diff options
| author | dos-reis <gdr@axiomatics.org> | 2010-04-20 16:10:58 +0000 |
|---|---|---|
| committer | dos-reis <gdr@axiomatics.org> | 2010-04-20 16:10:58 +0000 |
| commit | dca6da4bba9a14e544345d4b54f623450d47f283 (patch) | |
| tree | 2aa135df859572bc4e886e10ada08217c57ce413 /src/share | |
| parent | 6fa5b85a7a68ad4422b98eb982a2a44998d6ee53 (diff) | |
| download | open-axiom-dca6da4bba9a14e544345d4b54f623450d47f283.tar.gz | |
* interp/compiler.boot (joinIntegerModes): New.
(compIntegerValue): Likewise.
(compStepIterator): Likewise.
(compIterate): Use it.
* algebra/prtition.spad.pamphlet (Partition): Now CoercibleTo List
PositiveInteger.
* algebra/permgrps.spad.pamphlet (PermutationGroupExamples):
Operate on positive integers only.
* algebra/partperm.spad.pamphlet
(partitions$PartitionsAndPermutations): Operate on positive
integers only.
* algebra/cycles.spad.pamphlet (alternating$CycleIndicators): Now
accepts positive integer argument only.
(cyclic$CycleIndicators): Likewise.
(dihedral$CycleIndicators): Likewise.
Diffstat (limited to 'src/share')
| -rw-r--r-- | src/share/algebra/browse.daase | 636 | ||||
| -rw-r--r-- | src/share/algebra/category.daase | 1396 | ||||
| -rw-r--r-- | src/share/algebra/compress.daase | 1328 | ||||
| -rw-r--r-- | src/share/algebra/interp.daase | 9004 | ||||
| -rw-r--r-- | src/share/algebra/operation.daase | 26074 |
5 files changed, 19220 insertions, 19218 deletions
diff --git a/src/share/algebra/browse.daase b/src/share/algebra/browse.daase index 4fa3e44f..a041b7cb 100644 --- a/src/share/algebra/browse.daase +++ b/src/share/algebra/browse.daase @@ -1,5 +1,5 @@ -(2268134 . 3480583732) +(2268134 . 3480761524) (-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 -1674) +(-32 R -1707) ((|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 -1674 UP UPUP -2532) +(-40 -1707 UP UPUP -1552) ((|constructor| (NIL "Function field defined by \\spad{f}(\\spad{x},{} \\spad{y}) = 0.")) (|knownInfBasis| (((|Void|) (|NonNegativeInteger|)) "\\spad{knownInfBasis(n)} \\undocumented{}"))) ((-4442 |has| (-413 |#2|) (-368)) (-4447 |has| (-413 |#2|) (-368)) (-4441 |has| (-413 |#2|) (-368)) ((-4451 "*") . T) (-4443 . T) (-4444 . T) (-4446 . T)) -((|HasCategory| (-413 |#2|) (QUOTE (-146))) (|HasCategory| (-413 |#2|) (QUOTE (-148))) (|HasCategory| (-413 |#2|) (QUOTE (-354))) (-2740 (|HasCategory| (-413 |#2|) (QUOTE (-368))) (|HasCategory| (-413 |#2|) (QUOTE (-354)))) (|HasCategory| (-413 |#2|) (QUOTE (-368))) (|HasCategory| (-413 |#2|) (QUOTE (-373))) (-2740 (-12 (|HasCategory| (-413 |#2|) (QUOTE (-235))) (|HasCategory| (-413 |#2|) (QUOTE (-368)))) (|HasCategory| (-413 |#2|) (QUOTE (-354)))) (-2740 (-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)))) (-2740 (|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 -1674) +((|HasCategory| (-413 |#2|) (QUOTE (-146))) (|HasCategory| (-413 |#2|) (QUOTE (-148))) (|HasCategory| (-413 |#2|) (QUOTE (-354))) (-2892 (|HasCategory| (-413 |#2|) (QUOTE (-368))) (|HasCategory| (-413 |#2|) (QUOTE (-354)))) (|HasCategory| (-413 |#2|) (QUOTE (-368))) (|HasCategory| (-413 |#2|) (QUOTE (-373))) (-2892 (-12 (|HasCategory| (-413 |#2|) (QUOTE (-235))) (|HasCategory| (-413 |#2|) (QUOTE (-368)))) (|HasCategory| (-413 |#2|) (QUOTE (-354)))) (-2892 (-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)))) (-2892 (|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 -1707) ((|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."))) ((-4449 . T) (-4450 . T)) -((-2740 (-12 (|HasCategory| (-2 (|:| -2013 |#1|) (|:| -2224 |#2|)) (QUOTE (-856))) (|HasCategory| (-2 (|:| -2013 |#1|) (|:| -2224 |#2|)) (LIST (QUOTE -313) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -2013) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -2224) (|devaluate| |#2|)))))) (-12 (|HasCategory| (-2 (|:| -2013 |#1|) (|:| -2224 |#2|)) (QUOTE (-1109))) (|HasCategory| (-2 (|:| -2013 |#1|) (|:| -2224 |#2|)) (LIST (QUOTE -313) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -2013) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -2224) (|devaluate| |#2|))))))) (-2740 (|HasCategory| (-2 (|:| -2013 |#1|) (|:| -2224 |#2|)) (QUOTE (-856))) (|HasCategory| (-2 (|:| -2013 |#1|) (|:| -2224 |#2|)) (QUOTE (-1109))) (|HasCategory| (-2 (|:| -2013 |#1|) (|:| -2224 |#2|)) (LIST (QUOTE -619) (QUOTE (-868)))) (|HasCategory| |#2| (QUOTE (-1109))) (|HasCategory| |#2| (LIST (QUOTE -619) (QUOTE (-868))))) (|HasCategory| (-2 (|:| -2013 |#1|) (|:| -2224 |#2|)) (LIST (QUOTE -620) (QUOTE (-542)))) (-12 (|HasCategory| |#2| (QUOTE (-1109))) (|HasCategory| |#2| (LIST (QUOTE -313) (|devaluate| |#2|)))) (-2740 (|HasCategory| (-2 (|:| -2013 |#1|) (|:| -2224 |#2|)) (QUOTE (-856))) (|HasCategory| (-2 (|:| -2013 |#1|) (|:| -2224 |#2|)) (QUOTE (-1109))) (|HasCategory| |#2| (QUOTE (-1109)))) (|HasCategory| (-2 (|:| -2013 |#1|) (|:| -2224 |#2|)) (QUOTE (-856))) (|HasCategory| |#1| (QUOTE (-856))) (|HasCategory| |#2| (QUOTE (-1109))) (|HasCategory| (-570) (QUOTE (-856))) (|HasCategory| (-2 (|:| -2013 |#1|) (|:| -2224 |#2|)) (QUOTE (-1109))) (-2740 (|HasCategory| (-2 (|:| -2013 |#1|) (|:| -2224 |#2|)) (LIST (QUOTE -619) (QUOTE (-868)))) (|HasCategory| |#2| (LIST (QUOTE -619) (QUOTE (-868))))) (-2740 (|HasCategory| (-2 (|:| -2013 |#1|) (|:| -2224 |#2|)) (QUOTE (-1109))) (|HasCategory| |#2| (QUOTE (-1109)))) (|HasCategory| |#2| (LIST (QUOTE -619) (QUOTE (-868)))) (|HasCategory| (-2 (|:| -2013 |#1|) (|:| -2224 |#2|)) (LIST (QUOTE -619) (QUOTE (-868)))) (-12 (|HasCategory| (-2 (|:| -2013 |#1|) (|:| -2224 |#2|)) (QUOTE (-1109))) (|HasCategory| (-2 (|:| -2013 |#1|) (|:| -2224 |#2|)) (LIST (QUOTE -313) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -2013) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -2224) (|devaluate| |#2|))))))) +((-2892 (-12 (|HasCategory| (-2 (|:| -2106 |#1|) (|:| -2339 |#2|)) (QUOTE (-856))) (|HasCategory| (-2 (|:| -2106 |#1|) (|:| -2339 |#2|)) (LIST (QUOTE -313) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -2106) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -2339) (|devaluate| |#2|)))))) (-12 (|HasCategory| (-2 (|:| -2106 |#1|) (|:| -2339 |#2|)) (QUOTE (-1109))) (|HasCategory| (-2 (|:| -2106 |#1|) (|:| -2339 |#2|)) (LIST (QUOTE -313) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -2106) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -2339) (|devaluate| |#2|))))))) (-2892 (|HasCategory| (-2 (|:| -2106 |#1|) (|:| -2339 |#2|)) (QUOTE (-856))) (|HasCategory| (-2 (|:| -2106 |#1|) (|:| -2339 |#2|)) (QUOTE (-1109))) (|HasCategory| (-2 (|:| -2106 |#1|) (|:| -2339 |#2|)) (LIST (QUOTE -619) (QUOTE (-868)))) (|HasCategory| |#2| (QUOTE (-1109))) (|HasCategory| |#2| (LIST (QUOTE -619) (QUOTE (-868))))) (|HasCategory| (-2 (|:| -2106 |#1|) (|:| -2339 |#2|)) (LIST (QUOTE -620) (QUOTE (-542)))) (-12 (|HasCategory| |#2| (QUOTE (-1109))) (|HasCategory| |#2| (LIST (QUOTE -313) (|devaluate| |#2|)))) (-2892 (|HasCategory| (-2 (|:| -2106 |#1|) (|:| -2339 |#2|)) (QUOTE (-856))) (|HasCategory| (-2 (|:| -2106 |#1|) (|:| -2339 |#2|)) (QUOTE (-1109))) (|HasCategory| |#2| (QUOTE (-1109)))) (|HasCategory| (-2 (|:| -2106 |#1|) (|:| -2339 |#2|)) (QUOTE (-856))) (|HasCategory| |#1| (QUOTE (-856))) (|HasCategory| |#2| (QUOTE (-1109))) (|HasCategory| (-570) (QUOTE (-856))) (|HasCategory| (-2 (|:| -2106 |#1|) (|:| -2339 |#2|)) (QUOTE (-1109))) (-2892 (|HasCategory| (-2 (|:| -2106 |#1|) (|:| -2339 |#2|)) (LIST (QUOTE -619) (QUOTE (-868)))) (|HasCategory| |#2| (LIST (QUOTE -619) (QUOTE (-868))))) (-2892 (|HasCategory| (-2 (|:| -2106 |#1|) (|:| -2339 |#2|)) (QUOTE (-1109))) (|HasCategory| |#2| (QUOTE (-1109)))) (|HasCategory| |#2| (LIST (QUOTE -619) (QUOTE (-868)))) (|HasCategory| (-2 (|:| -2106 |#1|) (|:| -2339 |#2|)) (LIST (QUOTE -619) (QUOTE (-868)))) (-12 (|HasCategory| (-2 (|:| -2106 |#1|) (|:| -2339 |#2|)) (QUOTE (-1109))) (|HasCategory| (-2 (|:| -2106 |#1|) (|:| -2339 |#2|)) (LIST (QUOTE -313) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -2106) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -2339) (|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| $) "\\spad{leadingCoefficient(p)} returns the coefficient highest degree term of \\spad{p}."))) NIL @@ -144,7 +144,7 @@ NIL ((|constructor| (NIL "\\spad{ApplyUnivariateSkewPolynomial} (internal) allows univariate skew polynomials to be applied to appropriate modules.")) (|apply| ((|#2| |#3| (|Mapping| |#2| |#2|) |#2|) "\\spad{apply(p, f, m)} returns \\spad{p(m)} where the action is given by \\spad{x m = f(m)}. \\spad{f} must be an \\spad{R}-pseudo linear map on \\spad{M}."))) NIL NIL -(-54 |Base| R -1674) +(-54 |Base| R -1707) ((|constructor| (NIL "This package apply rewrite rules to expressions,{} calling the pattern matcher.")) (|localUnquote| ((|#3| |#3| (|List| (|Symbol|))) "\\spad{localUnquote(f,ls)} is a local function.")) (|applyRules| ((|#3| (|List| (|RewriteRule| |#1| |#2| |#3|)) |#3| (|PositiveInteger|)) "\\spad{applyRules([r1,...,rn], expr, n)} applies the rules \\spad{r1},{}...,{}\\spad{rn} to \\spad{f} a most \\spad{n} times.") ((|#3| (|List| (|RewriteRule| |#1| |#2| |#3|)) |#3|) "\\spad{applyRules([r1,...,rn], expr)} applies the rules \\spad{r1},{}...,{}\\spad{rn} to \\spad{f} an unlimited number of times,{} \\spadignore{i.e.} until none of \\spad{r1},{}...,{}\\spad{rn} is applicable to the expression."))) NIL NIL @@ -167,64 +167,64 @@ NIL (-59 S) ((|constructor| (NIL "This is the domain of 1-based one dimensional arrays")) (|oneDimensionalArray| (($ (|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}"))) ((-4450 . T) (-4449 . T)) -((-2740 (-12 (|HasCategory| |#1| (QUOTE (-856))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|))))) (-2740 (-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)))) (-2740 (|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|))))) +((-2892 (-12 (|HasCategory| |#1| (QUOTE (-856))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|))))) (-2892 (-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)))) (-2892 (|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}."))) ((-4449 . T) (-4450 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1109))) (-2740 (-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 -3504) +((-12 (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1109))) (-2892 (-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 -3599) ((|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 -3504) +(-62 -3599) ((|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 -3504) +(-63 -3599) ((|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 -3504) +(-64 -3599) ((|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 -3504) +(-65 -3599) ((|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 -3504) +(-66 -3599) ((|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 -3504) +(-67 -3599) ((|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 -3504) +(-68 -3599) ((|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 -3504) +(-69 -3599) ((|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 -3504) +(-70 -3599) ((|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 -3504) +(-71 -3599) ((|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 -3504) +(-72 -3599) ((|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 -3504) +(-73 -3599) ((|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 -3504) +(-74 -3599) ((|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 -3504) +(-77 -3599) ((|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 -3504) +(-78 -3599) ((|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 -3504) +(-79 -3599) ((|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 -3504) +(-80 -3599) ((|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 -3504) +(-81 -3599) ((|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 -3504) +(-82 -3599) ((|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 -3504) +(-83 -3599) ((|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 -3504) +(-84 -3599) ((|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 -3504) +(-85 -3599) ((|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 -3504) +(-86 -3599) ((|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 -3504) +(-87 -3599) ((|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 -3504) +(-88 -3599) ((|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 -3504) +(-89 -3599) ((|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}."))) ((-4449 . T) (-4450 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1109))) (-2740 (-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))) (-2892 (-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}."))) ((-4449 . T) (-4450 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1109))) (-2740 (-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))) (-2892 (-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."))) ((-4441 . T) (-4447 . T) (-4442 . T) ((-4451 "*") . T) (-4443 . T) (-4444 . T) (-4446 . 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))) (-2740 (|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)))) (-2740 (-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))) (-2892 (|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)))) (-2892 (-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 -1674 UP) +(-116 -1707 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}."))) ((-4441 . T) (-4447 . T) (-4442 . T) ((-4451 "*") . T) (-4443 . T) (-4444 . T) (-4446 . 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))) (-2740 (|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)))) (-2740 (-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))) (-2892 (|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)))) (-2892 (-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"))) ((-4449 . T) (-4450 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1109))) (-2740 (-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))) (-2892 (-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."))) ((-4449 . T) (-4450 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1109))) (-2740 (-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))) (-2892 (-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."))) ((-4449 . T) (-4450 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1109))) (-2740 (-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))) (-2892 (-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."))) ((-4450 . T) (-4449 . T)) -((-2740 (-12 (|HasCategory| (-130) (QUOTE (-856))) (|HasCategory| (-130) (LIST (QUOTE -313) (QUOTE (-130))))) (-12 (|HasCategory| (-130) (QUOTE (-1109))) (|HasCategory| (-130) (LIST (QUOTE -313) (QUOTE (-130)))))) (-2740 (-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)))) (-2740 (|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)))))) +((-2892 (-12 (|HasCategory| (-130) (QUOTE (-856))) (|HasCategory| (-130) (LIST (QUOTE -313) (QUOTE (-130))))) (-12 (|HasCategory| (-130) (QUOTE (-1109))) (|HasCategory| (-130) (LIST (QUOTE -313) (QUOTE (-130)))))) (-2892 (-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)))) (-2892 (|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") $ $) "\\spad{x - y} returns an element \\spad{z} such that \\spad{z+y=x} or \"failed\" if no such element exists.")) (|commutative| ((|attribute| "*") "a domain \\spad{D} has \\spad{commutative(\"*\")} if it has an operation \\spad{\"*\": (D,D) -> D} which is commutative."))) (((-4451 "*") . T)) NIL -(-136 |minix| -2408 S T$) +(-136 |minix| -2550 S T$) ((|constructor| (NIL "This package provides functions to enable conversion of tensors given conversion of the components.")) (|map| (((|CartesianTensor| |#1| |#2| |#4|) (|Mapping| |#4| |#3|) (|CartesianTensor| |#1| |#2| |#3|)) "\\spad{map(f,ts)} does a componentwise conversion of the tensor \\spad{ts} to a tensor with components of type \\spad{T}.")) (|reshape| (((|CartesianTensor| |#1| |#2| |#4|) (|List| |#4|) (|CartesianTensor| |#1| |#2| |#3|)) "\\spad{reshape(lt,ts)} organizes the list of components \\spad{lt} into a tensor with the same shape as \\spad{ts}."))) NIL NIL -(-137 |minix| -2408 R) +(-137 |minix| -2550 R) ((|constructor| (NIL "CartesianTensor(minix,{}dim,{}\\spad{R}) provides Cartesian tensors with components belonging to a commutative ring \\spad{R}. These tensors can have any number of indices. Each index takes values from \\spad{minix} to \\spad{minix + dim - 1}.")) (|sample| (($) "\\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| $ (|Integer|)) "\\spad{elt(t,i)} gives a component of a rank 1 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}."))) ((-4449 . T) (-4439 . T) (-4450 . T)) -((-2740 (-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)))))) +((-2892 (-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."))) ((-4446 . T)) NIL -(-149 -1674 UP UPUP) +(-149 -1707 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 -1674) +(-159 R -1707) ((|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 -4445)) (|HasAttribute| |#2| (QUOTE -4448)) (|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})"))) -((-4442 -2740 (|has| |#1| (-562)) (-12 (|has| |#1| (-311)) (|has| |#1| (-916)))) (-4447 |has| |#1| (-368)) (-4441 |has| |#1| (-368)) (-4445 |has| |#1| (-6 -4445)) (-4448 |has| |#1| (-6 -4448)) (-3035 . T) ((-4451 "*") . T) (-4443 . T) (-4444 . T) (-4446 . T)) +((-4442 -2892 (|has| |#1| (-562)) (-12 (|has| |#1| (-311)) (|has| |#1| (-916)))) (-4447 |has| |#1| (-368)) (-4441 |has| |#1| (-368)) (-4445 |has| |#1| (-6 -4445)) (-4448 |has| |#1| (-6 -4448)) (-3175 . T) ((-4451 "*") . T) (-4443 . T) (-4444 . T) (-4446 . 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}."))) -((-4442 -2740 (|has| |#1| (-562)) (-12 (|has| |#1| (-311)) (|has| |#1| (-916)))) (-4447 |has| |#1| (-368)) (-4441 |has| |#1| (-368)) (-4445 |has| |#1| (-6 -4445)) (-4448 |has| |#1| (-6 -4448)) (-3035 . T) ((-4451 "*") . T) (-4443 . T) (-4444 . T) (-4446 . 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T) ((-4451 "*") . T) (-4443 . T) (-4444 . T) (-4446 . T)) +((|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-148))) (|HasCategory| |#1| (QUOTE (-354))) (-2892 (|HasCategory| |#1| (QUOTE (-368))) (|HasCategory| |#1| (QUOTE (-354)))) (|HasCategory| |#1| (QUOTE (-562))) (|HasCategory| |#1| (QUOTE (-368))) (|HasCategory| |#1| (QUOTE (-373))) (-2892 (-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| (QUOTE (-311))) (|HasCategory| |#1| (QUOTE (-354)))) (-12 (|HasCategory| |#1| (QUOTE (-368))) (|HasCategory| |#1| (QUOTE (-354)))) (-12 (|HasCategory| |#1| (QUOTE (-354))) (|HasCategory| |#1| (LIST (QUOTE -290) (|devaluate| |#1|) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-354))) (|HasCategory| |#1| (LIST (QUOTE -645) (QUOTE (-570))))) (-12 (|HasCategory| |#1| (QUOTE (-354))) (|HasCategory| |#1| (LIST (QUOTE -907) (QUOTE (-1186))))) (-12 (|HasCategory| |#1| (QUOTE (-354))) (|HasCategory| |#1| (QUOTE (-373)))) (-12 (|HasCategory| |#1| (QUOTE (-354))) (|HasCategory| |#1| (QUOTE (-562)))) (-12 (|HasCategory| |#1| (QUOTE (-354))) (|HasCategory| |#1| (QUOTE (-834)))) (-12 (|HasCategory| |#1| (QUOTE (-354))) (|HasCategory| |#1| (QUOTE (-1031)))) (-12 (|HasCategory| |#1| (QUOTE (-354))) (|HasCategory| |#1| (QUOTE (-1212)))) (-12 (|HasCategory| |#1| (QUOTE (-354))) (|HasCategory| |#1| (LIST (QUOTE -620) (QUOTE (-542))))) (-12 (|HasCategory| |#1| (QUOTE (-354))) (|HasCategory| |#1| 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(|HasCategory| |#1| (QUOTE (-368))) (|HasCategory| |#1| (QUOTE (-916)))) (-12 (|HasCategory| |#1| (QUOTE (-354))) (|HasCategory| |#1| (QUOTE (-916))))) (-2892 (|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)))) (-2892 (|HasCategory| |#1| (QUOTE (-311))) (|HasCategory| |#1| (QUOTE (-368))) (|HasCategory| |#1| (QUOTE (-354))) (|HasCategory| |#1| (QUOTE (-562)))) (-2892 (|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))) (-2892 (-12 (|HasCategory| |#1| (QUOTE (-311))) (|HasCategory| |#1| (QUOTE (-916)))) (|HasCategory| |#1| (QUOTE (-368)))) (-2892 (-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 -4445)) (|HasAttribute| |#1| (QUOTE -4448)) (-12 (|HasCategory| |#1| (QUOTE (-235))) (|HasCategory| |#1| (QUOTE (-368)))) (-12 (|HasCategory| |#1| (QUOTE (-368))) (|HasCategory| |#1| (LIST (QUOTE -907) (QUOTE (-1186))))) (-2892 (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-311))) (|HasCategory| |#1| (QUOTE (-916)))) (|HasCategory| |#1| (QUOTE (-146)))) (-2892 (-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| $) (|Identifier|)) "\\spad{findConstructor(s)} attempts to find a constructor named \\spad{s}. If successful,{} returns that constructor; otherwise,{} returns \\spad{nothing}."))) NIL NIL -(-190 R -1674) +(-190 R -1707) ((|constructor| (NIL "\\spadtype{ComplexTrigonometricManipulations} provides function that compute the real and imaginary parts of complex functions.")) (|complexForm| (((|Complex| (|Expression| |#1|)) |#2|) "\\spad{complexForm(f)} returns \\spad{[real f, imag f]}.")) (|trigs| ((|#2| |#2|) "\\spad{trigs(f)} rewrites all the complex logs and exponentials appearing in \\spad{f} in terms of trigonometric functions.")) (|real?| (((|Boolean|) |#2|) "\\spad{real?(f)} returns \\spad{true} if \\spad{f = real f}.")) (|imag| (((|Expression| |#1|) |#2|) "\\spad{imag(f)} returns the imaginary part of \\spad{f} where \\spad{f} is a complex function.")) (|real| (((|Expression| |#1|) |#2|) "\\spad{real(f)} returns the real part of \\spad{f} where \\spad{f} is a complex function.")) (|complexElementary| ((|#2| |#2| (|Symbol|)) "\\spad{complexElementary(f, x)} rewrites the kernels of \\spad{f} involving \\spad{x} in terms of the 2 fundamental complex transcendental elementary functions: \\spad{log, exp}.") ((|#2| |#2|) "\\spad{complexElementary(f)} rewrites \\spad{f} in terms of the 2 fundamental complex transcendental elementary functions: \\spad{log, exp}.")) (|complexNormalize| ((|#2| |#2| (|Symbol|)) "\\spad{complexNormalize(f, x)} rewrites \\spad{f} using the least possible number of complex independent kernels involving \\spad{x}.") ((|#2| |#2|) "\\spad{complexNormalize(f)} rewrites \\spad{f} using the least possible number of complex independent kernels."))) NIL NIL @@ -796,23 +796,23 @@ NIL ((|constructor| (NIL "\\indented{1}{This domain implements a simple view of a database whose fields are} indexed by symbols")) (- (($ $ $) "\\spad{db1-db2} returns the difference of databases \\spad{db1} and \\spad{db2} \\spadignore{i.e.