diff options
Diffstat (limited to 'src')
-rw-r--r-- | src/ChangeLog | 11 | ||||
-rw-r--r-- | src/algebra/irsn.spad.pamphlet | 2 | ||||
-rw-r--r-- | src/algebra/perm.spad.pamphlet | 36 | ||||
-rw-r--r-- | src/algebra/permgrps.spad.pamphlet | 28 | ||||
-rw-r--r-- | src/algebra/rep1.spad.pamphlet | 2 | ||||
-rw-r--r-- | src/input/grpthry.input.pamphlet | 6 | ||||
-rw-r--r-- | src/input/perm.input.pamphlet | 8 | ||||
-rw-r--r-- | src/share/algebra/browse.daase | 644 | ||||
-rw-r--r-- | src/share/algebra/category.daase | 1407 | ||||
-rw-r--r-- | src/share/algebra/compress.daase | 1332 | ||||
-rw-r--r-- | src/share/algebra/interp.daase | 9040 | ||||
-rw-r--r-- | src/share/algebra/operation.daase | 31252 |
12 files changed, 21889 insertions, 21879 deletions
diff --git a/src/ChangeLog b/src/ChangeLog index 56d3b90b..4b6d92e6 100644 --- a/src/ChangeLog +++ b/src/ChangeLog @@ -1,5 +1,16 @@ 2010-06-12 Gabriel Dos Reis <gdr@cs.tamu.edu> + * algebra/permgrps.spad.pamphlet (PermutationGroup): Rename + movedPoints to support. Adjust call eval. + * algebra/perm.spad.pamphlet (PermutationCategory): Now extend + Eltable. Remove eval. Rename movedPoints to support. + (Permutation): Adjust. + * algebra/irsn.spad.pamphlet (listPermutationIrrRepSymNatPackage): + Change call to eval to elt. + * algebra/rep1.spad.pamphlet: Likewise. + +2010-06-12 Gabriel Dos Reis <gdr@cs.tamu.edu> + * interp/g-opt.boot (replaceableTemporary?): New. (optSEQ) [getRidOfTemps]: Use it to decide when to safely inline a temporary variable definition. diff --git a/src/algebra/irsn.spad.pamphlet b/src/algebra/irsn.spad.pamphlet index 95d9a257..5b2a4f48 100644 --- a/src/algebra/irsn.spad.pamphlet +++ b/src/algebra/irsn.spad.pamphlet @@ -171,7 +171,7 @@ IrrRepSymNatPackage(): public == private where listPermutation(pi) == li : L I := nil$(L I) for k in n..1 by -1 repeat - li := cons(eval(pi,k)$(PERM I),li) + li := cons(pi.k,li) li signum(numberOfRowTableau, numberOfColumnTableau,pi) == diff --git a/src/algebra/perm.spad.pamphlet b/src/algebra/perm.spad.pamphlet index 69f33f83..2dd9da5b 100644 --- a/src/algebra/perm.spad.pamphlet +++ b/src/algebra/perm.spad.pamphlet @@ -15,7 +15,7 @@ ++ Authors: Holger Gollan, Johannes Grabmeier, Gerhard Schneider ++ Date Created: 27 July 1989 ++ Date Last Updated: 29 March 1990 -++ Basic Operations: cycle, cycles, eval, orbit +++ Basic Operations: cycle, cycles, orbit ++ Related Constructors: PermutationGroup, PermutationGroupExamples ++ Also See: RepresentationTheoryPackage1 ++ AMS Classifications: @@ -24,7 +24,8 @@ ++ Description: PermutationCategory provides a categorial environment ++ for subgroups of bijections of a set (i.e. permutations) -PermutationCategory(S:SetCategory): Category == Group with +PermutationCategory(S:SetCategory): Category == + Join(Group,Eltable(S,S)) with cycle : List S -> % ++ cycle(ls) coerces a cycle {\em ls}, i.e. a list with not ++ repetitions to a permutation, which maps {\em ls.i} to @@ -37,12 +38,9 @@ PermutationCategory(S:SetCategory): Category == Group with ++ {\em ls.i} to {\em ls.i+1}, indices modulo the length of the list, ++ then these permutations are mutiplied. ++ Error: if repetitions occur in one cycle. - eval : (%,S) -> S - ++ eval(p, el) returns the image of {\em el} under the - ++ permutation p. - elt : (%,S) -> S - ++ elt(p, el) returns the image of {\em el} under the - ++ permutation p. + support: % -> Set S + ++ \spad{support p} returns the set of points not fixed by the + ++ permutation \spad{p}. orbit : (%,S) -> Set S ++ orbit(p, el) returns the orbit of {\em el} under the ++ permutation p, i.e. the set which is given by applications of @@ -61,7 +59,7 @@ PermutationCategory(S:SetCategory): Category == Group with ++ Authors: Johannes Grabmeier, Holger Gollan ++ Date Created: 19 May 1989 ++ Date Last Updated: 2 June 2006 -++ Basic Operations: _*, degree, movedPoints, cyclePartition, order, +++ Basic Operations: _*, degree, support, cyclePartition, order, ++ numberOfCycles, sign, even?, odd? ++ Related Constructors: PermutationGroup, PermutationGroupExamples ++ Also See: RepresentationTheoryPackage1 @@ -126,8 +124,6 @@ Permutation(S:SetCategory): public == private where degree : % -> NonNegativeInteger ++ degree(p) retuns the number of points moved by the ++ permutation p. - movedPoints : % -> Set S - ++ movedPoints(p) returns the set of points moved by the permutation p. cyclePartition : % -> Partition ++ cyclePartition(p) returns the cycle structure of a permutation ++ p including cycles of length 1 only if S is finite. @@ -300,7 +296,7 @@ Note that before [[patch--50]] this read coercePreimagesImages preImageAndImage == p : % := [preImageAndImage.1,preImageAndImage.2] \end{verbatim} -causing bugs when computing [[movedPoints]], [[fixedPoints]], [[even?]], +causing bugs when computing [[support]], [[fixedPoints]], [[even?]], [[odd?]], etc., as reported in Issue~\#295. The other coercion facilities check for fixed points. It also seems that [[*]] @@ -308,7 +304,7 @@ removes fixed points from its result. <<TEST PERM>>= p := coercePreimagesImages([[1,2,3],[1,2,3]]) - movedPoints p -- should return {} + support p -- should return {} even? p -- should return true p := coercePreimagesImages([[0,1,2,3],[3,0,2,1]])$PERM ZMOD 4 fixedPoints p -- should return {2} @@ -319,9 +315,9 @@ removes fixed points from its result. <<domain PERM Permutation>>= - movedPoints p == construct p.1 + support p == construct p.1 - degree p == #movedPoints p + degree p == #support p p = q == #(preimp := p.1) ~= #(preimq := q.1) => false @@ -334,12 +330,12 @@ removes fixed points from its result. orbit(p ,el) == -- start with a 1-element list: out : Set S := brace list el - el2 := eval(p, el) + el2 := p(el) while el2 ~= el repeat -- be carefull: insert adds one element -- as side effect to out insert!(el2, out) - el2 := eval(p, el2) + el2 := p(el2) out cyclePartition p == @@ -450,13 +446,11 @@ removes fixed points from its result. inv p == [p.2, p.1] - eval(p, el) == + elt(p,el) == pos := position(el, p.1) pos = 0 => el (p.2).pos - elt(p, el) == eval(p, el) - numberOfCycles p == #coerceToCycle(p, false) @@ -480,7 +474,7 @@ Up to [[patch--50]] we did not check for duplicates. Up to [[patch--50]] we did not check for duplicates. <<domain PERM Permutation>>= - fixedPoints ( p ) == complement movedPoints p + fixedPoints ( p ) == complement support p cyclePartition p == pt := partition([#c::PI for c in coerceToCycle(p, false)])$Partition diff --git a/src/algebra/permgrps.spad.pamphlet b/src/algebra/permgrps.spad.pamphlet index 5d69a574..98e2ab75 100644 --- a/src/algebra/permgrps.spad.pamphlet +++ b/src/algebra/permgrps.spad.pamphlet @@ -116,8 +116,8 @@ PermutationGroup(S:SetCategory): public == private where ++ wordInGenerators(p,gp) returns the word for the permutation p ++ in the original generators of the group {\em gp}, ++ represented by the indices of the list, given by {\em generators}. - movedPoints : % -> FSET S - ++ movedPoints(gp) returns the points moved by the group {\em gp}. + support : % -> FSET S + ++ support(gp) returns the points moved by the group {\em gp}. < : (%,%) -> B ++ gp1 < gp2 returns true if and only if {\em gp1} ++ is a proper subgroup of {\em gp2}. @@ -261,7 +261,7 @@ PermutationGroup(S:SetCategory): public == private where newList := nil()$(L S) workList := orbitList.pos for j in #workList..1 by -1 repeat - newList := cons ( eval ( gen , workList.j ) , newList ) + newList := cons (gen(workList.j) , newList ) if not member?( newList , orbitList ) then orbitList := cons ( newList , orbitList ) pos := pos + 1 @@ -298,10 +298,10 @@ PermutationGroup(S:SetCategory): public == private where true pointList(group : %) : L S == - support : FSET S := brace() -- empty set !! + s : FSET S := brace() -- empty set !! for perm in group.gens repeat - support := union(support, movedPoints perm) - parts support + s := union(s, support perm) + parts s orbitWithSvc ( group : L V NNI , point : NNI ) : REC == -- compute orbit with Schreier vector, "-2" means not in the orbit, @@ -469,7 +469,7 @@ PermutationGroup(S:SetCategory): public == private where for ggg in 1..#gp repeat q := new(degree,0)$(V NNI) for i in 1..degree repeat - newEl := eval ( gp.ggg , supp.i ) + newEl := elt(gp.ggg,supp.i) pos2 := position ( newEl , supp ) q.i := pos2 pretend NNI newGroup := cons ( q , newGroup ) @@ -597,7 +597,7 @@ PermutationGroup(S:SetCategory): public == private where -- internal membership testing supp := pointList gp outlist := nil()$(L NNI) - mP : L S := parts movedPoints p + mP : L S := parts support p for x in mP repeat not member? (x, supp) => return [ false , nil()$(L NNI) ] if flag then @@ -617,7 +617,7 @@ PermutationGroup(S:SetCategory): public == private where degree := # supp pp := new(degree,0)$(V NNI) for i in 1..degree repeat - el := eval ( p , supp.i ) + el := p(supp.i) pos := position ( el , supp ) pp.i := pos::NNI words := nil()$(L L NNI) @@ -649,7 +649,7 @@ PermutationGroup(S:SetCategory): public == private where elt ( gp , i ) == (gp.gens).i - movedPoints ( gp ) == brace pointList gp + support ( gp ) == brace pointList gp random ( group , maximalNumberOfFactors ) == maximalNumberOfFactors < 1 => 1$(PERM S) @@ -707,7 +707,7 @@ PermutationGroup(S:SetCategory): public == private where outSet orbits ( gp ) == - spp := movedPoints gp + spp := support gp orbits := nil()$(L FSET S) while cardinality spp > 0 repeat el := extract! spp @@ -734,17 +734,17 @@ PermutationGroup(S:SetCategory): public == private where shortenWord ( outlist , gp ) gp1 < gp2 == - not empty? difference ( movedPoints gp1 , movedPoints gp2 ) => false + not empty? difference ( support gp1 , support gp2 ) => false not subgroup ( gp1 , gp2 ) => false order gp1 = order gp2 => false true gp1 <= gp2 == - not empty? difference ( movedPoints gp1 , movedPoints gp2 ) => false + not empty? difference ( support gp1 , support gp2 ) => false subgroup ( gp1 , gp2 ) gp1 = gp2 == - movedPoints gp1 ~= movedPoints gp2 => false + support gp1 ~= support gp2 => false if #(gp1.gens) <= #(gp2.gens) then not subgroup ( gp1 , gp2 ) => return false else diff --git a/src/algebra/rep1.spad.pamphlet b/src/algebra/rep1.spad.pamphlet index f26ae02c..dde33bc9 100644 --- a/src/algebra/rep1.spad.pamphlet +++ b/src/algebra/rep1.spad.pamphlet @@ -302,7 +302,7 @@ RepresentationPackage1(R): public == private where -- permutations are assumed to permute {1,2,...,n} a : M I := zero(n :: NNI, n :: NNI) for i in 1..n repeat - a(eval(p,i)$(PERM I),i) := 1 + a(p.i,i) := 1 a diff --git a/src/input/grpthry.input.pamphlet b/src/input/grpthry.input.pamphlet index 2de5aa4e..e11ed503 100644 --- a/src/input/grpthry.input.pamphlet +++ b/src/input/grpthry.input.pamphlet @@ -22,7 +22,7 @@ g2 : PERMGRP INT := [ x , z ] g3 : PERMGRP INT := [ y , z ] order g1 degree g3 -movedPoints g2 +support g2 orbit (g1, 3) orbits g3 member? ( y , g2 ) @@ -72,9 +72,9 @@ px * pz py ** 3 inv px order px -movedPoints py +support py orbit ( pz , 3 ) -eval ( py , 7 ) +py 7 )sh PERM -- Input for page RepA6Page diff --git a/src/input/perm.input.pamphlet b/src/input/perm.input.pamphlet index 503c5c91..8b75c033 100644 --- a/src/input/perm.input.pamphlet +++ b/src/input/perm.input.pamphlet @@ -61,7 +61,7 @@ inv px -- or for the image of some element under a special permutation: -eval(px,17::PrimeField(29)) +elt(px,17::PrimeField(29)) -- you may try to build commutators: @@ -76,7 +76,7 @@ orbit(px,11::PrimeField(29)) -- or for the elements of the underlying set, which are permuted -- by a given permutation: -movedPoints(pk) +support(pk) -- Now we take a short look on permutation groups. -- They are represented as a list of generating permutations: @@ -129,9 +129,9 @@ el4 : PERM Vector PrimeField 2 := coerceListOfPairs ll4 -- Now we can do the same operations as before, e.g. -eval ( el3 , vl.5 ) +el3(vl.5) el2 * el1 -movedPoints el4 +support el4 -- Let's built the general linear group now diff --git a/src/share/algebra/browse.daase b/src/share/algebra/browse.daase index d2f1df71..5066fa82 100644 --- a/src/share/algebra/browse.daase +++ b/src/share/algebra/browse.daase @@ -1,5 +1,5 @@ -(2266417 . 3485084669) +(2266184 . 3485328466) (-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 \\spad{`d'}.")) (|base| (((|SpadAst|) $) "\\spad{base(d)} returns the base domain(\\spad{s}) of the add-domain expression."))) NIL NIL -(-32 R -1385) +(-32 R -2968) ((|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 -1047) (QUOTE (-570))))) @@ -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 a1,{}...,{}an."))) NIL NIL -(-40 -1385 UP UPUP -3808) +(-40 -2968 UP UPUP -3777) ((|constructor| (NIL "Function field defined by \\spad{f}(\\spad{x},{} \\spad{y}) = 0.")) (|knownInfBasis| (((|Void|) (|NonNegativeInteger|)) "\\spad{knownInfBasis(n)} \\undocumented{}"))) ((-4445 |has| (-413 |#2|) (-368)) (-4450 |has| (-413 |#2|) (-368)) (-4444 |has| (-413 |#2|) (-368)) ((-4454 "*") . T) (-4446 . T) (-4447 . T) (-4449 . T)) -((|HasCategory| (-413 |#2|) (QUOTE (-146))) (|HasCategory| (-413 |#2|) (QUOTE (-148))) (|HasCategory| (-413 |#2|) (QUOTE (-354))) (-2811 (|HasCategory| (-413 |#2|) (QUOTE (-368))) (|HasCategory| (-413 |#2|) (QUOTE (-354)))) (|HasCategory| (-413 |#2|) (QUOTE (-368))) (|HasCategory| (-413 |#2|) (QUOTE (-373))) (-2811 (-12 (|HasCategory| (-413 |#2|) (QUOTE (-235))) (|HasCategory| (-413 |#2|) (QUOTE (-368)))) (|HasCategory| (-413 |#2|) (QUOTE (-354)))) (-2811 (-12 (|HasCategory| (-413 |#2|) (LIST (QUOTE -907) (QUOTE (-1186)))) (|HasCategory| (-413 |#2|) (QUOTE (-368)))) (-12 (|HasCategory| (-413 |#2|) (LIST (QUOTE -907) (QUOTE (-1186)))) (|HasCategory| (-413 |#2|) (QUOTE (-354))))) (|HasCategory| (-413 |#2|) (LIST (QUOTE -645) (QUOTE (-570)))) (-2811 (|HasCategory| (-413 |#2|) (LIST (QUOTE -1047) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasCategory| (-413 |#2|) (QUOTE (-368)))) (|HasCategory| (-413 |#2|) (LIST (QUOTE -1047) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasCategory| (-413 |#2|) (LIST (QUOTE -1047) (QUOTE (-570)))) (|HasCategory| |#1| (QUOTE (-368))) (|HasCategory| |#1| (QUOTE (-373))) (-12 (|HasCategory| (-413 |#2|) (LIST (QUOTE -907) (QUOTE (-1186)))) (|HasCategory| (-413 |#2|) (QUOTE (-368)))) (-12 (|HasCategory| (-413 |#2|) (QUOTE (-235))) (|HasCategory| (-413 |#2|) (QUOTE (-368))))) -(-41 R -1385) +((|HasCategory| (-413 |#2|) (QUOTE (-146))) (|HasCategory| (-413 |#2|) (QUOTE (-148))) (|HasCategory| (-413 |#2|) (QUOTE (-354))) (-3684 (|HasCategory| (-413 |#2|) (QUOTE (-368))) (|HasCategory| (-413 |#2|) (QUOTE (-354)))) (|HasCategory| (-413 |#2|) (QUOTE (-368))) (|HasCategory| (-413 |#2|) (QUOTE (-373))) (-3684 (-12 (|HasCategory| (-413 |#2|) (QUOTE (-235))) (|HasCategory| (-413 |#2|) (QUOTE (-368)))) (|HasCategory| (-413 |#2|) (QUOTE (-354)))) (-3684 (-12 (|HasCategory| (-413 |#2|) (LIST (QUOTE -907) (QUOTE (-1186)))) (|HasCategory| (-413 |#2|) (QUOTE (-368)))) (-12 (|HasCategory| (-413 |#2|) (LIST (QUOTE -907) (QUOTE (-1186)))) (|HasCategory| (-413 |#2|) (QUOTE (-354))))) (|HasCategory| (-413 |#2|) (LIST (QUOTE -645) (QUOTE (-570)))) (-3684 (|HasCategory| (-413 |#2|) (LIST (QUOTE -1047) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasCategory| (-413 |#2|) (QUOTE (-368)))) (|HasCategory| (-413 |#2|) (LIST (QUOTE -1047) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasCategory| (-413 |#2|) (LIST (QUOTE -1047) (QUOTE (-570)))) (|HasCategory| |#1| (QUOTE (-368))) (|HasCategory| |#1| (QUOTE (-373))) (-12 (|HasCategory| (-413 |#2|) (LIST (QUOTE -907) (QUOTE (-1186)))) (|HasCategory| (-413 |#2|) (QUOTE (-368)))) (-12 (|HasCategory| (-413 |#2|) (QUOTE (-235))) (|HasCategory| (-413 |#2|) (QUOTE (-368))))) +(-41 R -2968) ((|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}\\spad{'s} which are algebraic from the denominators in \\spad{f}.") ((|#2| |#2| (|List| |#2|)) "\\spad{ratDenom(f, [a1,...,an])} removes the \\spad{ai}\\spad{'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 (-458))) (|HasCategory| |#1| (LIST (QUOTE -1047) (QUOTE (-570)))) (|HasCategory| |#2| (LIST (QUOTE -436) (|devaluate| |#1|))))) @@ -111,7 +111,7 @@ NIL (-45 |Key| |Entry|) ((|constructor| (NIL "\\spadtype{AssociationList} implements association lists. These may be viewed as lists of pairs where the first part is a key and the second is the stored value. For example,{} the key might be a string with a persons employee identification number and the value might be a record with personnel data."))) ((-4452 . T) (-4453 . T)) -((-2811 (-12 (|HasCategory| (-2 (|:| -3679 |#1|) (|:| -1409 |#2|)) (QUOTE (-856))) (|HasCategory| (-2 (|:| -3679 |#1|) (|:| -1409 |#2|)) (LIST (QUOTE -313) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -3679) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -1409) (|devaluate| |#2|)))))) (-12 (|HasCategory| (-2 (|:| -3679 |#1|) (|:| -1409 |#2|)) (QUOTE (-1109))) (|HasCategory| (-2 (|:| -3679 |#1|) (|:| -1409 |#2|)) (LIST (QUOTE -313) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -3679) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -1409) (|devaluate| |#2|))))))) (-2811 (|HasCategory| (-2 (|:| -3679 |#1|) (|:| -1409 |#2|)) (QUOTE (-856))) (|HasCategory| (-2 (|:| -3679 |#1|) (|:| -1409 |#2|)) (QUOTE (-1109))) (|HasCategory| (-2 (|:| -3679 |#1|) (|:| -1409 |#2|)) (LIST (QUOTE -619) (QUOTE (-868)))) (|HasCategory| |#2| (QUOTE (-1109))) (|HasCategory| |#2| (LIST (QUOTE -619) (QUOTE (-868))))) (|HasCategory| (-2 (|:| -3679 |#1|) (|:| -1409 |#2|)) (LIST (QUOTE -620) (QUOTE (-542)))) (-12 (|HasCategory| |#2| (QUOTE (-1109))) (|HasCategory| |#2| (LIST (QUOTE -313) (|devaluate| |#2|)))) (-2811 (|HasCategory| (-2 (|:| -3679 |#1|) (|:| -1409 |#2|)) (QUOTE (-856))) (|HasCategory| (-2 (|:| -3679 |#1|) (|:| -1409 |#2|)) (QUOTE (-1109))) (|HasCategory| |#2| (QUOTE (-1109)))) (|HasCategory| (-2 (|:| -3679 |#1|) (|:| -1409 |#2|)) (QUOTE (-856))) (|HasCategory| |#1| (QUOTE (-856))) (|HasCategory| |#2| (QUOTE (-1109))) (|HasCategory| (-570) (QUOTE (-856))) (|HasCategory| (-2 (|:| -3679 |#1|) (|:| -1409 |#2|)) (QUOTE (-1109))) (-2811 (|HasCategory| (-2 (|:| -3679 |#1|) (|:| -1409 |#2|)) (LIST (QUOTE -619) (QUOTE (-868)))) (|HasCategory| |#2| (LIST (QUOTE -619) (QUOTE (-868))))) (-2811 (|HasCategory| (-2 (|:| -3679 |#1|) (|:| -1409 |#2|)) (QUOTE (-1109))) (|HasCategory| |#2| (QUOTE (-1109)))) (|HasCategory| |#2| (LIST (QUOTE -619) (QUOTE (-868)))) (|HasCategory| (-2 (|:| -3679 |#1|) (|:| -1409 |#2|)) (LIST (QUOTE -619) (QUOTE (-868)))) (-12 (|HasCategory| (-2 (|:| -3679 |#1|) (|:| -1409 |#2|)) (QUOTE (-1109))) (|HasCategory| (-2 (|:| -3679 |#1|) (|:| -1409 |#2|)) (LIST (QUOTE -313) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -3679) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -1409) (|devaluate| |#2|))))))) +((-3684 (-12 (|HasCategory| (-2 (|:| -4111 |#1|) (|:| -3117 |#2|)) (QUOTE (-856))) (|HasCategory| (-2 (|:| -4111 |#1|) (|:| -3117 |#2|)) (LIST (QUOTE -313) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -4111) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -3117) (|devaluate| |#2|)))))) (-12 (|HasCategory| (-2 (|:| -4111 |#1|) (|:| -3117 |#2|)) (QUOTE (-1109))) (|HasCategory| (-2 (|:| -4111 |#1|) (|:| -3117 |#2|)) (LIST (QUOTE -313) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -4111) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -3117) (|devaluate| |#2|))))))) (-3684 (|HasCategory| (-2 (|:| -4111 |#1|) (|:| -3117 |#2|)) (QUOTE (-856))) (|HasCategory| (-2 (|:| -4111 |#1|) (|:| -3117 |#2|)) (QUOTE (-1109))) (|HasCategory| (-2 (|:| -4111 |#1|) (|:| -3117 |#2|)) (LIST (QUOTE -619) (QUOTE (-868)))) (|HasCategory| |#2| (QUOTE (-1109))) (|HasCategory| |#2| (LIST (QUOTE -619) (QUOTE (-868))))) (|HasCategory| (-2 (|:| -4111 |#1|) (|:| -3117 |#2|)) (LIST (QUOTE -620) (QUOTE (-542)))) (-12 (|HasCategory| |#2| (QUOTE (-1109))) (|HasCategory| |#2| (LIST (QUOTE -313) (|devaluate| |#2|)))) (-3684 (|HasCategory| (-2 (|:| -4111 |#1|) (|:| -3117 |#2|)) (QUOTE (-856))) (|HasCategory| (-2 (|:| -4111 |#1|) (|:| -3117 |#2|)) (QUOTE (-1109))) (|HasCategory| |#2| (QUOTE (-1109)))) (|HasCategory| (-2 (|:| -4111 |#1|) (|:| -3117 |#2|)) (QUOTE (-856))) (|HasCategory| |#1| (QUOTE (-856))) (|HasCategory| |#2| (QUOTE (-1109))) (|HasCategory| (-570) (QUOTE (-856))) (|HasCategory| (-2 (|:| -4111 |#1|) (|:| -3117 |#2|)) (QUOTE (-1109))) (-3684 (|HasCategory| (-2 (|:| -4111 |#1|) (|:| -3117 |#2|)) (LIST (QUOTE -619) (QUOTE (-868)))) (|HasCategory| |#2| (LIST (QUOTE -619) (QUOTE (-868))))) (-3684 (|HasCategory| (-2 (|:| -4111 |#1|) (|:| -3117 |#2|)) (QUOTE (-1109))) (|HasCategory| |#2| (QUOTE (-1109)))) (|HasCategory| |#2| (LIST (QUOTE -619) (QUOTE (-868)))) (|HasCategory| (-2 (|:| -4111 |#1|) (|:| -3117 |#2|)) (LIST (QUOTE -619) (QUOTE (-868)))) (-12 (|HasCategory| (-2 (|:| -4111 |#1|) (|:| -3117 |#2|)) (QUOTE (-1109))) (|HasCategory| (-2 (|:| -4111 |#1|) (|:| -3117 |#2|)) (LIST (QUOTE -313) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -4111) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -3117) (|devaluate| |#2|))))))) (-46 S R E) ((|constructor| (NIL "Abelian monoid ring elements (not necessarily of finite support) of this ring are of the form formal SUM (r_i * e_i) where the r_i are coefficents and the e_i,{} elements of the ordered abelian monoid,{} are thought of as exponents or monomials. The monomials commute with each other,{} and with the coefficients (which themselves may or may not be commutative). See \\spadtype{FiniteAbelianMonoidRing} for the case of finite support a useful common model for polynomials and power series. Conceptually at least,{} only the non-zero terms are ever operated on.")) (/ (($ $ |#2|) "\\spad{p/c} divides \\spad{p} by the coefficient \\spad{c}.")) (|coefficient| ((|#2| $ |#3|) "\\spad{coefficient(p,e)} extracts the coefficient of the monomial with exponent \\spad{e} from polynomial \\spad{p},{} or returns zero if exponent is not present.")) (|reductum| (($ $) "\\spad{reductum(u)} returns \\spad{u} minus its leading monomial returns zero if handed the zero element.")) (|monomial| (($ |#2| |#3|) "\\spad{monomial(r,e)} makes a term from a coefficient \\spad{r} and an exponent \\spad{e}.")) (|monomial?| (((|Boolean|) $) "\\spad{monomial?(p)} tests if \\spad{p} is a single monomial.")) (|map| (($ (|Mapping| |#2| |#2|) $) "\\spad{map(fn,u)} maps function \\spad{fn} onto the coefficients of the non-zero monomials of \\spad{u}.")) (|degree| ((|#3| $) "\\spad{degree(p)} returns the maximum of the exponents of the terms of \\spad{p}.")) (|leadingMonomial| (($ $) "\\spad{leadingMonomial(p)} returns the monomial of \\spad{p} with the highest degree.")) (|leadingCoefficient| ((|#2| $) "\\spad{leadingCoefficient(p)} returns the coefficient highest degree term of \\spad{p}."))) NIL @@ -144,7 +144,7 @@ NIL ((|constructor| (NIL "\\spad{ApplyUnivariateSkewPolynomial} (internal) allows univariate skew polynomials to be applied to appropriate modules.")) (|apply| ((|#2| |#3| (|Mapping| |#2| |#2|) |#2|) "\\spad{apply(p, f, m)} returns \\spad{p(m)} where the action is given by \\spad{x m = f(m)}. \\spad{f} must be an \\spad{R}-pseudo linear map on \\spad{M}."))) NIL NIL -(-54 |Base| R -1385) +(-54 |Base| R -2968) ((|constructor| (NIL "This package apply rewrite rules to expressions,{} calling the pattern matcher.")) (|localUnquote| ((|#3| |#3| (|List| (|Symbol|))) "\\spad{localUnquote(f,ls)} is a local function.")) (|applyRules| ((|#3| (|List| (|RewriteRule| |#1| |#2| |#3|)) |#3| (|PositiveInteger|)) "\\spad{applyRules([r1,...,rn], expr, n)} applies the rules \\spad{r1},{}...,{}\\spad{rn} to \\spad{f} a most \\spad{n} times.") ((|#3| (|List| (|RewriteRule| |#1| |#2| |#3|)) |#3|) "\\spad{applyRules([r1,...,rn], expr)} applies the rules \\spad{r1},{}...,{}\\spad{rn} to \\spad{f} an unlimited number of times,{} \\spadignore{i.e.} until none of \\spad{r1},{}...,{}\\spad{rn} is applicable to the expression."))) NIL NIL @@ -167,64 +167,64 @@ NIL (-59 S) ((|constructor| (NIL "This is the domain of 1-based one dimensional arrays")) (|oneDimensionalArray| (($ (|NonNegativeInteger|) |#1|) "\\spad{oneDimensionalArray(n,s)} creates an array from \\spad{n} copies of element \\spad{s}") (($ (|List| |#1|)) "\\spad{oneDimensionalArray(l)} creates an array from a list of elements \\spad{l}"))) ((-4453 . T) (-4452 . T)) -((-2811 (-12 (|HasCategory| |#1| (QUOTE (-856))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|))))) (-2811 (-12 (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-868))))) (|HasCategory| |#1| (LIST (QUOTE -620) (QUOTE (-542)))) (-2811 (|HasCategory| |#1| (QUOTE (-856))) (|HasCategory| |#1| (QUOTE (-1109)))) (|HasCategory| |#1| (QUOTE (-856))) (|HasCategory| (-570) (QUOTE (-856))) (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-868)))) (-12 (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|))))) +((-3684 (-12 (|HasCategory| |#1| (QUOTE (-856))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|))))) (-3684 (-12 (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-868))))) (|HasCategory| |#1| (LIST (QUOTE -620) (QUOTE (-542)))) (-3684 (|HasCategory| |#1| (QUOTE (-856))) (|HasCategory| |#1| (QUOTE (-1109)))) (|HasCategory| |#1| (QUOTE (-856))) (|HasCategory| (-570) (QUOTE (-856))) (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-868)))) (-12 (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|))))) (-60 R) ((|constructor| (NIL "\\indented{1}{A TwoDimensionalArray is a two dimensional array with} 1-based indexing for both rows and columns.")) (|shallowlyMutable| ((|attribute|) "One may destructively alter TwoDimensionalArray\\spad{'s}."))) ((-4452 . T) (-4453 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1109))) (-2811 (-12 (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-868))))) (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-868))))) -(-61 -2058) +((-12 (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1109))) (-3684 (-12 (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-868))))) (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-868))))) +(-61 -1800) ((|constructor| (NIL "\\spadtype{ASP10} produces Fortran for Type 10 ASPs,{} needed for NAG routine \\axiomOpFrom{d02kef}{d02Package}. This ASP computes the values of a set of functions,{} for example:\\begin{verbatim} SUBROUTINE COEFFN(P,Q,DQDL,X,ELAM,JINT) DOUBLE PRECISION ELAM,P,Q,X,DQDL INTEGER JINT P=1.0D0 Q=((-1.0D0*X**3)+ELAM*X*X-2.0D0)/(X*X) DQDL=1.0D0 RETURN END\\end{verbatim}")) (|coerce| (($ (|Vector| (|FortranExpression| (|construct| (QUOTE JINT) (QUOTE X) (QUOTE ELAM)) (|construct|) (|MachineFloat|)))) "\\spad{coerce(f)} takes objects from the appropriate instantiation of \\spadtype{FortranExpression} and turns them into an ASP."))) NIL NIL -(-62 -2058) +(-62 -1800) ((|constructor| (NIL "\\spadtype{Asp12} produces Fortran for Type 12 ASPs,{} needed for NAG routine \\axiomOpFrom{d02kef}{d02Package} etc.,{} for example:\\begin{verbatim} SUBROUTINE MONIT (MAXIT,IFLAG,ELAM,FINFO) DOUBLE PRECISION ELAM,FINFO(15) INTEGER MAXIT,IFLAG IF(MAXIT.EQ.-1)THEN PRINT*,\"Output from Monit\" ENDIF PRINT*,MAXIT,IFLAG,ELAM,(FINFO(I),I=1,4) RETURN END\\end{verbatim}")) (|outputAsFortran| (((|Void|)) "\\spad{outputAsFortran()} generates the default code for \\spadtype{ASP12}."))) NIL NIL -(-63 -2058) +(-63 -1800) ((|constructor| (NIL "\\spadtype{Asp19} produces Fortran for Type 19 ASPs,{} evaluating a set of functions and their jacobian at a given point,{} for example:\\begin{verbatim} SUBROUTINE LSFUN2(M,N,XC,FVECC,FJACC,LJC) DOUBLE PRECISION FVECC(M),FJACC(LJC,N),XC(N) INTEGER M,N,LJC INTEGER I,J DO 25003 I=1,LJC DO 25004 J=1,N FJACC(I,J)=0.0D025004 CONTINUE25003 CONTINUE FVECC(1)=((XC(1)-0.14D0)*XC(3)+(15.0D0*XC(1)-2.1D0)*XC(2)+1.0D0)/( &XC(3)+15.0D0*XC(2)) FVECC(2)=((XC(1)-0.18D0)*XC(3)+(7.0D0*XC(1)-1.26D0)*XC(2)+1.0D0)/( &XC(3)+7.0D0*XC(2)) FVECC(3)=((XC(1)-0.22D0)*XC(3)+(4.333333333333333D0*XC(1)-0.953333 &3333333333D0)*XC(2)+1.0D0)/(XC(3)+4.333333333333333D0*XC(2)) FVECC(4)=((XC(1)-0.25D0)*XC(3)+(3.0D0*XC(1)-0.75D0)*XC(2)+1.0D0)/( &XC(3)+3.0D0*XC(2)) FVECC(5)=((XC(1)-0.29D0)*XC(3)+(2.2D0*XC(1)-0.6379999999999999D0)* &XC(2)+1.0D0)/(XC(3)+2.2D0*XC(2)) FVECC(6)=((XC(1)-0.32D0)*XC(3)+(1.666666666666667D0*XC(1)-0.533333 &3333333333D0)*XC(2)+1.0D0)/(XC(3)+1.666666666666667D0*XC(2)) FVECC(7)=((XC(1)-0.35D0)*XC(3)+(1.285714285714286D0*XC(1)-0.45D0)* &XC(2)+1.0D0)/(XC(3)+1.285714285714286D0*XC(2)) FVECC(8)=((XC(1)-0.39D0)*XC(3)+(XC(1)-0.39D0)*XC(2)+1.0D0)/(XC(3)+ &XC(2)) FVECC(9)=((XC(1)-0.37D0)*XC(3)+(XC(1)-0.37D0)*XC(2)+1.285714285714 &286D0)/(XC(3)+XC(2)) FVECC(10)=((XC(1)-0.58D0)*XC(3)+(XC(1)-0.58D0)*XC(2)+1.66666666666 &6667D0)/(XC(3)+XC(2)) FVECC(11)=((XC(1)-0.73D0)*XC(3)+(XC(1)-0.73D0)*XC(2)+2.2D0)/(XC(3) &+XC(2)) FVECC(12)=((XC(1)-0.96D0)*XC(3)+(XC(1)-0.96D0)*XC(2)+3.0D0)/(XC(3) &+XC(2)) FVECC(13)=((XC(1)-1.34D0)*XC(3)+(XC(1)-1.34D0)*XC(2)+4.33333333333 &3333D0)/(XC(3)+XC(2)) FVECC(14)=((XC(1)-2.1D0)*XC(3)+(XC(1)-2.1D0)*XC(2)+7.0D0)/(XC(3)+X &C(2)) FVECC(15)=((XC(1)-4.39D0)*XC(3)+(XC(1)-4.39D0)*XC(2)+15.0D0)/(XC(3 &)+XC(2)) FJACC(1,1)=1.0D0 FJACC(1,2)=-15.0D0/(XC(3)**2+30.0D0*XC(2)*XC(3)+225.0D0*XC(2)**2) FJACC(1,3)=-1.0D0/(XC(3)**2+30.0D0*XC(2)*XC(3)+225.0D0*XC(2)**2) FJACC(2,1)=1.0D0 FJACC(2,2)=-7.0D0/(XC(3)**2+14.0D0*XC(2)*XC(3)+49.0D0*XC(2)**2) FJACC(2,3)=-1.0D0/(XC(3)**2+14.0D0*XC(2)*XC(3)+49.0D0*XC(2)**2) FJACC(3,1)=1.0D0 FJACC(3,2)=((-0.1110223024625157D-15*XC(3))-4.333333333333333D0)/( &XC(3)**2+8.666666666666666D0*XC(2)*XC(3)+18.77777777777778D0*XC(2) &**2) FJACC(3,3)=(0.1110223024625157D-15*XC(2)-1.0D0)/(XC(3)**2+8.666666 &666666666D0*XC(2)*XC(3)+18.77777777777778D0*XC(2)**2) FJACC(4,1)=1.0D0 FJACC(4,2)=-3.0D0/(XC(3)**2+6.0D0*XC(2)*XC(3)+9.0D0*XC(2)**2) FJACC(4,3)=-1.0D0/(XC(3)**2+6.0D0*XC(2)*XC(3)+9.0D0*XC(2)**2) FJACC(5,1)=1.0D0 FJACC(5,2)=((-0.1110223024625157D-15*XC(3))-2.2D0)/(XC(3)**2+4.399 &999999999999D0*XC(2)*XC(3)+4.839999999999998D0*XC(2)**2) FJACC(5,3)=(0.1110223024625157D-15*XC(2)-1.0D0)/(XC(3)**2+4.399999 &999999999D0*XC(2)*XC(3)+4.839999999999998D0*XC(2)**2) FJACC(6,1)=1.0D0 FJACC(6,2)=((-0.2220446049250313D-15*XC(3))-1.666666666666667D0)/( &XC(3)**2+3.333333333333333D0*XC(2)*XC(3)+2.777777777777777D0*XC(2) &**2) FJACC(6,3)=(0.2220446049250313D-15*XC(2)-1.0D0)/(XC(3)**2+3.333333 &333333333D0*XC(2)*XC(3)+2.777777777777777D0*XC(2)**2) FJACC(7,1)=1.0D0 FJACC(7,2)=((-0.5551115123125783D-16*XC(3))-1.285714285714286D0)/( &XC(3)**2+2.571428571428571D0*XC(2)*XC(3)+1.653061224489796D0*XC(2) &**2) FJACC(7,3)=(0.5551115123125783D-16*XC(2)-1.0D0)/(XC(3)**2+2.571428 &571428571D0*XC(2)*XC(3)+1.653061224489796D0*XC(2)**2) FJACC(8,1)=1.0D0 FJACC(8,2)=-1.0D0/(XC(3)**2+2.0D0*XC(2)*XC(3)+XC(2)**2) FJACC(8,3)=-1.0D0/(XC(3)**2+2.0D0*XC(2)*XC(3)+XC(2)**2) FJACC(9,1)=1.0D0 FJACC(9,2)=-1.285714285714286D0/(XC(3)**2+2.0D0*XC(2)*XC(3)+XC(2)* &*2) FJACC(9,3)=-1.285714285714286D0/(XC(3)**2+2.0D0*XC(2)*XC(3)+XC(2)* &*2) FJACC(10,1)=1.0D0 FJACC(10,2)=-1.666666666666667D0/(XC(3)**2+2.0D0*XC(2)*XC(3)+XC(2) &**2) FJACC(10,3)=-1.666666666666667D0/(XC(3)**2+2.0D0*XC(2)*XC(3)+XC(2) &**2) FJACC(11,1)=1.0D0 FJACC(11,2)=-2.2D0/(XC(3)**2+2.0D0*XC(2)*XC(3)+XC(2)**2) FJACC(11,3)=-2.2D0/(XC(3)**2+2.0D0*XC(2)*XC(3)+XC(2)**2) FJACC(12,1)=1.0D0 FJACC(12,2)=-3.0D0/(XC(3)**2+2.0D0*XC(2)*XC(3)+XC(2)**2) FJACC(12,3)=-3.0D0/(XC(3)**2+2.0D0*XC(2)*XC(3)+XC(2)**2) FJACC(13,1)=1.0D0 FJACC(13,2)=-4.333333333333333D0/(XC(3)**2+2.0D0*XC(2)*XC(3)+XC(2) &**2) FJACC(13,3)=-4.333333333333333D0/(XC(3)**2+2.0D0*XC(2)*XC(3)+XC(2) &**2) FJACC(14,1)=1.0D0 FJACC(14,2)=-7.0D0/(XC(3)**2+2.0D0*XC(2)*XC(3)+XC(2)**2) FJACC(14,3)=-7.0D0/(XC(3)**2+2.0D0*XC(2)*XC(3)+XC(2)**2) FJACC(15,1)=1.0D0 FJACC(15,2)=-15.0D0/(XC(3)**2+2.0D0*XC(2)*XC(3)+XC(2)**2) FJACC(15,3)=-15.0D0/(XC(3)**2+2.0D0*XC(2)*XC(3)+XC(2)**2) RETURN END\\end{verbatim}")) (|coerce| (($ (|Vector| (|FortranExpression| (|construct|) (|construct| (QUOTE XC)) (|MachineFloat|)))) "\\spad{coerce(f)} takes objects from the appropriate instantiation of \\spadtype{FortranExpression} and turns them into an ASP."))) NIL NIL -(-64 -2058) +(-64 -1800) ((|constructor| (NIL "\\spadtype{Asp1} produces Fortran for Type 1 ASPs,{} needed for various NAG routines. Type 1 ASPs take a univariate expression (in the symbol \\spad{X}) and turn it into a Fortran Function like the following:\\begin{verbatim} DOUBLE PRECISION FUNCTION F(X) DOUBLE PRECISION X F=DSIN(X) RETURN END\\end{verbatim}")) (|coerce| (($ (|FortranExpression| (|construct| (QUOTE X)) (|construct|) (|MachineFloat|))) "\\spad{coerce(f)} takes an object from the appropriate instantiation of \\spadtype{FortranExpression} and turns it into an ASP."))) NIL NIL -(-65 -2058) +(-65 -1800) ((|constructor| (NIL "\\spadtype{Asp20} produces Fortran for Type 20 ASPs,{} for example:\\begin{verbatim} SUBROUTINE QPHESS(N,NROWH,NCOLH,JTHCOL,HESS,X,HX) DOUBLE PRECISION HX(N),X(N),HESS(NROWH,NCOLH) INTEGER JTHCOL,N,NROWH,NCOLH HX(1)=2.0D0*X(1) HX(2)=2.0D0*X(2) HX(3)=2.0D0*X(4)+2.0D0*X(3) HX(4)=2.0D0*X(4)+2.0D0*X(3) HX(5)=2.0D0*X(5) HX(6)=(-2.0D0*X(7))+(-2.0D0*X(6)) HX(7)=(-2.0D0*X(7))+(-2.0D0*X(6)) RETURN END\\end{verbatim}"))) NIL NIL -(-66 -2058) +(-66 -1800) ((|constructor| (NIL "\\spadtype{Asp24} produces Fortran for Type 24 ASPs which evaluate a multivariate function at a point (needed for NAG routine \\axiomOpFrom{e04jaf}{e04Package}),{} for example:\\begin{verbatim} SUBROUTINE FUNCT1(N,XC,FC) DOUBLE PRECISION FC,XC(N) INTEGER N FC=10.0D0*XC(4)**4+(-40.0D0*XC(1)*XC(4)**3)+(60.0D0*XC(1)**2+5 &.0D0)*XC(4)**2+((-10.0D0*XC(3))+(-40.0D0*XC(1)**3))*XC(4)+16.0D0*X &C(3)**4+(-32.0D0*XC(2)*XC(3)**3)+(24.0D0*XC(2)**2+5.0D0)*XC(3)**2+ &(-8.0D0*XC(2)**3*XC(3))+XC(2)**4+100.0D0*XC(2)**2+20.0D0*XC(1)*XC( &2)+10.0D0*XC(1)**4+XC(1)**2 RETURN END\\end{verbatim}")) (|coerce| (($ (|FortranExpression| (|construct|) (|construct| (QUOTE XC)) (|MachineFloat|))) "\\spad{coerce(f)} takes an object from the appropriate instantiation of \\spadtype{FortranExpression} and turns it into an ASP."))) NIL NIL -(-67 -2058) +(-67 -1800) ((|constructor| (NIL "\\spadtype{Asp27} produces Fortran for Type 27 ASPs,{} needed for NAG routine \\axiomOpFrom{f02fjf}{f02Package} ,{}for example:\\begin{verbatim} FUNCTION DOT(IFLAG,N,Z,W,RWORK,LRWORK,IWORK,LIWORK) DOUBLE PRECISION W(N),Z(N),RWORK(LRWORK) INTEGER N,LIWORK,IFLAG,LRWORK,IWORK(LIWORK) DOT=(W(16)+(-0.5D0*W(15)))*Z(16)+((-0.5D0*W(16))+W(15)+(-0.5D0*W(1 &4)))*Z(15)+((-0.5D0*W(15))+W(14)+(-0.5D0*W(13)))*Z(14)+((-0.5D0*W( &14))+W(13)+(-0.5D0*W(12)))*Z(13)+((-0.5D0*W(13))+W(12)+(-0.5D0*W(1 &1)))*Z(12)+((-0.5D0*W(12))+W(11)+(-0.5D0*W(10)))*Z(11)+((-0.5D0*W( &11))+W(10)+(-0.5D0*W(9)))*Z(10)+((-0.5D0*W(10))+W(9)+(-0.5D0*W(8)) &)*Z(9)+((-0.5D0*W(9))+W(8)+(-0.5D0*W(7)))*Z(8)+((-0.5D0*W(8))+W(7) &+(-0.5D0*W(6)))*Z(7)+((-0.5D0*W(7))+W(6)+(-0.5D0*W(5)))*Z(6)+((-0. &5D0*W(6))+W(5)+(-0.5D0*W(4)))*Z(5)+((-0.5D0*W(5))+W(4)+(-0.5D0*W(3 &)))*Z(4)+((-0.5D0*W(4))+W(3)+(-0.5D0*W(2)))*Z(3)+((-0.5D0*W(3))+W( &2)+(-0.5D0*W(1)))*Z(2)+((-0.5D0*W(2))+W(1))*Z(1) RETURN END\\end{verbatim}"))) NIL NIL -(-68 -2058) +(-68 -1800) ((|constructor| (NIL "\\spadtype{Asp28} produces Fortran for Type 28 ASPs,{} used in NAG routine \\axiomOpFrom{f02fjf}{f02Package},{} for example:\\begin{verbatim} SUBROUTINE IMAGE(IFLAG,N,Z,W,RWORK,LRWORK,IWORK,LIWORK) DOUBLE PRECISION Z(N),W(N),IWORK(LRWORK),RWORK(LRWORK) INTEGER N,LIWORK,IFLAG,LRWORK W(1)=0.01707454969713436D0*Z(16)+0.001747395874954051D0*Z(15)+0.00 &2106973900813502D0*Z(14)+0.002957434991769087D0*Z(13)+(-0.00700554 &0882865317D0*Z(12))+(-0.01219194009813166D0*Z(11))+0.0037230647365 &3087D0*Z(10)+0.04932374658377151D0*Z(9)+(-0.03586220812223305D0*Z( &8))+(-0.04723268012114625D0*Z(7))+(-0.02434652144032987D0*Z(6))+0. &2264766947290192D0*Z(5)+(-0.1385343580686922D0*Z(4))+(-0.116530050 &8238904D0*Z(3))+(-0.2803531651057233D0*Z(2))+1.019463911841327D0*Z &(1) W(2)=0.0227345011107737D0*Z(16)+0.008812321197398072D0*Z(15)+0.010 &94012210519586D0*Z(14)+(-0.01764072463999744D0*Z(13))+(-0.01357136 &72105995D0*Z(12))+0.00157466157362272D0*Z(11)+0.05258889186338282D &0*Z(10)+(-0.01981532388243379D0*Z(9))+(-0.06095390688679697D0*Z(8) &)+(-0.04153119955569051D0*Z(7))+0.2176561076571465D0*Z(6)+(-0.0532 &5555586632358D0*Z(5))+(-0.1688977368984641D0*Z(4))+(-0.32440166056 &67343D0*Z(3))+0.9128222941872173D0*Z(2)+(-0.2419652703415429D0*Z(1 &)) W(3)=0.03371198197190302D0*Z(16)+0.02021603150122265D0*Z(15)+(-0.0 &06607305534689702D0*Z(14))+(-0.03032392238968179D0*Z(13))+0.002033 &305231024948D0*Z(12)+0.05375944956767728D0*Z(11)+(-0.0163213312502 &9967D0*Z(10))+(-0.05483186562035512D0*Z(9))+(-0.04901428822579872D &0*Z(8))+0.2091097927887612D0*Z(7)+(-0.05760560341383113D0*Z(6))+(- &0.1236679206156403D0*Z(5))+(-0.3523683853026259D0*Z(4))+0.88929961 &32269974D0*Z(3)+(-0.2995429545781457D0*Z(2))+(-0.02986582812574917 &D0*Z(1)) W(4)=0.05141563713660119D0*Z(16)+0.005239165960779299D0*Z(15)+(-0. &01623427735779699D0*Z(14))+(-0.01965809746040371D0*Z(13))+0.054688 &97337339577D0*Z(12)+(-0.014224695935687D0*Z(11))+(-0.0505181779315 &6355D0*Z(10))+(-0.04353074206076491D0*Z(9))+0.2012230497530726D0*Z &(8)+(-0.06630874514535952D0*Z(7))+(-0.1280829963720053D0*Z(6))+(-0 &.305169742604165D0*Z(5))+0.8600427128450191D0*Z(4)+(-0.32415033802 &68184D0*Z(3))+(-0.09033531980693314D0*Z(2))+0.09089205517109111D0* &Z(1) W(5)=0.04556369767776375D0*Z(16)+(-0.001822737697581869D0*Z(15))+( &-0.002512226501941856D0*Z(14))+0.02947046460707379D0*Z(13)+(-0.014 &45079632086177D0*Z(12))+(-0.05034242196614937D0*Z(11))+(-0.0376966 &3291725935D0*Z(10))+0.2171103102175198D0*Z(9)+(-0.0824949256021352 &4D0*Z(8))+(-0.1473995209288945D0*Z(7))+(-0.315042193418466D0*Z(6)) &+0.9591623347824002D0*Z(5)+(-0.3852396953763045D0*Z(4))+(-0.141718 &5427288274D0*Z(3))+(-0.03423495461011043D0*Z(2))+0.319820917706851 &6D0*Z(1) W(6)=0.04015147277405744D0*Z(16)+0.01328585741341559D0*Z(15)+0.048 &26082005465965D0*Z(14)+(-0.04319641116207706D0*Z(13))+(-0.04931323 &319055762D0*Z(12))+(-0.03526886317505474D0*Z(11))+0.22295383396730 &01D0*Z(10)+(-0.07375317649315155D0*Z(9))+(-0.1589391311991561D0*Z( &8))+(-0.328001910890377D0*Z(7))+0.952576555482747D0*Z(6)+(-0.31583 &09975786731D0*Z(5))+(-0.1846882042225383D0*Z(4))+(-0.0703762046700 &4427D0*Z(3))+0.2311852964327382D0*Z(2)+0.04254083491825025D0*Z(1) W(7)=0.06069778964023718D0*Z(16)+0.06681263884671322D0*Z(15)+(-0.0 &2113506688615768D0*Z(14))+(-0.083996867458326D0*Z(13))+(-0.0329843 &8523869648D0*Z(12))+0.2276878326327734D0*Z(11)+(-0.067356038933017 &95D0*Z(10))+(-0.1559813965382218D0*Z(9))+(-0.3363262957694705D0*Z( &8))+0.9442791158560948D0*Z(7)+(-0.3199955249404657D0*Z(6))+(-0.136 &2463839920727D0*Z(5))+(-0.1006185171570586D0*Z(4))+0.2057504515015 &423D0*Z(3)+(-0.02065879269286707D0*Z(2))+0.03160990266745513D0*Z(1 &) W(8)=0.126386868896738D0*Z(16)+0.002563370039476418D0*Z(15)+(-0.05 &581757739455641D0*Z(14))+(-0.07777893205900685D0*Z(13))+0.23117338 &45834199D0*Z(12)+(-0.06031581134427592D0*Z(11))+(-0.14805474755869 &52D0*Z(10))+(-0.3364014128402243D0*Z(9))+0.9364014128402244D0*Z(8) &+(-0.3269452524413048D0*Z(7))+(-0.1396841886557241D0*Z(6))+(-0.056 &1733845834199D0*Z(5))+0.1777789320590069D0*Z(4)+(-0.04418242260544 &359D0*Z(3))+(-0.02756337003947642D0*Z(2))+0.07361313110326199D0*Z( &1) W(9)=0.07361313110326199D0*Z(16)+(-0.02756337003947642D0*Z(15))+(- &0.04418242260544359D0*Z(14))+0.1777789320590069D0*Z(13)+(-0.056173 &3845834199D0*Z(12))+(-0.1396841886557241D0*Z(11))+(-0.326945252441 &3048D0*Z(10))+0.9364014128402244D0*Z(9)+(-0.3364014128402243D0*Z(8 &))+(-0.1480547475586952D0*Z(7))+(-0.06031581134427592D0*Z(6))+0.23 &11733845834199D0*Z(5)+(-0.07777893205900685D0*Z(4))+(-0.0558175773 &9455641D0*Z(3))+0.002563370039476418D0*Z(2)+0.126386868896738D0*Z( &1) W(10)=0.03160990266745513D0*Z(16)+(-0.02065879269286707D0*Z(15))+0 &.2057504515015423D0*Z(14)+(-0.1006185171570586D0*Z(13))+(-0.136246 &3839920727D0*Z(12))+(-0.3199955249404657D0*Z(11))+0.94427911585609 &48D0*Z(10)+(-0.3363262957694705D0*Z(9))+(-0.1559813965382218D0*Z(8 &))+(-0.06735603893301795D0*Z(7))+0.2276878326327734D0*Z(6)+(-0.032 &98438523869648D0*Z(5))+(-0.083996867458326D0*Z(4))+(-0.02113506688 &615768D0*Z(3))+0.06681263884671322D0*Z(2)+0.06069778964023718D0*Z( &1) W(11)=0.04254083491825025D0*Z(16)+0.2311852964327382D0*Z(15)+(-0.0 &7037620467004427D0*Z(14))+(-0.1846882042225383D0*Z(13))+(-0.315830 &9975786731D0*Z(12))+0.952576555482747D0*Z(11)+(-0.328001910890377D &0*Z(10))+(-0.1589391311991561D0*Z(9))+(-0.07375317649315155D0*Z(8) &)+0.2229538339673001D0*Z(7)+(-0.03526886317505474D0*Z(6))+(-0.0493 &1323319055762D0*Z(5))+(-0.04319641116207706D0*Z(4))+0.048260820054 &65965D0*Z(3)+0.01328585741341559D0*Z(2)+0.04015147277405744D0*Z(1) W(12)=0.3198209177068516D0*Z(16)+(-0.03423495461011043D0*Z(15))+(- &0.1417185427288274D0*Z(14))+(-0.3852396953763045D0*Z(13))+0.959162 &3347824002D0*Z(12)+(-0.315042193418466D0*Z(11))+(-0.14739952092889 &45D0*Z(10))+(-0.08249492560213524D0*Z(9))+0.2171103102175198D0*Z(8 &)+(-0.03769663291725935D0*Z(7))+(-0.05034242196614937D0*Z(6))+(-0. &01445079632086177D0*Z(5))+0.02947046460707379D0*Z(4)+(-0.002512226 &501941856D0*Z(3))+(-0.001822737697581869D0*Z(2))+0.045563697677763 &75D0*Z(1) W(13)=0.09089205517109111D0*Z(16)+(-0.09033531980693314D0*Z(15))+( &-0.3241503380268184D0*Z(14))+0.8600427128450191D0*Z(13)+(-0.305169 &742604165D0*Z(12))+(-0.1280829963720053D0*Z(11))+(-0.0663087451453 &5952D0*Z(10))+0.2012230497530726D0*Z(9)+(-0.04353074206076491D0*Z( &8))+(-0.05051817793156355D0*Z(7))+(-0.014224695935687D0*Z(6))+0.05 &468897337339577D0*Z(5)+(-0.01965809746040371D0*Z(4))+(-0.016234277 &35779699D0*Z(3))+0.005239165960779299D0*Z(2)+0.05141563713660119D0 &*Z(1) W(14)=(-0.02986582812574917D0*Z(16))+(-0.2995429545781457D0*Z(15)) &+0.8892996132269974D0*Z(14)+(-0.3523683853026259D0*Z(13))+(-0.1236 &679206156403D0*Z(12))+(-0.05760560341383113D0*Z(11))+0.20910979278 &87612D0*Z(10)+(-0.04901428822579872D0*Z(9))+(-0.05483186562035512D &0*Z(8))+(-0.01632133125029967D0*Z(7))+0.05375944956767728D0*Z(6)+0 &.002033305231024948D0*Z(5)+(-0.03032392238968179D0*Z(4))+(-0.00660 &7305534689702D0*Z(3))+0.02021603150122265D0*Z(2)+0.033711981971903 &02D0*Z(1) W(15)=(-0.2419652703415429D0*Z(16))+0.9128222941872173D0*Z(15)+(-0 &.3244016605667343D0*Z(14))+(-0.1688977368984641D0*Z(13))+(-0.05325 &555586632358D0*Z(12))+0.2176561076571465D0*Z(11)+(-0.0415311995556 &9051D0*Z(10))+(-0.06095390688679697D0*Z(9))+(-0.01981532388243379D &0*Z(8))+0.05258889186338282D0*Z(7)+0.00157466157362272D0*Z(6)+(-0. &0135713672105995D0*Z(5))+(-0.01764072463999744D0*Z(4))+0.010940122 &10519586D0*Z(3)+0.008812321197398072D0*Z(2)+0.0227345011107737D0*Z &(1) W(16)=1.019463911841327D0*Z(16)+(-0.2803531651057233D0*Z(15))+(-0. &1165300508238904D0*Z(14))+(-0.1385343580686922D0*Z(13))+0.22647669 &47290192D0*Z(12)+(-0.02434652144032987D0*Z(11))+(-0.04723268012114 &625D0*Z(10))+(-0.03586220812223305D0*Z(9))+0.04932374658377151D0*Z &(8)+0.00372306473653087D0*Z(7)+(-0.01219194009813166D0*Z(6))+(-0.0 &07005540882865317D0*Z(5))+0.002957434991769087D0*Z(4)+0.0021069739 &00813502D0*Z(3)+0.001747395874954051D0*Z(2)+0.01707454969713436D0* &Z(1) RETURN END\\end{verbatim}"))) NIL NIL -(-69 -2058) +(-69 -1800) ((|constructor| (NIL "\\spadtype{Asp29} produces Fortran for Type 29 ASPs,{} needed for NAG routine \\axiomOpFrom{f02fjf}{f02Package},{} for example:\\begin{verbatim} SUBROUTINE MONIT(ISTATE,NEXTIT,NEVALS,NEVECS,K,F,D) DOUBLE PRECISION D(K),F(K) INTEGER K,NEXTIT,NEVALS,NVECS,ISTATE CALL F02FJZ(ISTATE,NEXTIT,NEVALS,NEVECS,K,F,D) RETURN END\\end{verbatim}")) (|outputAsFortran| (((|Void|)) "\\spad{outputAsFortran()} generates the default code for \\spadtype{ASP29}."))) NIL NIL -(-70 -2058) +(-70 -1800) ((|constructor| (NIL "\\spadtype{Asp30} produces Fortran for Type 30 ASPs,{} needed for NAG routine \\axiomOpFrom{f04qaf}{f04Package},{} for example:\\begin{verbatim} SUBROUTINE APROD(MODE,M,N,X,Y,RWORK,LRWORK,IWORK,LIWORK) DOUBLE PRECISION X(N),Y(M),RWORK(LRWORK) INTEGER M,N,LIWORK,IFAIL,LRWORK,IWORK(LIWORK),MODE DOUBLE PRECISION A(5,5) EXTERNAL F06PAF A(1,1)=1.0D0 A(1,2)=0.0D0 A(1,3)=0.0D0 A(1,4)=-1.0D0 A(1,5)=0.0D0 A(2,1)=0.0D0 A(2,2)=1.0D0 A(2,3)=0.0D0 A(2,4)=0.0D0 A(2,5)=-1.0D0 A(3,1)=0.0D0 A(3,2)=0.0D0 A(3,3)=1.0D0 A(3,4)=-1.0D0 A(3,5)=0.0D0 A(4,1)=-1.0D0 A(4,2)=0.0D0 A(4,3)=-1.0D0 A(4,4)=4.0D0 A(4,5)=-1.0D0 A(5,1)=0.0D0 A(5,2)=-1.0D0 A(5,3)=0.0D0 A(5,4)=-1.0D0 A(5,5)=4.0D0 IF(MODE.EQ.1)THEN CALL F06PAF('N',M,N,1.0D0,A,M,X,1,1.0D0,Y,1) ELSEIF(MODE.EQ.2)THEN CALL F06PAF('T',M,N,1.0D0,A,M,Y,1,1.0D0,X,1) ENDIF RETURN END\\end{verbatim}"))) NIL NIL -(-71 -2058) +(-71 -1800) ((|constructor| (NIL "\\spadtype{Asp31} produces Fortran for Type 31 ASPs,{} needed for NAG routine \\axiomOpFrom{d02ejf}{d02Package},{} for example:\\begin{verbatim} SUBROUTINE PEDERV(X,Y,PW) DOUBLE PRECISION X,Y(*) DOUBLE PRECISION PW(3,3) PW(1,1)=-0.03999999999999999D0 PW(1,2)=10000.0D0*Y(3) PW(1,3)=10000.0D0*Y(2) PW(2,1)=0.03999999999999999D0 PW(2,2)=(-10000.0D0*Y(3))+(-60000000.0D0*Y(2)) PW(2,3)=-10000.0D0*Y(2) PW(3,1)=0.0D0 PW(3,2)=60000000.0D0*Y(2) PW(3,3)=0.0D0 RETURN END\\end{verbatim}")) (|coerce| (($ (|Vector| (|FortranExpression| (|construct| (QUOTE X)) (|construct| (QUOTE Y)) (|MachineFloat|)))) "\\spad{coerce(f)} takes objects from the appropriate instantiation of \\spadtype{FortranExpression} and turns them into an ASP."))) NIL NIL -(-72 -2058) +(-72 -1800) ((|constructor| (NIL "\\spadtype{Asp33} produces Fortran for Type 33 ASPs,{} needed for NAG routine \\axiomOpFrom{d02kef}{d02Package}. The code is a dummy ASP:\\begin{verbatim} SUBROUTINE REPORT(X,V,JINT) DOUBLE PRECISION V(3),X INTEGER JINT RETURN END\\end{verbatim}")) (|outputAsFortran| (((|Void|)) "\\spad{outputAsFortran()} generates the default code for \\spadtype{ASP33}."))) NIL NIL -(-73 -2058) +(-73 -1800) ((|constructor| (NIL "\\spadtype{Asp34} produces Fortran for Type 34 ASPs,{} needed for NAG routine \\axiomOpFrom{f04mbf}{f04Package},{} for example:\\begin{verbatim} SUBROUTINE MSOLVE(IFLAG,N,X,Y,RWORK,LRWORK,IWORK,LIWORK) DOUBLE PRECISION RWORK(LRWORK),X(N),Y(N) INTEGER I,J,N,LIWORK,IFLAG,LRWORK,IWORK(LIWORK) DOUBLE PRECISION W1(3),W2(3),MS(3,3) IFLAG=-1 MS(1,1)=2.0D0 MS(1,2)=1.0D0 MS(1,3)=0.0D0 MS(2,1)=1.0D0 MS(2,2)=2.0D0 MS(2,3)=1.0D0 MS(3,1)=0.0D0 MS(3,2)=1.0D0 MS(3,3)=2.0D0 CALL F04ASF(MS,N,X,N,Y,W1,W2,IFLAG) IFLAG=-IFLAG RETURN END\\end{verbatim}"))) NIL NIL -(-74 -2058) +(-74 -1800) ((|constructor| (NIL "\\spadtype{Asp35} produces Fortran for Type 35 ASPs,{} needed for NAG routines \\axiomOpFrom{c05pbf}{c05Package},{} \\axiomOpFrom{c05pcf}{c05Package},{} for example:\\begin{verbatim} SUBROUTINE FCN(N,X,FVEC,FJAC,LDFJAC,IFLAG) DOUBLE PRECISION X(N),FVEC(N),FJAC(LDFJAC,N) INTEGER LDFJAC,N,IFLAG IF(IFLAG.EQ.1)THEN FVEC(1)=(-1.0D0*X(2))+X(1) FVEC(2)=(-1.0D0*X(3))+2.0D0*X(2) FVEC(3)=3.0D0*X(3) ELSEIF(IFLAG.EQ.2)THEN FJAC(1,1)=1.0D0 FJAC(1,2)=-1.0D0 FJAC(1,3)=0.0D0 FJAC(2,1)=0.0D0 FJAC(2,2)=2.0D0 FJAC(2,3)=-1.0D0 FJAC(3,1)=0.0D0 FJAC(3,2)=0.0D0 FJAC(3,3)=3.0D0 ENDIF END\\end{verbatim}")) (|coerce| (($ (|Vector| (|FortranExpression| (|construct|) (|construct| (QUOTE X)) (|MachineFloat|)))) "\\spad{coerce(f)} takes objects from the appropriate instantiation of \\spadtype{FortranExpression} and turns them into an ASP."))) NIL NIL @@ -236,55 +236,55 @@ NIL ((|constructor| (NIL "\\spadtype{Asp42} produces Fortran for Type 42 ASPs,{} needed for NAG routines \\axiomOpFrom{d02raf}{d02Package} and \\axiomOpFrom{d02saf}{d02Package} in particular. These ASPs are in fact three Fortran routines which return a vector of functions,{} and their derivatives \\spad{wrt} \\spad{Y}(\\spad{i}) and also a continuation parameter EPS,{} for example:\\begin{verbatim} SUBROUTINE G(EPS,YA,YB,BC,N) DOUBLE PRECISION EPS,YA(N),YB(N),BC(N) INTEGER N BC(1)=YA(1) BC(2)=YA(2) BC(3)=YB(2)-1.0D0 RETURN END SUBROUTINE JACOBG(EPS,YA,YB,AJ,BJ,N) DOUBLE PRECISION EPS,YA(N),AJ(N,N),BJ(N,N),YB(N) INTEGER N AJ(1,1)=1.0D0 AJ(1,2)=0.0D0 AJ(1,3)=0.0D0 AJ(2,1)=0.0D0 AJ(2,2)=1.0D0 AJ(2,3)=0.0D0 AJ(3,1)=0.0D0 AJ(3,2)=0.0D0 AJ(3,3)=0.0D0 BJ(1,1)=0.0D0 BJ(1,2)=0.0D0 BJ(1,3)=0.0D0 BJ(2,1)=0.0D0 BJ(2,2)=0.0D0 BJ(2,3)=0.0D0 BJ(3,1)=0.0D0 BJ(3,2)=1.0D0 BJ(3,3)=0.0D0 RETURN END SUBROUTINE JACGEP(EPS,YA,YB,BCEP,N) DOUBLE PRECISION EPS,YA(N),YB(N),BCEP(N) INTEGER N BCEP(1)=0.0D0 BCEP(2)=0.0D0 BCEP(3)=0.0D0 RETURN END\\end{verbatim}")) (|coerce| (($ (|Vector| (|FortranExpression| (|construct| (QUOTE EPS)) (|construct| (QUOTE YA) (QUOTE YB)) (|MachineFloat|)))) "\\spad{coerce(f)} takes objects from the appropriate instantiation of \\spadtype{FortranExpression} and turns them into an ASP."))) NIL NIL -(-77 -2058) +(-77 -1800) ((|constructor| (NIL "\\spadtype{Asp49} produces Fortran for Type 49 ASPs,{} needed for NAG routines \\axiomOpFrom{e04dgf}{e04Package},{} \\axiomOpFrom{e04ucf}{e04Package},{} for example:\\begin{verbatim} SUBROUTINE OBJFUN(MODE,N,X,OBJF,OBJGRD,NSTATE,IUSER,USER) DOUBLE PRECISION X(N),OBJF,OBJGRD(N),USER(*) INTEGER N,IUSER(*),MODE,NSTATE OBJF=X(4)*X(9)+((-1.0D0*X(5))+X(3))*X(8)+((-1.0D0*X(3))+X(1))*X(7) &+(-1.0D0*X(2)*X(6)) OBJGRD(1)=X(7) OBJGRD(2)=-1.0D0*X(6) OBJGRD(3)=X(8)+(-1.0D0*X(7)) OBJGRD(4)=X(9) OBJGRD(5)=-1.0D0*X(8) OBJGRD(6)=-1.0D0*X(2) OBJGRD(7)=(-1.0D0*X(3))+X(1) OBJGRD(8)=(-1.0D0*X(5))+X(3) OBJGRD(9)=X(4) RETURN END\\end{verbatim}")) (|coerce| (($ (|FortranExpression| (|construct|) (|construct| (QUOTE X)) (|MachineFloat|))) "\\spad{coerce(f)} takes an object from the appropriate instantiation of \\spadtype{FortranExpression} and turns it into an ASP."))) NIL NIL -(-78 -2058) +(-78 -1800) ((|constructor| (NIL "\\spadtype{Asp4} produces Fortran for Type 4 ASPs,{} which take an expression in \\spad{X}(1) .. \\spad{X}(NDIM) and produce a real function of the form:\\begin{verbatim} DOUBLE PRECISION FUNCTION FUNCTN(NDIM,X) DOUBLE PRECISION X(NDIM) INTEGER NDIM FUNCTN=(4.0D0*X(1)*X(3)**2*DEXP(2.0D0*X(1)*X(3)))/(X(4)**2+(2.0D0* &X(2)+2.0D0)*X(4)+X(2)**2+2.0D0*X(2)+1.0D0) RETURN END\\end{verbatim}")) (|coerce| (($ (|FortranExpression| (|construct|) (|construct| (QUOTE X)) (|MachineFloat|))) "\\spad{coerce(f)} takes an object from the appropriate instantiation of \\spadtype{FortranExpression} and turns it into an ASP."))) NIL NIL -(-79 -2058) +(-79 -1800) ((|constructor| (NIL "\\spadtype{Asp50} produces Fortran for Type 50 ASPs,{} needed for NAG routine \\axiomOpFrom{e04fdf}{e04Package},{} for example:\\begin{verbatim} SUBROUTINE LSFUN1(M,N,XC,FVECC) DOUBLE PRECISION FVECC(M),XC(N) INTEGER I,M,N FVECC(1)=((XC(1)-2.4D0)*XC(3)+(15.0D0*XC(1)-36.0D0)*XC(2)+1.0D0)/( &XC(3)+15.0D0*XC(2)) FVECC(2)=((XC(1)-2.8D0)*XC(3)+(7.0D0*XC(1)-19.6D0)*XC(2)+1.0D0)/(X &C(3)+7.0D0*XC(2)) FVECC(3)=((XC(1)-3.2D0)*XC(3)+(4.333333333333333D0*XC(1)-13.866666 &66666667D0)*XC(2)+1.0D0)/(XC(3)+4.333333333333333D0*XC(2)) FVECC(4)=((XC(1)-3.5D0)*XC(3)+(3.0D0*XC(1)-10.5D0)*XC(2)+1.0D0)/(X &C(3)+3.0D0*XC(2)) FVECC(5)=((XC(1)-3.9D0)*XC(3)+(2.2D0*XC(1)-8.579999999999998D0)*XC &(2)+1.0D0)/(XC(3)+2.2D0*XC(2)) FVECC(6)=((XC(1)-4.199999999999999D0)*XC(3)+(1.666666666666667D0*X &C(1)-7.0D0)*XC(2)+1.0D0)/(XC(3)+1.666666666666667D0*XC(2)) FVECC(7)=((XC(1)-4.5D0)*XC(3)+(1.285714285714286D0*XC(1)-5.7857142 &85714286D0)*XC(2)+1.0D0)/(XC(3)+1.285714285714286D0*XC(2)) FVECC(8)=((XC(1)-4.899999999999999D0)*XC(3)+(XC(1)-4.8999999999999 &99D0)*XC(2)+1.0D0)/(XC(3)+XC(2)) FVECC(9)=((XC(1)-4.699999999999999D0)*XC(3)+(XC(1)-4.6999999999999 &99D0)*XC(2)+1.285714285714286D0)/(XC(3)+XC(2)) FVECC(10)=((XC(1)-6.8D0)*XC(3)+(XC(1)-6.8D0)*XC(2)+1.6666666666666 &67D0)/(XC(3)+XC(2)) FVECC(11)=((XC(1)-8.299999999999999D0)*XC(3)+(XC(1)-8.299999999999 &999D0)*XC(2)+2.2D0)/(XC(3)+XC(2)) FVECC(12)=((XC(1)-10.6D0)*XC(3)+(XC(1)-10.6D0)*XC(2)+3.0D0)/(XC(3) &+XC(2)) FVECC(13)=((XC(1)-1.34D0)*XC(3)+(XC(1)-1.34D0)*XC(2)+4.33333333333 &3333D0)/(XC(3)+XC(2)) FVECC(14)=((XC(1)-2.1D0)*XC(3)+(XC(1)-2.1D0)*XC(2)+7.0D0)/(XC(3)+X &C(2)) FVECC(15)=((XC(1)-4.39D0)*XC(3)+(XC(1)-4.39D0)*XC(2)+15.0D0)/(XC(3 &)+XC(2)) END\\end{verbatim}")) (|coerce| (($ (|Vector| (|FortranExpression| (|construct|) (|construct| (QUOTE XC)) (|MachineFloat|)))) "\\spad{coerce(f)} takes objects from the appropriate instantiation of \\spadtype{FortranExpression} and turns them into an ASP."))) NIL NIL -(-80 -2058) +(-80 -1800) ((|constructor| (NIL "\\spadtype{Asp55} produces Fortran for Type 55 ASPs,{} needed for NAG routines \\axiomOpFrom{e04dgf}{e04Package} and \\axiomOpFrom{e04ucf}{e04Package},{} for example:\\begin{verbatim} SUBROUTINE CONFUN(MODE,NCNLN,N,NROWJ,NEEDC,X,C,CJAC,NSTATE,IUSER &,USER) DOUBLE PRECISION C(NCNLN),X(N),CJAC(NROWJ,N),USER(*) INTEGER N,IUSER(*),NEEDC(NCNLN),NROWJ,MODE,NCNLN,NSTATE IF(NEEDC(1).GT.0)THEN C(1)=X(6)**2+X(1)**2 CJAC(1,1)=2.0D0*X(1) CJAC(1,2)=0.0D0 CJAC(1,3)=0.0D0 CJAC(1,4)=0.0D0 CJAC(1,5)=0.0D0 CJAC(1,6)=2.0D0*X(6) ENDIF IF(NEEDC(2).GT.0)THEN C(2)=X(2)**2+(-2.0D0*X(1)*X(2))+X(1)**2 CJAC(2,1)=(-2.0D0*X(2))+2.0D0*X(1) CJAC(2,2)=2.0D0*X(2)+(-2.0D0*X(1)) CJAC(2,3)=0.0D0 CJAC(2,4)=0.0D0 CJAC(2,5)=0.0D0 CJAC(2,6)=0.0D0 ENDIF IF(NEEDC(3).GT.0)THEN C(3)=X(3)**2+(-2.0D0*X(1)*X(3))+X(2)**2+X(1)**2 CJAC(3,1)=(-2.0D0*X(3))+2.0D0*X(1) CJAC(3,2)=2.0D0*X(2) CJAC(3,3)=2.0D0*X(3)+(-2.0D0*X(1)) CJAC(3,4)=0.0D0 CJAC(3,5)=0.0D0 CJAC(3,6)=0.0D0 ENDIF RETURN END\\end{verbatim}")) (|coerce| (($ (|Vector| (|FortranExpression| (|construct|) (|construct| (QUOTE X)) (|MachineFloat|)))) "\\spad{coerce(f)} takes objects from the appropriate instantiation of \\spadtype{FortranExpression} and turns them into an ASP."))) NIL NIL -(-81 -2058) +(-81 -1800) ((|constructor| (NIL "\\spadtype{Asp6} produces Fortran for Type 6 ASPs,{} needed for NAG routines \\axiomOpFrom{c05nbf}{c05Package},{} \\axiomOpFrom{c05ncf}{c05Package}. These represent vectors of functions of \\spad{X}(\\spad{i}) and look like:\\begin{verbatim} SUBROUTINE FCN(N,X,FVEC,IFLAG) DOUBLE PRECISION X(N),FVEC(N) INTEGER N,IFLAG FVEC(1)=(-2.0D0*X(2))+(-2.0D0*X(1)**2)+3.0D0*X(1)+1.0D0 FVEC(2)=(-2.0D0*X(3))+(-2.0D0*X(2)**2)+3.0D0*X(2)+(-1.0D0*X(1))+1. &0D0 FVEC(3)=(-2.0D0*X(4))+(-2.0D0*X(3)**2)+3.0D0*X(3)+(-1.0D0*X(2))+1. &0D0 FVEC(4)=(-2.0D0*X(5))+(-2.0D0*X(4)**2)+3.0D0*X(4)+(-1.0D0*X(3))+1. &0D0 FVEC(5)=(-2.0D0*X(6))+(-2.0D0*X(5)**2)+3.0D0*X(5)+(-1.0D0*X(4))+1. &0D0 FVEC(6)=(-2.0D0*X(7))+(-2.0D0*X(6)**2)+3.0D0*X(6)+(-1.0D0*X(5))+1. &0D0 FVEC(7)=(-2.0D0*X(8))+(-2.0D0*X(7)**2)+3.0D0*X(7)+(-1.0D0*X(6))+1. &0D0 FVEC(8)=(-2.0D0*X(9))+(-2.0D0*X(8)**2)+3.0D0*X(8)+(-1.0D0*X(7))+1. &0D0 FVEC(9)=(-2.0D0*X(9)**2)+3.0D0*X(9)+(-1.0D0*X(8))+1.0D0 RETURN END\\end{verbatim}"))) NIL NIL -(-82 -2058) +(-82 -1800) ((|constructor| (NIL "\\spadtype{Asp73} produces Fortran for Type 73 ASPs,{} needed for NAG routine \\axiomOpFrom{d03eef}{d03Package},{} for example:\\begin{verbatim} SUBROUTINE PDEF(X,Y,ALPHA,BETA,GAMMA,DELTA,EPSOLN,PHI,PSI) DOUBLE PRECISION ALPHA,EPSOLN,PHI,X,Y,BETA,DELTA,GAMMA,PSI ALPHA=DSIN(X) BETA=Y GAMMA=X*Y DELTA=DCOS(X)*DSIN(Y) EPSOLN=Y+X PHI=X PSI=Y RETURN END\\end{verbatim}")) (|coerce| (($ (|Vector| (|FortranExpression| (|construct| (QUOTE X) (QUOTE Y)) (|construct|) (|MachineFloat|)))) "\\spad{coerce(f)} takes objects from the appropriate instantiation of \\spadtype{FortranExpression} and turns them into an ASP."))) NIL NIL -(-83 -2058) +(-83 -1800) ((|constructor| (NIL "\\spadtype{Asp74} produces Fortran for Type 74 ASPs,{} needed for NAG routine \\axiomOpFrom{d03eef}{d03Package},{} for example:\\begin{verbatim} SUBROUTINE BNDY(X,Y,A,B,C,IBND) DOUBLE PRECISION A,B,C,X,Y INTEGER IBND IF(IBND.EQ.0)THEN A=0.0D0 B=1.0D0 C=-1.0D0*DSIN(X) ELSEIF(IBND.EQ.1)THEN A=1.0D0 B=0.0D0 C=DSIN(X)*DSIN(Y) ELSEIF(IBND.EQ.2)THEN A=1.0D0 B=0.0D0 C=DSIN(X)*DSIN(Y) ELSEIF(IBND.EQ.3)THEN A=0.0D0 B=1.0D0 C=-1.0D0*DSIN(Y) ENDIF END\\end{verbatim}")) (|coerce| (($ (|Matrix| (|FortranExpression| (|construct| (QUOTE X) (QUOTE Y)) (|construct|) (|MachineFloat|)))) "\\spad{coerce(f)} takes objects from the appropriate instantiation of \\spadtype{FortranExpression} and turns them into an ASP."))) NIL NIL -(-84 -2058) +(-84 -1800) ((|constructor| (NIL "\\spadtype{Asp77} produces Fortran for Type 77 ASPs,{} needed for NAG routine \\axiomOpFrom{d02gbf}{d02Package},{} for example:\\begin{verbatim} SUBROUTINE FCNF(X,F) DOUBLE PRECISION X DOUBLE PRECISION F(2,2) F(1,1)=0.0D0 F(1,2)=1.0D0 F(2,1)=0.0D0 F(2,2)=-10.0D0 RETURN END\\end{verbatim}")) (|coerce| (($ (|Matrix| (|FortranExpression| (|construct| (QUOTE X)) (|construct|) (|MachineFloat|)))) "\\spad{coerce(f)} takes objects from the appropriate instantiation of \\spadtype{FortranExpression} and turns them into an ASP."))) NIL NIL -(-85 -2058) +(-85 -1800) ((|constructor| (NIL "\\spadtype{Asp78} produces Fortran for Type 78 ASPs,{} needed for NAG routine \\axiomOpFrom{d02gbf}{d02Package},{} for example:\\begin{verbatim} SUBROUTINE FCNG(X,G) DOUBLE PRECISION G(*),X G(1)=0.0D0 G(2)=0.0D0 END\\end{verbatim}")) (|coerce| (($ (|Vector| (|FortranExpression| (|construct| (QUOTE X)) (|construct|) (|MachineFloat|)))) "\\spad{coerce(f)} takes objects from the appropriate instantiation of \\spadtype{FortranExpression} and turns them into an ASP."))) NIL NIL -(-86 -2058) +(-86 -1800) ((|constructor| (NIL "\\spadtype{Asp7} produces Fortran for Type 7 ASPs,{} needed for NAG routines \\axiomOpFrom{d02bbf}{d02Package},{} \\axiomOpFrom{d02gaf}{d02Package}. These represent a vector of functions of the scalar \\spad{X} and the array \\spad{Z},{} and look like:\\begin{verbatim} SUBROUTINE FCN(X,Z,F) DOUBLE PRECISION F(*),X,Z(*) F(1)=DTAN(Z(3)) F(2)=((-0.03199999999999999D0*DCOS(Z(3))*DTAN(Z(3)))+(-0.02D0*Z(2) &**2))/(Z(2)*DCOS(Z(3))) F(3)=-0.03199999999999999D0/(X*Z(2)**2) RETURN END\\end{verbatim}")) (|coerce| (($ (|Vector| (|FortranExpression| (|construct| (QUOTE X)) (|construct| (QUOTE Y)) (|MachineFloat|)))) "\\spad{coerce(f)} takes objects from the appropriate instantiation of \\spadtype{FortranExpression} and turns them into an ASP."))) NIL NIL -(-87 -2058) +(-87 -1800) ((|constructor| (NIL "\\spadtype{Asp80} produces Fortran for Type 80 ASPs,{} needed for NAG routine \\axiomOpFrom{d02kef}{d02Package},{} for example:\\begin{verbatim} SUBROUTINE BDYVAL(XL,XR,ELAM,YL,YR) DOUBLE PRECISION ELAM,XL,YL(3),XR,YR(3) YL(1)=XL YL(2)=2.0D0 YR(1)=1.0D0 YR(2)=-1.0D0*DSQRT(XR+(-1.0D0*ELAM)) RETURN END\\end{verbatim}")) (|coerce| (($ (|Matrix| (|FortranExpression| (|construct| (QUOTE XL) (QUOTE XR) (QUOTE ELAM)) (|construct|) (|MachineFloat|)))) "\\spad{coerce(f)} takes objects from the appropriate instantiation of \\spadtype{FortranExpression} and turns them into an ASP."))) NIL NIL -(-88 -2058) +(-88 -1800) ((|constructor| (NIL "\\spadtype{Asp8} produces Fortran for Type 8 ASPs,{} needed for NAG routine \\axiomOpFrom{d02bbf}{d02Package}. This ASP prints intermediate values of the computed solution of an ODE and might look like:\\begin{verbatim} SUBROUTINE OUTPUT(XSOL,Y,COUNT,M,N,RESULT,FORWRD) DOUBLE PRECISION Y(N),RESULT(M,N),XSOL INTEGER M,N,COUNT LOGICAL FORWRD DOUBLE PRECISION X02ALF,POINTS(8) EXTERNAL X02ALF INTEGER I POINTS(1)=1.0D0 POINTS(2)=2.0D0 POINTS(3)=3.0D0 POINTS(4)=4.0D0 POINTS(5)=5.0D0 POINTS(6)=6.0D0 POINTS(7)=7.0D0 POINTS(8)=8.0D0 COUNT=COUNT+1 DO 25001 I=1,N RESULT(COUNT,I)=Y(I)25001 CONTINUE IF(COUNT.EQ.M)THEN IF(FORWRD)THEN XSOL=X02ALF() ELSE XSOL=-X02ALF() ENDIF ELSE XSOL=POINTS(COUNT) ENDIF END\\end{verbatim}"))) NIL NIL -(-89 -2058) +(-89 -1800) ((|constructor| (NIL "\\spadtype{Asp9} produces Fortran for Type 9 ASPs,{} needed for NAG routines \\axiomOpFrom{d02bhf}{d02Package},{} \\axiomOpFrom{d02cjf}{d02Package},{} \\axiomOpFrom{d02ejf}{d02Package}. These ASPs represent a function of a scalar \\spad{X} and a vector \\spad{Y},{} for example:\\begin{verbatim} DOUBLE PRECISION FUNCTION G(X,Y) DOUBLE PRECISION X,Y(*) G=X+Y(1) RETURN END\\end{verbatim} If the user provides a constant value for \\spad{G},{} then extra information is added via COMMON blocks used by certain routines. This specifies that the value returned by \\spad{G} in this case is to be ignored.")) (|coerce| (($ (|FortranExpression| (|construct| (QUOTE X)) (|construct| (QUOTE Y)) (|MachineFloat|))) "\\spad{coerce(f)} takes an object from the appropriate instantiation of \\spadtype{FortranExpression} and turns it into an ASP."))) NIL NIL @@ -295,7 +295,7 @@ NIL (-91 S) ((|constructor| (NIL "A stack represented as a flexible array.")) (|arrayStack| (($ (|List| |#1|)) "\\spad{arrayStack([x,y,...,z])} creates an array stack with first (top) element \\spad{x},{} second element \\spad{y},{}...,{}and last element \\spad{z}."))) ((-4452 . T) (-4453 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1109))) (-2811 (-12 (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-868))))) (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-868))))) +((-12 (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1109))) (-3684 (-12 (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-868))))) (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-868))))) (-92 S) ((|constructor| (NIL "This is the category of Spad abstract syntax trees."))) NIL @@ -343,7 +343,7 @@ NIL (-103 S) ((|constructor| (NIL "\\spadtype{BalancedBinaryTree(S)} is the domain of balanced binary trees (bbtree). A balanced binary tree of \\spad{2**k} leaves,{} for some \\spad{k > 0},{} is symmetric,{} that is,{} the left and right subtree of each interior node have identical shape. In general,{} the left and right subtree of a given node can differ by at most leaf node.")) (|mapDown!| (($ $ |#1| (|Mapping| (|List| |#1|) |#1| |#1| |#1|)) "\\spad{mapDown!(t,p,f)} returns \\spad{t} after traversing \\spad{t} in \"preorder\" (node then left then right) fashion replacing the successive interior nodes as follows. Let \\spad{l} and \\spad{r} denote the left and right subtrees of \\spad{t}. The root value \\spad{x} of \\spad{t} is replaced by \\spad{p}. Then \\spad{f}(value \\spad{l},{} value \\spad{r},{} \\spad{p}),{} where \\spad{l} and \\spad{r} denote the left and right subtrees of \\spad{t},{} is evaluated producing two values \\spad{pl} and \\spad{pr}. Then \\spad{mapDown!(l,pl,f)} and \\spad{mapDown!(l,pr,f)} are evaluated.") (($ $ |#1| (|Mapping| |#1| |#1| |#1|)) "\\spad{mapDown!(t,p,f)} returns \\spad{t} after traversing \\spad{t} in \"preorder\" (node then left then right) fashion replacing the successive interior nodes as follows. The root value \\spad{x} is replaced by \\spad{q} \\spad{:=} \\spad{f}(\\spad{p},{}\\spad{x}). The mapDown!(\\spad{l},{}\\spad{q},{}\\spad{f}) and mapDown!(\\spad{r},{}\\spad{q},{}\\spad{f}) are evaluated for the left and right subtrees \\spad{l} and \\spad{r} of \\spad{t}.")) (|mapUp!| (($ $ $ (|Mapping| |#1| |#1| |#1| |#1| |#1|)) "\\spad{mapUp!(t,t1,f)} traverses \\spad{t} in an \"endorder\" (left then right then node) fashion returning \\spad{t} with the value at each successive interior node of \\spad{t} replaced by \\spad{f}(\\spad{l},{}\\spad{r},{}\\spad{l1},{}\\spad{r1}) where \\spad{l} and \\spad{r} are the values at the immediate left and right nodes. Values \\spad{l1} and \\spad{r1} are values at the corresponding nodes of a balanced binary tree \\spad{t1},{} of identical shape at \\spad{t}.") ((|#1| $ (|Mapping| |#1| |#1| |#1|)) "\\spad{mapUp!(t,f)} traverses balanced binary tree \\spad{t} in an \"endorder\" (left then right then node) fashion returning \\spad{t} with the value at each successive interior node of \\spad{t} replaced by \\spad{f}(\\spad{l},{}\\spad{r}) where \\spad{l} and \\spad{r} are the values at the immediate left and right nodes.")) (|setleaves!| (($ $ (|List| |#1|)) "\\spad{setleaves!(t, ls)} sets the leaves of \\spad{t} in left-to-right order to the elements of \\spad{ls}.")) (|balancedBinaryTree| (($ (|NonNegativeInteger|) |#1|) "\\spad{balancedBinaryTree(n, s)} creates a balanced binary tree with \\spad{n} nodes each with value \\spad{s}."))) ((-4452 . T) (-4453 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1109))) (-2811 (-12 (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-868))))) (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-868))))) +((-12 (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1109))) (-3684 (-12 (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-868))))) (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-868))))) (-104 R UP M |Row| |Col|) ((|constructor| (NIL "\\spadtype{BezoutMatrix} contains functions for computing resultants and discriminants using Bezout matrices.")) (|bezoutDiscriminant| ((|#1| |#2|) "\\spad{bezoutDiscriminant(p)} computes the discriminant of a polynomial \\spad{p} by computing the determinant of a Bezout matrix.")) (|bezoutResultant| ((|#1| |#2| |#2|) "\\spad{bezoutResultant(p,q)} computes the resultant of the two polynomials \\spad{p} and \\spad{q} by computing the determinant of a Bezout matrix.")) (|bezoutMatrix| ((|#3| |#2| |#2|) "\\spad{bezoutMatrix(p,q)} returns the Bezout matrix for the two polynomials \\spad{p} and \\spad{q}.")) (|sylvesterMatrix| ((|#3| |#2| |#2|) "\\spad{sylvesterMatrix(p,q)} returns the Sylvester matrix for the two polynomials \\spad{p} and \\spad{q}."))) NIL @@ -363,7 +363,7 @@ NIL (-108) ((|constructor| (NIL "This domain allows rational numbers to be presented as repeating binary expansions.")) (|binary| (($ (|Fraction| (|Integer|))) "\\spad{binary(r)} converts a rational number to a binary expansion.")) (|fractionPart| (((|Fraction| (|Integer|)) $) "\\spad{fractionPart(b)} returns the fractional part of a binary expansion."))) ((-4444 . T) (-4450 . T) (-4445 . T) ((-4454 "*") . T) (-4446 . T) (-4447 . T) (-4449 . T)) -((|HasCategory| (-570) (QUOTE (-916))) (|HasCategory| (-570) (LIST (QUOTE -1047) (QUOTE (-1186)))) (|HasCategory| (-570) (QUOTE (-146))) (|HasCategory| (-570) (QUOTE (-148))) (|HasCategory| (-570) (LIST (QUOTE -620) (QUOTE (-542)))) (|HasCategory| (-570) (QUOTE (-1031))) (|HasCategory| (-570) (QUOTE (-826))) (-2811 (|HasCategory| (-570) (QUOTE (-826))) (|HasCategory| (-570) (QUOTE (-856)))) (|HasCategory| (-570) (LIST (QUOTE -1047) (QUOTE (-570)))) (|HasCategory| (-570) (QUOTE (-1161))) (|HasCategory| (-570) (LIST (QUOTE -893) (QUOTE (-384)))) (|HasCategory| (-570) (LIST (QUOTE -893) (QUOTE (-570)))) (|HasCategory| (-570) (LIST (QUOTE -620) (LIST (QUOTE -899) (QUOTE (-384))))) (|HasCategory| (-570) (LIST (QUOTE -620) (LIST (QUOTE -899) (QUOTE (-570))))) (|HasCategory| (-570) (QUOTE (-235))) (|HasCategory| (-570) (LIST (QUOTE -907) (QUOTE (-1186)))) (|HasCategory| (-570) (LIST (QUOTE -520) (QUOTE (-1186)) (QUOTE (-570)))) (|HasCategory| (-570) (LIST (QUOTE -313) (QUOTE (-570)))) (|HasCategory| (-570) (LIST (QUOTE -290) (QUOTE (-570)) (QUOTE (-570)))) (|HasCategory| (-570) (QUOTE (-311))) (|HasCategory| (-570) (QUOTE (-551))) (|HasCategory| (-570) (QUOTE (-856))) (|HasCategory| (-570) (LIST (QUOTE -645) (QUOTE (-570)))) (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| (-570) (QUOTE (-916)))) (-2811 (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| (-570) (QUOTE (-916)))) (|HasCategory| (-570) (QUOTE (-146))))) +((|HasCategory| (-570) (QUOTE (-916))) (|HasCategory| (-570) (LIST (QUOTE -1047) (QUOTE (-1186)))) (|HasCategory| (-570) (QUOTE (-146))) (|HasCategory| (-570) (QUOTE (-148))) (|HasCategory| (-570) (LIST (QUOTE -620) (QUOTE (-542)))) (|HasCategory| (-570) (QUOTE (-1031))) (|HasCategory| (-570) (QUOTE (-826))) (-3684 (|HasCategory| (-570) (QUOTE (-826))) (|HasCategory| (-570) (QUOTE (-856)))) (|HasCategory| (-570) (LIST (QUOTE -1047) (QUOTE (-570)))) (|HasCategory| (-570) (QUOTE (-1161))) (|HasCategory| (-570) (LIST (QUOTE -893) (QUOTE (-384)))) (|HasCategory| (-570) (LIST (QUOTE -893) (QUOTE (-570)))) (|HasCategory| (-570) (LIST (QUOTE -620) (LIST (QUOTE -899) (QUOTE (-384))))) (|HasCategory| (-570) (LIST (QUOTE -620) (LIST (QUOTE -899) (QUOTE (-570))))) (|HasCategory| (-570) (QUOTE (-235))) (|HasCategory| (-570) (LIST (QUOTE -907) (QUOTE (-1186)))) (|HasCategory| (-570) (LIST (QUOTE -520) (QUOTE (-1186)) (QUOTE (-570)))) (|HasCategory| (-570) (LIST (QUOTE -313) (QUOTE (-570)))) (|HasCategory| (-570) (LIST (QUOTE -290) (QUOTE (-570)) (QUOTE (-570)))) (|HasCategory| (-570) (QUOTE (-311))) (|HasCategory| (-570) (QUOTE (-551))) (|HasCategory| (-570) (QUOTE (-856))) (|HasCategory| (-570) (LIST (QUOTE -645) (QUOTE (-570)))) (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| (-570) (QUOTE (-916)))) (-3684 (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| (-570) (QUOTE (-916)))) (|HasCategory| (-570) (QUOTE (-146))))) (-109) ((|constructor| (NIL "\\indented{1}{Author: Gabriel Dos Reis} Date Created: October 24,{} 2007 Date Last Modified: January 18,{} 2008. A `Binding' is a name asosciated with a collection of properties.")) (|binding| (($ (|Identifier|) (|List| (|Property|))) "\\spad{binding(n,props)} constructs a binding with name \\spad{`n'} and property list `props'.")) (|properties| (((|List| (|Property|)) $) "\\spad{properties(b)} returns the properties associated with binding \\spad{b}.")) (|name| (((|Identifier|) $) "\\spad{name(b)} returns the name of binding \\spad{b}"))) NIL @@ -392,7 +392,7 @@ NIL ((|constructor| (NIL "A basic operator is an object that can be applied to a list of arguments from a set,{} the result being a kernel over that set.")) (|setProperties| (($ $ (|AssociationList| (|String|) (|None|))) "\\spad{setProperties(op, l)} sets the property list of \\spad{op} to \\spad{l}. Argument \\spad{op} is modified \"in place\",{} \\spadignore{i.e.} no copy is made.")) (|setProperty| (($ $ (|Identifier|) (|None|)) "\\spad{setProperty(op, p, v)} attaches property \\spad{p} to \\spad{op},{} and sets its value to \\spad{v}. Argument \\spad{op} is modified \"in place\",{} \\spadignore{i.e.} no copy is made.") (($ $ (|String|) (|None|)) "\\spad{setProperty(op, s, v)} attaches property \\spad{s} to \\spad{op},{} and sets its value to \\spad{v}. Argument \\spad{op} is modified \"in place\",{} \\spadignore{i.e.} no copy is made.")) (|property| (((|Maybe| (|None|)) $ (|Identifier|)) "\\spad{property(op, p)} returns the value of property \\spad{p} if it is attached to \\spad{op},{} otherwise \\spad{nothing}.") (((|Union| (|None|) "failed") $ (|String|)) "\\spad{property(op, s)} returns the value of property \\spad{s} if it is attached to \\spad{op},{} and \"failed\" otherwise.")) (|deleteProperty!| (($ $ (|Identifier|)) "\\spad{deleteProperty!(op, p)} unattaches property \\spad{p} from \\spad{op}. Argument \\spad{op} is modified \"in place\",{} \\spadignore{i.e.} no copy is made.") (($ $ (|String|)) "\\spad{deleteProperty!(op, s)} unattaches property \\spad{s} from \\spad{op}. Argument \\spad{op} is modified \"in place\",{} \\spadignore{i.e.} no copy is made.")) (|assert| (($ $ (|Identifier|)) "\\spad{assert(op, p)} attaches property \\spad{p} to \\spad{op}. Argument \\spad{op} is modified \"in place\",{} \\spadignore{i.e.} no copy is made.")) (|has?| (((|Boolean|) $ (|Identifier|)) "\\spad{has?(op,p)} tests if property \\spad{s} is attached to \\spad{op}.")) (|input| (((|Union| (|Mapping| (|InputForm|) (|List| (|InputForm|))) "failed") $) "\\spad{input(op)} returns the \"\\%input\" property of \\spad{op} if it has one attached,{} \"failed\" otherwise.") (($ $ (|Mapping| (|InputForm|) (|List| (|InputForm|)))) "\\spad{input(op, foo)} attaches foo as the \"\\%input\" property of \\spad{op}. If \\spad{op} has a \"\\%input\" property \\spad{f},{} then \\spad{op(a1,...,an)} gets converted to InputForm as \\spad{f(a1,...,an)}.")) (|display| (($ $ (|Mapping| (|OutputForm|) (|OutputForm|))) "\\spad{display(op, foo)} attaches foo as the \"\\%display\" property of \\spad{op}. If \\spad{op} has a \"\\%display\" property \\spad{f},{} then \\spad{op(a)} gets converted to OutputForm as \\spad{f(a)}. Argument \\spad{op} must be unary.") (($ $ (|Mapping| (|OutputForm|) (|List| (|OutputForm|)))) "\\spad{display(op, foo)} attaches foo as the \"\\%display\" property of \\spad{op}. If \\spad{op} has a \"\\%display\" property \\spad{f},{} then \\spad{op(a1,...,an)} gets converted to OutputForm as \\spad{f(a1,...,an)}.") (((|Union| (|Mapping| (|OutputForm|) (|List| (|OutputForm|))) "failed") $) "\\spad{display(op)} returns the \"\\%display\" property of \\spad{op} if it has one attached,{} and \"failed\" otherwise.")) (|comparison| (($ $ (|Mapping| (|Boolean|) $ $)) "\\spad{comparison(op, foo?)} attaches foo? as the \"\\%less?\" property to \\spad{op}. If op1 and op2 have the same name,{} and one of them has a \"\\%less?\" property \\spad{f},{} then \\spad{f(op1, op2)} is called to decide whether \\spad{op1 < op2}.")) (|equality| (($ $ (|Mapping| (|Boolean|) $ $)) "\\spad{equality(op, foo?)} attaches foo? as the \"\\%equal?\" property to \\spad{op}. If op1 and op2 have the same name,{} and one of them has an \"\\%equal?\" property \\spad{f},{} then \\spad{f(op1, op2)} is called to decide whether op1 and op2 should be considered equal.")) (|weight| (($ $ (|NonNegativeInteger|)) "\\spad{weight(op, n)} attaches the weight \\spad{n} to \\spad{op}.") (((|NonNegativeInteger|) $) "\\spad{weight(op)} returns the weight attached to \\spad{op}.")) (|nary?| (((|Boolean|) $) "\\spad{nary?(op)} tests if \\spad{op} has arbitrary arity.")) (|unary?| (((|Boolean|) $) "\\spad{unary?(op)} tests if \\spad{op} is unary.")) (|nullary?| (((|Boolean|) $) "\\spad{nullary?(op)} tests if \\spad{op} is nullary.")) (|operator| (($ (|Symbol|) (|Arity|)) "\\spad{operator(f, a)} makes \\spad{f} into an operator of arity \\spad{a}.") (($ (|Symbol|) (|NonNegativeInteger|)) "\\spad{operator(f, n)} makes \\spad{f} into an \\spad{n}-ary operator.") (($ (|Symbol|)) "\\spad{operator(f)} makes \\spad{f} into an operator with arbitrary arity.")) (|copy| (($ $) "\\spad{copy(op)} returns a copy of \\spad{op}.")) (|properties| (((|AssociationList| (|String|) (|None|)) $) "\\spad{properties(op)} returns the list of all the properties currently attached to \\spad{op}."))) NIL NIL -(-116 -1385 UP) +(-116 -2968 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 @@ -403,7 +403,7 @@ NIL (-118 |p|) ((|constructor| (NIL "Stream-based implementation of \\spad{Qp:} numbers are represented as sum(\\spad{i} = \\spad{k}..,{} a[\\spad{i}] * p^i),{} where the a[\\spad{i}] lie in -(\\spad{p} - 1)\\spad{/2},{}...,{}(\\spad{p} - 1)\\spad{/2}."))) ((-4444 . T) (-4450 . T) (-4445 . T) ((-4454 "*") . T) (-4446 . T) (-4447 . T) (-4449 . T)) -((|HasCategory| (-117 |#1|) (QUOTE (-916))) (|HasCategory| (-117 |#1|) (LIST (QUOTE -1047) (QUOTE (-1186)))) (|HasCategory| (-117 |#1|) (QUOTE (-146))) (|HasCategory| (-117 |#1|) (QUOTE (-148))) (|HasCategory| (-117 |#1|) (LIST (QUOTE -620) (QUOTE (-542)))) (|HasCategory| (-117 |#1|) (QUOTE (-1031))) (|HasCategory| (-117 |#1|) (QUOTE (-826))) (-2811 (|HasCategory| (-117 |#1|) (QUOTE (-826))) (|HasCategory| (-117 |#1|) (QUOTE (-856)))) (|HasCategory| (-117 |#1|) (LIST (QUOTE -1047) (QUOTE (-570)))) (|HasCategory| (-117 |#1|) (QUOTE (-1161))) (|HasCategory| (-117 |#1|) (LIST (QUOTE -893) (QUOTE (-384)))) (|HasCategory| (-117 |#1|) (LIST (QUOTE -893) (QUOTE (-570)))) (|HasCategory| (-117 |#1|) (LIST (QUOTE -620) (LIST (QUOTE -899) (QUOTE (-384))))) (|HasCategory| (-117 |#1|) (LIST (QUOTE -620) (LIST (QUOTE -899) (QUOTE (-570))))) (|HasCategory| (-117 |#1|) (LIST (QUOTE -645) (QUOTE (-570)))) (|HasCategory| (-117 |#1|) (QUOTE (-235))) (|HasCategory| (-117 |#1|) (LIST (QUOTE -907) (QUOTE (-1186)))) (|HasCategory| (-117 |#1|) (LIST (QUOTE -520) (QUOTE (-1186)) (LIST (QUOTE -117) (|devaluate| |#1|)))) (|HasCategory| (-117 |#1|) (LIST (QUOTE -313) (LIST (QUOTE -117) (|devaluate| |#1|)))) (|HasCategory| (-117 |#1|) (LIST (QUOTE -290) (LIST (QUOTE -117) (|devaluate| |#1|)) (LIST (QUOTE -117) (|devaluate| |#1|)))) (|HasCategory| (-117 |#1|) (QUOTE (-311))) (|HasCategory| (-117 |#1|) (QUOTE (-551))) (|HasCategory| (-117 |#1|) (QUOTE (-856))) (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| (-117 |#1|) (QUOTE (-916)))) (-2811 (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| (-117 |#1|) (QUOTE (-916)))) (|HasCategory| (-117 |#1|) (QUOTE (-146))))) +((|HasCategory| (-117 |#1|) (QUOTE (-916))) (|HasCategory| (-117 |#1|) (LIST (QUOTE -1047) (QUOTE (-1186)))) (|HasCategory| (-117 |#1|) (QUOTE (-146))) (|HasCategory| (-117 |#1|) (QUOTE (-148))) (|HasCategory| (-117 |#1|) (LIST (QUOTE -620) (QUOTE (-542)))) (|HasCategory| (-117 |#1|) (QUOTE (-1031))) (|HasCategory| (-117 |#1|) (QUOTE (-826))) (-3684 (|HasCategory| (-117 |#1|) (QUOTE (-826))) (|HasCategory| (-117 |#1|) (QUOTE (-856)))) (|HasCategory| (-117 |#1|) (LIST (QUOTE -1047) (QUOTE (-570)))) (|HasCategory| (-117 |#1|) (QUOTE (-1161))) (|HasCategory| (-117 |#1|) (LIST (QUOTE -893) (QUOTE (-384)))) (|HasCategory| (-117 |#1|) (LIST (QUOTE -893) (QUOTE (-570)))) (|HasCategory| (-117 |#1|) (LIST (QUOTE -620) (LIST (QUOTE -899) (QUOTE (-384))))) (|HasCategory| (-117 |#1|) (LIST (QUOTE -620) (LIST (QUOTE -899) (QUOTE (-570))))) (|HasCategory| (-117 |#1|) (LIST (QUOTE -645) (QUOTE (-570)))) (|HasCategory| (-117 |#1|) (QUOTE (-235))) (|HasCategory| (-117 |#1|) (LIST (QUOTE -907) (QUOTE (-1186)))) (|HasCategory| (-117 |#1|) (LIST (QUOTE -520) (QUOTE (-1186)) (LIST (QUOTE -117) (|devaluate| |#1|)))) (|HasCategory| (-117 |#1|) (LIST (QUOTE -313) (LIST (QUOTE -117) (|devaluate| |#1|)))) (|HasCategory| (-117 |#1|) (LIST (QUOTE -290) (LIST (QUOTE -117) (|devaluate| |#1|)) (LIST (QUOTE -117) (|devaluate| |#1|)))) (|HasCategory| (-117 |#1|) (QUOTE (-311))) (|HasCategory| (-117 |#1|) (QUOTE (-551))) (|HasCategory| (-117 |#1|) (QUOTE (-856))) (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| (-117 |#1|) (QUOTE (-916)))) (-3684 (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| (-117 |#1|) (QUOTE (-916)))) (|HasCategory| (-117 |#1|) (QUOTE (-146))))) (-119 A S) ((|constructor| (NIL "A binary-recursive aggregate has 0,{} 1 or 2 children and serves as a model for a binary tree or a doubly-linked aggregate structure")) (|setright!| (($ $ $) "\\spad{setright!(a,x)} sets the right child of \\spad{t} to be \\spad{x}.")) (|setleft!| (($ $ $) "\\spad{setleft!(a,b)} sets the left child of \\axiom{a} to be \\spad{b}.")) (|setelt| (($ $ "right" $) "\\spad{setelt(a,\"right\",b)} (also written \\axiom{\\spad{b} . right \\spad{:=} \\spad{b}}) is equivalent to \\axiom{setright!(a,{}\\spad{b})}.") (($ $ "left" $) "\\spad{setelt(a,\"left\",b)} (also written \\axiom{a . left \\spad{:=} \\spad{b}}) is equivalent to \\axiom{setleft!(a,{}\\spad{b})}.")) (|right| (($ $) "\\spad{right(a)} returns the right child.")) (|elt| (($ $ "right") "\\spad{elt(a,\"right\")} (also written: \\axiom{a . right}) is equivalent to \\axiom{right(a)}.") (($ $ "left") "\\spad{elt(u,\"left\")} (also written: \\axiom{a . left}) is equivalent to \\axiom{left(a)}.")) (|left| (($ $) "\\spad{left(u)} returns the left child."))) NIL @@ -419,7 +419,7 @@ NIL (-122 S) ((|constructor| (NIL "BinarySearchTree(\\spad{S}) is the domain of a binary trees where elements are ordered across the tree. A binary search tree is either empty or has a value which is an \\spad{S},{} and a right and left which are both BinaryTree(\\spad{S}) Elements are ordered across the tree.")) (|split| (((|Record| (|:| |less| $) (|:| |greater| $)) |#1| $) "\\spad{split(x,b)} splits binary tree \\spad{b} into two trees,{} one with elements greater than \\spad{x},{} the other with elements less than \\spad{x}.")) (|insertRoot!| (($ |#1| $) "\\spad{insertRoot!(x,b)} inserts element \\spad{x} as a root of binary search tree \\spad{b}.")) (|insert!| (($ |#1| $) "\\spad{insert!(x,b)} inserts element \\spad{x} as leaves into binary search tree \\spad{b}.")) (|binarySearchTree| (($ (|List| |#1|)) "\\spad{binarySearchTree(l)} \\undocumented"))) ((-4452 . T) (-4453 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1109))) (-2811 (-12 (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-868))))) (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-868))))) +((-12 (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1109))) (-3684 (-12 (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-868))))) (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-868))))) (-123 S) ((|constructor| (NIL "The bit aggregate category models aggregates representing large quantities of Boolean data.")) (|xor| (($ $ $) "\\spad{xor(a,b)} returns the logical {\\em exclusive-or} of bit aggregates \\axiom{a} and \\axiom{\\spad{b}}.")) (|nor| (($ $ $) "\\spad{nor(a,b)} returns the logical {\\em nor} of bit aggregates \\axiom{a} and \\axiom{\\spad{b}}.")) (|nand| (($ $ $) "\\spad{nand(a,b)} returns the logical {\\em nand} of bit aggregates \\axiom{a} and \\axiom{\\spad{b}}."))) NIL @@ -439,15 +439,15 @@ NIL (-127 S) ((|constructor| (NIL "\\spadtype{BinaryTournament(S)} is the domain of binary trees where elements are ordered down the tree. A binary search tree is either empty or is a node containing a \\spadfun{value} of type \\spad{S},{} and a \\spadfun{right} and a \\spadfun{left} which are both \\spadtype{BinaryTree(S)}")) (|insert!| (($ |#1| $) "\\spad{insert!(x,b)} inserts element \\spad{x} as leaves into binary tournament \\spad{b}.")) (|binaryTournament| (($ (|List| |#1|)) "\\spad{binaryTournament(ls)} creates a binary tournament with the elements of \\spad{ls} as values at the nodes."))) ((-4452 . T) (-4453 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1109))) (-2811 (-12 (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-868))))) (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-868))))) +((-12 (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1109))) (-3684 (-12 (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-868))))) (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-868))))) (-128 S) ((|constructor| (NIL "\\spadtype{BinaryTree(S)} is the domain of all binary trees. A binary tree over \\spad{S} is either empty or has a \\spadfun{value} which is an \\spad{S} and a \\spadfun{right} and \\spadfun{left} which are both binary trees.")) (|binaryTree| (($ $ |#1| $) "\\spad{binaryTree(l,v,r)} creates a binary tree with value \\spad{v} with left subtree \\spad{l} and right subtree \\spad{r}.") (($ |#1|) "\\spad{binaryTree(v)} is an non-empty binary tree with value \\spad{v},{} and left and right empty."))) ((-4452 . T) (-4453 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1109))) (-2811 (-12 (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-868))))) (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-868))))) +((-12 (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1109))) (-3684 (-12 (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-868))))) (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-868))))) (-129) ((|constructor| (NIL "ByteBuffer provides datatype for buffers of bytes. This domain differs from PrimitiveArray Byte in that it is not as rigid as PrimitiveArray Byte. That is,{} the typical use of ByteBuffer is to pre-allocate a vector of Byte of some capacity \\spad{`n'}. The array can then store up to \\spad{`n'} bytes. The actual interesting bytes count (the length of the buffer) is therefore different from the capacity. The length is no more than the capacity,{} but it can be set dynamically as needed. This functionality is used for example when reading bytes from input/output devices where we use buffers to transfer data in and out of the system. Note: a value of type ByteBuffer is 0-based indexed,{} as opposed \\indented{6}{Vector,{} but not unlike PrimitiveArray Byte.}")) (|finiteAggregate| ((|attribute|) "A ByteBuffer object is a finite aggregate")) (|setLength!| (((|NonNegativeInteger|) $ (|NonNegativeInteger|)) "\\spad{setLength!(buf,n)} sets the number of active bytes in the `buf'. Error if \\spad{`n'} is more than the capacity.")) (|capacity| (((|NonNegativeInteger|) $) "\\spad{capacity(buf)} returns the pre-allocated maximum size of `buf'.")) (|byteBuffer| (($ (|NonNegativeInteger|)) "\\spad{byteBuffer(n)} creates a buffer of capacity \\spad{n},{} and length 0."))) ((-4453 . T) (-4452 . T)) -((-2811 (-12 (|HasCategory| (-130) (QUOTE (-856))) (|HasCategory| (-130) (LIST (QUOTE -313) (QUOTE (-130))))) (-12 (|HasCategory| (-130) (QUOTE (-1109))) (|HasCategory| (-130) (LIST (QUOTE -313) (QUOTE (-130)))))) (-2811 (-12 (|HasCategory| (-130) (QUOTE (-1109))) (|HasCategory| (-130) (LIST (QUOTE -313) (QUOTE (-130))))) (|HasCategory| (-130) (LIST (QUOTE -619) (QUOTE (-868))))) (|HasCategory| (-130) (LIST (QUOTE -620) (QUOTE (-542)))) (-2811 (|HasCategory| (-130) (QUOTE (-856))) (|HasCategory| (-130) (QUOTE (-1109)))) (|HasCategory| (-130) (QUOTE (-856))) (|HasCategory| (-570) (QUOTE (-856))) (|HasCategory| (-130) (QUOTE (-1109))) (|HasCategory| (-130) (LIST (QUOTE -619) (QUOTE (-868)))) (-12 (|HasCategory| (-130) (QUOTE (-1109))) (|HasCategory| (-130) (LIST (QUOTE -313) (QUOTE (-130)))))) +((-3684 (-12 (|HasCategory| (-130) (QUOTE (-856))) (|HasCategory| (-130) (LIST (QUOTE -313) (QUOTE (-130))))) (-12 (|HasCategory| (-130) (QUOTE (-1109))) (|HasCategory| (-130) (LIST (QUOTE -313) (QUOTE (-130)))))) (-3684 (-12 (|HasCategory| (-130) (QUOTE (-1109))) (|HasCategory| (-130) (LIST (QUOTE -313) (QUOTE (-130))))) (|HasCategory| (-130) (LIST (QUOTE -619) (QUOTE (-868))))) (|HasCategory| (-130) (LIST (QUOTE -620) (QUOTE (-542)))) (-3684 (|HasCategory| (-130) (QUOTE (-856))) (|HasCategory| (-130) (QUOTE (-1109)))) (|HasCategory| (-130) (QUOTE (-856))) (|HasCategory| (-570) (QUOTE (-856))) (|HasCategory| (-130) (QUOTE (-1109))) (|HasCategory| (-130) (LIST (QUOTE -619) (QUOTE (-868)))) (-12 (|HasCategory| (-130) (QUOTE (-1109))) (|HasCategory| (-130) (LIST (QUOTE -313) (QUOTE (-130)))))) (-130) ((|constructor| (NIL "Byte is the datatype of 8-bit sized unsigned integer values.")) (|sample| (($) "\\spad{sample} gives a sample datum of type Byte.")) (|bitior| (($ $ $) "bitor(\\spad{x},{}\\spad{y}) returns the bitwise `inclusive or' of \\spad{`x'} and \\spad{`y'}.")) (|bitand| (($ $ $) "\\spad{bitand(x,y)} returns the bitwise `and' of \\spad{`x'} and \\spad{`y'}.")) (|byte| (($ (|NonNegativeInteger|)) "\\spad{byte(x)} injects the unsigned integer value \\spad{`v'} into the Byte algebra. \\spad{`v'} must be non-negative and less than 256."))) NIL @@ -472,11 +472,11 @@ 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") $ $) "\\spad{x - y} returns an element \\spad{z} such that \\spad{z+y=x} or \"failed\" if no such element exists.")) (|commutative| ((|attribute| "*") "a domain \\spad{D} has \\spad{commutative(\"*\")} if it has an operation \\spad{\"*\": (D,D) -> D} which is commutative."))) (((-4454 "*") . T)) NIL -(-136 |minix| -2183 S T$) +(-136 |minix| -2795 S T$) ((|constructor| (NIL "This package provides functions to enable conversion of tensors given conversion of the components.")) (|map| (((|CartesianTensor| |#1| |#2| |#4|) (|Mapping| |#4| |#3|) (|CartesianTensor| |#1| |#2| |#3|)) "\\spad{map(f,ts)} does a componentwise conversion of the tensor \\spad{ts} to a tensor with components of type \\spad{T}.")) (|reshape| (((|CartesianTensor| |#1| |#2| |#4|) (|List| |#4|) (|CartesianTensor| |#1| |#2| |#3|)) "\\spad{reshape(lt,ts)} organizes the list of components \\spad{lt} into a tensor with the same shape as \\spad{ts}."))) NIL NIL -(-137 |minix| -2183 R) +(-137 |minix| -2795 R) ((|constructor| (NIL "CartesianTensor(minix,{}dim,{}\\spad{R}) provides Cartesian tensors with components belonging to a commutative ring \\spad{R}. These tensors can have any number of indices. Each index takes values from \\spad{minix} to \\spad{minix + dim - 1}.")) (|sample| (($) "\\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 @@ -499,7 +499,7 @@ NIL (-142) ((|constructor| (NIL "This domain allows classes of characters to be defined and manipulated efficiently.")) (|alphanumeric| (($) "\\spad{alphanumeric()} returns the class of all characters for which \\spadfunFrom{alphanumeric?}{Character} is \\spad{true}.")) (|alphabetic| (($) "\\spad{alphabetic()} returns the class of all characters for which \\spadfunFrom{alphabetic?}{Character} is \\spad{true}.")) (|lowerCase| (($) "\\spad{lowerCase()} returns the class of all characters for which \\spadfunFrom{lowerCase?}{Character} is \\spad{true}.")) (|upperCase| (($) "\\spad{upperCase()} returns the class of all characters for which \\spadfunFrom{upperCase?}{Character} is \\spad{true}.")) (|hexDigit| (($) "\\spad{hexDigit()} returns the class of all characters for which \\spadfunFrom{hexDigit?}{Character} is \\spad{true}.")) (|digit| (($) "\\spad{digit()} returns the class of all characters for which \\spadfunFrom{digit?}{Character} is \\spad{true}.")) (|charClass| (($ (|List| (|Character|))) "\\spad{charClass(l)} creates a character class which contains exactly the characters given in the list \\spad{l}.") (($ (|String|)) "\\spad{charClass(s)} creates a character class which contains exactly the characters given in the string \\spad{s}."))) ((-4452 . T) (-4442 . T) (-4453 . T)) -((-2811 (-12 (|HasCategory| (-145) (QUOTE (-373))) (|HasCategory| (-145) (LIST (QUOTE -313) (QUOTE (-145))))) (-12 (|HasCategory| (-145) (QUOTE (-1109))) (|HasCategory| (-145) (LIST (QUOTE -313) (QUOTE (-145)))))) (|HasCategory| (-145) (LIST (QUOTE -620) (QUOTE (-542)))) (|HasCategory| (-145) (QUOTE (-373))) (|HasCategory| (-145) (QUOTE (-856))) (|HasCategory| (-145) (QUOTE (-1109))) (|HasCategory| (-145) (LIST (QUOTE -619) (QUOTE (-868)))) (-12 (|HasCategory| (-145) (QUOTE (-1109))) (|HasCategory| (-145) (LIST (QUOTE -313) (QUOTE (-145)))))) +((-3684 (-12 (|HasCategory| (-145) (QUOTE (-373))) (|HasCategory| (-145) (LIST (QUOTE -313) (QUOTE (-145))))) (-12 (|HasCategory| (-145) (QUOTE (-1109))) (|HasCategory| (-145) (LIST (QUOTE -313) (QUOTE (-145)))))) (|HasCategory| (-145) (LIST (QUOTE -620) (QUOTE (-542)))) (|HasCategory| (-145) (QUOTE (-373))) (|HasCategory| (-145) (QUOTE (-856))) (|HasCategory| (-145) (QUOTE (-1109))) (|HasCategory| (-145) (LIST (QUOTE -619) (QUOTE (-868)))) (-12 (|HasCategory| (-145) (QUOTE (-1109))) (|HasCategory| (-145) (LIST (QUOTE -313) (QUOTE (-145)))))) (-143 R Q A) ((|constructor| (NIL "CommonDenominator 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|)) |#3|) "\\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}\\spad{'s}.")) (|clearDenominator| ((|#3| |#3|) "\\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}\\spad{'s}.")) (|commonDenominator| ((|#1| |#3|) "\\spad{commonDenominator([q1,...,qn])} returns a common denominator \\spad{d} for \\spad{q1},{}...,{}\\spad{qn}."))) NIL @@ -524,7 +524,7 @@ NIL ((|constructor| (NIL "Rings of Characteristic Zero."))) ((-4449 . T)) NIL -(-149 -1385 UP UPUP) +(-149 -2968 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 @@ -564,7 +564,7 @@ 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 -(-159 R -1385) +(-159 R -2968) ((|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})\\spad{/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.} \\spad{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.} \\spad{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.} \\spad{n!/}(\\spad{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 @@ -598,7 +598,7 @@ NIL ((|HasCategory| |#2| (QUOTE (-916))) (|HasCategory| |#2| (QUOTE (-551))) (|HasCategory| |#2| (QUOTE (-1011))) (|HasCategory| |#2| (QUOTE (-1212))) (|HasCategory| |#2| (QUOTE (-1069))) (|HasCategory| |#2| (QUOTE (-1031))) (|HasCategory| |#2| (QUOTE (-146))) (|HasCategory| |#2| (QUOTE (-148))) (|HasCategory| |#2| (LIST (QUOTE -620) (QUOTE (-542)))) (|HasCategory| |#2| (QUOTE (-368))) (|HasAttribute| |#2| (QUOTE -4448)) (|HasAttribute| |#2| (QUOTE -4451)) (|HasCategory| |#2| (QUOTE (-311))) (|HasCategory| |#2| (QUOTE (-562)))) (-167 R) ((|constructor| (NIL "This category represents the extension of a ring by a square root of \\spad{-1}.")) (|rationalIfCan| (((|Union| (|Fraction| (|Integer|)) "failed") $) "\\spad{rationalIfCan(x)} returns \\spad{x} as a rational number,{} or \"failed\" if \\spad{x} is not a rational number.")) (|rational| (((|Fraction| (|Integer|)) $) "\\spad{rational(x)} returns \\spad{x} as a rational number. Error: if \\spad{x} is not a rational number.")) (|rational?| (((|Boolean|) $) "\\spad{rational?(x)} tests if \\spad{x} is a rational number.")) (|polarCoordinates| (((|Record| (|:| |r| |#1|) (|:| |phi| |#1|)) $) "\\spad{polarCoordinates(x)} returns (\\spad{r},{} phi) such that \\spad{x} = \\spad{r} * exp(\\%\\spad{i} * phi).")) (|argument| ((|#1| $) "\\spad{argument(x)} returns the angle made by (0,{}1) and (0,{}\\spad{x}).")) (|abs| (($ $) "\\spad{abs(x)} returns the absolute value of \\spad{x} = sqrt(norm(\\spad{x})).")) (|exquo| (((|Union| $ "failed") $ |#1|) "\\spad{exquo(x, r)} returns the exact quotient of \\spad{x} by \\spad{r},{} or \"failed\" if \\spad{r} does not divide \\spad{x} exactly.")) (|norm| ((|#1| $) "\\spad{norm(x)} returns \\spad{x} * conjugate(\\spad{x})")) (|real| ((|#1| $) "\\spad{real(x)} returns real part of \\spad{x}.")) (|imag| ((|#1| $) "\\spad{imag(x)} returns imaginary part of \\spad{x}.")) (|conjugate| (($ $) "\\spad{conjugate(x + \\%i y)} returns \\spad{x} - \\%\\spad{i} \\spad{y}.")) (|imaginary| (($) "\\spad{imaginary()} = sqrt(\\spad{-1}) = \\%\\spad{i}.")) (|complex| (($ |#1| |#1|) "\\spad{complex(x,y)} constructs \\spad{x} + \\%i*y.") ((|attribute|) "indicates that \\% has sqrt(\\spad{-1})"))) -((-4445 -2811 (|has| |#1| (-562)) (-12 (|has| |#1| (-311)) (|has| |#1| (-916)))) (-4450 |has| |#1| (-368)) (-4444 |has| |#1| (-368)) (-4448 |has| |#1| (-6 -4448)) (-4451 |has| |#1| (-6 -4451)) (-3545 . T) ((-4454 "*") . T) (-4446 . T) (-4447 . T) (-4449 . T)) +((-4445 -3684 (|has| |#1| (-562)) (-12 (|has| |#1| (-311)) (|has| |#1| (-916)))) (-4450 |has| |#1| (-368)) (-4444 |has| |#1| (-368)) (-4448 |has| |#1| (-6 -4448)) (-4451 |has| |#1| (-6 -4451)) (-3420 . T) ((-4454 "*") . T) (-4446 . T) (-4447 . T) (-4449 . T)) NIL (-168 RR PR) ((|constructor| (NIL "\\indented{1}{Author:} Date Created: Date Last Updated: Basic Functions: Related Constructors: Complex,{} UnivariatePolynomial Also See: AMS Classifications: Keywords: complex,{} polynomial factorization,{} factor References:")) (|factor| (((|Factored| |#2|) |#2|) "\\spad{factor(p)} factorizes the polynomial \\spad{p} with complex coefficients."))) @@ -614,8 +614,8 @@ NIL NIL (-171 R) ((|constructor| (NIL "\\spadtype {Complex(R)} creates the domain of elements of the form \\spad{a + b * i} where \\spad{a} and \\spad{b} come from the ring \\spad{R},{} and \\spad{i} is a new element such that \\spad{i**2 = -1}."))) -((-4445 -2811 (|has| |#1| (-562)) (-12 (|has| |#1| (-311)) (|has| |#1| (-916)))) (-4450 |has| |#1| (-368)) (-4444 |has| |#1| (-368)) (-4448 |has| |#1| (-6 -4448)) (-4451 |has| |#1| (-6 -4451)) (-3545 . T) ((-4454 "*") . T) (-4446 . T) (-4447 . T) (-4449 . 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T) ((-4454 "*") . T) (-4446 . T) (-4447 . T) (-4449 . T)) +((|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-148))) (|HasCategory| |#1| (QUOTE (-354))) (-3684 (|HasCategory| |#1| (QUOTE (-368))) (|HasCategory| |#1| (QUOTE (-354)))) (|HasCategory| |#1| (QUOTE (-562))) (|HasCategory| |#1| (QUOTE (-368))) (|HasCategory| |#1| (QUOTE (-373))) (-3684 (-12 (|HasCategory| |#1| (LIST (QUOTE -620) (LIST (QUOTE -899) (QUOTE (-384))))) (|HasCategory| |#1| (QUOTE (-354)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -620) (LIST (QUOTE -899) (QUOTE (-570))))) (|HasCategory| |#1| (QUOTE (-354)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -520) (QUOTE (-1186)) (|devaluate| |#1|))) (|HasCategory| |#1| (QUOTE (-354)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -1047) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasCategory| |#1| (QUOTE (-354)))) (-12 (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-354)))) (-12 (|HasCategory| |#1| (QUOTE (-148))) (|HasCategory| |#1| (QUOTE (-354)))) (|HasCategory| |#1| (QUOTE (-235))) (-12 (|HasCategory| |#1| 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(|HasCategory| |#1| (QUOTE (-368))) (|HasCategory| |#1| (QUOTE (-916)))) (-12 (|HasCategory| |#1| (QUOTE (-354))) (|HasCategory| |#1| (QUOTE (-916))))) (-3684 (|HasCategory| |#1| (QUOTE (-368))) (|HasCategory| |#1| (QUOTE (-562)))) (-12 (|HasCategory| |#1| (QUOTE (-1011))) (|HasCategory| |#1| (QUOTE (-1212)))) (|HasCategory| |#1| (QUOTE (-1212))) (|HasCategory| |#1| (QUOTE (-1031))) (|HasCategory| |#1| (LIST (QUOTE -620) (QUOTE (-542)))) (-3684 (|HasCategory| |#1| (QUOTE (-311))) (|HasCategory| |#1| (QUOTE (-368))) (|HasCategory| |#1| (QUOTE (-354))) (|HasCategory| |#1| (QUOTE (-562)))) (-3684 (|HasCategory| |#1| (QUOTE (-311))) (|HasCategory| |#1| (QUOTE (-368))) (|HasCategory| |#1| (QUOTE (-354)))) (|HasCategory| |#1| (LIST (QUOTE -620) (LIST (QUOTE -899) (QUOTE (-384))))) (|HasCategory| |#1| (LIST (QUOTE -620) (LIST (QUOTE -899) (QUOTE (-570))))) (|HasCategory| |#1| (LIST (QUOTE -893) (QUOTE (-384)))) (|HasCategory| |#1| (LIST (QUOTE -893) (QUOTE (-570)))) (|HasCategory| |#1| (LIST (QUOTE -520) (QUOTE (-1186)) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -290) (|devaluate| |#1|) (|devaluate| |#1|))) (|HasCategory| |#1| (QUOTE (-834))) (|HasCategory| |#1| (QUOTE (-1069))) (-12 (|HasCategory| |#1| (QUOTE (-1069))) (|HasCategory| |#1| (QUOTE (-1212)))) (|HasCategory| |#1| (QUOTE (-551))) (|HasCategory| |#1| (QUOTE (-311))) (|HasCategory| |#1| (QUOTE (-916))) (-3684 (-12 (|HasCategory| |#1| (QUOTE (-311))) (|HasCategory| |#1| (QUOTE (-916)))) (|HasCategory| |#1| (QUOTE (-368)))) (-3684 (-12 (|HasCategory| |#1| (QUOTE (-311))) (|HasCategory| |#1| (QUOTE (-916)))) (|HasCategory| |#1| (QUOTE (-562)))) (|HasCategory| |#1| (QUOTE (-235))) (-12 (|HasCategory| |#1| (QUOTE (-311))) (|HasCategory| |#1| (QUOTE (-916)))) (|HasAttribute| |#1| (QUOTE -4448)) (|HasAttribute| |#1| (QUOTE -4451)) (-12 (|HasCategory| |#1| (QUOTE (-235))) (|HasCategory| |#1| (QUOTE (-368)))) (-12 (|HasCategory| |#1| (QUOTE (-368))) (|HasCategory| |#1| (LIST (QUOTE -907) (QUOTE (-1186))))) (-3684 (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-311))) (|HasCategory| |#1| (QUOTE (-916)))) (|HasCategory| |#1| (QUOTE (-146)))) (-3684 (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-311))) (|HasCategory| |#1| (QUOTE (-916)))) (|HasCategory| |#1| (QUOTE (-354))))) (-172 R S CS) ((|constructor| (NIL "This package supports converting complex expressions to patterns")) (|convert| (((|Pattern| |#1|) |#3|) "\\spad{convert(cs)} converts the complex expression \\spad{cs} to a pattern"))) NIL @@ -688,7 +688,7 @@ NIL ((|constructor| (NIL "This domain provides implementations for constructors.")) (|findConstructor| (((|Maybe| $) (|Identifier|)) "\\spad{findConstructor(s)} attempts to find a constructor named \\spad{s}. If successful,{} returns that constructor; otherwise,{} returns \\spad{nothing}."))) NIL NIL -(-190 R -1385) +(-190 R -2968) ((|constructor| (NIL "\\spadtype{ComplexTrigonometricManipulations} provides function that compute the real and imaginary parts of complex functions.")) (|complexForm| (((|Complex| (|Expression| |#1|)) |#2|) "\\spad{complexForm(f)} returns \\spad{[real f, imag f]}.")) (|trigs| ((|#2| |#2|) "\\spad{trigs(f)} rewrites all the complex logs and exponentials appearing in \\spad{f} in terms of trigonometric functions.")) (|real?| (((|Boolean|) |#2|) "\\spad{real?(f)} returns \\spad{true} if \\spad{f = real f}.")) (|imag| (((|Expression| |#1|) |#2|) "\\spad{imag(f)} returns the imaginary part of \\spad{f} where \\spad{f} is a complex function.")) (|real| (((|Expression| |#1|) |#2|) "\\spad{real(f)} returns the real part of \\spad{f} where \\spad{f} is a complex function.")) (|complexElementary| ((|#2| |#2| (|Symbol|)) "\\spad{complexElementary(f, x)} rewrites the kernels of \\spad{f} involving \\spad{x} in terms of the 2 fundamental complex transcendental elementary functions: \\spad{log, exp}.") ((|#2| |#2|) "\\spad{complexElementary(f)} rewrites \\spad{f} in terms of the 2 fundamental complex transcendental elementary functions: \\spad{log, exp}.")) (|complexNormalize| ((|#2| |#2| (|Symbol|)) "\\spad{complexNormalize(f, x)} rewrites \\spad{f} using the least possible number of complex independent kernels involving \\spad{x}.") ((|#2| |#2|) "\\spad{complexNormalize(f)} rewrites \\spad{f} using the least possible number of complex independent kernels."))) NIL NIL @@ -796,23 +796,23 @@ NIL ((|constructor| (NIL "\\indented{1}{This domain implements a simple view of a database whose fields are} indexed by symbols")) (- (($ $ $) "\\spad{db1-db2} returns the difference of databases \\spad{db1} and \\spad{db2} \\spadignore{i.e.} consisting of elements in \\spad{db1} but not in \\spad{db2}")) (+ (($ $ $) "\\spad{db1+db2} returns the merge of databases \\spad{db1} and \\spad{db2}")) (|fullDisplay| (((|Void|) $ (|PositiveInteger|) (|PositiveInteger|)) "\\spad{fullDisplay(db,start,end )} prints full details of entries in the range \\axiom{\\spad{start}..end} in \\axiom{\\spad{db}}.") (((|Void|) $) "\\spad{fullDisplay(db)} prints full details of each entry in \\axiom{\\spad{db}}.") (((|Void|) $) "\\spad{fullDisplay(x)} displays \\spad{x} in detail")) (|display| (((|Void|) $) "\\spad{display(db)} prints a summary line for each entry in \\axiom{\\spad{db}}.") (((|Void|) $) "\\spad{display(x)} displays \\spad{x} in some form")) (|elt| (((|DataList| (|String|)) $ (|Symbol|)) "\\spad{elt(db,s)} returns the \\axiom{\\spad{s}} field of each element of \\axiom{\\spad{db}}.") (($ $ (|QueryEquation|)) "\\spad{elt(db,q)} returns all elements of \\axiom{\\spad{db}} which satisfy \\axiom{\\spad{q}}.") (((|String|) $ (|Symbol|)) "\\spad{elt(x,s)} returns an element of \\spad{x} indexed by \\spad{s}"))) NIL NIL -(-217 -1385 UP UPUP R) +(-217 -2968 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 -(-218 -1385 FP) +(-218 -2968 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 \\spad{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 (-219) ((|constructor| (NIL "This domain allows rational numbers to be presented as repeating decimal expansions.")) (|decimal| (($ (|Fraction| (|Integer|))) "\\spad{decimal(r)} converts a rational number to a decimal expansion.")) (|fractionPart| (((|Fraction| (|Integer|)) $) "\\spad{fractionPart(d)} returns the fractional part of a decimal expansion."))) ((-4444 . T) (-4450 . T) (-4445 . T) ((-4454 "*") . T) (-4446 . T) (-4447 . T) (-4449 . T)) -((|HasCategory| (-570) (QUOTE (-916))) (|HasCategory| (-570) (LIST (QUOTE -1047) (QUOTE (-1186)))) (|HasCategory| (-570) (QUOTE (-146))) (|HasCategory| (-570) (QUOTE (-148))) (|HasCategory| (-570) (LIST (QUOTE -620) (QUOTE (-542)))) (|HasCategory| (-570) (QUOTE (-1031))) (|HasCategory| (-570) (QUOTE (-826))) (-2811 (|HasCategory| (-570) (QUOTE (-826))) (|HasCategory| (-570) (QUOTE (-856)))) (|HasCategory| (-570) (LIST (QUOTE -1047) (QUOTE (-570)))) (|HasCategory| (-570) (QUOTE (-1161))) (|HasCategory| (-570) (LIST (QUOTE -893) (QUOTE (-384)))) (|HasCategory| (-570) (LIST (QUOTE -893) (QUOTE (-570)))) (|HasCategory| (-570) (LIST (QUOTE -620) (LIST (QUOTE -899) (QUOTE (-384))))) (|HasCategory| (-570) (LIST (QUOTE -620) (LIST (QUOTE -899) (QUOTE (-570))))) (|HasCategory| (-570) (QUOTE (-235))) (|HasCategory| (-570) (LIST (QUOTE -907) (QUOTE (-1186)))) (|HasCategory| (-570) (LIST (QUOTE -520) (QUOTE (-1186)) (QUOTE (-570)))) (|HasCategory| (-570) (LIST (QUOTE -313) (QUOTE (-570)))) (|HasCategory| (-570) (LIST (QUOTE -290) (QUOTE (-570)) (QUOTE (-570)))) (|HasCategory| (-570) (QUOTE (-311))) (|HasCategory| (-570) (QUOTE (-551))) (|HasCategory| (-570) (QUOTE (-856))) (|HasCategory| (-570) (LIST (QUOTE -645) (QUOTE (-570)))) (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| (-570) (QUOTE (-916)))) (-2811 (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| (-570) (QUOTE (-916)))) (|HasCategory| (-570) (QUOTE (-146))))) +((|HasCategory| (-570) (QUOTE (-916))) (|HasCategory| (-570) (LIST (QUOTE -1047) (QUOTE (-1186)))) (|HasCategory| (-570) (QUOTE (-146))) (|HasCategory| (-570) (QUOTE (-148))) (|HasCategory| (-570) (LIST (QUOTE -620) (QUOTE (-542)))) (|HasCategory| (-570) (QUOTE (-1031))) (|HasCategory| (-570) (QUOTE (-826))) (-3684 (|HasCategory| (-570) (QUOTE (-826))) (|HasCategory| (-570) (QUOTE (-856)))) (|HasCategory| (-570) (LIST (QUOTE -1047) (QUOTE (-570)))) (|HasCategory| (-570) (QUOTE (-1161))) (|HasCategory| (-570) (LIST (QUOTE -893) (QUOTE (-384)))) (|HasCategory| (-570) (LIST (QUOTE -893) (QUOTE (-570)))) (|HasCategory| (-570) (LIST (QUOTE -620) (LIST (QUOTE -899) (QUOTE (-384))))) (|HasCategory| (-570) (LIST (QUOTE -620) (LIST (QUOTE -899) (QUOTE (-570))))) (|HasCategory| (-570) (QUOTE (-235))) (|HasCategory| (-570) (LIST (QUOTE -907) (QUOTE (-1186)))) (|HasCategory| (-570) (LIST (QUOTE -520) (QUOTE (-1186)) (QUOTE (-570)))) (|HasCategory| (-570) (LIST (QUOTE -313) (QUOTE (-570)))) (|HasCategory| (-570) (LIST (QUOTE -290) (QUOTE (-570)) (QUOTE (-570)))) (|HasCategory| (-570) (QUOTE (-311))) (|HasCategory| (-570) (QUOTE (-551))) (|HasCategory| (-570) (QUOTE (-856))) (|HasCategory| (-570) (LIST (QUOTE -645) (QUOTE (-570)))) (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| (-570) (QUOTE (-916)))) (-3684 (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| (-570) (QUOTE (-916)))) (|HasCategory| (-570) (QUOTE (-146))))) (-220) ((|constructor| (NIL "This domain represents the syntax of a definition.")) (|body| (((|SpadAst|) $) "\\spad{body(d)} returns the right hand side of the definition \\spad{`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|) $) "\\spad{head(d)} returns the head of the definition \\spad{`d'}. This is a list of identifiers starting with the name of the operation followed by the name of the parameters,{} if any."))) NIL NIL -(-221 R -1385) +(-221 R -2968) ((|constructor| (NIL "\\spadtype{ElementaryFunctionDefiniteIntegration} provides functions to compute definite integrals of elementary functions.")) (|innerint| (((|Union| (|:| |f1| (|OrderedCompletion| |#2|)) (|:| |f2| (|List| (|OrderedCompletion| |#2|))) (|:| |fail| "failed") (|:| |pole| "potentialPole")) |#2| (|Symbol|) (|OrderedCompletion| |#2|) (|OrderedCompletion| |#2|) (|Boolean|)) "\\spad{innerint(f, x, a, b, ignore?)} should be local but conditional")) (|integrate| (((|Union| (|:| |f1| (|OrderedCompletion| |#2|)) (|:| |f2| (|List| (|OrderedCompletion| |#2|))) (|:| |fail| "failed") (|:| |pole| "potentialPole")) |#2| (|SegmentBinding| (|OrderedCompletion| |#2|)) (|String|)) "\\spad{integrate(f, x = a..b, \"noPole\")} returns the integral of \\spad{f(x)dx} from a to \\spad{b}. If it is not possible to check whether \\spad{f} has a pole for \\spad{x} between a and \\spad{b} (because of parameters),{} then this function will assume that \\spad{f} has no such pole. Error: if \\spad{f} has a pole for \\spad{x} between a and \\spad{b} or if the last argument is not \"noPole\".") (((|Union| (|:| |f1| (|OrderedCompletion| |#2|)) (|:| |f2| (|List| (|OrderedCompletion| |#2|))) (|:| |fail| "failed") (|:| |pole| "potentialPole")) |#2| (|SegmentBinding| (|OrderedCompletion| |#2|))) "\\spad{integrate(f, x = a..b)} returns the integral of \\spad{f(x)dx} from a to \\spad{b}. Error: if \\spad{f} has a pole for \\spad{x} between a and \\spad{b}."))) NIL NIL @@ -827,18 +827,18 @@ NIL (-224 S) ((|constructor| (NIL "Linked list implementation of a Dequeue")) (|dequeue| (($ (|List| |#1|)) "\\spad{dequeue([x,y,...,z])} creates a dequeue with first (top or front) element \\spad{x},{} second element \\spad{y},{}...,{}and last (bottom or back) element \\spad{z}."))) ((-4452 . T) (-4453 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1109))) (-2811 (-12 (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-868))))) (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-868))))) +((-12 (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1109))) (-3684 (-12 (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-868))))) (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-868))))) (-225 |CoefRing| |listIndVar|) ((|constructor| (NIL "The deRham complex of Euclidean space,{} that is,{} the class of differential forms of arbitary degree over a coefficient ring. See Flanders,{} Harley,{} Differential Forms,{} With Applications to the Physical Sciences,{} New York,{} Academic Press,{} 1963.")) (|exteriorDifferential| (($ $) "\\spad{exteriorDifferential(df)} returns the exterior derivative (gradient,{} curl,{} divergence,{} ...) of the differential form \\spad{df}.")) (|totalDifferential| (($ (|Expression| |#1|)) "\\spad{totalDifferential(x)} returns the total differential (gradient) form for element \\spad{x}.")) (|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}."))) ((-4449 . T)) NIL -(-226 R -1385) +(-226 R -2968) ((|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 (-227) ((|constructor| (NIL "\\indented{1}{\\spadtype{DoubleFloat} is intended to make accessible} hardware floating point arithmetic in \\Language{},{} either native double precision,{} or IEEE. On most machines,{} there will be hardware support for the arithmetic operations: \\spadfunFrom{+}{DoubleFloat},{} \\spadfunFrom{*}{DoubleFloat},{} \\spadfunFrom{/}{DoubleFloat} and possibly also the \\spadfunFrom{sqrt}{DoubleFloat} operation. The operations \\spadfunFrom{exp}{DoubleFloat},{} \\spadfunFrom{log}{DoubleFloat},{} \\spadfunFrom{sin}{DoubleFloat},{} \\spadfunFrom{cos}{DoubleFloat},{} \\spadfunFrom{atan}{DoubleFloat} are normally coded in software based on minimax polynomial/rational approximations. Note that under Lisp/VM,{} \\spadfunFrom{atan}{DoubleFloat} is not available at this time. Some general comments about the accuracy of the operations: the operations \\spadfunFrom{+}{DoubleFloat},{} \\spadfunFrom{*}{DoubleFloat},{} \\spadfunFrom{/}{DoubleFloat} and \\spadfunFrom{sqrt}{DoubleFloat} are expected to be fully accurate. The operations \\spadfunFrom{exp}{DoubleFloat},{} \\spadfunFrom{log}{DoubleFloat},{} \\spadfunFrom{sin}{DoubleFloat},{} \\spadfunFrom{cos}{DoubleFloat} and \\spadfunFrom{atan}{DoubleFloat} are not expected to be fully accurate. In particular,{} \\spadfunFrom{sin}{DoubleFloat} and \\spadfunFrom{cos}{DoubleFloat} will lose all precision for large arguments. \\blankline The \\spadtype{Float} domain provides an alternative to the \\spad{DoubleFloat} domain. It provides an arbitrary precision model of floating point arithmetic. This means that accuracy problems like those above are eliminated by increasing the working precision where necessary. \\spadtype{Float} provides some special functions such as \\spadfunFrom{erf}{DoubleFloat},{} the error function in addition to the elementary functions. The disadvantage of \\spadtype{Float} is that it is much more expensive than small floats when the latter can be used.")) (|rationalApproximation| (((|Fraction| (|Integer|)) $ (|NonNegativeInteger|) (|NonNegativeInteger|)) "\\spad{rationalApproximation(f, n, b)} computes a rational approximation \\spad{r} to \\spad{f} with relative error \\spad{< b**(-n)} (that is,{} \\spad{|(r-f)/f| < b**(-n)}).") (((|Fraction| (|Integer|)) $ (|NonNegativeInteger|)) "\\spad{rationalApproximation(f, n)} computes a rational approximation \\spad{r} to \\spad{f} with relative error \\spad{< 10**(-n)}.")) (|Beta| (($ $ $) "\\spad{Beta(x,y)} is \\spad{Gamma(x) * Gamma(y)/Gamma(x+y)}.")) (|Gamma| (($ $) "\\spad{Gamma(x)} is the Euler Gamma function.")) (|atan| (($ $ $) "\\spad{atan(x,y)} computes the arc tangent from \\spad{x} with phase \\spad{y}.")) (|log10| (($ $) "\\spad{log10(x)} computes the logarithm with base 10 for \\spad{x}.")) (|log2| (($ $) "\\spad{log2(x)} computes the logarithm with base 2 for \\spad{x}.")) (|exp1| (($) "\\spad{exp1()} returns the natural log base \\spad{2.718281828...}.")) (** (($ $ $) "\\spad{x ** y} returns the \\spad{y}th power of \\spad{x} (equal to \\spad{exp(y log x)}).")) (/ (($ $ (|Integer|)) "\\spad{x / i} computes the division from \\spad{x} by an integer \\spad{i}."))) -((-3535 . T) (-4444 . T) (-4450 . T) (-4445 . T) ((-4454 "*") . T) (-4446 . T) (-4447 . T) (-4449 . T)) +((-3412 . T) (-4444 . T) (-4450 . T) (-4445 . T) ((-4454 "*") . T) (-4446 . T) (-4447 . T) (-4449 . T)) NIL (-228) ((|constructor| (NIL "This package provides special functions for double precision real and complex floating point.")) (|hypergeometric0F1| (((|Complex| (|DoubleFloat|)) (|Complex| (|DoubleFloat|)) (|Complex| (|DoubleFloat|))) "\\spad{hypergeometric0F1(c,z)} is the hypergeometric function \\spad{0F1(; c; z)}.") (((|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|)) "\\spad{hypergeometric0F1(c,z)} is the hypergeometric function \\spad{0F1(; c; z)}.")) (|airyBi| (((|Complex| (|DoubleFloat|)) (|Complex| (|DoubleFloat|))) "\\spad{airyBi(x)} is the Airy function \\spad{Bi(x)}. This function satisfies the differential equation: \\indented{2}{\\spad{Bi''(x) - x * Bi(x) = 0}.}") (((|DoubleFloat|) (|DoubleFloat|)) "\\spad{airyBi(x)} is the Airy function \\spad{Bi(x)}. This function satisfies the differential equation: \\indented{2}{\\spad{Bi''(x) - x * Bi(x) = 0}.}")) (|airyAi| (((|DoubleFloat|) (|DoubleFloat|)) "\\spad{airyAi(x)} is the Airy function \\spad{Ai(x)}. This function satisfies the differential equation: \\indented{2}{\\spad{Ai''(x) - x * Ai(x) = 0}.}") (((|Complex| (|DoubleFloat|)) (|Complex| (|DoubleFloat|))) "\\spad{airyAi(x)} is the Airy function \\spad{Ai(x)}. This function satisfies the differential equation: \\indented{2}{\\spad{Ai''(x) - x * Ai(x) = 0}.}")) (|besselK| (((|Complex| (|DoubleFloat|)) (|Complex| (|DoubleFloat|)) (|Complex| (|DoubleFloat|))) "\\spad{besselK(v,x)} is the modified Bessel function of the first kind,{} \\spad{K(v,x)}. This function satisfies the differential equation: \\indented{2}{\\spad{x^2 w''(x) + x w'(x) - (x^2+v^2)w(x) = 0}.} Note: The default implmentation uses the relation \\indented{2}{\\spad{K(v,x) = \\%pi/2*(I(-v,x) - I(v,x))/sin(v*\\%pi)}} so is not valid for integer values of \\spad{v}.") (((|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|)) "\\spad{besselK(v,x)} is the modified Bessel function of the first kind,{} \\spad{K(v,x)}. This function satisfies the differential equation: \\indented{2}{\\spad{x^2 w''(x) + x w'(x) - (x^2+v^2)w(x) = 0}.} Note: The default implmentation uses the relation \\indented{2}{\\spad{K(v,x) = \\%pi/2*(I(-v,x) - I(v,x))/sin(v*\\%pi)}.} so is not valid for integer values of \\spad{v}.")) (|besselI| (((|Complex| (|DoubleFloat|)) (|Complex| (|DoubleFloat|)) (|Complex| (|DoubleFloat|))) "\\spad{besselI(v,x)} is the modified Bessel function of the first kind,{} \\spad{I(v,x)}. This function satisfies the differential equation: \\indented{2}{\\spad{x^2 w''(x) + x w'(x) - (x^2+v^2)w(x) = 0}.}") (((|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|)) "\\spad{besselI(v,x)} is the modified Bessel function of the first kind,{} \\spad{I(v,x)}. This function satisfies the differential equation: \\indented{2}{\\spad{x^2 w''(x) + x w'(x) - (x^2+v^2)w(x) = 0}.}")) (|besselY| (((|Complex| (|DoubleFloat|)) (|Complex| (|DoubleFloat|)) (|Complex| (|DoubleFloat|))) "\\spad{besselY(v,x)} is the Bessel function of the second kind,{} \\spad{Y(v,x)}. This function satisfies the differential equation: \\indented{2}{\\spad{x^2 w''(x) + x w'(x) + (x^2-v^2)w(x) = 0}.} Note: The default implmentation uses the relation \\indented{2}{\\spad{Y(v,x) = (J(v,x) cos(v*\\%pi) - J(-v,x))/sin(v*\\%pi)}} so is not valid for integer values of \\spad{v}.") (((|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|)) "\\spad{besselY(v,x)} is the Bessel function of the second kind,{} \\spad{Y(v,x)}. This function satisfies the differential equation: \\indented{2}{\\spad{x^2 w''(x) + x w'(x) + (x^2-v^2)w(x) = 0}.} Note: The default implmentation uses the relation \\indented{2}{\\spad{Y(v,x) = (J(v,x) cos(v*\\%pi) - J(-v,x))/sin(v*\\%pi)}} so is not valid for integer values of \\spad{v}.")) (|besselJ| (((|Complex| (|DoubleFloat|)) (|Complex| (|DoubleFloat|)) (|Complex| (|DoubleFloat|))) "\\spad{besselJ(v,x)} is the Bessel function of the first kind,{} \\spad{J(v,x)}. This function satisfies the differential equation: \\indented{2}{\\spad{x^2 w''(x) + x w'(x) + (x^2-v^2)w(x) = 0}.}") (((|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|)) "\\spad{besselJ(v,x)} is the Bessel function of the first kind,{} \\spad{J(v,x)}. This function satisfies the differential equation: \\indented{2}{\\spad{x^2 w''(x) + x w'(x) + (x^2-v^2)w(x) = 0}.}")) (|polygamma| (((|Complex| (|DoubleFloat|)) (|NonNegativeInteger|) (|Complex| (|DoubleFloat|))) "\\spad{polygamma(n, x)} is the \\spad{n}-th derivative of \\spad{digamma(x)}.") (((|DoubleFloat|) (|NonNegativeInteger|) (|DoubleFloat|)) "\\spad{polygamma(n, x)} is the \\spad{n}-th derivative of \\spad{digamma(x)}.")) (|digamma| (((|Complex| (|DoubleFloat|)) (|Complex| (|DoubleFloat|))) "\\spad{digamma(x)} is the function,{} \\spad{psi(x)},{} defined by \\indented{2}{\\spad{psi(x) = Gamma'(x)/Gamma(x)}.}") (((|DoubleFloat|) (|DoubleFloat|)) "\\spad{digamma(x)} is the function,{} \\spad{psi(x)},{} defined by \\indented{2}{\\spad{psi(x) = Gamma'(x)/Gamma(x)}.}")) (|logGamma| (((|Complex| (|DoubleFloat|)) (|Complex| (|DoubleFloat|))) "\\spad{logGamma(x)} is the natural log of \\spad{Gamma(x)}. This can often be computed even if \\spad{Gamma(x)} cannot.") (((|DoubleFloat|) (|DoubleFloat|)) "\\spad{logGamma(x)} is the natural log of \\spad{Gamma(x)}. This can often be computed even if \\spad{Gamma(x)} cannot.")) (|Beta| (((|Complex| (|DoubleFloat|)) (|Complex| (|DoubleFloat|)) (|Complex| (|DoubleFloat|))) "\\spad{Beta(x, y)} is the Euler beta function,{} \\spad{B(x,y)},{} defined by \\indented{2}{\\spad{Beta(x,y) = integrate(t^(x-1)*(1-t)^(y-1), t=0..1)}.} This is related to \\spad{Gamma(x)} by \\indented{2}{\\spad{Beta(x,y) = Gamma(x)*Gamma(y) / Gamma(x + y)}.}") (((|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|)) "\\spad{Beta(x, y)} is the Euler beta function,{} \\spad{B(x,y)},{} defined by \\indented{2}{\\spad{Beta(x,y) = integrate(t^(x-1)*(1-t)^(y-1), t=0..1)}.} This is related to \\spad{Gamma(x)} by \\indented{2}{\\spad{Beta(x,y) = Gamma(x)*Gamma(y) / Gamma(x + y)}.}")) (|Gamma| (((|Complex| (|DoubleFloat|)) (|Complex| (|DoubleFloat|))) "\\spad{Gamma(x)} is the Euler gamma function,{} \\spad{Gamma(x)},{} defined by \\indented{2}{\\spad{Gamma(x) = integrate(t^(x-1)*exp(-t), t=0..\\%infinity)}.}") (((|DoubleFloat|) (|DoubleFloat|)) "\\spad{Gamma(x)} is the Euler gamma function,{} \\spad{Gamma(x)},{} defined by \\indented{2}{\\spad{Gamma(x) = integrate(t^(x-1)*exp(-t), t=0..\\%infinity)}.}"))) @@ -847,7 +847,7 @@ NIL (-229 R) ((|constructor| (NIL "\\indented{1}{A Denavit-Hartenberg Matrix is a 4x4 Matrix of the form:} \\indented{1}{\\spad{nx ox ax px}} \\indented{1}{\\spad{ny oy ay py}} \\indented{1}{\\spad{nz oz az pz}} \\indented{2}{\\spad{0\\space{2}0\\space{2}0\\space{2}1}} (\\spad{n},{} \\spad{o},{} and a are the direction cosines)")) (|translate| (($ |#1| |#1| |#1|) "\\spad{translate(X,Y,Z)} returns a dhmatrix for translation by \\spad{X},{} \\spad{Y},{} and \\spad{Z}")) (|scale| (($ |#1| |#1| |#1|) "\\spad{scale(sx,sy,sz)} returns a dhmatrix for scaling in the \\spad{X},{} \\spad{Y} and \\spad{Z} directions")) (|rotatez| (($ |#1|) "\\spad{rotatez(r)} returns a dhmatrix for rotation about axis \\spad{Z} for \\spad{r} degrees")) (|rotatey| (($ |#1|) "\\spad{rotatey(r)} returns a dhmatrix for rotation about axis \\spad{Y} for \\spad{r} degrees")) (|rotatex| (($ |#1|) "\\spad{rotatex(r)} returns a dhmatrix for rotation about axis \\spad{X} for \\spad{r} degrees")) (|identity| (($) "\\spad{identity()} create the identity dhmatrix")) (* (((|Point| |#1|) $ (|Point| |#1|)) "\\spad{t*p} applies the dhmatrix \\spad{t} to point \\spad{p}"))) ((-4452 . T) (-4453 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1109))) (-2811 (-12 (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-868))))) (|HasCategory| |#1| (QUOTE (-311))) (|HasCategory| |#1| (QUOTE (-562))) (|HasAttribute| |#1| (QUOTE (-4454 "*"))) (|HasCategory| |#1| (QUOTE (-368))) (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-868))))) +((-12 (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1109))) (-3684 (-12 (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-868))))) (|HasCategory| |#1| (QUOTE (-311))) (|HasCategory| |#1| (QUOTE (-562))) (|HasAttribute| |#1| (QUOTE (-4454 "*"))) (|HasCategory| |#1| (QUOTE (-368))) (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-868))))) (-230 A S) ((|constructor| (NIL "A dictionary is an aggregate in which entries can be inserted,{} searched for and removed. Duplicates are thrown away on insertion. This category models the usual notion of dictionary which involves large amounts of data where copying is impractical. Principal operations are thus destructive (non-copying) ones."))) NIL @@ -884,22 +884,22 @@ 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 -(-239 S -2183 R) +(-239 S -2795 R) ((|constructor| (NIL "\\indented{2}{This category represents a finite cartesian product of a given type.} Many categorical properties are preserved under this construction.")) (* (($ $ |#3|) "\\spad{y * r} multiplies each component of the vector \\spad{y} by the element \\spad{r}.") (($ |#3| $) "\\spad{r * y} multiplies the element \\spad{r} times each component of the vector \\spad{y}.")) (|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 (-368))) (|HasCategory| |#3| (QUOTE (-799))) (|HasCategory| |#3| (QUOTE (-854))) (|HasAttribute| |#3| (QUOTE -4449)) (|HasCategory| |#3| (QUOTE (-174))) (|HasCategory| |#3| (QUOTE (-373))) (|HasCategory| |#3| (QUOTE (-732))) (|HasCategory| |#3| (QUOTE (-132))) (|HasCategory| |#3| (QUOTE (-25))) (|HasCategory| |#3| (QUOTE (-1058))) (|HasCategory| |#3| (QUOTE (-1109)))) -(-240 -2183 R) +(-240 -2795 R) ((|constructor| (NIL "\\indented{2}{This category represents a finite cartesian product of a given type.} Many categorical properties are preserved under this construction.")) (* (($ $ |#2|) "\\spad{y * r} multiplies each component of the vector \\spad{y} by the element \\spad{r}.") (($ |#2| $) "\\spad{r * y} multiplies the element \\spad{r} times each component of the vector \\spad{y}.")) (|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"))) ((-4446 |has| |#2| (-1058)) (-4447 |has| |#2| (-1058)) (-4449 |has| |#2| (-6 -4449)) ((-4454 "*") |has| |#2| (-174)) (-4452 . T)) NIL -(-241 -2183 A B) +(-241 -2795 A B) ((|constructor| (NIL "\\indented{2}{This package provides operations which all take as arguments} direct products of elements of some type \\spad{A} and functions from \\spad{A} to another type \\spad{B}. The operations all iterate over their vector argument and either return a value of type \\spad{B} or a direct product over \\spad{B}.")) (|map| (((|DirectProduct| |#1| |#3|) (|Mapping| |#3| |#2|) (|DirectProduct| |#1| |#2|)) "\\spad{map(f, v)} applies the function \\spad{f} to every element of the vector \\spad{v} producing a new vector containing the values.")) (|reduce| ((|#3| (|Mapping| |#3| |#2| |#3|) (|DirectProduct| |#1| |#2|) |#3|) "\\spad{reduce(func,vec,ident)} combines the elements in \\spad{vec} using the binary function \\spad{func}. Argument \\spad{ident} is returned if the vector is empty.")) (|scan| (((|DirectProduct| |#1| |#3|) (|Mapping| |#3| |#2| |#3|) (|DirectProduct| |#1| |#2|) |#3|) "\\spad{scan(func,vec,ident)} creates a new vector whose elements are the result of applying reduce to the binary function \\spad{func},{} increasing initial subsequences of the vector \\spad{vec},{} and the element \\spad{ident}."))) NIL NIL -(-242 -2183 R) +(-242 -2795 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."))) ((-4446 |has| |#2| (-1058)) (-4447 |has| |#2| (-1058)) (-4449 |has| |#2| (-6 -4449)) ((-4454 "*") |has| |#2| (-174)) (-4452 . T)) -((-2811 (-12 (|HasCategory| |#2| (QUOTE (-25))) (|HasCategory| |#2| (LIST (QUOTE -313) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-132))) (|HasCategory| |#2| (LIST (QUOTE -313) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-174))) (|HasCategory| |#2| (LIST (QUOTE -313) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-235))) (|HasCategory| |#2| (LIST (QUOTE -313) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-368))) (|HasCategory| |#2| (LIST (QUOTE -313) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-373))) (|HasCategory| |#2| (LIST (QUOTE -313) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-732))) (|HasCategory| |#2| (LIST (QUOTE -313) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-799))) (|HasCategory| |#2| (LIST (QUOTE -313) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-854))) (|HasCategory| |#2| (LIST (QUOTE -313) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-1058))) (|HasCategory| |#2| (LIST 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(|sayLength| (((|Integer|) (|List| (|String|))) "\\spad{sayLength(l)} returns the length of a list of strings \\spad{l} as an integer.") (((|Integer|) (|String|)) "\\spad{sayLength(s)} returns the length of a string \\spad{s} as an integer.")) (|say| (((|Void|) (|List| (|String|))) "\\spad{say(l)} sends a list of strings \\spad{l} to output.") (((|Void|) (|String|)) "\\spad{say(s)} sends a string \\spad{s} to output.")) (|center| (((|List| (|String|)) (|List| (|String|)) (|Integer|) (|String|)) "\\spad{center(l,i,s)} takes a list of strings \\spad{l},{} and centers them within a list of strings which is \\spad{i} characters long,{} in which the remaining spaces are filled with strings composed of as many repetitions as possible of the last string parameter \\spad{s}.") (((|String|) (|String|) (|Integer|) (|String|)) "\\spad{center(s,i,s)} takes the first string \\spad{s},{} and centers it within a string of length \\spad{i},{} in which the other elements of the string are composed of as many replications as possible of the second indicated string,{} \\spad{s} which must have a length greater than that of an empty string.")) (|copies| (((|String|) (|Integer|) (|String|)) "\\spad{copies(i,s)} will take a string \\spad{s} and create a new string composed of \\spad{i} copies of \\spad{s}.")) (|newLine| (((|String|)) "\\spad{newLine()} sends a new line command to output.")) (|bright| (((|List| (|String|)) (|List| (|String|))) "\\spad{bright(l)} sets the font property of a list of strings,{} \\spad{l},{} to bold-face type.") (((|List| (|String|)) (|String|)) "\\spad{bright(s)} sets the font property of the string \\spad{s} to bold-face type."))) NIL @@ -919,7 +919,7 @@ NIL (-247 S) ((|constructor| (NIL "This domain provides some nice functions on lists")) (|elt| (((|NonNegativeInteger|) $ "count") "\\axiom{\\spad{l}.\"count\"} returns the number of elements in \\axiom{\\spad{l}}.") (($ $ "sort") "\\axiom{\\spad{l}.sort} returns \\axiom{\\spad{l}} with elements sorted. Note: \\axiom{\\spad{l}.sort = sort(\\spad{l})}") (($ $ "unique") "\\axiom{\\spad{l}.unique} returns \\axiom{\\spad{l}} with duplicates removed. Note: \\axiom{\\spad{l}.unique = removeDuplicates(\\spad{l})}.")) (|datalist| (($ (|List| |#1|)) "\\spad{datalist(l)} creates a datalist from \\spad{l}"))) ((-4453 . T) (-4452 . T)) -((-2811 (-12 (|HasCategory| |#1| (QUOTE (-856))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|))))) (-2811 (-12 (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-868))))) (|HasCategory| |#1| (LIST (QUOTE -620) (QUOTE (-542)))) (-2811 (|HasCategory| |#1| (QUOTE (-856))) (|HasCategory| |#1| (QUOTE (-1109)))) (|HasCategory| |#1| (QUOTE (-856))) (|HasCategory| (-570) (QUOTE (-856))) (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-868)))) (-12 (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|))))) +((-3684 (-12 (|HasCategory| |#1| (QUOTE (-856))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|))))) (-3684 (-12 (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-868))))) (|HasCategory| |#1| (LIST (QUOTE -620) (QUOTE (-542)))) (-3684 (|HasCategory| |#1| (QUOTE (-856))) (|HasCategory| |#1| (QUOTE (-1109)))) (|HasCategory| |#1| (QUOTE (-856))) (|HasCategory| (-570) (QUOTE (-856))) (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-868)))) (-12 (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|))))) (-248 M) ((|constructor| (NIL "DiscreteLogarithmPackage implements help functions for discrete logarithms in monoids using small cyclic groups.")) (|shanksDiscLogAlgorithm| (((|Union| (|NonNegativeInteger|) "failed") |#1| |#1| (|NonNegativeInteger|)) "\\spad{shanksDiscLogAlgorithm(b,a,p)} computes \\spad{s} with \\spad{b**s = a} for assuming that \\spad{a} and \\spad{b} are elements in a 'small' cyclic group of order \\spad{p} by Shank\\spad{'s} algorithm. Note: this is a subroutine of the function \\spadfun{discreteLog}.")) (** ((|#1| |#1| (|Integer|)) "\\spad{x ** n} returns \\spad{x} raised to the integer power \\spad{n}"))) NIL @@ -927,7 +927,7 @@ NIL (-249 |vl| R) ((|constructor| (NIL "\\indented{2}{This type supports distributed multivariate polynomials} whose variables are from a user specified list of symbols. The coefficient ring may be non commutative,{} but the variables are assumed to commute. The term ordering is lexicographic specified by the variable list parameter with the most significant variable first in the list.")) 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(|reflect| (($ (|ConstructorCall| (|DomainConstructor|))) "\\spad{reflect cc} returns the domain object designated by the ConstructorCall syntax `cc'. The constructor implied by `cc' must be known to the system since it is instantiated.")) (|reify| (((|ConstructorCall| (|DomainConstructor|)) $) "\\spad{reify(d)} returns the abstract syntax for the domain \\spad{`x'}.")) (|constructor| (NIL "\\indented{1}{Author: Gabriel Dos Reis} Date Create: October 18,{} 2007. Date Last Updated: December 20,{} 2008. Basic Operations: coerce,{} reify Related Constructors: Type,{} Syntax,{} OutputForm Also See: Type,{} ConstructorCall") (((|DomainConstructor|) $) "\\spad{constructor(d)} returns the domain constructor that is instantiated to the domain object \\spad{`d'}."))) 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(QUOTE -907) (QUOTE (-1186))))) (-12 (|HasCategory| |#3| (QUOTE (-235))) (|HasCategory| |#3| (QUOTE (-1058)))) (-3684 (-12 (|HasCategory| |#3| (QUOTE (-235))) (|HasCategory| |#3| (QUOTE (-1058)))) (|HasCategory| |#3| (QUOTE (-732))) (-12 (|HasCategory| |#3| (QUOTE (-1058))) (|HasCategory| |#3| (LIST (QUOTE -645) (QUOTE (-570))))) (-12 (|HasCategory| |#3| (QUOTE (-1058))) (|HasCategory| |#3| (LIST (QUOTE -907) (QUOTE (-1186)))))) (-12 (|HasCategory| |#3| (QUOTE (-1109))) (|HasCategory| |#3| (LIST (QUOTE -1047) (QUOTE (-570))))) (-3684 (|HasCategory| |#3| (QUOTE (-1058))) (-12 (|HasCategory| |#3| (QUOTE (-1109))) (|HasCategory| |#3| (LIST (QUOTE -1047) (QUOTE (-570)))))) (-12 (|HasCategory| |#3| (LIST (QUOTE -1047) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasCategory| |#3| (QUOTE (-1109)))) (-3684 (|HasAttribute| |#3| (QUOTE -4449)) (-12 (|HasCategory| |#3| (QUOTE (-235))) (|HasCategory| |#3| (QUOTE (-1058)))) (-12 (|HasCategory| |#3| (QUOTE (-1058))) (|HasCategory| |#3| (LIST (QUOTE -645) (QUOTE (-570))))) (-12 (|HasCategory| |#3| (QUOTE (-1058))) (|HasCategory| |#3| (LIST (QUOTE -907) (QUOTE (-1186)))))) (|HasCategory| |#3| (QUOTE (-132))) (|HasCategory| |#3| (QUOTE (-25))) (|HasCategory| |#3| (LIST (QUOTE -619) (QUOTE (-868)))) (-12 (|HasCategory| |#3| (QUOTE (-1109))) (|HasCategory| |#3| (LIST (QUOTE -313) (|devaluate| |#3|))))) (-255 A R S V E) ((|constructor| (NIL "\\spadtype{DifferentialPolynomialCategory} is a category constructor specifying basic functions in an ordinary differential polynomial ring with a given ordered set of differential indeterminates. In addition,{} it implements defaults for the basic functions. The functions \\spadfun{order} and \\spadfun{weight} are extended from the set of derivatives of differential indeterminates to the set of differential polynomials. Other operations provided on differential polynomials are \\spadfun{leader},{} \\spadfun{initial},{} \\spadfun{separant},{} \\spadfun{differentialVariables},{} and \\spadfun{isobaric?}. Furthermore,{} if the ground ring is a differential ring,{} then evaluation (substitution of differential indeterminates by elements of the ground ring or by differential polynomials) is provided by \\spadfun{eval}. A convenient way of referencing derivatives is provided by the functions \\spadfun{makeVariable}. \\blankline To construct a domain using this constructor,{} one needs to provide a ground ring \\spad{R},{} an ordered set \\spad{S} of differential indeterminates,{} a ranking \\spad{V} on the set of derivatives of the differential indeterminates,{} and a set \\spad{E} of exponents in bijection with the set of differential monomials in the given differential indeterminates. \\blankline")) (|separant| (($ $) "\\spad{separant(p)} returns the partial derivative of the differential polynomial \\spad{p} with respect to its leader.")) (|initial| (($ $) "\\spad{initial(p)} returns the leading coefficient when the differential polynomial \\spad{p} is written as a univariate polynomial in its leader.")) (|leader| ((|#4| $) "\\spad{leader(p)} returns the derivative of the highest rank appearing in the differential polynomial \\spad{p} Note: an error occurs if \\spad{p} is in the ground ring.")) (|isobaric?| (((|Boolean|) $) "\\spad{isobaric?(p)} returns \\spad{true} if every differential monomial appearing in the differential polynomial \\spad{p} has same weight,{} and returns \\spad{false} otherwise.")) (|weight| (((|NonNegativeInteger|) $ |#3|) "\\spad{weight(p, s)} returns the maximum weight of all differential monomials appearing in the differential polynomial \\spad{p} when \\spad{p} is viewed as a differential polynomial in the differential indeterminate \\spad{s} alone.") (((|NonNegativeInteger|) $) "\\spad{weight(p)} returns the maximum weight of all differential monomials appearing in the differential polynomial \\spad{p}.")) (|weights| (((|List| (|NonNegativeInteger|)) $ |#3|) "\\spad{weights(p, s)} returns a list of weights of differential monomials appearing in the differential polynomial \\spad{p} when \\spad{p} is viewed as a differential polynomial in the differential indeterminate \\spad{s} alone.") (((|List| (|NonNegativeInteger|)) $) "\\spad{weights(p)} returns a list of weights of differential monomials appearing in differential polynomial \\spad{p}.")) (|degree| (((|NonNegativeInteger|) $ |#3|) "\\spad{degree(p, s)} returns the maximum degree of the differential polynomial \\spad{p} viewed as a differential polynomial in the differential indeterminate \\spad{s} alone.")) (|order| (((|NonNegativeInteger|) $) "\\spad{order(p)} returns the order of the differential polynomial \\spad{p},{} which is the maximum number of differentiations of a differential indeterminate,{} among all those appearing in \\spad{p}.") (((|NonNegativeInteger|) $ |#3|) "\\spad{order(p,s)} returns the order of the differential polynomial \\spad{p} in differential indeterminate \\spad{s}.")) (|differentialVariables| (((|List| |#3|) $) "\\spad{differentialVariables(p)} returns a list of differential indeterminates occurring in a differential polynomial \\spad{p}.")) (|makeVariable| (((|Mapping| $ (|NonNegativeInteger|)) $) "\\spad{makeVariable(p)} views \\spad{p} as an element of a differential ring,{} in such a way that the \\spad{n}-th derivative of \\spad{p} may be simply referenced as \\spad{z}.\\spad{n} where \\spad{z} \\spad{:=} makeVariable(\\spad{p}). Note: In the interpreter,{} \\spad{z} is given as an internal map,{} which may be ignored.") (((|Mapping| $ (|NonNegativeInteger|)) |#3|) "\\spad{makeVariable(s)} views \\spad{s} as a differential indeterminate,{} in such a way that the \\spad{n}-th derivative of \\spad{s} may be simply referenced as \\spad{z}.