diff options
| author | dos-reis <gdr@axiomatics.org> | 2011-03-12 22:56:37 +0000 |
|---|---|---|
| committer | dos-reis <gdr@axiomatics.org> | 2011-03-12 22:56:37 +0000 |
| commit | 6c75a87d8ee00d48a0f5703aa9c86591078a50d3 (patch) | |
| tree | 28ff587bbc4d759dd0e3f96b156700ff01ba8c53 /src | |
| parent | a2e3e641bdbcb6e77bbb572aea25a748a967abca (diff) | |
| download | open-axiom-6c75a87d8ee00d48a0f5703aa9c86591078a50d3.tar.gz | |
* src/algebra/: Systematically use not one? when comparing for
equality with 1.
Diffstat (limited to 'src')
56 files changed, 17499 insertions, 17491 deletions
diff --git a/src/ChangeLog b/src/ChangeLog index 4ae5d86d..cade9727 100644 --- a/src/ChangeLog +++ b/src/ChangeLog @@ -1,5 +1,10 @@ 2011-03-12 Gabriel Dos Reis <gdr@cs.tamu.edu> + * src/algebra/: Systematically use not one? when comparing for + equality with 1. + +2011-03-12 Gabriel Dos Reis <gdr@cs.tamu.edu> + * src/algebra/: Systematically use negative? when comparing for equality with 0. diff --git a/src/algebra/algfunc.spad.pamphlet b/src/algebra/algfunc.spad.pamphlet index bf4c4b71..5cb93af1 100644 --- a/src/algebra/algfunc.spad.pamphlet +++ b/src/algebra/algfunc.spad.pamphlet @@ -277,7 +277,7 @@ test and give $$1/(-2)^(1/n) \ne (-1/2)^(1/n)$$ <<hackroot(x, n)>>= hackroot(x, n) == (n = 1) or (x = 1) => x - (((dx := denom x) ~= 1) and + (not one?(dx := denom x) and ((rx := retractIfCan(dx)@Union(Integer,"failed")) case Integer) and positive?(rx)) => hackroot((numer x)::F, n)/hackroot(rx::Integer::F, n) diff --git a/src/algebra/carten.spad.pamphlet b/src/algebra/carten.spad.pamphlet index 6d7de173..ed391bf4 100644 --- a/src/algebra/carten.spad.pamphlet +++ b/src/algebra/carten.spad.pamphlet @@ -372,7 +372,7 @@ CartesianTensor(minix, dim, R): Exports == Implementation where lengthRankOrElse n elt(x) == - #x ~= 1 => error "Index error (the rank is not 0)" + not one?(#x) => error "Index error (the rank is not 0)" get(x,0) elt(x, i: I) == #x ~= dim => error "Index error (the rank is not 1)" diff --git a/src/algebra/ddfact.spad.pamphlet b/src/algebra/ddfact.spad.pamphlet index 2fbc0ca5..80e8b3fd 100644 --- a/src/algebra/ddfact.spad.pamphlet +++ b/src/algebra/ddfact.spad.pamphlet @@ -101,12 +101,12 @@ DistinctDegreeFactorize(F,FP): C == T factlist : List(ParFact) :=empty() llf : List FFE fln :List(FP) := empty() - if (lcm:=leadingCoefficient m)~=1 then m:=(inv lcm)*m + if not one?(lcm:=leadingCoefficient m) then m:=(inv lcm)*m llf:= factorList(squareFree(m)) for lf in llf repeat d1:= lf.xpnt pol := lf.fctr - if (lcp:=leadingCoefficient pol)~=1 then pol := (inv lcp)*pol + if not one?(lcp:=leadingCoefficient pol) then pol := (inv lcp)*pol degree pol=1 => factlist:=cons([pol,d1]$ParFact,factlist) fln := appl(pol) factlist :=append([[pf,d1]$ParFact for pf in fln],factlist) @@ -159,7 +159,8 @@ DistinctDegreeFactorize(F,FP): C == T g := gcd(v-mon,u) dg := degree g dg =0 => "next k1" - if leadingCoefficient g ~=1 then g := (inv leadingCoefficient g)*g + if not one? leadingCoefficient g then + g := (inv leadingCoefficient g)*g ddfact := cons([k1,g]$fact,ddfact) testirr => return ddfact u := u quo g @@ -222,7 +223,7 @@ DistinctDegreeFactorize(F,FP): C == T fln : List(FP) :=empty() --make m monic - if (lcm := leadingCoefficient m) ~=1 then m := (inv lcm)*m + if not one?(lcm := leadingCoefficient m) then m := (inv lcm)*m --is x**d factor of m? if positive?(d := minimumDegree m) then diff --git a/src/algebra/derham.spad.pamphlet b/src/algebra/derham.spad.pamphlet index fe2a2e36..6e526e21 100644 --- a/src/algebra/derham.spad.pamphlet +++ b/src/algebra/derham.spad.pamphlet @@ -87,7 +87,8 @@ ExtAlgBasis(): Export == Implement where coerce(li:(L I)) == for x in li repeat - if x ~= 1 and x ~= 0 then error "coerce: values can only be 0 and 1" + if not one? x and not zero? x then + error "coerce: values can only be 0 and 1" li degree x == (_+/x)::NNI diff --git a/src/algebra/divisor.spad.pamphlet b/src/algebra/divisor.spad.pamphlet index 42056811..86feaf9e 100644 --- a/src/algebra/divisor.spad.pamphlet +++ b/src/algebra/divisor.spad.pamphlet @@ -440,7 +440,7 @@ ModularHermitianRowReduction(R): Exports == Implementation where qsetelt!(x, k, j, 0) un := unitNormal qelt(x,i,j) qsetelt!(x,i,j,un.canonical) - if un.associate ~= 1 then for jj in (j+1)..ncols repeat + if not one?(un.associate) then for jj in (j+1)..ncols repeat qsetelt!(x,i,jj,un.associate * qelt(x,i,jj)) xij := qelt(x,i,j) @@ -720,7 +720,7 @@ HyperellipticFiniteDivisor(F, UP, UPUP, R): Exports == Implementation where v::UP redpolyIfCan(h, a) == - degree(p := lift h) ~= 1 => "failed" + not one? degree(p := lift h) => "failed" q := - coefficient(p, 0) / coefficient(p, 1) rec := extendedEuclidean(denom q, a) not ground?(rec.generator) => "failed" diff --git a/src/algebra/elemntry.spad.pamphlet b/src/algebra/elemntry.spad.pamphlet index e102aade..ec9e0a56 100644 --- a/src/algebra/elemntry.spad.pamphlet +++ b/src/algebra/elemntry.spad.pamphlet @@ -647,7 +647,7 @@ ElementaryFunction(R, F): Exports == Implementation where ilog x ilog x == - ((num1 := one?(num := numer x)) or num = -1) and (den := denom x) ~= 1 + ((num1 := one?(num := numer x)) or num = -1) and not one?(den := denom x) and empty? variables x => - kernel(oplog, (num1 => den; -den)::F) kernel(oplog, x) diff --git a/src/algebra/ffpoly.spad.pamphlet b/src/algebra/ffpoly.spad.pamphlet index db79d30e..c4f0c586 100644 --- a/src/algebra/ffpoly.spad.pamphlet +++ b/src/algebra/ffpoly.spad.pamphlet @@ -345,7 +345,7 @@ FiniteFieldPolynomialPackage GF : Exports == Implementation where -- determine the multiplicative order of q modulo d e : PI := 1 qe : PI := q - while (qe rem d) ~= 1 repeat + while not one?(qe rem d) repeat e := e + 1 qe := qe * q prod := prod * _ @@ -361,7 +361,7 @@ FiniteFieldPolynomialPackage GF : Exports == Implementation where -- (cf. [LN] p.89, Th. 3.16, and p.87, following Th. 3.11) n : NNI := degree f n = 0 => false - leadingCoefficient f ~= 1 => false + not one? leadingCoefficient f => false coefficient(f, 0) = 0 => false q : PI := sizeGF qn1: PI := (q**n - 1) :: NNI :: PI @@ -371,7 +371,7 @@ FiniteFieldPolynomialPackage GF : Exports == Implementation where -- may be improved by tabulating the residues x**(i*q) -- for i = 0,...,n-1 : -- - lift(x ** qn1)$MM ~= 1 => false -- X**(q**n - 1) rem f in GF[X] + not one? lift(x ** qn1)$MM => false -- X**(q**n - 1) rem f in GF[X] lrec : L Record(factor:I, exponent:I) := factors(factor qn1) lfact : L PI := [] -- collect the prime factors for rec in lrec repeat -- of q**n - 1 @@ -387,7 +387,7 @@ FiniteFieldPolynomialPackage GF : Exports == Implementation where -- x, x**q, ... , x**(q**(n-1)) are linearly independent over GF n : NNI := degree f n = 0 => false - leadingCoefficient f ~= 1 => false + not one? leadingCoefficient f => false coefficient(f, 0) = 0 => false n = 1 => true not irreducible? f => false @@ -428,7 +428,7 @@ FiniteFieldPolynomialPackage GF : Exports == Implementation where n : NNI := degree f n = 0 => error "polynomial must have positive degree" -- make f monic - if (lcf := leadingCoefficient f) ~= 1 then f := (inv lcf) * f + if not one?(lcf := leadingCoefficient f) then f := (inv lcf) * f -- if f = fn*X**n + ... + f{i0}*X**{i0} with the fi non-zero -- then fRepr := [[n,fn], ... , [i0,f{i0}]] fRepr : Repr := f pretend Repr @@ -506,7 +506,7 @@ FiniteFieldPolynomialPackage GF : Exports == Implementation where n : NNI := degree f n = 0 => error "polynomial must have positive degree" -- make f monic - if (lcf := leadingCoefficient f) ~= 1 then f := (inv lcf) * f + if not one?(lcf := leadingCoefficient f) then f := (inv lcf) * f -- if f = fn*X**n + ... + f{i0}*X**{i0} with the fi non-zero -- then fRepr := [[n,fn], ... , [i0,f{i0}]] fRepr : Repr := f pretend Repr @@ -626,7 +626,7 @@ FiniteFieldPolynomialPackage GF : Exports == Implementation where n : NNI := degree f n = 0 => error "polynomial must have positive degree" -- make f monic - if (lcf := leadingCoefficient f) ~= 1 then f := (inv lcf) * f + if not one?(lcf := leadingCoefficient f) then f := (inv lcf) * f -- if f = fn*X**n + ... + f{i0}*X**{i0} with the fi non-zero -- then fRepr := [[n,fn], ... , [i0,f{i0}]] fRepr : Repr := f pretend Repr @@ -740,7 +740,7 @@ FiniteFieldPolynomialPackage GF : Exports == Implementation where n : NNI := degree f n = 0 => error "polynomial must have positive degree" -- make f monic - if (lcf := leadingCoefficient f) ~= 1 then f := (inv lcf) * f + if not one?(lcf := leadingCoefficient f) then f := (inv lcf) * f -- if f = fn*X**n + ... + f{i0}*X**{i0} with the fi non-zero -- then fRepr := [[n,fn], ... , [i0,f{i0}]] fRepr : Repr := f pretend Repr diff --git a/src/algebra/ffpoly2.spad.pamphlet b/src/algebra/ffpoly2.spad.pamphlet index 76c5780f..b4f6b767 100644 --- a/src/algebra/ffpoly2.spad.pamphlet +++ b/src/algebra/ffpoly2.spad.pamphlet @@ -108,7 +108,7 @@ FiniteFieldPolynomialPackage2(F,GF):Exports == Implementation where h:=gcd(stillToFactor,trModp +$(SUP F) _ (index(j pretend PI)$GF::F::(SUP F)))$(SUP F) -- make the gcd polynomial monic - if leadingCoefficient(h)$(SUP F) ~= 1$F then + if not one? leadingCoefficient(h)$(SUP F) then h:= (inv leadingCoefficient(h)) * h degh:=degree(h)$(SUP F) degSTF:=degree(stillToFactor)$(SUP F) diff --git a/src/algebra/fr.spad.pamphlet b/src/algebra/fr.spad.pamphlet index a77e5370..babaa801 100644 --- a/src/algebra/fr.spad.pamphlet +++ b/src/algebra/fr.spad.pamphlet @@ -187,7 +187,7 @@ Factored(R: IntegralDomain): Exports == Implementation where -- l := concat(convert(rec.fctr)@InputForm, l) -- l := concat(convert(rec.fctr)@InputForm ** rec.xpnt, l) empty? l => convert(unit x)@InputForm - if unit x ~= 1 then l := concat(convert(unit x)@InputForm,l) + if not one? unit x then l := concat(convert(unit x)@InputForm,l) empty? rest l => first l binary(convert(_*::Symbol)@InputForm, l)@InputForm diff --git a/src/algebra/gaussfac.spad.pamphlet b/src/algebra/gaussfac.spad.pamphlet index 8f922d92..bb4cb963 100644 --- a/src/algebra/gaussfac.spad.pamphlet +++ b/src/algebra/gaussfac.spad.pamphlet @@ -132,7 +132,7 @@ GaussianFactorizationPackage() : C == T result : List FFE :=[] unity:ZI:=1$ZI - if d~=1 then + if not one? d then a:=(a exquo d)::Z b:=(b exquo d)::Z r:= intfactor(d) @@ -163,13 +163,13 @@ GaussianFactorizationPackage() : C == T m:=m quo z result:=concat(part,result) - if m~=1 then unity:=unity * m + if not one? m then unity:=unity * m makeFR(unity,result) ---- write p prime like sum of two squares ---- sumSquares(p:Z) : List Z == p=2 => [1,1] - p rem 4 ~= 1 => error "no solutions" + not one?(p rem 4) => error "no solutions" sumsq1(p) diff --git a/src/algebra/gbeuclid.spad.pamphlet b/src/algebra/gbeuclid.spad.pamphlet index 95e7bb51..963e210b 100644 --- a/src/algebra/gbeuclid.spad.pamphlet +++ b/src/algebra/gbeuclid.spad.pamphlet @@ -252,7 +252,7 @@ EuclideanGroebnerBasisPackage(Dom, Expon, VarSet, Dpol): T == C where if xx2 = 1 then prinpolINFO(Pol) print(" THE GROEBNER BASIS over EUCLIDEAN DOMAIN"::Ex) - if xx1 = 1 and xx2 ~= 1 then + if xx1 = 1 and not one? xx2 then print(" THE GROEBNER BASIS over EUCLIDEAN DOMAIN"::Ex) H diff --git a/src/algebra/gbintern.spad.pamphlet b/src/algebra/gbintern.spad.pamphlet index a150f100..77e72e6f 100644 --- a/src/algebra/gbintern.spad.pamphlet +++ b/src/algebra/gbintern.spad.pamphlet @@ -168,7 +168,7 @@ GroebnerInternalPackage(Dom, Expon, VarSet, Dpol): T == C where if xx2 = 1 then prinpolINFO(Pol) messagePrint(" THE GROEBNER BASIS POLYNOMIALS") - if xx1 = 1 and xx2 ~= 1 then + if xx1 = 1 and not one? xx2 then messagePrint(" THE GROEBNER BASIS POLYNOMIALS") Pol diff --git a/src/algebra/gdpoly.spad.pamphlet b/src/algebra/gdpoly.spad.pamphlet index b169c548..2a212926 100644 --- a/src/algebra/gdpoly.spad.pamphlet +++ b/src/algebra/gdpoly.spad.pamphlet @@ -254,7 +254,7 @@ GeneralDistributedMultivariatePolynomial(vl,R,E): public == private where t.k.i = 1 => l := cons(vl1.i,l) l := cons(vl1.i ** t.k.i ::OutputForm,l) l := reverse l - if (t.c ~= 1) or (null l) then l := cons(t.c :: OutputForm,l) + if not one? t.c or (null l) then l := cons(t.c :: OutputForm,l) 1 = #l => lt := cons(first l,lt) lt := cons(reduce("*",l),lt) 1 = #lt => first lt diff --git a/src/algebra/geneez.spad.pamphlet b/src/algebra/geneez.spad.pamphlet index 453ae3bd..3c449fe1 100644 --- a/src/algebra/geneez.spad.pamphlet +++ b/src/algebra/geneez.spad.pamphlet @@ -146,7 +146,7 @@ GenExEuclid(R,BP) : C == T rpol := first redListPol redListPol := rest redListPol for rpol2 in redListPol repeat - gcd(rpol, rpol2) ~= 1 => return false + not one? gcd(rpol, rpol2) => return false true if R has Field then diff --git a/src/algebra/groebf.spad.pamphlet b/src/algebra/groebf.spad.pamphlet index 9d7c70a3..abda5441 100644 --- a/src/algebra/groebf.spad.pamphlet +++ b/src/algebra/groebf.spad.pamphlet @@ -260,7 +260,7 @@ GroebnerFactorizationPackage(Dom, Expon, VarSet, Dpol): T == C where doSplitting? => for fnP in allReducedFactors repeat - if fnP ~= 1$Dpol + if not one? fnP then newInputPolys : L Dpol := _ sort( degree #1 > degree #2 ,cons(fnP,inputPolys)) diff --git a/src/algebra/idecomp.spad.pamphlet b/src/algebra/idecomp.spad.pamphlet index cec341b3..8dd14b10 100644 --- a/src/algebra/idecomp.spad.pamphlet +++ b/src/algebra/idecomp.spad.pamphlet @@ -145,7 +145,7 @@ IdealDecompositionPackage(vl,nv) : C == T -- take away nv, now doesn't lf:=Id.first pv:DPoly:=0 pw:DPoly:=0 - while degree(lf,y)~=1 repeat + while not one? degree(lf,y) repeat val:=random()$Z rem 23 pv:=px+val*py pw:=px-val*py @@ -296,7 +296,7 @@ IdealDecompositionPackage(vl,nv) : C == T -- take away nv, now doesn't is0dimprimary(J:FIdeal,truelist:List OV) : Boolean == element?(1,J) => true Jd:=generators(groebner J) - #(factors factor Jd.last)~=1 => return false + not one?(#(factors factor Jd.last)) => return false i:=subtractIfCan(#truelist,1) (i case "failed") => return true JR:=(reverse Jd);JM:=groebnerIdeal([JR.first]);JP:List(DPoly):=[] @@ -356,7 +356,7 @@ IdealDecompositionPackage(vl,nv) : C == T -- take away nv, now doesn't #Jd~=n => false for f in Jd repeat if not ismonic(f,lvint.i) then return false - if i<n and (degree univariate(f,lvint.i))~=1 then return false + if i<n and not one?(degree univariate(f,lvint.i)) then return false i:=i+1 g:=Jd.n #(lfact:=factors(factor g)) >1 => false diff --git a/src/algebra/intaux.spad.pamphlet b/src/algebra/intaux.spad.pamphlet index 875fbcb8..d88eb62b 100644 --- a/src/algebra/intaux.spad.pamphlet +++ b/src/algebra/intaux.spad.pamphlet @@ -104,7 +104,7 @@ IntegrationResult(F:Field): Exports == Implementation where cc::O * logandp coeffp:O := (outputForm(rec.coeff, alpha) = 0::Z::O)@O logandp := alpha * prefix('log::O, [outputForm(rec.logand, alpha)]) - if (cc := Q2F(rec.scalar)) ~= 1 then + if not one?(cc := Q2F(rec.scalar)) then logandp := cc::O * logandp sum(logandp, coeffp) diff --git a/src/algebra/intpm.spad.pamphlet b/src/algebra/intpm.spad.pamphlet index 9d47548f..f529f043 100644 --- a/src/algebra/intpm.spad.pamphlet +++ b/src/algebra/intpm.spad.pamphlet @@ -117,7 +117,7 @@ PatternMatchIntegration(R, F): Exports == Implementation where [cc, nc] if (v := isPower f) case Record(val:F, exponent:Z) then vv := v::Record(val:F, exponent:Z) - (vv.exponent ~= 1) => + not one?(vv.exponent) => rec := splitConstant(vv.val, x) return [rec.const ** vv.exponent, rec.nconst ** vv.exponent] error "splitConstant: should not happen" @@ -248,7 +248,7 @@ PatternMatchIntegration(R, F): Exports == Implementation where rec.coef * sqrt(rec.radicand) pmintegrate(f, x) == - (rc := splitConstant(f, x)).const ~= 1 => + not one?((rc := splitConstant(f, x)).const) => (u := pmintegrate(rc.nconst, x)) case "failed" => "failed" rec := u::ANS [rc.const * rec.special, rc.const * rec.integrand] @@ -266,7 +266,7 @@ PatternMatchIntegration(R, F): Exports == Implementation where "failed" pmComplexintegrate(f, x) == - (rc := splitConstant(f, x)).const ~= 1 => + not one?((rc := splitConstant(f, x)).const) => (u := pmintegrate(rc.nconst, x)) case "failed" => "failed" rec := u::ANS [rc.const * rec.special, rc.const * rec.integrand] diff --git a/src/algebra/laplace.spad.pamphlet b/src/algebra/laplace.spad.pamphlet index 9bbabadb..8a04817b 100644 --- a/src/algebra/laplace.spad.pamphlet +++ b/src/algebra/laplace.spad.pamphlet @@ -134,7 +134,7 @@ LaplaceTransform(R, F): Exports == Implementation where [c, c1, c0] if (v := isPower f) case Record(val:F, exponent:Integer) then w := v::Record(val:F, exponent:Integer) - (w.exponent ~= 1) and + not one?(w.exponent) and ((r := aexp(w.val, t)) case Record(coef:F,coef1:F,coef0:F)) => rec := r::Record(coef:F, coef1:F, coef0:F) return [rec.coef ** w.exponent, w.exponent * rec.coef1, @@ -194,7 +194,7 @@ LaplaceTransform(R, F): Exports == Implementation where -- Use linearity (u := mkPlus f) case List(F) => +/[locallaplace(g, t, tt, s, ss) for g in u::List(F)] - (rec := splitConstant(f, t)).const ~= 1 => + not one?((rec := splitConstant(f, t)).const) => rec.const * locallaplace(rec.nconst, t, tt, s, ss) -- laplace(t^n*f(t),t,s) = (-1)^n*D(laplace(f(t),t,s), s, n)) diff --git a/src/algebra/leadcdet.spad.pamphlet b/src/algebra/leadcdet.spad.pamphlet index 47ac9d85..0c312914 100644 --- a/src/algebra/leadcdet.spad.pamphlet +++ b/src/algebra/leadcdet.spad.pamphlet @@ -62,7 +62,7 @@ LeadingCoefDetermination(OV,E,Z,P) : C == T q := unitNormal(lval.i).canonical for j in 0..(i-1)::NNI repeat y := distlist.((i-j)::NNI) - while y~=1 repeat + while not one? y repeat y := gcd(y,q) q := q quo y if q=1 then return false @@ -87,7 +87,7 @@ LeadingCoefDetermination(OV,E,Z,P) : C == T d := vl.i quo d unilist.i := d*unilist.i contm := contm quo d - if contm ~=1 then for i in 1..nf repeat pl.i := contm*pl.i + if not one? contm then for i in 1..nf repeat pl.i := contm*pl.i [pl,contm,unilist]$LeadFact distFact(contm:Z,unilist:List(BP),plead:FinalFact, diff --git a/src/algebra/limitps.spad.pamphlet b/src/algebra/limitps.spad.pamphlet index ac82fee8..74158c85 100644 --- a/src/algebra/limitps.spad.pamphlet +++ b/src/algebra/limitps.spad.pamphlet @@ -167,7 +167,7 @@ PowerSeriesLimitPackage(R,FE): Exports == Implementation where xkers := [k for k in tower fcn | member?(x,variables(k::FE))] # xkers ~= 2 => "failed" expKers := [k for k in xkers | is?(k, "exp" :: Symbol)] - # expKers ~= 1 => "failed" + not one?(# expKers) => "failed" -- fcn is a rational function of x and exp(g(x)) for some rational function g expKer := first expKers (fval := limitPlus(expKer::FE,x)) case "failed" => "failed" @@ -188,7 +188,7 @@ PowerSeriesLimitPackage(R,FE): Exports == Implementation where specialLimit1(fcn,x) == -- find the first interesting kernel in tower(fcn) xkers := [k for k in kernels fcn | member?(x,variables(k::FE))] - #xkers ~= 1 => "failed" + not one?(#xkers) => "failed" ker := first xkers vv := new()$SY; eq : EQ FE := equation(ker :: FE,vv :: FE) cc := eval(fcn,eq) diff --git a/src/algebra/lingrob.spad.pamphlet b/src/algebra/lingrob.spad.pamphlet index 2cb3aca7..41956dea 100644 --- a/src/algebra/lingrob.spad.pamphlet +++ b/src/algebra/lingrob.spad.pamphlet @@ -115,7 +115,7 @@ LinGroebnerPackage(lv,F) : C == T ofirstmon:DPoly:=1$DPoly orecfmon:Record(poly:HDPoly, mult:F) := [1,1] i:NNI:=2 - while (firstmon:=choosemon(firstmon,ltresult))~=1 repeat + while not one?(firstmon:=choosemon(firstmon,ltresult)) repeat if (v:=firstmon exquo ofirstmon) case "failed" then recfmon:=rRedPol(transform firstmon,B) else @@ -274,7 +274,7 @@ LinGroebnerPackage(lv,F) : C == T ofirstmon:DPoly:=1$DPoly orecfmon:Record(poly:HDPoly, mult:F) := [1,1] lx:= lvar.last - while (firstmon:=choosemon(firstmon,ltresult))~=1 repeat + while not one?(firstmon:=choosemon(firstmon,ltresult)) repeat if (v:=firstmon exquo ofirstmon) case "failed" then recfmon:=rRedPol(transform(eval(firstmon,lx,nval)),B) else diff --git a/src/algebra/matfuns.spad.pamphlet b/src/algebra/matfuns.spad.pamphlet index 23617e39..47cc96e3 100644 --- a/src/algebra/matfuns.spad.pamphlet +++ b/src/algebra/matfuns.spad.pamphlet @@ -737,7 +737,7 @@ MatrixLinearAlgebraFunctions(R,Row,Col,M):Exports == Implementation where un := unitNormal qelt(x,i,j) qsetelt!(x,i,j,un.canonical) - if un.associate ~= 1 then for jj in (j+1)..maxC repeat + if not one?(un.associate) then for jj in (j+1)..maxC repeat qsetelt!(x,i,jj,un.associate * qelt(x,i,jj)) xij := qelt(x,i,j) diff --git a/src/algebra/mathml.spad.pamphlet b/src/algebra/mathml.spad.pamphlet index ba186863..086d0d0f 100644 --- a/src/algebra/mathml.spad.pamphlet +++ b/src/algebra/mathml.spad.pamphlet @@ -1023,7 +1023,7 @@ have to be switched by swapping names. atomE : L E := atomize(expr) op : S := stringify first atomE op ~= "SUPERSUB" => "<mtext>Mistake in formatSuperSub: no SUPERSUB1</mtext>" - #args ~= 1 => "<mtext>Mistake in SuperSub1: #args <> 1</mtext>" + not one?(#args) => "<mtext>Mistake in SuperSub1: #args <> 1</mtext>" var : E := first args -- should be looking at something like {{SUPERSUB}{var}{ }{,,...,}} for -- example here's the second derivative of y w.r.t. x @@ -1052,7 +1052,7 @@ have to be switched by swapping names. atomE : L E := atomize(expr) op : S := stringify first atomE op ~= "SUPERSUB" => "<mtext>Mistake in formatSuperSub: no SUPERSUB</mtext>" - #args ~= 1 => "<mtext>Mistake in SuperSub: #args <> 1</mtext>" + not one?(#args) => "<mtext>Mistake in SuperSub: #args <> 1</mtext>" var : E := first args -- should be looking at something like {{SUPERSUB}{var}{ }{,,...,}} for -- example here's the second derivative of y w.r.t. x diff --git a/src/algebra/mfinfact.spad.pamphlet b/src/algebra/mfinfact.spad.pamphlet index 55153b57..73483b86 100644 --- a/src/algebra/mfinfact.spad.pamphlet +++ b/src/algebra/mfinfact.spad.pamphlet @@ -218,7 +218,7 @@ MultFiniteFactorize(OV,E,F,PG) : C == T x := lvar.1 lvar:=lvar.rest pc:= gcd coefficients um - if pc~=1 then + if not one? pc then um:=(um exquo pc)::SUP P ffactor:=multivariate(um,x) for lcterm in mFactor(pc,dx).factors repeat @@ -228,7 +228,7 @@ MultFiniteFactorize(OV,E,F,PG) : C == T -- should be unitNormal if unified, but for now it is easier lcum:F:= leadingCoefficient leadingCoefficient leadingCoefficient um - if lcum ~=1 then + if not one? lcum then um:=((inv lcum)::R::P) * um flead.contp := (lcum::R) *flead.contp @@ -286,13 +286,13 @@ MultFiniteFactorize(OV,E,F,PG) : C == T lpol:= dist.polfac dd := dist.correct unifact:=dist.corrfact - if dd~=1 then + if not one? dd then unifact := [dd*unifact.i for i in 1..nfact] um := ((dd**(nfact-1)::NNI)::P)*um (ffin:= lifting(um,lvar,unifact,lval,lpol,ldeg,pM(unifact))) case "failed" => intfact(um,lvar,ldeg,tleadpol,ltry) factfin: L SUP P:=ffin :: L SUP P - if dd~=1 then + if not one? dd then factfin:=[primitivePart ff for ff in factfin] factfin @@ -397,7 +397,7 @@ MultFiniteFactorize(OV,E,F,PG) : C == T -- else lcnm:F:=1 -- should be unitNormal if unified, but for now it is easier - if (lcnm:=leadingCoefficient leadingCoefficient newm)~=1 then + if not one?(lcnm:=leadingCoefficient leadingCoefficient newm) then newm:=((inv lcnm)::R)*newm dx:="max"/[degree uc for uc in coefficients newm] luniv:=generalTwoFactor(newm)$TwoFactorize(F) diff --git a/src/algebra/moddfact.spad.pamphlet b/src/algebra/moddfact.spad.pamphlet index 14795411..5cb2893d 100644 --- a/src/algebra/moddfact.spad.pamphlet +++ b/src/algebra/moddfact.spad.pamphlet @@ -114,7 +114,7 @@ ModularDistinctDegreeFactorizer(U):C == T where ans::U ddfactor(u) == - if (c:= lc(u)) ~= 1$I then u:= makeMonic(u) + if not one?(c:= lc(u)) then u:= makeMonic(u) ans:= sepfact(ddfact(u)) cons(c::EMR,[makeMonic(f) for f in ans | positive? degree(f)]) @@ -133,7 +133,7 @@ ModularDistinctDegreeFactorizer(U):C == T where w:= reduce(monomial(1,1)$U,p) m:= w d:I:= 1 - if (c:= lc(u)) ~= 1$I then u:= makeMonic u + if not one?(c:= lc(u)) then u:= makeMonic u ans:DDList:= [] repeat w:= exptmod(w,p,u) @@ -173,7 +173,7 @@ ModularDistinctDegreeFactorizer(U):C == T where u:= f.factor p:=modulus u (d := f.degree) = 0 => [u] - if (c:= lc(u)) ~= 1$I then u:= makeMonic(u) + if not one?(c:= lc(u)) then u:= makeMonic(u) d = (du := degree(u)) => [u] ans:L EMR:= [] x:U:= monomial(1,1) diff --git a/src/algebra/modmon.spad.pamphlet b/src/algebra/modmon.spad.pamphlet index 84c10d58..cb60793e 100644 --- a/src/algebra/modmon.spad.pamphlet +++ b/src/algebra/modmon.spad.pamphlet @@ -73,7 +73,7 @@ ModMonic(R,Rep): C == T setPoly (mon : Rep) == mon =$Rep m => mon oldm := m - leadingCoefficient mon ~= 1 => error "polynomial must be monic" + not one? leadingCoefficient mon => error "polynomial must be monic" -- following copy code needed since FFPOLY can modify mon copymon:Rep:= 0 while not zero? mon repeat diff --git a/src/algebra/mring.spad.pamphlet b/src/algebra/mring.spad.pamphlet index 6adb05f8..9521b586 100644 --- a/src/algebra/mring.spad.pamphlet +++ b/src/algebra/mring.spad.pamphlet @@ -186,13 +186,13 @@ MonoidRing(R: Ring, M: Monoid): MRcategory == MRdefinition where if M has Group then recip a == lt := terms a - #lt ~= 1 => "failed" + not one?(#lt) => "failed" (u := recip lt.first.Cf) case "failed" => "failed" --(u::R) * inv lt.first.Mn monomial((u::R), inv lt.first.Mn)$% else recip a == - #a ~= 1 or a.first.Mn ~= 1 => "failed" + not one?(#a) or not one?(a.first.Mn) => "failed" (u := recip a.first.Cf) case "failed" => "failed" u::R::% diff --git a/src/algebra/multfact.spad.pamphlet b/src/algebra/multfact.spad.pamphlet index b6009e97..de704ea2 100644 --- a/src/algebra/multfact.spad.pamphlet +++ b/src/algebra/multfact.spad.pamphlet @@ -325,7 +325,7 @@ InnerMultFact(OV,E,R,P) : C == T lpol:= dist.polfac dd := dist.correct unifact:=dist.corrfact - if dd~=1 then + if not one? dd then -- if polcase then lpol := [unitCanonical lp for lp in lpol] -- dd:=unitCanonical(dd) unifact := [dd * unif for unif in unifact] @@ -334,7 +334,7 @@ InnerMultFact(OV,E,R,P) : C == T (ffin:=lifting(umd,lvar,unifact,lval,lpol,ldeg,pmod)) case "failed" => intfact(um,lvar,ldeg,tleadpol,ltry,ufactor) factfin: L USP:=ffin :: L USP - if dd~=1 then + if not one? dd then factfin:=[primitivePart ff for ff in factfin] factfin @@ -425,7 +425,7 @@ InnerMultFact(OV,E,R,P) : C == T x := lvar.first lvar := lvar.rest pc:= gcd coefficients um - if pc~=1 then + if not one? pc then um:=(um exquo pc)::USP ffactor:=multivariate(um,x) for lcterm in mFactor(pc,ufactor).factors repeat diff --git a/src/algebra/multpoly.spad.pamphlet b/src/algebra/multpoly.spad.pamphlet index d7cb75c5..b558f0af 100644 --- a/src/algebra/multpoly.spad.pamphlet +++ b/src/algebra/multpoly.spad.pamphlet @@ -481,11 +481,11 @@ SparseMultivariatePolynomial(R: Ring,VarSet: OrderedSet): C == T where gcd(leadingCoefficient b, content a)::SUP $ conta := content a mona:SUP $ := monomial(conta, minimumDegree a) - if mona ~= 1 then + if not one? mona then a := (a exquo mona)::SUP $ contb := content b monb:SUP $ := monomial(contb, minimumDegree b) - if monb ~= 1 then + if not one? monb then b := (b exquo monb)::SUP $ mong:SUP $ := monomial(gcd(conta, contb), min(degree mona, degree monb)) diff --git a/src/algebra/multsqfr.spad.pamphlet b/src/algebra/multsqfr.spad.pamphlet index 7114c0f6..6c54e72c 100644 --- a/src/algebra/multsqfr.spad.pamphlet +++ b/src/algebra/multsqfr.spad.pamphlet @@ -111,13 +111,13 @@ MultivariateSquareFree (E,OV,R,P) : C == T where exp0:Z:=0 unitsq:P:=1 lcf:P:=leadingCoefficient f - if ctf~=1 then + if not one? ctf then f0:=ctf*f0 f:=(ctf::P)*f lcf:=ctf*lcf sqlead:List FFEP:= empty() sqlc:Factored P:=1 - if lcf~=1$P then + if not one? lcf then leadpol:=true sqlc:=squareFree lcf unitsq:=unitsq*(unit sqlc) @@ -132,7 +132,7 @@ MultivariateSquareFree (E,OV,R,P) : C == T where gg := unitNormal leadingCoefficient f sqdec:=cons([gg.associate*f,exp0],sqdec) return [gg.unit, sqdec]$squareForm - if ctf~=1 then g0:=ctf*g0 + if not one? ctf then g0:=ctf*g0 npol:=consnewpol(f,f0,exp0) (d,d0):=(npol.pol,npol.polval) if leadpol then lcoef:=coefChoose(exp0,sqlc) @@ -147,8 +147,8 @@ MultivariateSquareFree (E,OV,R,P) : C == T where f:=h::SUP f0:=completeEval(h,lvar,lval) lcr:P:=leadingCoefficient result0 - if leadpol and lcr~=1$P then - for lpfact in sqlead while lcr~=1 repeat + if leadpol and not one? lcr then + for lpfact in sqlead while not one? lcr repeat ground? lcr => unitsq:=(unitsq exquo lcr)::P lcr:=1$P @@ -195,7 +195,7 @@ MultivariateSquareFree (E,OV,R,P) : C == T where y:=lvar.im p:=p*monomial(1$P,y,n) result1:=cons(["sqfr",y::P,n],result1) - if p~=1$P then + if not one? p then f := (f exquo p)::P if ground? f then return makeFR(f, result1) lvar:=variables(f) diff --git a/src/algebra/nlode.spad.pamphlet b/src/algebra/nlode.spad.pamphlet index 4e4a7c25..ddb365b2 100644 --- a/src/algebra/nlode.spad.pamphlet +++ b/src/algebra/nlode.spad.pamphlet @@ -101,7 +101,7 @@ NonLinearFirstOrderODESolver(R, F): Exports == Implementation where r := denom(f := m / n)::F (not freeOf?(r, y := ky::F)) or (d := degree(p := univariate(numer f, ky))) < 2 - or degree(pp := reductum p) ~= 1 or reductum(pp) ~= 0 + or not one? degree(pp := reductum p) or reductum(pp) ~= 0 or (not freeOf?(a := (leadingCoefficient(pp)::F), y)) or (not freeOf?(b := (leadingCoefficient(p)::F), y)) => "failed" [a / r, b / r, d] diff --git a/src/algebra/npcoef.spad.pamphlet b/src/algebra/npcoef.spad.pamphlet index 7278870e..47710d88 100644 --- a/src/algebra/npcoef.spad.pamphlet +++ b/src/algebra/npcoef.spad.pamphlet @@ -63,7 +63,7 @@ NPCoef(BP,E,OV,R,P) : C == T where changed:Boolean:=true ltochange:List(NNI):=empty() ltodel:List(NNI):=empty() - while changed and ndet~=1 repeat + while changed and not one? ndet repeat changed :=false dt:=#tablecoef for i in 1..dt while not changed repeat diff --git a/src/algebra/numsolve.spad.pamphlet b/src/algebra/numsolve.spad.pamphlet index ae969619..04935b6b 100644 --- a/src/algebra/numsolve.spad.pamphlet +++ b/src/algebra/numsolve.spad.pamphlet @@ -148,7 +148,7 @@ InnerNumericFloatSolvePackage(K,F,Par): Cat == Cap where p0 := primitivePart multivariate(vec.0, mainvar) p1 := primitivePart(multivariate(vec.1, mainvar),mainvar) zero? p1 or - gcd(p0, leadingCoefficient(univariate(p1,mainvar))) ~=1 => + not one? gcd(p0, leadingCoefficient(univariate(p1,mainvar))) => innerSolve(cons(0,lp),empty(),lv,eps) findGenZeros([p1, p0], reverse lv, eps) @@ -286,12 +286,12 @@ FloatingRealPackage(Par): Cat == Cap where -- real zeros of the system of polynomial lp -- realRoots(lp:L RFI,lv:L SE,eps: Par) : L L Par == lnum:=[numer p for p in lp] - lden:=[dp for p in lp |(dp:=denom p)~=1] + lden:=[dp for p in lp |not one?(dp:=denom p)] innerSolve(lnum,lden,lv,eps)$INFSP(I,Par,Par) solve(lp:L RFI,eps : Par) : L L EQ P Par == lnum:=[numer p for p in lp] - lden:=[dp for p in lp |(dp:=denom p)~=1] + lden:=[dp for p in lp |not one?(dp:=denom p)] lv:="setUnion"/[variables np for np in lnum] if lden~=[] then lv:=setUnion(lv,"setUnion"/[variables dp for dp in lden]) @@ -301,7 +301,7 @@ FloatingRealPackage(Par): Cat == Cap where solve(le:L EQ RFI,eps : Par) : L L EQ P Par == lp:=[lhs ep - rhs ep for ep in le] lnum:=[numer p for p in lp] - lden:=[dp for p in lp |(dp:=denom p)~=1] + lden:=[dp for p in lp |not one?(dp:=denom p)] lv:="setUnion"/[variables np for np in lnum] if lden~=[] then lv:=setUnion(lv,"setUnion"/[variables dp for dp in lden]) @@ -406,12 +406,12 @@ FloatingComplexPackage(Par): Cat == Cap where -- find the complex zeros of an univariate polynomial -- complexRoots(lp:L FPK,lv:L SE,eps:Par) : L L C Par == lnum:=[numer p for p in lp] - lden:=[dp for p in lp |(dp:=denom p)~=1] + lden:=[dp for p in lp |not one?(dp:=denom p)] innerSolve(lnum,lden,lv,eps)$INFSP(K,C Par,Par) complexSolve(lp:L FPK,eps : Par) : L L EQ P C Par == lnum:=[numer p for p in lp] - lden:=[dp for p in lp |(dp:=denom p)~=1] + lden:=[dp for p in lp |not one?(dp:=denom p)] lv:="setUnion"/[variables np for np in lnum] if lden~=[] then lv:=setUnion(lv,"setUnion"/[variables dp for dp in lden]) @@ -421,7 +421,7 @@ FloatingComplexPackage(Par): Cat == Cap where complexSolve(le:L EQ FPK,eps : Par) : L L EQ P C Par == lp:=[lhs ep - rhs ep for ep in le] lnum:=[numer p for p in lp] - lden:=[dp for p in lp |(dp:=denom p)~=1] + lden:=[dp for p in lp |not one?(dp:=denom p)] lv:="setUnion"/[variables np for np in lnum] if lden~=[] then lv:=setUnion(lv,"setUnion"/[variables dp for dp in lden]) diff --git a/src/algebra/numtheor.spad.pamphlet b/src/algebra/numtheor.spad.pamphlet index 98a30591..0e40d82e 100644 --- a/src/algebra/numtheor.spad.pamphlet +++ b/src/algebra/numtheor.spad.pamphlet @@ -131,7 +131,7 @@ Using the half extended Euclidean algorithm we compute 1/a mod b. r:I := a-q*b (a,b):=(b,r) (c1,d1):=(d1,c1-q*d1) - a ~= 1 => error("moduli are not relatively prime") + not one? a => error("moduli are not relatively prime") positiveRemainder(c1,borg) @ @@ -155,11 +155,11 @@ inverse(a,b) == print [a, "=", q, "*(", b, ")+", r] (a,b):=(b,r) (c1,d1):=(d1,c1-q*d1) - a ~= 1 => error("moduli are not relatively prime") + not one? a => error("moduli are not relatively prime") positiveRemainder(c1,borg) -if ((inverse(26,15)*26)::IntegerMod(15) ~= 1) then print "DALY BUG" -if ((inverse(15,26)*15)::IntegerMod(26) ~= 1) then print "DALY BUG" +if not one?((inverse(26,15)*26)::IntegerMod(15)) then print "DALY BUG" +if not one?((inverse(15,26)*15)::IntegerMod(26)) then print "DALY BUG" @ \subsection{The Chinese Remainder Algorithm} @@ -566,7 +566,7 @@ PolynomialNumberTheoryFunctions(): Exports == Implementation where MonicQuotient: (SUP(I),SUP(I)) -> SUP(I) MonicQuotient (a,b) == - leadingCoefficient(b) ~= 1 => error "divisor must be monic" + not one? leadingCoefficient(b) => error "divisor must be monic" b = 1 => a da := degree a db := degree b -- assertion: degree b > 0 diff --git a/src/algebra/permgrps.spad.pamphlet b/src/algebra/permgrps.spad.pamphlet index ee5c746a..f3c8fa7d 100644 --- a/src/algebra/permgrps.spad.pamphlet +++ b/src/algebra/permgrps.spad.pamphlet @@ -350,7 +350,7 @@ PermutationGroup(S:SetCategory): public == private where ort := orbitWithSvc ( group , i ) k := ort.orb k1 := # k - if k1 ~= 1 then leave + if not one? k1 then leave gpsgs := nil()$(L V NNI) words2 := nil()$(L L NNI) gplength : NNI := #group diff --git a/src/algebra/pgcd.spad.pamphlet b/src/algebra/pgcd.spad.pamphlet index edbbccb0..2caf53de 100644 --- a/src/algebra/pgcd.spad.pamphlet +++ b/src/algebra/pgcd.spad.pamphlet @@ -322,7 +322,7 @@ PolynomialGcdPackage(E,OV,R,P):C == T where df:=degree f leadlist:List(P):=[] - if lgcd~=1 then + if not one? lgcd then leadpol:=true f:=lgcd*f ldeg:=[n0+n1 for n0 in ldeg for n1 in degree(lgcd,lvar)] diff --git a/src/algebra/poly.spad.pamphlet b/src/algebra/poly.spad.pamphlet index d055f03d..71a7d8df 100644 --- a/src/algebra/poly.spad.pamphlet +++ b/src/algebra/poly.spad.pamphlet @@ -618,7 +618,7 @@ SparseUnivariatePolynomial(R:Ring): UnivariatePolynomialCategory(R) with monicDivide(p1:%,p2:%) == null p2 => error "monicDivide: division by 0" - leadingCoefficient p2 ~= 1 => error "Divisor Not Monic" + not one? leadingCoefficient p2 => error "Divisor Not Monic" p2 = 1 => [p1,0] null p1 => [0,0] degree p1 < (n:=degree p2) => [0,p1] @@ -1045,7 +1045,7 @@ PolynomialSquareFree(VarSet:OrderedSet,E,RC:GcdDomain,P):C == T where cont1:=cont1*((unit listfin1)**uexp) pfaclist:=append(flistfin1,pfaclist) cont:=cont*cont1 - cont ~= 1 => + not one? cont => sqp := squareFree cont pfaclist:= append (factorList sqp,pfaclist) makeFR(unit(sqp)*coefficient(unit squf,0),pfaclist) @@ -1062,7 +1062,7 @@ PolynomialSquareFree(VarSet:OrderedSet,E,RC:GcdDomain,P):C == T where pfaclist:List FF := [[u.flg,multivariate(u.fctr,mv),u.xpnt] for u in factorList squp] - cont ~= 1 => + not one? cont => sqp := squareFree cont makeFR(unit(sqp)*coefficient(unit squp,0), append(factorList sqp, pfaclist)) diff --git a/src/algebra/primelt.spad.pamphlet b/src/algebra/primelt.spad.pamphlet index c72e09f6..9163b529 100644 --- a/src/algebra/primelt.spad.pamphlet +++ b/src/algebra/primelt.spad.pamphlet @@ -92,7 +92,7 @@ PrimitiveElement(F): Exports == Implementation where ll := nil()$List(UP) for v in lv repeat ((u := findUniv(l, v, w)) case "failed") or - (degree(p := univariate(u::P, v)) ~= 1) => return "failed" + not one? degree(p := univariate(u::P, v)) => return "failed" (bc := extendedEuclidean(univariate leadingCoefficient p, pw,1)) case "failed" => error "Should not happen" ll := concat(map(#1, diff --git a/src/algebra/rf.spad.pamphlet b/src/algebra/rf.spad.pamphlet index 26184004..ccb642c3 100644 --- a/src/algebra/rf.spad.pamphlet +++ b/src/algebra/rf.spad.pamphlet @@ -91,8 +91,8 @@ PolynomialCategoryQuotientFunctions(E, V, R, P, F): mymerge(variables numer f, variables denom f) isPower f == - (den := denom f) ~= 1 => - numer f ~= 1 => "failed" + not one?(den := denom f) => + not one? numer f => "failed" (ur := isExpt den) case "failed" => [den::F, -1] r := ur::Record(var:V, exponent:NonNegativeInteger) [r.var::P::F, - (r.exponent::Integer)] @@ -123,7 +123,7 @@ PolynomialCategoryQuotientFunctions(E, V, R, P, F): concat!(l::List(F), d) isPlus f == - denom f ~= 1 => "failed" + not one? denom f => "failed" (s := isPlus numer f) case "failed" => "failed" [x::F for x in s] diff --git a/src/algebra/rinterp.spad.pamphlet b/src/algebra/rinterp.spad.pamphlet index 73d12ede..468f9004 100644 --- a/src/algebra/rinterp.spad.pamphlet +++ b/src/algebra/rinterp.spad.pamphlet @@ -116,7 +116,7 @@ some of the data points may not be interpolated correctly. However, the solution is often still useful, thus we do not signal an error. <<RINTERP Implementation>>= - if #res~=1 then output("Warning: unattainable points!" _ + if not one?(#res) then output("Warning: unattainable points!" _ ::OutputForm)$OutputPackage @ diff --git a/src/algebra/space.spad.pamphlet b/src/algebra/space.spad.pamphlet index 6d688e47..60d4a13e 100644 --- a/src/algebra/space.spad.pamphlet +++ b/src/algebra/space.spad.pamphlet @@ -616,7 +616,7 @@ ThreeSpace(R:Ring):Exports == Implementation where numCurves := numCurves + 1 (#kid = 2) and _ (#children first kid = 1) and _ - (#children first rest kid ~= 1) => + not one?(#children first rest kid) => numPolys := numPolys + 1 numConstructs := numConstructs + 1 -- otherwise, a mathematical surface is assumed diff --git a/src/algebra/sregset.spad.pamphlet b/src/algebra/sregset.spad.pamphlet index dc961607..c301db79 100644 --- a/src/algebra/sregset.spad.pamphlet +++ b/src/algebra/sregset.spad.pamphlet @@ -1296,7 +1296,7 @@ SquareFreeRegularTriangularSet(R,E,V,P) : Exports == Implementation where not (mvar(ts) < mvar(p)) => "failed"::Union($,"failed") invertible?(init(p),ts)@Boolean => lts: Split := augment(p,ts) - #lts ~= 1 => "failed"::Union($,"failed") + not one?(#lts) => "failed"::Union($,"failed") (first lts)::Union($,"failed") "failed"::Union($,"failed") diff --git a/src/algebra/sttaylor.spad.pamphlet b/src/algebra/sttaylor.spad.pamphlet index 2de808ad..a3ddc781 100644 --- a/src/algebra/sttaylor.spad.pamphlet +++ b/src/algebra/sttaylor.spad.pamphlet @@ -558,7 +558,7 @@ Finally, we return the result with the correct order. powerre: (A,ST A,ST A) -> ST A powerre(s,x,c) == delay empty? x => zro() - frst x~=1 => error "**:constant coefficient should be 1" + not one? frst x => error "**:constant coefficient should be 1" concat(frst x,finteg((s+1)*(c*deriv x))-rst x * c) power(s,x) == YS(powerre(s,x,#1)) diff --git a/src/algebra/sum.spad.pamphlet b/src/algebra/sum.spad.pamphlet index e3d66075..aa5ae39f 100644 --- a/src/algebra/sum.spad.pamphlet +++ b/src/algebra/sum.spad.pamphlet @@ -269,13 +269,13 @@ GosperSummationMethod(E, V, R, P, Q): Exports == Impl where linearAndNNIntRoot(mp, v) == p := univariate(mp, v) - degree p ~= 1 => "failed" + not one? degree p => "failed" (p1 := retractIfCan(coefficient(p, 1))@Union(RN,"failed")) case "failed" or (p0 := retractIfCan(coefficient(p, 0))@Union(RN,"failed")) case "failed" => "failed" rt := -(p0::RN)/(p1::RN) - negative? rt or denom rt ~= 1 => "failed" + negative? rt or not one? denom rt => "failed" numer rt @ diff --git a/src/algebra/syssolp.spad.pamphlet b/src/algebra/syssolp.spad.pamphlet index 82218fa6..8fd97610 100644 --- a/src/algebra/syssolp.spad.pamphlet +++ b/src/algebra/syssolp.spad.pamphlet @@ -147,7 +147,7 @@ SystemSolvePackage(R): Cat == Cap where push:=PushVariables(R,DP,OV,dmp) lq : L dmp lvv:L OV:=[variable(vv)::OV for vv in lv] - lq:=[pushup(df::dmp,lvv)$push for f in lf|(df:=denom f)~=1] + lq:=[pushup(df::dmp,lvv)$push for f in lf|not one?(df:=denom f)] lp:=[pushup(numer(f)::dmp,lvv)$push for f in lf] parRes:=groebSolve(lp,lvv)$GroebnerSolve(lv,P R,R) if lq~=[] then diff --git a/src/algebra/twofact.spad.pamphlet b/src/algebra/twofact.spad.pamphlet index 2161c9a2..fb560b20 100644 --- a/src/algebra/twofact.spad.pamphlet +++ b/src/algebra/twofact.spad.pamphlet @@ -159,7 +159,7 @@ TwoFactorize(F) : C == T pfaclist) unitPart := unit(nfacs)**uexp * unitPart pfaclist := cons(u,pfaclist) - cont ~= 1 => + not one? cont => sqp := squareFree cont contlist:=[[w.flg,(w.fctr)::P,w.xpnt] for w in factorList sqp] pfaclist:= append(contlist, pfaclist) @@ -274,7 +274,7 @@ TwoFactorize(F) : C == T while not empty? lfacth repeat ff := first lfacth lfacth := rest lfacth - if (c:=leadingCoefficient leadingCoefficient ff) ~=1 then + if not one?(c:=leadingCoefficient leadingCoefficient ff) then ff:=((inv c)::SUEx)* ff not ((ffu:= retractIfCan(ff)$Normp) case "failed") => lfactk := cons(ffu::P, lfactk) diff --git a/src/algebra/unifact.spad.pamphlet b/src/algebra/unifact.spad.pamphlet index ab5a3e8e..f3437a81 100644 --- a/src/algebra/unifact.spad.pamphlet +++ b/src/algebra/unifact.spad.pamphlet @@ -136,7 +136,7 @@ UnivariateFactorize(ZP) : public == private where nm := (degree m)::NNI nmq2:NNI := nm quo 2 norm: Z := sqroot(+/[coefficient(m,k)**2 for k in 0..nm]) - if nmq2~=1 then nm := (nmq2-1):NNI + if not one? nmq2 then nm := (nmq2-1):NNI else nm := nmq2 bin0 := nm cbound := (bin0*norm+lcm)::PI @@ -219,7 +219,7 @@ UnivariateFactorize(ZP) : public == private where alpha: Z := coefficient(m,1)+d2 beta: Z := 2*coefficient(m,2) d := gcd(alpha,beta) - if d ~=1 then + if not one? d then alpha := alpha quo d beta := beta quo d m0: ZP := monomial(beta,1)+monomial(alpha,0) diff --git a/src/algebra/xlpoly.spad.pamphlet b/src/algebra/xlpoly.spad.pamphlet index 54526022..f607199d 100644 --- a/src/algebra/xlpoly.spad.pamphlet +++ b/src/algebra/xlpoly.spad.pamphlet @@ -254,7 +254,7 @@ LyndonWord(VarSet:OrderedSet):Public == Private where lyndon? w == w = 1$OFMON => false f: OFMON := rest w - while f ~= 1$OFMON repeat + while not one? f repeat not lexico(w,f) => return false f := rest f true @@ -807,7 +807,7 @@ PoincareBirkhoffWittLyndonBasis(VarSet: OrderedSet): Public == Private where null x.rest retract x == - #x ~= 1 => error "cannot convert to Lyndon word" + not one?(#x) => error "cannot convert to Lyndon word" x.first retractIfCan x == diff --git a/src/algebra/xpoly.spad.pamphlet b/src/algebra/xpoly.spad.pamphlet index b946d8bd..249a5e0e 100644 --- a/src/algebra/xpoly.spad.pamphlet +++ b/src/algebra/xpoly.spad.pamphlet @@ -267,7 +267,7 @@ FreeModule1(R:Ring,S:OrderedSet): FMcat == FMdef where monomials x == [ monom (t.k, t.c) for t in x] retractIfCan x == - numberOfMonomials(x) ~= 1 => "failed" + not one? numberOfMonomials(x) => "failed" x.first.c = 1 => x.first.k "failed" @@ -574,7 +574,7 @@ XPolynomialRing(R:Ring,E:OrderedMonoid): T == C where constant? p == (p = 0) or (maxdeg(p) = 1$E) constant p == coef(p,1$E) - quasiRegular? p == (p=0) or (last p).k ~= 1$E + quasiRegular? p == (p=0) or not one?((last p).k) quasiRegular p == quasiRegular?(p) => p [t for t in p | not(t.k = 1$E)] diff --git a/src/share/algebra/browse.daase b/src/share/algebra/browse.daase index 8eb96d66..8d325d93 100644 --- a/src/share/algebra/browse.daase +++ b/src/share/algebra/browse.daase @@ -1,5 +1,5 @@ -(2294709 . 3508949899) +(2294709 . 3508956485) (-18 A S) ((|constructor| (NIL "One-dimensional-array aggregates serves as models for one-dimensional arrays. Categorically,{} these aggregates are finite linear aggregates with the \\spadatt{shallowlyMutable} 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 @@ -56,7 +56,7 @@ NIL ((|constructor| (NIL "This domain represents the syntax for an add-expression.")) (|body| (((|SpadAst|) $) "base(\\spad{d}) returns the actual body of the add-domain expression `d'.")) (|base| (((|SpadAst|) $) "\\spad{base(d)} returns the base domain(\\spad{s}) of the add-domain expression."))) NIL NIL -(-32 R -1612) +(-32 R -1613) ((|constructor| (NIL "This package provides algebraic functions over an integral domain.")) (|iroot| ((|#2| |#1| (|Integer|)) "\\spad{iroot(p, n)} should be a non-exported function.")) (|definingPolynomial| ((|#2| |#2|) "\\spad{definingPolynomial(f)} returns the defining polynomial of \\spad{f} as an element of \\spad{F}. Error: if \\spad{f} is not a kernel.")) (|minPoly| (((|SparseUnivariatePolynomial| |#2|) (|Kernel| |#2|)) "\\spad{minPoly(k)} returns the defining polynomial of \\spad{k}.")) (** ((|#2| |#2| (|Fraction| (|Integer|))) "\\spad{x ** q} is \\spad{x} raised to the rational power \\spad{q}.")) (|droot| (((|OutputForm|) (|List| |#2|)) "\\spad{droot(l)} should be a non-exported function.")) (|inrootof| ((|#2| (|SparseUnivariatePolynomial| |#2|) |#2|) "\\spad{inrootof(p, x)} should be a non-exported function.")) (|belong?| (((|Boolean|) (|BasicOperator|)) "\\spad{belong?(op)} is \\spad{true} if \\spad{op} is an algebraic operator,{} that is,{} an \\spad{n}th root or implicit algebraic operator.")) (|operator| (((|BasicOperator|) (|BasicOperator|)) "\\spad{operator(op)} returns a copy of \\spad{op} with the domain-dependent properties appropriate for \\spad{F}. Error: if \\spad{op} is not an algebraic operator,{} that is,{} an \\spad{n}th root or implicit algebraic operator.")) (|rootOf| ((|#2| (|SparseUnivariatePolynomial| |#2|) (|Symbol|)) "\\spad{rootOf(p, y)} returns \\spad{y} such that \\spad{p(y) = 0}. The object returned displays as \\spad{'y}."))) NIL ((|HasCategory| |#1| (|%list| (QUOTE -1070) (QUOTE (-560))))) @@ -88,11 +88,11 @@ NIL ((|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."))) NIL NIL -(-40 -1612 UP UPUP -3168) +(-40 -1613 UP UPUP -3768) ((|constructor| (NIL "Function field defined by \\spad{f}(\\spad{x},{} \\spad{y}) = 0.")) (|knownInfBasis| (((|Void|) (|NonNegativeInteger|)) "\\spad{knownInfBasis(n)} \\undocumented{}"))) ((-4503 |has| (-421 |#2|) (-376)) (-4508 |has| (-421 |#2|) (-376)) (-4502 |has| (-421 |#2|) (-376)) ((-4512 "*") . T) (-4504 . T) (-4505 . T) (-4507 . T)) ((|HasCategory| (-421 |#2|) (QUOTE (-147))) (|HasCategory| (-421 |#2|) (QUOTE (-149))) (|HasCategory| (-421 |#2|) (QUOTE (-363))) (-2210 (|HasCategory| (-421 |#2|) (QUOTE (-376))) (|HasCategory| (-421 |#2|) (QUOTE (-363)))) (|HasCategory| (-421 |#2|) (QUOTE (-376))) (|HasCategory| (-421 |#2|) (QUOTE (-381))) (-2210 (-12 (|HasCategory| (-421 |#2|) (QUOTE (-240))) (|HasCategory| (-421 |#2|) (QUOTE (-376)))) (|HasCategory| (-421 |#2|) (QUOTE (-363)))) (-2210 (-12 (|HasCategory| (-421 |#2|) (QUOTE (-240))) (|HasCategory| (-421 |#2|) (QUOTE (-376)))) (-12 (|HasCategory| (-421 |#2|) (QUOTE (-239))) (|HasCategory| (-421 |#2|) (QUOTE (-376)))) (|HasCategory| (-421 |#2|) (QUOTE (-363)))) (-2210 (-12 (|HasCategory| (-421 |#2|) (|%list| (QUOTE -928) (QUOTE (-1209)))) (|HasCategory| (-421 |#2|) (QUOTE (-376)))) (-12 (|HasCategory| (-421 |#2|) (|%list| (QUOTE -928) (QUOTE (-1209)))) (|HasCategory| (-421 |#2|) (QUOTE (-363))))) (-2210 (-12 (|HasCategory| (-421 |#2|) (|%list| (QUOTE -928) (QUOTE (-1209)))) (|HasCategory| (-421 |#2|) (QUOTE (-376)))) (-12 (|HasCategory| (-421 |#2|) (|%list| (QUOTE -930) (QUOTE (-1209)))) (|HasCategory| (-421 |#2|) (QUOTE (-376))))) (|HasCategory| (-421 |#2|) (|%list| (QUOTE -660) (QUOTE (-560)))) (-2210 (|HasCategory| (-421 |#2|) (|%list| (QUOTE -1070) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| (-421 |#2|) (QUOTE (-376)))) (|HasCategory| (-421 |#2|) (|%list| (QUOTE -1070) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| (-421 |#2|) (|%list| (QUOTE -1070) (QUOTE (-560)))) (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (QUOTE (-381))) (-12 (|HasCategory| (-421 |#2|) (QUOTE (-239))) (|HasCategory| (-421 |#2|) (QUOTE (-376)))) (-12 (|HasCategory| (-421 |#2|) (|%list| (QUOTE -930) (QUOTE (-1209)))) (|HasCategory| (-421 |#2|) (QUOTE (-376)))) (-12 (|HasCategory| (-421 |#2|) (QUOTE (-240))) (|HasCategory| (-421 |#2|) (QUOTE (-376)))) (-12 (|HasCategory| (-421 |#2|) (|%list| (QUOTE -928) (QUOTE (-1209)))) (|HasCategory| (-421 |#2|) (QUOTE (-376))))) -(-41 R -1612) +(-41 R -1613) ((|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 ((-12 (|HasCategory| |#1| (QUOTE (-466))) (|HasCategory| |#1| (|%list| (QUOTE -1070) (QUOTE (-560)))) (|HasCategory| |#2| (|%list| (QUOTE -435) (|devaluate| |#1|))))) @@ -144,7 +144,7 @@ NIL ((|constructor| (NIL "\\spad{ApplyUnivariateSkewPolynomial} (internal) allows univariate skew polynomials to be applied to appropriate modules.")) (|apply| ((|#2| |#3| (|Mapping| |#2| |#2|) |#2|) "\\spad{apply(p, f, m)} returns \\spad{p(m)} where the action is given by \\spad{x m = f(m)}. \\spad{f} must be an \\spad{R}-pseudo linear map on \\spad{M}."))) NIL NIL -(-54 |Base| R -1612) +(-54 |Base| R -1613) ((|constructor| (NIL "This package apply rewrite rules to expressions,{} calling the pattern matcher.")) (|localUnquote| ((|#3| |#3| (|List| (|Symbol|))) "\\spad{localUnquote(f,ls)} is a local function.")) (|applyRules| ((|#3| (|List| (|RewriteRule| |#1| |#2| |#3|)) |#3| (|PositiveInteger|)) "\\spad{applyRules([r1,...,rn], expr, n)} applies the rules \\spad{r1},{}...,{}rn to \\spad{f} a most \\spad{n} times.") ((|#3| (|List| (|RewriteRule| |#1| |#2| |#3|)) |#3|) "\\spad{applyRules([r1,...,rn], expr)} applies the rules \\spad{r1},{}...,{}rn to \\spad{f} an unlimited number of times,{} \\spadignore{i.e.} until none of \\spad{r1},{}...,{}rn is applicable to the expression."))) NIL NIL @@ -396,7 +396,7 @@ NIL ((|constructor| (NIL "This package exports functions to set some commonly used properties of operators,{} including properties which contain functions.")) (|constantOpIfCan| (((|Union| |#1| "failed") (|BasicOperator|)) "\\spad{constantOpIfCan(op)} returns \\spad{a} if \\spad{op} is the constant nullary operator always returning \\spad{a},{} \"failed\" otherwise.")) (|constantOperator| (((|BasicOperator|) |#1|) "\\spad{constantOperator(a)} returns a nullary operator op such that \\spad{op()} always evaluate to \\spad{a}.")) (|derivative| (((|Union| (|List| (|Mapping| |#1| (|List| |#1|))) "failed") (|BasicOperator|)) "\\spad{derivative(op)} returns the value of the \"\\%diff\" property of \\spad{op} if it has one,{} and \"failed\" otherwise.") (((|BasicOperator|) (|BasicOperator|) (|Mapping| |#1| |#1|)) "\\spad{derivative(op, foo)} attaches foo as the \"\\%diff\" property of \\spad{op}. If \\spad{op} has an \"\\%diff\" property \\spad{f},{} then applying a derivation \\spad{D} to \\spad{op}(a) returns \\spad{f(a) * D(a)}. Argument \\spad{op} must be unary.") (((|BasicOperator|) (|BasicOperator|) (|List| (|Mapping| |#1| (|List| |#1|)))) "\\spad{derivative(op, [foo1,...,foon])} attaches [\\spad{foo1},{}...,{}foon] as the \"\\%diff\" property of \\spad{op}. If \\spad{op} has an \"\\%diff\" property \\spad{[f1,...,fn]} then applying a derivation \\spad{D} to \\spad{op(a1,...,an)} returns \\spad{f1(a1,...,an) * D(a1) + ... + fn(a1,...,an) * D(an)}.")) (|evaluate| (((|Union| (|Mapping| |#1| (|List| |#1|)) "failed") (|BasicOperator|)) "\\spad{evaluate(op)} returns the value of the \"\\%eval\" property of \\spad{op} if it has one,{} and \"failed\" otherwise.") (((|BasicOperator|) (|BasicOperator|) (|Mapping| |#1| |#1|)) "\\spad{evaluate(op, foo)} attaches foo as the \"\\%eval\" property of \\spad{op}. If \\spad{op} has an \"\\%eval\" property \\spad{f},{} then applying \\spad{op} to a returns the result of \\spad{f(a)}. Argument \\spad{op} must be unary.") (((|BasicOperator|) (|BasicOperator|) (|Mapping| |#1| (|List| |#1|))) "\\spad{evaluate(op, foo)} attaches foo as the \"\\%eval\" property of \\spad{op}. If \\spad{op} has an \"\\%eval\" property \\spad{f},{} then applying \\spad{op} to \\spad{(a1,...,an)} returns the result of \\spad{f(a1,...,an)}.") (((|Union| |#1| "failed") (|BasicOperator|) (|List| |#1|)) "\\spad{evaluate(op, [a1,...,an])} checks if \\spad{op} has an \"\\%eval\" property \\spad{f}. If it has,{} then \\spad{f(a1,...,an)} is returned,{} and \"failed\" otherwise."))) NIL NIL -(-117 -1612 UP) +(-117 -1613 UP) ((|constructor| (NIL "\\spadtype{BoundIntegerRoots} provides functions to find lower bounds on the integer roots of a polynomial.")) (|integerBound| (((|Integer|) |#2|) "\\spad{integerBound(p)} returns a lower bound on the negative integer roots of \\spad{p},{} and 0 if \\spad{p} has no negative integer roots."))) NIL NIL @@ -476,11 +476,11 @@ NIL ((|constructor| (NIL "Members of the domain CardinalNumber are values indicating the cardinality of sets,{} both finite and infinite. Arithmetic operations are defined on cardinal numbers as follows. \\blankline If \\spad{x = \\#X} and \\spad{y = \\#Y} then \\indented{2}{\\spad{x+y\\space{2}= \\#(X+Y)}\\space{3}\\tab{30}disjoint union} \\indented{2}{\\spad{x-y\\space{2}= \\#(X-Y)}\\space{3}\\tab{30}relative complement} \\indented{2}{\\spad{x*y\\space{2}= \\#(X*Y)}\\space{3}\\tab{30}cartesian product} \\indented{2}{\\spad{x**y = \\#(X**Y)}\\space{2}\\tab{30}\\spad{X**Y = \\{g| g:Y->X\\}}} \\blankline The non-negative integers have a natural construction as cardinals \\indented{2}{\\spad{0 = \\#\\{\\}},{} \\spad{1 = \\{0\\}},{} \\spad{2 = \\{0, 1\\}},{} ...,{} \\spad{n = \\{i| 0 <= i < n\\}}.} \\blankline That \\spad{0} acts as a zero for the multiplication of cardinals is equivalent to the axiom of choice. \\blankline The generalized continuum hypothesis asserts \\center{\\spad{2**Aleph i = Aleph(i+1)}} and is independent of the axioms of set theory [Goedel 1940]. \\blankline Three commonly encountered cardinal numbers are \\indented{3}{\\spad{a = \\#Z}\\space{7}\\tab{30}countable infinity} \\indented{3}{\\spad{c = \\#R}\\space{7}\\tab{30}the continuum} \\indented{3}{\\spad{f = \\#\\{g| g:[0,1]->R\\}}} \\blankline In this domain,{} these values are obtained using \\indented{3}{\\spad{a := Aleph 0},{} \\spad{c := 2**a},{} \\spad{f := 2**c}.} \\blankline")) (|generalizedContinuumHypothesisAssumed| (((|Boolean|) (|Boolean|)) "\\spad{generalizedContinuumHypothesisAssumed(bool)} is used to dictate whether the hypothesis is to be assumed.")) (|generalizedContinuumHypothesisAssumed?| (((|Boolean|)) "\\spad{generalizedContinuumHypothesisAssumed?()} tests if the hypothesis is currently assumed.")) (|countable?| (((|Boolean|) $) "\\spad{countable?(\\spad{a})} determines whether \\spad{a} is a countable cardinal,{} \\spadignore{i.e.} an integer or \\spad{Aleph 0}.")) (|finite?| (((|Boolean|) $) "\\spad{finite?(\\spad{a})} determines whether \\spad{a} is a finite cardinal,{} \\spadignore{i.e.} an integer.")) (|Aleph| (($ (|NonNegativeInteger|)) "\\spad{Aleph(n)} provides the named (infinite) cardinal number.")) (** (($ $ $) "\\spad{x**y} returns \\spad{\\#(X**Y)} where \\spad{X**Y} is defined \\indented{1}{as \\spad{\\{g| g:Y->X\\}}.}")) (- (((|Union| $ "failed") $ $) "\\spad{x - y} returns an element \\spad{z} such that \\spad{z+y=x} or \"failed\" if no such element exists.")) (|commutative| ((|attribute| "*") "a domain \\spad{D} has \\spad{commutative(\"*\")} if it has an operation \\spad{\"*\": (D,D) -> D} which is commutative."))) (((-4512 "*") . T)) NIL -(-137 |minix| -3048 R) +(-137 |minix| -3049 R) ((|constructor| (NIL "CartesianTensor(minix,{}dim,{}\\spad{R}) provides Cartesian tensors with components belonging to a commutative ring \\spad{R}. These tensors can have any number of indices. Each index takes values from \\spad{minix} to \\spad{minix + dim - 1}.")) (|sample| (($) "\\spad{sample()} returns an object of type \\%.")) (|unravel| (($ (|List| |#3|)) "\\spad{unravel(t)} produces a tensor from a list of components such that \\indented{2}{\\spad{unravel(ravel(t)) = t}.}")) (|ravel| (((|List| |#3|) $) "\\spad{ravel(t)} produces a list of components from a tensor such that \\indented{2}{\\spad{unravel(ravel(t)) = t}.}")) (|leviCivitaSymbol| (($) "\\spad{leviCivitaSymbol()} is the rank \\spad{dim} tensor defined by \\spad{leviCivitaSymbol()(i1,...idim) = +1/0/-1} if \\spad{i1,...,idim} is an even/is nota /is an odd permutation of \\spad{minix,...,minix+dim-1}.")) (|kroneckerDelta| (($) "\\spad{kroneckerDelta()} is the rank 2 tensor defined by \\indented{3}{\\spad{kroneckerDelta()(i,j)}} \\indented{6}{\\spad{= 1\\space{2}if i = j}} \\indented{6}{\\spad{= 0 if\\space{2}i \\~= j}}")) (|reindex| (($ $ (|List| (|Integer|))) "\\spad{reindex(t,[i1,...,idim])} permutes the indices of \\spad{t}. For example,{} if \\spad{r = reindex(t, [4,1,2,3])} for a rank 4 tensor \\spad{t},{} then \\spad{r} is the rank for tensor given by \\indented{4}{\\spad{r(i,j,k,l) = t(l,i,j,k)}.}")) (|transpose| (($ $ (|Integer|) (|Integer|)) "\\spad{transpose(t,i,j)} exchanges the \\spad{i}\\spad{-}th and \\spad{j}\\spad{-}th indices of \\spad{t}. For example,{} if \\spad{r = transpose(t,2,3)} for a rank 4 tensor \\spad{t},{} then \\spad{r} is the rank 4 tensor given by \\indented{4}{\\spad{r(i,j,k,l) = t(i,k,j,l)}.}") (($ $) "\\spad{transpose(t)} exchanges the first and last indices of \\spad{t}. For example,{} if \\spad{r = transpose(t)} for a rank 4 tensor \\spad{t},{} then \\spad{r} is the rank 4 tensor given by \\indented{4}{\\spad{r(i,j,k,l) = t(l,j,k,i)}.}")) (|contract| (($ $ (|Integer|) (|Integer|)) "\\spad{contract(t,i,j)} is the contraction of tensor \\spad{t} which sums along the \\spad{i}\\spad{-}th and \\spad{j}\\spad{-}th indices. For example,{} if \\spad{r = contract(t,1,3)} for a rank 4 tensor \\spad{t},{} then \\spad{r} is the rank 2 \\spad{(= 4 - 2)} tensor given by \\indented{4}{\\spad{r(i,j) = sum(h=1..dim,t(h,i,h,j))}.}") (($ $ (|Integer|) $ (|Integer|)) "\\spad{contract(t,i,s,j)} is the inner product of tenors \\spad{s} and \\spad{t} which sums along the \\spad{k1}\\spad{-}th index of \\spad{t} and the \\spad{k2}\\spad{-}th index of \\spad{s}. For example,{} if \\spad{r = contract(s,2,t,1)} for rank 3 tensors rank 3 tensors \\spad{s} and \\spad{t},{} then \\spad{r} is the rank 4 \\spad{(= 3 + 3 - 2)} tensor given by \\indented{4}{\\spad{r(i,j,k,l) = sum(h=1..dim,s(i,h,j)*t(h,k,l))}.}")) (* (($ $ $) "\\spad{s*t} is the inner product of the tensors \\spad{s} and \\spad{t} which contracts the last index of \\spad{s} with the first index of \\spad{t},{} \\spadignore{i.e.} \\indented{4}{\\spad{t*s = contract(t,rank t, s, 1)}} \\indented{4}{\\spad{t*s = sum(k=1..N, t[i1,..,iN,k]*s[k,j1,..,jM])}} This is compatible with the use of \\spad{M*v} to denote the matrix-vector inner product.")) (|product| (($ $ $) "\\spad{product(s,t)} is the outer product of the tensors \\spad{s} and \\spad{t}. For example,{} if \\spad{r = product(s,t)} for rank 2 tensors \\spad{s} and \\spad{t},{} then \\spad{r} is a rank 4 tensor given by \\indented{4}{\\spad{r(i,j,k,l) = s(i,j)*t(k,l)}.}")) (|elt| ((|#3| $ (|List| (|Integer|))) "\\spad{elt(t,[i1,...,iN])} gives a component of a rank \\spad{N} tensor.") ((|#3| $ (|Integer|) (|Integer|) (|Integer|) (|Integer|)) "\\spad{elt(t,i,j,k,l)} gives a component of a rank 4 tensor.") ((|#3| $ (|Integer|) (|Integer|) (|Integer|)) "\\spad{elt(t,i,j,k)} gives a component of a rank 3 tensor.") ((|#3| $ (|Integer|) (|Integer|)) "\\spad{elt(t,i,j)} gives a component of a rank 2 tensor.") ((|#3| $) "\\spad{elt(t)} gives the component of a rank 0 tensor.")) (|rank| (((|NonNegativeInteger|) $) "\\spad{rank(t)} returns the tensorial rank of \\spad{t} (that is,{} the number of indices). This is the same as the graded module degree.")) (|coerce| (($ (|List| $)) "\\spad{coerce([t_1,...,t_dim])} allows tensors to be constructed using lists.") (($ (|List| |#3|)) "\\spad{coerce([r_1,...,r_dim])} allows tensors to be constructed using lists.") (($ (|SquareMatrix| |#2| |#3|)) "\\spad{coerce(m)} views a matrix as a rank 2 tensor.") (($ (|DirectProduct| |#2| |#3|)) "\\spad{coerce(v)} views a vector as a rank 1 tensor."))) NIL NIL -(-138 |minix| -3048 S T$) +(-138 |minix| -3049 S T$) ((|constructor| (NIL "This package provides functions to enable conversion of tensors given conversion of the components.")) (|map| (((|CartesianTensor| |#1| |#2| |#4|) (|Mapping| |#4| |#3|) (|CartesianTensor| |#1| |#2| |#3|)) "\\spad{map(f,ts)} does a componentwise conversion of the tensor \\spad{ts} to a tensor with components of type \\spad{T}.")) (|reshape| (((|CartesianTensor| |#1| |#2| |#4|) (|List| |#4|) (|CartesianTensor| |#1| |#2| |#3|)) "\\spad{reshape(lt,ts)} organizes the list of components \\spad{lt} into a tensor with the same shape as \\spad{ts}."))) NIL NIL @@ -528,7 +528,7 @@ NIL ((|constructor| (NIL "Rings of Characteristic Zero."))) ((-4507 . T)) NIL -(-150 -1612 UP UPUP) +(-150 -1613 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}."))) NIL NIL @@ -568,7 +568,7 @@ NIL ((|constructor| (NIL "Color() specifies a domain of 27 colors provided in the \\Language{} system (the colors mix additively).")) (|color| (($ (|Integer|)) "\\spad{color(i)} returns a color of the indicated hue \\spad{i}.")) (|numberOfHues| (((|PositiveInteger|)) "\\spad{numberOfHues()} returns the number of total hues,{} set in totalHues.")) (|hue| (((|Integer|) $) "\\spad{hue(c)} returns the hue index of the indicated color \\spad{c}.")) (|blue| (($) "\\spad{blue()} returns the position of the blue hue from total hues.")) (|green| (($) "\\spad{green()} returns the position of the green hue from total hues.")) (|yellow| (($) "\\spad{yellow()} returns the position of the yellow hue from total hues.")) (|red| (($) "\\spad{red()} returns the position of the red hue from total hues.")) (+ (($ $ $) "\\spad{c1 + c2} additively mixes the two colors \\spad{c1} and \\spad{c2}.")) (* (($ (|DoubleFloat|) $) "\\spad{s * c},{} returns the color \\spad{c},{} whose weighted shade has been scaled by \\spad{s}.") (($ (|PositiveInteger|) $) "\\spad{s * c},{} returns the color \\spad{c},{} whose weighted shade has been scaled by \\spad{s}."))) NIL NIL -(-160 R -1612) +(-160 R -1613) ((|constructor| (NIL "Provides combinatorial functions over an integral domain.")) (|ipow| ((|#2| (|List| |#2|)) "\\spad{ipow(l)} should be local but conditional.")) (|iidprod| ((|#2| (|List| |#2|)) "\\spad{iidprod(l)} should be local but conditional.")) (|iidsum| ((|#2| (|List| |#2|)) "\\spad{iidsum(l)} should be local but conditional.")) (|iipow| ((|#2| (|List| |#2|)) "\\spad{iipow(l)} should be local but conditional.")) (|iiperm| ((|#2| (|List| |#2|)) "\\spad{iiperm(l)} should be local but conditional.")) (|iibinom| ((|#2| (|List| |#2|)) "\\spad{iibinom(l)} should be local but conditional.")) (|iifact| ((|#2| |#2|) "\\spad{iifact(x)} should be local but conditional.")) (|product| ((|#2| |#2| (|SegmentBinding| |#2|)) "\\spad{product(f(n), n = a..b)} returns \\spad{f}(a) * ... * \\spad{f}(\\spad{b}) as a formal product.") ((|#2| |#2| (|Symbol|)) "\\spad{product(f(n), n)} returns the formal product \\spad{P}(\\spad{n}) which verifies \\spad{P}(\\spad{n+1})/P(\\spad{n}) = \\spad{f}(\\spad{n}).")) (|summation| ((|#2| |#2| (|SegmentBinding| |#2|)) "\\spad{summation(f(n), n = a..b)} returns \\spad{f}(a) + ... + \\spad{f}(\\spad{b}) as a formal sum.") ((|#2| |#2| (|Symbol|)) "\\spad{summation(f(n), n)} returns the formal sum \\spad{S}(\\spad{n}) which verifies \\spad{S}(\\spad{n+1}) - \\spad{S}(\\spad{n}) = \\spad{f}(\\spad{n}).")) (|factorials| ((|#2| |#2| (|Symbol|)) "\\spad{factorials(f, x)} rewrites the permutations and binomials in \\spad{f} involving \\spad{x} in terms of factorials.") ((|#2| |#2|) "\\spad{factorials(f)} rewrites the permutations and binomials in \\spad{f} in terms of factorials.")) (|factorial| ((|#2| |#2|) "\\spad{factorial(n)} returns the factorial of \\spad{n},{} \\spadignore{i.e.} n!.")) (|permutation| ((|#2| |#2| |#2|) "\\spad{permutation(n, r)} returns the number of permutations of \\spad{n} objects taken \\spad{r} at a time,{} \\spadignore{i.e.} n!/(\\spad{n}-\\spad{r})!.")) (|binomial| ((|#2| |#2| |#2|) "\\spad{binomial(n, r)} returns the number of subsets of \\spad{r} objects taken among \\spad{n} objects,{} \\spadignore{i.e.} n!/(r! * (\\spad{n}-\\spad{r})!).")) (** ((|#2| |#2| |#2|) "\\spad{a ** b} is the formal exponential a**b.")) (|operator| (((|BasicOperator|) (|BasicOperator|)) "\\spad{operator(op)} returns a copy of \\spad{op} with the domain-dependent properties appropriate for \\spad{F}; error if \\spad{op} is not a combinatorial operator.")) (|belong?| (((|Boolean|) (|BasicOperator|)) "\\spad{belong?(op)} is \\spad{true} if \\spad{op} is a combinatorial operator."))) NIL NIL @@ -692,7 +692,7 @@ NIL ((|constructor| (NIL "This domain enumerates the three kinds of constructors available in OpenAxiom: category constructors,{} domain constructors,{} and package constructors.")) (|package| (($) "`package' is the kind of package constructors.")) (|domain| (($) "`domain' is the kind of domain constructors")) (|category| (($) "`category' is the kind of category constructors"))) NIL NIL -(-191 R -1612) +(-191 R -1613) ((|constructor| (NIL "\\spadtype{ComplexTrigonometricManipulations} provides function that compute the real and imaginary parts of complex functions.")) (|complexForm| (((|Complex| (|Expression| |#1|)) |#2|) "\\spad{complexForm(f)} returns \\spad{[real f, imag f]}.")) (|trigs| ((|#2| |#2|) "\\spad{trigs(f)} rewrites all the complex logs and exponentials appearing in \\spad{f} in terms of trigonometric functions.")) (|real?| (((|Boolean|) |#2|) "\\spad{real?(f)} returns \\spad{true} if \\spad{f = real f}.")) (|imag| (((|Expression| |#1|) |#2|) "\\spad{imag(f)} returns the imaginary part of \\spad{f} where \\spad{f} is a complex function.")) (|real| (((|Expression| |#1|) |#2|) "\\spad{real(f)} returns the real part of \\spad{f} where \\spad{f} is a complex function.")) (|complexElementary| ((|#2| |#2| (|Symbol|)) "\\spad{complexElementary(f, x)} rewrites the kernels of \\spad{f} involving \\spad{x} in terms of the 2 fundamental complex transcendental elementary functions: \\spad{log, exp}.") ((|#2| |#2|) "\\spad{complexElementary(f)} rewrites \\spad{f} in terms of the 2 fundamental complex transcendental elementary functions: \\spad{log, exp}.")) (|complexNormalize| ((|#2| |#2| (|Symbol|)) "\\spad{complexNormalize(f, x)} rewrites \\spad{f} using the least possible number of complex independent kernels involving \\spad{x}.") ((|#2| |#2|) "\\spad{complexNormalize(f)} rewrites \\spad{f} using the least possible number of complex independent kernels."))) NIL NIL @@ -804,11 +804,11 @@ NIL ((|constructor| (NIL "\\indented{1}{Author: Gabriel Dos Reis} Date Created: July 2,{} 2010 Date Last Modified: July 2,{} 2010 Descrption: \\indented{2}{Representation of a dual vector space basis,{} given by symbols.}")) (|dual| (($ (|LinearBasis| |#1|)) "\\spad{dual x} constructs the dual vector of a linear element which is part of a basis."))) NIL NIL -(-219 -1612 UP UPUP R) +(-219 -1613 UP UPUP R) ((|constructor| (NIL "This package provides functions for computing the residues of a function on an algebraic curve.")) (|doubleResultant| ((|#2| |#4| (|Mapping| |#2| |#2|)) "\\spad{doubleResultant(f, ')} returns \\spad{p}(\\spad{x}) whose roots are rational multiples of the residues of \\spad{f} at all its finite poles. Argument ' is the derivation to use."))) NIL NIL -(-220 -1612 FP) +(-220 -1613 FP) ((|constructor| (NIL "Package for the factorization of a univariate polynomial with coefficients in a finite field. The algorithm used is the \"distinct degree\" algorithm of Cantor-Zassenhaus,{} modified to use trace instead of the norm and a table for computing Frobenius as suggested by Naudin and Quitte .")) (|irreducible?| (((|Boolean|) |#2|) "\\spad{irreducible?(p)} tests whether the polynomial \\spad{p} is irreducible.")) (|tracePowMod| ((|#2| |#2| (|NonNegativeInteger|) |#2|) "\\spad{tracePowMod(u,k,v)} produces the sum of \\spad{u**(q**i)} for \\spad{i} running and q= size \\spad{F}")) (|trace2PowMod| ((|#2| |#2| (|NonNegativeInteger|) |#2|) "\\spad{trace2PowMod(u,k,v)} produces the sum of \\spad{u**(2**i)} for \\spad{i} running from 1 to \\spad{k} all computed modulo the polynomial \\spad{v}.")) (|exptMod| ((|#2| |#2| (|NonNegativeInteger|) |#2|) "\\spad{exptMod(u,k,v)} raises the polynomial \\spad{u} to the \\spad{k}th power modulo the polynomial \\spad{v}.")) (|separateFactors| (((|List| |#2|) (|List| (|Record| (|:| |deg| (|NonNegativeInteger|)) (|:| |prod| |#2|)))) "\\spad{separateFactors(lfact)} takes the list produced by \\spadfunFrom{separateDegrees}{DistinctDegreeFactorization} and produces the complete list of factors.")) (|separateDegrees| (((|List| (|Record| (|:| |deg| (|NonNegativeInteger|)) (|:| |prod| |#2|))) |#2|) "\\spad{separateDegrees(p)} splits the square free polynomial \\spad{p} into factors each of which is a product of irreducibles of the same degree.")) (|distdfact| (((|Record| (|:| |cont| |#1|) (|:| |factors| (|List| (|Record| (|:| |irr| |#2|) (|:| |pow| (|Integer|)))))) |#2| (|Boolean|)) "\\spad{distdfact(p,sqfrflag)} produces the complete factorization of the polynomial \\spad{p} returning an internal data structure. If argument \\spad{sqfrflag} is \\spad{true},{} the polynomial is assumed square free.")) (|factorSquareFree| (((|Factored| |#2|) |#2|) "\\spad{factorSquareFree(p)} produces the complete factorization of the square free polynomial \\spad{p}.")) (|factor| (((|Factored| |#2|) |#2|) "\\spad{factor(p)} produces the complete factorization of the polynomial \\spad{p}."))) NIL NIL @@ -820,7 +820,7 @@ NIL ((|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 NIL -(-223 R -1612) +(-223 R -1613) ((|constructor| (NIL "\\spadtype{ElementaryFunctionDefiniteIntegration} provides functions to compute definite integrals of elementary functions.")) (|innerint| (((|Union| (|:| |f1| (|OrderedCompletion| |#2|)) (|:| |f2| (|List| (|OrderedCompletion| |#2|))) (|:| |fail| "failed") (|:| |pole| "potentialPole")) |#2| (|Symbol|) (|OrderedCompletion| |#2|) (|OrderedCompletion| |#2|) (|Boolean|)) "\\spad{innerint(f, x, a, b, ignore?)} should be local but conditional")) (|integrate| (((|Union| (|:| |f1| (|OrderedCompletion| |#2|)) (|:| |f2| (|List| (|OrderedCompletion| |#2|))) (|:| |fail| "failed") (|:| |pole| "potentialPole")) |#2| (|SegmentBinding| (|OrderedCompletion| |#2|)) (|String|)) "\\spad{integrate(f, x = a..b, \"noPole\")} returns the integral of \\spad{f(x)dx} from a to \\spad{b}. If it is not possible to check whether \\spad{f} has a pole for \\spad{x} between a and \\spad{b} (because of parameters),{} then this function will assume that \\spad{f} has no such pole. Error: if \\spad{f} has a pole for \\spad{x} between a and \\spad{b} or if the last argument is not \"noPole\".") (((|Union| (|:| |f1| (|OrderedCompletion| |#2|)) (|:| |f2| (|List| (|OrderedCompletion| |#2|))) (|:| |fail| "failed") (|:| |pole| "potentialPole")) |#2| (|SegmentBinding| (|OrderedCompletion| |#2|))) "\\spad{integrate(f, x = a..b)} returns the integral of \\spad{f(x)dx} from a to \\spad{b}. Error: if \\spad{f} has a pole for \\spad{x} between a and \\spad{b}."))) NIL NIL @@ -840,7 +840,7 @@ NIL ((|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}.")) (|map| (($ (|Mapping| (|Expression| |#1|) (|Expression| |#1|)) $) "\\spad{map(f,df)} replaces each coefficient \\spad{x} of differential form \\spad{df} by \\spad{f(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}."))) ((-4507 . T)) NIL -(-228 R -1612) +(-228 R -1613) ((|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."))) NIL NIL @@ -904,19 +904,19 @@ NIL ((|constructor| (NIL "any solution of a homogeneous linear Diophantine equation can be represented as a sum of minimal solutions,{} which form a \"basis\" (a minimal solution cannot be represented as a nontrivial sum of solutions) in the case of an inhomogeneous linear Diophantine equation,{} each solution is the sum of a inhomogeneous solution and any number of homogeneous solutions therefore,{} it suffices to compute two sets: \\indented{3}{1. all minimal inhomogeneous solutions} \\indented{3}{2. all minimal homogeneous solutions} the algorithm implemented is a completion procedure,{} which enumerates all solutions in a recursive depth-first-search it can be seen as finding monotone paths in a graph for more details see Reference")) (|dioSolve| (((|Record| (|:| |varOrder| (|List| (|Symbol|))) (|:| |inhom| (|Union| (|List| (|Vector| (|NonNegativeInteger|))) "failed")) (|:| |hom| (|List| (|Vector| (|NonNegativeInteger|))))) (|Equation| (|Polynomial| (|Integer|)))) "\\spad{dioSolve(u)} computes a basis of all minimal solutions for linear homogeneous Diophantine equation \\spad{u},{} then all minimal solutions of inhomogeneous equation"))) NIL NIL -(-244 S -3048 R) +(-244 S -3049 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.")) (|finiteAggregate| ((|attribute|) "attribute to indicate an aggregate of finite size"))) NIL ((|HasCategory| |#3| (QUOTE (-376))) (|HasCategory| |#3| (QUOTE (-817))) (|HasCategory| |#3| (QUOTE (-872))) (|HasAttribute| |#3| (QUOTE -4507)) (|HasCategory| |#3| (QUOTE (-175))) (|HasCategory| |#3| (QUOTE (-381))) (|HasCategory| |#3| (QUOTE (-748))) (|HasCategory| |#3| (QUOTE (-21))) (|HasCategory| |#3| (QUOTE (-23))) (|HasCategory| |#3| (QUOTE (-133))) (|HasCategory| |#3| (QUOTE (-25))) (|HasCategory| |#3| (QUOTE (-1081))) (|HasCategory| |#3| (QUOTE (-1133)))) -(-245 -3048 R) +(-245 -3049 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.")) (|finiteAggregate| ((|attribute|) "attribute to indicate an aggregate of finite size"))) ((-4504 |has| |#2| (-1081)) (-4505 |has| |#2| (-1081)) (-4507 |has| |#2| (-6 -4507)) (-4510 . T)) NIL -(-246 -3048 R) +(-246 -3049 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."))) ((-4504 |has| |#2| (-1081)) (-4505 |has| |#2| (-1081)) (-4507 |has| |#2| (-6 -4507)) (-4510 . T)) ((-2210 (-12 (|HasCategory| |#2| (QUOTE (-21))) (|HasCategory| |#2| (|%list| (QUOTE -321) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-23))) (|HasCategory| |#2| (|%list| (QUOTE -321) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-25))) (|HasCategory| |#2| (|%list| (QUOTE -321) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-133))) (|HasCategory| |#2| (|%list| (QUOTE -321) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-175))) (|HasCategory| |#2| (|%list| (QUOTE -321) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-240))) (|HasCategory| |#2| (|%list| (QUOTE -321) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-376))) (|HasCategory| |#2| (|%list| (QUOTE -321) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-381))) (|HasCategory| |#2| (|%list| (QUOTE -321) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-748))) (|HasCategory| |#2| (|%list| (QUOTE -321) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-817))) 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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}."))) 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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."))) @@ -1076,11 +1076,11 @@ NIL ((|constructor| (NIL "A domain used in the construction of the exterior algebra on a set \\spad{X} over a ring \\spad{R}. This domain represents the set of all ordered subsets of the set \\spad{X},{} assumed to be in correspondance with {1,{}2,{}3,{} ...}. The ordered subsets are themselves ordered lexicographically and are in bijective correspondance with an ordered basis of the exterior algebra. In this domain we are dealing strictly with the exponents of basis elements which can only be 0 or 1. \\blankline The multiplicative identity element of the exterior algebra corresponds to the empty subset of \\spad{X}. A coerce from List Integer to an ordered basis element is provided to allow the convenient input of expressions. Another exported function forgets the ordered structure and simply returns the list corresponding to an ordered subset.")) (|Nul| (($ (|NonNegativeInteger|)) "\\spad{Nul()} gives the basis element 1 for the algebra generated by \\spad{n} generators.")) (|exponents| (((|List| (|Integer|)) $) "\\spad{exponents(x)} converts a domain element into a list of zeros and ones corresponding to the exponents in the basis element that \\spad{x} represents.")) (|degree| (((|NonNegativeInteger|) $) "\\spad{degree(x)} gives the numbers of 1's in \\spad{x},{} \\spadignore{i.e.} the number of non-zero exponents in the basis element that \\spad{x} represents.")) (|coerce| (($ (|List| (|Integer|))) "\\spad{coerce(l)} converts a list of 0's and 1's into a basis element,{} where 1 (respectively 0) designates that the variable of the corresponding index of \\spad{l} is (respectively,{} is not) present. Error: if an element of \\spad{l} is not 0 or 1."))) NIL NIL -(-287 R -1612) +(-287 R -1613) ((|constructor| (NIL "Provides elementary functions over an integral domain.")) (|localReal?| (((|Boolean|) |#2|) "\\spad{localReal?(x)} should be local but conditional")) (|specialTrigs| (((|Union| |#2| "failed") |#2| (|List| (|Record| (|:| |func| |#2|) (|:| |pole| (|Boolean|))))) "\\spad{specialTrigs(x,l)} should be local but conditional")) (|iiacsch| ((|#2| |#2|) "\\spad{iiacsch(x)} should be local but conditional")) (|iiasech| ((|#2| |#2|) "\\spad{iiasech(x)} should be local but conditional")) (|iiacoth| ((|#2| |#2|) "\\spad{iiacoth(x)} should be local but conditional")) (|iiatanh| ((|#2| |#2|) "\\spad{iiatanh(x)} should be local but conditional")) (|iiacosh| ((|#2| |#2|) "\\spad{iiacosh(x)} should be local but conditional")) (|iiasinh| ((|#2| |#2|) "\\spad{iiasinh(x)} should be local but conditional")) (|iicsch| ((|#2| |#2|) "\\spad{iicsch(x)} should be local but conditional")) (|iisech| ((|#2| |#2|) "\\spad{iisech(x)} should be local but conditional")) (|iicoth| ((|#2| |#2|) "\\spad{iicoth(x)} should be local but conditional")) (|iitanh| ((|#2| |#2|) "\\spad{iitanh(x)} should be local but conditional")) (|iicosh| ((|#2| |#2|) "\\spad{iicosh(x)} should be local but conditional")) (|iisinh| ((|#2| |#2|) "\\spad{iisinh(x)} should be local but conditional")) (|iiacsc| ((|#2| |#2|) "\\spad{iiacsc(x)} should be local but conditional")) (|iiasec| ((|#2| |#2|) "\\spad{iiasec(x)} should be local but conditional")) (|iiacot| ((|#2| |#2|) "\\spad{iiacot(x)} should be local but conditional")) (|iiatan| ((|#2| |#2|) "\\spad{iiatan(x)} should be local but conditional")) (|iiacos| ((|#2| |#2|) "\\spad{iiacos(x)} should be local but conditional")) (|iiasin| ((|#2| |#2|) "\\spad{iiasin(x)} should be local but conditional")) (|iicsc| ((|#2| |#2|) "\\spad{iicsc(x)} should be local but conditional")) (|iisec| ((|#2| |#2|) "\\spad{iisec(x)} should be local but conditional")) (|iicot| ((|#2| |#2|) "\\spad{iicot(x)} should be local but conditional")) (|iitan| ((|#2| |#2|) "\\spad{iitan(x)} should be local but conditional")) (|iicos| ((|#2| |#2|) "\\spad{iicos(x)} should be local but conditional")) (|iisin| ((|#2| |#2|) "\\spad{iisin(x)} should be local but conditional")) (|iilog| ((|#2| |#2|) "\\spad{iilog(x)} should be local but conditional")) (|iiexp| ((|#2| |#2|) "\\spad{iiexp(x)} should be local but conditional")) (|iisqrt3| ((|#2|) "\\spad{iisqrt3()} should be local but conditional")) (|iisqrt2| ((|#2|) "\\spad{iisqrt2()} should be local but conditional")) (|operator| (((|BasicOperator|) (|BasicOperator|)) "\\spad{operator(p)} returns an elementary operator with the same symbol as \\spad{p}")) (|belong?| (((|Boolean|) (|BasicOperator|)) "\\spad{belong?(p)} returns \\spad{true} if operator \\spad{p} is elementary")) (|pi| ((|#2|) "\\spad{pi()} returns the \\spad{pi} operator")) (|acsch| ((|#2| |#2|) "\\spad{acsch(x)} applies the inverse hyperbolic cosecant operator to \\spad{x}")) (|asech| ((|#2| |#2|) "\\spad{asech(x)} applies the inverse hyperbolic secant operator to \\spad{x}")) (|acoth| ((|#2| |#2|) "\\spad{acoth(x)} applies the inverse hyperbolic cotangent operator to \\spad{x}")) (|atanh| ((|#2| |#2|) "\\spad{atanh(x)} applies the inverse hyperbolic tangent operator to \\spad{x}")) (|acosh| ((|#2| |#2|) "\\spad{acosh(x)} applies the inverse hyperbolic cosine operator to \\spad{x}")) (|asinh| ((|#2| |#2|) "\\spad{asinh(x)} applies the inverse hyperbolic sine operator to \\spad{x}")) (|csch| ((|#2| |#2|) "\\spad{csch(x)} applies the hyperbolic cosecant operator to \\spad{x}")) (|sech| ((|#2| |#2|) "\\spad{sech(x)} applies the hyperbolic secant operator to \\spad{x}")) (|coth| ((|#2| |#2|) "\\spad{coth(x)} applies the hyperbolic cotangent operator to \\spad{x}")) (|tanh| ((|#2| |#2|) "\\spad{tanh(x)} applies the hyperbolic tangent operator to \\spad{x}")) (|cosh| ((|#2| |#2|) "\\spad{cosh(x)} applies the hyperbolic cosine operator to \\spad{x}")) (|sinh| ((|#2| |#2|) "\\spad{sinh(x)} applies the hyperbolic sine operator to \\spad{x}")) (|acsc| ((|#2| |#2|) "\\spad{acsc(x)} applies the inverse cosecant operator to \\spad{x}")) (|asec| ((|#2| |#2|) "\\spad{asec(x)} applies the inverse secant operator to \\spad{x}")) (|acot| ((|#2| |#2|) "\\spad{acot(x)} applies the inverse cotangent operator to \\spad{x}")) (|atan| ((|#2| |#2|) "\\spad{atan(x)} applies the inverse tangent operator to \\spad{x}")) (|acos| ((|#2| |#2|) "\\spad{acos(x)} applies the inverse cosine operator to \\spad{x}")) (|asin| ((|#2| |#2|) "\\spad{asin(x)} applies the inverse sine operator to \\spad{x}")) (|csc| ((|#2| |#2|) "\\spad{csc(x)} applies the cosecant operator to \\spad{x}")) (|sec| ((|#2| |#2|) "\\spad{sec(x)} applies the secant operator to \\spad{x}")) (|cot| ((|#2| |#2|) "\\spad{cot(x)} applies the cotangent operator to \\spad{x}")) (|tan| ((|#2| |#2|) "\\spad{tan(x)} applies the tangent operator to \\spad{x}")) (|cos| ((|#2| |#2|) "\\spad{cos(x)} applies the cosine operator to \\spad{x}")) (|sin| ((|#2| |#2|) "\\spad{sin(x)} applies the sine operator to \\spad{x}")) (|log| ((|#2| |#2|) "\\spad{log(x)} applies the logarithm operator to \\spad{x}")) (|exp| ((|#2| |#2|) "\\spad{exp(x)} applies the exponential operator to \\spad{x}"))) NIL NIL -(-288 R -1612) +(-288 R -1613) ((|constructor| (NIL "ElementaryFunctionStructurePackage provides functions to test the algebraic independence of various elementary functions,{} using the Risch structure theorem (real and complex versions). It also provides transformations on elementary functions which are not considered simplifications.")) (|tanQ| ((|#2| (|Fraction| (|Integer|)) |#2|) "\\spad{tanQ(q,a)} is a local function with a conditional implementation.")) (|rootNormalize| ((|#2| |#2| (|Kernel| |#2|)) "\\spad{rootNormalize(f, k)} returns \\spad{f} rewriting either \\spad{k} which must be an \\spad{n}th-root in terms of radicals already in \\spad{f},{} or some radicals in \\spad{f} in terms of \\spad{k}.")) (|validExponential| (((|Union| |#2| "failed") (|List| (|Kernel| |#2|)) |#2| (|Symbol|)) "\\spad{validExponential([k1,...,kn],f,x)} returns \\spad{g} if \\spad{exp(f)=g} and \\spad{g} involves only \\spad{k1...kn},{} and \"failed\" otherwise.")) (|realElementary| ((|#2| |#2| (|Symbol|)) "\\spad{realElementary(f,x)} rewrites the kernels of \\spad{f} involving \\spad{x} in terms of the 4 fundamental real transcendental elementary functions: \\spad{log, exp, tan, atan}.") ((|#2| |#2|) "\\spad{realElementary(f)} rewrites \\spad{f} in terms of the 4 fundamental real transcendental elementary functions: \\spad{log, exp, tan, atan}.")) (|rischNormalize| (((|Record| (|:| |func| |#2|) (|:| |kers| (|List| (|Kernel| |#2|))) (|:| |vals| (|List| |#2|))) |#2| (|Symbol|)) "\\spad{rischNormalize(f, x)} returns \\spad{[g, [k1,...,kn], [h1,...,hn]]} such that \\spad{g = normalize(f, x)} and each \\spad{ki} was rewritten as \\spad{hi} during the normalization.")) (|normalize| ((|#2| |#2| (|Symbol|)) "\\spad{normalize(f, x)} rewrites \\spad{f} using the least possible number of real algebraically independent kernels involving \\spad{x}.") ((|#2| |#2|) "\\spad{normalize(f)} rewrites \\spad{f} using the least possible number of real algebraically independent kernels."))) NIL NIL @@ -1132,7 +1132,7 @@ NIL ((|constructor| (NIL "An eltable aggregate is one which can be viewed as a function. For example,{} the list \\axiom{[1,{}7,{}4]} can applied to 0,{}1,{} and 2 respectively will return the integers 1,{}7,{} and 4; thus this list may be viewed as mapping 0 to 1,{} 1 to 7 and 2 to 4. In general,{} an aggregate can map members of a domain {\\em Dom} to an image domain {\\em Im}.")) (|qsetelt!| ((|#2| $ |#1| |#2|) "\\spad{qsetelt!(u,x,y)} sets the image of \\axiom{\\spad{x}} to be \\axiom{\\spad{y}} under \\axiom{\\spad{u}},{} without checking that \\axiom{\\spad{x}} is in the domain of \\axiom{\\spad{u}}. If such a check is required use the function \\axiom{setelt}.")) (|setelt| ((|#2| $ |#1| |#2|) "\\spad{setelt(u,x,y)} sets the image of \\spad{x} to be \\spad{y} under \\spad{u},{} assuming \\spad{x} is in the domain of \\spad{u}. Error: if \\spad{x} is not in the domain of \\spad{u}.")) (|qelt| ((|#2| $ |#1|) "\\spad{qelt(u, x)} applies \\axiom{\\spad{u}} to \\axiom{\\spad{x}} without checking whether \\axiom{\\spad{x}} is in the domain of \\axiom{\\spad{u}}. If \\axiom{\\spad{x}} is not in the domain of \\axiom{\\spad{u}} a memory-access violation may occur. If a check on whether \\axiom{\\spad{x}} is in the domain of \\axiom{\\spad{u}} is required,{} use the function \\axiom{elt}.")) (|elt| ((|#2| $ |#1| |#2|) "\\spad{elt(u, x, y)} applies \\spad{u} to \\spad{x} if \\spad{x} is in the domain of \\spad{u},{} and returns \\spad{y} otherwise. For example,{} if \\spad{u} is a polynomial in \\axiom{\\spad{x}} over the rationals,{} \\axiom{elt(\\spad{u},{}\\spad{n},{}0)} may define the coefficient of \\axiom{\\spad{x}} to the power \\spad{n},{} returning 0 when \\spad{n} is out of range."))) NIL NIL -(-301 S R |Mod| -3217 -1573 |exactQuo|) +(-301 S R |Mod| -4256 -2410 |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"))) ((-4503 . T) ((-4512 "*") . T) (-4504 . T) (-4505 . T) (-4507 . T)) NIL @@ -1172,11 +1172,11 @@ NIL ((|constructor| (NIL "An expression space is a set which is closed under certain operators.")) (|odd?| (((|Boolean|) $) "\\spad{odd? x} is \\spad{true} if \\spad{x} is an odd integer.")) (|even?| (((|Boolean|) $) "\\spad{even? x} is \\spad{true} if \\spad{x} is an even integer.")) (|definingPolynomial| (($ $) "\\spad{definingPolynomial(x)} returns an expression \\spad{p} such that \\spad{p(x) = 0}.")) (|minPoly| (((|SparseUnivariatePolynomial| $) (|Kernel| $)) "\\spad{minPoly(k)} returns \\spad{p} such that \\spad{p(k) = 0}.")) (|eval| (($ $ (|BasicOperator|) (|Mapping| $ $)) "\\spad{eval(x, s, f)} replaces every \\spad{s(a)} in \\spad{x} by \\spad{f(a)} for any \\spad{a}.") (($ $ (|BasicOperator|) (|Mapping| $ (|List| $))) "\\spad{eval(x, s, f)} replaces every \\spad{s(a1,..,am)} in \\spad{x} by \\spad{f(a1,..,am)} for any \\spad{a1},{}...,{}\\spad{am}.") (($ $ (|List| (|BasicOperator|)) (|List| (|Mapping| $ (|List| $)))) "\\spad{eval(x, [s1,...,sm], [f1,...,fm])} replaces every \\spad{si(a1,...,an)} in \\spad{x} by \\spad{fi(a1,...,an)} for any \\spad{a1},{}...,{}\\spad{an}.") (($ $ (|List| (|BasicOperator|)) (|List| (|Mapping| $ $))) "\\spad{eval(x, [s1,...,sm], [f1,...,fm])} replaces every \\spad{si(a)} in \\spad{x} by \\spad{fi(a)} for any \\spad{a}.") (($ $ (|Symbol|) (|Mapping| $ $)) "\\spad{eval(x, s, f)} replaces every \\spad{s(a)} in \\spad{x} by \\spad{f(a)} for any \\spad{a}.") (($ $ (|Symbol|) (|Mapping| $ (|List| $))) "\\spad{eval(x, s, f)} replaces every \\spad{s(a1,..,am)} in \\spad{x} by \\spad{f(a1,..,am)} for any \\spad{a1},{}...,{}\\spad{am}.") (($ $ (|List| (|Symbol|)) (|List| (|Mapping| $ (|List| $)))) "\\spad{eval(x, [s1,...,sm], [f1,...,fm])} replaces every \\spad{si(a1,...,an)} in \\spad{x} by \\spad{fi(a1,...,an)} for any \\spad{a1},{}...,{}\\spad{an}.") (($ $ (|List| (|Symbol|)) (|List| (|Mapping| $ $))) "\\spad{eval(x, [s1,...,sm], [f1,...,fm])} replaces every \\spad{si(a)} in \\spad{x} by \\spad{fi(a)} for any \\spad{a}.")) (|freeOf?| (((|Boolean|) $ (|Symbol|)) "\\spad{freeOf?(x, s)} tests if \\spad{x} does not contain any operator whose name is \\spad{s}.") (((|Boolean|) $ $) "\\spad{freeOf?(x, y)} tests if \\spad{x} does not contain any occurrence of \\spad{y},{} where \\spad{y} is a single kernel.")) (|map| (($ (|Mapping| $ $) (|Kernel| $)) "\\spad{map(f, k)} returns \\spad{op(f(x1),...,f(xn))} where \\spad{k = op(x1,...,xn)}.")) (|kernel| (($ (|BasicOperator|) (|List| $)) "\\spad{kernel(op, [f1,...,fn])} constructs \\spad{op(f1,...,fn)} without evaluating it.") (($ (|BasicOperator|) $) "\\spad{kernel(op, x)} constructs \\spad{op}(\\spad{x}) without evaluating it.")) (|is?| (((|Boolean|) $ (|Symbol|)) "\\spad{is?(x, s)} tests if \\spad{x} is a kernel and is the name of its operator is \\spad{s}.") (((|Boolean|) $ (|BasicOperator|)) "\\spad{is?(x, op)} tests if \\spad{x} is a kernel and is its operator is op.")) (|belong?| (((|Boolean|) (|BasicOperator|)) "\\spad{belong?(op)} tests if \\% accepts \\spad{op} as applicable to its elements.")) (|operator| (((|BasicOperator|) (|BasicOperator|)) "\\spad{operator(op)} returns a copy of \\spad{op} with the domain-dependent properties appropriate for \\%.")) (|operators| (((|List| (|BasicOperator|)) $) "\\spad{operators(f)} returns all the basic operators appearing in \\spad{f},{} no matter what their levels are.")) (|tower| (((|List| (|Kernel| $)) $) "\\spad{tower(f)} returns all the kernels appearing in \\spad{f},{} no matter what their levels are.")) (|kernels| (((|List| (|Kernel| $)) $) "\\spad{kernels(f)} returns the list of all the top-level kernels appearing in \\spad{f},{} but not the ones appearing in the arguments of the top-level kernels.")) (|mainKernel| (((|Union| (|Kernel| $) "failed") $) "\\spad{mainKernel(f)} returns a kernel of \\spad{f} with maximum nesting level,{} or if \\spad{f} has no kernels (\\spadignore{i.e.} \\spad{f} is a constant).")) (|height| (((|NonNegativeInteger|) $) "\\spad{height(f)} returns the highest nesting level appearing in \\spad{f}. Constants have height 0. Symbols have height 1. For any operator op and expressions \\spad{f1},{}...,{}fn,{} \\spad{op(f1,...,fn)} has height equal to \\spad{1 + max(height(f1),...,height(fn))}.")) (|distribute| (($ $ $) "\\spad{distribute(f, g)} expands all the kernels in \\spad{f} that contain \\spad{g} in their arguments and that are formally enclosed by a \\spadfunFrom{box}{ExpressionSpace} or a \\spadfunFrom{paren}{ExpressionSpace} expression.") (($ $) "\\spad{distribute(f)} expands all the kernels in \\spad{f} that are formally enclosed by a \\spadfunFrom{box}{ExpressionSpace} or \\spadfunFrom{paren}{ExpressionSpace} expression.")) (|paren| (($ (|List| $)) "\\spad{paren([f1,...,fn])} returns \\spad{(f1,...,fn)}. This prevents the \\spad{fi} from being evaluated when operators are applied to them,{} and makes them applicable to a unary operator. For example,{} \\spad{atan(paren [x, 2])} returns the formal kernel \\spad{atan((x, 2))}.") (($ $) "\\spad{paren(f)} returns (\\spad{f}). This prevents \\spad{f} from being evaluated when operators are applied to it. For example,{} \\spad{log(1)} returns 0,{} but \\spad{log(paren 1)} returns the formal kernel log((1)).")) (|box| (($ (|List| $)) "\\spad{box([f1,...,fn])} returns \\spad{(f1,...,fn)} with a 'box' around them that prevents the \\spad{fi} from being evaluated when operators are applied to them,{} and makes them applicable to a unary operator. For example,{} \\spad{atan(box [x, 2])} returns the formal kernel \\spad{atan(x, 2)}.") (($ $) "\\spad{box(f)} returns \\spad{f} with a 'box' around it that prevents \\spad{f} from being evaluated when operators are applied to it. For example,{} \\spad{log(1)} returns 0,{} but \\spad{log(box 1)} returns the formal kernel log(1).")) (|subst| (($ $ (|List| (|Kernel| $)) (|List| $)) "\\spad{subst(f, [k1...,kn], [g1,...,gn])} replaces the kernels \\spad{k1},{}...,{}kn by \\spad{g1},{}...,{}gn formally in \\spad{f}.") (($ $ (|List| (|Equation| $))) "\\spad{subst(f, [k1 = g1,...,kn = gn])} replaces the kernels \\spad{k1},{}...,{}kn by \\spad{g1},{}...,{}gn formally in \\spad{f}.") (($ $ (|Equation| $)) "\\spad{subst(f, k = g)} replaces the kernel \\spad{k} by \\spad{g} formally in \\spad{f}.")) (|elt| (($ (|BasicOperator|) (|List| $)) "\\spad{elt(op,[x1,...,xn])} or \\spad{op}([\\spad{x1},{}...,{}xn]) applies the \\spad{n}-ary operator \\spad{op} to \\spad{x1},{}...,{}xn.") (($ (|BasicOperator|) $ $ $ $) "\\spad{elt(op,x,y,z,t)} or \\spad{op}(\\spad{x},{} \\spad{y},{} \\spad{z},{} \\spad{t}) applies the 4-ary operator \\spad{op} to \\spad{x},{} \\spad{y},{} \\spad{z} and \\spad{t}.") (($ (|BasicOperator|) $ $ $) "\\spad{elt(op,x,y,z)} or \\spad{op}(\\spad{x},{} \\spad{y},{} \\spad{z}) applies the ternary operator \\spad{op} to \\spad{x},{} \\spad{y} and \\spad{z}.") (($ (|BasicOperator|) $ $) "\\spad{elt(op,x,y)} or \\spad{op}(\\spad{x},{} \\spad{y}) applies the binary operator \\spad{op} to \\spad{x} and \\spad{y}.") (($ (|BasicOperator|) $) "\\spad{elt(op,x)} or \\spad{op}(\\spad{x}) applies the unary operator \\spad{op} to \\spad{x}."))) NIL NIL -(-311 -1612 S) +(-311 -1613 S) ((|constructor| (NIL "This package allows a map from any expression space into any object to be lifted to a kernel over the expression set,{} using a given property of the operator of the kernel.")) (|map| ((|#2| (|Mapping| |#2| |#1|) (|String|) (|Kernel| |#1|)) "\\spad{map(f, p, k)} uses the property \\spad{p} of the operator of \\spad{k},{} in order to lift \\spad{f} and apply it to \\spad{k}."))) NIL NIL -(-312 E -1612) +(-312 E -1613) ((|constructor| (NIL "This package allows a mapping \\spad{E} -> \\spad{F} to be lifted to a kernel over \\spad{E}; This lifting can fail if the operator of the kernel cannot be applied in \\spad{F}; Do not use this package with \\spad{E} = \\spad{F},{} since this may drop some properties of the operators.")) (|map| ((|#2| (|Mapping| |#2| |#1|) (|Kernel| |#1|)) "\\spad{map(f, k)} returns \\spad{g = op(f(a1),...,f(an))} where \\spad{k = op(a1,...,an)}."))) NIL NIL @@ -1216,7 +1216,7 @@ NIL ((|constructor| (NIL "This category provides \\spadfun{eval} operations. A domain may belong to this category if it is possible to make ``evaluation'' substitutions.")) (|eval| (($ $ (|List| (|Equation| |#1|))) "\\spad{eval(f, [x1 = v1,...,xn = vn])} replaces \\spad{xi} by \\spad{vi} in \\spad{f}.") (($ $ (|Equation| |#1|)) "\\spad{eval(f,x = v)} replaces \\spad{x} by \\spad{v} in \\spad{f}."))) NIL NIL -(-322 -1612) +(-322 -1613) ((|constructor| (NIL "This package is to be used in conjuction with \\indented{12}{the CycleIndicators package. It provides an evaluation} \\indented{12}{function for SymmetricPolynomials.}")) (|eval| ((|#1| (|Mapping| |#1| (|Integer|)) (|SymmetricPolynomial| (|Fraction| (|Integer|)))) "\\spad{eval(f,s)} evaluates the cycle index \\spad{s} by applying \\indented{1}{the function \\spad{f} to each integer in a monomial partition,{}} \\indented{1}{forms their product and sums the results over all monomials.