} consisting of elements in \\spad{db1} but not in \\spad{db2}")) (+ (($ $ $) "\\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 -1674 UP UPUP R) +(-217 -1707 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 -1674 FP) +(-218 -1707 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."))) ((-4441 . T) (-4447 . T) (-4442 . T) ((-4451 "*") . T) (-4443 . T) (-4444 . T) (-4446 . 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))) (-2740 (|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)))) (-2740 (-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))) (-2892 (|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)))) (-2892 (-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|) $) "\\spad{head(d)} returns the head of the definition \\spad{`d'}. This is a list of identifiers starting with the name of the operation followed by the name of the parameters,{} if any."))) NIL NIL -(-221 R -1674) +(-221 R -1707) ((|constructor| (NIL "\\spadtype{ElementaryFunctionDefiniteIntegration} provides functions to compute definite integrals of elementary functions.")) (|innerint| (((|Union| (|:| |f1| (|OrderedCompletion| |#2|)) (|:| |f2| (|List| (|OrderedCompletion| |#2|))) (|:| |fail| "failed") (|:| |pole| "potentialPole")) |#2| (|Symbol|) (|OrderedCompletion| |#2|) (|OrderedCompletion| |#2|) (|Boolean|)) "\\spad{innerint(f, x, a, b, ignore?)} should be local but conditional")) (|integrate| (((|Union| (|:| |f1| (|OrderedCompletion| |#2|)) (|:| |f2| (|List| (|OrderedCompletion| |#2|))) (|:| |fail| "failed") (|:| |pole| "potentialPole")) |#2| (|SegmentBinding| (|OrderedCompletion| |#2|)) (|String|)) "\\spad{integrate(f, x = a..b, \"noPole\")} returns the integral of \\spad{f(x)dx} from a to \\spad{b}. If it is not possible to check whether \\spad{f} has a pole for \\spad{x} between a and \\spad{b} (because of parameters),{} then this function will assume that \\spad{f} has no such pole. Error: if \\spad{f} has a pole for \\spad{x} between a and \\spad{b} or if the last argument is not \"noPole\".") (((|Union| (|:| |f1| (|OrderedCompletion| |#2|)) (|:| |f2| (|List| (|OrderedCompletion| |#2|))) (|:| |fail| "failed") (|:| |pole| "potentialPole")) |#2| (|SegmentBinding| (|OrderedCompletion| |#2|))) "\\spad{integrate(f, x = a..b)} returns the integral of \\spad{f(x)dx} from a to \\spad{b}. Error: if \\spad{f} has a pole for \\spad{x} between a and \\spad{b}."))) NIL NIL @@ -827,18 +827,18 @@ NIL (-224 S) ((|constructor| (NIL "Linked list implementation of a Dequeue")) (|dequeue| (($ (|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}."))) ((-4449 . T) (-4450 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1109))) (-2740 (-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))) (-2892 (-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}."))) ((-4446 . T)) NIL -(-226 R -1674) +(-226 R -1707) ((|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}."))) -((-3026 . T) (-4441 . T) (-4447 . T) (-4442 . T) ((-4451 "*") . T) (-4443 . T) (-4444 . T) (-4446 . T)) +((-3167 . T) (-4441 . T) (-4447 . T) (-4442 . T) ((-4451 "*") . T) (-4443 . T) (-4444 . T) (-4446 . 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}"))) ((-4449 . T) (-4450 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1109))) (-2740 (-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 (-4451 "*"))) (|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))) (-2892 (-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 (-4451 "*"))) (|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 -2408 R) +(-239 S -2550 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 -4446)) (|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 -2408 R) +(-240 -2550 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"))) ((-4443 |has| |#2| (-1058)) (-4444 |has| |#2| (-1058)) (-4446 |has| |#2| (-6 -4446)) ((-4451 "*") |has| |#2| (-174)) (-4449 . T)) NIL -(-241 -2408 A B) +(-241 -2550 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 -2408 R) +(-242 -2550 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."))) ((-4443 |has| |#2| (-1058)) (-4444 |has| |#2| (-1058)) (-4446 |has| |#2| (-6 -4446)) ((-4451 "*") |has| |#2| (-174)) (-4449 . 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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}"))) ((-4450 . T) (-4449 . T)) -((-2740 (-12 (|HasCategory| |#1| (QUOTE (-856))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|))))) (-2740 (-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)))) (-2740 (|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|))))) +((-2892 (-12 (|HasCategory| |#1| (QUOTE (-856))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|))))) (-2892 (-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)))) (-2892 (|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)))) (-2892 (-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))))) (-2892 (|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)))) (-2892 (|HasAttribute| |#3| (QUOTE -4446)) (-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"))) (((-4451 "*") |has| |#1| (-174)) (-4442 |has| |#1| (-562)) (-4447 |has| |#1| (-6 -4447)) (-4444 . T) (-4443 . T) (-4446 . T)) -((|HasCategory| |#1| (QUOTE (-916))) (-2740 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-458))) (|HasCategory| |#1| (QUOTE (-562))) (|HasCategory| |#1| (QUOTE (-916)))) (-2740 (|HasCategory| |#1| (QUOTE (-458))) (|HasCategory| |#1| (QUOTE (-562))) (|HasCategory| |#1| (QUOTE (-916)))) (-2740 (|HasCategory| |#1| (QUOTE (-458))) (|HasCategory| |#1| (QUOTE (-916)))) (|HasCategory| |#1| (QUOTE (-562))) (|HasCategory| |#1| (QUOTE (-174))) (-2740 (|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)))) (-2740 (|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 -4447)) (|HasCategory| |#1| (QUOTE (-458))) (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-916)))) (-2740 (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-916)))) (|HasCategory| |#1| (QUOTE (-146))))) +((|HasCategory| |#1| (QUOTE (-916))) (-2892 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-458))) (|HasCategory| |#1| (QUOTE (-562))) (|HasCategory| |#1| (QUOTE (-916)))) (-2892 (|HasCategory| |#1| (QUOTE (-458))) (|HasCategory| |#1| (QUOTE (-562))) (|HasCategory| |#1| (QUOTE (-916)))) (-2892 (|HasCategory| |#1| (QUOTE (-458))) (|HasCategory| |#1| (QUOTE (-916)))) (|HasCategory| |#1| (QUOTE (-562))) (|HasCategory| |#1| (QUOTE (-174))) (-2892 (|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)))) (-2892 (|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 -4447)) (|HasCategory| |#1| (QUOTE (-458))) (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-916)))) (-2892 (-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 -1674) +(-279 R -1707) ((|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 -1674) +(-280 R -1707) ((|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| -2979 -2727 |exactQuo|) +(-293 S R |Mod| -1332 -2800 |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}")) (|elt| ((|#2| $ |#2|) "\\spad{elt(x,r)} or \\spad{x}.\\spad{r} \\undocumented")) (|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| $) "\\spad{modulus(x)} \\undocumented"))) ((-4442 . T) ((-4451 "*") . T) (-4443 . T) (-4444 . T) (-4446 . T)) NIL @@ -1122,21 +1122,21 @@ NIL NIL (-298 S) ((|constructor| (NIL "Equations as mathematical objects. All properties of the basis domain,{} \\spadignore{e.g.} being an abelian group are carried over the equation domain,{} by performing the structural operations on the left and on the right hand side.")) (|subst| (($ $ $) "\\spad{subst(eq1,eq2)} substitutes \\spad{eq2} into both sides of \\spad{eq1} the \\spad{lhs} of \\spad{eq2} should be a kernel")) (|inv| (($ $) "\\spad{inv(x)} returns the multiplicative inverse of \\spad{x}.")) (/ (($ $ $) "\\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."))) ((-4449 . T) (-4450 . T)) -((-12 (|HasCategory| (-2 (|:| -2013 |#1|) (|:| -2224 |#2|)) (QUOTE (-1109))) (|HasCategory| (-2 (|:| -2013 |#1|) (|:| -2224 |#2|)) (LIST (QUOTE -313) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -2013) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -2224) (|devaluate| |#2|)))))) (-2740 (|HasCategory| (-2 (|:| -2013 |#1|) (|:| -2224 |#2|)) (QUOTE (-1109))) (|HasCategory| |#2| (QUOTE (-1109)))) (-2740 (|HasCategory| (-2 (|:| -2013 |#1|) (|:| -2224 |#2|)) (QUOTE (-1109))) (|HasCategory| (-2 (|:| -2013 |#1|) (|:| -2224 |#2|)) (LIST (QUOTE -619) (QUOTE (-868)))) (|HasCategory| |#2| (QUOTE (-1109))) (|HasCategory| |#2| (LIST (QUOTE -619) (QUOTE (-868))))) (|HasCategory| (-2 (|:| -2013 |#1|) (|:| -2224 |#2|)) (LIST (QUOTE -620) (QUOTE (-542)))) (-12 (|HasCategory| |#2| (QUOTE (-1109))) (|HasCategory| |#2| (LIST (QUOTE -313) (|devaluate| |#2|)))) (|HasCategory| (-2 (|:| -2013 |#1|) (|:| -2224 |#2|)) (QUOTE (-1109))) (|HasCategory| |#1| (QUOTE (-856))) (|HasCategory| |#2| (QUOTE (-1109))) (-2740 (|HasCategory| (-2 (|:| -2013 |#1|) (|:| -2224 |#2|)) (LIST (QUOTE -619) (QUOTE (-868)))) (|HasCategory| |#2| (LIST (QUOTE -619) (QUOTE (-868))))) (|HasCategory| |#2| (LIST (QUOTE -619) (QUOTE (-868)))) (|HasCategory| (-2 (|:| -2013 |#1|) (|:| -2224 |#2|)) (LIST (QUOTE -619) (QUOTE (-868))))) +((-12 (|HasCategory| (-2 (|:| -2106 |#1|) (|:| -2339 |#2|)) (QUOTE (-1109))) (|HasCategory| (-2 (|:| -2106 |#1|) (|:| -2339 |#2|)) (LIST (QUOTE -313) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -2106) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -2339) (|devaluate| |#2|)))))) (-2892 (|HasCategory| (-2 (|:| -2106 |#1|) (|:| -2339 |#2|)) (QUOTE (-1109))) (|HasCategory| |#2| (QUOTE (-1109)))) (-2892 (|HasCategory| (-2 (|:| -2106 |#1|) (|:| -2339 |#2|)) (QUOTE (-1109))) (|HasCategory| (-2 (|:| -2106 |#1|) (|:| -2339 |#2|)) (LIST (QUOTE -619) (QUOTE (-868)))) (|HasCategory| |#2| (QUOTE (-1109))) (|HasCategory| |#2| (LIST (QUOTE -619) (QUOTE (-868))))) (|HasCategory| (-2 (|:| -2106 |#1|) (|:| -2339 |#2|)) (LIST (QUOTE -620) (QUOTE (-542)))) (-12 (|HasCategory| |#2| (QUOTE (-1109))) (|HasCategory| |#2| (LIST (QUOTE -313) (|devaluate| |#2|)))) (|HasCategory| (-2 (|:| -2106 |#1|) (|:| -2339 |#2|)) (QUOTE (-1109))) (|HasCategory| |#1| (QUOTE (-856))) (|HasCategory| |#2| (QUOTE (-1109))) (-2892 (|HasCategory| (-2 (|:| -2106 |#1|) (|:| -2339 |#2|)) (LIST (QUOTE -619) (QUOTE (-868)))) (|HasCategory| |#2| (LIST (QUOTE -619) (QUOTE (-868))))) (|HasCategory| |#2| (LIST (QUOTE -619) (QUOTE (-868)))) (|HasCategory| (-2 (|:| -2106 |#1|) (|:| -2339 |#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 -1674 S) +(-301 -1707 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 -1674) +(-302 E -1707) ((|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 -1674) +(-314 -1707) ((|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))}."))) ((-4441 . T) (-4447 . T) (-4442 . T) ((-4451 "*") . T) (-4443 . T) (-4444 . T) (-4446 . 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))) (-2740 (|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)))) (-2740 (|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))) (-2892 (|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)))) (-2892 (|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."))) -((-4446 -2740 (-1765 (|has| |#1| (-1058)) (|has| |#1| (-645 (-570)))) (-12 (|has| |#1| (-562)) (-2740 (-1765 (|has| |#1| (-1058)) (|has| |#1| (-645 (-570)))) (|has| |#1| (-1058)) (|has| |#1| (-479)))) (|has| |#1| (-1058)) (|has| |#1| (-479))) (-4444 |has| |#1| (-174)) (-4443 |has| |#1| (-174)) ((-4451 "*") |has| |#1| (-562)) (-4442 |has| |#1| (-562)) (-4447 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(-1121)))) (-2892 (|HasCategory| |#1| (QUOTE (-25))) (-12 (|HasCategory| |#1| (QUOTE (-1058))) (|HasCategory| |#1| (LIST (QUOTE -645) (QUOTE (-570)))))) (-2892 (|HasCategory| |#1| (QUOTE (-479))) (|HasCategory| |#1| (QUOTE (-1058)))) (-2892 (-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 -1707) ((|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."))) (((-4451 "*") |has| |#1| (-174)) (-4442 |has| |#1| (-562)) (-4447 |has| |#1| (-368)) (-4441 |has| |#1| (-368)) (-4443 . T) (-4444 . T) (-4446 . T)) -((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasCategory| |#1| (QUOTE (-562))) (|HasCategory| |#1| (QUOTE (-174))) (-2740 (|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))) (-2740 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-368))) (|HasCategory| |#1| (QUOTE (-562)))) (-2740 (|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 -3735) (LIST (|devaluate| |#1|) (QUOTE (-1186)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -413) (QUOTE (-570)))))) (-2740 (-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 -3722) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1186))))) (|HasSignature| |#1| (LIST (QUOTE -1713) (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))) (-2892 (|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))) (-2892 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-368))) (|HasCategory| |#1| (QUOTE (-562)))) (-2892 (|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 -3799) (LIST (|devaluate| |#1|) (QUOTE (-1186)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -413) (QUOTE (-570)))))) (-2892 (-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 -4201) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1186))))) (|HasSignature| |#1| (LIST (QUOTE -1754) (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."))) ((-4450 . T) (-4449 . T)) -((-2740 (-12 (|HasCategory| |#1| (QUOTE (-856))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|))))) (-2740 (-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)))) (-2740 (|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 -1674) +((-2892 (-12 (|HasCategory| |#1| (QUOTE (-856))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|))))) (-2892 (-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)))) (-2892 (|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 -1707) ((|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 -1674) +(-333 -1707) ((|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."))) ((-4441 . T) (-4447 . T) (-4442 . T) ((-4451 "*") . T) (-4443 . T) (-4444 . T) (-4446 . 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 -1674 UP UPUP R) +(-339 S -1707 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 -1674 UP UPUP R) +(-340 -1707 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 -1674 UP UPUP R) +(-341 -1707 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 -1674 UP UPUP) +(-346 S -1707 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 -1674 UP UPUP) +(-347 -1707 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."))) ((-4442 |has| (-413 |#2|) (-368)) (-4447 |has| (-413 |#2|) (-368)) (-4441 |has| (-413 |#2|) (-368)) ((-4451 "*") . T) (-4443 . T) (-4444 . T) (-4446 . 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."))) ((-4441 . T) (-4447 . T) (-4442 . T) ((-4451 "*") . T) (-4443 . T) (-4444 . T) (-4446 . T)) -((-2740 (|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)))) +((-2892 (|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."))) ((-4441 . T) (-4447 . T) (-4442 . T) ((-4451 "*") . T) (-4443 . T) (-4444 . T) (-4446 . T)) -((-2740 (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-373)))) (|HasCategory| |#1| (QUOTE (-148))) (|HasCategory| |#1| (QUOTE (-373))) (|HasCategory| |#1| (QUOTE (-146)))) +((-2892 (|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."))) ((-4441 . T) (-4447 . T) (-4442 . T) ((-4451 "*") . T) (-4443 . T) (-4444 . T) (-4446 . T)) -((-2740 (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-373)))) (|HasCategory| |#1| (QUOTE (-148))) (|HasCategory| |#1| (QUOTE (-373))) (|HasCategory| |#1| (QUOTE (-146)))) +((-2892 (|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."))) ((-4441 . T) (-4447 . T) (-4442 . T) ((-4451 "*") . T) (-4443 . T) (-4444 . T) (-4446 . T)) NIL -(-355 R UP -1674) +(-355 R UP -1707) ((|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."))) ((-4441 . T) (-4447 . T) (-4442 . T) ((-4451 "*") . T) (-4443 . T) (-4444 . T) (-4446 . T)) -((-2740 (|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)))) +((-2892 (|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."))) ((-4441 . T) (-4447 . T) (-4442 . T) ((-4451 "*") . T) (-4443 . T) (-4444 . T) (-4446 . T)) -((-2740 (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-373)))) (|HasCategory| |#1| (QUOTE (-148))) (|HasCategory| |#1| (QUOTE (-373))) (|HasCategory| |#1| (QUOTE (-146)))) +((-2892 (|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."))) ((-4441 . T) (-4447 . T) (-4442 . T) ((-4451 "*") . T) (-4443 . T) (-4444 . T) (-4446 . T)) -((-2740 (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-373)))) (|HasCategory| |#1| (QUOTE (-148))) (|HasCategory| |#1| (QUOTE (-373))) (|HasCategory| |#1| (QUOTE (-146)))) +((-2892 (|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}."))) ((-4441 . T) (-4447 . T) (-4442 . T) ((-4451 "*") . T) (-4443 . T) (-4444 . T) (-4446 . T)) -((-2740 (|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)))) +((-2892 (|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."))) ((-4441 . T) (-4447 . T) (-4442 . T) ((-4451 "*") . T) (-4443 . T) (-4444 . T) (-4446 . T)) -((-2740 (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-373)))) (|HasCategory| |#1| (QUOTE (-148))) (|HasCategory| |#1| (QUOTE (-373))) (|HasCategory| |#1| (QUOTE (-146)))) -(-361 -1674 GF) +((-2892 (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-373)))) (|HasCategory| |#1| (QUOTE (-148))) (|HasCategory| |#1| (QUOTE (-373))) (|HasCategory| |#1| (QUOTE (-146)))) +(-361 -1707 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 -1674 FP FPP) +(-363 -1707 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}."))) ((-4441 . T) (-4447 . T) (-4442 . T) ((-4451 "*") . T) (-4443 . T) (-4444 . T) (-4446 . T)) -((-2740 (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-373)))) (|HasCategory| |#1| (QUOTE (-148))) (|HasCategory| |#1| (QUOTE (-373))) (|HasCategory| |#1| (QUOTE (-146)))) +((-2892 (|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}."))) -((-4432 . T) (-4440 . T) (-3026 . T) (-4441 . T) (-4447 . T) (-4442 . T) ((-4451 "*") . T) (-4443 . T) (-4444 . T) (-4446 . T)) +((-4432 . T) (-4440 . T) (-3167 . T) (-4441 . T) (-4447 . T) (-4442 . T) ((-4451 "*") . T) (-4443 . T) (-4444 . T) (-4446 . 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 -1674 UP UPUP R) +(-398 -1707 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 -3504 |returnType| -3890 |symbols|) +(-404 -3599 |returnType| -3928 |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 -1674 UP) +(-405 -1707 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| $) "\\spad{p + x} returns the sum of \\spad{p} and \\spad{x}"))) NIL NIL @@ -1570,7 +1570,7 @@ NIL ((|HasAttribute| |#1| (QUOTE -4432)) (|HasAttribute| |#1| (QUOTE -4440))) (-410) ((|constructor| (NIL "This category is intended as a model for floating point systems. A floating point system is a model for the real numbers. In fact,{} it is an approximation in the sense that not all real numbers are exactly representable by floating point numbers. A floating point system is characterized by the following: \\blankline \\indented{2}{1: \\spadfunFrom{base}{FloatingPointSystem} of the \\spadfunFrom{exponent}{FloatingPointSystem}.} \\indented{9}{(actual implemenations are usually binary or decimal)} \\indented{2}{2: \\spadfunFrom{precision}{FloatingPointSystem} of the \\spadfunFrom{mantissa}{FloatingPointSystem} (arbitrary or fixed)} \\indented{2}{3: rounding error for operations} \\blankline Because a Float is an approximation to the real numbers,{} even though it is defined to be a join of a Field and OrderedRing,{} some of the attributes do not hold. In particular associative(\\spad{\"+\"}) does not hold. Algorithms defined over a field need special considerations when the field is a floating point system.")) (|max| (($) "\\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\"."))) -((-3026 . T) (-4441 . T) (-4447 . T) (-4442 . T) ((-4451 "*") . T) (-4443 . T) (-4444 . T) (-4446 . T)) +((-3167 . T) (-4441 . T) (-4447 . T) (-4442 . T) ((-4451 "*") . T) (-4443 . T) (-4444 . T) (-4446 . 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."))) ((-4436 -12 (|has| |#1| (-6 -4447)) (|has| |#1| (-458)) (|has| |#1| (-6 -4436))) (-4441 . T) (-4447 . T) (-4442 . T) ((-4451 "*") . T) (-4443 . T) (-4444 . T) (-4446 . T)) -((|HasCategory| |#1| (QUOTE (-916))) (|HasCategory| |#1| (LIST (QUOTE -1047) (QUOTE (-1186)))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-148))) (-2740 (-12 (|HasCategory| |#1| (QUOTE (-551))) (|HasCategory| |#1| (QUOTE (-834)))) (|HasCategory| |#1| (LIST (QUOTE -620) (QUOTE (-542))))) (|HasCategory| |#1| (QUOTE (-1031))) (|HasCategory| |#1| (QUOTE (-826))) (-2740 (|HasCategory| |#1| (QUOTE (-826))) (|HasCategory| |#1| (QUOTE (-856)))) (-2740 (-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)))) (-2740 (-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))))) (-2740 (|HasCategory| |#1| (LIST (QUOTE -620) (LIST (QUOTE -899) (QUOTE (-570))))) (-12 (|HasCategory| |#1| (QUOTE (-551))) (|HasCategory| |#1| (QUOTE (-834))))) (-2740 (|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 -4447)) (|HasAttribute| |#1| (QUOTE -4436)) (|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)))) (-2740 (-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))) (-2892 (-12 (|HasCategory| |#1| (QUOTE (-551))) (|HasCategory| |#1| (QUOTE (-834)))) (|HasCategory| |#1| (LIST (QUOTE -620) (QUOTE (-542))))) (|HasCategory| |#1| (QUOTE (-1031))) (|HasCategory| |#1| (QUOTE (-826))) (-2892 (|HasCategory| |#1| (QUOTE (-826))) (|HasCategory| |#1| (QUOTE (-856)))) (-2892 (-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)))) (-2892 (-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))))) (-2892 (|HasCategory| |#1| (LIST (QUOTE -620) (LIST (QUOTE -899) (QUOTE (-570))))) (-12 (|HasCategory| |#1| (QUOTE (-551))) (|HasCategory| |#1| (QUOTE (-834))))) (-2892 (|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 -4447)) (|HasAttribute| |#1| (QUOTE -4436)) (|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)))) (-2892 (-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| $)) "\\spad{basis()} returns the fixed \\spad{R}-module basis."))) NIL @@ -1604,11 +1604,11 @@ NIL ((|constructor| (NIL "\\indented{1}{Lifting of morphisms to fractional ideals.