\\spad{n} where \\spad{z} :=makeVariable(\\spad{s}). Note: In the interpreter,{} \\spad{z} is given as an internal map,{} which may be ignored."))) NIL @@ -999,7 +999,7 @@ NIL (-267 R S V) ((|constructor| (NIL "\\spadtype{DifferentialSparseMultivariatePolynomial} implements an ordinary differential polynomial ring by combining a domain belonging to the category \\spadtype{DifferentialVariableCategory} with the domain \\spadtype{SparseMultivariatePolynomial}. \\blankline"))) (((-4454 "*") |has| |#1| (-174)) (-4445 |has| |#1| (-562)) (-4450 |has| |#1| (-6 -4450)) (-4447 . T) (-4446 . T) (-4449 . T)) -((|HasCategory| |#1| (QUOTE (-916))) (-2811 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-458))) (|HasCategory| |#1| (QUOTE (-562))) (|HasCategory| |#1| (QUOTE (-916)))) (-2811 (|HasCategory| |#1| (QUOTE (-458))) (|HasCategory| |#1| (QUOTE (-562))) (|HasCategory| |#1| (QUOTE (-916)))) (-2811 (|HasCategory| |#1| (QUOTE (-458))) (|HasCategory| |#1| (QUOTE (-916)))) (|HasCategory| |#1| (QUOTE (-562))) (|HasCategory| |#1| (QUOTE (-174))) (-2811 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-562)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -893) (QUOTE (-384)))) (|HasCategory| |#3| (LIST (QUOTE -893) (QUOTE (-384))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -893) (QUOTE (-570)))) (|HasCategory| |#3| (LIST (QUOTE -893) (QUOTE (-570))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -620) (LIST (QUOTE -899) (QUOTE (-384))))) (|HasCategory| |#3| (LIST (QUOTE -620) (LIST (QUOTE -899) (QUOTE (-384)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -620) (LIST (QUOTE -899) (QUOTE (-570))))) (|HasCategory| |#3| (LIST (QUOTE -620) (LIST (QUOTE -899) (QUOTE (-570)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -620) (QUOTE (-542)))) (|HasCategory| |#3| (LIST (QUOTE -620) (QUOTE (-542))))) (|HasCategory| |#1| (LIST (QUOTE -645) (QUOTE (-570)))) (|HasCategory| |#1| (QUOTE (-148))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasCategory| |#1| (LIST (QUOTE -1047) (QUOTE (-570)))) (-2811 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasCategory| |#1| (LIST (QUOTE -1047) (LIST (QUOTE -413) (QUOTE (-570)))))) (|HasCategory| |#1| (LIST (QUOTE -1047) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasCategory| |#1| (QUOTE (-235))) (|HasCategory| |#1| (LIST (QUOTE -907) (QUOTE (-1186)))) (|HasCategory| |#1| (QUOTE (-368))) (|HasAttribute| |#1| (QUOTE -4450)) (|HasCategory| |#1| (QUOTE (-458))) (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-916)))) (-2811 (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-916)))) (|HasCategory| |#1| (QUOTE (-146))))) +((|HasCategory| |#1| (QUOTE (-916))) (-3684 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-458))) (|HasCategory| |#1| (QUOTE (-562))) (|HasCategory| |#1| (QUOTE (-916)))) (-3684 (|HasCategory| |#1| (QUOTE (-458))) (|HasCategory| |#1| (QUOTE (-562))) (|HasCategory| |#1| (QUOTE (-916)))) (-3684 (|HasCategory| |#1| (QUOTE (-458))) (|HasCategory| |#1| (QUOTE (-916)))) (|HasCategory| |#1| (QUOTE (-562))) (|HasCategory| |#1| (QUOTE (-174))) (-3684 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-562)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -893) (QUOTE (-384)))) (|HasCategory| |#3| (LIST (QUOTE -893) (QUOTE (-384))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -893) (QUOTE (-570)))) (|HasCategory| |#3| (LIST (QUOTE -893) (QUOTE (-570))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -620) (LIST (QUOTE -899) (QUOTE (-384))))) (|HasCategory| |#3| (LIST (QUOTE -620) (LIST (QUOTE -899) (QUOTE (-384)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -620) (LIST (QUOTE -899) (QUOTE (-570))))) (|HasCategory| |#3| (LIST (QUOTE -620) (LIST (QUOTE -899) (QUOTE (-570)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -620) (QUOTE (-542)))) (|HasCategory| |#3| (LIST (QUOTE -620) (QUOTE (-542))))) (|HasCategory| |#1| (LIST (QUOTE -645) (QUOTE (-570)))) (|HasCategory| |#1| (QUOTE (-148))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasCategory| |#1| (LIST (QUOTE -1047) (QUOTE (-570)))) (-3684 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasCategory| |#1| (LIST (QUOTE -1047) (LIST (QUOTE -413) (QUOTE (-570)))))) (|HasCategory| |#1| (LIST (QUOTE -1047) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasCategory| |#1| (QUOTE (-235))) (|HasCategory| |#1| (LIST (QUOTE -907) (QUOTE (-1186)))) (|HasCategory| |#1| (QUOTE (-368))) (|HasAttribute| |#1| (QUOTE -4450)) (|HasCategory| |#1| (QUOTE (-458))) (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-916)))) (-3684 (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-916)))) (|HasCategory| |#1| (QUOTE (-146))))) (-268 A S) ((|constructor| (NIL "\\spadtype{DifferentialVariableCategory} constructs the set of derivatives of a given set of (ordinary) differential indeterminates. If \\spad{x},{}...,{}\\spad{y} is an ordered set of differential indeterminates,{} and the prime notation is used for differentiation,{} then the set of derivatives (including zero-th order) of the differential indeterminates is \\spad{x},{}\\spad{x'},{}\\spad{x''},{}...,{} \\spad{y},{}\\spad{y'},{}\\spad{y''},{}... (Note: in the interpreter,{} the \\spad{n}-th derivative of \\spad{y} is displayed as \\spad{y} with a subscript \\spad{n}.) This set is viewed as a set of algebraic indeterminates,{} totally ordered in a way compatible with differentiation and the given order on the differential indeterminates. Such a total order is called a ranking of the differential indeterminates. \\blankline A domain in this category is needed to construct a differential polynomial domain. Differential polynomials are ordered by a ranking on the derivatives,{} and by an order (extending the ranking) on on the set of differential monomials. One may thus associate a domain in this category with a ranking of the differential indeterminates,{} just as one associates a domain in the category \\spadtype{OrderedAbelianMonoidSup} with an ordering of the set of monomials in a set of algebraic indeterminates. The ranking is specified through the binary relation \\spadfun{<}. For example,{} one may define one derivative to be less than another by lexicographically comparing first the \\spadfun{order},{} then the given order of the differential indeterminates appearing in the derivatives. This is the default implementation. \\blankline The notion of weight generalizes that of degree. A polynomial domain may be made into a graded ring if a weight function is given on the set of indeterminates,{} Very often,{} a grading is the first step in ordering the set of monomials. For differential polynomial domains,{} this constructor provides a function \\spadfun{weight},{} which allows the assignment of a non-negative number to each derivative of a differential indeterminate. For example,{} one may define the weight of a derivative to be simply its \\spadfun{order} (this is the default assignment). This weight function can then be extended to the set of all differential polynomials,{} providing a graded ring structure.")) (|coerce| (($ |#2|) "\\spad{coerce(s)} returns \\spad{s},{} viewed as the zero-th order derivative of \\spad{s}.")) (|differentiate| (($ $ (|NonNegativeInteger|)) "\\spad{differentiate(v, n)} returns the \\spad{n}-th derivative of \\spad{v}.") (($ $) "\\spad{differentiate(v)} returns the derivative of \\spad{v}.")) (|weight| (((|NonNegativeInteger|) $) "\\spad{weight(v)} returns the weight of the derivative \\spad{v}.")) (|variable| ((|#2| $) "\\spad{variable(v)} returns \\spad{s} if \\spad{v} is any derivative of the differential indeterminate \\spad{s}.")) (|order| (((|NonNegativeInteger|) $) "\\spad{order(v)} returns \\spad{n} if \\spad{v} is the \\spad{n}-th derivative of any differential indeterminate.")) (|makeVariable| (($ |#2| (|NonNegativeInteger|)) "\\spad{makeVariable(s, n)} returns the \\spad{n}-th derivative of a differential indeterminate \\spad{s} as an algebraic indeterminate."))) NIL @@ -1044,11 +1044,11 @@ 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|) $) "\\spad{degree(x)} gives the numbers of 1\\spad{'s} in \\spad{x},{} \\spadignore{i.e.} the number of non-zero exponents in the basis element that \\spad{x} represents.")) (|coerce| (($ (|List| (|Integer|))) "\\spad{coerce(l)} converts a list of 0\\spad{'s} and 1\\spad{'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 -(-279 R -1385) +(-279 R -2968) ((|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 -(-280 R -1385) +(-280 R -2968) ((|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 @@ -1100,7 +1100,7 @@ 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 -(-293 S R |Mod| -1576 -2523 |exactQuo|) +(-293 S R |Mod| -2228 -3055 |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| $) "\\spad{modulus(x)} \\undocumented"))) ((-4445 . T) ((-4454 "*") . T) (-4446 . T) (-4447 . T) (-4449 . T)) NIL @@ -1122,21 +1122,21 @@ NIL NIL (-298 S) ((|constructor| (NIL "Equations as mathematical objects. All properties of the basis domain,{} \\spadignore{e.g.} being an abelian group are carried over the equation domain,{} by performing the structural operations on the left and on the right hand side.")) (|subst| (($ $ $) "\\spad{subst(eq1,eq2)} substitutes \\spad{eq2} into both sides of \\spad{eq1} the \\spad{lhs} of \\spad{eq2} should be a kernel")) (|inv| (($ $) "\\spad{inv(x)} returns the multiplicative inverse of \\spad{x}.")) (/ (($ $ $) "\\spad{e1/e2} produces a new equation by dividing the left and right hand sides of equations e1 and e2.")) (|factorAndSplit| (((|List| $) $) "\\spad{factorAndSplit(eq)} make the right hand side 0 and factors the new left hand side. Each factor is equated to 0 and put into the resulting list without repetitions.")) (|rightOne| (((|Union| $ "failed") $) "\\spad{rightOne(eq)} divides by the right hand side.") (((|Union| $ "failed") $) "\\spad{rightOne(eq)} divides by the right hand side,{} if possible.")) (|leftOne| (((|Union| $ "failed") $) "\\spad{leftOne(eq)} divides by the left hand side.") (((|Union| $ "failed") $) "\\spad{leftOne(eq)} divides by the left hand side,{} if possible.")) (* (($ $ |#1|) "\\spad{eqn*x} produces a new equation by multiplying both sides of equation eqn by \\spad{x}.") (($ |#1| $) "\\spad{x*eqn} produces a new equation by multiplying both sides of equation eqn by \\spad{x}.")) (- (($ $ |#1|) "\\spad{eqn-x} produces a new equation by subtracting \\spad{x} from both sides of equation eqn.") (($ |#1| $) "\\spad{x-eqn} produces a new equation by subtracting both sides of equation eqn from \\spad{x}.")) (|rightZero| (($ $) "\\spad{rightZero(eq)} subtracts the right hand side.")) (|leftZero| (($ $) "\\spad{leftZero(eq)} subtracts the left hand side.")) (+ (($ $ |#1|) "\\spad{eqn+x} produces a new equation by adding \\spad{x} to both sides of equation eqn.") (($ |#1| $) "\\spad{x+eqn} produces a new equation by adding \\spad{x} to both sides of equation eqn.")) (|eval| (($ $ (|List| $)) "\\spad{eval(eqn, [x1=v1, ... xn=vn])} replaces \\spad{xi} by \\spad{vi} in equation \\spad{eqn}.") (($ $ $) "\\spad{eval(eqn, x=f)} replaces \\spad{x} by \\spad{f} in equation \\spad{eqn}.")) (|map| (($ (|Mapping| |#1| |#1|) $) "\\spad{map(f,eqn)} constructs a new equation by applying \\spad{f} to both sides of \\spad{eqn}.")) (|rhs| ((|#1| $) "\\spad{rhs(eqn)} returns the right hand side of equation \\spad{eqn}.")) (|lhs| ((|#1| $) "\\spad{lhs(eqn)} returns the left hand side of equation \\spad{eqn}.")) (|swap| (($ $) "\\spad{swap(eq)} interchanges left and right hand side of equation \\spad{eq}.")) (|equation| (($ |#1| |#1|) "\\spad{equation(a,b)} creates an equation.")) 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Thus keys are considered equal only if they are the same instance of a structure."))) ((-4452 . T) (-4453 . T)) -((-12 (|HasCategory| (-2 (|:| -3679 |#1|) (|:| -1409 |#2|)) (QUOTE (-1109))) (|HasCategory| (-2 (|:| -3679 |#1|) (|:| -1409 |#2|)) (LIST (QUOTE -313) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -3679) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -1409) (|devaluate| |#2|)))))) (-2811 (|HasCategory| (-2 (|:| -3679 |#1|) (|:| -1409 |#2|)) (QUOTE (-1109))) (|HasCategory| |#2| (QUOTE (-1109)))) (-2811 (|HasCategory| (-2 (|:| -3679 |#1|) (|:| -1409 |#2|)) (QUOTE (-1109))) (|HasCategory| (-2 (|:| -3679 |#1|) (|:| -1409 |#2|)) (LIST (QUOTE -619) (QUOTE (-868)))) (|HasCategory| |#2| (QUOTE (-1109))) (|HasCategory| |#2| (LIST (QUOTE -619) (QUOTE (-868))))) (|HasCategory| (-2 (|:| -3679 |#1|) (|:| -1409 |#2|)) (LIST (QUOTE -620) (QUOTE (-542)))) (-12 (|HasCategory| |#2| (QUOTE (-1109))) (|HasCategory| |#2| (LIST (QUOTE -313) (|devaluate| |#2|)))) (|HasCategory| (-2 (|:| -3679 |#1|) (|:| -1409 |#2|)) (QUOTE (-1109))) (|HasCategory| |#1| (QUOTE (-856))) (|HasCategory| |#2| (QUOTE (-1109))) (-2811 (|HasCategory| (-2 (|:| -3679 |#1|) (|:| -1409 |#2|)) (LIST (QUOTE -619) (QUOTE (-868)))) (|HasCategory| |#2| (LIST (QUOTE -619) (QUOTE (-868))))) (|HasCategory| |#2| (LIST (QUOTE -619) (QUOTE (-868)))) (|HasCategory| (-2 (|:| -3679 |#1|) (|:| -1409 |#2|)) (LIST (QUOTE -619) (QUOTE (-868))))) +((-12 (|HasCategory| (-2 (|:| -4111 |#1|) (|:| -3117 |#2|)) (QUOTE (-1109))) (|HasCategory| (-2 (|:| -4111 |#1|) (|:| -3117 |#2|)) (LIST (QUOTE -313) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -4111) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -3117) (|devaluate| |#2|)))))) (-3684 (|HasCategory| (-2 (|:| -4111 |#1|) (|:| -3117 |#2|)) (QUOTE (-1109))) (|HasCategory| |#2| (QUOTE (-1109)))) (-3684 (|HasCategory| (-2 (|:| -4111 |#1|) (|:| -3117 |#2|)) (QUOTE (-1109))) (|HasCategory| (-2 (|:| -4111 |#1|) (|:| -3117 |#2|)) (LIST (QUOTE -619) (QUOTE (-868)))) (|HasCategory| |#2| (QUOTE (-1109))) (|HasCategory| |#2| (LIST (QUOTE -619) (QUOTE (-868))))) (|HasCategory| (-2 (|:| -4111 |#1|) (|:| -3117 |#2|)) (LIST (QUOTE -620) (QUOTE (-542)))) (-12 (|HasCategory| |#2| (QUOTE (-1109))) (|HasCategory| |#2| (LIST (QUOTE -313) (|devaluate| |#2|)))) (|HasCategory| (-2 (|:| -4111 |#1|) (|:| -3117 |#2|)) (QUOTE (-1109))) (|HasCategory| |#1| (QUOTE (-856))) (|HasCategory| |#2| (QUOTE (-1109))) (-3684 (|HasCategory| (-2 (|:| -4111 |#1|) (|:| -3117 |#2|)) (LIST (QUOTE -619) (QUOTE (-868)))) (|HasCategory| |#2| (LIST (QUOTE -619) (QUOTE (-868))))) (|HasCategory| |#2| (LIST (QUOTE -619) (QUOTE (-868)))) (|HasCategory| (-2 (|:| -4111 |#1|) (|:| -3117 |#2|)) (LIST (QUOTE -619) (QUOTE (-868))))) (-300) ((|constructor| (NIL "ErrorFunctions implements error functions callable from the system interpreter. Typically,{} these functions would be called in user functions. The simple forms of the functions take one argument which is either a string (an error message) or a list of strings which all together make up a message. The list can contain formatting codes (see below). The more sophisticated versions takes two arguments where the first argument is the name of the function from which the error was invoked and the second argument is either a string or a list of strings,{} as above. When you use the one argument version in an interpreter function,{} the system will automatically insert the name of the function as the new first argument. Thus in the user interpreter function \\indented{2}{\\spad{f x == if x < 0 then error \"negative argument\" else x}} the call to error will actually be of the form \\indented{2}{\\spad{error(\"f\",\"negative argument\")}} because the interpreter will have created a new first argument. \\blankline Formatting codes: error messages may contain the following formatting codes (they should either start or end a string or else have blanks around them): \\indented{3}{\\spad{\\%l}\\space{6}start a new line} \\indented{3}{\\spad{\\%b}\\space{6}start printing in a bold font (where available)} \\indented{3}{\\spad{\\%d}\\space{6}stop\\space{2}printing in a bold font (where available)} \\indented{3}{\\spad{ \\%ceon}\\space{2}start centering message lines} \\indented{3}{\\spad{\\%ceoff}\\space{2}stop\\space{2}centering message lines} \\indented{3}{\\spad{\\%rjon}\\space{3}start displaying lines \"ragged left\"} \\indented{3}{\\spad{\\%rjoff}\\space{2}stop\\space{2}displaying lines \"ragged left\"} \\indented{3}{\\spad{\\%i}\\space{6}indent\\space{3}following lines 3 additional spaces} \\indented{3}{\\spad{\\%u}\\space{6}unindent following lines 3 additional spaces} \\indented{3}{\\spad{\\%xN}\\space{5}insert \\spad{N} blanks (eg,{} \\spad{\\%x10} inserts 10 blanks)} \\blankline")) (|error| (((|Exit|) (|String|) (|List| (|String|))) "\\spad{error(nam,lmsg)} displays error messages \\spad{lmsg} preceded by a message containing the name \\spad{nam} of the function in which the error is contained.") (((|Exit|) (|String|) (|String|)) "\\spad{error(nam,msg)} displays error message \\spad{msg} preceded by a message containing the name \\spad{nam} of the function in which the error is contained.") (((|Exit|) (|List| (|String|))) "\\spad{error(lmsg)} displays error message \\spad{lmsg} and terminates.") (((|Exit|) (|String|)) "\\spad{error(msg)} displays error message \\spad{msg} and terminates."))) NIL NIL -(-301 -1385 S) +(-301 -2968 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 -(-302 E -1385) +(-302 E -2968) ((|constructor| (NIL "This package allows a mapping \\spad{E} \\spad{->} \\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 @@ -1184,7 +1184,7 @@ NIL ((|constructor| (NIL "This category provides \\spadfun{eval} operations. A domain may belong to this category if it is possible to make ``evaluation\\spad{''} 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 -(-314 -1385) +(-314 -2968) ((|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 @@ -1199,7 +1199,7 @@ NIL (-317 R FE |var| |cen|) ((|constructor| (NIL "UnivariatePuiseuxSeriesWithExponentialSingularity is a domain used to represent essential singularities of functions. Objects in this domain are quotients of sums,{} where each term in the sum is a univariate Puiseux series times the exponential of a univariate Puiseux series.")) (|coerce| (($ (|UnivariatePuiseuxSeries| |#2| |#3| |#4|)) "\\spad{coerce(f)} converts a \\spadtype{UnivariatePuiseuxSeries} to an \\spadtype{ExponentialExpansion}.")) (|limitPlus| (((|Union| (|OrderedCompletion| |#2|) "failed") $) "\\spad{limitPlus(f(var))} returns \\spad{limit(var -> a+,f(var))}."))) ((-4444 . T) (-4450 . T) (-4445 . T) ((-4454 "*") . T) (-4446 . T) (-4447 . T) (-4449 . T)) -((|HasCategory| (-1263 |#1| |#2| |#3| |#4|) (QUOTE (-916))) (|HasCategory| (-1263 |#1| |#2| |#3| |#4|) (LIST (QUOTE -1047) (QUOTE (-1186)))) (|HasCategory| (-1263 |#1| |#2| |#3| |#4|) (QUOTE (-146))) (|HasCategory| (-1263 |#1| |#2| |#3| |#4|) (QUOTE (-148))) (|HasCategory| (-1263 |#1| |#2| |#3| |#4|) (LIST (QUOTE -620) (QUOTE (-542)))) (|HasCategory| (-1263 |#1| |#2| |#3| |#4|) (QUOTE (-1031))) (|HasCategory| (-1263 |#1| |#2| |#3| |#4|) (QUOTE (-826))) (-2811 (|HasCategory| (-1263 |#1| |#2| |#3| |#4|) (QUOTE (-826))) (|HasCategory| (-1263 |#1| |#2| |#3| |#4|) (QUOTE (-856)))) (|HasCategory| (-1263 |#1| |#2| |#3| |#4|) (LIST (QUOTE -1047) (QUOTE (-570)))) (|HasCategory| (-1263 |#1| |#2| |#3| |#4|) (QUOTE (-1161))) (|HasCategory| (-1263 |#1| |#2| |#3| |#4|) (LIST (QUOTE -893) (QUOTE (-384)))) (|HasCategory| (-1263 |#1| |#2| |#3| |#4|) (LIST (QUOTE -893) (QUOTE (-570)))) (|HasCategory| (-1263 |#1| |#2| |#3| |#4|) (LIST (QUOTE -620) (LIST (QUOTE -899) (QUOTE (-384))))) (|HasCategory| (-1263 |#1| |#2| |#3| |#4|) (LIST (QUOTE -620) (LIST (QUOTE -899) (QUOTE (-570))))) (|HasCategory| (-1263 |#1| |#2| |#3| |#4|) (LIST (QUOTE -645) (QUOTE (-570)))) (|HasCategory| (-1263 |#1| |#2| |#3| |#4|) (QUOTE (-235))) (|HasCategory| (-1263 |#1| |#2| |#3| |#4|) (LIST (QUOTE -907) (QUOTE (-1186)))) (|HasCategory| (-1263 |#1| |#2| |#3| |#4|) (LIST (QUOTE -520) (QUOTE (-1186)) (LIST (QUOTE -1263) (|devaluate| |#1|) (|devaluate| |#2|) (|devaluate| |#3|) (|devaluate| |#4|)))) (|HasCategory| (-1263 |#1| |#2| |#3| |#4|) (LIST (QUOTE -313) (LIST (QUOTE -1263) (|devaluate| |#1|) (|devaluate| |#2|) (|devaluate| |#3|) (|devaluate| |#4|)))) (|HasCategory| (-1263 |#1| |#2| |#3| |#4|) (LIST (QUOTE -290) (LIST (QUOTE -1263) (|devaluate| |#1|) (|devaluate| |#2|) (|devaluate| |#3|) (|devaluate| |#4|)) (LIST (QUOTE -1263) (|devaluate| |#1|) (|devaluate| |#2|) (|devaluate| |#3|) (|devaluate| |#4|)))) (|HasCategory| (-1263 |#1| |#2| |#3| |#4|) (QUOTE (-311))) (|HasCategory| (-1263 |#1| |#2| |#3| |#4|) (QUOTE (-551))) (|HasCategory| (-1263 |#1| |#2| |#3| |#4|) (QUOTE (-856))) (-12 (|HasCategory| (-1263 |#1| |#2| |#3| |#4|) (QUOTE (-916))) (|HasCategory| $ (QUOTE (-146)))) (-2811 (|HasCategory| (-1263 |#1| |#2| |#3| |#4|) (QUOTE (-146))) (-12 (|HasCategory| (-1263 |#1| |#2| |#3| |#4|) (QUOTE (-916))) (|HasCategory| $ (QUOTE (-146)))))) +((|HasCategory| (-1263 |#1| |#2| |#3| |#4|) (QUOTE (-916))) (|HasCategory| (-1263 |#1| |#2| |#3| |#4|) (LIST (QUOTE -1047) (QUOTE (-1186)))) (|HasCategory| (-1263 |#1| |#2| |#3| |#4|) (QUOTE (-146))) (|HasCategory| (-1263 |#1| |#2| |#3| |#4|) (QUOTE (-148))) (|HasCategory| (-1263 |#1| |#2| |#3| |#4|) (LIST (QUOTE -620) (QUOTE (-542)))) (|HasCategory| (-1263 |#1| |#2| |#3| |#4|) (QUOTE (-1031))) (|HasCategory| (-1263 |#1| |#2| |#3| |#4|) (QUOTE (-826))) (-3684 (|HasCategory| (-1263 |#1| |#2| |#3| |#4|) (QUOTE (-826))) (|HasCategory| (-1263 |#1| |#2| |#3| |#4|) (QUOTE (-856)))) (|HasCategory| (-1263 |#1| |#2| |#3| |#4|) (LIST (QUOTE -1047) (QUOTE (-570)))) (|HasCategory| (-1263 |#1| |#2| |#3| |#4|) (QUOTE (-1161))) (|HasCategory| (-1263 |#1| |#2| |#3| |#4|) (LIST (QUOTE -893) (QUOTE (-384)))) (|HasCategory| (-1263 |#1| |#2| |#3| |#4|) (LIST (QUOTE -893) (QUOTE (-570)))) (|HasCategory| (-1263 |#1| |#2| |#3| |#4|) (LIST (QUOTE -620) (LIST (QUOTE -899) (QUOTE (-384))))) (|HasCategory| (-1263 |#1| |#2| |#3| |#4|) (LIST (QUOTE -620) (LIST (QUOTE -899) (QUOTE (-570))))) (|HasCategory| (-1263 |#1| |#2| |#3| |#4|) (LIST (QUOTE -645) (QUOTE (-570)))) (|HasCategory| (-1263 |#1| |#2| |#3| |#4|) (QUOTE (-235))) (|HasCategory| (-1263 |#1| |#2| |#3| |#4|) (LIST (QUOTE -907) (QUOTE (-1186)))) (|HasCategory| (-1263 |#1| |#2| |#3| |#4|) (LIST (QUOTE -520) (QUOTE (-1186)) (LIST (QUOTE -1263) (|devaluate| |#1|) (|devaluate| |#2|) (|devaluate| |#3|) (|devaluate| |#4|)))) (|HasCategory| (-1263 |#1| |#2| |#3| |#4|) (LIST (QUOTE -313) (LIST (QUOTE -1263) (|devaluate| |#1|) (|devaluate| |#2|) (|devaluate| |#3|) (|devaluate| |#4|)))) (|HasCategory| (-1263 |#1| |#2| |#3| |#4|) (LIST (QUOTE -290) (LIST (QUOTE -1263) (|devaluate| |#1|) (|devaluate| |#2|) (|devaluate| |#3|) (|devaluate| |#4|)) (LIST (QUOTE -1263) (|devaluate| |#1|) (|devaluate| |#2|) (|devaluate| |#3|) (|devaluate| |#4|)))) (|HasCategory| (-1263 |#1| |#2| |#3| |#4|) (QUOTE (-311))) (|HasCategory| (-1263 |#1| |#2| |#3| |#4|) (QUOTE (-551))) (|HasCategory| (-1263 |#1| |#2| |#3| |#4|) (QUOTE (-856))) (-12 (|HasCategory| (-1263 |#1| |#2| |#3| |#4|) (QUOTE (-916))) (|HasCategory| $ (QUOTE (-146)))) (-3684 (|HasCategory| (-1263 |#1| |#2| |#3| |#4|) (QUOTE (-146))) (-12 (|HasCategory| (-1263 |#1| |#2| |#3| |#4|) (QUOTE (-916))) (|HasCategory| $ (QUOTE (-146)))))) (-318 R S) ((|constructor| (NIL "Lifting of maps to Expressions. Date Created: 16 Jan 1989 Date Last Updated: 22 Jan 1990")) (|map| (((|Expression| |#2|) (|Mapping| |#2| |#1|) (|Expression| |#1|)) "\\spad{map(f, e)} applies \\spad{f} to all the constants appearing in \\spad{e}."))) NIL @@ -1210,9 +1210,9 @@ NIL NIL (-320 R) ((|constructor| (NIL "Expressions involving symbolic functions.")) (|squareFreePolynomial| (((|Factored| (|SparseUnivariatePolynomial| $)) (|SparseUnivariatePolynomial| $)) "\\spad{squareFreePolynomial(p)} \\undocumented{}")) (|factorPolynomial| (((|Factored| (|SparseUnivariatePolynomial| $)) (|SparseUnivariatePolynomial| $)) "\\spad{factorPolynomial(p)} \\undocumented{}")) (|simplifyPower| (($ $ (|Integer|)) "simplifyPower?(\\spad{f},{}\\spad{n}) \\undocumented{}")) (|number?| (((|Boolean|) $) "\\spad{number?(f)} tests if \\spad{f} is rational")) (|reduce| (($ $) "\\spad{reduce(f)} simplifies all the unreduced algebraic quantities present in \\spad{f} by applying their defining relations."))) -((-4449 -2811 (-2115 (|has| |#1| (-1058)) (|has| |#1| (-645 (-570)))) (-12 (|has| |#1| (-562)) (-2811 (-2115 (|has| |#1| (-1058)) (|has| |#1| (-645 (-570)))) (|has| |#1| (-1058)) (|has| |#1| (-479)))) (|has| |#1| (-1058)) (|has| |#1| (-479))) (-4447 |has| |#1| (-174)) (-4446 |has| |#1| (-174)) ((-4454 "*") |has| |#1| (-562)) (-4445 |has| |#1| (-562)) (-4450 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(-1121)))) (-3684 (|HasCategory| |#1| (QUOTE (-25))) (-12 (|HasCategory| |#1| (QUOTE (-1058))) (|HasCategory| |#1| (LIST (QUOTE -645) (QUOTE (-570)))))) (-3684 (|HasCategory| |#1| (QUOTE (-479))) (|HasCategory| |#1| (QUOTE (-1058)))) (-3684 (-12 (|HasCategory| |#1| (LIST (QUOTE -1047) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasCategory| |#1| (QUOTE (-562)))) (-12 (|HasCategory| |#1| (QUOTE (-562))) (|HasCategory| |#1| (LIST (QUOTE -1047) (QUOTE (-570)))))) (|HasCategory| |#1| (QUOTE (-25))) (|HasCategory| |#1| (QUOTE (-1121))) (|HasCategory| |#1| (LIST (QUOTE -1047) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasCategory| $ (QUOTE (-1058))) (|HasCategory| $ (LIST (QUOTE -1047) (QUOTE (-570))))) +(-321 R -2968) ((|constructor| (NIL "Taylor series solutions of explicit ODE\\spad{'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 @@ -1223,7 +1223,7 @@ NIL (-323 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."))) (((-4454 "*") |has| |#1| (-174)) (-4445 |has| |#1| (-562)) (-4450 |has| |#1| (-368)) (-4444 |has| |#1| (-368)) (-4446 . T) (-4447 . T) (-4449 . T)) -((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasCategory| |#1| (QUOTE (-562))) (|HasCategory| |#1| (QUOTE (-174))) (-2811 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-562)))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-148))) (-12 (|HasCategory| |#1| (LIST (QUOTE -907) (QUOTE (-1186)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -413) (QUOTE (-570))) (|devaluate| |#1|))))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -413) (QUOTE (-570))) (|devaluate| |#1|)))) (|HasCategory| (-413 (-570)) (QUOTE (-1121))) (|HasCategory| |#1| (QUOTE (-368))) (-2811 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-368))) (|HasCategory| |#1| (QUOTE (-562)))) (-2811 (|HasCategory| |#1| (QUOTE (-368))) (|HasCategory| |#1| (QUOTE (-562)))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -413) (QUOTE (-570)))))) (|HasSignature| |#1| (LIST (QUOTE -2940) (LIST (|devaluate| |#1|) (QUOTE (-1186)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -413) (QUOTE (-570)))))) (-2811 (-12 (|HasCategory| |#1| (LIST (QUOTE -29) (QUOTE (-570)))) (|HasCategory| |#1| (QUOTE (-966))) (|HasCategory| |#1| (QUOTE (-1212))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -413) (QUOTE (-570)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasSignature| |#1| (LIST (QUOTE -3655) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1186))))) (|HasSignature| |#1| (LIST (QUOTE -2421) (LIST (LIST (QUOTE -650) (QUOTE (-1186))) (|devaluate| |#1|))))))) +((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasCategory| |#1| (QUOTE (-562))) (|HasCategory| |#1| (QUOTE (-174))) (-3684 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-562)))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-148))) (-12 (|HasCategory| |#1| (LIST (QUOTE -907) (QUOTE (-1186)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -413) (QUOTE (-570))) (|devaluate| |#1|))))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -413) (QUOTE (-570))) (|devaluate| |#1|)))) (|HasCategory| (-413 (-570)) (QUOTE (-1121))) (|HasCategory| |#1| (QUOTE (-368))) (-3684 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-368))) (|HasCategory| |#1| (QUOTE (-562)))) (-3684 (|HasCategory| |#1| (QUOTE (-368))) (|HasCategory| |#1| (QUOTE (-562)))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -413) (QUOTE (-570)))))) (|HasSignature| |#1| (LIST (QUOTE -2838) (LIST (|devaluate| |#1|) (QUOTE (-1186)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -413) (QUOTE (-570)))))) (-3684 (-12 (|HasCategory| |#1| (LIST (QUOTE -29) (QUOTE (-570)))) (|HasCategory| |#1| (QUOTE (-966))) (|HasCategory| |#1| (QUOTE (-1212))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -413) (QUOTE (-570)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasSignature| |#1| (LIST (QUOTE -2502) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1186))))) (|HasSignature| |#1| (LIST (QUOTE -1624) (LIST (LIST (QUOTE -650) (QUOTE (-1186))) (|devaluate| |#1|))))))) (-324 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},{}...,{}\\spad{rm} are distinct factors of \\spad{f},{} each of which has an exponent smaller than \\spad{p} in \\spad{f}."))) NIL @@ -1255,12 +1255,12 @@ NIL (-331 S) ((|constructor| (NIL "\\indented{1}{A FlexibleArray is the notion of an array intended to allow for growth} at the end only. Hence the following efficient operations \\indented{2}{\\spad{append(x,a)} meaning append item \\spad{x} at the end of the array \\spad{a}} \\indented{2}{\\spad{delete(a,n)} meaning delete the last item from the array \\spad{a}} Flexible arrays support the other operations inherited from \\spadtype{ExtensibleLinearAggregate}. However,{} these are not efficient. Flexible arrays combine the \\spad{O(1)} access time property of arrays with growing and shrinking at the end in \\spad{O(1)} (average) time. This is done by using an ordinary array which may have zero or more empty slots at the end. When the array becomes full it is copied into a new larger (50\\% larger) array. Conversely,{} when the array becomes less than 1/2 full,{} it is copied into a smaller array. Flexible arrays provide for an efficient implementation of many data structures in particular heaps,{} stacks and sets."))) ((-4453 . T) (-4452 . T)) -((-2811 (-12 (|HasCategory| |#1| (QUOTE (-856))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|))))) (-2811 (-12 (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-868))))) (|HasCategory| |#1| (LIST (QUOTE -620) (QUOTE (-542)))) (-2811 (|HasCategory| |#1| (QUOTE (-856))) (|HasCategory| |#1| (QUOTE (-1109)))) (|HasCategory| |#1| (QUOTE (-856))) (|HasCategory| (-570) (QUOTE (-856))) (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-868)))) (-12 (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|))))) -(-332 S -1385) +((-3684 (-12 (|HasCategory| |#1| (QUOTE (-856))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|))))) (-3684 (-12 (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-868))))) (|HasCategory| |#1| (LIST (QUOTE -620) (QUOTE (-542)))) (-3684 (|HasCategory| |#1| (QUOTE (-856))) (|HasCategory| |#1| (QUOTE (-1109)))) (|HasCategory| |#1| (QUOTE (-856))) (|HasCategory| (-570) (QUOTE (-856))) (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-868)))) (-12 (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|))))) +(-332 S -2968) ((|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})\\spad{\\$}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})\\spad{\\$}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**(\\spad{q**}(d*i)) for \\spad{i} in 0..\\spad{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},{}...,{}\\spad{vn} are the elements of the fixed basis.")) (|coordinates| (((|Matrix| |#2|) (|Vector| $)) "\\spad{coordinates([v1,...,vm])} returns the coordinates of the \\spad{vi}\\spad{'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| $) (|PositiveInteger|)) "\\spad{basis(n)} returns a fixed basis of a subfield of \\spad{\\$} as \\spad{F}-vectorspace.") (((|Vector| $)) "\\spad{basis()} returns a fixed basis of \\spad{\\$} as \\spad{F}-vectorspace."))) NIL ((|HasCategory| |#2| (QUOTE (-373)))) -(-333 -1385) +(-333 -2968) ((|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})\\spad{\\$}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})\\spad{\\$}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**(\\spad{q**}(d*i)) for \\spad{i} in 0..\\spad{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},{}...,{}\\spad{vn} are the elements of the fixed basis.")) (|coordinates| (((|Matrix| |#1|) (|Vector| $)) "\\spad{coordinates([v1,...,vm])} returns the coordinates of the \\spad{vi}\\spad{'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| $) (|PositiveInteger|)) "\\spad{basis(n)} returns a fixed basis of a subfield of \\spad{\\$} as \\spad{F}-vectorspace.") (((|Vector| $)) "\\spad{basis()} returns a fixed basis of \\spad{\\$} as \\spad{F}-vectorspace."))) ((-4444 . T) (-4450 . T) (-4445 . T) ((-4454 "*") . T) (-4446 . T) (-4447 . T) (-4449 . T)) NIL @@ -1284,15 +1284,15 @@ 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 -(-339 S -1385 UP UPUP R) +(-339 S -2968 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}\\spad{'s} are integers and the \\spad{P}\\spad{'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 \\spad{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 \\spad{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 -(-340 -1385 UP UPUP R) +(-340 -2968 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}\\spad{'s} are integers and the \\spad{P}\\spad{'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 \\spad{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 \\spad{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 -(-341 -1385 UP UPUP R) +(-341 -2968 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}\\spad{'s} are integers and the \\spad{P}\\spad{'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 @@ -1312,26 +1312,26 @@ NIL ((|constructor| (NIL "Lifts a map from rings to function fields over them.")) (|map| ((|#8| (|Mapping| |#5| |#1|) |#4|) "\\spad{map(f, p)} lifts \\spad{f} to \\spad{F1} and applies it to \\spad{p}."))) NIL NIL -(-346 S -1385 UP UPUP) +(-346 S -2968 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 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 (-373))) (|HasCategory| |#2| (QUOTE (-368)))) -(-347 -1385 UP UPUP) +(-347 -2968 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 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."))) ((-4445 |has| (-413 |#2|) (-368)) (-4450 |has| (-413 |#2|) (-368)) (-4444 |has| (-413 |#2|) (-368)) ((-4454 "*") . T) (-4446 . T) (-4447 . T) (-4449 . T)) NIL (-348 |p| |extdeg|) ((|constructor| (NIL "FiniteFieldCyclicGroup(\\spad{p},{}\\spad{n}) implements a finite field extension of degee \\spad{n} over the prime field with \\spad{p} elements. Its elements are represented by powers of a primitive element,{} \\spadignore{i.e.} a generator of the multiplicative (cyclic) group. As primitive element we choose the root of the extension polynomial,{} which is created by {\\em createPrimitivePoly} from \\spadtype{FiniteFieldPolynomialPackage}. The Zech logarithms are stored in a table of size half of the field size,{} and use \\spadtype{SingleInteger} for representing field elements,{} hence,{} there are restrictions on the size of the field.")) (|getZechTable| (((|PrimitiveArray| (|SingleInteger|))) "\\spad{getZechTable()} returns the zech logarithm table of the field. This table is used to perform additions in the field quickly."))) ((-4444 . T) (-4450 . T) (-4445 . T) ((-4454 "*") . T) (-4446 . T) (-4447 . T) (-4449 . T)) -((-2811 (|HasCategory| (-917 |#1|) (QUOTE (-146))) (|HasCategory| (-917 |#1|) (QUOTE (-373)))) (|HasCategory| (-917 |#1|) (QUOTE (-148))) (|HasCategory| (-917 |#1|) (QUOTE (-373))) (|HasCategory| (-917 |#1|) (QUOTE (-146)))) +((-3684 (|HasCategory| (-917 |#1|) (QUOTE (-146))) (|HasCategory| (-917 |#1|) (QUOTE (-373)))) (|HasCategory| (-917 |#1|) (QUOTE (-148))) (|HasCategory| (-917 |#1|) (QUOTE (-373))) (|HasCategory| (-917 |#1|) (QUOTE (-146)))) (-349 GF |defpol|) ((|constructor| (NIL "FiniteFieldCyclicGroupExtensionByPolynomial(\\spad{GF},{}defpol) implements a finite extension field of the ground field {\\em GF}. Its elements are represented by powers of a primitive element,{} \\spadignore{i.e.} a generator of the multiplicative (cyclic) group. As primitive element we choose the root of the extension polynomial {\\em defpol},{} which MUST be primitive (user responsibility). Zech logarithms are stored in a table of size half of the field size,{} and use \\spadtype{SingleInteger} for representing field elements,{} hence,{} there are restrictions on the size of the field.")) (|getZechTable| (((|PrimitiveArray| (|SingleInteger|))) "\\spad{getZechTable()} returns the zech logarithm table of the field it is used to perform additions in the field quickly."))) ((-4444 . T) (-4450 . T) (-4445 . T) ((-4454 "*") . T) (-4446 . T) (-4447 . T) (-4449 . T)) -((-2811 (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-373)))) (|HasCategory| |#1| (QUOTE (-148))) (|HasCategory| |#1| (QUOTE (-373))) (|HasCategory| |#1| (QUOTE (-146)))) +((-3684 (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-373)))) (|HasCategory| |#1| (QUOTE (-148))) (|HasCategory| |#1| (QUOTE (-373))) (|HasCategory| |#1| (QUOTE (-146)))) (-350 GF |extdeg|) ((|constructor| (NIL "FiniteFieldCyclicGroupExtension(\\spad{GF},{}\\spad{n}) implements a extension of degree \\spad{n} over the ground field {\\em GF}. Its elements are represented by powers of a primitive element,{} \\spadignore{i.e.} a generator of the multiplicative (cyclic) group. As primitive element we choose the root of the extension polynomial,{} which is created by {\\em createPrimitivePoly} from \\spadtype{FiniteFieldPolynomialPackage}. Zech logarithms are stored in a table of size half of the field size,{} and use \\spadtype{SingleInteger} for representing field elements,{} hence,{} there are restrictions on the size of the field.")) (|getZechTable| (((|PrimitiveArray| (|SingleInteger|))) "\\spad{getZechTable()} returns the zech logarithm table of the field. This table is used to perform additions in the field quickly."))) ((-4444 . T) (-4450 . T) (-4445 . T) ((-4454 "*") . T) (-4446 . T) (-4447 . T) (-4449 . T)) -((-2811 (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-373)))) (|HasCategory| |#1| (QUOTE (-148))) (|HasCategory| |#1| (QUOTE (-373))) (|HasCategory| |#1| (QUOTE (-146)))) +((-3684 (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-373)))) (|HasCategory| |#1| (QUOTE (-148))) (|HasCategory| |#1| (QUOTE (-373))) (|HasCategory| |#1| (QUOTE (-146)))) (-351 GF) ((|constructor| (NIL "FiniteFieldFunctions(\\spad{GF}) is a package with functions concerning finite extension fields of the finite ground field {\\em GF},{} \\spadignore{e.g.} Zech logarithms.")) (|createLowComplexityNormalBasis| (((|Union| (|SparseUnivariatePolynomial| |#1|) (|Vector| (|List| (|Record| (|:| |value| |#1|) (|:| |index| (|SingleInteger|)))))) (|PositiveInteger|)) "\\spad{createLowComplexityNormalBasis(n)} tries to find a a low complexity normal basis of degree {\\em n} over {\\em GF} and returns its multiplication matrix If no low complexity basis is found it calls \\axiomFunFrom{createNormalPoly}{FiniteFieldPolynomialPackage}(\\spad{n}) to produce a normal polynomial of degree {\\em n} over {\\em GF}")) (|createLowComplexityTable| (((|Union| (|Vector| (|List| (|Record| (|:| |value| |#1|) (|:| |index| (|SingleInteger|))))) "failed") (|PositiveInteger|)) "\\spad{createLowComplexityTable(n)} tries to find a low complexity normal basis of degree {\\em n} over {\\em GF} and returns its multiplication matrix Fails,{} if it does not find a low complexity basis")) (|sizeMultiplication| (((|NonNegativeInteger|) (|Vector| (|List| (|Record| (|:| |value| |#1|) (|:| |index| (|SingleInteger|)))))) "\\spad{sizeMultiplication(m)} returns the number of entries of the multiplication table {\\em m}.")) (|createMultiplicationMatrix| (((|Matrix| |#1|) (|Vector| (|List| (|Record| (|:| |value| |#1|) (|:| |index| (|SingleInteger|)))))) "\\spad{createMultiplicationMatrix(m)} forms the multiplication table {\\em m} into a matrix over the ground field.")) (|createMultiplicationTable| (((|Vector| (|List| (|Record| (|:| |value| |#1|) (|:| |index| (|SingleInteger|))))) (|SparseUnivariatePolynomial| |#1|)) "\\spad{createMultiplicationTable(f)} generates a multiplication table for the normal basis of the field extension determined by {\\em f}. This is needed to perform multiplications between elements represented as coordinate vectors to this basis. See \\spadtype{FFNBP},{} \\spadtype{FFNBX}.")) (|createZechTable| (((|PrimitiveArray| (|SingleInteger|)) (|SparseUnivariatePolynomial| |#1|)) "\\spad{createZechTable(f)} generates a Zech logarithm table for the cyclic group representation of a extension of the ground field by the primitive polynomial {\\em f(x)},{} \\spadignore{i.e.} \\spad{Z(i)},{} defined by {\\em x**Z(i) = 1+x**i} is stored at index \\spad{i}. This is needed in particular to perform addition of field elements in finite fields represented in this way. See \\spadtype{FFCGP},{} \\spadtype{FFCGX}."))) NIL @@ -1348,31 +1348,31 @@ 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|) $) "\\spad{primitive?(b)} tests whether the element \\spad{b} is a generator of the (cyclic) multiplicative group of the field,{} \\spadignore{i.e.} is a primitive element. Implementation Note: see \\spad{ch}.IX.1.3,{} th.2 in \\spad{D}. Lipson.")) (|primitiveElement| (($) "\\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."))) ((-4444 . T) (-4450 . T) (-4445 . T) ((-4454 "*") . T) (-4446 . T) (-4447 . T) (-4449 . T)) NIL -(-355 R UP -1385) +(-355 R UP -2968) ((|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 (-356 |p| |extdeg|) ((|constructor| (NIL "FiniteFieldNormalBasis(\\spad{p},{}\\spad{n}) implements a finite extension field of degree \\spad{n} over the prime field with \\spad{p} elements. The elements are represented by coordinate vectors with respect to a normal basis,{} \\spadignore{i.e.} a basis consisting of the conjugates (\\spad{q}-powers) of an element,{} in this case called normal element. This is chosen as a root of the extension polynomial created by \\spadfunFrom{createNormalPoly}{FiniteFieldPolynomialPackage}.")) (|sizeMultiplication| (((|NonNegativeInteger|)) "\\spad{sizeMultiplication()} returns the number of entries in the multiplication table of the field. Note: The time of multiplication of field elements depends on this size.")) (|getMultiplicationMatrix| (((|Matrix| (|PrimeField| |#1|))) "\\spad{getMultiplicationMatrix()} returns the multiplication table in form of a matrix.")) (|getMultiplicationTable| (((|Vector| (|List| (|Record| (|:| |value| (|PrimeField| |#1|)) (|:| |index| (|SingleInteger|)))))) "\\spad{getMultiplicationTable()} returns the multiplication table for the normal basis of the field. This table is used to perform multiplications between field elements."))) ((-4444 . T) (-4450 . T) (-4445 . T) ((-4454 "*") . T) (-4446 . T) (-4447 . T) (-4449 . T)) -((-2811 (|HasCategory| (-917 |#1|) (QUOTE (-146))) (|HasCategory| (-917 |#1|) (QUOTE (-373)))) (|HasCategory| (-917 |#1|) (QUOTE (-148))) (|HasCategory| (-917 |#1|) (QUOTE (-373))) (|HasCategory| (-917 |#1|) (QUOTE (-146)))) +((-3684 (|HasCategory| (-917 |#1|) (QUOTE (-146))) (|HasCategory| (-917 |#1|) (QUOTE (-373)))) (|HasCategory| (-917 |#1|) (QUOTE (-148))) (|HasCategory| (-917 |#1|) (QUOTE (-373))) (|HasCategory| (-917 |#1|) (QUOTE (-146)))) (-357 GF |uni|) ((|constructor| (NIL "FiniteFieldNormalBasisExtensionByPolynomial(\\spad{GF},{}uni) implements a finite extension of the ground field {\\em GF}. The elements are represented by coordinate vectors with respect to. a normal basis,{} \\spadignore{i.e.} a basis consisting of the conjugates (\\spad{q}-powers) of an element,{} in this case called normal element,{} where \\spad{q} is the size of {\\em GF}. The normal element is chosen as a root of the extension polynomial,{} which MUST be normal over {\\em GF} (user responsibility)")) (|sizeMultiplication| (((|NonNegativeInteger|)) "\\spad{sizeMultiplication()} returns the number of entries in the multiplication table of the field. Note: the time of multiplication of field elements depends on this size.")) (|getMultiplicationMatrix| (((|Matrix| |#1|)) "\\spad{getMultiplicationMatrix()} returns the multiplication table in form of a matrix.")) (|getMultiplicationTable| (((|Vector| (|List| (|Record| (|:| |value| |#1|) (|:| |index| (|SingleInteger|)))))) "\\spad{getMultiplicationTable()} returns the multiplication table for the normal basis of the field. This table is used to perform multiplications between field elements."))) ((-4444 . T) (-4450 . T) (-4445 . T) ((-4454 "*") . T) (-4446 . T) (-4447 . T) (-4449 . T)) -((-2811 (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-373)))) (|HasCategory| |#1| (QUOTE (-148))) (|HasCategory| |#1| (QUOTE (-373))) (|HasCategory| |#1| (QUOTE (-146)))) +((-3684 (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-373)))) (|HasCategory| |#1| (QUOTE (-148))) (|HasCategory| |#1| (QUOTE (-373))) (|HasCategory| |#1| (QUOTE (-146)))) (-358 GF |extdeg|) ((|constructor| (NIL "FiniteFieldNormalBasisExtensionByPolynomial(\\spad{GF},{}\\spad{n}) implements a finite extension field of degree \\spad{n} over the ground field {\\em GF}. The elements are represented by coordinate vectors with respect to a normal basis,{} \\spadignore{i.e.} a basis consisting of the conjugates (\\spad{q}-powers) of an element,{} in this case called normal element. This is chosen as a root of the extension polynomial,{} created by {\\em createNormalPoly} from \\spadtype{FiniteFieldPolynomialPackage}")) (|sizeMultiplication| (((|NonNegativeInteger|)) "\\spad{sizeMultiplication()} returns the number of entries in the multiplication table of the field. Note: the time of multiplication of field elements depends on this size.")) (|getMultiplicationMatrix| (((|Matrix| |#1|)) "\\spad{getMultiplicationMatrix()} returns the multiplication table in form of a matrix.")) (|getMultiplicationTable| (((|Vector| (|List| (|Record| (|:| |value| |#1|) (|:| |index| (|SingleInteger|)))))) "\\spad{getMultiplicationTable()} returns the multiplication table for the normal basis of the field. This table is used to perform multiplications between field elements."))) ((-4444 . T) (-4450 . T) (-4445 . T) ((-4454 "*") . T) (-4446 . T) (-4447 . T) (-4449 . T)) -((-2811 (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-373)))) (|HasCategory| |#1| (QUOTE (-148))) (|HasCategory| |#1| (QUOTE (-373))) (|HasCategory| |#1| (QUOTE (-146)))) +((-3684 (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-373)))) (|HasCategory| |#1| (QUOTE (-148))) (|HasCategory| |#1| (QUOTE (-373))) (|HasCategory| |#1| (QUOTE (-146)))) (-359 |p| |n|) ((|constructor| (NIL "FiniteField(\\spad{p},{}\\spad{n}) implements finite fields with p**n elements. This packages checks that \\spad{p} is prime. For a non-checking version,{} see \\spadtype{InnerFiniteField}."))) ((-4444 . T) (-4450 . T) (-4445 . T) ((-4454 "*") . T) (-4446 . T) (-4447 . T) (-4449 . T)) -((-2811 (|HasCategory| (-917 |#1|) (QUOTE (-146))) (|HasCategory| (-917 |#1|) (QUOTE (-373)))) (|HasCategory| (-917 |#1|) (QUOTE (-148))) (|HasCategory| (-917 |#1|) (QUOTE (-373))) (|HasCategory| (-917 |#1|) (QUOTE (-146)))) +((-3684 (|HasCategory| (-917 |#1|) (QUOTE (-146))) (|HasCategory| (-917 |#1|) (QUOTE (-373)))) (|HasCategory| (-917 |#1|) (QUOTE (-148))) (|HasCategory| (-917 |#1|) (QUOTE (-373))) (|HasCategory| (-917 |#1|) (QUOTE (-146)))) (-360 GF |defpol|) ((|constructor| (NIL "FiniteFieldExtensionByPolynomial(\\spad{GF},{} defpol) implements the extension of the finite field {\\em GF} generated by the extension polynomial {\\em defpol} which MUST be irreducible. Note: the user has the responsibility to ensure that {\\em defpol} is irreducible."))) ((-4444 . T) (-4450 . T) (-4445 . T) ((-4454 "*") . T) (-4446 . T) (-4447 . T) (-4449 . T)) -((-2811 (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-373)))) (|HasCategory| |#1| (QUOTE (-148))) (|HasCategory| |#1| (QUOTE (-373))) (|HasCategory| |#1| (QUOTE (-146)))) -(-361 -1385 GF) +((-3684 (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-373)))) (|HasCategory| |#1| (QUOTE (-148))) (|HasCategory| |#1| (QUOTE (-373))) (|HasCategory| |#1| (QUOTE (-146)))) +(-361 -2968 GF) ((|constructor| (NIL "FiniteFieldPolynomialPackage2(\\spad{F},{}\\spad{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 @@ -1380,14 +1380,14 @@ 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(\\spad{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(\\spad{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(\\spad{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(\\spad{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(\\spad{GF}) generates a normal polynomial of degree \\spad{n} over the finite field {\\em GF}.")) (|createPrimitivePoly| (((|SparseUnivariatePolynomial| |#1|) (|PositiveInteger|)) "\\spad{createPrimitivePoly(n)}\\$FFPOLY(\\spad{GF}) generates a primitive polynomial of degree \\spad{n} over the finite field {\\em GF}.")) (|createIrreduciblePoly| (((|SparseUnivariatePolynomial| |#1|) (|PositiveInteger|)) "\\spad{createIrreduciblePoly(n)}\\$FFPOLY(\\spad{GF}) generates a monic irreducible univariate polynomial of degree \\spad{n} over the finite field {\\em GF}.")) (|numberOfNormalPoly| (((|PositiveInteger|) (|PositiveInteger|)) "\\spad{numberOfNormalPoly(n)}\\$FFPOLY(\\spad{GF}) yields the number of normal polynomials of degree \\spad{n} over the finite field {\\em GF}.")) (|numberOfPrimitivePoly| (((|PositiveInteger|) (|PositiveInteger|)) "\\spad{numberOfPrimitivePoly(n)}\\$FFPOLY(\\spad{GF}) yields the number of primitive polynomials of degree \\spad{n} over the finite field {\\em GF}.")) (|numberOfIrreduciblePoly| (((|PositiveInteger|) (|PositiveInteger|)) "\\spad{numberOfIrreduciblePoly(n)}\\$FFPOLY(\\spad{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 -(-363 -1385 FP FPP) +(-363 -2968 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}\\spad{'s} exists."))) NIL NIL (-364 GF |n|) ((|constructor| (NIL "FiniteFieldExtensionByPolynomial(\\spad{GF},{} \\spad{n}) implements an extension of the finite field {\\em GF} of degree \\spad{n} generated by the extension polynomial constructed by \\spadfunFrom{createIrreduciblePoly}{FiniteFieldPolynomialPackage} from \\spadtype{FiniteFieldPolynomialPackage}."))) ((-4444 . T) (-4450 . T) (-4445 . T) ((-4454 "*") . T) (-4446 . T) (-4447 . T) (-4449 . T)) -((-2811 (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-373)))) (|HasCategory| |#1| (QUOTE (-148))) (|HasCategory| |#1| (QUOTE (-373))) (|HasCategory| |#1| (QUOTE (-146)))) +((-3684 (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-373)))) (|HasCategory| |#1| (QUOTE (-148))) (|HasCategory| |#1| (QUOTE (-373))) (|HasCategory| |#1| (QUOTE (-146)))) (-365 R |ls|) ((|constructor| (NIL "This is just an interface between several packages and domains. The goal is to compute lexicographical Groebner bases of sets of polynomial with type \\spadtype{Polynomial R} by the {\\em FGLM} algorithm if this is possible (\\spadignore{i.e.} if the input system generates a zero-dimensional ideal).")) (|groebner| (((|List| (|Polynomial| |#1|)) (|List| (|Polynomial| |#1|))) "\\axiom{groebner(\\spad{lq1})} returns the lexicographical Groebner basis of \\axiom{\\spad{lq1}}. If \\axiom{\\spad{lq1}} generates a zero-dimensional ideal then the {\\em FGLM} strategy is used,{} otherwise the {\\em Sugar} strategy is used.")) (|fglmIfCan| (((|Union| (|List| (|Polynomial| |#1|)) "failed") (|List| (|Polynomial| |#1|))) "\\axiom{fglmIfCan(\\spad{lq1})} returns the lexicographical Groebner basis of \\axiom{\\spad{lq1}} by using the {\\em FGLM} strategy,{} if \\axiom{zeroDimensional?(\\spad{lq1})} holds.")) (|zeroDimensional?| (((|Boolean|) (|List| (|Polynomial| |#1|))) "\\axiom{zeroDimensional?(\\spad{lq1})} returns \\spad{true} iff \\axiom{\\spad{lq1}} generates a zero-dimensional ideal \\spad{w}.\\spad{r}.\\spad{t}. the variables of \\axiom{\\spad{ls}}."))) NIL @@ -1466,7 +1466,7 @@ NIL NIL (-384) ((|constructor| (NIL "\\spadtype{Float} implements arbitrary precision floating point arithmetic. The number of significant digits of each operation can be set to an arbitrary value (the default is 20 decimal digits). The operation \\spad{float(mantissa,exponent,\\spadfunFrom{base}{FloatingPointSystem})} for integer \\spad{mantissa},{} \\spad{exponent} specifies the number \\spad{mantissa * \\spadfunFrom{base}{FloatingPointSystem} ** exponent} The underlying representation for floats is binary not decimal. The implications of this are described below. \\blankline The model adopted is that arithmetic operations are rounded to to nearest unit in the last place,{} that is,{} accurate to within \\spad{2**(-\\spadfunFrom{bits}{FloatingPointSystem})}. Also,{} the elementary functions and constants are accurate to one unit in the last place. A float is represented as a record of two integers,{} the mantissa and the exponent. The \\spadfunFrom{base}{FloatingPointSystem} of the representation is binary,{} hence a \\spad{Record(m:mantissa,e:exponent)} represents the number \\spad{m * 2 ** e}. Though it is not assumed that the underlying integers are represented with a binary \\spadfunFrom{base}{FloatingPointSystem},{} the code will be most efficient when this is the the case (this is \\spad{true} in most implementations of Lisp). The decision to choose the \\spadfunFrom{base}{FloatingPointSystem} to be binary has some unfortunate consequences. First,{} decimal numbers like 0.3 cannot be represented exactly. Second,{} there is a further loss of accuracy during conversion to decimal for output. To compensate for this,{} if \\spad{d} digits of precision are specified,{} \\spad{1 + ceiling(log2 d)} bits are used. Two numbers that are displayed identically may therefore be not equal. On the other hand,{} a significant efficiency loss would be incurred if we chose to use a decimal \\spadfunFrom{base}{FloatingPointSystem} when the underlying integer base is binary. \\blankline Algorithms used: For the elementary functions,{} the general approach is to apply identities so that the taylor series can be used,{} and,{} so that it will converge within \\spad{O( sqrt n )} steps. For example,{} using the identity \\spad{exp(x) = exp(x/2)**2},{} we can compute \\spad{exp(1/3)} to \\spad{n} digits of precision as follows. We have \\spad{exp(1/3) = exp(2 ** (-sqrt s) / 3) ** (2 ** sqrt s)}. The taylor series will converge in less than sqrt \\spad{n} steps and the exponentiation requires sqrt \\spad{n} multiplications for a total of \\spad{2 sqrt n} multiplications. Assuming integer multiplication costs \\spad{O( n**2 )} the overall running time is \\spad{O( sqrt(n) n**2 )}. This approach is the best known approach for precisions up to about 10,{}000 digits at which point the methods of Brent which are \\spad{O( log(n) n**2 )} become competitive. Note also that summing the terms of the taylor series for the elementary functions is done using integer operations. This avoids the overhead of floating point operations and results in efficient code at low precisions. This implementation makes no attempt to reuse storage,{} relying on the underlying system to do \\spadgloss{garbage collection}. \\spad{I} estimate that the efficiency of this package at low precisions could be improved by a factor of 2 if in-place operations were available. \\blankline Running times: in the following,{} \\spad{n} is the number of bits of precision \\indented{5}{\\spad{*},{} \\spad{/},{} \\spad{sqrt},{} \\spad{pi},{} \\spad{exp1},{} \\spad{log2},{} \\spad{log10}: \\spad{ O( n**2 )}} \\indented{5}{\\spad{exp},{} \\spad{log},{} \\spad{sin},{} \\spad{atan}:\\space{2}\\spad{ O( sqrt(n) n**2 )}} The other elementary functions are coded in terms of the ones above.")) (|outputSpacing| (((|Void|) (|NonNegativeInteger|)) "\\spad{outputSpacing(n)} inserts a space after \\spad{n} (default 10) digits on output; outputSpacing(0) means no spaces are inserted.")) (|outputGeneral| (((|Void|) (|NonNegativeInteger|)) "\\spad{outputGeneral(n)} sets the output mode to general notation with \\spad{n} significant digits displayed.") (((|Void|)) "\\spad{outputGeneral()} sets the output mode (default mode) to general notation; numbers will be displayed in either fixed or floating (scientific) notation depending on the magnitude.")) (|outputFixed| (((|Void|) (|NonNegativeInteger|)) "\\spad{outputFixed(n)} sets the output mode to fixed point notation,{} with \\spad{n} digits displayed after the decimal point.") (((|Void|)) "\\spad{outputFixed()} sets the output mode to fixed point notation; the output will contain a decimal point.")) (|outputFloating| (((|Void|) (|NonNegativeInteger|)) "\\spad{outputFloating(n)} sets the output mode to floating (scientific) notation with \\spad{n} significant digits displayed after the decimal point.") (((|Void|)) "\\spad{outputFloating()} sets the output mode to floating (scientific) notation,{} \\spadignore{i.e.} \\spad{mantissa * 10 exponent} is displayed as \\spad{0.mantissa E exponent}.")) (|atan| (($ $ $) "\\spad{atan(x,y)} computes the arc tangent from \\spad{x} with phase \\spad{y}.")) (|exp1| (($) "\\spad{exp1()} returns exp 1: \\spad{2.7182818284...}.")) (|log10| (($ $) "\\spad{log10(x)} computes the logarithm for \\spad{x} to base 10.") (($) "\\spad{log10()} returns \\spad{ln 10}: \\spad{2.3025809299...}.")) (|log2| (($ $) "\\spad{log2(x)} computes the logarithm for \\spad{x} to base 2.") (($) "\\spad{log2()} returns \\spad{ln 2},{} \\spadignore{i.e.} \\spad{0.6931471805...}.")) (|rationalApproximation| (((|Fraction| (|Integer|)) $ (|NonNegativeInteger|) (|NonNegativeInteger|)) "\\spad{rationalApproximation(f, n, b)} computes a rational approximation \\spad{r} to \\spad{f} with relative error \\spad{< b**(-n)},{} that is \\spad{|(r-f)/f| < b**(-n)}.") (((|Fraction| (|Integer|)) $ (|NonNegativeInteger|)) "\\spad{rationalApproximation(f, n)} computes a rational approximation \\spad{r} to \\spad{f} with relative error \\spad{< 10**(-n)}.")) (|shift| (($ $ (|Integer|)) "\\spad{shift(x,n)} adds \\spad{n} to the exponent of float \\spad{x}.")) (|relerror| (((|Integer|) $ $) "\\spad{relerror(x,y)} computes the absolute value of \\spad{x - y} divided by \\spad{y},{} when \\spad{y \\~= 0}.")) (|normalize| (($ $) "\\spad{normalize(x)} normalizes \\spad{x} at current precision.")) (** (($ $ $) "\\spad{x ** y} computes \\spad{exp(y log x)} where \\spad{x >= 0}.")) (/ (($ $ (|Integer|)) "\\spad{x / i} computes the division from \\spad{x} by an integer \\spad{i}."))) -((-4435 . T) (-4443 . T) (-3535 . T) (-4444 . T) (-4450 . T) (-4445 . T) ((-4454 "*") . T) (-4446 . T) (-4447 . T) (-4449 . T)) +((-4435 . T) (-4443 . T) (-3412 . T) (-4444 . T) (-4450 . T) (-4445 . T) ((-4454 "*") . T) (-4446 . T) (-4447 . T) (-4449 . T)) NIL (-385 |Par|) ((|constructor| (NIL "\\indented{3}{This is a package for the approximation of real solutions for} systems of polynomial equations over the rational numbers. The results are expressed as either rational numbers or floats depending on the type of the precision parameter which can be either a rational number or a floating point number.")) (|realRoots| (((|List| |#1|) (|Fraction| (|Polynomial| (|Integer|))) |#1|) "\\spad{realRoots(rf, eps)} finds the real zeros of a univariate rational function with precision given by eps.") (((|List| (|List| |#1|)) (|List| (|Fraction| (|Polynomial| (|Integer|)))) (|List| (|Symbol|)) |#1|) "\\spad{realRoots(lp,lv,eps)} computes the list of the real solutions of the list \\spad{lp} of rational functions with rational coefficients with respect to the variables in \\spad{lv},{} with precision \\spad{eps}. Each solution is expressed as a list of numbers in order corresponding to the variables in \\spad{lv}.")) (|solve| (((|List| (|Equation| (|Polynomial| |#1|))) (|Equation| (|Fraction| (|Polynomial| (|Integer|)))) |#1|) "\\spad{solve(eq,eps)} finds all of the real solutions of the univariate equation \\spad{eq} of rational functions with respect to the unique variables appearing in \\spad{eq},{} with precision \\spad{eps}.") (((|List| (|Equation| (|Polynomial| |#1|))) (|Fraction| (|Polynomial| (|Integer|))) |#1|) "\\spad{solve(p,eps)} finds all of the real solutions of the univariate rational function \\spad{p} with rational coefficients with respect to the unique variable appearing in \\spad{p},{} with precision \\spad{eps}.") (((|List| (|List| (|Equation| (|Polynomial| |#1|)))) (|List| (|Equation| (|Fraction| (|Polynomial| (|Integer|))))) |#1|) "\\spad{solve(leq,eps)} finds all of the real solutions of the system \\spad{leq} of equationas of rational functions with respect to all the variables appearing in \\spad{lp},{} with precision \\spad{eps}.") (((|List| (|List| (|Equation| (|Polynomial| |#1|)))) (|List| (|Fraction| (|Polynomial| (|Integer|)))) |#1|) "\\spad{solve(lp,eps)} finds all of the real solutions of the system \\spad{lp} of rational functions over the rational numbers with respect to all the variables appearing in \\spad{lp},{} with precision \\spad{eps}."))) @@ -1520,7 +1520,7 @@ 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 -(-398 -1385 UP UPUP R) +(-398 -2968 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 @@ -1544,11 +1544,11 @@ NIL ((|constructor| (NIL "provides an interface to the boot code for calling Fortran")) (|setLegalFortranSourceExtensions| (((|List| (|String|)) (|List| (|String|))) "\\spad{setLegalFortranSourceExtensions(l)} \\undocumented{}")) (|outputAsFortran| (((|Void|) (|FileName|)) "\\spad{outputAsFortran(fn)} \\undocumented{}")) (|linkToFortran| (((|SExpression|) (|Symbol|) (|List| (|Symbol|)) (|TheSymbolTable|) (|List| (|Symbol|))) "\\spad{linkToFortran(s,l,t,lv)} \\undocumented{}") (((|SExpression|) (|Symbol|) (|List| (|Union| (|:| |array| (|List| (|Symbol|))) (|:| |scalar| (|Symbol|)))) (|List| (|List| (|Union| (|:| |array| (|List| (|Symbol|))) (|:| |scalar| (|Symbol|))))) (|List| (|Symbol|)) (|Symbol|)) "\\spad{linkToFortran(s,l,ll,lv,t)} \\undocumented{}") (((|SExpression|) (|Symbol|) (|List| (|Union| (|:| |array| (|List| (|Symbol|))) (|:| |scalar| (|Symbol|)))) (|List| (|List| (|Union| (|:| |array| (|List| (|Symbol|))) (|:| |scalar| (|Symbol|))))) (|List| (|Symbol|))) "\\spad{linkToFortran(s,l,ll,lv)} \\undocumented{}"))) NIL NIL -(-404 -2058 |returnType| -4038 |symbols|) +(-404 -1800 |returnType| -4170 |symbols|) ((|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 -(-405 -1385 UP) +(-405 -2968 UP) ((|constructor| (NIL "\\indented{1}{Full partial fraction expansion of rational functions} Author: Manuel Bronstein Date Created: 9 December 1992 Date Last Updated: 6 October 1993 References: \\spad{M}.Bronstein & \\spad{B}.Salvy,{} \\indented{12}{Full Partial Fraction Decomposition of Rational Functions,{}} \\indented{12}{in Proceedings of ISSAC'93,{} Kiev,{} ACM Press.}")) (D (($ $ (|NonNegativeInteger|)) "\\spad{D(f, n)} returns the \\spad{n}-th derivative of \\spad{f}.") (($ $) "\\spad{D(f)} returns the derivative of \\spad{f}.")) (|differentiate| (($ $ (|NonNegativeInteger|)) "\\spad{differentiate(f, n)} returns the \\spad{n}-th derivative of \\spad{f}.") (($ $) "\\spad{differentiate(f)} returns the derivative of \\spad{f}.")) (|construct| (($ (|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| $) "\\spad{p + x} returns the sum of \\spad{p} and \\spad{x}"))) NIL NIL @@ -1570,7 +1570,7 @@ NIL ((|HasAttribute| |#1| (QUOTE -4435)) (|HasAttribute| |#1| (QUOTE -4443))) (-410) ((|constructor| (NIL "This category is intended as a model for floating point systems. A floating point system is a model for the real numbers. In fact,{} it is an approximation in the sense that not all real numbers are exactly representable by floating point numbers. A floating point system is characterized by the following: \\blankline \\indented{2}{1: \\spadfunFrom{base}{FloatingPointSystem} of the \\spadfunFrom{exponent}{FloatingPointSystem}.} \\indented{9}{(actual implemenations are usually binary or decimal)} \\indented{2}{2: \\spadfunFrom{precision}{FloatingPointSystem} of the \\spadfunFrom{mantissa}{FloatingPointSystem} (arbitrary or fixed)} \\indented{2}{3: rounding error for operations} \\blankline Because a Float is an approximation to the real numbers,{} even though it is defined to be a join of a Field and OrderedRing,{} some of the attributes do not hold. In particular associative(\\spad{\"+\"}) does not hold. Algorithms defined over a field need special considerations when the field is a floating point system.")) (|max| (($) "\\spad{max()} returns the maximum floating point number.")) (|min| (($) "\\spad{min()} returns the minimum floating point number.")) (|decreasePrecision| (((|PositiveInteger|) (|Integer|)) "\\spad{decreasePrecision(n)} decreases the current \\spadfunFrom{precision}{FloatingPointSystem} precision by \\spad{n} decimal digits.")) (|increasePrecision| (((|PositiveInteger|) (|Integer|)) "\\spad{increasePrecision(n)} increases the current \\spadfunFrom{precision}{FloatingPointSystem} by \\spad{n} decimal digits.")) (|precision| (((|PositiveInteger|) (|PositiveInteger|)) "\\spad{precision(n)} set the precision in the base to \\spad{n} decimal digits.") (((|PositiveInteger|)) "\\spad{precision()} returns the precision in digits base.")) (|digits| (((|PositiveInteger|) (|PositiveInteger|)) "\\spad{digits(d)} set the \\spadfunFrom{precision}{FloatingPointSystem} to \\spad{d} digits.") (((|PositiveInteger|)) "\\spad{digits()} returns ceiling\\spad{'s} precision in decimal digits.")) (|bits| (((|PositiveInteger|) (|PositiveInteger|)) "\\spad{bits(n)} set the \\spadfunFrom{precision}{FloatingPointSystem} to \\spad{n} bits.") (((|PositiveInteger|)) "\\spad{bits()} returns ceiling\\spad{'s} precision in bits.")) (|mantissa| (((|Integer|) $) "\\spad{mantissa(x)} returns the mantissa part of \\spad{x}.")) (|exponent| (((|Integer|) $) "\\spad{exponent(x)} returns the \\spadfunFrom{exponent}{FloatingPointSystem} part of \\spad{x}.")) (|base| (((|PositiveInteger|)) "\\spad{base()} returns the base of the \\spadfunFrom{exponent}{FloatingPointSystem}.")) (|order| (((|Integer|) $) "\\spad{order x} is the order of magnitude of \\spad{x}. Note: \\spad{base ** order x <= |x| < base ** (1 + order x)}.")) (|float| (($ (|Integer|) (|Integer|) (|PositiveInteger|)) "\\spad{float(a,e,b)} returns \\spad{a * b ** e}.") (($ (|Integer|) (|Integer|)) "\\spad{float(a,e)} returns \\spad{a * base() ** e}.")) (|approximate| ((|attribute|) "\\spad{approximate} means \"is an approximation to the real numbers\"."))) -((-3535 . T) (-4444 . T) (-4450 . T) (-4445 . T) ((-4454 "*") . T) (-4446 . T) (-4447 . T) (-4449 . T)) +((-3412 . T) (-4444 . T) (-4450 . T) (-4445 . T) ((-4454 "*") . T) (-4446 . T) (-4447 . T) (-4449 . T)) NIL (-411 R S) ((|constructor| (NIL "\\spadtype{FactoredFunctions2} contains functions that involve factored objects whose underlying domains may not be the same. For example,{} \\spadfun{map} might be used to coerce an object of type \\spadtype{Factored(Integer)} to \\spadtype{Factored(Complex(Integer))}.")) (|map| (((|Factored| |#2|) (|Mapping| |#2| |#1|) (|Factored| |#1|)) "\\spad{map(fn,u)} is used to apply the function \\userfun{\\spad{fn}} to every factor of \\spadvar{\\spad{u}}. The new factored object will have all its information flags set to \"nil\". This function is used,{} for example,{} to coerce every factor base to another type."))) @@ -1583,7 +1583,7 @@ NIL (-413 S) ((|constructor| (NIL "Fraction takes an IntegralDomain \\spad{S} and produces the domain of Fractions with numerators and denominators from \\spad{S}. If \\spad{S} is also a GcdDomain,{} then \\spad{gcd}\\spad{'s} between numerator and denominator will be cancelled during all operations.")) (|canonical| ((|attribute|) "\\spad{canonical} means that equal elements are in fact identical."))) ((-4439 -12 (|has| |#1| (-6 -4450)) (|has| |#1| (-458)) (|has| |#1| (-6 -4439))) (-4444 . T) (-4450 . T) (-4445 . T) ((-4454 "*") . T) (-4446 . T) (-4447 . T) (-4449 . T)) -((|HasCategory| |#1| (QUOTE (-916))) (|HasCategory| |#1| (LIST (QUOTE -1047) (QUOTE (-1186)))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-148))) (-2811 (-12 (|HasCategory| |#1| (QUOTE (-551))) (|HasCategory| |#1| (QUOTE (-834)))) (|HasCategory| |#1| (LIST (QUOTE -620) (QUOTE (-542))))) (|HasCategory| |#1| (QUOTE (-1031))) (|HasCategory| |#1| (QUOTE (-826))) (-2811 (|HasCategory| |#1| (QUOTE (-826))) (|HasCategory| |#1| (QUOTE (-856)))) (-2811 (-12 (|HasCategory| |#1| (QUOTE (-551))) (|HasCategory| |#1| (QUOTE (-834)))) (|HasCategory| |#1| (LIST (QUOTE -1047) (QUOTE (-570))))) (|HasCategory| |#1| (QUOTE (-1161))) (|HasCategory| |#1| (LIST (QUOTE -893) (QUOTE (-384)))) (-2811 (-12 (|HasCategory| |#1| (QUOTE (-551))) (|HasCategory| |#1| (QUOTE (-834)))) (|HasCategory| |#1| (LIST (QUOTE -893) (QUOTE (-570))))) (|HasCategory| |#1| (LIST (QUOTE -620) (LIST (QUOTE -899) (QUOTE (-384))))) (-2811 (|HasCategory| |#1| (LIST (QUOTE -620) (LIST (QUOTE -899) (QUOTE (-570))))) (-12 (|HasCategory| |#1| (QUOTE (-551))) (|HasCategory| |#1| (QUOTE (-834))))) (-2811 (|HasCategory| |#1| (LIST (QUOTE -645) (QUOTE (-570)))) (-12 (|HasCategory| |#1| (QUOTE (-551))) (|HasCategory| |#1| (QUOTE (-834))))) (|HasCategory| |#1| (QUOTE (-235))) (|HasCategory| |#1| (LIST (QUOTE -907) (QUOTE (-1186)))) (|HasCategory| |#1| (LIST (QUOTE -520) (QUOTE (-1186)) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -290) (|devaluate| |#1|) (|devaluate| |#1|))) (-12 (|HasCategory| |#1| (QUOTE (-551))) (|HasCategory| |#1| (QUOTE (-834)))) (|HasCategory| |#1| (QUOTE (-311))) (|HasCategory| |#1| (QUOTE (-551))) (-12 (|HasAttribute| |#1| (QUOTE -4450)) (|HasAttribute| |#1| (QUOTE -4439)) (|HasCategory| |#1| (QUOTE (-458)))) (|HasCategory| |#1| (LIST (QUOTE -620) (QUOTE (-542)))) (|HasCategory| |#1| (QUOTE (-856))) (|HasCategory| |#1| (LIST (QUOTE -1047) (QUOTE (-570)))) (|HasCategory| |#1| (LIST (QUOTE -893) (QUOTE (-570)))) (|HasCategory| |#1| (LIST (QUOTE -620) (LIST (QUOTE -899) (QUOTE (-570))))) (|HasCategory| |#1| (LIST (QUOTE -645) (QUOTE (-570)))) (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-916)))) (-2811 (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-916)))) (|HasCategory| |#1| (QUOTE (-146))))) +((|HasCategory| |#1| (QUOTE (-916))) (|HasCategory| |#1| (LIST (QUOTE -1047) (QUOTE (-1186)))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-148))) (-3684 (-12 (|HasCategory| |#1| (QUOTE (-551))) (|HasCategory| |#1| (QUOTE (-834)))) (|HasCategory| |#1| (LIST (QUOTE -620) (QUOTE (-542))))) (|HasCategory| |#1| (QUOTE (-1031))) (|HasCategory| |#1| (QUOTE (-826))) (-3684 (|HasCategory| |#1| (QUOTE (-826))) (|HasCategory| |#1| (QUOTE (-856)))) (-3684 (-12 (|HasCategory| |#1| (QUOTE (-551))) (|HasCategory| |#1| (QUOTE (-834)))) (|HasCategory| |#1| (LIST (QUOTE -1047) (QUOTE (-570))))) (|HasCategory| |#1| (QUOTE (-1161))) (|HasCategory| |#1| (LIST (QUOTE -893) (QUOTE (-384)))) (-3684 (-12 (|HasCategory| |#1| (QUOTE (-551))) (|HasCategory| |#1| (QUOTE (-834)))) (|HasCategory| |#1| (LIST (QUOTE -893) (QUOTE (-570))))) (|HasCategory| |#1| (LIST (QUOTE -620) (LIST (QUOTE -899) (QUOTE (-384))))) (-3684 (|HasCategory| |#1| (LIST (QUOTE -620) (LIST (QUOTE -899) (QUOTE (-570))))) (-12 (|HasCategory| |#1| (QUOTE (-551))) (|HasCategory| |#1| (QUOTE (-834))))) (-3684 (|HasCategory| |#1| (LIST (QUOTE -645) (QUOTE (-570)))) (-12 (|HasCategory| |#1| (QUOTE (-551))) (|HasCategory| |#1| (QUOTE (-834))))) (|HasCategory| |#1| (QUOTE (-235))) (|HasCategory| |#1| (LIST (QUOTE -907) (QUOTE (-1186)))) (|HasCategory| |#1| (LIST (QUOTE -520) (QUOTE (-1186)) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -290) (|devaluate| |#1|) (|devaluate| |#1|))) (-12 (|HasCategory| |#1| (QUOTE (-551))) (|HasCategory| |#1| (QUOTE (-834)))) (|HasCategory| |#1| (QUOTE (-311))) (|HasCategory| |#1| (QUOTE (-551))) (-12 (|HasAttribute| |#1| (QUOTE -4450)) (|HasAttribute| |#1| (QUOTE -4439)) (|HasCategory| |#1| (QUOTE (-458)))) (|HasCategory| |#1| (LIST (QUOTE -620) (QUOTE (-542)))) (|HasCategory| |#1| (QUOTE (-856))) (|HasCategory| |#1| (LIST (QUOTE -1047) (QUOTE (-570)))) (|HasCategory| |#1| (LIST (QUOTE -893) (QUOTE (-570)))) (|HasCategory| |#1| (LIST (QUOTE -620) (LIST (QUOTE -899) (QUOTE (-570))))) (|HasCategory| |#1| (LIST (QUOTE -645) (QUOTE (-570)))) (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-916)))) (-3684 (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-916)))) (|HasCategory| |#1| (QUOTE (-146))))) (-414 S R UP) ((|constructor| (NIL "A \\spadtype{FramedAlgebra} is a \\spadtype{FiniteRankAlgebra} together with a fixed \\spad{R}-module basis.")) (|regularRepresentation| (((|Matrix| |#2|) $) "\\spad{regularRepresentation(a)} returns the matrix of the linear map defined by left multiplication by \\spad{a} with respect to the fixed basis.")) (|discriminant| ((|#2|) "\\spad{discriminant()} = determinant(traceMatrix()).")) (|traceMatrix| (((|Matrix| |#2|)) "\\spad{traceMatrix()} is the \\spad{n}-by-\\spad{n} matrix ( \\spad{Tr(vi * vj)} ),{} where \\spad{v1},{} ...,{} \\spad{vn} are the elements of the fixed basis.")) (|convert| (($ (|Vector| |#2|)) "\\spad{convert([a1,..,an])} returns \\spad{a1*v1 + ... + an*vn},{} where \\spad{v1},{} ...,{} \\spad{vn} are the elements of the fixed basis.") (((|Vector| |#2|) $) "\\spad{convert(a)} returns the coordinates of \\spad{a} with respect to the fixed \\spad{R}-module basis.")) (|represents| (($ (|Vector| |#2|)) "\\spad{represents([a1,..,an])} returns \\spad{a1*v1 + ... + an*vn},{} where \\spad{v1},{} ...,{} \\spad{vn} are the elements of the fixed basis.")) (|coordinates| (((|Matrix| |#2|) (|Vector| $)) "\\spad{coordinates([v1,...,vm])} returns the coordinates of the \\spad{vi}\\spad{'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{R}-module basis.")) (|basis| (((|Vector| $)) "\\spad{basis()} returns the fixed \\spad{R}-module basis."))) NIL @@ -1604,11 +1604,11 @@ NIL ((|constructor| (NIL "\\indented{1}{Lifting of morphisms to fractional ideals.} Author: Manuel Bronstein Date Created: 1 Feb 1989 Date Last Updated: 27 Feb 1990 Keywords: ideal,{} algebra,{} module.")) (|map| (((|FractionalIdeal| |#5| |#6| |#7| |#8|) (|Mapping| |#5| |#1|) (|FractionalIdeal| |#1| |#2| |#3| |#4|)) "\\spad{map(f,i)} \\undocumented{}"))) NIL NIL -(-419 R -1385 UP A) +(-419 R -2968 UP A) ((|constructor| (NIL "Fractional ideals in a framed algebra.")) (|randomLC| ((|#4| (|NonNegativeInteger|) (|Vector| |#4|)) "\\spad{randomLC(n,x)} should be local but conditional.")) (|minimize| (($ $) "\\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)}."))) ((-4449 . T)) NIL -(-420 R -1385 UP A |ibasis|) +(-420 R -2968 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 -1047) (|devaluate| |#2|)))) @@ -1627,7 +1627,7 @@ NIL (-424 R) ((|constructor| (NIL "\\spadtype{Factored} creates a domain whose objects are kept in factored form as long as possible. Thus certain operations like multiplication and \\spad{gcd} are relatively easy to do. Others,{} like addition require somewhat more work,{} and unless the argument domain provides a factor function,{} the result may not be completely factored. Each object consists of a unit and a list of factors,{} where a factor has a member of \\spad{R} (the \"base\"),{} and exponent and a flag indicating what is known about the base. A flag may be one of \"nil\",{} \"sqfr\",{} \"irred\" or \"prime\",{} which respectively mean that nothing is known about the base,{} it is square-free,{} it is irreducible,{} or it is prime. The current restriction to integral domains allows simplification to be performed without worrying about multiplication order.")) (|rationalIfCan| (((|Union| (|Fraction| (|Integer|)) "failed") $) "\\spad{rationalIfCan(u)} returns a rational number if \\spad{u} really is one,{} and \"failed\" otherwise.")) (|rational| (((|Fraction| (|Integer|)) $) "\\spad{rational(u)} assumes spadvar{\\spad{u}} is actually a rational number and does the conversion to rational number (see \\spadtype{Fraction Integer}).")) (|rational?| (((|Boolean|) $) "\\spad{rational?(u)} tests if \\spadvar{\\spad{u}} is actually a rational number (see \\spadtype{Fraction Integer}).")) (|map| (($ (|Mapping| |#1| |#1|) $) "\\spad{map(fn,u)} maps the function \\userfun{\\spad{fn}} across the factors of \\spadvar{\\spad{u}} and creates a new factored object. Note: this clears the information flags (sets them to \"nil\") because the effect of \\userfun{\\spad{fn}} is clearly not known in general.")) (|unitNormalize| (($ $) "\\spad{unitNormalize(u)} normalizes the unit part of the factorization. For example,{} when working with factored integers,{} this operation will ensure that the bases are all positive integers.")) (|unit| ((|#1| $) "\\spad{unit(u)} extracts the unit part of the factorization.")) (|flagFactor| (($ |#1| (|Integer|) (|Union| "nil" "sqfr" "irred" "prime")) "\\spad{flagFactor(base,exponent,flag)} creates a factored object with a single factor whose \\spad{base} is asserted to be properly described by the information \\spad{flag}.")) (|sqfrFactor| (($ |#1| (|Integer|)) "\\spad{sqfrFactor(base,exponent)} creates a factored object with a single factor whose \\spad{base} is asserted to be square-free (flag = \"sqfr\").")) (|primeFactor| (($ |#1| (|Integer|)) "\\spad{primeFactor(base,exponent)} creates a factored object with a single factor whose \\spad{base} is asserted to be prime (flag = \"prime\").")) (|numberOfFactors| (((|NonNegativeInteger|) $) "\\spad{numberOfFactors(u)} returns the number of factors in \\spadvar{\\spad{u}}.")) (|nthFlag| (((|Union| "nil" "sqfr" "irred" "prime") $ (|Integer|)) "\\spad{nthFlag(u,n)} returns the information flag of the \\spad{n}th factor of \\spadvar{\\spad{u}}. If \\spadvar{\\spad{n}} is not a valid index for a factor (for example,{} less than 1 or too big),{} \"nil\" is returned.")) (|nthFactor| ((|#1| $ (|Integer|)) "\\spad{nthFactor(u,n)} returns the base of the \\spad{n}th factor of \\spadvar{\\spad{u}}. If \\spadvar{\\spad{n}} is not a valid index for a factor (for example,{} less than 1 or too big),{} 1 is returned. If \\spadvar{\\spad{u}} consists only of a unit,{} the unit is returned.")) (|nthExponent| (((|Integer|) $ (|Integer|)) "\\spad{nthExponent(u,n)} returns the exponent of the \\spad{n}th factor of \\spadvar{\\spad{u}}. If \\spadvar{\\spad{n}} is not a valid index for a factor (for example,{} less than 1 or too big),{} 0 is returned.")) (|irreducibleFactor| (($ |#1| (|Integer|)) "\\spad{irreducibleFactor(base,exponent)} creates a factored object with a single factor whose \\spad{base} is asserted to be irreducible (flag = \"irred\").")) (|factors| (((|List| (|Record| (|:| |factor| |#1|) (|:| |exponent| (|Integer|)))) $) "\\spad{factors(u)} returns a list of the factors in a form suitable for iteration. That is,{} it returns a list where each element is a record containing a base and exponent. The original object is the product of all the factors and the unit (which can be extracted by \\axiom{unit(\\spad{u})}).")) (|nilFactor| (($ |#1| (|Integer|)) "\\spad{nilFactor(base,exponent)} creates a factored object with a single factor with no information about the kind of \\spad{base} (flag = \"nil\").")) (|factorList| (((|List| (|Record| (|:| |flg| (|Union| "nil" "sqfr" "irred" "prime")) (|:| |fctr| |#1|) (|:| |xpnt| (|Integer|)))) $) "\\spad{factorList(u)} returns the list of factors with flags (for use by factoring code).")) (|makeFR| (($ |#1| (|List| (|Record| (|:| |flg| (|Union| "nil" "sqfr" "irred" "prime")) (|:| |fctr| |#1|) (|:| |xpnt| (|Integer|))))) "\\spad{makeFR(unit,listOfFactors)} creates a factored object (for use by factoring code).")) (|exponent| (((|Integer|) $) "\\spad{exponent(u)} returns the exponent of the first factor of \\spadvar{\\spad{u}},{} or 0 if the factored form consists solely of a unit.")) (|expand| ((|#1| $) "\\spad{expand(f)} multiplies the unit and factors together,{} yielding an \"unfactored\" object. Note: this is purposely not called \\spadfun{coerce} which would cause the interpreter to do this automatically."))) ((-4445 . T) ((-4454 "*") . T) (-4446 . T) (-4447 . T) (-4449 . T)) -((|HasCategory| |#1| (LIST (QUOTE -520) (QUOTE (-1186)) (QUOTE $))) (|HasCategory| |#1| (LIST (QUOTE -313) (QUOTE $))) (|HasCategory| |#1| (LIST (QUOTE -290) (QUOTE $) (QUOTE $))) (|HasCategory| |#1| (LIST (QUOTE -620) (QUOTE (-542)))) (|HasCategory| |#1| (QUOTE (-1231))) (-2811 (|HasCategory| |#1| (QUOTE (-458))) (|HasCategory| |#1| (QUOTE (-1231)))) (|HasCategory| |#1| (QUOTE (-1031))) (|HasCategory| |#1| (LIST (QUOTE -1047) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasCategory| |#1| (LIST (QUOTE -1047) (QUOTE (-570)))) (|HasCategory| |#1| (LIST (QUOTE -520) (QUOTE (-1186)) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|))) (-2811 (|HasCategory| |#1| (LIST (QUOTE -290) (|devaluate| |#1|) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -290) (QUOTE $) (QUOTE $)))) (|HasCategory| |#1| (LIST (QUOTE -290) (|devaluate| |#1|) (|devaluate| |#1|))) (|HasCategory| |#1| (QUOTE (-235))) (|HasCategory| |#1| (LIST (QUOTE -907) (QUOTE (-1186)))) (|HasCategory| |#1| (QUOTE (-551))) (|HasCategory| |#1| (QUOTE (-458)))) +((|HasCategory| |#1| (LIST (QUOTE -520) (QUOTE (-1186)) (QUOTE $))) (|HasCategory| |#1| (LIST (QUOTE -313) (QUOTE $))) (|HasCategory| |#1| (LIST (QUOTE -290) (QUOTE $) (QUOTE $))) (|HasCategory| |#1| (LIST (QUOTE -620) (QUOTE (-542)))) (|HasCategory| |#1| (QUOTE (-1231))) (-3684 (|HasCategory| |#1| (QUOTE (-458))) (|HasCategory| |#1| (QUOTE (-1231)))) (|HasCategory| |#1| (QUOTE (-1031))) (|HasCategory| |#1| (LIST (QUOTE -1047) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasCategory| |#1| (LIST (QUOTE -1047) (QUOTE (-570)))) (|HasCategory| |#1| (LIST (QUOTE -520) (QUOTE (-1186)) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|))) (-3684 (|HasCategory| |#1| (LIST (QUOTE -290) (|devaluate| |#1|) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -290) (QUOTE $) (QUOTE $)))) (|HasCategory| |#1| (LIST (QUOTE -290) (|devaluate| |#1|) (|devaluate| |#1|))) (|HasCategory| |#1| (QUOTE (-235))) (|HasCategory| |#1| (LIST (QUOTE -907) (QUOTE (-1186)))) (|HasCategory| |#1| (QUOTE (-551))) (|HasCategory| |#1| (QUOTE (-458)))) (-425 R) ((|constructor| (NIL "\\spadtype{FactoredFunctionUtilities} implements some utility functions for manipulating factored objects.")) (|mergeFactors| (((|Factored| |#1|) (|Factored| |#1|) (|Factored| |#1|)) "\\spad{mergeFactors(u,v)} is used when the factorizations of \\spadvar{\\spad{u}} and \\spadvar{\\spad{v}} are known to be disjoint,{} \\spadignore{e.g.} resulting from a content/primitive part split. Essentially,{} it creates a new factored object by multiplying the units together and appending the lists of factors.")) (|refine| (((|Factored| |#1|) (|Factored| |#1|) (|Mapping| (|Factored| |#1|) |#1|)) "\\spad{refine(u,fn)} is used to apply the function \\userfun{\\spad{fn}} to each factor of \\spadvar{\\spad{u}} and then build a new factored object from the results. For example,{} if \\spadvar{\\spad{u}} were created by calling \\spad{nilFactor(10,2)} then \\spad{refine(u,factor)} would create a factored object equal to that created by \\spad{factor(100)} or \\spad{primeFactor(2,2) * primeFactor(5,2)}."))) NIL @@ -1656,7 +1656,7 @@ NIL ((|constructor| (NIL "A finite-set aggregate models the notion of a finite set,{} that is,{} a collection of elements characterized by membership,{} but not by order or multiplicity. See \\spadtype{Set} for an example.")) (|min| ((|#1| $) "\\spad{min(u)} returns the smallest element of aggregate \\spad{u}.")) (|max| ((|#1| $) "\\spad{max(u)} returns the largest element of aggregate \\spad{u}.")) (|universe| (($) "\\spad{universe()}\\$\\spad{D} returns the universal set for finite set aggregate \\spad{D}.")) (|complement| (($ $) "\\spad{complement(u)} returns the complement of the set \\spad{u},{} \\spadignore{i.e.} the set of all values not in \\spad{u}.")) (|cardinality| (((|NonNegativeInteger|) $) "\\spad{cardinality(u)} returns the number of elements of \\spad{u}. Note: \\axiom{cardinality(\\spad{u}) = \\#u}."))) ((-4452 . T) (-4442 . T) (-4453 . T)) NIL -(-432 R -1385) +(-432 R -2968) ((|constructor| (NIL "\\spadtype{FunctionSpaceComplexIntegration} provides functions for the indefinite integration of complex-valued functions.")) (|complexIntegrate| ((|#2| |#2| (|Symbol|)) "\\spad{complexIntegrate(f, x)} returns the integral of \\spad{f(x)dx} where \\spad{x} is viewed as a complex variable.")) (|internalIntegrate0| (((|IntegrationResult| |#2|) |#2| (|Symbol|)) "\\spad{internalIntegrate0 should} be a local function,{} but is conditional.")) (|internalIntegrate| (((|IntegrationResult| |#2|) |#2| (|Symbol|)) "\\spad{internalIntegrate(f, x)} returns the integral of \\spad{f(x)dx} where \\spad{x} is viewed as a complex variable."))) NIL NIL @@ -1664,7 +1664,7 @@ NIL ((|constructor| (NIL "\\indented{1}{Author: James Davenport} Date Created: 17 April 1992 Date Last Updated: Basic Functions: Related Constructors: Also See: AMS Classifications: Keywords: References: Description:")) (|makeCos| (($ |#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"))) ((-4439 -12 (|has| |#1| (-6 -4439)) (|has| |#2| (-6 -4439))) (-4446 . T) (-4447 . T) (-4449 . T)) ((-12 (|HasAttribute| |#1| (QUOTE -4439)) (|HasAttribute| |#2| (QUOTE -4439)))) -(-434 R -1385) +(-434 R -2968) ((|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 @@ -1674,17 +1674,17 @@ NIL ((|HasCategory| |#2| (LIST (QUOTE -1047) (QUOTE (-570)))) (|HasCategory| |#2| (QUOTE (-562))) (|HasCategory| |#2| (QUOTE (-174))) (|HasCategory| |#2| (QUOTE (-146))) (|HasCategory| |#2| (QUOTE (-148))) (|HasCategory| |#2| (QUOTE (-1058))) (|HasCategory| |#2| (QUOTE (-21))) (|HasCategory| |#2| (QUOTE (-25))) (|HasCategory| |#2| (QUOTE (-479))) (|HasCategory| |#2| (QUOTE (-1121))) (|HasCategory| |#2| (LIST (QUOTE -620) (QUOTE (-542))))) (-436 R) ((|constructor| (NIL "A space of formal functions with arguments in an arbitrary ordered set.")) (|univariate| (((|Fraction| (|SparseUnivariatePolynomial| $)) $ (|Kernel| $)) "\\spad{univariate(f, k)} returns \\spad{f} viewed as a univariate fraction in \\spad{k}.")) (/ (($ (|SparseMultivariatePolynomial| |#1| (|Kernel| $)) (|SparseMultivariatePolynomial| |#1| (|Kernel| $))) "\\spad{p1/p2} returns the quotient of \\spad{p1} and \\spad{p2} as an element of \\%.")) (|denominator| (($ $) "\\spad{denominator(f)} returns the denominator of \\spad{f} converted to \\%.")) (|denom| (((|SparseMultivariatePolynomial| |#1| (|Kernel| $)) $) "\\spad{denom(f)} returns the denominator of \\spad{f} viewed as a polynomial in the kernels over \\spad{R}.")) (|convert| (($ (|Factored| $)) "\\spad{convert(f1\\^e1 ... fm\\^em)} returns \\spad{(f1)\\^e1 ... (fm)\\^em} as an element of \\%,{} using formal kernels created using a \\spadfunFrom{paren}{ExpressionSpace}.")) (|isPower| (((|Union| (|Record| (|:| |val| $) (|:| |exponent| (|Integer|))) "failed") $) "\\spad{isPower(p)} returns \\spad{[x, n]} if \\spad{p = x**n} and \\spad{n <> 0}.")) (|numerator| (($ $) "\\spad{numerator(f)} returns the numerator of \\spad{f} converted to \\%.")) (|numer| (((|SparseMultivariatePolynomial| |#1| (|Kernel| $)) $) "\\spad{numer(f)} returns the numerator of \\spad{f} viewed as a polynomial in the kernels over \\spad{R} if \\spad{R} is an integral domain. If not,{} then numer(\\spad{f}) = \\spad{f} viewed as a polynomial in the kernels over \\spad{R}.")) (|coerce| (($ (|Fraction| (|Polynomial| (|Fraction| |#1|)))) "\\spad{coerce(f)} returns \\spad{f} as an element of \\%.") (($ (|Polynomial| (|Fraction| |#1|))) "\\spad{coerce(p)} returns \\spad{p} as an element of \\%.") (($ (|Fraction| |#1|)) "\\spad{coerce(q)} returns \\spad{q} as an element of \\%.") (($ (|SparseMultivariatePolynomial| |#1| (|Kernel| $))) "\\spad{coerce(p)} returns \\spad{p} as an element of \\%.")) (|isMult| (((|Union| (|Record| (|:| |coef| (|Integer|)) (|:| |var| (|Kernel| $))) "failed") $) "\\spad{isMult(p)} returns \\spad{[n, x]} if \\spad{p = n * x} and \\spad{n <> 0}.")) (|isPlus| (((|Union| (|List| $) "failed") $) "\\spad{isPlus(p)} returns \\spad{[m1,...,mn]} if \\spad{p = m1 +...+ mn} and \\spad{n > 1}.")) (|isExpt| (((|Union| (|Record| (|:| |var| (|Kernel| $)) (|:| |exponent| (|Integer|))) "failed") $ (|Symbol|)) "\\spad{isExpt(p,f)} returns \\spad{[x, n]} if \\spad{p = x**n} and \\spad{n <> 0} and \\spad{x = f(a)}.") (((|Union| (|Record| (|:| |var| (|Kernel| $)) (|:| |exponent| (|Integer|))) "failed") $ (|BasicOperator|)) "\\spad{isExpt(p,op)} returns \\spad{[x, n]} if \\spad{p = x**n} and \\spad{n <> 0} and \\spad{x = op(a)}.") (((|Union| (|Record| (|:| |var| (|Kernel| $)) (|:| |exponent| (|Integer|))) "failed") $) "\\spad{isExpt(p)} returns \\spad{[x, n]} if \\spad{p = x**n} and \\spad{n <> 0}.")) (|isTimes| (((|Union| (|List| $) "failed") $) "\\spad{isTimes(p)} returns \\spad{[a1,...,an]} if \\spad{p = a1*...*an} and \\spad{n > 1}.")) (** (($ $ (|NonNegativeInteger|)) "\\spad{x**n} returns \\spad{x} * \\spad{x} * \\spad{x} * ... * \\spad{x} (\\spad{n} times).")) (|eval| (($ $ (|Symbol|) (|NonNegativeInteger|) (|Mapping| $ $)) "\\spad{eval(x, s, n, f)} replaces every \\spad{s(a)**n} in \\spad{x} by \\spad{f(a)} for any \\spad{a}.") (($ $ (|Symbol|) (|NonNegativeInteger|) (|Mapping| $ (|List| $))) "\\spad{eval(x, s, n, f)} replaces every \\spad{s(a1,...,am)**n} in \\spad{x} by \\spad{f(a1,...,am)} for any a1,{}...,{}am.") (($ $ (|List| (|Symbol|)) (|List| (|NonNegativeInteger|)) (|List| (|Mapping| $ (|List| $)))) "\\spad{eval(x, [s1,...,sm], [n1,...,nm], [f1,...,fm])} replaces every \\spad{si(a1,...,an)**ni} in \\spad{x} by \\spad{fi(a1,...,an)} for any a1,{}...,{}am.") (($ $ (|List| (|Symbol|)) (|List| (|NonNegativeInteger|)) (|List| (|Mapping| $ $))) "\\spad{eval(x, [s1,...,sm], [n1,...,nm], [f1,...,fm])} replaces every \\spad{si(a)**ni} in \\spad{x} by \\spad{fi(a)} for any \\spad{a}.") (($ $ (|List| (|BasicOperator|)) (|List| $) (|Symbol|)) "\\spad{eval(x, [s1,...,sm], [f1,...,fm], y)} replaces every \\spad{si(a)} in \\spad{x} by \\spad{fi(y)} with \\spad{y} replaced by \\spad{a} for any \\spad{a}.") (($ $ (|BasicOperator|) $ (|Symbol|)) "\\spad{eval(x, s, f, y)} replaces every \\spad{s(a)} in \\spad{x} by \\spad{f(y)} with \\spad{y} replaced by \\spad{a} for any \\spad{a}.") (($ $) "\\spad{eval(f)} unquotes all the quoted operators in \\spad{f}.") (($ $ (|List| (|Symbol|))) "\\spad{eval(f, [foo1,...,foon])} unquotes all the \\spad{fooi}\\spad{'s} in \\spad{f}.") (($ $ (|Symbol|)) "\\spad{eval(f, foo)} unquotes all the foo\\spad{'s} in \\spad{f}.")) (|applyQuote| (($ (|Symbol|) (|List| $)) "\\spad{applyQuote(foo, [x1,...,xn])} returns \\spad{'foo(x1,...,xn)}.") (($ (|Symbol|) $ $ $ $) "\\spad{applyQuote(foo, x, y, z, t)} returns \\spad{'foo(x,y,z,t)}.") (($ (|Symbol|) $ $ $) "\\spad{applyQuote(foo, x, y, z)} returns \\spad{'foo(x,y,z)}.") (($ (|Symbol|) $ $) "\\spad{applyQuote(foo, x, y)} returns \\spad{'foo(x,y)}.") (($ (|Symbol|) $) "\\spad{applyQuote(foo, x)} returns \\spad{'foo(x)}.")) (|variables| (((|List| (|Symbol|)) $) "\\spad{variables(f)} returns the list of all the variables of \\spad{f}.")) (|ground| ((|#1| $) "\\spad{ground(f)} returns \\spad{f} as an element of \\spad{R}. An error occurs if \\spad{f} is not an element of \\spad{R}.")) (|ground?| (((|Boolean|) $) "\\spad{ground?(f)} tests if \\spad{f} is an element of \\spad{R}."))) -((-4449 -2811 (|has| |#1| (-1058)) (|has| |#1| (-479))) (-4447 |has| |#1| (-174)) (-4446 |has| |#1| (-174)) ((-4454 "*") |has| |#1| (-562)) (-4445 |has| |#1| (-562)) (-4450 |has| |#1| (-562)) (-4444 |has| |#1| (-562))) +((-4449 -3684 (|has| |#1| (-1058)) (|has| |#1| (-479))) (-4447 |has| |#1| (-174)) (-4446 |has| |#1| (-174)) ((-4454 "*") |has| |#1| (-562)) (-4445 |has| |#1| (-562)) (-4450 |has| |#1| (-562)) (-4444 |has| |#1| (-562))) NIL -(-437 R -1385) +(-437 R -2968) ((|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 -(-438 R -1385) +(-438 R -2968) ((|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 a2 may involve \\spad{a1},{} but the minimal polynomial for \\spad{a1} may not involve 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)))) -(-439 R -1385) +(-439 R -2968) ((|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 @@ -1692,7 +1692,7 @@ 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 -(-441 R -1385 UP) +(-441 R -2968 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 -1047) (QUOTE (-48))))) @@ -1724,7 +1724,7 @@ 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\\spad{'s} criterion,{} \\spad{false} is inconclusive.")) (|useEisensteinCriterion| (((|Boolean|) (|Boolean|)) "\\spad{useEisensteinCriterion(b)} chooses whether factorizers check Eisenstein\\spad{'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\\spad{'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 -(-449 R UP -1385) +(-449 R UP -2968) ((|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 \\spad{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\\spad{'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\\spad{'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\\spad{'s} norm of \\spad{p}.") ((|#3| |#2|) "\\spad{bombieriNorm(p)} returns quadratic Bombieri\\spad{'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 @@ -1771,7 +1771,7 @@ NIL (-460 |vl| R E) ((|constructor| (NIL "\\indented{2}{This type supports distributed multivariate polynomials} whose variables are from a user specified list of symbols. The coefficient ring may be non commutative,{} but the variables are assumed to commute. The term ordering is specified by its third parameter. Suggested types which define term orderings include: \\spadtype{DirectProduct},{} \\spadtype{HomogeneousDirectProduct},{} \\spadtype{SplitHomogeneousDirectProduct} and finally \\spadtype{OrderedDirectProduct} which accepts an arbitrary user function to define a term ordering.")) (|reorder| (($ $ (|List| (|Integer|))) "\\spad{reorder(p, perm)} applies the permutation perm to the variables in a polynomial and returns the new correctly ordered polynomial"))) (((-4454 "*") |has| |#2| (-174)) (-4445 |has| |#2| (-562)) (-4450 |has| |#2| (-6 -4450)) (-4447 . T) (-4446 . T) (-4449 . T)) -((|HasCategory| |#2| (QUOTE (-916))) (-2811 (|HasCategory| |#2| (QUOTE (-174))) (|HasCategory| |#2| (QUOTE (-458))) (|HasCategory| |#2| (QUOTE (-562))) (|HasCategory| |#2| (QUOTE (-916)))) (-2811 (|HasCategory| |#2| (QUOTE (-458))) (|HasCategory| |#2| (QUOTE (-562))) (|HasCategory| |#2| (QUOTE (-916)))) (-2811 (|HasCategory| |#2| (QUOTE (-458))) (|HasCategory| |#2| (QUOTE (-916)))) (|HasCategory| |#2| (QUOTE (-562))) (|HasCategory| |#2| (QUOTE (-174))) (-2811 (|HasCategory| |#2| (QUOTE (-174))) (|HasCategory| |#2| (QUOTE (-562)))) (-12 (|HasCategory| (-870 |#1|) (LIST (QUOTE -893) (QUOTE (-384)))) (|HasCategory| |#2| (LIST (QUOTE -893) (QUOTE (-384))))) (-12 (|HasCategory| (-870 |#1|) (LIST (QUOTE -893) (QUOTE (-570)))) (|HasCategory| |#2| (LIST (QUOTE -893) (QUOTE (-570))))) (-12 (|HasCategory| (-870 |#1|) (LIST (QUOTE -620) (LIST (QUOTE -899) (QUOTE (-384))))) (|HasCategory| |#2| (LIST (QUOTE -620) (LIST (QUOTE -899) (QUOTE (-384)))))) (-12 (|HasCategory| (-870 |#1|) (LIST (QUOTE -620) (LIST (QUOTE -899) (QUOTE (-570))))) (|HasCategory| |#2| (LIST (QUOTE -620) (LIST (QUOTE -899) (QUOTE (-570)))))) (-12 (|HasCategory| (-870 |#1|) (LIST (QUOTE -620) (QUOTE (-542)))) (|HasCategory| |#2| (LIST (QUOTE -620) (QUOTE (-542))))) (|HasCategory| |#2| (LIST (QUOTE -645) (QUOTE (-570)))) (|HasCategory| |#2| (QUOTE (-148))) (|HasCategory| |#2| (QUOTE (-146))) (|HasCategory| |#2| (LIST (QUOTE -38) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasCategory| |#2| (LIST (QUOTE -1047) (QUOTE (-570)))) (-2811 (|HasCategory| |#2| (LIST (QUOTE -38) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasCategory| |#2| (LIST (QUOTE -1047) (LIST (QUOTE -413) (QUOTE (-570)))))) (|HasCategory| |#2| (LIST (QUOTE -1047) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasCategory| |#2| (QUOTE (-368))) (|HasAttribute| |#2| (QUOTE -4450)) (|HasCategory| |#2| (QUOTE (-458))) (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| |#2| (QUOTE (-916)))) (-2811 (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| |#2| (QUOTE (-916)))) (|HasCategory| |#2| (QUOTE (-146))))) +((|HasCategory| |#2| (QUOTE (-916))) (-3684 (|HasCategory| |#2| (QUOTE (-174))) (|HasCategory| |#2| (QUOTE (-458))) (|HasCategory| |#2| (QUOTE (-562))) (|HasCategory| |#2| (QUOTE (-916)))) (-3684 (|HasCategory| |#2| (QUOTE (-458))) (|HasCategory| |#2| (QUOTE (-562))) (|HasCategory| |#2| (QUOTE (-916)))) (-3684 (|HasCategory| |#2| (QUOTE (-458))) (|HasCategory| |#2| (QUOTE (-916)))) (|HasCategory| |#2| (QUOTE (-562))) (|HasCategory| |#2| (QUOTE (-174))) (-3684 (|HasCategory| |#2| (QUOTE (-174))) (|HasCategory| |#2| (QUOTE (-562)))) (-12 (|HasCategory| (-870 |#1|) (LIST (QUOTE -893) (QUOTE (-384)))) (|HasCategory| |#2| (LIST (QUOTE -893) (QUOTE (-384))))) (-12 (|HasCategory| (-870 |#1|) (LIST (QUOTE -893) (QUOTE (-570)))) (|HasCategory| |#2| (LIST (QUOTE -893) (QUOTE (-570))))) (-12 (|HasCategory| (-870 |#1|) (LIST (QUOTE -620) (LIST (QUOTE -899) (QUOTE (-384))))) (|HasCategory| |#2| (LIST (QUOTE -620) (LIST (QUOTE -899) (QUOTE (-384)))))) (-12 (|HasCategory| (-870 |#1|) (LIST (QUOTE -620) (LIST (QUOTE -899) (QUOTE (-570))))) (|HasCategory| |#2| (LIST (QUOTE -620) (LIST (QUOTE -899) (QUOTE (-570)))))) (-12 (|HasCategory| (-870 |#1|) (LIST (QUOTE -620) (QUOTE (-542)))) (|HasCategory| |#2| (LIST (QUOTE -620) (QUOTE (-542))))) (|HasCategory| |#2| (LIST (QUOTE -645) (QUOTE (-570)))) (|HasCategory| |#2| (QUOTE (-148))) (|HasCategory| |#2| (QUOTE (-146))) (|HasCategory| |#2| (LIST (QUOTE -38) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasCategory| |#2| (LIST (QUOTE -1047) (QUOTE (-570)))) (-3684 (|HasCategory| |#2| (LIST (QUOTE -38) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasCategory| |#2| (LIST (QUOTE -1047) (LIST (QUOTE -413) (QUOTE (-570)))))) (|HasCategory| |#2| (LIST (QUOTE -1047) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasCategory| |#2| (QUOTE (-368))) (|HasAttribute| |#2| (QUOTE -4450)) (|HasCategory| |#2| (QUOTE (-458))) (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| |#2| (QUOTE (-916)))) (-3684 (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| |#2| (QUOTE (-916)))) (|HasCategory| |#2| (QUOTE (-146))))) (-461 R BP) ((|constructor| (NIL "\\indented{1}{Author : \\spad{P}.Gianni.} January 1990 The equation \\spad{Af+Bg=h} and its generalization to \\spad{n} polynomials is solved for solutions over the \\spad{R},{} euclidean domain. A table containing the solutions of \\spad{Af+Bg=x**k} is used. The operations are performed modulus a prime which are in principle big enough,{} but the solutions are tested and,{} in case of failure,{} a hensel lifting process is used to get to the right solutions. It will be used in the factorization of multivariate polynomials over finite field,{} with \\spad{R=F[x]}.")) (|testModulus| (((|Boolean|) |#1| (|List| |#2|)) "\\spad{testModulus(p,lp)} returns \\spad{true} if the the prime \\spad{p} is valid for the list of polynomials \\spad{lp},{} \\spadignore{i.e.} preserves the degree and they remain relatively prime.")) (|solveid| (((|Union| (|List| |#2|) "failed") |#2| |#1| (|Vector| (|List| |#2|))) "\\spad{solveid(h,table)} computes the coefficients of the extended euclidean algorithm for a list of polynomials whose tablePow is \\spad{table} and with right side \\spad{h}.")) (|tablePow| (((|Union| (|Vector| (|List| |#2|)) "failed") (|NonNegativeInteger|) |#1| (|List| |#2|)) "\\spad{tablePow(maxdeg,prime,lpol)} constructs the table with the coefficients of the Extended Euclidean Algorithm for \\spad{lpol}. Here the right side is \\spad{x**k},{} for \\spad{k} less or equal to \\spad{maxdeg}. The operation returns \"failed\" when the elements are not coprime modulo \\spad{prime}.")) (|compBound| (((|NonNegativeInteger|) |#2| (|List| |#2|)) "\\spad{compBound(p,lp)} computes a bound for the coefficients of the solution polynomials. Given a polynomial right hand side \\spad{p},{} and a list \\spad{lp} of left hand side polynomials. Exported because it depends on the valuation.")) (|reduction| ((|#2| |#2| |#1|) "\\spad{reduction(p,prime)} reduces the polynomial \\spad{p} modulo \\spad{prime} of \\spad{R}. Note: this function is exported only because it\\spad{'s} conditional."))) NIL @@ -1836,7 +1836,7 @@ NIL ((|constructor| (NIL "GradedModule(\\spad{R},{}\\spad{E}) denotes ``E-graded \\spad{R}-module\\spad{''},{} \\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 -(-477 |lv| -1385 R) +(-477 |lv| -2968 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 @@ -1851,11 +1851,11 @@ NIL (-480 |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.")) (|differentiate| (($ $ (|Variable| |#2|)) "\\spad{differentiate(f(x),x)} returns the derivative of \\spad{f(x)} with respect to \\spad{x}.")) (|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."))) (((-4454 "*") |has| |#1| (-174)) (-4445 |has| |#1| (-562)) (-4450 |has| |#1| (-368)) (-4444 |has| |#1| (-368)) (-4446 . T) (-4447 . T) (-4449 . 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((-4453 . T)) -((-12 (|HasCategory| (-2 (|:| -3679 |#1|) (|:| -1409 |#2|)) (QUOTE (-1109))) (|HasCategory| (-2 (|:| -3679 |#1|) (|:| -1409 |#2|)) (LIST (QUOTE -313) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -3679) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -1409) (|devaluate| |#2|)))))) (-2811 (|HasCategory| (-2 (|:| -3679 |#1|) (|:| -1409 |#2|)) (QUOTE (-1109))) (|HasCategory| |#2| (QUOTE (-1109)))) (-2811 (|HasCategory| (-2 (|:| -3679 |#1|) (|:| -1409 |#2|)) (QUOTE (-1109))) (|HasCategory| (-2 (|:| -3679 |#1|) (|:| -1409 |#2|)) (LIST (QUOTE -619) (QUOTE (-868)))) (|HasCategory| |#2| (QUOTE (-1109))) (|HasCategory| |#2| (LIST (QUOTE -619) (QUOTE (-868))))) (|HasCategory| (-2 (|:| -3679 |#1|) (|:| -1409 |#2|)) (LIST (QUOTE -620) (QUOTE (-542)))) (-12 (|HasCategory| |#2| (QUOTE (-1109))) (|HasCategory| |#2| (LIST (QUOTE -313) (|devaluate| |#2|)))) (|HasCategory| |#1| (QUOTE (-856))) (-2811 (|HasCategory| (-2 (|:| -3679 |#1|) (|:| -1409 |#2|)) (LIST (QUOTE -619) (QUOTE (-868)))) (|HasCategory| |#2| (LIST (QUOTE -619) (QUOTE (-868))))) (|HasCategory| |#2| (QUOTE (-1109))) (|HasCategory| |#2| (LIST (QUOTE -619) (QUOTE (-868)))) (|HasCategory| (-2 (|:| -3679 |#1|) (|:| -1409 |#2|)) (LIST (QUOTE -619) (QUOTE (-868)))) (|HasCategory| (-2 (|:| -3679 |#1|) (|:| -1409 |#2|)) (QUOTE (-1109)))) +((-12 (|HasCategory| (-2 (|:| -4111 |#1|) (|:| -3117 |#2|)) (QUOTE (-1109))) (|HasCategory| (-2 (|:| -4111 |#1|) (|:| -3117 |#2|)) (LIST (QUOTE -313) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -4111) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -3117) (|devaluate| |#2|)))))) (-3684 (|HasCategory| (-2 (|:| -4111 |#1|) (|:| -3117 |#2|)) (QUOTE (-1109))) (|HasCategory| |#2| (QUOTE (-1109)))) (-3684 (|HasCategory| (-2 (|:| -4111 |#1|) (|:| -3117 |#2|)) (QUOTE (-1109))) (|HasCategory| (-2 (|:| -4111 |#1|) (|:| -3117 |#2|)) (LIST (QUOTE -619) (QUOTE (-868)))) (|HasCategory| |#2| (QUOTE (-1109))) (|HasCategory| |#2| (LIST (QUOTE -619) (QUOTE (-868))))) (|HasCategory| (-2 (|:| -4111 |#1|) (|:| -3117 |#2|)) (LIST (QUOTE -620) (QUOTE (-542)))) (-12 (|HasCategory| |#2| (QUOTE (-1109))) (|HasCategory| |#2| (LIST (QUOTE -313) (|devaluate| |#2|)))) (|HasCategory| |#1| (QUOTE (-856))) (-3684 (|HasCategory| (-2 (|:| -4111 |#1|) (|:| -3117 |#2|)) (LIST (QUOTE -619) (QUOTE (-868)))) (|HasCategory| |#2| (LIST (QUOTE -619) (QUOTE (-868))))) (|HasCategory| |#2| (QUOTE (-1109))) (|HasCategory| |#2| (LIST (QUOTE -619) (QUOTE (-868)))) (|HasCategory| (-2 (|:| -4111 |#1|) (|:| -3117 |#2|)) (LIST (QUOTE -619) (QUOTE (-868)))) (|HasCategory| (-2 (|:| -4111 |#1|) (|:| -3117 |#2|)) (QUOTE (-1109)))) (-482 R E V P) ((|constructor| (NIL "A domain constructor of the category \\axiomType{TriangularSetCategory}. The only requirement for a list of polynomials to be a member of such a domain is the following: no polynomial is constant and two distinct polynomials have distinct main variables. Such a triangular set may not be auto-reduced or consistent. Triangular sets are stored as sorted lists \\spad{w}.\\spad{r}.\\spad{t}. the main variables of their members but they are displayed in reverse order.\\newline References : \\indented{1}{[1] \\spad{P}. AUBRY,{} \\spad{D}. LAZARD and \\spad{M}. MORENO MAZA \"On the Theories} \\indented{5}{of Triangular Sets\" Journal of Symbol. Comp. (to appear)}"))) ((-4453 . T) (-4452 . T)) @@ -1871,7 +1871,7 @@ NIL (-485 |Key| |Entry| |hashfn|) ((|constructor| (NIL "This domain provides access to the underlying Lisp hash tables. By varying the hashfn parameter,{} tables suited for different purposes can be obtained."))) ((-4452 . T) (-4453 . T)) -((-12 (|HasCategory| (-2 (|:| -3679 |#1|) (|:| -1409 |#2|)) (QUOTE (-1109))) (|HasCategory| (-2 (|:| -3679 |#1|) (|:| -1409 |#2|)) (LIST (QUOTE -313) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -3679) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -1409) (|devaluate| |#2|)))))) (-2811 (|HasCategory| (-2 (|:| -3679 |#1|) (|:| -1409 |#2|)) (QUOTE (-1109))) (|HasCategory| |#2| (QUOTE (-1109)))) (-2811 (|HasCategory| (-2 (|:| -3679 |#1|) (|:| -1409 |#2|)) (QUOTE (-1109))) (|HasCategory| (-2 (|:| -3679 |#1|) (|:| -1409 |#2|)) (LIST (QUOTE -619) (QUOTE (-868)))) (|HasCategory| |#2| (QUOTE (-1109))) (|HasCategory| |#2| (LIST (QUOTE -619) (QUOTE (-868))))) (|HasCategory| (-2 (|:| -3679 |#1|) (|:| -1409 |#2|)) (LIST (QUOTE -620) (QUOTE (-542)))) (-12 (|HasCategory| |#2| (QUOTE (-1109))) (|HasCategory| |#2| (LIST (QUOTE -313) (|devaluate| |#2|)))) (|HasCategory| (-2 (|:| -3679 |#1|) (|:| -1409 |#2|)) (QUOTE (-1109))) (|HasCategory| |#1| (QUOTE (-856))) (|HasCategory| |#2| (QUOTE (-1109))) (-2811 (|HasCategory| (-2 (|:| -3679 |#1|) (|:| -1409 |#2|)) (LIST (QUOTE -619) (QUOTE (-868)))) (|HasCategory| |#2| (LIST (QUOTE -619) (QUOTE (-868))))) (|HasCategory| |#2| (LIST (QUOTE -619) (QUOTE (-868)))) (|HasCategory| (-2 (|:| -3679 |#1|) (|:| -1409 |#2|)) (LIST (QUOTE -619) (QUOTE (-868))))) +((-12 (|HasCategory| (-2 (|:| -4111 |#1|) (|:| -3117 |#2|)) (QUOTE (-1109))) (|HasCategory| (-2 (|:| -4111 |#1|) (|:| -3117 |#2|)) (LIST (QUOTE -313) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -4111) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -3117) (|devaluate| |#2|)))))) (-3684 (|HasCategory| (-2 (|:| -4111 |#1|) (|:| -3117 |#2|)) (QUOTE (-1109))) (|HasCategory| |#2| (QUOTE (-1109)))) (-3684 (|HasCategory| (-2 (|:| -4111 |#1|) (|:| -3117 |#2|)) (QUOTE (-1109))) (|HasCategory| (-2 (|:| -4111 |#1|) (|:| -3117 |#2|)) (LIST (QUOTE -619) (QUOTE (-868)))) (|HasCategory| |#2| (QUOTE (-1109))) (|HasCategory| |#2| (LIST (QUOTE -619) (QUOTE (-868))))) (|HasCategory| (-2 (|:| -4111 |#1|) (|:| -3117 |#2|)) (LIST (QUOTE -620) (QUOTE (-542)))) (-12 (|HasCategory| |#2| (QUOTE (-1109))) (|HasCategory| |#2| (LIST (QUOTE -313) (|devaluate| |#2|)))) (|HasCategory| (-2 (|:| -4111 |#1|) (|:| -3117 |#2|)) (QUOTE (-1109))) (|HasCategory| |#1| (QUOTE (-856))) (|HasCategory| |#2| (QUOTE (-1109))) (-3684 (|HasCategory| (-2 (|:| -4111 |#1|) (|:| -3117 |#2|)) (LIST (QUOTE -619) (QUOTE (-868)))) (|HasCategory| |#2| (LIST (QUOTE -619) (QUOTE (-868))))) (|HasCategory| |#2| (LIST (QUOTE -619) (QUOTE (-868)))) (|HasCategory| (-2 (|:| -4111 |#1|) (|:| -3117 |#2|)) (LIST (QUOTE -619) (QUOTE (-868))))) (-486) ((|constructor| (NIL "\\indented{1}{Author : Larry Lambe} Date Created : August 1988 Date Last Updated : March 9 1990 Related Constructors: OrderedSetInts,{} Commutator,{} FreeNilpotentLie AMS Classification: Primary 17B05,{} 17B30; Secondary 17A50 Keywords: free Lie algebra,{} Hall basis,{} basic commutators Description : Generate a basis for the free Lie algebra on \\spad{n} generators over a ring \\spad{R} with identity up to basic commutators of length \\spad{c} using the algorithm of \\spad{P}. Hall as given in Serre\\spad{'s} book Lie Groups \\spad{--} Lie Algebras")) (|generate| (((|Vector| (|List| (|Integer|))) (|NonNegativeInteger|) (|NonNegativeInteger|)) "\\spad{generate(numberOfGens, maximalWeight)} generates a vector of elements of the form [left,{}weight,{}right] which represents a \\spad{P}. Hall basis element for the free lie algebra on \\spad{numberOfGens} generators. We only generate those basis elements of weight less than or equal to maximalWeight")) (|inHallBasis?| (((|Boolean|) (|Integer|) (|Integer|) (|Integer|) (|Integer|)) "\\spad{inHallBasis?(numberOfGens, leftCandidate, rightCandidate, left)} tests to see if a new element should be added to the \\spad{P}. Hall basis being constructed. The list \\spad{[leftCandidate,wt,rightCandidate]} is included in the basis if in the unique factorization of \\spad{rightCandidate},{} we have left factor leftOfRight,{} and leftOfRight \\spad{<=} \\spad{leftCandidate}")) (|lfunc| (((|Integer|) (|Integer|) (|Integer|)) "\\spad{lfunc(d,n)} computes the rank of the \\spad{n}th factor in the lower central series of the free \\spad{d}-generated free Lie algebra; This rank is \\spad{d} if \\spad{n} = 1 and binom(\\spad{d},{}2) if \\spad{n} = 2"))) NIL @@ -1879,11 +1879,11 @@ NIL (-487 |vl| R) ((|constructor| (NIL "\\indented{2}{This type supports distributed multivariate polynomials} whose variables are from a user specified list of symbols. The coefficient ring may be non commutative,{} but the variables are assumed to commute. The term ordering is total degree ordering refined by reverse lexicographic ordering with respect to the position that the variables appear in the list of variables parameter.")) (|reorder| (($ $ (|List| (|Integer|))) "\\spad{reorder(p, perm)} applies the permutation perm to the variables in a polynomial and returns the new correctly ordered polynomial"))) (((-4454 "*") |has| |#2| (-174)) (-4445 |has| |#2| (-562)) (-4450 |has| |#2| (-6 -4450)) (-4447 . T) (-4446 . T) (-4449 . 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(QUOTE (-570))))) (-12 (|HasCategory| |#2| (QUOTE (-799))) (|HasCategory| |#2| (LIST (QUOTE -1047) (QUOTE (-570))))) (-12 (|HasCategory| |#2| (QUOTE (-854))) (|HasCategory| |#2| (LIST (QUOTE -1047) (QUOTE (-570))))) (-12 (|HasCategory| |#2| (QUOTE (-1058))) (|HasCategory| |#2| (LIST (QUOTE -1047) (QUOTE (-570))))) (-12 (|HasCategory| |#2| (QUOTE (-1109))) (|HasCategory| |#2| (LIST (QUOTE -1047) (QUOTE (-570)))))) (|HasCategory| (-570) (QUOTE (-856))) (-12 (|HasCategory| |#2| (QUOTE (-1058))) (|HasCategory| |#2| (LIST (QUOTE -645) (QUOTE (-570))))) (-12 (|HasCategory| |#2| (QUOTE (-235))) (|HasCategory| |#2| (QUOTE (-1058)))) (-12 (|HasCategory| |#2| (QUOTE (-1058))) (|HasCategory| |#2| (LIST (QUOTE -907) (QUOTE (-1186))))) (-3684 (|HasCategory| |#2| (QUOTE (-1058))) (-12 (|HasCategory| |#2| (QUOTE (-1109))) (|HasCategory| |#2| (LIST (QUOTE -1047) (QUOTE (-570)))))) (-12 (|HasCategory| |#2| (QUOTE (-1109))) (|HasCategory| |#2| (LIST (QUOTE -1047) (QUOTE (-570))))) (-12 (|HasCategory| |#2| (LIST (QUOTE -1047) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasCategory| |#2| (QUOTE (-1109)))) (|HasAttribute| |#2| (QUOTE -4449)) (|HasCategory| |#2| (QUOTE (-132))) (|HasCategory| |#2| (QUOTE (-25))) (|HasCategory| |#2| (LIST (QUOTE -619) (QUOTE (-868)))) (-12 (|HasCategory| |#2| (QUOTE (-1109))) (|HasCategory| |#2| (LIST (QUOTE -313) (|devaluate| |#2|))))) (-489) ((|constructor| (NIL "This domain represents the header of a definition.")) (|parameters| (((|List| (|ParameterAst|)) $) "\\spad{parameters(h)} gives the parameters specified in the definition header \\spad{`h'}.")) (|name| (((|Identifier|) $) "\\spad{name(h)} returns the name of the operation defined defined.")) (|headAst| (($ (|Identifier|) (|List| (|ParameterAst|))) "\\spad{headAst(f,[x1,..,xn])} constructs a function definition header."))) NIL @@ -1891,8 +1891,8 @@ NIL (-490 S) ((|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}."))) ((-4452 . T) (-4453 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1109))) (-2811 (-12 (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-868))))) (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-868))))) -(-491 -1385 UP UPUP R) +((-12 (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1109))) (-3684 (-12 (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-868))))) (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-868))))) +(-491 -2968 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}\\spad{'s} are integers and the \\spad{P}\\spad{'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 @@ -1903,7 +1903,7 @@ NIL (-493) ((|constructor| (NIL "This domain allows rational numbers to be presented as repeating hexadecimal expansions.")) (|hex| (($ (|Fraction| (|Integer|))) "\\spad{hex(r)} converts a rational number to a hexadecimal expansion.")) (|fractionPart| (((|Fraction| (|Integer|)) $) "\\spad{fractionPart(h)} returns the fractional part of a hexadecimal expansion."))) ((-4444 . T) (-4450 . T) (-4445 . T) ((-4454 "*") . T) (-4446 . T) (-4447 . T) (-4449 . T)) -((|HasCategory| (-570) (QUOTE (-916))) (|HasCategory| (-570) (LIST (QUOTE -1047) (QUOTE (-1186)))) (|HasCategory| (-570) (QUOTE (-146))) (|HasCategory| (-570) (QUOTE (-148))) (|HasCategory| (-570) (LIST (QUOTE -620) (QUOTE (-542)))) (|HasCategory| (-570) (QUOTE (-1031))) (|HasCategory| (-570) (QUOTE (-826))) (-2811 (|HasCategory| (-570) (QUOTE (-826))) (|HasCategory| (-570) (QUOTE (-856)))) (|HasCategory| (-570) (LIST (QUOTE -1047) (QUOTE (-570)))) (|HasCategory| (-570) (QUOTE (-1161))) (|HasCategory| (-570) (LIST (QUOTE -893) (QUOTE (-384)))) (|HasCategory| (-570) (LIST (QUOTE -893) (QUOTE (-570)))) (|HasCategory| (-570) (LIST (QUOTE -620) (LIST (QUOTE -899) (QUOTE (-384))))) (|HasCategory| (-570) (LIST (QUOTE -620) (LIST (QUOTE -899) (QUOTE (-570))))) (|HasCategory| (-570) (QUOTE (-235))) (|HasCategory| (-570) (LIST (QUOTE -907) (QUOTE (-1186)))) (|HasCategory| (-570) (LIST (QUOTE -520) (QUOTE (-1186)) (QUOTE (-570)))) (|HasCategory| (-570) (LIST (QUOTE -313) (QUOTE (-570)))) (|HasCategory| (-570) (LIST (QUOTE -290) (QUOTE (-570)) (QUOTE (-570)))) (|HasCategory| (-570) (QUOTE (-311))) (|HasCategory| (-570) (QUOTE (-551))) (|HasCategory| (-570) (QUOTE (-856))) (|HasCategory| (-570) (LIST (QUOTE -645) (QUOTE (-570)))) (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| (-570) (QUOTE (-916)))) (-2811 (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| (-570) (QUOTE (-916)))) (|HasCategory| (-570) (QUOTE (-146))))) +((|HasCategory| (-570) (QUOTE (-916))) (|HasCategory| (-570) (LIST (QUOTE -1047) (QUOTE (-1186)))) (|HasCategory| (-570) (QUOTE (-146))) (|HasCategory| (-570) (QUOTE (-148))) (|HasCategory| (-570) (LIST (QUOTE -620) (QUOTE (-542)))) (|HasCategory| (-570) (QUOTE (-1031))) (|HasCategory| (-570) (QUOTE (-826))) (-3684 (|HasCategory| (-570) (QUOTE (-826))) (|HasCategory| (-570) (QUOTE (-856)))) (|HasCategory| (-570) (LIST (QUOTE -1047) (QUOTE (-570)))) (|HasCategory| (-570) (QUOTE (-1161))) (|HasCategory| (-570) (LIST (QUOTE -893) (QUOTE (-384)))) (|HasCategory| (-570) (LIST (QUOTE -893) (QUOTE (-570)))) (|HasCategory| (-570) (LIST (QUOTE -620) (LIST (QUOTE -899) (QUOTE (-384))))) (|HasCategory| (-570) (LIST (QUOTE -620) (LIST (QUOTE -899) (QUOTE (-570))))) (|HasCategory| (-570) (QUOTE (-235))) (|HasCategory| (-570) (LIST (QUOTE -907) (QUOTE (-1186)))) (|HasCategory| (-570) (LIST (QUOTE -520) (QUOTE (-1186)) (QUOTE (-570)))) (|HasCategory| (-570) (LIST (QUOTE -313) (QUOTE (-570)))) (|HasCategory| (-570) (LIST (QUOTE -290) (QUOTE (-570)) (QUOTE (-570)))) (|HasCategory| (-570) (QUOTE (-311))) (|HasCategory| (-570) (QUOTE (-551))) (|HasCategory| (-570) (QUOTE (-856))) (|HasCategory| (-570) (LIST (QUOTE -645) (QUOTE (-570)))) (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| (-570) (QUOTE (-916)))) (-3684 (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| (-570) (QUOTE (-916)))) (|HasCategory| (-570) (QUOTE (-146))))) (-494 A S) ((|constructor| (NIL "A homogeneous aggregate is an aggregate of elements all of the same type. In the current system,{} all aggregates are homogeneous. Two attributes characterize classes of aggregates. Aggregates from domains with attribute \\spadatt{finiteAggregate} have a finite number of members. Those with attribute \\spadatt{shallowlyMutable} allow an element to be modified or updated without changing its overall value.")) (|member?| (((|Boolean|) |#2| $) "\\spad{member?(x,u)} tests if \\spad{x} is a member of \\spad{u}. For collections,{} \\axiom{member?(\\spad{x},{}\\spad{u}) = reduce(or,{}[x=y for \\spad{y} in \\spad{u}],{}\\spad{false})}.")) (|members| (((|List| |#2|) $) "\\spad{members(u)} returns a list of the consecutive elements of \\spad{u}. For collections,{} \\axiom{parts([\\spad{x},{}\\spad{y},{}...,{}\\spad{z}]) = (\\spad{x},{}\\spad{y},{}...,{}\\spad{z})}.")) (|parts| (((|List| |#2|) $) "\\spad{parts(u)} returns a list of the consecutive elements of \\spad{u}. For collections,{} \\axiom{parts([\\spad{x},{}\\spad{y},{}...,{}\\spad{z}]) = (\\spad{x},{}\\spad{y},{}...,{}\\spad{z})}.")) (|count| (((|NonNegativeInteger|) |#2| $) "\\spad{count(x,u)} returns the number of occurrences of \\spad{x} in \\spad{u}. For collections,{} \\axiom{count(\\spad{x},{}\\spad{u}) = reduce(+,{}[x=y for \\spad{y} in \\spad{u}],{}0)}.") (((|NonNegativeInteger|) (|Mapping| (|Boolean|) |#2|) $) "\\spad{count(p,u)} returns the number of elements \\spad{x} in \\spad{u} such that \\axiom{\\spad{p}(\\spad{x})} is \\spad{true}. For collections,{} \\axiom{count(\\spad{p},{}\\spad{u}) = reduce(+,{}[1 for \\spad{x} in \\spad{u} | \\spad{p}(\\spad{x})],{}0)}.")) (|every?| (((|Boolean|) (|Mapping| (|Boolean|) |#2|) $) "\\spad{every?(f,u)} tests if \\spad{p}(\\spad{x}) is \\spad{true} for all elements \\spad{x} of \\spad{u}. Note: for collections,{} \\axiom{every?(\\spad{p},{}\\spad{u}) = reduce(and,{}map(\\spad{f},{}\\spad{u}),{}\\spad{true},{}\\spad{false})}.")) (|any?| (((|Boolean|) (|Mapping| (|Boolean|) |#2|) $) "\\spad{any?(p,u)} tests if \\axiom{\\spad{p}(\\spad{x})} is \\spad{true} for any element \\spad{x} of \\spad{u}. Note: for collections,{} \\axiom{any?(\\spad{p},{}\\spad{u}) = reduce(or,{}map(\\spad{f},{}\\spad{u}),{}\\spad{false},{}\\spad{true})}.")) (|map!| (($ (|Mapping| |#2| |#2|) $) "\\spad{map!(f,u)} destructively replaces each element \\spad{x} of \\spad{u} by \\axiom{\\spad{f}(\\spad{x})}.")) (|map| (($ (|Mapping| |#2| |#2|) $) "\\spad{map(f,u)} returns a copy of \\spad{u} with each element \\spad{x} replaced by \\spad{f}(\\spad{x}). For collections,{} \\axiom{map(\\spad{f},{}\\spad{u}) = [\\spad{f}(\\spad{x}) for \\spad{x} in \\spad{u}]}."))) NIL @@ -1928,7 +1928,7 @@ NIL ((|constructor| (NIL "Category for the hyperbolic trigonometric functions.")) (|tanh| (($ $) "\\spad{tanh(x)} returns the hyperbolic tangent of \\spad{x}.")) (|sinh| (($ $) "\\spad{sinh(x)} returns the hyperbolic sine of \\spad{x}.")) (|sech| (($ $) "\\spad{sech(x)} returns the hyperbolic secant of \\spad{x}.")) (|csch| (($ $) "\\spad{csch(x)} returns the hyperbolic cosecant of \\spad{x}.")) (|coth| (($ $) "\\spad{coth(x)} returns the hyperbolic cotangent of \\spad{x}.")) (|cosh| (($ $) "\\spad{cosh(x)} returns the hyperbolic cosine of \\spad{x}."))) NIL NIL -(-500 -1385 UP |AlExt| |AlPol|) +(-500 -2968 UP |AlExt| |AlPol|) ((|constructor| (NIL "Factorization of univariate polynomials with coefficients in an algebraic extension of a field over which we can factor UP\\spad{'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 @@ -1939,16 +1939,16 @@ NIL (-502 S |mn|) ((|constructor| (NIL "\\indented{1}{Author Micheal Monagan Aug/87} This is the basic one dimensional array data type."))) ((-4453 . T) (-4452 . T)) -((-2811 (-12 (|HasCategory| |#1| (QUOTE (-856))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|))))) (-2811 (-12 (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-868))))) (|HasCategory| |#1| (LIST (QUOTE -620) (QUOTE (-542)))) (-2811 (|HasCategory| |#1| (QUOTE (-856))) (|HasCategory| |#1| (QUOTE (-1109)))) (|HasCategory| |#1| (QUOTE (-856))) (|HasCategory| (-570) (QUOTE (-856))) (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-868)))) (-12 (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|))))) +((-3684 (-12 (|HasCategory| |#1| (QUOTE (-856))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|))))) (-3684 (-12 (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-868))))) (|HasCategory| |#1| (LIST (QUOTE -620) (QUOTE (-542)))) (-3684 (|HasCategory| |#1| (QUOTE (-856))) (|HasCategory| |#1| (QUOTE (-1109)))) (|HasCategory| |#1| (QUOTE (-856))) (|HasCategory| (-570) (QUOTE (-856))) (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-868)))) (-12 (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|))))) (-503 R |mnRow| |mnCol|) ((|constructor| (NIL "\\indented{1}{An IndexedTwoDimensionalArray is a 2-dimensional array where} the minimal row and column indices are parameters of the type. Rows and columns are returned as IndexedOneDimensionalArray\\spad{'s} with minimal indices matching those of the IndexedTwoDimensionalArray. The index of the 'first' row may be obtained by calling the function 'minRowIndex'. The index of the 'first' column may be obtained by calling the function 'minColIndex'. The index of the first element of a 'Row' is the same as the index of the first column in an array and vice versa."))) ((-4452 . T) (-4453 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1109))) (-2811 (-12 (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-868))))) (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-868))))) +((-12 (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1109))) (-3684 (-12 (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-868))))) (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-868))))) (-504 K R UP) ((|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 -(-505 R UP -1385) +(-505 R UP -2968) ((|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 \\spad{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| $) $) "\\spad{squareFree(x)} returns a square-free factorisation of \\spad{x}"))) NIL NIL @@ -1968,7 +1968,7 @@ NIL ((|constructor| (NIL "InnerCommonDenominator provides functions to compute the common denominator of a finite linear aggregate of elements of the quotient field of an integral domain.")) (|splitDenominator| (((|Record| (|:| |num| |#3|) (|:| |den| |#1|)) |#4|) "\\spad{splitDenominator([q1,...,qn])} returns \\spad{[[p1,...,pn], d]} such that \\spad{qi = pi/d} and \\spad{d} is a common denominator for the \\spad{qi}\\spad{'s}.")) (|clearDenominator| ((|#3| |#4|) "\\spad{clearDenominator([q1,...,qn])} returns \\spad{[p1,...,pn]} such that \\spad{qi = pi/d} where \\spad{d} is a common denominator for the \\spad{qi}\\spad{'s}.")) (|commonDenominator| ((|#1| |#4|) "\\spad{commonDenominator([q1,...,qn])} returns a common denominator \\spad{d} for \\spad{q1},{}...,{}\\spad{qn}."))) NIL NIL -(-510 -1385 |Expon| |VarSet| |DPoly|) +(-510 -2968 |Expon| |VarSet| |DPoly|) ((|constructor| (NIL "This domain represents polynomial ideals with coefficients in any field and supports the basic ideal operations,{} including intersection sum and quotient. An ideal is represented by a list of polynomials (the generators of the ideal) and a boolean that is \\spad{true} if the generators are a Groebner basis. The algorithms used are based on Groebner basis computations. The ordering is determined by the datatype of the input polynomials. Users may use refinements of total degree orderings.")) (|relationsIdeal| (((|SuchThat| (|List| (|Polynomial| |#1|)) (|List| (|Equation| (|Polynomial| |#1|)))) (|List| |#4|)) "\\spad{relationsIdeal(polyList)} returns the ideal of relations among the polynomials in \\spad{polyList}.")) (|saturate| (($ $ |#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}.")) (* (($ $ $) "\\spad{I*J} computes the product of the ideal \\spad{I} and \\spad{J}."))) NIL ((|HasCategory| |#3| (LIST (QUOTE -620) (QUOTE (-1186))))) @@ -2019,7 +2019,7 @@ NIL (-522 S |mn|) ((|constructor| (NIL "\\indented{1}{Author: Michael Monagan July/87,{} modified \\spad{SMW} June/91} A FlexibleArray is the notion of an array intended to allow for growth at the end only. Hence the following efficient operations \\indented{2}{\\spad{append(x,a)} meaning append item \\spad{x} at the end of the array \\spad{a}} \\indented{2}{\\spad{delete(a,n)} meaning delete the last item from the array \\spad{a}} Flexible arrays support the other operations inherited from \\spadtype{ExtensibleLinearAggregate}. However,{} these are not efficient. Flexible arrays combine the \\spad{O(1)} access time property of arrays with growing and shrinking at the end in \\spad{O(1)} (average) time. This is done by using an ordinary array which may have zero or more empty slots at the end. When the array becomes full it is copied into a new larger (50\\% larger) array. Conversely,{} when the array becomes less than 1/2 full,{} it is copied into a smaller array. Flexible arrays provide for an efficient implementation of many data structures in particular heaps,{} stacks and sets.")) (|shrinkable| (((|Boolean|) (|Boolean|)) "\\spad{shrinkable(b)} sets the shrinkable attribute of flexible arrays to \\spad{b} and returns the previous value")) (|physicalLength!| (($ $ (|Integer|)) "\\spad{physicalLength!(x,n)} changes the physical length of \\spad{x} to be \\spad{n} and returns the new array.")) (|physicalLength| (((|NonNegativeInteger|) $) "\\spad{physicalLength(x)} returns the number of elements \\spad{x} can accomodate before growing")) (|flexibleArray| (($ (|List| |#1|)) "\\spad{flexibleArray(l)} creates a flexible array from the list of elements \\spad{l}"))) ((-4453 . T) (-4452 . T)) -((-2811 (-12 (|HasCategory| |#1| (QUOTE (-856))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|))))) (-2811 (-12 (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-868))))) (|HasCategory| |#1| (LIST (QUOTE -620) (QUOTE (-542)))) (-2811 (|HasCategory| |#1| (QUOTE (-856))) (|HasCategory| |#1| (QUOTE (-1109)))) (|HasCategory| |#1| (QUOTE (-856))) (|HasCategory| (-570) (QUOTE (-856))) (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-868)))) (-12 (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|))))) +((-3684 (-12 (|HasCategory| |#1| (QUOTE (-856))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|))))) (-3684 (-12 (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-868))))) (|HasCategory| |#1| (LIST (QUOTE -620) (QUOTE (-542)))) (-3684 (|HasCategory| |#1| (QUOTE (-856))) (|HasCategory| |#1| (QUOTE (-1109)))) (|HasCategory| |#1| (QUOTE (-856))) (|HasCategory| (-570) (QUOTE (-856))) (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-868)))) (-12 (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|))))) (-523) ((|constructor| (NIL "This domain represents AST for conditional expressions.")) (|elseBranch| (((|SpadAst|) $) "thenBranch(\\spad{e}) returns the `else-branch' of `e'.")) (|thenBranch| (((|SpadAst|) $) "\\spad{thenBranch(e)} returns the `then-branch' of `e'.")) (|condition| (((|SpadAst|) $) "\\spad{condition(e)} returns the condition of the if-expression `e'."))) NIL @@ -2027,15 +2027,15 @@ NIL (-524 |p| |n|) ((|constructor| (NIL "InnerFiniteField(\\spad{p},{}\\spad{n}) implements finite fields with \\spad{p**n} elements where \\spad{p} is assumed prime but does not check. For a version which checks that \\spad{p} is prime,{} see \\spadtype{FiniteField}."))) ((-4444 . T) (-4450 . T) (-4445 . T) ((-4454 "*") . T) (-4446 . T) (-4447 . T) (-4449 . T)) -((-2811 (|HasCategory| (-587 |#1|) (QUOTE (-146))) (|HasCategory| (-587 |#1|) (QUOTE (-373)))) (|HasCategory| (-587 |#1|) (QUOTE (-148))) (|HasCategory| (-587 |#1|) (QUOTE (-373))) (|HasCategory| (-587 |#1|) (QUOTE (-146)))) +((-3684 (|HasCategory| (-587 |#1|) (QUOTE (-146))) (|HasCategory| (-587 |#1|) (QUOTE (-373)))) (|HasCategory| (-587 |#1|) (QUOTE (-148))) (|HasCategory| (-587 |#1|) (QUOTE (-373))) (|HasCategory| (-587 |#1|) (QUOTE (-146)))) (-525 R |mnRow| |mnCol| |Row| |Col|) ((|constructor| (NIL "\\indented{1}{This is an internal type which provides an implementation of} 2-dimensional arrays as PrimitiveArray\\spad{'s} of PrimitiveArray\\spad{'s}."))) ((-4452 . T) (-4453 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1109))) (-2811 (-12 (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-868))))) (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-868))))) +((-12 (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1109))) (-3684 (-12 (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-868))))) (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-868))))) (-526 S |mn|) ((|constructor| (NIL "\\spadtype{IndexedList} is a basic implementation of the functions in \\spadtype{ListAggregate},{} often using functions in the underlying LISP system. The second parameter to the constructor (\\spad{mn}) is the beginning index of the list. That is,{} if \\spad{l} is a list,{} then \\spad{elt(l,mn)} is the first value. This constructor is probably best viewed as the implementation of singly-linked lists that are addressable by index rather than as a mere wrapper for LISP lists."))) ((-4453 . T) (-4452 . T)) -((-2811 (-12 (|HasCategory| |#1| (QUOTE (-856))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|))))) (-2811 (-12 (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-868))))) (|HasCategory| |#1| (LIST (QUOTE -620) (QUOTE (-542)))) (-2811 (|HasCategory| |#1| (QUOTE (-856))) (|HasCategory| |#1| (QUOTE (-1109)))) (|HasCategory| |#1| (QUOTE (-856))) (|HasCategory| (-570) (QUOTE (-856))) (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-868)))) (-12 (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|))))) +((-3684 (-12 (|HasCategory| |#1| (QUOTE (-856))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|))))) (-3684 (-12 (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-868))))) (|HasCategory| |#1| (LIST (QUOTE -620) (QUOTE (-542)))) (-3684 (|HasCategory| |#1| (QUOTE (-856))) (|HasCategory| |#1| (QUOTE (-1109)))) (|HasCategory| |#1| (QUOTE (-856))) (|HasCategory| (-570) (QUOTE (-856))) (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-868)))) (-12 (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|))))) (-527 R |Row| |Col| M) ((|constructor| (NIL "\\spadtype{InnerMatrixLinearAlgebraFunctions} is an internal package which provides standard linear algebra functions on domains in \\spad{MatrixCategory}")) (|inverse| (((|Union| |#4| "failed") |#4|) "\\spad{inverse(m)} returns the inverse of the matrix \\spad{m}. If the matrix is not invertible,{} \"failed\" is returned. Error: if the matrix is not square.")) (|generalizedInverse| ((|#4| |#4|) "\\spad{generalizedInverse(m)} returns the generalized (Moore--Penrose) inverse of the matrix \\spad{m},{} \\spadignore{i.e.} the matrix \\spad{h} such that m*h*m=h,{} h*m*h=m,{} \\spad{m*h} and \\spad{h*m} are both symmetric matrices.")) (|determinant| ((|#1| |#4|) "\\spad{determinant(m)} returns the determinant of the matrix \\spad{m}. an error message is returned if the matrix is not square.")) (|nullSpace| (((|List| |#3|) |#4|) "\\spad{nullSpace(m)} returns a basis for the null space of the matrix \\spad{m}.")) (|nullity| (((|NonNegativeInteger|) |#4|) "\\spad{nullity(m)} returns the mullity of the matrix \\spad{m}. This is the dimension of the null space of the matrix \\spad{m}.")) (|rank| (((|NonNegativeInteger|) |#4|) "\\spad{rank(m)} returns the rank of the matrix \\spad{m}.")) (|rowEchelon| ((|#4| |#4|) "\\spad{rowEchelon(m)} returns the row echelon form of the matrix \\spad{m}."))) NIL @@ -2047,7 +2047,7 @@ NIL (-529 R |mnRow| |mnCol|) ((|constructor| (NIL "An \\spad{IndexedMatrix} is a matrix where the minimal row and column indices are parameters of the type. The domains Row and Col are both IndexedVectors. The index of the 'first' row may be obtained by calling the function \\spadfun{minRowIndex}. The index of the 'first' column may be obtained by calling the function \\spadfun{minColIndex}. The index of the first element of a 'Row' is the same as the index of the first column in a matrix and vice versa."))) ((-4452 . T) (-4453 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1109))) (-2811 (-12 (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-868))))) (|HasCategory| |#1| (QUOTE (-311))) (|HasCategory| |#1| (QUOTE (-562))) (|HasAttribute| |#1| (QUOTE (-4454 "*"))) (|HasCategory| |#1| (QUOTE (-368))) (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-868))))) +((-12 (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1109))) (-3684 (-12 (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-868))))) (|HasCategory| |#1| (QUOTE (-311))) (|HasCategory| |#1| (QUOTE (-562))) (|HasAttribute| |#1| (QUOTE (-4454 "*"))) (|HasCategory| |#1| (QUOTE (-368))) (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-868))))) (-530) ((|constructor| (NIL "This domain represents an `import' of types.")) (|imports| (((|List| (|TypeAst|)) $) "\\spad{imports(x)} returns the list of imported types.")) (|coerce| (($ (|List| (|TypeAst|))) "ts::ImportAst constructs an ImportAst for the list if types `ts'."))) NIL @@ -2080,7 +2080,7 @@ 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 NIL -(-538 K -1385 |Par|) +(-538 K -2968 |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 \\spad{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 @@ -2104,7 +2104,7 @@ 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 -(-544 K -1385 |Par|) +(-544 K -2968 |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 @@ -2155,12 +2155,12 @@ NIL (-556 |Key| |Entry| |addDom|) ((|constructor| (NIL "This domain is used to provide a conditional \"add\" domain for the implementation of \\spadtype{Table}."))) ((-4452 . T) (-4453 . T)) -((-12 (|HasCategory| (-2 (|:| -3679 |#1|) (|:| -1409 |#2|)) (QUOTE (-1109))) (|HasCategory| (-2 (|:| -3679 |#1|) (|:| -1409 |#2|)) (LIST (QUOTE -313) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -3679) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -1409) (|devaluate| |#2|)))))) (-2811 (|HasCategory| (-2 (|:| -3679 |#1|) (|:| -1409 |#2|)) (QUOTE (-1109))) (|HasCategory| |#2| (QUOTE (-1109)))) (-2811 (|HasCategory| (-2 (|:| -3679 |#1|) (|:| -1409 |#2|)) (QUOTE (-1109))) (|HasCategory| (-2 (|:| -3679 |#1|) (|:| -1409 |#2|)) (LIST (QUOTE -619) (QUOTE (-868)))) (|HasCategory| |#2| (QUOTE (-1109))) (|HasCategory| |#2| (LIST (QUOTE -619) (QUOTE (-868))))) (|HasCategory| (-2 (|:| -3679 |#1|) (|:| -1409 |#2|)) (LIST (QUOTE -620) (QUOTE (-542)))) (-12 (|HasCategory| |#2| (QUOTE (-1109))) (|HasCategory| |#2| (LIST (QUOTE -313) (|devaluate| |#2|)))) (|HasCategory| (-2 (|:| -3679 |#1|) (|:| -1409 |#2|)) (QUOTE (-1109))) (|HasCategory| |#1| (QUOTE (-856))) (|HasCategory| |#2| (QUOTE (-1109))) (-2811 (|HasCategory| (-2 (|:| -3679 |#1|) (|:| -1409 |#2|)) (LIST (QUOTE -619) (QUOTE (-868)))) (|HasCategory| |#2| (LIST (QUOTE -619) (QUOTE (-868))))) (|HasCategory| |#2| (LIST (QUOTE -619) (QUOTE (-868)))) (|HasCategory| (-2 (|:| -3679 |#1|) (|:| -1409 |#2|)) (LIST (QUOTE -619) (QUOTE (-868))))) -(-557 R -1385) +((-12 (|HasCategory| (-2 (|:| -4111 |#1|) (|:| -3117 |#2|)) (QUOTE (-1109))) (|HasCategory| (-2 (|:| -4111 |#1|) (|:| -3117 |#2|)) (LIST (QUOTE -313) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -4111) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -3117) (|devaluate| |#2|)))))) (-3684 (|HasCategory| (-2 (|:| -4111 |#1|) (|:| -3117 |#2|)) (QUOTE (-1109))) (|HasCategory| |#2| (QUOTE (-1109)))) (-3684 (|HasCategory| (-2 (|:| -4111 |#1|) (|:| -3117 |#2|)) (QUOTE (-1109))) (|HasCategory| (-2 (|:| -4111 |#1|) (|:| -3117 |#2|)) (LIST (QUOTE -619) (QUOTE (-868)))) (|HasCategory| |#2| (QUOTE (-1109))) (|HasCategory| |#2| (LIST (QUOTE -619) (QUOTE (-868))))) (|HasCategory| (-2 (|:| -4111 |#1|) (|:| -3117 |#2|)) (LIST (QUOTE -620) (QUOTE (-542)))) (-12 (|HasCategory| |#2| (QUOTE (-1109))) (|HasCategory| |#2| (LIST (QUOTE -313) (|devaluate| |#2|)))) (|HasCategory| (-2 (|:| -4111 |#1|) (|:| -3117 |#2|)) (QUOTE (-1109))) (|HasCategory| |#1| (QUOTE (-856))) (|HasCategory| |#2| (QUOTE (-1109))) (-3684 (|HasCategory| (-2 (|:| -4111 |#1|) (|:| -3117 |#2|)) (LIST (QUOTE -619) (QUOTE (-868)))) (|HasCategory| |#2| (LIST (QUOTE -619) (QUOTE (-868))))) (|HasCategory| |#2| (LIST (QUOTE -619) (QUOTE (-868)))) (|HasCategory| (-2 (|:| -4111 |#1|) (|:| -3117 |#2|)) (LIST (QUOTE -619) (QUOTE (-868))))) +(-557 R -2968) ((|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 -(-558 R0 -1385 UP UPUP R) +(-558 R0 -2968 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 @@ -2170,7 +2170,7 @@ NIL NIL (-560 R) ((|constructor| (NIL "\\indented{1}{+ Author: Mike Dewar} + Date Created: November 1996 + Date Last Updated: + Basic Functions: + Related Constructors: + Also See: + AMS Classifications: + Keywords: + References: + Description: + This category implements of interval arithmetic and transcendental + functions over intervals.")) (|contains?| (((|Boolean|) $ |#1|) "\\spad{contains?(i,f)} returns \\spad{true} if \\axiom{\\spad{f}} is contained within the interval \\axiom{\\spad{i}},{} \\spad{false} otherwise.")) (|negative?| (((|Boolean|) $) "\\spad{negative?(u)} returns \\axiom{\\spad{true}} if every element of \\spad{u} is negative,{} \\axiom{\\spad{false}} otherwise.")) (|positive?| (((|Boolean|) $) "\\spad{positive?(u)} returns \\axiom{\\spad{true}} if every element of \\spad{u} is positive,{} \\axiom{\\spad{false}} otherwise.")) (|width| ((|#1| $) "\\spad{width(u)} returns \\axiom{sup(\\spad{u}) - inf(\\spad{u})}.")) (|sup| ((|#1| $) "\\spad{sup(u)} returns the supremum of \\axiom{\\spad{u}}.")) (|inf| ((|#1| $) "\\spad{inf(u)} returns the infinum of \\axiom{\\spad{u}}.")) (|qinterval| (($ |#1| |#1|) "\\spad{qinterval(inf,sup)} creates a new interval \\axiom{[\\spad{inf},{}\\spad{sup}]},{} without checking the ordering on the elements.")) (|interval| (($ (|Fraction| (|Integer|))) "\\spad{interval(f)} creates a new interval around \\spad{f}.") (($ |#1|) "\\spad{interval(f)} creates a new interval around \\spad{f}.") (($ |#1| |#1|) "\\spad{interval(inf,sup)} creates a new interval,{} either \\axiom{[\\spad{inf},{}\\spad{sup}]} if \\axiom{\\spad{inf} \\spad{<=} \\spad{sup}} or \\axiom{[\\spad{sup},{}in]} otherwise."))) -((-3535 . T) (-4445 . T) ((-4454 "*") . T) (-4446 . T) (-4447 . T) (-4449 . T)) +((-3412 . T) (-4445 . T) ((-4454 "*") . T) (-4446 . T) (-4447 . T) (-4449 . T)) NIL (-561 S) ((|constructor| (NIL "The category of commutative integral domains,{} \\spadignore{i.e.