}"))) NIL NIL @@ -1244,7 +1244,7 @@ NIL ((|constructor| (NIL "This package provides functions to convert functional expressions to power series.")) (|series| (((|Any|) |#2| (|Equation| |#2|) (|Fraction| (|Integer|))) "\\spad{series(f,x = a,n)} expands the expression \\spad{f} as a series in powers of (\\spad{x} - a); terms will be computed up to order at least \\spad{n}.") (((|Any|) |#2| (|Equation| |#2|)) "\\spad{series(f,x = a)} expands the expression \\spad{f} as a series in powers of (\\spad{x} - a).") (((|Any|) |#2| (|Fraction| (|Integer|))) "\\spad{series(f,n)} returns a series expansion of the expression \\spad{f}. Note: \\spad{f} should have only one variable; the series will be expanded in powers of that variable and terms will be computed up to order at least \\spad{n}.") (((|Any|) |#2|) "\\spad{series(f)} returns a series expansion of the expression \\spad{f}. Note: \\spad{f} should have only one variable; the series will be expanded in powers of that variable.") (((|Any|) (|Symbol|)) "\\spad{series(x)} returns \\spad{x} viewed as a series.")) (|puiseux| (((|Any|) |#2| (|Equation| |#2|) (|Fraction| (|Integer|))) "\\spad{puiseux(f,x = a,n)} expands the expression \\spad{f} as a Puiseux series in powers of \\spad{(x - a)}; terms will be computed up to order at least \\spad{n}.") (((|Any|) |#2| (|Equation| |#2|)) "\\spad{puiseux(f,x = a)} expands the expression \\spad{f} as a Puiseux series in powers of \\spad{(x - a)}.") (((|Any|) |#2| (|Fraction| (|Integer|))) "\\spad{puiseux(f,n)} returns a Puiseux expansion of the expression \\spad{f}. Note: \\spad{f} should have only one variable; the series will be expanded in powers of that variable and terms will be computed up to order at least \\spad{n}.") (((|Any|) |#2|) "\\spad{puiseux(f)} returns a Puiseux expansion of the expression \\spad{f}. Note: \\spad{f} should have only one variable; the series will be expanded in powers of that variable.") (((|Any|) (|Symbol|)) "\\spad{puiseux(x)} returns \\spad{x} viewed as a Puiseux series.")) (|laurent| (((|Any|) |#2| (|Equation| |#2|) (|Integer|)) "\\spad{laurent(f,x = a,n)} expands the expression \\spad{f} as a Laurent series in powers of \\spad{(x - a)}; terms will be computed up to order at least \\spad{n}.") (((|Any|) |#2| (|Equation| |#2|)) "\\spad{laurent(f,x = a)} expands the expression \\spad{f} as a Laurent series in powers of \\spad{(x - a)}.") (((|Any|) |#2| (|Integer|)) "\\spad{laurent(f,n)} returns a Laurent expansion of the expression \\spad{f}. Note: \\spad{f} should have only one variable; the series will be expanded in powers of that variable and terms will be computed up to order at least \\spad{n}.") (((|Any|) |#2|) "\\spad{laurent(f)} returns a Laurent expansion of the expression \\spad{f}. Note: \\spad{f} should have only one variable; the series will be expanded in powers of that variable.") (((|Any|) (|Symbol|)) "\\spad{laurent(x)} returns \\spad{x} viewed as a Laurent series.")) (|taylor| (((|Any|) |#2| (|Equation| |#2|) (|NonNegativeInteger|)) "\\spad{taylor(f,x = a)} expands the expression \\spad{f} as a Taylor series in powers of \\spad{(x - a)}; terms will be computed up to order at least \\spad{n}.") (((|Any|) |#2| (|Equation| |#2|)) "\\spad{taylor(f,x = a)} expands the expression \\spad{f} as a Taylor series in powers of \\spad{(x - a)}.") (((|Any|) |#2| (|NonNegativeInteger|)) "\\spad{taylor(f,n)} returns a Taylor expansion of the expression \\spad{f}. Note: \\spad{f} should have only one variable; the series will be expanded in powers of that variable and terms will be computed up to order at least \\spad{n}.") (((|Any|) |#2|) "\\spad{taylor(f)} returns a Taylor expansion of the expression \\spad{f}. Note: \\spad{f} should have only one variable; the series will be expanded in powers of that variable.") (((|Any|) (|Symbol|)) "\\spad{taylor(x)} returns \\spad{x} viewed as a Taylor series."))) NIL NIL -(-329 R -1612) +(-329 R -1613) ((|constructor| (NIL "Taylor series solutions of explicit ODE's.")) (|seriesSolve| (((|Any|) |#2| (|BasicOperator|) (|Equation| |#2|) (|List| |#2|)) "\\spad{seriesSolve(eq, y, x = a, [b0,...,bn])} is equivalent to \\spad{seriesSolve(eq = 0, y, x = a, [b0,...,b(n-1)])}.") (((|Any|) |#2| (|BasicOperator|) (|Equation| |#2|) (|Equation| |#2|)) "\\spad{seriesSolve(eq, y, x = a, y a = b)} is equivalent to \\spad{seriesSolve(eq=0, y, x=a, y a = b)}.") (((|Any|) |#2| (|BasicOperator|) (|Equation| |#2|) |#2|) "\\spad{seriesSolve(eq, y, x = a, b)} is equivalent to \\spad{seriesSolve(eq = 0, y, x = a, y a = b)}.") (((|Any|) (|Equation| |#2|) (|BasicOperator|) (|Equation| |#2|) |#2|) "\\spad{seriesSolve(eq,y, x=a, b)} is equivalent to \\spad{seriesSolve(eq, y, x=a, y a = b)}.") (((|Any|) (|List| |#2|) (|List| (|BasicOperator|)) (|Equation| |#2|) (|List| (|Equation| |#2|))) "\\spad{seriesSolve([eq1,...,eqn], [y1,...,yn], x = a,[y1 a = b1,..., yn a = bn])} is equivalent to \\spad{seriesSolve([eq1=0,...,eqn=0], [y1,...,yn], x = a, [y1 a = b1,..., yn a = bn])}.") (((|Any|) (|List| |#2|) (|List| (|BasicOperator|)) (|Equation| |#2|) (|List| |#2|)) "\\spad{seriesSolve([eq1,...,eqn], [y1,...,yn], x=a, [b1,...,bn])} is equivalent to \\spad{seriesSolve([eq1=0,...,eqn=0], [y1,...,yn], x=a, [b1,...,bn])}.") (((|Any|) (|List| (|Equation| |#2|)) (|List| (|BasicOperator|)) (|Equation| |#2|) (|List| |#2|)) "\\spad{seriesSolve([eq1,...,eqn], [y1,...,yn], x=a, [b1,...,bn])} is equivalent to \\spad{seriesSolve([eq1,...,eqn], [y1,...,yn], x = a, [y1 a = b1,..., yn a = bn])}.") (((|Any|) (|List| (|Equation| |#2|)) (|List| (|BasicOperator|)) (|Equation| |#2|) (|List| (|Equation| |#2|))) "\\spad{seriesSolve([eq1,...,eqn],[y1,...,yn],x = a,[y1 a = b1,...,yn a = bn])} returns a taylor series solution of \\spad{[eq1,...,eqn]} around \\spad{x = a} with initial conditions \\spad{yi(a) = bi}. Note: eqi must be of the form \\spad{fi(x, y1 x, y2 x,..., yn x) y1'(x) + gi(x, y1 x, y2 x,..., yn x) = h(x, y1 x, y2 x,..., yn x)}.") (((|Any|) (|Equation| |#2|) (|BasicOperator|) (|Equation| |#2|) (|List| |#2|)) "\\spad{seriesSolve(eq,y,x=a,[b0,...,b(n-1)])} returns a Taylor series solution of \\spad{eq} around \\spad{x = a} with initial conditions \\spad{y(a) = b0},{} \\spad{y'(a) = b1},{} \\spad{y''(a) = b2},{} ...,{}\\spad{y(n-1)(a) = b(n-1)} \\spad{eq} must be of the form \\spad{f(x, y x, y'(x),..., y(n-1)(x)) y(n)(x) + g(x,y x,y'(x),...,y(n-1)(x)) = h(x,y x, y'(x),..., y(n-1)(x))}.") (((|Any|) (|Equation| |#2|) (|BasicOperator|) (|Equation| |#2|) (|Equation| |#2|)) "\\spad{seriesSolve(eq,y,x=a, y a = b)} returns a Taylor series solution of \\spad{eq} around \\spad{x} = a with initial condition \\spad{y(a) = b}. Note: \\spad{eq} must be of the form \\spad{f(x, y x) y'(x) + g(x, y x) = h(x, y x)}."))) NIL NIL @@ -1255,7 +1255,7 @@ NIL (-331 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."))) (((-4512 "*") |has| |#1| (-175)) (-4503 |has| |#1| (-571)) (-4508 |has| |#1| (-376)) (-4502 |has| |#1| (-376)) (-4504 . T) (-4505 . T) (-4507 . T)) -((|HasCategory| |#1| (|%list| (QUOTE -38) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#1| (QUOTE (-571))) (|HasCategory| |#1| (QUOTE (-175))) (-2210 (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-571)))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-149))) (-12 (|HasCategory| |#1| (|%list| (QUOTE -928) (QUOTE (-1209)))) (|HasSignature| |#1| (|%list| (QUOTE *) (|%list| (|devaluate| |#1|) (|%list| (QUOTE -421) (QUOTE (-560))) (|devaluate| |#1|))))) (|HasSignature| |#1| (|%list| (QUOTE *) (|%list| (|devaluate| |#1|) (|%list| (QUOTE -421) (QUOTE (-560))) (|devaluate| |#1|)))) (|HasCategory| (-421 (-560)) (QUOTE (-1144))) (|HasCategory| |#1| (QUOTE (-376))) (-2210 (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (QUOTE (-571)))) (-2210 (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (QUOTE (-571)))) (-12 (|HasSignature| |#1| (|%list| (QUOTE **) (|%list| (|devaluate| |#1|) (|devaluate| |#1|) (|%list| (QUOTE -421) (QUOTE (-560)))))) (|HasSignature| |#1| (|%list| (QUOTE -2590) (|%list| (|devaluate| |#1|) (QUOTE (-1209)))))) (|HasSignature| |#1| (|%list| (QUOTE **) (|%list| (|devaluate| |#1|) (|devaluate| |#1|) (|%list| (QUOTE -421) (QUOTE (-560)))))) (-2210 (-12 (|HasCategory| |#1| (|%list| (QUOTE -29) (QUOTE (-560)))) (|HasCategory| |#1| (|%list| (QUOTE -38) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#1| (QUOTE (-990))) (|HasCategory| |#1| (QUOTE (-1235)))) (-12 (|HasCategory| |#1| (|%list| (QUOTE -38) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasSignature| |#1| (|%list| (QUOTE -1348) (|%list| (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1209))))) (|HasSignature| |#1| (|%list| (QUOTE -3589) (|%list| (|%list| (QUOTE -663) (QUOTE (-1209))) (|devaluate| |#1|))))))) +((|HasCategory| |#1| (|%list| (QUOTE -38) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#1| (QUOTE (-571))) (|HasCategory| |#1| (QUOTE (-175))) (-2210 (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-571)))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-149))) (-12 (|HasCategory| |#1| (|%list| (QUOTE -928) (QUOTE (-1209)))) (|HasSignature| |#1| (|%list| (QUOTE *) (|%list| (|devaluate| |#1|) (|%list| (QUOTE -421) (QUOTE (-560))) (|devaluate| |#1|))))) (|HasSignature| |#1| (|%list| (QUOTE *) (|%list| (|devaluate| |#1|) (|%list| (QUOTE -421) (QUOTE (-560))) (|devaluate| |#1|)))) (|HasCategory| (-421 (-560)) (QUOTE (-1144))) (|HasCategory| |#1| (QUOTE (-376))) (-2210 (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (QUOTE (-571)))) (-2210 (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (QUOTE (-571)))) (-12 (|HasSignature| |#1| (|%list| (QUOTE **) (|%list| (|devaluate| |#1|) (|devaluate| |#1|) (|%list| (QUOTE -421) (QUOTE (-560)))))) (|HasSignature| |#1| (|%list| (QUOTE -2590) (|%list| (|devaluate| |#1|) (QUOTE (-1209)))))) (|HasSignature| |#1| (|%list| (QUOTE **) (|%list| (|devaluate| |#1|) (|devaluate| |#1|) (|%list| (QUOTE -421) (QUOTE (-560)))))) (-2210 (-12 (|HasCategory| |#1| (|%list| (QUOTE -29) (QUOTE (-560)))) (|HasCategory| |#1| (|%list| (QUOTE -38) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#1| (QUOTE (-990))) (|HasCategory| |#1| (QUOTE (-1235)))) (-12 (|HasCategory| |#1| (|%list| (QUOTE -38) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasSignature| |#1| (|%list| (QUOTE -3270) (|%list| (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1209))))) (|HasSignature| |#1| (|%list| (QUOTE -3589) (|%list| (|%list| (QUOTE -663) (QUOTE (-1209))) (|devaluate| |#1|))))))) (-332 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}."))) NIL @@ -1288,11 +1288,11 @@ NIL ((|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."))) ((-4511 . T) (-4510 . T)) ((-2210 (-12 (|HasCategory| |#1| (QUOTE (-872))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|))))) (-2210 (-12 (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-888))))) (|HasCategory| |#1| (|%list| (QUOTE -633) (QUOTE (-549)))) (-2210 (|HasCategory| |#1| (QUOTE (-872))) (|HasCategory| |#1| (QUOTE (-1133)))) (|HasCategory| |#1| (QUOTE (-872))) (-2210 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-872))) (|HasCategory| |#1| (QUOTE (-1133)))) (|HasCategory| (-560) (QUOTE (-872))) (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-888)))) (|HasCategory| |#1| (QUOTE (-102))) (-12 (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|))))) -(-340 S -1612) +(-340 S -1613) ((|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| |#2|) "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| |#2|) $) "\\spad{linearAssociatedLog(a)} returns a polynomial {\\em g},{} such that \\spadfun{linearAssociatedExp}(normalElement(),{}\\spad{g}) equals {\\em a}.")) (|linearAssociatedOrder| (((|SparseUnivariatePolynomial| |#2|) $) "\\spad{linearAssociatedOrder(a)} retruns the monic polynomial {\\em g} of least degree,{} such that \\spadfun{linearAssociatedExp}(a,{}\\spad{g}) is 0.")) (|linearAssociatedExp| (($ $ (|SparseUnivariatePolynomial| |#2|)) "\\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])}.") ((|#2| $) "\\spad{trace(a)} computes the trace of \\spad{a} with respect to the field considered as an algebra with 1 over the ground field \\spad{F}.")) (|norm| (($ $ (|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])") ((|#2| $) "\\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| |#2|)) "\\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| |#2|) $) "\\spad{minimalPolynomial(a)} returns the minimal polynomial of an element \\spad{a} over the ground field \\spad{F}.")) (|represents| (($ (|Vector| |#2|)) "\\spad{represents([a1,..,an])} returns \\spad{a1*v1 + ... + an*vn},{} where \\spad{v1},{}...,{}vn are the elements of the fixed basis.")) (|coordinates| (((|Matrix| |#2|) (|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| |#2|) $) "\\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."))) NIL ((|HasCategory| |#2| (QUOTE (-381)))) -(-341 -1612) +(-341 -1613) ((|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."))) ((-4502 . T) (-4508 . T) (-4503 . T) ((-4512 "*") . T) (-4504 . T) (-4505 . T) (-4507 . T)) NIL @@ -1312,7 +1312,7 @@ NIL ((|constructor| (NIL "Represntation of data needed to instantiate a domain constructor.")) (|lookupFunction| (((|Identifier|) $) "\\spad{lookupFunction x} returns the name of the lookup function associated with the functor data \\spad{x}.")) (|categories| (((|PrimitiveArray| (|ConstructorCall| (|CategoryConstructor|))) $) "\\spad{categories x} returns the list of categories forms each domain object obtained from the domain data \\spad{x} belongs to.")) (|encodingDirectory| (((|PrimitiveArray| (|NonNegativeInteger|)) $) "\\spad{encodintDirectory x} returns the directory of domain-wide entity description.")) (|attributeData| (((|List| (|Pair| (|Syntax|) (|NonNegativeInteger|))) $) "\\spad{attributeData x} returns the list of attribute-predicate bit vector index pair associated with the functor data \\spad{x}.")) (|domainTemplate| (((|DomainTemplate|) $) "\\spad{domainTemplate x} returns the domain template vector associated with the functor data \\spad{x}."))) NIL NIL -(-346 -1612 UP UPUP R) +(-346 -1613 UP UPUP R) ((|constructor| (NIL "This domains implements finite rational divisors on a curve,{} that is finite formal sums SUM(\\spad{n} * \\spad{P}) where the \\spad{n}'s are integers and the \\spad{P}'s are finite rational points on the curve.")) (|lSpaceBasis| (((|Vector| |#4|) $) "\\spad{lSpaceBasis(d)} returns a basis for \\spad{L(d) = {f | (f) >= -d}} as a module over \\spad{K[x]}.")) (|finiteBasis| (((|Vector| |#4|) $) "\\spad{finiteBasis(d)} returns a basis for \\spad{d} as a module over {\\em K[x]}."))) NIL NIL @@ -1320,11 +1320,11 @@ NIL ((|constructor| (NIL "\\indented{1}{Lift a map to finite divisors.} Author: Manuel Bronstein Date Created: 1988 Date Last Updated: 19 May 1993")) (|map| (((|FiniteDivisor| |#5| |#6| |#7| |#8|) (|Mapping| |#5| |#1|) (|FiniteDivisor| |#1| |#2| |#3| |#4|)) "\\spad{map(f,d)} \\undocumented{}"))) NIL NIL -(-348 S -1612 UP UPUP R) +(-348 S -1613 UP UPUP R) ((|constructor| (NIL "This category describes finite rational divisors on a curve,{} that is finite formal sums SUM(\\spad{n} * \\spad{P}) where the \\spad{n}'s are integers and the \\spad{P}'s are finite rational points on the curve.")) (|generator| (((|Union| |#5| "failed") $) "\\spad{generator(d)} returns \\spad{f} if \\spad{(f) = d},{} \"failed\" if \\spad{d} is not principal.")) (|principal?| (((|Boolean|) $) "\\spad{principal?(D)} tests if the argument is the divisor of a function.")) (|reduce| (($ $) "\\spad{reduce(D)} converts \\spad{D} to some reduced form (the reduced forms can be differents in different implementations).")) (|decompose| (((|Record| (|:| |id| (|FractionalIdeal| |#3| (|Fraction| |#3|) |#4| |#5|)) (|:| |principalPart| |#5|)) $) "\\spad{decompose(d)} returns \\spad{[id, f]} where \\spad{d = (id) + div(f)}.")) (|divisor| (($ |#5| |#3| |#3| |#3| |#2|) "\\spad{divisor(h, d, d', g, r)} returns the sum of all the finite points where \\spad{h/d} has residue \\spad{r}. \\spad{h} must be integral. \\spad{d} must be squarefree. \\spad{d'} is some derivative of \\spad{d} (not necessarily dd/dx). \\spad{g = gcd(d,discriminant)} contains the ramified zeros of \\spad{d}") (($ |#2| |#2| (|Integer|)) "\\spad{divisor(a, b, n)} makes the divisor \\spad{nP} where P: \\spad{(x = a, y = b)}. \\spad{P} is allowed to be singular if \\spad{n} is a multiple of the rank.") (($ |#2| |#2|) "\\spad{divisor(a, b)} makes the divisor P: \\spad{(x = a, y = b)}. Error: if \\spad{P} is singular.") (($ |#5|) "\\spad{divisor(g)} returns the divisor of the function \\spad{g}.") (($ (|FractionalIdeal| |#3| (|Fraction| |#3|) |#4| |#5|)) "\\spad{divisor(I)} makes a divisor \\spad{D} from an ideal \\spad{I}.")) (|ideal| (((|FractionalIdeal| |#3| (|Fraction| |#3|) |#4| |#5|) $) "\\spad{ideal(D)} returns the ideal corresponding to a divisor \\spad{D}."))) NIL NIL -(-349 -1612 UP UPUP R) +(-349 -1613 UP UPUP R) ((|constructor| (NIL "This category describes finite rational divisors on a curve,{} that is finite formal sums SUM(\\spad{n} * \\spad{P}) where the \\spad{n}'s are integers and the \\spad{P}'s are finite rational points on the curve.")) (|generator| (((|Union| |#4| "failed") $) "\\spad{generator(d)} returns \\spad{f} if \\spad{(f) = d},{} \"failed\" if \\spad{d} is not principal.")) (|principal?| (((|Boolean|) $) "\\spad{principal?(D)} tests if the argument is the divisor of a function.")) (|reduce| (($ $) "\\spad{reduce(D)} converts \\spad{D} to some reduced form (the reduced forms can be differents in different implementations).")) (|decompose| (((|Record| (|:| |id| (|FractionalIdeal| |#2| (|Fraction| |#2|) |#3| |#4|)) (|:| |principalPart| |#4|)) $) "\\spad{decompose(d)} returns \\spad{[id, f]} where \\spad{d = (id) + div(f)}.")) (|divisor| (($ |#4| |#2| |#2| |#2| |#1|) "\\spad{divisor(h, d, d', g, r)} returns the sum of all the finite points where \\spad{h/d} has residue \\spad{r}. \\spad{h} must be integral. \\spad{d} must be squarefree. \\spad{d'} is some derivative of \\spad{d} (not necessarily dd/dx). \\spad{g = gcd(d,discriminant)} contains the ramified zeros of \\spad{d}") (($ |#1| |#1| (|Integer|)) "\\spad{divisor(a, b, n)} makes the divisor \\spad{nP} where P: \\spad{(x = a, y = b)}. \\spad{P} is allowed to be singular if \\spad{n} is a multiple of the rank.") (($ |#1| |#1|) "\\spad{divisor(a, b)} makes the divisor P: \\spad{(x = a, y = b)}. Error: if \\spad{P} is singular.") (($ |#4|) "\\spad{divisor(g)} returns the divisor of the function \\spad{g}.") (($ (|FractionalIdeal| |#2| (|Fraction| |#2|) |#3| |#4|)) "\\spad{divisor(I)} makes a divisor \\spad{D} from an ideal \\spad{I}.")) (|ideal| (((|FractionalIdeal| |#2| (|Fraction| |#2|) |#3| |#4|) $) "\\spad{ideal(D)} returns the ideal corresponding to a divisor \\spad{D}."))) NIL NIL @@ -1344,11 +1344,11 @@ NIL ((|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}."))) ((-4502 . T) (-4508 . T) (-4503 . T) ((-4512 "*") . T) (-4504 . T) (-4505 . T) (-4507 . T)) ((-2210 (|HasCategory| (-936 |#1|) (QUOTE (-147))) (|HasCategory| (-936 |#1|) (QUOTE (-381)))) (|HasCategory| (-936 |#1|) (QUOTE (-149))) (|HasCategory| (-936 |#1|) (QUOTE (-381))) (|HasCategory| (-936 |#1|) (QUOTE (-147)))) -(-354 S -1612 UP UPUP) +(-354 S -1613 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."))) NIL ((|HasCategory| |#2| (QUOTE (-381))) (|HasCategory| |#2| (QUOTE (-376)))) -(-355 -1612 UP UPUP) +(-355 -1613 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."))) ((-4503 |has| (-421 |#2|) (-376)) (-4508 |has| (-421 |#2|) (-376)) (-4502 |has| (-421 |#2|) (-376)) ((-4512 "*") . T) (-4504 . T) (-4505 . T) (-4507 . T)) NIL @@ -1384,7 +1384,7 @@ NIL ((|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."))) ((-4502 . T) (-4508 . T) (-4503 . T) ((-4512 "*") . T) (-4504 . T) (-4505 . T) (-4507 . T)) NIL -(-364 R UP -1612) +(-364 R UP -1613) ((|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| $) $) "\\spad{squareFree(x)} returns a square-free factorisation of \\spad{x}"))) NIL NIL @@ -1408,11 +1408,11 @@ NIL ((|constructor| (NIL "This package provides a number of functions for generating,{} counting and testing irreducible,{} normal,{} primitive,{} random polynomials over finite fields.")) (|reducedQPowers| (((|PrimitiveArray| (|SparseUnivariatePolynomial| |#1|)) (|SparseUnivariatePolynomial| |#1|)) "\\spad{reducedQPowers(f)} generates \\spad{[x,x**q,x**(q**2),...,x**(q**(n-1))]} reduced modulo \\spad{f} where \\spad{q = size()\\$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."))) NIL NIL -(-370 -1612 GF) +(-370 -1613 GF) ((|constructor| (NIL "\\spad{FiniteFieldPolynomialPackage2}(\\spad{F},{}GF) exports some functions concerning finite fields,{} which depend on a finite field {\\em GF} and an algebraic extension \\spad{F} of {\\em GF},{} \\spadignore{e.g.} a zero of a polynomial over {\\em GF} in \\spad{F}.")) (|rootOfIrreduciblePoly| ((|#1| (|SparseUnivariatePolynomial| |#2|)) "\\spad{rootOfIrreduciblePoly(f)} computes one root of the monic,{} irreducible polynomial \\spad{f},{} which degree must divide the extension degree of {\\em F} over {\\em GF},{} \\spadignore{i.e.} \\spad{f} splits into linear factors over {\\em F}.")) (|Frobenius| ((|#1| |#1|) "\\spad{Frobenius(x)} \\undocumented{}")) (|basis| (((|Vector| |#1|) (|PositiveInteger|)) "\\spad{basis(n)} \\undocumented{}")) (|lookup| (((|PositiveInteger|) |#1|) "\\spad{lookup(x)} \\undocumented{}")) (|coerce| ((|#1| |#2|) "\\spad{coerce(x)} \\undocumented{}"))) NIL NIL -(-371 -1612 FP FPP) +(-371 -1613 FP FPP) ((|constructor| (NIL "This package solves linear diophantine equations for Bivariate polynomials over finite fields")) (|solveLinearPolynomialEquation| (((|Union| (|List| |#3|) "failed") (|List| |#3|) |#3|) "\\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."))) NIL NIL @@ -1552,7 +1552,7 @@ NIL ((|constructor| (NIL "Code to manipulate Fortran Output Stack")) (|topFortranOutputStack| (((|String|)) "\\spad{topFortranOutputStack()} returns the top element of the Fortran output stack")) (|pushFortranOutputStack| (((|Void|) (|String|)) "\\spad{pushFortranOutputStack(f)} pushes \\spad{f} onto the Fortran output stack") (((|Void|) (|FileName|)) "\\spad{pushFortranOutputStack(f)} pushes \\spad{f} onto the Fortran output stack")) (|popFortranOutputStack| (((|Void|)) "\\spad{popFortranOutputStack()} pops the Fortran output stack")) (|showFortranOutputStack| (((|Stack| (|String|))) "\\spad{showFortranOutputStack()} returns the Fortran output stack")) (|clearFortranOutputStack| (((|Stack| (|String|))) "\\spad{clearFortranOutputStack()} clears the Fortran output stack"))) NIL NIL -(-406 -1612 UP UPUP R) +(-406 -1613 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"))) NIL NIL @@ -1580,7 +1580,7 @@ NIL ((|constructor| (NIL "\\axiomType{FortranProgram} allows the user to build and manipulate simple models of FORTRAN subprograms. These can then be transformed into actual FORTRAN notation.")) (|coerce| (($ (|Equation| (|Expression| (|Complex| (|Float|))))) "\\spad{coerce(eq)} \\undocumented{}") (($ (|Equation| (|Expression| (|Float|)))) "\\spad{coerce(eq)} \\undocumented{}") (($ (|Equation| (|Expression| (|Integer|)))) "\\spad{coerce(eq)} \\undocumented{}") (($ (|Expression| (|Complex| (|Float|)))) "\\spad{coerce(e)} \\undocumented{}") (($ (|Expression| (|Float|))) "\\spad{coerce(e)} \\undocumented{}") (($ (|Expression| (|Integer|))) "\\spad{coerce(e)} \\undocumented{}") (($ (|Equation| (|Expression| (|MachineComplex|)))) "\\spad{coerce(eq)} \\undocumented{}") (($ (|Equation| (|Expression| (|MachineFloat|)))) "\\spad{coerce(eq)} \\undocumented{}") (($ (|Equation| (|Expression| (|MachineInteger|)))) "\\spad{coerce(eq)} \\undocumented{}") (($ (|Expression| (|MachineComplex|))) "\\spad{coerce(e)} \\undocumented{}") (($ (|Expression| (|MachineFloat|))) "\\spad{coerce(e)} \\undocumented{}") (($ (|Expression| (|MachineInteger|))) "\\spad{coerce(e)} \\undocumented{}") (($ (|Record| (|:| |localSymbols| (|SymbolTable|)) (|:| |code| (|List| (|FortranCode|))))) "\\spad{coerce(r)} \\undocumented{}") (($ (|List| (|FortranCode|))) "\\spad{coerce(lfc)} \\undocumented{}") (($ (|FortranCode|)) "\\spad{coerce(fc)} \\undocumented{}"))) NIL NIL -(-413 -1612 UP) +(-413 -1613 UP) ((|constructor| (NIL "\\indented{1}{Full partial fraction expansion of rational functions} Author: Manuel Bronstein Date Created: 9 December 1992 Date Last Updated: June 18,{} 2010 References: \\spad{M}.Bronstein & \\spad{B}.Salvy,{} \\indented{12}{Full Partial Fraction Decomposition of Rational Functions,{}} \\indented{12}{in Proceedings of \\spad{ISSAC'93},{} Kiev,{} ACM Press.}")) (|construct| (($ (|List| (|Record| (|:| |exponent| (|NonNegativeInteger|)) (|:| |center| |#2|) (|:| |num| |#2|)))) "\\spad{construct(l)} is the inverse of fracPart.")) (|fracPart| (((|List| (|Record| (|:| |exponent| (|NonNegativeInteger|)) (|:| |center| |#2|) (|:| |num| |#2|))) $) "\\spad{fracPart(f)} returns the list of summands of the fractional part of \\spad{f}.")) (|polyPart| ((|#2| $) "\\spad{polyPart(f)} returns the polynomial part of \\spad{f}.")) (|fullPartialFraction| (($ (|Fraction| |#2|)) "\\spad{fullPartialFraction(f)} returns \\spad{[p, [[j, Dj, Hj]...]]} such that \\spad{f = p(x) + \\sum_{[j,Dj,Hj] in l} \\sum_{Dj(a)=0} Hj(a)/(x - a)\\^j}.")) (+ (($ |#2| $) "\\spad{p + x} returns the sum of \\spad{p} and \\spad{x}"))) NIL NIL @@ -1636,7 +1636,7 @@ NIL ((|constructor| (NIL "\\indented{2}{A is fully retractable to \\spad{B} means that A is retractable to \\spad{B},{} and,{}} \\indented{2}{in addition,{} if \\spad{B} is retractable to the integers or rational} \\indented{2}{numbers then so is A.} \\indented{2}{In particular,{} what we are asserting is that there are no integers} \\indented{2}{(rationals) in A which don't retract into \\spad{B}.} Date Created: March 1990 Date Last Updated: 9 April 1991"))) NIL NIL -(-427 R -1612 UP A) +(-427 R -1613 UP A) ((|constructor| (NIL "Fractional ideals in a framed algebra.")) (|randomLC| ((|#4| (|NonNegativeInteger|) (|Vector| |#4|)) "\\spad{randomLC(n,x)} should be local but conditional.")) (|minimize| (($ $) "\\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)}."))) ((-4507 . T)) NIL @@ -1644,7 +1644,7 @@ NIL ((|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{}"))) NIL NIL -(-429 R -1612 UP A |ibasis|) +(-429 R -1613 UP A |ibasis|) ((|constructor| (NIL "Module representation of fractional ideals.")) (|module| (($ (|FractionalIdeal| |#1| |#2| |#3| |#4|)) "\\spad{module(I)} returns \\spad{I} viewed has a module over \\spad{R}.") (($ (|Vector| |#4|)) "\\spad{module([f1,...,fn])} = the module generated by \\spad{(f1,...,fn)} over \\spad{R}.")) (|norm| ((|#2| $) "\\spad{norm(f)} returns the norm of the module \\spad{f}.")) (|basis| (((|Vector| |#4|) $) "\\spad{basis((f1,...,fn))} = the vector \\spad{[f1,...,fn]}."))) NIL ((|HasCategory| |#4| (|%list| (QUOTE -1070) (|devaluate| |#2|)))) @@ -1696,7 +1696,7 @@ NIL ((|constructor| (NIL "\\spad{FiniteSetAggregateFunctions2} provides functions involving two finite set aggregates where the underlying domains might be different. An example of this is to create a set of rational numbers by mapping a function across a set of integers,{} where the function divides each integer by 1000.")) (|scan| ((|#4| (|Mapping| |#3| |#1| |#3|) |#2| |#3|) "\\spad{scan(f,a,r)} successively applies \\spad{reduce(f,x,r)} to more and more leading sub-aggregates \\spad{x} of aggregate \\spad{a}. More precisely,{} if \\spad{a} is \\spad{[a1,a2,...]},{} then \\spad{scan(f,a,r)} returns \\spad {[reduce(f,[a1],r),reduce(f,[a1,a2],r),...]}.")) (|reduce| ((|#3| (|Mapping| |#3| |#1| |#3|) |#2| |#3|) "\\spad{reduce(f,a,r)} applies function \\spad{f} to each successive element of the aggregate \\spad{a} and an accumulant initialised to \\spad{r}. For example,{} \\spad{reduce(_+\\$Integer,[1,2,3],0)} does a \\spad{3+(2+(1+0))}. Note: third argument \\spad{r} may be regarded as an identity element for the function.")) (|map| ((|#4| (|Mapping| |#3| |#1|) |#2|) "\\spad{map(f,a)} applies function \\spad{f} to each member of aggregate \\spad{a},{} creating a new aggregate with a possibly different underlying domain."))) NIL NIL -(-442 R -1612) +(-442 R -1613) ((|constructor| (NIL "\\spadtype{FunctionSpaceComplexIntegration} provides functions for the indefinite integration of complex-valued functions.")) (|complexIntegrate| ((|#2| |#2| (|Symbol|)) "\\spad{complexIntegrate(f, x)} returns the integral of \\spad{f(x)dx} where \\spad{x} is viewed as a complex variable.")) (|internalIntegrate0| (((|IntegrationResult| |#2|) |#2| (|Symbol|)) "\\spad{internalIntegrate0 should} be a local function,{} but is conditional.")) (|internalIntegrate| (((|IntegrationResult| |#2|) |#2| (|Symbol|)) "\\spad{internalIntegrate(f, x)} returns the integral of \\spad{f(x)dx} where \\spad{x} is viewed as a complex variable."))) NIL NIL @@ -1704,19 +1704,19 @@ NIL ((|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"))) ((-4497 -12 (|has| |#1| (-6 -4497)) (|has| |#2| (-6 -4497))) (-4504 . T) (-4505 . T) (-4507 . T)) ((-12 (|HasAttribute| |#1| (QUOTE -4497)) (|HasAttribute| |#2| (QUOTE -4497)))) -(-444 R -1612) +(-444 R -1613) ((|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."))) NIL NIL -(-445 R -1612) +(-445 R -1613) ((|constructor| (NIL "Provides some special functions over an integral domain.")) (|iiabs| ((|#2| |#2|) "\\spad{iiabs(x)} should be local but conditional.")) (|iiGamma| ((|#2| |#2|) "\\spad{iiGamma(x)} should be local but conditional.")) (|airyBi| ((|#2| |#2|) "\\spad{airyBi(x)} returns the airybi function applied to \\spad{x}")) (|airyAi| ((|#2| |#2|) "\\spad{airyAi(x)} returns the airyai function applied to \\spad{x}")) (|besselK| ((|#2| |#2| |#2|) "\\spad{besselK(x,y)} returns the besselk function applied to \\spad{x} and \\spad{y}")) (|besselI| ((|#2| |#2| |#2|) "\\spad{besselI(x,y)} returns the besseli function applied to \\spad{x} and \\spad{y}")) (|besselY| ((|#2| |#2| |#2|) "\\spad{besselY(x,y)} returns the bessely function applied to \\spad{x} and \\spad{y}")) (|besselJ| ((|#2| |#2| |#2|) "\\spad{besselJ(x,y)} returns the besselj function applied to \\spad{x} and \\spad{y}")) (|polygamma| ((|#2| |#2| |#2|) "\\spad{polygamma(x,y)} returns the polygamma function applied to \\spad{x} and \\spad{y}")) (|digamma| ((|#2| |#2|) "\\spad{digamma(x)} returns the digamma function applied to \\spad{x}")) (|Beta| ((|#2| |#2| |#2|) "\\spad{Beta(x,y)} returns the beta function applied to \\spad{x} and \\spad{y}")) (|Gamma| ((|#2| |#2| |#2|) "\\spad{Gamma(a,x)} returns the incomplete Gamma function applied to a and \\spad{x}") ((|#2| |#2|) "\\spad{Gamma(f)} returns the formal Gamma function applied to \\spad{f}")) (|abs| ((|#2| |#2|) "\\spad{abs(f)} returns the absolute value operator applied to \\spad{f}")) (|operator| (((|BasicOperator|) (|BasicOperator|)) "\\spad{operator(op)} returns a copy of \\spad{op} with the domain-dependent properties appropriate for \\spad{F}; error if \\spad{op} is not a special function operator")) (|belong?| (((|Boolean|) (|BasicOperator|)) "\\spad{belong?(op)} is \\spad{true} if \\spad{op} is a special function operator."))) NIL NIL -(-446 R -1612) +(-446 R -1613) ((|constructor| (NIL "FunctionsSpacePrimitiveElement provides functions to compute primitive elements in functions spaces.")) (|primitiveElement| (((|Record| (|:| |primelt| |#2|) (|:| |pol1| (|SparseUnivariatePolynomial| |#2|)) (|:| |pol2| (|SparseUnivariatePolynomial| |#2|)) (|:| |prim| (|SparseUnivariatePolynomial| |#2|))) |#2| |#2|) "\\spad{primitiveElement(a1, a2)} returns \\spad{[a, q1, q2, q]} such that \\spad{k(a1, a2) = k(a)},{} \\spad{ai = qi(a)},{} and \\spad{q(a) = 0}. The minimal polynomial for \\spad{a2} may involve \\spad{a1},{} but the minimal polynomial for \\spad{a1} may not involve \\spad{a2}; This operations uses \\spadfun{resultant}.") (((|Record| (|:| |primelt| |#2|) (|:| |poly| (|List| (|SparseUnivariatePolynomial| |#2|))) (|:| |prim| (|SparseUnivariatePolynomial| |#2|))) (|List| |#2|)) "\\spad{primitiveElement([a1,...,an])} returns \\spad{[a, [q1,...,qn], q]} such that then \\spad{k(a1,...,an) = k(a)},{} \\spad{ai = qi(a)},{} and \\spad{q(a) = 0}. This operation uses the technique of \\spadglossSee{groebner bases}{Groebner basis}."))) NIL ((|HasCategory| |#2| (QUOTE (-27)))) -(-447 R -1612) +(-447 R -1613) ((|constructor| (NIL "This package provides function which replaces transcendental kernels in a function space by random integers. The correspondence between the kernels and the integers is fixed between calls to new().")) (|newReduc| (((|Void|)) "\\spad{newReduc()} \\undocumented")) (|bringDown| (((|SparseUnivariatePolynomial| (|Fraction| (|Integer|))) |#2| (|Kernel| |#2|)) "\\spad{bringDown(f,k)} \\undocumented") (((|Fraction| (|Integer|)) |#2|) "\\spad{bringDown(f)} \\undocumented"))) NIL NIL @@ -1724,7 +1724,7 @@ NIL ((|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\""))) NIL NIL -(-449 R -1612 UP) +(-449 R -1613 UP) ((|constructor| (NIL "\\indented{1}{Used internally by IR2F} Author: Manuel Bronstein Date Created: 12 May 1988 Date Last Updated: 22 September 1993 Keywords: function,{} space,{} polynomial,{} factoring")) (|anfactor| (((|Union| (|Factored| (|SparseUnivariatePolynomial| (|AlgebraicNumber|))) "failed") |#3|) "\\spad{anfactor(p)} tries to factor \\spad{p} over algebraic numbers,{} returning \"failed\" if it cannot")) (|UP2ifCan| (((|Union| (|:| |overq| (|SparseUnivariatePolynomial| (|Fraction| (|Integer|)))) (|:| |overan| (|SparseUnivariatePolynomial| (|AlgebraicNumber|))) (|:| |failed| (|Boolean|))) |#3|) "\\spad{UP2ifCan(x)} should be local but conditional.")) (|qfactor| (((|Union| (|Factored| (|SparseUnivariatePolynomial| (|Fraction| (|Integer|)))) "failed") |#3|) "\\spad{qfactor(p)} tries to factor \\spad{p} over fractions of integers,{} returning \"failed\" if it cannot")) (|ffactor| (((|Factored| |#3|) |#3|) "\\spad{ffactor(p)} tries to factor a univariate polynomial \\spad{p} over \\spad{F}"))) NIL ((|HasCategory| |#2| (|%list| (QUOTE -1070) (QUOTE (-48))))) @@ -1756,7 +1756,7 @@ NIL ((|constructor| (NIL "\\spadtype{GaloisGroupFactorizer} provides functions to factor resolvents.")) (|btwFact| (((|Record| (|:| |contp| (|Integer|)) (|:| |factors| (|List| (|Record| (|:| |irr| |#1|) (|:| |pow| (|Integer|)))))) |#1| (|Boolean|) (|Set| (|NonNegativeInteger|)) (|NonNegativeInteger|)) "\\spad{btwFact(p,sqf,pd,r)} returns the factorization of \\spad{p},{} the result is a Record such that \\spad{contp=}content \\spad{p},{} \\spad{factors=}List of irreducible factors of \\spad{p} with exponent. If \\spad{sqf=true} the polynomial is assumed to be square free (\\spadignore{i.e.} without repeated factors). \\spad{pd} is the \\spadtype{Set} of possible degrees. \\spad{r} is a lower bound for the number of factors of \\spad{p}. Please do not use this function in your code because its design may change.")) (|henselFact| (((|Record| (|:| |contp| (|Integer|)) (|:| |factors| (|List| (|Record| (|:| |irr| |#1|) (|:| |pow| (|Integer|)))))) |#1| (|Boolean|)) "\\spad{henselFact(p,sqf)} returns the factorization of \\spad{p},{} the result is a Record such that \\spad{contp=}content \\spad{p},{} \\spad{factors=}List of irreducible factors of \\spad{p} with exponent. If \\spad{sqf=true} the polynomial is assumed to be square free (\\spadignore{i.e.} without repeated factors).")) (|factorOfDegree| (((|Union| |#1| "failed") (|PositiveInteger|) |#1| (|List| (|NonNegativeInteger|)) (|NonNegativeInteger|) (|Boolean|)) "\\spad{factorOfDegree(d,p,listOfDegrees,r,sqf)} returns a factor of \\spad{p} of degree \\spad{d} knowing that \\spad{p} has for possible splitting of its degree \\spad{listOfDegrees},{} and that \\spad{p} has at least \\spad{r} factors. If \\spad{sqf=true} the polynomial is assumed to be square free (\\spadignore{i.e.} without repeated factors).") (((|Union| |#1| "failed") (|PositiveInteger|) |#1| (|List| (|NonNegativeInteger|)) (|NonNegativeInteger|)) "\\spad{factorOfDegree(d,p,listOfDegrees,r)} returns a factor of \\spad{p} of degree \\spad{d} knowing that \\spad{p} has for possible splitting of its degree \\spad{listOfDegrees},{} and that \\spad{p} has at least \\spad{r} factors.") (((|Union| |#1| "failed") (|PositiveInteger|) |#1| (|List| (|NonNegativeInteger|))) "\\spad{factorOfDegree(d,p,listOfDegrees)} returns a factor of \\spad{p} of degree \\spad{d} knowing that \\spad{p} has for possible splitting of its degree \\spad{listOfDegrees}.") (((|Union| |#1| "failed") (|PositiveInteger|) |#1| (|NonNegativeInteger|)) "\\spad{factorOfDegree(d,p,r)} returns a factor of \\spad{p} of degree \\spad{d} knowing that \\spad{p} has at least \\spad{r} factors.") (((|Union| |#1| "failed") (|PositiveInteger|) |#1|) "\\spad{factorOfDegree(d,p)} returns a factor of \\spad{p} of degree \\spad{d}.")) (|factorSquareFree| (((|Factored| |#1|) |#1| (|NonNegativeInteger|) (|NonNegativeInteger|)) "\\spad{factorSquareFree(p,d,r)} factorizes the polynomial \\spad{p} using the single factor bound algorithm,{} knowing that \\spad{d} divides the degree of all factors of \\spad{p} and that \\spad{p} has at least \\spad{r} factors. \\spad{f} is supposed not having any repeated factor (this is not checked).") (((|Factored| |#1|) |#1| (|List| (|NonNegativeInteger|)) (|NonNegativeInteger|)) "\\spad{factorSquareFree(p,listOfDegrees,r)} factorizes the polynomial \\spad{p} using the single factor bound algorithm,{} knowing that \\spad{p} has for possible splitting of its degree \\spad{listOfDegrees} and that \\spad{p} has at least \\spad{r} factors. \\spad{f} is supposed not having any repeated factor (this is not checked).") (((|Factored| |#1|) |#1| (|List| (|NonNegativeInteger|))) "\\spad{factorSquareFree(p,listOfDegrees)} factorizes the polynomial \\spad{p} using the single factor bound algorithm and knowing that \\spad{p} has for possible splitting of its degree \\spad{listOfDegrees}. \\spad{f} is supposed not having any repeated factor (this is not checked).") (((|Factored| |#1|) |#1| (|NonNegativeInteger|)) "\\spad{factorSquareFree(p,r)} factorizes the polynomial \\spad{p} using the single factor bound algorithm and knowing that \\spad{p} has at least \\spad{r} factors. \\spad{f} is supposed not having any repeated factor (this is not checked).") (((|Factored| |#1|) |#1|) "\\spad{factorSquareFree(p)} returns the factorization of \\spad{p} which is supposed not having any repeated factor (this is not checked).")) (|factor| (((|Factored| |#1|) |#1| (|NonNegativeInteger|) (|NonNegativeInteger|)) "\\spad{factor(p,d,r)} factorizes the polynomial \\spad{p} using the single factor bound algorithm,{} knowing that \\spad{d} divides the degree of all factors of \\spad{p} and that \\spad{p} has at least \\spad{r} factors.") (((|Factored| |#1|) |#1| (|List| (|NonNegativeInteger|)) (|NonNegativeInteger|)) "\\spad{factor(p,listOfDegrees,r)} factorizes the polynomial \\spad{p} using the single factor bound algorithm,{} knowing that \\spad{p} has for possible splitting of its degree \\spad{listOfDegrees} and that \\spad{p} has at least \\spad{r} factors.") (((|Factored| |#1|) |#1| (|List| (|NonNegativeInteger|))) "\\spad{factor(p,listOfDegrees)} factorizes the polynomial \\spad{p} using the single factor bound algorithm and knowing that \\spad{p} has for possible splitting of its degree \\spad{listOfDegrees}.") (((|Factored| |#1|) |#1| (|NonNegativeInteger|)) "\\spad{factor(p,r)} factorizes the polynomial \\spad{p} using the single factor bound algorithm and knowing that \\spad{p} has at least \\spad{r} factors.") (((|Factored| |#1|) |#1|) "\\spad{factor(p)} returns the factorization of \\spad{p} over the integers.")) (|tryFunctionalDecomposition| (((|Boolean|) (|Boolean|)) "\\spad{tryFunctionalDecomposition(b)} chooses whether factorizers have to look for functional decomposition of polynomials (\\spad{true}) or not (\\spad{false}). Returns the previous value.")) (|tryFunctionalDecomposition?| (((|Boolean|)) "\\spad{tryFunctionalDecomposition?()} returns \\spad{true} if factorizers try functional decomposition of polynomials before factoring them.")) (|eisensteinIrreducible?| (((|Boolean|) |#1|) "\\spad{eisensteinIrreducible?(p)} returns \\spad{true} if \\spad{p} can be shown to be irreducible by Eisenstein's criterion,{} \\spad{false} is inconclusive.")) (|useEisensteinCriterion| (((|Boolean|) (|Boolean|)) "\\spad{useEisensteinCriterion(b)} chooses whether factorizers check Eisenstein's criterion before factoring: \\spad{true} for using it,{} \\spad{false} else. Returns the previous value.")) (|useEisensteinCriterion?| (((|Boolean|)) "\\spad{useEisensteinCriterion?()} returns \\spad{true} if factorizers check Eisenstein's criterion before factoring.")) (|useSingleFactorBound| (((|Boolean|) (|Boolean|)) "\\spad{useSingleFactorBound(b)} chooses the algorithm to be used by the factorizers: \\spad{true} for algorithm with single factor bound,{} \\spad{false} for algorithm with overall bound. Returns the previous value.")) (|useSingleFactorBound?| (((|Boolean|)) "\\spad{useSingleFactorBound?()} returns \\spad{true} if algorithm with single factor bound is used for factorization,{} \\spad{false} for algorithm with overall bound.")) (|modularFactor| (((|Record| (|:| |prime| (|Integer|)) (|:| |factors| (|List| |#1|))) |#1|) "\\spad{modularFactor(f)} chooses a \"good\" prime and returns the factorization of \\spad{f} modulo this prime in a form that may be used by \\spadfunFrom{completeHensel}{GeneralHenselPackage}. If prime is zero it means that \\spad{f} has been proved to be irreducible over the integers or that \\spad{f} is a unit (\\spadignore{i.e.} 1 or \\spad{-1}). \\spad{f} shall be primitive (\\spadignore{i.e.} content(\\spad{p})\\spad{=1}) and square free (\\spadignore{i.e.} without repeated factors).")) (|numberOfFactors| (((|NonNegativeInteger|) (|List| (|Record| (|:| |factor| |#1|) (|:| |degree| (|Integer|))))) "\\spad{numberOfFactors(ddfactorization)} returns the number of factors of the polynomial \\spad{f} modulo \\spad{p} where \\spad{ddfactorization} is the distinct degree factorization of \\spad{f} computed by \\spadfunFrom{ddFact}{ModularDistinctDegreeFactorizer} for some prime \\spad{p}.")) (|stopMusserTrials| (((|PositiveInteger|) (|PositiveInteger|)) "\\spad{stopMusserTrials(n)} sets to \\spad{n} the bound on the number of factors for which \\spadfun{modularFactor} stops to look for an other prime. You will have to remember that the step of recombining the extraneous factors may take up to \\spad{2**n} trials. Returns the previous value.") (((|PositiveInteger|)) "\\spad{stopMusserTrials()} returns the bound on the number of factors for which \\spadfun{modularFactor} stops to look for an other prime. You will have to remember that the step of recombining the extraneous factors may take up to \\spad{2**stopMusserTrials()} trials.")) (|musserTrials| (((|PositiveInteger|) (|PositiveInteger|)) "\\spad{musserTrials(n)} sets to \\spad{n} the number of primes to be tried in \\spadfun{modularFactor} and returns the previous value.") (((|PositiveInteger|)) "\\spad{musserTrials()} returns the number of primes that are tried in \\spadfun{modularFactor}.")) (|degreePartition| (((|Multiset| (|NonNegativeInteger|)) (|List| (|Record| (|:| |factor| |#1|) (|:| |degree| (|Integer|))))) "\\spad{degreePartition(ddfactorization)} returns the degree partition of the polynomial \\spad{f} modulo \\spad{p} where \\spad{ddfactorization} is the distinct degree factorization of \\spad{f} computed by \\spadfunFrom{ddFact}{ModularDistinctDegreeFactorizer} for some prime \\spad{p}.")) (|makeFR| (((|Factored| |#1|) (|Record| (|:| |contp| (|Integer|)) (|:| |factors| (|List| (|Record| (|:| |irr| |#1|) (|:| |pow| (|Integer|))))))) "\\spad{makeFR(flist)} turns the final factorization of henselFact into a \\spadtype{Factored} object."))) NIL NIL -(-457 R UP -1612) +(-457 R UP -1613) ((|constructor| (NIL "\\spadtype{GaloisGroupFactorizationUtilities} provides functions that will be used by the factorizer.")) (|length| ((|#3| |#2|) "\\spad{length(p)} returns the sum of the absolute values of the coefficients of the polynomial \\spad{p}.")) (|height| ((|#3| |#2|) "\\spad{height(p)} returns the maximal absolute value of the coefficients of the polynomial \\spad{p}.")) (|infinityNorm| ((|#3| |#2|) "\\spad{infinityNorm(f)} returns the maximal absolute value of the coefficients of the polynomial \\spad{f}.")) (|quadraticNorm| ((|#3| |#2|) "\\spad{quadraticNorm(f)} returns the \\spad{l2} norm of the polynomial \\spad{f}.")) (|norm| ((|#3| |#2| (|PositiveInteger|)) "\\spad{norm(f,p)} returns the lp norm of the polynomial \\spad{f}.")) (|singleFactorBound| (((|Integer|) |#2|) "\\spad{singleFactorBound(p,r)} returns a bound on the infinite norm of the factor of \\spad{p} with smallest Bombieri's norm. \\spad{p} shall be of degree higher or equal to 2.") (((|Integer|) |#2| (|NonNegativeInteger|)) "\\spad{singleFactorBound(p,r)} returns a bound on the infinite norm of the factor of \\spad{p} with smallest Bombieri's norm. \\spad{r} is a lower bound for the number of factors of \\spad{p}. \\spad{p} shall be of degree higher or equal to 2.")) (|rootBound| (((|Integer|) |#2|) "\\spad{rootBound(p)} returns a bound on the largest norm of the complex roots of \\spad{p}.")) (|bombieriNorm| ((|#3| |#2| (|PositiveInteger|)) "\\spad{bombieriNorm(p,n)} returns the \\spad{n}th Bombieri's norm of \\spad{p}.") ((|#3| |#2|) "\\spad{bombieriNorm(p)} returns quadratic Bombieri's norm of \\spad{p}.")) (|beauzamyBound| (((|Integer|) |#2|) "\\spad{beauzamyBound(p)} returns a bound on the larger coefficient of any factor of \\spad{p}."))) NIL NIL @@ -1868,7 +1868,7 @@ NIL ((|constructor| (NIL "GradedModule(\\spad{R},{}\\spad{E}) denotes ``E-graded \\spad{R}-module'',{} \\spadignore{i.e.} collection of \\spad{R}-modules indexed by an abelian monoid \\spad{E}. An element \\spad{g} of \\spad{G[s]} for some specific \\spad{s} in \\spad{E} is said to be an element of \\spad{G} with {\\em degree} \\spad{s}. Sums are defined in each module \\spad{G[s]} so two elements of \\spad{G} have a sum if they have the same degree. \\blankline Morphisms can be defined and composed by degree to give the mathematical category of graded modules.")) (+ (($ $ $) "\\spad{g+h} is the sum of \\spad{g} and \\spad{h} in the module of elements of the same degree as \\spad{g} and \\spad{h}. Error: if \\spad{g} and \\spad{h} have different degrees.")) (- (($ $ $) "\\spad{g-h} is the difference of \\spad{g} and \\spad{h} in the module of elements of the same degree as \\spad{g} and \\spad{h}. Error: if \\spad{g} and \\spad{h} have different degrees.") (($ $) "\\spad{-g} is the additive inverse of \\spad{g} in the module of elements of the same grade as \\spad{g}.")) (* (($ $ |#1|) "\\spad{g*r} is right module multiplication.") (($ |#1| $) "\\spad{r*g} is left module multiplication.")) ((|Zero|) (($) "0 denotes the zero of degree 0.")) (|degree| ((|#2| $) "\\spad{degree(g)} names the degree of \\spad{g}. The set of all elements of a given degree form an \\spad{R}-module."))) NIL NIL -(-485 |lv| -1612 R) +(-485 |lv| -1613 R) ((|constructor| (NIL "\\indented{1}{Author : \\spad{P}.Gianni,{} Summer \\spad{'88},{} revised November \\spad{'89}} Solve systems of polynomial equations using Groebner bases Total order Groebner bases are computed and then converted to lex ones This package is mostly intended for internal use.")) (|genericPosition| (((|Record| (|:| |dpolys| (|List| (|DistributedMultivariatePolynomial| |#1| |#2|))) (|:| |coords| (|List| (|Integer|)))) (|List| (|DistributedMultivariatePolynomial| |#1| |#2|)) (|List| (|OrderedVariableList| |#1|))) "\\spad{genericPosition(lp,lv)} puts a radical zero dimensional ideal in general position,{} for system \\spad{lp} in variables \\spad{lv}.")) (|testDim| (((|Union| (|List| (|HomogeneousDistributedMultivariatePolynomial| |#1| |#2|)) "failed") (|List| (|HomogeneousDistributedMultivariatePolynomial| |#1| |#2|)) (|List| (|OrderedVariableList| |#1|))) "\\spad{testDim(lp,lv)} tests if the polynomial system \\spad{lp} in variables \\spad{lv} is zero dimensional.")) (|groebSolve| (((|List| (|List| (|DistributedMultivariatePolynomial| |#1| |#2|))) (|List| (|DistributedMultivariatePolynomial| |#1| |#2|)) (|List| (|OrderedVariableList| |#1|))) "\\spad{groebSolve(lp,lv)} reduces the polynomial system \\spad{lp} in variables \\spad{lv} to triangular form. Algorithm based on groebner bases algorithm with linear algebra for change of ordering. Preprocessing for the general solver. The polynomials in input are of type \\spadtype{DMP}."))) NIL NIL @@ -1883,7 +1883,7 @@ NIL (-488 |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."))) (((-4512 "*") |has| |#1| (-175)) (-4503 |has| |#1| (-571)) (-4508 |has| |#1| (-376)) (-4502 |has| |#1| (-376)) (-4504 . T) (-4505 . T) (-4507 . 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(QUOTE (-1081)))) (-12 (|HasCategory| |#2| (QUOTE (-1081))) (|HasCategory| |#2| (|%list| (QUOTE -930) (QUOTE (-1209))))) (-2210 (|HasCategory| |#2| (QUOTE (-1081))) (-12 (|HasCategory| |#2| (QUOTE (-1133))) (|HasCategory| |#2| (|%list| (QUOTE -1070) (QUOTE (-560)))))) (-12 (|HasCategory| |#2| (QUOTE (-1133))) (|HasCategory| |#2| (|%list| (QUOTE -1070) (QUOTE (-560))))) (-12 (|HasCategory| |#2| (|%list| (QUOTE -1070) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#2| (QUOTE (-1133)))) (|HasAttribute| |#2| (QUOTE -4507)) (-12 (|HasCategory| |#2| (QUOTE (-240))) (|HasCategory| |#2| (QUOTE (-1081)))) (-12 (|HasCategory| |#2| (QUOTE (-1081))) (|HasCategory| |#2| (|%list| (QUOTE -928) (QUOTE (-1209))))) (|HasCategory| |#2| (QUOTE (-175))) (|HasCategory| |#2| (QUOTE (-23))) (|HasCategory| |#2| (QUOTE (-133))) (|HasCategory| |#2| (QUOTE (-25))) (|HasCategory| |#2| (|%list| (QUOTE -632) (QUOTE (-888)))) (|HasCategory| |#2| (QUOTE (-102))) (-12 (|HasCategory| |#2| (QUOTE (-1133))) (|HasCategory| |#2| (|%list| (QUOTE -321) (|devaluate| |#2|))))) @@ -1924,7 +1924,7 @@ NIL ((|constructor| (NIL "Heap implemented in a flexible array to allow for insertions")) (|heap| (($ (|List| |#1|)) "\\spad{heap(ls)} creates a heap of elements consisting of the elements of \\spad{ls}."))) ((-4510 . T) (-4511 . T)) ((-12 (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1133))) (-2210 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-1133)))) (-2210 (-12 (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-888))))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-888)))) (|HasCategory| |#1| (QUOTE (-102)))) -(-499 -1612 UP UPUP R) +(-499 -1613 UP UPUP R) ((|constructor| (NIL "This domains implements finite rational divisors on an hyperelliptic curve,{} that is finite formal sums SUM(\\spad{n} * \\spad{P}) where the \\spad{n}'s are integers and the \\spad{P}'s are finite rational points on the curve. The equation of the curve must be \\spad{y^2} = \\spad{f}(\\spad{x}) and \\spad{f} must have odd degree."))) NIL NIL @@ -1960,7 +1960,7 @@ NIL ((|constructor| (NIL "Category for the hyperbolic trigonometric functions.")) (|tanh| (($ $) "\\spad{tanh(x)} returns the hyperbolic tangent of \\spad{x}.")) (|sinh| (($ $) "\\spad{sinh(x)} returns the hyperbolic sine of \\spad{x}.")) (|sech| (($ $) "\\spad{sech(x)} returns the hyperbolic secant of \\spad{x}.")) (|csch| (($ $) "\\spad{csch(x)} returns the hyperbolic cosecant of \\spad{x}.")) (|coth| (($ $) "\\spad{coth(x)} returns the hyperbolic cotangent of \\spad{x}.")) (|cosh| (($ $) "\\spad{cosh(x)} returns the hyperbolic cosine of \\spad{x}."))) NIL NIL -(-508 -1612 UP |AlExt| |AlPol|) +(-508 -1613 UP |AlExt| |AlPol|) ((|constructor| (NIL "Factorization of univariate polynomials with coefficients in an algebraic extension of a field over which we can factor UP's.")) (|factor| (((|Factored| |#4|) |#4| (|Mapping| (|Factored| |#2|) |#2|)) "\\spad{factor(p, f)} returns a prime factorisation of \\spad{p}; \\spad{f} is a factorisation map for elements of UP."))) NIL NIL @@ -1980,7 +1980,7 @@ NIL ((|constructor| (NIL "\\indented{1}{Author: Clifton Williamson} Date Created: 9 August 1993 Date Last Updated: 3 December 1993 Basic Operations: chineseRemainder,{} factorList Related Domains: PAdicWildFunctionFieldIntegralBasis(\\spad{K},{}\\spad{R},{}UP,{}\\spad{F}) Also See: WildFunctionFieldIntegralBasis,{} FunctionFieldIntegralBasis AMS Classifications: Keywords: function field,{} finite field,{} integral basis Examples: References: Description:")) (|chineseRemainder| (((|Record| (|:| |basis| (|Matrix| |#2|)) (|:| |basisDen| |#2|) (|:| |basisInv| (|Matrix| |#2|))) (|List| |#3|) (|List| (|Record| (|:| |basis| (|Matrix| |#2|)) (|:| |basisDen| |#2|) (|:| |basisInv| (|Matrix| |#2|)))) (|NonNegativeInteger|)) "\\spad{chineseRemainder(lu,lr,n)} \\undocumented")) (|listConjugateBases| (((|List| (|Record| (|:| |basis| (|Matrix| |#2|)) (|:| |basisDen| |#2|) (|:| |basisInv| (|Matrix| |#2|)))) (|Record| (|:| |basis| (|Matrix| |#2|)) (|:| |basisDen| |#2|) (|:| |basisInv| (|Matrix| |#2|))) (|NonNegativeInteger|) (|NonNegativeInteger|)) "\\spad{listConjugateBases(bas,q,n)} returns the list \\spad{[bas,bas^Frob,bas^(Frob^2),...bas^(Frob^(n-1))]},{} where \\spad{Frob} raises the coefficients of all polynomials appearing in the basis \\spad{bas} to the \\spad{q}th power.")) (|factorList| (((|List| (|SparseUnivariatePolynomial| |#1|)) |#1| (|NonNegativeInteger|) (|NonNegativeInteger|) (|NonNegativeInteger|)) "\\spad{factorList(k,n,m,j)} \\undocumented"))) NIL NIL -(-513 R UP -1612) +(-513 R UP -1613) ((|constructor| (NIL "This package contains functions used in the packages FunctionFieldIntegralBasis and NumberFieldIntegralBasis.")) (|moduleSum| (((|Record| (|:| |basis| (|Matrix| |#1|)) (|:| |basisDen| |#1|) (|:| |basisInv| (|Matrix| |#1|))) (|Record| (|:| |basis| (|Matrix| |#1|)) (|:| |basisDen| |#1|) (|:| |basisInv| (|Matrix| |#1|))) (|Record| (|:| |basis| (|Matrix| |#1|)) (|:| |basisDen| |#1|) (|:| |basisInv| (|Matrix| |#1|)))) "\\spad{moduleSum(m1,m2)} returns the sum of two modules in the framed algebra \\spad{F}. Each module \\spad{mi} is represented as follows: \\spad{F} is a framed algebra with \\spad{R}-module basis \\spad{w1,w2,...,wn} and \\spad{mi} is a record \\spad{[basis,basisDen,basisInv]}. If \\spad{basis} is the matrix \\spad{(aij, i = 1..n, j = 1..n)},{} then a basis \\spad{v1,...,vn} for \\spad{mi} is given by \\spad{vi = (1/basisDen) * sum(aij * wj, j = 1..n)},{} \\spadignore{i.e.} the \\spad{i}th row of '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)}.")) (|idealiserMatrix| (((|Matrix| |#1|) (|Matrix| |#1|) (|Matrix| |#1|)) "\\spad{idealiserMatrix(m1, m2)} returns the matrix representing the linear conditions on the Ring associatied with an ideal defined by \\spad{m1} and \\spad{m2}.")) (|idealiser| (((|Matrix| |#1|) (|Matrix| |#1|) (|Matrix| |#1|) |#1|) "\\spad{idealiser(m1,m2,d)} computes the order of an ideal defined by \\spad{m1} and \\spad{m2} where \\spad{d} is the known part of the denominator") (((|Matrix| |#1|) (|Matrix| |#1|) (|Matrix| |#1|)) "\\spad{idealiser(m1,m2)} computes the order of an ideal defined by \\spad{m1} and \\spad{m2}")) (|leastPower| (((|NonNegativeInteger|) (|NonNegativeInteger|) (|NonNegativeInteger|)) "\\spad{leastPower(p,n)} returns \\spad{e},{} where \\spad{e} is the smallest integer such that \\spad{p **e >= n}")) (|divideIfCan!| ((|#1| (|Matrix| |#1|) (|Matrix| |#1|) |#1| (|Integer|)) "\\spad{divideIfCan!(matrix,matrixOut,prime,n)} attempts to divide the entries of \\spad{matrix} by \\spad{prime} and store the result in \\spad{matrixOut}. If it is successful,{} 1 is returned and if not,{} \\spad{prime} is returned. Here both \\spad{matrix} and \\spad{matrixOut} are \\spad{n}-by-\\spad{n} upper triangular matrices.")) (|matrixGcd| ((|#1| (|Matrix| |#1|) |#1| (|NonNegativeInteger|)) "\\spad{matrixGcd(mat,sing,n)} is \\spad{gcd(sing,g)} where \\spad{g} is the gcd of the entries of the \\spad{n}-by-\\spad{n} upper-triangular matrix \\spad{mat}.")) (|diagonalProduct| ((|#1| (|Matrix| |#1|)) "\\spad{diagonalProduct(m)} returns the product of the elements on the diagonal of the matrix \\spad{m}")) (|squareFree| (((|Factored| $) $) "\\spad{squareFree(x)} returns a square-free factorisation of \\spad{x}"))) NIL NIL @@ -2000,7 +2000,7 @@ NIL ((|constructor| (NIL "InnerCommonDenominator provides functions to compute the common denominator of a finite linear aggregate of elements of the quotient field of an integral domain.")) (|splitDenominator| (((|Record| (|:| |num| |#3|) (|:| |den| |#1|)) |#4|) "\\spad{splitDenominator([q1,...,qn])} returns \\spad{[[p1,...,pn], d]} such that \\spad{qi = pi/d} and \\spad{d} is a common denominator for the \\spad{qi}'s.")) (|clearDenominator| ((|#3| |#4|) "\\spad{clearDenominator([q1,...,qn])} returns \\spad{[p1,...,pn]} such that \\spad{qi = pi/d} where \\spad{d} is a common denominator for the \\spad{qi}'s.")) (|commonDenominator| ((|#1| |#4|) "\\spad{commonDenominator([q1,...,qn])} returns a common denominator \\spad{d} for \\spad{q1},{}...,{}qn."))) NIL NIL -(-518 -1612 |Expon| |VarSet| |DPoly|) +(-518 -1613 |Expon| |VarSet| |DPoly|) ((|constructor| (NIL "This domain represents polynomial ideals with coefficients in any field and supports the basic ideal operations,{} including intersection sum and quotient. An ideal is represented by a list of polynomials (the generators of the ideal) and a boolean that is \\spad{true} if the generators are a Groebner basis. The algorithms used are based on Groebner basis computations. The ordering is determined by the datatype of the input polynomials. Users may use refinements of total degree orderings.")) (|relationsIdeal| (((|SuchThat| (|List| (|Polynomial| |#1|)) (|List| (|Equation| (|Polynomial| |#1|)))) (|List| |#4|)) "\\spad{relationsIdeal(polyList)} returns the ideal of relations among the polynomials in \\spad{polyList}.")) (|saturate| (($ $ |#4| (|List| |#3|)) "\\spad{saturate(I,f,lvar)} is the saturation with respect to the prime principal ideal which is generated by \\spad{f} in the polynomial ring \\spad{F[lvar]}.") (($ $ |#4|) "\\spad{saturate(I,f)} is the saturation of the ideal \\spad{I} with respect to the multiplicative set generated by the polynomial \\spad{f}.")) (|coerce| (($ (|List| |#4|)) "\\spad{coerce(polyList)} converts the list of polynomials \\spad{polyList} to an ideal.")) (|generators| (((|List| |#4|) $) "\\spad{generators(I)} returns a list of generators for the ideal \\spad{I}.")) (|groebner?| (((|Boolean|) $) "\\spad{groebner?(I)} tests if the generators of the ideal \\spad{I} are a Groebner basis.")) (|groebnerIdeal| (($ (|List| |#4|)) "\\spad{groebnerIdeal(polyList)} constructs the ideal generated by the list of polynomials \\spad{polyList} which are assumed to be a Groebner basis. Note: this operation avoids a Groebner basis computation.")) (|ideal| (($ (|List| |#4|)) "\\spad{ideal(polyList)} constructs the ideal generated by the list of polynomials \\spad{polyList}.")) (|leadingIdeal| (($ $) "\\spad{leadingIdeal(I)} is the ideal generated by the leading terms of the elements of the ideal \\spad{I}.")) (|dimension| (((|Integer|) $) "\\spad{dimension(I)} gives the dimension of the ideal \\spad{I}. in the ring \\spad{F[lvar]},{} where lvar are the variables appearing in \\spad{I}") (((|Integer|) $ (|List| |#3|)) "\\spad{dimension(I,lvar)} gives the dimension of the ideal \\spad{I},{} in the ring \\spad{F[lvar]}")) (|backOldPos| (($ (|Record| (|:| |mval| (|Matrix| |#1|)) (|:| |invmval| (|Matrix| |#1|)) (|:| |genIdeal| $))) "\\spad{backOldPos(genPos)} takes the result produced by \\spadfunFrom{generalPosition}{PolynomialIdeals} and performs the inverse transformation,{} returning the original ideal \\spad{backOldPos(generalPosition(I,listvar))} = \\spad{I}.")) (|generalPosition| (((|Record| (|:| |mval| (|Matrix| |#1|)) (|:| |invmval| (|Matrix| |#1|)) (|:| |genIdeal| $)) $ (|List| |#3|)) "\\spad{generalPosition(I,listvar)} perform a random linear transformation on the variables in \\spad{listvar} and returns the transformed ideal along with the change of basis matrix.")) (|groebner| (($ $) "\\spad{groebner(I)} returns a set of generators of \\spad{I} that are a Groebner basis for \\spad{I}.")) (|quotient| (($ $ |#4|) "\\spad{quotient(I,f)} computes the quotient of the ideal \\spad{I} by the principal ideal generated by the polynomial \\spad{f},{} \\spad{(I:(f))}.") (($ $ $) "\\spad{quotient(I,J)} computes the quotient of the ideals \\spad{I} and \\spad{J},{} \\spad{(I:J)}.")) (|intersect| (($ (|List| $)) "\\spad{intersect(LI)} computes the intersection of the list of ideals \\spad{LI}.") (($ $ $) "\\spad{intersect(I,J)} computes the intersection of the ideals \\spad{I} and \\spad{J}.")) (|zeroDim?| (((|Boolean|) $) "\\spad{zeroDim?(I)} tests if the ideal \\spad{I} is zero dimensional,{} \\spadignore{i.e.} all its associated primes are maximal,{} in the ring \\spad{F[lvar]},{} where lvar are the variables appearing in \\spad{I}") (((|Boolean|) $ (|List| |#3|)) "\\spad{zeroDim?(I,lvar)} tests if the ideal \\spad{I} is zero dimensional,{} \\spadignore{i.e.} all its associated primes are maximal,{} in the ring \\spad{F[lvar]}")) (|inRadical?| (((|Boolean|) |#4| $) "\\spad{inRadical?(f,I)} tests if some power of the polynomial \\spad{f} belongs to the ideal \\spad{I}.")) (|in?| (((|Boolean|) $ $) "\\spad{in?(I,J)} tests if the ideal \\spad{I} is contained in the ideal \\spad{J}.")) (|element?| (((|Boolean|) |#4| $) "\\spad{element?(f,I)} tests whether the polynomial \\spad{f} belongs to the ideal \\spad{I}.")) (|zero?| (((|Boolean|) $) "\\spad{zero?(I)} tests whether the ideal \\spad{I} is the zero ideal")) (|one?| (((|Boolean|) $) "\\spad{one?(I)} tests whether the ideal \\spad{I} is the unit ideal,{} \\spadignore{i.e.} contains 1.")) (+ (($ $ $) "\\spad{I+J} computes the ideal generated by the union of \\spad{I} and \\spad{J}.")) (** (($ $ (|NonNegativeInteger|)) "\\spad{I**n} computes the \\spad{n}th power of the ideal \\spad{I}.")) (* (($ $ $) "\\spad{I*J} computes the product of the ideal \\spad{I} and \\spad{J}."))) NIL ((|HasCategory| |#3| (|%list| (QUOTE -633) (QUOTE (-1209))))) @@ -2112,7 +2112,7 @@ NIL ((|constructor| (NIL "\\indented{2}{IndexedExponents of an ordered set of variables gives a representation} for the degree of polynomials in commuting variables. It gives an ordered pairing of non negative integer exponents with variables"))) NIL ((-12 (|HasCategory| (-793) (QUOTE (-1133))) (|HasCategory| |#1| (QUOTE (-1133))))) -(-546 K -1612 |Par|) +(-546 K -1613 |Par|) ((|constructor| (NIL "This package is the inner package to be used by NumericRealEigenPackage and NumericComplexEigenPackage for the computation of numeric eigenvalues and eigenvectors.")) (|innerEigenvectors| (((|List| (|Record| (|:| |outval| |#2|) (|:| |outmult| (|Integer|)) (|:| |outvect| (|List| (|Matrix| |#2|))))) (|Matrix| |#1|) |#3| (|Mapping| (|Factored| (|SparseUnivariatePolynomial| |#1|)) (|SparseUnivariatePolynomial| |#1|))) "\\spad{innerEigenvectors(m,eps,factor)} computes explicitly the eigenvalues and the correspondent eigenvectors of the matrix \\spad{m}. The parameter \\spad{eps} determines the type of the output,{} \\spad{factor} is the univariate factorizer to br used to reduce the characteristic polynomial into irreducible factors.")) (|solve1| (((|List| |#2|) (|SparseUnivariatePolynomial| |#1|) |#3|) "\\spad{solve1(pol, eps)} finds the roots of the univariate polynomial polynomial \\spad{pol} to precision eps. If \\spad{K} is \\spad{Fraction Integer} then only the real roots are returned,{} if \\spad{K} is \\spad{Complex Fraction Integer} then all roots are found.")) (|charpol| (((|SparseUnivariatePolynomial| |#1|) (|Matrix| |#1|)) "\\spad{charpol(m)} computes the characteristic polynomial of a matrix \\spad{m} with entries in \\spad{K}. This function returns a polynomial over \\spad{K},{} while the general one (that is in EiegenPackage) returns Fraction \\spad{P} \\spad{K}"))) NIL NIL @@ -2136,7 +2136,7 @@ NIL ((|constructor| (NIL "This package computes infinite products of univariate Taylor series over an integral domain of characteristic 0.")) (|generalInfiniteProduct| ((|#2| |#2| (|Integer|) (|Integer|)) "\\spad{generalInfiniteProduct(f(x),a,d)} computes \\spad{product(n=a,a+d,a+2*d,...,f(x**n))}. The series \\spad{f(x)} should have constant coefficient 1.")) (|oddInfiniteProduct| ((|#2| |#2|) "\\spad{oddInfiniteProduct(f(x))} computes \\spad{product(n=1,3,5...,f(x**n))}. The series \\spad{f(x)} should have constant coefficient 1.")) (|evenInfiniteProduct| ((|#2| |#2|) "\\spad{evenInfiniteProduct(f(x))} computes \\spad{product(n=2,4,6...,f(x**n))}. The series \\spad{f(x)} should have constant coefficient 1.")) (|infiniteProduct| ((|#2| |#2|) "\\spad{infiniteProduct(f(x))} computes \\spad{product(n=1,2,3...,f(x**n))}. The series \\spad{f(x)} should have constant coefficient 1."))) NIL NIL -(-552 K -1612 |Par|) +(-552 K -1613 |Par|) ((|constructor| (NIL "This is an internal package for computing approximate solutions to systems of polynomial equations. The parameter \\spad{K} specifies the coefficient field of the input polynomials and must be either \\spad{Fraction(Integer)} or \\spad{Complex(Fraction Integer)}. The parameter \\spad{F} specifies where the solutions must lie and can be one of the following: \\spad{Float},{} \\spad{Fraction(Integer)},{} \\spad{Complex(Float)},{} \\spad{Complex(Fraction Integer)}. The last parameter specifies the type of the precision operand and must be either \\spad{Fraction(Integer)} or \\spad{Float}.")) (|makeEq| (((|List| (|Equation| (|Polynomial| |#2|))) (|List| |#2|) (|List| (|Symbol|))) "\\spad{makeEq(lsol,lvar)} returns a list of equations formed by corresponding members of \\spad{lvar} and \\spad{lsol}.")) (|innerSolve| (((|List| (|List| |#2|)) (|List| (|Polynomial| |#1|)) (|List| (|Polynomial| |#1|)) (|List| (|Symbol|)) |#3|) "\\spad{innerSolve(lnum,lden,lvar,eps)} returns a list of solutions of the system of polynomials \\spad{lnum},{} with the side condition that none of the members of \\spad{lden} vanish identically on any solution. Each solution is expressed as a list corresponding to the list of variables in \\spad{lvar} and with precision specified by \\spad{eps}.")) (|innerSolve1| (((|List| |#2|) (|Polynomial| |#1|) |#3|) "\\spad{innerSolve1(p,eps)} returns the list of the zeros of the polynomial \\spad{p} with precision \\spad{eps}.") (((|List| |#2|) (|SparseUnivariatePolynomial| |#1|) |#3|) "\\spad{innerSolve1(up,eps)} returns the list of the zeros of the univariate polynomial \\spad{up} with precision \\spad{eps}."))) NIL NIL @@ -2192,11 +2192,11 @@ NIL ((|constructor| (NIL "This domain is used to provide a conditional \"add\" domain for the implementation of \\spadtype{Table}."))) ((-4510 . T) (-4511 . T)) ((-12 (|HasCategory| (-2 (|:| -3837 |#1|) (|:| -2715 |#2|)) (QUOTE (-1133))) (|HasCategory| (-2 (|:| -3837 |#1|) (|:| -2715 |#2|)) (|%list| (QUOTE -321) (|%list| (QUOTE -2) (|%list| (QUOTE |:|) (QUOTE -3837) (|devaluate| |#1|)) (|%list| (QUOTE |:|) (QUOTE -2715) (|devaluate| |#2|)))))) (-2210 (|HasCategory| (-2 (|:| -3837 |#1|) (|:| -2715 |#2|)) (QUOTE (-1133))) (|HasCategory| |#2| (QUOTE (-1133)))) (-2210 (|HasCategory| (-2 (|:| -3837 |#1|) (|:| -2715 |#2|)) (QUOTE (-102))) (|HasCategory| (-2 (|:| -3837 |#1|) (|:| -2715 |#2|)) (QUOTE (-1133))) (|HasCategory| |#2| (QUOTE (-102))) (|HasCategory| |#2| (QUOTE (-1133)))) (-2210 (|HasCategory| (-2 (|:| -3837 |#1|) (|:| -2715 |#2|)) (QUOTE (-1133))) (|HasCategory| (-2 (|:| -3837 |#1|) (|:| -2715 |#2|)) (|%list| (QUOTE -632) (QUOTE (-888)))) (|HasCategory| |#2| (QUOTE (-1133))) (|HasCategory| |#2| (|%list| (QUOTE -632) (QUOTE (-888))))) (|HasCategory| (-2 (|:| -3837 |#1|) (|:| -2715 |#2|)) (|%list| (QUOTE -633) (QUOTE (-549)))) (-12 (|HasCategory| |#2| (QUOTE (-1133))) (|HasCategory| |#2| (|%list| (QUOTE -321) (|devaluate| |#2|)))) (|HasCategory| (-2 (|:| -3837 |#1|) (|:| -2715 |#2|)) (QUOTE (-1133))) (|HasCategory| |#1| (QUOTE (-872))) (|HasCategory| |#2| (QUOTE (-1133))) (-2210 (|HasCategory| (-2 (|:| -3837 |#1|) (|:| -2715 |#2|)) (|%list| (QUOTE -632) (QUOTE (-888)))) (|HasCategory| |#2| (|%list| (QUOTE -632) (QUOTE (-888))))) (-2210 (|HasCategory| (-2 (|:| -3837 |#1|) (|:| -2715 |#2|)) (QUOTE (-102))) (|HasCategory| |#2| (QUOTE (-102)))) (|HasCategory| |#2| (QUOTE (-102))) (|HasCategory| |#2| (|%list| (QUOTE -632) (QUOTE (-888)))) (|HasCategory| (-2 (|:| -3837 |#1|) (|:| -2715 |#2|)) (|%list| (QUOTE -632) (QUOTE (-888)))) (|HasCategory| (-2 (|:| -3837 |#1|) (|:| -2715 |#2|)) (QUOTE (-102)))) -(-566 R -1612) +(-566 R -1613) ((|constructor| (NIL "This package provides functions for the integration of algebraic integrands over transcendental functions.")) (|algint| (((|IntegrationResult| |#2|) |#2| (|Kernel| |#2|) (|Kernel| |#2|) (|Mapping| (|SparseUnivariatePolynomial| |#2|) (|SparseUnivariatePolynomial| |#2|))) "\\spad{algint(f, x, y, d)} returns the integral of \\spad{f(x,y)dx} where \\spad{y} is an algebraic function of \\spad{x}; \\spad{d} is the derivation to use on \\spad{k[x]}."))) NIL NIL -(-567 R0 -1612 UP UPUP R) +(-567 R0 -1613 UP UPUP R) ((|constructor| (NIL "This package provides functions for integrating a function on an algebraic curve.")) (|palginfieldint| (((|Union| |#5| "failed") |#5| (|Mapping| |#3| |#3|)) "\\spad{palginfieldint(f, d)} returns an algebraic function \\spad{g} such that \\spad{dg = f} if such a \\spad{g} exists,{} \"failed\" otherwise. Argument \\spad{f} must be a pure algebraic function.")) (|palgintegrate| (((|IntegrationResult| |#5|) |#5| (|Mapping| |#3| |#3|)) "\\spad{palgintegrate(f, d)} integrates \\spad{f} with respect to the derivation \\spad{d}. Argument \\spad{f} must be a pure algebraic function.")) (|algintegrate| (((|IntegrationResult| |#5|) |#5| (|Mapping| |#3| |#3|)) "\\spad{algintegrate(f, d)} integrates \\spad{f} with respect to the derivation \\spad{d}."))) NIL NIL @@ -2216,7 +2216,7 @@ NIL ((|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."))) ((-4503 . T) ((-4512 "*") . T) (-4504 . T) (-4505 . T) (-4507 . T)) NIL -(-572 R -1612) +(-572 R -1613) ((|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|)) "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|)) "failed") |#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."))) NIL NIL @@ -2228,7 +2228,7 @@ NIL ((|constructor| (NIL "\\blankline")) (|entry| (((|Record| (|:| |endPointContinuity| (|Union| (|:| |continuous| "Continuous at the end points") (|:| |lowerSingular| "There is a singularity at the lower end point") (|:| |upperSingular| "There is a singularity at the upper end point") (|:| |bothSingular| "There are singularities at both end points") (|:| |notEvaluated| "End point continuity not yet evaluated"))) (|:| |singularitiesStream| (|Union| (|:| |str| (|Stream| (|DoubleFloat|))) (|:| |notEvaluated| "Internal singularities not yet evaluated"))) (|:| |range| (|Union| (|:| |finite| "The range is finite") (|:| |lowerInfinite| "The bottom of range is infinite") (|:| |upperInfinite| "The top of range is infinite") (|:| |bothInfinite| "Both top and bottom points are infinite") (|:| |notEvaluated| "Range not yet evaluated")))) (|Record| (|:| |var| (|Symbol|)) (|:| |fn| (|Expression| (|DoubleFloat|))) (|:| |range| (|Segment| (|OrderedCompletion| (|DoubleFloat|)))) (|:| |abserr| (|DoubleFloat|)) (|:| |relerr| (|DoubleFloat|)))) "\\spad{entry(n)} \\undocumented{}")) (|entries| (((|List| (|Record| (|:| |key| (|Record| (|:| |var| (|Symbol|)) (|:| |fn| (|Expression| (|DoubleFloat|))) (|:| |range| (|Segment| (|OrderedCompletion| (|DoubleFloat|)))) (|:| |abserr| (|DoubleFloat|)) (|:| |relerr| (|DoubleFloat|)))) (|:| |entry| (|Record| (|:| |endPointContinuity| (|Union| (|:| |continuous| "Continuous at the end points") (|:| |lowerSingular| "There is a singularity at the lower end point") (|:| |upperSingular| "There is a singularity at the upper end point") (|:| |bothSingular| "There are singularities at both end points") (|:| |notEvaluated| "End point continuity not yet evaluated"))) (|:| |singularitiesStream| (|Union| (|:| |str| (|Stream| (|DoubleFloat|))) (|:| |notEvaluated| "Internal singularities not yet evaluated"))) (|:| |range| (|Union| (|:| |finite| "The range is finite") (|:| |lowerInfinite| "The bottom of range is infinite") (|:| |upperInfinite| "The top of range is infinite") (|:| |bothInfinite| "Both top and bottom points are infinite") (|:| |notEvaluated| "Range not yet evaluated"))))))) $) "\\spad{entries(x)} \\undocumented{}")) (|showAttributes| (((|Union| (|Record| (|:| |endPointContinuity| (|Union| (|:| |continuous| "Continuous at the end points") (|:| |lowerSingular| "There is a singularity at the lower end point") (|:| |upperSingular| "There is a singularity at the upper end point") (|:| |bothSingular| "There are singularities at both end points") (|:| |notEvaluated| "End point continuity not yet evaluated"))) (|:| |singularitiesStream| (|Union| (|:| |str| (|Stream| (|DoubleFloat|))) (|:| |notEvaluated| "Internal singularities not yet evaluated"))) (|:| |range| (|Union| (|:| |finite| "The range is finite") (|:| |lowerInfinite| "The bottom of range is infinite") (|:| |upperInfinite| "The top of range is infinite") (|:| |bothInfinite| "Both top and bottom points are infinite") (|:| |notEvaluated| "Range not yet evaluated")))) "failed") (|Record| (|:| |var| (|Symbol|)) (|:| |fn| (|Expression| (|DoubleFloat|))) (|:| |range| (|Segment| (|OrderedCompletion| (|DoubleFloat|)))) (|:| |abserr| (|DoubleFloat|)) (|:| |relerr| (|DoubleFloat|)))) "\\spad{showAttributes(x)} \\undocumented{}")) (|insert!| (($ (|Record| (|:| |key| (|Record| (|:| |var| (|Symbol|)) (|:| |fn| (|Expression| (|DoubleFloat|))) (|:| |range| (|Segment| (|OrderedCompletion| (|DoubleFloat|)))) (|:| |abserr| (|DoubleFloat|)) (|:| |relerr| (|DoubleFloat|)))) (|:| |entry| (|Record| (|:| |endPointContinuity| (|Union| (|:| |continuous| "Continuous at the end points") (|:| |lowerSingular| "There is a singularity at the lower end point") (|:| |upperSingular| "There is a singularity at the upper end point") (|:| |bothSingular| "There are singularities at both end points") (|:| |notEvaluated| "End point continuity not yet evaluated"))) (|:| |singularitiesStream| (|Union| (|:| |str| (|Stream| (|DoubleFloat|))) (|:| |notEvaluated| "Internal singularities not yet evaluated"))) (|:| |range| (|Union| (|:| |finite| "The range is finite") (|:| |lowerInfinite| "The bottom of range is infinite") (|:| |upperInfinite| "The top of range is infinite") (|:| |bothInfinite| "Both top and bottom points are infinite") (|:| |notEvaluated| "Range not yet evaluated"))))))) "\\spad{insert!(r)} inserts an entry \\spad{r} into theIFTable")) (|fTable| (($ (|List| (|Record| (|:| |key| (|Record| (|:| |var| (|Symbol|)) (|:| |fn| (|Expression| (|DoubleFloat|))) (|:| |range| (|Segment| (|OrderedCompletion| (|DoubleFloat|)))) (|:| |abserr| (|DoubleFloat|)) (|:| |relerr| (|DoubleFloat|)))) (|:| |entry| (|Record| (|:| |endPointContinuity| (|Union| (|:| |continuous| "Continuous at the end points") (|:| |lowerSingular| "There is a singularity at the lower end point") (|:| |upperSingular| "There is a singularity at the upper end point") (|:| |bothSingular| "There are singularities at both end points") (|:| |notEvaluated| "End point continuity not yet evaluated"))) (|:| |singularitiesStream| (|Union| (|:| |str| (|Stream| (|DoubleFloat|))) (|:| |notEvaluated| "Internal singularities not yet evaluated"))) (|:| |range| (|Union| (|:| |finite| "The range is finite") (|:| |lowerInfinite| "The bottom of range is infinite") (|:| |upperInfinite| "The top of range is infinite") (|:| |bothInfinite| "Both top and bottom points are infinite") (|:| |notEvaluated| "Range not yet evaluated")))))))) "\\spad{fTable(l)} creates a functions table from the elements of \\spad{l}.")) (|keys| (((|List| (|Record| (|:| |var| (|Symbol|)) (|:| |fn| (|Expression| (|DoubleFloat|))) (|:| |range| (|Segment| (|OrderedCompletion| (|DoubleFloat|)))) (|:| |abserr| (|DoubleFloat|)) (|:| |relerr| (|DoubleFloat|)))) $) "\\spad{keys(f)} returns the list of keys of \\spad{f}")) (|clearTheFTable| (((|Void|)) "\\spad{clearTheFTable()} clears the current table of functions.")) (|showTheFTable| (($) "\\spad{showTheFTable()} returns the current table of functions."))) NIL NIL -(-575 R -1612 L) +(-575 R -1613 L) ((|constructor| (NIL "This internal package rationalises integrands on curves of the form: \\indented{2}{\\spad{y\\^2 = a x\\^2 + b x + c}} \\indented{2}{\\spad{y\\^2 = (a x + b) / (c x + d)}} \\indented{2}{\\spad{f(x, y) = 0} where \\spad{f} has degree 1 in \\spad{x}} The rationalization is done for integration,{} limited integration,{} extended integration and the risch differential equation.")) (|palgLODE0| (((|Record| (|:| |particular| (|Union| |#2| "failed")) (|:| |basis| (|List| |#2|))) |#3| |#2| (|Kernel| |#2|) (|Kernel| |#2|) (|Kernel| |#2|) |#2| (|Fraction| (|SparseUnivariatePolynomial| |#2|))) "\\spad{palgLODE0(op,g,x,y,z,t,c)} returns the solution of \\spad{op f = g} Argument \\spad{y} is an algebraic function of \\spad{x} satisfying \\spad{f(x,y)dx = c f(t,y) dy}; \\spad{c} and \\spad{t} are rational functions of \\spad{y}.") (((|Record| (|:| |particular| (|Union| |#2| "failed")) (|:| |basis| (|List| |#2|))) |#3| |#2| (|Kernel| |#2|) (|Kernel| |#2|) |#2| (|SparseUnivariatePolynomial| |#2|)) "\\spad{palgLODE0(op, g, x, y, d, p)} returns the solution of \\spad{op f = g}. Argument \\spad{y} is an algebraic function of \\spad{x} satisfying \\spad{d(x)\\^2y(x)\\^2 = P(x)}.")) (|lift| (((|SparseUnivariatePolynomial| (|Fraction| (|SparseUnivariatePolynomial| |#2|))) (|SparseUnivariatePolynomial| |#2|) (|Kernel| |#2|)) "\\spad{lift(u,k)} \\undocumented")) (|multivariate| ((|#2| (|SparseUnivariatePolynomial| (|Fraction| (|SparseUnivariatePolynomial| |#2|))) (|Kernel| |#2|) |#2|) "\\spad{multivariate(u,k,f)} \\undocumented")) (|univariate| (((|SparseUnivariatePolynomial| (|Fraction| (|SparseUnivariatePolynomial| |#2|))) |#2| (|Kernel| |#2|) (|Kernel| |#2|) (|SparseUnivariatePolynomial| |#2|)) "\\spad{univariate(f,k,k,p)} \\undocumented")) (|palgRDE0| (((|Union| |#2| "failed") |#2| |#2| (|Kernel| |#2|) (|Kernel| |#2|) (|Mapping| (|Union| |#2| "failed") |#2| |#2| (|Symbol|)) (|Kernel| |#2|) |#2| (|Fraction| (|SparseUnivariatePolynomial| |#2|))) "\\spad{palgRDE0(f, g, x, y, foo, t, c)} returns a function \\spad{z(x,y)} such that \\spad{dz/dx + n * df/dx z(x,y) = g(x,y)} if such a \\spad{z} exists,{} and \"failed\" otherwise. Argument \\spad{y} is an algebraic function of \\spad{x} satisfying \\spad{f(x,y)dx = c f(t,y) dy}; \\spad{c} and \\spad{t} are rational functions of \\spad{y}. Argument \\spad{foo},{} called by \\spad{foo(a, b, x)},{} is a function that solves \\spad{du/dx + n * da/dx u(x) = u(x)} for an unknown \\spad{u(x)} not involving \\spad{y}.") (((|Union| |#2| "failed") |#2| |#2| (|Kernel| |#2|) (|Kernel| |#2|) (|Mapping| (|Union| |#2| "failed") |#2| |#2| (|Symbol|)) |#2| (|SparseUnivariatePolynomial| |#2|)) "\\spad{palgRDE0(f, g, x, y, foo, d, p)} returns a function \\spad{z(x,y)} such that \\spad{dz/dx + n * df/dx z(x,y) = g(x,y)} if such a \\spad{z} exists,{} and \"failed\" otherwise. Argument \\spad{y} is an algebraic function of \\spad{x} satisfying \\spad{d(x)\\^2y(x)\\^2 = P(x)}. Argument \\spad{foo},{} called by \\spad{foo(a, b, x)},{} is a function that solves \\spad{du/dx + n * da/dx u(x) = u(x)} for an unknown \\spad{u(x)} not involving \\spad{y}.")) (|palglimint0| (((|Union| (|Record| (|:| |mainpart| |#2|) (|:| |limitedlogs| (|List| (|Record| (|:| |coeff| |#2|) (|:| |logand| |#2|))))) "failed") |#2| (|Kernel| |#2|) (|Kernel| |#2|) (|List| |#2|) (|Kernel| |#2|) |#2| (|Fraction| (|SparseUnivariatePolynomial| |#2|))) "\\spad{palglimint0(f, x, y, [u1,...,un], z, t, c)} returns functions \\spad{[h,[[ci, ui]]]} such that the \\spad{ui}'s are among \\spad{[u1,...,un]} and \\spad{d(h + sum(ci log(ui)))/dx = f(x,y)} if such functions exist,{} and \"failed\" otherwise. Argument \\spad{y} is an algebraic function of \\spad{x} satisfying \\spad{f(x,y)dx = c f(t,y) dy}; \\spad{c} and \\spad{t} are rational functions of \\spad{y}.") (((|Union| (|Record| (|:| |mainpart| |#2|) (|:| |limitedlogs| (|List| (|Record| (|:| |coeff| |#2|) (|:| |logand| |#2|))))) "failed") |#2| (|Kernel| |#2|) (|Kernel| |#2|) (|List| |#2|) |#2| (|SparseUnivariatePolynomial| |#2|)) "\\spad{palglimint0(f, x, y, [u1,...,un], d, p)} returns functions \\spad{[h,[[ci, ui]]]} such that the \\spad{ui}'s are among \\spad{[u1,...,un]} and \\spad{d(h + sum(ci log(ui)))/dx = f(x,y)} if such functions exist,{} and \"failed\" otherwise. Argument \\spad{y} is an algebraic function of \\spad{x} satisfying \\spad{d(x)\\^2y(x)\\^2 = P(x)}.")) (|palgextint0| (((|Union| (|Record| (|:| |ratpart| |#2|) (|:| |coeff| |#2|)) "failed") |#2| (|Kernel| |#2|) (|Kernel| |#2|) |#2| (|Kernel| |#2|) |#2| (|Fraction| (|SparseUnivariatePolynomial| |#2|))) "\\spad{palgextint0(f, x, y, g, z, t, c)} returns functions \\spad{[h, d]} such that \\spad{dh/dx = f(x,y) - d g},{} where \\spad{y} is an algebraic function of \\spad{x} satisfying \\spad{f(x,y)dx = c f(t,y) dy},{} and \\spad{c} and \\spad{t} are rational functions of \\spad{y}. Argument \\spad{z} is a dummy variable not appearing in \\spad{f(x,y)}. The operation returns \"failed\" if no such functions exist.") (((|Union| (|Record| (|:| |ratpart| |#2|) (|:| |coeff| |#2|)) "failed") |#2| (|Kernel| |#2|) (|Kernel| |#2|) |#2| |#2| (|SparseUnivariatePolynomial| |#2|)) "\\spad{palgextint0(f, x, y, g, d, p)} returns functions \\spad{[h, c]} such that \\spad{dh/dx = f(x,y) - c g},{} where \\spad{y} is an algebraic function of \\spad{x} satisfying \\spad{d(x)\\^2 y(x)\\^2 = P(x)},{} or \"failed\" if no such functions exist.")) (|palgint0| (((|IntegrationResult| |#2|) |#2| (|Kernel| |#2|) (|Kernel| |#2|) (|Kernel| |#2|) |#2| (|Fraction| (|SparseUnivariatePolynomial| |#2|))) "\\spad{palgint0(f, x, y, z, t, c)} returns the integral of \\spad{f(x,y)dx} where \\spad{y} is an algebraic function of \\spad{x} satisfying \\spad{f(x,y)dx = c f(t,y) dy}; \\spad{c} and \\spad{t} are rational functions of \\spad{y}. Argument \\spad{z} is a dummy variable not appearing in \\spad{f(x,y)}.") (((|IntegrationResult| |#2|) |#2| (|Kernel| |#2|) (|Kernel| |#2|) |#2| (|SparseUnivariatePolynomial| |#2|)) "\\spad{palgint0(f, x, y, d, p)} returns the integral of \\spad{f(x,y)dx} where \\spad{y} is an algebraic function of \\spad{x} satisfying \\spad{d(x)\\^2 y(x)\\^2 = P(x)}."))) NIL ((|HasCategory| |#3| (|%list| (QUOTE -680) (|devaluate| |#2|)))) @@ -2236,11 +2236,11 @@ NIL ((|constructor| (NIL "This package provides various number theoretic functions on the integers.")) (|sumOfKthPowerDivisors| (((|Integer|) (|Integer|) (|NonNegativeInteger|)) "\\spad{sumOfKthPowerDivisors(n,k)} returns the sum of the \\spad{k}th powers of the integers between 1 and \\spad{n} (inclusive) which divide \\spad{n}. the sum of the \\spad{k}th powers of the divisors of \\spad{n} is often denoted by \\spad{sigma_k(n)}.")) (|sumOfDivisors| (((|Integer|) (|Integer|)) "\\spad{sumOfDivisors(n)} returns the sum of the integers between 1 and \\spad{n} (inclusive) which divide \\spad{n}. The sum of the divisors of \\spad{n} is often denoted by \\spad{sigma(n)}.")) (|numberOfDivisors| (((|Integer|) (|Integer|)) "\\spad{numberOfDivisors(n)} returns the number of integers between 1 and \\spad{n} (inclusive) which divide \\spad{n}. The number of divisors of \\spad{n} is often denoted by \\spad{tau(n)}.")) (|moebiusMu| (((|Integer|) (|Integer|)) "\\spad{moebiusMu(n)} returns the Moebius function \\spad{mu(n)}. \\spad{mu(n)} is either \\spad{-1},{}0 or 1 as follows: \\spad{mu(n) = 0} if \\spad{n} is divisible by a square > 1,{} \\spad{mu(n) = (-1)^k} if \\spad{n} is square-free and has \\spad{k} distinct prime divisors.")) (|legendre| (((|Integer|) (|Integer|) (|Integer|)) "\\spad{legendre(a,p)} returns the Legendre symbol \\spad{L(a/p)}. \\spad{L(a/p) = (-1)**((p-1)/2) mod p} (\\spad{p} prime),{} which is 0 if \\spad{a} is 0,{} 1 if \\spad{a} is a quadratic residue \\spad{mod p} and \\spad{-1} otherwise. Note: because the primality test is expensive,{} if it is known that \\spad{p} is prime then use \\spad{jacobi(a,p)}.")) (|jacobi| (((|Integer|) (|Integer|) (|Integer|)) "\\spad{jacobi(a,b)} returns the Jacobi symbol \\spad{J(a/b)}. When \\spad{b} is odd,{} \\spad{J(a/b) = product(L(a/p) for p in factor b )}. Note: by convention,{} 0 is returned if \\spad{gcd(a,b) ~= 1}. Iterative \\spad{O(log(b)^2)} version coded by Michael Monagan June 1987.")) (|harmonic| (((|Fraction| (|Integer|)) (|Integer|)) "\\spad{harmonic(n)} returns the \\spad{n}th harmonic number. This is \\spad{H[n] = sum(1/k,k=1..n)}.")) (|fibonacci| (((|Integer|) (|Integer|)) "\\spad{fibonacci(n)} returns the \\spad{n}th Fibonacci number. the Fibonacci numbers \\spad{F[n]} are defined by \\spad{F[0] = F[1] = 1} and \\spad{F[n] = F[n-1] + F[n-2]}. The algorithm has running time \\spad{O(log(n)^3)}. Reference: Knuth,{} The Art of Computer Programming Vol 2,{} Semi-Numerical Algorithms.")) (|eulerPhi| (((|Integer|) (|Integer|)) "\\spad{eulerPhi(n)} returns the number of integers between 1 and \\spad{n} (including 1) which are relatively prime to \\spad{n}. This is the Euler phi function \\spad{\\phi(n)} is also called the totient function.")) (|euler| (((|Integer|) (|Integer|)) "\\spad{euler(n)} returns the \\spad{n}th Euler number. This is \\spad{2^n E(n,1/2)},{} where \\spad{E(n,x)} is the \\spad{n}th Euler polynomial.")) (|divisors| (((|List| (|Integer|)) (|Integer|)) "\\spad{divisors(n)} returns a list of the divisors of \\spad{n}.")) (|chineseRemainder| (((|Integer|) (|Integer|) (|Integer|) (|Integer|) (|Integer|)) "\\spad{chineseRemainder(x1,m1,x2,m2)} returns \\spad{w},{} where \\spad{w} is such that \\spad{w = x1 mod m1} and \\spad{w = x2 mod m2}. Note: \\spad{m1} and \\spad{m2} must be relatively prime.")) (|bernoulli| (((|Fraction| (|Integer|)) (|Integer|)) "\\spad{bernoulli(n)} returns the \\spad{n}th Bernoulli number. this is \\spad{B(n,0)},{} where \\spad{B(n,x)} is the \\spad{n}th Bernoulli polynomial."))) NIL NIL -(-577 -1612 UP UPUP R) +(-577 -1613 UP UPUP R) ((|constructor| (NIL "algebraic Hermite redution.")) (|HermiteIntegrate| (((|Record| (|:| |answer| |#4|) (|:| |logpart| |#4|)) |#4| (|Mapping| |#2| |#2|)) "\\spad{HermiteIntegrate(f, ')} returns \\spad{[g,h]} such that \\spad{f = g' + h} and \\spad{h} has a only simple finite normal poles."))) NIL NIL -(-578 -1612 UP) +(-578 -1613 UP) ((|constructor| (NIL "Hermite integration,{} transcendental case.")) (|HermiteIntegrate| (((|Record| (|:| |answer| (|Fraction| |#2|)) (|:| |logpart| (|Fraction| |#2|)) (|:| |specpart| (|Fraction| |#2|)) (|:| |polypart| |#2|)) (|Fraction| |#2|) (|Mapping| |#2| |#2|)) "\\spad{HermiteIntegrate(f, D)} returns \\spad{[g, h, s, p]} such that \\spad{f = Dg + h + s + p},{} \\spad{h} has a squarefree denominator normal \\spad{w}.\\spad{r}.\\spad{t}. \\spad{D},{} and all the squarefree factors of the denominator of \\spad{s} are special \\spad{w}.\\spad{r}.\\spad{t}. \\spad{D}. Furthermore,{} \\spad{h} and \\spad{s} have no polynomial parts. \\spad{D} is the derivation to use on \\spadtype{UP}."))) NIL NIL @@ -2248,15 +2248,15 @@ NIL ((|measure| (((|Record| (|:| |measure| (|Float|)) (|:| |name| (|String|)) (|:| |explanations| (|List| (|String|))) (|:| |extra| (|Result|))) (|NumericalIntegrationProblem|) (|RoutinesTable|)) "\\spad{measure(prob,R)} is a top level ANNA function for identifying the most appropriate numerical routine from those in the routines table provided for solving the numerical integration problem defined by \\axiom{\\spad{prob}}. \\blankline It calls each \\axiom{domain} listed in \\axiom{\\spad{R}} of \\axiom{category} \\axiomType{NumericalIntegrationCategory} in turn to calculate all measures and returns the best \\spadignore{i.e.} the name of the most appropriate domain and any other relevant information.") (((|Record| (|:| |measure| (|Float|)) (|:| |name| (|String|)) (|:| |explanations| (|List| (|String|))) (|:| |extra| (|Result|))) (|NumericalIntegrationProblem|)) "\\spad{measure(prob)} is a top level ANNA function for identifying the most appropriate numerical routine for solving the numerical integration problem defined by \\axiom{\\spad{prob}}. \\blankline It calls each \\axiom{domain} of \\axiom{category} \\axiomType{NumericalIntegrationCategory} in turn to calculate all measures and returns the best \\spadignore{i.e.} the name of the most appropriate domain and any other relevant information.")) (|integrate| (((|Union| (|Result|) "failed") (|Expression| (|Float|)) (|SegmentBinding| (|OrderedCompletion| (|Float|))) (|Symbol|)) "\\spad{integrate(exp, x = a..b, numerical)} is a top level ANNA function to integrate an expression,{} {\\tt \\spad{exp}},{} over a given range,{} {\\tt a} to {\\tt \\spad{b}}. \\blankline It iterates over the \\axiom{domains} of \\axiomType{NumericalIntegrationCategory} to get the name and other relevant information of the the (domain of the) numerical routine likely to be the most appropriate,{} \\spadignore{i.e.} have the best \\axiom{measure}. \\blankline It then performs the integration of the given expression on that \\axiom{domain}.\\newline \\blankline Default values for the absolute and relative error are used. \\blankline It is an error if the last argument is not {\\tt numerical}.") (((|Union| (|Result|) "failed") (|Expression| (|Float|)) (|SegmentBinding| (|OrderedCompletion| (|Float|))) (|String|)) "\\spad{integrate(exp, x = a..b, \"numerical\")} is a top level ANNA function to integrate an expression,{} {\\tt \\spad{exp}},{} over a given range,{} {\\tt a} to {\\tt \\spad{b}}. \\blankline It iterates over the \\axiom{domains} of \\axiomType{NumericalIntegrationCategory} to get the name and other relevant information of the the (domain of the) numerical routine likely to be the most appropriate,{} \\spadignore{i.e.} have the best \\axiom{measure}. \\blankline It then performs the integration of the given expression on that \\axiom{domain}.\\newline \\blankline Default values for the absolute and relative error are used. \\blankline It is an error of the last argument is not {\\tt \"numerical\"}.") (((|Result|) (|Expression| (|Float|)) (|List| (|Segment| (|OrderedCompletion| (|Float|)))) (|Float|) (|Float|) (|RoutinesTable|)) "\\spad{integrate(exp, [a..b,c..d,...], epsabs, epsrel, routines)} is a top level ANNA function to integrate a multivariate expression,{} {\\tt \\spad{exp}},{} over a given set of ranges to the required absolute and relative accuracy,{} using the routines available in the RoutinesTable provided. \\blankline It iterates over the \\axiom{domains} of \\axiomType{NumericalIntegrationCategory} to get the name and other relevant information of the the (domain of the) numerical routine likely to be the most appropriate,{} \\spadignore{i.e.} have the best \\axiom{measure}. \\blankline It then performs the integration of the given expression on that \\axiom{domain}.") (((|Result|) (|Expression| (|Float|)) (|List| (|Segment| (|OrderedCompletion| (|Float|)))) (|Float|) (|Float|)) "\\spad{integrate(exp, [a..b,c..d,...], epsabs, epsrel)} is a top level ANNA function to integrate a multivariate expression,{} {\\tt \\spad{exp}},{} over a given set of ranges to the required absolute and relative accuracy. \\blankline It iterates over the \\axiom{domains} of \\axiomType{NumericalIntegrationCategory} to get the name and other relevant information of the the (domain of the) numerical routine likely to be the most appropriate,{} \\spadignore{i.e.} have the best \\axiom{measure}. \\blankline It then performs the integration of the given expression on that \\axiom{domain}.") (((|Result|) (|Expression| (|Float|)) (|List| (|Segment| (|OrderedCompletion| (|Float|)))) (|Float|)) "\\spad{integrate(exp, [a..b,c..d,...], epsrel)} is a top level ANNA function to integrate a multivariate expression,{} {\\tt \\spad{exp}},{} over a given set of ranges to the required relative accuracy. \\blankline It iterates over the \\axiom{domains} of \\axiomType{NumericalIntegrationCategory} to get the name and other relevant information of the the (domain of the) numerical routine likely to be the most appropriate,{} \\spadignore{i.e.} have the best \\axiom{measure}. \\blankline It then performs the integration of the given expression on that \\axiom{domain}. \\blankline If epsrel = 0,{} a default absolute accuracy is used.") (((|Result|) (|Expression| (|Float|)) (|List| (|Segment| (|OrderedCompletion| (|Float|))))) "\\spad{integrate(exp, [a..b,c..d,...])} is a top level ANNA function to integrate a multivariate expression,{} {\\tt \\spad{exp}},{} over a given set of ranges. \\blankline It iterates over the \\axiom{domains} of \\axiomType{NumericalIntegrationCategory} to get the name and other relevant information of the the (domain of the) numerical routine likely to be the most appropriate,{} \\spadignore{i.e.} have the best \\axiom{measure}. \\blankline It then performs the integration of the given expression on that \\axiom{domain}. \\blankline Default values for the absolute and relative error are used.") (((|Result|) (|Expression| (|Float|)) (|Segment| (|OrderedCompletion| (|Float|)))) "\\spad{integrate(exp, a..b)} is a top level ANNA function to integrate an expression,{} {\\tt \\spad{exp}},{} over a given range {\\tt a} to {\\tt \\spad{b}}. \\blankline It iterates over the \\axiom{domains} of \\axiomType{NumericalIntegrationCategory} to get the name and other relevant information of the the (domain of the) numerical routine likely to be the most appropriate,{} \\spadignore{i.e.} have the best \\axiom{measure}. \\blankline It then performs the integration of the given expression on that \\axiom{domain}. \\blankline Default values for the absolute and relative error are used.") (((|Result|) (|Expression| (|Float|)) (|Segment| (|OrderedCompletion| (|Float|))) (|Float|)) "\\spad{integrate(exp, a..b, epsrel)} is a top level ANNA function to integrate an expression,{} {\\tt \\spad{exp}},{} over a given range {\\tt a} to {\\tt \\spad{b}} to the required relative accuracy. \\blankline It iterates over the \\axiom{domains} of \\axiomType{NumericalIntegrationCategory} to get the name and other relevant information of the the (domain of the) numerical routine likely to be the most appropriate,{} \\spadignore{i.e.} have the best \\axiom{measure}. \\blankline It then performs the integration of the given expression on that \\axiom{domain}. \\blankline If epsrel = 0,{} a default absolute accuracy is used.") (((|Result|) (|Expression| (|Float|)) (|Segment| (|OrderedCompletion| (|Float|))) (|Float|) (|Float|)) "\\spad{integrate(exp, a..b, epsabs, epsrel)} is a top level ANNA function to integrate an expression,{} {\\tt \\spad{exp}},{} over a given range {\\tt a} to {\\tt \\spad{b}} to the required absolute and relative accuracy. \\blankline It iterates over the \\axiom{domains} of \\axiomType{NumericalIntegrationCategory} to get the name and other relevant information of the the (domain of the) numerical routine likely to be the most appropriate,{} \\spadignore{i.e.} have the best \\axiom{measure}. \\blankline It then performs the integration of the given expression on that \\axiom{domain}.") (((|Result|) (|NumericalIntegrationProblem|)) "\\spad{integrate(IntegrationProblem)} is a top level ANNA function to integrate an expression over a given range or ranges to the required absolute and relative accuracy. \\blankline It iterates over the \\axiom{domains} of \\axiomType{NumericalIntegrationCategory} to get the name and other relevant information of the the (domain of the) numerical routine likely to be the most appropriate,{} \\spadignore{i.e.} have the best \\axiom{measure}. \\blankline It then performs the integration of the given expression on that \\axiom{domain}.") (((|Result|) (|Expression| (|Float|)) (|Segment| (|OrderedCompletion| (|Float|))) (|Float|) (|Float|) (|RoutinesTable|)) "\\spad{integrate(exp, a..b, epsrel, routines)} is a top level ANNA function to integrate an expression,{} {\\tt \\spad{exp}},{} over a given range {\\tt a} to {\\tt \\spad{b}} to the required absolute and relative accuracy using the routines available in the RoutinesTable provided. \\blankline It iterates over the \\axiom{domains} of \\axiomType{NumericalIntegrationCategory} to get the name and other relevant information of the the (domain of the) numerical routine likely to be the most appropriate,{} \\spadignore{i.e.