} Author: Manuel Bronstein Date Created: 1 Feb 1989 Date Last Updated: 27 Feb 1990 Keywords: ideal,{} algebra,{} module.")) (|map| (((|FractionalIdeal| |#5| |#6| |#7| |#8|) (|Mapping| |#5| |#1|) (|FractionalIdeal| |#1| |#2| |#3| |#4|)) "\\spad{map(f,i)} \\undocumented{}"))) NIL NIL -(-419 R -1674 UP A) +(-419 R -1707 UP A) ((|constructor| (NIL "Fractional ideals in a framed algebra.")) (|randomLC| ((|#4| (|NonNegativeInteger|) (|Vector| |#4|)) "\\spad{randomLC(n,x)} should be local but conditional.")) (|minimize| (($ $) "\\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)}."))) ((-4446 . T)) NIL -(-420 R -1674 UP A |ibasis|) +(-420 R -1707 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."))) ((-4442 . T) ((-4451 "*") . T) (-4443 . T) (-4444 . T) (-4446 . 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))) (-2740 (|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|))) (|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))) (-2892 (|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|))) (|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|) $) "\\spad{cardinality(u)} returns the number of elements of \\spad{u}. Note: \\axiom{cardinality(\\spad{u}) = \\#u}."))) ((-4449 . T) (-4439 . T) (-4450 . T)) NIL -(-432 R -1674) +(-432 R -1707) ((|constructor| (NIL "\\spadtype{FunctionSpaceComplexIntegration} provides functions for the indefinite integration of complex-valued functions.")) (|complexIntegrate| ((|#2| |#2| (|Symbol|)) "\\spad{complexIntegrate(f, x)} returns the integral of \\spad{f(x)dx} where \\spad{x} is viewed as a complex variable.")) (|internalIntegrate0| (((|IntegrationResult| |#2|) |#2| (|Symbol|)) "\\spad{internalIntegrate0 should} be a local function,{} but is conditional.")) (|internalIntegrate| (((|IntegrationResult| |#2|) |#2| (|Symbol|)) "\\spad{internalIntegrate(f, x)} returns the integral of \\spad{f(x)dx} where \\spad{x} is viewed as a complex variable."))) NIL NIL @@ -1664,7 +1664,7 @@ NIL ((|constructor| (NIL "\\indented{1}{Author: James Davenport} Date Created: 17 April 1992 Date Last Updated: Basic Functions: Related Constructors: Also See: AMS Classifications: Keywords: References: Description:")) (|makeCos| (($ |#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"))) ((-4436 -12 (|has| |#1| (-6 -4436)) (|has| |#2| (-6 -4436))) (-4443 . T) (-4444 . T) (-4446 . T)) ((-12 (|HasAttribute| |#1| (QUOTE -4436)) (|HasAttribute| |#2| (QUOTE -4436)))) -(-434 R -1674) +(-434 R -1707) ((|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}."))) -((-4446 -2740 (|has| |#1| (-1058)) (|has| |#1| (-479))) (-4444 |has| |#1| (-174)) (-4443 |has| |#1| (-174)) ((-4451 "*") |has| |#1| (-562)) (-4442 |has| |#1| (-562)) (-4447 |has| |#1| (-562)) (-4441 |has| |#1| (-562))) +((-4446 -2892 (|has| |#1| (-1058)) (|has| |#1| (-479))) (-4444 |has| |#1| (-174)) (-4443 |has| |#1| (-174)) ((-4451 "*") |has| |#1| (-562)) (-4442 |has| |#1| (-562)) (-4447 |has| |#1| (-562)) (-4441 |has| |#1| (-562))) NIL -(-437 R -1674) +(-437 R -1707) ((|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 -1674) +(-438 R -1707) ((|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 -1674) +(-439 R -1707) ((|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 -1674 UP) +(-441 R -1707 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 -1674) +(-449 R UP -1707) ((|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"))) (((-4451 "*") |has| |#2| (-174)) (-4442 |has| |#2| (-562)) (-4447 |has| |#2| (-6 -4447)) (-4444 . T) (-4443 . T) (-4446 . T)) -((|HasCategory| |#2| (QUOTE (-916))) (-2740 (|HasCategory| |#2| (QUOTE (-174))) (|HasCategory| |#2| (QUOTE (-458))) (|HasCategory| |#2| (QUOTE (-562))) (|HasCategory| |#2| (QUOTE (-916)))) (-2740 (|HasCategory| |#2| (QUOTE (-458))) (|HasCategory| |#2| (QUOTE (-562))) (|HasCategory| |#2| (QUOTE (-916)))) (-2740 (|HasCategory| |#2| (QUOTE (-458))) (|HasCategory| |#2| (QUOTE (-916)))) (|HasCategory| |#2| (QUOTE (-562))) (|HasCategory| |#2| (QUOTE (-174))) (-2740 (|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)))) (-2740 (|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 -4447)) (|HasCategory| |#2| (QUOTE (-458))) (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| |#2| (QUOTE (-916)))) (-2740 (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| |#2| (QUOTE (-916)))) (|HasCategory| |#2| (QUOTE (-146))))) +((|HasCategory| |#2| (QUOTE (-916))) (-2892 (|HasCategory| |#2| (QUOTE (-174))) (|HasCategory| |#2| (QUOTE (-458))) (|HasCategory| |#2| (QUOTE (-562))) (|HasCategory| |#2| (QUOTE (-916)))) (-2892 (|HasCategory| |#2| (QUOTE (-458))) (|HasCategory| |#2| (QUOTE (-562))) (|HasCategory| |#2| (QUOTE (-916)))) (-2892 (|HasCategory| |#2| (QUOTE (-458))) (|HasCategory| |#2| (QUOTE (-916)))) (|HasCategory| |#2| (QUOTE (-562))) (|HasCategory| |#2| (QUOTE (-174))) (-2892 (|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)))) (-2892 (|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 -4447)) (|HasCategory| |#2| (QUOTE (-458))) (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| |#2| (QUOTE (-916)))) (-2892 (-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| -1674 R) +(-477 |lv| -1707 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."))) (((-4451 "*") |has| |#1| (-174)) (-4442 |has| |#1| (-562)) (-4447 |has| |#1| (-368)) (-4441 |has| |#1| (-368)) (-4443 . T) (-4444 . T) (-4446 . 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T)) -((-12 (|HasCategory| (-2 (|:| -2013 |#1|) (|:| -2224 |#2|)) (QUOTE (-1109))) (|HasCategory| (-2 (|:| -2013 |#1|) (|:| -2224 |#2|)) (LIST (QUOTE -313) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -2013) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -2224) (|devaluate| |#2|)))))) (-2740 (|HasCategory| (-2 (|:| -2013 |#1|) (|:| -2224 |#2|)) (QUOTE (-1109))) (|HasCategory| |#2| (QUOTE (-1109)))) (-2740 (|HasCategory| (-2 (|:| -2013 |#1|) (|:| -2224 |#2|)) (QUOTE (-1109))) (|HasCategory| (-2 (|:| -2013 |#1|) (|:| -2224 |#2|)) (LIST (QUOTE -619) (QUOTE (-868)))) (|HasCategory| |#2| (QUOTE (-1109))) (|HasCategory| |#2| (LIST (QUOTE -619) (QUOTE (-868))))) (|HasCategory| (-2 (|:| -2013 |#1|) (|:| -2224 |#2|)) (LIST (QUOTE -620) (QUOTE (-542)))) (-12 (|HasCategory| |#2| (QUOTE (-1109))) (|HasCategory| |#2| (LIST (QUOTE -313) (|devaluate| |#2|)))) (|HasCategory| |#1| (QUOTE (-856))) (-2740 (|HasCategory| (-2 (|:| -2013 |#1|) (|:| -2224 |#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 (|:| -2013 |#1|) (|:| -2224 |#2|)) (LIST (QUOTE -619) (QUOTE (-868)))) (|HasCategory| (-2 (|:| -2013 |#1|) (|:| -2224 |#2|)) (QUOTE (-1109)))) +((-12 (|HasCategory| (-2 (|:| -2106 |#1|) (|:| -2339 |#2|)) (QUOTE (-1109))) (|HasCategory| (-2 (|:| -2106 |#1|) (|:| -2339 |#2|)) (LIST (QUOTE -313) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -2106) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -2339) (|devaluate| |#2|)))))) (-2892 (|HasCategory| (-2 (|:| -2106 |#1|) (|:| -2339 |#2|)) (QUOTE (-1109))) (|HasCategory| |#2| (QUOTE (-1109)))) (-2892 (|HasCategory| (-2 (|:| -2106 |#1|) (|:| -2339 |#2|)) (QUOTE (-1109))) (|HasCategory| (-2 (|:| -2106 |#1|) (|:| -2339 |#2|)) (LIST (QUOTE -619) (QUOTE (-868)))) (|HasCategory| |#2| (QUOTE (-1109))) (|HasCategory| |#2| (LIST (QUOTE -619) (QUOTE (-868))))) (|HasCategory| (-2 (|:| -2106 |#1|) (|:| -2339 |#2|)) (LIST (QUOTE -620) (QUOTE (-542)))) (-12 (|HasCategory| |#2| (QUOTE (-1109))) (|HasCategory| |#2| (LIST (QUOTE -313) (|devaluate| |#2|)))) (|HasCategory| |#1| (QUOTE (-856))) (-2892 (|HasCategory| (-2 (|:| -2106 |#1|) (|:| -2339 |#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 (|:| -2106 |#1|) (|:| -2339 |#2|)) (LIST (QUOTE -619) (QUOTE (-868)))) (|HasCategory| (-2 (|:| -2106 |#1|) (|:| -2339 |#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)}"))) ((-4450 . T) (-4449 . 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."))) ((-4449 . T) (-4450 . T)) -((-12 (|HasCategory| (-2 (|:| -2013 |#1|) (|:| -2224 |#2|)) (QUOTE (-1109))) (|HasCategory| (-2 (|:| -2013 |#1|) (|:| -2224 |#2|)) (LIST (QUOTE -313) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -2013) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -2224) (|devaluate| |#2|)))))) (-2740 (|HasCategory| (-2 (|:| -2013 |#1|) (|:| -2224 |#2|)) (QUOTE (-1109))) (|HasCategory| |#2| (QUOTE (-1109)))) (-2740 (|HasCategory| (-2 (|:| -2013 |#1|) (|:| -2224 |#2|)) (QUOTE (-1109))) (|HasCategory| (-2 (|:| -2013 |#1|) (|:| -2224 |#2|)) (LIST (QUOTE -619) (QUOTE (-868)))) (|HasCategory| |#2| (QUOTE (-1109))) (|HasCategory| |#2| (LIST (QUOTE -619) (QUOTE (-868))))) (|HasCategory| (-2 (|:| -2013 |#1|) (|:| -2224 |#2|)) (LIST (QUOTE -620) (QUOTE (-542)))) (-12 (|HasCategory| |#2| (QUOTE (-1109))) (|HasCategory| |#2| (LIST (QUOTE -313) (|devaluate| |#2|)))) (|HasCategory| (-2 (|:| -2013 |#1|) (|:| -2224 |#2|)) (QUOTE (-1109))) (|HasCategory| |#1| (QUOTE (-856))) (|HasCategory| |#2| (QUOTE (-1109))) (-2740 (|HasCategory| (-2 (|:| -2013 |#1|) (|:| -2224 |#2|)) (LIST (QUOTE -619) (QUOTE (-868)))) (|HasCategory| |#2| (LIST (QUOTE -619) (QUOTE (-868))))) (|HasCategory| |#2| (LIST (QUOTE -619) (QUOTE (-868)))) (|HasCategory| (-2 (|:| -2013 |#1|) (|:| -2224 |#2|)) (LIST (QUOTE -619) (QUOTE (-868))))) +((-12 (|HasCategory| (-2 (|:| -2106 |#1|) (|:| -2339 |#2|)) (QUOTE (-1109))) (|HasCategory| (-2 (|:| -2106 |#1|) (|:| -2339 |#2|)) (LIST (QUOTE -313) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -2106) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -2339) (|devaluate| |#2|)))))) (-2892 (|HasCategory| (-2 (|:| -2106 |#1|) (|:| -2339 |#2|)) (QUOTE (-1109))) (|HasCategory| |#2| (QUOTE (-1109)))) (-2892 (|HasCategory| (-2 (|:| -2106 |#1|) (|:| -2339 |#2|)) (QUOTE (-1109))) (|HasCategory| (-2 (|:| -2106 |#1|) (|:| -2339 |#2|)) (LIST (QUOTE -619) (QUOTE (-868)))) (|HasCategory| |#2| (QUOTE (-1109))) (|HasCategory| |#2| (LIST (QUOTE -619) (QUOTE (-868))))) (|HasCategory| (-2 (|:| -2106 |#1|) (|:| -2339 |#2|)) (LIST (QUOTE -620) (QUOTE (-542)))) (-12 (|HasCategory| |#2| (QUOTE (-1109))) (|HasCategory| |#2| (LIST (QUOTE -313) (|devaluate| |#2|)))) (|HasCategory| (-2 (|:| -2106 |#1|) (|:| -2339 |#2|)) (QUOTE (-1109))) (|HasCategory| |#1| (QUOTE (-856))) (|HasCategory| |#2| (QUOTE (-1109))) (-2892 (|HasCategory| (-2 (|:| -2106 |#1|) (|:| -2339 |#2|)) (LIST (QUOTE -619) (QUOTE (-868)))) (|HasCategory| |#2| (LIST (QUOTE -619) (QUOTE (-868))))) (|HasCategory| |#2| (LIST (QUOTE -619) (QUOTE (-868)))) (|HasCategory| (-2 (|:| -2106 |#1|) (|:| -2339 |#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.")) 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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))))) (-2892 (|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 -4446)) (|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}."))) ((-4449 . T) (-4450 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1109))) (-2740 (-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 -1674 UP UPUP R) +((-12 (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1109))) (-2892 (-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 -1707 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."))) ((-4441 . T) (-4447 . T) (-4442 . T) ((-4451 "*") . T) (-4443 . T) (-4444 . T) (-4446 . 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))) (-2740 (|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)))) (-2740 (-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))) (-2892 (|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)))) (-2892 (-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 -1674 UP |AlExt| |AlPol|) +(-500 -1707 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."))) ((-4450 . T) (-4449 . T)) -((-2740 (-12 (|HasCategory| |#1| (QUOTE (-856))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|))))) (-2740 (-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)))) (-2740 (|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|))))) +((-2892 (-12 (|HasCategory| |#1| (QUOTE (-856))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|))))) (-2892 (-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)))) (-2892 (|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."))) ((-4449 . T) (-4450 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1109))) (-2740 (-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))) (-2892 (-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 -1674) +(-505 R UP -1707) ((|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| $) $) "\\spad{squareFree(x)} returns a square-free factorisation of \\spad{x}"))) NIL NIL @@ -1968,7 +1968,7 @@ NIL ((|constructor| (NIL "InnerCommonDenominator provides functions to compute the common denominator of a finite linear aggregate of elements of the quotient field of an integral domain.")) (|splitDenominator| (((|Record| (|:| |num| |#3|) (|:| |den| |#1|)) |#4|) "\\spad{splitDenominator([q1,...,qn])} returns \\spad{[[p1,...,pn], d]} such that \\spad{qi = pi/d} and \\spad{d} is a common denominator for the \\spad{qi}\\spad{'s}.")) (|clearDenominator| ((|#3| |#4|) "\\spad{clearDenominator([q1,...,qn])} returns \\spad{[p1,...,pn]} such that \\spad{qi = pi/d} where \\spad{d} is a common denominator for the \\spad{qi}\\spad{'s}.")) (|commonDenominator| ((|#1| |#4|) "\\spad{commonDenominator([q1,...,qn])} returns a common denominator \\spad{d} for \\spad{q1},{}...,{}\\spad{qn}."))) NIL NIL -(-510 -1674 |Expon| |VarSet| |DPoly|) +(-510 -1707 |Expon| |VarSet| |DPoly|) ((|constructor| (NIL "This domain represents polynomial ideals with coefficients in any field and supports the basic ideal operations,{} including intersection sum and quotient. An ideal is represented by a list of polynomials (the generators of the ideal) and a boolean that is \\spad{true} if the generators are a Groebner basis. The algorithms used are based on Groebner basis computations. The ordering is determined by the datatype of the input polynomials. Users may use refinements of total degree orderings.")) (|relationsIdeal| (((|SuchThat| (|List| (|Polynomial| |#1|)) (|List| (|Equation| (|Polynomial| |#1|)))) (|List| |#4|)) "\\spad{relationsIdeal(polyList)} returns the ideal of relations among the polynomials in \\spad{polyList}.")) (|saturate| (($ $ |#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}"))) ((-4450 . T) (-4449 . T)) -((-2740 (-12 (|HasCategory| |#1| (QUOTE (-856))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|))))) (-2740 (-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)))) (-2740 (|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|))))) +((-2892 (-12 (|HasCategory| |#1| (QUOTE (-856))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|))))) (-2892 (-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)))) (-2892 (|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}."))) ((-4441 . T) (-4447 . T) (-4442 . T) ((-4451 "*") . T) (-4443 . T) (-4444 . T) (-4446 . T)) -((-2740 (|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)))) +((-2892 (|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}."))) ((-4449 . T) (-4450 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1109))) (-2740 (-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))) (-2892 (-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."))) ((-4450 . T) (-4449 . T)) -((-2740 (-12 (|HasCategory| |#1| (QUOTE (-856))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|))))) (-2740 (-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)))) (-2740 (|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|))))) +((-2892 (-12 (|HasCategory| |#1| (QUOTE (-856))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|))))) (-2892 (-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)))) (-2892 (|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."))) ((-4449 . T) (-4450 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1109))) (-2740 (-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 (-4451 "*"))) (|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))) (-2892 (-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 (-4451 "*"))) (|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 -1674 |Par|) +(-538 K -1707 |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 -1674 |Par|) +(-544 K -1707 |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}."))) ((-4449 . T) (-4450 . T)) -((-12 (|HasCategory| (-2 (|:| -2013 |#1|) (|:| -2224 |#2|)) (QUOTE (-1109))) (|HasCategory| (-2 (|:| -2013 |#1|) (|:| -2224 |#2|)) (LIST (QUOTE -313) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -2013) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -2224) (|devaluate| |#2|)))))) (-2740 (|HasCategory| (-2 (|:| -2013 |#1|) (|:| -2224 |#2|)) (QUOTE (-1109))) (|HasCategory| |#2| (QUOTE (-1109)))) (-2740 (|HasCategory| (-2 (|:| -2013 |#1|) (|:| -2224 |#2|)) (QUOTE (-1109))) (|HasCategory| (-2 (|:| -2013 |#1|) (|:| -2224 |#2|)) (LIST (QUOTE -619) (QUOTE (-868)))) (|HasCategory| |#2| (QUOTE (-1109))) (|HasCategory| |#2| (LIST (QUOTE -619) (QUOTE (-868))))) (|HasCategory| (-2 (|:| -2013 |#1|) (|:| -2224 |#2|)) (LIST (QUOTE -620) (QUOTE (-542)))) (-12 (|HasCategory| |#2| (QUOTE (-1109))) (|HasCategory| |#2| (LIST (QUOTE -313) (|devaluate| |#2|)))) (|HasCategory| (-2 (|:| -2013 |#1|) (|:| -2224 |#2|)) (QUOTE (-1109))) (|HasCategory| |#1| (QUOTE (-856))) (|HasCategory| |#2| (QUOTE (-1109))) (-2740 (|HasCategory| (-2 (|:| -2013 |#1|) (|:| -2224 |#2|)) (LIST (QUOTE -619) (QUOTE (-868)))) (|HasCategory| |#2| (LIST (QUOTE -619) (QUOTE (-868))))) (|HasCategory| |#2| (LIST (QUOTE -619) (QUOTE (-868)))) (|HasCategory| (-2 (|:| -2013 |#1|) (|:| -2224 |#2|)) (LIST (QUOTE -619) (QUOTE (-868))))) -(-557 R -1674) +((-12 (|HasCategory| (-2 (|:| -2106 |#1|) (|:| -2339 |#2|)) (QUOTE (-1109))) (|HasCategory| (-2 (|:| -2106 |#1|) (|:| -2339 |#2|)) (LIST (QUOTE -313) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -2106) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -2339) (|devaluate| |#2|)))))) (-2892 (|HasCategory| (-2 (|:| -2106 |#1|) (|:| -2339 |#2|)) (QUOTE (-1109))) (|HasCategory| |#2| (QUOTE (-1109)))) (-2892 (|HasCategory| (-2 (|:| -2106 |#1|) (|:| -2339 |#2|)) (QUOTE (-1109))) (|HasCategory| (-2 (|:| -2106 |#1|) (|:| -2339 |#2|)) (LIST (QUOTE -619) (QUOTE (-868)))) (|HasCategory| |#2| (QUOTE (-1109))) (|HasCategory| |#2| (LIST (QUOTE -619) (QUOTE (-868))))) (|HasCategory| (-2 (|:| -2106 |#1|) (|:| -2339 |#2|)) (LIST (QUOTE -620) (QUOTE (-542)))) (-12 (|HasCategory| |#2| (QUOTE (-1109))) (|HasCategory| |#2| (LIST (QUOTE -313) (|devaluate| |#2|)))) (|HasCategory| (-2 (|:| -2106 |#1|) (|:| -2339 |#2|)) (QUOTE (-1109))) (|HasCategory| |#1| (QUOTE (-856))) (|HasCategory| |#2| (QUOTE (-1109))) (-2892 (|HasCategory| (-2 (|:| -2106 |#1|) (|:| -2339 |#2|)) (LIST (QUOTE -619) (QUOTE (-868)))) (|HasCategory| |#2| (LIST (QUOTE -619) (QUOTE (-868))))) (|HasCategory| |#2| (LIST (QUOTE -619) (QUOTE (-868)))) (|HasCategory| (-2 (|:| -2106 |#1|) (|:| -2339 |#2|)) (LIST (QUOTE -619) (QUOTE (-868))))) +(-557 R -1707) ((|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 -1674 UP UPUP R) +(-558 R0 -1707 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."))) -((-3026 . T) (-4442 . T) ((-4451 "*") . T) (-4443 . T) (-4444 . T) (-4446 . T)) +((-3167 . T) (-4442 . T) ((-4451 "*") . T) (-4443 . T) (-4444 . T) (-4446 . 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."))) ((-4442 . T) ((-4451 "*") . T) (-4443 . T) (-4444 . T) (-4446 . T)) NIL -(-563 R -1674) +(-563 R -1707) ((|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 -1674 L) +(-566 R -1707 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 -1674 UP UPUP R) +(-568 -1707 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 -1674 UP) +(-569 -1707 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 -1674 L) +(-572 R -1707 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 -1674) +(-573 R -1707) ((|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 -1674 UP) +(-574 -1707 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 -1674) +(-576 -1707) ((|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."))) -((-3026 . T) (-4442 . T) ((-4451 "*") . T) (-4443 . T) (-4444 . T) (-4446 . T)) +((-3167 . T) (-4442 . T) ((-4451 "*") . T) (-4443 . T) (-4444 . T) (-4446 . 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 -1674) +(-579 R -1707) ((|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 -1674 UP) +(-580 -1707 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 -1674) +(-581 R -1707) ((|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 -1674) +(-589 R -1707) ((|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 -1674) +(-590 E -1707) ((|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 -1674) +(-592 -1707) ((|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}."))) ((-4444 . T) (-4443 . 