} commutative rings with no zero divisors. \\blankline Conditional attributes: \\indented{2}{canonicalUnitNormal\\tab{20}the canonical field is the same for all associates} \\indented{2}{canonicalsClosed\\tab{20}the product of two canonicals is itself canonical}")) (|unit?| (((|Boolean|) $) "\\spad{unit?(x)} tests whether \\spad{x} is a unit,{} \\spadignore{i.e.} is invertible.")) (|associates?| (((|Boolean|) $ $) "\\spad{associates?(x,y)} tests whether \\spad{x} and \\spad{y} are associates,{} \\spadignore{i.e.} differ by a unit factor.")) (|unitCanonical| (($ $) "\\spad{unitCanonical(x)} returns \\spad{unitNormal(x).canonical}.")) (|unitNormal| (((|Record| (|:| |unit| $) (|:| |canonical| $) (|:| |associate| $)) $) "\\spad{unitNormal(x)} tries to choose a canonical element from the associate class of \\spad{x}. The attribute canonicalUnitNormal,{} if asserted,{} means that the \"canonical\" element is the same across all associates of \\spad{x} if \\spad{unitNormal(x) = [u,c,a]} then \\spad{u*c = x},{} \\spad{a*u = 1}.")) (|exquo| (((|Union| $ "failed") $ $) "\\spad{exquo(a,b)} either returns an element \\spad{c} such that \\spad{c*b=a} or \"failed\" if no such element can be found."))) @@ -2180,7 +2180,7 @@ 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."))) ((-4445 . T) ((-4454 "*") . T) (-4446 . T) (-4447 . T) (-4449 . T)) NIL -(-563 R -1385) +(-563 R -2968) ((|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},{}...,{}\\spad{kn} (the \\spad{ki}\\spad{'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}\\spad{'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 @@ -2192,7 +2192,7 @@ 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 -(-566 R -1385 L) +(-566 R -2968 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}\\spad{'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}\\spad{'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 -662) (|devaluate| |#2|)))) @@ -2200,11 +2200,11 @@ 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 -(-568 -1385 UP UPUP R) +(-568 -2968 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 -(-569 -1385 UP) +(-569 -2968 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 @@ -2216,15 +2216,15 @@ 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,{} {\\spad{\\tt} \\spad{exp}},{} over a given range,{} {\\spad{\\tt} a} to {\\spad{\\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 {\\spad{\\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,{} {\\spad{\\tt} \\spad{exp}},{} over a given range,{} {\\spad{\\tt} a} to {\\spad{\\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 {\\spad{\\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,{} {\\spad{\\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,{} {\\spad{\\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,{} {\\spad{\\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,{} {\\spad{\\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,{} {\\spad{\\tt} \\spad{exp}},{} over a given range {\\spad{\\tt} a} to {\\spad{\\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,{} {\\spad{\\tt} \\spad{exp}},{} over a given range {\\spad{\\tt} a} to {\\spad{\\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,{} {\\spad{\\tt} \\spad{exp}},{} over a given range {\\spad{\\tt} a} to {\\spad{\\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,{} {\\spad{\\tt} \\spad{exp}},{} over a given range {\\spad{\\tt} a} to {\\spad{\\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 -(-572 R -1385 L) +(-572 R -2968 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}\\spad{'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 -662) (|devaluate| |#2|)))) -(-573 R -1385) +(-573 R -2968) ((|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 -620) (LIST (QUOTE -899) (QUOTE (-570))))) (|HasCategory| |#1| (LIST (QUOTE -893) (QUOTE (-570)))) (|HasCategory| |#2| (QUOTE (-1148)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -620) (LIST (QUOTE -899) (QUOTE (-570))))) (|HasCategory| |#1| (LIST (QUOTE -893) (QUOTE (-570)))) (|HasCategory| |#2| (QUOTE (-635))))) -(-574 -1385 UP) +(-574 -2968 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}\\spad{'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 @@ -2232,27 +2232,27 @@ 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 -(-576 -1385) +(-576 -2968) ((|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}\\spad{'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 (-577 R) ((|constructor| (NIL "\\indented{1}{+ Author: Mike Dewar} + Date Created: November 1996 + Date Last Updated: + Basic Functions: + Related Constructors: + Also See: + AMS Classifications: + Keywords: + References: + Description: + This domain is an implementation of interval arithmetic and transcendental + functions over intervals."))) -((-3535 . T) (-4445 . T) ((-4454 "*") . T) (-4446 . T) (-4447 . T) (-4449 . T)) +((-3412 . T) (-4445 . T) ((-4454 "*") . T) (-4446 . T) (-4447 . T) (-4449 . T)) NIL (-578) ((|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}\\spad{'s} exists."))) NIL NIL -(-579 R -1385) +(-579 R -2968) ((|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 -620) (LIST (QUOTE -899) (QUOTE (-570))))) (|HasCategory| |#1| (QUOTE (-458))) (|HasCategory| |#1| (LIST (QUOTE -893) (QUOTE (-570)))) (|HasCategory| |#2| (QUOTE (-288))) (|HasCategory| |#2| (QUOTE (-635))) (|HasCategory| |#2| (LIST (QUOTE -1047) (QUOTE (-1186))))) (-12 (|HasCategory| |#1| (QUOTE (-458))) (|HasCategory| |#2| (QUOTE (-288)))) (|HasCategory| |#1| (QUOTE (-562)))) -(-580 -1385 UP) +(-580 -2968 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 -(-581 R -1385) +(-581 R -2968) ((|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 @@ -2284,11 +2284,11 @@ 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 -(-589 R -1385) +(-589 R -2968) ((|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},{}...,{}\\spad{Pn} are the factors of \\spad{P}."))) NIL NIL -(-590 E -1385) +(-590 E -2968) ((|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 @@ -2296,7 +2296,7 @@ NIL ((|constructor| (NIL "This domain provides representations for the intermediate form data structure used by the Spad elaborator.")) (|irDef| (($ (|Identifier|) (|InternalTypeForm|) $) "\\spad{irDef(f,ts,e)} returns an IR representation for a definition of a function named \\spad{f},{} with signature \\spad{ts} and body \\spad{e}.")) (|irCtor| (($ (|Identifier|) (|InternalTypeForm|)) "\\spad{irCtor(n,t)} returns an IR for a constructor reference of type designated by the type form \\spad{t}")) (|irVar| (($ (|Identifier|) (|InternalTypeForm|)) "\\spad{irVar(x,t)} returns an IR for a variable reference of type designated by the type form \\spad{t}"))) NIL NIL -(-592 -1385) +(-592 -2968) ((|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 \\spad{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}."))) ((-4447 . T) (-4446 . T)) ((|HasCategory| |#1| (LIST (QUOTE -907) (QUOTE (-1186)))) (|HasCategory| |#1| (LIST (QUOTE -1047) (QUOTE (-1186))))) @@ -2327,7 +2327,7 @@ NIL (-599 |mn|) ((|constructor| (NIL "This domain implements low-level strings"))) ((-4453 . T) (-4452 . T)) -((-2811 (-12 (|HasCategory| (-145) (QUOTE (-856))) (|HasCategory| (-145) (LIST (QUOTE -313) (QUOTE (-145))))) (-12 (|HasCategory| (-145) (QUOTE (-1109))) (|HasCategory| (-145) (LIST (QUOTE -313) (QUOTE (-145)))))) (-2811 (|HasCategory| (-145) (LIST (QUOTE -619) (QUOTE (-868)))) (-12 (|HasCategory| (-145) (QUOTE (-1109))) (|HasCategory| (-145) (LIST (QUOTE -313) (QUOTE (-145)))))) (|HasCategory| (-145) (LIST (QUOTE -620) (QUOTE (-542)))) (-2811 (|HasCategory| (-145) (QUOTE (-856))) (|HasCategory| (-145) (QUOTE (-1109)))) (|HasCategory| (-145) (QUOTE (-856))) (|HasCategory| (-570) (QUOTE (-856))) (|HasCategory| (-145) (QUOTE (-1109))) (|HasCategory| (-145) (LIST (QUOTE -619) (QUOTE (-868)))) (-12 (|HasCategory| (-145) (QUOTE (-1109))) (|HasCategory| (-145) (LIST (QUOTE -313) (QUOTE (-145)))))) +((-3684 (-12 (|HasCategory| (-145) (QUOTE (-856))) (|HasCategory| (-145) (LIST (QUOTE -313) (QUOTE (-145))))) (-12 (|HasCategory| (-145) (QUOTE (-1109))) (|HasCategory| (-145) (LIST (QUOTE -313) (QUOTE (-145)))))) (-3684 (|HasCategory| (-145) (LIST (QUOTE -619) (QUOTE (-868)))) (-12 (|HasCategory| (-145) (QUOTE (-1109))) (|HasCategory| (-145) (LIST (QUOTE -313) (QUOTE (-145)))))) (|HasCategory| (-145) (LIST (QUOTE -620) (QUOTE (-542)))) (-3684 (|HasCategory| (-145) (QUOTE (-856))) (|HasCategory| (-145) (QUOTE (-1109)))) (|HasCategory| (-145) (QUOTE (-856))) (|HasCategory| (-570) (QUOTE (-856))) (|HasCategory| (-145) (QUOTE (-1109))) (|HasCategory| (-145) (LIST (QUOTE -619) (QUOTE (-868)))) (-12 (|HasCategory| (-145) (QUOTE (-1109))) (|HasCategory| (-145) (LIST (QUOTE -313) (QUOTE (-145)))))) (-600 E V R P) ((|constructor| (NIL "tools for the summation packages.")) (|sum| (((|Record| (|:| |num| |#4|) (|:| |den| (|Integer|))) |#4| |#2|) "\\spad{sum(p(n), n)} returns \\spad{P(n)},{} the indefinite sum of \\spad{p(n)} with respect to upward difference on \\spad{n},{} \\spadignore{i.e.} \\spad{P(n+1) - P(n) = a(n)}.") (((|Record| (|:| |num| |#4|) (|:| |den| (|Integer|))) |#4| |#2| (|Segment| |#4|)) "\\spad{sum(p(n), n = a..b)} returns \\spad{p(a) + p(a+1) + ... + p(b)}."))) NIL @@ -2335,7 +2335,7 @@ NIL (-601 |Coef|) ((|constructor| (NIL "InnerSparseUnivariatePowerSeries is an internal domain \\indented{2}{used for creating sparse Taylor and Laurent series.}")) (|cAcsch| (($ $) "\\spad{cAcsch(f)} computes the inverse hyperbolic cosecant of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cAsech| (($ $) "\\spad{cAsech(f)} computes the inverse hyperbolic secant of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cAcoth| (($ $) "\\spad{cAcoth(f)} computes the inverse hyperbolic cotangent of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cAtanh| (($ $) "\\spad{cAtanh(f)} computes the inverse hyperbolic tangent of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cAcosh| (($ $) "\\spad{cAcosh(f)} computes the inverse hyperbolic cosine of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cAsinh| (($ $) "\\spad{cAsinh(f)} computes the inverse hyperbolic sine of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cCsch| (($ $) "\\spad{cCsch(f)} computes the hyperbolic cosecant of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cSech| (($ $) "\\spad{cSech(f)} computes the hyperbolic secant of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cCoth| (($ $) "\\spad{cCoth(f)} computes the hyperbolic cotangent of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cTanh| (($ $) "\\spad{cTanh(f)} computes the hyperbolic tangent of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cCosh| (($ $) "\\spad{cCosh(f)} computes the hyperbolic cosine of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cSinh| (($ $) "\\spad{cSinh(f)} computes the hyperbolic sine of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cAcsc| (($ $) "\\spad{cAcsc(f)} computes the arccosecant of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cAsec| (($ $) "\\spad{cAsec(f)} computes the arcsecant of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cAcot| (($ $) "\\spad{cAcot(f)} computes the arccotangent of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cAtan| (($ $) "\\spad{cAtan(f)} computes the arctangent of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cAcos| (($ $) "\\spad{cAcos(f)} computes the arccosine of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cAsin| (($ $) "\\spad{cAsin(f)} computes the arcsine of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cCsc| (($ $) "\\spad{cCsc(f)} computes the cosecant of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cSec| (($ $) "\\spad{cSec(f)} computes the secant of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cCot| (($ $) "\\spad{cCot(f)} computes the cotangent of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cTan| (($ $) "\\spad{cTan(f)} computes the tangent of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cCos| (($ $) "\\spad{cCos(f)} computes the cosine of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cSin| (($ $) "\\spad{cSin(f)} computes the sine of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cLog| (($ $) "\\spad{cLog(f)} computes the logarithm of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cExp| (($ $) "\\spad{cExp(f)} computes the exponential of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cRationalPower| (($ $ (|Fraction| (|Integer|))) "\\spad{cRationalPower(f,r)} computes \\spad{f^r}. For use when the coefficient ring is commutative.")) (|cPower| (($ $ |#1|) "\\spad{cPower(f,r)} computes \\spad{f^r},{} where \\spad{f} has constant coefficient 1. For use when the coefficient ring is commutative.")) (|integrate| (($ $) "\\spad{integrate(f(x))} returns an anti-derivative of the power series \\spad{f(x)} with constant coefficient 0. Warning: function does not check for a term of degree \\spad{-1}.")) (|seriesToOutputForm| (((|OutputForm|) (|Stream| (|Record| (|:| |k| (|Integer|)) (|:| |c| |#1|))) (|Reference| (|OrderedCompletion| (|Integer|))) (|Symbol|) |#1| (|Fraction| (|Integer|))) "\\spad{seriesToOutputForm(st,refer,var,cen,r)} prints the series \\spad{f((var - cen)^r)}.")) (|iCompose| (($ $ $) "\\spad{iCompose(f,g)} returns \\spad{f(g(x))}. This is an internal function which should only be called for Taylor series \\spad{f(x)} and \\spad{g(x)} such that the constant coefficient of \\spad{g(x)} is zero.")) (|taylorQuoByVar| (($ $) "\\spad{taylorQuoByVar(a0 + a1 x + a2 x**2 + ...)} returns \\spad{a1 + a2 x + a3 x**2 + ...}")) (|iExquo| (((|Union| $ "failed") $ $ (|Boolean|)) "\\spad{iExquo(f,g,taylor?)} is the quotient of the power series \\spad{f} and \\spad{g}. If \\spad{taylor?} is \\spad{true},{} then we must have \\spad{order(f) >= order(g)}.")) (|multiplyCoefficients| (($ (|Mapping| |#1| (|Integer|)) $) "\\spad{multiplyCoefficients(fn,f)} returns the series \\spad{sum(fn(n) * an * x^n,n = n0..)},{} where \\spad{f} is the series \\spad{sum(an * x^n,n = n0..)}.")) (|monomial?| (((|Boolean|) $) "\\spad{monomial?(f)} tests if \\spad{f} is a single monomial.")) (|series| (($ (|Stream| (|Record| (|:| |k| (|Integer|)) (|:| |c| |#1|)))) "\\spad{series(st)} creates a series from a stream of non-zero terms,{} where a term is an exponent-coefficient pair. The terms in the stream should be ordered by increasing order of exponents.")) (|getStream| (((|Stream| (|Record| (|:| |k| (|Integer|)) (|:| |c| |#1|))) $) "\\spad{getStream(f)} returns the stream of terms representing the series \\spad{f}.")) (|getRef| (((|Reference| (|OrderedCompletion| (|Integer|))) $) "\\spad{getRef(f)} returns a reference containing the order to which the terms of \\spad{f} have been computed.")) (|makeSeries| (($ (|Reference| (|OrderedCompletion| (|Integer|))) (|Stream| (|Record| (|:| |k| (|Integer|)) (|:| |c| |#1|)))) "\\spad{makeSeries(refer,str)} creates a power series from the reference \\spad{refer} and the stream \\spad{str}."))) (((-4454 "*") |has| |#1| (-174)) (-4445 |has| |#1| (-562)) (-4446 . T) (-4447 . T) (-4449 . T)) -((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasCategory| |#1| (QUOTE (-562))) (-2811 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-562)))) (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-148))) (-12 (|HasCategory| |#1| (LIST (QUOTE -907) (QUOTE (-1186)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (QUOTE (-570)) (|devaluate| |#1|))))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (QUOTE (-570)) (|devaluate| |#1|)))) (|HasCategory| (-570) (QUOTE (-1121))) (|HasCategory| |#1| (QUOTE (-368))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-570))))) (|HasSignature| |#1| (LIST (QUOTE -2940) (LIST (|devaluate| |#1|) (QUOTE (-1186)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-570)))))) +((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasCategory| |#1| (QUOTE (-562))) (-3684 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-562)))) (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-148))) (-12 (|HasCategory| |#1| (LIST (QUOTE -907) (QUOTE (-1186)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (QUOTE (-570)) (|devaluate| |#1|))))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (QUOTE (-570)) (|devaluate| |#1|)))) (|HasCategory| (-570) (QUOTE (-1121))) (|HasCategory| |#1| (QUOTE (-368))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-570))))) (|HasSignature| |#1| (LIST (QUOTE -2838) (LIST (|devaluate| |#1|) (QUOTE (-1186)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-570)))))) (-602 |Coef|) ((|constructor| (NIL "Internal package for dense Taylor series. This is an internal Taylor series type in which Taylor series are represented by a \\spadtype{Stream} of \\spadtype{Ring} elements. For univariate series,{} the \\spad{Stream} elements are the Taylor coefficients. For multivariate series,{} the \\spad{n}th Stream element is a form of degree \\spad{n} in the power series variables.")) (* (($ $ (|Integer|)) "\\spad{x*i} returns the product of integer \\spad{i} and the series \\spad{x}.")) (|order| (((|NonNegativeInteger|) $ (|NonNegativeInteger|)) "\\spad{order(x,n)} returns the minimum of \\spad{n} and the order of \\spad{x}.") (((|NonNegativeInteger|) $) "\\spad{order(x)} returns the order of a power series \\spad{x},{} \\indented{1}{\\spadignore{i.e.} the degree of the first non-zero term of the series.}")) (|pole?| (((|Boolean|) $) "\\spad{pole?(x)} tests if the series \\spad{x} has a pole. \\indented{1}{Note: this is \\spad{false} when \\spad{x} is a Taylor series.}")) (|series| (($ (|Stream| |#1|)) "\\spad{series(s)} creates a power series from a stream of \\indented{1}{ring elements.} \\indented{1}{For univariate series types,{} the stream \\spad{s} should be a stream} \\indented{1}{of Taylor coefficients. For multivariate series types,{} the} \\indented{1}{stream \\spad{s} should be a stream of forms the \\spad{n}th element} \\indented{1}{of which is a} \\indented{1}{form of degree \\spad{n} in the power series variables.}")) (|coefficients| (((|Stream| |#1|) $) "\\spad{coefficients(x)} returns a stream of ring elements. \\indented{1}{When \\spad{x} is a univariate series,{} this is a stream of Taylor} \\indented{1}{coefficients. When \\spad{x} is a multivariate series,{} the} \\indented{1}{\\spad{n}th element of the stream is a form of} \\indented{1}{degree \\spad{n} in the power series variables.}"))) (((-4454 "*") |has| |#1| (-562)) (-4445 |has| |#1| (-562)) (-4446 . T) (-4447 . T) (-4449 . T)) @@ -2352,7 +2352,7 @@ 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 -(-606 R -1385 FG) +(-606 R -2968 FG) ((|constructor| (NIL "This package provides transformations from trigonometric functions to exponentials and logarithms,{} and back. \\spad{F} and \\spad{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 @@ -2363,7 +2363,7 @@ NIL (-608 R |mn|) ((|constructor| (NIL "\\indented{2}{This type represents vector like objects with varying lengths} and a user-specified initial index."))) ((-4453 . T) (-4452 . T)) -((-2811 (-12 (|HasCategory| |#1| (QUOTE (-856))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|))))) (-2811 (-12 (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-868))))) (|HasCategory| |#1| (LIST (QUOTE -620) (QUOTE (-542)))) (-2811 (|HasCategory| |#1| (QUOTE (-856))) (|HasCategory| |#1| (QUOTE (-1109)))) (|HasCategory| |#1| (QUOTE (-856))) (|HasCategory| (-570) (QUOTE (-856))) (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (QUOTE (-25))) (|HasCategory| |#1| (QUOTE (-23))) (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-732))) (|HasCategory| |#1| (QUOTE (-1058))) (-12 (|HasCategory| |#1| (QUOTE (-1011))) (|HasCategory| |#1| (QUOTE (-1058)))) (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-868)))) (-12 (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|))))) +((-3684 (-12 (|HasCategory| |#1| (QUOTE (-856))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|))))) (-3684 (-12 (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-868))))) (|HasCategory| |#1| (LIST (QUOTE -620) (QUOTE (-542)))) (-3684 (|HasCategory| |#1| (QUOTE (-856))) (|HasCategory| |#1| (QUOTE (-1109)))) (|HasCategory| |#1| (QUOTE (-856))) (|HasCategory| (-570) (QUOTE (-856))) (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (QUOTE (-25))) (|HasCategory| |#1| (QUOTE (-23))) (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-732))) (|HasCategory| |#1| (QUOTE (-1058))) (-12 (|HasCategory| |#1| (QUOTE (-1011))) (|HasCategory| |#1| (QUOTE (-1058)))) (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-868)))) (-12 (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|))))) (-609 S |Index| |Entry|) ((|constructor| (NIL "An indexed aggregate is a many-to-one mapping of indices to entries. For example,{} a one-dimensional-array is an indexed aggregate where the index is an integer. Also,{} a table is an indexed aggregate where the indices and entries may have any type.")) (|swap!| (((|Void|) $ |#2| |#2|) "\\spad{swap!(u,i,j)} interchanges elements \\spad{i} and \\spad{j} of aggregate \\spad{u}. No meaningful value is returned.")) (|fill!| (($ $ |#3|) "\\spad{fill!(u,x)} replaces each entry in aggregate \\spad{u} by \\spad{x}. The modified \\spad{u} is returned as value.")) (|first| ((|#3| $) "\\spad{first(u)} returns the first element \\spad{x} of \\spad{u}. Note: for collections,{} \\axiom{first([\\spad{x},{}\\spad{y},{}...,{}\\spad{z}]) = \\spad{x}}. Error: if \\spad{u} is empty.")) (|minIndex| ((|#2| $) "\\spad{minIndex(u)} returns the minimum index \\spad{i} of aggregate \\spad{u}. Note: in general,{} \\axiom{minIndex(a) = reduce(min,{}[\\spad{i} for \\spad{i} in indices a])}; for lists,{} \\axiom{minIndex(a) = 1}.")) (|maxIndex| ((|#2| $) "\\spad{maxIndex(u)} returns the maximum index \\spad{i} of aggregate \\spad{u}. Note: in general,{} \\axiom{maxIndex(\\spad{u}) = reduce(max,{}[\\spad{i} for \\spad{i} in indices \\spad{u}])}; if \\spad{u} is a list,{} \\axiom{maxIndex(\\spad{u}) = \\#u}.")) (|entry?| (((|Boolean|) |#3| $) "\\spad{entry?(x,u)} tests if \\spad{x} equals \\axiom{\\spad{u} . \\spad{i}} for some index \\spad{i}.")) (|indices| (((|List| |#2|) $) "\\spad{indices(u)} returns a list of indices of aggregate \\spad{u} in no particular order.")) (|index?| (((|Boolean|) |#2| $) "\\spad{index?(i,u)} tests if \\spad{i} is an index of aggregate \\spad{u}.")) (|entries| (((|List| |#3|) $) "\\spad{entries(u)} returns a list of all the entries of aggregate \\spad{u} in no assumed order."))) NIL @@ -2382,12 +2382,12 @@ NIL NIL (-613 R A) ((|constructor| (NIL "\\indented{1}{AssociatedJordanAlgebra takes an algebra \\spad{A} and uses \\spadfun{*\\$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)."))) -((-4449 -2811 (-2115 (|has| |#2| (-372 |#1|)) (|has| |#1| (-562))) (-12 (|has| |#2| (-423 |#1|)) (|has| |#1| (-562)))) (-4447 . T) (-4446 . T)) -((-2811 (|HasCategory| |#2| (LIST (QUOTE -372) (|devaluate| |#1|))) (|HasCategory| |#2| (LIST (QUOTE -423) (|devaluate| |#1|)))) (|HasCategory| |#2| (LIST (QUOTE -423) (|devaluate| |#1|))) (-12 (|HasCategory| |#1| (QUOTE (-368))) (|HasCategory| |#2| (LIST (QUOTE -423) (|devaluate| |#1|)))) (-2811 (-12 (|HasCategory| |#1| (QUOTE (-562))) (|HasCategory| |#2| (LIST (QUOTE -372) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-562))) (|HasCategory| |#2| (LIST (QUOTE -423) (|devaluate| |#1|))))) (|HasCategory| |#2| (LIST (QUOTE -372) (|devaluate| |#1|)))) +((-4449 -3684 (-3163 (|has| |#2| (-372 |#1|)) (|has| |#1| (-562))) (-12 (|has| |#2| (-423 |#1|)) (|has| |#1| (-562)))) (-4447 . T) (-4446 . T)) +((-3684 (|HasCategory| |#2| (LIST (QUOTE -372) (|devaluate| |#1|))) (|HasCategory| |#2| (LIST (QUOTE -423) (|devaluate| |#1|)))) (|HasCategory| |#2| (LIST (QUOTE -423) (|devaluate| |#1|))) (-12 (|HasCategory| |#1| (QUOTE (-368))) (|HasCategory| |#2| (LIST (QUOTE -423) (|devaluate| |#1|)))) (-3684 (-12 (|HasCategory| |#1| (QUOTE (-562))) (|HasCategory| |#2| (LIST (QUOTE -372) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-562))) (|HasCategory| |#2| (LIST (QUOTE -423) (|devaluate| |#1|))))) (|HasCategory| |#2| (LIST (QUOTE -372) (|devaluate| |#1|)))) (-614 |Entry|) ((|constructor| (NIL "This domain allows a random access file to be viewed both as a table and as a file object.")) (|pack!| (($ $) "\\spad{pack!(f)} reorganizes the file \\spad{f} on disk to recover unused space."))) ((-4452 . T) (-4453 . T)) -((-12 (|HasCategory| (-2 (|:| -3679 (-1168)) (|:| -1409 |#1|)) (QUOTE (-1109))) (|HasCategory| (-2 (|:| -3679 (-1168)) (|:| -1409 |#1|)) (LIST (QUOTE -313) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -3679) (QUOTE (-1168))) (LIST (QUOTE |:|) (QUOTE -1409) (|devaluate| |#1|)))))) (|HasCategory| (-2 (|:| -3679 (-1168)) (|:| -1409 |#1|)) (LIST (QUOTE -620) (QUOTE (-542)))) (-12 (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| (-1168) (QUOTE (-856))) (|HasCategory| (-2 (|:| -3679 (-1168)) (|:| -1409 |#1|)) (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-868)))) (|HasCategory| (-2 (|:| -3679 (-1168)) (|:| -1409 |#1|)) (LIST (QUOTE -619) (QUOTE (-868))))) +((-12 (|HasCategory| (-2 (|:| -4111 (-1168)) (|:| -3117 |#1|)) (QUOTE (-1109))) (|HasCategory| (-2 (|:| -4111 (-1168)) (|:| -3117 |#1|)) (LIST (QUOTE -313) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -4111) (QUOTE (-1168))) (LIST (QUOTE |:|) (QUOTE -3117) (|devaluate| |#1|)))))) (|HasCategory| (-2 (|:| -4111 (-1168)) (|:| -3117 |#1|)) (LIST (QUOTE -620) (QUOTE (-542)))) (-12 (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| (-1168) (QUOTE (-856))) (|HasCategory| (-2 (|:| -4111 (-1168)) (|:| -3117 |#1|)) (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-868)))) (|HasCategory| (-2 (|:| -4111 (-1168)) (|:| -3117 |#1|)) (LIST (QUOTE -619) (QUOTE (-868))))) (-615 S |Key| |Entry|) ((|constructor| (NIL "A keyed dictionary is a dictionary of key-entry pairs for which there is a unique entry for each key.")) (|search| (((|Union| |#3| "failed") |#2| $) "\\spad{search(k,t)} searches the table \\spad{t} for the key \\spad{k},{} returning the entry stored in \\spad{t} for key \\spad{k}. If \\spad{t} has no such key,{} \\axiom{search(\\spad{k},{}\\spad{t})} returns \"failed\".")) (|remove!| (((|Union| |#3| "failed") |#2| $) "\\spad{remove!(k,t)} searches the table \\spad{t} for the key \\spad{k} removing (and return) the entry if there. If \\spad{t} has no such key,{} \\axiom{remove!(\\spad{k},{}\\spad{t})} returns \"failed\".")) (|keys| (((|List| |#2|) $) "\\spad{keys(t)} returns the list the keys in table \\spad{t}.")) (|key?| (((|Boolean|) |#2| $) "\\spad{key?(k,t)} tests if \\spad{k} is a key in table \\spad{t}."))) NIL @@ -2412,7 +2412,7 @@ 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| $) "\\spad{convert(a)} transforms a into an element of \\spad{S}."))) NIL NIL -(-621 -1385 UP) +(-621 -2968 UP) ((|constructor| (NIL "\\spadtype{Kovacic} provides a modified Kovacic\\spad{'s} algorithm for solving explicitely irreducible 2nd order linear ordinary differential equations.")) (|kovacic| (((|Union| (|SparseUnivariatePolynomial| (|Fraction| |#2|)) "failed") (|Fraction| |#2|) (|Fraction| |#2|) (|Fraction| |#2|) (|Mapping| (|Factored| |#2|) |#2|)) "\\spad{kovacic(a_0,a_1,a_2,ezfactor)} returns either \"failed\" or \\spad{P}(\\spad{u}) such that \\spad{\\$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 @@ -2440,7 +2440,7 @@ NIL ((|constructor| (NIL "LocalAlgebra produces the localization of an algebra,{} \\spadignore{i.e.} fractions whose numerators come from some \\spad{R} algebra.")) (|denom| ((|#3| $) "\\spad{denom x} returns the denominator of \\spad{x}.")) (|numer| ((|#1| $) "\\spad{numer x} returns the numerator of \\spad{x}.")) (/ (($ |#1| |#3|) "\\spad{a / d} divides the element \\spad{a} by \\spad{d}.") (($ $ |#3|) "\\spad{x / d} divides the element \\spad{x} by \\spad{d}."))) ((-4446 . T) (-4447 . T) (-4449 . T)) ((|HasCategory| |#1| (QUOTE (-854)))) -(-628 R -1385) +(-628 R -2968) ((|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 @@ -2472,18 +2472,18 @@ 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 -(-636 R -1385) +(-636 R -2968) ((|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 -(-637 |lv| -1385) +(-637 |lv| -2968) ((|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 (-638) ((|constructor| (NIL "This domain provides a simple way to save values in files.")) (|setelt| (((|Any|) $ (|Symbol|) (|Any|)) "\\spad{lib.k := v} saves the value \\spad{v} in the library \\spad{lib}. It can later be extracted using the key \\spad{k}.")) (|pack!| (($ $) "\\spad{pack!(f)} reorganizes the file \\spad{f} on disk to recover unused space.")) (|library| (($ (|FileName|)) "\\spad{library(ln)} creates a new library file."))) ((-4453 . T)) -((-12 (|HasCategory| (-2 (|:| -3679 (-1168)) (|:| -1409 (-52))) (QUOTE (-1109))) (|HasCategory| (-2 (|:| -3679 (-1168)) (|:| -1409 (-52))) (LIST (QUOTE -313) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -3679) (QUOTE (-1168))) (LIST (QUOTE |:|) (QUOTE -1409) (QUOTE (-52))))))) (-2811 (|HasCategory| (-2 (|:| -3679 (-1168)) (|:| -1409 (-52))) (QUOTE (-1109))) (|HasCategory| (-52) (QUOTE (-1109)))) (-2811 (|HasCategory| (-2 (|:| -3679 (-1168)) (|:| -1409 (-52))) (QUOTE (-1109))) (|HasCategory| (-2 (|:| -3679 (-1168)) (|:| -1409 (-52))) (LIST (QUOTE -619) (QUOTE (-868)))) (|HasCategory| (-52) (QUOTE (-1109))) (|HasCategory| (-52) (LIST (QUOTE -619) (QUOTE (-868))))) (|HasCategory| (-2 (|:| -3679 (-1168)) (|:| -1409 (-52))) (LIST (QUOTE -620) (QUOTE (-542)))) (-12 (|HasCategory| (-52) (QUOTE (-1109))) (|HasCategory| (-52) (LIST (QUOTE -313) (QUOTE (-52))))) (|HasCategory| (-1168) (QUOTE (-856))) (-2811 (|HasCategory| (-2 (|:| -3679 (-1168)) (|:| -1409 (-52))) (LIST (QUOTE -619) (QUOTE (-868)))) (|HasCategory| (-52) (LIST (QUOTE -619) (QUOTE (-868))))) (|HasCategory| (-52) (QUOTE (-1109))) (|HasCategory| (-52) (LIST (QUOTE -619) (QUOTE (-868)))) (|HasCategory| (-2 (|:| -3679 (-1168)) (|:| -1409 (-52))) (LIST (QUOTE -619) (QUOTE (-868)))) (|HasCategory| (-2 (|:| -3679 (-1168)) (|:| -1409 (-52))) (QUOTE (-1109)))) +((-12 (|HasCategory| (-2 (|:| -4111 (-1168)) (|:| -3117 (-52))) (QUOTE (-1109))) (|HasCategory| (-2 (|:| -4111 (-1168)) (|:| -3117 (-52))) (LIST (QUOTE -313) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -4111) (QUOTE (-1168))) (LIST (QUOTE |:|) (QUOTE -3117) (QUOTE (-52))))))) (-3684 (|HasCategory| (-2 (|:| -4111 (-1168)) (|:| -3117 (-52))) (QUOTE (-1109))) (|HasCategory| (-52) (QUOTE (-1109)))) (-3684 (|HasCategory| (-2 (|:| -4111 (-1168)) (|:| -3117 (-52))) (QUOTE (-1109))) (|HasCategory| (-2 (|:| -4111 (-1168)) (|:| -3117 (-52))) (LIST (QUOTE -619) (QUOTE (-868)))) (|HasCategory| (-52) (QUOTE (-1109))) (|HasCategory| (-52) (LIST (QUOTE -619) (QUOTE (-868))))) (|HasCategory| (-2 (|:| -4111 (-1168)) (|:| -3117 (-52))) (LIST (QUOTE -620) (QUOTE (-542)))) (-12 (|HasCategory| (-52) (QUOTE (-1109))) (|HasCategory| (-52) (LIST (QUOTE -313) (QUOTE (-52))))) (|HasCategory| (-1168) (QUOTE (-856))) (-3684 (|HasCategory| (-2 (|:| -4111 (-1168)) (|:| -3117 (-52))) (LIST (QUOTE -619) (QUOTE (-868)))) (|HasCategory| (-52) (LIST (QUOTE -619) (QUOTE (-868))))) (|HasCategory| (-52) (QUOTE (-1109))) (|HasCategory| (-52) (LIST (QUOTE -619) (QUOTE (-868)))) (|HasCategory| (-2 (|:| -4111 (-1168)) (|:| -3117 (-52))) (LIST (QUOTE -619) (QUOTE (-868)))) (|HasCategory| (-2 (|:| -4111 (-1168)) (|:| -3117 (-52))) (QUOTE (-1109)))) (-639 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{\\spad{x/r}} returns the division of \\axiom{\\spad{x}} by \\axiom{\\spad{r}}.")) (|construct| (($ $ $) "\\axiom{construct(\\spad{x},{}\\spad{y})} returns the Lie bracket of \\axiom{\\spad{x}} and \\axiom{\\spad{y}}."))) NIL @@ -2494,8 +2494,8 @@ NIL NIL (-641 R A) ((|constructor| (NIL "AssociatedLieAlgebra takes an algebra \\spad{A} and uses \\spadfun{*\\$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)."))) -((-4449 -2811 (-2115 (|has| |#2| (-372 |#1|)) (|has| |#1| (-562))) (-12 (|has| |#2| (-423 |#1|)) (|has| |#1| (-562)))) (-4447 . T) (-4446 . T)) -((-2811 (|HasCategory| |#2| (LIST (QUOTE -372) (|devaluate| |#1|))) (|HasCategory| |#2| (LIST (QUOTE -423) (|devaluate| |#1|)))) (|HasCategory| |#2| (LIST (QUOTE -423) (|devaluate| |#1|))) (-12 (|HasCategory| |#1| (QUOTE (-368))) (|HasCategory| |#2| (LIST (QUOTE -423) (|devaluate| |#1|)))) (-2811 (-12 (|HasCategory| |#1| (QUOTE (-562))) (|HasCategory| |#2| (LIST (QUOTE -372) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-562))) (|HasCategory| |#2| (LIST (QUOTE -423) (|devaluate| |#1|))))) (|HasCategory| |#2| (LIST (QUOTE -372) (|devaluate| |#1|)))) +((-4449 -3684 (-3163 (|has| |#2| (-372 |#1|)) (|has| |#1| (-562))) (-12 (|has| |#2| (-423 |#1|)) (|has| |#1| (-562)))) (-4447 . T) (-4446 . T)) +((-3684 (|HasCategory| |#2| (LIST (QUOTE -372) (|devaluate| |#1|))) (|HasCategory| |#2| (LIST (QUOTE -423) (|devaluate| |#1|)))) (|HasCategory| |#2| (LIST (QUOTE -423) (|devaluate| |#1|))) (-12 (|HasCategory| |#1| (QUOTE (-368))) (|HasCategory| |#2| (LIST (QUOTE -423) (|devaluate| |#1|)))) (-3684 (-12 (|HasCategory| |#1| (QUOTE (-562))) (|HasCategory| |#2| (LIST (QUOTE -372) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-562))) (|HasCategory| |#2| (LIST (QUOTE -423) (|devaluate| |#1|))))) (|HasCategory| |#2| (LIST (QUOTE -372) (|devaluate| |#1|)))) (-642 R FE) ((|constructor| (NIL "PowerSeriesLimitPackage implements limits of expressions in one or more variables as one of the variables approaches a limiting value. Included are two-sided limits,{} left- and right- hand limits,{} and limits at plus or minus infinity.")) (|complexLimit| (((|Union| (|OnePointCompletion| |#2|) "failed") |#2| (|Equation| (|OnePointCompletion| |#2|))) "\\spad{complexLimit(f(x),x = a)} computes the complex limit \\spad{lim(x -> a,f(x))}.")) (|limit| (((|Union| (|OrderedCompletion| |#2|) "failed") |#2| (|Equation| |#2|) (|String|)) "\\spad{limit(f(x),x=a,\"left\")} computes the left hand real limit \\spad{lim(x -> a-,f(x))}; \\spad{limit(f(x),x=a,\"right\")} computes the right hand real limit \\spad{lim(x -> a+,f(x))}.") (((|Union| (|OrderedCompletion| |#2|) (|Record| (|:| |leftHandLimit| (|Union| (|OrderedCompletion| |#2|) "failed")) (|:| |rightHandLimit| (|Union| (|OrderedCompletion| |#2|) "failed"))) "failed") |#2| (|Equation| (|OrderedCompletion| |#2|))) "\\spad{limit(f(x),x = a)} computes the real limit \\spad{lim(x -> a,f(x))}."))) NIL @@ -2507,7 +2507,7 @@ NIL (-644 S R) ((|constructor| (NIL "Test for linear dependence.")) (|solveLinear| (((|Union| (|Vector| (|Fraction| |#1|)) "failed") (|Vector| |#2|) |#2|) "\\spad{solveLinear([v1,...,vn], u)} returns \\spad{[c1,...,cn]} such that \\spad{c1*v1 + ... + cn*vn = u},{} \"failed\" if no such \\spad{ci}\\spad{'s} exist in the quotient field of \\spad{S}.") (((|Union| (|Vector| |#1|) "failed") (|Vector| |#2|) |#2|) "\\spad{solveLinear([v1,...,vn], u)} returns \\spad{[c1,...,cn]} such that \\spad{c1*v1 + ... + cn*vn = u},{} \"failed\" if no such \\spad{ci}\\spad{'s} exist in \\spad{S}.")) (|linearDependence| (((|Union| (|Vector| |#1|) "failed") (|Vector| |#2|)) "\\spad{linearDependence([v1,...,vn])} returns \\spad{[c1,...,cn]} if \\spad{c1*v1 + ... + cn*vn = 0} and not all the \\spad{ci}\\spad{'s} are 0,{} \"failed\" if the \\spad{vi}\\spad{'s} are linearly independent over \\spad{S}.")) (|linearlyDependent?| (((|Boolean|) (|Vector| |#2|)) "\\spad{linearlyDependent?([v1,...,vn])} returns \\spad{true} if the \\spad{vi}\\spad{'s} are linearly dependent over \\spad{S},{} \\spad{false} otherwise."))) NIL -((-2104 (|HasCategory| |#1| (QUOTE (-368)))) (|HasCategory| |#1| (QUOTE (-368)))) +((-3152 (|HasCategory| |#1| (QUOTE (-368)))) (|HasCategory| |#1| (QUOTE (-368)))) (-645 R) ((|constructor| (NIL "An extension ring with an explicit linear dependence test.")) (|reducedSystem| (((|Record| (|:| |mat| (|Matrix| |#1|)) (|:| |vec| (|Vector| |#1|))) (|Matrix| $) (|Vector| $)) "\\spad{reducedSystem(A, v)} returns a matrix \\spad{B} and a vector \\spad{w} such that \\spad{A x = v} and \\spad{B x = w} have the same solutions in \\spad{R}.") (((|Matrix| |#1|) (|Matrix| $)) "\\spad{reducedSystem(A)} returns a matrix \\spad{B} such that \\spad{A x = 0} and \\spad{B x = 0} have the same solutions in \\spad{R}."))) ((-4449 . T)) @@ -2531,7 +2531,7 @@ NIL (-650 S) ((|constructor| (NIL "\\spadtype{List} implements singly-linked lists that are addressable by indices; the index of the first element is 1. In addition to the operations provided by \\spadtype{IndexedList},{} this constructor provides some LISP-like functions such as \\spadfun{null} and \\spadfun{cons}.")) (|setDifference| (($ $ $) "\\spad{setDifference(u1,u2)} returns a list of the elements of \\spad{u1} that are not also in \\spad{u2}. The order of elements in the resulting list is unspecified.")) (|setIntersection| (($ $ $) "\\spad{setIntersection(u1,u2)} returns a list of the elements that lists \\spad{u1} and \\spad{u2} have in common. The order of elements in the resulting list is unspecified.")) (|setUnion| (($ $ $) "\\spad{setUnion(u1,u2)} appends the two lists \\spad{u1} and \\spad{u2},{} then removes all duplicates. The order of elements in the resulting list is unspecified.")) (|append| (($ $ $) "\\spad{append(u1,u2)} appends the elements of list \\spad{u1} onto the front of list \\spad{u2}. This new list and \\spad{u2} will share some structure.")) (|cons| (($ |#1| $) "\\spad{cons(element,u)} appends \\spad{element} onto the front of list \\spad{u} and returns the new list. This new list and the old one will share some structure.")) (|null| (((|Boolean|) $) "\\spad{null(u)} tests if list \\spad{u} is the empty list.")) (|nil| (($) "\\spad{nil} is the empty list."))) ((-4453 . T) (-4452 . T)) -((-2811 (-12 (|HasCategory| |#1| (QUOTE (-856))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|))))) (-2811 (-12 (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-868))))) (|HasCategory| |#1| (LIST (QUOTE -620) (QUOTE (-542)))) (-2811 (|HasCategory| |#1| (QUOTE (-856))) (|HasCategory| |#1| (QUOTE (-1109)))) (|HasCategory| |#1| (QUOTE (-856))) (|HasCategory| |#1| (QUOTE (-834))) (|HasCategory| (-570) (QUOTE (-856))) (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-868)))) (-12 (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|))))) +((-3684 (-12 (|HasCategory| |#1| (QUOTE (-856))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|))))) (-3684 (-12 (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-868))))) (|HasCategory| |#1| (LIST (QUOTE -620) (QUOTE (-542)))) (-3684 (|HasCategory| |#1| (QUOTE (-856))) (|HasCategory| |#1| (QUOTE (-1109)))) (|HasCategory| |#1| (QUOTE (-856))) (|HasCategory| |#1| (QUOTE (-834))) (|HasCategory| (-570) (QUOTE (-856))) (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-868)))) (-12 (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|))))) (-651 T$) ((|constructor| (NIL "This domain represents AST for Spad literals."))) NIL @@ -2543,7 +2543,7 @@ NIL (-653 S) ((|substitute| (($ |#1| |#1| $) "\\spad{substitute(x,y,d)} replace \\spad{x}\\spad{'s} with \\spad{y}\\spad{'s} in dictionary \\spad{d}.")) (|duplicates?| (((|Boolean|) $) "\\spad{duplicates?(d)} tests if dictionary \\spad{d} has duplicate entries."))) ((-4452 . T) (-4453 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1109))) (-2811 (-12 (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-868))))) (|HasCategory| |#1| (LIST (QUOTE -620) (QUOTE (-542)))) (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-868))))) +((-12 (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1109))) (-3684 (-12 (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-868))))) (|HasCategory| |#1| (LIST (QUOTE -620) (QUOTE (-542)))) (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-868))))) (-654 R) ((|constructor| (NIL "The category of left modules over an \\spad{rng} (ring not necessarily with unit). This is an abelian group which supports left multiplation by elements of the \\spad{rng}. \\blankline"))) NIL @@ -2560,7 +2560,7 @@ NIL ((|constructor| (NIL "A linear aggregate is an aggregate whose elements are indexed by integers. Examples of linear aggregates are strings,{} lists,{} and arrays. Most of the exported operations for linear aggregates are non-destructive but are not always efficient for a particular aggregate. For example,{} \\spadfun{concat} of two lists needs only to copy its first argument,{} whereas \\spadfun{concat} of two arrays needs to copy both arguments. Most of the operations exported here apply to infinite objects (\\spadignore{e.g.} streams) as well to finite ones. For finite linear aggregates,{} see \\spadtype{FiniteLinearAggregate}.")) (|setelt| ((|#1| $ (|UniversalSegment| (|Integer|)) |#1|) "\\spad{setelt(u,i..j,x)} (also written: \\axiom{\\spad{u}(\\spad{i}..\\spad{j}) \\spad{:=} \\spad{x}}) destructively replaces each element in the segment \\axiom{\\spad{u}(\\spad{i}..\\spad{j})} by \\spad{x}. The value \\spad{x} is returned. Note: \\spad{u} is destructively change so that \\axiom{\\spad{u}.\\spad{k} \\spad{:=} \\spad{x} for \\spad{k} in \\spad{i}..\\spad{j}}; its length remains unchanged.")) (|insert| (($ $ $ (|Integer|)) "\\spad{insert(v,u,k)} returns a copy of \\spad{u} having \\spad{v} inserted beginning at the \\axiom{\\spad{i}}th element. Note: \\axiom{insert(\\spad{v},{}\\spad{u},{}\\spad{k}) = concat( \\spad{u}(0..\\spad{k}-1),{} \\spad{v},{} \\spad{u}(\\spad{k}..) )}.") (($ |#1| $ (|Integer|)) "\\spad{insert(x,u,i)} returns a copy of \\spad{u} having \\spad{x} as its \\axiom{\\spad{i}}th element. Note: \\axiom{insert(\\spad{x},{}a,{}\\spad{k}) = concat(concat(a(0..\\spad{k}-1),{}\\spad{x}),{}a(\\spad{k}..))}.")) (|delete| (($ $ (|UniversalSegment| (|Integer|))) "\\spad{delete(u,i..j)} returns a copy of \\spad{u} with the \\axiom{\\spad{i}}th through \\axiom{\\spad{j}}th element deleted. Note: \\axiom{delete(a,{}\\spad{i}..\\spad{j}) = concat(a(0..\\spad{i}-1),{}a(\\spad{j+1}..))}.") (($ $ (|Integer|)) "\\spad{delete(u,i)} returns a copy of \\spad{u} with the \\axiom{\\spad{i}}th element deleted. Note: for lists,{} \\axiom{delete(a,{}\\spad{i}) \\spad{==} concat(a(0..\\spad{i} - 1),{}a(\\spad{i} + 1,{}..))}.")) (|map| (($ (|Mapping| |#1| |#1| |#1|) $ $) "\\spad{map(f,u,v)} returns a new collection \\spad{w} with elements \\axiom{\\spad{z} = \\spad{f}(\\spad{x},{}\\spad{y})} for corresponding elements \\spad{x} and \\spad{y} from \\spad{u} and \\spad{v}. Note: for linear aggregates,{} \\axiom{\\spad{w}.\\spad{i} = \\spad{f}(\\spad{u}.\\spad{i},{}\\spad{v}.\\spad{i})}.")) (|concat| (($ (|List| $)) "\\spad{concat(u)},{} where \\spad{u} is a lists of aggregates \\axiom{[a,{}\\spad{b},{}...,{}\\spad{c}]},{} returns a single aggregate consisting of the elements of \\axiom{a} followed by those of \\spad{b} followed ... by the elements of \\spad{c}. Note: \\axiom{concat(a,{}\\spad{b},{}...,{}\\spad{c}) = concat(a,{}concat(\\spad{b},{}...,{}\\spad{c}))}.") (($ $ $) "\\spad{concat(u,v)} returns an aggregate consisting of the elements of \\spad{u} followed by the elements of \\spad{v}. Note: if \\axiom{\\spad{w} = concat(\\spad{u},{}\\spad{v})} then \\axiom{\\spad{w}.\\spad{i} = \\spad{u}.\\spad{i} for \\spad{i} in indices \\spad{u}} and \\axiom{\\spad{w}.(\\spad{j} + maxIndex \\spad{u}) = \\spad{v}.\\spad{j} for \\spad{j} in indices \\spad{v}}.") (($ |#1| $) "\\spad{concat(x,u)} returns aggregate \\spad{u} with additional element at the front. Note: for lists: \\axiom{concat(\\spad{x},{}\\spad{u}) \\spad{==} concat([\\spad{x}],{}\\spad{u})}.") (($ $ |#1|) "\\spad{concat(u,x)} returns aggregate \\spad{u} with additional element \\spad{x} at the end. Note: for lists,{} \\axiom{concat(\\spad{u},{}\\spad{x}) \\spad{==} concat(\\spad{u},{}[\\spad{x}])}")) (|new| (($ (|NonNegativeInteger|) |#1|) "\\spad{new(n,x)} returns \\axiom{fill!(new \\spad{n},{}\\spad{x})}."))) NIL NIL -(-658 R -1385 L) +(-658 R -2968 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 @@ -2580,11 +2580,11 @@ 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}."))) ((-4446 . T) (-4447 . T) (-4449 . T)) NIL -(-663 -1385 UP) +(-663 -2968 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)))) -(-664 A -3757) +(-664 A -1498) ((|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}}"))) ((-4446 . T) (-4447 . T) (-4449 . T)) ((|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (LIST (QUOTE -1047) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasCategory| |#1| (LIST (QUOTE -1047) (QUOTE (-570)))) (|HasCategory| |#1| (QUOTE (-562))) (|HasCategory| |#1| (QUOTE (-458))) (|HasCategory| |#1| (QUOTE (-368)))) @@ -2620,11 +2620,11 @@ 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}."))) ((-4453 . T) (-4452 . T)) NIL -(-673 -1385) +(-673 -2968) ((|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\\spad{'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 -(-674 -1385 |Row| |Col| M) +(-674 -2968 |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 @@ -2635,7 +2635,7 @@ NIL (-676 |n| R) ((|constructor| (NIL "LieSquareMatrix(\\spad{n},{}\\spad{R}) implements the Lie algebra of the \\spad{n} by \\spad{n} matrices over the commutative ring \\spad{R}. The Lie bracket (commutator) of the algebra is given by \\spad{a*b := (a *\\$SQMATRIX(n,R) b - b *\\$SQMATRIX(n,R) a)},{} where \\spadfun{*\\$SQMATRIX(\\spad{n},{}\\spad{R})} is the usual matrix multiplication."))) ((-4449 . T) (-4452 . T) (-4446 . T) (-4447 . T)) -((|HasCategory| |#2| (LIST (QUOTE -907) (QUOTE (-1186)))) (|HasCategory| |#2| (QUOTE (-235))) (|HasAttribute| |#2| (QUOTE (-4454 "*"))) (|HasCategory| |#2| (LIST (QUOTE -645) (QUOTE (-570)))) (|HasCategory| |#2| (LIST (QUOTE -1047) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasCategory| |#2| (LIST (QUOTE -1047) (QUOTE (-570)))) (-2811 (-12 (|HasCategory| |#2| (QUOTE (-235))) (|HasCategory| |#2| (LIST (QUOTE -313) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-1109))) (|HasCategory| |#2| (LIST (QUOTE -313) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (LIST (QUOTE -313) (|devaluate| |#2|))) (|HasCategory| |#2| (LIST (QUOTE -645) (QUOTE (-570))))) (-12 (|HasCategory| |#2| (LIST (QUOTE -313) (|devaluate| |#2|))) (|HasCategory| |#2| (LIST (QUOTE -907) (QUOTE (-1186)))))) (|HasCategory| |#2| (QUOTE (-311))) (|HasCategory| |#2| (QUOTE (-1109))) (|HasCategory| |#2| (QUOTE (-368))) (|HasCategory| |#2| (QUOTE (-562))) (-2811 (|HasAttribute| |#2| (QUOTE (-4454 "*"))) (|HasCategory| |#2| (LIST (QUOTE -645) (QUOTE (-570)))) (|HasCategory| |#2| (LIST (QUOTE -907) (QUOTE (-1186)))) (|HasCategory| |#2| (QUOTE (-235)))) (|HasCategory| |#2| (LIST (QUOTE -619) (QUOTE (-868)))) (-12 (|HasCategory| |#2| (QUOTE (-1109))) (|HasCategory| |#2| (LIST (QUOTE -313) (|devaluate| |#2|)))) (|HasCategory| |#2| (QUOTE (-174)))) +((|HasCategory| |#2| (LIST (QUOTE -907) (QUOTE (-1186)))) (|HasCategory| |#2| (QUOTE (-235))) (|HasAttribute| |#2| (QUOTE (-4454 "*"))) (|HasCategory| |#2| (LIST (QUOTE -645) (QUOTE (-570)))) (|HasCategory| |#2| (LIST (QUOTE -1047) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasCategory| |#2| (LIST (QUOTE -1047) (QUOTE (-570)))) (-3684 (-12 (|HasCategory| |#2| (QUOTE (-235))) (|HasCategory| |#2| (LIST (QUOTE -313) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-1109))) (|HasCategory| |#2| (LIST (QUOTE -313) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (LIST (QUOTE -313) (|devaluate| |#2|))) (|HasCategory| |#2| (LIST (QUOTE -645) (QUOTE (-570))))) (-12 (|HasCategory| |#2| (LIST (QUOTE -313) (|devaluate| |#2|))) (|HasCategory| |#2| (LIST (QUOTE -907) (QUOTE (-1186)))))) (|HasCategory| |#2| (QUOTE (-311))) (|HasCategory| |#2| (QUOTE (-1109))) (|HasCategory| |#2| (QUOTE (-368))) (|HasCategory| |#2| (QUOTE (-562))) (-3684 (|HasAttribute| |#2| (QUOTE (-4454 "*"))) (|HasCategory| |#2| (LIST (QUOTE -645) (QUOTE (-570)))) (|HasCategory| |#2| (LIST (QUOTE -907) (QUOTE (-1186)))) (|HasCategory| |#2| (QUOTE (-235)))) (|HasCategory| |#2| (LIST (QUOTE -619) (QUOTE (-868)))) (-12 (|HasCategory| |#2| (QUOTE (-1109))) (|HasCategory| |#2| (LIST (QUOTE -313) (|devaluate| |#2|)))) (|HasCategory| |#2| (QUOTE (-174)))) (-677) ((|constructor| (NIL "This domain represents `literal sequence' syntax.")) (|elements| (((|List| (|SpadAst|)) $) "\\spad{elements(e)} returns the list of expressions in the `literal' list `e'."))) NIL @@ -2655,7 +2655,7 @@ NIL (-681 R) ((|constructor| (NIL "This domain represents three dimensional matrices over a general object type")) (|matrixDimensions| (((|Vector| (|NonNegativeInteger|)) $) "\\spad{matrixDimensions(x)} returns the dimensions of a matrix")) (|matrixConcat3D| (($ (|Symbol|) $ $) "\\spad{matrixConcat3D(s,x,y)} concatenates two 3-\\spad{D} matrices along a specified axis")) (|coerce| (((|PrimitiveArray| (|PrimitiveArray| (|PrimitiveArray| |#1|))) $) "\\spad{coerce(x)} moves from the domain to the representation type") (($ (|PrimitiveArray| (|PrimitiveArray| (|PrimitiveArray| |#1|)))) "\\spad{coerce(p)} moves from the representation type (PrimitiveArray PrimitiveArray PrimitiveArray \\spad{R}) to the domain")) (|setelt!| ((|#1| $ (|NonNegativeInteger|) (|NonNegativeInteger|) (|NonNegativeInteger|) |#1|) "\\spad{setelt!(x,i,j,k,s)} (or \\spad{x}.\\spad{i}.\\spad{j}.k:=s) sets a specific element of the array to some value of type \\spad{R}")) (|elt| ((|#1| $ (|NonNegativeInteger|) (|NonNegativeInteger|) (|NonNegativeInteger|)) "\\spad{elt(x,i,j,k)} extract an element from the matrix \\spad{x}")) (|construct| (($ (|List| (|List| (|List| |#1|)))) "\\spad{construct(lll)} creates a 3-\\spad{D} matrix from a List List List \\spad{R} \\spad{lll}")) (|plus| (($ $ $) "\\spad{plus(x,y)} adds two matrices,{} term by term we note that they must be the same size")) (|identityMatrix| (($ (|NonNegativeInteger|)) "\\spad{identityMatrix(n)} create an identity matrix we note that this must be square")) (|zeroMatrix| (($ (|NonNegativeInteger|) (|NonNegativeInteger|) (|NonNegativeInteger|)) "\\spad{zeroMatrix(i,j,k)} create a matrix with all zero terms"))) NIL -((-2811 (-12 (|HasCategory| |#1| (QUOTE (-1058))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|))))) (|HasCategory| |#1| (QUOTE (-1109))) (-2811 (-12 (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-868))))) (|HasCategory| |#1| (QUOTE (-1058))) (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-868)))) (-12 (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|))))) +((-3684 (-12 (|HasCategory| |#1| (QUOTE (-1058))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|))))) (|HasCategory| |#1| (QUOTE (-1109))) (-3684 (-12 (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-868))))) (|HasCategory| |#1| (QUOTE (-1058))) (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-868)))) (-12 (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|))))) (-682) ((|constructor| (NIL "This domain represents the syntax of a macro definition.")) (|body| (((|SpadAst|) $) "\\spad{body(m)} returns the right hand side of the definition \\spad{`m'}.")) (|head| (((|HeadAst|) $) "\\spad{head(m)} returns the head of the macro definition \\spad{`m'}. This is a list of identifiers starting with the name of the macro followed by the name of the parameters,{} if any."))) NIL @@ -2711,7 +2711,7 @@ NIL (-695 R) ((|constructor| (NIL "\\spadtype{Matrix} is a matrix domain where 1-based indexing is used for both rows and columns.")) (|inverse| (((|Union| $ "failed") $) "\\spad{inverse(m)} returns the inverse of the matrix \\spad{m}. If the matrix is not invertible,{} \"failed\" is returned. Error: if the matrix is not square.")) (|diagonalMatrix| (($ (|Vector| |#1|)) "\\spad{diagonalMatrix(v)} returns a diagonal matrix where the elements of \\spad{v} appear on the diagonal."))) ((-4452 . T) (-4453 . T)) -((-2811 (-12 (|HasCategory| |#1| (QUOTE (-368))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|))))) (|HasCategory| |#1| (QUOTE (-1109))) (-2811 (-12 (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-868))))) (|HasCategory| |#1| (LIST (QUOTE -620) (QUOTE (-542)))) (|HasCategory| |#1| (QUOTE (-311))) (|HasCategory| |#1| (QUOTE (-562))) (|HasAttribute| |#1| (QUOTE (-4454 "*"))) (|HasCategory| |#1| (QUOTE (-368))) (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-868)))) (-12 (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|))))) +((-3684 (-12 (|HasCategory| |#1| (QUOTE (-368))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|))))) (|HasCategory| |#1| (QUOTE (-1109))) (-3684 (-12 (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-868))))) (|HasCategory| |#1| (LIST (QUOTE -620) (QUOTE (-542)))) (|HasCategory| |#1| (QUOTE (-311))) (|HasCategory| |#1| (QUOTE (-562))) (|HasAttribute| |#1| (QUOTE (-4454 "*"))) (|HasCategory| |#1| (QUOTE (-368))) (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-868)))) (-12 (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|))))) (-696 R) ((|constructor| (NIL "This package provides standard arithmetic operations on matrices. The functions in this package store the results of computations in existing matrices,{} rather than creating new matrices. This package works only for matrices of type Matrix and uses the internal representation of this type.")) (** (((|Matrix| |#1|) (|Matrix| |#1|) (|NonNegativeInteger|)) "\\spad{x ** n} computes the \\spad{n}-th power of a square matrix. The power \\spad{n} is assumed greater than 1.")) (|power!| (((|Matrix| |#1|) (|Matrix| |#1|) (|Matrix| |#1|) (|Matrix| |#1|) (|Matrix| |#1|) (|NonNegativeInteger|)) "\\spad{power!(a,b,c,m,n)} computes \\spad{m} \\spad{**} \\spad{n} and stores the result in \\spad{a}. The matrices \\spad{b} and \\spad{c} are used to store intermediate results. Error: if \\spad{a},{} \\spad{b},{} \\spad{c},{} and \\spad{m} are not square and of the same dimensions.")) (|times!| (((|Matrix| |#1|) (|Matrix| |#1|) (|Matrix| |#1|) (|Matrix| |#1|)) "\\spad{times!(c,a,b)} computes the matrix product \\spad{a * b} and stores the result in the matrix \\spad{c}. Error: if \\spad{a},{} \\spad{b},{} and \\spad{c} do not have compatible dimensions.")) (|rightScalarTimes!| (((|Matrix| |#1|) (|Matrix| |#1|) (|Matrix| |#1|) |#1|) "\\spad{rightScalarTimes!(c,a,r)} computes the scalar product \\spad{a * r} and stores the result in the matrix \\spad{c}. Error: if \\spad{a} and \\spad{c} do not have the same dimensions.")) (|leftScalarTimes!| (((|Matrix| |#1|) (|Matrix| |#1|) |#1| (|Matrix| |#1|)) "\\spad{leftScalarTimes!(c,r,a)} computes the scalar product \\spad{r * a} and stores the result in the matrix \\spad{c}. Error: if \\spad{a} and \\spad{c} do not have the same dimensions.")) (|minus!| (((|Matrix| |#1|) (|Matrix| |#1|) (|Matrix| |#1|) (|Matrix| |#1|)) "\\spad{!minus!(c,a,b)} computes the matrix difference \\spad{a - b} and stores the result in the matrix \\spad{c}. Error: if \\spad{a},{} \\spad{b},{} and \\spad{c} do not have the same dimensions.") (((|Matrix| |#1|) (|Matrix| |#1|) (|Matrix| |#1|)) "\\spad{minus!(c,a)} computes \\spad{-a} and stores the result in the matrix \\spad{c}. Error: if a and \\spad{c} do not have the same dimensions.")) (|plus!| (((|Matrix| |#1|) (|Matrix| |#1|) (|Matrix| |#1|) (|Matrix| |#1|)) "\\spad{plus!(c,a,b)} computes the matrix sum \\spad{a + b} and stores the result in the matrix \\spad{c}. Error: if \\spad{a},{} \\spad{b},{} and \\spad{c} do not have the same dimensions.")) (|copy!| (((|Matrix| |#1|) (|Matrix| |#1|) (|Matrix| |#1|)) "\\spad{copy!(c,a)} copies the matrix \\spad{a} into the matrix \\spad{c}. Error: if \\spad{a} and \\spad{c} do not have the same dimensions."))) NIL @@ -2720,7 +2720,7 @@ 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 \\spad{`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 \\spad{`x'} into \\%."))) NIL NIL -(-698 S -1385 FLAF FLAS) +(-698 S -2968 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,{} kl+ku+1 being actual bandwidth. Stores the nonzero band in a matrix,{} dimensions kl+ku+1 by \\#xlist. The upper triangle is in the top \\spad{ku} rows,{} the diagonal is in row 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 @@ -2730,8 +2730,8 @@ NIL NIL (-700) ((|constructor| (NIL "A domain which models the complex number representation used by machines in the AXIOM-NAG link.")) (|coerce| (((|Complex| (|Float|)) $) "\\spad{coerce(u)} transforms \\spad{u} into a COmplex Float") (($ (|Complex| (|MachineInteger|))) "\\spad{coerce(u)} transforms \\spad{u} into a MachineComplex") (($ (|Complex| (|MachineFloat|))) "\\spad{coerce(u)} transforms \\spad{u} into a MachineComplex") (($ (|Complex| (|Integer|))) "\\spad{coerce(u)} transforms \\spad{u} into a MachineComplex") (($ (|Complex| (|Float|))) "\\spad{coerce(u)} transforms \\spad{u} into a MachineComplex"))) -((-4445 . T) (-4450 |has| (-705) (-368)) (-4444 |has| (-705) (-368)) (-3545 . T) (-4451 |has| (-705) (-6 -4451)) (-4448 |has| (-705) (-6 -4448)) ((-4454 "*") . T) (-4446 . T) (-4447 . T) (-4449 . T)) -((|HasCategory| (-705) (QUOTE (-148))) (|HasCategory| (-705) (QUOTE (-146))) (|HasCategory| (-705) (LIST (QUOTE -1047) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasCategory| (-705) (LIST (QUOTE -645) (QUOTE (-570)))) (|HasCategory| (-705) (QUOTE (-373))) (|HasCategory| (-705) (QUOTE (-368))) (-2811 (|HasCategory| (-705) (LIST (QUOTE -1047) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasCategory| (-705) (QUOTE (-368)))) (|HasCategory| (-705) (LIST (QUOTE -907) (QUOTE (-1186)))) (|HasCategory| (-705) (QUOTE (-235))) (-2811 (|HasCategory| (-705) (QUOTE (-368))) (|HasCategory| (-705) (QUOTE (-354)))) (|HasCategory| (-705) (QUOTE (-354))) (|HasCategory| (-705) (LIST (QUOTE -290) (QUOTE (-705)) (QUOTE (-705)))) (|HasCategory| (-705) (LIST (QUOTE -313) (QUOTE (-705)))) (|HasCategory| (-705) (LIST (QUOTE -520) (QUOTE (-1186)) (QUOTE (-705)))) (|HasCategory| (-705) (LIST (QUOTE -893) (QUOTE (-570)))) (|HasCategory| (-705) (LIST (QUOTE -893) (QUOTE (-384)))) (|HasCategory| (-705) (LIST (QUOTE -620) (LIST (QUOTE -899) (QUOTE (-570))))) (|HasCategory| (-705) (LIST (QUOTE -620) (LIST (QUOTE -899) (QUOTE (-384))))) (-2811 (|HasCategory| (-705) (QUOTE (-311))) (|HasCategory| (-705) (QUOTE (-368))) (|HasCategory| (-705) (QUOTE (-354)))) (|HasCategory| (-705) (LIST (QUOTE -620) (QUOTE (-542)))) (|HasCategory| (-705) (QUOTE (-1031))) (|HasCategory| (-705) (QUOTE (-1212))) (-12 (|HasCategory| (-705) (QUOTE (-1011))) (|HasCategory| (-705) (QUOTE (-1212)))) (-2811 (-12 (|HasCategory| (-705) (QUOTE (-311))) (|HasCategory| (-705) (QUOTE (-916)))) (|HasCategory| (-705) (QUOTE (-368))) (-12 (|HasCategory| (-705) (QUOTE (-354))) (|HasCategory| (-705) (QUOTE (-916))))) (-2811 (-12 (|HasCategory| (-705) (QUOTE (-311))) (|HasCategory| (-705) (QUOTE (-916)))) (-12 (|HasCategory| (-705) (QUOTE (-368))) (|HasCategory| (-705) (QUOTE (-916)))) (-12 (|HasCategory| (-705) (QUOTE (-354))) (|HasCategory| (-705) (QUOTE (-916))))) (|HasCategory| (-705) (QUOTE (-551))) (-12 (|HasCategory| (-705) (QUOTE (-1069))) (|HasCategory| (-705) (QUOTE (-1212)))) (|HasCategory| (-705) (QUOTE (-1069))) (|HasCategory| (-705) (QUOTE (-311))) (|HasCategory| (-705) (QUOTE (-916))) (-2811 (-12 (|HasCategory| (-705) (QUOTE (-311))) (|HasCategory| (-705) (QUOTE (-916)))) (|HasCategory| (-705) (QUOTE (-368)))) (-2811 (-12 (|HasCategory| (-705) (QUOTE (-311))) (|HasCategory| (-705) (QUOTE (-916)))) (|HasCategory| (-705) (QUOTE (-562)))) (-12 (|HasCategory| (-705) (QUOTE (-235))) (|HasCategory| (-705) (QUOTE (-368)))) (-12 (|HasCategory| (-705) (LIST (QUOTE -907) (QUOTE (-1186)))) (|HasCategory| (-705) (QUOTE (-368)))) (|HasCategory| (-705) (LIST (QUOTE -1047) (QUOTE (-570)))) (|HasCategory| (-705) (QUOTE (-562))) (|HasAttribute| (-705) (QUOTE -4451)) (|HasAttribute| (-705) (QUOTE -4448)) (-12 (|HasCategory| (-705) (QUOTE (-311))) (|HasCategory| (-705) (QUOTE (-916)))) (-2811 (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| (-705) (QUOTE (-311))) (|HasCategory| (-705) (QUOTE (-916)))) (|HasCategory| (-705) (QUOTE (-146)))) (-2811 (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| (-705) (QUOTE (-311))) (|HasCategory| (-705) (QUOTE (-916)))) (|HasCategory| (-705) (QUOTE (-354))))) +((-4445 . T) (-4450 |has| (-705) (-368)) (-4444 |has| (-705) (-368)) (-3420 . T) (-4451 |has| (-705) (-6 -4451)) (-4448 |has| (-705) (-6 -4448)) ((-4454 "*") . T) (-4446 . T) (-4447 . T) (-4449 . T)) +((|HasCategory| (-705) (QUOTE (-148))) (|HasCategory| (-705) (QUOTE (-146))) (|HasCategory| (-705) (LIST (QUOTE -1047) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasCategory| (-705) (LIST (QUOTE -645) (QUOTE (-570)))) (|HasCategory| (-705) (QUOTE (-373))) (|HasCategory| (-705) (QUOTE (-368))) (-3684 (|HasCategory| (-705) (LIST (QUOTE -1047) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasCategory| (-705) (QUOTE (-368)))) (|HasCategory| (-705) (LIST (QUOTE -907) (QUOTE (-1186)))) (|HasCategory| (-705) (QUOTE (-235))) (-3684 (|HasCategory| (-705) (QUOTE (-368))) (|HasCategory| (-705) (QUOTE (-354)))) (|HasCategory| (-705) (QUOTE (-354))) (|HasCategory| (-705) (LIST (QUOTE -290) (QUOTE (-705)) (QUOTE (-705)))) (|HasCategory| (-705) (LIST (QUOTE -313) (QUOTE (-705)))) (|HasCategory| (-705) (LIST (QUOTE -520) (QUOTE (-1186)) (QUOTE (-705)))) (|HasCategory| (-705) (LIST (QUOTE -893) (QUOTE (-570)))) (|HasCategory| (-705) (LIST (QUOTE -893) (QUOTE (-384)))) (|HasCategory| (-705) (LIST (QUOTE -620) (LIST (QUOTE -899) (QUOTE (-570))))) (|HasCategory| (-705) (LIST (QUOTE -620) (LIST (QUOTE -899) (QUOTE (-384))))) (-3684 (|HasCategory| (-705) (QUOTE (-311))) (|HasCategory| (-705) (QUOTE (-368))) (|HasCategory| (-705) (QUOTE (-354)))) (|HasCategory| (-705) (LIST (QUOTE -620) (QUOTE (-542)))) (|HasCategory| (-705) (QUOTE (-1031))) (|HasCategory| (-705) (QUOTE (-1212))) (-12 (|HasCategory| (-705) (QUOTE (-1011))) (|HasCategory| (-705) (QUOTE (-1212)))) (-3684 (-12 (|HasCategory| (-705) (QUOTE (-311))) (|HasCategory| (-705) (QUOTE (-916)))) (|HasCategory| (-705) (QUOTE (-368))) (-12 (|HasCategory| (-705) (QUOTE (-354))) (|HasCategory| (-705) (QUOTE (-916))))) (-3684 (-12 (|HasCategory| (-705) (QUOTE (-311))) (|HasCategory| (-705) (QUOTE (-916)))) (-12 (|HasCategory| (-705) (QUOTE (-368))) (|HasCategory| (-705) (QUOTE (-916)))) (-12 (|HasCategory| (-705) (QUOTE (-354))) (|HasCategory| (-705) (QUOTE (-916))))) (|HasCategory| (-705) (QUOTE (-551))) (-12 (|HasCategory| (-705) (QUOTE (-1069))) (|HasCategory| (-705) (QUOTE (-1212)))) (|HasCategory| (-705) (QUOTE (-1069))) (|HasCategory| (-705) (QUOTE (-311))) (|HasCategory| (-705) (QUOTE (-916))) (-3684 (-12 (|HasCategory| (-705) (QUOTE (-311))) (|HasCategory| (-705) (QUOTE (-916)))) (|HasCategory| (-705) (QUOTE (-368)))) (-3684 (-12 (|HasCategory| (-705) (QUOTE (-311))) (|HasCategory| (-705) (QUOTE (-916)))) (|HasCategory| (-705) (QUOTE (-562)))) (-12 (|HasCategory| (-705) (QUOTE (-235))) (|HasCategory| (-705) (QUOTE (-368)))) (-12 (|HasCategory| (-705) (LIST (QUOTE -907) (QUOTE (-1186)))) (|HasCategory| (-705) (QUOTE (-368)))) (|HasCategory| (-705) (LIST (QUOTE -1047) (QUOTE (-570)))) (|HasCategory| (-705) (QUOTE (-562))) (|HasAttribute| (-705) (QUOTE -4451)) (|HasAttribute| (-705) (QUOTE -4448)) (-12 (|HasCategory| (-705) (QUOTE (-311))) (|HasCategory| (-705) (QUOTE (-916)))) (-3684 (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| (-705) (QUOTE (-311))) (|HasCategory| (-705) (QUOTE (-916)))) (|HasCategory| (-705) (QUOTE (-146)))) (-3684 (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| (-705) (QUOTE (-311))) (|HasCategory| (-705) (QUOTE (-916)))) (|HasCategory| (-705) (QUOTE (-354))))) (-701 S) ((|constructor| (NIL "A multi-dictionary is a dictionary which may contain duplicates. As for any dictionary,{} its size is assumed large so that copying (non-destructive) operations are generally to be avoided.")) (|duplicates| (((|List| (|Record| (|:| |entry| |#1|) (|:| |count| (|NonNegativeInteger|)))) $) "\\spad{duplicates(d)} returns a list of values which have duplicates in \\spad{d}")) (|removeDuplicates!| (($ $) "\\spad{removeDuplicates!(d)} destructively removes any duplicate values in dictionary \\spad{d}.")) (|insert!| (($ |#1| $ (|NonNegativeInteger|)) "\\spad{insert!(x,d,n)} destructively inserts \\spad{n} copies of \\spad{x} into dictionary \\spad{d}."))) ((-4453 . T)) @@ -2744,13 +2744,13 @@ NIL ((|constructor| (NIL "\\indented{1}{<description of package>} Author: Jim Wen Date Created: \\spad{??} 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 -(-704 OV E -1385 PG) +(-704 OV E -2968 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 (-705) ((|constructor| (NIL "A domain which models the floating point representation used by machines in the AXIOM-NAG link.")) (|changeBase| (($ (|Integer|) (|Integer|) (|PositiveInteger|)) "\\spad{changeBase(exp,man,base)} \\undocumented{}")) (|exponent| (((|Integer|) $) "\\spad{exponent(u)} returns the exponent of \\spad{u}")) (|mantissa| (((|Integer|) $) "\\spad{mantissa(u)} returns the mantissa of \\spad{u}")) (|coerce| (($ (|MachineInteger|)) "\\spad{coerce(u)} transforms a MachineInteger into a MachineFloat") (((|Float|) $) "\\spad{coerce(u)} transforms a MachineFloat to a standard Float")) (|minimumExponent| (((|Integer|)) "\\spad{minimumExponent()} returns the minimum exponent in the model") (((|Integer|) (|Integer|)) "\\spad{minimumExponent(e)} sets the minimum exponent in the model to \\spad{e}")) (|maximumExponent| (((|Integer|)) "\\spad{maximumExponent()} returns the maximum exponent in the model") (((|Integer|) (|Integer|)) "\\spad{maximumExponent(e)} sets the maximum exponent in the model to \\spad{e}")) (|base| (((|PositiveInteger|) (|PositiveInteger|)) "\\spad{base(b)} sets the base of the model to \\spad{b}")) (|precision| (((|PositiveInteger|)) "\\spad{precision()} returns the number of digits in the model") (((|PositiveInteger|) (|PositiveInteger|)) "\\spad{precision(p)} sets the number of digits in the model to \\spad{p}"))) -((-3535 . T) (-4444 . T) (-4450 . T) (-4445 . T) ((-4454 "*") . T) (-4446 . T) (-4447 . T) (-4449 . T)) +((-3412 . T) (-4444 . T) (-4450 . T) (-4445 . T) ((-4454 "*") . T) (-4446 . T) (-4447 . T) (-4449 . T)) NIL (-706 R) ((|constructor| (NIL "\\indented{1}{Modular hermitian row reduction.} Author: Manuel Bronstein Date Created: 22 February 1989 Date Last Updated: 24 November 1993 Keywords: matrix,{} reduction.")) (|normalizedDivide| (((|Record| (|:| |quotient| |#1|) (|:| |remainder| |#1|)) |#1| |#1|) "\\spad{normalizedDivide(n,d)} returns a normalized quotient and remainder such that consistently unique representatives for the residue class are chosen,{} \\spadignore{e.g.} positive remainders")) (|rowEchelonLocal| (((|Matrix| |#1|) (|Matrix| |#1|) |#1| |#1|) "\\spad{rowEchelonLocal(m, d, p)} computes the row-echelon form of \\spad{m} concatenated with \\spad{d} times the identity matrix over a local ring where \\spad{p} is the only prime.")) (|rowEchLocal| (((|Matrix| |#1|) (|Matrix| |#1|) |#1|) "\\spad{rowEchLocal(m,p)} computes a modular row-echelon form of \\spad{m},{} finding an appropriate modulus over a local ring where \\spad{p} is the only prime.")) (|rowEchelon| (((|Matrix| |#1|) (|Matrix| |#1|) |#1|) "\\spad{rowEchelon(m, d)} computes a modular row-echelon form mod \\spad{d} of \\indented{3}{[\\spad{d}\\space{5}]} \\indented{3}{[\\space{2}\\spad{d}\\space{3}]} \\indented{3}{[\\space{4}. ]} \\indented{3}{[\\space{5}\\spad{d}]} \\indented{3}{[\\space{3}\\spad{M}\\space{2}]} where \\spad{M = m mod d}.")) (|rowEch| (((|Matrix| |#1|) (|Matrix| |#1|)) "\\spad{rowEch(m)} computes a modular row-echelon form of \\spad{m},{} finding an appropriate modulus."))) @@ -2776,7 +2776,7 @@ 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 part1 is \\spad{a} and part2 is \\spad{b}."))) NIL NIL -(-712 S -3651 I) +(-712 S -3347 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 @@ -2796,14 +2796,14 @@ 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 -(-717 R |Mod| -1576 -2523 |exactQuo|) +(-717 R |Mod| -2228 -3055 |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| $) "\\spad{modulus(x)} \\undocumented"))) ((-4444 . T) (-4450 . T) (-4445 . T) ((-4454 "*") . T) (-4446 . T) (-4447 . T) (-4449 . T)) NIL (-718 R |Rep|) ((|constructor| (NIL "This package \\undocumented")) (|frobenius| (($ $) "\\spad{frobenius(x)} \\undocumented")) (|computePowers| (((|PrimitiveArray| $)) "\\spad{computePowers()} \\undocumented")) (|pow| (((|PrimitiveArray| $)) "\\spad{pow()} \\undocumented")) (|An| (((|Vector| |#1|) $) "\\spad{An(x)} \\undocumented")) (|UnVectorise| (($ (|Vector| |#1|)) "\\spad{UnVectorise(v)} \\undocumented")) (|Vectorise| (((|Vector| |#1|) $) "\\spad{Vectorise(x)} \\undocumented")) (|lift| ((|#2| $) "\\spad{lift(x)} \\undocumented")) (|reduce| (($ |#2|) "\\spad{reduce(x)} \\undocumented")) (|modulus| ((|#2|) "\\spad{modulus()} \\undocumented")) (|setPoly| ((|#2| |#2|) "\\spad{setPoly(x)} \\undocumented"))) (((-4454 "*") |has| |#1| (-174)) (-4445 |has| |#1| (-562)) (-4448 |has| |#1| (-368)) (-4450 |has| |#1| (-6 -4450)) (-4447 . T) (-4446 . T) (-4449 . T)) -((|HasCategory| |#1| (QUOTE (-916))) (|HasCategory| |#1| (QUOTE (-562))) (|HasCategory| |#1| (QUOTE (-174))) (-2811 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-562)))) (-12 (|HasCategory| (-1091) (LIST (QUOTE -893) (QUOTE (-384)))) (|HasCategory| |#1| (LIST (QUOTE -893) (QUOTE (-384))))) (-12 (|HasCategory| (-1091) (LIST (QUOTE -893) (QUOTE (-570)))) (|HasCategory| |#1| (LIST (QUOTE -893) (QUOTE (-570))))) (-12 (|HasCategory| (-1091) (LIST (QUOTE -620) (LIST (QUOTE -899) (QUOTE (-384))))) (|HasCategory| |#1| (LIST (QUOTE -620) (LIST (QUOTE -899) (QUOTE (-384)))))) (-12 (|HasCategory| (-1091) (LIST (QUOTE -620) (LIST (QUOTE -899) (QUOTE (-570))))) (|HasCategory| |#1| (LIST (QUOTE -620) (LIST (QUOTE -899) (QUOTE (-570)))))) (-12 (|HasCategory| (-1091) (LIST (QUOTE -620) (QUOTE (-542)))) (|HasCategory| |#1| (LIST (QUOTE -620) (QUOTE (-542))))) (|HasCategory| |#1| (LIST (QUOTE -645) (QUOTE (-570)))) (|HasCategory| |#1| (QUOTE (-148))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasCategory| |#1| (LIST (QUOTE -1047) (QUOTE (-570)))) (-2811 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasCategory| |#1| (LIST (QUOTE -1047) (LIST (QUOTE -413) (QUOTE (-570)))))) (|HasCategory| |#1| (LIST (QUOTE -1047) (LIST (QUOTE -413) (QUOTE (-570))))) (-2811 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-368))) (|HasCategory| |#1| (QUOTE (-458))) (|HasCategory| |#1| (QUOTE (-562))) (|HasCategory| |#1| (QUOTE (-916)))) (-2811 (|HasCategory| |#1| (QUOTE (-368))) (|HasCategory| |#1| (QUOTE (-458))) (|HasCategory| |#1| (QUOTE (-562))) (|HasCategory| |#1| (QUOTE (-916)))) (-2811 (|HasCategory| |#1| (QUOTE (-368))) (|HasCategory| |#1| (QUOTE (-458))) (|HasCategory| |#1| (QUOTE (-916)))) (|HasCategory| |#1| (QUOTE (-368))) (|HasCategory| |#1| (QUOTE (-1161))) (|HasCategory| |#1| (LIST (QUOTE -907) (QUOTE (-1186)))) (|HasCategory| |#1| (QUOTE (-373))) (|HasCategory| |#1| (QUOTE (-354))) (|HasCategory| |#1| (QUOTE (-235))) (|HasAttribute| |#1| (QUOTE -4450)) (|HasCategory| |#1| (QUOTE (-458))) (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-916)))) (-2811 (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-916)))) (|HasCategory| |#1| (QUOTE (-146))))) +((|HasCategory| |#1| (QUOTE (-916))) (|HasCategory| |#1| (QUOTE (-562))) (|HasCategory| |#1| (QUOTE (-174))) (-3684 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-562)))) (-12 (|HasCategory| (-1091) (LIST (QUOTE -893) (QUOTE (-384)))) (|HasCategory| |#1| (LIST (QUOTE -893) (QUOTE (-384))))) (-12 (|HasCategory| (-1091) (LIST (QUOTE -893) (QUOTE (-570)))) (|HasCategory| |#1| (LIST (QUOTE -893) (QUOTE (-570))))) (-12 (|HasCategory| (-1091) (LIST (QUOTE -620) (LIST (QUOTE -899) (QUOTE (-384))))) (|HasCategory| |#1| (LIST (QUOTE -620) (LIST (QUOTE -899) (QUOTE (-384)))))) (-12 (|HasCategory| (-1091) (LIST (QUOTE -620) (LIST (QUOTE -899) (QUOTE (-570))))) (|HasCategory| |#1| (LIST (QUOTE -620) (LIST (QUOTE -899) (QUOTE (-570)))))) (-12 (|HasCategory| (-1091) (LIST (QUOTE -620) (QUOTE (-542)))) (|HasCategory| |#1| (LIST (QUOTE -620) (QUOTE (-542))))) (|HasCategory| |#1| (LIST (QUOTE -645) (QUOTE (-570)))) (|HasCategory| |#1| (QUOTE (-148))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasCategory| |#1| (LIST (QUOTE -1047) (QUOTE (-570)))) (-3684 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasCategory| |#1| (LIST (QUOTE -1047) (LIST (QUOTE -413) (QUOTE (-570)))))) (|HasCategory| |#1| (LIST (QUOTE -1047) (LIST (QUOTE -413) (QUOTE (-570))))) (-3684 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-368))) (|HasCategory| |#1| (QUOTE (-458))) (|HasCategory| |#1| (QUOTE (-562))) (|HasCategory| |#1| (QUOTE (-916)))) (-3684 (|HasCategory| |#1| (QUOTE (-368))) (|HasCategory| |#1| (QUOTE (-458))) (|HasCategory| |#1| (QUOTE (-562))) (|HasCategory| |#1| (QUOTE (-916)))) (-3684 (|HasCategory| |#1| (QUOTE (-368))) (|HasCategory| |#1| (QUOTE (-458))) (|HasCategory| |#1| (QUOTE (-916)))) (|HasCategory| |#1| (QUOTE (-368))) (|HasCategory| |#1| (QUOTE (-1161))) (|HasCategory| |#1| (LIST (QUOTE -907) (QUOTE (-1186)))) (|HasCategory| |#1| (QUOTE (-373))) (|HasCategory| |#1| (QUOTE (-354))) (|HasCategory| |#1| (QUOTE (-235))) (|HasAttribute| |#1| (QUOTE -4450)) (|HasCategory| |#1| (QUOTE (-458))) (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-916)))) (-3684 (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-916)))) (|HasCategory| |#1| (QUOTE (-146))))) (-719 IS E |ff|) ((|constructor| (NIL "This package \\undocumented")) (|construct| (($ |#1| |#2|) "\\spad{construct(i,e)} \\undocumented")) (|index| ((|#1| $) "\\spad{index(x)} \\undocumented")) (|exponent| ((|#2| $) "\\spad{exponent(x)} \\undocumented"))) NIL @@ -2812,7 +2812,7 @@ NIL ((|constructor| (NIL "Algebra of ADDITIVE operators on a module.")) (|makeop| (($ |#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| (($ $ $) "\\spad{adjoint(op1, op2)} sets the adjoint of \\spad{op1} to be op2. \\spad{op1} must be a basic operator") (($ $) "\\spad{adjoint(op)} returns the adjoint of the operator \\spad{op}."))) ((-4447 |has| |#1| (-174)) (-4446 |has| |#1| (-174)) (-4449 . T)) ((|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-148)))) -(-721 R |Mod| -1576 -2523 |exactQuo|) +(-721 R |Mod| -2228 -3055 |exactQuo|) ((|constructor| (NIL "These domains are used for the factorization and gcds of univariate polynomials over the integers in order to work modulo different primes. See \\spadtype{EuclideanModularRing} ,{}\\spadtype{ModularField}")) (|inv| (($ $) "\\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"))) ((-4449 . T)) NIL @@ -2824,7 +2824,7 @@ NIL ((|constructor| (NIL "The category of modules over a commutative ring. \\blankline"))) ((-4447 . T) (-4446 . T)) NIL -(-724 -1385) +(-724 -2968) ((|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]]}."))) ((-4449 . T)) NIL @@ -2860,7 +2860,7 @@ 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 -(-733 -1385 UP) +(-733 -2968 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 @@ -2879,7 +2879,7 @@ NIL (-737 |vl| R) ((|constructor| (NIL "\\indented{2}{This type is the basic representation of sparse recursive multivariate} polynomials whose variables are from a user specified list of symbols. The ordering is specified by the position of the variable in the list. The coefficient ring may be non commutative,{} but the variables are assumed to commute."))) (((-4454 "*") |has| |#2| (-174)) (-4445 |has| |#2| (-562)) (-4450 |has| |#2| (-6 -4450)) (-4447 . T) (-4446 . T) (-4449 . T)) -((|HasCategory| |#2| (QUOTE (-916))) (-2811 (|HasCategory| |#2| (QUOTE (-174))) (|HasCategory| |#2| (QUOTE (-458))) (|HasCategory| |#2| (QUOTE (-562))) (|HasCategory| |#2| (QUOTE (-916)))) (-2811 (|HasCategory| |#2| (QUOTE (-458))) (|HasCategory| |#2| (QUOTE (-562))) (|HasCategory| |#2| (QUOTE (-916)))) (-2811 (|HasCategory| |#2| (QUOTE (-458))) (|HasCategory| |#2| (QUOTE (-916)))) (|HasCategory| |#2| (QUOTE (-562))) (|HasCategory| |#2| (QUOTE (-174))) (-2811 (|HasCategory| |#2| (QUOTE (-174))) (|HasCategory| |#2| (QUOTE (-562)))) (-12 (|HasCategory| (-870 |#1|) (LIST (QUOTE -893) (QUOTE (-384)))) (|HasCategory| |#2| (LIST (QUOTE -893) (QUOTE (-384))))) (-12 (|HasCategory| (-870 |#1|) (LIST (QUOTE -893) (QUOTE (-570)))) (|HasCategory| |#2| (LIST (QUOTE -893) (QUOTE (-570))))) (-12 (|HasCategory| (-870 |#1|) (LIST (QUOTE -620) (LIST (QUOTE -899) (QUOTE (-384))))) (|HasCategory| |#2| (LIST (QUOTE -620) (LIST (QUOTE -899) (QUOTE (-384)))))) (-12 (|HasCategory| (-870 |#1|) (LIST (QUOTE -620) (LIST (QUOTE -899) (QUOTE (-570))))) (|HasCategory| |#2| (LIST (QUOTE -620) (LIST (QUOTE -899) (QUOTE (-570)))))) (-12 (|HasCategory| (-870 |#1|) (LIST (QUOTE -620) (QUOTE (-542)))) (|HasCategory| |#2| (LIST (QUOTE -620) (QUOTE (-542))))) (|HasCategory| |#2| (LIST (QUOTE -645) (QUOTE (-570)))) (|HasCategory| |#2| (QUOTE (-148))) (|HasCategory| |#2| (QUOTE (-146))) (|HasCategory| |#2| (LIST (QUOTE -38) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasCategory| |#2| (LIST (QUOTE -1047) (QUOTE (-570)))) (-2811 (|HasCategory| |#2| (LIST (QUOTE -38) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasCategory| |#2| (LIST (QUOTE -1047) (LIST (QUOTE -413) (QUOTE (-570)))))) (|HasCategory| |#2| (LIST (QUOTE -1047) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasCategory| |#2| (QUOTE (-368))) (|HasAttribute| |#2| (QUOTE -4450)) (|HasCategory| |#2| (QUOTE (-458))) (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| |#2| (QUOTE (-916)))) (-2811 (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| |#2| (QUOTE (-916)))) (|HasCategory| |#2| (QUOTE (-146))))) +((|HasCategory| |#2| (QUOTE (-916))) (-3684 (|HasCategory| |#2| (QUOTE (-174))) (|HasCategory| |#2| (QUOTE (-458))) (|HasCategory| |#2| (QUOTE (-562))) (|HasCategory| |#2| (QUOTE (-916)))) (-3684 (|HasCategory| |#2| (QUOTE (-458))) (|HasCategory| |#2| (QUOTE (-562))) (|HasCategory| |#2| (QUOTE (-916)))) (-3684 (|HasCategory| |#2| (QUOTE (-458))) (|HasCategory| |#2| (QUOTE (-916)))) (|HasCategory| |#2| (QUOTE (-562))) (|HasCategory| |#2| (QUOTE (-174))) (-3684 (|HasCategory| |#2| (QUOTE (-174))) (|HasCategory| |#2| (QUOTE (-562)))) (-12 (|HasCategory| (-870 |#1|) (LIST (QUOTE -893) (QUOTE (-384)))) (|HasCategory| |#2| (LIST (QUOTE -893) (QUOTE (-384))))) (-12 (|HasCategory| (-870 |#1|) (LIST (QUOTE -893) (QUOTE (-570)))) (|HasCategory| |#2| (LIST (QUOTE -893) (QUOTE (-570))))) (-12 (|HasCategory| (-870 |#1|) (LIST (QUOTE -620) (LIST (QUOTE -899) (QUOTE (-384))))) (|HasCategory| |#2| (LIST (QUOTE -620) (LIST (QUOTE -899) (QUOTE (-384)))))) (-12 (|HasCategory| (-870 |#1|) (LIST (QUOTE -620) (LIST (QUOTE -899) (QUOTE (-570))))) (|HasCategory| |#2| (LIST (QUOTE -620) (LIST (QUOTE -899) (QUOTE (-570)))))) (-12 (|HasCategory| (-870 |#1|) (LIST (QUOTE -620) (QUOTE (-542)))) (|HasCategory| |#2| (LIST (QUOTE -620) (QUOTE (-542))))) (|HasCategory| |#2| (LIST (QUOTE -645) (QUOTE (-570)))) (|HasCategory| |#2| (QUOTE (-148))) (|HasCategory| |#2| (QUOTE (-146))) (|HasCategory| |#2| (LIST (QUOTE -38) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasCategory| |#2| (LIST (QUOTE -1047) (QUOTE (-570)))) (-3684 (|HasCategory| |#2| (LIST (QUOTE -38) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasCategory| |#2| (LIST (QUOTE -1047) (LIST (QUOTE -413) (QUOTE (-570)))))) (|HasCategory| |#2| (LIST (QUOTE -1047) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasCategory| |#2| (QUOTE (-368))) (|HasAttribute| |#2| (QUOTE -4450)) (|HasCategory| |#2| (QUOTE (-458))) (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| |#2| (QUOTE (-916)))) (-3684 (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| |#2| (QUOTE (-916)))) (|HasCategory| |#2| (QUOTE (-146))))) (-738 E OV R PRF) ((|constructor| (NIL "\\indented{3}{This package exports a factor operation for multivariate polynomials} with coefficients which are rational functions over some ring \\spad{R} over which we can factor. It is used internally by packages such as primary decomposition which need to work with polynomials with rational function coefficients,{} \\spadignore{i.e.} themselves fractions of polynomials.")) (|factor| (((|Factored| |#4|) |#4|) "\\spad{factor(prf)} factors a polynomial with rational function coefficients.")) (|pushuconst| ((|#4| (|Fraction| (|Polynomial| |#3|)) |#2|) "\\spad{pushuconst(r,var)} takes a rational function and raises all occurances of the variable \\spad{var} to the polynomial level.")) (|pushucoef| ((|#4| (|SparseUnivariatePolynomial| (|Polynomial| |#3|)) |#2|) "\\spad{pushucoef(upoly,var)} converts the anonymous univariate polynomial \\spad{upoly} to a polynomial in \\spad{var} over rational functions.")) (|pushup| ((|#4| |#4| |#2|) "\\spad{pushup(prf,var)} raises all occurences of the variable \\spad{var} in the coefficients of the polynomial \\spad{prf} back to the polynomial level.")) (|pushdterm| ((|#4| (|SparseUnivariatePolynomial| |#4|) |#2|) "\\spad{pushdterm(monom,var)} pushes all top level occurences of the variable \\spad{var} into the coefficient domain for the monomial \\spad{monom}.")) (|pushdown| ((|#4| |#4| |#2|) "\\spad{pushdown(prf,var)} pushes all top level occurences of the variable \\spad{var} into the coefficient domain for the polynomial \\spad{prf}.")) (|totalfract| (((|Record| (|:| |sup| (|Polynomial| |#3|)) (|:| |inf| (|Polynomial| |#3|))) |#4|) "\\spad{totalfract(prf)} takes a polynomial whose coefficients are themselves fractions of polynomials and returns a record containing the numerator and denominator resulting from putting \\spad{prf} over a common denominator.")) (|convert| (((|Symbol|) $) "\\spad{convert(x)} converts \\spad{x} to a symbol"))) NIL @@ -3012,11 +3012,11 @@ 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 -(-771 -1385) +(-771 -2968) ((|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 -(-772 P -1385) +(-772 P -2968) ((|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\\spad{''}."))) NIL NIL @@ -3024,7 +3024,7 @@ NIL NIL NIL NIL -(-774 UP -1385) +(-774 UP -2968) ((|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 @@ -3040,7 +3040,7 @@ 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."))) (((-4454 "*") . T)) NIL -(-778 R -1385) +(-778 R -2968) ((|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 @@ -3060,7 +3060,7 @@ 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 \\spad{gcd} over} \\indented{5}{algebraic towers of simple extensions\" In proceedings of 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},{}\\spad{ts})} is an internal subroutine,{} exported only for developement.")) (|outputArgs| (((|Void|) (|String|) (|String|) |#4| |#5|) "\\axiom{outputArgs(\\spad{s1},{}\\spad{s2},{}\\spad{p},{}\\spad{ts})} is an internal subroutine,{} exported only for developement.")) (|normalize| (((|List| (|Record| (|:| |val| |#4|) (|:| |tower| |#5|))) |#4| |#5|) "\\axiom{normalize(\\spad{p},{}\\spad{ts})} normalizes \\axiom{\\spad{p}} \\spad{w}.\\spad{r}.\\spad{t} \\spad{ts}.")) (|normalizedAssociate| ((|#4| |#4| |#5|) "\\axiom{normalizedAssociate(\\spad{p},{}\\spad{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},{}\\spad{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 -(-783 -1385 |ExtF| |SUEx| |ExtP| |n|) +(-783 -2968 |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 @@ -3075,7 +3075,7 @@ NIL (-786 R |VarSet|) ((|constructor| (NIL "A post-facto extension for \\axiomType{\\spad{SMP}} in order to speed up operations related to pseudo-division and \\spad{gcd}. This domain is based on the \\axiomType{NSUP} constructor which is itself a post-facto extension of the \\axiomType{SUP} constructor."))) (((-4454 "*") |has| |#1| (-174)) (-4445 |has| |#1| (-562)) (-4450 |has| |#1| (-6 -4450)) (-4447 . T) (-4446 . T) (-4449 . 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(-570))))))) (-12 (|HasCategory| |#2| (LIST (QUOTE -620) (QUOTE (-1186)))) (-3152 (|HasCategory| |#1| (LIST (QUOTE -38) (QUOTE (-570))))) (-3152 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -413) (QUOTE (-570))))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasCategory| |#2| (LIST (QUOTE -620) (QUOTE (-1186)))) (-3152 (|HasCategory| |#1| (LIST (QUOTE -1001) (QUOTE (-570))))))) (|HasAttribute| |#1| (QUOTE -4450)) (|HasCategory| |#1| (QUOTE (-458))) (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-916)))) (-3684 (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-916)))) (|HasCategory| |#1| (QUOTE (-146))))) (-787 R S) ((|constructor| (NIL "This package lifts a mapping from coefficient rings \\spad{R} to \\spad{S} to a mapping from sparse univariate polynomial over \\spad{R} to a sparse univariate polynomial over \\spad{S}. Note that the mapping is assumed to send zero to zero,{} since it will only be applied to the non-zero coefficients of the polynomial.")) (|map| (((|NewSparseUnivariatePolynomial| |#2|) (|Mapping| |#2| |#1|) (|NewSparseUnivariatePolynomial| |#1|)) "\\axiom{map(func,{} poly)} creates a new polynomial by applying func to every non-zero coefficient of the polynomial poly."))) NIL @@ -3083,7 +3083,7 @@ NIL (-788 R) ((|constructor| (NIL "A post-facto extension for \\axiomType{SUP} in order to speed up operations related to pseudo-division and \\spad{gcd} for both \\axiomType{SUP} and,{} consequently,{} \\axiomType{NSMP}.")) (|halfExtendedResultant2| (((|Record| (|:| |resultant| |#1|) (|:| |coef2| $)) $ $) "\\axiom{halfExtendedResultant2(a,{}\\spad{b})} returns \\axiom{[\\spad{r},{}ca]} such that \\axiom{extendedResultant(a,{}\\spad{b})} returns \\axiom{[\\spad{r},{}ca,{} \\spad{cb}]}")) (|halfExtendedResultant1| (((|Record| (|:| |resultant| |#1|) (|:| |coef1| $)) $ $) "\\axiom{halfExtendedResultant1(a,{}\\spad{b})} returns \\axiom{[\\spad{r},{}ca]} such that \\axiom{extendedResultant(a,{}\\spad{b})} returns \\axiom{[\\spad{r},{}ca,{} \\spad{cb}]}")) (|extendedResultant| (((|Record| (|:| |resultant| |#1|) (|:| |coef1| $) (|:| |coef2| $)) $ $) "\\axiom{extendedResultant(a,{}\\spad{b})} returns \\axiom{[\\spad{r},{}ca,{}\\spad{cb}]} such that \\axiom{\\spad{r}} is the resultant of \\axiom{a} and \\axiom{\\spad{b}} and \\axiom{\\spad{r} = ca * a + \\spad{cb} * \\spad{b}}")) (|halfExtendedSubResultantGcd2| (((|Record| (|:| |gcd| $) (|:| |coef2| $)) $ $) "\\axiom{halfExtendedSubResultantGcd2(a,{}\\spad{b})} returns \\axiom{[\\spad{g},{}\\spad{cb}]} such that \\axiom{extendedSubResultantGcd(a,{}\\spad{b})} returns \\axiom{[\\spad{g},{}ca,{} \\spad{cb}]}")) (|halfExtendedSubResultantGcd1| (((|Record| (|:| |gcd| $) (|:| |coef1| $)) $ $) "\\axiom{halfExtendedSubResultantGcd1(a,{}\\spad{b})} returns \\axiom{[\\spad{g},{}ca]} such that \\axiom{extendedSubResultantGcd(a,{}\\spad{b})} returns \\axiom{[\\spad{g},{}ca,{} \\spad{cb}]}")) (|extendedSubResultantGcd| (((|Record| (|:| |gcd| $) (|:| |coef1| $) (|:| |coef2| $)) $ $) "\\axiom{extendedSubResultantGcd(a,{}\\spad{b})} returns \\axiom{[\\spad{g},{}ca,{} \\spad{cb}]} such that \\axiom{\\spad{g}} is a \\spad{gcd} of \\axiom{a} and \\axiom{\\spad{b}} in \\axiom{\\spad{R^}(\\spad{-1}) \\spad{P}} and \\axiom{\\spad{g} = ca * a + \\spad{cb} * \\spad{b}}")) (|lastSubResultant| (($ $ $) "\\axiom{lastSubResultant(a,{}\\spad{b})} returns \\axiom{resultant(a,{}\\spad{b})} if \\axiom{a} and \\axiom{\\spad{b}} has no non-trivial \\spad{gcd} in \\axiom{\\spad{R^}(\\spad{-1}) \\spad{P}} otherwise the non-zero sub-resultant with smallest index.")) (|subResultantsChain| (((|List| $) $ $) "\\axiom{subResultantsChain(a,{}\\spad{b})} returns the list of the non-zero sub-resultants of \\axiom{a} and \\axiom{\\spad{b}} sorted by increasing degree.")) (|lazyPseudoQuotient| (($ $ $) "\\axiom{lazyPseudoQuotient(a,{}\\spad{b})} returns \\axiom{\\spad{q}} if \\axiom{lazyPseudoDivide(a,{}\\spad{b})} returns \\axiom{[\\spad{c},{}\\spad{g},{}\\spad{q},{}\\spad{r}]}")) (|lazyPseudoDivide| (((|Record| (|:| |coef| |#1|) (|:| |gap| (|NonNegativeInteger|)) (|:| |quotient| $) (|:| |remainder| $)) $ $) "\\axiom{lazyPseudoDivide(a,{}\\spad{b})} returns \\axiom{[\\spad{c},{}\\spad{g},{}\\spad{q},{}\\spad{r}]} such that \\axiom{\\spad{c^n} * a = \\spad{q*b} \\spad{+r}} and \\axiom{lazyResidueClass(a,{}\\spad{b})} returns \\axiom{[\\spad{r},{}\\spad{c},{}\\spad{n}]} where \\axiom{\\spad{n} + \\spad{g} = max(0,{} degree(\\spad{b}) - degree(a) + 1)}.")) (|lazyPseudoRemainder| (($ $ $) "\\axiom{lazyPseudoRemainder(a,{}\\spad{b})} returns \\axiom{\\spad{r}} if \\axiom{lazyResidueClass(a,{}\\spad{b})} returns \\axiom{[\\spad{r},{}\\spad{c},{}\\spad{n}]}. This lazy pseudo-remainder is computed by means of the \\axiomOpFrom{fmecg}{NewSparseUnivariatePolynomial} operation.")) (|lazyResidueClass| (((|Record| (|:| |polnum| $) (|:| |polden| |#1|) (|:| |power| (|NonNegativeInteger|))) $ $) "\\axiom{lazyResidueClass(a,{}\\spad{b})} returns \\axiom{[\\spad{r},{}\\spad{c},{}\\spad{n}]} such that \\axiom{\\spad{r}} is reduced \\spad{w}.\\spad{r}.\\spad{t}. \\axiom{\\spad{b}} and \\axiom{\\spad{b}} divides \\axiom{\\spad{c^n} * a - \\spad{r}} where \\axiom{\\spad{c}} is \\axiom{leadingCoefficient(\\spad{b})} and \\axiom{\\spad{n}} is as small as possible with the previous properties.")) (|monicModulo| (($ $ $) "\\axiom{monicModulo(a,{}\\spad{b})} returns \\axiom{\\spad{r}} such that \\axiom{\\spad{r}} is reduced \\spad{w}.\\spad{r}.\\spad{t}. \\axiom{\\spad{b}} and \\axiom{\\spad{b}} divides \\axiom{a \\spad{-r}} where \\axiom{\\spad{b}} is monic.")) (|fmecg| (($ $ (|NonNegativeInteger|) |#1| $) "\\axiom{fmecg(\\spad{p1},{}\\spad{e},{}\\spad{r},{}\\spad{p2})} returns \\axiom{\\spad{p1} - \\spad{r} * X**e * \\spad{p2}} where \\axiom{\\spad{X}} is \\axiom{monomial(1,{}1)}"))) (((-4454 "*") |has| |#1| (-174)) (-4445 |has| |#1| (-562)) (-4448 |has| |#1| (-368)) (-4450 |has| |#1| (-6 -4450)) (-4447 . T) (-4446 . T) (-4449 . 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(|eulerE| ((|#1| (|NonNegativeInteger|) |#1|) "\\spad{eulerE(n,r)} \\undocumented")) (|bernoulliB| ((|#1| (|NonNegativeInteger|) |#1|) "\\spad{bernoulliB(n,r)} \\undocumented")) (|cyclotomic| ((|#1| (|NonNegativeInteger|) |#1|) "\\spad{cyclotomic(n,r)} \\undocumented"))) NIL @@ -3144,23 +3144,23 @@ NIL ((|constructor| (NIL "OctonionCategory gives the categorial frame for the octonions,{} and eight-dimensional non-associative algebra,{} doubling the the quaternions in the same way as doubling the Complex numbers to get the quaternions.")) (|inv| (($ $) "\\spad{inv(o)} returns the inverse of \\spad{o} if it exists.")) (|rationalIfCan| (((|Union| (|Fraction| (|Integer|)) "failed") $) "\\spad{rationalIfCan(o)} returns the real part if all seven imaginary parts are 0,{} and \"failed\" otherwise.")) (|rational| (((|Fraction| (|Integer|)) $) "\\spad{rational(o)} returns the real part if all seven imaginary parts are 0. Error: if \\spad{o} is not rational.")) (|rational?| (((|Boolean|) $) "\\spad{rational?(o)} tests if \\spad{o} is rational,{} \\spadignore{i.e.} that all seven imaginary parts are 0.")) (|abs| ((|#1| $) "\\spad{abs(o)} computes the absolute value of an octonion,{} equal to the square root of the \\spadfunFrom{norm}{Octonion}.")) (|octon| (($ |#1| |#1| |#1| |#1| |#1| |#1| |#1| |#1|) "\\spad{octon(re,ri,rj,rk,rE,rI,rJ,rK)} constructs an octonion from scalars.")) (|norm| ((|#1| $) "\\spad{norm(o)} returns the norm of an octonion,{} equal to the sum of the squares of its coefficients.")) (|imagK| ((|#1| $) "\\spad{imagK(o)} extracts the imaginary \\spad{K} part of octonion \\spad{o}.")) (|imagJ| ((|#1| $) "\\spad{imagJ(o)} extracts the imaginary \\spad{J} part of octonion \\spad{o}.")) (|imagI| ((|#1| $) "\\spad{imagI(o)} extracts the imaginary \\spad{I} part of octonion \\spad{o}.")) (|imagE| ((|#1| $) "\\spad{imagE(o)} extracts the imaginary \\spad{E} part of octonion \\spad{o}.")) (|imagk| ((|#1| $) "\\spad{imagk(o)} extracts the \\spad{k} part of octonion \\spad{o}.")) (|imagj| ((|#1| $) "\\spad{imagj(o)} extracts the \\spad{j} part of octonion \\spad{o}.")) (|imagi| ((|#1| $) "\\spad{imagi(o)} extracts the \\spad{i} part of octonion \\spad{o}.")) (|real| ((|#1| $) "\\spad{real(o)} extracts real part of octonion \\spad{o}.")) (|conjugate| (($ $) "\\spad{conjugate(o)} negates the imaginary parts \\spad{i},{}\\spad{j},{}\\spad{k},{}\\spad{E},{}\\spad{I},{}\\spad{J},{}\\spad{K} of octonian \\spad{o}."))) ((-4446 . T) (-4447 . T) (-4449 . T)) NIL -(-804 -2811 R OS S) +(-804 -3684 R OS S) ((|constructor| (NIL "OctonionCategoryFunctions2 implements functions between two octonion domains defined over different rings. The function map is used to coerce between octonion types.")) (|map| ((|#3| (|Mapping| |#4| |#2|) |#1|) "\\spad{map(f,u)} maps \\spad{f} onto the component parts of the octonion \\spad{u}."))) NIL NIL (-805 R) ((|constructor| (NIL "Octonion implements octonions (Cayley-Dixon algebra) over a commutative ring,{} an eight-dimensional non-associative algebra,{} doubling the quaternions in the same way as doubling the complex numbers to get the quaternions the main constructor function is {\\em octon} which takes 8 arguments: the real part,{} the \\spad{i} imaginary part,{} the \\spad{j} imaginary part,{} the \\spad{k} imaginary part,{} (as with quaternions) and in addition the imaginary parts \\spad{E},{} \\spad{I},{} \\spad{J},{} \\spad{K}.")) (|octon| (($ (|Quaternion| |#1|) (|Quaternion| |#1|)) "\\spad{octon(qe,qE)} constructs an octonion from two quaternions using the relation {\\em O = Q + QE}."))) ((-4446 . T) (-4447 . T) (-4449 . T)) -((|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-148))) (|HasCategory| |#1| (LIST (QUOTE -620) (QUOTE (-542)))) (|HasCategory| |#1| (QUOTE (-856))) (|HasCategory| |#1| (QUOTE (-373))) (|HasCategory| |#1| (LIST (QUOTE -520) (QUOTE (-1186)) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -290) (|devaluate| |#1|) (|devaluate| |#1|))) (-2811 (|HasCategory| (-1008 |#1|) (LIST (QUOTE -1047) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasCategory| |#1| (LIST (QUOTE -1047) (LIST (QUOTE -413) (QUOTE (-570)))))) (-2811 (|HasCategory| (-1008 |#1|) (LIST (QUOTE -1047) (QUOTE (-570)))) (|HasCategory| |#1| (LIST (QUOTE -1047) (QUOTE (-570))))) (|HasCategory| |#1| (QUOTE (-1069))) (|HasCategory| |#1| (QUOTE (-551))) (|HasCategory| |#1| (QUOTE (-368))) (|HasCategory| (-1008 |#1|) (LIST (QUOTE -1047) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasCategory| (-1008 |#1|) (LIST (QUOTE -1047) (QUOTE (-570)))) (|HasCategory| |#1| (LIST (QUOTE -1047) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasCategory| |#1| (LIST (QUOTE -1047) (QUOTE (-570))))) +((|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-148))) (|HasCategory| |#1| (LIST (QUOTE -620) (QUOTE (-542)))) (|HasCategory| |#1| (QUOTE (-856))) (|HasCategory| |#1| (QUOTE (-373))) (|HasCategory| |#1| (LIST (QUOTE -520) (QUOTE (-1186)) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -290) (|devaluate| |#1|) (|devaluate| |#1|))) (-3684 (|HasCategory| (-1008 |#1|) (LIST (QUOTE -1047) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasCategory| |#1| (LIST (QUOTE -1047) (LIST (QUOTE -413) (QUOTE (-570)))))) (-3684 (|HasCategory| (-1008 |#1|) (LIST (QUOTE -1047) (QUOTE (-570)))) (|HasCategory| |#1| (LIST (QUOTE -1047) (QUOTE (-570))))) (|HasCategory| |#1| (QUOTE (-1069))) (|HasCategory| |#1| (QUOTE (-551))) (|HasCategory| |#1| (QUOTE (-368))) (|HasCategory| (-1008 |#1|) (LIST (QUOTE -1047) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasCategory| (-1008 |#1|) (LIST (QUOTE -1047) (QUOTE (-570)))) (|HasCategory| |#1| (LIST (QUOTE -1047) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasCategory| |#1| (LIST (QUOTE -1047) (QUOTE (-570))))) (-806) ((|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 -(-807 R -1385 L) +(-807 R -2968 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}\\spad{'s} form a basis for the solutions of \\spad{op y = 0}."))) NIL NIL -(-808 R -1385) +(-808 R -2968) ((|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 @@ -3168,7 +3168,7 @@ NIL ((|constructor| (NIL "\\axiom{ODEIntensityFunctionsTable()} provides a dynamic table and a set of functions to store details found out about sets of ODE\\spad{'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 -(-810 R -1385) +(-810 R -2968) ((|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 @@ -3176,11 +3176,11 @@ 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\\spad{'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\\spad{'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\\spad{'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\\spad{'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\\spad{'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\\spad{'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\\spad{'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\\spad{'s} and calculating a measure of compatibility of each routine to these attributes. \\blankline It then calls the resulting `best' routine."))) NIL NIL -(-812 -1385 UP UPUP R) +(-812 -2968 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 -(-813 -1385 UP L LQ) +(-813 -2968 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}\\spad{'s} are the affine singularities of \\spad{op} above the roots of \\spad{p},{} and the \\spad{e_i}\\spad{'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}\\spad{'s} are the affine singularities of \\spad{op},{} and the \\spad{e_i}\\spad{'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}\\spad{'s} are the affine singularities of \\spad{op} above the roots of \\spad{p},{} and the \\spad{e_i}\\spad{'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}\\spad{'s} are the affine singularities of \\spad{op},{} and the \\spad{e_i}\\spad{'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 @@ -3188,38 +3188,38 @@ 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 -(-815 -1385 UP L LQ) +(-815 -2968 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}\\spad{'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)}\\spad{'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}\\spad{'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}\\spad{'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 \\spad{mj} for some \\spad{j},{} and its leading coefficient is then a zero of \\spad{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 {\\spad{gcd}(\\spad{d},{}\\spad{q}) = 1}."))) NIL NIL -(-816 -1385 UP) +(-816 -2968 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}\\spad{'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}\\spad{'s} form a basis for the rational solutions of the homogeneous equation."))) NIL NIL -(-817 -1385 L UP A LO) +(-817 -2968 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 -(-818 -1385 UP) +(-818 -2968 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}\\spad{'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 \\spad{++} part of any rational solution of the associated Riccati equation of \\spad{op y = 0} must be one of the \\spad{fi}\\spad{'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)))) -(-819 -1385 LO) +(-819 -2968 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}.") 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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)]}."))) 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The ranking on the differential indeterminate is orderly. This is analogous to the domain \\spadtype{Polynomial}. \\blankline"))) (((-4454 "*") |has| |#1| (-174)) (-4445 |has| |#1| (-562)) (-4450 |has| |#1| (-6 -4450)) (-4447 . T) (-4446 . T) (-4449 . 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(((-4454 "*") |has| |#2| (-368)) (-4445 |has| |#2| (-368)) (-4450 |has| |#2| (-368)) (-4444 |has| |#2| (-368)) (-4449 . T) (-4447 . T) (-4446 . T)) @@ -3287,7 +3287,7 @@ NIL (-839 R) ((|constructor| (NIL "Adjunction of a complex infinity to a set. Date Created: 4 Oct 1989 Date Last Updated: 1 Nov 1989")) (|rationalIfCan| (((|Union| (|Fraction| (|Integer|)) "failed") $) "\\spad{rationalIfCan(x)} returns \\spad{x} as a finite rational number if it is one,{} \"failed\" otherwise.")) (|rational| (((|Fraction| (|Integer|)) $) "\\spad{rational(x)} returns \\spad{x} as a finite rational number. Error: if \\spad{x} is not a rational number.")) (|rational?| (((|Boolean|) $) "\\spad{rational?(x)} tests if \\spad{x} is a finite rational number.")) (|infinite?| (((|Boolean|) $) "\\spad{infinite?(x)} tests if \\spad{x} is infinite.")) (|finite?| (((|Boolean|) $) "\\spad{finite?(x)} tests if \\spad{x} is finite.")) (|infinity| (($) "\\spad{infinity()} returns infinity."))) ((-4449 |has| |#1| (-854))) -((|HasCategory| |#1| (QUOTE (-854))) (|HasCategory| |#1| (QUOTE (-21))) (-2811 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-854)))) (|HasCategory| |#1| (LIST (QUOTE -1047) (LIST (QUOTE -413) (QUOTE (-570))))) (-2811 (|HasCategory| |#1| (QUOTE (-854))) (|HasCategory| |#1| (LIST (QUOTE -1047) (QUOTE (-570))))) (|HasCategory| |#1| (LIST (QUOTE -1047) (QUOTE (-570)))) (|HasCategory| |#1| (QUOTE (-551)))) +((|HasCategory| |#1| (QUOTE (-854))) (|HasCategory| |#1| (QUOTE (-21))) (-3684 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-854)))) (|HasCategory| |#1| (LIST (QUOTE -1047) (LIST (QUOTE -413) (QUOTE (-570))))) (-3684 (|HasCategory| |#1| (QUOTE (-854))) (|HasCategory| |#1| (LIST (QUOTE -1047) (QUOTE (-570))))) (|HasCategory| |#1| (LIST (QUOTE -1047) (QUOTE (-570)))) (|HasCategory| |#1| (QUOTE (-551)))) (-840 A S) ((|constructor| (NIL "This category specifies the interface for operators used to build terms,{} in the sense of Universal Algebra. The domain parameter \\spad{S} provides representation for the `external name' of an operator.")) (|is?| (((|Boolean|) $ |#2|) "\\spad{is?(op,n)} holds if the name of the operator \\spad{op} is \\spad{n}.")) (|arity| (((|Arity|) $) "\\spad{arity(op)} returns the arity of the operator \\spad{op}.")) (|name| ((|#2| $) "\\spad{name(op)} returns the externam name of \\spad{op}."))) NIL @@ -3327,12 +3327,12 @@ NIL (-849 R) ((|constructor| (NIL "Adjunction of two real infinites quantities to a set. Date Created: 4 Oct 1989 Date Last Updated: 1 Nov 1989")) (|rationalIfCan| (((|Union| (|Fraction| (|Integer|)) "failed") $) "\\spad{rationalIfCan(x)} returns \\spad{x} as a finite rational number if it is one and \"failed\" otherwise.")) (|rational| (((|Fraction| (|Integer|)) $) "\\spad{rational(x)} returns \\spad{x} as a finite rational number. Error: if \\spad{x} cannot be so converted.")) (|rational?| (((|Boolean|) $) "\\spad{rational?(x)} tests if \\spad{x} is a finite rational number.")) (|whatInfinity| (((|SingleInteger|) $) "\\spad{whatInfinity(x)} returns 0 if \\spad{x} is finite,{} 1 if \\spad{x} is +infinity,{} and \\spad{-1} if \\spad{x} is -infinity.")) (|infinite?| (((|Boolean|) $) "\\spad{infinite?(x)} tests if \\spad{x} is +infinity or -infinity,{}")) (|finite?| (((|Boolean|) $) "\\spad{finite?(x)} tests if \\spad{x} is finite.")) (|minusInfinity| (($) "\\spad{minusInfinity()} returns -infinity.")) (|plusInfinity| (($) "\\spad{plusInfinity()} returns +infinity."))) ((-4449 |has| |#1| (-854))) -((|HasCategory| |#1| (QUOTE (-854))) (|HasCategory| |#1| (QUOTE (-21))) (-2811 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-854)))) (|HasCategory| |#1| (LIST (QUOTE -1047) (LIST (QUOTE -413) (QUOTE (-570))))) (-2811 (|HasCategory| |#1| (QUOTE (-854))) (|HasCategory| |#1| (LIST (QUOTE -1047) (QUOTE (-570))))) (|HasCategory| |#1| (LIST (QUOTE -1047) (QUOTE (-570)))) (|HasCategory| |#1| (QUOTE (-551)))) +((|HasCategory| |#1| (QUOTE (-854))) (|HasCategory| |#1| (QUOTE (-21))) (-3684 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-854)))) (|HasCategory| |#1| (LIST (QUOTE -1047) (LIST (QUOTE -413) (QUOTE (-570))))) (-3684 (|HasCategory| |#1| (QUOTE (-854))) (|HasCategory| |#1| (LIST (QUOTE -1047) (QUOTE (-570))))) (|HasCategory| |#1| (LIST (QUOTE -1047) (QUOTE (-570)))) (|HasCategory| |#1| (QUOTE (-551)))) (-850) ((|constructor| (NIL "Ordered finite sets.")) (|max| (($) "\\spad{max} is the maximum value of \\%.")) (|min| (($) "\\spad{min} is the minimum value of \\%."))) NIL NIL -(-851 -2183 S) +(-851 -2795 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 @@ -3368,11 +3368,11 @@ 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{''}. \\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{''}. \\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{''}. \\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{''}. \\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 (-368))) (|HasCategory| |#1| (QUOTE (-562)))) -(-860 R |sigma| -2227) +(-860 R |sigma| -3502) ((|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."))) ((-4446 . T) (-4447 . T) (-4449 . T)) ((|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (LIST (QUOTE -1047) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasCategory| |#1| (LIST (QUOTE -1047) (QUOTE (-570)))) (|HasCategory| |#1| (QUOTE (-562))) (|HasCategory| |#1| (QUOTE (-458))) (|HasCategory| |#1| (QUOTE (-368)))) -(-861 |x| R |sigma| -2227) +(-861 |x| R |sigma| -3502) ((|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}."))) ((-4446 . T) (-4447 . T) (-4449 . T)) ((|HasCategory| |#2| (QUOTE (-174))) (|HasCategory| |#2| (LIST (QUOTE -1047) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasCategory| |#2| (LIST (QUOTE -1047) (QUOTE (-570)))) (|HasCategory| |#2| (QUOTE (-562))) (|HasCategory| |#2| (QUOTE (-458))) (|HasCategory| |#2| (QUOTE (-368)))) @@ -3439,15 +3439,15 @@ NIL (-877 |p|) ((|constructor| (NIL "Stream-based implementation of \\spad{Qp:} numbers are represented as sum(\\spad{i} = \\spad{k}..,{} a[\\spad{i}] * p^i) where the a[\\spad{i}] lie in 0,{}1,{}...,{}(\\spad{p} - 1)."))) ((-4444 . T) (-4450 . T) (-4445 . T) ((-4454 "*") . T) (-4446 . T) (-4447 . T) (-4449 . T)) -((|HasCategory| (-876 |#1|) (QUOTE (-916))) (|HasCategory| (-876 |#1|) (LIST (QUOTE -1047) (QUOTE (-1186)))) (|HasCategory| (-876 |#1|) (QUOTE (-146))) (|HasCategory| (-876 |#1|) (QUOTE (-148))) (|HasCategory| (-876 |#1|) (LIST (QUOTE -620) (QUOTE (-542)))) (|HasCategory| (-876 |#1|) (QUOTE (-1031))) (|HasCategory| (-876 |#1|) (QUOTE (-826))) (-2811 (|HasCategory| (-876 |#1|) (QUOTE (-826))) (|HasCategory| (-876 |#1|) (QUOTE (-856)))) (|HasCategory| (-876 |#1|) (LIST (QUOTE -1047) (QUOTE (-570)))) (|HasCategory| (-876 |#1|) (QUOTE (-1161))) (|HasCategory| (-876 |#1|) (LIST (QUOTE -893) (QUOTE (-384)))) (|HasCategory| (-876 |#1|) (LIST (QUOTE -893) (QUOTE (-570)))) (|HasCategory| (-876 |#1|) (LIST (QUOTE -620) (LIST (QUOTE -899) (QUOTE (-384))))) (|HasCategory| (-876 |#1|) (LIST (QUOTE -620) (LIST (QUOTE -899) (QUOTE (-570))))) (|HasCategory| (-876 |#1|) (LIST (QUOTE -645) (QUOTE (-570)))) (|HasCategory| (-876 |#1|) (QUOTE (-235))) (|HasCategory| (-876 |#1|) (LIST (QUOTE -907) (QUOTE (-1186)))) (|HasCategory| (-876 |#1|) (LIST (QUOTE -520) (QUOTE (-1186)) (LIST (QUOTE -876) (|devaluate| |#1|)))) (|HasCategory| (-876 |#1|) (LIST (QUOTE -313) (LIST (QUOTE -876) (|devaluate| |#1|)))) (|HasCategory| (-876 |#1|) (LIST (QUOTE -290) (LIST (QUOTE -876) (|devaluate| |#1|)) (LIST (QUOTE -876) (|devaluate| |#1|)))) (|HasCategory| (-876 |#1|) (QUOTE (-311))) (|HasCategory| (-876 |#1|) (QUOTE (-551))) (|HasCategory| (-876 |#1|) (QUOTE (-856))) (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| (-876 |#1|) (QUOTE (-916)))) (-2811 (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| (-876 |#1|) (QUOTE (-916)))) (|HasCategory| (-876 |#1|) (QUOTE (-146))))) +((|HasCategory| (-876 |#1|) (QUOTE (-916))) (|HasCategory| (-876 |#1|) (LIST (QUOTE -1047) (QUOTE (-1186)))) (|HasCategory| (-876 |#1|) (QUOTE (-146))) (|HasCategory| (-876 |#1|) (QUOTE (-148))) (|HasCategory| (-876 |#1|) (LIST (QUOTE -620) (QUOTE (-542)))) (|HasCategory| (-876 |#1|) (QUOTE (-1031))) (|HasCategory| (-876 |#1|) (QUOTE (-826))) (-3684 (|HasCategory| (-876 |#1|) (QUOTE (-826))) (|HasCategory| (-876 |#1|) (QUOTE (-856)))) (|HasCategory| (-876 |#1|) (LIST (QUOTE -1047) (QUOTE (-570)))) (|HasCategory| (-876 |#1|) (QUOTE (-1161))) (|HasCategory| (-876 |#1|) (LIST (QUOTE -893) (QUOTE (-384)))) (|HasCategory| (-876 |#1|) (LIST (QUOTE -893) (QUOTE (-570)))) (|HasCategory| (-876 |#1|) (LIST (QUOTE -620) (LIST (QUOTE -899) (QUOTE (-384))))) (|HasCategory| (-876 |#1|) (LIST (QUOTE -620) (LIST (QUOTE -899) (QUOTE (-570))))) (|HasCategory| (-876 |#1|) (LIST (QUOTE -645) (QUOTE (-570)))) (|HasCategory| (-876 |#1|) (QUOTE (-235))) (|HasCategory| (-876 |#1|) (LIST (QUOTE -907) (QUOTE (-1186)))) (|HasCategory| (-876 |#1|) (LIST (QUOTE -520) (QUOTE (-1186)) (LIST (QUOTE -876) (|devaluate| |#1|)))) (|HasCategory| (-876 |#1|) (LIST (QUOTE -313) (LIST (QUOTE -876) (|devaluate| |#1|)))) (|HasCategory| (-876 |#1|) (LIST (QUOTE -290) (LIST (QUOTE -876) (|devaluate| |#1|)) (LIST (QUOTE -876) (|devaluate| |#1|)))) (|HasCategory| (-876 |#1|) (QUOTE (-311))) (|HasCategory| (-876 |#1|) (QUOTE (-551))) (|HasCategory| (-876 |#1|) (QUOTE (-856))) (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| (-876 |#1|) (QUOTE (-916)))) (-3684 (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| (-876 |#1|) (QUOTE (-916)))) (|HasCategory| (-876 |#1|) (QUOTE (-146))))) (-878 |p| PADIC) ((|constructor| (NIL "This is the category of stream-based representations of \\spad{Qp}.")) (|removeZeroes| (($ (|Integer|) $) "\\spad{removeZeroes(n,x)} removes up to \\spad{n} leading zeroes from the \\spad{p}-adic rational \\spad{x}.") (($ $) "\\spad{removeZeroes(x)} removes leading zeroes from the representation of the \\spad{p}-adic rational \\spad{x}. A \\spad{p}-adic rational is represented by (1) an exponent and (2) a \\spad{p}-adic integer which may have leading zero digits. When the \\spad{p}-adic integer has a leading zero digit,{} a 'leading zero' is removed from the \\spad{p}-adic rational as follows: the number is rewritten by increasing the exponent by 1 and dividing the \\spad{p}-adic integer by \\spad{p}. Note: \\spad{removeZeroes(f)} removes all leading zeroes from \\spad{f}.")) (|continuedFraction| (((|ContinuedFraction| (|Fraction| (|Integer|))) $) "\\spad{continuedFraction(x)} converts the \\spad{p}-adic rational number \\spad{x} to a continued fraction.")) (|approximate| (((|Fraction| (|Integer|)) $ (|Integer|)) "\\spad{approximate(x,n)} returns a rational number \\spad{y} such that \\spad{y = x (mod p^n)}."))) ((-4444 . T) (-4450 . T) (-4445 . T) ((-4454 "*") . T) (-4446 . T) (-4447 . T) (-4449 . T)) -((|HasCategory| |#2| (QUOTE (-916))) (|HasCategory| |#2| (LIST (QUOTE -1047) (QUOTE (-1186)))) (|HasCategory| |#2| (QUOTE (-146))) (|HasCategory| |#2| (QUOTE (-148))) (|HasCategory| |#2| (LIST (QUOTE -620) (QUOTE (-542)))) (|HasCategory| |#2| (QUOTE (-1031))) (|HasCategory| |#2| (QUOTE (-826))) (-2811 (|HasCategory| |#2| (QUOTE (-826))) (|HasCategory| |#2| (QUOTE (-856)))) (|HasCategory| |#2| (LIST (QUOTE -1047) (QUOTE (-570)))) (|HasCategory| |#2| (QUOTE (-1161))) (|HasCategory| |#2| (LIST (QUOTE -893) (QUOTE (-384)))) (|HasCategory| |#2| (LIST (QUOTE -893) (QUOTE (-570)))) (|HasCategory| |#2| (LIST (QUOTE -620) (LIST (QUOTE -899) (QUOTE (-384))))) (|HasCategory| |#2| (LIST (QUOTE -620) (LIST (QUOTE -899) (QUOTE (-570))))) (|HasCategory| |#2| (LIST (QUOTE -645) (QUOTE (-570)))) (|HasCategory| |#2| (QUOTE (-235))) (|HasCategory| |#2| (LIST (QUOTE -907) (QUOTE (-1186)))) (|HasCategory| |#2| (LIST (QUOTE -520) (QUOTE (-1186)) (|devaluate| |#2|))) (|HasCategory| |#2| (LIST (QUOTE -313) (|devaluate| |#2|))) (|HasCategory| |#2| (LIST (QUOTE -290) (|devaluate| |#2|) (|devaluate| |#2|))) (|HasCategory| |#2| (QUOTE (-311))) (|HasCategory| |#2| (QUOTE (-551))) (|HasCategory| |#2| (QUOTE (-856))) (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| |#2| (QUOTE (-916)))) (-2811 (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| |#2| (QUOTE (-916)))) (|HasCategory| |#2| (QUOTE (-146))))) +((|HasCategory| |#2| (QUOTE (-916))) (|HasCategory| |#2| (LIST (QUOTE -1047) (QUOTE (-1186)))) (|HasCategory| |#2| (QUOTE (-146))) (|HasCategory| |#2| (QUOTE (-148))) (|HasCategory| |#2| (LIST (QUOTE -620) (QUOTE (-542)))) (|HasCategory| |#2| (QUOTE (-1031))) (|HasCategory| |#2| (QUOTE (-826))) (-3684 (|HasCategory| |#2| (QUOTE (-826))) (|HasCategory| |#2| (QUOTE (-856)))) (|HasCategory| |#2| (LIST (QUOTE -1047) (QUOTE (-570)))) (|HasCategory| |#2| (QUOTE (-1161))) (|HasCategory| |#2| (LIST (QUOTE -893) (QUOTE (-384)))) (|HasCategory| |#2| (LIST (QUOTE -893) (QUOTE (-570)))) (|HasCategory| |#2| (LIST (QUOTE -620) (LIST (QUOTE -899) (QUOTE (-384))))) (|HasCategory| |#2| (LIST (QUOTE -620) (LIST (QUOTE -899) (QUOTE (-570))))) (|HasCategory| |#2| (LIST (QUOTE -645) (QUOTE (-570)))) (|HasCategory| |#2| (QUOTE (-235))) (|HasCategory| |#2| (LIST (QUOTE -907) (QUOTE (-1186)))) (|HasCategory| |#2| (LIST (QUOTE -520) (QUOTE (-1186)) (|devaluate| |#2|))) (|HasCategory| |#2| (LIST (QUOTE -313) (|devaluate| |#2|))) (|HasCategory| |#2| (LIST (QUOTE -290) (|devaluate| |#2|) (|devaluate| |#2|))) (|HasCategory| |#2| (QUOTE (-311))) (|HasCategory| |#2| (QUOTE (-551))) (|HasCategory| |#2| (QUOTE (-856))) (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| |#2| (QUOTE (-916)))) (-3684 (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| |#2| (QUOTE (-916)))) (|HasCategory| |#2| (QUOTE (-146))))) (-879 S T$) ((|constructor| (NIL "\\indented{1}{This domain provides a very simple representation} of the notion of `pair of objects'. It does not try to achieve all possible imaginable things.")) (|second| ((|#2| $) "\\spad{second(p)} extracts the second components of \\spad{`p'}.")) (|first| ((|#1| $) "\\spad{first(p)} extracts the first component of \\spad{`p'}.")) (|construct| (($ |#1| |#2|) "\\spad{construct(s,t)} is same as pair(\\spad{s},{}\\spad{t}),{} with syntactic sugar.")) (|pair| (($ |#1| |#2|) "\\spad{pair(s,t)} returns a pair object composed of \\spad{`s'} and \\spad{`t'}."))) NIL -((-12 (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#2| (QUOTE (-1109)))) (-2811 (-12 (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#2| (QUOTE (-1109)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-868)))) (|HasCategory| |#2| (LIST (QUOTE -619) (QUOTE (-868)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-868)))) (|HasCategory| |#2| (LIST (QUOTE -619) (QUOTE (-868)))))) +((-12 (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#2| (QUOTE (-1109)))) (-3684 (-12 (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#2| (QUOTE (-1109)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-868)))) (|HasCategory| |#2| (LIST (QUOTE -619) (QUOTE (-868)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-868)))) (|HasCategory| |#2| (LIST (QUOTE -619) (QUOTE (-868)))))) (-880) ((|constructor| (NIL "This domain describes four groups of color shades (palettes).")) (|coerce| (($ (|Color|)) "\\spad{coerce(c)} sets the average shade for the palette to that of the indicated color \\spad{c}.")) (|shade| (((|Integer|) $) "\\spad{shade(p)} returns the shade index of the indicated palette \\spad{p}.")) (|hue| (((|Color|) $) "\\spad{hue(p)} returns the hue field of the indicated palette \\spad{p}.")) (|light| (($ (|Color|)) "\\spad{light(c)} sets the shade of a hue,{} \\spad{c},{} to it\\spad{'s} highest value.")) (|pastel| (($ (|Color|)) "\\spad{pastel(c)} sets the shade of a hue,{} \\spad{c},{} above bright,{} but below light.")) (|bright| (($ (|Color|)) "\\spad{bright(c)} sets the shade of a hue,{} \\spad{c},{} above dim,{} but below pastel.")) (|dim| (($ (|Color|)) "\\spad{dim(c)} sets the shade of a hue,{} \\spad{c},{} above dark,{} but below bright.")) (|dark| (($ (|Color|)) "\\spad{dark(c)} sets the shade of the indicated hue of \\spad{c} to it\\spad{'s} lowest value."))) NIL @@ -3507,7 +3507,7 @@ NIL (-894 |Base| |Subject| |Pat|) ((|constructor| (NIL "This package provides the top-level pattern macthing functions.")) (|Is| (((|PatternMatchResult| |#1| |#2|) |#2| |#3|) "\\spad{Is(expr, pat)} matches the pattern pat on the expression \\spad{expr} and returns a match of the form \\spad{[v1 = e1,...,vn = en]}; returns an empty match if \\spad{expr} is exactly equal to pat. returns a \\spadfun{failed} match if pat does not match \\spad{expr}.") (((|List| (|Equation| (|Polynomial| |#2|))) |#2| |#3|) "\\spad{Is(expr, pat)} matches the pattern pat on the expression \\spad{expr} and returns a list of matches \\spad{[v1 = e1,...,vn = en]}; returns an empty list if either \\spad{expr} is exactly equal to pat or if pat does not match \\spad{expr}.") (((|List| (|Equation| |#2|)) |#2| |#3|) "\\spad{Is(expr, pat)} matches the pattern pat on the expression \\spad{expr} and returns a list of matches \\spad{[v1 = e1,...,vn = en]}; returns an empty list if either \\spad{expr} is exactly equal to pat or if pat does not match \\spad{expr}.") (((|PatternMatchListResult| |#1| |#2| (|List| |#2|)) (|List| |#2|) |#3|) "\\spad{Is([e1,...,en], pat)} matches the pattern pat on the list of expressions \\spad{[e1,...,en]} and returns the result.")) (|is?| (((|Boolean|) (|List| |#2|) |#3|) "\\spad{is?([e1,...,en], pat)} tests if the list of expressions \\spad{[e1,...,en]} matches the pattern pat.") (((|Boolean|) |#2| |#3|) "\\spad{is?(expr, pat)} tests if the expression \\spad{expr} matches the pattern pat."))) NIL -((-12 (-2104 (|HasCategory| |#2| (QUOTE (-1058)))) (-2104 (|HasCategory| |#2| (LIST (QUOTE -1047) (QUOTE (-1186)))))) (-12 (|HasCategory| |#2| (QUOTE (-1058))) (-2104 (|HasCategory| |#2| (LIST (QUOTE -1047) (QUOTE (-1186)))))) (|HasCategory| |#2| (LIST (QUOTE -1047) (QUOTE (-1186))))) +((-12 (-3152 (|HasCategory| |#2| (QUOTE (-1058)))) (-3152 (|HasCategory| |#2| (LIST (QUOTE -1047) (QUOTE (-1186)))))) (-12 (|HasCategory| |#2| (QUOTE (-1058))) (-3152 (|HasCategory| |#2| (LIST (QUOTE -1047) (QUOTE (-1186)))))) (|HasCategory| |#2| (LIST (QUOTE -1047) (QUOTE (-1186))))) (-895 R A B) ((|constructor| (NIL "Lifts maps to pattern matching results.")) (|map| (((|PatternMatchResult| |#1| |#3|) (|Mapping| |#3| |#2|) (|PatternMatchResult| |#1| |#2|)) "\\spad{map(f, [(v1,a1),...,(vn,an)])} returns the matching result [(\\spad{v1},{}\\spad{f}(a1)),{}...,{}(\\spad{vn},{}\\spad{f}(an))]."))) NIL @@ -3516,7 +3516,7 @@ NIL ((|constructor| (NIL "A PatternMatchResult is an object internally returned by the pattern matcher; It is either a failed match,{} or a list of matches of the form (var,{} expr) meaning that the variable var matches the expression expr.")) (|satisfy?| (((|Union| (|Boolean|) "failed") $ (|Pattern| |#1|)) "\\spad{satisfy?(r, p)} returns \\spad{true} if the matches satisfy the top-level predicate of \\spad{p},{} \\spad{false} if they don\\spad{'t},{} and \"failed\" if not enough variables of \\spad{p} are matched in \\spad{r} to decide.")) (|construct| (($ (|List| (|Record| (|:| |key| (|Symbol|)) (|:| |entry| |#2|)))) "\\spad{construct([v1,e1],...,[vn,en])} returns the match result containing the matches (\\spad{v1},{}e1),{}...,{}(\\spad{vn},{}en).")) (|destruct| (((|List| (|Record| (|:| |key| (|Symbol|)) (|:| |entry| |#2|))) $) "\\spad{destruct(r)} returns the list of matches (var,{} expr) in \\spad{r}. Error: if \\spad{r} is a failed match.")) (|addMatchRestricted| (($ (|Pattern| |#1|) |#2| $ |#2|) "\\spad{addMatchRestricted(var, expr, r, val)} adds the match (\\spad{var},{} \\spad{expr}) in \\spad{r},{} provided that \\spad{expr} satisfies the predicates attached to \\spad{var},{} that \\spad{var} is not matched to another expression already,{} and that either \\spad{var} is an optional pattern variable or that \\spad{expr} is not equal to val (usually an identity).")) (|insertMatch| (($ (|Pattern| |#1|) |#2| $) "\\spad{insertMatch(var, expr, r)} adds the match (\\spad{var},{} \\spad{expr}) in \\spad{r},{} without checking predicates or previous matches for \\spad{var}.")) (|addMatch| (($ (|Pattern| |#1|) |#2| $) "\\spad{addMatch(var, expr, r)} adds the match (\\spad{var},{} \\spad{expr}) in \\spad{r},{} provided that \\spad{expr} satisfies the predicates attached to \\spad{var},{} and that \\spad{var} is not matched to another expression already.")) (|getMatch| (((|Union| |#2| "failed") (|Pattern| |#1|) $) "\\spad{getMatch(var, r)} returns the expression that \\spad{var} matches in the result \\spad{r},{} and \"failed\" if \\spad{var} is not matched in \\spad{r}.")) (|union| (($ $ $) "\\spad{union(a, b)} makes the set-union of two match results.")) (|new| (($) "\\spad{new()} returns a new empty match result.")) (|failed| (($) "\\spad{failed()} returns a failed match.")) (|failed?| (((|Boolean|) $) "\\spad{failed?(r)} tests if \\spad{r} is a failed match."))) NIL NIL -(-897 R -3651) +(-897 R -3347) ((|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 \\spad{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 @@ -3540,7 +3540,7 @@ 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 -(-903 UP -1385) +(-903 UP -2968) ((|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 @@ -3563,23 +3563,23 @@ NIL (-908 S) ((|constructor| (NIL "\\indented{1}{A PendantTree(\\spad{S})is either a leaf? and is an \\spad{S} or has} a left and a right both PendantTree(\\spad{S})\\spad{'s}")) (|ptree| (($ $ $) "\\spad{ptree(x,y)} \\undocumented") (($ |#1|) "\\spad{ptree(s)} is a leaf? pendant tree"))) NIL -((-12 (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1109))) (-2811 (-12 (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-868))))) (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-868))))) +((-12 (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1109))) (-3684 (-12 (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-868))))) (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-868))))) (-909 |n| R) ((|constructor| (NIL "Permanent implements the functions {\\em permanent},{} the permanent for square matrices.")) (|permanent| ((|#2| (|SquareMatrix| |#1| |#2|)) "\\spad{permanent(x)} computes the permanent of a square matrix \\spad{x}. The {\\em permanent} is equivalent to the \\spadfun{determinant} except that coefficients have no change of sign. This function is much more difficult to compute than the {\\em determinant}. The formula used is by \\spad{H}.\\spad{J}. Ryser,{} improved by [Nijenhuis and Wilf,{} \\spad{Ch}. 19]. Note: permanent(\\spad{x}) choose one of three algorithms,{} depending on the underlying ring \\spad{R} and on \\spad{n},{} the number of rows (and columns) of \\spad{x:}\\begin{items} \\item 1. if 2 has an inverse in \\spad{R} we can use the algorithm of \\indented{3}{[Nijenhuis and Wilf,{} \\spad{ch}.19,{}\\spad{p}.158]; if 2 has no inverse,{}} \\indented{3}{some modifications are necessary:} \\item 2. if {\\em n > 6} and \\spad{R} is an integral domain with characteristic \\indented{3}{different from 2 (the algorithm works if and only 2 is not a} \\indented{3}{zero-divisor of \\spad{R} and {\\em characteristic()\\$R ~= 2},{}} \\indented{3}{but how to check that for any given \\spad{R} ?),{}} \\indented{3}{the local function {\\em permanent2} is called;} \\item 3. else,{} the local function {\\em permanent3} is called \\indented{3}{(works for all commutative rings \\spad{R}).} \\end{items}"))) NIL NIL (-910 S) -((|constructor| (NIL "PermutationCategory provides a categorial environment \\indented{1}{for subgroups of bijections of a set (\\spadignore{i.e.} permutations)}")) (< (((|Boolean|) $ $) "\\spad{p < q} is an order relation on permutations. Note: this order is only total if and only if \\spad{S} is totally ordered or \\spad{S} is finite.")) (|orbit| (((|Set| |#1|) $ |#1|) "\\spad{orbit(p, el)} returns the orbit of {\\em el} under the permutation \\spad{p},{} \\spadignore{i.e.} the set which is given by applications of the powers of \\spad{p} to {\\em el}.")) (|elt| ((|#1| $ |#1|) "\\spad{elt(p, el)} returns the image of {\\em el} under the permutation \\spad{p}.")) (|eval| ((|#1| $ |#1|) "\\spad{eval(p, el)} returns the image of {\\em el} under the permutation \\spad{p}.")) (|cycles| (($ (|List| (|List| |#1|))) "\\spad{cycles(lls)} coerces a list list of cycles {\\em lls} to a permutation,{} each cycle being a list with not repetitions,{} is coerced to the permutation,{} which maps {\\em ls.i} to {\\em ls.i+1},{} indices modulo the length of the list,{} then these permutations are mutiplied. Error: if repetitions occur in one cycle.")) (|cycle| (($ (|List| |#1|)) "\\spad{cycle(ls)} coerces a cycle {\\em ls},{} \\spadignore{i.e.} a list with not repetitions to a permutation,{} which maps {\\em ls.i} to {\\em ls.i+1},{} indices modulo the length of the list. Error: if repetitions occur."))) +((|constructor| (NIL "PermutationCategory provides a categorial environment \\indented{1}{for subgroups of bijections of a set (\\spadignore{i.e.} permutations)}")) (< (((|Boolean|) $ $) "\\spad{p < q} is an order relation on permutations. Note: this order is only total if and only if \\spad{S} is totally ordered or \\spad{S} is finite.")) (|orbit| (((|Set| |#1|) $ |#1|) "\\spad{orbit(p, el)} returns the orbit of {\\em el} under the permutation \\spad{p},{} \\spadignore{i.e.} the set which is given by applications of the powers of \\spad{p} to {\\em el}.")) (|support| (((|Set| |#1|) $) "\\spad{support p} returns the set of points not fixed by the permutation \\spad{p}.")) (|cycles| (($ (|List| (|List| |#1|))) "\\spad{cycles(lls)} coerces a list list of cycles {\\em lls} to a permutation,{} each cycle being a list with not repetitions,{} is coerced to the permutation,{} which maps {\\em ls.i} to {\\em ls.i+1},{} indices modulo the length of the list,{} then these permutations are mutiplied. Error: if repetitions occur in one cycle.")) (|cycle| (($ (|List| |#1|)) "\\spad{cycle(ls)} coerces a cycle {\\em ls},{} \\spadignore{i.e.} a list with not repetitions to a permutation,{} which maps {\\em ls.i} to {\\em ls.i+1},{} indices modulo the length of the list. Error: if repetitions occur."))) ((-4449 . T)) NIL (-911 S) -((|constructor| (NIL "PermutationGroup implements permutation groups acting on a set \\spad{S},{} \\spadignore{i.e.} all subgroups of the symmetric group of \\spad{S},{} represented as a list of permutations (generators). Note that therefore the objects are not members of the \\Language category \\spadtype{Group}. Using the idea of base and strong generators by Sims,{} basic routines and algorithms are implemented so that the word problem for permutation groups can be solved.")) (|initializeGroupForWordProblem| (((|Void|) $ (|Integer|) (|Integer|)) "\\spad{initializeGroupForWordProblem(gp,m,n)} initializes the group {\\em gp} for the word problem. Notes: (1) with a small integer you get shorter words,{} but the routine takes longer than the standard routine for longer words. (2) be careful: invoking this routine will destroy the possibly stored information about your group (but will recompute it again). (3) users need not call this function normally for the soultion of the word problem.") (((|Void|) $) "\\spad{initializeGroupForWordProblem(gp)} initializes the group {\\em gp} for the word problem. Notes: it calls the other function of this name with parameters 0 and 1: {\\em initializeGroupForWordProblem(gp,0,1)}. Notes: (1) be careful: invoking this routine will destroy the possibly information about your group (but will recompute it again) (2) users need not call this function normally for the soultion of the word problem.")) (<= (((|Boolean|) $ $) "\\spad{gp1 <= gp2} returns \\spad{true} if and only if {\\em gp1} is a subgroup of {\\em gp2}. Note: because of a bug in the parser you have to call this function explicitly by {\\em gp1 <=\\$(PERMGRP S) gp2}.")) (< (((|Boolean|) $ $) "\\spad{gp1 < gp2} returns \\spad{true} if and only if {\\em gp1} is a proper subgroup of {\\em gp2}.")) (|movedPoints| (((|Set| |#1|) $) "\\spad{movedPoints(gp)} returns the points moved by the group {\\em gp}.")) (|wordInGenerators| (((|List| (|NonNegativeInteger|)) (|Permutation| |#1|) $) "\\spad{wordInGenerators(p,gp)} returns the word for the permutation \\spad{p} in the original generators of the group {\\em gp},{} represented by the indices of the list,{} given by {\\em generators}.")) (|wordInStrongGenerators| (((|List| (|NonNegativeInteger|)) (|Permutation| |#1|) $) "\\spad{wordInStrongGenerators(p,gp)} returns the word for the permutation \\spad{p} in the strong generators of the group {\\em gp},{} represented by the indices of the list,{} given by {\\em strongGenerators}.")) (|member?| (((|Boolean|) (|Permutation| |#1|) $) "\\spad{member?(pp,gp)} answers the question,{} whether the permutation {\\em pp} is in the group {\\em gp} or not.")) (|orbits| (((|Set| (|Set| |#1|)) $) "\\spad{orbits(gp)} returns the orbits of the group {\\em gp},{} \\spadignore{i.e.} it partitions the (finite) of all moved points.")) (|orbit| (((|Set| (|List| |#1|)) $ (|List| |#1|)) "\\spad{orbit(gp,ls)} returns the orbit of the ordered list {\\em ls} under the group {\\em gp}. Note: return type is \\spad{L} \\spad{L} \\spad{S} temporarily because FSET \\spad{L} \\spad{S} has an error.") (((|Set| (|Set| |#1|)) $ (|Set| |#1|)) "\\spad{orbit(gp,els)} returns the orbit of the unordered set {\\em els} under the group {\\em gp}.") (((|Set| |#1|) $ |#1|) "\\spad{orbit(gp,el)} returns the orbit of the element {\\em el} under the group {\\em gp},{} \\spadignore{i.e.} the set of all points gained by applying each group element to {\\em el}.")) (|permutationGroup| (($ (|List| (|Permutation| |#1|))) "\\spad{permutationGroup(ls)} coerces a list of permutations {\\em ls} to the group generated by this list.")) (|wordsForStrongGenerators| (((|List| (|List| (|NonNegativeInteger|))) $) "\\spad{wordsForStrongGenerators(gp)} returns the words for the strong generators of the group {\\em gp} in the original generators of {\\em gp},{} represented by their indices in the list,{} given by {\\em generators}.")) (|strongGenerators| (((|List| (|Permutation| |#1|)) $) "\\spad{strongGenerators(gp)} returns strong generators for the group {\\em gp}.")) (|base| (((|List| |#1|) $) "\\spad{base(gp)} returns a base for the group {\\em gp}.")) (|degree| (((|NonNegativeInteger|) $) "\\spad{degree(gp)} returns the number of points moved by all permutations of the group {\\em gp}.")) (|order| (((|NonNegativeInteger|) $) "\\spad{order(gp)} returns the order of the group {\\em gp}.")) (|random| (((|Permutation| |#1|) $) "\\spad{random(gp)} returns a random product of maximal 20 generators of the group {\\em gp}. Note: {\\em random(gp)=random(gp,20)}.") (((|Permutation| |#1|) $ (|Integer|)) "\\spad{random(gp,i)} returns a random product of maximal \\spad{i} generators of the group {\\em gp}.")) (|elt| (((|Permutation| |#1|) $ (|NonNegativeInteger|)) "\\spad{elt(gp,i)} returns the \\spad{i}-th generator of the group {\\em gp}.")) (|generators| (((|List| (|Permutation| |#1|)) $) "\\spad{generators(gp)} returns the generators of the group {\\em gp}.")) (|coerce| (($ (|List| (|Permutation| |#1|))) "\\spad{coerce(ls)} coerces a list of permutations {\\em ls} to the group generated by this list.") (((|List| (|Permutation| |#1|)) $) "\\spad{coerce(gp)} returns the generators of the group {\\em gp}."))) +((|constructor| (NIL "PermutationGroup implements permutation groups acting on a set \\spad{S},{} \\spadignore{i.e.} all subgroups of the symmetric group of \\spad{S},{} represented as a list of permutations (generators). Note that therefore the objects are not members of the \\Language category \\spadtype{Group}. Using the idea of base and strong generators by Sims,{} basic routines and algorithms are implemented so that the word problem for permutation groups can be solved.")) (|initializeGroupForWordProblem| (((|Void|) $ (|Integer|) (|Integer|)) "\\spad{initializeGroupForWordProblem(gp,m,n)} initializes the group {\\em gp} for the word problem. Notes: (1) with a small integer you get shorter words,{} but the routine takes longer than the standard routine for longer words. (2) be careful: invoking this routine will destroy the possibly stored information about your group (but will recompute it again). (3) users need not call this function normally for the soultion of the word problem.") (((|Void|) $) "\\spad{initializeGroupForWordProblem(gp)} initializes the group {\\em gp} for the word problem. Notes: it calls the other function of this name with parameters 0 and 1: {\\em initializeGroupForWordProblem(gp,0,1)}. Notes: (1) be careful: invoking this routine will destroy the possibly information about your group (but will recompute it again) (2) users need not call this function normally for the soultion of the word problem.")) (<= (((|Boolean|) $ $) "\\spad{gp1 <= gp2} returns \\spad{true} if and only if {\\em gp1} is a subgroup of {\\em gp2}. Note: because of a bug in the parser you have to call this function explicitly by {\\em gp1 <=\\$(PERMGRP S) gp2}.")) (< (((|Boolean|) $ $) "\\spad{gp1 < gp2} returns \\spad{true} if and only if {\\em gp1} is a proper subgroup of {\\em gp2}.")) (|support| (((|Set| |#1|) $) "\\spad{support(gp)} returns the points moved by the group {\\em gp}.")) (|wordInGenerators| (((|List| (|NonNegativeInteger|)) (|Permutation| |#1|) $) "\\spad{wordInGenerators(p,gp)} returns the word for the permutation \\spad{p} in the original generators of the group {\\em gp},{} represented by the indices of the list,{} given by {\\em generators}.")) (|wordInStrongGenerators| (((|List| (|NonNegativeInteger|)) (|Permutation| |#1|) $) "\\spad{wordInStrongGenerators(p,gp)} returns the word for the permutation \\spad{p} in the strong generators of the group {\\em gp},{} represented by the indices of the list,{} given by {\\em strongGenerators}.")) (|member?| (((|Boolean|) (|Permutation| |#1|) $) "\\spad{member?(pp,gp)} answers the question,{} whether the permutation {\\em pp} is in the group {\\em gp} or not.")) (|orbits| (((|Set| (|Set| |#1|)) $) "\\spad{orbits(gp)} returns the orbits of the group {\\em gp},{} \\spadignore{i.e.} it partitions the (finite) of all moved points.")) (|orbit| (((|Set| (|List| |#1|)) $ (|List| |#1|)) "\\spad{orbit(gp,ls)} returns the orbit of the ordered list {\\em ls} under the group {\\em gp}. Note: return type is \\spad{L} \\spad{L} \\spad{S} temporarily because FSET \\spad{L} \\spad{S} has an error.") (((|Set| (|Set| |#1|)) $ (|Set| |#1|)) "\\spad{orbit(gp,els)} returns the orbit of the unordered set {\\em els} under the group {\\em gp}.") (((|Set| |#1|) $ |#1|) "\\spad{orbit(gp,el)} returns the orbit of the element {\\em el} under the group {\\em gp},{} \\spadignore{i.e.} the set of all points gained by applying each group element to {\\em el}.")) (|permutationGroup| (($ (|List| (|Permutation| |#1|))) "\\spad{permutationGroup(ls)} coerces a list of permutations {\\em ls} to the group generated by this list.")) (|wordsForStrongGenerators| (((|List| (|List| (|NonNegativeInteger|))) $) "\\spad{wordsForStrongGenerators(gp)} returns the words for the strong generators of the group {\\em gp} in the original generators of {\\em gp},{} represented by their indices in the list,{} given by {\\em generators}.")) (|strongGenerators| (((|List| (|Permutation| |#1|)) $) "\\spad{strongGenerators(gp)} returns strong generators for the group {\\em gp}.")) (|base| (((|List| |#1|) $) "\\spad{base(gp)} returns a base for the group {\\em gp}.")) (|degree| (((|NonNegativeInteger|) $) "\\spad{degree(gp)} returns the number of points moved by all permutations of the group {\\em gp}.")) (|order| (((|NonNegativeInteger|) $) "\\spad{order(gp)} returns the order of the group {\\em gp}.")) (|random| (((|Permutation| |#1|) $) "\\spad{random(gp)} returns a random product of maximal 20 generators of the group {\\em gp}. Note: {\\em random(gp)=random(gp,20)}.") (((|Permutation| |#1|) $ (|Integer|)) "\\spad{random(gp,i)} returns a random product of maximal \\spad{i} generators of the group {\\em gp}.")) (|elt| (((|Permutation| |#1|) $ (|NonNegativeInteger|)) "\\spad{elt(gp,i)} returns the \\spad{i}-th generator of the group {\\em gp}.")) (|generators| (((|List| (|Permutation| |#1|)) $) "\\spad{generators(gp)} returns the generators of the group {\\em gp}.")) (|coerce| (($ (|List| (|Permutation| |#1|))) "\\spad{coerce(ls)} coerces a list of permutations {\\em ls} to the group generated by this list.") (((|List| (|Permutation| |#1|)) $) "\\spad{coerce(gp)} returns the generators of the group {\\em gp}."))) NIL NIL (-912 S) -((|constructor| (NIL "Permutation(\\spad{S}) implements the group of all bijections \\indented{2}{on a set \\spad{S},{} which move only a finite number of points.} \\indented{2}{A permutation is considered as a map from \\spad{S} into \\spad{S}. In particular} \\indented{2}{multiplication is defined as composition of maps:} \\indented{2}{{\\em pi1 * pi2 = pi1 o pi2}.} \\indented{2}{The internal representation of permuatations are two lists} \\indented{2}{of equal length representing preimages and images.}")) (|coerceImages| (($ (|List| |#1|)) "\\spad{coerceImages(ls)} coerces the list {\\em ls} to a permutation whose image is given by {\\em ls} and the preimage is fixed to be {\\em [1,...,n]}. Note: {coerceImages(\\spad{ls})=coercePreimagesImages([1,{}...,{}\\spad{n}],{}\\spad{ls})}. We assume that both preimage and image do not contain repetitions.")) (|fixedPoints| (((|Set| |#1|) $) "\\spad{fixedPoints(p)} returns the points fixed by the permutation \\spad{p}.")) (|sort| (((|List| $) (|List| $)) "\\spad{sort(lp)} sorts a list of permutations {\\em lp} according to cycle structure first according to length of cycles,{} second,{} if \\spad{S} has \\spadtype{Finite} or \\spad{S} has \\spadtype{OrderedSet} according to lexicographical order of entries in cycles of equal length.")) (|odd?