} have the best \\axiom{measure}. \\blankline It then performs the integration of the given expression on that \\axiom{domain}."))) NIL NIL -(-580 R -1612 L) +(-580 R -1613 L) ((|constructor| (NIL "This package provides functions for integration,{} limited integration,{} extended integration and the risch differential equation for pure algebraic integrands.")) (|palgLODE| (((|Record| (|:| |particular| (|Union| |#2| "failed")) (|:| |basis| (|List| |#2|))) |#3| |#2| (|Kernel| |#2|) (|Kernel| |#2|) (|Symbol|)) "\\spad{palgLODE(op, g, kx, y, x)} returns the solution of \\spad{op f = g}. \\spad{y} is an algebraic function of \\spad{x}.")) (|palgRDE| (((|Union| |#2| "failed") |#2| |#2| |#2| (|Kernel| |#2|) (|Kernel| |#2|) (|Mapping| (|Union| |#2| "failed") |#2| |#2| (|Symbol|))) "\\spad{palgRDE(nfp, f, g, x, y, foo)} returns a function \\spad{z(x,y)} such that \\spad{dz/dx + n * df/dx z(x,y) = g(x,y)} if such a \\spad{z} exists,{} \"failed\" otherwise; \\spad{y} is an algebraic function of \\spad{x}; \\spad{foo(a, b, x)} is a function that solves \\spad{du/dx + n * da/dx u(x) = u(x)} for an unknown \\spad{u(x)} not involving \\spad{y}. \\spad{nfp} is \\spad{n * df/dx}.")) (|palglimint| (((|Union| (|Record| (|:| |mainpart| |#2|) (|:| |limitedlogs| (|List| (|Record| (|:| |coeff| |#2|) (|:| |logand| |#2|))))) "failed") |#2| (|Kernel| |#2|) (|Kernel| |#2|) (|List| |#2|)) "\\spad{palglimint(f, x, y, [u1,...,un])} returns functions \\spad{[h,[[ci, ui]]]} such that the \\spad{ui}'s are among \\spad{[u1,...,un]} and \\spad{d(h + sum(ci log(ui)))/dx = f(x,y)} if such functions exist,{} \"failed\" otherwise; \\spad{y} is an algebraic function of \\spad{x}.")) (|palgextint| (((|Union| (|Record| (|:| |ratpart| |#2|) (|:| |coeff| |#2|)) "failed") |#2| (|Kernel| |#2|) (|Kernel| |#2|) |#2|) "\\spad{palgextint(f, x, y, g)} returns functions \\spad{[h, c]} such that \\spad{dh/dx = f(x,y) - c g},{} where \\spad{y} is an algebraic function of \\spad{x}; returns \"failed\" if no such functions exist.")) (|palgint| (((|IntegrationResult| |#2|) |#2| (|Kernel| |#2|) (|Kernel| |#2|)) "\\spad{palgint(f, x, y)} returns the integral of \\spad{f(x,y)dx} where \\spad{y} is an algebraic function of \\spad{x}."))) NIL ((|HasCategory| |#3| (|%list| (QUOTE -680) (|devaluate| |#2|)))) -(-581 R -1612) +(-581 R -1613) ((|constructor| (NIL "\\spadtype{PatternMatchIntegration} provides functions that use the pattern matcher to find some indefinite and definite integrals involving special functions and found in the litterature.")) (|pmintegrate| (((|Union| |#2| "failed") |#2| (|Symbol|) (|OrderedCompletion| |#2|) (|OrderedCompletion| |#2|)) "\\spad{pmintegrate(f, x = a..b)} returns the integral of \\spad{f(x)dx} from a to \\spad{b} if it can be found by the built-in pattern matching rules.") (((|Union| (|Record| (|:| |special| |#2|) (|:| |integrand| |#2|)) "failed") |#2| (|Symbol|)) "\\spad{pmintegrate(f, x)} returns either \"failed\" or \\spad{[g,h]} such that \\spad{integrate(f,x) = g + integrate(h,x)}.")) (|pmComplexintegrate| (((|Union| (|Record| (|:| |special| |#2|) (|:| |integrand| |#2|)) "failed") |#2| (|Symbol|)) "\\spad{pmComplexintegrate(f, x)} returns either \"failed\" or \\spad{[g,h]} such that \\spad{integrate(f,x) = g + integrate(h,x)}. It only looks for special complex integrals that pmintegrate does not return.")) (|splitConstant| (((|Record| (|:| |const| |#2|) (|:| |nconst| |#2|)) |#2| (|Symbol|)) "\\spad{splitConstant(f, x)} returns \\spad{[c, g]} such that \\spad{f = c * g} and \\spad{c} does not involve \\spad{t}."))) NIL ((-12 (|HasCategory| |#1| (|%list| (QUOTE -633) (|%list| (QUOTE -916) (QUOTE (-560))))) (|HasCategory| |#1| (|%list| (QUOTE -912) (QUOTE (-560)))) (|HasCategory| |#2| (QUOTE (-1171)))) (-12 (|HasCategory| |#1| (|%list| (QUOTE -633) (|%list| (QUOTE -916) (QUOTE (-560))))) (|HasCategory| |#1| (|%list| (QUOTE -912) (QUOTE (-560)))) (|HasCategory| |#2| (QUOTE (-649))))) -(-582 -1612 UP) +(-582 -1613 UP) ((|constructor| (NIL "This package provides functions for the base case of the Risch algorithm.")) (|limitedint| (((|Union| (|Record| (|:| |mainpart| (|Fraction| |#2|)) (|:| |limitedlogs| (|List| (|Record| (|:| |coeff| (|Fraction| |#2|)) (|:| |logand| (|Fraction| |#2|)))))) "failed") (|Fraction| |#2|) (|List| (|Fraction| |#2|))) "\\spad{limitedint(f, [g1,...,gn])} returns fractions \\spad{[h,[[ci, gi]]]} such that the \\spad{gi}'s are among \\spad{[g1,...,gn]},{} \\spad{ci' = 0},{} and \\spad{(h+sum(ci log(gi)))' = f},{} if possible,{} \"failed\" otherwise.")) (|extendedint| (((|Union| (|Record| (|:| |ratpart| (|Fraction| |#2|)) (|:| |coeff| (|Fraction| |#2|))) "failed") (|Fraction| |#2|) (|Fraction| |#2|)) "\\spad{extendedint(f, g)} returns fractions \\spad{[h, c]} such that \\spad{c' = 0} and \\spad{h' = f - cg},{} if \\spad{(h, c)} exist,{} \"failed\" otherwise.")) (|infieldint| (((|Union| (|Fraction| |#2|) "failed") (|Fraction| |#2|)) "\\spad{infieldint(f)} returns \\spad{g} such that \\spad{g' = f} or \"failed\" if the integral of \\spad{f} is not a rational function.")) (|integrate| (((|IntegrationResult| (|Fraction| |#2|)) (|Fraction| |#2|)) "\\spad{integrate(f)} returns \\spad{g} such that \\spad{g' = f}."))) NIL NIL @@ -2264,7 +2264,7 @@ NIL ((|constructor| (NIL "Provides integer testing and retraction functions. Date Created: March 1990 Date Last Updated: 9 April 1991")) (|integerIfCan| (((|Union| (|Integer|) "failed") |#1|) "\\spad{integerIfCan(x)} returns \\spad{x} as an integer,{} \"failed\" if \\spad{x} is not an integer.")) (|integer?| (((|Boolean|) |#1|) "\\spad{integer?(x)} is \\spad{true} if \\spad{x} is an integer,{} \\spad{false} otherwise.")) (|integer| (((|Integer|) |#1|) "\\spad{integer(x)} returns \\spad{x} as an integer; error if \\spad{x} is not an integer."))) NIL NIL -(-584 -1612) +(-584 -1613) ((|constructor| (NIL "This package provides functions for the integration of rational functions.")) (|extendedIntegrate| (((|Union| (|Record| (|:| |ratpart| (|Fraction| (|Polynomial| |#1|))) (|:| |coeff| (|Fraction| (|Polynomial| |#1|)))) "failed") (|Fraction| (|Polynomial| |#1|)) (|Symbol|) (|Fraction| (|Polynomial| |#1|))) "\\spad{extendedIntegrate(f, x, g)} returns fractions \\spad{[h, c]} such that \\spad{dc/dx = 0} and \\spad{dh/dx = f - cg},{} if \\spad{(h, c)} exist,{} \"failed\" otherwise.")) (|limitedIntegrate| (((|Union| (|Record| (|:| |mainpart| (|Fraction| (|Polynomial| |#1|))) (|:| |limitedlogs| (|List| (|Record| (|:| |coeff| (|Fraction| (|Polynomial| |#1|))) (|:| |logand| (|Fraction| (|Polynomial| |#1|))))))) "failed") (|Fraction| (|Polynomial| |#1|)) (|Symbol|) (|List| (|Fraction| (|Polynomial| |#1|)))) "\\spad{limitedIntegrate(f, x, [g1,...,gn])} returns fractions \\spad{[h, [[ci,gi]]]} such that the \\spad{gi}'s are among \\spad{[g1,...,gn]},{} \\spad{dci/dx = 0},{} and \\spad{d(h + sum(ci log(gi)))/dx = f} if possible,{} \"failed\" otherwise.")) (|infieldIntegrate| (((|Union| (|Fraction| (|Polynomial| |#1|)) "failed") (|Fraction| (|Polynomial| |#1|)) (|Symbol|)) "\\spad{infieldIntegrate(f, x)} returns a fraction \\spad{g} such that \\spad{dg/dx = f} if \\spad{g} exists,{} \"failed\" otherwise.")) (|internalIntegrate| (((|IntegrationResult| (|Fraction| (|Polynomial| |#1|))) (|Fraction| (|Polynomial| |#1|)) (|Symbol|)) "\\spad{internalIntegrate(f, x)} returns \\spad{g} such that \\spad{dg/dx = f}."))) NIL NIL @@ -2276,15 +2276,15 @@ NIL ((|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."))) NIL NIL -(-587 R -1612) +(-587 R -1613) ((|constructor| (NIL "\\indented{1}{Tools for the integrator} Author: Manuel Bronstein Date Created: 25 April 1990 Date Last Updated: 9 June 1993 Keywords: elementary,{} function,{} integration.")) (|intPatternMatch| (((|IntegrationResult| |#2|) |#2| (|Symbol|) (|Mapping| (|IntegrationResult| |#2|) |#2| (|Symbol|)) (|Mapping| (|Union| (|Record| (|:| |special| |#2|) (|:| |integrand| |#2|)) "failed") |#2| (|Symbol|))) "\\spad{intPatternMatch(f, x, int, pmint)} tries to integrate \\spad{f} first by using the integration function \\spad{int},{} and then by using the pattern match intetgration function \\spad{pmint} on any remaining unintegrable part.")) (|mkPrim| ((|#2| |#2| (|Symbol|)) "\\spad{mkPrim(f, x)} makes the logs in \\spad{f} which are linear in \\spad{x} primitive with respect to \\spad{x}.")) (|removeConstantTerm| ((|#2| |#2| (|Symbol|)) "\\spad{removeConstantTerm(f, x)} returns \\spad{f} minus any additive constant with respect to \\spad{x}.")) (|vark| (((|List| (|Kernel| |#2|)) (|List| |#2|) (|Symbol|)) "\\spad{vark([f1,...,fn],x)} returns the set-theoretic union of \\spad{(varselect(f1,x),...,varselect(fn,x))}.")) (|union| (((|List| (|Kernel| |#2|)) (|List| (|Kernel| |#2|)) (|List| (|Kernel| |#2|))) "\\spad{union(l1, l2)} returns set-theoretic union of \\spad{l1} and \\spad{l2}.")) (|ksec| (((|Kernel| |#2|) (|Kernel| |#2|) (|List| (|Kernel| |#2|)) (|Symbol|)) "\\spad{ksec(k, [k1,...,kn], x)} returns the second top-level \\spad{ki} after \\spad{k} involving \\spad{x}.")) (|kmax| (((|Kernel| |#2|) (|List| (|Kernel| |#2|))) "\\spad{kmax([k1,...,kn])} returns the top-level \\spad{ki} for integration.")) (|varselect| (((|List| (|Kernel| |#2|)) (|List| (|Kernel| |#2|)) (|Symbol|)) "\\spad{varselect([k1,...,kn], x)} returns the \\spad{ki} which involve \\spad{x}."))) NIL ((-12 (|HasCategory| |#1| (|%list| (QUOTE -633) (|%list| (QUOTE -916) (QUOTE (-560))))) (|HasCategory| |#1| (QUOTE (-466))) (|HasCategory| |#1| (|%list| (QUOTE -912) (QUOTE (-560)))) (|HasCategory| |#2| (QUOTE (-296))) (|HasCategory| |#2| (QUOTE (-649))) (|HasCategory| |#2| (|%list| (QUOTE -1070) (QUOTE (-1209))))) (-12 (|HasCategory| |#1| (QUOTE (-466))) (|HasCategory| |#2| (QUOTE (-296)))) (|HasCategory| |#1| (QUOTE (-571)))) -(-588 -1612 UP) +(-588 -1613 UP) ((|constructor| (NIL "This package provides functions for the transcendental case of the Risch algorithm.")) (|monomialIntPoly| (((|Record| (|:| |answer| |#2|) (|:| |polypart| |#2|)) |#2| (|Mapping| |#2| |#2|)) "\\spad{monomialIntPoly(p, ')} returns [\\spad{q},{} \\spad{r}] such that \\spad{p = q' + r} and \\spad{degree(r) < degree(t')}. Error if \\spad{degree(t') < 2}.")) (|monomialIntegrate| (((|Record| (|:| |ir| (|IntegrationResult| (|Fraction| |#2|))) (|:| |specpart| (|Fraction| |#2|)) (|:| |polypart| |#2|)) (|Fraction| |#2|) (|Mapping| |#2| |#2|)) "\\spad{monomialIntegrate(f, ')} returns \\spad{[ir, s, p]} such that \\spad{f = ir' + s + p} and all the squarefree factors of the denominator of \\spad{s} are special \\spad{w}.\\spad{r}.\\spad{t} the derivation '.")) (|expintfldpoly| (((|Union| (|LaurentPolynomial| |#1| |#2|) "failed") (|LaurentPolynomial| |#1| |#2|) (|Mapping| (|Record| (|:| |ans| |#1|) (|:| |right| |#1|) (|:| |sol?| (|Boolean|))) (|Integer|) |#1|)) "\\spad{expintfldpoly(p, foo)} returns \\spad{q} such that \\spad{p' = q} or \"failed\" if no such \\spad{q} exists. Argument foo is a Risch differential equation function on \\spad{F}.")) (|primintfldpoly| (((|Union| |#2| "failed") |#2| (|Mapping| (|Union| (|Record| (|:| |ratpart| |#1|) (|:| |coeff| |#1|)) "failed") |#1|) |#1|) "\\spad{primintfldpoly(p, ', t')} returns \\spad{q} such that \\spad{p' = q} or \"failed\" if no such \\spad{q} exists. Argument \\spad{t'} is the derivative of the primitive generating the extension.")) (|primlimintfrac| (((|Union| (|Record| (|:| |mainpart| (|Fraction| |#2|)) (|:| |limitedlogs| (|List| (|Record| (|:| |coeff| (|Fraction| |#2|)) (|:| |logand| (|Fraction| |#2|)))))) "failed") (|Fraction| |#2|) (|Mapping| |#2| |#2|) (|List| (|Fraction| |#2|))) "\\spad{primlimintfrac(f, ', [u1,...,un])} returns \\spad{[v, [c1,...,cn]]} such that \\spad{ci' = 0} and \\spad{f = v' + +/[ci * ui'/ui]}. Error: if \\spad{degree numer f >= degree denom f}.")) (|primextintfrac| (((|Union| (|Record| (|:| |ratpart| (|Fraction| |#2|)) (|:| |coeff| (|Fraction| |#2|))) "failed") (|Fraction| |#2|) (|Mapping| |#2| |#2|) (|Fraction| |#2|)) "\\spad{primextintfrac(f, ', g)} returns \\spad{[v, c]} such that \\spad{f = v' + c g} and \\spad{c' = 0}. Error: if \\spad{degree numer f >= degree denom f} or if \\spad{degree numer g >= degree denom g} or if \\spad{denom g} is not squarefree.")) (|explimitedint| (((|Union| (|Record| (|:| |answer| (|Record| (|:| |mainpart| (|Fraction| |#2|)) (|:| |limitedlogs| (|List| (|Record| (|:| |coeff| (|Fraction| |#2|)) (|:| |logand| (|Fraction| |#2|))))))) (|:| |a0| |#1|)) "failed") (|Fraction| |#2|) (|Mapping| |#2| |#2|) (|Mapping| (|Record| (|:| |ans| |#1|) (|:| |right| |#1|) (|:| |sol?| (|Boolean|))) (|Integer|) |#1|) (|List| (|Fraction| |#2|))) "\\spad{explimitedint(f, ', foo, [u1,...,un])} returns \\spad{[v, [c1,...,cn], a]} such that \\spad{ci' = 0},{} \\spad{f = v' + a + reduce(+,[ci * ui'/ui])},{} and \\spad{a = 0} or \\spad{a} has no integral in \\spad{F}. Returns \"failed\" if no such \\spad{v},{} \\spad{ci},{} a exist. Argument \\spad{foo} is a Risch differential equation function on \\spad{F}.")) (|primlimitedint| (((|Union| (|Record| (|:| |answer| (|Record| (|:| |mainpart| (|Fraction| |#2|)) (|:| |limitedlogs| (|List| (|Record| (|:| |coeff| (|Fraction| |#2|)) (|:| |logand| (|Fraction| |#2|))))))) (|:| |a0| |#1|)) "failed") (|Fraction| |#2|) (|Mapping| |#2| |#2|) (|Mapping| (|Union| (|Record| (|:| |ratpart| |#1|) (|:| |coeff| |#1|)) "failed") |#1|) (|List| (|Fraction| |#2|))) "\\spad{primlimitedint(f, ', foo, [u1,...,un])} returns \\spad{[v, [c1,...,cn], a]} such that \\spad{ci' = 0},{} \\spad{f = v' + a + reduce(+,[ci * ui'/ui])},{} and \\spad{a = 0} or \\spad{a} has no integral in UP. Returns \"failed\" if no such \\spad{v},{} \\spad{ci},{} a exist. Argument \\spad{foo} is an extended integration function on \\spad{F}.")) (|expextendedint| (((|Union| (|Record| (|:| |answer| (|Fraction| |#2|)) (|:| |a0| |#1|)) (|Record| (|:| |ratpart| (|Fraction| |#2|)) (|:| |coeff| (|Fraction| |#2|))) "failed") (|Fraction| |#2|) (|Mapping| |#2| |#2|) (|Mapping| (|Record| (|:| |ans| |#1|) (|:| |right| |#1|) (|:| |sol?| (|Boolean|))) (|Integer|) |#1|) (|Fraction| |#2|)) "\\spad{expextendedint(f, ', foo, g)} returns either \\spad{[v, c]} such that \\spad{f = v' + c g} and \\spad{c' = 0},{} or \\spad{[v, a]} such that \\spad{f = g' + a},{} and \\spad{a = 0} or \\spad{a} has no integral in \\spad{F}. Returns \"failed\" if neither case can hold. Argument \\spad{foo} is a Risch differential equation function on \\spad{F}.")) (|primextendedint| (((|Union| (|Record| (|:| |answer| (|Fraction| |#2|)) (|:| |a0| |#1|)) (|Record| (|:| |ratpart| (|Fraction| |#2|)) (|:| |coeff| (|Fraction| |#2|))) "failed") (|Fraction| |#2|) (|Mapping| |#2| |#2|) (|Mapping| (|Union| (|Record| (|:| |ratpart| |#1|) (|:| |coeff| |#1|)) "failed") |#1|) (|Fraction| |#2|)) "\\spad{primextendedint(f, ', foo, g)} returns either \\spad{[v, c]} such that \\spad{f = v' + c g} and \\spad{c' = 0},{} or \\spad{[v, a]} such that \\spad{f = g' + a},{} and \\spad{a = 0} or \\spad{a} has no integral in UP. Returns \"failed\" if neither case can hold. Argument \\spad{foo} is an extended integration function on \\spad{F}.")) (|tanintegrate| (((|Record| (|:| |answer| (|IntegrationResult| (|Fraction| |#2|))) (|:| |a0| |#1|)) (|Fraction| |#2|) (|Mapping| |#2| |#2|) (|Mapping| (|Union| (|List| |#1|) "failed") (|Integer|) |#1| |#1|)) "\\spad{tanintegrate(f, ', foo)} returns \\spad{[g, a]} such that \\spad{f = g' + a},{} and \\spad{a = 0} or \\spad{a} has no integral in \\spad{F}; Argument foo is a Risch differential system solver on \\spad{F}.")) (|expintegrate| (((|Record| (|:| |answer| (|IntegrationResult| (|Fraction| |#2|))) (|:| |a0| |#1|)) (|Fraction| |#2|) (|Mapping| |#2| |#2|) (|Mapping| (|Record| (|:| |ans| |#1|) (|:| |right| |#1|) (|:| |sol?| (|Boolean|))) (|Integer|) |#1|)) "\\spad{expintegrate(f, ', foo)} returns \\spad{[g, a]} such that \\spad{f = g' + a},{} and \\spad{a = 0} or \\spad{a} has no integral in \\spad{F}; Argument foo is a Risch differential equation solver on \\spad{F}.")) (|primintegrate| (((|Record| (|:| |answer| (|IntegrationResult| (|Fraction| |#2|))) (|:| |a0| |#1|)) (|Fraction| |#2|) (|Mapping| |#2| |#2|) (|Mapping| (|Union| (|Record| (|:| |ratpart| |#1|) (|:| |coeff| |#1|)) "failed") |#1|)) "\\spad{primintegrate(f, ', foo)} returns \\spad{[g, a]} such that \\spad{f = g' + a},{} and \\spad{a = 0} or \\spad{a} has no integral in UP. Argument foo is an extended integration function on \\spad{F}."))) NIL NIL -(-589 R -1612) +(-589 R -1613) ((|constructor| (NIL "This package computes the inverse Laplace Transform.")) (|inverseLaplace| (((|Union| |#2| "failed") |#2| (|Symbol|) (|Symbol|)) "\\spad{inverseLaplace(f, s, t)} returns the Inverse Laplace transform of \\spad{f(s)} using \\spad{t} as the new variable or \"failed\" if unable to find a closed form."))) NIL NIL @@ -2316,15 +2316,15 @@ NIL ((|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."))) NIL NIL -(-597 -1612) +(-597 -1613) ((|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}."))) ((-4505 . T) (-4504 . T)) ((|HasCategory| |#1| (|%list| (QUOTE -928) (QUOTE (-1209)))) (|HasCategory| |#1| (|%list| (QUOTE -1070) (QUOTE (-1209))))) -(-598 E -1612) +(-598 E -1613) ((|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"))) NIL NIL -(-599 R -1612) +(-599 R -1613) ((|constructor| (NIL "This package allows a sum of logs over the roots of a polynomial to be expressed as explicit logarithms and arc tangents,{} provided that the indexing polynomial can be factored into quadratics.")) (|complexExpand| ((|#2| (|IntegrationResult| |#2|)) "\\spad{complexExpand(i)} returns the expanded complex function corresponding to \\spad{i}.")) (|expand| (((|List| |#2|) (|IntegrationResult| |#2|)) "\\spad{expand(i)} returns the list of possible real functions corresponding to \\spad{i}.")) (|split| (((|IntegrationResult| |#2|) (|IntegrationResult| |#2|)) "\\spad{split(u(x) + sum_{P(a)=0} Q(a,x))} returns \\spad{u(x) + sum_{P1(a)=0} Q(a,x) + ... + sum_{Pn(a)=0} Q(a,x)} where \\spad{P1},{}...,{}Pn are the factors of \\spad{P}."))) NIL NIL @@ -2384,7 +2384,7 @@ NIL ((|constructor| (NIL "Functions defined on streams with entries in two sets.")) (|map| (((|Stream| |#3|) (|Mapping| |#3| |#1| |#2|) (|InfiniteTuple| |#1|) (|Stream| |#2|)) "\\spad{map(f,a,b)} \\undocumented") (((|Stream| |#3|) (|Mapping| |#3| |#1| |#2|) (|Stream| |#1|) (|InfiniteTuple| |#2|)) "\\spad{map(f,a,b)} \\undocumented") (((|InfiniteTuple| |#3|) (|Mapping| |#3| |#1| |#2|) (|InfiniteTuple| |#1|) (|InfiniteTuple| |#2|)) "\\spad{map(f,a,b)} \\undocumented"))) NIL NIL -(-614 R -1612 FG) +(-614 R -1613 FG) ((|constructor| (NIL "This package provides transformations from trigonometric functions to exponentials and logarithms,{} and back. \\spad{F} and FG should be the same type of function space.")) (|trigs2explogs| ((|#3| |#3| (|List| (|Kernel| |#3|)) (|List| (|Symbol|))) "\\spad{trigs2explogs(f, [k1,...,kn], [x1,...,xm])} rewrites all the trigonometric functions appearing in \\spad{f} and involving one of the \\spad{xi's} in terms of complex logarithms and exponentials. A kernel of the form \\spad{tan(u)} is expressed using \\spad{exp(u)**2} if it is one of the \\spad{ki's},{} in terms of \\spad{exp(2*u)} otherwise.")) (|explogs2trigs| (((|Complex| |#2|) |#3|) "\\spad{explogs2trigs(f)} rewrites all the complex logs and exponentials appearing in \\spad{f} in terms of trigonometric functions.")) (F2FG ((|#3| |#2|) "\\spad{F2FG(a + sqrt(-1) b)} returns \\spad{a + i b}.")) (FG2F ((|#2| |#3|) "\\spad{FG2F(a + i b)} returns \\spad{a + sqrt(-1) b}.")) (GF2FG ((|#3| (|Complex| |#2|)) "\\spad{GF2FG(a + i b)} returns \\spad{a + i b} viewed as a function with the \\spad{i} pushed down into the coefficient domain."))) NIL NIL @@ -2410,7 +2410,7 @@ NIL NIL (-620 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)."))) -((-4507 -2210 (-1385 (|has| |#2| (-380 |#1|)) (|has| |#1| (-571))) (-12 (|has| |#2| (-432 |#1|)) (|has| |#1| (-571)))) (-4505 . T) (-4504 . T)) +((-4507 -2210 (-1384 (|has| |#2| (-380 |#1|)) (|has| |#1| (-571))) (-12 (|has| |#2| (-432 |#1|)) (|has| |#1| (-571)))) (-4505 . T) (-4504 . T)) ((-2210 (|HasCategory| |#2| (|%list| (QUOTE -380) (|devaluate| |#1|))) (|HasCategory| |#2| (|%list| (QUOTE -432) (|devaluate| |#1|)))) (|HasCategory| |#2| (|%list| (QUOTE -432) (|devaluate| |#1|))) (-12 (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#2| (|%list| (QUOTE -432) (|devaluate| |#1|)))) (-2210 (-12 (|HasCategory| |#1| (QUOTE (-571))) (|HasCategory| |#2| (|%list| (QUOTE -380) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-571))) (|HasCategory| |#2| (|%list| (QUOTE -432) (|devaluate| |#1|))))) (|HasCategory| |#2| (|%list| (QUOTE -380) (|devaluate| |#1|)))) (-621) ((|constructor| (NIL "This is the datatype for the JVM bytecodes."))) @@ -2464,7 +2464,7 @@ NIL ((|constructor| (NIL "A is convertible to \\spad{B} means any element of A can be converted into an element of \\spad{B},{} but not automatically by the interpreter.")) (|convert| ((|#1| $) "\\spad{convert(a)} transforms a into an element of \\spad{S}."))) NIL NIL -(-634 -1612 UP) +(-634 -1613 UP) ((|constructor| (NIL "\\spadtype{Kovacic} provides a modified Kovacic's algorithm for solving explicitely irreducible 2nd order linear ordinary differential equations.")) (|kovacic| (((|Union| (|SparseUnivariatePolynomial| (|Fraction| |#2|)) "failed") (|Fraction| |#2|) (|Fraction| |#2|) (|Fraction| |#2|) (|Mapping| (|Factored| |#2|) |#2|)) "\\spad{kovacic(a_0,a_1,a_2,ezfactor)} returns either \"failed\" or \\spad{P}(\\spad{u}) such that \\spad{\\$e^{\\int(-a_1/2a_2)} e^{\\int u}\\$} is a solution of \\indented{5}{\\spad{\\$a_2 y'' + a_1 y' + a0 y = 0\\$}} whenever \\spad{u} is a solution of \\spad{P u = 0}. The equation must be already irreducible over the rational functions. Argument \\spad{ezfactor} is a factorisation in \\spad{UP},{} not necessarily into irreducibles.") (((|Union| (|SparseUnivariatePolynomial| (|Fraction| |#2|)) "failed") (|Fraction| |#2|) (|Fraction| |#2|) (|Fraction| |#2|)) "\\spad{kovacic(a_0,a_1,a_2)} returns either \"failed\" or \\spad{P}(\\spad{u}) such that \\spad{\\$e^{\\int(-a_1/2a_2)} e^{\\int u}\\$} is a solution of \\indented{5}{\\spad{a_2 y'' + a_1 y' + a0 y = 0}} whenever \\spad{u} is a solution of \\spad{P u = 0}. The equation must be already irreducible over the rational functions."))) NIL NIL @@ -2492,7 +2492,7 @@ NIL ((|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."))) ((-4507 . T)) NIL -(-641 R -1612) +(-641 R -1613) ((|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."))) NIL NIL @@ -2520,7 +2520,7 @@ NIL ((|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}."))) NIL NIL -(-648 R -1612) +(-648 R -1613) ((|constructor| (NIL "This package provides liouvillian functions over an integral domain.")) (|integral| ((|#2| |#2| (|SegmentBinding| |#2|)) "\\spad{integral(f,x = a..b)} denotes the definite integral of \\spad{f} with respect to \\spad{x} from \\spad{a} to \\spad{b}.") ((|#2| |#2| (|Symbol|)) "\\spad{integral(f,x)} indefinite integral of \\spad{f} with respect to \\spad{x}.")) (|dilog| ((|#2| |#2|) "\\spad{dilog(f)} denotes the dilogarithm")) (|erf| ((|#2| |#2|) "\\spad{erf(f)} denotes the error function")) (|li| ((|#2| |#2|) "\\spad{li(f)} denotes the logarithmic integral")) (|Ci| ((|#2| |#2|) "\\spad{Ci(f)} denotes the cosine integral")) (|Si| ((|#2| |#2|) "\\spad{Si(f)} denotes the sine integral")) (|Ei| ((|#2| |#2|) "\\spad{Ei(f)} denotes the exponential integral")) (|operator| (((|BasicOperator|) (|BasicOperator|)) "\\spad{operator(op)} returns the Liouvillian operator based on \\spad{op}")) (|belong?| (((|Boolean|) (|BasicOperator|)) "\\spad{belong?(op)} checks if \\spad{op} is Liouvillian"))) NIL NIL @@ -2528,7 +2528,7 @@ NIL ((|constructor| (NIL "Category for the transcendental Liouvillian functions.")) (|erf| (($ $) "\\spad{erf(x)} returns the error function of \\spad{x},{} \\spadignore{i.e.} \\spad{2 / sqrt(\\%pi)} times the integral of \\spad{exp(-x**2) dx}.")) (|dilog| (($ $) "\\spad{dilog(x)} returns the dilogarithm of \\spad{x},{} \\spadignore{i.e.} the integral of \\spad{log(x) / (1 - x) dx}.")) (|li| (($ $) "\\spad{li(x)} returns the logarithmic integral of \\spad{x},{} \\spadignore{i.e.} the integral of \\spad{dx / log(x)}.")) (|Ci| (($ $) "\\spad{Ci(x)} returns the cosine integral of \\spad{x},{} \\spadignore{i.e.} the integral of \\spad{cos(x) / x dx}.")) (|Si| (($ $) "\\spad{Si(x)} returns the sine integral of \\spad{x},{} \\spadignore{i.e.} the integral of \\spad{sin(x) / x dx}.")) (|Ei| (($ $) "\\spad{Ei(x)} returns the exponential integral of \\spad{x},{} \\spadignore{i.e.} the integral of \\spad{exp(x)/x dx}."))) NIL NIL -(-650 |lv| -1612) +(-650 |lv| -1613) ((|constructor| (NIL "\\indented{1}{Given a Groebner basis \\spad{B} with respect to the total degree ordering for} a zero-dimensional ideal \\spad{I},{} compute a Groebner basis with respect to the lexicographical ordering by using linear algebra.")) (|transform| (((|HomogeneousDistributedMultivariatePolynomial| |#1| |#2|) (|DistributedMultivariatePolynomial| |#1| |#2|)) "\\spad{transform }\\undocumented")) (|choosemon| (((|DistributedMultivariatePolynomial| |#1| |#2|) (|DistributedMultivariatePolynomial| |#1| |#2|) (|List| (|DistributedMultivariatePolynomial| |#1| |#2|))) "\\spad{choosemon }\\undocumented")) (|intcompBasis| (((|List| (|HomogeneousDistributedMultivariatePolynomial| |#1| |#2|)) (|OrderedVariableList| |#1|) (|List| (|HomogeneousDistributedMultivariatePolynomial| |#1| |#2|)) (|List| (|HomogeneousDistributedMultivariatePolynomial| |#1| |#2|))) "\\spad{intcompBasis }\\undocumented")) (|anticoord| (((|DistributedMultivariatePolynomial| |#1| |#2|) (|List| |#2|) (|DistributedMultivariatePolynomial| |#1| |#2|) (|List| (|DistributedMultivariatePolynomial| |#1| |#2|))) "\\spad{anticoord }\\undocumented")) (|coord| (((|Vector| |#2|) (|HomogeneousDistributedMultivariatePolynomial| |#1| |#2|) (|List| (|HomogeneousDistributedMultivariatePolynomial| |#1| |#2|))) "\\spad{coord }\\undocumented")) (|computeBasis| (((|List| (|HomogeneousDistributedMultivariatePolynomial| |#1| |#2|)) (|List| (|HomogeneousDistributedMultivariatePolynomial| |#1| |#2|))) "\\spad{computeBasis }\\undocumented")) (|minPol| (((|HomogeneousDistributedMultivariatePolynomial| |#1| |#2|) (|List| (|HomogeneousDistributedMultivariatePolynomial| |#1| |#2|)) (|OrderedVariableList| |#1|)) "\\spad{minPol }\\undocumented") (((|HomogeneousDistributedMultivariatePolynomial| |#1| |#2|) (|List| (|HomogeneousDistributedMultivariatePolynomial| |#1| |#2|)) (|List| (|HomogeneousDistributedMultivariatePolynomial| |#1| |#2|)) (|OrderedVariableList| |#1|)) "\\spad{minPol }\\undocumented")) (|totolex| (((|List| (|DistributedMultivariatePolynomial| |#1| |#2|)) (|List| (|HomogeneousDistributedMultivariatePolynomial| |#1| |#2|))) "\\spad{totolex }\\undocumented")) (|groebgen| (((|Record| (|:| |glbase| (|List| (|DistributedMultivariatePolynomial| |#1| |#2|))) (|:| |glval| (|List| (|Integer|)))) (|List| (|DistributedMultivariatePolynomial| |#1| |#2|))) "\\spad{groebgen }\\undocumented")) (|linGenPos| (((|Record| (|:| |gblist| (|List| (|DistributedMultivariatePolynomial| |#1| |#2|))) (|:| |gvlist| (|List| (|Integer|)))) (|List| (|HomogeneousDistributedMultivariatePolynomial| |#1| |#2|))) "\\spad{linGenPos }\\undocumented"))) NIL NIL @@ -2538,7 +2538,7 @@ NIL ((-12 (|HasCategory| (-2 (|:| -3837 (-1191)) (|:| -2715 (-51))) (QUOTE (-1133))) (|HasCategory| (-2 (|:| -3837 (-1191)) (|:| -2715 (-51))) (|%list| (QUOTE -321) (|%list| (QUOTE -2) (|%list| (QUOTE |:|) (QUOTE -3837) (QUOTE (-1191))) (|%list| (QUOTE |:|) (QUOTE -2715) (QUOTE (-51))))))) (-2210 (|HasCategory| (-2 (|:| -3837 (-1191)) (|:| -2715 (-51))) (QUOTE (-1133))) (|HasCategory| (-51) (QUOTE (-1133)))) (-2210 (|HasCategory| (-2 (|:| -3837 (-1191)) (|:| -2715 (-51))) (QUOTE (-102))) (|HasCategory| (-2 (|:| -3837 (-1191)) (|:| -2715 (-51))) (QUOTE (-1133))) (|HasCategory| (-51) (QUOTE (-102))) (|HasCategory| (-51) (QUOTE (-1133)))) (-2210 (|HasCategory| (-2 (|:| -3837 (-1191)) (|:| -2715 (-51))) (QUOTE (-1133))) (|HasCategory| (-2 (|:| -3837 (-1191)) (|:| -2715 (-51))) (|%list| (QUOTE -632) (QUOTE (-888)))) (|HasCategory| (-51) (QUOTE (-1133))) (|HasCategory| (-51) (|%list| (QUOTE -632) (QUOTE (-888))))) (|HasCategory| (-2 (|:| -3837 (-1191)) (|:| -2715 (-51))) (|%list| (QUOTE -633) (QUOTE (-549)))) (-12 (|HasCategory| (-51) (QUOTE (-1133))) (|HasCategory| (-51) (|%list| (QUOTE -321) (QUOTE (-51))))) (|HasCategory| (-1191) (QUOTE (-872))) (-2210 (|HasCategory| (-2 (|:| -3837 (-1191)) (|:| -2715 (-51))) (|%list| (QUOTE -632) (QUOTE (-888)))) (|HasCategory| (-51) (|%list| (QUOTE -632) (QUOTE (-888))))) (-2210 (|HasCategory| (-2 (|:| -3837 (-1191)) (|:| -2715 (-51))) (QUOTE (-102))) (|HasCategory| (-51) (QUOTE (-102)))) (|HasCategory| (-51) (QUOTE (-1133))) (|HasCategory| (-51) (QUOTE (-102))) (|HasCategory| (-51) (|%list| (QUOTE -632) (QUOTE (-888)))) (|HasCategory| (-2 (|:| -3837 (-1191)) (|:| -2715 (-51))) (|%list| (QUOTE -632) (QUOTE (-888)))) (|HasCategory| (-2 (|:| -3837 (-1191)) (|:| -2715 (-51))) (QUOTE (-102))) (|HasCategory| (-2 (|:| -3837 (-1191)) (|:| -2715 (-51))) (QUOTE (-1133)))) (-652 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)."))) -((-4507 -2210 (-1385 (|has| |#2| (-380 |#1|)) (|has| |#1| (-571))) (-12 (|has| |#2| (-432 |#1|)) (|has| |#1| (-571)))) (-4505 . T) (-4504 . T)) +((-4507 -2210 (-1384 (|has| |#2| (-380 |#1|)) (|has| |#1| (-571))) (-12 (|has| |#2| (-432 |#1|)) (|has| |#1| (-571)))) (-4505 . T) (-4504 . T)) ((-2210 (|HasCategory| |#2| (|%list| (QUOTE -380) (|devaluate| |#1|))) (|HasCategory| |#2| (|%list| (QUOTE -432) (|devaluate| |#1|)))) (|HasCategory| |#2| (|%list| (QUOTE -432) (|devaluate| |#1|))) (-12 (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#2| (|%list| (QUOTE -432) (|devaluate| |#1|)))) (-2210 (-12 (|HasCategory| |#1| (QUOTE (-571))) (|HasCategory| |#2| (|%list| (QUOTE -380) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-571))) (|HasCategory| |#2| (|%list| (QUOTE -432) (|devaluate| |#1|))))) (|HasCategory| |#2| (|%list| (QUOTE -380) (|devaluate| |#1|)))) (-653 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}}."))) @@ -2628,11 +2628,11 @@ NIL ((|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}."))) ((-4505 . T) (-4504 . T)) ((|HasCategory| |#1| (QUOTE (-814)))) -(-675 R -1612 L) +(-675 R -1613 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."))) NIL NIL -(-676 A -4216) +(-676 A -3257) ((|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}}"))) ((-4504 . T) (-4505 . T) (-4507 . T)) ((|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (|%list| (QUOTE -1070) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#1| (|%list| (QUOTE -1070) (QUOTE (-560)))) (|HasCategory| |#1| (QUOTE (-571))) (|HasCategory| |#1| (QUOTE (-466))) (|HasCategory| |#1| (QUOTE (-376)))) @@ -2652,7 +2652,7 @@ NIL ((|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}."))) ((-4504 . T) (-4505 . T) (-4507 . T)) NIL -(-681 -1612 UP) +(-681 -1613 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}."))) NIL ((|HasCategory| |#1| (QUOTE (-27)))) @@ -2684,11 +2684,11 @@ NIL ((|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| (($ |#1|) "\\spad{list(x)} returns the list of one element \\spad{x}."))) ((-4511 . T) (-4510 . T)) NIL -(-689 -1612 |Row| |Col| M) +(-689 -1613 |Row| |Col| M) ((|constructor| (NIL "This package solves linear system in the matrix form \\spad{AX = B}.")) (|rank| (((|NonNegativeInteger|) |#4| |#3|) "\\spad{rank(A,B)} computes the rank of the complete matrix \\spad{(A|B)} of the linear system \\spad{AX = B}.")) (|hasSolution?| (((|Boolean|) |#4| |#3|) "\\spad{hasSolution?(A,B)} tests if the linear system \\spad{AX = B} has a solution.")) (|particularSolution| (((|Union| |#3| "failed") |#4| |#3|) "\\spad{particularSolution(A,B)} finds a particular solution of the linear system \\spad{AX = B}.")) (|solve| (((|List| (|Record| (|:| |particular| (|Union| |#3| "failed")) (|:| |basis| (|List| |#3|)))) |#4| (|List| |#3|)) "\\spad{solve(A,LB)} finds a particular soln of the systems \\spad{AX = B} and a basis of the associated homogeneous systems \\spad{AX = 0} where \\spad{B} varies in the list of column vectors \\spad{LB}.") (((|Record| (|:| |particular| (|Union| |#3| "failed")) (|:| |basis| (|List| |#3|))) |#4| |#3|) "\\spad{solve(A,B)} finds a particular solution of the system \\spad{AX = B} and a basis of the associated homogeneous system \\spad{AX = 0}."))) NIL NIL -(-690 -1612) +(-690 -1613) ((|constructor| (NIL "This package solves linear system in the matrix form \\spad{AX = B}. It is essentially a particular instantiation of the package \\spadtype{LinearSystemMatrixPackage} for Matrix and Vector. This package's existence makes it easier to use \\spadfun{solve} in the AXIOM interpreter.")) (|rank| (((|NonNegativeInteger|) (|Matrix| |#1|) (|Vector| |#1|)) "\\spad{rank(A,B)} computes the rank of the complete matrix \\spad{(A|B)} of the linear system \\spad{AX = B}.")) (|hasSolution?| (((|Boolean|) (|Matrix| |#1|) (|Vector| |#1|)) "\\spad{hasSolution?(A,B)} tests if the linear system \\spad{AX = B} has a solution.")) (|particularSolution| (((|Union| (|Vector| |#1|) "failed") (|Matrix| |#1|) (|Vector| |#1|)) "\\spad{particularSolution(A,B)} finds a particular solution of the linear system \\spad{AX = B}.")) (|solve| (((|List| (|Record| (|:| |particular| (|Union| (|Vector| |#1|) "failed")) (|:| |basis| (|List| (|Vector| |#1|))))) (|List| (|List| |#1|)) (|List| (|Vector| |#1|))) "\\spad{solve(A,LB)} finds a particular soln of the systems \\spad{AX = B} and a basis of the associated homogeneous systems \\spad{AX = 0} where \\spad{B} varies in the list of column vectors \\spad{LB}.") (((|List| (|Record| (|:| |particular| (|Union| (|Vector| |#1|) "failed")) (|:| |basis| (|List| (|Vector| |#1|))))) (|Matrix| |#1|) (|List| (|Vector| |#1|))) "\\spad{solve(A,LB)} finds a particular soln of the systems \\spad{AX = B} and a basis of the associated homogeneous systems \\spad{AX = 0} where \\spad{B} varies in the list of column vectors \\spad{LB}.") (((|Record| (|:| |particular| (|Union| (|Vector| |#1|) "failed")) (|:| |basis| (|List| (|Vector| |#1|)))) (|List| (|List| |#1|)) (|Vector| |#1|)) "\\spad{solve(A,B)} finds a particular solution of the system \\spad{AX = B} and a basis of the associated homogeneous system \\spad{AX = 0}.") (((|Record| (|:| |particular| (|Union| (|Vector| |#1|) "failed")) (|:| |basis| (|List| (|Vector| |#1|)))) (|Matrix| |#1|) (|Vector| |#1|)) "\\spad{solve(A,B)} finds a particular solution of the system \\spad{AX = B} and a basis of the associated homogeneous system \\spad{AX = 0}."))) NIL NIL @@ -2784,7 +2784,7 @@ NIL ((|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 -(-714 S -1612 FLAF FLAS) +(-714 S -1613 FLAF FLAS) ((|constructor| (NIL "\\indented{1}{\\spadtype{MultiVariableCalculusFunctions} Package provides several} \\indented{1}{functions for multivariable calculus.} These include gradient,{} hessian and jacobian,{} divergence and laplacian. Various forms for banded and sparse storage of matrices are included.")) (|bandedJacobian| (((|Matrix| |#2|) |#3| |#4| (|NonNegativeInteger|) (|NonNegativeInteger|)) "\\spad{bandedJacobian(vf,xlist,kl,ku)} computes the jacobian,{} the matrix of first partial derivatives,{} of the vector field \\spad{vf},{} \\spad{vf} a vector function of the variables listed in \\spad{xlist},{} \\spad{kl} is the number of nonzero subdiagonals,{} \\spad{ku} is the number of nonzero superdiagonals,{} \\spad{kl+ku+1} being actual bandwidth. Stores the nonzero band in a matrix,{} dimensions \\spad{kl+ku+1} by \\#xlist. The upper triangle is in the top \\spad{ku} rows,{} the diagonal is in row \\spad{ku+1},{} the lower triangle in the last \\spad{kl} rows. Entries in a column in the band store correspond to entries in same column of full store. (The notation conforms to LAPACK/NAG-\\spad{F07} conventions.)")) (|jacobian| (((|Matrix| |#2|) |#3| |#4|) "\\spad{jacobian(vf,xlist)} computes the jacobian,{} the matrix of first partial derivatives,{} of the vector field \\spad{vf},{} \\spad{vf} a vector function of the variables listed in \\spad{xlist}.")) (|bandedHessian| (((|Matrix| |#2|) |#2| |#4| (|NonNegativeInteger|)) "\\spad{bandedHessian(v,xlist,k)} computes the hessian,{} the matrix of second partial derivatives,{} of the scalar field \\spad{v},{} \\spad{v} a function of the variables listed in \\spad{xlist},{} \\spad{k} is the semi-bandwidth,{} the number of nonzero subdiagonals,{} 2*k+1 being actual bandwidth. Stores the nonzero band in lower triangle in a matrix,{} dimensions \\spad{k+1} by \\#xlist,{} whose rows are the vectors formed by diagonal,{} subdiagonal,{} etc. of the real,{} full-matrix,{} hessian. (The notation conforms to LAPACK/NAG-\\spad{F07} conventions.)")) (|hessian| (((|Matrix| |#2|) |#2| |#4|) "\\spad{hessian(v,xlist)} computes the hessian,{} the matrix of second partial derivatives,{} of the scalar field \\spad{v},{} \\spad{v} a function of the variables listed in \\spad{xlist}.")) (|laplacian| ((|#2| |#2| |#4|) "\\spad{laplacian(v,xlist)} computes the laplacian of the scalar field \\spad{v},{} \\spad{v} a function of the variables listed in \\spad{xlist}.")) (|divergence| ((|#2| |#3| |#4|) "\\spad{divergence(vf,xlist)} computes the divergence of the vector field \\spad{vf},{} \\spad{vf} a vector function of the variables listed in \\spad{xlist}.")) (|gradient| (((|Vector| |#2|) |#2| |#4|) "\\spad{gradient(v,xlist)} computes the gradient,{} the vector of first partial derivatives,{} of the scalar field \\spad{v},{} \\spad{v} a function of the variables listed in \\spad{xlist}."))) NIL NIL @@ -2808,7 +2808,7 @@ NIL ((|constructor| (NIL "\\indented{1}{<description of package>} Author: Jim Wen Date Created: ?? Date Last Updated: October 1991 by Jon Steinbach Keywords: Examples: References:")) (|ptFunc| (((|Mapping| (|Point| (|DoubleFloat|)) (|DoubleFloat|) (|DoubleFloat|)) (|Mapping| (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|)) (|Mapping| (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|)) (|Mapping| (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|)) (|Mapping| (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|))) "\\spad{ptFunc(a,b,c,d)} is an internal function exported in order to compile packages.")) (|meshPar1Var| (((|ThreeSpace| (|DoubleFloat|)) (|Expression| (|Integer|)) (|Expression| (|Integer|)) (|Expression| (|Integer|)) (|Mapping| (|DoubleFloat|) (|DoubleFloat|)) (|Segment| (|DoubleFloat|)) (|List| (|DrawOption|))) "\\spad{meshPar1Var(s,t,u,f,s1,l)} \\undocumented")) (|meshFun2Var| (((|ThreeSpace| (|DoubleFloat|)) (|Mapping| (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|)) (|Union| (|Mapping| (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|)) "undefined") (|Segment| (|DoubleFloat|)) (|Segment| (|DoubleFloat|)) (|List| (|DrawOption|))) "\\spad{meshFun2Var(f,g,s1,s2,l)} \\undocumented")) (|meshPar2Var| (((|ThreeSpace| (|DoubleFloat|)) (|ThreeSpace| (|DoubleFloat|)) (|Mapping| (|Point| (|DoubleFloat|)) (|DoubleFloat|) (|DoubleFloat|)) (|Segment| (|DoubleFloat|)) (|Segment| (|DoubleFloat|)) (|List| (|DrawOption|))) "\\spad{meshPar2Var(sp,f,s1,s2,l)} \\undocumented") (((|ThreeSpace| (|DoubleFloat|)) (|Mapping| (|Point| (|DoubleFloat|)) (|DoubleFloat|) (|DoubleFloat|)) (|Segment| (|DoubleFloat|)) (|Segment| (|DoubleFloat|)) (|List| (|DrawOption|))) "\\spad{meshPar2Var(f,s1,s2,l)} \\undocumented") (((|ThreeSpace| (|DoubleFloat|)) (|Mapping| (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|)) (|Mapping| (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|)) (|Mapping| (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|)) (|Union| (|Mapping| (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|)) "undefined") (|Segment| (|DoubleFloat|)) (|Segment| (|DoubleFloat|)) (|List| (|DrawOption|))) "\\spad{meshPar2Var(f,g,h,j,s1,s2,l)} \\undocumented"))) NIL NIL -(-720 OV E -1612 PG) +(-720 OV E -1613 PG) ((|constructor| (NIL "Package for factorization of multivariate polynomials over finite fields.")) (|factor| (((|Factored| (|SparseUnivariatePolynomial| |#4|)) (|SparseUnivariatePolynomial| |#4|)) "\\spad{factor(p)} produces the complete factorization of the multivariate polynomial \\spad{p} over a finite field. \\spad{p} is represented as a univariate polynomial with multivariate coefficients over a finite field.") (((|Factored| |#4|) |#4|) "\\spad{factor(p)} produces the complete factorization of the multivariate polynomial \\spad{p} over a finite field."))) NIL NIL @@ -2840,7 +2840,7 @@ NIL ((|constructor| (NIL "MakeRecord is used internally by the interpreter to create record types which are used for doing parallel iterations on streams.")) (|makeRecord| (((|Record| (|:| |part1| |#1|) (|:| |part2| |#2|)) |#1| |#2|) "\\spad{makeRecord(a,b)} creates a record object with type Record(part1:S,{} part2:R),{} where \\spad{part1} is \\spad{a} and \\spad{part2} is \\spad{b}."))) NIL NIL -(-728 S -4350 I) +(-728 S -4349 I) ((|constructor| (NIL "transforms top-level objects into compiled functions.")) (|compiledFunction| (((|Mapping| |#3| |#2|) |#1| (|Symbol|)) "\\spad{compiledFunction(expr, x)} returns a function \\spad{f: D -> I} defined by \\spad{f(x) == expr}. Function \\spad{f} is compiled and directly applicable to objects of type \\spad{D}.")) (|unaryFunction| (((|Mapping| |#3| |#2|) (|Symbol|)) "\\spad{unaryFunction(a)} is a local function"))) NIL NIL @@ -2860,7 +2860,7 @@ NIL ((|constructor| (NIL "\\spadtype{MathMLFormat} provides a coercion from \\spadtype{OutputForm} to MathML format.")) (|display| (((|Void|) (|String|)) "prints the string returned by coerce,{} adding <math ...> tags.")) (|exprex| (((|String|) (|OutputForm|)) "coverts \\spadtype{OutputForm} to \\spadtype{String} with the structure preserved with braces. Actually this is not quite accurate. The function \\spadfun{precondition} is first applied to the \\spadtype{OutputForm} expression before \\spadfun{exprex}. The raw \\spadtype{OutputForm} and the nature of the \\spadfun{precondition} function is still obscure to me at the time of this writing (2007-02-14).")) (|coerceL| (((|String|) (|OutputForm|)) "coerceS(\\spad{o}) changes \\spad{o} in the standard output format to MathML format and displays result as one long string.")) (|coerceS| (((|String|) (|OutputForm|)) "\\spad{coerceS(o)} changes \\spad{o} in the standard output format to MathML format and displays formatted result.")) (|coerce| (((|String|) (|OutputForm|)) "coerceS(\\spad{o}) changes \\spad{o} in the standard output format to MathML format."))) NIL NIL -(-733 R |Mod| -3217 -1573 |exactQuo|) +(-733 R |Mod| -4256 -2410 |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| $) "\\spad{modulus(x)} \\undocumented"))) ((-4502 . T) (-4508 . T) (-4503 . T) ((-4512 "*") . T) (-4504 . T) (-4505 . T) (-4507 . T)) NIL @@ -2876,7 +2876,7 @@ NIL ((|constructor| (NIL "Algebra of ADDITIVE operators on a module.")) (|makeop| (($ |#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| (($ $ $) "\\spad{adjoint(op1, op2)} sets the adjoint of \\spad{op1} to be \\spad{op2}. \\spad{op1} must be a basic operator") (($ $) "\\spad{adjoint(op)} returns the adjoint of the operator \\spad{op}."))) ((-4505 |has| |#1| (-175)) (-4504 |has| |#1| (-175)) (-4507 . T)) ((|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-149)))) -(-737 R |Mod| -3217 -1573 |exactQuo|) +(-737 R |Mod| -4256 -2410 |exactQuo|) ((|constructor| (NIL "These domains are used for the factorization and gcds of univariate polynomials over the integers in order to work modulo different primes. See \\spadtype{EuclideanModularRing} ,{}\\spadtype{ModularField}")) (|inv| (($ $) "\\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"))) ((-4507 . T)) NIL @@ -2888,7 +2888,7 @@ NIL ((|constructor| (NIL "The category of modules over a commutative ring. \\blankline"))) ((-4505 . T) (-4504 . T)) NIL -(-740 -1612) +(-740 -1613) ((|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]]}."))) ((-4507 . T)) NIL @@ -2924,7 +2924,7 @@ NIL ((|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."))) NIL NIL -(-749 -1612 UP) +(-749 -1613 UP) ((|constructor| (NIL "Tools for handling monomial extensions.")) (|decompose| (((|Record| (|:| |poly| |#2|) (|:| |normal| (|Fraction| |#2|)) (|:| |special| (|Fraction| |#2|))) (|Fraction| |#2|) (|Mapping| |#2| |#2|)) "\\spad{decompose(f, D)} returns \\spad{[p,n,s]} such that \\spad{f = p+n+s},{} all the squarefree factors of \\spad{denom(n)} are normal \\spad{w}.\\spad{r}.\\spad{t}. \\spad{D},{} \\spad{denom(s)} is special \\spad{w}.\\spad{r}.\\spad{t}. \\spad{D},{} and \\spad{n} and \\spad{s} are proper fractions (no pole at infinity). \\spad{D} is the derivation to use.")) (|normalDenom| ((|#2| (|Fraction| |#2|) (|Mapping| |#2| |#2|)) "\\spad{normalDenom(f, D)} returns the product of all the normal factors of \\spad{denom(f)}. \\spad{D} is the derivation to use.")) (|splitSquarefree| (((|Record| (|:| |normal| (|Factored| |#2|)) (|:| |special| (|Factored| |#2|))) |#2| (|Mapping| |#2| |#2|)) "\\spad{splitSquarefree(p, D)} returns \\spad{[n_1 n_2\\^2 ... n_m\\^m, s_1 s_2\\^2 ... s_q\\^q]} such that \\spad{p = n_1 n_2\\^2 ... n_m\\^m s_1 s_2\\^2 ... s_q\\^q},{} each \\spad{n_i} is normal \\spad{w}.\\spad{r}.\\spad{t}. \\spad{D} and each \\spad{s_i} is special \\spad{w}.\\spad{r}.\\spad{t} \\spad{D}. \\spad{D} is the derivation to use.")) (|split| (((|Record| (|:| |normal| |#2|) (|:| |special| |#2|)) |#2| (|Mapping| |#2| |#2|)) "\\spad{split(p, D)} returns \\spad{[n,s]} such that \\spad{p = n s},{} all the squarefree factors of \\spad{n} are normal \\spad{w}.\\spad{r}.\\spad{t}. \\spad{D},{} and \\spad{s} is special \\spad{w}.\\spad{r}.\\spad{t}. \\spad{D}. \\spad{D} is the derivation to use."))) NIL NIL @@ -3076,11 +3076,11 @@ NIL ((|constructor| (NIL "This package computes explicitly eigenvalues and eigenvectors of matrices with entries over the complex rational numbers. The results are expressed either as complex floating numbers or as complex rational numbers depending on the type of the precision parameter.")) (|complexEigenvectors| (((|List| (|Record| (|:| |outval| (|Complex| |#1|)) (|:| |outmult| (|Integer|)) (|:| |outvect| (|List| (|Matrix| (|Complex| |#1|)))))) (|Matrix| (|Complex| (|Fraction| (|Integer|)))) |#1|) "\\spad{complexEigenvectors(m,eps)} returns a list of records each one containing a complex eigenvalue,{} its algebraic multiplicity,{} and a list of associated eigenvectors. All these results are computed to precision \\spad{eps} and are expressed as complex floats or complex rational numbers depending on the type of \\spad{eps} (float or rational).")) (|complexEigenvalues| (((|List| (|Complex| |#1|)) (|Matrix| (|Complex| (|Fraction| (|Integer|)))) |#1|) "\\spad{complexEigenvalues(m,eps)} computes the eigenvalues of the matrix \\spad{m} to precision \\spad{eps}. The eigenvalues are expressed as complex floats or complex rational numbers depending on the type of \\spad{eps} (float or rational).")) (|characteristicPolynomial| (((|Polynomial| (|Complex| (|Fraction| (|Integer|)))) (|Matrix| (|Complex| (|Fraction| (|Integer|)))) (|Symbol|)) "\\spad{characteristicPolynomial(m,x)} returns the characteristic polynomial of the matrix \\spad{m} expressed as polynomial over Complex Rationals with variable \\spad{x}.") (((|Polynomial| (|Complex| (|Fraction| (|Integer|)))) (|Matrix| (|Complex| (|Fraction| (|Integer|))))) "\\spad{characteristicPolynomial(m)} returns the characteristic polynomial of the matrix \\spad{m} expressed as polynomial over complex rationals with a new symbol as variable."))) NIL NIL -(-787 -1612) +(-787 -1613) ((|constructor| (NIL "\\spadtype{NumericContinuedFraction} provides functions \\indented{2}{for converting floating point numbers to continued fractions.}")) (|continuedFraction| (((|ContinuedFraction| (|Integer|)) |#1|) "\\spad{continuedFraction(f)} converts the floating point number \\spad{f} to a reduced continued fraction."))) NIL NIL -(-788 P -1612) +(-788 P -1613) ((|constructor| (NIL "This package provides a division and related operations for \\spadtype{MonogenicLinearOperator}\\spad{s} over a \\spadtype{Field}. Since the multiplication is in general non-commutative,{} these operations all have left- and right-hand versions. This package provides the operations based on left-division.")) (|leftLcm| ((|#1| |#1| |#1|) "\\spad{leftLcm(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.")) (|leftGcd| ((|#1| |#1| |#1|) "\\spad{leftGcd(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 left-division.")) (|leftExactQuotient| (((|Union| |#1| "failed") |#1| |#1|) "\\spad{leftExactQuotient(a,b)} computes the value \\spad{q},{} if it exists,{} \\indented{1}{such that \\spad{a = b*q}.}")) (|leftRemainder| ((|#1| |#1| |#1|) "\\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| ((|#1| |#1| |#1|) "\\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| |#1|) (|:| |remainder| |#1|)) |#1| |#1|) "\\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''."))) NIL NIL @@ -3088,7 +3088,7 @@ NIL NIL NIL NIL -(-790 UP -1612) +(-790 UP -1613) ((|constructor| (NIL "In this package \\spad{F} is a framed algebra over the integers (typically \\spad{F = Z[a]} for some algebraic integer a). The package provides functions to compute the integral closure of \\spad{Z} in the quotient quotient field of \\spad{F}.")) (|localIntegralBasis| (((|Record| (|:| |basis| (|Matrix| (|Integer|))) (|:| |basisDen| (|Integer|)) (|:| |basisInv| (|Matrix| (|Integer|)))) (|Integer|)) "\\spad{integralBasis(p)} returns a record \\spad{[basis,basisDen,basisInv]} containing information regarding the local integral closure of \\spad{Z} at the prime \\spad{p} in the quotient field of \\spad{F},{} where \\spad{F} is a framed algebra with \\spad{Z}-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)}.")) (|integralBasis| (((|Record| (|:| |basis| (|Matrix| (|Integer|))) (|:| |basisDen| (|Integer|)) (|:| |basisInv| (|Matrix| (|Integer|))))) "\\spad{integralBasis()} returns a record \\spad{[basis,basisDen,basisInv]} containing information regarding the integral closure of \\spad{Z} in the quotient field of \\spad{F},{} where \\spad{F} is a framed algebra with \\spad{Z}-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)}.")) (|discriminant| (((|Integer|)) "\\spad{discriminant()} returns the discriminant of the integral closure of \\spad{Z} in the quotient field of the framed algebra \\spad{F}."))) NIL NIL @@ -3104,7 +3104,7 @@ NIL ((|constructor| (NIL "\\spadtype{NonNegativeInteger} provides functions for non \\indented{2}{negative integers.}")) (|commutative| ((|attribute| "*") "\\spad{commutative(\"*\")} means multiplication is commutative : \\spad{x*y = y*x}.")) (|random| (($ $) "\\spad{random(n)} returns a random integer from 0 to \\spad{n-1}.")) (|shift| (($ $ (|Integer|)) "\\spad{shift(a,i)} shift \\spad{a} by \\spad{i} bits.")) (|exquo| (((|Union| $ "failed") $ $) "\\spad{exquo(a,b)} returns the quotient of \\spad{a} and \\spad{b},{} or \"failed\" if \\spad{b} is zero or \\spad{a} rem \\spad{b} is zero.")) (|divide| (((|Record| (|:| |quotient| $) (|:| |remainder| $)) $ $) "\\spad{divide(a,b)} returns a record containing both remainder and quotient.")) (|gcd| (($ $ $) "\\spad{gcd(a,b)} computes the greatest common divisor of two non negative integers \\spad{a} and \\spad{b}.")) (|rem| (($ $ $) "\\spad{a rem b} returns the remainder of \\spad{a} and \\spad{b}.")) (|quo| (($ $ $) "\\spad{a quo b} returns the quotient of \\spad{a} and \\spad{b},{} forgetting the remainder."))) (((-4512 "*") . T)) NIL -(-794 R -1612) +(-794 R -1613) ((|constructor| (NIL "NonLinearFirstOrderODESolver provides a function for finding closed form first integrals of nonlinear ordinary differential equations of order 1.")) (|solve| (((|Union| |#2| "failed") |#2| |#2| (|BasicOperator|) (|Symbol|)) "\\spad{solve(M(x,y), N(x,y), y, x)} returns \\spad{F(x,y)} such that \\spad{F(x,y) = c} for a constant \\spad{c} is a first integral of the equation \\spad{M(x,y) dx + N(x,y) dy = 0},{} or \"failed\" if no first-integral can be found."))) NIL NIL @@ -3124,7 +3124,7 @@ NIL ((|constructor| (NIL "A package for computing normalized assocites of univariate polynomials with coefficients in a tower of simple extensions of a field.\\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 and \\spad{R}. RIOBOO \"Computations of gcd over} \\indented{5}{algebraic towers of simple extensions\" In proceedings of \\spad{AAECC11}} \\indented{5}{Paris,{} 1995.} \\indented{1}{[3] \\spad{M}. MORENO MAZA \"Calculs de pgcd au-dessus des tours} \\indented{5}{d'extensions simples et resolution des systemes d'equations} \\indented{5}{algebriques\" These,{} Universite \\spad{P}.etM. Curie,{} Paris,{} 1997.}")) (|normInvertible?| (((|List| (|Record| (|:| |val| (|Boolean|)) (|:| |tower| |#5|))) |#4| |#5|) "\\axiom{normInvertible?(\\spad{p},{}ts)} is an internal subroutine,{} exported only for developement.")) (|outputArgs| (((|Void|) (|String|) (|String|) |#4| |#5|) "\\axiom{outputArgs(\\spad{s1},{}\\spad{s2},{}\\spad{p},{}ts)} is an internal subroutine,{} exported only for developement.")) (|normalize| (((|List| (|Record| (|:| |val| |#4|) (|:| |tower| |#5|))) |#4| |#5|) "\\axiom{normalize(\\spad{p},{}ts)} normalizes \\axiom{\\spad{p}} \\spad{w}.\\spad{r}.\\spad{t} \\spad{ts}.")) (|normalizedAssociate| ((|#4| |#4| |#5|) "\\axiom{normalizedAssociate(\\spad{p},{}ts)} returns a normalized polynomial \\axiom{\\spad{n}} \\spad{w}.\\spad{r}.\\spad{t}. \\spad{ts} such that \\axiom{\\spad{n}} and \\axiom{\\spad{p}} are associates \\spad{w}.\\spad{r}.\\spad{t} \\spad{ts} and assuming that \\axiom{\\spad{p}} is invertible \\spad{w}.\\spad{r}.\\spad{t} \\spad{ts}.")) (|recip| (((|Record| (|:| |num| |#4|) (|:| |den| |#4|)) |#4| |#5|) "\\axiom{recip(\\spad{p},{}ts)} returns the inverse of \\axiom{\\spad{p}} \\spad{w}.\\spad{r}.\\spad{t} \\spad{ts} assuming that \\axiom{\\spad{p}} is invertible \\spad{w}.\\spad{r}.\\spad{t} \\spad{ts}."))) NIL NIL -(-799 -1612 |ExtF| |SUEx| |ExtP| |n|) +(-799 -1613 |ExtF| |SUEx| |ExtP| |n|) ((|constructor| (NIL "This package \\undocumented")) (|Frobenius| ((|#4| |#4|) "\\spad{Frobenius(x)} \\undocumented")) (|retractIfCan| (((|Union| (|SparseUnivariatePolynomial| (|SparseUnivariatePolynomial| |#1|)) "failed") |#4|) "\\spad{retractIfCan(x)} \\undocumented")) (|normFactors| (((|List| |#4|) |#4|) "\\spad{normFactors(x)} \\undocumented"))) NIL NIL @@ -3228,11 +3228,11 @@ NIL ((|ODESolve| (((|Result|) (|Record| (|:| |xinit| (|DoubleFloat|)) (|:| |xend| (|DoubleFloat|)) (|:| |fn| (|Vector| (|Expression| (|DoubleFloat|)))) (|:| |yinit| (|List| (|DoubleFloat|))) (|:| |intvals| (|List| (|DoubleFloat|))) (|:| |g| (|Expression| (|DoubleFloat|))) (|:| |abserr| (|DoubleFloat|)) (|:| |relerr| (|DoubleFloat|)))) "\\spad{ODESolve(args)} performs the integration of the function given the strategy or method returned by \\axiomFun{measure}.")) (|measure| (((|Record| (|:| |measure| (|Float|)) (|:| |explanations| (|String|))) (|RoutinesTable|) (|Record| (|:| |xinit| (|DoubleFloat|)) (|:| |xend| (|DoubleFloat|)) (|:| |fn| (|Vector| (|Expression| (|DoubleFloat|)))) (|:| |yinit| (|List| (|DoubleFloat|))) (|:| |intvals| (|List| (|DoubleFloat|))) (|:| |g| (|Expression| (|DoubleFloat|))) (|:| |abserr| (|DoubleFloat|)) (|:| |relerr| (|DoubleFloat|)))) "\\spad{measure(R,args)} calculates an estimate of the ability of a particular method to solve a problem. \\blankline This method may be either a specific NAG routine or a strategy (such as transforming the function from one which is difficult to one which is easier to solve). \\blankline It will call whichever agents are needed to perform analysis on the problem in order to calculate the measure. There is a parameter,{} labelled \\axiom{sofar},{} which would contain the best compatibility found so far."))) NIL NIL -(-825 R -1612 L) +(-825 R -1613 L) ((|constructor| (NIL "Solution of linear ordinary differential equations,{} constant coefficient case.")) (|constDsolve| (((|Record| (|:| |particular| |#2|) (|:| |basis| (|List| |#2|))) |#3| |#2| (|Symbol|)) "\\spad{constDsolve(op, g, x)} returns \\spad{[f, [y1,...,ym]]} where \\spad{f} is a particular solution of the equation \\spad{op y = g},{} and the \\spad{yi}'s form a basis for the solutions of \\spad{op y = 0}."))) NIL NIL -(-826 R -1612) +(-826 R -1613) ((|constructor| (NIL "\\spad{ElementaryFunctionODESolver} provides the top-level functions for finding closed form solutions of ordinary differential equations and initial value problems.")) (|solve| (((|Union| |#2| "failed") |#2| (|BasicOperator|) (|Equation| |#2|) (|List| |#2|)) "\\spad{solve(eq, y, x = a, [y0,...,ym])} returns either the solution of the initial value problem \\spad{eq, y(a) = y0, y'(a) = y1,...} or \"failed\" if the solution cannot be found; error if the equation is not one linear ordinary or of the form \\spad{dy/dx = f(x,y)}.") (((|Union| |#2| "failed") (|Equation| |#2|) (|BasicOperator|) (|Equation| |#2|) (|List| |#2|)) "\\spad{solve(eq, y, x = a, [y0,...,ym])} returns either the solution of the initial value problem \\spad{eq, y(a) = y0, y'(a) = y1,...} or \"failed\" if the solution cannot be found; error if the equation is not one linear ordinary or of the form \\spad{dy/dx = f(x,y)}.") (((|Union| (|Record| (|:| |particular| |#2|) (|:| |basis| (|List| |#2|))) |#2| "failed") |#2| (|BasicOperator|) (|Symbol|)) "\\spad{solve(eq, y, x)} returns either a solution of the ordinary differential equation \\spad{eq} or \"failed\" if no non-trivial solution can be found; If the equation is linear ordinary,{} a solution is of 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{f(x,y) = 0}; A full basis for the solutions of the homogenuous equation is not always returned,{} only the solutions which were found; If the equation is of the form {dy/dx = \\spad{f}(\\spad{x},{}\\spad{y})},{} a solution is of the form \\spad{h(x,y)} where \\spad{h(x,y) = c} is a first integral of the equation for any constant \\spad{c}.") (((|Union| (|Record| (|:| |particular| |#2|) (|:| |basis| (|List| |#2|))) |#2| "failed") (|Equation| |#2|) (|BasicOperator|) (|Symbol|)) "\\spad{solve(eq, y, x)} returns either a solution of the ordinary differential equation \\spad{eq} or \"failed\" if no non-trivial solution can be found; If the equation is linear ordinary,{} a solution is of the form \\spad{[h, [b1,...,bm]]} where \\spad{h} is a particular solution and \\spad{[b1,...bm]} are linearly independent solutions of the associated homogenuous equation \\spad{f(x,y) = 0}; A full basis for the solutions of the homogenuous equation is not always returned,{} only the solutions which were found; If the equation is of the form {dy/dx = \\spad{f}(\\spad{x},{}\\spad{y})},{} a solution is of the form \\spad{h(x,y)} where \\spad{h(x,y) = c} is a first integral of the equation for any constant \\spad{c}; error if the equation is not one of those 2 forms.") (((|Union| (|Record| (|:| |particular| (|Vector| |#2|)) (|:| |basis| (|List| (|Vector| |#2|)))) "failed") (|List| |#2|) (|List| (|BasicOperator|)) (|Symbol|)) "\\spad{solve([eq_1,...,eq_n], [y_1,...,y_n], x)} returns either \"failed\" or,{} if the equations form a fist order linear system,{} a solution of the form \\spad{[y_p, [b_1,...,b_n]]} where \\spad{h_p} is a particular solution and \\spad{[b_1,...b_m]} are linearly independent solutions of the associated homogenuous system. error if the equations do not form a first order linear system") (((|Union| (|Record| (|:| |particular| (|Vector| |#2|)) (|:| |basis| (|List| (|Vector| |#2|)))) "failed") (|List| (|Equation| |#2|)) (|List| (|BasicOperator|)) (|Symbol|)) "\\spad{solve([eq_1,...,eq_n], [y_1,...,y_n], x)} returns either \"failed\" or,{} if the equations form a fist order linear system,{} a solution of the form \\spad{[y_p, [b_1,...,b_n]]} where \\spad{h_p} is a particular solution and \\spad{[b_1,...b_m]} are linearly independent solutions of the associated homogenuous system. error if the equations do not form a first order linear system") (((|Union| (|List| (|Vector| |#2|)) "failed") (|Matrix| |#2|) (|Symbol|)) "\\spad{solve(m, x)} returns a basis for the solutions of \\spad{D y = m y}. \\spad{x} is the dependent variable.") (((|Union| (|Record| (|:| |particular| (|Vector| |#2|)) (|:| |basis| (|List| (|Vector| |#2|)))) "failed") (|Matrix| |#2|) (|Vector| |#2|) (|Symbol|)) "\\spad{solve(m, v, x)} returns \\spad{[v_p, [v_1,...,v_m]]} such that the solutions of the system \\spad{D y = m y + v} are \\spad{v_p + c_1 v_1 + ... + c_m v_m} where the \\spad{c_i's} are constants,{} and the \\spad{v_i's} form a basis for the solutions of \\spad{D y = m y}. \\spad{x} is the dependent variable."))) NIL NIL @@ -3240,7 +3240,7 @@ NIL ((|constructor| (NIL "\\axiom{ODEIntensityFunctionsTable()} provides a dynamic table and a set of functions to store details found out about sets of ODE's.")) (|showIntensityFunctions| (((|Union| (|Record| (|:| |stiffness| (|Float|)) (|:| |stability| (|Float|)) (|:| |expense| (|Float|)) (|:| |accuracy| (|Float|)) (|:| |intermediateResults| (|Float|))) "failed") (|Record| (|:| |xinit| (|DoubleFloat|)) (|:| |xend| (|DoubleFloat|)) (|:| |fn| (|Vector| (|Expression| (|DoubleFloat|)))) (|:| |yinit| (|List| (|DoubleFloat|))) (|:| |intvals| (|List| (|DoubleFloat|))) (|:| |g| (|Expression| (|DoubleFloat|))) (|:| |abserr| (|DoubleFloat|)) (|:| |relerr| (|DoubleFloat|)))) "\\spad{showIntensityFunctions(k)} returns the entries in the table of intensity functions \\spad{k}.")) (|insert!| (($ (|Record| (|:| |key| (|Record| (|:| |xinit| (|DoubleFloat|)) (|:| |xend| (|DoubleFloat|)) (|:| |fn| (|Vector| (|Expression| (|DoubleFloat|)))) (|:| |yinit| (|List| (|DoubleFloat|))) (|:| |intvals| (|List| (|DoubleFloat|))) (|:| |g| (|Expression| (|DoubleFloat|))) (|:| |abserr| (|DoubleFloat|)) (|:| |relerr| (|DoubleFloat|)))) (|:| |entry| (|Record| (|:| |stiffness| (|Float|)) (|:| |stability| (|Float|)) (|:| |expense| (|Float|)) (|:| |accuracy| (|Float|)) (|:| |intermediateResults| (|Float|)))))) "\\spad{insert!(r)} inserts an entry \\spad{r} into theIFTable")) (|iFTable| (($ (|List| (|Record| (|:| |key| (|Record| (|:| |xinit| (|DoubleFloat|)) (|:| |xend| (|DoubleFloat|)) (|:| |fn| (|Vector| (|Expression| (|DoubleFloat|)))) (|:| |yinit| (|List| (|DoubleFloat|))) (|:| |intvals| (|List| (|DoubleFloat|))) (|:| |g| (|Expression| (|DoubleFloat|))) (|:| |abserr| (|DoubleFloat|)) (|:| |relerr| (|DoubleFloat|)))) (|:| |entry| (|Record| (|:| |stiffness| (|Float|)) (|:| |stability| (|Float|)) (|:| |expense| (|Float|)) (|:| |accuracy| (|Float|)) (|:| |intermediateResults| (|Float|))))))) "\\spad{iFTable(l)} creates an intensity-functions table from the elements of \\spad{l}.")) (|keys| (((|List| (|Record| (|:| |xinit| (|DoubleFloat|)) (|:| |xend| (|DoubleFloat|)) (|:| |fn| (|Vector| (|Expression| (|DoubleFloat|)))) (|:| |yinit| (|List| (|DoubleFloat|))) (|:| |intvals| (|List| (|DoubleFloat|))) (|:| |g| (|Expression| (|DoubleFloat|))) (|:| |abserr| (|DoubleFloat|)) (|:| |relerr| (|DoubleFloat|)))) $) "\\spad{keys(tab)} returns the list of keys of \\spad{f}")) (|clearTheIFTable| (((|Void|)) "\\spad{clearTheIFTable()} clears the current table of intensity functions.")) (|showTheIFTable| (($) "\\spad{showTheIFTable()} returns the current table of intensity functions."))) NIL NIL -(-828 R -1612) +(-828 R -1613) ((|constructor| (NIL "\\spadtype{ODEIntegration} provides an interface to the integrator. This package is intended for use by the differential equations solver but not at top-level.")) (|diff| (((|Mapping| |#2| |#2|) (|Symbol|)) "\\spad{diff(x)} returns the derivation with respect to \\spad{x}.")) (|expint| ((|#2| |#2| (|Symbol|)) "\\spad{expint(f, x)} returns e^{the integral of \\spad{f} with respect to \\spad{x}}.")) (|int| ((|#2| |#2| (|Symbol|)) "\\spad{int(f, x)} returns the integral of \\spad{f} with respect to \\spad{x}."))) NIL NIL @@ -3248,11 +3248,11 @@ NIL ((|measure| (((|Record| (|:| |measure| (|Float|)) (|:| |name| (|String|)) (|:| |explanations| (|List| (|String|)))) (|NumericalODEProblem|) (|RoutinesTable|)) "\\spad{measure(prob,R)} is a top level ANNA function for identifying the most appropriate numerical routine from those in the routines table provided for solving the numerical ODE problem defined by \\axiom{\\spad{prob}}. \\blankline It calls each \\axiom{domain} listed in \\axiom{\\spad{R}} of \\axiom{category} \\axiomType{OrdinaryDifferentialEquationsSolverCategory} in turn to calculate all measures and returns the best \\spadignore{i.e.} the name of the most appropriate domain and any other relevant information. It predicts the likely most effective NAG numerical Library routine to solve the input set of ODEs by checking various attributes of the system of ODEs and calculating a measure of compatibility of each routine to these attributes.") (((|Record| (|:| |measure| (|Float|)) (|:| |name| (|String|)) (|:| |explanations| (|List| (|String|)))) (|NumericalODEProblem|)) "\\spad{measure(prob)} is a top level ANNA function for identifying the most appropriate numerical routine from those in the routines table provided for solving the numerical ODE problem defined by \\axiom{\\spad{prob}}. \\blankline It calls each \\axiom{domain} of \\axiom{category} \\axiomType{OrdinaryDifferentialEquationsSolverCategory} in turn to calculate all measures and returns the best \\spadignore{i.e.} the name of the most appropriate domain and any other relevant information. It predicts the likely most effective NAG numerical Library routine to solve the input set of ODEs by checking various attributes of the system of ODEs and calculating a measure of compatibility of each routine to these attributes.")) (|solve| (((|Result|) (|Vector| (|Expression| (|Float|))) (|Float|) (|Float|) (|List| (|Float|)) (|Expression| (|Float|)) (|List| (|Float|)) (|Float|) (|Float|)) "\\spad{solve(f,xStart,xEnd,yInitial,G,intVals,epsabs,epsrel)} is a top level ANNA function to solve numerically a system of ordinary differential equations,{} \\axiom{\\spad{f}},{} \\spadignore{i.e.} equations for the derivatives \\spad{Y}[1]'..\\spad{Y}[\\spad{n}]' defined in terms of \\spad{X},{}\\spad{Y}[1]..\\spad{Y}[\\spad{n}] from \\axiom{\\spad{xStart}} to \\axiom{\\spad{xEnd}} with the initial values for \\spad{Y}[1]..\\spad{Y}[\\spad{n}] (\\axiom{\\spad{yInitial}}) to an absolute error requirement \\axiom{\\spad{epsabs}} and relative error \\axiom{\\spad{epsrel}}. The values of \\spad{Y}[1]..\\spad{Y}[\\spad{n}] will be output for the values of \\spad{X} in \\axiom{\\spad{intVals}}. The calculation will stop if the function \\spad{G}(\\spad{X},{}\\spad{Y}[1],{}..,{}\\spad{Y}[\\spad{n}]) evaluates to zero before \\spad{X} = \\spad{xEnd}. \\blankline It iterates over the \\axiom{domains} of \\axiomType{OrdinaryDifferentialEquationsSolverCategory} contained in the table of routines \\axiom{\\spad{R}} to get the name and other relevant information of the the (domain of the) numerical routine likely to be the most appropriate,{} \\spadignore{i.e.} have the best \\axiom{measure}. \\blankline The method used to perform the numerical process will be one of the routines contained in the NAG numerical Library. The function predicts the likely most effective routine by checking various attributes of the system of ODE's and calculating a measure of compatibility of each routine to these attributes. \\blankline It then calls the resulting `best' routine.") (((|Result|) (|Vector| (|Expression| (|Float|))) (|Float|) (|Float|) (|List| (|Float|)) (|Expression| (|Float|)) (|List| (|Float|)) (|Float|)) "\\spad{solve(f,xStart,xEnd,yInitial,G,intVals,tol)} is a top level ANNA function to solve numerically a system of ordinary differential equations,{} \\axiom{\\spad{f}},{} \\spadignore{i.e.} equations for the derivatives \\spad{Y}[1]'..\\spad{Y}[\\spad{n}]' defined in terms of \\spad{X},{}\\spad{Y}[1]..\\spad{Y}[\\spad{n}] from \\axiom{\\spad{xStart}} to \\axiom{\\spad{xEnd}} with the initial values for \\spad{Y}[1]..\\spad{Y}[\\spad{n}] (\\axiom{\\spad{yInitial}}) to a tolerance \\axiom{\\spad{tol}}. The values of \\spad{Y}[1]..\\spad{Y}[\\spad{n}] will be output for the values of \\spad{X} in \\axiom{\\spad{intVals}}. The calculation will stop if the function \\spad{G}(\\spad{X},{}\\spad{Y}[1],{}..,{}\\spad{Y}[\\spad{n}]) evaluates to zero before \\spad{X} = \\spad{xEnd}. \\blankline It iterates over the \\axiom{domains} of \\axiomType{OrdinaryDifferentialEquationsSolverCategory} contained in the table of routines \\axiom{\\spad{R}} to get the name and other relevant information of the the (domain of the) numerical routine likely to be the most appropriate,{} \\spadignore{i.e.} have the best \\axiom{measure}. \\blankline The method used to perform the numerical process will be one of the routines contained in the NAG numerical Library. The function predicts the likely most effective routine by checking various attributes of the system of ODE's and calculating a measure of compatibility of each routine to these attributes. \\blankline It then calls the resulting `best' routine.") (((|Result|) (|Vector| (|Expression| (|Float|))) (|Float|) (|Float|) (|List| (|Float|)) (|List| (|Float|)) (|Float|)) "\\spad{solve(f,xStart,xEnd,yInitial,intVals,tol)} is a top level ANNA function to solve numerically a system of ordinary differential equations,{} \\axiom{\\spad{f}},{} \\spadignore{i.e.} equations for the derivatives \\spad{Y}[1]'..\\spad{Y}[\\spad{n}]' defined in terms of \\spad{X},{}\\spad{Y}[1]..\\spad{Y}[\\spad{n}] from \\axiom{\\spad{xStart}} to \\axiom{\\spad{xEnd}} with the initial values for \\spad{Y}[1]..\\spad{Y}[\\spad{n}] (\\axiom{\\spad{yInitial}}) to a tolerance \\axiom{\\spad{tol}}. The values of \\spad{Y}[1]..\\spad{Y}[\\spad{n}] will be output for the values of \\spad{X} in \\axiom{\\spad{intVals}}. \\blankline It iterates over the \\axiom{domains} of \\axiomType{OrdinaryDifferentialEquationsSolverCategory} contained in the table of routines \\axiom{\\spad{R}} to get the name and other relevant information of the the (domain of the) numerical routine likely to be the most appropriate,{} \\spadignore{i.e.} have the best \\axiom{measure}. \\blankline The method used to perform the numerical process will be one of the routines contained in the NAG numerical Library. The function predicts the likely most effective routine by checking various attributes of the system of ODE's and calculating a measure of compatibility of each routine to these attributes. \\blankline It then calls the resulting `best' routine.") (((|Result|) (|Vector| (|Expression| (|Float|))) (|Float|) (|Float|) (|List| (|Float|)) (|Expression| (|Float|)) (|Float|)) "\\spad{solve(f,xStart,xEnd,yInitial,G,tol)} is a top level ANNA function to solve numerically a system of ordinary differential equations,{} \\axiom{\\spad{f}},{} \\spadignore{i.e.} equations for the derivatives \\spad{Y}[1]'..\\spad{Y}[\\spad{n}]' defined in terms of \\spad{X},{}\\spad{Y}[1]..\\spad{Y}[\\spad{n}] from \\axiom{\\spad{xStart}} to \\axiom{\\spad{xEnd}} with the initial values for \\spad{Y}[1]..\\spad{Y}[\\spad{n}] (\\axiom{\\spad{yInitial}}) to a tolerance \\axiom{\\spad{tol}}. The calculation will stop if the function \\spad{G}(\\spad{X},{}\\spad{Y}[1],{}..,{}\\spad{Y}[\\spad{n}]) evaluates to zero before \\spad{X} = \\spad{xEnd}. \\blankline It iterates over the \\axiom{domains} of \\axiomType{OrdinaryDifferentialEquationsSolverCategory} contained in the table of routines \\axiom{\\spad{R}} to get the name and other relevant information of the the (domain of the) numerical routine likely to be the most appropriate,{} \\spadignore{i.e.} have the best \\axiom{measure}. \\blankline The method used to perform the numerical process will be one of the routines contained in the NAG numerical Library. The function predicts the likely most effective routine by checking various attributes of the system of ODE's and calculating a measure of compatibility of each routine to these attributes. \\blankline It then calls the resulting `best' routine.") (((|Result|) (|Vector| (|Expression| (|Float|))) (|Float|) (|Float|) (|List| (|Float|)) (|Float|)) "\\spad{solve(f,xStart,xEnd,yInitial,tol)} is a top level ANNA function to solve numerically a system of ordinary differential equations,{} \\axiom{\\spad{f}},{} \\spadignore{i.e.} equations for the derivatives \\spad{Y}[1]'..\\spad{Y}[\\spad{n}]' defined in terms of \\spad{X},{}\\spad{Y}[1]..\\spad{Y}[\\spad{n}] from \\axiom{\\spad{xStart}} to \\axiom{\\spad{xEnd}} with the initial values for \\spad{Y}[1]..\\spad{Y}[\\spad{n}] (\\axiom{\\spad{yInitial}}) to a tolerance \\axiom{\\spad{tol}}. \\blankline It iterates over the \\axiom{domains} of \\axiomType{OrdinaryDifferentialEquationsSolverCategory} contained in the table of routines \\axiom{\\spad{R}} to get the name and other relevant information of the the (domain of the) numerical routine likely to be the most appropriate,{} \\spadignore{i.e.} have the best \\axiom{measure}. \\blankline The method used to perform the numerical process will be one of the routines contained in the NAG numerical Library. The function predicts the likely most effective routine by checking various attributes of the system of ODE's and calculating a measure of compatibility of each routine to these attributes. \\blankline It then calls the resulting `best' routine.") (((|Result|) (|Vector| (|Expression| (|Float|))) (|Float|) (|Float|) (|List| (|Float|))) "\\spad{solve(f,xStart,xEnd,yInitial)} is a top level ANNA function to solve numerically a system of ordinary differential equations \\spadignore{i.e.} equations for the derivatives \\spad{Y}[1]'..\\spad{Y}[\\spad{n}]' defined in terms of \\spad{X},{}\\spad{Y}[1]..\\spad{Y}[\\spad{n}],{} together with a starting value for \\spad{X} and \\spad{Y}[1]..\\spad{Y}[\\spad{n}] (called the initial conditions) and a final value of \\spad{X}. A default value is used for the accuracy requirement. \\blankline It iterates over the \\axiom{domains} of \\axiomType{OrdinaryDifferentialEquationsSolverCategory} contained in the table of routines \\axiom{\\spad{R}} to get the name and other relevant information of the the (domain of the) numerical routine likely to be the most appropriate,{} \\spadignore{i.e.} have the best \\axiom{measure}. \\blankline The method used to perform the numerical process will be one of the routines contained in the NAG numerical Library. The function predicts the likely most effective routine by checking various attributes of the system of ODE's and calculating a measure of compatibility of each routine to these attributes. \\blankline It then calls the resulting `best' routine.") (((|Result|) (|NumericalODEProblem|) (|RoutinesTable|)) "\\spad{solve(odeProblem,R)} is a top level ANNA function to solve numerically a system of ordinary differential equations \\spadignore{i.e.} equations for the derivatives \\spad{Y}[1]'..\\spad{Y}[\\spad{n}]' defined in terms of \\spad{X},{}\\spad{Y}[1]..\\spad{Y}[\\spad{n}],{} together with starting values for \\spad{X} and \\spad{Y}[1]..\\spad{Y}[\\spad{n}] (called the initial conditions),{} a final value of \\spad{X},{} an accuracy requirement and any intermediate points at which the result is required. \\blankline It iterates over the \\axiom{domains} of \\axiomType{OrdinaryDifferentialEquationsSolverCategory} contained in the table of routines \\axiom{\\spad{R}} to get the name and other relevant information of the the (domain of the) numerical routine likely to be the most appropriate,{} \\spadignore{i.e.} have the best \\axiom{measure}. \\blankline The method used to perform the numerical process will be one of the routines contained in the NAG numerical Library. The function predicts the likely most effective routine by checking various attributes of the system of ODE's and calculating a measure of compatibility of each routine to these attributes. \\blankline It then calls the resulting `best' routine.") (((|Result|) (|NumericalODEProblem|)) "\\spad{solve(odeProblem)} is a top level ANNA function to solve numerically a system of ordinary differential equations \\spadignore{i.e.} equations for the derivatives \\spad{Y}[1]'..\\spad{Y}[\\spad{n}]' defined in terms of \\spad{X},{}\\spad{Y}[1]..\\spad{Y}[\\spad{n}],{} together with starting values for \\spad{X} and \\spad{Y}[1]..\\spad{Y}[\\spad{n}] (called the initial conditions),{} a final value of \\spad{X},{} an accuracy requirement and any intermediate points at which the result is required. \\blankline It iterates over the \\axiom{domains} of \\axiomType{OrdinaryDifferentialEquationsSolverCategory} to get the name and other relevant information of the the (domain of the) numerical routine likely to be the most appropriate,{} \\spadignore{i.e.} have the best \\axiom{measure}. \\blankline The method used to perform the numerical process will be one of the routines contained in the NAG numerical Library. The function predicts the likely most effective routine by checking various attributes of the system of ODE's and calculating a measure of compatibility of each routine to these attributes. \\blankline It then calls the resulting `best' routine."))) NIL NIL -(-830 -1612 UP UPUP R) +(-830 -1613 UP UPUP R) ((|constructor| (NIL "In-field solution of an linear ordinary differential equation,{} pure algebraic case.")) (|algDsolve| (((|Record| (|:| |particular| (|Union| |#4| "failed")) (|:| |basis| (|List| |#4|))) (|LinearOrdinaryDifferentialOperator1| |#4|) |#4|) "\\spad{algDsolve(op, g)} returns \\spad{[\"failed\", []]} if the equation \\spad{op y = g} has no solution in \\spad{R}. Otherwise,{} it returns \\spad{[f, [y1,...,ym]]} where \\spad{f} is a particular rational solution and the \\spad{y_i's} form a basis for the solutions in \\spad{R} of the homogeneous equation."))) NIL NIL -(-831 -1612 UP L LQ) +(-831 -1613 UP L LQ) ((|constructor| (NIL "\\spad{PrimitiveRatDE} provides functions for in-field solutions of linear \\indented{1}{ordinary differential equations,{} in the transcendental case.} \\indented{1}{The derivation to use is given by the parameter \\spad{L}.}")) (|splitDenominator| (((|Record| (|:| |eq| |#3|) (|:| |rh| (|List| (|Fraction| |#2|)))) |#4| (|List| (|Fraction| |#2|))) "\\spad{splitDenominator(op, [g1,...,gm])} returns \\spad{op0, [h1,...,hm]} such that the equations \\spad{op y = c1 g1 + ... + cm gm} and \\spad{op0 y = c1 h1 + ... + cm hm} have the same solutions.")) (|indicialEquation| ((|#2| |#4| |#1|) "\\spad{indicialEquation(op, a)} returns the indicial equation of \\spad{op} at \\spad{a}.") ((|#2| |#3| |#1|) "\\spad{indicialEquation(op, a)} returns the indicial equation of \\spad{op} at \\spad{a}.")) (|indicialEquations| (((|List| (|Record| (|:| |center| |#2|) (|:| |equation| |#2|))) |#4| |#2|) "\\spad{indicialEquations(op, p)} returns \\spad{[[d1,e1],...,[dq,eq]]} where the \\spad{d_i}'s are the affine singularities of \\spad{op} above the roots of \\spad{p},{} and the \\spad{e_i}'s are the indicial equations at each \\spad{d_i}.") (((|List| (|Record| (|:| |center| |#2|) (|:| |equation| |#2|))) |#4|) "\\spad{indicialEquations op} returns \\spad{[[d1,e1],...,[dq,eq]]} where the \\spad{d_i}'s are the affine singularities of \\spad{op},{} and the \\spad{e_i}'s are the indicial equations at each \\spad{d_i}.") (((|List| (|Record| (|:| |center| |#2|) (|:| |equation| |#2|))) |#3| |#2|) "\\spad{indicialEquations(op, p)} returns \\spad{[[d1,e1],...,[dq,eq]]} where the \\spad{d_i}'s are the affine singularities of \\spad{op} above the roots of \\spad{p},{} and the \\spad{e_i}'s are the indicial equations at each \\spad{d_i}.") (((|List| (|Record| (|:| |center| |#2|) (|:| |equation| |#2|))) |#3|) "\\spad{indicialEquations op} returns \\spad{[[d1,e1],...,[dq,eq]]} where the \\spad{d_i}'s are the affine singularities of \\spad{op},{} and the \\spad{e_i}'s are the indicial equations at each \\spad{d_i}.")) (|denomLODE| ((|#2| |#3| (|List| (|Fraction| |#2|))) "\\spad{denomLODE(op, [g1,...,gm])} returns a polynomial \\spad{d} such that any rational solution of \\spad{op y = c1 g1 + ... + cm gm} is of the form \\spad{p/d} for some polynomial \\spad{p}.") (((|Union| |#2| "failed") |#3| (|Fraction| |#2|)) "\\spad{denomLODE(op, g)} returns a polynomial \\spad{d} such that any rational solution of \\spad{op y = g} is of the form \\spad{p/d} for some polynomial \\spad{p},{} and \"failed\",{} if the equation has no rational solution."))) NIL NIL @@ -3260,31 +3260,31 @@ NIL ((|retract| (((|Record| (|:| |xinit| (|DoubleFloat|)) (|:| |xend| (|DoubleFloat|)) (|:| |fn| (|Vector| (|Expression| (|DoubleFloat|)))) (|:| |yinit| (|List| (|DoubleFloat|))) (|:| |intvals| (|List| (|DoubleFloat|))) (|:| |g| (|Expression| (|DoubleFloat|))) (|:| |abserr| (|DoubleFloat|)) (|:| |relerr| (|DoubleFloat|))) $) "\\spad{retract(x)} \\undocumented{}")) (|coerce| (($ (|Record| (|:| |xinit| (|DoubleFloat|)) (|:| |xend| (|DoubleFloat|)) (|:| |fn| (|Vector| (|Expression| (|DoubleFloat|)))) (|:| |yinit| (|List| (|DoubleFloat|))) (|:| |intvals| (|List| (|DoubleFloat|))) (|:| |g| (|Expression| (|DoubleFloat|))) (|:| |abserr| (|DoubleFloat|)) (|:| |relerr| (|DoubleFloat|)))) "\\spad{coerce(x)} \\undocumented{}"))) NIL NIL -(-833 -1612 UP L LQ) +(-833 -1613 UP L LQ) ((|constructor| (NIL "In-field solution of Riccati equations,{} primitive case.")) (|changeVar| ((|#3| |#3| (|Fraction| |#2|)) "\\spad{changeVar(+/[ai D^i], a)} returns the operator \\spad{+/[ai (D+a)^i]}.") ((|#3| |#3| |#2|) "\\spad{changeVar(+/[ai D^i], a)} returns the operator \\spad{+/[ai (D+a)^i]}.")) (|singRicDE| (((|List| (|Record| (|:| |frac| (|Fraction| |#2|)) (|:| |eq| |#3|))) |#3| (|Mapping| (|List| |#2|) |#2| (|SparseUnivariatePolynomial| |#2|)) (|Mapping| (|Factored| |#2|) |#2|)) "\\spad{singRicDE(op, zeros, ezfactor)} returns \\spad{[[f1, L1], [f2, L2], ... , [fk, Lk]]} such that the singular part of any rational solution of the associated Riccati equation of \\spad{op y=0} must be one of the \\spad{fi}'s (up to the constant coefficient),{} in which case the equation for \\spad{z=y e^{-int p}} is \\spad{Li z=0}. \\spad{zeros(C(x),H(x,y))} returns all the \\spad{P_i(x)}'s such that \\spad{H(x,P_i(x)) = 0 modulo C(x)}. Argument \\spad{ezfactor} is a factorisation in \\spad{UP},{} not necessarily into irreducibles.")) (|polyRicDE| (((|List| (|Record| (|:| |poly| |#2|) (|:| |eq| |#3|))) |#3| (|Mapping| (|List| |#1|) |#2|)) "\\spad{polyRicDE(op, zeros)} returns \\spad{[[p1, L1], [p2, L2], ... , [pk, Lk]]} such that the polynomial part of any rational solution of the associated Riccati equation of \\spad{op y=0} must be one of the \\spad{pi}'s (up to the constant coefficient),{} in which case the equation for \\spad{z=y e^{-int p}} is \\spad{Li z =0}. \\spad{zeros} is a zero finder in \\spad{UP}.")) (|constantCoefficientRicDE| (((|List| (|Record| (|:| |constant| |#1|) (|:| |eq| |#3|))) |#3| (|Mapping| (|List| |#1|) |#2|)) "\\spad{constantCoefficientRicDE(op, ric)} returns \\spad{[[a1, L1], [a2, L2], ... , [ak, Lk]]} such that any rational solution with no polynomial part of the associated Riccati equation of \\spad{op y = 0} must be one of the \\spad{ai}'s in which case the equation for \\spad{z = y e^{-int ai}} is \\spad{Li z = 0}. \\spad{ric} is a Riccati equation solver over \\spad{F},{} whose input is the associated linear equation.")) (|leadingCoefficientRicDE| (((|List| (|Record| (|:| |deg| (|NonNegativeInteger|)) (|:| |eq| |#2|))) |#3|) "\\spad{leadingCoefficientRicDE(op)} returns \\spad{[[m1, p1], [m2, p2], ... , [mk, pk]]} such that the polynomial part of any rational solution of the associated Riccati equation of \\spad{op y = 0} must have degree mj for some \\spad{j},{} and its leading coefficient is then a zero of pj. In addition,{}\\spad{m1>m2> ... >mk}.")) (|denomRicDE| ((|#2| |#3|) "\\spad{denomRicDE(op)} returns a polynomial \\spad{d} such that any rational solution of the associated Riccati equation of \\spad{op y = 0} is of the form \\spad{p/d + q'/q + r} for some polynomials \\spad{p} and \\spad{q} and a reduced \\spad{r}. Also,{} \\spad{deg(p) < deg(d)} and {gcd(\\spad{d},{}\\spad{q}) = 1}."))) NIL NIL -(-834 -1612 UP) +(-834 -1613 UP) ((|constructor| (NIL "\\spad{RationalLODE} provides functions for in-field solutions of linear \\indented{1}{ordinary differential equations,{} in the rational case.}")) (|indicialEquationAtInfinity| ((|#2| (|LinearOrdinaryDifferentialOperator2| |#2| (|Fraction| |#2|))) "\\spad{indicialEquationAtInfinity op} returns the indicial equation of \\spad{op} at infinity.") ((|#2| (|LinearOrdinaryDifferentialOperator1| (|Fraction| |#2|))) "\\spad{indicialEquationAtInfinity op} returns the indicial equation of \\spad{op} at infinity.")) (|ratDsolve| (((|Record| (|:| |basis| (|List| (|Fraction| |#2|))) (|:| |mat| (|Matrix| |#1|))) (|LinearOrdinaryDifferentialOperator2| |#2| (|Fraction| |#2|)) (|List| (|Fraction| |#2|))) "\\spad{ratDsolve(op, [g1,...,gm])} returns \\spad{[[h1,...,hq], M]} such that any rational solution of \\spad{op y = c1 g1 + ... + cm gm} is of the form \\spad{d1 h1 + ... + dq hq} where \\spad{M [d1,...,dq,c1,...,cm] = 0}.") (((|Record| (|:| |particular| (|Union| (|Fraction| |#2|) "failed")) (|:| |basis| (|List| (|Fraction| |#2|)))) (|LinearOrdinaryDifferentialOperator2| |#2| (|Fraction| |#2|)) (|Fraction| |#2|)) "\\spad{ratDsolve(op, g)} returns \\spad{[\"failed\", []]} if the equation \\spad{op y = g} has no rational solution. Otherwise,{} it returns \\spad{[f, [y1,...,ym]]} where \\spad{f} is a particular rational solution and the \\spad{yi}'s form a basis for the rational solutions of the homogeneous equation.") (((|Record| (|:| |basis| (|List| (|Fraction| |#2|))) (|:| |mat| (|Matrix| |#1|))) (|LinearOrdinaryDifferentialOperator1| (|Fraction| |#2|)) (|List| (|Fraction| |#2|))) "\\spad{ratDsolve(op, [g1,...,gm])} returns \\spad{[[h1,...,hq], M]} such that any rational solution of \\spad{op y = c1 g1 + ... + cm gm} is of the form \\spad{d1 h1 + ... + dq hq} where \\spad{M [d1,...,dq,c1,...,cm] = 0}.") (((|Record| (|:| |particular| (|Union| (|Fraction| |#2|) "failed")) (|:| |basis| (|List| (|Fraction| |#2|)))) (|LinearOrdinaryDifferentialOperator1| (|Fraction| |#2|)) (|Fraction| |#2|)) "\\spad{ratDsolve(op, g)} returns \\spad{[\"failed\", []]} if the equation \\spad{op y = g} has no rational solution. Otherwise,{} it returns \\spad{[f, [y1,...,ym]]} where \\spad{f} is a particular rational solution and the \\spad{yi}'s form a basis for the rational solutions of the homogeneous equation."))) NIL NIL -(-835 -1612 L UP A LO) +(-835 -1613 L UP A LO) ((|constructor| (NIL "Elimination of an algebraic from the coefficentss of a linear ordinary differential equation.")) (|reduceLODE| (((|Record| (|:| |mat| (|Matrix| |#2|)) (|:| |vec| (|Vector| |#1|))) |#5| |#4|) "\\spad{reduceLODE(op, g)} returns \\spad{[m, v]} such that any solution in \\spad{A} of \\spad{op z = g} is of the form \\spad{z = (z_1,...,z_m) . (b_1,...,b_m)} where the \\spad{b_i's} are the basis of \\spad{A} over \\spad{F} returned by \\spadfun{basis}() from \\spad{A},{} and the \\spad{z_i's} satisfy the differential system \\spad{M.z = v}."))) NIL NIL -(-836 -1612 UP) +(-836 -1613 UP) ((|constructor| (NIL "In-field solution of Riccati equations,{} rational case.")) (|polyRicDE| (((|List| (|Record| (|:| |poly| |#2|) (|:| |eq| (|LinearOrdinaryDifferentialOperator2| |#2| (|Fraction| |#2|))))) (|LinearOrdinaryDifferentialOperator2| |#2| (|Fraction| |#2|)) (|Mapping| (|List| |#1|) |#2|)) "\\spad{polyRicDE(op, zeros)} returns \\spad{[[p1, L1], [p2, L2], ... , [pk,Lk]]} such that the polynomial part of any rational solution of the associated Riccati equation of \\spad{op y = 0} must be one of the \\spad{pi}'s (up to the constant coefficient),{} in which case the equation for \\spad{z = y e^{-int p}} is \\spad{Li z = 0}. \\spad{zeros} is a zero finder in \\spad{UP}.")) (|singRicDE| (((|List| (|Record| (|:| |frac| (|Fraction| |#2|)) (|:| |eq| (|LinearOrdinaryDifferentialOperator2| |#2| (|Fraction| |#2|))))) (|LinearOrdinaryDifferentialOperator2| |#2| (|Fraction| |#2|)) (|Mapping| (|Factored| |#2|) |#2|)) "\\spad{singRicDE(op, ezfactor)} returns \\spad{[[f1,L1], [f2,L2],..., [fk,Lk]]} such that the singular ++ part of any rational solution of the associated Riccati equation of \\spad{op y = 0} must be one of the \\spad{fi}'s (up to the constant coefficient),{} in which case the equation for \\spad{z = y e^{-int ai}} is \\spad{Li z = 0}. Argument \\spad{ezfactor} is a factorisation in \\spad{UP},{} not necessarily into irreducibles.")) (|ricDsolve| (((|List| (|Fraction| |#2|)) (|LinearOrdinaryDifferentialOperator2| |#2| (|Fraction| |#2|)) (|Mapping| (|Factored| |#2|) |#2|)) "\\spad{ricDsolve(op, ezfactor)} returns the rational solutions of the associated Riccati equation of \\spad{op y = 0}. Argument \\spad{ezfactor} is a factorisation in \\spad{UP},{} not necessarily into irreducibles.") (((|List| (|Fraction| |#2|)) (|LinearOrdinaryDifferentialOperator2| |#2| (|Fraction| |#2|))) "\\spad{ricDsolve(op)} returns the rational solutions of the associated Riccati equation of \\spad{op y = 0}.") (((|List| (|Fraction| |#2|)) (|LinearOrdinaryDifferentialOperator1| (|Fraction| |#2|)) (|Mapping| (|Factored| |#2|) |#2|)) "\\spad{ricDsolve(op, ezfactor)} returns the rational solutions of the associated Riccati equation of \\spad{op y = 0}. Argument \\spad{ezfactor} is a factorisation in \\spad{UP},{} not necessarily into irreducibles.") (((|List| (|Fraction| |#2|)) (|LinearOrdinaryDifferentialOperator1| (|Fraction| |#2|))) "\\spad{ricDsolve(op)} returns the rational solutions of the associated Riccati equation of \\spad{op y = 0}.") (((|List| (|Fraction| |#2|)) (|LinearOrdinaryDifferentialOperator2| |#2| (|Fraction| |#2|)) (|Mapping| (|List| |#1|) |#2|) (|Mapping| (|Factored| |#2|) |#2|)) "\\spad{ricDsolve(op, zeros, ezfactor)} returns the rational solutions of the associated Riccati equation of \\spad{op y = 0}. \\spad{zeros} is a zero finder in \\spad{UP}. Argument \\spad{ezfactor} is a factorisation in \\spad{UP},{} not necessarily into irreducibles.") (((|List| (|Fraction| |#2|)) (|LinearOrdinaryDifferentialOperator2| |#2| (|Fraction| |#2|)) (|Mapping| (|List| |#1|) |#2|)) "\\spad{ricDsolve(op, zeros)} returns the rational solutions of the associated Riccati equation of \\spad{op y = 0}. \\spad{zeros} is a zero finder in \\spad{UP}.") (((|List| (|Fraction| |#2|)) (|LinearOrdinaryDifferentialOperator1| (|Fraction| |#2|)) (|Mapping| (|List| |#1|) |#2|) (|Mapping| (|Factored| |#2|) |#2|)) "\\spad{ricDsolve(op, zeros, ezfactor)} returns the rational solutions of the associated Riccati equation of \\spad{op y = 0}. \\spad{zeros} is a zero finder in \\spad{UP}. Argument \\spad{ezfactor} is a factorisation in \\spad{UP},{} not necessarily into irreducibles.") (((|List| (|Fraction| |#2|)) (|LinearOrdinaryDifferentialOperator1| (|Fraction| |#2|)) (|Mapping| (|List| |#1|) |#2|)) "\\spad{ricDsolve(op, zeros)} returns the rational solutions of the associated Riccati equation of \\spad{op y = 0}. \\spad{zeros} is a zero finder in \\spad{UP}."))) NIL ((|HasCategory| |#1| (QUOTE (-27)))) -(-837 -1612 LO) +(-837 -1613 LO) ((|constructor| (NIL "SystemODESolver provides tools for triangulating and solving some systems of linear ordinary differential equations.")) (|solveInField| (((|Record| (|:| |particular| (|Union| (|Vector| |#1|) "failed")) (|:| |basis| (|List| (|Vector| |#1|)))) (|Matrix| |#2|) (|Vector| |#1|) (|Mapping| (|Record| (|:| |particular| (|Union| |#1| "failed")) (|:| |basis| (|List| |#1|))) |#2| |#1|)) "\\spad{solveInField(m, v, solve)} returns \\spad{[[v_1,...,v_m], v_p]} such that the solutions in \\spad{F} of the system \\spad{m x = v} are \\spad{v_p + c_1 v_1 + ... + c_m v_m} where the \\spad{c_i's} are constants,{} and the \\spad{v_i's} form a basis for the solutions of \\spad{m x = 0}. Argument \\spad{solve} is a function for solving a single linear ordinary differential equation in \\spad{F}.")) (|solve| (((|Union| (|Record| (|:| |particular| (|Vector| |#1|)) (|:| |basis| (|Matrix| |#1|))) "failed") (|Matrix| |#1|) (|Vector| |#1|) (|Mapping| (|Union| (|Record| (|:| |particular| |#1|) (|:| |basis| (|List| |#1|))) "failed") |#2| |#1|)) "\\spad{solve(m, v, solve)} returns \\spad{[[v_1,...,v_m], v_p]} such that the solutions in \\spad{F} of the system \\spad{D x = m x + v} are \\spad{v_p + c_1 v_1 + ... + c_m v_m} where the \\spad{c_i's} are constants,{} and the \\spad{v_i's} form a basis for the solutions of \\spad{D x = m x}. Argument \\spad{solve} is a function for solving a single linear ordinary differential equation in \\spad{F}.")) (|triangulate| (((|Record| (|:| |mat| (|Matrix| |#2|)) (|:| |vec| (|Vector| |#1|))) (|Matrix| |#2|) (|Vector| |#1|)) "\\spad{triangulate(m, v)} returns \\spad{[m_0, v_0]} such that \\spad{m_0} is upper triangular and the system \\spad{m_0 x = v_0} is equivalent to \\spad{m x = v}.") (((|Record| (|:| A (|Matrix| |#1|)) (|:| |eqs| (|List| (|Record| (|:| C (|Matrix| |#1|)) (|:| |g| (|Vector| |#1|)) (|:| |eq| |#2|) (|:| |rh| |#1|))))) (|Matrix| |#1|) (|Vector| |#1|)) "\\spad{triangulate(M,v)} returns \\spad{A,[[C_1,g_1,L_1,h_1],...,[C_k,g_k,L_k,h_k]]} such that under the change of variable \\spad{y = A z},{} the first order linear system \\spad{D y = M y + v} is uncoupled as \\spad{D z_i = C_i z_i + g_i} and each \\spad{C_i} is a companion matrix corresponding to the scalar equation \\spad{L_i z_j = h_i}."))) NIL NIL -(-838 -1612 LODO) +(-838 -1613 LODO) ((|constructor| (NIL "\\spad{ODETools} provides tools for the linear ODE solver.")) (|particularSolution| (((|Union| |#1| "failed") |#2| |#1| (|List| |#1|) (|Mapping| |#1| |#1|)) "\\spad{particularSolution(op, g, [f1,...,fm], I)} returns a particular solution \\spad{h} of the equation \\spad{op y = g} where \\spad{[f1,...,fm]} are linearly independent and \\spad{op(fi)=0}. The value \"failed\" is returned if no particular solution is found. Note: the method of variations of parameters is used.")) (|variationOfParameters| (((|Union| (|Vector| |#1|) "failed") |#2| |#1| (|List| |#1|)) "\\spad{variationOfParameters(op, g, [f1,...,fm])} returns \\spad{[u1,...,um]} such that a particular solution of the equation \\spad{op y = g} is \\spad{f1 int(u1) + ... + fm int(um)} where \\spad{[f1,...,fm]} are linearly independent and \\spad{op(fi)=0}. The value \"failed\" is returned if \\spad{m < n} and no particular solution is found.")) (|wronskianMatrix| (((|Matrix| |#1|) (|List| |#1|) (|NonNegativeInteger|)) "\\spad{wronskianMatrix([f1,...,fn], q, D)} returns the \\spad{q x n} matrix \\spad{m} whose i^th row is \\spad{[f1^(i-1),...,fn^(i-1)]}.") (((|Matrix| |#1|) (|List| |#1|)) "\\spad{wronskianMatrix([f1,...,fn])} returns the \\spad{n x n} matrix \\spad{m} whose i^th row is \\spad{[f1^(i-1),...,fn^(i-1)]}."))) NIL NIL -(-839 -3048 S |f|) +(-839 -3049 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}."))) ((-4504 |has| |#2| (-1081)) (-4505 |has| |#2| (-1081)) (-4507 |has| |#2| (-6 -4507)) (-4510 . 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(|HasCategory| |#2| (|%list| (QUOTE -321) (|devaluate| |#2|))))) @@ -3404,7 +3404,7 @@ NIL ((|constructor| (NIL "Ordered finite sets.")) (|max| (($) "\\spad{max} is the maximum value of \\%.")) (|min| (($) "\\spad{min} is the minimum value of \\%."))) NIL NIL -(-869 -3048 S) +(-869 -3049 S) ((|constructor| (NIL "\\indented{3}{This package provides ordering functions on vectors which} are suitable parameters for OrderedDirectProduct.")) (|reverseLex| (((|Boolean|) (|Vector| |#2|) (|Vector| |#2|)) "\\spad{reverseLex(v1,v2)} return \\spad{true} if the vector \\spad{v1} is less than the vector \\spad{v2} in the ordering which is total degree refined by the reverse lexicographic ordering.")) (|totalLex| (((|Boolean|) (|Vector| |#2|) (|Vector| |#2|)) "\\spad{totalLex(v1,v2)} return \\spad{true} if the vector \\spad{v1} is less than the vector \\spad{v2} in the ordering which is total degree refined by lexicographic ordering.")) (|pureLex| (((|Boolean|) (|Vector| |#2|) (|Vector| |#2|)) "\\spad{pureLex(v1,v2)} return \\spad{true} if the vector \\spad{v1} is less than the vector \\spad{v2} in the lexicographic ordering."))) NIL NIL @@ -3444,11 +3444,11 @@ NIL ((|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."))) NIL ((|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (QUOTE (-571)))) -(-879 R |sigma| -3733) +(-879 R |sigma| -3732) ((|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."))) ((-4504 . T) (-4505 . T) (-4507 . T)) ((|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (|%list| (QUOTE -1070) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#1| (|%list| (QUOTE -1070) (QUOTE (-560)))) (|HasCategory| |#1| (QUOTE (-571))) (|HasCategory| |#1| (QUOTE (-466))) (|HasCategory| |#1| (QUOTE (-376)))) -(-880 |x| R |sigma| -3733) +(-880 |x| R |sigma| -3732) ((|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}."))) ((-4504 . T) (-4505 . T) (-4507 . T)) ((|HasCategory| |#2| (QUOTE (-175))) (|HasCategory| |#2| (|%list| (QUOTE -1070) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#2| (|%list| (QUOTE -1070) (QUOTE (-560)))) (|HasCategory| |#2| (QUOTE (-571))) (|HasCategory| |#2| (QUOTE (-466))) (|HasCategory| |#2| (QUOTE (-376)))) @@ -3596,7 +3596,7 @@ NIL ((|constructor| (NIL "Patterns for use by the pattern matcher.")) (|optpair| (((|Union| (|List| $) "failed") (|List| $)) "\\spad{optpair(l)} returns \\spad{l} has the form \\spad{[a, b]} and a is optional,{} and \"failed\" otherwise.")) (|variables| (((|List| $) $) "\\spad{variables(p)} returns the list of matching variables appearing in \\spad{p}.")) (|getBadValues| (((|List| (|Any|)) $) "\\spad{getBadValues(p)} returns the list of \"bad values\" for \\spad{p}. Note: \\spad{p} is not allowed to match any of its \"bad values\".")) (|addBadValue| (($ $ (|Any|)) "\\spad{addBadValue(p, v)} adds \\spad{v} to the list of \"bad values\" for \\spad{p}. Note: \\spad{p} is not allowed to match any of its \"bad values\".")) (|resetBadValues| (($ $) "\\spad{resetBadValues(p)} initializes the list of \"bad values\" for \\spad{p} to \\spad{[]}. Note: \\spad{p} is not allowed to match any of its \"bad values\".")) (|hasTopPredicate?| (((|Boolean|) $) "\\spad{hasTopPredicate?(p)} tests if \\spad{p} has a top-level predicate.")) (|topPredicate| (((|Record| (|:| |var| (|List| (|Symbol|))) (|:| |pred| (|Any|))) $) "\\spad{topPredicate(x)} returns \\spad{[[a1,...,an], f]} where the top-level predicate of \\spad{x} is \\spad{f(a1,...,an)}. Note: \\spad{n} is 0 if \\spad{x} has no top-level predicate.")) (|setTopPredicate| (($ $ (|List| (|Symbol|)) (|Any|)) "\\spad{setTopPredicate(x, [a1,...,an], f)} returns \\spad{x} with the top-level predicate set to \\spad{f(a1,...,an)}.")) (|patternVariable| (($ (|Symbol|) (|Boolean|) (|Boolean|) (|Boolean|)) "\\spad{patternVariable(x, c?, o?, m?)} creates a pattern variable \\spad{x},{} which is constant if \\spad{c? = true},{} optional if \\spad{o? = true},{} and multiple if \\spad{m? = true}.")) (|withPredicates| (($ $ (|List| (|Any|))) "\\spad{withPredicates(p, [p1,...,pn])} makes a copy of \\spad{p} and attaches the predicate \\spad{p1} and ... and pn to the copy,{} which is returned.")) (|setPredicates| (($ $ (|List| (|Any|))) "\\spad{setPredicates(p, [p1,...,pn])} attaches the predicate \\spad{p1} and ... and pn to \\spad{p}.")) (|predicates| (((|List| (|Any|)) $) "\\spad{predicates(p)} returns \\spad{[p1,...,pn]} such that the predicate attached to \\spad{p} is \\spad{p1} and ... and pn.")) (|hasPredicate?| (((|Boolean|) $) "\\spad{hasPredicate?(p)} tests if \\spad{p} has predicates attached to it.")) (|optional?| (((|Boolean|) $) "\\spad{optional?(p)} tests if \\spad{p} is a single matching variable which can match an identity.")) (|multiple?| (((|Boolean|) $) "\\spad{multiple?(p)} tests if \\spad{p} is a single matching variable allowing list matching or multiple term matching in a sum or product.")) (|generic?| (((|Boolean|) $) "\\spad{generic?