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"))) ((-4450 . T) (-4449 . T)) -((-2740 (-12 (|HasCategory| (-145) (QUOTE (-856))) (|HasCategory| (-145) (LIST (QUOTE -313) (QUOTE (-145))))) (-12 (|HasCategory| (-145) (QUOTE (-1109))) (|HasCategory| (-145) (LIST (QUOTE -313) (QUOTE (-145)))))) (-2740 (|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)))) (-2740 (|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)))))) +((-2892 (-12 (|HasCategory| (-145) (QUOTE (-856))) (|HasCategory| (-145) (LIST (QUOTE -313) (QUOTE (-145))))) (-12 (|HasCategory| (-145) (QUOTE (-1109))) (|HasCategory| (-145) (LIST (QUOTE -313) (QUOTE (-145)))))) (-2892 (|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)))) (-2892 (|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}."))) (((-4451 "*") |has| |#1| (-174)) (-4442 |has| |#1| (-562)) (-4443 . T) (-4444 . T) (-4446 . T)) -((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasCategory| |#1| (QUOTE (-562))) (-2740 (|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 -3735) (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))) (-2892 (|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 -3799) (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.}"))) (((-4451 "*") |has| |#1| (-562)) (-4442 |has| |#1| (-562)) (-4443 . T) (-4444 . T) (-4446 . 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 -1674 FG) +(-606 R -1707 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."))) ((-4450 . T) (-4449 . T)) -((-2740 (-12 (|HasCategory| |#1| (QUOTE (-856))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|))))) (-2740 (-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)))) (-2740 (|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|))))) +((-2892 (-12 (|HasCategory| |#1| (QUOTE (-856))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|))))) (-2892 (-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)))) (-2892 (|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)."))) -((-4446 -2740 (-1765 (|has| |#2| (-372 |#1|)) (|has| |#1| (-562))) (-12 (|has| |#2| (-423 |#1|)) (|has| |#1| (-562)))) (-4444 . T) (-4443 . T)) -((-2740 (|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|)))) (-2740 (-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|)))) +((-4446 -2892 (-1807 (|has| |#2| (-372 |#1|)) (|has| |#1| (-562))) (-12 (|has| |#2| (-423 |#1|)) (|has| |#1| (-562)))) (-4444 . T) (-4443 . T)) +((-2892 (|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|)))) (-2892 (-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."))) ((-4449 . T) (-4450 . T)) -((-12 (|HasCategory| (-2 (|:| -2013 (-1168)) (|:| -2224 |#1|)) (QUOTE (-1109))) (|HasCategory| (-2 (|:| -2013 (-1168)) (|:| -2224 |#1|)) (LIST (QUOTE -313) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -2013) (QUOTE (-1168))) (LIST (QUOTE |:|) (QUOTE -2224) (|devaluate| |#1|)))))) (|HasCategory| (-2 (|:| -2013 (-1168)) (|:| -2224 |#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 (|:| -2013 (-1168)) (|:| -2224 |#1|)) (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-868)))) (|HasCategory| (-2 (|:| -2013 (-1168)) (|:| -2224 |#1|)) (LIST (QUOTE -619) (QUOTE (-868))))) +((-12 (|HasCategory| (-2 (|:| -2106 (-1168)) (|:| -2339 |#1|)) (QUOTE (-1109))) (|HasCategory| (-2 (|:| -2106 (-1168)) (|:| -2339 |#1|)) (LIST (QUOTE -313) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -2106) (QUOTE (-1168))) (LIST (QUOTE |:|) (QUOTE -2339) (|devaluate| |#1|)))))) (|HasCategory| (-2 (|:| -2106 (-1168)) (|:| -2339 |#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 (|:| -2106 (-1168)) (|:| -2339 |#1|)) (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-868)))) (|HasCategory| (-2 (|:| -2106 (-1168)) (|:| -2339 |#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| $) "\\spad{convert(a)} transforms a into an element of \\spad{S}."))) NIL NIL -(-621 -1674 UP) +(-621 -1707 UP) ((|constructor| (NIL "\\spadtype{Kovacic} provides a modified Kovacic\\spad{'s} algorithm for solving explicitely irreducible 2nd order linear ordinary differential equations.")) (|kovacic| (((|Union| (|SparseUnivariatePolynomial| (|Fraction| |#2|)) "failed") (|Fraction| |#2|) (|Fraction| |#2|) (|Fraction| |#2|) (|Mapping| (|Factored| |#2|) |#2|)) "\\spad{kovacic(a_0,a_1,a_2,ezfactor)} returns either \"failed\" or \\spad{P}(\\spad{u}) such that \\spad{\\$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}."))) ((-4443 . T) (-4444 . T) (-4446 . T)) ((|HasCategory| |#1| (QUOTE (-854)))) -(-628 R -1674) +(-628 R -1707) ((|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 -1674) +(-636 R -1707) ((|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| -1674) +(-637 |lv| -1707) ((|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}.")) (|elt| (((|Any|) $ (|Symbol|)) "\\spad{elt(lib,k)} or \\spad{lib}.\\spad{k} extracts the value corresponding to the key \\spad{k} from the library \\spad{lib}.")) (|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."))) ((-4450 . T)) -((-12 (|HasCategory| (-2 (|:| -2013 (-1168)) (|:| -2224 (-52))) (QUOTE (-1109))) (|HasCategory| (-2 (|:| -2013 (-1168)) (|:| -2224 (-52))) (LIST (QUOTE -313) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -2013) (QUOTE (-1168))) (LIST (QUOTE |:|) (QUOTE -2224) (QUOTE (-52))))))) (-2740 (|HasCategory| (-2 (|:| -2013 (-1168)) (|:| -2224 (-52))) (QUOTE (-1109))) (|HasCategory| (-52) (QUOTE (-1109)))) (-2740 (|HasCategory| (-2 (|:| -2013 (-1168)) (|:| -2224 (-52))) (QUOTE (-1109))) (|HasCategory| (-2 (|:| -2013 (-1168)) (|:| -2224 (-52))) (LIST (QUOTE -619) (QUOTE (-868)))) (|HasCategory| (-52) (QUOTE (-1109))) (|HasCategory| (-52) (LIST (QUOTE -619) (QUOTE (-868))))) (|HasCategory| (-2 (|:| -2013 (-1168)) (|:| -2224 (-52))) (LIST (QUOTE -620) (QUOTE (-542)))) (-12 (|HasCategory| (-52) (QUOTE (-1109))) (|HasCategory| (-52) (LIST (QUOTE -313) (QUOTE (-52))))) (|HasCategory| (-1168) (QUOTE (-856))) (-2740 (|HasCategory| (-2 (|:| -2013 (-1168)) (|:| -2224 (-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 (|:| -2013 (-1168)) (|:| -2224 (-52))) (LIST (QUOTE -619) (QUOTE (-868)))) (|HasCategory| (-2 (|:| -2013 (-1168)) (|:| -2224 (-52))) (QUOTE (-1109)))) +((-12 (|HasCategory| (-2 (|:| -2106 (-1168)) (|:| -2339 (-52))) (QUOTE (-1109))) (|HasCategory| (-2 (|:| -2106 (-1168)) (|:| -2339 (-52))) (LIST (QUOTE -313) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -2106) (QUOTE (-1168))) (LIST (QUOTE |:|) (QUOTE -2339) (QUOTE (-52))))))) (-2892 (|HasCategory| (-2 (|:| -2106 (-1168)) (|:| -2339 (-52))) (QUOTE (-1109))) (|HasCategory| (-52) (QUOTE (-1109)))) (-2892 (|HasCategory| (-2 (|:| -2106 (-1168)) (|:| -2339 (-52))) (QUOTE (-1109))) (|HasCategory| (-2 (|:| -2106 (-1168)) (|:| -2339 (-52))) (LIST (QUOTE -619) (QUOTE (-868)))) (|HasCategory| (-52) (QUOTE (-1109))) (|HasCategory| (-52) (LIST (QUOTE -619) (QUOTE (-868))))) (|HasCategory| (-2 (|:| -2106 (-1168)) (|:| -2339 (-52))) (LIST (QUOTE -620) (QUOTE (-542)))) (-12 (|HasCategory| (-52) (QUOTE (-1109))) (|HasCategory| (-52) (LIST (QUOTE -313) (QUOTE (-52))))) (|HasCategory| (-1168) (QUOTE (-856))) (-2892 (|HasCategory| (-2 (|:| -2106 (-1168)) (|:| -2339 (-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 (|:| -2106 (-1168)) (|:| -2339 (-52))) (LIST (QUOTE -619) (QUOTE (-868)))) (|HasCategory| (-2 (|:| -2106 (-1168)) (|:| -2339 (-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)."))) -((-4446 -2740 (-1765 (|has| |#2| (-372 |#1|)) (|has| |#1| (-562))) (-12 (|has| |#2| (-423 |#1|)) (|has| |#1| (-562)))) (-4444 . T) (-4443 . T)) -((-2740 (|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|)))) (-2740 (-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|)))) +((-4446 -2892 (-1807 (|has| |#2| (-372 |#1|)) (|has| |#1| (-562))) (-12 (|has| |#2| (-423 |#1|)) (|has| |#1| (-562)))) (-4444 . T) (-4443 . T)) +((-2892 (|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|)))) (-2892 (-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 -((-1753 (|HasCategory| |#1| (QUOTE (-368)))) (|HasCategory| |#1| (QUOTE (-368)))) +((-1796 (|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| $)) "\\spad{reducedSystem(A)} returns a matrix \\spad{B} such that \\spad{A x = 0} and \\spad{B x = 0} have the same solutions in \\spad{R}."))) ((-4446 . T)) @@ -2531,7 +2531,7 @@ NIL (-650 S) ((|constructor| (NIL "\\spadtype{List} implements singly-linked lists that are addressable by indices; the index of the first element is 1. In addition to the operations provided by \\spadtype{IndexedList},{} this constructor provides some LISP-like functions such as \\spadfun{null} and \\spadfun{cons}.")) (|setDifference| (($ $ $) "\\spad{setDifference(u1,u2)} returns a list of the elements of \\spad{u1} that are not also in \\spad{u2}. The order of elements in the resulting list is unspecified.")) (|setIntersection| (($ $ $) "\\spad{setIntersection(u1,u2)} returns a list of the elements that lists \\spad{u1} and \\spad{u2} have in common. The order of elements in the resulting list is unspecified.")) (|setUnion| (($ $ $) "\\spad{setUnion(u1,u2)} appends the two lists \\spad{u1} and \\spad{u2},{} then removes all duplicates. The order of elements in the resulting list is unspecified.")) (|append| (($ $ $) "\\spad{append(u1,u2)} appends the elements of list \\spad{u1} onto the front of list \\spad{u2}. This new list and \\spad{u2} will share some structure.")) (|cons| (($ |#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."))) ((-4450 . T) (-4449 . T)) -((-2740 (-12 (|HasCategory| |#1| (QUOTE (-856))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|))))) (-2740 (-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)))) (-2740 (|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|))))) +((-2892 (-12 (|HasCategory| |#1| (QUOTE (-856))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|))))) (-2892 (-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)))) (-2892 (|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."))) ((-4449 . T) (-4450 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1109))) (-2740 (-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))) (-2892 (-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,{}..))}.")) (|elt| (($ $ (|UniversalSegment| (|Integer|))) "\\spad{elt(u,i..j)} (also written: \\axiom{a(\\spad{i}..\\spad{j})}) returns the aggregate of elements \\axiom{\\spad{u}} for \\spad{k} from \\spad{i} to \\spad{j} in that order. Note: in general,{} \\axiom{a.\\spad{s} = [a.\\spad{k} for \\spad{i} in \\spad{s}]}.")) (|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 -1674 L) +(-658 R -1707 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}."))) ((-4443 . T) (-4444 . T) (-4446 . T)) NIL -(-663 -1674 UP) +(-663 -1707 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 -1541) +(-664 A -2212) ((|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}}"))) ((-4443 . T) (-4444 . T) (-4446 . 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}."))) ((-4450 . T) (-4449 . T)) NIL -(-673 -1674) +(-673 -1707) ((|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 -1674 |Row| |Col| M) +(-674 -1707 |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."))) ((-4446 . T) (-4449 . T) (-4443 . T) (-4444 . T)) -((|HasCategory| |#2| (LIST (QUOTE -907) (QUOTE (-1186)))) (|HasCategory| |#2| (QUOTE (-235))) (|HasAttribute| |#2| (QUOTE (-4451 "*"))) (|HasCategory| |#2| (LIST (QUOTE -645) (QUOTE (-570)))) (|HasCategory| |#2| (LIST (QUOTE -1047) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasCategory| |#2| (LIST (QUOTE -1047) (QUOTE (-570)))) (-2740 (-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))) (-2740 (|HasAttribute| |#2| (QUOTE (-4451 "*"))) (|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 (-4451 "*"))) (|HasCategory| |#2| (LIST (QUOTE -645) (QUOTE (-570)))) (|HasCategory| |#2| (LIST (QUOTE -1047) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasCategory| |#2| (LIST (QUOTE -1047) (QUOTE (-570)))) (-2892 (-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))) (-2892 (|HasAttribute| |#2| (QUOTE (-4451 "*"))) (|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 -((-2740 (-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))) (-2740 (-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|))))) +((-2892 (-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))) (-2892 (-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."))) ((-4449 . T) (-4450 . T)) -((-2740 (-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))) (-2740 (-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 (-4451 "*"))) (|HasCategory| |#1| (QUOTE (-368))) (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-868)))) (-12 (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|))))) +((-2892 (-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))) (-2892 (-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 (-4451 "*"))) (|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 -1674 FLAF FLAS) +(-698 S -1707 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"))) -((-4442 . T) (-4447 |has| (-705) (-368)) (-4441 |has| (-705) (-368)) (-3035 . T) (-4448 |has| (-705) (-6 -4448)) (-4445 |has| (-705) (-6 -4445)) ((-4451 "*") . T) (-4443 . T) (-4444 . T) (-4446 . 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))) (-2740 (|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))) (-2740 (|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))))) (-2740 (|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)))) (-2740 (-12 (|HasCategory| (-705) (QUOTE (-311))) (|HasCategory| (-705) (QUOTE (-916)))) (|HasCategory| (-705) (QUOTE (-368))) (-12 (|HasCategory| (-705) (QUOTE (-354))) (|HasCategory| (-705) (QUOTE (-916))))) (-2740 (-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))) (-2740 (-12 (|HasCategory| (-705) (QUOTE (-311))) (|HasCategory| (-705) (QUOTE (-916)))) (|HasCategory| (-705) (QUOTE (-368)))) (-2740 (-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 -4448)) (|HasAttribute| (-705) (QUOTE -4445)) (-12 (|HasCategory| (-705) (QUOTE (-311))) (|HasCategory| (-705) (QUOTE (-916)))) (-2740 (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| (-705) (QUOTE (-311))) (|HasCategory| (-705) (QUOTE (-916)))) (|HasCategory| (-705) (QUOTE (-146)))) (-2740 (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| (-705) (QUOTE (-311))) (|HasCategory| (-705) (QUOTE (-916)))) (|HasCategory| (-705) (QUOTE (-354))))) +((-4442 . T) (-4447 |has| (-705) (-368)) (-4441 |has| (-705) (-368)) (-3175 . T) (-4448 |has| (-705) (-6 -4448)) (-4445 |has| (-705) (-6 -4445)) ((-4451 "*") . T) (-4443 . T) (-4444 . T) (-4446 . 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))) (-2892 (|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))) (-2892 (|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))))) (-2892 (|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)))) (-2892 (-12 (|HasCategory| (-705) (QUOTE (-311))) (|HasCategory| (-705) (QUOTE (-916)))) (|HasCategory| (-705) (QUOTE (-368))) (-12 (|HasCategory| (-705) (QUOTE (-354))) (|HasCategory| (-705) (QUOTE (-916))))) (-2892 (-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))) (-2892 (-12 (|HasCategory| (-705) (QUOTE (-311))) (|HasCategory| (-705) (QUOTE (-916)))) (|HasCategory| (-705) (QUOTE (-368)))) (-2892 (-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 -4448)) (|HasAttribute| (-705) (QUOTE -4445)) (-12 (|HasCategory| (-705) (QUOTE (-311))) (|HasCategory| (-705) (QUOTE (-916)))) (-2892 (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| (-705) (QUOTE (-311))) (|HasCategory| (-705) (QUOTE (-916)))) (|HasCategory| (-705) (QUOTE (-146)))) (-2892 (-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}."))) ((-4450 . 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 -1674 PG) +(-704 OV E -1707 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}"))) -((-3026 . T) (-4441 . T) (-4447 . T) (-4442 . T) ((-4451 "*") . T) (-4443 . T) (-4444 . T) (-4446 . T)) +((-3167 . T) (-4441 . T) (-4447 . T) (-4442 . T) ((-4451 "*") . T) (-4443 . T) (-4444 . T) (-4446 . 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 -2791 I) +(-712 S -2942 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| -2979 -2727 |exactQuo|) +(-717 R |Mod| -1332 -2800 |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| $) "\\spad{modulus(x)} \\undocumented"))) ((-4441 . T) (-4447 . T) (-4442 . T) ((-4451 "*") . T) (-4443 . T) (-4444 . T) (-4446 . T)) NIL (-718 R |Rep|) ((|constructor| (NIL "This package \\undocumented")) (|frobenius| (($ $) "\\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"))) (((-4451 "*") |has| |#1| (-174)) (-4442 |has| |#1| (-562)) (-4445 |has| |#1| (-368)) (-4447 |has| |#1| (-6 -4447)) (-4444 . T) (-4443 . T) (-4446 . T)) -((|HasCategory| |#1| (QUOTE (-916))) (|HasCategory| |#1| (QUOTE (-562))) (|HasCategory| |#1| (QUOTE (-174))) (-2740 (|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)))) (-2740 (|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))))) (-2740 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-368))) (|HasCategory| |#1| (QUOTE (-458))) (|HasCategory| |#1| (QUOTE (-562))) (|HasCategory| |#1| (QUOTE (-916)))) (-2740 (|HasCategory| |#1| (QUOTE (-368))) (|HasCategory| |#1| (QUOTE (-458))) (|HasCategory| |#1| (QUOTE (-562))) (|HasCategory| |#1| (QUOTE (-916)))) (-2740 (|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 -4447)) (|HasCategory| |#1| (QUOTE (-458))) (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-916)))) (-2740 (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-916)))) (|HasCategory| |#1| (QUOTE (-146))))) +((|HasCategory| |#1| (QUOTE (-916))) (|HasCategory| |#1| (QUOTE (-562))) (|HasCategory| |#1| (QUOTE (-174))) (-2892 (|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)))) (-2892 (|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))))) (-2892 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-368))) (|HasCategory| |#1| (QUOTE (-458))) (|HasCategory| |#1| (QUOTE (-562))) (|HasCategory| |#1| (QUOTE (-916)))) (-2892 (|HasCategory| |#1| (QUOTE (-368))) (|HasCategory| |#1| (QUOTE (-458))) (|HasCategory| |#1| (QUOTE (-562))) (|HasCategory| |#1| (QUOTE (-916)))) (-2892 (|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 -4447)) (|HasCategory| |#1| (QUOTE (-458))) (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-916)))) (-2892 (-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| (($ $ $) "\\spad{adjoint(op1, op2)} sets the adjoint of \\spad{op1} to be op2. \\spad{op1} must be a basic operator") (($ $) "\\spad{adjoint(op)} returns the adjoint of the operator \\spad{op}."))) ((-4444 |has| |#1| (-174)) (-4443 |has| |#1| (-174)) (-4446 . T)) ((|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-148)))) -(-721 R |Mod| -2979 -2727 |exactQuo|) +(-721 R |Mod| -1332 -2800 |exactQuo|) ((|constructor| (NIL "These domains are used for the factorization and gcds of univariate polynomials over the integers in order to work modulo different primes. See \\spadtype{EuclideanModularRing} ,{}\\spadtype{ModularField}")) (|inv| (($ $) "\\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"))) ((-4446 . T)) NIL @@ -2824,7 +2824,7 @@ NIL ((|constructor| (NIL "The category of modules over a commutative ring. \\blankline"))) ((-4444 . T) (-4443 . T)) NIL -(-724 -1674) +(-724 -1707) ((|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]]}."))) ((-4446 . 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 -1674 UP) +(-733 -1707 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."))) (((-4451 "*") |has| |#2| (-174)) (-4442 |has| |#2| (-562)) (-4447 |has| |#2| (-6 -4447)) (-4444 . T) (-4443 . T) (-4446 . T)) -((|HasCategory| |#2| (QUOTE (-916))) (-2740 (|HasCategory| |#2| (QUOTE (-174))) (|HasCategory| |#2| (QUOTE (-458))) (|HasCategory| |#2| (QUOTE (-562))) (|HasCategory| |#2| (QUOTE (-916)))) (-2740 (|HasCategory| |#2| (QUOTE (-458))) (|HasCategory| |#2| (QUOTE (-562))) (|HasCategory| |#2| (QUOTE (-916)))) (-2740 (|HasCategory| |#2| (QUOTE (-458))) (|HasCategory| |#2| (QUOTE (-916)))) (|HasCategory| |#2| (QUOTE (-562))) (|HasCategory| |#2| (QUOTE (-174))) (-2740 (|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)))) (-2740 (|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 -4447)) (|HasCategory| |#2| (QUOTE (-458))) (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| |#2| (QUOTE (-916)))) (-2740 (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| |#2| (QUOTE (-916)))) (|HasCategory| |#2| (QUOTE (-146))))) +((|HasCategory| |#2| (QUOTE (-916))) (-2892 (|HasCategory| |#2| (QUOTE (-174))) (|HasCategory| |#2| (QUOTE (-458))) (|HasCategory| |#2| (QUOTE (-562))) (|HasCategory| |#2| (QUOTE (-916)))) (-2892 (|HasCategory| |#2| (QUOTE (-458))) (|HasCategory| |#2| (QUOTE (-562))) (|HasCategory| |#2| (QUOTE (-916)))) (-2892 (|HasCategory| |#2| (QUOTE (-458))) (|HasCategory| |#2| (QUOTE (-916)))) (|HasCategory| |#2| (QUOTE (-562))) (|HasCategory| |#2| (QUOTE (-174))) (-2892 (|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)))) (-2892 (|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 -4447)) (|HasCategory| |#2| (QUOTE (-458))) (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| |#2| (QUOTE (-916)))) (-2892 (-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 -1674) +(-771 -1707) ((|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 -1674) +(-772 P -1707) ((|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 -1674) +(-774 UP -1707) ((|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."))) (((-4451 "*") . T)) NIL -(-778 R -1674) +(-778 R -1707) ((|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 -1674 |ExtF| |SUEx| |ExtP| |n|) +(-783 -1707 |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."))) (((-4451 "*") |has| |#1| (-174)) (-4442 |has| |#1| (-562)) (-4447 |has| |#1| (-6 -4447)) (-4444 . T) (-4443 . T) (-4446 . 