| (((|Boolean|) $) "\\spad{odd?(p)} returns \\spad{true} if and only if \\spad{p} is an odd permutation \\spadignore{i.e.} {\\em sign(p)} is {\\em -1}.")) (|even?| (((|Boolean|) $) "\\spad{even?(p)} returns \\spad{true} if and only if \\spad{p} is an even permutation,{} \\spadignore{i.e.} {\\em sign(p)} is 1.")) (|sign| (((|Integer|) $) "\\spad{sign(p)} returns the signum of the permutation \\spad{p},{} \\spad{+1} or \\spad{-1}.")) (|numberOfCycles| (((|NonNegativeInteger|) $) "\\spad{numberOfCycles(p)} returns the number of non-trivial cycles of the permutation \\spad{p}.")) (|order| (((|NonNegativeInteger|) $) "\\spad{order(p)} returns the order of a permutation \\spad{p} as a group element.")) (|cyclePartition| (((|Partition|) $) "\\spad{cyclePartition(p)} returns the cycle structure of a permutation \\spad{p} including cycles of length 1 only if \\spad{S} is finite.")) (|movedPoints| (((|Set| |#1|) $) "\\spad{movedPoints(p)} returns the set of points moved by the permutation \\spad{p}.")) (|degree| (((|NonNegativeInteger|) $) "\\spad{degree(p)} retuns the number of points moved by the permutation \\spad{p}.")) (|coerceListOfPairs| (($ (|List| (|List| |#1|))) "\\spad{coerceListOfPairs(lls)} coerces a list of pairs {\\em lls} to a permutation. Error: if not consistent,{} \\spadignore{i.e.} the set of the first elements coincides with the set of second elements. coerce(\\spad{p}) generates output of the permutation \\spad{p} with domain OutputForm.")) (|coerce| (($ (|List| |#1|)) "\\spad{coerce(ls)} coerces a cycle {\\em ls},{} \\spadignore{i.e.} a list with not repetitions to a permutation,{} which maps {\\em ls.i} to {\\em ls.i+1},{} indices modulo the length of the list. Error: if repetitions occur.") (($ (|List| (|List| |#1|))) "\\spad{coerce(lls)} coerces a list of cycles {\\em lls} to a permutation,{} each cycle being a list with no repetitions,{} is coerced to the permutation,{} which maps {\\em ls.i} to {\\em ls.i+1},{} indices modulo the length of the list,{} then these permutations are mutiplied. Error: if repetitions occur in one cycle.")) (|coercePreimagesImages| (($ (|List| (|List| |#1|))) "\\spad{coercePreimagesImages(lls)} coerces the representation {\\em lls} of a permutation as a list of preimages and images to a permutation. We assume that both preimage and image do not contain repetitions.")) (|listRepresentation| (((|Record| (|:| |preimage| (|List| |#1|)) (|:| |image| (|List| |#1|))) $) "\\spad{listRepresentation(p)} produces a representation {\\em rep} of the permutation \\spad{p} as a list of preimages and images,{} \\spad{i}.\\spad{e} \\spad{p} maps {\\em (rep.preimage).k} to {\\em (rep.image).k} for all indices \\spad{k}. Elements of \\spad{S} not in {\\em (rep.preimage).k} are fixed points,{} and these are the only fixed points of the permutation."))) +((|constructor| (NIL "Permutation(\\spad{S}) implements the group of all bijections \\indented{2}{on a set \\spad{S},{} which move only a finite number of points.} \\indented{2}{A permutation is considered as a map from \\spad{S} into \\spad{S}. In particular} \\indented{2}{multiplication is defined as composition of maps:} \\indented{2}{{\\em pi1 * pi2 = pi1 o pi2}.} \\indented{2}{The internal representation of permuatations are two lists} \\indented{2}{of equal length representing preimages and images.}")) (|coerceImages| (($ (|List| |#1|)) "\\spad{coerceImages(ls)} coerces the list {\\em ls} to a permutation whose image is given by {\\em ls} and the preimage is fixed to be {\\em [1,...,n]}. Note: {coerceImages(\\spad{ls})=coercePreimagesImages([1,{}...,{}\\spad{n}],{}\\spad{ls})}. We assume that both preimage and image do not contain repetitions.")) (|fixedPoints| (((|Set| |#1|) $) "\\spad{fixedPoints(p)} returns the points fixed by the permutation \\spad{p}.")) (|sort| (((|List| $) (|List| $)) "\\spad{sort(lp)} sorts a list of permutations {\\em lp} according to cycle structure first according to length of cycles,{} second,{} if \\spad{S} has \\spadtype{Finite} or \\spad{S} has \\spadtype{OrderedSet} according to lexicographical order of entries in cycles of equal length.")) (|odd?| (((|Boolean|) $) "\\spad{odd?(p)} returns \\spad{true} if and only if \\spad{p} is an odd permutation \\spadignore{i.e.} {\\em sign(p)} is {\\em -1}.")) (|even?| (((|Boolean|) $) "\\spad{even?(p)} returns \\spad{true} if and only if \\spad{p} is an even permutation,{} \\spadignore{i.e.} {\\em sign(p)} is 1.")) (|sign| (((|Integer|) $) "\\spad{sign(p)} returns the signum of the permutation \\spad{p},{} \\spad{+1} or \\spad{-1}.")) (|numberOfCycles| (((|NonNegativeInteger|) $) "\\spad{numberOfCycles(p)} returns the number of non-trivial cycles of the permutation \\spad{p}.")) (|order| (((|NonNegativeInteger|) $) "\\spad{order(p)} returns the order of a permutation \\spad{p} as a group element.")) (|cyclePartition| (((|Partition|) $) "\\spad{cyclePartition(p)} returns the cycle structure of a permutation \\spad{p} including cycles of length 1 only if \\spad{S} is finite.")) (|degree| (((|NonNegativeInteger|) $) "\\spad{degree(p)} retuns the number of points moved by the permutation \\spad{p}.")) (|coerceListOfPairs| (($ (|List| (|List| |#1|))) "\\spad{coerceListOfPairs(lls)} coerces a list of pairs {\\em lls} to a permutation. Error: if not consistent,{} \\spadignore{i.e.} the set of the first elements coincides with the set of second elements. coerce(\\spad{p}) generates output of the permutation \\spad{p} with domain OutputForm.")) (|coerce| (($ (|List| |#1|)) "\\spad{coerce(ls)} coerces a cycle {\\em ls},{} \\spadignore{i.e.} a list with not repetitions to a permutation,{} which maps {\\em ls.i} to {\\em ls.i+1},{} indices modulo the length of the list. Error: if repetitions occur.") (($ (|List| (|List| |#1|))) "\\spad{coerce(lls)} coerces a list of cycles {\\em lls} to a permutation,{} each cycle being a list with no repetitions,{} is coerced to the permutation,{} which maps {\\em ls.i} to {\\em ls.i+1},{} indices modulo the length of the list,{} then these permutations are mutiplied. Error: if repetitions occur in one cycle.")) (|coercePreimagesImages| (($ (|List| (|List| |#1|))) "\\spad{coercePreimagesImages(lls)} coerces the representation {\\em lls} of a permutation as a list of preimages and images to a permutation. We assume that both preimage and image do not contain repetitions.")) (|listRepresentation| (((|Record| (|:| |preimage| (|List| |#1|)) (|:| |image| (|List| |#1|))) $) "\\spad{listRepresentation(p)} produces a representation {\\em rep} of the permutation \\spad{p} as a list of preimages and images,{} \\spad{i}.\\spad{e} \\spad{p} maps {\\em (rep.preimage).k} to {\\em (rep.image).k} for all indices \\spad{k}. Elements of \\spad{S} not in {\\em (rep.preimage).k} are fixed points,{} and these are the only fixed points of the permutation."))) ((-4449 . T)) -((-2811 (|HasCategory| |#1| (QUOTE (-373))) (|HasCategory| |#1| (QUOTE (-856)))) (|HasCategory| |#1| (QUOTE (-373))) (|HasCategory| |#1| (QUOTE (-856)))) +((-3684 (|HasCategory| |#1| (QUOTE (-373))) (|HasCategory| |#1| (QUOTE (-856)))) (|HasCategory| |#1| (QUOTE (-373))) (|HasCategory| |#1| (QUOTE (-856)))) (-913 R E |VarSet| S) ((|constructor| (NIL "PolynomialFactorizationByRecursion(\\spad{R},{}\\spad{E},{}\\spad{VarSet},{}\\spad{S}) is used for factorization of sparse univariate polynomials over a domain \\spad{S} of multivariate polynomials over \\spad{R}.")) (|factorSFBRlcUnit| (((|Factored| (|SparseUnivariatePolynomial| |#4|)) (|List| |#3|) (|SparseUnivariatePolynomial| |#4|)) "\\spad{factorSFBRlcUnit(p)} returns the square free factorization of polynomial \\spad{p} (see \\spadfun{factorSquareFreeByRecursion}{PolynomialFactorizationByRecursionUnivariate}) in the case where the leading coefficient of \\spad{p} is a unit.")) (|bivariateSLPEBR| (((|Union| (|List| (|SparseUnivariatePolynomial| |#4|)) "failed") (|List| (|SparseUnivariatePolynomial| |#4|)) (|SparseUnivariatePolynomial| |#4|) |#3|) "\\spad{bivariateSLPEBR(lp,p,v)} implements the bivariate case of \\spadfunFrom{solveLinearPolynomialEquationByRecursion}{PolynomialFactorizationByRecursionUnivariate}; its implementation depends on \\spad{R}")) (|randomR| ((|#1|) "\\spad{randomR produces} a random element of \\spad{R}")) (|factorSquareFreeByRecursion| (((|Factored| (|SparseUnivariatePolynomial| |#4|)) (|SparseUnivariatePolynomial| |#4|)) "\\spad{factorSquareFreeByRecursion(p)} returns the square free factorization of \\spad{p}. This functions performs the recursion step for factorSquareFreePolynomial,{} as defined in \\spadfun{PolynomialFactorizationExplicit} category (see \\spadfun{factorSquareFreePolynomial}).")) (|factorByRecursion| (((|Factored| (|SparseUnivariatePolynomial| |#4|)) (|SparseUnivariatePolynomial| |#4|)) "\\spad{factorByRecursion(p)} factors polynomial \\spad{p}. This function performs the recursion step for factorPolynomial,{} as defined in \\spadfun{PolynomialFactorizationExplicit} category (see \\spadfun{factorPolynomial})")) (|solveLinearPolynomialEquationByRecursion| (((|Union| (|List| (|SparseUnivariatePolynomial| |#4|)) "failed") (|List| (|SparseUnivariatePolynomial| |#4|)) (|SparseUnivariatePolynomial| |#4|)) "\\spad{solveLinearPolynomialEquationByRecursion([p1,...,pn],p)} returns the list of polynomials \\spad{[q1,...,qn]} such that \\spad{sum qi/pi = p / prod pi},{} a recursion step for solveLinearPolynomialEquation as defined in \\spadfun{PolynomialFactorizationExplicit} category (see \\spadfun{solveLinearPolynomialEquation}). If no such list of \\spad{qi} exists,{} then \"failed\" is returned."))) NIL @@ -3600,7 +3600,7 @@ NIL ((|constructor| (NIL "PrimeField(\\spad{p}) implements the field with \\spad{p} elements if \\spad{p} is a prime number. Error: if \\spad{p} is not prime. Note: this domain does not check that argument is a prime."))) ((-4444 . T) (-4450 . T) (-4445 . T) ((-4454 "*") . T) (-4446 . T) (-4447 . T) (-4449 . T)) ((|HasCategory| $ (QUOTE (-148))) (|HasCategory| $ (QUOTE (-146))) (|HasCategory| $ (QUOTE (-373)))) -(-918 R0 -1385 UP UPUP R) +(-918 R0 -2968 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 @@ -3628,7 +3628,7 @@ 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\\spad{'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\\spad{'s} Cube acting on integers {\\em 10*i+j} for {\\em 1 <= i <= 6},{} {\\em 1 <= j <= 8}. The faces of Rubik\\spad{'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\\spad{'s} Cube acting on integers 10*i+j for 1 \\spad{<=} \\spad{i} \\spad{<=} 6,{} 1 \\spad{<=} \\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 -(-925 -1385) +(-925 -2968) ((|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 \\spad{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 @@ -3644,11 +3644,11 @@ NIL ((|constructor| (NIL "\\spadtype{PositiveInteger} provides functions for \\indented{2}{positive integers.}")) (|commutative| ((|attribute| "*") "\\spad{commutative(\"*\")} means multiplication is commutative : x*y = \\spad{y*x}")) (|gcd| (($ $ $) "\\spad{gcd(a,b)} computes the greatest common divisor of two positive integers \\spad{a} and \\spad{b}."))) (((-4454 "*") . T)) NIL -(-929 -1385 P) +(-929 -2968 P) ((|constructor| (NIL "This package exports interpolation algorithms")) (|LagrangeInterpolation| ((|#2| (|List| |#1|) (|List| |#1|)) "\\spad{LagrangeInterpolation(l1,l2)} \\undocumented"))) NIL NIL -(-930 |xx| -1385) +(-930 |xx| -2968) ((|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 @@ -3672,7 +3672,7 @@ NIL ((|constructor| (NIL "This package exports plotting tools")) (|calcRanges| (((|List| (|Segment| (|DoubleFloat|))) (|List| (|List| (|Point| (|DoubleFloat|))))) "\\spad{calcRanges(l)} \\undocumented"))) NIL NIL -(-936 R -1385) +(-936 R -2968) ((|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 \\spad{'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 @@ -3684,7 +3684,7 @@ 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 -(-939 S R -1385) +(-939 S R -2968) ((|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 @@ -3704,11 +3704,11 @@ 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 -893) (|devaluate| |#1|)))) -(-944 R -1385 -3651) +(-944 R -2968 -3347) ((|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 \\spad{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 -(-945 -3651) +(-945 -3347) ((|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 \\spad{fn} to \\spad{x}.") (((|Expression| (|Integer|)) (|Symbol|) (|Mapping| (|Boolean|) |#1|)) "\\spad{suchThat(x, foo)} attaches the predicate foo to \\spad{x}."))) NIL NIL @@ -3731,7 +3731,7 @@ NIL (-950 R) ((|constructor| (NIL "This domain implements points in coordinate space"))) ((-4453 . T) (-4452 . T)) -((-2811 (-12 (|HasCategory| |#1| (QUOTE (-856))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|))))) (-2811 (-12 (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-868))))) (|HasCategory| |#1| (LIST (QUOTE -620) (QUOTE (-542)))) (-2811 (|HasCategory| |#1| (QUOTE (-856))) (|HasCategory| |#1| (QUOTE (-1109)))) (|HasCategory| |#1| (QUOTE (-856))) (|HasCategory| (-570) (QUOTE (-856))) (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (QUOTE (-25))) (|HasCategory| |#1| (QUOTE (-23))) (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-732))) (|HasCategory| |#1| (QUOTE (-1058))) (-12 (|HasCategory| |#1| (QUOTE (-1011))) (|HasCategory| |#1| (QUOTE (-1058)))) (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-868)))) (-12 (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|))))) +((-3684 (-12 (|HasCategory| |#1| (QUOTE (-856))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|))))) (-3684 (-12 (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-868))))) (|HasCategory| |#1| (LIST (QUOTE -620) (QUOTE (-542)))) (-3684 (|HasCategory| |#1| (QUOTE (-856))) (|HasCategory| |#1| (QUOTE (-1109)))) (|HasCategory| |#1| (QUOTE (-856))) (|HasCategory| (-570) (QUOTE (-856))) (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (QUOTE (-25))) (|HasCategory| |#1| (QUOTE (-23))) (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-732))) (|HasCategory| |#1| (QUOTE (-1058))) (-12 (|HasCategory| |#1| (QUOTE (-1011))) (|HasCategory| |#1| (QUOTE (-1058)))) (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-868)))) (-12 (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|))))) (-951 |lv| R) ((|constructor| (NIL "Package with the conversion functions among different kind of polynomials")) (|pToDmp| (((|DistributedMultivariatePolynomial| |#1| |#2|) (|Polynomial| |#2|)) "\\spad{pToDmp(p)} converts \\spad{p} from a \\spadtype{POLY} to a \\spadtype{DMP}.")) (|dmpToP| (((|Polynomial| |#2|) (|DistributedMultivariatePolynomial| |#1| |#2|)) "\\spad{dmpToP(p)} converts \\spad{p} from a \\spadtype{DMP} to a \\spadtype{POLY}.")) (|hdmpToP| (((|Polynomial| |#2|) (|HomogeneousDistributedMultivariatePolynomial| |#1| |#2|)) "\\spad{hdmpToP(p)} converts \\spad{p} from a \\spadtype{HDMP} to a \\spadtype{POLY}.")) (|pToHdmp| (((|HomogeneousDistributedMultivariatePolynomial| |#1| |#2|) (|Polynomial| |#2|)) "\\spad{pToHdmp(p)} converts \\spad{p} from a \\spadtype{POLY} to a \\spadtype{HDMP}.")) (|hdmpToDmp| (((|DistributedMultivariatePolynomial| |#1| |#2|) (|HomogeneousDistributedMultivariatePolynomial| |#1| |#2|)) "\\spad{hdmpToDmp(p)} converts \\spad{p} from a \\spadtype{HDMP} to a \\spadtype{DMP}.")) (|dmpToHdmp| (((|HomogeneousDistributedMultivariatePolynomial| |#1| |#2|) (|DistributedMultivariatePolynomial| |#1| |#2|)) "\\spad{dmpToHdmp(p)} converts \\spad{p} from a \\spadtype{DMP} to a \\spadtype{HDMP}."))) NIL @@ -3756,7 +3756,7 @@ 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 \\spad{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 \\spad{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 \\spad{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 \\spad{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}."))) (((-4454 "*") |has| |#1| (-174)) (-4445 |has| |#1| (-562)) (-4450 |has| |#1| (-6 -4450)) (-4447 . T) (-4446 . T) (-4449 . T)) NIL -(-957 E V R P -1385) +(-957 E V R P -2968) ((|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},{}...,{}\\spad{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 @@ -3767,8 +3767,8 @@ NIL (-959 R) ((|constructor| (NIL "\\indented{2}{This type is the basic representation of sparse recursive multivariate} polynomials whose variables are arbitrary symbols. The ordering is alphabetic determined by the Symbol type. The coefficient ring may be non commutative,{} but the variables are assumed to commute.")) (|integrate| (($ $ (|Symbol|)) "\\spad{integrate(p,x)} computes the integral of \\spad{p*dx},{} \\spadignore{i.e.} integrates the polynomial \\spad{p} with respect to the variable \\spad{x}."))) (((-4454 "*") |has| |#1| (-174)) (-4445 |has| |#1| (-562)) (-4450 |has| |#1| (-6 -4450)) (-4447 . T) (-4446 . T) (-4449 . T)) -((|HasCategory| |#1| (QUOTE (-916))) (-2811 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-458))) (|HasCategory| |#1| (QUOTE (-562))) (|HasCategory| |#1| (QUOTE (-916)))) (-2811 (|HasCategory| |#1| (QUOTE (-458))) (|HasCategory| |#1| (QUOTE (-562))) (|HasCategory| |#1| (QUOTE (-916)))) (-2811 (|HasCategory| |#1| (QUOTE (-458))) (|HasCategory| |#1| (QUOTE (-916)))) (|HasCategory| |#1| (QUOTE (-562))) (|HasCategory| |#1| (QUOTE (-174))) (-2811 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-562)))) (-12 (|HasCategory| (-1186) (LIST (QUOTE -893) (QUOTE (-384)))) (|HasCategory| |#1| (LIST (QUOTE -893) (QUOTE (-384))))) (-12 (|HasCategory| (-1186) (LIST (QUOTE -893) (QUOTE (-570)))) (|HasCategory| |#1| (LIST (QUOTE -893) (QUOTE (-570))))) (-12 (|HasCategory| (-1186) (LIST (QUOTE -620) (LIST (QUOTE -899) (QUOTE (-384))))) (|HasCategory| |#1| (LIST (QUOTE -620) (LIST (QUOTE -899) (QUOTE (-384)))))) (-12 (|HasCategory| (-1186) (LIST (QUOTE -620) (LIST (QUOTE -899) (QUOTE (-570))))) (|HasCategory| |#1| (LIST (QUOTE -620) (LIST (QUOTE -899) (QUOTE (-570)))))) (-12 (|HasCategory| (-1186) (LIST (QUOTE -620) (QUOTE (-542)))) (|HasCategory| |#1| (LIST (QUOTE -620) (QUOTE (-542))))) (|HasCategory| |#1| (LIST (QUOTE -645) (QUOTE (-570)))) (|HasCategory| |#1| (QUOTE (-148))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasCategory| |#1| (LIST (QUOTE -1047) (QUOTE (-570)))) (-2811 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasCategory| |#1| (LIST (QUOTE -1047) (LIST (QUOTE -413) (QUOTE (-570)))))) (|HasCategory| |#1| (LIST (QUOTE -1047) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasCategory| |#1| (QUOTE (-368))) (|HasAttribute| |#1| (QUOTE -4450)) (|HasCategory| |#1| (QUOTE (-458))) (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-916)))) (-2811 (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-916)))) (|HasCategory| |#1| (QUOTE (-146))))) -(-960 E V R P -1385) +((|HasCategory| |#1| (QUOTE (-916))) (-3684 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-458))) (|HasCategory| |#1| (QUOTE (-562))) (|HasCategory| |#1| (QUOTE (-916)))) (-3684 (|HasCategory| |#1| (QUOTE (-458))) (|HasCategory| |#1| (QUOTE (-562))) (|HasCategory| |#1| (QUOTE (-916)))) (-3684 (|HasCategory| |#1| (QUOTE (-458))) (|HasCategory| |#1| (QUOTE (-916)))) (|HasCategory| |#1| (QUOTE (-562))) (|HasCategory| |#1| (QUOTE (-174))) (-3684 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-562)))) (-12 (|HasCategory| (-1186) (LIST (QUOTE -893) (QUOTE (-384)))) (|HasCategory| |#1| (LIST (QUOTE -893) (QUOTE (-384))))) (-12 (|HasCategory| (-1186) (LIST (QUOTE -893) (QUOTE (-570)))) (|HasCategory| |#1| (LIST (QUOTE -893) (QUOTE (-570))))) (-12 (|HasCategory| (-1186) (LIST (QUOTE -620) (LIST (QUOTE -899) (QUOTE (-384))))) (|HasCategory| |#1| (LIST (QUOTE -620) (LIST (QUOTE -899) (QUOTE (-384)))))) (-12 (|HasCategory| (-1186) (LIST (QUOTE -620) (LIST (QUOTE -899) (QUOTE (-570))))) (|HasCategory| |#1| (LIST (QUOTE -620) (LIST (QUOTE -899) (QUOTE (-570)))))) (-12 (|HasCategory| (-1186) (LIST (QUOTE -620) (QUOTE (-542)))) (|HasCategory| |#1| (LIST (QUOTE -620) (QUOTE (-542))))) (|HasCategory| |#1| (LIST (QUOTE -645) (QUOTE (-570)))) (|HasCategory| |#1| (QUOTE (-148))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasCategory| |#1| (LIST (QUOTE -1047) (QUOTE (-570)))) (-3684 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasCategory| |#1| (LIST (QUOTE -1047) (LIST (QUOTE -413) (QUOTE (-570)))))) (|HasCategory| |#1| (LIST (QUOTE -1047) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasCategory| |#1| (QUOTE (-368))) (|HasAttribute| |#1| (QUOTE -4450)) (|HasCategory| |#1| (QUOTE (-458))) (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-916)))) (-3684 (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-916)))) (|HasCategory| |#1| (QUOTE (-146))))) +(-960 E V R P -2968) ((|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| $) "\\spad{numer(x)} \\undocumented"))) NIL ((|HasCategory| |#3| (QUOTE (-458)))) @@ -3791,12 +3791,12 @@ NIL (-965 S) ((|constructor| (NIL "\\indented{1}{This provides a fast array type with no bound checking on elt\\spad{'s}.} Minimum index is 0 in this type,{} cannot be changed"))) ((-4453 . T) (-4452 . T)) -((-2811 (-12 (|HasCategory| |#1| (QUOTE (-856))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|))))) (-2811 (-12 (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-868))))) (|HasCategory| |#1| (LIST (QUOTE -620) (QUOTE (-542)))) (-2811 (|HasCategory| |#1| (QUOTE (-856))) (|HasCategory| |#1| (QUOTE (-1109)))) (|HasCategory| |#1| (QUOTE (-856))) (|HasCategory| (-570) (QUOTE (-856))) (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-868)))) (-12 (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|))))) +((-3684 (-12 (|HasCategory| |#1| (QUOTE (-856))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|))))) (-3684 (-12 (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-868))))) (|HasCategory| |#1| (LIST (QUOTE -620) (QUOTE (-542)))) (-3684 (|HasCategory| |#1| (QUOTE (-856))) (|HasCategory| |#1| (QUOTE (-1109)))) (|HasCategory| |#1| (QUOTE (-856))) (|HasCategory| (-570) (QUOTE (-856))) (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-868)))) (-12 (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|))))) (-966) ((|constructor| (NIL "Category for the functions defined by integrals.")) (|integral| (($ $ (|SegmentBinding| $)) "\\spad{integral(f, x = a..b)} returns the formal definite integral of \\spad{f} \\spad{dx} for \\spad{x} between \\spad{a} and \\spad{b}.") (($ $ (|Symbol|)) "\\spad{integral(f, x)} returns the formal integral of \\spad{f} \\spad{dx}."))) NIL NIL -(-967 -1385) +(-967 -2968) ((|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}\\spad{'s} are the defining polynomials for the \\spad{ai}\\spad{'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}\\spad{'s} are the defining polynomials for the \\spad{ai}\\spad{'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}\\spad{'s} are the defining polynomials for the \\spad{ai}\\spad{'s}. The \\spad{p2} may involve \\spad{a1},{} but \\spad{p1} must not involve a2. This operation uses \\spadfun{resultant}."))) NIL NIL @@ -3811,11 +3811,11 @@ NIL (-970 R E) ((|constructor| (NIL "This domain represents generalized polynomials with coefficients (from a not necessarily commutative ring),{} and terms indexed by their exponents (from an arbitrary ordered abelian monoid). This type is used,{} for example,{} by the \\spadtype{DistributedMultivariatePolynomial} domain where the exponent domain is a direct product of non negative integers.")) (|canonicalUnitNormal| ((|attribute|) "canonicalUnitNormal guarantees that the function unitCanonical returns the same representative for all associates of any particular element.")) (|fmecg| (($ $ |#2| |#1| $) "\\spad{fmecg(p1,e,r,p2)} finds \\spad{X} : \\spad{p1} - \\spad{r} * X**e * \\spad{p2}"))) (((-4454 "*") |has| |#1| (-174)) (-4445 |has| |#1| (-562)) (-4450 |has| |#1| (-6 -4450)) (-4446 . T) (-4447 . T) (-4449 . T)) -((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasCategory| |#1| (QUOTE (-562))) (-2811 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-562)))) (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-148))) (-2811 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasCategory| |#1| (LIST (QUOTE -1047) (LIST (QUOTE -413) (QUOTE (-570)))))) (|HasCategory| |#1| (LIST (QUOTE -1047) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasCategory| |#1| (LIST (QUOTE -1047) (QUOTE (-570)))) (|HasCategory| |#1| (QUOTE (-368))) (|HasCategory| |#1| (QUOTE (-458))) (-12 (|HasCategory| |#1| (QUOTE (-562))) (|HasCategory| |#2| (QUOTE (-132)))) (|HasAttribute| |#1| (QUOTE -4450))) +((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasCategory| |#1| (QUOTE (-562))) (-3684 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-562)))) (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-148))) (-3684 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasCategory| |#1| (LIST (QUOTE -1047) (LIST (QUOTE -413) (QUOTE (-570)))))) (|HasCategory| |#1| (LIST (QUOTE -1047) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasCategory| |#1| (LIST (QUOTE -1047) (QUOTE (-570)))) (|HasCategory| |#1| (QUOTE (-368))) (|HasCategory| |#1| (QUOTE (-458))) (-12 (|HasCategory| |#1| (QUOTE (-562))) (|HasCategory| |#2| (QUOTE (-132)))) (|HasAttribute| |#1| (QUOTE -4450))) (-971 A B) ((|constructor| (NIL "This domain implements cartesian product")) (|selectsecond| ((|#2| $) "\\spad{selectsecond(x)} \\undocumented")) (|selectfirst| ((|#1| $) "\\spad{selectfirst(x)} \\undocumented")) (|makeprod| (($ |#1| |#2|) "\\spad{makeprod(a,b)} \\undocumented"))) ((-4449 -12 (|has| |#2| (-479)) (|has| |#1| (-479)))) -((-2811 (-12 (|HasCategory| |#1| (QUOTE (-799))) (|HasCategory| |#2| (QUOTE (-799)))) (-12 (|HasCategory| |#1| (QUOTE (-856))) (|HasCategory| |#2| (QUOTE (-856))))) (-12 (|HasCategory| |#1| (QUOTE (-799))) (|HasCategory| |#2| (QUOTE (-799)))) (-2811 (-12 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#2| (QUOTE (-21)))) (-12 (|HasCategory| |#1| (QUOTE (-132))) (|HasCategory| |#2| (QUOTE (-132)))) (-12 (|HasCategory| |#1| (QUOTE (-799))) (|HasCategory| |#2| (QUOTE (-799))))) (-12 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#2| (QUOTE (-21)))) (-2811 (-12 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#2| (QUOTE (-21)))) (-12 (|HasCategory| |#1| (QUOTE (-23))) (|HasCategory| |#2| (QUOTE (-23)))) (-12 (|HasCategory| |#1| (QUOTE (-132))) (|HasCategory| |#2| (QUOTE (-132)))) (-12 (|HasCategory| |#1| (QUOTE (-799))) (|HasCategory| |#2| (QUOTE (-799))))) (-12 (|HasCategory| |#1| (QUOTE (-479))) (|HasCategory| |#2| (QUOTE (-479)))) (-2811 (-12 (|HasCategory| |#1| (QUOTE (-479))) (|HasCategory| |#2| (QUOTE (-479)))) (-12 (|HasCategory| |#1| (QUOTE (-732))) (|HasCategory| |#2| (QUOTE (-732))))) (-12 (|HasCategory| |#1| (QUOTE (-373))) (|HasCategory| |#2| (QUOTE (-373)))) (-2811 (-12 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#2| (QUOTE (-21)))) (-12 (|HasCategory| |#1| (QUOTE (-23))) (|HasCategory| |#2| (QUOTE (-23)))) (-12 (|HasCategory| |#1| (QUOTE (-132))) (|HasCategory| |#2| (QUOTE (-132)))) (-12 (|HasCategory| |#1| (QUOTE (-479))) (|HasCategory| |#2| (QUOTE (-479)))) (-12 (|HasCategory| |#1| (QUOTE (-732))) (|HasCategory| |#2| (QUOTE (-732)))) (-12 (|HasCategory| |#1| (QUOTE (-799))) (|HasCategory| |#2| (QUOTE (-799))))) (-12 (|HasCategory| |#1| (QUOTE (-732))) (|HasCategory| |#2| (QUOTE (-732)))) (-12 (|HasCategory| |#1| (QUOTE (-23))) (|HasCategory| |#2| (QUOTE (-23)))) (-12 (|HasCategory| |#1| (QUOTE (-132))) (|HasCategory| |#2| (QUOTE (-132)))) (-12 (|HasCategory| |#1| (QUOTE (-856))) (|HasCategory| |#2| (QUOTE (-856))))) +((-3684 (-12 (|HasCategory| |#1| (QUOTE (-799))) (|HasCategory| |#2| (QUOTE (-799)))) (-12 (|HasCategory| |#1| (QUOTE (-856))) (|HasCategory| |#2| (QUOTE (-856))))) (-12 (|HasCategory| |#1| (QUOTE (-799))) (|HasCategory| |#2| (QUOTE (-799)))) (-3684 (-12 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#2| (QUOTE (-21)))) (-12 (|HasCategory| |#1| (QUOTE (-132))) (|HasCategory| |#2| (QUOTE (-132)))) (-12 (|HasCategory| |#1| (QUOTE (-799))) (|HasCategory| |#2| (QUOTE (-799))))) (-12 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#2| (QUOTE (-21)))) (-3684 (-12 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#2| (QUOTE (-21)))) (-12 (|HasCategory| |#1| (QUOTE (-23))) (|HasCategory| |#2| (QUOTE (-23)))) (-12 (|HasCategory| |#1| (QUOTE (-132))) (|HasCategory| |#2| (QUOTE (-132)))) (-12 (|HasCategory| |#1| (QUOTE (-799))) (|HasCategory| |#2| (QUOTE (-799))))) (-12 (|HasCategory| |#1| (QUOTE (-479))) (|HasCategory| |#2| (QUOTE (-479)))) (-3684 (-12 (|HasCategory| |#1| (QUOTE (-479))) (|HasCategory| |#2| (QUOTE (-479)))) (-12 (|HasCategory| |#1| (QUOTE (-732))) (|HasCategory| |#2| (QUOTE (-732))))) (-12 (|HasCategory| |#1| (QUOTE (-373))) (|HasCategory| |#2| (QUOTE (-373)))) (-3684 (-12 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#2| (QUOTE (-21)))) (-12 (|HasCategory| |#1| (QUOTE (-23))) (|HasCategory| |#2| (QUOTE (-23)))) (-12 (|HasCategory| |#1| (QUOTE (-132))) (|HasCategory| |#2| (QUOTE (-132)))) (-12 (|HasCategory| |#1| (QUOTE (-479))) (|HasCategory| |#2| (QUOTE (-479)))) (-12 (|HasCategory| |#1| (QUOTE (-732))) (|HasCategory| |#2| (QUOTE (-732)))) (-12 (|HasCategory| |#1| (QUOTE (-799))) (|HasCategory| |#2| (QUOTE (-799))))) (-12 (|HasCategory| |#1| (QUOTE (-732))) (|HasCategory| |#2| (QUOTE (-732)))) (-12 (|HasCategory| |#1| (QUOTE (-23))) (|HasCategory| |#2| (QUOTE (-23)))) (-12 (|HasCategory| |#1| (QUOTE (-132))) (|HasCategory| |#2| (QUOTE (-132)))) (-12 (|HasCategory| |#1| (QUOTE (-856))) (|HasCategory| |#2| (QUOTE (-856))))) (-972) ((|constructor| (NIL "\\indented{1}{Author: Gabriel Dos Reis} Date Created: October 24,{} 2007 Date Last Modified: January 18,{} 2008. An `Property' is a pair of name and value.")) (|property| (($ (|Identifier|) (|SExpression|)) "\\spad{property(n,val)} constructs a property with name \\spad{`n'} and value `val'.")) (|value| (((|SExpression|) $) "\\spad{value(p)} returns value of property \\spad{p}")) (|name| (((|Identifier|) $) "\\spad{name(p)} returns the name of property \\spad{p}"))) NIL @@ -3904,7 +3904,7 @@ 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 -(-994 K R UP -1385) +(-994 K R UP -2968) ((|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 @@ -3963,11 +3963,11 @@ NIL (-1008 R) ((|constructor| (NIL "\\spadtype{Quaternion} implements quaternions over a \\indented{2}{commutative ring. The main constructor function is \\spadfun{quatern}} \\indented{2}{which takes 4 arguments: the real part,{} the \\spad{i} imaginary part,{} the \\spad{j}} \\indented{2}{imaginary part and the \\spad{k} imaginary part.}"))) ((-4445 |has| |#1| (-294)) (-4446 . T) (-4447 . T) (-4449 . T)) -((|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-148))) (|HasCategory| |#1| (LIST (QUOTE -620) (QUOTE (-542)))) (|HasCategory| |#1| (QUOTE (-368))) (-2811 (|HasCategory| |#1| (QUOTE (-294))) (|HasCategory| |#1| (QUOTE (-368)))) (|HasCategory| |#1| (QUOTE (-294))) (|HasCategory| |#1| (QUOTE (-856))) (|HasCategory| |#1| (LIST (QUOTE -645) (QUOTE (-570)))) (|HasCategory| |#1| (LIST (QUOTE -520) (QUOTE (-1186)) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -290) (|devaluate| |#1|) (|devaluate| |#1|))) (|HasCategory| |#1| (QUOTE (-235))) (|HasCategory| |#1| (LIST (QUOTE -907) (QUOTE (-1186)))) (-2811 (|HasCategory| |#1| (LIST (QUOTE -1047) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasCategory| |#1| (QUOTE (-368)))) (|HasCategory| |#1| (LIST (QUOTE -1047) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasCategory| |#1| (LIST (QUOTE -1047) (QUOTE (-570)))) (|HasCategory| |#1| (QUOTE (-1069))) (|HasCategory| |#1| (QUOTE (-551)))) +((|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-148))) (|HasCategory| |#1| (LIST (QUOTE -620) (QUOTE (-542)))) (|HasCategory| |#1| (QUOTE (-368))) (-3684 (|HasCategory| |#1| (QUOTE (-294))) (|HasCategory| |#1| (QUOTE (-368)))) (|HasCategory| |#1| (QUOTE (-294))) (|HasCategory| |#1| (QUOTE (-856))) (|HasCategory| |#1| (LIST (QUOTE -645) (QUOTE (-570)))) (|HasCategory| |#1| (LIST (QUOTE -520) (QUOTE (-1186)) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -290) (|devaluate| |#1|) (|devaluate| |#1|))) (|HasCategory| |#1| (QUOTE (-235))) (|HasCategory| |#1| (LIST (QUOTE -907) (QUOTE (-1186)))) (-3684 (|HasCategory| |#1| (LIST (QUOTE -1047) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasCategory| |#1| (QUOTE (-368)))) (|HasCategory| |#1| (LIST (QUOTE -1047) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasCategory| |#1| (LIST (QUOTE -1047) (QUOTE (-570)))) (|HasCategory| |#1| (QUOTE (-1069))) (|HasCategory| |#1| (QUOTE (-551)))) (-1009 S) ((|constructor| (NIL "Linked List implementation of a Queue")) (|queue| (($ (|List| |#1|)) "\\spad{queue([x,y,...,z])} creates a queue with first (top) element \\spad{x},{} second element \\spad{y},{}...,{}and last (bottom) element \\spad{z}."))) ((-4452 . T) (-4453 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1109))) (-2811 (-12 (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-868))))) (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-868))))) +((-12 (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1109))) (-3684 (-12 (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-868))))) (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-868))))) (-1010 S) ((|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| (($ $) "\\spad{sqrt(x)} returns the square root of \\spad{x}."))) NIL @@ -3976,14 +3976,14 @@ NIL ((|constructor| (NIL "The \\spad{RadicalCategory} is a model for the rational numbers.")) (** (($ $ (|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 -(-1012 -1385 UP UPUP |radicnd| |n|) +(-1012 -2968 UP UPUP |radicnd| |n|) ((|constructor| (NIL "Function field defined by y**n = \\spad{f}(\\spad{x})."))) ((-4445 |has| (-413 |#2|) (-368)) (-4450 |has| (-413 |#2|) (-368)) (-4444 |has| (-413 |#2|) (-368)) ((-4454 "*") . T) (-4446 . T) (-4447 . T) (-4449 . T)) -((|HasCategory| (-413 |#2|) (QUOTE (-146))) (|HasCategory| (-413 |#2|) (QUOTE (-148))) (|HasCategory| (-413 |#2|) (QUOTE (-354))) (-2811 (|HasCategory| (-413 |#2|) (QUOTE (-368))) (|HasCategory| (-413 |#2|) (QUOTE (-354)))) (|HasCategory| (-413 |#2|) (QUOTE (-368))) (|HasCategory| (-413 |#2|) (QUOTE (-373))) (-2811 (-12 (|HasCategory| (-413 |#2|) (QUOTE (-235))) (|HasCategory| (-413 |#2|) (QUOTE (-368)))) (|HasCategory| (-413 |#2|) (QUOTE (-354)))) (-2811 (-12 (|HasCategory| (-413 |#2|) (LIST (QUOTE -907) (QUOTE (-1186)))) (|HasCategory| (-413 |#2|) (QUOTE (-368)))) (-12 (|HasCategory| (-413 |#2|) (LIST (QUOTE -907) (QUOTE (-1186)))) (|HasCategory| (-413 |#2|) (QUOTE (-354))))) (|HasCategory| (-413 |#2|) (LIST (QUOTE -645) (QUOTE (-570)))) (-2811 (|HasCategory| (-413 |#2|) (LIST (QUOTE -1047) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasCategory| (-413 |#2|) (QUOTE (-368)))) (|HasCategory| (-413 |#2|) (LIST (QUOTE -1047) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasCategory| (-413 |#2|) (LIST (QUOTE -1047) (QUOTE (-570)))) (|HasCategory| |#1| (QUOTE (-368))) (|HasCategory| |#1| (QUOTE (-373))) (-12 (|HasCategory| (-413 |#2|) (LIST (QUOTE -907) (QUOTE (-1186)))) (|HasCategory| (-413 |#2|) (QUOTE (-368)))) (-12 (|HasCategory| (-413 |#2|) (QUOTE (-235))) (|HasCategory| (-413 |#2|) (QUOTE (-368))))) +((|HasCategory| (-413 |#2|) (QUOTE (-146))) (|HasCategory| (-413 |#2|) (QUOTE (-148))) (|HasCategory| (-413 |#2|) (QUOTE (-354))) (-3684 (|HasCategory| (-413 |#2|) (QUOTE (-368))) (|HasCategory| (-413 |#2|) (QUOTE (-354)))) (|HasCategory| (-413 |#2|) (QUOTE (-368))) (|HasCategory| (-413 |#2|) (QUOTE (-373))) (-3684 (-12 (|HasCategory| (-413 |#2|) (QUOTE (-235))) (|HasCategory| (-413 |#2|) (QUOTE (-368)))) (|HasCategory| (-413 |#2|) (QUOTE (-354)))) (-3684 (-12 (|HasCategory| (-413 |#2|) (LIST (QUOTE -907) (QUOTE (-1186)))) (|HasCategory| (-413 |#2|) (QUOTE (-368)))) (-12 (|HasCategory| (-413 |#2|) (LIST (QUOTE -907) (QUOTE (-1186)))) (|HasCategory| (-413 |#2|) (QUOTE (-354))))) (|HasCategory| (-413 |#2|) (LIST (QUOTE -645) (QUOTE (-570)))) (-3684 (|HasCategory| (-413 |#2|) (LIST (QUOTE -1047) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasCategory| (-413 |#2|) (QUOTE (-368)))) (|HasCategory| (-413 |#2|) (LIST (QUOTE -1047) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasCategory| (-413 |#2|) (LIST (QUOTE -1047) (QUOTE (-570)))) (|HasCategory| |#1| (QUOTE (-368))) (|HasCategory| |#1| (QUOTE (-373))) (-12 (|HasCategory| (-413 |#2|) (LIST (QUOTE -907) (QUOTE (-1186)))) (|HasCategory| (-413 |#2|) (QUOTE (-368)))) (-12 (|HasCategory| (-413 |#2|) (QUOTE (-235))) (|HasCategory| (-413 |#2|) (QUOTE (-368))))) (-1013 |bb|) ((|constructor| (NIL "This domain allows rational numbers to be presented as repeating decimal expansions or more generally as repeating expansions in any base.")) (|fractRadix| (($ (|List| (|Integer|)) (|List| (|Integer|))) "\\spad{fractRadix(pre,cyc)} creates a fractional radix expansion from a list of prefix ragits and a list of cyclic ragits. For example,{} \\spad{fractRadix([1],[6])} will return \\spad{0.16666666...}.")) (|wholeRadix| (($ (|List| (|Integer|))) "\\spad{wholeRadix(l)} creates an integral radix expansion from a list of ragits. For example,{} \\spad{wholeRadix([1,3,4])} will return \\spad{134}.")) (|cycleRagits| (((|List| (|Integer|)) $) "\\spad{cycleRagits(rx)} returns the cyclic part of the ragits of the fractional part of a radix expansion. For example,{} if \\spad{x = 3/28 = 0.10 714285 714285 ...},{} then \\spad{cycleRagits(x) = [7,1,4,2,8,5]}.")) (|prefixRagits| (((|List| (|Integer|)) $) "\\spad{prefixRagits(rx)} returns the non-cyclic part of the ragits of the fractional part of a radix expansion. For example,{} if \\spad{x = 3/28 = 0.10 714285 714285 ...},{} then \\spad{prefixRagits(x)=[1,0]}.")) (|fractRagits| (((|Stream| (|Integer|)) $) "\\spad{fractRagits(rx)} returns the ragits of the fractional part of a radix expansion.")) (|wholeRagits| (((|List| (|Integer|)) $) "\\spad{wholeRagits(rx)} returns the ragits of the integer part of a radix expansion.")) (|fractionPart| (((|Fraction| (|Integer|)) $) "\\spad{fractionPart(rx)} returns the fractional part of a radix expansion."))) ((-4444 . T) (-4450 . T) (-4445 . T) ((-4454 "*") . T) (-4446 . T) (-4447 . T) (-4449 . T)) -((|HasCategory| (-570) (QUOTE (-916))) (|HasCategory| (-570) (LIST (QUOTE -1047) (QUOTE (-1186)))) (|HasCategory| (-570) (QUOTE (-146))) (|HasCategory| (-570) (QUOTE (-148))) (|HasCategory| (-570) (LIST (QUOTE -620) (QUOTE (-542)))) (|HasCategory| (-570) (QUOTE (-1031))) (|HasCategory| (-570) (QUOTE (-826))) (-2811 (|HasCategory| (-570) (QUOTE (-826))) (|HasCategory| (-570) (QUOTE (-856)))) (|HasCategory| (-570) (LIST (QUOTE -1047) (QUOTE (-570)))) (|HasCategory| (-570) (QUOTE (-1161))) (|HasCategory| (-570) (LIST (QUOTE -893) (QUOTE (-384)))) (|HasCategory| (-570) (LIST (QUOTE -893) (QUOTE (-570)))) (|HasCategory| (-570) (LIST (QUOTE -620) (LIST (QUOTE -899) (QUOTE (-384))))) (|HasCategory| (-570) (LIST (QUOTE -620) (LIST (QUOTE -899) (QUOTE (-570))))) (|HasCategory| (-570) (QUOTE (-235))) (|HasCategory| (-570) (LIST (QUOTE -907) (QUOTE (-1186)))) (|HasCategory| (-570) (LIST (QUOTE -520) (QUOTE (-1186)) (QUOTE (-570)))) (|HasCategory| (-570) (LIST (QUOTE -313) (QUOTE (-570)))) (|HasCategory| (-570) (LIST (QUOTE -290) (QUOTE (-570)) (QUOTE (-570)))) (|HasCategory| (-570) (QUOTE (-311))) (|HasCategory| (-570) (QUOTE (-551))) (|HasCategory| (-570) (QUOTE (-856))) (|HasCategory| (-570) (LIST (QUOTE -645) (QUOTE (-570)))) (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| (-570) (QUOTE (-916)))) (-2811 (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| (-570) (QUOTE (-916)))) (|HasCategory| (-570) (QUOTE (-146))))) +((|HasCategory| (-570) (QUOTE (-916))) (|HasCategory| (-570) (LIST (QUOTE -1047) (QUOTE (-1186)))) (|HasCategory| (-570) (QUOTE (-146))) (|HasCategory| (-570) (QUOTE (-148))) (|HasCategory| (-570) (LIST (QUOTE -620) (QUOTE (-542)))) (|HasCategory| (-570) (QUOTE (-1031))) (|HasCategory| (-570) (QUOTE (-826))) (-3684 (|HasCategory| (-570) (QUOTE (-826))) (|HasCategory| (-570) (QUOTE (-856)))) (|HasCategory| (-570) (LIST (QUOTE -1047) (QUOTE (-570)))) (|HasCategory| (-570) (QUOTE (-1161))) (|HasCategory| (-570) (LIST (QUOTE -893) (QUOTE (-384)))) (|HasCategory| (-570) (LIST (QUOTE -893) (QUOTE (-570)))) (|HasCategory| (-570) (LIST (QUOTE -620) (LIST (QUOTE -899) (QUOTE (-384))))) (|HasCategory| (-570) (LIST (QUOTE -620) (LIST (QUOTE -899) (QUOTE (-570))))) (|HasCategory| (-570) (QUOTE (-235))) (|HasCategory| (-570) (LIST (QUOTE -907) (QUOTE (-1186)))) (|HasCategory| (-570) (LIST (QUOTE -520) (QUOTE (-1186)) (QUOTE (-570)))) (|HasCategory| (-570) (LIST (QUOTE -313) (QUOTE (-570)))) (|HasCategory| (-570) (LIST (QUOTE -290) (QUOTE (-570)) (QUOTE (-570)))) (|HasCategory| (-570) (QUOTE (-311))) (|HasCategory| (-570) (QUOTE (-551))) (|HasCategory| (-570) (QUOTE (-856))) (|HasCategory| (-570) (LIST (QUOTE -645) (QUOTE (-570)))) (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| (-570) (QUOTE (-916)))) (-3684 (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| (-570) (QUOTE (-916)))) (|HasCategory| (-570) (QUOTE (-146))))) (-1014) ((|constructor| (NIL "This package provides tools for creating radix expansions.")) (|radix| (((|Any|) (|Fraction| (|Integer|)) (|Integer|)) "\\spad{radix(x,b)} converts \\spad{x} to a radix expansion in base \\spad{b}."))) NIL @@ -4016,19 +4016,19 @@ 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} \\spad{**} (1/2)}") (($ (|Fraction| (|Integer|))) "\\axiom{sqrt(\\spad{x})} is \\axiom{\\spad{x} \\spad{**} (1/2)}") (($ $) "\\axiom{sqrt(\\spad{x})} is \\axiom{\\spad{x} \\spad{**} (1/2)}") (($ $ (|PositiveInteger|)) "\\axiom{sqrt(\\spad{x},{}\\spad{n})} is \\axiom{\\spad{x} \\spad{**} (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}}"))) ((-4445 . T) (-4450 . T) (-4444 . T) (-4447 . T) (-4446 . T) ((-4454 "*") . T) (-4449 . T)) NIL -(-1022 R -1385) +(-1022 R -2968) ((|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 -(-1023 R -1385) +(-1023 R -2968) ((|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 -(-1024 -1385 UP) +(-1024 -2968 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 -(-1025 -1385 UP) +(-1025 -2968 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 @@ -4063,8 +4063,8 @@ NIL (-1033 |TheField|) ((|constructor| (NIL "This domain implements the real closure of an ordered field.")) (|relativeApprox| (((|Fraction| (|Integer|)) $ $) "\\axiom{relativeApprox(\\spad{n},{}\\spad{p})} gives a relative approximation of \\axiom{\\spad{n}} that has precision \\axiom{\\spad{p}}")) (|mainCharacterization| (((|Union| (|RightOpenIntervalRootCharacterization| $ (|SparseUnivariatePolynomial| $)) "failed") $) "\\axiom{mainCharacterization(\\spad{x})} is the main algebraic quantity of \\axiom{\\spad{x}} (\\axiom{SEG})")) (|algebraicOf| (($ (|RightOpenIntervalRootCharacterization| $ (|SparseUnivariatePolynomial| $)) (|OutputForm|)) "\\axiom{algebraicOf(char)} is the external number"))) ((-4445 . T) (-4450 . T) (-4444 . T) (-4447 . T) (-4446 . T) ((-4454 "*") . T) (-4449 . T)) -((-2811 (|HasCategory| (-413 (-570)) (LIST (QUOTE -1047) (QUOTE (-570)))) (|HasCategory| |#1| (LIST (QUOTE -1047) (QUOTE (-570))))) (|HasCategory| |#1| (LIST (QUOTE -1047) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasCategory| |#1| (LIST (QUOTE -1047) (QUOTE (-570)))) (|HasCategory| (-413 (-570)) (LIST (QUOTE -1047) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasCategory| (-413 (-570)) (LIST (QUOTE -1047) (QUOTE (-570))))) -(-1034 -1385 L) +((-3684 (|HasCategory| (-413 (-570)) (LIST (QUOTE -1047) (QUOTE (-570)))) (|HasCategory| |#1| (LIST (QUOTE -1047) (QUOTE (-570))))) (|HasCategory| |#1| (LIST (QUOTE -1047) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasCategory| |#1| (LIST (QUOTE -1047) (QUOTE (-570)))) (|HasCategory| (-413 (-570)) (LIST (QUOTE -1047) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasCategory| (-413 (-570)) (LIST (QUOTE -1047) (QUOTE (-570))))) +(-1034 -2968 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 @@ -4100,14 +4100,14 @@ 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 -(-1043 -1385 |Expon| |VarSet| |FPol| |LFPol|) +(-1043 -2968 |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"))) (((-4454 "*") . T) (-4446 . T) (-4447 . T) (-4449 . T)) NIL (-1044) ((|constructor| (NIL "A domain used to return the results from a call to the NAG Library. It prints as a list of names and types,{} though the user may choose to display values automatically if he or she wishes.")) (|showArrayValues| (((|Boolean|) (|Boolean|)) "\\spad{showArrayValues(true)} forces the values of array components to be \\indented{1}{displayed rather than just their types.}")) (|showScalarValues| (((|Boolean|) (|Boolean|)) "\\spad{showScalarValues(true)} forces the values of scalar components to be \\indented{1}{displayed rather than just their types.}"))) ((-4452 . T) (-4453 . T)) -((-12 (|HasCategory| (-2 (|:| -3679 (-1186)) (|:| -1409 (-52))) (QUOTE (-1109))) (|HasCategory| (-2 (|:| -3679 (-1186)) (|:| -1409 (-52))) (LIST (QUOTE -313) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -3679) (QUOTE (-1186))) (LIST (QUOTE |:|) (QUOTE -1409) (QUOTE (-52))))))) (-2811 (|HasCategory| (-2 (|:| -3679 (-1186)) (|:| -1409 (-52))) (QUOTE (-1109))) (|HasCategory| (-52) (QUOTE (-1109)))) (-2811 (|HasCategory| (-2 (|:| -3679 (-1186)) (|:| -1409 (-52))) (QUOTE (-1109))) (|HasCategory| (-2 (|:| -3679 (-1186)) (|:| -1409 (-52))) (LIST (QUOTE -619) (QUOTE (-868)))) (|HasCategory| (-52) (QUOTE (-1109))) (|HasCategory| (-52) (LIST (QUOTE -619) (QUOTE (-868))))) (|HasCategory| (-2 (|:| -3679 (-1186)) (|:| -1409 (-52))) (LIST (QUOTE -620) (QUOTE (-542)))) (-12 (|HasCategory| (-52) (QUOTE (-1109))) (|HasCategory| (-52) (LIST (QUOTE -313) (QUOTE (-52))))) (|HasCategory| (-2 (|:| -3679 (-1186)) (|:| -1409 (-52))) (QUOTE (-1109))) (|HasCategory| (-1186) (QUOTE (-856))) (|HasCategory| (-52) (QUOTE (-1109))) (-2811 (|HasCategory| (-2 (|:| -3679 (-1186)) (|:| -1409 (-52))) (LIST (QUOTE -619) (QUOTE (-868)))) (|HasCategory| (-52) (LIST (QUOTE -619) (QUOTE (-868))))) (|HasCategory| (-52) (LIST (QUOTE -619) (QUOTE (-868)))) (|HasCategory| (-2 (|:| -3679 (-1186)) (|:| -1409 (-52))) (LIST (QUOTE -619) (QUOTE (-868))))) +((-12 (|HasCategory| (-2 (|:| -4111 (-1186)) (|:| -3117 (-52))) (QUOTE (-1109))) (|HasCategory| (-2 (|:| -4111 (-1186)) (|:| -3117 (-52))) (LIST (QUOTE -313) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -4111) (QUOTE (-1186))) (LIST (QUOTE |:|) (QUOTE -3117) (QUOTE (-52))))))) (-3684 (|HasCategory| (-2 (|:| -4111 (-1186)) (|:| -3117 (-52))) (QUOTE (-1109))) (|HasCategory| (-52) (QUOTE (-1109)))) (-3684 (|HasCategory| (-2 (|:| -4111 (-1186)) (|:| -3117 (-52))) (QUOTE (-1109))) (|HasCategory| (-2 (|:| -4111 (-1186)) (|:| -3117 (-52))) (LIST (QUOTE -619) (QUOTE (-868)))) (|HasCategory| (-52) (QUOTE (-1109))) (|HasCategory| (-52) (LIST (QUOTE -619) (QUOTE (-868))))) (|HasCategory| (-2 (|:| -4111 (-1186)) (|:| -3117 (-52))) (LIST (QUOTE -620) (QUOTE (-542)))) (-12 (|HasCategory| (-52) (QUOTE (-1109))) (|HasCategory| (-52) (LIST (QUOTE -313) (QUOTE (-52))))) (|HasCategory| (-2 (|:| -4111 (-1186)) (|:| -3117 (-52))) (QUOTE (-1109))) (|HasCategory| (-1186) (QUOTE (-856))) (|HasCategory| (-52) (QUOTE (-1109))) (-3684 (|HasCategory| (-2 (|:| -4111 (-1186)) (|:| -3117 (-52))) (LIST (QUOTE -619) (QUOTE (-868)))) (|HasCategory| (-52) (LIST (QUOTE -619) (QUOTE (-868))))) (|HasCategory| (-52) (LIST (QUOTE -619) (QUOTE (-868)))) (|HasCategory| (-2 (|:| -4111 (-1186)) (|:| -3117 (-52))) (LIST (QUOTE -619) (QUOTE (-868))))) (-1045) ((|constructor| (NIL "This domain represents `return' expressions.")) (|expression| (((|SpadAst|) $) "\\spad{expression(e)} returns the expression returned by `e'."))) NIL @@ -4164,7 +4164,7 @@ NIL ((|constructor| (NIL "The category of rings with unity,{} always associative,{} but not necessarily commutative.")) (|unitsKnown| ((|attribute|) "recip truly yields reciprocal or \"failed\" if not a unit. Note: \\spad{recip(0) = \"failed\"}.")) (|characteristic| (((|NonNegativeInteger|)) "\\spad{characteristic()} returns the characteristic of the ring this is the smallest positive integer \\spad{n} such that \\spad{n*x=0} for all \\spad{x} in the ring,{} or zero if no such \\spad{n} exists."))) ((-4449 . T)) NIL -(-1059 |xx| -1385) +(-1059 |xx| -2968) ((|constructor| (NIL "This package exports rational interpolation algorithms"))) NIL NIL @@ -4183,7 +4183,7 @@ NIL (-1063 |m| |n| R) ((|constructor| (NIL "\\spadtype{RectangularMatrix} is a matrix domain where the number of rows and the number of columns are parameters of the domain.")) (|rectangularMatrix| (($ (|Matrix| |#3|)) "\\spad{rectangularMatrix(m)} converts a matrix of type \\spadtype{Matrix} to a matrix of type \\spad{RectangularMatrix}."))) ((-4452 . T) (-4447 . T) (-4446 . T)) -((|HasCategory| |#3| (QUOTE (-174))) (-2811 (-12 (|HasCategory| |#3| (QUOTE (-174))) (|HasCategory| |#3| (LIST (QUOTE -313) (|devaluate| |#3|)))) (-12 (|HasCategory| |#3| (QUOTE (-368))) (|HasCategory| |#3| (LIST (QUOTE -313) (|devaluate| |#3|)))) (-12 (|HasCategory| |#3| (QUOTE (-1109))) (|HasCategory| |#3| (LIST (QUOTE -313) (|devaluate| |#3|))))) (|HasCategory| |#3| (LIST (QUOTE -620) (QUOTE (-542)))) (-2811 (|HasCategory| |#3| (QUOTE (-174))) (|HasCategory| |#3| (QUOTE (-368)))) (|HasCategory| |#3| (QUOTE (-368))) (|HasCategory| |#3| (QUOTE (-1109))) (|HasCategory| |#3| (QUOTE (-311))) (|HasCategory| |#3| (QUOTE (-562))) (-12 (|HasCategory| |#3| (QUOTE (-1109))) (|HasCategory| |#3| (LIST (QUOTE -313) (|devaluate| |#3|)))) (|HasCategory| |#3| (LIST (QUOTE -619) (QUOTE (-868))))) +((|HasCategory| |#3| (QUOTE (-174))) (-3684 (-12 (|HasCategory| |#3| (QUOTE (-174))) (|HasCategory| |#3| (LIST (QUOTE -313) (|devaluate| |#3|)))) (-12 (|HasCategory| |#3| (QUOTE (-368))) (|HasCategory| |#3| (LIST (QUOTE -313) (|devaluate| |#3|)))) (-12 (|HasCategory| |#3| (QUOTE (-1109))) (|HasCategory| |#3| (LIST (QUOTE -313) (|devaluate| |#3|))))) (|HasCategory| |#3| (LIST (QUOTE -620) (QUOTE (-542)))) (-3684 (|HasCategory| |#3| (QUOTE (-174))) (|HasCategory| |#3| (QUOTE (-368)))) (|HasCategory| |#3| (QUOTE (-368))) (|HasCategory| |#3| (QUOTE (-1109))) (|HasCategory| |#3| (QUOTE (-311))) (|HasCategory| |#3| (QUOTE (-562))) (-12 (|HasCategory| |#3| (QUOTE (-1109))) (|HasCategory| |#3| (LIST (QUOTE -313) (|devaluate| |#3|)))) (|HasCategory| |#3| (LIST (QUOTE -619) (QUOTE (-868))))) (-1064 |m| |n| R1 |Row1| |Col1| M1 R2 |Row2| |Col2| M2) ((|constructor| (NIL "\\spadtype{RectangularMatrixCategoryFunctions2} provides functions between two matrix domains. The functions provided are \\spadfun{map} and \\spadfun{reduce}.")) (|reduce| ((|#7| (|Mapping| |#7| |#3| |#7|) |#6| |#7|) "\\spad{reduce(f,m,r)} returns a matrix \\spad{n} where \\spad{n[i,j] = f(m[i,j],r)} for all indices spad{\\spad{i}} and \\spad{j}.")) (|map| ((|#10| (|Mapping| |#7| |#3|) |#6|) "\\spad{map(f,m)} applies the function \\spad{f} to the elements of the matrix \\spad{m}."))) NIL @@ -4219,7 +4219,7 @@ NIL (-1072) ((|constructor| (NIL "\\axiomType{RoutinesTable} implements a database and associated tuning mechanisms for a set of known NAG routines")) (|recoverAfterFail| (((|Union| (|String|) "failed") $ (|String|) (|Integer|)) "\\spad{recoverAfterFail(routs,routineName,ifailValue)} acts on the instructions given by the ifail list")) (|showTheRoutinesTable| (($) "\\spad{showTheRoutinesTable()} returns the current table of NAG routines.")) (|deleteRoutine!| (($ $ (|Symbol|)) "\\spad{deleteRoutine!(R,s)} destructively deletes the given routine from the current database of NAG routines")) (|getExplanations| (((|List| (|String|)) $ (|String|)) "\\spad{getExplanations(R,s)} gets the explanations of the output parameters for the given NAG routine.")) (|getMeasure| (((|Float|) $ (|Symbol|)) "\\spad{getMeasure(R,s)} gets the current value of the maximum measure for the given NAG routine.")) (|changeMeasure| (($ $ (|Symbol|) (|Float|)) "\\spad{changeMeasure(R,s,newValue)} changes the maximum value for a measure of the given NAG routine.")) (|changeThreshhold| (($ $ (|Symbol|) (|Float|)) "\\spad{changeThreshhold(R,s,newValue)} changes the value below which,{} given a NAG routine generating a higher measure,{} the routines will make no attempt to generate a measure.")) (|selectMultiDimensionalRoutines| (($ $) "\\spad{selectMultiDimensionalRoutines(R)} chooses only those routines from the database which are designed for use with multi-dimensional expressions")) (|selectNonFiniteRoutines| (($ $) "\\spad{selectNonFiniteRoutines(R)} chooses only those routines from the database which are designed for use with non-finite expressions.")) (|selectSumOfSquaresRoutines| (($ $) "\\spad{selectSumOfSquaresRoutines(R)} chooses only those routines from the database which are designed for use with sums of squares")) (|selectFiniteRoutines| (($ $) "\\spad{selectFiniteRoutines(R)} chooses only those routines from the database which are designed for use with finite expressions")) (|selectODEIVPRoutines| (($ $) "\\spad{selectODEIVPRoutines(R)} chooses only those routines from the database which are for the solution of ODE\\spad{'s}")) (|selectPDERoutines| (($ $) "\\spad{selectPDERoutines(R)} chooses only those routines from the database which are for the solution of PDE\\spad{'s}")) (|selectOptimizationRoutines| (($ $) "\\spad{selectOptimizationRoutines(R)} chooses only those routines from the database which are for integration")) (|selectIntegrationRoutines| (($ $) "\\spad{selectIntegrationRoutines(R)} chooses only those routines from the database which are for integration")) (|routines| (($) "\\spad{routines()} initialises a database of known NAG routines")) (|concat| (($ $ $) "\\spad{concat(x,y)} merges two tables \\spad{x} and \\spad{y}"))) ((-4452 . T) (-4453 . T)) -((-12 (|HasCategory| (-2 (|:| -3679 (-1186)) (|:| -1409 (-52))) (QUOTE (-1109))) (|HasCategory| (-2 (|:| -3679 (-1186)) (|:| -1409 (-52))) (LIST (QUOTE -313) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -3679) (QUOTE (-1186))) (LIST (QUOTE |:|) (QUOTE -1409) (QUOTE (-52))))))) (-2811 (|HasCategory| (-2 (|:| -3679 (-1186)) (|:| -1409 (-52))) (QUOTE (-1109))) (|HasCategory| (-52) (QUOTE (-1109)))) (-2811 (|HasCategory| (-2 (|:| -3679 (-1186)) (|:| -1409 (-52))) (QUOTE (-1109))) (|HasCategory| (-2 (|:| -3679 (-1186)) (|:| -1409 (-52))) (LIST (QUOTE -619) (QUOTE (-868)))) (|HasCategory| (-52) (QUOTE (-1109))) (|HasCategory| (-52) (LIST (QUOTE -619) (QUOTE (-868))))) (|HasCategory| (-2 (|:| -3679 (-1186)) (|:| -1409 (-52))) (LIST (QUOTE -620) (QUOTE (-542)))) (-12 (|HasCategory| (-52) (QUOTE (-1109))) (|HasCategory| (-52) (LIST (QUOTE -313) (QUOTE (-52))))) (|HasCategory| (-2 (|:| -3679 (-1186)) (|:| -1409 (-52))) (QUOTE (-1109))) (|HasCategory| (-1186) (QUOTE (-856))) (|HasCategory| (-52) (QUOTE (-1109))) (-2811 (|HasCategory| (-2 (|:| -3679 (-1186)) (|:| -1409 (-52))) (LIST (QUOTE -619) (QUOTE (-868)))) (|HasCategory| (-52) (LIST (QUOTE -619) (QUOTE (-868))))) (|HasCategory| (-52) (LIST (QUOTE -619) (QUOTE (-868)))) (|HasCategory| (-2 (|:| -3679 (-1186)) (|:| -1409 (-52))) (LIST (QUOTE -619) (QUOTE (-868))))) +((-12 (|HasCategory| (-2 (|:| -4111 (-1186)) (|:| -3117 (-52))) (QUOTE (-1109))) (|HasCategory| (-2 (|:| -4111 (-1186)) (|:| -3117 (-52))) (LIST (QUOTE -313) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -4111) (QUOTE (-1186))) (LIST (QUOTE |:|) (QUOTE -3117) (QUOTE (-52))))))) (-3684 (|HasCategory| (-2 (|:| -4111 (-1186)) (|:| -3117 (-52))) (QUOTE (-1109))) (|HasCategory| (-52) (QUOTE (-1109)))) (-3684 (|HasCategory| (-2 (|:| -4111 (-1186)) (|:| -3117 (-52))) (QUOTE (-1109))) (|HasCategory| (-2 (|:| -4111 (-1186)) (|:| -3117 (-52))) (LIST (QUOTE -619) (QUOTE (-868)))) (|HasCategory| (-52) (QUOTE (-1109))) (|HasCategory| (-52) (LIST (QUOTE -619) (QUOTE (-868))))) (|HasCategory| (-2 (|:| -4111 (-1186)) (|:| -3117 (-52))) (LIST (QUOTE -620) (QUOTE (-542)))) (-12 (|HasCategory| (-52) (QUOTE (-1109))) (|HasCategory| (-52) (LIST (QUOTE -313) (QUOTE (-52))))) (|HasCategory| (-2 (|:| -4111 (-1186)) (|:| -3117 (-52))) (QUOTE (-1109))) (|HasCategory| (-1186) (QUOTE (-856))) (|HasCategory| (-52) (QUOTE (-1109))) (-3684 (|HasCategory| (-2 (|:| -4111 (-1186)) (|:| -3117 (-52))) (LIST (QUOTE -619) (QUOTE (-868)))) (|HasCategory| (-52) (LIST (QUOTE -619) (QUOTE (-868))))) (|HasCategory| (-52) (LIST (QUOTE -619) (QUOTE (-868)))) (|HasCategory| (-2 (|:| -4111 (-1186)) (|:| -3117 (-52))) (LIST (QUOTE -619) (QUOTE (-868))))) (-1073 S R E V) ((|constructor| (NIL "A category for general multi-variate polynomials with coefficients in a ring,{} variables in an ordered set,{} and exponents from an ordered abelian monoid,{} with a \\axiomOp{sup} operation. When not constant,{} such a polynomial is viewed as a univariate polynomial in its main variable \\spad{w}. \\spad{r}. \\spad{t}. to the total ordering on the elements in the ordered set,{} so that some operations usually defined for univariate polynomials make sense here.")) (|mainSquareFreePart| (($ $) "\\axiom{mainSquareFreePart(\\spad{p})} returns the square free part of \\axiom{\\spad{p}} viewed as a univariate polynomial in its main variable and with coefficients in the polynomial ring generated by its other variables over \\axiom{\\spad{R}}.")) (|mainPrimitivePart| (($ $) "\\axiom{mainPrimitivePart(\\spad{p})} returns the primitive part of \\axiom{\\spad{p}} viewed as a univariate polynomial in its main variable and with coefficients in the polynomial ring generated by its other variables over \\axiom{\\spad{R}}.")) (|mainContent| (($ $) "\\axiom{mainContent(\\spad{p})} returns the content of \\axiom{\\spad{p}} viewed as a univariate polynomial in its main variable and with coefficients in the polynomial ring generated by its other variables over \\axiom{\\spad{R}}.")) (|primitivePart!| (($ $) "\\axiom{primitivePart!(\\spad{p})} replaces \\axiom{\\spad{p}} by its primitive part.")) (|gcd| ((|#2| |#2| $) "\\axiom{\\spad{gcd}(\\spad{r},{}\\spad{p})} returns the \\spad{gcd} of \\axiom{\\spad{r}} and the content of \\axiom{\\spad{p}}.")) (|nextsubResultant2| (($ $ $ $ $) "\\axiom{nextsubResultant2(\\spad{p},{}\\spad{q},{}\\spad{z},{}\\spad{s})} is the multivariate version of the operation \\axiomOpFrom{next_sousResultant2}{PseudoRemainderSequence} from the \\axiomType{PseudoRemainderSequence} constructor.")) (|LazardQuotient2| (($ $ $ $ (|NonNegativeInteger|)) "\\axiom{LazardQuotient2(\\spad{p},{}a,{}\\spad{b},{}\\spad{n})} returns \\axiom{(a**(\\spad{n}-1) * \\spad{p}) exquo \\spad{b**}(\\spad{n}-1)} assuming that this quotient does not fail.")) (|LazardQuotient| (($ $ $ (|NonNegativeInteger|)) "\\axiom{LazardQuotient(a,{}\\spad{b},{}\\spad{n})} returns \\axiom{a**n exquo \\spad{b**}(\\spad{n}-1)} assuming that this quotient does not fail.")) (|lastSubResultant| (($ $ $) "\\axiom{lastSubResultant(a,{}\\spad{b})} returns the last non-zero subresultant of \\axiom{a} and \\axiom{\\spad{b}} where \\axiom{a} and \\axiom{\\spad{b}} are assumed to have the same main variable \\axiom{\\spad{v}} and are viewed as univariate polynomials in \\axiom{\\spad{v}}.")) (|subResultantChain| (((|List| $) $ $) "\\axiom{subResultantChain(a,{}\\spad{b})},{} where \\axiom{a} and \\axiom{\\spad{b}} are not contant polynomials with the same main variable,{} returns the subresultant chain of \\axiom{a} and \\axiom{\\spad{b}}.")) (|resultant| (($ $ $) "\\axiom{resultant(a,{}\\spad{b})} computes the resultant of \\axiom{a} and \\axiom{\\spad{b}} where \\axiom{a} and \\axiom{\\spad{b}} are assumed to have the same main variable \\axiom{\\spad{v}} and are viewed as univariate polynomials in \\axiom{\\spad{v}}.")) (|halfExtendedSubResultantGcd2| (((|Record| (|:| |gcd| $) (|:| |coef2| $)) $ $) "\\axiom{halfExtendedSubResultantGcd2(a,{}\\spad{b})} returns \\axiom{[\\spad{g},{}\\spad{cb}]} if \\axiom{extendedSubResultantGcd(a,{}\\spad{b})} returns \\axiom{[\\spad{g},{}ca,{}\\spad{cb}]} otherwise produces an error.")) (|halfExtendedSubResultantGcd1| (((|Record| (|:| |gcd| $) (|:| |coef1| $)) $ $) "\\axiom{halfExtendedSubResultantGcd1(a,{}\\spad{b})} returns \\axiom{[\\spad{g},{}ca]} if \\axiom{extendedSubResultantGcd(a,{}\\spad{b})} returns \\axiom{[\\spad{g},{}ca,{}\\spad{cb}]} otherwise produces an error.")) (|extendedSubResultantGcd| (((|Record| (|:| |gcd| $) (|:| |coef1| $) (|:| |coef2| $)) $ $) "\\axiom{extendedSubResultantGcd(a,{}\\spad{b})} returns \\axiom{[ca,{}\\spad{cb},{}\\spad{r}]} such that \\axiom{\\spad{r}} is \\axiom{subResultantGcd(a,{}\\spad{b})} and we have \\axiom{ca * a + \\spad{cb} * \\spad{cb} = \\spad{r}} .")) (|subResultantGcd| (($ $ $) "\\axiom{subResultantGcd(a,{}\\spad{b})} computes a \\spad{gcd} of \\axiom{a} and \\axiom{\\spad{b}} where \\axiom{a} and \\axiom{\\spad{b}} are assumed to have the same main variable \\axiom{\\spad{v}} and are viewed as univariate polynomials in \\axiom{\\spad{v}} with coefficients in the fraction field of the polynomial ring generated by their other variables over \\axiom{\\spad{R}}.")) (|exactQuotient!| (($ $ $) "\\axiom{exactQuotient!(a,{}\\spad{b})} replaces \\axiom{a} by \\axiom{exactQuotient(a,{}\\spad{b})}") (($ $ |#2|) "\\axiom{exactQuotient!(\\spad{p},{}\\spad{r})} replaces \\axiom{\\spad{p}} by \\axiom{exactQuotient(\\spad{p},{}\\spad{r})}.")) (|exactQuotient| (($ $ $) "\\axiom{exactQuotient(a,{}\\spad{b})} computes the exact quotient of \\axiom{a} by \\axiom{\\spad{b}},{} which is assumed to be a divisor of \\axiom{a}. No error is returned if this exact quotient fails!") (($ $ |#2|) "\\axiom{exactQuotient(\\spad{p},{}\\spad{r})} computes the exact quotient of \\axiom{\\spad{p}} by \\axiom{\\spad{r}},{} which is assumed to be a divisor of \\axiom{\\spad{p}}. No error is returned if this exact quotient fails!")) (|primPartElseUnitCanonical!| (($ $) "\\axiom{primPartElseUnitCanonical!(\\spad{p})} replaces \\axiom{\\spad{p}} by \\axiom{primPartElseUnitCanonical(\\spad{p})}.")) (|primPartElseUnitCanonical| (($ $) "\\axiom{primPartElseUnitCanonical(\\spad{p})} returns \\axiom{primitivePart(\\spad{p})} if \\axiom{\\spad{R}} is a \\spad{gcd}-domain,{} otherwise \\axiom{unitCanonical(\\spad{p})}.")) (|convert| (($ (|Polynomial| |#2|)) "\\axiom{convert(\\spad{p})} returns \\axiom{\\spad{p}} as an element of the current domain if all its variables belong to \\axiom{\\spad{V}},{} otherwise an error is produced.") (($ (|Polynomial| (|Integer|))) "\\axiom{convert(\\spad{p})} returns the same as \\axiom{retract(\\spad{p})}.") (($ (|Polynomial| (|Integer|))) "\\axiom{convert(\\spad{p})} returns the same as \\axiom{retract(\\spad{p})}") (($ (|Polynomial| (|Fraction| (|Integer|)))) "\\axiom{convert(\\spad{p})} returns the same as \\axiom{retract(\\spad{p})}.")) (|retract| (($ (|Polynomial| |#2|)) "\\axiom{retract(\\spad{p})} returns \\axiom{\\spad{p}} as an element of the current domain if \\axiom{retractIfCan(\\spad{p})} does not return \"failed\",{} otherwise an error is produced.") (($ (|Polynomial| |#2|)) "\\axiom{retract(\\spad{p})} returns \\axiom{\\spad{p}} as an element of the current domain if \\axiom{retractIfCan(\\spad{p})} does not return \"failed\",{} otherwise an error is produced.") (($ (|Polynomial| (|Integer|))) "\\axiom{retract(\\spad{p})} returns \\axiom{\\spad{p}} as an element of the current domain if \\axiom{retractIfCan(\\spad{p})} does not return \"failed\",{} otherwise an error is produced.") (($ (|Polynomial| |#2|)) "\\axiom{retract(\\spad{p})} returns \\axiom{\\spad{p}} as an element of the current domain if \\axiom{retractIfCan(\\spad{p})} does not return \"failed\",{} otherwise an error is produced.") (($ (|Polynomial| (|Integer|))) "\\axiom{retract(\\spad{p})} returns \\axiom{\\spad{p}} as an element of the current domain if \\axiom{retractIfCan(\\spad{p})} does not return \"failed\",{} otherwise an error is produced.") (($ (|Polynomial| (|Fraction| (|Integer|)))) "\\axiom{retract(\\spad{p})} returns \\axiom{\\spad{p}} as an element of the current domain if \\axiom{retractIfCan(\\spad{p})} does not return \"failed\",{} otherwise an error is produced.")) (|retractIfCan| (((|Union| $ "failed") (|Polynomial| |#2|)) "\\axiom{retractIfCan(\\spad{p})} returns \\axiom{\\spad{p}} as an element of the current domain if all its variables belong to \\axiom{\\spad{V}}.") (((|Union| $ "failed") (|Polynomial| |#2|)) "\\axiom{retractIfCan(\\spad{p})} returns \\axiom{\\spad{p}} as an element of the current domain if all its variables belong to \\axiom{\\spad{V}}.") (((|Union| $ "failed") (|Polynomial| (|Integer|))) "\\axiom{retractIfCan(\\spad{p})} returns \\axiom{\\spad{p}} as an element of the current domain if all its variables belong to \\axiom{\\spad{V}}.") (((|Union| $ "failed") (|Polynomial| |#2|)) "\\axiom{retractIfCan(\\spad{p})} returns \\axiom{\\spad{p}} as an element of the current domain if all its variables belong to \\axiom{\\spad{V}}.") (((|Union| $ "failed") (|Polynomial| (|Integer|))) "\\axiom{retractIfCan(\\spad{p})} returns \\axiom{\\spad{p}} as an element of the current domain if all its variables belong to \\axiom{\\spad{V}}.") (((|Union| $ "failed") (|Polynomial| (|Fraction| (|Integer|)))) "\\axiom{retractIfCan(\\spad{p})} returns \\axiom{\\spad{p}} as an element of the current domain if all its variables belong to \\axiom{\\spad{V}}.")) (|initiallyReduce| (($ $ $) "\\axiom{initiallyReduce(a,{}\\spad{b})} returns a polynomial \\axiom{\\spad{r}} such that \\axiom{initiallyReduced?(\\spad{r},{}\\spad{b})} holds and there exists an integer \\axiom{\\spad{e}} such that \\axiom{init(\\spad{b})^e a - \\spad{r}} is zero modulo \\axiom{\\spad{b}}.")) (|headReduce| (($ $ $) "\\axiom{headReduce(a,{}\\spad{b})} returns a polynomial \\axiom{\\spad{r}} such that \\axiom{headReduced?(\\spad{r},{}\\spad{b})} holds and there exists an integer \\axiom{\\spad{e}} such that \\axiom{init(\\spad{b})^e a - \\spad{r}} is zero modulo \\axiom{\\spad{b}}.")) (|lazyResidueClass| (((|Record| (|:| |polnum| $) (|:| |polden| $) (|:| |power| (|NonNegativeInteger|))) $ $) "\\axiom{lazyResidueClass(a,{}\\spad{b})} returns \\axiom{[\\spad{p},{}\\spad{q},{}\\spad{n}]} where \\axiom{\\spad{p} / q**n} represents the residue class of \\axiom{a} modulo \\axiom{\\spad{b}} and \\axiom{\\spad{p}} is reduced \\spad{w}.\\spad{r}.\\spad{t}. \\axiom{\\spad{b}} and \\axiom{\\spad{q}} is \\axiom{init(\\spad{b})}.")) (|monicModulo| (($ $ $) "\\axiom{monicModulo(a,{}\\spad{b})} computes \\axiom{a mod \\spad{b}},{} if \\axiom{\\spad{b}} is monic as univariate polynomial in its main variable.")) (|pseudoDivide| (((|Record| (|:| |quotient| $) (|:| |remainder| $)) $ $) "\\axiom{pseudoDivide(a,{}\\spad{b})} computes \\axiom{[pquo(a,{}\\spad{b}),{}prem(a,{}\\spad{b})]},{} both polynomials viewed as univariate polynomials in the main variable of \\axiom{\\spad{b}},{} if \\axiom{\\spad{b}} is not a constant polynomial.")) (|lazyPseudoDivide| (((|Record| (|:| |coef| $) (|:| |gap| (|NonNegativeInteger|)) (|:| |quotient| $) (|:| |remainder| $)) $ $ |#4|) "\\axiom{lazyPseudoDivide(a,{}\\spad{b},{}\\spad{v})} returns \\axiom{[\\spad{c},{}\\spad{g},{}\\spad{q},{}\\spad{r}]} such that \\axiom{\\spad{r} = lazyPrem(a,{}\\spad{b},{}\\spad{v})},{} \\axiom{(c**g)\\spad{*r} = prem(a,{}\\spad{b},{}\\spad{v})} and \\axiom{\\spad{q}} is the pseudo-quotient computed in this lazy pseudo-division.") (((|Record| (|:| |coef| $) (|:| |gap| (|NonNegativeInteger|)) (|:| |quotient| $) (|:| |remainder| $)) $ $) "\\axiom{lazyPseudoDivide(a,{}\\spad{b})} returns \\axiom{[\\spad{c},{}\\spad{g},{}\\spad{q},{}\\spad{r}]} such that \\axiom{[\\spad{c},{}\\spad{g},{}\\spad{r}] = lazyPremWithDefault(a,{}\\spad{b})} and \\axiom{\\spad{q}} is the pseudo-quotient computed in this lazy pseudo-division.")) (|lazyPremWithDefault| (((|Record| (|:| |coef| $) (|:| |gap| (|NonNegativeInteger|)) (|:| |remainder| $)) $ $ |#4|) "\\axiom{lazyPremWithDefault(a,{}\\spad{b},{}\\spad{v})} returns \\axiom{[\\spad{c},{}\\spad{g},{}\\spad{r}]} such that \\axiom{\\spad{r} = lazyPrem(a,{}\\spad{b},{}\\spad{v})} and \\axiom{(c**g)\\spad{*r} = prem(a,{}\\spad{b},{}\\spad{v})}.") (((|Record| (|:| |coef| $) (|:| |gap| (|NonNegativeInteger|)) (|:| |remainder| $)) $ $) "\\axiom{lazyPremWithDefault(a,{}\\spad{b})} returns \\axiom{[\\spad{c},{}\\spad{g},{}\\spad{r}]} such that \\axiom{\\spad{r} = lazyPrem(a,{}\\spad{b})} and \\axiom{(c**g)\\spad{*r} = prem(a,{}\\spad{b})}.")) (|lazyPquo| (($ $ $ |#4|) "\\axiom{lazyPquo(a,{}\\spad{b},{}\\spad{v})} returns the polynomial \\axiom{\\spad{q}} such that \\axiom{lazyPseudoDivide(a,{}\\spad{b},{}\\spad{v})} returns \\axiom{[\\spad{c},{}\\spad{g},{}\\spad{q},{}\\spad{r}]}.") (($ $ $) "\\axiom{lazyPquo(a,{}\\spad{b})} returns the polynomial \\axiom{\\spad{q}} such that \\axiom{lazyPseudoDivide(a,{}\\spad{b})} returns \\axiom{[\\spad{c},{}\\spad{g},{}\\spad{q},{}\\spad{r}]}.")) (|lazyPrem| (($ $ $ |#4|) "\\axiom{lazyPrem(a,{}\\spad{b},{}\\spad{v})} returns the polynomial \\axiom{\\spad{r}} reduced \\spad{w}.\\spad{r}.\\spad{t}. \\axiom{\\spad{b}} viewed as univariate polynomials in the variable \\axiom{\\spad{v}} such that \\axiom{\\spad{b}} divides \\axiom{init(\\spad{b})^e a - \\spad{r}} where \\axiom{\\spad{e}} is the number of steps of this pseudo-division.") (($ $ $) "\\axiom{lazyPrem(a,{}\\spad{b})} returns the polynomial \\axiom{\\spad{r}} reduced \\spad{w}.\\spad{r}.\\spad{t}. \\axiom{\\spad{b}} and such that \\axiom{\\spad{b}} divides \\axiom{init(\\spad{b})^e a - \\spad{r}} where \\axiom{\\spad{e}} is the number of steps of this pseudo-division.")) (|pquo| (($ $ $ |#4|) "\\axiom{pquo(a,{}\\spad{b},{}\\spad{v})} computes the pseudo-quotient of \\axiom{a} by \\axiom{\\spad{b}},{} both viewed as univariate polynomials in \\axiom{\\spad{v}}.") (($ $ $) "\\axiom{pquo(a,{}\\spad{b})} computes the pseudo-quotient of \\axiom{a} by \\axiom{\\spad{b}},{} both viewed as univariate polynomials in the main variable of \\axiom{\\spad{b}}.")) (|prem| (($ $ $ |#4|) "\\axiom{prem(a,{}\\spad{b},{}\\spad{v})} computes the pseudo-remainder of \\axiom{a} by \\axiom{\\spad{b}},{} both viewed as univariate polynomials in \\axiom{\\spad{v}}.") (($ $ $) "\\axiom{prem(a,{}\\spad{b})} computes the pseudo-remainder of \\axiom{a} by \\axiom{\\spad{b}},{} both viewed as univariate polynomials in the main variable of \\axiom{\\spad{b}}.")) (|normalized?| (((|Boolean|) $ (|List| $)) "\\axiom{normalized?(\\spad{q},{}\\spad{lp})} returns \\spad{true} iff \\axiom{normalized?(\\spad{q},{}\\spad{p})} holds for every \\axiom{\\spad{p}} in \\axiom{\\spad{lp}}.") (((|Boolean|) $ $) "\\axiom{normalized?(a,{}\\spad{b})} returns \\spad{true} iff \\axiom{a} and its iterated initials have degree zero \\spad{w}.\\spad{r}.\\spad{t}. the main variable of \\axiom{\\spad{b}}")) (|initiallyReduced?| (((|Boolean|) $ (|List| $)) "\\axiom{initiallyReduced?(\\spad{q},{}\\spad{lp})} returns \\spad{true} iff \\axiom{initiallyReduced?(\\spad{q},{}\\spad{p})} holds for every \\axiom{\\spad{p}} in \\axiom{\\spad{lp}}.") (((|Boolean|) $ $) "\\axiom{initiallyReduced?(a,{}\\spad{b})} returns \\spad{false} iff there exists an iterated initial of \\axiom{a} which is not reduced \\spad{w}.\\spad{r}.\\spad{t} \\axiom{\\spad{b}}.")) (|headReduced?| (((|Boolean|) $ (|List| $)) "\\axiom{headReduced?(\\spad{q},{}\\spad{lp})} returns \\spad{true} iff \\axiom{headReduced?(\\spad{q},{}\\spad{p})} holds for every \\axiom{\\spad{p}} in \\axiom{\\spad{lp}}.") (((|Boolean|) $ $) "\\axiom{headReduced?(a,{}\\spad{b})} returns \\spad{true} iff \\axiom{degree(head(a),{}mvar(\\spad{b})) < mdeg(\\spad{b})}.")) (|reduced?| (((|Boolean|) $ (|List| $)) "\\axiom{reduced?(\\spad{q},{}\\spad{lp})} returns \\spad{true} iff \\axiom{reduced?(\\spad{q},{}\\spad{p})} holds for every \\axiom{\\spad{p}} in \\axiom{\\spad{lp}}.") (((|Boolean|) $ $) "\\axiom{reduced?(a,{}\\spad{b})} returns \\spad{true} iff \\axiom{degree(a,{}mvar(\\spad{b})) < mdeg(\\spad{b})}.")) (|supRittWu?| (((|Boolean|) $ $) "\\axiom{supRittWu?(a,{}\\spad{b})} returns \\spad{true} if \\axiom{a} is greater than \\axiom{\\spad{b}} \\spad{w}.\\spad{r}.\\spad{t}. the Ritt and Wu Wen Tsun ordering using the refinement of Lazard.")) (|infRittWu?| (((|Boolean|) $ $) "\\axiom{infRittWu?(a,{}\\spad{b})} returns \\spad{true} if \\axiom{a} is less than \\axiom{\\spad{b}} \\spad{w}.\\spad{r}.\\spad{t}. the Ritt and Wu Wen Tsun ordering using the refinement of Lazard.")) (|RittWuCompare| (((|Union| (|Boolean|) "failed") $ $) "\\axiom{RittWuCompare(a,{}\\spad{b})} returns \\axiom{\"failed\"} if \\axiom{a} and \\axiom{\\spad{b}} have same rank \\spad{w}.\\spad{r}.\\spad{t}. Ritt and Wu Wen Tsun ordering using the refinement of Lazard,{} otherwise returns \\axiom{infRittWu?(a,{}\\spad{b})}.")) (|mainMonomials| (((|List| $) $) "\\axiom{mainMonomials(\\spad{p})} returns an error if \\axiom{\\spad{p}} is \\axiom{\\spad{O}},{} otherwise,{} if \\axiom{\\spad{p}} belongs to \\axiom{\\spad{R}} returns [1],{} otherwise returns the list of the monomials of \\axiom{\\spad{p}},{} where \\axiom{\\spad{p}} is viewed as a univariate polynomial in its main variable.")) (|mainCoefficients| (((|List| $) $) "\\axiom{mainCoefficients(\\spad{p})} returns an error if \\axiom{\\spad{p}} is \\axiom{\\spad{O}},{} otherwise,{} if \\axiom{\\spad{p}} belongs to \\axiom{\\spad{R}} returns [\\spad{p}],{} otherwise returns the list of the coefficients of \\axiom{\\spad{p}},{} where \\axiom{\\spad{p}} is viewed as a univariate polynomial in its main variable.")) (|leastMonomial| (($ $) "\\axiom{leastMonomial(\\spad{p})} returns an error if \\axiom{\\spad{p}} is \\axiom{\\spad{O}},{} otherwise,{} if \\axiom{\\spad{p}} belongs to \\axiom{\\spad{R}} returns \\axiom{1},{} otherwise,{} the monomial of \\axiom{\\spad{p}} with lowest degree,{} where \\axiom{\\spad{p}} is viewed as a univariate polynomial in its main variable.")) (|mainMonomial| (($ $) "\\axiom{mainMonomial(\\spad{p})} returns an error if \\axiom{\\spad{p}} is \\axiom{\\spad{O}},{} otherwise,{} if \\axiom{\\spad{p}} belongs to \\axiom{\\spad{R}} returns \\axiom{1},{} otherwise,{} \\axiom{mvar(\\spad{p})} raised to the power \\axiom{mdeg(\\spad{p})}.")) (|quasiMonic?| (((|Boolean|) $) "\\axiom{quasiMonic?(\\spad{p})} returns \\spad{false} if \\axiom{\\spad{p}} belongs to \\axiom{\\spad{R}},{} otherwise returns \\spad{true} iff the initial of \\axiom{\\spad{p}} lies in the base ring \\axiom{\\spad{R}}.")) (|monic?| (((|Boolean|) $) "\\axiom{monic?(\\spad{p})} returns \\spad{false} if \\axiom{\\spad{p}} belongs to \\axiom{\\spad{R}},{} otherwise returns \\spad{true} iff \\axiom{\\spad{p}} is monic as a univariate polynomial in its main variable.")) (|reductum| (($ $ |#4|) "\\axiom{reductum(\\spad{p},{}\\spad{v})} returns the reductum of \\axiom{\\spad{p}},{} where \\axiom{\\spad{p}} is viewed as a univariate polynomial in \\axiom{\\spad{v}}.")) (|leadingCoefficient| (($ $ |#4|) "\\axiom{leadingCoefficient(\\spad{p},{}\\spad{v})} returns the leading coefficient of \\axiom{\\spad{p}},{} where \\axiom{\\spad{p}} is viewed as A univariate polynomial in \\axiom{\\spad{v}}.")) (|deepestInitial| (($ $) "\\axiom{deepestInitial(\\spad{p})} returns an error if \\axiom{\\spad{p}} belongs to \\axiom{\\spad{R}},{} otherwise returns the last term of \\axiom{iteratedInitials(\\spad{p})}.")) (|iteratedInitials| (((|List| $) $) "\\axiom{iteratedInitials(\\spad{p})} returns \\axiom{[]} if \\axiom{\\spad{p}} belongs to \\axiom{\\spad{R}},{} otherwise returns the list of the iterated initials of \\axiom{\\spad{p}}.")) (|deepestTail| (($ $) "\\axiom{deepestTail(\\spad{p})} returns \\axiom{0} if \\axiom{\\spad{p}} belongs to \\axiom{\\spad{R}},{} otherwise returns tail(\\spad{p}),{} if \\axiom{tail(\\spad{p})} belongs to \\axiom{\\spad{R}} or \\axiom{mvar(tail(\\spad{p})) < mvar(\\spad{p})},{} otherwise returns \\axiom{deepestTail(tail(\\spad{p}))}.")) (|tail| (($ $) "\\axiom{tail(\\spad{p})} returns its reductum,{} where \\axiom{\\spad{p}} is viewed as a univariate polynomial in its main variable.")) (|head| (($ $) "\\axiom{head(\\spad{p})} returns \\axiom{\\spad{p}} if \\axiom{\\spad{p}} belongs to \\axiom{\\spad{R}},{} otherwise returns its leading term (monomial in the AXIOM sense),{} where \\axiom{\\spad{p}} is viewed as a univariate polynomial in its main variable.")) (|init| (($ $) "\\axiom{init(\\spad{p})} returns an error if \\axiom{\\spad{p}} belongs to \\axiom{\\spad{R}},{} otherwise returns its leading coefficient,{} where \\axiom{\\spad{p}} is viewed as a univariate polynomial in its main variable.")) (|mdeg| (((|NonNegativeInteger|) $) "\\axiom{mdeg(\\spad{p})} returns an error if \\axiom{\\spad{p}} is \\axiom{0},{} otherwise,{} if \\axiom{\\spad{p}} belongs to \\axiom{\\spad{R}} returns \\axiom{0},{} otherwise,{} returns the degree of \\axiom{\\spad{p}} in its main variable.")) (|mvar| ((|#4| $) "\\axiom{mvar(\\spad{p})} returns an error if \\axiom{\\spad{p}} belongs to \\axiom{\\spad{R}},{} otherwise returns its main variable \\spad{w}. \\spad{r}. \\spad{t}. to the total ordering on the elements in \\axiom{\\spad{V}}."))) NIL @@ -4268,11 +4268,11 @@ NIL ((|constructor| (NIL "This domain implements named rules")) (|name| (((|Symbol|) $) "\\spad{name(x)} returns the symbol"))) NIL NIL -(-1085 |Base| R -1385) +(-1085 |Base| R -2968) ((|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},{}...,{}\\spad{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 -(-1086 |Base| R -1385) +(-1086 |Base| R -2968) ((|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 @@ -4287,7 +4287,7 @@ NIL (-1089 R UP M) ((|constructor| (NIL "Domain which represents simple algebraic extensions of arbitrary rings. The first argument to the domain,{} \\spad{R},{} is the underlying ring,{} the second argument is a domain of univariate polynomials over \\spad{K},{} while the last argument specifies the defining minimal polynomial. The elements of the domain are canonically represented as polynomials of degree less than that of the minimal polynomial with coefficients in \\spad{R}. The second argument is both the type of the third argument and the underlying representation used by \\spadtype{SAE} itself."))) ((-4445 |has| |#1| (-368)) (-4450 |has| |#1| (-368)) (-4444 |has| |#1| (-368)) ((-4454 "*") . T) (-4446 . T) (-4447 . T) (-4449 . T)) -((|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-148))) (|HasCategory| |#1| (QUOTE (-354))) (-2811 (|HasCategory| |#1| (QUOTE (-368))) (|HasCategory| |#1| (QUOTE (-354)))) (|HasCategory| |#1| (QUOTE (-368))) (|HasCategory| |#1| (QUOTE (-373))) (-2811 (-12 (|HasCategory| |#1| (QUOTE (-235))) (|HasCategory| |#1| (QUOTE (-368)))) (|HasCategory| |#1| (QUOTE (-354)))) (-2811 (-12 (|HasCategory| |#1| (QUOTE (-368))) (|HasCategory| |#1| (LIST (QUOTE -907) (QUOTE (-1186))))) (-12 (|HasCategory| |#1| (QUOTE (-354))) (|HasCategory| |#1| (LIST (QUOTE -907) (QUOTE (-1186)))))) (|HasCategory| |#1| (LIST (QUOTE -645) (QUOTE (-570)))) (-2811 (|HasCategory| |#1| (LIST (QUOTE -1047) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasCategory| |#1| (QUOTE (-368)))) (|HasCategory| |#1| (LIST (QUOTE -1047) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasCategory| |#1| (LIST (QUOTE -1047) (QUOTE (-570)))) (-12 (|HasCategory| |#1| (QUOTE (-368))) (|HasCategory| |#1| (LIST (QUOTE -907) (QUOTE (-1186))))) (-12 (|HasCategory| |#1| (QUOTE (-235))) (|HasCategory| |#1| (QUOTE (-368))))) +((|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-148))) (|HasCategory| |#1| (QUOTE (-354))) (-3684 (|HasCategory| |#1| (QUOTE (-368))) (|HasCategory| |#1| (QUOTE (-354)))) (|HasCategory| |#1| (QUOTE (-368))) (|HasCategory| |#1| (QUOTE (-373))) (-3684 (-12 (|HasCategory| |#1| (QUOTE (-235))) (|HasCategory| |#1| (QUOTE (-368)))) (|HasCategory| |#1| (QUOTE (-354)))) (-3684 (-12 (|HasCategory| |#1| (QUOTE (-368))) (|HasCategory| |#1| (LIST (QUOTE -907) (QUOTE (-1186))))) (-12 (|HasCategory| |#1| (QUOTE (-354))) (|HasCategory| |#1| (LIST (QUOTE -907) (QUOTE (-1186)))))) (|HasCategory| |#1| (LIST (QUOTE -645) (QUOTE (-570)))) (-3684 (|HasCategory| |#1| (LIST (QUOTE -1047) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasCategory| |#1| (QUOTE (-368)))) (|HasCategory| |#1| (LIST (QUOTE -1047) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasCategory| |#1| (LIST (QUOTE -1047) (QUOTE (-570)))) (-12 (|HasCategory| |#1| (QUOTE (-368))) (|HasCategory| |#1| (LIST (QUOTE -907) (QUOTE (-1186))))) (-12 (|HasCategory| |#1| (QUOTE (-235))) (|HasCategory| |#1| (QUOTE (-368))))) (-1090 UP SAE UPA) ((|constructor| (NIL "Factorization of univariate polynomials with coefficients in an algebraic extension of \\spadtype{Fraction Polynomial Integer}.")) (|factor| (((|Factored| |#3|) |#3|) "\\spad{factor(p)} returns a prime factorisation of \\spad{p}."))) NIL @@ -4315,7 +4315,7 @@ NIL (-1096 R) ((|constructor| (NIL "\\spadtype{SequentialDifferentialPolynomial} implements an ordinary differential polynomial ring in arbitrary number of differential indeterminates,{} with coefficients in a ring. The ranking on the differential indeterminate is sequential. \\blankline"))) (((-4454 "*") |has| |#1| (-174)) (-4445 |has| |#1| (-562)) (-4450 |has| |#1| (-6 -4450)) (-4447 . T) (-4446 . T) (-4449 . 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A sequential ranking is a ranking \\spadfun{<} of the derivatives with the property that for any derivative \\spad{v},{} there are only a finite number of derivatives \\spad{u} with \\spad{u} \\spadfun{<} \\spad{v}. This domain belongs to \\spadtype{DifferentialVariableCategory}. It defines \\spadfun{weight} to be just \\spadfun{order},{} and it defines a sequential ranking \\spadfun{<} on derivatives \\spad{u} by the lexicographic order on the pair (\\spadfun{variable}(\\spad{u}),{} \\spadfun{order}(\\spad{u}))."))) NIL @@ -4375,7 +4375,7 @@ NIL (-1111 S) ((|constructor| (NIL "A set over a domain \\spad{D} models the usual mathematical notion of a finite set of elements from \\spad{D}. Sets are unordered collections of distinct elements (that is,{} order and duplication does not matter). The notation \\spad{set [a,b,c]} can be used to create a set and the usual operations such as union and intersection are available to form new sets. In our implementation,{} \\Language{} maintains the entries in sorted order. Specifically,{} the parts function returns the entries as a list in ascending order and the extract operation returns the maximum entry. Given two sets \\spad{s} and \\spad{t} where \\spad{\\#s = m} and \\spad{\\#t = n},{} the complexity of \\indented{2}{\\spad{s = t} is \\spad{O(min(n,m))}} \\indented{2}{\\spad{s < t} is \\spad{O(max(n,m))}} \\indented{2}{\\spad{union(s,t)},{} \\spad{intersect(s,t)},{} \\spad{minus(s,t)},{} \\spad{symmetricDifference(s,t)} is \\spad{O(max(n,m))}} \\indented{2}{\\spad{member(x,t)} is \\spad{O(n log n)}} \\indented{2}{\\spad{insert(x,t)} and \\spad{remove(x,t)} is \\spad{O(n)}}"))) ((-4452 . T) (-4442 . T) (-4453 . T)) -((-2811 (-12 (|HasCategory| |#1| (QUOTE (-373))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|))))) (|HasCategory| |#1| (LIST (QUOTE -620) (QUOTE (-542)))) (|HasCategory| |#1| (QUOTE (-373))) (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (QUOTE (-856))) (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-868)))) (-12 (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|))))) +((-3684 (-12 (|HasCategory| |#1| (QUOTE (-373))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|))))) (|HasCategory| |#1| (LIST (QUOTE -620) (QUOTE (-542)))) (|HasCategory| |#1| (QUOTE (-373))) (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (QUOTE (-856))) (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-868)))) (-12 (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|))))) (-1112 |Str| |Sym| |Int| |Flt| |Expr|) ((|constructor| (NIL "This category allows the manipulation of Lisp values while keeping the grunge fairly localized.")) (|#| (((|Integer|) $) "\\spad{\\#((a1,...,an))} returns \\spad{n}.")) (|cdr| (($ $) "\\spad{cdr((a1,...,an))} returns \\spad{(a2,...,an)}.")) (|car| (($ $) "\\spad{car((a1,...,an))} returns a1.")) (|expr| ((|#5| $) "\\spad{expr(s)} returns \\spad{s} as an element of Expr; Error: if \\spad{s} is not an atom that also belongs to Expr.")) (|float| ((|#4| $) "\\spad{float(s)} returns \\spad{s} as an element of \\spad{Flt}; Error: if \\spad{s} is not an atom that also belongs to \\spad{Flt}.")) (|integer| ((|#3| $) "\\spad{integer(s)} returns \\spad{s} as an element of Int. Error: if \\spad{s} is not an atom that also belongs to Int.")) (|symbol| ((|#2| $) "\\spad{symbol(s)} returns \\spad{s} as an element of \\spad{Sym}. Error: if \\spad{s} is not an atom that also belongs to \\spad{Sym}.")) (|string| ((|#1| $) "\\spad{string(s)} returns \\spad{s} as an element of \\spad{Str}. Error: if \\spad{s} is not an atom that also belongs to \\spad{Str}.")) (|destruct| (((|List| $) $) "\\spad{destruct((a1,...,an))} returns the list [a1,{}...,{}an].")) (|float?| (((|Boolean|) $) "\\spad{float?(s)} is \\spad{true} if \\spad{s} is an atom and belong to \\spad{Flt}.")) (|integer?| (((|Boolean|) $) "\\spad{integer?(s)} is \\spad{true} if \\spad{s} is an atom and belong to Int.")) (|symbol?| (((|Boolean|) $) "\\spad{symbol?(s)} is \\spad{true} if \\spad{s} is an atom and belong to \\spad{Sym}.")) (|string?| (((|Boolean|) $) "\\spad{string?(s)} is \\spad{true} if \\spad{s} is an atom and belong to \\spad{Str}.")) (|list?| (((|Boolean|) $) "\\spad{list?(s)} is \\spad{true} if \\spad{s} is a Lisp list,{} possibly ().")) (|pair?| (((|Boolean|) $) "\\spad{pair?(s)} is \\spad{true} if \\spad{s} has is a non-null Lisp list.")) (|atom?| (((|Boolean|) $) "\\spad{atom?(s)} is \\spad{true} if \\spad{s} is a Lisp atom.")) (|null?| (((|Boolean|) $) "\\spad{null?(s)} is \\spad{true} if \\spad{s} is the \\spad{S}-expression ().")) 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|#3| (LIST (QUOTE -1047) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasCategory| |#3| (QUOTE (-1109)))) (|HasAttribute| |#3| (QUOTE -4449)) (|HasCategory| |#3| (QUOTE (-132))) (|HasCategory| |#3| (QUOTE (-25))) (|HasCategory| |#3| (LIST (QUOTE -619) (QUOTE (-868)))) (-12 (|HasCategory| |#3| (QUOTE (-1109))) (|HasCategory| |#3| (LIST (QUOTE -313) (|devaluate| |#3|))))) (-1123 R |x|) ((|constructor| (NIL "This package produces functions for counting etc. real roots of univariate polynomials in \\spad{x} over \\spad{R},{} which must be an OrderedIntegralDomain")) (|countRealRootsMultiple| (((|Integer|) (|UnivariatePolynomial| |#2| |#1|)) "\\spad{countRealRootsMultiple(p)} says how many real roots \\spad{p} has,{} counted with multiplicity")) (|SturmHabichtMultiple| (((|Integer|) (|UnivariatePolynomial| |#2| |#1|) (|UnivariatePolynomial| |#2| |#1|)) "\\spad{SturmHabichtMultiple(p1,p2)} computes \\spad{c_}{+}\\spad{-c_}{-} where \\spad{c_}{+} is the number of real roots of \\spad{p1} with p2>0 and \\spad{c_}{-} is the number of real roots of \\spad{p1} with p2<0. If p2=1 what you get is the number of real roots of \\spad{p1}.")) (|countRealRoots| (((|Integer|) (|UnivariatePolynomial| |#2| |#1|)) "\\spad{countRealRoots(p)} says how many real roots \\spad{p} has")) (|SturmHabicht| (((|Integer|) (|UnivariatePolynomial| |#2| |#1|) (|UnivariatePolynomial| |#2| |#1|)) "\\spad{SturmHabicht(p1,p2)} computes \\spad{c_}{+}\\spad{-c_}{-} where \\spad{c_}{+} is the number of real roots of \\spad{p1} with p2>0 and \\spad{c_}{-} is the number of real roots of \\spad{p1} with p2<0. If p2=1 what you get is the number of real roots of \\spad{p1}.")) (|SturmHabichtCoefficients| (((|List| |#1|) (|UnivariatePolynomial| |#2| |#1|) (|UnivariatePolynomial| |#2| |#1|)) "\\spad{SturmHabichtCoefficients(p1,p2)} computes the principal Sturm-Habicht coefficients of \\spad{p1} and \\spad{p2}")) (|SturmHabichtSequence| (((|List| (|UnivariatePolynomial| |#2| |#1|)) (|UnivariatePolynomial| |#2| |#1|) (|UnivariatePolynomial| |#2| |#1|)) "\\spad{SturmHabichtSequence(p1,p2)} computes the Sturm-Habicht sequence of \\spad{p1} and \\spad{p2}")) (|subresultantSequence| (((|List| (|UnivariatePolynomial| |#2| |#1|)) (|UnivariatePolynomial| |#2| |#1|) (|UnivariatePolynomial| |#2| |#1|)) "\\spad{subresultantSequence(p1,p2)} computes the (standard) subresultant sequence of \\spad{p1} and \\spad{p2}"))) NIL @@ -4428,7 +4428,7 @@ 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 \\spad{`s'}.")) (|name| (((|Identifier|) $) "\\spad{name(s)} returns the name of the signature \\spad{`s'}.")) (|signatureAst| (($ (|Identifier|) (|Signature|)) "\\spad{signatureAst(n,s,t)} builds the signature AST \\spad{n:} \\spad{s} \\spad{->} \\spad{t}"))) NIL NIL -(-1125 R -1385) +(-1125 R -2968) ((|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 @@ -4467,16 +4467,16 @@ NIL (-1134 R |VarSet|) ((|constructor| (NIL "\\indented{2}{This type is the basic representation of sparse recursive multivariate} polynomials. It is parameterized by the coefficient ring and the variable set which may be infinite. The variable ordering is determined by the variable set parameter. The coefficient ring may be non-commutative,{} but the variables are assumed to commute."))) (((-4454 "*") |has| |#1| (-174)) (-4445 |has| |#1| (-562)) (-4450 |has| |#1| (-6 -4450)) (-4447 . T) (-4446 . T) (-4449 . T)) -((|HasCategory| |#1| (QUOTE (-916))) (-2811 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-458))) (|HasCategory| |#1| (QUOTE (-562))) (|HasCategory| |#1| (QUOTE (-916)))) (-2811 (|HasCategory| |#1| (QUOTE (-458))) (|HasCategory| |#1| (QUOTE (-562))) (|HasCategory| |#1| (QUOTE (-916)))) (-2811 (|HasCategory| |#1| (QUOTE (-458))) (|HasCategory| |#1| (QUOTE (-916)))) (|HasCategory| |#1| (QUOTE (-562))) (|HasCategory| |#1| (QUOTE (-174))) (-2811 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-562)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -893) (QUOTE (-384)))) (|HasCategory| |#2| (LIST (QUOTE -893) (QUOTE (-384))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -893) (QUOTE (-570)))) (|HasCategory| |#2| (LIST (QUOTE -893) (QUOTE (-570))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -620) (LIST (QUOTE -899) (QUOTE (-384))))) (|HasCategory| |#2| (LIST (QUOTE -620) (LIST (QUOTE -899) (QUOTE (-384)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -620) (LIST (QUOTE -899) (QUOTE (-570))))) (|HasCategory| |#2| (LIST (QUOTE -620) (LIST (QUOTE -899) (QUOTE (-570)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -620) (QUOTE (-542)))) (|HasCategory| |#2| (LIST (QUOTE -620) (QUOTE (-542))))) (|HasCategory| |#1| (LIST (QUOTE -645) (QUOTE (-570)))) (|HasCategory| |#1| (QUOTE (-148))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasCategory| |#1| (LIST (QUOTE -1047) (QUOTE (-570)))) (-2811 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasCategory| |#1| (LIST (QUOTE -1047) (LIST (QUOTE -413) (QUOTE (-570)))))) (|HasCategory| |#1| (LIST (QUOTE -1047) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasCategory| |#1| (QUOTE (-368))) (|HasAttribute| |#1| (QUOTE -4450)) (|HasCategory| |#1| (QUOTE (-458))) (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-916)))) (-2811 (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-916)))) (|HasCategory| |#1| (QUOTE (-146))))) +((|HasCategory| |#1| (QUOTE (-916))) (-3684 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-458))) (|HasCategory| |#1| (QUOTE (-562))) (|HasCategory| |#1| (QUOTE (-916)))) (-3684 (|HasCategory| |#1| (QUOTE (-458))) (|HasCategory| |#1| (QUOTE (-562))) (|HasCategory| |#1| (QUOTE (-916)))) (-3684 (|HasCategory| |#1| (QUOTE (-458))) (|HasCategory| |#1| (QUOTE (-916)))) (|HasCategory| |#1| (QUOTE (-562))) (|HasCategory| |#1| (QUOTE (-174))) (-3684 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-562)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -893) (QUOTE (-384)))) (|HasCategory| |#2| (LIST (QUOTE -893) (QUOTE (-384))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -893) (QUOTE (-570)))) (|HasCategory| |#2| (LIST (QUOTE -893) (QUOTE (-570))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -620) (LIST (QUOTE -899) (QUOTE (-384))))) (|HasCategory| |#2| (LIST (QUOTE -620) (LIST (QUOTE -899) (QUOTE (-384)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -620) (LIST (QUOTE -899) (QUOTE (-570))))) (|HasCategory| |#2| (LIST (QUOTE -620) (LIST (QUOTE -899) (QUOTE (-570)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -620) (QUOTE (-542)))) (|HasCategory| |#2| (LIST (QUOTE -620) (QUOTE (-542))))) (|HasCategory| |#1| (LIST (QUOTE -645) (QUOTE (-570)))) (|HasCategory| |#1| (QUOTE (-148))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasCategory| |#1| (LIST (QUOTE -1047) (QUOTE (-570)))) (-3684 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasCategory| |#1| (LIST (QUOTE -1047) (LIST (QUOTE -413) (QUOTE (-570)))))) (|HasCategory| |#1| (LIST (QUOTE -1047) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasCategory| |#1| (QUOTE (-368))) (|HasAttribute| |#1| (QUOTE -4450)) (|HasCategory| |#1| (QUOTE (-458))) (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-916)))) (-3684 (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-916)))) (|HasCategory| |#1| (QUOTE (-146))))) (-1135 |Coef| |Var| SMP) ((|constructor| (NIL "This domain provides multivariate Taylor series with variables from an arbitrary ordered set. A Taylor series is represented by a stream of polynomials from the polynomial domain \\spad{SMP}. The \\spad{n}th element of the stream is a form of degree \\spad{n}. SMTS is an internal domain.")) (|fintegrate| (($ (|Mapping| $) |#2| |#1|) "\\spad{fintegrate(f,v,c)} is the integral of \\spad{f()} with respect \\indented{1}{to \\spad{v} and having \\spad{c} as the constant of integration.} \\indented{1}{The evaluation of \\spad{f()} is delayed.}")) (|integrate| (($ $ |#2| |#1|) "\\spad{integrate(s,v,c)} is the integral of \\spad{s} with respect \\indented{1}{to \\spad{v} and having \\spad{c} as the constant of integration.}")) (|csubst| (((|Mapping| (|Stream| |#3|) |#3|) (|List| |#2|) (|List| (|Stream| |#3|))) "\\spad{csubst(a,b)} is for internal use only")) (* (($ |#3| $) "\\spad{smp*ts} multiplies a TaylorSeries by a monomial \\spad{SMP}.")) (|coerce| (($ |#3|) "\\spad{coerce(poly)} regroups the terms by total degree and forms a series.") (($ |#2|) "\\spad{coerce(var)} converts a variable to a Taylor series")) (|coefficient| ((|#3| $ (|NonNegativeInteger|)) "\\spad{coefficient(s, n)} gives the terms of total degree \\spad{n}."))) (((-4454 "*") |has| |#1| (-174)) (-4445 |has| |#1| (-562)) (-4447 . T) (-4446 . T) (-4449 . T)) -((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-148))) (|HasCategory| |#1| (QUOTE (-146))) (-2811 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-562)))) (|HasCategory| |#1| (QUOTE (-562))) (|HasCategory| |#1| (QUOTE (-368)))) +((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-148))) (|HasCategory| |#1| (QUOTE (-146))) (-3684 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-562)))) (|HasCategory| |#1| (QUOTE (-562))) (|HasCategory| |#1| (QUOTE (-368)))) (-1136 R E V P) ((|constructor| (NIL "The category of square-free and normalized triangular sets. Thus,{} up to the primitivity axiom of [1],{} these sets are Lazard triangular sets.\\newline References : \\indented{1}{[1] \\spad{D}. LAZARD \"A new method for solving algebraic systems of} \\indented{5}{positive dimension\" Discr. App. Math. 33:147-160,{}1991}"))) ((-4453 . T) (-4452 . T)) NIL -(-1137 UP -1385) +(-1137 UP -2968) ((|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 @@ -4531,11 +4531,11 @@ NIL (-1150 V C) ((|constructor| (NIL "This domain exports a modest implementation of splitting trees. Spliiting trees are needed when the evaluation of some quantity under some hypothesis requires to split the hypothesis into sub-cases. For instance by adding some new hypothesis on one hand and its negation on another hand. The computations are terminated is a splitting tree \\axiom{a} when \\axiom{status(value(a))} is \\axiom{\\spad{true}}. Thus,{} if for the splitting tree \\axiom{a} the flag \\axiom{status(value(a))} is \\axiom{\\spad{true}},{} then \\axiom{status(value(\\spad{d}))} is \\axiom{\\spad{true}} for any subtree \\axiom{\\spad{d}} of \\axiom{a}. This property of splitting trees is called the termination condition. If no vertex in a splitting tree \\axiom{a} is equal to another,{} \\axiom{a} is said to satisfy the no-duplicates condition. The splitting tree \\axiom{a} will satisfy this condition if nodes are added to \\axiom{a} by mean of \\axiom{splitNodeOf!} and if \\axiom{construct} is only used to create the root of \\axiom{a} with no children.")) (|splitNodeOf!| (($ $ $ (|List| (|SplittingNode| |#1| |#2|)) (|Mapping| (|Boolean|) |#2| |#2|)) "\\axiom{splitNodeOf!(\\spad{l},{}a,{}\\spad{ls},{}sub?)} returns \\axiom{a} where the children list of \\axiom{\\spad{l}} has been set to \\axiom{[[\\spad{s}]\\$\\% for \\spad{s} in \\spad{ls} | not subNodeOf?(\\spad{s},{}a,{}sub?)]}. Thus,{} if \\axiom{\\spad{l}} is not a node of \\axiom{a},{} this latter splitting tree is unchanged.") (($ $ $ (|List| (|SplittingNode| |#1| |#2|))) "\\axiom{splitNodeOf!(\\spad{l},{}a,{}\\spad{ls})} returns \\axiom{a} where the children list of \\axiom{\\spad{l}} has been set to \\axiom{[[\\spad{s}]\\$\\% for \\spad{s} in \\spad{ls} | not nodeOf?(\\spad{s},{}a)]}. Thus,{} if \\axiom{\\spad{l}} is not a node of \\axiom{a},{} this latter splitting tree is unchanged.")) (|remove!| (($ (|SplittingNode| |#1| |#2|) $) "\\axiom{remove!(\\spad{s},{}a)} replaces a by remove(\\spad{s},{}a)")) (|remove| (($ (|SplittingNode| |#1| |#2|) $) "\\axiom{remove(\\spad{s},{}a)} returns the splitting tree obtained from a by removing every sub-tree \\axiom{\\spad{b}} such that \\axiom{value(\\spad{b})} and \\axiom{\\spad{s}} have the same value,{} condition and status.")) (|subNodeOf?| (((|Boolean|) (|SplittingNode| |#1| |#2|) $ (|Mapping| (|Boolean|) |#2| |#2|)) "\\axiom{subNodeOf?(\\spad{s},{}a,{}sub?)} returns \\spad{true} iff for some node \\axiom{\\spad{n}} in \\axiom{a} we have \\axiom{\\spad{s} = \\spad{n}} or \\axiom{status(\\spad{n})} and \\axiom{subNode?(\\spad{s},{}\\spad{n},{}sub?)}.")) (|nodeOf?| (((|Boolean|) (|SplittingNode| |#1| |#2|) $) "\\axiom{nodeOf?(\\spad{s},{}a)} returns \\spad{true} iff some node of \\axiom{a} is equal to \\axiom{\\spad{s}}")) (|result| (((|List| (|Record| (|:| |val| |#1|) (|:| |tower| |#2|))) $) "\\axiom{result(a)} where \\axiom{\\spad{ls}} is the leaves list of \\axiom{a} returns \\axiom{[[value(\\spad{s}),{}condition(\\spad{s})]\\$\\spad{VT} for \\spad{s} in \\spad{ls}]} if the computations are terminated in \\axiom{a} else an error is produced.")) (|conditions| (((|List| |#2|) $) "\\axiom{conditions(a)} returns the list of the conditions of the leaves of a")) (|construct| (($ |#1| |#2| |#1| (|List| |#2|)) "\\axiom{construct(\\spad{v1},{}\\spad{t},{}\\spad{v2},{}\\spad{lt})} creates a splitting tree with value (\\spadignore{i.e.} root vertex) given by \\axiom{[\\spad{v},{}\\spad{t}]\\$\\spad{S}} and with children list given by \\axiom{[[[\\spad{v},{}\\spad{t}]\\$\\spad{S}]\\$\\% for \\spad{s} in \\spad{ls}]}.") (($ |#1| |#2| (|List| (|SplittingNode| |#1| |#2|))) "\\axiom{construct(\\spad{v},{}\\spad{t},{}\\spad{ls})} creates a splitting tree with value (\\spadignore{i.e.} root vertex) given by \\axiom{[\\spad{v},{}\\spad{t}]\\$\\spad{S}} and with children list given by \\axiom{[[\\spad{s}]\\$\\% for \\spad{s} in \\spad{ls}]}.") (($ |#1| |#2| (|List| $)) "\\axiom{construct(\\spad{v},{}\\spad{t},{}la)} creates a splitting tree with value (\\spadignore{i.e.} root vertex) given by \\axiom{[\\spad{v},{}\\spad{t}]\\$\\spad{S}} and with \\axiom{la} as children list.") (($ (|SplittingNode| |#1| |#2|)) "\\axiom{construct(\\spad{s})} creates a splitting tree with value (\\spadignore{i.e.} root vertex) given by \\axiom{\\spad{s}} and no children. Thus,{} if the status of \\axiom{\\spad{s}} is \\spad{false},{} \\axiom{[\\spad{s}]} represents the starting point of the evaluation \\axiom{value(\\spad{s})} under the hypothesis \\axiom{condition(\\spad{s})}.")) (|updateStatus!| (($ $) "\\axiom{updateStatus!(a)} returns a where the status of the vertices are updated to satisfy the \"termination condition\".")) (|extractSplittingLeaf| (((|Union| $ "failed") $) "\\axiom{extractSplittingLeaf(a)} returns the left most leaf (as a tree) whose status is \\spad{false} if any,{} else \"failed\" is returned."))) ((-4452 . T) (-4453 . T)) -((-12 (|HasCategory| (-1149 |#1| |#2|) (LIST (QUOTE -313) (LIST (QUOTE -1149) (|devaluate| |#1|) (|devaluate| |#2|)))) (|HasCategory| (-1149 |#1| |#2|) (QUOTE (-1109)))) (|HasCategory| (-1149 |#1| |#2|) (QUOTE (-1109))) (-2811 (|HasCategory| (-1149 |#1| |#2|) (LIST (QUOTE -619) (QUOTE (-868)))) (-12 (|HasCategory| (-1149 |#1| |#2|) (LIST (QUOTE -313) (LIST (QUOTE -1149) (|devaluate| |#1|) (|devaluate| |#2|)))) (|HasCategory| (-1149 |#1| |#2|) (QUOTE (-1109))))) (|HasCategory| (-1149 |#1| |#2|) (LIST (QUOTE -619) (QUOTE (-868))))) +((-12 (|HasCategory| (-1149 |#1| |#2|) (LIST (QUOTE -313) (LIST (QUOTE -1149) (|devaluate| |#1|) (|devaluate| |#2|)))) (|HasCategory| (-1149 |#1| |#2|) (QUOTE (-1109)))) (|HasCategory| (-1149 |#1| |#2|) (QUOTE (-1109))) (-3684 (|HasCategory| (-1149 |#1| |#2|) (LIST (QUOTE -619) (QUOTE (-868)))) (-12 (|HasCategory| (-1149 |#1| |#2|) (LIST (QUOTE -313) (LIST (QUOTE -1149) (|devaluate| |#1|) (|devaluate| |#2|)))) (|HasCategory| (-1149 |#1| |#2|) (QUOTE (-1109))))) (|HasCategory| (-1149 |#1| |#2|) (LIST (QUOTE -619) (QUOTE (-868))))) (-1151 |ndim| R) ((|constructor| (NIL "\\spadtype{SquareMatrix} is a matrix domain of square matrices,{} where the number of rows (= number of columns) is a parameter of the type.")) (|unitsKnown| ((|attribute|) "the invertible matrices are simply the matrices whose determinants are units in the Ring \\spad{R}.")) (|central| ((|attribute|) "the elements of the Ring \\spad{R},{} viewed as diagonal matrices,{} commute with all matrices and,{} indeed,{} are the only matrices which commute with all matrices.")) (|squareMatrix| (($ (|Matrix| |#2|)) "\\spad{squareMatrix(m)} converts a matrix of type \\spadtype{Matrix} to a matrix of type \\spadtype{SquareMatrix}.")) (|transpose| (($ $) "\\spad{transpose(m)} returns the transpose of the matrix \\spad{m}.")) (|new| (($ |#2|) "\\spad{new(c)} constructs a new \\spadtype{SquareMatrix} object of dimension \\spad{ndim} with initial entries equal to \\spad{c}."))) ((-4449 . T) (-4441 |has| |#2| (-6 (-4454 "*"))) (-4452 . T) (-4446 . T) (-4447 . T)) -((|HasCategory| |#2| (LIST (QUOTE -907) (QUOTE (-1186)))) (|HasCategory| |#2| (QUOTE (-235))) (|HasAttribute| |#2| (QUOTE (-4454 "*"))) (|HasCategory| |#2| (LIST (QUOTE -645) (QUOTE (-570)))) (|HasCategory| |#2| (LIST (QUOTE -1047) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasCategory| |#2| (LIST (QUOTE -1047) (QUOTE (-570)))) (-2811 (-12 (|HasCategory| |#2| (QUOTE (-235))) (|HasCategory| |#2| (LIST (QUOTE -313) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-1109))) (|HasCategory| |#2| (LIST (QUOTE -313) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (LIST (QUOTE -313) (|devaluate| |#2|))) (|HasCategory| |#2| (LIST (QUOTE -645) (QUOTE (-570))))) (-12 (|HasCategory| |#2| (LIST (QUOTE -313) (|devaluate| |#2|))) (|HasCategory| |#2| (LIST (QUOTE -907) (QUOTE (-1186)))))) (|HasCategory| |#2| (LIST (QUOTE -620) (QUOTE (-542)))) (|HasCategory| |#2| (QUOTE (-311))) (|HasCategory| |#2| (QUOTE (-562))) (|HasCategory| |#2| (QUOTE (-1109))) (|HasCategory| |#2| (QUOTE (-368))) (-2811 (|HasAttribute| |#2| (QUOTE (-4454 "*"))) (|HasCategory| |#2| (LIST (QUOTE -645) (QUOTE (-570)))) (|HasCategory| |#2| (LIST (QUOTE -907) (QUOTE (-1186)))) (|HasCategory| |#2| (QUOTE (-235)))) (|HasCategory| |#2| (LIST (QUOTE -619) (QUOTE (-868)))) (-12 (|HasCategory| |#2| (QUOTE (-1109))) (|HasCategory| |#2| (LIST (QUOTE -313) (|devaluate| |#2|)))) (|HasCategory| |#2| (QUOTE (-174)))) +((|HasCategory| |#2| (LIST (QUOTE -907) (QUOTE (-1186)))) (|HasCategory| |#2| (QUOTE (-235))) (|HasAttribute| |#2| (QUOTE (-4454 "*"))) (|HasCategory| |#2| (LIST (QUOTE -645) (QUOTE (-570)))) (|HasCategory| |#2| (LIST (QUOTE -1047) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasCategory| |#2| (LIST (QUOTE -1047) (QUOTE (-570)))) (-3684 (-12 (|HasCategory| |#2| (QUOTE (-235))) (|HasCategory| |#2| (LIST (QUOTE -313) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-1109))) (|HasCategory| |#2| (LIST (QUOTE -313) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (LIST (QUOTE -313) (|devaluate| |#2|))) (|HasCategory| |#2| (LIST (QUOTE -645) (QUOTE (-570))))) (-12 (|HasCategory| |#2| (LIST (QUOTE -313) (|devaluate| |#2|))) (|HasCategory| |#2| (LIST (QUOTE -907) (QUOTE (-1186)))))) (|HasCategory| |#2| (LIST (QUOTE -620) (QUOTE (-542)))) (|HasCategory| |#2| (QUOTE (-311))) (|HasCategory| |#2| (QUOTE (-562))) (|HasCategory| |#2| (QUOTE (-1109))) (|HasCategory| |#2| (QUOTE (-368))) (-3684 (|HasAttribute| |#2| (QUOTE (-4454 "*"))) (|HasCategory| |#2| (LIST (QUOTE -645) (QUOTE (-570)))) (|HasCategory| |#2| (LIST (QUOTE -907) (QUOTE (-1186)))) (|HasCategory| |#2| (QUOTE (-235)))) (|HasCategory| |#2| (LIST (QUOTE -619) (QUOTE (-868)))) (-12 (|HasCategory| |#2| (QUOTE (-1109))) (|HasCategory| |#2| (LIST (QUOTE -313) (|devaluate| |#2|)))) (|HasCategory| |#2| (QUOTE (-174)))) (-1152 S) ((|constructor| (NIL "A string aggregate is a category for strings,{} that is,{} one dimensional arrays of characters.")) (|elt| (($ $ $) "\\spad{elt(s,t)} returns the concatenation of \\spad{s} and \\spad{t}. It is provided to allow juxtaposition of strings to work as concatenation. For example,{} \\axiom{\"smoo\" \"shed\"} returns \\axiom{\"smooshed\"}.")) (|rightTrim| (($ $ (|CharacterClass|)) "\\spad{rightTrim(s,cc)} returns \\spad{s} with all trailing occurences of characters in \\spad{cc} deleted. For example,{} \\axiom{rightTrim(\"(abc)\",{} charClass \"()\")} returns \\axiom{\"(abc\"}.") (($ $ (|Character|)) "\\spad{rightTrim(s,c)} returns \\spad{s} with all trailing occurrences of \\spad{c} deleted. For example,{} \\axiom{rightTrim(\" abc \",{} char \" \")} returns \\axiom{\" abc\"}.")) (|leftTrim| (($ $ (|CharacterClass|)) "\\spad{leftTrim(s,cc)} returns \\spad{s} with all leading characters in \\spad{cc} deleted. For example,{} \\axiom{leftTrim(\"(abc)\",{} charClass \"()\")} returns \\axiom{\"abc)\"}.") (($ $ (|Character|)) "\\spad{leftTrim(s,c)} returns \\spad{s} with all leading characters \\spad{c} deleted. For example,{} \\axiom{leftTrim(\" abc \",{} char \" \")} returns \\axiom{\"abc \"}.")) (|trim| (($ $ (|CharacterClass|)) "\\spad{trim(s,cc)} returns \\spad{s} with all characters in \\spad{cc} deleted from right and left ends. For example,{} \\axiom{trim(\"(abc)\",{} charClass \"()\")} returns \\axiom{\"abc\"}.") (($ $ (|Character|)) "\\spad{trim(s,c)} returns \\spad{s} with all characters \\spad{c} deleted from right and left ends. For example,{} \\axiom{trim(\" abc \",{} char \" \")} returns \\axiom{\"abc\"}.")) (|split| (((|List| $) $ (|CharacterClass|)) "\\spad{split(s,cc)} returns a list of substrings delimited by characters in \\spad{cc}.") (((|List| $) $ (|Character|)) "\\spad{split(s,c)} returns a list of substrings delimited by character \\spad{c}.")) (|coerce| (($ (|Character|)) "\\spad{coerce(c)} returns \\spad{c} as a string \\spad{s} with the character \\spad{c}.")) (|position| (((|Integer|) (|CharacterClass|) $ (|Integer|)) "\\spad{position(cc,t,i)} returns the position \\axiom{\\spad{j} \\spad{>=} \\spad{i}} in \\spad{t} of the first character belonging to \\spad{cc}.") (((|Integer|) $ $ (|Integer|)) "\\spad{position(s,t,i)} returns the position \\spad{j} of the substring \\spad{s} in string \\spad{t},{} where \\axiom{\\spad{j} \\spad{>=} \\spad{i}} is required.")) (|replace| (($ $ (|UniversalSegment| (|Integer|)) $) "\\spad{replace(s,i..j,t)} replaces the substring \\axiom{\\spad{s}(\\spad{i}..\\spad{j})} of \\spad{s} by string \\spad{t}.")) (|match?| (((|Boolean|) $ $ (|Character|)) "\\spad{match?(s,t,c)} tests if \\spad{s} matches \\spad{t} except perhaps for multiple and consecutive occurrences of character \\spad{c}. Typically \\spad{c} is the blank character.")) (|match| (((|NonNegativeInteger|) $ $ (|Character|)) "\\spad{match(p,s,wc)} tests if pattern \\axiom{\\spad{p}} matches subject \\axiom{\\spad{s}} where \\axiom{\\spad{wc}} is a wild card character. If no match occurs,{} the index \\axiom{0} is returned; otheriwse,{} the value returned is the first index of the first character in the subject matching the subject (excluding that matched by an initial wild-card). For example,{} \\axiom{match(\"*to*\",{}\"yorktown\",{}\\spad{\"*\"})} returns \\axiom{5} indicating a successful match starting at index \\axiom{5} of \\axiom{\"yorktown\"}.")) (|substring?| (((|Boolean|) $ $ (|Integer|)) "\\spad{substring?(s,t,i)} tests if \\spad{s} is a substring of \\spad{t} beginning at index \\spad{i}. Note: \\axiom{substring?(\\spad{s},{}\\spad{t},{}0) = prefix?(\\spad{s},{}\\spad{t})}.")) (|suffix?| (((|Boolean|) $ $) "\\spad{suffix?(s,t)} tests if the string \\spad{s} is the final substring of \\spad{t}. Note: \\axiom{suffix?(\\spad{s},{}\\spad{t}) \\spad{==} reduce(and,{}[\\spad{s}.\\spad{i} = \\spad{t}.(\\spad{n} - \\spad{m} + \\spad{i}) for \\spad{i} in 0..maxIndex \\spad{s}])} where \\spad{m} and \\spad{n} denote the maxIndex of \\spad{s} and \\spad{t} respectively.")) (|prefix?| (((|Boolean|) $ $) "\\spad{prefix?(s,t)} tests if the string \\spad{s} is the initial substring of \\spad{t}. Note: \\axiom{prefix?(\\spad{s},{}\\spad{t}) \\spad{==} reduce(and,{}[\\spad{s}.\\spad{i} = \\spad{t}.\\spad{i} for \\spad{i} in 0..maxIndex \\spad{s}])}.")) (|upperCase!| (($ $) "\\spad{upperCase!(s)} destructively replaces the alphabetic characters in \\spad{s} by upper case characters.")) (|upperCase| (($ $) "\\spad{upperCase(s)} returns the string with all characters in upper case.")) (|lowerCase!| (($ $) "\\spad{lowerCase!(s)} destructively replaces the alphabetic characters in \\spad{s} by lower case.")) (|lowerCase| (($ $) "\\spad{lowerCase(s)} returns the string with all characters in lower case."))) NIL @@ -4555,7 +4555,7 @@ NIL (-1156 S) ((|constructor| (NIL "Linked List implementation of a Stack")) (|stack| (($ (|List| |#1|)) "\\spad{stack([x,y,...,z])} creates a stack with first (top) element \\spad{x},{} second element \\spad{y},{}...,{}and last element \\spad{z}."))) ((-4452 . T) (-4453 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1109))) (-2811 (-12 (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-868))))) (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-868))))) +((-12 (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1109))) (-3684 (-12 (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-868))))) (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-868))))) (-1157 A S) ((|constructor| (NIL "A stream aggregate is a linear aggregate which possibly has an infinite number of elements. A basic domain constructor which builds stream aggregates is \\spadtype{Stream}. From streams,{} a number of infinite structures such power series can be built. A stream aggregate may also be infinite since it may be cyclic. For example,{} see \\spadtype{DecimalExpansion}.")) (|possiblyInfinite?| (((|Boolean|) $) "\\spad{possiblyInfinite?(s)} tests if the stream \\spad{s} could possibly have an infinite number of elements. Note: for many datatypes,{} \\axiom{possiblyInfinite?(\\spad{s}) = not explictlyFinite?(\\spad{s})}.")) (|explicitlyFinite?| (((|Boolean|) $) "\\spad{explicitlyFinite?(s)} tests if the stream has a finite number of elements,{} and \\spad{false} otherwise. Note: for many datatypes,{} \\axiom{explicitlyFinite?(\\spad{s}) = not possiblyInfinite?(\\spad{s})}."))) NIL @@ -4567,7 +4567,7 @@ NIL (-1159 |Key| |Ent| |dent|) ((|constructor| (NIL "A sparse table has a default entry,{} which is returned if no other value has been explicitly stored for a key."))) ((-4453 . T)) -((-12 (|HasCategory| (-2 (|:| -3679 |#1|) (|:| -1409 |#2|)) (QUOTE (-1109))) (|HasCategory| (-2 (|:| -3679 |#1|) (|:| -1409 |#2|)) (LIST (QUOTE -313) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -3679) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -1409) (|devaluate| |#2|)))))) (-2811 (|HasCategory| (-2 (|:| -3679 |#1|) (|:| -1409 |#2|)) (QUOTE (-1109))) (|HasCategory| |#2| (QUOTE (-1109)))) (-2811 (|HasCategory| (-2 (|:| -3679 |#1|) (|:| -1409 |#2|)) (QUOTE (-1109))) (|HasCategory| (-2 (|:| -3679 |#1|) (|:| -1409 |#2|)) (LIST (QUOTE -619) (QUOTE (-868)))) (|HasCategory| |#2| (QUOTE (-1109))) (|HasCategory| |#2| (LIST (QUOTE -619) (QUOTE (-868))))) (|HasCategory| (-2 (|:| -3679 |#1|) (|:| -1409 |#2|)) (LIST (QUOTE -620) (QUOTE (-542)))) (-12 (|HasCategory| |#2| (QUOTE (-1109))) (|HasCategory| |#2| (LIST (QUOTE -313) (|devaluate| |#2|)))) (|HasCategory| |#1| (QUOTE (-856))) (-2811 (|HasCategory| (-2 (|:| -3679 |#1|) (|:| -1409 |#2|)) (LIST (QUOTE -619) (QUOTE (-868)))) (|HasCategory| |#2| (LIST (QUOTE -619) (QUOTE (-868))))) (|HasCategory| |#2| (QUOTE (-1109))) (|HasCategory| |#2| (LIST (QUOTE -619) (QUOTE (-868)))) (|HasCategory| (-2 (|:| -3679 |#1|) (|:| -1409 |#2|)) (LIST (QUOTE -619) (QUOTE (-868)))) (|HasCategory| (-2 (|:| -3679 |#1|) (|:| -1409 |#2|)) (QUOTE (-1109)))) +((-12 (|HasCategory| (-2 (|:| -4111 |#1|) (|:| -3117 |#2|)) (QUOTE (-1109))) (|HasCategory| (-2 (|:| -4111 |#1|) (|:| -3117 |#2|)) (LIST (QUOTE -313) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -4111) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -3117) (|devaluate| |#2|)))))) (-3684 (|HasCategory| (-2 (|:| -4111 |#1|) (|:| -3117 |#2|)) (QUOTE (-1109))) (|HasCategory| |#2| (QUOTE (-1109)))) (-3684 (|HasCategory| (-2 (|:| -4111 |#1|) (|:| -3117 |#2|)) (QUOTE (-1109))) (|HasCategory| (-2 (|:| -4111 |#1|) (|:| -3117 |#2|)) (LIST (QUOTE -619) (QUOTE (-868)))) (|HasCategory| |#2| (QUOTE (-1109))) (|HasCategory| |#2| (LIST (QUOTE -619) (QUOTE (-868))))) (|HasCategory| (-2 (|:| -4111 |#1|) (|:| -3117 |#2|)) (LIST (QUOTE -620) (QUOTE (-542)))) (-12 (|HasCategory| |#2| (QUOTE (-1109))) (|HasCategory| |#2| (LIST (QUOTE -313) (|devaluate| |#2|)))) (|HasCategory| |#1| (QUOTE (-856))) (-3684 (|HasCategory| (-2 (|:| -4111 |#1|) (|:| -3117 |#2|)) (LIST (QUOTE -619) (QUOTE (-868)))) (|HasCategory| |#2| (LIST (QUOTE -619) (QUOTE (-868))))) (|HasCategory| |#2| (QUOTE (-1109))) (|HasCategory| |#2| (LIST (QUOTE -619) (QUOTE (-868)))) (|HasCategory| (-2 (|:| -4111 |#1|) (|:| -3117 |#2|)) (LIST (QUOTE -619) (QUOTE (-868)))) (|HasCategory| (-2 (|:| -4111 |#1|) (|:| -3117 |#2|)) (QUOTE (-1109)))) (-1160) ((|constructor| (NIL "This domain represents an arithmetic progression iterator syntax.")) (|step| (((|SpadAst|) $) "\\spad{step(i)} returns the Spad AST denoting the step of the arithmetic progression represented by the iterator \\spad{i}.")) (|upperBound| (((|Maybe| (|SpadAst|)) $) "If the set of values assumed by the iteration variable is bounded from above,{} \\spad{upperBound(i)} returns the upper bound. Otherwise,{} its returns \\spad{nothing}.")) (|lowerBound| (((|SpadAst|) $) "\\spad{lowerBound(i)} returns the lower bound on the values assumed by the iteration variable.")) (|iterationVar| (((|Identifier|) $) "\\spad{iterationVar(i)} returns the name of the iterating variable of the arithmetic progression iterator \\spad{i}."))) NIL @@ -4595,7 +4595,7 @@ NIL (-1166 S) ((|constructor| (NIL "A stream is an implementation of an infinite sequence using a list of terms that have been computed and a function closure to compute additional terms when needed.")) (|filterUntil| (($ (|Mapping| (|Boolean|) |#1|) $) "\\spad{filterUntil(p,s)} returns \\spad{[x0,x1,...,x(n)]} where \\spad{s = [x0,x1,x2,..]} and \\spad{n} is the smallest index such that \\spad{p(xn) = true}.")) (|filterWhile| (($ (|Mapping| (|Boolean|) |#1|) $) "\\spad{filterWhile(p,s)} returns \\spad{[x0,x1,...,x(n-1)]} where \\spad{s = [x0,x1,x2,..]} and \\spad{n} is the smallest index such that \\spad{p(xn) = false}.")) (|generate| (($ (|Mapping| |#1| |#1|) |#1|) "\\spad{generate(f,x)} creates an infinite stream whose first element is \\spad{x} and whose \\spad{n}th element (\\spad{n > 1}) is \\spad{f} applied to the previous element. Note: \\spad{generate(f,x) = [x,f(x),f(f(x)),...]}.") (($ (|Mapping| |#1|)) "\\spad{generate(f)} creates an infinite stream all of whose elements are equal to \\spad{f()}. Note: \\spad{generate(f) = [f(),f(),f(),...]}.")) (|setrest!| (($ $ (|Integer|) $) "\\spad{setrest!(x,n,y)} sets rest(\\spad{x},{}\\spad{n}) to \\spad{y}. The function will expand cycles if necessary.")) (|showAll?| (((|Boolean|)) "\\spad{showAll?()} returns \\spad{true} if all computed entries of streams will be displayed.")) (|showAllElements| (((|OutputForm|) $) "\\spad{showAllElements(s)} creates an output form which displays all computed elements.")) (|output| (((|Void|) (|Integer|) $) "\\spad{output(n,st)} computes and displays the first \\spad{n} entries of \\spad{st}.")) (|cons| (($ |#1| $) "\\spad{cons(a,s)} returns a stream whose \\spad{first} is \\spad{a} and whose \\spad{rest} is \\spad{s}. Note: \\spad{cons(a,s) = concat(a,s)}.")) (|delay| (($ (|Mapping| $)) "\\spad{delay(f)} creates a stream with a lazy evaluation defined by function \\spad{f}. Caution: This function can only be called in compiled code.")) (|findCycle| (((|Record| (|:| |cycle?| (|Boolean|)) (|:| |prefix| (|NonNegativeInteger|)) (|:| |period| (|NonNegativeInteger|))) (|NonNegativeInteger|) $) "\\spad{findCycle(n,st)} determines if \\spad{st} is periodic within \\spad{n}.")) (|repeating?| (((|Boolean|) (|List| |#1|) $) "\\spad{repeating?(l,s)} returns \\spad{true} if a stream \\spad{s} is periodic with period \\spad{l},{} and \\spad{false} otherwise.")) (|repeating| (($ (|List| |#1|)) "\\spad{repeating(l)} is a repeating stream whose period is the list \\spad{l}.")) (|shallowlyMutable| ((|attribute|) "one may destructively alter a stream by assigning new values to its entries."))) ((-4453 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1109))) (-2811 (-12 (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-868))))) (|HasCategory| |#1| (LIST (QUOTE -620) (QUOTE (-542)))) (|HasCategory| (-570) (QUOTE (-856))) (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-868))))) +((-12 (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1109))) (-3684 (-12 (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-868))))) (|HasCategory| |#1| (LIST (QUOTE -620) (QUOTE (-542)))) (|HasCategory| (-570) (QUOTE (-856))) (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-868))))) (-1167) ((|constructor| (NIL "A category for string-like objects")) (|string| (($ (|Integer|)) "\\spad{string(i)} returns the decimal representation of \\spad{i} in a string"))) ((-4453 . T) (-4452 . T)) @@ -4603,11 +4603,11 @@ NIL (-1168) NIL ((-4453 . T) (-4452 . T)) -((-2811 (-12 (|HasCategory| (-145) (QUOTE (-856))) (|HasCategory| (-145) (LIST (QUOTE -313) (QUOTE (-145))))) (-12 (|HasCategory| (-145) (QUOTE (-1109))) (|HasCategory| (-145) (LIST (QUOTE -313) (QUOTE (-145)))))) (|HasCategory| (-145) (LIST (QUOTE -620) (QUOTE (-542)))) (|HasCategory| (-145) (QUOTE (-856))) (|HasCategory| (-570) (QUOTE (-856))) (|HasCategory| (-145) (QUOTE (-1109))) (|HasCategory| (-145) (LIST (QUOTE -619) (QUOTE (-868)))) (-12 (|HasCategory| (-145) (QUOTE (-1109))) (|HasCategory| (-145) (LIST (QUOTE -313) (QUOTE (-145)))))) +((-3684 (-12 (|HasCategory| (-145) (QUOTE (-856))) (|HasCategory| (-145) (LIST (QUOTE -313) (QUOTE (-145))))) (-12 (|HasCategory| (-145) (QUOTE (-1109))) (|HasCategory| (-145) (LIST (QUOTE -313) (QUOTE (-145)))))) (|HasCategory| (-145) (LIST (QUOTE -620) (QUOTE (-542)))) (|HasCategory| (-145) (QUOTE (-856))) (|HasCategory| (-570) (QUOTE (-856))) (|HasCategory| (-145) (QUOTE (-1109))) (|HasCategory| (-145) (LIST (QUOTE -619) (QUOTE (-868)))) (-12 (|HasCategory| (-145) (QUOTE (-1109))) (|HasCategory| (-145) (LIST (QUOTE -313) (QUOTE (-145)))))) (-1169 |Entry|) ((|constructor| (NIL "This domain provides tables where the keys are strings. A specialized hash function for strings is used."))) ((-4452 . T) (-4453 . 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(|power| (((|Stream| |#1|) |#1| (|Stream| |#1|)) "\\spad{power(a,f)} returns the power series \\spad{f} raised to the power \\spad{a}.")) (|lazyGintegrate| (((|Stream| |#1|) (|Mapping| |#1| (|Integer|)) |#1| (|Mapping| (|Stream| |#1|))) "\\spad{lazyGintegrate(f,r,g)} is used for fixed point computations.")) (|mapdiv| (((|Stream| |#1|) (|Stream| |#1|) (|Stream| |#1|)) "\\spad{mapdiv([a0,a1,..],[b0,b1,..])} returns \\spad{[a0/b0,a1/b1,..]}.")) (|powern| (((|Stream| |#1|) (|Fraction| (|Integer|)) (|Stream| |#1|)) "\\spad{powern(r,f)} raises power series \\spad{f} to the power \\spad{r}.")) (|nlde| (((|Stream| |#1|) (|Stream| (|Stream| |#1|))) "\\spad{nlde(u)} solves a first order non-linear differential equation described by \\spad{u} of the form \\spad{[[b<0,0>,b<0,1>,...],[b<1,0>,b<1,1>,.],...]}. the differential equation has the form \\spad{y' = sum(i=0 to infinity,j=0 to infinity,b<i,j>*(x**i)*(y**j))}.")) (|lazyIntegrate| (((|Stream| |#1|) |#1| (|Mapping| (|Stream| |#1|))) "\\spad{lazyIntegrate(r,f)} is a local function used for fixed point computations.")) (|integrate| (((|Stream| |#1|) |#1| (|Stream| |#1|)) "\\spad{integrate(r,a)} returns the integral of the power series \\spad{a} with respect to the power series variableintegration where \\spad{r} denotes the constant of integration. Thus \\spad{integrate(a,[a0,a1,a2,...]) = [a,a0,a1/2,a2/3,...]}.")) (|invmultisect| (((|Stream| |#1|) (|Integer|) (|Integer|) (|Stream| |#1|)) "\\spad{invmultisect(a,b,st)} substitutes \\spad{x**((a+b)*n)} for \\spad{x**n} and multiplies by \\spad{x**b}.")) (|multisect| (((|Stream| |#1|) (|Integer|) (|Integer|) (|Stream| |#1|)) "\\spad{multisect(a,b,st)} selects the coefficients of \\spad{x**((a+b)*n+a)},{} and changes them to \\spad{x**n}.")) (|generalLambert| (((|Stream| |#1|) (|Stream| |#1|) (|Integer|) (|Integer|)) "\\spad{generalLambert(f(x),a,d)} returns \\spad{f(x**a) + f(x**(a + d)) + f(x**(a + 2 d)) + ...}. \\spad{f(x)} should have zero constant coefficient and \\spad{a} and \\spad{d} should be positive.")) (|evenlambert| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{evenlambert(st)} computes \\spad{f(x**2) + f(x**4) + f(x**6) + ...} if \\spad{st} is a stream representing \\spad{f(x)}. This function is used for computing infinite products. If \\spad{f(x)} is a power series with constant coefficient 1,{} then \\spad{prod(f(x**(2*n)),n=1..infinity) = exp(evenlambert(log(f(x))))}.")) (|oddlambert| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{oddlambert(st)} computes \\spad{f(x) + f(x**3) + f(x**5) + ...} if \\spad{st} is a stream representing \\spad{f(x)}. This function is used for computing infinite products. If \\spad{f}(\\spad{x}) is a power series with constant coefficient 1 then \\spad{prod(f(x**(2*n-1)),n=1..infinity) = exp(oddlambert(log(f(x))))}.")) (|lambert| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{lambert(st)} computes \\spad{f(x) + f(x**2) + f(x**3) + ...} if \\spad{st} is a stream representing \\spad{f(x)}. This function is used for computing infinite products. If \\spad{f(x)} is a power series with constant coefficient 1 then \\spad{prod(f(x**n),n = 1..infinity) = exp(lambert(log(f(x))))}.")) (|addiag| (((|Stream| |#1|) (|Stream| (|Stream| |#1|))) "\\spad{addiag(x)} performs diagonal addition of a stream of streams. if \\spad{x} = \\spad{[[a<0,0>,a<0,1>,..],[a<1,0>,a<1,1>,..],[a<2,0>,a<2,1>,..],..]} and \\spad{addiag(x) = [b<0,b<1>,...], then b<k> = sum(i+j=k,a<i,j>)}.")) (|revert| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{revert(a)} computes the inverse of a power series \\spad{a} with respect to composition. the series should have constant coefficient 0 and first order coefficient should be invertible.")) (|lagrange| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{lagrange(g)} produces the power series for \\spad{f} where \\spad{f} is implicitly defined as \\spad{f(z) = z*g(f(z))}.")) (|compose| (((|Stream| |#1|) (|Stream| |#1|) (|Stream| |#1|)) "\\spad{compose(a,b)} composes the power series \\spad{a} with the power series \\spad{b}.")) (|eval| (((|Stream| |#1|) (|Stream| |#1|) |#1|) "\\spad{eval(a,r)} returns a stream of partial sums of the power series \\spad{a} evaluated at the power series variable equal to \\spad{r}.")) (|coerce| (((|Stream| |#1|) |#1|) "\\spad{coerce(r)} converts a ring element \\spad{r} to a stream with one element.")) (|gderiv| (((|Stream| |#1|) (|Mapping| |#1| (|Integer|)) (|Stream| |#1|)) "\\spad{gderiv(f,[a0,a1,a2,..])} returns \\spad{[f(0)*a0,f(1)*a1,f(2)*a2,..]}.")) (|deriv| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{deriv(a)} returns the derivative of the power series with respect to the power series variable. Thus \\spad{deriv([a0,a1,a2,...])} returns \\spad{[a1,2 a2,3 a3,...]}.")) (|mapmult| (((|Stream| |#1|) (|Stream| |#1|) (|Stream| |#1|)) "\\spad{mapmult([a0,a1,..],[b0,b1,..])} returns \\spad{[a0*b0,a1*b1,..]}.")) (|int| (((|Stream| |#1|) |#1|) "\\spad{int(r)} returns [\\spad{r},{}\\spad{r+1},{}\\spad{r+2},{}...],{} where \\spad{r} is a ring element.")) (|oddintegers| (((|Stream| (|Integer|)) (|Integer|)) "\\spad{oddintegers(n)} returns \\spad{[n,n+2,n+4,...]}.")) (|integers| (((|Stream| (|Integer|)) (|Integer|)) "\\spad{integers(n)} returns \\spad{[n,n+1,n+2,...]}.")) (|monom| (((|Stream| |#1|) |#1| (|Integer|)) "\\spad{monom(deg,coef)} is a monomial of degree \\spad{deg} with coefficient \\spad{coef}.")) (|recip| (((|Union| (|Stream| |#1|) "failed") (|Stream| |#1|)) "\\spad{recip(a)} returns the power series reciprocal of \\spad{a},{} or \"failed\" if not possible.")) (/ (((|Stream| |#1|) (|Stream| |#1|) (|Stream| |#1|)) "\\spad{a / b} returns the power series quotient of \\spad{a} by \\spad{b}. An error message is returned if \\spad{b} is not invertible. This function is used in fixed point computations.")) (|exquo| (((|Union| (|Stream| |#1|) "failed") (|Stream| |#1|) (|Stream| |#1|)) "\\spad{exquo(a,b)} returns the power series quotient of \\spad{a} by \\spad{b},{} if the quotient exists,{} and \"failed\" otherwise")) (* (((|Stream| |#1|) (|Stream| |#1|) |#1|) "\\spad{a * r} returns the power series scalar multiplication of \\spad{a} by \\spad{r:} \\spad{[a0,a1,...] * r = [a0 * r,a1 * r,...]}") (((|Stream| |#1|) |#1| (|Stream| |#1|)) "\\spad{r * a} returns the power series scalar multiplication of \\spad{r} by \\spad{a}: \\spad{r * [a0,a1,...] = [r * a0,r * a1,...]}") (((|Stream| |#1|) (|Stream| |#1|) (|Stream| |#1|)) "\\spad{a * b} returns the power series (Cauchy) product of \\spad{a} and \\spad{b:} \\spad{[a0,a1,...] * [b0,b1,...] = [c0,c1,...]} where \\spad{ck = sum(i + j = k,ai * bk)}.")) (- (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{- a} returns the power series negative of \\spad{a}: \\spad{- [a0,a1,...] = [- a0,- a1,...]}") (((|Stream| |#1|) (|Stream| |#1|) (|Stream| |#1|)) "\\spad{a - b} returns the power series difference of \\spad{a} and \\spad{b}: \\spad{[a0,a1,..] - [b0,b1,..] = [a0 - b0,a1 - b1,..]}")) (+ (((|Stream| |#1|) (|Stream| |#1|) (|Stream| |#1|)) "\\spad{a + b} returns the power series sum of \\spad{a} and \\spad{b}: \\spad{[a0,a1,..] + [b0,b1,..] = [a0 + b0,a1 + b1,..]}"))) NIL @@ -4638,9 +4638,9 @@ NIL NIL (-1177 |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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(|HasCategory| |#1| (QUOTE (-368))) (|HasCategory| |#1| (QUOTE (-458))) (|HasCategory| |#1| (QUOTE (-916)))) (|HasCategory| |#1| (QUOTE (-368))) (|HasCategory| |#1| (QUOTE (-1161))) (|HasCategory| |#1| (LIST (QUOTE -907) (QUOTE (-1186)))) (|HasCategory| |#1| (QUOTE (-235))) (|HasAttribute| |#1| (QUOTE -4450)) (|HasCategory| |#1| (QUOTE (-458))) (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-916)))) (-3684 (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-916)))) (|HasCategory| |#1| (QUOTE (-146))))) (-1183 |Coef| |var| |cen|) ((|constructor| (NIL "Sparse Puiseux series in one variable \\indented{2}{\\spadtype{SparseUnivariatePuiseuxSeries} is a domain representing Puiseux} \\indented{2}{series in one variable with coefficients in an arbitrary ring.\\space{2}The} \\indented{2}{parameters of the type specify the coefficient ring,{} the power series} \\indented{2}{variable,{} and the center of the power series expansion.\\space{2}For example,{}} \\indented{2}{\\spad{SparseUnivariatePuiseuxSeries(Integer,x,3)} represents Puiseux} \\indented{2}{series in \\spad{(x - 3)} with \\spadtype{Integer} coefficients.}")) (|integrate| (($ $ (|Variable| |#2|)) "\\spad{integrate(f(x))} returns an anti-derivative of the power series \\spad{f(x)} with constant coefficient 0. We may integrate a series when we can divide coefficients by integers.")) (|differentiate| (($ $ (|Variable| |#2|)) "\\spad{differentiate(f(x),x)} returns the derivative of \\spad{f(x)} with respect to \\spad{x}."))) (((-4454 "*") |has| |#1| (-174)) (-4445 |has| |#1| (-562)) (-4450 |has| |#1| (-368)) (-4444 |has| |#1| (-368)) (-4446 . T) (-4447 . T) (-4449 . T)) -((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasCategory| |#1| (QUOTE (-562))) (|HasCategory| |#1| (QUOTE (-174))) (-2811 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-562)))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-148))) (-12 (|HasCategory| |#1| (LIST (QUOTE -907) (QUOTE (-1186)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -413) (QUOTE (-570))) (|devaluate| |#1|))))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -413) (QUOTE (-570))) (|devaluate| |#1|)))) (|HasCategory| (-413 (-570)) (QUOTE (-1121))) (|HasCategory| |#1| (QUOTE (-368))) (-2811 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-368))) (|HasCategory| |#1| (QUOTE (-562)))) (-2811 (|HasCategory| |#1| (QUOTE (-368))) (|HasCategory| |#1| (QUOTE (-562)))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -413) (QUOTE (-570)))))) (|HasSignature| |#1| (LIST (QUOTE -2940) (LIST (|devaluate| |#1|) (QUOTE (-1186)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -413) (QUOTE (-570)))))) (-2811 (-12 (|HasCategory| |#1| (LIST (QUOTE -29) (QUOTE (-570)))) (|HasCategory| |#1| (QUOTE (-966))) (|HasCategory| |#1| (QUOTE (-1212))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -413) (QUOTE (-570)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasSignature| |#1| (LIST (QUOTE -3655) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1186))))) (|HasSignature| |#1| (LIST (QUOTE -2421) (LIST (LIST (QUOTE -650) (QUOTE (-1186))) (|devaluate| |#1|))))))) +((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasCategory| |#1| (QUOTE (-562))) (|HasCategory| |#1| (QUOTE (-174))) (-3684 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-562)))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-148))) (-12 (|HasCategory| |#1| (LIST (QUOTE -907) (QUOTE (-1186)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -413) (QUOTE (-570))) (|devaluate| |#1|))))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -413) (QUOTE (-570))) (|devaluate| |#1|)))) (|HasCategory| (-413 (-570)) (QUOTE (-1121))) (|HasCategory| |#1| (QUOTE (-368))) (-3684 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-368))) (|HasCategory| |#1| (QUOTE (-562)))) (-3684 (|HasCategory| |#1| (QUOTE (-368))) (|HasCategory| |#1| (QUOTE (-562)))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -413) (QUOTE (-570)))))) (|HasSignature| |#1| (LIST (QUOTE -2838) (LIST (|devaluate| |#1|) (QUOTE (-1186)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -413) (QUOTE (-570)))))) (-3684 (-12 (|HasCategory| |#1| (LIST (QUOTE -29) (QUOTE (-570)))) (|HasCategory| |#1| (QUOTE (-966))) (|HasCategory| |#1| (QUOTE (-1212))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -413) (QUOTE (-570)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasSignature| |#1| (LIST (QUOTE -2502) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1186))))) (|HasSignature| |#1| (LIST (QUOTE -1624) (LIST (LIST (QUOTE -650) (QUOTE (-1186))) (|devaluate| |#1|))))))) (-1184 |Coef| |var| |cen|) ((|constructor| (NIL "Sparse Taylor series in one variable \\indented{2}{\\spadtype{SparseUnivariateTaylorSeries} is a domain representing Taylor} \\indented{2}{series in one variable with coefficients in an arbitrary ring.\\space{2}The} \\indented{2}{parameters of the type specify the coefficient ring,{} the power series} \\indented{2}{variable,{} and the center of the power series expansion.\\space{2}For example,{}} \\indented{2}{\\spadtype{SparseUnivariateTaylorSeries}(Integer,{}\\spad{x},{}3) represents Taylor} \\indented{2}{series in \\spad{(x - 3)} with \\spadtype{Integer} coefficients.}")) (|integrate| (($ $ (|Variable| |#2|)) "\\spad{integrate(f(x),x)} returns an anti-derivative of the power series \\spad{f(x)} with constant coefficient 0. We may integrate a series when we can divide coefficients by integers.")) (|differentiate| (($ $ (|Variable| |#2|)) "\\spad{differentiate(f(x),x)} computes the derivative of \\spad{f(x)} with respect to \\spad{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}."))) (((-4454 "*") |has| |#1| (-174)) (-4445 |has| |#1| (-562)) (-4446 . T) (-4447 . T) (-4449 . T)) -((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasCategory| |#1| (QUOTE (-562))) (-2811 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-562)))) (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-148))) (-12 (|HasCategory| |#1| (LIST (QUOTE -907) (QUOTE (-1186)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (QUOTE (-777)) (|devaluate| |#1|))))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (QUOTE (-777)) (|devaluate| |#1|)))) (|HasCategory| (-777) (QUOTE (-1121))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-777))))) (|HasSignature| |#1| (LIST (QUOTE -2940) (LIST (|devaluate| |#1|) (QUOTE (-1186)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-777))))) (|HasCategory| |#1| (QUOTE (-368))) (-2811 (-12 (|HasCategory| |#1| (LIST (QUOTE -29) (QUOTE (-570)))) (|HasCategory| |#1| (QUOTE (-966))) (|HasCategory| |#1| (QUOTE (-1212))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -413) (QUOTE (-570)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasSignature| |#1| (LIST (QUOTE -3655) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1186))))) (|HasSignature| |#1| (LIST (QUOTE -2421) (LIST (LIST (QUOTE -650) (QUOTE (-1186))) (|devaluate| |#1|))))))) +((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasCategory| |#1| (QUOTE (-562))) (-3684 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-562)))) (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-148))) (-12 (|HasCategory| |#1| (LIST (QUOTE -907) (QUOTE (-1186)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (QUOTE (-777)) (|devaluate| |#1|))))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (QUOTE (-777)) (|devaluate| |#1|)))) (|HasCategory| (-777) (QUOTE (-1121))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-777))))) (|HasSignature| |#1| (LIST (QUOTE -2838) (LIST (|devaluate| |#1|) (QUOTE (-1186)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-777))))) (|HasCategory| |#1| (QUOTE (-368))) (-3684 (-12 (|HasCategory| |#1| (LIST (QUOTE -29) (QUOTE (-570)))) (|HasCategory| |#1| (QUOTE (-966))) (|HasCategory| |#1| (QUOTE (-1212))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -413) (QUOTE (-570)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasSignature| |#1| (LIST (QUOTE -2502) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1186))))) (|HasSignature| |#1| (LIST (QUOTE -1624) (LIST (LIST (QUOTE -650) (QUOTE (-1186))) (|devaluate| |#1|))))))) (-1185) ((|constructor| (NIL "This domain builds representations of boolean expressions for use with the \\axiomType{FortranCode} domain.")) (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 @@ -4683,7 +4683,7 @@ NIL (-1188 R) ((|constructor| (NIL "This domain implements symmetric polynomial"))) (((-4454 "*") |has| |#1| (-174)) (-4445 |has| |#1| (-562)) (-4450 |has| |#1| (-6 -4450)) (-4446 . T) (-4447 . T) (-4449 . T)) -((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasCategory| |#1| (QUOTE (-562))) (-2811 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-562)))) (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-148))) (-2811 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasCategory| |#1| (LIST (QUOTE -1047) (LIST (QUOTE -413) (QUOTE (-570)))))) (|HasCategory| |#1| (LIST (QUOTE -1047) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasCategory| |#1| (LIST (QUOTE -1047) (QUOTE (-570)))) (|HasCategory| |#1| (QUOTE (-368))) (|HasCategory| |#1| (QUOTE (-458))) (-12 (|HasCategory| (-980) (QUOTE (-132))) (|HasCategory| |#1| (QUOTE (-562)))) (|HasAttribute| |#1| (QUOTE -4450))) +((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasCategory| |#1| (QUOTE (-562))) (-3684 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-562)))) (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-148))) (-3684 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasCategory| |#1| (LIST (QUOTE -1047) (LIST (QUOTE -413) (QUOTE (-570)))))) (|HasCategory| |#1| (LIST (QUOTE -1047) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasCategory| |#1| (LIST (QUOTE -1047) (QUOTE (-570)))) (|HasCategory| |#1| (QUOTE (-368))) (|HasCategory| |#1| (QUOTE (-458))) (-12 (|HasCategory| (-980) (QUOTE (-132))) (|HasCategory| |#1| (QUOTE (-562)))) (|HasAttribute| |#1| (QUOTE -4450))) (-1189) ((|constructor| (NIL "Creates and manipulates one global symbol table for FORTRAN code generation,{} containing details of types,{} dimensions,{} and argument lists.")) (|symbolTableOf| (((|SymbolTable|) (|Symbol|) $) "\\spad{symbolTableOf(f,tab)} returns the symbol table of \\spad{f}")) (|argumentListOf| (((|List| (|Symbol|)) (|Symbol|) $) "\\spad{argumentListOf(f,tab)} returns the argument list of \\spad{f}")) (|returnTypeOf| (((|Union| (|:| |fst| (|FortranScalarType|)) (|:| |void| "void")) (|Symbol|) $) "\\spad{returnTypeOf(f,tab)} returns the type of the object returned by \\spad{f}")) (|empty| (($) "\\spad{empty()} creates a new,{} empty symbol table.")) (|printTypes| (((|Void|) (|Symbol|)) "\\spad{printTypes(tab)} produces FORTRAN type declarations from \\spad{tab},{} on the current FORTRAN output stream")) (|printHeader| (((|Void|)) "\\spad{printHeader()} produces the FORTRAN header for the current subprogram in the global symbol table on the current FORTRAN output stream.") (((|Void|) (|Symbol|)) "\\spad{printHeader(f)} produces the FORTRAN header for subprogram \\spad{f} in the global symbol table on the current FORTRAN output stream.") (((|Void|) (|Symbol|) $) "\\spad{printHeader(f,tab)} produces the FORTRAN header for subprogram \\spad{f} in symbol table \\spad{tab} on the current FORTRAN output stream.")) (|returnType!