(p)} tests if \\spad{p} is a single matching variable.")) (|constant?| (((|Boolean|) $) "\\spad{constant?(p)} tests if \\spad{p} contains no matching variables.")) (|symbol?| (((|Boolean|) $) "\\spad{symbol?(p)} tests if \\spad{p} is a symbol.")) (|quoted?| (((|Boolean|) $) "\\spad{quoted?(p)} tests if \\spad{p} is of the form 's for a symbol \\spad{s}.")) (|inR?| (((|Boolean|) $) "\\spad{inR?(p)} tests if \\spad{p} is an atom (\\spadignore{i.e.} an element of \\spad{R}).")) (|copy| (($ $) "\\spad{copy(p)} returns a recursive copy of \\spad{p}.")) (|convert| (($ (|List| $)) "\\spad{convert([a1,...,an])} returns the pattern \\spad{[a1,...,an]}.")) (|depth| (((|NonNegativeInteger|) $) "\\spad{depth(p)} returns the nesting level of \\spad{p}.")) (/ (($ $ $) "\\spad{a / b} returns the pattern \\spad{a / b}.")) (** (($ $ $) "\\spad{a ** b} returns the pattern \\spad{a ** b}.") (($ $ (|NonNegativeInteger|)) "\\spad{a ** n} returns the pattern \\spad{a ** n}.")) (* (($ $ $) "\\spad{a * b} returns the pattern \\spad{a * b}.")) (+ (($ $ $) "\\spad{a + b} returns the pattern \\spad{a + b}.")) (|elt| (($ (|BasicOperator|) (|List| $)) "\\spad{elt(op, [a1,...,an])} returns \\spad{op(a1,...,an)}.")) (|isPower| (((|Union| (|Record| (|:| |val| $) (|:| |exponent| $)) "failed") $) "\\spad{isPower(p)} returns \\spad{[a, b]} if \\spad{p = a ** b},{} and \"failed\" otherwise.")) (|isList| (((|Union| (|List| $) "failed") $) "\\spad{isList(p)} returns \\spad{[a1,...,an]} if \\spad{p = [a1,...,an]},{} \"failed\" otherwise.")) (|isQuotient| (((|Union| (|Record| (|:| |num| $) (|:| |den| $)) "failed") $) "\\spad{isQuotient(p)} returns \\spad{[a, b]} if \\spad{p = a / b},{} and \"failed\" otherwise.")) (|isExpt| (((|Union| (|Record| (|:| |val| $) (|:| |exponent| (|NonNegativeInteger|))) "failed") $) "\\spad{isExpt(p)} returns \\spad{[q, n]} if \\spad{n > 0} and \\spad{p = q ** n},{} and \"failed\" otherwise.")) (|isOp| (((|Union| (|Record| (|:| |op| (|BasicOperator|)) (|:| |arg| (|List| $))) "failed") $) "\\spad{isOp(p)} returns \\spad{[op, [a1,...,an]]} if \\spad{p = op(a1,...,an)},{} and \"failed\" otherwise.") (((|Union| (|List| $) "failed") $ (|BasicOperator|)) "\\spad{isOp(p, op)} returns \\spad{[a1,...,an]} if \\spad{p = op(a1,...,an)},{} and \"failed\" otherwise.")) (|isTimes| (((|Union| (|List| $) "failed") $) "\\spad{isTimes(p)} returns \\spad{[a1,...,an]} if \\spad{n > 1} and \\spad{p = a1 * ... * an},{} and \"failed\" otherwise.")) (|isPlus| (((|Union| (|List| $) "failed") $) "\\spad{isPlus(p)} returns \\spad{[a1,...,an]} if \\spad{n > 1} \\indented{1}{and \\spad{p = a1 + ... + an},{}} and \"failed\" otherwise.")) ((|One|) (($) "1")) ((|Zero|) (($) "0"))) NIL NIL -(-917 R -4350) +(-917 R -4349) ((|constructor| (NIL "Tools for patterns.")) (|badValues| (((|List| |#2|) (|Pattern| |#1|)) "\\spad{badValues(p)} returns the list of \"bad values\" for \\spad{p}; \\spad{p} is not allowed to match any of its \"bad values\".")) (|addBadValue| (((|Pattern| |#1|) (|Pattern| |#1|) |#2|) "\\spad{addBadValue(p, v)} adds \\spad{v} to the list of \"bad values\" for \\spad{p}; \\spad{p} is not allowed to match any of its \"bad values\".")) (|satisfy?| (((|Boolean|) (|List| |#2|) (|Pattern| |#1|)) "\\spad{satisfy?([v1,...,vn], p)} returns \\spad{f(v1,...,vn)} where \\spad{f} is the top-level predicate attached to \\spad{p}.") (((|Boolean|) |#2| (|Pattern| |#1|)) "\\spad{satisfy?(v, p)} returns \\spad{f}(\\spad{v}) where \\spad{f} is the predicate attached to \\spad{p}.")) (|predicate| (((|Mapping| (|Boolean|) |#2|) (|Pattern| |#1|)) "\\spad{predicate(p)} returns the predicate attached to \\spad{p},{} the constant function \\spad{true} if \\spad{p} has no predicates attached to it.")) (|suchThat| (((|Pattern| |#1|) (|Pattern| |#1|) (|List| (|Symbol|)) (|Mapping| (|Boolean|) (|List| |#2|))) "\\spad{suchThat(p, [a1,...,an], f)} returns a copy of \\spad{p} with the top-level predicate set to \\spad{f(a1,...,an)}.") (((|Pattern| |#1|) (|Pattern| |#1|) (|List| (|Mapping| (|Boolean|) |#2|))) "\\spad{suchThat(p, [f1,...,fn])} makes a copy of \\spad{p} and adds the predicate \\spad{f1} and ... and fn to the copy,{} which is returned.") (((|Pattern| |#1|) (|Pattern| |#1|) (|Mapping| (|Boolean|) |#2|)) "\\spad{suchThat(p, f)} makes a copy of \\spad{p} and adds the predicate \\spad{f} to the copy,{} which is returned."))) NIL NIL @@ -3624,7 +3624,7 @@ NIL ((|PDESolve| (((|Result|) (|Record| (|:| |pde| (|List| (|Expression| (|DoubleFloat|)))) (|:| |constraints| (|List| (|Record| (|:| |start| (|DoubleFloat|)) (|:| |finish| (|DoubleFloat|)) (|:| |grid| (|NonNegativeInteger|)) (|:| |boundaryType| (|Integer|)) (|:| |dStart| (|Matrix| (|DoubleFloat|))) (|:| |dFinish| (|Matrix| (|DoubleFloat|)))))) (|:| |f| (|List| (|List| (|Expression| (|DoubleFloat|))))) (|:| |st| (|String|)) (|:| |tol| (|DoubleFloat|)))) "\\spad{PDESolve(args)} performs the integration of the function given the strategy or method returned by \\axiomFun{measure}.")) (|measure| (((|Record| (|:| |measure| (|Float|)) (|:| |explanations| (|String|))) (|RoutinesTable|) (|Record| (|:| |pde| (|List| (|Expression| (|DoubleFloat|)))) (|:| |constraints| (|List| (|Record| (|:| |start| (|DoubleFloat|)) (|:| |finish| (|DoubleFloat|)) (|:| |grid| (|NonNegativeInteger|)) (|:| |boundaryType| (|Integer|)) (|:| |dStart| (|Matrix| (|DoubleFloat|))) (|:| |dFinish| (|Matrix| (|DoubleFloat|)))))) (|:| |f| (|List| (|List| (|Expression| (|DoubleFloat|))))) (|:| |st| (|String|)) (|:| |tol| (|DoubleFloat|)))) "\\spad{measure(R,args)} calculates an estimate of the ability of a particular method to solve a problem. \\blankline This method may be either a specific NAG routine or a strategy (such as transforming the function from one which is difficult to one which is easier to solve). \\blankline It will call whichever agents are needed to perform analysis on the problem in order to calculate the measure. There is a parameter,{} labelled \\axiom{sofar},{} which would contain the best compatibility found so far."))) NIL NIL -(-924 UP -1612) +(-924 UP -1613) ((|constructor| (NIL "This package \\undocumented")) (|rightFactorCandidate| ((|#1| |#1| (|NonNegativeInteger|)) "\\spad{rightFactorCandidate(p,n)} \\undocumented")) (|leftFactor| (((|Union| |#1| "failed") |#1| |#1|) "\\spad{leftFactor(p,q)} \\undocumented")) (|decompose| (((|Union| (|Record| (|:| |left| |#1|) (|:| |right| |#1|)) "failed") |#1| (|NonNegativeInteger|) (|NonNegativeInteger|)) "\\spad{decompose(up,m,n)} \\undocumented") (((|List| |#1|) |#1|) "\\spad{decompose(up)} \\undocumented"))) NIL NIL @@ -3692,7 +3692,7 @@ NIL ((|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}."))) ((-4503 . T) ((-4512 "*") . T) (-4504 . T) (-4505 . T) (-4507 . T)) NIL -(-941 R0 -1612 UP UPUP R) +(-941 R0 -1613 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"))) NIL NIL @@ -3720,7 +3720,7 @@ NIL ((|constructor| (NIL "PermutationGroupExamples provides permutation groups for some classes of groups: symmetric,{} alternating,{} dihedral,{} cyclic,{} direct products of cyclic,{} which are in fact the finite abelian groups of symmetric groups called Young subgroups. Furthermore,{} Rubik's group as permutation group of 48 integers and a list of sporadic simple groups derived from the atlas of finite groups.")) (|youngGroup| (((|PermutationGroup| (|Integer|)) (|Partition|)) "\\spad{youngGroup(lambda)} constructs the direct product of the symmetric groups given by the parts of the partition {\\em lambda}.") (((|PermutationGroup| (|Integer|)) (|List| (|Integer|))) "\\spad{youngGroup([n1,...,nk])} constructs the direct product of the symmetric groups {\\em Sn1},{}...,{}{\\em Snk}.")) (|rubiksGroup| (((|PermutationGroup| (|Integer|))) "\\spad{rubiksGroup constructs} the permutation group representing Rubic's Cube acting on integers {\\em 10*i+j} for {\\em 1 <= i <= 6},{} {\\em 1 <= j <= 8}. The faces of Rubik's Cube are labelled in the obvious way Front,{} Right,{} Up,{} Down,{} Left,{} Back and numbered from 1 to 6 in this given ordering,{} the pieces on each face (except the unmoveable center piece) are clockwise numbered from 1 to 8 starting with the piece in the upper left corner. The moves of the cube are represented as permutations on these pieces,{} represented as a two digit integer {\\em ij} where \\spad{i} is the numer of theface (1 to 6) and \\spad{j} is the number of the piece on this face. The remaining ambiguities are resolved by looking at the 6 generators,{} which represent a 90 degree turns of the faces,{} or from the following pictorial description. Permutation group representing Rubic's Cube acting on integers 10*i+j for 1 <= \\spad{i} <= 6,{} 1 <= \\spad{j} \\spad{<=8}. \\blankline\\begin{verbatim}Rubik's Cube: +-----+ +-- B where: marks Side # : / U /|/ / / | F(ront) <-> 1 L --> +-----+ R| R(ight) <-> 2 | | + U(p) <-> 3 | F | / D(own) <-> 4 | |/ L(eft) <-> 5 +-----+ B(ack) <-> 6 ^ | DThe Cube's surface: The pieces on each side +---+ (except the unmoveable center |567| piece) are clockwise numbered |4U8| from 1 to 8 starting with the |321| piece in the upper left +---+---+---+ corner (see figure on the |781|123|345| left). The moves of the cube |6L2|8F4|2R6| are represented as |543|765|187| permutations on these pieces. +---+---+---+ Each of the pieces is |123| represented as a two digit |8D4| integer ij where i is the |765| # of the side ( 1 to 6 for +---+ F to B (see table above )) |567| and j is the # of the piece. |4B8| |321| +---+\\end{verbatim}")) (|janko2| (((|PermutationGroup| (|Integer|))) "\\spad{janko2 constructs} the janko group acting on the integers 1,{}...,{}100.") (((|PermutationGroup| (|Integer|)) (|List| (|Integer|))) "\\spad{janko2(li)} constructs the janko group acting on the 100 integers given in the list {\\em li}. Note: duplicates in the list will be removed. Error: if {\\em li} has less or more than 100 different entries")) (|mathieu24| (((|PermutationGroup| (|Integer|))) "\\spad{mathieu24 constructs} the mathieu group acting on the integers 1,{}...,{}24.") (((|PermutationGroup| (|Integer|)) (|List| (|Integer|))) "\\spad{mathieu24(li)} constructs the mathieu group acting on the 24 integers given in the list {\\em li}. Note: duplicates in the list will be removed. Error: if {\\em li} has less or more than 24 different entries.")) (|mathieu23| (((|PermutationGroup| (|Integer|))) "\\spad{mathieu23 constructs} the mathieu group acting on the integers 1,{}...,{}23.") (((|PermutationGroup| (|Integer|)) (|List| (|Integer|))) "\\spad{mathieu23(li)} constructs the mathieu group acting on the 23 integers given in the list {\\em li}. Note: duplicates in the list will be removed. Error: if {\\em li} has less or more than 23 different entries.")) (|mathieu22| (((|PermutationGroup| (|Integer|))) "\\spad{mathieu22 constructs} the mathieu group acting on the integers 1,{}...,{}22.") (((|PermutationGroup| (|Integer|)) (|List| (|Integer|))) "\\spad{mathieu22(li)} constructs the mathieu group acting on the 22 integers given in the list {\\em li}. Note: duplicates in the list will be removed. Error: if {\\em li} has less or more than 22 different entries.")) (|mathieu12| (((|PermutationGroup| (|Integer|))) "\\spad{mathieu12 constructs} the mathieu group acting on the integers 1,{}...,{}12.") (((|PermutationGroup| (|Integer|)) (|List| (|Integer|))) "\\spad{mathieu12(li)} constructs the mathieu group acting on the 12 integers given in the list {\\em li}. Note: duplicates in the list will be removed Error: if {\\em li} has less or more than 12 different entries.")) (|mathieu11| (((|PermutationGroup| (|Integer|))) "\\spad{mathieu11 constructs} the mathieu group acting on the integers 1,{}...,{}11.") (((|PermutationGroup| (|Integer|)) (|List| (|Integer|))) "\\spad{mathieu11(li)} constructs the mathieu group acting on the 11 integers given in the list {\\em li}. Note: duplicates in the list will be removed. error,{} if {\\em li} has less or more than 11 different entries.")) (|dihedralGroup| (((|PermutationGroup| (|Integer|)) (|List| (|Integer|))) "\\spad{dihedralGroup([i1,...,ik])} constructs the dihedral group of order 2k acting on the integers out of {\\em i1},{}...,{}{\\em ik}. Note: duplicates in the list will be removed.") (((|PermutationGroup| (|Integer|)) (|PositiveInteger|)) "\\spad{dihedralGroup(n)} constructs the dihedral group of order 2n acting on integers 1,{}...,{}\\spad{N}.")) (|cyclicGroup| (((|PermutationGroup| (|Integer|)) (|List| (|Integer|))) "\\spad{cyclicGroup([i1,...,ik])} constructs the cyclic group of order \\spad{k} acting on the integers {\\em i1},{}...,{}{\\em ik}. Note: duplicates in the list will be removed.") (((|PermutationGroup| (|Integer|)) (|PositiveInteger|)) "\\spad{cyclicGroup(n)} constructs the cyclic group of order \\spad{n} acting on the integers 1,{}...,{}\\spad{n}.")) (|abelianGroup| (((|PermutationGroup| (|Integer|)) (|List| (|PositiveInteger|))) "\\spad{abelianGroup([n1,...,nk])} constructs the abelian group that is the direct product of cyclic groups with order {\\em ni}.")) (|alternatingGroup| (((|PermutationGroup| (|Integer|)) (|List| (|Integer|))) "\\spad{alternatingGroup(li)} constructs the alternating group acting on the integers in the list {\\em li},{} generators are in general the {\\em n-2}-cycle {\\em (li.3,...,li.n)} and the 3-cycle {\\em (li.1,li.2,li.3)},{} if \\spad{n} is odd and product of the 2-cycle {\\em (li.1,li.2)} with {\\em n-2}-cycle {\\em (li.3,...,li.n)} and the 3-cycle {\\em (li.1,li.2,li.3)},{} if \\spad{n} is even. Note: duplicates in the list will be removed.") (((|PermutationGroup| (|Integer|)) (|PositiveInteger|)) "\\spad{alternatingGroup(n)} constructs the alternating group {\\em An} acting on the integers 1,{}...,{}\\spad{n},{} generators are in general the {\\em n-2}-cycle {\\em (3,...,n)} and the 3-cycle {\\em (1,2,3)} if \\spad{n} is odd and the product of the 2-cycle {\\em (1,2)} with {\\em n-2}-cycle {\\em (3,...,n)} and the 3-cycle {\\em (1,2,3)} if \\spad{n} is even.")) (|symmetricGroup| (((|PermutationGroup| (|Integer|)) (|List| (|Integer|))) "\\spad{symmetricGroup(li)} constructs the symmetric group acting on the integers in the list {\\em li},{} generators are the cycle given by {\\em li} and the 2-cycle {\\em (li.1,li.2)}. Note: duplicates in the list will be removed.") (((|PermutationGroup| (|Integer|)) (|PositiveInteger|)) "\\spad{symmetricGroup(n)} constructs the symmetric group {\\em Sn} acting on the integers 1,{}...,{}\\spad{n},{} generators are the {\\em n}-cycle {\\em (1,...,n)} and the 2-cycle {\\em (1,2)}."))) NIL NIL -(-948 -1612) +(-948 -1613) ((|constructor| (NIL "Groebner functions for \\spad{P} \\spad{F} \\indented{2}{This package is an interface package to the groebner basis} package which allows you to compute groebner bases for polynomials in either lexicographic ordering or total degree ordering refined by reverse lex. The input is the ordinary polynomial type which is internally converted to a type with the required ordering. The resulting grobner basis is converted back to ordinary polynomials. The ordering among the variables is controlled by an explicit list of variables which is passed as a second argument. The coefficient domain is allowed to be any gcd domain,{} but the groebner basis is computed as if the polynomials were over a field.")) (|totalGroebner| (((|List| (|Polynomial| |#1|)) (|List| (|Polynomial| |#1|)) (|List| (|Symbol|))) "\\spad{totalGroebner(lp,lv)} computes Groebner basis for the list of polynomials \\spad{lp} with the terms ordered first by total degree and then refined by reverse lexicographic ordering. The variables are ordered by their position in the list \\spad{lv}.")) (|lexGroebner| (((|List| (|Polynomial| |#1|)) (|List| (|Polynomial| |#1|)) (|List| (|Symbol|))) "\\spad{lexGroebner(lp,lv)} computes Groebner basis for the list of polynomials \\spad{lp} in lexicographic order. The variables are ordered by their position in the list \\spad{lv}."))) NIL NIL @@ -3736,11 +3736,11 @@ NIL ((|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)}"))) ((-4503 . T) ((-4512 "*") . T) (-4504 . T) (-4505 . T) (-4507 . T)) NIL -(-952 |xx| -1612) +(-952 |xx| -1613) ((|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"))) NIL NIL -(-953 -1612 P) +(-953 -1613 P) ((|constructor| (NIL "This package exports interpolation algorithms")) (|LagrangeInterpolation| ((|#2| (|List| |#1|) (|List| |#1|)) "\\spad{LagrangeInterpolation(l1,l2)} \\undocumented"))) NIL NIL @@ -3768,7 +3768,7 @@ NIL ((|constructor| (NIL "Attaching assertions to symbols for pattern matching. Date Created: 21 Mar 1989 Date Last Updated: 23 May 1990")) (|multiple| (((|Expression| (|Integer|)) (|Symbol|)) "\\spad{multiple(x)} tells the pattern matcher that \\spad{x} should preferably match a multi-term quantity in a sum or product. For matching on lists,{} multiple(\\spad{x}) tells the pattern matcher that \\spad{x} should match a list instead of an element of a list.")) (|optional| (((|Expression| (|Integer|)) (|Symbol|)) "\\spad{optional(x)} tells the pattern matcher that \\spad{x} can match an identity (0 in a sum,{} 1 in a product or exponentiation)..")) (|constant| (((|Expression| (|Integer|)) (|Symbol|)) "\\spad{constant(x)} tells the pattern matcher that \\spad{x} should match only the symbol 'x and no other quantity.")) (|assert| (((|Expression| (|Integer|)) (|Symbol|) (|Identifier|)) "\\spad{assert(x, s)} makes the assertion \\spad{s} about \\spad{x}."))) NIL NIL -(-960 R -1612) +(-960 R -1613) ((|constructor| (NIL "Attaching assertions to symbols for pattern matching; Date Created: 21 Mar 1989 Date Last Updated: 23 May 1990")) (|multiple| ((|#2| |#2|) "\\spad{multiple(x)} tells the pattern matcher that \\spad{x} should preferably match a multi-term quantity in a sum or product. For matching on lists,{} multiple(\\spad{x}) tells the pattern matcher that \\spad{x} should match a list instead of an element of a list. Error: if \\spad{x} is not a symbol.")) (|optional| ((|#2| |#2|) "\\spad{optional(x)} tells the pattern matcher that \\spad{x} can match an identity (0 in a sum,{} 1 in a product or exponentiation). Error: if \\spad{x} is not a symbol.")) (|constant| ((|#2| |#2|) "\\spad{constant(x)} tells the pattern matcher that \\spad{x} should match only the symbol 'x and no other quantity. Error: if \\spad{x} is not a symbol.")) (|assert| ((|#2| |#2| (|Identifier|)) "\\spad{assert(x, s)} makes the assertion \\spad{s} about \\spad{x}. Error: if \\spad{x} is not a symbol."))) NIL NIL @@ -3776,7 +3776,7 @@ NIL ((|constructor| (NIL "This packages provides tools for matching recursively in type towers.")) (|patternMatch| (((|PatternMatchResult| |#1| |#3|) |#2| (|Pattern| |#1|) (|PatternMatchResult| |#1| |#3|)) "\\spad{patternMatch(expr, pat, res)} matches the pattern \\spad{pat} to the expression \\spad{expr}; res contains the variables of \\spad{pat} which are already matched and their matches. Note: this function handles type towers by changing the predicates and calling the matching function provided by \\spad{A}.")) (|fixPredicate| (((|Mapping| (|Boolean|) |#2|) (|Mapping| (|Boolean|) |#3|)) "\\spad{fixPredicate(f)} returns \\spad{g} defined by \\spad{g}(a) = \\spad{f}(a::B)."))) NIL NIL -(-962 S R -1612) +(-962 S R -1613) ((|constructor| (NIL "This package provides pattern matching functions on function spaces.")) (|patternMatch| (((|PatternMatchResult| |#1| |#3|) |#3| (|Pattern| |#1|) (|PatternMatchResult| |#1| |#3|)) "\\spad{patternMatch(expr, pat, res)} matches the pattern \\spad{pat} to the expression \\spad{expr}; res contains the variables of \\spad{pat} which are already matched and their matches."))) NIL NIL @@ -3796,11 +3796,11 @@ NIL ((|constructor| (NIL "This package provides pattern matching functions on polynomials.")) (|patternMatch| (((|PatternMatchResult| |#1| |#5|) |#5| (|Pattern| |#1|) (|PatternMatchResult| |#1| |#5|)) "\\spad{patternMatch(p, pat, res)} matches the pattern \\spad{pat} to the polynomial \\spad{p}; res contains the variables of \\spad{pat} which are already matched and their matches.") (((|PatternMatchResult| |#1| |#5|) |#5| (|Pattern| |#1|) (|PatternMatchResult| |#1| |#5|) (|Mapping| (|PatternMatchResult| |#1| |#5|) |#3| (|Pattern| |#1|) (|PatternMatchResult| |#1| |#5|))) "\\spad{patternMatch(p, pat, res, vmatch)} matches the pattern \\spad{pat} to the polynomial \\spad{p}. \\spad{res} contains the variables of \\spad{pat} which are already matched and their matches; vmatch is the matching function to use on the variables."))) NIL ((|HasCategory| |#3| (|%list| (QUOTE -912) (|devaluate| |#1|)))) -(-967 -4350) +(-967 -4349) ((|constructor| (NIL "Attaching predicates to symbols for pattern matching. Date Created: 21 Mar 1989 Date Last Updated: 23 May 1990")) (|suchThat| (((|Expression| (|Integer|)) (|Symbol|) (|List| (|Mapping| (|Boolean|) |#1|))) "\\spad{suchThat(x, [f1, f2, ..., fn])} attaches the predicate \\spad{f1} and \\spad{f2} and ... and fn to \\spad{x}.") (((|Expression| (|Integer|)) (|Symbol|) (|Mapping| (|Boolean|) |#1|)) "\\spad{suchThat(x, foo)} attaches the predicate foo to \\spad{x}."))) NIL NIL -(-968 R -1612 -4350) +(-968 R -1613 -4349) ((|constructor| (NIL "Attaching predicates to symbols for pattern matching. Date Created: 21 Mar 1989 Date Last Updated: 23 May 1990")) (|suchThat| ((|#2| |#2| (|List| (|Mapping| (|Boolean|) |#3|))) "\\spad{suchThat(x, [f1, f2, ..., fn])} attaches the predicate \\spad{f1} and \\spad{f2} and ... and fn to \\spad{x}. Error: if \\spad{x} is not a symbol.") ((|#2| |#2| (|Mapping| (|Boolean|) |#3|)) "\\spad{suchThat(x, foo)} attaches the predicate foo to \\spad{x}; error if \\spad{x} is not a symbol."))) NIL NIL @@ -3852,7 +3852,7 @@ NIL ((|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}."))) (((-4512 "*") |has| |#1| (-175)) (-4503 |has| |#1| (-571)) (-4508 |has| |#1| (-6 -4508)) (-4505 . T) (-4504 . T) (-4507 . T)) NIL -(-981 E V R P -1612) +(-981 E V R P -1613) ((|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}."))) NIL NIL @@ -3860,7 +3860,7 @@ NIL ((|constructor| (NIL "This package provides a very general map function,{} which given a set \\spad{S} and polynomials over \\spad{R} with maps from the variables into \\spad{S} and the coefficients into \\spad{S},{} maps polynomials into \\spad{S}. \\spad{S} is assumed to support \\spad{+},{} \\spad{*} and \\spad{**}.")) (|map| ((|#5| (|Mapping| |#5| |#2|) (|Mapping| |#5| |#3|) |#4|) "\\spad{map(varmap, coefmap, p)} takes a \\spad{varmap},{} a mapping from the variables of polynomial \\spad{p} into \\spad{S},{} \\spad{coefmap},{} a mapping from coefficients of \\spad{p} into \\spad{S},{} and \\spad{p},{} and produces a member of \\spad{S} using the corresponding arithmetic. in \\spad{S}"))) NIL NIL -(-983 E V R P -1612) +(-983 E V R P -1613) ((|constructor| (NIL "computes \\spad{n}-th roots of quotients of multivariate polynomials")) (|nthr| (((|Record| (|:| |exponent| (|NonNegativeInteger|)) (|:| |coef| |#4|) (|:| |radicand| (|List| |#4|))) |#4| (|NonNegativeInteger|)) "\\spad{nthr(p,n)} should be local but conditional")) (|froot| (((|Record| (|:| |exponent| (|NonNegativeInteger|)) (|:| |coef| |#5|) (|:| |radicand| |#5|)) |#5| (|NonNegativeInteger|)) "\\spad{froot(f, n)} returns \\spad{[m,c,r]} such that \\spad{f**(1/n) = c * r**(1/m)}.")) (|qroot| (((|Record| (|:| |exponent| (|NonNegativeInteger|)) (|:| |coef| |#5|) (|:| |radicand| |#5|)) (|Fraction| (|Integer|)) (|NonNegativeInteger|)) "\\spad{qroot(f, n)} returns \\spad{[m,c,r]} such that \\spad{f**(1/n) = c * r**(1/m)}.")) (|rroot| (((|Record| (|:| |exponent| (|NonNegativeInteger|)) (|:| |coef| |#5|) (|:| |radicand| |#5|)) |#3| (|NonNegativeInteger|)) "\\spad{rroot(f, n)} returns \\spad{[m,c,r]} such that \\spad{f**(1/n) = c * r**(1/m)}.")) (|denom| ((|#4| $) "\\spad{denom(x)} \\undocumented")) (|numer| ((|#4| $) "\\spad{numer(x)} \\undocumented"))) NIL ((|HasCategory| |#3| (QUOTE (-466)))) @@ -3892,7 +3892,7 @@ NIL ((|constructor| (NIL "Category for the functions defined by integrals.")) (|integral| (($ $ (|SegmentBinding| $)) "\\spad{integral(f, x = a..b)} returns the formal definite integral of \\spad{f} dx for \\spad{x} between \\spad{a} and \\spad{b}.") (($ $ (|Symbol|)) "\\spad{integral(f, x)} returns the formal integral of \\spad{f} dx."))) NIL NIL -(-991 -1612) +(-991 -1613) ((|constructor| (NIL "PrimitiveElement provides functions to compute primitive elements in algebraic extensions.")) (|primitiveElement| (((|Record| (|:| |coef| (|List| (|Integer|))) (|:| |poly| (|List| (|SparseUnivariatePolynomial| |#1|))) (|:| |prim| (|SparseUnivariatePolynomial| |#1|))) (|List| (|Polynomial| |#1|)) (|List| (|Symbol|)) (|Symbol|)) "\\spad{primitiveElement([p1,...,pn], [a1,...,an], a)} returns \\spad{[[c1,...,cn], [q1,...,qn], q]} such that then \\spad{k(a1,...,an) = k(a)},{} where \\spad{a = a1 c1 + ... + an cn},{} \\spad{ai = qi(a)},{} and \\spad{q(a) = 0}. The \\spad{pi}'s are the defining polynomials for the \\spad{ai}'s. This operation uses the technique of \\spadglossSee{groebner bases}{Groebner basis}.") (((|Record| (|:| |coef| (|List| (|Integer|))) (|:| |poly| (|List| (|SparseUnivariatePolynomial| |#1|))) (|:| |prim| (|SparseUnivariatePolynomial| |#1|))) (|List| (|Polynomial| |#1|)) (|List| (|Symbol|))) "\\spad{primitiveElement([p1,...,pn], [a1,...,an])} returns \\spad{[[c1,...,cn], [q1,...,qn], q]} such that then \\spad{k(a1,...,an) = k(a)},{} where \\spad{a = a1 c1 + ... + an cn},{} \\spad{ai = qi(a)},{} and \\spad{q(a) = 0}. The \\spad{pi}'s are the defining polynomials for the \\spad{ai}'s. This operation uses the technique of \\spadglossSee{groebner bases}{Groebner basis}.") (((|Record| (|:| |coef1| (|Integer|)) (|:| |coef2| (|Integer|)) (|:| |prim| (|SparseUnivariatePolynomial| |#1|))) (|Polynomial| |#1|) (|Symbol|) (|Polynomial| |#1|) (|Symbol|)) "\\spad{primitiveElement(p1, a1, p2, a2)} returns \\spad{[c1, c2, q]} such that \\spad{k(a1, a2) = k(a)} where \\spad{a = c1 a1 + c2 a2, and q(a) = 0}. The \\spad{pi}'s are the defining polynomials for the \\spad{ai}'s. The \\spad{p2} may involve \\spad{a1},{} but \\spad{p1} must not involve \\spad{a2}. This operation uses \\spadfun{resultant}."))) NIL NIL @@ -3996,7 +3996,7 @@ NIL ((|constructor| (NIL "This package \\undocumented{}")) (|map| ((|#4| (|Mapping| |#4| (|Polynomial| |#1|)) |#4|) "\\spad{map(f,p)} \\undocumented{}")) (|pushup| ((|#4| |#4| (|List| |#3|)) "\\spad{pushup(p,lv)} \\undocumented{}") ((|#4| |#4| |#3|) "\\spad{pushup(p,v)} \\undocumented{}")) (|pushdown| ((|#4| |#4| (|List| |#3|)) "\\spad{pushdown(p,lv)} \\undocumented{}") ((|#4| |#4| |#3|) "\\spad{pushdown(p,v)} \\undocumented{}")) (|variable| (((|Union| $ "failed") (|Symbol|)) "\\spad{variable(s)} makes an element from symbol \\spad{s} or fails")) (|convert| (((|Symbol|) $) "\\spad{convert(x)} converts \\spad{x} to a symbol"))) NIL NIL -(-1017 K R UP -1612) +(-1017 K R UP -1613) ((|constructor| (NIL "In this package \\spad{K} is a finite field,{} \\spad{R} is a ring of univariate polynomials over \\spad{K},{} and \\spad{F} is a monogenic algebra over \\spad{R}. We require that \\spad{F} is monogenic,{} \\spadignore{i.e.} that \\spad{F = K[x,y]/(f(x,y))},{} because the integral basis algorithm used will factor the polynomial \\spad{f(x,y)}. The package provides a function to compute the integral closure of \\spad{R} in the quotient field of \\spad{F} as well as a function to compute a \"local integral basis\" at a specific prime.")) (|reducedDiscriminant| ((|#2| |#3|) "\\spad{reducedDiscriminant(up)} \\undocumented")) (|localIntegralBasis| (((|Record| (|:| |basis| (|Matrix| |#2|)) (|:| |basisDen| |#2|) (|:| |basisInv| (|Matrix| |#2|))) |#2|) "\\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 the framed algebra \\spad{F}. \\spad{F} is a framed algebra with \\spad{R}-module basis \\spad{w1,w2,...,wn}. If '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 'basis' contains the coordinates of the \\spad{i}th basis vector. Similarly,{} the \\spad{i}th row of the matrix 'basisInv' contains the coordinates of \\spad{wi} with respect to the basis \\spad{v1,...,vn}: if '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| |#2|)) (|:| |basisDen| |#2|) (|:| |basisInv| (|Matrix| |#2|)))) "\\spad{integralBasis()} returns a record \\spad{[basis,basisDen,basisInv] } containing information regarding the integral closure of \\spad{R} in the quotient field of the framed algebra \\spad{F}. \\spad{F} is a framed algebra with \\spad{R}-module basis \\spad{w1,w2,...,wn}. If '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 'basis' contains the coordinates of the \\spad{i}th basis vector. Similarly,{} the \\spad{i}th row of the matrix 'basisInv' contains the coordinates of \\spad{wi} with respect to the basis \\spad{v1,...,vn}: if 'basisInv' is the matrix \\spad{(bij, i = 1..n, j = 1..n)},{} then \\spad{wi = sum(bij * vj, j = 1..n)}."))) NIL NIL @@ -4068,7 +4068,7 @@ NIL ((|constructor| (NIL "The \\spad{RadicalCategory} is a model for the rational numbers.")) (** (($ $ (|Fraction| (|Integer|))) "\\spad{x ** y} is the rational exponentiation of \\spad{x} by the power \\spad{y}.")) (|nthRoot| (($ $ (|Integer|)) "\\spad{nthRoot(x,n)} returns the \\spad{n}th root of \\spad{x}.")) (|sqrt| (($ $) "\\spad{sqrt(x)} returns the square root of \\spad{x}."))) NIL NIL -(-1035 -1612 UP UPUP |radicnd| |n|) +(-1035 -1613 UP UPUP |radicnd| |n|) ((|constructor| (NIL "Function field defined by y**n = \\spad{f}(\\spad{x})."))) ((-4503 |has| (-421 |#2|) (-376)) (-4508 |has| (-421 |#2|) (-376)) (-4502 |has| (-421 |#2|) (-376)) ((-4512 "*") . T) (-4504 . T) (-4505 . T) (-4507 . T)) ((|HasCategory| (-421 |#2|) (QUOTE (-147))) (|HasCategory| (-421 |#2|) (QUOTE (-149))) (|HasCategory| (-421 |#2|) (QUOTE (-363))) (-2210 (|HasCategory| (-421 |#2|) (QUOTE (-376))) (|HasCategory| (-421 |#2|) (QUOTE (-363)))) (|HasCategory| (-421 |#2|) (QUOTE (-376))) (|HasCategory| (-421 |#2|) (QUOTE (-381))) (-2210 (-12 (|HasCategory| (-421 |#2|) (QUOTE (-240))) (|HasCategory| (-421 |#2|) (QUOTE (-376)))) (|HasCategory| (-421 |#2|) (QUOTE (-363)))) (-2210 (-12 (|HasCategory| (-421 |#2|) (QUOTE (-240))) (|HasCategory| (-421 |#2|) (QUOTE (-376)))) (-12 (|HasCategory| (-421 |#2|) (QUOTE (-239))) (|HasCategory| (-421 |#2|) (QUOTE (-376)))) (|HasCategory| (-421 |#2|) (QUOTE (-363)))) (-2210 (-12 (|HasCategory| (-421 |#2|) (|%list| (QUOTE -928) (QUOTE (-1209)))) (|HasCategory| (-421 |#2|) (QUOTE (-376)))) (-12 (|HasCategory| (-421 |#2|) (|%list| (QUOTE -928) (QUOTE (-1209)))) (|HasCategory| (-421 |#2|) (QUOTE (-363))))) (-2210 (-12 (|HasCategory| (-421 |#2|) (|%list| (QUOTE -928) (QUOTE (-1209)))) (|HasCategory| (-421 |#2|) (QUOTE (-376)))) (-12 (|HasCategory| (-421 |#2|) (|%list| (QUOTE -930) (QUOTE (-1209)))) (|HasCategory| (-421 |#2|) (QUOTE (-376))))) (|HasCategory| (-421 |#2|) (|%list| (QUOTE -660) (QUOTE (-560)))) (-2210 (|HasCategory| (-421 |#2|) (|%list| (QUOTE -1070) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| (-421 |#2|) (QUOTE (-376)))) (|HasCategory| (-421 |#2|) (|%list| (QUOTE -1070) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| (-421 |#2|) (|%list| (QUOTE -1070) (QUOTE (-560)))) (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (QUOTE (-381))) (-12 (|HasCategory| (-421 |#2|) (QUOTE (-239))) (|HasCategory| (-421 |#2|) (QUOTE (-376)))) (-12 (|HasCategory| (-421 |#2|) (|%list| (QUOTE -930) (QUOTE (-1209)))) (|HasCategory| (-421 |#2|) (QUOTE (-376)))) (-12 (|HasCategory| (-421 |#2|) (QUOTE (-240))) (|HasCategory| (-421 |#2|) (QUOTE (-376)))) (-12 (|HasCategory| (-421 |#2|) (|%list| (QUOTE -928) (QUOTE (-1209)))) (|HasCategory| (-421 |#2|) (QUOTE (-376))))) @@ -4108,19 +4108,19 @@ NIL ((|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}}"))) ((-4503 . T) (-4508 . T) (-4502 . T) (-4505 . T) (-4504 . T) ((-4512 "*") . T) (-4507 . T)) NIL -(-1045 R -1612) +(-1045 R -1613) ((|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."))) NIL NIL -(-1046 R -1612) +(-1046 R -1613) ((|constructor| (NIL "\\indented{1}{Risch differential equation,{} elementary case.} Author: Manuel Bronstein Date Created: 12 August 1992 Date Last Updated: 17 August 1992 Keywords: elementary,{} function,{} integration.")) (|rischDEsys| (((|Union| (|List| |#2|) "failed") (|Integer|) |#2| |#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{rischDEsys(n, f, g_1, g_2, x,lim,ext)} returns \\spad{y_1.y_2} such that \\spad{(dy1/dx,dy2/dx) + ((0, - n df/dx),(n df/dx,0)) (y1,y2) = (g1,g2)} if \\spad{y_1,y_2} exist,{} \"failed\" otherwise. \\spad{lim} is a limited integration function,{} \\spad{ext} is an extended integration function."))) NIL NIL -(-1047 -1612 UP) +(-1047 -1613 UP) ((|constructor| (NIL "\\indented{1}{Risch differential equation,{} transcendental case.} Author: Manuel Bronstein Date Created: Jan 1988 Date Last Updated: 2 November 1995")) (|polyRDE| (((|Union| (|:| |ans| (|Record| (|:| |ans| |#2|) (|:| |nosol| (|Boolean|)))) (|:| |eq| (|Record| (|:| |b| |#2|) (|:| |c| |#2|) (|:| |m| (|Integer|)) (|:| |alpha| |#2|) (|:| |beta| |#2|)))) |#2| |#2| |#2| (|Integer|) (|Mapping| |#2| |#2|)) "\\spad{polyRDE(a, B, C, n, D)} returns either: 1. \\spad{[Q, b]} such that \\spad{degree(Q) <= n} and \\indented{3}{\\spad{a Q'+ B Q = C} if \\spad{b = true},{} \\spad{Q} is a partial solution} \\indented{3}{otherwise.} 2. \\spad{[B1, C1, m, \\alpha, \\beta]} such that any polynomial solution \\indented{3}{of degree at most \\spad{n} of \\spad{A Q' + BQ = C} must be of the form} \\indented{3}{\\spad{Q = \\alpha H + \\beta} where \\spad{degree(H) <= m} and} \\indented{3}{\\spad{H} satisfies \\spad{H' + B1 H = C1}.} \\spad{D} is the derivation to use.")) (|baseRDE| (((|Record| (|:| |ans| (|Fraction| |#2|)) (|:| |nosol| (|Boolean|))) (|Fraction| |#2|) (|Fraction| |#2|)) "\\spad{baseRDE(f, g)} returns a \\spad{[y, b]} such that \\spad{y' + fy = g} if \\spad{b = true},{} \\spad{y} is a partial solution otherwise (no solution in that case). \\spad{D} is the derivation to use.")) (|monomRDE| (((|Union| (|Record| (|:| |a| |#2|) (|:| |b| (|Fraction| |#2|)) (|:| |c| (|Fraction| |#2|)) (|:| |t| |#2|)) "failed") (|Fraction| |#2|) (|Fraction| |#2|) (|Mapping| |#2| |#2|)) "\\spad{monomRDE(f,g,D)} returns \\spad{[A, B, C, T]} such that \\spad{y' + f y = g} has a solution if and only if \\spad{y = Q / T},{} where \\spad{Q} satisfies \\spad{A Q' + B Q = C} and has no normal pole. A and \\spad{T} are polynomials and \\spad{B} and \\spad{C} have no normal poles. \\spad{D} is the derivation to use."))) NIL NIL -(-1048 -1612 UP) +(-1048 -1613 UP) ((|constructor| (NIL "\\indented{1}{Risch differential equation system,{} transcendental case.} Author: Manuel Bronstein Date Created: 17 August 1992 Date Last Updated: 3 February 1994")) (|baseRDEsys| (((|Union| (|List| (|Fraction| |#2|)) "failed") (|Fraction| |#2|) (|Fraction| |#2|) (|Fraction| |#2|)) "\\spad{baseRDEsys(f, g1, g2)} returns fractions \\spad{y_1.y_2} such that \\spad{(y1', y2') + ((0, -f), (f, 0)) (y1,y2) = (g1,g2)} if \\spad{y_1,y_2} exist,{} \"failed\" otherwise.")) (|monomRDEsys| (((|Union| (|Record| (|:| |a| |#2|) (|:| |b| (|Fraction| |#2|)) (|:| |h| |#2|) (|:| |c1| (|Fraction| |#2|)) (|:| |c2| (|Fraction| |#2|)) (|:| |t| |#2|)) "failed") (|Fraction| |#2|) (|Fraction| |#2|) (|Fraction| |#2|) (|Mapping| |#2| |#2|)) "\\spad{monomRDEsys(f,g1,g2,D)} returns \\spad{[A, B, H, C1, C2, T]} such that \\spad{(y1', y2') + ((0, -f), (f, 0)) (y1,y2) = (g1,g2)} has a solution if and only if \\spad{y1 = Q1 / T, y2 = Q2 / T},{} where \\spad{B,C1,C2,Q1,Q2} have no normal poles and satisfy A \\spad{(Q1', Q2') + ((H, -B), (B, H)) (Q1,Q2) = (C1,C2)} \\spad{D} is the derivation to use."))) NIL NIL @@ -4156,7 +4156,7 @@ NIL ((|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"))) ((-4503 . T) (-4508 . T) (-4502 . T) (-4505 . T) (-4504 . T) ((-4512 "*") . T) (-4507 . T)) ((-2210 (|HasCategory| (-421 (-560)) (|%list| (QUOTE -1070) (QUOTE (-560)))) (|HasCategory| |#1| (|%list| (QUOTE -1070) (QUOTE (-560))))) (|HasCategory| |#1| (|%list| (QUOTE -1070) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#1| (|%list| (QUOTE -1070) (QUOTE (-560)))) (|HasCategory| (-421 (-560)) (|%list| (QUOTE -1070) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| (-421 (-560)) (|%list| (QUOTE -1070) (QUOTE (-560))))) -(-1057 -1612 L) +(-1057 -1613 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}."))) NIL NIL @@ -4192,7 +4192,7 @@ NIL ((|constructor| (NIL "This package provides coercions for the special types \\spadtype{Exit} and \\spadtype{Void}.")) (|coerce| ((|#1| (|Exit|)) "\\spad{coerce(e)} is never really evaluated. This coercion is used for formal type correctness when a function will not return directly to its caller.") (((|Void|) |#1|) "\\spad{coerce(s)} throws all information about \\spad{s} away. This coercion allows values of any type to appear in contexts where they will not be used. For example,{} it allows the resolution of different types in the \\spad{then} and \\spad{else} branches when an \\spad{if} is in a context where the resulting value is not used."))) NIL NIL -(-1066 -1612 |Expon| |VarSet| |FPol| |LFPol|) +(-1066 -1613 |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"))) (((-4512 "*") . T) (-4504 . T) (-4505 . T) (-4507 . T)) NIL @@ -4256,7 +4256,7 @@ NIL ((|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."))) ((-4507 . T)) NIL -(-1082 |xx| -1612) +(-1082 |xx| -1613) ((|constructor| (NIL "This package exports rational interpolation algorithms"))) NIL NIL @@ -4356,7 +4356,7 @@ NIL ((|constructor| (NIL "This is the datatype of OpenAxiom runtime values. It exists solely for internal purposes.")) (|eq| (((|Boolean|) $ $) "\\spad{eq(x,y)} holds if both values \\spad{x} and \\spad{y} resides at the same address in memory."))) NIL NIL -(-1107 |Base| R -1612) +(-1107 |Base| R -1613) ((|constructor| (NIL "\\indented{1}{Rules for the pattern matcher} Author: Manuel Bronstein Date Created: 24 Oct 1988 Date Last Updated: 26 October 1993 Keywords: pattern,{} matching,{} rule.")) (|quotedOperators| (((|List| (|Symbol|)) $) "\\spad{quotedOperators(r)} returns the list of operators on the right hand side of \\spad{r} that are considered quoted,{} that is they are not evaluated during any rewrite,{} but just applied formally to their arguments.")) (|elt| ((|#3| $ |#3| (|PositiveInteger|)) "\\spad{elt(r,f,n)} or \\spad{r}(\\spad{f},{} \\spad{n}) applies the rule \\spad{r} to \\spad{f} at most \\spad{n} times.")) (|rhs| ((|#3| $) "\\spad{rhs(r)} returns the right hand side of the rule \\spad{r}.")) (|lhs| ((|#3| $) "\\spad{lhs(r)} returns the left hand side of the rule \\spad{r}.")) (|pattern| (((|Pattern| |#1|) $) "\\spad{pattern(r)} returns the pattern corresponding to the left hand side of the rule \\spad{r}.")) (|suchThat| (($ $ (|List| (|Symbol|)) (|Mapping| (|Boolean|) (|List| |#3|))) "\\spad{suchThat(r, [a1,...,an], f)} returns the rewrite rule \\spad{r} with the predicate \\spad{f(a1,...,an)} attached to it.")) (|rule| (($ |#3| |#3| (|List| (|Symbol|))) "\\spad{rule(f, g, [f1,...,fn])} creates the rewrite rule \\spad{f == eval(eval(g, g is f), [f1,...,fn])},{} that is a rule with left-hand side \\spad{f} and right-hand side \\spad{g}; The symbols \\spad{f1},{}...,{}fn are the operators that are considered quoted,{} that is they are not evaluated during any rewrite,{} but just applied formally to their arguments.") (($ |#3| |#3|) "\\spad{rule(f, g)} creates the rewrite rule: \\spad{f == eval(g, g is f)},{} with left-hand side \\spad{f} and right-hand side \\spad{g}."))) NIL NIL @@ -4364,7 +4364,7 @@ NIL ((|constructor| (NIL "This domain implements named rules")) (|name| (((|Symbol|) $) "\\spad{name(x)} returns the symbol"))) NIL NIL -(-1109 |Base| R -1612) +(-1109 |Base| R -1613) ((|constructor| (NIL "A ruleset is a set of pattern matching rules grouped together.")) (|elt| ((|#3| $ |#3| (|PositiveInteger|)) "\\spad{elt(r,f,n)} or \\spad{r}(\\spad{f},{} \\spad{n}) applies all the rules of \\spad{r} to \\spad{f} at most \\spad{n} times.")) (|rules| (((|List| (|RewriteRule| |#1| |#2| |#3|)) $) "\\spad{rules(r)} returns the rules contained in \\spad{r}.")) (|ruleset| (($ (|List| (|RewriteRule| |#1| |#2| |#3|))) "\\spad{ruleset([r1,...,rn])} creates the rule set \\spad{{r1,...,rn}}."))) NIL NIL @@ -4524,7 +4524,7 @@ NIL ((|constructor| (NIL "This domain represents a signature AST. A signature AST \\indented{2}{is a description of an exported operation,{} \\spadignore{e.g.} its name,{} result} \\indented{2}{type,{} and the list of its argument types.}")) (|signature| (((|Signature|) $) "\\spad{signature(s)} returns AST of the declared signature for `s'.")) (|name| (((|Identifier|) $) "\\spad{name(s)} returns the name of the signature `s'.")) (|signatureAst| (($ (|Identifier|) (|Signature|)) "\\spad{signatureAst(n,s,t)} builds the signature AST n: \\spad{s} -> \\spad{t}"))) NIL NIL -(-1149 R -1612) +(-1149 R -1613) ((|constructor| (NIL "This package provides functions to determine the sign of an elementary function around a point or infinity.")) (|sign| (((|Union| (|Integer|) "failed") |#2| (|Symbol|) |#2| (|String|)) "\\spad{sign(f, x, a, s)} returns the sign of \\spad{f} as \\spad{x} nears \\spad{a} from below if \\spad{s} is \"left\",{} or above if \\spad{s} is \"right\".") (((|Union| (|Integer|) "failed") |#2| (|Symbol|) (|OrderedCompletion| |#2|)) "\\spad{sign(f, x, a)} returns the sign of \\spad{f} as \\spad{x} nears \\spad{a},{} from both sides if \\spad{a} is finite.") (((|Union| (|Integer|) "failed") |#2|) "\\spad{sign(f)} returns the sign of \\spad{f} if it is constant everywhere."))) NIL NIL @@ -4568,7 +4568,7 @@ NIL ((|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}"))) ((-4511 . T) (-4510 . T)) NIL -(-1160 UP -1612) +(-1160 UP -1613) ((|constructor| (NIL "This package factors the formulas out of the general solve code,{} allowing their recursive use over different domains. Care is taken to introduce few radicals so that radical extension domains can more easily simplify the results.")) (|aQuartic| ((|#2| |#2| |#2| |#2| |#2| |#2|) "\\spad{aQuartic(f,g,h,i,k)} \\undocumented")) (|aCubic| ((|#2| |#2| |#2| |#2| |#2|) "\\spad{aCubic(f,g,h,j)} \\undocumented")) (|aQuadratic| ((|#2| |#2| |#2| |#2|) "\\spad{aQuadratic(f,g,h)} \\undocumented")) (|aLinear| ((|#2| |#2| |#2|) "\\spad{aLinear(f,g)} \\undocumented")) (|quartic| (((|List| |#2|) |#2| |#2| |#2| |#2| |#2|) "\\spad{quartic(f,g,h,i,j)} \\undocumented") (((|List| |#2|) |#1|) "\\spad{quartic(u)} \\undocumented")) (|cubic| (((|List| |#2|) |#2| |#2| |#2| |#2|) "\\spad{cubic(f,g,h,i)} \\undocumented") (((|List| |#2|) |#1|) "\\spad{cubic(u)} \\undocumented")) (|quadratic| (((|List| |#2|) |#2| |#2| |#2|) "\\spad{quadratic(f,g,h)} \\undocumented") (((|List| |#2|) |#1|) "\\spad{quadratic(u)} \\undocumented")) (|linear| (((|List| |#2|) |#2| |#2|) "\\spad{linear(f,g)} \\undocumented") (((|List| |#2|) |#1|) "\\spad{linear(u)} \\undocumented")) (|mapSolve| (((|Record| (|:| |solns| (|List| |#2|)) (|:| |maps| (|List| (|Record| (|:| |arg| |#2|) (|:| |res| |#2|))))) |#1| (|Mapping| |#2| |#2|)) "\\spad{mapSolve(u,f)} \\undocumented")) (|particularSolution| ((|#2| |#1|) "\\spad{particularSolution(u)} \\undocumented")) (|solve| (((|List| |#2|) |#1|) "\\spad{solve(u)} \\undocumented"))) NIL NIL @@ -4730,9 +4730,9 @@ NIL NIL (-1200 |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. 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(NOT (($ $) "\\spad{NOT(x)} returns the \\axiomType{Switch} expression representing \\spad{\\~~x}.") (($ (|Union| (|:| I (|Expression| (|Integer|))) (|:| F (|Expression| (|Float|))) (|:| CF (|Expression| (|Complex| (|Float|)))) (|:| |switch| $))) "\\spad{NOT(x)} returns the \\axiomType{Switch} expression representing \\spad{\\~~x}.")) (AND (($ (|Union| (|:| I (|Expression| (|Integer|))) (|:| F (|Expression| (|Float|))) (|:| CF (|Expression| (|Complex| (|Float|)))) (|:| |switch| $)) (|Union| (|:| I (|Expression| (|Integer|))) (|:| F (|Expression| (|Float|))) (|:| CF (|Expression| (|Complex| (|Float|)))) (|:| |switch| $))) "\\spad{AND(x,y)} returns the \\axiomType{Switch} expression representing \\spad{x and y}.")) (EQ (($ (|Union| (|:| I (|Expression| (|Integer|))) (|:| F (|Expression| (|Float|))) (|:| CF (|Expression| (|Complex| (|Float|)))) (|:| |switch| $)) (|Union| (|:| I (|Expression| (|Integer|))) (|:| F (|Expression| (|Float|))) (|:| CF (|Expression| (|Complex| (|Float|)))) (|:| |switch| $))) "\\spad{EQ(x,y)} returns the \\axiomType{Switch} expression representing \\spad{x = y}.")) (OR (($ (|Union| (|:| I (|Expression| (|Integer|))) (|:| F (|Expression| (|Float|))) (|:| CF (|Expression| (|Complex| (|Float|)))) (|:| |switch| $)) (|Union| (|:| I (|Expression| (|Integer|))) (|:| F (|Expression| (|Float|))) (|:| CF (|Expression| (|Complex| (|Float|)))) (|:| |switch| $))) "\\spad{OR(x,y)} returns the \\axiomType{Switch} expression representing \\spad{x or y}.")) (GE (($ (|Union| (|:| I (|Expression| (|Integer|))) (|:| F (|Expression| (|Float|))) (|:| CF (|Expression| (|Complex| (|Float|)))) (|:| |switch| $)) (|Union| (|:| I (|Expression| (|Integer|))) (|:| F (|Expression| (|Float|))) (|:| CF (|Expression| (|Complex| (|Float|)))) (|:| |switch| $))) "\\spad{GE(x,y)} returns the \\axiomType{Switch} expression representing \\spad{x>=y}.")) (LE (($ (|Union| (|:| I (|Expression| (|Integer|))) (|:| F (|Expression| (|Float|))) (|:| CF (|Expression| (|Complex| (|Float|)))) (|:| |switch| $)) (|Union| (|:| I (|Expression| (|Integer|))) (|:| F (|Expression| (|Float|))) (|:| CF (|Expression| (|Complex| (|Float|)))) (|:| |switch| $))) "\\spad{LE(x,y)} returns the \\axiomType{Switch} expression representing \\spad{x<=y}.")) (GT (($ (|Union| (|:| I (|Expression| (|Integer|))) (|:| F (|Expression| (|Float|))) (|:| CF (|Expression| (|Complex| (|Float|)))) (|:| |switch| $)) (|Union| (|:| I (|Expression| (|Integer|))) (|:| F (|Expression| (|Float|))) (|:| CF (|Expression| (|Complex| (|Float|)))) (|:| |switch| $))) "\\spad{GT(x,y)} returns the \\axiomType{Switch} expression representing \\spad{x>y}.")) (LT (($ (|Union| (|:| I (|Expression| (|Integer|))) (|:| F (|Expression| (|Float|))) (|:| CF (|Expression| (|Complex| (|Float|)))) (|:| |switch| $)) (|Union| (|:| I (|Expression| (|Integer|))) (|:| F (|Expression| (|Float|))) (|:| CF (|Expression| (|Complex| (|Float|)))) (|:| |switch| $))) "\\spad{LT(x,y)} returns the \\axiomType{Switch} expression representing \\spad{x<y}.")) (|coerce| (($ (|Symbol|)) "\\spad{coerce(s)} \\undocumented{}"))) NIL @@ -4884,7 +4884,7 @@ NIL ((|constructor| (NIL "Category for the trigonometric functions.")) (|tan| (($ $) "\\spad{tan(x)} returns the tangent of \\spad{x}.")) (|sin| (($ $) "\\spad{sin(x)} returns the sine of \\spad{x}.")) (|sec| (($ $) "\\spad{sec(x)} returns the secant of \\spad{x}.")) (|csc| (($ $) "\\spad{csc(x)} returns the cosecant of \\spad{x}.")) (|cot| (($ $) "\\spad{cot(x)} returns the cotangent of \\spad{x}.")) (|cos| (($ $) "\\spad{cos(x)} returns the cosine of \\spad{x}."))) NIL NIL -(-1239 R -1612) +(-1239 R -1613) ((|constructor| (NIL "\\spadtype{TrigonometricManipulations} provides transformations from trigonometric functions to complex exponentials and logarithms,{} and back.")) (|complexForm| (((|Complex| |#2|) |#2|) "\\spad{complexForm(f)} returns \\spad{[real f, imag f]}.")) (|real?| (((|Boolean|) |#2|) "\\spad{real?(f)} returns \\spad{true} if \\spad{f = real f}.")) (|imag| ((|#2| |#2|) "\\spad{imag(f)} returns the imaginary part of \\spad{f} where \\spad{f} is a complex function.")) (|real| ((|#2| |#2|) "\\spad{real(f)} returns the real part of \\spad{f} where \\spad{f} is a complex function.")) (|trigs| ((|#2| |#2|) "\\spad{trigs(f)} rewrites all the complex logs and exponentials appearing in \\spad{f} in terms of trigonometric functions.")) (|complexElementary| ((|#2| |#2| (|Symbol|)) "\\spad{complexElementary(f, x)} rewrites the kernels of \\spad{f} involving \\spad{x} in terms of the 2 fundamental complex transcendental elementary functions: \\spad{log, exp}.") ((|#2| |#2|) "\\spad{complexElementary(f)} rewrites \\spad{f} in terms of the 2 fundamental complex transcendental elementary functions: \\spad{log, exp}.")) (|complexNormalize| ((|#2| |#2| (|Symbol|)) "\\spad{complexNormalize(f, x)} rewrites \\spad{f} using the least possible number of complex independent kernels involving \\spad{x}.") ((|#2| |#2|) "\\spad{complexNormalize(f)} rewrites \\spad{f} using the least possible number of complex independent kernels."))) NIL NIL @@ -4892,7 +4892,7 @@ NIL ((|constructor| (NIL "This package provides functions that compute \"fraction-free\" inverses of upper and lower triangular matrices over a integral domain. By \"fraction-free inverses\" we mean the following: given a matrix \\spad{B} with entries in \\spad{R} and an element \\spad{d} of \\spad{R} such that \\spad{d} * inv(\\spad{B}) also has entries in \\spad{R},{} we return \\spad{d} * inv(\\spad{B}). Thus,{} it is not necessary to pass to the quotient field in any of our computations.")) (|LowTriBddDenomInv| ((|#4| |#4| |#1|) "\\spad{LowTriBddDenomInv(B,d)} returns \\spad{M},{} where \\spad{B} is a non-singular lower triangular matrix and \\spad{d} is an element of \\spad{R} such that \\spad{M = d * inv(B)} has entries in \\spad{R}.")) (|UpTriBddDenomInv| ((|#4| |#4| |#1|) "\\spad{UpTriBddDenomInv(B,d)} returns \\spad{M},{} where \\spad{B} is a non-singular upper triangular matrix and \\spad{d} is an element of \\spad{R} such that \\spad{M = d * inv(B)} has entries in \\spad{R}."))) NIL NIL -(-1241 R -1612) +(-1241 R -1613) ((|constructor| (NIL "TranscendentalManipulations provides functions to simplify and expand expressions involving transcendental operators.")) (|expandTrigProducts| ((|#2| |#2|) "\\spad{expandTrigProducts(e)} replaces \\axiom{sin(\\spad{x})*sin(\\spad{y})} by \\spad{(cos(x-y)-cos(x+y))/2},{} \\axiom{cos(\\spad{x})*cos(\\spad{y})} by \\spad{(cos(x-y)+cos(x+y))/2},{} and \\axiom{sin(\\spad{x})*cos(\\spad{y})} by \\spad{(sin(x-y)+sin(x+y))/2}. Note that this operation uses the pattern matcher and so is relatively expensive. To avoid getting into an infinite loop the transformations are applied at most ten times.")) (|removeSinhSq| ((|#2| |#2|) "\\spad{removeSinhSq(f)} converts every \\spad{sinh(u)**2} appearing in \\spad{f} into \\spad{1 - cosh(x)**2},{} and also reduces higher powers of \\spad{sinh(u)} with that formula.")) (|removeCoshSq| ((|#2| |#2|) "\\spad{removeCoshSq(f)} converts every \\spad{cosh(u)**2} appearing in \\spad{f} into \\spad{1 - sinh(x)**2},{} and also reduces higher powers of \\spad{cosh(u)} with that formula.")) (|removeSinSq| ((|#2| |#2|) "\\spad{removeSinSq(f)} converts every \\spad{sin(u)**2} appearing in \\spad{f} into \\spad{1 - cos(x)**2},{} and also reduces higher powers of \\spad{sin(u)} with that formula.")) (|removeCosSq| ((|#2| |#2|) "\\spad{removeCosSq(f)} converts every \\spad{cos(u)**2} appearing in \\spad{f} into \\spad{1 - sin(x)**2},{} and also reduces higher powers of \\spad{cos(u)} with that formula.")) (|coth2tanh| ((|#2| |#2|) "\\spad{coth2tanh(f)} converts every \\spad{coth(u)} appearing in \\spad{f} into \\spad{1/tanh(u)}.")) (|cot2tan| ((|#2| |#2|) "\\spad{cot2tan(f)} converts every \\spad{cot(u)} appearing in \\spad{f} into \\spad{1/tan(u)}.")) (|tanh2coth| ((|#2| |#2|) "\\spad{tanh2coth(f)} converts every \\spad{tanh(u)} appearing in \\spad{f} into \\spad{1/coth(u)}.")) (|tan2cot| ((|#2| |#2|) "\\spad{tan2cot(f)} converts every \\spad{tan(u)} appearing in \\spad{f} into \\spad{1/cot(u)}.")) (|tanh2trigh| ((|#2| |#2|) "\\spad{tanh2trigh(f)} converts every \\spad{tanh(u)} appearing in \\spad{f} into \\spad{sinh(u)/cosh(u)}.")) (|tan2trig| ((|#2| |#2|) "\\spad{tan2trig(f)} converts every \\spad{tan(u)} appearing in \\spad{f} into \\spad{sin(u)/cos(u)}.")) (|sinh2csch| ((|#2| |#2|) "\\spad{sinh2csch(f)} converts every \\spad{sinh(u)} appearing in \\spad{f} into \\spad{1/csch(u)}.")) (|sin2csc| ((|#2| |#2|) "\\spad{sin2csc(f)} converts every \\spad{sin(u)} appearing in \\spad{f} into \\spad{1/csc(u)}.")) (|sech2cosh| ((|#2| |#2|) "\\spad{sech2cosh(f)} converts every \\spad{sech(u)} appearing in \\spad{f} into \\spad{1/cosh(u)}.")) (|sec2cos| ((|#2| |#2|) "\\spad{sec2cos(f)} converts every \\spad{sec(u)} appearing in \\spad{f} into \\spad{1/cos(u)}.")) (|csch2sinh| ((|#2| |#2|) "\\spad{csch2sinh(f)} converts every \\spad{csch(u)} appearing in \\spad{f} into \\spad{1/sinh(u)}.")) (|csc2sin| ((|#2| |#2|) "\\spad{csc2sin(f)} converts every \\spad{csc(u)} appearing in \\spad{f} into \\spad{1/sin(u)}.")) (|coth2trigh| ((|#2| |#2|) "\\spad{coth2trigh(f)} converts every \\spad{coth(u)} appearing in \\spad{f} into \\spad{cosh(u)/sinh(u)}.")) (|cot2trig| ((|#2| |#2|) "\\spad{cot2trig(f)} converts every \\spad{cot(u)} appearing in \\spad{f} into \\spad{cos(u)/sin(u)}.")) (|cosh2sech| ((|#2| |#2|) "\\spad{cosh2sech(f)} converts every \\spad{cosh(u)} appearing in \\spad{f} into \\spad{1/sech(u)}.")) (|cos2sec| ((|#2| |#2|) "\\spad{cos2sec(f)} converts every \\spad{cos(u)} appearing in \\spad{f} into \\spad{1/sec(u)}.")) (|expandLog| ((|#2| |#2|) "\\spad{expandLog(f)} converts every \\spad{log(a/b)} appearing in \\spad{f} into \\spad{log(a) - log(b)},{} and every \\spad{log(a*b)} into \\spad{log(a) + log(b)}..")) (|expandPower| ((|#2| |#2|) "\\spad{expandPower(f)} converts every power \\spad{(a/b)**c} appearing in \\spad{f} into \\spad{a**c * b**(-c)}.")) (|simplifyLog| ((|#2| |#2|) "\\spad{simplifyLog(f)} converts every \\spad{log(a) - log(b)} appearing in \\spad{f} into \\spad{log(a/b)},{} every \\spad{log(a) + log(b)} into \\spad{log(a*b)} and every \\spad{n*log(a)} into \\spad{log(a^n)}.")) (|simplifyExp| ((|#2| |#2|) "\\spad{simplifyExp(f)} converts every product \\spad{exp(a)*exp(b)} appearing in \\spad{f} into \\spad{exp(a+b)}.")) (|htrigs| ((|#2| |#2|) "\\spad{htrigs(f)} converts all the exponentials in \\spad{f} into hyperbolic sines and cosines.")) (|simplify| ((|#2| |#2|) "\\spad{simplify(f)} performs the following simplifications on f:\\begin{items} \\item 1. rewrites trigs and hyperbolic trigs in terms of \\spad{sin} ,{}\\spad{cos},{} \\spad{sinh},{} \\spad{cosh}. \\item 2. rewrites \\spad{sin**2} and \\spad{sinh**2} in terms of \\spad{cos} and \\spad{cosh},{} \\item 3. rewrites \\spad{exp(a)*exp(b)} as \\spad{exp(a+b)}. \\item 4. rewrites \\spad{(a**(1/n))**m * (a**(1/s))**t} as a single power of a single radical of \\spad{a}. \\end{items}")) (|expand| ((|#2| |#2|) "\\spad{expand(f)} performs the following expansions on f:\\begin{items} \\item 1. logs of products are expanded into sums of logs,{} \\item 2. trigonometric and hyperbolic trigonometric functions of sums are expanded into sums of products of trigonometric and hyperbolic trigonometric functions. \\item 3. formal powers of the form \\spad{(a/b)**c} are expanded into \\spad{a**c * b**(-c)}. \\end{items}"))) NIL ((-12 (|HasCategory| |#1| (|%list| (QUOTE -633) (|%list| (QUOTE -916) (|devaluate| |#1|)))) (|HasCategory| |#1| (|%list| (QUOTE -912) (|devaluate| |#1|))) (|HasCategory| |#2| (|%list| (QUOTE -633) (|%list| (QUOTE -916) (|devaluate| |#1|)))) (|HasCategory| |#2| (|%list| (QUOTE -912) (|devaluate| |#1|))))) @@ -4920,7 +4920,7 @@ NIL ((|constructor| (NIL "\\indented{1}{This domain is used to interface with the interpreter's notion} of comma-delimited sequences of values.")) (|length| (((|NonNegativeInteger|) $) "\\spad{length(x)} returns the number of elements in tuple \\spad{x}")) (|select| ((|#1| $ (|NonNegativeInteger|)) "\\spad{select(x,n)} returns the \\spad{n}-th element of tuple \\spad{x}. tuples are 0-based"))) NIL ((|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-888))))) -(-1248 -1612) +(-1248 -1613) ((|constructor| (NIL "A basic package for the factorization of bivariate polynomials over a finite field. The functions here represent the base step for the multivariate factorizer.")) (|twoFactor| (((|Factored| (|SparseUnivariatePolynomial| (|SparseUnivariatePolynomial| |#1|))) (|SparseUnivariatePolynomial| (|SparseUnivariatePolynomial| |#1|)) (|Integer|)) "\\spad{twoFactor(p,n)} returns the factorisation of polynomial \\spad{p},{} a sparse univariate polynomial (sup) over a sup over \\spad{F}. Also,{} \\spad{p} is assumed primitive and square-free and \\spad{n} is the degree of the inner variable of \\spad{p} (maximum of the degrees of the coefficients of \\spad{p}).")) (|generalSqFr| (((|Factored| (|SparseUnivariatePolynomial| (|SparseUnivariatePolynomial| |#1|))) (|SparseUnivariatePolynomial| (|SparseUnivariatePolynomial| |#1|))) "\\spad{generalSqFr(p)} returns the square-free factorisation of polynomial \\spad{p},{} a sparse univariate polynomial (sup) over a sup over \\spad{F}.")) (|generalTwoFactor| (((|Factored| (|SparseUnivariatePolynomial| (|SparseUnivariatePolynomial| |#1|))) (|SparseUnivariatePolynomial| (|SparseUnivariatePolynomial| |#1|))) "\\spad{generalTwoFactor(p)} returns the factorisation of polynomial \\spad{p},{} a sparse univariate polynomial (sup) over a sup over \\spad{F}."))) NIL NIL @@ -4966,8 +4966,8 @@ NIL NIL (-1259 |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.")) 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(|HasCategory| $ (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#2| (QUOTE (-940)))) (|HasCategory| |#1| (QUOTE (-147))) (-12 (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#2| (QUOTE (-147)))))) (-1265 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 @@ -5051,7 +5051,7 @@ NIL (-1280 |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."))) (((-4512 "*") |has| |#1| (-175)) (-4503 |has| |#1| (-571)) (-4508 |has| |#1| (-376)) (-4502 |has| |#1| (-376)) (-4504 . T) (-4505 . T) (-4507 . T)) -((|HasCategory| |#1| (|%list| (QUOTE -38) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#1| (QUOTE (-571))) (|HasCategory| |#1| (QUOTE (-175))) (-2210 (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-571)))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-149))) (-12 (|HasCategory| |#1| (|%list| (QUOTE -928) (QUOTE (-1209)))) (|HasSignature| |#1| (|%list| (QUOTE *) (|%list| (|devaluate| |#1|) (|%list| (QUOTE -421) (QUOTE (-560))) (|devaluate| |#1|))))) (|HasSignature| |#1| (|%list| (QUOTE *) (|%list| (|devaluate| |#1|) (|%list| (QUOTE -421) (QUOTE (-560))) (|devaluate| |#1|)))) (|HasCategory| (-421 (-560)) (QUOTE (-1144))) (|HasCategory| |#1| (QUOTE (-376))) (-2210 (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (QUOTE (-571)))) (-2210 (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (QUOTE (-571)))) (-12 (|HasSignature| |#1| (|%list| (QUOTE **) (|%list| (|devaluate| |#1|) (|devaluate| |#1|) (|%list| (QUOTE -421) (QUOTE (-560)))))) (|HasSignature| |#1| (|%list| (QUOTE -2590) (|%list| (|devaluate| |#1|) (QUOTE (-1209)))))) (|HasSignature| |#1| (|%list| (QUOTE **) (|%list| (|devaluate| |#1|) (|devaluate| |#1|) (|%list| (QUOTE -421) (QUOTE (-560)))))) (-2210 (-12 (|HasCategory| |#1| (|%list| (QUOTE -29) (QUOTE (-560)))) (|HasCategory| |#1| (|%list| (QUOTE -38) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#1| (QUOTE (-990))) (|HasCategory| |#1| (QUOTE (-1235)))) (-12 (|HasCategory| |#1| (|%list| (QUOTE -38) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasSignature| |#1| (|%list| (QUOTE -1348) (|%list| (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1209))))) (|HasSignature| |#1| (|%list| (QUOTE -3589) (|%list| (|%list| (QUOTE -663) (QUOTE (-1209))) (|devaluate| |#1|))))))) +((|HasCategory| |#1| (|%list| (QUOTE -38) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#1| (QUOTE (-571))) (|HasCategory| |#1| (QUOTE (-175))) (-2210 (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-571)))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-149))) (-12 (|HasCategory| |#1| (|%list| (QUOTE -928) (QUOTE (-1209)))) (|HasSignature| |#1| (|%list| (QUOTE *) (|%list| (|devaluate| |#1|) (|%list| (QUOTE -421) (QUOTE (-560))) (|devaluate| |#1|))))) (|HasSignature| |#1| (|%list| (QUOTE *) (|%list| (|devaluate| |#1|) (|%list| (QUOTE -421) (QUOTE (-560))) (|devaluate| |#1|)))) (|HasCategory| (-421 (-560)) (QUOTE (-1144))) (|HasCategory| |#1| (QUOTE (-376))) (-2210 (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (QUOTE (-571)))) (-2210 (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (QUOTE (-571)))) (-12 (|HasSignature| |#1| (|%list| (QUOTE **) (|%list| (|devaluate| |#1|) (|devaluate| |#1|) (|%list| (QUOTE -421) (QUOTE (-560)))))) (|HasSignature| |#1| (|%list| (QUOTE -2590) (|%list| (|devaluate| |#1|) (QUOTE (-1209)))))) (|HasSignature| |#1| (|%list| (QUOTE **) (|%list| (|devaluate| |#1|) (|devaluate| |#1|) (|%list| (QUOTE -421) (QUOTE (-560)))))) (-2210 (-12 (|HasCategory| |#1| (|%list| (QUOTE -29) (QUOTE (-560)))) (|HasCategory| |#1| (|%list| (QUOTE -38) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#1| (QUOTE (-990))) (|HasCategory| |#1| (QUOTE (-1235)))) (-12 (|HasCategory| |#1| (|%list| (QUOTE -38) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasSignature| |#1| (|%list| (QUOTE -3270) (|%list| (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1209))))) (|HasSignature| |#1| (|%list| (QUOTE -3589) (|%list| (|%list| (QUOTE -663) (QUOTE (-1209))) (|devaluate| |#1|))))))) (-1281 |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)}."))) NIL @@ -5071,7 +5071,7 @@ NIL (-1285 |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)}."))) (((-4512 "*") |has| |#1| (-175)) (-4503 |has| |#1| (-571)) (-4508 |has| |#1| (-376)) (-4502 |has| |#1| (-376)) (-4504 . T) (-4505 . T) (-4507 . T)) -((|HasCategory| |#1| (QUOTE (-571))) (|HasCategory| |#1| (QUOTE (-175))) (-2210 (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-571)))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-149))) (-12 (|HasCategory| |#1| (|%list| (QUOTE -928) (QUOTE (-1209)))) (|HasSignature| |#1| (|%list| (QUOTE *) (|%list| (|devaluate| |#1|) (|%list| (QUOTE -421) (QUOTE (-560))) (|devaluate| |#1|))))) (|HasSignature| |#1| (|%list| (QUOTE *) (|%list| (|devaluate| |#1|) (|%list| (QUOTE -421) (QUOTE (-560))) (|devaluate| |#1|)))) (|HasCategory| (-421 (-560)) (QUOTE (-1144))) (|HasCategory| |#1| (QUOTE (-376))) (-2210 (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (QUOTE (-571)))) (-2210 (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (QUOTE (-571)))) (-12 (|HasSignature| |#1| (|%list| (QUOTE **) (|%list| (|devaluate| |#1|) (|devaluate| |#1|) (|%list| (QUOTE -421) (QUOTE (-560)))))) (|HasSignature| |#1| (|%list| (QUOTE -2590) (|%list| (|devaluate| |#1|) (QUOTE (-1209)))))) (|HasSignature| |#1| (|%list| (QUOTE **) (|%list| (|devaluate| |#1|) (|devaluate| |#1|) (|%list| (QUOTE -421) (QUOTE (-560)))))) (-2210 (-12 (|HasCategory| |#1| (|%list| (QUOTE -29) (QUOTE (-560)))) (|HasCategory| |#1| (|%list| (QUOTE -38) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#1| (QUOTE (-990))) (|HasCategory| |#1| (QUOTE (-1235)))) (-12 (|HasCategory| |#1| (|%list| (QUOTE -38) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasSignature| |#1| (|%list| (QUOTE -1348) (|%list| (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1209))))) (|HasSignature| |#1| (|%list| (QUOTE -3589) (|%list| (|%list| (QUOTE -663) (QUOTE (-1209))) (|devaluate| |#1|)))))) (|HasCategory| |#1| (|%list| (QUOTE -38) (|%list| (QUOTE -421) (QUOTE (-560)))))) +((|HasCategory| |#1| (QUOTE (-571))) (|HasCategory| |#1| (QUOTE (-175))) (-2210 (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-571)))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-149))) (-12 (|HasCategory| |#1| (|%list| (QUOTE -928) (QUOTE (-1209)))) (|HasSignature| |#1| (|%list| (QUOTE *) (|%list| (|devaluate| |#1|) (|%list| (QUOTE -421) (QUOTE (-560))) (|devaluate| |#1|))))) (|HasSignature| |#1| (|%list| (QUOTE *) (|%list| (|devaluate| |#1|) (|%list| (QUOTE -421) (QUOTE (-560))) (|devaluate| |#1|)))) (|HasCategory| (-421 (-560)) (QUOTE (-1144))) (|HasCategory| |#1| (QUOTE (-376))) (-2210 (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (QUOTE (-571)))) (-2210 (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (QUOTE (-571)))) (-12 (|HasSignature| |#1| (|%list| (QUOTE **) (|%list| (|devaluate| |#1|) (|devaluate| |#1|) (|%list| (QUOTE -421) (QUOTE (-560)))))) (|HasSignature| |#1| (|%list| (QUOTE -2590) (|%list| (|devaluate| |#1|) (QUOTE (-1209)))))) (|HasSignature| |#1| (|%list| (QUOTE **) (|%list| (|devaluate| |#1|) (|devaluate| |#1|) (|%list| (QUOTE -421) (QUOTE (-560)))))) (-2210 (-12 (|HasCategory| |#1| (|%list| (QUOTE -29) (QUOTE (-560)))) (|HasCategory| |#1| (|%list| (QUOTE -38) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#1| (QUOTE (-990))) (|HasCategory| |#1| (QUOTE (-1235)))) (-12 (|HasCategory| |#1| (|%list| (QUOTE -38) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasSignature| |#1| (|%list| (QUOTE -3270) (|%list| (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1209))))) (|HasSignature| |#1| (|%list| (QUOTE -3589) (|%list| (|%list| (QUOTE -663) (QUOTE (-1209))) (|devaluate| |#1|)))))) (|HasCategory| |#1| (|%list| (QUOTE -38) (|%list| (QUOTE -421) (QUOTE (-560)))))) (-1286 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") $) "\\spad{limitPlus(f(var))} returns \\spad{limit(var -> cen+,f(var))}."))) (((-4512 "*") |has| (-1280 |#2| |#3| |#4|) (-175)) (-4503 |has| (-1280 |#2| |#3| |#4|) (-571)) (-4504 . T) (-4505 . T) (-4507 . T)) @@ -5087,7 +5087,7 @@ NIL (-1289 |Coef| |var| |cen|) ((|constructor| (NIL "Dense Taylor series in one variable \\spadtype{UnivariateTaylorSeries} is a domain representing Taylor series in one variable with coefficients in an arbitrary ring. The parameters of the type specify the coefficient ring,{} the power series variable,{} and the center of the power series expansion. For example,{} \\spadtype{UnivariateTaylorSeries}(Integer,{}\\spad{x},{}3) represents Taylor series in \\spad{(x - 3)} with \\spadtype{Integer} coefficients.")) (|integrate| (($ $ (|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}."))) (((-4512 "*") |has| |#1| (-175)) (-4503 |has| |#1| (-571)) (-4504 . T) (-4505 . T) (-4507 . 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(|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}.") (($ $) "\\spad{integrate(f(x))} returns an anti-derivative of the power series \\spad{f(x)} with constant coefficient 0. We may integrate a series when we can divide coefficients by integers.")) (** (($ $ |#2|) "\\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| |#2|) $ (|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| |#2|) $ (|NonNegativeInteger|)) "\\spad{polynomial(f,k)} returns a polynomial consisting of the sum of all terms of \\spad{f} of degree \\spad{<= k}.")) (|multiplyCoefficients| (($ (|Mapping| |#2| (|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| |#2|) $) "\\spad{coefficients(a0 + a1 x + a2 x**2 + ...)} returns a stream of coefficients: \\spad{[a0,a1,a2,...]}. The entries of the stream may be zero.")) (|series| (($ (|Stream| |#2|)) "\\spad{series([a0,a1,a2,...])} is the Taylor series \\spad{a0 + a1 x + a2 x**2 + ...}.") (($ (|Stream| (|Record| (|:| |k| (|NonNegativeInteger|)) (|:| |c| |#2|)))) "\\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."))) NIL -((|HasCategory| |#2| (|%list| (QUOTE -29) (QUOTE (-560)))) (|HasCategory| |#2| (QUOTE (-990))) (|HasCategory| |#2| (QUOTE (-1235))) (|HasSignature| |#2| (|%list| (QUOTE -3589) (|%list| (|%list| (QUOTE -663) (QUOTE (-1209))) (|devaluate| |#2|)))) (|HasSignature| |#2| (|%list| (QUOTE -1348) (|%list| (|devaluate| |#2|) (|devaluate| |#2|) (QUOTE (-1209))))) (|HasCategory| |#2| (|%list| (QUOTE -38) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#2| (QUOTE (-376)))) +((|HasCategory| |#2| (|%list| (QUOTE -29) (QUOTE (-560)))) (|HasCategory| |#2| (QUOTE (-990))) (|HasCategory| |#2| (QUOTE (-1235))) (|HasSignature| |#2| (|%list| (QUOTE -3589) (|%list| (|%list| (QUOTE -663) (QUOTE (-1209))) (|devaluate| |#2|)))) (|HasSignature| |#2| (|%list| (QUOTE -3270) (|%list| (|devaluate| |#2|) (|devaluate| |#2|) (QUOTE (-1209))))) (|HasCategory| |#2| (|%list| (QUOTE -38) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#2| (QUOTE (-376)))) (-1292 |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."))) (((-4512 "*") |has| |#1| (-175)) (-4503 |has| |#1| (-571)) (-4504 . T) (-4505 . T) (-4507 . T)) @@ -5104,7 +5104,7 @@ NIL ((|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."))) NIL NIL -(-1294 -1612 UP L UTS) +(-1294 -1613 UP L UTS) ((|constructor| (NIL "\\spad{RUTSodetools} provides tools to interface with the series \\indented{1}{ODE solver when presented with linear ODEs.}")) (RF2UTS ((|#4| (|Fraction| |#2|)) "\\spad{RF2UTS(f)} converts \\spad{f} to a Taylor series.")) (LODO2FUN (((|Mapping| |#4| (|List| |#4|)) |#3|) "\\spad{LODO2FUN(op)} returns the function to pass to the series ODE solver in order to solve \\spad{op y = 0}.")) (UTS2UP ((|#2| |#4| (|NonNegativeInteger|)) "\\spad{UTS2UP(s, n)} converts the first \\spad{n} terms of \\spad{s} to a univariate polynomial.")) (UP2UTS ((|#4| |#2|) "\\spad{UP2UTS(p)} converts \\spad{p} to a Taylor series."))) NIL ((|HasCategory| |#1| (QUOTE (-571)))) @@ -5164,7 +5164,7 @@ NIL ((|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."))) NIL NIL -(-1309 K R UP -1612) +(-1309 K R UP -1613) ((|constructor| (NIL "In this package \\spad{K} is a finite field,{} \\spad{R} is a ring of univariate polynomials over \\spad{K},{} and \\spad{F} is a framed algebra over \\spad{R}. The package provides a function to compute the integral closure of \\spad{R} in the quotient field of \\spad{F} as well as a function to compute a \"local integral basis\" at a specific prime.")) (|localIntegralBasis| (((|Record| (|:| |basis| (|Matrix| |#2|)) (|:| |basisDen| |#2|) (|:| |basisInv| (|Matrix| |#2|))) |#2|) "\\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| |#2|)) (|:| |basisDen| |#2|) (|:| |basisInv| (|Matrix| |#2|)))) "\\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)}."))) NIL NIL @@ -5196,11 +5196,11 @@ NIL ((|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}}."))) NIL NIL -(-1317 S -1612) +(-1317 S -1613) ((|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|) $) "\\spad{algebraic?(a)} tests whether an element \\spad{a} is algebraic with respect to the ground field \\spad{F}."))) NIL ((|HasCategory| |#2| (QUOTE (-381))) (|HasCategory| |#2| (QUOTE (-147))) (|HasCategory| |#2| (QUOTE (-149)))) -(-1318 -1612) +(-1318 -1613) ((|constructor| (NIL "ExtensionField {\\em F} is the category of fields which extend the field \\spad{F}")) (|Frobenius| (($ $ (|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|) $) "\\spad{algebraic?(a)} tests whether an element \\spad{a} is algebraic with respect to the ground field \\spad{F}."))) ((-4502 . T) (-4508 . T) (-4503 . T) ((-4512 "*") . T) (-4504 . T) (-4505 . T) (-4507 . T)) NIL diff --git a/src/share/algebra/category.daase b/src/share/algebra/category.daase index 5b51d29d..1b8351f6 100644 --- a/src/share/algebra/category.daase +++ b/src/share/algebra/category.daase @@ -1,5 +1,5 @@ -(205732 . 3508949904) +(205732 . 3508956490) (((|#2| |#2|) -12 (|has| |#2| (-321 |#2|)) (|has| |#2| (-1133))) ((#0=(-2 (|:| -3837 |#1|) (|:| -2715 |#2|)) #0#) |has| (-2 (|:| -3837 |#1|) (|:| -2715 |#2|)) (-321 (-2 (|:| -3837 |#1|) (|:| -2715 |#2|))))) ((((-560)) . T) (($) -2210 (|has| |#1| (-319)) (|has| |#1| (-376)) (|has| |#1| (-363)) (|has| |#1| (-571))) (((-421 (-560))) -2210 (|has| |#1| (-376)) (|has| |#1| (-363)) (|has| |#1| (-1070 (-421 (-560))))) ((|#1|) . T)) (((|#2| |#2|) . T)) @@ -78,7 +78,7 @@ ((((-560)) . T) (((-421 (-560))) -2210 (|has| |#2| (-38 (-421 (-560)))) (|has| |#2| (-1070 (-421 (-560))))) ((|#2|) . T) (($) -2210 (|has| |#2| (-466)) (|has| |#2| (-571)) (|has| |#2| (-940))) (((-889 |#1|)) . T)) (-2210 (|has| |#1| (-376)) (|has| |#1| (-571))) (-2210 (|has| |#1| (-376)) (|has| |#1| (-571))) -((((-2 (|:| -4021 |#1|) (|:| -2790 |#2|))) . T)) +((((-2 (|:| -4019 |#1|) (|:| -4400 |#2|))) . T)) ((($) . T)) ((((-888)) |has| |#1| (-632 (-888))) ((|#1|) . T)) ((((-560)) . T) (((-421 (-560))) -2210 (|has| |#1| (-38 (-421 (-560)))) (|has| |#1| (-1070 (-421 (-560))))) ((|#1|) . T) (($) -2210 (|has| |#1| (-466)) (|has| |#1| (-571)) (|has| |#1| (-940))) (((-1209)) . T)) @@ -314,11 +314,11 @@ ((((-549)) |has| |#2| (-633 (-549))) (((-916 (-391))) |has| |#2| (-633 (-916 (-391)))) (((-916 (-560))) |has| |#2| (-633 (-916 (-560))))) ((((-888)) . T)) (((|#1| |#2| |#3| |#4|) . T)) -((((-2 (|:| -4021 |#1|) (|:| -2790 |#2|))) . T) (((-888)) . T)) +((((-2 (|:| -4019 |#1|) (|:| -4400 |#2|))) . T) (((-888)) . T)) ((((-549)) |has| |#1| (-633 (-549))) (((-916 (-391))) |has| |#1| (-633 (-916 (-391)))) (((-916 (-560))) |has| |#1| (-633 (-916 (-560))))) (((|#4|) -2210 (|has| |#4| (-175)) (|has| |#4| (-376)) (|has| |#4| (-1081)))) (((|#3|) -2210 (|has| |#3| (-175)) (|has| |#3| (-376)) (|has| |#3| (-1081)))) -((((-2 (|:| -4021 |#1|) (|:| -2790 |#2|))) . T)) +((((-2 (|:| -4019 |#1|) (|:| -4400 |#2|))) . T)) ((((-888)) . T)) ((((-888)) . T)) ((((-549)) . T) (((-560)) . T) (((-916 (-560))) . T) (((-391)) . T) (((-229)) . T)) diff --git a/src/share/algebra/compress.daase b/src/share/algebra/compress.daase index 29f8d74f..a233d3de 100644 --- a/src/share/algebra/compress.daase +++ b/src/share/algebra/compress.daase @@ -1,5 +1,5 @@ -(30 . 3508949898) +(30 . 3508956483) (4513 |Enumeration| |Mapping| |Record| |Union| |ofCategory| |isDomain| ATTRIBUTE |package| |domain| |category| CATEGORY |nobranch| AND |Join| |ofType| SIGNATURE "failed" "algebra" |OneDimensionalArrayAggregate&| @@ -489,675 +489,676 @@ |XPolynomialsCat| |XPolynomialRing| |XRecursivePolynomial| |YoungDiagram| |ParadoxicalCombinatorsForStreams| |ZeroDimensionalSolvePackage| |IntegerLinearDependence| |IntegerMod| - |Enumeration| |Mapping| |Record| |Union| |s19adf| |jvmPublic| - |modifyPoint| |fortranLiteral| |pureLex| |interReduce| |critMonD1| - |s19aaf| |e| |extractIndex| |rootsOf| |factorsOfCyclicGroupSize| - |escape| |errorInfo| |integrate| |sqfree| |isOr| |showTheIFTable| - |knownInfBasis| |normFactors| |kernel| |headReduce| |makeResult| - |latex| |coth2tanh| |setButtonValue| |denominator| |null| - |setEpilogue!| |overlap| |pquo| |useSingleFactorBound| |list| - |oblateSpheroidal| |isNot| |cosh2sech| |radicalOfLeftTraceForm| - |tensorProduct| |convergents| |not| |draw| |rational| |flagFactor| - |s17akf| |tanh2coth| |startPolynomial| |horizConcat| |inverse| |even?| - |bright| |LiePoly| |and| |supDimElseRittWu?| |coordinate| - |usingTable?| |antisymmetricTensors| |setPosition| |exp1| |asechIfCan| - |commonDenominator| |getMultiplicationTable| |or| |iiGamma| - |rightTrace| |taylorIfCan| |hitherPlane| |coerceImages| |aLinear| - |cCos| |setCondition!| |isList| |xor| |removeZeroes| |cache| - |multMonom| |s17aef| |subspace| |debug3D| |bubbleSort!| - |fortranLinkerArgs| |cyclicParents| |binomial| |case| |makeObject| - |primintegrate| |laplacian| |vconcat| |contract| |squareTop| - |pointLists| |qroot| |basisOfLeftNucloid| |integralRepresents| - |isOpen?| |Zero| |binaryTournament| |positiveRemainder| |shiftLeft| - |coef| |safetyMargin| |complexExpand| |readByte!| |limitedIntegrate| - |traverse| |squareFreePart| |One| |simplify| |cycleLength| - |checkForZero| |ddFact| |removeRoughlyRedundantFactorsInPol| |graphs| - |makeMulti| |ceiling| |edf2fi| |contractSolve| |coerceListOfPairs| - |factorSquareFreePolynomial| |df2ef| |compactFraction| |gradient| - |generators| |brillhartTrials| |selectPDERoutines| |moebiusMu| - |expandPower| |difference| |prefixRagits| |sizeLess?| - |var1StepsDefault| |janko2| |left| |rename| |minIndex| |triangular?| - |eisensteinIrreducible?| |groebnerIdeal| |normalForm| |retractIfCan| - |bumprow| |has?| |invmod| |discriminant| |right| |dictionary| |size| - |basisOfLeftNucleus| |clikeUniv| |factorGroebnerBasis| |stopTable!| - |nonQsign| |nthFactor| |fortranCompilerName| |shuffle| - |noncommutativeJordanAlgebra?| |edf2ef| |purelyAlgebraic?| |d01aqf| - |polygon| |cyclicGroup| |elt| |acoshIfCan| |remainder| |currentScope| - |degreeSubResultantEuclidean| EQ |divide| |createThreeSpace| |more?| - |constantCoefficientRicDE| |integers| |fortranDoubleComplex| - 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|generalizedEigenvectors| |quasiMonicPolynomials| |realRoots| - |symbol?| |leadingExponent| |iicos| |argument| |tanhIfCan| - |associative?| |paren| |viewPhiDefault| |exponent| |autoCoerce| - |maxIndex| |setIntersection| |readLineIfCan!| |whatInfinity| - |integer?| |basisOfCentroid| |numberOfComponents| - |createIrreduciblePoly| |binarySearchTree| |radicalSimplify| - |dominantTerm| |port| |shufflein| |weights| |writeUInt8!| |untab| - |LowTriBddDenomInv| |leftLcm| |top| |eval| |readInt16!| |totolex| - |rightExtendedGcd| |invertibleElseSplit?| |s17adf| |algebraic?| - |innerint| |factorsOfDegree| |printTypes| |continue| - |changeThreshhold| |e01daf| |wronskianMatrix| |anticoord| |e01sff| - |measure| |printStatement| |elRow2!| |complement| - |basisOfRightAnnihilator| |generalInfiniteProduct| |quadratic| |t| - |doublyTransitive?| |orbits| |ricDsolve| |negative?| |irVar| - |indiceSubResultant| |setrest!| |modTree| |badNum| |shade| - |nextSubsetGray| |inf| |antiCommutative?| |indicialEquationAtInfinity| - |csubst| |localUnquote| |s21baf| |primextendedint| |reflect| |rk4a| - |showTheRoutinesTable| |init| |f02bjf| |rightQuotient| |deepExpand| - |irreducible?| |nextPrime| |PDESolve| |polygon?| |basisOfRightNucleus| - |duplicates| |connectTo| |floor| |backspace| |rootKerSimp| - |evaluateInverse| |elRow1!| |e01sbf| |listRepresentation| |enumerate| - |rootOf| |prologue| |selectfirst| |normalizedDivide| - |leftExactQuotient| |OMputAtp| |sign| |divideIfCan| |shallowCopy| - |e04naf| |Beta| |writeByte!| |fglmIfCan| |hostByteOrder| |external?| - |splitNodeOf!| |linkToFortran| |irreducibleRepresentation| - |possiblyInfinite?| |squareFree| |shallowExpand| |interpret| - |lfextendedint| |constantRight| |f01maf| |controlPanel| |e02agf| - |vedf2vef| |s13acf| |fortranTypeOf| |f04qaf| |stoseInvertibleSet| - |addPoint| |getOperands| |linearAssociatedLog| |dmpToHdmp| |makeFR| - |rdregime| |directSum| |imagE| |nullSpace| |categoryMode| |nil| - |mkIntegral| |subResultantGcdEuclidean| |unitCanonical| |Gamma| - 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|rombergo| |insertMatch| |c06gcf| |generic?| |sumOfSquares| |nary?| - |subresultantSequence| |algDsolve| |byteBuffer| |LyndonWordsList1| - |systemSizeIF| |superscript| |drawComplex| |retract| |cAcot| |s17dgf| - |pdf2df| |bindings| |mappingMode| |lazyPrem| |processTemplate| - |lazyPquo| |createNormalPrimitivePoly| |froot| |color| - |leadingBasisTerm| |jokerMode| |children| |d01fcf| |segment| - |stronglyReduced?| |physicalLength!| |OMUnknownSymbol?| |f01brf| - |norm| |getCurve| |rightFactorIfCan| |tubePlot| |getGoodPrime| - |associatedEquations| |hclf| |OMputObject| |mindeg| |quatern| - |interpretString| |previous| |ratpart| |tValues| |zeroMatrix| - |swapRows!| |stiffnessAndStabilityFactor| |createPrimitivePoly| - |complexZeros| |generalLambert| |nullary?| |scalarTypeOf| |sn| - |s17dhf| |initTable!| |d01akf| |countRealRoots| |leader| |torsion?| - |perfectSquare?| |lazyIrreducibleFactors| |headRemainder| |imagK| - |getProperty| |maxdeg| |outputMeasure| |OMputEndBVar| |typeLists| - |mainVariables| |basisOfMiddleNucleus| |setleft!| |rotatey| - |OMputEndAtp| |ListOfTerms| |rewriteIdealWithQuasiMonicGenerators| - |jvmStatic| |invertible?| |internalDecompose| |sylvesterMatrix| - |numberOfIrreduciblePoly| |selectPolynomials| |getPickedPoints| - |category| |readUInt16!| |lflimitedint| |signatureAst| - |lookupFunction| |divisor| |modulus| |spherical| |closed?| |domain| - |cCoth| |insertBottom!| |componentUpperBound| |trapezoidalo| - |hermiteH| |hash| |viewWriteDefault| |cSin| |jvmFinal| - |cyclicSubmodule| |mapDown!| |curveColor| |alphanumeric?| - |fortranCarriageReturn| |package| |tanIfCan| |substring?| - |nthExponent| |count| |expPot| |infix| |resultantReduit| |medialSet| - |nativeModuleExtension| |getCode| |limitedint| |xn| |second| |sin?| - |s13adf| |convert| |sayLength| |makeop| |nodeOf?| |jvmTransient| - |triangulate| |df2st| |pade| |ratDsolve| |xCoord| |third| |s18aef| - |replace| |suffix?| |makeCos| |reduction| |algebraicCoefficients?| - |generator| |e02akf| |simplifyPower| |edf2efi| |exportedOperators| - |primitiveElement| |readBytes!| |expandTrigProducts| |vark| |d01bbf| - 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|sort!| |cAsech| |imag| |packageCall| |findBinding| |solve1| |delete| - |omError| |SturmHabichtCoefficients| |algebraicVariables| |ran| - |perfectSqrt| |asec| |directProduct| |unit| |moebius| |ocf2ocdf| - |augment| |semiResultantEuclidean1| |cyclic| |OMputApp| |sinh2csch| - |top!| |ridHack1| |explicitlyEmpty?| |irForm| |bitLength| |s17def| - |unitsColorDefault| |outputFloating| |OMencodingUnknown| |tree| - |readInt32!| |OMgetVariable| |droot| |skewSFunction| - |innerEigenvectors| |OMgetAtp| |brace| |clipBoolean| |create| - |exactQuotient| |d02raf| |cTanh| |odd?| |pToDmp| |geometric| - |functorData| |destruct| |parametersOf| |setright!| |var2Steps| - |carriageReturn| |isQuotient| |phiCoord| |reduced?| |genericLeftTrace| - |airyBi| |sum| |evenlambert| |qqq| |pdf2ef| |coefChoose| |intChoose| - |genericLeftTraceForm| |minPoints| |computeBasis| |singRicDE| |f2df| - |optpair| |zeroDimPrimary?| |linearDependence| |wholeRagits| |minPoly| - |wrregime| |shiftRight| |prod| |components| |stirling1| |pointPlot| - 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|OMputSymbol| |partition| |tanh| |e04mbf| |nodes| |rowEchelon| - |subscript| |stack| |acosIfCan| |hexDigit?| |iiperm| |log10| |select| - |polyred| |reopen!| |resultantnaif| |coth| - |combineFeatureCompatibility| |patternVariable| |getIdentifier| - |df2mf| |radicalEigenvectors| |child| |e02bdf| |setProperty| |bitand| - |normal01| |divideIfCan!| |defineProperty| |sech| |f02abf| |monomials| - |infiniteProduct| |taylor| |qfactor| |e02ahf| |showSummary| |cPower| - |rootPower| |HenselLift| |bitior| |solid?| |partialQuotients| |csch| - |choosemon| |mapBivariate| |initializeGroupForWordProblem| - |leadingCoefficientRicDE| |symmetricSquare| |refine| - |encodingDirectory| |standardBasisOfCyclicSubmodule| |asinh| - |invertIfCan| |symbolTableOf| |normalizeAtInfinity| |isAtom| - |showAttributes| |ode2| |kroneckerDelta| |denomRicDE| |nthCoef| - |extension| |acosh| |compdegd| |cycleTail| |algint| |members| |cAcosh| - |alphabetic?| |tube| |OMgetType| |upperCase!| |atanh| - |fillPascalTriangle| |numFunEvals| F2FG |normalizeIfCan| |linSolve| - |makeRecord| |groebner?| |deleteRoutine!| |acoth| |iiatanh| - |viewDefaults| |e01sef| |normalizedAssociate| |interpolate| |e02ajf| - |merge!| |internalIntegrate| |imagi| |open| |asech| |listOfMonoms| - |viewThetaDefault| |typeForm| |splitConstant| |OMclose| |cAsec| - |clearFortranOutputStack| |po| |squareFreeFactors| |gderiv| - |diagonalMatrix| |subresultantVector| |mathieu12| |cycleRagits| - |delta| |palginfieldint| |isImplies| |rspace| |trunc| - |numberOfMonomials| |OMputInteger| |multiple| |multinomial| - |dimensions| |curve?| |eyeDistance| |weight| |bivariatePolynomials| - |primlimitedint| |toseInvertibleSet| |domainTemplate| |applyQuote| - |startTable!| |lazyPremWithDefault| |product| |tail| |iitan| |pushup| - |highCommonTerms| |f02akf| |ranges| |isOp| |operations| |nthFlag| - |leadingSupport| |ord| |differentialVariables| |isAnd| |closedCurve?| - |OMwrite| |besselK| |initial| |zeroDimPrime?| |endOfFile?| - |figureUnits| |vspace| |nullity| |viewpoint| - |rightCharacteristicPolynomial| |semiDegreeSubResultantEuclidean| - |expint| |bivariate?| |ruleset| |superHeight| |lowerBound| - |alphabetic| |lllp| |reducedDiscriminant| |laguerreL| |writable?| - |complete| |hex| |sylvesterSequence| |double?| |rootBound| - |zeroVector| |laplace| |lazyResidueClass| |apply| |zag| |iidprod| - |OMsupportsSymbol?| |inputBinaryFile| |BumInSepFFE| |solid| - |homogeneous?| |arity| |romberg| Y |eulerPhi| |swapColumns!| |infLex?| - |first| |rank| |transcendentalDecompose| |varList| |elaborate| - |sec2cos| |tubeRadius| |suchThat| |mathieu23| |ReduceOrder| - |stopTableInvSet!| |nextItem| |cubic| |rest| |lazyEvaluate| |insert!| - |digit?| |numberOfCycles| |iicsch| |rightOne| |trigs| |module| - |leftRegularRepresentation| |collectUnder| |palgint0| - |integralLastSubResultant| |key| |s21bcf| |asimpson| |leftExtendedGcd| - |linear?| |separateDegrees| |idealiser| |elseBranch| - |PollardSmallFactor| |vertConcat| |sequences| |quadraticForm| - |toseSquareFreePart| |idealSimplify| |scan| |rootRadius| |cycleSplit!| - |kmax| |internal?| |ratPoly| |imagI| |absolutelyIrreducible?| - |mappingAst| |rootOfIrreduciblePoly| |filename| |bipolar| |colorDef| - |associatorDependence| |palgLODE0| |unaryFunction| |deref| - |reciprocalPolynomial| |identitySquareMatrix| |divergence| - |primintfldpoly| |hcrf| |inR?| |intermediateResultsIF| |initials| - |f02wef| |hypergeometric0F1| |symmetricRemainder| - |numberOfComputedEntries| |selectOrPolynomials| |identity| |input| - |parse| |oddInfiniteProduct| |isMult| |region| |indices| - |factorPolynomial| |split!| |cCosh| |leftFactor| |curryRight| - |OMlistSymbols| |library| |besselI| |ef2edf| |inverseColeman| - |tryFunctionalDecomposition?| |lists| |extract!| |c06fpf| |central?| - |OMputBind| |atoms| |select!| |discreteLog| |nextPrimitiveNormalPoly| - |genericRightNorm| |capacity| |clipPointsDefault| |baseRDE| - |endSubProgram| |measure2Result| |palglimint0| |prem| |palgRDE| - |sincos| |showIntensityFunctions| |internalLastSubResultant| - |inverseIntegralMatrixAtInfinity| |numberOfPrimitivePoly| |isTimes| - |whitePoint| |chebyshevT| |numberOfFractionalTerms| |deepestTail| - |paraboloidal| |s19abf| |decompose| |binomThmExpt| |normalElement| - |plus| |crest| |resetAttributeButtons| |rotate| - |halfExtendedSubResultantGcd2| |unary?| |in?| |probablyZeroDim?| - |selectODEIVPRoutines| |imagk| |OMgetEndObject| |localAbs| - |palgextint0| |ip4Address| |indicialEquation| |bracket| |s18dcf| - |dual| |value| |distdfact| |host| |regime| |quasiComponent| |lllip| - |zeroSetSplit| |pomopo!| |setLegalFortranSourceExtensions| |pushdown| - |matrixDimensions| |mesh| |noLinearFactor?| |f04mbf| |graeffe| - |yCoordinates| |checkRur| |resultantReduitEuclidean| |cAcsc| |times| - |red| |name| |reset| |showClipRegion| |bumptab| |cyclic?| |unravel| - |minPoints3D| |relationsIdeal| |kind| |linearForm| |sts2stst| - |consnewpol| |f02aef| |back| |body| |stripCommentsAndBlanks| - |constantOperator| |linefeed| |e04fdf| |parent| |screenResolution| - |setImagSteps| |f04atf| |s18adf| |restorePrecision| - |constantToUnaryFunction| |KrullNumber| |divisorCascade| |write| - |makeFloatFunction| |showRegion| |chebyshevU| |readIfCan!| |s14aaf| - 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|besselJ| |ffactor| |trace| |blankSeparate| |bfKeys| |solve| - |Vectorise| |lagrange| |mainPrimitivePart| |delete!| |leadingIndex| - |bezoutDiscriminant| |rightRemainder| |sturmVariationsOf| |reverse| - |resetBadValues| |jvmAbstract| |removeRoughlyRedundantFactorsInPols| - |crushedSet| |generalTwoFactor| |zeroDim?| |totalDifferential| - |insertTop!| |parabolic| |integralAtInfinity?| |dihedral| - |basisOfCommutingElements| |sechIfCan| |say| - |jvmInterfaceMethodConstantTag| |useSingleFactorBound?| - |removeConstantTerm| |totalDegree| |mapSolve| |upperBound| - |fortranLiteralLine| |d01apf| |structuralConstants| |qelt| |interval| - |makeCrit| |linearlyDependent?| |ksec| |torsionIfCan| |fractRadix| - |setAttributeButtonStep| |next| |groebner| |iicoth| |makeEq| |iilog| - |qsetelt| |rangeIsFinite| |SFunction| |powers| |univariate?| UP2UTS - |symFunc| |shanksDiscLogAlgorithm| |characteristicPolynomial| - |padicallyExpand| |evenInfiniteProduct| |rk4qc| |xRange| |arguments| - |square?| |complex?| |getMatch| |iFTable| - |semiLastSubResultantEuclidean| |basis| |pastel| |schema| |iisqrt2| - |wholeRadix| |factor1| |union| |yRange| |fibonacci| |cothIfCan| - |c06fqf| |parts| |OMgetString| |stoseLastSubResultant| |twist| - |extendedIntegrate| |quasiRegular| |ipow| |signAround| |predicates| - |zRange| |c06gqf| |nextsousResultant2| |irreducibleFactors| |subNode?| - |powern| |bounds| |parents| |inputOutputBinaryFile| |search| - |RittWuCompare| |rightRecip| |mapmult| |se2rfi| |boundOfCauchy| |map!| - |rubiksGroup| |quoted?| |supRittWu?| |leadingIdeal| |extractPoint| - |nextsubResultant2| |setColumn!| |plenaryPower| - |genericLeftDiscriminant| |bernoulli| |expextendedint| - |particularSolution| |qsetelt!| |linearAssociatedExp| |pushdterm| - |zoom| |size?| |youngGroup| |mapdiv| |e02daf| |OMsetEncoding| - |asinhIfCan| |extractClosed| |compound?| |sech2cosh| |ScanRoman| - |decomposeFunc| |socf2socdf| |rroot| |asecIfCan| |read!| |diff| - |brillhartIrreducible?| |Aleph| |curry| |e01bgf| |primlimintfrac| - |reducedQPowers| |outlineRender| |e04gcf| |tanh2trigh| - |radicalEigenvalues| |datalist| |pushucoef| |closeComponent| - |firstUncouplingMatrix| |upDateBranches| |permutations| |generalSqFr| - |unitNormal| |internalZeroSetSplit| |iitanh| |OMconnOutDevice| - |prolateSpheroidal| |nextIrreduciblePoly| |nextColeman| |f04jgf| - |subSet| |head| |nextPrimitivePoly| |finiteBound| - |solveLinearPolynomialEquationByRecursion| |singularitiesOf| - |matrixConcat3D| |f02xef| |mapMatrixIfCan| |diag| - |linearAssociatedOrder| |hasoln| |changeWeightLevel| |trigs2explogs| - |minimize| |round| |exponential| |getOrder| |d01ajf| |c02agf| - |wordInGenerators| |makeUnit| |monicRightFactorIfCan| |intersect| - |symmetricProduct| |basicSet| |mpsode| |variable?| |separate| - |inspect| |OMencodingXML| |UpTriBddDenomInv| |charthRoot| - |mainDefiningPolynomial| |isAbsolutelyIrreducible?| - |nthFractionalTerm| |nextLatticePermutation| |completeHermite| - |mainVariable| |setlast!| |pleskenSplit| |d02cjf| |push!| - |maxPoints3D| |insertionSort!| |argscript| |multiplyExponents| - |plusInfinity| |compose| |points| |bringDown| |jvmFloatConstantTag| - |setTopPredicate| |cAcoth| |rischDEsys| |submod| |hessian| - |jvmIntegerConstantTag| |zeroSquareMatrix| |leftUnit| |minusInfinity| - |rootProduct| |light| |alphanumeric| |createPrimitiveNormalPoly| - |modularFactor| |mainValue| |removeRedundantFactorsInPols| |setClosed| - |fixPredicate| |fi2df| |argumentList!| |iisinh| |pole?| |factors| - |safeCeiling| |power| |loopPoints| |exprToGenUPS| |getDatabase| - |transcendenceDegree| |iisech| |symmetricGroup| |scanOneDimSubspaces| - |lineColorDefault| |qPot| |expenseOfEvaluationIF| |repSq| - |complexNumericIfCan| |createNormalPoly| |palgRDE0| |compiledFunction| - |underscore| |radPoly| |parseString| |qinterval| |externalList| - |pattern| |debug| |dihedralGroup| |sinIfCan| |gcdPolynomial| - |checkPrecision| |reseed| |coefficient| |principal?| - |useEisensteinCriterion?| |OMserve| D |constant?| |mainVariable?| - |minColIndex| |fortranReal| |type| |any?| |s15adf| - |rationalApproximation| |cyclicEqual?| |component| |clearTheIFTable| - |extractIfCan| |pseudoDivide| |OMputVariable| |minRowIndex| - |quadraticNorm| |resultantEuclidean| |getMultiplicationMatrix| - |UP2ifCan| |approxSqrt| |leftCharacteristicPolynomial| |drawToScale| - |drawStyle| |factorList| |countRealRootsMultiple| |pushuconst| - |startStats!| |LyndonBasis| |concat| |cAcsch| |coefficients| - |createNormalElement| |stoseIntegralLastSubResultant| - |definingPolynomial| |headReduced?| |dequeue| |moduloP| - |genericRightTraceForm| |range| |listYoungTableaus| |f01bsf| |root| - |voidMode| |resultantEuclideannaif| |selectMultiDimensionalRoutines| - |stoseSquareFreePart| |setPoly| |shellSort| |quoByVar| |iiasin| - |f04asf| |clearCache| |factorByRecursion| |karatsubaOnce| |constant| - |lintgcd| |subCase?| |rotatez| |branchIfCan| |maxRowIndex| - |decreasePrecision| |setOrder| |changeName| |minus!| - |setScreenResolution| |matrixGcd| |direction| |patternMatchTimes| - |linearPart| |resultant| |extractBottom!| |realZeros| - |univariatePolynomial| |reduceLODE| |rootDirectory| |print| - |algebraicOf| |const| |fintegrate| |extendedSubResultantGcd| - |intcompBasis| |ode1| |resolve| |leaf?| GF2FG |s01eaf| - |basisOfLeftAnnihilator| |normal?| |makeTerm| |rootSplit| - |rightExactQuotient| |scopes| |nullary| |corrPoly| |numer| - |lastSubResultantElseSplit| |computeInt| |slex| |dAndcExp| |s21bbf| - |unrankImproperPartitions0| |numericalOptimization| |denom| - |symmetricDifference| |ptree| |incrementKthElement| |reindex| - |viewSizeDefault| |selectsecond| |showScalarValues| |removeCoshSq| - |oddlambert| |operators| |isEquiv| |eigenvector| |rischDE| |f07aef| - |addPoint2| |setprevious!| |genericLeftNorm| |seriesToOutputForm| - |title| |characteristic| |pi| |createRandomElement| |iCompose| - |outputList| |null?| |polynomialZeros| |meshPar1Var| - |removeRoughlyRedundantFactorsInContents| |bigEndian| - |numberOfNormalPoly| |infinity| |noKaratsuba| |integralCoordinates| - |listConjugateBases| |mkPrim| |OMputError| |atom?| |nil| |infinite| - |arbitraryExponent| |approximate| |complex| |shallowMutable| - |canonical| |noetherian| |central| |partiallyOrderedSet| - |arbitraryPrecision| |canonicalsClosed| |noZeroDivisors| - |rightUnitary| |leftUnitary| |additiveValuation| |unitsKnown| - |canonicalUnitNormal| |multiplicativeValuation| |finiteAggregate| - |shallowlyMutable| |commutative|)