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(-570))))))) (-12 (|HasCategory| |#2| (LIST (QUOTE -620) (QUOTE (-1186)))) (-1796 (|HasCategory| |#1| (LIST (QUOTE -38) (QUOTE (-570))))) (-1796 (|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)))) (-1796 (|HasCategory| |#1| (LIST (QUOTE -1001) (QUOTE (-570))))))) (|HasAttribute| |#1| (QUOTE -4447)) (|HasCategory| |#1| (QUOTE (-458))) (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-916)))) (-2892 (-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| $) "\\axiom{fmecg(\\spad{p1},{}\\spad{e},{}\\spad{r},{}\\spad{p2})} returns \\axiom{\\spad{p1} - \\spad{r} * X**e * \\spad{p2}} where \\axiom{\\spad{X}} is \\axiom{monomial(1,{}1)}"))) (((-4451 "*") |has| |#1| (-174)) (-4442 |has| |#1| (-562)) (-4445 |has| |#1| (-368)) (-4447 |has| |#1| (-6 -4447)) (-4444 . T) (-4443 . T) (-4446 . 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(|eulerE| ((|#1| (|NonNegativeInteger|) |#1|) "\\spad{eulerE(n,r)} \\undocumented")) (|bernoulliB| ((|#1| (|NonNegativeInteger|) |#1|) "\\spad{bernoulliB(n,r)} \\undocumented")) (|cyclotomic| ((|#1| (|NonNegativeInteger|) |#1|) "\\spad{cyclotomic(n,r)} \\undocumented"))) NIL @@ -3144,23 +3144,23 @@ NIL ((|constructor| (NIL "OctonionCategory gives the categorial frame for the octonions,{} and eight-dimensional non-associative algebra,{} doubling the the quaternions in the same way as doubling the Complex numbers to get the quaternions.")) (|inv| (($ $) "\\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| $) "\\spad{real(o)} extracts real part of octonion \\spad{o}.")) (|conjugate| (($ $) "\\spad{conjugate(o)} negates the imaginary parts \\spad{i},{}\\spad{j},{}\\spad{k},{}\\spad{E},{}\\spad{I},{}\\spad{J},{}\\spad{K} of octonian \\spad{o}."))) ((-4443 . T) (-4444 . T) (-4446 . T)) NIL -(-804 -2740 R OS S) +(-804 -2892 R OS S) ((|constructor| (NIL "OctonionCategoryFunctions2 implements functions between two octonion domains defined over different rings. The function map is used to coerce between octonion types.")) (|map| ((|#3| (|Mapping| |#4| |#2|) |#1|) "\\spad{map(f,u)} maps \\spad{f} onto the component parts of the octonion \\spad{u}."))) NIL NIL (-805 R) ((|constructor| (NIL "Octonion implements octonions (Cayley-Dixon algebra) over a commutative ring,{} an eight-dimensional non-associative algebra,{} doubling the quaternions in the same way as doubling the complex numbers to get the quaternions the main constructor function is {\\em octon} which takes 8 arguments: the real part,{} the \\spad{i} imaginary part,{} the \\spad{j} imaginary part,{} the \\spad{k} imaginary part,{} (as with quaternions) and in addition the imaginary parts \\spad{E},{} \\spad{I},{} \\spad{J},{} \\spad{K}.")) (|octon| (($ (|Quaternion| |#1|) (|Quaternion| |#1|)) "\\spad{octon(qe,qE)} constructs an octonion from two quaternions using the relation {\\em O = Q + QE}."))) ((-4443 . T) (-4444 . T) (-4446 . 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|))) (-2740 (|HasCategory| (-1008 |#1|) (LIST (QUOTE -1047) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasCategory| |#1| (LIST (QUOTE -1047) (LIST (QUOTE -413) (QUOTE (-570)))))) (-2740 (|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|))) (-2892 (|HasCategory| (-1008 |#1|) (LIST (QUOTE -1047) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasCategory| |#1| (LIST (QUOTE -1047) (LIST (QUOTE -413) (QUOTE (-570)))))) (-2892 (|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 -1674 L) +(-807 R -1707 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 -1674) +(-808 R -1707) ((|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 -1674) +(-810 R -1707) ((|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 -1674 UP UPUP R) +(-812 -1707 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 -1674 UP L LQ) +(-813 -1707 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 -1674 UP L LQ) +(-815 -1707 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 -1674 UP) +(-816 -1707 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 -1674 L UP A LO) +(-817 -1707 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 -1674 UP) +(-818 -1707 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 -1674 LO) +(-819 -1707 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"))) (((-4451 "*") |has| |#1| (-174)) (-4442 |has| |#1| (-562)) (-4447 |has| |#1| (-6 -4447)) (-4444 . T) (-4443 . T) (-4446 . 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(((-4451 "*") |has| |#2| (-368)) (-4442 |has| |#2| (-368)) (-4447 |has| |#2| (-368)) (-4441 |has| |#2| (-368)) (-4446 . T) (-4444 . T) (-4443 . 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."))) ((-4446 |has| |#1| (-854))) -((|HasCategory| |#1| (QUOTE (-854))) (|HasCategory| |#1| (QUOTE (-21))) (-2740 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-854)))) (|HasCategory| |#1| (LIST (QUOTE -1047) (LIST (QUOTE -413) (QUOTE (-570))))) (-2740 (|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))) (-2892 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-854)))) (|HasCategory| |#1| (LIST (QUOTE -1047) (LIST (QUOTE -413) (QUOTE (-570))))) (-2892 (|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| (($) "\\spad{plusInfinity()} returns +infinity."))) ((-4446 |has| |#1| (-854))) -((|HasCategory| |#1| (QUOTE (-854))) (|HasCategory| |#1| (QUOTE (-21))) (-2740 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-854)))) (|HasCategory| |#1| (LIST (QUOTE -1047) (LIST (QUOTE -413) (QUOTE (-570))))) (-2740 (|HasCategory| |#1| (QUOTE (-854))) (|HasCategory| |#1| (LIST (QUOTE -1047) (QUOTE (-570))))) (|HasCategory| |#1| (LIST (QUOTE -1047) (QUOTE (-570)))) (|HasCategory| |#1| (QUOTE (-551)))) +((|HasCategory| |#1| (QUOTE (-854))) (|HasCategory| |#1| (QUOTE (-21))) (-2892 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-854)))) (|HasCategory| |#1| (LIST (QUOTE -1047) (LIST (QUOTE -413) (QUOTE (-570))))) (-2892 (|HasCategory| |#1| (QUOTE (-854))) (|HasCategory| |#1| (LIST (QUOTE -1047) (QUOTE (-570))))) (|HasCategory| |#1| (LIST (QUOTE -1047) (QUOTE (-570)))) (|HasCategory| |#1| (QUOTE (-551)))) (-850) ((|constructor| (NIL "Ordered finite sets.")) (|max| (($) "\\spad{max} is the maximum value of \\%.")) (|min| (($) "\\spad{min} is the minimum value of \\%."))) NIL NIL -(-851 -2408 S) +(-851 -2550 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| -3049) +(-860 R |sigma| -3225) ((|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."))) ((-4443 . T) (-4444 . T) (-4446 . 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| -3049) +(-861 |x| R |sigma| -3225) ((|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}."))) ((-4443 . T) (-4444 . T) (-4446 . 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)."))) ((-4441 . T) (-4447 . T) (-4442 . T) ((-4451 "*") . T) (-4443 . T) (-4444 . T) (-4446 . 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))) (-2740 (|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)))) (-2740 (-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))) (-2892 (|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)))) (-2892 (-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)}."))) ((-4441 . T) (-4447 . T) (-4442 . T) ((-4451 "*") . T) (-4443 . T) (-4444 . T) (-4446 . 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))) (-2740 (|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)))) (-2740 (-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))) (-2892 (|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)))) (-2892 (-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)))) (-2740 (-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)))) (-2892 (-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 (-1753 (|HasCategory| |#2| (QUOTE (-1058)))) (-1753 (|HasCategory| |#2| (LIST (QUOTE -1047) (QUOTE (-1186)))))) (-12 (|HasCategory| |#2| (QUOTE (-1058))) (-1753 (|HasCategory| |#2| (LIST (QUOTE -1047) (QUOTE (-1186)))))) (|HasCategory| |#2| (LIST (QUOTE -1047) (QUOTE (-1186))))) +((-12 (-1796 (|HasCategory| |#2| (QUOTE (-1058)))) (-1796 (|HasCategory| |#2| (LIST (QUOTE -1047) (QUOTE (-1186)))))) (-12 (|HasCategory| |#2| (QUOTE (-1058))) (-1796 (|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 -2791) +(-897 R -2942) ((|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 -1674) +(-903 UP -1707) ((|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 @@ -3563,7 +3563,7 @@ 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))) (-2740 (-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))) (-2892 (-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 @@ -3579,7 +3579,7 @@ 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."))) ((-4446 . T)) -((-2740 (|HasCategory| |#1| (QUOTE (-373))) (|HasCategory| |#1| (QUOTE (-856)))) (|HasCategory| |#1| (QUOTE (-373))) (|HasCategory| |#1| (QUOTE (-856)))) +((-2892 (|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."))) ((-4441 . T) (-4447 . T) (-4442 . T) ((-4451 "*") . T) (-4443 . T) (-4444 . T) (-4446 . T)) ((|HasCategory| $ (QUOTE (-148))) (|HasCategory| $ (QUOTE (-146))) (|HasCategory| $ (QUOTE (-373)))) -(-918 R0 -1674 UP UPUP R) +(-918 R0 -1707 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 -1674) +(-925 -1707) ((|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}."))) (((-4451 "*") . T)) NIL -(-929 -1674 P) +(-929 -1707 P) ((|constructor| (NIL "This package exports interpolation algorithms")) (|LagrangeInterpolation| ((|#2| (|List| |#1|) (|List| |#1|)) "\\spad{LagrangeInterpolation(l1,l2)} \\undocumented"))) NIL NIL -(-930 |xx| -1674) +(-930 |xx| -1707) ((|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 -1674) +(-936 R -1707) ((|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 -1674) +(-939 S R -1707) ((|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 -1674 -2791) +(-944 R -1707 -2942) ((|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 -2791) +(-945 -2942) ((|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"))) ((-4450 . T) (-4449 . T)) -((-2740 (-12 (|HasCategory| |#1| (QUOTE (-856))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|))))) (-2740 (-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)))) (-2740 (|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|))))) +((-2892 (-12 (|HasCategory| |#1| (QUOTE (-856))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|))))) (-2892 (-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)))) (-2892 (|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}."))) (((-4451 "*") |has| |#1| (-174)) (-4442 |has| |#1| (-562)) (-4447 |has| |#1| (-6 -4447)) (-4444 . T) (-4443 . T) (-4446 . T)) NIL -(-957 E V R P -1674) +(-957 E V R P -1707) ((|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}."))) (((-4451 "*") |has| |#1| (-174)) (-4442 |has| |#1| (-562)) (-4447 |has| |#1| (-6 -4447)) (-4444 . T) (-4443 . T) (-4446 . T)) -((|HasCategory| |#1| (QUOTE (-916))) (-2740 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-458))) (|HasCategory| |#1| (QUOTE (-562))) (|HasCategory| |#1| (QUOTE (-916)))) (-2740 (|HasCategory| |#1| (QUOTE (-458))) (|HasCategory| |#1| (QUOTE (-562))) (|HasCategory| |#1| (QUOTE (-916)))) (-2740 (|HasCategory| |#1| (QUOTE (-458))) (|HasCategory| |#1| (QUOTE (-916)))) (|HasCategory| |#1| (QUOTE (-562))) (|HasCategory| |#1| (QUOTE (-174))) (-2740 (|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)))) (-2740 (|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 -4447)) (|HasCategory| |#1| (QUOTE (-458))) (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-916)))) (-2740 (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-916)))) (|HasCategory| |#1| (QUOTE (-146))))) -(-960 E V R P -1674) +((|HasCategory| |#1| (QUOTE (-916))) (-2892 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-458))) (|HasCategory| |#1| (QUOTE (-562))) (|HasCategory| |#1| (QUOTE (-916)))) (-2892 (|HasCategory| |#1| (QUOTE (-458))) (|HasCategory| |#1| (QUOTE (-562))) (|HasCategory| |#1| (QUOTE (-916)))) (-2892 (|HasCategory| |#1| (QUOTE (-458))) (|HasCategory| |#1| (QUOTE (-916)))) (|HasCategory| |#1| (QUOTE (-562))) (|HasCategory| |#1| (QUOTE (-174))) (-2892 (|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)))) (-2892 (|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 -4447)) (|HasCategory| |#1| (QUOTE (-458))) (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-916)))) (-2892 (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-916)))) (|HasCategory| |#1| (QUOTE (-146))))) +(-960 E V R P -1707) ((|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| $) "\\spad{numer(x)} \\undocumented"))) NIL ((|HasCategory| |#3| (QUOTE (-458)))) @@ -3791,12 +3791,12 @@ NIL (-965 S) ((|constructor| (NIL "\\indented{1}{This provides a fast array type with no bound checking on elt\\spad{'s}.} Minimum index is 0 in this type,{} cannot be changed"))) ((-4450 . T) (-4449 . T)) -((-2740 (-12 (|HasCategory| |#1| (QUOTE (-856))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|))))) (-2740 (-12 (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-868))))) (|HasCategory| |#1| (LIST (QUOTE -620) (QUOTE (-542)))) (-2740 (|HasCategory| |#1| (QUOTE (-856))) (|HasCategory| |#1| (QUOTE (-1109)))) (|HasCategory| |#1| (QUOTE (-856))) (|HasCategory| (-570) (QUOTE (-856))) (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-868)))) (-12 (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|))))) +((-2892 (-12 (|HasCategory| |#1| (QUOTE (-856))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|))))) (-2892 (-12 (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-868))))) (|HasCategory| |#1| (LIST (QUOTE -620) (QUOTE (-542)))) (-2892 (|HasCategory| |#1| (QUOTE (-856))) (|HasCategory| |#1| (QUOTE (-1109)))) (|HasCategory| |#1| (QUOTE (-856))) (|HasCategory| (-570) (QUOTE (-856))) (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-868)))) (-12 (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|))))) (-966) ((|constructor| (NIL "Category for the functions defined by integrals.")) (|integral| (($ $ (|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 -1674) +(-967 -1707) ((|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}"))) (((-4451 "*") |has| |#1| (-174)) (-4442 |has| |#1| (-562)) (-4447 |has| |#1| (-6 -4447)) (-4443 . T) (-4444 . T) (-4446 . T)) -((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasCategory| |#1| (QUOTE (-562))) (-2740 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-562)))) (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-148))) (-2740 (|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 -4447))) +((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasCategory| |#1| (QUOTE (-562))) (-2892 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-562)))) (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-148))) (-2892 (|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 -4447))) (-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"))) ((-4446 -12 (|has| |#2| (-479)) (|has| |#1| (-479)))) -((-2740 (-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)))) (-2740 (-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)))) (-2740 (-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)))) (-2740 (-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)))) (-2740 (-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))))) +((-2892 (-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)))) (-2892 (-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)))) (-2892 (-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)))) (-2892 (-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)))) (-2892 (-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 -1674) +(-994 K R UP -1707) ((|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.}"))) ((-4442 |has| |#1| (-294)) (-4443 . T) (-4444 . T) (-4446 . T)) -((|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-148))) (|HasCategory| |#1| (LIST (QUOTE -620) (QUOTE (-542)))) (|HasCategory| |#1| (QUOTE (-368))) (-2740 (|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)))) (-2740 (|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))) (-2892 (|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)))) (-2892 (|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}."))) ((-4449 . T) (-4450 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1109))) (-2740 (-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))) (-2892 (-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 -1674 UP UPUP |radicnd| |n|) +(-1012 -1707 UP UPUP |radicnd| |n|) ((|constructor| (NIL "Function field defined by y**n = \\spad{f}(\\spad{x})."))) ((-4442 |has| (-413 |#2|) (-368)) (-4447 |has| (-413 |#2|) (-368)) (-4441 |has| (-413 |#2|) (-368)) ((-4451 "*") . T) (-4443 . T) (-4444 . T) (-4446 . T)) -((|HasCategory| (-413 |#2|) (QUOTE (-146))) (|HasCategory| (-413 |#2|) (QUOTE (-148))) (|HasCategory| (-413 |#2|) (QUOTE (-354))) (-2740 (|HasCategory| (-413 |#2|) (QUOTE (-368))) (|HasCategory| (-413 |#2|) (QUOTE (-354)))) (|HasCategory| (-413 |#2|) (QUOTE (-368))) (|HasCategory| (-413 |#2|) (QUOTE (-373))) (-2740 (-12 (|HasCategory| (-413 |#2|) (QUOTE (-235))) (|HasCategory| (-413 |#2|) (QUOTE (-368)))) (|HasCategory| (-413 |#2|) (QUOTE (-354)))) (-2740 (-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)))) (-2740 (|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))) (-2892 (|HasCategory| (-413 |#2|) (QUOTE (-368))) (|HasCategory| (-413 |#2|) (QUOTE (-354)))) (|HasCategory| (-413 |#2|) (QUOTE (-368))) (|HasCategory| (-413 |#2|) (QUOTE (-373))) (-2892 (-12 (|HasCategory| (-413 |#2|) (QUOTE (-235))) (|HasCategory| (-413 |#2|) (QUOTE (-368)))) (|HasCategory| (-413 |#2|) (QUOTE (-354)))) (-2892 (-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)))) (-2892 (|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."))) ((-4441 . T) (-4447 . T) (-4442 . T) ((-4451 "*") . T) (-4443 . T) (-4444 . T) (-4446 . 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))) (-2740 (|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)))) (-2740 (-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))) (-2892 (|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)))) (-2892 (-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}}"))) ((-4442 . T) (-4447 . T) (-4441 . T) (-4444 . T) (-4443 . T) ((-4451 "*") . T) (-4446 . T)) NIL -(-1022 R -1674) +(-1022 R -1707) ((|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 -1674) +(-1023 R -1707) ((|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 -1674 UP) +(-1024 -1707 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 -1674 UP) +(-1025 -1707 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"))) ((-4442 . T) (-4447 . T) (-4441 . T) (-4444 . T) (-4443 . T) ((-4451 "*") . T) (-4446 . T)) -((-2740 (|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 -1674 L) +((-2892 (|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 -1707 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 -1674 |Expon| |VarSet| |FPol| |LFPol|) +(-1043 -1707 |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"))) (((-4451 "*") . T) (-4443 . T) (-4444 . T) (-4446 . 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.