| (((|Void|) (|Union| (|:| |fst| (|FortranScalarType|)) (|:| |void| "void"))) "\\spad{returnType!(t)} declares that the return type of he current subprogram in the global symbol table is \\spad{t}.") (((|Void|) (|Symbol|) (|Union| (|:| |fst| (|FortranScalarType|)) (|:| |void| "void"))) "\\spad{returnType!(f,t)} declares that the return type of subprogram \\spad{f} in the global symbol table is \\spad{t}.") (((|Void|) (|Symbol|) (|Union| (|:| |fst| (|FortranScalarType|)) (|:| |void| "void")) $) "\\spad{returnType!(f,t,tab)} declares that the return type of subprogram \\spad{f} in symbol table \\spad{tab} is \\spad{t}.")) (|argumentList!| (((|Void|) (|List| (|Symbol|))) "\\spad{argumentList!(l)} declares that the argument list for the current subprogram in the global symbol table is \\spad{l}.") (((|Void|) (|Symbol|) (|List| (|Symbol|))) "\\spad{argumentList!(f,l)} declares that the argument list for subprogram \\spad{f} in the global symbol table is \\spad{l}.") (((|Void|) (|Symbol|) (|List| (|Symbol|)) $) "\\spad{argumentList!(f,l,tab)} declares that the argument list for subprogram \\spad{f} in symbol table \\spad{tab} is \\spad{l}.")) (|endSubProgram| (((|Symbol|)) "\\spad{endSubProgram()} asserts that we are no longer processing the current subprogram.")) (|currentSubProgram| (((|Symbol|)) "\\spad{currentSubProgram()} returns the name of the current subprogram being processed")) (|newSubProgram| (((|Void|) (|Symbol|)) "\\spad{newSubProgram(f)} asserts that from now on type declarations are part of subprogram \\spad{f}.")) (|declare!| (((|FortranType|) (|Symbol|) (|FortranType|) (|Symbol|)) "\\spad{declare!(u,t,asp)} declares the parameter \\spad{u} to have type \\spad{t} in \\spad{asp}.") (((|FortranType|) (|Symbol|) (|FortranType|)) "\\spad{declare!(u,t)} declares the parameter \\spad{u} to have type \\spad{t} in the current level of the symbol table.") (((|FortranType|) (|List| (|Symbol|)) (|FortranType|) (|Symbol|) $) "\\spad{declare!(u,t,asp,tab)} declares the parameters \\spad{u} of subprogram \\spad{asp} to have type \\spad{t} in symbol table \\spad{tab}.") (((|FortranType|) (|Symbol|) (|FortranType|) (|Symbol|) $) "\\spad{declare!(u,t,asp,tab)} declares the parameter \\spad{u} of subprogram \\spad{asp} to have type \\spad{t} in symbol table \\spad{tab}.")) (|clearTheSymbolTable| (((|Void|) (|Symbol|)) "\\spad{clearTheSymbolTable(x)} removes the symbol \\spad{x} from the table") (((|Void|)) "\\spad{clearTheSymbolTable()} clears the current symbol table.")) (|showTheSymbolTable| (($) "\\spad{showTheSymbolTable()} returns the current symbol table."))) NIL @@ -4727,7 +4727,7 @@ NIL (-1199 |Key| |Entry|) ((|constructor| (NIL "This is the general purpose table type. The keys are hashed to look up the entries. This creates a \\spadtype{HashTable} if equal for the Key domain is consistent with Lisp EQUAL otherwise an \\spadtype{AssociationList}"))) ((-4452 . T) (-4453 . T)) -((-12 (|HasCategory| (-2 (|:| -3679 |#1|) (|:| -1409 |#2|)) (QUOTE (-1109))) (|HasCategory| (-2 (|:| -3679 |#1|) (|:| -1409 |#2|)) (LIST (QUOTE -313) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -3679) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -1409) (|devaluate| |#2|)))))) (-2811 (|HasCategory| (-2 (|:| -3679 |#1|) (|:| -1409 |#2|)) (QUOTE (-1109))) (|HasCategory| |#2| (QUOTE (-1109)))) (-2811 (|HasCategory| (-2 (|:| -3679 |#1|) (|:| -1409 |#2|)) (QUOTE (-1109))) (|HasCategory| (-2 (|:| -3679 |#1|) (|:| -1409 |#2|)) (LIST (QUOTE -619) (QUOTE (-868)))) (|HasCategory| |#2| (QUOTE (-1109))) (|HasCategory| |#2| (LIST (QUOTE -619) (QUOTE (-868))))) (|HasCategory| (-2 (|:| -3679 |#1|) (|:| -1409 |#2|)) (LIST (QUOTE -620) (QUOTE (-542)))) (-12 (|HasCategory| |#2| (QUOTE (-1109))) (|HasCategory| |#2| (LIST (QUOTE -313) (|devaluate| |#2|)))) (|HasCategory| (-2 (|:| -3679 |#1|) (|:| -1409 |#2|)) (QUOTE (-1109))) (|HasCategory| |#1| (QUOTE (-856))) (|HasCategory| |#2| (QUOTE (-1109))) (-2811 (|HasCategory| (-2 (|:| -3679 |#1|) (|:| -1409 |#2|)) (LIST (QUOTE -619) (QUOTE (-868)))) (|HasCategory| |#2| (LIST (QUOTE -619) (QUOTE (-868))))) (|HasCategory| |#2| (LIST (QUOTE -619) (QUOTE (-868)))) (|HasCategory| (-2 (|:| -3679 |#1|) (|:| -1409 |#2|)) (LIST (QUOTE -619) (QUOTE (-868))))) +((-12 (|HasCategory| (-2 (|:| -4111 |#1|) (|:| -3117 |#2|)) (QUOTE (-1109))) (|HasCategory| (-2 (|:| -4111 |#1|) (|:| -3117 |#2|)) (LIST (QUOTE -313) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -4111) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -3117) (|devaluate| |#2|)))))) (-3684 (|HasCategory| (-2 (|:| -4111 |#1|) (|:| -3117 |#2|)) (QUOTE (-1109))) (|HasCategory| |#2| (QUOTE (-1109)))) (-3684 (|HasCategory| (-2 (|:| -4111 |#1|) (|:| -3117 |#2|)) (QUOTE (-1109))) (|HasCategory| (-2 (|:| -4111 |#1|) (|:| -3117 |#2|)) (LIST (QUOTE -619) (QUOTE (-868)))) (|HasCategory| |#2| (QUOTE (-1109))) (|HasCategory| |#2| (LIST (QUOTE -619) (QUOTE (-868))))) (|HasCategory| (-2 (|:| -4111 |#1|) (|:| -3117 |#2|)) (LIST (QUOTE -620) (QUOTE (-542)))) (-12 (|HasCategory| |#2| (QUOTE (-1109))) (|HasCategory| |#2| (LIST (QUOTE -313) (|devaluate| |#2|)))) (|HasCategory| (-2 (|:| -4111 |#1|) (|:| -3117 |#2|)) (QUOTE (-1109))) (|HasCategory| |#1| (QUOTE (-856))) (|HasCategory| |#2| (QUOTE (-1109))) (-3684 (|HasCategory| (-2 (|:| -4111 |#1|) (|:| -3117 |#2|)) (LIST (QUOTE -619) (QUOTE (-868)))) (|HasCategory| |#2| (LIST (QUOTE -619) (QUOTE (-868))))) (|HasCategory| |#2| (LIST (QUOTE -619) (QUOTE (-868)))) (|HasCategory| (-2 (|:| -4111 |#1|) (|:| -3117 |#2|)) (LIST (QUOTE -619) (QUOTE (-868))))) (-1200 S) ((|constructor| (NIL "\\indented{1}{Author: Gabriel Dos Reis} Date Created: April 17,{} 2010 Date Last Modified: April 17,{} 2010")) (|operator| (($ |#1| (|Arity|)) "\\spad{operator(n,a)} returns an operator named \\spad{n} and with arity \\spad{a}."))) NIL @@ -4783,7 +4783,7 @@ NIL (-1213 S) ((|constructor| (NIL "\\spadtype{Tree(S)} is a basic domains of tree structures. Each tree is either empty or else is a {\\it node} consisting of a value and a list of (sub)trees.")) (|cyclicParents| (((|List| $) $) "\\spad{cyclicParents(t)} returns a list of cycles that are parents of \\spad{t}.")) (|cyclicEqual?| (((|Boolean|) $ $) "\\spad{cyclicEqual?(t1, t2)} tests of two cyclic trees have the same structure.")) (|cyclicEntries| (((|List| $) $) "\\spad{cyclicEntries(t)} returns a list of top-level cycles in tree \\spad{t}.")) (|cyclicCopy| (($ $) "\\spad{cyclicCopy(l)} makes a copy of a (possibly) cyclic tree \\spad{l}.")) (|cyclic?| (((|Boolean|) $) "\\spad{cyclic?(t)} tests if \\spad{t} is a cyclic tree.")) (|tree| (($ |#1|) "\\spad{tree(nd)} creates a tree with value \\spad{nd},{} and no children") (($ (|List| |#1|)) "\\spad{tree(ls)} creates a tree from a list of elements of \\spad{s}.") (($ |#1| (|List| $)) "\\spad{tree(nd,ls)} creates a tree with value \\spad{nd},{} and children \\spad{ls}."))) ((-4453 . T) (-4452 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1109))) (-2811 (-12 (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-868))))) (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-868))))) +((-12 (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1109))) (-3684 (-12 (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-868))))) (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-868))))) (-1214 S) ((|constructor| (NIL "Category for the trigonometric functions.")) (|tan| (($ $) "\\spad{tan(x)} returns the tangent of \\spad{x}.")) (|sin| (($ $) "\\spad{sin(x)} returns the sine of \\spad{x}.")) (|sec| (($ $) "\\spad{sec(x)} returns the secant of \\spad{x}.")) (|csc| (($ $) "\\spad{csc(x)} returns the cosecant of \\spad{x}.")) (|cot| (($ $) "\\spad{cot(x)} returns the cotangent of \\spad{x}.")) (|cos| (($ $) "\\spad{cos(x)} returns the cosine of \\spad{x}."))) NIL @@ -4792,7 +4792,7 @@ NIL ((|constructor| (NIL "Category for the trigonometric functions.")) (|tan| (($ $) "\\spad{tan(x)} returns the tangent of \\spad{x}.")) (|sin| (($ $) "\\spad{sin(x)} returns the sine of \\spad{x}.")) (|sec| (($ $) "\\spad{sec(x)} returns the secant of \\spad{x}.")) (|csc| (($ $) "\\spad{csc(x)} returns the cosecant of \\spad{x}.")) (|cot| (($ $) "\\spad{cot(x)} returns the cotangent of \\spad{x}.")) (|cos| (($ $) "\\spad{cos(x)} returns the cosine of \\spad{x}."))) NIL NIL -(-1216 R -1385) +(-1216 R -2968) ((|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 @@ -4800,7 +4800,7 @@ 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 -(-1218 R -1385) +(-1218 R -2968) ((|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 \\spad{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 \\spad{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 -620) (LIST (QUOTE -899) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -893) (|devaluate| |#1|))) (|HasCategory| |#2| (LIST (QUOTE -620) (LIST (QUOTE -899) (|devaluate| |#1|)))) (|HasCategory| |#2| (LIST (QUOTE -893) (|devaluate| |#1|))))) @@ -4815,7 +4815,7 @@ NIL (-1221 |Coef|) ((|constructor| (NIL "\\spadtype{TaylorSeries} is a general multivariate Taylor series domain over the ring Coef and with variables of type Symbol.")) (|fintegrate| (($ (|Mapping| $) (|Symbol|) |#1|) "\\spad{fintegrate(f,v,c)} is the integral of \\spad{f()} with respect \\indented{1}{to \\spad{v} and having \\spad{c} as the constant of integration.} \\indented{1}{The evaluation of \\spad{f()} is delayed.}")) (|integrate| (($ $ (|Symbol|) |#1|) "\\spad{integrate(s,v,c)} is the integral of \\spad{s} with respect \\indented{1}{to \\spad{v} and having \\spad{c} as the constant of integration.}")) (|coerce| (($ (|Polynomial| |#1|)) "\\spad{coerce(s)} regroups terms of \\spad{s} by total degree \\indented{1}{and forms a series.}") (($ (|Symbol|)) "\\spad{coerce(s)} converts a variable to a Taylor series")) (|coefficient| (((|Polynomial| |#1|) $ (|NonNegativeInteger|)) "\\spad{coefficient(s, n)} gives the terms of total degree \\spad{n}."))) (((-4454 "*") |has| |#1| (-174)) (-4445 |has| |#1| (-562)) (-4447 . T) (-4446 . T) (-4449 . T)) -((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-148))) (|HasCategory| |#1| (QUOTE (-146))) (-2811 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-562)))) (|HasCategory| |#1| (QUOTE (-562))) (|HasCategory| |#1| (QUOTE (-368)))) +((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-148))) (|HasCategory| |#1| (QUOTE (-146))) (-3684 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-562)))) (|HasCategory| |#1| (QUOTE (-562))) (|HasCategory| |#1| (QUOTE (-368)))) (-1222 |Curve|) ((|constructor| (NIL "\\indented{2}{Package for constructing tubes around 3-dimensional parametric curves.} Domain of tubes around 3-dimensional parametric curves.")) (|tube| (($ |#1| (|List| (|List| (|Point| (|DoubleFloat|)))) (|Boolean|)) "\\spad{tube(c,ll,b)} creates a tube of the domain \\spadtype{TubePlot} from a space curve \\spad{c} of the category \\spadtype{PlottableSpaceCurveCategory},{} a list of lists of points (loops) \\spad{ll} and a boolean \\spad{b} which if \\spad{true} indicates a closed tube,{} or if \\spad{false} an open tube.")) (|setClosed| (((|Boolean|) $ (|Boolean|)) "\\spad{setClosed(t,b)} declares the given tube plot \\spad{t} to be closed if \\spad{b} is \\spad{true},{} or if \\spad{b} is \\spad{false},{} \\spad{t} is set to be open.")) (|open?| (((|Boolean|) $) "\\spad{open?(t)} tests whether the given tube plot \\spad{t} is open.")) (|closed?| (((|Boolean|) $) "\\spad{closed?(t)} tests whether the given tube plot \\spad{t} is closed.")) (|listLoops| (((|List| (|List| (|Point| (|DoubleFloat|)))) $) "\\spad{listLoops(t)} returns the list of lists of points,{} or the 'loops',{} of the given tube plot \\spad{t}.")) (|getCurve| ((|#1| $) "\\spad{getCurve(t)} returns the \\spadtype{PlottableSpaceCurveCategory} representing the parametric curve of the given tube plot \\spad{t}."))) NIL @@ -4828,7 +4828,7 @@ NIL ((|constructor| (NIL "\\indented{1}{This domain is used to interface with the interpreter\\spad{'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 (-1109))) (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-868))))) -(-1225 -1385) +(-1225 -2968) ((|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}.")) 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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 @@ -4931,7 +4931,7 @@ NIL (-1250 |x| R) ((|constructor| (NIL "This domain represents univariate polynomials in some symbol over arbitrary (not necessarily commutative) coefficient rings. The representation is sparse in the sense that only non-zero terms are represented.")) (|fmecg| (($ $ (|NonNegativeInteger|) |#2| $) "\\spad{fmecg(p1,e,r,p2)} finds \\spad{X} : \\spad{p1} - \\spad{r} * X**e * \\spad{p2}"))) (((-4454 "*") |has| |#2| (-174)) (-4445 |has| |#2| (-562)) (-4448 |has| |#2| (-368)) (-4450 |has| |#2| (-6 -4450)) (-4447 . T) (-4446 . T) (-4449 . T)) -((|HasCategory| |#2| (QUOTE (-916))) (|HasCategory| |#2| (QUOTE (-562))) (|HasCategory| |#2| (QUOTE (-174))) (-2811 (|HasCategory| |#2| (QUOTE (-174))) (|HasCategory| |#2| (QUOTE (-562)))) (-12 (|HasCategory| (-1091) (LIST (QUOTE -893) (QUOTE (-384)))) (|HasCategory| |#2| (LIST (QUOTE -893) (QUOTE (-384))))) (-12 (|HasCategory| (-1091) (LIST (QUOTE -893) (QUOTE (-570)))) (|HasCategory| |#2| (LIST (QUOTE -893) (QUOTE (-570))))) (-12 (|HasCategory| (-1091) (LIST (QUOTE -620) (LIST (QUOTE -899) (QUOTE (-384))))) (|HasCategory| |#2| (LIST (QUOTE -620) (LIST (QUOTE -899) (QUOTE (-384)))))) (-12 (|HasCategory| (-1091) (LIST (QUOTE -620) (LIST (QUOTE -899) (QUOTE (-570))))) (|HasCategory| |#2| (LIST (QUOTE -620) (LIST (QUOTE -899) (QUOTE (-570)))))) (-12 (|HasCategory| (-1091) (LIST (QUOTE -620) (QUOTE (-542)))) (|HasCategory| |#2| (LIST (QUOTE -620) (QUOTE (-542))))) (|HasCategory| |#2| (LIST (QUOTE -645) (QUOTE (-570)))) (|HasCategory| |#2| (QUOTE (-148))) (|HasCategory| |#2| (QUOTE (-146))) (|HasCategory| |#2| (LIST (QUOTE -38) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasCategory| |#2| (LIST (QUOTE -1047) (QUOTE (-570)))) (-2811 (|HasCategory| |#2| (LIST (QUOTE -38) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasCategory| |#2| (LIST (QUOTE -1047) (LIST (QUOTE -413) (QUOTE (-570)))))) (|HasCategory| |#2| (LIST (QUOTE -1047) (LIST (QUOTE -413) (QUOTE (-570))))) (-2811 (|HasCategory| |#2| (QUOTE (-174))) (|HasCategory| |#2| (QUOTE (-368))) (|HasCategory| |#2| (QUOTE (-458))) (|HasCategory| |#2| (QUOTE (-562))) (|HasCategory| |#2| (QUOTE (-916)))) (-2811 (|HasCategory| |#2| (QUOTE (-368))) (|HasCategory| |#2| (QUOTE (-458))) (|HasCategory| |#2| (QUOTE (-562))) (|HasCategory| |#2| (QUOTE (-916)))) (-2811 (|HasCategory| |#2| (QUOTE (-368))) (|HasCategory| |#2| (QUOTE (-458))) (|HasCategory| |#2| (QUOTE (-916)))) (|HasCategory| |#2| (QUOTE (-368))) (|HasCategory| |#2| (QUOTE (-1161))) (|HasCategory| |#2| (LIST (QUOTE -907) (QUOTE (-1186)))) (|HasCategory| |#2| (QUOTE (-235))) (|HasAttribute| |#2| (QUOTE -4450)) (|HasCategory| |#2| (QUOTE (-458))) (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| |#2| (QUOTE (-916)))) (-2811 (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| |#2| (QUOTE (-916)))) (|HasCategory| |#2| (QUOTE (-146))))) +((|HasCategory| |#2| (QUOTE (-916))) (|HasCategory| |#2| (QUOTE (-562))) (|HasCategory| |#2| (QUOTE (-174))) (-3684 (|HasCategory| |#2| (QUOTE (-174))) (|HasCategory| |#2| (QUOTE (-562)))) (-12 (|HasCategory| (-1091) (LIST (QUOTE -893) (QUOTE (-384)))) (|HasCategory| |#2| (LIST (QUOTE -893) (QUOTE (-384))))) (-12 (|HasCategory| (-1091) (LIST (QUOTE -893) (QUOTE (-570)))) (|HasCategory| |#2| (LIST (QUOTE -893) (QUOTE (-570))))) (-12 (|HasCategory| (-1091) (LIST (QUOTE -620) (LIST (QUOTE -899) (QUOTE (-384))))) (|HasCategory| |#2| (LIST (QUOTE -620) (LIST (QUOTE -899) (QUOTE (-384)))))) (-12 (|HasCategory| (-1091) (LIST (QUOTE -620) (LIST (QUOTE -899) (QUOTE (-570))))) (|HasCategory| |#2| (LIST (QUOTE -620) (LIST (QUOTE -899) (QUOTE (-570)))))) (-12 (|HasCategory| (-1091) (LIST (QUOTE -620) (QUOTE (-542)))) (|HasCategory| |#2| (LIST (QUOTE -620) (QUOTE (-542))))) (|HasCategory| |#2| (LIST (QUOTE -645) (QUOTE (-570)))) (|HasCategory| |#2| (QUOTE (-148))) (|HasCategory| |#2| (QUOTE (-146))) (|HasCategory| |#2| (LIST (QUOTE -38) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasCategory| |#2| (LIST (QUOTE -1047) (QUOTE (-570)))) (-3684 (|HasCategory| |#2| (LIST (QUOTE -38) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasCategory| |#2| (LIST (QUOTE -1047) (LIST (QUOTE -413) (QUOTE (-570)))))) (|HasCategory| |#2| (LIST (QUOTE -1047) (LIST (QUOTE -413) (QUOTE (-570))))) (-3684 (|HasCategory| |#2| (QUOTE (-174))) (|HasCategory| |#2| (QUOTE (-368))) (|HasCategory| |#2| (QUOTE (-458))) (|HasCategory| |#2| (QUOTE (-562))) (|HasCategory| |#2| (QUOTE (-916)))) (-3684 (|HasCategory| |#2| (QUOTE (-368))) (|HasCategory| |#2| (QUOTE (-458))) (|HasCategory| |#2| (QUOTE (-562))) (|HasCategory| |#2| (QUOTE (-916)))) (-3684 (|HasCategory| |#2| (QUOTE (-368))) (|HasCategory| |#2| (QUOTE (-458))) (|HasCategory| |#2| (QUOTE (-916)))) (|HasCategory| |#2| (QUOTE (-368))) (|HasCategory| |#2| (QUOTE (-1161))) (|HasCategory| |#2| (LIST (QUOTE -907) (QUOTE (-1186)))) (|HasCategory| |#2| (QUOTE (-235))) (|HasAttribute| |#2| (QUOTE -4450)) (|HasCategory| |#2| (QUOTE (-458))) (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| |#2| (QUOTE (-916)))) (-3684 (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| |#2| (QUOTE (-916)))) (|HasCategory| |#2| (QUOTE (-146))))) (-1251 R PR S PS) ((|constructor| (NIL "Mapping from polynomials over \\spad{R} to polynomials over \\spad{S} given a map from \\spad{R} to \\spad{S} assumed to send zero to zero.")) (|map| ((|#4| (|Mapping| |#3| |#1|) |#2|) "\\spad{map(f, p)} takes a function \\spad{f} from \\spad{R} to \\spad{S},{} and applies it to each (non-zero) coefficient of a polynomial \\spad{p} over \\spad{R},{} getting a new polynomial over \\spad{S}. Note: since the map is not applied to zero elements,{} it may map zero to zero."))) NIL @@ -4947,7 +4947,7 @@ NIL (-1254 S |Coef| |Expon|) ((|constructor| (NIL "\\spadtype{UnivariatePowerSeriesCategory} is the most general univariate power series category with exponents in an ordered abelian monoid. Note: this category exports a substitution function if it is possible to multiply exponents. Note: this category exports a derivative operation if it is possible to multiply coefficients by exponents.")) (|eval| (((|Stream| |#2|) $ |#2|) "\\spad{eval(f,a)} evaluates a power series at a value in the ground ring by returning a stream of partial sums.")) (|extend| (($ $ |#3|) "\\spad{extend(f,n)} causes all terms of \\spad{f} of degree \\spad{<=} \\spad{n} to be computed.")) (|approximate| ((|#2| $ |#3|) "\\spad{approximate(f)} returns a truncated power series with the series variable viewed as an element of the coefficient domain.")) (|truncate| (($ $ |#3| |#3|) "\\spad{truncate(f,k1,k2)} returns a (finite) power series consisting of the sum of all terms of \\spad{f} of degree \\spad{d} with \\spad{k1 <= d <= k2}.") (($ $ |#3|) "\\spad{truncate(f,k)} returns a (finite) power series consisting of the sum of all terms of \\spad{f} of degree \\spad{<= k}.")) (|order| ((|#3| $ |#3|) "\\spad{order(f,n) = min(m,n)},{} where \\spad{m} is the degree of the lowest order non-zero term in \\spad{f}.") ((|#3| $) "\\spad{order(f)} is the degree of the lowest order non-zero term in \\spad{f}. This will result in an infinite loop if \\spad{f} has no non-zero terms.")) (|multiplyExponents| (($ $ (|PositiveInteger|)) "\\spad{multiplyExponents(f,n)} multiplies all exponents of the power series \\spad{f} by the positive integer \\spad{n}.")) (|center| ((|#2| $) "\\spad{center(f)} returns the point about which the series \\spad{f} is expanded.")) (|variable| (((|Symbol|) $) "\\spad{variable(f)} returns the (unique) power series variable of the power series \\spad{f}.")) (|terms| (((|Stream| (|Record| (|:| |k| |#3|) (|:| |c| |#2|))) $) "\\spad{terms(f(x))} returns a stream of non-zero terms,{} where a a term is an exponent-coefficient pair. The terms in the stream are ordered by increasing order of exponents."))) NIL -((|HasCategory| |#2| (LIST (QUOTE -907) (QUOTE (-1186)))) (|HasSignature| |#2| (LIST (QUOTE *) (LIST (|devaluate| |#2|) (|devaluate| |#3|) (|devaluate| |#2|)))) (|HasCategory| |#3| (QUOTE (-1121))) (|HasSignature| |#2| (LIST (QUOTE **) (LIST (|devaluate| |#2|) (|devaluate| |#2|) (|devaluate| |#3|)))) (|HasSignature| |#2| (LIST (QUOTE -2940) (LIST (|devaluate| |#2|) (QUOTE (-1186)))))) +((|HasCategory| |#2| (LIST (QUOTE -907) (QUOTE (-1186)))) (|HasSignature| |#2| (LIST (QUOTE *) (LIST (|devaluate| |#2|) (|devaluate| |#3|) (|devaluate| |#2|)))) (|HasCategory| |#3| (QUOTE (-1121))) (|HasSignature| |#2| (LIST (QUOTE **) (LIST (|devaluate| |#2|) (|devaluate| |#2|) (|devaluate| |#3|)))) (|HasSignature| |#2| (LIST (QUOTE -2838) (LIST (|devaluate| |#2|) (QUOTE (-1186)))))) (-1255 |Coef| |Expon|) ((|constructor| (NIL "\\spadtype{UnivariatePowerSeriesCategory} is the most general univariate power series category with exponents in an ordered abelian monoid. Note: this category exports a substitution function if it is possible to multiply exponents. Note: this category exports a derivative operation if it is possible to multiply coefficients by exponents.")) (|eval| (((|Stream| |#1|) $ |#1|) "\\spad{eval(f,a)} evaluates a power series at a value in the ground ring by returning a stream of partial sums.")) (|extend| (($ $ |#2|) "\\spad{extend(f,n)} causes all terms of \\spad{f} of degree \\spad{<=} \\spad{n} to be computed.")) (|approximate| ((|#1| $ |#2|) "\\spad{approximate(f)} returns a truncated power series with the series variable viewed as an element of the coefficient domain.")) (|truncate| (($ $ |#2| |#2|) "\\spad{truncate(f,k1,k2)} returns a (finite) power series consisting of the sum of all terms of \\spad{f} of degree \\spad{d} with \\spad{k1 <= d <= k2}.") (($ $ |#2|) "\\spad{truncate(f,k)} returns a (finite) power series consisting of the sum of all terms of \\spad{f} of degree \\spad{<= k}.")) (|order| ((|#2| $ |#2|) "\\spad{order(f,n) = min(m,n)},{} where \\spad{m} is the degree of the lowest order non-zero term in \\spad{f}.") ((|#2| $) "\\spad{order(f)} is the degree of the lowest order non-zero term in \\spad{f}. This will result in an infinite loop if \\spad{f} has no non-zero terms.")) (|multiplyExponents| (($ $ (|PositiveInteger|)) "\\spad{multiplyExponents(f,n)} multiplies all exponents of the power series \\spad{f} by the positive integer \\spad{n}.")) (|center| ((|#1| $) "\\spad{center(f)} returns the point about which the series \\spad{f} is expanded.")) (|variable| (((|Symbol|) $) "\\spad{variable(f)} returns the (unique) power series variable of the power series \\spad{f}.")) (|terms| (((|Stream| (|Record| (|:| |k| |#2|) (|:| |c| |#1|))) $) "\\spad{terms(f(x))} returns a stream of non-zero terms,{} where a a term is an exponent-coefficient pair. The terms in the stream are ordered by increasing order of exponents."))) (((-4454 "*") |has| |#1| (-174)) (-4445 |has| |#1| (-562)) (-4446 . T) (-4447 . T) (-4449 . T)) @@ -4975,15 +4975,15 @@ NIL (-1261 |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)}."))) (((-4454 "*") |has| |#1| (-174)) (-4445 |has| |#1| (-562)) (-4450 |has| |#1| (-368)) (-4444 |has| |#1| (-368)) (-4446 . T) (-4447 . T) (-4449 . T)) -((|HasCategory| |#1| (QUOTE (-562))) (|HasCategory| |#1| (QUOTE (-174))) (-2811 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-562)))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-148))) (-12 (|HasCategory| |#1| (LIST (QUOTE -907) (QUOTE (-1186)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -413) (QUOTE (-570))) (|devaluate| |#1|))))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -413) (QUOTE (-570))) (|devaluate| |#1|)))) (|HasCategory| (-413 (-570)) (QUOTE (-1121))) (|HasCategory| |#1| (QUOTE (-368))) (-2811 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-368))) (|HasCategory| |#1| (QUOTE (-562)))) (-2811 (|HasCategory| |#1| (QUOTE (-368))) (|HasCategory| |#1| (QUOTE (-562)))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -413) (QUOTE (-570)))))) (|HasSignature| |#1| (LIST (QUOTE -2940) (LIST (|devaluate| |#1|) (QUOTE (-1186)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -413) (QUOTE (-570)))))) (-2811 (-12 (|HasCategory| |#1| (LIST (QUOTE -29) (QUOTE (-570)))) (|HasCategory| |#1| (QUOTE (-966))) (|HasCategory| |#1| (QUOTE (-1212))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -413) (QUOTE (-570)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasSignature| |#1| (LIST (QUOTE -3655) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1186))))) (|HasSignature| |#1| (LIST (QUOTE -2421) (LIST (LIST (QUOTE -650) (QUOTE (-1186))) (|devaluate| |#1|)))))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -413) (QUOTE (-570)))))) +((|HasCategory| |#1| (QUOTE (-562))) (|HasCategory| |#1| (QUOTE (-174))) (-3684 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-562)))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-148))) (-12 (|HasCategory| |#1| (LIST (QUOTE -907) (QUOTE (-1186)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -413) (QUOTE (-570))) (|devaluate| |#1|))))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -413) (QUOTE (-570))) (|devaluate| |#1|)))) (|HasCategory| (-413 (-570)) (QUOTE (-1121))) (|HasCategory| |#1| (QUOTE (-368))) (-3684 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-368))) (|HasCategory| |#1| (QUOTE (-562)))) (-3684 (|HasCategory| |#1| (QUOTE (-368))) (|HasCategory| |#1| (QUOTE (-562)))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -413) (QUOTE (-570)))))) (|HasSignature| |#1| (LIST (QUOTE -2838) (LIST (|devaluate| |#1|) (QUOTE (-1186)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -413) (QUOTE (-570)))))) (-3684 (-12 (|HasCategory| |#1| (LIST (QUOTE -29) (QUOTE (-570)))) (|HasCategory| |#1| (QUOTE (-966))) (|HasCategory| |#1| (QUOTE (-1212))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -413) (QUOTE (-570)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasSignature| |#1| (LIST (QUOTE -2502) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1186))))) (|HasSignature| |#1| (LIST (QUOTE -1624) (LIST (LIST (QUOTE -650) (QUOTE (-1186))) (|devaluate| |#1|)))))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -413) (QUOTE (-570)))))) (-1262 |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.")) (|differentiate| (($ $ (|Variable| |#2|)) "\\spad{differentiate(f(x),x)} returns the derivative of \\spad{f(x)} with respect to \\spad{x}."))) (((-4454 "*") |has| |#1| (-174)) (-4445 |has| |#1| (-562)) (-4450 |has| |#1| (-368)) (-4444 |has| |#1| (-368)) (-4446 . T) (-4447 . T) (-4449 . T)) -((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasCategory| |#1| (QUOTE (-562))) (|HasCategory| |#1| (QUOTE (-174))) (-2811 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-562)))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-148))) (-12 (|HasCategory| |#1| (LIST (QUOTE -907) (QUOTE (-1186)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -413) (QUOTE (-570))) (|devaluate| |#1|))))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -413) (QUOTE (-570))) (|devaluate| |#1|)))) (|HasCategory| (-413 (-570)) (QUOTE (-1121))) (|HasCategory| |#1| (QUOTE (-368))) (-2811 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-368))) (|HasCategory| |#1| (QUOTE (-562)))) (-2811 (|HasCategory| |#1| (QUOTE (-368))) (|HasCategory| |#1| (QUOTE (-562)))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -413) (QUOTE (-570)))))) (|HasSignature| |#1| (LIST (QUOTE -2940) (LIST (|devaluate| |#1|) (QUOTE (-1186)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -413) (QUOTE (-570)))))) (-2811 (-12 (|HasCategory| |#1| (LIST (QUOTE -29) (QUOTE (-570)))) (|HasCategory| |#1| (QUOTE (-966))) (|HasCategory| |#1| (QUOTE (-1212))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -413) (QUOTE (-570)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasSignature| |#1| (LIST (QUOTE -3655) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1186))))) (|HasSignature| |#1| (LIST (QUOTE -2421) (LIST (LIST (QUOTE -650) (QUOTE (-1186))) (|devaluate| |#1|))))))) +((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasCategory| |#1| (QUOTE (-562))) (|HasCategory| |#1| (QUOTE (-174))) (-3684 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-562)))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-148))) (-12 (|HasCategory| |#1| (LIST (QUOTE -907) (QUOTE (-1186)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -413) (QUOTE (-570))) (|devaluate| |#1|))))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -413) (QUOTE (-570))) (|devaluate| |#1|)))) (|HasCategory| (-413 (-570)) (QUOTE (-1121))) (|HasCategory| |#1| (QUOTE (-368))) (-3684 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-368))) (|HasCategory| |#1| (QUOTE (-562)))) (-3684 (|HasCategory| |#1| (QUOTE (-368))) (|HasCategory| |#1| (QUOTE (-562)))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -413) (QUOTE (-570)))))) (|HasSignature| |#1| (LIST (QUOTE -2838) (LIST (|devaluate| |#1|) (QUOTE (-1186)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -413) (QUOTE (-570)))))) (-3684 (-12 (|HasCategory| |#1| (LIST (QUOTE -29) (QUOTE (-570)))) (|HasCategory| |#1| (QUOTE (-966))) (|HasCategory| |#1| (QUOTE (-1212))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -413) (QUOTE (-570)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasSignature| |#1| (LIST (QUOTE -2502) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1186))))) (|HasSignature| |#1| (LIST (QUOTE -1624) (LIST (LIST (QUOTE -650) (QUOTE (-1186))) (|devaluate| |#1|))))))) (-1263 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))}."))) (((-4454 "*") |has| (-1262 |#2| |#3| |#4|) (-174)) (-4445 |has| (-1262 |#2| |#3| |#4|) (-562)) (-4446 . T) (-4447 . T) (-4449 . T)) -((|HasCategory| (-1262 |#2| |#3| |#4|) (LIST (QUOTE -38) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasCategory| (-1262 |#2| |#3| |#4|) (QUOTE (-146))) (|HasCategory| (-1262 |#2| |#3| |#4|) (QUOTE (-148))) (|HasCategory| (-1262 |#2| |#3| |#4|) (QUOTE (-174))) (-2811 (|HasCategory| (-1262 |#2| |#3| |#4|) (LIST (QUOTE -38) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasCategory| (-1262 |#2| |#3| |#4|) (LIST (QUOTE -1047) (LIST (QUOTE -413) (QUOTE (-570)))))) (|HasCategory| (-1262 |#2| |#3| |#4|) (LIST (QUOTE -1047) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasCategory| (-1262 |#2| |#3| |#4|) (LIST (QUOTE -1047) (QUOTE (-570)))) (|HasCategory| (-1262 |#2| |#3| |#4|) (QUOTE (-368))) (|HasCategory| (-1262 |#2| |#3| |#4|) (QUOTE (-458))) (|HasCategory| (-1262 |#2| |#3| |#4|) (QUOTE (-562)))) +((|HasCategory| (-1262 |#2| |#3| |#4|) (LIST (QUOTE -38) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasCategory| (-1262 |#2| |#3| |#4|) (QUOTE (-146))) (|HasCategory| (-1262 |#2| |#3| |#4|) (QUOTE (-148))) (|HasCategory| (-1262 |#2| |#3| |#4|) (QUOTE (-174))) (-3684 (|HasCategory| (-1262 |#2| |#3| |#4|) (LIST (QUOTE -38) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasCategory| (-1262 |#2| |#3| |#4|) (LIST (QUOTE -1047) (LIST (QUOTE -413) (QUOTE (-570)))))) (|HasCategory| (-1262 |#2| |#3| |#4|) (LIST (QUOTE -1047) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasCategory| (-1262 |#2| |#3| |#4|) (LIST (QUOTE -1047) (QUOTE (-570)))) (|HasCategory| (-1262 |#2| |#3| |#4|) (QUOTE (-368))) (|HasCategory| (-1262 |#2| |#3| |#4|) (QUOTE (-458))) (|HasCategory| (-1262 |#2| |#3| |#4|) (QUOTE (-562)))) (-1264 A S) ((|constructor| (NIL "A unary-recursive aggregate is a one where nodes may have either 0 or 1 children. This aggregate models,{} though not precisely,{} a linked list possibly with a single cycle. A node with one children models a non-empty list,{} with the \\spadfun{value} of the list designating the head,{} or \\spadfun{first},{} of the list,{} and the child designating the tail,{} or \\spadfun{rest},{} of the list. A node with no child then designates the empty list. Since these aggregates are recursive aggregates,{} they may be cyclic.")) (|split!| (($ $ (|Integer|)) "\\spad{split!(u,n)} splits \\spad{u} into two aggregates: \\axiom{\\spad{v} = rest(\\spad{u},{}\\spad{n})} and \\axiom{\\spad{w} = first(\\spad{u},{}\\spad{n})},{} returning \\axiom{\\spad{v}}. Note: afterwards \\axiom{rest(\\spad{u},{}\\spad{n})} returns \\axiom{empty()}.")) (|setlast!| ((|#2| $ |#2|) "\\spad{setlast!(u,x)} destructively changes the last element of \\spad{u} to \\spad{x}.")) (|setrest!| (($ $ $) "\\spad{setrest!(u,v)} destructively changes the rest of \\spad{u} to \\spad{v}.")) (|setelt| ((|#2| $ "last" |#2|) "\\spad{setelt(u,\"last\",x)} (also written: \\axiom{\\spad{u}.last \\spad{:=} \\spad{b}}) is equivalent to \\axiom{setlast!(\\spad{u},{}\\spad{v})}.") (($ $ "rest" $) "\\spad{setelt(u,\"rest\",v)} (also written: \\axiom{\\spad{u}.rest \\spad{:=} \\spad{v}}) is equivalent to \\axiom{setrest!(\\spad{u},{}\\spad{v})}.") ((|#2| $ "first" |#2|) "\\spad{setelt(u,\"first\",x)} (also written: \\axiom{\\spad{u}.first \\spad{:=} \\spad{x}}) is equivalent to \\axiom{setfirst!(\\spad{u},{}\\spad{x})}.")) (|setfirst!| ((|#2| $ |#2|) "\\spad{setfirst!(u,x)} destructively changes the first element of a to \\spad{x}.")) (|cycleSplit!| (($ $) "\\spad{cycleSplit!(u)} splits the aggregate by dropping off the cycle. The value returned is the cycle entry,{} or nil if none exists. For example,{} if \\axiom{\\spad{w} = concat(\\spad{u},{}\\spad{v})} is the cyclic list where \\spad{v} is the head of the cycle,{} \\axiom{cycleSplit!(\\spad{w})} will drop \\spad{v} off \\spad{w} thus destructively changing \\spad{w} to \\spad{u},{} and returning \\spad{v}.")) (|concat!| (($ $ |#2|) "\\spad{concat!(u,x)} destructively adds element \\spad{x} to the end of \\spad{u}. Note: \\axiom{concat!(a,{}\\spad{x}) = setlast!(a,{}[\\spad{x}])}.") (($ $ $) "\\spad{concat!(u,v)} destructively concatenates \\spad{v} to the end of \\spad{u}. Note: \\axiom{concat!(\\spad{u},{}\\spad{v}) = setlast!(\\spad{u},{}\\spad{v})}.")) (|cycleTail| (($ $) "\\spad{cycleTail(u)} returns the last node in the cycle,{} or empty if none exists.")) (|cycleLength| (((|NonNegativeInteger|) $) "\\spad{cycleLength(u)} returns the length of a top-level cycle contained in aggregate \\spad{u},{} or 0 is \\spad{u} has no such cycle.")) (|cycleEntry| (($ $) "\\spad{cycleEntry(u)} returns the head of a top-level cycle contained in aggregate \\spad{u},{} or \\axiom{empty()} if none exists.")) (|third| ((|#2| $) "\\spad{third(u)} returns the third element of \\spad{u}. Note: \\axiom{third(\\spad{u}) = first(rest(rest(\\spad{u})))}.")) (|second| ((|#2| $) "\\spad{second(u)} returns the second element of \\spad{u}. Note: \\axiom{second(\\spad{u}) = first(rest(\\spad{u}))}.")) (|tail| (($ $) "\\spad{tail(u)} returns the last node of \\spad{u}. Note: if \\spad{u} is \\axiom{shallowlyMutable},{} \\axiom{setrest(tail(\\spad{u}),{}\\spad{v}) = concat(\\spad{u},{}\\spad{v})}.")) (|last| (($ $ (|NonNegativeInteger|)) "\\spad{last(u,n)} returns a copy of the last \\spad{n} (\\axiom{\\spad{n} \\spad{>=} 0}) nodes of \\spad{u}. Note: \\axiom{last(\\spad{u},{}\\spad{n})} is a list of \\spad{n} elements.") ((|#2| $) "\\spad{last(u)} resturn the last element of \\spad{u}. Note: for lists,{} \\axiom{last(\\spad{u}) = \\spad{u} . (maxIndex \\spad{u}) = \\spad{u} . (\\# \\spad{u} - 1)}.")) (|rest| (($ $ (|NonNegativeInteger|)) "\\spad{rest(u,n)} returns the \\axiom{\\spad{n}}th (\\spad{n} \\spad{>=} 0) node of \\spad{u}. Note: \\axiom{rest(\\spad{u},{}0) = \\spad{u}}.") (($ $) "\\spad{rest(u)} returns an aggregate consisting of all but the first element of \\spad{u} (equivalently,{} the next node of \\spad{u}).")) (|elt| ((|#2| $ "last") "\\spad{elt(u,\"last\")} (also written: \\axiom{\\spad{u} . last}) is equivalent to last \\spad{u}.") (($ $ "rest") "\\spad{elt(\\%,\"rest\")} (also written: \\axiom{\\spad{u}.rest}) is equivalent to \\axiom{rest \\spad{u}}.") ((|#2| $ "first") "\\spad{elt(u,\"first\")} (also written: \\axiom{\\spad{u} . first}) is equivalent to first \\spad{u}.")) (|first| (($ $ (|NonNegativeInteger|)) "\\spad{first(u,n)} returns a copy of the first \\spad{n} (\\axiom{\\spad{n} \\spad{>=} 0}) elements of \\spad{u}.") ((|#2| $) "\\spad{first(u)} returns the first element of \\spad{u} (equivalently,{} the value at the current node).")) (|concat| (($ |#2| $) "\\spad{concat(x,u)} returns aggregate consisting of \\spad{x} followed by the elements of \\spad{u}. Note: if \\axiom{\\spad{v} = concat(\\spad{x},{}\\spad{u})} then \\axiom{\\spad{x} = first \\spad{v}} and \\axiom{\\spad{u} = rest \\spad{v}}.") (($ $ $) "\\spad{concat(u,v)} returns an aggregate \\spad{w} consisting of the elements of \\spad{u} followed by the elements of \\spad{v}. Note: \\axiom{\\spad{v} = rest(\\spad{w},{}\\#a)}."))) NIL @@ -4999,7 +4999,7 @@ NIL (-1267 S |Coef|) ((|constructor| (NIL "\\spadtype{UnivariateTaylorSeriesCategory} is the category of Taylor series in one variable.")) (|integrate| (($ $ (|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}.") (($ $) "\\spad{integrate(f(x))} returns an anti-derivative of the power series \\spad{f(x)} with constant coefficient 0. We may integrate a series when we can divide coefficients by integers.")) (** (($ $ |#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 (-570)))) (|HasCategory| |#2| (QUOTE (-966))) (|HasCategory| |#2| (QUOTE (-1212))) (|HasSignature| |#2| (LIST (QUOTE -2421) (LIST (LIST (QUOTE -650) (QUOTE (-1186))) (|devaluate| |#2|)))) (|HasSignature| |#2| (LIST (QUOTE -3655) (LIST (|devaluate| |#2|) (|devaluate| |#2|) (QUOTE (-1186))))) (|HasCategory| |#2| (LIST (QUOTE -38) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasCategory| |#2| (QUOTE (-368)))) +((|HasCategory| |#2| (LIST (QUOTE -29) (QUOTE (-570)))) (|HasCategory| |#2| (QUOTE (-966))) (|HasCategory| |#2| (QUOTE (-1212))) (|HasSignature| |#2| (LIST (QUOTE -1624) (LIST (LIST (QUOTE -650) (QUOTE (-1186))) (|devaluate| |#2|)))) (|HasSignature| |#2| (LIST (QUOTE -2502) (LIST (|devaluate| |#2|) (|devaluate| |#2|) (QUOTE (-1186))))) (|HasCategory| |#2| (LIST (QUOTE -38) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasCategory| |#2| (QUOTE (-368)))) (-1268 |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."))) (((-4454 "*") |has| |#1| (-174)) (-4445 |has| |#1| (-562)) (-4446 . T) (-4447 . T) (-4449 . T)) @@ -5007,12 +5007,12 @@ NIL (-1269 |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| (($ $) "\\spad{evenlambert(f(x))} returns \\spad{f(x^2) + f(x^4) + f(x^6) + ...}. \\indented{1}{\\spad{f(x)} should have a zero constant coefficient.} \\indented{1}{This function is used for computing infinite products.} \\indented{1}{If \\spad{f(x)} is a Taylor series with constant term 1,{} then} \\indented{1}{\\spad{product(n=1..infinity,f(x^(2*n))) = exp(log(evenlambert(f(x))))}.}")) (|oddlambert| (($ $) "\\spad{oddlambert(f(x))} returns \\spad{f(x) + f(x^3) + f(x^5) + ...}. \\indented{1}{\\spad{f(x)} should have a zero constant coefficient.} \\indented{1}{This function is used for computing infinite products.} \\indented{1}{If \\spad{f(x)} is a Taylor series with constant term 1,{} then} \\indented{1}{\\spad{product(n=1..infinity,f(x^(2*n-1)))=exp(log(oddlambert(f(x))))}.}")) (|lambert| (($ $) "\\spad{lambert(f(x))} returns \\spad{f(x) + f(x^2) + f(x^3) + ...}. \\indented{1}{This function is used for computing infinite products.} \\indented{1}{\\spad{f(x)} should have zero constant coefficient.} \\indented{1}{If \\spad{f(x)} is a Taylor series with constant term 1,{} then} \\indented{1}{\\spad{product(n = 1..infinity,f(x^n)) = exp(log(lambert(f(x))))}.}")) (|lagrange| (($ $) "\\spad{lagrange(g(x))} produces the Taylor series for \\spad{f(x)} \\indented{1}{where \\spad{f(x)} is implicitly defined as \\spad{f(x) = x*g(f(x))}.}")) (|differentiate| (($ $ (|Variable| |#2|)) "\\spad{differentiate(f(x),x)} computes the derivative of \\spad{f(x)} with respect to \\spad{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}."))) (((-4454 "*") |has| |#1| (-174)) (-4445 |has| |#1| (-562)) (-4446 . T) (-4447 . T) (-4449 . T)) -((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasCategory| |#1| (QUOTE (-562))) (-2811 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-562)))) (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-148))) (-12 (|HasCategory| |#1| (LIST (QUOTE -907) (QUOTE (-1186)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (QUOTE (-777)) (|devaluate| |#1|))))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (QUOTE (-777)) (|devaluate| |#1|)))) (|HasCategory| (-777) (QUOTE (-1121))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-777))))) (|HasSignature| |#1| (LIST (QUOTE -2940) (LIST (|devaluate| |#1|) (QUOTE (-1186)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-777))))) (|HasCategory| |#1| (QUOTE (-368))) (-2811 (-12 (|HasCategory| |#1| (LIST (QUOTE -29) (QUOTE (-570)))) (|HasCategory| |#1| (QUOTE (-966))) (|HasCategory| |#1| (QUOTE (-1212))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -413) (QUOTE (-570)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasSignature| |#1| (LIST (QUOTE -3655) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1186))))) (|HasSignature| |#1| (LIST (QUOTE -2421) (LIST (LIST (QUOTE -650) (QUOTE (-1186))) (|devaluate| |#1|))))))) +((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasCategory| |#1| (QUOTE (-562))) (-3684 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-562)))) (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-148))) (-12 (|HasCategory| |#1| (LIST (QUOTE -907) (QUOTE (-1186)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (QUOTE (-777)) (|devaluate| |#1|))))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (QUOTE (-777)) (|devaluate| |#1|)))) (|HasCategory| (-777) (QUOTE (-1121))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-777))))) (|HasSignature| |#1| (LIST (QUOTE -2838) (LIST (|devaluate| |#1|) (QUOTE (-1186)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-777))))) (|HasCategory| |#1| (QUOTE (-368))) (-3684 (-12 (|HasCategory| |#1| (LIST (QUOTE -29) (QUOTE (-570)))) (|HasCategory| |#1| (QUOTE (-966))) (|HasCategory| |#1| (QUOTE (-1212))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -413) (QUOTE (-570)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasSignature| |#1| (LIST (QUOTE -2502) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1186))))) (|HasSignature| |#1| (LIST (QUOTE -1624) (LIST (LIST (QUOTE -650) (QUOTE (-1186))) (|devaluate| |#1|))))))) (-1270 |Coef| UTS) ((|constructor| (NIL "\\indented{1}{This package provides Taylor series solutions to regular} linear or non-linear ordinary differential equations of arbitrary order.")) (|mpsode| (((|List| |#2|) (|List| |#1|) (|List| (|Mapping| |#2| (|List| |#2|)))) "\\spad{mpsode(r,f)} solves the system of differential equations \\spad{dy[i]/dx =f[i] [x,y[1],y[2],...,y[n]]},{} \\spad{y[i](a) = r[i]} for \\spad{i} in 1..\\spad{n}.")) (|ode| ((|#2| (|Mapping| |#2| (|List| |#2|)) (|List| |#1|)) "\\spad{ode(f,cl)} is the solution to \\spad{y<n>=f(y,y',..,y<n-1>)} such that \\spad{y<i>(a) = cl.i} for \\spad{i} in 1..\\spad{n}.")) (|ode2| ((|#2| (|Mapping| |#2| |#2| |#2|) |#1| |#1|) "\\spad{ode2(f,c0,c1)} is the solution to \\spad{y'' = f(y,y')} such that \\spad{y(a) = c0} and \\spad{y'(a) = c1}.")) (|ode1| ((|#2| (|Mapping| |#2| |#2|) |#1|) "\\spad{ode1(f,c)} is the solution to \\spad{y' = f(y)} such that \\spad{y(a) = c}.")) (|fixedPointExquo| ((|#2| |#2| |#2|) "\\spad{fixedPointExquo(f,g)} computes the exact quotient of \\spad{f} and \\spad{g} using a fixed point computation.")) (|stFuncN| (((|Mapping| (|Stream| |#1|) (|List| (|Stream| |#1|))) (|Mapping| |#2| (|List| |#2|))) "\\spad{stFuncN(f)} is a local function xported due to compiler problem. This function is of no interest to the top-level user.")) (|stFunc2| (((|Mapping| (|Stream| |#1|) (|Stream| |#1|) (|Stream| |#1|)) (|Mapping| |#2| |#2| |#2|)) "\\spad{stFunc2(f)} is a local function exported due to compiler problem. This function is of no interest to the top-level user.")) (|stFunc1| (((|Mapping| (|Stream| |#1|) (|Stream| |#1|)) (|Mapping| |#2| |#2|)) "\\spad{stFunc1(f)} is a local function exported due to compiler problem. This function is of no interest to the top-level user."))) NIL NIL -(-1271 -1385 UP L UTS) +(-1271 -2968 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 (-562)))) @@ -5039,7 +5039,7 @@ NIL (-1277 R) ((|constructor| (NIL "This type represents vector like objects with varying lengths and indexed by a finite segment of integers starting at 1.")) (|vector| (($ (|List| |#1|)) "\\spad{vector(l)} converts the list \\spad{l} to a vector."))) ((-4453 . T) (-4452 . T)) -((-2811 (-12 (|HasCategory| |#1| (QUOTE (-856))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|))))) (-2811 (-12 (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-868))))) (|HasCategory| |#1| (LIST (QUOTE -620) (QUOTE (-542)))) (-2811 (|HasCategory| |#1| (QUOTE (-856))) (|HasCategory| |#1| (QUOTE (-1109)))) (|HasCategory| |#1| (QUOTE (-856))) (|HasCategory| (-570) (QUOTE (-856))) (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (QUOTE (-25))) (|HasCategory| |#1| (QUOTE (-23))) (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-732))) (|HasCategory| |#1| (QUOTE (-1058))) (-12 (|HasCategory| |#1| (QUOTE (-1011))) (|HasCategory| |#1| (QUOTE (-1058)))) (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-868)))) (-12 (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|))))) +((-3684 (-12 (|HasCategory| |#1| (QUOTE (-856))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|))))) (-3684 (-12 (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-868))))) (|HasCategory| |#1| (LIST (QUOTE -620) (QUOTE (-542)))) (-3684 (|HasCategory| |#1| (QUOTE (-856))) (|HasCategory| |#1| (QUOTE (-1109)))) (|HasCategory| |#1| (QUOTE (-856))) (|HasCategory| (-570) (QUOTE (-856))) (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (QUOTE (-25))) (|HasCategory| |#1| (QUOTE (-23))) (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-732))) (|HasCategory| |#1| (QUOTE (-1058))) (-12 (|HasCategory| |#1| (QUOTE (-1011))) (|HasCategory| |#1| (QUOTE (-1058)))) (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-868)))) (-12 (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|))))) (-1278) ((|constructor| (NIL "TwoDimensionalViewport creates viewports to display graphs.")) (|coerce| (((|OutputForm|) $) "\\spad{coerce(v)} returns the given two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport} as output of the domain \\spadtype{OutputForm}.")) (|key| (((|Integer|) $) "\\spad{key(v)} returns the process ID number of the given two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport}.")) (|reset| (((|Void|) $) "\\spad{reset(v)} sets the current state of the graph characteristics of the given two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport},{} back to their initial settings.")) (|write| (((|String|) $ (|String|) (|List| (|String|))) "\\spad{write(v,s,lf)} takes the given two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport},{} and creates a directory indicated by \\spad{s},{} which contains the graph data files for \\spad{v} and the optional file types indicated by the list \\spad{lf}.") (((|String|) $ (|String|) (|String|)) "\\spad{write(v,s,f)} takes the given two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport},{} and creates a directory indicated by \\spad{s},{} which contains the graph data files for \\spad{v} and an optional file type \\spad{f}.") (((|String|) $ (|String|)) "\\spad{write(v,s)} takes the given two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport},{} and creates a directory indicated by \\spad{s},{} which contains the graph data files for \\spad{v}.")) (|resize| (((|Void|) $ (|PositiveInteger|) (|PositiveInteger|)) "\\spad{resize(v,w,h)} displays the two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport},{} with a width of \\spad{w} and a height of \\spad{h},{} keeping the upper left-hand corner position unchanged.")) (|update| (((|Void|) $ (|GraphImage|) (|PositiveInteger|)) "\\spad{update(v,gr,n)} drops the graph \\spad{gr} in slot \\spad{n} of viewport \\spad{v}. The graph \\spad{gr} must have been transmitted already and acquired an integer key.")) (|move| (((|Void|) $ (|NonNegativeInteger|) (|NonNegativeInteger|)) "\\spad{move(v,x,y)} displays the two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport},{} with the upper left-hand corner of the viewport window at the screen coordinate position \\spad{x},{} \\spad{y}.")) (|show| (((|Void|) $ (|PositiveInteger|) (|String|)) "\\spad{show(v,n,s)} displays the graph in field \\spad{n} of the given two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport},{} if \\spad{s} is \"on\",{} or does not display the graph if \\spad{s} is \"off\".")) (|translate| (((|Void|) $ (|PositiveInteger|) (|Float|) (|Float|)) "\\spad{translate(v,n,dx,dy)} displays the graph in field \\spad{n} of the given two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport},{} translated by \\spad{dx} in the \\spad{x}-coordinate direction from the center of the viewport,{} and by \\spad{dy} in the \\spad{y}-coordinate direction from the center. Setting \\spad{dx} and \\spad{dy} to \\spad{0} places the center of the graph at the center of the viewport.")) (|scale| (((|Void|) $ (|PositiveInteger|) (|Float|) (|Float|)) "\\spad{scale(v,n,sx,sy)} displays the graph in field \\spad{n} of the given two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport},{} scaled by the factor \\spad{sx} in the \\spad{x}-coordinate direction and by the factor \\spad{sy} in the \\spad{y}-coordinate direction.")) (|dimensions| (((|Void|) $ (|NonNegativeInteger|) (|NonNegativeInteger|) (|PositiveInteger|) (|PositiveInteger|)) "\\spad{dimensions(v,x,y,width,height)} sets the position of the upper left-hand corner of the two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport},{} to the window coordinate \\spad{x},{} \\spad{y},{} and sets the dimensions of the window to that of \\spad{width},{} \\spad{height}. The new dimensions are not displayed until the function \\spadfun{makeViewport2D} is executed again for \\spad{v}.")) (|close| (((|Void|) $) "\\spad{close(v)} closes the viewport window of the given two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport},{} and terminates the corresponding process ID.")) (|controlPanel| (((|Void|) $ (|String|)) "\\spad{controlPanel(v,s)} displays the control panel of the given two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport},{} if \\spad{s} is \"on\",{} or hides the control panel if \\spad{s} is \"off\".")) (|connect| (((|Void|) $ (|PositiveInteger|) (|String|)) "\\spad{connect(v,n,s)} displays the lines connecting the graph points in field \\spad{n} of the given two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport},{} if \\spad{s} is \"on\",{} or does not display the lines if \\spad{s} is \"off\".")) (|region| (((|Void|) $ (|PositiveInteger|) (|String|)) "\\spad{region(v,n,s)} displays the bounding box of the graph in field \\spad{n} of the given two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport},{} if \\spad{s} is \"on\",{} or does not display the bounding box if \\spad{s} is \"off\".")) (|points| (((|Void|) $ (|PositiveInteger|) (|String|)) "\\spad{points(v,n,s)} displays the points of the graph in field \\spad{n} of the given two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport},{} if \\spad{s} is \"on\",{} or does not display the points if \\spad{s} is \"off\".")) (|units| (((|Void|) $ (|PositiveInteger|) (|Palette|)) "\\spad{units(v,n,c)} displays the units of the graph in field \\spad{n} of the given two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport},{} with the units color set to the given palette color \\spad{c}.") (((|Void|) $ (|PositiveInteger|) (|String|)) "\\spad{units(v,n,s)} displays the units of the graph in field \\spad{n} of the given two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport},{} if \\spad{s} is \"on\",{} or does not display the units if \\spad{s} is \"off\".")) (|axes| (((|Void|) $ (|PositiveInteger|) (|Palette|)) "\\spad{axes(v,n,c)} displays the axes of the graph in field \\spad{n} of the given two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport},{} with the axes color set to the given palette color \\spad{c}.") (((|Void|) $ (|PositiveInteger|) (|String|)) "\\spad{axes(v,n,s)} displays the axes of the graph in field \\spad{n} of the given two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport},{} if \\spad{s} is \"on\",{} or does not display the axes if \\spad{s} is \"off\".")) (|getGraph| (((|GraphImage|) $ (|PositiveInteger|)) "\\spad{getGraph(v,n)} returns the graph which is of the domain \\spadtype{GraphImage} which is located in graph field \\spad{n} of the given two-dimensional viewport,{} \\spad{v},{} which is of the domain \\spadtype{TwoDimensionalViewport}.")) (|putGraph| (((|Void|) $ (|GraphImage|) (|PositiveInteger|)) "\\spad{putGraph(v,gi,n)} sets the graph field indicated by \\spad{n},{} of the indicated two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport},{} to be the graph,{} \\spad{gi} of domain \\spadtype{GraphImage}. The contents of viewport,{} \\spad{v},{} will contain \\spad{gi} when the function \\spadfun{makeViewport2D} is called to create the an updated viewport \\spad{v}.")) (|title| (((|Void|) $ (|String|)) "\\spad{title(v,s)} changes the title which is shown in the two-dimensional viewport window,{} \\spad{v} of domain \\spadtype{TwoDimensionalViewport}.")) (|graphs| (((|Vector| (|Union| (|GraphImage|) "undefined")) $) "\\spad{graphs(v)} returns a vector,{} or list,{} which is a union of all the graphs,{} of the domain \\spadtype{GraphImage},{} which are allocated for the two-dimensional viewport,{} \\spad{v},{} of domain \\spadtype{TwoDimensionalViewport}. Those graphs which have no data are labeled \"undefined\",{} otherwise their contents are shown.")) (|graphStates| (((|Vector| (|Record| (|:| |scaleX| (|DoubleFloat|)) (|:| |scaleY| (|DoubleFloat|)) (|:| |deltaX| (|DoubleFloat|)) (|:| |deltaY| (|DoubleFloat|)) (|:| |points| (|Integer|)) (|:| |connect| (|Integer|)) (|:| |spline| (|Integer|)) (|:| |axes| (|Integer|)) (|:| |axesColor| (|Palette|)) (|:| |units| (|Integer|)) (|:| |unitsColor| (|Palette|)) (|:| |showing| (|Integer|)))) $) "\\spad{graphStates(v)} returns and shows a listing of a record containing the current state of the characteristics of each of the ten graph records in the given two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport}.")) (|graphState| (((|Void|) $ (|PositiveInteger|) (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|) (|Integer|) (|Integer|) (|Integer|) (|Integer|) (|Palette|) (|Integer|) (|Palette|) (|Integer|)) "\\spad{graphState(v,num,sX,sY,dX,dY,pts,lns,box,axes,axesC,un,unC,cP)} sets the state of the characteristics for the graph indicated by \\spad{num} in the given two-dimensional viewport \\spad{v},{} of domain \\spadtype{TwoDimensionalViewport},{} to the values given as parameters. The scaling of the graph in the \\spad{x} and \\spad{y} component directions is set to be \\spad{sX} and \\spad{sY}; the window translation in the \\spad{x} and \\spad{y} component directions is set to be \\spad{dX} and \\spad{dY}; The graph points,{} lines,{} bounding \\spad{box},{} \\spad{axes},{} or units will be shown in the viewport if their given parameters \\spad{pts},{} \\spad{lns},{} \\spad{box},{} \\spad{axes} or \\spad{un} are set to be \\spad{1},{} but will not be shown if they are set to \\spad{0}. The color of the \\spad{axes} and the color of the units are indicated by the palette colors \\spad{axesC} and \\spad{unC} respectively. To display the control panel when the viewport window is displayed,{} set \\spad{cP} to \\spad{1},{} otherwise set it to \\spad{0}.")) (|options| (($ $ (|List| (|DrawOption|))) "\\spad{options(v,lopt)} takes the given two-dimensional viewport,{} \\spad{v},{} of the domain \\spadtype{TwoDimensionalViewport} and returns \\spad{v} with it\\spad{'s} draw options modified to be those which are indicated in the given list,{} \\spad{lopt} of domain \\spadtype{DrawOption}.") (((|List| (|DrawOption|)) $) "\\spad{options(v)} takes the given two-dimensional viewport,{} \\spad{v},{} of the domain \\spadtype{TwoDimensionalViewport} and returns a list containing the draw options from the domain \\spadtype{DrawOption} for \\spad{v}.")) (|makeViewport2D| (($ (|GraphImage|) (|List| (|DrawOption|))) "\\spad{makeViewport2D(gi,lopt)} creates and displays a viewport window of the domain \\spadtype{TwoDimensionalViewport} whose graph field is assigned to be the given graph,{} \\spad{gi},{} of domain \\spadtype{GraphImage},{} and whose options field is set to be the list of options,{} \\spad{lopt} of domain \\spadtype{DrawOption}.") (($ $) "\\spad{makeViewport2D(v)} takes the given two-dimensional viewport,{} \\spad{v},{} of the domain \\spadtype{TwoDimensionalViewport} and displays a viewport window on the screen which contains the contents of \\spad{v}.")) (|viewport2D| (($) "\\spad{viewport2D()} returns an undefined two-dimensional viewport of the domain \\spadtype{TwoDimensionalViewport} whose contents are empty.")) (|getPickedPoints| (((|List| (|Point| (|DoubleFloat|))) $) "\\spad{getPickedPoints(x)} returns a list of small floats for the points the user interactively picked on the viewport for full integration into the system,{} some design issues need to be addressed: \\spadignore{e.g.} how to go through the GraphImage interface,{} how to default to graphs,{} etc."))) NIL @@ -5072,7 +5072,7 @@ 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]\\spad{*v} + A[2]*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 -(-1286 K R UP -1385) +(-1286 K R UP -2968) ((|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 @@ -5108,11 +5108,11 @@ NIL ((|constructor| (NIL "This category specifies opeations for polynomials and formal series with non-commutative variables.")) (|varList| (((|List| |#1|) $) "\\spad{varList(x)} returns the list of variables which appear in \\spad{x}.")) (|map| (($ (|Mapping| |#2| |#2|) $) "\\spad{map(fn,x)} returns \\spad{Sum(fn(r_i) w_i)} if \\spad{x} writes \\spad{Sum(r_i w_i)}.")) (|sh| (($ $ (|NonNegativeInteger|)) "\\spad{sh(x,n)} returns the shuffle power of \\spad{x} to the \\spad{n}.") (($ $ $) "\\spad{sh(x,y)} returns the shuffle-product of \\spad{x} by \\spad{y}. This multiplication is associative and commutative.")) (|quasiRegular| (($ $) "\\spad{quasiRegular(x)} return \\spad{x} minus its constant term.")) (|quasiRegular?| (((|Boolean|) $) "\\spad{quasiRegular?(x)} return \\spad{true} if \\spad{constant(x)} is zero.")) (|constant| ((|#2| $) "\\spad{constant(x)} returns the constant term of \\spad{x}.")) (|constant?| (((|Boolean|) $) "\\spad{constant?(x)} returns \\spad{true} if \\spad{x} is constant.")) (|coerce| (($ |#1|) "\\spad{coerce(v)} returns \\spad{v}.")) (|mirror| (($ $) "\\spad{mirror(x)} returns \\spad{Sum(r_i mirror(w_i))} if \\spad{x} writes \\spad{Sum(r_i w_i)}.")) (|monomial?| (((|Boolean|) $) "\\spad{monomial?(x)} returns \\spad{true} if \\spad{x} is a monomial")) (|monom| (($ (|OrderedFreeMonoid| |#1|) |#2|) "\\spad{monom(w,r)} returns the product of the word \\spad{w} by the coefficient \\spad{r}.")) (|rquo| (($ $ $) "\\spad{rquo(x,y)} returns the right simplification of \\spad{x} by \\spad{y}.") (($ $ (|OrderedFreeMonoid| |#1|)) "\\spad{rquo(x,w)} returns the right simplification of \\spad{x} by \\spad{w}.") (($ $ |#1|) "\\spad{rquo(x,v)} returns the right simplification of \\spad{x} by the variable \\spad{v}.")) (|lquo| (($ $ $) "\\spad{lquo(x,y)} returns the left simplification of \\spad{x} by \\spad{y}.") (($ $ (|OrderedFreeMonoid| |#1|)) "\\spad{lquo(x,w)} returns the left simplification of \\spad{x} by the word \\spad{w}.") (($ $ |#1|) "\\spad{lquo(x,v)} returns the left simplification of \\spad{x} by the variable \\spad{v}.")) (|coef| ((|#2| $ $) "\\spad{coef(x,y)} returns scalar product of \\spad{x} by \\spad{y},{} the set of words being regarded as an orthogonal basis.") ((|#2| $ (|OrderedFreeMonoid| |#1|)) "\\spad{coef(x,w)} returns the coefficient of the word \\spad{w} in \\spad{x}.")) (|mindegTerm| (((|Record| (|:| |k| (|OrderedFreeMonoid| |#1|)) (|:| |c| |#2|)) $) "\\spad{mindegTerm(x)} returns the term whose word is \\spad{mindeg(x)}.")) (|mindeg| (((|OrderedFreeMonoid| |#1|) $) "\\spad{mindeg(x)} returns the little word which appears in \\spad{x}. Error if \\spad{x=0}.")) (* (($ $ |#2|) "\\spad{x * r} returns the product of \\spad{x} by \\spad{r}. Usefull if \\spad{R} is a non-commutative Ring.") (($ |#1| $) "\\spad{v * x} returns the product of a variable \\spad{x} by \\spad{x}."))) ((-4445 |has| |#2| (-6 -4445)) (-4447 . T) (-4446 . T) (-4449 . T)) NIL -(-1295 S -1385) +(-1295 S -2968) ((|constructor| (NIL "ExtensionField {\\em F} is the category of fields which extend the field \\spad{F}")) (|Frobenius| (($ $ (|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|) $) "\\spad{algebraic?(a)} tests whether an element \\spad{a} is algebraic with respect to the ground field \\spad{F}."))) NIL ((|HasCategory| |#2| (QUOTE (-373))) (|HasCategory| |#2| (QUOTE (-146))) (|HasCategory| |#2| (QUOTE (-148)))) -(-1296 -1385) +(-1296 -2968) ((|constructor| (NIL "ExtensionField {\\em F} is the category of fields which extend the field \\spad{F}")) (|Frobenius| (($ $ (|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}."))) ((-4444 . T) (-4450 . T) (-4445 . T) ((-4454 "*") . T) (-4446 . T) (-4447 . T) (-4449 . T)) NIL @@ -5172,4 +5172,4 @@ NIL NIL NIL NIL -((-3 NIL 2266397 2266402 2266407 2266412) (-2 NIL 2266377 2266382 2266387 2266392) (-1 NIL 2266357 2266362 2266367 2266372) (0 NIL 2266337 2266342 2266347 2266352) (-1306 "ZMOD.spad" 2266146 2266159 2266275 2266332) (-1305 "ZLINDEP.spad" 2265212 2265223 2266136 2266141) (-1304 "ZDSOLVE.spad" 2255157 2255179 2265202 2265207) (-1303 "YSTREAM.spad" 2254652 2254663 2255147 2255152) (-1302 "YDIAGRAM.spad" 2254286 2254295 2254642 2254647) (-1301 "XRPOLY.spad" 2253506 2253526 2254142 2254211) (-1300 "XPR.spad" 2251301 2251314 2253224 2253323) (-1299 "XPOLY.spad" 2250856 2250867 2251157 2251226) (-1298 "XPOLYC.spad" 2250175 2250191 2250782 2250851) (-1297 "XPBWPOLY.spad" 2248612 2248632 2249955 2250024) (-1296 "XF.spad" 2247075 2247090 2248514 2248607) (-1295 "XF.spad" 2245518 2245535 2246959 2246964) (-1294 "XFALG.spad" 2242566 2242582 2245444 2245513) (-1293 "XEXPPKG.spad" 2241817 2241843 2242556 2242561) (-1292 "XDPOLY.spad" 2241431 2241447 2241673 2241742) (-1291 "XALG.spad" 2241091 2241102 2241387 2241426) (-1290 "WUTSET.spad" 2236930 2236947 2240737 2240764) (-1289 "WP.spad" 2236129 2236173 2236788 2236855) (-1288 "WHILEAST.spad" 2235927 2235936 2236119 2236124) (-1287 "WHEREAST.spad" 2235598 2235607 2235917 2235922) (-1286 "WFFINTBS.spad" 2233261 2233283 2235588 2235593) (-1285 "WEIER.spad" 2231483 2231494 2233251 2233256) (-1284 "VSPACE.spad" 2231156 2231167 2231451 2231478) (-1283 "VSPACE.spad" 2230849 2230862 2231146 2231151) (-1282 "VOID.spad" 2230526 2230535 2230839 2230844) (-1281 "VIEW.spad" 2228206 2228215 2230516 2230521) (-1280 "VIEWDEF.spad" 2223407 2223416 2228196 2228201) (-1279 "VIEW3D.spad" 2207368 2207377 2223397 2223402) (-1278 "VIEW2D.spad" 2195259 2195268 2207358 2207363) (-1277 "VECTOR.spad" 2193933 2193944 2194184 2194211) (-1276 "VECTOR2.spad" 2192572 2192585 2193923 2193928) (-1275 "VECTCAT.spad" 2190476 2190487 2192540 2192567) (-1274 "VECTCAT.spad" 2188187 2188200 2190253 2190258) (-1273 "VARIABLE.spad" 2187967 2187982 2188177 2188182) (-1272 "UTYPE.spad" 2187611 2187620 2187957 2187962) (-1271 "UTSODETL.spad" 2186906 2186930 2187567 2187572) (-1270 "UTSODE.spad" 2185122 2185142 2186896 2186901) (-1269 "UTS.spad" 2179926 2179954 2183589 2183686) (-1268 "UTSCAT.spad" 2177405 2177421 2179824 2179921) (-1267 "UTSCAT.spad" 2174528 2174546 2176949 2176954) (-1266 "UTS2.spad" 2174123 2174158 2174518 2174523) (-1265 "URAGG.spad" 2168796 2168807 2174113 2174118) (-1264 "URAGG.spad" 2163433 2163446 2168752 2168757) (-1263 "UPXSSING.spad" 2161078 2161104 2162514 2162647) (-1262 "UPXS.spad" 2158232 2158260 2159210 2159359) (-1261 "UPXSCONS.spad" 2155991 2156011 2156364 2156513) (-1260 "UPXSCCA.spad" 2154562 2154582 2155837 2155986) (-1259 "UPXSCCA.spad" 2153275 2153297 2154552 2154557) (-1258 "UPXSCAT.spad" 2151864 2151880 2153121 2153270) (-1257 "UPXS2.spad" 2151407 2151460 2151854 2151859) (-1256 "UPSQFREE.spad" 2149821 2149835 2151397 2151402) (-1255 "UPSCAT.spad" 2147608 2147632 2149719 2149816) (-1254 "UPSCAT.spad" 2145101 2145127 2147214 2147219) (-1253 "UPOLYC.spad" 2140141 2140152 2144943 2145096) (-1252 "UPOLYC.spad" 2135073 2135086 2139877 2139882) (-1251 "UPOLYC2.spad" 2134544 2134563 2135063 2135068) (-1250 "UP.spad" 2131743 2131758 2132130 2132283) (-1249 "UPMP.spad" 2130643 2130656 2131733 2131738) (-1248 "UPDIVP.spad" 2130208 2130222 2130633 2130638) (-1247 "UPDECOMP.spad" 2128453 2128467 2130198 2130203) (-1246 "UPCDEN.spad" 2127662 2127678 2128443 2128448) (-1245 "UP2.spad" 2127026 2127047 2127652 2127657) (-1244 "UNISEG.spad" 2126379 2126390 2126945 2126950) (-1243 "UNISEG2.spad" 2125876 2125889 2126335 2126340) (-1242 "UNIFACT.spad" 2124979 2124991 2125866 2125871) (-1241 "ULS.spad" 2115537 2115565 2116624 2117053) (-1240 "ULSCONS.spad" 2107933 2107953 2108303 2108452) (-1239 "ULSCCAT.spad" 2105670 2105690 2107779 2107928) (-1238 "ULSCCAT.spad" 2103515 2103537 2105626 2105631) (-1237 "ULSCAT.spad" 2101747 2101763 2103361 2103510) (-1236 "ULS2.spad" 2101261 2101314 2101737 2101742) (-1235 "UINT8.spad" 2101138 2101147 2101251 2101256) (-1234 "UINT64.spad" 2101014 2101023 2101128 2101133) (-1233 "UINT32.spad" 2100890 2100899 2101004 2101009) (-1232 "UINT16.spad" 2100766 2100775 2100880 2100885) (-1231 "UFD.spad" 2099831 2099840 2100692 2100761) (-1230 "UFD.spad" 2098958 2098969 2099821 2099826) (-1229 "UDVO.spad" 2097839 2097848 2098948 2098953) (-1228 "UDPO.spad" 2095332 2095343 2097795 2097800) (-1227 "TYPE.spad" 2095264 2095273 2095322 2095327) (-1226 "TYPEAST.spad" 2095183 2095192 2095254 2095259) (-1225 "TWOFACT.spad" 2093835 2093850 2095173 2095178) (-1224 "TUPLE.spad" 2093321 2093332 2093734 2093739) (-1223 "TUBETOOL.spad" 2090188 2090197 2093311 2093316) (-1222 "TUBE.spad" 2088835 2088852 2090178 2090183) (-1221 "TS.spad" 2087434 2087450 2088400 2088497) (-1220 "TSETCAT.spad" 2074561 2074578 2087402 2087429) (-1219 "TSETCAT.spad" 2061674 2061693 2074517 2074522) (-1218 "TRMANIP.spad" 2056040 2056057 2061380 2061385) (-1217 "TRIMAT.spad" 2055003 2055028 2056030 2056035) (-1216 "TRIGMNIP.spad" 2053530 2053547 2054993 2054998) (-1215 "TRIGCAT.spad" 2053042 2053051 2053520 2053525) (-1214 "TRIGCAT.spad" 2052552 2052563 2053032 2053037) (-1213 "TREE.spad" 2051127 2051138 2052159 2052186) (-1212 "TRANFUN.spad" 2050966 2050975 2051117 2051122) (-1211 "TRANFUN.spad" 2050803 2050814 2050956 2050961) (-1210 "TOPSP.spad" 2050477 2050486 2050793 2050798) (-1209 "TOOLSIGN.spad" 2050140 2050151 2050467 2050472) (-1208 "TEXTFILE.spad" 2048701 2048710 2050130 2050135) (-1207 "TEX.spad" 2045847 2045856 2048691 2048696) (-1206 "TEX1.spad" 2045403 2045414 2045837 2045842) (-1205 "TEMUTL.spad" 2044958 2044967 2045393 2045398) (-1204 "TBCMPPK.spad" 2043051 2043074 2044948 2044953) (-1203 "TBAGG.spad" 2042101 2042124 2043031 2043046) (-1202 "TBAGG.spad" 2041159 2041184 2042091 2042096) (-1201 "TANEXP.spad" 2040567 2040578 2041149 2041154) (-1200 "TALGOP.spad" 2040291 2040302 2040557 2040562) (-1199 "TABLE.spad" 2038702 2038725 2038972 2038999) (-1198 "TABLEAU.spad" 2038183 2038194 2038692 2038697) (-1197 "TABLBUMP.spad" 2034986 2034997 2038173 2038178) (-1196 "SYSTEM.spad" 2034214 2034223 2034976 2034981) (-1195 "SYSSOLP.spad" 2031697 2031708 2034204 2034209) (-1194 "SYSPTR.spad" 2031596 2031605 2031687 2031692) (-1193 "SYSNNI.spad" 2030778 2030789 2031586 2031591) (-1192 "SYSINT.spad" 2030182 2030193 2030768 2030773) (-1191 "SYNTAX.spad" 2026388 2026397 2030172 2030177) (-1190 "SYMTAB.spad" 2024456 2024465 2026378 2026383) (-1189 "SYMS.spad" 2020479 2020488 2024446 2024451) (-1188 "SYMPOLY.spad" 2019486 2019497 2019568 2019695) (-1187 "SYMFUNC.spad" 2018987 2018998 2019476 2019481) (-1186 "SYMBOL.spad" 2016490 2016499 2018977 2018982) (-1185 "SWITCH.spad" 2013261 2013270 2016480 2016485) (-1184 "SUTS.spad" 2010166 2010194 2011728 2011825) (-1183 "SUPXS.spad" 2007307 2007335 2008298 2008447) (-1182 "SUP.spad" 2004120 2004131 2004893 2005046) (-1181 "SUPFRACF.spad" 2003225 2003243 2004110 2004115) (-1180 "SUP2.spad" 2002617 2002630 2003215 2003220) (-1179 "SUMRF.spad" 2001591 2001602 2002607 2002612) (-1178 "SUMFS.spad" 2001228 2001245 2001581 2001586) (-1177 "SULS.spad" 1991773 1991801 1992873 1993302) (-1176 "SUCHTAST.spad" 1991542 1991551 1991763 1991768) (-1175 "SUCH.spad" 1991224 1991239 1991532 1991537) (-1174 "SUBSPACE.spad" 1983339 1983354 1991214 1991219) (-1173 "SUBRESP.spad" 1982509 1982523 1983295 1983300) (-1172 "STTF.spad" 1978608 1978624 1982499 1982504) (-1171 "STTFNC.spad" 1975076 1975092 1978598 1978603) (-1170 "STTAYLOR.spad" 1967711 1967722 1974957 1974962) (-1169 "STRTBL.spad" 1966216 1966233 1966365 1966392) (-1168 "STRING.spad" 1965625 1965634 1965639 1965666) (-1167 "STRICAT.spad" 1965413 1965422 1965593 1965620) (-1166 "STREAM.spad" 1962331 1962342 1964938 1964953) (-1165 "STREAM3.spad" 1961904 1961919 1962321 1962326) (-1164 "STREAM2.spad" 1961032 1961045 1961894 1961899) (-1163 "STREAM1.spad" 1960738 1960749 1961022 1961027) (-1162 "STINPROD.spad" 1959674 1959690 1960728 1960733) (-1161 "STEP.spad" 1958875 1958884 1959664 1959669) (-1160 "STEPAST.spad" 1958109 1958118 1958865 1958870) (-1159 "STBL.spad" 1956635 1956663 1956802 1956817) (-1158 "STAGG.spad" 1955710 1955721 1956625 1956630) (-1157 "STAGG.spad" 1954783 1954796 1955700 1955705) (-1156 "STACK.spad" 1954140 1954151 1954390 1954417) (-1155 "SREGSET.spad" 1951844 1951861 1953786 1953813) (-1154 "SRDCMPK.spad" 1950405 1950425 1951834 1951839) (-1153 "SRAGG.spad" 1945548 1945557 1950373 1950400) (-1152 "SRAGG.spad" 1940711 1940722 1945538 1945543) (-1151 "SQMATRIX.spad" 1938327 1938345 1939243 1939330) (-1150 "SPLTREE.spad" 1932879 1932892 1937763 1937790) (-1149 "SPLNODE.spad" 1929467 1929480 1932869 1932874) (-1148 "SPFCAT.spad" 1928276 1928285 1929457 1929462) (-1147 "SPECOUT.spad" 1926828 1926837 1928266 1928271) (-1146 "SPADXPT.spad" 1918423 1918432 1926818 1926823) (-1145 "spad-parser.spad" 1917888 1917897 1918413 1918418) (-1144 "SPADAST.spad" 1917589 1917598 1917878 1917883) (-1143 "SPACEC.spad" 1901788 1901799 1917579 1917584) (-1142 "SPACE3.spad" 1901564 1901575 1901778 1901783) (-1141 "SORTPAK.spad" 1901113 1901126 1901520 1901525) (-1140 "SOLVETRA.spad" 1898876 1898887 1901103 1901108) (-1139 "SOLVESER.spad" 1897404 1897415 1898866 1898871) (-1138 "SOLVERAD.spad" 1893430 1893441 1897394 1897399) (-1137 "SOLVEFOR.spad" 1891892 1891910 1893420 1893425) (-1136 "SNTSCAT.spad" 1891492 1891509 1891860 1891887) (-1135 "SMTS.spad" 1889764 1889790 1891057 1891154) (-1134 "SMP.spad" 1887239 1887259 1887629 1887756) (-1133 "SMITH.spad" 1886084 1886109 1887229 1887234) (-1132 "SMATCAT.spad" 1884194 1884224 1886028 1886079) (-1131 "SMATCAT.spad" 1882236 1882268 1884072 1884077) (-1130 "SKAGG.spad" 1881199 1881210 1882204 1882231) (-1129 "SINT.spad" 1880139 1880148 1881065 1881194) (-1128 "SIMPAN.spad" 1879867 1879876 1880129 1880134) (-1127 "SIG.spad" 1879197 1879206 1879857 1879862) (-1126 "SIGNRF.spad" 1878315 1878326 1879187 1879192) (-1125 "SIGNEF.spad" 1877594 1877611 1878305 1878310) (-1124 "SIGAST.spad" 1876979 1876988 1877584 1877589) (-1123 "SHP.spad" 1874907 1874922 1876935 1876940) (-1122 "SHDP.spad" 1864618 1864645 1865127 1865258) (-1121 "SGROUP.spad" 1864226 1864235 1864608 1864613) (-1120 "SGROUP.spad" 1863832 1863843 1864216 1864221) (-1119 "SGCF.spad" 1856971 1856980 1863822 1863827) (-1118 "SFRTCAT.spad" 1855901 1855918 1856939 1856966) (-1117 "SFRGCD.spad" 1854964 1854984 1855891 1855896) (-1116 "SFQCMPK.spad" 1849601 1849621 1854954 1854959) (-1115 "SFORT.spad" 1849040 1849054 1849591 1849596) (-1114 "SEXOF.spad" 1848883 1848923 1849030 1849035) (-1113 "SEX.spad" 1848775 1848784 1848873 1848878) (-1112 "SEXCAT.spad" 1846556 1846596 1848765 1848770) (-1111 "SET.spad" 1844880 1844891 1845977 1846016) (-1110 "SETMN.spad" 1843330 1843347 1844870 1844875) (-1109 "SETCAT.spad" 1842652 1842661 1843320 1843325) (-1108 "SETCAT.spad" 1841972 1841983 1842642 1842647) (-1107 "SETAGG.spad" 1838521 1838532 1841952 1841967) (-1106 "SETAGG.spad" 1835078 1835091 1838511 1838516) (-1105 "SEQAST.spad" 1834781 1834790 1835068 1835073) (-1104 "SEGXCAT.spad" 1833937 1833950 1834771 1834776) (-1103 "SEG.spad" 1833750 1833761 1833856 1833861) (-1102 "SEGCAT.spad" 1832675 1832686 1833740 1833745) (-1101 "SEGBIND.spad" 1832433 1832444 1832622 1832627) (-1100 "SEGBIND2.spad" 1832131 1832144 1832423 1832428) (-1099 "SEGAST.spad" 1831845 1831854 1832121 1832126) (-1098 "SEG2.spad" 1831280 1831293 1831801 1831806) (-1097 "SDVAR.spad" 1830556 1830567 1831270 1831275) (-1096 "SDPOL.spad" 1827982 1827993 1828273 1828400) (-1095 "SCPKG.spad" 1826071 1826082 1827972 1827977) (-1094 "SCOPE.spad" 1825224 1825233 1826061 1826066) (-1093 "SCACHE.spad" 1823920 1823931 1825214 1825219) (-1092 "SASTCAT.spad" 1823829 1823838 1823910 1823915) (-1091 "SAOS.spad" 1823701 1823710 1823819 1823824) (-1090 "SAERFFC.spad" 1823414 1823434 1823691 1823696) (-1089 "SAE.spad" 1821589 1821605 1822200 1822335) (-1088 "SAEFACT.spad" 1821290 1821310 1821579 1821584) (-1087 "RURPK.spad" 1818949 1818965 1821280 1821285) (-1086 "RULESET.spad" 1818402 1818426 1818939 1818944) (-1085 "RULE.spad" 1816642 1816666 1818392 1818397) (-1084 "RULECOLD.spad" 1816494 1816507 1816632 1816637) (-1083 "RTVALUE.spad" 1816229 1816238 1816484 1816489) (-1082 "RSTRCAST.spad" 1815946 1815955 1816219 1816224) (-1081 "RSETGCD.spad" 1812324 1812344 1815936 1815941) (-1080 "RSETCAT.spad" 1802260 1802277 1812292 1812319) (-1079 "RSETCAT.spad" 1792216 1792235 1802250 1802255) (-1078 "RSDCMPK.spad" 1790668 1790688 1792206 1792211) (-1077 "RRCC.spad" 1789052 1789082 1790658 1790663) (-1076 "RRCC.spad" 1787434 1787466 1789042 1789047) (-1075 "RPTAST.spad" 1787136 1787145 1787424 1787429) (-1074 "RPOLCAT.spad" 1766496 1766511 1787004 1787131) (-1073 "RPOLCAT.spad" 1745569 1745586 1766079 1766084) (-1072 "ROUTINE.spad" 1741452 1741461 1744216 1744243) (-1071 "ROMAN.spad" 1740780 1740789 1741318 1741447) (-1070 "ROIRC.spad" 1739860 1739892 1740770 1740775) (-1069 "RNS.spad" 1738763 1738772 1739762 1739855) (-1068 "RNS.spad" 1737752 1737763 1738753 1738758) (-1067 "RNG.spad" 1737487 1737496 1737742 1737747) (-1066 "RNGBIND.spad" 1736647 1736661 1737442 1737447) (-1065 "RMODULE.spad" 1736412 1736423 1736637 1736642) (-1064 "RMCAT2.spad" 1735832 1735889 1736402 1736407) (-1063 "RMATRIX.spad" 1734656 1734675 1734999 1735038) (-1062 "RMATCAT.spad" 1730235 1730266 1734612 1734651) (-1061 "RMATCAT.spad" 1725704 1725737 1730083 1730088) (-1060 "RLINSET.spad" 1725098 1725109 1725694 1725699) (-1059 "RINTERP.spad" 1724986 1725006 1725088 1725093) (-1058 "RING.spad" 1724456 1724465 1724966 1724981) (-1057 "RING.spad" 1723934 1723945 1724446 1724451) (-1056 "RIDIST.spad" 1723326 1723335 1723924 1723929) (-1055 "RGCHAIN.spad" 1721909 1721925 1722811 1722838) (-1054 "RGBCSPC.spad" 1721690 1721702 1721899 1721904) (-1053 "RGBCMDL.spad" 1721220 1721232 1721680 1721685) (-1052 "RF.spad" 1718862 1718873 1721210 1721215) (-1051 "RFFACTOR.spad" 1718324 1718335 1718852 1718857) (-1050 "RFFACT.spad" 1718059 1718071 1718314 1718319) (-1049 "RFDIST.spad" 1717055 1717064 1718049 1718054) (-1048 "RETSOL.spad" 1716474 1716487 1717045 1717050) (-1047 "RETRACT.spad" 1715902 1715913 1716464 1716469) (-1046 "RETRACT.spad" 1715328 1715341 1715892 1715897) (-1045 "RETAST.spad" 1715140 1715149 1715318 1715323) (-1044 "RESULT.spad" 1713200 1713209 1713787 1713814) (-1043 "RESRING.spad" 1712547 1712594 1713138 1713195) (-1042 "RESLATC.spad" 1711871 1711882 1712537 1712542) (-1041 "REPSQ.spad" 1711602 1711613 1711861 1711866) (-1040 "REP.spad" 1709156 1709165 1711592 1711597) (-1039 "REPDB.spad" 1708863 1708874 1709146 1709151) (-1038 "REP2.spad" 1698521 1698532 1708705 1708710) (-1037 "REP1.spad" 1692717 1692728 1698471 1698476) (-1036 "REGSET.spad" 1690514 1690531 1692363 1692390) (-1035 "REF.spad" 1689849 1689860 1690469 1690474) (-1034 "REDORDER.spad" 1689055 1689072 1689839 1689844) (-1033 "RECLOS.spad" 1687838 1687858 1688542 1688635) (-1032 "REALSOLV.spad" 1686978 1686987 1687828 1687833) (-1031 "REAL.spad" 1686850 1686859 1686968 1686973) (-1030 "REAL0Q.spad" 1684148 1684163 1686840 1686845) (-1029 "REAL0.spad" 1680992 1681007 1684138 1684143) (-1028 "RDUCEAST.spad" 1680713 1680722 1680982 1680987) (-1027 "RDIV.spad" 1680368 1680393 1680703 1680708) (-1026 "RDIST.spad" 1679935 1679946 1680358 1680363) (-1025 "RDETRS.spad" 1678799 1678817 1679925 1679930) (-1024 "RDETR.spad" 1676938 1676956 1678789 1678794) (-1023 "RDEEFS.spad" 1676037 1676054 1676928 1676933) (-1022 "RDEEF.spad" 1675047 1675064 1676027 1676032) (-1021 "RCFIELD.spad" 1672233 1672242 1674949 1675042) (-1020 "RCFIELD.spad" 1669505 1669516 1672223 1672228) (-1019 "RCAGG.spad" 1667433 1667444 1669495 1669500) (-1018 "RCAGG.spad" 1665288 1665301 1667352 1667357) (-1017 "RATRET.spad" 1664648 1664659 1665278 1665283) (-1016 "RATFACT.spad" 1664340 1664352 1664638 1664643) (-1015 "RANDSRC.spad" 1663659 1663668 1664330 1664335) (-1014 "RADUTIL.spad" 1663415 1663424 1663649 1663654) (-1013 "RADIX.spad" 1660336 1660350 1661882 1661975) (-1012 "RADFF.spad" 1658749 1658786 1658868 1659024) (-1011 "RADCAT.spad" 1658344 1658353 1658739 1658744) (-1010 "RADCAT.spad" 1657937 1657948 1658334 1658339) (-1009 "QUEUE.spad" 1657285 1657296 1657544 1657571) (-1008 "QUAT.spad" 1655866 1655877 1656209 1656274) (-1007 "QUATCT2.spad" 1655486 1655505 1655856 1655861) (-1006 "QUATCAT.spad" 1653656 1653667 1655416 1655481) (-1005 "QUATCAT.spad" 1651577 1651590 1653339 1653344) (-1004 "QUAGG.spad" 1650404 1650415 1651545 1651572) (-1003 "QQUTAST.spad" 1650172 1650181 1650394 1650399) (-1002 "QFORM.spad" 1649790 1649805 1650162 1650167) (-1001 "QFCAT.spad" 1648492 1648503 1649692 1649785) (-1000 "QFCAT.spad" 1646785 1646798 1647987 1647992) (-999 "QFCAT2.spad" 1646478 1646494 1646775 1646780) (-998 "QEQUAT.spad" 1646037 1646045 1646468 1646473) (-997 "QCMPACK.spad" 1640784 1640803 1646027 1646032) (-996 "QALGSET.spad" 1636863 1636895 1640698 1640703) (-995 "QALGSET2.spad" 1634859 1634877 1636853 1636858) (-994 "PWFFINTB.spad" 1632275 1632296 1634849 1634854) (-993 "PUSHVAR.spad" 1631614 1631633 1632265 1632270) (-992 "PTRANFN.spad" 1627742 1627752 1631604 1631609) (-991 "PTPACK.spad" 1624830 1624840 1627732 1627737) (-990 "PTFUNC2.spad" 1624653 1624667 1624820 1624825) (-989 "PTCAT.spad" 1623908 1623918 1624621 1624648) (-988 "PSQFR.spad" 1623215 1623239 1623898 1623903) (-987 "PSEUDLIN.spad" 1622101 1622111 1623205 1623210) (-986 "PSETPK.spad" 1607534 1607550 1621979 1621984) (-985 "PSETCAT.spad" 1601454 1601477 1607514 1607529) (-984 "PSETCAT.spad" 1595348 1595373 1601410 1601415) (-983 "PSCURVE.spad" 1594331 1594339 1595338 1595343) (-982 "PSCAT.spad" 1593114 1593143 1594229 1594326) (-981 "PSCAT.spad" 1591987 1592018 1593104 1593109) (-980 "PRTITION.spad" 1590685 1590693 1591977 1591982) (-979 "PRTDAST.spad" 1590404 1590412 1590675 1590680) (-978 "PRS.spad" 1579966 1579983 1590360 1590365) (-977 "PRQAGG.spad" 1579401 1579411 1579934 1579961) (-976 "PROPLOG.spad" 1578973 1578981 1579391 1579396) (-975 "PROPFUN2.spad" 1578596 1578609 1578963 1578968) (-974 "PROPFUN1.spad" 1577994 1578005 1578586 1578591) (-973 "PROPFRML.spad" 1576562 1576573 1577984 1577989) (-972 "PROPERTY.spad" 1576050 1576058 1576552 1576557) (-971 "PRODUCT.spad" 1573732 1573744 1574016 1574071) (-970 "PR.spad" 1572124 1572136 1572823 1572950) (-969 "PRINT.spad" 1571876 1571884 1572114 1572119) (-968 "PRIMES.spad" 1570129 1570139 1571866 1571871) (-967 "PRIMELT.spad" 1568210 1568224 1570119 1570124) (-966 "PRIMCAT.spad" 1567837 1567845 1568200 1568205) (-965 "PRIMARR.spad" 1566842 1566852 1567020 1567047) (-964 "PRIMARR2.spad" 1565609 1565621 1566832 1566837) (-963 "PREASSOC.spad" 1564991 1565003 1565599 1565604) (-962 "PPCURVE.spad" 1564128 1564136 1564981 1564986) (-961 "PORTNUM.spad" 1563903 1563911 1564118 1564123) (-960 "POLYROOT.spad" 1562752 1562774 1563859 1563864) (-959 "POLY.spad" 1560087 1560097 1560602 1560729) (-958 "POLYLIFT.spad" 1559352 1559375 1560077 1560082) (-957 "POLYCATQ.spad" 1557470 1557492 1559342 1559347) (-956 "POLYCAT.spad" 1550940 1550961 1557338 1557465) (-955 "POLYCAT.spad" 1543748 1543771 1550148 1550153) (-954 "POLY2UP.spad" 1543200 1543214 1543738 1543743) (-953 "POLY2.spad" 1542797 1542809 1543190 1543195) (-952 "POLUTIL.spad" 1541738 1541767 1542753 1542758) (-951 "POLTOPOL.spad" 1540486 1540501 1541728 1541733) (-950 "POINT.spad" 1539324 1539334 1539411 1539438) (-949 "PNTHEORY.spad" 1536026 1536034 1539314 1539319) (-948 "PMTOOLS.spad" 1534801 1534815 1536016 1536021) (-947 "PMSYM.spad" 1534350 1534360 1534791 1534796) (-946 "PMQFCAT.spad" 1533941 1533955 1534340 1534345) (-945 "PMPRED.spad" 1533420 1533434 1533931 1533936) (-944 "PMPREDFS.spad" 1532874 1532896 1533410 1533415) (-943 "PMPLCAT.spad" 1531954 1531972 1532806 1532811) (-942 "PMLSAGG.spad" 1531539 1531553 1531944 1531949) (-941 "PMKERNEL.spad" 1531118 1531130 1531529 1531534) (-940 "PMINS.spad" 1530698 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"FINITE.spad" 599827 599835 600665 600670) (-372 "FINAALG.spad" 588948 588958 599769 599822) (-371 "FINAALG.spad" 578081 578093 588904 588909) (-370 "FILE.spad" 577664 577674 578071 578076) (-369 "FILECAT.spad" 576190 576207 577654 577659) (-368 "FIELD.spad" 575596 575604 576092 576185) (-367 "FIELD.spad" 575088 575098 575586 575591) (-366 "FGROUP.spad" 573735 573745 575068 575083) (-365 "FGLMICPK.spad" 572522 572537 573725 573730) (-364 "FFX.spad" 571897 571912 572238 572331) (-363 "FFSLPE.spad" 571400 571421 571887 571892) (-362 "FFPOLY.spad" 562662 562673 571390 571395) (-361 "FFPOLY2.spad" 561722 561739 562652 562657) (-360 "FFP.spad" 561119 561139 561438 561531) (-359 "FF.spad" 560567 560583 560800 560893) (-358 "FFNBX.spad" 559079 559099 560283 560376) (-357 "FFNBP.spad" 557592 557609 558795 558888) (-356 "FFNB.spad" 556057 556078 557273 557366) (-355 "FFINTBAS.spad" 553571 553590 556047 556052) (-354 "FFIELDC.spad" 551148 551156 553473 553566) (-353 "FFIELDC.spad" 548811 548821 551138 551143) (-352 "FFHOM.spad" 547559 547576 548801 548806) (-351 "FFF.spad" 544994 545005 547549 547554) (-350 "FFCGX.spad" 543841 543861 544710 544803) (-349 "FFCGP.spad" 542730 542750 543557 543650) (-348 "FFCG.spad" 541522 541543 542411 542504) (-347 "FFCAT.spad" 534695 534717 541361 541517) (-346 "FFCAT.spad" 527947 527971 534615 534620) (-345 "FFCAT2.spad" 527694 527734 527937 527942) (-344 "FEXPR.spad" 519411 519457 527450 527489) (-343 "FEVALAB.spad" 519119 519129 519401 519406) (-342 "FEVALAB.spad" 518612 518624 518896 518901) (-341 "FDIV.spad" 518054 518078 518602 518607) (-340 "FDIVCAT.spad" 516118 516142 518044 518049) (-339 "FDIVCAT.spad" 514180 514206 516108 516113) (-338 "FDIV2.spad" 513836 513876 514170 514175) (-337 "FCTRDATA.spad" 512844 512852 513826 513831) (-336 "FCPAK1.spad" 511411 511419 512834 512839) (-335 "FCOMP.spad" 510790 510800 511401 511406) (-334 "FC.spad" 500797 500805 510780 510785) (-333 "FAXF.spad" 493768 493782 500699 500792) (-332 "FAXF.spad" 486791 486807 493724 493729) (-331 "FARRAY.spad" 484941 484951 485974 486001) (-330 "FAMR.spad" 483077 483089 484839 484936) (-329 "FAMR.spad" 481197 481211 482961 482966) (-328 "FAMONOID.spad" 480865 480875 481151 481156) (-327 "FAMONC.spad" 479161 479173 480855 480860) (-326 "FAGROUP.spad" 478785 478795 479057 479084) (-325 "FACUTIL.spad" 476989 477006 478775 478780) (-324 "FACTFUNC.spad" 476183 476193 476979 476984) (-323 "EXPUPXS.spad" 473016 473039 474315 474464) (-322 "EXPRTUBE.spad" 470304 470312 473006 473011) (-321 "EXPRODE.spad" 467464 467480 470294 470299) (-320 "EXPR.spad" 462739 462749 463453 463860) (-319 "EXPR2UPS.spad" 458861 458874 462729 462734) (-318 "EXPR2.spad" 458566 458578 458851 458856) (-317 "EXPEXPAN.spad" 455506 455531 456138 456231) (-316 "EXIT.spad" 455177 455185 455496 455501) (-315 "EXITAST.spad" 454913 454921 455167 455172) (-314 "EVALCYC.spad" 454373 454387 454903 454908) (-313 "EVALAB.spad" 453945 453955 454363 454368) (-312 "EVALAB.spad" 453515 453527 453935 453940) (-311 "EUCDOM.spad" 451089 451097 453441 453510) (-310 "EUCDOM.spad" 448725 448735 451079 451084) (-309 "ESTOOLS.spad" 440571 440579 448715 448720) (-308 "ESTOOLS2.spad" 440174 440188 440561 440566) (-307 "ESTOOLS1.spad" 439859 439870 440164 440169) (-306 "ES.spad" 432674 432682 439849 439854) (-305 "ES.spad" 425395 425405 432572 432577) (-304 "ESCONT.spad" 422188 422196 425385 425390) (-303 "ESCONT1.spad" 421937 421949 422178 422183) (-302 "ES2.spad" 421442 421458 421927 421932) (-301 "ES1.spad" 421012 421028 421432 421437) (-300 "ERROR.spad" 418339 418347 421002 421007) (-299 "EQTBL.spad" 416811 416833 417020 417047) (-298 "EQ.spad" 411616 411626 414403 414515) (-297 "EQ2.spad" 411334 411346 411606 411611) (-296 "EP.spad" 407660 407670 411324 411329) (-295 "ENV.spad" 406338 406346 407650 407655) (-294 "ENTIRER.spad" 406006 406014 406282 406333) (-293 "EMR.spad" 405294 405335 405932 406001) (-292 "ELTAGG.spad" 403548 403567 405284 405289) (-291 "ELTAGG.spad" 401766 401787 403504 403509) (-290 "ELTAB.spad" 401241 401254 401756 401761) (-289 "ELFUTS.spad" 400628 400647 401231 401236) (-288 "ELEMFUN.spad" 400317 400325 400618 400623) (-287 "ELEMFUN.spad" 400004 400014 400307 400312) (-286 "ELAGG.spad" 397975 397985 399984 399999) (-285 "ELAGG.spad" 395883 395895 397894 397899) (-284 "ELABOR.spad" 395229 395237 395873 395878) (-283 "ELABEXPR.spad" 394161 394169 395219 395224) (-282 "EFUPXS.spad" 390937 390967 394117 394122) (-281 "EFULS.spad" 387773 387796 390893 390898) (-280 "EFSTRUC.spad" 385788 385804 387763 387768) (-279 "EF.spad" 380564 380580 385778 385783) (-278 "EAB.spad" 378840 378848 380554 380559) (-277 "E04UCFA.spad" 378376 378384 378830 378835) (-276 "E04NAFA.spad" 377953 377961 378366 378371) (-275 "E04MBFA.spad" 377533 377541 377943 377948) (-274 "E04JAFA.spad" 377069 377077 377523 377528) (-273 "E04GCFA.spad" 376605 376613 377059 377064) (-272 "E04FDFA.spad" 376141 376149 376595 376600) (-271 "E04DGFA.spad" 375677 375685 376131 376136) (-270 "E04AGNT.spad" 371527 371535 375667 375672) (-269 "DVARCAT.spad" 368216 368226 371517 371522) (-268 "DVARCAT.spad" 364903 364915 368206 368211) (-267 "DSMP.spad" 362370 362384 362675 362802) (-266 "DROPT.spad" 356329 356337 362360 362365) (-265 "DROPT1.spad" 355994 356004 356319 356324) (-264 "DROPT0.spad" 350851 350859 355984 355989) (-263 "DRAWPT.spad" 349024 349032 350841 350846) (-262 "DRAW.spad" 341900 341913 349014 349019) (-261 "DRAWHACK.spad" 341208 341218 341890 341895) (-260 "DRAWCX.spad" 338678 338686 341198 341203) (-259 "DRAWCURV.spad" 338225 338240 338668 338673) (-258 "DRAWCFUN.spad" 327757 327765 338215 338220) (-257 "DQAGG.spad" 325935 325945 327725 327752) (-256 "DPOLCAT.spad" 321284 321300 325803 325930) (-255 "DPOLCAT.spad" 316719 316737 321240 321245) (-254 "DPMO.spad" 308945 308961 309083 309384) (-253 "DPMM.spad" 301184 301202 301309 301610) (-252 "DOMTMPLT.spad" 300955 300963 301174 301179) (-251 "DOMCTOR.spad" 300710 300718 300945 300950) (-250 "DOMAIN.spad" 299797 299805 300700 300705) (-249 "DMP.spad" 297057 297072 297627 297754) (-248 "DLP.spad" 296409 296419 297047 297052) (-247 "DLIST.spad" 294988 294998 295592 295619) (-246 "DLAGG.spad" 293405 293415 294978 294983) (-245 "DIVRING.spad" 292947 292955 293349 293400) (-244 "DIVRING.spad" 292533 292543 292937 292942) (-243 "DISPLAY.spad" 290723 290731 292523 292528) (-242 "DIRPROD.spad" 280303 280319 280943 281074) (-241 "DIRPROD2.spad" 279121 279139 280293 280298) (-240 "DIRPCAT.spad" 278065 278081 278985 279116) (-239 "DIRPCAT.spad" 276738 276756 277660 277665) (-238 "DIOSP.spad" 275563 275571 276728 276733) (-237 "DIOPS.spad" 274559 274569 275543 275558) (-236 "DIOPS.spad" 273529 273541 274515 274520) (-235 "DIFRING.spad" 272825 272833 273509 273524) (-234 "DIFRING.spad" 272129 272139 272815 272820) (-233 "DIFEXT.spad" 271300 271310 272109 272124) (-232 "DIFEXT.spad" 270388 270400 271199 271204) (-231 "DIAGG.spad" 270018 270028 270368 270383) (-230 "DIAGG.spad" 269656 269668 270008 270013) (-229 "DHMATRIX.spad" 267968 267978 269113 269140) (-228 "DFSFUN.spad" 261608 261616 267958 267963) (-227 "DFLOAT.spad" 258339 258347 261498 261603) (-226 "DFINTTLS.spad" 256570 256586 258329 258334) (-225 "DERHAM.spad" 254484 254516 256550 256565) (-224 "DEQUEUE.spad" 253808 253818 254091 254118) (-223 "DEGRED.spad" 253425 253439 253798 253803) (-222 "DEFINTRF.spad" 250962 250972 253415 253420) (-221 "DEFINTEF.spad" 249472 249488 250952 250957) (-220 "DEFAST.spad" 248840 248848 249462 249467) (-219 "DECIMAL.spad" 246946 246954 247307 247400) (-218 "DDFACT.spad" 244759 244776 246936 246941) (-217 "DBLRESP.spad" 244359 244383 244749 244754) (-216 "DBASE.spad" 243023 243033 244349 244354) (-215 "DATAARY.spad" 242485 242498 243013 243018) (-214 "D03FAFA.spad" 242313 242321 242475 242480) (-213 "D03EEFA.spad" 242133 242141 242303 242308) (-212 "D03AGNT.spad" 241219 241227 242123 242128) (-211 "D02EJFA.spad" 240681 240689 241209 241214) (-210 "D02CJFA.spad" 240159 240167 240671 240676) (-209 "D02BHFA.spad" 239649 239657 240149 240154) (-208 "D02BBFA.spad" 239139 239147 239639 239644) (-207 "D02AGNT.spad" 233953 233961 239129 239134) (-206 "D01WGTS.spad" 232272 232280 233943 233948) (-205 "D01TRNS.spad" 232249 232257 232262 232267) (-204 "D01GBFA.spad" 231771 231779 232239 232244) (-203 "D01FCFA.spad" 231293 231301 231761 231766) (-202 "D01ASFA.spad" 230761 230769 231283 231288) (-201 "D01AQFA.spad" 230207 230215 230751 230756) (-200 "D01APFA.spad" 229631 229639 230197 230202) (-199 "D01ANFA.spad" 229125 229133 229621 229626) (-198 "D01AMFA.spad" 228635 228643 229115 229120) (-197 "D01ALFA.spad" 228175 228183 228625 228630) (-196 "D01AKFA.spad" 227701 227709 228165 228170) (-195 "D01AJFA.spad" 227224 227232 227691 227696) (-194 "D01AGNT.spad" 223291 223299 227214 227219) (-193 "CYCLOTOM.spad" 222797 222805 223281 223286) (-192 "CYCLES.spad" 219589 219597 222787 222792) (-191 "CVMP.spad" 219006 219016 219579 219584) (-190 "CTRIGMNP.spad" 217506 217522 218996 219001) (-189 "CTOR.spad" 217197 217205 217496 217501) (-188 "CTORKIND.spad" 216800 216808 217187 217192) (-187 "CTORCAT.spad" 216049 216057 216790 216795) (-186 "CTORCAT.spad" 215296 215306 216039 216044) (-185 "CTORCALL.spad" 214885 214895 215286 215291) (-184 "CSTTOOLS.spad" 214130 214143 214875 214880) (-183 "CRFP.spad" 207854 207867 214120 214125) (-182 "CRCEAST.spad" 207574 207582 207844 207849) (-181 "CRAPACK.spad" 206625 206635 207564 207569) (-180 "CPMATCH.spad" 206129 206144 206550 206555) (-179 "CPIMA.spad" 205834 205853 206119 206124) (-178 "COORDSYS.spad" 200843 200853 205824 205829) (-177 "CONTOUR.spad" 200254 200262 200833 200838) (-176 "CONTFRAC.spad" 196004 196014 200156 200249) (-175 "CONDUIT.spad" 195762 195770 195994 195999) (-174 "COMRING.spad" 195436 195444 195700 195757) (-173 "COMPPROP.spad" 194954 194962 195426 195431) (-172 "COMPLPAT.spad" 194721 194736 194944 194949) (-171 "COMPLEX.spad" 188858 188868 189102 189363) (-170 "COMPLEX2.spad" 188573 188585 188848 188853) (-169 "COMPILER.spad" 188122 188130 188563 188568) (-168 "COMPFACT.spad" 187724 187738 188112 188117) (-167 "COMPCAT.spad" 185796 185806 187458 187719) (-166 "COMPCAT.spad" 183596 183608 185260 185265) (-165 "COMMUPC.spad" 183344 183362 183586 183591) (-164 "COMMONOP.spad" 182877 182885 183334 183339) (-163 "COMM.spad" 182688 182696 182867 182872) (-162 "COMMAAST.spad" 182451 182459 182678 182683) (-161 "COMBOPC.spad" 181366 181374 182441 182446) (-160 "COMBINAT.spad" 180133 180143 181356 181361) (-159 "COMBF.spad" 177515 177531 180123 180128) (-158 "COLOR.spad" 176352 176360 177505 177510) (-157 "COLONAST.spad" 176018 176026 176342 176347) (-156 "CMPLXRT.spad" 175729 175746 176008 176013) (-155 "CLLCTAST.spad" 175391 175399 175719 175724) (-154 "CLIP.spad" 171499 171507 175381 175386) (-153 "CLIF.spad" 170154 170170 171455 171494) (-152 "CLAGG.spad" 166659 166669 170144 170149) (-151 "CLAGG.spad" 163035 163047 166522 166527) (-150 "CINTSLPE.spad" 162366 162379 163025 163030) (-149 "CHVAR.spad" 160504 160526 162356 162361) (-148 "CHARZ.spad" 160419 160427 160484 160499) (-147 "CHARPOL.spad" 159929 159939 160409 160414) (-146 "CHARNZ.spad" 159682 159690 159909 159924) (-145 "CHAR.spad" 157556 157564 159672 159677) (-144 "CFCAT.spad" 156884 156892 157546 157551) (-143 "CDEN.spad" 156080 156094 156874 156879) (-142 "CCLASS.spad" 154229 154237 155491 155530) (-141 "CATEGORY.spad" 153271 153279 154219 154224) (-140 "CATCTOR.spad" 153162 153170 153261 153266) (-139 "CATAST.spad" 152780 152788 153152 153157) (-138 "CASEAST.spad" 152494 152502 152770 152775) (-137 "CARTEN.spad" 147861 147885 152484 152489) (-136 "CARTEN2.spad" 147251 147278 147851 147856) (-135 "CARD.spad" 144546 144554 147225 147246) (-134 "CAPSLAST.spad" 144320 144328 144536 144541) (-133 "CACHSET.spad" 143944 143952 144310 144315) (-132 "CABMON.spad" 143499 143507 143934 143939) (-131 "BYTEORD.spad" 143174 143182 143489 143494) (-130 "BYTE.spad" 142601 142609 143164 143169) (-129 "BYTEBUF.spad" 140460 140468 141770 141797) (-128 "BTREE.spad" 139533 139543 140067 140094) (-127 "BTOURN.spad" 138538 138548 139140 139167) (-126 "BTCAT.spad" 137930 137940 138506 138533) (-125 "BTCAT.spad" 137342 137354 137920 137925) (-124 "BTAGG.spad" 136808 136816 137310 137337) (-123 "BTAGG.spad" 136294 136304 136798 136803) (-122 "BSTREE.spad" 135035 135045 135901 135928) (-121 "BRILL.spad" 133232 133243 135025 135030) (-120 "BRAGG.spad" 132172 132182 133222 133227) (-119 "BRAGG.spad" 131076 131088 132128 132133) (-118 "BPADICRT.spad" 129057 129069 129312 129405) (-117 "BPADIC.spad" 128721 128733 128983 129052) (-116 "BOUNDZRO.spad" 128377 128394 128711 128716) (-115 "BOP.spad" 123559 123567 128367 128372) (-114 "BOP1.spad" 121025 121035 123549 123554) (-113 "BOOLE.spad" 120675 120683 121015 121020) (-112 "BOOLEAN.spad" 120113 120121 120665 120670) (-111 "BMODULE.spad" 119825 119837 120081 120108) (-110 "BITS.spad" 119246 119254 119461 119488) (-109 "BINDING.spad" 118659 118667 119236 119241) (-108 "BINARY.spad" 116770 116778 117126 117219) (-107 "BGAGG.spad" 115975 115985 116750 116765) (-106 "BGAGG.spad" 115188 115200 115965 115970) (-105 "BFUNCT.spad" 114752 114760 115168 115183) (-104 "BEZOUT.spad" 113892 113919 114702 114707) (-103 "BBTREE.spad" 110737 110747 113499 113526) (-102 "BASTYPE.spad" 110409 110417 110727 110732) (-101 "BASTYPE.spad" 110079 110089 110399 110404) (-100 "BALFACT.spad" 109538 109551 110069 110074) (-99 "AUTOMOR.spad" 108989 108998 109518 109533) (-98 "ATTREG.spad" 105712 105719 108741 108984) (-97 "ATTRBUT.spad" 101735 101742 105692 105707) (-96 "ATTRAST.spad" 101452 101459 101725 101730) (-95 "ATRIG.spad" 100922 100929 101442 101447) (-94 "ATRIG.spad" 100390 100399 100912 100917) (-93 "ASTCAT.spad" 100294 100301 100380 100385) (-92 "ASTCAT.spad" 100196 100205 100284 100289) (-91 "ASTACK.spad" 99535 99544 99803 99830) (-90 "ASSOCEQ.spad" 98361 98372 99491 99496) (-89 "ASP9.spad" 97442 97455 98351 98356) (-88 "ASP8.spad" 96485 96498 97432 97437) (-87 "ASP80.spad" 95807 95820 96475 96480) (-86 "ASP7.spad" 94967 94980 95797 95802) (-85 "ASP78.spad" 94418 94431 94957 94962) (-84 "ASP77.spad" 93787 93800 94408 94413) (-83 "ASP74.spad" 92879 92892 93777 93782) (-82 "ASP73.spad" 92150 92163 92869 92874) (-81 "ASP6.spad" 91017 91030 92140 92145) (-80 "ASP55.spad" 89526 89539 91007 91012) (-79 "ASP50.spad" 87343 87356 89516 89521) (-78 "ASP4.spad" 86638 86651 87333 87338) (-77 "ASP49.spad" 85637 85650 86628 86633) (-76 "ASP42.spad" 84044 84083 85627 85632) (-75 "ASP41.spad" 82623 82662 84034 84039) (-74 "ASP35.spad" 81611 81624 82613 82618) (-73 "ASP34.spad" 80912 80925 81601 81606) (-72 "ASP33.spad" 80472 80485 80902 80907) (-71 "ASP31.spad" 79612 79625 80462 80467) (-70 "ASP30.spad" 78504 78517 79602 79607) (-69 "ASP29.spad" 77970 77983 78494 78499) (-68 "ASP28.spad" 69243 69256 77960 77965) (-67 "ASP27.spad" 68140 68153 69233 69238) (-66 "ASP24.spad" 67227 67240 68130 68135) (-65 "ASP20.spad" 66691 66704 67217 67222) (-64 "ASP1.spad" 66072 66085 66681 66686) (-63 "ASP19.spad" 60758 60771 66062 66067) (-62 "ASP12.spad" 60172 60185 60748 60753) (-61 "ASP10.spad" 59443 59456 60162 60167) (-60 "ARRAY2.spad" 58803 58812 59050 59077) (-59 "ARRAY1.spad" 57640 57649 57986 58013) (-58 "ARRAY12.spad" 56353 56364 57630 57635) (-57 "ARR2CAT.spad" 52127 52148 56321 56348) (-56 "ARR2CAT.spad" 47921 47944 52117 52122) (-55 "ARITY.spad" 47293 47300 47911 47916) (-54 "APPRULE.spad" 46553 46575 47283 47288) (-53 "APPLYORE.spad" 46172 46185 46543 46548) (-52 "ANY.spad" 45031 45038 46162 46167) (-51 "ANY1.spad" 44102 44111 45021 45026) (-50 "ANTISYM.spad" 42547 42563 44082 44097) (-49 "ANON.spad" 42240 42247 42537 42542) (-48 "AN.spad" 40549 40556 42056 42149) (-47 "AMR.spad" 38734 38745 40447 40544) (-46 "AMR.spad" 36756 36769 38471 38476) (-45 "ALIST.spad" 34168 34189 34518 34545) (-44 "ALGSC.spad" 33303 33329 34040 34093) (-43 "ALGPKG.spad" 29086 29097 33259 33264) (-42 "ALGMFACT.spad" 28279 28293 29076 29081) (-41 "ALGMANIP.spad" 25753 25768 28112 28117) (-40 "ALGFF.spad" 24068 24095 24285 24441) (-39 "ALGFACT.spad" 23195 23205 24058 24063) (-38 "ALGEBRA.spad" 23028 23037 23151 23190) (-37 "ALGEBRA.spad" 22893 22904 23018 23023) (-36 "ALAGG.spad" 22405 22426 22861 22888) (-35 "AHYP.spad" 21786 21793 22395 22400) (-34 "AGG.spad" 20103 20110 21776 21781) (-33 "AGG.spad" 18384 18393 20059 20064) (-32 "AF.spad" 16815 16830 18319 18324) (-31 "ADDAST.spad" 16493 16500 16805 16810) (-30 "ACPLOT.spad" 15084 15091 16483 16488) (-29 "ACFS.spad" 12893 12902 14986 15079) (-28 "ACFS.spad" 10788 10799 12883 12888) (-27 "ACF.spad" 7470 7477 10690 10783) (-26 "ACF.spad" 4238 4247 7460 7465) (-25 "ABELSG.spad" 3779 3786 4228 4233) (-24 "ABELSG.spad" 3318 3327 3769 3774) (-23 "ABELMON.spad" 2861 2868 3308 3313) (-22 "ABELMON.spad" 2402 2411 2851 2856) (-21 "ABELGRP.spad" 2067 2074 2392 2397) (-20 "ABELGRP.spad" 1730 1739 2057 2062) (-19 "A1AGG.spad" 870 879 1698 1725) (-18 "A1AGG.spad" 30 41 860 865))
\ No newline at end of file +((-3 NIL 2266164 2266169 2266174 2266179) (-2 NIL 2266144 2266149 2266154 2266159) (-1 NIL 2266124 2266129 2266134 2266139) (0 NIL 2266104 2266109 2266114 2266119) (-1306 "ZMOD.spad" 2265913 2265926 2266042 2266099) (-1305 "ZLINDEP.spad" 2264979 2264990 2265903 2265908) (-1304 "ZDSOLVE.spad" 2254924 2254946 2264969 2264974) (-1303 "YSTREAM.spad" 2254419 2254430 2254914 2254919) (-1302 "YDIAGRAM.spad" 2254053 2254062 2254409 2254414) (-1301 "XRPOLY.spad" 2253273 2253293 2253909 2253978) (-1300 "XPR.spad" 2251068 2251081 2252991 2253090) (-1299 "XPOLY.spad" 2250623 2250634 2250924 2250993) (-1298 "XPOLYC.spad" 2249942 2249958 2250549 2250618) (-1297 "XPBWPOLY.spad" 2248379 2248399 2249722 2249791) (-1296 "XF.spad" 2246842 2246857 2248281 2248374) (-1295 "XF.spad" 2245285 2245302 2246726 2246731) (-1294 "XFALG.spad" 2242333 2242349 2245211 2245280) (-1293 "XEXPPKG.spad" 2241584 2241610 2242323 2242328) (-1292 "XDPOLY.spad" 2241198 2241214 2241440 2241509) (-1291 "XALG.spad" 2240858 2240869 2241154 2241193) (-1290 "WUTSET.spad" 2236697 2236714 2240504 2240531) (-1289 "WP.spad" 2235896 2235940 2236555 2236622) (-1288 "WHILEAST.spad" 2235694 2235703 2235886 2235891) (-1287 "WHEREAST.spad" 2235365 2235374 2235684 2235689) (-1286 "WFFINTBS.spad" 2233028 2233050 2235355 2235360) (-1285 "WEIER.spad" 2231250 2231261 2233018 2233023) (-1284 "VSPACE.spad" 2230923 2230934 2231218 2231245) (-1283 "VSPACE.spad" 2230616 2230629 2230913 2230918) (-1282 "VOID.spad" 2230293 2230302 2230606 2230611) (-1281 "VIEW.spad" 2227973 2227982 2230283 2230288) (-1280 "VIEWDEF.spad" 2223174 2223183 2227963 2227968) (-1279 "VIEW3D.spad" 2207135 2207144 2223164 2223169) (-1278 "VIEW2D.spad" 2195026 2195035 2207125 2207130) (-1277 "VECTOR.spad" 2193700 2193711 2193951 2193978) (-1276 "VECTOR2.spad" 2192339 2192352 2193690 2193695) (-1275 "VECTCAT.spad" 2190243 2190254 2192307 2192334) (-1274 "VECTCAT.spad" 2187954 2187967 2190020 2190025) (-1273 "VARIABLE.spad" 2187734 2187749 2187944 2187949) (-1272 "UTYPE.spad" 2187378 2187387 2187724 2187729) (-1271 "UTSODETL.spad" 2186673 2186697 2187334 2187339) (-1270 "UTSODE.spad" 2184889 2184909 2186663 2186668) (-1269 "UTS.spad" 2179693 2179721 2183356 2183453) (-1268 "UTSCAT.spad" 2177172 2177188 2179591 2179688) (-1267 "UTSCAT.spad" 2174295 2174313 2176716 2176721) (-1266 "UTS2.spad" 2173890 2173925 2174285 2174290) (-1265 "URAGG.spad" 2168563 2168574 2173880 2173885) (-1264 "URAGG.spad" 2163200 2163213 2168519 2168524) (-1263 "UPXSSING.spad" 2160845 2160871 2162281 2162414) (-1262 "UPXS.spad" 2157999 2158027 2158977 2159126) (-1261 "UPXSCONS.spad" 2155758 2155778 2156131 2156280) (-1260 "UPXSCCA.spad" 2154329 2154349 2155604 2155753) (-1259 "UPXSCCA.spad" 2153042 2153064 2154319 2154324) (-1258 "UPXSCAT.spad" 2151631 2151647 2152888 2153037) (-1257 "UPXS2.spad" 2151174 2151227 2151621 2151626) (-1256 "UPSQFREE.spad" 2149588 2149602 2151164 2151169) (-1255 "UPSCAT.spad" 2147375 2147399 2149486 2149583) (-1254 "UPSCAT.spad" 2144868 2144894 2146981 2146986) (-1253 "UPOLYC.spad" 2139908 2139919 2144710 2144863) (-1252 "UPOLYC.spad" 2134840 2134853 2139644 2139649) (-1251 "UPOLYC2.spad" 2134311 2134330 2134830 2134835) (-1250 "UP.spad" 2131510 2131525 2131897 2132050) (-1249 "UPMP.spad" 2130410 2130423 2131500 2131505) (-1248 "UPDIVP.spad" 2129975 2129989 2130400 2130405) (-1247 "UPDECOMP.spad" 2128220 2128234 2129965 2129970) (-1246 "UPCDEN.spad" 2127429 2127445 2128210 2128215) (-1245 "UP2.spad" 2126793 2126814 2127419 2127424) (-1244 "UNISEG.spad" 2126146 2126157 2126712 2126717) (-1243 "UNISEG2.spad" 2125643 2125656 2126102 2126107) (-1242 "UNIFACT.spad" 2124746 2124758 2125633 2125638) (-1241 "ULS.spad" 2115304 2115332 2116391 2116820) (-1240 "ULSCONS.spad" 2107700 2107720 2108070 2108219) (-1239 "ULSCCAT.spad" 2105437 2105457 2107546 2107695) (-1238 "ULSCCAT.spad" 2103282 2103304 2105393 2105398) (-1237 "ULSCAT.spad" 2101514 2101530 2103128 2103277) (-1236 "ULS2.spad" 2101028 2101081 2101504 2101509) (-1235 "UINT8.spad" 2100905 2100914 2101018 2101023) (-1234 "UINT64.spad" 2100781 2100790 2100895 2100900) (-1233 "UINT32.spad" 2100657 2100666 2100771 2100776) (-1232 "UINT16.spad" 2100533 2100542 2100647 2100652) (-1231 "UFD.spad" 2099598 2099607 2100459 2100528) (-1230 "UFD.spad" 2098725 2098736 2099588 2099593) (-1229 "UDVO.spad" 2097606 2097615 2098715 2098720) (-1228 "UDPO.spad" 2095099 2095110 2097562 2097567) (-1227 "TYPE.spad" 2095031 2095040 2095089 2095094) (-1226 "TYPEAST.spad" 2094950 2094959 2095021 2095026) (-1225 "TWOFACT.spad" 2093602 2093617 2094940 2094945) (-1224 "TUPLE.spad" 2093088 2093099 2093501 2093506) (-1223 "TUBETOOL.spad" 2089955 2089964 2093078 2093083) (-1222 "TUBE.spad" 2088602 2088619 2089945 2089950) (-1221 "TS.spad" 2087201 2087217 2088167 2088264) (-1220 "TSETCAT.spad" 2074328 2074345 2087169 2087196) (-1219 "TSETCAT.spad" 2061441 2061460 2074284 2074289) (-1218 "TRMANIP.spad" 2055807 2055824 2061147 2061152) (-1217 "TRIMAT.spad" 2054770 2054795 2055797 2055802) (-1216 "TRIGMNIP.spad" 2053297 2053314 2054760 2054765) (-1215 "TRIGCAT.spad" 2052809 2052818 2053287 2053292) (-1214 "TRIGCAT.spad" 2052319 2052330 2052799 2052804) (-1213 "TREE.spad" 2050894 2050905 2051926 2051953) (-1212 "TRANFUN.spad" 2050733 2050742 2050884 2050889) (-1211 "TRANFUN.spad" 2050570 2050581 2050723 2050728) (-1210 "TOPSP.spad" 2050244 2050253 2050560 2050565) (-1209 "TOOLSIGN.spad" 2049907 2049918 2050234 2050239) (-1208 "TEXTFILE.spad" 2048468 2048477 2049897 2049902) (-1207 "TEX.spad" 2045614 2045623 2048458 2048463) (-1206 "TEX1.spad" 2045170 2045181 2045604 2045609) (-1205 "TEMUTL.spad" 2044725 2044734 2045160 2045165) (-1204 "TBCMPPK.spad" 2042818 2042841 2044715 2044720) (-1203 "TBAGG.spad" 2041868 2041891 2042798 2042813) (-1202 "TBAGG.spad" 2040926 2040951 2041858 2041863) (-1201 "TANEXP.spad" 2040334 2040345 2040916 2040921) (-1200 "TALGOP.spad" 2040058 2040069 2040324 2040329) (-1199 "TABLE.spad" 2038469 2038492 2038739 2038766) (-1198 "TABLEAU.spad" 2037950 2037961 2038459 2038464) (-1197 "TABLBUMP.spad" 2034753 2034764 2037940 2037945) (-1196 "SYSTEM.spad" 2033981 2033990 2034743 2034748) (-1195 "SYSSOLP.spad" 2031464 2031475 2033971 2033976) (-1194 "SYSPTR.spad" 2031363 2031372 2031454 2031459) (-1193 "SYSNNI.spad" 2030545 2030556 2031353 2031358) (-1192 "SYSINT.spad" 2029949 2029960 2030535 2030540) (-1191 "SYNTAX.spad" 2026155 2026164 2029939 2029944) (-1190 "SYMTAB.spad" 2024223 2024232 2026145 2026150) (-1189 "SYMS.spad" 2020246 2020255 2024213 2024218) (-1188 "SYMPOLY.spad" 2019253 2019264 2019335 2019462) (-1187 "SYMFUNC.spad" 2018754 2018765 2019243 2019248) (-1186 "SYMBOL.spad" 2016257 2016266 2018744 2018749) (-1185 "SWITCH.spad" 2013028 2013037 2016247 2016252) (-1184 "SUTS.spad" 2009933 2009961 2011495 2011592) (-1183 "SUPXS.spad" 2007074 2007102 2008065 2008214) (-1182 "SUP.spad" 2003887 2003898 2004660 2004813) (-1181 "SUPFRACF.spad" 2002992 2003010 2003877 2003882) (-1180 "SUP2.spad" 2002384 2002397 2002982 2002987) (-1179 "SUMRF.spad" 2001358 2001369 2002374 2002379) (-1178 "SUMFS.spad" 2000995 2001012 2001348 2001353) (-1177 "SULS.spad" 1991540 1991568 1992640 1993069) (-1176 "SUCHTAST.spad" 1991309 1991318 1991530 1991535) (-1175 "SUCH.spad" 1990991 1991006 1991299 1991304) (-1174 "SUBSPACE.spad" 1983106 1983121 1990981 1990986) (-1173 "SUBRESP.spad" 1982276 1982290 1983062 1983067) (-1172 "STTF.spad" 1978375 1978391 1982266 1982271) (-1171 "STTFNC.spad" 1974843 1974859 1978365 1978370) (-1170 "STTAYLOR.spad" 1967478 1967489 1974724 1974729) (-1169 "STRTBL.spad" 1965983 1966000 1966132 1966159) (-1168 "STRING.spad" 1965392 1965401 1965406 1965433) (-1167 "STRICAT.spad" 1965180 1965189 1965360 1965387) (-1166 "STREAM.spad" 1962098 1962109 1964705 1964720) (-1165 "STREAM3.spad" 1961671 1961686 1962088 1962093) (-1164 "STREAM2.spad" 1960799 1960812 1961661 1961666) (-1163 "STREAM1.spad" 1960505 1960516 1960789 1960794) (-1162 "STINPROD.spad" 1959441 1959457 1960495 1960500) (-1161 "STEP.spad" 1958642 1958651 1959431 1959436) (-1160 "STEPAST.spad" 1957876 1957885 1958632 1958637) (-1159 "STBL.spad" 1956402 1956430 1956569 1956584) (-1158 "STAGG.spad" 1955477 1955488 1956392 1956397) (-1157 "STAGG.spad" 1954550 1954563 1955467 1955472) (-1156 "STACK.spad" 1953907 1953918 1954157 1954184) (-1155 "SREGSET.spad" 1951611 1951628 1953553 1953580) (-1154 "SRDCMPK.spad" 1950172 1950192 1951601 1951606) (-1153 "SRAGG.spad" 1945315 1945324 1950140 1950167) (-1152 "SRAGG.spad" 1940478 1940489 1945305 1945310) (-1151 "SQMATRIX.spad" 1938094 1938112 1939010 1939097) (-1150 "SPLTREE.spad" 1932646 1932659 1937530 1937557) (-1149 "SPLNODE.spad" 1929234 1929247 1932636 1932641) (-1148 "SPFCAT.spad" 1928043 1928052 1929224 1929229) (-1147 "SPECOUT.spad" 1926595 1926604 1928033 1928038) (-1146 "SPADXPT.spad" 1918190 1918199 1926585 1926590) (-1145 "spad-parser.spad" 1917655 1917664 1918180 1918185) (-1144 "SPADAST.spad" 1917356 1917365 1917645 1917650) (-1143 "SPACEC.spad" 1901555 1901566 1917346 1917351) (-1142 "SPACE3.spad" 1901331 1901342 1901545 1901550) (-1141 "SORTPAK.spad" 1900880 1900893 1901287 1901292) (-1140 "SOLVETRA.spad" 1898643 1898654 1900870 1900875) (-1139 "SOLVESER.spad" 1897171 1897182 1898633 1898638) (-1138 "SOLVERAD.spad" 1893197 1893208 1897161 1897166) (-1137 "SOLVEFOR.spad" 1891659 1891677 1893187 1893192) (-1136 "SNTSCAT.spad" 1891259 1891276 1891627 1891654) (-1135 "SMTS.spad" 1889531 1889557 1890824 1890921) (-1134 "SMP.spad" 1887006 1887026 1887396 1887523) (-1133 "SMITH.spad" 1885851 1885876 1886996 1887001) (-1132 "SMATCAT.spad" 1883961 1883991 1885795 1885846) (-1131 "SMATCAT.spad" 1882003 1882035 1883839 1883844) (-1130 "SKAGG.spad" 1880966 1880977 1881971 1881998) (-1129 "SINT.spad" 1879906 1879915 1880832 1880961) (-1128 "SIMPAN.spad" 1879634 1879643 1879896 1879901) (-1127 "SIG.spad" 1878964 1878973 1879624 1879629) (-1126 "SIGNRF.spad" 1878082 1878093 1878954 1878959) (-1125 "SIGNEF.spad" 1877361 1877378 1878072 1878077) (-1124 "SIGAST.spad" 1876746 1876755 1877351 1877356) (-1123 "SHP.spad" 1874674 1874689 1876702 1876707) (-1122 "SHDP.spad" 1864385 1864412 1864894 1865025) (-1121 "SGROUP.spad" 1863993 1864002 1864375 1864380) (-1120 "SGROUP.spad" 1863599 1863610 1863983 1863988) (-1119 "SGCF.spad" 1856738 1856747 1863589 1863594) (-1118 "SFRTCAT.spad" 1855668 1855685 1856706 1856733) (-1117 "SFRGCD.spad" 1854731 1854751 1855658 1855663) (-1116 "SFQCMPK.spad" 1849368 1849388 1854721 1854726) (-1115 "SFORT.spad" 1848807 1848821 1849358 1849363) (-1114 "SEXOF.spad" 1848650 1848690 1848797 1848802) (-1113 "SEX.spad" 1848542 1848551 1848640 1848645) (-1112 "SEXCAT.spad" 1846323 1846363 1848532 1848537) (-1111 "SET.spad" 1844647 1844658 1845744 1845783) (-1110 "SETMN.spad" 1843097 1843114 1844637 1844642) (-1109 "SETCAT.spad" 1842419 1842428 1843087 1843092) (-1108 "SETCAT.spad" 1841739 1841750 1842409 1842414) (-1107 "SETAGG.spad" 1838288 1838299 1841719 1841734) (-1106 "SETAGG.spad" 1834845 1834858 1838278 1838283) (-1105 "SEQAST.spad" 1834548 1834557 1834835 1834840) (-1104 "SEGXCAT.spad" 1833704 1833717 1834538 1834543) (-1103 "SEG.spad" 1833517 1833528 1833623 1833628) (-1102 "SEGCAT.spad" 1832442 1832453 1833507 1833512) (-1101 "SEGBIND.spad" 1832200 1832211 1832389 1832394) (-1100 "SEGBIND2.spad" 1831898 1831911 1832190 1832195) (-1099 "SEGAST.spad" 1831612 1831621 1831888 1831893) (-1098 "SEG2.spad" 1831047 1831060 1831568 1831573) (-1097 "SDVAR.spad" 1830323 1830334 1831037 1831042) (-1096 "SDPOL.spad" 1827749 1827760 1828040 1828167) (-1095 "SCPKG.spad" 1825838 1825849 1827739 1827744) (-1094 "SCOPE.spad" 1824991 1825000 1825828 1825833) (-1093 "SCACHE.spad" 1823687 1823698 1824981 1824986) (-1092 "SASTCAT.spad" 1823596 1823605 1823677 1823682) (-1091 "SAOS.spad" 1823468 1823477 1823586 1823591) (-1090 "SAERFFC.spad" 1823181 1823201 1823458 1823463) (-1089 "SAE.spad" 1821356 1821372 1821967 1822102) (-1088 "SAEFACT.spad" 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1740542) (-1069 "RNS.spad" 1738530 1738539 1739529 1739622) (-1068 "RNS.spad" 1737519 1737530 1738520 1738525) (-1067 "RNG.spad" 1737254 1737263 1737509 1737514) (-1066 "RNGBIND.spad" 1736414 1736428 1737209 1737214) (-1065 "RMODULE.spad" 1736179 1736190 1736404 1736409) (-1064 "RMCAT2.spad" 1735599 1735656 1736169 1736174) (-1063 "RMATRIX.spad" 1734423 1734442 1734766 1734805) (-1062 "RMATCAT.spad" 1730002 1730033 1734379 1734418) (-1061 "RMATCAT.spad" 1725471 1725504 1729850 1729855) (-1060 "RLINSET.spad" 1724865 1724876 1725461 1725466) (-1059 "RINTERP.spad" 1724753 1724773 1724855 1724860) (-1058 "RING.spad" 1724223 1724232 1724733 1724748) (-1057 "RING.spad" 1723701 1723712 1724213 1724218) (-1056 "RIDIST.spad" 1723093 1723102 1723691 1723696) (-1055 "RGCHAIN.spad" 1721676 1721692 1722578 1722605) (-1054 "RGBCSPC.spad" 1721457 1721469 1721666 1721671) (-1053 "RGBCMDL.spad" 1720987 1720999 1721447 1721452) (-1052 "RF.spad" 1718629 1718640 1720977 1720982) (-1051 "RFFACTOR.spad" 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(-1032 "REALSOLV.spad" 1686745 1686754 1687595 1687600) (-1031 "REAL.spad" 1686617 1686626 1686735 1686740) (-1030 "REAL0Q.spad" 1683915 1683930 1686607 1686612) (-1029 "REAL0.spad" 1680759 1680774 1683905 1683910) (-1028 "RDUCEAST.spad" 1680480 1680489 1680749 1680754) (-1027 "RDIV.spad" 1680135 1680160 1680470 1680475) (-1026 "RDIST.spad" 1679702 1679713 1680125 1680130) (-1025 "RDETRS.spad" 1678566 1678584 1679692 1679697) (-1024 "RDETR.spad" 1676705 1676723 1678556 1678561) (-1023 "RDEEFS.spad" 1675804 1675821 1676695 1676700) (-1022 "RDEEF.spad" 1674814 1674831 1675794 1675799) (-1021 "RCFIELD.spad" 1672000 1672009 1674716 1674809) (-1020 "RCFIELD.spad" 1669272 1669283 1671990 1671995) (-1019 "RCAGG.spad" 1667200 1667211 1669262 1669267) (-1018 "RCAGG.spad" 1665055 1665068 1667119 1667124) (-1017 "RATRET.spad" 1664415 1664426 1665045 1665050) (-1016 "RATFACT.spad" 1664107 1664119 1664405 1664410) (-1015 "RANDSRC.spad" 1663426 1663435 1664097 1664102) (-1014 "RADUTIL.spad" 1663182 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(-901 "PCOMP.spad" 1450901 1450914 1451038 1451043) (-900 "PBWLB.spad" 1449489 1449506 1450891 1450896) (-899 "PATTERN.spad" 1444028 1444038 1449479 1449484) (-898 "PATTERN2.spad" 1443766 1443778 1444018 1444023) (-897 "PATTERN1.spad" 1442102 1442118 1443756 1443761) (-896 "PATRES.spad" 1439677 1439689 1442092 1442097) (-895 "PATRES2.spad" 1439349 1439363 1439667 1439672) (-894 "PATMATCH.spad" 1437546 1437577 1439057 1439062) (-893 "PATMAB.spad" 1436975 1436985 1437536 1437541) (-892 "PATLRES.spad" 1436061 1436075 1436965 1436970) (-891 "PATAB.spad" 1435825 1435835 1436051 1436056) (-890 "PARTPERM.spad" 1433833 1433841 1435815 1435820) (-889 "PARSURF.spad" 1433267 1433295 1433823 1433828) (-888 "PARSU2.spad" 1433064 1433080 1433257 1433262) (-887 "script-parser.spad" 1432584 1432592 1433054 1433059) (-886 "PARSCURV.spad" 1432018 1432046 1432574 1432579) (-885 "PARSC2.spad" 1431809 1431825 1432008 1432013) (-884 "PARPCURV.spad" 1431271 1431299 1431799 1431804) (-883 "PARPC2.spad" 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1378094) (-845 "OPTCAT.spad" 1368187 1368195 1370498 1370503) (-844 "OPSIG.spad" 1367841 1367849 1368177 1368182) (-843 "OPQUERY.spad" 1367390 1367398 1367831 1367836) (-842 "OP.spad" 1367132 1367142 1367212 1367279) (-841 "OPERCAT.spad" 1366598 1366608 1367122 1367127) (-840 "OPERCAT.spad" 1366062 1366074 1366588 1366593) (-839 "ONECOMP.spad" 1364807 1364817 1365609 1365638) (-838 "ONECOMP2.spad" 1364231 1364243 1364797 1364802) (-837 "OMSERVER.spad" 1363237 1363245 1364221 1364226) (-836 "OMSAGG.spad" 1363025 1363035 1363193 1363232) (-835 "OMPKG.spad" 1361641 1361649 1363015 1363020) (-834 "OM.spad" 1360614 1360622 1361631 1361636) (-833 "OMLO.spad" 1360039 1360051 1360500 1360539) (-832 "OMEXPR.spad" 1359873 1359883 1360029 1360034) (-831 "OMERR.spad" 1359418 1359426 1359863 1359868) (-830 "OMERRK.spad" 1358452 1358460 1359408 1359413) (-829 "OMENC.spad" 1357796 1357804 1358442 1358447) (-828 "OMDEV.spad" 1352105 1352113 1357786 1357791) (-827 "OMCONN.spad" 1351514 1351522 1352095 1352100) (-826 "OINTDOM.spad" 1351277 1351285 1351440 1351509) (-825 "OFMONOID.spad" 1349400 1349410 1351233 1351238) (-824 "ODVAR.spad" 1348661 1348671 1349390 1349395) (-823 "ODR.spad" 1348305 1348331 1348473 1348622) (-822 "ODPOL.spad" 1345687 1345697 1346027 1346154) (-821 "ODP.spad" 1335534 1335554 1335907 1336038) (-820 "ODETOOLS.spad" 1334183 1334202 1335524 1335529) (-819 "ODESYS.spad" 1331877 1331894 1334173 1334178) (-818 "ODERTRIC.spad" 1327886 1327903 1331834 1331839) (-817 "ODERED.spad" 1327285 1327309 1327876 1327881) (-816 "ODERAT.spad" 1324900 1324917 1327275 1327280) (-815 "ODEPRRIC.spad" 1321937 1321959 1324890 1324895) (-814 "ODEPROB.spad" 1321194 1321202 1321927 1321932) (-813 "ODEPRIM.spad" 1318528 1318550 1321184 1321189) (-812 "ODEPAL.spad" 1317914 1317938 1318518 1318523) (-811 "ODEPACK.spad" 1304580 1304588 1317904 1317909) (-810 "ODEINT.spad" 1304015 1304031 1304570 1304575) (-809 "ODEIFTBL.spad" 1301410 1301418 1304005 1304010) (-808 "ODEEF.spad" 1296901 1296917 1301400 1301405) (-807 "ODECONST.spad" 1296438 1296456 1296891 1296896) (-806 "ODECAT.spad" 1295036 1295044 1296428 1296433) (-805 "OCT.spad" 1293172 1293182 1293886 1293925) (-804 "OCTCT2.spad" 1292818 1292839 1293162 1293167) (-803 "OC.spad" 1290614 1290624 1292774 1292813) (-802 "OC.spad" 1288135 1288147 1290297 1290302) (-801 "OCAMON.spad" 1287983 1287991 1288125 1288130) (-800 "OASGP.spad" 1287798 1287806 1287973 1287978) (-799 "OAMONS.spad" 1287320 1287328 1287788 1287793) (-798 "OAMON.spad" 1287181 1287189 1287310 1287315) (-797 "OAGROUP.spad" 1287043 1287051 1287171 1287176) (-796 "NUMTUBE.spad" 1286634 1286650 1287033 1287038) (-795 "NUMQUAD.spad" 1274610 1274618 1286624 1286629) (-794 "NUMODE.spad" 1265964 1265972 1274600 1274605) (-793 "NUMINT.spad" 1263530 1263538 1265954 1265959) (-792 "NUMFMT.spad" 1262370 1262378 1263520 1263525) (-791 "NUMERIC.spad" 1254484 1254494 1262175 1262180) (-790 "NTSCAT.spad" 1252992 1253008 1254452 1254479) (-789 "NTPOLFN.spad" 1252543 1252553 1252909 1252914) (-788 "NSUP.spad" 1245589 1245599 1250129 1250282) (-787 "NSUP2.spad" 1244981 1244993 1245579 1245584) (-786 "NSMP.spad" 1241211 1241230 1241519 1241646) (-785 "NREP.spad" 1239589 1239603 1241201 1241206) (-784 "NPCOEF.spad" 1238835 1238855 1239579 1239584) (-783 "NORMRETR.spad" 1238433 1238472 1238825 1238830) (-782 "NORMPK.spad" 1236335 1236354 1238423 1238428) (-781 "NORMMA.spad" 1236023 1236049 1236325 1236330) (-780 "NONE.spad" 1235764 1235772 1236013 1236018) (-779 "NONE1.spad" 1235440 1235450 1235754 1235759) (-778 "NODE1.spad" 1234927 1234943 1235430 1235435) (-777 "NNI.spad" 1233822 1233830 1234901 1234922) (-776 "NLINSOL.spad" 1232448 1232458 1233812 1233817) (-775 "NIPROB.spad" 1230989 1230997 1232438 1232443) (-774 "NFINTBAS.spad" 1228549 1228566 1230979 1230984) (-773 "NETCLT.spad" 1228523 1228534 1228539 1228544) (-772 "NCODIV.spad" 1226739 1226755 1228513 1228518) (-771 "NCNTFRAC.spad" 1226381 1226395 1226729 1226734) (-770 "NCEP.spad" 1224547 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"FMTC.spad" 637467 637475 637595 637664) (-392 "FMONOID.spad" 637132 637142 637423 637428) (-391 "FMONCAT.spad" 634285 634295 637122 637127) (-390 "FM.spad" 633980 633992 634219 634246) (-389 "FMFUN.spad" 631010 631018 633970 633975) (-388 "FMC.spad" 630062 630070 631000 631005) (-387 "FMCAT.spad" 627730 627748 630030 630057) (-386 "FM1.spad" 627087 627099 627664 627691) (-385 "FLOATRP.spad" 624822 624836 627077 627082) (-384 "FLOAT.spad" 618136 618144 624688 624817) (-383 "FLOATCP.spad" 615567 615581 618126 618131) (-382 "FLINEXP.spad" 615279 615289 615547 615562) (-381 "FLINEXP.spad" 614945 614957 615215 615220) (-380 "FLASORT.spad" 614271 614283 614935 614940) (-379 "FLALG.spad" 611917 611936 614197 614266) (-378 "FLAGG.spad" 608959 608969 611897 611912) (-377 "FLAGG.spad" 605902 605914 608842 608847) (-376 "FLAGG2.spad" 604627 604643 605892 605897) (-375 "FINRALG.spad" 602688 602701 604583 604622) (-374 "FINRALG.spad" 600675 600690 602572 602577) (-373 "FINITE.spad" 599827 599835 600665 600670) (-372 "FINAALG.spad" 588948 588958 599769 599822) (-371 "FINAALG.spad" 578081 578093 588904 588909) (-370 "FILE.spad" 577664 577674 578071 578076) (-369 "FILECAT.spad" 576190 576207 577654 577659) (-368 "FIELD.spad" 575596 575604 576092 576185) (-367 "FIELD.spad" 575088 575098 575586 575591) (-366 "FGROUP.spad" 573735 573745 575068 575083) (-365 "FGLMICPK.spad" 572522 572537 573725 573730) (-364 "FFX.spad" 571897 571912 572238 572331) (-363 "FFSLPE.spad" 571400 571421 571887 571892) (-362 "FFPOLY.spad" 562662 562673 571390 571395) (-361 "FFPOLY2.spad" 561722 561739 562652 562657) (-360 "FFP.spad" 561119 561139 561438 561531) (-359 "FF.spad" 560567 560583 560800 560893) (-358 "FFNBX.spad" 559079 559099 560283 560376) (-357 "FFNBP.spad" 557592 557609 558795 558888) (-356 "FFNB.spad" 556057 556078 557273 557366) (-355 "FFINTBAS.spad" 553571 553590 556047 556052) (-354 "FFIELDC.spad" 551148 551156 553473 553566) (-353 "FFIELDC.spad" 548811 548821 551138 551143) (-352 "FFHOM.spad" 547559 547576 548801 548806) (-351 "FFF.spad" 544994 545005 547549 547554) (-350 "FFCGX.spad" 543841 543861 544710 544803) (-349 "FFCGP.spad" 542730 542750 543557 543650) (-348 "FFCG.spad" 541522 541543 542411 542504) (-347 "FFCAT.spad" 534695 534717 541361 541517) (-346 "FFCAT.spad" 527947 527971 534615 534620) (-345 "FFCAT2.spad" 527694 527734 527937 527942) (-344 "FEXPR.spad" 519411 519457 527450 527489) (-343 "FEVALAB.spad" 519119 519129 519401 519406) (-342 "FEVALAB.spad" 518612 518624 518896 518901) (-341 "FDIV.spad" 518054 518078 518602 518607) (-340 "FDIVCAT.spad" 516118 516142 518044 518049) (-339 "FDIVCAT.spad" 514180 514206 516108 516113) (-338 "FDIV2.spad" 513836 513876 514170 514175) (-337 "FCTRDATA.spad" 512844 512852 513826 513831) (-336 "FCPAK1.spad" 511411 511419 512834 512839) (-335 "FCOMP.spad" 510790 510800 511401 511406) (-334 "FC.spad" 500797 500805 510780 510785) (-333 "FAXF.spad" 493768 493782 500699 500792) (-332 "FAXF.spad" 486791 486807 493724 493729) (-331 "FARRAY.spad" 484941 484951 485974 486001) (-330 "FAMR.spad" 483077 483089 484839 484936) (-329 "FAMR.spad" 481197 481211 482961 482966) (-328 "FAMONOID.spad" 480865 480875 481151 481156) (-327 "FAMONC.spad" 479161 479173 480855 480860) (-326 "FAGROUP.spad" 478785 478795 479057 479084) (-325 "FACUTIL.spad" 476989 477006 478775 478780) (-324 "FACTFUNC.spad" 476183 476193 476979 476984) (-323 "EXPUPXS.spad" 473016 473039 474315 474464) (-322 "EXPRTUBE.spad" 470304 470312 473006 473011) (-321 "EXPRODE.spad" 467464 467480 470294 470299) (-320 "EXPR.spad" 462739 462749 463453 463860) (-319 "EXPR2UPS.spad" 458861 458874 462729 462734) (-318 "EXPR2.spad" 458566 458578 458851 458856) (-317 "EXPEXPAN.spad" 455506 455531 456138 456231) (-316 "EXIT.spad" 455177 455185 455496 455501) (-315 "EXITAST.spad" 454913 454921 455167 455172) (-314 "EVALCYC.spad" 454373 454387 454903 454908) (-313 "EVALAB.spad" 453945 453955 454363 454368) (-312 "EVALAB.spad" 453515 453527 453935 453940) (-311 "EUCDOM.spad" 451089 451097 453441 453510) (-310 "EUCDOM.spad" 448725 448735 451079 451084) (-309 "ESTOOLS.spad" 440571 440579 448715 448720) (-308 "ESTOOLS2.spad" 440174 440188 440561 440566) (-307 "ESTOOLS1.spad" 439859 439870 440164 440169) (-306 "ES.spad" 432674 432682 439849 439854) (-305 "ES.spad" 425395 425405 432572 432577) (-304 "ESCONT.spad" 422188 422196 425385 425390) (-303 "ESCONT1.spad" 421937 421949 422178 422183) (-302 "ES2.spad" 421442 421458 421927 421932) (-301 "ES1.spad" 421012 421028 421432 421437) (-300 "ERROR.spad" 418339 418347 421002 421007) (-299 "EQTBL.spad" 416811 416833 417020 417047) (-298 "EQ.spad" 411616 411626 414403 414515) (-297 "EQ2.spad" 411334 411346 411606 411611) (-296 "EP.spad" 407660 407670 411324 411329) (-295 "ENV.spad" 406338 406346 407650 407655) (-294 "ENTIRER.spad" 406006 406014 406282 406333) (-293 "EMR.spad" 405294 405335 405932 406001) (-292 "ELTAGG.spad" 403548 403567 405284 405289) (-291 "ELTAGG.spad" 401766 401787 403504 403509) (-290 "ELTAB.spad" 401241 401254 401756 401761) (-289 "ELFUTS.spad" 400628 400647 401231 401236) (-288 "ELEMFUN.spad" 400317 400325 400618 400623) (-287 "ELEMFUN.spad" 400004 400014 400307 400312) (-286 "ELAGG.spad" 397975 397985 399984 399999) (-285 "ELAGG.spad" 395883 395895 397894 397899) (-284 "ELABOR.spad" 395229 395237 395873 395878) (-283 "ELABEXPR.spad" 394161 394169 395219 395224) (-282 "EFUPXS.spad" 390937 390967 394117 394122) (-281 "EFULS.spad" 387773 387796 390893 390898) (-280 "EFSTRUC.spad" 385788 385804 387763 387768) (-279 "EF.spad" 380564 380580 385778 385783) (-278 "EAB.spad" 378840 378848 380554 380559) (-277 "E04UCFA.spad" 378376 378384 378830 378835) (-276 "E04NAFA.spad" 377953 377961 378366 378371) (-275 "E04MBFA.spad" 377533 377541 377943 377948) (-274 "E04JAFA.spad" 377069 377077 377523 377528) (-273 "E04GCFA.spad" 376605 376613 377059 377064) (-272 "E04FDFA.spad" 376141 376149 376595 376600) (-271 "E04DGFA.spad" 375677 375685 376131 376136) (-270 "E04AGNT.spad" 371527 371535 375667 375672) (-269 "DVARCAT.spad" 368216 368226 371517 371522) (-268 "DVARCAT.spad" 364903 364915 368206 368211) (-267 "DSMP.spad" 362370 362384 362675 362802) (-266 "DROPT.spad" 356329 356337 362360 362365) (-265 "DROPT1.spad" 355994 356004 356319 356324) (-264 "DROPT0.spad" 350851 350859 355984 355989) (-263 "DRAWPT.spad" 349024 349032 350841 350846) (-262 "DRAW.spad" 341900 341913 349014 349019) (-261 "DRAWHACK.spad" 341208 341218 341890 341895) (-260 "DRAWCX.spad" 338678 338686 341198 341203) (-259 "DRAWCURV.spad" 338225 338240 338668 338673) (-258 "DRAWCFUN.spad" 327757 327765 338215 338220) (-257 "DQAGG.spad" 325935 325945 327725 327752) (-256 "DPOLCAT.spad" 321284 321300 325803 325930) (-255 "DPOLCAT.spad" 316719 316737 321240 321245) (-254 "DPMO.spad" 308945 308961 309083 309384) (-253 "DPMM.spad" 301184 301202 301309 301610) (-252 "DOMTMPLT.spad" 300955 300963 301174 301179) (-251 "DOMCTOR.spad" 300710 300718 300945 300950) (-250 "DOMAIN.spad" 299797 299805 300700 300705) (-249 "DMP.spad" 297057 297072 297627 297754) (-248 "DLP.spad" 296409 296419 297047 297052) (-247 "DLIST.spad" 294988 294998 295592 295619) (-246 "DLAGG.spad" 293405 293415 294978 294983) (-245 "DIVRING.spad" 292947 292955 293349 293400) (-244 "DIVRING.spad" 292533 292543 292937 292942) (-243 "DISPLAY.spad" 290723 290731 292523 292528) (-242 "DIRPROD.spad" 280303 280319 280943 281074) (-241 "DIRPROD2.spad" 279121 279139 280293 280298) (-240 "DIRPCAT.spad" 278065 278081 278985 279116) (-239 "DIRPCAT.spad" 276738 276756 277660 277665) (-238 "DIOSP.spad" 275563 275571 276728 276733) (-237 "DIOPS.spad" 274559 274569 275543 275558) (-236 "DIOPS.spad" 273529 273541 274515 274520) (-235 "DIFRING.spad" 272825 272833 273509 273524) (-234 "DIFRING.spad" 272129 272139 272815 272820) (-233 "DIFEXT.spad" 271300 271310 272109 272124) (-232 "DIFEXT.spad" 270388 270400 271199 271204) (-231 "DIAGG.spad" 270018 270028 270368 270383) (-230 "DIAGG.spad" 269656 269668 270008 270013) (-229 "DHMATRIX.spad" 267968 267978 269113 269140) (-228 "DFSFUN.spad" 261608 261616 267958 267963) (-227 "DFLOAT.spad" 258339 258347 261498 261603) (-226 "DFINTTLS.spad" 256570 256586 258329 258334) (-225 "DERHAM.spad" 254484 254516 256550 256565) (-224 "DEQUEUE.spad" 253808 253818 254091 254118) (-223 "DEGRED.spad" 253425 253439 253798 253803) (-222 "DEFINTRF.spad" 250962 250972 253415 253420) (-221 "DEFINTEF.spad" 249472 249488 250952 250957) (-220 "DEFAST.spad" 248840 248848 249462 249467) (-219 "DECIMAL.spad" 246946 246954 247307 247400) (-218 "DDFACT.spad" 244759 244776 246936 246941) (-217 "DBLRESP.spad" 244359 244383 244749 244754) (-216 "DBASE.spad" 243023 243033 244349 244354) (-215 "DATAARY.spad" 242485 242498 243013 243018) (-214 "D03FAFA.spad" 242313 242321 242475 242480) (-213 "D03EEFA.spad" 242133 242141 242303 242308) (-212 "D03AGNT.spad" 241219 241227 242123 242128) (-211 "D02EJFA.spad" 240681 240689 241209 241214) (-210 "D02CJFA.spad" 240159 240167 240671 240676) (-209 "D02BHFA.spad" 239649 239657 240149 240154) (-208 "D02BBFA.spad" 239139 239147 239639 239644) (-207 "D02AGNT.spad" 233953 233961 239129 239134) (-206 "D01WGTS.spad" 232272 232280 233943 233948) (-205 "D01TRNS.spad" 232249 232257 232262 232267) (-204 "D01GBFA.spad" 231771 231779 232239 232244) (-203 "D01FCFA.spad" 231293 231301 231761 231766) (-202 "D01ASFA.spad" 230761 230769 231283 231288) (-201 "D01AQFA.spad" 230207 230215 230751 230756) (-200 "D01APFA.spad" 229631 229639 230197 230202) (-199 "D01ANFA.spad" 229125 229133 229621 229626) (-198 "D01AMFA.spad" 228635 228643 229115 229120) (-197 "D01ALFA.spad" 228175 228183 228625 228630) (-196 "D01AKFA.spad" 227701 227709 228165 228170) (-195 "D01AJFA.spad" 227224 227232 227691 227696) (-194 "D01AGNT.spad" 223291 223299 227214 227219) (-193 "CYCLOTOM.spad" 222797 222805 223281 223286) (-192 "CYCLES.spad" 219589 219597 222787 222792) (-191 "CVMP.spad" 219006 219016 219579 219584) (-190 "CTRIGMNP.spad" 217506 217522 218996 219001) (-189 "CTOR.spad" 217197 217205 217496 217501) (-188 "CTORKIND.spad" 216800 216808 217187 217192) (-187 "CTORCAT.spad" 216049 216057 216790 216795) (-186 "CTORCAT.spad" 215296 215306 216039 216044) (-185 "CTORCALL.spad" 214885 214895 215286 215291) (-184 "CSTTOOLS.spad" 214130 214143 214875 214880) (-183 "CRFP.spad" 207854 207867 214120 214125) (-182 "CRCEAST.spad" 207574 207582 207844 207849) (-181 "CRAPACK.spad" 206625 206635 207564 207569) (-180 "CPMATCH.spad" 206129 206144 206550 206555) (-179 "CPIMA.spad" 205834 205853 206119 206124) (-178 "COORDSYS.spad" 200843 200853 205824 205829) (-177 "CONTOUR.spad" 200254 200262 200833 200838) (-176 "CONTFRAC.spad" 196004 196014 200156 200249) (-175 "CONDUIT.spad" 195762 195770 195994 195999) (-174 "COMRING.spad" 195436 195444 195700 195757) (-173 "COMPPROP.spad" 194954 194962 195426 195431) (-172 "COMPLPAT.spad" 194721 194736 194944 194949) (-171 "COMPLEX.spad" 188858 188868 189102 189363) (-170 "COMPLEX2.spad" 188573 188585 188848 188853) (-169 "COMPILER.spad" 188122 188130 188563 188568) (-168 "COMPFACT.spad" 187724 187738 188112 188117) (-167 "COMPCAT.spad" 185796 185806 187458 187719) (-166 "COMPCAT.spad" 183596 183608 185260 185265) (-165 "COMMUPC.spad" 183344 183362 183586 183591) (-164 "COMMONOP.spad" 182877 182885 183334 183339) (-163 "COMM.spad" 182688 182696 182867 182872) (-162 "COMMAAST.spad" 182451 182459 182678 182683) (-161 "COMBOPC.spad" 181366 181374 182441 182446) (-160 "COMBINAT.spad" 180133 180143 181356 181361) (-159 "COMBF.spad" 177515 177531 180123 180128) (-158 "COLOR.spad" 176352 176360 177505 177510) (-157 "COLONAST.spad" 176018 176026 176342 176347) (-156 "CMPLXRT.spad" 175729 175746 176008 176013) (-155 "CLLCTAST.spad" 175391 175399 175719 175724) (-154 "CLIP.spad" 171499 171507 175381 175386) (-153 "CLIF.spad" 170154 170170 171455 171494) (-152 "CLAGG.spad" 166659 166669 170144 170149) (-151 "CLAGG.spad" 163035 163047 166522 166527) (-150 "CINTSLPE.spad" 162366 162379 163025 163030) (-149 "CHVAR.spad" 160504 160526 162356 162361) (-148 "CHARZ.spad" 160419 160427 160484 160499) (-147 "CHARPOL.spad" 159929 159939 160409 160414) (-146 "CHARNZ.spad" 159682 159690 159909 159924) (-145 "CHAR.spad" 157556 157564 159672 159677) (-144 "CFCAT.spad" 156884 156892 157546 157551) (-143 "CDEN.spad" 156080 156094 156874 156879) (-142 "CCLASS.spad" 154229 154237 155491 155530) (-141 "CATEGORY.spad" 153271 153279 154219 154224) (-140 "CATCTOR.spad" 153162 153170 153261 153266) (-139 "CATAST.spad" 152780 152788 153152 153157) (-138 "CASEAST.spad" 152494 152502 152770 152775) (-137 "CARTEN.spad" 147861 147885 152484 152489) (-136 "CARTEN2.spad" 147251 147278 147851 147856) (-135 "CARD.spad" 144546 144554 147225 147246) (-134 "CAPSLAST.spad" 144320 144328 144536 144541) (-133 "CACHSET.spad" 143944 143952 144310 144315) (-132 "CABMON.spad" 143499 143507 143934 143939) (-131 "BYTEORD.spad" 143174 143182 143489 143494) (-130 "BYTE.spad" 142601 142609 143164 143169) (-129 "BYTEBUF.spad" 140460 140468 141770 141797) (-128 "BTREE.spad" 139533 139543 140067 140094) (-127 "BTOURN.spad" 138538 138548 139140 139167) (-126 "BTCAT.spad" 137930 137940 138506 138533) (-125 "BTCAT.spad" 137342 137354 137920 137925) (-124 "BTAGG.spad" 136808 136816 137310 137337) (-123 "BTAGG.spad" 136294 136304 136798 136803) (-122 "BSTREE.spad" 135035 135045 135901 135928) (-121 "BRILL.spad" 133232 133243 135025 135030) (-120 "BRAGG.spad" 132172 132182 133222 133227) (-119 "BRAGG.spad" 131076 131088 132128 132133) (-118 "BPADICRT.spad" 129057 129069 129312 129405) (-117 "BPADIC.spad" 128721 128733 128983 129052) (-116 "BOUNDZRO.spad" 128377 128394 128711 128716) (-115 "BOP.spad" 123559 123567 128367 128372) (-114 "BOP1.spad" 121025 121035 123549 123554) (-113 "BOOLE.spad" 120675 120683 121015 121020) (-112 "BOOLEAN.spad" 120113 120121 120665 120670) (-111 "BMODULE.spad" 119825 119837 120081 120108) (-110 "BITS.spad" 119246 119254 119461 119488) (-109 "BINDING.spad" 118659 118667 119236 119241) (-108 "BINARY.spad" 116770 116778 117126 117219) (-107 "BGAGG.spad" 115975 115985 116750 116765) (-106 "BGAGG.spad" 115188 115200 115965 115970) (-105 "BFUNCT.spad" 114752 114760 115168 115183) (-104 "BEZOUT.spad" 113892 113919 114702 114707) (-103 "BBTREE.spad" 110737 110747 113499 113526) (-102 "BASTYPE.spad" 110409 110417 110727 110732) (-101 "BASTYPE.spad" 110079 110089 110399 110404) (-100 "BALFACT.spad" 109538 109551 110069 110074) (-99 "AUTOMOR.spad" 108989 108998 109518 109533) (-98 "ATTREG.spad" 105712 105719 108741 108984) (-97 "ATTRBUT.spad" 101735 101742 105692 105707) (-96 "ATTRAST.spad" 101452 101459 101725 101730) (-95 "ATRIG.spad" 100922 100929 101442 101447) (-94 "ATRIG.spad" 100390 100399 100912 100917) (-93 "ASTCAT.spad" 100294 100301 100380 100385) (-92 "ASTCAT.spad" 100196 100205 100284 100289) (-91 "ASTACK.spad" 99535 99544 99803 99830) (-90 "ASSOCEQ.spad" 98361 98372 99491 99496) (-89 "ASP9.spad" 97442 97455 98351 98356) (-88 "ASP8.spad" 96485 96498 97432 97437) (-87 "ASP80.spad" 95807 95820 96475 96480) (-86 "ASP7.spad" 94967 94980 95797 95802) (-85 "ASP78.spad" 94418 94431 94957 94962) (-84 "ASP77.spad" 93787 93800 94408 94413) (-83 "ASP74.spad" 92879 92892 93777 93782) (-82 "ASP73.spad" 92150 92163 92869 92874) (-81 "ASP6.spad" 91017 91030 92140 92145) (-80 "ASP55.spad" 89526 89539 91007 91012) (-79 "ASP50.spad" 87343 87356 89516 89521) (-78 "ASP4.spad" 86638 86651 87333 87338) (-77 "ASP49.spad" 85637 85650 86628 86633) (-76 "ASP42.spad" 84044 84083 85627 85632) (-75 "ASP41.spad" 82623 82662 84034 84039) (-74 "ASP35.spad" 81611 81624 82613 82618) (-73 "ASP34.spad" 80912 80925 81601 81606) (-72 "ASP33.spad" 80472 80485 80902 80907) (-71 "ASP31.spad" 79612 79625 80462 80467) (-70 "ASP30.spad" 78504 78517 79602 79607) (-69 "ASP29.spad" 77970 77983 78494 78499) (-68 "ASP28.spad" 69243 69256 77960 77965) (-67 "ASP27.spad" 68140 68153 69233 69238) (-66 "ASP24.spad" 67227 67240 68130 68135) (-65 "ASP20.spad" 66691 66704 67217 67222) (-64 "ASP1.spad" 66072 66085 66681 66686) (-63 "ASP19.spad" 60758 60771 66062 66067) (-62 "ASP12.spad" 60172 60185 60748 60753) (-61 "ASP10.spad" 59443 59456 60162 60167) (-60 "ARRAY2.spad" 58803 58812 59050 59077) (-59 "ARRAY1.spad" 57640 57649 57986 58013) (-58 "ARRAY12.spad" 56353 56364 57630 57635) (-57 "ARR2CAT.spad" 52127 52148 56321 56348) (-56 "ARR2CAT.spad" 47921 47944 52117 52122) (-55 "ARITY.spad" 47293 47300 47911 47916) (-54 "APPRULE.spad" 46553 46575 47283 47288) (-53 "APPLYORE.spad" 46172 46185 46543 46548) (-52 "ANY.spad" 45031 45038 46162 46167) (-51 "ANY1.spad" 44102 44111 45021 45026) (-50 "ANTISYM.spad" 42547 42563 44082 44097) (-49 "ANON.spad" 42240 42247 42537 42542) (-48 "AN.spad" 40549 40556 42056 42149) (-47 "AMR.spad" 38734 38745 40447 40544) (-46 "AMR.spad" 36756 36769 38471 38476) (-45 "ALIST.spad" 34168 34189 34518 34545) (-44 "ALGSC.spad" 33303 33329 34040 34093) (-43 "ALGPKG.spad" 29086 29097 33259 33264) (-42 "ALGMFACT.spad" 28279 28293 29076 29081) (-41 "ALGMANIP.spad" 25753 25768 28112 28117) (-40 "ALGFF.spad" 24068 24095 24285 24441) (-39 "ALGFACT.spad" 23195 23205 24058 24063) (-38 "ALGEBRA.spad" 23028 23037 23151 23190) (-37 "ALGEBRA.spad" 22893 22904 23018 23023) (-36 "ALAGG.spad" 22405 22426 22861 22888) (-35 "AHYP.spad" 21786 21793 22395 22400) (-34 "AGG.spad" 20103 20110 21776 21781) (-33 "AGG.spad" 18384 18393 20059 20064) (-32 "AF.spad" 16815 16830 18319 18324) (-31 "ADDAST.spad" 16493 16500 16805 16810) (-30 "ACPLOT.spad" 15084 15091 16483 16488) (-29 "ACFS.spad" 12893 12902 14986 15079) (-28 "ACFS.spad" 10788 10799 12883 12888) (-27 "ACF.spad" 7470 7477 10690 10783) (-26 "ACF.spad" 4238 4247 7460 7465) (-25 "ABELSG.spad" 3779 3786 4228 4233) (-24 "ABELSG.spad" 3318 3327 3769 3774) (-23 "ABELMON.spad" 2861 2868 3308 3313) (-22 "ABELMON.spad" 2402 2411 2851 2856) (-21 "ABELGRP.spad" 2067 2074 2392 2397) (-20 "ABELGRP.spad" 1730 1739 2057 2062) (-19 "A1AGG.spad" 870 879 1698 1725) (-18 "A1AGG.spad" 30 41 860 865))