\ No newline at end of file + |Enumeration| |Mapping| |Record| |Union| |low| |solveLinear| + |OMgetInteger| |blankSeparate| |hclf| |mainMonomial| |getStream| + |nullity| |e| |repeating| |stiffnessAndStabilityOfODEIF| |putProperty| + |bfKeys| |OMputObject| |hasTopPredicate?| |subResultantChain| + |viewpoint| |definingPolynomial| |palglimint| |mapGen| |kernel| + |isPlus| |solve| |scripted?| |mindeg| |rightCharacteristicPolynomial| + |OMopenString| |null| |headReduced?| |meshPar2Var| |d03eef| + |plotPolar| |list| |Vectorise| |quatern| |sh| |realEigenvalues| + |semiDegreeSubResultantEuclidean| |dequeue| |not| |draw| |space| + |expressIdealMember| |lprop| |lagrange| |branchPointAtInfinity?| + |f01qef| |interpretString| |expint| |bright| |and| |moduloP| + |realSolve| |identification| |f02aaf| |mainPrimitivePart| + |findConstructor| |ratpart| |sturmSequence| |bivariate?| + |genericRightTraceForm| |or| |mathieu22| |sequence| |quartic| + |delete!| |outputFixed| |tValues| |taylorQuoByVar| |superHeight| + |range| |xor| |mvar| |cache| |primitive?| |f07fdf| |leadingIndex| + |zeroMatrix| |d01gbf| |OMgetEndAtp| |lowerBound| |listYoungTableaus| + |case| |makeObject| |semiSubResultantGcdEuclidean1| |legendre| + |closedCurve| |bezoutDiscriminant| |exp1| |leviCivitaSymbol| + |swapRows!| |alphabetic| |elaboration| |f01bsf| |Zero| |basisOfCenter| + |removeDuplicates| |showTheSymbolTable| |coef| |rightRemainder| + |asechIfCan| |stiffnessAndStabilityFactor| |freeOf?| |lllp| + |mindegTerm| |root| |One| |antisymmetric?| |outputSpacing| + |infinityNorm| |sturmVariationsOf| |commonDenominator| + |integralBasisAtInfinity| |createPrimitivePoly| |prinb| + |reducedDiscriminant| |voidMode| |autoReduced?| |OMgetEndError| + |leftGcd| |resetBadValues| |edf2ef| |complexZeros| |lieAdmissible?| + |jvmNative| |laguerreL| |resultantEuclideannaif| |jacobian| + |rightAlternative?| |rightPower| |jvmAbstract| |left| + |purelyAlgebraic?| |outputGeneral| |generalLambert| |writable?| + |badValues| |selectMultiDimensionalRoutines| |retractIfCan| + |outputArgs| |distribute| |credPol| + |removeRoughlyRedundantFactorsInPols| |right| |d01aqf| |size| + |nullary?| |aQuadratic| |associatedSystem| |complete| + |stoseSquareFreePart| |distance| |rightDivide| + |stosePrepareSubResAlgo| |crushedSet| |scalarTypeOf| |implies| |hex| + |lazyIntegrate| |setPoly| |elt| |polCase| |dfRange| |OMgetObject| EQ + |generalTwoFactor| |s17dhf| |ScanFloatIgnoreSpaces| + |factorSquareFreePolynomial| |wordInStrongGenerators| + |sylvesterSequence| |shellSort| |overset?| |jvmVolatile| |parametric?| + |zeroDim?| |df2ef| |adaptive| |initTable!| |double?| |printStats!| + |quoByVar| |enterInCache| |BasicMethod| |addMatchRestricted| + |totalDifferential| |d01akf| |compactFraction| |solveRetract| + |rootBound| |optional?| |iiasin| |internalAugment| |zeroDimensional?| + |axesColorDefault| |insertTop!| |removeRedundantFactorsInContents| + |countRealRoots| |zeroVector| |e04ycf| |f04asf| |signature| + |rewriteIdealWithRemainder| |eq?| |conjugates| |parabolic| + |numberOfDivisors| |torsion?| |laplace| |semiResultantEuclideannaif| + |factorByRecursion| |primaryDecomp| |prinpolINFO| |testModulus| + |integralAtInfinity?| |perfectSquare?| FG2F |factorset| + |lazyResidueClass| |karatsubaOnce| |setFieldInfo| |sort!| + |monicCompleteDecompose| |dihedral| |slash| |lazyIrreducibleFactors| + |zag| |equiv| |lintgcd| |SturmHabichtMultiple| |redPo| |cAsech| + |basisOfCommutingElements| |operation| |node| |setMinPoints| + |headRemainder| |setleaves!| |iidprod| |subCase?| |every?| + |packageCall| |removeSquaresIfCan| |sechIfCan| |returns| |imagK| + |doubleRank| |OMsupportsSymbol?| |rotatez| |lazyPseudoDivide| + |expintegrate| |findBinding| |jvmInterfaceMethodConstantTag| |symbol| + |getProperty| |cyclePartition| |inputBinaryFile| |quasiAlgebraicSet| + |branchIfCan| |solve1| |stoseInternalLastSubResultant| SEGMENT |inc| + |lazyPseudoQuotient| |useSingleFactorBound?| |expression| + |monomialIntegrate| |maxdeg| |BumInSepFFE| |cfirst| |maxRowIndex| + |zerosOf| |updateStatus!| |unknown| |omError| |removeConstantTerm| + |integer| |outputMeasure| |jvmSuper| F |solid| |fixedDivisor| + |decreasePrecision| |exprHasWeightCosWXorSinWX| |log2| + |SturmHabichtCoefficients| |totalDegree| |OMputEndBVar| |removeCosSq| + |permutation| |homogeneous?| |setOrder| |palgextint| |precision| |Ci| + |algebraicVariables| |mapSolve| |check| |typeLists| |mkcomm| |arity| + |changeName| |s18aff| |sortConstraints| |ran| |upperBound| |s17aef| + |mainVariables| |numberOfChildren| |romberg| |hermite| |minus!| + |minset| |perfectSqrt| |lowerCase| |fortranLiteralLine| + |basisOfMiddleNucleus| |generic| |subspace| |eulerPhi| |digamma| + |setScreenResolution| |cond| |call| |fixedPoint| |unit| |nlde| + |d01apf| |setleft!| |numerator| |debug3D| |fortranInteger| + |swapColumns!| |matrixGcd| |totalfract| |moebius| |degree| |comp| + |structuralConstants| |rotatey| |monomialIntPoly| |symbolTable| + |totalLex| |infLex?| |direction| |inconsistent?| |ocf2ocdf| + |LyndonCoordinates| |interval| |innerSolve1| |OMputEndAtp| + |leftDiscriminant| |transcendentalDecompose| |patternMatchTimes| + |unitVector| |augment| |cot2tan| |makeCrit| |pushFortranOutputStack| + |isConnected?| |ListOfTerms| |elaborate| |squareFreePolynomial| + |linearPart| |cAsinh| |pmComplexintegrate| |semiResultantEuclidean1| + |linearlyDependent?| |popFortranOutputStack| |equation| + |rewriteIdealWithQuasiMonicGenerators| |rationalPower| |simplifyLog| + |sec2cos| |resultant| |cschIfCan| |cyclic| |splitDenominator| |ksec| + |jvmStatic| |bubbleSort!| |numberOfComposites| |outputAsFortran| + |reify| |tubeRadius| |extractBottom!| |relativeApprox| |OMputApp| + |newSubProgram| |torsionIfCan| |infieldint| |fortranLinkerArgs| + |invertible?| |digits| |mathieu23| |realZeros| |indicialEquations| + |cSec| |sinh2csch| |fractRadix| |selectPDERoutines| |cyclicParents| + |conditionP| |internalDecompose| |coord| |ReduceOrder| + |univariatePolynomial| |mesh?| |goodPoint| |top!| + |setAttributeButtonStep| |moebiusMu| |sylvesterMatrix| |rquo| + |stopTableInvSet!| |magnitude| |reduceLODE| |f02aff| |ridHack1| + |groebner| |expandPower| |reducedForm| |numberOfIrreduciblePoly| + |writeInt8!| |nextItem| |rootDirectory| |bag| |any| + |minimalPolynomial| |explicitlyEmpty?| |iicoth| |insert| |rst| + |selectPolynomials| |minimumDegree| |cubic| |algebraicOf| |genus| + |specialTrigs| |irForm| |makeEq| |swap!| |getPickedPoints| + |lazyEvaluate| |leftQuotient| |const| |arbitrary| |bitLength| |just| + |iilog| |clip| |insert!| |fintegrate| |binaryTree| |factorial| |super| + |s17def| |assert| |rangeIsFinite| |finiteBasis| |currentSubProgram| + |digit?| |iisin| |extendedSubResultantGcd| |stop| |leftFactorIfCan| + |parabolicCylindrical| |unitsColorDefault| |SFunction| |dioSolve| + |singularAtInfinity?| |LyndonWordsList| |numberOfCycles| + |intcompBasis| |orthonormalBasis| |summation| |outputFloating| + |systemCommand| |powers| |tablePow| |quotientByP| |formula| |iicsch| + |intPatternMatch| |ode1| |sin2csc| |univariate?| |tracePowMod| + |groebgen| |rightOne| |companionBlocks| |leaf?| |sub| |bitCoef| + |setStatus!| |normal| UP2UTS |e04ucf| |OMreceive| |lowerCase?| |trigs| + |integralRepresents| GF2FG |primeFactor| |cSinh| |leftMult| |symFunc| + |integralMatrixAtInfinity| |jvmClassConstantTag| |module| |uniform01| + |s01eaf| |isOpen?| |beauzamyBound| |leftPower| |diophantineSystem| + |shanksDiscLogAlgorithm| |difference| |areEquivalent?| |weierstrass| + |nrows| |basisOfLeftAnnihilator| |binaryTournament| |updatD| |fortran| + |flexible?| |solveInField| |characteristicPolynomial| |close| + |normalizeIfCan| |prefixRagits| |randnum| |rationalFunction| |ncols| + |adjoint| |normal?| |OMread| |assign| |removeZero| |padicallyExpand| + |sizeLess?| |high| |graphStates| |linSolve| |bsolve| |eq| |makeTerm| + |iiacoth| |f02bbf| |OMputEndApp| |log| |evenInfiniteProduct| |display| + |cSech| |hasHi| |groebner?| |infRittWu?| |iter| |rootSplit| + |OMputEndObject| |element?| |tab1| |iomode| |c02aff| |setnext!| + |deleteRoutine!| |rightExactQuotient| |harmonic| |isList| |lifting| + |OMencodingSGML| |transpose| |continuedFraction| |monicDivide| + |iiatanh| |d01alf| |scopes| |weakBiRank| |removeZeroes| |getConstant| + |associates?| |diagonal| |createMultiplicationTable| |listBranches| + |e01bff| |viewDefaults| |nullary| |multMonom| |realEigenvectors| + |accuracyIF| |anfactor| |rationalPoints| |quotedOperators| |multisect| + |e01sef| |argumentListOf| |normalize| |addPointLast| |radicalSolve| + |length| |leftScalarTimes!| |squareFreeLexTriangular| + |normalizedAssociate| |lhs| |returnTypeOf| |binomial| + |complexElementary| |transcendenceDegree| |localReal?| + |splitSquarefree| |rk4| |linear| |predicate| |scripts| |OMgetEndBind| + |output| |primintegrate| |reverseLex| + |semiIndiceSubResultantEuclidean| |rhs| |exQuo| |interpolate| |iisech| + |readByte!| |test| |stopTable!| |algebraicSort| |getZechTable| + |viewport3D| |exp| |contours| |point| |laplacian| |true| + |semiSubResultantGcdEuclidean2| |divideExponents| |e02ajf| + |commutator| |limitedIntegrate| |symmetricGroup| |noValueMode| |arg1| + |nonQsign| |polynomial| |bombieriNorm| |linGenPos| |lambda| |routines| + |ignore?| |currentEnv| |width| |positiveSolve| |merge!| |leaves| + |deepCopy| |scanOneDimSubspaces| |traverse| |printCode| |nthFactor| + |arg2| |d03faf| |epilogue| |normalized?| |map| |setsubMatrix!| + |startTableInvSet!| |internalIntegrate| + |removeIrreducibleRedundantFactors| |lineColorDefault| + |jvmLongConstantTag| |script| |optAttributes| |rationalPoint?| + |OMgetFloat| |series| |nilFactor| |maxint| |integralBasis| + |loadNativeModule| |imagi| |qPot| |li| |conditions| |printingInfo?| + |createLowComplexityNormalBasis| |Si| |compBound| |message| |ldf2lst| + |belong?| |listOfMonoms| |setPrologue!| |squareFreePart| + |expenseOfEvaluationIF| |selectFiniteRoutines| |match| |extendedint| + |recur| |real?| |d02kef| |e02bbf| |createGenericMatrix| |simplify| + |viewThetaDefault| |repSq| |exptMod| |tableForDiscreteLogarithm| + |zCoord| |pol| |decimal| |fprindINFO| |splitConstant| |OMgetApp| + |cycleLength| |complexNumericIfCan| |s17acf| |quote| + |selectSumOfSquaresRoutines| |vectorise| |min| |identityMatrix| + |optional| |tan2trig| |chvar| |OMclose| |createNormalPoly| |decrease| + |setTex!| |parameters| |myDegree| |algebraicDecompose| |ref| + |outputAsScript| |cAsec| |roman| |palgRDE0| |pointColorPalette| + |OMunhandledSymbol| |infinite?| |remove| |makeGraphImage| |divide| + |hdmpToP| |getVariableOrder| |clearFortranOutputStack| |mapUnivariate| + |compiledFunction| |result| |shift| |jacobiIdentity?| |ODESolve| + |lastSubResultant| |csc2sin| |subtractIfCan| |rowEch| |po| |weighted| + |underscore| |maximumExponent| |setOfMinN| |OMopenFile| |last| + |userOrdered?| |createThreeSpace| |mr| |f04maf| |simpsono| |cartesian| + |squareFreeFactors| |radPoly| |extend| |primeFrobenius| + |currentCategoryFrame| |f01qcf| |more?| |univariatePolynomialsGcds| + |definingEquations| |solveid| |gderiv| |parseString| |primitivePart!| + |complexSolve| |fortranDouble| |besselY| |balancedBinaryTree| + |constantCoefficientRicDE| |regularRepresentation| |perfectNthPower?| + |diagonalMatrix| BY |qinterval| |pseudoRemainder| |OMsend| + |rewriteIdealWithHeadRemainder| LODO2FUN |expr| |primitivePart| + |youngDiagram| |fortranLogical| |subresultantVector| |externalList| + |modularGcd| |internalSubPolSet?| |clearTable!| |clipWithRanges| + |cardinality| |completeEchelonBasis| |unparse| |mathieu12| + |dihedralGroup| |lift| |label| |whileLoop| |numberOfFactors| |dec| + |diagonal?| |row| |cycleRagits| |rombergo| |monic?| + |unrankImproperPartitions1| |sinIfCan| |reduce| |condition| |e01bhf| + |numeric| |lp| |symmetricPower| |setStatus| |jacobi| + |exponentialOrder| |depth| |palginfieldint| |insertMatch| + |trapezoidal| |rules| |gcdPolynomial| |prefix| |radical| + |constantLeft| |mapUp!| |bandedHessian| |OMReadError?| |variable| + |c06gcf| |definingInequation| |iiatan| |isImplies| |reseed| + |showAllElements| |linearElement| |OMgetBVar| |cross| |iterators| + |before?| |generic?| |OMgetEndApp| |rspace| |coefficient| + |reducedSystem| |numberOfImproperPartitions| GT |pile| + |euclideanGroebner| NOT |integers| |sumOfSquares| |redPol| |stFunc1| + |trunc| |principal?| |rightRank| |cyclotomic| |toroidal| LE + |setLength!| OR |fortranDoubleComplex| |nary?| |chiSquare1| |eof?| + |numberOfMonomials| |useEisensteinCriterion?| |conjugate| |bits| + |times!| |jvmProtected| LT |leftAlternative?| AND |bothWays| + |subresultantSequence| |root?| |setDifference| |OMputInteger| + |OMserve| |option| |euler| |sumOfKthPowerDivisors| |integerIfCan| + |ParCondList| |algDsolve| |zero?| |multinomial| |acschIfCan| + |constant?| |bytes| |copy!| |center| |lastSubResultantEuclidean| + |radicalRoots| |byteBuffer| |addmod| |cCot| |dimensions| + |mainVariable?| |antiAssociative?| |hMonic| |update| |removeSinSq| + |newTypeLists| |LyndonWordsList1| |rur| |curve?| |htrigs| + |minColIndex| |asinIfCan| |traceMatrix| |dimension| |comparison| |rem| + |meatAxe| |rootPoly| |systemSizeIF| |GospersMethod| |eyeDistance| + |fortranReal| |gcdcofactprim| |fortranCharacter| |lexico| |ideal| + |quo| |selectAndPolynomials| |superscript| |weight| |e01bef| |any?| + |overlabel| |exactQuotient!| |limitPlus| |f01qdf| |drawComplex| + |karatsuba| |integralDerivationMatrix| |bivariatePolynomials| |s15adf| + |chainSubResultants| |setFormula!| |mapUnivariateIfCan| + |makeViewport3D| |div| |extendedEuclidean| |cAcot| |primlimitedint| + |jvmStringConstantTag| |byte| |rationalApproximation| |increase| + |cyclicCopy| |mantissa| |scale| |calcRanges| |exquo| |binaryFunction| + |s17dgf| |iidsum| |toseInvertibleSet| |cyclicEqual?| |disjunction| + |showTheFTable| |minPol| |getProperties| * ~= |pdf2df| |nthRootIfCan| + |domainTemplate| |mathieu11| |component| |internalInfRittWu?| |s17aff| + |OMputFloat| |writeBytes!| |#| |virtualDegree| |mappingMode| + |startTable!| |viewDeltaYDefault| |clearTheIFTable| |jordanAlgebra?| + |surface| |cscIfCan| |printInfo!| ~ + |unprotectedRemoveRedundantFactors| |lazyPrem| |f02adf| + |lazyPremWithDefault| |extractIfCan| |symbolIfCan| |doubleDisc| + |getExplanations| |nonLinearPart| = |processTemplate| |categories| + |simplifyExp| |f04faf| |product| |pseudoDivide| |ParCond| |unit?| + |irCtor| |getMultiplicationTable| |henselFact| |tex| + |doubleFloatFormat| |lazyPquo| |iitan| |repeating?| |OMputVariable| + |representationType| |lfintegrate| |function| |goodnessOfFit| + |iiGamma| |less?| |/\\| < |createNormalPrimitivePoly| |lighting| + |pushup| |expandLog| |minRowIndex| |int| |bit?| |OMputBVar| + |constantOpIfCan| |rightTrace| |\\/| > |froot| |karatsubaDivide| + |highCommonTerms| |subMatrix| |quadraticNorm| |extractTop!| + |polyRicDE| |preprocess| |leastPower| <= |color| |extractProperty| + |f02akf| |lazyVariations| |resultantEuclidean| |integral?| + |innerSolve| |irDef| |curveColorPalette| >= |leadingBasisTerm| |radix| + |getButtonValue| |ranges| |getMultiplicationMatrix| |merge| |edf2fi| + |constantKernel| |commutativeEquality| |viewPosDefault| |updatF| + |isOp| |UP2ifCan| |jordanAdmissible?| |sizeMultiplication| + |atrapezoidal| |contractSolve| |drawCurves| |factorSFBRlcUnit| + |selectNonFiniteRoutines| |laurent| |nthFlag| |mightHaveRoots| + |approxSqrt| |fill!| |coerceListOfPairs| |radicalEigenvector| + |typeList| |empty| |swap| + |fixedPoints| |puiseux| + |uncouplingMatrices| |leadingSupport| |leftCharacteristicPolynomial| + |c05pbf| |oddintegers| |extendIfCan| |minimumExponent| - + |palgintegrate| |prevPrime| |ord| |extensionDegree| |drawToScale| + |selectOptimizationRoutines| |constantIfCan| |c06ekf| |cons| / + |e01saf| |inv| |differentialVariables| |recip| |drawStyle| |jvmStrict| + |OMputEndError| |setMaxPoints| |declare| |mathieu24| |ground?| + |atanIfCan| |stopTableGcd!| |randomR| |isAnd| |factorList| + |makeViewport2D| |leftNorm| |node?| |ravel| |univariateSolve| + |putProperties| |ground| |flatten| |separateFactors| + |fractionFreeGauss!| |closedCurve?| |countRealRootsMultiple| + |palgLODE| |callForm?| |dot| |lcm| |perfectNthRoot| + |partialNumerators| |reshape| |leadingMonomial| |llprop| |pushuconst| + |genericRightMinimalPolynomial| |c06gbf| |rightScalarTimes!| |vector| + |hexDigit| |set| |mainKernel| |c06ecf| |leadingCoefficient| + |rightRankPolynomial| |acosIfCan| |startStats!| |OMputAttr| |rotate!| + |tab| |differentiate| |append| |genericPosition| + |numericalIntegration| |source| |primitiveMonomials| |rdHack1| + |hexDigit?| |complementaryBasis| |LyndonBasis| |readLine!| + |fullPartialFraction| |linears| |gcd| |nextPartition| |s20acf| + |leftRemainder| |reductum| |iiperm| |hasPredicate?| |cAcsch| |cAtan| + |jvmSynchronized| |screenResolution3D| |false| |OMlistCDs| |taylorRep| + |polyred| |reduceByQuasiMonic| |coefficients| |removeSinhSq| + |OMgetEndAttr| |setValue!| |regime| |target| |att2Result| |opeval| + |reopen!| |quickSort| |createNormalElement| |cycleElt| |sumSquares| + |complexNormalize| |quasiComponent| |polyRDE| |leastMonomial| + |resultantnaif| |connect| |stoseIntegralLastSubResultant| |tubePoints| + |expintfldpoly| |mainSquareFreePart| |lllip| |makeSketch| + |makeVariable| |combineFeatureCompatibility| |linearlyDependentOverZ?| + |symmetric?| |dimensionsOf| |writeLine!| |zeroSetSplit| |imaginary| + |outerProduct| |table| |patternVariable| |modifyPointData| + |subQuasiComponent?| |printInfo| |monicRightFactorIfCan| |monomRDE| + |multiplyCoefficients| |quasiRegular?| |pomopo!| |cup| |new| + |rightRegularRepresentation| |position| |getIdentifier| + |stoseInvertible?| |intersect| |normalise| |coerce| |minGbasis| + |OMreadFile| |setLegalFortranSourceExtensions| |f02ajf| |npcoef| + |df2mf| |getMeasure| |symmetricProduct| |wholePart| |construct| + |powerAssociative?| |OMputEndBind| |pushdown| |subResultantsChain| + |delay| |iipow| |radicalEigenvectors| |basicSet| |digit| |universe| + |f04arf| |matrixDimensions| |polygon| |presuper| |OMUnknownCD?| + |monicLeftDivide| |child| |void| |mpsode| |composite| |iprint| + |scalarMatrix| |mesh| |poisson| |bumptab1| |e02bdf| + |tubeRadiusDefault| |variable?| |coshIfCan| |rk4f| |failed?| + |noLinearFactor?| |cyclicGroup| |reduceBasisAtInfinity| |nthRoot| + |setProperty| |reorder| |separate| |computeCycleLength| |trim| + |laurentIfCan| |f04mbf| |zero| |critMTonD1| |abs| |setErrorBound| + |normal01| |inspect| |coHeight| |elaborateFile| |ldf2vmf| |graeffe| + |leftRankPolynomial| |clipSurface| |irreducibleFactor| |divideIfCan!| + |properties| |OMencodingXML| |initiallyReduced?| |countable?| |primes| + |yCoordinates| |And| |comment| |sdf2lst| |createLowComplexityTable| + |balancedFactorisation| |defineProperty| |translate| + |UpTriBddDenomInv| |normalForm| |checkRur| |toseInvertible?| |d01asf| + |float?| |acoshIfCan| |Or| |e02def| |OMsupportsCD?| |f02abf| + |invmultisect| |charthRoot| |bumprow| |iifact| |csch2sinh| |logical?| + |failed| |resultantReduitEuclidean| |Not| |firstSubsetGray| |green| + |topPredicate| |monomials| |mainDefiningPolynomial| |has?| |stFuncN| + |abelianGroup| |setref| |cAcsc| |seed| |point?| |showArrayValues| + |infiniteProduct| |isAbsolutelyIrreducible?| |directory| |forLoop| + |OMgetEndBVar| |replaceKthElement| |red| |iiacsc| |getlo| |qfactor| + |subTriSet?| |nthFractionalTerm| |entry| |outputAsTex| |insertRoot!| + |halfExtendedSubResultantGcd1| |showClipRegion| |match?| + |categoryFrame| |useEisensteinCriterion| |e02ahf| |bat| + |nextLatticePermutation| |error| |birth| |ramifiedAtInfinity?| |dn| + |backOldPos| |bumptab| |bernoulliB| |setAdaptive3D| |leftUnits| + |cPower| |completeHermite| |reducedContinuedFraction| |divisors| + |jvmDoubleConstantTag| |complexEigenvalues| |remainder| |cyclic?| + |mat| |graphImage| |rootPower| |is?| |mainVariable| |ScanArabic| + |c05adf| |setelt| |HermiteIntegrate| |c06gsf| |unravel| |maxPoints| + |nthr| |HenselLift| |roughUnitIdeal?| |setlast!| |status| |satisfy?| + |subPolSet?| |minPoints3D| |solid?| |OMconnectTCP| |front| + |checkForZero| |fractionPart| |pleskenSplit| |bfEntry| |copy| + |recolor| |rectangularMatrix| |relationsIdeal| |inrootof| + |partialQuotients| |createZechTable| |ddFact| |psolve| |d02cjf| + |f04adf| |zeroOf| |makingStats?| |linearForm| |biRank| |messagePrint| + |SturmHabicht| |choosemon| |removeRoughlyRedundantFactorsInPol| + |push!| |cCsc| |autoCoerce| |environment| |gcdcofact| |sts2stst| + |exprex| |stoseInvertible?sqfreg| |mapBivariate| |meshFun2Var| + |maxPoints3D| |newline| |constDsolve| |var2StepsDefault| |port| + |consnewpol| |c06eaf| |viewport2D| |initializeGroupForWordProblem| + |zeroSetSplitIntoTriangularSystems| |insertionSort!| |top| |eval| + |jvmUTF8ConstantTag| |algSplitSimple| |leftMinimalPolynomial| |f02aef| + |moduleSum| |bat1| |pascalTriangle| |leadingCoefficientRicDE| + |argscript| |continue| |possiblyNewVariety?| |gensym| |nextSublist| + |back| |rightMult| |OMbindTCP| |sparsityIF| |symmetricSquare| + |multiplyExponents| |df2fi| |iiabs| |trivialIdeal?| |t| + |stripCommentsAndBlanks| |var1StepsDefault| |c05nbf| |adaptive3D?| + |imports| |refine| |compose| |enqueue!| |mainCharacterization| + |tubePointsDefault| |constantOperator| |currentScope| |janko2| + |pr2dmp| |startTableGcd!| |unknownEndian| |encodingDirectory| |points| + |iroot| |pointColorDefault| |init| |rewriteSetWithReduction| + |linefeed| |degreeSubResultantEuclidean| |rename| |varselect| + |lazyGintegrate| |jvmPrivate| |standardBasisOfCyclicSubmodule| + |bringDown| |alternating| |blue| |cot2trig| |e04fdf| |leftRank| + |bitTruth| |entries| |invertIfCan| |jvmFloatConstantTag| + |nonSingularModel| |d02ejf| |showAll?| |parent| |f04mcf| + |cyclicEntries| |upperCase?| |symbolTableOf| |setTopPredicate| + |e01baf| |formfeed| |moreAlgebraic?| |screenResolution| + |polarCoordinates| |makeSUP| |normalizeAtInfinity| |cosIfCan| |cAcoth| + |singular?| |curve| |RemainderList| |setImagSteps| |interpret| + |s17dlf| |addMatch| |isAtom| |numberOfVariables| |rischDEsys| + |polyPart| |genericRightTrace| |support| |f04atf| |usingTable?| + |firstDenom| |gcdPrimitive| |complexForm| |ode2| |submod| |character?| + |presub| |Is| |s18adf| |nil| |antisymmetricTensors| |cap| + |setPredicates| |kroneckerDelta| |c06fuf| |hessian| + |stoseInvertibleSetsqfreg| |leftZero| |buildSyntax| |restorePrecision| + |setPosition| |macroExpand| |roughSubIdeal?| |mainContent| + |denomRicDE| |minrank| |jvmIntegerConstantTag| |basisOfRightNucloid| + |f02awf| |s18def| |constantToUnaryFunction| |d02bbf| + |setVariableOrder| |nthCoef| |generalizedInverse| |zeroSquareMatrix| + |qualifier| |charClass| |finite?| |KrullNumber| |approximate| |rule| + |complexLimit| |derivationCoordinates| |extension| |midpoint| + |leftUnit| |internalIntegrate0| |eigenvectors| |diagonals| + |divisorCascade| |complex| |dualSignature| |inGroundField?| + |functionIsFracPolynomial?| |compdegd| |rootProduct| |f01rcf| + |copyInto!| |OMreadStr| |makeFloatFunction| |level| |fTable| + |mergeDifference| |prindINFO| |cycleTail| |light| |multiEuclideanTree| + |e02bef| |showRegion| |subst| |permanent| |midpoints| |double| + |exponents| |algint| |alphanumeric| |Ei| |OMputString| |chebyshevU| + |Lazard| |monomRDEsys| |cAsin| |members| |createPrimitiveNormalPoly| + |fortranCompilerName| |sorted?| |graphState| |readIfCan!| |dom| + |octon| |sample| |cAcosh| |discriminantEuclidean| |modularFactor| + |shuffle| |bandedJacobian| |acscIfCan| |s14aaf| |obj| |alphabetic?| + |dark| |mainValue| |noncommutativeJordanAlgebra?| |acsch| |makeSeries| + |lazyPseudoRemainder| |hyperelliptic| |imagE| |aQuartic| |objects| + |tube| |prime?| |removeRedundantFactorsInPols| |cn| + |removeSuperfluousQuasiComponents| |mainExpression| |alternative?| + |removeRedundantFactors| |nullSpace| |op| |base| |integralMatrix| + |OMgetType| |setClosed| |leastAffineMultiple| |aromberg| + |euclideanNormalForm| |categoryMode| |setchildren!| |collectUpper| + |upperCase!| |fixPredicate| |variationOfParameters| |integerBound| + |mkIntegral| |integral| |declare!| |fillPascalTriangle| + |LazardQuotient2| |fi2df| |removeDuplicates!| |dim| |cycles| + |optimize| |determinant| |subResultantGcdEuclidean| |pop!| |mdeg| + |s17ajf| |numFunEvals| |argumentList!| |drawComplexVectorField| + |supersub| |SturmHabichtSequence| |denominators| |unitCanonical| + |conditionsForIdempotents| F2FG |iisinh| |f02agf| |initiallyReduce| + |purelyTranscendental?| |errorKind| |Gamma| |pole?| + |computeCycleEntry| |leftRecip| |dmp2rfi| |notelem| |postfix| |push| + |frst| |factors| |makeSin| |chineseRemainder| |move| + |sizePascalTriangle| |imagj| |headAst| + |dimensionOfIrreducibleRepresentation| |safeCeiling| |retract| |iiexp| + |lepol| |coerceS| |bindings| |exists?| |FormatRoman| |OMgetError| + |elements| |power| |s14abf| |Frobenius| |setClipValue| |changeMeasure| + |mainMonomials| |rischNormalize| |segment| |loopPoints| |padecf| + |maxrank| |OMlistSymbols| |whatInfinity| |empty?| |perspective| + |elliptic| |aCubic| |exprToGenUPS| |s19adf| |bivariateSLPEBR| + |exponential1| |integer?| |besselI| |newLine| |previous| + |generateIrredPoly| |iiacosh| |clearTheSymbolTable| |getDatabase| + |jvmPublic| |colorFunction| |setAdaptive| |basisOfCentroid| |ef2edf| + |sn| |nthExpon| |rewriteSetByReducingWithParticularGenerators| + |setvalue!| |tanAn| |leader| |modifyPoint| |multiset| |patternMatch| + |inverseColeman| |numberOfComponents| |iflist2Result| |airyAi| |limit| + |s18acf| |extractClosed| |fortranLiteral| |derivative| |musserTrials| + |createIrreduciblePoly| |tryFunctionalDecomposition?| |lookup| + |ScanFloatIgnoreSpacesIfCan| |unmakeSUP| |terms| |compound?| + |extract!| |pureLex| |coerceL| |unvectorise| |binarySearchTree| + |category| |principalAncestors| |clearDenominator| |iiacos| + |getBadValues| |sech2cosh| |domain| |interReduce| |increasePrecision| + |unitNormalize| |c06fpf| |radicalSimplify| |one?| |e02bcf| |vconcat| + |hash| |interactiveEnv| |thenBranch| |ScanRoman| |package| |critMonD1| + |realElementary| |computePowers| |central?| |dominantTerm| + |substring?| |nor| |count| |contract| |plus!| |rCoord| |part?| + |decomposeFunc| |sqfrFactor| |s19aaf| |normInvertible?| |second| + |OMputBind| |shufflein| |convert| |polar| |critM| |squareTop| |s19acf| + |subResultantGcd| |socf2socdf| |pdct| |extractIndex| |third| + |localIntegralBasis| |weights| |atoms| |suffix?| |lowerPolynomial| + |pmintegrate| |sup| |generator| |LiePolyIfCan| |rroot| |rootsOf| + |cyclotomicDecomposition| |roughEqualIdeals?| |select!| |writeUInt8!| + |positiveRemainder| |jvmNameAndTypeConstantTag| |twoFactor| + |rightNorm| |internalSubQuasiComponent?| |asecIfCan| |char| + |factorsOfCyclicGroupSize| |lyndonIfCan| |revert| |discreteLog| + |untab| |prefix?| |ratDenom| |mkAnswer| |rightTrim| |completeEval| + |quasiMonic?| |read!| |escape| |univcase| |e02dcf| + |nextPrimitiveNormalPoly| |LowTriBddDenomInv| |shiftLeft| + |completeHensel| |leftTrim| |setfirst!| |pointColor| |rightUnit| + |diff| |errorInfo| |tanQ| |critBonD| |genericRightNorm| |leftLcm| + |safetyMargin| |yellow| |tower| |critpOrder| |logpart| + |extendedResultant| |brillhartIrreducible?| |integrate| + |jvmMethodrefConstantTag| |B1solve| |capacity| |readInt16!| + |complexExpand| |inverseLaplace| |fractRagits| |lyndon| + |numFunEvals3D| |Aleph| |bottom!| |clipPointsDefault| |sqfree| + |printHeader| |box| |totolex| |float| |pointLists| |option?| + |rightDiscriminant| |sumOfDivisors| |sinhIfCan| |curry| |isOr| + |branchPoint?| |gcdprim| |rightExtendedGcd| |baseRDE| |erf| |qroot| + |critT| |d01amf| |car| |deriv| |e01bgf| |showTheIFTable| |rowEchLocal| + |rationalIfCan| |invertibleElseSplit?| |endSubProgram| |infix?| + |basisOfLeftNucloid| |mapCoef| |createPrimitiveElement| |relerror| + |linearDependenceOverZ| |primlimintfrac| |knownInfBasis| + |nextNormalPoly| |f02fjf| |measure2Result| |s17adf| |mask| |units| + |matrix| |exprToUPS| |setEmpty!| |represents| |normalDenom| + |reducedQPowers| |normFactors| |mapExponents| |expt| |palglimint0| + |algebraic?| |dilog| |complexNumeric| |incr| |rational?| |truncate| + |commaSeparate| |content| |outlineRender| |headReduce| + |semicolonSeparate| |LagrangeInterpolation| |innerint| |prem| |sin| + |cylindrical| |elementary| |semiResultantReduitEuclidean| |list?| + |e04gcf| |makeResult| |copies| |e02baf| |factorsOfDegree| |palgRDE| + |cos| |iisec| |kernels| |complexIntegrate| + |solveLinearPolynomialEquation| |yCoord| |tanh2trigh| |latex| + |idealiserMatrix| |certainlySubVariety?| |sincos| |printTypes| |tan| + |littleEndian| |sort| |clearTheFTable| |operator| |physicalLength| + |member?| |radicalEigenvalues| |listexp| |keys| |coth2tanh| |cotIfCan| + |showIntensityFunctions| |changeThreshhold| GE |code| |cot| + |OMmakeConn| |univariate| |getOperator| |stopMusserTrials| |open?| + |pushucoef| |options| |setButtonValue| |sncndn| |over| |e01daf| + |internalLastSubResultant| |sec| |constructor| |random| + |createMultiplicationMatrix| |toseLastSubResultant| |sPol| |build| + |closeComponent| |fortranComplex| |denominator| |leftReducedSystem| + |hi| |inverseIntegralMatrixAtInfinity| |wronskianMatrix| |csc| + |roughBase?| |roughBasicSet| |s14baf| |largest| + |firstUncouplingMatrix| |string| |setEpilogue!| |inRadical?| + |explicitEntries?| |numberOfPrimitivePoly| |anticoord| |asin| |wreath| + |separant| |factor| |linearMatrix| |upperCase| |upDateBranches| + |invmod| |overlap| |cAtanh| |subHeight| |e01sff| |isTimes| |acos| + |lexTriangular| |rightLcm| |sqrt| |factorials| |getRef| |permutations| + |discriminant| |pquo| |schwerpunkt| |redmat| |measure| |whitePoint| + |atan| |lieAlgebra?| |hspace| |real| |cExp| |denomLODE| |generalSqFr| + |dictionary| |useSingleFactorBound| |lambert| |characteristicSerie| + |printStatement| |chebyshevT| |acot| |transform| |laguerre| |imag| + |setelt!| |OMParseError?| |unitNormal| |oblateSpheroidal| |readable?| + |delete| |solveLinearPolynomialEquationByFractions| |elRow2!| + |numberOfFractionalTerms| |asec| |directProduct| |setLabelValue| + |OMputEndAttr| |elColumn2!| |atanhIfCan| |internalZeroSetSplit| + |isNot| |redpps| |outputForm| |complement| |deepestTail| |minIndex| + |gbasis| |e02aef| |setRow!| |purelyAlgebraicLeadingMonomial?| |iitanh| + |tree| |cosh2sech| |find| |hconcat| |basisOfRightAnnihilator| + |paraboloidal| |s17dcf| |tRange| |brace| + |functionIsContinuousAtEndPoints| |padicFraction| |OMconnOutDevice| + |radicalOfLeftTraceForm| |multiple?| |logIfCan| |s19abf| + |generalInfiniteProduct| |setMaxPoints3D| |hdmpToDmp| |destruct| + |var1Steps| |gethi| |prolateSpheroidal| |isQuotient| |remove!| + |mirror| |quadratic| |decompose| |sum| |primPartElseUnitCanonical| + |enterPointData| |iicsc| |groebSolve| |nextIrreduciblePoly| + |rootNormalize| |linearPolynomials| |doublyTransitive?| |binomThmExpt| + |normalDeriv| |rightTraceMatrix| |lexGroebner| |lex| |nextColeman| + |block| |cLog| |secIfCan| |normalElement| |orbits| |doubleComplex?| + |f01rdf| |exprToXXP| |cAcos| |f04jgf| |explimitedint| |gradient| + |generate| |collect| |prepareDecompose| |ricDsolve| |crest| + |coercePreimagesImages| |monomial| |chiSquare| |quadratic?| |resetNew| + |subSet| |closed| |generators| |recoverAfterFail| |concat!| + |resetAttributeButtons| |negative?| |iExquo| |OMcloseConn| + |multivariate| |putGraph| |OMgetSymbol| |taylorIfCan| |head| + |brillhartTrials| |logGamma| |trailingCoefficient| |height| + |incrementBy| |tanintegrate| |irVar| |rotate| + |exprHasLogarithmicWeights| |acsc| |id| |expIfCan| |baseRDEsys| + |variables| |monicDecomposeIfCan| |hitherPlane| |nextPrimitivePoly| + |nand| |numerators| |expand| |indiceSubResultant| + |halfExtendedSubResultantGcd2| |nothing| |sinh| |shrinkable| |lo| + |coerceImages| |smith| |fmecg| |laurentRep| |finiteBound| |unary?| + |cCsch| |tensorProduct| |explogs2trigs| |filterWhile| |compile| + |setrest!| |cosh| |s17akf| |step| |tan2cot| |stronglyReduce| + |acotIfCan| |tanSum| |solveLinearPolynomialEquationByRecursion| + |readUInt8!| |e02dff| |filterUntil| |modTree| |in?| |tanh| |stack| + |stFunc2| |split| |viewWriteAvailable| |pointSizeDefault| |tanh2coth| + |singularitiesOf| |write!| |log10| |select| |cycleEntry| |badNum| + |probablyZeroDim?| |coth| |verticalTab| |LiePoly| |startPolynomial| + |topFortranOutputStack| |returnType!| |unexpand| |matrixConcat3D| + |kovacic| |d01gaf| |bitand| |shade| |selectODEIVPRoutines| |sech| + |scaleRoots| |supDimElseRittWu?| |modularGcdPrimitive| |taylor| + |e02adf| |stoseInvertibleSetreg| |showSummary| |f02xef| |seriesSolve| + |associator| |bitior| |nextSubsetGray| |imagk| |csch| |coordinate| + |simpson| |evaluate| |mapMatrixIfCan| |stirling2| + |univariatePolynomials| |inf| |OMgetEndObject| |asinh| + |exteriorDifferential| |f02bjf| |OMputSymbol| + |semiResultantEuclidean2| |showAttributes| |diag| |isobaric?| + |contains?| |antiCommutative?| |localAbs| |acosh| |aspFilename| + |rightQuotient| |partition| |ode| |linearAssociatedOrder| |reverse!| + |s17ahf| |palgextint0| |indicialEquationAtInfinity| |atanh| + |splitLinear| |deepExpand| |leftTrace| |e04mbf| |hasoln| |makeRecord| + |ip4Address| |csubst| |acoth| |irreducible?| |resize| |nodes| + |coordinates| |changeWeightLevel| |readUInt16!| |cRationalPower| + |localUnquote| |indicialEquation| |open| |asech| |f02axf| |nextPrime| + |typeForm| |rightZero| |rowEchelon| |trigs2explogs| |lflimitedint| + |isExpt| |s21baf| |bracket| |f2st| |PDESolve| |frobenius| |delta| + |subscript| |minimize| |acothIfCan| |signatureAst| |addiag| + |primextendedint| |s18dcf| |multiple| |randomLC| |polygon?| |round| + |uniform| |lookupFunction| |outputBinaryFile| |reflect| |dual| + |basisOfRightNucleus| |applyQuote| |OMencodingUnknown| + |stoseInvertible?reg| |middle| |tail| |exponential| |position!| + |coerceP| |divisor| |distdfact| |rk4a| |operations| + |generalizedEigenvector| |duplicates| |simpleBounds?| |readInt32!| + |getOrder| |cos2sec| |modulus| |LazardQuotient| |initial| |host| + |showTheRoutinesTable| |iiasinh| |connectTo| + |tryFunctionalDecomposition| |OMgetVariable| |d01ajf| |factorAndSplit| + |spherical| |generalPosition| |ruleset| |floor| |hostPlatform| |droot| + |pointData| |c02agf| |algintegrate| |composites| |closed?| + |leftRegularRepresentation| |iterationVar| |backspace| |leftDivide| + |skewSFunction| |lowerCase!| |wordInGenerators| |lifting1| |apply| + |trace2PowMod| |cCoth| |heap| |collectUnder| |rootKerSimp| + |innerEigenvectors| |Hausdorff| |curryLeft| Y |insertBottom!| + |ramified?| |makeUnit| |getSyntaxFormsFromFile| |first| |rank| + |varList| |palgint0| |c06frf| |f01ref| |suchThat| |evaluateInverse| + |nil?| |OMgetAtp| |graphs| |d03edf| |rest| |primextintfrac| + |componentUpperBound| |iiasech| |integralLastSubResultant| + |functionIsOscillatory| |problemPoints| |elRow1!| |clipBoolean| + |makeMulti| |rk4qc| |convergents| |e04jaf| |key| |trapezoidalo| + |OMgetAttr| |lazy?| |s21bcf| |iiasec| |readInt8!| |e01sbf| |ceiling| + |create| |square?| |rational| |primPartElseUnitCanonical!| |hermiteH| + |degreeSubResultant| |bipolarCylindrical| |asimpson| |leftOne| + |listRepresentation| |iisqrt3| |exactQuotient| |complex?| |flagFactor| + |conical| |filename| |UnVectorise| |viewWriteDefault| + |leftExtendedGcd| |addBadValue| |enumerate| |pair?| |duplicates?| + |d02raf| |getMatch| |cyclotomicFactorization| |cSin| |f07adf| |s15aef| + |linear?| |corrPoly| |powerSum| |rootOf| |cTanh| |FormatArabic| + |input| |iFTable| |degreePartition| |parse| |jvmFinal| |monicModulo| + |separateDegrees| |symmetricTensors| |lastSubResultantElseSplit| + |fracPart| |prologue| |odd?| |getGraph| |library| + |semiLastSubResultantEuclidean| |setProperties| |subNodeOf?| |lists| + |cyclicSubmodule| |euclideanSize| |idealiser| |computeInt| + |eigenvalues| |selectfirst| |setScreenResolution3D| |pToDmp| |basis| + |multiEuclidean| |mapDown!| |complexRoots| |rightUnits| |elseBranch| + |slex| |normalizedDivide| |cycle| |geometric| |maxrow| |pastel| + |sinhcosh| |curveColor| |mergeFactors| |PollardSmallFactor| + |principalIdeal| |dAndcExp| |leftExactQuotient| |diagonalProduct| + |functorData| |shiftRoots| |schema| |alphanumeric?| |someBasis| |plus| + |rightFactorCandidate| |mulmod| |vertConcat| |s21bbf| + |groebnerFactorize| |OMputAtp| |factorFraction| |parametersOf| + |iisqrt2| |key?| |edf2df| |fortranCarriageReturn| |arrayStack| + |sequences| |unrankImproperPartitions0| |semiDiscriminantEuclidean| + |value| |sign| |setright!| |column| |wholeRadix| |cdr| |tanIfCan| + |collectQuasiMonic| |critB| |quadraticForm| |numericalOptimization| + |coleman| |divideIfCan| |var2Steps| |singleFactorBound| |factor1| + |heapSort| |nthExponent| |distFact| |elem?| |times| + |toseSquareFreePart| |name| |reset| |symmetricDifference| |neglist| + |shallowCopy| |carriageReturn| |newReduc| |fibonacci| |kind| + |factorOfDegree| |positive?| |expPot| |d02gbf| |idealSimplify| |body| + |incrementKthElement| |expenseOfEvaluation| |e04naf| |putColorInfo| + |phiCoord| |cothIfCan| |setRealSteps| |deepestInitial| |infix| + |aLinear| |s13aaf| |scan| |reindex| |write| |Beta| |listOfLists| + |create3Space| |reduced?| |c06fqf| |rootRadius| |lfinfieldint| |cCos| + |wordsForStrongGenerators| |resultantReduit| |complexEigenvectors| ** + |save| |viewSizeDefault| |writeByte!| |viewDeltaXDefault| + |genericLeftTrace| |permutationRepresentation| |OMgetString| |index| + |f07fef| |dequeue!| |setCondition!| |medialSet| |monom| + |rangePascalTriangle| |cycleSplit!| |selectsecond| |fglmIfCan| |An| + |readUInt32!| |airyBi| |stoseLastSubResultant| |polygamma| |makeprod| + |nativeModuleExtension| |kmax| |rarrow| |showScalarValues| + |ellipticCylindrical| |hostByteOrder| |OMgetBind| |evenlambert| + |twist| |e02gaf| |pair| |getCode| |setUnion| |internal?| + |fixedPointExquo| |removeCoshSq| |assoc| |subscriptedVariables| + |external?| |approximants| |qqq| |extendedIntegrate| |show| |common| + |lfunc| |limitedint| |ptFunc| |ratPoly| |removeSuperfluousCases| + |oddlambert| |clipParametric| |splitNodeOf!| |pdf2ef| |OMconnInDevice| + |quasiRegular| |triangSolve| |safeFloor| |xn| |s17agf| |imagI| + |operators| |applyRules| |linkToFortran| |equality| |coefChoose| + |ipow| |trace| |number?| |sin?| |characteristicSet| + |absolutelyIrreducible?| |gramschmidt| |isEquiv| |trueEqual| + |irreducibleRepresentation| |intChoose| |e02zaf| |signAround| + |reverse| |thetaCoord| |s13adf| |iteratedInitials| |mappingAst| + |mainForm| |eigenvector| |leadingTerm| |possiblyInfinite?| |rotatex| + |genericLeftTraceForm| |predicates| |binding| |resetVariableOrder| + |say| |sayLength| |style| |rootOfIrreduciblePoly| |rischDE| + |showFortranOutputStack| |squareFree| |minPoints| |squareMatrix| + |c06gqf| |qelt| |shape| |makeop| |totalGroebner| |bipolar| + |normDeriv2| |f07aef| |next| |shallowExpand| |extractSplittingLeaf| + |computeBasis| |s21bdf| |nextsousResultant2| |qsetelt| |dflist| + |partialDenominators| |nodeOf?| |firstNumer| |colorDef| |addPoint2| + |lfextendedint| |cosSinInfo| |singRicDE| |queue| |irreducibleFactors| + |xRange| |arguments| |factorSquareFree| |repeatUntilLoop| + |jvmTransient| |goto| |associatorDependence| |setprevious!| |index?| + |constantRight| |f2df| |pushNewContour| |subNode?| |union| |yRange| + |changeNameToObjf| |explicitlyFinite?| |triangulate| |parts| + |palgLODE0| |max| |genericLeftNorm| |f01maf| |coth2trigh| |iiacot| + |optpair| |powern| |zRange| |validExponential| |df2st| + |jvmFieldrefConstantTag| |unaryFunction| |hue| |seriesToOutputForm| + |parents| |exprHasAlgebraicWeight| |search| |controlPanel| + |zeroDimPrimary?| |adaptive?| |bounds| |monomial?| |map!| + |infieldIntegrate| |pade| |axes| |iiacsch| |deref| |characteristic| + |rowEchelonLocal| |e02agf| |cTan| |linearDependence| |flexibleArray| + |inputOutputBinaryFile| |qsetelt!| |maxColIndex| |attributeData| + |ratDsolve| |reciprocalPolynomial| |Nul| |createRandomElement| + |vedf2vef| |nsqfree| |numberOfOperations| |wholeRagits| + |RittWuCompare| |subset?| |xCoord| |imagJ| |identitySquareMatrix| + |nextNormalPrimitivePoly| |iCompose| |basisOfNucleus| |s13acf| + |minPoly| |d01anf| |rightRecip| |mix| |approxNthRoot| |s18aef| + |findCycle| |lSpaceBasis| |divergence| |null?| |datalist| |quotient| + |fortranTypeOf| |halfExtendedResultant2| |wrregime| |mapmult| |prime| + |lyndon?| |replace| |elliptic?| |primintfldpoly| |polynomialZeros| + |numberOfHues| |f04qaf| |rename!| |shiftRight| |se2rfi| + |leftTraceMatrix| |makeCos| |retractable?| |hcrf| |prinshINFO| + |meshPar1Var| |iicot| |stoseInvertibleSet| |prod| |conjunction| + |boundOfCauchy| |selectIntegrationRoutines| |reduction| + |monicRightDivide| |palgint| |inR?| + |removeRoughlyRedundantFactorsInContents| |hasSolution?| |addPoint| + |eigenMatrix| |components| |rubiksGroup| |bezoutResultant| + |algebraicCoefficients?| |minordet| |intermediateResultsIF| |powmod| + |bigEndian| |OMencodingBinary| |getOperands| |stirling1| |legendreP| + |quoted?| |doubleResultant| |power!| |e02akf| |partitions| |initials| + |numberOfNormalPoly| |linearAssociatedLog| |tanNa| |e04dgf| + |pointPlot| |supRittWu?| |morphism| |property| |simplifyPower| + |plusInfinity| |generalizedEigenvectors| |f02wef| |noKaratsuba| + |d02gaf| |dmpToHdmp| |oneDimensionalArray| |btwFact| |leadingIdeal| + |edf2efi| |minusInfinity| |factorSquareFreeByRecursion| + |hypergeometric0F1| |quasiMonicPolynomials| |integralCoordinates| + |makeFR| |horizConcat| |withPredicates| |f04axf| |allRootsOf| + |extractPoint| |exportedOperators| |order| |realRoots| + |symmetricRemainder| |listConjugateBases| |rootSimp| |rdregime| + |inverse| |appendPoint| |inHallBasis?| |nextsubResultant2| + |bezoutMatrix| |primitiveElement| |numberOfComputedEntries| |symbol?| + |mkPrim| |directSum| |eulerE| |even?| |useNagFunctions| + |antiCommutator| |setColumn!| |iibinom| |leadingExponent| |readBytes!| + |selectOrPolynomials| |pattern| |OMputError| |debug| + |mainCoefficients| |prepareSubResAlgo| |plenaryPower| |checkPrecision| + |conjug| |expandTrigProducts| |identity| |iicos| D |atom?| + |alternatingGroup| |deleteProperty!| |plot| |genericLeftDiscriminant| + |generalizedContinuumHypothesisAssumed| |type| |vark| |argument| + |oddInfiniteProduct| |close!| |changeBase| RF2UTS |bernoulli| |d01bbf| + |Lazard2| |isMult| |tanhIfCan| |genericRightDiscriminant| + |horizontalTab| |d02bhf| |expextendedint| |associative?| |region| + |basisOfLeftNucleus| |tableau| |strongGenerators| |dmpToP| + |particularSolution| |concat| |jokerMode| |makeYoungTableau| |indices| + |paren| |graphCurves| |clikeUniv| |rightMinimalPolynomial| |isPower| + |linearAssociatedExp| |genericLeftMinimalPolynomial| |children| + |factorPolynomial| |viewPhiDefault| |factorGroebnerBasis| |pToHdmp| + |increment| |listLoops| |pushdterm| |saturate| |d01fcf| |exponent| + |split!| |clearCache| |changeVar| |zoom| |constant| |lfextlimint| + |stronglyReduced?| |cCosh| |maxIndex| |completeSmith| |testDim| UTS2UP + |size?| |physicalLength!| |c06ebf| |setIntersection| |leftFactor| + |fullDisplay| |pack!| |solveLinearlyOverQ| |youngGroup| + |OMUnknownSymbol?| |triangularSystems| |curryRight| |readLineIfCan!| + |print| |rightGcd| |f01mcf| |string?| |mapdiv| |f01brf| |intensity| + |resolve| |setMinPoints3D| |iicosh| |jvmInterface| |e02daf| + |generalizedContinuumHypothesisAssumed?| |norm| |s20adf| |OMwrite| + |raisePolynomial| |mapExpon| |charpol| |numer| |OMsetEncoding| + |getCurve| |pseudoQuotient| |numericIfCan| |besselK| |binary| + |halfExtendedResultant1| |permutationGroup| |denom| |ptree| + |asinhIfCan| |squareFreePrim| |rightFactorIfCan| |zeroDimPrime?| + |partialFraction| |triangular?| |lquo| |toScale| |invertibleSet| + |tubePlot| |indiceSubResultantEuclidean| |overbar| |endOfFile?| + |commutative?| |eisensteinIrreducible?| |orbit| |title| |pi| + |viewZoomDefault| |besselJ| |entry?| |outputList| |getGoodPrime| + |figureUnits| |pow| |groebnerIdeal| |inverseIntegralMatrix| |child?| + |substitute| |infinity| |ffactor| |associatedEquations| |e02ddf| + |vspace| |transcendent?| |nil| |infinite| |arbitraryExponent| + |approximate| |complex| |shallowMutable| |canonical| |noetherian| + |central| |partiallyOrderedSet| |arbitraryPrecision| + |canonicalsClosed| |noZeroDivisors| |rightUnitary| |leftUnitary| + |additiveValuation| |unitsKnown| |canonicalUnitNormal| + |multiplicativeValuation| |finiteAggregate| |shallowlyMutable| + |commutative|)
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T) ((-102) -2210 (|has| |#2| (-1133)) (|has| |#2| (-1081)) (|has| |#2| (-872)) (|has| |#2| (-817)) (|has| |#2| (-748)) (|has| |#2| (-381)) (|has| |#2| (-376)) (|has| |#2| (-175)) (|has| |#2| (-133)) (|has| |#2| (-102)) (|has| |#2| (-25)) (|has| |#2| (-23)) (|has| |#2| (-21))) ((-111 |#2| |#2|) -2210 (|has| |#2| (-1081)) (|has| |#2| (-376)) (|has| |#2| (-175))) ((-133) -2210 (|has| |#2| (-1081)) (|has| |#2| (-817)) (|has| |#2| (-376)) (|has| |#2| (-175)) (|has| |#2| (-133)) (|has| |#2| (-21))) ((-635 #0=(-421 (-560))) -12 (|has| |#2| (-1070 (-421 (-560)))) (|has| |#2| (-1133))) ((-635 (-560)) -2210 (|has| |#2| (-1081)) (-12 (|has| |#2| (-1070 (-560))) (|has| |#2| (-1133)))) ((-635 |#2|) |has| |#2| (-1133)) ((-632 (-888)) -2210 (|has| |#2| (-1133)) (|has| |#2| (-1081)) (|has| |#2| (-872)) (|has| |#2| (-817)) (|has| |#2| (-748)) (|has| |#2| (-381)) (|has| |#2| (-376)) (|has| |#2| (-175)) (|has| |#2| (-632 (-888))) (|has| |#2| (-133)) (|has| |#2| (-25)) (|has| |#2| (-23)) (|has| |#2| (-21))) ((-632 (-1299 |#2|)) . 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T) ((-528 |#2| |#2|) -12 (|has| |#2| (-321 |#2|)) (|has| |#2| (-1133))) ((-668 (-560)) -2210 (|has| |#2| (-1081)) (|has| |#2| (-376)) (|has| |#2| (-175)) (|has| |#2| (-21))) ((-668 |#2|) -2210 (|has| |#2| (-1081)) (|has| |#2| (-748)) (|has| |#2| (-376)) (|has| |#2| (-175))) ((-668 $) |has| |#2| (-1081)) ((-670 #2=(-560)) -12 (|has| |#2| (-660 (-560))) (|has| |#2| (-1081))) ((-670 |#2|) -2210 (|has| |#2| (-1081)) (|has| |#2| (-376)) (|has| |#2| (-175))) ((-670 $) |has| |#2| (-1081)) ((-662 |#2|) -2210 (|has| |#2| (-748)) (|has| |#2| (-376)) (|has| |#2| (-175))) ((-660 #2#) -12 (|has| |#2| (-660 (-560))) (|has| |#2| (-1081))) ((-660 |#2|) |has| |#2| (-1081)) ((-739 |#2|) -2210 (|has| |#2| (-376)) (|has| |#2| (-175))) ((-748) |has| |#2| (-1081)) ((-816) |has| |#2| (-817)) ((-817) |has| |#2| (-817)) ((-818) |has| |#2| (-817)) ((-821) |has| |#2| (-817)) ((-872) -2210 (|has| |#2| (-872)) (|has| |#2| (-817))) ((-875) -2210 (|has| |#2| (-872)) (|has| |#2| (-817))) ((-922 $ #3=(-1209)) -2210 (-12 (|has| |#2| (-930 (-1209))) (|has| |#2| (-1081))) (-12 (|has| |#2| (-928 (-1209))) (|has| |#2| (-1081)))) ((-928 (-1209)) -12 (|has| |#2| (-928 (-1209))) (|has| |#2| (-1081))) ((-930 #3#) -2210 (-12 (|has| |#2| (-930 (-1209))) (|has| |#2| (-1081))) (-12 (|has| |#2| (-928 (-1209))) (|has| |#2| (-1081)))) ((-1070 #0#) -12 (|has| |#2| (-1070 (-421 (-560)))) (|has| |#2| (-1133))) ((-1070 (-560)) -12 (|has| |#2| (-1070 (-560))) (|has| |#2| (-1133))) ((-1070 |#2|) |has| |#2| (-1133)) ((-1083 |#2|) -2210 (|has| |#2| (-1081)) (|has| |#2| (-748)) (|has| |#2| (-376)) (|has| |#2| (-175))) ((-1088 |#2|) -2210 (|has| |#2| (-1081)) (|has| |#2| (-376)) (|has| |#2| (-175))) ((-1081) |has| |#2| (-1081)) ((-1089) |has| |#2| (-1081)) ((-1144) |has| |#2| (-1081)) ((-1133) -2210 (|has| |#2| (-1133)) (|has| |#2| (-1081)) (|has| |#2| (-872)) (|has| |#2| (-817)) (|has| |#2| (-748)) (|has| |#2| (-381)) (|has| |#2| (-376)) (|has| |#2| (-175)) (|has| |#2| (-133)) (|has| |#2| (-25)) (|has| |#2| (-23)) (|has| |#2| (-21))) ((-1249) . 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T) ((-23) . T) ((-25) . T) ((-38 |#1|) . T) ((-102) . T) ((-111 |#1| |#1|) . T) ((-133) . T) ((-147) |has| |#1| (-147)) ((-149) |has| |#1| (-149)) ((-635 (-560)) . T) ((-635 |#1|) . T) ((-632 (-888)) . T) ((-383 |#1| |#2|) . T) ((-668 (-560)) . T) ((-668 |#1|) . T) ((-668 $) . T) ((-670 |#1|) . T) ((-670 $) . T) ((-662 |#1|) . T) ((-739 |#1|) . T) ((-748) . T) ((-1083 |#1|) . T) ((-1088 |#1|) . T) ((-1081) . T) ((-1089) . T) ((-1144) . T) ((-1133) . T) ((-1249) . 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T) ((-310) . T) ((-376) |has| |#1| (-571)) ((-390 |#1|) |has| |#1| (-1081)) ((-414 |#1|) . T) ((-426 |#1|) . T) ((-466) |has| |#1| (-571)) ((-487) |has| |#1| (-487)) ((-528 (-630 $) $) . T) ((-528 $ $) . 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range is infinite") (|:| |bothInfinite| "Both top and bottom points are infinite") (|:| |notEvaluated| "Range not yet evaluated"))))))) $)) (-15 -2715 ((-2 (|:| |endPointContinuity| (-3 (|:| |continuous| "Continuous at the end points") (|:| |lowerSingular| "There is a singularity at the lower end point") (|:| |upperSingular| "There is a singularity at the upper end point") (|:| |bothSingular| "There are singularities at both end points") (|:| |notEvaluated| "End point continuity not yet evaluated"))) (|:| |singularitiesStream| (-3 (|:| |str| (-1187 (-229))) (|:| |notEvaluated| "Internal singularities not yet evaluated"))) (|:| -4389 (-3 (|:| |finite| "The range is finite") (|:| |lowerInfinite| "The bottom of range is infinite") (|:| |upperInfinite| "The top of range is infinite") (|:| |bothInfinite| "Both top and bottom points are infinite") (|:| |notEvaluated| "Range not yet evaluated")))) (-2 (|:| |var| (-1209)) (|:| |fn| (-326 (-229))) (|:| -4389 (-1121 (-866 (-229)))) (|:| |abserr| (-229)) (|:| |relerr| (-229))))))) (T -574)) -((-2715 (*1 *2 *3) (-12 (-5 *3 (-2 (|:| |var| (-1209)) (|:| |fn| (-326 (-229))) (|:| -4389 (-1121 (-866 (-229)))) (|:| |abserr| (-229)) (|:| |relerr| (-229)))) (-5 *2 (-2 (|:| |endPointContinuity| (-3 (|:| |continuous| "Continuous at the end points") (|:| |lowerSingular| "There is a singularity at the lower end point") (|:| |upperSingular| "There is a singularity at the upper end point") (|:| |bothSingular| "There are singularities at both end points") (|:| |notEvaluated| "End point continuity not yet evaluated"))) (|:| |singularitiesStream| (-3 (|:| |str| (-1187 (-229))) (|:| |notEvaluated| "Internal singularities not yet evaluated"))) (|:| -4389 (-3 (|:| |finite| "The range is finite") (|:| |lowerInfinite| "The bottom of range is infinite") (|:| |upperInfinite| "The top of range is infinite") (|:| |bothInfinite| "Both top and bottom points are infinite") (|:| |notEvaluated| "Range not yet evaluated"))))) (-5 *1 (-574)))) (-2588 (*1 *2 *1) (-12 (-5 *2 (-663 (-2 (|:| -3837 (-2 (|:| |var| (-1209)) (|:| |fn| (-326 (-229))) (|:| -4389 (-1121 (-866 (-229)))) (|:| |abserr| (-229)) (|:| |relerr| (-229)))) (|:| -2715 (-2 (|:| |endPointContinuity| (-3 (|:| |continuous| "Continuous at the end points") (|:| |lowerSingular| "There is a singularity at the lower end point") (|:| |upperSingular| "There is a singularity at the upper end point") (|:| |bothSingular| "There are singularities at both end points") (|:| |notEvaluated| "End point continuity not yet evaluated"))) (|:| |singularitiesStream| (-3 (|:| |str| (-1187 (-229))) (|:| |notEvaluated| "Internal singularities not yet evaluated"))) (|:| -4389 (-3 (|:| |finite| "The range is finite") (|:| |lowerInfinite| "The bottom of range is infinite") (|:| |upperInfinite| "The top of range is infinite") (|:| |bothInfinite| "Both top and bottom points are infinite") (|:| |notEvaluated| "Range not yet evaluated")))))))) (-5 *1 (-574)))) (-3682 (*1 *2 *3) (|partial| -12 (-5 *3 (-2 (|:| |var| 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(-1121 (-866 (-229)))) (|:| |abserr| (-229)) (|:| |relerr| (-229)))) (|:| -2715 (-2 (|:| |endPointContinuity| (-3 (|:| |continuous| "Continuous at the end points") (|:| |lowerSingular| "There is a singularity at the lower end point") (|:| |upperSingular| "There is a singularity at the upper end point") (|:| |bothSingular| "There are singularities at both end points") (|:| |notEvaluated| "End point continuity not yet evaluated"))) (|:| |singularitiesStream| (-3 (|:| |str| (-1187 (-229))) (|:| |notEvaluated| "Internal singularities not yet evaluated"))) (|:| -4389 (-3 (|:| |finite| "The range is finite") (|:| |lowerInfinite| "The bottom of range is infinite") (|:| |upperInfinite| "The top of range is infinite") (|:| |bothInfinite| "Both top and bottom points are infinite") (|:| |notEvaluated| "Range not yet evaluated"))))))) (-5 *1 (-574)))) (-3037 (*1 *1 *2) (-12 (-5 *2 (-663 (-2 (|:| -3837 (-2 (|:| |var| (-1209)) (|:| |fn| (-326 (-229))) (|:| -4389 (-1121 (-866 (-229)))) (|:| |abserr| 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|lowerInfinite| "The bottom of range is infinite") (|:| |upperInfinite| "The top of range is infinite") (|:| |bothInfinite| "Both top and bottom points are infinite") (|:| |notEvaluated| "Range not yet evaluated"))))))))) (-15 -3826 ($ (-2 (|:| -3837 (-2 (|:| |var| (-1209)) (|:| |fn| (-326 (-229))) (|:| -4389 (-1121 (-866 (-229)))) (|:| |abserr| (-229)) (|:| |relerr| (-229)))) (|:| -2715 (-2 (|:| |endPointContinuity| (-3 (|:| |continuous| "Continuous at the end points") (|:| |lowerSingular| "There is a singularity at the lower end point") (|:| |upperSingular| "There is a singularity at the upper end point") (|:| |bothSingular| "There are singularities at both end points") (|:| |notEvaluated| "End point continuity not yet evaluated"))) (|:| |singularitiesStream| (-3 (|:| |str| (-1187 (-229))) (|:| |notEvaluated| "Internal singularities not yet evaluated"))) (|:| -4389 (-3 (|:| |finite| "The range is finite") (|:| |lowerInfinite| "The bottom of range is infinite") (|:| |upperInfinite| "The top of range is infinite") (|:| |bothInfinite| "Both top and bottom points are infinite") (|:| |notEvaluated| "Range not yet evaluated")))))))) (-15 -3682 ((-3 (-2 (|:| |endPointContinuity| (-3 (|:| |continuous| "Continuous at the end points") (|:| |lowerSingular| "There is a singularity at the lower end point") (|:| |upperSingular| "There is a singularity at the upper end point") (|:| |bothSingular| "There are singularities at both end points") (|:| |notEvaluated| "End point continuity not yet evaluated"))) (|:| |singularitiesStream| (-3 (|:| |str| (-1187 (-229))) (|:| |notEvaluated| "Internal singularities not yet evaluated"))) (|:| -4389 (-3 (|:| |finite| "The range is finite") (|:| |lowerInfinite| "The bottom of range is infinite") (|:| |upperInfinite| "The top of range is infinite") (|:| |bothInfinite| "Both top and bottom points are infinite") (|:| |notEvaluated| "Range not yet evaluated")))) "failed") (-2 (|:| |var| (-1209)) (|:| |fn| (-326 (-229))) (|:| -4389 (-1121 (-866 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((-2 (|:| |endPointContinuity| (-3 (|:| |continuous| "Continuous at the end points") (|:| |lowerSingular| "There is a singularity at the lower end point") (|:| |upperSingular| "There is a singularity at the upper end point") (|:| |bothSingular| "There are singularities at both end points") (|:| |notEvaluated| "End point continuity not yet evaluated"))) (|:| |singularitiesStream| (-3 (|:| |str| (-1187 (-229))) (|:| |notEvaluated| "Internal singularities not yet evaluated"))) (|:| -4389 (-3 (|:| |finite| "The range is finite") (|:| |lowerInfinite| "The bottom of range is infinite") (|:| |upperInfinite| "The top of range is infinite") (|:| |bothInfinite| "Both top and bottom points are infinite") (|:| |notEvaluated| "Range not yet evaluated")))) (-2 (|:| |var| (-1209)) (|:| |fn| (-326 (-229))) (|:| -4389 (-1121 (-866 (-229)))) (|:| |abserr| (-229)) (|:| |relerr| (-229)))))) -((-3390 (((-1203 (-421 (-1203 |#2|))) |#2| (-630 |#2|) (-630 |#2|) (-1203 |#2|)) 35 T ELT)) (-3914 (((-3 (-2 (|:| 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T) ((-23) . T) ((-47 |#1| #0=(-560)) . T) ((-25) . T) ((-38 #1=(-421 (-560))) -2210 (|has| |#1| (-376)) (|has| |#1| (-38 (-421 (-560))))) ((-38 |#1|) |has| |#1| (-175)) ((-38 |#2|) |has| |#1| (-376)) ((-38 $) -2210 (|has| |#1| (-571)) (|has| |#1| (-376))) ((-35) |has| |#1| (-38 (-421 (-560)))) ((-95) |has| |#1| (-38 (-421 (-560)))) ((-102) . T) ((-111 #1# #1#) -2210 (|has| |#1| (-376)) (|has| |#1| (-38 (-421 (-560))))) ((-111 |#1| |#1|) . T) ((-111 |#2| |#2|) |has| |#1| (-376)) ((-111 $ $) -2210 (|has| |#1| (-571)) (|has| |#1| (-376)) (|has| |#1| (-175))) ((-133) . T) ((-147) -2210 (-12 (|has| |#1| (-376)) (|has| |#2| (-147))) (|has| |#1| (-147))) ((-149) -2210 (-12 (|has| |#1| (-376)) (|has| |#2| (-149))) (|has| |#1| (-149))) ((-635 #1#) -2210 (|has| |#1| (-376)) (|has| |#1| (-38 (-421 (-560))))) ((-635 (-560)) . T) ((-635 #2=(-1209)) -12 (|has| |#1| (-376)) (|has| |#2| (-1070 (-1209)))) ((-635 |#1|) |has| |#1| (-175)) ((-635 |#2|) . T) ((-635 $) -2210 (|has| |#1| (-571)) (|has| |#1| (-376))) ((-632 (-888)) . T) ((-175) -2210 (|has| |#1| (-571)) (|has| |#1| (-376)) (|has| |#1| (-175))) ((-633 (-229)) -12 (|has| |#1| (-376)) (|has| |#2| (-1052))) ((-633 (-391)) -12 (|has| |#1| (-376)) (|has| |#2| (-1052))) ((-633 (-549)) -12 (|has| |#1| (-376)) (|has| |#2| (-633 (-549)))) ((-633 (-916 (-391))) -12 (|has| |#1| (-376)) (|has| |#2| (-633 (-916 (-391))))) ((-633 (-916 (-560))) -12 (|has| |#1| (-376)) (|has| |#2| (-633 (-916 (-560))))) ((-236 $) -2210 (-12 (|has| |#1| (-376)) (|has| |#2| (-239))) (-12 (|has| |#1| (-376)) (|has| |#2| (-240))) (|has| |#1| (-15 * (|#1| (-560) |#1|)))) ((-234 |#2|) |has| |#1| (-376)) ((-240) -2210 (-12 (|has| |#1| (-376)) (|has| |#2| (-240))) (|has| |#1| (-15 * (|#1| (-560) |#1|)))) ((-239) -2210 (-12 (|has| |#1| (-376)) (|has| |#2| (-239))) (-12 (|has| |#1| (-376)) (|has| |#2| (-240))) (|has| |#1| (-15 * (|#1| (-560) |#1|)))) ((-274 |#2|) |has| |#1| (-376)) ((-250) |has| |#1| (-376)) ((-296) |has| |#1| (-38 (-421 (-560)))) ((-298 #0# |#1|) . T) ((-298 |#2| $) -12 (|has| |#1| (-376)) (|has| |#2| (-298 |#2| |#2|))) ((-298 $ $) |has| (-560) (-1144)) ((-302) -2210 (|has| |#1| (-571)) (|has| |#1| (-376))) ((-319) |has| |#1| (-376)) ((-321 |#2|) -12 (|has| |#1| (-376)) (|has| |#2| (-321 |#2|))) ((-376) |has| |#1| (-376)) ((-351 |#2|) |has| |#1| (-376)) ((-390 |#2|) |has| |#1| (-376)) ((-414 |#2|) |has| |#1| (-376)) ((-466) |has| |#1| (-376)) ((-507) |has| |#1| (-38 (-421 (-560)))) ((-528 (-1209) |#2|) -12 (|has| |#1| (-376)) (|has| |#2| (-528 (-1209) |#2|))) ((-528 |#2| |#2|) -12 (|has| |#1| (-376)) (|has| |#2| (-321 |#2|))) ((-571) -2210 (|has| |#1| (-571)) (|has| |#1| (-376))) ((-668 #1#) -2210 (|has| |#1| (-376)) (|has| |#1| (-38 (-421 (-560))))) ((-668 (-560)) . T) ((-668 |#1|) . T) ((-668 |#2|) |has| |#1| (-376)) ((-668 $) . T) ((-670 #1#) -2210 (|has| |#1| (-376)) (|has| |#1| (-38 (-421 (-560))))) ((-670 #3=(-560)) -12 (|has| |#1| (-376)) (|has| |#2| (-660 (-560)))) ((-670 |#1|) . T) ((-670 |#2|) |has| |#1| (-376)) ((-670 $) . T) ((-662 #1#) -2210 (|has| |#1| (-376)) (|has| |#1| (-38 (-421 (-560))))) ((-662 |#1|) |has| |#1| (-175)) ((-662 |#2|) |has| |#1| (-376)) ((-662 $) -2210 (|has| |#1| (-571)) (|has| |#1| (-376))) ((-660 #3#) -12 (|has| |#1| (-376)) (|has| |#2| (-660 (-560)))) ((-660 |#2|) |has| |#1| (-376)) ((-739 #1#) -2210 (|has| |#1| (-376)) (|has| |#1| (-38 (-421 (-560))))) ((-739 |#1|) |has| |#1| (-175)) ((-739 |#2|) |has| |#1| (-376)) ((-739 $) -2210 (|has| |#1| (-571)) (|has| |#1| (-376))) ((-748) . T) ((-814) -12 (|has| |#1| (-376)) (|has| |#2| (-844))) ((-816) -12 (|has| |#1| (-376)) (|has| |#2| (-844))) ((-818) -12 (|has| |#1| (-376)) (|has| |#2| (-844))) ((-821) -12 (|has| |#1| (-376)) (|has| |#2| (-844))) ((-844) -12 (|has| |#1| (-376)) (|has| |#2| (-844))) ((-871) -12 (|has| |#1| (-376)) (|has| |#2| (-844))) ((-872) -2210 (-12 (|has| |#1| (-376)) (|has| |#2| (-872))) (-12 (|has| |#1| (-376)) (|has| |#2| (-844)))) ((-875) -2210 (-12 (|has| |#1| (-376)) (|has| |#2| (-872))) (-12 (|has| |#1| (-376)) (|has| |#2| (-844)))) ((-922 $ #4=(-1209)) -2210 (-12 (|has| |#1| (-376)) (|has| |#2| (-930 (-1209)))) (-12 (|has| |#1| (-376)) (|has| |#2| (-928 (-1209)))) (-12 (|has| |#1| (-15 * (|#1| (-560) |#1|))) (|has| |#1| (-928 (-1209))))) ((-928 (-1209)) -2210 (-12 (|has| |#1| (-376)) (|has| |#2| (-928 (-1209)))) (-12 (|has| |#1| (-15 * (|#1| (-560) |#1|))) (|has| |#1| (-928 (-1209))))) ((-930 #4#) -2210 (-12 (|has| |#1| (-376)) (|has| |#2| (-930 (-1209)))) (-12 (|has| |#1| (-376)) (|has| |#2| (-928 (-1209)))) (-12 (|has| |#1| (-15 * (|#1| (-560) |#1|))) (|has| |#1| (-928 (-1209))))) ((-912 (-391)) -12 (|has| |#1| (-376)) (|has| |#2| (-912 (-391)))) ((-912 (-560)) -12 (|has| |#1| (-376)) (|has| |#2| (-912 (-560)))) ((-910 |#2|) |has| |#1| (-376)) ((-940) -12 (|has| |#1| (-376)) (|has| |#2| (-940))) ((-1005 |#1| #0# (-1114)) . T) ((-951) |has| |#1| (-376)) ((-1023 |#2|) |has| |#1| (-376)) ((-1034) |has| |#1| (-38 (-421 (-560)))) ((-1052) -12 (|has| |#1| (-376)) (|has| |#2| (-1052))) ((-1070 (-421 (-560))) -12 (|has| |#1| (-376)) (|has| |#2| (-1070 (-560)))) ((-1070 (-560)) -12 (|has| |#1| (-376)) (|has| |#2| (-1070 (-560)))) ((-1070 #2#) -12 (|has| |#1| (-376)) (|has| |#2| (-1070 (-1209)))) ((-1070 |#2|) . T) ((-1083 #1#) -2210 (|has| |#1| (-376)) (|has| |#1| (-38 (-421 (-560))))) ((-1083 |#1|) . T) ((-1083 |#2|) |has| |#1| (-376)) ((-1083 $) -2210 (|has| |#1| (-571)) (|has| |#1| (-376)) (|has| |#1| (-175))) ((-1088 #1#) -2210 (|has| |#1| (-376)) (|has| |#1| (-38 (-421 (-560))))) ((-1088 |#1|) . T) ((-1088 |#2|) |has| |#1| (-376)) ((-1088 $) -2210 (|has| |#1| (-571)) (|has| |#1| (-376)) (|has| |#1| (-175))) ((-1081) . T) ((-1089) . T) ((-1144) . T) ((-1133) . T) ((-1184) -12 (|has| |#1| (-376)) (|has| |#2| (-1184))) ((-1235) |has| |#1| (-38 (-421 (-560)))) ((-1238) |has| |#1| (-38 (-421 (-560)))) ((-1249) . 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T) ((-23) . T) ((-47 |#1| #0=(-793)) . T) ((-25) . T) ((-38 #1=(-421 (-560))) |has| |#1| (-38 (-421 (-560)))) ((-38 |#1|) |has| |#1| (-175)) ((-38 $) -2210 (|has| |#1| (-940)) (|has| |#1| (-571)) (|has| |#1| (-466)) (|has| |#1| (-376))) ((-102) . T) ((-111 #1# #1#) |has| |#1| (-38 (-421 (-560)))) ((-111 |#1| |#1|) . T) ((-111 $ $) -2210 (|has| |#1| (-940)) (|has| |#1| (-571)) (|has| |#1| (-466)) (|has| |#1| (-376)) (|has| |#1| (-175))) ((-133) . T) ((-147) |has| |#1| (-147)) ((-149) |has| |#1| (-149)) ((-635 #1#) -2210 (|has| |#1| (-1070 (-421 (-560)))) (|has| |#1| (-38 (-421 (-560))))) ((-635 (-560)) . T) ((-635 #2=(-1114)) . T) ((-635 |#1|) . T) ((-635 $) -2210 (|has| |#1| (-940)) (|has| |#1| (-571)) (|has| |#1| (-466)) (|has| |#1| (-376))) ((-632 (-888)) . 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T) ((-571) -2210 (|has| |#1| (-940)) (|has| |#1| (-571)) (|has| |#1| (-466)) (|has| |#1| (-376))) ((-668 #1#) |has| |#1| (-38 (-421 (-560)))) ((-668 (-560)) . T) ((-668 |#1|) . T) ((-668 $) . T) ((-670 #1#) |has| |#1| (-38 (-421 (-560)))) ((-670 #3=(-560)) |has| |#1| (-660 (-560))) ((-670 |#1|) . T) ((-670 $) . T) ((-662 #1#) |has| |#1| (-38 (-421 (-560)))) ((-662 |#1|) |has| |#1| (-175)) ((-662 $) -2210 (|has| |#1| (-940)) (|has| |#1| (-571)) (|has| |#1| (-466)) (|has| |#1| (-376))) ((-660 #3#) |has| |#1| (-660 (-560))) ((-660 |#1|) . T) ((-739 #1#) |has| |#1| (-38 (-421 (-560)))) ((-739 |#1|) |has| |#1| (-175)) ((-739 $) -2210 (|has| |#1| (-940)) (|has| |#1| (-571)) (|has| |#1| (-466)) (|has| |#1| (-376))) ((-748) . T) ((-922 $ #2#) . T) ((-922 $ #4=(-1209)) -2210 (|has| |#1| (-930 (-1209))) (|has| |#1| (-928 (-1209)))) ((-928 #2#) . T) ((-928 (-1209)) |has| |#1| (-928 (-1209))) ((-930 #2#) . T) ((-930 #4#) -2210 (|has| |#1| (-930 (-1209))) (|has| |#1| (-928 (-1209)))) ((-912 (-391)) -12 (|has| (-1114) (-912 (-391))) (|has| |#1| (-912 (-391)))) ((-912 (-560)) -12 (|has| (-1114) (-912 (-560))) (|has| |#1| (-912 (-560)))) ((-980 |#1| #0# #2#) . T) ((-940) |has| |#1| (-940)) ((-951) |has| |#1| (-376)) ((-1070 (-421 (-560))) |has| |#1| (-1070 (-421 (-560)))) ((-1070 (-560)) |has| |#1| (-1070 (-560))) ((-1070 #2#) . T) ((-1070 |#1|) . T) ((-1083 #1#) |has| |#1| (-38 (-421 (-560)))) ((-1083 |#1|) . T) ((-1083 $) -2210 (|has| |#1| (-940)) (|has| |#1| (-571)) (|has| |#1| (-466)) (|has| |#1| (-376)) (|has| |#1| (-175))) ((-1088 #1#) |has| |#1| (-38 (-421 (-560)))) ((-1088 |#1|) . T) ((-1088 $) -2210 (|has| |#1| (-940)) (|has| |#1| (-571)) (|has| |#1| (-466)) (|has| |#1| (-376)) (|has| |#1| (-175))) ((-1081) . T) ((-1089) . T) ((-1144) . T) ((-1133) . T) ((-1184) |has| |#1| (-1184)) ((-1249) . 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NIL) -8 NIL NIL NIL) (-1311 3418936 3419210 3419280 "WHILEAST" 3419340 T WHILEAST (NIL) -8 NIL NIL NIL) (-1310 3418348 3418653 3418747 "WHEREAST" 3418864 T WHEREAST (NIL) -8 NIL NIL NIL) (-1309 3417222 3417432 3417727 "WFFINTBS" 3418145 NIL WFFINTBS (NIL T T T T) -7 NIL NIL NIL) (-1308 3415090 3415553 3416015 "WEIER" 3416794 NIL WEIER (NIL T) -7 NIL NIL NIL) (-1307 3414014 3414572 3414614 "VSPACE" 3414750 NIL VSPACE (NIL T) -9 NIL 3414824 NIL) (-1306 3413846 3413879 3413970 "VSPACE-" 3413975 NIL VSPACE- (NIL T T) -8 NIL NIL NIL) (-1305 3413643 3413697 3413765 "VOID" 3413800 T VOID (NIL) -8 NIL NIL NIL) (-1304 3409911 3410706 3411443 "VIEWDEF" 3412928 T VIEWDEF (NIL) -7 NIL NIL NIL) (-1303 3398855 3401459 3403632 "VIEW3D" 3407760 T VIEW3D (NIL) -8 NIL NIL NIL) (-1302 3390872 3392766 3394345 "VIEW2D" 3397298 T VIEW2D (NIL) -8 NIL NIL NIL) (-1301 3388972 3389367 3389773 "VIEW" 3390488 T VIEW (NIL) -7 NIL NIL NIL) (-1300 3387525 3387808 3388126 "VECTOR2" 3388702 NIL VECTOR2 (NIL T T) -7 NIL NIL NIL) (-1299 3382431 3387295 3387387 "VECTOR" 3387468 NIL VECTOR (NIL T) -8 NIL NIL NIL) (-1298 3375376 3380135 3380178 "VECTCAT" 3381173 NIL VECTCAT (NIL T) -9 NIL 3381760 NIL) (-1297 3374318 3374644 3375034 "VECTCAT-" 3375039 NIL VECTCAT- (NIL T T) -8 NIL NIL NIL) (-1296 3373724 3373969 3374089 "VARIABLE" 3374233 NIL VARIABLE (NIL NIL) -8 NIL NIL NIL) (-1295 3373657 3373662 3373692 "UTYPE" 3373697 T UTYPE (NIL) -9 NIL NIL NIL) (-1294 3372465 3372641 3372903 "UTSODETL" 3373483 NIL UTSODETL (NIL T T T T) -7 NIL NIL NIL) (-1293 3369857 3370365 3370889 "UTSODE" 3372006 NIL UTSODE (NIL T T) -7 NIL NIL NIL) (-1292 3359867 3365790 3365833 "UTSCAT" 3366945 NIL UTSCAT (NIL T) -9 NIL 3367703 NIL) (-1291 3356993 3357937 3358926 "UTSCAT-" 3358931 NIL UTSCAT- (NIL T T) -8 NIL NIL NIL) (-1290 3356614 3356663 3356796 "UTS2" 3356944 NIL UTS2 (NIL T T T T) -7 NIL NIL NIL) (-1289 3347931 3354375 3354855 "UTS" 3356192 NIL UTS (NIL T NIL NIL) -8 NIL NIL NIL) (-1288 3341798 3344741 3344784 "URAGG" 3346854 NIL URAGG (NIL T) -9 NIL 3347577 NIL) (-1287 3338521 3339600 3340723 "URAGG-" 3340728 NIL URAGG- (NIL T T) -8 NIL NIL NIL) (-1286 3333897 3337156 3337621 "UPXSSING" 3338185 NIL UPXSSING (NIL T T NIL NIL) -8 NIL NIL NIL) (-1285 3326326 3333801 3333873 "UPXSCONS" 3333878 NIL UPXSCONS (NIL T T) -8 NIL NIL NIL) (-1284 3315084 3322528 3322590 "UPXSCCA" 3323164 NIL UPXSCCA (NIL T T) -9 NIL 3323397 NIL) (-1283 3314704 3314807 3314981 "UPXSCCA-" 3314986 NIL UPXSCCA- (NIL T T T) -8 NIL NIL NIL) (-1282 3303362 3310531 3310574 "UPXSCAT" 3311222 NIL UPXSCAT (NIL T) -9 NIL 3311831 NIL) (-1281 3302786 3302871 3303050 "UPXS2" 3303277 NIL UPXS2 (NIL T T NIL NIL NIL NIL) -7 NIL NIL NIL) (-1280 3294278 3302168 3302432 "UPXS" 3302580 NIL UPXS (NIL T NIL NIL) -8 NIL NIL NIL) (-1279 3292914 3293185 3293536 "UPSQFREE" 3294021 NIL UPSQFREE (NIL T T) -7 NIL NIL NIL) (-1278 3285745 3289180 3289235 "UPSCAT" 3290315 NIL UPSCAT (NIL T T) -9 NIL 3291081 NIL) (-1277 3284901 3285156 3285483 "UPSCAT-" 3285488 NIL UPSCAT- (NIL T T T) -8 NIL NIL NIL) (-1276 3284522 3284571 3284704 "UPOLYC2" 3284852 NIL UPOLYC2 (NIL T T T T) -7 NIL NIL NIL) (-1275 3268670 3277649 3277692 "UPOLYC" 3279793 NIL UPOLYC (NIL T) -9 NIL 3281014 NIL) (-1274 3259539 3262438 3265578 "UPOLYC-" 3265583 NIL UPOLYC- (NIL T T) -8 NIL NIL NIL) (-1273 3258860 3258985 3259149 "UPMP" 3259428 NIL UPMP (NIL T T) -7 NIL NIL NIL) (-1272 3258407 3258494 3258633 "UPDIVP" 3258773 NIL UPDIVP (NIL T T) -7 NIL NIL NIL) (-1271 3256945 3257224 3257540 "UPDECOMP" 3258156 NIL UPDECOMP (NIL T T) -7 NIL NIL NIL) (-1270 3256158 3256288 3256474 "UPCDEN" 3256829 NIL UPCDEN (NIL T T T) -7 NIL NIL NIL) (-1269 3255671 3255746 3255895 "UP2" 3256083 NIL UP2 (NIL NIL T NIL T) -7 NIL NIL NIL) (-1268 3246267 3255354 3255483 "UP" 3255590 NIL UP (NIL NIL T) -8 NIL NIL NIL) (-1267 3245472 3245609 3245814 "UNISEG2" 3246110 NIL UNISEG2 (NIL T T) -7 NIL NIL NIL) (-1266 3243825 3244676 3244953 "UNISEG" 3245230 NIL UNISEG (NIL T) -8 NIL NIL NIL) (-1265 3242867 3243065 3243291 "UNIFACT" 3243641 NIL UNIFACT (NIL T) -7 NIL NIL NIL) (-1264 3229598 3242771 3242843 "ULSCONS" 3242848 NIL ULSCONS (NIL T T) -8 NIL NIL NIL) (-1263 3209415 3222678 3222740 "ULSCCAT" 3223378 NIL ULSCCAT (NIL T T) -9 NIL 3223667 NIL) (-1262 3208411 3208710 3209098 "ULSCCAT-" 3209103 NIL ULSCCAT- (NIL T T T) -8 NIL NIL NIL) (-1261 3196866 3203957 3204000 "ULSCAT" 3204863 NIL ULSCAT (NIL T) -9 NIL 3205594 NIL) (-1260 3196290 3196375 3196554 "ULS2" 3196781 NIL ULS2 (NIL T T NIL NIL NIL NIL) -7 NIL NIL NIL) (-1259 3178121 3195602 3195844 "ULS" 3196106 NIL ULS (NIL T NIL NIL) -8 NIL NIL NIL) (-1258 3177040 3177740 3177854 "UINT8" 3177965 T UINT8 (NIL) -8 NIL NIL 3178057) (-1257 3175958 3176658 3176772 "UINT64" 3176883 T UINT64 (NIL) -8 NIL NIL 3176975) (-1256 3174876 3175576 3175690 "UINT32" 3175801 T UINT32 (NIL) -8 NIL NIL 3175893) (-1255 3173794 3174494 3174608 "UINT16" 3174719 T UINT16 (NIL) -8 NIL NIL 3174811) (-1254 3171873 3173040 3173070 "UFD" 3173282 T UFD (NIL) -9 NIL 3173396 NIL) (-1253 3171655 3171713 3171808 "UFD-" 3171813 NIL UFD- (NIL T) -8 NIL NIL NIL) (-1252 3170713 3170920 3171136 "UDVO" 3171461 T UDVO (NIL) -7 NIL NIL NIL) (-1251 3168479 3168938 3169409 "UDPO" 3170277 NIL UDPO (NIL T) -7 NIL NIL NIL) (-1250 3168191 3168434 3168465 "TYPEAST" 3168470 T TYPEAST (NIL) -8 NIL NIL NIL) (-1249 3168124 3168129 3168159 "TYPE" 3168164 T TYPE (NIL) -9 NIL NIL NIL) (-1248 3167077 3167297 3167537 "TWOFACT" 3167918 NIL TWOFACT (NIL T) -7 NIL NIL NIL) (-1247 3166052 3166486 3166721 "TUPLE" 3166877 NIL TUPLE (NIL T) -8 NIL NIL NIL) (-1246 3163689 3164262 3164801 "TUBETOOL" 3165535 T TUBETOOL (NIL) -7 NIL NIL NIL) (-1245 3162495 3162736 3162978 "TUBE" 3163482 NIL TUBE (NIL T) -8 NIL NIL NIL) (-1244 3150630 3155252 3155349 "TSETCAT" 3160618 NIL TSETCAT (NIL T T T T) -9 NIL 3162150 NIL) (-1243 3145098 3146962 3148853 "TSETCAT-" 3148858 NIL TSETCAT- (NIL T T T T T) -8 NIL NIL NIL) (-1242 3139284 3144070 3144353 "TS" 3144850 NIL TS (NIL T) -8 NIL NIL NIL) (-1241 3133757 3134770 3135699 "TRMANIP" 3138420 NIL TRMANIP (NIL T T) -7 NIL NIL NIL) (-1240 3133186 3133261 3133424 "TRIMAT" 3133689 NIL TRIMAT (NIL T T T T) -7 NIL NIL NIL) (-1239 3130998 3131289 3131646 "TRIGMNIP" 3132935 NIL TRIGMNIP (NIL T T) -7 NIL NIL NIL) (-1238 3130482 3130631 3130661 "TRIGCAT" 3130874 T TRIGCAT (NIL) -9 NIL NIL NIL) (-1237 3130127 3130230 3130371 "TRIGCAT-" 3130376 NIL TRIGCAT- (NIL T) -8 NIL NIL NIL) (-1236 3126741 3128985 3129266 "TREE" 3129881 NIL TREE (NIL T) -8 NIL NIL NIL) (-1235 3125847 3126543 3126573 "TRANFUN" 3126608 T TRANFUN (NIL) -9 NIL 3126674 NIL) (-1234 3125066 3125317 3125597 "TRANFUN-" 3125602 NIL TRANFUN- (NIL T) -8 NIL NIL NIL) (-1233 3124864 3124902 3124963 "TOPSP" 3125027 T TOPSP (NIL) -7 NIL NIL NIL) (-1232 3124194 3124327 3124481 "TOOLSIGN" 3124745 NIL TOOLSIGN (NIL T) -7 NIL NIL NIL) (-1231 3122708 3123371 3123610 "TEXTFILE" 3123977 T TEXTFILE (NIL) -8 NIL NIL NIL) (-1230 3122483 3122520 3122592 "TEX1" 3122671 NIL TEX1 (NIL T) -7 NIL NIL NIL) (-1229 3120287 3120936 3121365 "TEX" 3122076 T TEX (NIL) -8 NIL NIL NIL) (-1228 3119923 3119998 3120088 "TEMUTL" 3120219 T TEMUTL (NIL) -7 NIL NIL NIL) (-1227 3118017 3118357 3118682 "TBCMPPK" 3119646 NIL TBCMPPK (NIL T T) -7 NIL NIL NIL) (-1226 3109337 3116103 3116159 "TBAGG" 3116559 NIL TBAGG (NIL T T) -9 NIL 3116770 NIL) (-1225 3104221 3105895 3107649 "TBAGG-" 3107654 NIL TBAGG- (NIL T T T) -8 NIL NIL NIL) (-1224 3103587 3103712 3103857 "TANEXP" 3104110 NIL TANEXP (NIL T) -7 NIL NIL NIL) (-1223 3103038 3103362 3103452 "TALGOP" 3103532 NIL TALGOP (NIL T) -8 NIL NIL NIL) (-1222 3102432 3102549 3102687 "TABLEAU" 3102935 NIL TABLEAU (NIL T) -8 NIL NIL NIL) (-1221 3095446 3102289 3102382 "TABLE" 3102387 NIL TABLE (NIL T T) -8 NIL NIL NIL) (-1220 3089976 3091274 3092522 "TABLBUMP" 3094232 NIL TABLBUMP (NIL T) -7 NIL NIL NIL) (-1219 3089186 3089345 3089526 "SYSTEM" 3089817 T SYSTEM (NIL) -8 NIL NIL NIL) (-1218 3085591 3086344 3087127 "SYSSOLP" 3088437 NIL SYSSOLP (NIL T) -7 NIL NIL NIL) (-1217 3085353 3085546 3085577 "SYSPTR" 3085582 T SYSPTR (NIL) -8 NIL NIL NIL) (-1216 3084192 3084884 3085010 "SYSNNI" 3085196 NIL SYSNNI (NIL NIL) -8 NIL NIL 3085288) (-1215 3083399 3083954 3084033 "SYSINT" 3084093 NIL SYSINT (NIL NIL) -8 NIL NIL 3084138) (-1214 3079497 3080677 3081387 "SYNTAX" 3082711 T SYNTAX (NIL) -8 NIL NIL NIL) (-1213 3076577 3077257 3077889 "SYMTAB" 3078887 T SYMTAB (NIL) -8 NIL NIL NIL) (-1212 3071676 3072728 3073711 "SYMS" 3075616 T SYMS (NIL) -8 NIL NIL NIL) (-1211 3068582 3071127 3071360 "SYMPOLY" 3071478 NIL SYMPOLY (NIL T) -8 NIL NIL NIL) (-1210 3068087 3068174 3068297 "SYMFUNC" 3068494 NIL SYMFUNC (NIL T) -7 NIL NIL NIL) (-1209 3063885 3065399 3066212 "SYMBOL" 3067296 T SYMBOL (NIL) -8 NIL NIL NIL) (-1208 3057358 3059113 3060833 "SWITCH" 3062187 T SWITCH (NIL) -8 NIL NIL NIL) (-1207 3050119 3056314 3056608 "SUTS" 3057122 NIL SUTS (NIL T NIL NIL) -8 NIL NIL NIL) (-1206 3041611 3049501 3049765 "SUPXS" 3049913 NIL SUPXS (NIL T NIL NIL) -8 NIL NIL NIL) (-1205 3040758 3040897 3041114 "SUPFRACF" 3041479 NIL SUPFRACF (NIL T T T T) -7 NIL NIL NIL) (-1204 3040373 3040438 3040551 "SUP2" 3040693 NIL SUP2 (NIL T T) -7 NIL NIL NIL) (-1203 3030917 3039991 3040117 "SUP" 3040282 NIL SUP (NIL T) -8 NIL NIL NIL) (-1202 3029341 3029639 3029995 "SUMRF" 3030616 NIL SUMRF (NIL T) -7 NIL NIL NIL) (-1201 3028664 3028742 3028934 "SUMFS" 3029262 NIL SUMFS (NIL T T) -7 NIL NIL NIL) (-1200 3010530 3027976 3028218 "SULS" 3028480 NIL SULS (NIL T NIL NIL) -8 NIL NIL NIL) (-1199 3010078 3010352 3010422 "SUCHTAST" 3010482 T SUCHTAST (NIL) -8 NIL NIL NIL) (-1198 3009319 3009603 3009743 "SUCH" 3009986 NIL SUCH (NIL T T) -8 NIL NIL NIL) (-1197 3002958 3004225 3005184 "SUBSPACE" 3008407 NIL SUBSPACE (NIL NIL T) -8 NIL NIL NIL) (-1196 3002378 3002478 3002642 "SUBRESP" 3002846 NIL SUBRESP (NIL T T) -7 NIL NIL NIL) (-1195 2996389 2997671 2998818 "STTFNC" 3001278 NIL STTFNC (NIL T) -7 NIL NIL NIL) (-1194 2989583 2991054 2992365 "STTF" 2995125 NIL STTF (NIL T) -7 NIL NIL NIL) (-1193 2980699 2982765 2984559 "STTAYLOR" 2987824 NIL STTAYLOR (NIL T) -7 NIL NIL NIL) (-1192 2973453 2980563 2980646 "STRTBL" 2980651 NIL STRTBL (NIL T) -8 NIL NIL NIL) (-1191 2967850 2973162 2973261 "STRING" 2973376 T STRING (NIL) -8 NIL NIL NIL) (-1190 2967354 2967437 2967581 "STREAM3" 2967767 NIL STREAM3 (NIL T T T) -7 NIL NIL NIL) (-1189 2966318 2966519 2966754 "STREAM2" 2967167 NIL STREAM2 (NIL T T) -7 NIL NIL NIL) (-1188 2966000 2966058 2966151 "STREAM1" 2966260 NIL STREAM1 (NIL T) -7 NIL NIL NIL) (-1187 2958114 2963619 2964230 "STREAM" 2965424 NIL STREAM (NIL T) -8 NIL NIL NIL) (-1186 2957106 2957311 2957542 "STINPROD" 2957930 NIL STINPROD (NIL T) -7 NIL NIL NIL) (-1185 2956221 2956595 2956743 "STEPAST" 2956980 T STEPAST (NIL) -8 NIL NIL NIL) (-1184 2955717 2955962 2955992 "STEP" 2956086 T STEP (NIL) -9 NIL 2956157 NIL) (-1183 2948773 2955616 2955693 "STBL" 2955698 NIL STBL (NIL T T NIL) -8 NIL NIL NIL) (-1182 2943323 2947936 2947979 "STAGG" 2948132 NIL STAGG (NIL T) -9 NIL 2948221 NIL) (-1181 2940875 2941627 2942499 "STAGG-" 2942504 NIL STAGG- (NIL T T) -8 NIL NIL NIL) (-1180 2938847 2940645 2940737 "STACK" 2940818 NIL STACK (NIL T) -8 NIL NIL NIL) (-1179 2938164 2938677 2938707 "SRING" 2938712 T SRING (NIL) -9 NIL 2938732 NIL) (-1178 2930171 2936305 2936761 "SREGSET" 2937794 NIL SREGSET (NIL T T T T) -8 NIL NIL NIL) (-1177 2922518 2923965 2925478 "SRDCMPK" 2928777 NIL SRDCMPK (NIL T T T T T) -7 NIL NIL NIL) (-1176 2914818 2919877 2919907 "SRAGG" 2921210 T SRAGG (NIL) -9 NIL 2921818 NIL) (-1175 2913769 2914090 2914469 "SRAGG-" 2914474 NIL SRAGG- (NIL T) -8 NIL NIL NIL) (-1174 2907353 2912716 2913137 "SQMATRIX" 2913395 NIL SQMATRIX (NIL NIL T) -8 NIL NIL NIL) (-1173 2900765 2904071 2904798 "SPLTREE" 2906698 NIL SPLTREE (NIL T T) -8 NIL NIL NIL) (-1172 2896590 2897421 2898067 "SPLNODE" 2900191 NIL SPLNODE (NIL T T) -8 NIL NIL NIL) (-1171 2895565 2895870 2895900 "SPFCAT" 2896344 T SPFCAT (NIL) -9 NIL NIL NIL) (-1170 2894260 2894512 2894776 "SPECOUT" 2895323 T SPECOUT (NIL) -7 NIL NIL NIL) (-1169 2884906 2887224 2887254 "SPADXPT" 2891932 T SPADXPT (NIL) -9 NIL 2894098 NIL) (-1168 2884661 2884707 2884776 "SPADPRSR" 2884859 T SPADPRSR (NIL) -7 NIL NIL NIL) (-1167 2882264 2884616 2884647 "SPADAST" 2884652 T SPADAST (NIL) -8 NIL NIL NIL) (-1166 2873865 2875968 2876011 "SPACEC" 2880384 NIL SPACEC (NIL T) -9 NIL 2882200 NIL) (-1165 2871665 2873797 2873846 "SPACE3" 2873851 NIL SPACE3 (NIL T) -8 NIL NIL NIL) (-1164 2870397 2870588 2870879 "SORTPAK" 2871470 NIL SORTPAK (NIL T T) -7 NIL NIL NIL) (-1163 2868459 2868792 2869204 "SOLVETRA" 2870061 NIL SOLVETRA (NIL T) -7 NIL NIL NIL) (-1162 2867497 2867731 2867992 "SOLVESER" 2868232 NIL SOLVESER (NIL T) -7 NIL NIL NIL) (-1161 2862729 2863689 2864684 "SOLVERAD" 2866549 NIL SOLVERAD (NIL T) -7 NIL NIL NIL) (-1160 2858454 2859153 2859882 "SOLVEFOR" 2862096 NIL SOLVEFOR (NIL T T) -7 NIL NIL NIL) (-1159 2852058 2857802 2857899 "SNTSCAT" 2857904 NIL SNTSCAT (NIL T T T T) -9 NIL 2857974 NIL) (-1158 2845609 2850381 2850772 "SMTS" 2851748 NIL SMTS (NIL T T T) -8 NIL NIL NIL) (-1157 2839331 2845497 2845574 "SMP" 2845579 NIL SMP (NIL T T) -8 NIL NIL NIL) (-1156 2837460 2837791 2838189 "SMITH" 2839028 NIL SMITH (NIL T T T T) -7 NIL NIL NIL) (-1155 2828985 2834039 2834142 "SMATCAT" 2835493 NIL SMATCAT (NIL NIL T T T) -9 NIL 2836043 NIL) (-1154 2825757 2826748 2827926 "SMATCAT-" 2827931 NIL SMATCAT- (NIL T NIL T T T) -8 NIL NIL NIL) (-1153 2823226 2824965 2825008 "SKAGG" 2825269 NIL SKAGG (NIL T) -9 NIL 2825404 NIL) (-1152 2818746 2822709 2822886 "SINT" 2823038 T SINT (NIL) -8 NIL NIL 2823193) (-1151 2818512 2818556 2818622 "SIMPAN" 2818702 T SIMPAN (NIL) -7 NIL NIL NIL) (-1150 2817332 2817571 2817846 "SIGNRF" 2818271 NIL SIGNRF (NIL T) -7 NIL NIL NIL) (-1149 2816147 2816316 2816600 "SIGNEF" 2817161 NIL SIGNEF (NIL T T) -7 NIL NIL NIL) (-1148 2815387 2815730 2815854 "SIGAST" 2816045 T SIGAST (NIL) -8 NIL NIL NIL) (-1147 2814612 2814922 2815062 "SIG" 2815269 T SIG (NIL) -8 NIL NIL NIL) (-1146 2812264 2812756 2813262 "SHP" 2814153 NIL SHP (NIL T NIL) -7 NIL NIL NIL) (-1145 2805588 2812165 2812241 "SHDP" 2812246 NIL SHDP (NIL NIL NIL T) -8 NIL NIL NIL) (-1144 2805099 2805339 2805369 "SGROUP" 2805462 T SGROUP (NIL) -9 NIL 2805524 NIL) (-1143 2804951 2804983 2805056 "SGROUP-" 2805061 NIL SGROUP- (NIL T) -8 NIL NIL NIL) (-1142 2801670 2802440 2803163 "SGCF" 2804250 T SGCF (NIL) -7 NIL NIL NIL) (-1141 2795372 2801116 2801213 "SFRTCAT" 2801218 NIL SFRTCAT (NIL T T T T) -9 NIL 2801257 NIL) (-1140 2788691 2789811 2790947 "SFRGCD" 2794355 NIL SFRGCD (NIL T T T T T) -7 NIL NIL NIL) (-1139 2781709 2782890 2784076 "SFQCMPK" 2787624 NIL SFQCMPK (NIL T T T T T) -7 NIL NIL NIL) (-1138 2781311 2781418 2781529 "SFORT" 2781650 NIL SFORT (NIL T T) -8 NIL NIL NIL) (-1137 2780237 2781151 2781272 "SEXOF" 2781277 NIL SEXOF (NIL T T T T T) -8 NIL NIL NIL) (-1136 2775826 2776733 2776828 "SEXCAT" 2779450 NIL SEXCAT (NIL T T T T T) -9 NIL 2780010 NIL) (-1135 2774741 2775707 2775775 "SEX" 2775780 T SEX (NIL) -8 NIL NIL NIL) (-1134 2772863 2773454 2773759 "SETMN" 2774482 NIL SETMN (NIL NIL NIL) -8 NIL NIL NIL) (-1133 2772393 2772581 2772611 "SETCAT" 2772728 T SETCAT (NIL) -9 NIL 2772813 NIL) (-1132 2772161 2772225 2772324 "SETCAT-" 2772329 NIL SETCAT- (NIL T) -8 NIL NIL NIL) (-1131 2768264 2770622 2770665 "SETAGG" 2771535 NIL SETAGG (NIL T) -9 NIL 2771875 NIL) (-1130 2767686 2767838 2768075 "SETAGG-" 2768080 NIL SETAGG- (NIL T T) -8 NIL NIL NIL) (-1129 2764495 2767620 2767668 "SET" 2767673 NIL SET (NIL T) -8 NIL NIL NIL) (-1128 2763878 2764191 2764292 "SEQAST" 2764416 T SEQAST (NIL) -8 NIL NIL NIL) (-1127 2763005 2763371 2763432 "SEGXCAT" 2763718 NIL SEGXCAT (NIL T T) -9 NIL 2763838 NIL) (-1126 2761930 2762198 2762241 "SEGCAT" 2762763 NIL SEGCAT (NIL T) -9 NIL 2762984 NIL) (-1125 2761545 2761610 2761723 "SEGBIND2" 2761865 NIL SEGBIND2 (NIL T T) -7 NIL NIL NIL) (-1124 2760435 2760908 2761116 "SEGBIND" 2761372 NIL SEGBIND (NIL T) -8 NIL NIL NIL) (-1123 2759954 2760236 2760313 "SEGAST" 2760380 T SEGAST (NIL) -8 NIL NIL NIL) (-1122 2759163 2759299 2759503 "SEG2" 2759798 NIL SEG2 (NIL T T) -7 NIL NIL NIL) (-1121 2758079 2758829 2759011 "SEG" 2759016 NIL SEG (NIL T) -8 NIL NIL NIL) (-1120 2757312 2758014 2758061 "SDVAR" 2758066 NIL SDVAR (NIL T) -8 NIL NIL NIL) (-1119 2748670 2757082 2757212 "SDPOL" 2757217 NIL SDPOL (NIL T) -8 NIL NIL NIL) (-1118 2747239 2747529 2747848 "SCPKG" 2748385 NIL SCPKG (NIL T) -7 NIL NIL NIL) (-1117 2746361 2746575 2746767 "SCOPE" 2747069 T SCOPE (NIL) -8 NIL NIL NIL) (-1116 2745557 2745715 2745894 "SCACHE" 2746216 NIL SCACHE (NIL T) -7 NIL NIL NIL) (-1115 2745141 2745375 2745405 "SASTCAT" 2745410 T SASTCAT (NIL) -9 NIL 2745423 NIL) (-1114 2744544 2744976 2745052 "SAOS" 2745087 T SAOS (NIL) -8 NIL NIL NIL) (-1113 2744103 2744144 2744317 "SAERFFC" 2744503 NIL SAERFFC (NIL T T T) -7 NIL NIL NIL) (-1112 2743690 2743731 2743890 "SAEFACT" 2744062 NIL SAEFACT (NIL T T T) -7 NIL NIL NIL) (-1111 2736738 2743587 2743667 "SAE" 2743672 NIL SAE (NIL T T NIL) -8 NIL NIL NIL) (-1110 2735041 2735373 2735774 "RURPK" 2736404 NIL RURPK (NIL T NIL) -7 NIL NIL NIL) (-1109 2733618 2733984 2734289 "RULESET" 2734875 NIL RULESET (NIL T T T) -8 NIL NIL NIL) (-1108 2733188 2733412 2733495 "RULECOLD" 2733570 NIL RULECOLD (NIL NIL) -8 NIL NIL NIL) (-1107 2730303 2730941 2731399 "RULE" 2732869 NIL RULE (NIL T T T) -8 NIL NIL NIL) (-1106 2730087 2730121 2730192 "RTVALUE" 2730254 T RTVALUE (NIL) -8 NIL NIL NIL) (-1105 2729498 2729804 2729898 "RSTRCAST" 2730015 T RSTRCAST (NIL) -8 NIL NIL NIL) (-1104 2724268 2725141 2726061 "RSETGCD" 2728697 NIL RSETGCD (NIL T T T T T) -7 NIL NIL NIL) (-1103 2712832 2718576 2718673 "RSETCAT" 2722792 NIL RSETCAT (NIL T T T T) -9 NIL 2723889 NIL) (-1102 2710651 2711298 2712122 "RSETCAT-" 2712127 NIL RSETCAT- (NIL T T T T T) -8 NIL NIL NIL) (-1101 2702959 2704413 2705933 "RSDCMPK" 2709250 NIL RSDCMPK (NIL T T T T T) -7 NIL NIL NIL) (-1100 2700828 2701391 2701465 "RRCC" 2702551 NIL RRCC (NIL T T) -9 NIL 2702895 NIL) (-1099 2700149 2700353 2700632 "RRCC-" 2700637 NIL RRCC- (NIL T T T) -8 NIL NIL NIL) (-1098 2699532 2699845 2699946 "RPTAST" 2700070 T RPTAST (NIL) -8 NIL NIL NIL) (-1097 2671918 2682644 2682711 "RPOLCAT" 2693377 NIL RPOLCAT (NIL T T T) -9 NIL 2696537 NIL) (-1096 2662888 2665756 2668878 "RPOLCAT-" 2668883 NIL RPOLCAT- (NIL T T T T) -8 NIL NIL NIL) (-1095 2653341 2661099 2661581 "ROUTINE" 2662428 T ROUTINE (NIL) -8 NIL NIL NIL) (-1094 2649404 2652967 2653107 "ROMAN" 2653223 T ROMAN (NIL) -8 NIL NIL NIL) (-1093 2647516 2648264 2648524 "ROIRC" 2649209 NIL ROIRC (NIL T T) -8 NIL NIL NIL) (-1092 2643236 2646005 2646035 "RNS" 2646339 T RNS (NIL) -9 NIL 2646613 NIL) (-1091 2641643 2642128 2642662 "RNS-" 2642737 NIL RNS- (NIL T) -8 NIL NIL NIL) (-1090 2640604 2641008 2641210 "RNGBIND" 2641494 NIL RNGBIND (NIL T T) -8 NIL NIL NIL) (-1089 2639897 2640401 2640431 "RNG" 2640436 T RNG (NIL) -9 NIL 2640457 NIL) (-1088 2639192 2639670 2639713 "RMODULE" 2639718 NIL RMODULE (NIL T) -9 NIL 2639745 NIL) (-1087 2638016 2638122 2638458 "RMCAT2" 2639093 NIL RMCAT2 (NIL NIL NIL T T T T T T T T) -7 NIL NIL NIL) (-1086 2634518 2637362 2637659 "RMATRIX" 2637778 NIL RMATRIX (NIL NIL NIL T) -8 NIL NIL NIL) (-1085 2627017 2629605 2629720 "RMATCAT" 2633079 NIL RMATCAT (NIL NIL NIL T T T) -9 NIL 2634061 NIL) (-1084 2626356 2626539 2626846 "RMATCAT-" 2626851 NIL RMATCAT- (NIL T NIL NIL T T T) -8 NIL NIL NIL) (-1083 2625929 2626143 2626186 "RLINSET" 2626248 NIL RLINSET (NIL T) -9 NIL 2626292 NIL) (-1082 2625490 2625571 2625699 "RINTERP" 2625848 NIL RINTERP (NIL NIL T) -7 NIL NIL NIL) (-1081 2624414 2625088 2625118 "RING" 2625174 T RING (NIL) -9 NIL 2625266 NIL) (-1080 2624194 2624250 2624347 "RING-" 2624352 NIL RING- (NIL T) -8 NIL NIL NIL) (-1079 2623005 2623272 2623530 "RIDIST" 2623958 T RIDIST (NIL) -7 NIL NIL NIL) (-1078 2613630 2622473 2622679 "RGCHAIN" 2622853 NIL RGCHAIN (NIL T NIL) -8 NIL NIL NIL) (-1077 2612888 2613372 2613413 "RGBCSPC" 2613471 NIL RGBCSPC (NIL T) -9 NIL 2613523 NIL) (-1076 2611954 2612413 2612454 "RGBCMDL" 2612686 NIL RGBCMDL (NIL T) -9 NIL 2612800 NIL) (-1075 2611594 2611663 2611766 "RFFACTOR" 2611885 NIL RFFACTOR (NIL T) -7 NIL NIL NIL) (-1074 2611313 2611354 2611451 "RFFACT" 2611553 NIL RFFACT (NIL T) -7 NIL NIL NIL) (-1073 2609364 2609794 2610176 "RFDIST" 2610953 T RFDIST (NIL) -7 NIL NIL NIL) (-1072 2606304 2606972 2607642 "RF" 2608728 NIL RF (NIL T) -7 NIL NIL NIL) (-1071 2605751 2605849 2606012 "RETSOL" 2606206 NIL RETSOL (NIL T T) -7 NIL NIL NIL) (-1070 2605369 2605467 2605510 "RETRACT" 2605643 NIL RETRACT (NIL T) -9 NIL 2605730 NIL) (-1069 2605212 2605243 2605330 "RETRACT-" 2605335 NIL RETRACT- (NIL T T) -8 NIL NIL NIL) (-1068 2604760 2605034 2605104 "RETAST" 2605164 T RETAST (NIL) -8 NIL NIL NIL) (-1067 2597110 2604413 2604540 "RESULT" 2604655 T RESULT (NIL) -8 NIL NIL NIL) (-1066 2595545 2596379 2596578 "RESRING" 2597013 NIL RESRING (NIL T T T T NIL) -8 NIL NIL NIL) (-1065 2595169 2595230 2595328 "RESLATC" 2595482 NIL RESLATC (NIL T) -7 NIL NIL NIL) (-1064 2594868 2594909 2595016 "REPSQ" 2595128 NIL REPSQ (NIL T) -7 NIL NIL NIL) (-1063 2594559 2594600 2594711 "REPDB" 2594827 NIL REPDB (NIL T) -7 NIL NIL NIL) (-1062 2588391 2589848 2591071 "REP2" 2593371 NIL REP2 (NIL T) -7 NIL NIL NIL) (-1061 2584694 2585449 2586257 "REP1" 2587618 NIL REP1 (NIL T) -7 NIL NIL NIL) (-1060 2582074 2582696 2583298 "REP" 2584114 T REP (NIL) -7 NIL NIL NIL) (-1059 2574082 2580215 2580671 "REGSET" 2581704 NIL REGSET (NIL T T T T) -8 NIL NIL NIL) (-1058 2572791 2573230 2573480 "REF" 2573867 NIL REF (NIL T) -8 NIL NIL NIL) (-1057 2572156 2572271 2572438 "REDORDER" 2572675 NIL REDORDER (NIL T T) -7 NIL NIL NIL) (-1056 2567527 2571369 2571596 "RECLOS" 2571984 NIL RECLOS (NIL T) -8 NIL NIL NIL) (-1055 2566561 2566760 2566975 "REALSOLV" 2567334 T REALSOLV (NIL) -7 NIL NIL NIL) (-1054 2563008 2563846 2564730 "REAL0Q" 2565726 NIL REAL0Q (NIL T) -7 NIL NIL NIL) (-1053 2558561 2559597 2560658 "REAL0" 2561989 NIL REAL0 (NIL T) -7 NIL NIL NIL) (-1052 2558395 2558448 2558478 "REAL" 2558483 T REAL (NIL) -9 NIL 2558518 NIL) (-1051 2557806 2558112 2558206 "RDUCEAST" 2558323 T RDUCEAST (NIL) -8 NIL NIL NIL) (-1050 2557205 2557283 2557490 "RDIV" 2557728 NIL RDIV (NIL T T T T T) -7 NIL NIL NIL) (-1049 2556255 2556447 2556660 "RDIST" 2557027 NIL RDIST (NIL T) -7 NIL NIL NIL) (-1048 2554840 2555139 2555511 "RDETRS" 2555963 NIL RDETRS (NIL T T) -7 NIL NIL NIL) (-1047 2552634 2553106 2553644 "RDETR" 2554382 NIL RDETR (NIL T T) -7 NIL NIL NIL) (-1046 2551253 2551537 2551934 "RDEEFS" 2552350 NIL RDEEFS (NIL T T) -7 NIL NIL NIL) (-1045 2549756 2550068 2550493 "RDEEF" 2550941 NIL RDEEF (NIL T T) -7 NIL NIL NIL) (-1044 2543235 2546710 2546740 "RCFIELD" 2548035 T RCFIELD (NIL) -9 NIL 2548766 NIL) (-1043 2541191 2541803 2542499 "RCFIELD-" 2542574 NIL RCFIELD- (NIL T) -8 NIL NIL NIL) (-1042 2537243 2539264 2539307 "RCAGG" 2540391 NIL RCAGG (NIL T) -9 NIL 2540856 NIL) (-1041 2536853 2536965 2537128 "RCAGG-" 2537133 NIL RCAGG- (NIL T T) -8 NIL NIL NIL) (-1040 2536170 2536300 2536465 "RATRET" 2536737 NIL RATRET (NIL T) -7 NIL NIL NIL) (-1039 2535711 2535790 2535911 "RATFACT" 2536098 NIL RATFACT (NIL T) -7 NIL NIL NIL) (-1038 2534989 2535139 2535291 "RANDSRC" 2535581 T RANDSRC (NIL) -7 NIL NIL NIL) (-1037 2534717 2534767 2534840 "RADUTIL" 2534938 T RADUTIL (NIL) -7 NIL NIL NIL) (-1036 2526862 2533548 2533859 "RADIX" 2534440 NIL RADIX (NIL NIL) -8 NIL NIL NIL) (-1035 2516477 2526704 2526834 "RADFF" 2526839 NIL RADFF (NIL T T T NIL NIL) -8 NIL NIL NIL) (-1034 2516106 2516199 2516229 "RADCAT" 2516389 T RADCAT (NIL) -9 NIL NIL NIL) (-1033 2515876 2515936 2516036 "RADCAT-" 2516041 NIL RADCAT- (NIL T) -8 NIL NIL NIL) (-1032 2513787 2515646 2515738 "QUEUE" 2515819 NIL QUEUE (NIL T) -8 NIL NIL NIL) (-1031 2513412 2513461 2513592 "QUATCT2" 2513738 NIL QUATCT2 (NIL T T T T) -7 NIL NIL NIL) (-1030 2505790 2509835 2509877 "QUATCAT" 2510668 NIL QUATCAT (NIL T) -9 NIL 2511434 NIL) (-1029 2501671 2502966 2504356 "QUATCAT-" 2504452 NIL QUATCAT- (NIL T T) -8 NIL NIL NIL) (-1028 2497517 2501604 2501652 "QUAT" 2501657 NIL QUAT (NIL T) -8 NIL NIL NIL) (-1027 2494773 2496565 2496608 "QUAGG" 2496989 NIL QUAGG (NIL T) -9 NIL 2497164 NIL) (-1026 2494321 2494595 2494665 "QQUTAST" 2494725 T QQUTAST (NIL) -8 NIL NIL NIL) (-1025 2493232 2493834 2493999 "QFORM" 2494202 NIL QFORM (NIL NIL T) -8 NIL NIL NIL) (-1024 2492857 2492906 2493037 "QFCAT2" 2493183 NIL QFCAT2 (NIL T T T T) -7 NIL NIL NIL) (-1023 2482554 2488704 2488746 "QFCAT" 2489414 NIL QFCAT (NIL T) -9 NIL 2490415 NIL) (-1022 2477888 2479336 2480923 "QFCAT-" 2481019 NIL QFCAT- (NIL T T) -8 NIL NIL NIL) (-1021 2477319 2477453 2477585 "QEQUAT" 2477778 T QEQUAT (NIL) -8 NIL NIL NIL) (-1020 2470337 2471518 2472704 "QCMPACK" 2476252 NIL QCMPACK (NIL T T T T T) -7 NIL NIL NIL) (-1019 2469566 2469748 2469984 "QALGSET2" 2470155 NIL QALGSET2 (NIL NIL NIL) -7 NIL NIL NIL) (-1018 2467016 2467552 2467982 "QALGSET" 2469221 NIL QALGSET (NIL T T T T) -8 NIL NIL NIL) (-1017 2465683 2465925 2466244 "PWFFINTB" 2466789 NIL PWFFINTB (NIL T T T T) -7 NIL NIL NIL) (-1016 2463828 2464026 2464382 "PUSHVAR" 2465497 NIL PUSHVAR (NIL T T T T) -7 NIL NIL NIL) (-1015 2459555 2460771 2460814 "PTRANFN" 2462725 NIL PTRANFN (NIL T) -9 NIL NIL NIL) (-1014 2457892 2458237 2458561 "PTPACK" 2459266 NIL PTPACK (NIL T) -7 NIL NIL NIL) (-1013 2457515 2457578 2457689 "PTFUNC2" 2457829 NIL PTFUNC2 (NIL T T) -7 NIL NIL NIL) (-1012 2451431 2456304 2456347 "PTCAT" 2456647 NIL PTCAT (NIL T) -9 NIL 2456800 NIL) (-1011 2451080 2451121 2451247 "PSQFR" 2451390 NIL PSQFR (NIL T T T T) -7 NIL NIL NIL) (-1010 2449652 2449968 2450304 "PSEUDLIN" 2450778 NIL PSEUDLIN (NIL T) -7 NIL NIL NIL) (-1009 2436172 2438747 2441073 "PSETPK" 2447412 NIL PSETPK (NIL T T T T) -7 NIL NIL NIL) (-1008 2428880 2431908 2432006 "PSETCAT" 2435047 NIL PSETCAT (NIL T T T T) -9 NIL 2435861 NIL) (-1007 2426605 2427347 2428171 "PSETCAT-" 2428176 NIL PSETCAT- (NIL T T T T T) -8 NIL NIL NIL) (-1006 2425918 2426113 2426143 "PSCURVE" 2426415 T PSCURVE (NIL) -9 NIL 2426582 NIL) (-1005 2421641 2423408 2423475 "PSCAT" 2424327 NIL PSCAT (NIL T T T) -9 NIL 2424567 NIL) (-1004 2420635 2420917 2421320 "PSCAT-" 2421325 NIL PSCAT- (NIL T T T T) -8 NIL NIL NIL) (-1003 2418803 2419694 2419959 "PRTITION" 2420392 T PRTITION (NIL) -8 NIL NIL NIL) (-1002 2418214 2418520 2418614 "PRTDAST" 2418731 T PRTDAST (NIL) -8 NIL NIL NIL) (-1001 2407058 2409480 2411670 "PRS" 2416076 NIL PRS (NIL T T) -7 NIL NIL NIL) (-1000 2404673 2406375 2406417 "PRQAGG" 2406603 NIL PRQAGG (NIL T) -9 NIL 2406705 NIL) (-999 2403852 2404301 2404329 "PROPLOG" 2404468 T PROPLOG (NIL) -9 NIL 2404583 NIL) (-998 2403450 2403513 2403636 "PROPFUN2" 2403775 NIL PROPFUN2 (NIL T T) -8 NIL NIL NIL) (-997 2402747 2402886 2403058 "PROPFUN1" 2403311 NIL PROPFUN1 (NIL T) -8 NIL NIL NIL) (-996 2400728 2401494 2401791 "PROPFRML" 2402483 NIL PROPFRML (NIL T) -8 NIL NIL NIL) (-995 2400173 2400304 2400432 "PROPERTY" 2400620 T PROPERTY (NIL) -8 NIL NIL NIL) (-994 2393986 2398339 2399159 "PRODUCT" 2399399 NIL PRODUCT (NIL T T) -8 NIL NIL NIL) (-993 2393776 2393814 2393873 "PRINT" 2393947 T PRINT (NIL) -7 NIL NIL NIL) (-992 2393092 2393233 2393385 "PRIMES" 2393656 NIL PRIMES (NIL T) -7 NIL NIL NIL) (-991 2391139 2391558 2392024 "PRIMELT" 2392671 NIL PRIMELT (NIL T) -7 NIL NIL NIL) (-990 2390856 2390917 2390945 "PRIMCAT" 2391069 T PRIMCAT (NIL) -9 NIL NIL NIL) (-989 2389845 2390041 2390269 "PRIMARR2" 2390674 NIL PRIMARR2 (NIL T T) -7 NIL NIL NIL) (-988 2385567 2389783 2389828 "PRIMARR" 2389833 NIL PRIMARR (NIL T) -8 NIL NIL NIL) (-987 2385204 2385266 2385377 "PREASSOC" 2385505 NIL PREASSOC (NIL T T) -7 NIL NIL NIL) (-986 2382169 2384662 2384896 "PR" 2385015 NIL PR (NIL T T) -8 NIL NIL NIL) (-985 2381620 2381777 2381805 "PPCURVE" 2382010 T PPCURVE (NIL) -9 NIL 2382146 NIL) (-984 2381167 2381415 2381498 "PORTNUM" 2381557 T PORTNUM (NIL) -8 NIL NIL NIL) (-983 2378504 2378925 2379517 "POLYROOT" 2380748 NIL POLYROOT (NIL T T T T T) -7 NIL NIL NIL) (-982 2377881 2377945 2378179 "POLYLIFT" 2378440 NIL POLYLIFT (NIL T T T T T) -7 NIL NIL NIL) (-981 2374102 2374605 2375234 "POLYCATQ" 2377426 NIL POLYCATQ (NIL T T T T T) -7 NIL NIL NIL) (-980 2359750 2365849 2365914 "POLYCAT" 2369428 NIL POLYCAT (NIL T T T) -9 NIL 2371306 NIL) (-979 2352890 2355075 2357452 "POLYCAT-" 2357457 NIL POLYCAT- (NIL T T T T) -8 NIL NIL NIL) (-978 2352471 2352545 2352665 "POLY2UP" 2352816 NIL POLY2UP (NIL NIL T) -7 NIL NIL NIL) (-977 2352097 2352160 2352269 "POLY2" 2352408 NIL POLY2 (NIL T T) -7 NIL NIL NIL) (-976 2345312 2351701 2351861 "POLY" 2351970 NIL POLY (NIL T) -8 NIL NIL NIL) (-975 2343973 2344236 2344512 "POLUTIL" 2345086 NIL POLUTIL (NIL T T) -7 NIL NIL NIL) (-974 2342292 2342605 2342936 "POLTOPOL" 2343695 NIL POLTOPOL (NIL NIL T) -7 NIL NIL NIL) (-973 2337288 2342226 2342273 "POINT" 2342278 NIL POINT (NIL T) -8 NIL NIL NIL) (-972 2335421 2335832 2336207 "PNTHEORY" 2336933 T PNTHEORY (NIL) -7 NIL NIL NIL) (-971 2333867 2334176 2334575 "PMTOOLS" 2335119 NIL PMTOOLS (NIL T T T) -7 NIL NIL NIL) (-970 2333454 2333538 2333655 "PMSYM" 2333783 NIL PMSYM (NIL T) -7 NIL NIL NIL) (-969 2332956 2333031 2333206 "PMQFCAT" 2333379 NIL PMQFCAT (NIL T T T) -7 NIL NIL NIL) (-968 2332337 2332435 2332597 "PMPREDFS" 2332857 NIL PMPREDFS (NIL T T T) -7 NIL NIL NIL) (-967 2331680 2331802 2331958 "PMPRED" 2332214 NIL PMPRED (NIL T) -7 NIL NIL NIL) (-966 2330334 2330552 2330930 "PMPLCAT" 2331442 NIL PMPLCAT (NIL T T T T T) -7 NIL NIL NIL) (-965 2329860 2329945 2330097 "PMLSAGG" 2330249 NIL PMLSAGG (NIL T T T) -7 NIL NIL NIL) (-964 2329327 2329409 2329591 "PMKERNEL" 2329778 NIL PMKERNEL (NIL T T) -7 NIL NIL NIL) (-963 2328938 2329019 2329132 "PMINS" 2329246 NIL PMINS (NIL T) -7 NIL NIL NIL) (-962 2328374 2328449 2328658 "PMFS" 2328863 NIL PMFS (NIL T T T) -7 NIL NIL NIL) (-961 2327590 2327720 2327925 "PMDOWN" 2328251 NIL PMDOWN (NIL T T T) -7 NIL NIL NIL) (-960 2326839 2326973 2327136 "PMASSFS" 2327477 NIL PMASSFS (NIL T T) -7 NIL NIL NIL) (-959 2325982 2326164 2326345 "PMASS" 2326678 T PMASS (NIL) -7 NIL NIL NIL) (-958 2325631 2325705 2325799 "PLOTTOOL" 2325908 T PLOTTOOL (NIL) -7 NIL NIL NIL) (-957 2321283 2322477 2323399 "PLOT3D" 2324729 T PLOT3D (NIL) -8 NIL NIL NIL) (-956 2320171 2320372 2320607 "PLOT1" 2321087 NIL PLOT1 (NIL T) -7 NIL NIL NIL) (-955 2314592 2315982 2317130 "PLOT" 2319043 T PLOT (NIL) -8 NIL NIL NIL) (-954 2289767 2294658 2299509 "PLEQN" 2309858 NIL PLEQN (NIL T T T T) -7 NIL NIL NIL) (-953 2289454 2289507 2289610 "PINTERPA" 2289714 NIL PINTERPA (NIL T T) -7 NIL NIL NIL) (-952 2288760 2288894 2289074 "PINTERP" 2289319 NIL PINTERP (NIL NIL T) -7 NIL NIL NIL) (-951 2286844 2288010 2288038 "PID" 2288235 T PID (NIL) -9 NIL 2288362 NIL) (-950 2286589 2286632 2286707 "PICOERCE" 2286801 NIL PICOERCE (NIL T) -7 NIL NIL NIL) (-949 2285685 2286353 2286440 "PI" 2286480 T PI (NIL) -8 NIL NIL 2286547) (-948 2284993 2285144 2285320 "PGROEB" 2285541 NIL PGROEB (NIL T) -7 NIL NIL NIL) (-947 2280432 2281391 2282297 "PGE" 2284107 T PGE (NIL) -7 NIL NIL NIL) (-946 2278513 2278802 2279168 "PGCD" 2280149 NIL PGCD (NIL T T T T) -7 NIL NIL NIL) (-945 2277839 2277954 2278115 "PFRPAC" 2278397 NIL PFRPAC (NIL T) -7 NIL NIL NIL) (-944 2274097 2276387 2276740 "PFR" 2277518 NIL PFR (NIL T) -8 NIL NIL NIL) (-943 2272450 2272730 2273055 "PFOTOOLS" 2273844 NIL PFOTOOLS (NIL T T) -7 NIL NIL NIL) (-942 2270965 2271222 2271573 "PFOQ" 2272207 NIL PFOQ (NIL T T T) -7 NIL NIL NIL) (-941 2269448 2269678 2270034 "PFO" 2270749 NIL PFO (NIL T T T T T) -7 NIL NIL NIL) (-940 2266532 2268038 2268066 "PFECAT" 2268659 T PFECAT (NIL) -9 NIL 2269036 NIL) (-939 2265980 2266145 2266352 "PFECAT-" 2266357 NIL PFECAT- (NIL T) -8 NIL NIL NIL) (-938 2264553 2264835 2265136 "PFBRU" 2265729 NIL PFBRU (NIL T T) -7 NIL NIL NIL) (-937 2262382 2262771 2263203 "PFBR" 2264204 NIL PFBR (NIL T T T T) -7 NIL NIL NIL) (-936 2258328 2262271 2262340 "PF" 2262345 NIL PF (NIL NIL) -8 NIL NIL NIL) (-935 2253382 2254535 2255405 "PERMGRP" 2257491 NIL PERMGRP (NIL T) -8 NIL NIL NIL) (-934 2251294 2252406 2252447 "PERMCAT" 2252847 NIL PERMCAT (NIL T) -9 NIL 2253145 NIL) (-933 2250941 2250988 2251112 "PERMAN" 2251247 NIL PERMAN (NIL NIL T) -7 NIL NIL NIL) (-932 2246743 2248450 2249098 "PERM" 2250326 NIL PERM (NIL T) -8 NIL NIL NIL) (-931 2243984 2246408 2246530 "PENDTREE" 2246654 NIL PENDTREE (NIL T) -8 NIL NIL NIL) (-930 2242865 2243128 2243169 "PDSPC" 2243702 NIL PDSPC (NIL T) -9 NIL 2243947 NIL) (-929 2241920 2242186 2242548 "PDSPC-" 2242553 NIL PDSPC- (NIL T T) -8 NIL NIL NIL) (-928 2240634 2241570 2241611 "PDRING" 2241616 NIL PDRING (NIL T) -9 NIL 2241644 NIL) (-927 2239377 2240139 2240193 "PDMOD" 2240198 NIL PDMOD (NIL T T) -9 NIL 2240302 NIL) (-926 2236544 2237370 2238038 "PDEPROB" 2238729 T PDEPROB (NIL) -8 NIL NIL NIL) (-925 2234053 2234593 2235148 "PDEPACK" 2236009 T PDEPACK (NIL) -7 NIL NIL NIL) (-924 2232941 2233155 2233406 "PDECOMP" 2233852 NIL PDECOMP (NIL T T) -7 NIL NIL NIL) (-923 2230458 2231349 2231377 "PDECAT" 2232164 T PDECAT (NIL) -9 NIL 2232877 NIL) (-922 2230075 2230142 2230196 "PDDOM" 2230361 NIL PDDOM (NIL T T) -9 NIL 2230441 NIL) (-921 2229888 2229924 2230031 "PDDOM-" 2230036 NIL PDDOM- (NIL T T T) -8 NIL NIL NIL) (-920 2229633 2229672 2229762 "PCOMP" 2229849 NIL PCOMP (NIL T T) -7 NIL NIL NIL) (-919 2227673 2228434 2228731 "PBWLB" 2229362 NIL PBWLB (NIL T) -8 NIL NIL NIL) (-918 2227299 2227362 2227471 "PATTERN2" 2227610 NIL PATTERN2 (NIL T T) -7 NIL NIL NIL) (-917 2225008 2225444 2225901 "PATTERN1" 2226888 NIL PATTERN1 (NIL T T) -7 NIL NIL NIL) (-916 2217187 2219081 2220419 "PATTERN" 2223691 NIL PATTERN (NIL T) -8 NIL NIL NIL) (-915 2216745 2216818 2216950 "PATRES2" 2217114 NIL PATRES2 (NIL T T T) -7 NIL NIL NIL) (-914 2214011 2214694 2215175 "PATRES" 2216310 NIL PATRES (NIL T T) -8 NIL NIL NIL) (-913 2211864 2212299 2212706 "PATMATCH" 2213678 NIL PATMATCH (NIL T T T) -7 NIL NIL NIL) (-912 2211318 2211569 2211610 "PATMAB" 2211717 NIL PATMAB (NIL T) -9 NIL 2211800 NIL) (-911 2209764 2210172 2210430 "PATLRES" 2211123 NIL PATLRES (NIL T T T) -8 NIL NIL NIL) (-910 2209302 2209433 2209474 "PATAB" 2209479 NIL PATAB (NIL T) -9 NIL 2209651 NIL) (-909 2207442 2207879 2208302 "PARTPERM" 2208899 T PARTPERM (NIL) -7 NIL NIL NIL) (-908 2207051 2207126 2207228 "PARSURF" 2207373 NIL PARSURF (NIL T) -8 NIL NIL NIL) (-907 2206677 2206740 2206849 "PARSU2" 2206988 NIL PARSU2 (NIL T T) -7 NIL NIL NIL) (-906 2206435 2206481 2206548 "PARSER" 2206630 T PARSER (NIL) -7 NIL NIL NIL) (-905 2206044 2206119 2206221 "PARSCURV" 2206366 NIL PARSCURV (NIL T) -8 NIL NIL NIL) (-904 2205670 2205733 2205842 "PARSC2" 2205981 NIL PARSC2 (NIL T T) -7 NIL NIL NIL) (-903 2205297 2205367 2205464 "PARPCURV" 2205606 NIL PARPCURV (NIL T) -8 NIL NIL NIL) (-902 2204923 2204986 2205095 "PARPC2" 2205234 NIL PARPC2 (NIL T T) -7 NIL NIL NIL) (-901 2203912 2204296 2204478 "PARAMAST" 2204761 T PARAMAST (NIL) -8 NIL NIL NIL) (-900 2203420 2203518 2203637 "PAN2EXPR" 2203813 T PAN2EXPR (NIL) -7 NIL NIL NIL) (-899 2202113 2202541 2202769 "PALETTE" 2203212 T PALETTE (NIL) -8 NIL NIL NIL) (-898 2200458 2201118 2201478 "PAIR" 2201799 NIL PAIR (NIL T T) -8 NIL NIL NIL) (-897 2193391 2199715 2199910 "PADICRC" 2200312 NIL PADICRC (NIL NIL T) -8 NIL NIL NIL) (-896 2185648 2192735 2192920 "PADICRAT" 2193238 NIL PADICRAT (NIL NIL) -8 NIL NIL NIL) (-895 2182445 2184308 2184348 "PADICCT" 2184929 NIL PADICCT (NIL NIL) -9 NIL 2185211 NIL) (-894 2180461 2182382 2182427 "PADIC" 2182432 NIL PADIC (NIL NIL) -8 NIL NIL NIL) (-893 2179406 2179618 2179886 "PADEPAC" 2180248 NIL PADEPAC (NIL T NIL NIL) -7 NIL NIL NIL) (-892 2178606 2178751 2178957 "PADE" 2179268 NIL PADE (NIL T T T) -7 NIL NIL NIL) (-891 2176839 2177814 2178094 "OWP" 2178410 NIL OWP (NIL T NIL NIL NIL) -8 NIL NIL NIL) (-890 2176284 2176545 2176642 "OVERSET" 2176762 T OVERSET (NIL) -8 NIL NIL NIL) (-889 2175204 2175889 2176061 "OVAR" 2176152 NIL OVAR (NIL NIL) -8 NIL NIL NIL) (-888 2163440 2166313 2168513 "OUTFORM" 2173024 T OUTFORM (NIL) -8 NIL NIL NIL) (-887 2162722 2163037 2163164 "OUTBFILE" 2163333 T OUTBFILE (NIL) -8 NIL NIL NIL) (-886 2161999 2162194 2162222 "OUTBCON" 2162540 T OUTBCON (NIL) -9 NIL 2162706 NIL) (-885 2161582 2161712 2161869 "OUTBCON-" 2161874 NIL OUTBCON- (NIL T) -8 NIL NIL NIL) (-884 2160822 2160967 2161128 "OUT" 2161441 T OUT (NIL) -7 NIL NIL NIL) (-883 2160118 2160551 2160640 "OSI" 2160753 T OSI (NIL) -8 NIL NIL NIL) (-882 2159537 2159959 2159987 "OSGROUP" 2159992 T OSGROUP (NIL) -9 NIL 2160014 NIL) (-881 2158248 2158509 2158794 "ORTHPOL" 2159284 NIL ORTHPOL (NIL T) -7 NIL NIL NIL) (-880 2155499 2158083 2158204 "OREUP" 2158209 NIL OREUP (NIL NIL T NIL NIL) -8 NIL NIL NIL) (-879 2152602 2155190 2155317 "ORESUP" 2155441 NIL ORESUP (NIL T NIL NIL) -8 NIL NIL NIL) (-878 2150102 2150630 2151191 "OREPCTO" 2152091 NIL OREPCTO (NIL T T) -7 NIL NIL NIL) (-877 2143480 2145975 2146016 "OREPCAT" 2148364 NIL OREPCAT (NIL T) -9 NIL 2149468 NIL) (-876 2140453 2141409 2142467 "OREPCAT-" 2142472 NIL OREPCAT- (NIL T T) -8 NIL NIL NIL) (-875 2139645 2139923 2139951 "ORDTYPE" 2140260 T ORDTYPE (NIL) -9 NIL 2140423 NIL) (-874 2138946 2139162 2139417 "ORDTYPE-" 2139422 NIL ORDTYPE- (NIL T) -8 NIL NIL NIL) (-873 2138302 2138685 2138843 "ORDSTRCT" 2138848 NIL ORDSTRCT (NIL T NIL) -8 NIL NIL NIL) (-872 2137800 2138170 2138198 "ORDSET" 2138203 T ORDSET (NIL) -9 NIL 2138225 NIL) (-871 2136451 2137422 2137450 "ORDRING" 2137455 T ORDRING (NIL) -9 NIL 2137484 NIL) (-870 