}"))) ((-4449 . T) (-4450 . T)) -((-12 (|HasCategory| (-2 (|:| -2013 (-1186)) (|:| -2224 (-52))) (QUOTE (-1109))) (|HasCategory| (-2 (|:| -2013 (-1186)) (|:| -2224 (-52))) (LIST (QUOTE -313) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -2013) (QUOTE (-1186))) (LIST (QUOTE |:|) (QUOTE -2224) (QUOTE (-52))))))) (-2740 (|HasCategory| (-2 (|:| -2013 (-1186)) (|:| -2224 (-52))) (QUOTE (-1109))) (|HasCategory| (-52) (QUOTE (-1109)))) (-2740 (|HasCategory| (-2 (|:| -2013 (-1186)) (|:| -2224 (-52))) (QUOTE (-1109))) (|HasCategory| (-2 (|:| -2013 (-1186)) (|:| -2224 (-52))) (LIST (QUOTE -619) (QUOTE (-868)))) (|HasCategory| (-52) (QUOTE (-1109))) (|HasCategory| (-52) (LIST (QUOTE -619) (QUOTE (-868))))) (|HasCategory| (-2 (|:| -2013 (-1186)) (|:| -2224 (-52))) (LIST (QUOTE -620) (QUOTE (-542)))) (-12 (|HasCategory| (-52) (QUOTE (-1109))) (|HasCategory| (-52) (LIST (QUOTE -313) (QUOTE (-52))))) (|HasCategory| (-2 (|:| -2013 (-1186)) (|:| -2224 (-52))) (QUOTE (-1109))) (|HasCategory| (-1186) (QUOTE (-856))) (|HasCategory| (-52) (QUOTE (-1109))) (-2740 (|HasCategory| (-2 (|:| -2013 (-1186)) (|:| -2224 (-52))) (LIST (QUOTE -619) (QUOTE (-868)))) (|HasCategory| (-52) (LIST (QUOTE -619) (QUOTE (-868))))) (|HasCategory| (-52) (LIST (QUOTE -619) (QUOTE (-868)))) (|HasCategory| (-2 (|:| -2013 (-1186)) (|:| -2224 (-52))) (LIST (QUOTE -619) (QUOTE (-868))))) +((-12 (|HasCategory| (-2 (|:| -2106 (-1186)) (|:| -2339 (-52))) (QUOTE (-1109))) (|HasCategory| (-2 (|:| -2106 (-1186)) (|:| -2339 (-52))) (LIST (QUOTE -313) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -2106) (QUOTE (-1186))) (LIST (QUOTE |:|) (QUOTE -2339) (QUOTE (-52))))))) (-2892 (|HasCategory| (-2 (|:| -2106 (-1186)) (|:| -2339 (-52))) (QUOTE (-1109))) (|HasCategory| (-52) (QUOTE (-1109)))) (-2892 (|HasCategory| (-2 (|:| -2106 (-1186)) (|:| -2339 (-52))) (QUOTE (-1109))) (|HasCategory| (-2 (|:| -2106 (-1186)) (|:| -2339 (-52))) (LIST (QUOTE -619) (QUOTE (-868)))) (|HasCategory| (-52) (QUOTE (-1109))) (|HasCategory| (-52) (LIST (QUOTE -619) (QUOTE (-868))))) (|HasCategory| (-2 (|:| -2106 (-1186)) (|:| -2339 (-52))) (LIST (QUOTE -620) (QUOTE (-542)))) (-12 (|HasCategory| (-52) (QUOTE (-1109))) (|HasCategory| (-52) (LIST (QUOTE -313) (QUOTE (-52))))) (|HasCategory| (-2 (|:| -2106 (-1186)) (|:| -2339 (-52))) (QUOTE (-1109))) (|HasCategory| (-1186) (QUOTE (-856))) (|HasCategory| (-52) (QUOTE (-1109))) (-2892 (|HasCategory| (-2 (|:| -2106 (-1186)) (|:| -2339 (-52))) (LIST (QUOTE -619) (QUOTE (-868)))) (|HasCategory| (-52) (LIST (QUOTE -619) (QUOTE (-868))))) (|HasCategory| (-52) (LIST (QUOTE -619) (QUOTE (-868)))) (|HasCategory| (-2 (|:| -2106 (-1186)) (|:| -2339 (-52))) (LIST (QUOTE -619) (QUOTE (-868))))) (-1045) ((|constructor| (NIL "This domain represents `return' expressions.")) (|expression| (((|SpadAst|) $) "\\spad{expression(e)} returns the expression returned by `e'."))) NIL @@ -4164,7 +4164,7 @@ NIL ((|constructor| (NIL "The category of rings with unity,{} always associative,{} but not necessarily commutative.")) (|unitsKnown| ((|attribute|) "recip truly yields reciprocal or \"failed\" if not a unit. Note: \\spad{recip(0) = \"failed\"}.")) (|characteristic| (((|NonNegativeInteger|)) "\\spad{characteristic()} returns the characteristic of the ring this is the smallest positive integer \\spad{n} such that \\spad{n*x=0} for all \\spad{x} in the ring,{} or zero if no such \\spad{n} exists."))) ((-4446 . T)) NIL -(-1059 |xx| -1674) +(-1059 |xx| -1707) ((|constructor| (NIL "This package exports rational interpolation algorithms"))) NIL NIL @@ -4183,7 +4183,7 @@ NIL (-1063 |m| |n| R) ((|constructor| (NIL "\\spadtype{RectangularMatrix} is a matrix domain where the number of rows and the number of columns are parameters of the domain.")) (|rectangularMatrix| (($ (|Matrix| |#3|)) "\\spad{rectangularMatrix(m)} converts a matrix of type \\spadtype{Matrix} to a matrix of type \\spad{RectangularMatrix}."))) ((-4449 . T) (-4444 . T) (-4443 . T)) -((|HasCategory| |#3| (QUOTE (-174))) (-2740 (-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)))) (-2740 (|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))) (-2892 (-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)))) (-2892 (|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}"))) ((-4449 . T) (-4450 . T)) -((-12 (|HasCategory| (-2 (|:| -2013 (-1186)) (|:| -2224 (-52))) (QUOTE (-1109))) (|HasCategory| (-2 (|:| -2013 (-1186)) (|:| -2224 (-52))) (LIST (QUOTE -313) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -2013) (QUOTE (-1186))) (LIST (QUOTE |:|) (QUOTE -2224) (QUOTE (-52))))))) (-2740 (|HasCategory| (-2 (|:| -2013 (-1186)) (|:| -2224 (-52))) (QUOTE (-1109))) (|HasCategory| (-52) (QUOTE (-1109)))) (-2740 (|HasCategory| (-2 (|:| -2013 (-1186)) (|:| -2224 (-52))) (QUOTE (-1109))) (|HasCategory| (-2 (|:| -2013 (-1186)) (|:| -2224 (-52))) (LIST (QUOTE -619) (QUOTE (-868)))) (|HasCategory| (-52) (QUOTE (-1109))) (|HasCategory| (-52) (LIST (QUOTE -619) (QUOTE (-868))))) (|HasCategory| (-2 (|:| -2013 (-1186)) (|:| -2224 (-52))) (LIST (QUOTE -620) (QUOTE (-542)))) (-12 (|HasCategory| (-52) (QUOTE (-1109))) (|HasCategory| (-52) (LIST (QUOTE -313) (QUOTE (-52))))) (|HasCategory| (-2 (|:| -2013 (-1186)) (|:| -2224 (-52))) (QUOTE (-1109))) (|HasCategory| (-1186) (QUOTE (-856))) (|HasCategory| (-52) (QUOTE (-1109))) (-2740 (|HasCategory| (-2 (|:| -2013 (-1186)) (|:| -2224 (-52))) (LIST (QUOTE -619) (QUOTE (-868)))) (|HasCategory| (-52) (LIST (QUOTE -619) (QUOTE (-868))))) (|HasCategory| (-52) (LIST (QUOTE -619) (QUOTE (-868)))) (|HasCategory| (-2 (|:| -2013 (-1186)) (|:| -2224 (-52))) (LIST (QUOTE -619) (QUOTE (-868))))) +((-12 (|HasCategory| (-2 (|:| -2106 (-1186)) (|:| -2339 (-52))) (QUOTE (-1109))) (|HasCategory| (-2 (|:| -2106 (-1186)) (|:| -2339 (-52))) (LIST (QUOTE -313) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -2106) (QUOTE (-1186))) (LIST (QUOTE |:|) (QUOTE -2339) (QUOTE (-52))))))) (-2892 (|HasCategory| (-2 (|:| -2106 (-1186)) (|:| -2339 (-52))) (QUOTE (-1109))) (|HasCategory| (-52) (QUOTE (-1109)))) (-2892 (|HasCategory| (-2 (|:| -2106 (-1186)) (|:| -2339 (-52))) (QUOTE (-1109))) (|HasCategory| (-2 (|:| -2106 (-1186)) (|:| -2339 (-52))) (LIST (QUOTE -619) (QUOTE (-868)))) (|HasCategory| (-52) (QUOTE (-1109))) (|HasCategory| (-52) (LIST (QUOTE -619) (QUOTE (-868))))) (|HasCategory| (-2 (|:| -2106 (-1186)) (|:| -2339 (-52))) (LIST (QUOTE -620) (QUOTE (-542)))) (-12 (|HasCategory| (-52) (QUOTE (-1109))) (|HasCategory| (-52) (LIST (QUOTE -313) (QUOTE (-52))))) (|HasCategory| (-2 (|:| -2106 (-1186)) (|:| -2339 (-52))) (QUOTE (-1109))) (|HasCategory| (-1186) (QUOTE (-856))) (|HasCategory| (-52) (QUOTE (-1109))) (-2892 (|HasCategory| (-2 (|:| -2106 (-1186)) (|:| -2339 (-52))) (LIST (QUOTE -619) (QUOTE (-868)))) (|HasCategory| (-52) (LIST (QUOTE -619) (QUOTE (-868))))) (|HasCategory| (-52) (LIST (QUOTE -619) (QUOTE (-868)))) (|HasCategory| (-2 (|:| -2106 (-1186)) (|:| -2339 (-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 -1674) +(-1085 |Base| R -1707) ((|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 -1674) +(-1086 |Base| R -1707) ((|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."))) ((-4442 |has| |#1| (-368)) (-4447 |has| |#1| (-368)) (-4441 |has| |#1| (-368)) ((-4451 "*") . T) (-4443 . T) (-4444 . T) (-4446 . T)) -((|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-148))) (|HasCategory| |#1| (QUOTE (-354))) (-2740 (|HasCategory| |#1| (QUOTE (-368))) (|HasCategory| |#1| (QUOTE (-354)))) (|HasCategory| |#1| (QUOTE (-368))) (|HasCategory| |#1| (QUOTE (-373))) (-2740 (-12 (|HasCategory| |#1| (QUOTE (-235))) (|HasCategory| |#1| (QUOTE (-368)))) (|HasCategory| |#1| (QUOTE (-354)))) (-2740 (-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)))) (-2740 (|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))) (-2892 (|HasCategory| |#1| (QUOTE (-368))) (|HasCategory| |#1| (QUOTE (-354)))) (|HasCategory| |#1| (QUOTE (-368))) (|HasCategory| |#1| (QUOTE (-373))) (-2892 (-12 (|HasCategory| |#1| (QUOTE (-235))) (|HasCategory| |#1| (QUOTE (-368)))) (|HasCategory| |#1| (QUOTE (-354)))) (-2892 (-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)))) (-2892 (|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"))) (((-4451 "*") |has| |#1| (-174)) (-4442 |has| |#1| (-562)) (-4447 |has| |#1| (-6 -4447)) (-4444 . T) (-4443 . T) (-4446 . T)) -((|HasCategory| |#1| (QUOTE (-916))) (-2740 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-458))) (|HasCategory| |#1| (QUOTE (-562))) (|HasCategory| |#1| (QUOTE (-916)))) (-2740 (|HasCategory| |#1| (QUOTE (-458))) (|HasCategory| |#1| (QUOTE (-562))) (|HasCategory| |#1| (QUOTE (-916)))) (-2740 (|HasCategory| |#1| (QUOTE (-458))) (|HasCategory| |#1| (QUOTE (-916)))) (|HasCategory| |#1| (QUOTE (-562))) (|HasCategory| |#1| (QUOTE (-174))) (-2740 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-562)))) (-12 (|HasCategory| (-1097 (-1186)) (LIST (QUOTE -893) (QUOTE (-384)))) (|HasCategory| |#1| (LIST (QUOTE -893) (QUOTE (-384))))) (-12 (|HasCategory| (-1097 (-1186)) (LIST (QUOTE -893) (QUOTE (-570)))) (|HasCategory| |#1| (LIST (QUOTE -893) (QUOTE (-570))))) (-12 (|HasCategory| (-1097 (-1186)) (LIST (QUOTE -620) (LIST (QUOTE -899) (QUOTE (-384))))) (|HasCategory| |#1| (LIST (QUOTE -620) (LIST (QUOTE -899) (QUOTE (-384)))))) (-12 (|HasCategory| (-1097 (-1186)) (LIST (QUOTE -620) (LIST (QUOTE -899) (QUOTE (-570))))) (|HasCategory| |#1| (LIST (QUOTE -620) (LIST (QUOTE -899) (QUOTE (-570)))))) (-12 (|HasCategory| (-1097 (-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)))) (-2740 (|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 -4447)) (|HasCategory| |#1| (QUOTE (-458))) (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-916)))) (-2740 (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-916)))) (|HasCategory| |#1| (QUOTE (-146))))) +((|HasCategory| |#1| (QUOTE (-916))) (-2892 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-458))) (|HasCategory| |#1| (QUOTE (-562))) (|HasCategory| |#1| (QUOTE (-916)))) (-2892 (|HasCategory| |#1| (QUOTE (-458))) (|HasCategory| |#1| (QUOTE (-562))) (|HasCategory| |#1| (QUOTE (-916)))) (-2892 (|HasCategory| |#1| (QUOTE (-458))) (|HasCategory| |#1| (QUOTE (-916)))) (|HasCategory| |#1| (QUOTE (-562))) (|HasCategory| |#1| (QUOTE (-174))) (-2892 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-562)))) (-12 (|HasCategory| (-1097 (-1186)) (LIST (QUOTE -893) (QUOTE (-384)))) (|HasCategory| |#1| (LIST (QUOTE -893) (QUOTE (-384))))) (-12 (|HasCategory| (-1097 (-1186)) (LIST (QUOTE -893) (QUOTE (-570)))) (|HasCategory| |#1| (LIST (QUOTE -893) (QUOTE (-570))))) (-12 (|HasCategory| (-1097 (-1186)) (LIST (QUOTE -620) (LIST (QUOTE -899) (QUOTE (-384))))) (|HasCategory| |#1| (LIST (QUOTE -620) (LIST (QUOTE -899) (QUOTE (-384)))))) (-12 (|HasCategory| (-1097 (-1186)) (LIST (QUOTE -620) (LIST (QUOTE -899) (QUOTE (-570))))) (|HasCategory| |#1| (LIST (QUOTE -620) (LIST (QUOTE -899) (QUOTE (-570)))))) (-12 (|HasCategory| (-1097 (-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)))) (-2892 (|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 -4447)) (|HasCategory| |#1| (QUOTE (-458))) (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-916)))) (-2892 (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-916)))) (|HasCategory| |#1| (QUOTE (-146))))) (-1097 S) ((|constructor| (NIL "\\spadtype{OrderlyDifferentialVariable} adds a commonly used sequential ranking to the set of derivatives of an ordered list of differential indeterminates. A sequential ranking is a ranking \\spadfun{<} of the derivatives with the property that for any derivative \\spad{v},{} there are only a finite number of derivatives \\spad{u} with \\spad{u} \\spadfun{<} \\spad{v}. This domain belongs to \\spadtype{DifferentialVariableCategory}. It defines \\spadfun{weight} to be just \\spadfun{order},{} and it defines a sequential ranking \\spadfun{<} on derivatives \\spad{u} by the lexicographic order on the pair (\\spadfun{variable}(\\spad{u}),{} \\spadfun{order}(\\spad{u}))."))) NIL @@ -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)}}"))) ((-4449 . T) (-4439 . T) (-4450 . T)) -((-2740 (-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|))))) +((-2892 (-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.")) (|elt| (($ $ (|List| (|Integer|))) "\\spad{elt((a1,...,an), [i1,...,im])} returns \\spad{(a_i1,...,a_im)}.") (($ $ (|Integer|)) "\\spad{elt((a1,...,an), i)} returns \\spad{ai}.")) (|#| (((|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.")) 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(QUOTE (-570))))) (-12 (|HasCategory| |#3| (QUOTE (-799))) (|HasCategory| |#3| (LIST (QUOTE -1047) (QUOTE (-570))))) (-12 (|HasCategory| |#3| (QUOTE (-854))) (|HasCategory| |#3| (LIST (QUOTE -1047) (QUOTE (-570))))) (-12 (|HasCategory| |#3| (QUOTE (-1058))) (|HasCategory| |#3| (LIST (QUOTE -1047) (QUOTE (-570))))) (-12 (|HasCategory| |#3| (QUOTE (-1109))) (|HasCategory| |#3| (LIST (QUOTE -1047) (QUOTE (-570)))))) (|HasCategory| (-570) (QUOTE (-856))) (-12 (|HasCategory| |#3| (QUOTE (-1058))) (|HasCategory| |#3| (LIST (QUOTE -645) (QUOTE (-570))))) (-12 (|HasCategory| |#3| (QUOTE (-235))) (|HasCategory| |#3| (QUOTE (-1058)))) (-12 (|HasCategory| |#3| (QUOTE (-1058))) (|HasCategory| |#3| (LIST (QUOTE -907) (QUOTE (-1186))))) (-2892 (|HasCategory| |#3| (QUOTE (-1058))) (-12 (|HasCategory| |#3| (QUOTE (-1109))) (|HasCategory| |#3| (LIST (QUOTE -1047) (QUOTE (-570)))))) (-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)))) (|HasAttribute| |#3| (QUOTE -4446)) (|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 -1674) +(-1125 R -1707) ((|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."))) (((-4451 "*") |has| |#1| (-174)) (-4442 |has| |#1| (-562)) (-4447 |has| |#1| (-6 -4447)) (-4444 . T) (-4443 . T) (-4446 . T)) -((|HasCategory| |#1| (QUOTE (-916))) (-2740 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-458))) (|HasCategory| |#1| (QUOTE (-562))) (|HasCategory| |#1| (QUOTE (-916)))) (-2740 (|HasCategory| |#1| (QUOTE (-458))) (|HasCategory| |#1| (QUOTE (-562))) (|HasCategory| |#1| (QUOTE (-916)))) (-2740 (|HasCategory| |#1| (QUOTE (-458))) (|HasCategory| |#1| (QUOTE (-916)))) (|HasCategory| |#1| (QUOTE (-562))) (|HasCategory| |#1| (QUOTE (-174))) (-2740 (|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)))) (-2740 (|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 -4447)) (|HasCategory| |#1| (QUOTE (-458))) (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-916)))) (-2740 (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-916)))) (|HasCategory| |#1| (QUOTE (-146))))) +((|HasCategory| |#1| (QUOTE (-916))) (-2892 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-458))) (|HasCategory| |#1| (QUOTE (-562))) (|HasCategory| |#1| (QUOTE (-916)))) (-2892 (|HasCategory| |#1| (QUOTE (-458))) (|HasCategory| |#1| (QUOTE (-562))) (|HasCategory| |#1| (QUOTE (-916)))) (-2892 (|HasCategory| |#1| (QUOTE (-458))) (|HasCategory| |#1| (QUOTE (-916)))) (|HasCategory| |#1| (QUOTE (-562))) (|HasCategory| |#1| (QUOTE (-174))) (-2892 (|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)))) (-2892 (|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 -4447)) (|HasCategory| |#1| (QUOTE (-458))) (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-916)))) (-2892 (-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}."))) (((-4451 "*") |has| |#1| (-174)) (-4442 |has| |#1| (-562)) (-4444 . T) (-4443 . T) (-4446 . T)) -((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-148))) (|HasCategory| |#1| (QUOTE (-146))) (-2740 (|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))) (-2892 (|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}"))) ((-4450 . T) (-4449 . T)) NIL -(-1137 UP -1674) +(-1137 UP -1707) ((|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") $) "\\axiom{extractSplittingLeaf(a)} returns the left most leaf (as a tree) whose status is \\spad{false} if any,{} else \"failed\" is returned."))) ((-4449 . T) (-4450 . T)) -((-12 (|HasCategory| (-1149 |#1| |#2|) (LIST (QUOTE -313) (LIST (QUOTE -1149) (|devaluate| |#1|) (|devaluate| |#2|)))) (|HasCategory| (-1149 |#1| |#2|) (QUOTE (-1109)))) (|HasCategory| (-1149 |#1| |#2|) (QUOTE (-1109))) (-2740 (|HasCategory| (-1149 |#1| |#2|) (LIST (QUOTE -619) (QUOTE (-868)))) (-12 (|HasCategory| (-1149 |#1| |#2|) (LIST (QUOTE -313) (LIST (QUOTE -1149) (|devaluate| |#1|) (|devaluate| |#2|)))) (|HasCategory| (-1149 |#1| |#2|) (QUOTE (-1109))))) (|HasCategory| (-1149 |#1| |#2|) (LIST (QUOTE -619) (QUOTE (-868))))) +((-12 (|HasCategory| (-1149 |#1| |#2|) (LIST (QUOTE -313) (LIST (QUOTE -1149) (|devaluate| |#1|) (|devaluate| |#2|)))) (|HasCategory| (-1149 |#1| |#2|) (QUOTE (-1109)))) (|HasCategory| (-1149 |#1| |#2|) (QUOTE (-1109))) (-2892 (|HasCategory| (-1149 |#1| |#2|) (LIST (QUOTE -619) (QUOTE (-868)))) (-12 (|HasCategory| (-1149 |#1| |#2|) (LIST (QUOTE -313) (LIST (QUOTE -1149) (|devaluate| |#1|) (|devaluate| |#2|)))) (|HasCategory| (-1149 |#1| |#2|) (QUOTE (-1109))))) (|HasCategory| (-1149 |#1| |#2|) (LIST (QUOTE -619) (QUOTE (-868))))) (-1151 |ndim| R) ((|constructor| (NIL "\\spadtype{SquareMatrix} is a matrix domain of square matrices,{} where the number of rows (= number of columns) is a parameter of the type.")) (|unitsKnown| ((|attribute|) "the invertible matrices are simply the matrices whose determinants are units in the Ring \\spad{R}.")) (|central| ((|attribute|) "the elements of the Ring \\spad{R},{} viewed as diagonal matrices,{} commute with all matrices and,{} indeed,{} are the only matrices which commute with all matrices.")) (|squareMatrix| (($ (|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}."))) ((-4446 . T) (-4438 |has| |#2| (-6 (-4451 "*"))) (-4449 . T) (-4443 . T) (-4444 . T)) -((|HasCategory| |#2| (LIST (QUOTE -907) (QUOTE (-1186)))) (|HasCategory| |#2| (QUOTE (-235))) (|HasAttribute| |#2| (QUOTE (-4451 "*"))) (|HasCategory| |#2| (LIST (QUOTE -645) (QUOTE (-570)))) (|HasCategory| |#2| (LIST (QUOTE -1047) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasCategory| |#2| (LIST (QUOTE -1047) (QUOTE (-570)))) (-2740 (-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))) (-2740 (|HasAttribute| |#2| (QUOTE (-4451 "*"))) (|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 (-4451 "*"))) (|HasCategory| |#2| (LIST (QUOTE -645) (QUOTE (-570)))) (|HasCategory| |#2| (LIST (QUOTE -1047) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasCategory| |#2| (LIST (QUOTE -1047) (QUOTE (-570)))) (-2892 (-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))) (-2892 (|HasAttribute| |#2| (QUOTE (-4451 "*"))) (|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}."))) ((-4449 . T) (-4450 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1109))) (-2740 (-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))) (-2892 (-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."))) ((-4450 . T)) -((-12 (|HasCategory| (-2 (|:| -2013 |#1|) (|:| -2224 |#2|)) (QUOTE (-1109))) (|HasCategory| (-2 (|:| -2013 |#1|) (|:| -2224 |#2|)) (LIST (QUOTE -313) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -2013) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -2224) (|devaluate| |#2|)))))) (-2740 (|HasCategory| (-2 (|:| -2013 |#1|) (|:| -2224 |#2|)) (QUOTE (-1109))) (|HasCategory| |#2| (QUOTE (-1109)))) (-2740 (|HasCategory| (-2 (|:| -2013 |#1|) (|:| -2224 |#2|)) (QUOTE (-1109))) (|HasCategory| (-2 (|:| -2013 |#1|) (|:| -2224 |#2|)) (LIST (QUOTE -619) (QUOTE (-868)))) (|HasCategory| |#2| (QUOTE (-1109))) (|HasCategory| |#2| (LIST (QUOTE -619) (QUOTE (-868))))) (|HasCategory| (-2 (|:| -2013 |#1|) (|:| -2224 |#2|)) (LIST (QUOTE -620) (QUOTE (-542)))) (-12 (|HasCategory| |#2| (QUOTE (-1109))) (|HasCategory| |#2| (LIST (QUOTE -313) (|devaluate| |#2|)))) (|HasCategory| |#1| (QUOTE (-856))) (-2740 (|HasCategory| (-2 (|:| -2013 |#1|) (|:| -2224 |#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 (|:| -2013 |#1|) (|:| -2224 |#2|)) (LIST (QUOTE -619) (QUOTE (-868)))) (|HasCategory| (-2 (|:| -2013 |#1|) (|:| -2224 |#2|)) (QUOTE (-1109)))) +((-12 (|HasCategory| (-2 (|:| -2106 |#1|) (|:| -2339 |#2|)) (QUOTE (-1109))) (|HasCategory| (-2 (|:| -2106 |#1|) (|:| -2339 |#2|)) (LIST (QUOTE -313) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -2106) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -2339) (|devaluate| |#2|)))))) (-2892 (|HasCategory| (-2 (|:| -2106 |#1|) (|:| -2339 |#2|)) (QUOTE (-1109))) (|HasCategory| |#2| (QUOTE (-1109)))) (-2892 (|HasCategory| (-2 (|:| -2106 |#1|) (|:| -2339 |#2|)) (QUOTE (-1109))) (|HasCategory| (-2 (|:| -2106 |#1|) (|:| -2339 |#2|)) (LIST (QUOTE -619) (QUOTE (-868)))) (|HasCategory| |#2| (QUOTE (-1109))) (|HasCategory| |#2| (LIST (QUOTE -619) (QUOTE (-868))))) (|HasCategory| (-2 (|:| -2106 |#1|) (|:| -2339 |#2|)) (LIST (QUOTE -620) (QUOTE (-542)))) (-12 (|HasCategory| |#2| (QUOTE (-1109))) (|HasCategory| |#2| (LIST (QUOTE -313) (|devaluate| |#2|)))) (|HasCategory| |#1| (QUOTE (-856))) (-2892 (|HasCategory| (-2 (|:| -2106 |#1|) (|:| -2339 |#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 (|:| -2106 |#1|) (|:| -2339 |#2|)) (LIST (QUOTE -619) (QUOTE (-868)))) (|HasCategory| (-2 (|:| -2106 |#1|) (|:| -2339 |#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."))) ((-4450 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1109))) (-2740 (-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))) (-2892 (-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"))) ((-4450 . T) (-4449 . T)) @@ -4603,11 +4603,11 @@ NIL (-1168) NIL ((-4450 . T) (-4449 . T)) -((-2740 (-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)))))) +((-2892 (-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."))) ((-4449 . T) (-4450 . T)) -((-12 (|HasCategory| (-2 (|:| -2013 (-1168)) (|:| -2224 |#1|)) (QUOTE (-1109))) (|HasCategory| (-2 (|:| -2013 (-1168)) (|:| -2224 |#1|)) (LIST (QUOTE -313) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -2013) (QUOTE (-1168))) (LIST (QUOTE |:|) (QUOTE -2224) (|devaluate| |#1|)))))) (-2740 (|HasCategory| (-2 (|:| -2013 (-1168)) (|:| -2224 |#1|)) (QUOTE (-1109))) (|HasCategory| |#1| (QUOTE (-1109)))) (-2740 (|HasCategory| (-2 (|:| -2013 (-1168)) (|:| -2224 |#1|)) (QUOTE (-1109))) (|HasCategory| (-2 (|:| -2013 (-1168)) (|:| -2224 |#1|)) (LIST (QUOTE -619) (QUOTE (-868)))) (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-868))))) (|HasCategory| (-2 (|:| -2013 (-1168)) (|:| -2224 |#1|)) (LIST (QUOTE -620) (QUOTE (-542)))) (-12 (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|)))) (|HasCategory| (-2 (|:| -2013 (-1168)) (|:| -2224 |#1|)) (QUOTE (-1109))) (|HasCategory| (-1168) (QUOTE (-856))) (|HasCategory| |#1| (QUOTE (-1109))) (-2740 (|HasCategory| (-2 (|:| -2013 (-1168)) (|:| -2224 |#1|)) (LIST (QUOTE -619) (QUOTE (-868)))) (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-868))))) (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-868)))) (|HasCategory| (-2 (|:| -2013 (-1168)) (|:| -2224 |#1|)) (LIST (QUOTE -619) (QUOTE (-868))))) +((-12 (|HasCategory| (-2 (|:| -2106 (-1168)) (|:| -2339 |#1|)) (QUOTE (-1109))) (|HasCategory| (-2 (|:| -2106 (-1168)) (|:| -2339 |#1|)) (LIST (QUOTE -313) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -2106) (QUOTE (-1168))) (LIST (QUOTE |:|) (QUOTE -2339) (|devaluate| |#1|)))))) (-2892 (|HasCategory| (-2 (|:| -2106 (-1168)) (|:| -2339 |#1|)) (QUOTE (-1109))) (|HasCategory| |#1| (QUOTE (-1109)))) (-2892 (|HasCategory| (-2 (|:| -2106 (-1168)) (|:| -2339 |#1|)) (QUOTE (-1109))) (|HasCategory| (-2 (|:| -2106 (-1168)) (|:| -2339 |#1|)) (LIST (QUOTE -619) (QUOTE (-868)))) (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-868))))) (|HasCategory| (-2 (|:| -2106 (-1168)) (|:| -2339 |#1|)) (LIST (QUOTE -620) (QUOTE (-542)))) (-12 (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|)))) (|HasCategory| (-2 (|:| -2106 (-1168)) (|:| -2339 |#1|)) (QUOTE (-1109))) (|HasCategory| (-1168) (QUOTE (-856))) (|HasCategory| |#1| (QUOTE (-1109))) (-2892 (|HasCategory| (-2 (|:| -2106 (-1168)) (|:| -2339 |#1|)) (LIST (QUOTE -619) (QUOTE (-868)))) (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-868))))) (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-868)))) (|HasCategory| (-2 (|:| -2106 (-1168)) (|:| -2339 |#1|)) (LIST (QUOTE -619) (QUOTE (-868))))) (-1170 A) ((|constructor| (NIL "StreamTaylorSeriesOperations implements Taylor series arithmetic,{} where a Taylor series is represented by a stream of its coefficients.")) (|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. 