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T) (((-413 (-570))) -3684 (|has| |#1| (-38 (-413 (-570)))) (|has| |#1| (-1047 (-413 (-570)))))) (((|#1|) . T) (($) . T)) ((((-570)) . T)) ((((-570)) . T)) -((($) -2811 (|has| |#1| (-368)) (|has| |#1| (-562))) (((-413 (-570))) -2811 (|has| |#1| (-38 (-413 (-570)))) (|has| |#1| (-368))) ((|#1|) |has| |#1| (-174))) +((($) -3684 (|has| |#1| (-368)) (|has| |#1| (-562))) (((-413 (-570))) -3684 (|has| |#1| (-38 (-413 (-570)))) (|has| |#1| (-368))) ((|#1|) |has| |#1| (-174))) ((((-570)) . T)) ((((-570)) . T)) ((((-413 (-570))) . T) (($) . T)) @@ -233,13 +233,13 @@ ((((-868)) . T)) ((((-868)) . T)) (((|#1| |#1|) . T)) -(((#0=(-413 (-570)) #0#) |has| |#1| (-38 (-413 (-570)))) ((|#1| |#1|) . T) (($ $) -2811 (|has| |#1| (-174)) (|has| |#1| (-458)) (|has| |#1| (-562)) (|has| |#1| (-916)))) -((($ $) -2811 (|has| |#1| (-174)) (|has| |#1| (-368)) (|has| |#1| (-458)) (|has| |#1| (-562)) (|has| |#1| (-916))) ((|#1| |#1|) . T) ((#0=(-413 (-570)) #0#) |has| |#1| (-38 (-413 (-570))))) +(((#0=(-413 (-570)) #0#) |has| |#1| (-38 (-413 (-570)))) ((|#1| |#1|) . T) (($ $) -3684 (|has| |#1| (-174)) (|has| |#1| (-458)) (|has| |#1| (-562)) (|has| |#1| (-916)))) +((($ $) -3684 (|has| |#1| (-174)) (|has| |#1| (-368)) (|has| |#1| (-458)) (|has| |#1| (-562)) (|has| |#1| (-916))) ((|#1| |#1|) . T) ((#0=(-413 (-570)) #0#) |has| |#1| (-38 (-413 (-570))))) (((|#1|) . T)) (((|#1|) . T)) -((((-413 (-570))) |has| |#1| (-38 (-413 (-570)))) ((|#1|) . T) (($) -2811 (|has| |#1| (-174)) (|has| |#1| (-458)) (|has| |#1| (-562)) (|has| |#1| (-916)))) -((($) -2811 (|has| |#1| (-174)) (|has| |#1| (-368)) (|has| |#1| (-458)) (|has| |#1| (-562)) (|has| |#1| (-916))) ((|#1|) . T) (((-413 (-570))) |has| |#1| (-38 (-413 (-570))))) -((($) -2811 (|has| |#2| (-174)) (|has| |#2| (-854)) (|has| |#2| (-1058))) ((|#2|) -2811 (|has| |#2| (-174)) (|has| |#2| (-368)) (|has| |#2| (-1058)))) +((((-413 (-570))) |has| |#1| (-38 (-413 (-570)))) ((|#1|) . T) (($) -3684 (|has| |#1| (-174)) (|has| |#1| (-458)) (|has| |#1| (-562)) (|has| |#1| (-916)))) +((($) -3684 (|has| |#1| (-174)) (|has| |#1| (-368)) (|has| |#1| (-458)) (|has| |#1| (-562)) (|has| |#1| (-916))) ((|#1|) . T) (((-413 (-570))) |has| |#1| (-38 (-413 (-570))))) +((($) -3684 (|has| |#2| (-174)) (|has| |#2| (-854)) (|has| |#2| (-1058))) ((|#2|) -3684 (|has| |#2| (-174)) (|has| |#2| (-368)) (|has| |#2| (-1058)))) ((((-868)) . T)) ((((-868)) . T)) ((((-868)) . T)) @@ -250,10 +250,10 @@ ((((-171 (-227))) |has| |#1| (-1031)) (((-171 (-384))) |has| |#1| (-1031)) (((-542)) |has| |#1| (-620 (-542))) (((-1182 |#1|)) . T) (((-899 (-570))) |has| |#1| (-620 (-899 (-570)))) (((-899 (-384))) |has| |#1| (-620 (-899 (-384))))) (((|#1| |#1|) -12 (|has| |#1| (-313 |#1|)) (|has| |#1| (-1109)))) (((|#1|) . T)) -(-2811 (|has| |#1| (-21)) (|has| |#1| (-854))) -(-2811 (|has| |#1| (-21)) (|has| |#1| (-854))) -((((-413 (-570))) -2811 (|has| |#1| (-38 (-413 (-570)))) (|has| |#1| (-368))) (($) -2811 (|has| |#1| (-368)) (|has| |#1| (-562))) ((|#2|) |has| |#1| (-368)) ((|#1|) |has| |#1| (-174))) -(((|#1|) |has| |#1| (-174)) (((-413 (-570))) -2811 (|has| |#1| (-38 (-413 (-570)))) (|has| |#1| (-368))) (($) -2811 (|has| |#1| (-368)) (|has| |#1| (-562)))) +(-3684 (|has| |#1| (-21)) (|has| |#1| (-854))) +(-3684 (|has| |#1| (-21)) (|has| |#1| (-854))) +((((-413 (-570))) -3684 (|has| |#1| (-38 (-413 (-570)))) (|has| |#1| (-368))) (($) -3684 (|has| |#1| (-368)) (|has| |#1| (-562))) ((|#2|) |has| |#1| (-368)) ((|#1|) |has| |#1| (-174))) +(((|#1|) |has| |#1| (-174)) (((-413 (-570))) -3684 (|has| |#1| (-38 (-413 (-570)))) (|has| |#1| (-368))) (($) -3684 (|has| |#1| (-368)) (|has| |#1| (-562)))) (|has| |#1| (-368)) ((((-868)) . T)) ((($) . T)) @@ -261,8 +261,8 @@ ((((-130)) . T)) (-12 (|has| |#4| (-235)) (|has| |#4| (-1058))) (-12 (|has| |#3| (-235)) (|has| |#3| (-1058))) -(-2811 (|has| |#4| (-174)) (|has| |#4| (-854)) (|has| |#4| (-1058))) -(-2811 (|has| |#3| (-174)) (|has| |#3| (-854)) (|has| |#3| (-1058))) +(-3684 (|has| |#4| (-174)) (|has| |#4| (-854)) (|has| |#4| (-1058))) +(-3684 (|has| |#3| (-174)) (|has| |#3| (-854)) (|has| |#3| (-1058))) ((((-868)) . T) (((-1191)) . T)) ((((-868)) . T) (((-1191)) . T)) ((((-1191)) . T)) @@ -271,14 +271,14 @@ (((|#1|) . T)) ((((-413 (-570))) |has| |#1| (-1047 (-413 (-570)))) (((-570)) |has| |#1| (-1047 (-570))) ((|#1|) . T)) (((|#1|) . T) (((-570)) |has| |#1| (-645 (-570)))) -(((|#2|) . T) (((-2 (|:| -3679 |#1|) (|:| -1409 |#2|))) . T)) -(((|#1|) . T) (((-2 (|:| -3679 (-1168)) (|:| -1409 |#1|))) . T)) +(((|#2|) . T) (((-2 (|:| -4111 |#1|) (|:| -3117 |#2|))) . T)) +(((|#1|) . T) (((-2 (|:| -4111 (-1168)) (|:| -3117 |#1|))) . 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T)) (|has| |#1| (-562)) (|has| |#1| (-562)) @@ -291,21 +291,21 @@ ((((-413 |#2|)) . T) (((-413 (-570))) . T) (($) . T)) (-12 (|has| |#1| (-1109)) (|has| |#2| (-1109))) ((($) . T) (((-413 (-570))) |has| |#1| (-38 (-413 (-570)))) ((|#1|) . T)) -((((-413 (-570))) -2811 (|has| |#1| (-38 (-413 (-570)))) (|has| |#1| (-368))) (((-1184 |#1| |#2| |#3|)) |has| |#1| (-368)) (($) . T) ((|#1|) . T)) -(((|#1|) . T) (((-413 (-570))) -2811 (|has| |#1| (-38 (-413 (-570)))) (|has| |#1| (-368))) (($) . T)) +((((-413 (-570))) -3684 (|has| |#1| (-38 (-413 (-570)))) (|has| |#1| (-368))) (((-1184 |#1| |#2| |#3|)) |has| |#1| (-368)) (($) . T) ((|#1|) . T)) +(((|#1|) . T) (((-413 (-570))) -3684 (|has| |#1| (-38 (-413 (-570)))) (|has| |#1| (-368))) (($) . T)) (((|#1|) . T) (((-413 (-570))) |has| |#1| (-38 (-413 (-570)))) (($) . 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T)) ((((-542)) |has| |#1| (-620 (-542))) (((-899 (-384))) |has| |#1| (-620 (-899 (-384)))) (((-899 (-570))) |has| |#1| (-620 (-899 (-570))))) -(((|#4|) -2811 (|has| |#4| (-174)) (|has| |#4| (-368)) (|has| |#4| (-1058))) (($) |has| |#4| (-174))) -(((|#3|) -2811 (|has| |#3| (-174)) (|has| |#3| (-368)) (|has| |#3| (-1058))) (($) |has| |#3| (-174))) -((((-2 (|:| -2594 |#1|) (|:| -1459 |#2|))) . T)) +(((|#4|) -3684 (|has| |#4| (-174)) (|has| |#4| (-368)) (|has| |#4| (-1058))) (($) |has| |#4| (-174))) +(((|#3|) -3684 (|has| |#3| (-174)) (|has| |#3| (-368)) (|has| |#3| (-1058))) (($) |has| |#3| (-174))) +((((-2 (|:| -4285 |#1|) (|:| -2092 |#2|))) . T)) ((((-868)) . T)) ((((-868)) . T)) ((((-542)) . T) (((-570)) . T) (((-899 (-570))) . T) (((-384)) . T) (((-227)) . T)) @@ -313,14 +313,14 @@ (((|#1|) . T) (((-570)) |has| |#1| (-1047 (-570))) (((-413 (-570))) |has| |#1| (-1047 (-413 (-570))))) ((($) . T) (((-413 (-570))) |has| |#2| (-38 (-413 (-570)))) ((|#2|) . T)) ((((-413 $) (-413 $)) |has| |#2| (-562)) (($ $) . T) ((|#2| |#2|) . T)) -((((-2 (|:| -3679 (-1168)) (|:| -1409 (-52)))) . T)) +((((-2 (|:| -4111 (-1168)) (|:| -3117 (-52)))) . T)) (((|#1|) . T)) (|has| |#2| (-916)) ((((-1168) (-52)) . T)) ((((-570)) |has| #0=(-413 |#2|) (-645 (-570))) ((#0#) . T)) ((((-542)) . T) (((-227)) . T) (((-384)) . T) (((-899 (-384))) . T)) ((((-868)) . T)) -(-2811 (|has| |#1| (-21)) (|has| |#1| (-174)) (|has| |#1| (-368)) (|has| |#1| (-907 (-1186))) (|has| |#1| (-1058))) +(-3684 (|has| |#1| (-21)) (|has| |#1| (-174)) (|has| |#1| (-368)) (|has| |#1| (-907 (-1186))) (|has| |#1| (-1058))) (((|#1|) |has| |#1| (-174))) (((|#1| $) |has| |#1| (-290 |#1| |#1|))) ((((-868)) . T)) @@ -334,15 +334,15 @@ (|has| |#1| (-1109)) ((((-917 |#1|)) . T) (($) . T) (((-413 (-570))) . T)) (((|#1|) . 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T)) (((|#1| (-980)) . T)) ((((-570)) . T) ((|#2|) . T)) @@ -352,7 +352,7 @@ (((|#1|) . T)) (((|#2| |#2|) . T)) (|has| |#1| (-1161)) -((((-2 (|:| -3679 (-1168)) (|:| -1409 |#1|))) . T)) +((((-2 (|:| -4111 (-1168)) (|:| -3117 |#1|))) . T)) (|has| (-1263 |#1| |#2| |#3| |#4|) (-146)) (|has| (-1263 |#1| |#2| |#3| |#4|) (-148)) (|has| |#1| (-146)) @@ -364,27 +364,27 @@ (((|#2|) . T)) (((|#1|) . T)) (((|#2|) . T) (((-570)) |has| |#2| (-645 (-570)))) -((((-1134 |#1| (-1186))) . T) (((-570)) . T) (((-824 (-1186))) . T) (($) -2811 (|has| |#1| (-458)) (|has| |#1| (-562)) (|has| |#1| (-916))) ((|#1|) . T) (((-413 (-570))) -2811 (|has| |#1| (-38 (-413 (-570)))) (|has| |#1| (-1047 (-413 (-570))))) (((-1186)) . T)) +((((-1134 |#1| (-1186))) . T) (((-570)) . T) (((-824 (-1186))) . T) (($) -3684 (|has| |#1| (-458)) (|has| |#1| (-562)) (|has| |#1| (-916))) ((|#1|) . T) (((-413 (-570))) -3684 (|has| |#1| (-38 (-413 (-570)))) (|has| |#1| (-1047 (-413 (-570))))) (((-1186)) . 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T)) (|has| (-413 |#2|) (-148)) (|has| (-413 |#2|) (-146)) @@ -856,15 +856,15 @@ (|has| |#1| (-562)) (|has| |#1| (-38 (-413 (-570)))) (|has| |#1| (-38 (-413 (-570)))) -((((-2 (|:| -3679 |#1|) (|:| -1409 |#2|))) . T)) +((((-2 (|:| -4111 |#1|) (|:| -3117 |#2|))) . T)) ((((-868)) . T)) -((((-2 (|:| -3679 (-1168)) (|:| -1409 |#1|))) . T)) +((((-2 (|:| -4111 (-1168)) (|:| -3117 |#1|))) . T)) (|has| |#1| (-38 (-413 (-570)))) -((((-394) (-2 (|:| -3679 (-1168)) (|:| -1409 |#1|))) . T)) +((((-394) (-2 (|:| -4111 (-1168)) (|:| -3117 |#1|))) . T)) (|has| |#1| (-38 (-413 (-570)))) (|has| |#2| (-1161)) -(-2811 (|has| |#1| (-368)) (|has| |#1| (-562))) -(-2811 (|has| |#1| (-368)) (|has| |#1| (-562))) +(-3684 (|has| |#1| (-368)) (|has| |#1| (-562))) +(-3684 (|has| |#1| (-368)) (|has| |#1| (-562))) ((((-868)) . T) (((-1191)) . T)) ((((-868)) . T) (((-1191)) . T)) ((((-1191)) . T)) @@ -882,7 +882,7 @@ ((((-394) (-1168)) . T)) (|has| |#1| (-562)) ((((-1244 (-570)) $) . T) (((-570) |#1|) . T)) -(-2811 (|has| |#1| (-174)) (|has| |#1| (-458)) (|has| |#1| (-562)) (|has| |#1| (-916))) +(-3684 (|has| |#1| (-174)) (|has| |#1| (-458)) (|has| |#1| (-562)) (|has| |#1| (-916))) ((((-570)) . T) (($) . T) (((-413 (-570))) . T)) ((((-570)) . T) (($) . T) (((-413 (-570))) . T)) (((|#2|) . T)) @@ -899,7 +899,7 @@ ((((-650 |#1|)) . T)) ((((-868)) . T)) ((((-542)) |has| |#1| (-620 (-542)))) -(-2811 (|has| |#1| (-856)) (|has| |#1| (-1109))) +(-3684 (|has| |#1| (-856)) (|has| |#1| (-1109))) (((|#2|) |has| |#2| (-313 |#2|))) (((#0=(-570) #0#) . T) ((#1=(-413 (-570)) #1#) . T) (($ $) . T)) (((|#1|) . T)) @@ -909,14 +909,14 @@ (((#0=(-570) #0#) . T) ((#1=(-413 (-570)) #1#) . T) (($ $) . T)) ((($) . T) (((-570)) . T) (((-413 (-570))) . T)) (|has| |#2| (-373)) -(-2811 (|has| |#1| (-856)) (|has| |#1| (-1109))) +(-3684 (|has| |#1| (-856)) (|has| |#1| (-1109))) (((|#1|) . T) (((-413 (-570))) . T) (($) . T)) (((|#1|) . T) (((-413 (-570))) . T) (($) . T)) (((|#1|) . T) (((-413 (-570))) . T) (($) . T)) ((((-570)) . T) (((-413 (-570))) . T) (($) . T)) -((($) -2811 (|has| |#1| (-368)) (|has| |#1| (-562))) (((-413 (-570))) -2811 (|has| |#1| (-38 (-413 (-570)))) (|has| |#1| (-368))) ((|#1|) |has| |#1| (-174))) +((($) -3684 (|has| |#1| (-368)) (|has| |#1| (-562))) (((-413 (-570))) -3684 (|has| |#1| (-38 (-413 (-570)))) (|has| |#1| (-368))) ((|#1|) |has| |#1| (-174))) (((|#1| |#2|) . T)) -((((-413 (-570))) -2811 (|has| |#1| (-38 (-413 (-570)))) (|has| |#1| (-368))) (($) -2811 (|has| |#1| (-174)) (|has| |#1| (-368)) (|has| |#1| (-562))) ((|#1|) . T)) +((((-413 (-570))) -3684 (|has| |#1| (-38 (-413 (-570)))) (|has| |#1| (-368))) (($) -3684 (|has| |#1| (-174)) (|has| |#1| (-368)) (|has| |#1| (-562))) ((|#1|) . T)) ((((-570)) . T) (((-413 (-570))) . T) (($) . T)) (((|#1| |#2|) . T)) ((((-868)) . T)) @@ -924,8 +924,8 @@ ((((-868)) . T)) ((((-868)) . T)) ((((-542)) |has| |#1| (-620 (-542)))) -((((-868)) -2811 (|has| |#1| (-619 (-868))) (|has| |#1| (-1109)))) -((($) . 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T) (((-570)) . T)) ((((-570) (-145)) . T)) ((((-145)) . T)) (((|#1|) . T)) -(-2811 (|has| |#1| (-21)) (|has| |#1| (-146)) (|has| |#1| (-148)) (|has| |#1| (-174)) (|has| |#1| (-562)) (|has| |#1| (-1058))) +(-3684 (|has| |#1| (-21)) (|has| |#1| (-146)) (|has| |#1| (-148)) (|has| |#1| (-174)) (|has| |#1| (-562)) (|has| |#1| (-1058))) ((((-112)) . T)) (((|#1|) -12 (|has| |#1| (-313 |#1|)) (|has| |#1| (-1109)))) ((((-112)) . T)) @@ -953,31 +953,31 @@ ((((-868)) . T)) ((((-1191)) . T)) (|has| |#1| (-826)) -(-2811 (|has| |#1| (-368)) (|has| |#1| (-458)) (|has| |#1| (-562)) (|has| |#1| (-916))) -((($) -2811 (|has| |#1| (-174)) (|has| |#1| (-368)) (|has| |#1| (-562))) (((-413 (-570))) -2811 (|has| |#1| (-38 (-413 (-570)))) (|has| |#1| (-368))) ((|#2|) |has| |#1| (-368)) ((|#1|) . T)) -((((-413 (-570))) -2811 (|has| |#1| (-38 (-413 (-570)))) (|has| |#1| (-368))) (($) -2811 (|has| |#1| (-368)) (|has| |#1| (-562))) ((|#2|) |has| |#1| (-368)) ((|#1|) |has| |#1| (-174))) -(((|#1|) . 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T)) (((|#1|) -12 (|has| |#1| (-313 |#1|)) (|has| |#1| (-1109)))) (|has| |#2| (-854)) (-12 (|has| |#1| (-799)) (|has| |#2| (-799))) (-12 (|has| |#1| (-799)) (|has| |#2| (-799))) -(-2811 (-12 (|has| |#1| (-479)) (|has| |#2| (-479))) (-12 (|has| |#1| (-732)) (|has| |#2| (-732)))) +(-3684 (-12 (|has| |#1| (-479)) (|has| |#2| (-479))) (-12 (|has| |#1| (-732)) (|has| |#2| (-732)))) (((|#1| |#2|) . T)) (((|#1|) |has| |#1| (-174)) ((|#4|) . T) (((-570)) . T)) (((|#2|) |has| |#2| (-174))) @@ -1010,7 +1010,7 @@ (((|#1|) . T)) ((((-413 (-570))) . T) (($) . T)) (((|#2|) . T) (($) . T) (((-413 (-570))) . T)) -((($) . T) (((-413 (-570))) -2811 (|has| |#1| (-38 (-413 (-570)))) (|has| |#1| (-368))) ((|#1|) . T)) +((($) . T) (((-413 (-570))) -3684 (|has| |#1| (-38 (-413 (-570)))) (|has| |#1| (-368))) ((|#1|) . T)) (|has| |#1| (-834)) ((((-413 (-570))) |has| |#1| (-1047 (-413 (-570)))) (((-570)) |has| |#1| (-1047 (-570))) ((|#1|) . T)) (|has| |#1| (-1109)) @@ -1021,13 +1021,13 @@ (((|#4|) |has| |#4| (-1109))) (((|#3|) |has| |#3| (-1109))) (|has| |#3| (-373)) -((($) |has| |#1| (-562)) ((|#1|) . T) (((-413 (-570))) -2811 (|has| |#1| (-38 (-413 (-570)))) (|has| |#1| (-1047 (-413 (-570))))) (((-570)) . T)) -((((-413 (-570))) -2811 (|has| |#1| (-38 (-413 (-570)))) (|has| |#1| (-368))) (($) -2811 (|has| |#1| (-368)) (|has| |#1| (-562))) (((-1269 |#1| |#2| |#3|)) |has| |#1| (-368)) ((|#1|) |has| |#1| (-174))) +((($) |has| |#1| (-562)) ((|#1|) . T) (((-413 (-570))) -3684 (|has| |#1| (-38 (-413 (-570)))) (|has| |#1| (-1047 (-413 (-570))))) (((-570)) . T)) +((((-413 (-570))) -3684 (|has| |#1| (-38 (-413 (-570)))) (|has| |#1| (-368))) (($) -3684 (|has| |#1| (-368)) (|has| |#1| (-562))) (((-1269 |#1| |#2| |#3|)) |has| |#1| (-368)) ((|#1|) |has| |#1| (-174))) ((((-868)) . T)) ((((-868)) . T)) (((|#2|) . T)) (((|#1| |#2|) . 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T)) -(-2811 (|has| |#1| (-21)) (|has| |#1| (-25)) (|has| |#1| (-146)) (|has| |#1| (-148)) (|has| |#1| (-174)) (|has| |#1| (-562)) (|has| |#1| (-1058))) +(-3684 (|has| |#1| (-21)) (|has| |#1| (-25)) (|has| |#1| (-146)) (|has| |#1| (-148)) (|has| |#1| (-174)) (|has| |#1| (-562)) (|has| |#1| (-1058))) (((|#1|) |has| |#1| (-174))) (|has| $ (-148)) (|has| $ (-148)) @@ -1057,15 +1057,15 @@ ((((-868)) . T)) (|has| |#1| (-38 (-413 (-570)))) (|has| |#1| (-38 (-413 (-570)))) -(-2811 (|has| |#1| (-146)) (|has| |#1| (-148)) (|has| |#1| (-174)) (|has| |#1| (-479)) (|has| |#1| (-562)) (|has| |#1| (-1058)) (|has| |#1| (-1121))) +(-3684 (|has| |#1| (-146)) (|has| |#1| (-148)) (|has| |#1| (-174)) (|has| |#1| (-479)) (|has| |#1| (-562)) (|has| |#1| (-1058)) (|has| |#1| (-1121))) ((($ $) |has| |#1| (-290 $ $)) ((|#1| $) |has| |#1| (-290 |#1| |#1|))) (((|#1| (-413 (-570))) . T)) (((|#1|) . T)) ((((-413 (-570))) . T) (((-570)) . T) (($) . T)) ((((-1186)) . 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T)) (((|#1|) |has| |#1| (-313 |#1|))) @@ -1261,11 +1262,11 @@ (|has| |#1| (-373)) ((((-1186) $) |has| |#1| (-520 (-1186) $)) (($ $) |has| |#1| (-313 $)) ((|#1| |#1|) |has| |#1| (-313 |#1|)) (((-1186) |#1|) |has| |#1| (-520 (-1186) |#1|))) ((((-1186)) |has| |#1| (-907 (-1186)))) -(-2811 (-12 (|has| |#1| (-235)) (|has| |#1| (-368))) (|has| |#1| (-354))) +(-3684 (-12 (|has| |#1| (-235)) (|has| |#1| (-368))) (|has| |#1| (-354))) (((|#1| |#4|) . T)) (((|#1| |#3|) . T)) ((((-394) |#1|) . T)) -(-2811 (|has| |#1| (-368)) (|has| |#1| (-354))) +(-3684 (|has| |#1| (-368)) (|has| |#1| (-354))) (|has| |#1| (-1109)) (((|#2|) . T) (((-868)) . T)) ((((-868)) . T)) @@ -1273,8 +1274,8 @@ ((((-917 |#1|)) . T)) ((((-868)) . T) (((-1191)) . T)) ((((-1191)) . 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T)) (|has| |#1| (-1212)) (((#0=(-570) #0#) . T) ((#1=(-413 (-570)) #1#) . T) (($ $) . T)) @@ -1304,8 +1305,8 @@ (((|#1| |#1|) . T) (($ $) . T) ((#0=(-413 (-570)) #0#) . T)) (|has| |#1| (-368)) ((((-570)) . T) (((-413 (-570))) . T) (($) . T)) -((($ $) . T) ((#0=(-413 (-570)) #0#) -2811 (|has| |#1| (-368)) (|has| |#1| (-354))) ((|#1| |#1|) . T)) -((((-868)) -2811 (|has| |#1| (-619 (-868))) (|has| |#1| (-1109)))) +((($ $) . T) ((#0=(-413 (-570)) #0#) -3684 (|has| |#1| (-368)) (|has| |#1| (-354))) ((|#1| |#1|) . T)) +((((-868)) -3684 (|has| |#1| (-619 (-868))) (|has| |#1| (-1109)))) (((|#1|) . T) (($) . T) (((-413 (-570))) . T)) ((((-868)) . T)) ((((-868)) . T)) @@ -1320,29 +1321,29 @@ (((|#1| |#2|) . T)) (|has| |#1| (-854)) (|has| |#1| (-854)) -((($) . T) (((-413 (-570))) -2811 (|has| |#1| (-368)) (|has| |#1| (-354))) ((|#1|) . T)) -(-2811 (|has| |#1| (-174)) (|has| |#1| (-562))) +((($) . T) (((-413 (-570))) -3684 (|has| |#1| (-368)) (|has| |#1| (-354))) ((|#1|) . 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T)) -((((-570) (-2 (|:| -3679 |#1|) (|:| -1409 |#2|))) . T) ((|#1| |#2|) . T)) +((((-570) (-2 (|:| -4111 |#1|) (|:| -3117 |#2|))) . T) ((|#1| |#2|) . T)) ((((-413 (-570))) . T) (($) . T)) (((|#1|) . T)) -((((-2 (|:| -3679 |#1|) (|:| -1409 |#2|))) . T)) +((((-2 (|:| -4111 |#1|) (|:| -3117 |#2|))) . T)) ((((-868)) . T)) ((((-917 |#1|)) . T)) (|has| |#1| (-368)) @@ -1350,11 +1351,11 @@ (|has| |#1| (-368)) (|has| |#1| (-15 * (|#1| (-413 (-570)) |#1|))) (|has| |#1| (-854)) -((($) -2811 (|has| |#1| (-311)) (|has| |#1| (-368)) (|has| |#1| (-354)) (|has| |#1| (-562))) (((-413 (-570))) -2811 (|has| |#1| (-368)) (|has| |#1| (-354))) ((|#1|) . T)) +((($) -3684 (|has| |#1| (-311)) (|has| |#1| (-368)) (|has| |#1| (-354)) (|has| |#1| (-562))) (((-413 (-570))) -3684 (|has| |#1| (-368)) (|has| |#1| (-354))) ((|#1|) . T)) (|has| |#1| (-368)) (((|#1|) . T) (($) . T)) (|has| |#1| (-854)) -((($) . T) (((-413 (-570))) -2811 (|has| |#1| (-368)) (|has| |#1| (-354))) ((|#1|) . T)) +((($) . 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T)) -(((|#2|) -2811 (|has| |#2| (-174)) (|has| |#2| (-368)) (|has| |#2| (-1058))) (($) |has| |#2| (-174))) +(((|#2|) -3684 (|has| |#2| (-174)) (|has| |#2| (-368)) (|has| |#2| (-1058))) (($) |has| |#2| (-174))) (|has| $ (-148)) ((((-413 |#2|)) . T)) ((((-413 (-570))) |has| #0=(-413 |#2|) (-1047 (-413 (-570)))) (((-570)) |has| #0# (-1047 (-570))) ((#0#) . T)) @@ -1491,11 +1492,11 @@ (((|#3|) |has| |#3| (-174))) (|has| |#1| (-148)) (|has| |#1| (-146)) -(-2811 (|has| |#1| (-146)) (|has| |#1| (-373))) +(-3684 (|has| |#1| (-146)) (|has| |#1| (-373))) (|has| |#1| (-148)) -(-2811 (|has| |#1| (-146)) (|has| |#1| (-373))) +(-3684 (|has| |#1| (-146)) (|has| |#1| (-373))) (|has| |#1| (-148)) -(-2811 (|has| |#1| (-146)) (|has| |#1| (-373))) +(-3684 (|has| |#1| (-146)) (|has| |#1| (-373))) (|has| |#1| (-148)) (((|#1|) . T)) (|has| |#2| (-235)) @@ -1533,7 +1534,7 @@ ((((-1008 |#1|)) . T) ((|#1|) . T)) ((((-868)) . T)) ((((-868)) . T)) -((((-2 (|:| -3679 |#1|) (|:| -1409 |#2|))) . T)) +((((-2 (|:| -4111 |#1|) (|:| -3117 |#2|))) . T)) ((((-413 (-570))) . T) (((-413 |#1|)) . T) ((|#1|) . T) (($) . T)) (((|#1| (-1182 |#1|)) . T)) ((((-570)) . T) (($) . T) (((-413 (-570))) . T)) @@ -1542,8 +1543,8 @@ (((|#1|) . T) (((-570)) . T) (($) . T)) (((|#2|) . T)) ((((-570)) . T) (($) . T) (((-413 (-570))) . T)) -((((-2 (|:| -3679 (-1168)) (|:| -1409 |#1|))) . T)) -((((-868)) -2811 (|has| |#1| (-619 (-868))) (|has| |#1| (-1109)))) +((((-2 (|:| -4111 (-1168)) (|:| -3117 |#1|))) . T)) +((((-868)) -3684 (|has| |#1| (-619 (-868))) (|has| |#1| (-1109)))) ((((-570) |#2|) . T)) (((|#1|) . T) (((-413 (-570))) . T) (((-570)) . T) (($) . T)) ((($) . T) (((-570)) . T) (((-413 (-570))) . T)) @@ -1556,7 +1557,7 @@ (|has| |#1| (-38 (-413 (-570)))) (|has| |#1| (-38 (-413 (-570)))) ((((-1269 |#1| |#2| |#3|)) |has| |#1| (-368))) -(((|#2| |#2|) -12 (|has| |#2| (-313 |#2|)) (|has| |#2| (-1109))) ((#0=(-2 (|:| -3679 |#1|) (|:| -1409 |#2|)) #0#) |has| (-2 (|:| -3679 |#1|) (|:| -1409 |#2|)) (-313 (-2 (|:| -3679 |#1|) (|:| -1409 |#2|))))) +(((|#2| |#2|) -12 (|has| |#2| (-313 |#2|)) (|has| |#2| (-1109))) ((#0=(-2 (|:| -4111 |#1|) (|:| -3117 |#2|)) #0#) |has| (-2 (|:| -4111 |#1|) (|:| -3117 |#2|)) (-313 (-2 (|:| -4111 |#1|) (|:| -3117 |#2|))))) (((|#2| |#2|) . T)) (|has| |#1| (-1109)) (|has| |#2| (-368)) @@ -1566,16 +1567,16 @@ (|has| |#1| (-38 (-413 (-570)))) (|has| |#1| (-38 (-413 (-570)))) (((|#1|) |has| |#1| (-174))) -((((-413 (-570))) |has| |#1| (-38 (-413 (-570)))) ((|#1|) |has| |#1| (-174)) (($) -2811 (|has| |#1| (-458)) (|has| |#1| (-562)) (|has| |#1| (-916)))) -((($) -2811 (|has| |#1| (-368)) (|has| |#1| (-458)) (|has| |#1| (-562)) (|has| |#1| (-916))) ((|#1|) |has| |#1| (-174)) (((-413 (-570))) |has| |#1| (-38 (-413 (-570))))) +((((-413 (-570))) |has| |#1| (-38 (-413 (-570)))) ((|#1|) |has| |#1| (-174)) (($) -3684 (|has| |#1| (-458)) (|has| |#1| (-562)) (|has| |#1| (-916)))) +((($) -3684 (|has| |#1| (-368)) (|has| |#1| (-458)) (|has| |#1| (-562)) (|has| |#1| (-916))) ((|#1|) |has| |#1| (-174)) (((-413 (-570))) |has| |#1| (-38 (-413 (-570))))) (((|#2|) . T)) (((|#1|) . T)) ((((-1168) (-52)) . T)) (((|#1|) . T)) -((((-413 (-570))) |has| |#1| (-38 (-413 (-570)))) ((|#1|) . 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T) (((-413 (-570))) |has| |#1| (-38 (-413 (-570))))) (((|#2|) |has| |#2| (-174))) -((($) -2811 (|has| |#2| (-174)) (|has| |#2| (-854)) (|has| |#2| (-1058))) (((-570)) -2811 (|has| |#2| (-174)) (|has| |#2| (-368)) (|has| |#2| (-854)) (|has| |#2| (-1058))) ((|#2|) -2811 (|has| |#2| (-174)) (|has| |#2| (-368)) (|has| |#2| (-1058)))) +((($) -3684 (|has| |#2| (-174)) (|has| |#2| (-854)) (|has| |#2| (-1058))) (((-570)) -3684 (|has| |#2| (-174)) (|has| |#2| (-368)) (|has| |#2| (-854)) (|has| |#2| (-1058))) ((|#2|) -3684 (|has| |#2| (-174)) (|has| |#2| (-368)) (|has| |#2| (-1058)))) ((((-570) |#3|) . T)) ((((-570) (-145)) . T)) ((((-145)) . T)) @@ -1601,19 +1602,19 @@ (((|#1|) -12 (|has| |#1| (-313 |#1|)) (|has| |#1| (-1109)))) (((|#1| |#2|) . T)) ((((-1244 (-570)) $) . T) (((-570) (-145)) . T)) -(((#0=(-2 (|:| -3679 |#1|) (|:| -1409 |#2|)) #0#) |has| (-2 (|:| -3679 |#1|) (|:| -1409 |#2|)) (-313 (-2 (|:| -3679 |#1|) (|:| -1409 |#2|)))) ((|#2| |#2|) -12 (|has| |#2| (-313 |#2|)) (|has| |#2| (-1109)))) -((($) -2811 (|has| |#1| (-458)) (|has| |#1| (-562)) (|has| |#1| (-916))) ((|#1|) |has| |#1| (-174)) (((-413 (-570))) |has| |#1| (-38 (-413 (-570))))) +(((#0=(-2 (|:| -4111 |#1|) (|:| -3117 |#2|)) #0#) |has| (-2 (|:| -4111 |#1|) (|:| -3117 |#2|)) (-313 (-2 (|:| -4111 |#1|) (|:| -3117 |#2|)))) ((|#2| |#2|) -12 (|has| |#2| (-313 |#2|)) (|has| |#2| (-1109)))) +((($) -3684 (|has| |#1| (-458)) (|has| |#1| (-562)) (|has| |#1| (-916))) ((|#1|) |has| |#1| (-174)) (((-413 (-570))) |has| |#1| (-38 (-413 (-570))))) (|has| |#1| (-856)) (((|#2| (-777) (-1091)) . T)) (((|#1| |#2|) . T)) -(-2811 (|has| |#1| (-174)) (|has| |#1| (-562))) +(-3684 (|has| |#1| (-174)) (|has| |#1| (-562))) (|has| |#1| (-797)) (((|#1|) |has| |#1| (-174))) (((|#4|) . T)) (((|#4|) . T)) (((|#1| |#2|) . T)) -(-2811 (|has| |#1| (-148)) (-12 (|has| |#1| (-368)) (|has| |#2| (-148)))) -(-2811 (|has| |#1| (-146)) (-12 (|has| |#1| (-368)) (|has| |#2| (-146)))) +(-3684 (|has| |#1| (-148)) (-12 (|has| |#1| (-368)) (|has| |#2| (-148)))) +(-3684 (|has| |#1| (-146)) (-12 (|has| |#1| (-368)) (|has| |#2| (-146)))) (((|#4|) . T)) (|has| |#1| (-146)) ((((-1168) |#1|) . T)) @@ -1627,24 +1628,24 @@ (((|#3|) . T)) ((((-1269 |#1| |#2| |#3|)) |has| |#1| (-368))) ((($) . T) (((-570)) . T) (((-413 (-570))) |has| |#1| (-38 (-413 (-570)))) ((|#1|) . T)) -((((-413 (-570))) -2811 (|has| |#1| (-38 (-413 (-570)))) (|has| |#1| (-368))) (((-1184 |#1| |#2| |#3|)) |has| |#1| (-368)) (((-570)) . T) (($) . T) ((|#1|) . T)) -(((|#1|) . T) (((-413 (-570))) -2811 (|has| |#1| (-38 (-413 (-570)))) (|has| |#1| (-368))) (((-570)) . T) (($) . T)) +((((-413 (-570))) -3684 (|has| |#1| (-38 (-413 (-570)))) (|has| |#1| (-368))) (((-1184 |#1| |#2| |#3|)) |has| |#1| (-368)) (((-570)) . T) (($) . T) ((|#1|) . T)) +(((|#1|) . 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T)) -(((|#4|) -2811 (|has| |#4| (-174)) (|has| |#4| (-368)))) -(((|#3|) -2811 (|has| |#3| (-174)) (|has| |#3| (-368)))) +(((|#4|) -3684 (|has| |#4| (-174)) (|has| |#4| (-368)))) +(((|#3|) -3684 (|has| |#3| (-174)) (|has| |#3| (-368)))) (|has| |#2| (-368)) (((|#1|) |has| |#1| (-174))) -(((|#4|) -2811 (|has| |#4| (-174)) (|has| |#4| (-368)) (|has| |#4| (-1058))) (($) |has| |#4| (-174))) -(((|#3|) -2811 (|has| |#3| (-174)) (|has| |#3| (-368)) (|has| |#3| (-1058))) (($) |has| |#3| (-174))) +(((|#4|) -3684 (|has| |#4| (-174)) (|has| |#4| (-368)) (|has| |#4| (-1058))) (($) |has| |#4| (-174))) +(((|#3|) -3684 (|has| |#3| (-174)) (|has| |#3| (-368)) (|has| |#3| (-1058))) (($) |has| |#3| (-174))) (((|#2|) |has| |#2| (-1058))) ((((-1168) |#1|) . T)) (((|#3| |#3|) -12 (|has| |#3| (-313 |#3|)) (|has| |#3| (-1109)))) @@ -1653,8 +1654,8 @@ ((($) . T) (((-570)) . T) (((-413 (-570))) |has| |#2| (-38 (-413 (-570)))) ((|#2|) . T)) ((((-394) (-1168)) . T)) ((($) |has| |#1| (-562)) ((|#1|) |has| |#1| (-174)) (((-413 (-570))) |has| |#1| (-38 (-413 (-570))))) -((((-868)) -2811 (|has| |#2| (-25)) (|has| |#2| (-132)) (|has| |#2| (-619 (-868))) (|has| |#2| (-174)) (|has| |#2| (-368)) (|has| |#2| (-373)) (|has| |#2| (-732)) (|has| |#2| (-799)) (|has| |#2| (-854)) (|has| |#2| (-1058)) (|has| |#2| (-1109))) (((-1277 |#2|)) . T)) -(((#0=(-52)) . T) (((-2 (|:| -3679 (-1168)) (|:| -1409 #0#))) . T)) +((((-868)) -3684 (|has| |#2| (-25)) (|has| |#2| (-132)) (|has| |#2| (-619 (-868))) (|has| |#2| (-174)) (|has| |#2| (-368)) (|has| |#2| (-373)) (|has| |#2| (-732)) (|has| |#2| (-799)) (|has| |#2| (-854)) (|has| |#2| (-1058)) (|has| |#2| (-1109))) (((-1277 |#2|)) . T)) +(((#0=(-52)) . T) (((-2 (|:| -4111 (-1168)) (|:| -3117 #0#))) . T)) (((|#1|) . T)) ((((-868)) . T)) (((|#2| |#2|) -12 (|has| |#2| (-313 |#2|)) (|has| |#2| (-1109)))) @@ -1663,7 +1664,7 @@ ((((-570)) . T)) (|has| |#2| (-148)) (|has| |#1| (-479)) -(-2811 (|has| |#1| (-479)) (|has| |#1| (-732)) (|has| |#1| (-907 (-1186))) (|has| |#1| (-1058))) +(-3684 (|has| |#1| (-479)) (|has| |#1| (-732)) (|has| |#1| (-907 (-1186))) (|has| |#1| (-1058))) (|has| |#1| (-368)) ((((-868)) . T)) (|has| |#1| (-38 (-413 (-570)))) @@ -1674,8 +1675,8 @@ (|has| |#1| (-854)) ((((-868)) . T)) (((|#2|) . T)) -((((-413 (-570))) -2811 (|has| |#1| (-38 (-413 (-570)))) (|has| |#1| (-368))) (($) -2811 (|has| |#1| (-368)) (|has| |#1| (-562))) (((-1269 |#1| |#2| |#3|)) |has| |#1| (-368)) ((|#1|) |has| |#1| (-174))) -(((|#1|) |has| |#1| (-174)) (((-413 (-570))) -2811 (|has| |#1| (-38 (-413 (-570)))) (|has| |#1| (-368))) (($) -2811 (|has| |#1| (-368)) (|has| |#1| (-562)))) +((((-413 (-570))) -3684 (|has| |#1| (-38 (-413 (-570)))) (|has| |#1| (-368))) (($) -3684 (|has| |#1| (-368)) (|has| |#1| (-562))) (((-1269 |#1| |#2| |#3|)) |has| |#1| (-368)) ((|#1|) |has| |#1| (-174))) +(((|#1|) |has| |#1| (-174)) (((-413 (-570))) -3684 (|has| |#1| (-38 (-413 (-570)))) (|has| |#1| (-368))) (($) -3684 (|has| |#1| (-368)) (|has| |#1| (-562)))) ((($) |has| |#1| (-562)) ((|#1|) |has| |#1| (-174)) (((-413 (-570))) |has| |#1| (-38 (-413 (-570))))) (((|#2|) . T) (((-570)) . T) (((-825 |#1|)) . T)) (((|#1| |#2|) . T)) @@ -1685,7 +1686,7 @@ ((((-868)) . T)) ((((-868)) . T)) (|has| |#1| (-1109)) -(((|#2| (-488 (-2865 |#1|) (-777)) (-870 |#1|)) . T)) +(((|#2| (-488 (-2827 |#1|) (-777)) (-870 |#1|)) . T)) ((((-413 (-570))) . #0=(|has| |#2| (-368))) (($) . #0#)) (((|#1| (-537 (-1186)) (-1186)) . T)) (((|#1|) . T)) @@ -1706,17 +1707,17 @@ (((|#2|) |has| |#2| (-174))) (((|#1|) . T)) (((|#2|) . T)) -(((|#1|) . T) (((-2 (|:| -3679 (-1168)) (|:| -1409 |#1|))) . T)) -((((-2 (|:| -3679 |#1|) (|:| -1409 |#2|))) . T)) +(((|#1|) . T) (((-2 (|:| -4111 (-1168)) (|:| -3117 |#1|))) . T)) +((((-2 (|:| -4111 |#1|) (|:| -3117 |#2|))) . T)) (((|#2|) . T)) -((((-2 (|:| -3679 (-1186)) (|:| -1409 (-52)))) . T)) +((((-2 (|:| -4111 (-1186)) (|:| -3117 (-52)))) . T)) ((((-1184 |#1| |#2| |#3|)) |has| |#1| (-368))) -((((-2 (|:| -3679 |#1|) (|:| -1409 |#2|))) . T)) +((((-2 (|:| -4111 |#1|) (|:| -3117 |#2|))) . T)) ((((-1186) (-52)) . T)) ((((-413 (-570)) |#1|) . T) (($ $) . T)) (((|#1| (-570)) . T)) ((((-917 |#1|)) . T)) -(((|#1|) -2811 (|has| |#1| (-174)) (|has| |#1| (-368)) (|has| |#1| (-1058))) (($) -2811 (|has| |#1| (-907 (-1186))) (|has| |#1| (-1058)))) +(((|#1|) -3684 (|has| |#1| (-174)) (|has| |#1| (-368)) (|has| |#1| (-1058))) (($) -3684 (|has| |#1| (-907 (-1186))) (|has| |#1| (-1058)))) (((|#1|) . T) (((-570)) |has| |#1| (-1047 (-570))) (((-413 (-570))) |has| |#1| (-1047 (-413 (-570))))) (|has| |#1| (-856)) (|has| |#1| (-856)) @@ -1736,13 +1737,13 @@ (((|#1|) |has| |#1| (-174))) (|has| |#1| (-290 |#1| |#1|)) (((|#4| |#4|) -12 (|has| |#4| (-313 |#4|)) (|has| |#4| (-1109)))) -(((|#3|) -2811 (|has| |#3| (-174)) (|has| |#3| (-368)))) -((($) -2811 (|has| |#1| (-458)) (|has| |#1| (-562)) (|has| |#1| (-916))) ((|#1|) |has| |#1| (-174)) (((-413 (-570))) |has| |#1| (-38 (-413 (-570))))) -(-2811 (|has| |#2| (-368)) (|has| |#2| (-458)) (|has| |#2| (-916))) -((($) -2811 (|has| |#1| (-174)) (|has| |#1| (-458)) (|has| |#1| (-562)) (|has| |#1| (-916))) ((|#1|) . T) (((-413 (-570))) |has| |#1| (-38 (-413 (-570))))) +(((|#3|) -3684 (|has| |#3| (-174)) (|has| |#3| (-368)))) +((($) -3684 (|has| |#1| (-458)) (|has| |#1| (-562)) (|has| |#1| (-916))) ((|#1|) |has| |#1| (-174)) (((-413 (-570))) |has| |#1| (-38 (-413 (-570))))) +(-3684 (|has| |#2| (-368)) (|has| |#2| (-458)) (|has| |#2| (-916))) +((($) -3684 (|has| |#1| (-174)) (|has| |#1| (-458)) (|has| |#1| (-562)) (|has| |#1| (-916))) ((|#1|) . T) (((-413 (-570))) |has| |#1| (-38 (-413 (-570))))) ((($ $) . T) ((#0=(-413 (-570)) #0#) . T)) ((((-570) |#2|) . T)) -(((|#2|) -2811 (|has| |#2| (-174)) (|has| |#2| (-368)))) +(((|#2|) -3684 (|has| |#2| (-174)) (|has| |#2| (-368)))) (|has| |#1| (-354)) (((|#3| |#3|) -12 (|has| |#3| (-313 |#3|)) (|has| |#3| (-1109)))) (((|#2|) . T) (((-570)) . T)) @@ -1751,7 +1752,7 @@ (|has| |#1| (-826)) (|has| |#1| (-826)) (((|#1|) . T)) -(-2811 (|has| |#1| (-311)) (|has| |#1| (-368)) (|has| |#1| (-354))) +(-3684 (|has| |#1| (-311)) (|has| |#1| (-368)) (|has| |#1| (-354))) (|has| |#1| (-854)) (|has| |#1| (-854)) (|has| |#1| (-854)) @@ -1760,14 +1761,14 @@ ((((-570)) . T) (($) . T) (((-413 (-570))) . T)) (|has| |#1| (-38 (-413 (-570)))) (|has| |#1| (-38 (-413 (-570)))) -(-2811 (|has| |#1| (-368)) (|has| |#1| (-354))) +(-3684 (|has| |#1| (-368)) (|has| |#1| (-354))) (|has| |#1| (-38 (-413 (-570)))) (|has| |#1| (-38 (-413 (-570)))) -((((-2 (|:| -3679 |#1|) (|:| -1409 |#2|))) . T)) +((((-2 (|:| -4111 |#1|) (|:| -3117 |#2|))) . T)) ((((-1186)) |has| |#1| (-907 (-1186))) (((-1091)) . T)) (((|#1|) . 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T)) +((((-2 (|:| -4111 (-1186)) (|:| -3117 (-52)))) . T)) ((((-413 |#2|)) . T) (((-413 (-570))) . T) (($) . T)) ((((-678 |#1|)) . T)) (((|#1| |#2| |#3| |#4|) . T)) @@ -1864,7 +1865,7 @@ ((((-868)) . T)) (((|#1|) -12 (|has| |#1| (-313 |#1|)) (|has| |#1| (-1109)))) ((((-868)) . T)) -((((-413 (-570))) |has| |#2| (-38 (-413 (-570)))) ((|#2|) |has| |#2| (-174)) (($) -2811 (|has| |#2| (-458)) (|has| |#2| (-562)) (|has| |#2| (-916)))) +((((-413 (-570))) |has| |#2| (-38 (-413 (-570)))) ((|#2|) |has| |#2| (-174)) (($) -3684 (|has| |#2| (-458)) (|has| |#2| (-562)) (|has| |#2| (-916)))) ((((-1191)) . T)) ((((-413 (-570))) . T) (($) . T) (((-413 |#1|)) . T) ((|#1|) . T) (((-570)) . T)) (((|#3|) . T) (((-570)) . T) (((-618 $)) . T)) @@ -1872,12 +1873,12 @@ ((((-868)) . T)) ((((-868)) . T)) (((|#2|) . T)) -(-2811 (|has| |#3| (-25)) (|has| |#3| (-132)) (|has| |#3| (-174)) (|has| |#3| (-368)) (|has| |#3| (-373)) (|has| |#3| (-732)) (|has| |#3| (-799)) (|has| |#3| (-854)) (|has| |#3| (-1058)) (|has| |#3| (-1109))) -(-2811 (|has| |#2| (-174)) (|has| |#2| (-854)) (|has| |#2| (-1058))) +(-3684 (|has| |#3| (-25)) (|has| |#3| (-132)) (|has| |#3| (-174)) (|has| |#3| (-368)) (|has| |#3| (-373)) (|has| |#3| (-732)) (|has| |#3| (-799)) (|has| |#3| (-854)) (|has| |#3| (-1058)) (|has| |#3| (-1109))) +(-3684 (|has| |#2| (-174)) (|has| |#2| (-854)) (|has| |#2| (-1058))) ((((-413 (-570))) |has| |#1| (-1047 (-413 (-570)))) (((-570)) |has| |#1| (-1047 (-570))) ((|#1|) . T)) (|has| |#1| (-1212)) (|has| |#1| (-1212)) -(-2811 (|has| |#2| (-25)) (|has| |#2| (-132)) (|has| |#2| (-174)) (|has| |#2| (-368)) (|has| |#2| (-373)) (|has| |#2| (-732)) (|has| |#2| (-799)) (|has| |#2| (-854)) (|has| |#2| (-1058)) (|has| |#2| (-1109))) +(-3684 (|has| |#2| (-25)) (|has| |#2| (-132)) (|has| |#2| (-174)) (|has| |#2| (-368)) (|has| |#2| (-373)) (|has| |#2| (-732)) (|has| |#2| (-799)) (|has| |#2| (-854)) (|has| |#2| (-1058)) (|has| |#2| (-1109))) (|has| |#1| (-1212)) (|has| |#1| (-1212)) ((((-570)) . T) (($) . T) (((-413 (-570))) . T)) @@ -1895,7 +1896,7 @@ ((((-1168) (-52)) . T)) (|has| |#1| (-1109)) (((|#1|) |has| |#1| (-174)) (($) . T)) -(-2811 (|has| |#2| (-826)) (|has| |#2| (-856))) +(-3684 (|has| |#2| (-826)) (|has| |#2| (-856))) (((|#1|) . T) (($) . T) (((-413 (-570))) . T)) (((|#1|) . T) (((-413 (-570))) . T) (($) . T)) (((|#1|) . T)) @@ -1903,7 +1904,7 @@ ((((-570)) . T) (((-413 (-570))) . T) (($) . T)) ((((-570)) . T) (($) . T)) ((((-777)) . T)) -(-2811 (|has| |#2| (-458)) (|has| |#2| (-562)) (|has| |#2| (-916))) +(-3684 (|has| |#2| (-458)) (|has| |#2| (-562)) (|has| |#2| (-916))) (((|#1| |#1|) -12 (|has| |#1| (-313 |#1|)) (|has| |#1| (-1109)))) ((((-868)) . T)) ((($) . T) (((-570)) . T)) @@ -1911,38 +1912,38 @@ (|has| |#2| (-916)) (|has| |#1| (-368)) (((|#2|) |has| |#2| (-1109))) -(-2811 (|has| |#1| (-458)) (|has| |#1| (-562)) (|has| |#1| (-916))) -(-2811 (|has| |#1| (-368)) (|has| |#1| (-458)) (|has| |#1| (-562)) (|has| |#1| (-916))) -((($) -2811 (|has| |#1| (-368)) (|has| |#1| (-354))) (((-413 (-570))) -2811 (|has| |#1| (-368)) (|has| |#1| (-354))) ((|#1|) . T)) +(-3684 (|has| |#1| (-458)) (|has| |#1| (-562)) (|has| |#1| (-916))) +(-3684 (|has| |#1| (-368)) (|has| |#1| (-458)) (|has| |#1| (-562)) (|has| |#1| (-916))) +((($) -3684 (|has| |#1| (-368)) (|has| |#1| (-354))) (((-413 (-570))) -3684 (|has| |#1| (-368)) (|has| |#1| (-354))) ((|#1|) . T)) ((((-542)) . T) (((-413 (-1182 (-570)))) . T) (((-227)) . T) (((-384)) . T)) ((((-384)) . T) (((-227)) . T) (((-868)) . T)) (|has| |#1| (-916)) (|has| |#1| (-916)) (|has| |#1| (-916)) -(-2811 (|has| |#1| (-458)) (|has| |#1| (-562)) (|has| |#1| (-916))) -(-2811 (|has| |#1| (-458)) (|has| |#1| (-916))) -(-2811 (|has| |#1| (-856)) (|has| |#1| (-1109))) +(-3684 (|has| |#1| (-458)) (|has| |#1| (-562)) (|has| |#1| (-916))) +(-3684 (|has| |#1| (-458)) (|has| |#1| (-916))) +(-3684 (|has| |#1| (-856)) (|has| |#1| (-1109))) ((($) . T)) ((($) . T) ((|#2|) . T)) -(((|#2|) -2811 (|has| |#2| (-174)) (|has| |#2| (-368)))) +(((|#2|) -3684 (|has| |#2| (-174)) (|has| |#2| (-368)))) ((((-1184 |#1| |#2| |#3|)) -12 (|has| (-1184 |#1| |#2| |#3|) (-313 (-1184 |#1| |#2| |#3|))) (|has| |#1| (-368)))) (((|#1|) . 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T)) -((((-2 (|:| -3679 |#1|) (|:| -1409 |#2|))) . T)) +((((-2 (|:| -4111 |#1|) (|:| -3117 |#2|))) . T)) (|has| |#1| (-1109)) ((((-1168) |#1|) . T)) ((($) . T)) @@ -1985,19 +1986,19 @@ (((|#1|) . T)) ((((-570)) . T)) ((((-868)) . T)) -(-2811 (|has| |#1| (-146)) (|has| |#1| (-354))) +(-3684 (|has| |#1| (-146)) (|has| |#1| (-354))) ((((-868)) . T)) (|has| |#1| (-148)) (((|#3|) . T)) -(-2811 (|has| |#3| (-174)) (|has| |#3| (-854)) (|has| |#3| (-1058))) +(-3684 (|has| |#3| (-174)) (|has| |#3| (-854)) (|has| |#3| (-1058))) ((((-868)) . T)) ((((-1262 |#2| |#3| |#4|)) . T) (((-1263 |#1| |#2| |#3| |#4|)) . T)) ((((-868)) . T)) -((((-48)) -12 (|has| |#1| (-562)) (|has| |#1| (-1047 (-570)))) (((-618 $)) . T) ((|#1|) . T) (((-570)) |has| |#1| (-1047 (-570))) (((-413 (-570))) -2811 (-12 (|has| |#1| (-562)) (|has| |#1| (-1047 (-570)))) (|has| |#1| (-1047 (-413 (-570))))) (((-413 (-959 |#1|))) |has| |#1| (-562)) (((-959 |#1|)) |has| |#1| (-1058)) (((-1186)) . 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T)) ((((-570)) |has| |#1| (-893 (-570))) (((-384)) |has| |#1| (-893 (-384)))) @@ -2006,14 +2007,14 @@ (|has| |#1| (-562)) ((((-413 (-570))) |has| |#1| (-38 (-413 (-570)))) ((|#1|) |has| |#1| (-174)) (($) |has| |#1| (-562))) (((|#1|) . 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T)) +((((-2 (|:| -4111 (-1168)) (|:| -3117 (-52)))) . T)) (((|#1|) . T) (((-413 (-570))) . T) (((-570)) . T) (($) . T)) (((|#1|) . T) (((-413 (-570))) . T) (((-570)) . T) (($) . T)) (((|#1|) . T) (((-413 (-570))) . T) (((-570)) . T) (($) . T)) @@ -2203,17 +2204,17 @@ ((((-705)) . T) (((-413 (-570))) . T) (((-570)) . T)) (((|#1| |#1|) |has| |#1| (-174))) (((|#2|) . T)) -((($) . T) (((-570)) . T) (((-413 (-570))) -2811 (|has| |#1| (-368)) (|has| |#1| (-354))) ((|#1|) . T)) +((($) . T) (((-570)) . T) (((-413 (-570))) -3684 (|has| |#1| (-368)) (|has| |#1| (-354))) ((|#1|) . T)) ((((-570) |#1|) . 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T)) @@ -2489,10 +2490,10 @@ ((((-868)) . T)) ((((-868)) . T)) ((((-542)) |has| |#1| (-620 (-542)))) -((((-2 (|:| -3679 |#1|) (|:| -1409 |#2|))) . T)) +((((-2 (|:| -4111 |#1|) (|:| -3117 |#2|))) . T)) ((((-570)) . T) (($) . T) (((-413 (-570))) . T)) ((((-1186) |#1|) |has| |#1| (-520 (-1186) |#1|)) ((|#1| |#1|) |has| |#1| (-313 |#1|))) -(((|#1|) -2811 (|has| |#1| (-174)) (|has| |#1| (-368)))) +(((|#1|) -3684 (|has| |#1| (-174)) (|has| |#1| (-368)))) (((|#1|) . T) (((-413 (-570))) . T) (($) . T)) ((((-570)) . T) (((-413 (-570))) . T) (($) . T)) (((|#1|) . T) (((-413 (-570))) . T) (($) . T)) @@ -2502,10 +2503,10 @@ (((|#1|) . T) (($) . T) (((-413 (-570))) . T)) (((|#1|) . T) (($) . T) (((-413 (-570))) . T)) (((|#2|) |has| |#2| (-368))) -((($) -2811 (|has| |#1| (-368)) (|has| |#1| (-354))) (((-413 (-570))) -2811 (|has| |#1| (-368)) (|has| |#1| (-354))) ((|#1|) . T)) +((($) -3684 (|has| |#1| (-368)) (|has| |#1| (-354))) (((-413 (-570))) -3684 (|has| |#1| (-368)) (|has| |#1| (-354))) ((|#1|) . T)) (((|#2|) . T)) ((((-413 (-570))) . T) (((-705)) . T) (($) . T)) -((($) . T) (((-413 (-570))) -2811 (|has| |#1| (-368)) (|has| |#1| (-354))) ((|#1|) . T)) +((($) . T) (((-413 (-570))) -3684 (|has| |#1| (-368)) (|has| |#1| (-354))) ((|#1|) . T)) (((|#1|) -12 (|has| |#1| (-313 |#1|)) (|has| |#1| (-1109)))) (((#0=(-786 |#1| (-870 |#2|)) #0#) |has| (-786 |#1| (-870 |#2|)) (-313 (-786 |#1| (-870 |#2|))))) ((((-570)) . T) (($) . T)) @@ -2524,13 +2525,13 @@ (|has| |#1| (-146)) (|has| |#1| (-148)) ((($ $) . 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T)) ((((-413 (-570))) |has| |#2| (-1047 (-413 (-570)))) (((-570)) |has| |#2| (-1047 (-570))) ((|#2|) . T) (((-870 |#1|)) . T)) ((($) . T) (((-117 |#1|)) . T) (((-413 (-570))) . T)) ((((-1134 |#1| |#2|)) . T) ((|#2|) . T) ((|#1|) . T) (((-570)) |has| |#1| (-1047 (-570))) (((-413 (-570))) |has| |#1| (-1047 (-413 (-570))))) @@ -2563,22 +2564,22 @@ (((|#1| |#2|) . T)) ((((-1186) |#1|) . T)) (((|#4|) . T)) -(-2811 (|has| |#1| (-368)) (|has| |#1| (-354))) +(-3684 (|has| |#1| (-368)) (|has| |#1| (-354))) ((((-1186) (-52)) . T)) ((((-1262 |#2| |#3| |#4|) (-323 |#2| |#3| |#4|)) . T)) ((((-413 (-570))) |has| |#1| (-1047 (-413 (-570)))) (((-570)) |has| |#1| (-1047 (-570))) ((|#1|) . T)) ((((-868)) . 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T)) (((|#1| $) |has| |#1| (-290 |#1| |#1|))) ((((-1263 |#1| |#2| |#3| |#4|)) . T) (((-413 (-570))) . T) (($) . T)) (((|#1|) |has| |#1| (-174)) (((-413 (-570))) |has| |#1| (-562)) (($) |has| |#1| (-562))) -((((-413 (-570))) -2811 (|has| |#1| (-38 (-413 (-570)))) (|has| |#1| (-368))) (($) -2811 (|has| |#1| (-174)) (|has| |#1| (-368)) (|has| |#1| (-562))) ((|#1|) . T)) +((((-413 (-570))) -3684 (|has| |#1| (-38 (-413 (-570)))) (|has| |#1| (-368))) (($) -3684 (|has| |#1| (-174)) (|has| |#1| (-368)) (|has| |#1| (-562))) ((|#1|) . T)) (|has| |#1| (-368)) -((($) |has| |#1| (-854)) (((-570)) -2811 (|has| |#1| (-21)) (|has| |#1| (-854)))) +((($) |has| |#1| (-854)) (((-570)) -3684 (|has| |#1| (-21)) (|has| |#1| (-854)))) (|has| |#1| (-146)) (|has| |#1| (-148)) (|has| |#1| (-148)) @@ -2591,17 +2592,17 @@ (((|#1|) . T)) (((|#2| |#2|) -12 (|has| |#2| (-313 |#2|)) (|has| |#2| (-1109)))) (((|#2| |#3|) . T)) -(-2811 (|has| |#2| (-368)) (|has| |#2| (-458)) (|has| |#2| (-562)) (|has| |#2| (-916))) +(-3684 (|has| |#2| (-368)) (|has| |#2| (-458)) (|has| |#2| (-562)) (|has| |#2| (-916))) (((|#1| (-537 |#2|)) . T)) (((|#1| (-777)) . T)) (((|#1| (-537 (-1097 (-1186)))) . T)) (((|#1|) |has| |#1| (-174))) (((|#1|) . T)) (|has| |#2| (-916)) -(-2811 (|has| |#2| (-799)) (|has| |#2| (-854))) +(-3684 (|has| |#2| (-799)) (|has| |#2| (-854))) ((((-868)) . T)) -(((|#2|) -2811 (|has| |#2| (-174)) (|has| |#2| (-368)))) -(((|#2|) -2811 (|has| |#2| (-174)) (|has| |#2| (-368)) (|has| |#2| (-1058))) (($) |has| |#2| (-174))) +(((|#2|) -3684 (|has| |#2| (-174)) (|has| |#2| (-368)))) +(((|#2|) -3684 (|has| |#2| (-174)) (|has| |#2| (-368)) (|has| |#2| (-1058))) (($) |has| |#2| (-174))) ((($ $) . T) ((#0=(-1262 |#2| |#3| |#4|) #0#) . T) ((#1=(-413 (-570)) #1#) |has| #0# (-38 (-413 (-570))))) ((((-917 |#1|)) . T)) (-12 (|has| |#1| (-368)) (|has| |#2| (-826))) @@ -2609,14 +2610,14 @@ ((((-868)) . T)) ((($) . T)) ((($) . T)) -(-2811 (|has| |#1| (-311)) (|has| |#1| (-368)) (|has| |#1| (-354)) (|has| |#1| (-562))) +(-3684 (|has| |#1| (-311)) (|has| |#1| (-368)) (|has| |#1| (-354)) (|has| |#1| (-562))) (|has| |#1| (-368)) (|has| |#1| (-368)) (((|#1| |#2|) . T)) ((($) . T) ((#0=(-1262 |#2| |#3| |#4|)) . T) (((-413 (-570))) |has| #0# (-38 (-413 (-570))))) ((((-1184 |#1| |#2| |#3|)) |has| |#1| (-368))) -(-2811 (-12 (|has| |#1| (-311)) (|has| |#1| (-916))) (|has| |#1| (-368)) (|has| |#1| (-354))) -(-2811 (|has| |#1| (-907 (-1186))) (|has| |#1| (-1058))) +(-3684 (-12 (|has| |#1| (-311)) (|has| |#1| (-916))) (|has| |#1| (-368)) (|has| |#1| (-354))) +(-3684 (|has| |#1| (-907 (-1186))) (|has| |#1| (-1058))) ((((-570)) |has| |#1| (-645 (-570))) ((|#1|) . T)) (((|#1| |#2|) . T)) ((((-868)) . T)) @@ -2661,28 +2662,28 @@ (((|#2|) . T)) (((|#4| |#4|) -12 (|has| |#4| (-313 |#4|)) (|has| |#4| (-1109)))) (((|#2|) . T)) -(((|#2|) -2811 (|has| |#2| (-6 (-4454 "*"))) (|has| |#2| (-174)))) -(-2811 (|has| |#2| (-458)) (|has| |#2| (-562)) (|has| |#2| (-916))) -(-2811 (|has| |#1| (-458)) (|has| |#1| (-562)) (|has| |#1| (-916))) +(((|#2|) -3684 (|has| |#2| (-6 (-4454 "*"))) (|has| |#2| (-174)))) +(-3684 (|has| |#2| (-458)) (|has| |#2| (-562)) (|has| |#2| (-916))) +(-3684 (|has| |#1| (-458)) (|has| |#1| (-562)) (|has| |#1| (-916))) (|has| |#2| (-916)) (|has| |#1| (-916)) (((|#2|) |has| |#2| (-174))) -((((-2 (|:| -3679 |#1|) (|:| -1409 |#2|))) . T)) +((((-2 (|:| -4111 |#1|) (|:| -3117 |#2|))) . T)) ((((-1269 |#1| |#2| |#3|)) |has| |#1| (-368))) ((((-868)) . T)) ((((-868)) . T)) ((((-542)) . T) (((-570)) . T) (((-899 (-570))) . T) (((-384)) . T) (((-227)) . T)) (((|#1| |#2|) . T)) ((($) . T) (((-570)) . T)) -((((-2 (|:| -3679 (-1168)) (|:| -1409 (-52)))) . T)) +((((-2 (|:| -4111 (-1168)) (|:| -3117 (-52)))) . T)) (((|#1|) . T)) -((((-2 (|:| -3679 |#1|) (|:| -1409 |#2|))) . T)) +((((-2 (|:| -4111 |#1|) (|:| -3117 |#2|))) . T)) ((((-868)) . T)) (((|#1| |#2|) . T)) ((($) . T) (((-570)) . T)) (((|#1| (-413 (-570))) . T)) (((|#1|) . T)) -(-2811 (|has| |#1| (-294)) (|has| |#1| (-368))) +(-3684 (|has| |#1| (-294)) (|has| |#1| (-368))) ((((-145)) . T)) ((((-413 |#2|)) . T) (((-413 (-570))) . T) (($) . T)) (|has| |#1| (-854)) @@ -2698,7 +2699,7 @@ ((((-868)) . T)) ((((-868)) . T)) ((((-189)) . T) (((-868)) . T)) -((((-2 (|:| -3679 |#1|) (|:| -1409 |#2|))) . T)) +((((-2 (|:| -4111 |#1|) (|:| -3117 |#2|))) . T)) (((|#2| |#2|) . T) ((|#1| |#1|) . T)) ((((-868)) . T)) ((((-868)) . T)) @@ -2711,7 +2712,7 @@ ((((-868)) . T)) ((((-1168)) . T)) ((((-1186) |#1|) |has| |#1| (-520 (-1186) |#1|)) ((|#1| |#1|) |has| |#1| (-313 |#1|))) -((((-2 (|:| -3679 (-1168)) (|:| -1409 |#1|))) . T)) +((((-2 (|:| -4111 (-1168)) (|:| -3117 |#1|))) . T)) (|has| |#1| (-856)) ((((-868)) . T)) ((((-542)) |has| |#1| (-620 (-542)))) @@ -2723,16 +2724,16 @@ (((|#2|) . T)) ((((-917 |#1|)) . T) (((-413 (-570))) . T) (($) . T)) ((($) . T) (((-570)) . T) (((-413 (-570))) . T) (((-618 $)) . T)) -(-2811 (|has| |#4| (-174)) (|has| |#4| (-732)) (|has| |#4| (-854)) (|has| |#4| (-1058))) -(-2811 (|has| |#3| (-174)) (|has| |#3| (-732)) (|has| |#3| (-854)) (|has| |#3| (-1058))) +(-3684 (|has| |#4| (-174)) (|has| |#4| (-732)) (|has| |#4| (-854)) (|has| |#4| (-1058))) +(-3684 (|has| |#3| (-174)) (|has| |#3| (-732)) (|has| |#3| (-854)) (|has| |#3| (-1058))) ((((-1186) (-52)) . T)) -(-2811 (|has| |#1| (-458)) (|has| |#1| (-562)) (|has| |#1| (-916))) -(-2811 (|has| |#1| (-368)) (|has| |#1| (-458)) (|has| |#1| (-562)) (|has| |#1| (-916))) +(-3684 (|has| |#1| (-458)) (|has| |#1| (-562)) (|has| |#1| (-916))) +(-3684 (|has| |#1| (-368)) (|has| |#1| (-458)) (|has| |#1| (-562)) (|has| |#1| (-916))) (((|#1|) . T)) (((|#1|) . T)) (((|#1|) . T)) -(-2811 (|has| |#2| (-25)) (|has| |#2| (-132)) (|has| |#2| (-174)) (|has| |#2| (-368)) (|has| |#2| (-799)) (|has| |#2| (-854)) (|has| |#2| (-1058))) -(-2811 (|has| |#2| (-174)) (|has| |#2| (-368)) (|has| |#2| (-854)) (|has| |#2| (-1058))) +(-3684 (|has| |#2| (-25)) (|has| |#2| (-132)) (|has| |#2| (-174)) (|has| |#2| (-368)) (|has| |#2| (-799)) (|has| |#2| (-854)) (|has| |#2| (-1058))) +(-3684 (|has| |#2| (-174)) (|has| |#2| (-368)) (|has| |#2| (-854)) (|has| |#2| (-1058))) (|has| |#1| (-916)) ((((-917 |#1|)) . T) (((-413 (-570))) . T) (($) . T) (((-570)) . T)) (|has| |#1| (-916)) @@ -2749,12 +2750,12 @@ (|has| |#1| (-38 (-413 (-570)))) (|has| |#1| (-38 (-413 (-570)))) (|has| |#1| (-38 (-413 (-570)))) -(-2811 (|has| |#1| (-368)) (|has| |#1| (-458)) (|has| |#1| (-562)) (|has| |#1| (-916))) +(-3684 (|has| |#1| (-368)) (|has| |#1| (-458)) (|has| |#1| (-562)) (|has| |#1| (-916))) (|has| |#1| (-826)) (((#0=(-917 |#1|) #0#) . T) (($ $) . T) ((#1=(-413 (-570)) #1#) . T)) ((((-413 |#2|)) . T)) (|has| |#1| (-854)) -((((-1213 |#1|)) . T) (((-868)) -2811 (|has| |#1| (-619 (-868))) (|has| |#1| (-1109)))) +((((-1213 |#1|)) . T) (((-868)) -3684 (|has| |#1| (-619 (-868))) (|has| |#1| (-1109)))) (((|#1| |#1|) . T) ((#0=(-413 (-570)) #0#) . T) ((#1=(-570) #1#) . T) (($ $) . T)) ((((-917 |#1|)) . T) (($) . T) (((-413 (-570))) . T)) (((|#2|) |has| |#2| (-1058)) (((-570)) -12 (|has| |#2| (-645 (-570))) (|has| |#2| (-1058)))) @@ -2770,29 +2771,29 @@ (((|#2|) |has| |#2| (-174))) (((|#1|) . T)) (((|#2|) . T)) -(-2811 (|has| |#1| (-146)) (|has| |#1| (-373))) -(-2811 (|has| |#1| (-146)) (|has| |#1| (-373))) -(-2811 (|has| |#1| (-146)) (|has| |#1| (-373))) -((((-2 (|:| -3679 (-1186)) (|:| -1409 (-52)))) . T)) +(-3684 (|has| |#1| (-146)) (|has| |#1| (-373))) +(-3684 (|has| |#1| (-146)) (|has| |#1| (-373))) +(-3684 (|has| |#1| (-146)) (|has| |#1| (-373))) +((((-2 (|:| -4111 (-1186)) (|:| -3117 (-52)))) . T)) ((((-570) |#3|) . T)) -(((#0=(-52)) . T) (((-2 (|:| -3679 (-1186)) (|:| -1409 #0#))) . T)) +(((#0=(-52)) . T) (((-2 (|:| -4111 (-1186)) (|:| -3117 #0#))) . T)) (|has| |#1| (-354)) ((((-570)) . T)) ((((-868)) . T)) (((|#1|) . T)) (((#0=(-1263 |#1| |#2| |#3| |#4|) $) |has| #0# (-290 #0# #0#))) (|has| |#1| (-368)) -(((|#1|) -2811 (|has| |#1| (-174)) (|has| |#1| (-368)) (|has| |#1| (-1058))) (($) -2811 (|has| |#1| (-907 (-1186))) (|has| |#1| (-1058))) (((-570)) -2811 (|has| |#1| (-21)) (|has| |#1| (-174)) (|has| |#1| (-368)) (|has| |#1| (-907 (-1186))) (|has| |#1| (-1058)))) +(((|#1|) -3684 (|has| |#1| (-174)) (|has| |#1| (-368)) (|has| |#1| (-1058))) (($) -3684 (|has| |#1| (-907 (-1186))) (|has| |#1| (-1058))) (((-570)) -3684 (|has| |#1| (-21)) (|has| |#1| (-174)) (|has| |#1| (-368)) (|has| |#1| (-907 (-1186))) (|has| |#1| (-1058)))) (((#0=(-1091) |#1|) . T) ((#0# $) . T) (($ $) . T)) -(-2811 (|has| |#1| (-368)) (|has| |#1| (-354))) +(-3684 (|has| |#1| (-368)) (|has| |#1| (-354))) (((#0=(-413 (-570)) #0#) . T) ((#1=(-705) #1#) . T) (($ $) . T)) ((((-320 |#1|)) . T) (($) . T)) (((|#1|) . T) (((-413 (-570))) |has| |#1| (-368))) ((((-868)) . T)) (|has| |#1| (-1109)) (((|#1|) . T)) -(((|#1|) -2811 (|has| |#2| (-372 |#1|)) (|has| |#2| (-423 |#1|)))) -(((|#1|) -2811 (|has| |#2| (-372 |#1|)) (|has| |#2| (-423 |#1|)))) +(((|#1|) -3684 (|has| |#2| (-372 |#1|)) (|has| |#2| (-423 |#1|)))) +(((|#1|) -3684 (|has| |#2| (-372 |#1|)) (|has| |#2| (-423 |#1|)))) (((|#2|) . T)) ((((-413 (-570))) . T) (((-705)) . T) (($) . T)) ((((-585)) . T)) @@ -2817,7 +2818,7 @@ (((|#1|) . T)) ((((-570)) . T)) (((|#2|) . T) (((-413 (-570))) |has| |#1| (-1047 (-413 (-570)))) ((|#1|) . T) (($) . T) (((-570)) . T)) -(-2811 (|has| |#1| (-174)) (|has| |#1| (-368)) (|has| |#1| (-458)) (|has| |#1| (-562)) (|has| |#1| (-916))) +(-3684 (|has| |#1| (-174)) (|has| |#1| (-368)) (|has| |#1| (-458)) (|has| |#1| (-562)) (|has| |#1| (-916))) (((|#2|) . T) (((-570)) |has| |#2| (-645 (-570)))) (((|#1| |#2|) . T)) ((($) . T)) @@ -2861,7 +2862,7 @@ (|has| |#2| (-1031)) ((($) . T)) (|has| |#1| (-916)) -((((-2 (|:| -3679 |#1|) (|:| -1409 |#2|))) . T)) +((((-2 (|:| -4111 |#1|) (|:| -3117 |#2|))) . T)) ((($) . T)) (((|#2|) . T)) (((|#1|) . T)) @@ -2870,10 +2871,10 @@ (|has| |#1| (-368)) ((((-917 |#1|)) . T)) ((($) . T) (((-570)) . T) ((|#1|) . T) (((-413 (-570))) . T)) -((($) -2811 (|has| |#1| (-368)) (|has| |#1| (-458)) (|has| |#1| (-562)) (|has| |#1| (-916))) ((|#1|) |has| |#1| (-174)) (((-413 (-570))) |has| |#1| (-38 (-413 (-570))))) -((($) |has| |#1| (-854)) (((-570)) -2811 (|has| |#1| (-21)) (|has| |#1| (-854)))) +((($) -3684 (|has| |#1| (-368)) (|has| |#1| (-458)) (|has| |#1| (-562)) (|has| |#1| (-916))) ((|#1|) |has| |#1| (-174)) (((-413 (-570))) |has| |#1| (-38 (-413 (-570))))) +((($) |has| |#1| (-854)) (((-570)) -3684 (|has| |#1| (-21)) (|has| |#1| (-854)))) ((($ $) . T) ((#0=(-413 (-570)) #0#) . T)) -(-2811 (|has| |#1| (-373)) (|has| |#1| (-856))) +(-3684 (|has| |#1| (-373)) (|has| |#1| (-856))) (((|#1|) . T)) ((((-777)) . T)) ((((-868)) . T)) @@ -2884,17 +2885,17 @@ ((((-570)) . T) (($) . T)) ((((-570)) . T) (($) . T)) ((((-777) |#1|) . T)) -(((|#2| (-242 (-2865 |#1|) (-777))) . T)) +(((|#2| (-242 (-2827 |#1|) (-777))) . T)) (((|#1| (-537 |#3|)) . T)) ((((-413 (-570))) . T)) -(-2811 (|has| |#1| (-458)) (|has| |#1| (-562)) (|has| |#1| (-916))) +(-3684 (|has| |#1| (-458)) (|has| |#1| (-562)) (|has| |#1| (-916))) ((((-1168)) . T) (((-868)) . T)) -(((#0=(-2 (|:| -3679 (-1186)) (|:| -1409 (-52))) #0#) |has| (-2 (|:| -3679 (-1186)) (|:| -1409 (-52))) (-313 (-2 (|:| -3679 (-1186)) (|:| -1409 (-52)))))) +(((#0=(-2 (|:| -4111 (-1186)) (|:| -3117 (-52))) #0#) |has| (-2 (|:| -4111 (-1186)) (|:| -3117 (-52))) (-313 (-2 (|:| -4111 (-1186)) (|:| -3117 (-52)))))) ((((-1168)) . T)) (|has| |#1| (-916)) (|has| |#2| (-368)) (((|#1|) . T) (($) . T) (((-570)) . T)) -(-2811 (|has| |#2| (-132)) (|has| |#2| (-174)) (|has| |#2| (-368)) (|has| |#2| (-799)) (|has| |#2| (-854)) (|has| |#2| (-1058))) +(-3684 (|has| |#2| (-132)) (|has| |#2| (-174)) (|has| |#2| (-368)) (|has| |#2| (-799)) (|has| |#2| (-854)) (|has| |#2| (-1058))) ((((-171 (-384))) . T) (((-227)) . T) (((-384)) . T)) ((((-868)) . T)) (((|#1|) . T)) @@ -2911,11 +2912,11 @@ (|has| |#1| (-38 (-413 (-570)))) (|has| |#1| (-38 (-413 (-570)))) (|has| |#1| (-38 (-413 (-570)))) -(-2811 (|has| |#1| (-311)) (|has| |#1| (-368)) (|has| |#1| (-354))) +(-3684 (|has| |#1| (-311)) (|has| |#1| (-368)) (|has| |#1| (-354))) (|has| |#1| (-38 (-413 (-570)))) (-12 (|has| |#1| (-551)) (|has| |#1| (-834))) ((((-868)) . T)) -((((-1186)) -2811 (-12 (|has| |#1| (-15 * (|#1| (-570) |#1|))) (|has| |#1| (-907 (-1186)))) (-12 (|has| |#1| (-368)) (|has| |#2| (-907 (-1186)))))) +((((-1186)) -3684 (-12 (|has| |#1| (-15 * (|#1| (-570) |#1|))) (|has| |#1| (-907 (-1186)))) (-12 (|has| |#1| (-368)) (|has| |#2| (-907 (-1186)))))) (|has| |#1| (-368)) ((((-1186)) -12 (|has| |#1| (-15 * (|#1| (-413 (-570)) |#1|))) (|has| |#1| (-907 (-1186))))) (|has| |#1| (-368)) @@ -2927,7 +2928,7 @@ (((|#2|) |has| |#1| (-368))) (((|#2|) |has| |#1| (-368))) ((((-570)) . T) (($) . T)) -((((-2 (|:| -3679 |#1|) (|:| -1409 |#2|))) . T)) +((((-2 (|:| -4111 |#1|) (|:| -3117 |#2|))) . T)) (((|#1|) . T)) (((|#1|) |has| |#1| (-174))) (((|#1|) . T)) @@ -2956,11 +2957,11 @@ (((|#1| |#1|) -12 (|has| |#1| (-313 |#1|)) (|has| |#1| (-1109)))) (((|#2|) |has| |#1| (-368))) ((((-384)) -12 (|has| |#1| (-368)) (|has| |#2| (-893 (-384)))) (((-570)) -12 (|has| |#1| (-368)) (|has| |#2| (-893 (-570))))) -(-2811 (|has| |#1| (-368)) (|has| |#1| (-562))) +(-3684 (|has| |#1| (-368)) (|has| |#1| (-562))) (|has| |#1| (-368)) (((|#1|) . T)) ((($) . T) (((-570)) . T) ((|#2|) . T)) -(-2811 (|has| |#1| (-368)) (|has| |#1| (-562))) +(-3684 (|has| |#1| (-368)) (|has| |#1| (-562))) (((|#3|) . T)) ((((-1168)) . T) (((-512)) . T) (((-227)) . T) (((-570)) . T)) (((|#1|) . T)) @@ -2968,23 +2969,23 @@ (|has| |#1| (-562)) (((|#4| |#4|) -12 (|has| |#4| (-313 |#4|)) (|has| |#4| (-1109)))) ((((-413 |#2|)) . T) (((-413 (-570))) . T) (($) . T) (((-570)) . T)) -(-2811 (|has| |#2| (-132)) (|has| |#2| (-174)) (|has| |#2| (-368)) (|has| |#2| (-799)) (|has| |#2| (-854)) (|has| |#2| (-1058))) +(-3684 (|has| |#2| (-132)) (|has| |#2| (-174)) (|has| |#2| (-368)) (|has| |#2| (-799)) (|has| |#2| (-854)) (|has| |#2| (-1058))) (((|#2|) . T)) (((|#2|) . T)) -(-2811 (|has| |#2| (-174)) (|has| |#2| (-732)) (|has| |#2| (-854)) (|has| |#2| (-1058))) -((((-2 (|:| -3679 |#1|) (|:| -1409 |#2|))) . T)) -((((-2 (|:| -3679 (-1168)) (|:| -1409 |#1|))) . T)) -((((-2 (|:| -3679 |#1|) (|:| -1409 |#2|))) . T)) +(-3684 (|has| |#2| (-174)) (|has| |#2| (-732)) (|has| |#2| (-854)) (|has| |#2| (-1058))) +((((-2 (|:| -4111 |#1|) (|:| -3117 |#2|))) . T)) +((((-2 (|:| -4111 (-1168)) (|:| -3117 |#1|))) . T)) +((((-2 (|:| -4111 |#1|) (|:| -3117 |#2|))) . T)) (|has| |#1| (-38 (-413 (-570)))) (((|#1| |#2|) . T)) (|has| |#1| (-38 (-413 (-570)))) -(-2811 (|has| |#1| (-146)) (|has| |#1| (-373))) +(-3684 (|has| |#1| (-146)) (|has| |#1| (-373))) ((($) . T)) ((((-1168) |#1|) . T)) (|has| |#1| (-148)) -(-2811 (|has| |#1| (-146)) (|has| |#1| (-373))) +(-3684 (|has| |#1| (-146)) (|has| |#1| (-373))) (|has| |#1| (-148)) -(-2811 (|has| |#1| (-146)) (|has| |#1| (-373))) +(-3684 (|has| |#1| (-146)) (|has| |#1| (-373))) ((($) . T)) (|has| |#1| (-148)) ((((-587 |#1|)) . T)) @@ -2998,7 +2999,7 @@ ((((-413 (-570))) |has| |#2| (-1047 (-570))) (((-570)) |has| |#2| (-1047 (-570))) (((-1186)) |has| |#2| (-1047 (-1186))) ((|#2|) . T)) (((#0=(-413 |#2|) #0#) . T) ((#1=(-413 (-570)) #1#) . T) (($ $) . T)) (((|#1|) . T)) -(-2811 (|has| |#1| (-146)) (|has| |#1| (-354))) +(-3684 (|has| |#1| (-146)) (|has| |#1| (-354))) (|has| |#1| (-148)) ((((-868)) . T)) ((($) . T)) @@ -3024,7 +3025,7 @@ ((((-917 |#1|)) . T) (((-413 (-570))) . T) (($) . T) (((-570)) . T)) ((((-868)) . T)) ((((-542)) |has| |#1| (-620 (-542)))) -((((-868)) -2811 (|has| |#1| (-619 (-868))) (|has| |#1| (-856)) (|has| |#1| (-1109)))) +((((-868)) -3684 (|has| |#1| (-619 (-868))) (|has| |#1| (-856)) (|has| |#1| (-1109)))) ((((-115)) . T) ((|#1|) . T)) (((|#1|) . T)) (((|#1|) . T)) @@ -3046,7 +3047,7 @@ ((((-570)) . T)) ((((-868)) . T)) ((((-570)) . T)) -(-2811 (|has| |#2| (-799)) (|has| |#2| (-854))) +(-3684 (|has| |#2| (-799)) (|has| |#2| (-854))) ((((-171 (-384))) . T) (((-227)) . T) (((-384)) . T)) ((((-868)) . T)) ((((-868)) . T)) @@ -3058,10 +3059,10 @@ (((|#1|) . T) (($) . T) (((-413 (-570))) . T)) (|has| |#1| (-368)) (|has| |#1| (-368)) -((((-868)) -2811 (|has| |#1| (-619 (-868))) (|has| |#1| (-1109)))) -((((-868)) -2811 (|has| |#1| (-619 (-868))) (|has| |#1| (-1109)))) +((((-868)) -3684 (|has| |#1| (-619 (-868))) (|has| |#1| (-1109)))) +((((-868)) -3684 (|has| |#1| (-619 (-868))) (|has| |#1| (-1109)))) ((((-570) $) . T) (((-650 (-570)) $) . T)) -(-2811 (|has| |#1| (-21)) (|has| |#1| (-25)) (|has| |#1| (-174)) (|has| |#1| (-368)) (|has| |#1| (-479)) (|has| |#1| (-732)) (|has| |#1| (-907 (-1186))) (|has| |#1| (-1058)) (|has| |#1| (-1121)) (|has| |#1| (-1109))) +(-3684 (|has| |#1| (-21)) (|has| |#1| (-25)) (|has| |#1| (-174)) (|has| |#1| (-368)) (|has| |#1| (-479)) (|has| |#1| (-732)) (|has| |#1| (-907 (-1186))) (|has| |#1| (-1058)) (|has| |#1| (-1121)) (|has| |#1| (-1109))) (|has| |#1| (-1161)) ((((-917 |#1|)) . T) (((-413 (-570))) . T) (($) . T)) ((((-917 |#1|)) . T) (($) . T) (((-413 (-570))) . T)) @@ -3078,9 +3079,9 @@ (((|#1|) |has| |#1| (-313 |#1|))) ((((-570) |#1|) . T) (((-1244 (-570)) $) . T)) ((((-1186) |#1|) . T)) -(((|#1|) -2811 (|has| |#1| (-174)) (|has| |#1| (-368)))) +(((|#1|) -3684 (|has| |#1| (-174)) (|has| |#1| (-368)))) (((|#1|) . T)) -(((|#1|) -2811 (|has| |#1| (-174)) (|has| |#1| (-368)) (|has| |#1| (-1058)))) +(((|#1|) -3684 (|has| |#1| (-174)) (|has| |#1| (-368)) (|has| |#1| (-1058)))) ((((-570)) . T) (((-413 (-570))) . T)) (((|#1|) . T)) (|has| |#1| (-562)) @@ -3089,14 +3090,14 @@ ((((-384)) . T)) (((|#1|) . T)) (((|#1|) . T)) -(-2811 (|has| |#1| (-368)) (|has| |#1| (-562))) +(-3684 (|has| |#1| (-368)) (|has| |#1| (-562))) (|has| |#1| (-368)) -(-2811 (|has| |#1| (-368)) (|has| |#1| (-562))) +(-3684 (|has| |#1| (-368)) (|has| |#1| (-562))) (|has| |#1| (-368)) (|has| |#1| (-562)) (|has| |#1| (-1109)) ((((-786 |#1| (-870 |#2|))) |has| (-786 |#1| (-870 |#2|)) (-313 (-786 |#1| (-870 |#2|))))) -(-2811 (|has| |#2| (-458)) (|has| |#2| (-562)) (|has| |#2| (-916))) +(-3684 (|has| |#2| (-458)) (|has| |#2| (-562)) (|has| |#2| (-916))) (((|#1|) . T)) (((|#2| |#3|) . T)) (((|#1|) . T)) @@ -3108,13 +3109,13 @@ (|has| |#2| (-368)) ((((-587 |#1|)) . T) (((-413 (-570))) . T) (($) . T) (((-570)) . T)) ((((-570)) . T) (((-413 (-570))) . T) (($) . T)) -((((-2 (|:| -3679 (-1168)) (|:| -1409 (-52)))) . T)) +((((-2 (|:| -4111 (-1168)) (|:| -3117 (-52)))) . T)) (((|#1|) . T)) (((|#1|) . T) (((-570)) . 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T)) (((|#1|) |has| |#1| (-174))) -(-2811 (|has| |#2| (-25)) (|has| |#2| (-132)) (|has| |#2| (-174)) (|has| |#2| (-368)) (|has| |#2| (-799)) (|has| |#2| (-854)) (|has| |#2| (-1058))) +(-3684 (|has| |#2| (-25)) (|has| |#2| (-132)) (|has| |#2| (-174)) (|has| |#2| (-368)) (|has| |#2| (-799)) (|has| |#2| (-854)) (|has| |#2| (-1058))) (((|#1|) . T)) (((|#1|) . T)) -(-2811 (|has| |#2| (-174)) (|has| |#2| (-368)) (|has| |#2| (-854)) (|has| |#2| (-1058))) +(-3684 (|has| |#2| (-174)) (|has| |#2| (-368)) (|has| |#2| (-854)) (|has| |#2| (-1058))) (((|#1|) . T)) ((((-413 (-570))) . T) (((-570)) . T) (($) . T)) ((((-542)) . T)) @@ -3211,14 +3212,14 @@ ((($ $) . T) ((#0=(-413 (-570)) #0#) . T)) ((((-1186)) |has| |#1| (-907 (-1186)))) ((((-917 |#1|)) . T) (((-413 (-570))) . T) (($) . T)) -((($) . T) (((-413 (-570))) -2811 (|has| |#1| (-38 (-413 (-570)))) (|has| |#1| (-368))) ((|#1|) . T)) -(((#0=(-413 (-570)) #0#) |has| |#1| (-38 (-413 (-570)))) ((|#1| |#1|) . 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T)) (|has| |#2| (-826)) (|has| |#2| (-826)) -((((-413 (-570))) -2811 (|has| |#1| (-38 (-413 (-570)))) (|has| |#1| (-368))) ((|#2|) |has| |#1| (-368)) (($) . T) ((|#1|) . T)) -(((|#1|) . T) (((-413 (-570))) -2811 (|has| |#1| (-38 (-413 (-570)))) (|has| |#1| (-368))) (($) . T)) +((((-413 (-570))) -3684 (|has| |#1| (-38 (-413 (-570)))) (|has| |#1| (-368))) ((|#2|) |has| |#1| (-368)) (($) . T) ((|#1|) . T)) +(((|#1|) . T) (((-413 (-570))) -3684 (|has| |#1| (-38 (-413 (-570)))) (|has| |#1| (-368))) (($) . T)) (((|#1| |#1|) -12 (|has| |#1| (-313 |#1|)) (|has| |#1| (-1109)))) (((|#1|) . T) (((-570)) |has| |#1| (-1047 (-570))) (((-413 (-570))) |has| |#1| (-1047 (-413 (-570))))) ((((-570)) |has| |#1| (-893 (-570))) (((-384)) |has| |#1| (-893 (-384)))) @@ -3255,7 +3256,7 @@ (((|#1|) . 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T)) -(-2811 (|has| |#1| (-368)) (|has| |#1| (-354))) -((((-868)) -2811 (|has| |#1| (-619 (-868))) (|has| |#1| (-856)) (|has| |#1| (-1109)))) +(-3684 (|has| |#1| (-368)) (|has| |#1| (-354))) +((((-868)) -3684 (|has| |#1| (-619 (-868))) (|has| |#1| (-856)) (|has| |#1| (-1109)))) ((((-542)) |has| |#1| (-620 (-542)))) -((((-868)) -2811 (|has| |#1| (-619 (-868))) (|has| |#1| (-1109)))) -((((-868)) -2811 (|has| |#1| (-619 (-868))) (|has| |#1| (-856)) (|has| |#1| (-1109)))) +((((-868)) -3684 (|has| |#1| (-619 (-868))) (|has| |#1| (-1109)))) +((((-868)) -3684 (|has| |#1| (-619 (-868))) (|has| |#1| (-856)) (|has| |#1| (-1109)))) ((((-542)) |has| |#1| (-620 (-542)))) -((((-868)) -2811 (|has| |#1| (-619 (-868))) (|has| |#1| (-856)) (|has| |#1| (-1109)))) +((((-868)) -3684 (|has| |#1| (-619 (-868))) (|has| |#1| (-856)) (|has| |#1| (-1109)))) ((((-542)) |has| |#1| (-620 (-542)))) -((((-868)) -2811 (|has| |#1| (-619 (-868))) (|has| |#1| (-1109)))) +((((-868)) -3684 (|has| |#1| (-619 (-868))) (|has| |#1| (-1109)))) (((|#1|) . T)) (((|#2| |#2|) . T) ((#0=(-413 (-570)) #0#) . T) (($ $) . T)) (((|#2|) . T) (((-413 (-570))) . T) (($) . T)) @@ -3639,21 +3640,21 @@ (((|#1| (-537 (-870 |#2|)) (-870 |#2|) (-786 |#1| (-870 |#2|))) . T)) (((|#1| |#2| (-242 |#1| |#2|) (-242 |#1| |#2|)) . T)) ((((-868)) . T)) -((((-413 (-570))) |has| |#2| (-38 (-413 (-570)))) ((|#2|) |has| |#2| (-174)) (($) -2811 (|has| |#2| (-458)) (|has| |#2| (-562)) (|has| |#2| (-916)))) +((((-413 (-570))) |has| |#2| (-38 (-413 (-570)))) ((|#2|) |has| |#2| (-174)) (($) -3684 (|has| |#2| (-458)) (|has| |#2| (-562)) (|has| |#2| (-916)))) (((|#2|) . T) ((|#6|) . T)) ((($) . T) (((-413 (-570))) |has| |#2| (-38 (-413 (-570)))) ((|#2|) . T)) ((($) . T) (((-570)) . T)) -((($) -2811 (|has| |#1| (-458)) (|has| |#1| (-562)) (|has| |#1| (-916))) ((|#1|) |has| |#1| (-174)) (((-413 (-570))) |has| |#1| (-38 (-413 (-570))))) +((($) -3684 (|has| |#1| (-458)) (|has| |#1| (-562)) (|has| |#1| (-916))) ((|#1|) |has| |#1| (-174)) (((-413 (-570))) |has| |#1| (-38 (-413 (-570))))) ((((-1113)) . T)) ((((-868)) . T)) ((((-1191)) . T) (((-868)) . T)) ((((-1191)) . T) (((-868)) . T)) -((($) -2811 (|has| |#1| (-368)) (|has| |#1| (-458)) (|has| |#1| (-562)) (|has| |#1| (-916))) ((|#1|) |has| |#1| (-174)) (((-413 (-570))) |has| |#1| (-38 (-413 (-570))))) +((($) -3684 (|has| |#1| (-368)) (|has| |#1| (-458)) (|has| |#1| (-562)) (|has| |#1| (-916))) ((|#1|) |has| |#1| (-174)) (((-413 (-570))) |has| |#1| (-38 (-413 (-570))))) ((((-1191)) . T)) ((((-1191)) . T)) ((($) . T) (((-413 (-570))) |has| |#1| (-38 (-413 (-570)))) ((|#1|) . T)) ((($) . T)) -((($) -2811 (|has| |#1| (-458)) (|has| |#1| (-562)) (|has| |#1| (-916))) ((|#1|) |has| |#1| (-174)) (((-413 (-570))) |has| |#1| (-38 (-413 (-570))))) +((($) -3684 (|has| |#1| (-458)) (|has| |#1| (-562)) (|has| |#1| (-916))) ((|#1|) |has| |#1| (-174)) (((-413 (-570))) |has| |#1| (-38 (-413 (-570))))) ((($ $) . T) (((-1186) $) . T)) (|has| |#2| (-916)) ((((-1269 |#1| |#2| |#3|)) . T)) @@ -3666,7 +3667,7 @@ (((|#1|) . T)) (((|#1| |#1|) |has| |#1| (-174))) ((((-705)) . T)) -((((-868)) -2811 (|has| |#1| (-619 (-868))) (|has| |#1| (-1109)))) +((((-868)) -3684 (|has| |#1| (-619 (-868))) (|has| |#1| (-1109)))) ((((-1191)) . T)) (((|#1|) |has| |#1| (-174))) ((((-1191)) . T)) @@ -3683,13 +3684,13 @@ ((((-1191)) . T)) ((((-1191)) . T)) ((((-1191)) . T)) -(-2811 (|has| |#1| (-368)) (|has| |#1| (-354))) -(-2811 (|has| |#1| (-368)) (|has| |#1| (-354))) +(-3684 (|has| |#1| (-368)) (|has| |#1| (-354))) +(-3684 (|has| |#1| (-368)) (|has| |#1| (-354))) ((((-1191)) . T)) ((((-1191)) . T)) (|has| |#1| (-368)) (|has| |#1| (-368)) -(-2811 (|has| |#1| (-174)) (|has| |#1| (-562))) +(-3684 (|has| |#1| (-174)) (|has| |#1| (-562))) (((|#1| (-570)) . T)) (((|#1| (-413 (-570))) . T)) (((|#1| (-777)) . T)) @@ -3704,16 +3705,16 @@ ((((-899 (-384))) . T) (((-899 (-570))) . T) (((-1186)) . T) (((-542)) . T)) (((|#1|) . T)) ((((-868)) . T)) -(-2811 (|has| |#2| (-132)) (|has| |#2| (-174)) (|has| |#2| (-368)) (|has| |#2| (-799)) (|has| |#2| (-854)) (|has| |#2| (-1058))) -(-2811 (-12 (|has| |#1| (-21)) (|has| |#2| (-21))) (-12 (|has| |#1| (-23)) (|has| |#2| (-23))) (-12 (|has| |#1| (-132)) (|has| |#2| (-132))) (-12 (|has| |#1| (-799)) (|has| |#2| (-799)))) +(-3684 (|has| |#2| (-132)) (|has| |#2| (-174)) (|has| |#2| (-368)) (|has| |#2| (-799)) (|has| |#2| (-854)) (|has| |#2| (-1058))) +(-3684 (-12 (|has| |#1| (-21)) (|has| |#2| (-21))) (-12 (|has| |#1| (-23)) (|has| |#2| (-23))) (-12 (|has| |#1| (-132)) (|has| |#2| (-132))) (-12 (|has| |#1| (-799)) (|has| |#2| (-799)))) ((((-570)) . T)) ((((-570)) . T)) -((((-2 (|:| -3679 |#1|) (|:| -1409 |#2|))) . T)) +((((-2 (|:| -4111 |#1|) (|:| -3117 |#2|))) . T)) (((|#1| |#2|) . T)) (((|#1|) . T)) -(-2811 (|has| |#2| (-174)) (|has| |#2| (-732)) (|has| |#2| (-854)) (|has| |#2| (-1058))) +(-3684 (|has| |#2| (-174)) (|has| |#2| (-732)) (|has| |#2| (-854)) (|has| |#2| (-1058))) ((((-1186)) -12 (|has| |#2| (-907 (-1186))) (|has| |#2| (-1058)))) -(-2811 (-12 (|has| |#1| (-479)) (|has| |#2| (-479))) (-12 (|has| |#1| (-732)) (|has| |#2| (-732)))) +(-3684 (-12 (|has| |#1| (-479)) (|has| |#2| (-479))) (-12 (|has| |#1| (-732)) (|has| |#2| (-732)))) (|has| |#1| (-146)) (|has| |#1| (-148)) (|has| |#1| (-368)) @@ -3744,7 +3745,7 @@ (((|#1| |#2|) . T)) ((((-570)) . T) ((|#2|) |has| |#2| (-174))) ((((-115)) . T) ((|#1|) . T) (((-570)) . T)) -(-2811 (|has| |#1| (-354)) (|has| |#1| (-373))) +(-3684 (|has| |#1| (-354)) (|has| |#1| (-373))) (((|#1| |#2|) . T)) ((((-227)) . T)) ((((-413 (-570))) . T) (($) . T) (((-570)) . T)) @@ -3756,7 +3757,7 @@ (((|#1|) . T)) (((|#1|) . T)) ((((-542)) |has| |#1| (-620 (-542)))) -((((-868)) -2811 (|has| |#1| (-619 (-868))) (|has| |#1| (-856)) (|has| |#1| (-1109)))) +((((-868)) -3684 (|has| |#1| (-619 (-868))) (|has| |#1| (-856)) (|has| |#1| (-1109)))) ((((-570) $) . T) (((-650 (-570)) $) . T)) ((($) . T) (((-413 (-570))) . T)) (|has| |#1| (-916)) @@ -3768,14 +3769,14 @@ (((|#1| |#1|) |has| |#1| (-174))) (((|#1|) . T) (((-570)) . T)) ((((-1191)) . T)) -(-2811 (|has| |#1| (-368)) (|has| |#1| (-562))) -(-2811 (|has| |#1| (-21)) (|has| |#1| (-854))) +(-3684 (|has| |#1| (-368)) (|has| |#1| (-562))) +(-3684 (|has| |#1| (-21)) (|has| |#1| (-854))) (((|#2|) . T)) -(-2811 (|has| |#1| (-21)) (|has| |#1| (-854))) +(-3684 (|has| |#1| (-21)) (|has| |#1| (-854))) (((|#1|) |has| |#1| (-174))) (((|#1|) . T)) (((|#1|) . T)) -((((-868)) -2811 (-12 (|has| |#1| (-619 (-868))) (|has| |#2| (-619 (-868)))) (-12 (|has| |#1| (-1109)) (|has| |#2| (-1109))))) +((((-868)) -3684 (-12 (|has| |#1| (-619 (-868))) (|has| |#2| (-619 (-868)))) (-12 (|has| |#1| (-1109)) (|has| |#2| (-1109))))) ((((-413 |#2|) |#3|) . T)) ((((-413 (-570))) . T) (($) . T)) (|has| |#1| (-38 (-413 (-570)))) @@ -3789,19 +3790,19 @@ (((|#1|) . T) (((-413 (-570))) . T) (((-570)) . T) (($) . T)) (((#0=(-570) #0#) . T)) ((($) . T) (((-413 (-570))) . T)) -(-2811 (|has| |#4| (-174)) (|has| |#4| (-732)) (|has| |#4| (-854)) (|has| |#4| (-1058))) -(-2811 (|has| |#3| (-174)) (|has| |#3| (-732)) (|has| |#3| (-854)) (|has| |#3| (-1058))) +(-3684 (|has| |#4| (-174)) (|has| |#4| (-732)) (|has| |#4| (-854)) (|has| |#4| (-1058))) +(-3684 (|has| |#3| (-174)) (|has| |#3| (-732)) (|has| |#3| (-854)) (|has| |#3| (-1058))) ((((-868)) . T) (((-1191)) . T)) (|has| |#4| (-799)) -(-2811 (|has| |#4| (-799)) (|has| |#4| (-854))) +(-3684 (|has| |#4| (-799)) (|has| |#4| (-854))) (|has| |#4| (-854)) (|has| |#3| (-799)) ((((-1191)) . T)) -(-2811 (|has| |#3| (-799)) (|has| |#3| (-854))) +(-3684 (|has| |#3| (-799)) (|has| |#3| (-854))) (|has| |#3| (-854)) ((((-570)) . T)) (((|#2|) . T)) -((((-1186)) -2811 (-12 (|has| (-1184 |#1| |#2| |#3|) (-907 (-1186))) (|has| |#1| (-368))) (-12 (|has| |#1| (-15 * (|#1| (-570) |#1|))) (|has| |#1| (-907 (-1186)))))) +((((-1186)) -3684 (-12 (|has| (-1184 |#1| |#2| |#3|) (-907 (-1186))) (|has| |#1| (-368))) (-12 (|has| |#1| (-15 * (|#1| (-570) |#1|))) (|has| |#1| (-907 (-1186)))))) ((((-1186)) -12 (|has| |#1| (-15 * (|#1| (-413 (-570)) |#1|))) (|has| |#1| (-907 (-1186))))) ((((-1186)) -12 (|has| |#1| (-15 * (|#1| (-777) |#1|))) (|has| |#1| (-907 (-1186))))) (((|#1| |#1|) . T) (($ $) . T)) @@ -3816,11 +3817,11 @@ ((((-1184 |#1| |#2| |#3|)) |has| |#1| (-368))) ((((-1149 |#1| |#2|)) . T)) ((((-1184 |#1| |#2| |#3|)) |has| |#1| (-368))) -(((|#2|) . T) (((-2 (|:| -3679 |#1|) (|:| -1409 |#2|))) . T)) -((((-2 (|:| -3679 (-1186)) (|:| -1409 (-52)))) . T)) +(((|#2|) . T) (((-2 (|:| -4111 |#1|) (|:| -3117 |#2|))) . T)) +((((-2 (|:| -4111 (-1186)) (|:| -3117 (-52)))) . T)) ((($) . T)) (|has| |#1| (-1031)) -(((|#2|) . T) (((-2 (|:| -3679 |#1|) (|:| -1409 |#2|))) . T)) +(((|#2|) . T) (((-2 (|:| -4111 |#1|) (|:| -3117 |#2|))) . T)) ((((-868)) . T)) ((((-542)) |has| |#2| (-620 (-542))) (((-899 (-570))) |has| |#2| (-620 (-899 (-570)))) (((-899 (-384))) |has| |#2| (-620 (-899 (-384)))) (((-384)) . #0=(|has| |#2| (-1031))) (((-227)) . #0#)) ((((-298 |#3|)) . T)) @@ -3837,15 +3838,15 @@ ((((-1184 |#1| |#2| |#3|)) . T)) ((((-1184 |#1| |#2| |#3|)) . T) (((-1177 |#1| |#2| |#3|)) . T)) ((((-868)) . T)) -((((-868)) -2811 (|has| |#1| (-619 (-868))) (|has| |#1| (-1109)))) +((((-868)) -3684 (|has| |#1| (-619 (-868))) (|has| |#1| (-1109)))) ((((-570) |#1|) . T)) ((((-1184 |#1| |#2| |#3|)) |has| |#1| (-368))) (((|#1| |#2| |#3| |#4|) . T)) (((|#1|) . T)) (((|#2|) . T)) (|has| |#2| (-368)) -(((|#3|) . T) ((|#2|) . T) (($) -2811 (|has| |#4| (-174)) (|has| |#4| (-854)) (|has| |#4| (-1058))) ((|#4|) -2811 (|has| |#4| (-174)) (|has| |#4| (-368)) (|has| |#4| (-1058)))) -(((|#2|) . T) (($) -2811 (|has| |#3| (-174)) (|has| |#3| (-854)) (|has| |#3| (-1058))) ((|#3|) -2811 (|has| |#3| (-174)) (|has| |#3| (-368)) (|has| |#3| (-1058)))) +(((|#3|) . T) ((|#2|) . T) (($) -3684 (|has| |#4| (-174)) (|has| |#4| (-854)) (|has| |#4| (-1058))) ((|#4|) -3684 (|has| |#4| (-174)) (|has| |#4| (-368)) (|has| |#4| (-1058)))) +(((|#2|) . T) (($) -3684 (|has| |#3| (-174)) (|has| |#3| (-854)) (|has| |#3| (-1058))) ((|#3|) -3684 (|has| |#3| (-174)) (|has| |#3| (-368)) (|has| |#3| (-1058)))) (((|#1|) . T)) (((|#1|) . T)) ((((-117 |#1|)) . T)) @@ -3859,7 +3860,7 @@ ((((-189)) . T) (((-868)) . T)) ((((-868)) . T)) (((|#1|) . T)) -((((-868)) -2811 (|has| |#1| (-619 (-868))) (|has| |#1| (-1109)))) +((((-868)) -3684 (|has| |#1| (-619 (-868))) (|has| |#1| (-1109)))) ((((-130)) . T) (((-868)) . T)) ((((-570) |#1|) . T) (((-1244 (-570)) $) . T)) ((((-130)) . T)) @@ -3868,13 +3869,13 @@ (((|#1|) . T)) (((|#2| $) -12 (|has| |#1| (-368)) (|has| |#2| (-290 |#2| |#2|))) (($ $) . T) (((-570) |#1|) . T)) ((($ $) . T) (((-413 (-570)) |#1|) . T)) -(-2811 (|has| |#1| (-368)) (|has| |#1| (-458)) (|has| |#1| (-916))) -(-2811 (|has| |#1| (-856)) (|has| |#1| (-1109))) +(-3684 (|has| |#1| (-368)) (|has| |#1| (-458)) (|has| |#1| (-916))) +(-3684 (|has| |#1| (-856)) (|has| |#1| (-1109))) ((((-868)) . T)) ((((-868)) . T)) ((((-868)) . T)) (((|#1| (-537 |#2|)) . T)) -((((-2 (|:| -3679 (-1186)) (|:| -1409 (-52)))) . T)) +((((-2 (|:| -4111 (-1186)) (|:| -3117 (-52)))) . T)) ((((-570) (-130)) . T)) (((|#1| (-570)) . T)) (((|#1| (-413 (-570))) . T)) @@ -3889,8 +3890,8 @@ ((((-1191)) . T)) ((((-868)) . T) (((-1191)) . T)) ((((-868)) . T) (((-1191)) . T)) -(-2811 (|has| |#2| (-458)) (|has| |#2| (-562)) (|has| |#2| (-916))) -(-2811 (|has| |#1| (-458)) (|has| |#1| (-562)) (|has| |#1| (-916))) +(-3684 (|has| |#2| (-458)) (|has| |#2| (-562)) (|has| |#2| (-916))) +(-3684 (|has| |#1| (-458)) (|has| |#1| (-562)) (|has| |#1| (-916))) ((($) . T)) (((|#2| (-537 (-870 |#1|))) . T)) ((((-1191)) . T)) @@ -3905,13 +3906,13 @@ ((((-1191)) . T)) ((((-868)) . T) (((-1191)) . T)) ((((-1191)) . T)) -((((-868)) -2811 (|has| |#1| (-619 (-868))) (|has| |#1| (-1109)))) +((((-868)) -3684 (|has| |#1| (-619 (-868))) (|has| |#1| (-1109)))) (((|#1|) . T)) (((|#2| (-777)) . T)) (((|#1| |#2|) . T)) ((((-1168) |#1|) . T)) ((((-413 |#2|)) . T)) -((((-2 (|:| -3679 |#1|) (|:| -1409 |#2|))) . T)) +((((-2 (|:| -4111 |#1|) (|:| -3117 |#2|))) . T)) (|has| |#1| (-562)) (|has| |#1| (-562)) ((($) . T) ((|#2|) . T)) @@ -3922,14 +3923,14 @@ ((((-570)) . T) (($) . 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T) (((-570)) -2811 (|has| (-1008 |#1|) (-1047 (-570))) (|has| |#1| (-1047 (-570)))) (((-413 (-570))) -2811 (|has| (-1008 |#1|) (-1047 (-413 (-570)))) (|has| |#1| (-1047 (-413 (-570)))))) +((((-1008 |#1|)) . T) ((|#1|) . T) (((-570)) -3684 (|has| (-1008 |#1|) (-1047 (-570))) (|has| |#1| (-1047 (-570)))) (((-413 (-570))) -3684 (|has| (-1008 |#1|) (-1047 (-413 (-570)))) (|has| |#1| (-1047 (-413 (-570)))))) ((((-917 |#1|)) . T) (((-413 (-570))) . T) (($) . T)) (((|#1| |#1|) -12 (|has| |#1| (-313 |#1|)) (|has| |#1| (-1109)))) (((|#1| |#1|) -12 (|has| |#1| (-313 |#1|)) (|has| |#1| (-1109)))) @@ -3945,11 +3946,11 @@ (((|#1| |#2| |#3| |#4|) . T)) (((#0=(-1149 |#1| |#2|) #0#) |has| (-1149 |#1| |#2|) (-313 (-1149 |#1| |#2|)))) (((|#1|) . 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. -562) 165479) ((-254 . -1047) 165306) ((-253 . -1047) 165133) ((-127 . -120) 165117) ((-917 . -1065) 165082) ((-718 . -102) T) ((-705 . -1067) T) ((-603 . -622) 165063) ((-591 . -622) 165044) ((-542 . -624) 164947) ((-348 . -174) T) ((-88 . -619) 164929) ((-153 . -21) T) ((-153 . -25) T) ((-917 . -111) 164885) ((-40 . -723) 164830) ((-876 . -1109) T) ((-670 . -622) 164807) ((-651 . -622) 164788) ((-360 . -622) 164725) ((-357 . -622) 164662) ((-553 . -1109) T) ((-349 . -622) 164599) ((-331 . -620) 164560) ((-331 . -619) 164472) ((-267 . -622) 164225) ((-249 . -622) 164010) ((-1240 . -798) 163963) ((-1240 . -801) 163916) ((-254 . -382) 163885) ((-253 . -382) 163854) ((-660 . -38) 163824) ((-614 . -34) T) ((-488 . -1121) 163734) ((-481 . -34) T) ((-1122 . -132) 163604) ((-971 . -25) 163415) ((-917 . -622) 163365) ((-880 . -619) 163347) ((-971 . -21) 163302) ((-821 . -21) 163212) ((-821 . -25) 163063) ((-1233 . -373) T) ((-629 . -1067) T) ((-1188 . -562) 163042) ((-1182 . -47) 163019) 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155502) ((-48 . -1109) T) ((-718 . -233) 155486) ((-877 . -907) NIL) ((-1250 . -893) NIL) ((-896 . -102) T) ((-892 . -102) T) ((-394 . -1109) T) ((-171 . -382) 155470) ((-171 . -343) 155454) ((-1250 . -1047) 155334) ((-861 . -1047) 155230) ((-1151 . -102) T) ((-668 . -798) 155209) ((-659 . -132) T) ((-668 . -801) 155188) ((-118 . -520) 155096) ((-577 . -1047) 155078) ((-298 . -1284) 155048) ((-872 . -102) T) ((-970 . -562) 155027) ((-1221 . -1065) 154910) ((-1012 . -1060) 154855) ((-488 . -645) 154761) ((-911 . -1109) T) ((-1033 . -723) 154698) ((-717 . -1065) 154663) ((-1012 . -646) 154608) ((-623 . -102) T) ((-608 . -34) T) ((-1156 . -1227) T) ((-1221 . -111) 154477) ((-480 . -654) 154374) ((-359 . -723) 154319) ((-171 . -907) 154278) ((-705 . -294) T) ((-700 . -174) T) ((-717 . -111) 154234) ((-1306 . -1067) T) ((-1250 . -382) 154218) ((-424 . -1231) 154196) ((-1127 . -619) 154178) ((-317 . -854) NIL) ((-424 . -562) T) ((-227 . -311) T) ((-1240 . -797) 154131) ((-1240 . -800) 154084) ((-1261 . -732) T) ((-1240 . -732) T) ((-48 . -723) 154049) ((-227 . -1031) T) ((-356 . -1284) 154026) ((-1263 . -417) 153992) ((-724 . -732) T) ((-337 . -619) 153974) ((-1250 . -907) 153917) ((-1221 . -622) 153799) ((-112 . -619) 153781) ((-112 . -620) 153763) ((-724 . -479) T) ((-717 . -622) 153713) ((-1300 . -1060) 153697) ((-488 . -21) 153607) ((-128 . -495) 153591) ((-122 . -495) 153575) ((-488 . -25) 153426) ((-1300 . -646) 153396) ((-629 . -294) T) ((-592 . -1065) 153371) ((-443 . -1109) T) ((-1071 . -311) T) ((-118 . -294) T) ((-1113 . -102) T) ((-1012 . -102) T) ((-592 . -111) 153339) ((-1151 . -313) 153277) ((-1221 . -1058) T) ((-1071 . -1031) T) ((-66 . -1227) T) ((-1063 . -25) T) ((-1063 . -21) T) ((-717 . -1058) T) ((-390 . -21) T) ((-390 . -25) T) ((-700 . -520) NIL) ((-1033 . -174) T) ((-717 . -245) T) ((-1071 . -551) T) ((-718 . -652) 153187) ((-512 . -102) T) ((-508 . -102) T) ((-359 . -174) T) ((-348 . -619) 153169) ((-413 . -1060) 153121) ((-400 . -619) 153103) ((-1129 . -854) T) ((-480 . -732) T) ((-899 . -1047) 153071) ((-413 . -646) 153023) ((-108 . -856) T) ((-664 . -1065) 153007) ((-493 . -132) T) ((-1263 . -1067) T) ((-219 . -132) T) ((-1166 . -102) 152985) ((-99 . -1109) T) ((-247 . -672) 152969) ((-247 . -657) 152953) ((-664 . -111) 152932) ((-592 . -622) 152916) ((-320 . -417) 152900) ((-247 . -378) 152884) ((-1169 . -237) 152831) ((-1008 . -233) 152815) ((-74 . -1227) T) ((-48 . -174) T) ((-707 . -393) T) ((-707 . -144) T) ((-1300 . -102) T) ((-1207 . -622) 152797) ((-1096 . -1065) 152640) ((-1085 . -1227) T) ((-267 . -916) 152619) ((-249 . -916) 152598) ((-788 . -1065) 152421) ((-786 . -1065) 152264) ((-614 . -1227) T) ((-1174 . -619) 152246) ((-1096 . -111) 152075) ((-1055 . -102) T) ((-481 . -1227) T) ((-467 . -1065) 152046) ((-460 . -1065) 151889) ((-670 . -654) 151873) ((-877 . -311) T) ((-788 . -111) 151682) ((-786 . -111) 151511) ((-360 . -654) 151463) ((-357 . -654) 151415) ((-349 . -654) 151367) ((-267 . -654) 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-620) 131490) ((-444 . -619) 131472) ((-219 . -148) T) ((-219 . -146) NIL) ((-1129 . -619) 131454) ((-130 . -102) T) ((-52 . -102) T) ((-1241 . -645) 131406) ((-485 . -107) 131356) ((-1002 . -23) T) ((-1301 . -38) 131326) ((-1182 . -1121) T) ((-1134 . -1121) T) ((-1071 . -1231) T) ((-315 . -102) T) ((-860 . -1121) T) ((-959 . -1231) 131305) ((-487 . -1231) 131284) ((-1071 . -562) T) ((-959 . -562) 131215) ((-1182 . -23) T) ((-1160 . -1092) T) ((-1134 . -23) T) ((-860 . -23) T) ((-487 . -562) 131146) ((-1151 . -723) 131078) ((-676 . -1060) 131062) ((-1155 . -520) 130995) ((-676 . -646) 130979) ((-1044 . -620) NIL) ((-1044 . -619) 130961) ((-96 . -1092) T) ((-872 . -723) 130931) ((-1221 . -47) 130900) ((-254 . -132) T) ((-253 . -132) T) ((-1113 . -1109) T) ((-1012 . -1109) T) ((-62 . -619) 130882) ((-1177 . -856) NIL) ((-1033 . -798) T) ((-1033 . -801) T) ((-1306 . -1065) 130869) ((-1306 . -111) 130854) ((-1269 . -25) T) ((-1269 . -21) T) ((-876 . -654) 130841) ((-1262 . -21) T) ((-1262 . -25) T) ((-1241 . -21) T) ((-1241 . -25) T) ((-1036 . -152) 130825) ((-878 . -826) 130804) ((-878 . -927) T) ((-718 . -290) 130731) ((-602 . -21) T) ((-344 . -652) 130690) ((-602 . -25) T) ((-601 . -21) T) ((-176 . -652) 130607) ((-40 . -732) T) ((-224 . -520) 130540) ((-601 . -25) T) ((-482 . -152) 130524) ((-469 . -152) 130508) ((-928 . -800) T) ((-928 . -732) T) ((-777 . -799) T) ((-777 . -800) T) ((-512 . -1109) T) ((-508 . -1109) T) ((-777 . -732) T) ((-227 . -368) T) ((-1299 . -1060) 130492) ((-1297 . -1060) 130476) ((-1299 . -646) 130446) ((-1166 . -1109) 130424) ((-877 . -1231) T) ((-1297 . -646) 130394) ((-660 . -619) 130376) ((-877 . -562) T) ((-700 . -373) NIL) ((-44 . -1060) 130360) ((-1306 . -622) 130342) ((-1300 . -1109) T) ((-676 . -102) T) ((-364 . -1284) 130326) ((-358 . -1284) 130310) ((-44 . -646) 130294) ((-350 . -1284) 130278) ((-554 . -102) T) ((-526 . -856) 130257) ((-1055 . -1109) T) ((-823 . -458) 130236) ((-153 . -1060) 130220) ((-1055 . -1080) 130149) 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119999) ((-839 . -417) 119983) ((-1129 . -801) T) ((-1129 . -798) T) ((-707 . -1109) T) ((-584 . -619) 119965) ((-384 . -368) T) ((-171 . -499) 119943) ((-224 . -619) 119875) ((-135 . -1109) T) ((-117 . -1109) T) ((-973 . -1227) T) ((-48 . -732) T) ((-1055 . -495) 119840) ((-142 . -431) 119822) ((-142 . -373) T) ((-1036 . -102) T) ((-518 . -515) 119801) ((-718 . -622) 119557) ((-482 . -102) T) ((-469 . -102) T) ((-1043 . -1121) T) ((-1234 . -619) 119539) ((-1191 . -1047) 119475) ((-1184 . -35) 119441) ((-1184 . -95) 119407) ((-1184 . -1215) 119373) ((-1184 . -1212) 119339) ((-1183 . -1212) 119305) ((-1168 . -313) NIL) ((-89 . -402) T) ((-89 . -401) T) ((-1089 . -1161) 119284) ((-1183 . -1215) 119250) ((-1183 . -95) 119216) ((-1043 . -23) T) ((-1183 . -35) 119182) ((-577 . -499) T) ((-1177 . -1212) 119148) ((-1177 . -1215) 119114) ((-1177 . -95) 119080) ((-1177 . -35) 119046) ((-366 . -1121) T) ((-364 . -1161) 119025) ((-358 . -1161) 119004) ((-350 . -1161) 118983) ((-1113 . -290) 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. -1060) 114008) ((-45 . -102) T) ((-823 . -102) T) ((-1188 . -646) 113905) ((-1250 . -25) T) ((-1250 . -21) T) ((-861 . -25) T) ((-44 . -372) 113889) ((-861 . -21) T) ((-737 . -458) 113840) ((-1300 . -619) 113822) ((-1289 . -1060) 113792) ((-1063 . -313) 113730) ((-677 . -1092) T) ((-612 . -1092) T) ((-396 . -1109) T) ((-577 . -25) T) ((-577 . -21) T) ((-182 . -1092) T) ((-162 . -1092) T) ((-157 . -1092) T) ((-155 . -1092) T) ((-1289 . -646) 113700) ((-627 . -1109) T) ((-705 . -893) 113682) ((-1277 . -1227) T) ((-229 . -313) 113620) ((-145 . -373) T) ((-1055 . -620) 113562) ((-1055 . -619) 113505) ((-317 . -916) NIL) ((-1235 . -850) T) ((-705 . -1047) 113450) ((-717 . -927) T) ((-480 . -1231) 113429) ((-1183 . -458) 113408) ((-1177 . -458) 113387) ((-334 . -102) T) ((-878 . -1121) T) ((-323 . -652) 113269) ((-320 . -654) 113090) ((-317 . -654) 113019) ((-480 . -562) 112970) ((-344 . -520) 112936) ((-556 . -152) 112886) ((-40 . -311) T) ((-849 . -619) 112868) ((-707 . -294) T) ((-878 . 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. -1237) 105497) ((-521 . -25) T) ((-501 . -306) T) ((-517 . -23) T) ((-516 . -25) T) ((-514 . -25) T) ((-513 . -23) T) ((-424 . -1060) 105471) ((-413 . -1058) T) ((-323 . -1067) T) ((-700 . -311) T) ((-424 . -646) 105445) ((-108 . -854) T) ((-718 . -732) T) ((-413 . -245) T) ((-413 . -235) 105424) ((-493 . -38) 105374) ((-219 . -38) 105324) ((-480 . -499) 105290) ((-1234 . -373) T) ((-1168 . -1153) T) ((-1110 . -102) T) ((-707 . -619) 105272) ((-707 . -620) 105187) ((-720 . -21) T) ((-720 . -25) T) ((-1144 . -102) T) ((-488 . -652) 104937) ((-135 . -619) 104919) ((-117 . -619) 104901) ((-158 . -25) T) ((-1299 . -1109) T) ((-878 . -645) 104849) ((-1297 . -1109) T) ((-970 . -102) T) ((-741 . -102) T) ((-721 . -102) T) ((-459 . -102) T) ((-822 . -458) 104800) ((-44 . -1109) T) ((-1097 . -856) T) ((-1072 . -313) 104651) ((-670 . -132) T) ((-1063 . -652) 104620) ((-676 . -723) 104604) ((-293 . -1067) T) ((-360 . -132) T) ((-357 . -132) T) ((-349 . -132) T) ((-267 . -132) T) ((-249 . -132) 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-657) 100403) ((-1135 . -646) 100300) ((-1221 . -562) 100279) ((-825 . -391) 100263) ((-717 . -562) T) ((-320 . -891) 100247) ((-320 . -893) 100172) ((-137 . -1227) T) ((-317 . -891) 100133) ((-317 . -893) NIL) ((-805 . -313) 100098) ((-323 . -723) 99939) ((-392 . -391) 99923) ((-328 . -327) 99900) ((-491 . -102) T) ((-480 . -25) T) ((-480 . -21) T) ((-424 . -38) 99874) ((-320 . -1047) 99537) ((-227 . -1212) T) ((-227 . -1215) T) ((-3 . -619) 99519) ((-317 . -1047) 99449) ((-2 . -1109) T) ((-2 . |RecordCategory|) T) ((-839 . -619) 99431) ((-1122 . -1067) 99361) ((-586 . -927) T) ((-570 . -826) T) ((-570 . -927) T) ((-501 . -927) T) ((-137 . -1047) 99345) ((-227 . -95) T) ((-171 . -148) 99324) ((-75 . -447) T) ((0 . -619) 99306) ((-75 . -401) T) ((-171 . -146) 99257) ((-227 . -35) T) ((-49 . -619) 99239) ((-483 . -1067) T) ((-493 . -233) 99221) ((-490 . -977) 99205) ((-488 . -854) 99184) ((-219 . -233) 99166) ((-81 . -447) T) ((-81 . -401) T) ((-1155 . -34) T) ((-821 . -174) 99145) 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88680) ((-483 . -1065) 88645) ((-664 . -132) T) ((-627 . -622) 88614) ((-1122 . -520) 88547) ((-341 . -132) T) ((-171 . -408) 88526) ((-488 . -723) 88468) ((-821 . -290) 88445) ((-483 . -111) 88401) ((-659 . -1067) T) ((-822 . -1060) 88244) ((-1288 . -1092) T) ((-1250 . -458) 88175) ((-822 . -646) 88024) ((-1287 . -1092) T) ((-1096 . -132) T) ((-1063 . -723) 87966) ((-788 . -132) T) ((-786 . -132) T) ((-577 . -458) T) ((-1036 . -520) 87899) ((-627 . -1058) T) ((-598 . -1109) T) ((-539 . -175) T) ((-467 . -132) T) ((-460 . -132) T) ((-1008 . -1227) 87868) ((-45 . -1109) T) ((-390 . -723) 87838) ((-823 . -1109) T) ((-482 . -520) 87771) ((-469 . -520) 87704) ((-1302 . -622) 87686) ((-459 . -372) 87656) ((-45 . -616) 87635) ((-320 . -306) T) ((-483 . -622) 87585) ((-1241 . -313) 87470) ((-676 . -619) 87432) ((-59 . -856) 87411) ((-1013 . -406) 87393) ((-554 . -619) 87375) ((-805 . -652) 87334) ((-821 . -610) 87311) ((-522 . -856) 87290) ((-502 . -856) 87269) ((-40 . -1231) T) ((-1008 . 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-313) 81728) ((-970 . -417) 81712) ((-705 . -1231) T) ((-638 . -290) 81665) ((-1096 . -645) 81613) ((-788 . -645) 81561) ((-786 . -645) 81509) ((-348 . -132) T) ((-293 . -619) 81491) ((-912 . -1109) T) ((-705 . -562) T) ((-130 . -622) 81473) ((-876 . -1121) T) ((-460 . -645) 81421) ((-912 . -910) 81405) ((-384 . -458) T) ((-493 . -1109) T) ((-950 . -313) 81343) ((-707 . -654) 81330) ((-555 . -850) T) ((-219 . -1109) T) ((-320 . -927) 81309) ((-317 . -927) T) ((-317 . -826) NIL) ((-396 . -726) T) ((-876 . -23) T) ((-117 . -654) 81296) ((-480 . -146) 81275) ((-424 . -417) 81259) ((-480 . -148) 81238) ((-110 . -495) 81220) ((-315 . -622) 81201) ((-2 . -619) 81183) ((-188 . -102) T) ((-1168 . -19) 81165) ((-1168 . -610) 81140) ((-664 . -21) T) ((-664 . -25) T) ((-599 . -1153) T) ((-1122 . -290) 81117) ((-341 . -25) T) ((-341 . -21) T) ((-242 . -652) 80867) ((-501 . -368) T) ((-1292 . -38) 80837) ((-1182 . -1060) 80660) ((-1151 . -1227) T) ((-1134 . -1060) 80503) ((-860 . -1060) 80487) 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. -292) 168276) ((-331 . -610) 168253) ((-502 . -292) 168230) ((-460 . -294) 168161) ((-1044 . -313) 168012) ((-882 . -496) 167993) ((-882 . -619) 167959) ((-687 . -496) 167940) ((-577 . -732) T) ((-682 . -496) 167921) ((-687 . -619) 167871) ((-682 . -619) 167837) ((-668 . -619) 167819) ((-484 . -496) 167800) ((-484 . -619) 167766) ((-247 . -620) 167727) ((-247 . -496) 167704) ((-139 . -496) 167685) ((-138 . -496) 167666) ((-134 . -496) 167647) ((-247 . -619) 167539) ((-215 . -102) T) ((-139 . -619) 167505) ((-138 . -619) 167471) ((-134 . -619) 167437) ((-1156 . -34) T) ((-950 . -1227) T) ((-348 . -723) 167382) ((-676 . -25) T) ((-676 . -21) T) ((-1186 . -622) 167363) ((-480 . -1058) T) ((-641 . -423) 167328) ((-613 . -423) 167293) ((-1129 . -1161) T) ((-718 . -1060) 167116) ((-587 . -294) T) ((-524 . -294) T) ((-1262 . -311) 167095) ((-480 . -235) 167047) ((-480 . -245) 167026) ((-1241 . -311) 167005) ((-718 . -646) 166834) ((-1241 . -1031) NIL) ((-1089 . -132) T) ((-878 . -801) 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. -231) 161139) ((-384 . -800) T) ((-384 . -797) T) ((-876 . -174) T) ((-384 . -732) T) ((-717 . -619) 161121) ((-718 . -38) 160950) ((-1277 . -1275) 160934) ((-356 . -408) T) ((-1277 . -1109) 160884) ((-1200 . -1109) T) ((-586 . -723) 160871) ((-570 . -723) 160858) ((-501 . -723) 160823) ((-1263 . -652) 160713) ((-320 . -635) 160692) ((-842 . -732) T) ((-833 . -732) T) ((-650 . -1227) T) ((-1089 . -645) 160640) ((-1182 . -907) 160583) ((-1134 . -907) 160567) ((-668 . -1065) 160551) ((-108 . -645) 160533) ((-488 . -132) 160403) ((-1188 . -1121) T) ((-959 . -47) 160372) ((-629 . -1109) T) ((-668 . -111) 160351) ((-497 . -619) 160317) ((-331 . -292) 160294) ((-487 . -47) 160251) ((-1188 . -23) T) ((-118 . -1109) T) ((-103 . -102) 160229) ((-1289 . -1121) T) ((-554 . -856) T) ((-1063 . -132) T) ((-1033 . -1067) T) ((-825 . -1047) 160213) ((-1012 . -730) 160185) ((-1289 . -23) T) ((-705 . -723) 160150) ((-592 . -619) 160132) ((-392 . -1047) 160116) ((-359 . -1067) T) ((-390 . -132) T) 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-798) T) ((-1012 . -417) 134608) ((-359 . -111) 134537) ((-384 . -927) T) ((-413 . -854) 134516) ((-718 . -294) 134427) ((-225 . -732) T) ((-1269 . -499) 134393) ((-1262 . -499) 134359) ((-1241 . -499) 134325) ((-584 . -1109) T) ((-320 . -1011) 134304) ((-224 . -1109) 134282) ((-1234 . -850) T) ((-323 . -982) 134244) ((-105 . -102) T) ((-48 . -1065) 134209) ((-1301 . -102) T) ((-386 . -102) T) ((-48 . -111) 134165) ((-1013 . -645) 134147) ((-1263 . -619) 134129) ((-537 . -102) T) ((-506 . -102) T) ((-1142 . -1143) 134113) ((-153 . -1284) 134097) ((-247 . -1227) T) ((-1226 . -102) T) ((-1033 . -622) 134034) ((-1182 . -1231) 134013) ((-359 . -622) 133943) ((-1134 . -1231) 133922) ((-242 . -21) 133832) ((-242 . -25) 133683) ((-128 . -120) 133667) ((-122 . -120) 133651) ((-44 . -750) 133635) ((-1182 . -562) 133546) ((-1134 . -562) 133477) ((-1234 . -1109) T) ((-1044 . -290) 133452) ((-1176 . -1092) T) ((-1003 . -1092) T) ((-822 . -132) T) ((-118 . -801) NIL) ((-118 . -798) NIL) ((-360 . -311) T) ((-357 . -311) T) ((-349 . -311) T) ((-254 . -1121) 133362) ((-253 . -1121) 133272) ((-1033 . -1058) T) ((-1012 . -1067) T) ((-48 . -622) 133205) ((-348 . -654) 133150) ((-627 . -38) 133134) ((-1290 . -619) 133096) ((-1290 . -620) 133057) ((-1086 . -619) 133039) ((-1033 . -245) T) ((-359 . -1058) T) ((-821 . -1284) 133009) ((-254 . -23) T) ((-253 . -23) T) ((-996 . -619) 132991) ((-743 . -620) 132952) ((-743 . -619) 132934) ((-805 . -856) 132913) ((-1169 . -152) 132860) ((-1008 . -520) 132772) ((-359 . -235) T) ((-359 . -245) T) ((-394 . -622) 132753) ((-1013 . -25) T) ((-142 . -619) 132735) ((-142 . -620) 132694) ((-917 . -311) T) ((-1013 . -21) T) ((-980 . -25) T) ((-921 . -21) T) ((-921 . -25) T) ((-433 . -21) T) ((-433 . -25) T) ((-849 . -417) 132678) ((-48 . -1058) T) ((-1299 . -1291) 132662) ((-1297 . -1291) 132646) ((-1044 . -610) 132621) ((-320 . -620) 132482) ((-320 . -619) 132464) ((-317 . -620) NIL) ((-317 . -619) 132446) ((-48 . -245) T) ((-48 . -235) T) ((-660 . -290) 132407) ((-556 . -237) 132357) ((-140 . -619) 132324) ((-137 . -619) 132306) ((-115 . -619) 132288) ((-483 . -38) 132253) ((-1301 . -1298) 132232) ((-1292 . -132) T) ((-1300 . -1067) T) ((-1091 . -102) T) ((-88 . -1227) T) ((-506 . -313) NIL) ((-1009 . -107) 132216) ((-896 . -1109) T) ((-892 . -1109) T) ((-1277 . -657) 132200) ((-1277 . -378) 132184) ((-331 . -1227) T) ((-599 . -856) T) ((-1151 . -1109) T) ((-1151 . -1062) 132124) ((-103 . -520) 132057) ((-934 . -619) 132039) ((-348 . -732) T) ((-30 . -619) 132021) ((-872 . -1109) T) ((-849 . -1067) 132000) ((-40 . -654) 131945) ((-227 . -1231) T) ((-413 . -1067) T) ((-1168 . -152) 131927) ((-1008 . -294) 131878) ((-623 . -1109) T) ((-227 . -562) T) ((-323 . -1258) 131862) ((-323 . -1255) 131832) ((-707 . -652) 131804) ((-1199 . -1203) 131783) ((-1084 . -619) 131765) ((-1199 . -107) 131715) ((-653 . -152) 131699) ((-638 . -152) 131645) ((-117 . -652) 131617) ((-485 . -1203) 131596) ((-493 . -148) T) ((-493 . -146) NIL) ((-1129 . -620) 131511) ((-444 . -619) 131493) ((-219 . -148) T) ((-219 . -146) NIL) ((-1129 . -619) 131475) ((-130 . -102) T) ((-52 . -102) T) ((-1241 . -645) 131427) ((-485 . -107) 131377) ((-1002 . -23) T) ((-1301 . -38) 131347) ((-1182 . -1121) T) ((-1134 . -1121) T) ((-1071 . -1231) T) ((-315 . -102) T) ((-860 . -1121) T) ((-959 . -1231) 131326) ((-487 . -1231) 131305) ((-1071 . -562) T) ((-959 . -562) 131236) ((-1182 . -23) T) ((-1160 . -1092) T) ((-1134 . -23) T) ((-860 . -23) T) ((-487 . -562) 131167) ((-1151 . -723) 131099) ((-676 . -1060) 131083) ((-1155 . -520) 131016) ((-676 . -646) 131000) ((-1044 . -620) NIL) ((-1044 . -619) 130982) ((-96 . -1092) T) ((-872 . -723) 130952) ((-1221 . -47) 130921) ((-254 . -132) T) ((-253 . -132) T) ((-1113 . -1109) T) ((-1012 . -1109) T) ((-62 . -619) 130903) ((-1177 . -856) NIL) ((-1033 . -798) T) ((-1033 . -801) T) ((-1306 . -1065) 130890) ((-1306 . -111) 130875) ((-1269 . -25) T) ((-1269 . -21) T) ((-876 . -654) 130862) ((-1262 . -21) T) ((-1262 . -25) T) ((-1241 . -21) T) ((-1241 . -25) T) ((-1036 . -152) 130846) ((-878 . -826) 130825) ((-878 . -927) T) ((-718 . -290) 130752) ((-602 . -21) T) ((-344 . -652) 130711) ((-602 . -25) T) ((-601 . -21) T) ((-176 . -652) 130628) ((-40 . -732) T) ((-224 . -520) 130561) ((-601 . -25) T) ((-482 . -152) 130545) ((-469 . -152) 130529) ((-928 . -800) T) ((-928 . -732) T) ((-777 . -799) T) ((-777 . -800) T) ((-512 . -1109) T) ((-508 . -1109) T) ((-777 . -732) T) ((-227 . -368) T) ((-1299 . -1060) 130513) ((-1297 . -1060) 130497) ((-1299 . -646) 130467) ((-1166 . -1109) 130445) ((-877 . -1231) T) ((-1297 . -646) 130415) ((-660 . -619) 130397) ((-877 . -562) T) ((-700 . -373) NIL) ((-44 . -1060) 130381) ((-1306 . -622) 130363) ((-1300 . -1109) T) ((-676 . -102) T) ((-364 . -1284) 130347) ((-358 . -1284) 130331) ((-44 . -646) 130315) ((-350 . -1284) 130299) ((-554 . -102) T) ((-526 . -856) 130278) ((-1055 . -1109) T) ((-823 . -458) 130257) ((-153 . -1060) 130241) ((-1055 . -1080) 130170) 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-723) 128879) ((-1096 . -47) 128840) ((-1071 . -1121) T) ((-959 . -1121) T) ((-128 . -34) T) ((-122 . -34) T) ((-788 . -47) 128817) ((-786 . -47) 128789) ((-1250 . -562) 128700) ((-359 . -373) T) ((-487 . -1121) T) ((-1182 . -132) T) ((-1134 . -132) T) ((-460 . -47) 128679) ((-877 . -368) T) ((-860 . -132) T) ((-153 . -102) T) ((-1071 . -23) T) ((-959 . -23) T) ((-577 . -562) T) ((-822 . -25) T) ((-822 . -21) T) ((-1151 . -520) 128612) ((-598 . -1092) T) ((-592 . -1047) 128596) ((-1263 . -622) 128470) ((-487 . -23) T) ((-356 . -1067) T) ((-1221 . -907) 128451) ((-676 . -313) 128389) ((-1122 . -1284) 128359) ((-705 . -654) 128324) ((-1013 . -856) T) ((-1012 . -174) T) ((-970 . -146) 128303) ((-641 . -1109) T) ((-613 . -1109) T) ((-970 . -148) 128282) ((-741 . -148) 128261) ((-741 . -146) 128240) ((-664 . -1227) T) ((-980 . -856) T) ((-839 . -652) 128157) ((-480 . -927) 128136) ((-323 . -1060) 127971) ((-320 . -1065) 127881) ((-317 . -1065) 127810) ((-1008 . -290) 127768) ((-413 . -723) 127720) ((-323 . -646) 127561) ((-707 . -854) T) ((-1263 . -1058) T) ((-320 . -111) 127457) ((-317 . -111) 127370) ((-971 . -102) T) ((-821 . -102) 127160) ((-718 . -620) NIL) ((-718 . -619) 127142) ((-664 . -1047) 127038) ((-1263 . -330) 126982) ((-1044 . -292) 126957) ((-586 . -732) T) ((-570 . -800) T) ((-171 . -368) 126908) ((-570 . -797) T) ((-570 . -732) T) ((-501 . -732) T) ((-788 . -1227) T) ((-1155 . -495) 126892) ((-1096 . -893) NIL) ((-877 . -1121) T) ((-118 . -916) NIL) ((-1299 . -1298) 126868) ((-1297 . -1298) 126847) ((-788 . -893) NIL) ((-786 . -893) 126706) ((-1292 . -25) T) ((-1292 . -21) T) ((-1224 . -102) 126684) ((-1115 . -401) T) ((-629 . -654) 126671) ((-460 . -893) NIL) ((-681 . -102) 126649) ((-1096 . -1047) 126476) ((-877 . -23) T) ((-788 . -1047) 126335) ((-786 . -1047) 126192) ((-118 . -654) 126137) ((-460 . -1047) 126013) ((-320 . -622) 125577) ((-317 . -622) 125460) ((-396 . -652) 125429) ((-655 . -1047) 125413) ((-633 . -102) T) ((-224 . -495) 125397) 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123310) ((-364 . -646) 123262) ((-225 . -1047) 123239) ((-358 . -646) 123191) ((-108 . -1060) 123141) ((-350 . -646) 123093) ((-298 . -723) 123035) ((-707 . -1067) T) ((-493 . -458) T) ((-413 . -520) 122947) ((-108 . -646) 122897) ((-219 . -458) T) ((-1129 . -235) T) ((-299 . -152) 122847) ((-1008 . -620) 122808) ((-1008 . -619) 122790) ((-998 . -619) 122772) ((-117 . -1067) T) ((-660 . -1065) 122756) ((-227 . -499) T) ((-405 . -619) 122738) ((-405 . -620) 122715) ((-1063 . -1284) 122685) ((-660 . -111) 122664) ((-1151 . -495) 122648) ((-1301 . -652) 122607) ((-386 . -652) 122576) ((-821 . -38) 122546) ((-63 . -447) T) ((-63 . -401) T) ((-1169 . -102) T) ((-877 . -132) T) ((-490 . -102) 122524) ((-1306 . -373) T) ((-1089 . -102) T) ((-1070 . -102) T) ((-356 . -723) 122469) ((-737 . -148) 122448) ((-737 . -146) 122427) ((-660 . -622) 122345) ((-1033 . -654) 122282) ((-529 . -1109) 122260) ((-364 . -102) T) ((-358 . -102) T) ((-350 . -102) T) ((-108 . -102) T) ((-510 . -1109) T) ((-359 . -654) 122205) ((-1182 . -645) 122153) ((-1134 . -645) 122101) ((-390 . -515) 122080) ((-839 . -854) 122059) ((-384 . -1231) T) ((-700 . -732) T) ((-1241 . -1001) 122011) ((-344 . -1067) T) ((-112 . -1227) T) ((-176 . -1067) T) ((-103 . -619) 121943) ((-1184 . -146) 121922) ((-1184 . -148) 121901) ((-384 . -562) T) ((-1183 . -148) 121880) ((-1183 . -146) 121859) ((-1177 . -146) 121766) ((-413 . -294) T) ((-1177 . -148) 121673) ((-1135 . -148) 121652) ((-1135 . -146) 121631) ((-323 . -38) 121472) ((-171 . -132) T) ((-317 . -801) NIL) ((-317 . -798) NIL) ((-660 . -1058) T) ((-48 . -654) 121437) ((-1122 . -1060) 121334) ((-900 . -622) 121311) ((-1122 . -646) 121253) ((-1176 . -102) T) ((-1003 . -102) T) ((-1002 . -21) T) ((-128 . -1019) 121237) ((-122 . -1019) 121221) ((-1002 . -25) T) ((-908 . -120) 121205) ((-1168 . -102) T) ((-1250 . -132) T) ((-1182 . -25) T) ((-1182 . -21) T) ((-861 . -132) T) ((-1134 . -25) T) ((-1134 . -21) T) ((-860 . -25) T) ((-860 . -21) T) ((-788 . -311) 121184) 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120020) ((-839 . -417) 120004) ((-1129 . -801) T) ((-1129 . -798) T) ((-707 . -1109) T) ((-584 . -619) 119986) ((-384 . -368) T) ((-171 . -499) 119964) ((-224 . -619) 119896) ((-135 . -1109) T) ((-117 . -1109) T) ((-973 . -1227) T) ((-48 . -732) T) ((-1055 . -495) 119861) ((-142 . -431) 119843) ((-142 . -373) T) ((-1036 . -102) T) ((-518 . -515) 119822) ((-718 . -622) 119578) ((-482 . -102) T) ((-469 . -102) T) ((-1043 . -1121) T) ((-1234 . -619) 119560) ((-1191 . -1047) 119496) ((-1184 . -35) 119462) ((-1184 . -95) 119428) ((-1184 . -1215) 119394) ((-1184 . -1212) 119360) ((-1183 . -1212) 119326) ((-1168 . -313) NIL) ((-89 . -402) T) ((-89 . -401) T) ((-1089 . -1161) 119305) ((-1183 . -1215) 119271) ((-1183 . -95) 119237) ((-1043 . -23) T) ((-1183 . -35) 119203) ((-577 . -499) T) ((-1177 . -1212) 119169) ((-1177 . -1215) 119135) ((-1177 . -95) 119101) ((-1177 . -35) 119067) ((-366 . -1121) T) ((-364 . -1161) 119046) ((-358 . -1161) 119025) ((-350 . -1161) 119004) ((-1113 . -290) 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. -1060) 114029) ((-45 . -102) T) ((-823 . -102) T) ((-1188 . -646) 113926) ((-1250 . -25) T) ((-1250 . -21) T) ((-861 . -25) T) ((-44 . -372) 113910) ((-861 . -21) T) ((-737 . -458) 113861) ((-1300 . -619) 113843) ((-1289 . -1060) 113813) ((-1063 . -313) 113751) ((-677 . -1092) T) ((-612 . -1092) T) ((-396 . -1109) T) ((-577 . -25) T) ((-577 . -21) T) ((-182 . -1092) T) ((-162 . -1092) T) ((-157 . -1092) T) ((-155 . -1092) T) ((-1289 . -646) 113721) ((-627 . -1109) T) ((-705 . -893) 113703) ((-1277 . -1227) T) ((-229 . -313) 113641) ((-145 . -373) T) ((-1055 . -620) 113583) ((-1055 . -619) 113526) ((-317 . -916) NIL) ((-1235 . -850) T) ((-705 . -1047) 113471) ((-717 . -927) T) ((-480 . -1231) 113450) ((-1183 . -458) 113429) ((-1177 . -458) 113408) ((-334 . -102) T) ((-878 . -1121) T) ((-323 . -652) 113290) ((-320 . -654) 113111) ((-317 . -654) 113040) ((-480 . -562) 112991) ((-344 . -520) 112957) ((-556 . -152) 112907) ((-40 . -311) T) ((-849 . -619) 112889) ((-707 . -294) T) ((-878 . 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. -1237) 105518) ((-521 . -25) T) ((-501 . -306) T) ((-517 . -23) T) ((-516 . -25) T) ((-514 . -25) T) ((-513 . -23) T) ((-424 . -1060) 105492) ((-413 . -1058) T) ((-323 . -1067) T) ((-700 . -311) T) ((-424 . -646) 105466) ((-108 . -854) T) ((-718 . -732) T) ((-413 . -245) T) ((-413 . -235) 105445) ((-493 . -38) 105395) ((-219 . -38) 105345) ((-480 . -499) 105311) ((-1234 . -373) T) ((-1168 . -1153) T) ((-1110 . -102) T) ((-707 . -619) 105293) ((-707 . -620) 105208) ((-720 . -21) T) ((-720 . -25) T) ((-1144 . -102) T) ((-488 . -652) 104958) ((-135 . -619) 104940) ((-117 . -619) 104922) ((-158 . -25) T) ((-1299 . -1109) T) ((-878 . -645) 104870) ((-1297 . -1109) T) ((-970 . -102) T) ((-741 . -102) T) ((-721 . -102) T) ((-459 . -102) T) ((-822 . -458) 104821) ((-44 . -1109) T) ((-1097 . -856) T) ((-1072 . -313) 104672) ((-670 . -132) T) ((-1063 . -652) 104641) ((-676 . -723) 104625) ((-293 . -1067) T) ((-360 . -132) T) ((-357 . -132) T) ((-349 . -132) T) ((-267 . -132) T) ((-249 . -132) 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-38) 98282) ((-267 . -645) 98230) ((-249 . -645) 98178) ((-707 . -1065) 98165) ((-601 . -1255) 98142) ((-1135 . -288) 98108) ((-323 . -174) 98039) ((-364 . -1109) T) ((-358 . -1109) T) ((-350 . -1109) T) ((-506 . -19) 98021) ((-1129 . -1047) 98003) ((-1111 . -152) 97987) ((-108 . -1109) T) ((-117 . -1065) 97974) ((-717 . -368) T) ((-506 . -610) 97949) ((-707 . -111) 97934) ((-442 . -102) T) ((-882 . -1272) T) ((-252 . -102) T) ((-45 . -1158) 97884) ((-117 . -111) 97869) ((-1302 . -619) 97836) ((-641 . -726) T) ((-613 . -726) T) ((-1302 . -496) 97818) ((-1279 . -619) 97800) ((-1235 . -619) 97782) ((-1233 . -856) T) ((-1221 . -1121) T) ((-821 . -520) 97715) ((-1044 . -1227) T) ((-242 . -1060) 97612) ((-1221 . -23) T) ((-1182 . -458) 97543) ((-950 . -152) 97527) ((-1177 . -313) 97412) ((-1176 . -1109) T) ((-242 . -646) 97354) ((-1168 . -1109) T) ((-1151 . -654) 97328) ((-1135 . -313) 97315) ((-531 . -102) T) ((-526 . -102) 97265) ((-1134 . -458) 97216) ((-1096 . -562) 97147) ((-1096 . 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88701) ((-483 . -1065) 88666) ((-664 . -132) T) ((-627 . -622) 88635) ((-1122 . -520) 88568) ((-341 . -132) T) ((-171 . -408) 88547) ((-488 . -723) 88489) ((-821 . -290) 88466) ((-483 . -111) 88422) ((-659 . -1067) T) ((-822 . -1060) 88265) ((-1288 . -1092) T) ((-1250 . -458) 88196) ((-822 . -646) 88045) ((-1287 . -1092) T) ((-1096 . -132) T) ((-1063 . -723) 87987) ((-788 . -132) T) ((-786 . -132) T) ((-577 . -458) T) ((-1036 . -520) 87920) ((-627 . -1058) T) ((-598 . -1109) T) ((-539 . -175) T) ((-467 . -132) T) ((-460 . -132) T) ((-1008 . -1227) 87889) ((-45 . -1109) T) ((-390 . -723) 87859) ((-823 . -1109) T) ((-482 . -520) 87792) ((-469 . -520) 87725) ((-1302 . -622) 87707) ((-459 . -372) 87677) ((-45 . -616) 87656) ((-320 . -306) T) ((-483 . -622) 87606) ((-1241 . -313) 87491) ((-676 . -619) 87453) ((-59 . -856) 87432) ((-1013 . -406) 87414) ((-554 . -619) 87396) ((-805 . -652) 87355) ((-821 . -610) 87332) ((-522 . -856) 87311) ((-502 . -856) 87290) ((-40 . -1231) T) ((-1008 . -1047) 87186) ((-50 . -132) T) ((-587 . -132) T) ((-524 . -132) T) ((-298 . -654) 87046) ((-348 . -333) 87023) ((-348 . -368) T) ((-326 . -327) 87000) ((-323 . -290) 86958) ((-40 . -562) T) ((-384 . -1212) T) ((-384 . -1215) T) ((-1044 . -1203) 86933) ((-1199 . -237) 86883) ((-1177 . -233) 86835) ((-334 . -1109) T) ((-384 . -95) T) ((-384 . -35) T) ((-1044 . -107) 86781) ((-483 . -1058) T) ((-1301 . -1065) 86765) ((-485 . -237) 86715) ((-1169 . -495) 86649) ((-1292 . -1060) 86633) ((-386 . -1065) 86617) ((-1292 . -646) 86587) ((-483 . -245) T) ((-822 . -102) T) ((-720 . -148) 86566) ((-720 . -146) 86545) ((-490 . -495) 86529) ((-491 . -340) 86498) ((-1301 . -111) 86477) ((-518 . -1109) T) ((-488 . -174) 86456) ((-1008 . -382) 86440) ((-419 . -102) T) ((-386 . -111) 86419) ((-1008 . -343) 86403) ((-282 . -992) 86387) ((-281 . -992) 86371) ((-1299 . -619) 86353) ((-1297 . -619) 86335) ((-110 . -520) NIL) ((-1182 . -1253) 86319) ((-860 . -858) 86303) ((-1188 . -1109) T) ((-103 . -1227) T) 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\ No newline at end of file diff --git a/src/share/algebra/compress.daase b/src/share/algebra/compress.daase index e6ac108b..d51d8a13 100644 --- a/src/share/algebra/compress.daase +++ b/src/share/algebra/compress.daase @@ -1,5 +1,5 @@ -(30 . 3485084667) +(30 . 3485328463) (4455 |Enumeration| |Mapping| |Record| |Union| |ofCategory| |isDomain| ATTRIBUTE |package| |domain| |category| CATEGORY |nobranch| AND |Join| |ofType| SIGNATURE "failed" "algebra" |OneDimensionalArrayAggregate&| @@ -484,665 +484,671 @@ |XPolynomial| |XPolynomialRing| |XRecursivePolynomial| |YoungDiagram| |ParadoxicalCombinatorsForStreams| |ZeroDimensionalSolvePackage| |IntegerLinearDependence| |IntegerMod| |Enumeration| |Mapping| - |Record| |Union| |primeFrobenius| |fixedPoints| |printingInfo?| - |rangePascalTriangle| |exponential| |biRank| |unaryFunction| |Beta| - |graphImage| |compdegd| |antisymmetric?| |initials| |subTriSet?| - |graphState| |spherical| |scopes| |match?| |style| |rule| |endOfFile?| - |createLowComplexityNormalBasis| |dmpToP| |autoCoerce| |nthRoot| - 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|gramschmidt| |nilFactor| |fixedPointExquo| |minPoly| |hessian| - |npcoef| |forLoop| |OMwrite| |createPrimitivePoly| |makeCos| |row| - |mainSquareFreePart| |findCycle| |parseString| |unitNormalize| - |stoseInvertible?sqfreg| |rightQuotient| |rightTraceMatrix| - |dmpToHdmp| |dark| |coleman| |redPo| |root?| |getOperands| |orbits| - |s21baf| |charthRoot| |log10| |partitions| |jacobi| - |transcendentalDecompose| |numericalIntegration| |remove!| - |leastMonomial| |string?| |flexible?| |definingEquations| - |fullDisplay| |f04maf| |normalize| |bitand| |localUnquote| - |radicalSimplify| |ffactor| |minimalPolynomial| - |stosePrepareSubResAlgo| |decomposeFunc| |qfactor| |completeEval| - |innerEigenvectors| |plus| |changeVar| |critBonD| |bitior| |fTable| - |f07aef| |listRepresentation| |rationalFunction| - |genericRightMinimalPolynomial| |palgint0| |OMgetEndBVar| |groebner?| - |lazyPseudoRemainder| |patternMatchTimes| |maxrow| |obj| - |extractBottom!| |odd?| |stopTable!| |iterationVar| |f01ref| - |viewDeltaXDefault| |parabolic| |clearTheFTable| |OMunhandledSymbol| - |countRealRoots| |pade| |HenselLift| |cache| |roughBase?| - |outputAsScript| |algebraicVariables| |prolateSpheroidal| |conjugate| - |setelt!| |makeCrit| |representationType| |adaptive3D?| - |continuedFraction| |expenseOfEvaluation| |eisensteinIrreducible?| - |perfectNthRoot| |s19aaf| |findConstructor| |dimensionsOf| |multisect| - |imagE| |times| |degreeSubResultant| |empty?| |factorials| |leftNorm| - |d01akf| |d01asf| |generic?| |rowEchelonLocal| |weierstrass| - |hypergeometric0F1| |monomRDEsys| |rootKerSimp| |d01anf| |crest| - |polynomialZeros| |quoted?| |singularAtInfinity?| |c06gqf| |voidMode| - |node?| |multMonom| |rotatey| |expPot| |f02awf| |var1Steps| - |numberOfChildren| |variationOfParameters| |nthRootIfCan| - |leftFactorIfCan| |setAttributeButtonStep| |constantKernel| - |rangeIsFinite| |declare!| |removeSquaresIfCan| |singular?| - |karatsubaDivide| |testModulus| |divisor| |OMsetEncoding| |airyBi| - |graphStates| |decimal| |measure| |distdfact| |repSq| |inverseColeman| - |complexNumericIfCan| |monom| |optional?| |iflist2Result| |bivariate?| - |lookupFunction| |internalAugment| - |generalizedContinuumHypothesisAssumed| |meshFun2Var| |rationalIfCan| - |d01amf| |nary?| |car| |denomRicDE| |shift| |changeWeightLevel| - |solveInField| |legendre| |pseudoDivide| |alternatingGroup| - |roughBasicSet| |rational?| |print| |roughEqualIdeals?| - |factorsOfDegree| |dot| |showClipRegion| |dom| |setClipValue| - |rationalApproximation| |sqfree| |disjunction| - |squareFreeLexTriangular| |printTypes| |sinhcosh| |resolve| |common| - |lagrange| |column| |symbol?| |before?| |getButtonValue| |check| - |shade| |more?| |addMatch| Y |squareTop| |balancedBinaryTree| - |var2Steps| |functionIsFracPolynomial?| |vectorise| |implies| - |position!| |viewZoomDefault| |OMconnectTCP| |transpose| |fintegrate| - |monomialIntegrate| |f01rcf| |semiSubResultantGcdEuclidean1| |ef2edf| - |vedf2vef| |label| |component| |halfExtendedSubResultantGcd1| |lookup| - |consnewpol| |overlap| |segment| |c06ecf| |leastPower| |findBinding| - |OMputEndAttr| |makeSketch| |getRef| |multiplyExponents| - |identification| |conjugates| |midpoints| |inverseLaplace| |mantissa| - |lieAdmissible?| |monicRightFactorIfCan| |infieldIntegrate| |cosIfCan| - |closed| |f01maf| |mapDown!| |startTableInvSet!| |c06gsf| |df2mf| - |conical| |sinIfCan| |cCosh| |closedCurve?| |ideal| |torsionIfCan| - |elliptic?| |cycle| |f02akf| |pdct| |iicot| |region| |mathieu12| - |rotatez| |eulerPhi| |separant| |zeroDim?| |recoverAfterFail| - |epilogue| |bytes| |leadingCoefficientRicDE| |rdregime| - |certainlySubVariety?| |associatorDependence| |totalDifferential| - |maxPoints| |minColIndex| |iiacsch| |exprex| |iicosh| |coefficient| - |slex| |positive?| |bsolve| |algebraic?| |principalIdeal| - |quadraticNorm| |wordInGenerators| |numberOfCycles| |shape| - |encodingDirectory| |sylvesterSequence| |numberOfDivisors| - |constructor| |lintgcd| |exponents| |cdr| |callForm?| |dec| - |meshPar2Var| |selectsecond| |reseed| |changeBase| |iteratedInitials| - |halfExtendedResultant1| |computePowers| |mat| |s17ahf| |divisors| - |option| |setCondition!| |cap| |var2StepsDefault| |compound?| - |positiveSolve| |shufflein| |showSummary| |keys| |factorPolynomial| - |tubeRadius| |split| |ellipticCylindrical| |changeMeasure| - |beauzamyBound| |putColorInfo| |lyndon?| |stoseInvertibleSetsqfreg| - |iiacsc| |collect| |rational| |maxColIndex| |e01bff| - |tableForDiscreteLogarithm| |harmonic| |LyndonWordsList1| |center| - |limit| |removeCoshSq| |elements| |showAttributes| |numFunEvals3D| - |fractionFreeGauss!| |imagk| |moduleSum| |scaleRoots| |evaluate| - |trim| |mapGen| |isConnected?| |bag| |quotient| |packageCall| |d01bbf| - |linearAssociatedLog| |realZeros| |setEmpty!| |curveColor| |sequences| - |complexEigenvectors| |asinhIfCan| |checkRur| |previous| |putProperty| - |bitCoef| |symmetricRemainder| |s13acf| |sturmVariationsOf| |name| - |expintfldpoly| |ramified?| |lyndon| |leviCivitaSymbol| |permutation| - |atoms| |rename| |attributeData| |simplifyExp| |f02fjf| |body| - |upperCase| |palgRDE| |ddFact| |getConstant| |s21bcf| |OMgetEndObject| - UP2UTS |dihedral| |createMultiplicationMatrix| |create| |leaf?| - |chainSubResultants| |startTable!| |reopen!| |frst| |times!| |units| - |subQuasiComponent?| |inputBinaryFile| |besselJ| |imagK| |arbitrary| - |null| |outputForm| EQ |rootOf| |integers| |pointColorPalette| - |leftRegularRepresentation| |HermiteIntegrate| |setDifference| - |cyclic?| |identity| |unexpand| |not| |integralAtInfinity?| - |asinIfCan| |FormatRoman| |OMgetAtp| |integralLastSubResultant| - |solveRetract| |shallowCopy| |sayLength| |makeFR| - |trailingCoefficient| |and| |satisfy?| |randomR| |poisson| |df2st| - |rationalPower| |squareFreePart| |mesh?| |Lazard| |e04mbf| |OMputAtp| - |or| |d02cjf| |mapmult| |conditionsForIdempotents| |s17aef| - |derivationCoordinates| |explogs2trigs| |ScanArabic| |xor| |cup| - |antiCommutator| |assert| |code| |minPoints3D| |tower| |normalDeriv| - |invertibleSet| |s19adf| |port| |particularSolution| |pattern| - |viewWriteAvailable| |case| |associates?| |zag| |complementaryBasis| - |e04gcf| |determinant| |fortranCarriageReturn| |ramifiedAtInfinity?| - |rowEchLocal| |Zero| |readUInt8!| |OMlistSymbols| |cAcosh| - |oddInfiniteProduct| |bat1| |logGamma| |t| |One| |sorted?| - |indiceSubResultant| |search| |transcendent?| |exprHasAlgebraicWeight| - |eq| |lighting| |monicRightDivide| |shiftRoots| |returnType!| - |companionBlocks| |currentSubProgram| |predicate| |entries| - |setIntersection| |iter| |plus!| |dim| |subresultantSequence| |d01gbf| - |e01saf| |message| |nullSpace| |monicDivide| |f04jgf| |lifting1| - |complexNumeric| |setTex!| |symmetricPower| |bivariatePolynomials| - |laurentRep| |OMgetSymbol| |points| |ord| |OMreadStr| |pushucoef| - |iiacot| |exactQuotient| |hdmpToP| |expandTrigProducts| - |linearDependence| |unvectorise| |bindings| |iicoth| |kernels| - |completeEchelonBasis| |OMputEndError| |lex| |elt| |chvar| |uniform| - |OMgetInteger| |sum| |s17akf| |screenResolution3D| |operator| - |generators| |f02aef| |pseudoRemainder| |showTheFTable| - |interpretString| |delta| |topPredicate| |associatedEquations| - |mainPrimitivePart| |divideIfCan| |typeForm| |backOldPos| |ParCond| - |lyndonIfCan| |setMinPoints3D| |c06ebf| |cons| |univariate| - |dimensions| |increase| |coshIfCan| |tryFunctionalDecomposition| - |semiSubResultantGcdEuclidean2| |randomLC| |linearMatrix| |divide| - |rightDiscriminant| |pomopo!| |tab1| |changeName| |extractIfCan| - |f04axf| |getCode| |sup| |lllip| |cn| |semiLastSubResultantEuclidean| - |lllp| |nextIrreduciblePoly| |startStats!| |parameters| |coefficients| - |edf2ef| |screenResolution| |factor| |updatF| |leftMult| - |absolutelyIrreducible?| |cTanh| |exprHasLogarithmicWeights| - |quickSort| |useNagFunctions| |stronglyReduce| |redpps| |sqrt| - |power!| |qroot| |writeByte!| |B1solve| |rootPower| |linearPart| - |sin?| |e01bgf| |po| |real| |close!| |tablePow| |initTable!| - |expandPower| |startPolynomial| |lambda| |elliptic| |doubleComplex?| - |s17ajf| |source| |e02akf| |imag| |retract| |e04jaf| - |wordInStrongGenerators| |contract| |drawCurves| |directProduct| - |nothing| |numberOfVariables| |setsubMatrix!| |OMputVariable| - |getMatch| |cosSinInfo| |gcdcofactprim| |mapdiv| |gradient| - |expandLog| |addPoint| |iroot| |lfunc| |horizConcat| |zero| |isAnd| - |listexp| |plusInfinity| |part?| |viewport2D| |stopMusserTrials| - |cot2tan| |arity| |useEisensteinCriterion| |leftScalarTimes!| - |removeRedundantFactorsInContents| |minusInfinity| |fortranTypeOf| - |listOfLists| |brace| |argument| |getMeasure| |critB| - |chineseRemainder| |char| |clearFortranOutputStack| |alternating| - |tubePoints| |topFortranOutputStack| |padicallyExpand| |And| - |invertibleElseSplit?| |destruct| |basisOfCentroid| |upperCase!| - |symmetricTensors| |lazyPrem| |OMputBind| |stirling1| |writable?| - |discriminant| |target| |Or| |OMputSymbol| |prologue| - |removeRoughlyRedundantFactorsInPol| |stoseInvertibleSet| |isExpt| - |generalTwoFactor| |realRoots| |gethi| |reduceBasisAtInfinity| - |checkPrecision| |movedPoints| |f02bjf| |Not| |coerceListOfPairs| - |substring?| |setButtonValue| |BasicMethod| |aQuartic| - |numberOfNormalPoly| |selectMultiDimensionalRoutines| |conjug| - |relationsIdeal| |iisech| LODO2FUN |kovacic| |tanNa| |approximants| - |ldf2lst| |integer?| |polyRDE| |incrementKthElement| |lepol| - |combineFeatureCompatibility| |type| |double?| |PollardSmallFactor| - |index?| |hasHi| |monomial| |suffix?| |xn| |cCos| |superscript| - |stack| |nextColeman| |coerceL| |exteriorDifferential| - |complexIntegrate| |iisqrt2| |finiteBasis| |firstNumer| |multivariate| - |computeCycleLength| |diag| |balancedFactorisation| |noValueMode| - |structuralConstants| |float| |constantToUnaryFunction| |e02ahf| - |resultantReduit| |root| |degreeSubResultantEuclidean| |variables| - |prefix?| |rightCharacteristicPolynomial| |OMgetEndError| |unparse| - |boundOfCauchy| |normalizeAtInfinity| |decreasePrecision| |jacobian| - |besselY| |components| |rootDirectory| |palglimint| |goodnessOfFit| - |zero?| |tubeRadiusDefault| |palgRDE0| |generalizedInverse| - |interactiveEnv| |definingPolynomial| |factorOfDegree| |octon| - |approxNthRoot| |integralBasis| |redmat| |deepCopy| |baseRDEsys| - |OMgetApp| |mapUnivariate| |d01fcf| |principal?| - |selectFiniteRoutines| |ratDenom| |quartic| |bezoutMatrix| |elem?| - |fortranLiteralLine| |operators| |highCommonTerms| |OMserve| - |sizePascalTriangle| |lastSubResultantElseSplit| |has?| |rowEch| - |s18aff| |pair?| |palgLODE| |dflist| |explimitedint| - |internalIntegrate0| |nextPrime| |minimumDegree| |taylor| |cPower| - |wholeRagits| |clipBoolean| |extractProperty| |resetBadValues| - |fortranInteger| |ref| |setAdaptive3D| |OMgetObject| |rCoord| |infix?| - |laurent| |mapMatrixIfCan| |insertMatch| |antiAssociative?| |expt| - |computeInt| |chebyshevU| |iicsc| |lift| |factorSFBRlcUnit| |init| - |mask| |isEquiv| |headReduce| |puiseux| |ptree| |mappingMode| |ptFunc| - |basisOfCommutingElements| |moebius| |mapUp!| GE |reduce| |flatten| - |computeBasis| |shrinkable| |roman| |factorAndSplit| - |primitiveElement| |partition| |algebraicSort| - |resultantEuclideannaif| |ReduceOrder| |leftUnit| GT |sncndn| - |outputSpacing| |perfectSqrt| |merge| |cyclicEqual?| |inv| |operation| - |irForm| |irreducibleRepresentation| |perfectNthPower?| |normal01| - |middle| LE |rightUnit| |leftPower| |ground?| |finite?| |factorList| - |identityMatrix| |normal?| |stFunc2| |indicialEquation| |tan2trig| - |putProperties| LT |subscriptedVariables| |f04mcf| |ground| - |meshPar1Var| |dAndcExp| |norm| |point| |genericLeftMinimalPolynomial| - |univariatePolynomialsGcds| |createGenericMatrix| - |removeSuperfluousQuasiComponents| |cschIfCan| |e02ajf| |leftGcd| - |lazyPquo| |escape| |lazyPseudoDivide| |useSingleFactorBound| - |OMputEndObject| |simplifyPower| |collectQuasiMonic| |palgextint| - |subCase?| |s17dgf| |extendedSubResultantGcd| |generalPosition| - |sin2csc| |e01sbf| |expressIdealMember| |lieAlgebra?| |BumInSepFFE| - |headReduced?| |heap| |permanent| |sinhIfCan| |bipolarCylindrical| - |normalizedAssociate| |series| |capacity| |solve| |submod| - |primextintfrac| |hasSolution?| |reducedSystem| - |generalizedEigenvectors| |sPol| |totalfract| |deriv| |cartesian| - |index| |upperBound| |exprToXXP| |karatsuba| |setfirst!| |insert!| - |integerIfCan| |status| |elementary| |primitive?| |associatedSystem| - |numberOfFractionalTerms| |partialFraction| |maxPoints3D| |f02axf| - |generalInfiniteProduct| |outerProduct| |extendedIntegrate| - |cyclicCopy| |insertTop!| |userOrdered?| |hconcat| |fractRagits| - |applyRules| |getIdentifier| |unrankImproperPartitions0| - |stopTableGcd!| |rightTrim| |eq?| |binarySearchTree| |socf2socdf| - |rectangularMatrix| |min| |maximumExponent| |pair| |order| |linSolve| - |d01aqf| |iiperm| |byte| |polar| |mathieu24| |leftTrim| |extractPoint| - |bright| |hasTopPredicate?| |polygamma| |ParCondList| - |extensionDegree| |yellow| |mainVariable?| |s17dlf| - |semiDiscriminantEuclidean| |matrixConcat3D| |constantLeft| |s14baf| - |imagJ| |sylvesterMatrix| |f04mbf| |derivative| |rightTrace| - |showScalarValues| |lfinfieldint| |getPickedPoints| |fglmIfCan| - |slash| |midpoint| |eval| |f02wef| |unmakeSUP| |leftRankPolynomial| - |monomials| |leftRank| |rightLcm| |sizeLess?| |s21bdf| |readInt32!| - |tab| |laguerre| |graphs| |powmod| |e02def| |lazyPseudoQuotient| - |hspace| |complexEigenvalues| |algebraicCoefficients?| GF2FG - |permutations| |selectOptimizationRoutines| |usingTable?| |nthCoef| - |triangular?| |mergeDifference| |noLinearFactor?| |refine| |error| - |lastSubResultant| |leadingExponent| |point?| |mainExpression| - |solveLinearlyOverQ| |FormatArabic| |asechIfCan| |alphabetic| - |unitVector| |removeIrreducibleRedundantFactors| |mpsode| |f01brf| - |hasPredicate?| |brillhartTrials| |denominator| |palgintegrate| - |removeSuperfluousCases| |hexDigit| |regime| |rootPoly| |cosh2sech| - |variable?| |complexLimit| |writeBytes!| |quatern| |f2st| - |getDatabase| |minPol| |function| |optimize| |dihedralGroup| - |noncommutativeJordanAlgebra?| |groebSolve| |rightPower| |c06fqf| - |binaryTournament| |makeVariable| |ListOfTerms| |sn| |minPoints| - |nextSublist| |froot| BY |complexRoots| |nextItem| |binaryTree| - |delete!| |lazyPremWithDefault| |compose| |alphanumeric| - |selectPolynomials| |primintfldpoly| |intensity| |rspace| |expIfCan| - |interpolate| |showRegion| |inGroundField?| |triangSolve| |solid?| - |rotatex| |univariatePolynomials| |OMputApp| |child| |cCoth| |trunc| - |rightRemainder| |univariate?| |measure2Result| |enqueue!| - |zeroVector| |bandedJacobian| |rischNormalize| |categoryFrame| - |s17aff| |tanh2coth| |tanQ| |overlabel| |testDim| |s18aef| - |toseSquareFreePart| |e02aef| |rightRank| |f01rdf| - |fullPartialFraction| |minus!| |jordanAlgebra?| |hdmpToDmp| - |varselect| |totalGroebner| |OMputBVar| |remainder| |cCsc| |dequeue!| - |doubleFloatFormat| |lazyGintegrate| |binaryFunction| |buildSyntax| - |intersect| |radicalRoots| |flexibleArray| |rem| |result| - |getGoodPrime| |safetyMargin| |dimension| |f04asf| |numericIfCan| NOT - |extendedEuclidean| |degree| |cSinh| |li| |tableau| |quo| |errorKind| - |wholeRadix| |sequence| |sign| |kmax| |sample| OR |constantRight| - |d03edf| |argumentListOf| |complexForm| |basisOfLeftNucleus| - |readUInt16!| |f02ajf| |setAdaptive| |pack!| |laplacian| AND - |monicLeftDivide| |imagI| |fractRadix| |multiset| |div| |addPoint2| - |getOperator| |every?| |wrregime| |critMTonD1| |normalise| |lcm| - |compiledFunction| |f02bbf| |recolor| |aLinear| - |genericLeftDiscriminant| |exquo| |delete| |padecf| |lfextendedint| - |id| |invmultisect| |aspFilename| |enterPointData| - |SturmHabichtMultiple| |listYoungTableaus| |coHeight| |tube| ~= - |nsqfree| |moduloP| |anfactor| |transform| |lo| |setRow!| - |factorFraction| |append| |elRow2!| |distance| |linearlyDependent?| - |subResultantGcdEuclidean| |#| |c06ekf| |mainVariables| |sdf2lst| - |e01bef| |badNum| |gcd| |hexDigit?| |ScanFloatIgnoreSpaces| |getGraph| - ~ |edf2df| |symbolIfCan| |leadingSupport| |e04ucf| |divergence| - |nthFractionalTerm| |false| |collectUnder| |s13aaf| |select!| - |setStatus!| |f04atf| |KrullNumber| |branchPoint?| |nextSubsetGray| - |toScale| |rubiksGroup| |stiffnessAndStabilityOfODEIF| - |selectODEIVPRoutines| |df2fi| |rischDEsys| |test| |scalarTypeOf| - |mainContent| |triangularSystems| |viewDefaults| |quasiRegular?| - |associative?| |setlast!| |resetAttributeButtons| |aCubic| - |integralDerivationMatrix| |loopPoints| |/\\| |copies| |Is| |overset?| - |setErrorBound| |fortranDouble| |e04fdf| |basisOfRightNucloid| - |setPrologue!| |leftOne| |createPrimitiveElement| |\\/| |OMputEndBVar| - |d02ejf| |acotIfCan| |numer| |squareFreePolynomial| |newSubProgram| * - |nthExponent| |retractIfCan| |powers| |complement| |isOp| |bit?| - |pmintegrate| |firstSubsetGray| |d02bbf| |denom| - |setScreenResolution3D| |SturmHabichtSequence| |coerce| |readByte!| - |hermiteH| |mathieu11| |bumptab| |iicsch| |nodeOf?| - |internalIntegrate| |f01mcf| |restorePrecision| |getCurve| |construct| - |knownInfBasis| |freeOf?| |radicalSolve| |drawToScale| |OMgetString| - |bfEntry| |digit?| |makeSUP| |factorSquareFreePolynomial| |pi| = - |revert| |prefix| |f02adf| |ceiling| |Frobenius| |OMgetEndApp| - |opeval| |modularFactor| |singRicDE| |stripCommentsAndBlanks| - |infinity| |roughUnitIdeal?| |maxIndex| |inverseIntegralMatrix| - |groebnerIdeal| |atanIfCan| |rightUnits| |minIndex| - |regularRepresentation| |rk4| |e02dff| |constantCoefficientRicDE| - |unit| < |changeNameToObjf| |doubleDisc| |cos2sec| |unitNormal| - |infinite?| |genericRightDiscriminant| |subNodeOf?| |blankSeparate| - |paren| > |dominantTerm| |se2rfi| |clearTable!| |cycleLength| |d03faf| - |stoseInvertibleSetreg| |element?| |outputList| |unit?| |OMputObject| - |kernel| |relativeApprox| |fortranLinkerArgs| <= |groebgen| - |setLabelValue| |traceMatrix| |symmetricGroup| |quasiComponent| - |unravel| |declare| |sort| |linearPolynomials| |completeSmith| |just| - |list| |Nul| >= |map| |rk4qc| |modularGcd| |pseudoQuotient| - |partialDenominators| |besselK| |cyclotomicDecomposition| |draw| - |LyndonCoordinates| |multiple?| |bubbleSort!| |f02aff| |tan2cot| - |leader| |create3Space| |outputMeasure| |sechIfCan| |s20adf| - |createThreeSpace| |nodes| |halfExtendedSubResultantGcd2| - |setTopPredicate| |showAllElements| |number?| |addMatchRestricted| - |cycleElt| |iiasech| |leadingTerm| |primextendedint| |categories| - |rombergo| |basisOfNucleus| |invmod| |explicitlyEmpty?| |UP2ifCan| - |updatD| |mulmod| + |head| |value| |c06gcf| |hitherPlane| - |euclideanSize| |mapUnivariateIfCan| |subst| |cardinality| |width| - |complete| |random| |showTheRoutinesTable| |processTemplate| - |LazardQuotient| - |ridHack1| |stoseIntegralLastSubResultant| - |specialTrigs| |halfExtendedResultant2| |leftTraceMatrix| |commutator| - |central?| |gensym| |infix| |makeObject| |crushedSet| / - |resultantEuclidean| |convert| |isOpen?| |level| |setref| |largest| - |OMgetEndAttr| |cyclicGroup| |ratPoly| |readable?| |genericPosition| - |polyPart| |coef| |iisec| |qinterval| |oblateSpheroidal| - |idealSimplify| |trivialIdeal?| |queue| |extractTop!| |distribute| - |asimpson| |log| |maxdeg| |monicCompleteDecompose| |generateIrredPoly| - |e04naf| |numberOfComposites| |reindex| |quadratic| |normDeriv2| - |isList| |integerBound| |s17agf| |optAttributes| |toseInvertibleSet| - |multiEuclideanTree| |d02bhf| |iifact| |rowEchelon| |inrootof| - |cyclicSubmodule| |ode2| |infLex?| |setelt| |algebraicDecompose| - |assign| |iiasin| |f07fef| |oneDimensionalArray| |e02bef| |iiatanh| - |prinshINFO| |cExp| |subspace| |objects| |iidprod| |drawStyle| |mr| - |getStream| |makeop| |indicialEquations| |radix| - |parabolicCylindrical| |heapSort| |infiniteProduct| |OMread| - |optional| |base| |copy| |semiResultantReduitEuclidean| |yCoordinates| - |atrapezoidal| |ricDsolve| |numberOfComputedEntries| |terms| - |partialNumerators| |pr2dmp| |qelt| |linkToFortran| |OMopenFile| - |eyeDistance| |stFunc1| |eigenvector| |exponential1| |toroidal| - |infinityNorm| |qsetelt| |LagrangeInterpolation| |prefixRagits| - |rootsOf| |iidsum| |primes| |prod| |front| |repeating?| - |factorByRecursion| |dmp2rfi| |fi2df| |localAbs| |xRange| |e02daf| - |parent| |build| |pascalTriangle| |OMUnknownCD?| |digits| |setnext!| - |edf2fi| |getMultiplicationTable| |selectfirst| |yRange| |s19abf| - |lazyVariations| |reorder| |OMclose| |setProperties| |subPolSet?| - |bipolar| |binary| |rightExactQuotient| |fixPredicate| |zRange| - |pole?| |viewThetaDefault| |addmod| |listConjugateBases| - |genericLeftTraceForm| |reducedDiscriminant| |OMgetEndAtp| - |orthonormalBasis| |map!| |physicalLength| |rightFactorCandidate| - |elaborateFile| |cylindrical| |s17acf| |isAbsolutelyIrreducible?| |dn| - |twoFactor| |integralCoordinates| |LiePolyIfCan| |systemCommand| - 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|latex| UTS2UP |mindeg| |popFortranOutputStack| |prinb| |sub| |iiabs| - |countRealRootsMultiple| |push| |createZechTable| |directSum| |pop!| - |say| |littleEndian| |An| |outputAsFortran| - |stoseInternalLastSubResultant| |rk4f| |presuper| |hyperelliptic| - |youngDiagram| |cotIfCan| |basisOfLeftNucloid| |max| |gcdcofact| - |getProperty| |semiResultantEuclidean1| |resultantnaif| - |leadingMonomial| |ratpart| |reset| |isAtom| |putGraph| |cyclic| - |maxRowIndex| |elRow1!| |cSin| |duplicates| |fractionPart| - |leadingCoefficient| |nil| |cothIfCan| |nextPartition| |inc| - |patternVariable| |elColumn2!| |selectOrPolynomials| |c06frf| |bfKeys| - |d02raf| |primitiveMonomials| |basicSet| |write| |rules| - |discriminantEuclidean| |pushup| |createMultiplicationTable| - |deepExpand| |df2ef| |fortranReal| |maxint| |reductum| |save| |Si| - |collectUpper| |innerSolve| |subHeight| |normalized?| |stop| |s13adf| - |OMsupportsCD?| |imports| |distFact| |approximate| |c06gbf| |isOr| - |back| |innerint| |inR?| |unrankImproperPartitions1| |headRemainder| - 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|symmetricDifference| |doubleRank| |constant| |pointColor| |factorset| - |iiacoth| |monic?| |predicates| |rightDivide| |scanOneDimSubspaces| - |critpOrder| |exp| |endSubProgram| |makeMulti| |modifyPoint| |iitanh| - |pToHdmp| |binomial| |nextNormalPrimitivePoly| |pmComplexintegrate| - |pointSizeDefault| |nextPrimitiveNormalPoly| |debug| - |showFortranOutputStack| |factorSquareFree| |d03eef| |tanSum| - |bandedHessian| |meatAxe| |internalZeroSetSplit| |second| |taylorRep| - |copyInto!| D |GospersMethod| |f02abf| |printStatement| |integrate| - |algSplitSimple| |reducedQPowers| |d01ajf| |third| |neglist| - |lowerCase?| |isNot| |listLoops| |listOfMonoms| |cyclicParents| - |eulerE| |fillPascalTriangle| |cubic| |adaptive?| |any| |LyndonBasis| - |any?| |unitCanonical| |exprToUPS| |eigenMatrix| |constantOperator| - |pol| |rightMult| |key| |factorial| |edf2efi| |sumOfDivisors| - |truncate| |e02bcf| |polygon| |parents| |leaves| |swapRows!| |s18adf| - |readLine!| |schema| |subResultantGcd| |symmetric?| - 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|showArrayValues| |dequeue| |setPoly| |selectPDERoutines| - |setprevious!| |swap| |graphCurves| |readInt16!| |subResultantsChain| - |hclf| |generator| |surface| |prime?| |bounds| - |internalSubQuasiComponent?| |f01qef| |leftQuotient| |evenlambert| - |exponentialOrder| |bitTruth| |exQuo| |e04dgf| |stFuncN| |pow| - |transcendenceDegree| |ocf2ocdf| |host| |nullity| |updateStatus!| - |axes| |options| |content| |cyclotomicFactorization| - |nativeModuleExtension| |constantIfCan| |linearAssociatedExp| |module| - |expintegrate| |lazy?| |connect| |modulus| |presub| |composite| - |oddintegers| |antiCommutative?| |flagFactor| |branchIfCan| - |simpleBounds?| |rewriteIdealWithQuasiMonicGenerators| |table| - |numberOfIrreduciblePoly| |nullary?| |child?| |color| |mesh| - |numberOfMonomials| |indiceSubResultantEuclidean| |unknownEndian| - |monomial?| |string| |new| |nextNormalPoly| |pastel| |Gamma| - |nthFactor| |hostByteOrder| |categoryMode| |setMaxPoints3D| - |external?| |solveid| |qualifier| |palgextint0| |generalSqFr| - |numerator| |length| |s17dhf| |setOrder| |split!| |binomThmExpt| - |minimumExponent| |fortranLogical| |jokerMode| |clearTheIFTable| - |jordanAdmissible?| |scripts| |intermediateResultsIF| |irreducible?| - |cAsinh| |title| |complexExpand| |OMmakeConn| |hcrf| |laplace| - |c02aff| |critT| |arg1| |gbasis| |bumprow| |characteristicSerie| - |vertConcat| |myDegree| |incr| |subSet| |OMreadFile| |round| |swap!| - |arg2| |makeTerm| |lazyEvaluate| |mappingAst| |in?| |outputArgs| - |cAtan| |hi| |complex?| |innerSolve1| |leftCharacteristicPolynomial| - |tail| |e| |shanksDiscLogAlgorithm| |dual| |characteristic| - |realSolve| |printInfo| |resultant| |square?| |headAst| - |UpTriBddDenomInv| |represents| |conditions| |arrayStack| - |LyndonWordsList| |subMatrix| |indices| |scalarMatrix| - |functionIsOscillatory| |partialQuotients| |substitute| - |leftDiscriminant| |parts| |match| |genericRightTraceForm| |rotate| - |modifyPointData| |rootOfIrreduciblePoly| |prepareDecompose| - |idealiserMatrix| |log2| |youngGroup| |apply| |extractIndex| - |medialSet| |rightScalarTimes!| |imagi| |groebnerFactorize| - |tensorProduct| |comment| |leftRecip| |changeThreshhold| - |selectNonFiniteRoutines| |htrigs| |first| |supersub| |iiacosh| - |c05nbf| |resultantReduitEuclidean| |less?| |left| |convergents| - |increasePrecision| |domainTemplate| |augment| |fortran| |rest| - |cAcos| |seriesSolve| |iCompose| |iipow| |moreAlgebraic?| |right| - |thenBranch| |bitLength| |scripted?| |hash| |currentCategoryFrame| - |generalizedEigenvector| |redPol| |comp| |initiallyReduced?| |light| - |csch2sinh| |count| |splitDenominator| |perfectSquare?| |polyred| - |mainCoefficients| |curryRight| |normalElement| |PDESolve| - |createIrreduciblePoly| |setPredicates| |integralBasisAtInfinity| - |lifting| |resetVariableOrder| |leftExtendedGcd| |laurentIfCan| - |elaborate| |bernoulli| |UnVectorise| |red| |coth2tanh| |pile| - |secIfCan| |integralMatrix| |unprotectedRemoveRedundantFactors| - |unary?| |e02zaf| |inverseIntegralMatrixAtInfinity| |normalDenom| - |quote| |removeDuplicates| |lastSubResultantEuclidean| |newTypeLists| - |semicolonSeparate| |compactFraction| |primlimintfrac| |integral| - |OMcloseConn| |high| |signAround| |padicFraction| |clipWithRanges| - |mkIntegral| |prindINFO| |mainMonomial| |atanhIfCan| |lquo| - |isobaric?| |mkcomm| |generate| |f02xef| |subResultantChain| |ksec| - |intcompBasis| |rationalPoint?| |cAcsc| |differentialVariables| - |hMonic| |real?| |comparison| |standardBasisOfCyclicSubmodule| - |mapExpon| |frobenius| |nonLinearPart| |strongGenerators| |c06fpf| - |lineColorDefault| |incrementBy| |att2Result| |appendPoint| |bottom!| - |iFTable| |primPartElseUnitCanonical!| |lowerBound| |nonSingularModel| - |trueEqual| |irCtor| |expand| |triangulate| |complexElementary| - |arguments| |curry| |kroneckerDelta| |one?| |showTheIFTable| - |normFactors| |patternMatch| |mainDefiningPolynomial| |symbol| - |filterWhile| |symmetricProduct| |purelyTranscendental?| |polCase| - |next| |preprocess| |totalDegree| |constant?| |basis| |vconcat| - |colorFunction| |erf| |expression| |filterUntil| |outputFloating| - |upDateBranches| |iiexp| |script| |skewSFunction| |swapColumns!| - |asecIfCan| |generic| |integer| |select| - |solveLinearPolynomialEquationByRecursion| |fixedDivisor| |shuffle| - |rewriteIdealWithRemainder| |setright!| |mainMonomials| |cSech| - |e02baf| |mapExponents| |shellSort| |OMgetFloat| |factors| - |primitivePart| |inspect| |numberOfComponents| |replace| - |cyclicEntries| |iomode| |dilog| |morphism| |cRationalPower| |linear?| - |tex| |getProperties| |OMUnknownSymbol?| |overbar| |pdf2df| - |singleFactorBound| |psolve| |sin| |OMgetType| |pureLex| - |sturmSequence| |semiResultantEuclidean2| |top| |makeGraphImage| - |d02gbf| |deref| |cos| |internalLastSubResultant| |resetNew| |getlo| - |continue| |removeRedundantFactorsInPols| |allRootsOf| |cycleEntry| - |sqfrFactor| |interval| |leftZero| |tan| |numFunEvals| - |internalInfRittWu?| |lprop| |fprindINFO| |zerosOf| |showAll?| - |primlimitedint| |ip4Address| |exprHasWeightCosWXorSinWX| |compBound| - |cot| |makeRecord| |mainCharacterization| |step| RF2UTS |leftLcm| - |leftMinimalPolynomial| |inf| |iExquo| |c05pbf| |push!| |sec| |int| - |concat| |LiePoly| |vspace| |reify| |deleteRoutine!| - |stopTableInvSet!| |diophantineSystem| |OMParseError?| |csc| - |getOrder| |henselFact| |stronglyReduced?| |rootProduct| |acothIfCan| - |bringDown| |solveLinearPolynomialEquation| |setFormula!| |output| - |condition| |curve?| |asin| |basisOfLeftAnnihilator| - |functionIsContinuousAtEndPoints| |logIfCan| |argumentList!| - |palginfieldint| |list?| |tracePowMod| |readIfCan!| - |getSyntaxFormsFromFile| |acos| |pointLists| |s18acf| |e02gaf| FG2F - |cycleTail| |externalList| |makeViewport2D| |interpret| |belong?| - |atan| |basisOfCenter| |jacobiIdentity?| |setchildren!| |rightGcd| - |OMgetBVar| |quotedOperators| |mkAnswer| |hasoln| |acot| - |outlineRender| |addBadValue| |xCoord| |abs| |numberOfOperations| - |purelyAlgebraicLeadingMonomial?| |smith| |rightZero| |laguerreL| - |asec| |squareFree| |paraboloidal| |virtualDegree| |infieldint| - |csc2sin| |bernoulliB| |showIntensityFunctions| |bezoutDiscriminant| - |Hausdorff| |outputBinaryFile| |acsc| |unitsColorDefault| |matrixGcd| - |viewWriteDefault| |withPredicates| |viewPosDefault| |credPol| - |zeroSetSplit| |factor1| |internalSubPolSet?| |connectTo| |dioSolve| - |sinh| |parametric?| |negative?| |reducedForm| |reciprocalPolynomial| - |mainForm| |coordinates| |inconsistent?| |nonQsign| |normalizedDivide| - |cosh| |makeSin| |pointColorDefault| |phiCoord| |subresultantVector| - |property| |evenInfiniteProduct| |setProperty| |optpair| |rank| |tanh| - |cot2trig| |setUnion| |acoshIfCan| |radPoly| |const| |upperCase?| - |prem| |clipParametric| |indicialEquationAtInfinity| |coth| - |makeViewport3D| |linears| |fortranCompilerName| |hex| |OMputString| - |bracket| |e01sff| |gcdPrimitive| |goodPoint| |iibinom| |lexico| - |sech| |powerAssociative?| |genericRightNorm| |choosemon| - |checkForZero| |environment| |low| |integral?| - |rewriteIdealWithHeadRemainder| |relerror| SEGMENT - |reduceByQuasiMonic| |csch| |symFunc| |computeCycleEntry| - |lfextlimint| |setPosition| |kind| |bat| |Aleph| |logical?| - 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|removeRoughlyRedundantFactorsInContents| |setColumn!| |sumOfSquares| - |numberOfFactors| |printStats!| |writeInt8!| |merge!| |directory| - |ncols| |suchThat| |contractSolve| |genus| |denomLODE| |clip| |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 + |Record| |Union| |sinIfCan| |oddlambert| |element?| |cycleEntry| + |genericRightTrace| |makeop| |showFortranOutputStack| + |linearDependenceOverZ| |genus| |changeThreshhold| |getProperty| |set| + |prime| |alternating| |prinb| |d02gaf| |neglist| |euclideanNormalForm| + |c05nbf| |minus!| |hdmpToP| |rootProduct| |ode1| |compiledFunction| + |OMputInteger| |lfunc| |associatorDependence| |recoverAfterFail| + |resetNew| |cap| |setCondition!| |iiexp| |primintfldpoly| + |brillhartIrreducible?| |extractTop!| |idealiser| |f2st| |imagj| + |getMeasure| |listOfMonoms| |c02aff| |lists| |setLabelValue| |cAtan| + |conditionsForIdempotents| |makeUnit| |firstUncouplingMatrix| + |dominantTerm| |invertibleSet| |hasHi| |s15aef| |hconcat| + |modularFactor| |OMlistCDs| |rightFactorCandidate| |nlde| + |mainContent| |mapGen| |resetAttributeButtons| |numFunEvals3D| |reify| + |decreasePrecision| |createZechTable| |dmpToP| |bandedHessian| + |internalAugment| |cyclic| |lazyPseudoQuotient| |signature| + |subMatrix| |asecIfCan| |dimensionsOf| |interpolate| |drawComplex| + |htrigs| |rootsOf| |selectfirst| |inverseColeman| |mergeDifference| + |schwerpunkt| |leftTraceMatrix| |repeatUntilLoop| |cubic| + |tanintegrate| |search| |hasoln| |s18adf| |chiSquare1| |realRoots| + |expr| |partition| |leftDivide| |reducedDiscriminant| |identification| + |incrementKthElement| |explicitlyEmpty?| |minset| + |createPrimitivePoly| |f01rcf| |conjugate| |makeFR| + |toseLastSubResultant| |sts2stst| |critBonD| |aLinear| |outputList| + |nodes| |midpoints| |regularRepresentation| |leftExactQuotient| + |infLex?