 82897) (|void| . 82859) + (|dimension| . 81355) (|crest| . 81103) (|cfirst| . 80851) + (|sts2stst| . 80601) (|clikeUniv| . 80333) (|weierstrass| . 80103) + (|qqq| . 79817) (|integralBasis| . 77755) (|localIntegralBasis| . 76008) + (|qualifier| . 75929) (|mainExpression| . 75850) (|condition| . 75507) + (|changeWeightLevel| . 74818) (|characteristicSerie| . 73941) + (|characteristicSet| . 73234) (|medialSet| . 72527) (|Hausdorff| . 72232) + (|Frobenius| . 71579) (|transcendenceDegree| . 71232) + (|extensionDegree| . 70484) (|inGroundField?| . 70357) + (|transcendent?| . 70230) (|algebraic?| . 69784) (|varList| . 68593) + (|sh| . 68189) (|mirror| . 67435) (|monomial?| . 66439) (|monom| . 65945) + (|rquo| . 65068) (|lquo| . 64191) (|mindegTerm| . 63969) (|log| . 61558) + (|exp| . 59245) (|product| . 58089) (|LiePolyIfCan| . 57699) + (|coerce| . 45959) (|trunc| . 45583) (|degree| . 41161) (/ . 37328) + (|quasiRegular| . 37062) (|quasiRegular?| . 36733) (|constant| . 35948) + (|constant?| . 35406) (|coef| . 34753) (|mindeg| . 34439) (|maxdeg| . 34122) + (|#| . 33312) (|reductum| . 31135) (* . 23431) (|RemainderList| . 23017) (|unexpand| . 22675) (|expand| . 20495) (|shape| . 20408) (|youngDiagram| . 20299) (Y . 19838) (|triangSolve| . 18514) (|univariateSolve| . 15694) (|realSolve| . 13158) (|positiveSolve| . 11340) |