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| (($ (|Variable| |#2|)) "\\spad{coerce(var)} converts the series variable \\spad{var} into a Laurent series."))) -(((-4451 "*") -2740 (-1765 (|has| |#1| (-368)) (|has| (-1184 |#1| |#2| |#3|) (-826))) (|has| |#1| (-174)) (-1765 (|has| |#1| (-368)) (|has| (-1184 |#1| |#2| |#3|) (-916)))) (-4442 -2740 (-1765 (|has| |#1| (-368)) (|has| (-1184 |#1| |#2| |#3|) (-826))) (|has| |#1| (-562)) (-1765 (|has| |#1| (-368)) (|has| (-1184 |#1| |#2| |#3|) (-916)))) (-4447 |has| |#1| (-368)) (-4441 |has| |#1| (-368)) (-4443 . T) (-4444 . T) (-4446 . T)) -((-2740 (-12 (|HasCategory| (-1184 |#1| |#2| |#3|) (QUOTE (-826))) (|HasCategory| |#1| (QUOTE (-368)))) (-12 (|HasCategory| (-1184 |#1| |#2| |#3|) (QUOTE (-856))) (|HasCategory| |#1| (QUOTE (-368)))) (-12 (|HasCategory| (-1184 |#1| |#2| |#3|) (QUOTE (-916))) (|HasCategory| |#1| (QUOTE (-368)))) (-12 (|HasCategory| (-1184 |#1| |#2| |#3|) (QUOTE (-1031))) (|HasCategory| |#1| (QUOTE (-368)))) (-12 (|HasCategory| (-1184 |#1| |#2| |#3|) (QUOTE (-1161))) (|HasCategory| |#1| (QUOTE (-368)))) (-12 (|HasCategory| (-1184 |#1| |#2| |#3|) (LIST (QUOTE -620) (QUOTE (-542)))) (|HasCategory| |#1| (QUOTE (-368)))) (-12 (|HasCategory| (-1184 |#1| |#2| |#3|) (LIST (QUOTE -620) (LIST (QUOTE -899) (QUOTE (-384))))) (|HasCategory| |#1| (QUOTE (-368)))) (-12 (|HasCategory| (-1184 |#1| |#2| |#3|) (LIST (QUOTE -620) (LIST (QUOTE -899) (QUOTE (-570))))) (|HasCategory| |#1| (QUOTE (-368)))) (-12 (|HasCategory| (-1184 |#1| |#2| |#3|) (LIST (QUOTE -290) (LIST (QUOTE -1184) (|devaluate| |#1|) (|devaluate| 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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 -4447)) (|HasCategory| |#1| (QUOTE (-458))) (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-916)))) (-2892 (-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}."))) (((-4451 "*") |has| |#1| (-174)) (-4442 |has| |#1| (-562)) (-4447 |has| |#1| (-368)) (-4441 |has| |#1| (-368)) (-4443 . T) (-4444 . T) (-4446 . T)) -((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasCategory| |#1| (QUOTE (-562))) (|HasCategory| |#1| (QUOTE (-174))) (-2740 (|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))) (-2740 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-368))) (|HasCategory| |#1| (QUOTE (-562)))) (-2740 (|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 -3735) (LIST (|devaluate| |#1|) (QUOTE (-1186)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -413) (QUOTE (-570)))))) (-2740 (-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 -3722) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1186))))) (|HasSignature| |#1| (LIST (QUOTE -1713) (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))) (-2892 (|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))) (-2892 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-368))) (|HasCategory| |#1| (QUOTE (-562)))) (-2892 (|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 -3799) (LIST (|devaluate| |#1|) (QUOTE (-1186)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -413) (QUOTE (-570)))))) (-2892 (-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 -4201) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1186))))) (|HasSignature| |#1| (LIST (QUOTE -1754) (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}."))) (((-4451 "*") |has| |#1| (-174)) (-4442 |has| |#1| (-562)) (-4443 . T) (-4444 . T) (-4446 . T)) -((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasCategory| |#1| (QUOTE (-562))) (-2740 (|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 -3735) (LIST (|devaluate| |#1|) (QUOTE (-1186)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-777))))) (|HasCategory| |#1| (QUOTE (-368))) (-2740 (-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 -3722) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1186))))) (|HasSignature| |#1| (LIST (QUOTE -1713) (LIST (LIST (QUOTE -650) (QUOTE (-1186))) (|devaluate| |#1|))))))) +((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasCategory| |#1| (QUOTE (-562))) (-2892 (|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 -3799) (LIST (|devaluate| |#1|) (QUOTE (-1186)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-777))))) (|HasCategory| |#1| (QUOTE (-368))) (-2892 (-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 -4201) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1186))))) (|HasSignature| |#1| (LIST (QUOTE -1754) (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}.")) 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T)) -((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasCategory| |#1| (QUOTE (-562))) (-2740 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-562)))) (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-148))) (-2740 (|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 -4447))) +((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasCategory| |#1| (QUOTE (-562))) (-2892 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-562)))) (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-148))) (-2892 (|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 -4447))) (-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}"))) ((-4449 . T) (-4450 . T)) -((-12 (|HasCategory| (-2 (|:| -2013 |#1|) (|:| -2224 |#2|)) (QUOTE (-1109))) (|HasCategory| (-2 (|:| -2013 |#1|) (|:| -2224 |#2|)) (LIST (QUOTE -313) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -2013) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -2224) (|devaluate| |#2|)))))) (-2740 (|HasCategory| (-2 (|:| -2013 |#1|) (|:| -2224 |#2|)) (QUOTE (-1109))) (|HasCategory| |#2| (QUOTE (-1109)))) (-2740 (|HasCategory| (-2 (|:| -2013 |#1|) (|:| -2224 |#2|)) (QUOTE (-1109))) (|HasCategory| (-2 (|:| -2013 |#1|) (|:| -2224 |#2|)) (LIST (QUOTE -619) (QUOTE (-868)))) (|HasCategory| |#2| (QUOTE (-1109))) (|HasCategory| |#2| (LIST (QUOTE -619) (QUOTE (-868))))) (|HasCategory| (-2 (|:| -2013 |#1|) (|:| -2224 |#2|)) (LIST (QUOTE -620) (QUOTE (-542)))) (-12 (|HasCategory| |#2| (QUOTE (-1109))) (|HasCategory| |#2| (LIST (QUOTE -313) (|devaluate| |#2|)))) (|HasCategory| (-2 (|:| -2013 |#1|) (|:| -2224 |#2|)) (QUOTE (-1109))) (|HasCategory| |#1| (QUOTE (-856))) (|HasCategory| |#2| (QUOTE (-1109))) (-2740 (|HasCategory| (-2 (|:| -2013 |#1|) (|:| -2224 |#2|)) (LIST (QUOTE -619) (QUOTE (-868)))) (|HasCategory| |#2| (LIST (QUOTE -619) (QUOTE (-868))))) (|HasCategory| |#2| (LIST (QUOTE -619) (QUOTE (-868)))) (|HasCategory| (-2 (|:| -2013 |#1|) (|:| -2224 |#2|)) (LIST (QUOTE -619) (QUOTE (-868))))) +((-12 (|HasCategory| (-2 (|:| -2106 |#1|) (|:| -2339 |#2|)) (QUOTE (-1109))) (|HasCategory| (-2 (|:| -2106 |#1|) (|:| -2339 |#2|)) (LIST (QUOTE -313) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -2106) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -2339) (|devaluate| |#2|)))))) (-2892 (|HasCategory| (-2 (|:| -2106 |#1|) (|:| -2339 |#2|)) (QUOTE (-1109))) (|HasCategory| |#2| (QUOTE (-1109)))) (-2892 (|HasCategory| (-2 (|:| -2106 |#1|) (|:| -2339 |#2|)) (QUOTE (-1109))) (|HasCategory| (-2 (|:| -2106 |#1|) (|:| -2339 |#2|)) (LIST (QUOTE -619) (QUOTE (-868)))) (|HasCategory| |#2| (QUOTE (-1109))) (|HasCategory| |#2| (LIST (QUOTE -619) (QUOTE (-868))))) (|HasCategory| (-2 (|:| -2106 |#1|) (|:| -2339 |#2|)) (LIST (QUOTE -620) (QUOTE (-542)))) (-12 (|HasCategory| |#2| (QUOTE (-1109))) (|HasCategory| |#2| (LIST (QUOTE -313) (|devaluate| |#2|)))) (|HasCategory| (-2 (|:| -2106 |#1|) (|:| -2339 |#2|)) (QUOTE (-1109))) (|HasCategory| |#1| (QUOTE (-856))) (|HasCategory| |#2| (QUOTE (-1109))) (-2892 (|HasCategory| (-2 (|:| -2106 |#1|) (|:| -2339 |#2|)) (LIST (QUOTE -619) (QUOTE (-868)))) (|HasCategory| |#2| (LIST (QUOTE -619) (QUOTE (-868))))) (|HasCategory| |#2| (LIST (QUOTE -619) (QUOTE (-868)))) (|HasCategory| (-2 (|:| -2106 |#1|) (|:| -2339 |#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| $)) "\\spad{tree(nd,ls)} creates a tree with value \\spad{nd},{} and children \\spad{ls}."))) ((-4450 . T) (-4449 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1109))) (-2740 (-12 (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-868))))) (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-868))))) +((-12 (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1109))) (-2892 (-12 (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-868))))) (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-868))))) (-1214 S) ((|constructor| (NIL "Category for the trigonometric functions.")) (|tan| (($ $) "\\spad{tan(x)} returns the tangent of \\spad{x}.")) (|sin| (($ $) "\\spad{sin(x)} returns the sine of \\spad{x}.")) (|sec| (($ $) "\\spad{sec(x)} returns the secant of \\spad{x}.")) (|csc| (($ $) "\\spad{csc(x)} returns the cosecant of \\spad{x}.")) (|cot| (($ $) "\\spad{cot(x)} returns the cotangent of \\spad{x}.")) (|cos| (($ $) "\\spad{cos(x)} returns the cosine of \\spad{x}."))) NIL @@ -4792,7 +4792,7 @@ NIL ((|constructor| (NIL "Category for the trigonometric functions.")) (|tan| (($ $) "\\spad{tan(x)} returns the tangent of \\spad{x}.")) (|sin| (($ $) "\\spad{sin(x)} returns the sine of \\spad{x}.")) (|sec| (($ $) "\\spad{sec(x)} returns the secant of \\spad{x}.")) (|csc| (($ $) "\\spad{csc(x)} returns the cosecant of \\spad{x}.")) (|cot| (($ $) "\\spad{cot(x)} returns the cotangent of \\spad{x}.")) (|cos| (($ $) "\\spad{cos(x)} returns the cosine of \\spad{x}."))) NIL NIL -(-1216 R -1674) +(-1216 R -1707) ((|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 -1674) +(-1218 R -1707) ((|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}."))) (((-4451 "*") |has| |#1| (-174)) (-4442 |has| |#1| (-562)) (-4444 . T) (-4443 . T) (-4446 . T)) -((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-148))) (|HasCategory| |#1| (QUOTE (-146))) (-2740 (|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))) (-2892 (|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 -1674) +(-1225 -1707) ((|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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(LIST (QUOTE -1047) (QUOTE (-570)))) (|HasCategory| |#1| (QUOTE (-368)))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -413) (QUOTE (-570)))))) (-2892 (-12 (|HasCategory| (-1269 |#1| |#2| |#3|) (QUOTE (-826))) (|HasCategory| |#1| (QUOTE (-368)))) (-12 (|HasCategory| (-1269 |#1| |#2| |#3|) (QUOTE (-916))) (|HasCategory| |#1| (QUOTE (-368)))) (|HasCategory| |#1| (QUOTE (-174)))) (-12 (|HasCategory| (-1269 |#1| |#2| |#3|) (QUOTE (-856))) (|HasCategory| |#1| (QUOTE (-368)))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -413) (QUOTE (-570))))) (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| (-1269 |#1| |#2| |#3|) (QUOTE (-916))) (|HasCategory| |#1| (QUOTE (-368)))) (-2892 (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| (-1269 |#1| |#2| |#3|) (QUOTE (-916))) (|HasCategory| |#1| (QUOTE (-368)))) (-12 (|HasCategory| (-1269 |#1| |#2| |#3|) (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-368)))) (|HasCategory| |#1| (QUOTE (-146))))) (-1242 ZP) ((|constructor| (NIL "Package for the factorization of univariate polynomials with integer coefficients. The factorization is done by \"lifting\" (HENSEL) the factorization over a finite field.")) (|henselFact| (((|Record| (|:| |contp| (|Integer|)) (|:| |factors| (|List| (|Record| (|:| |irr| |#1|) (|:| |pow| (|Integer|)))))) |#1| (|Boolean|)) "\\spad{henselFact(m,flag)} returns the factorization of \\spad{m},{} FinalFact is a Record \\spad{s}.\\spad{t}. FinalFact.contp=content \\spad{m},{} FinalFact.factors=List of irreducible factors of \\spad{m} with exponent ,{} if \\spad{flag} =true the polynomial is assumed square free.")) (|factorSquareFree| (((|Factored| |#1|) |#1|) "\\spad{factorSquareFree(m)} returns the factorization of \\spad{m} square free polynomial")) (|factor| (((|Factored| |#1|) |#1|) "\\spad{factor(m)} returns the factorization of \\spad{m}"))) NIL @@ -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}"))) (((-4451 "*") |has| |#2| (-174)) (-4442 |has| |#2| (-562)) (-4445 |has| |#2| (-368)) (-4447 |has| |#2| (-6 -4447)) (-4444 . T) (-4443 . T) (-4446 . T)) -((|HasCategory| |#2| (QUOTE (-916))) (|HasCategory| |#2| (QUOTE (-562))) (|HasCategory| |#2| (QUOTE (-174))) (-2740 (|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)))) (-2740 (|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))))) (-2740 (|HasCategory| |#2| (QUOTE (-174))) (|HasCategory| |#2| (QUOTE (-368))) (|HasCategory| |#2| (QUOTE (-458))) (|HasCategory| |#2| (QUOTE (-562))) (|HasCategory| |#2| (QUOTE (-916)))) (-2740 (|HasCategory| |#2| (QUOTE (-368))) (|HasCategory| |#2| (QUOTE (-458))) (|HasCategory| |#2| (QUOTE (-562))) (|HasCategory| |#2| (QUOTE (-916)))) (-2740 (|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 -4447)) (|HasCategory| |#2| (QUOTE (-458))) (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| |#2| (QUOTE (-916)))) (-2740 (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| |#2| (QUOTE (-916)))) (|HasCategory| |#2| (QUOTE (-146))))) +((|HasCategory| |#2| (QUOTE (-916))) (|HasCategory| |#2| (QUOTE (-562))) (|HasCategory| |#2| (QUOTE (-174))) (-2892 (|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)))) (-2892 (|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))))) (-2892 (|HasCategory| |#2| (QUOTE (-174))) (|HasCategory| |#2| (QUOTE (-368))) (|HasCategory| |#2| (QUOTE (-458))) (|HasCategory| |#2| (QUOTE (-562))) (|HasCategory| |#2| (QUOTE (-916)))) (-2892 (|HasCategory| |#2| (QUOTE (-368))) (|HasCategory| |#2| (QUOTE (-458))) (|HasCategory| |#2| (QUOTE (-562))) (|HasCategory| |#2| (QUOTE (-916)))) (-2892 (|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 -4447)) (|HasCategory| |#2| (QUOTE (-458))) (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| |#2| (QUOTE (-916)))) (-2892 (-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}.")) (|elt| ((|#2| $ |#3|) "\\spad{elt(f(x),r)} returns the coefficient of the term of degree \\spad{r} in \\spad{f(x)}. This is the same as the function \\spadfun{coefficient}.")) (|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 -3735) (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 -3799) (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}.")) (|elt| ((|#1| $ |#2|) "\\spad{elt(f(x),r)} returns the coefficient of the term of degree \\spad{r} in \\spad{f(x)}. This is the same as the function \\spadfun{coefficient}.")) (|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."))) (((-4451 "*") |has| |#1| (-174)) (-4442 |has| |#1| (-562)) (-4443 . T) (-4444 . T) (-4446 . 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)}."))) (((-4451 "*") |has| |#1| (-174)) (-4442 |has| |#1| (-562)) (-4447 |has| |#1| (-368)) (-4441 |has| |#1| (-368)) (-4443 . T) (-4444 . T) (-4446 . T)) -((|HasCategory| |#1| (QUOTE (-562))) (|HasCategory| |#1| (QUOTE (-174))) (-2740 (|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))) (-2740 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-368))) (|HasCategory| |#1| (QUOTE (-562)))) (-2740 (|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 -3735) (LIST (|devaluate| |#1|) (QUOTE (-1186)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -413) (QUOTE (-570)))))) (-2740 (-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 -3722) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1186))))) (|HasSignature| |#1| (LIST (QUOTE -1713) (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))) (-2892 (|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))) (-2892 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-368))) (|HasCategory| |#1| (QUOTE (-562)))) (-2892 (|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 -3799) (LIST (|devaluate| |#1|) (QUOTE (-1186)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -413) (QUOTE (-570)))))) (-2892 (-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 -4201) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1186))))) (|HasSignature| |#1| (LIST (QUOTE -1754) (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}."))) (((-4451 "*") |has| |#1| (-174)) (-4442 |has| |#1| (-562)) (-4447 |has| |#1| (-368)) (-4441 |has| |#1| (-368)) (-4443 . T) (-4444 . T) (-4446 . T)) -((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasCategory| |#1| (QUOTE (-562))) (|HasCategory| |#1| (QUOTE (-174))) (-2740 (|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))) (-2740 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-368))) (|HasCategory| |#1| (QUOTE (-562)))) (-2740 (|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 -3735) (LIST (|devaluate| |#1|) (QUOTE (-1186)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -413) (QUOTE (-570)))))) (-2740 (-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 -3722) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1186))))) (|HasSignature| |#1| (LIST (QUOTE -1713) (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))) (-2892 (|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))) (-2892 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-368))) (|HasCategory| |#1| (QUOTE (-562)))) (-2892 (|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 -3799) (LIST (|devaluate| |#1|) (QUOTE (-1186)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -413) (QUOTE (-570)))))) (-2892 (-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 -4201) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1186))))) (|HasSignature| |#1| (LIST (QUOTE -1754) (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))}."))) (((-4451 "*") |has| (-1262 |#2| |#3| |#4|) (-174)) (-4442 |has| (-1262 |#2| |#3| |#4|) (-562)) (-4443 . T) (-4444 . T) (-4446 . 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))) (-2740 (|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))) (-2892 (|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 -1713) (LIST (LIST (QUOTE -650) (QUOTE (-1186))) (|devaluate| |#2|)))) (|HasSignature| |#2| (LIST (QUOTE -3722) (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 -1754) (LIST (LIST (QUOTE -650) (QUOTE (-1186))) (|devaluate| |#2|)))) (|HasSignature| |#2| (LIST (QUOTE -4201) (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."))) (((-4451 "*") |has| |#1| (-174)) (-4442 |has| |#1| (-562)) (-4443 . T) (-4444 . T) (-4446 . 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}."))) (((-4451 "*") |has| |#1| (-174)) (-4442 |has| |#1| (-562)) (-4443 . T) (-4444 . T) (-4446 . T)) -((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasCategory| |#1| (QUOTE (-562))) (-2740 (|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 -3735) (LIST (|devaluate| |#1|) (QUOTE (-1186)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-777))))) (|HasCategory| |#1| (QUOTE (-368))) (-2740 (-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 -3722) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1186))))) (|HasSignature| |#1| (LIST (QUOTE -1713) (LIST (LIST (QUOTE -650) (QUOTE (-1186))) (|devaluate| |#1|))))))) +((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasCategory| |#1| (QUOTE (-562))) (-2892 (|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 -3799) (LIST (|devaluate| |#1|) (QUOTE (-1186)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-777))))) (|HasCategory| |#1| (QUOTE (-368))) (-2892 (-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 -4201) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1186))))) (|HasSignature| |#1| (LIST (QUOTE -1754) (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 -1674 UP L UTS) +(-1271 -1707 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."))) ((-4450 . T) (-4449 . T)) -((-2740 (-12 (|HasCategory| |#1| (QUOTE (-856))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|))))) (-2740 (-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)))) (-2740 (|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|))))) +((-2892 (-12 (|HasCategory| |#1| (QUOTE (-856))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|))))) (-2892 (-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)))) (-2892 (|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 -1674) +(-1286 K R UP -1707) ((|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| $) "\\spad{v * x} returns the product of a variable \\spad{x} by \\spad{x}."))) ((-4442 |has| |#2| (-6 -4442)) (-4444 . T) (-4443 . T) (-4446 . T)) NIL -(-1295 S -1674) +(-1295 S -1707) ((|constructor| (NIL "ExtensionField {\\em F} is the category of fields which extend the field \\spad{F}")) (|Frobenius| (($ $ (|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|) $) "\\spad{algebraic?(a)} tests whether an element \\spad{a} is algebraic with respect to the ground field \\spad{F}."))) NIL ((|HasCategory| |#2| (QUOTE (-373))) (|HasCategory| |#2| (QUOTE (-146))) (|HasCategory| |#2| (QUOTE (-148)))) -(-1296 -1674) +(-1296 -1707) ((|constructor| (NIL "ExtensionField {\\em F} is the category of fields which extend the field \\spad{F}")) (|Frobenius| (($ $ (|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|) $) "\\spad{algebraic?(a)} tests whether an element \\spad{a} is algebraic with respect to the ground field \\spad{F}."))) ((-4441 . T) (-4447 . T) (-4442 . T) ((-4451 "*") . T) (-4443 . T) (-4444 . T) (-4446 . T)) NIL diff --git a/src/share/algebra/category.daase b/src/share/algebra/category.daase index 63d69f49..c1c235c9 100644 --- a/src/share/algebra/category.daase +++ b/src/share/algebra/category.daase @@ -1,15 +1,15 @@ -(188596 . 3480583739) -(((|#2| |#2|) -12 (|has| |#2| (-313 |#2|)) (|has| |#2| (-1109))) ((#0=(-2 (|:| -2013 |#1|) (|:| -2224 |#2|)) #0#) |has| (-2 (|:| -2013 |#1|) (|:| -2224 |#2|)) (-313 (-2 (|:| -2013 |#1|) (|:| -2224 |#2|))))) -((((-570)) . T) (($) -2740 (|has| |#1| (-311)) (|has| |#1| (-368)) (|has| |#1| (-354)) (|has| |#1| (-562))) (((-413 (-570))) -2740 (|has| |#1| (-368)) (|has| |#1| (-354)) (|has| |#1| (-1047 (-413 (-570))))) ((|#1|) . T)) +(188596 . 