| |leviCivitaSymbol| |strongGenerators| + |genericLeftDiscriminant| |expint| |variationOfParameters| |parts| + |leftAlternative?| |represents| |show| |isPlus| |round| |qroot| + |stoseInvertible?| |associatedSystem| |polCase| |nthRootIfCan| + |maxdeg| |identity| |firstNumer| |rightRank| |plus!| |droot| + |variable| |cardinality| |iicoth| |aspFilename| |principalAncestors| + |monicCompleteDecompose| |datalist| |trace| |screenResolution3D| + |color| |mat| |solveRetract| |heap| |iterators| |cyclicEqual?| + |meshPar1Var| |getlo| |vertConcat| |exp1| |lighting| |trueEqual| + |iifact| |subst| |nextPrimitivePoly| |ldf2vmf| |numberOfVariables| + |bivariatePolynomials| |jordanAdmissible?| |systemCommand| |axes| + |shanksDiscLogAlgorithm| |newTypeLists| |findConstructor| |iiacsch| + |untab| |char| |checkPrecision| |redPo| |lookup| |iicsc| |s17dgf| + |limitedIntegrate| |realEigenvectors| |readInt32!| |d03edf| + |deepExpand| |selectOrPolynomials| |bitior| |parabolicCylindrical| + |changeNameToObjf| |bipolar| |maxPoints3D| |lowerBound| |precision| + |diff| |isPower| |univariatePolynomials| |denominators| |superHeight| + |d02gbf| |dot| |attributeData| |subQuasiComponent?| |leadingIdeal| + |normal| |showArrayValues| |leftExtendedGcd| |positive?| + |sylvesterMatrix| |sin2csc| |nilFactor| |figureUnits| |s17def| + |OMopenString| |setTopPredicate| |push| |cond| |adaptive| |e02bcf| + |branchPointAtInfinity?| |concat| |permutationGroup| |randomR| + |printCode| |complexExpand| |complexZeros| |green| |sech| |toroidal| + |retractable?| |selectNonFiniteRoutines| |coefficients| |edf2efi| + |hasSolution?| |objects| |OMgetType| |lazyGintegrate| |getIdentifier| + |clipPointsDefault| |csch| |unitNormal| |empty| |solid| |invertIfCan| + |exprToXXP| |GospersMethod| |base| |float| |column| |birth| |iitanh| + |permanent| |OMputAtp| |asinh| |extendedEuclidean| + |ScanFloatIgnoreSpacesIfCan| |f04mbf| |returnTypeOf| |solveid| + |constantLeft| |constantToUnaryFunction| |cAcosh| |nextSubsetGray| + |acosh| |createMultiplicationTable| |remainder| |cyclicSubmodule| + |asechIfCan| |sign| |kind| |stopTable!| |stronglyReduced?| + |setErrorBound| |outputMeasure| |mapExpon| |arg1| |viewPhiDefault| + |certainlySubVariety?| |atanh| |key?| |currentSubProgram| |vspace| + |LazardQuotient| |evenInfiniteProduct| |leftRank| |edf2ef| |op| + |setnext!| |pquo| |bat| |arg2| |wordsForStrongGenerators| |mix| + |acoth| |eq?| |OMencodingXML| |associatedEquations| + |tubeRadiusDefault| |ramifiedAtInfinity?| |groebgen| |palgint| + |branchIfCan| |exists?| |radicalSimplify| |firstDenom| |asech| + |sncndn| |numer| |airyAi| |unit| |quotient| |fortranLiteralLine| + |host| |integers| |conditions| |compactFraction| |mdeg| |pop!| |Beta| + |box| |variables| |zeroOf| |linearAssociatedLog| |denom| + |makeGraphImage| |opeval| |iisec| |complexEigenvalues| |lex| |match| + |options| |multiple| |trim| |fractRadix| |unvectorise| |lepol| + |e02zaf| |dn| |pdf2ef| |partialNumerators| |modTree| |mesh?| + |setProperty| |applyQuote| |minPoly| |selectMultiDimensionalRoutines| + |s18aff| |pi| |pair?| |tree| |mkAnswer| |powern| |whatInfinity| |any| + |surface| |categoryFrame| |complexNormalize| |infinity| |zoom| + |viewDeltaYDefault| |algintegrate| |e01sbf| |union| |mathieu12| + |replaceKthElement| |compBound| |intermediateResultsIF| |string| + |LyndonWordsList| |OMconnOutDevice| |localReal?| |UpTriBddDenomInv| + |biRank| |cCot| |minIndex| |setIntersection| |SturmHabicht| + |idealSimplify| |ruleset| |integralAtInfinity?| |symbolTableOf| + |selectPolynomials| |routines| |previous| |acotIfCan| |child?| + |physicalLength| |psolve| |signAround| |setImagSteps| |localAbs| |qqq| + |kernel| |seriesSolve| |SturmHabichtCoefficients| |computePowers| + |plot| |e02ajf| |setMinPoints| |f02aef| |OMputEndObject| + |linearAssociatedOrder| |expIfCan| |list| |complexNumeric| + |finiteBasis| |rightAlternative?| |mapmult| |tanSum| |schema| + |laguerre| |suchThat| |optional?| |exportedOperators| |swapColumns!| + |imports| |resize| |draw| |Ei| |halfExtendedSubResultantGcd1| + |lowerCase?| |partialFraction| |initials| |arbitrary| |makeCrit| + |polarCoordinates| |insertMatch| |charpol| |linSolve| |gcdcofactprim| + |moebiusMu| |flagFactor| |tanhIfCan| |reopen!| |iiacosh| |rombergo| + |e02dff| |multiplyExponents| |setColumn!| |algint| |c06fuf| |check| + |s18def| |allRootsOf| |makeResult| |zeroDimensional?| |weight| + |supRittWu?| |exteriorDifferential| |setStatus| F2FG |mainValue| + |radix| |viewport3D| |besselJ| |prolateSpheroidal| |drawStyle| + |prepareDecompose| |returnType!| |polyRDE| |addiag| |makeObject| + |satisfy?| |gramschmidt| |OMputEndBind| |viewWriteAvailable| + |selectIntegrationRoutines| |genericLeftTraceForm| |s18aef| + |acschIfCan| |center| |colorFunction| |hue| |coef| |power!| + |quadraticForm| |numberOfHues| |corrPoly| |separant| |stack| |e04gcf| + |iteratedInitials| |OMParseError?| |gderiv| |numberOfChildren| |label| + |d01amf| |children| |checkRur| |aCubic| |putGraph| + |integralMatrixAtInfinity| |status| |colorDef| |headAst| |outputAsTex| + |name| |primeFactor| |anfactor| |integralLastSubResultant| |lagrange| + |tab| |typeForm| |coerceS| |internalLastSubResultant| + |resetVariableOrder| |knownInfBasis| |f02aaf| |body| |gcdcofact| + |cyclic?| |cAsinh| |lowerCase!| |generalTwoFactor| + |generalInfiniteProduct| |OMgetAttr| |invmultisect| + |normalizeAtInfinity| |weierstrass| |setPosition| |escape| |d02bhf| + |interpret| |queue| |sumOfKthPowerDivisors| |rotatez| |normalDeriv| + |primitivePart!| |generalPosition| |s19aaf| + |inverseIntegralMatrixAtInfinity| |outputArgs| |create3Space| + |LowTriBddDenomInv| |maxIndex| |OMclose| |argument| UP2UTS |iisinh| + |irreducibleFactor| |exponentialOrder| |setPoly| |convergents| + |quickSort| |fortranLogical| |inrootof| |froot| |point| + |constantRight| |length| |sizeMultiplication| |nsqfree| |reverse!| + |resultantEuclideannaif| |variable?| |chebyshevU| |meshPar2Var| + |bezoutDiscriminant| |nthCoef| |rotatex| |scripts| |leftTrace| + |cotIfCan| |cup| |zeroVector| |OMreadFile| |rootOf| |tab1| + |setClipValue| |leftFactor| |option| |halfExtendedResultant2| + |before?| |ode| |nextItem| |removeRedundantFactorsInContents| + |simplifyLog| SEGMENT |constant?| |exprHasWeightCosWXorSinWX| |d01gbf| + |series| |hexDigit?| |quadratic?| |sequence| |extend| |port| + |linearMatrix| |squareFreePrim| |basisOfLeftNucleus| |hspace| + |clikeUniv| |leastMonomial| |df2st| |lyndon| |imagJ| |baseRDEsys| + |d02bbf| |radicalSolve| |constantOperator| |perfectNthPower?| + |UP2ifCan| |multMonom| |addMatch| |expandLog| |makeSeries| |polygon?| + |t| |OMconnectTCP| |recip| |external?| |terms| |cschIfCan| |s17dlf| + |iiacos| |OMputBVar| |meshFun2Var| |internalZeroSetSplit| |lprop| + |viewThetaDefault| |matrixConcat3D| |drawCurves| |bumptab1| |recur| + |min| |tValues| |purelyTranscendental?| |rangePascalTriangle| + |elColumn2!| |nextNormalPrimitivePoly| |getGoodPrime| + |genericLeftTrace| |e02aef| |unitsColorDefault| |c06ekf| |f04axf| + |bfEntry| |OMputEndAtp| |lazyEvaluate| |goodnessOfFit| + |stoseInvertibleSetsqfreg| |triangularSystems| |positiveRemainder| + |normalizedAssociate| |OMgetVariable| |normalizeIfCan| |setfirst!| + |module| |nthFactor| |stiffnessAndStabilityFactor| |topPredicate| + |finite?| |refine| |removeRoughlyRedundantFactorsInPols| + |prefixRagits| |sqfree| |sdf2lst| |factorFraction| |slex| |rootRadius| + |coerceP| |unknown| |apply| |sturmVariationsOf| |nonQsign| + |rightMinimalPolynomial| |listYoungTableaus| |commaSeparate| + |difference| |getZechTable| |oneDimensionalArray| |mathieu23| + |palginfieldint| |rowEch| |first| |s17dhf| |insertionSort!| + |integerBound| |subPolSet?| |changeBase| |tanh2coth| |oddintegers| + |xor| |imag| |rational| |exponential1| |logical?| |sturmSequence| + |rest| |controlPanel| |lineColorDefault| |doubleFloatFormat| + |printHeader| |laurentIfCan| |directProduct| |degreePartition| + |cRationalPower| |case| |cos2sec| |getButtonValue| |removeCosSq| + |irDef| |blue| |functionIsOscillatory| + |removeIrreducibleRedundantFactors| |stirling1| |reindex| |invmod| + |Zero| |stripCommentsAndBlanks| |countRealRootsMultiple| + |axesColorDefault| |comp| |keys| |overset?| |true| |graphStates| + |cCoth| |magnitude| |readUInt8!| |void| |bottom!| |f04adf| |One| |top| + |characteristicSerie| |putColorInfo| |semiLastSubResultantEuclidean| + |startPolynomial| |getConstant| |sizePascalTriangle| + |standardBasisOfCyclicSubmodule| |build| |continue| |members| + |denomRicDE| |LiePolyIfCan| |modularGcdPrimitive| |intersect| + |mappingMode| |clearTable!| |increase| |yCoord| |modifyPoint| |sort| + |plusInfinity| |nand| |cyclotomicDecomposition| |Si| |LiePoly| |eof?| + |systemSizeIF| |nextNormalPoly| |deleteProperty!| + |ellipticCylindrical| |prinshINFO| |minusInfinity| |highCommonTerms| + |genericLeftNorm| |contours| |measure2Result| |pushup| |HenselLift| + |ideal| |coleman| |linearPart| |abelianGroup| |sumOfDivisors| |entry?| + |squareFreeFactors| |id| |rightPower| |f04qaf| |floor| |wreath| + |reduceBasisAtInfinity| |characteristicSet| + |functionIsFracPolynomial?| |badNum| |perfectSqrt| |hexDigit| + |createIrreduciblePoly| |UnVectorise| |elt| |moreAlgebraic?| + |rightUnit| |lo| |upperCase?| |exponent| |rename| |prepareSubResAlgo| + |semiResultantReduitEuclidean| |random| |OMgetBind| |lSpaceBasis| + |outputFixed| |linkToFortran| |constantCoefficientRicDE| |next| + |rootKerSimp| |eyeDistance| |rightRegularRepresentation| |testModulus| + |singularAtInfinity?| |leftMinimalPolynomial| |rangeIsFinite| + |elements| |OMgetBVar| |univariateSolve| |critT| |numberOfDivisors| + |quadraticNorm| |bounds| |ParCondList| |initiallyReduced?| + |binomThmExpt| |shufflein| |newReduc| |argscript| + |integralBasisAtInfinity| |patternMatch| |cot2trig| |pseudoDivide| + |sinh2csch| |remove!| |readable?| |moebius| |secIfCan| + |toseInvertibleSet| |insertTop!| |acosIfCan| |expPot| |d01asf| + |identitySquareMatrix| |prologue| |lieAdmissible?| + |unrankImproperPartitions0| |freeOf?| |lfextlimint| |rightDivide| + |stoseSquareFreePart| |homogeneous?| |pushuconst| |minRowIndex| + |leftDiscriminant| |insert| |writeByte!| |empty?| |getMatch| |isEquiv| + |call| |factorByRecursion| |ocf2ocdf| |s20acf| |choosemon| + |coerceListOfPairs| |parabolic| |lyndonIfCan| |maxPoints| |composites| + |leader| |singularitiesOf| |inGroundField?| |sorted?| |isTimes| + |create| |resultantReduit| |useEisensteinCriterion?| |normal?| + |outputAsScript| |shellSort| |OMputAttr| |shuffle| |f01qdf| + |OMgetObject| |primeFrobenius| |bivariateSLPEBR| |imagk| + |leftCharacteristicPolynomial| |e04dgf| |radPoly| |leftPower| + |sequences| |ODESolve| |showAllElements| |subNodeOf?| |csch2sinh| + |closed?| |monicDecomposeIfCan| |pol| |setLength!| |s21bdf| + |symmetricRemainder| |semiResultantEuclidean2| |cTan| + |definingEquations| |f02agf| |wholeRagits| |numericalOptimization| + |extractClosed| |eigenvectors| |digit?| |internalIntegrate0| + |fortranInteger| |chebyshevT| |d01fcf| |denominator| |digit| |revert| + |setEmpty!| |reorder| |ratDenom| |monicModulo| |leftRankPolynomial| + |possiblyNewVariety?| |infix| |printStats!| |bezoutMatrix| |composite| + |symbolTable| |explicitEntries?| |cdr| |rationalIfCan| + |selectODEIVPRoutines| |reduction| |ipow| |normalized?| |torsion?| + |llprop| |printStatement| |e02akf| |extension| + |semiSubResultantGcdEuclidean2| |mapUnivariate| |symbolIfCan| + |makeprod| |localIntegralBasis| |usingTable?| |pushFortranOutputStack| + |fortranDouble| |splitDenominator| |brillhartTrials| |minrank| + |sylvesterSequence| |e02agf| |digamma| |setleft!| |insert!| + |popFortranOutputStack| |width| |showTheRoutinesTable| + |closeComponent| |separateFactors| |prindINFO| |super| + |createRandomElement| |makeVariable| |createPrimitiveNormalPoly| + |wrregime| |outputAsFortran| |areEquivalent?| |paraboloidal| + |vedf2vef| |leastAffineMultiple| |pointColor| |expenseOfEvaluation| + |rationalPoint?| Y |latex| |setRow!| |quote| |realElementary| + |monomialIntPoly| |predicates| |groebner?| |OMgetEndError| |rootBound| + |setleaves!| |linearAssociatedExp| |OMencodingUnknown| |mergeFactors| + |removeSinSq| |internalInfRittWu?| |cSinh| |operators| |f07fef| + |loopPoints| |nullary?| |leftQuotient| |range| |alphabetic?| + |unitVector| |lazyIntegrate| |f02aff| |eigenvector| |rowEchelon| + |clearCache| |useEisensteinCriterion| |setDifference| |flexibleArray| + |lift| |table| |isList| |trivialIdeal?| |badValues| + |oddInfiniteProduct| |groebner| |more?| |df2mf| |rquo| |flexible?| + |reduce| |new| |dictionary| |toseSquareFreePart| |readInt16!| |obj| + |multiEuclidean| |symmetricProduct| |d01bbf| |nullSpace| + |approxNthRoot| |primPartElseUnitCanonical| |subresultantVector| + |ratPoly| |imagK| |cache| |totalGroebner| |rightGcd| |deepCopy| |li| + |monomRDEsys| |f04faf| |outputForm| |headRemainder| + |numericalIntegration| |car| |split!| |e04ucf| |sechIfCan| |largest| + |dimensions| |product| |generalLambert| |OMputSymbol| |f02abf| + |diophantineSystem| |stirling2| |createPrimitiveElement| + |setPredicates| |legendreP| |optpair| |factor| |pdf2df| |Gamma| + |expandPower| |cycleElt| |implies| |semiIndiceSubResultantEuclidean| + |genericRightDiscriminant| |prime?| |mainExpression| |medialSet| + |iipow| |cAcoth| |computeCycleEntry| |youngDiagram| + |expenseOfEvaluationIF| |rotatey| |atoms| |numberOfImproperPartitions| + |mapCoef| |groebSolve| |vector| |quasiRegular?| |push!| + |printingInfo?| |ddFact| |solve1| |semiDiscriminantEuclidean| + |quartic| |basisOfNucleus| |integralRepresents| |equiv| + |differentiate| |mapExponents| |clipSurface| |dark| + |curveColorPalette| |split| |rootSimp| |predicate| |d01ajf| + |factorial| |removeCoshSq| |iiacot| |exprToGenUPS| |comparison| + |findCycle| |sort!| |e01bef| |powers| |hMonic| |setprevious!| + |ramified?| |primextendedint| |f01brf| |countable?| |size| |monomial| + |left| ** |factorSquareFreePolynomial| |selectOptimizationRoutines| + |RittWuCompare| |parent| |dom| |test| |redPol| |makeSin| + |identityMatrix| |arity| |argumentList!| |byte| |BasicMethod| |d01akf| + |right| |multivariate| |viewpoint| |fractionFreeGauss!| |roughBase?| + |innerint| |numberOfComposites| |ceiling| |typeLists| |ord| + |printInfo!| |edf2df| |linear| |OMputBind| |retractIfCan| + |LyndonWordsList1| |definingInequation| |exponents| |bumprow| + |romberg| |solve| |numberOfFactors| |c06gbf| |primlimintfrac| |close| + |semiDegreeSubResultantEuclidean| |characteristicPolynomial| + |basisOfCommutingElements| |drawComplexVectorField| + |totalDifferential| |atanhIfCan| |basisOfRightNucloid| + |nthFractionalTerm| |ran| |polynomial| |traverse| |sqrt| |atanIfCan| + |specialTrigs| |subResultantChain| |iiacoth| |iprint| |doubleRank| + |universe| |thetaCoord| |leaves| |display| |e02gaf| |real| |title| + |ravel| |safeFloor| |critpOrder| |degreeSubResultant| |interval| + |failed?| |units| |iisqrt3| |gcdPrimitive| |prefix| |cosh2sech| + |limitPlus| |makeTerm| |makeViewport2D| |ParCond| |viewDeltaXDefault| + |reshape| |cycle| |repeating?| |rightCharacteristicPolynomial| + |cPower| |parameters| |integrate| |sinhIfCan| |innerSolve1| + |constantKernel| |ef2edf| |unmakeSUP| |iicos| |discriminant| |int| + |slash| |light| |repSq| |e| |pmintegrate| |cAsin| |exQuo| + |insertRoot!| |createLowComplexityTable| |node| |gensym| + |invertibleElseSplit?| |makeEq| |atrapezoidal| |binaryTournament| + |cSin| |leadingExponent| |separate| |getMultiplicationMatrix| |cCosh| + |extendedint| |fixedPoint| |input| |legendre| |bits| |map| |critM| + |mainVariables| |cLog| |positiveSolve| |f01qef| |brace| |kernels| + |code| |library| |laplacian| |subHeight| |decomposeFunc| |generic| + |mkPrim| |rewriteIdealWithRemainder| |besselI| |writeUInt8!| |rischDE| + |update| |eq| |operator| |iiperm| |showSummary| |fortran| |dfRange| + |mainCoefficients| |bit?| |dual| |signatureAst| |interactiveEnv| + |crest| |f02fjf| |autoReduced?| |iter| |optimize| |coth2trigh| + |mkIntegral| |OMserve| |localUnquote| |generalizedEigenvector| + |complexEigenvectors| |select!| |coefficient| |f04mcf| |listLoops| + |conjugates| |logGamma| |tan2trig| |numerators| |assert| |printTypes| + |newSubProgram| |rewriteSetWithReduction| |leftRegularRepresentation| + |buildSyntax| |mkcomm| |continuedFraction| |transcendenceDegree| + |iroot| |convert| |listexp| |clipParametric| |diag| + |componentUpperBound| |RemainderList| |cyclotomicFactorization| + |splitLinear| |showAttributes| |fractionPart| |weighted| |level| + |cylindrical| |hostPlatform| |univariatePolynomialsGcds| + |removeSuperfluousCases| |complete| |position| |iiasec| + |removeRoughlyRedundantFactorsInPol| |karatsubaDivide| + |dimensionOfIrreducibleRepresentation| |makeFloatFunction| + |readUInt32!| |f04asf| |OMputObject| |primitiveElement| + |setAdaptive3D| |basisOfLeftAnnihilator| |approximants| |elliptic?| + |spherical| |explimitedint| |stoseInvertible?sqfreg| |cAsec| + |OMputVariable| |delay| |shrinkable| |OMreceive| |hermiteH| + |representationType| |compile| |saturate| |internalSubPolSet?| + |derivationCoordinates| |diagonal?| |exp| |basisOfCenter| + |createLowComplexityNormalBasis| |numeric| |principalIdeal| + |showTheFTable| |root| |maxint| |lifting1| |one?| |coefChoose| + |equation| |uncouplingMatrices| |rotate| |radical| |OMputEndAttr| + |lazy?| |lexTriangular| |selectFiniteRoutines| |removeZeroes| + |bracket| |merge!| |trace2PowMod| |bytes| |algebraicOf| |e01bff| + |irForm| |overlap| |extractPoint| |primes| + |halfExtendedSubResultantGcd2| |tracePowMod| |bfKeys| + |fortranCompilerName| |degree| |ricDsolve| |integerIfCan| + |gcdPolynomial| |OMgetError| |resetBadValues| |script| + |pseudoQuotient| |inf| |OMgetEndBVar| |getProperties| + |tryFunctionalDecomposition?| |e01daf| |measure| |sayLength| + |transcendent?| |tablePow| |printInfo| |clearFortranOutputStack| + |mainMonomials| |symmetricPower| |irCtor| |lexico| + |listRepresentation| |nonLinearPart| |rightExactQuotient| |cAtanh| + |imagi| |purelyAlgebraicLeadingMonomial?| |alphanumeric?| + |antisymmetric?| |totolex| |resultantnaif| + |rewriteIdealWithQuasiMonicGenerators| |mainForm| |minPol| |tex| + |socf2socdf| |mindeg| |over| |mapUnivariateIfCan| |symmetricTensors| + |showScalarValues| GF2FG |PDESolve| |nothing| |infieldint| |write!| + |cycleSplit!| |f04atf| |integral?| |elaboration| |getOperands| + |recolor| |quatern| |upDateBranches| |negative?| |viewport2D| + |applyRules| |leftLcm| |bringDown| |f04maf| |hcrf| |divideExponents| + |factorsOfDegree| |red| |completeSmith| |qelt| |bitLength| |e02def| + |setValue!| |defineProperty| |fillPascalTriangle| |row| |qsetelt| + |reverseLex| |cyclicEntries| |lookupFunction| |c06gcf| + |OMunhandledSymbol| |viewPosDefault| |pointLists| |symmetricGroup| + |innerEigenvectors| |airyBi| |type| |powerSum| + |getMultiplicationTable| |cCos| |isAnd| |rem| |xRange| + |addMatchRestricted| |alphabetic| |PollardSmallFactor| |e01baf| + |palgextint0| |divisors| |block| |besselY| |possiblyInfinite?| |quo| + |yRange| |charthRoot| |constantOpIfCan| |initial| |rightDiscriminant| + |diagonal| |commutativeEquality| |cons| |copyInto!| + |monomialIntegrate| |OMwrite| |zRange| |ode2| |pleskenSplit| + |getVariableOrder| |isOpen?| |wholeRadix| |dim| |map!| |qPot| |s17akf| + |baseRDE| |div| |high| |addBadValue| |SturmHabichtSequence| + |indiceSubResultantEuclidean| |mainVariable| |space| |qsetelt!| + |null?| |normalise| |exquo| |log2| |OMputFloat| |showAll?| + |lazyPremWithDefault| |updateStatus!| |prevPrime| |scale| ~= + |relationsIdeal| |s17ajf| |mindegTerm| |internal?| |cfirst| + |multiEuclideanTree| |complexElementary| |extendIfCan| |#| + |primPartElseUnitCanonical!| |univcase| |tubePointsDefault| + |topFortranOutputStack| |fullPartialFraction| |coercePreimagesImages| + |mapDown!| |zero| ~ |subCase?| |coerce| |setVariableOrder| + |nextPrimitiveNormalPoly| |iiabs| |showTheSymbolTable| |zCoord| + |source| |basisOfRightAnnihilator| |swapRows!| |f01mcf| |construct| + |completeHermite| |leftRecip| |univariate?| |eulerPhi| |relerror| + |And| |rk4f| |acsch| |elementary| |LyndonBasis| |nil?| |redpps| + |shape| |radicalOfLeftTraceForm| |/\\| |Or| |times!| |OMputEndError| + |primaryDecomp| |decrease| |mathieu24| |reducedSystem| |rk4qc| + |replace| |\\/| |Not| |c06eaf| |stoseInvertibleSetreg| |distance| + |clip| |back| |asimpson| |uniform| |cTanh| |structuralConstants| + |dflist| |supDimElseRittWu?| |nor| |maxrow| |target| |splitNodeOf!| + |numberOfOperations| |euler| |nthFlag| |rightTrace| |character?| + |s19acf| |square?| |taylorRep| |forLoop| |leadingTerm| |repeating| + |computeCycleLength| |debug3D| |normalForm| |squareFree| |close!| + |splitConstant| |parametric?| |initializeGroupForWordProblem| + |trigs2explogs| |shiftRoots| |scanOneDimSubspaces| |c05adf| |central?| + |factorSquareFree| |nonSingularModel| |addPoint2| |iisin| + |musserTrials| |elaborateFile| |f02bbf| |second| |open| |front| + |curve?| |tanNa| |Lazard| |polyPart| |generalizedInverse| |dimension| + |distribute| |f01bsf| |third| |fortranComplex| |linearPolynomials| + |points| |reducedQPowers| |squareFreePart| |inspect| + |rootOfIrreduciblePoly| |Nul| |s17aef| |ref| |cCsc| |epilogue| + |bumptab| |numberOfNormalPoly| |totalfract| |f02axf| |tanIfCan| |bag| + |critMonD1| |preprocess| |leftGcd| |mightHaveRoots| |iiGamma| |e01sef| + |reset| |iidsum| |resultant| |discreteLog| |bright| |operations| + |trailingCoefficient| |stoseInternalLastSubResultant| |bat1| + |mainCharacterization| |purelyAlgebraic?| F |lfextendedint| + |curryLeft| |simpleBounds?| |simplify| |digits| |OMgetEndApp| + |chineseRemainder| |pdct| |algebraicDecompose| |addPoint| |f07aef| + |getSyntaxFormsFromFile| |write| |tubePoints| |binary| |inc| |low| + |eval| |minordet| |duplicates| |rdHack1| |viewWriteDefault| + |createThreeSpace| |setelt| |save| |completeHensel| |s13aaf| + |binaryFunction| |algebraicCoefficients?| |taylorQuoByVar| |pade| |sn| + |quasiRegular| |adaptive3D?| |closedCurve| + |setLegalFortranSourceExtensions| |rowEchLocal| |iibinom| + |startStats!| |eigenvalues| |sub| |subResultantGcdEuclidean| + |roughSubIdeal?| |reduceLODE| |lowerCase| |thenBranch| + |removeRoughlyRedundantFactorsInContents| |copy| + |fortranDoubleComplex| |radicalEigenvector| |frobenius| + |tensorProduct| |lambert| |error| |isobaric?| |critMTonD1| + |algebraic?| |qinterval| |c06fqf| |semiResultantEuclidean1| + |acothIfCan| EQ |f01rdf| |shallowCopy| |truncate| |findBinding| + |support| UTS2UP |readLineIfCan!| |mainPrimitivePart| |extractIfCan| + |mesh| |upperCase!| |getRef| |s17ahf| |yCoordinates| |byteBuffer| + |content| |tubeRadius| |antiAssociative?| |rationalApproximation| + |cosIfCan| |reducedContinuedFraction| |root?| |lllip| |readLine!| + |merge| |virtualDegree| |myDegree| |numberOfFractionalTerms| + |factorGroebnerBasis| |OMgetEndBind| |traceMatrix| |fortranLiteral| + |generalizedContinuumHypothesisAssumed| |chvar| + |inputOutputBinaryFile| |match?| |seriesToOutputForm| + |firstSubsetGray| |completeEchelonBasis| |OMUnknownCD?| |iFTable| + |autoCoerce| |double?| |imagI| |delete!| |simplifyExp| |cycleTail| + |jacobian| |indicialEquations| |intChoose| |s14aaf| |pToHdmp| + |rationalPower| |linearDependence| |semicolonSeparate| |makeCos| + |numberOfMonomials| |polyRicDE| |roughEqualIdeals?| + |degreeSubResultantEuclidean| |stoseLastSubResultant| |scaleRoots| + |primextintfrac| |rischNormalize| + |rewriteSetByReducingWithParticularGenerators| |pushdterm| + |explicitlyFinite?| |sumSquares| |entries| |isAbsolutelyIrreducible?| + |nthExpon| |leftRemainder| |safeCeiling| |fractRagits| |decompose| + |outlineRender| |fill!| |rk4| |e02ahf| |weakBiRank| |cosSinInfo| + |binarySearchTree| |useSingleFactorBound?| |ffactor| |clearTheFTable| + |scalarTypeOf| |entry| |invertible?| |rightRemainder| |integer?| + |isOp| |randomLC| |rightScalarTimes!| |OMgetAtp| |elRow2!| + |laurentRep| |skewSFunction| |startTableGcd!| |shallowExpand| + |numberOfCycles| |currentCategoryFrame| |d02ejf| |top!| |palgextint| + |factors| |clearTheIFTable| |zerosOf| |listConjugateBases| |null| + |OMmakeConn| |meatAxe| |simpson| |odd?| |leftMult| + |removeRedundantFactorsInPols| |callForm?| |reseed| |goto| + |userOrdered?| |intensity| |pile| |not| |fixedDivisor| |se2rfi| + |normDeriv2| |polygon| |bubbleSort!| |roughUnitIdeal?| + |useSingleFactorBound| |euclideanGroebner| |c02agf| |getCurve| |and| + |initiallyReduce| |fortranCarriageReturn| |radicalEigenvalues| |real?| + |zeroDimPrime?| |linear?| |categories| |finiteBound| |d01apf| + |maxrank| |writeBytes!| |or| |delete| |lyndon?| |edf2fi| |rotate!| + |environment| |minimumExponent| |morphism| |directSum| |OMsetEncoding| + |rspace| |noLinearFactor?| |c06frf| |particularSolution| + |chainSubResultants| |cyclicParents| |singRicDE| |sincos| + |diagonalProduct| |shiftRight| |algebraicSort| |c06ebf| |sec2cos| + |graphs| |cycles| |graphState| |gradient| |whitePoint| |gcdprim| + |subresultantSequence| |factorSquareFreeByRecursion| + |singleFactorBound| |seed| |noValueMode| |subspace| |hclf| + |oblateSpheroidal| |s21bbf| |fixedPointExquo| |resultantEuclidean| + |symbol?| |numerator| |rightUnits| |orthonormalBasis| + |algebraicVariables| |var1Steps| |inverseLaplace| |OMputError| + |isQuotient| |qualifier| |setMaxPoints| |d03eef| |makingStats?| + |outputSpacing| |arrayStack| |rightRecip| |s14baf| + |extendedSubResultantGcd| |iisqrt2| |computeInt| |member?| |OMread| + |e04mbf| |fi2df| |lowerPolynomial| |basisOfMiddleNucleus| + |lazyIrreducibleFactors| |symmetric?| + |generalizedContinuumHypothesisAssumed?| |antiCommutative?| + |genericPosition| |generators| |rroot| |domainTemplate| + |factorSFBRlcUnit| |depth| |vark| |rewriteIdealWithHeadRemainder| + |SturmHabichtMultiple| |s17aff| |charClass| |sizeLess?| |palglimint| + |nullity| |cn| |viewZoomDefault| |s14abf| |totalDegree| |palglimint0| + |mapMatrixIfCan| |consnewpol| |vconcat| |height| |patternVariable| + |exponential| |numberOfComputedEntries| |dequeue!| |makeMulti| + |supersub| |nthRoot| |quasiMonic?| |extractProperty| |dequeue| |dec| + |coord| |sinhcosh| |zeroSetSplitIntoTriangularSystems| |conditionP| + |showClipRegion| |substitute| |pureLex| |inconsistent?| |fibonacci| + |scalarMatrix| |isAtom| |integralCoordinates| |rst| |rowEchelonLocal| + |middle| |log10| |c06fpf| |rarrow| |setMaxPoints3D| |algDsolve| + |minPoints3D| |antisymmetricTensors| |has?| |e02dcf| |bitand| + |enqueue!| |commutative?| |lastSubResultantEuclidean| |isExpt| + |besselK| |sample| |Aleph| |physicalLength!| |leadingIndex| + |internalIntegrate| |taylorIfCan| |anticoord| |doubleComplex?| + |d02kef| |logpart| |omError| |cyclicCopy| |complexRoots| |float?| + |realZeros| |OMgetEndObject| |unexpand| |patternMatchTimes| |curve| + |dAndcExp| |notelem| |karatsuba| |intPatternMatch| |updatF| + |removeRedundantFactors| |perfectNthRoot| |tube| |debug| |failed| + |max| |polyred| |less?| |quoted?| |optAttributes| + |showIntensityFunctions| |pointSizeDefault| |boundOfCauchy| + |substring?| D |in?| |contains?| |irreducibleRepresentation| + |subtractIfCan| |doubleDisc| |collect| |s17dcf| |laguerreL| + |numberOfPrimitivePoly| |monomials| |asinhIfCan| |subSet| + |trapezoidalo| |leftUnit| |bitCoef| |deref| |f02ajf| |suffix?| + |transcendentalDecompose| |bombieriNorm| |irreducible?| |contract| + |ip4Address| |heapSort| |listOfLists| |f07adf| |OMsupportsCD?| |nil| + |halfExtendedResultant1| |removeSuperfluousQuasiComponents| + |complexForm| |tail| |log| |appendPoint| |univariate| |prefix?| + |direction| |tanh2trigh| |order| |solveLinear| |coordinates| + |setProperties| |child| |rightTraceMatrix| |init| |OMgetString| + |poisson| |tryFunctionalDecomposition| |tRange| |mvar| |yellow| + |nullary| |macroExpand| |bivariate?| |setlast!| |outputBinaryFile| + |solid?| |lieAlgebra?| |c06gsf| |e01bgf| |varList| |s17acf| + |overlabel| |frst| |approximate| |extractSplittingLeaf| |phiCoord| + |binomial| |complexSolve| |coerceL| |toScale| |rootPower| |complex| + |is?| RF2UTS |graphCurves| |fprindINFO| |kmax| |paren| |orbit| + |extendedIntegrate| |var2Steps| |getGraph| |unrankImproperPartitions1| + |fortranCharacter| |mapBivariate| |complementaryBasis| + |discriminantEuclidean| |extractBottom!| |print| + |LagrangeInterpolation| |setScreenResolution| |polygamma| |properties| + |cAcot| |subscript| |beauzamyBound| |infix?| |interpretString| + |resolve| |squareFreeLexTriangular| |monic?| |nextIrreduciblePoly| + |translate| |iiacsc| |pmComplexintegrate| |iicot| |mask| |pr2dmp| + |declare| |solveLinearPolynomialEquationByFractions| |overbar| + |FormatRoman| |hostByteOrder| |intcompBasis| |screenResolution| + |rCoord| |roughBasicSet| |acoshIfCan| |triangular?| |squareTop| + |setStatus!| |createMultiplicationMatrix| |packageCall| |OMsend| + |f2df| |limitedint| |presub| |iilog| |lflimitedint| |e02ddf| + |genericRightNorm| |constDsolve| |shade| |mirror| |squareMatrix| + |regime| |resultantReduitEuclidean| |iiatanh| |SFunction| |mapdiv| GE + |weights| |basis| |encodingDirectory| |factorPolynomial| |concat!| + |externalList| |s15adf| |rootNormalize| GT |twoFactor| + |partialQuotients| |f02awf| |delta| |sortConstraints| |generalSqFr| + |branchPoint?| |s21baf| |dualSignature| |say| |eulerE| + |expressIdealMember| LE |wordInGenerators| |pushdown| |ScanRoman| + |iflist2Result| |maxColIndex| |nary?| |iCompose| LT + |startTableInvSet!| |trunc| |subResultantGcd| |factorials| |indices| + |processTemplate| |elliptic| |initTable!| |doubleResultant| + |removeConstantTerm| |plus| |basisOfLeftNucloid| |commutator| + |stopTableGcd!| |zero?| |addmod| |s21bcf| |size?| |leftOne| |e01sff| + |OMgetEndAtp| |setMinPoints3D| |find| |unaryFunction| |normalDenom| + |shift| |eisensteinIrreducible?| |complexLimit| |e01saf| |readBytes!| + |pushNewContour| |makeYoungTableau| |remove| |lazyPseudoDivide| + |cross| |wronskianMatrix| |coHeight| |graeffe| |string?| + |exactQuotient!| |stFuncN| |infiniteProduct| |palgintegrate| + |ReduceOrder| |putProperty| |divisor| |tanQ| |times| + |hypergeometric0F1| |permutation| |removeSquaresIfCan| |newLine| + |last| |exptMod| |listBranches| |selectPDERoutines| |e02bbf| + |normal01| |generator| |youngGroup| |iicsch| |mantissa| |setref| + |quadratic| |enterPointData| |quotedOperators| |assoc| |att2Result| + |antiCommutator| |readUInt16!| |lastSubResultantElseSplit| + |selectsecond| |getCode| |palgLODE0| |cAsech| |elRow1!| |df2fi| + |bandedJacobian| |fortranTypeOf| |s13adf| |infRittWu?| |elaborate| + |zeroSquareMatrix| BY |any?| |shiftLeft| |nthExponent| |condition| + |trigs| |sech2cosh| |capacity| |crushedSet| |multinomial| |monom| + |complexIntegrate| |nodeOf?| |argumentListOf| |chiSquare| + |drawToScale| |transform| |iiasinh| |open?| |ratDsolve| |OMgetInteger| + |factorOfDegree| |categoryMode| |minColIndex| |f02xef| |simpsono| + |sin?| |cycleRagits| |checkForZero| |approxSqrt| |elseBranch| |bsolve| + |exprToUPS| |erf| |lazyPseudoRemainder| |pastel| |dmp2rfi| |output| + |rootDirectory| |common| |pascalTriangle| |mappingAst| + |perfectSquare?| |realEigenvalues| |OMgetFloat| |bernoulliB| + |eigenMatrix| |increment| |blankSeparate| |matrixGcd| |setButtonValue| + |genericRightMinimalPolynomial| |lexGroebner| |swap| |constant| + |s01eaf| |rightLcm| |clipBoolean| |setUnion| |constructor| + |removeDuplicates!| |internalDecompose| |balancedBinaryTree| |stFunc2| + |pointColorDefault| |dilog| |normalizedDivide| NOT |viewDefaults| + |f02wef| |internalSubQuasiComponent?| |OMcloseConn| |incr| |distFact| + |infinityNorm| |nextPrime| |cyclotomic| |sin| |factorList| |function| + |lastSubResultant| OR |mainKernel| |f02adf| |iisech| |hi| + |duplicates?| |solveInField| |getPickedPoints| |acscIfCan| |cos| + |lintgcd| |expintfldpoly| |maximumExponent| AND |rightTrim| + |diagonals| |getOperator| |aromberg| |d01alf| |OMputApp| + |nextsousResultant2| |tan| |gbasis| |setOrder| |generic?| |isNot| + |leftTrim| |jokerMode| |pointPlot| |postfix| |deriv| |ksec| |cot| + |lifting| |mainDefiningPolynomial| |probablyZeroDim?| |coshIfCan| + |getExplanations| |irreducibleFactors| |LyndonCoordinates| |e04jaf| + |component| |sec| |unary?| |noncommutativeJordanAlgebra?| |rightNorm| + |unparse| |matrixDimensions| |numFunEvals| |rootPoly| |collectUpper| + |upperBound| |csc| |symbol| |ptFunc| |squareFreePolynomial| + |hyperelliptic| |basicSet| |raisePolynomial| |plenaryPower| |inverse| + |minGbasis| |B1solve| |subset?| |asin| |expression| |enumerate| + |transpose| |e02baf| |vectorise| |updatD| |deepestInitial| + |padicallyExpand| |ScanFloatIgnoreSpaces| |infinite?| |point?| |acos| + |iiasin| |integer| |stopTableInvSet!| |destruct| |iiatan| |rightZero| + |inputBinaryFile| |radicalRoots| |singular?| |toseInvertible?| |iitan| + |atan| |rur| |triangSolve| |s17agf| |mpsode| |modulus| + |genericRightTraceForm| |fglmIfCan| |abs| |ScanArabic| |acot| + |number?| |geometric| |alternatingGroup| |setchildren!| |moduleSum| + |readInt8!| |leftNorm| |expt| |lllp| |asec| |f07fdf| + |nextsubResultant2| * |redmat| |addPointLast| |d01gaf| |lhs| |d01aqf| + |typeList| |makeSUP| |distdfact| |acsc| |principal?| |lcm| + |lazyResidueClass| |removeDuplicates| |cscIfCan| |Is| |rhs| |OMgetApp| + |noKaratsuba| |setrest!| |powerAssociative?| |sinh| |cyclicGroup| + |stFunc1| |selectSumOfSquaresRoutines| |fmecg| |inverseIntegralMatrix| + |generate| |e04ycf| |unravel| |monicRightFactorIfCan| |primlimitedint| + |varselect| |cosh| |append| |var1StepsDefault| |hash| |coordinate| = + |mainMonomial| |currentEnv| |OMencodingSGML| |clipWithRanges| + |useNagFunctions| |copies| |pattern| |fortranLinkerArgs| |tanh| + |subscriptedVariables| |decimal| |e04naf| |gcd| |count| + |nextPartition| |incrementBy| |c06gqf| |sumOfSquares| |karatsubaOnce| + |pow| |extractIndex| |quasiMonicPolynomials| |fracPart| |coth| + |constantIfCan| |false| |lp| < |nextColeman| |symFunc| + |extensionDegree| |expand| |category| |palgRDE| |s17adf| + |indicialEquation| |ptree| LODO2FUN |atom?| |summation| |flatten| + |subResultantsChain| |aQuadratic| |cycleLength| > |mapSolve| + |changeName| |filterWhile| |domain| |separateDegrees| |cAcos| + |adjoint| |loadNativeModule| |leftScalarTimes!| |iicosh| |limit| + |pushucoef| |property| <= |changeMeasure| |writable?| |filterUntil| + |package| |factorsOfCyclicGroupSize| |outputFloating| |quotientByP| + |message| |rk4a| |factorAndSplit| |irVar| |normInvertible?| |imagE| + |writeInt8!| >= |zeroDim?| |select| |dmpToHdmp| |computeBasis| + |setClosed| |integralMatrix| |rootSplit| |horizConcat| |f04jgf| + |nextSublist| |e01bhf| |s18dcf| |cSec| |double| |pack!| |setFormula!| + |innerSolve| |readByte!| |validExponential| |torsionIfCan| |lazyPquo| + |quoByVar| |logIfCan| |cot2tan| |setvalue!| |endOfFile?| + |wordInStrongGenerators| |coerceImages| |dihedral| |parents| + |stiffnessAndStabilityOfODEIF| |createNormalElement| |leadingSupport| + |bitTruth| |complexNumericIfCan| + |leaf?| |list?| |leastPower| + |headReduced?| |nthr| |euclideanSize| |associative?| |d01anf| |prem| + |setelt!| - |cExp| |reduced?| |functorData| |e04fdf| |scan| + |setAttributeButtonStep| |sqfrFactor| |divide| |indiceSubResultant| / + |stronglyReduce| |createNormalPrimitivePoly| |someBasis| |palgint0| + |rule| |normalize| |setScreenResolution3D| |compound?| + |pointColorPalette| |factorset| |makeRecord| |OMUnknownSymbol?| + |getDatabase| |s19adf| |symmetricDifference| |setTex!| + |genericLeftMinimalPolynomial| |ranges| |swap!| |c05pbf| + |outerProduct| |disjunction| |moduloP| |doublyTransitive?| |npcoef| + |jordanAlgebra?| |factor1| |f01ref| |unit?| |fixedPoints| + |basisOfRightNucleus| |declare!| |inHallBasis?| |minimumDegree| + |groebnerIdeal| |normFactors| |unitNormalize| |fortranReal| + |completeEval| |commonDenominator| |elem?| |Lazard2| |operation| + |interReduce| |move| |bothWays| |perspective| |complex?| + |stoseIntegralLastSubResultant| |setsubMatrix!| |wholePart| + |Vectorise| |cartesian| |octon| |henselFact| |bigEndian| |fullDisplay| + |backOldPos| |kroneckerDelta| |rename!| |primitive?| |rules| + |associator| |removeSinhSq| |collectQuasiMonic| |e02daf| + |outputGeneral| |normalElement| |maxRowIndex| |jacobi| |cCsch| + |prinpolINFO| |head| |diagonalMatrix| |generateIrredPoly| + |OMgetEndAttr| |harmonic| |step| |errorInfo| |rdregime| + |OMlistSymbols| |extract!| |xn| |stosePrepareSubResAlgo| + |rightRankPolynomial| |cyclePartition| |hdmpToDmp| |f04arf| + |errorKind| |s19abf| |setright!| |critB| |linears| |idealiserMatrix| + |zeroDimPrimary?| |alternative?| |janko2| |OMputString| |even?| + |ListOfTerms| |style| |segment| |voidMode| |conjug| |dihedralGroup| + |zeroSetSplit| |zag| |radicalEigenvectors| |integral| |setAdaptive| + |balancedFactorisation| |indicialEquationAtInfinity| |conical| |norm| + |deleteRoutine!| |semiSubResultantGcdEuclidean1| + |permutationRepresentation| |clearDenominator| |leftZero| + |createGenericMatrix| |rationalFunction| |reflect| |parseString| + |multisect| |reciprocalPolynomial| |splitSquarefree| |insertBottom!| + |unitCanonical| |lfinfieldint| |cAcsch| |expintegrate| |option?| + |messagePrint| |curveColor| |belong?| |numericIfCan| |trapezoidal| + |pseudoRemainder| |sPol| |conjunction| |midpoint| |stoseInvertibleSet| + |zeroMatrix| |randnum| |connectTo| |changeWeightLevel| |key| |pToDmp| + |e02adf| |monicDivide| |ignore?| |power| |subNode?| |f01maf| + |polynomialZeros| |rightExtendedGcd| |multiset| |polar| + |jacobiIdentity?| |denomLODE| |totalLex| |value| |KrullNumber| + |augment| |OMReadError?| |definingPolynomial| |filename| |calcRanges| + |leftFactorIfCan| |OMreadStr| |evaluateInverse| |gethi| + |exprHasAlgebraicWeight| |po| |c06ecf| |BumInSepFFE| |const| + |optional| |formula| |extendedResultant| |var2StepsDefault| + |stopMusserTrials| |integralBasis| |absolutelyIrreducible?| |d03faf| + |littleEndian| |padicFraction| |numberOfIrreduciblePoly| |s13acf| + |parse| |unprotectedRemoveRedundantFactors| |linearlyDependentOverZ?| + |exprHasLogarithmicWeights| |sup| |cAcsc| |f02bjf| |ratpart| |twist| + |HermiteIntegrate| |OMconnInDevice| |df2ef| |stop| |tanAn| + |curryRight| |tableau| |arguments| |isImplies| |rational?| + |endSubProgram| |mr| |plotPolar| |relativeApprox| |goodPoint| + |rationalPoints| |d02raf| |setPrologue!| |infieldIntegrate| + |numberOfComponents| |rightQuotient| |xCoord| |lfintegrate| + |headReduce| |nrows| |symmetricSquare| |nativeModuleExtension| + |putProperties| |cothIfCan| |complement| |every?| |expextendedint| + |orbits| |selectAndPolynomials| |alphanumeric| |hasPredicate?| |ncols| + |result| |basisOfCentroid| |exprex| |cSech| |presuper| + |linearlyDependent?| |mapUp!| |explogs2trigs| |part?| |e02bdf| + |solveLinearPolynomialEquation| |pole?| |evaluate| |adaptive?| + |csc2sin| |qfactor| |nextLatticePermutation| |connect| |btwFact| + |tan2cot| |hasTopPredicate?| |monomRDE| |divergence| + |rightFactorIfCan| |monicLeftDivide| |divideIfCan| |getBadValues| + |smith| |tower| |solveLinearPolynomialEquationByRecursion| + |minimalPolynomial| |OMputEndBVar| |inR?| |quasiComponent| |s20adf| + |OMbindTCP| |fTable| |aQuartic| |Ci| |roman| |characteristic| + |bindings| |prod| |testDim| |divideIfCan!| |OMopenFile| |fixPredicate| + |accuracyIF| |expandTrigProducts| |functionIsContinuousAtEndPoints| + |OMencodingBinary| |quasiAlgebraicSet| |taylor| |comment| |index?| + |enterInCache| |pointData| |mainSquareFreePart| |compose| + |mainVariable?| |bezoutResultant| |isOr| |rubiksGroup| + |rectangularMatrix| |divisorCascade| |laurent| |imaginary| |scopes| + |iiasech| |returns| |setFieldInfo| |determinant| |derivative| + |collectUnder| |makeSketch| |realSolve| |whileLoop| |puiseux| + |credPol| |hessian| |fintegrate| |Hausdorff| |permutations| |matrix| + |region| |index| |compdegd| |integralDerivationMatrix| |rischDEsys| + |hex| |iExquo| |solveLinearlyOverQ| |lambda| |read!| |isConnected?| + |isMult| |removeZero| |primintegrate| |exactQuotient| + |differentialVariables| |leadingBasisTerm| + |semiResultantEuclideannaif| |leadingCoefficientRicDE| |components| + |equality| |inv| |sparsityIF| |Frobenius| |leftUnits| |currentScope| + |contractSolve| |showRegion| |ground?| FG2F |monicRightDivide| + |uniform01| |hermite| |superscript| |bernoulli| |subTriSet?| |laplace| + |d02cjf| |stoseInvertible?reg| |setEpilogue!| |closedCurve?| + |startTable!| |pair| |ldf2lst| |ground| |palgRDE0| |iterationVar| + |associates?| |linGenPos| |FormatArabic| |multiple?| |simplifyPower| + |triangulate| |tubePlot| |pomopo!| |showTheIFTable| + |clearTheSymbolTable| |directory| |safetyMargin| |ridHack1| + |groebnerFactorize| |writeLine!| |setRealSteps| |leadingMonomial| + |binding| |bipolarCylindrical| |minimize| |mulmod| |submod| |csubst| + |sum| |reducedForm| |mathieu22| |univariatePolynomial| |problemPoints| + |reverse| |mathieu11| |leadingCoefficient| |createNormalPoly| |lquo| + |inRadical?| |An| |rightMult| |evenlambert| |iidprod| |iomode| + |primitivePart| |rightOne| |curry| |primitiveMonomials| + |countRealRoots| |unknownEndian| |position!| |f01qcf| |makeViewport3D| + |kovacic| |setOfMinN| |powmod| |retract| |combineFeatureCompatibility| + |modifyPointData| |coth2tanh| |multiplyCoefficients| |scripted?| + |reductum| |copy!| |e02bef| |upperCase| |assign| |deepestTail| + |parametersOf| |OMgetSymbol| |rank| |OMsupportsSymbol?| |padecf| + |just| |restorePrecision| |tableForDiscreteLogarithm| |graphImage| + |f02akf| |companionBlocks| |lazyPrem| |withPredicates| |monomial?| + |node?| |palgLODE| |readIfCan!| |binaryTree| |hitherPlane| + |partitions| |dioSolve| |generalizedEigenvectors| |getStream| + |asinIfCan| |minPoints| |sh| |LazardQuotient2| |partialDenominators| + |viewSizeDefault| |increasePrecision| |reduceByQuasiMonic| + |algSplitSimple| |modularGcd| |closed| |OMputEndApp| |s18acf| + |getOrder| |changeVar| |lazyVariations| |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) ((-907 (-1186)) |has| |#1| (-907 (-1186))) ((-893 (-384)) |has| |#1| (-893 (-384))) ((-893 (-570)) |has| |#1| (-893 (-570))) ((-891 |#1|) . T) ((-916) -12 (|has| |#1| (-311)) (|has| |#1| (-916))) ((-927) -3684 (|has| |#1| (-354)) (|has| |#1| (-368)) (|has| |#1| (-311))) ((-1011) -12 (|has| |#1| (-1011)) (|has| |#1| (-1212))) ((-1047 (-413 (-570))) |has| |#1| (-1047 (-413 (-570)))) ((-1047 (-570)) |has| |#1| (-1047 (-570))) ((-1047 |#1|) . T) ((-1060 #0#) -3684 (|has| |#1| (-354)) (|has| |#1| (-368))) ((-1060 |#1|) . T) ((-1060 $) . T) ((-1065 #0#) -3684 (|has| |#1| (-354)) (|has| |#1| (-368))) ((-1065 |#1|) . T) ((-1065 $) . T) ((-1058) . T) ((-1067) . T) ((-1121) . T) ((-1109) . T) ((-1161) |has| |#1| (-354)) ((-1212) |has| |#1| (-1212)) ((-1215) |has| |#1| (-1212)) ((-1227) . 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T) ((-174) |has| |#2| (-174)) ((-233 |#2|) |has| |#2| (-1058)) ((-235) -12 (|has| |#2| (-235)) (|has| |#2| (-1058))) ((-290 #1=(-570) |#2|) . T) ((-292 #1# |#2|) . T) ((-313 |#2|) -12 (|has| |#2| (-313 |#2|)) (|has| |#2| (-1109))) ((-373) |has| |#2| (-373)) ((-382 |#2|) |has| |#2| (-1058)) ((-417 |#2|) |has| |#2| (-1109)) ((-495 |#2|) . T) ((-610 #1# |#2|) . T) ((-520 |#2| |#2|) -12 (|has| |#2| (-313 |#2|)) (|has| |#2| (-1109))) ((-652 (-570)) -2811 (|has| |#2| (-1058)) (|has| |#2| (-854)) (|has| |#2| (-368)) (|has| |#2| (-174))) ((-652 |#2|) -2811 (|has| |#2| (-1058)) (|has| |#2| (-368)) (|has| |#2| (-174))) ((-652 $) -2811 (|has| |#2| (-1058)) (|has| |#2| (-854)) (|has| |#2| (-174))) ((-654 |#2|) -2811 (|has| |#2| (-1058)) (|has| |#2| (-368)) (|has| |#2| (-174))) ((-654 $) -2811 (|has| |#2| (-1058)) (|has| |#2| (-854)) (|has| |#2| (-174))) ((-646 |#2|) -2811 (|has| |#2| (-368)) (|has| |#2| (-174))) ((-645 (-570)) -12 (|has| |#2| (-645 (-570))) (|has| |#2| (-1058))) ((-645 |#2|) |has| |#2| (-1058)) ((-723 |#2|) -2811 (|has| |#2| (-368)) (|has| |#2| (-174))) ((-732) -2811 (|has| |#2| (-1058)) (|has| |#2| (-854)) (|has| |#2| (-732)) (|has| |#2| (-174))) ((-797) |has| |#2| (-854)) ((-798) -2811 (|has| |#2| (-854)) (|has| |#2| (-799))) ((-799) |has| |#2| (-799)) ((-800) -2811 (|has| |#2| (-854)) (|has| |#2| (-799))) ((-801) -2811 (|has| |#2| (-854)) (|has| |#2| (-799))) ((-854) |has| |#2| (-854)) ((-856) -2811 (|has| |#2| (-854)) (|has| |#2| (-799))) ((-907 (-1186)) -12 (|has| |#2| (-907 (-1186))) (|has| |#2| (-1058))) ((-1047 #0#) -12 (|has| |#2| (-1047 (-413 (-570)))) (|has| |#2| (-1109))) ((-1047 (-570)) -12 (|has| |#2| (-1047 (-570))) (|has| |#2| (-1109))) ((-1047 |#2|) |has| |#2| (-1109)) ((-1060 |#2|) -2811 (|has| |#2| (-1058)) (|has| |#2| (-368)) (|has| |#2| (-174))) ((-1060 $) |has| |#2| (-174)) ((-1065 |#2|) -2811 (|has| |#2| (-1058)) (|has| |#2| (-368)) (|has| |#2| (-174))) ((-1065 $) |has| |#2| (-174)) ((-1058) -2811 (|has| |#2| (-1058)) (|has| |#2| (-854)) (|has| |#2| (-174))) ((-1067) -2811 (|has| |#2| (-1058)) (|has| |#2| (-854)) (|has| |#2| (-174))) ((-1121) -2811 (|has| |#2| (-1058)) (|has| |#2| (-854)) (|has| |#2| (-732)) (|has| |#2| (-174))) ((-1109) -2811 (|has| |#2| (-1109)) (|has| |#2| (-1058)) (|has| |#2| (-854)) (|has| |#2| (-799)) (|has| |#2| (-732)) (|has| |#2| (-373)) (|has| |#2| (-368)) (|has| |#2| (-174)) (|has| |#2| (-132)) (|has| |#2| (-25))) ((-1227) . T) ((-1284 |#2|) |has| |#2| (-368))) -((-4406 (((-242 |#1| |#3|) (-1 |#3| |#2| |#3|) (-242 |#1| |#2|) |#3|) 21)) (-2507 ((|#3| (-1 |#3| |#2| |#3|) (-242 |#1| |#2|) |#3|) 23)) (-3025 (((-242 |#1| |#3|) (-1 |#3| |#2|) (-242 |#1| |#2|)) 18))) -(((-241 |#1| |#2| |#3|) (-10 -7 (-15 -4406 ((-242 |#1| |#3|) (-1 |#3| |#2| |#3|) (-242 |#1| |#2|) |#3|)) (-15 -2507 (|#3| (-1 |#3| |#2| |#3|) (-242 |#1| |#2|) |#3|)) (-15 -3025 ((-242 |#1| |#3|) (-1 |#3| |#2|) (-242 |#1| |#2|)))) (-777) (-1227) (-1227)) (T -241)) -((-3025 (*1 *2 *3 *4) (-12 (-5 *3 (-1 *7 *6)) (-5 *4 (-242 *5 *6)) (-14 *5 (-777)) (-4 *6 (-1227)) (-4 *7 (-1227)) (-5 *2 (-242 *5 *7)) (-5 *1 (-241 *5 *6 *7)))) (-2507 (*1 *2 *3 *4 *2) (-12 (-5 *3 (-1 *2 *6 *2)) (-5 *4 (-242 *5 *6)) (-14 *5 (-777)) (-4 *6 (-1227)) (-4 *2 (-1227)) (-5 *1 (-241 *5 *6 *2)))) (-4406 (*1 *2 *3 *4 *5) (-12 (-5 *3 (-1 *5 *7 *5)) (-5 *4 (-242 *6 *7)) (-14 *6 (-777)) (-4 *7 (-1227)) (-4 *5 (-1227)) (-5 *2 (-242 *6 *5)) (-5 *1 (-241 *6 *7 *5))))) -(-10 -7 (-15 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(|has| |t#2| (-132)) (-6 (-132)) |%noBranch|) (IF (|has| |t#2| (-732)) (PROGN (-6 (-732)) (-15 * ($ |t#2| $)) (-15 * ($ $ |t#2|))) |%noBranch|) (IF (|has| |t#2| (-373)) (-6 (-373)) |%noBranch|) (IF (|has| |t#2| (-174)) (PROGN (-6 (-38 |t#2|)) (-6 (-174))) |%noBranch|) (IF (|has| |t#2| (-6 -4449)) (-6 -4449) |%noBranch|) (IF (|has| |t#2| (-854)) (-6 (-854)) |%noBranch|) (IF (|has| |t#2| (-799)) (-6 (-799)) |%noBranch|) (IF (|has| |t#2| (-368)) (-6 (-1284 |t#2|)) |%noBranch|))) +(((-21) -3684 (|has| |#2| (-1058)) (|has| |#2| (-854)) (|has| |#2| (-368)) (|has| |#2| (-174))) ((-23) -3684 (|has| |#2| (-1058)) (|has| |#2| (-854)) (|has| |#2| (-799)) (|has| |#2| (-368)) (|has| |#2| (-174)) (|has| |#2| (-132))) ((-25) -3684 (|has| |#2| (-1058)) (|has| |#2| (-854)) (|has| |#2| (-799)) (|has| |#2| (-368)) (|has| |#2| (-174)) (|has| |#2| (-132)) (|has| |#2| (-25))) ((-34) . T) ((-38 |#2|) |has| |#2| (-174)) ((-102) -3684 (|has| |#2| (-1109)) (|has| |#2| (-1058)) (|has| |#2| (-854)) (|has| |#2| (-799)) (|has| |#2| (-732)) (|has| |#2| (-373)) (|has| |#2| (-368)) (|has| |#2| (-174)) (|has| |#2| (-132)) (|has| |#2| (-25))) ((-111 |#2| |#2|) -3684 (|has| |#2| (-1058)) (|has| |#2| (-368)) (|has| |#2| (-174))) ((-111 $ $) |has| |#2| (-174)) ((-132) -3684 (|has| |#2| (-1058)) (|has| |#2| (-854)) (|has| |#2| (-799)) (|has| |#2| (-368)) (|has| |#2| (-174)) (|has| |#2| (-132))) ((-622 #0=(-413 (-570))) -12 (|has| |#2| (-1047 (-413 (-570)))) (|has| |#2| (-1109))) ((-622 (-570)) -3684 (|has| |#2| (-1058)) (-12 (|has| |#2| (-1047 (-570))) (|has| |#2| (-1109))) (|has| |#2| (-854)) (|has| |#2| (-174))) ((-622 |#2|) -3684 (|has| |#2| (-1109)) (|has| |#2| (-174))) ((-619 (-868)) -3684 (|has| |#2| (-1109)) (|has| |#2| (-1058)) (|has| |#2| (-854)) (|has| |#2| (-799)) (|has| |#2| (-732)) (|has| |#2| (-373)) (|has| |#2| (-368)) (|has| |#2| (-174)) (|has| |#2| (-619 (-868))) (|has| |#2| (-132)) (|has| |#2| (-25))) ((-619 (-1277 |#2|)) . T) ((-174) |has| |#2| (-174)) ((-233 |#2|) |has| |#2| (-1058)) ((-235) -12 (|has| |#2| (-235)) (|has| |#2| (-1058))) ((-290 #1=(-570) |#2|) . T) ((-292 #1# |#2|) . T) ((-313 |#2|) -12 (|has| |#2| (-313 |#2|)) (|has| |#2| (-1109))) ((-373) |has| |#2| (-373)) ((-382 |#2|) |has| |#2| (-1058)) ((-417 |#2|) |has| |#2| (-1109)) ((-495 |#2|) . T) ((-610 #1# |#2|) . T) ((-520 |#2| |#2|) -12 (|has| |#2| (-313 |#2|)) (|has| |#2| (-1109))) ((-652 (-570)) -3684 (|has| |#2| (-1058)) (|has| |#2| (-854)) (|has| |#2| (-368)) (|has| |#2| (-174))) ((-652 |#2|) -3684 (|has| |#2| (-1058)) (|has| |#2| (-368)) (|has| |#2| (-174))) ((-652 $) -3684 (|has| |#2| (-1058)) (|has| |#2| (-854)) (|has| |#2| (-174))) ((-654 |#2|) -3684 (|has| |#2| (-1058)) (|has| |#2| (-368)) (|has| |#2| (-174))) ((-654 $) -3684 (|has| |#2| (-1058)) (|has| |#2| (-854)) (|has| |#2| (-174))) ((-646 |#2|) -3684 (|has| |#2| (-368)) (|has| |#2| (-174))) ((-645 (-570)) -12 (|has| |#2| (-645 (-570))) (|has| |#2| (-1058))) ((-645 |#2|) |has| |#2| (-1058)) ((-723 |#2|) -3684 (|has| |#2| (-368)) (|has| |#2| (-174))) ((-732) -3684 (|has| |#2| (-1058)) (|has| |#2| (-854)) (|has| |#2| (-732)) (|has| |#2| (-174))) ((-797) |has| |#2| (-854)) ((-798) -3684 (|has| |#2| (-854)) (|has| |#2| (-799))) ((-799) |has| |#2| (-799)) ((-800) -3684 (|has| |#2| (-854)) (|has| |#2| (-799))) ((-801) -3684 (|has| |#2| (-854)) (|has| |#2| (-799))) ((-854) |has| |#2| (-854)) ((-856) -3684 (|has| |#2| (-854)) (|has| |#2| (-799))) ((-907 (-1186)) -12 (|has| |#2| (-907 (-1186))) (|has| |#2| (-1058))) ((-1047 #0#) -12 (|has| |#2| (-1047 (-413 (-570)))) (|has| |#2| (-1109))) ((-1047 (-570)) -12 (|has| |#2| (-1047 (-570))) (|has| |#2| (-1109))) ((-1047 |#2|) |has| |#2| (-1109)) ((-1060 |#2|) -3684 (|has| |#2| (-1058)) (|has| |#2| (-368)) (|has| |#2| (-174))) ((-1060 $) |has| |#2| (-174)) ((-1065 |#2|) -3684 (|has| |#2| (-1058)) (|has| |#2| (-368)) (|has| |#2| (-174))) ((-1065 $) |has| |#2| (-174)) ((-1058) -3684 (|has| |#2| (-1058)) (|has| |#2| (-854)) (|has| |#2| (-174))) ((-1067) -3684 (|has| |#2| (-1058)) (|has| |#2| (-854)) (|has| |#2| (-174))) ((-1121) -3684 (|has| |#2| (-1058)) (|has| |#2| (-854)) (|has| |#2| (-732)) (|has| |#2| (-174))) ((-1109) -3684 (|has| |#2| (-1109)) (|has| |#2| (-1058)) (|has| |#2| (-854)) (|has| |#2| (-799)) (|has| |#2| (-732)) (|has| |#2| (-373)) (|has| |#2| (-368)) (|has| |#2| (-174)) (|has| |#2| (-132)) (|has| |#2| (-25))) ((-1227) . 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T) ((-23) . T) ((-47 |#1| #0=(-413 (-570))) . T) ((-25) . T) ((-38 #1=(-413 (-570))) -2811 (|has| |#1| (-368)) (|has| |#1| (-38 (-413 (-570))))) ((-38 |#1|) |has| |#1| (-174)) ((-38 $) -2811 (|has| |#1| (-562)) (|has| |#1| (-368))) ((-35) |has| |#1| (-38 (-413 (-570)))) ((-95) |has| |#1| (-38 (-413 (-570)))) ((-102) . T) ((-111 #1# #1#) -2811 (|has| |#1| (-368)) (|has| |#1| (-38 (-413 (-570))))) ((-111 |#1| |#1|) . T) ((-111 $ $) -2811 (|has| |#1| (-562)) (|has| |#1| (-368)) (|has| |#1| (-174))) ((-132) . T) ((-146) |has| |#1| (-146)) ((-148) |has| |#1| (-148)) ((-622 #1#) -2811 (|has| |#1| (-368)) (|has| |#1| (-38 (-413 (-570))))) ((-622 (-570)) . T) ((-622 |#1|) |has| |#1| (-174)) ((-622 $) -2811 (|has| |#1| (-562)) (|has| |#1| (-368))) ((-619 (-868)) . T) ((-174) -2811 (|has| |#1| (-562)) (|has| |#1| (-368)) (|has| |#1| (-174))) ((-235) |has| |#1| (-15 * (|#1| (-413 (-570)) |#1|))) ((-245) |has| |#1| (-368)) ((-288) |has| |#1| (-38 (-413 (-570)))) ((-290 #0# |#1|) . 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"TS" 2941683 NIL TS (NIL T) -8 NIL NIL NIL) (-1220 2925300 2929419 2929516 "TSETCAT" 2934785 NIL TSETCAT (NIL T T T T) -9 NIL 2936316 NIL) (-1219 2920032 2921632 2923523 "TSETCAT-" 2923528 NIL TSETCAT- (NIL T T T T T) -8 NIL NIL NIL) (-1218 2914671 2915518 2916447 "TRMANIP" 2919168 NIL TRMANIP (NIL T T) -7 NIL NIL NIL) (-1217 2914112 2914175 2914338 "TRIMAT" 2914603 NIL TRIMAT (NIL T T T T) -7 NIL NIL NIL) (-1216 2911978 2912215 2912572 "TRIGMNIP" 2913861 NIL TRIGMNIP (NIL T T) -7 NIL NIL NIL) (-1215 2911498 2911611 2911641 "TRIGCAT" 2911854 T TRIGCAT (NIL) -9 NIL NIL NIL) (-1214 2911167 2911246 2911387 "TRIGCAT-" 2911392 NIL TRIGCAT- (NIL T) -8 NIL NIL NIL) (-1213 2908012 2910025 2910306 "TREE" 2910921 NIL TREE (NIL T) -8 NIL NIL NIL) (-1212 2907286 2907814 2907844 "TRANFUN" 2907879 T TRANFUN (NIL) -9 NIL 2907945 NIL) (-1211 2906565 2906756 2907036 "TRANFUN-" 2907041 NIL TRANFUN- (NIL T) -8 NIL NIL NIL) (-1210 2906369 2906401 2906462 "TOPSP" 2906526 T TOPSP (NIL) -7 NIL NIL NIL) (-1209 2905717 2905832 2905986 "TOOLSIGN" 2906250 NIL TOOLSIGN (NIL T) -7 NIL NIL NIL) (-1208 2904351 2904894 2905133 "TEXTFILE" 2905500 T TEXTFILE (NIL) -8 NIL NIL NIL) (-1207 2902263 2902804 2903233 "TEX" 2903944 T TEX (NIL) -8 NIL NIL NIL) (-1206 2902044 2902075 2902147 "TEX1" 2902226 NIL TEX1 (NIL T) -7 NIL NIL NIL) (-1205 2901692 2901755 2901845 "TEMUTL" 2901976 T TEMUTL (NIL) -7 NIL NIL NIL) (-1204 2899846 2900126 2900451 "TBCMPPK" 2901415 NIL TBCMPPK (NIL T T) -7 NIL NIL NIL) (-1203 2891623 2898006 2898062 "TBAGG" 2898462 NIL TBAGG (NIL T T) -9 NIL 2898673 NIL) (-1202 2886693 2888181 2889935 "TBAGG-" 2889940 NIL TBAGG- (NIL T T T) -8 NIL NIL NIL) (-1201 2886077 2886184 2886329 "TANEXP" 2886582 NIL TANEXP (NIL T) -7 NIL NIL NIL) (-1200 2885588 2885852 2885942 "TALGOP" 2886022 NIL TALGOP (NIL T) -8 NIL NIL NIL) (-1199 2878978 2885445 2885538 "TABLE" 2885543 NIL TABLE (NIL T T) -8 NIL NIL NIL) (-1198 2878390 2878489 2878627 "TABLEAU" 2878875 NIL TABLEAU (NIL T) -8 NIL NIL NIL) (-1197 2872998 2874218 2875466 "TABLBUMP" 2877176 NIL TABLBUMP (NIL T) -7 NIL NIL NIL) (-1196 2872220 2872367 2872548 "SYSTEM" 2872839 T SYSTEM (NIL) -8 NIL NIL NIL) (-1195 2868679 2869378 2870161 "SYSSOLP" 2871471 NIL SYSSOLP (NIL T) -7 NIL NIL NIL) (-1194 2868477 2868634 2868665 "SYSPTR" 2868670 T SYSPTR (NIL) -8 NIL NIL NIL) (-1193 2867516 2868021 2868140 "SYSNNI" 2868326 NIL SYSNNI (NIL NIL) -8 NIL NIL 2868411) (-1192 2866818 2867277 2867356 "SYSINT" 2867416 NIL SYSINT (NIL NIL) -8 NIL NIL 2867461) (-1191 2863150 2864096 2864806 "SYNTAX" 2866130 T SYNTAX (NIL) -8 NIL NIL NIL) (-1190 2860308 2860910 2861542 "SYMTAB" 2862540 T SYMTAB (NIL) -8 NIL NIL NIL) (-1189 2855557 2856459 2857442 "SYMS" 2859347 T SYMS (NIL) -8 NIL NIL NIL) (-1188 2852792 2855015 2855245 "SYMPOLY" 2855362 NIL SYMPOLY (NIL T) -8 NIL NIL NIL) (-1187 2852309 2852384 2852507 "SYMFUNC" 2852704 NIL SYMFUNC (NIL T) -7 NIL NIL NIL) (-1186 2848329 2849621 2850434 "SYMBOL" 2851518 T SYMBOL (NIL) -8 NIL NIL NIL) (-1185 2841868 2843557 2845277 "SWITCH" 2846631 T SWITCH (NIL) -8 NIL NIL NIL) (-1184 2835102 2840689 2840992 "SUTS" 2841623 NIL SUTS (NIL T NIL NIL) -8 NIL NIL NIL) (-1183 2827168 2834349 2834622 "SUPXS" 2834887 NIL SUPXS (NIL T NIL NIL) -8 NIL NIL NIL) (-1182 2818927 2826786 2826912 "SUP" 2827077 NIL SUP (NIL T) -8 NIL NIL NIL) (-1181 2818086 2818213 2818430 "SUPFRACF" 2818795 NIL SUPFRACF (NIL T T T T) -7 NIL NIL NIL) (-1180 2817707 2817766 2817879 "SUP2" 2818021 NIL SUP2 (NIL T T) -7 NIL NIL NIL) (-1179 2816155 2816429 2816785 "SUMRF" 2817406 NIL SUMRF (NIL T) -7 NIL NIL NIL) (-1178 2815490 2815556 2815748 "SUMFS" 2816076 NIL SUMFS (NIL T T) -7 NIL NIL NIL) (-1177 2799457 2814667 2814918 "SULS" 2815297 NIL SULS (NIL T NIL NIL) -8 NIL NIL NIL) (-1176 2799059 2799279 2799349 "SUCHTAST" 2799409 T SUCHTAST (NIL) -8 NIL NIL NIL) (-1175 2798354 2798584 2798724 "SUCH" 2798967 NIL SUCH (NIL T T) -8 NIL NIL NIL) (-1174 2792221 2793260 2794219 "SUBSPACE" 2797442 NIL SUBSPACE (NIL NIL T) -8 NIL NIL NIL) (-1173 2791651 2791741 2791905 "SUBRESP" 2792109 NIL SUBRESP (NIL T T) -7 NIL NIL NIL) (-1172 2785019 2786316 2787627 "STTF" 2790387 NIL STTF (NIL T) -7 NIL NIL NIL) (-1171 2779192 2780312 2781459 "STTFNC" 2783919 NIL STTFNC (NIL T) -7 NIL NIL NIL) (-1170 2770505 2772374 2774168 "STTAYLOR" 2777433 NIL STTAYLOR (NIL T) -7 NIL NIL NIL) (-1169 2763635 2770369 2770452 "STRTBL" 2770457 NIL STRTBL (NIL T) -8 NIL NIL NIL) (-1168 2758999 2763590 2763621 "STRING" 2763626 T STRING (NIL) -8 NIL NIL NIL) (-1167 2753828 2758342 2758372 "STRICAT" 2758431 T STRICAT (NIL) -9 NIL 2758493 NIL) (-1166 2746581 2751447 2752058 "STREAM" 2753252 NIL STREAM (NIL T) -8 NIL NIL NIL) (-1165 2746091 2746168 2746312 "STREAM3" 2746498 NIL STREAM3 (NIL T T T) -7 NIL NIL NIL) (-1164 2745073 2745256 2745491 "STREAM2" 2745904 NIL STREAM2 (NIL T T) -7 NIL NIL NIL) (-1163 2744761 2744813 2744906 "STREAM1" 2745015 NIL STREAM1 (NIL T) -7 NIL NIL NIL) (-1162 2743777 2743958 2744189 "STINPROD" 2744577 NIL STINPROD (NIL T) -7 NIL NIL NIL) (-1161 2743329 2743539 2743569 "STEP" 2743649 T STEP (NIL) -9 NIL 2743727 NIL) (-1160 2742516 2742818 2742966 "STEPAST" 2743203 T STEPAST (NIL) -8 NIL NIL NIL) (-1159 2735948 2742415 2742492 "STBL" 2742497 NIL STBL (NIL T T NIL) -8 NIL NIL NIL) (-1158 2731043 2735139 2735182 "STAGG" 2735335 NIL STAGG (NIL T) -9 NIL 2735424 NIL) (-1157 2728745 2729347 2730219 "STAGG-" 2730224 NIL STAGG- (NIL T T) -8 NIL NIL NIL) (-1156 2726892 2728515 2728607 "STACK" 2728688 NIL STACK (NIL T) -8 NIL NIL NIL) (-1155 2719587 2725033 2725489 "SREGSET" 2726522 NIL SREGSET (NIL T T T T) -8 NIL NIL NIL) (-1154 2712012 2713381 2714894 "SRDCMPK" 2718193 NIL SRDCMPK (NIL T T T T T) -7 NIL NIL NIL) (-1153 2704897 2709422 2709452 "SRAGG" 2710755 T SRAGG (NIL) -9 NIL 2711363 NIL) (-1152 2703914 2704169 2704548 "SRAGG-" 2704553 NIL SRAGG- (NIL T) -8 NIL NIL NIL) (-1151 2698374 2702861 2703282 "SQMATRIX" 2703540 NIL SQMATRIX (NIL NIL T) -8 NIL NIL NIL) (-1150 2692059 2695092 2695819 "SPLTREE" 2697719 NIL SPLTREE (NIL T T) -8 NIL NIL NIL) (-1149 2688022 2688715 2689361 "SPLNODE" 2691485 NIL SPLNODE (NIL T T) -8 NIL NIL NIL) (-1148 2687069 2687302 2687332 "SPFCAT" 2687776 T SPFCAT (NIL) -9 NIL NIL NIL) (-1147 2685806 2686016 2686280 "SPECOUT" 2686827 T SPECOUT (NIL) -7 NIL NIL NIL) (-1146 2676916 2678788 2678818 "SPADXPT" 2683494 T SPADXPT (NIL) -9 NIL 2685658 NIL) (-1145 2676677 2676717 2676786 "SPADPRSR" 2676869 T SPADPRSR (NIL) -7 NIL NIL NIL) (-1144 2674726 2676632 2676663 "SPADAST" 2676668 T SPADAST (NIL) -8 NIL NIL NIL) (-1143 2666671 2668444 2668487 "SPACEC" 2672860 NIL SPACEC (NIL T) -9 NIL 2674676 NIL) (-1142 2664801 2666603 2666652 "SPACE3" 2666657 NIL SPACE3 (NIL T) -8 NIL NIL NIL) (-1141 2663553 2663724 2664015 "SORTPAK" 2664606 NIL SORTPAK (NIL T T) -7 NIL NIL NIL) (-1140 2661645 2661948 2662360 "SOLVETRA" 2663217 NIL SOLVETRA (NIL T) -7 NIL NIL NIL) (-1139 2660695 2660917 2661178 "SOLVESER" 2661418 NIL SOLVESER (NIL T) -7 NIL NIL NIL) (-1138 2655999 2656887 2657882 "SOLVERAD" 2659747 NIL SOLVERAD (NIL T) -7 NIL NIL NIL) (-1137 2651814 2652423 2653152 "SOLVEFOR" 2655366 NIL SOLVEFOR (NIL T T) -7 NIL NIL NIL) (-1136 2646084 2651163 2651260 "SNTSCAT" 2651265 NIL SNTSCAT (NIL T T T T) -9 NIL 2651335 NIL) (-1135 2640190 2644407 2644798 "SMTS" 2645774 NIL SMTS (NIL T T T) -8 NIL NIL NIL) (-1134 2634875 2640078 2640155 "SMP" 2640160 NIL SMP (NIL T T) -8 NIL NIL NIL) (-1133 2633034 2633335 2633733 "SMITH" 2634572 NIL SMITH (NIL T T T T) -7 NIL NIL NIL) (-1132 2625747 2629943 2630046 "SMATCAT" 2631397 NIL SMATCAT (NIL NIL T T T) -9 NIL 2631947 NIL) (-1131 2622687 2623510 2624688 "SMATCAT-" 2624693 NIL SMATCAT- (NIL T NIL T T T) -8 NIL NIL NIL) (-1130 2620353 2621923 2621966 "SKAGG" 2622227 NIL SKAGG (NIL T) -9 NIL 2622362 NIL) (-1129 2616679 2619826 2620010 "SINT" 2620162 T SINT (NIL) -8 NIL NIL 2620324) (-1128 2616451 2616489 2616555 "SIMPAN" 2616635 T SIMPAN (NIL) -7 NIL NIL NIL) (-1127 2615730 2615986 2616126 "SIG" 2616333 T SIG (NIL) -8 NIL NIL NIL) (-1126 2614568 2614789 2615064 "SIGNRF" 2615489 NIL SIGNRF (NIL T) -7 NIL NIL NIL) (-1125 2613401 2613552 2613836 "SIGNEF" 2614397 NIL SIGNEF (NIL T T) -7 NIL NIL NIL) (-1124 2612707 2612984 2613108 "SIGAST" 2613299 T SIGAST (NIL) -8 NIL NIL NIL) (-1123 2610397 2610851 2611357 "SHP" 2612248 NIL SHP (NIL T NIL) -7 NIL NIL NIL) (-1122 2604249 2610298 2610374 "SHDP" 2610379 NIL SHDP (NIL NIL NIL T) -8 NIL NIL NIL) (-1121 2603822 2604014 2604044 "SGROUP" 2604137 T SGROUP (NIL) -9 NIL 2604199 NIL) (-1120 2603680 2603706 2603779 "SGROUP-" 2603784 NIL SGROUP- (NIL T) -8 NIL NIL NIL) (-1119 2600471 2601169 2601892 "SGCF" 2602979 T SGCF (NIL) -7 NIL NIL NIL) (-1118 2594839 2599918 2600015 "SFRTCAT" 2600020 NIL SFRTCAT (NIL T T T T) -9 NIL 2600059 NIL) (-1117 2588260 2589278 2590414 "SFRGCD" 2593822 NIL SFRGCD (NIL T T T T T) -7 NIL NIL NIL) (-1116 2581386 2582459 2583645 "SFQCMPK" 2587193 NIL SFQCMPK (NIL T T T T T) -7 NIL NIL NIL) (-1115 2581006 2581095 2581206 "SFORT" 2581327 NIL SFORT (NIL T T) -8 NIL NIL NIL) (-1114 2580124 2580846 2580967 "SEXOF" 2580972 NIL SEXOF (NIL T T T T T) -8 NIL NIL NIL) (-1113 2579231 2580005 2580073 "SEX" 2580078 T SEX (NIL) -8 NIL NIL NIL) (-1112 2575012 2575727 2575822 "SEXCAT" 2578444 NIL SEXCAT (NIL T T T T T) -9 NIL 2579004 NIL) (-1111 2572165 2574946 2574994 "SET" 2574999 NIL SET (NIL T) -8 NIL NIL NIL) (-1110 2570389 2570878 2571183 "SETMN" 2571906 NIL SETMN (NIL NIL NIL) -8 NIL NIL NIL) (-1109 2569885 2570037 2570067 "SETCAT" 2570243 T SETCAT (NIL) -9 NIL 2570353 NIL) (-1108 2569577 2569655 2569785 "SETCAT-" 2569790 NIL SETCAT- (NIL T) -8 NIL NIL NIL) (-1107 2565938 2568038 2568081 "SETAGG" 2568951 NIL SETAGG (NIL T) -9 NIL 2569291 NIL) (-1106 2565396 2565512 2565749 "SETAGG-" 2565754 NIL SETAGG- (NIL T T) -8 NIL NIL NIL) (-1105 2564839 2565092 2565193 "SEQAST" 2565317 T SEQAST (NIL) -8 NIL NIL NIL) (-1104 2564038 2564332 2564393 "SEGXCAT" 2564679 NIL SEGXCAT (NIL T T) -9 NIL 2564799 NIL) (-1103 2563044 2563704 2563886 "SEG" 2563891 NIL SEG (NIL T) -8 NIL NIL NIL) (-1102 2562023 2562237 2562280 "SEGCAT" 2562802 NIL SEGCAT (NIL T) -9 NIL 2563023 NIL) (-1101 2560955 2561386 2561594 "SEGBIND" 2561850 NIL SEGBIND (NIL T) -8 NIL NIL NIL) (-1100 2560576 2560635 2560748 "SEGBIND2" 2560890 NIL SEGBIND2 (NIL T T) -7 NIL NIL NIL) (-1099 2560149 2560377 2560454 "SEGAST" 2560521 T SEGAST (NIL) -8 NIL NIL NIL) (-1098 2559368 2559494 2559698 "SEG2" 2559993 NIL SEG2 (NIL T T) -7 NIL NIL NIL) (-1097 2558778 2559303 2559350 "SDVAR" 2559355 NIL SDVAR (NIL T) -8 NIL NIL NIL) (-1096 2551305 2558548 2558678 "SDPOL" 2558683 NIL SDPOL (NIL T) -8 NIL NIL NIL) (-1095 2549898 2550164 2550483 "SCPKG" 2551020 NIL SCPKG (NIL T) -7 NIL NIL NIL) (-1094 2549062 2549234 2549426 "SCOPE" 2549728 T SCOPE (NIL) -8 NIL NIL NIL) (-1093 2548282 2548416 2548595 "SCACHE" 2548917 NIL SCACHE (NIL T) -7 NIL NIL NIL) (-1092 2547928 2548114 2548144 "SASTCAT" 2548149 T SASTCAT (NIL) -9 NIL 2548162 NIL) (-1091 2547415 2547763 2547839 "SAOS" 2547874 T SAOS (NIL) -8 NIL NIL NIL) (-1090 2546980 2547015 2547188 "SAERFFC" 2547374 NIL SAERFFC (NIL T T T) -7 NIL NIL NIL) (-1089 2540919 2546877 2546957 "SAE" 2546962 NIL SAE (NIL T T NIL) -8 NIL NIL NIL) (-1088 2540512 2540547 2540706 "SAEFACT" 2540878 NIL SAEFACT (NIL T T T) -7 NIL NIL NIL) (-1087 2538833 2539147 2539548 "RURPK" 2540178 NIL RURPK (NIL T NIL) -7 NIL NIL NIL) (-1086 2537470 2537776 2538081 "RULESET" 2538667 NIL RULESET (NIL T T T) -8 NIL NIL NIL) (-1085 2534693 2535223 2535681 "RULE" 2537151 NIL RULE (NIL T T T) -8 NIL NIL NIL) (-1084 2534305 2534487 2534570 "RULECOLD" 2534645 NIL RULECOLD (NIL NIL) -8 NIL NIL NIL) (-1083 2534095 2534123 2534194 "RTVALUE" 2534256 T RTVALUE (NIL) -8 NIL NIL NIL) (-1082 2533566 2533812 2533906 "RSTRCAST" 2534023 T RSTRCAST (NIL) -8 NIL NIL NIL) (-1081 2528414 2529209 2530129 "RSETGCD" 2532765 NIL RSETGCD (NIL T T T T T) -7 NIL NIL NIL) (-1080 2517644 2522723 2522820 "RSETCAT" 2526939 NIL RSETCAT (NIL T T T T) -9 NIL 2528036 NIL) (-1079 2515571 2516110 2516934 "RSETCAT-" 2516939 NIL RSETCAT- (NIL T T T T T) -8 NIL NIL NIL) (-1078 2507957 2509333 2510853 "RSDCMPK" 2514170 NIL RSDCMPK (NIL T T T T T) -7 NIL NIL NIL) (-1077 2505936 2506403 2506477 "RRCC" 2507563 NIL RRCC (NIL T T) -9 NIL 2507907 NIL) (-1076 2505287 2505461 2505740 "RRCC-" 2505745 NIL RRCC- (NIL T T T) -8 NIL NIL NIL) (-1075 2504730 2504983 2505084 "RPTAST" 2505208 T RPTAST (NIL) -8 NIL NIL NIL) (-1074 2478576 2487935 2488002 "RPOLCAT" 2498668 NIL RPOLCAT (NIL T T T) -9 NIL 2501828 NIL) (-1073 2470074 2472414 2475536 "RPOLCAT-" 2475541 NIL RPOLCAT- (NIL T T T T) -8 NIL NIL NIL) (-1072 2461005 2468285 2468767 "ROUTINE" 2469614 T ROUTINE (NIL) -8 NIL NIL NIL) (-1071 2457803 2460631 2460771 "ROMAN" 2460887 T ROMAN (NIL) -8 NIL NIL NIL) (-1070 2456047 2456663 2456923 "ROIRC" 2457608 NIL ROIRC (NIL T T) -8 NIL NIL NIL) (-1069 2452279 2454563 2454593 "RNS" 2454897 T RNS (NIL) -9 NIL 2455171 NIL) (-1068 2450788 2451171 2451705 "RNS-" 2451780 NIL RNS- (NIL T) -8 NIL NIL NIL) (-1067 2450191 2450599 2450629 "RNG" 2450634 T RNG (NIL) -9 NIL 2450655 NIL) (-1066 2449194 2449556 2449758 "RNGBIND" 2450042 NIL RNGBIND (NIL T T) -8 NIL NIL NIL) (-1065 2448593 2448981 2449024 "RMODULE" 2449029 NIL RMODULE (NIL T) -9 NIL 2449056 NIL) (-1064 2447429 2447523 2447859 "RMCAT2" 2448494 NIL RMCAT2 (NIL NIL NIL T T T T T T T T) -7 NIL NIL NIL) (-1063 2444279 2446775 2447072 "RMATRIX" 2447191 NIL RMATRIX (NIL NIL NIL T) -8 NIL NIL NIL) (-1062 2437106 2439366 2439481 "RMATCAT" 2442840 NIL RMATCAT (NIL NIL NIL T T T) -9 NIL 2443822 NIL) (-1061 2436481 2436628 2436935 "RMATCAT-" 2436940 NIL RMATCAT- (NIL T NIL NIL T T T) -8 NIL NIL NIL) (-1060 2435882 2436103 2436146 "RLINSET" 2436340 NIL RLINSET (NIL T) -9 NIL 2436431 NIL) (-1059 2435449 2435524 2435652 "RINTERP" 2435801 NIL RINTERP (NIL NIL T) -7 NIL NIL NIL) (-1058 2434507 2435061 2435091 "RING" 2435147 T RING (NIL) -9 NIL 2435239 NIL) (-1057 2434299 2434343 2434440 "RING-" 2434445 NIL RING- (NIL T) -8 NIL NIL NIL) (-1056 2433140 2433377 2433635 "RIDIST" 2434063 T RIDIST (NIL) -7 NIL NIL NIL) (-1055 2424429 2432608 2432814 "RGCHAIN" 2432988 NIL RGCHAIN (NIL T NIL) -8 NIL NIL NIL) (-1054 2423779 2424185 2424226 "RGBCSPC" 2424284 NIL RGBCSPC (NIL T) -9 NIL 2424336 NIL) (-1053 2422937 2423318 2423359 "RGBCMDL" 2423591 NIL RGBCMDL (NIL T) -9 NIL 2423705 NIL) (-1052 2419931 2420545 2421215 "RF" 2422301 NIL RF (NIL T) -7 NIL NIL NIL) (-1051 2419577 2419640 2419743 "RFFACTOR" 2419862 NIL RFFACTOR (NIL T) -7 NIL NIL NIL) (-1050 2419302 2419337 2419434 "RFFACT" 2419536 NIL RFFACT (NIL T) -7 NIL NIL NIL) (-1049 2417419 2417783 2418165 "RFDIST" 2418942 T RFDIST (NIL) -7 NIL NIL NIL) (-1048 2416872 2416964 2417127 "RETSOL" 2417321 NIL RETSOL (NIL T T) -7 NIL NIL NIL) (-1047 2416508 2416588 2416631 "RETRACT" 2416764 NIL RETRACT (NIL T) -9 NIL 2416851 NIL) (-1046 2416357 2416382 2416469 "RETRACT-" 2416474 NIL RETRACT- (NIL T T) -8 NIL NIL NIL) (-1045 2415959 2416179 2416249 "RETAST" 2416309 T RETAST (NIL) -8 NIL NIL NIL) (-1044 2408697 2415612 2415739 "RESULT" 2415854 T RESULT (NIL) -8 NIL NIL NIL) (-1043 2407288 2407966 2408165 "RESRING" 2408600 NIL RESRING (NIL T T T T NIL) -8 NIL NIL NIL) (-1042 2406924 2406973 2407071 "RESLATC" 2407225 NIL RESLATC (NIL T) -7 NIL NIL NIL) (-1041 2406629 2406664 2406771 "REPSQ" 2406883 NIL REPSQ (NIL T) -7 NIL NIL NIL) (-1040 2404051 2404631 2405233 "REP" 2406049 T REP (NIL) -7 NIL NIL NIL) (-1039 2403748 2403783 2403894 "REPDB" 2404010 NIL REPDB (NIL T) -7 NIL NIL NIL) (-1038 2397648 2399037 2400260 "REP2" 2402560 NIL REP2 (NIL T) -7 NIL NIL NIL) (-1037 2394025 2394706 2395514 "REP1" 2396875 NIL REP1 (NIL T) -7 NIL NIL NIL) (-1036 2386721 2392166 2392622 "REGSET" 2393655 NIL REGSET (NIL T T T T) -8 NIL NIL NIL) (-1035 2385486 2385869 2386119 "REF" 2386506 NIL REF (NIL T) -8 NIL NIL NIL) (-1034 2384863 2384966 2385133 "REDORDER" 2385370 NIL REDORDER (NIL T T) -7 NIL NIL NIL) (-1033 2380831 2384076 2384303 "RECLOS" 2384691 NIL RECLOS (NIL T) -8 NIL NIL NIL) (-1032 2379883 2380064 2380279 "REALSOLV" 2380638 T REALSOLV (NIL) -7 NIL NIL NIL) (-1031 2379729 2379770 2379800 "REAL" 2379805 T REAL (NIL) -9 NIL 2379840 NIL) (-1030 2376212 2377014 2377898 "REAL0Q" 2378894 NIL REAL0Q (NIL T) -7 NIL NIL NIL) (-1029 2371813 2372801 2373862 "REAL0" 2375193 NIL REAL0 (NIL T) -7 NIL NIL NIL) (-1028 2371284 2371530 2371624 "RDUCEAST" 2371741 T RDUCEAST (NIL) -8 NIL NIL NIL) (-1027 2370689 2370761 2370968 "RDIV" 2371206 NIL RDIV (NIL T T T T T) -7 NIL NIL NIL) (-1026 2369757 2369931 2370144 "RDIST" 2370511 NIL RDIST (NIL T) -7 NIL NIL NIL) (-1025 2368354 2368641 2369013 "RDETRS" 2369465 NIL RDETRS (NIL T T) -7 NIL NIL NIL) (-1024 2366166 2366620 2367158 "RDETR" 2367896 NIL RDETR (NIL T T) -7 NIL NIL NIL) (-1023 2364791 2365069 2365466 "RDEEFS" 2365882 NIL RDEEFS (NIL T T) -7 NIL NIL NIL) (-1022 2363300 2363606 2364031 "RDEEF" 2364479 NIL RDEEF (NIL T T) -7 NIL NIL NIL) (-1021 2357361 2360281 2360311 "RCFIELD" 2361606 T RCFIELD (NIL) -9 NIL 2362337 NIL) (-1020 2355425 2355929 2356625 "RCFIELD-" 2356700 NIL RCFIELD- (NIL T) -8 NIL NIL NIL) (-1019 2351694 2353526 2353569 "RCAGG" 2354653 NIL RCAGG (NIL T) -9 NIL 2355118 NIL) (-1018 2351322 2351416 2351579 "RCAGG-" 2351584 NIL RCAGG- (NIL T T) -8 NIL NIL NIL) (-1017 2350657 2350769 2350934 "RATRET" 2351206 NIL RATRET (NIL T) -7 NIL NIL NIL) (-1016 2350210 2350277 2350398 "RATFACT" 2350585 NIL RATFACT (NIL T) -7 NIL NIL NIL) (-1015 2349518 2349638 2349790 "RANDSRC" 2350080 T RANDSRC (NIL) -7 NIL NIL NIL) (-1014 2349252 2349296 2349369 "RADUTIL" 2349467 T RADUTIL (NIL) -7 NIL NIL NIL) (-1013 2342366 2348083 2348394 "RADIX" 2348975 NIL RADIX (NIL NIL) -8 NIL NIL NIL) (-1012 2333985 2342208 2342338 "RADFF" 2342343 NIL RADFF (NIL T T T NIL NIL) -8 NIL NIL NIL) (-1011 2333632 2333707 2333737 "RADCAT" 2333897 T RADCAT (NIL) -9 NIL NIL NIL) (-1010 2333414 2333462 2333562 "RADCAT-" 2333567 NIL RADCAT- (NIL T) -8 NIL NIL NIL) (-1009 2331512 2333184 2333276 "QUEUE" 2333357 NIL QUEUE (NIL T) -8 NIL NIL NIL) (-1008 2328049 2331445 2331493 "QUAT" 2331498 NIL QUAT (NIL T) -8 NIL NIL NIL) (-1007 2327680 2327723 2327854 "QUATCT2" 2328000 NIL QUATCT2 (NIL T T T T) -7 NIL NIL NIL) (-1006 2321091 2324436 2324478 "QUATCAT" 2325269 NIL QUATCAT (NIL T) -9 NIL 2326035 NIL) (-1005 2317230 2318267 2319657 "QUATCAT-" 2319753 NIL QUATCAT- (NIL T T) -8 NIL NIL NIL) (-1004 2314695 2316306 2316349 "QUAGG" 2316730 NIL QUAGG (NIL T) -9 NIL 2316905 NIL) (-1003 2314297 2314517 2314587 "QQUTAST" 2314647 T QQUTAST (NIL) -8 NIL NIL NIL) (-1002 2313310 2313810 2313975 "QFORM" 2314178 NIL QFORM (NIL NIL T) -8 NIL NIL NIL) (-1001 2304303 2309542 2309584 "QFCAT" 2310252 NIL QFCAT (NIL T) -9 NIL 2311253 NIL) (-1000 2299870 2301071 2302665 "QFCAT-" 2302761 NIL QFCAT- (NIL T T) -8 NIL NIL NIL) (-999 2299504 2299547 2299676 "QFCAT2" 2299821 NIL QFCAT2 (NIL T T T T) -7 NIL NIL NIL) (-998 2298964 2299074 2299204 "QEQUAT" 2299394 T QEQUAT (NIL) -8 NIL NIL NIL) (-997 2292110 2293183 2294367 "QCMPACK" 2297897 NIL QCMPACK (NIL T T T T T) -7 NIL NIL NIL) (-996 2289659 2290107 2290535 "QALGSET" 2291765 NIL QALGSET (NIL T T T T) -8 NIL NIL NIL) (-995 2288904 2289078 2289310 "QALGSET2" 2289479 NIL QALGSET2 (NIL NIL NIL) -7 NIL NIL NIL) (-994 2287594 2287818 2288135 "PWFFINTB" 2288677 NIL PWFFINTB (NIL T T T T) -7 NIL NIL NIL) (-993 2285776 2285944 2286298 "PUSHVAR" 2287408 NIL PUSHVAR (NIL T T T T) -7 NIL NIL NIL) (-992 2281694 2282748 2282789 "PTRANFN" 2284673 NIL PTRANFN (NIL T) -9 NIL NIL NIL) (-991 2280096 2280387 2280709 "PTPACK" 2281405 NIL PTPACK (NIL T) -7 NIL NIL NIL) (-990 2279728 2279785 2279894 "PTFUNC2" 2280033 NIL PTFUNC2 (NIL T T) -7 NIL NIL NIL) (-989 2274173 2278570 2278611 "PTCAT" 2278907 NIL PTCAT (NIL T) -9 NIL 2279060 NIL) (-988 2273831 2273866 2273990 "PSQFR" 2274132 NIL PSQFR (NIL T T T T) -7 NIL NIL NIL) (-987 2272426 2272724 2273058 "PSEUDLIN" 2273529 NIL PSEUDLIN (NIL T) -7 NIL NIL NIL) (-986 2259189 2261560 2263884 "PSETPK" 2270186 NIL PSETPK (NIL T T T T) -7 NIL NIL NIL) (-985 2252207 2254947 2255043 "PSETCAT" 2258064 NIL PSETCAT (NIL T T T T) -9 NIL 2258878 NIL) (-984 2250043 2250677 2251498 "PSETCAT-" 2251503 NIL PSETCAT- (NIL T T T T T) -8 NIL NIL NIL) (-983 2249392 2249557 2249585 "PSCURVE" 2249853 T PSCURVE (NIL) -9 NIL 2250020 NIL) (-982 2245390 2246906 2246971 "PSCAT" 2247815 NIL PSCAT (NIL T T T) -9 NIL 2248055 NIL) (-981 2244453 2244669 2245069 "PSCAT-" 2245074 NIL PSCAT- (NIL T T T T) -8 NIL NIL NIL) (-980 2242812 2243522 2243785 "PRTITION" 2244210 T PRTITION (NIL) -8 NIL NIL NIL) (-979 2242287 2242533 2242625 "PRTDAST" 2242740 T PRTDAST (NIL) -8 NIL NIL NIL) (-978 2231377 2233591 2235779 "PRS" 2240149 NIL PRS (NIL T T) -7 NIL NIL NIL) (-977 2229188 2230727 2230767 "PRQAGG" 2230950 NIL PRQAGG (NIL T) -9 NIL 2231052 NIL) (-976 2228524 2228829 2228857 "PROPLOG" 2228996 T PROPLOG (NIL) -9 NIL 2229111 NIL) (-975 2228128 2228185 2228308 "PROPFUN2" 2228447 NIL PROPFUN2 (NIL T T) -8 NIL NIL NIL) (-974 2227443 2227564 2227736 "PROPFUN1" 2227989 NIL 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2064785 2065628 2065656 "PDECAT" 2066443 T PDECAT (NIL) -9 NIL 2067156 NIL) (-901 2064536 2064569 2064659 "PCOMP" 2064746 NIL PCOMP (NIL T T) -7 NIL NIL NIL) (-900 2062714 2063337 2063634 "PBWLB" 2064265 NIL PBWLB (NIL T) -8 NIL NIL NIL) (-899 2055187 2056787 2058125 "PATTERN" 2061397 NIL PATTERN (NIL T) -8 NIL NIL NIL) (-898 2054819 2054876 2054985 "PATTERN2" 2055124 NIL PATTERN2 (NIL T T) -7 NIL NIL NIL) (-897 2052576 2052964 2053421 "PATTERN1" 2054408 NIL PATTERN1 (NIL T T) -7 NIL NIL NIL) (-896 2049944 2050525 2051006 "PATRES" 2052141 NIL PATRES (NIL T T) -8 NIL NIL NIL) (-895 2049508 2049575 2049707 "PATRES2" 2049871 NIL PATRES2 (NIL T T T) -7 NIL NIL NIL) (-894 2047391 2047796 2048203 "PATMATCH" 2049175 NIL PATMATCH (NIL T T T) -7 NIL NIL NIL) (-893 2046901 2047110 2047151 "PATMAB" 2047258 NIL PATMAB (NIL T) -9 NIL 2047341 NIL) (-892 2045419 2045755 2046013 "PATLRES" 2046706 NIL PATLRES (NIL T T T) -8 NIL NIL NIL) (-891 2044965 2045088 2045129 "PATAB" 2045134 NIL PATAB (NIL T) -9 NIL 2045306 NIL) (-890 2043147 2043542 2043965 "PARTPERM" 2044562 T PARTPERM (NIL) -7 NIL NIL NIL) (-889 2042768 2042831 2042933 "PARSURF" 2043078 NIL PARSURF (NIL T) -8 NIL NIL NIL) (-888 2042400 2042457 2042566 "PARSU2" 2042705 NIL PARSU2 (NIL T T) -7 NIL NIL NIL) (-887 2042164 2042204 2042271 "PARSER" 2042353 T PARSER (NIL) -7 NIL NIL NIL) (-886 2041785 2041848 2041950 "PARSCURV" 2042095 NIL PARSCURV (NIL T) -8 NIL NIL NIL) (-885 2041417 2041474 2041583 "PARSC2" 2041722 NIL PARSC2 (NIL T T) -7 NIL NIL NIL) (-884 2041056 2041114 2041211 "PARPCURV" 2041353 NIL PARPCURV (NIL T) -8 NIL NIL NIL) (-883 2040688 2040745 2040854 "PARPC2" 2040993 NIL PARPC2 (NIL T T) -7 NIL NIL NIL) (-882 2039749 2040061 2040243 "PARAMAST" 2040526 T PARAMAST (NIL) -8 NIL NIL NIL) (-881 2039269 2039355 2039474 "PAN2EXPR" 2039650 T PAN2EXPR (NIL) -7 NIL NIL NIL) (-880 2038046 2038390 2038618 "PALETTE" 2039061 T PALETTE (NIL) -8 NIL NIL NIL) (-879 2036439 2037051 2037411 "PAIR" 2037732 NIL PAIR (NIL T T) -8 NIL NIL NIL) (-878 2030307 2035696 2035891 "PADICRC" 2036293 NIL PADICRC (NIL NIL T) -8 NIL NIL NIL) (-877 2023534 2029651 2029836 "PADICRAT" 2030154 NIL PADICRAT (NIL NIL) -8 NIL NIL NIL) (-876 2021849 2023471 2023516 "PADIC" 2023521 NIL PADIC (NIL NIL) -8 NIL NIL NIL) (-875 2018959 2020523 2020563 "PADICCT" 2021144 NIL PADICCT (NIL NIL) -9 NIL 2021426 NIL) (-874 2017916 2018116 2018384 "PADEPAC" 2018746 NIL PADEPAC (NIL T NIL NIL) -7 NIL NIL NIL) (-873 2017128 2017261 2017467 "PADE" 2017778 NIL PADE (NIL T T T) -7 NIL NIL NIL) (-872 2015515 2016336 2016616 "OWP" 2016932 NIL OWP (NIL T NIL NIL NIL) -8 NIL NIL NIL) (-871 2015008 2015221 2015318 "OVERSET" 2015438 T OVERSET (NIL) -8 NIL NIL NIL) (-870 2014054 2014613 2014785 "OVAR" 2014876 NIL OVAR (NIL NIL) -8 NIL NIL NIL) (-869 2013318 2013439 2013600 "OUT" 2013913 T OUT (NIL) -7 NIL NIL NIL) (-868 2002190 2004427 2006627 "OUTFORM" 2011138 T OUTFORM (NIL) -8 NIL NIL NIL) (-867 2001526 2001787 2001914 "OUTBFILE" 2002083 T OUTBFILE (NIL) -8 NIL NIL NIL) (-866 2000833 2000998 2001026 "OUTBCON" 2001344 T OUTBCON (NIL) -9 NIL 2001510 NIL) (-865 2000434 2000546 2000703 "OUTBCON-" 2000708 NIL OUTBCON- (NIL T) -8 NIL NIL NIL) (-864 1999814 2000163 2000252 "OSI" 2000365 T OSI (NIL) -8 NIL NIL NIL) (-863 1999344 1999682 1999710 "OSGROUP" 1999715 T OSGROUP (NIL) -9 NIL 1999737 NIL) (-862 1998089 1998316 1998601 "ORTHPOL" 1999091 NIL ORTHPOL (NIL T) -7 NIL NIL NIL) (-861 1995640 1997924 1998045 "OREUP" 1998050 NIL OREUP (NIL NIL T NIL NIL) -8 NIL NIL NIL) (-860 1993043 1995331 1995458 "ORESUP" 1995582 NIL ORESUP (NIL T NIL NIL) -8 NIL NIL NIL) (-859 1990571 1991071 1991632 "OREPCTO" 1992532 NIL OREPCTO (NIL T T) -7 NIL NIL NIL) (-858 1984257 1986458 1986499 "OREPCAT" 1988847 NIL OREPCAT (NIL T) -9 NIL 1989951 NIL) (-857 1981404 1982186 1983244 "OREPCAT-" 1983249 NIL OREPCAT- (NIL T T) -8 NIL NIL NIL) (-856 1980555 1980853 1980881 "ORDSET" 1981190 T ORDSET (NIL) -9 NIL 1981354 NIL) (-855 1979986 1980134 1980358 "ORDSET-" 1980363 NIL ORDSET- (NIL T) -8 NIL NIL NIL) (-854 1978551 1979342 1979370 "ORDRING" 1979572 T ORDRING (NIL) -9 NIL 1979697 NIL) (-853 1978196 1978290 1978434 "ORDRING-" 1978439 NIL ORDRING- (NIL T) -8 NIL NIL NIL) (-852 1977576 1978039 1978067 "ORDMON" 1978072 T ORDMON (NIL) -9 NIL 1978093 NIL) (-851 1976738 1976885 1977080 "ORDFUNS" 1977425 NIL ORDFUNS (NIL NIL T) -7 NIL NIL NIL) (-850 1976076 1976495 1976523 "ORDFIN" 1976588 T ORDFIN (NIL) -9 NIL 1976662 NIL) (-849 1972635 1974662 1975071 "ORDCOMP" 1975700 NIL ORDCOMP (NIL T) -8 NIL NIL NIL) (-848 1971901 1972028 1972214 "ORDCOMP2" 1972495 NIL ORDCOMP2 (NIL T T) -7 NIL NIL NIL) (-847 1968482 1969392 1970206 "OPTPROB" 1971107 T OPTPROB (NIL) -8 NIL NIL NIL) (-846 1965284 1965923 1966627 "OPTPACK" 1967798 T OPTPACK (NIL) -7 NIL NIL NIL) (-845 1962971 1963737 1963765 "OPTCAT" 1964584 T OPTCAT (NIL) -9 NIL 1965234 NIL) (-844 1962355 1962648 1962753 "OPSIG" 1962886 T OPSIG (NIL) -8 NIL NIL NIL) (-843 1962123 1962162 1962228 "OPQUERY" 1962309 T OPQUERY (NIL) -7 NIL NIL NIL) (-842 1959254 1960434 1960938 "OP" 1961652 NIL OP (NIL T) -8 NIL NIL NIL) (-841 1958628 1958854 1958895 "OPERCAT" 1959107 NIL OPERCAT (NIL T) -9 NIL 1959204 NIL) (-840 1958383 1958439 1958556 "OPERCAT-" 1958561 NIL OPERCAT- (NIL T T) -8 NIL NIL NIL) (-839 1955196 1957180 1957549 "ONECOMP" 1958047 NIL ONECOMP (NIL T) -8 NIL NIL NIL) (-838 1954501 1954616 1954790 "ONECOMP2" 1955068 NIL ONECOMP2 (NIL T T) -7 NIL NIL NIL) (-837 1953920 1954026 1954156 "OMSERVER" 1954391 T OMSERVER (NIL) -7 NIL NIL NIL) (-836 1950782 1953360 1953400 "OMSAGG" 1953461 NIL OMSAGG (NIL T) -9 NIL 1953525 NIL) (-835 1949405 1949668 1949950 "OMPKG" 1950520 T OMPKG (NIL) -7 NIL NIL NIL) (-834 1948835 1948938 1948966 "OM" 1949265 T OM (NIL) -9 NIL NIL NIL) (-833 1947382 1948384 1948553 "OMLO" 1948716 NIL OMLO (NIL T T) -8 NIL NIL NIL) (-832 1946342 1946489 1946709 "OMEXPR" 1947208 NIL OMEXPR (NIL T) -7 NIL NIL NIL) (-831 1945633 1945888 1946024 "OMERR" 1946226 T OMERR (NIL) -8 NIL NIL NIL) (-830 1944784 1945054 1945214 "OMERRK" 1945493 T OMERRK (NIL) -8 NIL NIL NIL) (-829 1944235 1944461 1944569 "OMENC" 1944696 T OMENC (NIL) -8 NIL NIL NIL) (-828 1938130 1939315 1940486 "OMDEV" 1943084 T OMDEV (NIL) -8 NIL NIL NIL) (-827 1937199 1937370 1937564 "OMCONN" 1937956 T OMCONN (NIL) -8 NIL NIL NIL) (-826 1935720 1936696 1936724 "OINTDOM" 1936729 T OINTDOM (NIL) -9 NIL 1936750 NIL) (-825 1933058 1934408 1934745 "OFMONOID" 1935415 NIL OFMONOID (NIL T) -8 NIL NIL NIL) (-824 1932469 1932995 1933040 "ODVAR" 1933045 NIL ODVAR (NIL T) -8 NIL NIL NIL) (-823 1929892 1932214 1932369 "ODR" 1932374 NIL ODR (NIL T T NIL) -8 NIL NIL NIL) (-822 1922473 1929668 1929794 "ODPOL" 1929799 NIL ODPOL (NIL T) -8 NIL NIL NIL) (-821 1916295 1922345 1922450 "ODP" 1922455 NIL ODP (NIL NIL T NIL) -8 NIL NIL NIL) (-820 1915061 1915276 1915551 "ODETOOLS" 1916069 NIL ODETOOLS (NIL T T) -7 NIL NIL NIL) (-819 1912028 1912686 1913402 "ODESYS" 1914394 NIL ODESYS (NIL T T) -7 NIL NIL NIL) (-818 1906910 1907818 1908843 "ODERTRIC" 1911103 NIL ODERTRIC (NIL T T) -7 NIL NIL NIL) (-817 1906336 1906418 1906612 "ODERED" 1906822 NIL ODERED (NIL T T T T T) -7 NIL NIL NIL) (-816 1903224 1903772 1904449 "ODERAT" 1905759 NIL ODERAT (NIL T T) -7 NIL NIL NIL) (-815 1900183 1900648 1901245 "ODEPRRIC" 1902753 NIL ODEPRRIC (NIL T T T T) -7 NIL NIL NIL) (-814 1898126 1898722 1899208 "ODEPROB" 1899717 T ODEPROB (NIL) -8 NIL NIL NIL) (-813 1894646 1895131 1895778 "ODEPRIM" 1897605 NIL ODEPRIM (NIL T T T T) -7 NIL NIL NIL) (-812 1893895 1893997 1894257 "ODEPAL" 1894538 NIL ODEPAL (NIL T T T T) -7 NIL NIL NIL) (-811 1890057 1890848 1891712 "ODEPACK" 1893051 T ODEPACK (NIL) -7 NIL NIL NIL) (-810 1889118 1889225 1889447 "ODEINT" 1889946 NIL ODEINT (NIL T T) -7 NIL NIL NIL) (-809 1883219 1884644 1886091 "ODEIFTBL" 1887691 T ODEIFTBL (NIL) -8 NIL NIL NIL) (-808 1878617 1879403 1880355 "ODEEF" 1882378 NIL ODEEF (NIL T T) -7 NIL NIL NIL) (-807 1877966 1878055 1878278 "ODECONST" 1878522 NIL ODECONST (NIL T T T) -7 NIL NIL NIL) (-806 1876091 1876752 1876780 "ODECAT" 1877385 T ODECAT (NIL) -9 NIL 1877916 NIL) (-805 1872946 1875796 1875918 "OCT" 1876001 NIL OCT (NIL T) -8 NIL NIL NIL) (-804 1872584 1872627 1872754 "OCTCT2" 1872897 NIL OCTCT2 (NIL T T T T) -7 NIL NIL NIL) (-803 1867195 1869630 1869670 "OC" 1870767 NIL OC (NIL T) -9 NIL 1871625 NIL) (-802 1864422 1865170 1866160 "OC-" 1866254 NIL OC- (NIL T T) -8 NIL NIL NIL) (-801 1863774 1864242 1864270 "OCAMON" 1864275 T OCAMON (NIL) -9 NIL 1864296 NIL) (-800 1863305 1863646 1863674 "OASGP" 1863679 T OASGP (NIL) -9 NIL 1863699 NIL) (-799 1862566 1863055 1863083 "OAMONS" 1863123 T OAMONS (NIL) -9 NIL 1863166 NIL) (-798 1861980 1862413 1862441 "OAMON" 1862446 T OAMON (NIL) -9 NIL 1862466 NIL) (-797 1861238 1861756 1861784 "OAGROUP" 1861789 T OAGROUP (NIL) -9 NIL 1861809 NIL) (-796 1860928 1860978 1861066 "NUMTUBE" 1861182 NIL NUMTUBE (NIL T) -7 NIL NIL NIL) (-795 1854501 1856019 1857555 "NUMQUAD" 1859412 T NUMQUAD (NIL) -7 NIL NIL NIL) (-794 1850257 1851245 1852270 "NUMODE" 1853496 T NUMODE (NIL) -7 NIL NIL NIL) (-793 1847612 1848492 1848520 "NUMINT" 1849443 T NUMINT (NIL) -9 NIL 1850207 NIL) (-792 1846560 1846757 1846975 "NUMFMT" 1847414 T NUMFMT (NIL) -7 NIL NIL NIL) (-791 1832919 1835864 1838396 "NUMERIC" 1844067 NIL NUMERIC (NIL T) -7 NIL NIL NIL) (-790 1827289 1832368 1832463 "NTSCAT" 1832468 NIL NTSCAT (NIL T T T T) -9 NIL 1832507 NIL) (-789 1826483 1826648 1826841 "NTPOLFN" 1827128 NIL NTPOLFN (NIL T) -7 NIL NIL NIL) (-788 1814560 1823308 1824120 "NSUP" 1825704 NIL NSUP (NIL T) -8 NIL NIL NIL) (-787 1814192 1814249 1814358 "NSUP2" 1814497 NIL NSUP2 (NIL T T) -7 NIL NIL NIL) (-786 1804418 1813966 1814099 "NSMP" 1814104 NIL NSMP (NIL T T) -8 NIL NIL NIL) (-785 1802850 1803151 1803508 "NREP" 1804106 NIL NREP (NIL T) -7 NIL NIL NIL) (-784 1801441 1801693 1802051 "NPCOEF" 1802593 NIL NPCOEF (NIL T T T T T) -7 NIL NIL NIL) (-783 1800507 1800622 1800838 "NORMRETR" 1801322 NIL NORMRETR (NIL T T T T NIL) -7 NIL NIL NIL) (-782 1798548 1798838 1799247 "NORMPK" 1800215 NIL NORMPK (NIL T T T T T) -7 NIL NIL NIL) (-781 1798233 1798261 1798385 "NORMMA" 1798514 NIL NORMMA (NIL T T T T) -7 NIL NIL NIL) (-780 1798033 1798190 1798219 "NONE" 1798224 T NONE (NIL) -8 NIL NIL NIL) (-779 1797822 1797851 1797920 "NONE1" 1797997 NIL NONE1 (NIL T) -7 NIL NIL NIL) (-778 1797319 1797381 1797560 "NODE1" 1797754 NIL NODE1 (NIL T T) -7 NIL NIL NIL) (-777 1795600 1796451 1796706 "NNI" 1797053 T NNI (NIL) -8 NIL NIL 1797288) (-776 1794020 1794333 1794697 "NLINSOL" 1795268 NIL NLINSOL (NIL T) -7 NIL NIL NIL) (-775 1790261 1791256 1792155 "NIPROB" 1793141 T NIPROB (NIL) -8 NIL NIL NIL) (-774 1789018 1789252 1789554 "NFINTBAS" 1790023 NIL NFINTBAS (NIL T T) -7 NIL NIL NIL) (-773 1788192 1788668 1788709 "NETCLT" 1788881 NIL NETCLT (NIL T) -9 NIL 1788963 NIL) (-772 1786900 1787131 1787412 "NCODIV" 1787960 NIL NCODIV (NIL T T) -7 NIL NIL NIL) (-771 1786662 1786699 1786774 "NCNTFRAC" 1786857 NIL NCNTFRAC (NIL T) -7 NIL NIL NIL) (-770 1784842 1785206 1785626 "NCEP" 1786287 NIL NCEP (NIL T) -7 NIL NIL NIL) (-769 1783693 1784466 1784494 "NASRING" 1784604 T NASRING (NIL) -9 NIL 1784684 NIL) (-768 1783488 1783532 1783626 "NASRING-" 1783631 NIL NASRING- (NIL T) -8 NIL NIL NIL) (-767 1782595 1783120 1783148 "NARNG" 1783265 T NARNG (NIL) -9 NIL 1783356 NIL) (-766 1782287 1782354 1782488 "NARNG-" 1782493 NIL NARNG- (NIL T) -8 NIL NIL NIL) (-765 1781166 1781373 1781608 "NAGSP" 1782072 T NAGSP (NIL) -7 NIL NIL NIL) (-764 1772438 1774122 1775795 "NAGS" 1779513 T NAGS (NIL) -7 NIL NIL NIL) (-763 1770986 1771294 1771625 "NAGF07" 1772127 T NAGF07 (NIL) -7 NIL NIL NIL) (-762 1765524 1766815 1768122 "NAGF04" 1769699 T NAGF04 (NIL) -7 NIL NIL NIL) (-761 1758492 1760106 1761739 "NAGF02" 1763911 T NAGF02 (NIL) -7 NIL NIL NIL) (-760 1753716 1754816 1755933 "NAGF01" 1757395 T NAGF01 (NIL) -7 NIL NIL NIL) (-759 1747344 1748910 1750495 "NAGE04" 1752151 T NAGE04 (NIL) -7 NIL NIL NIL) (-758 1738513 1740634 1742764 "NAGE02" 1745234 T NAGE02 (NIL) -7 NIL NIL NIL) (-757 1734466 1735413 1736377 "NAGE01" 1737569 T NAGE01 (NIL) -7 NIL NIL NIL) (-756 1732261 1732795 1733353 "NAGD03" 1733928 T NAGD03 (NIL) -7 NIL NIL NIL) (-755 1724011 1725939 1727893 "NAGD02" 1730327 T NAGD02 (NIL) -7 NIL NIL NIL) (-754 1717822 1719247 1720687 "NAGD01" 1722591 T NAGD01 (NIL) -7 NIL NIL NIL) (-753 1714031 1714853 1715690 "NAGC06" 1717005 T NAGC06 (NIL) -7 NIL NIL NIL) (-752 1712496 1712828 1713184 "NAGC05" 1713695 T NAGC05 (NIL) -7 NIL NIL NIL) (-751 1711872 1711991 1712135 "NAGC02" 1712372 T NAGC02 (NIL) -7 NIL NIL NIL) (-750 1710831 1711414 1711454 "NAALG" 1711533 NIL NAALG (NIL T) -9 NIL 1711594 NIL) (-749 1710666 1710695 1710785 "NAALG-" 1710790 NIL NAALG- (NIL T T) -8 NIL NIL NIL) (-748 1704616 1705724 1706911 "MULTSQFR" 1709562 NIL MULTSQFR (NIL T T T T) -7 NIL NIL NIL) (-747 1703935 1704010 1704194 "MULTFACT" 1704528 NIL MULTFACT (NIL T T T T) -7 NIL NIL NIL) (-746 1696659 1700572 1700625 "MTSCAT" 1701695 NIL MTSCAT (NIL T T) -9 NIL 1702210 NIL) (-745 1696371 1696425 1696517 "MTHING" 1696599 NIL MTHING (NIL T) -7 NIL NIL NIL) (-744 1696163 1696196 1696256 "MSYSCMD" 1696331 T MSYSCMD (NIL) -7 NIL NIL NIL) (-743 1692245 1694918 1695238 "MSET" 1695876 NIL MSET (NIL T) -8 NIL NIL NIL) (-742 1689314 1691806 1691847 "MSETAGG" 1691852 NIL MSETAGG (NIL T) -9 NIL 1691886 NIL) (-741 1685156 1686693 1687438 "MRING" 1688614 NIL MRING (NIL T T) -8 NIL NIL NIL) (-740 1684722 1684789 1684920 "MRF2" 1685083 NIL MRF2 (NIL T T T) -7 NIL NIL NIL) (-739 1684340 1684375 1684519 "MRATFAC" 1684681 NIL MRATFAC (NIL T T T T) -7 NIL NIL NIL) (-738 1681952 1682247 1682678 "MPRFF" 1684045 NIL MPRFF (NIL T T T T) -7 NIL NIL NIL) (-737 1676249 1681806 1681903 "MPOLY" 1681908 NIL MPOLY (NIL NIL T) -8 NIL NIL NIL) (-736 1675739 1675774 1675982 "MPCPF" 1676208 NIL MPCPF (NIL T T T T) -7 NIL NIL NIL) (-735 1675253 1675296 1675480 "MPC3" 1675690 NIL MPC3 (NIL T T T T T T T) -7 NIL NIL NIL) (-734 1674448 1674529 1674750 "MPC2" 1675168 NIL MPC2 (NIL T T T T T T T) -7 NIL NIL NIL) (-733 1672749 1673086 1673476 "MONOTOOL" 1674108 NIL MONOTOOL (NIL T T) -7 NIL NIL NIL) (-732 1671974 1672291 1672319 "MONOID" 1672538 T MONOID (NIL) -9 NIL 1672685 NIL) (-731 1671520 1671639 1671820 "MONOID-" 1671825 NIL MONOID- (NIL T) -8 NIL NIL NIL) (-730 1661995 1667946 1668005 "MONOGEN" 1668679 NIL MONOGEN (NIL T T) -9 NIL 1669135 NIL) (-729 1659213 1659948 1660948 "MONOGEN-" 1661067 NIL MONOGEN- (NIL T T T) -8 NIL NIL NIL) (-728 1658046 1658492 1658520 "MONADWU" 1658912 T MONADWU (NIL) -9 NIL 1659150 NIL) (-727 1657418 1657577 1657825 "MONADWU-" 1657830 NIL MONADWU- (NIL T) -8 NIL NIL NIL) (-726 1656777 1657021 1657049 "MONAD" 1657256 T MONAD (NIL) -9 NIL 1657368 NIL) (-725 1656462 1656540 1656672 "MONAD-" 1656677 NIL MONAD- (NIL T) -8 NIL NIL NIL) (-724 1654751 1655375 1655654 "MOEBIUS" 1656215 NIL MOEBIUS (NIL T) -8 NIL NIL NIL) (-723 1654029 1654433 1654473 "MODULE" 1654478 NIL MODULE (NIL T) -9 NIL 1654517 NIL) (-722 1653597 1653693 1653883 "MODULE-" 1653888 NIL MODULE- (NIL T T) -8 NIL NIL NIL) (-721 1651277 1651961 1652288 "MODRING" 1653421 NIL MODRING (NIL T T NIL NIL NIL) -8 NIL NIL NIL) (-720 1648221 1649382 1649903 "MODOP" 1650806 NIL MODOP (NIL T T) -8 NIL NIL NIL) (-719 1646809 1647288 1647565 "MODMONOM" 1648084 NIL MODMONOM (NIL T T NIL) -8 NIL NIL NIL) (-718 1636853 1645100 1645514 "MODMON" 1646446 NIL MODMON (NIL T T) -8 NIL NIL NIL) (-717 1634009 1635697 1635973 "MODFIELD" 1636728 NIL MODFIELD (NIL T T NIL NIL NIL) -8 NIL NIL NIL) (-716 1632986 1633290 1633480 "MMLFORM" 1633839 T MMLFORM (NIL) -8 NIL NIL NIL) (-715 1632512 1632555 1632734 "MMAP" 1632937 NIL MMAP (NIL T T T T T T) -7 NIL NIL NIL) (-714 1630591 1631358 1631399 "MLO" 1631822 NIL MLO (NIL T) -9 NIL 1632064 NIL) (-713 1627957 1628473 1629075 "MLIFT" 1630072 NIL MLIFT (NIL T T T T) -7 NIL NIL NIL) (-712 1627348 1627432 1627586 "MKUCFUNC" 1627868 NIL MKUCFUNC (NIL T T T) -7 NIL NIL NIL) (-711 1626947 1627017 1627140 "MKRECORD" 1627271 NIL MKRECORD (NIL T T) -7 NIL NIL NIL) (-710 1625994 1626156 1626384 "MKFUNC" 1626758 NIL MKFUNC (NIL T) -7 NIL NIL NIL) (-709 1625382 1625486 1625642 "MKFLCFN" 1625877 NIL MKFLCFN (NIL T) -7 NIL NIL NIL) (-708 1624659 1624761 1624946 "MKBCFUNC" 1625275 NIL MKBCFUNC (NIL T T T T) -7 NIL NIL NIL) (-707 1621366 1624213 1624349 "MINT" 1624543 T MINT (NIL) -8 NIL NIL NIL) (-706 1620178 1620421 1620698 "MHROWRED" 1621121 NIL MHROWRED (NIL T) -7 NIL NIL NIL) (-705 1615558 1618713 1619118 "MFLOAT" 1619793 T MFLOAT (NIL) -8 NIL NIL NIL) (-704 1614915 1614991 1615162 "MFINFACT" 1615470 NIL MFINFACT (NIL T T T T) -7 NIL NIL NIL) (-703 1611230 1612078 1612962 "MESH" 1614051 T MESH (NIL) -7 NIL NIL NIL) (-702 1609620 1609932 1610285 "MDDFACT" 1610917 NIL MDDFACT (NIL T) -7 NIL NIL NIL) (-701 1606415 1608779 1608820 "MDAGG" 1609075 NIL MDAGG (NIL T) -9 NIL 1609218 NIL) (-700 1596155 1605708 1605915 "MCMPLX" 1606228 T MCMPLX (NIL) -8 NIL NIL NIL) (-699 1595292 1595438 1595639 "MCDEN" 1596004 NIL MCDEN (NIL T T) -7 NIL NIL NIL) (-698 1593182 1593452 1593832 "MCALCFN" 1595022 NIL MCALCFN (NIL T T T T) -7 NIL NIL NIL) (-697 1592107 1592347 1592580 "MAYBE" 1592988 NIL MAYBE (NIL T) -8 NIL NIL NIL) (-696 1589719 1590242 1590804 "MATSTOR" 1591578 NIL MATSTOR (NIL T) -7 NIL NIL NIL) (-695 1585676 1589091 1589339 "MATRIX" 1589504 NIL MATRIX (NIL T) -8 NIL NIL NIL) (-694 1581442 1582149 1582885 "MATLIN" 1585033 NIL MATLIN (NIL T T T T) -7 NIL NIL NIL) (-693 1571548 1574734 1574811 "MATCAT" 1579691 NIL MATCAT (NIL T T T) -9 NIL 1581108 NIL) (-692 1567904 1568925 1570281 "MATCAT-" 1570286 NIL MATCAT- (NIL T T T T) -8 NIL NIL NIL) (-691 1566498 1566651 1566984 "MATCAT2" 1567739 NIL MATCAT2 (NIL T T T T T T T T) -7 NIL NIL NIL) (-690 1564610 1564934 1565318 "MAPPKG3" 1566173 NIL MAPPKG3 (NIL T T T) -7 NIL NIL NIL) (-689 1563591 1563764 1563986 "MAPPKG2" 1564434 NIL MAPPKG2 (NIL T T) -7 NIL NIL NIL) (-688 1562090 1562374 1562701 "MAPPKG1" 1563297 NIL MAPPKG1 (NIL T) -7 NIL NIL NIL) (-687 1561169 1561496 1561673 "MAPPAST" 1561933 T MAPPAST (NIL) -8 NIL NIL NIL) (-686 1560780 1560838 1560961 "MAPHACK3" 1561105 NIL MAPHACK3 (NIL T T T) -7 NIL NIL NIL) (-685 1560372 1560433 1560547 "MAPHACK2" 1560712 NIL MAPHACK2 (NIL T T) -7 NIL NIL NIL) (-684 1559810 1559913 1560055 "MAPHACK1" 1560263 NIL MAPHACK1 (NIL T) -7 NIL NIL NIL) (-683 1557889 1558510 1558814 "MAGMA" 1559538 NIL MAGMA (NIL T) -8 NIL NIL NIL) (-682 1557368 1557613 1557704 "MACROAST" 1557818 T MACROAST (NIL) -8 NIL NIL NIL) (-681 1553786 1555607 1556068 "M3D" 1556940 NIL M3D (NIL T) -8 NIL NIL NIL) (-680 1547861 1552125 1552166 "LZSTAGG" 1552948 NIL LZSTAGG (NIL T) -9 NIL 1553243 NIL) (-679 1543819 1544992 1546449 "LZSTAGG-" 1546454 NIL LZSTAGG- (NIL T T) -8 NIL NIL NIL) (-678 1540906 1541710 1542197 "LWORD" 1543364 NIL LWORD (NIL T) -8 NIL NIL NIL) (-677 1540482 1540710 1540785 "LSTAST" 1540851 T LSTAST (NIL) -8 NIL NIL NIL) (-676 1533648 1540253 1540387 "LSQM" 1540392 NIL LSQM (NIL NIL T) -8 NIL NIL NIL) (-675 1532872 1533011 1533239 "LSPP" 1533503 NIL LSPP (NIL T T T T) -7 NIL NIL NIL) (-674 1530684 1530985 1531441 "LSMP" 1532561 NIL LSMP (NIL T T T T) -7 NIL NIL NIL) (-673 1527463 1528137 1528867 "LSMP1" 1529986 NIL LSMP1 (NIL T) -7 NIL NIL NIL) (-672 1521309 1526600 1526641 "LSAGG" 1526703 NIL LSAGG (NIL T) -9 NIL 1526781 NIL) (-671 1518004 1518928 1520141 "LSAGG-" 1520146 NIL LSAGG- (NIL T T) -8 NIL NIL NIL) (-670 1515603 1517148 1517397 "LPOLY" 1517799 NIL LPOLY (NIL T T) -8 NIL NIL NIL) (-669 1515185 1515270 1515393 "LPEFRAC" 1515512 NIL LPEFRAC (NIL T) -7 NIL NIL NIL) (-668 1513506 1514279 1514532 "LO" 1515017 NIL LO (NIL T T T) -8 NIL NIL NIL) (-667 1513158 1513270 1513298 "LOGIC" 1513409 T LOGIC (NIL) -9 NIL 1513490 NIL) (-666 1513020 1513043 1513114 "LOGIC-" 1513119 NIL LOGIC- (NIL T) -8 NIL NIL NIL) (-665 1512213 1512353 1512546 "LODOOPS" 1512876 NIL LODOOPS (NIL T T) -7 NIL NIL NIL) (-664 1509636 1512129 1512195 "LODO" 1512200 NIL LODO (NIL T NIL) -8 NIL NIL NIL) (-663 1508174 1508409 1508762 "LODOF" 1509383 NIL LODOF (NIL T T) -7 NIL NIL NIL) (-662 1504378 1506809 1506850 "LODOCAT" 1507288 NIL LODOCAT (NIL T) -9 NIL 1507499 NIL) (-661 1504111 1504169 1504296 "LODOCAT-" 1504301 NIL LODOCAT- (NIL T T) -8 NIL NIL NIL) (-660 1501431 1503952 1504070 "LODO2" 1504075 NIL LODO2 (NIL T T) -8 NIL NIL NIL) (-659 1498866 1501368 1501413 "LODO1" 1501418 NIL LODO1 (NIL T) -8 NIL NIL NIL) (-658 1497747 1497912 1498217 "LODEEF" 1498689 NIL LODEEF (NIL T T T) -7 NIL NIL NIL) (-657 1493050 1495941 1495982 "LNAGG" 1496844 NIL LNAGG (NIL T) -9 NIL 1497279 NIL) (-656 1492197 1492411 1492753 "LNAGG-" 1492758 NIL LNAGG- (NIL T T) -8 NIL NIL NIL) (-655 1488333 1489122 1489761 "LMOPS" 1491612 NIL LMOPS (NIL T T NIL) -8 NIL NIL NIL) (-654 1487736 1488124 1488165 "LMODULE" 1488170 NIL LMODULE (NIL T) -9 NIL 1488196 NIL) (-653 1484934 1487381 1487504 "LMDICT" 1487646 NIL LMDICT (NIL T) -8 NIL NIL NIL) (-652 1484340 1484561 1484602 "LLINSET" 1484793 NIL LLINSET (NIL T) -9 NIL 1484884 NIL) (-651 1484039 1484248 1484308 "LITERAL" 1484313 NIL LITERAL (NIL T) -8 NIL NIL NIL) (-650 1477202 1482973 1483277 "LIST" 1483768 NIL LIST (NIL T) -8 NIL NIL NIL) (-649 1476727 1476801 1476940 "LIST3" 1477122 NIL LIST3 (NIL T T T) -7 NIL NIL NIL) (-648 1475734 1475912 1476140 "LIST2" 1476545 NIL LIST2 (NIL T T) -7 NIL NIL NIL) (-647 1473868 1474180 1474579 "LIST2MAP" 1475381 NIL LIST2MAP (NIL T T) -7 NIL NIL NIL) (-646 1473464 1473701 1473742 "LINSET" 1473747 NIL LINSET (NIL T) -9 NIL 1473781 NIL) (-645 1472125 1472795 1472836 "LINEXP" 1473091 NIL LINEXP (NIL T) -9 NIL 1473240 NIL) (-644 1470772 1471032 1471329 "LINDEP" 1471877 NIL LINDEP (NIL T T) -7 NIL NIL NIL) (-643 1467539 1468258 1469035 "LIMITRF" 1470027 NIL LIMITRF (NIL T) -7 NIL NIL NIL) (-642 1465842 1466138 1466547 "LIMITPS" 1467234 NIL LIMITPS (NIL T T) -7 NIL NIL NIL) (-641 1460270 1465353 1465581 "LIE" 1465663 NIL LIE (NIL T T) -8 NIL NIL NIL) (-640 1459218 1459687 1459727 "LIECAT" 1459867 NIL LIECAT (NIL T) -9 NIL 1460018 NIL) (-639 1459059 1459086 1459174 "LIECAT-" 1459179 NIL LIECAT- (NIL T T) -8 NIL NIL NIL) (-638 1451646 1458599 1458755 "LIB" 1458923 T LIB (NIL) -8 NIL NIL NIL) (-637 1447281 1448164 1449099 "LGROBP" 1450763 NIL LGROBP (NIL NIL T) -7 NIL NIL NIL) (-636 1445279 1445553 1445903 "LF" 1447002 NIL LF (NIL T T) -7 NIL NIL NIL) (-635 1444119 1444811 1444839 "LFCAT" 1445046 T LFCAT (NIL) -9 NIL 1445185 NIL) (-634 1441021 1441651 1442339 "LEXTRIPK" 1443483 NIL LEXTRIPK (NIL T NIL) -7 NIL NIL NIL) (-633 1437765 1438591 1439094 "LEXP" 1440601 NIL LEXP (NIL T T NIL) -8 NIL NIL NIL) (-632 1437241 1437486 1437578 "LETAST" 1437693 T LETAST (NIL) -8 NIL NIL NIL) (-631 1435639 1435952 1436353 "LEADCDET" 1436923 NIL LEADCDET (NIL T T T T) -7 NIL NIL NIL) (-630 1434829 1434903 1435132 "LAZM3PK" 1435560 NIL LAZM3PK (NIL T T T T T T) -7 NIL NIL NIL) (-629 1429746 1432906 1433444 "LAUPOL" 1434341 NIL LAUPOL (NIL T T) -8 NIL NIL NIL) (-628 1429325 1429369 1429530 "LAPLACE" 1429696 NIL LAPLACE (NIL T T) -7 NIL NIL NIL) (-627 1427264 1428426 1428677 "LA" 1429158 NIL LA (NIL T T T) -8 NIL NIL NIL) (-626 1426258 1426842 1426883 "LALG" 1426945 NIL LALG (NIL T) -9 NIL 1427004 NIL) (-625 1425972 1426031 1426167 "LALG-" 1426172 NIL LALG- (NIL T T) -8 NIL NIL NIL) (-624 1425807 1425831 1425872 "KVTFROM" 1425934 NIL KVTFROM (NIL T) -9 NIL NIL NIL) (-623 1424730 1425174 1425359 "KTVLOGIC" 1425642 T KTVLOGIC (NIL) -8 NIL NIL NIL) (-622 1424565 1424589 1424630 "KRCFROM" 1424692 NIL KRCFROM (NIL T) -9 NIL NIL NIL) (-621 1423469 1423656 1423955 "KOVACIC" 1424365 NIL KOVACIC (NIL T T) -7 NIL NIL NIL) (-620 1423304 1423328 1423369 "KONVERT" 1423431 NIL KONVERT (NIL T) -9 NIL NIL NIL) (-619 1423139 1423163 1423204 "KOERCE" 1423266 NIL KOERCE (NIL T) -9 NIL NIL NIL) (-618 1420969 1421732 1422109 "KERNEL" 1422795 NIL KERNEL (NIL T) -8 NIL NIL NIL) (-617 1420465 1420546 1420678 "KERNEL2" 1420883 NIL KERNEL2 (NIL T T) -7 NIL NIL NIL) (-616 1414235 1419004 1419058 "KDAGG" 1419435 NIL KDAGG (NIL T T) -9 NIL 1419641 NIL) (-615 1413764 1413888 1414093 "KDAGG-" 1414098 NIL KDAGG- (NIL T T T) -8 NIL NIL NIL) (-614 1406912 1413425 1413580 "KAFILE" 1413642 NIL KAFILE (NIL T) -8 NIL NIL NIL) (-613 1401340 1406423 1406651 "JORDAN" 1406733 NIL JORDAN (NIL T T) -8 NIL NIL NIL) (-612 1400719 1400989 1401110 "JOINAST" 1401239 T JOINAST (NIL) -8 NIL NIL NIL) (-611 1400565 1400624 1400679 "JAVACODE" 1400684 T JAVACODE (NIL) -8 NIL NIL NIL) (-610 1396817 1398770 1398824 "IXAGG" 1399753 NIL IXAGG (NIL T T) -9 NIL 1400212 NIL) (-609 1395736 1396042 1396461 "IXAGG-" 1396466 NIL IXAGG- (NIL T T T) -8 NIL NIL NIL) (-608 1391266 1395658 1395717 "IVECTOR" 1395722 NIL IVECTOR (NIL T NIL) -8 NIL NIL NIL) (-607 1390032 1390269 1390535 "ITUPLE" 1391033 NIL ITUPLE (NIL T) -8 NIL NIL NIL) (-606 1388534 1388711 1389006 "ITRIGMNP" 1389854 NIL ITRIGMNP (NIL T T T) -7 NIL NIL NIL) (-605 1387279 1387483 1387766 "ITFUN3" 1388310 NIL ITFUN3 (NIL T T T) -7 NIL NIL NIL) (-604 1386911 1386968 1387077 "ITFUN2" 1387216 NIL ITFUN2 (NIL T T) -7 NIL NIL NIL) (-603 1386070 1386391 1386565 "ITFORM" 1386757 T ITFORM (NIL) -8 NIL NIL NIL) (-602 1384031 1385090 1385368 "ITAYLOR" 1385825 NIL ITAYLOR (NIL T) -8 NIL NIL NIL) (-601 1372976 1378168 1379331 "ISUPS" 1382901 NIL ISUPS (NIL T) -8 NIL NIL NIL) (-600 1372080 1372220 1372456 "ISUMP" 1372823 NIL ISUMP (NIL T T T T) -7 NIL NIL NIL) (-599 1367455 1372025 1372066 "ISTRING" 1372071 NIL ISTRING (NIL NIL) -8 NIL NIL NIL) (-598 1366931 1367176 1367268 "ISAST" 1367383 T ISAST (NIL) -8 NIL NIL NIL) (-597 1366140 1366222 1366438 "IRURPK" 1366845 NIL IRURPK (NIL T T T T T) -7 NIL NIL NIL) (-596 1365076 1365277 1365517 "IRSN" 1365920 T IRSN (NIL) -7 NIL NIL NIL) (-595 1363147 1363502 1363931 "IRRF2F" 1364714 NIL IRRF2F (NIL T) -7 NIL NIL NIL) (-594 1362894 1362932 1363008 "IRREDFFX" 1363103 NIL IRREDFFX (NIL T) -7 NIL NIL NIL) (-593 1361509 1361768 1362067 "IROOT" 1362627 NIL IROOT (NIL T) -7 NIL NIL NIL) (-592 1358113 1359193 1359885 "IR" 1360849 NIL IR (NIL T) -8 NIL NIL NIL) (-591 1357318 1357606 1357757 "IRFORM" 1357982 T IRFORM (NIL) -8 NIL NIL NIL) (-590 1354931 1355426 1355992 "IR2" 1356796 NIL IR2 (NIL T T) -7 NIL NIL NIL) (-589 1354031 1354144 1354358 "IR2F" 1354814 NIL IR2F (NIL T T) -7 NIL NIL NIL) (-588 1353822 1353856 1353916 "IPRNTPK" 1353991 T IPRNTPK (NIL) -7 NIL NIL NIL) (-587 1350403 1353711 1353780 "IPF" 1353785 NIL IPF (NIL NIL) -8 NIL NIL NIL) (-586 1348730 1350328 1350385 "IPADIC" 1350390 NIL IPADIC (NIL NIL NIL) -8 NIL NIL NIL) (-585 1348042 1348290 1348420 "IP4ADDR" 1348620 T IP4ADDR (NIL) -8 NIL NIL NIL) (-584 1347416 1347671 1347803 "IOMODE" 1347930 T IOMODE (NIL) -8 NIL NIL NIL) (-583 1346489 1347013 1347140 "IOBFILE" 1347309 T IOBFILE (NIL) -8 NIL NIL NIL) (-582 1345977 1346393 1346421 "IOBCON" 1346426 T IOBCON (NIL) -9 NIL 1346447 NIL) (-581 1345488 1345546 1345729 "INVLAPLA" 1345913 NIL INVLAPLA (NIL T T) -7 NIL NIL NIL) (-580 1335136 1337490 1339876 "INTTR" 1343152 NIL INTTR (NIL T T) -7 NIL NIL NIL) (-579 1331471 1332213 1333078 "INTTOOLS" 1334321 NIL INTTOOLS (NIL T T) -7 NIL NIL NIL) (-578 1331057 1331148 1331265 "INTSLPE" 1331374 T INTSLPE (NIL) -7 NIL NIL NIL) (-577 1329010 1330980 1331039 "INTRVL" 1331044 NIL INTRVL (NIL T) -8 NIL NIL NIL) (-576 1326612 1327124 1327699 "INTRF" 1328495 NIL INTRF (NIL T) -7 NIL NIL NIL) (-575 1326023 1326120 1326262 "INTRET" 1326510 NIL INTRET (NIL T) -7 NIL NIL NIL) (-574 1324020 1324409 1324879 "INTRAT" 1325631 NIL INTRAT (NIL T T) -7 NIL NIL NIL) (-573 1321283 1321866 1322485 "INTPM" 1323505 NIL INTPM (NIL T T) -7 NIL NIL NIL) (-572 1318028 1318627 1319365 "INTPAF" 1320669 NIL INTPAF (NIL T T T) -7 NIL NIL NIL) (-571 1313207 1314169 1315220 "INTPACK" 1316997 T INTPACK (NIL) -7 NIL NIL NIL) (-570 1310155 1313004 1313113 "INT" 1313118 T INT (NIL) -8 NIL NIL NIL) (-569 1309407 1309559 1309767 "INTHERTR" 1309997 NIL INTHERTR (NIL T T) -7 NIL NIL NIL) (-568 1308846 1308926 1309114 "INTHERAL" 1309321 NIL INTHERAL (NIL T T T T) -7 NIL NIL NIL) (-567 1306692 1307135 1307592 "INTHEORY" 1308409 T INTHEORY (NIL) -7 NIL NIL NIL) (-566 1298098 1299719 1301491 "INTG0" 1305044 NIL INTG0 (NIL T T T) -7 NIL NIL NIL) (-565 1278671 1283461 1288271 "INTFTBL" 1293308 T INTFTBL (NIL) -8 NIL NIL NIL) (-564 1277920 1278058 1278231 "INTFACT" 1278530 NIL INTFACT (NIL T) -7 NIL NIL NIL) (-563 1275347 1275793 1276350 "INTEF" 1277474 NIL INTEF (NIL T T) -7 NIL NIL NIL) (-562 1273714 1274453 1274481 "INTDOM" 1274782 T INTDOM (NIL) -9 NIL 1274989 NIL) (-561 1273083 1273257 1273499 "INTDOM-" 1273504 NIL INTDOM- (NIL T) -8 NIL NIL NIL) (-560 1269471 1271399 1271453 "INTCAT" 1272252 NIL INTCAT (NIL T) -9 NIL 1272573 NIL) (-559 1268943 1269046 1269174 "INTBIT" 1269363 T INTBIT (NIL) -7 NIL NIL NIL) (-558 1267642 1267796 1268103 "INTALG" 1268788 NIL INTALG (NIL T T T T T) -7 NIL NIL NIL) (-557 1267125 1267215 1267372 "INTAF" 1267546 NIL INTAF (NIL T T) -7 NIL NIL NIL) (-556 1260468 1266935 1267075 "INTABL" 1267080 NIL INTABL (NIL T T T) -8 NIL NIL NIL) (-555 1259809 1260275 1260340 "INT8" 1260374 T INT8 (NIL) -8 NIL NIL 1260419) (-554 1259149 1259615 1259680 "INT64" 1259714 T INT64 (NIL) -8 NIL NIL 1259759) (-553 1258489 1258955 1259020 "INT32" 1259054 T INT32 (NIL) -8 NIL NIL 1259099) (-552 1257829 1258295 1258360 "INT16" 1258394 T INT16 (NIL) -8 NIL NIL 1258439) (-551 1252739 1255452 1255480 "INS" 1256414 T INS (NIL) -9 NIL 1257079 NIL) (-550 1249979 1250750 1251724 "INS-" 1251797 NIL INS- (NIL T) -8 NIL NIL NIL) (-549 1248754 1248981 1249279 "INPSIGN" 1249732 NIL INPSIGN (NIL T T) -7 NIL NIL NIL) (-548 1247872 1247989 1248186 "INPRODPF" 1248634 NIL INPRODPF (NIL T T) -7 NIL NIL NIL) (-547 1246766 1246883 1247120 "INPRODFF" 1247752 NIL INPRODFF (NIL T T T T) -7 NIL NIL NIL) (-546 1245766 1245918 1246178 "INNMFACT" 1246602 NIL INNMFACT (NIL T T T T) -7 NIL NIL NIL) (-545 1244963 1245060 1245248 "INMODGCD" 1245665 NIL INMODGCD (NIL T T NIL NIL) -7 NIL NIL NIL) (-544 1243471 1243716 1244040 "INFSP" 1244708 NIL INFSP (NIL T T T) -7 NIL NIL NIL) (-543 1242655 1242772 1242955 "INFPROD0" 1243351 NIL INFPROD0 (NIL T T) -7 NIL NIL NIL) (-542 1239510 1240720 1241235 "INFORM" 1242148 T INFORM (NIL) -8 NIL NIL NIL) (-541 1239120 1239180 1239278 "INFORM1" 1239445 NIL INFORM1 (NIL T) -7 NIL NIL NIL) (-540 1238643 1238732 1238846 "INFINITY" 1239026 T INFINITY (NIL) -7 NIL NIL NIL) (-539 1237819 1238363 1238464 "INETCLTS" 1238562 T INETCLTS (NIL) -8 NIL NIL NIL) (-538 1236435 1236685 1237006 "INEP" 1237567 NIL INEP (NIL T T T) -7 NIL NIL NIL) (-537 1235684 1236332 1236397 "INDE" 1236402 NIL INDE (NIL T) -8 NIL NIL NIL) (-536 1235248 1235316 1235433 "INCRMAPS" 1235611 NIL INCRMAPS (NIL T) -7 NIL NIL NIL) (-535 1234066 1234517 1234723 "INBFILE" 1235062 T INBFILE (NIL) -8 NIL NIL NIL) (-534 1229365 1230302 1231246 "INBFF" 1233154 NIL INBFF (NIL T) -7 NIL NIL NIL) (-533 1228273 1228542 1228570 "INBCON" 1229083 T INBCON (NIL) -9 NIL 1229349 NIL) (-532 1227525 1227748 1228024 "INBCON-" 1228029 NIL INBCON- (NIL T) -8 NIL NIL NIL) (-531 1227004 1227249 1227340 "INAST" 1227454 T INAST (NIL) -8 NIL NIL NIL) (-530 1226431 1226683 1226789 "IMPTAST" 1226918 T IMPTAST (NIL) -8 NIL NIL NIL) (-529 1222877 1226275 1226379 "IMATRIX" 1226384 NIL IMATRIX (NIL T NIL NIL) -8 NIL NIL NIL) (-528 1221585 1221708 1222024 "IMATQF" 1222733 NIL IMATQF (NIL T T T T T T T T) -7 NIL NIL NIL) (-527 1219805 1220032 1220369 "IMATLIN" 1221341 NIL IMATLIN (NIL T T T T) -7 NIL NIL NIL) (-526 1214383 1219729 1219787 "ILIST" 1219792 NIL ILIST (NIL T NIL) -8 NIL NIL NIL) (-525 1212288 1214243 1214356 "IIARRAY2" 1214361 NIL IIARRAY2 (NIL T NIL NIL T T) -8 NIL NIL NIL) (-524 1207686 1212199 1212263 "IFF" 1212268 NIL IFF (NIL NIL NIL) -8 NIL NIL NIL) (-523 1207033 1207303 1207419 "IFAST" 1207590 T IFAST (NIL) -8 NIL NIL NIL) (-522 1202028 1206325 1206513 "IFARRAY" 1206890 NIL IFARRAY (NIL T NIL) -8 NIL NIL NIL) (-521 1201208 1201932 1202005 "IFAMON" 1202010 NIL IFAMON (NIL T T NIL) -8 NIL NIL NIL) (-520 1200792 1200857 1200911 "IEVALAB" 1201118 NIL IEVALAB (NIL T T) -9 NIL NIL NIL) (-519 1200467 1200535 1200695 "IEVALAB-" 1200700 NIL IEVALAB- (NIL T T T) -8 NIL NIL NIL) (-518 1200098 1200381 1200444 "IDPO" 1200449 NIL IDPO (NIL T T) -8 NIL NIL NIL) (-517 1199348 1199987 1200062 "IDPOAMS" 1200067 NIL IDPOAMS (NIL T T) -8 NIL NIL NIL) (-516 1198655 1199237 1199312 "IDPOAM" 1199317 NIL IDPOAM (NIL T T) -8 NIL NIL NIL) (-515 1197714 1197990 1198043 "IDPC" 1198456 NIL IDPC (NIL T T) -9 NIL 1198605 NIL) (-514 1197183 1197606 1197679 "IDPAM" 1197684 NIL IDPAM (NIL T T) -8 NIL NIL NIL) (-513 1196559 1197075 1197148 "IDPAG" 1197153 NIL IDPAG (NIL T T) -8 NIL NIL NIL) (-512 1196204 1196395 1196470 "IDENT" 1196504 T IDENT (NIL) -8 NIL NIL NIL) (-511 1192459 1193307 1194202 "IDECOMP" 1195361 NIL IDECOMP (NIL NIL NIL) -7 NIL NIL NIL) (-510 1185296 1186382 1187429 "IDEAL" 1191495 NIL IDEAL (NIL T T T T) -8 NIL NIL NIL) (-509 1184456 1184568 1184768 "ICDEN" 1185180 NIL ICDEN (NIL T T T T) -7 NIL NIL NIL) (-508 1183527 1183936 1184083 "ICARD" 1184329 T ICARD (NIL) -8 NIL NIL NIL) (-507 1181587 1181900 1182305 "IBPTOOLS" 1183204 NIL IBPTOOLS (NIL T T T T) -7 NIL NIL NIL) (-506 1177194 1181207 1181320 "IBITS" 1181506 NIL IBITS (NIL NIL) -8 NIL NIL NIL) (-505 1173917 1174493 1175188 "IBATOOL" 1176611 NIL IBATOOL (NIL T T T) -7 NIL NIL NIL) (-504 1171696 1172158 1172691 "IBACHIN" 1173452 NIL IBACHIN (NIL T T T) -7 NIL NIL NIL) (-503 1169525 1171542 1171645 "IARRAY2" 1171650 NIL IARRAY2 (NIL T NIL NIL) -8 NIL NIL NIL) (-502 1165631 1169451 1169508 "IARRAY1" 1169513 NIL IARRAY1 (NIL T NIL) -8 NIL NIL NIL) (-501 1159740 1164043 1164524 "IAN" 1165170 T IAN (NIL) -8 NIL NIL NIL) (-500 1159251 1159308 1159481 "IALGFACT" 1159677 NIL IALGFACT (NIL T T T T) -7 NIL NIL NIL) (-499 1158779 1158892 1158920 "HYPCAT" 1159127 T HYPCAT (NIL) -9 NIL NIL NIL) (-498 1158317 1158434 1158620 "HYPCAT-" 1158625 NIL HYPCAT- (NIL T) -8 NIL NIL NIL) (-497 1157912 1158112 1158195 "HOSTNAME" 1158254 T HOSTNAME (NIL) -8 NIL NIL NIL) (-496 1157757 1157794 1157835 "HOMOTOP" 1157840 NIL HOMOTOP (NIL T) -9 NIL 1157873 NIL) (-495 1154389 1155767 1155808 "HOAGG" 1156789 NIL HOAGG (NIL T) -9 NIL 1157468 NIL) (-494 1152983 1153382 1153908 "HOAGG-" 1153913 NIL HOAGG- (NIL T T) -8 NIL NIL NIL) (-493 1146985 1152576 1152726 "HEXADEC" 1152853 T HEXADEC (NIL) -8 NIL NIL NIL) (-492 1145733 1145955 1146218 "HEUGCD" 1146762 NIL HEUGCD (NIL T) -7 NIL NIL NIL) (-491 1144809 1145570 1145700 "HELLFDIV" 1145705 NIL HELLFDIV (NIL T T T T) -8 NIL NIL NIL) (-490 1142988 1144586 1144674 "HEAP" 1144753 NIL HEAP (NIL T) -8 NIL NIL NIL) (-489 1142251 1142540 1142674 "HEADAST" 1142874 T HEADAST (NIL) -8 NIL NIL NIL) (-488 1136117 1142166 1142228 "HDP" 1142233 NIL HDP (NIL NIL T) -8 NIL NIL NIL) (-487 1130105 1135752 1135904 "HDMP" 1136018 NIL HDMP (NIL NIL T) -8 NIL NIL NIL) (-486 1129429 1129569 1129733 "HB" 1129961 T HB (NIL) -7 NIL NIL NIL) (-485 1122815 1129275 1129379 "HASHTBL" 1129384 NIL HASHTBL (NIL T T NIL) -8 NIL NIL NIL) (-484 1122291 1122536 1122628 "HASAST" 1122743 T HASAST (NIL) -8 NIL NIL NIL) (-483 1120069 1121913 1122095 "HACKPI" 1122129 T HACKPI (NIL) -8 NIL NIL NIL) (-482 1115737 1119922 1120035 "GTSET" 1120040 NIL GTSET (NIL T T T T) -8 NIL NIL NIL) (-481 1109152 1115615 1115713 "GSTBL" 1115718 NIL GSTBL (NIL T T T NIL) -8 NIL NIL NIL) (-480 1101430 1108183 1108448 "GSERIES" 1108943 NIL GSERIES (NIL T NIL NIL) -8 NIL NIL NIL) (-479 1100571 1100988 1101016 "GROUP" 1101219 T GROUP (NIL) -9 NIL 1101353 NIL) (-478 1099937 1100096 1100347 "GROUP-" 1100352 NIL GROUP- (NIL T) -8 NIL NIL NIL) (-477 1098304 1098625 1099012 "GROEBSOL" 1099614 NIL GROEBSOL (NIL NIL T T) -7 NIL NIL NIL) (-476 1097218 1097506 1097557 "GRMOD" 1098086 NIL GRMOD (NIL T T) -9 NIL 1098254 NIL) (-475 1096986 1097022 1097150 "GRMOD-" 1097155 NIL GRMOD- (NIL T T T) -8 NIL NIL NIL) (-474 1092276 1093340 1094340 "GRIMAGE" 1096006 T GRIMAGE (NIL) -8 NIL NIL NIL) (-473 1090742 1091003 1091327 "GRDEF" 1091972 T GRDEF (NIL) -7 NIL NIL NIL) (-472 1090186 1090302 1090443 "GRAY" 1090621 T GRAY (NIL) -7 NIL NIL NIL) (-471 1089373 1089779 1089830 "GRALG" 1089983 NIL GRALG (NIL T T) -9 NIL 1090076 NIL) (-470 1089034 1089107 1089270 "GRALG-" 1089275 NIL GRALG- (NIL T T T) -8 NIL NIL NIL) (-469 1085811 1088619 1088797 "GPOLSET" 1088941 NIL GPOLSET (NIL T T T T) -8 NIL NIL NIL) (-468 1085165 1085222 1085480 "GOSPER" 1085748 NIL GOSPER (NIL T T T T T) -7 NIL NIL NIL) (-467 1080897 1081603 1082129 "GMODPOL" 1084864 NIL GMODPOL (NIL NIL T T T NIL T) -8 NIL NIL NIL) (-466 1079902 1080086 1080324 "GHENSEL" 1080709 NIL GHENSEL (NIL T T) -7 NIL NIL NIL) (-465 1074058 1074901 1075921 "GENUPS" 1078986 NIL GENUPS (NIL T T) -7 NIL NIL NIL) (-464 1073755 1073806 1073895 "GENUFACT" 1074001 NIL GENUFACT (NIL T) -7 NIL NIL NIL) (-463 1073167 1073244 1073409 "GENPGCD" 1073673 NIL GENPGCD (NIL T T T T) -7 NIL NIL NIL) (-462 1072641 1072676 1072889 "GENMFACT" 1073126 NIL GENMFACT (NIL T T T T T) -7 NIL NIL NIL) (-461 1071207 1071464 1071771 "GENEEZ" 1072384 NIL GENEEZ (NIL T T) -7 NIL NIL NIL) (-460 1065355 1070818 1070980 "GDMP" 1071130 NIL GDMP (NIL NIL T T) -8 NIL NIL NIL) (-459 1054698 1059126 1060232 "GCNAALG" 1064338 NIL GCNAALG (NIL T NIL NIL NIL) -8 NIL NIL NIL) (-458 1053025 1053887 1053915 "GCDDOM" 1054170 T GCDDOM (NIL) -9 NIL 1054327 NIL) (-457 1052495 1052622 1052837 "GCDDOM-" 1052842 NIL GCDDOM- (NIL T) -8 NIL NIL NIL) (-456 1051167 1051352 1051656 "GB" 1052274 NIL GB (NIL T T T T) -7 NIL NIL NIL) (-455 1039783 1042113 1044505 "GBINTERN" 1048858 NIL GBINTERN (NIL T T T T) -7 NIL NIL NIL) (-454 1037620 1037912 1038333 "GBF" 1039458 NIL GBF (NIL T T T T) -7 NIL NIL NIL) (-453 1036401 1036566 1036833 "GBEUCLID" 1037436 NIL GBEUCLID (NIL T T T T) -7 NIL NIL NIL) (-452 1035750 1035875 1036024 "GAUSSFAC" 1036272 T GAUSSFAC (NIL) -7 NIL NIL NIL) (-451 1034117 1034419 1034733 "GALUTIL" 1035469 NIL GALUTIL (NIL T) -7 NIL NIL NIL) (-450 1032425 1032699 1033023 "GALPOLYU" 1033844 NIL GALPOLYU (NIL T T) -7 NIL NIL NIL) (-449 1029790 1030080 1030487 "GALFACTU" 1032122 NIL GALFACTU (NIL T T T) -7 NIL NIL NIL) (-448 1021596 1023095 1024703 "GALFACT" 1028222 NIL GALFACT (NIL T) -7 NIL NIL NIL) (-447 1018984 1019642 1019670 "FVFUN" 1020826 T FVFUN (NIL) -9 NIL 1021546 NIL) (-446 1018250 1018432 1018460 "FVC" 1018751 T FVC (NIL) -9 NIL 1018934 NIL) (-445 1017893 1018075 1018143 "FUNDESC" 1018202 T FUNDESC (NIL) -8 NIL NIL NIL) (-444 1017508 1017690 1017771 "FUNCTION" 1017845 NIL FUNCTION (NIL NIL) -8 NIL NIL NIL) (-443 1015252 1015830 1016296 "FT" 1017062 T FT (NIL) -8 NIL NIL NIL) (-442 1014043 1014553 1014756 "FTEM" 1015069 T FTEM (NIL) -8 NIL NIL NIL) (-441 1012334 1012623 1013020 "FSUPFACT" 1013734 NIL FSUPFACT (NIL T T T) -7 NIL NIL NIL) (-440 1010731 1011020 1011352 "FST" 1012022 T FST (NIL) -8 NIL NIL NIL) (-439 1009930 1010036 1010224 "FSRED" 1010613 NIL FSRED (NIL T T) -7 NIL NIL NIL) (-438 1008629 1008885 1009232 "FSPRMELT" 1009645 NIL FSPRMELT (NIL T T) -7 NIL NIL NIL) (-437 1005935 1006373 1006859 "FSPECF" 1008192 NIL FSPECF (NIL T T) -7 NIL NIL NIL) (-436 987573 995904 995945 "FS" 999829 NIL FS (NIL T) -9 NIL 1002118 NIL) (-435 976216 979209 983266 "FS-" 983566 NIL FS- (NIL T T) -8 NIL NIL NIL) (-434 975744 975798 975968 "FSINT" 976157 NIL FSINT (NIL T T) -7 NIL NIL NIL) (-433 974036 974737 975040 "FSERIES" 975523 NIL FSERIES (NIL T T) -8 NIL NIL NIL) (-432 973078 973194 973418 "FSCINT" 973916 NIL FSCINT (NIL T T) -7 NIL NIL NIL) (-431 969286 972022 972063 "FSAGG" 972433 NIL FSAGG (NIL T) -9 NIL 972692 NIL) (-430 967048 967649 968445 "FSAGG-" 968540 NIL FSAGG- (NIL T T) -8 NIL NIL NIL) (-429 966090 966233 966460 "FSAGG2" 966901 NIL FSAGG2 (NIL T T T T) -7 NIL NIL NIL) (-428 963772 964052 964599 "FS2UPS" 965808 NIL FS2UPS (NIL T T T T T NIL) -7 NIL NIL NIL) (-427 963406 963449 963578 "FS2" 963723 NIL FS2 (NIL T T T T) -7 NIL NIL NIL) (-426 962284 962455 962757 "FS2EXPXP" 963231 NIL FS2EXPXP (NIL T T NIL NIL) -7 NIL NIL NIL) (-425 961710 961825 961977 "FRUTIL" 962164 NIL FRUTIL (NIL T) -7 NIL NIL NIL) (-424 953123 957205 958563 "FR" 960384 NIL FR (NIL T) -8 NIL NIL NIL) (-423 948137 950812 950852 "FRNAALG" 952172 NIL FRNAALG (NIL T) -9 NIL 952770 NIL) (-422 943810 944886 946161 "FRNAALG-" 946911 NIL FRNAALG- (NIL T T) -8 NIL NIL NIL) (-421 943448 943491 943618 "FRNAAF2" 943761 NIL FRNAAF2 (NIL T T T T) -7 NIL NIL NIL) (-420 941823 942297 942593 "FRMOD" 943260 NIL FRMOD (NIL T T T T NIL) -8 NIL NIL NIL) (-419 939566 940198 940516 "FRIDEAL" 941614 NIL FRIDEAL (NIL T T T T) -8 NIL NIL NIL) (-418 938757 938844 939135 "FRIDEAL2" 939473 NIL FRIDEAL2 (NIL T T T T T T T T) -7 NIL NIL NIL) (-417 937890 938304 938345 "FRETRCT" 938350 NIL FRETRCT (NIL T) -9 NIL 938526 NIL) (-416 937002 937233 937584 "FRETRCT-" 937589 NIL FRETRCT- (NIL T T) -8 NIL NIL NIL) (-415 934090 935300 935359 "FRAMALG" 936241 NIL FRAMALG (NIL T T) -9 NIL 936533 NIL) (-414 932224 932679 933309 "FRAMALG-" 933532 NIL FRAMALG- (NIL T T T) -8 NIL NIL NIL) (-413 926143 931697 931974 "FRAC" 931979 NIL FRAC (NIL T) -8 NIL NIL NIL) (-412 925779 925836 925943 "FRAC2" 926080 NIL FRAC2 (NIL T T) -7 NIL NIL NIL) (-411 925415 925472 925579 "FR2" 925716 NIL FR2 (NIL T T) -7 NIL NIL NIL) (-410 919928 922821 922849 "FPS" 923968 T FPS (NIL) -9 NIL 924525 NIL) (-409 919377 919486 919650 "FPS-" 919796 NIL FPS- (NIL T) -8 NIL NIL NIL) (-408 916679 918348 918376 "FPC" 918601 T FPC (NIL) -9 NIL 918743 NIL) (-407 916472 916512 916609 "FPC-" 916614 NIL FPC- (NIL T) -8 NIL NIL NIL) (-406 915262 915960 916001 "FPATMAB" 916006 NIL FPATMAB (NIL T) -9 NIL 916158 NIL) (-405 912935 913438 913864 "FPARFRAC" 914899 NIL FPARFRAC (NIL T T) -8 NIL NIL NIL) (-404 908329 908827 909509 "FORTRAN" 912367 NIL FORTRAN (NIL NIL NIL NIL NIL) -8 NIL NIL NIL) (-403 906045 906545 907084 "FORT" 907810 T FORT (NIL) -7 NIL NIL NIL) (-402 903721 904283 904311 "FORTFN" 905371 T FORTFN (NIL) -9 NIL 905995 NIL) (-401 903485 903535 903563 "FORTCAT" 903622 T FORTCAT (NIL) -9 NIL 903684 NIL) (-400 901591 902101 902491 "FORMULA" 903115 T FORMULA (NIL) -8 NIL NIL NIL) (-399 901379 901409 901478 "FORMULA1" 901555 NIL FORMULA1 (NIL T) -7 NIL NIL NIL) (-398 900902 900954 901127 "FORDER" 901321 NIL FORDER (NIL T T T T) -7 NIL NIL NIL) (-397 899998 900162 900355 "FOP" 900729 T FOP (NIL) -7 NIL NIL NIL) (-396 898579 899278 899452 "FNLA" 899880 NIL FNLA (NIL NIL NIL T) -8 NIL NIL NIL) (-395 897308 897723 897751 "FNCAT" 898211 T FNCAT (NIL) -9 NIL 898471 NIL) (-394 896847 897267 897295 "FNAME" 897300 T FNAME (NIL) -8 NIL NIL NIL) (-393 895410 896373 896401 "FMTC" 896406 T FMTC (NIL) -9 NIL 896442 NIL) (-392 894156 895346 895392 "FMONOID" 895397 NIL FMONOID (NIL T) -8 NIL NIL NIL) (-391 890984 892152 892193 "FMONCAT" 893410 NIL FMONCAT (NIL T) -9 NIL 894015 NIL) (-390 890176 890726 890875 "FM" 890880 NIL FM (NIL T T) -8 NIL NIL NIL) (-389 887600 888246 888274 "FMFUN" 889418 T FMFUN (NIL) -9 NIL 890126 NIL) (-388 886869 887050 887078 "FMC" 887368 T FMC (NIL) -9 NIL 887550 NIL) (-387 883948 884808 884862 "FMCAT" 886057 NIL FMCAT (NIL T T) -9 NIL 886552 NIL) (-386 882814 883714 883814 "FM1" 883893 NIL FM1 (NIL T T) -8 NIL NIL NIL) (-385 880588 881004 881498 "FLOATRP" 882365 NIL FLOATRP (NIL T) -7 NIL NIL NIL) (-384 874166 878317 878938 "FLOAT" 879987 T FLOAT (NIL) -8 NIL NIL NIL) (-383 871604 872104 872682 "FLOATCP" 873633 NIL FLOATCP (NIL T) -7 NIL NIL NIL) (-382 870344 871182 871223 "FLINEXP" 871228 NIL FLINEXP (NIL T) -9 NIL 871321 NIL) (-381 869498 869733 870061 "FLINEXP-" 870066 NIL FLINEXP- (NIL T T) -8 NIL NIL NIL) (-380 868574 868718 868942 "FLASORT" 869350 NIL FLASORT (NIL T T) -7 NIL NIL NIL) (-379 865690 866558 866610 "FLALG" 867837 NIL FLALG (NIL T T) -9 NIL 868304 NIL) (-378 859394 863146 863187 "FLAGG" 864449 NIL FLAGG (NIL T) -9 NIL 865101 NIL) (-377 858120 858459 858949 "FLAGG-" 858954 NIL FLAGG- (NIL T T) -8 NIL NIL NIL) (-376 857162 857305 857532 "FLAGG2" 857973 NIL FLAGG2 (NIL T T T T) -7 NIL NIL NIL) (-375 854013 855021 855080 "FINRALG" 856208 NIL FINRALG (NIL T T) -9 NIL 856716 NIL) (-374 853173 853402 853741 "FINRALG-" 853746 NIL FINRALG- (NIL T T T) -8 NIL NIL NIL) (-373 852553 852792 852820 "FINITE" 853016 T FINITE (NIL) -9 NIL 853123 NIL) (-372 844910 847097 847137 "FINAALG" 850804 NIL FINAALG (NIL T) -9 NIL 852257 NIL) (-371 840242 841292 842436 "FINAALG-" 843815 NIL FINAALG- (NIL T T) -8 NIL NIL NIL) (-370 839610 839997 840100 "FILE" 840172 NIL FILE (NIL T) -8 NIL NIL NIL) (-369 838268 838606 838660 "FILECAT" 839344 NIL FILECAT (NIL T T) -9 NIL 839560 NIL) (-368 835984 837512 837540 "FIELD" 837580 T FIELD (NIL) -9 NIL 837660 NIL) (-367 834604 834989 835500 "FIELD-" 835505 NIL FIELD- (NIL T) -8 NIL NIL NIL) (-366 832454 833239 833586 "FGROUP" 834290 NIL FGROUP (NIL T) -8 NIL NIL NIL) (-365 831544 831708 831928 "FGLMICPK" 832286 NIL FGLMICPK (NIL T NIL) -7 NIL NIL NIL) (-364 827376 831469 831526 "FFX" 831531 NIL FFX (NIL T NIL) -8 NIL NIL NIL) (-363 826977 827038 827173 "FFSLPE" 827309 NIL FFSLPE (NIL T T T) -7 NIL NIL NIL) (-362 822967 823749 824545 "FFPOLY" 826213 NIL FFPOLY (NIL T) -7 NIL NIL NIL) (-361 822471 822507 822716 "FFPOLY2" 822925 NIL FFPOLY2 (NIL T T) -7 NIL NIL NIL) (-360 818317 822390 822453 "FFP" 822458 NIL FFP (NIL T NIL) -8 NIL NIL NIL) (-359 813715 818228 818292 "FF" 818297 NIL FF (NIL NIL NIL) -8 NIL NIL NIL) (-358 808841 813058 813248 "FFNBX" 813569 NIL FFNBX (NIL T NIL) -8 NIL NIL NIL) (-357 803769 807976 808234 "FFNBP" 808695 NIL FFNBP (NIL T NIL) -8 NIL NIL NIL) (-356 798402 803053 803264 "FFNB" 803602 NIL FFNB (NIL NIL NIL) -8 NIL NIL NIL) (-355 797234 797432 797747 "FFINTBAS" 798199 NIL FFINTBAS (NIL T T T) -7 NIL NIL NIL) (-354 793303 795523 795551 "FFIELDC" 796171 T FFIELDC (NIL) -9 NIL 796547 NIL) (-353 791965 792336 792833 "FFIELDC-" 792838 NIL FFIELDC- (NIL T) -8 NIL NIL NIL) (-352 791534 791580 791704 "FFHOM" 791907 NIL FFHOM (NIL T T T) -7 NIL NIL NIL) (-351 789229 789716 790233 "FFF" 791049 NIL FFF (NIL T) -7 NIL NIL NIL) (-350 784847 788971 789072 "FFCGX" 789172 NIL FFCGX (NIL T NIL) -8 NIL NIL NIL) (-349 780469 784579 784686 "FFCGP" 784790 NIL FFCGP (NIL T NIL) -8 NIL NIL NIL) (-348 775652 780196 780304 "FFCG" 780405 NIL FFCG (NIL NIL NIL) -8 NIL NIL NIL) (-347 757048 766129 766215 "FFCAT" 771380 NIL FFCAT (NIL T T T) -9 NIL 772831 NIL) (-346 752245 753293 754607 "FFCAT-" 755837 NIL FFCAT- (NIL T T T T) -8 NIL NIL NIL) (-345 751656 751699 751934 "FFCAT2" 752196 NIL FFCAT2 (NIL T T T T T T T T) -7 NIL NIL NIL) (-344 740979 744628 745848 "FEXPR" 750508 NIL FEXPR (NIL NIL NIL T) -8 NIL NIL NIL) (-343 739941 740376 740417 "FEVALAB" 740501 NIL FEVALAB (NIL T) -9 NIL 740762 NIL) (-342 739100 739310 739648 "FEVALAB-" 739653 NIL FEVALAB- (NIL T T) -8 NIL NIL NIL) (-341 737666 738483 738686 "FDIV" 738999 NIL FDIV (NIL T T T T) -8 NIL NIL NIL) (-340 734686 735427 735542 "FDIVCAT" 737110 NIL FDIVCAT (NIL T T T T) -9 NIL 737547 NIL) (-339 734448 734475 734645 "FDIVCAT-" 734650 NIL FDIVCAT- (NIL T T T T T) -8 NIL NIL NIL) (-338 733668 733755 734032 "FDIV2" 734355 NIL FDIV2 (NIL T T T T T T T T) -7 NIL NIL NIL) (-337 732642 732963 733165 "FCTRDATA" 733486 T FCTRDATA (NIL) -8 NIL NIL NIL) (-336 731328 731587 731876 "FCPAK1" 732373 T FCPAK1 (NIL) -7 NIL NIL NIL) (-335 730427 730828 730969 "FCOMP" 731219 NIL FCOMP (NIL T) -8 NIL NIL NIL) (-334 714132 717577 721115 "FC" 726909 T FC (NIL) -8 NIL NIL NIL) (-333 706495 710523 710563 "FAXF" 712365 NIL FAXF (NIL T) -9 NIL 713057 NIL) (-332 703772 704429 705254 "FAXF-" 705719 NIL FAXF- (NIL T T) -8 NIL NIL NIL) (-331 698824 703148 703324 "FARRAY" 703629 NIL FARRAY (NIL T) -8 NIL NIL NIL) (-330 693718 695785 695838 "FAMR" 696861 NIL FAMR (NIL T T) -9 NIL 697321 NIL) (-329 692608 692910 693345 "FAMR-" 693350 NIL FAMR- (NIL T T T) -8 NIL NIL NIL) (-328 691777 692530 692583 "FAMONOID" 692588 NIL FAMONOID (NIL T) -8 NIL NIL NIL) (-327 689563 690273 690326 "FAMONC" 691267 NIL FAMONC (NIL T T) -9 NIL 691653 NIL) (-326 688227 689317 689454 "FAGROUP" 689459 NIL FAGROUP (NIL T) -8 NIL NIL NIL) (-325 686022 686341 686744 "FACUTIL" 687908 NIL FACUTIL (NIL T T T T) -7 NIL NIL NIL) (-324 685121 685306 685528 "FACTFUNC" 685832 NIL FACTFUNC (NIL T) -7 NIL NIL NIL) (-323 677543 684424 684623 "EXPUPXS" 684977 NIL EXPUPXS (NIL T NIL NIL) -8 NIL NIL NIL) (-322 675026 675566 676152 "EXPRTUBE" 676977 T EXPRTUBE (NIL) -7 NIL NIL NIL) (-321 671297 671889 672619 "EXPRODE" 674365 NIL EXPRODE (NIL T T) -7 NIL NIL NIL) (-320 656782 669946 670375 "EXPR" 670901 NIL EXPR (NIL T) -8 NIL NIL NIL) (-319 651336 651923 652729 "EXPR2UPS" 656080 NIL EXPR2UPS (NIL T T) -7 NIL NIL NIL) (-318 650968 651025 651134 "EXPR2" 651273 NIL EXPR2 (NIL T T) -7 NIL NIL NIL) (-317 642356 650119 650410 "EXPEXPAN" 650804 NIL EXPEXPAN (NIL T T NIL NIL) -8 NIL NIL NIL) (-316 642156 642313 642342 "EXIT" 642347 T EXIT (NIL) -8 NIL NIL NIL) (-315 641636 641880 641971 "EXITAST" 642085 T EXITAST (NIL) -8 NIL NIL NIL) (-314 641263 641325 641438 "EVALCYC" 641568 NIL EVALCYC (NIL T) -7 NIL NIL NIL) (-313 640804 640922 640963 "EVALAB" 641133 NIL EVALAB (NIL T) -9 NIL 641237 NIL) (-312 640285 640407 640628 "EVALAB-" 640633 NIL EVALAB- (NIL T T) -8 NIL NIL NIL) (-311 637653 638955 638983 "EUCDOM" 639538 T EUCDOM (NIL) -9 NIL 639888 NIL) (-310 636058 636500 637090 "EUCDOM-" 637095 NIL EUCDOM- (NIL T) -8 NIL NIL NIL) (-309 623597 626356 629106 "ESTOOLS" 633328 T ESTOOLS (NIL) -7 NIL NIL NIL) (-308 623229 623286 623395 "ESTOOLS2" 623534 NIL ESTOOLS2 (NIL T T) -7 NIL NIL NIL) (-307 622980 623022 623102 "ESTOOLS1" 623181 NIL ESTOOLS1 (NIL T) -7 NIL NIL NIL) (-306 617017 618625 618653 "ES" 621421 T ES (NIL) -9 NIL 622831 NIL) (-305 611964 613251 615068 "ES-" 615232 NIL ES- (NIL T) -8 NIL NIL NIL) (-304 608338 609099 609879 "ESCONT" 611204 T ESCONT (NIL) -7 NIL NIL NIL) (-303 608083 608115 608197 "ESCONT1" 608300 NIL ESCONT1 (NIL NIL NIL) -7 NIL NIL NIL) (-302 607758 607808 607908 "ES2" 608027 NIL ES2 (NIL T T) -7 NIL NIL NIL) (-301 607388 607446 607555 "ES1" 607694 NIL ES1 (NIL T T) -7 NIL NIL NIL) (-300 606604 606733 606909 "ERROR" 607232 T ERROR (NIL) -7 NIL NIL NIL) (-299 599996 606463 606554 "EQTBL" 606559 NIL EQTBL (NIL T T) -8 NIL NIL NIL) (-298 592499 595310 596759 "EQ" 598580 NIL -2094 (NIL T) -8 NIL NIL NIL) (-297 592131 592188 592297 "EQ2" 592436 NIL EQ2 (NIL T T) -7 NIL NIL NIL) (-296 587422 588469 589562 "EP" 591070 NIL EP (NIL T) -7 NIL NIL NIL) (-295 586022 586313 586619 "ENV" 587136 T ENV (NIL) -8 NIL NIL NIL) (-294 585116 585670 585698 "ENTIRER" 585703 T ENTIRER (NIL) -9 NIL 585749 NIL) (-293 581810 583298 583659 "EMR" 584924 NIL EMR (NIL T T T NIL NIL NIL) -8 NIL NIL NIL) (-292 580940 581125 581179 "ELTAGG" 581559 NIL ELTAGG (NIL T T) -9 NIL 581770 NIL) (-291 580659 580721 580862 "ELTAGG-" 580867 NIL ELTAGG- (NIL T T T) -8 NIL NIL NIL) (-290 580423 580452 580506 "ELTAB" 580590 NIL ELTAB (NIL T T) -9 NIL 580642 NIL) (-289 579549 579695 579894 "ELFUTS" 580274 NIL ELFUTS (NIL T T) -7 NIL NIL NIL) (-288 579291 579347 579375 "ELEMFUN" 579480 T ELEMFUN (NIL) -9 NIL NIL NIL) (-287 579161 579182 579250 "ELEMFUN-" 579255 NIL ELEMFUN- (NIL T) -8 NIL NIL NIL) (-286 573975 577231 577272 "ELAGG" 578212 NIL ELAGG (NIL T) -9 NIL 578675 NIL) (-285 572260 572694 573357 "ELAGG-" 573362 NIL ELAGG- (NIL T T) -8 NIL NIL NIL) (-284 571572 571709 571865 "ELABOR" 572124 T ELABOR (NIL) -8 NIL NIL NIL) (-283 570233 570512 570806 "ELABEXPR" 571298 T ELABEXPR (NIL) -8 NIL NIL NIL) (-282 563097 564900 565727 "EFUPXS" 569509 NIL EFUPXS (NIL T T T T) -8 NIL NIL NIL) (-281 556547 558348 559158 "EFULS" 562373 NIL EFULS (NIL T T T) -8 NIL NIL NIL) (-280 554032 554390 554862 "EFSTRUC" 556179 NIL EFSTRUC (NIL T T) -7 NIL NIL NIL) (-279 543823 545389 546937 "EF" 552547 NIL EF (NIL T T) -7 NIL NIL NIL) (-278 542897 543308 543457 "EAB" 543694 T EAB (NIL) -8 NIL NIL NIL) (-277 542079 542856 542884 "E04UCFA" 542889 T E04UCFA (NIL) -8 NIL NIL NIL) (-276 541261 542038 542066 "E04NAFA" 542071 T E04NAFA (NIL) -8 NIL NIL NIL) (-275 540443 541220 541248 "E04MBFA" 541253 T E04MBFA (NIL) -8 NIL NIL NIL) (-274 539625 540402 540430 "E04JAFA" 540435 T E04JAFA (NIL) -8 NIL NIL NIL) (-273 538809 539584 539612 "E04GCFA" 539617 T E04GCFA (NIL) -8 NIL NIL NIL) (-272 537993 538768 538796 "E04FDFA" 538801 T E04FDFA (NIL) -8 NIL NIL NIL) (-271 537175 537952 537980 "E04DGFA" 537985 T E04DGFA (NIL) -8 NIL NIL NIL) (-270 531348 532700 534064 "E04AGNT" 535831 T E04AGNT (NIL) -7 NIL NIL NIL) (-269 530028 530534 530574 "DVARCAT" 531049 NIL DVARCAT (NIL T) -9 NIL 531248 NIL) (-268 529232 529444 529758 "DVARCAT-" 529763 NIL DVARCAT- (NIL T T) -8 NIL NIL NIL) (-267 522369 529031 529160 "DSMP" 529165 NIL DSMP (NIL T T T) -8 NIL NIL NIL) (-266 517150 518314 519382 "DROPT" 521321 T DROPT (NIL) -8 NIL NIL NIL) (-265 516815 516874 516972 "DROPT1" 517085 NIL DROPT1 (NIL T) -7 NIL NIL NIL) (-264 511930 513056 514193 "DROPT0" 515698 T DROPT0 (NIL) -7 NIL NIL NIL) (-263 510275 510600 510986 "DRAWPT" 511564 T DRAWPT (NIL) -7 NIL NIL NIL) (-262 504862 505785 506864 "DRAW" 509249 NIL DRAW (NIL T) -7 NIL NIL NIL) (-261 504495 504548 504666 "DRAWHACK" 504803 NIL DRAWHACK (NIL T) -7 NIL NIL NIL) (-260 503226 503495 503786 "DRAWCX" 504224 T DRAWCX (NIL) -7 NIL NIL NIL) (-259 502741 502810 502961 "DRAWCURV" 503152 NIL DRAWCURV (NIL T T) -7 NIL NIL NIL) (-258 493209 495171 497286 "DRAWCFUN" 500646 T DRAWCFUN (NIL) -7 NIL NIL NIL) (-257 489973 491902 491943 "DQAGG" 492572 NIL DQAGG (NIL T) -9 NIL 492846 NIL) (-256 478097 484566 484649 "DPOLCAT" 486501 NIL DPOLCAT (NIL T T T T) -9 NIL 487046 NIL) (-255 472934 474282 476240 "DPOLCAT-" 476245 NIL DPOLCAT- (NIL T T T T T) -8 NIL NIL NIL) (-254 466056 472795 472893 "DPMO" 472898 NIL DPMO (NIL NIL T T) -8 NIL NIL NIL) (-253 459081 465836 466003 "DPMM" 466008 NIL DPMM (NIL NIL T T T) -8 NIL NIL NIL) (-252 458651 458865 458954 "DOMTMPLT" 459012 T DOMTMPLT (NIL) -8 NIL NIL NIL) (-251 458084 458453 458533 "DOMCTOR" 458591 T DOMCTOR (NIL) -8 NIL NIL NIL) (-250 457296 457564 457715 "DOMAIN" 457953 T DOMAIN (NIL) -8 NIL NIL NIL) (-249 451284 456931 457083 "DMP" 457197 NIL DMP (NIL NIL T) -8 NIL NIL NIL) (-248 450884 450940 451084 "DLP" 451222 NIL DLP (NIL T) -7 NIL NIL NIL) (-247 444706 450211 450401 "DLIST" 450726 NIL DLIST (NIL T) -8 NIL NIL NIL) (-246 441503 443559 443600 "DLAGG" 444150 NIL DLAGG (NIL T) -9 NIL 444380 NIL) (-245 440179 440843 440871 "DIVRING" 440963 T DIVRING (NIL) -9 NIL 441046 NIL) (-244 439416 439606 439906 "DIVRING-" 439911 NIL DIVRING- (NIL T) -8 NIL NIL NIL) (-243 437518 437875 438281 "DISPLAY" 439030 T DISPLAY (NIL) -7 NIL NIL NIL) (-242 431404 437432 437495 "DIRPROD" 437500 NIL DIRPROD (NIL NIL T) -8 NIL NIL NIL) (-241 430252 430455 430720 "DIRPROD2" 431197 NIL DIRPROD2 (NIL NIL T T) -7 NIL NIL NIL) (-240 419027 425033 425086 "DIRPCAT" 425496 NIL DIRPCAT (NIL NIL T) -9 NIL 426336 NIL) (-239 416353 416995 417876 "DIRPCAT-" 418213 NIL DIRPCAT- (NIL T NIL T) -8 NIL NIL NIL) (-238 415640 415800 415986 "DIOSP" 416187 T DIOSP (NIL) -7 NIL NIL NIL) (-237 412295 414552 414593 "DIOPS" 415027 NIL DIOPS (NIL T) -9 NIL 415256 NIL) (-236 411844 411958 412149 "DIOPS-" 412154 NIL DIOPS- (NIL T T) -8 NIL NIL NIL) (-235 410667 411295 411323 "DIFRING" 411510 T DIFRING (NIL) -9 NIL 411620 NIL) (-234 410313 410390 410542 "DIFRING-" 410547 NIL DIFRING- (NIL T) -8 NIL NIL NIL) (-233 408049 409321 409362 "DIFEXT" 409725 NIL DIFEXT (NIL T) -9 NIL 410019 NIL) (-232 406334 406762 407428 "DIFEXT-" 407433 NIL DIFEXT- (NIL T T) -8 NIL NIL NIL) (-231 403609 405866 405907 "DIAGG" 405912 NIL DIAGG (NIL T) -9 NIL 405932 NIL) (-230 402993 403150 403402 "DIAGG-" 403407 NIL DIAGG- (NIL T T) -8 NIL NIL NIL) (-229 398410 401952 402229 "DHMATRIX" 402762 NIL DHMATRIX (NIL T) -8 NIL NIL NIL) (-228 394022 394931 395941 "DFSFUN" 397420 T DFSFUN (NIL) -7 NIL NIL NIL) (-227 389102 392953 393265 "DFLOAT" 393730 T DFLOAT (NIL) -8 NIL NIL NIL) (-226 387365 387646 388035 "DFINTTLS" 388810 NIL DFINTTLS (NIL T T) -7 NIL NIL NIL) (-225 384394 385386 385786 "DERHAM" 387031 NIL DERHAM (NIL T NIL) -8 NIL NIL NIL) (-224 382195 384169 384258 "DEQUEUE" 384338 NIL DEQUEUE (NIL T) -8 NIL NIL NIL) (-223 381449 381582 381765 "DEGRED" 382057 NIL DEGRED (NIL T T) -7 NIL NIL NIL) (-222 377879 378624 379470 "DEFINTRF" 380677 NIL DEFINTRF (NIL T) -7 NIL NIL NIL) (-221 375434 375903 376495 "DEFINTEF" 377398 NIL DEFINTEF (NIL T T) -7 NIL NIL NIL) (-220 374784 375054 375169 "DEFAST" 375339 T DEFAST (NIL) -8 NIL NIL NIL) (-219 368786 374377 374527 "DECIMAL" 374654 T DECIMAL (NIL) -8 NIL NIL NIL) (-218 366298 366756 367262 "DDFACT" 368330 NIL DDFACT (NIL T T) -7 NIL NIL NIL) (-217 365894 365937 366088 "DBLRESP" 366249 NIL DBLRESP (NIL T T T T) -7 NIL NIL NIL) (-216 363766 364127 364487 "DBASE" 365661 NIL DBASE (NIL T) -8 NIL NIL NIL) (-215 363008 363246 363392 "DATAARY" 363665 NIL DATAARY (NIL NIL T) -8 NIL NIL NIL) (-214 362114 362967 362995 "D03FAFA" 363000 T D03FAFA (NIL) -8 NIL NIL NIL) (-213 361221 362073 362101 "D03EEFA" 362106 T D03EEFA (NIL) -8 NIL NIL NIL) (-212 359171 359637 360126 "D03AGNT" 360752 T D03AGNT (NIL) -7 NIL NIL NIL) (-211 358460 359130 359158 "D02EJFA" 359163 T D02EJFA (NIL) -8 NIL NIL NIL) (-210 357749 358419 358447 "D02CJFA" 358452 T D02CJFA (NIL) -8 NIL NIL NIL) (-209 357038 357708 357736 "D02BHFA" 357741 T D02BHFA (NIL) -8 NIL NIL NIL) (-208 356327 356997 357025 "D02BBFA" 357030 T D02BBFA (NIL) -8 NIL NIL NIL) (-207 349524 351113 352719 "D02AGNT" 354741 T D02AGNT (NIL) -7 NIL NIL NIL) (-206 347292 347815 348361 "D01WGTS" 348998 T D01WGTS (NIL) -7 NIL NIL NIL) (-205 346359 347251 347279 "D01TRNS" 347284 T D01TRNS (NIL) -8 NIL NIL NIL) (-204 345427 346318 346346 "D01GBFA" 346351 T D01GBFA (NIL) -8 NIL NIL NIL) (-203 344495 345386 345414 "D01FCFA" 345419 T D01FCFA (NIL) -8 NIL NIL NIL) (-202 343563 344454 344482 "D01ASFA" 344487 T D01ASFA (NIL) -8 NIL NIL NIL) (-201 342631 343522 343550 "D01AQFA" 343555 T D01AQFA (NIL) -8 NIL NIL NIL) (-200 341699 342590 342618 "D01APFA" 342623 T D01APFA (NIL) -8 NIL NIL NIL) (-199 340767 341658 341686 "D01ANFA" 341691 T D01ANFA (NIL) -8 NIL NIL NIL) (-198 339835 340726 340754 "D01AMFA" 340759 T D01AMFA (NIL) -8 NIL NIL NIL) (-197 338903 339794 339822 "D01ALFA" 339827 T D01ALFA (NIL) -8 NIL NIL NIL) (-196 337971 338862 338890 "D01AKFA" 338895 T D01AKFA (NIL) -8 NIL NIL NIL) (-195 337039 337930 337958 "D01AJFA" 337963 T D01AJFA (NIL) -8 NIL NIL NIL) (-194 330334 331887 333448 "D01AGNT" 335498 T D01AGNT (NIL) -7 NIL NIL NIL) (-193 329671 329799 329951 "CYCLOTOM" 330202 T CYCLOTOM (NIL) -7 NIL NIL NIL) (-192 326404 327119 327846 "CYCLES" 328964 T CYCLES (NIL) -7 NIL NIL NIL) (-191 325716 325850 326021 "CVMP" 326265 NIL CVMP (NIL T) -7 NIL NIL NIL) (-190 323557 323815 324184 "CTRIGMNP" 325444 NIL CTRIGMNP (NIL T T) -7 NIL NIL NIL) (-189 322993 323351 323424 "CTOR" 323504 T CTOR (NIL) -8 NIL NIL NIL) (-188 322502 322724 322825 "CTORKIND" 322912 T CTORKIND (NIL) -8 NIL NIL NIL) (-187 321793 322109 322137 "CTORCAT" 322319 T CTORCAT (NIL) -9 NIL 322432 NIL) (-186 321391 321502 321661 "CTORCAT-" 321666 NIL CTORCAT- (NIL T) -8 NIL NIL NIL) (-185 320853 321065 321173 "CTORCALL" 321315 NIL CTORCALL (NIL T) -8 NIL NIL NIL) (-184 320227 320326 320479 "CSTTOOLS" 320750 NIL CSTTOOLS (NIL T T) -7 NIL NIL NIL) (-183 316026 316683 317441 "CRFP" 319539 NIL CRFP (NIL T T) -7 NIL NIL NIL) (-182 315501 315747 315839 "CRCEAST" 315954 T CRCEAST (NIL) -8 NIL NIL NIL) (-181 314548 314733 314961 "CRAPACK" 315305 NIL CRAPACK (NIL T) -7 NIL NIL NIL) (-180 313932 314033 314237 "CPMATCH" 314424 NIL CPMATCH (NIL T T T) -7 NIL NIL NIL) (-179 313657 313685 313791 "CPIMA" 313898 NIL CPIMA (NIL T T T) -7 NIL NIL NIL) (-178 310005 310677 311396 "COORDSYS" 312992 NIL COORDSYS (NIL T) -7 NIL NIL NIL) (-177 309417 309538 309680 "CONTOUR" 309883 T CONTOUR (NIL) -8 NIL NIL NIL) (-176 305308 307420 307912 "CONTFRAC" 308957 NIL CONTFRAC (NIL T) -8 NIL NIL NIL) (-175 305188 305209 305237 "CONDUIT" 305274 T CONDUIT (NIL) -9 NIL NIL NIL) (-174 304276 304830 304858 "COMRING" 304863 T COMRING (NIL) -9 NIL 304915 NIL) (-173 303330 303634 303818 "COMPPROP" 304112 T COMPPROP (NIL) -8 NIL NIL NIL) (-172 302991 303026 303154 "COMPLPAT" 303289 NIL COMPLPAT (NIL T T T) -7 NIL NIL NIL) (-171 293282 302800 302909 "COMPLEX" 302914 NIL COMPLEX (NIL T) -8 NIL NIL NIL) (-170 292918 292975 293082 "COMPLEX2" 293219 NIL COMPLEX2 (NIL T T) -7 NIL NIL NIL) (-169 292257 292378 292538 "COMPILER" 292778 T COMPILER (NIL) -8 NIL NIL NIL) (-168 291975 292010 292108 "COMPFACT" 292216 NIL COMPFACT (NIL T T) -7 NIL NIL NIL) (-167 276055 286049 286089 "COMPCAT" 287093 NIL COMPCAT (NIL T) -9 NIL 288441 NIL) (-166 265567 268494 272121 "COMPCAT-" 272477 NIL COMPCAT- (NIL T T) -8 NIL NIL NIL) (-165 265296 265324 265427 "COMMUPC" 265533 NIL COMMUPC (NIL T T T) -7 NIL NIL NIL) (-164 265090 265124 265183 "COMMONOP" 265257 T COMMONOP (NIL) -7 NIL NIL NIL) (-163 264646 264841 264928 "COMM" 265023 T COMM (NIL) -8 NIL NIL NIL) (-162 264222 264450 264525 "COMMAAST" 264591 T COMMAAST (NIL) -8 NIL NIL NIL) (-161 263471 263665 263693 "COMBOPC" 264031 T COMBOPC (NIL) -9 NIL 264206 NIL) (-160 262367 262577 262819 "COMBINAT" 263261 NIL COMBINAT (NIL T) -7 NIL NIL NIL) (-159 258824 259398 260025 "COMBF" 261789 NIL COMBF (NIL T T) -7 NIL NIL NIL) (-158 257582 257940 258175 "COLOR" 258609 T COLOR (NIL) -8 NIL NIL NIL) (-157 257058 257303 257395 "COLONAST" 257510 T COLONAST (NIL) -8 NIL NIL NIL) (-156 256698 256745 256870 "CMPLXRT" 257005 NIL CMPLXRT (NIL T T) -7 NIL NIL NIL) (-155 256146 256398 256497 "CLLCTAST" 256619 T CLLCTAST (NIL) -8 NIL NIL NIL) (-154 251648 252676 253756 "CLIP" 255086 T CLIP (NIL) -7 NIL NIL NIL) (-153 249989 250749 250989 "CLIF" 251475 NIL CLIF (NIL NIL T NIL) -8 NIL NIL NIL) (-152 246164 248135 248176 "CLAGG" 249105 NIL CLAGG (NIL T) -9 NIL 249641 NIL) (-151 244586 245043 245626 "CLAGG-" 245631 NIL CLAGG- (NIL T T) -8 NIL NIL NIL) (-150 244130 244215 244355 "CINTSLPE" 244495 NIL CINTSLPE (NIL T T) -7 NIL NIL NIL) (-149 241631 242102 242650 "CHVAR" 243658 NIL CHVAR (NIL T T T) -7 NIL NIL NIL) (-148 240805 241359 241387 "CHARZ" 241392 T CHARZ (NIL) -9 NIL 241407 NIL) (-147 240559 240599 240677 "CHARPOL" 240759 NIL CHARPOL (NIL T) -7 NIL NIL NIL) (-146 239617 240204 240232 "CHARNZ" 240279 T CHARNZ (NIL) -9 NIL 240335 NIL) (-145 237523 238271 238624 "CHAR" 239284 T CHAR (NIL) -8 NIL NIL NIL) (-144 237249 237310 237338 "CFCAT" 237449 T CFCAT (NIL) -9 NIL NIL NIL) (-143 236490 236601 236784 "CDEN" 237133 NIL CDEN (NIL T T T) -7 NIL NIL NIL) (-142 232455 235643 235923 "CCLASS" 236230 T CCLASS (NIL) -8 NIL NIL NIL) (-141 231706 231863 232040 "CATEGORY" 232298 T -10 (NIL) -8 NIL NIL NIL) (-140 231279 231625 231673 "CATCTOR" 231678 T CATCTOR (NIL) -8 NIL NIL NIL) (-139 230730 230982 231080 "CATAST" 231201 T CATAST (NIL) -8 NIL NIL NIL) (-138 230206 230451 230543 "CASEAST" 230658 T CASEAST (NIL) -8 NIL NIL NIL) (-137 225344 226363 227107 "CARTEN" 229518 NIL CARTEN (NIL NIL NIL T) -8 NIL NIL NIL) (-136 224452 224600 224821 "CARTEN2" 225191 NIL CARTEN2 (NIL NIL NIL T T) -7 NIL NIL NIL) (-135 222768 223602 223859 "CARD" 224215 T CARD (NIL) -8 NIL NIL NIL) (-134 222344 222572 222647 "CAPSLAST" 222713 T CAPSLAST (NIL) -8 NIL NIL NIL) (-133 221848 222056 222084 "CACHSET" 222216 T CACHSET (NIL) -9 NIL 222294 NIL) (-132 221318 221640 221668 "CABMON" 221718 T CABMON (NIL) -9 NIL 221774 NIL) (-131 220791 221022 221132 "BYTEORD" 221228 T BYTEORD (NIL) -8 NIL NIL NIL) (-130 219768 220320 220462 "BYTE" 220625 T BYTE (NIL) -8 NIL NIL 220747) (-129 215118 219273 219445 "BYTEBUF" 219616 T BYTEBUF (NIL) -8 NIL NIL NIL) (-128 212627 214810 214917 "BTREE" 215044 NIL BTREE (NIL T) -8 NIL NIL NIL) (-127 210076 212275 212397 "BTOURN" 212537 NIL BTOURN (NIL T) -8 NIL NIL NIL) (-126 207446 209546 209587 "BTCAT" 209655 NIL BTCAT (NIL T) -9 NIL 209732 NIL) (-125 207113 207193 207342 "BTCAT-" 207347 NIL BTCAT- (NIL T T) -8 NIL NIL NIL) (-124 202492 206372 206400 "BTAGG" 206514 T BTAGG (NIL) -9 NIL 206624 NIL) (-123 201982 202107 202313 "BTAGG-" 202318 NIL BTAGG- (NIL T) -8 NIL NIL NIL) (-122 198977 201260 201475 "BSTREE" 201799 NIL BSTREE (NIL T) -8 NIL NIL NIL) (-121 198115 198241 198425 "BRILL" 198833 NIL BRILL (NIL T) -7 NIL NIL NIL) (-120 194767 196841 196882 "BRAGG" 197531 NIL BRAGG (NIL T) -9 NIL 197789 NIL) (-119 193296 193702 194257 "BRAGG-" 194262 NIL BRAGG- (NIL T T) -8 NIL NIL NIL) (-118 186523 192640 192825 "BPADICRT" 193143 NIL BPADICRT (NIL NIL) -8 NIL NIL NIL) (-117 184838 186460 186505 "BPADIC" 186510 NIL BPADIC (NIL NIL) -8 NIL NIL NIL) (-116 184536 184566 184680 "BOUNDZRO" 184802 NIL BOUNDZRO (NIL T T) -7 NIL NIL NIL) (-115 179764 180962 181874 "BOP" 183644 T BOP (NIL) -8 NIL NIL NIL) (-114 177545 177949 178424 "BOP1" 179322 NIL BOP1 (NIL T) -7 NIL NIL NIL) (-113 177246 177307 177335 "BOOLE" 177446 T BOOLE (NIL) -9 NIL 177528 NIL) (-112 176071 176820 176969 "BOOLEAN" 177117 T BOOLEAN (NIL) -8 NIL NIL NIL) (-111 175350 175754 175808 "BMODULE" 175813 NIL BMODULE (NIL T T) -9 NIL 175878 NIL) (-110 171151 175148 175221 "BITS" 175297 T BITS (NIL) -8 NIL NIL NIL) (-109 170572 170691 170831 "BINDING" 171031 T BINDING (NIL) -8 NIL NIL NIL) (-108 164577 170167 170316 "BINARY" 170443 T BINARY (NIL) -8 NIL NIL NIL) (-107 162357 163832 163873 "BGAGG" 164133 NIL BGAGG (NIL T) -9 NIL 164270 NIL) (-106 162188 162220 162311 "BGAGG-" 162316 NIL BGAGG- (NIL T T) -8 NIL NIL NIL) (-105 161259 161572 161777 "BFUNCT" 162003 T BFUNCT (NIL) -8 NIL NIL NIL) (-104 159949 160127 160415 "BEZOUT" 161083 NIL BEZOUT (NIL T T T T T) -7 NIL NIL NIL) (-103 156418 158801 159131 "BBTREE" 159652 NIL BBTREE (NIL T) -8 NIL NIL NIL) (-102 156152 156205 156233 "BASTYPE" 156352 T BASTYPE (NIL) -9 NIL NIL NIL) (-101 156004 156033 156106 "BASTYPE-" 156111 NIL BASTYPE- (NIL T) -8 NIL NIL NIL) (-100 155438 155514 155666 "BALFACT" 155915 NIL BALFACT (NIL T T) -7 NIL NIL NIL) (-99 154294 154853 155039 "AUTOMOR" 155283 NIL AUTOMOR (NIL T) -8 NIL NIL NIL) (-98 154020 154025 154051 "ATTREG" 154056 T ATTREG (NIL) -9 NIL NIL NIL) (-97 152272 152717 153069 "ATTRBUT" 153686 T ATTRBUT (NIL) -8 NIL NIL NIL) (-96 151880 152100 152166 "ATTRAST" 152224 T ATTRAST (NIL) -8 NIL NIL NIL) (-95 151416 151529 151555 "ATRIG" 151756 T ATRIG (NIL) -9 NIL NIL NIL) (-94 151225 151266 151353 "ATRIG-" 151358 NIL ATRIG- (NIL T) -8 NIL NIL NIL) (-93 150870 151056 151082 "ASTCAT" 151087 T ASTCAT (NIL) -9 NIL 151117 NIL) (-92 150597 150656 150775 "ASTCAT-" 150780 NIL ASTCAT- (NIL T) -8 NIL NIL NIL) (-91 148746 150373 150461 "ASTACK" 150540 NIL ASTACK (NIL T) -8 NIL NIL NIL) (-90 147251 147548 147913 "ASSOCEQ" 148428 NIL ASSOCEQ (NIL T T) -7 NIL NIL NIL) (-89 146283 146910 147034 "ASP9" 147158 NIL ASP9 (NIL NIL) -8 NIL NIL NIL) (-88 146046 146231 146270 "ASP8" 146275 NIL ASP8 (NIL NIL) -8 NIL NIL NIL) (-87 144914 145651 145793 "ASP80" 145935 NIL ASP80 (NIL NIL) -8 NIL NIL NIL) (-86 143812 144549 144681 "ASP7" 144813 NIL ASP7 (NIL NIL) -8 NIL NIL NIL) (-85 142766 143489 143607 "ASP78" 143725 NIL ASP78 (NIL NIL) -8 NIL NIL NIL) (-84 141735 142446 142563 "ASP77" 142680 NIL ASP77 (NIL NIL) -8 NIL NIL NIL) (-83 140647 141373 141504 "ASP74" 141635 NIL ASP74 (NIL NIL) -8 NIL NIL NIL) (-82 139547 140282 140414 "ASP73" 140546 NIL ASP73 (NIL NIL) -8 NIL NIL NIL) (-81 138651 139373 139473 "ASP6" 139478 NIL ASP6 (NIL NIL) -8 NIL NIL NIL) (-80 137598 138328 138446 "ASP55" 138564 NIL ASP55 (NIL NIL) -8 NIL NIL NIL) (-79 136547 137272 137391 "ASP50" 137510 NIL ASP50 (NIL NIL) -8 NIL NIL NIL) (-78 135635 136248 136358 "ASP4" 136468 NIL ASP4 (NIL NIL) -8 NIL NIL NIL) (-77 134723 135336 135446 "ASP49" 135556 NIL ASP49 (NIL NIL) -8 NIL NIL NIL) (-76 133507 134262 134430 "ASP42" 134612 NIL ASP42 (NIL NIL NIL NIL) -8 NIL NIL NIL) (-75 132284 133040 133210 "ASP41" 133394 NIL ASP41 (NIL NIL NIL NIL) -8 NIL NIL NIL) (-74 131234 131961 132079 "ASP35" 132197 NIL ASP35 (NIL NIL) -8 NIL NIL NIL) (-73 130999 131182 131221 "ASP34" 131226 NIL ASP34 (NIL NIL) -8 NIL NIL NIL) (-72 130736 130803 130879 "ASP33" 130954 NIL ASP33 (NIL NIL) -8 NIL NIL NIL) (-71 129630 130371 130503 "ASP31" 130635 NIL ASP31 (NIL NIL) -8 NIL NIL NIL) (-70 129395 129578 129617 "ASP30" 129622 NIL ASP30 (NIL NIL) -8 NIL NIL NIL) (-69 129130 129199 129275 "ASP29" 129350 NIL ASP29 (NIL NIL) -8 NIL NIL NIL) (-68 128895 129078 129117 "ASP28" 129122 NIL ASP28 (NIL NIL) -8 NIL NIL NIL) (-67 128660 128843 128882 "ASP27" 128887 NIL ASP27 (NIL NIL) -8 NIL NIL NIL) (-66 127744 128358 128469 "ASP24" 128580 NIL ASP24 (NIL NIL) -8 NIL NIL NIL) (-65 126821 127546 127658 "ASP20" 127663 NIL ASP20 (NIL NIL) -8 NIL NIL NIL) (-64 125909 126522 126632 "ASP1" 126742 NIL ASP1 (NIL NIL) -8 NIL NIL NIL) (-63 124852 125583 125702 "ASP19" 125821 NIL ASP19 (NIL NIL) -8 NIL NIL NIL) (-62 124589 124656 124732 "ASP12" 124807 NIL ASP12 (NIL NIL) -8 NIL NIL NIL) (-61 123441 124188 124332 "ASP10" 124476 NIL ASP10 (NIL NIL) -8 NIL NIL NIL) (-60 121292 123285 123376 "ARRAY2" 123381 NIL ARRAY2 (NIL T) -8 NIL NIL NIL) (-59 117057 120940 121054 "ARRAY1" 121209 NIL ARRAY1 (NIL T) -8 NIL NIL NIL) (-58 116089 116262 116483 "ARRAY12" 116880 NIL ARRAY12 (NIL T T) -7 NIL NIL NIL) (-57 110401 112319 112394 "ARR2CAT" 115024 NIL ARR2CAT (NIL T T T) -9 NIL 115782 NIL) (-56 107835 108579 109533 "ARR2CAT-" 109538 NIL ARR2CAT- (NIL T T T T) -8 NIL NIL NIL) (-55 107152 107462 107587 "ARITY" 107728 T ARITY (NIL) -8 NIL NIL NIL) (-54 105928 106080 106379 "APPRULE" 106988 NIL APPRULE (NIL T T T) -7 NIL NIL NIL) (-53 105579 105627 105746 "APPLYORE" 105874 NIL APPLYORE (NIL T T T) -7 NIL NIL NIL) (-52 104933 105172 105292 "ANY" 105477 T ANY (NIL) -8 NIL NIL NIL) (-51 104211 104334 104491 "ANY1" 104807 NIL ANY1 (NIL T) -7 NIL NIL NIL) (-50 101741 102648 102975 "ANTISYM" 103935 NIL ANTISYM (NIL T NIL) -8 NIL NIL NIL) (-49 101233 101448 101544 "ANON" 101663 T ANON (NIL) -8 NIL NIL NIL) (-48 95482 99772 100226 "AN" 100797 T AN (NIL) -8 NIL NIL NIL) (-47 91380 92768 92819 "AMR" 93567 NIL AMR (NIL T T) -9 NIL 94167 NIL) (-46 90492 90713 91076 "AMR-" 91081 NIL AMR- (NIL T T T) -8 NIL NIL NIL) (-45 74931 90409 90470 "ALIST" 90475 NIL ALIST (NIL T T) -8 NIL NIL NIL) (-44 71736 74525 74694 "ALGSC" 74849 NIL ALGSC (NIL T NIL NIL NIL) -8 NIL NIL NIL) (-43 68292 68846 69453 "ALGPKG" 71176 NIL ALGPKG (NIL T T) -7 NIL NIL NIL) (-42 67569 67670 67854 "ALGMFACT" 68178 NIL ALGMFACT (NIL T T T) -7 NIL NIL NIL) (-41 63604 64183 64777 "ALGMANIP" 67153 NIL ALGMANIP (NIL T T) -7 NIL NIL NIL) (-40 54974 63230 63380 "ALGFF" 63537 NIL ALGFF (NIL T T T NIL) -8 NIL NIL NIL) (-39 54170 54301 54480 "ALGFACT" 54832 NIL ALGFACT (NIL T) -7 NIL NIL NIL) (-38 53111 53711 53749 "ALGEBRA" 53754 NIL ALGEBRA (NIL T) -9 NIL 53795 NIL) (-37 52829 52888 53020 "ALGEBRA-" 53025 NIL ALGEBRA- (NIL T T) -8 NIL NIL NIL) (-36 34892 50801 50853 "ALAGG" 50989 NIL ALAGG (NIL T T) -9 NIL 51150 NIL) (-35 34428 34541 34567 "AHYP" 34768 T AHYP (NIL) -9 NIL NIL NIL) (-34 33359 33607 33633 "AGG" 34132 T AGG (NIL) -9 NIL 34411 NIL) (-33 32793 32955 33169 "AGG-" 33174 NIL AGG- (NIL T) -8 NIL NIL NIL) (-32 30599 31022 31427 "AF" 32435 NIL AF (NIL T T) -7 NIL NIL NIL) (-31 30079 30324 30414 "ADDAST" 30527 T ADDAST (NIL) -8 NIL NIL NIL) (-30 29347 29606 29762 "ACPLOT" 29941 T ACPLOT (NIL) -8 NIL NIL NIL) (-29 18670 26474 26512 "ACFS" 27119 NIL ACFS (NIL T) -9 NIL 27358 NIL) (-28 16697 17187 17949 "ACFS-" 17954 NIL ACFS- (NIL T T) -8 NIL NIL NIL) (-27 12815 14744 14770 "ACF" 15649 T ACF (NIL) -9 NIL 16062 NIL) (-26 11519 11853 12346 "ACF-" 12351 NIL ACF- (NIL T) -8 NIL NIL NIL) (-25 11091 11286 11312 "ABELSG" 11404 T ABELSG (NIL) -9 NIL 11469 NIL) (-24 10958 10983 11049 "ABELSG-" 11054 NIL ABELSG- (NIL T) -8 NIL NIL NIL) (-23 10301 10588 10614 "ABELMON" 10784 T ABELMON (NIL) -9 NIL 10896 NIL) (-22 9965 10049 10187 "ABELMON-" 10192 NIL ABELMON- (NIL T) -8 NIL NIL NIL) (-21 9313 9685 9711 "ABELGRP" 9783 T ABELGRP (NIL) -9 NIL 9858 NIL) (-20 8776 8905 9121 "ABELGRP-" 9126 NIL ABELGRP- (NIL T) -8 NIL NIL NIL) (-19 4333 8085 8124 "A1AGG" 8129 NIL A1AGG (NIL T) -9 NIL 8169 NIL) (-18 30 1251 2813 "A1AGG-" 2818 NIL A1AGG- (NIL T T) -8 NIL NIL NIL))