2135702 2136267 2136295 "ORDMON" 2136300 T ORDMON (NIL) -9 NIL 2136321 NIL) (-869 2134846 2135011 2135206 "ORDFUNS" 2135551 NIL ORDFUNS (NIL NIL T) -7 NIL NIL NIL) (-868 2134061 2134576 2134604 "ORDFIN" 2134669 T ORDFIN (NIL) -9 NIL 2134743 NIL) (-867 2133315 2133454 2133640 "ORDCOMP2" 2133921 NIL ORDCOMP2 (NIL T T) -7 NIL NIL NIL) (-866 2129662 2131901 2132310 "ORDCOMP" 2132939 NIL ORDCOMP (NIL T) -8 NIL NIL NIL) (-865 2126183 2127153 2127967 "OPTPROB" 2128868 T OPTPROB (NIL) -8 NIL NIL NIL) (-864 2122925 2123624 2124328 "OPTPACK" 2125499 T OPTPACK (NIL) -7 NIL NIL NIL) (-863 2120538 2121364 2121392 "OPTCAT" 2122211 T OPTCAT (NIL) -9 NIL 2122861 NIL) (-862 2119856 2120215 2120320 "OPSIG" 2120453 T OPSIG (NIL) -8 NIL NIL NIL) (-861 2119618 2119663 2119729 "OPQUERY" 2119810 T OPQUERY (NIL) -7 NIL NIL NIL) (-860 2118924 2119204 2119245 "OPERCAT" 2119457 NIL OPERCAT (NIL T) -9 NIL 2119554 NIL) (-859 2118667 2118735 2118852 "OPERCAT-" 2118857 NIL OPERCAT- (NIL T T) -8 NIL NIL NIL) (-858 2115583 2116978 2117482 "OP" 2118196 NIL OP (NIL T) -8 NIL NIL NIL) (-857 2114876 2115003 2115177 "ONECOMP2" 2115455 NIL ONECOMP2 (NIL T T) -7 NIL NIL NIL) (-856 2111489 2113673 2114042 "ONECOMP" 2114540 NIL ONECOMP (NIL T) -8 NIL NIL NIL) (-855 2110890 2111014 2111144 "OMSERVER" 2111379 T OMSERVER (NIL) -7 NIL NIL NIL) (-854 2107402 2110328 2110368 "OMSAGG" 2110429 NIL OMSAGG (NIL T) -9 NIL 2110494 NIL) (-853 2105977 2106288 2106570 "OMPKG" 2107140 T OMPKG (NIL) -7 NIL NIL NIL) (-852 2104324 2105526 2105695 "OMLO" 2105858 NIL OMLO (NIL T T) -8 NIL NIL NIL) (-851 2103260 2103431 2103651 "OMEXPR" 2104150 NIL OMEXPR (NIL T) -7 NIL NIL NIL) (-850 2102345 2102681 2102841 "OMERRK" 2103120 T OMERRK (NIL) -8 NIL NIL NIL) (-849 2101582 2101891 2102027 "OMERR" 2102229 T OMERR (NIL) -8 NIL NIL NIL) (-848 2100973 2101259 2101367 "OMENC" 2101494 T OMENC (NIL) -8 NIL NIL NIL) (-847 2094610 2096053 2097224 "OMDEV" 2099822 T OMDEV (NIL) -8 NIL NIL NIL) (-846 2093643 2093850 2094044 "OMCONN" 2094436 T OMCONN (NIL) -8 NIL NIL NIL) (-845 2093049 2093176 2093204 "OM" 2093503 T OM (NIL) -9 NIL NIL NIL) (-844 2091327 2092519 2092547 "OINTDOM" 2092552 T OINTDOM (NIL) -9 NIL 2092573 NIL) (-843 2088402 2090015 2090352 "OFMONOID" 2091022 NIL OFMONOID (NIL T) -8 NIL NIL NIL) (-842 2087636 2088339 2088384 "ODVAR" 2088389 NIL ODVAR (NIL T) -8 NIL NIL NIL) (-841 2084780 2087381 2087536 "ODR" 2087541 NIL ODR (NIL T T NIL) -8 NIL NIL NIL) (-840 2076192 2084556 2084682 "ODPOL" 2084687 NIL ODPOL (NIL T) -8 NIL NIL NIL) (-839 2069486 2076064 2076169 "ODP" 2076174 NIL ODP (NIL NIL T NIL) -8 NIL NIL NIL) (-838 2068228 2068467 2068742 "ODETOOLS" 2069260 NIL ODETOOLS (NIL T T) -7 NIL NIL NIL) (-837 2065171 2065853 2066569 "ODESYS" 2067561 NIL ODESYS (NIL T T) -7 NIL NIL NIL) (-836 2060001 2060961 2061986 "ODERTRIC" 2064246 NIL ODERTRIC (NIL T T) -7 NIL NIL NIL) (-835 2059421 2059509 2059703 "ODERED" 2059913 NIL ODERED (NIL T T T T T) -7 NIL NIL NIL) (-834 2056273 2056857 2057534 "ODERAT" 2058844 NIL ODERAT (NIL T T) -7 NIL NIL NIL) (-833 2053189 2053697 2054294 "ODEPRRIC" 2055802 NIL ODEPRRIC (NIL T T T T) -7 NIL NIL NIL) (-832 2051084 2051728 2052214 "ODEPROB" 2052723 T ODEPROB (NIL) -8 NIL NIL NIL) (-831 2047550 2048089 2048736 "ODEPRIM" 2050563 NIL ODEPRIM (NIL T T T T) -7 NIL NIL NIL) (-830 2046793 2046901 2047161 "ODEPAL" 2047442 NIL ODEPAL (NIL T T T T) -7 NIL NIL NIL) (-829 2042895 2043746 2044610 "ODEPACK" 2045949 T ODEPACK (NIL) -7 NIL NIL NIL) (-828 2041938 2042063 2042285 "ODEINT" 2042784 NIL ODEINT (NIL T T) -7 NIL NIL NIL) (-827 2036003 2037464 2038911 "ODEIFTBL" 2040511 T ODEIFTBL (NIL) -8 NIL NIL NIL) (-826 2031353 2032187 2033139 "ODEEF" 2035162 NIL ODEEF (NIL T T) -7 NIL NIL NIL) (-825 2030696 2030791 2031014 "ODECONST" 2031258 NIL ODECONST (NIL T T T) -7 NIL NIL NIL) (-824 2028759 2029468 2029496 "ODECAT" 2030101 T ODECAT (NIL) -9 NIL 2030632 NIL) (-823 2028391 2028440 2028567 "OCTCT2" 2028710 NIL OCTCT2 (NIL T T T T) -7 NIL NIL NIL) (-822 2024891 2028096 2028218 "OCT" 2028301 NIL OCT (NIL T) -8 NIL NIL NIL) (-821 2024084 2024684 2024712 "OCAMON" 2024717 T OCAMON (NIL) -9 NIL 2024738 NIL) (-820 2018355 2021127 2021167 "OC" 2022264 NIL OC (NIL T) -9 NIL 2023122 NIL) (-819 2015390 2016330 2017320 "OC-" 2017414 NIL OC- (NIL T T) -8 NIL NIL NIL) (-818 2014810 2015235 2015263 "OASGP" 2015268 T OASGP (NIL) -9 NIL 2015288 NIL) (-817 2013906 2014533 2014561 "OAMONS" 2014601 T OAMONS (NIL) -9 NIL 2014644 NIL) (-816 2013082 2013641 2013669 "OAMON" 2013727 T OAMON (NIL) -9 NIL 2013779 NIL) (-815 2012940 2012973 2013041 "OAMON-" 2013046 NIL OAMON- (NIL T) -8 NIL NIL NIL) (-814 2011721 2012474 2012502 "OAGROUP" 2012649 T OAGROUP (NIL) -9 NIL 2012742 NIL) (-813 2011424 2011512 2011630 "OAGROUP-" 2011635 NIL OAGROUP- (NIL T) -8 NIL NIL NIL) (-812 2011106 2011162 2011251 "NUMTUBE" 2011368 NIL NUMTUBE (NIL T) -7 NIL NIL NIL) (-811 2004625 2006197 2007733 "NUMQUAD" 2009590 T NUMQUAD (NIL) -7 NIL NIL NIL) (-810 2000305 2001339 2002374 "NUMODE" 2003610 T NUMODE (NIL) -7 NIL NIL NIL) (-809 1997586 1998526 1998554 "NUMINT" 1999477 T NUMINT (NIL) -9 NIL 2000241 NIL) (-808 1996498 1996731 1996949 "NUMFMT" 1997388 T NUMFMT (NIL) -7 NIL NIL NIL) (-807 1982681 1985802 1988334 "NUMERIC" 1994005 NIL NUMERIC (NIL T) -7 NIL NIL NIL) (-806 1976385 1982129 1982224 "NTSCAT" 1982229 NIL NTSCAT (NIL T T T T) -9 NIL 1982268 NIL) (-805 1975565 1975744 1975937 "NTPOLFN" 1976224 NIL NTPOLFN (NIL T) -7 NIL NIL NIL) (-804 1975191 1975254 1975363 "NSUP2" 1975502 NIL NSUP2 (NIL T T) -7 NIL NIL NIL) (-803 1961973 1972016 1972828 "NSUP" 1974412 NIL NSUP (NIL T) -8 NIL NIL NIL) (-802 1950816 1961747 1961880 "NSMP" 1961885 NIL NSMP (NIL T T) -8 NIL NIL NIL) (-801 1949224 1949549 1949906 "NREP" 1950504 NIL NREP (NIL T) -7 NIL NIL NIL) (-800 1947803 1948067 1948425 "NPCOEF" 1948967 NIL NPCOEF (NIL T T T T T) -7 NIL NIL NIL) (-799 1946851 1946984 1947200 "NORMRETR" 1947684 NIL NORMRETR (NIL T T T T NIL) -7 NIL NIL NIL) (-798 1944862 1945182 1945591 "NORMPK" 1946559 NIL NORMPK (NIL T T T T T) -7 NIL NIL NIL) (-797 1944541 1944575 1944699 "NORMMA" 1944828 NIL NORMMA (NIL T T T T) -7 NIL NIL NIL) (-796 1944324 1944359 1944428 "NONE1" 1944505 NIL NONE1 (NIL T) -7 NIL NIL NIL) (-795 1944088 1944281 1944310 "NONE" 1944315 T NONE (NIL) -8 NIL NIL NIL) (-794 1943579 1943647 1943826 "NODE1" 1944020 NIL NODE1 (NIL T T) -7 NIL NIL NIL) (-793 1941640 1942702 1942957 "NNI" 1943304 T NNI (NIL) -8 NIL NIL 1943539) (-792 1940036 1940373 1940737 "NLINSOL" 1941308 NIL NLINSOL (NIL T) -7 NIL NIL NIL) (-791 1936217 1937272 1938171 "NIPROB" 1939157 T NIPROB (NIL) -8 NIL NIL NIL) (-790 1934956 1935208 1935510 "NFINTBAS" 1935979 NIL NFINTBAS (NIL T T) -7 NIL NIL NIL) (-789 1934040 1934606 1934647 "NETCLT" 1934819 NIL NETCLT (NIL T) -9 NIL 1934901 NIL) (-788 1932712 1932979 1933260 "NCODIV" 1933808 NIL NCODIV (NIL T T) -7 NIL NIL NIL) (-787 1932468 1932511 1932586 "NCNTFRAC" 1932669 NIL NCNTFRAC (NIL T) -7 NIL NIL NIL) (-786 1930624 1931012 1931432 "NCEP" 1932093 NIL NCEP (NIL T) -7 NIL NIL NIL) (-785 1929287 1930234 1930262 "NASRING" 1930372 T NASRING (NIL) -9 NIL 1930452 NIL) (-784 1929070 1929126 1929220 "NASRING-" 1929225 NIL NASRING- (NIL T) -8 NIL NIL NIL) (-783 1928037 1928688 1928716 "NARNG" 1928833 T NARNG (NIL) -9 NIL 1928924 NIL) (-782 1927711 1927796 1927930 "NARNG-" 1927935 NIL NARNG- (NIL T) -8 NIL NIL NIL) (-781 1926548 1926797 1927032 "NAGSP" 1927496 T NAGSP (NIL) -7 NIL NIL NIL) (-780 1917592 1919504 1921177 "NAGS" 1924895 T NAGS (NIL) -7 NIL NIL NIL) (-779 1916116 1916448 1916779 "NAGF07" 1917281 T NAGF07 (NIL) -7 NIL NIL NIL) (-778 1910588 1911945 1913252 "NAGF04" 1914829 T NAGF04 (NIL) -7 NIL NIL NIL) (-777 1903460 1905170 1906803 "NAGF02" 1908975 T NAGF02 (NIL) -7 NIL NIL NIL) (-776 1898624 1899784 1900901 "NAGF01" 1902363 T NAGF01 (NIL) -7 NIL NIL NIL) (-775 1892204 1893818 1895403 "NAGE04" 1897059 T NAGE04 (NIL) -7 NIL NIL NIL) (-774 1883265 1885494 1887624 "NAGE02" 1890094 T NAGE02 (NIL) -7 NIL NIL NIL) (-773 1879158 1880165 1881129 "NAGE01" 1882321 T NAGE01 (NIL) -7 NIL NIL NIL) (-772 1876935 1877487 1878045 "NAGD03" 1878620 T NAGD03 (NIL) -7 NIL NIL NIL) (-771 1868631 1870613 1872567 "NAGD02" 1875001 T NAGD02 (NIL) -7 NIL NIL NIL) (-770 1862370 1863867 1865307 "NAGD01" 1867211 T NAGD01 (NIL) -7 NIL NIL NIL) (-769 1858507 1859401 1860238 "NAGC06" 1861553 T NAGC06 (NIL) -7 NIL NIL NIL) (-768 1856954 1857304 1857660 "NAGC05" 1858171 T NAGC05 (NIL) -7 NIL NIL NIL) (-767 1856318 1856449 1856593 "NAGC02" 1856830 T NAGC02 (NIL) -7 NIL NIL NIL) (-766 1855119 1855846 1855886 "NAALG" 1855965 NIL NAALG (NIL T) -9 NIL 1856026 NIL) (-765 1854948 1854983 1855073 "NAALG-" 1855078 NIL NAALG- (NIL T T) -8 NIL NIL NIL) (-764 1848820 1850006 1851193 "MULTSQFR" 1853844 NIL MULTSQFR (NIL T T T T) -7 NIL NIL NIL) (-763 1848127 1848214 1848398 "MULTFACT" 1848732 NIL MULTFACT (NIL T T T T) -7 NIL NIL NIL) (-762 1840272 1844710 1844763 "MTSCAT" 1845833 NIL MTSCAT (NIL T T) -9 NIL 1846349 NIL) (-761 1839978 1840038 1840130 "MTHING" 1840212 NIL MTHING (NIL T) -7 NIL NIL NIL) (-760 1839764 1839803 1839863 "MSYSCMD" 1839938 T MSYSCMD (NIL) -7 NIL NIL NIL) (-759 1836509 1839325 1839366 "MSETAGG" 1839371 NIL MSETAGG (NIL T) -9 NIL 1839405 NIL) (-758 1832223 1835264 1835584 "MSET" 1836222 NIL MSET (NIL T) -8 NIL NIL NIL) (-757 1827822 1829602 1830347 "MRING" 1831523 NIL MRING (NIL T T) -8 NIL NIL NIL) (-756 1827382 1827455 1827586 "MRF2" 1827749 NIL MRF2 (NIL T T T) -7 NIL NIL NIL) (-755 1826994 1827035 1827179 "MRATFAC" 1827341 NIL MRATFAC (NIL T T T T) -7 NIL NIL NIL) (-754 1824564 1824901 1825332 "MPRFF" 1826699 NIL MPRFF (NIL T T T T) -7 NIL NIL NIL) (-753 1817898 1824418 1824515 "MPOLY" 1824520 NIL MPOLY (NIL NIL T) -8 NIL NIL NIL) (-752 1817382 1817423 1817631 "MPCPF" 1817857 NIL MPCPF (NIL T T T T) -7 NIL NIL NIL) (-751 1816890 1816939 1817123 "MPC3" 1817333 NIL MPC3 (NIL T T T T T T T) -7 NIL NIL NIL) (-750 1816073 1816166 1816387 "MPC2" 1816805 NIL MPC2 (NIL T T T T T T T) -7 NIL NIL NIL) (-749 1814350 1814711 1815101 "MONOTOOL" 1815733 NIL MONOTOOL (NIL T T) -7 NIL NIL NIL) (-748 1813495 1813878 1813906 "MONOID" 1814125 T MONOID (NIL) -9 NIL 1814272 NIL) (-747 1813011 1813160 1813341 "MONOID-" 1813346 NIL MONOID- (NIL T) -8 NIL NIL NIL) (-746 1801984 1808831 1808890 "MONOGEN" 1809564 NIL MONOGEN (NIL T T) -9 NIL 1810020 NIL) (-745 1799034 1799937 1800937 "MONOGEN-" 1801056 NIL MONOGEN- (NIL T T T) -8 NIL NIL NIL) (-744 1797751 1798299 1798327 "MONADWU" 1798719 T MONADWU (NIL) -9 NIL 1798957 NIL) (-743 1797081 1797282 1797530 "MONADWU-" 1797535 NIL MONADWU- (NIL T) -8 NIL NIL NIL) (-742 1796366 1796670 1796698 "MONAD" 1796905 T MONAD (NIL) -9 NIL 1797017 NIL) (-741 1796033 1796129 1796261 "MONAD-" 1796266 NIL MONAD- (NIL T) -8 NIL NIL NIL) (-740 1794172 1794946 1795225 "MOEBIUS" 1795786 NIL MOEBIUS (NIL T) -8 NIL NIL NIL) (-739 1793340 1793840 1793880 "MODULE" 1793885 NIL MODULE (NIL T) -9 NIL 1793924 NIL) (-738 1792878 1793004 1793194 "MODULE-" 1793199 NIL MODULE- (NIL T T) -8 NIL NIL NIL) (-737 1790408 1791242 1791569 "MODRING" 1792702 NIL MODRING (NIL T T NIL NIL NIL) -8 NIL NIL NIL) (-736 1787137 1788513 1789034 "MODOP" 1789937 NIL MODOP (NIL T T) -8 NIL NIL NIL) (-735 1785623 1786204 1786481 "MODMONOM" 1787000 NIL MODMONOM (NIL T T NIL) -8 NIL NIL NIL) (-734 1774384 1783914 1784328 "MODMON" 1785260 NIL MODMON (NIL T T) -8 NIL NIL NIL) (-733 1771217 1773228 1773504 "MODFIELD" 1774259 NIL MODFIELD (NIL T T NIL NIL NIL) -8 NIL NIL NIL) (-732 1770128 1770498 1770688 "MMLFORM" 1771047 T MMLFORM (NIL) -8 NIL NIL NIL) (-731 1769648 1769697 1769876 "MMAP" 1770079 NIL MMAP (NIL T T T T T T) -7 NIL NIL NIL) (-730 1767541 1768480 1768521 "MLO" 1768944 NIL MLO (NIL T) -9 NIL 1769186 NIL) (-729 1764889 1765423 1766025 "MLIFT" 1767022 NIL MLIFT (NIL T T T T) -7 NIL NIL NIL) (-728 1764268 1764364 1764518 "MKUCFUNC" 1764800 NIL MKUCFUNC (NIL T T T) -7 NIL NIL NIL) (-727 1763861 1763937 1764060 "MKRECORD" 1764191 NIL MKRECORD (NIL T T) -7 NIL NIL NIL) (-726 1762884 1763070 1763298 "MKFUNC" 1763672 NIL MKFUNC (NIL T) -7 NIL NIL NIL) (-725 1762260 1762376 1762532 "MKFLCFN" 1762767 NIL MKFLCFN (NIL T) -7 NIL NIL NIL) (-724 1761525 1761639 1761824 "MKBCFUNC" 1762153 NIL MKBCFUNC (NIL T T T T) -7 NIL NIL NIL) (-723 1757522 1761079 1761215 "MINT" 1761409 T MINT (NIL) -8 NIL NIL NIL) (-722 1756304 1756577 1756854 "MHROWRED" 1757277 NIL MHROWRED (NIL T) -7 NIL NIL NIL) (-721 1751055 1754839 1755244 "MFLOAT" 1755919 T MFLOAT (NIL) -8 NIL NIL NIL) (-720 1750400 1750488 1750659 "MFINFACT" 1750967 NIL MFINFACT (NIL T T T T) -7 NIL NIL NIL) (-719 1746679 1747563 1748447 "MESH" 1749536 T MESH (NIL) -7 NIL NIL NIL) (-718 1745033 1745381 1745734 "MDDFACT" 1746366 NIL MDDFACT (NIL T) -7 NIL NIL NIL) (-717 1741569 1744164 1744205 "MDAGG" 1744460 NIL MDAGG (NIL T) -9 NIL 1744603 NIL) (-716 1729292 1740862 1741069 "MCMPLX" 1741382 T MCMPLX (NIL) -8 NIL NIL NIL) (-715 1728411 1728575 1728776 "MCDEN" 1729141 NIL MCDEN (NIL T T) -7 NIL NIL NIL) (-714 1726259 1726571 1726951 "MCALCFN" 1728141 NIL MCALCFN (NIL T T T T) -7 NIL NIL NIL) (-713 1725136 1725424 1725657 "MAYBE" 1726065 NIL MAYBE (NIL T) -8 NIL NIL NIL) (-712 1722694 1723271 1723833 "MATSTOR" 1724607 NIL MATSTOR (NIL T) -7 NIL NIL NIL) (-711 1718116 1722066 1722314 "MATRIX" 1722479 NIL MATRIX (NIL T) -8 NIL NIL NIL) (-710 1713816 1714589 1715325 "MATLIN" 1717473 NIL MATLIN (NIL T T T T) -7 NIL NIL NIL) (-709 1712392 1712563 1712896 "MATCAT2" 1713651 NIL MATCAT2 (NIL T T T T T T T T) -7 NIL NIL NIL) (-708 1701731 1705449 1705526 "MATCAT" 1710558 NIL MATCAT (NIL T T T) -9 NIL 1712030 NIL) (-707 1697684 1698994 1700407 "MATCAT-" 1700412 NIL MATCAT- (NIL T T T T) -8 NIL NIL NIL) (-706 1695760 1696120 1696504 "MAPPKG3" 1697359 NIL MAPPKG3 (NIL T T T) -7 NIL NIL NIL) (-705 1694717 1694914 1695136 "MAPPKG2" 1695584 NIL MAPPKG2 (NIL T T) -7 NIL NIL NIL) (-704 1693174 1693500 1693827 "MAPPKG1" 1694423 NIL MAPPKG1 (NIL T) -7 NIL NIL NIL) (-703 1692175 1692580 1692757 "MAPPAST" 1693017 T MAPPAST (NIL) -8 NIL NIL NIL) (-702 1691780 1691844 1691967 "MAPHACK3" 1692111 NIL MAPHACK3 (NIL T T T) -7 NIL NIL NIL) (-701 1691360 1691433 1691547 "MAPHACK2" 1691712 NIL MAPHACK2 (NIL T T) -7 NIL NIL NIL) (-700 1690786 1690901 1691043 "MAPHACK1" 1691251 NIL MAPHACK1 (NIL T) -7 NIL NIL NIL) (-699 1688709 1689486 1689790 "MAGMA" 1690514 NIL MAGMA (NIL T) -8 NIL NIL NIL) (-698 1688128 1688433 1688524 "MACROAST" 1688638 T MACROAST (NIL) -8 NIL NIL NIL) (-697 1684371 1686367 1686828 "M3D" 1687700 NIL M3D (NIL T) -8 NIL NIL NIL) (-696 1677843 1682682 1682723 "LZSTAGG" 1683505 NIL LZSTAGG (NIL T) -9 NIL 1683800 NIL) (-695 1673525 1674974 1676431 "LZSTAGG-" 1676436 NIL LZSTAGG- (NIL T T) -8 NIL NIL NIL) (-694 1670438 1671416 1671903 "LWORD" 1673070 NIL LWORD (NIL T) -8 NIL NIL NIL) (-693 1669960 1670242 1670317 "LSTAST" 1670383 T LSTAST (NIL) -8 NIL NIL NIL) (-692 1661888 1669731 1669865 "LSQM" 1669870 NIL LSQM (NIL NIL T) -8 NIL NIL NIL) (-691 1661106 1661251 1661479 "LSPP" 1661743 NIL LSPP (NIL T T T T) -7 NIL NIL NIL) (-690 1657843 1658559 1659289 "LSMP1" 1660408 NIL LSMP1 (NIL T) -7 NIL NIL NIL) (-689 1655625 1655956 1656412 "LSMP" 1657532 NIL LSMP (NIL T T T T) -7 NIL NIL NIL) (-688 1648753 1654715 1654756 "LSAGG" 1654818 NIL LSAGG (NIL T) -9 NIL 1654896 NIL) (-687 1645262 1646372 1647585 "LSAGG-" 1647590 NIL LSAGG- (NIL T T) -8 NIL NIL NIL) (-686 1642557 1644406 1644655 "LPOLY" 1645057 NIL LPOLY (NIL T T) -8 NIL NIL NIL) (-685 1642133 1642224 1642347 "LPEFRAC" 1642466 NIL LPEFRAC (NIL T) -7 NIL NIL NIL) (-684 1641816 1641895 1641923 "LOGIC" 1642034 T LOGIC (NIL) -9 NIL 1642116 NIL) (-683 1641672 1641701 1641772 "LOGIC-" 1641777 NIL LOGIC- (NIL T) -8 NIL NIL NIL) (-682 1640847 1641005 1641198 "LODOOPS" 1641528 NIL LODOOPS (NIL T T) -7 NIL NIL NIL) (-681 1639371 1639620 1639973 "LODOF" 1640594 NIL LODOF (NIL T T) -7 NIL NIL NIL) (-680 1635247 1638006 1638047 "LODOCAT" 1638485 NIL LODOCAT (NIL T) -9 NIL 1638696 NIL) (-679 1634962 1635038 1635165 "LODOCAT-" 1635170 NIL LODOCAT- (NIL T T) -8 NIL NIL NIL) (-678 1631948 1634803 1634921 "LODO2" 1634926 NIL LODO2 (NIL T T) -8 NIL NIL NIL) (-677 1629055 1631885 1631930 "LODO1" 1631935 NIL LODO1 (NIL T) -8 NIL NIL NIL) (-676 1626150 1628971 1629037 "LODO" 1629042 NIL LODO (NIL T NIL) -8 NIL NIL NIL) (-675 1625019 1625196 1625501 "LODEEF" 1625973 NIL LODEEF (NIL T T T) -7 NIL NIL NIL) (-674 1623005 1624113 1624366 "LO" 1624851 NIL LO (NIL T T T) -8 NIL NIL NIL) (-673 1617977 1621171 1621212 "LNAGG" 1622074 NIL LNAGG (NIL T) -9 NIL 1622509 NIL) (-672 1617070 1617338 1617680 "LNAGG-" 1617685 NIL LNAGG- (NIL T T) -8 NIL NIL NIL) (-671 1613050 1613995 1614634 "LMOPS" 1616485 NIL LMOPS (NIL T T NIL) -8 NIL NIL NIL) (-670 1612349 1612827 1612868 "LMODULE" 1612873 NIL LMODULE (NIL T) -9 NIL 1612899 NIL) (-669 1609304 1611994 1612117 "LMDICT" 1612259 NIL LMDICT (NIL T) -8 NIL NIL NIL) (-668 1608880 1609094 1609135 "LLINSET" 1609196 NIL LLINSET (NIL T) -9 NIL 1609240 NIL) (-667 1608525 1608788 1608848 "LITERAL" 1608853 NIL LITERAL (NIL T) -8 NIL NIL NIL) (-666 1608044 1608124 1608263 "LIST3" 1608445 NIL LIST3 (NIL T T T) -7 NIL NIL NIL) (-665 1606142 1606490 1606889 "LIST2MAP" 1607691 NIL LIST2MAP (NIL T T) -7 NIL NIL NIL) (-664 1605131 1605327 1605555 "LIST2" 1605960 NIL LIST2 (NIL T T) -7 NIL NIL NIL) (-663 1597585 1604065 1604369 "LIST" 1604860 NIL LIST (NIL T) -8 NIL NIL NIL) (-662 1597168 1597404 1597445 "LINSET" 1597450 NIL LINSET (NIL T) -9 NIL 1597484 NIL) (-661 1595982 1596676 1596843 "LINFORM" 1597053 NIL LINFORM (NIL T NIL) -8 NIL NIL NIL) (-660 1594281 1595009 1595050 "LINEXP" 1595540 NIL LINEXP (NIL T) -9 NIL 1595813 NIL) (-659 1592857 1593761 1593942 "LINELT" 1594152 NIL LINELT (NIL T NIL) -8 NIL NIL NIL) (-658 1591414 1591694 1592005 "LINDEP" 1592609 NIL LINDEP (NIL T T) -7 NIL NIL NIL) (-657 1590550 1591146 1591256 "LINBASIS" 1591344 NIL LINBASIS (NIL NIL) -8 NIL NIL NIL) (-656 1587287 1588036 1588813 "LIMITRF" 1589805 NIL LIMITRF (NIL T) -7 NIL NIL NIL) (-655 1585572 1585886 1586295 "LIMITPS" 1586982 NIL LIMITPS (NIL T T) -7 NIL NIL NIL) (-654 1584400 1584975 1585015 "LIECAT" 1585155 NIL LIECAT (NIL T) -9 NIL 1585306 NIL) (-653 1584235 1584268 1584356 "LIECAT-" 1584361 NIL LIECAT- (NIL T T) -8 NIL NIL NIL) (-652 1578255 1583746 1583974 "LIE" 1584056 NIL LIE (NIL T T) -8 NIL NIL NIL) (-651 1570440 1577795 1577951 "LIB" 1578119 T LIB (NIL) -8 NIL NIL NIL) (-650 1566009 1566958 1567893 "LGROBP" 1569557 NIL LGROBP (NIL NIL T) -7 NIL NIL NIL) (-649 1564633 1565541 1565569 "LFCAT" 1565776 T LFCAT (NIL) -9 NIL 1565915 NIL) (-648 1562571 1562905 1563255 "LF" 1564354 NIL LF (NIL T T) -7 NIL NIL NIL) (-647 1559431 1560103 1560791 "LEXTRIPK" 1561935 NIL LEXTRIPK (NIL T NIL) -7 NIL NIL NIL) (-646 1556019 1557001 1557504 "LEXP" 1559011 NIL LEXP (NIL T T NIL) -8 NIL NIL NIL) (-645 1555435 1555740 1555832 "LETAST" 1555947 T LETAST (NIL) -8 NIL NIL NIL) (-644 1553821 1554146 1554547 "LEADCDET" 1555117 NIL LEADCDET (NIL T T T T) -7 NIL NIL NIL) (-643 1552999 1553085 1553314 "LAZM3PK" 1553742 NIL LAZM3PK (NIL T T T T T T) -7 NIL NIL NIL) (-642 1547524 1551076 1551614 "LAUPOL" 1552511 NIL LAUPOL (NIL T T) -8 NIL NIL NIL) (-641 1547097 1547147 1547308 "LAPLACE" 1547474 NIL LAPLACE (NIL T T) -7 NIL NIL NIL) (-640 1545945 1546661 1546702 "LALG" 1546764 NIL LALG (NIL T) -9 NIL 1546823 NIL) (-639 1545641 1545718 1545854 "LALG-" 1545859 NIL LALG- (NIL T T) -8 NIL NIL NIL) (-638 1543378 1544742 1544993 "LA" 1545474 NIL LA (NIL T T T) -8 NIL NIL NIL) (-637 1543207 1543237 1543278 "KVTFROM" 1543340 NIL KVTFROM (NIL T) -9 NIL NIL NIL) (-636 1541964 1542574 1542759 "KTVLOGIC" 1543042 T KTVLOGIC (NIL) -8 NIL NIL NIL) (-635 1541793 1541823 1541864 "KRCFROM" 1541926 NIL KRCFROM (NIL T) -9 NIL NIL NIL) (-634 1540685 1540884 1541183 "KOVACIC" 1541593 NIL KOVACIC (NIL T T) -7 NIL NIL NIL) (-633 1540514 1540544 1540585 "KONVERT" 1540647 NIL KONVERT (NIL T) -9 NIL NIL NIL) (-632 1540343 1540373 1540414 "KOERCE" 1540476 NIL KOERCE (NIL T) -9 NIL NIL NIL) (-631 1539827 1539920 1540052 "KERNEL2" 1540257 NIL KERNEL2 (NIL T T) -7 NIL NIL NIL) (-630 1537514 1538420 1538797 "KERNEL" 1539483 NIL KERNEL (NIL T) -8 NIL NIL NIL) (-629 1530985 1535991 1536045 "KDAGG" 1536422 NIL KDAGG (NIL T T) -9 NIL 1536628 NIL) (-628 1530496 1530638 1530843 "KDAGG-" 1530848 NIL KDAGG- (NIL T T T) -8 NIL NIL NIL) (-627 1523196 1530157 1530312 "KAFILE" 1530374 NIL KAFILE (NIL T) -8 NIL NIL NIL) (-626 1522800 1523085 1523148 "JVMOP" 1523153 T JVMOP (NIL) -8 NIL NIL NIL) (-625 1521536 1522040 1522289 "JVMMDACC" 1522571 T JVMMDACC (NIL) -8 NIL NIL NIL) (-624 1520472 1520926 1521131 "JVMFDACC" 1521351 T JVMFDACC (NIL) -8 NIL NIL NIL) (-623 1519053 1519548 1519848 "JVMCSTTG" 1520192 T JVMCSTTG (NIL) -8 NIL NIL NIL) (-622 1518189 1518593 1518754 "JVMCFACC" 1518912 T JVMCFACC (NIL) -8 NIL NIL NIL) (-621 1517867 1518106 1518155 "JVMBCODE" 1518160 T JVMBCODE (NIL) -8 NIL NIL NIL) (-620 1511886 1517378 1517606 "JORDAN" 1517688 NIL JORDAN (NIL T T) -8 NIL NIL NIL) (-619 1511199 1511535 1511656 "JOINAST" 1511785 T JOINAST (NIL) -8 NIL NIL NIL) (-618 1507234 1509376 1509430 "IXAGG" 1510359 NIL IXAGG (NIL T T) -9 NIL 1510818 NIL) (-617 1506087 1506459 1506878 "IXAGG-" 1506883 NIL IXAGG- (NIL T T T) -8 NIL NIL NIL) (-616 1501176 1506009 1506068 "IVECTOR" 1506073 NIL IVECTOR (NIL T NIL) -8 NIL NIL NIL) (-615 1499901 1500179 1500445 "ITUPLE" 1500943 NIL ITUPLE (NIL T) -8 NIL NIL NIL) (-614 1498373 1498580 1498875 "ITRIGMNP" 1499723 NIL ITRIGMNP (NIL T T T) -7 NIL NIL NIL) (-613 1497100 1497322 1497605 "ITFUN3" 1498149 NIL ITFUN3 (NIL T T T) -7 NIL NIL NIL) (-612 1496698 1496761 1496884 "ITFUN2" 1497023 NIL ITFUN2 (NIL T T) -8 NIL NIL NIL) (-611 1495803 1496178 1496352 "ITFORM" 1496544 T ITFORM (NIL) -8 NIL NIL NIL) (-610 1493572 1494823 1495101 "ITAYLOR" 1495558 NIL ITAYLOR (NIL T) -8 NIL NIL NIL) (-609 1481976 1487709 1488872 "ISUPS" 1492442 NIL ISUPS (NIL T) -8 NIL NIL NIL) (-608 1481068 1481220 1481456 "ISUMP" 1481823 NIL ISUMP (NIL T T T T) -7 NIL NIL NIL) (-607 1475918 1481013 1481054 "ISTRING" 1481059 NIL ISTRING (NIL NIL) -8 NIL NIL NIL) (-606 1475334 1475639 1475731 "ISAST" 1475846 T ISAST (NIL) -8 NIL NIL NIL) (-605 1474532 1474625 1474841 "IRURPK" 1475248 NIL IRURPK (NIL T T T T T) -7 NIL NIL NIL) (-604 1473444 1473669 1473909 "IRSN" 1474312 T IRSN (NIL) -7 NIL NIL NIL) (-603 1471489 1471870 1472299 "IRRF2F" 1473082 NIL IRRF2F (NIL T) -7 NIL NIL NIL) (-602 1471230 1471274 1471350 "IRREDFFX" 1471445 NIL IRREDFFX (NIL T) -7 NIL NIL NIL) (-601 1469803 1470104 1470403 "IROOT" 1470963 NIL IROOT (NIL T) -7 NIL NIL NIL) (-600 1468942 1469296 1469447 "IRFORM" 1469672 T IRFORM (NIL) -8 NIL NIL NIL) (-599 1468024 1468155 1468369 "IR2F" 1468825 NIL IR2F (NIL T T) -7 NIL NIL NIL) (-598 1465613 1466132 1466698 "IR2" 1467502 NIL IR2 (NIL T T) -7 NIL NIL NIL) (-597 1462053 1463297 1463989 "IR" 1464953 NIL IR (NIL T) -8 NIL NIL NIL) (-596 1461838 1461878 1461938 "IPRNTPK" 1462013 T IPRNTPK (NIL) -7 NIL NIL NIL) (-595 1457812 1461727 1461796 "IPF" 1461801 NIL IPF (NIL NIL) -8 NIL NIL NIL) (-594 1455840 1457737 1457794 "IPADIC" 1457799 NIL IPADIC (NIL NIL NIL) -8 NIL NIL NIL) (-593 1455098 1455400 1455530 "IP4ADDR" 1455730 T IP4ADDR (NIL) -8 NIL NIL NIL) (-592 1454436 1454727 1454859 "IOMODE" 1454986 T IOMODE (NIL) -8 NIL NIL NIL) (-591 1453407 1454033 1454160 "IOBFILE" 1454329 T IOBFILE (NIL) -8 NIL NIL NIL) (-590 1452817 1453311 1453339 "IOBCON" 1453344 T IOBCON (NIL) -9 NIL 1453365 NIL) (-589 1452322 1452386 1452569 "INVLAPLA" 1452753 NIL INVLAPLA (NIL T T) -7 NIL NIL NIL) (-588 1441892 1444324 1446710 "INTTR" 1449986 NIL INTTR (NIL T T) -7 NIL NIL NIL) (-587 1438185 1438969 1439834 "INTTOOLS" 1441077 NIL INTTOOLS (NIL T T) -7 NIL NIL NIL) (-586 1437765 1437862 1437979 "INTSLPE" 1438088 T INTSLPE (NIL) -7 NIL NIL NIL) (-585 1435232 1437688 1437747 "INTRVL" 1437752 NIL INTRVL (NIL T) -8 NIL NIL NIL) (-584 1432810 1433346 1433921 "INTRF" 1434717 NIL INTRF (NIL T) -7 NIL NIL NIL) (-583 1432203 1432318 1432460 "INTRET" 1432708 NIL INTRET (NIL T) -7 NIL NIL NIL) (-582 1430176 1430589 1431059 "INTRAT" 1431811 NIL INTRAT (NIL T T) -7 NIL NIL NIL) (-581 1427421 1428022 1428641 "INTPM" 1429661 NIL INTPM (NIL T T) -7 NIL NIL NIL) (-580 1424138 1424765 1425503 "INTPAF" 1426807 NIL INTPAF (NIL T T T) -7 NIL NIL NIL) (-579 1419239 1420279 1421330 "INTPACK" 1423107 T INTPACK (NIL) -7 NIL NIL NIL) (-578 1418485 1418643 1418851 "INTHERTR" 1419081 NIL INTHERTR (NIL T T) -7 NIL NIL NIL) (-577 1417918 1418004 1418192 "INTHERAL" 1418399 NIL INTHERAL (NIL T T T T) -7 NIL NIL NIL) (-576 1415686 1416207 1416664 "INTHEORY" 1417481 T INTHEORY (NIL) -7 NIL NIL NIL) (-575 1407018 1408713 1410485 "INTG0" 1414038 NIL INTG0 (NIL T T T) -7 NIL NIL NIL) (-574 1387543 1392381 1397191 "INTFTBL" 1402228 T INTFTBL (NIL) -8 NIL NIL NIL) (-573 1386768 1386930 1387103 "INTFACT" 1387402 NIL INTFACT (NIL T) -7 NIL NIL NIL) (-572 1384165 1384641 1385198 "INTEF" 1386322 NIL INTEF (NIL T T) -7 NIL NIL NIL) (-571 1382362 1383257 1383285 "INTDOM" 1383586 T INTDOM (NIL) -9 NIL 1383793 NIL) (-570 1381701 1381905 1382147 "INTDOM-" 1382152 NIL INTDOM- (NIL T) -8 NIL NIL NIL) (-569 1377569 1379990 1380044 "INTCAT" 1380843 NIL INTCAT (NIL T) -9 NIL 1381164 NIL) (-568 1377023 1377144 1377272 "INTBIT" 1377461 T INTBIT (NIL) -7 NIL NIL NIL) (-567 1375704 1375876 1376183 "INTALG" 1376868 NIL INTALG (NIL T T T T T) -7 NIL NIL NIL) (-566 1375181 1375277 1375434 "INTAF" 1375608 NIL INTAF (NIL T T) -7 NIL NIL NIL) (-565 1368148 1374991 1375131 "INTABL" 1375136 NIL INTABL (NIL T T T) -8 NIL NIL NIL) (-564 1367389 1367951 1368016 "INT8" 1368050 T INT8 (NIL) -8 NIL NIL 1368095) (-563 1366629 1367191 1367256 "INT64" 1367290 T INT64 (NIL) -8 NIL NIL 1367335) (-562 1365869 1366431 1366496 "INT32" 1366530 T INT32 (NIL) -8 NIL NIL 1366575) (-561 1365109 1365671 1365736 "INT16" 1365770 T INT16 (NIL) -8 NIL NIL 1365815) (-560 1361313 1364906 1365015 "INT" 1365020 T INT (NIL) -8 NIL NIL NIL) (-559 1355422 1358861 1358889 "INS" 1359823 T INS (NIL) -9 NIL 1360488 NIL) (-558 1352579 1353499 1354440 "INS-" 1354513 NIL INS- (NIL T) -8 NIL NIL NIL) (-557 1351336 1351581 1351879 "INPSIGN" 1352332 NIL INPSIGN (NIL T T) -7 NIL NIL NIL) (-556 1350430 1350571 1350768 "INPRODPF" 1351216 NIL INPRODPF (NIL T T) -7 NIL NIL NIL) (-555 1349300 1349441 1349678 "INPRODFF" 1350310 NIL INPRODFF (NIL T T T T) -7 NIL NIL NIL) (-554 1348288 1348452 1348712 "INNMFACT" 1349136 NIL INNMFACT (NIL T T T T) -7 NIL NIL NIL) (-553 1347467 1347582 1347770 "INMODGCD" 1348187 NIL INMODGCD (NIL T T NIL NIL) -7 NIL NIL NIL) (-552 1345951 1346220 1346544 "INFSP" 1347212 NIL INFSP (NIL T T T) -7 NIL NIL NIL) (-551 1345111 1345252 1345435 "INFPROD0" 1345831 NIL INFPROD0 (NIL T T) -7 NIL NIL NIL) (-550 1344709 1344781 1344879 "INFORM1" 1345046 NIL INFORM1 (NIL T) -7 NIL NIL NIL) (-549 1341276 1342774 1343289 "INFORM" 1344202 T INFORM (NIL) -8 NIL NIL NIL) (-548 1340781 1340888 1341002 "INFINITY" 1341182 T INFINITY (NIL) -7 NIL NIL NIL) (-547 1339855 1340501 1340602 "INETCLTS" 1340700 T INETCLTS (NIL) -8 NIL NIL NIL) (-546 1338453 1338721 1339042 "INEP" 1339603 NIL INEP (NIL T T T) -7 NIL NIL NIL) (-545 1337483 1338350 1338415 "INDE" 1338420 NIL INDE (NIL T) -8 NIL NIL NIL) (-544 1337035 1337115 1337232 "INCRMAPS" 1337410 NIL INCRMAPS (NIL T) -7 NIL NIL NIL) (-543 1335757 1336304 1336510 "INBFILE" 1336849 T INBFILE (NIL) -8 NIL NIL NIL) (-542 1330936 1331993 1332937 "INBFF" 1334845 NIL INBFF (NIL T) -7 NIL NIL NIL) (-541 1329790 1330113 1330141 "INBCON" 1330654 T INBCON (NIL) -9 NIL 1330920 NIL) (-540 1329000 1329265 1329541 "INBCON-" 1329546 NIL INBCON- (NIL T) -8 NIL NIL NIL) (-539 1328419 1328724 1328815 "INAST" 1328929 T INAST (NIL) -8 NIL NIL NIL) (-538 1327786 1328098 1328204 "IMPTAST" 1328333 T IMPTAST (NIL) -8 NIL NIL NIL) (-537 1323707 1327630 1327734 "IMATRIX" 1327739 NIL IMATRIX (NIL T NIL NIL) -8 NIL NIL NIL) (-536 1322399 1322538 1322854 "IMATQF" 1323563 NIL IMATQF (NIL T T T T T T T T) -7 NIL NIL NIL) (-535 1320579 1320846 1321183 "IMATLIN" 1322155 NIL IMATLIN (NIL T T T T) -7 NIL NIL NIL) (-534 1314494 1320503 1320561 "ILIST" 1320566 NIL ILIST (NIL T NIL) -8 NIL NIL NIL) (-533 1312160 1314354 1314467 "IIARRAY2" 1314472 NIL IIARRAY2 (NIL T NIL NIL T T) -8 NIL NIL NIL) (-532 1306981 1312071 1312135 "IFF" 1312140 NIL IFF (NIL NIL NIL) -8 NIL NIL NIL) (-531 1306262 1306598 1306714 "IFAST" 1306885 T IFAST (NIL) -8 NIL NIL NIL) (-530 1300774 1305554 1305742 "IFARRAY" 1306119 NIL IFARRAY (NIL T NIL) -8 NIL NIL NIL) (-529 1299812 1300678 1300751 "IFAMON" 1300756 NIL IFAMON (NIL T T NIL) -8 NIL NIL NIL) (-528 1299384 1299461 1299515 "IEVALAB" 1299722 NIL IEVALAB (NIL T T) -9 NIL NIL NIL) (-527 1299047 1299127 1299287 "IEVALAB-" 1299292 NIL IEVALAB- (NIL T T T) -8 NIL NIL NIL) (-526 1298080 1298936 1299011 "IDPOAMS" 1299016 NIL IDPOAMS (NIL T T) -8 NIL NIL NIL) (-525 1297182 1297969 1298044 "IDPOAM" 1298049 NIL IDPOAM (NIL T T) -8 NIL NIL NIL) (-524 1296563 1297097 1297159 "IDPO" 1297164 NIL IDPO (NIL T T) -8 NIL NIL NIL) (-523 1295043 1295570 1295622 "IDPC" 1296134 NIL IDPC (NIL T T) -9 NIL 1296415 NIL) (-522 1294375 1294935 1295008 "IDPAM" 1295013 NIL IDPAM (NIL T T) -8 NIL NIL NIL) (-521 1293590 1294267 1294340 "IDPAG" 1294345 NIL IDPAG (NIL T T) -8 NIL NIL NIL) (-520 1293134 1293396 1293486 "IDENT" 1293520 T IDENT (NIL) -8 NIL NIL NIL) (-519 1289353 1290237 1291132 "IDECOMP" 1292291 NIL IDECOMP (NIL NIL NIL) -7 NIL NIL NIL) (-518 1281988 1283276 1284323 "IDEAL" 1288389 NIL IDEAL (NIL T T T T) -8 NIL NIL NIL) (-517 1281130 1281260 1281460 "ICDEN" 1281872 NIL ICDEN (NIL T T T T) -7 NIL NIL NIL) (-516 1280105 1280610 1280757 "ICARD" 1281003 T ICARD (NIL) -8 NIL NIL NIL) (-515 1278135 1278478 1278883 "IBPTOOLS" 1279782 NIL IBPTOOLS (NIL T T T T) -7 NIL NIL NIL) (-514 1273250 1277755 1277868 "IBITS" 1278054 NIL IBITS (NIL NIL) -8 NIL NIL NIL) (-513 1269925 1270549 1271244 "IBATOOL" 1272667 NIL IBATOOL (NIL T T T) -7 NIL NIL NIL) (-512 1267686 1268166 1268699 "IBACHIN" 1269460 NIL IBACHIN (NIL T T T) -7 NIL NIL NIL) (-511 1265276 1267532 1267635 "IARRAY2" 1267640 NIL IARRAY2 (NIL T NIL NIL) -8 NIL NIL NIL) (-510 1260989 1265202 1265259 "IARRAY1" 1265264 NIL IARRAY1 (NIL T NIL) -8 NIL NIL NIL) (-509 1254006 1259401 1259882 "IAN" 1260528 T IAN (NIL) -8 NIL NIL NIL) (-508 1253511 1253574 1253747 "IALGFACT" 1253943 NIL IALGFACT (NIL T T T T) -7 NIL NIL NIL) (-507 1253003 1253152 1253180 "HYPCAT" 1253387 T HYPCAT (NIL) -9 NIL NIL NIL) (-506 1252505 1252658 1252844 "HYPCAT-" 1252849 NIL HYPCAT- (NIL T) -8 NIL NIL NIL) (-505 1252052 1252300 1252383 "HOSTNAME" 1252442 T HOSTNAME (NIL) -8 NIL NIL NIL) (-504 1251885 1251934 1251975 "HOMOTOP" 1251980 NIL HOMOTOP (NIL T) -9 NIL 1252013 NIL) (-503 1248318 1249817 1249858 "HOAGG" 1250839 NIL HOAGG (NIL T) -9 NIL 1251568 NIL) (-502 1246834 1247311 1247837 "HOAGG-" 1247842 NIL HOAGG- (NIL T T) -8 NIL NIL NIL) (-501 1239891 1246427 1246577 "HEXADEC" 1246704 T HEXADEC (NIL) -8 NIL NIL NIL) (-500 1238603 1238861 1239124 "HEUGCD" 1239668 NIL HEUGCD (NIL T) -7 NIL NIL NIL) (-499 1237535 1238440 1238570 "HELLFDIV" 1238575 NIL HELLFDIV (NIL T T T T) -8 NIL NIL NIL) (-498 1235543 1237310 1237399 "HEAP" 1237478 NIL HEAP (NIL T) -8 NIL NIL NIL) (-497 1234740 1235095 1235229 "HEADAST" 1235429 T HEADAST (NIL) -8 NIL NIL NIL) (-496 1228078 1234655 1234717 "HDP" 1234722 NIL HDP (NIL NIL T) -8 NIL NIL NIL) (-495 1221097 1227713 1227865 "HDMP" 1227979 NIL HDMP (NIL NIL T) -8 NIL NIL NIL) (-494 1220403 1220561 1220725 "HB" 1220953 T HB (NIL) -7 NIL NIL NIL) (-493 1213413 1220249 1220353 "HASHTBL" 1220358 NIL HASHTBL (NIL T T NIL) -8 NIL NIL NIL) (-492 1212829 1213134 1213226 "HASAST" 1213341 T HASAST (NIL) -8 NIL NIL NIL) (-491 1210242 1212451 1212633 "HACKPI" 1212667 T HACKPI (NIL) -8 NIL NIL NIL) (-490 1205414 1210095 1210208 "GTSET" 1210213 NIL GTSET (NIL T T T T) -8 NIL NIL NIL) (-489 1198453 1205292 1205390 "GSTBL" 1205395 NIL GSTBL (NIL T T T NIL) -8 NIL NIL NIL) (-488 1190216 1197618 1197874 "GSERIES" 1198253 NIL GSERIES (NIL T NIL NIL) -8 NIL NIL NIL) (-487 1189247 1189760 1189788 "GROUP" 1189991 T GROUP (NIL) -9 NIL 1190125 NIL) (-486 1188571 1188772 1189023 "GROUP-" 1189028 NIL GROUP- (NIL T) -8 NIL NIL NIL) (-485 1186920 1187259 1187646 "GROEBSOL" 1188248 NIL GROEBSOL (NIL NIL T T) -7 NIL NIL NIL) (-484 1185748 1186108 1186159 "GRMOD" 1186688 NIL GRMOD (NIL T T) -9 NIL 1186856 NIL) (-483 1185504 1185552 1185680 "GRMOD-" 1185685 NIL GRMOD- (NIL T T T) -8 NIL NIL NIL) (-482 1180644 1181858 1182858 "GRIMAGE" 1184524 T GRIMAGE (NIL) -8 NIL NIL NIL) (-481 1179038 1179371 1179695 "GRDEF" 1180340 T GRDEF (NIL) -7 NIL NIL NIL) (-480 1178470 1178598 1178739 "GRAY" 1178917 T GRAY (NIL) -7 NIL NIL NIL) (-479 1177547 1178049 1178100 "GRALG" 1178253 NIL GRALG (NIL T T) -9 NIL 1178346 NIL) (-478 1177184 1177281 1177444 "GRALG-" 1177449 NIL GRALG- (NIL T T T) -8 NIL NIL NIL) (-477 1173665 1176767 1176946 "GPOLSET" 1177090 NIL GPOLSET (NIL T T T T) -8 NIL NIL NIL) (-476 1173013 1173076 1173334 "GOSPER" 1173602 NIL GOSPER (NIL T T T T T) -7 NIL NIL NIL) (-475 1168583 1169451 1169977 "GMODPOL" 1172712 NIL GMODPOL (NIL NIL T T T NIL T) -8 NIL NIL NIL) (-474 1167570 1167772 1168010 "GHENSEL" 1168395 NIL GHENSEL (NIL T T) -7 NIL NIL NIL) (-473 1161642 1162569 1163589 "GENUPS" 1166654 NIL GENUPS (NIL T T) -7 NIL NIL NIL) (-472 1161333 1161390 1161479 "GENUFACT" 1161585 NIL GENUFACT (NIL T) -7 NIL NIL NIL) (-471 1160733 1160822 1160987 "GENPGCD" 1161251 NIL GENPGCD (NIL T T T T) -7 NIL NIL NIL) (-470 1160201 1160242 1160455 "GENMFACT" 1160692 NIL GENMFACT (NIL T T T T T) -7 NIL NIL NIL) (-469 1158737 1159024 1159331 "GENEEZ" 1159944 NIL GENEEZ (NIL T T) -7 NIL NIL NIL) (-468 1151916 1158348 1158510 "GDMP" 1158660 NIL GDMP (NIL NIL T T) -8 NIL NIL NIL) (-467 1140654 1145687 1146793 "GCNAALG" 1150899 NIL GCNAALG (NIL T NIL NIL NIL) -8 NIL NIL NIL) (-466 1138781 1139829 1139857 "GCDDOM" 1140112 T GCDDOM (NIL) -9 NIL 1140269 NIL) (-465 1138221 1138378 1138593 "GCDDOM-" 1138598 NIL GCDDOM- (NIL T) -8 NIL NIL NIL) (-464 1126693 1129167 1131559 "GBINTERN" 1135912 NIL GBINTERN (NIL T T T T) -7 NIL NIL NIL) (-463 1124494 1124822 1125243 "GBF" 1126368 NIL GBF (NIL T T T T) -7 NIL NIL NIL) (-462 1123251 1123440 1123707 "GBEUCLID" 1124310 NIL GBEUCLID (NIL T T T T) -7 NIL NIL NIL) (-461 1121901 1122108 1122412 "GB" 1123030 NIL GB (NIL T T T T) -7 NIL NIL NIL) (-460 1121232 1121375 1121524 "GAUSSFAC" 1121772 T GAUSSFAC (NIL) -7 NIL NIL NIL) (-459 1119553 1119901 1120215 "GALUTIL" 1120951 NIL GALUTIL (NIL T) -7 NIL NIL NIL) (-458 1117813 1118135 1118459 "GALPOLYU" 1119280 NIL GALPOLYU (NIL T T) -7 NIL NIL NIL) (-457 1115112 1115468 1115875 "GALFACTU" 1117510 NIL GALFACTU (NIL T T T) -7 NIL NIL NIL) (-456 1106726 1108417 1110025 "GALFACT" 1113544 NIL GALFACT (NIL T) -7 NIL NIL NIL) (-455 1104012 1104772 1104800 "FVFUN" 1105956 T FVFUN (NIL) -9 NIL 1106676 NIL) (-454 1103242 1103460 1103488 "FVC" 1103779 T FVC (NIL) -9 NIL 1103962 NIL) (-453 1102843 1103067 1103135 "FUNDESC" 1103194 T FUNDESC (NIL) -8 NIL NIL NIL) (-452 1102416 1102640 1102721 "FUNCTION" 1102795 NIL FUNCTION (NIL NIL) -8 NIL NIL NIL) (-451 1101093 1101717 1101920 "FTEM" 1102233 T FTEM (NIL) -8 NIL NIL NIL) (-450 1098723 1099415 1099881 "FT" 1100647 T FT (NIL) -8 NIL NIL NIL) (-449 1096992 1097303 1097700 "FSUPFACT" 1098414 NIL FSUPFACT (NIL T T T) -7 NIL NIL NIL) (-448 1095311 1095678 1096010 "FST" 1096680 T FST (NIL) -8 NIL NIL NIL) (-447 1094492 1094616 1094804 "FSRED" 1095193 NIL FSRED (NIL T T) -7 NIL NIL NIL) (-446 1093181 1093447 1093794 "FSPRMELT" 1094207 NIL FSPRMELT (NIL T T) -7 NIL NIL NIL) (-445 1090391 1090925 1091411 "FSPECF" 1092744 NIL FSPECF (NIL T T) -7 NIL NIL NIL) (-444 1089913 1089973 1090143 "FSINT" 1090332 NIL FSINT (NIL T T) -7 NIL NIL NIL) (-443 1088049 1088906 1089209 "FSERIES" 1089692 NIL FSERIES (NIL T T) -8 NIL NIL NIL) (-442 1087073 1087207 1087431 "FSCINT" 1087929 NIL FSCINT (NIL T T) -7 NIL NIL NIL) (-441 1086097 1086258 1086485 "FSAGG2" 1086926 NIL FSAGG2 (NIL T T T T) -7 NIL NIL NIL) (-440 1081961 1085041 1085082 "FSAGG" 1085452 NIL FSAGG (NIL T) -9 NIL 1085711 NIL) (-439 1079561 1080324 1081120 "FSAGG-" 1081215 NIL FSAGG- (NIL T T) -8 NIL NIL NIL) (-438 1077221 1077519 1078067 "FS2UPS" 1079279 NIL FS2UPS (NIL T T T T T NIL) -7 NIL NIL NIL) (-437 1076087 1076270 1076572 "FS2EXPXP" 1077046 NIL FS2EXPXP (NIL T T NIL NIL) -7 NIL NIL NIL) (-436 1075715 1075764 1075893 "FS2" 1076038 NIL FS2 (NIL T T T T) -7 NIL NIL NIL) (-435 1055953 1065489 1065530 "FS" 1069414 NIL FS (NIL T) -9 NIL 1071703 NIL) (-434 1044014 1047589 1051646 "FS-" 1051946 NIL FS- (NIL T T) -8 NIL NIL NIL) (-433 1043428 1043555 1043707 "FRUTIL" 1043894 NIL FRUTIL (NIL T) -7 NIL NIL NIL) (-432 1037939 1041117 1041157 "FRNAALG" 1042477 NIL FRNAALG (NIL T) -9 NIL 1043075 NIL) (-431 1033420 1034688 1035963 "FRNAALG-" 1036713 NIL FRNAALG- (NIL T T) -8 NIL NIL NIL) (-430 1033052 1033101 1033228 "FRNAAF2" 1033371 NIL FRNAAF2 (NIL T T T T) -7 NIL NIL NIL) (-429 1031339 1031901 1032197 "FRMOD" 1032864 NIL FRMOD (NIL T T T T NIL) -8 NIL NIL NIL) (-428 1030524 1030617 1030908 "FRIDEAL2" 1031246 NIL FRIDEAL2 (NIL T T T T T T T T) -7 NIL NIL NIL) (-427 1028129 1028899 1029217 "FRIDEAL" 1030315 NIL FRIDEAL (NIL T T T T) -8 NIL NIL NIL) (-426 1027220 1027676 1027717 "FRETRCT" 1027722 NIL FRETRCT (NIL T) -9 NIL 1027898 NIL) (-425 1026278 1026563 1026914 "FRETRCT-" 1026919 NIL FRETRCT- (NIL T T) -8 NIL NIL NIL) (-424 1023099 1024562 1024621 "FRAMALG" 1025503 NIL FRAMALG (NIL T T) -9 NIL 1025795 NIL) (-423 1021137 1021688 1022318 "FRAMALG-" 1022541 NIL FRAMALG- (NIL T T T) -8 NIL NIL NIL) (-422 1020767 1020830 1020937 "FRAC2" 1021074 NIL FRAC2 (NIL T T) -7 NIL NIL NIL) (-421 1013760 1020240 1020517 "FRAC" 1020522 NIL FRAC (NIL T) -8 NIL NIL NIL) (-420 1013390 1013453 1013560 "FR2" 1013697 NIL FR2 (NIL T T) -7 NIL NIL NIL) (-419 1004307 1008885 1010243 "FR" 1012064 NIL FR (NIL T) -8 NIL NIL NIL) (-418 998226 1001686 1001714 "FPS" 1002833 T FPS (NIL) -9 NIL 1003390 NIL) (-417 997651 997784 997948 "FPS-" 998094 NIL FPS- (NIL T) -8 NIL NIL NIL) (-416 994617 996608 996636 "FPC" 996861 T FPC (NIL) -9 NIL 997003 NIL) (-415 994398 994450 994547 "FPC-" 994552 NIL FPC- (NIL T) -8 NIL NIL NIL) (-414 993156 993886 993927 "FPATMAB" 993932 NIL FPATMAB (NIL T) -9 NIL 994084 NIL) (-413 991299 991898 992245 "FPARFRAC" 992872 NIL FPARFRAC (NIL T T) -8 NIL NIL NIL) (-412 986591 987191 987873 "FORTRAN" 990731 NIL FORTRAN (NIL NIL NIL NIL NIL) -8 NIL NIL NIL) (-411 984165 984829 984857 "FORTFN" 985917 T FORTFN (NIL) -9 NIL 986541 NIL) (-410 983917 983979 984007 "FORTCAT" 984066 T FORTCAT (NIL) -9 NIL 984128 NIL) (-409 981603 982133 982672 "FORT" 983398 T FORT (NIL) -7 NIL NIL NIL) (-408 981385 981421 981490 "FORMULA1" 981567 NIL FORMULA1 (NIL T) -7 NIL NIL NIL) (-407 979389 980001 980391 "FORMULA" 981015 T FORMULA (NIL) -8 NIL NIL NIL) (-406 978906 978964 979137 "FORDER" 979331 NIL FORDER (NIL T T T T) -7 NIL NIL NIL) (-405 977966 978166 978359 "FOP" 978733 T FOP (NIL) -7 NIL NIL NIL) (-404 976379 977246 977420 "FNLA" 977848 NIL FNLA (NIL NIL NIL T) -8 NIL NIL NIL) (-403 974998 975509 975537 "FNCAT" 975997 T FNCAT (NIL) -9 NIL 976257 NIL) (-402 974441 974957 974985 "FNAME" 974990 T FNAME (NIL) -8 NIL NIL NIL) (-401 972767 973940 973968 "FMTC" 973973 T FMTC (NIL) -9 NIL 974009 NIL) (-400 971316 972703 972749 "FMONOID" 972754 NIL FMONOID (NIL T) -8 NIL NIL NIL) (-399 967905 969271 969312 "FMONCAT" 970529 NIL FMONCAT (NIL T) -9 NIL 971134 NIL) (-398 965227 965975 966003 "FMFUN" 967147 T FMFUN (NIL) -9 NIL 967855 NIL) (-397 962100 963152 963206 "FMCAT" 964401 NIL FMCAT (NIL T T) -9 NIL 964896 NIL) (-396 961333 961550 961578 "FMC" 961868 T FMC (NIL) -9 NIL 962050 NIL) (-395 960001 961099 961199 "FM1" 961278 NIL FM1 (NIL T T) -8 NIL NIL NIL) (-394 959019 959743 959892 "FM" 959897 NIL FM (NIL T T) -8 NIL NIL NIL) (-393 956757 957209 957703 "FLOATRP" 958570 NIL FLOATRP (NIL T) -7 NIL NIL NIL) (-392 954159 954695 955273 "FLOATCP" 956224 NIL FLOATCP (NIL T) -7 NIL NIL NIL) (-391 946822 951888 952509 "FLOAT" 953558 T FLOAT (NIL) -8 NIL NIL NIL) (-390 945340 946414 946455 "FLINEXP" 946460 NIL FLINEXP (NIL T) -9 NIL 946553 NIL) (-389 944470 944729 945057 "FLINEXP-" 945062 NIL FLINEXP- (NIL T T) -8 NIL NIL NIL) (-388 943528 943690 943914 "FLASORT" 944322 NIL FLASORT (NIL T T) -7 NIL NIL NIL) (-387 940446 941498 941550 "FLALG" 942777 NIL FLALG (NIL T T) -9 NIL 943244 NIL) (-386 939470 939631 939858 "FLAGG2" 940299 NIL FLAGG2 (NIL T T T T) -7 NIL NIL NIL) (-385 932725 936879 936920 "FLAGG" 938182 NIL FLAGG (NIL T) -9 NIL 938834 NIL) (-384 931379 931790 932280 "FLAGG-" 932285 NIL FLAGG- (NIL T T) -8 NIL NIL NIL) (-383 928017 929224 929283 "FINRALG" 930411 NIL FINRALG (NIL T T) -9 NIL 930919 NIL) (-382 927141 927406 927745 "FINRALG-" 927750 NIL FINRALG- (NIL T T T) -8 NIL NIL NIL) (-381 926447 926746 926774 "FINITE" 926970 T FINITE (NIL) -9 NIL 927077 NIL) (-380 918398 920977 921017 "FINAALG" 924684 NIL FINAALG (NIL T) -9 NIL 926137 NIL) (-379 913514 914780 915924 "FINAALG-" 917303 NIL FINAALG- (NIL T T) -8 NIL NIL NIL) (-378 912074 912496 912550 "FILECAT" 913234 NIL FILECAT (NIL T T) -9 NIL 913450 NIL) (-377 911352 911829 911932 "FILE" 912004 NIL FILE (NIL T) -8 NIL NIL NIL) (-376 908755 910582 910610 "FIELD" 910650 T FIELD (NIL) -9 NIL 910730 NIL) (-375 907297 907760 908271 "FIELD-" 908276 NIL FIELD- (NIL T) -8 NIL NIL NIL) (-374 904980 905932 906279 "FGROUP" 906983 NIL FGROUP (NIL T) -8 NIL NIL NIL) (-373 904052 904234 904454 "FGLMICPK" 904812 NIL FGLMICPK (NIL T NIL) -7 NIL NIL NIL) (-372 899307 903977 904034 "FFX" 904039 NIL FFX (NIL T NIL) -8 NIL NIL NIL) (-371 898902 898969 899104 "FFSLPE" 899240 NIL FFSLPE (NIL T T T) -7 NIL NIL NIL) (-370 898400 898442 898651 "FFPOLY2" 898860 NIL FFPOLY2 (NIL T T) -7 NIL NIL NIL) (-369 894276 895172 895968 "FFPOLY" 897636 NIL FFPOLY (NIL T) -7 NIL NIL NIL) (-368 889545 894195 894258 "FFP" 894263 NIL FFP (NIL T NIL) -8 NIL NIL NIL) (-367 884076 888888 889078 "FFNBX" 889399 NIL FFNBX (NIL T NIL) -8 NIL NIL NIL) (-366 878409 883211 883469 "FFNBP" 883930 NIL FFNBP (NIL T NIL) -8 NIL NIL NIL) (-365 872447 877693 877904 "FFNB" 878242 NIL FFNB (NIL NIL NIL) -8 NIL NIL NIL) (-364 871267 871477 871792 "FFINTBAS" 872244 NIL FFINTBAS (NIL T T T) -7 NIL NIL NIL) (-363 866860 869514 869542 "FFIELDC" 870162 T FFIELDC (NIL) -9 NIL 870538 NIL) (-362 865480 865921 866404 "FFIELDC-" 866409 NIL FFIELDC- (NIL T) -8 NIL NIL NIL) (-361 865037 865095 865219 "FFHOM" 865422 NIL FFHOM (NIL T T T) -7 NIL NIL NIL) (-360 862696 863219 863736 "FFF" 864552 NIL FFF (NIL T) -7 NIL NIL NIL) (-359 857731 862438 862539 "FFCGX" 862639 NIL FFCGX (NIL T NIL) -8 NIL NIL NIL) (-358 852770 857463 857570 "FFCGP" 857674 NIL FFCGP (NIL T NIL) -8 NIL NIL NIL) (-357 847370 852497 852605 "FFCG" 852706 NIL FFCG (NIL NIL NIL) -8 NIL NIL NIL) (-356 846775 846824 847059 "FFCAT2" 847321 NIL FFCAT2 (NIL T T T T T T T T) -7 NIL NIL NIL) (-355 825457 836507 836593 "FFCAT" 841758 NIL FFCAT (NIL T T T) -9 NIL 843209 NIL) (-354 820468 821702 823016 "FFCAT-" 824246 NIL FFCAT- (NIL T T T T) -8 NIL NIL NIL) (-353 815289 820379 820443 "FF" 820448 NIL FF (NIL NIL NIL) -8 NIL NIL NIL) (-352 803942 808261 809481 "FEXPR" 814141 NIL FEXPR (NIL NIL NIL T) -8 NIL NIL NIL) (-351 802870 803339 803380 "FEVALAB" 803464 NIL FEVALAB (NIL T) -9 NIL 803725 NIL) (-350 801987 802239 802577 "FEVALAB-" 802582 NIL FEVALAB- (NIL T T) -8 NIL NIL NIL) (-349 798849 799734 799849 "FDIVCAT" 801417 NIL FDIVCAT (NIL T T T T) -9 NIL 801854 NIL) (-348 798605 798638 798808 "FDIVCAT-" 798813 NIL FDIVCAT- (NIL T T T T T) -8 NIL NIL NIL) (-347 797819 797912 798189 "FDIV2" 798512 NIL FDIV2 (NIL T T T T T T T T) -7 NIL NIL NIL) (-346 796229 797202 797405 "FDIV" 797718 NIL FDIV (NIL T T T T) -8 NIL NIL NIL) (-345 795137 795524 795726 "FCTRDATA" 796047 T FCTRDATA (NIL) -8 NIL NIL NIL) (-344 793793 794082 794371 "FCPAK1" 794868 T FCPAK1 (NIL) -7 NIL NIL NIL) (-343 792796 793293 793434 "FCOMP" 793684 NIL FCOMP (NIL T) -8 NIL NIL NIL) (-342 776110 779946 783484 "FC" 789278 T FC (NIL) -8 NIL NIL NIL) (-341 767819 772431 772471 "FAXF" 774273 NIL FAXF (NIL T) -9 NIL 774965 NIL) (-340 764960 765767 766585 "FAXF-" 767050 NIL FAXF- (NIL T T) -8 NIL NIL NIL) (-339 759529 764336 764512 "FARRAY" 764817 NIL FARRAY (NIL T) -8 NIL NIL NIL) (-338 754094 756476 756529 "FAMR" 757552 NIL FAMR (NIL T T) -9 NIL 758012 NIL) (-337 752918 753286 753721 "FAMR-" 753726 NIL FAMR- (NIL T T T) -8 NIL NIL NIL) (-336 751945 752840 752893 "FAMONOID" 752898 NIL FAMONOID (NIL T) -8 NIL NIL NIL) (-335 749575 750427 750480 "FAMONC" 751421 NIL FAMONC (NIL T T) -9 NIL 751807 NIL) (-334 748049 749329 749466 "FAGROUP" 749471 NIL FAGROUP (NIL T) -8 NIL NIL NIL) (-333 745802 746163 746566 "FACUTIL" 747730 NIL FACUTIL (NIL T T T T) -7 NIL NIL NIL) (-332 744889 745086 745308 "FACTFUNC" 745612 NIL FACTFUNC (NIL T) -7 NIL NIL NIL) (-331 736630 744192 744391 "EXPUPXS" 744745 NIL EXPUPXS (NIL T NIL NIL) -8 NIL NIL NIL) (-330 734083 734653 735239 "EXPRTUBE" 736064 T EXPRTUBE (NIL) -7 NIL NIL NIL) (-329 730294 730946 731676 "EXPRODE" 733422 NIL EXPRODE (NIL T T) -7 NIL NIL NIL) (-328 724728 725435 726241 "EXPR2UPS" 729592 NIL EXPR2UPS (NIL T T) -7 NIL NIL NIL) (-327 724354 724417 724526 "EXPR2" 724665 NIL EXPR2 (NIL T T) -7 NIL NIL NIL) (-326 708662 723003 723432 "EXPR" 723958 NIL EXPR (NIL T) -8 NIL NIL NIL) (-325 699000 707813 708104 "EXPEXPAN" 708498 NIL EXPEXPAN (NIL T T NIL NIL) -8 NIL NIL NIL) (-324 698420 698724 698815 "EXITAST" 698929 T EXITAST (NIL) -8 NIL NIL NIL) (-323 698184 698377 698406 "EXIT" 698411 T EXIT (NIL) -8 NIL NIL NIL) (-322 697805 697873 697986 "EVALCYC" 698116 NIL EVALCYC (NIL T) -7 NIL NIL NIL) (-321 697322 697464 697505 "EVALAB" 697675 NIL EVALAB (NIL T) -9 NIL 697779 NIL) (-320 696779 696925 697146 "EVALAB-" 697151 NIL EVALAB- (NIL T T) -8 NIL NIL NIL) (-319 693894 695435 695463 "EUCDOM" 696018 T EUCDOM (NIL) -9 NIL 696368 NIL) (-318 692254 692755 693338 "EUCDOM-" 693343 NIL EUCDOM- (NIL T) -8 NIL NIL NIL) (-317 691880 691943 692052 "ESTOOLS2" 692191 NIL ESTOOLS2 (NIL T T) -7 NIL NIL NIL) (-316 691625 691673 691753 "ESTOOLS1" 691832 NIL ESTOOLS1 (NIL T) -7 NIL NIL NIL) (-315 678942 681923 684673 "ESTOOLS" 688895 T ESTOOLS (NIL) -7 NIL NIL NIL) (-314 678681 678719 678801 "ESCONT1" 678904 NIL ESCONT1 (NIL NIL NIL) -7 NIL NIL NIL) (-313 674989 675816 676596 "ESCONT" 677921 T ESCONT (NIL) -7 NIL NIL NIL) (-312 674658 674714 674814 "ES2" 674933 NIL ES2 (NIL T T) -7 NIL NIL NIL) (-311 674282 674346 674455 "ES1" 674594 NIL ES1 (NIL T T) -7 NIL NIL NIL) (-310 667983 669913 669941 "ES" 672709 T ES (NIL) -9 NIL 674119 NIL) (-309 662660 664217 666034 "ES-" 666198 NIL ES- (NIL T) -8 NIL NIL NIL) (-308 661852 662005 662181 "ERROR" 662504 T ERROR (NIL) -7 NIL NIL NIL) (-307 654868 661711 661802 "EQTBL" 661807 NIL EQTBL (NIL T T) -8 NIL NIL NIL) (-306 654494 654557 654666 "EQ2" 654805 NIL EQ2 (NIL T T) -7 NIL NIL NIL) (-305 646753 649808 651257 "EQ" 653078 NIL -1499 (NIL T) -8 NIL NIL NIL) (-304 641996 643091 644184 "EP" 645692 NIL EP (NIL T) -7 NIL NIL NIL) (-303 640536 640887 641193 "ENV" 641710 T ENV (NIL) -8 NIL NIL NIL) (-302 639496 640170 640198 "ENTIRER" 640203 T ENTIRER (NIL) -9 NIL 640249 NIL) (-301 635915 637678 638039 "EMR" 639304 NIL EMR (NIL T T T NIL NIL NIL) -8 NIL NIL NIL) (-300 635019 635230 635284 "ELTAGG" 635664 NIL ELTAGG (NIL T T) -9 NIL 635875 NIL) (-299 634726 634800 634941 "ELTAGG-" 634946 NIL ELTAGG- (NIL T T T) -8 NIL NIL NIL) (-298 634484 634519 634573 "ELTAB" 634657 NIL ELTAB (NIL T T) -9 NIL 634709 NIL) (-297 633586 633756 633955 "ELFUTS" 634335 NIL ELFUTS (NIL T T) -7 NIL NIL NIL) (-296 633310 633384 633412 "ELEMFUN" 633517 T ELEMFUN (NIL) -9 NIL NIL NIL) (-295 633174 633201 633269 "ELEMFUN-" 633274 NIL ELEMFUN- (NIL T) -8 NIL NIL NIL) (-294 627585 631216 631257 "ELAGG" 632197 NIL ELAGG (NIL T) -9 NIL 632660 NIL) (-293 625762 626304 626967 "ELAGG-" 626972 NIL ELAGG- (NIL T T) -8 NIL NIL NIL) (-292 625044 625211 625367 "ELABOR" 625626 T ELABOR (NIL) -8 NIL NIL NIL) (-291 623650 623984 624278 "ELABEXPR" 624770 T ELABEXPR (NIL) -8 NIL NIL NIL) (-290 616162 618287 619116 "EFUPXS" 622925 NIL EFUPXS (NIL T T T T) -8 NIL NIL NIL) (-289 609288 611411 612222 "EFULS" 615437 NIL EFULS (NIL T T T) -8 NIL NIL NIL) (-288 606725 607131 607603 "EFSTRUC" 608920 NIL EFSTRUC (NIL T T) -7 NIL NIL NIL) (-287 596163 598082 599630 "EF" 605240 NIL EF (NIL T T) -7 NIL NIL NIL) (-286 595141 595648 595797 "EAB" 596034 T EAB (NIL) -8 NIL NIL NIL) (-285 594263 595100 595128 "E04UCFA" 595133 T E04UCFA (NIL) -8 NIL NIL NIL) (-284 593385 594222 594250 "E04NAFA" 594255 T E04NAFA (NIL) -8 NIL NIL NIL) (-283 592507 593344 593372 "E04MBFA" 593377 T E04MBFA (NIL) -8 NIL NIL NIL) (-282 591629 592466 592494 "E04JAFA" 592499 T E04JAFA (NIL) -8 NIL NIL NIL) (-281 590753 591588 591616 "E04GCFA" 591621 T E04GCFA (NIL) -8 NIL NIL NIL) (-280 589877 590712 590740 "E04FDFA" 590745 T E04FDFA (NIL) -8 NIL NIL NIL) (-279 588999 589836 589864 "E04DGFA" 589869 T E04DGFA (NIL) -8 NIL NIL NIL) (-278 583076 584524 585888 "E04AGNT" 587655 T E04AGNT (NIL) -7 NIL NIL NIL) (-277 581696 582377 582417 "DVARCAT" 582758 NIL DVARCAT (NIL T) -9 NIL 582921 NIL) (-276 580846 581112 581426 "DVARCAT-" 581431 NIL DVARCAT- (NIL T T) -8 NIL NIL NIL) (-275 572814 580645 580774 "DSMP" 580779 NIL DSMP (NIL T T T) -8 NIL NIL NIL) (-274 571165 571956 571997 "DSEXT" 572360 NIL DSEXT (NIL T) -9 NIL 572654 NIL) (-273 569354 569878 570544 "DSEXT-" 570549 NIL DSEXT- (NIL T T) -8 NIL NIL NIL) (-272 569013 569078 569176 "DROPT1" 569289 NIL DROPT1 (NIL T) -7 NIL NIL NIL) (-271 564032 565254 566391 "DROPT0" 567896 T DROPT0 (NIL) -7 NIL NIL NIL) (-270 558615 559977 561045 "DROPT" 562984 T DROPT (NIL) -8 NIL NIL NIL) (-269 556924 557285 557671 "DRAWPT" 558249 T DRAWPT (NIL) -7 NIL NIL NIL) (-268 556551 556610 556728 "DRAWHACK" 556865 NIL DRAWHACK (NIL T) -7 NIL NIL NIL) (-267 555252 555551 555842 "DRAWCX" 556280 T DRAWCX (NIL) -7 NIL NIL NIL) (-266 554761 554836 554987 "DRAWCURV" 555178 NIL DRAWCURV (NIL T T) -7 NIL NIL NIL) (-265 545079 547191 549306 "DRAWCFUN" 552666 T DRAWCFUN (NIL) -7 NIL NIL NIL) (-264 539570 540589 541668 "DRAW" 544053 NIL DRAW (NIL T) -7 NIL NIL NIL) (-263 536041 538235 538276 "DQAGG" 538905 NIL DQAGG (NIL T) -9 NIL 539179 NIL) (-262 522624 530252 530335 "DPOLCAT" 532187 NIL DPOLCAT (NIL T T T T) -9 NIL 532732 NIL) (-261 517143 518809 520767 "DPOLCAT-" 520772 NIL DPOLCAT- (NIL T T T T T) -8 NIL NIL NIL) (-260 509951 517004 517102 "DPMO" 517107 NIL DPMO (NIL NIL T T) -8 NIL NIL NIL) (-259 502656 509731 509898 "DPMM" 509903 NIL DPMM (NIL NIL T T T) -8 NIL NIL NIL) (-258 502178 502440 502529 "DOMTMPLT" 502587 T DOMTMPLT (NIL) -8 NIL NIL NIL) (-257 501527 501980 502060 "DOMCTOR" 502118 T DOMCTOR (NIL) -8 NIL NIL NIL) (-256 500679 501007 501158 "DOMAIN" 501396 T DOMAIN (NIL) -8 NIL NIL NIL) (-255 493698 500314 500466 "DMP" 500580 NIL DMP (NIL NIL T) -8 NIL NIL NIL) (-254 491475 492765 492806 "DMEXT" 492811 NIL DMEXT (NIL T) -9 NIL 492987 NIL) (-253 491069 491131 491275 "DLP" 491413 NIL DLP (NIL T) -7 NIL NIL NIL) (-252 484192 490396 490586 "DLIST" 490911 NIL DLIST (NIL T) -8 NIL NIL NIL) (-251 480730 483017 483058 "DLAGG" 483608 NIL DLAGG (NIL T) -9 NIL 483838 NIL) (-250 479242 480056 480084 "DIVRING" 480176 T DIVRING (NIL) -9 NIL 480259 NIL) (-249 478425 478669 478969 "DIVRING-" 478974 NIL DIVRING- (NIL T) -8 NIL NIL NIL) (-248 476467 476884 477290 "DISPLAY" 478039 T DISPLAY (NIL) -7 NIL NIL NIL) (-247 475297 475518 475783 "DIRPROD2" 476260 NIL DIRPROD2 (NIL NIL T T) -7 NIL NIL NIL) (-246 468655 475211 475274 "DIRPROD" 475279 NIL DIRPROD (NIL NIL T) -8 NIL NIL NIL) (-245 456818 463366 463419 "DIRPCAT" 463677 NIL DIRPCAT (NIL NIL T) -9 NIL 464552 NIL) (-244 454018 454786 455667 "DIRPCAT-" 456004 NIL DIRPCAT- (NIL T NIL T) -8 NIL NIL NIL) (-243 453299 453465 453651 "DIOSP" 453852 T DIOSP (NIL) -7 NIL NIL NIL) (-242 449713 452183 452224 "DIOPS" 452658 NIL DIOPS (NIL T) -9 NIL 452887 NIL) (-241 449232 449376 449567 "DIOPS-" 449572 NIL DIOPS- (NIL T T) -8 NIL NIL NIL) (-240 448139 448911 448939 "DIFRING" 448944 T DIFRING (NIL) -9 NIL 448966 NIL) (-239 447787 447885 447913 "DIFFSPC" 448032 T DIFFSPC (NIL) -9 NIL 448107 NIL) (-238 447408 447510 447662 "DIFFSPC-" 447667 NIL DIFFSPC- (NIL T) -8 NIL NIL NIL) (-237 446344 446942 446983 "DIFFMOD" 446988 NIL DIFFMOD (NIL T) -9 NIL 447086 NIL) (-236 446040 446097 446138 "DIFFDOM" 446259 NIL DIFFDOM (NIL T) -9 NIL 446327 NIL) (-235 445887 445917 446001 "DIFFDOM-" 446006 NIL DIFFDOM- (NIL T T) -8 NIL NIL NIL) (-234 443627 445091 445132 "DIFEXT" 445137 NIL DIFEXT (NIL T) -9 NIL 445290 NIL) (-233 440661 443131 443172 "DIAGG" 443177 NIL DIAGG (NIL T) -9 NIL 443197 NIL) (-232 440009 440202 440454 "DIAGG-" 440459 NIL DIAGG- (NIL T T) -8 NIL NIL NIL) (-231 434859 438968 439245 "DHMATRIX" 439778 NIL DHMATRIX (NIL T) -8 NIL NIL NIL) (-230 430327 431380 432390 "DFSFUN" 433869 T DFSFUN (NIL) -7 NIL NIL NIL) (-229 424568 429258 429570 "DFLOAT" 430035 T DFLOAT (NIL) -8 NIL NIL NIL) (-228 422807 423112 423501 "DFINTTLS" 424276 NIL DFINTTLS (NIL T T) -7 NIL NIL NIL) (-227 419626 420828 421228 "DERHAM" 422473 NIL DERHAM (NIL T NIL) -8 NIL NIL NIL) (-226 417162 419401 419490 "DEQUEUE" 419570 NIL DEQUEUE (NIL T) -8 NIL NIL NIL) (-225 416404 416549 416732 "DEGRED" 417024 NIL DEGRED (NIL T T) -7 NIL NIL NIL) (-224 412810 413579 414425 "DEFINTRF" 415632 NIL DEFINTRF (NIL T) -7 NIL NIL NIL) (-223 410347 410834 411426 "DEFINTEF" 412329 NIL DEFINTEF (NIL T T) -7 NIL NIL NIL) (-222 409631 409967 410082 "DEFAST" 410252 T DEFAST (NIL) -8 NIL NIL NIL) (-221 402688 409224 409374 "DECIMAL" 409501 T DECIMAL (NIL) -8 NIL NIL NIL) (-220 400146 400658 401164 "DDFACT" 402232 NIL DDFACT (NIL T T) -7 NIL NIL NIL) (-219 399736 399785 399936 "DBLRESP" 400097 NIL DBLRESP (NIL T T T T) -7 NIL NIL NIL) (-218 398937 399506 399597 "DBASIS" 399685 NIL DBASIS (NIL NIL) -8 NIL NIL NIL) (-217 396721 397167 397528 "DBASE" 398703 NIL DBASE (NIL T) -8 NIL NIL NIL) (-216 395909 396201 396347 "DATAARY" 396620 NIL DATAARY (NIL NIL T) -8 NIL NIL NIL) (-215 394967 395868 395896 "D03FAFA" 395901 T D03FAFA (NIL) -8 NIL NIL NIL) (-214 394026 394926 394954 "D03EEFA" 394959 T D03EEFA (NIL) -8 NIL NIL NIL) (-213 391952 392442 392931 "D03AGNT" 393557 T D03AGNT (NIL) -7 NIL NIL NIL) (-212 391193 391911 391939 "D02EJFA" 391944 T D02EJFA (NIL) -8 NIL NIL NIL) (-211 390434 391152 391180 "D02CJFA" 391185 T D02CJFA (NIL) -8 NIL NIL NIL) (-210 389675 390393 390421 "D02BHFA" 390426 T D02BHFA (NIL) -8 NIL NIL NIL) (-209 388916 389634 389662 "D02BBFA" 389667 T D02BBFA (NIL) -8 NIL NIL NIL) (-208 382047 383702 385308 "D02AGNT" 387330 T D02AGNT (NIL) -7 NIL NIL NIL) (-207 379797 380338 380884 "D01WGTS" 381521 T D01WGTS (NIL) -7 NIL NIL NIL) (-206 378804 379756 379784 "D01TRNS" 379789 T D01TRNS (NIL) -8 NIL NIL NIL) (-205 377812 378763 378791 "D01GBFA" 378796 T D01GBFA (NIL) -8 NIL NIL NIL) (-204 376820 377771 377799 "D01FCFA" 377804 T D01FCFA (NIL) -8 NIL NIL NIL) (-203 375828 376779 376807 "D01ASFA" 376812 T D01ASFA (NIL) -8 NIL NIL NIL) (-202 374836 375787 375815 "D01AQFA" 375820 T D01AQFA (NIL) -8 NIL NIL NIL) (-201 373844 374795 374823 "D01APFA" 374828 T D01APFA (NIL) -8 NIL NIL NIL) (-200 372852 373803 373831 "D01ANFA" 373836 T D01ANFA (NIL) -8 NIL NIL NIL) (-199 371860 372811 372839 "D01AMFA" 372844 T D01AMFA (NIL) -8 NIL NIL NIL) (-198 370868 371819 371847 "D01ALFA" 371852 T D01ALFA (NIL) -8 NIL NIL NIL) (-197 369876 370827 370855 "D01AKFA" 370860 T D01AKFA (NIL) -8 NIL NIL NIL) (-196 368884 369835 369863 "D01AJFA" 369868 T D01AJFA (NIL) -8 NIL NIL NIL) (-195 362107 363732 365293 "D01AGNT" 367343 T D01AGNT (NIL) -7 NIL NIL NIL) (-194 361426 361572 361724 "CYCLOTOM" 361975 T CYCLOTOM (NIL) -7 NIL NIL NIL) (-193 358081 358874 359601 "CYCLES" 360719 T CYCLES (NIL) -7 NIL NIL NIL) (-192 357381 357527 357698 "CVMP" 357942 NIL CVMP (NIL T) -7 NIL NIL NIL) (-191 355168 355480 355849 "CTRIGMNP" 357109 NIL CTRIGMNP (NIL T T) -7 NIL NIL NIL) (-190 354641 354899 355000 "CTORKIND" 355087 T CTORKIND (NIL) -8 NIL NIL NIL) (-189 353846 354234 354262 "CTORCAT" 354444 T CTORCAT (NIL) -9 NIL 354557 NIL) (-188 353420 353555 353714 "CTORCAT-" 353719 NIL CTORCAT- (NIL T) -8 NIL NIL NIL) (-187 352834 353094 353202 "CTORCALL" 353344 NIL CTORCALL (NIL T) -8 NIL NIL NIL) (-186 352192 352628 352701 "CTOR" 352781 T CTOR (NIL) -8 NIL NIL NIL) (-185 351548 351665 351818 "CSTTOOLS" 352089 NIL CSTTOOLS (NIL T T) -7 NIL NIL NIL) (-184 347245 348004 348762 "CRFP" 350860 NIL CRFP (NIL T T) -7 NIL NIL NIL) (-183 346660 346966 347058 "CRCEAST" 347173 T CRCEAST (NIL) -8 NIL NIL NIL) (-182 345683 345892 346120 "CRAPACK" 346464 NIL CRAPACK (NIL T) -7 NIL NIL NIL) (-181 345063 345168 345372 "CPMATCH" 345559 NIL CPMATCH (NIL T T T) -7 NIL NIL NIL) (-180 344782 344816 344922 "CPIMA" 345029 NIL CPIMA (NIL T T T) -7 NIL NIL NIL) (-179 341040 341802 342521 "COORDSYS" 344117 NIL COORDSYS (NIL T) -7 NIL NIL NIL) (-178 340428 340573 340715 "CONTOUR" 340918 T CONTOUR (NIL) -8 NIL NIL NIL) (-177 335899 338431 338923 "CONTFRAC" 339968 NIL CONTFRAC (NIL T) -8 NIL NIL NIL) (-176 335773 335800 335828 "CONDUIT" 335865 T CONDUIT (NIL) -9 NIL NIL NIL) (-175 334727 335401 335429 "COMRING" 335434 T COMRING (NIL) -9 NIL 335486 NIL) (-174 333709 334085 334269 "COMPPROP" 334563 T COMPPROP (NIL) -8 NIL NIL NIL) (-173 333364 333405 333533 "COMPLPAT" 333668 NIL COMPLPAT (NIL T T T) -7 NIL NIL NIL) (-172 332994 333057 333164 "COMPLEX2" 333301 NIL COMPLEX2 (NIL T T) -7 NIL NIL NIL) (-171 321398 332803 332912 "COMPLEX" 332917 NIL COMPLEX (NIL T) -8 NIL NIL NIL) (-170 320719 320858 321018 "COMPILER" 321258 T COMPILER (NIL) -8 NIL NIL NIL) (-169 320431 320472 320570 "COMPFACT" 320678 NIL COMPFACT (NIL T T) -7 NIL NIL NIL) (-168 301825 314135 314175 "COMPCAT" 315179 NIL COMPCAT (NIL T) -9 NIL 316527 NIL) (-167 290713 294264 297891 "COMPCAT-" 298247 NIL COMPCAT- (NIL T T) -8 NIL NIL NIL) (-166 290436 290470 290573 "COMMUPC" 290679 NIL COMMUPC (NIL T T T) -7 NIL NIL NIL) (-165 290224 290264 290323 "COMMONOP" 290397 T COMMONOP (NIL) -7 NIL NIL NIL) (-164 289746 290028 290103 "COMMAAST" 290169 T COMMAAST (NIL) -8 NIL NIL NIL) (-163 289253 289497 289584 "COMM" 289679 T COMM (NIL) -8 NIL NIL NIL) (-162 288448 288696 288724 "COMBOPC" 289062 T COMBOPC (NIL) -9 NIL 289237 NIL) (-161 287302 287554 287796 "COMBINAT" 288238 NIL COMBINAT (NIL T) -7 NIL NIL NIL) (-160 283645 284333 284960 "COMBF" 286724 NIL COMBF (NIL T T) -7 NIL NIL NIL) (-159 282307 282761 282996 "COLOR" 283430 T COLOR (NIL) -8 NIL NIL NIL) (-158 281723 282028 282120 "COLONAST" 282235 T COLONAST (NIL) -8 NIL NIL NIL) (-157 281357 281410 281535 "CMPLXRT" 281670 NIL CMPLXRT (NIL T T) -7 NIL NIL NIL) (-156 280745 281057 281156 "CLLCTAST" 281278 T CLLCTAST (NIL) -8 NIL NIL NIL) (-155 276204 277275 278355 "CLIP" 279685 T CLIP (NIL) -7 NIL NIL NIL) (-154 274377 275305 275545 "CLIF" 276031 NIL CLIF (NIL NIL T NIL) -8 NIL NIL NIL) (-153 270359 272495 272536 "CLAGG" 273465 NIL CLAGG (NIL T) -9 NIL 274001 NIL) (-152 268703 269238 269821 "CLAGG-" 269826 NIL CLAGG- (NIL T T) -8 NIL NIL NIL) (-151 268241 268332 268472 "CINTSLPE" 268612 NIL CINTSLPE (NIL T T) -7 NIL NIL NIL) (-150 265706 266213 266761 "CHVAR" 267769 NIL CHVAR (NIL T T T) -7 NIL NIL NIL) (-149 264746 265420 265448 "CHARZ" 265453 T CHARZ (NIL) -9 NIL 265468 NIL) (-148 264494 264540 264618 "CHARPOL" 264700 NIL CHARPOL (NIL T) -7 NIL NIL NIL) (-147 263412 264118 264146 "CHARNZ" 264207 T CHARNZ (NIL) -9 NIL 264256 NIL) (-146 260356 261466 261995 "CHAR" 262903 T CHAR (NIL) -8 NIL NIL NIL) (-145 260064 260143 260171 "CFCAT" 260282 T CFCAT (NIL) -9 NIL NIL NIL) (-144 259287 259416 259599 "CDEN" 259948 NIL CDEN (NIL T T T) -7 NIL NIL NIL) (-143 254884 258440 258720 "CCLASS" 259027 T CCLASS (NIL) -8 NIL NIL NIL) (-142 254105 254292 254469 "CATEGORY" 254727 T -10 (NIL) -8 NIL NIL NIL) (-141 253600 254024 254072 "CATCTOR" 254077 T CATCTOR (NIL) -8 NIL NIL NIL) (-140 252991 253303 253401 "CATAST" 253522 T CATAST (NIL) -8 NIL NIL NIL) (-139 252407 252712 252804 "CASEAST" 252919 T CASEAST (NIL) -8 NIL NIL NIL) (-138 251503 251663 251884 "CARTEN2" 252254 NIL CARTEN2 (NIL NIL NIL T T) -7 NIL NIL NIL) (-137 246400 247660 248404 "CARTEN" 250815 NIL CARTEN (NIL NIL NIL T) -8 NIL NIL NIL) (-136 244530 245550 245807 "CARD" 246163 T CARD (NIL) -8 NIL NIL NIL) (-135 244052 244334 244409 "CAPSLAST" 244475 T CAPSLAST (NIL) -8 NIL NIL NIL) (-134 243494 243750 243778 "CACHSET" 243910 T CACHSET (NIL) -9 NIL 243988 NIL) (-133 242884 243272 243300 "CABMON" 243350 T CABMON (NIL) -9 NIL 243406 NIL) (-132 242321 242588 242698 "BYTEORD" 242794 T BYTEORD (NIL) -8 NIL NIL NIL) (-131 237248 241826 241998 "BYTEBUF" 242169 T BYTEBUF (NIL) -8 NIL NIL NIL) (-130 236006 236763 236912 "BYTE" 237075 T BYTE (NIL) -8 NIL NIL 237204) (-129 233268 235698 235805 "BTREE" 235932 NIL BTREE (NIL T) -8 NIL NIL NIL) (-128 230470 232916 233038 "BTOURN" 233178 NIL BTOURN (NIL T) -8 NIL NIL NIL) (-127 227577 229912 229953 "BTCAT" 230021 NIL BTCAT (NIL T) -9 NIL 230098 NIL) (-126 227226 227324 227473 "BTCAT-" 227478 NIL BTCAT- (NIL T T) -8 NIL NIL NIL) (-125 222115 226472 226500 "BTAGG" 226614 T BTAGG (NIL) -9 NIL 226724 NIL) (-124 221569 221730 221936 "BTAGG-" 221941 NIL BTAGG- (NIL T) -8 NIL NIL NIL) (-123 218305 220847 221062 "BSTREE" 221386 NIL BSTREE (NIL T) -8 NIL NIL NIL) (-122 217413 217569 217753 "BRILL" 218161 NIL BRILL (NIL T) -7 NIL NIL NIL) (-121 213808 216111 216152 "BRAGG" 216801 NIL BRAGG (NIL T) -9 NIL 217059 NIL) (-120 212241 212743 213298 "BRAGG-" 213303 NIL BRAGG- (NIL T T) -8 NIL NIL NIL) (-119 204498 211585 211770 "BPADICRT" 212088 NIL BPADICRT (NIL NIL) -8 NIL NIL NIL) (-118 202514 204435 204480 "BPADIC" 204485 NIL BPADIC (NIL NIL) -8 NIL NIL NIL) (-117 202206 202242 202356 "BOUNDZRO" 202478 NIL BOUNDZRO (NIL T T) -7 NIL NIL NIL) (-116 199933 200391 200866 "BOP1" 201764 NIL BOP1 (NIL T) -7 NIL NIL NIL) (-115 194915 196359 197271 "BOP" 199041 T BOP (NIL) -8 NIL NIL NIL) (-114 193580 194503 194645 "BOOLEAN" 194793 T BOOLEAN (NIL) -8 NIL NIL NIL) (-113 193173 193330 193358 "BOOLE" 193469 T BOOLE (NIL) -9 NIL 193550 NIL) (-112 193041 193068 193134 "BOOLE-" 193139 NIL BOOLE- (NIL T) -8 NIL NIL NIL) (-111 192210 192710 192764 "BMODULE" 192769 NIL BMODULE (NIL T T) -9 NIL 192834 NIL) (-110 187531 192008 192081 "BITS" 192157 T BITS (NIL) -8 NIL NIL NIL) (-109 186928 187071 187211 "BINDING" 187411 T BINDING (NIL) -8 NIL NIL NIL) (-108 179988 186523 186672 "BINARY" 186799 T BINARY (NIL) -8 NIL NIL NIL) (-107 177595 179215 179256 "BGAGG" 179516 NIL BGAGG (NIL T) -9 NIL 179653 NIL) (-106 177420 177458 177549 "BGAGG-" 177554 NIL BGAGG- (NIL T T) -8 NIL NIL NIL) (-105 176443 176804 177009 "BFUNCT" 177235 T BFUNCT (NIL) -8 NIL NIL NIL) (-104 175113 175311 175599 "BEZOUT" 176267 NIL BEZOUT (NIL T T T T T) -7 NIL NIL NIL) (-103 171311 173965 174295 "BBTREE" 174816 NIL BBTREE (NIL T) -8 NIL NIL NIL) (-102 170894 170990 171018 "BASTYPE" 171195 T BASTYPE (NIL) -9 NIL 171294 NIL) (-101 170552 170651 170786 "BASTYPE-" 170791 NIL BASTYPE- (NIL T) -8 NIL NIL NIL) (-100 169974 170062 170214 "BALFACT" 170463 NIL BALFACT (NIL T T) -7 NIL NIL NIL) (-99 168710 169389 169575 "AUTOMOR" 169819 NIL AUTOMOR (NIL T) -8 NIL NIL NIL) (-98 168436 168441 168467 "ATTREG" 168472 T ATTREG (NIL) -9 NIL NIL NIL) (-97 166598 167133 167485 "ATTRBUT" 168102 T ATTRBUT (NIL) -8 NIL NIL NIL) (-96 166152 166426 166492 "ATTRAST" 166550 T ATTRAST (NIL) -8 NIL NIL NIL) (-95 165652 165801 165827 "ATRIG" 166028 T ATRIG (NIL) -9 NIL NIL NIL) (-94 165449 165502 165589 "ATRIG-" 165594 NIL ATRIG- (NIL T) -8 NIL NIL NIL) (-93 165032 165266 165292 "ASTCAT" 165297 T ASTCAT (NIL) -9 NIL 165327 NIL) (-92 164741 164818 164937 "ASTCAT-" 164942 NIL ASTCAT- (NIL T) -8 NIL NIL NIL) (-91 162715 164517 164605 "ASTACK" 164684 NIL ASTACK (NIL T) -8 NIL NIL NIL) (-90 161204 161517 161882 "ASSOCEQ" 162397 NIL ASSOCEQ (NIL T T) -7 NIL NIL NIL) (-89 160128 160863 160987 "ASP9" 161111 NIL ASP9 (NIL NIL) -8 NIL NIL NIL) (-88 158888 159733 159875 "ASP80" 160017 NIL ASP80 (NIL NIL) -8 NIL NIL NIL) (-87 158615 158836 158875 "ASP8" 158880 NIL ASP8 (NIL NIL) -8 NIL NIL NIL) (-86 157461 158292 158410 "ASP78" 158528 NIL ASP78 (NIL NIL) -8 NIL NIL NIL) (-85 156322 157141 157258 "ASP77" 157375 NIL ASP77 (NIL NIL) -8 NIL NIL NIL) (-84 155126 155960 156091 "ASP74" 156222 NIL ASP74 (NIL NIL) -8 NIL NIL NIL) (-83 153918 154761 154893 "ASP73" 155025 NIL ASP73 (NIL NIL) -8 NIL NIL NIL) (-82 152708 153553 153685 "ASP7" 153817 NIL ASP7 (NIL NIL) -8 NIL NIL NIL) (-81 151704 152534 152634 "ASP6" 152639 NIL ASP6 (NIL NIL) -8 NIL NIL NIL) (-80 150543 151381 151499 "ASP55" 151617 NIL ASP55 (NIL NIL) -8 NIL NIL NIL) (-79 149384 150217 150336 "ASP50" 150455 NIL ASP50 (NIL NIL) -8 NIL NIL NIL) (-78 148364 149085 149195 "ASP49" 149305 NIL ASP49 (NIL NIL) -8 NIL NIL NIL) (-77 147040 147903 148071 "ASP42" 148253 NIL ASP42 (NIL NIL NIL NIL) -8 NIL NIL NIL) (-76 145709 146573 146743 "ASP41" 146927 NIL ASP41 (NIL NIL NIL NIL) -8 NIL NIL NIL) (-75 144689 145410 145520 "ASP4" 145630 NIL ASP4 (NIL NIL) -8 NIL NIL NIL) (-74 143531 144366 144484 "ASP35" 144602 NIL ASP35 (NIL NIL) -8 NIL NIL NIL) (-73 143260 143479 143518 "ASP34" 143523 NIL ASP34 (NIL NIL) -8 NIL NIL NIL) (-72 142979 143064 143140 "ASP33" 143215 NIL ASP33 (NIL NIL) -8 NIL NIL NIL) (-71 141765 142614 142746 "ASP31" 142878 NIL ASP31 (NIL NIL) -8 NIL NIL NIL) (-70 141494 141713 141752 "ASP30" 141757 NIL ASP30 (NIL NIL) -8 NIL NIL NIL) (-69 141211 141298 141374 "ASP29" 141449 NIL ASP29 (NIL NIL) -8 NIL NIL NIL) (-68 140940 141159 141198 "ASP28" 141203 NIL ASP28 (NIL NIL) -8 NIL NIL NIL) (-67 140669 140888 140927 "ASP27" 140932 NIL ASP27 (NIL NIL) -8 NIL NIL NIL) (-66 139645 140367 140478 "ASP24" 140589 NIL ASP24 (NIL NIL) -8 NIL NIL NIL) (-65 138614 139447 139559 "ASP20" 139564 NIL ASP20 (NIL NIL) -8 NIL NIL NIL) (-64 137449 138288 138407 "ASP19" 138526 NIL ASP19 (NIL NIL) -8 NIL NIL NIL) (-63 137168 137253 137329 "ASP12" 137404 NIL ASP12 (NIL NIL) -8 NIL NIL NIL) (-62 135912 136767 136911 "ASP10" 137055 NIL ASP10 (NIL NIL) -8 NIL NIL NIL) (-61 134892 135613 135723 "ASP1" 135833 NIL ASP1 (NIL NIL) -8 NIL NIL NIL) (-60 132504 134736 134827 "ARRAY2" 134832 NIL ARRAY2 (NIL T) -8 NIL NIL NIL) (-59 131518 131709 131930 "ARRAY12" 132327 NIL ARRAY12 (NIL T T) -7 NIL NIL NIL) (-58 126878 131166 131280 "ARRAY1" 131435 NIL ARRAY1 (NIL T) -8 NIL NIL NIL) (-57 120923 123080 123155 "ARR2CAT" 125785 NIL ARR2CAT (NIL T T T) -9 NIL 126543 NIL) (-56 118213 119101 120055 "ARR2CAT-" 120060 NIL ARR2CAT- (NIL T T T T) -8 NIL NIL NIL) (-55 117464 117840 117965 "ARITY" 118106 T ARITY (NIL) -8 NIL NIL NIL) (-54 116222 116392 116691 "APPRULE" 117300 NIL APPRULE (NIL T T T) -7 NIL NIL NIL) (-53 115867 115921 116040 "APPLYORE" 116168 NIL APPLYORE (NIL T T T) -7 NIL NIL NIL) (-52 115121 115268 115425 "ANY1" 115741 NIL ANY1 (NIL T) -7 NIL NIL NIL) (-51 114421 114714 114834 "ANY" 115019 T ANY (NIL) -8 NIL NIL NIL) (-50 111747 112858 113185 "ANTISYM" 114145 NIL ANTISYM (NIL T NIL) -8 NIL NIL NIL) (-49 111191 111454 111550 "ANON" 111669 T ANON (NIL) -8 NIL NIL NIL) (-48 104354 109730 110184 "AN" 110755 T AN (NIL) -8 NIL NIL NIL) (-47 100017 101626 101677 "AMR" 102425 NIL AMR (NIL T T) -9 NIL 103025 NIL) (-46 99069 99350 99713 "AMR-" 99718 NIL AMR- (NIL T T T) -8 NIL NIL NIL) (-45 82538 98986 99047 "ALIST" 99052 NIL ALIST (NIL T T) -8 NIL NIL NIL) (-44 78835 82132 82301 "ALGSC" 82456 NIL ALGSC (NIL T NIL NIL NIL) -8 NIL NIL NIL) (-43 75285 75945 76552 "ALGPKG" 78275 NIL ALGPKG (NIL T T) -7 NIL NIL NIL) (-42 74550 74663 74847 "ALGMFACT" 75171 NIL ALGMFACT (NIL T T T) -7 NIL NIL NIL) (-41 70533 71164 71758 "ALGMANIP" 74134 NIL ALGMANIP (NIL T T) -7 NIL NIL NIL) (-40 59893 70159 70309 "ALGFF" 70466 NIL ALGFF (NIL T T T NIL) -8 NIL NIL NIL) (-39 59065 59220 59399 "ALGFACT" 59751 NIL ALGFACT (NIL T) -7 NIL NIL NIL) (-38 57854 58592 58630 "ALGEBRA" 58635 NIL ALGEBRA (NIL T) -9 NIL 58676 NIL) (-37 57554 57631 57763 "ALGEBRA-" 57768 NIL ALGEBRA- (NIL T T) -8 NIL NIL NIL) (-36 38508 55391 55443 "ALAGG" 55579 NIL ALAGG (NIL T T) -9 NIL 55740 NIL) (-35 38008 38157 38183 "AHYP" 38384 T AHYP (NIL) -9 NIL NIL NIL) (-34 36893 37187 37213 "AGG" 37712 T AGG (NIL) -9 NIL 37991 NIL) (-33 36291 36489 36703 "AGG-" 36708 NIL AGG- (NIL T) -8 NIL NIL NIL) (-32 34051 34520 34925 "AF" 35933 NIL AF (NIL T T) -7 NIL NIL NIL) (-31 33471 33776 33866 "ADDAST" 33979 T ADDAST (NIL) -8 NIL NIL NIL) (-30 32703 32998 33154 "ACPLOT" 33333 T ACPLOT (NIL) -8 NIL NIL NIL) (-29 20267 29635 29673 "ACFS" 30280 NIL ACFS (NIL T) -9 NIL 30519 NIL) (-28 18174 18784 19546 "ACFS-" 19551 NIL ACFS- (NIL T T) -8 NIL NIL NIL) (-27 13882 16207 16233 "ACF" 17112 T ACF (NIL) -9 NIL 17525 NIL) (-26 12514 12920 13413 "ACF-" 13418 NIL ACF- (NIL T) -8 NIL NIL NIL) (-25 12024 12267 12293 "ABELSG" 12385 T ABELSG (NIL) -9 NIL 12450 NIL) (-24 11885 11916 11982 "ABELSG-" 11987 NIL ABELSG- (NIL T) -8 NIL NIL NIL) (-23 11154 11501 11527 "ABELMON" 11697 T ABELMON (NIL) -9 NIL 11809 NIL) (-22 10794 10902 11040 "ABELMON-" 11045 NIL ABELMON- (NIL T) -8 NIL NIL NIL) (-21 10044 10500 10526 "ABELGRP" 10598 T ABELGRP (NIL) -9 NIL 10673 NIL) (-20 9471 9636 9852 "ABELGRP-" 9857 NIL ABELGRP- (NIL T) -8 NIL NIL NIL) (-19 4579 8733 8772 "A1AGG" 8777 NIL A1AGG (NIL T) -9 NIL 8817 NIL) (-18 30 1497 3059 "A1AGG-" 3064 NIL A1AGG- (NIL T T) -8 NIL NIL NIL))
\ No newline at end of file +((-3 3472968 3472973 3472978 NIL NIL NIL NIL (NIL) -8 NIL NIL NIL) (-2 3472953 3472958 3472963 NIL NIL NIL NIL (NIL) -8 NIL NIL NIL) (-1 3472938 3472943 3472948 NIL NIL NIL NIL (NIL) -8 NIL NIL NIL) (0 3472923 3472928 3472933 NIL NIL NIL NIL (NIL) -8 NIL NIL NIL) (-1329 3471916 3472798 3472875 "ZMOD" 3472880 NIL ZMOD (NIL NIL) -8 NIL NIL NIL) (-1328 3470952 3471134 3471357 "ZLINDEP" 3471748 NIL ZLINDEP (NIL T) -7 NIL NIL NIL) (-1327 3460114 3462020 3463992 "ZDSOLVE" 3469082 NIL ZDSOLVE (NIL T NIL NIL) -7 NIL NIL NIL) (-1326 3459348 3459501 3459690 "YSTREAM" 3459960 NIL YSTREAM (NIL T) -7 NIL NIL NIL) (-1325 3458708 3459017 3459132 "YDIAGRAM" 3459255 T YDIAGRAM (NIL) -8 NIL NIL NIL) (-1324 3456156 3458009 3458213 "XRPOLY" 3458551 NIL XRPOLY (NIL T T) -8 NIL NIL NIL) (-1323 3452423 3454027 3454602 "XPR" 3455628 NIL XPR (NIL T T) -8 NIL NIL NIL) (-1322 3449754 3451430 3451485 "XPOLYC" 3451773 NIL XPOLYC (NIL T T) -9 NIL 3451886 NIL) (-1321 3447149 3449085 3449289 "XPOLY" 3449585 NIL XPOLY (NIL T) -8 NIL NIL NIL) (-1320 3443095 3445666 3446054 "XPBWPOLY" 3446807 NIL XPBWPOLY (NIL T T) -8 NIL NIL NIL) (-1319 3437987 3439566 3439621 "XFALG" 3441793 NIL XFALG (NIL T T) -9 NIL 3442582 NIL) (-1318 3433263 3435963 3436005 "XF" 3436626 NIL XF (NIL T) -9 NIL 3437026 NIL) (-1317 3432860 3432972 3433141 "XF-" 3433146 NIL XF- (NIL T T) -8 NIL NIL NIL) (-1316 3431975 3432097 3432302 "XEXPPKG" 3432752 NIL XEXPPKG (NIL T T T) -7 NIL NIL NIL) (-1315 3429716 3431825 3431921 "XDPOLY" 3431926 NIL XDPOLY (NIL T T) -8 NIL NIL NIL) (-1314 3428371 3429109 3429152 "XALG" 3429157 NIL XALG (NIL T) -9 NIL 3429268 NIL) (-1313 3421281 3426348 3426842 "WUTSET" 3427963 NIL WUTSET (NIL T T T T) -8 NIL NIL NIL) (-1312 3419383 3420333 3420656 "WP" 3421092 NIL WP (NIL T T T T NIL NIL NIL) -8 NIL NIL NIL) (-1311 3418931 3419205 3419275 "WHILEAST" 3419335 T WHILEAST (NIL) -8 NIL NIL NIL) (-1310 3418343 3418648 3418742 "WHEREAST" 3418859 T WHEREAST (NIL) -8 NIL NIL NIL) (-1309 3417217 3417427 3417722 "WFFINTBS" 3418140 NIL WFFINTBS (NIL T T T T) -7 NIL NIL NIL) (-1308 3415085 3415548 3416010 "WEIER" 3416789 NIL WEIER (NIL T) -7 NIL NIL NIL) (-1307 3414009 3414567 3414609 "VSPACE" 3414745 NIL VSPACE (NIL T) -9 NIL 3414819 NIL) (-1306 3413841 3413874 3413965 "VSPACE-" 3413970 NIL VSPACE- (NIL T T) -8 NIL NIL NIL) (-1305 3413638 3413692 3413760 "VOID" 3413795 T VOID (NIL) -8 NIL NIL NIL) (-1304 3409906 3410701 3411438 "VIEWDEF" 3412923 T VIEWDEF (NIL) -7 NIL NIL NIL) (-1303 3398850 3401454 3403627 "VIEW3D" 3407755 T VIEW3D (NIL) -8 NIL NIL NIL) (-1302 3390867 3392761 3394340 "VIEW2D" 3397293 T VIEW2D (NIL) -8 NIL NIL NIL) (-1301 3388967 3389362 3389768 "VIEW" 3390483 T VIEW (NIL) -7 NIL NIL NIL) (-1300 3387520 3387803 3388121 "VECTOR2" 3388697 NIL VECTOR2 (NIL T T) -7 NIL NIL NIL) (-1299 3382426 3387290 3387382 "VECTOR" 3387463 NIL VECTOR (NIL T) -8 NIL NIL NIL) (-1298 3375371 3380130 3380173 "VECTCAT" 3381168 NIL VECTCAT (NIL T) -9 NIL 3381755 NIL) (-1297 3374313 3374639 3375029 "VECTCAT-" 3375034 NIL VECTCAT- (NIL T T) -8 NIL NIL NIL) (-1296 3373719 3373964 3374084 "VARIABLE" 3374228 NIL VARIABLE (NIL NIL) -8 NIL NIL NIL) (-1295 3373652 3373657 3373687 "UTYPE" 3373692 T UTYPE (NIL) -9 NIL NIL NIL) (-1294 3372460 3372636 3372898 "UTSODETL" 3373478 NIL UTSODETL (NIL T T T T) -7 NIL NIL NIL) (-1293 3369852 3370360 3370884 "UTSODE" 3372001 NIL UTSODE (NIL T T) -7 NIL NIL NIL) (-1292 3359862 3365785 3365828 "UTSCAT" 3366940 NIL UTSCAT (NIL T) -9 NIL 3367698 NIL) (-1291 3356988 3357932 3358921 "UTSCAT-" 3358926 NIL UTSCAT- (NIL T T) -8 NIL NIL NIL) (-1290 3356609 3356658 3356791 "UTS2" 3356939 NIL UTS2 (NIL T T T T) -7 NIL NIL NIL) (-1289 3347926 3354370 3354850 "UTS" 3356187 NIL UTS (NIL T NIL NIL) -8 NIL NIL NIL) (-1288 3341793 3344736 3344779 "URAGG" 3346849 NIL URAGG (NIL T) -9 NIL 3347572 NIL) (-1287 3338516 3339595 3340718 "URAGG-" 3340723 NIL URAGG- (NIL T T) -8 NIL NIL NIL) (-1286 3333892 3337151 3337616 "UPXSSING" 3338180 NIL UPXSSING (NIL T T NIL NIL) -8 NIL NIL NIL) (-1285 3326321 3333796 3333868 "UPXSCONS" 3333873 NIL UPXSCONS (NIL T T) -8 NIL NIL NIL) (-1284 3315079 3322523 3322585 "UPXSCCA" 3323159 NIL UPXSCCA (NIL T T) -9 NIL 3323392 NIL) (-1283 3314699 3314802 3314976 "UPXSCCA-" 3314981 NIL UPXSCCA- (NIL T T T) -8 NIL NIL NIL) (-1282 3303357 3310526 3310569 "UPXSCAT" 3311217 NIL UPXSCAT (NIL T) -9 NIL 3311826 NIL) (-1281 3302781 3302866 3303045 "UPXS2" 3303272 NIL UPXS2 (NIL T T NIL NIL NIL NIL) -7 NIL NIL NIL) (-1280 3294273 3302163 3302427 "UPXS" 3302575 NIL UPXS (NIL T NIL NIL) -8 NIL NIL NIL) (-1279 3292909 3293180 3293531 "UPSQFREE" 3294016 NIL UPSQFREE (NIL T T) -7 NIL NIL NIL) (-1278 3285740 3289175 3289230 "UPSCAT" 3290310 NIL UPSCAT (NIL T T) -9 NIL 3291076 NIL) (-1277 3284896 3285151 3285478 "UPSCAT-" 3285483 NIL UPSCAT- (NIL T T T) -8 NIL NIL NIL) (-1276 3284517 3284566 3284699 "UPOLYC2" 3284847 NIL UPOLYC2 (NIL T T T T) -7 NIL NIL NIL) (-1275 3268665 3277644 3277687 "UPOLYC" 3279788 NIL UPOLYC (NIL T) -9 NIL 3281009 NIL) (-1274 3259534 3262433 3265573 "UPOLYC-" 3265578 NIL UPOLYC- (NIL T T) -8 NIL NIL NIL) (-1273 3258855 3258980 3259144 "UPMP" 3259423 NIL UPMP (NIL T T) -7 NIL NIL NIL) (-1272 3258402 3258489 3258628 "UPDIVP" 3258768 NIL UPDIVP (NIL T T) -7 NIL NIL NIL) (-1271 3256940 3257219 3257535 "UPDECOMP" 3258151 NIL UPDECOMP (NIL T T) -7 NIL NIL NIL) (-1270 3256153 3256283 3256469 "UPCDEN" 3256824 NIL UPCDEN (NIL T T T) -7 NIL NIL NIL) (-1269 3255666 3255741 3255890 "UP2" 3256078 NIL UP2 (NIL NIL T NIL T) -7 NIL NIL NIL) (-1268 3246262 3255349 3255478 "UP" 3255585 NIL UP (NIL NIL T) -8 NIL NIL NIL) (-1267 3245467 3245604 3245809 "UNISEG2" 3246105 NIL UNISEG2 (NIL T T) -7 NIL NIL NIL) (-1266 3243820 3244671 3244948 "UNISEG" 3245225 NIL UNISEG (NIL T) -8 NIL NIL NIL) (-1265 3242862 3243060 3243286 "UNIFACT" 3243636 NIL UNIFACT (NIL T) -7 NIL NIL NIL) (-1264 3229593 3242766 3242838 "ULSCONS" 3242843 NIL ULSCONS (NIL T T) -8 NIL NIL NIL) (-1263 3209410 3222673 3222735 "ULSCCAT" 3223373 NIL ULSCCAT (NIL T T) -9 NIL 3223662 NIL) (-1262 3208406 3208705 3209093 "ULSCCAT-" 3209098 NIL ULSCCAT- (NIL T T T) -8 NIL NIL NIL) (-1261 3196861 3203952 3203995 "ULSCAT" 3204858 NIL ULSCAT (NIL T) -9 NIL 3205589 NIL) (-1260 3196285 3196370 3196549 "ULS2" 3196776 NIL ULS2 (NIL T T NIL NIL NIL NIL) -7 NIL NIL NIL) (-1259 3178116 3195597 3195839 "ULS" 3196101 NIL ULS (NIL T NIL NIL) -8 NIL NIL NIL) (-1258 3177035 3177735 3177849 "UINT8" 3177960 T UINT8 (NIL) -8 NIL NIL 3178052) (-1257 3175953 3176653 3176767 "UINT64" 3176878 T UINT64 (NIL) -8 NIL NIL 3176970) (-1256 3174871 3175571 3175685 "UINT32" 3175796 T UINT32 (NIL) -8 NIL NIL 3175888) (-1255 3173789 3174489 3174603 "UINT16" 3174714 T UINT16 (NIL) -8 NIL NIL 3174806) (-1254 3171868 3173035 3173065 "UFD" 3173277 T UFD (NIL) -9 NIL 3173391 NIL) (-1253 3171650 3171708 3171803 "UFD-" 3171808 NIL UFD- (NIL T) -8 NIL NIL NIL) (-1252 3170708 3170915 3171131 "UDVO" 3171456 T UDVO (NIL) -7 NIL NIL NIL) (-1251 3168474 3168933 3169404 "UDPO" 3170272 NIL UDPO (NIL T) -7 NIL NIL NIL) (-1250 3168186 3168429 3168460 "TYPEAST" 3168465 T TYPEAST (NIL) -8 NIL NIL NIL) (-1249 3168119 3168124 3168154 "TYPE" 3168159 T TYPE (NIL) -9 NIL NIL NIL) (-1248 3167072 3167292 3167532 "TWOFACT" 3167913 NIL TWOFACT (NIL T) -7 NIL NIL NIL) (-1247 3166047 3166481 3166716 "TUPLE" 3166872 NIL TUPLE (NIL T) -8 NIL NIL NIL) (-1246 3163684 3164257 3164796 "TUBETOOL" 3165530 T TUBETOOL (NIL) -7 NIL NIL NIL) (-1245 3162490 3162731 3162973 "TUBE" 3163477 NIL TUBE (NIL T) -8 NIL NIL NIL) (-1244 3150625 3155247 3155344 "TSETCAT" 3160613 NIL TSETCAT (NIL T T T T) -9 NIL 3162145 NIL) (-1243 3145093 3146957 3148848 "TSETCAT-" 3148853 NIL TSETCAT- (NIL T T T T T) -8 NIL NIL NIL) (-1242 3139279 3144065 3144348 "TS" 3144845 NIL TS (NIL T) -8 NIL NIL NIL) (-1241 3133752 3134765 3135694 "TRMANIP" 3138415 NIL TRMANIP (NIL T T) -7 NIL NIL NIL) (-1240 3133181 3133256 3133419 "TRIMAT" 3133684 NIL TRIMAT (NIL T T T T) -7 NIL NIL NIL) (-1239 3130993 3131284 3131641 "TRIGMNIP" 3132930 NIL TRIGMNIP (NIL T T) -7 NIL NIL NIL) (-1238 3130477 3130626 3130656 "TRIGCAT" 3130869 T TRIGCAT (NIL) -9 NIL NIL NIL) (-1237 3130122 3130225 3130366 "TRIGCAT-" 3130371 NIL TRIGCAT- (NIL T) -8 NIL NIL NIL) (-1236 3126736 3128980 3129261 "TREE" 3129876 NIL TREE (NIL T) -8 NIL NIL NIL) (-1235 3125842 3126538 3126568 "TRANFUN" 3126603 T TRANFUN (NIL) -9 NIL 3126669 NIL) (-1234 3125061 3125312 3125592 "TRANFUN-" 3125597 NIL TRANFUN- (NIL T) -8 NIL NIL NIL) (-1233 3124859 3124897 3124958 "TOPSP" 3125022 T TOPSP (NIL) -7 NIL NIL NIL) (-1232 3124189 3124322 3124476 "TOOLSIGN" 3124740 NIL TOOLSIGN (NIL T) -7 NIL NIL NIL) (-1231 3122703 3123366 3123605 "TEXTFILE" 3123972 T TEXTFILE (NIL) -8 NIL NIL NIL) (-1230 3122478 3122515 3122587 "TEX1" 3122666 NIL TEX1 (NIL T) -7 NIL NIL NIL) (-1229 3120282 3120931 3121360 "TEX" 3122071 T TEX (NIL) -8 NIL NIL NIL) (-1228 3119918 3119993 3120083 "TEMUTL" 3120214 T TEMUTL (NIL) -7 NIL NIL NIL) (-1227 3118012 3118352 3118677 "TBCMPPK" 3119641 NIL TBCMPPK (NIL T T) -7 NIL NIL NIL) (-1226 3109332 3116098 3116154 "TBAGG" 3116554 NIL TBAGG (NIL T T) -9 NIL 3116765 NIL) (-1225 3104216 3105890 3107644 "TBAGG-" 3107649 NIL TBAGG- (NIL T T T) -8 NIL NIL NIL) (-1224 3103582 3103707 3103852 "TANEXP" 3104105 NIL TANEXP (NIL T) -7 NIL NIL NIL) (-1223 3103033 3103357 3103447 "TALGOP" 3103527 NIL TALGOP (NIL T) -8 NIL NIL NIL) (-1222 3102427 3102544 3102682 "TABLEAU" 3102930 NIL TABLEAU (NIL T) -8 NIL NIL NIL) (-1221 3095441 3102284 3102377 "TABLE" 3102382 NIL TABLE (NIL T T) -8 NIL NIL NIL) (-1220 3089971 3091269 3092517 "TABLBUMP" 3094227 NIL TABLBUMP (NIL T) -7 NIL NIL NIL) (-1219 3089181 3089340 3089521 "SYSTEM" 3089812 T SYSTEM (NIL) -8 NIL NIL NIL) (-1218 3085586 3086339 3087122 "SYSSOLP" 3088432 NIL SYSSOLP (NIL T) -7 NIL NIL NIL) (-1217 3085348 3085541 3085572 "SYSPTR" 3085577 T SYSPTR (NIL) -8 NIL NIL NIL) (-1216 3084187 3084879 3085005 "SYSNNI" 3085191 NIL SYSNNI (NIL NIL) -8 NIL NIL 3085283) (-1215 3083394 3083949 3084028 "SYSINT" 3084088 NIL SYSINT (NIL NIL) -8 NIL NIL 3084133) (-1214 3079492 3080672 3081382 "SYNTAX" 3082706 T SYNTAX (NIL) -8 NIL NIL NIL) (-1213 3076572 3077252 3077884 "SYMTAB" 3078882 T SYMTAB (NIL) -8 NIL NIL NIL) (-1212 3071671 3072723 3073706 "SYMS" 3075611 T SYMS (NIL) -8 NIL NIL NIL) (-1211 3068577 3071122 3071355 "SYMPOLY" 3071473 NIL SYMPOLY (NIL T) -8 NIL NIL NIL) (-1210 3068082 3068169 3068292 "SYMFUNC" 3068489 NIL SYMFUNC (NIL T) -7 NIL NIL NIL) (-1209 3063880 3065394 3066207 "SYMBOL" 3067291 T SYMBOL (NIL) -8 NIL NIL NIL) (-1208 3057353 3059108 3060828 "SWITCH" 3062182 T SWITCH (NIL) -8 NIL NIL NIL) (-1207 3050114 3056309 3056603 "SUTS" 3057117 NIL SUTS (NIL T NIL NIL) -8 NIL NIL NIL) (-1206 3041606 3049496 3049760 "SUPXS" 3049908 NIL SUPXS (NIL T NIL NIL) -8 NIL NIL NIL) (-1205 3040753 3040892 3041109 "SUPFRACF" 3041474 NIL SUPFRACF (NIL T T T T) -7 NIL NIL NIL) (-1204 3040368 3040433 3040546 "SUP2" 3040688 NIL SUP2 (NIL T T) -7 NIL NIL NIL) (-1203 3030912 3039986 3040112 "SUP" 3040277 NIL SUP (NIL T) -8 NIL NIL NIL) (-1202 3029336 3029634 3029990 "SUMRF" 3030611 NIL SUMRF (NIL T) -7 NIL NIL NIL) (-1201 3028659 3028737 3028929 "SUMFS" 3029257 NIL SUMFS (NIL T T) -7 NIL NIL NIL) (-1200 3010525 3027971 3028213 "SULS" 3028475 NIL SULS (NIL T NIL NIL) -8 NIL NIL NIL) (-1199 3010073 3010347 3010417 "SUCHTAST" 3010477 T SUCHTAST (NIL) -8 NIL NIL NIL) (-1198 3009314 3009598 3009738 "SUCH" 3009981 NIL SUCH (NIL T T) -8 NIL NIL NIL) (-1197 3002953 3004220 3005179 "SUBSPACE" 3008402 NIL SUBSPACE (NIL NIL T) -8 NIL NIL NIL) (-1196 3002373 3002473 3002637 "SUBRESP" 3002841 NIL SUBRESP (NIL T T) -7 NIL NIL NIL) (-1195 2996384 2997666 2998813 "STTFNC" 3001273 NIL STTFNC (NIL T) -7 NIL NIL NIL) (-1194 2989578 2991049 2992360 "STTF" 2995120 NIL STTF (NIL T) -7 NIL NIL NIL) (-1193 2980694 2982760 2984554 "STTAYLOR" 2987819 NIL STTAYLOR (NIL T) -7 NIL NIL NIL) (-1192 2973448 2980558 2980641 "STRTBL" 2980646 NIL STRTBL (NIL T) -8 NIL NIL NIL) (-1191 2967845 2973157 2973256 "STRING" 2973371 T STRING (NIL) -8 NIL NIL NIL) (-1190 2967349 2967432 2967576 "STREAM3" 2967762 NIL STREAM3 (NIL T T T) -7 NIL NIL NIL) (-1189 2966313 2966514 2966749 "STREAM2" 2967162 NIL STREAM2 (NIL T T) -7 NIL NIL NIL) (-1188 2965995 2966053 2966146 "STREAM1" 2966255 NIL STREAM1 (NIL T) -7 NIL NIL NIL) (-1187 2958109 2963614 2964225 "STREAM" 2965419 NIL STREAM (NIL T) -8 NIL NIL NIL) (-1186 2957101 2957306 2957537 "STINPROD" 2957925 NIL STINPROD (NIL T) -7 NIL NIL NIL) (-1185 2956216 2956590 2956738 "STEPAST" 2956975 T STEPAST (NIL) -8 NIL NIL NIL) (-1184 2955712 2955957 2955987 "STEP" 2956081 T STEP (NIL) -9 NIL 2956152 NIL) (-1183 2948768 2955611 2955688 "STBL" 2955693 NIL STBL (NIL T T NIL) -8 NIL NIL NIL) (-1182 2943318 2947931 2947974 "STAGG" 2948127 NIL STAGG (NIL T) -9 NIL 2948216 NIL) (-1181 2940870 2941622 2942494 "STAGG-" 2942499 NIL STAGG- (NIL T T) -8 NIL NIL NIL) (-1180 2938842 2940640 2940732 "STACK" 2940813 NIL STACK (NIL T) -8 NIL NIL NIL) (-1179 2938159 2938672 2938702 "SRING" 2938707 T SRING (NIL) -9 NIL 2938727 NIL) (-1178 2930167 2936300 2936756 "SREGSET" 2937789 NIL SREGSET (NIL T T T T) -8 NIL NIL NIL) (-1177 2922514 2923961 2925474 "SRDCMPK" 2928773 NIL SRDCMPK (NIL T T T T T) -7 NIL NIL NIL) (-1176 2914814 2919873 2919903 "SRAGG" 2921206 T SRAGG (NIL) -9 NIL 2921814 NIL) (-1175 2913765 2914086 2914465 "SRAGG-" 2914470 NIL SRAGG- (NIL T) -8 NIL NIL NIL) (-1174 2907349 2912712 2913133 "SQMATRIX" 2913391 NIL SQMATRIX (NIL NIL T) -8 NIL NIL NIL) (-1173 2900761 2904067 2904794 "SPLTREE" 2906694 NIL SPLTREE (NIL T T) -8 NIL NIL NIL) (-1172 2896586 2897417 2898063 "SPLNODE" 2900187 NIL SPLNODE (NIL T T) -8 NIL NIL NIL) (-1171 2895561 2895866 2895896 "SPFCAT" 2896340 T SPFCAT (NIL) -9 NIL NIL NIL) (-1170 2894256 2894508 2894772 "SPECOUT" 2895319 T SPECOUT (NIL) -7 NIL NIL NIL) (-1169 2884902 2887220 2887250 "SPADXPT" 2891928 T SPADXPT (NIL) -9 NIL 2894094 NIL) (-1168 2884657 2884703 2884772 "SPADPRSR" 2884855 T SPADPRSR (NIL) -7 NIL NIL NIL) (-1167 2882260 2884612 2884643 "SPADAST" 2884648 T SPADAST (NIL) -8 NIL NIL NIL) (-1166 2873861 2875964 2876007 "SPACEC" 2880380 NIL SPACEC (NIL T) -9 NIL 2882196 NIL) (-1165 2871661 2873793 2873842 "SPACE3" 2873847 NIL SPACE3 (NIL T) -8 NIL NIL NIL) (-1164 2870393 2870584 2870875 "SORTPAK" 2871466 NIL SORTPAK (NIL T T) -7 NIL NIL NIL) (-1163 2868455 2868788 2869200 "SOLVETRA" 2870057 NIL SOLVETRA (NIL T) -7 NIL NIL NIL) (-1162 2867493 2867727 2867988 "SOLVESER" 2868228 NIL SOLVESER (NIL T) -7 NIL NIL NIL) (-1161 2862725 2863685 2864680 "SOLVERAD" 2866545 NIL SOLVERAD (NIL T) -7 NIL NIL NIL) (-1160 2858450 2859149 2859878 "SOLVEFOR" 2862092 NIL SOLVEFOR (NIL T T) -7 NIL NIL NIL) (-1159 2852054 2857798 2857895 "SNTSCAT" 2857900 NIL SNTSCAT (NIL T T T T) -9 NIL 2857970 NIL) (-1158 2845605 2850377 2850768 "SMTS" 2851744 NIL SMTS (NIL T T T) -8 NIL NIL NIL) (-1157 2839327 2845493 2845570 "SMP" 2845575 NIL SMP (NIL T T) -8 NIL NIL NIL) (-1156 2837456 2837787 2838185 "SMITH" 2839024 NIL SMITH (NIL T T T T) -7 NIL NIL NIL) (-1155 2828981 2834035 2834138 "SMATCAT" 2835489 NIL SMATCAT (NIL NIL T T T) -9 NIL 2836039 NIL) (-1154 2825753 2826744 2827922 "SMATCAT-" 2827927 NIL SMATCAT- (NIL T NIL T T T) -8 NIL NIL NIL) (-1153 2823222 2824961 2825004 "SKAGG" 2825265 NIL SKAGG (NIL T) -9 NIL 2825400 NIL) (-1152 2818742 2822705 2822882 "SINT" 2823034 T SINT (NIL) -8 NIL NIL 2823189) (-1151 2818508 2818552 2818618 "SIMPAN" 2818698 T SIMPAN (NIL) -7 NIL NIL NIL) (-1150 2817328 2817567 2817842 "SIGNRF" 2818267 NIL SIGNRF (NIL T) -7 NIL NIL NIL) (-1149 2816143 2816312 2816596 "SIGNEF" 2817157 NIL SIGNEF (NIL T T) -7 NIL NIL NIL) (-1148 2815383 2815726 2815850 "SIGAST" 2816041 T SIGAST (NIL) -8 NIL NIL NIL) (-1147 2814608 2814918 2815058 "SIG" 2815265 T SIG (NIL) -8 NIL NIL NIL) (-1146 2812260 2812752 2813258 "SHP" 2814149 NIL SHP (NIL T NIL) -7 NIL NIL NIL) (-1145 2805584 2812161 2812237 "SHDP" 2812242 NIL SHDP (NIL NIL NIL T) -8 NIL NIL NIL) (-1144 2805095 2805335 2805365 "SGROUP" 2805458 T SGROUP (NIL) -9 NIL 2805520 NIL) (-1143 2804947 2804979 2805052 "SGROUP-" 2805057 NIL SGROUP- (NIL T) -8 NIL NIL NIL) (-1142 2801666 2802436 2803159 "SGCF" 2804246 T SGCF (NIL) -7 NIL NIL NIL) (-1141 2795368 2801112 2801209 "SFRTCAT" 2801214 NIL SFRTCAT (NIL T T T T) -9 NIL 2801253 NIL) (-1140 2788687 2789807 2790943 "SFRGCD" 2794351 NIL SFRGCD (NIL T T T T T) -7 NIL NIL NIL) (-1139 2781705 2782886 2784072 "SFQCMPK" 2787620 NIL SFQCMPK (NIL T T T T T) -7 NIL NIL NIL) (-1138 2781307 2781414 2781525 "SFORT" 2781646 NIL SFORT (NIL T T) -8 NIL NIL NIL) (-1137 2780233 2781147 2781268 "SEXOF" 2781273 NIL SEXOF (NIL T T T T T) -8 NIL NIL NIL) (-1136 2775822 2776729 2776824 "SEXCAT" 2779446 NIL SEXCAT (NIL T T T T T) -9 NIL 2780006 NIL) (-1135 2774737 2775703 2775771 "SEX" 2775776 T SEX (NIL) -8 NIL NIL NIL) (-1134 2772859 2773450 2773755 "SETMN" 2774478 NIL SETMN (NIL NIL NIL) -8 NIL NIL NIL) (-1133 2772389 2772577 2772607 "SETCAT" 2772724 T SETCAT (NIL) -9 NIL 2772809 NIL) (-1132 2772157 2772221 2772320 "SETCAT-" 2772325 NIL SETCAT- (NIL T) -8 NIL NIL NIL) (-1131 2768260 2770618 2770661 "SETAGG" 2771531 NIL SETAGG (NIL T) -9 NIL 2771871 NIL) (-1130 2767682 2767834 2768071 "SETAGG-" 2768076 NIL SETAGG- (NIL T T) -8 NIL NIL NIL) (-1129 2764491 2767616 2767664 "SET" 2767669 NIL SET (NIL T) -8 NIL NIL NIL) (-1128 2763874 2764187 2764288 "SEQAST" 2764412 T SEQAST (NIL) -8 NIL NIL NIL) (-1127 2763001 2763367 2763428 "SEGXCAT" 2763714 NIL SEGXCAT (NIL T T) -9 NIL 2763834 NIL) (-1126 2761926 2762194 2762237 "SEGCAT" 2762759 NIL SEGCAT (NIL T) -9 NIL 2762980 NIL) (-1125 2761541 2761606 2761719 "SEGBIND2" 2761861 NIL SEGBIND2 (NIL T T) -7 NIL NIL NIL) (-1124 2760431 2760904 2761112 "SEGBIND" 2761368 NIL SEGBIND (NIL T) -8 NIL NIL NIL) (-1123 2759950 2760232 2760309 "SEGAST" 2760376 T SEGAST (NIL) -8 NIL NIL NIL) (-1122 2759159 2759295 2759499 "SEG2" 2759794 NIL SEG2 (NIL T T) -7 NIL NIL NIL) (-1121 2758075 2758825 2759007 "SEG" 2759012 NIL SEG (NIL T) -8 NIL NIL NIL) (-1120 2757308 2758010 2758057 "SDVAR" 2758062 NIL SDVAR (NIL T) -8 NIL NIL NIL) (-1119 2748666 2757078 2757208 "SDPOL" 2757213 NIL SDPOL (NIL T) -8 NIL NIL NIL) (-1118 2747235 2747525 2747844 "SCPKG" 2748381 NIL SCPKG (NIL T) -7 NIL NIL NIL) (-1117 2746357 2746571 2746763 "SCOPE" 2747065 T SCOPE (NIL) -8 NIL NIL NIL) (-1116 2745553 2745711 2745890 "SCACHE" 2746212 NIL SCACHE (NIL T) -7 NIL NIL NIL) (-1115 2745137 2745371 2745401 "SASTCAT" 2745406 T SASTCAT (NIL) -9 NIL 2745419 NIL) (-1114 2744540 2744972 2745048 "SAOS" 2745083 T SAOS (NIL) -8 NIL NIL NIL) (-1113 2744099 2744140 2744313 "SAERFFC" 2744499 NIL SAERFFC (NIL T T T) -7 NIL NIL NIL) (-1112 2743686 2743727 2743886 "SAEFACT" 2744058 NIL SAEFACT (NIL T T T) -7 NIL NIL NIL) (-1111 2736734 2743583 2743663 "SAE" 2743668 NIL SAE (NIL T T NIL) -8 NIL NIL NIL) (-1110 2735037 2735369 2735770 "RURPK" 2736400 NIL RURPK (NIL T NIL) -7 NIL NIL NIL) (-1109 2733614 2733980 2734285 "RULESET" 2734871 NIL RULESET (NIL T T T) -8 NIL NIL NIL) (-1108 2733184 2733408 2733491 "RULECOLD" 2733566 NIL RULECOLD (NIL NIL) -8 NIL NIL NIL) (-1107 2730299 2730937 2731395 "RULE" 2732865 NIL RULE (NIL T T T) -8 NIL NIL NIL) (-1106 2730083 2730117 2730188 "RTVALUE" 2730250 T RTVALUE (NIL) -8 NIL NIL NIL) (-1105 2729494 2729800 2729894 "RSTRCAST" 2730011 T RSTRCAST (NIL) -8 NIL NIL NIL) (-1104 2724264 2725137 2726057 "RSETGCD" 2728693 NIL RSETGCD (NIL T T T T T) -7 NIL NIL NIL) (-1103 2712828 2718572 2718669 "RSETCAT" 2722788 NIL RSETCAT (NIL T T T T) -9 NIL 2723885 NIL) (-1102 2710647 2711294 2712118 "RSETCAT-" 2712123 NIL RSETCAT- (NIL T T T T T) -8 NIL NIL NIL) (-1101 2702955 2704409 2705929 "RSDCMPK" 2709246 NIL RSDCMPK (NIL T T T T T) -7 NIL NIL NIL) (-1100 2700824 2701387 2701461 "RRCC" 2702547 NIL RRCC (NIL T T) -9 NIL 2702891 NIL) (-1099 2700145 2700349 2700628 "RRCC-" 2700633 NIL RRCC- (NIL T T T) -8 NIL NIL NIL) (-1098 2699528 2699841 2699942 "RPTAST" 2700066 T RPTAST (NIL) -8 NIL NIL NIL) (-1097 2671914 2682640 2682707 "RPOLCAT" 2693373 NIL RPOLCAT (NIL T T T) -9 NIL 2696533 NIL) (-1096 2662884 2665752 2668874 "RPOLCAT-" 2668879 NIL RPOLCAT- (NIL T T T T) -8 NIL NIL NIL) (-1095 2653337 2661095 2661577 "ROUTINE" 2662424 T ROUTINE (NIL) -8 NIL NIL NIL) (-1094 2649400 2652963 2653103 "ROMAN" 2653219 T ROMAN (NIL) -8 NIL NIL NIL) (-1093 2647512 2648260 2648520 "ROIRC" 2649205 NIL ROIRC (NIL T T) -8 NIL NIL NIL) (-1092 2643232 2646001 2646031 "RNS" 2646335 T RNS (NIL) -9 NIL 2646609 NIL) (-1091 2641639 2642124 2642658 "RNS-" 2642733 NIL RNS- (NIL T) -8 NIL NIL NIL) (-1090 2640600 2641004 2641206 "RNGBIND" 2641490 NIL RNGBIND (NIL T T) -8 NIL NIL NIL) (-1089 2639893 2640397 2640427 "RNG" 2640432 T RNG (NIL) -9 NIL 2640453 NIL) (-1088 2639188 2639666 2639709 "RMODULE" 2639714 NIL RMODULE (NIL T) -9 NIL 2639741 NIL) (-1087 2638012 2638118 2638454 "RMCAT2" 2639089 NIL RMCAT2 (NIL NIL NIL T T T T T T T T) -7 NIL NIL NIL) (-1086 2634514 2637358 2637655 "RMATRIX" 2637774 NIL RMATRIX (NIL NIL NIL T) -8 NIL NIL NIL) (-1085 2627013 2629601 2629716 "RMATCAT" 2633075 NIL RMATCAT (NIL NIL NIL T T T) -9 NIL 2634057 NIL) (-1084 2626352 2626535 2626842 "RMATCAT-" 2626847 NIL RMATCAT- (NIL T NIL NIL T T T) -8 NIL NIL NIL) (-1083 2625925 2626139 2626182 "RLINSET" 2626244 NIL RLINSET (NIL T) -9 NIL 2626288 NIL) (-1082 2625486 2625567 2625695 "RINTERP" 2625844 NIL RINTERP (NIL NIL T) -7 NIL NIL NIL) (-1081 2624410 2625084 2625114 "RING" 2625170 T RING (NIL) -9 NIL 2625262 NIL) (-1080 2624190 2624246 2624343 "RING-" 2624348 NIL RING- (NIL T) -8 NIL NIL NIL) (-1079 2623001 2623268 2623526 "RIDIST" 2623954 T RIDIST (NIL) -7 NIL NIL NIL) (-1078 2613626 2622469 2622675 "RGCHAIN" 2622849 NIL RGCHAIN (NIL T NIL) -8 NIL NIL NIL) (-1077 2612884 2613368 2613409 "RGBCSPC" 2613467 NIL RGBCSPC (NIL T) -9 NIL 2613519 NIL) (-1076 2611950 2612409 2612450 "RGBCMDL" 2612682 NIL RGBCMDL (NIL T) -9 NIL 2612796 NIL) (-1075 2611590 2611659 2611762 "RFFACTOR" 2611881 NIL RFFACTOR (NIL T) -7 NIL NIL NIL) (-1074 2611309 2611350 2611447 "RFFACT" 2611549 NIL RFFACT (NIL T) -7 NIL NIL NIL) (-1073 2609360 2609790 2610172 "RFDIST" 2610949 T RFDIST (NIL) -7 NIL NIL NIL) (-1072 2606300 2606968 2607638 "RF" 2608724 NIL RF (NIL T) -7 NIL NIL NIL) (-1071 2605747 2605845 2606008 "RETSOL" 2606202 NIL RETSOL (NIL T T) -7 NIL NIL NIL) (-1070 2605365 2605463 2605506 "RETRACT" 2605639 NIL RETRACT (NIL T) -9 NIL 2605726 NIL) (-1069 2605208 2605239 2605326 "RETRACT-" 2605331 NIL RETRACT- (NIL T T) -8 NIL NIL NIL) (-1068 2604756 2605030 2605100 "RETAST" 2605160 T RETAST (NIL) -8 NIL NIL NIL) (-1067 2597106 2604409 2604536 "RESULT" 2604651 T RESULT (NIL) -8 NIL NIL NIL) (-1066 2595541 2596375 2596574 "RESRING" 2597009 NIL RESRING (NIL T T T T NIL) -8 NIL NIL NIL) (-1065 2595165 2595226 2595324 "RESLATC" 2595478 NIL RESLATC (NIL T) -7 NIL NIL NIL) (-1064 2594864 2594905 2595012 "REPSQ" 2595124 NIL REPSQ (NIL T) -7 NIL NIL NIL) (-1063 2594555 2594596 2594707 "REPDB" 2594823 NIL REPDB (NIL T) -7 NIL NIL NIL) (-1062 2588387 2589844 2591067 "REP2" 2593367 NIL REP2 (NIL T) -7 NIL NIL NIL) (-1061 2584690 2585445 2586253 "REP1" 2587614 NIL REP1 (NIL T) -7 NIL NIL NIL) (-1060 2582070 2582692 2583294 "REP" 2584110 T REP (NIL) -7 NIL NIL NIL) (-1059 2574078 2580211 2580667 "REGSET" 2581700 NIL REGSET (NIL T T T T) -8 NIL NIL NIL) (-1058 2572787 2573226 2573476 "REF" 2573863 NIL REF (NIL T) -8 NIL NIL NIL) (-1057 2572152 2572267 2572434 "REDORDER" 2572671 NIL REDORDER (NIL T T) -7 NIL NIL NIL) (-1056 2567523 2571365 2571592 "RECLOS" 2571980 NIL RECLOS (NIL T) -8 NIL NIL NIL) (-1055 2566557 2566756 2566971 "REALSOLV" 2567330 T REALSOLV (NIL) -7 NIL NIL NIL) (-1054 2563004 2563842 2564726 "REAL0Q" 2565722 NIL REAL0Q (NIL T) -7 NIL NIL NIL) (-1053 2558557 2559593 2560654 "REAL0" 2561985 NIL REAL0 (NIL T) -7 NIL NIL NIL) (-1052 2558391 2558444 2558474 "REAL" 2558479 T REAL (NIL) -9 NIL 2558514 NIL) (-1051 2557802 2558108 2558202 "RDUCEAST" 2558319 T RDUCEAST (NIL) -8 NIL NIL NIL) (-1050 2557201 2557279 2557486 "RDIV" 2557724 NIL RDIV (NIL T T T T T) -7 NIL NIL NIL) (-1049 2556251 2556443 2556656 "RDIST" 2557023 NIL RDIST (NIL T) -7 NIL NIL NIL) (-1048 2554836 2555135 2555507 "RDETRS" 2555959 NIL RDETRS (NIL T T) -7 NIL NIL NIL) (-1047 2552630 2553102 2553640 "RDETR" 2554378 NIL RDETR (NIL T T) -7 NIL NIL NIL) (-1046 2551249 2551533 2551930 "RDEEFS" 2552346 NIL RDEEFS (NIL T T) -7 NIL NIL NIL) (-1045 2549752 2550064 2550489 "RDEEF" 2550937 NIL RDEEF (NIL T T) -7 NIL NIL NIL) (-1044 2543231 2546706 2546736 "RCFIELD" 2548031 T RCFIELD (NIL) -9 NIL 2548762 NIL) (-1043 2541187 2541799 2542495 "RCFIELD-" 2542570 NIL RCFIELD- (NIL T) -8 NIL NIL NIL) (-1042 2537239 2539260 2539303 "RCAGG" 2540387 NIL RCAGG (NIL T) -9 NIL 2540852 NIL) (-1041 2536849 2536961 2537124 "RCAGG-" 2537129 NIL RCAGG- (NIL T T) -8 NIL NIL NIL) (-1040 2536166 2536296 2536461 "RATRET" 2536733 NIL RATRET (NIL T) -7 NIL NIL NIL) (-1039 2535707 2535786 2535907 "RATFACT" 2536094 NIL RATFACT (NIL T) -7 NIL NIL NIL) (-1038 2534985 2535135 2535287 "RANDSRC" 2535577 T RANDSRC (NIL) -7 NIL NIL NIL) (-1037 2534713 2534763 2534836 "RADUTIL" 2534934 T RADUTIL (NIL) -7 NIL NIL NIL) (-1036 2526858 2533544 2533855 "RADIX" 2534436 NIL RADIX (NIL NIL) -8 NIL NIL NIL) (-1035 2516473 2526700 2526830 "RADFF" 2526835 NIL RADFF (NIL T T T NIL NIL) -8 NIL NIL NIL) (-1034 2516102 2516195 2516225 "RADCAT" 2516385 T RADCAT (NIL) -9 NIL NIL NIL) (-1033 2515872 2515932 2516032 "RADCAT-" 2516037 NIL RADCAT- (NIL T) -8 NIL NIL NIL) (-1032 2513783 2515642 2515734 "QUEUE" 2515815 NIL QUEUE (NIL T) -8 NIL NIL NIL) (-1031 2513408 2513457 2513588 "QUATCT2" 2513734 NIL QUATCT2 (NIL T T T T) -7 NIL NIL NIL) (-1030 2505786 2509831 2509873 "QUATCAT" 2510664 NIL QUATCAT (NIL T) -9 NIL 2511430 NIL) (-1029 2501667 2502962 2504352 "QUATCAT-" 2504448 NIL QUATCAT- (NIL T T) -8 NIL NIL NIL) (-1028 2497513 2501600 2501648 "QUAT" 2501653 NIL QUAT (NIL T) -8 NIL NIL NIL) (-1027 2494769 2496561 2496604 "QUAGG" 2496985 NIL QUAGG (NIL T) -9 NIL 2497160 NIL) (-1026 2494317 2494591 2494661 "QQUTAST" 2494721 T QQUTAST (NIL) -8 NIL NIL NIL) (-1025 2493228 2493830 2493995 "QFORM" 2494198 NIL QFORM (NIL NIL T) -8 NIL NIL NIL) (-1024 2492853 2492902 2493033 "QFCAT2" 2493179 NIL QFCAT2 (NIL T T T T) -7 NIL NIL NIL) (-1023 2482550 2488700 2488742 "QFCAT" 2489410 NIL QFCAT (NIL T) -9 NIL 2490411 NIL) (-1022 2477884 2479332 2480919 "QFCAT-" 2481015 NIL QFCAT- (NIL T T) -8 NIL NIL NIL) (-1021 2477315 2477449 2477581 "QEQUAT" 2477774 T QEQUAT (NIL) -8 NIL NIL NIL) (-1020 2470333 2471514 2472700 "QCMPACK" 2476248 NIL QCMPACK (NIL T T T T T) -7 NIL NIL NIL) (-1019 2469562 2469744 2469980 "QALGSET2" 2470151 NIL QALGSET2 (NIL NIL NIL) -7 NIL NIL NIL) (-1018 2467012 2467548 2467978 "QALGSET" 2469217 NIL QALGSET (NIL T T T T) -8 NIL NIL NIL) (-1017 2465679 2465921 2466240 "PWFFINTB" 2466785 NIL PWFFINTB (NIL T T T T) -7 NIL NIL NIL) (-1016 2463824 2464022 2464378 "PUSHVAR" 2465493 NIL PUSHVAR (NIL T T T T) -7 NIL NIL NIL) (-1015 2459551 2460767 2460810 "PTRANFN" 2462721 NIL PTRANFN (NIL T) -9 NIL NIL NIL) (-1014 2457888 2458233 2458557 "PTPACK" 2459262 NIL PTPACK (NIL T) -7 NIL NIL NIL) (-1013 2457511 2457574 2457685 "PTFUNC2" 2457825 NIL PTFUNC2 (NIL T T) -7 NIL NIL NIL) (-1012 2451427 2456300 2456343 "PTCAT" 2456643 NIL PTCAT (NIL T) -9 NIL 2456796 NIL) (-1011 2451076 2451117 2451243 "PSQFR" 2451386 NIL PSQFR (NIL T T T T) -7 NIL NIL NIL) (-1010 2449648 2449964 2450300 "PSEUDLIN" 2450774 NIL PSEUDLIN (NIL T) -7 NIL NIL NIL) (-1009 2436168 2438743 2441069 "PSETPK" 2447408 NIL PSETPK (NIL T T T T) -7 NIL NIL NIL) (-1008 2428876 2431904 2432002 "PSETCAT" 2435043 NIL PSETCAT (NIL T T T T) -9 NIL 2435857 NIL) (-1007 2426601 2427343 2428167 "PSETCAT-" 2428172 NIL PSETCAT- (NIL T T T T T) -8 NIL NIL NIL) (-1006 2425914 2426109 2426139 "PSCURVE" 2426411 T PSCURVE (NIL) -9 NIL 2426578 NIL) (-1005 2421637 2423404 2423471 "PSCAT" 2424323 NIL PSCAT (NIL T T T) -9 NIL 2424563 NIL) (-1004 2420631 2420913 2421316 "PSCAT-" 2421321 NIL PSCAT- (NIL T T T T) -8 NIL NIL NIL) (-1003 2418799 2419690 2419955 "PRTITION" 2420388 T PRTITION (NIL) -8 NIL NIL NIL) (-1002 2418210 2418516 2418610 "PRTDAST" 2418727 T PRTDAST (NIL) -8 NIL NIL NIL) (-1001 2407054 2409476 2411666 "PRS" 2416072 NIL PRS (NIL T T) -7 NIL NIL NIL) (-1000 2404669 2406371 2406413 "PRQAGG" 2406599 NIL PRQAGG (NIL T) -9 NIL 2406701 NIL) (-999 2403848 2404297 2404325 "PROPLOG" 2404464 T PROPLOG (NIL) -9 NIL 2404579 NIL) (-998 2403446 2403509 2403632 "PROPFUN2" 2403771 NIL PROPFUN2 (NIL T T) -8 NIL NIL NIL) (-997 2402743 2402882 2403054 "PROPFUN1" 2403307 NIL PROPFUN1 (NIL T) -8 NIL NIL NIL) (-996 2400724 2401490 2401787 "PROPFRML" 2402479 NIL PROPFRML (NIL T) -8 NIL NIL NIL) (-995 2400169 2400300 2400428 "PROPERTY" 2400616 T PROPERTY (NIL) -8 NIL NIL NIL) (-994 2393982 2398335 2399155 "PRODUCT" 2399395 NIL PRODUCT (NIL T T) -8 NIL NIL NIL) (-993 2393772 2393810 2393869 "PRINT" 2393943 T PRINT (NIL) -7 NIL NIL NIL) (-992 2393088 2393229 2393381 "PRIMES" 2393652 NIL PRIMES (NIL T) -7 NIL NIL NIL) (-991 2391135 2391554 2392020 "PRIMELT" 2392667 NIL PRIMELT (NIL T) -7 NIL NIL NIL) (-990 2390852 2390913 2390941 "PRIMCAT" 2391065 T PRIMCAT (NIL) -9 NIL NIL NIL) (-989 2389841 2390037 2390265 "PRIMARR2" 2390670 NIL PRIMARR2 (NIL T T) -7 NIL NIL NIL) (-988 2385563 2389779 2389824 "PRIMARR" 2389829 NIL PRIMARR (NIL T) -8 NIL NIL NIL) (-987 2385200 2385262 2385373 "PREASSOC" 2385501 NIL PREASSOC (NIL T T) -7 NIL NIL NIL) (-986 2382165 2384658 2384892 "PR" 2385011 NIL PR (NIL T T) -8 NIL NIL NIL) (-985 2381616 2381773 2381801 "PPCURVE" 2382006 T PPCURVE (NIL) -9 NIL 2382142 NIL) (-984 2381163 2381411 2381494 "PORTNUM" 2381553 T PORTNUM (NIL) -8 NIL NIL NIL) (-983 2378500 2378921 2379513 "POLYROOT" 2380744 NIL POLYROOT (NIL T T T T T) -7 NIL NIL NIL) (-982 2377877 2377941 2378175 "POLYLIFT" 2378436 NIL POLYLIFT (NIL T T T T T) -7 NIL NIL NIL) (-981 2374098 2374601 2375230 "POLYCATQ" 2377422 NIL POLYCATQ (NIL T T T T T) -7 NIL NIL NIL) (-980 2359746 2365845 2365910 "POLYCAT" 2369424 NIL POLYCAT (NIL T T T) -9 NIL 2371302 NIL) (-979 2352886 2355071 2357448 "POLYCAT-" 2357453 NIL POLYCAT- (NIL T T T T) -8 NIL NIL NIL) (-978 2352467 2352541 2352661 "POLY2UP" 2352812 NIL POLY2UP (NIL NIL T) -7 NIL NIL NIL) (-977 2352093 2352156 2352265 "POLY2" 2352404 NIL POLY2 (NIL T T) -7 NIL NIL NIL) (-976 2345308 2351697 2351857 "POLY" 2351966 NIL POLY (NIL T) -8 NIL NIL NIL) (-975 2343969 2344232 2344508 "POLUTIL" 2345082 NIL POLUTIL (NIL T T) -7 NIL NIL NIL) (-974 2342288 2342601 2342932 "POLTOPOL" 2343691 NIL POLTOPOL (NIL NIL T) -7 NIL NIL NIL) (-973 2337284 2342222 2342269 "POINT" 2342274 NIL POINT (NIL T) -8 NIL NIL NIL) (-972 2335417 2335828 2336203 "PNTHEORY" 2336929 T PNTHEORY (NIL) -7 NIL NIL NIL) (-971 2333863 2334172 2334571 "PMTOOLS" 2335115 NIL PMTOOLS (NIL T T T) -7 NIL NIL NIL) (-970 2333450 2333534 2333651 "PMSYM" 2333779 NIL PMSYM (NIL T) -7 NIL NIL NIL) (-969 2332952 2333027 2333202 "PMQFCAT" 2333375 NIL PMQFCAT (NIL T T T) -7 NIL NIL NIL) (-968 2332333 2332431 2332593 "PMPREDFS" 2332853 NIL PMPREDFS (NIL T T T) -7 NIL NIL NIL) (-967 2331676 2331798 2331954 "PMPRED" 2332210 NIL PMPRED (NIL T) -7 NIL NIL NIL) (-966 2330330 2330548 2330926 "PMPLCAT" 2331438 NIL PMPLCAT (NIL T T T T T) -7 NIL NIL NIL) (-965 2329856 2329941 2330093 "PMLSAGG" 2330245 NIL PMLSAGG (NIL T T T) -7 NIL NIL NIL) (-964 2329323 2329405 2329587 "PMKERNEL" 2329774 NIL PMKERNEL (NIL T T) -7 NIL NIL NIL) (-963 2328934 2329015 2329128 "PMINS" 2329242 NIL PMINS (NIL T) -7 NIL NIL NIL) (-962 2328370 2328445 2328654 "PMFS" 2328859 NIL PMFS (NIL T T T) -7 NIL NIL NIL) (-961 2327586 2327716 2327921 "PMDOWN" 2328247 NIL PMDOWN (NIL T T T) -7 NIL NIL NIL) (-960 2326835 2326969 2327132 "PMASSFS" 2327473 NIL PMASSFS (NIL T T) -7 NIL NIL NIL) (-959 2325978 2326160 2326341 "PMASS" 2326674 T PMASS (NIL) -7 NIL NIL NIL) (-958 2325627 2325701 2325795 "PLOTTOOL" 2325904 T PLOTTOOL (NIL) -7 NIL NIL NIL) (-957 2321279 2322473 2323395 "PLOT3D" 2324725 T PLOT3D (NIL) -8 NIL NIL NIL) (-956 2320167 2320368 2320603 "PLOT1" 2321083 NIL PLOT1 (NIL T) -7 NIL NIL NIL) (-955 2314588 2315978 2317126 "PLOT" 2319039 T PLOT (NIL) -8 NIL NIL NIL) (-954 2289763 2294654 2299505 "PLEQN" 2309854 NIL PLEQN (NIL T T T T) -7 NIL NIL NIL) (-953 2289450 2289503 2289606 "PINTERPA" 2289710 NIL PINTERPA (NIL T T) -7 NIL NIL NIL) (-952 2288756 2288890 2289070 "PINTERP" 2289315 NIL PINTERP (NIL NIL T) -7 NIL NIL NIL) (-951 2286840 2288006 2288034 "PID" 2288231 T PID (NIL) -9 NIL 2288358 NIL) (-950 2286585 2286628 2286703 "PICOERCE" 2286797 NIL PICOERCE (NIL T) -7 NIL NIL NIL) (-949 2285681 2286349 2286436 "PI" 2286476 T PI (NIL) -8 NIL NIL 2286543) (-948 2284989 2285140 2285316 "PGROEB" 2285537 NIL PGROEB (NIL T) -7 NIL NIL NIL) (-947 2280428 2281387 2282293 "PGE" 2284103 T PGE (NIL) -7 NIL NIL NIL) (-946 2278509 2278798 2279164 "PGCD" 2280145 NIL PGCD (NIL T T T T) -7 NIL NIL NIL) (-945 2277835 2277950 2278111 "PFRPAC" 2278393 NIL PFRPAC (NIL T) -7 NIL NIL NIL) (-944 2274093 2276383 2276736 "PFR" 2277514 NIL PFR (NIL T) -8 NIL NIL NIL) (-943 2272446 2272726 2273051 "PFOTOOLS" 2273840 NIL PFOTOOLS (NIL T T) -7 NIL NIL NIL) (-942 2270961 2271218 2271569 "PFOQ" 2272203 NIL PFOQ (NIL T T T) -7 NIL NIL NIL) (-941 2269444 2269674 2270030 "PFO" 2270745 NIL PFO (NIL T T T T T) -7 NIL NIL NIL) (-940 2266528 2268034 2268062 "PFECAT" 2268655 T PFECAT (NIL) -9 NIL 2269032 NIL) (-939 2265976 2266141 2266348 "PFECAT-" 2266353 NIL PFECAT- (NIL T) -8 NIL NIL NIL) (-938 2264549 2264831 2265132 "PFBRU" 2265725 NIL PFBRU (NIL T T) -7 NIL NIL NIL) (-937 2262378 2262767 2263199 "PFBR" 2264200 NIL PFBR (NIL T T T T) -7 NIL NIL NIL) (-936 2258324 2262267 2262336 "PF" 2262341 NIL PF (NIL NIL) -8 NIL NIL NIL) (-935 2253378 2254531 2255401 "PERMGRP" 2257487 NIL PERMGRP (NIL T) -8 NIL NIL NIL) (-934 2251290 2252402 2252443 "PERMCAT" 2252843 NIL PERMCAT (NIL T) -9 NIL 2253141 NIL) (-933 2250937 2250984 2251108 "PERMAN" 2251243 NIL PERMAN (NIL NIL T) -7 NIL NIL NIL) (-932 2246739 2248446 2249094 "PERM" 2250322 NIL PERM (NIL T) -8 NIL NIL NIL) (-931 2243980 2246404 2246526 "PENDTREE" 2246650 NIL PENDTREE (NIL T) -8 NIL NIL NIL) (-930 2242861 2243124 2243165 "PDSPC" 2243698 NIL PDSPC (NIL T) -9 NIL 2243943 NIL) (-929 2241916 2242182 2242544 "PDSPC-" 2242549 NIL PDSPC- (NIL T T) -8 NIL NIL NIL) (-928 2240630 2241566 2241607 "PDRING" 2241612 NIL PDRING (NIL T) -9 NIL 2241640 NIL) (-927 2239373 2240135 2240189 "PDMOD" 2240194 NIL PDMOD (NIL T T) -9 NIL 2240298 NIL) (-926 2236540 2237366 2238034 "PDEPROB" 2238725 T PDEPROB (NIL) -8 NIL NIL NIL) (-925 2234049 2234589 2235144 "PDEPACK" 2236005 T PDEPACK (NIL) -7 NIL NIL NIL) (-924 2232937 2233151 2233402 "PDECOMP" 2233848 NIL PDECOMP (NIL T T) -7 NIL NIL NIL) (-923 2230454 2231345 2231373 "PDECAT" 2232160 T PDECAT (NIL) -9 NIL 2232873 NIL) (-922 2230071 2230138 2230192 "PDDOM" 2230357 NIL PDDOM (NIL T T) -9 NIL 2230437 NIL) (-921 2229884 2229920 2230027 "PDDOM-" 2230032 NIL PDDOM- (NIL T T T) -8 NIL NIL NIL) (-920 2229629 2229668 2229758 "PCOMP" 2229845 NIL PCOMP (NIL T T) -7 NIL NIL NIL) (-919 2227669 2228430 2228727 "PBWLB" 2229358 NIL PBWLB (NIL T) -8 NIL NIL NIL) (-918 2227295 2227358 2227467 "PATTERN2" 2227606 NIL PATTERN2 (NIL T T) -7 NIL NIL NIL) (-917 2225004 2225440 2225897 "PATTERN1" 2226884 NIL PATTERN1 (NIL T T) -7 NIL NIL NIL) (-916 2217183 2219077 2220415 "PATTERN" 2223687 NIL PATTERN (NIL T) -8 NIL NIL NIL) (-915 2216741 2216814 2216946 "PATRES2" 2217110 NIL PATRES2 (NIL T T T) -7 NIL NIL NIL) (-914 2214007 2214690 2215171 "PATRES" 2216306 NIL PATRES (NIL T T) -8 NIL NIL NIL) (-913 2211860 2212295 2212702 "PATMATCH" 2213674 NIL PATMATCH (NIL T T T) -7 NIL NIL NIL) (-912 2211314 2211565 2211606 "PATMAB" 2211713 NIL PATMAB (NIL T) -9 NIL 2211796 NIL) (-911 2209760 2210168 2210426 "PATLRES" 2211119 NIL PATLRES (NIL T T T) -8 NIL NIL NIL) (-910 2209298 2209429 2209470 "PATAB" 2209475 NIL PATAB (NIL T) -9 NIL 2209647 NIL) (-909 2207438 2207875 2208298 "PARTPERM" 2208895 T PARTPERM (NIL) -7 NIL NIL NIL) (-908 2207047 2207122 2207224 "PARSURF" 2207369 NIL PARSURF (NIL T) -8 NIL NIL NIL) (-907 2206673 2206736 2206845 "PARSU2" 2206984 NIL PARSU2 (NIL T T) -7 NIL NIL NIL) (-906 2206431 2206477 2206544 "PARSER" 2206626 T PARSER (NIL) -7 NIL NIL NIL) (-905 2206040 2206115 2206217 "PARSCURV" 2206362 NIL PARSCURV (NIL T) -8 NIL NIL NIL) (-904 2205666 2205729 2205838 "PARSC2" 2205977 NIL PARSC2 (NIL T T) -7 NIL NIL NIL) (-903 2205293 2205363 2205460 "PARPCURV" 2205602 NIL PARPCURV (NIL T) -8 NIL NIL NIL) (-902 2204919 2204982 2205091 "PARPC2" 2205230 NIL PARPC2 (NIL T T) -7 NIL NIL NIL) (-901 2203908 2204292 2204474 "PARAMAST" 2204757 T PARAMAST (NIL) -8 NIL NIL NIL) (-900 2203416 2203514 2203633 "PAN2EXPR" 2203809 T PAN2EXPR (NIL) -7 NIL NIL NIL) (-899 2202109 2202537 2202765 "PALETTE" 2203208 T PALETTE (NIL) -8 NIL NIL NIL) (-898 2200454 2201114 2201474 "PAIR" 2201795 NIL PAIR (NIL T T) -8 NIL NIL NIL) (-897 2193387 2199711 2199906 "PADICRC" 2200308 NIL PADICRC (NIL NIL T) -8 NIL NIL NIL) (-896 2185644 2192731 2192916 "PADICRAT" 2193234 NIL PADICRAT (NIL NIL) -8 NIL NIL NIL) (-895 2182441 2184304 2184344 "PADICCT" 2184925 NIL PADICCT (NIL NIL) -9 NIL 2185207 NIL) (-894 2180457 2182378 2182423 "PADIC" 2182428 NIL PADIC (NIL NIL) -8 NIL NIL NIL) (-893 2179402 2179614 2179882 "PADEPAC" 2180244 NIL PADEPAC (NIL T NIL NIL) -7 NIL NIL NIL) (-892 2178602 2178747 2178953 "PADE" 2179264 NIL PADE (NIL T T T) -7 NIL NIL NIL) (-891 2176835 2177810 2178090 "OWP" 2178406 NIL OWP (NIL T NIL NIL NIL) -8 NIL NIL NIL) (-890 2176280 2176541 2176638 "OVERSET" 2176758 T OVERSET (NIL) -8 NIL NIL NIL) (-889 2175200 2175885 2176057 "OVAR" 2176148 NIL OVAR (NIL NIL) -8 NIL NIL NIL) (-888 2163436 2166309 2168509 "OUTFORM" 2173020 T OUTFORM (NIL) -8 NIL NIL NIL) (-887 2162718 2163033 2163160 "OUTBFILE" 2163329 T OUTBFILE (NIL) -8 NIL NIL NIL) (-886 2161995 2162190 2162218 "OUTBCON" 2162536 T OUTBCON (NIL) -9 NIL 2162702 NIL) (-885 2161578 2161708 2161865 "OUTBCON-" 2161870 NIL OUTBCON- (NIL T) -8 NIL NIL NIL) (-884 2160818 2160963 2161124 "OUT" 2161437 T OUT (NIL) -7 NIL NIL NIL) (-883 2160114 2160547 2160636 "OSI" 2160749 T OSI (NIL) -8 NIL NIL NIL) (-882 2159533 2159955 2159983 "OSGROUP" 2159988 T OSGROUP (NIL) -9 NIL 2160010 NIL) (-881 2158244 2158505 2158790 "ORTHPOL" 2159280 NIL ORTHPOL (NIL T) -7 NIL NIL NIL) (-880 2155495 2158079 2158200 "OREUP" 2158205 NIL OREUP (NIL NIL T NIL NIL) -8 NIL NIL NIL) (-879 2152598 2155186 2155313 "ORESUP" 2155437 NIL ORESUP (NIL T NIL NIL) -8 NIL NIL NIL) (-878 2150098 2150626 2151187 "OREPCTO" 2152087 NIL OREPCTO (NIL T T) -7 NIL NIL NIL) (-877 2143476 2145971 2146012 "OREPCAT" 2148360 NIL OREPCAT (NIL T) -9 NIL 2149464 NIL) (-876 2140449 2141405 2142463 "OREPCAT-" 2142468 NIL OREPCAT- (NIL T T) -8 NIL NIL NIL) (-875 2139641 2139919 2139947 "ORDTYPE" 2140256 T ORDTYPE (NIL) -9 NIL 2140419 NIL) (-874 2138942 2139158 2139413 "ORDTYPE-" 2139418 NIL ORDTYPE- (NIL T) -8 NIL NIL NIL) (-873 2138298 2138681 2138839 "ORDSTRCT" 2138844 NIL ORDSTRCT (NIL T NIL) -8 NIL NIL NIL) (-872 2137796 2138166 2138194 "ORDSET" 2138199 T ORDSET (NIL) -9 NIL 2138221 NIL) (-871 2136447 2137418 2137446 "ORDRING" 2137451 T ORDRING (NIL) -9 NIL 2137480 NIL) (-870 2135698 2136263 2136291 "ORDMON" 2136296 T ORDMON (NIL) -9 NIL 2136317 NIL) (-869 2134842 2135007 2135202 "ORDFUNS" 2135547 NIL ORDFUNS (NIL NIL T) -7 NIL NIL NIL) (-868 2134057 2134572 2134600 "ORDFIN" 2134665 T ORDFIN (NIL) -9 NIL 2134739 NIL) (-867 2133311 2133450 2133636 "ORDCOMP2" 2133917 NIL ORDCOMP2 (NIL T T) -7 NIL NIL NIL) (-866 2129658 2131897 2132306 "ORDCOMP" 2132935 NIL ORDCOMP (NIL T) -8 NIL NIL NIL) (-865 2126179 2127149 2127963 "OPTPROB" 2128864 T OPTPROB (NIL) -8 NIL NIL NIL) (-864 2122921 2123620 2124324 "OPTPACK" 2125495 T OPTPACK (NIL) -7 NIL NIL NIL) (-863 2120534 2121360 2121388 "OPTCAT" 2122207 T OPTCAT (NIL) -9 NIL 2122857 NIL) (-862 2119852 2120211 2120316 "OPSIG" 2120449 T OPSIG (NIL) -8 NIL NIL NIL) (-861 2119614 2119659 2119725 "OPQUERY" 2119806 T OPQUERY (NIL) -7 NIL NIL NIL) (-860 2118920 2119200 2119241 "OPERCAT" 2119453 NIL OPERCAT (NIL T) -9 NIL 2119550 NIL) (-859 2118663 2118731 2118848 "OPERCAT-" 2118853 NIL OPERCAT- (NIL T T) -8 NIL NIL NIL) (-858 2115579 2116974 2117478 "OP" 2118192 NIL OP (NIL T) -8 NIL NIL NIL) (-857 2114872 2114999 2115173 "ONECOMP2" 2115451 NIL ONECOMP2 (NIL T T) -7 NIL NIL NIL) (-856 2111485 2113669 2114038 "ONECOMP" 2114536 NIL ONECOMP (NIL T) -8 NIL NIL NIL) (-855 2110886 2111010 2111140 "OMSERVER" 2111375 T OMSERVER (NIL) -7 NIL NIL NIL) (-854 2107398 2110324 2110364 "OMSAGG" 2110425 NIL OMSAGG (NIL T) -9 NIL 2110490 NIL) (-853 2105973 2106284 2106566 "OMPKG" 2107136 T OMPKG (NIL) -7 NIL NIL NIL) (-852 2104320 2105522 2105691 "OMLO" 2105854 NIL OMLO (NIL T T) -8 NIL NIL NIL) (-851 2103256 2103427 2103647 "OMEXPR" 2104146 NIL OMEXPR (NIL T) -7 NIL NIL NIL) (-850 2102341 2102677 2102837 "OMERRK" 2103116 T OMERRK (NIL) -8 NIL NIL NIL) (-849 2101578 2101887 2102023 "OMERR" 2102225 T OMERR (NIL) -8 NIL NIL NIL) (-848 2100969 2101255 2101363 "OMENC" 2101490 T OMENC (NIL) -8 NIL NIL NIL) (-847 2094606 2096049 2097220 "OMDEV" 2099818 T OMDEV (NIL) -8 NIL NIL NIL) (-846 2093639 2093846 2094040 "OMCONN" 2094432 T OMCONN (NIL) -8 NIL NIL NIL) (-845 2093045 2093172 2093200 "OM" 2093499 T OM (NIL) -9 NIL NIL NIL) (-844 2091323 2092515 2092543 "OINTDOM" 2092548 T OINTDOM (NIL) -9 NIL 2092569 NIL) (-843 2088398 2090011 2090348 "OFMONOID" 2091018 NIL OFMONOID (NIL T) -8 NIL NIL NIL) (-842 2087632 2088335 2088380 "ODVAR" 2088385 NIL ODVAR (NIL T) -8 NIL NIL NIL) (-841 2084776 2087377 2087532 "ODR" 2087537 NIL ODR (NIL T T NIL) -8 NIL NIL NIL) (-840 2076188 2084552 2084678 "ODPOL" 2084683 NIL ODPOL (NIL T) -8 NIL NIL NIL) (-839 2069482 2076060 2076165 "ODP" 2076170 NIL ODP (NIL NIL T NIL) -8 NIL NIL NIL) (-838 2068224 2068463 2068738 "ODETOOLS" 2069256 NIL ODETOOLS (NIL T T) -7 NIL NIL NIL) (-837 2065167 2065849 2066565 "ODESYS" 2067557 NIL ODESYS (NIL T T) -7 NIL NIL NIL) (-836 2059997 2060957 2061982 "ODERTRIC" 2064242 NIL ODERTRIC (NIL T T) -7 NIL NIL NIL) (-835 2059417 2059505 2059699 "ODERED" 2059909 NIL ODERED (NIL T T T T T) -7 NIL NIL NIL) (-834 2056269 2056853 2057530 "ODERAT" 2058840 NIL ODERAT (NIL T T) -7 NIL NIL NIL) (-833 2053185 2053693 2054290 "ODEPRRIC" 2055798 NIL ODEPRRIC (NIL T T T T) -7 NIL NIL NIL) (-832 2051080 2051724 2052210 "ODEPROB" 2052719 T ODEPROB (NIL) -8 NIL NIL NIL) (-831 2047546 2048085 2048732 "ODEPRIM" 2050559 NIL ODEPRIM (NIL T T T T) -7 NIL NIL NIL) (-830 2046789 2046897 2047157 "ODEPAL" 2047438 NIL ODEPAL (NIL T T T T) -7 NIL NIL NIL) (-829 2042891 2043742 2044606 "ODEPACK" 2045945 T ODEPACK (NIL) -7 NIL NIL NIL) (-828 2041934 2042059 2042281 "ODEINT" 2042780 NIL ODEINT (NIL T T) -7 NIL NIL NIL) (-827 2035999 2037460 2038907 "ODEIFTBL" 2040507 T ODEIFTBL (NIL) -8 NIL NIL NIL) (-826 2031349 2032183 2033135 "ODEEF" 2035158 NIL ODEEF (NIL T T) -7 NIL NIL NIL) (-825 2030692 2030787 2031010 "ODECONST" 2031254 NIL ODECONST (NIL T T T) -7 NIL NIL NIL) (-824 2028755 2029464 2029492 "ODECAT" 2030097 T ODECAT (NIL) -9 NIL 2030628 NIL) (-823 2028387 2028436 2028563 "OCTCT2" 2028706 NIL OCTCT2 (NIL T T T T) -7 NIL NIL NIL) (-822 2024887 2028092 2028214 "OCT" 2028297 NIL OCT (NIL T) -8 NIL NIL NIL) (-821 2024080 2024680 2024708 "OCAMON" 2024713 T OCAMON (NIL) -9 NIL 2024734 NIL) (-820 2018351 2021123 2021163 "OC" 2022260 NIL OC (NIL T) -9 NIL 2023118 NIL) (-819 2015386 2016326 2017316 "OC-" 2017410 NIL OC- (NIL T T) -8 NIL NIL NIL) (-818 2014806 2015231 2015259 "OASGP" 2015264 T OASGP (NIL) -9 NIL 2015284 NIL) (-817 2013902 2014529 2014557 "OAMONS" 2014597 T OAMONS (NIL) -9 NIL 2014640 NIL) (-816 2013078 2013637 2013665 "OAMON" 2013723 T OAMON (NIL) -9 NIL 2013775 NIL) (-815 2012936 2012969 2013037 "OAMON-" 2013042 NIL OAMON- (NIL T) -8 NIL NIL NIL) (-814 2011717 2012470 2012498 "OAGROUP" 2012645 T OAGROUP (NIL) -9 NIL 2012738 NIL) (-813 2011420 2011508 2011626 "OAGROUP-" 2011631 NIL OAGROUP- (NIL T) -8 NIL NIL NIL) (-812 2011102 2011158 2011247 "NUMTUBE" 2011364 NIL NUMTUBE (NIL T) -7 NIL NIL NIL) (-811 2004621 2006193 2007729 "NUMQUAD" 2009586 T NUMQUAD (NIL) -7 NIL NIL NIL) (-810 2000301 2001335 2002370 "NUMODE" 2003606 T NUMODE (NIL) -7 NIL NIL NIL) (-809 1997582 1998522 1998550 "NUMINT" 1999473 T NUMINT (NIL) -9 NIL 2000237 NIL) (-808 1996494 1996727 1996945 "NUMFMT" 1997384 T NUMFMT (NIL) -7 NIL NIL NIL) (-807 1982677 1985798 1988330 "NUMERIC" 1994001 NIL NUMERIC (NIL T) -7 NIL NIL NIL) (-806 1976381 1982125 1982220 "NTSCAT" 1982225 NIL NTSCAT (NIL T T T T) -9 NIL 1982264 NIL) (-805 1975561 1975740 1975933 "NTPOLFN" 1976220 NIL NTPOLFN (NIL T) -7 NIL NIL NIL) (-804 1975187 1975250 1975359 "NSUP2" 1975498 NIL NSUP2 (NIL T T) -7 NIL NIL NIL) (-803 1961969 1972012 1972824 "NSUP" 1974408 NIL NSUP (NIL T) -8 NIL NIL NIL) (-802 1950812 1961743 1961876 "NSMP" 1961881 NIL NSMP (NIL T T) -8 NIL NIL NIL) (-801 1949220 1949545 1949902 "NREP" 1950500 NIL NREP (NIL T) -7 NIL NIL NIL) (-800 1947799 1948063 1948421 "NPCOEF" 1948963 NIL NPCOEF (NIL T T T T T) -7 NIL NIL NIL) (-799 1946847 1946980 1947196 "NORMRETR" 1947680 NIL NORMRETR (NIL T T T T NIL) -7 NIL NIL NIL) (-798 1944858 1945178 1945587 "NORMPK" 1946555 NIL NORMPK (NIL T T T T T) -7 NIL NIL NIL) (-797 1944537 1944571 1944695 "NORMMA" 1944824 NIL NORMMA (NIL T T T T) -7 NIL NIL NIL) (-796 1944320 1944355 1944424 "NONE1" 1944501 NIL NONE1 (NIL T) -7 NIL NIL NIL) (-795 1944084 1944277 1944306 "NONE" 1944311 T NONE (NIL) -8 NIL NIL NIL) (-794 1943575 1943643 1943822 "NODE1" 1944016 NIL NODE1 (NIL T T) -7 NIL NIL NIL) (-793 1941636 1942698 1942953 "NNI" 1943300 T NNI (NIL) -8 NIL NIL 1943535) (-792 1940032 1940369 1940733 "NLINSOL" 1941304 NIL NLINSOL (NIL T) -7 NIL NIL NIL) (-791 1936213 1937268 1938167 "NIPROB" 1939153 T NIPROB (NIL) -8 NIL NIL NIL) (-790 1934952 1935204 1935506 "NFINTBAS" 1935975 NIL NFINTBAS (NIL T T) -7 NIL NIL NIL) (-789 1934036 1934602 1934643 "NETCLT" 1934815 NIL NETCLT (NIL T) -9 NIL 1934897 NIL) (-788 1932708 1932975 1933256 "NCODIV" 1933804 NIL NCODIV (NIL T T) -7 NIL NIL NIL) (-787 1932464 1932507 1932582 "NCNTFRAC" 1932665 NIL NCNTFRAC (NIL T) -7 NIL NIL NIL) (-786 1930620 1931008 1931428 "NCEP" 1932089 NIL NCEP (NIL T) -7 NIL NIL NIL) (-785 1929283 1930230 1930258 "NASRING" 1930368 T NASRING (NIL) -9 NIL 1930448 NIL) (-784 1929066 1929122 1929216 "NASRING-" 1929221 NIL NASRING- (NIL T) -8 NIL NIL NIL) (-783 1928033 1928684 1928712 "NARNG" 1928829 T NARNG (NIL) -9 NIL 1928920 NIL) (-782 1927707 1927792 1927926 "NARNG-" 1927931 NIL NARNG- (NIL T) -8 NIL NIL NIL) (-781 1926544 1926793 1927028 "NAGSP" 1927492 T NAGSP (NIL) -7 NIL NIL NIL) (-780 1917588 1919500 1921173 "NAGS" 1924891 T NAGS (NIL) -7 NIL NIL NIL) (-779 1916112 1916444 1916775 "NAGF07" 1917277 T NAGF07 (NIL) -7 NIL NIL NIL) (-778 1910584 1911941 1913248 "NAGF04" 1914825 T NAGF04 (NIL) -7 NIL NIL NIL) (-777 1903456 1905166 1906799 "NAGF02" 1908971 T NAGF02 (NIL) -7 NIL NIL NIL) (-776 1898620 1899780 1900897 "NAGF01" 1902359 T NAGF01 (NIL) -7 NIL NIL NIL) (-775 1892200 1893814 1895399 "NAGE04" 1897055 T NAGE04 (NIL) -7 NIL NIL NIL) (-774 1883261 1885490 1887620 "NAGE02" 1890090 T NAGE02 (NIL) -7 NIL NIL NIL) (-773 1879154 1880161 1881125 "NAGE01" 1882317 T NAGE01 (NIL) -7 NIL NIL NIL) (-772 1876931 1877483 1878041 "NAGD03" 1878616 T NAGD03 (NIL) -7 NIL NIL NIL) (-771 1868627 1870609 1872563 "NAGD02" 1874997 T NAGD02 (NIL) -7 NIL NIL NIL) (-770 1862366 1863863 1865303 "NAGD01" 1867207 T NAGD01 (NIL) -7 NIL NIL NIL) (-769 1858503 1859397 1860234 "NAGC06" 1861549 T NAGC06 (NIL) -7 NIL NIL NIL) (-768 1856950 1857300 1857656 "NAGC05" 1858167 T NAGC05 (NIL) -7 NIL NIL NIL) (-767 1856314 1856445 1856589 "NAGC02" 1856826 T NAGC02 (NIL) -7 NIL NIL NIL) (-766 1855115 1855842 1855882 "NAALG" 1855961 NIL NAALG (NIL T) -9 NIL 1856022 NIL) (-765 1854944 1854979 1855069 "NAALG-" 1855074 NIL NAALG- (NIL T T) -8 NIL NIL NIL) (-764 1848816 1850002 1851189 "MULTSQFR" 1853840 NIL MULTSQFR (NIL T T T T) -7 NIL NIL NIL) (-763 1848123 1848210 1848394 "MULTFACT" 1848728 NIL MULTFACT (NIL T T T T) -7 NIL NIL NIL) (-762 1840268 1844706 1844759 "MTSCAT" 1845829 NIL MTSCAT (NIL T T) -9 NIL 1846345 NIL) (-761 1839974 1840034 1840126 "MTHING" 1840208 NIL MTHING (NIL T) -7 NIL NIL NIL) (-760 1839760 1839799 1839859 "MSYSCMD" 1839934 T MSYSCMD (NIL) -7 NIL NIL NIL) (-759 1836505 1839321 1839362 "MSETAGG" 1839367 NIL MSETAGG (NIL T) -9 NIL 1839401 NIL) (-758 1832219 1835260 1835580 "MSET" 1836218 NIL MSET (NIL T) -8 NIL NIL NIL) (-757 1827821 1829598 1830343 "MRING" 1831519 NIL MRING (NIL T T) -8 NIL NIL NIL) (-756 1827381 1827454 1827585 "MRF2" 1827748 NIL MRF2 (NIL T T T) -7 NIL NIL NIL) (-755 1826993 1827034 1827178 "MRATFAC" 1827340 NIL MRATFAC (NIL T T T T) -7 NIL NIL NIL) (-754 1824563 1824900 1825331 "MPRFF" 1826698 NIL MPRFF (NIL T T T T) -7 NIL NIL NIL) (-753 1817897 1824417 1824514 "MPOLY" 1824519 NIL MPOLY (NIL NIL T) -8 NIL NIL NIL) (-752 1817381 1817422 1817630 "MPCPF" 1817856 NIL MPCPF (NIL T T T T) -7 NIL NIL NIL) (-751 1816889 1816938 1817122 "MPC3" 1817332 NIL MPC3 (NIL T T T T T T T) -7 NIL NIL NIL) (-750 1816072 1816165 1816386 "MPC2" 1816804 NIL MPC2 (NIL T T T T T T T) -7 NIL NIL NIL) (-749 1814349 1814710 1815100 "MONOTOOL" 1815732 NIL MONOTOOL (NIL T T) -7 NIL NIL NIL) (-748 1813494 1813877 1813905 "MONOID" 1814124 T MONOID (NIL) -9 NIL 1814271 NIL) (-747 1813010 1813159 1813340 "MONOID-" 1813345 NIL MONOID- (NIL T) -8 NIL NIL NIL) (-746 1801983 1808830 1808889 "MONOGEN" 1809563 NIL MONOGEN (NIL T T) -9 NIL 1810019 NIL) (-745 1799033 1799936 1800936 "MONOGEN-" 1801055 NIL MONOGEN- (NIL T T T) -8 NIL NIL NIL) (-744 1797750 1798298 1798326 "MONADWU" 1798718 T MONADWU (NIL) -9 NIL 1798956 NIL) (-743 1797080 1797281 1797529 "MONADWU-" 1797534 NIL MONADWU- (NIL T) -8 NIL NIL NIL) (-742 1796365 1796669 1796697 "MONAD" 1796904 T MONAD (NIL) -9 NIL 1797016 NIL) (-741 1796032 1796128 1796260 "MONAD-" 1796265 NIL MONAD- (NIL T) -8 NIL NIL NIL) (-740 1794171 1794945 1795224 "MOEBIUS" 1795785 NIL MOEBIUS (NIL T) -8 NIL NIL NIL) (-739 1793339 1793839 1793879 "MODULE" 1793884 NIL MODULE (NIL T) -9 NIL 1793923 NIL) (-738 1792877 1793003 1793193 "MODULE-" 1793198 NIL MODULE- (NIL T T) -8 NIL NIL NIL) (-737 1790407 1791241 1791568 "MODRING" 1792701 NIL MODRING (NIL T T NIL NIL NIL) -8 NIL NIL NIL) (-736 1787136 1788512 1789033 "MODOP" 1789936 NIL MODOP (NIL T T) -8 NIL NIL NIL) (-735 1785622 1786203 1786480 "MODMONOM" 1786999 NIL MODMONOM (NIL T T NIL) -8 NIL NIL NIL) (-734 1774383 1783913 1784327 "MODMON" 1785259 NIL MODMON (NIL T T) -8 NIL NIL NIL) (-733 1771216 1773227 1773503 "MODFIELD" 1774258 NIL MODFIELD (NIL T T NIL NIL NIL) -8 NIL NIL NIL) (-732 1770127 1770497 1770687 "MMLFORM" 1771046 T MMLFORM (NIL) -8 NIL NIL NIL) (-731 1769647 1769696 1769875 "MMAP" 1770078 NIL MMAP (NIL T T T T T T) -7 NIL NIL NIL) (-730 1767540 1768479 1768520 "MLO" 1768943 NIL MLO (NIL T) -9 NIL 1769185 NIL) (-729 1764888 1765422 1766024 "MLIFT" 1767021 NIL MLIFT (NIL T T T T) -7 NIL NIL NIL) (-728 1764267 1764363 1764517 "MKUCFUNC" 1764799 NIL MKUCFUNC (NIL T T T) -7 NIL NIL NIL) (-727 1763860 1763936 1764059 "MKRECORD" 1764190 NIL MKRECORD (NIL T T) -7 NIL NIL NIL) (-726 1762883 1763069 1763297 "MKFUNC" 1763671 NIL MKFUNC (NIL T) -7 NIL NIL NIL) (-725 1762259 1762375 1762531 "MKFLCFN" 1762766 NIL MKFLCFN (NIL T) -7 NIL NIL NIL) (-724 1761524 1761638 1761823 "MKBCFUNC" 1762152 NIL MKBCFUNC (NIL T T T T) -7 NIL NIL NIL) (-723 1757521 1761078 1761214 "MINT" 1761408 T MINT (NIL) -8 NIL NIL NIL) (-722 1756303 1756576 1756853 "MHROWRED" 1757276 NIL MHROWRED (NIL T) -7 NIL NIL NIL) (-721 1751054 1754838 1755243 "MFLOAT" 1755918 T MFLOAT (NIL) -8 NIL NIL NIL) (-720 1750399 1750487 1750658 "MFINFACT" 1750966 NIL MFINFACT (NIL T T T T) -7 NIL NIL NIL) (-719 1746678 1747562 1748446 "MESH" 1749535 T MESH (NIL) -7 NIL NIL NIL) (-718 1745032 1745380 1745733 "MDDFACT" 1746365 NIL MDDFACT (NIL T) -7 NIL NIL NIL) (-717 1741568 1744163 1744204 "MDAGG" 1744459 NIL MDAGG (NIL T) -9 NIL 1744602 NIL) (-716 1729291 1740861 1741068 "MCMPLX" 1741381 T MCMPLX (NIL) -8 NIL NIL NIL) (-715 1728410 1728574 1728775 "MCDEN" 1729140 NIL MCDEN (NIL T T) -7 NIL NIL NIL) (-714 1726258 1726570 1726950 "MCALCFN" 1728140 NIL MCALCFN (NIL T T T T) -7 NIL NIL NIL) (-713 1725135 1725423 1725656 "MAYBE" 1726064 NIL MAYBE (NIL T) -8 NIL NIL NIL) (-712 1722693 1723270 1723832 "MATSTOR" 1724606 NIL MATSTOR (NIL T) -7 NIL NIL NIL) (-711 1718115 1722065 1722313 "MATRIX" 1722478 NIL MATRIX (NIL T) -8 NIL NIL NIL) (-710 1713815 1714588 1715324 "MATLIN" 1717472 NIL MATLIN (NIL T T T T) -7 NIL NIL NIL) (-709 1712391 1712562 1712895 "MATCAT2" 1713650 NIL MATCAT2 (NIL T T T T T T T T) -7 NIL NIL NIL) (-708 1701730 1705448 1705525 "MATCAT" 1710557 NIL MATCAT (NIL T T T) -9 NIL 1712029 NIL) (-707 1697683 1698993 1700406 "MATCAT-" 1700411 NIL MATCAT- (NIL T T T T) -8 NIL NIL NIL) (-706 1695759 1696119 1696503 "MAPPKG3" 1697358 NIL MAPPKG3 (NIL T T T) -7 NIL NIL NIL) (-705 1694716 1694913 1695135 "MAPPKG2" 1695583 NIL MAPPKG2 (NIL T T) -7 NIL NIL NIL) (-704 1693173 1693499 1693826 "MAPPKG1" 1694422 NIL MAPPKG1 (NIL T) -7 NIL NIL NIL) (-703 1692174 1692579 1692756 "MAPPAST" 1693016 T MAPPAST (NIL) -8 NIL NIL NIL) (-702 1691779 1691843 1691966 "MAPHACK3" 1692110 NIL MAPHACK3 (NIL T T T) -7 NIL NIL NIL) (-701 1691359 1691432 1691546 "MAPHACK2" 1691711 NIL MAPHACK2 (NIL T T) -7 NIL NIL NIL) (-700 1690785 1690900 1691042 "MAPHACK1" 1691250 NIL MAPHACK1 (NIL T) -7 NIL NIL NIL) (-699 1688708 1689485 1689789 "MAGMA" 1690513 NIL MAGMA (NIL T) -8 NIL NIL NIL) (-698 1688127 1688432 1688523 "MACROAST" 1688637 T MACROAST (NIL) -8 NIL NIL NIL) (-697 1684370 1686366 1686827 "M3D" 1687699 NIL M3D (NIL T) -8 NIL NIL NIL) (-696 1677842 1682681 1682722 "LZSTAGG" 1683504 NIL LZSTAGG (NIL T) -9 NIL 1683799 NIL) (-695 1673524 1674973 1676430 "LZSTAGG-" 1676435 NIL LZSTAGG- (NIL T T) -8 NIL NIL NIL) (-694 1670437 1671415 1671902 "LWORD" 1673069 NIL LWORD (NIL T) -8 NIL NIL NIL) (-693 1669959 1670241 1670316 "LSTAST" 1670382 T LSTAST (NIL) -8 NIL NIL NIL) (-692 1661887 1669730 1669864 "LSQM" 1669869 NIL LSQM (NIL NIL T) -8 NIL NIL NIL) (-691 1661105 1661250 1661478 "LSPP" 1661742 NIL LSPP (NIL T T T T) -7 NIL NIL NIL) (-690 1657842 1658558 1659288 "LSMP1" 1660407 NIL LSMP1 (NIL T) -7 NIL NIL NIL) (-689 1655624 1655955 1656411 "LSMP" 1657531 NIL LSMP (NIL T T T T) -7 NIL NIL NIL) (-688 1648752 1654714 1654755 "LSAGG" 1654817 NIL LSAGG (NIL T) -9 NIL 1654895 NIL) (-687 1645261 1646371 1647584 "LSAGG-" 1647589 NIL LSAGG- (NIL T T) -8 NIL NIL NIL) (-686 1642556 1644405 1644654 "LPOLY" 1645056 NIL LPOLY (NIL T T) -8 NIL NIL NIL) (-685 1642132 1642223 1642346 "LPEFRAC" 1642465 NIL LPEFRAC (NIL T) -7 NIL NIL NIL) (-684 1641815 1641894 1641922 "LOGIC" 1642033 T LOGIC (NIL) -9 NIL 1642115 NIL) (-683 1641671 1641700 1641771 "LOGIC-" 1641776 NIL LOGIC- (NIL T) -8 NIL NIL NIL) (-682 1640846 1641004 1641197 "LODOOPS" 1641527 NIL LODOOPS (NIL T T) -7 NIL NIL NIL) (-681 1639370 1639619 1639972 "LODOF" 1640593 NIL LODOF (NIL T T) -7 NIL NIL NIL) (-680 1635246 1638005 1638046 "LODOCAT" 1638484 NIL LODOCAT (NIL T) -9 NIL 1638695 NIL) (-679 1634961 1635037 1635164 "LODOCAT-" 1635169 NIL LODOCAT- (NIL T T) -8 NIL NIL NIL) (-678 1631947 1634802 1634920 "LODO2" 1634925 NIL LODO2 (NIL T T) -8 NIL NIL NIL) (-677 1629054 1631884 1631929 "LODO1" 1631934 NIL LODO1 (NIL T) -8 NIL NIL NIL) (-676 1626149 1628970 1629036 "LODO" 1629041 NIL LODO (NIL T NIL) -8 NIL NIL NIL) (-675 1625018 1625195 1625500 "LODEEF" 1625972 NIL LODEEF (NIL T T T) -7 NIL NIL NIL) (-674 1623004 1624112 1624365 "LO" 1624850 NIL LO (NIL T T T) -8 NIL NIL NIL) (-673 1617976 1621170 1621211 "LNAGG" 1622073 NIL LNAGG (NIL T) -9 NIL 1622508 NIL) (-672 1617069 1617337 1617679 "LNAGG-" 1617684 NIL LNAGG- (NIL T T) -8 NIL NIL NIL) (-671 1613049 1613994 1614633 "LMOPS" 1616484 NIL LMOPS (NIL T T NIL) -8 NIL NIL NIL) (-670 1612348 1612826 1612867 "LMODULE" 1612872 NIL LMODULE (NIL T) -9 NIL 1612898 NIL) (-669 1609303 1611993 1612116 "LMDICT" 1612258 NIL LMDICT (NIL T) -8 NIL NIL NIL) (-668 1608879 1609093 1609134 "LLINSET" 1609195 NIL LLINSET (NIL T) -9 NIL 1609239 NIL) (-667 1608524 1608787 1608847 "LITERAL" 1608852 NIL LITERAL (NIL T) -8 NIL NIL NIL) (-666 1608043 1608123 1608262 "LIST3" 1608444 NIL LIST3 (NIL T T T) -7 NIL NIL NIL) (-665 1606141 1606489 1606888 "LIST2MAP" 1607690 NIL LIST2MAP (NIL T T) -7 NIL NIL NIL) (-664 1605130 1605326 1605554 "LIST2" 1605959 NIL LIST2 (NIL T T) -7 NIL NIL NIL) (-663 1597584 1604064 1604368 "LIST" 1604859 NIL LIST (NIL T) -8 NIL NIL NIL) (-662 1597167 1597403 1597444 "LINSET" 1597449 NIL LINSET (NIL T) -9 NIL 1597483 NIL) (-661 1595981 1596675 1596842 "LINFORM" 1597052 NIL LINFORM (NIL T NIL) -8 NIL NIL NIL) (-660 1594280 1595008 1595049 "LINEXP" 1595539 NIL LINEXP (NIL T) -9 NIL 1595812 NIL) (-659 1592856 1593760 1593941 "LINELT" 1594151 NIL LINELT (NIL T NIL) -8 NIL NIL NIL) (-658 1591413 1591693 1592004 "LINDEP" 1592608 NIL LINDEP (NIL T T) -7 NIL NIL NIL) (-657 1590549 1591145 1591255 "LINBASIS" 1591343 NIL LINBASIS (NIL NIL) -8 NIL NIL NIL) (-656 1587286 1588035 1588812 "LIMITRF" 1589804 NIL LIMITRF (NIL T) -7 NIL NIL NIL) (-655 1585571 1585885 1586294 "LIMITPS" 1586981 NIL LIMITPS (NIL T T) -7 NIL NIL NIL) (-654 1584399 1584974 1585014 "LIECAT" 1585154 NIL LIECAT (NIL T) -9 NIL 1585305 NIL) (-653 1584234 1584267 1584355 "LIECAT-" 1584360 NIL LIECAT- (NIL T T) -8 NIL NIL NIL) (-652 1578254 1583745 1583973 "LIE" 1584055 NIL LIE (NIL T T) -8 NIL NIL NIL) (-651 1570439 1577794 1577950 "LIB" 1578118 T LIB (NIL) -8 NIL NIL NIL) (-650 1566008 1566957 1567892 "LGROBP" 1569556 NIL LGROBP (NIL NIL T) -7 NIL NIL NIL) (-649 1564632 1565540 1565568 "LFCAT" 1565775 T LFCAT (NIL) -9 NIL 1565914 NIL) (-648 1562570 1562904 1563254 "LF" 1564353 NIL LF (NIL T T) -7 NIL NIL NIL) (-647 1559430 1560102 1560790 "LEXTRIPK" 1561934 NIL LEXTRIPK (NIL T NIL) -7 NIL NIL NIL) (-646 1556018 1557000 1557503 "LEXP" 1559010 NIL LEXP (NIL T T NIL) -8 NIL NIL NIL) (-645 1555434 1555739 1555831 "LETAST" 1555946 T LETAST (NIL) -8 NIL NIL NIL) (-644 1553820 1554145 1554546 "LEADCDET" 1555116 NIL LEADCDET (NIL T T T T) -7 NIL NIL NIL) (-643 1552998 1553084 1553313 "LAZM3PK" 1553741 NIL LAZM3PK (NIL T T T T T T) -7 NIL NIL NIL) (-642 1547523 1551075 1551613 "LAUPOL" 1552510 NIL LAUPOL (NIL T T) -8 NIL NIL NIL) (-641 1547096 1547146 1547307 "LAPLACE" 1547473 NIL LAPLACE (NIL T T) -7 NIL NIL NIL) (-640 1545944 1546660 1546701 "LALG" 1546763 NIL LALG (NIL T) -9 NIL 1546822 NIL) (-639 1545640 1545717 1545853 "LALG-" 1545858 NIL LALG- (NIL T T) -8 NIL NIL NIL) (-638 1543377 1544741 1544992 "LA" 1545473 NIL LA (NIL T T T) -8 NIL NIL NIL) (-637 1543206 1543236 1543277 "KVTFROM" 1543339 NIL KVTFROM (NIL T) -9 NIL NIL NIL) (-636 1541963 1542573 1542758 "KTVLOGIC" 1543041 T KTVLOGIC (NIL) -8 NIL NIL NIL) (-635 1541792 1541822 1541863 "KRCFROM" 1541925 NIL KRCFROM (NIL T) -9 NIL NIL NIL) (-634 1540684 1540883 1541182 "KOVACIC" 1541592 NIL KOVACIC (NIL T T) -7 NIL NIL NIL) (-633 1540513 1540543 1540584 "KONVERT" 1540646 NIL KONVERT (NIL T) -9 NIL NIL NIL) (-632 1540342 1540372 1540413 "KOERCE" 1540475 NIL KOERCE (NIL T) -9 NIL NIL NIL) (-631 1539826 1539919 1540051 "KERNEL2" 1540256 NIL KERNEL2 (NIL T T) -7 NIL NIL NIL) (-630 1537513 1538419 1538796 "KERNEL" 1539482 NIL KERNEL (NIL T) -8 NIL NIL NIL) (-629 1530984 1535990 1536044 "KDAGG" 1536421 NIL KDAGG (NIL T T) -9 NIL 1536627 NIL) (-628 1530495 1530637 1530842 "KDAGG-" 1530847 NIL KDAGG- (NIL T T T) -8 NIL NIL NIL) (-627 1523195 1530156 1530311 "KAFILE" 1530373 NIL KAFILE (NIL T) -8 NIL NIL NIL) (-626 1522799 1523084 1523147 "JVMOP" 1523152 T JVMOP (NIL) -8 NIL NIL NIL) (-625 1521535 1522039 1522288 "JVMMDACC" 1522570 T JVMMDACC (NIL) -8 NIL NIL NIL) (-624 1520471 1520925 1521130 "JVMFDACC" 1521350 T JVMFDACC (NIL) -8 NIL NIL NIL) (-623 1519052 1519547 1519847 "JVMCSTTG" 1520191 T JVMCSTTG (NIL) -8 NIL NIL NIL) (-622 1518188 1518592 1518753 "JVMCFACC" 1518911 T JVMCFACC (NIL) -8 NIL NIL NIL) (-621 1517866 1518105 1518154 "JVMBCODE" 1518159 T JVMBCODE (NIL) -8 NIL NIL NIL) (-620 1511885 1517377 1517605 "JORDAN" 1517687 NIL JORDAN (NIL T T) -8 NIL NIL NIL) (-619 1511198 1511534 1511655 "JOINAST" 1511784 T JOINAST (NIL) -8 NIL NIL NIL) (-618 1507233 1509375 1509429 "IXAGG" 1510358 NIL IXAGG (NIL T T) -9 NIL 1510817 NIL) (-617 1506086 1506458 1506877 "IXAGG-" 1506882 NIL IXAGG- (NIL T T T) -8 NIL NIL NIL) (-616 1501175 1506008 1506067 "IVECTOR" 1506072 NIL IVECTOR (NIL T NIL) -8 NIL NIL NIL) (-615 1499900 1500178 1500444 "ITUPLE" 1500942 NIL ITUPLE (NIL T) -8 NIL NIL NIL) (-614 1498372 1498579 1498874 "ITRIGMNP" 1499722 NIL ITRIGMNP (NIL T T T) -7 NIL NIL NIL) (-613 1497099 1497321 1497604 "ITFUN3" 1498148 NIL ITFUN3 (NIL T T T) -7 NIL NIL NIL) (-612 1496697 1496760 1496883 "ITFUN2" 1497022 NIL ITFUN2 (NIL T T) -8 NIL NIL NIL) (-611 1495802 1496177 1496351 "ITFORM" 1496543 T ITFORM (NIL) -8 NIL NIL NIL) (-610 1493571 1494822 1495100 "ITAYLOR" 1495557 NIL ITAYLOR (NIL T) -8 NIL NIL NIL) (-609 1481975 1487708 1488871 "ISUPS" 1492441 NIL ISUPS (NIL T) -8 NIL NIL NIL) (-608 1481067 1481219 1481455 "ISUMP" 1481822 NIL ISUMP (NIL T T T T) -7 NIL NIL NIL) (-607 1475917 1481012 1481053 "ISTRING" 1481058 NIL ISTRING (NIL NIL) -8 NIL NIL NIL) (-606 1475333 1475638 1475730 "ISAST" 1475845 T ISAST (NIL) -8 NIL NIL NIL) (-605 1474531 1474624 1474840 "IRURPK" 1475247 NIL IRURPK (NIL T T T T T) -7 NIL NIL NIL) (-604 1473443 1473668 1473908 "IRSN" 1474311 T IRSN (NIL) -7 NIL NIL NIL) (-603 1471488 1471869 1472298 "IRRF2F" 1473081 NIL IRRF2F (NIL T) -7 NIL NIL NIL) (-602 1471229 1471273 1471349 "IRREDFFX" 1471444 NIL IRREDFFX (NIL T) -7 NIL NIL NIL) (-601 1469802 1470103 1470402 "IROOT" 1470962 NIL IROOT (NIL T) -7 NIL NIL NIL) (-600 1468941 1469295 1469446 "IRFORM" 1469671 T IRFORM (NIL) -8 NIL NIL NIL) (-599 1468023 1468154 1468368 "IR2F" 1468824 NIL IR2F (NIL T T) -7 NIL NIL NIL) (-598 1465612 1466131 1466697 "IR2" 1467501 NIL IR2 (NIL T T) -7 NIL NIL NIL) (-597 1462052 1463296 1463988 "IR" 1464952 NIL IR (NIL T) -8 NIL NIL NIL) (-596 1461837 1461877 1461937 "IPRNTPK" 1462012 T IPRNTPK (NIL) -7 NIL NIL NIL) (-595 1457811 1461726 1461795 "IPF" 1461800 NIL IPF (NIL NIL) -8 NIL NIL NIL) (-594 1455839 1457736 1457793 "IPADIC" 1457798 NIL IPADIC (NIL NIL NIL) -8 NIL NIL NIL) (-593 1455097 1455399 1455529 "IP4ADDR" 1455729 T IP4ADDR (NIL) -8 NIL NIL NIL) (-592 1454435 1454726 1454858 "IOMODE" 1454985 T IOMODE (NIL) -8 NIL NIL NIL) (-591 1453406 1454032 1454159 "IOBFILE" 1454328 T IOBFILE (NIL) -8 NIL NIL NIL) (-590 1452816 1453310 1453338 "IOBCON" 1453343 T IOBCON (NIL) -9 NIL 1453364 NIL) (-589 1452321 1452385 1452568 "INVLAPLA" 1452752 NIL INVLAPLA (NIL T T) -7 NIL NIL NIL) (-588 1441891 1444323 1446709 "INTTR" 1449985 NIL INTTR (NIL T T) -7 NIL NIL NIL) (-587 1438184 1438968 1439833 "INTTOOLS" 1441076 NIL INTTOOLS (NIL T T) -7 NIL NIL NIL) (-586 1437764 1437861 1437978 "INTSLPE" 1438087 T INTSLPE (NIL) -7 NIL NIL NIL) (-585 1435231 1437687 1437746 "INTRVL" 1437751 NIL INTRVL (NIL T) -8 NIL NIL NIL) (-584 1432809 1433345 1433920 "INTRF" 1434716 NIL INTRF (NIL T) -7 NIL NIL NIL) (-583 1432202 1432317 1432459 "INTRET" 1432707 NIL INTRET (NIL T) -7 NIL NIL NIL) (-582 1430175 1430588 1431058 "INTRAT" 1431810 NIL INTRAT (NIL T T) -7 NIL NIL NIL) (-581 1427420 1428021 1428640 "INTPM" 1429660 NIL INTPM (NIL T T) -7 NIL NIL NIL) (-580 1424137 1424764 1425502 "INTPAF" 1426806 NIL INTPAF (NIL T T T) -7 NIL NIL NIL) (-579 1419238 1420278 1421329 "INTPACK" 1423106 T INTPACK (NIL) -7 NIL NIL NIL) (-578 1418484 1418642 1418850 "INTHERTR" 1419080 NIL INTHERTR (NIL T T) -7 NIL NIL NIL) (-577 1417917 1418003 1418191 "INTHERAL" 1418398 NIL INTHERAL (NIL T T T T) -7 NIL NIL NIL) (-576 1415685 1416206 1416663 "INTHEORY" 1417480 T INTHEORY (NIL) -7 NIL NIL NIL) (-575 1407017 1408712 1410484 "INTG0" 1414037 NIL INTG0 (NIL T T T) -7 NIL NIL NIL) (-574 1387542 1392380 1397190 "INTFTBL" 1402227 T INTFTBL (NIL) -8 NIL NIL NIL) (-573 1386767 1386929 1387102 "INTFACT" 1387401 NIL INTFACT (NIL T) -7 NIL NIL NIL) (-572 1384164 1384640 1385197 "INTEF" 1386321 NIL INTEF (NIL T T) -7 NIL NIL NIL) (-571 1382361 1383256 1383284 "INTDOM" 1383585 T INTDOM (NIL) -9 NIL 1383792 NIL) (-570 1381700 1381904 1382146 "INTDOM-" 1382151 NIL INTDOM- (NIL T) -8 NIL NIL NIL) (-569 1377568 1379989 1380043 "INTCAT" 1380842 NIL INTCAT (NIL T) -9 NIL 1381163 NIL) (-568 1377022 1377143 1377271 "INTBIT" 1377460 T INTBIT (NIL) -7 NIL NIL NIL) (-567 1375703 1375875 1376182 "INTALG" 1376867 NIL INTALG (NIL T T T T T) -7 NIL NIL NIL) (-566 1375180 1375276 1375433 "INTAF" 1375607 NIL INTAF (NIL T T) -7 NIL NIL NIL) (-565 1368147 1374990 1375130 "INTABL" 1375135 NIL INTABL (NIL T T T) -8 NIL NIL NIL) (-564 1367388 1367950 1368015 "INT8" 1368049 T INT8 (NIL) -8 NIL NIL 1368094) (-563 1366628 1367190 1367255 "INT64" 1367289 T INT64 (NIL) -8 NIL NIL 1367334) (-562 1365868 1366430 1366495 "INT32" 1366529 T INT32 (NIL) -8 NIL NIL 1366574) (-561 1365108 1365670 1365735 "INT16" 1365769 T INT16 (NIL) -8 NIL NIL 1365814) (-560 1361312 1364905 1365014 "INT" 1365019 T INT (NIL) -8 NIL NIL NIL) (-559 1355421 1358860 1358888 "INS" 1359822 T INS (NIL) -9 NIL 1360487 NIL) (-558 1352578 1353498 1354439 "INS-" 1354512 NIL INS- (NIL T) -8 NIL NIL NIL) (-557 1351335 1351580 1351878 "INPSIGN" 1352331 NIL INPSIGN (NIL T T) -7 NIL NIL NIL) (-556 1350429 1350570 1350767 "INPRODPF" 1351215 NIL INPRODPF (NIL T T) -7 NIL NIL NIL) (-555 1349299 1349440 1349677 "INPRODFF" 1350309 NIL INPRODFF (NIL T T T T) -7 NIL NIL NIL) (-554 1348287 1348451 1348711 "INNMFACT" 1349135 NIL INNMFACT (NIL T T T T) -7 NIL NIL NIL) (-553 1347466 1347581 1347769 "INMODGCD" 1348186 NIL INMODGCD (NIL T T NIL NIL) -7 NIL NIL NIL) (-552 1345950 1346219 1346543 "INFSP" 1347211 NIL INFSP (NIL T T T) -7 NIL NIL NIL) (-551 1345110 1345251 1345434 "INFPROD0" 1345830 NIL INFPROD0 (NIL T T) -7 NIL NIL NIL) (-550 1344708 1344780 1344878 "INFORM1" 1345045 NIL INFORM1 (NIL T) -7 NIL NIL NIL) (-549 1341275 1342773 1343288 "INFORM" 1344201 T INFORM (NIL) -8 NIL NIL NIL) (-548 1340780 1340887 1341001 "INFINITY" 1341181 T INFINITY (NIL) -7 NIL NIL NIL) (-547 1339854 1340500 1340601 "INETCLTS" 1340699 T INETCLTS (NIL) -8 NIL NIL NIL) (-546 1338452 1338720 1339041 "INEP" 1339602 NIL INEP (NIL T T T) -7 NIL NIL NIL) (-545 1337482 1338349 1338414 "INDE" 1338419 NIL INDE (NIL T) -8 NIL NIL NIL) (-544 1337034 1337114 1337231 "INCRMAPS" 1337409 NIL INCRMAPS (NIL T) -7 NIL NIL NIL) (-543 1335756 1336303 1336509 "INBFILE" 1336848 T INBFILE (NIL) -8 NIL NIL NIL) (-542 1330935 1331992 1332936 "INBFF" 1334844 NIL INBFF (NIL T) -7 NIL NIL NIL) (-541 1329789 1330112 1330140 "INBCON" 1330653 T INBCON (NIL) -9 NIL 1330919 NIL) (-540 1328999 1329264 1329540 "INBCON-" 1329545 NIL INBCON- (NIL T) -8 NIL NIL NIL) (-539 1328418 1328723 1328814 "INAST" 1328928 T INAST (NIL) -8 NIL NIL NIL) (-538 1327785 1328097 1328203 "IMPTAST" 1328332 T IMPTAST (NIL) -8 NIL NIL NIL) (-537 1323706 1327629 1327733 "IMATRIX" 1327738 NIL IMATRIX (NIL T NIL NIL) -8 NIL NIL NIL) (-536 1322398 1322537 1322853 "IMATQF" 1323562 NIL IMATQF (NIL T T T T T T T T) -7 NIL NIL NIL) (-535 1320578 1320845 1321182 "IMATLIN" 1322154 NIL IMATLIN (NIL T T T T) -7 NIL NIL NIL) (-534 1314493 1320502 1320560 "ILIST" 1320565 NIL ILIST (NIL T NIL) -8 NIL NIL NIL) (-533 1312159 1314353 1314466 "IIARRAY2" 1314471 NIL IIARRAY2 (NIL T NIL NIL T T) -8 NIL NIL NIL) (-532 1306980 1312070 1312134 "IFF" 1312139 NIL IFF (NIL NIL NIL) -8 NIL NIL NIL) (-531 1306261 1306597 1306713 "IFAST" 1306884 T IFAST (NIL) -8 NIL NIL NIL) (-530 1300773 1305553 1305741 "IFARRAY" 1306118 NIL IFARRAY (NIL T NIL) -8 NIL NIL NIL) (-529 1299811 1300677 1300750 "IFAMON" 1300755 NIL IFAMON (NIL T T NIL) -8 NIL NIL NIL) (-528 1299383 1299460 1299514 "IEVALAB" 1299721 NIL IEVALAB (NIL T T) -9 NIL NIL NIL) (-527 1299046 1299126 1299286 "IEVALAB-" 1299291 NIL IEVALAB- (NIL T T T) -8 NIL NIL NIL) (-526 1298079 1298935 1299010 "IDPOAMS" 1299015 NIL IDPOAMS (NIL T T) -8 NIL NIL NIL) (-525 1297181 1297968 1298043 "IDPOAM" 1298048 NIL IDPOAM (NIL T T) -8 NIL NIL NIL) (-524 1296562 1297096 1297158 "IDPO" 1297163 NIL IDPO (NIL T T) -8 NIL NIL NIL) (-523 1295042 1295569 1295621 "IDPC" 1296133 NIL IDPC (NIL T T) -9 NIL 1296414 NIL) (-522 1294374 1294934 1295007 "IDPAM" 1295012 NIL IDPAM (NIL T T) -8 NIL NIL NIL) (-521 1293589 1294266 1294339 "IDPAG" 1294344 NIL IDPAG (NIL T T) -8 NIL NIL NIL) (-520 1293133 1293395 1293485 "IDENT" 1293519 T IDENT (NIL) -8 NIL NIL NIL) (-519 1289352 1290236 1291131 "IDECOMP" 1292290 NIL IDECOMP (NIL NIL NIL) -7 NIL NIL NIL) (-518 1281987 1283275 1284322 "IDEAL" 1288388 NIL IDEAL (NIL T T T T) -8 NIL NIL NIL) (-517 1281129 1281259 1281459 "ICDEN" 1281871 NIL ICDEN (NIL T T T T) -7 NIL NIL NIL) (-516 1280104 1280609 1280756 "ICARD" 1281002 T ICARD (NIL) -8 NIL NIL NIL) (-515 1278134 1278477 1278882 "IBPTOOLS" 1279781 NIL IBPTOOLS (NIL T T T T) -7 NIL NIL NIL) (-514 1273249 1277754 1277867 "IBITS" 1278053 NIL IBITS (NIL NIL) -8 NIL NIL NIL) (-513 1269924 1270548 1271243 "IBATOOL" 1272666 NIL IBATOOL (NIL T T T) -7 NIL NIL NIL) (-512 1267685 1268165 1268698 "IBACHIN" 1269459 NIL IBACHIN (NIL T T T) -7 NIL NIL NIL) (-511 1265275 1267531 1267634 "IARRAY2" 1267639 NIL IARRAY2 (NIL T NIL NIL) -8 NIL NIL NIL) (-510 1260988 1265201 1265258 "IARRAY1" 1265263 NIL IARRAY1 (NIL T NIL) -8 NIL NIL NIL) (-509 1254005 1259400 1259881 "IAN" 1260527 T IAN (NIL) -8 NIL NIL NIL) (-508 1253510 1253573 1253746 "IALGFACT" 1253942 NIL IALGFACT (NIL T T T T) -7 NIL NIL NIL) (-507 1253002 1253151 1253179 "HYPCAT" 1253386 T HYPCAT (NIL) -9 NIL NIL NIL) (-506 1252504 1252657 1252843 "HYPCAT-" 1252848 NIL HYPCAT- (NIL T) -8 NIL NIL NIL) (-505 1252051 1252299 1252382 "HOSTNAME" 1252441 T HOSTNAME (NIL) -8 NIL NIL NIL) (-504 1251884 1251933 1251974 "HOMOTOP" 1251979 NIL HOMOTOP (NIL T) -9 NIL 1252012 NIL) (-503 1248317 1249816 1249857 "HOAGG" 1250838 NIL HOAGG (NIL T) -9 NIL 1251567 NIL) (-502 1246833 1247310 1247836 "HOAGG-" 1247841 NIL HOAGG- (NIL T T) -8 NIL NIL NIL) (-501 1239890 1246426 1246576 "HEXADEC" 1246703 T HEXADEC (NIL) -8 NIL NIL NIL) (-500 1238602 1238860 1239123 "HEUGCD" 1239667 NIL HEUGCD (NIL T) -7 NIL NIL NIL) (-499 1237534 1238439 1238569 "HELLFDIV" 1238574 NIL HELLFDIV (NIL T T T T) -8 NIL NIL NIL) (-498 1235542 1237309 1237398 "HEAP" 1237477 NIL HEAP (NIL T) -8 NIL NIL NIL) (-497 1234739 1235094 1235228 "HEADAST" 1235428 T HEADAST (NIL) -8 NIL NIL NIL) (-496 1228077 1234654 1234716 "HDP" 1234721 NIL HDP (NIL NIL T) -8 NIL NIL NIL) (-495 1221096 1227712 1227864 "HDMP" 1227978 NIL HDMP (NIL NIL T) -8 NIL NIL NIL) (-494 1220402 1220560 1220724 "HB" 1220952 T HB (NIL) -7 NIL NIL NIL) (-493 1213412 1220248 1220352 "HASHTBL" 1220357 NIL HASHTBL (NIL T T NIL) -8 NIL NIL NIL) (-492 1212828 1213133 1213225 "HASAST" 1213340 T HASAST (NIL) -8 NIL NIL NIL) (-491 1210241 1212450 1212632 "HACKPI" 1212666 T HACKPI (NIL) -8 NIL NIL NIL) (-490 1205413 1210094 1210207 "GTSET" 1210212 NIL GTSET (NIL T T T T) -8 NIL NIL NIL) (-489 1198452 1205291 1205389 "GSTBL" 1205394 NIL GSTBL (NIL T T T NIL) -8 NIL NIL NIL) (-488 1190215 1197617 1197873 "GSERIES" 1198252 NIL GSERIES (NIL T NIL NIL) -8 NIL NIL NIL) (-487 1189246 1189759 1189787 "GROUP" 1189990 T GROUP (NIL) -9 NIL 1190124 NIL) (-486 1188570 1188771 1189022 "GROUP-" 1189027 NIL GROUP- (NIL T) -8 NIL NIL NIL) (-485 1186919 1187258 1187645 "GROEBSOL" 1188247 NIL GROEBSOL (NIL NIL T T) -7 NIL NIL NIL) (-484 1185747 1186107 1186158 "GRMOD" 1186687 NIL GRMOD (NIL T T) -9 NIL 1186855 NIL) (-483 1185503 1185551 1185679 "GRMOD-" 1185684 NIL GRMOD- (NIL T T T) -8 NIL NIL NIL) (-482 1180643 1181857 1182857 "GRIMAGE" 1184523 T GRIMAGE (NIL) -8 NIL NIL NIL) (-481 1179037 1179370 1179694 "GRDEF" 1180339 T GRDEF (NIL) -7 NIL NIL NIL) (-480 1178469 1178597 1178738 "GRAY" 1178916 T GRAY (NIL) -7 NIL NIL NIL) (-479 1177546 1178048 1178099 "GRALG" 1178252 NIL GRALG (NIL T T) -9 NIL 1178345 NIL) (-478 1177183 1177280 1177443 "GRALG-" 1177448 NIL GRALG- (NIL T T T) -8 NIL NIL NIL) (-477 1173664 1176766 1176945 "GPOLSET" 1177089 NIL GPOLSET (NIL T T T T) -8 NIL NIL NIL) (-476 1173012 1173075 1173333 "GOSPER" 1173601 NIL GOSPER (NIL T T T T T) -7 NIL NIL NIL) (-475 1168582 1169450 1169976 "GMODPOL" 1172711 NIL GMODPOL (NIL NIL T T T NIL T) -8 NIL NIL NIL) (-474 1167569 1167771 1168009 "GHENSEL" 1168394 NIL GHENSEL (NIL T T) -7 NIL NIL NIL) (-473 1161641 1162568 1163588 "GENUPS" 1166653 NIL GENUPS (NIL T T) -7 NIL NIL NIL) (-472 1161332 1161389 1161478 "GENUFACT" 1161584 NIL GENUFACT (NIL T) -7 NIL NIL NIL) (-471 1160732 1160821 1160986 "GENPGCD" 1161250 NIL GENPGCD (NIL T T T T) -7 NIL NIL NIL) (-470 1160200 1160241 1160454 "GENMFACT" 1160691 NIL GENMFACT (NIL T T T T T) -7 NIL NIL NIL) (-469 1158737 1159023 1159330 "GENEEZ" 1159943 NIL GENEEZ (NIL T T) -7 NIL NIL NIL) (-468 1151916 1158348 1158510 "GDMP" 1158660 NIL GDMP (NIL NIL T T) -8 NIL NIL NIL) (-467 1140654 1145687 1146793 "GCNAALG" 1150899 NIL GCNAALG (NIL T NIL NIL NIL) -8 NIL NIL NIL) (-466 1138781 1139829 1139857 "GCDDOM" 1140112 T GCDDOM (NIL) -9 NIL 1140269 NIL) (-465 1138221 1138378 1138593 "GCDDOM-" 1138598 NIL GCDDOM- (NIL T) -8 NIL NIL NIL) (-464 1126693 1129167 1131559 "GBINTERN" 1135912 NIL GBINTERN (NIL T T T T) -7 NIL NIL NIL) (-463 1124494 1124822 1125243 "GBF" 1126368 NIL GBF (NIL T T T T) -7 NIL NIL NIL) (-462 1123251 1123440 1123707 "GBEUCLID" 1124310 NIL GBEUCLID (NIL T T T T) -7 NIL NIL NIL) (-461 1121901 1122108 1122412 "GB" 1123030 NIL GB (NIL T T T T) -7 NIL NIL NIL) (-460 1121232 1121375 1121524 "GAUSSFAC" 1121772 T GAUSSFAC (NIL) -7 NIL NIL NIL) (-459 1119553 1119901 1120215 "GALUTIL" 1120951 NIL GALUTIL (NIL T) -7 NIL NIL NIL) (-458 1117813 1118135 1118459 "GALPOLYU" 1119280 NIL GALPOLYU (NIL T T) -7 NIL NIL NIL) (-457 1115112 1115468 1115875 "GALFACTU" 1117510 NIL GALFACTU (NIL T T T) -7 NIL NIL NIL) (-456 1106726 1108417 1110025 "GALFACT" 1113544 NIL GALFACT (NIL T) -7 NIL NIL NIL) (-455 1104012 1104772 1104800 "FVFUN" 1105956 T FVFUN (NIL) -9 NIL 1106676 NIL) (-454 1103242 1103460 1103488 "FVC" 1103779 T FVC (NIL) -9 NIL 1103962 NIL) (-453 1102843 1103067 1103135 "FUNDESC" 1103194 T FUNDESC (NIL) -8 NIL NIL NIL) (-452 1102416 1102640 1102721 "FUNCTION" 1102795 NIL FUNCTION (NIL NIL) -8 NIL NIL NIL) (-451 1101093 1101717 1101920 "FTEM" 1102233 T FTEM (NIL) -8 NIL NIL NIL) (-450 1098723 1099415 1099881 "FT" 1100647 T FT (NIL) -8 NIL NIL NIL) (-449 1096992 1097303 1097700 "FSUPFACT" 1098414 NIL FSUPFACT (NIL T T T) -7 NIL NIL NIL) (-448 1095311 1095678 1096010 "FST" 1096680 T FST (NIL) -8 NIL NIL NIL) (-447 1094492 1094616 1094804 "FSRED" 1095193 NIL FSRED (NIL T T) -7 NIL NIL NIL) (-446 1093181 1093447 1093794 "FSPRMELT" 1094207 NIL FSPRMELT (NIL T T) -7 NIL NIL NIL) (-445 1090391 1090925 1091411 "FSPECF" 1092744 NIL FSPECF (NIL T T) -7 NIL NIL NIL) (-444 1089913 1089973 1090143 "FSINT" 1090332 NIL FSINT (NIL T T) -7 NIL NIL NIL) (-443 1088049 1088906 1089209 "FSERIES" 1089692 NIL FSERIES (NIL T T) -8 NIL NIL NIL) (-442 1087073 1087207 1087431 "FSCINT" 1087929 NIL FSCINT (NIL T T) -7 NIL NIL NIL) (-441 1086097 1086258 1086485 "FSAGG2" 1086926 NIL FSAGG2 (NIL T T T T) -7 NIL NIL NIL) (-440 1081961 1085041 1085082 "FSAGG" 1085452 NIL FSAGG (NIL T) -9 NIL 1085711 NIL) (-439 1079561 1080324 1081120 "FSAGG-" 1081215 NIL FSAGG- (NIL T T) -8 NIL NIL NIL) (-438 1077221 1077519 1078067 "FS2UPS" 1079279 NIL FS2UPS (NIL T T T T T NIL) -7 NIL NIL NIL) (-437 1076087 1076270 1076572 "FS2EXPXP" 1077046 NIL FS2EXPXP (NIL T T NIL NIL) -7 NIL NIL NIL) (-436 1075715 1075764 1075893 "FS2" 1076038 NIL FS2 (NIL T T T T) -7 NIL NIL NIL) (-435 1055953 1065489 1065530 "FS" 1069414 NIL FS (NIL T) -9 NIL 1071703 NIL) (-434 1044014 1047589 1051646 "FS-" 1051946 NIL FS- (NIL T T) -8 NIL NIL NIL) (-433 1043428 1043555 1043707 "FRUTIL" 1043894 NIL FRUTIL (NIL T) -7 NIL NIL NIL) (-432 1037939 1041117 1041157 "FRNAALG" 1042477 NIL FRNAALG (NIL T) -9 NIL 1043075 NIL) (-431 1033420 1034688 1035963 "FRNAALG-" 1036713 NIL FRNAALG- (NIL T T) -8 NIL NIL NIL) (-430 1033052 1033101 1033228 "FRNAAF2" 1033371 NIL FRNAAF2 (NIL T T T T) -7 NIL NIL NIL) (-429 1031339 1031901 1032197 "FRMOD" 1032864 NIL FRMOD (NIL T T T T NIL) -8 NIL NIL NIL) (-428 1030524 1030617 1030908 "FRIDEAL2" 1031246 NIL FRIDEAL2 (NIL T T T T T T T T) -7 NIL NIL NIL) (-427 1028129 1028899 1029217 "FRIDEAL" 1030315 NIL FRIDEAL (NIL T T T T) -8 NIL NIL NIL) (-426 1027220 1027676 1027717 "FRETRCT" 1027722 NIL FRETRCT (NIL T) -9 NIL 1027898 NIL) (-425 1026278 1026563 1026914 "FRETRCT-" 1026919 NIL FRETRCT- (NIL T T) -8 NIL NIL NIL) (-424 1023099 1024562 1024621 "FRAMALG" 1025503 NIL FRAMALG (NIL T T) -9 NIL 1025795 NIL) (-423 1021137 1021688 1022318 "FRAMALG-" 1022541 NIL FRAMALG- (NIL T T T) -8 NIL NIL NIL) (-422 1020767 1020830 1020937 "FRAC2" 1021074 NIL FRAC2 (NIL T T) -7 NIL NIL NIL) (-421 1013760 1020240 1020517 "FRAC" 1020522 NIL FRAC (NIL T) -8 NIL NIL NIL) (-420 1013390 1013453 1013560 "FR2" 1013697 NIL FR2 (NIL T T) -7 NIL NIL NIL) (-419 1004307 1008885 1010243 "FR" 1012064 NIL FR (NIL T) -8 NIL NIL NIL) (-418 998226 1001686 1001714 "FPS" 1002833 T FPS (NIL) -9 NIL 1003390 NIL) (-417 997651 997784 997948 "FPS-" 998094 NIL FPS- (NIL T) -8 NIL NIL NIL) (-416 994617 996608 996636 "FPC" 996861 T FPC (NIL) -9 NIL 997003 NIL) (-415 994398 994450 994547 "FPC-" 994552 NIL FPC- (NIL T) -8 NIL NIL NIL) (-414 993156 993886 993927 "FPATMAB" 993932 NIL FPATMAB (NIL T) -9 NIL 994084 NIL) (-413 991299 991898 992245 "FPARFRAC" 992872 NIL FPARFRAC (NIL T T) -8 NIL NIL NIL) (-412 986591 987191 987873 "FORTRAN" 990731 NIL FORTRAN (NIL NIL NIL NIL NIL) -8 NIL NIL NIL) (-411 984165 984829 984857 "FORTFN" 985917 T FORTFN (NIL) -9 NIL 986541 NIL) (-410 983917 983979 984007 "FORTCAT" 984066 T FORTCAT (NIL) -9 NIL 984128 NIL) (-409 981603 982133 982672 "FORT" 983398 T FORT (NIL) -7 NIL NIL NIL) (-408 981385 981421 981490 "FORMULA1" 981567 NIL FORMULA1 (NIL T) -7 NIL NIL NIL) (-407 979389 980001 980391 "FORMULA" 981015 T FORMULA (NIL) -8 NIL NIL NIL) (-406 978906 978964 979137 "FORDER" 979331 NIL FORDER (NIL T T T T) -7 NIL NIL NIL) (-405 977966 978166 978359 "FOP" 978733 T FOP (NIL) -7 NIL NIL NIL) (-404 976379 977246 977420 "FNLA" 977848 NIL FNLA (NIL NIL NIL T) -8 NIL NIL NIL) (-403 974998 975509 975537 "FNCAT" 975997 T FNCAT (NIL) -9 NIL 976257 NIL) (-402 974441 974957 974985 "FNAME" 974990 T FNAME (NIL) -8 NIL NIL NIL) (-401 972767 973940 973968 "FMTC" 973973 T FMTC (NIL) -9 NIL 974009 NIL) (-400 971316 972703 972749 "FMONOID" 972754 NIL FMONOID (NIL T) -8 NIL NIL NIL) (-399 967905 969271 969312 "FMONCAT" 970529 NIL FMONCAT (NIL T) -9 NIL 971134 NIL) (-398 965227 965975 966003 "FMFUN" 967147 T FMFUN (NIL) -9 NIL 967855 NIL) (-397 962100 963152 963206 "FMCAT" 964401 NIL FMCAT (NIL T T) -9 NIL 964896 NIL) (-396 961333 961550 961578 "FMC" 961868 T FMC (NIL) -9 NIL 962050 NIL) (-395 960001 961099 961199 "FM1" 961278 NIL FM1 (NIL T T) -8 NIL NIL NIL) (-394 959019 959743 959892 "FM" 959897 NIL FM (NIL T T) -8 NIL NIL NIL) (-393 956757 957209 957703 "FLOATRP" 958570 NIL FLOATRP (NIL T) -7 NIL NIL NIL) (-392 954159 954695 955273 "FLOATCP" 956224 NIL FLOATCP (NIL T) -7 NIL NIL NIL) (-391 946822 951888 952509 "FLOAT" 953558 T FLOAT (NIL) -8 NIL NIL NIL) (-390 945340 946414 946455 "FLINEXP" 946460 NIL FLINEXP (NIL T) -9 NIL 946553 NIL) (-389 944470 944729 945057 "FLINEXP-" 945062 NIL FLINEXP- (NIL T T) -8 NIL NIL NIL) (-388 943528 943690 943914 "FLASORT" 944322 NIL FLASORT (NIL T T) -7 NIL NIL NIL) (-387 940446 941498 941550 "FLALG" 942777 NIL FLALG (NIL T T) -9 NIL 943244 NIL) (-386 939470 939631 939858 "FLAGG2" 940299 NIL FLAGG2 (NIL T T T T) -7 NIL NIL NIL) (-385 932725 936879 936920 "FLAGG" 938182 NIL FLAGG (NIL T) -9 NIL 938834 NIL) (-384 931379 931790 932280 "FLAGG-" 932285 NIL FLAGG- (NIL T T) -8 NIL NIL NIL) (-383 928017 929224 929283 "FINRALG" 930411 NIL FINRALG (NIL T T) -9 NIL 930919 NIL) (-382 927141 927406 927745 "FINRALG-" 927750 NIL FINRALG- (NIL T T T) -8 NIL NIL NIL) (-381 926447 926746 926774 "FINITE" 926970 T FINITE (NIL) -9 NIL 927077 NIL) (-380 918398 920977 921017 "FINAALG" 924684 NIL FINAALG (NIL T) -9 NIL 926137 NIL) (-379 913514 914780 915924 "FINAALG-" 917303 NIL FINAALG- (NIL T T) -8 NIL NIL NIL) (-378 912074 912496 912550 "FILECAT" 913234 NIL FILECAT (NIL T T) -9 NIL 913450 NIL) (-377 911352 911829 911932 "FILE" 912004 NIL FILE (NIL T) -8 NIL NIL NIL) (-376 908755 910582 910610 "FIELD" 910650 T FIELD (NIL) -9 NIL 910730 NIL) (-375 907297 907760 908271 "FIELD-" 908276 NIL FIELD- (NIL T) -8 NIL NIL NIL) (-374 904980 905932 906279 "FGROUP" 906983 NIL FGROUP (NIL T) -8 NIL NIL NIL) (-373 904052 904234 904454 "FGLMICPK" 904812 NIL FGLMICPK (NIL T NIL) -7 NIL NIL NIL) (-372 899307 903977 904034 "FFX" 904039 NIL FFX (NIL T NIL) -8 NIL NIL NIL) (-371 898902 898969 899104 "FFSLPE" 899240 NIL FFSLPE (NIL T T T) -7 NIL NIL NIL) (-370 898400 898442 898651 "FFPOLY2" 898860 NIL FFPOLY2 (NIL T T) -7 NIL NIL NIL) (-369 894276 895172 895968 "FFPOLY" 897636 NIL FFPOLY (NIL T) -7 NIL NIL NIL) (-368 889545 894195 894258 "FFP" 894263 NIL FFP (NIL T NIL) -8 NIL NIL NIL) (-367 884076 888888 889078 "FFNBX" 889399 NIL FFNBX (NIL T NIL) -8 NIL NIL NIL) (-366 878409 883211 883469 "FFNBP" 883930 NIL FFNBP (NIL T NIL) -8 NIL NIL NIL) (-365 872447 877693 877904 "FFNB" 878242 NIL FFNB (NIL NIL NIL) -8 NIL NIL NIL) (-364 871267 871477 871792 "FFINTBAS" 872244 NIL FFINTBAS (NIL T T T) -7 NIL NIL NIL) (-363 866860 869514 869542 "FFIELDC" 870162 T FFIELDC (NIL) -9 NIL 870538 NIL) (-362 865480 865921 866404 "FFIELDC-" 866409 NIL FFIELDC- (NIL T) -8 NIL NIL NIL) (-361 865037 865095 865219 "FFHOM" 865422 NIL FFHOM (NIL T T T) -7 NIL NIL NIL) (-360 862696 863219 863736 "FFF" 864552 NIL FFF (NIL T) -7 NIL NIL NIL) (-359 857731 862438 862539 "FFCGX" 862639 NIL FFCGX (NIL T NIL) -8 NIL NIL NIL) (-358 852770 857463 857570 "FFCGP" 857674 NIL FFCGP (NIL T NIL) -8 NIL NIL NIL) (-357 847370 852497 852605 "FFCG" 852706 NIL FFCG (NIL NIL NIL) -8 NIL NIL NIL) (-356 846775 846824 847059 "FFCAT2" 847321 NIL FFCAT2 (NIL T T T T T T T T) -7 NIL NIL NIL) (-355 825457 836507 836593 "FFCAT" 841758 NIL FFCAT (NIL T T T) -9 NIL 843209 NIL) (-354 820468 821702 823016 "FFCAT-" 824246 NIL FFCAT- (NIL T T T T) -8 NIL NIL NIL) (-353 815289 820379 820443 "FF" 820448 NIL FF (NIL NIL NIL) -8 NIL NIL NIL) (-352 803942 808261 809481 "FEXPR" 814141 NIL FEXPR (NIL NIL NIL T) -8 NIL NIL NIL) (-351 802870 803339 803380 "FEVALAB" 803464 NIL FEVALAB (NIL T) -9 NIL 803725 NIL) (-350 801987 802239 802577 "FEVALAB-" 802582 NIL FEVALAB- (NIL T T) -8 NIL NIL NIL) (-349 798849 799734 799849 "FDIVCAT" 801417 NIL FDIVCAT (NIL T T T T) -9 NIL 801854 NIL) (-348 798605 798638 798808 "FDIVCAT-" 798813 NIL FDIVCAT- (NIL T T T T T) -8 NIL NIL NIL) (-347 797819 797912 798189 "FDIV2" 798512 NIL FDIV2 (NIL T T T T T T T T) -7 NIL NIL NIL) (-346 796229 797202 797405 "FDIV" 797718 NIL FDIV (NIL T T T T) -8 NIL NIL NIL) (-345 795137 795524 795726 "FCTRDATA" 796047 T FCTRDATA (NIL) -8 NIL NIL NIL) (-344 793793 794082 794371 "FCPAK1" 794868 T FCPAK1 (NIL) -7 NIL NIL NIL) (-343 792796 793293 793434 "FCOMP" 793684 NIL FCOMP (NIL T) -8 NIL NIL NIL) (-342 776110 779946 783484 "FC" 789278 T FC (NIL) -8 NIL NIL NIL) (-341 767819 772431 772471 "FAXF" 774273 NIL FAXF (NIL T) -9 NIL 774965 NIL) (-340 764960 765767 766585 "FAXF-" 767050 NIL FAXF- (NIL T T) -8 NIL NIL NIL) (-339 759529 764336 764512 "FARRAY" 764817 NIL FARRAY (NIL T) -8 NIL NIL NIL) (-338 754094 756476 756529 "FAMR" 757552 NIL FAMR (NIL T T) -9 NIL 758012 NIL) (-337 752918 753286 753721 "FAMR-" 753726 NIL FAMR- (NIL T T T) -8 NIL NIL NIL) (-336 751945 752840 752893 "FAMONOID" 752898 NIL FAMONOID (NIL T) -8 NIL NIL NIL) (-335 749575 750427 750480 "FAMONC" 751421 NIL FAMONC (NIL T T) -9 NIL 751807 NIL) (-334 748049 749329 749466 "FAGROUP" 749471 NIL FAGROUP (NIL T) -8 NIL NIL NIL) (-333 745802 746163 746566 "FACUTIL" 747730 NIL FACUTIL (NIL T T T T) -7 NIL NIL NIL) (-332 744889 745086 745308 "FACTFUNC" 745612 NIL FACTFUNC (NIL T) -7 NIL NIL NIL) (-331 736630 744192 744391 "EXPUPXS" 744745 NIL EXPUPXS (NIL T NIL NIL) -8 NIL NIL NIL) (-330 734083 734653 735239 "EXPRTUBE" 736064 T EXPRTUBE (NIL) -7 NIL NIL NIL) (-329 730294 730946 731676 "EXPRODE" 733422 NIL EXPRODE (NIL T T) -7 NIL NIL NIL) (-328 724728 725435 726241 "EXPR2UPS" 729592 NIL EXPR2UPS (NIL T T) -7 NIL NIL NIL) (-327 724354 724417 724526 "EXPR2" 724665 NIL EXPR2 (NIL T T) -7 NIL NIL NIL) (-326 708662 723003 723432 "EXPR" 723958 NIL EXPR (NIL T) -8 NIL NIL NIL) (-325 699000 707813 708104 "EXPEXPAN" 708498 NIL EXPEXPAN (NIL T T NIL NIL) -8 NIL NIL NIL) (-324 698420 698724 698815 "EXITAST" 698929 T EXITAST (NIL) -8 NIL NIL NIL) (-323 698184 698377 698406 "EXIT" 698411 T EXIT (NIL) -8 NIL NIL NIL) (-322 697805 697873 697986 "EVALCYC" 698116 NIL EVALCYC (NIL T) -7 NIL NIL NIL) (-321 697322 697464 697505 "EVALAB" 697675 NIL EVALAB (NIL T) -9 NIL 697779 NIL) (-320 696779 696925 697146 "EVALAB-" 697151 NIL EVALAB- (NIL T T) -8 NIL NIL NIL) (-319 693894 695435 695463 "EUCDOM" 696018 T EUCDOM (NIL) -9 NIL 696368 NIL) (-318 692254 692755 693338 "EUCDOM-" 693343 NIL EUCDOM- (NIL T) -8 NIL NIL NIL) (-317 691880 691943 692052 "ESTOOLS2" 692191 NIL ESTOOLS2 (NIL T T) -7 NIL NIL NIL) (-316 691625 691673 691753 "ESTOOLS1" 691832 NIL ESTOOLS1 (NIL T) -7 NIL NIL NIL) (-315 678942 681923 684673 "ESTOOLS" 688895 T ESTOOLS (NIL) -7 NIL NIL NIL) (-314 678681 678719 678801 "ESCONT1" 678904 NIL ESCONT1 (NIL NIL NIL) -7 NIL NIL NIL) (-313 674989 675816 676596 "ESCONT" 677921 T ESCONT (NIL) -7 NIL NIL NIL) (-312 674658 674714 674814 "ES2" 674933 NIL ES2 (NIL T T) -7 NIL NIL NIL) (-311 674282 674346 674455 "ES1" 674594 NIL ES1 (NIL T T) -7 NIL NIL NIL) (-310 667983 669913 669941 "ES" 672709 T ES (NIL) -9 NIL 674119 NIL) (-309 662660 664217 666034 "ES-" 666198 NIL ES- (NIL T) -8 NIL NIL NIL) (-308 661852 662005 662181 "ERROR" 662504 T ERROR (NIL) -7 NIL NIL NIL) (-307 654868 661711 661802 "EQTBL" 661807 NIL EQTBL (NIL T T) -8 NIL NIL NIL) (-306 654494 654557 654666 "EQ2" 654805 NIL EQ2 (NIL T T) -7 NIL NIL NIL) (-305 646753 649808 651257 "EQ" 653078 NIL -1498 (NIL T) -8 NIL NIL NIL) (-304 641996 643091 644184 "EP" 645692 NIL EP (NIL T) -7 NIL NIL NIL) (-303 640536 640887 641193 "ENV" 641710 T ENV (NIL) -8 NIL NIL NIL) (-302 639496 640170 640198 "ENTIRER" 640203 T ENTIRER (NIL) -9 NIL 640249 NIL) (-301 635915 637678 638039 "EMR" 639304 NIL EMR (NIL T T T NIL NIL NIL) -8 NIL NIL NIL) (-300 635019 635230 635284 "ELTAGG" 635664 NIL ELTAGG (NIL T T) -9 NIL 635875 NIL) (-299 634726 634800 634941 "ELTAGG-" 634946 NIL ELTAGG- (NIL T T T) -8 NIL NIL NIL) (-298 634484 634519 634573 "ELTAB" 634657 NIL ELTAB (NIL T T) -9 NIL 634709 NIL) (-297 633586 633756 633955 "ELFUTS" 634335 NIL ELFUTS (NIL T T) -7 NIL NIL NIL) (-296 633310 633384 633412 "ELEMFUN" 633517 T ELEMFUN (NIL) -9 NIL NIL NIL) (-295 633174 633201 633269 "ELEMFUN-" 633274 NIL ELEMFUN- (NIL T) -8 NIL NIL NIL) (-294 627585 631216 631257 "ELAGG" 632197 NIL ELAGG (NIL T) -9 NIL 632660 NIL) (-293 625762 626304 626967 "ELAGG-" 626972 NIL ELAGG- (NIL T T) -8 NIL NIL NIL) (-292 625044 625211 625367 "ELABOR" 625626 T ELABOR (NIL) -8 NIL NIL NIL) (-291 623650 623984 624278 "ELABEXPR" 624770 T ELABEXPR (NIL) -8 NIL NIL NIL) (-290 616162 618287 619116 "EFUPXS" 622925 NIL EFUPXS (NIL T T T T) -8 NIL NIL NIL) (-289 609288 611411 612222 "EFULS" 615437 NIL EFULS (NIL T T T) -8 NIL NIL NIL) (-288 606725 607131 607603 "EFSTRUC" 608920 NIL EFSTRUC (NIL T T) -7 NIL NIL NIL) (-287 596163 598082 599630 "EF" 605240 NIL EF (NIL T T) -7 NIL NIL NIL) (-286 595141 595648 595797 "EAB" 596034 T EAB (NIL) -8 NIL NIL NIL) (-285 594263 595100 595128 "E04UCFA" 595133 T E04UCFA (NIL) -8 NIL NIL NIL) (-284 593385 594222 594250 "E04NAFA" 594255 T E04NAFA (NIL) -8 NIL NIL NIL) (-283 592507 593344 593372 "E04MBFA" 593377 T E04MBFA (NIL) -8 NIL NIL NIL) (-282 591629 592466 592494 "E04JAFA" 592499 T E04JAFA (NIL) -8 NIL NIL NIL) (-281 590753 591588 591616 "E04GCFA" 591621 T E04GCFA (NIL) -8 NIL NIL NIL) (-280 589877 590712 590740 "E04FDFA" 590745 T E04FDFA (NIL) -8 NIL NIL NIL) (-279 588999 589836 589864 "E04DGFA" 589869 T E04DGFA (NIL) -8 NIL NIL NIL) (-278 583076 584524 585888 "E04AGNT" 587655 T E04AGNT (NIL) -7 NIL NIL NIL) (-277 581696 582377 582417 "DVARCAT" 582758 NIL DVARCAT (NIL T) -9 NIL 582921 NIL) (-276 580846 581112 581426 "DVARCAT-" 581431 NIL DVARCAT- (NIL T T) -8 NIL NIL NIL) (-275 572814 580645 580774 "DSMP" 580779 NIL DSMP (NIL T T T) -8 NIL NIL NIL) (-274 571165 571956 571997 "DSEXT" 572360 NIL DSEXT (NIL T) -9 NIL 572654 NIL) (-273 569354 569878 570544 "DSEXT-" 570549 NIL DSEXT- (NIL T T) -8 NIL NIL NIL) (-272 569013 569078 569176 "DROPT1" 569289 NIL DROPT1 (NIL T) -7 NIL NIL NIL) (-271 564032 565254 566391 "DROPT0" 567896 T DROPT0 (NIL) -7 NIL NIL NIL) (-270 558615 559977 561045 "DROPT" 562984 T DROPT (NIL) -8 NIL NIL NIL) (-269 556924 557285 557671 "DRAWPT" 558249 T DRAWPT (NIL) -7 NIL NIL NIL) (-268 556551 556610 556728 "DRAWHACK" 556865 NIL DRAWHACK (NIL T) -7 NIL NIL NIL) (-267 555252 555551 555842 "DRAWCX" 556280 T DRAWCX (NIL) -7 NIL NIL NIL) (-266 554761 554836 554987 "DRAWCURV" 555178 NIL DRAWCURV (NIL T T) -7 NIL NIL NIL) (-265 545079 547191 549306 "DRAWCFUN" 552666 T DRAWCFUN (NIL) -7 NIL NIL NIL) (-264 539570 540589 541668 "DRAW" 544053 NIL DRAW (NIL T) -7 NIL NIL NIL) (-263 536041 538235 538276 "DQAGG" 538905 NIL DQAGG (NIL T) -9 NIL 539179 NIL) (-262 522624 530252 530335 "DPOLCAT" 532187 NIL DPOLCAT (NIL T T T T) -9 NIL 532732 NIL) (-261 517143 518809 520767 "DPOLCAT-" 520772 NIL DPOLCAT- (NIL T T T T T) -8 NIL NIL NIL) (-260 509951 517004 517102 "DPMO" 517107 NIL DPMO (NIL NIL T T) -8 NIL NIL NIL) (-259 502656 509731 509898 "DPMM" 509903 NIL DPMM (NIL NIL T T T) -8 NIL NIL NIL) (-258 502178 502440 502529 "DOMTMPLT" 502587 T DOMTMPLT (NIL) -8 NIL NIL NIL) (-257 501527 501980 502060 "DOMCTOR" 502118 T DOMCTOR (NIL) -8 NIL NIL NIL) (-256 500679 501007 501158 "DOMAIN" 501396 T DOMAIN (NIL) -8 NIL NIL NIL) (-255 493698 500314 500466 "DMP" 500580 NIL DMP (NIL NIL T) -8 NIL NIL NIL) (-254 491475 492765 492806 "DMEXT" 492811 NIL DMEXT (NIL T) -9 NIL 492987 NIL) (-253 491069 491131 491275 "DLP" 491413 NIL DLP (NIL T) -7 NIL NIL NIL) (-252 484192 490396 490586 "DLIST" 490911 NIL DLIST (NIL T) -8 NIL NIL NIL) (-251 480730 483017 483058 "DLAGG" 483608 NIL DLAGG (NIL T) -9 NIL 483838 NIL) (-250 479242 480056 480084 "DIVRING" 480176 T DIVRING (NIL) -9 NIL 480259 NIL) (-249 478425 478669 478969 "DIVRING-" 478974 NIL DIVRING- (NIL T) -8 NIL NIL NIL) (-248 476467 476884 477290 "DISPLAY" 478039 T DISPLAY (NIL) -7 NIL NIL NIL) (-247 475297 475518 475783 "DIRPROD2" 476260 NIL DIRPROD2 (NIL NIL T T) -7 NIL NIL NIL) (-246 468655 475211 475274 "DIRPROD" 475279 NIL DIRPROD (NIL NIL T) -8 NIL NIL NIL) (-245 456818 463366 463419 "DIRPCAT" 463677 NIL DIRPCAT (NIL NIL T) -9 NIL 464552 NIL) (-244 454018 454786 455667 "DIRPCAT-" 456004 NIL DIRPCAT- (NIL T NIL T) -8 NIL NIL NIL) (-243 453299 453465 453651 "DIOSP" 453852 T DIOSP (NIL) -7 NIL NIL NIL) (-242 449713 452183 452224 "DIOPS" 452658 NIL DIOPS (NIL T) -9 NIL 452887 NIL) (-241 449232 449376 449567 "DIOPS-" 449572 NIL DIOPS- (NIL T T) -8 NIL NIL NIL) (-240 448139 448911 448939 "DIFRING" 448944 T DIFRING (NIL) -9 NIL 448966 NIL) (-239 447787 447885 447913 "DIFFSPC" 448032 T DIFFSPC (NIL) -9 NIL 448107 NIL) (-238 447408 447510 447662 "DIFFSPC-" 447667 NIL DIFFSPC- (NIL T) -8 NIL NIL NIL) (-237 446344 446942 446983 "DIFFMOD" 446988 NIL DIFFMOD (NIL T) -9 NIL 447086 NIL) (-236 446040 446097 446138 "DIFFDOM" 446259 NIL DIFFDOM (NIL T) -9 NIL 446327 NIL) (-235 445887 445917 446001 "DIFFDOM-" 446006 NIL DIFFDOM- (NIL T T) -8 NIL NIL NIL) (-234 443627 445091 445132 "DIFEXT" 445137 NIL DIFEXT (NIL T) -9 NIL 445290 NIL) (-233 440661 443131 443172 "DIAGG" 443177 NIL DIAGG (NIL T) -9 NIL 443197 NIL) (-232 440009 440202 440454 "DIAGG-" 440459 NIL DIAGG- (NIL T T) -8 NIL NIL NIL) (-231 434859 438968 439245 "DHMATRIX" 439778 NIL DHMATRIX (NIL T) -8 NIL NIL NIL) (-230 430327 431380 432390 "DFSFUN" 433869 T DFSFUN (NIL) -7 NIL NIL NIL) (-229 424568 429258 429570 "DFLOAT" 430035 T DFLOAT (NIL) -8 NIL NIL NIL) (-228 422807 423112 423501 "DFINTTLS" 424276 NIL DFINTTLS (NIL T T) -7 NIL NIL NIL) (-227 419626 420828 421228 "DERHAM" 422473 NIL DERHAM (NIL T NIL) -8 NIL NIL NIL) (-226 417162 419401 419490 "DEQUEUE" 419570 NIL DEQUEUE (NIL T) -8 NIL NIL NIL) (-225 416404 416549 416732 "DEGRED" 417024 NIL DEGRED (NIL T T) -7 NIL NIL NIL) (-224 412810 413579 414425 "DEFINTRF" 415632 NIL DEFINTRF (NIL T) -7 NIL NIL NIL) (-223 410347 410834 411426 "DEFINTEF" 412329 NIL DEFINTEF (NIL T T) -7 NIL NIL NIL) (-222 409631 409967 410082 "DEFAST" 410252 T DEFAST (NIL) -8 NIL NIL NIL) (-221 402688 409224 409374 "DECIMAL" 409501 T DECIMAL (NIL) -8 NIL NIL NIL) (-220 400146 400658 401164 "DDFACT" 402232 NIL DDFACT (NIL T T) -7 NIL NIL NIL) (-219 399736 399785 399936 "DBLRESP" 400097 NIL DBLRESP (NIL T T T T) -7 NIL NIL NIL) (-218 398937 399506 399597 "DBASIS" 399685 NIL DBASIS (NIL NIL) -8 NIL NIL NIL) (-217 396721 397167 397528 "DBASE" 398703 NIL DBASE (NIL T) -8 NIL NIL NIL) (-216 395909 396201 396347 "DATAARY" 396620 NIL DATAARY (NIL NIL T) -8 NIL NIL NIL) (-215 394967 395868 395896 "D03FAFA" 395901 T D03FAFA (NIL) -8 NIL NIL NIL) (-214 394026 394926 394954 "D03EEFA" 394959 T D03EEFA (NIL) -8 NIL NIL NIL) (-213 391952 392442 392931 "D03AGNT" 393557 T D03AGNT (NIL) -7 NIL NIL NIL) (-212 391193 391911 391939 "D02EJFA" 391944 T D02EJFA (NIL) -8 NIL NIL NIL) (-211 390434 391152 391180 "D02CJFA" 391185 T D02CJFA (NIL) -8 NIL NIL NIL) (-210 389675 390393 390421 "D02BHFA" 390426 T D02BHFA (NIL) -8 NIL NIL NIL) (-209 388916 389634 389662 "D02BBFA" 389667 T D02BBFA (NIL) -8 NIL NIL NIL) (-208 382047 383702 385308 "D02AGNT" 387330 T D02AGNT (NIL) -7 NIL NIL NIL) (-207 379797 380338 380884 "D01WGTS" 381521 T D01WGTS (NIL) -7 NIL NIL NIL) (-206 378804 379756 379784 "D01TRNS" 379789 T D01TRNS (NIL) -8 NIL NIL NIL) (-205 377812 378763 378791 "D01GBFA" 378796 T D01GBFA (NIL) -8 NIL NIL NIL) (-204 376820 377771 377799 "D01FCFA" 377804 T D01FCFA (NIL) -8 NIL NIL NIL) (-203 375828 376779 376807 "D01ASFA" 376812 T D01ASFA (NIL) -8 NIL NIL NIL) (-202 374836 375787 375815 "D01AQFA" 375820 T D01AQFA (NIL) -8 NIL NIL NIL) (-201 373844 374795 374823 "D01APFA" 374828 T D01APFA (NIL) -8 NIL NIL NIL) (-200 372852 373803 373831 "D01ANFA" 373836 T D01ANFA (NIL) -8 NIL NIL NIL) (-199 371860 372811 372839 "D01AMFA" 372844 T D01AMFA (NIL) -8 NIL NIL NIL) (-198 370868 371819 371847 "D01ALFA" 371852 T D01ALFA (NIL) -8 NIL NIL NIL) (-197 369876 370827 370855 "D01AKFA" 370860 T D01AKFA (NIL) -8 NIL NIL NIL) (-196 368884 369835 369863 "D01AJFA" 369868 T D01AJFA (NIL) -8 NIL NIL NIL) (-195 362107 363732 365293 "D01AGNT" 367343 T D01AGNT (NIL) -7 NIL NIL NIL) (-194 361426 361572 361724 "CYCLOTOM" 361975 T CYCLOTOM (NIL) -7 NIL NIL NIL) (-193 358081 358874 359601 "CYCLES" 360719 T CYCLES (NIL) -7 NIL NIL NIL) (-192 357381 357527 357698 "CVMP" 357942 NIL CVMP (NIL T) -7 NIL NIL NIL) (-191 355168 355480 355849 "CTRIGMNP" 357109 NIL CTRIGMNP (NIL T T) -7 NIL NIL NIL) (-190 354641 354899 355000 "CTORKIND" 355087 T CTORKIND (NIL) -8 NIL NIL NIL) (-189 353846 354234 354262 "CTORCAT" 354444 T CTORCAT (NIL) -9 NIL 354557 NIL) (-188 353420 353555 353714 "CTORCAT-" 353719 NIL CTORCAT- (NIL T) -8 NIL NIL NIL) (-187 352834 353094 353202 "CTORCALL" 353344 NIL CTORCALL (NIL T) -8 NIL NIL NIL) (-186 352192 352628 352701 "CTOR" 352781 T CTOR (NIL) -8 NIL NIL NIL) (-185 351548 351665 351818 "CSTTOOLS" 352089 NIL CSTTOOLS (NIL T T) -7 NIL NIL NIL) (-184 347245 348004 348762 "CRFP" 350860 NIL CRFP (NIL T T) -7 NIL NIL NIL) (-183 346660 346966 347058 "CRCEAST" 347173 T CRCEAST (NIL) -8 NIL NIL NIL) (-182 345683 345892 346120 "CRAPACK" 346464 NIL CRAPACK (NIL T) -7 NIL NIL NIL) (-181 345063 345168 345372 "CPMATCH" 345559 NIL CPMATCH (NIL T T T) -7 NIL NIL NIL) (-180 344782 344816 344922 "CPIMA" 345029 NIL CPIMA (NIL T T T) -7 NIL NIL NIL) (-179 341040 341802 342521 "COORDSYS" 344117 NIL COORDSYS (NIL T) -7 NIL NIL NIL) (-178 340428 340573 340715 "CONTOUR" 340918 T CONTOUR (NIL) -8 NIL NIL NIL) (-177 335899 338431 338923 "CONTFRAC" 339968 NIL CONTFRAC (NIL T) -8 NIL NIL NIL) (-176 335773 335800 335828 "CONDUIT" 335865 T CONDUIT (NIL) -9 NIL NIL NIL) (-175 334727 335401 335429 "COMRING" 335434 T COMRING (NIL) -9 NIL 335486 NIL) (-174 333709 334085 334269 "COMPPROP" 334563 T COMPPROP (NIL) -8 NIL NIL NIL) (-173 333364 333405 333533 "COMPLPAT" 333668 NIL COMPLPAT (NIL T T T) -7 NIL NIL NIL) (-172 332994 333057 333164 "COMPLEX2" 333301 NIL COMPLEX2 (NIL T T) -7 NIL NIL NIL) (-171 321398 332803 332912 "COMPLEX" 332917 NIL COMPLEX (NIL T) -8 NIL NIL NIL) (-170 320719 320858 321018 "COMPILER" 321258 T COMPILER (NIL) -8 NIL NIL NIL) (-169 320431 320472 320570 "COMPFACT" 320678 NIL COMPFACT (NIL T T) -7 NIL NIL NIL) (-168 301825 314135 314175 "COMPCAT" 315179 NIL COMPCAT (NIL T) -9 NIL 316527 NIL) (-167 290713 294264 297891 "COMPCAT-" 298247 NIL COMPCAT- (NIL T T) -8 NIL NIL NIL) (-166 290436 290470 290573 "COMMUPC" 290679 NIL COMMUPC (NIL T T T) -7 NIL NIL NIL) (-165 290224 290264 290323 "COMMONOP" 290397 T COMMONOP (NIL) -7 NIL NIL NIL) (-164 289746 290028 290103 "COMMAAST" 290169 T COMMAAST (NIL) -8 NIL NIL NIL) (-163 289253 289497 289584 "COMM" 289679 T COMM (NIL) -8 NIL NIL NIL) (-162 288448 288696 288724 "COMBOPC" 289062 T COMBOPC (NIL) -9 NIL 289237 NIL) (-161 287302 287554 287796 "COMBINAT" 288238 NIL COMBINAT (NIL T) -7 NIL NIL NIL) (-160 283645 284333 284960 "COMBF" 286724 NIL COMBF (NIL T T) -7 NIL NIL NIL) (-159 282307 282761 282996 "COLOR" 283430 T COLOR (NIL) -8 NIL NIL NIL) (-158 281723 282028 282120 "COLONAST" 282235 T COLONAST (NIL) -8 NIL NIL NIL) (-157 281357 281410 281535 "CMPLXRT" 281670 NIL CMPLXRT (NIL T T) -7 NIL NIL NIL) (-156 280745 281057 281156 "CLLCTAST" 281278 T CLLCTAST (NIL) -8 NIL NIL NIL) (-155 276204 277275 278355 "CLIP" 279685 T CLIP (NIL) -7 NIL NIL NIL) (-154 274377 275305 275545 "CLIF" 276031 NIL CLIF (NIL NIL T NIL) -8 NIL NIL NIL) (-153 270359 272495 272536 "CLAGG" 273465 NIL CLAGG (NIL T) -9 NIL 274001 NIL) (-152 268703 269238 269821 "CLAGG-" 269826 NIL CLAGG- (NIL T T) -8 NIL NIL NIL) (-151 268241 268332 268472 "CINTSLPE" 268612 NIL CINTSLPE (NIL T T) -7 NIL NIL NIL) (-150 265706 266213 266761 "CHVAR" 267769 NIL CHVAR (NIL T T T) -7 NIL NIL NIL) (-149 264746 265420 265448 "CHARZ" 265453 T CHARZ (NIL) -9 NIL 265468 NIL) (-148 264494 264540 264618 "CHARPOL" 264700 NIL CHARPOL (NIL T) -7 NIL NIL NIL) (-147 263412 264118 264146 "CHARNZ" 264207 T CHARNZ (NIL) -9 NIL 264256 NIL) (-146 260356 261466 261995 "CHAR" 262903 T CHAR (NIL) -8 NIL NIL NIL) (-145 260064 260143 260171 "CFCAT" 260282 T CFCAT (NIL) -9 NIL NIL NIL) (-144 259287 259416 259599 "CDEN" 259948 NIL CDEN (NIL T T T) -7 NIL NIL NIL) (-143 254884 258440 258720 "CCLASS" 259027 T CCLASS (NIL) -8 NIL NIL NIL) (-142 254105 254292 254469 "CATEGORY" 254727 T -10 (NIL) -8 NIL NIL NIL) (-141 253600 254024 254072 "CATCTOR" 254077 T CATCTOR (NIL) -8 NIL NIL NIL) (-140 252991 253303 253401 "CATAST" 253522 T CATAST (NIL) -8 NIL NIL NIL) (-139 252407 252712 252804 "CASEAST" 252919 T CASEAST (NIL) -8 NIL NIL NIL) (-138 251503 251663 251884 "CARTEN2" 252254 NIL CARTEN2 (NIL NIL NIL T T) -7 NIL NIL NIL) (-137 246400 247660 248404 "CARTEN" 250815 NIL CARTEN (NIL NIL NIL T) -8 NIL NIL NIL) (-136 244530 245550 245807 "CARD" 246163 T CARD (NIL) -8 NIL NIL NIL) (-135 244052 244334 244409 "CAPSLAST" 244475 T CAPSLAST (NIL) -8 NIL NIL NIL) (-134 243494 243750 243778 "CACHSET" 243910 T CACHSET (NIL) -9 NIL 243988 NIL) (-133 242884 243272 243300 "CABMON" 243350 T CABMON (NIL) -9 NIL 243406 NIL) (-132 242321 242588 242698 "BYTEORD" 242794 T BYTEORD (NIL) -8 NIL NIL NIL) (-131 237248 241826 241998 "BYTEBUF" 242169 T BYTEBUF (NIL) -8 NIL NIL NIL) (-130 236006 236763 236912 "BYTE" 237075 T BYTE (NIL) -8 NIL NIL 237204) (-129 233268 235698 235805 "BTREE" 235932 NIL BTREE (NIL T) -8 NIL NIL NIL) (-128 230470 232916 233038 "BTOURN" 233178 NIL BTOURN (NIL T) -8 NIL NIL NIL) (-127 227577 229912 229953 "BTCAT" 230021 NIL BTCAT (NIL T) -9 NIL 230098 NIL) (-126 227226 227324 227473 "BTCAT-" 227478 NIL BTCAT- (NIL T T) -8 NIL NIL NIL) (-125 222115 226472 226500 "BTAGG" 226614 T BTAGG (NIL) -9 NIL 226724 NIL) (-124 221569 221730 221936 "BTAGG-" 221941 NIL BTAGG- (NIL T) -8 NIL NIL NIL) (-123 218305 220847 221062 "BSTREE" 221386 NIL BSTREE (NIL T) -8 NIL NIL NIL) (-122 217413 217569 217753 "BRILL" 218161 NIL BRILL (NIL T) -7 NIL NIL NIL) (-121 213808 216111 216152 "BRAGG" 216801 NIL BRAGG (NIL T) -9 NIL 217059 NIL) (-120 212241 212743 213298 "BRAGG-" 213303 NIL BRAGG- (NIL T T) -8 NIL NIL NIL) (-119 204498 211585 211770 "BPADICRT" 212088 NIL BPADICRT (NIL NIL) -8 NIL NIL NIL) (-118 202514 204435 204480 "BPADIC" 204485 NIL BPADIC (NIL NIL) -8 NIL NIL NIL) (-117 202206 202242 202356 "BOUNDZRO" 202478 NIL BOUNDZRO (NIL T T) -7 NIL NIL NIL) (-116 199933 200391 200866 "BOP1" 201764 NIL BOP1 (NIL T) -7 NIL NIL NIL) (-115 194915 196359 197271 "BOP" 199041 T BOP (NIL) -8 NIL NIL NIL) (-114 193580 194503 194645 "BOOLEAN" 194793 T BOOLEAN (NIL) -8 NIL NIL NIL) (-113 193173 193330 193358 "BOOLE" 193469 T BOOLE (NIL) -9 NIL 193550 NIL) (-112 193041 193068 193134 "BOOLE-" 193139 NIL BOOLE- (NIL T) -8 NIL NIL NIL) (-111 192210 192710 192764 "BMODULE" 192769 NIL BMODULE (NIL T T) -9 NIL 192834 NIL) (-110 187531 192008 192081 "BITS" 192157 T BITS (NIL) -8 NIL NIL NIL) (-109 186928 187071 187211 "BINDING" 187411 T BINDING (NIL) -8 NIL NIL NIL) (-108 179988 186523 186672 "BINARY" 186799 T BINARY (NIL) -8 NIL NIL NIL) (-107 177595 179215 179256 "BGAGG" 179516 NIL BGAGG (NIL T) -9 NIL 179653 NIL) (-106 177420 177458 177549 "BGAGG-" 177554 NIL BGAGG- (NIL T T) -8 NIL NIL NIL) (-105 176443 176804 177009 "BFUNCT" 177235 T BFUNCT (NIL) -8 NIL NIL NIL) (-104 175113 175311 175599 "BEZOUT" 176267 NIL BEZOUT (NIL T T T T T) -7 NIL NIL NIL) (-103 171311 173965 174295 "BBTREE" 174816 NIL BBTREE (NIL T) -8 NIL NIL NIL) (-102 170894 170990 171018 "BASTYPE" 171195 T BASTYPE (NIL) -9 NIL 171294 NIL) (-101 170552 170651 170786 "BASTYPE-" 170791 NIL BASTYPE- (NIL T) -8 NIL NIL NIL) (-100 169974 170062 170214 "BALFACT" 170463 NIL BALFACT (NIL T T) -7 NIL NIL NIL) (-99 168710 169389 169575 "AUTOMOR" 169819 NIL AUTOMOR (NIL T) -8 NIL NIL NIL) (-98 168436 168441 168467 "ATTREG" 168472 T ATTREG (NIL) -9 NIL NIL NIL) (-97 166598 167133 167485 "ATTRBUT" 168102 T ATTRBUT (NIL) -8 NIL NIL NIL) (-96 166152 166426 166492 "ATTRAST" 166550 T ATTRAST (NIL) -8 NIL NIL NIL) (-95 165652 165801 165827 "ATRIG" 166028 T ATRIG (NIL) -9 NIL NIL NIL) (-94 165449 165502 165589 "ATRIG-" 165594 NIL ATRIG- (NIL T) -8 NIL NIL NIL) (-93 165032 165266 165292 "ASTCAT" 165297 T ASTCAT (NIL) -9 NIL 165327 NIL) (-92 164741 164818 164937 "ASTCAT-" 164942 NIL ASTCAT- (NIL T) -8 NIL NIL NIL) (-91 162715 164517 164605 "ASTACK" 164684 NIL ASTACK (NIL T) -8 NIL NIL NIL) (-90 161204 161517 161882 "ASSOCEQ" 162397 NIL ASSOCEQ (NIL T T) -7 NIL NIL NIL) (-89 160128 160863 160987 "ASP9" 161111 NIL ASP9 (NIL NIL) -8 NIL NIL NIL) (-88 158888 159733 159875 "ASP80" 160017 NIL ASP80 (NIL NIL) -8 NIL NIL NIL) (-87 158615 158836 158875 "ASP8" 158880 NIL ASP8 (NIL NIL) -8 NIL NIL NIL) (-86 157461 158292 158410 "ASP78" 158528 NIL ASP78 (NIL NIL) -8 NIL NIL NIL) (-85 156322 157141 157258 "ASP77" 157375 NIL ASP77 (NIL NIL) -8 NIL NIL NIL) (-84 155126 155960 156091 "ASP74" 156222 NIL ASP74 (NIL NIL) -8 NIL NIL NIL) (-83 153918 154761 154893 "ASP73" 155025 NIL ASP73 (NIL NIL) -8 NIL NIL NIL) (-82 152708 153553 153685 "ASP7" 153817 NIL ASP7 (NIL NIL) -8 NIL NIL NIL) (-81 151704 152534 152634 "ASP6" 152639 NIL ASP6 (NIL NIL) -8 NIL NIL NIL) (-80 150543 151381 151499 "ASP55" 151617 NIL ASP55 (NIL NIL) -8 NIL NIL NIL) (-79 149384 150217 150336 "ASP50" 150455 NIL ASP50 (NIL NIL) -8 NIL NIL NIL) (-78 148364 149085 149195 "ASP49" 149305 NIL ASP49 (NIL NIL) -8 NIL NIL NIL) (-77 147040 147903 148071 "ASP42" 148253 NIL ASP42 (NIL NIL NIL NIL) -8 NIL NIL NIL) (-76 145709 146573 146743 "ASP41" 146927 NIL ASP41 (NIL NIL NIL NIL) -8 NIL NIL NIL) (-75 144689 145410 145520 "ASP4" 145630 NIL ASP4 (NIL NIL) -8 NIL NIL NIL) (-74 143531 144366 144484 "ASP35" 144602 NIL ASP35 (NIL NIL) -8 NIL NIL NIL) (-73 143260 143479 143518 "ASP34" 143523 NIL ASP34 (NIL NIL) -8 NIL NIL NIL) (-72 142979 143064 143140 "ASP33" 143215 NIL ASP33 (NIL NIL) -8 NIL NIL NIL) (-71 141765 142614 142746 "ASP31" 142878 NIL ASP31 (NIL NIL) -8 NIL NIL NIL) (-70 141494 141713 141752 "ASP30" 141757 NIL ASP30 (NIL NIL) -8 NIL NIL NIL) (-69 141211 141298 141374 "ASP29" 141449 NIL ASP29 (NIL NIL) -8 NIL NIL NIL) (-68 140940 141159 141198 "ASP28" 141203 NIL ASP28 (NIL NIL) -8 NIL NIL NIL) (-67 140669 140888 140927 "ASP27" 140932 NIL ASP27 (NIL NIL) -8 NIL NIL NIL) (-66 139645 140367 140478 "ASP24" 140589 NIL ASP24 (NIL NIL) -8 NIL NIL NIL) (-65 138614 139447 139559 "ASP20" 139564 NIL ASP20 (NIL NIL) -8 NIL NIL NIL) (-64 137449 138288 138407 "ASP19" 138526 NIL ASP19 (NIL NIL) -8 NIL NIL NIL) (-63 137168 137253 137329 "ASP12" 137404 NIL ASP12 (NIL NIL) -8 NIL NIL NIL) (-62 135912 136767 136911 "ASP10" 137055 NIL ASP10 (NIL NIL) -8 NIL NIL NIL) (-61 134892 135613 135723 "ASP1" 135833 NIL ASP1 (NIL NIL) -8 NIL NIL NIL) (-60 132504 134736 134827 "ARRAY2" 134832 NIL ARRAY2 (NIL T) -8 NIL NIL NIL) (-59 131518 131709 131930 "ARRAY12" 132327 NIL ARRAY12 (NIL T T) -7 NIL NIL NIL) (-58 126878 131166 131280 "ARRAY1" 131435 NIL ARRAY1 (NIL T) -8 NIL NIL NIL) (-57 120923 123080 123155 "ARR2CAT" 125785 NIL ARR2CAT (NIL T T T) -9 NIL 126543 NIL) (-56 118213 119101 120055 "ARR2CAT-" 120060 NIL ARR2CAT- (NIL T T T T) -8 NIL NIL NIL) (-55 117464 117840 117965 "ARITY" 118106 T ARITY (NIL) -8 NIL NIL NIL) (-54 116222 116392 116691 "APPRULE" 117300 NIL APPRULE (NIL T T T) -7 NIL NIL NIL) (-53 115867 115921 116040 "APPLYORE" 116168 NIL APPLYORE (NIL T T T) -7 NIL NIL NIL) (-52 115121 115268 115425 "ANY1" 115741 NIL ANY1 (NIL T) -7 NIL NIL NIL) (-51 114421 114714 114834 "ANY" 115019 T ANY (NIL) -8 NIL NIL NIL) (-50 111747 112858 113185 "ANTISYM" 114145 NIL ANTISYM (NIL T NIL) -8 NIL NIL NIL) (-49 111191 111454 111550 "ANON" 111669 T ANON (NIL) -8 NIL NIL NIL) (-48 104354 109730 110184 "AN" 110755 T AN (NIL) -8 NIL NIL NIL) (-47 100017 101626 101677 "AMR" 102425 NIL AMR (NIL T T) -9 NIL 103025 NIL) (-46 99069 99350 99713 "AMR-" 99718 NIL AMR- (NIL T T T) -8 NIL NIL NIL) (-45 82538 98986 99047 "ALIST" 99052 NIL ALIST (NIL T T) -8 NIL NIL NIL) (-44 78835 82132 82301 "ALGSC" 82456 NIL ALGSC (NIL T NIL NIL NIL) -8 NIL NIL NIL) (-43 75285 75945 76552 "ALGPKG" 78275 NIL ALGPKG (NIL T T) -7 NIL NIL NIL) (-42 74550 74663 74847 "ALGMFACT" 75171 NIL ALGMFACT (NIL T T T) -7 NIL NIL NIL) (-41 70533 71164 71758 "ALGMANIP" 74134 NIL ALGMANIP (NIL T T) -7 NIL NIL NIL) (-40 59893 70159 70309 "ALGFF" 70466 NIL ALGFF (NIL T T T NIL) -8 NIL NIL NIL) (-39 59065 59220 59399 "ALGFACT" 59751 NIL ALGFACT (NIL T) -7 NIL NIL NIL) (-38 57854 58592 58630 "ALGEBRA" 58635 NIL ALGEBRA (NIL T) -9 NIL 58676 NIL) (-37 57554 57631 57763 "ALGEBRA-" 57768 NIL ALGEBRA- (NIL T T) -8 NIL NIL NIL) (-36 38508 55391 55443 "ALAGG" 55579 NIL ALAGG (NIL T T) -9 NIL 55740 NIL) (-35 38008 38157 38183 "AHYP" 38384 T AHYP (NIL) -9 NIL NIL NIL) (-34 36893 37187 37213 "AGG" 37712 T AGG (NIL) -9 NIL 37991 NIL) (-33 36291 36489 36703 "AGG-" 36708 NIL AGG- (NIL T) -8 NIL NIL NIL) (-32 34051 34520 34925 "AF" 35933 NIL AF (NIL T T) -7 NIL NIL NIL) (-31 33471 33776 33866 "ADDAST" 33979 T ADDAST (NIL) -8 NIL NIL NIL) (-30 32703 32998 33154 "ACPLOT" 33333 T ACPLOT (NIL) -8 NIL NIL NIL) (-29 20267 29635 29673 "ACFS" 30280 NIL ACFS (NIL T) -9 NIL 30519 NIL) (-28 18174 18784 19546 "ACFS-" 19551 NIL ACFS- (NIL T T) -8 NIL NIL NIL) (-27 13882 16207 16233 "ACF" 17112 T ACF (NIL) -9 NIL 17525 NIL) (-26 12514 12920 13413 "ACF-" 13418 NIL ACF- (NIL T) -8 NIL NIL NIL) (-25 12024 12267 12293 "ABELSG" 12385 T ABELSG (NIL) -9 NIL 12450 NIL) (-24 11885 11916 11982 "ABELSG-" 11987 NIL ABELSG- (NIL T) -8 NIL NIL NIL) (-23 11154 11501 11527 "ABELMON" 11697 T ABELMON (NIL) -9 NIL 11809 NIL) (-22 10794 10902 11040 "ABELMON-" 11045 NIL ABELMON- (NIL T) -8 NIL NIL NIL) (-21 10044 10500 10526 "ABELGRP" 10598 T ABELGRP (NIL) -9 NIL 10673 NIL) (-20 9471 9636 9852 "ABELGRP-" 9857 NIL ABELGRP- (NIL T) -8 NIL NIL NIL) (-19 4579 8733 8772 "A1AGG" 8777 NIL A1AGG (NIL T) -9 NIL 8817 NIL) (-18 30 1497 3059 "A1AGG-" 3064 NIL A1AGG- (NIL T T) -8 NIL NIL NIL))
\ No newline at end of file diff --git a/src/share/algebra/operation.daase b/src/share/algebra/operation.daase index aa9949d1..49a6b1cf 100644 --- a/src/share/algebra/operation.daase +++ b/src/share/algebra/operation.daase @@ -1,52 +1,51 @@ -(733417 . 3508949900) -(((*1 *2 *1) - (-12 (-4 *1 (-1136 *3 *4 *5 *6 *7)) (-4 *3 (-1133)) (-4 *4 (-1133)) - (-4 *5 (-1133)) (-4 *6 (-1133)) (-4 *7 (-1133)) (-5 *2 (-114))))) -(((*1 *2 *1) (-12 (-5 *2 (-1305)) (-5 *1 (-847))))) -(((*1 *2 *2 *3) - (-12 (-5 *3 (-1209)) (-4 *4 (-466)) (-4 *4 (-1133)) - (-5 *1 (-587 *4 *2)) (-4 *2 (-296)) (-4 *2 (-435 *4))))) -(((*1 *2 *3 *4 *4) - (-12 (-5 *4 (-793)) (-4 *5 (-363)) (-4 *6 (-1275 *5)) +(733417 . 3508956486) +(((*1 *2 *1) (-12 (-4 *1 (-1318 *3)) (-4 *3 (-376)) (-5 *2 (-114))))) +(((*1 *1 *2) (-12 (-5 *2 (-560)) (-5 *1 (-888))))) +(((*1 *2 *3 *4 *5 *5 *5 *5 *6 *4 *4 *4 *4 *4 *5 *4 *5 *5 *4) + (-12 (-5 *3 (-1191)) (-5 *4 (-560)) (-5 *5 (-711 (-229))) + (-5 *6 (-229)) (-5 *2 (-1067)) (-5 *1 (-774))))) +(((*1 *2 *3 *4) + (-12 (-4 *5 (-376)) (-4 *5 (-571)) (-5 *2 - (-663 - (-2 (|:| -4149 (-711 *6)) (|:| |basisDen| *6) - (|:| |basisInv| (-711 *6))))) - (-5 *1 (-512 *5 *6 *7)) - (-5 *3 - (-2 (|:| -4149 (-711 *6)) (|:| |basisDen| *6) - (|:| |basisInv| (-711 *6)))) - (-4 *7 (-1275 *6))))) -(((*1 *2 *1) - (-12 (-4 *1 (-355 *3 *4 *5)) (-4 *3 (-1254)) (-4 *4 (-1275 *3)) - (-4 *5 (-1275 (-421 *4))) - (-5 *2 (-2 (|:| |num| (-1299 *4)) (|:| |den| *4)))))) -(((*1 *2 *2 *2) - (-12 (-4 *3 (-1081)) (-5 *1 (-1273 *3 *2)) (-4 *2 (-1275 *3))))) + (-2 (|:| |minor| (-663 (-949))) (|:| -1879 *3) + (|:| |minors| (-663 (-663 (-949)))) (|:| |ops| (-663 *3)))) + (-5 *1 (-90 *5 *3)) (-5 *4 (-949)) (-4 *3 (-680 *5))))) +(((*1 *2 *3) + (-12 (-4 *4 (-13 (-571) (-1070 (-560)))) (-4 *5 (-435 *4)) + (-5 *2 (-419 *3)) (-5 *1 (-449 *4 *5 *3)) (-4 *3 (-1275 *5))))) (((*1 *2) (-12 (-5 *2 (-856 (-560))) (-5 *1 (-548)))) ((*1 *1) (-12 (-5 *1 (-856 *2)) (-4 *2 (-1133))))) -(((*1 *2 *2) (-12 (-5 *2 (-949)) (-5 *1 (-369 *3)) (-4 *3 (-363))))) -(((*1 *1) (-5 *1 (-132)))) -(((*1 *2 *2 *2) - (-12 (-5 *2 (-663 *6)) (-4 *6 (-1097 *3 *4 *5)) (-4 *3 (-466)) - (-4 *3 (-571)) (-4 *4 (-817)) (-4 *5 (-872)) - (-5 *1 (-1009 *3 *4 *5 *6))))) -(((*1 *2 *3 *3 *3 *4 *5 *6) - (-12 (-5 *3 (-326 (-560))) (-5 *4 (-1 (-229) (-229))) - (-5 *5 (-1121 (-229))) (-5 *6 (-663 (-270))) (-5 *2 (-1165 (-229))) - (-5 *1 (-719))))) -(((*1 *2 *3 *4 *5) - (-12 (-5 *3 (-976 (-421 (-560)))) (-5 *4 (-1209)) - (-5 *5 (-1121 (-866 (-229)))) (-5 *2 (-663 (-229))) (-5 *1 (-313))))) -(((*1 *2 *1) - (-12 (-4 *1 (-1136 *3 *4 *5 *6 *7)) (-4 *3 (-1133)) (-4 *4 (-1133)) - (-4 *5 (-1133)) (-4 *6 (-1133)) (-4 *7 (-1133)) (-5 *2 (-114))))) +(((*1 *1 *2 *2 *1) (-12 (-5 *1 (-669 *2)) (-4 *2 (-1133))))) +(((*1 *2 *1 *1) + (-12 (-4 *1 (-1042 *3)) (-4 *3 (-1249)) (-4 *3 (-1133)) + (-5 *2 (-114))))) +(((*1 *2) + (-12 (-4 *1 (-355 *3 *4 *5)) (-4 *3 (-1254)) (-4 *4 (-1275 *3)) + (-4 *5 (-1275 (-421 *4))) (-5 *2 (-711 (-421 *4)))))) +(((*1 *1 *2) + (-12 (-5 *2 (-663 *6)) (-4 *6 (-980 *3 *4 *5)) (-4 *3 (-376)) + (-4 *4 (-817)) (-4 *5 (-872)) (-5 *1 (-518 *3 *4 *5 *6))))) +(((*1 *2) + (-12 (-4 *3 (-1081)) (-5 *2 (-988 (-734 *3 *4))) (-5 *1 (-734 *3 *4)) + (-4 *4 (-1275 *3))))) +(((*1 *2 *3) + (-12 (-5 *3 (-663 (-663 (-973 (-229))))) (-5 *2 (-663 (-229))) + (-5 *1 (-482))))) +(((*1 *2 *3) + (-12 (-5 *3 (-560)) (-4 *4 (-1275 (-421 *3))) (-5 *2 (-949)) + (-5 *1 (-943 *4 *5)) (-4 *5 (-1275 (-421 *4)))))) (((*1 *2 *3) (-12 (-5 *3 (-663 (-51))) (-5 *2 (-1305)) (-5 *1 (-884))))) -(((*1 *1 *1 *1) (-12 (-5 *1 (-609 *2)) (-4 *2 (-1081))))) -(((*1 *2 *3 *2) - (-12 (-5 *3 (-663 (-711 *4))) (-5 *2 (-711 *4)) (-4 *4 (-1081)) - (-5 *1 (-1062 *4))))) +(((*1 *2 *3 *1) + (-12 (|has| *1 (-6 -4510)) (-4 *1 (-618 *4 *3)) (-4 *4 (-1133)) + (-4 *3 (-1249)) (-4 *3 (-1133)) (-5 *2 (-114))))) +(((*1 *2 *2 *2) (-12 (-5 *2 (-229)) (-5 *1 (-230)))) + ((*1 *2 *2 *2) (-12 (-5 *2 (-171 (-229))) (-5 *1 (-230)))) + ((*1 *2 *2 *2) + (-12 (-4 *3 (-571)) (-5 *1 (-445 *3 *2)) (-4 *2 (-435 *3)))) + ((*1 *1 *1 *1) (-4 *1 (-1171)))) +(((*1 *2 *2) (-12 (-5 *2 (-391)) (-5 *1 (-1303)))) + ((*1 *2) (-12 (-5 *2 (-391)) (-5 *1 (-1303))))) (((*1 *2) (-12 (-4 *2 (-13 (-435 *3) (-1034))) (-5 *1 (-287 *3 *2)) (-4 *3 (-571)))) @@ -54,96 +53,97 @@ (-12 (-5 *1 (-352 *2 *3 *4)) (-14 *2 (-663 (-1209))) (-14 *3 (-663 (-1209))) (-4 *4 (-401)))) ((*1 *1) (-5 *1 (-491))) ((*1 *1) (-4 *1 (-1235)))) -(((*1 *2) - (-12 (-4 *4 (-175)) (-5 *2 (-793)) (-5 *1 (-167 *3 *4)) - (-4 *3 (-168 *4)))) - ((*1 *2) - (-12 (-14 *4 *2) (-4 *5 (-1249)) (-5 *2 (-793)) - (-5 *1 (-244 *3 *4 *5)) (-4 *3 (-245 *4 *5)))) - ((*1 *2) - (-12 (-4 *4 (-1133)) (-5 *2 (-793)) (-5 *1 (-434 *3 *4)) - (-4 *3 (-435 *4)))) - ((*1 *2) (-12 (-5 *2 (-793)) (-5 *1 (-558 *3)) (-4 *3 (-559)))) - ((*1 *2) (-12 (-4 *1 (-785)) (-5 *2 (-793)))) - ((*1 *2) - (-12 (-4 *4 (-175)) (-5 *2 (-793)) (-5 *1 (-819 *3 *4)) - (-4 *3 (-820 *4)))) - ((*1 *2) - (-12 (-4 *4 (-571)) (-5 *2 (-793)) (-5 *1 (-1022 *3 *4)) - (-4 *3 (-1023 *4)))) - ((*1 *2) - (-12 (-4 *4 (-175)) (-5 *2 (-793)) (-5 *1 (-1029 *3 *4)) - (-4 *3 (-1030 *4)))) - ((*1 *2) (-12 (-5 *2 (-793)) (-5 *1 (-1043 *3)) (-4 *3 (-1044)))) - ((*1 *2) (-12 (-4 *1 (-1081)) (-5 *2 (-793)))) - ((*1 *2) (-12 (-5 *2 (-793)) (-5 *1 (-1091 *3)) (-4 *3 (-1092))))) (((*1 *1 *2) (-12 (-5 *2 (-1191)) (-5 *1 (-270)))) ((*1 *2 *3 *2) (-12 (-5 *2 (-1191)) (-5 *3 (-663 (-270))) (-5 *1 (-271)))) ((*1 *2 *1 *3) (-12 (-5 *3 (-1191)) (-5 *2 (-1305)) (-5 *1 (-1302)))) ((*1 *2 *1 *3) (-12 (-5 *3 (-1191)) (-5 *2 (-1305)) (-5 *1 (-1303))))) -(((*1 *2 *3 *4 *5 *6 *7) - (-12 (-5 *3 (-1187 (-2 (|:| |k| (-560)) (|:| |c| *6)))) - (-5 *4 (-1058 (-866 (-560)))) (-5 *5 (-1209)) (-5 *7 (-421 (-560))) - (-4 *6 (-1081)) (-5 *2 (-888)) (-5 *1 (-609 *6))))) -(((*1 *2 *1) - (-12 (-5 *2 (-421 (-976 *3))) (-5 *1 (-467 *3 *4 *5 *6)) - (-4 *3 (-571)) (-4 *3 (-175)) (-14 *4 (-949)) - (-14 *5 (-663 (-1209))) (-14 *6 (-1299 (-711 *3)))))) -(((*1 *1 *1 *1) - (-12 (|has| *1 (-6 -4511)) (-4 *1 (-251 *2)) (-4 *2 (-1249))))) -(((*1 *1 *1 *2) - (-12 (-5 *2 (-973 *4)) (-4 *4 (-1081)) (-5 *1 (-1197 *3 *4)) - (-14 *3 (-949))))) -(((*1 *2 *3 *4 *4 *5 *4 *6 *4 *5) - (-12 (-5 *3 (-1191)) (-5 *5 (-711 (-229))) (-5 *6 (-711 (-560))) - (-5 *4 (-560)) (-5 *2 (-1067)) (-5 *1 (-779))))) -(((*1 *2 *3 *4 *4 *5 *6 *7) - (-12 (-5 *5 (-1209)) - (-5 *6 - (-1 - (-3 - (-2 (|:| |mainpart| *4) - (|:| |limitedlogs| - (-663 (-2 (|:| |coeff| *4) (|:| |logand| *4))))) - "failed") - *4 (-663 *4))) - (-5 *7 - (-1 (-3 (-2 (|:| -3122 *4) (|:| |coeff| *4)) "failed") *4 *4)) - (-4 *4 (-13 (-1235) (-27) (-435 *8))) - (-4 *8 (-13 (-466) (-149) (-1070 *3) (-660 *3))) (-5 *3 (-560)) - (-5 *2 (-2 (|:| |ans| *4) (|:| -1477 *4) (|:| |sol?