\ No newline at end of file +((-3 3228420 3228425 3228430 NIL NIL NIL NIL (NIL) -8 NIL NIL NIL) (-2 3228405 3228410 3228415 NIL NIL NIL NIL (NIL) -8 NIL NIL NIL) (-1 3228390 3228395 3228400 NIL NIL NIL NIL (NIL) -8 NIL NIL NIL) (0 3228375 3228380 3228385 NIL NIL NIL NIL (NIL) -8 NIL NIL NIL) (-1306 3227518 3228250 3228327 "ZMOD" 3228332 NIL ZMOD (NIL NIL) -8 NIL NIL NIL) (-1305 3226628 3226792 3227001 "ZLINDEP" 3227350 NIL ZLINDEP (NIL T) -7 NIL NIL NIL) (-1304 3215928 3217696 3219668 "ZDSOLVE" 3224758 NIL ZDSOLVE (NIL T NIL NIL) -7 NIL NIL NIL) (-1303 3215174 3215315 3215504 "YSTREAM" 3215774 NIL YSTREAM (NIL T) -7 NIL NIL NIL) (-1302 3214602 3214848 3214961 "YDIAGRAM" 3215083 T YDIAGRAM (NIL) -8 NIL NIL NIL) (-1301 3212376 3213903 3214107 "XRPOLY" 3214445 NIL XRPOLY (NIL T T) -8 NIL NIL NIL) (-1300 3208929 3210247 3210822 "XPR" 3211848 NIL XPR (NIL T T) -8 NIL NIL NIL) (-1299 3206650 3208260 3208464 "XPOLY" 3208760 NIL XPOLY (NIL T) -8 NIL NIL NIL) (-1298 3204303 3205671 3205726 "XPOLYC" 3206014 NIL XPOLYC (NIL T T) -9 NIL 3206127 NIL) (-1297 3200679 3202820 3203208 "XPBWPOLY" 3203961 NIL XPBWPOLY (NIL T T) -8 NIL NIL NIL) (-1296 3196374 3198669 3198711 "XF" 3199332 NIL XF (NIL T) -9 NIL 3199732 NIL) (-1295 3195995 3196083 3196252 "XF-" 3196257 NIL XF- (NIL T T) -8 NIL NIL NIL) (-1294 3191191 3192480 3192535 "XFALG" 3194707 NIL XFALG (NIL T T) -9 NIL 3195496 NIL) (-1293 3190324 3190428 3190633 "XEXPPKG" 3191083 NIL XEXPPKG (NIL T T T) -7 NIL NIL NIL) (-1292 3188433 3190174 3190270 "XDPOLY" 3190275 NIL XDPOLY (NIL T T) -8 NIL NIL NIL) (-1291 3187240 3187840 3187883 "XALG" 3187888 NIL XALG (NIL T) -9 NIL 3187999 NIL) (-1290 3180682 3185217 3185711 "WUTSET" 3186832 NIL WUTSET (NIL T T T T) -8 NIL NIL NIL) (-1289 3178938 3179734 3180057 "WP" 3180493 NIL WP (NIL T T T T NIL NIL NIL) -8 NIL NIL NIL) (-1288 3178540 3178760 3178830 "WHILEAST" 3178890 T WHILEAST (NIL) -8 NIL NIL NIL) (-1287 3178012 3178257 3178351 "WHEREAST" 3178468 T WHEREAST (NIL) -8 NIL NIL NIL) (-1286 3176898 3177096 3177391 "WFFINTBS" 3177809 NIL WFFINTBS (NIL T T T T) -7 NIL NIL NIL) (-1285 3174802 3175229 3175691 "WEIER" 3176470 NIL WEIER (NIL T) -7 NIL NIL NIL) (-1284 3173848 3174298 3174340 "VSPACE" 3174476 NIL VSPACE (NIL T) -9 NIL 3174550 NIL) (-1283 3173686 3173713 3173804 "VSPACE-" 3173809 NIL VSPACE- (NIL T T) -8 NIL NIL NIL) (-1282 3173495 3173537 3173605 "VOID" 3173640 T VOID (NIL) -8 NIL NIL NIL) (-1281 3171631 3171990 3172396 "VIEW" 3173111 T VIEW (NIL) -7 NIL NIL NIL) (-1280 3168055 3168694 3169431 "VIEWDEF" 3170916 T VIEWDEF (NIL) -7 NIL NIL NIL) (-1279 3157359 3159603 3161776 "VIEW3D" 3165904 T VIEW3D (NIL) -8 NIL NIL NIL) (-1278 3149610 3151270 3152849 "VIEW2D" 3155802 T VIEW2D (NIL) -8 NIL NIL NIL) (-1277 3144963 3149380 3149472 "VECTOR" 3149553 NIL VECTOR (NIL T) -8 NIL NIL NIL) (-1276 3143540 3143799 3144117 "VECTOR2" 3144693 NIL VECTOR2 (NIL T T) -7 NIL NIL NIL) (-1275 3136982 3141291 3141334 "VECTCAT" 3142329 NIL VECTCAT (NIL T) -9 NIL 3142916 NIL) (-1274 3135996 3136250 3136640 "VECTCAT-" 3136645 NIL VECTCAT- (NIL T T) -8 NIL NIL NIL) (-1273 3135450 3135647 3135767 "VARIABLE" 3135911 NIL VARIABLE (NIL NIL) -8 NIL NIL NIL) (-1272 3135383 3135388 3135418 "UTYPE" 3135423 T UTYPE (NIL) -9 NIL NIL NIL) (-1271 3134213 3134367 3134629 "UTSODETL" 3135209 NIL UTSODETL (NIL T T T T) -7 NIL NIL NIL) (-1270 3131653 3132113 3132637 "UTSODE" 3133754 NIL UTSODE (NIL T T) -7 NIL NIL NIL) (-1269 3123491 3129279 3129768 "UTS" 3131222 NIL UTS (NIL T NIL NIL) -8 NIL NIL NIL) (-1268 3114328 3119696 3119739 "UTSCAT" 3120851 NIL UTSCAT (NIL T) -9 NIL 3121609 NIL) (-1267 3111676 3112398 3113387 "UTSCAT-" 3113392 NIL UTSCAT- (NIL T T) -8 NIL NIL NIL) (-1266 3111303 3111346 3111479 "UTS2" 3111627 NIL UTS2 (NIL T T T T) -7 NIL NIL NIL) (-1265 3105529 3108141 3108184 "URAGG" 3110254 NIL URAGG (NIL T) -9 NIL 3110977 NIL) (-1264 3102468 3103331 3104454 "URAGG-" 3104459 NIL URAGG- (NIL T T) -8 NIL NIL NIL) (-1263 3098177 3101103 3101568 "UPXSSING" 3102132 NIL UPXSSING (NIL T T NIL NIL) -8 NIL NIL NIL) (-1262 3090243 3097424 3097697 "UPXS" 3097962 NIL UPXS (NIL T NIL NIL) -8 NIL NIL NIL) (-1261 3083316 3090147 3090219 "UPXSCONS" 3090224 NIL UPXSCONS (NIL T T) -8 NIL NIL NIL) (-1260 3073024 3079818 3079880 "UPXSCCA" 3080454 NIL UPXSCCA (NIL T T) -9 NIL 3080687 NIL) (-1259 3072662 3072747 3072921 "UPXSCCA-" 3072926 NIL UPXSCCA- (NIL T T T) -8 NIL NIL NIL) (-1258 3062222 3068789 3068832 "UPXSCAT" 3069480 NIL UPXSCAT (NIL T) -9 NIL 3070089 NIL) (-1257 3061652 3061731 3061910 "UPXS2" 3062137 NIL UPXS2 (NIL T T NIL NIL NIL NIL) -7 NIL NIL NIL) (-1256 3060306 3060559 3060910 "UPSQFREE" 3061395 NIL UPSQFREE (NIL T T) -7 NIL NIL NIL) (-1255 3053779 3056837 3056892 "UPSCAT" 3057972 NIL UPSCAT (NIL T T) -9 NIL 3058737 NIL) (-1254 3052983 3053190 3053517 "UPSCAT-" 3053522 NIL UPSCAT- (NIL T T T) -8 NIL NIL NIL) (-1253 3038624 3046392 3046435 "UPOLYC" 3048536 NIL UPOLYC (NIL T) -9 NIL 3049757 NIL) (-1252 3029952 3032378 3035525 "UPOLYC-" 3035530 NIL UPOLYC- (NIL T T) -8 NIL NIL NIL) (-1251 3029579 3029622 3029755 "UPOLYC2" 3029903 NIL UPOLYC2 (NIL T T T T) -7 NIL NIL NIL) (-1250 3021390 3029262 3029391 "UP" 3029498 NIL UP (NIL NIL T) -8 NIL NIL NIL) (-1249 3020729 3020836 3021000 "UPMP" 3021279 NIL UPMP (NIL T T) -7 NIL NIL NIL) (-1248 3020282 3020363 3020502 "UPDIVP" 3020642 NIL UPDIVP (NIL T T) -7 NIL NIL NIL) (-1247 3018850 3019099 3019415 "UPDECOMP" 3020031 NIL UPDECOMP (NIL T T) -7 NIL NIL NIL) (-1246 3018081 3018193 3018379 "UPCDEN" 3018734 NIL UPCDEN (NIL T T T) -7 NIL NIL NIL) (-1245 3017600 3017669 3017818 "UP2" 3018006 NIL UP2 (NIL NIL T NIL T) -7 NIL NIL NIL) (-1244 3016067 3016804 3017081 "UNISEG" 3017358 NIL UNISEG (NIL T) -8 NIL NIL NIL) (-1243 3015282 3015409 3015614 "UNISEG2" 3015910 NIL UNISEG2 (NIL T T) -7 NIL NIL NIL) (-1242 3014342 3014522 3014748 "UNIFACT" 3015098 NIL UNIFACT (NIL T) -7 NIL NIL NIL) (-1241 2998274 3013519 3013770 "ULS" 3014149 NIL ULS (NIL T NIL NIL) -8 NIL NIL NIL) (-1240 2986272 2998178 2998250 "ULSCONS" 2998255 NIL ULSCONS (NIL T T) -8 NIL NIL NIL) (-1239 2968280 2980266 2980328 "ULSCCAT" 2980966 NIL ULSCCAT (NIL T T) -9 NIL 2981255 NIL) (-1238 2967330 2967575 2967963 "ULSCCAT-" 2967968 NIL ULSCCAT- (NIL T T T) -8 NIL NIL NIL) (-1237 2956667 2963148 2963191 "ULSCAT" 2964054 NIL ULSCAT (NIL T) -9 NIL 2964785 NIL) (-1236 2956097 2956176 2956355 "ULS2" 2956582 NIL ULS2 (NIL T T NIL NIL NIL NIL) -7 NIL NIL NIL) (-1235 2955216 2955726 2955833 "UINT8" 2955944 T UINT8 (NIL) -8 NIL NIL 2956029) (-1234 2954334 2954844 2954951 "UINT64" 2955062 T UINT64 (NIL) -8 NIL NIL 2955147) (-1233 2953452 2953962 2954069 "UINT32" 2954180 T UINT32 (NIL) -8 NIL NIL 2954265) (-1232 2952570 2953080 2953187 "UINT16" 2953298 T UINT16 (NIL) -8 NIL NIL 2953383) (-1231 2950873 2951830 2951860 "UFD" 2952072 T UFD (NIL) -9 NIL 2952186 NIL) (-1230 2950667 2950713 2950808 "UFD-" 2950813 NIL UFD- (NIL T) -8 NIL NIL NIL) (-1229 2949749 2949932 2950148 "UDVO" 2950473 T UDVO (NIL) -7 NIL NIL NIL) (-1228 2947565 2947974 2948445 "UDPO" 2949313 NIL UDPO (NIL T) -7 NIL NIL NIL) (-1227 2947498 2947503 2947533 "TYPE" 2947538 T TYPE (NIL) -9 NIL NIL NIL) (-1226 2947258 2947453 2947484 "TYPEAST" 2947489 T TYPEAST (NIL) -8 NIL NIL NIL) (-1225 2946229 2946431 2946671 "TWOFACT" 2947052 NIL TWOFACT (NIL T) -7 NIL NIL NIL) (-1224 2945252 2945638 2945873 "TUPLE" 2946029 NIL TUPLE (NIL T) -8 NIL NIL NIL) (-1223 2942943 2943462 2944001 "TUBETOOL" 2944735 T TUBETOOL (NIL) -7 NIL NIL NIL) (-1222 2941792 2941997 2942238 "TUBE" 2942736 NIL TUBE (NIL T) -8 NIL NIL NIL) (-1221 2936521 2940764 2941047 "TS" 2941544 NIL TS (NIL T) -8 NIL NIL NIL) (-1220 2925161 2929280 2929377 "TSETCAT" 2934646 NIL TSETCAT (NIL T T T T) -9 NIL 2936177 NIL) (-1219 2919893 2921493 2923384 "TSETCAT-" 2923389 NIL TSETCAT- (NIL T T T T T) -8 NIL NIL NIL) (-1218 2914532 2915379 2916308 "TRMANIP" 2919029 NIL TRMANIP (NIL T T) -7 NIL NIL NIL) (-1217 2913973 2914036 2914199 "TRIMAT" 2914464 NIL TRIMAT (NIL T T T T) -7 NIL NIL NIL) (-1216 2911839 2912076 2912433 "TRIGMNIP" 2913722 NIL TRIGMNIP (NIL T T) -7 NIL NIL NIL) (-1215 2911359 2911472 2911502 "TRIGCAT" 2911715 T TRIGCAT (NIL) -9 NIL NIL NIL) (-1214 2911028 2911107 2911248 "TRIGCAT-" 2911253 NIL TRIGCAT- (NIL T) -8 NIL NIL NIL) (-1213 2907873 2909886 2910167 "TREE" 2910782 NIL TREE (NIL T) -8 NIL NIL NIL) (-1212 2907147 2907675 2907705 "TRANFUN" 2907740 T TRANFUN (NIL) -9 NIL 2907806 NIL) (-1211 2906426 2906617 2906897 "TRANFUN-" 2906902 NIL TRANFUN- (NIL T) -8 NIL NIL NIL) (-1210 2906230 2906262 2906323 "TOPSP" 2906387 T TOPSP (NIL) -7 NIL NIL NIL) (-1209 2905578 2905693 2905847 "TOOLSIGN" 2906111 NIL TOOLSIGN (NIL T) -7 NIL NIL NIL) (-1208 2904212 2904755 2904994 "TEXTFILE" 2905361 T TEXTFILE (NIL) -8 NIL NIL NIL) (-1207 2902124 2902665 2903094 "TEX" 2903805 T TEX (NIL) -8 NIL NIL NIL) (-1206 2901905 2901936 2902008 "TEX1" 2902087 NIL TEX1 (NIL T) -7 NIL NIL NIL) (-1205 2901553 2901616 2901706 "TEMUTL" 2901837 T TEMUTL (NIL) -7 NIL NIL NIL) (-1204 2899707 2899987 2900312 "TBCMPPK" 2901276 NIL TBCMPPK (NIL T T) -7 NIL NIL NIL) (-1203 2891484 2897867 2897923 "TBAGG" 2898323 NIL TBAGG (NIL T T) -9 NIL 2898534 NIL) (-1202 2886554 2888042 2889796 "TBAGG-" 2889801 NIL TBAGG- (NIL T T T) -8 NIL NIL NIL) (-1201 2885938 2886045 2886190 "TANEXP" 2886443 NIL TANEXP (NIL T) -7 NIL NIL NIL) (-1200 2885449 2885713 2885803 "TALGOP" 2885883 NIL TALGOP (NIL T) -8 NIL NIL NIL) (-1199 2878839 2885306 2885399 "TABLE" 2885404 NIL TABLE (NIL T T) -8 NIL NIL NIL) (-1198 2878251 2878350 2878488 "TABLEAU" 2878736 NIL TABLEAU (NIL T) -8 NIL NIL NIL) (-1197 2872859 2874079 2875327 "TABLBUMP" 2877037 NIL TABLBUMP (NIL T) -7 NIL NIL NIL) (-1196 2872081 2872228 2872409 "SYSTEM" 2872700 T SYSTEM (NIL) -8 NIL NIL NIL) (-1195 2868540 2869239 2870022 "SYSSOLP" 2871332 NIL SYSSOLP (NIL T) -7 NIL NIL NIL) (-1194 2868338 2868495 2868526 "SYSPTR" 2868531 T SYSPTR (NIL) -8 NIL NIL NIL) (-1193 2867374 2867879 2867998 "SYSNNI" 2868184 NIL SYSNNI (NIL NIL) -8 NIL NIL 2868269) (-1192 2866673 2867132 2867211 "SYSINT" 2867271 NIL SYSINT (NIL NIL) -8 NIL NIL 2867316) (-1191 2863005 2863951 2864661 "SYNTAX" 2865985 T SYNTAX (NIL) -8 NIL NIL NIL) (-1190 2860163 2860765 2861397 "SYMTAB" 2862395 T SYMTAB (NIL) -8 NIL NIL NIL) (-1189 2855412 2856314 2857297 "SYMS" 2859202 T SYMS (NIL) -8 NIL NIL NIL) (-1188 2852647 2854870 2855100 "SYMPOLY" 2855217 NIL SYMPOLY (NIL T) -8 NIL NIL NIL) (-1187 2852164 2852239 2852362 "SYMFUNC" 2852559 NIL SYMFUNC (NIL T) -7 NIL NIL NIL) (-1186 2848184 2849476 2850289 "SYMBOL" 2851373 T SYMBOL (NIL) -8 NIL NIL NIL) (-1185 2841723 2843412 2845132 "SWITCH" 2846486 T SWITCH (NIL) -8 NIL NIL NIL) (-1184 2834957 2840544 2840847 "SUTS" 2841478 NIL SUTS (NIL T NIL NIL) -8 NIL NIL NIL) (-1183 2827023 2834204 2834477 "SUPXS" 2834742 NIL SUPXS (NIL T NIL NIL) -8 NIL NIL NIL) (-1182 2818782 2826641 2826767 "SUP" 2826932 NIL SUP (NIL T) -8 NIL NIL NIL) (-1181 2817941 2818068 2818285 "SUPFRACF" 2818650 NIL SUPFRACF (NIL T T T T) -7 NIL NIL NIL) (-1180 2817562 2817621 2817734 "SUP2" 2817876 NIL SUP2 (NIL T T) -7 NIL NIL NIL) (-1179 2816010 2816284 2816640 "SUMRF" 2817261 NIL SUMRF (NIL T) -7 NIL NIL NIL) (-1178 2815345 2815411 2815603 "SUMFS" 2815931 NIL SUMFS (NIL T T) -7 NIL NIL NIL) (-1177 2799312 2814522 2814773 "SULS" 2815152 NIL SULS (NIL T NIL NIL) -8 NIL NIL NIL) (-1176 2798914 2799134 2799204 "SUCHTAST" 2799264 T SUCHTAST (NIL) -8 NIL NIL NIL) (-1175 2798209 2798439 2798579 "SUCH" 2798822 NIL SUCH (NIL T T) -8 NIL NIL NIL) (-1174 2792076 2793115 2794074 "SUBSPACE" 2797297 NIL SUBSPACE (NIL NIL T) -8 NIL NIL NIL) (-1173 2791506 2791596 2791760 "SUBRESP" 2791964 NIL SUBRESP (NIL T T) -7 NIL NIL NIL) (-1172 2784874 2786171 2787482 "STTF" 2790242 NIL STTF (NIL T) -7 NIL NIL NIL) (-1171 2779047 2780167 2781314 "STTFNC" 2783774 NIL STTFNC (NIL T) -7 NIL NIL NIL) (-1170 2770360 2772229 2774023 "STTAYLOR" 2777288 NIL STTAYLOR (NIL T) -7 NIL NIL NIL) (-1169 2763490 2770224 2770307 "STRTBL" 2770312 NIL STRTBL (NIL T) -8 NIL NIL NIL) (-1168 2758854 2763445 2763476 "STRING" 2763481 T STRING (NIL) -8 NIL NIL NIL) (-1167 2753683 2758197 2758227 "STRICAT" 2758286 T STRICAT (NIL) -9 NIL 2758348 NIL) (-1166 2746436 2751302 2751913 "STREAM" 2753107 NIL STREAM (NIL T) -8 NIL NIL NIL) (-1165 2745946 2746023 2746167 "STREAM3" 2746353 NIL STREAM3 (NIL T T T) -7 NIL NIL NIL) (-1164 2744928 2745111 2745346 "STREAM2" 2745759 NIL STREAM2 (NIL T T) -7 NIL NIL NIL) (-1163 2744616 2744668 2744761 "STREAM1" 2744870 NIL STREAM1 (NIL T) -7 NIL NIL NIL) (-1162 2743632 2743813 2744044 "STINPROD" 2744432 NIL STINPROD (NIL T) -7 NIL NIL NIL) (-1161 2743184 2743394 2743424 "STEP" 2743504 T STEP (NIL) -9 NIL 2743582 NIL) (-1160 2742371 2742673 2742821 "STEPAST" 2743058 T STEPAST (NIL) -8 NIL NIL NIL) (-1159 2735803 2742270 2742347 "STBL" 2742352 NIL STBL (NIL T T NIL) -8 NIL NIL NIL) (-1158 2730898 2734994 2735037 "STAGG" 2735190 NIL STAGG (NIL T) -9 NIL 2735279 NIL) (-1157 2728600 2729202 2730074 "STAGG-" 2730079 NIL STAGG- (NIL T T) -8 NIL NIL NIL) (-1156 2726747 2728370 2728462 "STACK" 2728543 NIL STACK (NIL T) -8 NIL NIL NIL) (-1155 2719442 2724888 2725344 "SREGSET" 2726377 NIL SREGSET (NIL T T T T) -8 NIL NIL NIL) (-1154 2711867 2713236 2714749 "SRDCMPK" 2718048 NIL SRDCMPK (NIL T T T T T) -7 NIL NIL NIL) (-1153 2704752 2709277 2709307 "SRAGG" 2710610 T SRAGG (NIL) -9 NIL 2711218 NIL) (-1152 2703769 2704024 2704403 "SRAGG-" 2704408 NIL SRAGG- (NIL T) -8 NIL NIL NIL) (-1151 2698229 2702716 2703137 "SQMATRIX" 2703395 NIL SQMATRIX (NIL NIL T) -8 NIL NIL NIL) (-1150 2691914 2694947 2695674 "SPLTREE" 2697574 NIL SPLTREE (NIL T T) -8 NIL NIL NIL) (-1149 2687877 2688570 2689216 "SPLNODE" 2691340 NIL SPLNODE (NIL T T) -8 NIL NIL NIL) (-1148 2686924 2687157 2687187 "SPFCAT" 2687631 T SPFCAT (NIL) -9 NIL NIL NIL) (-1147 2685661 2685871 2686135 "SPECOUT" 2686682 T SPECOUT (NIL) -7 NIL NIL NIL) (-1146 2676771 2678643 2678673 "SPADXPT" 2683349 T SPADXPT (NIL) -9 NIL 2685513 NIL) (-1145 2676532 2676572 2676641 "SPADPRSR" 2676724 T SPADPRSR (NIL) -7 NIL NIL NIL) (-1144 2674581 2676487 2676518 "SPADAST" 2676523 T SPADAST (NIL) -8 NIL NIL NIL) (-1143 2666526 2668299 2668342 "SPACEC" 2672715 NIL SPACEC (NIL T) -9 NIL 2674531 NIL) (-1142 2664656 2666458 2666507 "SPACE3" 2666512 NIL SPACE3 (NIL T) -8 NIL NIL NIL) (-1141 2663408 2663579 2663870 "SORTPAK" 2664461 NIL SORTPAK (NIL T T) -7 NIL NIL NIL) (-1140 2661500 2661803 2662215 "SOLVETRA" 2663072 NIL SOLVETRA (NIL T) -7 NIL NIL NIL) (-1139 2660550 2660772 2661033 "SOLVESER" 2661273 NIL SOLVESER (NIL T) -7 NIL NIL NIL) (-1138 2655854 2656742 2657737 "SOLVERAD" 2659602 NIL SOLVERAD (NIL T) -7 NIL NIL NIL) (-1137 2651669 2652278 2653007 "SOLVEFOR" 2655221 NIL SOLVEFOR (NIL T T) -7 NIL NIL NIL) (-1136 2645939 2651018 2651115 "SNTSCAT" 2651120 NIL SNTSCAT (NIL T T T T) -9 NIL 2651190 NIL) (-1135 2640045 2644262 2644653 "SMTS" 2645629 NIL SMTS (NIL T T T) -8 NIL NIL NIL) (-1134 2634730 2639933 2640010 "SMP" 2640015 NIL SMP (NIL T T) -8 NIL NIL NIL) (-1133 2632889 2633190 2633588 "SMITH" 2634427 NIL SMITH (NIL T T T T) -7 NIL NIL NIL) (-1132 2625602 2629798 2629901 "SMATCAT" 2631252 NIL SMATCAT (NIL NIL T T T) -9 NIL 2631802 NIL) (-1131 2622542 2623365 2624543 "SMATCAT-" 2624548 NIL SMATCAT- (NIL T NIL T T T) -8 NIL NIL NIL) (-1130 2620208 2621778 2621821 "SKAGG" 2622082 NIL SKAGG (NIL T) -9 NIL 2622217 NIL) (-1129 2616534 2619681 2619865 "SINT" 2620017 T SINT (NIL) -8 NIL NIL 2620179) (-1128 2616306 2616344 2616410 "SIMPAN" 2616490 T SIMPAN (NIL) -7 NIL NIL NIL) (-1127 2615585 2615841 2615981 "SIG" 2616188 T SIG (NIL) -8 NIL NIL NIL) (-1126 2614423 2614644 2614919 "SIGNRF" 2615344 NIL SIGNRF (NIL T) -7 NIL NIL NIL) (-1125 2613256 2613407 2613691 "SIGNEF" 2614252 NIL SIGNEF (NIL T T) -7 NIL NIL NIL) (-1124 2612562 2612839 2612963 "SIGAST" 2613154 T SIGAST (NIL) -8 NIL NIL NIL) (-1123 2610252 2610706 2611212 "SHP" 2612103 NIL SHP (NIL T NIL) -7 NIL NIL NIL) (-1122 2604104 2610153 2610229 "SHDP" 2610234 NIL SHDP (NIL NIL NIL T) -8 NIL NIL NIL) (-1121 2603677 2603869 2603899 "SGROUP" 2603992 T SGROUP (NIL) -9 NIL 2604054 NIL) (-1120 2603535 2603561 2603634 "SGROUP-" 2603639 NIL SGROUP- (NIL T) -8 NIL NIL NIL) (-1119 2600326 2601024 2601747 "SGCF" 2602834 T SGCF (NIL) -7 NIL NIL NIL) (-1118 2594694 2599773 2599870 "SFRTCAT" 2599875 NIL SFRTCAT (NIL T T T T) -9 NIL 2599914 NIL) (-1117 2588115 2589133 2590269 "SFRGCD" 2593677 NIL SFRGCD (NIL T T T T T) -7 NIL NIL NIL) (-1116 2581241 2582314 2583500 "SFQCMPK" 2587048 NIL SFQCMPK (NIL T T T T T) -7 NIL NIL NIL) (-1115 2580861 2580950 2581061 "SFORT" 2581182 NIL SFORT (NIL T T) -8 NIL NIL NIL) (-1114 2579979 2580701 2580822 "SEXOF" 2580827 NIL SEXOF (NIL T T T T T) -8 NIL NIL NIL) (-1113 2579086 2579860 2579928 "SEX" 2579933 T SEX (NIL) -8 NIL NIL NIL) (-1112 2574867 2575582 2575677 "SEXCAT" 2578299 NIL SEXCAT (NIL T T T T T) -9 NIL 2578859 NIL) (-1111 2572020 2574801 2574849 "SET" 2574854 NIL SET (NIL T) -8 NIL NIL NIL) (-1110 2570244 2570733 2571038 "SETMN" 2571761 NIL SETMN (NIL NIL NIL) -8 NIL NIL NIL) (-1109 2569740 2569892 2569922 "SETCAT" 2570098 T SETCAT (NIL) -9 NIL 2570208 NIL) (-1108 2569432 2569510 2569640 "SETCAT-" 2569645 NIL SETCAT- (NIL T) -8 NIL NIL NIL) (-1107 2565793 2567893 2567936 "SETAGG" 2568806 NIL SETAGG (NIL T) -9 NIL 2569146 NIL) (-1106 2565251 2565367 2565604 "SETAGG-" 2565609 NIL SETAGG- (NIL T T) -8 NIL NIL NIL) (-1105 2564694 2564947 2565048 "SEQAST" 2565172 T SEQAST (NIL) -8 NIL NIL NIL) (-1104 2563893 2564187 2564248 "SEGXCAT" 2564534 NIL SEGXCAT (NIL T T) -9 NIL 2564654 NIL) (-1103 2562899 2563559 2563741 "SEG" 2563746 NIL SEG (NIL T) -8 NIL NIL NIL) (-1102 2561878 2562092 2562135 "SEGCAT" 2562657 NIL SEGCAT (NIL T) -9 NIL 2562878 NIL) (-1101 2560810 2561241 2561449 "SEGBIND" 2561705 NIL SEGBIND (NIL T) -8 NIL NIL NIL) (-1100 2560431 2560490 2560603 "SEGBIND2" 2560745 NIL SEGBIND2 (NIL T T) -7 NIL NIL NIL) (-1099 2560004 2560232 2560309 "SEGAST" 2560376 T SEGAST (NIL) -8 NIL NIL NIL) (-1098 2559223 2559349 2559553 "SEG2" 2559848 NIL SEG2 (NIL T T) -7 NIL NIL NIL) (-1097 2558633 2559158 2559205 "SDVAR" 2559210 NIL SDVAR (NIL T) -8 NIL NIL NIL) (-1096 2551160 2558403 2558533 "SDPOL" 2558538 NIL SDPOL (NIL T) -8 NIL NIL NIL) (-1095 2549753 2550019 2550338 "SCPKG" 2550875 NIL SCPKG (NIL T) -7 NIL NIL NIL) (-1094 2548917 2549089 2549281 "SCOPE" 2549583 T SCOPE (NIL) -8 NIL NIL NIL) (-1093 2548137 2548271 2548450 "SCACHE" 2548772 NIL SCACHE (NIL T) -7 NIL NIL NIL) (-1092 2547783 2547969 2547999 "SASTCAT" 2548004 T SASTCAT (NIL) -9 NIL 2548017 NIL) (-1091 2547270 2547618 2547694 "SAOS" 2547729 T SAOS (NIL) -8 NIL NIL NIL) (-1090 2546835 2546870 2547043 "SAERFFC" 2547229 NIL SAERFFC (NIL T T T) -7 NIL NIL NIL) (-1089 2540774 2546732 2546812 "SAE" 2546817 NIL SAE (NIL T T NIL) -8 NIL NIL NIL) (-1088 2540367 2540402 2540561 "SAEFACT" 2540733 NIL SAEFACT (NIL T T T) -7 NIL NIL NIL) (-1087 2538688 2539002 2539403 "RURPK" 2540033 NIL RURPK (NIL T NIL) -7 NIL NIL NIL) (-1086 2537325 2537631 2537936 "RULESET" 2538522 NIL RULESET (NIL T T T) -8 NIL NIL NIL) (-1085 2534548 2535078 2535536 "RULE" 2537006 NIL RULE (NIL T T T) -8 NIL NIL NIL) (-1084 2534160 2534342 2534425 "RULECOLD" 2534500 NIL RULECOLD (NIL NIL) -8 NIL NIL NIL) (-1083 2533950 2533978 2534049 "RTVALUE" 2534111 T RTVALUE (NIL) -8 NIL NIL NIL) (-1082 2533421 2533667 2533761 "RSTRCAST" 2533878 T RSTRCAST (NIL) -8 NIL NIL NIL) (-1081 2528269 2529064 2529984 "RSETGCD" 2532620 NIL RSETGCD (NIL T T T T T) -7 NIL NIL NIL) (-1080 2517499 2522578 2522675 "RSETCAT" 2526794 NIL RSETCAT (NIL T T T T) -9 NIL 2527891 NIL) (-1079 2515426 2515965 2516789 "RSETCAT-" 2516794 NIL RSETCAT- (NIL T T T T T) -8 NIL NIL NIL) (-1078 2507812 2509188 2510708 "RSDCMPK" 2514025 NIL RSDCMPK (NIL T T T T T) -7 NIL NIL NIL) (-1077 2505791 2506258 2506332 "RRCC" 2507418 NIL RRCC (NIL T T) -9 NIL 2507762 NIL) (-1076 2505142 2505316 2505595 "RRCC-" 2505600 NIL RRCC- (NIL T T T) -8 NIL NIL NIL) (-1075 2504585 2504838 2504939 "RPTAST" 2505063 T RPTAST (NIL) -8 NIL NIL NIL) (-1074 2478431 2487790 2487857 "RPOLCAT" 2498523 NIL RPOLCAT (NIL T T T) -9 NIL 2501683 NIL) (-1073 2469929 2472269 2475391 "RPOLCAT-" 2475396 NIL RPOLCAT- (NIL T T T T) -8 NIL NIL NIL) (-1072 2460860 2468140 2468622 "ROUTINE" 2469469 T ROUTINE (NIL) -8 NIL NIL NIL) (-1071 2457658 2460486 2460626 "ROMAN" 2460742 T ROMAN (NIL) -8 NIL NIL NIL) (-1070 2455902 2456518 2456778 "ROIRC" 2457463 NIL ROIRC (NIL T T) -8 NIL NIL NIL) (-1069 2452134 2454418 2454448 "RNS" 2454752 T RNS (NIL) -9 NIL 2455026 NIL) (-1068 2450643 2451026 2451560 "RNS-" 2451635 NIL RNS- (NIL T) -8 NIL NIL NIL) (-1067 2450046 2450454 2450484 "RNG" 2450489 T RNG (NIL) -9 NIL 2450510 NIL) (-1066 2449049 2449411 2449613 "RNGBIND" 2449897 NIL RNGBIND (NIL T T) -8 NIL NIL NIL) (-1065 2448448 2448836 2448879 "RMODULE" 2448884 NIL RMODULE (NIL T) -9 NIL 2448911 NIL) (-1064 2447284 2447378 2447714 "RMCAT2" 2448349 NIL RMCAT2 (NIL NIL NIL T T T T T T T T) -7 NIL NIL NIL) (-1063 2444134 2446630 2446927 "RMATRIX" 2447046 NIL RMATRIX (NIL NIL NIL T) -8 NIL NIL NIL) (-1062 2436961 2439221 2439336 "RMATCAT" 2442695 NIL RMATCAT (NIL NIL NIL T T T) -9 NIL 2443677 NIL) (-1061 2436336 2436483 2436790 "RMATCAT-" 2436795 NIL RMATCAT- (NIL T NIL NIL T T T) -8 NIL NIL NIL) (-1060 2435737 2435958 2436001 "RLINSET" 2436195 NIL RLINSET (NIL T) -9 NIL 2436286 NIL) (-1059 2435304 2435379 2435507 "RINTERP" 2435656 NIL RINTERP (NIL NIL T) -7 NIL NIL NIL) (-1058 2434362 2434916 2434946 "RING" 2435002 T RING (NIL) -9 NIL 2435094 NIL) (-1057 2434154 2434198 2434295 "RING-" 2434300 NIL RING- (NIL T) -8 NIL NIL NIL) (-1056 2432995 2433232 2433490 "RIDIST" 2433918 T RIDIST (NIL) -7 NIL NIL NIL) (-1055 2424284 2432463 2432669 "RGCHAIN" 2432843 NIL RGCHAIN (NIL T NIL) -8 NIL NIL NIL) (-1054 2423634 2424040 2424081 "RGBCSPC" 2424139 NIL RGBCSPC (NIL T) -9 NIL 2424191 NIL) (-1053 2422792 2423173 2423214 "RGBCMDL" 2423446 NIL RGBCMDL (NIL T) -9 NIL 2423560 NIL) (-1052 2419786 2420400 2421070 "RF" 2422156 NIL RF (NIL T) -7 NIL NIL NIL) (-1051 2419432 2419495 2419598 "RFFACTOR" 2419717 NIL RFFACTOR (NIL T) -7 NIL NIL NIL) (-1050 2419157 2419192 2419289 "RFFACT" 2419391 NIL RFFACT (NIL T) -7 NIL NIL NIL) (-1049 2417274 2417638 2418020 "RFDIST" 2418797 T RFDIST (NIL) -7 NIL NIL NIL) (-1048 2416727 2416819 2416982 "RETSOL" 2417176 NIL RETSOL (NIL T T) -7 NIL NIL NIL) (-1047 2416363 2416443 2416486 "RETRACT" 2416619 NIL RETRACT (NIL T) -9 NIL 2416706 NIL) (-1046 2416212 2416237 2416324 "RETRACT-" 2416329 NIL RETRACT- (NIL T T) -8 NIL NIL NIL) (-1045 2415814 2416034 2416104 "RETAST" 2416164 T RETAST (NIL) -8 NIL NIL NIL) (-1044 2408552 2415467 2415594 "RESULT" 2415709 T RESULT (NIL) -8 NIL NIL NIL) (-1043 2407143 2407821 2408020 "RESRING" 2408455 NIL RESRING (NIL T T T T NIL) -8 NIL NIL NIL) (-1042 2406779 2406828 2406926 "RESLATC" 2407080 NIL RESLATC (NIL T) -7 NIL NIL NIL) (-1041 2406484 2406519 2406626 "REPSQ" 2406738 NIL REPSQ (NIL T) -7 NIL NIL NIL) (-1040 2403906 2404486 2405088 "REP" 2405904 T REP (NIL) -7 NIL NIL NIL) (-1039 2403603 2403638 2403749 "REPDB" 2403865 NIL REPDB (NIL T) -7 NIL NIL NIL) (-1038 2397503 2398892 2400115 "REP2" 2402415 NIL REP2 (NIL T) -7 NIL NIL NIL) (-1037 2393880 2394561 2395369 "REP1" 2396730 NIL REP1 (NIL T) -7 NIL NIL NIL) (-1036 2386576 2392021 2392477 "REGSET" 2393510 NIL REGSET (NIL T T T T) -8 NIL NIL NIL) (-1035 2385341 2385724 2385974 "REF" 2386361 NIL REF (NIL T) -8 NIL NIL NIL) (-1034 2384718 2384821 2384988 "REDORDER" 2385225 NIL REDORDER (NIL T T) -7 NIL NIL NIL) (-1033 2380686 2383931 2384158 "RECLOS" 2384546 NIL RECLOS (NIL T) -8 NIL NIL NIL) (-1032 2379738 2379919 2380134 "REALSOLV" 2380493 T REALSOLV (NIL) -7 NIL NIL NIL) (-1031 2379584 2379625 2379655 "REAL" 2379660 T REAL (NIL) -9 NIL 2379695 NIL) (-1030 2376067 2376869 2377753 "REAL0Q" 2378749 NIL REAL0Q (NIL T) -7 NIL NIL NIL) (-1029 2371668 2372656 2373717 "REAL0" 2375048 NIL REAL0 (NIL T) -7 NIL NIL NIL) (-1028 2371139 2371385 2371479 "RDUCEAST" 2371596 T RDUCEAST (NIL) -8 NIL NIL NIL) (-1027 2370544 2370616 2370823 "RDIV" 2371061 NIL RDIV (NIL T T T T T) -7 NIL NIL NIL) (-1026 2369612 2369786 2369999 "RDIST" 2370366 NIL RDIST (NIL T) -7 NIL NIL NIL) (-1025 2368209 2368496 2368868 "RDETRS" 2369320 NIL RDETRS (NIL T T) -7 NIL NIL NIL) (-1024 2366021 2366475 2367013 "RDETR" 2367751 NIL RDETR (NIL T T) -7 NIL NIL NIL) (-1023 2364646 2364924 2365321 "RDEEFS" 2365737 NIL RDEEFS (NIL T T) -7 NIL NIL NIL) (-1022 2363155 2363461 2363886 "RDEEF" 2364334 NIL RDEEF (NIL T T) -7 NIL NIL NIL) (-1021 2357216 2360136 2360166 "RCFIELD" 2361461 T RCFIELD (NIL) -9 NIL 2362192 NIL) (-1020 2355280 2355784 2356480 "RCFIELD-" 2356555 NIL RCFIELD- (NIL T) -8 NIL NIL NIL) (-1019 2351549 2353381 2353424 "RCAGG" 2354508 NIL RCAGG (NIL T) -9 NIL 2354973 NIL) (-1018 2351177 2351271 2351434 "RCAGG-" 2351439 NIL RCAGG- (NIL T T) -8 NIL NIL NIL) (-1017 2350512 2350624 2350789 "RATRET" 2351061 NIL RATRET (NIL T) -7 NIL NIL NIL) (-1016 2350065 2350132 2350253 "RATFACT" 2350440 NIL RATFACT (NIL T) -7 NIL NIL NIL) (-1015 2349373 2349493 2349645 "RANDSRC" 2349935 T RANDSRC (NIL) -7 NIL NIL NIL) (-1014 2349107 2349151 2349224 "RADUTIL" 2349322 T RADUTIL (NIL) -7 NIL NIL NIL) (-1013 2342221 2347938 2348249 "RADIX" 2348830 NIL RADIX (NIL NIL) -8 NIL NIL NIL) (-1012 2333840 2342063 2342193 "RADFF" 2342198 NIL RADFF (NIL T T T NIL NIL) -8 NIL NIL NIL) (-1011 2333487 2333562 2333592 "RADCAT" 2333752 T RADCAT (NIL) -9 NIL NIL NIL) (-1010 2333269 2333317 2333417 "RADCAT-" 2333422 NIL RADCAT- (NIL T) -8 NIL NIL NIL) (-1009 2331367 2333039 2333131 "QUEUE" 2333212 NIL QUEUE (NIL T) -8 NIL NIL NIL) (-1008 2327904 2331300 2331348 "QUAT" 2331353 NIL QUAT (NIL T) -8 NIL NIL NIL) (-1007 2327535 2327578 2327709 "QUATCT2" 2327855 NIL QUATCT2 (NIL T T T T) -7 NIL NIL NIL) (-1006 2320946 2324291 2324333 "QUATCAT" 2325124 NIL QUATCAT (NIL T) -9 NIL 2325890 NIL) (-1005 2317085 2318122 2319512 "QUATCAT-" 2319608 NIL QUATCAT- (NIL T T) -8 NIL NIL NIL) (-1004 2314550 2316161 2316204 "QUAGG" 2316585 NIL QUAGG (NIL T) -9 NIL 2316760 NIL) (-1003 2314152 2314372 2314442 "QQUTAST" 2314502 T QQUTAST (NIL) -8 NIL NIL NIL) (-1002 2313165 2313665 2313830 "QFORM" 2314033 NIL QFORM (NIL NIL T) -8 NIL NIL NIL) (-1001 2304158 2309397 2309439 "QFCAT" 2310107 NIL QFCAT (NIL T) -9 NIL 2311108 NIL) (-1000 2299725 2300926 2302520 "QFCAT-" 2302616 NIL QFCAT- (NIL T T) -8 NIL NIL NIL) (-999 2299359 2299402 2299531 "QFCAT2" 2299676 NIL QFCAT2 (NIL T T T T) -7 NIL NIL NIL) (-998 2298819 2298929 2299059 "QEQUAT" 2299249 T QEQUAT (NIL) -8 NIL NIL NIL) (-997 2291965 2293038 2294222 "QCMPACK" 2297752 NIL QCMPACK (NIL T T T T T) -7 NIL NIL NIL) (-996 2289514 2289962 2290390 "QALGSET" 2291620 NIL QALGSET (NIL T T T T) -8 NIL NIL NIL) (-995 2288759 2288933 2289165 "QALGSET2" 2289334 NIL QALGSET2 (NIL NIL NIL) -7 NIL NIL NIL) (-994 2287449 2287673 2287990 "PWFFINTB" 2288532 NIL PWFFINTB (NIL T T T T) -7 NIL NIL NIL) (-993 2285631 2285799 2286153 "PUSHVAR" 2287263 NIL PUSHVAR (NIL T T T T) -7 NIL NIL NIL) (-992 2281549 2282603 2282644 "PTRANFN" 2284528 NIL PTRANFN (NIL T) -9 NIL NIL NIL) (-991 2279951 2280242 2280564 "PTPACK" 2281260 NIL PTPACK (NIL T) -7 NIL NIL NIL) (-990 2279583 2279640 2279749 "PTFUNC2" 2279888 NIL PTFUNC2 (NIL T T) -7 NIL NIL NIL) (-989 2274028 2278425 2278466 "PTCAT" 2278762 NIL PTCAT (NIL T) -9 NIL 2278915 NIL) (-988 2273686 2273721 2273845 "PSQFR" 2273987 NIL PSQFR (NIL T T T T) -7 NIL NIL NIL) (-987 2272281 2272579 2272913 "PSEUDLIN" 2273384 NIL PSEUDLIN (NIL T) -7 NIL NIL NIL) (-986 2259044 2261415 2263739 "PSETPK" 2270041 NIL PSETPK (NIL T T T T) -7 NIL NIL NIL) (-985 2252062 2254802 2254898 "PSETCAT" 2257919 NIL PSETCAT (NIL T T T T) -9 NIL 2258733 NIL) (-984 2249898 2250532 2251353 "PSETCAT-" 2251358 NIL PSETCAT- (NIL T T T T T) -8 NIL NIL NIL) (-983 2249247 2249412 2249440 "PSCURVE" 2249708 T PSCURVE (NIL) -9 NIL 2249875 NIL) (-982 2245245 2246761 2246826 "PSCAT" 2247670 NIL PSCAT (NIL T T T) -9 NIL 2247910 NIL) (-981 2244308 2244524 2244924 "PSCAT-" 2244929 NIL PSCAT- (NIL T T T T) -8 NIL NIL NIL) (-980 2242667 2243377 2243640 "PRTITION" 2244065 T PRTITION (NIL) -8 NIL NIL NIL) (-979 2242142 2242388 2242480 "PRTDAST" 2242595 T PRTDAST (NIL) -8 NIL NIL NIL) (-978 2231232 2233446 2235634 "PRS" 2240004 NIL PRS (NIL T T) -7 NIL NIL NIL) (-977 2229043 2230582 2230622 "PRQAGG" 2230805 NIL PRQAGG (NIL T) -9 NIL 2230907 NIL) (-976 2228379 2228684 2228712 "PROPLOG" 2228851 T PROPLOG (NIL) -9 NIL 2228966 NIL) (-975 2227983 2228040 2228163 "PROPFUN2" 2228302 NIL PROPFUN2 (NIL T T) -8 NIL NIL NIL) (-974 2227298 2227419 2227591 "PROPFUN1" 2227844 NIL PROPFUN1 (NIL T) -8 NIL NIL NIL) (-973 2225479 2226045 2226342 "PROPFRML" 2227034 NIL PROPFRML (NIL T) -8 NIL NIL NIL) (-972 2224948 2225055 2225183 "PROPERTY" 2225371 T PROPERTY (NIL) -8 NIL NIL NIL) (-971 2219006 2223114 2223934 "PRODUCT" 2224174 NIL PRODUCT (NIL T T) -8 NIL NIL NIL) (-970 2216284 2218464 2218698 "PR" 2218817 NIL PR (NIL T T) -8 NIL NIL NIL) (-969 2216080 2216112 2216171 "PRINT" 2216245 T PRINT (NIL) -7 NIL NIL NIL) (-968 2215420 2215537 2215689 "PRIMES" 2215960 NIL PRIMES (NIL T) -7 NIL NIL NIL) (-967 2213485 2213886 2214352 "PRIMELT" 2214999 NIL PRIMELT (NIL T) -7 NIL NIL NIL) (-966 2213214 2213263 2213291 "PRIMCAT" 2213415 T PRIMCAT (NIL) -9 NIL NIL NIL) (-965 2209329 2213152 2213197 "PRIMARR" 2213202 NIL PRIMARR (NIL T) -8 NIL NIL NIL) (-964 2208336 2208514 2208742 "PRIMARR2" 2209147 NIL PRIMARR2 (NIL T T) -7 NIL NIL NIL) (-963 2207979 2208035 2208146 "PREASSOC" 2208274 NIL PREASSOC (NIL T T) -7 NIL NIL NIL) (-962 2207454 2207587 2207615 "PPCURVE" 2207820 T PPCURVE (NIL) -9 NIL 2207956 NIL) (-961 2207049 2207249 2207332 "PORTNUM" 2207391 T PORTNUM (NIL) -8 NIL NIL NIL) (-960 2204408 2204807 2205399 "POLYROOT" 2206630 NIL POLYROOT (NIL T T T T T) -7 NIL NIL NIL) (-959 2198590 2204012 2204172 "POLY" 2204281 NIL POLY (NIL T) -8 NIL NIL NIL) (-958 2197973 2198031 2198265 "POLYLIFT" 2198526 NIL POLYLIFT (NIL T T T T T) -7 NIL NIL NIL) (-957 2194248 2194697 2195326 "POLYCATQ" 2197518 NIL POLYCATQ (NIL T T T T T) -7 NIL NIL NIL) (-956 2180960 2186088 2186153 "POLYCAT" 2189667 NIL POLYCAT (NIL T T T) -9 NIL 2191545 NIL) (-955 2174409 2176271 2178655 "POLYCAT-" 2178660 NIL POLYCAT- (NIL T T T T) -8 NIL NIL NIL) (-954 2173996 2174064 2174184 "POLY2UP" 2174335 NIL POLY2UP (NIL NIL T) -7 NIL NIL NIL) (-953 2173628 2173685 2173794 "POLY2" 2173933 NIL POLY2 (NIL T T) -7 NIL NIL NIL) (-952 2172313 2172552 2172828 "POLUTIL" 2173402 NIL POLUTIL (NIL T T) -7 NIL NIL NIL) (-951 2170668 2170945 2171276 "POLTOPOL" 2172035 NIL POLTOPOL (NIL NIL T) -7 NIL NIL NIL) (-950 2166133 2170604 2170650 "POINT" 2170655 NIL POINT (NIL T) -8 NIL NIL NIL) (-949 2164320 2164677 2165052 "PNTHEORY" 2165778 T PNTHEORY (NIL) -7 NIL NIL NIL) (-948 2162778 2163075 2163474 "PMTOOLS" 2164018 NIL PMTOOLS (NIL T T T) -7 NIL NIL NIL) (-947 2162371 2162449 2162566 "PMSYM" 2162694 NIL PMSYM (NIL T) -7 NIL NIL NIL) (-946 2161879 2161948 2162123 "PMQFCAT" 2162296 NIL PMQFCAT (NIL T T T) -7 NIL NIL NIL) (-945 2161234 2161344 2161500 "PMPRED" 2161756 NIL PMPRED (NIL T) -7 NIL NIL NIL) (-944 2160627 2160713 2160875 "PMPREDFS" 2161135 NIL PMPREDFS (NIL T T T) -7 NIL NIL NIL) (-943 2159291 2159499 2159877 "PMPLCAT" 2160389 NIL PMPLCAT (NIL T T T T T) -7 NIL NIL NIL) (-942 2158823 2158902 2159054 "PMLSAGG" 2159206 NIL PMLSAGG (NIL T T T) -7 NIL NIL NIL) (-941 2158296 2158372 2158554 "PMKERNEL" 2158741 NIL PMKERNEL (NIL T T) -7 NIL NIL NIL) (-940 2157913 2157988 2158101 "PMINS" 2158215 NIL PMINS (NIL T) -7 NIL NIL NIL) (-939 2157355 2157424 2157633 "PMFS" 2157838 NIL PMFS (NIL T T T) -7 NIL NIL NIL) (-938 2156583 2156701 2156906 "PMDOWN" 2157232 NIL PMDOWN (NIL T T T) -7 NIL NIL NIL) (-937 2155750 2155908 2156089 "PMASS" 2156422 T PMASS (NIL) -7 NIL NIL NIL) (-936 2155023 2155133 2155296 "PMASSFS" 2155637 NIL PMASSFS (NIL T T) -7 NIL NIL NIL) (-935 2154678 2154746 2154840 "PLOTTOOL" 2154949 T PLOTTOOL (NIL) -7 NIL NIL NIL) (-934 2149285 2150489 2151637 "PLOT" 2153550 T PLOT (NIL) -8 NIL NIL NIL) (-933 2145089 2146133 2147054 "PLOT3D" 2148384 T PLOT3D (NIL) -8 NIL NIL NIL) (-932 2144001 2144178 2144413 "PLOT1" 2144893 NIL PLOT1 (NIL T) -7 NIL NIL NIL) (-931 2119392 2124067 2128918 "PLEQN" 2139267 NIL PLEQN (NIL T T T T) -7 NIL NIL NIL) (-930 2118710 2118832 2119012 "PINTERP" 2119257 NIL PINTERP (NIL NIL T) -7 NIL NIL NIL) (-929 2118403 2118450 2118553 "PINTERPA" 2118657 NIL PINTERPA (NIL T T) -7 NIL NIL NIL) (-928 2117619 2118167 2118254 "PI" 2118294 T PI (NIL) -8 NIL NIL 2118361) (-927 2115916 2116891 2116919 "PID" 2117101 T PID (NIL) -9 NIL 2117235 NIL) (-926 2115667 2115704 2115779 "PICOERCE" 2115873 NIL PICOERCE (NIL T) -7 NIL NIL NIL) (-925 2114987 2115126 2115302 "PGROEB" 2115523 NIL PGROEB (NIL T) -7 NIL NIL NIL) (-924 2110574 2111388 2112293 "PGE" 2114102 T PGE (NIL) -7 NIL NIL NIL) (-923 2108697 2108944 2109310 "PGCD" 2110291 NIL PGCD (NIL T T T T) -7 NIL NIL NIL) (-922 2108035 2108138 2108299 "PFRPAC" 2108581 NIL PFRPAC (NIL T) -7 NIL NIL NIL) (-921 2104675 2106583 2106936 "PFR" 2107714 NIL PFR (NIL T) -8 NIL NIL NIL) (-920 2103064 2103308 2103633 "PFOTOOLS" 2104422 NIL PFOTOOLS (NIL T T) -7 NIL NIL NIL) (-919 2101597 2101836 2102187 "PFOQ" 2102821 NIL PFOQ (NIL T T T) -7 NIL NIL NIL) (-918 2100098 2100310 2100666 "PFO" 2101381 NIL PFO (NIL T T T T T) -7 NIL NIL NIL) (-917 2096651 2099987 2100056 "PF" 2100061 NIL PF (NIL NIL) -8 NIL NIL NIL) (-916 2093985 2095256 2095284 "PFECAT" 2095869 T PFECAT (NIL) -9 NIL 2096253 NIL) (-915 2093430 2093584 2093798 "PFECAT-" 2093803 NIL PFECAT- (NIL T) -8 NIL NIL NIL) (-914 2092033 2092285 2092586 "PFBRU" 2093179 NIL PFBRU (NIL T T) -7 NIL NIL NIL) (-913 2089899 2090251 2090683 "PFBR" 2091684 NIL PFBR (NIL T T T T) -7 NIL NIL NIL) (-912 2085945 2087411 2088058 "PERM" 2089285 NIL PERM (NIL T) -8 NIL NIL NIL) (-911 2081179 2082152 2083022 "PERMGRP" 2085108 NIL PERMGRP (NIL T) -8 NIL NIL NIL) (-910 2079298 2080258 2080299 "PERMCAT" 2080699 NIL PERMCAT (NIL T) -9 NIL 2080997 NIL) (-909 2078951 2078992 2079116 "PERMAN" 2079251 NIL PERMAN (NIL NIL T) -7 NIL NIL NIL) (-908 2076439 2078616 2078738 "PENDTREE" 2078862 NIL PENDTREE (NIL T) -8 NIL NIL NIL) (-907 2074463 2075231 2075272 "PDRING" 2075929 NIL PDRING (NIL T) -9 NIL 2076215 NIL) (-906 2073566 2073784 2074146 "PDRING-" 2074151 NIL PDRING- (NIL T T) -8 NIL NIL NIL) (-905 2070781 2071559 2072227 "PDEPROB" 2072918 T PDEPROB (NIL) -8 NIL NIL NIL) (-904 2068326 2068830 2069385 "PDEPACK" 2070246 T PDEPACK (NIL) -7 NIL NIL NIL) (-903 2067238 2067428 2067679 "PDECOMP" 2068125 NIL PDECOMP (NIL T T) -7 NIL NIL NIL) (-902 2064817 2065660 2065688 "PDECAT" 2066475 T PDECAT (NIL) -9 NIL 2067188 NIL) (-901 2064568 2064601 2064691 "PCOMP" 2064778 NIL PCOMP (NIL T T) -7 NIL NIL NIL) (-900 2062746 2063369 2063666 "PBWLB" 2064297 NIL PBWLB (NIL T) -8 NIL NIL NIL) (-899 2055219 2056819 2058157 "PATTERN" 2061429 NIL PATTERN (NIL T) -8 NIL NIL NIL) (-898 2054851 2054908 2055017 "PATTERN2" 2055156 NIL PATTERN2 (NIL T T) -7 NIL NIL NIL) (-897 2052608 2052996 2053453 "PATTERN1" 2054440 NIL PATTERN1 (NIL T T) -7 NIL NIL NIL) (-896 2049976 2050557 2051038 "PATRES" 2052173 NIL PATRES (NIL T T) -8 NIL NIL NIL) (-895 2049540 2049607 2049739 "PATRES2" 2049903 NIL PATRES2 (NIL T T T) -7 NIL NIL NIL) (-894 2047423 2047828 2048235 "PATMATCH" 2049207 NIL PATMATCH (NIL T T T) -7 NIL NIL NIL) (-893 2046933 2047142 2047183 "PATMAB" 2047290 NIL PATMAB (NIL T) -9 NIL 2047373 NIL) (-892 2045451 2045787 2046045 "PATLRES" 2046738 NIL PATLRES (NIL T T T) -8 NIL NIL NIL) (-891 2044997 2045120 2045161 "PATAB" 2045166 NIL PATAB (NIL T) -9 NIL 2045338 NIL) (-890 2043179 2043574 2043997 "PARTPERM" 2044594 T PARTPERM (NIL) -7 NIL NIL NIL) (-889 2042800 2042863 2042965 "PARSURF" 2043110 NIL PARSURF (NIL T) -8 NIL NIL NIL) (-888 2042432 2042489 2042598 "PARSU2" 2042737 NIL PARSU2 (NIL T T) -7 NIL NIL NIL) (-887 2042196 2042236 2042303 "PARSER" 2042385 T PARSER (NIL) -7 NIL NIL NIL) (-886 2041817 2041880 2041982 "PARSCURV" 2042127 NIL PARSCURV (NIL T) -8 NIL NIL NIL) (-885 2041449 2041506 2041615 "PARSC2" 2041754 NIL PARSC2 (NIL T T) -7 NIL NIL NIL) (-884 2041088 2041146 2041243 "PARPCURV" 2041385 NIL PARPCURV (NIL T) -8 NIL NIL NIL) (-883 2040720 2040777 2040886 "PARPC2" 2041025 NIL PARPC2 (NIL T T) -7 NIL NIL NIL) (-882 2039781 2040093 2040275 "PARAMAST" 2040558 T PARAMAST (NIL) -8 NIL NIL NIL) (-881 2039301 2039387 2039506 "PAN2EXPR" 2039682 T PAN2EXPR (NIL) -7 NIL NIL NIL) (-880 2038078 2038422 2038650 "PALETTE" 2039093 T PALETTE (NIL) -8 NIL NIL NIL) (-879 2036471 2037083 2037443 "PAIR" 2037764 NIL PAIR (NIL T T) -8 NIL NIL NIL) (-878 2030339 2035728 2035923 "PADICRC" 2036325 NIL PADICRC (NIL NIL T) -8 NIL NIL NIL) (-877 2023566 2029683 2029868 "PADICRAT" 2030186 NIL PADICRAT (NIL NIL) -8 NIL NIL NIL) (-876 2021881 2023503 2023548 "PADIC" 2023553 NIL PADIC (NIL NIL) -8 NIL NIL NIL) (-875 2018991 2020555 2020595 "PADICCT" 2021176 NIL PADICCT (NIL NIL) -9 NIL 2021458 NIL) (-874 2017948 2018148 2018416 "PADEPAC" 2018778 NIL PADEPAC (NIL T NIL NIL) -7 NIL NIL NIL) (-873 2017160 2017293 2017499 "PADE" 2017810 NIL PADE (NIL T T T) -7 NIL NIL NIL) (-872 2015547 2016368 2016648 "OWP" 2016964 NIL OWP (NIL T NIL NIL NIL) -8 NIL NIL NIL) (-871 2015040 2015253 2015350 "OVERSET" 2015470 T OVERSET (NIL) -8 NIL NIL NIL) (-870 2014086 2014645 2014817 "OVAR" 2014908 NIL OVAR (NIL NIL) -8 NIL NIL NIL) (-869 2013350 2013471 2013632 "OUT" 2013945 T OUT (NIL) -7 NIL NIL NIL) (-868 2002222 2004459 2006659 "OUTFORM" 2011170 T OUTFORM (NIL) -8 NIL NIL NIL) (-867 2001558 2001819 2001946 "OUTBFILE" 2002115 T OUTBFILE (NIL) -8 NIL NIL NIL) (-866 2000865 2001030 2001058 "OUTBCON" 2001376 T OUTBCON (NIL) -9 NIL 2001542 NIL) (-865 2000466 2000578 2000735 "OUTBCON-" 2000740 NIL OUTBCON- (NIL T) -8 NIL NIL NIL) (-864 1999846 2000195 2000284 "OSI" 2000397 T OSI (NIL) -8 NIL NIL NIL) (-863 1999376 1999714 1999742 "OSGROUP" 1999747 T OSGROUP (NIL) -9 NIL 1999769 NIL) (-862 1998121 1998348 1998633 "ORTHPOL" 1999123 NIL ORTHPOL (NIL T) -7 NIL NIL NIL) (-861 1995672 1997956 1998077 "OREUP" 1998082 NIL OREUP (NIL NIL T NIL NIL) -8 NIL NIL NIL) (-860 1993075 1995363 1995490 "ORESUP" 1995614 NIL ORESUP (NIL T NIL NIL) -8 NIL NIL NIL) (-859 1990603 1991103 1991664 "OREPCTO" 1992564 NIL OREPCTO (NIL T T) -7 NIL NIL NIL) (-858 1984289 1986490 1986531 "OREPCAT" 1988879 NIL OREPCAT (NIL T) -9 NIL 1989983 NIL) (-857 1981436 1982218 1983276 "OREPCAT-" 1983281 NIL OREPCAT- (NIL T T) -8 NIL NIL NIL) (-856 1980587 1980885 1980913 "ORDSET" 1981222 T ORDSET (NIL) -9 NIL 1981386 NIL) (-855 1980018 1980166 1980390 "ORDSET-" 1980395 NIL ORDSET- (NIL T) -8 NIL NIL NIL) (-854 1978583 1979374 1979402 "ORDRING" 1979604 T ORDRING (NIL) -9 NIL 1979729 NIL) (-853 1978228 1978322 1978466 "ORDRING-" 1978471 NIL ORDRING- (NIL T) -8 NIL NIL NIL) (-852 1977608 1978071 1978099 "ORDMON" 1978104 T ORDMON (NIL) -9 NIL 1978125 NIL) (-851 1976770 1976917 1977112 "ORDFUNS" 1977457 NIL ORDFUNS (NIL NIL T) -7 NIL NIL NIL) (-850 1976108 1976527 1976555 "ORDFIN" 1976620 T ORDFIN (NIL) -9 NIL 1976694 NIL) (-849 1972667 1974694 1975103 "ORDCOMP" 1975732 NIL ORDCOMP (NIL T) -8 NIL NIL NIL) (-848 1971933 1972060 1972246 "ORDCOMP2" 1972527 NIL ORDCOMP2 (NIL T T) -7 NIL NIL NIL) (-847 1968514 1969424 1970238 "OPTPROB" 1971139 T OPTPROB (NIL) -8 NIL NIL NIL) (-846 1965316 1965955 1966659 "OPTPACK" 1967830 T OPTPACK (NIL) -7 NIL NIL NIL) (-845 1963003 1963769 1963797 "OPTCAT" 1964616 T OPTCAT (NIL) -9 NIL 1965266 NIL) (-844 1962387 1962680 1962785 "OPSIG" 1962918 T OPSIG (NIL) -8 NIL NIL NIL) (-843 1962155 1962194 1962260 "OPQUERY" 1962341 T OPQUERY (NIL) -7 NIL NIL NIL) (-842 1959286 1960466 1960970 "OP" 1961684 NIL OP (NIL T) -8 NIL NIL NIL) (-841 1958660 1958886 1958927 "OPERCAT" 1959139 NIL OPERCAT (NIL T) -9 NIL 1959236 NIL) (-840 1958415 1958471 1958588 "OPERCAT-" 1958593 NIL OPERCAT- (NIL T T) -8 NIL NIL NIL) (-839 1955228 1957212 1957581 "ONECOMP" 1958079 NIL ONECOMP (NIL T) -8 NIL NIL NIL) (-838 1954533 1954648 1954822 "ONECOMP2" 1955100 NIL ONECOMP2 (NIL T T) -7 NIL NIL NIL) (-837 1953952 1954058 1954188 "OMSERVER" 1954423 T OMSERVER (NIL) -7 NIL NIL NIL) (-836 1950814 1953392 1953432 "OMSAGG" 1953493 NIL OMSAGG (NIL T) -9 NIL 1953557 NIL) (-835 1949437 1949700 1949982 "OMPKG" 1950552 T OMPKG (NIL) -7 NIL NIL NIL) (-834 1948867 1948970 1948998 "OM" 1949297 T OM (NIL) -9 NIL NIL NIL) (-833 1947414 1948416 1948585 "OMLO" 1948748 NIL OMLO (NIL T T) -8 NIL NIL NIL) (-832 1946374 1946521 1946741 "OMEXPR" 1947240 NIL OMEXPR (NIL T) -7 NIL NIL NIL) (-831 1945665 1945920 1946056 "OMERR" 1946258 T OMERR (NIL) -8 NIL NIL NIL) (-830 1944816 1945086 1945246 "OMERRK" 1945525 T OMERRK (NIL) -8 NIL NIL NIL) (-829 1944267 1944493 1944601 "OMENC" 1944728 T OMENC (NIL) -8 NIL NIL NIL) (-828 1938162 1939347 1940518 "OMDEV" 1943116 T OMDEV (NIL) -8 NIL NIL NIL) (-827 1937231 1937402 1937596 "OMCONN" 1937988 T OMCONN (NIL) -8 NIL NIL NIL) (-826 1935752 1936728 1936756 "OINTDOM" 1936761 T OINTDOM (NIL) -9 NIL 1936782 NIL) (-825 1933090 1934440 1934777 "OFMONOID" 1935447 NIL OFMONOID (NIL T) -8 NIL NIL NIL) (-824 1932501 1933027 1933072 "ODVAR" 1933077 NIL ODVAR (NIL T) -8 NIL NIL NIL) (-823 1929924 1932246 1932401 "ODR" 1932406 NIL ODR (NIL T T NIL) -8 NIL NIL NIL) (-822 1922505 1929700 1929826 "ODPOL" 1929831 NIL ODPOL (NIL T) -8 NIL NIL NIL) (-821 1916327 1922377 1922482 "ODP" 1922487 NIL ODP (NIL NIL T NIL) -8 NIL NIL NIL) (-820 1915093 1915308 1915583 "ODETOOLS" 1916101 NIL ODETOOLS (NIL T T) -7 NIL NIL NIL) (-819 1912060 1912718 1913434 "ODESYS" 1914426 NIL ODESYS (NIL T T) -7 NIL NIL NIL) (-818 1906942 1907850 1908875 "ODERTRIC" 1911135 NIL ODERTRIC (NIL T T) -7 NIL NIL NIL) (-817 1906368 1906450 1906644 "ODERED" 1906854 NIL ODERED (NIL T T T T T) -7 NIL NIL NIL) (-816 1903256 1903804 1904481 "ODERAT" 1905791 NIL ODERAT (NIL T T) -7 NIL NIL NIL) (-815 1900215 1900680 1901277 "ODEPRRIC" 1902785 NIL ODEPRRIC (NIL T T T T) -7 NIL NIL NIL) (-814 1898158 1898754 1899240 "ODEPROB" 1899749 T ODEPROB (NIL) -8 NIL NIL NIL) (-813 1894678 1895163 1895810 "ODEPRIM" 1897637 NIL ODEPRIM (NIL T T T T) -7 NIL NIL NIL) (-812 1893927 1894029 1894289 "ODEPAL" 1894570 NIL ODEPAL (NIL T T T T) -7 NIL NIL NIL) (-811 1890089 1890880 1891744 "ODEPACK" 1893083 T ODEPACK (NIL) -7 NIL NIL NIL) (-810 1889150 1889257 1889479 "ODEINT" 1889978 NIL ODEINT (NIL T T) -7 NIL NIL NIL) (-809 1883251 1884676 1886123 "ODEIFTBL" 1887723 T ODEIFTBL (NIL) -8 NIL NIL NIL) (-808 1878649 1879435 1880387 "ODEEF" 1882410 NIL ODEEF (NIL T T) -7 NIL NIL NIL) (-807 1877998 1878087 1878310 "ODECONST" 1878554 NIL ODECONST (NIL T T T) -7 NIL NIL NIL) (-806 1876123 1876784 1876812 "ODECAT" 1877417 T ODECAT (NIL) -9 NIL 1877948 NIL) (-805 1872978 1875828 1875950 "OCT" 1876033 NIL OCT (NIL T) -8 NIL NIL NIL) (-804 1872616 1872659 1872786 "OCTCT2" 1872929 NIL OCTCT2 (NIL T T T T) -7 NIL NIL NIL) (-803 1867227 1869662 1869702 "OC" 1870799 NIL OC (NIL T) -9 NIL 1871657 NIL) (-802 1864454 1865202 1866192 "OC-" 1866286 NIL OC- (NIL T T) -8 NIL NIL NIL) (-801 1863806 1864274 1864302 "OCAMON" 1864307 T OCAMON (NIL) -9 NIL 1864328 NIL) (-800 1863337 1863678 1863706 "OASGP" 1863711 T OASGP (NIL) -9 NIL 1863731 NIL) (-799 1862598 1863087 1863115 "OAMONS" 1863155 T OAMONS (NIL) -9 NIL 1863198 NIL) (-798 1862012 1862445 1862473 "OAMON" 1862478 T OAMON (NIL) -9 NIL 1862498 NIL) (-797 1861270 1861788 1861816 "OAGROUP" 1861821 T OAGROUP (NIL) -9 NIL 1861841 NIL) (-796 1860960 1861010 1861098 "NUMTUBE" 1861214 NIL NUMTUBE (NIL T) -7 NIL NIL NIL) (-795 1854533 1856051 1857587 "NUMQUAD" 1859444 T NUMQUAD (NIL) -7 NIL NIL NIL) (-794 1850289 1851277 1852302 "NUMODE" 1853528 T NUMODE (NIL) -7 NIL NIL NIL) (-793 1847644 1848524 1848552 "NUMINT" 1849475 T NUMINT (NIL) -9 NIL 1850239 NIL) (-792 1846592 1846789 1847007 "NUMFMT" 1847446 T NUMFMT (NIL) -7 NIL NIL NIL) (-791 1832951 1835896 1838428 "NUMERIC" 1844099 NIL NUMERIC (NIL T) -7 NIL NIL NIL) (-790 1827321 1832400 1832495 "NTSCAT" 1832500 NIL NTSCAT (NIL T T T T) -9 NIL 1832539 NIL) (-789 1826515 1826680 1826873 "NTPOLFN" 1827160 NIL NTPOLFN (NIL T) -7 NIL NIL NIL) (-788 1814592 1823340 1824152 "NSUP" 1825736 NIL NSUP (NIL T) -8 NIL NIL NIL) (-787 1814224 1814281 1814390 "NSUP2" 1814529 NIL NSUP2 (NIL T T) -7 NIL NIL NIL) (-786 1804450 1813998 1814131 "NSMP" 1814136 NIL NSMP (NIL T T) -8 NIL NIL NIL) (-785 1802882 1803183 1803540 "NREP" 1804138 NIL NREP (NIL T) -7 NIL NIL NIL) (-784 1801473 1801725 1802083 "NPCOEF" 1802625 NIL NPCOEF (NIL T T T T T) -7 NIL NIL NIL) (-783 1800539 1800654 1800870 "NORMRETR" 1801354 NIL NORMRETR (NIL T T T T NIL) -7 NIL NIL NIL) (-782 1798580 1798870 1799279 "NORMPK" 1800247 NIL NORMPK (NIL T T T T T) -7 NIL NIL NIL) (-781 1798265 1798293 1798417 "NORMMA" 1798546 NIL NORMMA (NIL T T T T) -7 NIL NIL NIL) (-780 1798065 1798222 1798251 "NONE" 1798256 T NONE (NIL) -8 NIL NIL NIL) (-779 1797854 1797883 1797952 "NONE1" 1798029 NIL NONE1 (NIL T) -7 NIL NIL NIL) (-778 1797351 1797413 1797592 "NODE1" 1797786 NIL NODE1 (NIL T T) -7 NIL NIL NIL) (-777 1795632 1796483 1796738 "NNI" 1797085 T NNI (NIL) -8 NIL NIL 1797320) (-776 1794052 1794365 1794729 "NLINSOL" 1795300 NIL NLINSOL (NIL T) -7 NIL NIL NIL) (-775 1790293 1791288 1792187 "NIPROB" 1793173 T NIPROB (NIL) -8 NIL NIL NIL) (-774 1789050 1789284 1789586 "NFINTBAS" 1790055 NIL NFINTBAS (NIL T T) -7 NIL NIL NIL) (-773 1788224 1788700 1788741 "NETCLT" 1788913 NIL NETCLT (NIL T) -9 NIL 1788995 NIL) (-772 1786932 1787163 1787444 "NCODIV" 1787992 NIL NCODIV (NIL T T) -7 NIL NIL NIL) (-771 1786694 1786731 1786806 "NCNTFRAC" 1786889 NIL NCNTFRAC (NIL T) -7 NIL NIL NIL) (-770 1784874 1785238 1785658 "NCEP" 1786319 NIL NCEP (NIL T) -7 NIL NIL NIL) (-769 1783725 1784498 1784526 "NASRING" 1784636 T NASRING (NIL) -9 NIL 1784716 NIL) (-768 1783520 1783564 1783658 "NASRING-" 1783663 NIL NASRING- (NIL T) -8 NIL NIL NIL) (-767 1782627 1783152 1783180 "NARNG" 1783297 T NARNG (NIL) -9 NIL 1783388 NIL) (-766 1782319 1782386 1782520 "NARNG-" 1782525 NIL NARNG- (NIL T) -8 NIL NIL NIL) (-765 1781198 1781405 1781640 "NAGSP" 1782104 T NAGSP (NIL) -7 NIL NIL NIL) (-764 1772470 1774154 1775827 "NAGS" 1779545 T NAGS (NIL) -7 NIL NIL NIL) (-763 1771018 1771326 1771657 "NAGF07" 1772159 T NAGF07 (NIL) -7 NIL NIL NIL) (-762 1765556 1766847 1768154 "NAGF04" 1769731 T NAGF04 (NIL) -7 NIL NIL NIL) (-761 1758524 1760138 1761771 "NAGF02" 1763943 T NAGF02 (NIL) -7 NIL NIL NIL) (-760 1753748 1754848 1755965 "NAGF01" 1757427 T NAGF01 (NIL) -7 NIL NIL NIL) (-759 1747376 1748942 1750527 "NAGE04" 1752183 T NAGE04 (NIL) -7 NIL NIL NIL) (-758 1738545 1740666 1742796 "NAGE02" 1745266 T NAGE02 (NIL) -7 NIL NIL NIL) (-757 1734498 1735445 1736409 "NAGE01" 1737601 T NAGE01 (NIL) -7 NIL NIL NIL) (-756 1732293 1732827 1733385 "NAGD03" 1733960 T NAGD03 (NIL) -7 NIL NIL NIL) (-755 1724043 1725971 1727925 "NAGD02" 1730359 T NAGD02 (NIL) -7 NIL NIL NIL) (-754 1717854 1719279 1720719 "NAGD01" 1722623 T NAGD01 (NIL) -7 NIL NIL NIL) (-753 1714063 1714885 1715722 "NAGC06" 1717037 T NAGC06 (NIL) -7 NIL NIL NIL) (-752 1712528 1712860 1713216 "NAGC05" 1713727 T NAGC05 (NIL) -7 NIL NIL NIL) (-751 1711904 1712023 1712167 "NAGC02" 1712404 T NAGC02 (NIL) -7 NIL NIL NIL) (-750 1710863 1711446 1711486 "NAALG" 1711565 NIL NAALG (NIL T) -9 NIL 1711626 NIL) (-749 1710698 1710727 1710817 "NAALG-" 1710822 NIL NAALG- (NIL T T) -8 NIL NIL NIL) (-748 1704648 1705756 1706943 "MULTSQFR" 1709594 NIL MULTSQFR (NIL T T T T) -7 NIL NIL NIL) (-747 1703967 1704042 1704226 "MULTFACT" 1704560 NIL MULTFACT (NIL T T T T) -7 NIL NIL NIL) (-746 1696691 1700604 1700657 "MTSCAT" 1701727 NIL MTSCAT (NIL T T) -9 NIL 1702242 NIL) (-745 1696403 1696457 1696549 "MTHING" 1696631 NIL MTHING (NIL T) -7 NIL NIL NIL) (-744 1696195 1696228 1696288 "MSYSCMD" 1696363 T MSYSCMD (NIL) -7 NIL NIL NIL) (-743 1692277 1694950 1695270 "MSET" 1695908 NIL MSET (NIL T) -8 NIL NIL NIL) (-742 1689346 1691838 1691879 "MSETAGG" 1691884 NIL MSETAGG (NIL T) -9 NIL 1691918 NIL) (-741 1685188 1686725 1687470 "MRING" 1688646 NIL MRING (NIL T T) -8 NIL NIL NIL) (-740 1684754 1684821 1684952 "MRF2" 1685115 NIL MRF2 (NIL T T T) -7 NIL NIL NIL) (-739 1684372 1684407 1684551 "MRATFAC" 1684713 NIL MRATFAC (NIL T T T T) -7 NIL NIL NIL) (-738 1681984 1682279 1682710 "MPRFF" 1684077 NIL MPRFF (NIL T T T T) -7 NIL NIL NIL) (-737 1676281 1681838 1681935 "MPOLY" 1681940 NIL MPOLY (NIL NIL T) -8 NIL NIL NIL) (-736 1675771 1675806 1676014 "MPCPF" 1676240 NIL MPCPF (NIL T T T T) -7 NIL NIL NIL) (-735 1675285 1675328 1675512 "MPC3" 1675722 NIL MPC3 (NIL T T T T T T T) -7 NIL NIL NIL) (-734 1674480 1674561 1674782 "MPC2" 1675200 NIL MPC2 (NIL T T T T T T T) -7 NIL NIL NIL) (-733 1672781 1673118 1673508 "MONOTOOL" 1674140 NIL MONOTOOL (NIL T T) -7 NIL NIL NIL) (-732 1672006 1672323 1672351 "MONOID" 1672570 T MONOID (NIL) -9 NIL 1672717 NIL) (-731 1671552 1671671 1671852 "MONOID-" 1671857 NIL MONOID- (NIL T) -8 NIL NIL NIL) (-730 1662027 1667978 1668037 "MONOGEN" 1668711 NIL MONOGEN (NIL T T) -9 NIL 1669167 NIL) (-729 1659245 1659980 1660980 "MONOGEN-" 1661099 NIL MONOGEN- (NIL T T T) -8 NIL NIL NIL) (-728 1658078 1658524 1658552 "MONADWU" 1658944 T MONADWU (NIL) -9 NIL 1659182 NIL) (-727 1657450 1657609 1657857 "MONADWU-" 1657862 NIL MONADWU- (NIL T) -8 NIL NIL NIL) (-726 1656809 1657053 1657081 "MONAD" 1657288 T MONAD (NIL) -9 NIL 1657400 NIL) (-725 1656494 1656572 1656704 "MONAD-" 1656709 NIL MONAD- (NIL T) -8 NIL NIL NIL) (-724 1654783 1655407 1655686 "MOEBIUS" 1656247 NIL MOEBIUS (NIL T) -8 NIL NIL NIL) (-723 1654061 1654465 1654505 "MODULE" 1654510 NIL MODULE (NIL T) -9 NIL 1654549 NIL) (-722 1653629 1653725 1653915 "MODULE-" 1653920 NIL MODULE- (NIL T T) -8 NIL NIL NIL) (-721 1651309 1651993 1652320 "MODRING" 1653453 NIL MODRING (NIL T T NIL NIL NIL) -8 NIL NIL NIL) (-720 1648253 1649414 1649935 "MODOP" 1650838 NIL MODOP (NIL T T) -8 NIL NIL NIL) (-719 1646841 1647320 1647597 "MODMONOM" 1648116 NIL MODMONOM (NIL T T NIL) -8 NIL NIL NIL) (-718 1636885 1645132 1645546 "MODMON" 1646478 NIL MODMON (NIL T T) -8 NIL NIL NIL) (-717 1634041 1635729 1636005 "MODFIELD" 1636760 NIL MODFIELD (NIL T T NIL NIL NIL) -8 NIL NIL NIL) (-716 1633018 1633322 1633512 "MMLFORM" 1633871 T MMLFORM (NIL) -8 NIL NIL NIL) (-715 1632544 1632587 1632766 "MMAP" 1632969 NIL MMAP (NIL T T T T T T) -7 NIL NIL NIL) (-714 1630623 1631390 1631431 "MLO" 1631854 NIL MLO (NIL T) -9 NIL 1632096 NIL) (-713 1627989 1628505 1629107 "MLIFT" 1630104 NIL MLIFT (NIL T T T T) -7 NIL NIL NIL) (-712 1627380 1627464 1627618 "MKUCFUNC" 1627900 NIL MKUCFUNC (NIL T T T) -7 NIL NIL NIL) (-711 1626979 1627049 1627172 "MKRECORD" 1627303 NIL MKRECORD (NIL T T) -7 NIL NIL NIL) (-710 1626026 1626188 1626416 "MKFUNC" 1626790 NIL MKFUNC (NIL T) -7 NIL NIL NIL) (-709 1625414 1625518 1625674 "MKFLCFN" 1625909 NIL MKFLCFN (NIL T) -7 NIL NIL NIL) (-708 1624691 1624793 1624978 "MKBCFUNC" 1625307 NIL MKBCFUNC (NIL T T T T) -7 NIL NIL NIL) (-707 1621398 1624245 1624381 "MINT" 1624575 T MINT (NIL) -8 NIL NIL NIL) (-706 1620210 1620453 1620730 "MHROWRED" 1621153 NIL MHROWRED (NIL T) -7 NIL NIL NIL) (-705 1615590 1618745 1619150 "MFLOAT" 1619825 T MFLOAT (NIL) -8 NIL NIL NIL) (-704 1614947 1615023 1615194 "MFINFACT" 1615502 NIL MFINFACT (NIL T T T T) -7 NIL NIL NIL) (-703 1611262 1612110 1612994 "MESH" 1614083 T MESH (NIL) -7 NIL NIL NIL) (-702 1609652 1609964 1610317 "MDDFACT" 1610949 NIL MDDFACT (NIL T) -7 NIL NIL NIL) (-701 1606447 1608811 1608852 "MDAGG" 1609107 NIL MDAGG (NIL T) -9 NIL 1609250 NIL) (-700 1596187 1605740 1605947 "MCMPLX" 1606260 T MCMPLX (NIL) -8 NIL NIL NIL) (-699 1595324 1595470 1595671 "MCDEN" 1596036 NIL MCDEN (NIL T T) -7 NIL NIL NIL) (-698 1593214 1593484 1593864 "MCALCFN" 1595054 NIL MCALCFN (NIL T T T T) -7 NIL NIL NIL) (-697 1592139 1592379 1592612 "MAYBE" 1593020 NIL MAYBE (NIL T) -8 NIL NIL NIL) (-696 1589751 1590274 1590836 "MATSTOR" 1591610 NIL MATSTOR (NIL T) -7 NIL NIL NIL) (-695 1585708 1589123 1589371 "MATRIX" 1589536 NIL MATRIX (NIL T) -8 NIL NIL NIL) (-694 1581474 1582181 1582917 "MATLIN" 1585065 NIL MATLIN (NIL T T T T) -7 NIL NIL NIL) (-693 1571580 1574766 1574843 "MATCAT" 1579723 NIL MATCAT (NIL T T T) -9 NIL 1581140 NIL) (-692 1567936 1568957 1570313 "MATCAT-" 1570318 NIL MATCAT- (NIL T T T T) -8 NIL NIL NIL) (-691 1566530 1566683 1567016 "MATCAT2" 1567771 NIL MATCAT2 (NIL T T T T T T T T) -7 NIL NIL NIL) (-690 1564642 1564966 1565350 "MAPPKG3" 1566205 NIL MAPPKG3 (NIL T T T) -7 NIL NIL NIL) (-689 1563623 1563796 1564018 "MAPPKG2" 1564466 NIL MAPPKG2 (NIL T T) -7 NIL NIL NIL) (-688 1562122 1562406 1562733 "MAPPKG1" 1563329 NIL MAPPKG1 (NIL T) -7 NIL NIL NIL) (-687 1561201 1561528 1561705 "MAPPAST" 1561965 T MAPPAST (NIL) -8 NIL NIL NIL) (-686 1560812 1560870 1560993 "MAPHACK3" 1561137 NIL MAPHACK3 (NIL T T T) -7 NIL NIL NIL) (-685 1560404 1560465 1560579 "MAPHACK2" 1560744 NIL MAPHACK2 (NIL T T) -7 NIL NIL NIL) (-684 1559842 1559945 1560087 "MAPHACK1" 1560295 NIL MAPHACK1 (NIL T) -7 NIL NIL NIL) (-683 1557921 1558542 1558846 "MAGMA" 1559570 NIL MAGMA (NIL T) -8 NIL NIL NIL) (-682 1557400 1557645 1557736 "MACROAST" 1557850 T MACROAST (NIL) -8 NIL NIL NIL) (-681 1553818 1555639 1556100 "M3D" 1556972 NIL M3D (NIL T) -8 NIL NIL NIL) (-680 1547893 1552157 1552198 "LZSTAGG" 1552980 NIL LZSTAGG (NIL T) -9 NIL 1553275 NIL) (-679 1543851 1545024 1546481 "LZSTAGG-" 1546486 NIL LZSTAGG- (NIL T T) -8 NIL NIL NIL) (-678 1540938 1541742 1542229 "LWORD" 1543396 NIL LWORD (NIL T) -8 NIL NIL NIL) (-677 1540514 1540742 1540817 "LSTAST" 1540883 T LSTAST (NIL) -8 NIL NIL NIL) (-676 1533680 1540285 1540419 "LSQM" 1540424 NIL LSQM (NIL NIL T) -8 NIL NIL NIL) (-675 1532904 1533043 1533271 "LSPP" 1533535 NIL LSPP (NIL T T T T) -7 NIL NIL NIL) (-674 1530716 1531017 1531473 "LSMP" 1532593 NIL LSMP (NIL T T T T) -7 NIL NIL NIL) (-673 1527495 1528169 1528899 "LSMP1" 1530018 NIL LSMP1 (NIL T) -7 NIL NIL NIL) (-672 1521341 1526632 1526673 "LSAGG" 1526735 NIL LSAGG (NIL T) -9 NIL 1526813 NIL) (-671 1518036 1518960 1520173 "LSAGG-" 1520178 NIL LSAGG- (NIL T T) -8 NIL NIL NIL) (-670 1515635 1517180 1517429 "LPOLY" 1517831 NIL LPOLY (NIL T T) -8 NIL NIL NIL) (-669 1515217 1515302 1515425 "LPEFRAC" 1515544 NIL LPEFRAC (NIL T) -7 NIL NIL NIL) (-668 1513538 1514311 1514564 "LO" 1515049 NIL LO (NIL T T T) -8 NIL NIL NIL) (-667 1513190 1513302 1513330 "LOGIC" 1513441 T LOGIC (NIL) -9 NIL 1513522 NIL) (-666 1513052 1513075 1513146 "LOGIC-" 1513151 NIL LOGIC- (NIL T) -8 NIL NIL NIL) (-665 1512245 1512385 1512578 "LODOOPS" 1512908 NIL LODOOPS (NIL T T) -7 NIL NIL NIL) (-664 1509668 1512161 1512227 "LODO" 1512232 NIL LODO (NIL T NIL) -8 NIL NIL NIL) (-663 1508206 1508441 1508794 "LODOF" 1509415 NIL LODOF (NIL T T) -7 NIL NIL NIL) (-662 1504410 1506841 1506882 "LODOCAT" 1507320 NIL LODOCAT (NIL T) -9 NIL 1507531 NIL) (-661 1504143 1504201 1504328 "LODOCAT-" 1504333 NIL LODOCAT- (NIL T T) -8 NIL NIL NIL) (-660 1501463 1503984 1504102 "LODO2" 1504107 NIL LODO2 (NIL T T) -8 NIL NIL NIL) (-659 1498898 1501400 1501445 "LODO1" 1501450 NIL LODO1 (NIL T) -8 NIL NIL NIL) (-658 1497779 1497944 1498249 "LODEEF" 1498721 NIL LODEEF (NIL T T T) -7 NIL NIL NIL) (-657 1493082 1495973 1496014 "LNAGG" 1496876 NIL LNAGG (NIL T) -9 NIL 1497311 NIL) (-656 1492229 1492443 1492785 "LNAGG-" 1492790 NIL LNAGG- (NIL T T) -8 NIL NIL NIL) (-655 1488365 1489154 1489793 "LMOPS" 1491644 NIL LMOPS (NIL T T NIL) -8 NIL NIL NIL) (-654 1487768 1488156 1488197 "LMODULE" 1488202 NIL LMODULE (NIL T) -9 NIL 1488228 NIL) (-653 1484966 1487413 1487536 "LMDICT" 1487678 NIL LMDICT (NIL T) -8 NIL NIL NIL) (-652 1484372 1484593 1484634 "LLINSET" 1484825 NIL LLINSET (NIL T) -9 NIL 1484916 NIL) (-651 1484071 1484280 1484340 "LITERAL" 1484345 NIL LITERAL (NIL T) -8 NIL NIL NIL) (-650 1477234 1483005 1483309 "LIST" 1483800 NIL LIST (NIL T) -8 NIL NIL NIL) (-649 1476759 1476833 1476972 "LIST3" 1477154 NIL LIST3 (NIL T T T) -7 NIL NIL NIL) (-648 1475766 1475944 1476172 "LIST2" 1476577 NIL LIST2 (NIL T T) -7 NIL NIL NIL) (-647 1473900 1474212 1474611 "LIST2MAP" 1475413 NIL LIST2MAP (NIL T T) -7 NIL NIL NIL) (-646 1473496 1473733 1473774 "LINSET" 1473779 NIL LINSET (NIL T) -9 NIL 1473813 NIL) (-645 1472157 1472827 1472868 "LINEXP" 1473123 NIL LINEXP (NIL T) -9 NIL 1473272 NIL) (-644 1470804 1471064 1471361 "LINDEP" 1471909 NIL LINDEP (NIL T T) -7 NIL NIL NIL) (-643 1467571 1468290 1469067 "LIMITRF" 1470059 NIL LIMITRF (NIL T) -7 NIL NIL NIL) (-642 1465874 1466170 1466579 "LIMITPS" 1467266 NIL LIMITPS (NIL T T) -7 NIL NIL NIL) (-641 1460302 1465385 1465613 "LIE" 1465695 NIL LIE (NIL T T) -8 NIL NIL NIL) (-640 1459250 1459719 1459759 "LIECAT" 1459899 NIL LIECAT (NIL T) -9 NIL 1460050 NIL) (-639 1459091 1459118 1459206 "LIECAT-" 1459211 NIL LIECAT- (NIL T T) -8 NIL NIL NIL) (-638 1451678 1458631 1458787 "LIB" 1458955 T LIB (NIL) -8 NIL NIL NIL) (-637 1447313 1448196 1449131 "LGROBP" 1450795 NIL LGROBP (NIL NIL T) -7 NIL NIL NIL) (-636 1445311 1445585 1445935 "LF" 1447034 NIL LF (NIL T T) -7 NIL NIL NIL) (-635 1444151 1444843 1444871 "LFCAT" 1445078 T LFCAT (NIL) -9 NIL 1445217 NIL) (-634 1441053 1441683 1442371 "LEXTRIPK" 1443515 NIL LEXTRIPK (NIL T NIL) -7 NIL NIL NIL) (-633 1437797 1438623 1439126 "LEXP" 1440633 NIL LEXP (NIL T T NIL) -8 NIL NIL NIL) (-632 1437273 1437518 1437610 "LETAST" 1437725 T LETAST (NIL) -8 NIL NIL NIL) (-631 1435671 1435984 1436385 "LEADCDET" 1436955 NIL LEADCDET (NIL T T T T) -7 NIL NIL NIL) (-630 1434861 1434935 1435164 "LAZM3PK" 1435592 NIL LAZM3PK (NIL T T T T T T) -7 NIL NIL NIL) (-629 1429778 1432938 1433476 "LAUPOL" 1434373 NIL LAUPOL (NIL T T) -8 NIL NIL NIL) (-628 1429357 1429401 1429562 "LAPLACE" 1429728 NIL LAPLACE (NIL T T) -7 NIL NIL NIL) (-627 1427296 1428458 1428709 "LA" 1429190 NIL LA (NIL T T T) -8 NIL NIL NIL) (-626 1426290 1426874 1426915 "LALG" 1426977 NIL LALG (NIL T) -9 NIL 1427036 NIL) (-625 1426004 1426063 1426199 "LALG-" 1426204 NIL LALG- (NIL T T) -8 NIL NIL NIL) (-624 1425839 1425863 1425904 "KVTFROM" 1425966 NIL KVTFROM (NIL T) -9 NIL NIL NIL) (-623 1424762 1425206 1425391 "KTVLOGIC" 1425674 T KTVLOGIC (NIL) -8 NIL NIL NIL) (-622 1424597 1424621 1424662 "KRCFROM" 1424724 NIL KRCFROM (NIL T) -9 NIL NIL NIL) (-621 1423501 1423688 1423987 "KOVACIC" 1424397 NIL KOVACIC (NIL T T) -7 NIL NIL NIL) (-620 1423336 1423360 1423401 "KONVERT" 1423463 NIL KONVERT (NIL T) -9 NIL NIL NIL) (-619 1423171 1423195 1423236 "KOERCE" 1423298 NIL KOERCE (NIL T) -9 NIL NIL NIL) (-618 1421001 1421764 1422141 "KERNEL" 1422827 NIL KERNEL (NIL T) -8 NIL NIL NIL) (-617 1420497 1420578 1420710 "KERNEL2" 1420915 NIL KERNEL2 (NIL T T) -7 NIL NIL NIL) (-616 1414267 1419036 1419090 "KDAGG" 1419467 NIL KDAGG (NIL T T) -9 NIL 1419673 NIL) (-615 1413796 1413920 1414125 "KDAGG-" 1414130 NIL KDAGG- (NIL T T T) -8 NIL NIL NIL) (-614 1406944 1413457 1413612 "KAFILE" 1413674 NIL KAFILE (NIL T) -8 NIL NIL NIL) (-613 1401372 1406455 1406683 "JORDAN" 1406765 NIL JORDAN (NIL T T) -8 NIL NIL NIL) (-612 1400751 1401021 1401142 "JOINAST" 1401271 T JOINAST (NIL) -8 NIL NIL NIL) (-611 1400597 1400656 1400711 "JAVACODE" 1400716 T JAVACODE (NIL) -8 NIL NIL NIL) (-610 1396849 1398802 1398856 "IXAGG" 1399785 NIL IXAGG (NIL T T) -9 NIL 1400244 NIL) (-609 1395768 1396074 1396493 "IXAGG-" 1396498 NIL IXAGG- (NIL T T T) -8 NIL NIL NIL) (-608 1391298 1395690 1395749 "IVECTOR" 1395754 NIL IVECTOR (NIL T NIL) -8 NIL NIL NIL) (-607 1390064 1390301 1390567 "ITUPLE" 1391065 NIL ITUPLE (NIL T) -8 NIL NIL NIL) (-606 1388566 1388743 1389038 "ITRIGMNP" 1389886 NIL ITRIGMNP (NIL T T T) -7 NIL NIL NIL) (-605 1387311 1387515 1387798 "ITFUN3" 1388342 NIL ITFUN3 (NIL T T T) -7 NIL NIL NIL) (-604 1386943 1387000 1387109 "ITFUN2" 1387248 NIL ITFUN2 (NIL T T) -7 NIL NIL NIL) (-603 1386102 1386423 1386597 "ITFORM" 1386789 T ITFORM (NIL) -8 NIL NIL NIL) (-602 1384063 1385122 1385400 "ITAYLOR" 1385857 NIL ITAYLOR (NIL T) -8 NIL NIL NIL) (-601 1373008 1378200 1379363 "ISUPS" 1382933 NIL ISUPS (NIL T) -8 NIL NIL NIL) (-600 1372112 1372252 1372488 "ISUMP" 1372855 NIL ISUMP (NIL T T T T) -7 NIL NIL NIL) (-599 1367487 1372057 1372098 "ISTRING" 1372103 NIL ISTRING (NIL NIL) -8 NIL NIL NIL) (-598 1366963 1367208 1367300 "ISAST" 1367415 T ISAST (NIL) -8 NIL NIL NIL) (-597 1366172 1366254 1366470 "IRURPK" 1366877 NIL IRURPK (NIL T T T T T) -7 NIL NIL NIL) (-596 1365108 1365309 1365549 "IRSN" 1365952 T IRSN (NIL) -7 NIL NIL NIL) (-595 1363179 1363534 1363963 "IRRF2F" 1364746 NIL IRRF2F (NIL T) -7 NIL NIL NIL) (-594 1362926 1362964 1363040 "IRREDFFX" 1363135 NIL IRREDFFX (NIL T) -7 NIL NIL NIL) (-593 1361541 1361800 1362099 "IROOT" 1362659 NIL IROOT (NIL T) -7 NIL NIL NIL) (-592 1358145 1359225 1359917 "IR" 1360881 NIL IR (NIL T) -8 NIL NIL NIL) (-591 1357350 1357638 1357789 "IRFORM" 1358014 T IRFORM (NIL) -8 NIL NIL NIL) (-590 1354963 1355458 1356024 "IR2" 1356828 NIL IR2 (NIL T T) -7 NIL NIL NIL) (-589 1354063 1354176 1354390 "IR2F" 1354846 NIL IR2F (NIL T T) -7 NIL NIL NIL) (-588 1353854 1353888 1353948 "IPRNTPK" 1354023 T IPRNTPK (NIL) -7 NIL NIL NIL) (-587 1350435 1353743 1353812 "IPF" 1353817 NIL IPF (NIL NIL) -8 NIL NIL NIL) (-586 1348762 1350360 1350417 "IPADIC" 1350422 NIL IPADIC (NIL NIL NIL) -8 NIL NIL NIL) (-585 1348074 1348322 1348452 "IP4ADDR" 1348652 T IP4ADDR (NIL) -8 NIL NIL NIL) (-584 1347448 1347703 1347835 "IOMODE" 1347962 T IOMODE (NIL) -8 NIL NIL NIL) (-583 1346521 1347045 1347172 "IOBFILE" 1347341 T IOBFILE (NIL) -8 NIL NIL NIL) (-582 1346009 1346425 1346453 "IOBCON" 1346458 T IOBCON (NIL) -9 NIL 1346479 NIL) (-581 1345520 1345578 1345761 "INVLAPLA" 1345945 NIL INVLAPLA (NIL T T) -7 NIL NIL NIL) (-580 1335168 1337522 1339908 "INTTR" 1343184 NIL INTTR (NIL T T) -7 NIL NIL NIL) (-579 1331503 1332245 1333110 "INTTOOLS" 1334353 NIL INTTOOLS (NIL T T) -7 NIL NIL NIL) (-578 1331089 1331180 1331297 "INTSLPE" 1331406 T INTSLPE (NIL) -7 NIL NIL NIL) (-577 1329042 1331012 1331071 "INTRVL" 1331076 NIL INTRVL (NIL T) -8 NIL NIL NIL) (-576 1326644 1327156 1327731 "INTRF" 1328527 NIL INTRF (NIL T) -7 NIL NIL NIL) (-575 1326055 1326152 1326294 "INTRET" 1326542 NIL INTRET (NIL T) -7 NIL NIL NIL) (-574 1324052 1324441 1324911 "INTRAT" 1325663 NIL INTRAT (NIL T T) -7 NIL NIL NIL) (-573 1321315 1321898 1322517 "INTPM" 1323537 NIL INTPM (NIL T T) -7 NIL NIL NIL) (-572 1318060 1318659 1319397 "INTPAF" 1320701 NIL INTPAF (NIL T T T) -7 NIL NIL NIL) (-571 1313239 1314201 1315252 "INTPACK" 1317029 T INTPACK (NIL) -7 NIL NIL NIL) (-570 1310187 1313036 1313145 "INT" 1313150 T INT (NIL) -8 NIL NIL NIL) (-569 1309439 1309591 1309799 "INTHERTR" 1310029 NIL INTHERTR (NIL T T) -7 NIL NIL NIL) (-568 1308878 1308958 1309146 "INTHERAL" 1309353 NIL INTHERAL (NIL T T T T) -7 NIL NIL NIL) (-567 1306724 1307167 1307624 "INTHEORY" 1308441 T INTHEORY (NIL) -7 NIL NIL NIL) (-566 1298130 1299751 1301523 "INTG0" 1305076 NIL INTG0 (NIL T T T) -7 NIL NIL NIL) (-565 1278703 1283493 1288303 "INTFTBL" 1293340 T INTFTBL (NIL) -8 NIL NIL NIL) (-564 1277952 1278090 1278263 "INTFACT" 1278562 NIL INTFACT (NIL T) -7 NIL NIL NIL) (-563 1275379 1275825 1276382 "INTEF" 1277506 NIL INTEF (NIL T T) -7 NIL NIL NIL) (-562 1273746 1274485 1274513 "INTDOM" 1274814 T INTDOM (NIL) -9 NIL 1275021 NIL) (-561 1273115 1273289 1273531 "INTDOM-" 1273536 NIL INTDOM- (NIL T) -8 NIL NIL NIL) (-560 1269503 1271431 1271485 "INTCAT" 1272284 NIL INTCAT (NIL T) -9 NIL 1272605 NIL) (-559 1268975 1269078 1269206 "INTBIT" 1269395 T INTBIT (NIL) -7 NIL NIL NIL) (-558 1267674 1267828 1268135 "INTALG" 1268820 NIL INTALG (NIL T T T T T) -7 NIL NIL NIL) (-557 1267157 1267247 1267404 "INTAF" 1267578 NIL INTAF (NIL T T) -7 NIL NIL NIL) (-556 1260500 1266967 1267107 "INTABL" 1267112 NIL INTABL (NIL T T T) -8 NIL NIL NIL) (-555 1259833 1260299 1260364 "INT8" 1260398 T INT8 (NIL) -8 NIL NIL 1260443) (-554 1259165 1259631 1259696 "INT64" 1259730 T INT64 (NIL) -8 NIL NIL 1259775) (-553 1258497 1258963 1259028 "INT32" 1259062 T INT32 (NIL) -8 NIL NIL 1259107) (-552 1257829 1258295 1258360 "INT16" 1258394 T INT16 (NIL) -8 NIL NIL 1258439) (-551 1252739 1255452 1255480 "INS" 1256414 T INS (NIL) -9 NIL 1257079 NIL) (-550 1249979 1250750 1251724 "INS-" 1251797 NIL INS- (NIL T) -8 NIL NIL NIL) (-549 1248754 1248981 1249279 "INPSIGN" 1249732 NIL INPSIGN (NIL T T) -7 NIL NIL NIL) (-548 1247872 1247989 1248186 "INPRODPF" 1248634 NIL INPRODPF (NIL T T) -7 NIL NIL NIL) (-547 1246766 1246883 1247120 "INPRODFF" 1247752 NIL INPRODFF (NIL T T T T) -7 NIL NIL NIL) (-546 1245766 1245918 1246178 "INNMFACT" 1246602 NIL INNMFACT (NIL T T T T) -7 NIL NIL NIL) (-545 1244963 1245060 1245248 "INMODGCD" 1245665 NIL INMODGCD (NIL T T NIL NIL) -7 NIL NIL NIL) (-544 1243471 1243716 1244040 "INFSP" 1244708 NIL INFSP (NIL T T T) -7 NIL NIL NIL) (-543 1242655 1242772 1242955 "INFPROD0" 1243351 NIL INFPROD0 (NIL T T) -7 NIL NIL NIL) (-542 1239510 1240720 1241235 "INFORM" 1242148 T INFORM (NIL) -8 NIL NIL NIL) (-541 1239120 1239180 1239278 "INFORM1" 1239445 NIL INFORM1 (NIL T) -7 NIL NIL NIL) (-540 1238643 1238732 1238846 "INFINITY" 1239026 T INFINITY (NIL) -7 NIL NIL NIL) (-539 1237819 1238363 1238464 "INETCLTS" 1238562 T INETCLTS (NIL) -8 NIL NIL NIL) (-538 1236435 1236685 1237006 "INEP" 1237567 NIL INEP (NIL T T T) -7 NIL NIL NIL) (-537 1235684 1236332 1236397 "INDE" 1236402 NIL INDE (NIL T) -8 NIL NIL NIL) (-536 1235248 1235316 1235433 "INCRMAPS" 1235611 NIL INCRMAPS (NIL T) -7 NIL NIL NIL) (-535 1234066 1234517 1234723 "INBFILE" 1235062 T INBFILE (NIL) -8 NIL NIL NIL) (-534 1229365 1230302 1231246 "INBFF" 1233154 NIL INBFF (NIL T) -7 NIL NIL NIL) (-533 1228273 1228542 1228570 "INBCON" 1229083 T INBCON (NIL) -9 NIL 1229349 NIL) (-532 1227525 1227748 1228024 "INBCON-" 1228029 NIL INBCON- (NIL T) -8 NIL NIL NIL) (-531 1227004 1227249 1227340 "INAST" 1227454 T INAST (NIL) -8 NIL NIL NIL) (-530 1226431 1226683 1226789 "IMPTAST" 1226918 T IMPTAST (NIL) -8 NIL NIL NIL) (-529 1222877 1226275 1226379 "IMATRIX" 1226384 NIL IMATRIX (NIL T NIL NIL) -8 NIL NIL NIL) (-528 1221585 1221708 1222024 "IMATQF" 1222733 NIL IMATQF (NIL T T T T T T T T) -7 NIL NIL NIL) (-527 1219805 1220032 1220369 "IMATLIN" 1221341 NIL IMATLIN (NIL T T T T) -7 NIL NIL NIL) (-526 1214383 1219729 1219787 "ILIST" 1219792 NIL ILIST (NIL T NIL) -8 NIL NIL NIL) (-525 1212288 1214243 1214356 "IIARRAY2" 1214361 NIL IIARRAY2 (NIL T NIL NIL T T) -8 NIL NIL NIL) (-524 1207686 1212199 1212263 "IFF" 1212268 NIL IFF (NIL NIL NIL) -8 NIL NIL NIL) (-523 1207033 1207303 1207419 "IFAST" 1207590 T IFAST (NIL) -8 NIL NIL NIL) (-522 1202028 1206325 1206513 "IFARRAY" 1206890 NIL IFARRAY (NIL T NIL) -8 NIL NIL NIL) (-521 1201208 1201932 1202005 "IFAMON" 1202010 NIL IFAMON (NIL T T NIL) -8 NIL NIL NIL) (-520 1200792 1200857 1200911 "IEVALAB" 1201118 NIL IEVALAB (NIL T T) -9 NIL NIL NIL) (-519 1200467 1200535 1200695 "IEVALAB-" 1200700 NIL IEVALAB- (NIL T T T) -8 NIL NIL NIL) (-518 1200098 1200381 1200444 "IDPO" 1200449 NIL IDPO (NIL T T) -8 NIL NIL NIL) (-517 1199348 1199987 1200062 "IDPOAMS" 1200067 NIL IDPOAMS (NIL T T) -8 NIL NIL NIL) (-516 1198655 1199237 1199312 "IDPOAM" 1199317 NIL IDPOAM (NIL T T) -8 NIL NIL NIL) (-515 1197714 1197990 1198043 "IDPC" 1198456 NIL IDPC (NIL T T) -9 NIL 1198605 NIL) (-514 1197183 1197606 1197679 "IDPAM" 1197684 NIL IDPAM (NIL T T) -8 NIL NIL NIL) (-513 1196559 1197075 1197148 "IDPAG" 1197153 NIL IDPAG (NIL T T) -8 NIL NIL NIL) (-512 1196204 1196395 1196470 "IDENT" 1196504 T IDENT (NIL) -8 NIL NIL NIL) (-511 1192459 1193307 1194202 "IDECOMP" 1195361 NIL IDECOMP (NIL NIL NIL) -7 NIL NIL NIL) (-510 1185296 1186382 1187429 "IDEAL" 1191495 NIL IDEAL (NIL T T T T) -8 NIL NIL NIL) (-509 1184456 1184568 1184768 "ICDEN" 1185180 NIL ICDEN (NIL T T T T) -7 NIL NIL NIL) (-508 1183527 1183936 1184083 "ICARD" 1184329 T ICARD (NIL) -8 NIL NIL NIL) (-507 1181587 1181900 1182305 "IBPTOOLS" 1183204 NIL IBPTOOLS (NIL T T T T) -7 NIL NIL NIL) (-506 1177194 1181207 1181320 "IBITS" 1181506 NIL IBITS (NIL NIL) -8 NIL NIL NIL) (-505 1173917 1174493 1175188 "IBATOOL" 1176611 NIL IBATOOL (NIL T T T) -7 NIL NIL NIL) (-504 1171696 1172158 1172691 "IBACHIN" 1173452 NIL IBACHIN (NIL T T T) -7 NIL NIL NIL) (-503 1169525 1171542 1171645 "IARRAY2" 1171650 NIL IARRAY2 (NIL T NIL NIL) -8 NIL NIL NIL) (-502 1165631 1169451 1169508 "IARRAY1" 1169513 NIL IARRAY1 (NIL T NIL) -8 NIL NIL NIL) (-501 1159740 1164043 1164524 "IAN" 1165170 T IAN (NIL) -8 NIL NIL NIL) (-500 1159251 1159308 1159481 "IALGFACT" 1159677 NIL IALGFACT (NIL T T T T) -7 NIL NIL NIL) (-499 1158779 1158892 1158920 "HYPCAT" 1159127 T HYPCAT (NIL) -9 NIL NIL NIL) (-498 1158317 1158434 1158620 "HYPCAT-" 1158625 NIL HYPCAT- (NIL T) -8 NIL NIL NIL) (-497 1157912 1158112 1158195 "HOSTNAME" 1158254 T HOSTNAME (NIL) -8 NIL NIL NIL) (-496 1157757 1157794 1157835 "HOMOTOP" 1157840 NIL HOMOTOP (NIL T) -9 NIL 1157873 NIL) (-495 1154389 1155767 1155808 "HOAGG" 1156789 NIL HOAGG (NIL T) -9 NIL 1157468 NIL) (-494 1152983 1153382 1153908 "HOAGG-" 1153913 NIL HOAGG- (NIL T T) -8 NIL NIL NIL) (-493 1146985 1152576 1152726 "HEXADEC" 1152853 T HEXADEC (NIL) -8 NIL NIL NIL) (-492 1145733 1145955 1146218 "HEUGCD" 1146762 NIL HEUGCD (NIL T) -7 NIL NIL NIL) (-491 1144809 1145570 1145700 "HELLFDIV" 1145705 NIL HELLFDIV (NIL T T T T) -8 NIL NIL NIL) (-490 1142988 1144586 1144674 "HEAP" 1144753 NIL HEAP (NIL T) -8 NIL NIL NIL) (-489 1142251 1142540 1142674 "HEADAST" 1142874 T HEADAST (NIL) -8 NIL NIL NIL) (-488 1136117 1142166 1142228 "HDP" 1142233 NIL HDP (NIL NIL T) -8 NIL NIL NIL) (-487 1130105 1135752 1135904 "HDMP" 1136018 NIL HDMP (NIL NIL T) -8 NIL NIL NIL) (-486 1129429 1129569 1129733 "HB" 1129961 T HB (NIL) -7 NIL NIL NIL) (-485 1122815 1129275 1129379 "HASHTBL" 1129384 NIL HASHTBL (NIL T T NIL) -8 NIL NIL NIL) (-484 1122291 1122536 1122628 "HASAST" 1122743 T HASAST (NIL) -8 NIL NIL NIL) (-483 1120069 1121913 1122095 "HACKPI" 1122129 T HACKPI (NIL) -8 NIL NIL NIL) (-482 1115737 1119922 1120035 "GTSET" 1120040 NIL GTSET (NIL T T T T) -8 NIL NIL NIL) (-481 1109152 1115615 1115713 "GSTBL" 1115718 NIL GSTBL (NIL T T T NIL) -8 NIL NIL NIL) (-480 1101430 1108183 1108448 "GSERIES" 1108943 NIL GSERIES (NIL T NIL NIL) -8 NIL NIL NIL) (-479 1100571 1100988 1101016 "GROUP" 1101219 T GROUP (NIL) -9 NIL 1101353 NIL) (-478 1099937 1100096 1100347 "GROUP-" 1100352 NIL GROUP- (NIL T) -8 NIL NIL NIL) (-477 1098304 1098625 1099012 "GROEBSOL" 1099614 NIL GROEBSOL (NIL NIL T T) -7 NIL NIL NIL) (-476 1097218 1097506 1097557 "GRMOD" 1098086 NIL GRMOD (NIL T T) -9 NIL 1098254 NIL) (-475 1096986 1097022 1097150 "GRMOD-" 1097155 NIL GRMOD- (NIL T T T) -8 NIL NIL NIL) (-474 1092276 1093340 1094340 "GRIMAGE" 1096006 T GRIMAGE (NIL) -8 NIL NIL NIL) (-473 1090742 1091003 1091327 "GRDEF" 1091972 T GRDEF (NIL) -7 NIL NIL NIL) (-472 1090186 1090302 1090443 "GRAY" 1090621 T GRAY (NIL) -7 NIL NIL NIL) (-471 1089373 1089779 1089830 "GRALG" 1089983 NIL GRALG (NIL T T) -9 NIL 1090076 NIL) (-470 1089034 1089107 1089270 "GRALG-" 1089275 NIL GRALG- (NIL T T T) -8 NIL NIL NIL) (-469 1085811 1088619 1088797 "GPOLSET" 1088941 NIL GPOLSET (NIL T T T T) -8 NIL NIL NIL) (-468 1085165 1085222 1085480 "GOSPER" 1085748 NIL GOSPER (NIL T T T T T) -7 NIL NIL NIL) (-467 1080897 1081603 1082129 "GMODPOL" 1084864 NIL GMODPOL (NIL NIL T T T NIL T) -8 NIL NIL NIL) (-466 1079902 1080086 1080324 "GHENSEL" 1080709 NIL GHENSEL (NIL T T) -7 NIL NIL NIL) (-465 1074058 1074901 1075921 "GENUPS" 1078986 NIL GENUPS (NIL T T) -7 NIL NIL NIL) (-464 1073755 1073806 1073895 "GENUFACT" 1074001 NIL GENUFACT (NIL T) -7 NIL NIL NIL) (-463 1073167 1073244 1073409 "GENPGCD" 1073673 NIL GENPGCD (NIL T T T T) -7 NIL NIL NIL) (-462 1072641 1072676 1072889 "GENMFACT" 1073126 NIL GENMFACT (NIL T T T T T) -7 NIL NIL NIL) (-461 1071207 1071464 1071771 "GENEEZ" 1072384 NIL GENEEZ (NIL T T) -7 NIL NIL NIL) (-460 1065355 1070818 1070980 "GDMP" 1071130 NIL GDMP (NIL NIL T T) -8 NIL NIL NIL) (-459 1054698 1059126 1060232 "GCNAALG" 1064338 NIL GCNAALG (NIL T NIL NIL NIL) -8 NIL NIL NIL) (-458 1053025 1053887 1053915 "GCDDOM" 1054170 T GCDDOM (NIL) -9 NIL 1054327 NIL) (-457 1052495 1052622 1052837 "GCDDOM-" 1052842 NIL GCDDOM- (NIL T) -8 NIL NIL NIL) (-456 1051167 1051352 1051656 "GB" 1052274 NIL GB (NIL T T T T) -7 NIL NIL NIL) (-455 1039783 1042113 1044505 "GBINTERN" 1048858 NIL GBINTERN (NIL T T T T) -7 NIL NIL NIL) (-454 1037620 1037912 1038333 "GBF" 1039458 NIL GBF (NIL T T T T) -7 NIL NIL NIL) (-453 1036401 1036566 1036833 "GBEUCLID" 1037436 NIL GBEUCLID (NIL T T T T) -7 NIL NIL NIL) (-452 1035750 1035875 1036024 "GAUSSFAC" 1036272 T GAUSSFAC (NIL) -7 NIL NIL NIL) (-451 1034117 1034419 1034733 "GALUTIL" 1035469 NIL GALUTIL (NIL T) -7 NIL NIL NIL) (-450 1032425 1032699 1033023 "GALPOLYU" 1033844 NIL GALPOLYU (NIL T T) -7 NIL NIL NIL) (-449 1029790 1030080 1030487 "GALFACTU" 1032122 NIL GALFACTU (NIL T T T) -7 NIL NIL NIL) (-448 1021596 1023095 1024703 "GALFACT" 1028222 NIL GALFACT (NIL T) -7 NIL NIL NIL) (-447 1018984 1019642 1019670 "FVFUN" 1020826 T FVFUN (NIL) -9 NIL 1021546 NIL) (-446 1018250 1018432 1018460 "FVC" 1018751 T FVC (NIL) -9 NIL 1018934 NIL) (-445 1017893 1018075 1018143 "FUNDESC" 1018202 T FUNDESC (NIL) -8 NIL NIL NIL) (-444 1017508 1017690 1017771 "FUNCTION" 1017845 NIL FUNCTION (NIL NIL) -8 NIL NIL NIL) (-443 1015252 1015830 1016296 "FT" 1017062 T FT (NIL) -8 NIL NIL NIL) (-442 1014043 1014553 1014756 "FTEM" 1015069 T FTEM (NIL) -8 NIL NIL NIL) (-441 1012334 1012623 1013020 "FSUPFACT" 1013734 NIL FSUPFACT (NIL T T T) -7 NIL NIL NIL) (-440 1010731 1011020 1011352 "FST" 1012022 T FST (NIL) -8 NIL NIL NIL) (-439 1009930 1010036 1010224 "FSRED" 1010613 NIL FSRED (NIL T T) -7 NIL NIL NIL) (-438 1008629 1008885 1009232 "FSPRMELT" 1009645 NIL FSPRMELT (NIL T T) -7 NIL NIL NIL) (-437 1005935 1006373 1006859 "FSPECF" 1008192 NIL FSPECF (NIL T T) -7 NIL NIL NIL) (-436 987573 995904 995945 "FS" 999829 NIL FS (NIL T) -9 NIL 1002118 NIL) (-435 976216 979209 983266 "FS-" 983566 NIL FS- (NIL T T) -8 NIL NIL NIL) (-434 975744 975798 975968 "FSINT" 976157 NIL FSINT (NIL T T) -7 NIL NIL NIL) (-433 974036 974737 975040 "FSERIES" 975523 NIL FSERIES (NIL T T) -8 NIL NIL NIL) (-432 973078 973194 973418 "FSCINT" 973916 NIL FSCINT (NIL T T) -7 NIL NIL NIL) (-431 969286 972022 972063 "FSAGG" 972433 NIL FSAGG (NIL T) -9 NIL 972692 NIL) (-430 967048 967649 968445 "FSAGG-" 968540 NIL FSAGG- (NIL T T) -8 NIL NIL NIL) (-429 966090 966233 966460 "FSAGG2" 966901 NIL FSAGG2 (NIL T T T T) -7 NIL NIL NIL) (-428 963772 964052 964599 "FS2UPS" 965808 NIL FS2UPS (NIL T T T T T NIL) -7 NIL NIL NIL) (-427 963406 963449 963578 "FS2" 963723 NIL FS2 (NIL T T T T) -7 NIL NIL NIL) (-426 962284 962455 962757 "FS2EXPXP" 963231 NIL FS2EXPXP (NIL T T NIL NIL) -7 NIL NIL NIL) (-425 961710 961825 961977 "FRUTIL" 962164 NIL FRUTIL (NIL T) -7 NIL NIL NIL) (-424 953123 957205 958563 "FR" 960384 NIL FR (NIL T) -8 NIL NIL NIL) (-423 948137 950812 950852 "FRNAALG" 952172 NIL FRNAALG (NIL T) -9 NIL 952770 NIL) (-422 943810 944886 946161 "FRNAALG-" 946911 NIL FRNAALG- (NIL T T) -8 NIL NIL NIL) (-421 943448 943491 943618 "FRNAAF2" 943761 NIL FRNAAF2 (NIL T T T T) -7 NIL NIL NIL) (-420 941823 942297 942593 "FRMOD" 943260 NIL FRMOD (NIL T T T T NIL) -8 NIL NIL NIL) (-419 939566 940198 940516 "FRIDEAL" 941614 NIL FRIDEAL (NIL T T T T) -8 NIL NIL NIL) (-418 938757 938844 939135 "FRIDEAL2" 939473 NIL FRIDEAL2 (NIL T T T T T T T T) -7 NIL NIL NIL) (-417 937890 938304 938345 "FRETRCT" 938350 NIL FRETRCT (NIL T) -9 NIL 938526 NIL) (-416 937002 937233 937584 "FRETRCT-" 937589 NIL FRETRCT- (NIL T T) -8 NIL NIL NIL) (-415 934090 935300 935359 "FRAMALG" 936241 NIL FRAMALG (NIL T T) -9 NIL 936533 NIL) (-414 932224 932679 933309 "FRAMALG-" 933532 NIL FRAMALG- (NIL T T T) -8 NIL NIL NIL) (-413 926143 931697 931974 "FRAC" 931979 NIL FRAC (NIL T) -8 NIL NIL NIL) (-412 925779 925836 925943 "FRAC2" 926080 NIL FRAC2 (NIL T T) -7 NIL NIL NIL) (-411 925415 925472 925579 "FR2" 925716 NIL FR2 (NIL T T) -7 NIL NIL NIL) (-410 919928 922821 922849 "FPS" 923968 T FPS (NIL) -9 NIL 924525 NIL) (-409 919377 919486 919650 "FPS-" 919796 NIL FPS- (NIL T) -8 NIL NIL NIL) (-408 916679 918348 918376 "FPC" 918601 T FPC (NIL) -9 NIL 918743 NIL) (-407 916472 916512 916609 "FPC-" 916614 NIL FPC- (NIL T) -8 NIL NIL NIL) (-406 915262 915960 916001 "FPATMAB" 916006 NIL FPATMAB (NIL T) -9 NIL 916158 NIL) (-405 912935 913438 913864 "FPARFRAC" 914899 NIL FPARFRAC (NIL T T) -8 NIL NIL NIL) (-404 908329 908827 909509 "FORTRAN" 912367 NIL FORTRAN (NIL NIL NIL NIL NIL) -8 NIL NIL NIL) (-403 906045 906545 907084 "FORT" 907810 T FORT (NIL) -7 NIL NIL NIL) (-402 903721 904283 904311 "FORTFN" 905371 T FORTFN (NIL) -9 NIL 905995 NIL) (-401 903485 903535 903563 "FORTCAT" 903622 T FORTCAT (NIL) -9 NIL 903684 NIL) (-400 901591 902101 902491 "FORMULA" 903115 T FORMULA (NIL) -8 NIL NIL NIL) (-399 901379 901409 901478 "FORMULA1" 901555 NIL FORMULA1 (NIL T) -7 NIL NIL NIL) (-398 900902 900954 901127 "FORDER" 901321 NIL FORDER (NIL T T T T) -7 NIL NIL NIL) (-397 899998 900162 900355 "FOP" 900729 T FOP (NIL) -7 NIL NIL NIL) (-396 898579 899278 899452 "FNLA" 899880 NIL FNLA (NIL NIL NIL T) -8 NIL NIL NIL) (-395 897308 897723 897751 "FNCAT" 898211 T FNCAT (NIL) -9 NIL 898471 NIL) (-394 896847 897267 897295 "FNAME" 897300 T FNAME (NIL) -8 NIL NIL NIL) (-393 895410 896373 896401 "FMTC" 896406 T FMTC (NIL) -9 NIL 896442 NIL) (-392 894156 895346 895392 "FMONOID" 895397 NIL FMONOID (NIL T) -8 NIL NIL NIL) (-391 890984 892152 892193 "FMONCAT" 893410 NIL FMONCAT (NIL T) -9 NIL 894015 NIL) (-390 890176 890726 890875 "FM" 890880 NIL FM (NIL T T) -8 NIL NIL NIL) (-389 887600 888246 888274 "FMFUN" 889418 T FMFUN (NIL) -9 NIL 890126 NIL) (-388 886869 887050 887078 "FMC" 887368 T FMC (NIL) -9 NIL 887550 NIL) (-387 883948 884808 884862 "FMCAT" 886057 NIL FMCAT (NIL T T) -9 NIL 886552 NIL) (-386 882814 883714 883814 "FM1" 883893 NIL FM1 (NIL T T) -8 NIL NIL NIL) (-385 880588 881004 881498 "FLOATRP" 882365 NIL FLOATRP (NIL T) -7 NIL NIL NIL) (-384 874166 878317 878938 "FLOAT" 879987 T FLOAT (NIL) -8 NIL NIL NIL) (-383 871604 872104 872682 "FLOATCP" 873633 NIL FLOATCP (NIL T) -7 NIL NIL NIL) (-382 870344 871182 871223 "FLINEXP" 871228 NIL FLINEXP (NIL T) -9 NIL 871321 NIL) (-381 869498 869733 870061 "FLINEXP-" 870066 NIL FLINEXP- (NIL T T) -8 NIL NIL NIL) (-380 868574 868718 868942 "FLASORT" 869350 NIL FLASORT (NIL T T) -7 NIL NIL NIL) (-379 865690 866558 866610 "FLALG" 867837 NIL FLALG (NIL T T) -9 NIL 868304 NIL) (-378 859394 863146 863187 "FLAGG" 864449 NIL FLAGG (NIL T) -9 NIL 865101 NIL) (-377 858120 858459 858949 "FLAGG-" 858954 NIL FLAGG- (NIL T T) -8 NIL NIL NIL) (-376 857162 857305 857532 "FLAGG2" 857973 NIL FLAGG2 (NIL T T T T) -7 NIL NIL NIL) (-375 854013 855021 855080 "FINRALG" 856208 NIL FINRALG (NIL T T) -9 NIL 856716 NIL) (-374 853173 853402 853741 "FINRALG-" 853746 NIL FINRALG- (NIL T T T) -8 NIL NIL NIL) (-373 852553 852792 852820 "FINITE" 853016 T FINITE (NIL) -9 NIL 853123 NIL) (-372 844910 847097 847137 "FINAALG" 850804 NIL FINAALG (NIL T) -9 NIL 852257 NIL) (-371 840242 841292 842436 "FINAALG-" 843815 NIL FINAALG- (NIL T T) -8 NIL NIL NIL) (-370 839610 839997 840100 "FILE" 840172 NIL FILE (NIL T) -8 NIL NIL NIL) (-369 838268 838606 838660 "FILECAT" 839344 NIL FILECAT (NIL T T) -9 NIL 839560 NIL) (-368 835984 837512 837540 "FIELD" 837580 T FIELD (NIL) -9 NIL 837660 NIL) (-367 834604 834989 835500 "FIELD-" 835505 NIL FIELD- (NIL T) -8 NIL NIL NIL) (-366 832454 833239 833586 "FGROUP" 834290 NIL FGROUP (NIL T) -8 NIL NIL NIL) (-365 831544 831708 831928 "FGLMICPK" 832286 NIL FGLMICPK (NIL T NIL) -7 NIL NIL NIL) (-364 827376 831469 831526 "FFX" 831531 NIL FFX (NIL T NIL) -8 NIL NIL NIL) (-363 826977 827038 827173 "FFSLPE" 827309 NIL FFSLPE (NIL T T T) -7 NIL NIL NIL) (-362 822967 823749 824545 "FFPOLY" 826213 NIL FFPOLY (NIL T) -7 NIL NIL NIL) (-361 822471 822507 822716 "FFPOLY2" 822925 NIL FFPOLY2 (NIL T T) -7 NIL NIL NIL) (-360 818317 822390 822453 "FFP" 822458 NIL FFP (NIL T NIL) -8 NIL NIL NIL) (-359 813715 818228 818292 "FF" 818297 NIL FF (NIL NIL NIL) -8 NIL NIL NIL) (-358 808841 813058 813248 "FFNBX" 813569 NIL FFNBX (NIL T NIL) -8 NIL NIL NIL) (-357 803769 807976 808234 "FFNBP" 808695 NIL FFNBP (NIL T NIL) -8 NIL NIL NIL) (-356 798402 803053 803264 "FFNB" 803602 NIL FFNB (NIL NIL NIL) -8 NIL NIL NIL) (-355 797234 797432 797747 "FFINTBAS" 798199 NIL FFINTBAS (NIL T T T) -7 NIL NIL NIL) (-354 793303 795523 795551 "FFIELDC" 796171 T FFIELDC (NIL) -9 NIL 796547 NIL) (-353 791965 792336 792833 "FFIELDC-" 792838 NIL FFIELDC- (NIL T) -8 NIL NIL NIL) (-352 791534 791580 791704 "FFHOM" 791907 NIL FFHOM (NIL T T T) -7 NIL NIL NIL) (-351 789229 789716 790233 "FFF" 791049 NIL FFF (NIL T) -7 NIL NIL NIL) (-350 784847 788971 789072 "FFCGX" 789172 NIL FFCGX (NIL T NIL) -8 NIL NIL NIL) (-349 780469 784579 784686 "FFCGP" 784790 NIL FFCGP (NIL T NIL) -8 NIL NIL NIL) (-348 775652 780196 780304 "FFCG" 780405 NIL FFCG (NIL NIL NIL) -8 NIL NIL NIL) (-347 757048 766129 766215 "FFCAT" 771380 NIL FFCAT (NIL T T T) -9 NIL 772831 NIL) (-346 752245 753293 754607 "FFCAT-" 755837 NIL FFCAT- (NIL T T T T) -8 NIL NIL NIL) (-345 751656 751699 751934 "FFCAT2" 752196 NIL FFCAT2 (NIL T T T T T T T T) -7 NIL NIL NIL) (-344 740979 744628 745848 "FEXPR" 750508 NIL FEXPR (NIL NIL NIL T) -8 NIL NIL NIL) (-343 739941 740376 740417 "FEVALAB" 740501 NIL FEVALAB (NIL T) -9 NIL 740762 NIL) (-342 739100 739310 739648 "FEVALAB-" 739653 NIL FEVALAB- (NIL T T) -8 NIL NIL NIL) (-341 737666 738483 738686 "FDIV" 738999 NIL FDIV (NIL T T T T) -8 NIL NIL NIL) (-340 734686 735427 735542 "FDIVCAT" 737110 NIL FDIVCAT (NIL T T T T) -9 NIL 737547 NIL) (-339 734448 734475 734645 "FDIVCAT-" 734650 NIL FDIVCAT- (NIL T T T T T) -8 NIL NIL NIL) (-338 733668 733755 734032 "FDIV2" 734355 NIL FDIV2 (NIL T T T T T T T T) -7 NIL NIL NIL) (-337 732642 732963 733165 "FCTRDATA" 733486 T FCTRDATA (NIL) -8 NIL NIL NIL) (-336 731328 731587 731876 "FCPAK1" 732373 T FCPAK1 (NIL) -7 NIL NIL NIL) (-335 730427 730828 730969 "FCOMP" 731219 NIL FCOMP (NIL T) -8 NIL NIL NIL) (-334 714132 717577 721115 "FC" 726909 T FC (NIL) -8 NIL NIL NIL) (-333 706495 710523 710563 "FAXF" 712365 NIL FAXF (NIL T) -9 NIL 713057 NIL) (-332 703772 704429 705254 "FAXF-" 705719 NIL FAXF- (NIL T T) -8 NIL NIL NIL) (-331 698824 703148 703324 "FARRAY" 703629 NIL FARRAY (NIL T) -8 NIL NIL NIL) (-330 693718 695785 695838 "FAMR" 696861 NIL FAMR (NIL T T) -9 NIL 697321 NIL) (-329 692608 692910 693345 "FAMR-" 693350 NIL FAMR- (NIL T T T) -8 NIL NIL NIL) (-328 691777 692530 692583 "FAMONOID" 692588 NIL FAMONOID (NIL T) -8 NIL NIL NIL) (-327 689563 690273 690326 "FAMONC" 691267 NIL FAMONC (NIL T T) -9 NIL 691653 NIL) (-326 688227 689317 689454 "FAGROUP" 689459 NIL FAGROUP (NIL T) -8 NIL NIL NIL) (-325 686022 686341 686744 "FACUTIL" 687908 NIL FACUTIL (NIL T T T T) -7 NIL NIL NIL) (-324 685121 685306 685528 "FACTFUNC" 685832 NIL FACTFUNC (NIL T) -7 NIL NIL NIL) (-323 677543 684424 684623 "EXPUPXS" 684977 NIL EXPUPXS (NIL T NIL NIL) -8 NIL NIL NIL) (-322 675026 675566 676152 "EXPRTUBE" 676977 T EXPRTUBE (NIL) -7 NIL NIL NIL) (-321 671297 671889 672619 "EXPRODE" 674365 NIL EXPRODE (NIL T T) -7 NIL NIL NIL) (-320 656782 669946 670375 "EXPR" 670901 NIL EXPR (NIL T) -8 NIL NIL NIL) (-319 651336 651923 652729 "EXPR2UPS" 656080 NIL EXPR2UPS (NIL T T) -7 NIL NIL NIL) (-318 650968 651025 651134 "EXPR2" 651273 NIL EXPR2 (NIL T T) -7 NIL NIL NIL) (-317 642356 650119 650410 "EXPEXPAN" 650804 NIL EXPEXPAN (NIL T T NIL NIL) -8 NIL NIL NIL) (-316 642156 642313 642342 "EXIT" 642347 T EXIT (NIL) -8 NIL NIL NIL) (-315 641636 641880 641971 "EXITAST" 642085 T EXITAST (NIL) -8 NIL NIL NIL) (-314 641263 641325 641438 "EVALCYC" 641568 NIL EVALCYC (NIL T) -7 NIL NIL NIL) (-313 640804 640922 640963 "EVALAB" 641133 NIL EVALAB (NIL T) -9 NIL 641237 NIL) (-312 640285 640407 640628 "EVALAB-" 640633 NIL EVALAB- (NIL T T) -8 NIL NIL NIL) (-311 637653 638955 638983 "EUCDOM" 639538 T EUCDOM (NIL) -9 NIL 639888 NIL) (-310 636058 636500 637090 "EUCDOM-" 637095 NIL EUCDOM- (NIL T) -8 NIL NIL NIL) (-309 623597 626356 629106 "ESTOOLS" 633328 T ESTOOLS (NIL) -7 NIL NIL NIL) (-308 623229 623286 623395 "ESTOOLS2" 623534 NIL ESTOOLS2 (NIL T T) -7 NIL NIL NIL) (-307 622980 623022 623102 "ESTOOLS1" 623181 NIL ESTOOLS1 (NIL T) -7 NIL NIL NIL) (-306 617017 618625 618653 "ES" 621421 T ES (NIL) -9 NIL 622831 NIL) (-305 611964 613251 615068 "ES-" 615232 NIL ES- (NIL T) -8 NIL NIL NIL) (-304 608338 609099 609879 "ESCONT" 611204 T ESCONT (NIL) -7 NIL NIL NIL) (-303 608083 608115 608197 "ESCONT1" 608300 NIL ESCONT1 (NIL NIL NIL) -7 NIL NIL NIL) (-302 607758 607808 607908 "ES2" 608027 NIL ES2 (NIL T T) -7 NIL NIL NIL) (-301 607388 607446 607555 "ES1" 607694 NIL ES1 (NIL T T) -7 NIL NIL NIL) (-300 606604 606733 606909 "ERROR" 607232 T ERROR (NIL) -7 NIL NIL NIL) (-299 599996 606463 606554 "EQTBL" 606559 NIL EQTBL (NIL T T) -8 NIL NIL NIL) (-298 592499 595310 596759 "EQ" 598580 NIL -3030 (NIL T) -8 NIL NIL NIL) (-297 592131 592188 592297 "EQ2" 592436 NIL EQ2 (NIL T T) -7 NIL NIL NIL) (-296 587422 588469 589562 "EP" 591070 NIL EP (NIL T) -7 NIL NIL NIL) (-295 586022 586313 586619 "ENV" 587136 T ENV (NIL) -8 NIL NIL NIL) (-294 585116 585670 585698 "ENTIRER" 585703 T ENTIRER (NIL) -9 NIL 585749 NIL) (-293 581810 583298 583659 "EMR" 584924 NIL EMR (NIL T T T NIL NIL NIL) -8 NIL NIL NIL) (-292 580940 581125 581179 "ELTAGG" 581559 NIL ELTAGG (NIL T T) -9 NIL 581770 NIL) (-291 580659 580721 580862 "ELTAGG-" 580867 NIL ELTAGG- (NIL T T T) -8 NIL NIL NIL) (-290 580423 580452 580506 "ELTAB" 580590 NIL ELTAB (NIL T T) -9 NIL 580642 NIL) (-289 579549 579695 579894 "ELFUTS" 580274 NIL ELFUTS (NIL T T) -7 NIL NIL NIL) (-288 579291 579347 579375 "ELEMFUN" 579480 T ELEMFUN (NIL) -9 NIL NIL NIL) (-287 579161 579182 579250 "ELEMFUN-" 579255 NIL ELEMFUN- (NIL T) -8 NIL NIL NIL) (-286 573975 577231 577272 "ELAGG" 578212 NIL ELAGG (NIL T) -9 NIL 578675 NIL) (-285 572260 572694 573357 "ELAGG-" 573362 NIL ELAGG- (NIL T T) -8 NIL NIL NIL) (-284 571572 571709 571865 "ELABOR" 572124 T ELABOR (NIL) -8 NIL NIL NIL) (-283 570233 570512 570806 "ELABEXPR" 571298 T ELABEXPR (NIL) -8 NIL NIL NIL) (-282 563097 564900 565727 "EFUPXS" 569509 NIL EFUPXS (NIL T T T T) -8 NIL NIL NIL) (-281 556547 558348 559158 "EFULS" 562373 NIL EFULS (NIL T T T) -8 NIL NIL NIL) (-280 554032 554390 554862 "EFSTRUC" 556179 NIL EFSTRUC (NIL T T) -7 NIL NIL NIL) (-279 543823 545389 546937 "EF" 552547 NIL EF (NIL T T) -7 NIL NIL NIL) (-278 542897 543308 543457 "EAB" 543694 T EAB (NIL) -8 NIL NIL NIL) (-277 542079 542856 542884 "E04UCFA" 542889 T E04UCFA (NIL) -8 NIL NIL NIL) (-276 541261 542038 542066 "E04NAFA" 542071 T E04NAFA (NIL) -8 NIL NIL NIL) (-275 540443 541220 541248 "E04MBFA" 541253 T E04MBFA (NIL) -8 NIL NIL NIL) (-274 539625 540402 540430 "E04JAFA" 540435 T E04JAFA (NIL) -8 NIL NIL NIL) (-273 538809 539584 539612 "E04GCFA" 539617 T E04GCFA (NIL) -8 NIL NIL NIL) (-272 537993 538768 538796 "E04FDFA" 538801 T E04FDFA (NIL) -8 NIL NIL NIL) (-271 537175 537952 537980 "E04DGFA" 537985 T E04DGFA (NIL) -8 NIL NIL NIL) (-270 531348 532700 534064 "E04AGNT" 535831 T E04AGNT (NIL) -7 NIL NIL NIL) (-269 530028 530534 530574 "DVARCAT" 531049 NIL DVARCAT (NIL T) -9 NIL 531248 NIL) (-268 529232 529444 529758 "DVARCAT-" 529763 NIL DVARCAT- (NIL T T) -8 NIL NIL NIL) (-267 522369 529031 529160 "DSMP" 529165 NIL DSMP (NIL T T T) -8 NIL NIL NIL) (-266 517150 518314 519382 "DROPT" 521321 T DROPT (NIL) -8 NIL NIL NIL) (-265 516815 516874 516972 "DROPT1" 517085 NIL DROPT1 (NIL T) -7 NIL NIL NIL) (-264 511930 513056 514193 "DROPT0" 515698 T DROPT0 (NIL) -7 NIL NIL NIL) (-263 510275 510600 510986 "DRAWPT" 511564 T DRAWPT (NIL) -7 NIL NIL NIL) (-262 504862 505785 506864 "DRAW" 509249 NIL DRAW (NIL T) -7 NIL NIL NIL) (-261 504495 504548 504666 "DRAWHACK" 504803 NIL DRAWHACK (NIL T) -7 NIL NIL NIL) (-260 503226 503495 503786 "DRAWCX" 504224 T DRAWCX (NIL) -7 NIL NIL NIL) (-259 502741 502810 502961 "DRAWCURV" 503152 NIL DRAWCURV (NIL T T) -7 NIL NIL NIL) (-258 493209 495171 497286 "DRAWCFUN" 500646 T DRAWCFUN (NIL) -7 NIL NIL NIL) (-257 489973 491902 491943 "DQAGG" 492572 NIL DQAGG (NIL T) -9 NIL 492846 NIL) (-256 478097 484566 484649 "DPOLCAT" 486501 NIL DPOLCAT (NIL T T T T) -9 NIL 487046 NIL) (-255 472934 474282 476240 "DPOLCAT-" 476245 NIL DPOLCAT- (NIL T T T T T) -8 NIL NIL NIL) (-254 466056 472795 472893 "DPMO" 472898 NIL DPMO (NIL NIL T T) -8 NIL NIL NIL) (-253 459081 465836 466003 "DPMM" 466008 NIL DPMM (NIL NIL T T T) -8 NIL NIL NIL) (-252 458651 458865 458954 "DOMTMPLT" 459012 T DOMTMPLT (NIL) -8 NIL NIL NIL) (-251 458084 458453 458533 "DOMCTOR" 458591 T DOMCTOR (NIL) -8 NIL NIL NIL) (-250 457296 457564 457715 "DOMAIN" 457953 T DOMAIN (NIL) -8 NIL NIL NIL) (-249 451284 456931 457083 "DMP" 457197 NIL DMP (NIL NIL T) -8 NIL NIL NIL) (-248 450884 450940 451084 "DLP" 451222 NIL DLP (NIL T) -7 NIL NIL NIL) (-247 444706 450211 450401 "DLIST" 450726 NIL DLIST (NIL T) -8 NIL NIL NIL) (-246 441503 443559 443600 "DLAGG" 444150 NIL DLAGG (NIL T) -9 NIL 444380 NIL) (-245 440179 440843 440871 "DIVRING" 440963 T DIVRING (NIL) -9 NIL 441046 NIL) (-244 439416 439606 439906 "DIVRING-" 439911 NIL DIVRING- (NIL T) -8 NIL NIL NIL) (-243 437518 437875 438281 "DISPLAY" 439030 T DISPLAY (NIL) -7 NIL NIL NIL) (-242 431404 437432 437495 "DIRPROD" 437500 NIL DIRPROD (NIL NIL T) -8 NIL NIL NIL) (-241 430252 430455 430720 "DIRPROD2" 431197 NIL DIRPROD2 (NIL NIL T T) -7 NIL NIL NIL) (-240 419027 425033 425086 "DIRPCAT" 425496 NIL DIRPCAT (NIL NIL T) -9 NIL 426336 NIL) (-239 416353 416995 417876 "DIRPCAT-" 418213 NIL DIRPCAT- (NIL T NIL T) -8 NIL NIL NIL) (-238 415640 415800 415986 "DIOSP" 416187 T DIOSP (NIL) -7 NIL NIL NIL) (-237 412295 414552 414593 "DIOPS" 415027 NIL DIOPS (NIL T) -9 NIL 415256 NIL) (-236 411844 411958 412149 "DIOPS-" 412154 NIL DIOPS- (NIL T T) -8 NIL NIL NIL) (-235 410667 411295 411323 "DIFRING" 411510 T DIFRING (NIL) -9 NIL 411620 NIL) (-234 410313 410390 410542 "DIFRING-" 410547 NIL DIFRING- (NIL T) -8 NIL NIL NIL) (-233 408049 409321 409362 "DIFEXT" 409725 NIL DIFEXT (NIL T) -9 NIL 410019 NIL) (-232 406334 406762 407428 "DIFEXT-" 407433 NIL DIFEXT- (NIL T T) -8 NIL NIL NIL) (-231 403609 405866 405907 "DIAGG" 405912 NIL DIAGG (NIL T) -9 NIL 405932 NIL) (-230 402993 403150 403402 "DIAGG-" 403407 NIL DIAGG- (NIL T T) -8 NIL NIL NIL) (-229 398410 401952 402229 "DHMATRIX" 402762 NIL DHMATRIX (NIL T) -8 NIL NIL NIL) (-228 394022 394931 395941 "DFSFUN" 397420 T DFSFUN (NIL) -7 NIL NIL NIL) (-227 389102 392953 393265 "DFLOAT" 393730 T DFLOAT (NIL) -8 NIL NIL NIL) (-226 387365 387646 388035 "DFINTTLS" 388810 NIL DFINTTLS (NIL T T) -7 NIL NIL NIL) (-225 384394 385386 385786 "DERHAM" 387031 NIL DERHAM (NIL T NIL) -8 NIL NIL NIL) (-224 382195 384169 384258 "DEQUEUE" 384338 NIL DEQUEUE (NIL T) -8 NIL NIL NIL) (-223 381449 381582 381765 "DEGRED" 382057 NIL DEGRED (NIL T T) -7 NIL NIL NIL) (-222 377879 378624 379470 "DEFINTRF" 380677 NIL DEFINTRF (NIL T) -7 NIL NIL NIL) (-221 375434 375903 376495 "DEFINTEF" 377398 NIL DEFINTEF (NIL T T) -7 NIL NIL NIL) (-220 374784 375054 375169 "DEFAST" 375339 T DEFAST (NIL) -8 NIL NIL NIL) (-219 368786 374377 374527 "DECIMAL" 374654 T DECIMAL (NIL) -8 NIL NIL NIL) (-218 366298 366756 367262 "DDFACT" 368330 NIL DDFACT (NIL T T) -7 NIL NIL NIL) (-217 365894 365937 366088 "DBLRESP" 366249 NIL DBLRESP (NIL T T T T) -7 NIL NIL NIL) (-216 363766 364127 364487 "DBASE" 365661 NIL DBASE (NIL T) -8 NIL NIL NIL) (-215 363008 363246 363392 "DATAARY" 363665 NIL DATAARY (NIL NIL T) -8 NIL NIL NIL) (-214 362114 362967 362995 "D03FAFA" 363000 T D03FAFA (NIL) -8 NIL NIL NIL) (-213 361221 362073 362101 "D03EEFA" 362106 T D03EEFA (NIL) -8 NIL NIL NIL) (-212 359171 359637 360126 "D03AGNT" 360752 T D03AGNT (NIL) -7 NIL NIL NIL) (-211 358460 359130 359158 "D02EJFA" 359163 T D02EJFA (NIL) -8 NIL NIL NIL) (-210 357749 358419 358447 "D02CJFA" 358452 T D02CJFA (NIL) -8 NIL NIL NIL) (-209 357038 357708 357736 "D02BHFA" 357741 T D02BHFA (NIL) -8 NIL NIL NIL) (-208 356327 356997 357025 "D02BBFA" 357030 T D02BBFA (NIL) -8 NIL NIL NIL) (-207 349524 351113 352719 "D02AGNT" 354741 T D02AGNT (NIL) -7 NIL NIL NIL) (-206 347292 347815 348361 "D01WGTS" 348998 T D01WGTS (NIL) -7 NIL NIL NIL) (-205 346359 347251 347279 "D01TRNS" 347284 T D01TRNS (NIL) -8 NIL NIL NIL) (-204 345427 346318 346346 "D01GBFA" 346351 T D01GBFA (NIL) -8 NIL NIL NIL) (-203 344495 345386 345414 "D01FCFA" 345419 T D01FCFA (NIL) -8 NIL NIL NIL) (-202 343563 344454 344482 "D01ASFA" 344487 T D01ASFA (NIL) -8 NIL NIL NIL) (-201 342631 343522 343550 "D01AQFA" 343555 T D01AQFA (NIL) -8 NIL NIL NIL) (-200 341699 342590 342618 "D01APFA" 342623 T D01APFA (NIL) -8 NIL NIL NIL) (-199 340767 341658 341686 "D01ANFA" 341691 T D01ANFA (NIL) -8 NIL NIL NIL) (-198 339835 340726 340754 "D01AMFA" 340759 T D01AMFA (NIL) -8 NIL NIL NIL) (-197 338903 339794 339822 "D01ALFA" 339827 T D01ALFA (NIL) -8 NIL NIL NIL) (-196 337971 338862 338890 "D01AKFA" 338895 T D01AKFA (NIL) -8 NIL NIL NIL) (-195 337039 337930 337958 "D01AJFA" 337963 T D01AJFA (NIL) -8 NIL NIL NIL) (-194 330334 331887 333448 "D01AGNT" 335498 T D01AGNT (NIL) -7 NIL NIL NIL) (-193 329671 329799 329951 "CYCLOTOM" 330202 T CYCLOTOM (NIL) -7 NIL NIL NIL) (-192 326404 327119 327846 "CYCLES" 328964 T CYCLES (NIL) -7 NIL NIL NIL) (-191 325716 325850 326021 "CVMP" 326265 NIL CVMP (NIL T) -7 NIL NIL NIL) (-190 323557 323815 324184 "CTRIGMNP" 325444 NIL CTRIGMNP (NIL T T) -7 NIL NIL NIL) (-189 322993 323351 323424 "CTOR" 323504 T CTOR (NIL) -8 NIL NIL NIL) (-188 322502 322724 322825 "CTORKIND" 322912 T CTORKIND (NIL) -8 NIL NIL NIL) (-187 321793 322109 322137 "CTORCAT" 322319 T CTORCAT (NIL) -9 NIL 322432 NIL) (-186 321391 321502 321661 "CTORCAT-" 321666 NIL CTORCAT- (NIL T) -8 NIL NIL NIL) (-185 320853 321065 321173 "CTORCALL" 321315 NIL CTORCALL (NIL T) -8 NIL NIL NIL) (-184 320227 320326 320479 "CSTTOOLS" 320750 NIL CSTTOOLS (NIL T T) -7 NIL NIL NIL) (-183 316026 316683 317441 "CRFP" 319539 NIL CRFP (NIL T T) -7 NIL NIL NIL) (-182 315501 315747 315839 "CRCEAST" 315954 T CRCEAST (NIL) -8 NIL NIL NIL) (-181 314548 314733 314961 "CRAPACK" 315305 NIL CRAPACK (NIL T) -7 NIL NIL NIL) (-180 313932 314033 314237 "CPMATCH" 314424 NIL CPMATCH (NIL T T T) -7 NIL NIL NIL) (-179 313657 313685 313791 "CPIMA" 313898 NIL CPIMA (NIL T T T) -7 NIL NIL NIL) (-178 310005 310677 311396 "COORDSYS" 312992 NIL COORDSYS (NIL T) -7 NIL NIL NIL) (-177 309417 309538 309680 "CONTOUR" 309883 T CONTOUR (NIL) -8 NIL NIL NIL) (-176 305308 307420 307912 "CONTFRAC" 308957 NIL CONTFRAC (NIL T) -8 NIL NIL NIL) (-175 305188 305209 305237 "CONDUIT" 305274 T CONDUIT (NIL) -9 NIL NIL NIL) (-174 304276 304830 304858 "COMRING" 304863 T COMRING (NIL) -9 NIL 304915 NIL) (-173 303330 303634 303818 "COMPPROP" 304112 T COMPPROP (NIL) -8 NIL NIL NIL) (-172 302991 303026 303154 "COMPLPAT" 303289 NIL COMPLPAT (NIL T T T) -7 NIL NIL NIL) (-171 293282 302800 302909 "COMPLEX" 302914 NIL COMPLEX (NIL T) -8 NIL NIL NIL) (-170 292918 292975 293082 "COMPLEX2" 293219 NIL COMPLEX2 (NIL T T) -7 NIL NIL NIL) (-169 292257 292378 292538 "COMPILER" 292778 T COMPILER (NIL) -8 NIL NIL NIL) (-168 291975 292010 292108 "COMPFACT" 292216 NIL COMPFACT (NIL T T) -7 NIL NIL NIL) (-167 276055 286049 286089 "COMPCAT" 287093 NIL COMPCAT (NIL T) -9 NIL 288441 NIL) (-166 265567 268494 272121 "COMPCAT-" 272477 NIL COMPCAT- (NIL T T) -8 NIL NIL NIL) (-165 265296 265324 265427 "COMMUPC" 265533 NIL COMMUPC (NIL T T T) -7 NIL NIL NIL) (-164 265090 265124 265183 "COMMONOP" 265257 T COMMONOP (NIL) -7 NIL NIL NIL) (-163 264646 264841 264928 "COMM" 265023 T COMM (NIL) -8 NIL NIL NIL) (-162 264222 264450 264525 "COMMAAST" 264591 T COMMAAST (NIL) -8 NIL NIL NIL) (-161 263471 263665 263693 "COMBOPC" 264031 T COMBOPC (NIL) -9 NIL 264206 NIL) (-160 262367 262577 262819 "COMBINAT" 263261 NIL COMBINAT (NIL T) -7 NIL NIL NIL) (-159 258824 259398 260025 "COMBF" 261789 NIL COMBF (NIL T T) -7 NIL NIL NIL) (-158 257582 257940 258175 "COLOR" 258609 T COLOR (NIL) -8 NIL NIL NIL) (-157 257058 257303 257395 "COLONAST" 257510 T COLONAST (NIL) -8 NIL NIL NIL) (-156 256698 256745 256870 "CMPLXRT" 257005 NIL CMPLXRT (NIL T T) -7 NIL NIL NIL) (-155 256146 256398 256497 "CLLCTAST" 256619 T CLLCTAST (NIL) -8 NIL NIL NIL) (-154 251648 252676 253756 "CLIP" 255086 T CLIP (NIL) -7 NIL NIL NIL) (-153 249989 250749 250989 "CLIF" 251475 NIL CLIF (NIL NIL T NIL) -8 NIL NIL NIL) (-152 246164 248135 248176 "CLAGG" 249105 NIL CLAGG (NIL T) -9 NIL 249641 NIL) (-151 244586 245043 245626 "CLAGG-" 245631 NIL CLAGG- (NIL T T) -8 NIL NIL NIL) (-150 244130 244215 244355 "CINTSLPE" 244495 NIL CINTSLPE (NIL T T) -7 NIL NIL NIL) (-149 241631 242102 242650 "CHVAR" 243658 NIL CHVAR (NIL T T T) -7 NIL NIL NIL) (-148 240805 241359 241387 "CHARZ" 241392 T CHARZ (NIL) -9 NIL 241407 NIL) (-147 240559 240599 240677 "CHARPOL" 240759 NIL CHARPOL (NIL T) -7 NIL NIL NIL) (-146 239617 240204 240232 "CHARNZ" 240279 T CHARNZ (NIL) -9 NIL 240335 NIL) (-145 237523 238271 238624 "CHAR" 239284 T CHAR (NIL) -8 NIL NIL NIL) (-144 237249 237310 237338 "CFCAT" 237449 T CFCAT (NIL) -9 NIL NIL NIL) (-143 236490 236601 236784 "CDEN" 237133 NIL CDEN (NIL T T T) -7 NIL NIL NIL) (-142 232455 235643 235923 "CCLASS" 236230 T CCLASS (NIL) -8 NIL NIL NIL) (-141 231706 231863 232040 "CATEGORY" 232298 T -10 (NIL) -8 NIL NIL NIL) (-140 231279 231625 231673 "CATCTOR" 231678 T CATCTOR (NIL) -8 NIL NIL NIL) (-139 230730 230982 231080 "CATAST" 231201 T CATAST (NIL) -8 NIL NIL NIL) (-138 230206 230451 230543 "CASEAST" 230658 T CASEAST (NIL) -8 NIL NIL NIL) (-137 225344 226363 227107 "CARTEN" 229518 NIL CARTEN (NIL NIL NIL T) -8 NIL NIL NIL) (-136 224452 224600 224821 "CARTEN2" 225191 NIL CARTEN2 (NIL NIL NIL T T) -7 NIL NIL NIL) (-135 222768 223602 223859 "CARD" 224215 T CARD (NIL) -8 NIL NIL NIL) (-134 222344 222572 222647 "CAPSLAST" 222713 T CAPSLAST (NIL) -8 NIL NIL NIL) (-133 221848 222056 222084 "CACHSET" 222216 T CACHSET (NIL) -9 NIL 222294 NIL) (-132 221318 221640 221668 "CABMON" 221718 T CABMON (NIL) -9 NIL 221774 NIL) (-131 220791 221022 221132 "BYTEORD" 221228 T BYTEORD (NIL) -8 NIL NIL NIL) (-130 219768 220320 220462 "BYTE" 220625 T BYTE (NIL) -8 NIL NIL 220747) (-129 215118 219273 219445 "BYTEBUF" 219616 T BYTEBUF (NIL) -8 NIL NIL NIL) (-128 212627 214810 214917 "BTREE" 215044 NIL BTREE 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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 (-194))))) +(((*1 *2 *2) + (-12 (-4 *3 (-620 (-899 *3))) (-4 *3 (-893 *3)) (-4 *3 (-458)) + (-5 *1 (-1218 *3 *2)) (-4 *2 (-620 (-899 *3))) (-4 *2 (-893 *3)) + (-4 *2 (-13 (-436 *3) (-1212)))))) +(((*1 *2 *3) + (-12 + (-5 *3 + (-2 (|:| |xinit| (-227)) (|:| |xend| (-227)) + (|:| |fn| (-1277 (-320 (-227)))) (|:| |yinit| (-650 (-227))) + (|:| |intvals| (-650 (-227))) (|:| |g| (-320 (-227))) + (|:| |abserr| (-227)) (|:| |relerr| (-227)))) + (-5 *2 (-384)) (-5 *1 (-207))))) +(((*1 *2 *3) + (-12 (-5 *3 (-1 (-112) *6)) (-4 *6 (-13 (-1109) (-1047 *5))) + (-4 *5 (-893 *4)) (-4 *4 (-1109)) (-5 *2 (-1 (-112) *5)) + (-5 *1 (-938 *4 *5 *6))))) +(((*1 *1 *2 *2 *3) (-12 (-5 *2 (-1168)) (-5 *3 (-829)) (-5 *1 (-828))))) +(((*1 *2 *3 *3 *2 *4) + (-12 (-5 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"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| (-1166 (-227))) + (|:| |notEvaluated| + "Internal singularities not yet evaluated"))) + (|:| -2293 + (-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 (-565))))) +(((*1 *2 *1 *3) (-12 (-5 *3 (-1129)) (-5 *2 (-112)) (-5 *1 (-827))))) +(((*1 *2 *3 *4) + (-12 (-5 *3 (-227)) (-5 *4 (-570)) (-5 *2 (-1044)) (-5 *1 (-764))))) +(((*1 *2 *1) + (-12 (-4 *1 (-1220 *3 *4 *5 *6)) (-4 *3 (-562)) (-4 *4 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(-5 *2 - (-650 (-1155 *4 (-537 (-870 *6)) (-870 *6) (-786 *4 (-870 *6))))) - (-5 *1 (-1304 *4 *5 *6)) (-14 *6 (-650 (-1186)))))) + (-2 (|:| -3491 (-695 *3)) (|:| |basisDen| *3) + (|:| |basisInv| (-695 *3)))) + (-4 *3 (-13 (-311) (-10 -8 (-15 -2904 ((-424 $) $))))) + (-4 *4 (-1253 *3)) (-5 *1 (-505 *3 *4 *5)) (-4 *5 (-415 *3 *4))))) +(((*1 *1 *1 *2) + (-12 (-5 *2 (-650 *1)) (|has| *1 (-6 -4453)) (-4 *1 (-1019 *3)) + (-4 *3 (-1227))))) +(((*1 *2 *3) (-12 (-5 *3 (-928)) (-5 *2 (-911 (-570))) (-5 *1 (-924)))) + ((*1 *2 *3) + (-12 (-5 *3 (-650 (-570))) (-5 *2 (-911 (-570))) (-5 *1 (-924))))) +(((*1 *2 *3) + (-12 (-5 *3 |RationalNumber|) (-5 *2 (-1 (-570))) (-5 *1 (-1056))))) +(((*1 *2 *1) + (-12 (-5 *2 (-112)) (-5 *1 (-320 *3)) (-4 *3 (-562)) (-4 *3 (-1109))))) (((*1 *1 *1) (-4 *1 (-95))) ((*1 *2 *2) (-12 (-4 *3 (-562)) (-5 *1 (-279 *3 *2)) @@ -1279,22 +3573,7 @@ ((*1 *2 *2) (-12 (-5 *2 (-1166 *3)) (-4 *3 (-38 (-413 (-570)))) (-5 *1 (-1172 *3))))) -(((*1 *2 *3 *2) (-12 (-5 *3 (-777)) (-5 *1 (-862 *2)) (-4 *2 (-174)))) - ((*1 *2 *3 *3 *2) - (-12 (-5 *3 (-777)) (-5 *1 (-862 *2)) (-4 *2 (-174))))) -(((*1 *1 *1) (-12 (-5 *1 (-298 *2)) (-4 *2 (-21)) (-4 *2 (-1227))))) -(((*1 *2 *2) - (-12 (-4 *3 (-311)) (-4 *4 (-378 *3)) (-4 *5 (-378 *3)) - (-5 *1 (-1133 *3 *4 *5 *2)) (-4 *2 (-693 *3 *4 *5))))) -(((*1 *2 *3 *1) - (-12 (-4 *1 (-1080 *4 *5 *6 *3)) (-4 *4 (-458)) (-4 *5 (-799)) - (-4 *6 (-856)) (-4 *3 (-1074 *4 *5 *6)) (-5 *2 (-112))))) -(((*1 *2 *3) - (-12 (-5 *3 (-1277 (-320 (-227)))) - (-5 *2 - (-2 (|:| |additions| (-570)) (|:| |multiplications| (-570)) - (|:| |exponentiations| (-570)) (|:| |functionCalls| (-570)))) - (-5 *1 (-309))))) +(((*1 *2 *3) (-12 (-5 *3 (-1168)) (-5 *2 (-928)) (-5 *1 (-792))))) (((*1 *1 *1) (-12 (-4 *1 (-167 *2)) (-4 *2 (-174)) (-4 *2 (-1069)))) ((*1 *1 *1) (-12 (-5 *1 (-344 *2 *3 *4)) (-14 *2 (-650 (-1186))) @@ -1305,58 +3584,75 @@ ((*1 *1 *1) (-4 *1 (-854))) ((*1 *2 *1) (-12 (-4 *1 (-1006 *2)) (-4 *2 (-174)) (-4 *2 (-1069)))) ((*1 *1 *1) (-4 *1 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(-227))) ((*1 *2 *2) (-12 (-4 *3 (-562)) (-5 *1 (-279 *3 *2)) @@ -1377,44 +3673,59 @@ ((*1 *2 *2) (-12 (-5 *2 (-1166 *3)) (-4 *3 (-38 (-413 (-570)))) (-5 *1 (-1172 *3))))) +(((*1 *2 *2) + (-12 (-4 *3 (-562)) (-5 *1 (-279 *3 *2)) + (-4 *2 (-13 (-436 *3) (-1011)))))) +(((*1 *2 *3 *4) + (-12 (-4 *5 (-458)) (-4 *6 (-799)) (-4 *7 (-856)) + (-4 *3 (-1074 *5 *6 *7)) (-5 *2 (-112)) + (-5 *1 (-1081 *5 *6 *7 *3 *4)) (-4 *4 (-1080 *5 *6 *7 *3)))) + ((*1 *2 *3 *4) + (-12 (-4 *5 (-458)) (-4 *6 (-799)) (-4 *7 (-856)) + (-4 *3 (-1074 *5 *6 *7)) + (-5 *2 (-650 (-2 (|:| |val| (-112)) (|:| -4228 *4)))) + (-5 *1 (-1081 *5 *6 *7 *3 *4)) (-4 *4 (-1080 *5 *6 *7 *3))))) (((*1 *2 *3) - (-12 (-5 *3 (-115)) (-4 *4 (-562)) (-5 *2 (-112)) (-5 *1 (-32 *4 *5)) - (-4 *5 (-436 *4)))) - ((*1 *2 *3) - (-12 (-5 *3 (-115)) (-4 *4 (-562)) (-5 *2 (-112)) - (-5 *1 (-159 *4 *5)) (-4 *5 (-436 *4)))) - ((*1 *2 *3) - (-12 (-5 *3 (-115)) (-4 *4 (-562)) (-5 *2 (-112)) - (-5 *1 (-279 *4 *5)) (-4 *5 (-13 (-436 *4) (-1011))))) - 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(-4 *3 (-562)) (-5 *1 (-279 *3 *2)) + (-4 *2 (-13 (-436 *3) (-1011)))))) +(((*1 *2 *1) + (-12 (-5 *2 (-650 (-2 (|:| -4111 (-1186)) (|:| -3117 *4)))) + (-5 *1 (-896 *3 *4)) (-4 *3 (-1109)) (-4 *4 (-1109)))) + ((*1 *2 *1) + (-12 (-4 *3 (-1109)) (-4 *4 (-1109)) (-4 *5 (-1109)) (-4 *6 (-1109)) + (-4 *7 (-1109)) (-5 *2 (-650 *1)) (-4 *1 (-1112 *3 *4 *5 *6 *7))))) +(((*1 *2) + (-12 (-4 *3 (-458)) (-4 *4 (-799)) (-4 *5 (-856)) + (-4 *6 (-1074 *3 *4 *5)) (-5 *2 (-1282)) + (-5 *1 (-1081 *3 *4 *5 *6 *7)) (-4 *7 (-1080 *3 *4 *5 *6)))) + ((*1 *2) + (-12 (-4 *3 (-458)) (-4 *4 (-799)) (-4 *5 (-856)) + (-4 *6 (-1074 *3 *4 *5)) (-5 *2 (-1282)) + (-5 *1 (-1117 *3 *4 *5 *6 *7)) (-4 *7 (-1080 *3 *4 *5 *6))))) +(((*1 *2 *3) (-12 (-5 *2 (-570)) (-5 *1 (-575 *3)) (-4 *3 (-1047 *2)))) + ((*1 *2 *1) + (-12 (-4 *1 (-1112 *3 *4 *2 *5 *6)) (-4 *3 (-1109)) (-4 *4 (-1109)) + (-4 *5 (-1109)) (-4 *6 (-1109)) (-4 *2 (-1109))))) +(((*1 *2 *2) + (-12 (-4 *3 (-562)) (-5 *1 (-279 *3 *2)) + (-4 *2 (-13 (-436 *3) (-1011)))))) (((*1 *1 *1) (-4 *1 (-95))) ((*1 *2 *2) (-12 (-4 *3 (-562)) (-5 *1 (-279 *3 *2)) @@ -1434,48 +3745,52 @@ ((*1 *2 *2) (-12 (-5 *2 (-1166 *3)) (-4 *3 (-38 (-413 (-570)))) (-5 *1 (-1172 *3))))) -(((*1 *2 *3) - (-12 (-5 *3 (-1168)) (-5 *2 (-650 (-1191))) (-5 *1 (-887))))) -(((*1 *2 *1) (|partial| -12 (-5 *1 (-370 *2)) (-4 *2 (-1109)))) - ((*1 *2 *1) (|partial| -12 (-5 *2 (-1168)) (-5 *1 (-1208))))) -(((*1 *2 *2 *3 *2) - (-12 (-5 *3 (-777)) (-4 *4 (-354)) (-5 *1 (-218 *4 *2)) - (-4 *2 (-1253 *4))))) -(((*1 *2 *1) - (-12 (-4 *1 (-1112 *3 *4 *5 *6 *7)) (-4 *3 (-1109)) (-4 *4 (-1109)) - (-4 *5 (-1109)) (-4 *6 (-1109)) (-4 *7 (-1109)) (-5 *2 (-112))))) -(((*1 *2 *2 *3) - (|partial| -12 (-5 *3 (-1 *6 *6)) (-4 *6 (-1253 *5)) - (-4 *5 (-13 (-27) (-436 *4))) (-4 *4 (-13 (-562) (-1047 (-570)))) - (-4 *7 (-1253 (-413 *6))) (-5 *1 (-558 *4 *5 *6 *7 *2)) - (-4 *2 (-347 *5 *6 *7))))) -(((*1 *2 *3) - (-12 (-5 *3 (-650 (-1186))) (-5 *2 (-1282)) (-5 *1 (-1189)))) - ((*1 *2 *3 *4) - (-12 (-5 *4 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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 (-194))))) -(((*1 *2 *3) - (-12 (-4 *4 (-562)) (-5 *2 (-650 *3)) (-5 *1 (-43 *4 *3)) - (-4 *3 (-423 *4))))) + (-650 + (-2 (|:| |lcmfij| *4) (|:| |totdeg| (-777)) (|:| |poli| *6) + (|:| |polj| *6)))) + (-4 *4 (-799)) (-4 *6 (-956 *3 *4 *5)) (-4 *3 (-458)) (-4 *5 (-856)) + (-5 *1 (-455 *3 *4 *5 *6))))) +(((*1 *2 *1 *3) + (-12 (-5 *3 (-777)) (-4 *1 (-1253 *4)) (-4 *4 (-1058)) + (-5 *2 (-1277 *4))))) +(((*1 *2 *3 *3 *4 *4 *4 *4 *3) + (-12 (-5 *3 (-570)) (-5 *4 (-695 (-227))) (-5 *2 (-1044)) + (-5 *1 (-758))))) +(((*1 *1 *1 *2 *2) + (-12 (-5 *2 (-570)) (-5 *1 (-137 *3 *4 *5)) (-14 *3 *2) + (-14 *4 (-777)) (-4 *5 (-174)))) + ((*1 *1 *1) + (-12 (-5 *1 (-137 *2 *3 *4)) (-14 *2 (-570)) (-14 *3 (-777)) + (-4 *4 (-174)))) + ((*1 *1 *1) + (-12 (-4 *1 (-693 *2 *3 *4)) (-4 *2 (-1058)) (-4 *3 (-378 *2)) + (-4 *4 (-378 *2)))) + ((*1 *1 *2) + (-12 (-4 *3 (-1058)) (-4 *1 (-693 *3 *2 *4)) (-4 *2 (-378 *3)) + (-4 *4 (-378 *3)))) + ((*1 *1 *1) + (-12 (-5 *1 (-1151 *2 *3)) (-14 *2 (-777)) (-4 *3 (-1058))))) +(((*1 *2) + (-12 (-5 *2 (-1277 (-1110 *3 *4))) (-5 *1 (-1110 *3 *4)) + (-14 *3 (-928)) (-14 *4 (-928))))) +(((*1 *2 *1) (-12 (-5 *2 (-1144)) (-5 *1 (-182)))) + ((*1 *2 *1) (-12 (-5 *2 (-1144)) (-5 *1 (-315)))) + ((*1 *2 *1) (-12 (-5 *2 (-1144)) (-5 *1 (-979)))) + ((*1 *2 *1) (-12 (-5 *2 (-1144)) (-5 *1 (-1003)))) + ((*1 *2 *1) (-12 (-5 *2 (-1144)) (-5 *1 (-1045)))) + ((*1 *2 *1) (-12 (-5 *2 (-1144)) (-5 *1 (-1082))))) (((*1 *1 *1) (-4 *1 (-95))) ((*1 *2 *2) (-12 (-4 *3 (-562)) (-5 *1 (-279 *3 *2)) @@ -1495,70 +3810,78 @@ ((*1 *2 *2) (-12 (-5 *2 (-1166 *3)) (-4 *3 (-38 (-413 (-570)))) (-5 *1 (-1172 *3))))) -(((*1 *2 *1) (-12 (-4 *1 (-1143 *3)) (-4 *3 (-1058)) (-5 *2 (-112))))) -(((*1 *2 *1) (-12 (-5 *2 (-1144)) (-5 *1 (-523)))) - ((*1 *2 *1) - (-12 (-4 *2 (-13 (-1109) (-34))) (-5 *1 (-1149 *3 *2)) - (-4 *3 (-13 (-1109) (-34))))) - ((*1 *2 *1) (-12 (-5 *2 (-1144)) (-5 *1 (-1288))))) -(((*1 *1) (-5 *1 (-584))) - ((*1 *2 *3) (-12 (-5 *3 (-1168)) (-5 *2 (-1282)) (-5 *1 (-869)))) - ((*1 *2 *3) (-12 (-5 *3 (-868)) (-5 *2 (-1282)) (-5 *1 (-869)))) - ((*1 *2 *3 *4) - (-12 (-5 *3 (-1168)) (-5 *4 (-868)) (-5 *2 (-1282)) (-5 *1 (-869)))) - ((*1 *2 *3 *1) - (-12 (-5 *3 (-570)) (-5 *2 (-1282)) (-5 *1 (-1166 *4)) - (-4 *4 (-1109)) (-4 *4 (-1227))))) -(((*1 *2 *1 *2) (-12 (-5 *2 (-650 (-1168))) (-5 *1 (-400))))) -(((*1 *2 *2 *3) - (|partial| -12 (-5 *2 (-650 (-1182 *5))) (-5 *3 (-1182 *5)) - (-4 *5 (-167 *4)) (-4 *4 (-551)) (-5 *1 (-150 *4 *5)))) - ((*1 *2 *2 *3) - (|partial| -12 (-5 *2 (-650 *3)) (-4 *3 (-1253 *5)) - (-4 *5 (-1253 *4)) (-4 *4 (-354)) (-5 *1 (-363 *4 *5 *3)))) - ((*1 *2 *2 *3) - (|partial| -12 (-5 *2 (-650 (-1182 (-570)))) (-5 *3 (-1182 (-570))) - (-5 *1 (-578)))) - ((*1 *2 *2 *3) - (|partial| -12 (-5 *2 (-650 (-1182 *1))) (-5 *3 (-1182 *1)) - (-4 *1 (-916))))) +(((*1 *2 *1 *1) + (-12 (-4 *1 (-1107 *3)) (-4 *3 (-1109)) (-5 *2 (-112))))) (((*1 *2 *3) - (-12 (-4 *4 (-13 (-562) (-1047 (-570)))) (-5 *2 (-413 (-570))) - (-5 *1 (-439 *4 *3)) (-4 *3 (-436 *4)))) - ((*1 *2 *3 *4) - (-12 (-5 *4 (-618 *3)) (-4 *3 (-436 *5)) - (-4 *5 (-13 (-562) (-1047 (-570)))) (-5 *2 (-1182 (-413 (-570)))) - (-5 *1 (-439 *5 *3))))) -(((*1 *2 *2) (|partial| -12 (-4 *1 (-992 *2)) (-4 *2 (-1212))))) -(((*1 *2 *2) - (-12 (-4 *3 (-13 (-458) (-1047 (-570)))) (-4 *3 (-562)) - (-5 *1 (-41 *3 *2)) (-4 *2 (-436 *3)) - (-4 *2 - (-13 (-368) (-306) - (-10 -8 (-15 -2924 ((-1134 *3 (-618 $)) $)) - (-15 -2937 ((-1134 *3 (-618 $)) $)) - (-15 -2940 ($ (-1134 *3 (-618 $)))))))))) -(((*1 *2 *1) - (-12 (-4 *1 (-1220 *3 *4 *5 *6)) (-4 *3 (-562)) (-4 *4 (-799)) - (-4 *5 (-856)) (-4 *6 (-1074 *3 *4 *5)) (-5 *2 (-112)))) - ((*1 *2 *3 *1) - (-12 (-4 *1 (-1220 *4 *5 *6 *3)) (-4 *4 (-562)) (-4 *5 (-799)) - (-4 *6 (-856)) (-4 *3 (-1074 *4 *5 *6)) (-5 *2 (-112))))) -(((*1 *2 *3 *4) - (-12 (-5 *4 (-112)) + (-12 + (-5 *3 + (-2 (|:| -1454 (-695 (-413 (-959 *4)))) + (|:| |vec| (-650 (-413 (-959 *4)))) (|:| -4396 (-777)) + (|:| |rows| (-650 (-570))) (|:| |cols| (-650 (-570))))) + (-4 *4 (-13 (-311) (-148))) (-4 *5 (-13 (-856) (-620 (-1186)))) + (-4 *6 (-799)) (-5 *2 - (-2 (|:| |contp| (-570)) - (|:| -4082 (-650 (-2 (|:| |irr| *3) (|:| -3791 (-570))))))) - (-5 *1 (-448 *3)) (-4 *3 (-1253 (-570))))) + (-2 (|:| |partsol| (-1277 (-413 (-959 *4)))) + (|:| -3491 (-650 (-1277 (-413 (-959 *4))))))) + (-5 *1 (-931 *4 *5 *6 *7)) (-4 *7 (-956 *4 *6 *5))))) +(((*1 *2 *2) + (-12 (-5 *2 (-650 *6)) (-4 *6 (-956 *3 *4 *5)) (-4 *3 (-458)) + (-4 *4 (-799)) (-4 *5 (-856)) (-5 *1 (-455 *3 *4 *5 *6))))) +(((*1 *2 *2) + (|partial| -12 (-4 *3 (-368)) (-4 *4 (-378 *3)) (-4 *5 (-378 *3)) + (-5 *1 (-527 *3 *4 *5 *2)) (-4 *2 (-693 *3 *4 *5)))) + ((*1 *2 *3) + (|partial| -12 (-4 *4 (-562)) (-4 *5 (-378 *4)) (-4 *6 (-378 *4)) + (-4 *7 (-1001 *4)) (-4 *2 (-693 *7 *8 *9)) + (-5 *1 (-528 *4 *5 *6 *3 *7 *8 *9 *2)) (-4 *3 (-693 *4 *5 *6)) + (-4 *8 (-378 *7)) (-4 *9 (-378 *7)))) + ((*1 *1 *1) + (|partial| -12 (-4 *1 (-693 *2 *3 *4)) (-4 *2 (-1058)) + (-4 *3 (-378 *2)) (-4 *4 (-378 *2)) (-4 *2 (-368)))) + ((*1 *2 *2) + (|partial| -12 (-4 *3 (-368)) (-4 *3 (-174)) (-4 *4 (-378 *3)) + (-4 *5 (-378 *3)) (-5 *1 (-694 *3 *4 *5 *2)) + (-4 *2 (-693 *3 *4 *5)))) + ((*1 *1 *1) + (|partial| -12 (-5 *1 (-695 *2)) (-4 *2 (-368)) (-4 *2 (-1058)))) + ((*1 *1 *1) + (|partial| -12 (-4 *1 (-1132 *2 *3 *4 *5)) (-4 *3 (-1058)) + (-4 *4 (-240 *2 *3)) (-4 *5 (-240 *2 *3)) (-4 *3 (-368)))) + ((*1 *2 *2) (-12 (-5 *2 (-650 *3)) (-4 *3 (-856)) (-5 *1 (-1197 *3))))) +(((*1 *1 *1 *2) (-12 (-5 *2 (-928)) (-4 *1 (-750 *3)) (-4 *3 (-174))))) +(((*1 *2 *3) + (-12 (-5 *3 (-1182 *6)) (-4 *6 (-1058)) (-4 *4 (-799)) (-4 *5 (-856)) + (-5 *2 (-1182 *7)) (-5 *1 (-325 *4 *5 *6 *7)) + (-4 *7 (-956 *6 *4 *5))))) +(((*1 *2 *3 *4 *5) + (|partial| -12 (-5 *4 (-1 (-112) *9)) (-5 *5 (-1 (-112) *9 *9)) + (-4 *9 (-1074 *6 *7 *8)) (-4 *6 (-562)) (-4 *7 (-799)) + (-4 *8 (-856)) (-5 *2 (-2 (|:| |bas| *1) (|:| -2028 (-650 *9)))) + (-5 *3 (-650 *9)) (-4 *1 (-1220 *6 *7 *8 *9)))) ((*1 *2 *3 *4) - (-12 (-5 *4 (-112)) - (-5 *2 - (-2 (|:| |contp| (-570)) - (|:| -4082 (-650 (-2 (|:| |irr| *3) (|:| -3791 (-570))))))) - (-5 *1 (-1242 *3)) (-4 *3 (-1253 (-570)))))) + (|partial| -12 (-5 *4 (-1 (-112) *8 *8)) (-4 *8 (-1074 *5 *6 *7)) + (-4 *5 (-562)) (-4 *6 (-799)) (-4 *7 (-856)) + (-5 *2 (-2 (|:| |bas| *1) (|:| -2028 (-650 *8)))) + (-5 *3 (-650 *8)) (-4 *1 (-1220 *5 *6 *7 *8))))) (((*1 *2) - (-12 (-5 *2 (-2 (|:| -4274 (-650 *3)) (|:| -3996 (-650 *3)))) - (-5 *1 (-1228 *3)) (-4 *3 (-1109))))) + (|partial| -12 (-4 *4 (-1231)) (-4 *5 (-1253 (-413 *2))) + (-4 *2 (-1253 *4)) (-5 *1 (-346 *3 *4 *2 *5)) + (-4 *3 (-347 *4 *2 *5)))) + ((*1 *2) + (|partial| -12 (-4 *1 (-347 *3 *2 *4)) (-4 *3 (-1231)) + (-4 *4 (-1253 (-413 *2))) (-4 *2 (-1253 *3))))) +(((*1 *2 *3) + (-12 (-5 *2 (-424 (-1182 *1))) (-5 *1 (-320 *4)) (-5 *3 (-1182 *1)) + (-4 *4 (-458)) (-4 *4 (-562)) (-4 *4 (-1109)))) + ((*1 *2 *3) + (-12 (-4 *1 (-916)) (-5 *2 (-424 (-1182 *1))) (-5 *3 (-1182 *1))))) +(((*1 *2 *3 *3 *3 *4) + (-12 (-5 *3 (-1 (-227) (-227) (-227))) + (-5 *4 (-1 (-227) (-227) (-227) (-227))) + (-5 *2 (-1 (-950 (-227)) (-227) (-227))) (-5 *1 (-703))))) +(((*1 *2 *1) + (-12 (-4 *1 (-1112 *3 *2 *4 *5 *6)) (-4 *3 (-1109)) (-4 *4 (-1109)) + (-4 *5 (-1109)) (-4 *6 (-1109)) (-4 *2 (-1109))))) (((*1 *2 *2) (-12 (-4 *3 (-562)) (-5 *1 (-279 *3 *2)) (-4 *2 (-13 (-436 *3) (-1011))))) @@ -1575,47 +3898,24 @@ (-12 (-5 *2 (-1166 *3)) (-4 *3 (-38 (-413 (-570)))) (-5 *1 (-1172 *3)))) ((*1 *1 *1) (-4 *1 (-1215)))) -(((*1 *2 *1) (-12 (-5 *2 (-112)) (-5 *1 (-830))))) +(((*1 *2 *1) (-12 (-5 *2 (-697 (-1144))) (-5 *1 (-1160))))) +(((*1 *1 *1 *2) + (-12 (-4 *1 (-985 *3 *4 *2 *5)) (-4 *3 (-1058)) (-4 *4 (-799)) + (-4 *2 (-856)) (-4 *5 (-1074 *3 *4 *2))))) (((*1 *2 *3 *4) - (-12 (-4 *5 (-311)) (-4 *6 (-378 *5)) (-4 *4 (-378 *5)) - (-5 *2 - (-2 (|:| |particular| (-3 *4 "failed")) (|:| -4055 (-650 *4)))) - (-5 *1 (-1133 *5 *6 *4 *3)) (-4 *3 (-693 *5 *6 *4))))) + (-12 (-5 *3 (-413 *6)) (-4 *5 (-1231)) (-4 *6 (-1253 *5)) + (-5 *2 (-2 (|:| -2092 (-777)) (|:| -1777 *3) (|:| |radicand| *6))) + (-5 *1 (-149 *5 *6 *7)) (-5 *4 (-777)) (-4 *7 (-1253 *3))))) +(((*1 *2) (-12 (-5 *2 (-570)) (-5 *1 (-934))))) +(((*1 *2 *1) + (-12 (-5 *2 (-1277 (-777))) (-5 *1 (-681 *3)) (-4 *3 (-1109))))) +(((*1 *2 *1) (-12 (-5 *2 (-1168)) (-5 *1 (-542))))) +(((*1 *2 *1) (-12 (-4 *1 (-372 *2)) (-4 *2 (-174))))) (((*1 *2) - (-12 (-4 *3 (-458)) (-4 *4 (-799)) (-4 *5 (-856)) - (-4 *6 (-1074 *3 *4 *5)) (-5 *2 (-1282)) - (-5 *1 (-1081 *3 *4 *5 *6 *7)) (-4 *7 (-1080 *3 *4 *5 *6)))) - ((*1 *2) - (-12 (-4 *3 (-458)) (-4 *4 (-799)) (-4 *5 (-856)) - (-4 *6 (-1074 *3 *4 *5)) (-5 *2 (-1282)) - (-5 *1 (-1117 *3 *4 *5 *6 *7)) (-4 *7 (-1080 *3 *4 *5 *6))))) -(((*1 *1 *1 *2) (-12 (-5 *2 (-1186)) (-5 *1 (-1072))))) -(((*1 *2 *1) (-12 (-5 *2 (-185 (-251))) (-5 *1 (-250))))) -(((*1 *1 *2) (-12 (-5 *2 (-570)) (-5 *1 (-868))))) -(((*1 *1 *2) - (-12 (-5 *2 (-678 *3)) (-4 *3 (-856)) (-4 *1 (-379 *3 *4)) - (-4 *4 (-174))))) -(((*1 *2 *2 *2) (-12 (-5 *2 (-1044)) (-5 *1 (-309)))) - ((*1 *2 *3) - (-12 (-5 *3 (-650 (-1044))) (-5 *2 (-1044)) (-5 *1 (-309)))) - ((*1 *1 *2) (-12 (-5 *2 (-650 *1)) (-4 *1 (-657 *3)) (-4 *3 (-1227)))) - ((*1 *1 *1 *1) (-12 (-4 *1 (-657 *2)) (-4 *2 (-1227)))) - ((*1 *1 *2 *1) (-12 (-4 *1 (-657 *2)) (-4 *2 (-1227)))) - ((*1 *1 *1 *2) (-12 (-4 *1 (-657 *2)) (-4 *2 (-1227)))) - ((*1 *1 *1 *1) (-5 *1 (-1072))) - ((*1 *2 *3) - (-12 (-5 *3 (-1166 (-1166 *4))) (-5 *2 (-1166 *4)) (-5 *1 (-1163 *4)) - (-4 *4 (-1227)))) - ((*1 *1 *2 *1) (-12 (-4 *1 (-1265 *2)) (-4 *2 (-1227)))) - ((*1 *1 *1 *1) (-12 (-4 *1 (-1265 *2)) (-4 *2 (-1227))))) -(((*1 *2 *2 *3) - (-12 (-5 *3 (-1186)) - (-4 *4 (-13 (-311) (-1047 (-570)) (-645 (-570)) (-148))) - (-5 *1 (-810 *4 *2)) (-4 *2 (-13 (-29 *4) (-1212) (-966))))) - ((*1 *1 *1 *1 *1) (-5 *1 (-868))) ((*1 *1 *1 *1) (-5 *1 (-868))) - ((*1 *1 *1) (-5 *1 (-868))) - ((*1 *2 *3) - (-12 (-5 *2 (-1166 *3)) (-5 *1 (-1170 *3)) (-4 *3 (-1058))))) + (-12 (-4 *4 (-174)) (-5 *2 (-112)) (-5 *1 (-371 *3 *4)) + (-4 *3 (-372 *4)))) + ((*1 *2) (-12 (-4 *1 (-372 *3)) (-4 *3 (-174)) (-5 *2 (-112))))) +(((*1 *2 *1) (-12 (-5 *2 (-112)) (-5 *1 (-115))))) (((*1 *2 *2) (-12 (-4 *3 (-562)) (-5 *1 (-279 *3 *2)) (-4 *2 (-13 (-436 *3) (-1011))))) @@ -1632,31 +3932,40 @@ (-12 (-5 *2 (-1166 *3)) (-4 *3 (-38 (-413 (-570)))) (-5 *1 (-1172 *3)))) ((*1 *1 *1) (-4 *1 (-1215)))) -(((*1 *2 *2 *1) (-12 (-4 *1 (-1130 *2)) (-4 *2 (-1227))))) -(((*1 *2 *3 *3 *3 *4 *5 *3 *6) - (-12 (-5 *3 (-570)) (-5 *4 (-695 (-227))) (-5 *5 (-227)) - (-5 *6 (-3 (|:| |fn| (-394)) (|:| |fp| (-74 FCN)))) (-5 *2 (-1044)) - (-5 *1 (-752))))) -(((*1 *1 *1 *1 *2) - (|partial| -12 (-5 *2 (-112)) (-5 *1 (-601 *3)) (-4 *3 (-1058))))) -(((*1 *2 *1) (-12 (-4 *1 (-560 *2)) (-4 *2 (-13 (-410) (-1212)))))) +(((*1 *2 *1 *3 *4 *4 *5) + (-12 (-5 *3 (-950 (-227))) (-5 *4 (-880)) (-5 *5 (-928)) + (-5 *2 (-1282)) (-5 *1 (-474)))) + ((*1 *2 *1 *3) + (-12 (-5 *3 (-950 (-227))) (-5 *2 (-1282)) (-5 *1 (-474)))) + ((*1 *2 *1 *3 *4 *4 *5) + (-12 (-5 *3 (-650 (-950 (-227)))) (-5 *4 (-880)) (-5 *5 (-928)) + (-5 *2 (-1282)) (-5 *1 (-474))))) +(((*1 *2 *3 *3 *3 *3 *4 *4 *4 *3 *5) + (-12 (-5 *3 (-570)) (-5 *4 (-695 (-227))) + (-5 *5 (-3 (|:| |fn| (-394)) (|:| |fp| (-66 FUNCT1)))) + (-5 *2 (-1044)) (-5 *1 (-759))))) (((*1 *2 *1) - (-12 (-4 *1 (-372 *3)) (-4 *3 (-174)) (-4 *3 (-562)) - (-5 *2 (-1182 *3))))) -(((*1 *2 *2 *2) - (-12 (-4 *3 (-368)) (-5 *1 (-772 *2 *3)) (-4 *2 (-714 *3)))) - ((*1 *1 *1 *1) (-12 (-4 *1 (-858 *2)) (-4 *2 (-1058)) (-4 *2 (-368))))) + (-12 (-5 *2 (-650 (-2 (|:| |k| (-678 *3)) (|:| |c| *4)))) + (-5 *1 (-633 *3 *4 *5)) (-4 *3 (-856)) + (-4 *4 (-13 (-174) (-723 (-413 (-570))))) (-14 *5 (-928))))) +(((*1 *2 *2) + (-12 (-5 *2 (-650 *6)) (-4 *6 (-1074 *3 *4 *5)) (-4 *3 (-148)) + (-4 *3 (-311)) (-4 *3 (-562)) (-4 *4 (-799)) (-4 *5 (-856)) + (-5 *1 (-986 *3 *4 *5 *6))))) +(((*1 *2 *1 *3) + (-12 (-5 *2 (-650 (-1168))) (-5 *1 (-1072)) (-5 *3 (-1168))))) +(((*1 *2 *2) (|partial| -12 (-4 *1 (-992 *2)) (-4 *2 (-1212))))) (((*1 *2 *3) - (-12 (-5 *3 (-413 *5)) (-4 *5 (-1253 *4)) (-4 *4 (-562)) - (-4 *4 (-1058)) (-4 *2 (-1268 *4)) (-5 *1 (-1271 *4 *5 *6 *2)) - (-4 *6 (-662 *5))))) -(((*1 *2 *1) (-12 (-5 *2 (-1144)) (-5 *1 (-1160))))) -(((*1 *2 *1) - (|partial| -12 (-5 *2 (-1070 (-1033 *3) (-1182 (-1033 *3)))) - (-5 *1 (-1033 *3)) (-4 *3 (-13 (-854) (-368) (-1031)))))) -(((*1 *2 *3 *4) - (-12 (-5 *2 (-2 (|:| |part1| *3) (|:| |part2| *4))) - (-5 *1 (-711 *3 *4)) (-4 *3 (-1227)) (-4 *4 (-1227))))) + (-12 (-5 *3 (-650 *7)) (-4 *7 (-1074 *4 *5 *6)) (-4 *4 (-562)) + (-4 *5 (-799)) (-4 *6 (-856)) (-5 *2 (-112)) + (-5 *1 (-986 *4 *5 *6 *7))))) +(((*1 *2 *1) (|partial| -12 (-5 *2 (-1182 *1)) (-4 *1 (-1021))))) +(((*1 *2 *3 *4 *5 *6 *7 *8 *9) + (|partial| -12 (-5 *4 (-650 *11)) (-5 *5 (-650 (-1182 *9))) + (-5 *6 (-650 *9)) (-5 *7 (-650 *12)) (-5 *8 (-650 (-777))) + (-4 *11 (-856)) (-4 *9 (-311)) (-4 *12 (-956 *9 *10 *11)) + (-4 *10 (-799)) (-5 *2 (-650 (-1182 *12))) + (-5 *1 (-713 *10 *11 *9 *12)) (-5 *3 (-1182 *12))))) (((*1 *2 *2) (-12 (-4 *3 (-562)) (-5 *1 (-279 *3 *2)) (-4 *2 (-13 (-436 *3) (-1011))))) @@ -1673,64 +3982,40 @@ (-12 (-5 *2 (-1166 *3)) (-4 *3 (-38 (-413 (-570)))) (-5 *1 (-1172 *3)))) ((*1 *1 *1) (-4 *1 (-1215)))) -(((*1 *2 *3 *4) - (-12 (-5 *4 (-650 *3)) (-4 *3 (-1253 *5)) (-4 *5 (-311)) - (-5 *2 (-777)) (-5 *1 (-461 *5 *3))))) -(((*1 *2 *3) - (|partial| -12 - (-5 *3 - (-2 (|:| |var| (-1186)) (|:| |fn| (-320 (-227))) - (|:| -4388 (-1103 (-849 (-227)))) (|:| |abserr| (-227)) - (|:| |relerr| (-227)))) - (-5 *2 (-2 (|:| -4296 (-115)) (|:| |w| (-227)))) (-5 *1 (-206))))) -(((*1 *1 *2) (-12 (-5 *2 (-1168)) (-5 *1 (-585))))) -(((*1 *2 *3 *4 *5 *6) - (|partial| -12 (-5 *4 (-1 *8 *8)) - (-5 *5 - (-1 (-3 (-2 (|:| -3491 *7) (|:| |coeff| *7)) "failed") *7)) - (-5 *6 (-650 (-413 *8))) (-4 *7 (-368)) (-4 *8 (-1253 *7)) - (-5 *3 (-413 *8)) - (-5 *2 - (-2 - (|:| |answer| - (-2 (|:| |mainpart| *3) - (|:| |limitedlogs| - (-650 (-2 (|:| |coeff| *3) (|:| |logand| *3)))))) - (|:| |a0| *7))) - (-5 *1 (-580 *7 *8))))) -(((*1 *2) - (-12 (-5 *2 (-112)) (-5 *1 (-1166 *3)) (-4 *3 (-1109)) - (-4 *3 (-1227))))) -(((*1 *2 *3 *4) - (-12 (-5 *3 (-1182 *1)) (-5 *4 (-1186)) (-4 *1 (-27)) - (-5 *2 (-650 *1)))) - ((*1 *2 *3) (-12 (-5 *3 (-1182 *1)) (-4 *1 (-27)) (-5 *2 (-650 *1)))) - ((*1 *2 *3) (-12 (-5 *3 (-959 *1)) (-4 *1 (-27)) (-5 *2 (-650 *1)))) - ((*1 *2 *1 *3) - (-12 (-5 *3 (-1186)) (-4 *4 (-562)) (-5 *2 (-650 *1)) - (-4 *1 (-29 *4)))) - ((*1 *2 *1) (-12 (-4 *3 (-562)) (-5 *2 (-650 *1)) (-4 *1 (-29 *3)))) - ((*1 *2 *3 *4 *5) - (-12 (-5 *3 (-320 (-227))) (-5 *4 (-650 (-1186))) - (-5 *5 (-1103 (-849 (-227)))) (-5 *2 (-1166 (-227))) (-5 *1 (-304))))) -(((*1 *2 *3 *4 *4 *2 *2 *2 *2) - (-12 (-5 *2 (-570)) - (-5 *3 - (-2 (|:| |lcmfij| *6) (|:| |totdeg| (-777)) (|:| |poli| *4) - (|:| |polj| *4))) - (-4 *6 (-799)) (-4 *4 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*2 *3 *3 *4 *5 *5) - (-12 (-5 *5 (-112)) (-4 *6 (-458)) (-4 *7 (-799)) (-4 *8 (-856)) - (-4 *3 (-1074 *6 *7 *8)) - (-5 *2 (-650 (-2 (|:| |val| *3) (|:| -2140 *4)))) - (-5 *1 (-1081 *6 *7 *8 *3 *4)) (-4 *4 (-1080 *6 *7 *8 *3)))) - ((*1 *2 *3 *4 *5) - (-12 (-5 *3 (-650 (-2 (|:| |val| (-650 *8)) (|:| -2140 *9)))) - (-5 *5 (-112)) (-4 *8 (-1074 *6 *7 *4)) (-4 *9 (-1080 *6 *7 *4 *8)) - (-4 *6 (-458)) (-4 *7 (-799)) (-4 *4 (-856)) - (-5 *2 (-650 (-2 (|:| |val| *8) (|:| -2140 *9)))) - (-5 *1 (-1081 *6 *7 *4 *8 *9))))) + (-12 (-5 *3 (-650 (-570))) (-5 *2 (-570)) (-5 *1 (-492 *4)) + (-4 *4 (-1253 *2))))) (((*1 *2 *2) (-12 (-4 *3 (-562)) (-5 *1 (-279 *3 *2)) (-4 *2 (-13 (-436 *3) (-1011))))) @@ -1815,31 +4092,72 @@ (-12 (-5 *2 (-1166 *3)) (-4 *3 (-38 (-413 (-570)))) (-5 *1 (-1172 *3)))) ((*1 *1 *1) (-4 *1 (-1215)))) -(((*1 *2 *1) (-12 (-5 *1 (-1035 *2)) (-4 *2 (-1227))))) -(((*1 *2 *3 *3 *4 *3 *4 *4 *4 *5 *5 *5 *5 *4 *4 *6 *7) - (-12 (-5 *4 (-570)) (-5 *5 (-695 (-227))) - (-5 *6 (-3 (|:| |fn| 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+ (-12 (-5 *2 (-1186)) (-5 *1 (-710 *3)) (-4 *3 (-620 (-542))))) + ((*1 *2 *3 *2 *4) + (-12 (-5 *4 (-650 (-1186))) (-5 *2 (-1186)) (-5 *1 (-710 *3)) + (-4 *3 (-620 (-542)))))) +(((*1 *2 *1) + (-12 + (-5 *2 + (-650 + (-2 (|:| |flg| (-3 "nil" "sqfr" "irred" "prime")) (|:| |fctr| *3) + (|:| |xpnt| (-570))))) + (-5 *1 (-424 *3)) (-4 *3 (-562)))) + ((*1 *2 *3 *4 *4 *4) + (-12 (-5 *4 (-777)) (-4 *3 (-354)) (-4 *5 (-1253 *3)) + (-5 *2 (-650 (-1182 *3))) (-5 *1 (-504 *3 *5 *6)) + (-4 *6 (-1253 *5))))) (((*1 *2 *2) (-12 (-4 *3 (-562)) (-5 *1 (-279 *3 *2)) (-4 *2 (-13 (-436 *3) (-1011))))) @@ -1860,533 +4178,413 @@ (-12 (-5 *2 (-1166 *3)) (-4 *3 (-38 (-413 (-570)))) (-5 *1 (-1172 *3)))) ((*1 *1 *1) (-4 *1 (-1215)))) -(((*1 *2 *3 *4) - (-12 (-5 *3 (-695 *8)) (-4 *8 (-956 *5 *7 *6)) - (-4 *5 (-13 (-311) (-148))) (-4 *6 (-13 (-856) (-620 (-1186)))) - (-4 *7 (-799)) - (-5 *2 - (-650 - (-2 (|:| |eqzro| (-650 *8)) (|:| |neqzro| (-650 *8)) - (|:| |wcond| (-650 (-959 *5))) - (|:| |bsoln| - (-2 (|:| 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(-1190)))) ((*1 *1 *2) (-12 (-5 *2 (-335 *4)) (-4 *4 (-13 (-856) (-21))) @@ -8310,14 +8475,14 @@ ((*1 *1 *2) (-12 (-5 *2 (-440)) (-5 *1 (-443)))) ((*1 *1 *2) (-12 - (-5 *2 (-2 (|:| |localSymbols| (-1190)) (|:| -2138 (-650 (-334))))) + (-5 *2 (-2 (|:| |localSymbols| (-1190)) (|:| -2544 (-650 (-334))))) (-4 *1 (-446)))) ((*1 *1 *2) (-12 (-5 *2 (-334)) (-4 *1 (-446)))) ((*1 *1 *2) (-12 (-5 *2 (-650 (-334))) (-4 *1 (-446)))) ((*1 *1 *2) (-12 (-5 *2 (-1277 (-705))) (-4 *1 (-446)))) ((*1 *1 *2) (-12 - (-5 *2 (-2 (|:| |localSymbols| (-1190)) (|:| -2138 (-650 (-334))))) + (-5 *2 (-2 (|:| |localSymbols| (-1190)) (|:| -2544 (-650 (-334))))) (-4 *1 (-447)))) ((*1 *1 *2) (-12 (-5 *2 (-334)) (-4 *1 (-447)))) ((*1 *1 *2) (-12 (-5 *2 (-650 (-334))) (-4 *1 (-447)))) @@ -8386,7 +8551,7 @@ (-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 *2) - (-12 (-5 *2 (-650 (-2 (|:| -3102 *3) (|:| -1850 *4)))) + (-12 (-5 *2 (-650 (-2 (|:| -1777 *3) (|:| 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(-775)))) ((*1 *2 *3) (-12 (-5 *2 (-780)) (-5 *1 (-779 *3)) (-4 *3 (-1227)))) @@ -8431,23 +8596,23 @@ (-5 *2 (-3 (|:| |noa| - (-2 (|:| |fn| (-320 (-227))) (|:| -2495 (-650 (-227))) + (-2 (|:| |fn| (-320 (-227))) (|:| -3392 (-650 (-227))) (|:| |lb| (-650 (-849 (-227)))) (|:| |cf| (-650 (-320 (-227)))) (|:| |ub| (-650 (-849 (-227)))))) (|:| |lsa| (-2 (|:| |lfn| (-650 (-320 (-227)))) - (|:| -2495 (-650 (-227))))))) + (|:| -3392 (-650 (-227))))))) (-5 *1 (-847)))) ((*1 *1 *2) (-12 (-5 *2 - (-2 (|:| |lfn| (-650 (-320 (-227)))) (|:| -2495 (-650 (-227))))) + (-2 (|:| |lfn| (-650 (-320 (-227)))) (|:| -3392 (-650 (-227))))) (-5 *1 (-847)))) ((*1 *1 *2) (-12 (-5 *2 - (-2 (|:| |fn| (-320 (-227))) (|:| -2495 (-650 (-227))) + (-2 (|:| |fn| (-320 (-227))) (|:| -3392 (-650 (-227))) (|:| |lb| (-650 (-849 (-227)))) (|:| |cf| (-650 (-320 (-227)))) (|:| |ub| (-650 (-849 (-227)))))) (-5 *1 (-847)))) @@ -8549,504 +8714,40 @@ (-12 (-5 *2 (-670 *3 *4)) (-4 *3 (-856)) (-4 *4 (-174)) (-5 *1 (-1297 *3 *4))))) 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*3 *4 *5) + (|partial| -12 (-5 *4 (-1 *7 *7)) (-5 *5 (-650 (-413 *7))) + (-4 *7 (-1253 *6)) (-5 *3 (-413 *7)) (-4 *6 (-368)) + (-5 *2 + (-2 (|:| |mainpart| *3) + (|:| |limitedlogs| + (-650 (-2 (|:| |coeff| *3) (|:| |logand| *3)))))) + (-5 *1 (-580 *6 *7))))) (((*1 *2 *3 *4 *3) - (|partial| -12 (-5 *4 (-1 *6 *6)) (-4 *6 (-1253 *5)) (-4 *5 (-368)) - (-5 *2 (-2 (|:| -3491 (-413 *6)) (|:| |coeff| (-413 *6)))) - (-5 *1 (-580 *5 *6)) (-5 *3 (-413 *6))))) -(((*1 *1 *1 *1 *1) (-4 *1 (-551)))) + (-12 (-5 *3 (-570)) (-5 *4 (-695 (-227))) (-5 *2 (-1044)) + (-5 *1 (-753))))) +(((*1 *2 *1) (-12 (-5 *2 (-777)) (-5 *1 (-424 *3)) (-4 *3 (-562)))) + ((*1 *2 *3) + (-12 (-5 *3 (-650 (-2 (|:| -2356 *4) (|:| -2676 (-570))))) + (-4 *4 (-1253 (-570))) (-5 *2 (-777)) (-5 *1 (-448 *4))))) (((*1 *2 *3 *4) (-12 (-5 *3 (-650 (-413 (-959 (-570))))) (-5 *2 (-650 (-650 (-298 (-959 *4))))) (-5 *1 (-385 *4)) @@ -10471,7 +11226,7 @@ (|partial| -12 (-5 *5 (-1186)) (-4 *6 (-13 (-311) (-1047 (-570)) (-645 (-570)) (-148))) (-4 *4 (-13 (-29 *6) (-1212) (-966))) - (-5 *2 (-2 (|:| |particular| *4) (|:| -4055 (-650 *4)))) + (-5 *2 (-2 (|:| |particular| *4) (|:| -3491 (-650 *4)))) (-5 *1 (-658 *6 *4 *3)) (-4 *3 (-662 *4)))) ((*1 *2 *3 *2 *4 *2 *5) (|partial| -12 (-5 *4 (-1186)) (-5 *5 (-650 *2)) @@ -10482,40 +11237,40 @@ (-12 (-5 *3 (-695 *5)) (-4 *5 (-368)) (-5 *2 (-2 (|:| |particular| (-3 (-1277 *5) "failed")) - (|:| -4055 (-650 (-1277 *5))))) + (|:| -3491 (-650 (-1277 *5))))) (-5 *1 (-673 *5)) (-5 *4 (-1277 *5)))) ((*1 *2 *3 *4) (-12 (-5 *3 (-650 (-650 *5))) (-4 *5 (-368)) (-5 *2 (-2 (|:| |particular| (-3 (-1277 *5) "failed")) - (|:| -4055 (-650 (-1277 *5))))) + (|:| -3491 (-650 (-1277 *5))))) (-5 *1 (-673 *5)) (-5 *4 (-1277 *5)))) ((*1 *2 *3 *4) (-12 (-5 *3 (-695 *5)) (-4 *5 (-368)) (-5 *2 (-650 (-2 (|:| |particular| (-3 (-1277 *5) "failed")) - (|:| -4055 (-650 (-1277 *5)))))) + (|:| -3491 (-650 (-1277 *5)))))) (-5 *1 (-673 *5)) (-5 *4 (-650 (-1277 *5))))) ((*1 *2 *3 *4) (-12 (-5 *3 (-650 (-650 *5))) (-4 *5 (-368)) (-5 *2 (-650 (-2 (|:| |particular| (-3 (-1277 *5) "failed")) - (|:| -4055 (-650 (-1277 *5)))))) + (|:| -3491 (-650 (-1277 *5)))))) (-5 *1 (-673 *5)) (-5 *4 (-650 (-1277 *5))))) ((*1 *2 *3 *4) (-12 (-4 *5 (-368)) (-4 *6 (-13 (-378 *5) (-10 -7 (-6 -4453)))) (-4 *4 (-13 (-378 *5) (-10 -7 (-6 -4453)))) (-5 *2 - (-2 (|:| |particular| (-3 *4 "failed")) (|:| -4055 (-650 *4)))) + (-2 (|:| |particular| (-3 *4 "failed")) (|:| -3491 (-650 *4)))) (-5 *1 (-674 *5 *6 *4 *3)) (-4 *3 (-693 *5 *6 *4)))) ((*1 *2 *3 *4) (-12 (-4 *5 (-368)) (-4 *6 (-13 (-378 *5) (-10 -7 (-6 -4453)))) (-4 *7 (-13 (-378 *5) (-10 -7 (-6 -4453)))) (-5 *2 (-650 - (-2 (|:| |particular| (-3 *7 "failed")) (|:| -4055 (-650 *7))))) + (-2 (|:| |particular| (-3 *7 "failed")) (|:| -3491 (-650 *7))))) (-5 *1 (-674 *5 *6 *7 *3)) (-5 *4 (-650 *7)) (-4 *3 (-693 *5 *6 *7)))) ((*1 *2 *3 *4) @@ -10533,7 +11288,7 @@ (-4 *7 (-13 (-29 *6) (-1212) (-966))) (-4 *6 (-13 (-311) (-1047 (-570)) (-645 (-570)) (-148))) (-5 *2 - (-2 (|:| |particular| (-1277 *7)) (|:| -4055 (-650 (-1277 *7))))) + (-2 (|:| |particular| (-1277 *7)) (|:| -3491 (-650 (-1277 *7))))) (-5 *1 (-808 *6 *7)) (-5 *4 (-1277 *7)))) ((*1 *2 *3 *4) (|partial| -12 (-5 *3 (-695 *6)) (-5 *4 (-1186)) @@ -10545,27 +11300,27 @@ (-5 *5 (-1186)) (-4 *7 (-13 (-29 *6) (-1212) (-966))) (-4 *6 (-13 (-311) (-1047 (-570)) (-645 (-570)) (-148))) (-5 *2 - (-2 (|:| |particular| (-1277 *7)) (|:| -4055 (-650 (-1277 *7))))) + (-2 (|:| |particular| (-1277 *7)) (|:| -3491 (-650 (-1277 *7))))) (-5 *1 (-808 *6 *7)))) ((*1 *2 *3 *4 *5) (|partial| -12 (-5 *3 (-650 *7)) (-5 *4 (-650 (-115))) (-5 *5 (-1186)) (-4 *7 (-13 (-29 *6) (-1212) (-966))) (-4 *6 (-13 (-311) (-1047 (-570)) (-645 (-570)) (-148))) (-5 *2 - (-2 (|:| |particular| (-1277 *7)) (|:| -4055 (-650 (-1277 *7))))) + (-2 (|:| |particular| (-1277 *7)) (|:| -3491 (-650 (-1277 *7))))) (-5 *1 (-808 *6 *7)))) ((*1 *2 *3 *4 *5) (-12 (-5 *3 (-298 *7)) (-5 *4 (-115)) (-5 *5 (-1186)) (-4 *7 (-13 (-29 *6) (-1212) (-966))) (-4 *6 (-13 (-311) (-1047 (-570)) (-645 (-570)) (-148))) (-5 *2 - (-3 (-2 (|:| |particular| *7) (|:| -4055 (-650 *7))) *7 "failed")) + (-3 (-2 (|:| |particular| *7) (|:| -3491 (-650 *7))) *7 "failed")) (-5 *1 (-808 *6 *7)))) ((*1 *2 *3 *4 *5) (-12 (-5 *4 (-115)) (-5 *5 (-1186)) (-4 *6 (-13 (-311) (-1047 (-570)) (-645 (-570)) (-148))) (-5 *2 - (-3 (-2 (|:| |particular| *3) (|:| -4055 (-650 *3))) *3 "failed")) + (-3 (-2 (|:| |particular| *3) (|:| -3491 (-650 *3))) *3 "failed")) (-5 *1 (-808 *6 *3)) (-4 *3 (-13 (-29 *6) (-1212) (-966))))) ((*1 *2 *3 *4 *3 *5) (|partial| -12 (-5 *3 (-298 *2)) (-5 *4 (-115)) (-5 *5 (-650 *2)) @@ -10601,10 +11356,10 @@ (|partial| -12 (-5 *5 (-1 - (-3 (-2 (|:| |particular| *6) (|:| -4055 (-650 *6))) "failed") + (-3 (-2 (|:| |particular| *6) (|:| -3491 (-650 *6))) "failed") *7 *6)) (-4 *6 (-368)) (-4 *7 (-662 *6)) - (-5 *2 (-2 (|:| |particular| (-1277 *6)) (|:| -4055 (-695 *6)))) + (-5 *2 (-2 (|:| |particular| (-1277 *6)) (|:| -3491 (-695 *6)))) (-5 *1 (-819 *6 *7)) (-5 *3 (-695 *6)) (-5 *4 (-1277 *6)))) ((*1 *2 *3) (-12 (-5 *3 (-905)) (-5 *2 (-1044)) (-5 *1 (-904)))) ((*1 *2 *3 *4) @@ -10677,1127 +11432,202 @@ ((*1 *2 *3) (-12 (-4 *4 (-562)) (-5 *2 (-650 (-298 (-413 (-959 *4))))) (-5 *1 (-1195 *4)) (-5 *3 (-298 (-413 (-959 *4))))))) -(((*1 *2 *1) (-12 (-5 *2 (-777)) (-5 *1 (-129))))) +(((*1 *2 *3 *4 *4 *4 *4 *5 *5) + (-12 (-5 *3 (-1 (-384) (-384))) (-5 *4 (-384)) + (-5 *2 + (-2 (|:| -4126 *4) (|:| -3022 *4) (|:| |totalpts| (-570)) + (|:| |success| (-112)))) + (-5 *1 (-795)) (-5 *5 (-570))))) +(((*1 *2 *3 *4 *5) + (-12 (-5 *3 (-1 (-112) *6 *6)) (-4 *6 (-856)) (-5 *4 (-650 *6)) + (-5 *2 (-2 (|:| |fs| (-112)) (|:| |sd| *4) (|:| |td| (-650 *4)))) + (-5 *1 (-1197 *6)) (-5 *5 (-650 *4))))) +(((*1 *2 *1) (-12 (-5 *2 (-650 (-570))) (-5 *1 (-278))))) +(((*1 *2 *1) + (-12 (-4 *2 (-956 *3 *5 *4)) (-5 *1 (-996 *3 *4 *5 *2)) + (-4 *3 (-458)) (-4 *4 (-856)) (-4 *5 (-799))))) +(((*1 *2 *3 *4) + (-12 (-5 *3 (-650 *5)) (-5 *4 (-928)) (-4 *5 (-856)) + (-5 *2 (-59 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\ No newline at end of file |