| (-114)))) - (-5 *1 (-1045 *8 *4))))) -(((*1 *2 *3 *4) - (-12 (-5 *3 (-3 (-421 (-976 *5)) (-1198 (-1209) (-976 *5)))) - (-4 *5 (-466)) (-5 *2 (-663 (-711 (-421 (-976 *5))))) - (-5 *1 (-304 *5)) (-5 *4 (-711 (-421 (-976 *5))))))) -(((*1 *2 *1) - (-12 (-5 *2 (-713 (-898 (-996 *3) (-996 *3)))) (-5 *1 (-996 *3)) - (-4 *3 (-1133))))) -(((*1 *2 *1) (-12 (-4 *1 (-310)) (-5 *2 (-663 (-115)))))) -(((*1 *2 *2) - (-12 (-5 *2 (-1187 *3)) (-4 *3 (-1081)) (-5 *1 (-1193 *3)))) - ((*1 *1 *1) - (-12 (-5 *1 (-1289 *2 *3 *4)) (-4 *2 (-1081)) (-14 *3 (-1209)) - (-14 *4 *2)))) -(((*1 *2 *2) - (-12 (-4 *3 (-466)) (-5 *1 (-1241 *3 *2)) - (-4 *2 (-13 (-435 *3) (-1235)))))) -(((*1 *2 *2) (-12 (-5 *2 (-114)) (-5 *1 (-1067))))) +(((*1 *2 *1 *3) + (-12 (-4 *1 (-934 *3)) (-4 *3 (-1133)) (-5 *2 (-1129 *3)))) + ((*1 *2 *1 *3) + (-12 (-4 *4 (-1133)) (-5 *2 (-1129 (-663 *4))) (-5 *1 (-935 *4)) + (-5 *3 (-663 *4)))) + ((*1 *2 *1 *3) + (-12 (-4 *4 (-1133)) (-5 *2 (-1129 (-1129 *4))) (-5 *1 (-935 *4)) + (-5 *3 (-1129 *4)))) + ((*1 *2 *1 *3) + (-12 (-5 *2 (-1129 *3)) (-5 *1 (-935 *3)) (-4 *3 (-1133))))) +(((*1 *2 *3) + (-12 (-5 *2 (-114)) (-5 *1 (-456 *3)) (-4 *3 (-1275 (-560)))))) +(((*1 *2) + (-12 (-4 *4 (-175)) (-5 *2 (-114)) (-5 *1 (-379 *3 *4)) + (-4 *3 (-380 *4)))) + ((*1 *2) (-12 (-4 *1 (-380 *3)) (-4 *3 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*2 (-1245 (-957))) (-5 *1 (-330))))) +(((*1 *2 *3 *1) + (-12 (-4 *4 (-466)) (-4 *5 (-817)) (-4 *6 (-872)) + (-4 *3 (-1097 *4 *5 *6)) (-5 *2 (-663 *1)) + (-4 *1 (-1103 *4 *5 *6 *3))))) +(((*1 *1 *2) (-12 (-5 *2 (-114)) (-5 *1 (-270)))) + ((*1 *2 *3 *2) + (-12 (-5 *2 (-114)) (-5 *3 (-663 (-270))) (-5 *1 (-271))))) +(((*1 *2 *2 *1) + (-12 (-5 *2 (-1324 *3 *4)) (-4 *1 (-387 *3 *4)) (-4 *3 (-872)) + (-4 *4 (-175)))) + ((*1 *1 *1 *1) (|partial| -12 (-4 *1 (-399 *2)) (-4 *2 (-1133)))) + ((*1 *1 *1 *2) (|partial| -12 (-5 *1 (-843 *2)) (-4 *2 (-872)))) + ((*1 *1 *1 *1) + (-12 (-4 *1 (-1319 *2 *3)) (-4 *2 (-872)) (-4 *3 (-1081)))) + ((*1 *1 *1 *2) + (-12 (-5 *2 (-843 *3)) (-4 *1 (-1319 *3 *4)) (-4 *3 (-872)) + (-4 *4 (-1081)))) + ((*1 *1 *1 *2) + (-12 (-4 *1 (-1319 *2 *3)) (-4 *2 (-872)) (-4 *3 (-1081))))) (((*1 *2 *1) - (-12 (-4 *2 (-1133)) (-5 *1 (-994 *3 *2)) (-4 *3 (-1133))))) -(((*1 *2) (-12 (-5 *2 (-663 (-949))) (-5 *1 (-1304)))) - ((*1 *2 *2) (-12 (-5 *2 (-663 (-949))) (-5 *1 (-1304))))) 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*2 *2) - (-12 (-4 *3 (-13 (-571) (-1070 (-560)))) (-5 *1 (-191 *3 *2)) - (-4 *2 (-13 (-27) (-1235) (-435 (-171 *3)))))) - ((*1 *2 *2) - (-12 (-4 *3 (-13 (-466) (-1070 (-560)) (-660 (-560)))) - (-5 *1 (-1239 *3 *2)) (-4 *2 (-13 (-27) (-1235) (-435 *3)))))) -(((*1 *1 *1) - (|partial| -12 (-5 *1 (-305 *2)) (-4 *2 (-748)) (-4 *2 (-1249))))) (((*1 *2 *2) (-12 (-4 *3 (-571)) (-5 *1 (-287 *3 *2)) (-4 *2 (-13 (-435 *3) (-1034)))))) -(((*1 *2 *1) (-12 (-5 *2 (-793)) (-5 *1 (-932 *3)) (-4 *3 (-1133))))) -(((*1 *2 *1) (-12 (-5 *2 (-114)) (-5 *1 (-146))))) -(((*1 *1 *2 *1) (-12 (-4 *1 (-107 *2)) (-4 *2 (-1249)))) - ((*1 *1 *2 *1) (-12 (-5 *1 (-123 *2)) (-4 *2 (-872)))) - ((*1 *1 *2 *1) (-12 (-5 *1 (-128 *2)) (-4 *2 (-872)))) - ((*1 *1 *1 *1 *2) - (-12 (-5 *2 (-560)) (-4 *1 (-294 *3)) (-4 *3 (-1249)))) - ((*1 *1 *2 *1 *3) - (-12 (-5 *3 (-560)) (-4 *1 (-294 *2)) (-4 *2 (-1249)))) - ((*1 *1 *2) - (-12 - (-5 *2 - (-2 - (|:| -3837 - (-2 (|:| |var| (-1209)) (|:| |fn| (-326 (-229))) - (|:| -4389 (-1121 (-866 (-229)))) (|:| |abserr| (-229)) - (|:| |relerr| (-229)))) - (|:| -2715 - (-2 - (|:| |endPointContinuity| - (-3 (|:| |continuous| "Continuous at the end points") - (|:| |lowerSingular| - "There is a singularity at the lower end point") - (|:| |upperSingular| - "There is a singularity at the upper end point") - (|:| |bothSingular| - "There are singularities at both end points") - (|:| |notEvaluated| - "End point continuity not yet evaluated"))) - (|:| |singularitiesStream| - (-3 (|:| |str| (-1187 (-229))) - (|:| |notEvaluated| - "Internal singularities not yet evaluated"))) - (|:| -4389 - (-3 (|:| |finite| "The range is finite") - (|:| |lowerInfinite| - "The bottom of range is infinite") - (|:| |upperInfinite| "The top of range is infinite") - (|:| |bothInfinite| - "Both top and bottom points are infinite") - (|:| |notEvaluated| "Range not yet evaluated"))))))) - (-5 *1 (-574)))) - ((*1 *1 *2 *1 *3) - (-12 (-5 *3 (-793)) (-4 *1 (-717 *2)) (-4 *2 (-1133)))) - ((*1 *1 *2) - (-12 - (-5 *2 - (-2 - (|:| -3837 - (-2 (|:| |xinit| (-229)) (|:| |xend| (-229)) - (|:| |fn| (-1299 (-326 (-229)))) (|:| |yinit| (-663 (-229))) - (|:| |intvals| (-663 (-229))) (|:| |g| (-326 (-229))) - (|:| |abserr| (-229)) (|:| |relerr| (-229)))) - (|:| -2715 - (-2 (|:| |stiffness| (-391)) (|:| |stability| (-391)) - (|:| |expense| (-391)) (|:| |accuracy| (-391)) - (|:| |intermediateResults| (-391)))))) - (-5 *1 (-827)))) - ((*1 *2 *3 *4) - (-12 (-5 *2 (-1305)) (-5 *1 (-1227 *3 *4)) (-4 *3 (-1133)) - (-4 *4 (-1133))))) -(((*1 *1 *1) (-12 (-4 *1 (-696 *2)) (-4 *2 (-1249))))) +(((*1 *2) (-12 (-4 *1 (-1076 *2)) (-4 *2 (-23))))) +(((*1 *2 *3 *4 *3) + (|partial| -12 (-5 *4 (-1 *6 *6)) (-4 *6 (-1275 *5)) (-4 *5 (-376)) + (-5 *2 (-2 (|:| -1391 (-421 *6)) (|:| |coeff| (-421 *6)))) + (-5 *1 (-588 *5 *6)) (-5 *3 (-421 *6))))) (((*1 *1 *1) (-12 (-5 *1 (-699 *2)) (-4 *2 (-872)))) ((*1 *1 *1) (-12 (-5 *1 (-843 *2)) (-4 *2 (-872)))) ((*1 *1 *1) (-12 (-5 *1 (-919 *2)) (-4 *2 (-872)))) @@ -3393,29 +2986,20 @@ ((*1 *1 *1 *2) (-12 (-5 *2 (-793)) (-4 *1 (-1288 *3)) (-4 *3 (-1249)))) ((*1 *1 *1) (-12 (-4 *1 (-1288 *2)) (-4 *2 (-1249))))) +(((*1 *2 *3 *3 *3 *3 *4 *3 *5 *5 *5 *3) + (-12 (-5 *3 (-560)) (-5 *5 (-711 (-229))) (-5 *4 (-229)) + (-5 *2 (-1067)) (-5 *1 (-772))))) (((*1 *2 *3) - (-12 (-4 *4 (-13 (-376) (-10 -8 (-15 ** ($ $ (-421 (-560))))))) - (-5 *2 (-663 *4)) (-5 *1 (-1160 *3 *4)) (-4 *3 (-1275 *4)))) - ((*1 *2 *3 *3 *3 *3) - (-12 (-4 *3 (-13 (-376) (-10 -8 (-15 ** ($ $ (-421 (-560))))))) - (-5 *2 (-663 *3)) (-5 *1 (-1160 *4 *3)) (-4 *4 (-1275 *3))))) -(((*1 *2 *1) (-12 (-5 *2 (-713 *1)) (-4 *1 (-1184))))) -(((*1 *2) - (-12 (-4 *3 (-466)) (-4 *4 (-817)) (-4 *5 (-872)) - (-4 *6 (-1097 *3 *4 *5)) (-5 *2 (-1305)) - (-5 *1 (-1104 *3 *4 *5 *6 *7)) (-4 *7 (-1103 *3 *4 *5 *6)))) - ((*1 *2) - (-12 (-4 *3 (-466)) (-4 *4 (-817)) (-4 *5 (-872)) - (-4 *6 (-1097 *3 *4 *5)) (-5 *2 (-1305)) - (-5 *1 (-1140 *3 *4 *5 *6 *7)) (-4 *7 (-1103 *3 *4 *5 *6))))) -(((*1 *2 *2 *3) - (-12 (-4 *3 (-376)) (-5 *1 (-1057 *3 *2)) (-4 *2 (-680 *3)))) - ((*1 *2 *3 *4) - (-12 (-4 *5 (-376)) (-5 *2 (-2 (|:| -1879 *3) (|:| -3027 (-663 *5)))) - (-5 *1 (-1057 *5 *3)) (-5 *4 (-663 *5)) (-4 *3 (-680 *5))))) -(((*1 *2 *3) - (-12 (-5 *3 (-663 (-560))) (-5 *2 (-935 (-560))) (-5 *1 (-947)))) - ((*1 *2) (-12 (-5 *2 (-935 (-560))) (-5 *1 (-947))))) + (-12 (-5 *3 (-949)) (-5 *2 (-1211 (-421 (-560)))) (-5 *1 (-193)))) + ((*1 *2 *1) + (-12 (-5 *2 (-1299 (-3 (-482) "undefined"))) (-5 *1 (-1302))))) +(((*1 *2 *1) (-12 (-5 *2 (-1305)) (-5 *1 (-847))))) +(((*1 *2 *1) (-12 (-5 *2 (-114)) (-5 *1 (-1214))))) +(((*1 *1 *1 *2) + (-12 (-5 *2 (-1 *4 *4)) (-4 *4 (-670 *3)) (-4 *3 (-1081)) + (-5 *1 (-736 *3 *4)))) + ((*1 *1 *1 *2) + (-12 (-5 *2 (-1 *3 *3)) (-4 *3 (-1081)) (-5 *1 (-858 *3))))) (((*1 *2 *2 *3) (-12 (-5 *2 (-916 *4)) (-5 *3 (-1 (-114) *5)) (-4 *4 (-1133)) (-4 *5 (-1249)) (-5 *1 (-917 *4 *5)))) @@ -3443,14 +3027,22 @@ (-4 *6 (-13 (-435 *5) (-912 *4) (-633 (-916 *4)))) (-4 *4 (-1133)) (-4 *5 (-13 (-1081) (-912 *4) (-633 (-916 *4)))) (-5 *1 (-1107 *4 *5 *6))))) -(((*1 *1 *2) (-12 (-5 *2 (-391)) (-5 *1 (-270)))) - ((*1 *2 *3 *2) - (-12 (-5 *2 (-391)) (-5 *3 (-663 (-270))) (-5 *1 (-271))))) -(((*1 *2 *2) - (-12 (-4 *3 (-466)) (-5 *1 (-1241 *3 *2)) - (-4 *2 (-13 (-435 *3) (-1235)))))) -(((*1 *2 *3) - (-12 (-5 *3 (-1167)) (-5 *2 (-713 (-292))) (-5 *1 (-170))))) +(((*1 *2 *3 *4 *4 *4 *4 *5 *5 *4) + (-12 (-5 *3 (-1191)) (-5 *4 (-560)) (-5 *5 (-711 (-171 (-229)))) + (-5 *2 (-1067)) (-5 *1 (-776))))) +(((*1 *2 *3 *3 *4 *5 *5 *5 *3) + (-12 (-5 *3 (-560)) (-5 *4 (-1191)) (-5 *5 (-711 (-229))) + (-5 *2 (-1067)) (-5 *1 (-769))))) +(((*1 *2 *3 *4 *4 *3 *5) + (-12 (-5 *4 (-630 *3)) (-5 *5 (-1203 *3)) + (-4 *3 (-13 (-435 *6) (-27) (-1235))) + (-4 *6 (-13 (-466) (-1070 (-560)) (-149) (-660 (-560)))) + (-5 *2 (-597 *3)) (-5 *1 (-575 *6 *3 *7)) (-4 *7 (-1133)))) + ((*1 *2 *3 *4 *4 *4 *3 *5) + (-12 (-5 *4 (-630 *3)) (-5 *5 (-421 (-1203 *3))) + (-4 *3 (-13 (-435 *6) (-27) (-1235))) + (-4 *6 (-13 (-466) (-1070 (-560)) (-149) (-660 (-560)))) + (-5 *2 (-597 *3)) (-5 *1 (-575 *6 *3 *7)) (-4 *7 (-1133))))) (((*1 *2 *3 *4) (-12 (-5 *4 (-793)) (-5 *2 (-663 (-1209))) (-5 *1 (-213)) (-5 *3 (-1209)))) @@ -3470,34 +3062,6 @@ ((*1 *2 *1) (-12 (-4 *1 (-1319 *3 *4)) (-4 *3 (-872)) (-4 *4 (-1081)) (-5 *2 (-663 *3))))) -(((*1 *2 *3 *4 *5) - (-12 (-5 *5 (-793)) (-4 *6 (-466)) (-4 *7 (-817)) (-4 *8 (-872)) - (-4 *3 (-1097 *6 *7 *8)) - (-5 *2 - (-2 (|:| |done| (-663 *4)) - (|:| |todo| (-663 (-2 (|:| |val| (-663 *3)) (|:| -3265 *4)))))) - (-5 *1 (-1101 *6 *7 *8 *3 *4)) (-4 *4 (-1103 *6 *7 *8 *3)))) - ((*1 *2 *3 *4) - (-12 (-4 *5 (-466)) (-4 *6 (-817)) (-4 *7 (-872)) - (-4 *3 (-1097 *5 *6 *7)) - (-5 *2 - (-2 (|:| |done| (-663 *4)) - (|:| |todo| (-663 (-2 (|:| |val| (-663 *3)) (|:| -3265 *4)))))) - (-5 *1 (-1101 *5 *6 *7 *3 *4)) (-4 *4 (-1103 *5 *6 *7 *3)))) - ((*1 *2 *3 *4 *5) - (-12 (-5 *5 (-793)) (-4 *6 (-466)) (-4 *7 (-817)) (-4 *8 (-872)) - (-4 *3 (-1097 *6 *7 *8)) - (-5 *2 - (-2 (|:| |done| (-663 *4)) - (|:| |todo| (-663 (-2 (|:| |val| (-663 *3)) (|:| -3265 *4)))))) - (-5 *1 (-1177 *6 *7 *8 *3 *4)) (-4 *4 (-1141 *6 *7 *8 *3)))) - ((*1 *2 *3 *4) - (-12 (-4 *5 (-466)) (-4 *6 (-817)) (-4 *7 (-872)) - (-4 *3 (-1097 *5 *6 *7)) - (-5 *2 - (-2 (|:| |done| (-663 *4)) - (|:| |todo| (-663 (-2 (|:| |val| (-663 *3)) (|:| -3265 *4)))))) - (-5 *1 (-1177 *5 *6 *7 *3 *4)) (-4 *4 (-1141 *5 *6 *7 *3))))) (((*1 *2 *1) (-12 (-5 *2 (-793)) (-5 *1 (-137 *3 *4 *5)) (-14 *3 (-560)) (-14 *4 *2) (-4 *5 (-175)))) @@ -3543,48 +3107,56 @@ ((*1 *1 *1 *2) (-12 (-5 *2 (-793)) (-4 *1 (-1288 *3)) (-4 *3 (-1249)))) ((*1 *2 *1) (-12 (-4 *1 (-1288 *2)) (-4 *2 (-1249))))) -(((*1 *2 *1 *1 *3 *4) - (-12 (-5 *3 (-1 (-114) *5 *5)) (-5 *4 (-1 (-114) *6 *6)) - (-4 *5 (-13 (-1133) (-34))) (-4 *6 (-13 (-1133) (-34))) - (-5 *2 (-114)) (-5 *1 (-1172 *5 *6))))) -(((*1 *1 *1 *2 *2) - (-12 (-5 *2 (-560)) (-4 *1 (-708 *3 *4 *5)) (-4 *3 (-1081)) - (-4 *4 (-385 *3)) (-4 *5 (-385 *3))))) -(((*1 *2 *2) (-12 (-5 *2 (-560)) (-5 *1 (-576))))) +(((*1 *2 *3) + (-12 (-5 *3 (-1191)) (-5 *2 (-663 (-1214))) (-5 *1 (-906))))) +(((*1 *1) + (-12 (-5 *1 (-671 *2 *3 *4)) (-4 *2 (-1133)) (-4 *3 (-23)) + (-14 *4 *3)))) +(((*1 *2 *3) + (-12 (-4 *1 (-355 *4 *3 *5)) (-4 *4 (-1254)) (-4 *3 (-1275 *4)) + (-4 *5 (-1275 (-421 *3))) (-5 *2 (-114)))) + ((*1 *2 *3) + (-12 (-4 *1 (-355 *3 *4 *5)) (-4 *3 (-1254)) (-4 *4 (-1275 *3)) + (-4 *5 (-1275 (-421 *4))) (-5 *2 (-114))))) +(((*1 *2 *2 *1) (-12 (-4 *1 (-263 *2)) (-4 *2 (-1249))))) (((*1 *2 *3) (-12 (-5 *3 (-1 (-1187 *4) (-1187 *4))) (-5 *2 (-1187 *4)) (-5 *1 (-1326 *4)) (-4 *4 (-1249)))) ((*1 *2 *3 *4) (-12 (-5 *3 (-1 (-663 (-1187 *5)) (-663 (-1187 *5)))) (-5 *4 (-560)) (-5 *2 (-663 (-1187 *5))) (-5 *1 (-1326 *5)) (-4 *5 (-1249))))) -(((*1 *2 *3 *4 *4 *4 *4 *5 *5) - (-12 (-5 *3 (-1 (-391) (-391))) (-5 *4 (-391)) - (-5 *2 - (-2 (|:| -3950 *4) (|:| -2726 *4) (|:| |totalpts| (-560)) - (|:| |success| (-114)))) - (-5 *1 (-811)) (-5 *5 (-560))))) -(((*1 *2 *1) (-12 (-4 *1 (-860 *3)) (-4 *3 (-1133)) (-5 *2 (-55))))) -(((*1 *2 *1) - (-12 (-5 *2 (-114)) (-5 *1 (-50 *3 *4)) (-4 *3 (-1081)) - (-14 *4 (-663 (-1209))))) - ((*1 *2 *1) - (-12 (-5 *2 (-114)) (-5 *1 (-227 *3 *4)) (-4 *3 (-13 (-1081) (-872))) - (-14 *4 (-663 (-1209)))))) -(((*1 *2 *1 *2) (-12 (-5 *2 (-114)) (-5 *1 (-174))))) -(((*1 *2 *2) - (-12 +(((*1 *2 *3 *4) + (-12 (-5 *3 (-1 *6 *4 *5)) (-4 *4 (-1133)) (-4 *5 (-1133)) + (-4 *6 (-1133)) (-5 *2 (-1 *6 *5)) (-5 *1 (-706 *4 *5 *6))))) +(((*1 *2 *2 *2 *3) + (-12 (-5 *3 (-793)) (-4 *4 (-13 (-1081) (-739 (-421 (-560))))) + (-4 *5 (-872)) (-5 *1 (-1316 *4 *5 *2)) (-4 *2 (-1322 *5 *4))))) +(((*1 *2 *3 *4 *5) + (-12 (-5 *3 (-711 *6)) (-5 *5 (-1 (-419 (-1203 *6)) (-1203 *6))) + (-4 *6 (-376)) (-5 *2 - (-2 (|:| |flg| (-3 "nil" "sqfr" "irred" "prime")) (|:| |fctr| *4) - (|:| |xpnt| (-560)))) - (-4 *4 (-13 (-1275 *3) (-571) (-10 -8 (-15 -2522 ($ $ $))))) - (-4 *3 (-571)) (-5 *1 (-1279 *3 *4))))) -(((*1 *1 *2) (-12 (-5 *2 (-1191)) (-5 *1 (-543)))) - ((*1 *1 *2) (-12 (-5 *2 (-402)) (-5 *1 (-543))))) -(((*1 *2 *3 *3) (-12 (-5 *3 (-1191)) (-5 *2 (-114)) (-5 *1 (-853))))) -(((*1 *2 *3) - (-12 (-5 *3 (-663 *2)) (-4 *2 (-435 *4)) (-5 *1 (-160 *4 *2)) - (-4 *4 (-571))))) -(((*1 *1 *1 *1) (-5 *1 (-888)))) + (-663 + (-2 (|:| |outval| *7) (|:| |outmult| (-560)) + (|:| |outvect| (-663 (-711 *7)))))) + (-5 *1 (-546 *6 *7 *4)) (-4 *7 (-376)) (-4 *4 (-13 (-376) (-871)))))) +(((*1 *2 *3 *2 *4) + (-12 (-5 *3 (-115)) (-5 *4 (-793)) + (-4 *5 (-13 (-466) (-1070 (-560)))) (-4 *5 (-571)) + (-5 *1 (-41 *5 *2)) (-4 *2 (-435 *5)) + (-4 *2 + (-13 (-376) (-310) + (-10 -8 (-15 -4445 ((-1157 *5 (-630 $)) $)) + (-15 -4454 ((-1157 *5 (-630 $)) $)) + (-15 -2590 ($ (-1157 *5 (-630 $)))))))))) +(((*1 *1 *1 *2) + (-12 (-4 *1 (-1008 *3 *4 *2 *5)) (-4 *3 (-1081)) (-4 *4 (-817)) + (-4 *2 (-872)) (-4 *5 (-1097 *3 *4 *2))))) +(((*1 *1 *2) (-12 (-5 *2 (-663 *3)) (-4 *3 (-872)) (-5 *1 (-498 *3))))) +(((*1 *1 *1) + (-12 (-5 *1 (-609 *2)) (-4 *2 (-38 (-421 (-560)))) (-4 *2 (-1081))))) +(((*1 *2 *2 *3 *2) + 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(-1209))))) + ((*1 *2 *3 *4) + (-12 (-5 *4 (-663 (-711 *5))) (-5 *3 (-711 *5)) (-4 *5 (-376)) + (-5 *2 (-1299 *5)) (-5 *1 (-1118 *5))))) +(((*1 *2 *1) + (-12 (-4 *3 (-1249)) (-5 *2 (-663 *1)) (-4 *1 (-1042 *3))))) +(((*1 *2 *1 *3 *3) + (-12 (-5 *3 (-949)) (-5 *2 (-1305)) (-5 *1 (-1302)))) + ((*1 *2 *1 *3 *3) + (-12 (-5 *3 (-949)) (-5 *2 (-1305)) (-5 *1 (-1303))))) +(((*1 *2 *3) + (-12 (-4 *4 (-363)) (-5 *2 (-114)) (-5 *1 (-220 *4 *3)) + (-4 *3 (-1275 *4))))) (((*1 *1 *1) (-4 *1 (-35))) ((*1 *2 *2) (-12 (-4 *3 (-571)) (-5 *1 (-287 *3 *2)) @@ -4036,29 +3606,28 @@ ((*1 *2 *2) (-12 (-5 *2 (-1187 *3)) (-4 *3 (-38 (-421 (-560)))) (-5 *1 (-1195 *3))))) -(((*1 *1 *1 *2) (-12 (-5 *2 (-1209)) (-5 *1 (-1095))))) -(((*1 *2 *1) - (-12 (-4 *3 (-376)) (-4 *4 (-817)) (-4 *5 (-872)) (-5 *2 (-114)) - (-5 *1 (-518 *3 *4 *5 *6)) (-4 *6 (-980 *3 *4 *5))))) +(((*1 *2 *3 *4) + (-12 (-5 *3 (-663 *6)) (-5 *4 (-663 (-1187 *7))) (-4 *6 (-872)) + (-4 *7 (-980 *5 (-545 *6) *6)) (-4 *5 (-1081)) + (-5 *2 (-1 (-1187 *7) *7)) (-5 *1 (-1158 *5 *6 *7))))) +(((*1 *1 *2) (-12 (-5 *2 (-1191)) (-5 *1 (-593))))) (((*1 *2 *3 *4) (-12 (-5 *2 (-2 (|:| |part1| *3) (|:| |part2| *4))) (-5 *1 (-727 *3 *4)) (-4 *3 (-1249)) (-4 *4 (-1249))))) -(((*1 *2 *3 *4) - (-12 (-5 *3 (-663 *8)) (-5 *4 (-663 *7)) (-4 *7 (-872)) - (-4 *8 (-980 *5 *6 *7)) (-4 *5 (-571)) (-4 *6 (-817)) +(((*1 *2 *3 *3) + (-12 (-4 *4 (-13 (-319) (-149))) (-4 *5 (-13 (-872) (-633 (-1209)))) + (-4 *6 (-817)) (-4 *7 (-980 *4 *6 *5)) (-5 *2 - (-2 (|:| |particular| (-3 (-1299 (-421 *8)) "failed")) - (|:| -4149 (-663 (-1299 (-421 *8)))))) - (-5 *1 (-691 *5 *6 *7 *8))))) -(((*1 *2 *2) - (-12 (-4 *3 (-466)) (-4 *4 (-817)) (-4 *5 (-872)) - (-4 *6 (-1097 *3 *4 *5)) (-5 *1 (-643 *3 *4 *5 *6 *7 *2)) - (-4 *7 (-1103 *3 *4 *5 *6)) (-4 *2 (-1141 *3 *4 *5 *6))))) -(((*1 *2 *3) - (-12 (-4 *4 (-571)) (-4 *2 (-13 (-435 (-171 *4)) (-1034) (-1235))) - (-5 *1 (-614 *4 *3 *2)) (-4 *3 (-13 (-435 *4) (-1034) (-1235)))))) -(((*1 *2) (-12 (-5 *2 (-560)) (-5 *1 (-955))))) -(((*1 *2) (-12 (-5 *2 (-1305)) (-5 *1 (-459 *3)) (-4 *3 (-1081))))) + (-2 (|:| |sysok| (-114)) (|:| |z0| (-663 *7)) (|:| |n0| (-663 *7)))) + (-5 *1 (-954 *4 *5 *6 *7)) (-5 *3 (-663 *7))))) +(((*1 *2 *3 *3 *3 *3 *3 *3 *4 *4 *4 *4 *5 *3 *3 *4 *3) + (-12 (-5 *3 (-560)) (-5 *4 (-711 (-229))) (-5 *5 (-114)) + (-5 *2 (-1067)) (-5 *1 (-775))))) +(((*1 *2 *1) (-12 (-4 *1 (-380 *2)) (-4 *2 (-175))))) +(((*1 *2 *1) + (-12 (-5 *2 (-888)) (-5 *1 (-404 *3 *4 *5)) (-14 *3 (-793)) + (-14 *4 (-793)) (-4 *5 (-175))))) +(((*1 *2 *2) (-12 (-5 *2 (-326 (-229))) (-5 *1 (-278))))) (((*1 *1 *1) (-4 *1 (-35))) ((*1 *2 *2) (-12 (-4 *3 (-571)) (-5 *1 (-287 *3 *2)) @@ -4075,31 +3644,44 @@ ((*1 *2 *2) (-12 (-5 *2 (-1187 *3)) (-4 *3 (-38 (-421 (-560)))) (-5 *1 (-1195 *3))))) -(((*1 *1 *1) (-4 *1 (-1176)))) -(((*1 *2 *1) (-12 (-5 *2 (-1209)) (-5 *1 (-847))))) -(((*1 *2 *3 *4 *5) - (-12 (-5 *4 (-229)) (-5 *5 (-560)) (-5 *2 (-1245 *3)) - (-5 *1 (-812 *3)) (-4 *3 (-1006)))) - ((*1 *1 *2 *3 *4) - (-12 (-5 *3 (-663 (-663 (-973 (-229))))) (-5 *4 (-114)) - (-5 *1 (-1245 *2)) (-4 *2 (-1006))))) -(((*1 *2 *1) (-12 (-5 *2 (-114)) (-5 *1 (-146))))) -(((*1 *1 *1) - (-12 (-5 *1 (-609 *2)) (-4 *2 (-38 (-421 (-560)))) (-4 *2 (-1081))))) -(((*1 *2 *1) - (-12 (|has| *1 (-6 -4510)) (-4 *1 (-503 *3)) (-4 *3 (-1249)) - (-5 *2 (-663 *3)))) - ((*1 *2 *1) (-12 (-5 *2 (-663 *3)) (-5 *1 (-758 *3)) (-4 *3 (-1133)))) - ((*1 *2 *1) (-12 (-5 *2 (-663 (-453))) (-5 *1 (-890))))) -(((*1 *2 *3 *4 *4 *5) - (-12 (-5 *4 (-630 *3)) (-5 *5 (-1 (-1203 *3) (-1203 *3))) - (-4 *3 (-13 (-27) (-435 *6))) (-4 *6 (-571)) (-5 *2 (-597 *3)) - (-5 *1 (-566 *6 *3))))) -(((*1 *1 *1) (-12 (-4 *1 (-1288 *2)) (-4 *2 (-1249))))) (((*1 *2 *3) - (-12 (-5 *3 (-663 (-2 (|:| -3430 (-1203 *6)) (|:| -2790 (-560))))) - (-4 *6 (-319)) (-4 *4 (-817)) (-4 *5 (-872)) (-5 *2 (-560)) - (-5 *1 (-764 *4 *5 *6 *7)) (-4 *7 (-980 *6 *4 *5))))) + (-12 (-5 *3 (-677 (-421 *2))) (-4 *2 (-1275 *4)) (-5 *1 (-834 *4 *2)) + (-4 *4 (-13 (-376) (-149) (-1070 (-560)) (-1070 (-421 (-560))))))) + ((*1 *2 *3) + (-12 (-5 *3 (-678 *2 (-421 *2))) (-4 *2 (-1275 *4)) + (-5 *1 (-834 *4 *2)) + (-4 *4 (-13 (-376) (-149) (-1070 (-560)) (-1070 (-421 (-560)))))))) +(((*1 *2 *3 *4 *4 *3 *3 *5) + (|partial| -12 (-5 *4 (-630 *3)) (-5 *5 (-1203 *3)) + (-4 *3 (-13 (-435 *6) (-27) (-1235))) + (-4 *6 (-13 (-466) (-1070 (-560)) (-149) (-660 (-560)))) + (-5 *2 (-2 (|:| -1391 *3) (|:| |coeff| *3))) + (-5 *1 (-575 *6 *3 *7)) (-4 *7 (-1133)))) + ((*1 *2 *3 *4 *4 *3 *4 *3 *5) + (|partial| -12 (-5 *4 (-630 *3)) (-5 *5 (-421 (-1203 *3))) + (-4 *3 (-13 (-435 *6) (-27) (-1235))) + (-4 *6 (-13 (-466) (-1070 (-560)) (-149) (-660 (-560)))) + (-5 *2 (-2 (|:| -1391 *3) (|:| |coeff| *3))) + (-5 *1 (-575 *6 *3 *7)) (-4 *7 (-1133))))) +(((*1 *2 *3 *4) + (-12 (-5 *3 (-229)) (-5 *4 (-560)) (-5 *2 (-1067)) (-5 *1 (-780))))) +(((*1 *1 *1) (-12 (-4 *1 (-263 *2)) (-4 *2 (-1249)))) + ((*1 *1 *1) + (-12 (|has| *1 (-6 -4511)) (-4 *1 (-385 *2)) (-4 *2 (-1249)))) + ((*1 *1 *1) + (-12 (-5 *1 (-671 *2 *3 *4)) (-4 *2 (-1133)) (-4 *3 (-23)) + (-14 *4 *3)))) +(((*1 *2 *1) + (-12 (-4 *1 (-341 *3)) (-4 *3 (-376)) (-4 *3 (-381)) + (-5 *2 (-1203 *3))))) +(((*1 *2 *3 *4) + (-12 (-5 *3 (-1 *2 (-663 *2))) (-5 *4 (-663 *5)) + (-4 *5 (-38 (-421 (-560)))) (-4 *2 (-1292 *5)) + (-5 *1 (-1293 *5 *2))))) +(((*1 *2 *2) (-12 (-5 *1 (-161 *2)) (-4 *2 (-559)))) + ((*1 *1 *2) (-12 (-5 *2 (-663 (-949))) (-5 *1 (-1003))))) +(((*1 *1 *1 *1) (-12 (-4 *1 (-877 *2)) (-4 *2 (-1081)) (-4 *2 (-376))))) +(((*1 *2 *2) (-12 (-5 *2 (-1191)) (-5 *1 (-781))))) (((*1 *1 *1) (-4 *1 (-35))) ((*1 *2 *2) (-12 (-4 *3 (-571)) (-5 *1 (-287 *3 *2)) @@ -4116,25 +3698,36 @@ ((*1 *2 *2) (-12 (-5 *2 (-1187 *3)) (-4 *3 (-38 (-421 (-560)))) (-5 *1 (-1195 *3))))) -(((*1 *2 *1) (-12 (-4 *1 (-403)) (-5 *2 (-1191))))) +(((*1 *2 *2) + (-12 (-4 *3 (-13 (-466) (-1070 (-560)) (-660 (-560)))) + (-5 *1 (-437 *3 *2 *4 *5)) (-4 *2 (-13 (-27) (-1235) (-435 *3))) + (-14 *4 (-1209)) (-14 *5 *2))) + ((*1 *2 *2) + (-12 (-4 *3 (-13 (-466) (-1070 (-560)) (-660 (-560)))) + (-4 *2 (-13 (-27) (-1235) (-435 *3) (-10 -8 (-15 -2590 ($ *4))))) + (-4 *4 (-871)) + (-4 *5 + (-13 (-1278 *2 *4) (-376) (-1235) + (-10 -8 (-15 -2509 ($ $)) (-15 -3270 ($ $))))) + (-5 *1 (-438 *3 *2 *4 *5 *6 *7)) (-4 *6 (-1015 *5)) + (-14 *7 (-1209))))) +(((*1 *2) + (-12 (-4 *4 (-175)) (-5 *2 (-114)) (-5 *1 (-379 *3 *4)) + (-4 *3 (-380 *4)))) + ((*1 *2) (-12 (-4 *1 (-380 *3)) (-4 *3 (-175)) (-5 *2 (-114))))) (((*1 *2 *1 *3) - (-12 (-5 *3 (-560)) (-4 *1 (-335 *4 *2)) (-4 *4 (-1133)) - (-4 *2 (-133))))) + (-12 (-4 *1 (-569 *3)) (-4 *3 (-13 (-418) (-1235))) (-5 *2 (-114))))) +(((*1 *2 *1) + (-12 (-4 *1 (-262 *3 *4 *5 *6)) (-4 *3 (-1081)) (-4 *4 (-872)) + (-4 *5 (-277 *4)) (-4 *6 (-817)) (-5 *2 (-114))))) (((*1 *2 *3) - (-12 (-4 *2 (-1275 *4)) (-5 *1 (-833 *4 *2 *3 *5)) - (-4 *4 (-13 (-376) (-149) (-1070 (-421 (-560))))) (-4 *3 (-680 *2)) - (-4 *5 (-680 (-421 *2)))))) -(((*1 *1) - (-12 (-5 *1 (-137 *2 *3 *4)) (-14 *2 (-560)) (-14 *3 (-793)) - (-4 *4 (-175))))) -(((*1 *2 *3 *4 *4) - (-12 (-5 *3 (-1 *2 *2 *2)) (-4 *2 (-1292 *4)) (-5 *1 (-1293 *4 *2)) - (-4 *4 (-38 (-421 (-560))))))) + (-12 (-5 *3 (-1 *5 *4 *4)) (-4 *4 (-1133)) (-4 *5 (-1133)) + (-5 *2 (-1 *5 *4)) (-5 *1 (-705 *4 *5))))) (((*1 *2 *3) (|partial| -12 (-5 *3 (-2 (|:| |var| (-1209)) (|:| |fn| (-326 (-229))) - (|:| -4389 (-1121 (-866 (-229)))) (|:| |abserr| (-229)) + (|:| -1404 (-1121 (-866 (-229)))) (|:| |abserr| (-229)) (|:| |relerr| (-229)))) (-5 *2 (-2 @@ -4152,7 +3745,7 @@ (-3 (|:| |str| (-1187 (-229))) (|:| |notEvaluated| "Internal singularities not yet evaluated"))) - (|:| -4389 + (|:| -1404 (-3 (|:| |finite| "The range is finite") (|:| |lowerInfinite| "The bottom of range is infinite") (|:| |upperInfinite| "The top of range is infinite") @@ -4160,15 +3753,17 @@ "Both top and bottom points are infinite") (|:| |notEvaluated| "Range not yet evaluated"))))) (-5 *1 (-574))))) -(((*1 *2 *1) (-12 (-5 *2 (-713 *3)) (-5 *1 (-996 *3)) (-4 *3 (-1133))))) -(((*1 *2 *2) - (-12 (-5 *2 (-1299 *1)) (-4 *1 (-355 *3 *4 *5)) (-4 *3 (-1254)) - (-4 *4 (-1275 *3)) (-4 *5 (-1275 (-421 *4)))))) -(((*1 *2 *3 *1) (-12 (-5 *3 (-1209)) (-5 *2 (-1213)) (-5 *1 (-1212))))) -(((*1 *2 *2) - (|partial| -12 (-4 *3 (-571)) (-4 *3 (-175)) (-4 *4 (-385 *3)) - (-4 *5 (-385 *3)) (-5 *1 (-710 *3 *4 *5 *2)) - (-4 *2 (-708 *3 *4 *5))))) +(((*1 *2 *3 *3) + (-12 (-4 *4 (-571)) (-5 *2 (-2 (|:| |coef2| *3) (|:| -1708 *4))) + (-5 *1 (-1001 *4 *3)) (-4 *3 (-1275 *4))))) +(((*1 *2 *1 *3 *3) + (-12 (-5 *3 (-1191)) (-5 *2 (-1305)) (-5 *1 (-847))))) +(((*1 *2 *3 *3 *3 *4 *5 *3 *6 *6 *3) + (-12 (-5 *3 (-560)) (-5 *5 (-114)) (-5 *6 (-711 (-229))) + (-5 *4 (-229)) (-5 *2 (-1067)) (-5 *1 (-777))))) +(((*1 *1 *1) + (-12 (-5 *1 (-227 *2 *3)) (-4 *2 (-13 (-1081) (-872))) + (-14 *3 (-663 (-1209)))))) (((*1 *1 *1) (-4 *1 (-35))) ((*1 *2 *2) (-12 (-4 *3 (-571)) (-5 *1 (-287 *3 *2)) @@ -4185,53 +3780,45 @@ ((*1 *2 *2) (-12 (-5 *2 (-1187 *3)) (-4 *3 (-38 (-421 (-560)))) (-5 *1 (-1195 *3))))) -(((*1 *2 *3 *4) - (-12 (-5 *3 (-663 (-711 *5))) (-5 *4 (-1299 *5)) (-4 *5 (-319)) - (-4 *5 (-1081)) (-5 *2 (-711 *5)) (-5 *1 (-1062 *5))))) -(((*1 *2 *1) (-12 (-5 *2 (-988 (-793))) (-5 *1 (-345))))) -(((*1 *1 *1 *2) (-12 (-5 *2 (-229)) (-5 *1 (-30)))) - ((*1 *2 *2 *3) - (-12 (-5 *3 (-1 (-419 *4) *4)) (-4 *4 (-571)) (-5 *2 (-419 *4)) - (-5 *1 (-433 *4)))) - ((*1 *1 *1) (-5 *1 (-955))) - ((*1 *1 *1 *2) (-12 (-5 *2 (-1121 (-229))) (-5 *1 (-955)))) - ((*1 *1 *1) (-5 *1 (-957))) - ((*1 *1 *1 *2) (-12 (-5 *2 (-1121 (-229))) (-5 *1 (-957)))) - ((*1 *2 *3 *2 *4) - (-12 (-5 *2 (-2 (|:| -1465 (-421 (-560))) (|:| -1477 (-421 (-560))))) - (-5 *4 (-421 (-560))) (-5 *1 (-1053 *3)) (-4 *3 (-1275 (-560))))) - ((*1 *2 *3 *2 *2) - (|partial| -12 - (-5 *2 (-2 (|:| -1465 (-421 (-560))) (|:| -1477 (-421 (-560))))) - (-5 *1 (-1053 *3)) (-4 *3 (-1275 (-560))))) - ((*1 *2 *3 *2 *4) - (-12 (-5 *2 (-2 (|:| -1465 (-421 (-560))) (|:| -1477 (-421 (-560))))) - (-5 *4 (-421 (-560))) (-5 *1 (-1054 *3)) (-4 *3 (-1275 *4)))) - ((*1 *2 *3 *2 *2) - (|partial| -12 - (-5 *2 (-2 (|:| -1465 (-421 (-560))) (|:| -1477 (-421 (-560))))) - (-5 *1 (-1054 *3)) (-4 *3 (-1275 (-421 (-560)))))) - ((*1 *1 *1) - (-12 (-4 *2 (-13 (-871) (-376))) (-5 *1 (-1093 *2 *3)) - (-4 *3 (-1275 *2))))) -(((*1 *1 *1) (-12 (-4 *1 (-680 *2)) (-4 *2 (-1081)) (-4 *2 (-376))))) +(((*1 *2 *1) (-12 (-5 *2 (-1305)) (-5 *1 (-847))))) +(((*1 *2 *1) (-12 (-4 *1 (-569 *2)) (-4 *2 (-13 (-418) (-1235)))))) (((*1 *2 *3) - (-12 (-4 *4 (-13 (-376) (-149) (-1070 (-421 (-560))))) - (-4 *5 (-1275 *4)) - (-5 *2 (-663 (-2 (|:| |deg| (-793)) (|:| -1879 *5)))) - (-5 *1 (-833 *4 *5 *3 *6)) (-4 *3 (-680 *5)) - (-4 *6 (-680 (-421 *5)))))) -(((*1 *2 *1 *3 *3) - (-12 (-5 *3 (-560)) (-5 *2 (-1305)) (-5 *1 (-935 *4)) - (-4 *4 (-1133)))) - ((*1 *2 *1) (-12 (-5 *2 (-1305)) (-5 *1 (-935 *3)) (-4 *3 (-1133))))) + (-12 (-4 *4 (-571)) (-4 *5 (-817)) (-4 *6 (-872)) + (-4 *7 (-1097 *4 *5 *6)) + (-5 *2 (-2 (|:| |goodPols| (-663 *7)) (|:| |badPols| (-663 *7)))) + (-5 *1 (-1009 *4 *5 *6 *7)) (-5 *3 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((*1 *1 *1 *2) + (-12 (-5 *2 (-1 *4 *4)) (-4 *4 (-670 *3)) (-4 *3 (-1081)) + (-5 *1 (-736 *3 *4)))) + ((*1 *1 *1 *2) + (-12 (-5 *2 (-1 *3 *3)) (-4 *3 (-1081)) (-5 *1 (-858 *3))))) +(((*1 *2 *3 *4 *4 *4 *4 *5 *5) + (-12 (-5 *3 (-1 (-391) (-391))) (-5 *4 (-391)) + (-5 *2 + (-2 (|:| -3949 *4) (|:| -2726 *4) (|:| |totalpts| (-560)) + (|:| |success| (-114)))) + (-5 *1 (-811)) (-5 *5 (-560))))) +(((*1 *2 *1 *3) (-12 (-5 *3 (-793)) (-5 *1 (-903 *2)) (-4 *2 (-1249)))) + ((*1 *2 *1 *3) (-12 (-5 *3 (-793)) (-5 *1 (-905 *2)) (-4 *2 (-1249)))) + ((*1 *2 *1 *3) (-12 (-5 *3 (-793)) (-5 *1 (-908 *2)) (-4 *2 (-1249))))) (((*1 *2 *2) (-12 (-4 *3 (-571)) (-5 *1 (-287 *3 *2)) (-4 *2 (-13 (-435 *3) (-1034))))) @@ -4248,34 +3835,67 @@ ((*1 *2 *2) (-12 (-5 *2 (-1187 *3)) (-4 *3 (-38 (-421 (-560)))) (-5 *1 (-1195 *3))))) -(((*1 *2 *1) (-12 (-5 *2 (-1187 *3)) (-5 *1 (-177 *3)) (-4 *3 (-319))))) -(((*1 *2 *1) (-12 (-5 *2 (-114)) (-5 *1 (-174))))) +(((*1 *2 *1) (-12 (-4 *1 (-820 *2)) (-4 *2 (-175))))) +(((*1 *2 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(|partial| -12 (-4 *4 (-13 (-571) (-1070 (-560)))) (-4 *5 (-435 *4)) - (-5 *2 (-419 (-1203 (-421 (-560))))) (-5 *1 (-449 *4 *5 *3)) - (-4 *3 (-1275 *5))))) +(((*1 *2 *3 *4) + (-12 (-4 *5 (-466)) (-4 *6 (-817)) (-4 *7 (-872)) + (-4 *3 (-1097 *5 *6 *7)) (-5 *2 (-663 *4)) + (-5 *1 (-1140 *5 *6 *7 *3 *4)) (-4 *4 (-1103 *5 *6 *7 *3))))) +(((*1 *2 *3 *3 *3 *4 *4 *4 *3) + (-12 (-5 *3 (-560)) (-5 *4 (-711 (-229))) (-5 *2 (-1067)) + (-5 *1 (-774))))) (((*1 *2 *3) (-12 (-5 *3 (-1209)) (-4 *4 (-13 (-466) (-1070 (-560)) (-660 (-560)))) (-5 *2 (-51)) @@ -4318,30 +3938,19 @@ (-5 *1 (-473 *7 *3)))) ((*1 *2 *1) (-12 (-4 *1 (-1263 *3 *2)) (-4 *3 (-1081)) (-4 *2 (-1292 *3))))) -(((*1 *2 *2) - (-12 (-4 *3 (-13 (-571) (-149))) (-5 *1 (-551 *3 *2)) - (-4 *2 (-1292 *3)))) - ((*1 *2 *2) - (-12 (-4 *3 (-13 (-376) (-381) (-633 (-560)))) (-4 *4 (-1275 *3)) - (-4 *5 (-746 *3 *4)) (-5 *1 (-555 *3 *4 *5 *2)) (-4 *2 (-1292 *5)))) - ((*1 *2 *2) - (-12 (-4 *3 (-13 (-376) (-381) (-633 (-560)))) (-5 *1 (-556 *3 *2)) - 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*3 (-1103 *4 *5 *6 *7))))) +(((*1 *2 *2 *3) + (-12 (-4 *3 (-1081)) (-5 *1 (-458 *3 *2)) (-4 *2 (-1275 *3))))) (((*1 *2 *2) (-12 (-4 *3 (-571)) (-5 *1 (-287 *3 *2)) (-4 *2 (-13 (-435 *3) (-1034))))) @@ -4358,41 +3967,53 @@ ((*1 *2 *2) (-12 (-5 *2 (-1187 *3)) (-4 *3 (-38 (-421 (-560)))) (-5 *1 (-1195 *3))))) -(((*1 *1 *1 *2 *3) - (-12 (-5 *2 (-663 (-793))) (-5 *3 (-174)) (-5 *1 (-1197 *4 *5)) - (-14 *4 (-949)) (-4 *5 (-1081))))) -(((*1 *2 *3 *3 *2 *4) - (-12 (-5 *3 (-711 *2)) (-5 *4 (-560)) - (-4 *2 (-13 (-319) (-10 -8 (-15 -2894 ((-419 $) $))))) - (-4 *5 (-1275 *2)) (-5 *1 (-513 *2 *5 *6)) (-4 *6 (-424 *2 *5))))) -(((*1 *2) (-12 (-5 *2 (-391)) (-5 *1 (-1073))))) +(((*1 *1 *1) (-5 *1 (-1095)))) +(((*1 *2 *1) (-12 (-5 *2 (-560)) (-5 *1 (-899)))) + ((*1 *2 *3) + (-12 (-5 *3 (-973 *2)) (-5 *1 (-1014 *2)) (-4 *2 (-1081))))) (((*1 *1 *1 *1) (-5 *1 (-130))) ((*1 *1 *1 *1) (-12 (-5 *1 (-1216 *2)) (-14 *2 (-949)))) ((*1 *1 *1 *1) (-5 *1 (-1255))) ((*1 *1 *1 *1) (-5 *1 (-1256))) ((*1 *1 *1 *1) 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*1 *2) + (-12 (-5 *2 (-1315 (-1209) *3)) (-4 *3 (-1081)) (-5 *1 (-1321 *3)))) + ((*1 *1 *2) + (-12 (-5 *2 (-1315 *3 *4)) (-4 *3 (-872)) (-4 *4 (-1081)) + (-5 *1 (-1324 *3 *4))))) (((*1 *2 *3) - (-12 (-5 *3 (-711 (-421 (-976 (-560))))) - (-5 *2 - (-663 - (-2 (|:| |radval| (-326 (-560))) (|:| |radmult| (-560)) - (|:| |radvect| (-663 (-711 (-326 (-560)))))))) - (-5 *1 (-1060))))) -(((*1 *2 *3) (-12 (-5 *3 (-229)) (-5 *2 (-721)) (-5 *1 (-315))))) -(((*1 *2 *1) (|partial| -12 (-5 *2 (-520)) (-5 *1 (-291))))) -(((*1 *1 *2 *3 *3 *3) - (-12 (-5 *2 (-1209)) (-5 *3 (-114)) (-5 *1 (-916 *4)) - (-4 *4 (-1133))))) -(((*1 *2 *2 *2) (-12 (-5 *2 (-391)) (-5 *1 (-208)))) - ((*1 *2 *2 *3) - (-12 (-5 *3 (-663 (-391))) (-5 *2 (-391)) (-5 *1 (-208))))) + (-12 (-5 *3 (-3 (|:| |fst| (-448)) (|:| -2618 "void"))) + (-5 *2 (-1305)) (-5 *1 (-1212)))) + ((*1 *2 *3 *4) + (-12 (-5 *3 (-1209)) + (-5 *4 (-3 (|:| |fst| (-448)) (|:| -2618 "void"))) (-5 *2 (-1305)) + (-5 *1 (-1212)))) + ((*1 *2 *3 *4 *1) + (-12 (-5 *3 (-1209)) + (-5 *4 (-3 (|:| |fst| (-448)) (|:| -2618 "void"))) (-5 *2 (-1305)) + (-5 *1 (-1212))))) +(((*1 *2) (-12 (-5 *2 (-1191)) (-5 *1 (-405))))) +(((*1 *2 *3) + (-12 (-4 *4 (-13 (-376) (-871))) + (-5 *2 (-2 (|:| |start| *3) (|:| -3080 (-419 *3)))) + (-5 *1 (-184 *4 *3)) (-4 *3 (-1275 (-171 *4)))))) +(((*1 *1 *2) + (-12 (-5 *2 (-694 *3)) (-4 *3 (-872)) (-4 *1 (-387 *3 *4)) + (-4 *4 (-175))))) +(((*1 *1) (-5 *1 (-146)))) (((*1 *2 *2) (-12 (-4 *3 (-571)) (-5 *1 (-287 *3 *2)) (-4 *2 (-13 (-435 *3) (-1034))))) @@ -4409,14 +4030,18 @@ ((*1 *2 *2) (-12 (-5 *2 (-1187 *3)) (-4 *3 (-38 (-421 (-560)))) (-5 *1 (-1195 *3))))) -(((*1 *2 *3 *3) - (-12 (-4 *2 (-571)) (-5 *1 (-1001 *2 *3)) (-4 *3 (-1275 *2))))) -(((*1 *1 *1 *2) - (-12 (-5 *2 (-1191)) (-4 *1 (-378 *3 *4)) (-4 *3 (-1133)) - (-4 *4 (-1133))))) -(((*1 *2 *2) - (-12 (-4 *3 (-1275 (-421 (-560)))) (-5 *1 (-943 *3 *2)) - (-4 *2 (-1275 (-421 *3)))))) +(((*1 *2 *3) + (-12 (-5 *3 (-663 *7)) (-4 *7 (-1097 *4 *5 *6)) (-4 *4 (-571)) + (-4 *5 (-817)) (-4 *6 (-872)) (-5 *2 (-114)) + (-5 *1 (-1009 *4 *5 *6 *7))))) +(((*1 *2 *3) + (-12 (-4 *3 (-1275 (-421 (-560)))) + (-5 *2 (-2 (|:| |den| (-560)) (|:| |gcdnum| (-560)))) + (-5 *1 (-943 *3 *4)) (-4 *4 (-1275 (-421 *3))))) + ((*1 *2 *3) + (-12 (-4 *4 (-1275 (-421 *2))) (-5 *2 (-560)) (-5 *1 (-943 *4 *3)) + (-4 *3 (-1275 (-421 *4)))))) +(((*1 *1 *1) (-12 (-4 *1 (-1288 *2)) (-4 *2 (-1249))))) (((*1 *1 *2 *1) (-12 (-5 *2 (-1 (-114) *3)) (|has| *1 (-6 -4510)) (-4 *1 (-153 *3)) (-4 *3 (-1249)))) @@ -4434,39 +4059,58 @@ (-12 (-5 *1 (-352 *2 *3 *4)) (-14 *2 (-663 (-1209))) (-14 *3 (-663 (-1209))) (-4 *4 (-401)))) ((*1 *1 *1) (-5 *1 (-391))) ((*1 *1) (-5 *1 (-391)))) +(((*1 *2 *1 *2) + (-12 (-4 *1 (-378 *3 *2)) (-4 *3 (-1133)) (-4 *2 (-1133))))) (((*1 *2 *3) - (-12 (-5 *3 (-663 *2)) (-4 *2 (-435 *4)) (-5 *1 (-160 *4 *2)) - (-4 *4 (-571))))) -(((*1 *2 *1) (-12 (-5 *2 (-114)) (-5 *1 (-146))))) -(((*1 *2 *2) (|partial| -12 (-4 *1 (-1015 *2)) (-4 *2 (-1235))))) -(((*1 *1 *2) - (-12 (-5 *2 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(-5 *3 (-560)) (-5 *4 (-711 (-229))) (-5 *5 (-114)) - (-5 *2 (-1067)) (-5 *1 (-775))))) + (-12 (-5 *2 (-597 *4)) (-4 *4 (-13 (-29 *3) (-1235))) + (-4 *3 (-13 (-466) (-1070 (-560)) (-660 (-560)))) + (-5 *1 (-599 *3 *4)))) + ((*1 *2 *2) + (-12 (-5 *2 (-597 (-421 (-976 *3)))) + (-4 *3 (-13 (-466) (-1070 (-560)) (-660 (-560)))) (-5 *1 (-603 *3)))) + ((*1 *2 *3 *4) + (-12 (-5 *4 (-1 *3 *3)) (-4 *3 (-1275 *5)) (-4 *5 (-376)) + (-5 *2 (-2 (|:| -1829 *3) (|:| |special| *3))) (-5 *1 (-749 *5 *3)))) + ((*1 *2 *3 *4) + (-12 (-5 *4 (-1299 *5)) (-4 *5 (-376)) (-4 *5 (-1081)) + (-5 *2 (-663 (-663 (-711 *5)))) (-5 *1 (-1062 *5)) + (-5 *3 (-663 (-711 *5))))) + ((*1 *2 *3 *4) + (-12 (-5 *4 (-1299 (-1299 *5))) (-4 *5 (-376)) (-4 *5 (-1081)) + (-5 *2 (-663 (-663 (-711 *5)))) (-5 *1 (-1062 *5)) + (-5 *3 (-663 (-711 *5))))) + ((*1 *2 *1 *3) (-12 (-5 *3 (-143)) (-5 *2 (-663 *1)) (-4 *1 (-1176)))) + ((*1 *2 *1 *3) (-12 (-5 *3 (-146)) (-5 *2 (-663 *1)) (-4 *1 (-1176))))) +(((*1 *2 *3) + (-12 (-5 *3 (-1 *5 *5 *5)) (-4 *5 (-1292 *4)) + (-4 *4 (-38 (-421 (-560)))) + (-5 *2 (-1 (-1187 *4) (-1187 *4) (-1187 *4))) (-5 *1 (-1293 *4 *5))))) +(((*1 *1 *2) + (-12 (-5 *2 (-663 *3)) (-4 *3 (-1249)) (-5 *1 (-1180 *3))))) (((*1 *2 *2) (-12 (-4 *3 (-571)) (-5 *1 (-287 *3 *2)) (-4 *2 (-13 (-435 *3) (-1034))))) @@ -4486,54 +4130,43 @@ ((*1 *2 *2) (-12 (-5 *2 (-1187 *3)) (-4 *3 (-38 (-421 (-560)))) (-5 *1 (-1195 *3))))) -(((*1 *2 *2) (-12 (-5 *1 (-161 *2)) (-4 *2 (-559)))) - ((*1 *1 *2) (-12 (-5 *2 (-663 (-949))) (-5 *1 (-1003))))) -(((*1 *2 *1 *3 *3) - (-12 (-5 *3 (-1191)) (-5 *2 (-1305)) (-5 *1 (-847))))) -(((*1 *2 *3 *4 *4 *4 *4 *5 *5) - (-12 (-5 *3 (-1 (-391) (-391))) (-5 *4 (-391)) - (-5 *2 - (-2 (|:| -3950 *4) (|:| -2726 *4) (|:| |totalpts| (-560)) - (|:| |success| (-114)))) - (-5 *1 (-811)) (-5 *5 (-560))))) +(((*1 *2 *3) + (-12 (-5 *3 (-229)) (-5 *2 (-114)) (-5 *1 (-314 *4 *5)) (-14 *4 *3) + (-14 *5 *3))) + ((*1 *2 *3 *4) + (-12 (-5 *4 (-1121 (-866 (-229)))) (-5 *3 (-229)) (-5 *2 (-114)) + (-5 *1 (-315)))) + ((*1 *2 *1 *1) + (-12 (-4 *3 (-376)) (-4 *4 (-817)) (-4 *5 (-872)) (-5 *2 (-114)) + (-5 *1 (-518 *3 *4 *5 *6)) (-4 *6 (-980 *3 *4 *5))))) +(((*1 *2 *3 *2) + (-12 (-5 *2 (-663 *3)) (-4 *3 (-319)) (-5 *1 (-182 *3))))) (((*1 *1 *2 *1) (-12 (-5 *2 (-1 (-114) *3)) (-4 *3 (-1249)) (-5 *1 (-615 *3)))) ((*1 *1 *2 *1) (-12 (-5 *2 (-1 (-114) *3)) (-4 *3 (-1249)) (-5 *1 (-1187 *3))))) -(((*1 *2 *3 *3 *3 *4 *4 *4 *3) +(((*1 *2 *3 *3 *3 *3 *4 *4 *4 *4 *4 *3 *3 *3) (-12 (-5 *3 (-560)) (-5 *4 (-711 (-229))) (-5 *2 (-1067)) (-5 *1 (-774))))) -(((*1 *2 *3) - (-12 (-5 *3 (-3 (|:| |fst| (-448)) (|:| -2618 "void"))) - (-5 *2 (-1305)) (-5 *1 (-1212)))) - ((*1 *2 *3 *4) - (-12 (-5 *3 (-1209)) - (-5 *4 (-3 (|:| |fst| (-448)) (|:| -2618 "void"))) (-5 *2 (-1305)) - (-5 *1 (-1212)))) - ((*1 *2 *3 *4 *1) - (-12 (-5 *3 (-1209)) - (-5 *4 (-3 (|:| |fst| (-448)) (|:| -2618 "void"))) (-5 *2 (-1305)) - (-5 *1 (-1212))))) -(((*1 *2) (-12 (-5 *2 (-949)) (-5 *1 (-1304)))) - ((*1 *2 *2) (-12 (-5 *2 (-949)) (-5 *1 (-1304))))) -(((*1 *2 *2) (|partial| -12 (-4 *1 (-1015 *2)) (-4 *2 (-1235))))) -(((*1 *1 *1 *2 *3 *1) - (-12 (-5 *2 (-793)) (-5 *1 (-803 *3)) (-4 *3 (-1081)))) - ((*1 *1 *1 *2 *3 *1) - (-12 (-5 *1 (-986 *3 *2)) (-4 *2 (-133)) (-4 *3 (-571)) - (-4 *3 (-1081)) (-4 *2 (-816)))) - ((*1 *1 *1 *2 *3 *1) - (-12 (-5 *2 (-793)) (-5 *1 (-1203 *3)) (-4 *3 (-1081)))) - ((*1 *1 *1 *2 *3 *1) - (-12 (-5 *2 (-1003)) (-4 *2 (-133)) (-5 *1 (-1211 *3)) (-4 *3 (-571)) - (-4 *3 (-1081)))) - ((*1 *1 *1 *2 *3 *1) - (-12 (-5 *2 (-793)) (-5 *1 (-1268 *4 *3)) (-14 *4 (-1209)) - (-4 *3 (-1081))))) +(((*1 *2 *1) (-12 (-4 *1 (-541)) (-5 *2 (-713 (-1258)))))) +(((*1 *2 *2 *3) + (|partial| -12 (-5 *2 (-663 (-1203 *7))) (-5 *3 (-1203 *7)) + (-4 *7 (-980 *4 *5 *6)) (-4 *4 (-940)) (-4 *5 (-817)) + (-4 *6 (-872)) (-5 *1 (-937 *4 *5 *6 *7)))) + ((*1 *2 *2 *3) + (|partial| -12 (-5 *2 (-663 (-1203 *5))) (-5 *3 (-1203 *5)) + (-4 *5 (-1275 *4)) (-4 *4 (-940)) (-5 *1 (-938 *4 *5))))) +(((*1 *2 *3) (-12 (-5 *3 (-663 *2)) (-5 *1 (-1224 *2)) (-4 *2 (-376))))) (((*1 *2 *2) (|partial| -12 (-4 *1 (-1015 *2)) (-4 *2 (-1235))))) +(((*1 *2 *2 *1) + (-12 (-4 *1 (-1244 *3 *4 *5 *2)) (-4 *3 (-571)) (-4 *4 (-817)) + (-4 *5 (-872)) (-4 *2 (-1097 *3 *4 *5))))) +(((*1 *2 *2) + (-12 (-4 *3 (-466)) (-5 *1 (-1241 *3 *2)) + (-4 *2 (-13 (-435 *3) (-1235)))))) (((*1 *2 *1) (-12 (-5 *2 (-1167)) (-5 *1 (-1185))))) -(((*1 *1 *1 *1 *2) - (|partial| -12 (-5 *2 (-114)) (-5 *1 (-609 *3)) (-4 *3 (-1081))))) +(((*1 *2 *3 *4) + (-12 (-5 *3 (-229)) (-5 *4 (-560)) (-5 *2 (-1067)) (-5 *1 (-780))))) (((*1 *2 *2) (-12 (-4 *3 (-571)) (-5 *1 (-287 *3 *2)) (-4 *2 (-13 (-435 *3) (-1034))))) @@ -4553,58 +4186,58 @@ ((*1 *2 *2) (-12 (-5 *2 (-1187 *3)) (-4 *3 (-38 (-421 (-560)))) (-5 *1 (-1195 *3))))) -(((*1 *2) (-12 (-5 *2 (-1305)) (-5 *1 (-1209))))) +(((*1 *1 *1 *2 *1) + (-12 (-5 *2 (-560)) (-5 *1 (-1187 *3)) (-4 *3 (-1249)))) + ((*1 *1 *1 *1) + (-12 (|has| *1 (-6 -4511)) (-4 *1 (-1288 *2)) (-4 *2 (-1249))))) (((*1 *2 *2 *3) (-12 (-5 *2 (-1209)) (-5 *3 (-663 (-549))) (-5 *1 (-549))))) (((*1 *1 *2 *1) (-12 (-5 *2 (-1 (-114) *3)) (-4 *3 (-1249)) (-5 *1 (-615 *3)))) ((*1 *1 *2 *1) (-12 (-5 *2 (-1 (-114) *3)) (-4 *3 (-1249)) (-5 *1 (-1187 *3))))) -(((*1 *1 *1) - (-12 (-5 *1 (-609 *2)) (-4 *2 (-38 (-421 (-560)))) (-4 *2 (-1081))))) -(((*1 *2 *2) - (-12 (-5 *2 (-663 (-663 *3))) (-4 *3 (-872)) (-5 *1 (-1220 *3))))) -(((*1 *2 *3 *4) - (-12 (-5 *4 (-663 (-889 *5))) (-14 *5 (-663 (-1209))) (-4 *6 (-466)) - (-5 *2 (-663 (-663 (-255 *5 *6)))) (-5 *1 (-485 *5 *6 *7)) - (-5 *3 (-663 (-255 *5 *6))) (-4 *7 (-466))))) (((*1 *2 *3) - (-12 (-5 *3 (-1121 (-866 (-229)))) (-5 *2 (-229)) (-5 *1 (-195)))) - ((*1 *2 *3) - (-12 (-5 *3 (-1121 (-866 (-229)))) (-5 *2 (-229)) (-5 *1 (-313)))) - ((*1 *2 *3) - (-12 (-5 *3 (-1121 (-866 (-229)))) (-5 *2 (-229)) (-5 *1 (-315))))) -(((*1 *2 *3) - (-12 - (-5 *3 - (-2 (|:| |var| (-1209)) (|:| |fn| (-326 (-229))) - (|:| -4389 (-1121 (-866 (-229)))) (|:| |abserr| (-229)) - (|:| |relerr| (-229)))) - (-5 *2 - (-3 (|:| |continuous| "Continuous at the end points") - (|:| |lowerSingular| - "There is a singularity at the lower end point") - (|:| |upperSingular| - "There is a singularity at the upper end point") - (|:| |bothSingular| "There are singularities at both end points") - (|:| |notEvaluated| "End point continuity not yet evaluated"))) - (-5 *1 (-195))))) -(((*1 *2 *3 *1) - (-12 (-4 *1 (-1103 *4 *5 *6 *3)) (-4 *4 (-466)) (-4 *5 (-817)) - (-4 *6 (-872)) (-4 *3 (-1097 *4 *5 *6)) (-5 *2 (-114))))) -(((*1 *2 *2) (|partial| -12 (-4 *1 (-1015 *2)) (-4 *2 (-1235))))) -(((*1 *2 *1 *3 *3 *3 *2) - (-12 (-5 *3 (-793)) (-5 *1 (-697 *2)) (-4 *2 (-1133))))) + (-12 (-4 *4 (-571)) (-5 *2 (-171 *5)) (-5 *1 (-614 *4 *5 *3)) + (-4 *5 (-13 (-435 *4) (-1034) (-1235))) + (-4 *3 (-13 (-435 (-171 *4)) (-1034) (-1235)))))) +(((*1 *2 *2 *2) + (-12 (-5 *2 (-711 *3)) (-4 *3 (-1081)) (-5 *1 (-1061 *3)))) + ((*1 *2 *2 *2) + (-12 (-5 *2 (-663 (-711 *3))) (-4 *3 (-1081)) (-5 *1 (-1061 *3)))) + ((*1 *2 *2) + (-12 (-5 *2 (-711 *3)) (-4 *3 (-1081)) (-5 *1 (-1061 *3)))) + ((*1 *2 *2) + (-12 (-5 *2 (-663 (-711 *3))) (-4 *3 (-1081)) (-5 *1 (-1061 *3))))) (((*1 *1 *1) (-12 (-5 *1 (-609 *2)) (-4 *2 (-38 (-421 (-560)))) (-4 *2 (-1081))))) -(((*1 *2 *1) (-12 (-4 *1 (-1126 *2)) (-4 *2 (-1249))))) +(((*1 *2 *1) (-12 (-5 *2 (-114)) (-5 *1 (-115))))) +(((*1 *2 *3 *4) + (-12 (-5 *3 (-663 (-866 (-229)))) (-5 *4 (-229)) (-5 *2 (-663 *4)) + (-5 *1 (-278))))) +(((*1 *2 *1) + (-12 (-4 *1 (-1284 *3 *2)) (-4 *3 (-1081)) (-4 *2 (-1261 *3))))) +(((*1 *1 *1 *2 *3 *1) + (-12 (-5 *2 (-793)) (-5 *1 (-803 *3)) (-4 *3 (-1081)))) + ((*1 *1 *1 *2 *3 *1) + (-12 (-5 *1 (-986 *3 *2)) (-4 *2 (-133)) (-4 *3 (-571)) + (-4 *3 (-1081)) (-4 *2 (-816)))) + ((*1 *1 *1 *2 *3 *1) + (-12 (-5 *2 (-793)) (-5 *1 (-1203 *3)) (-4 *3 (-1081)))) + ((*1 *1 *1 *2 *3 *1) + (-12 (-5 *2 (-1003)) (-4 *2 (-133)) (-5 *1 (-1211 *3)) (-4 *3 (-571)) + (-4 *3 (-1081)))) + ((*1 *1 *1 *2 *3 *1) + (-12 (-5 *2 (-793)) (-5 *1 (-1268 *4 *3)) (-14 *4 (-1209)) + (-4 *3 (-1081))))) (((*1 *2 *2) - (-12 (-4 *3 (-571)) (-5 *1 (-160 *3 *2)) (-4 *2 (-435 *3)))) - ((*1 *2 *2 *3) - (-12 (-5 *3 (-1209)) (-4 *4 (-571)) (-5 *1 (-160 *4 *2)) - (-4 *2 (-435 *4)))) - ((*1 *1 *1 *2) (-12 (-4 *1 (-162)) (-5 *2 (-1209)))) - ((*1 *1 *1) (-4 *1 (-162)))) + (-12 (-4 *3 (-319)) (-4 *4 (-385 *3)) (-4 *5 (-385 *3)) + (-5 *1 (-1156 *3 *4 *5 *2)) (-4 *2 (-708 *3 *4 *5))))) +(((*1 *1 *2) (-12 (-5 *2 (-663 *3)) (-4 *3 (-1133)) (-5 *1 (-932 *3))))) +(((*1 *2 *1) (-12 (-4 *1 (-1126 *2)) (-4 *2 (-1249))))) +(((*1 *2 *2) (-12 (-5 *2 (-114)) (-5 *1 (-339 *3)) (-4 *3 (-1249)))) + ((*1 *2 *2) + (-12 (-5 *2 (-114)) (-5 *1 (-530 *3 *4)) (-4 *3 (-1249)) + (-14 *4 (-560))))) (((*1 *2 *2) (-12 (-4 *3 (-571)) (-5 *1 (-287 *3 *2)) (-4 *2 (-13 (-435 *3) (-1034))))) @@ -4625,10 +4258,16 @@ (-12 (-5 *2 (-1187 *3)) (-4 *3 (-38 (-421 (-560)))) (-5 *1 (-1195 *3))))) (((*1 *1) (-12 (-5 *1 (-713 *2)) (-4 *2 (-632 (-888)))))) -(((*1 *1) (-5 *1 (-143))) ((*1 *1 *1) (-5 *1 (-146))) - ((*1 *1 *1) (-4 *1 (-1176)))) -(((*1 *2 *3 *3 *3 *4) - (-12 (-5 *3 (-229)) (-5 *4 (-560)) (-5 *2 (-1067)) (-5 *1 (-780))))) +(((*1 *2 *1 *1) + (-12 (-5 *2 (-2 (|:| -2522 (-803 *3)) (|:| |coef2| (-803 *3)))) + (-5 *1 (-803 *3)) (-4 *3 (-571)) (-4 *3 (-1081)))) + ((*1 *2 *1 *1) + (-12 (-4 *3 (-571)) (-4 *3 (-1081)) (-4 *4 (-817)) (-4 *5 (-872)) + (-5 *2 (-2 (|:| -2522 *1) (|:| |coef2| *1))) + (-4 *1 (-1097 *3 *4 *5))))) +(((*1 *2 *2 *2 *3) + (-12 (-5 *3 (-793)) (-4 *4 (-571)) (-5 *1 (-1001 *4 *2)) + (-4 *2 (-1275 *4))))) (((*1 *2 *3 *4) (-12 (-5 *4 (-949)) (-4 *6 (-571)) (-5 *2 (-663 (-326 *6))) (-5 *1 (-225 *5 *6)) (-5 *3 (-326 *6)) (-4 *5 (-1081)))) @@ -4654,31 +4293,19 @@ ((*1 *2 *1) (-12 (-5 *2 (-1315 *3 *4)) (-5 *1 (-1324 *3 *4)) (-4 *3 (-872)) (-4 *4 (-1081))))) +(((*1 *2 *1) (-12 (-5 *2 (-1187 *3)) (-5 *1 (-177 *3)) (-4 *3 (-319))))) +(((*1 *1 *1 *1) (-5 *1 (-114))) ((*1 *1 *1 *1) (-4 *1 (-125)))) +(((*1 *2 *2) + (|partial| -12 (-5 *2 (-1203 *3)) (-4 *3 (-363)) (-5 *1 (-369 *3))))) +(((*1 *2 *1 *3) (-12 (-5 *3 (-391)) (-5 *2 (-1305)) (-5 *1 (-1303))))) (((*1 *2 *3) - (-12 - (-5 *3 - (-2 (|:| |lcmfij| *5) (|:| |totdeg| (-793)) (|:| |poli| *2) - (|:| |polj| *2))) - (-4 *5 (-817)) (-4 *2 (-980 *4 *5 *6)) (-5 *1 (-464 *4 *5 *6 *2)) - (-4 *4 (-466)) (-4 *6 (-872))))) -(((*1 *2) - (-12 (-5 *2 (-949)) (-5 *1 (-456 *3)) (-4 *3 (-1275 (-560))))) - ((*1 *2 *2) - (-12 (-5 *2 (-949)) (-5 *1 (-456 *3)) (-4 *3 (-1275 (-560)))))) -(((*1 *2 *1) (-12 (-5 *2 (-793)) (-5 *1 (-339 *3)) (-4 *3 (-1249)))) - ((*1 *2 *1) - (-12 (-5 *2 (-793)) (-5 *1 (-530 *3 *4)) (-4 *3 (-1249)) - (-14 *4 (-560))))) -(((*1 *2 *3) - (-12 (-5 *3 (-973 *2)) (-5 *1 (-1014 *2)) (-4 *2 (-1081))))) -(((*1 *2 *3 *3) - (-12 (-4 *4 (-466)) (-4 *4 (-571)) - (-5 *2 (-2 (|:| |coef2| *3) (|:| -3193 *4))) (-5 *1 (-1001 *4 *3)) - (-4 *3 (-1275 *4))))) + (|partial| -12 (-4 *4 (-13 (-571) (-149))) + (-5 *2 (-2 (|:| -1465 *3) (|:| -1477 *3))) (-5 *1 (-1271 *4 *3)) + (-4 *3 (-1275 *4))))) (((*1 *2 *3) (-12 (-5 *3 - (-2 (|:| |lfn| (-663 (-326 (-229)))) (|:| -2856 (-663 (-229))))) + (-2 (|:| |lfn| (-663 (-326 (-229)))) (|:| -2855 (-663 (-229))))) (-5 *2 (-663 (-1209))) (-5 *1 (-278)))) ((*1 *2 *3) (-12 (-5 *3 (-1203 *7)) (-4 *7 (-980 *6 *4 *5)) (-4 *4 (-817)) @@ -4700,7 +4327,7 @@ (-5 *1 (-981 *4 *5 *6 *7 *3)) (-4 *3 (-13 (-376) - (-10 -8 (-15 -2590 ($ *7)) (-15 -4445 (*7 $)) (-15 -4453 (*7 $))))))) + (-10 -8 (-15 -2590 ($ *7)) (-15 -4445 (*7 $)) (-15 -4454 (*7 $))))))) ((*1 *2 *1) (-12 (-4 *1 (-1005 *3 *4 *5)) (-4 *3 (-1081)) (-4 *4 (-816)) (-4 *5 (-872)) (-5 *2 (-663 *5)))) @@ -4710,19 +4337,11 @@ ((*1 *2 *3) (-12 (-5 *3 (-421 (-976 *4))) (-4 *4 (-571)) (-5 *2 (-663 (-1209))) (-5 *1 (-1072 *4))))) -(((*1 *2 *1) - (-12 (-4 *1 (-338 *2 *3)) (-4 *3 (-816)) (-4 *2 (-1081)) - (-4 *2 (-466)))) - ((*1 *2 *3) - (-12 (-5 *3 (-663 *4)) (-4 *4 (-1275 (-560))) (-5 *2 (-663 (-560))) - (-5 *1 (-500 *4)))) - ((*1 *2 *1) (-12 (-4 *1 (-877 *2)) (-4 *2 (-1081)) (-4 *2 (-466)))) - ((*1 *1 *1 *2) - (-12 (-4 *1 (-980 *3 *4 *2)) (-4 *3 (-1081)) (-4 *4 (-817)) - (-4 *2 (-872)) (-4 *3 (-466))))) -(((*1 *2 *3 *4) - (-12 (-5 *3 (-421 *2)) (-5 *4 (-1 *2 *2)) (-4 *2 (-1275 *5)) - (-5 *1 (-749 *5 *2)) (-4 *5 (-376))))) +(((*1 *2 *3 *3 *3) + (|partial| -12 (-4 *4 (-13 (-376) (-149) (-1070 (-560)))) + (-4 *5 (-1275 *4)) (-5 *2 (-663 (-421 *5))) (-5 *1 (-1048 *4 *5)) + (-5 *3 (-421 *5))))) +(((*1 *2 *2) (|partial| -12 (-4 *1 (-1015 *2)) (-4 *2 (-1235))))) (((*1 *2 *2) (-12 (-5 *1 (-704 *2)) (-4 *2 (-1133))))) (((*1 *1 *1) (-4 *1 (-95))) ((*1 *2 *2) @@ -4740,11 +4359,24 @@ ((*1 *2 *2) (-12 (-5 *2 (-1187 *3)) (-4 *3 (-38 (-421 (-560)))) (-5 *1 (-1195 *3))))) -(((*1 *2 *1 *1) (-12 (-5 *2 (-560)) (-5 *1 (-391))))) -(((*1 *2 *2) - (-12 (-5 *2 (-1187 *3)) (-4 *3 (-1081)) (-5 *1 (-1193 *3))))) -(((*1 *2 *2) (-12 (-5 *2 (-560)) (-5 *1 (-576))))) -(((*1 *2) (-12 (-5 *2 (-560)) (-5 *1 (-957))))) +(((*1 *2 *3) + (-12 + (-5 *3 + (-2 (|:| |var| (-1209)) (|:| |fn| (-326 (-229))) + (|:| -1404 (-1121 (-866 (-229)))) (|:| |abserr| (-229)) + (|:| |relerr| (-229)))) + (-5 *2 (-560)) (-5 *1 (-207))))) +(((*1 *2 *1 *3 *3) + (-12 (-5 *3 (-560)) (-5 *2 (-1305)) (-5 *1 (-1303)))) + ((*1 *2 *1 *3 *3) + (-12 (-5 *3 (-391)) (-5 *2 (-1305)) (-5 *1 (-1303))))) +(((*1 *1 *2 *3) (-12 (-5 *2 (-520)) (-5 *3 (-611)) (-5 *1 (-600))))) +(((*1 *2 *3 *4 *5) + (-12 (-5 *4 (-1 *7 *7)) + (-5 *5 (-1 (-3 (-663 *6) "failed") (-560) *6 *6)) (-4 *6 (-376)) + (-4 *7 (-1275 *6)) + (-5 *2 (-2 (|:| |answer| (-597 (-421 *7))) (|:| |a0| *6))) + (-5 *1 (-588 *6 *7)) (-5 *3 (-421 *7))))) (((*1 *2 *3) (-12 (-5 *2 (-1 *3 *3)) (-5 *1 (-544 *3)) (-4 *3 (-13 (-748) (-25)))))) (((*1 *2 *1) (-12 (-4 *1 (-263 *3)) (-4 *3 (-1249)) (-5 *2 (-793)))) @@ -4756,31 +4388,28 @@ ((*1 *2 *1) (-12 (-5 *2 (-793)) (-5 *1 (-630 *3)) (-4 *3 (-1133)))) ((*1 *2) (-12 (-5 *2 (-560)) (-5 *1 (-888)))) ((*1 *2 *1) (-12 (-5 *2 (-560)) (-5 *1 (-888))))) -(((*1 *2 *1 *1) - (-12 - (-5 *2 - (-2 (|:| -4420 *3) (|:| |coef1| (-803 *3)) (|:| |coef2| (-803 *3)))) - (-5 *1 (-803 *3)) (-4 *3 (-571)) (-4 *3 (-1081))))) -(((*1 *1) - (|partial| -12 (-4 *1 (-380 *2)) (-4 *2 (-571)) (-4 *2 (-175))))) -(((*1 *2 *3 *4 *5) - (-12 (-5 *3 (-1203 *9)) (-5 *4 (-663 *7)) (-5 *5 (-663 *8)) - (-4 *7 (-872)) (-4 *8 (-1081)) (-4 *9 (-980 *8 *6 *7)) - (-4 *6 (-817)) (-5 *2 (-1203 *8)) (-5 *1 (-333 *6 *7 *8 *9))))) -(((*1 *2 *1) (-12 (-4 *1 (-380 *2)) (-4 *2 (-175))))) -(((*1 *1 *2) - (|partial| -12 (-5 *2 (-1315 *3 *4)) (-4 *3 (-872)) (-4 *4 (-175)) - (-5 *1 (-686 *3 *4)))) - ((*1 *2 *1) - (|partial| -12 (-5 *2 (-686 *3 *4)) (-5 *1 (-1320 *3 *4)) - (-4 *3 (-872)) (-4 *4 (-175))))) -(((*1 *2 *2 *2) - (-12 (-4 *3 (-571)) (-5 *1 (-1001 *3 *2)) (-4 *2 (-1275 *3)))) - ((*1 *1 *1 *1) +(((*1 *2 *1) + (-12 (-4 *2 (-571)) (-5 *1 (-642 *2 *3)) (-4 *3 (-1275 *2))))) +(((*1 *2 *2) (-12 (-5 *2 (-229)) (-5 *1 (-230)))) + ((*1 *2 *2) (-12 (-5 *2 (-171 (-229))) (-5 *1 (-230))))) +(((*1 *2) + (-12 (-5 *2 (-793)) (-5 *1 (-122 *3)) (-4 *3 (-1275 (-560))))) + ((*1 *2 *2) + (-12 (-5 *2 (-793)) (-5 *1 (-122 *3)) (-4 *3 (-1275 (-560)))))) +(((*1 *2 *1) (-12 (-5 *2 (-497)) (-5 *1 (-222)))) + ((*1 *1 *1) (-12 (-4 *1 (-251 *2)) (-4 *2 (-1249)))) + ((*1 *2 *1) (-12 (-5 *2 (-497)) (-5 *1 (-698)))) + ((*1 *1 *1) (-12 (-4 *1 (-1097 *2 *3 *4)) (-4 *2 (-1081)) (-4 *3 (-817)) - (-4 *4 (-872)) (-4 *2 (-571)))) - ((*1 *1 *1 *1) - (-12 (-4 *1 (-1275 *2)) (-4 *2 (-1081)) (-4 *2 (-571))))) + (-4 *4 (-872))))) +(((*1 *2 *1) + (|partial| -12 (-4 *1 (-1263 *3 *2)) (-4 *3 (-1081)) + (-4 *2 (-1292 *3))))) +(((*1 *2 *1) + (-12 (-5 *2 (-2 (|:| |cd| (-1191)) (|:| -3971 (-1191)))) + (-5 *1 (-847))))) +(((*1 *2 *1 *3 *4) + (-12 (-5 *3 (-482)) (-5 *4 (-949)) (-5 *2 (-1305)) (-5 *1 (-1302))))) (((*1 *2 *3 *4 *2) (-12 (-5 *3 (-1203 (-421 (-1203 *2)))) (-5 *4 (-630 *2)) (-4 *2 (-13 (-435 *5) (-27) (-1235))) @@ -4797,73 +4426,42 @@ (-4 *6 (-1081)) (-4 *2 (-13 (-376) - (-10 -8 (-15 -2590 ($ *7)) (-15 -4445 (*7 $)) (-15 -4453 (*7 $))))) + (-10 -8 (-15 -2590 ($ *7)) (-15 -4445 (*7 $)) (-15 -4454 (*7 $))))) (-5 *1 (-981 *5 *4 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(-114)) (-4 *10 (-1103 *6 *7 *8 *9)) + (-4 *6 (-466)) (-4 *7 (-817)) (-4 *8 (-872)) + (-4 *9 (-1097 *6 *7 *8)) + (-5 *2 + (-663 + (-2 (|:| -1879 (-663 *9)) (|:| -3265 *10) (|:| |ineq| (-663 *9))))) + (-5 *1 (-1139 *6 *7 *8 *9 *10)) (-5 *3 (-663 *9))))) +(((*1 *1 *1 *2) + (-12 (-4 *1 (-1008 *3 *4 *2 *5)) (-4 *3 (-1081)) (-4 *4 (-817)) + (-4 *2 (-872)) (-4 *5 (-1097 *3 *4 *2))))) (((*1 *2 *3 *3) (-12 (-5 *3 (-793)) (-5 *2 (-1299 (-663 (-560)))) (-5 *1 (-494)))) ((*1 *1 *2 *3) @@ -4964,118 +4569,98 @@ ((*1 *1 *2 *3) (-12 (-5 *2 (-1 *3 *3)) (-4 *3 (-1249)) (-5 *1 (-1187 *3)))) ((*1 *1 *2) (-12 (-5 *2 (-1 *3)) (-4 *3 (-1249)) (-5 *1 (-1187 *3))))) -(((*1 *2 *2) - (-12 (-5 *2 (-114)) (-5 *1 (-352 *3 *4 *5)) (-14 *3 (-663 (-1209))) - (-14 *4 (-663 (-1209))) (-4 *5 (-401)))) - ((*1 *2) - (-12 (-5 *2 (-114)) (-5 *1 (-352 *3 *4 *5)) (-14 *3 (-663 (-1209))) - (-14 *4 (-663 (-1209))) (-4 *5 (-401))))) -(((*1 *2 *3 *3 *3 *3) - (-12 (-5 *3 (-560)) (-5 *2 (-114)) (-5 *1 (-494))))) -(((*1 *2 *3 *4 *3 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(-1299 *4)) (-4 *4 (-1249)) (-4 *1 (-245 *3 *4))))) (((*1 *1 *1) (-4 *1 (-95))) @@ -5264,31 +4933,27 @@ ((*1 *2 *2) (-12 (-5 *2 (-1187 *3)) (-4 *3 (-38 (-421 (-560)))) (-5 *1 (-1195 *3))))) -(((*1 *2 *2) (|partial| -12 (-5 *1 (-601 *2)) (-4 *2 (-559))))) -(((*1 *2 *3) - (-12 (-5 *3 (-560)) (-4 *4 (-817)) (-4 *5 (-872)) (-4 *2 (-1081)) - (-5 *1 (-333 *4 *5 *2 *6)) (-4 *6 (-980 *2 *4 *5))))) -(((*1 *2 *1) - (-12 (-4 *1 (-1244 *3 *4 *5 *6)) (-4 *3 (-571)) (-4 *4 (-817)) - (-4 *5 (-872)) (-4 *6 (-1097 *3 *4 *5)) (-5 *2 (-663 *5))))) -(((*1 *2 *3 *3) - (-12 (-5 *3 (-1268 *5 *4)) (-4 *4 (-844)) (-14 *5 (-1209)) - (-5 *2 (-663 *4)) (-5 *1 (-1146 *4 *5))))) -(((*1 *1 *2 *3) - (-12 (-5 *2 (-850)) (-5 *3 (-663 (-1209))) (-5 *1 (-849))))) +(((*1 *2 *1) (-12 (-5 *2 (-560)) (-5 *1 (-944 *3)) (-4 *3 (-319))))) +(((*1 *2 *2 *3 *4 *4) + (-12 (-5 *4 (-560)) (-4 *3 (-175)) (-4 *5 (-385 *3)) + (-4 *6 (-385 *3)) (-5 *1 (-710 *3 *5 *6 *2)) + (-4 *2 (-708 *3 *5 *6))))) +(((*1 *2 *2 *3) + (|partial| -12 (-5 *2 (-663 (-1203 *4))) (-5 *3 (-1203 *4)) + (-4 *4 (-940)) (-5 *1 (-685 *4))))) (((*1 *1 *1 *2) (-12 (-5 *2 (-1266 (-560))) (-4 *1 (-673 *3)) (-4 *3 (-1249)))) ((*1 *1 *1 *2) (-12 (-5 *2 (-560)) (-4 *1 (-673 *3)) (-4 *3 (-1249))))) -(((*1 *2 *3 *4) - (-12 (-5 *3 (-1203 *5)) (-4 *5 (-376)) (-5 *2 (-663 *6)) - (-5 *1 (-546 *5 *6 *4)) (-4 *6 (-376)) (-4 *4 (-13 (-376) (-871)))))) -(((*1 *2 *3 *1) - (-12 (-5 *3 (-520)) (-5 *2 (-713 (-109))) (-5 *1 (-178)))) - ((*1 *2 *3 *1) - (-12 (-5 *3 (-520)) (-5 *2 (-713 (-109))) (-5 *1 (-1117))))) +(((*1 *2 *1) (-12 (-4 *1 (-403)) (-5 *2 (-114))))) (((*1 *2 *3) - (-12 (-5 *3 (-1209)) (-5 *2 (-549)) (-5 *1 (-550 *4)) - (-4 *4 (-1249))))) + (-12 (-5 *2 (-1 (-973 *3) (-973 *3))) (-5 *1 (-179 *3)) + (-4 *3 (-13 (-376) (-1235) (-1034)))))) +(((*1 *2 *1) + (-12 (-5 *2 (-2 (|:| -1659 *1) (|:| -4497 *1) (|:| |associate| *1))) + (-4 *1 (-571))))) +(((*1 *2 *1) (-12 (-5 *2 (-114)) (-5 *1 (-850))))) +(((*1 *2 *1 *3 *3 *3 *2) + (-12 (-5 *3 (-793)) (-5 *1 (-697 *2)) (-4 *2 (-1133))))) (((*1 *2 *1) (-12 (-4 *1 (-168 *2)) (-4 *2 (-175)))) ((*1 *2 *3) (-12 (-4 *4 (-13 (-571) (-1070 (-560)))) (-5 *2 (-326 *4)) @@ -5296,14 +4961,11 @@ ((*1 *2 *2) (-12 (-4 *3 (-13 (-466) (-1070 (-560)) (-660 (-560)))) (-5 *1 (-1239 *3 *2)) (-4 *2 (-13 (-27) (-1235) (-435 *3)))))) -(((*1 *1 *1) - (-12 (-5 *1 (-609 *2)) (-4 *2 (-38 (-421 (-560)))) (-4 *2 (-1081))))) -(((*1 *1 *1) - (-12 (|has| *1 (-6 -4511)) (-4 *1 (-385 *2)) (-4 *2 (-1249)) - (-4 *2 (-872)))) - ((*1 *1 *2 *1) - (-12 (-5 *2 (-1 (-114) *3 *3)) (|has| *1 (-6 -4511)) - (-4 *1 (-385 *3)) (-4 *3 (-1249))))) +(((*1 *2 *3) + (-12 (-5 *2 (-1203 (-560))) (-5 *1 (-972)) (-5 *3 (-560))))) +(((*1 *2 *3) + (-12 (-5 *3 (-255 *4 *5)) (-14 *4 (-663 (-1209))) (-4 *5 (-466)) + (-5 *2 (-495 *4 *5)) (-5 *1 (-650 *4 *5))))) (((*1 *1 *1) (-4 *1 (-95))) ((*1 *2 *2) (-12 (-4 *3 (-571)) (-5 *1 (-287 *3 *2)) @@ -5320,31 +4982,43 @@ ((*1 *2 *2) (-12 (-5 *2 (-1187 *3)) (-4 *3 (-38 (-421 (-560)))) (-5 *1 (-1195 *3))))) +(((*1 *2 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*6 *2))))) -(((*1 *2) - (-12 (-4 *4 (-175)) (-5 *2 (-114)) (-5 *1 (-379 *3 *4)) - (-4 *3 (-380 *4)))) - ((*1 *2) (-12 (-4 *1 (-380 *3)) (-4 *3 (-175)) (-5 *2 (-114))))) + (|partial| -12 (-5 *4 (-421 *2)) (-4 *2 (-1275 *5)) + (-5 *1 (-831 *5 *2 *3 *6)) + (-4 *5 (-13 (-376) (-149) (-1070 (-421 (-560))))) + (-4 *3 (-680 *2)) (-4 *6 (-680 *4)))) + ((*1 *2 *3 *4) + (-12 (-5 *4 (-663 (-421 *2))) (-4 *2 (-1275 *5)) + (-5 *1 (-831 *5 *2 *3 *6)) + (-4 *5 (-13 (-376) (-149) (-1070 (-421 (-560))))) (-4 *3 (-680 *2)) + (-4 *6 (-680 (-421 *2)))))) +(((*1 *1 *1) + (-12 (-5 *1 (-609 *2)) (-4 *2 (-38 (-421 (-560)))) (-4 *2 (-1081))))) (((*1 *2 *1) (-12 (-4 *1 (-168 *2)) (-4 *2 (-175)))) ((*1 *2 *3) (-12 (-4 *4 (-13 (-571) (-1070 (-560)))) (-5 *2 (-326 *4)) @@ -5354,13 +5028,11 @@ ((*1 *2 *2) (-12 (-4 *3 (-13 (-466) (-1070 (-560)) (-660 (-560)))) (-5 *1 (-1239 *3 *2)) (-4 *2 (-13 (-27) (-1235) (-435 *3)))))) -(((*1 *2 *2 *2) - (-12 (-4 *3 (-376)) (-5 *1 (-788 *2 *3)) (-4 *2 (-730 *3)))) - ((*1 *1 *1 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(-1081))))) +(((*1 *2 *2) + (-12 (-4 *3 (-571)) (-5 *1 (-160 *3 *2)) (-4 *2 (-435 *3)))) + ((*1 *2 *2 *3) + (-12 (-5 *3 (-1209)) (-4 *4 (-571)) (-5 *1 (-160 *4 *2)) + (-4 *2 (-435 *4)))) + ((*1 *1 *1 *2) (-12 (-4 *1 (-162)) (-5 *2 (-1209)))) + ((*1 *1 *1) (-4 *1 (-162)))) (((*1 *1 *1) (-12 (-5 *1 (-352 *2 *3 *4)) (-14 *2 (-663 (-1209))) (-14 *3 (-663 (-1209))) (-4 *4 (-401)))) @@ -5437,10 +5202,11 @@ ((*1 *1 *2) (-12 (-5 *2 (-421 (-560))) (-4 *1 (-1044)))) ((*1 *1 *1 *2) (-12 (-4 *1 (-1044)) (-5 *2 (-949)))) ((*1 *1 *1) (-4 *1 (-1044)))) -(((*1 *2 *1) (-12 (-5 *2 (-560)) (-5 *1 (-847))))) -(((*1 *2) - (-12 (-4 *1 (-355 *3 *4 *5)) (-4 *3 (-1254)) (-4 *4 (-1275 *3)) - (-4 *5 (-1275 (-421 *4))) (-5 *2 (-711 (-421 *4)))))) +(((*1 *1 *1 *1) (-12 (-4 *1 (-877 *2)) (-4 *2 (-1081)) (-4 *2 (-376))))) +(((*1 *2 *3 *4) + (-12 (-5 *3 (-663 (-802 *5 (-889 *6)))) (-5 *4 (-114)) (-4 *5 (-466)) + (-14 *6 (-663 (-1209))) (-5 *2 (-663 (-1078 *5 *6))) + (-5 *1 (-647 *5 *6))))) (((*1 *1 *1) (-4 *1 (-95))) ((*1 *2 *2) (-12 (-4 *3 (-571)) (-5 *1 (-287 *3 *2)) @@ -5460,32 +5226,59 @@ ((*1 *2 *2) (-12 (-5 *2 (-1187 *3)) (-4 *3 (-38 (-421 (-560)))) (-5 *1 (-1195 *3))))) -(((*1 *2) - (-12 (-4 *4 (-175)) (-5 *2 (-114)) (-5 *1 (-379 *3 *4)) - (-4 *3 (-380 *4)))) - ((*1 *2) (-12 (-4 *1 (-380 *3)) (-4 *3 (-175)) (-5 *2 (-114))))) -(((*1 *1 *2) (-12 (-5 *2 (-114)) (-5 *1 (-270)))) - ((*1 *2 *3 *2) - (-12 (-5 *2 (-114)) (-5 *3 (-663 (-270))) (-5 *1 (-271))))) -(((*1 *1 *2) - (-12 (-5 *2 (-663 (-932 *3))) (-4 *3 (-1133)) (-5 *1 (-935 *3))))) -(((*1 *2 *3) - (-12 (-5 *3 (-1203 *6)) (-4 *6 (-1081)) (-4 *4 (-817)) (-4 *5 (-872)) - (-5 *2 (-1203 *7)) (-5 *1 (-333 *4 *5 *6 *7)) - (-4 *7 (-980 *6 *4 *5))))) -(((*1 *1) (-5 *1 (-622)))) -(((*1 *2 *3 *4 *3 *5 *3) - (-12 (-5 *4 (-711 (-229))) (-5 *5 (-711 (-560))) (-5 *3 (-560)) - (-5 *2 (-1067)) (-5 *1 (-776))))) -(((*1 *2 *3 *4) - (|partial| -12 (-5 *3 (-1299 *4)) (-4 *4 (-13 (-1081) (-660 (-560)))) - (-5 *2 (-1299 (-421 (-560)))) (-5 *1 (-1328 *4))))) 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+(((*1 *2 *3 *4 *2 *5 *6) + (-12 + (-5 *5 + (-2 (|:| |done| (-663 *11)) + (|:| |todo| (-663 (-2 (|:| |val| *3) (|:| -3265 *11)))))) + (-5 *6 (-793)) + (-5 *2 (-663 (-2 (|:| |val| (-663 *10)) (|:| -3265 *11)))) + (-5 *3 (-663 *10)) (-5 *4 (-663 *11)) (-4 *10 (-1097 *7 *8 *9)) + (-4 *11 (-1103 *7 *8 *9 *10)) (-4 *7 (-466)) (-4 *8 (-817)) + (-4 *9 (-872)) (-5 *1 (-1101 *7 *8 *9 *10 *11)))) + ((*1 *2 *3 *4 *2 *5 *6) + (-12 + (-5 *5 + (-2 (|:| |done| (-663 *11)) + (|:| |todo| (-663 (-2 (|:| |val| *3) (|:| -3265 *11)))))) + (-5 *6 (-793)) + (-5 *2 (-663 (-2 (|:| |val| (-663 *10)) (|:| -3265 *11)))) + (-5 *3 (-663 *10)) (-5 *4 (-663 *11)) (-4 *10 (-1097 *7 *8 *9)) + (-4 *11 (-1141 *7 *8 *9 *10)) (-4 *7 (-466)) (-4 *8 (-817)) + (-4 *9 (-872)) (-5 *1 (-1177 *7 *8 *9 *10 *11))))) +(((*1 *1) (-5 *1 (-143))) ((*1 *1 *1) (-5 *1 (-146))) + ((*1 *1 *1) (-4 *1 (-1176)))) (((*1 *2 *3 *4) - (-12 (-5 *4 (-793)) (-4 *5 (-1081)) (-4 *2 (-1275 *5)) - (-5 *1 (-1294 *5 *2 *6 *3)) (-4 *6 (-680 *2)) (-4 *3 (-1292 *5))))) -(((*1 *1 *1 *2) - (|partial| -12 (-4 *1 (-1244 *3 *4 *5 *2)) (-4 *3 (-571)) - (-4 *4 (-817)) (-4 *5 (-872)) (-4 *2 (-1097 *3 *4 *5))))) + (-12 (-5 *3 (-663 (-326 (-229)))) (-5 *4 (-793)) + (-5 *2 (-711 (-229))) (-5 *1 (-278))))) (((*1 *2 *3 *4) (-12 (-5 *4 (-663 (-48))) (-5 *2 (-419 *3)) (-5 *1 (-39 *3)) (-4 *3 (-1275 (-48))))) @@ -5626,24 +5419,10 @@ ((*1 *2 *1) (-12 (-5 *2 (-419 *1)) (-4 *1 (-1254)))) ((*1 *2 *3) (-12 (-5 *2 (-419 *3)) (-5 *1 (-1265 *3)) (-4 *3 (-1275 (-560)))))) -(((*1 *2 *3 *4) - (-12 (-5 *4 (-711 (-421 (-976 (-560))))) - (-5 *2 (-663 (-711 (-326 (-560))))) (-5 *1 (-1060)) - (-5 *3 (-326 (-560)))))) -(((*1 *2 *3) - (-12 (-5 *3 (-1299 (-663 (-2 (|:| -3950 *4) (|:| -4021 (-1152)))))) - (-4 *4 (-363)) (-5 *2 (-793)) (-5 *1 (-360 *4)))) - ((*1 *2) - (-12 (-5 *2 (-793)) (-5 *1 (-365 *3 *4)) (-14 *3 (-949)) - (-14 *4 (-949)))) - ((*1 *2) - (-12 (-5 *2 (-793)) (-5 *1 (-366 *3 *4)) (-4 *3 (-363)) - (-14 *4 - (-3 (-1203 *3) - (-1299 (-663 (-2 (|:| -3950 *3) (|:| -4021 (-1152))))))))) - ((*1 *2) - (-12 (-5 *2 (-793)) (-5 *1 (-367 *3 *4)) (-4 *3 (-363)) - (-14 *4 (-949))))) +(((*1 *1 *1) + (-12 (-4 *1 (-262 *2 *3 *4 *5)) (-4 *2 (-1081)) (-4 *3 (-872)) + (-4 *4 (-277 *3)) (-4 *5 (-817))))) +(((*1 *2 *2 *2) (-12 (-5 *2 (-1211 (-421 (-560)))) (-5 *1 (-193))))) (((*1 *1 *1) (-4 *1 (-95))) ((*1 *2 *2) (-12 (-4 *3 (-571)) (-5 *1 (-287 *3 *2)) @@ -5663,29 +5442,16 @@ ((*1 *2 *2) (-12 (-5 *2 (-1187 *3)) (-4 *3 (-38 (-421 (-560)))) (-5 *1 (-1195 *3))))) -(((*1 *2 *3) - (-12 (-5 *2 (-630 *4)) (-5 *1 (-631 *3 *4)) (-4 *3 (-1133)) - (-4 *4 (-1133))))) -(((*1 *1 *2 *3 *1) (-12 (-5 *2 (-520)) (-5 *3 (-611)) (-5 *1 (-600))))) -(((*1 *2 *3 *4 *4) - (-12 (-5 *4 (-114)) (-4 *5 (-466)) (-4 *6 (-817)) (-4 *7 (-872)) - (-4 *8 (-1097 *5 *6 *7)) - (-5 *2 - (-2 (|:| |val| (-663 *8)) - (|:| |towers| (-663 (-1059 *5 *6 *7 *8))))) - (-5 *1 (-1059 *5 *6 *7 *8)) (-5 *3 (-663 *8)))) - ((*1 *2 *3 *4 *4) - (-12 (-5 *4 (-114)) (-4 *5 (-466)) (-4 *6 (-817)) (-4 *7 (-872)) - (-4 *8 (-1097 *5 *6 *7)) - (-5 *2 - (-2 (|:| |val| (-663 *8)) - (|:| |towers| (-663 (-1178 *5 *6 *7 *8))))) - (-5 *1 (-1178 *5 *6 *7 *8)) (-5 *3 (-663 *8))))) -(((*1 *2 *1 *1) (-12 (-4 *1 (-559)) (-5 *2 (-114))))) -(((*1 *2 *3) (-12 (-5 *3 (-865)) (-5 *2 (-1067)) (-5 *1 (-864)))) - ((*1 *2 *3 *4) - (-12 (-5 *3 (-663 (-326 (-391)))) (-5 *4 (-663 (-391))) - (-5 *2 (-1067)) (-5 *1 (-864))))) +(((*1 *2 *3 *2 *4) + (-12 (-5 *3 (-663 *6)) (-5 *4 (-663 (-255 *5 *6))) (-4 *6 (-466)) + (-5 *2 (-255 *5 *6)) (-14 *5 (-663 (-1209))) (-5 *1 (-650 *5 *6))))) +(((*1 *2 *2) (-12 (-5 *2 (-949)) (-5 *1 (-369 *3)) (-4 *3 (-363))))) +(((*1 *2 *1) (-12 (-4 *1 (-696 *3)) (-4 *3 (-1249)) (-5 *2 (-114))))) +(((*1 *2 *3 *1) + (-12 (-4 *4 (-376)) (-4 *5 (-817)) (-4 *6 (-872)) (-5 *2 (-114)) + (-5 *1 (-518 *4 *5 *6 *3)) (-4 *3 (-980 *4 *5 *6))))) +(((*1 *2 *1 *2) (-12 (-5 *2 (-663 (-1191))) (-5 *1 (-407)))) + ((*1 *2 *1 *2) (-12 (-5 *2 (-663 (-1191))) (-5 *1 (-1229))))) (((*1 *1 *1) (-5 *1 (-888))) ((*1 *2 *1) (-12 (-4 *1 (-1136 *2 *3 *4 *5 *6)) (-4 *3 (-1133)) (-4 *4 (-1133)) @@ -5693,20 +5459,26 @@ ((*1 *1 *2) (-12 (-5 *2 (-229)) (-5 *1 (-1191)))) ((*1 *1 *2) (-12 (-5 *2 (-560)) (-5 *1 (-1191)))) ((*1 *2 *1) (-12 (-5 *2 (-1191)) (-5 *1 (-1209))))) -(((*1 *2 *1) (-12 (-4 *1 (-571)) (-5 *2 (-114))))) -(((*1 *2 *1 *3) - (-12 (-5 *2 (-663 (-1191))) (-5 *1 (-1095)) (-5 *3 (-1191))))) -(((*1 *1 *2 *2 *2) (-12 (-5 *1 (-908 *2)) (-4 *2 (-1249))))) (((*1 *2 *3 *4) + (|partial| -12 (-5 *4 (-949)) (-4 *5 (-571)) (-5 *2 (-711 *5)) + (-5 *1 (-987 *5 *3)) (-4 *3 (-680 *5))))) +(((*1 *2 *3 *4) + (-12 (-5 *3 (-663 *2)) (-5 *4 (-1 (-114) *2 *2)) (-5 *1 (-1251 *2)) + (-4 *2 (-1133)))) + ((*1 *2 *3) + (-12 (-5 *3 (-663 *2)) (-4 *2 (-1133)) (-4 *2 (-872)) + (-5 *1 (-1251 *2))))) +(((*1 *2 *3 *3 *3 *4) (-12 (-5 *3 (-229)) (-5 *4 (-560)) (-5 *2 (-1067)) (-5 *1 (-780))))) -(((*1 *2 *3 *3 *4) - (-12 (-5 *3 (-663 (-495 *5 *6))) (-5 *4 (-889 *5)) - (-14 *5 (-663 (-1209))) (-5 *2 (-495 *5 *6)) (-5 *1 (-650 *5 *6)) - (-4 *6 (-466)))) - ((*1 *2 *3 *4) - (-12 (-5 *3 (-663 (-495 *5 *6))) (-5 *4 (-889 *5)) - (-14 *5 (-663 (-1209))) (-5 *2 (-495 *5 *6)) (-5 *1 (-650 *5 *6)) - (-4 *6 (-466))))) +(((*1 *2 *3) + (|partial| -12 (-4 *4 (-571)) (-4 *5 (-817)) (-4 *6 (-872)) + (-4 *7 (-1097 *4 *5 *6)) + (-5 *2 (-2 (|:| |bas| (-490 *4 *5 *6 *7)) (|:| -2810 (-663 *7)))) + (-5 *1 (-1009 *4 *5 *6 *7)) (-5 *3 (-663 *7))))) +(((*1 *2 *1) + (-12 (-4 *1 (-1008 *3 *4 *5 *6)) (-4 *3 (-1081)) (-4 *4 (-817)) + (-4 *5 (-872)) (-4 *6 (-1097 *3 *4 *5)) (-4 *3 (-571)) + (-5 *2 (-114))))) (((*1 *2 *2) (-12 (-4 *3 (-571)) (-5 *1 (-287 *3 *2)) (-4 *2 (-13 (-435 *3) (-1034))))) @@ -5723,45 +5495,51 @@ (-12 (-5 *2 (-1187 *3)) (-4 *3 (-38 (-421 (-560)))) (-5 *1 (-1195 *3)))) ((*1 *1 *1) (-4 *1 (-1238)))) -(((*1 *1 *2 *2 *2) - (-12 (-5 *1 (-231 *2)) (-4 *2 (-13 (-376) (-1235))))) - ((*1 *1 *1 *2) (-12 (-5 *1 (-740 *2)) (-4 *2 (-376)))) - ((*1 *1 *2) (-12 (-5 *1 (-740 *2)) (-4 *2 (-376)))) - ((*1 *2 *1 *3 *4 *4) - (-12 (-5 *3 (-949)) 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(-976 *6)) *5 *4)) (-5 *1 (-754 *5 *4 *6 *2)) + (-4 *5 (-817)) + (-4 *4 (-13 (-872) (-10 -8 (-15 -3202 ((-1209) $)))))))) +(((*1 *2 *1) (-12 (-5 *2 (-114)) (-5 *1 (-1245 *3)) (-4 *3 (-1006))))) +(((*1 *2) + (-12 (-5 *2 (-949)) (-5 *1 (-456 *3)) (-4 *3 (-1275 (-560))))) + ((*1 *2 *2) + (-12 (-5 *2 (-949)) (-5 *1 (-456 *3)) (-4 *3 (-1275 (-560)))))) +(((*1 *2 *1) (|partial| -12 (-5 *2 (-520)) (-5 *1 (-291)))) + ((*1 *2 *1) + (-12 (-5 *2 (-3 (-560) (-229) (-520) (-1191) (-1214))) + (-5 *1 (-1214))))) (((*1 *2 *1 *3) (-12 (-5 *3 (-630 *1)) (-4 *1 (-435 *4)) (-4 *4 (-1133)) (-4 *4 (-571)) (-5 *2 (-421 (-1203 *1))))) @@ -5861,20 +5637,19 @@ (-5 *1 (-981 *5 *4 *6 *7 *3)) (-4 *3 (-13 (-376) - (-10 -8 (-15 -2590 ($ *7)) (-15 -4445 (*7 $)) (-15 -4453 (*7 $))))))) + (-10 -8 (-15 -2590 ($ *7)) (-15 -4445 (*7 $)) (-15 -4454 (*7 $))))))) ((*1 *2 *3 *4 *2) (-12 (-5 *2 (-1203 *3)) (-4 *3 (-13 (-376) - (-10 -8 (-15 -2590 ($ *7)) (-15 -4445 (*7 $)) (-15 -4453 (*7 $))))) + (-10 -8 (-15 -2590 ($ *7)) (-15 -4445 (*7 $)) (-15 -4454 (*7 $))))) (-4 *7 (-980 *6 *5 *4)) (-4 *5 (-817)) (-4 *4 (-872)) (-4 *6 (-1081)) (-5 *1 (-981 *5 *4 *6 *7 *3)))) ((*1 *2 *3 *4) (-12 (-5 *4 (-1209)) (-4 *5 (-571)) (-5 *2 (-421 (-1203 (-421 (-976 *5))))) (-5 *1 (-1072 *5)) (-5 *3 (-421 (-976 *5)))))) -(((*1 *2) (-12 (-5 *2 (-560)) (-5 *1 (-721)))) - ((*1 *2 *2) (-12 (-5 *2 (-560)) (-5 *1 (-721))))) +(((*1 *1 *2) (-12 (-5 *2 (-1152)) (-5 *1 (-846))))) (((*1 *2 *2) (-12 (-4 *3 (-571)) (-5 *1 (-287 *3 *2)) (-4 *2 (-13 (-435 *3) (-1034))))) @@ -5907,13 +5682,13 @@ (-2 (|:| |switch| (-1208)) (|:| |thenClause| (-342)) (|:| |elseClause| (-342)))) (|:| |returnBranch| - (-2 (|:| -2926 (-114)) - (|:| -3950 + (-2 (|:| -3111 (-114)) + (|:| -3949 (-2 (|:| |ints2Floats?| (-114)) (|:| -2129 (-888)))))) (|:| |blockBranch| (-663 (-342))) (|:| |commentBranch| (-663 (-1191))) (|:| |callBranch| (-1191)) (|:| |forBranch| - (-2 (|:| -4389 (-1124 (-976 (-560)))) + (-2 (|:| -1404 (-1124 (-976 (-560)))) (|:| |span| (-976 (-560))) (|:| -3985 (-342)))) (|:| |labelBranch| (-1152)) (|:| |loopBranch| (-2 (|:| |switch| (-1208)) (|:| -3985 (-342)))) @@ -5924,32 +5699,33 @@ (((*1 *1 *2 *2) (-12 (-5 *2 - (-3 (|:| I (-326 (-560))) (|:| -1612 (-326 (-391))) + (-3 (|:| I (-326 (-560))) (|:| -1613 (-326 (-391))) (|:| CF (-326 (-171 (-391)))) (|:| |switch| (-1208)))) (-5 *1 (-1208))))) -(((*1 *1 *1 *1) (-12 (-5 *1 (-803 *2)) (-4 *2 (-571)) (-4 *2 (-1081)))) - ((*1 *2 *2 *2) - (-12 (-4 *3 (-571)) (-5 *1 (-1001 *3 *2)) (-4 *2 (-1275 *3)))) - ((*1 *1 *1 *1) - (-12 (-4 *1 (-1097 *2 *3 *4)) (-4 *2 (-1081)) (-4 *3 (-817)) - (-4 *4 (-872)) (-4 *2 (-571)))) - ((*1 *2 *3 *3 *1) - (-12 (-4 *4 (-466)) (-4 *5 (-817)) (-4 *6 (-872)) - (-4 *3 (-1097 *4 *5 *6)) - (-5 *2 (-663 (-2 (|:| |val| *3) (|:| -3265 *1)))) - (-4 *1 (-1103 *4 *5 *6 *3))))) -(((*1 *2 *3 *3) (-12 (-5 *3 (-1191)) (-5 *2 (-323)) (-5 *1 (-853))))) -(((*1 *2 *3 *4 *5) - (-12 (-5 *3 (-1203 *9)) (-5 *4 (-663 *7)) (-4 *7 (-872)) - (-4 *9 (-980 *8 *6 *7)) (-4 *6 (-817)) (-4 *8 (-319)) - (-5 *2 (-663 (-793))) (-5 *1 (-764 *6 *7 *8 *9)) (-5 *5 (-793))))) -(((*1 *1 *1) (-5 *1 (-1095)))) +(((*1 *1 *1 *2 *3) + (-12 (-5 *2 (-1209)) (-5 *3 (-391)) (-5 *1 (-1095))))) +(((*1 *2 *3) + (|partial| -12 + (-5 *3 + (-2 (|:| |xinit| (-229)) (|:| |xend| (-229)) + (|:| |fn| (-1299 (-326 (-229)))) (|:| |yinit| (-663 (-229))) + (|:| |intvals| (-663 (-229))) (|:| |g| (-326 (-229))) + (|:| |abserr| (-229)) (|:| |relerr| (-229)))) + (-5 *2 + (-2 (|:| |stiffness| (-391)) (|:| |stability| (-391)) + (|:| |expense| (-391)) (|:| |accuracy| (-391)) + (|:| |intermediateResults| (-391)))) + (-5 *1 (-827))))) +(((*1 *2 *2) (|partial| -12 (-4 *1 (-1015 *2)) (-4 *2 (-1235))))) +(((*1 *2 *2) + (-12 (-4 *3 (-466)) (-5 *1 (-1241 *3 *2)) + (-4 *2 (-13 (-435 *3) (-1235)))))) (((*1 *2 *1) (-12 (-5 *2 (-663 (-2 (|:| |var| (-1209)) (|:| |fn| (-326 (-229))) - (|:| -4389 (-1121 (-866 (-229)))) (|:| |abserr| (-229)) + (|:| -1404 (-1121 (-866 (-229)))) (|:| |abserr| (-229)) (|:| |relerr| (-229))))) (-5 *1 (-574)))) ((*1 *2 *1) @@ -5965,22 +5741,25 @@ (|:| |abserr| (-229)) (|:| |relerr| (-229))))) (-5 *1 (-827))))) (((*1 *2 *3) - (-12 (-4 *1 (-363)) (-5 *3 (-560)) (-5 *2 (-1221 (-949) (-793)))))) -(((*1 *2 *3 *4 *2) - (-12 (-5 *3 (-1 *2 (-793) *2)) (-5 *4 (-793)) (-4 *2 (-1133)) - (-5 *1 (-700 *2)))) - ((*1 *2 *2) - (-12 (-5 *2 (-1 *3 (-793) *3)) (-4 *3 (-1133)) (-5 *1 (-704 *3))))) -(((*1 *2 *2) - (-12 (-4 *3 (-571)) (-5 *1 (-648 *3 *2)) - (-4 *2 (-13 (-435 *3) (-1034) (-1235))))) - ((*1 *1 *1) (-4 *1 (-649)))) -(((*1 *2 *3 *3) - (-12 (-4 *3 (-1254)) (-4 *5 (-1275 *3)) (-4 *6 (-1275 (-421 *5))) - (-5 *2 (-114)) (-5 *1 (-354 *4 *3 *5 *6)) (-4 *4 (-355 *3 *5 *6)))) - ((*1 *2 *3 *3) - (-12 (-4 *1 (-355 *3 *4 *5)) (-4 *3 (-1254)) (-4 *4 (-1275 *3)) - (-4 *5 (-1275 (-421 *4))) (-5 *2 (-114))))) + (-12 (-4 *4 (-817)) (-4 *5 (-872)) (-4 *6 (-319)) + (-5 *2 (-663 (-793))) (-5 *1 (-800 *3 *4 *5 *6 *7)) + (-4 *3 (-1275 *6)) (-4 *7 (-980 *6 *4 *5))))) +(((*1 *2 *3) + (-12 (-5 *3 (-711 (-421 (-976 (-560))))) (-5 *2 (-663 (-326 (-560)))) + (-5 *1 (-1060))))) +(((*1 *2 *3 *1) + (-12 (|has| *1 (-6 -4510)) (-4 *1 (-503 *3)) (-4 *3 (-1249)) + (-4 *3 (-1133)) (-5 *2 (-114)))) + ((*1 *2 *3 *1) + (-12 (-5 *3 (-932 *4)) (-4 *4 (-1133)) (-5 *2 (-114)) + (-5 *1 (-935 *4)))) + ((*1 *2 *3 *1) + (-12 (-5 *3 (-949)) (-5 *2 (-114)) (-5 *1 (-1134 *4 *5)) (-14 *4 *3) + (-14 *5 *3)))) +(((*1 *2 *1) (-12 (-5 *2 (-793)) (-5 *1 (-339 *3)) (-4 *3 (-1249)))) + ((*1 *2 *1) + (-12 (-5 *2 (-793)) (-5 *1 (-530 *3 *4)) (-4 *3 (-1249)) + (-14 *4 (-560))))) (((*1 *2 *2) (-12 (-5 *2 (-115)) (-4 *3 (-571)) (-5 *1 (-32 *3 *4)) (-4 *4 (-435 *3)))) @@ -6008,10 +5787,7 @@ (-4 *4 (-13 (-435 *3) (-1034) (-1235))))) ((*1 *2 *1) (-12 (-5 *2 (-1167)) (-5 *1 (-1051)))) ((*1 *1 *2 *3) (-12 (-5 *3 (-55)) (-5 *1 (-1223 *2)) (-4 *2 (-1133))))) -(((*1 *2 *3 *3 *4 *4 *5 *5 *3 *3 *4 *4 *5 *5 *3 *3 *4 *4 *5 *5 *3 *4 *4 - *4 *6 *4) - (-12 (-5 *4 (-560)) (-5 *5 (-711 (-229))) (-5 *6 (-697 (-229))) - (-5 *3 (-229)) (-5 *2 (-1067)) (-5 *1 (-772))))) +(((*1 *2) (-12 (-5 *2 (-1305)) (-5 *1 (-574))))) (((*1 *1 *1) (-12 (-4 *1 (-385 *2)) (-4 *2 (-1249)) (-4 *2 (-872)))) ((*1 *1 *2 *1) (-12 (-5 *2 (-1 (-114) *3 *3)) (-4 *1 (-385 *3)) (-4 *3 (-1249)))) @@ -6020,15 +5796,9 @@ ((*1 *2 *1 *3) (-12 (-4 *4 (-1081)) (-4 *5 (-817)) (-4 *3 (-872)) (-4 *6 (-1097 *4 *5 *3)) - (-5 *2 (-2 (|:| |under| *1) (|:| -2867 *1) (|:| |upper| *1))) + (-5 *2 (-2 (|:| |under| *1) (|:| -3782 *1) (|:| |upper| *1))) (-4 *1 (-1008 *4 *5 *3 *6))))) -(((*1 *2 *3) - (-12 (-5 *3 (-663 (-495 *4 *5))) (-14 *4 (-663 (-1209))) - (-4 *5 (-466)) - (-5 *2 - (-2 (|:| |gblist| (-663 (-255 *4 *5))) - (|:| |gvlist| (-663 (-560))))) - (-5 *1 (-650 *4 *5))))) +(((*1 *1) (-5 *1 (-132)))) (((*1 *2 *2) (-12 (-4 *3 (-571)) (-5 *1 (-287 *3 *2)) (-4 *2 (-13 (-435 *3) (-1034))))) @@ -6048,147 +5818,50 @@ (-12 (-5 *2 (-1187 *3)) (-4 *3 (-38 (-421 (-560)))) (-5 *1 (-1195 *3)))) ((*1 *1 *1) (-4 *1 (-1238)))) -(((*1 *1) (-5 *1 (-1303)))) -(((*1 *2 *3 *4 *5 *5 *6) - (-12 (-5 *4 (-560)) (-5 *6 (-1 (-1305) (-1299 *5) (-1299 *5) (-391))) - (-5 *3 (-1299 (-391))) (-5 *5 (-391)) (-5 *2 (-1305)) - (-5 *1 (-810)))) - ((*1 *2 *3 *4 *5 *5 *6 *3 *3 *3 *3) - (-12 (-5 *4 (-560)) (-5 *6 (-1 (-1305) (-1299 *5) (-1299 *5) (-391))) - (-5 *3 (-1299 (-391))) (-5 *5 (-391)) (-5 *2 (-1305)) - (-5 *1 (-810))))) -(((*1 *2 *3 *4) - (-12 (-5 *3 (-421 (-976 *5))) (-5 *4 (-1209)) - (-4 *5 (-13 (-319) (-149))) (-5 *2 (-663 (-305 (-326 *5)))) - (-5 *1 (-1161 *5)))) - ((*1 *2 *3) - (-12 (-5 *3 (-421 (-976 *4))) (-4 *4 (-13 (-319) (-149))) - (-5 *2 (-663 (-305 (-326 *4)))) (-5 *1 (-1161 *4)))) - ((*1 *2 *3 *4) - (-12 (-5 *3 (-305 (-421 (-976 *5)))) (-5 *4 (-1209)) - (-4 *5 (-13 (-319) (-149))) (-5 *2 (-663 (-305 (-326 *5)))) - (-5 *1 (-1161 *5)))) - ((*1 *2 *3) - (-12 (-5 *3 (-305 (-421 (-976 *4)))) (-4 *4 (-13 (-319) (-149))) - (-5 *2 (-663 (-305 (-326 *4)))) (-5 *1 (-1161 *4)))) - ((*1 *2 *3 *4) - (-12 (-5 *3 (-663 (-421 (-976 *5)))) (-5 *4 (-663 (-1209))) - (-4 *5 (-13 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+ (-5 *2 (-663 (-2 (|:| -4400 (-793)) (|:| -2242 *4) (|:| |num| *4)))) (-4 *4 (-1275 *3)) (-4 *3 (-13 (-376) (-149))) (-5 *1 (-413 *3 *4)))) ((*1 *1 *2 *3 *4) (-12 (-5 *2 (-3 (|:| |fst| (-448)) (|:| -2618 "void"))) @@ -9980,8 +9701,8 @@ ((*1 *1 *2 *3) (-12 (-5 *1 (-735 *2 *3 *4)) (-4 *2 (-872)) (-4 *3 (-1133)) (-14 *4 - (-1 (-114) (-2 (|:| -4021 *2) (|:| -2790 *3)) - (-2 (|:| -4021 *2) (|:| -2790 *3)))))) + (-1 (-114) (-2 (|:| -4019 *2) (|:| -4400 *3)) + (-2 (|:| -4019 *2) (|:| -4400 *3)))))) ((*1 *1 *2 *3) (-12 (-5 *2 (-520)) (-5 *3 (-1147)) (-5 *1 (-862)))) ((*1 *1 *2 *3) (-12 (-5 *1 (-898 *2 *3)) (-4 *2 (-1249)) (-4 *3 (-1249)))) @@ -10020,58 +9741,34 @@ (-4 *4 (-13 (-1133) (-34))) (-5 *1 (-1173 *3 *4)))) ((*1 *1 *2 *3) (-12 (-5 *1 (-1198 *2 *3)) (-4 *2 (-1133)) (-4 *3 (-1133))))) -(((*1 *2 *3 *4 *4 *2 *2 *2) - (-12 (-5 *2 (-560)) - (-5 *3 - (-2 (|:| |lcmfij| *6) (|:| |totdeg| (-793)) (|:| |poli| *4) - (|:| |polj| *4))) - (-4 *6 (-817)) (-4 *4 (-980 *5 *6 *7)) (-4 *5 (-466)) (-4 *7 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(-817)) (-4 *8 (-872)) (-4 *9 (-319)) + (-4 *10 (-980 *9 *7 *8)) + (-5 *2 + (-2 (|:| |deter| (-663 (-1203 *10))) + (|:| |dterm| + (-663 (-663 (-2 (|:| -3333 (-793)) (|:| |pcoef| *10))))) + (|:| |nfacts| (-663 *6)) (|:| |nlead| (-663 *10)))) + (-5 *1 (-800 *6 *7 *8 *9 *10)) (-5 *3 (-1203 *10)) (-5 *4 (-663 *6)) + (-5 *5 (-663 *10))))) +(((*1 *2 *3 *3 *3 *4 *4 *3) + (-12 (-5 *3 (-560)) (-5 *4 (-711 (-229))) (-5 *2 (-1067)) + (-5 *1 (-777))))) +(((*1 *2 *2) (-12 (-5 *2 (-663 (-1191))) (-5 *1 (-409))))) +(((*1 *2 *3) (-12 (-5 *3 (-1191)) (-5 *2 (-51)) (-5 *1 (-853))))) (((*1 *2 *2) - (-12 (-4 *3 (-376)) (-4 *4 (-385 *3)) (-4 *5 (-385 *3)) - (-5 *1 (-535 *3 *4 *5 *2)) (-4 *2 (-708 *3 *4 *5))))) -(((*1 *2 *3) - (-12 - (-5 *3 - (-663 - (-2 (|:| -3812 (-793)) - (|:| |eqns| - (-663 - (-2 (|:| |det| *7) (|:| |rows| (-663 (-560))) - (|:| |cols| (-663 (-560)))))) - (|:| |fgb| (-663 *7))))) - (-4 *7 (-980 *4 *6 *5)) (-4 *4 (-13 (-319) (-149))) - (-4 *5 (-13 (-872) (-633 (-1209)))) (-4 *6 (-817)) (-5 *2 (-793)) - (-5 *1 (-954 *4 *5 *6 *7))))) -(((*1 *2 *3 *3 *4 *5 *5 *5 *5 *3) - (-12 (-5 *3 (-560)) (-5 *4 (-1191)) (-5 *5 (-711 (-229))) - (-5 *2 (-1067)) (-5 *1 (-769))))) -(((*1 *2 *3) - (-12 (-4 *4 (-13 (-571) (-1070 (-560)))) (-5 *2 (-171 (-326 *4))) - (-5 *1 (-191 *4 *3)) (-4 *3 (-13 (-27) (-1235) (-435 (-171 *4)))))) - ((*1 *2 *3) - (-12 (-4 *4 (-13 (-466) (-1070 (-560)) (-660 (-560)))) - (-5 *2 (-171 *3)) (-5 *1 (-1239 *4 *3)) - (-4 *3 (-13 (-27) (-1235) (-435 *4)))))) -(((*1 *2 *3 *4) - (-12 (-5 *3 (-663 *8)) (-5 *4 (-663 *9)) (-4 *8 (-1097 *5 *6 *7)) - (-4 *9 (-1103 *5 *6 *7 *8)) (-4 *5 (-466)) (-4 *6 (-817)) - (-4 *7 (-872)) (-5 *2 (-793)) (-5 *1 (-1101 *5 *6 *7 *8 *9)))) - ((*1 *2 *3 *4) - (-12 (-5 *3 (-663 *8)) (-5 *4 (-663 *9)) (-4 *8 (-1097 *5 *6 *7)) - (-4 *9 (-1141 *5 *6 *7 *8)) (-4 *5 (-466)) (-4 *6 (-817)) - (-4 *7 (-872)) (-5 *2 (-793)) (-5 *1 (-1177 *5 *6 *7 *8 *9))))) -(((*1 *2 *2) (|partial| -12 (-4 *1 (-1015 *2)) (-4 *2 (-1235))))) + (-12 (-5 *2 (-663 *6)) (-4 *6 (-980 *3 *4 *5)) (-4 *3 (-466)) + (-4 *4 (-817)) (-4 *5 (-872)) (-5 *1 (-464 *3 *4 *5 *6))))) (((*1 *1 *2) (-12 (-5 *2 (-1299 *3)) (-4 *3 (-376)) (-14 *6 (-1299 (-711 *3))) (-5 *1 (-44 *3 *4 *5 *6)) (-14 *4 (-949)) (-14 *5 (-663 (-1209))))) @@ -10375,25 +10072,25 @@ (-3 (|:| |nia| (-2 (|:| |var| (-1209)) (|:| |fn| (-326 (-229))) - (|:| -4389 (-1121 (-866 (-229)))) (|:| |abserr| (-229)) + (|:| -1404 (-1121 (-866 (-229)))) (|:| |abserr| (-229)) (|:| |relerr| (-229)))) (|:| |mdnia| (-2 (|:| |fn| (-326 (-229))) - (|:| -4389 (-663 (-1121 (-866 (-229))))) + (|:| -1404 (-663 (-1121 (-866 (-229))))) (|:| |abserr| (-229)) (|:| |relerr| (-229)))))) (-5 *1 (-791)))) ((*1 *1 *2) (-12 (-5 *2 (-2 (|:| |fn| (-326 (-229))) - (|:| -4389 (-663 (-1121 (-866 (-229))))) (|:| |abserr| (-229)) + (|:| -1404 (-663 (-1121 (-866 (-229))))) (|:| |abserr| (-229)) (|:| |relerr| (-229)))) (-5 *1 (-791)))) ((*1 *1 *2) (-12 (-5 *2 (-2 (|:| |var| (-1209)) (|:| |fn| (-326 (-229))) - (|:| -4389 (-1121 (-866 (-229)))) (|:| |abserr| (-229)) + (|:| -1404 (-1121 (-866 (-229)))) (|:| |abserr| (-229)) (|:| |relerr| (-229)))) (-5 *1 (-791)))) ((*1 *2 *3) (-12 (-5 *2 (-795)) (-5 *1 (-796 *3)) (-4 *3 (-1249)))) @@ -10411,23 +10108,23 @@ (-5 *2 (-3 (|:| |noa| - (-2 (|:| |fn| (-326 (-229))) (|:| -2856 (-663 (-229))) + (-2 (|:| |fn| (-326 (-229))) (|:| -2855 (-663 (-229))) (|:| |lb| (-663 (-866 (-229)))) (|:| |cf| (-663 (-326 (-229)))) (|:| |ub| (-663 (-866 (-229)))))) (|:| |lsa| (-2 (|:| |lfn| (-663 (-326 (-229)))) - (|:| -2856 (-663 (-229))))))) + (|:| -2855 (-663 (-229))))))) (-5 *1 (-865)))) ((*1 *1 *2) (-12 (-5 *2 - (-2 (|:| |lfn| (-663 (-326 (-229)))) (|:| -2856 (-663 (-229))))) + (-2 (|:| |lfn| (-663 (-326 (-229)))) (|:| -2855 (-663 (-229))))) (-5 *1 (-865)))) ((*1 *1 *2) (-12 (-5 *2 - (-2 (|:| |fn| (-326 (-229))) (|:| -2856 (-663 (-229))) + (-2 (|:| |fn| (-326 (-229))) (|:| -2855 (-663 (-229))) (|:| |lb| (-663 (-866 (-229)))) (|:| |cf| (-663 (-326 (-229)))) (|:| |ub| (-663 (-866 (-229)))))) (-5 *1 (-865)))) @@ -10528,46 +10225,39 @@ ((*1 *1 *2) (-12 (-5 *2 (-686 *3 *4)) (-4 *3 (-872)) (-4 *4 (-175)) (-5 *1 (-1320 *3 *4))))) -(((*1 *2 *1) (-12 (-5 *2 (-114)) (-5 *1 (-146))))) -(((*1 *2 *1) - (-12 - (-5 *2 - (-663 - (-2 - (|:| -3837 - (-2 (|:| |var| (-1209)) (|:| |fn| (-326 (-229))) - (|:| -4389 (-1121 (-866 (-229)))) (|:| |abserr| (-229)) - (|:| |relerr| (-229)))) - (|:| -2715 - (-2 - (|:| |endPointContinuity| - (-3 (|:| |continuous| "Continuous at the end points") - (|:| |lowerSingular| - "There is a singularity at the lower end point") - (|:| |upperSingular| - "There is a singularity at the upper end point") - (|:| |bothSingular| - "There are singularities at both end points") - (|:| |notEvaluated| - "End point continuity not yet evaluated"))) - (|:| |singularitiesStream| - (-3 (|:| |str| (-1187 (-229))) - (|:| |notEvaluated| - "Internal singularities not yet evaluated"))) - (|:| -4389 - (-3 (|:| |finite| "The range is finite") - (|:| |lowerInfinite| - "The bottom of range is infinite") - (|:| |upperInfinite| "The top of range is infinite") - (|:| |bothInfinite| - "Both top and bottom points are infinite") - (|:| |notEvaluated| "Range not yet evaluated")))))))) - (-5 *1 (-574)))) - ((*1 *2 *1) - (-12 (-4 *1 (-618 *3 *4)) (-4 *3 (-1133)) (-4 *4 (-1249)) - (-5 *2 (-663 *4))))) -(((*1 *1) (-5 *1 (-624))) ((*1 *1) (-5 *1 (-625)))) -(((*1 *1) (-5 *1 (-132)))) +(((*1 *2 *2) (-12 (-5 *2 (-711 (-326 (-560)))) (-5 *1 (-1060))))) +(((*1 *1 *2) + (-12 (-5 *2 (-663 (-518 *3 *4 *5 *6))) (-4 *3 (-376)) (-4 *4 (-817)) + (-4 *5 (-872)) (-5 *1 (-518 *3 *4 *5 *6)) (-4 *6 (-980 *3 *4 *5)))) + ((*1 *1 *1 *1) + (-12 (-4 *2 (-376)) (-4 *3 (-817)) (-4 *4 (-872)) + (-5 *1 (-518 *2 *3 *4 *5)) (-4 *5 (-980 *2 *3 *4)))) + ((*1 *2 *3 *2) + (-12 (-5 *2 (-663 *1)) (-4 *1 (-1103 *4 *5 *6 *3)) (-4 *4 (-466)) + (-4 *5 (-817)) (-4 *6 (-872)) (-4 *3 (-1097 *4 *5 *6)))) + ((*1 *2 *3 *2) + (-12 (-5 *2 (-663 *1)) (-5 *3 (-663 *7)) (-4 *1 (-1103 *4 *5 *6 *7)) + (-4 *4 (-466)) (-4 *5 (-817)) (-4 *6 (-872)) + (-4 *7 (-1097 *4 *5 *6)))) + ((*1 *2 *3 *1) + (-12 (-5 *3 (-663 *7)) (-4 *7 (-1097 *4 *5 *6)) (-4 *4 (-466)) + (-4 *5 (-817)) (-4 *6 (-872)) (-5 *2 (-663 *1)) + (-4 *1 (-1103 *4 *5 *6 *7)))) + ((*1 *2 *3 *1) + (-12 (-4 *4 (-466)) (-4 *5 (-817)) (-4 *6 (-872)) + (-4 *3 (-1097 *4 *5 *6)) (-5 *2 (-663 *1)) + (-4 *1 (-1103 *4 *5 *6 *3)))) + ((*1 *1 *1 *1) (-12 (-4 *1 (-1131 *2)) (-4 *2 (-1133))))) +(((*1 *2 *3 *4) + (-12 (-4 *5 (-466)) (-4 *6 (-817)) (-4 *7 (-872)) + (-4 *3 (-1097 *5 *6 *7)) (-5 *2 (-114)) + (-5 *1 (-1140 *5 *6 *7 *3 *4)) (-4 *4 (-1103 *5 *6 *7 *3)))) + ((*1 *2 *3 *4) + (-12 (-4 *5 (-466)) (-4 *6 (-817)) (-4 *7 (-872)) + (-4 *3 (-1097 *5 *6 *7)) + (-5 *2 (-663 (-2 (|:| |val| (-114)) (|:| -3265 *4)))) + (-5 *1 (-1140 *5 *6 *7 *3 *4)) (-4 *4 (-1103 *5 *6 *7 *3))))) +(((*1 *2 *1) (|partial| -12 (-5 *2 (-520)) (-5 *1 (-291))))) (((*1 *2 *1) (-12 (-4 *1 (-134)) (-5 *2 (-793)))) ((*1 *2 *3 *1 *2) (-12 (-5 *2 (-560)) (-4 *1 (-385 *3)) (-4 *3 (-1249)) @@ -10581,7 +10271,10 @@ ((*1 *2 *1) (-12 (-5 *2 (-1152)) (-5 *1 (-543)))) ((*1 *2 *3 *1 *2) (-12 (-4 *1 (-1176)) (-5 *2 (-560)) (-5 *3 (-143)))) ((*1 *2 *1 *1 *2) (-12 (-4 *1 (-1176)) (-5 *2 (-560))))) -(((*1 *2 *1) (-12 (-5 *2 (-663 (-1250))) (-5 *1 (-538))))) +(((*1 *2 *1 *3) + (-12 (-5 *3 (-1299 *1)) (-4 *1 (-380 *4)) (-4 *4 (-175)) + (-5 *2 (-711 *4)))) + ((*1 *2 *1) (-12 (-4 *1 (-432 *3)) (-4 *3 (-175)) (-5 *2 (-711 *3))))) (((*1 *1 *2 *2 *3) (-12 (-5 *2 (-793)) (-4 *3 (-1249)) (-4 *1 (-57 *3 *4 *5)) (-4 *4 (-385 *3)) (-4 *5 (-385 *3)))) @@ -10599,124 +10292,31 @@ ((*1 *1) (-12 (-5 *1 (-1197 *2 *3)) (-14 *2 (-949)) (-4 *3 (-1081)))) ((*1 *1 *1) (-5 *1 (-1209))) ((*1 *1) (-5 *1 (-1209))) ((*1 *1) (-5 *1 (-1229)))) -(((*1 *2 *3) - (-12 (-5 *3 (-711 (-326 (-229)))) (-5 *2 (-391)) (-5 *1 (-208))))) -(((*1 *2 *3 *4) - (-12 (-5 *3 (-793)) (-5 *4 (-560)) (-5 *1 (-459 *2)) (-4 *2 (-1081))))) -(((*1 *2 *3) - (-12 (-4 *4 (-571)) (-4 *5 (-817)) (-4 *6 (-872)) - (-4 *7 (-1097 *4 *5 *6)) - (-5 *2 (-663 (-2 (|:| -1862 *1) (|:| -3717 (-663 *7))))) - (-5 *3 (-663 *7)) (-4 *1 (-1244 *4 *5 *6 *7))))) -(((*1 *2 *3 *4 *5 *5 *6) - (-12 (-5 *3 (-1 (-229) (-229) (-229))) - (-5 *4 (-3 (-1 (-229) (-229) (-229) (-229)) "undefined")) - (-5 *5 (-1121 (-229))) (-5 *6 (-663 (-270))) (-5 *2 (-1165 (-229))) - (-5 *1 (-719))))) -(((*1 *2 *3) - (-12 (-4 *4 (-571)) (-5 *2 (-793)) (-5 *1 (-43 *4 *3)) - (-4 *3 (-432 *4))))) -(((*1 *2 *3 *4) - (-12 (-5 *3 (-711 *8)) (-4 *8 (-980 *5 *7 *6)) - (-4 *5 (-13 (-319) (-149))) (-4 *6 (-13 (-872) (-633 (-1209)))) - (-4 *7 (-817)) - (-5 *2 - (-663 - (-2 (|:| |eqzro| (-663 *8)) (|:| |neqzro| (-663 *8)) - (|:| |wcond| (-663 (-976 *5))) - (|:| |bsoln| - (-2 (|:| |partsol| (-1299 (-421 (-976 *5)))) - (|:| -4149 (-663 (-1299 (-421 (-976 *5)))))))))) - (-5 *1 (-954 *5 *6 *7 *8)) (-5 *4 (-663 *8)))) - ((*1 *2 *3 *4) - (-12 (-5 *3 (-711 *8)) (-5 *4 (-663 (-1209))) (-4 *8 (-980 *5 *7 *6)) - (-4 *5 (-13 (-319) (-149))) (-4 *6 (-13 (-872) (-633 (-1209)))) - (-4 *7 (-817)) - (-5 *2 - (-663 - (-2 (|:| |eqzro| (-663 *8)) (|:| |neqzro| (-663 *8)) - (|:| |wcond| (-663 (-976 *5))) - (|:| |bsoln| - (-2 (|:| |partsol| (-1299 (-421 (-976 *5)))) - (|:| -4149 (-663 (-1299 (-421 (-976 *5)))))))))) - (-5 *1 (-954 *5 *6 *7 *8)))) - ((*1 *2 *3) - (-12 (-5 *3 (-711 *7)) (-4 *7 (-980 *4 *6 *5)) - (-4 *4 (-13 (-319) (-149))) (-4 *5 (-13 (-872) (-633 (-1209)))) - (-4 *6 (-817)) - (-5 *2 - (-663 - (-2 (|:| |eqzro| (-663 *7)) (|:| |neqzro| (-663 *7)) - (|:| |wcond| (-663 (-976 *4))) - (|:| |bsoln| - (-2 (|:| |partsol| (-1299 (-421 (-976 *4)))) - (|:| -4149 (-663 (-1299 (-421 (-976 *4)))))))))) - (-5 *1 (-954 *4 *5 *6 *7)))) - ((*1 *2 *3 *4 *5) - (-12 (-5 *3 (-711 *9)) (-5 *5 (-949)) (-4 *9 (-980 *6 *8 *7)) - (-4 *6 (-13 (-319) (-149))) (-4 *7 (-13 (-872) (-633 (-1209)))) - (-4 *8 (-817)) - (-5 *2 - (-663 - (-2 (|:| |eqzro| (-663 *9)) (|:| |neqzro| (-663 *9)) - (|:| |wcond| (-663 (-976 *6))) - (|:| |bsoln| - (-2 (|:| |partsol| (-1299 (-421 (-976 *6)))) - (|:| -4149 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(-1 *6 *6)) (-4 *6 (-1275 *5)) + (-4 *5 (-13 (-376) (-149) (-1070 (-560)))) + (-5 *2 + (-2 (|:| |a| *6) (|:| |b| (-421 *6)) (|:| |c| (-421 *6)) + (|:| -2834 *6))) + (-5 *1 (-1047 *5 *6)) (-5 *3 (-421 *6))))) +(((*1 *2 *2 *3) + (|partial| -12 (-5 *3 (-793)) (-4 *4 (-13 (-571) (-149))) + (-5 *1 (-1271 *4 *2)) (-4 *2 (-1275 *4))))) (((*1 *2 *3 *4) (-12 (-5 *3 (-663 (-2 (|:| |val| (-663 *8)) (|:| -3265 *9)))) (-5 *4 (-793)) (-4 *8 (-1097 *5 *6 *7)) (-4 *9 (-1103 *5 *6 *7 *8)) @@ -10727,106 +10327,6 @@ (-5 *4 (-793)) (-4 *8 (-1097 *5 *6 *7)) (-4 *9 (-1141 *5 *6 *7 *8)) (-4 *5 (-466)) (-4 *6 (-817)) (-4 *7 (-872)) (-5 *2 (-1305)) (-5 *1 (-1177 *5 *6 *7 *8 *9))))) -(((*1 *2 *1) (-12 (-5 *2 (-421 (-560))) (-5 *1 (-108)))) - ((*1 *2 *1) (-12 (-5 *2 (-421 (-560))) (-5 *1 (-221)))) - ((*1 *2 *1) (-12 (-5 *2 (-421 (-560))) (-5 *1 (-501)))) - ((*1 *1 *1) (-12 (-4 *1 (-1023 *2)) (-4 *2 (-571)) (-4 *2 (-319)))) - ((*1 *2 *1) - (-12 (-5 *2 (-421 (-560))) (-5 *1 (-1036 *3)) (-14 *3 (-560)))) - ((*1 *1 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(-1133)) + (-4 *4 (-1133))))) +(((*1 *2 *3 *2) + (-12 (-5 *3 (-115)) (-4 *4 (-1081)) (-5 *1 (-736 *4 *2)) + (-4 *2 (-670 *4)))) + ((*1 *2 *3 *2) (-12 (-5 *3 (-115)) (-5 *1 (-858 *2)) (-4 *2 (-1081))))) +(((*1 *2 *3) + (-12 + (-5 *3 + (-2 + (|:| |endPointContinuity| + (-3 (|:| |continuous| "Continuous at the end points") + (|:| |lowerSingular| + "There is a singularity at the lower end point") + (|:| |upperSingular| + "There is a singularity at the upper end point") + (|:| |bothSingular| + "There are singularities at both end points") + (|:| |notEvaluated| + "End point continuity not yet evaluated"))) + (|:| |singularitiesStream| + (-3 (|:| |str| (-1187 (-229))) + (|:| |notEvaluated| + "Internal singularities not yet evaluated"))) + (|:| -1404 + (-3 (|:| |finite| "The range is finite") + (|:| |lowerInfinite| "The bottom of range is infinite") + (|:| |upperInfinite| "The top of range is infinite") + (|:| |bothInfinite| + "Both top and bottom points are infinite") + (|:| |notEvaluated| "Range not yet evaluated"))))) + (-5 *2 (-1067)) (-5 *1 (-315))))) (((*1 *2 *1) (-12 (-5 *2 (-1250)) (-5 *1 (-183)))) ((*1 *2 *1) (-12 (-5 *2 (-1250)) (-5 *1 (-703)))) ((*1 *2 *1) (-12 (-5 *2 (-1250)) (-5 *1 (-1002)))) ((*1 *2 *1) (-12 (-5 *2 (-1250)) (-5 *1 (-1105)))) ((*1 *2 *1) (-12 (-5 *2 (-1214)) (-5 *1 (-1147))))) -(((*1 *2 *3 *4) - (-12 (-5 *3 (-1 *2 (-663 *2))) (-5 *4 (-663 *5)) - (-4 *5 (-38 (-421 (-560)))) (-4 *2 (-1292 *5)) - (-5 *1 (-1293 *5 *2))))) -(((*1 *2 *3 *3) - (-12 (-4 *4 (-571)) (-5 *2 (-2 (|:| |coef2| *3) (|:| -4420 *4))) - (-5 *1 (-1001 *4 *3)) (-4 *3 (-1275 *4))))) -(((*1 *2 *3 *4) - (|partial| -12 (-5 *3 (-115)) (-5 *4 (-663 *2)) (-5 *1 (-116 *2)) - (-4 *2 (-1133)))) - ((*1 *2 *2 *3) - (-12 (-5 *2 (-115)) (-5 *3 (-1 *4 (-663 *4))) (-4 *4 (-1133)) - (-5 *1 (-116 *4)))) - ((*1 *2 *2 *3) - (-12 (-5 *2 (-115)) (-5 *3 (-1 *4 *4)) (-4 *4 (-1133)) - (-5 *1 (-116 *4)))) - ((*1 *2 *3) - (|partial| -12 (-5 *3 (-115)) (-5 *2 (-1 *4 (-663 *4))) - (-5 *1 (-116 *4)) (-4 *4 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*3)) - (-4 *3 (-1275 *4))))) -(((*1 *1) (-4 *1 (-999)))) -(((*1 *2 *1) - (-12 (-5 *2 (-2 (|:| |cd| (-1191)) (|:| -3971 (-1191)))) - (-5 *1 (-847))))) -(((*1 *2 *3) (-12 (-5 *3 (-326 (-229))) (-5 *2 (-114)) (-5 *1 (-278))))) -(((*1 *2 *3 *4) - (-12 (-5 *4 (-114)) (-4 *5 (-13 (-466) (-1070 (-560)) (-660 (-560)))) +(((*1 *2 *3 *4 *5 *6 *7 *7 *8) + (-12 + (-5 *3 + (-2 (|:| |det| *12) (|:| |rows| (-663 (-560))) + (|:| |cols| (-663 (-560))))) + (-5 *4 (-711 *12)) (-5 *5 (-663 (-421 (-976 *9)))) + (-5 *6 (-663 (-663 *12))) (-5 *7 (-793)) (-5 *8 (-560)) + (-4 *9 (-13 (-319) (-149))) (-4 *12 (-980 *9 *11 *10)) + (-4 *10 (-13 (-872) (-633 (-1209)))) (-4 *11 (-817)) (-5 *2 - (-3 (|:| |%expansion| (-325 *5 *3 *6 *7)) - (|:| |%problem| (-2 (|:| |func| (-1191)) (|:| |prob| (-1191)))))) - (-5 *1 (-437 *5 *3 *6 *7)) (-4 *3 (-13 (-27) (-1235) (-435 *5))) - (-14 *6 (-1209)) (-14 *7 *3)))) -(((*1 *2 *2 *3) - (-12 (-5 *2 (-663 (-976 *4))) (-5 *3 (-663 (-1209))) (-4 *4 (-466)) - (-5 *1 (-948 *4))))) + (-2 (|:| |eqzro| (-663 *12)) (|:| |neqzro| (-663 *12)) + (|:| |wcond| (-663 (-976 *9))) + (|:| |bsoln| + (-2 (|:| |partsol| (-1299 (-421 (-976 *9)))) + (|:| -3907 (-663 (-1299 (-421 (-976 *9))))))))) + (-5 *1 (-954 *9 *10 *11 *12))))) +(((*1 *1 *1 *2) + (-12 (-5 *1 (-1172 *2 *3)) (-4 *2 (-13 (-1133) (-34))) + (-4 *3 (-13 (-1133) (-34)))))) +(((*1 *2 *1) (-12 (-5 *2 (-1305)) (-5 *1 (-847))))) (((*1 *2 *2) - (-12 (-4 *3 (-571)) (-5 *1 (-287 *3 *2)) - (-4 *2 (-13 (-435 *3) (-1034)))))) -(((*1 *1 *2) (-12 (-5 *2 (-949)) (-5 *1 (-270)))) - ((*1 *2 *3 *2) - (-12 (-5 *2 (-949)) (-5 *3 (-663 (-270))) (-5 *1 (-271))))) + (-12 (-4 *3 (-466)) (-5 *1 (-1241 *3 *2)) + (-4 *2 (-13 (-435 *3) (-1235)))))) +(((*1 *2 *1) + (-12 (-4 *1 (-338 *3 *4)) (-4 *3 (-1081)) (-4 *4 (-816)) + (-5 *2 (-663 *3)))) + ((*1 *2 *1) + (-12 (-4 *1 (-397 *3 *4)) (-4 *3 (-1081)) (-4 *4 (-1133)) + (-5 *2 (-663 *3)))) + ((*1 *2 *1) + (-12 (-5 *2 (-1187 *3)) (-5 *1 (-610 *3)) (-4 *3 (-1081)))) + ((*1 *2 *1) + (-12 (-5 *2 (-663 *3)) (-5 *1 (-757 *3 *4)) (-4 *3 (-1081)) + (-4 *4 (-748)))) + ((*1 *2 *1) (-12 (-4 *1 (-877 *3)) (-4 *3 (-1081)) (-5 *2 (-663 *3)))) + ((*1 *2 *1) + (-12 (-4 *1 (-1292 *3)) (-4 *3 (-1081)) (-5 *2 (-1187 *3))))) +(((*1 *2 *2 *1) + (-12 (-4 *1 (-1244 *3 *4 *5 *2)) (-4 *3 (-571)) (-4 *4 (-817)) + (-4 *5 (-872)) (-4 *2 (-1097 *3 *4 *5))))) +(((*1 *2 *2) + (-12 (-4 *3 (-1275 (-421 (-560)))) (-5 *1 (-943 *3 *2)) + (-4 *2 (-1275 (-421 *3)))))) +(((*1 *2 *1) + (-12 (-4 *1 (-1263 *3 *2)) (-4 *3 (-1081)) (-4 *2 (-1292 *3))))) +(((*1 *2) (-12 (-5 *2 (-663 (-1191))) (-5 *1 (-853))))) +(((*1 *1) (-4 *1 (-999)))) +(((*1 *2) (-12 (-5 *2 (-560)) (-5 *1 (-957))))) +(((*1 *1) (-5 *1 (-625)))) +(((*1 *1 *1) + (-12 (-5 *1 (-609 *2)) (-4 *2 (-38 (-421 (-560)))) (-4 *2 (-1081))))) +(((*1 *1 *1) + (-12 (-5 *1 (-609 *2)) (-4 *2 (-38 (-421 (-560)))) (-4 *2 (-1081))))) +(((*1 *2 *1) (-12 (-5 *2 (-114)) (-5 *1 (-916 *3)) (-4 *3 (-1133))))) +(((*1 *2 *3) + (-12 (-5 *3 (-663 *2)) (-4 *2 (-435 *4)) (-5 *1 (-160 *4 *2)) + (-4 *4 (-571))))) (((*1 *1 *1) (-12 (-4 *1 (-47 *2 *3)) (-4 *2 (-1081)) (-4 *3 (-816)))) ((*1 *1 *1) (-12 (-5 *1 (-50 *2 *3)) (-4 *2 (-1081)) (-14 *3 (-663 (-1209))))) @@ -10992,8 +10602,8 @@ (-12 (-14 *2 (-663 (-1209))) (-4 *3 (-175)) (-4 *5 (-245 (-2327 *2) (-793))) (-14 *6 - (-1 (-114) (-2 (|:| -4021 *4) (|:| -2790 *5)) - (-2 (|:| -4021 *4) (|:| -2790 *5)))) + (-1 (-114) (-2 (|:| -4019 *4) (|:| -4400 *5)) + (-2 (|:| -4019 *4) (|:| -4400 *5)))) (-5 *1 (-475 *2 *3 *4 *5 *6 *7)) (-4 *4 (-872)) (-4 *7 (-980 *3 *5 (-889 *2))))) ((*1 *1 *1) (-12 (-4 *1 (-523 *2 *3)) (-4 *2 (-102)) (-4 *3 (-875)))) @@ -11009,14 +10619,16 @@ (-4 *2 (-872)))) ((*1 *1 *1) (-12 (-5 *1 (-1323 *2 *3)) (-4 *2 (-1081)) (-4 *3 (-870))))) -(((*1 *1 *1) (-12 (-5 *1 (-944 *2)) (-4 *2 (-319))))) -(((*1 *1 *1 *2 *3) - (-12 (-5 *2 (-560)) (-4 *1 (-57 *4 *3 *5)) (-4 *4 (-1249)) - (-4 *3 (-385 *4)) (-4 *5 (-385 *4))))) -(((*1 *2 *2 *3 *4 *4) - (-12 (-5 *4 (-560)) (-4 *3 (-175)) (-4 *5 (-385 *3)) - (-4 *6 (-385 *3)) (-5 *1 (-710 *3 *5 *6 *2)) - (-4 *2 (-708 *3 *5 *6))))) +(((*1 *2 *2 *2) + (-12 (-4 *3 (-376)) (-5 *1 (-788 *2 *3)) (-4 *2 (-730 *3)))) + ((*1 *1 *1 *1) (-12 (-4 *1 (-877 *2)) (-4 *2 (-1081)) (-4 *2 (-376))))) +(((*1 *2 *3 *4) + (-12 (-5 *3 (-229)) (-5 *4 (-560)) (-5 *2 (-1067)) (-5 *1 (-780))))) +(((*1 *2 *2 *2 *3) + (-12 (-5 *2 (-1299 (-560))) (-5 *3 (-560)) (-5 *1 (-1142)))) + ((*1 *2 *3 *2 *4) + (-12 (-5 *2 (-1299 (-560))) (-5 *3 (-663 (-560))) (-5 *4 (-560)) + (-5 *1 (-1142))))) (((*1 *1 *2) (-12 (-5 *2 (-663 *1)) (-4 *1 (-466)))) ((*1 *1 *1 *1) (-4 *1 (-466))) ((*1 *2 *3) @@ -11045,63 +10657,46 @@ ((*1 *2 *2 *1) (-12 (-4 *1 (-1097 *2 *3 *4)) (-4 *2 (-1081)) (-4 *3 (-817)) (-4 *4 (-872)) (-4 *2 (-466))))) -(((*1 *2 *1) (-12 (-5 *2 (-114)) (-5 *1 (-850))))) -(((*1 *2 *3 *4) - (|partial| -12 (-5 *4 (-421 *2)) (-4 *2 (-1275 *5)) - (-5 *1 (-831 *5 *2 *3 *6)) - (-4 *5 (-13 (-376) (-149) (-1070 (-421 (-560))))) - (-4 *3 (-680 *2)) (-4 *6 (-680 *4)))) - ((*1 *2 *3 *4) - (-12 (-5 *4 (-663 (-421 *2))) (-4 *2 (-1275 *5)) - (-5 *1 (-831 *5 *2 *3 *6)) - (-4 *5 (-13 (-376) (-149) (-1070 (-421 (-560))))) (-4 *3 (-680 *2)) - (-4 *6 (-680 (-421 *2)))))) -(((*1 *2 *1) - (-12 (-5 *2 (-1058 (-866 (-560)))) (-5 *1 (-609 *3)) (-4 *3 (-1081))))) -(((*1 *2 *3 *4) - (-12 (-5 *3 (-663 (-326 (-229)))) (-5 *4 (-793)) - (-5 *2 (-711 (-229))) (-5 *1 (-278))))) -(((*1 *2 *3 *4) - (-12 (-5 *3 (-663 *2)) (-5 *4 (-1 (-114) *2 *2)) (-5 *1 (-1251 *2)) - (-4 *2 (-1133)))) - ((*1 *2 *3) - (-12 (-5 *3 (-663 *2)) (-4 *2 (-1133)) (-4 *2 (-872)) - (-5 *1 (-1251 *2))))) -(((*1 *1 *2 *3 *4) - (-12 (-14 *5 (-663 (-1209))) (-4 *2 (-175)) - (-4 *4 (-245 (-2327 *5) (-793))) - (-14 *6 - (-1 (-114) (-2 (|:| -4021 *3) (|:| -2790 *4)) - (-2 (|:| -4021 *3) (|:| -2790 *4)))) - (-5 *1 (-475 *5 *2 *3 *4 *6 *7)) (-4 *3 (-872)) - (-4 *7 (-980 *2 *4 (-889 *5)))))) -(((*1 *2 *1) (-12 (-5 *2 (-114)) (-5 *1 (-1245 *3)) (-4 *3 (-1006))))) -(((*1 *2 *3 *1) - (-12 (|has| *1 (-6 -4510)) (-4 *1 (-503 *3)) (-4 *3 (-1249)) - (-4 *3 (-1133)) (-5 *2 (-114)))) - ((*1 *2 *3 *1) - (-12 (-5 *3 (-932 *4)) (-4 *4 (-1133)) (-5 *2 (-114)) - (-5 *1 (-935 *4)))) - ((*1 *2 *3 *1) - (-12 (-5 *3 (-949)) (-5 *2 (-114)) (-5 *1 (-1134 *4 *5)) (-14 *4 *3) - (-14 *5 *3)))) +(((*1 *2 *2 *3) + (-12 (-5 *3 (-560)) (-5 *1 (-718 *2)) (-4 *2 (-1275 *3))))) +(((*1 *1 *2) + (-12 (-5 *2 (-421 *4)) (-4 *4 (-1275 *3)) (-4 *3 (-13 (-376) (-149))) + (-5 *1 (-413 *3 *4))))) +(((*1 *2 *1) (-12 (-5 *2 (-1191)) (-5 *1 (-1231))))) +(((*1 *2 *3) + (-12 (-5 *3 (-663 *4)) (-4 *4 (-872)) (-5 *2 (-663 (-686 *4 *5))) + (-5 *1 (-646 *4 *5 *6)) (-4 *5 (-13 (-175) (-739 (-421 (-560))))) + (-14 *6 (-949))))) +(((*1 *2 *2) + (-12 (-5 *2 (-1299 *1)) (-4 *1 (-355 *3 *4 *5)) (-4 *3 (-1254)) + (-4 *4 (-1275 *3)) (-4 *5 (-1275 (-421 *4)))))) +(((*1 *2 *1) (-12 (-5 *2 (-114)) (-5 *1 (-146))))) +(((*1 *2 *3 *4 *5) + (-12 (-5 *3 (-1299 *6)) (-5 *4 (-1299 (-560))) (-5 *5 (-560)) + (-4 *6 (-1133)) (-5 *2 (-1 *6)) (-5 *1 (-1049 *6))))) (((*1 *2 *1) (-12 (-4 *3 (-1081)) (-4 *4 (-817)) (-4 *5 (-872)) (-5 *2 (-663 *1)) (-4 *1 (-980 *3 *4 *5))))) (((*1 *2 *1) (-12 (-5 *2 (-663 (-1250))) (-5 *1 (-703)))) ((*1 *2 *1) (-12 (-5 *2 (-663 (-1214))) (-5 *1 (-1147))))) -(((*1 *2 *2 *3) - (|partial| -12 (-5 *2 (-663 (-1203 *5))) (-5 *3 (-1203 *5)) - (-4 *5 (-168 *4)) (-4 *4 (-559)) (-5 *1 (-151 *4 *5)))) - ((*1 *2 *2 *3) - (|partial| -12 (-5 *2 (-663 *3)) (-4 *3 (-1275 *5)) - (-4 *5 (-1275 *4)) (-4 *4 (-363)) (-5 *1 (-371 *4 *5 *3)))) - ((*1 *2 *2 *3) - (|partial| -12 (-5 *2 (-663 (-1203 (-560)))) (-5 *3 (-1203 (-560))) - (-5 *1 (-586)))) - ((*1 *2 *2 *3) - (|partial| -12 (-5 *2 (-663 (-1203 *1))) (-5 *3 (-1203 *1)) - (-4 *1 (-940))))) +(((*1 *2 *3 *2) + (-12 (-4 *1 (-809)) (-5 *2 (-1067)) + (-5 *3 + (-2 (|:| |fn| (-326 (-229))) + (|:| -1404 (-663 (-1121 (-866 (-229))))) (|:| |abserr| (-229)) + (|:| |relerr| (-229)))))) + ((*1 *2 *3 *2) + (-12 (-4 *1 (-809)) (-5 *2 (-1067)) + (-5 *3 + (-2 (|:| |var| (-1209)) (|:| |fn| (-326 (-229))) + (|:| -1404 (-1121 (-866 (-229)))) (|:| |abserr| (-229)) + (|:| |relerr| (-229))))))) +(((*1 *2 *3 *4) + (-12 (-5 *4 (-663 (-889 *5))) (-14 *5 (-663 (-1209))) (-4 *6 (-466)) + (-5 *2 + (-2 (|:| |dpolys| (-663 (-255 *5 *6))) + (|:| |coords| (-663 (-560))))) + (-5 *1 (-485 *5 *6 *7)) (-5 *3 (-663 (-255 *5 *6))) (-4 *7 (-466))))) (((*1 *1 *1 *1) (-12 (-5 *1 (-663 *2)) (-4 *2 (-1249))))) (((*1 *2 *1) (-12 (-4 *1 (-236 *2)) (-4 *2 (-1249)))) ((*1 *1 *1 *2) (-12 (-4 *1 (-239)) (-5 *2 (-793)))) @@ -11130,33 +10725,25 @@ (-12 (-5 *2 (-663 *3)) (-4 *1 (-930 *3)) (-4 *3 (-1133)))) ((*1 *1 *1 *2 *1) (-12 (-5 *2 (-1 *3 *3)) (-4 *1 (-1275 *3)) (-4 *3 (-1081))))) -(((*1 *2 *1) - (-12 (-4 *1 (-1136 *3 *4 *5 *6 *7)) (-4 *3 (-1133)) (-4 *4 (-1133)) - (-4 *5 (-1133)) (-4 *6 (-1133)) (-4 *7 (-1133)) (-5 *2 (-114))))) (((*1 *2 *3) - (-12 (-5 *3 (-663 (-1191))) (-5 *2 (-1191)) (-5 *1 (-195)))) - ((*1 *1 *2) (-12 (-5 *2 (-663 (-888))) (-5 *1 (-888))))) -(((*1 *1 *2) (-12 (-5 *2 (-1299 *3)) (-4 *3 (-376)) (-4 *1 (-341 *3)))) - ((*1 *1 *2 *3) - (-12 (-5 *2 (-1299 *3)) (-4 *3 (-1275 *4)) (-4 *4 (-1254)) - (-4 *1 (-355 *4 *3 *5)) (-4 *5 (-1275 (-421 *3))))) - ((*1 *1 *2 *3) - (-12 (-5 *2 (-1299 *4)) (-5 *3 (-1299 *1)) (-4 *4 (-175)) - (-4 *1 (-380 *4)))) - ((*1 *1 *2 *3) - (-12 (-5 *2 (-1299 *4)) (-5 *3 (-1299 *1)) (-4 *4 (-175)) - (-4 *1 (-383 *4 *5)) (-4 *5 (-1275 *4)))) - ((*1 *1 *2) - (-12 (-5 *2 (-1299 *3)) (-4 *3 (-175)) (-4 *1 (-424 *3 *4)) - (-4 *4 (-1275 *3)))) - ((*1 *1 *2) (-12 (-5 *2 (-1299 *3)) (-4 *3 (-175)) (-4 *1 (-432 *3))))) + (-12 (-4 *4 (-872)) (-5 *2 (-1222 (-663 *4))) (-5 *1 (-1220 *4)) + (-5 *3 (-663 *4))))) +(((*1 *1 *1) (-12 (-4 *1 (-1027 *2)) (-4 *2 (-1249))))) +(((*1 *2 *1) (-12 (-5 *2 (-1305)) (-5 *1 (-847))))) (((*1 *2 *3) - (|partial| -12 (-5 *3 (-1299 *4)) (-4 *4 (-13 (-1081) (-660 (-560)))) - (-5 *2 (-1299 (-560))) (-5 *1 (-1328 *4))))) -(((*1 *1 *1) - (-12 (-4 *1 (-1136 *2 *3 *4 *5 *6)) (-4 *2 (-1133)) (-4 *3 (-1133)) - (-4 *4 (-1133)) (-4 *5 (-1133)) (-4 *6 (-1133))))) + (-12 (-5 *3 (-1191)) (-5 *2 (-1305)) (-5 *1 (-1227 *4 *5)) + (-4 *4 (-1133)) (-4 *5 (-1133))))) (((*1 *2 *2) (|partial| -12 (-4 *1 (-1015 *2)) (-4 *2 (-1235))))) +(((*1 *2) + (-12 (-4 *4 (-175)) (-5 *2 (-1203 (-976 *4))) (-5 *1 (-431 *3 *4)) + (-4 *3 (-432 *4)))) + ((*1 *2) + (-12 (-4 *1 (-432 *3)) (-4 *3 (-175)) (-4 *3 (-376)) + (-5 *2 (-1203 (-976 *3))))) + ((*1 *2) + (-12 (-5 *2 (-1203 (-421 (-976 *3)))) (-5 *1 (-467 *3 *4 *5 *6)) + (-4 *3 (-571)) (-4 *3 (-175)) (-14 *4 (-949)) + (-14 *5 (-663 (-1209))) (-14 *6 (-1299 (-711 *3)))))) (((*1 *2 *1) (-12 (-4 *1 (-47 *2 *3)) (-4 *3 (-816)) (-4 *2 (-1081)))) ((*1 *2 *1) (-12 (-4 *2 (-1081)) (-5 *1 (-50 *2 *3)) (-14 *3 (-663 (-1209))))) @@ -11168,8 +10755,8 @@ ((*1 *2 *1) (-12 (-14 *3 (-663 (-1209))) (-4 *5 (-245 (-2327 *3) (-793))) (-14 *6 - (-1 (-114) (-2 (|:| -4021 *4) (|:| -2790 *5)) - (-2 (|:| -4021 *4) (|:| -2790 *5)))) + (-1 (-114) (-2 (|:| -4019 *4) (|:| -4400 *5)) + (-2 (|:| -4019 *4) (|:| -4400 *5)))) (-4 *2 (-175)) (-5 *1 (-475 *3 *2 *4 *5 *6 *7)) (-4 *4 (-872)) (-4 *7 (-980 *2 *5 (-889 *3))))) ((*1 *2 *1) (-12 (-4 *1 (-523 *2 *3)) (-4 *3 (-875)) (-4 *2 (-102)))) @@ -11186,40 +10773,31 @@ ((*1 *1 *1 *2) (-12 (-4 *1 (-1097 *3 *4 *2)) (-4 *3 (-1081)) (-4 *4 (-817)) (-4 *2 (-872))))) -(((*1 *1 *2) (-12 (-5 *2 (-843 *3)) (-4 *3 (-872)) (-5 *1 (-694 *3))))) -(((*1 *2 *1) - (-12 - (-5 *2 - (-663 - (-2 (|:| |scalar| (-421 (-560))) (|:| |coeff| (-1203 *3)) - (|:| |logand| (-1203 *3))))) - (-5 *1 (-597 *3)) (-4 *3 (-376))))) +(((*1 *2 *3 *4 *4 *3) + (-12 (-5 *3 (-560)) (-5 *4 (-711 (-229))) (-5 *2 (-1067)) + (-5 *1 (-769))))) +(((*1 *2 *1) (|partial| -12 (-5 *2 (-630 *1)) (-4 *1 (-310))))) (((*1 *1 *2) (-12 (-5 *2 (-663 *3)) (-4 *3 (-1133)) (-4 *1 (-1131 *3)))) ((*1 *1) (-12 (-4 *1 (-1131 *2)) (-4 *2 (-1133))))) -(((*1 *1 *2) (-12 (-5 *2 (-899)) (-5 *1 (-270)))) - ((*1 *1 *2) (-12 (-5 *2 (-391)) (-5 *1 (-270))))) +(((*1 *1) (-5 *1 (-143)))) (((*1 *1 *2) (-12 (-5 *2 (-663 *3)) (-4 *3 (-1249)) (-5 *1 (-1299 *3))))) +(((*1 *2 *2 *2 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*2 (-175)) (-5 *1 (-301 *2 *3 *4 *5 *6 *7)) @@ -11382,6 +10999,9 @@ (-14 *4 (-1 *2 *2 *3)) (-14 *5 (-1 (-3 *3 "failed") *3 *3)) (-14 *6 (-1 (-3 *2 "failed") *2 *2 *3)))) ((*1 *1 *1) (-12 (-4 *1 (-820 *2)) (-4 *2 (-175)) (-4 *2 (-376))))) +(((*1 *2 *3 *4 *4 *4 *3) + (-12 (-5 *3 (-560)) (-5 *4 (-711 (-229))) (-5 *2 (-1067)) + (-5 *1 (-773))))) (((*1 *1 *1 *2) (-12 (-4 *1 (-47 *2 *3)) (-4 *2 (-1081)) (-4 *3 (-816)) (-4 *2 (-376)))) @@ -11437,28 +11057,31 @@ (-4 *3 (-870))))) (((*1 *1 *2 *1) (-12 (-5 *1 (-663 *2)) (-4 *2 (-1249)))) ((*1 *1 *2 *1) (-12 (-5 *1 (-1187 *2)) (-4 *2 (-1249))))) -(((*1 *2 *1 *1) - (-12 (-5 *2 (-2 (|:| -4420 *3) (|:| |coef2| (-803 *3)))) - (-5 *1 (-803 *3)) (-4 *3 (-571)) (-4 *3 (-1081))))) -(((*1 *2 *3 *3 *3 *4 *3 *3 *4 *4 *4 *5) - (-12 (-5 *3 (-229)) (-5 *4 (-560)) - (-5 *5 (-3 (|:| |fn| (-402)) (|:| |fp| (-61 G)))) (-5 *2 (-1067)) - (-5 *1 (-770))))) +(((*1 *2 *3 *3 *4 *4 *3) + (-12 (-5 *3 (-560)) (-5 *4 (-711 (-229))) (-5 *2 (-1067)) + (-5 *1 (-769))))) (((*1 *2 *3) - (-12 (-5 *3 (-1299 (-326 (-229)))) - (-5 *2 - (-2 (|:| |additions| (-560)) (|:| |multiplications| (-560)) - (|:| |exponentiations| (-560)) (|:| |functionCalls| (-560)))) - (-5 *1 (-315))))) -(((*1 *1 *1) - (-12 (-5 *1 (-609 *2)) (-4 *2 (-38 (-421 (-560)))) (-4 *2 (-1081))))) -(((*1 *2) (-12 (-5 *2 (-114)) (-5 *1 (-955))))) -(((*1 *2 *2) - (-12 (-4 *3 (-571)) (-5 *1 (-287 *3 *2)) - (-4 *2 (-13 (-435 *3) (-1034)))))) -(((*1 *1 *2 *1) (-12 (-5 *2 (-109)) (-5 *1 (-1117))))) -(((*1 *1 *2) - (-12 (-5 *2 (-663 *3)) (-4 *3 (-1133)) (-5 *1 (-1032 *3))))) + (|partial| -12 (-5 *3 (-630 *4)) (-4 *4 (-1133)) (-4 *2 (-1133)) + (-5 *1 (-631 *2 *4))))) +(((*1 *1 *1) (-5 *1 (-1095)))) +(((*1 *2) (-12 (-5 *2 (-114)) (-5 *1 (-481)))) + ((*1 *2 *2) (-12 (-5 *2 (-114)) (-5 *1 (-481))))) +(((*1 *2) + (-12 (-4 *4 (-376)) (-5 *2 (-949)) (-5 *1 (-340 *3 *4)) + (-4 *3 (-341 *4)))) + ((*1 *2) + (-12 (-4 *4 (-376)) (-5 *2 (-856 (-949))) (-5 *1 (-340 *3 *4)) + (-4 *3 (-341 *4)))) + ((*1 *2) (-12 (-4 *1 (-341 *3)) (-4 *3 (-376)) (-5 *2 (-949)))) + ((*1 *2) + (-12 (-4 *1 (-1318 *3)) (-4 *3 (-376)) (-5 *2 (-856 (-949)))))) +(((*1 *2 *1) (-12 (-5 *2 (-793)) (-5 *1 (-146))))) +(((*1 *2 *2) (-12 (-5 *1 (-992 *2)) (-4 *2 (-559))))) +(((*1 *2 *3 *4) + (-12 (-5 *4 (-1 *7 *7)) (-4 *7 (-1275 *6)) + (-4 *6 (-13 (-27) (-435 *5))) (-4 *5 (-13 (-571) (-1070 (-560)))) + (-4 *8 (-1275 (-421 *7))) (-5 *2 (-597 *3)) + (-5 *1 (-567 *5 *6 *7 *8 *3)) (-4 *3 (-355 *6 *7 *8))))) (((*1 *1 *1 *1) (-4 *1 (-21))) ((*1 *1 *1) (-4 *1 (-21))) ((*1 *1 *1 *1) (|partial| -5 *1 (-136))) ((*1 *1 *1 *1) @@ -11466,7 +11089,7 @@ (-4 *2 (-13 (-872) (-10 -8 (-15 -1494 ((-1191) $ (-1209))) (-15 -1886 ((-1305) $)) - (-15 -1706 ((-1305) $))))))) + (-15 -4418 ((-1305) $))))))) ((*1 *1 *1 *2) (-12 (-5 *1 (-305 *2)) (-4 *2 (-21)) (-4 *2 (-1249)))) ((*1 *1 *2 *1) (-12 (-5 *1 (-305 *2)) (-4 *2 (-21)) (-4 *2 (-1249)))) ((*1 *1 *1 *1) @@ -11486,19 +11109,23 @@ ((*1 *2 *2 *2) (-12 (-5 *2 (-973 (-229))) (-5 *1 (-1246)))) ((*1 *1 *1 *1) (-12 (-4 *1 (-1298 *2)) (-4 *2 (-1249)) (-4 *2 (-21)))) ((*1 *1 *1) (-12 (-4 *1 (-1298 *2)) (-4 *2 (-1249)) (-4 *2 (-21))))) -(((*1 *2 *3 *3 *3 *3 *4) - (-12 (-5 *3 (-229)) (-5 *4 (-560)) (-5 *2 (-1067)) (-5 *1 (-780))))) -(((*1 *1 *2) - (-12 (-5 *2 (-711 *4)) (-4 *4 (-1081)) (-5 *1 (-1174 *3 *4)) - (-14 *3 (-793))))) -(((*1 *1 *2) (-12 (-5 *1 (-231 *2)) (-4 *2 (-13 (-376) (-1235)))))) -(((*1 *2 *3 *3 *4 *4 *3 *4 *4 *3 *3 *3) - (-12 (-5 *3 (-560)) (-5 *4 (-711 (-229))) (-5 *2 (-1067)) - (-5 *1 (-774))))) -(((*1 *1 *1 *2) (-12 (-5 *2 (-1 (-114) (-115) (-115))) (-5 *1 (-115))))) -(((*1 *2 *1) (-12 (-5 *2 (-847)) (-5 *1 (-846))))) -(((*1 *2 *1) - (-12 (-5 *2 (-1187 (-421 *3))) (-5 *1 (-177 *3)) (-4 *3 (-319))))) +(((*1 *2) (-12 (-5 *2 (-560)) (-5 *1 (-721)))) + ((*1 *2 *2) (-12 (-5 *2 (-560)) (-5 *1 (-721))))) +(((*1 *1 *1 *2) + (|partial| -12 (-4 *1 (-1244 *3 *4 *5 *2)) (-4 *3 (-571)) + (-4 *4 (-817)) (-4 *5 (-872)) (-4 *2 (-1097 *3 *4 *5))))) +(((*1 *2 *3) + (-12 (-5 *2 (-1187 (-560))) (-5 *1 (-1193 *4)) (-4 *4 (-1081)) + (-5 *3 (-560))))) +(((*1 *2 *3 *3 *3 *4 *5 *3 *6) + (-12 (-5 *3 (-560)) (-5 *4 (-711 (-229))) (-5 *5 (-229)) + (-5 *6 (-3 (|:| |fn| (-402)) (|:| |fp| (-74 FCN)))) (-5 *2 (-1067)) + (-5 *1 (-768))))) +(((*1 *2 *1) (-12 (-4 *1 (-380 *3)) (-4 *3 (-175)) (-5 *2 (-1203 *3))))) +(((*1 *2 *1) (-12 (-4 *1 (-523 *3 *2)) (-4 *3 (-102)) (-4 *2 (-875))))) +(((*1 *2 *3) + (-12 (-4 *4 (-571)) (-5 *2 (-1299 (-711 *4))) (-5 *1 (-90 *4 *5)) + (-5 *3 (-711 *4)) (-4 *5 (-680 *4))))) (((*1 *2 *3) (-12 (-5 *3 (-1209)) (-4 *4 (-13 (-466) (-1070 (-560)) (-660 (-560)))) (-5 *2 (-51)) @@ -11533,14 +11160,16 @@ ((*1 *1 *2 *3) (-12 (-5 *2 (-421 (-560))) (-4 *4 (-1081)) (-4 *1 (-1284 *4 *3)) (-4 *3 (-1261 *4))))) -(((*1 *2 *1) (-12 (-5 *2 (-1305)) (-5 *1 (-847))))) +(((*1 *2 *1) + (-12 (-5 *2 (-1129 *3)) (-5 *1 (-932 *3)) (-4 *3 (-381)) + (-4 *3 (-1133))))) (((*1 *1 *1 *1) (-4 *1 (-25))) ((*1 *1 *1 *1) (-5 *1 (-159))) ((*1 *1 *1 *1) (-12 (-5 *1 (-217 *2)) (-4 *2 (-13 (-872) (-10 -8 (-15 -1494 ((-1191) $ (-1209))) (-15 -1886 ((-1305) $)) - (-15 -1706 ((-1305) $))))))) + (-15 -4418 ((-1305) $))))))) ((*1 *1 *1 *2) (-12 (-5 *1 (-305 *2)) (-4 *2 (-25)) (-4 *2 (-1249)))) ((*1 *1 *2 *1) (-12 (-5 *1 (-305 *2)) (-4 *2 (-25)) (-4 *2 (-1249)))) ((*1 *1 *2 *1) @@ -11563,47 +11192,46 @@ (-12 (-5 *2 (-1187 *3)) (-4 *3 (-1081)) (-5 *1 (-1193 *3)))) ((*1 *2 *2 *2) (-12 (-5 *2 (-973 (-229))) (-5 *1 (-1246)))) ((*1 *1 *1 *1) (-12 (-4 *1 (-1298 *2)) (-4 *2 (-1249)) (-4 *2 (-25))))) -(((*1 *2 *1) (-12 (-4 *1 (-541)) (-5 *2 (-713 (-1256)))))) +(((*1 *2 *2) + (-12 (-4 *3 (-1081)) (-4 *4 (-1275 *3)) (-5 *1 (-166 *3 *4 *2)) + (-4 *2 (-1275 *4)))) + ((*1 *1 *1) (-12 (-5 *1 (-305 *2)) (-4 *2 (-1249))))) +(((*1 *1) (-4 *1 (-34))) ((*1 *1) (-5 *1 (-303))) + ((*1 *1) (-5 *1 (-888))) + ((*1 *1) + (-12 (-4 *2 (-466)) (-4 *3 (-872)) (-4 *4 (-817)) + (-5 *1 (-1018 *2 *3 *4 *5)) (-4 *5 (-980 *2 *4 *3)))) + ((*1 *1) (-5 *1 (-1117))) + ((*1 *1) + (-12 (-5 *1 (-1172 *2 *3)) (-4 *2 (-13 (-1133) (-34))) + (-4 *3 (-13 (-1133) (-34))))) + ((*1 *1) (-5 *1 (-1212))) ((*1 *1) (-5 *1 (-1213)))) +(((*1 *2 *3 *1) + (-12 (-5 *3 (-448)) + (-5 *2 + (-663 + (-3 (|:| -3971 (-1209)) + (|:| -4182 (-663 (-3 (|:| S (-1209)) (|:| P (-976 (-560))))))))) + (-5 *1 (-1213))))) (((*1 *2 *3 *4) - (-12 (-5 *3 (-932 (-560))) (-5 *4 (-560)) (-5 *2 (-711 *4)) - (-5 *1 (-1061 *5)) (-4 *5 (-1081)))) - ((*1 *2 *3) - (-12 (-5 *3 (-663 (-560))) (-5 *2 (-711 (-560))) (-5 *1 (-1061 *4)) - (-4 *4 (-1081)))) - ((*1 *2 *3 *4) - (-12 (-5 *3 (-663 (-932 (-560)))) (-5 *4 (-560)) - (-5 *2 (-663 (-711 *4))) (-5 *1 (-1061 *5)) (-4 *5 (-1081)))) - ((*1 *2 *3) - (-12 (-5 *3 (-663 (-663 (-560)))) (-5 *2 (-663 (-711 (-560)))) - (-5 *1 (-1061 *4)) (-4 *4 (-1081))))) + (-12 (-5 *4 (-711 (-421 (-976 (-560))))) + (-5 *2 (-663 (-711 (-326 (-560))))) (-5 *1 (-1060)) + (-5 *3 (-326 (-560)))))) (((*1 *1 *2) - (-12 (-5 *2 (-1197 3 *3)) (-4 *3 (-1081)) (-4 *1 (-1166 *3)))) - ((*1 *1) (-12 (-4 *1 (-1166 *2)) (-4 *2 (-1081))))) -(((*1 *2 *2 *3) - (-12 (-5 *2 (-663 (-663 (-973 (-229))))) (-5 *3 (-663 (-899))) - (-5 *1 (-482))))) -(((*1 *2) - (-12 (-4 *3 (-13 (-571) (-1070 (-560)))) (-5 *2 (-1305)) - (-5 *1 (-447 *3 *4)) (-4 *4 (-435 *3))))) -(((*1 *2 *3 *4) - (-12 (-5 *4 (-793)) (-4 *5 (-1081)) (-5 *2 (-560)) - (-5 *1 (-457 *5 *3 *6)) (-4 *3 (-1275 *5)) - (-4 *6 (-13 (-418) (-1070 *5) (-376) (-1235) (-296))))) - ((*1 *2 *3) - (-12 (-4 *4 (-1081)) (-5 *2 (-560)) (-5 *1 (-457 *4 *3 *5)) - (-4 *3 (-1275 *4)) - (-4 *5 (-13 (-418) (-1070 *4) (-376) (-1235) (-296)))))) + (-12 (-5 *2 (-663 (-663 *3))) (-4 *3 (-1133)) (-5 *1 (-932 *3))))) +(((*1 *1 *1 *2) + (-12 (-4 *1 (-57 *2 *3 *4)) (-4 *2 (-1249)) (-4 *3 (-385 *2)) + (-4 *4 (-385 *2)))) + ((*1 *1 *1 *2) + (-12 (|has| *1 (-6 -4511)) (-4 *1 (-618 *3 *2)) (-4 *3 (-1133)) + (-4 *2 (-1249))))) +(((*1 *2 *2) (-12 (-5 *1 (-601 *2)) (-4 *2 (-559))))) +(((*1 *2 *3 *1) + (-12 (-4 *4 (-13 (-871) (-376))) (-5 *2 (-114)) (-5 *1 (-1093 *4 *3)) + (-4 *3 (-1275 *4))))) (((*1 *2 *1 *3) - (-12 (-5 *3 (-560)) (-4 *1 (-57 *4 *5 *2)) (-4 *4 (-1249)) - (-4 *5 (-385 *4)) (-4 *2 (-385 *4)))) - ((*1 *2 *1 *3) - (-12 (-5 *3 (-560)) (-4 *1 (-1085 *4 *5 *6 *7 *2)) (-4 *6 (-1081)) - (-4 *7 (-245 *5 *6)) (-4 *2 (-245 *4 *6))))) -(((*1 *2 *3) - (-12 (-5 *3 (-421 (-976 *4))) (-4 *4 (-319)) - (-5 *2 (-421 (-419 (-976 *4)))) (-5 *1 (-1075 *4))))) -(((*1 *2 *2 *3) - (-12 (-4 *3 (-1081)) (-5 *1 (-458 *3 *2)) (-4 *2 (-1275 *3))))) + (-12 (-5 *3 (-560)) (-5 *2 (-3 "nil" "sqfr" "irred" "prime")) + (-5 *1 (-419 *4)) (-4 *4 (-571))))) (((*1 *2 *3) (-12 (-5 *3 (-1209)) (-4 *4 (-13 (-466) (-1070 (-560)) (-660 (-560)))) (-5 *2 (-51)) @@ -11638,232 +11266,217 @@ (-4 *3 (-1292 *4)))) ((*1 *2 *1) (-12 (-4 *1 (-1284 *3 *2)) (-4 *3 (-1081)) (-4 *2 (-1261 *3))))) -(((*1 *2 *3 *4 *5 *4 *4 *4) - (-12 (-4 *6 (-872)) (-5 *3 (-663 *6)) (-5 *5 (-663 *3)) +(((*1 *1 *1) (-5 *1 (-1095)))) +(((*1 *2 *3 *4) + (-12 (-5 *3 (-663 *7)) (-4 *7 (-872)) (-4 *5 (-940)) (-4 *6 (-817)) + (-4 *8 (-980 *5 *6 *7)) (-5 *2 (-419 (-1203 *8))) + (-5 *1 (-937 *5 *6 *7 *8)) (-5 *4 (-1203 *8)))) + ((*1 *2 *3) + (-12 (-4 *4 (-940)) (-4 *5 (-1275 *4)) (-5 *2 (-419 (-1203 *5))) + (-5 *1 (-938 *4 *5)) (-5 *3 (-1203 *5))))) +(((*1 *2 *3 *4 *4 *5 *6) + (-12 (-5 *3 (-663 (-663 (-973 (-229))))) (-5 *4 (-899)) + (-5 *5 (-949)) (-5 *6 (-663 (-270))) (-5 *2 (-1302)) + (-5 *1 (-1301)))) + ((*1 *2 *3 *4) + (-12 (-5 *3 (-663 (-663 (-973 (-229))))) (-5 *4 (-663 (-270))) + (-5 *2 (-1302)) (-5 *1 (-1301))))) +(((*1 *2 *3 *4) + (-12 (-5 *3 (-305 (-421 (-976 *5)))) (-5 *4 (-1209)) + (-4 *5 (-13 (-319) (-149))) + (-5 *2 (-1198 (-663 (-326 *5)) (-663 (-305 (-326 *5))))) + (-5 *1 (-1161 *5)))) + ((*1 *2 *3 *4) + (-12 (-5 *3 (-421 (-976 *5))) (-5 *4 (-1209)) + (-4 *5 (-13 (-319) (-149))) + (-5 *2 (-1198 (-663 (-326 *5)) (-663 (-305 (-326 *5))))) + (-5 *1 (-1161 *5))))) +(((*1 *2 *3 *4 *4 *4 *4 *5 *5 *5) + (-12 (-5 *3 (-1 (-391) (-391))) (-5 *4 (-391)) (-5 *2 - (-2 (|:| |f1| *3) (|:| |f2| (-663 *5)) (|:| |f3| *5) - (|:| |f4| (-663 *5)))) - (-5 *1 (-1220 *6)) (-5 *4 (-663 *5))))) -(((*1 *2 *2) (-12 (-5 *2 (-560)) (-5 *1 (-957))))) -(((*1 *2 *1 *3) (-12 (-5 *3 (-949)) (-5 *2 (-482)) (-5 *1 (-1302))))) -(((*1 *2 *3) (-12 (-5 *3 (-949)) (-5 *2 (-1191)) (-5 *1 (-808))))) -(((*1 *2 *1) (-12 (-5 *2 (-114)) (-5 *1 (-669 *3)) (-4 *3 (-1133))))) -(((*1 *2) - (-12 (-4 *2 (-13 (-435 *3) (-1034))) (-5 *1 (-287 *3 *2)) - (-4 *3 (-571))))) -(((*1 *2 *1) (-12 (-4 *1 (-541)) (-5 *2 (-713 (-564)))))) + (-2 (|:| -3949 *4) (|:| -2726 *4) (|:| |totalpts| (-560)) + (|:| |success| (-114)))) + (-5 *1 (-811)) (-5 *5 (-560))))) (((*1 *2 *3) - (-12 - (-5 *3 - (-2 (|:| |var| (-1209)) (|:| |fn| (-326 (-229))) - (|:| -4389 (-1121 (-866 (-229)))) (|:| |abserr| (-229)) - (|:| |relerr| (-229)))) - (-5 *2 (-391)) (-5 *1 (-195))))) -(((*1 *2 *3 *4 *4 *4 *4 *5 *5 *4) - (-12 (-5 *3 (-1191)) (-5 *4 (-560)) (-5 *5 (-711 (-171 (-229)))) - (-5 *2 (-1067)) (-5 *1 (-776))))) -(((*1 *2 *3 *4) - (-12 (-5 *3 (-1 *6 *4 *5)) (-4 *4 (-1133)) (-4 *5 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(-1191)) (-5 *2 (-1305)) (-5 *1 (-884)))) ((*1 *2 *3) (-12 (-5 *3 (-888)) (-5 *2 (-1305)) (-5 *1 (-884)))) @@ -14363,13 +14036,13 @@ ((*1 *2 *3 *1) (-12 (-5 *3 (-560)) (-5 *2 (-1305)) (-5 *1 (-1187 *4)) (-4 *4 (-1133)) (-4 *4 (-1249))))) -(((*1 *2 *3) (-12 (-5 *3 (-846)) (-5 *2 (-51)) (-5 *1 (-855))))) +(((*1 *2 *1) (-12 (-5 *2 (-1305)) (-5 *1 (-847))))) (((*1 *1 *1 *2) (-12 (-5 *2 (-663 (-888))) (-5 *1 (-888)))) ((*1 *2 *1) (-12 (-5 *2 - (-2 (|:| -1642 (-663 (-888))) (|:| -2936 (-663 (-888))) - (|:| |presup| (-663 (-888))) (|:| -2265 (-663 (-888))) + (-2 (|:| -1826 (-663 (-888))) (|:| -3218 (-663 (-888))) + (|:| |presup| (-663 (-888))) (|:| -2913 (-663 (-888))) (|:| |args| (-663 (-888))))) (-5 *1 (-1209))))) (((*1 *2 *3) @@ -14382,41 +14055,49 @@ ((*1 *2 *3 *3) (-12 (-4 *3 (-13 (-376) (-10 -8 (-15 ** ($ $ (-421 (-560))))))) (-5 *2 (-663 *3)) (-5 *1 (-1160 *4 *3)) (-4 *4 (-1275 *3))))) +(((*1 *2 *3 *4 *5 *5 *6) + (-12 (-5 *4 (-560)) (-5 *6 (-1 (-1305) (-1299 *5) (-1299 *5) (-391))) + 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*2 *1) (-12 (-5 *2 (-114)) (-5 *1 (-115))))) (((*1 *2) (-12 (-14 *4 *2) (-4 *5 (-1249)) (-5 *2 (-793)) (-5 *1 (-244 *3 *4 *5)) (-4 *3 (-245 *4 *5)))) @@ -16510,8 +16432,10 @@ ((*1 *2 *1) (-12 (-4 *2 (-13 (-871) (-376))) (-5 *1 (-1093 *2 *3)) (-4 *3 (-1275 *2))))) -(((*1 *1 *2) (-12 (-5 *2 (-663 *3)) (-4 *3 (-1133)) (-4 *1 (-242 *3)))) - ((*1 *1) (-12 (-4 *1 (-242 *2)) (-4 *2 (-1133))))) +(((*1 *2 *3 *3 *3 *3 *3 *4 *4 *4 *5) + (-12 (-5 *3 (-229)) (-5 *4 (-560)) + (-5 *5 (-3 (|:| |fn| (-402)) (|:| |fp| (-61 G)))) (-5 *2 (-1067)) + (-5 *1 (-770))))) (((*1 *1 *1) (-12 (-4 *1 (-121 *2)) (-4 *2 (-1249)))) ((*1 *1 *1) (-12 (-5 *1 (-694 *2)) (-4 *2 (-872)))) ((*1 *1 *1) (-12 (-5 *1 (-699 *2)) (-4 *2 (-872)))) @@ -16520,29 +16444,21 @@ ((*1 *2 *1) (-12 (-4 *2 (-13 (-871) (-376))) (-5 *1 (-1093 *2 *3)) (-4 *3 (-1275 *2))))) -(((*1 *2) (-12 (-4 *2 (-175)) (-5 *1 (-167 *3 *2)) (-4 *3 (-168 *2)))) - ((*1 *2 *3) - (-12 (-5 *3 (-1299 *1)) (-4 *1 (-383 *2 *4)) (-4 *4 (-1275 *2)) - (-4 *2 (-175)))) - 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\ No newline at end of file |