3480761531) +(((|#2| |#2|) -12 (|has| |#2| (-313 |#2|)) (|has| |#2| (-1109))) ((#0=(-2 (|:| -2106 |#1|) (|:| -2339 |#2|)) #0#) |has| (-2 (|:| -2106 |#1|) (|:| -2339 |#2|)) (-313 (-2 (|:| -2106 |#1|) (|:| -2339 |#2|))))) +((((-570)) . T) (($) -2892 (|has| |#1| (-311)) (|has| |#1| (-368)) (|has| |#1| (-354)) (|has| |#1| (-562))) (((-413 (-570))) -2892 (|has| |#1| (-368)) (|has| |#1| (-354)) (|has| |#1| (-1047 (-413 (-570))))) ((|#1|) . T)) (((|#2| |#2|) . T)) ((((-570)) . T)) -((($ $) -2740 (|has| |#2| (-174)) (|has| |#2| (-368)) (|has| |#2| (-458)) (|has| |#2| (-562)) (|has| |#2| (-916))) ((|#2| |#2|) . T) ((#0=(-413 (-570)) #0#) |has| |#2| (-38 (-413 (-570))))) +((($ $) -2892 (|has| |#2| (-174)) (|has| |#2| (-368)) (|has| |#2| (-458)) (|has| |#2| (-562)) (|has| |#2| (-916))) ((|#2| |#2|) . T) ((#0=(-413 (-570)) #0#) |has| |#2| (-38 (-413 (-570))))) ((($) . T)) (((|#1|) . T)) ((($) . T) ((|#1|) . T) (((-413 (-570))) |has| |#1| (-38 (-413 (-570))))) (((|#2|) . T)) -((($) -2740 (|has| |#2| (-174)) (|has| |#2| (-368)) (|has| |#2| (-458)) (|has| |#2| (-562)) (|has| |#2| (-916))) ((|#2|) . T) (((-413 (-570))) |has| |#2| (-38 (-413 (-570))))) +((($) -2892 (|has| |#2| (-174)) (|has| |#2| (-368)) (|has| |#2| (-458)) (|has| |#2| (-562)) (|has| |#2| (-916))) ((|#2|) . T) (((-413 (-570))) |has| |#2| (-38 (-413 (-570))))) (|has| |#1| (-916)) ((((-868)) . T)) ((((-868)) . T)) @@ -24,19 +24,19 @@ ((((-227)) . T) (((-868)) . T)) (((|#1|) -12 (|has| |#1| (-313 |#1|)) (|has| |#1| (-1109)))) (((|#1|) . T)) -(-2740 (|has| |#1| (-21)) (|has| |#1| (-854))) -((($ $) . T) ((#0=(-413 (-570)) #0#) -2740 (|has| |#1| (-368)) (|has| |#1| (-354))) ((|#1| |#1|) . T)) -(-2740 (|has| |#1| (-826)) (|has| |#1| (-856))) +(-2892 (|has| |#1| (-21)) (|has| |#1| (-854))) +((($ $) . T) ((#0=(-413 (-570)) #0#) -2892 (|has| |#1| (-368)) (|has| |#1| (-354))) ((|#1| |#1|) . T)) +(-2892 (|has| |#1| (-826)) (|has| |#1| (-856))) ((((-413 (-570))) |has| |#1| (-1047 (-413 (-570)))) (((-570)) |has| |#1| (-1047 (-570))) ((|#1|) . T)) ((((-868)) . T)) ((((-868)) . 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T) ((#0=(-413 (-570)) #0#) |has| |#1| (-38 (-413 (-570))))) +(((#0=(-413 (-570)) #0#) |has| |#1| (-38 (-413 (-570)))) ((|#1| |#1|) . T) (($ $) -2892 (|has| |#1| (-174)) (|has| |#1| (-458)) (|has| |#1| (-562)) (|has| |#1| (-916)))) +((($ $) -2892 (|has| |#1| (-174)) (|has| |#1| (-368)) (|has| |#1| (-458)) (|has| |#1| (-562)) (|has| |#1| (-916))) ((|#1| |#1|) . T) ((#0=(-413 (-570)) #0#) |has| |#1| (-38 (-413 (-570))))) (((|#1|) . T)) (((|#1|) . T)) -((((-413 (-570))) |has| |#1| (-38 (-413 (-570)))) ((|#1|) . T) (($) -2740 (|has| |#1| (-174)) (|has| |#1| (-458)) (|has| |#1| (-562)) (|has| |#1| (-916)))) -((($) -2740 (|has| |#1| (-174)) (|has| |#1| (-368)) (|has| |#1| (-458)) (|has| |#1| (-562)) (|has| |#1| (-916))) ((|#1|) . T) (((-413 (-570))) |has| |#1| (-38 (-413 (-570))))) -((($) -2740 (|has| |#2| (-174)) (|has| |#2| (-854)) (|has| |#2| (-1058))) ((|#2|) -2740 (|has| |#2| (-174)) (|has| |#2| (-368)) (|has| |#2| (-1058)))) +((((-413 (-570))) |has| |#1| (-38 (-413 (-570)))) ((|#1|) . T) (($) -2892 (|has| |#1| (-174)) (|has| |#1| (-458)) (|has| |#1| (-562)) (|has| |#1| (-916)))) +((($) -2892 (|has| |#1| (-174)) (|has| |#1| (-368)) (|has| |#1| (-458)) (|has| |#1| (-562)) (|has| |#1| (-916))) ((|#1|) . T) (((-413 (-570))) |has| |#1| (-38 (-413 (-570))))) +((($) -2892 (|has| |#2| (-174)) (|has| |#2| (-854)) (|has| |#2| (-1058))) ((|#2|) -2892 (|has| |#2| (-174)) (|has| |#2| (-368)) (|has| |#2| (-1058)))) ((((-868)) . T)) ((((-868)) . T)) ((((-868)) . T)) @@ -249,10 +249,10 @@ ((((-171 (-227))) |has| |#1| (-1031)) (((-171 (-384))) |has| |#1| (-1031)) (((-542)) |has| |#1| (-620 (-542))) (((-1182 |#1|)) . T) (((-899 (-570))) |has| |#1| (-620 (-899 (-570)))) (((-899 (-384))) |has| |#1| (-620 (-899 (-384))))) (((|#1| |#1|) -12 (|has| |#1| (-313 |#1|)) (|has| |#1| (-1109)))) (((|#1|) . 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T)) (-12 (|has| |#4| (-235)) (|has| |#4| (-1058))) (-12 (|has| |#3| (-235)) (|has| |#3| (-1058))) -(-2740 (|has| |#4| (-174)) (|has| |#4| (-854)) (|has| |#4| (-1058))) -(-2740 (|has| |#3| (-174)) (|has| |#3| (-854)) (|has| |#3| (-1058))) +(-2892 (|has| |#4| (-174)) (|has| |#4| (-854)) (|has| |#4| (-1058))) +(-2892 (|has| |#3| (-174)) (|has| |#3| (-854)) (|has| |#3| (-1058))) ((((-868)) . T) (((-1191)) . T)) ((((-868)) . T) (((-1191)) . T)) ((((-1191)) . T)) @@ -270,14 +270,14 @@ (((|#1|) . T)) ((((-413 (-570))) |has| |#1| (-1047 (-413 (-570)))) (((-570)) |has| |#1| (-1047 (-570))) ((|#1|) . T)) (((|#1|) . T) (((-570)) |has| |#1| (-645 (-570)))) -(((|#2|) . T) (((-2 (|:| -2013 |#1|) (|:| -2224 |#2|))) . T)) -(((|#1|) . T) (((-2 (|:| -2013 (-1168)) (|:| -2224 |#1|))) . T)) +(((|#2|) . T) (((-2 (|:| -2106 |#1|) (|:| -2339 |#2|))) . T)) +(((|#1|) . T) (((-2 (|:| -2106 (-1168)) (|:| -2339 |#1|))) . 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T)) (|has| |#1| (-562)) (|has| |#1| (-562)) @@ -290,21 +290,21 @@ ((((-413 |#2|)) . T) (((-413 (-570))) . T) (($) . T)) (-12 (|has| |#1| (-1109)) (|has| |#2| (-1109))) ((($) . T) (((-413 (-570))) |has| |#1| (-38 (-413 (-570)))) ((|#1|) . T)) -((((-413 (-570))) -2740 (|has| |#1| (-38 (-413 (-570)))) (|has| |#1| (-368))) (((-1184 |#1| |#2| |#3|)) |has| |#1| (-368)) (($) . T) ((|#1|) . T)) -(((|#1|) . T) (((-413 (-570))) -2740 (|has| |#1| (-38 (-413 (-570)))) (|has| |#1| (-368))) (($) . T)) +((((-413 (-570))) -2892 (|has| |#1| (-38 (-413 (-570)))) (|has| |#1| (-368))) (((-1184 |#1| |#2| |#3|)) |has| |#1| (-368)) (($) . T) ((|#1|) . T)) +(((|#1|) . T) (((-413 (-570))) -2892 (|has| |#1| (-38 (-413 (-570)))) (|has| |#1| (-368))) (($) . T)) (((|#1|) . T) (((-413 (-570))) |has| |#1| (-38 (-413 (-570)))) (($) . 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T)) (((|#1| (-980)) . T)) ((((-570)) . T) ((|#2|) . T)) @@ -351,7 +351,7 @@ (((|#1|) . T)) (((|#2| |#2|) . T)) (|has| |#1| (-1161)) -((((-2 (|:| -2013 (-1168)) (|:| -2224 |#1|))) . T)) +((((-2 (|:| -2106 (-1168)) (|:| -2339 |#1|))) . T)) (|has| (-1263 |#1| |#2| |#3| |#4|) (-146)) (|has| (-1263 |#1| |#2| |#3| |#4|) (-148)) (|has| |#1| (-146)) @@ -363,27 +363,27 @@ (((|#2|) . T)) (((|#1|) . T)) (((|#2|) . T) (((-570)) |has| |#2| (-645 (-570)))) -((((-1134 |#1| (-1186))) . T) (((-570)) . T) (((-824 (-1186))) . T) (($) -2740 (|has| |#1| (-458)) (|has| |#1| (-562)) (|has| |#1| (-916))) ((|#1|) . T) (((-413 (-570))) -2740 (|has| |#1| (-38 (-413 (-570)))) (|has| |#1| (-1047 (-413 (-570))))) (((-1186)) . T)) +((((-1134 |#1| (-1186))) . T) (((-570)) . T) (((-824 (-1186))) . T) (($) -2892 (|has| |#1| (-458)) (|has| |#1| (-562)) (|has| |#1| (-916))) ((|#1|) . T) (((-413 (-570))) -2892 (|has| |#1| (-38 (-413 (-570)))) (|has| |#1| (-1047 (-413 (-570))))) (((-1186)) . 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T)) -((($) -2740 (|has| |#1| (-174)) (|has| |#1| (-458)) (|has| |#1| (-562)) (|has| |#1| (-916))) ((|#1|) . T) (((-413 (-570))) |has| |#1| (-38 (-413 (-570))))) +((($) -2892 (|has| |#1| (-174)) (|has| |#1| (-458)) (|has| |#1| (-562)) (|has| |#1| (-916))) ((|#1|) . T) (((-413 (-570))) |has| |#1| (-38 (-413 (-570))))) ((((-868)) . T)) ((((-868)) . T)) (|has| (-1262 |#2| |#3| |#4|) (-148)) @@ -394,16 +394,16 @@ ((((-868)) . T)) (((|#1|) . T)) (((|#1|) . T)) -(-2740 (|has| |#1| (-21)) (|has| |#1| (-174)) (|has| |#1| (-368)) (|has| |#1| (-907 (-1186))) (|has| |#1| (-1058))) +(-2892 (|has| |#1| (-21)) (|has| |#1| (-174)) (|has| |#1| (-368)) (|has| |#1| (-907 (-1186))) (|has| |#1| (-1058))) (((|#1|) . T)) ((((-570) |#1|) . T)) (((|#2|) |has| |#2| (-174))) (((|#1|) |has| |#1| (-174))) (((|#1|) . 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T)) ((((-868)) . T)) ((((-868)) . T)) @@ -815,34 +815,34 @@ (|has| |#1| (-1109)) (((|#2|) . T)) ((((-542)) |has| |#2| (-620 (-542))) (((-899 (-384))) |has| |#2| (-620 (-899 (-384)))) (((-899 (-570))) |has| |#2| (-620 (-899 (-570))))) -(((|#4|) -2740 (|has| |#4| (-174)) (|has| |#4| (-368)))) -(((|#3|) -2740 (|has| |#3| (-174)) (|has| |#3| (-368)))) +(((|#4|) -2892 (|has| |#4| (-174)) (|has| |#4| (-368)))) +(((|#3|) -2892 (|has| |#3| (-174)) (|has| |#3| (-368)))) ((((-868)) . T)) (((|#1|) . 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T)) (|has| (-413 |#2|) (-148)) (|has| (-413 |#2|) (-146)) @@ -855,15 +855,15 @@ (|has| |#1| (-562)) (|has| |#1| (-38 (-413 (-570)))) (|has| |#1| (-38 (-413 (-570)))) -((((-2 (|:| -2013 |#1|) (|:| -2224 |#2|))) . T)) +((((-2 (|:| -2106 |#1|) (|:| -2339 |#2|))) . T)) ((((-868)) . T)) -((((-2 (|:| -2013 (-1168)) (|:| -2224 |#1|))) . T)) +((((-2 (|:| -2106 (-1168)) (|:| -2339 |#1|))) . T)) (|has| |#1| (-38 (-413 (-570)))) -((((-394) (-2 (|:| -2013 (-1168)) (|:| -2224 |#1|))) . T)) +((((-394) (-2 (|:| -2106 (-1168)) (|:| -2339 |#1|))) . T)) (|has| |#1| (-38 (-413 (-570)))) (|has| |#2| (-1161)) -(-2740 (|has| |#1| (-368)) (|has| |#1| (-562))) -(-2740 (|has| |#1| (-368)) (|has| |#1| (-562))) +(-2892 (|has| |#1| (-368)) (|has| |#1| (-562))) +(-2892 (|has| |#1| (-368)) (|has| |#1| (-562))) ((((-868)) . T) (((-1191)) . T)) ((((-868)) . T) (((-1191)) . T)) ((((-868)) . T) (((-1191)) . T)) @@ -881,7 +881,7 @@ ((((-394) (-1168)) . T)) (|has| |#1| (-562)) ((((-570) |#1|) . T)) -(-2740 (|has| |#1| (-174)) (|has| |#1| (-458)) (|has| |#1| (-562)) (|has| |#1| (-916))) +(-2892 (|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)) @@ -897,7 +897,7 @@ ((((-650 |#1|)) . T)) ((((-868)) . T)) ((((-542)) |has| |#1| (-620 (-542)))) -(-2740 (|has| |#1| (-856)) (|has| |#1| (-1109))) +(-2892 (|has| |#1| (-856)) (|has| |#1| (-1109))) (((|#2|) |has| |#2| (-313 |#2|))) (((#0=(-570) #0#) . T) ((#1=(-413 (-570)) #1#) . T) (($ $) . T)) (((|#1|) . T)) @@ -907,14 +907,14 @@ (((#0=(-570) #0#) . T) ((#1=(-413 (-570)) #1#) . T) (($ $) . T)) ((($) . T) (((-570)) . T) (((-413 (-570))) . T)) (|has| |#2| (-373)) -(-2740 (|has| |#1| (-856)) (|has| |#1| (-1109))) +(-2892 (|has| |#1| (-856)) (|has| |#1| (-1109))) (((|#1|) . T) (((-413 (-570))) . T) (($) . T)) (((|#1|) . T) (((-413 (-570))) . T) (($) . T)) (((|#1|) . T) (((-413 (-570))) . T) (($) . 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T)) -(-2740 (|has| |#1| (-174)) (|has| |#1| (-368)) (|has| |#1| (-562))) -(-2740 (|has| |#1| (-174)) (|has| |#1| (-368)) (|has| |#1| (-562))) -(-2740 (|has| |#1| (-174)) (|has| |#1| (-562))) +(-2892 (|has| |#1| (-174)) (|has| |#1| (-368)) (|has| |#1| (-562))) +(-2892 (|has| |#1| (-174)) (|has| |#1| (-368)) (|has| |#1| (-562))) +(-2892 (|has| |#1| (-174)) (|has| |#1| (-562))) ((((-868)) . T)) ((((-868)) . T)) ((((-868)) . T)) (((|#1| (-1277 |#1|) (-1277 |#1|)) . T)) ((((-570) (-145)) . T)) ((($) . T)) -(-2740 (|has| |#4| (-174)) (|has| |#4| (-854)) (|has| |#4| (-1058))) -(-2740 (|has| |#3| (-174)) (|has| |#3| (-854)) (|has| |#3| (-1058))) +(-2892 (|has| |#4| (-174)) (|has| |#4| (-854)) (|has| |#4| (-1058))) +(-2892 (|has| |#3| (-174)) (|has| |#3| (-854)) (|has| |#3| (-1058))) ((((-1191)) . T) (((-868)) . T)) ((((-1191)) . T)) ((((-868)) . T)) @@ -983,20 +983,20 @@ (((|#1| (-980)) . T)) (((|#1| |#1|) . T)) ((($) . T)) -(-2740 (|has| |#2| (-799)) (|has| |#2| (-854))) -(-2740 (|has| |#2| (-799)) (|has| |#2| (-854))) +(-2892 (|has| |#2| (-799)) (|has| |#2| (-854))) +(-2892 (|has| |#2| (-799)) (|has| |#2| (-854))) (-12 (|has| |#1| (-479)) (|has| |#2| (-479))) -(-2740 (|has| |#2| (-174)) (|has| |#2| (-732)) (|has| |#2| (-854)) (|has| |#2| (-1058))) +(-2892 (|has| |#2| (-174)) (|has| |#2| (-732)) (|has| |#2| (-854)) (|has| |#2| (-1058))) ((($) . T) (((-570)) . T) (((-876 |#1|)) . T) (((-413 (-570))) . T)) (((|#1|) . T)) (|has| |#2| (-799)) -(-2740 (|has| |#2| (-799)) (|has| |#2| (-854))) +(-2892 (|has| |#2| (-799)) (|has| |#2| (-854))) (((|#1| |#2|) . 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))) -(-2740 (-12 (|has| |#1| (-479)) (|has| |#2| (-479))) (-12 (|has| |#1| (-732)) (|has| |#2| (-732)))) +(-2892 (-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))) @@ -1008,7 +1008,7 @@ (((|#1|) . T)) ((((-413 (-570))) . T) (($) . T)) (((|#2|) . T) (($) . T) (((-413 (-570))) . T)) -((($) . T) (((-413 (-570))) -2740 (|has| |#1| (-38 (-413 (-570)))) (|has| |#1| (-368))) ((|#1|) . T)) +((($) . T) (((-413 (-570))) -2892 (|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)) @@ -1019,13 +1019,13 @@ (((|#4|) |has| |#4| (-1109))) (((|#3|) |has| |#3| (-1109))) (|has| |#3| (-373)) -((($) |has| |#1| (-562)) ((|#1|) . T) (((-413 (-570))) -2740 (|has| |#1| (-38 (-413 (-570)))) (|has| |#1| (-1047 (-413 (-570))))) (((-570)) . T)) -((((-413 (-570))) -2740 (|has| |#1| (-38 (-413 (-570)))) (|has| |#1| (-368))) (($) -2740 (|has| |#1| (-368)) (|has| |#1| (-562))) (((-1269 |#1| |#2| |#3|)) |has| |#1| (-368)) ((|#1|) |has| |#1| (-174))) +((($) |has| |#1| (-562)) ((|#1|) . T) (((-413 (-570))) -2892 (|has| |#1| (-38 (-413 (-570)))) (|has| |#1| (-1047 (-413 (-570))))) (((-570)) . T)) +((((-413 (-570))) -2892 (|has| |#1| (-38 (-413 (-570)))) (|has| |#1| (-368))) (($) -2892 (|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|) . T)) -(((|#1|) |has| |#1| (-174)) (((-413 (-570))) -2740 (|has| |#1| (-38 (-413 (-570)))) (|has| |#1| (-368))) (($) -2740 (|has| |#1| (-368)) (|has| |#1| (-562)))) +(((|#1|) |has| |#1| (-174)) (((-413 (-570))) -2892 (|has| |#1| (-38 (-413 (-570)))) (|has| |#1| (-368))) (($) -2892 (|has| |#1| (-368)) (|has| |#1| (-562)))) ((($) |has| |#1| (-562)) ((|#1|) |has| |#1| (-174)) (((-413 (-570))) |has| |#1| (-38 (-413 (-570))))) (((|#1| |#1|) |has| |#1| (-174))) (|has| |#2| (-368)) @@ -1033,19 +1033,19 @@ (((|#1|) |has| |#1| (-174))) ((((-413 (-570))) . T) (((-570)) . T)) ((($) . T) (((-570)) . T) (((-413 (-570))) |has| |#2| (-38 (-413 (-570)))) ((|#2|) . T)) -((($ $) -2740 (|has| |#1| (-174)) (|has| |#1| (-562))) ((|#1| |#1|) . T) ((#0=(-413 (-570)) #0#) |has| |#1| (-38 (-413 (-570))))) +((($ $) -2892 (|has| |#1| (-174)) (|has| |#1| (-562))) ((|#1| |#1|) . T) ((#0=(-413 (-570)) #0#) |has| |#1| (-38 (-413 (-570))))) ((($) . T) (((-570)) . 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T)) -(-2740 (|has| |#1| (-21)) (|has| |#1| (-25)) (|has| |#1| (-146)) (|has| |#1| (-148)) (|has| |#1| (-174)) (|has| |#1| (-562)) (|has| |#1| (-1058))) +(-2892 (|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)) @@ -1055,15 +1055,15 @@ ((((-868)) . T)) (|has| |#1| (-38 (-413 (-570)))) (|has| |#1| (-38 (-413 (-570)))) -(-2740 (|has| |#1| (-146)) (|has| |#1| (-148)) (|has| |#1| (-174)) (|has| |#1| (-479)) (|has| |#1| (-562)) (|has| |#1| (-1058)) (|has| |#1| (-1121))) +(-2892 (|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)) . T)) (|has| |#1| (-562)) -(-2740 (|has| |#1| (-368)) (|has| |#1| (-562))) -(-2740 (|has| |#1| (-368)) (|has| |#1| (-562))) +(-2892 (|has| |#1| (-368)) (|has| |#1| (-562))) +(-2892 (|has| |#1| (-368)) (|has| |#1| (-562))) (|has| |#1| (-562)) (|has| |#1| (-38 (-413 (-570)))) (|has| |#1| (-38 (-413 (-570)))) @@ -1074,7 +1074,7 @@ (|has| |#1| (-148)) (|has| |#1| (-146)) (|has| |#4| (-854)) -(((|#2| (-242 (-2426 |#1|) (-777)) (-870 |#1|)) . T)) +(((|#2| (-242 (-2569 |#1|) (-777)) (-870 |#1|)) . T)) (|has| |#3| (-854)) (((|#1| (-537 |#3|) |#3|) . T)) (|has| |#1| (-148)) @@ -1088,21 +1088,21 @@ (|has| |#1| (-148)) ((((-413 (-570))) |has| |#2| (-368)) (($) . 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T)) -(-2740 (|has| |#2| (-174)) (|has| |#2| (-854)) (|has| |#2| (-1058))) +(-2892 (|has| |#2| (-174)) (|has| |#2| (-854)) (|has| |#2| (-1058))) (|has| |#1| (-562)) (((|#1|) . T)) (((|#1|) . T)) @@ -1126,11 +1126,11 @@ (((|#1| (-413 (-570))) . T)) (((|#3|) . T) (((-618 $)) . T)) (((|#1| |#2|) . T)) -((((-2 (|:| -2013 |#1|) (|:| -2224 |#2|))) . T)) +((((-2 (|:| -2106 |#1|) (|:| -2339 |#2|))) . T)) (((|#1|) . T)) (((|#1|) -12 (|has| |#1| (-313 |#1|)) (|has| |#1| (-1109)))) -((((-2 (|:| -2013 |#1|) (|:| -2224 |#2|))) . T)) -((((-570)) -2740 (|has| |#2| (-174)) (|has| |#2| (-854)) (-12 (|has| |#2| (-1047 (-570))) (|has| |#2| (-1109))) (|has| |#2| (-1058))) ((|#2|) -2740 (|has| |#2| (-174)) (|has| |#2| (-1109))) (((-413 (-570))) -12 (|has| |#2| (-1047 (-413 (-570)))) (|has| |#2| (-1109)))) +((((-2 (|:| -2106 |#1|) (|:| -2339 |#2|))) . T)) +((((-570)) -2892 (|has| |#2| (-174)) (|has| |#2| (-854)) (-12 (|has| |#2| (-1047 (-570))) (|has| |#2| (-1109))) (|has| |#2| (-1058))) ((|#2|) -2892 (|has| |#2| (-174)) (|has| |#2| (-1109))) (((-413 (-570))) -12 (|has| |#2| (-1047 (-413 (-570)))) (|has| |#2| (-1109)))) (((|#1|) . T) (((-413 (-570))) . T) (($) . T)) ((($ $) . T) ((|#2| $) . T)) ((((-570)) . T) (($) . T) (((-413 (-570))) . T)) @@ -1138,8 +1138,8 @@ ((((-868)) . T)) ((((-868)) . T)) (((|#1| |#1|) . T)) -(((|#2|) -12 (|has| |#2| (-313 |#2|)) (|has| |#2| (-1109))) (((-2 (|:| -2013 |#1|) (|:| -2224 |#2|))) |has| (-2 (|:| -2013 |#1|) (|:| -2224 |#2|)) (-313 (-2 (|:| -2013 |#1|) (|:| -2224 |#2|))))) -(((|#1|) -12 (|has| |#1| (-313 |#1|)) (|has| |#1| (-1109))) (((-2 (|:| -2013 (-1168)) (|:| -2224 |#1|))) |has| (-2 (|:| -2013 (-1168)) (|:| -2224 |#1|)) (-313 (-2 (|:| -2013 (-1168)) (|:| -2224 |#1|))))) +(((|#2|) -12 (|has| |#2| (-313 |#2|)) (|has| |#2| (-1109))) (((-2 (|:| -2106 |#1|) (|:| -2339 |#2|))) |has| (-2 (|:| -2106 |#1|) (|:| -2339 |#2|)) (-313 (-2 (|:| -2106 |#1|) (|:| -2339 |#2|))))) +(((|#1|) -12 (|has| |#1| (-313 |#1|)) (|has| |#1| (-1109))) (((-2 (|:| -2106 (-1168)) (|:| -2339 |#1|))) |has| (-2 (|:| -2106 (-1168)) (|:| -2339 |#1|)) (-313 (-2 (|:| -2106 (-1168)) (|:| -2339 |#1|))))) ((((-868)) . T)) (((|#1|) . T)) (((|#3| |#3|) . T)) @@ -1153,10 +1153,10 @@ ((($) . T) (((-570)) . T) (((-413 (-570))) |has| |#1| (-38 (-413 (-570)))) ((|#1|) . T)) ((((-570)) . T) (($) . 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T)) -((($) -2740 (|has| |#1| (-311)) (|has| |#1| (-368)) (|has| |#1| (-354)) (|has| |#1| (-562))) (((-413 (-570))) -2740 (|has| |#1| (-368)) (|has| |#1| (-354))) ((|#1|) . T)) +((($) -2892 (|has| |#1| (-311)) (|has| |#1| (-368)) (|has| |#1| (-354)) (|has| |#1| (-562))) (((-413 (-570))) -2892 (|has| |#1| (-368)) (|has| |#1| (-354))) ((|#1|) . T)) ((((-570) |#2|) . T)) (((|#1| |#2|) . T)) (((|#1| |#2|) . T)) @@ -1214,41 +1214,41 @@ (-12 (|has| |#1| (-373)) (|has| |#2| (-373))) ((((-868)) . T)) ((((-1186) |#1|) |has| |#1| (-520 (-1186) |#1|)) ((|#1| |#1|) |has| |#1| (-313 |#1|))) -(-2740 (|has| |#1| (-146)) (|has| |#1| (-373))) -(-2740 (|has| |#1| (-146)) (|has| |#1| (-373))) -(-2740 (|has| |#1| (-146)) (|has| |#1| (-373))) +(-2892 (|has| |#1| (-146)) (|has| |#1| (-373))) +(-2892 (|has| |#1| (-146)) (|has| |#1| (-373))) +(-2892 (|has| |#1| (-146)) (|has| |#1| (-373))) (((|#1|) . 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T)) (((|#1|) |has| |#1| (-313 |#1|))) @@ -1258,11 +1258,11 @@ (|has| |#1| (-373)) ((((-1186) $) |has| |#1| (-520 (-1186) $)) (($ $) |has| |#1| (-313 $)) ((|#1| |#1|) |has| |#1| (-313 |#1|)) (((-1186) |#1|) |has| |#1| (-520 (-1186) |#1|))) ((((-1186)) |has| |#1| (-907 (-1186)))) -(-2740 (-12 (|has| |#1| (-235)) (|has| |#1| (-368))) (|has| |#1| (-354))) +(-2892 (-12 (|has| |#1| (-235)) (|has| |#1| (-368))) (|has| |#1| (-354))) (((|#1| |#4|) . T)) (((|#1| |#3|) . T)) ((((-394) |#1|) . T)) -(-2740 (|has| |#1| (-368)) (|has| |#1| (-354))) +(-2892 (|has| |#1| (-368)) (|has| |#1| (-354))) (|has| |#1| (-1109)) (((|#2|) . T) (((-868)) . T)) ((((-868)) . T)) @@ -1270,8 +1270,8 @@ ((((-917 |#1|)) . T)) ((((-868)) . T) (((-1191)) . T)) ((((-1191)) . T)) -((((-413 (-570))) |has| |#2| (-38 (-413 (-570)))) ((|#2|) |has| |#2| (-174)) (($) -2740 (|has| |#2| (-458)) (|has| |#2| (-562)) (|has| |#2| (-916)))) -((((-413 (-570))) |has| |#1| (-38 (-413 (-570)))) ((|#1|) |has| |#1| (-174)) (($) -2740 (|has| |#1| (-458)) (|has| |#1| (-562)) (|has| |#1| (-916)))) +((((-413 (-570))) |has| |#2| (-38 (-413 (-570)))) ((|#2|) |has| |#2| (-174)) (($) -2892 (|has| |#2| (-458)) (|has| |#2| (-562)) (|has| |#2| (-916)))) +((((-413 (-570))) |has| |#1| (-38 (-413 (-570)))) ((|#1|) |has| |#1| (-174)) (($) -2892 (|has| |#1| (-458)) (|has| |#1| (-562)) (|has| |#1| (-916)))) (((|#1| |#2|) . T)) ((($) . T)) ((((-570)) . T) (($) . T) (((-413 (-570))) . T)) @@ -1280,16 +1280,16 @@ (((|#1|) . T) (((-413 (-570))) . T) (($) . T) (((-570)) . T)) (((|#1| |#1|) . T)) (((#0=(-876 |#1|)) |has| #0# (-313 #0#))) -((((-570)) . 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T)) (|has| |#1| (-1212)) (((#0=(-570) #0#) . T) ((#1=(-413 (-570)) #1#) . T) (($ $) . T)) @@ -1301,8 +1301,8 @@ (((|#1| |#1|) . T) (($ $) . T) ((#0=(-413 (-570)) #0#) . T)) (|has| |#1| (-368)) ((((-570)) . T) (((-413 (-570))) . T) (($) . T)) -((($ $) . T) ((#0=(-413 (-570)) #0#) -2740 (|has| |#1| (-368)) (|has| |#1| (-354))) ((|#1| |#1|) . T)) -((((-868)) -2740 (|has| |#1| (-619 (-868))) (|has| |#1| (-1109)))) +((($ $) . T) ((#0=(-413 (-570)) #0#) -2892 (|has| |#1| (-368)) (|has| |#1| (-354))) ((|#1| |#1|) . T)) +((((-868)) -2892 (|has| |#1| (-619 (-868))) (|has| |#1| (-1109)))) (((|#1|) . T) (($) . T) (((-413 (-570))) . T)) ((((-868)) . T)) ((((-868)) . T)) @@ -1317,29 +1317,29 @@ (((|#1| |#2|) . T)) (|has| |#1| (-854)) (|has| |#1| (-854)) -((($) . T) (((-413 (-570))) -2740 (|has| |#1| (-368)) (|has| |#1| (-354))) ((|#1|) . T)) -(-2740 (|has| |#1| (-174)) (|has| |#1| (-562))) +((($) . T) (((-413 (-570))) -2892 (|has| |#1| (-368)) (|has| |#1| (-354))) ((|#1|) . 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T)) +((((-2 (|:| -2106 |#1|) (|:| -2339 |#2|))) . T)) ((((-413 (-570))) . T) (((-413 |#1|)) . T) ((|#1|) . T) (($) . T)) (((|#1| (-1182 |#1|)) . T)) ((((-570)) . T) (($) . T) (((-413 (-570))) . T)) @@ -1537,8 +1537,8 @@ (((|#1|) . T) (((-570)) . T) (($) . T)) (((|#2|) . T)) ((((-570)) . T) (($) . T) (((-413 (-570))) . T)) -((((-2 (|:| -2013 (-1168)) (|:| -2224 |#1|))) . T)) -((((-868)) -2740 (|has| |#1| (-619 (-868))) (|has| |#1| (-1109)))) +((((-2 (|:| -2106 (-1168)) (|:| -2339 |#1|))) . T)) +((((-868)) -2892 (|has| |#1| (-619 (-868))) (|has| |#1| (-1109)))) ((((-570) |#2|) . T)) (((|#1|) . T) (((-413 (-570))) . T) (((-570)) . T) (($) . T)) ((($) . T) (((-570)) . T) (((-413 (-570))) . T)) @@ -1551,7 +1551,7 @@ (|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 (|:| -2013 |#1|) (|:| -2224 |#2|)) #0#) |has| (-2 (|:| -2013 |#1|) (|:| -2224 |#2|)) (-313 (-2 (|:| -2013 |#1|) (|:| -2224 |#2|))))) +(((|#2| |#2|) -12 (|has| |#2| (-313 |#2|)) (|has| |#2| (-1109))) ((#0=(-2 (|:| -2106 |#1|) (|:| -2339 |#2|)) #0#) |has| (-2 (|:| -2106 |#1|) (|:| -2339 |#2|)) (-313 (-2 (|:| -2106 |#1|) (|:| -2339 |#2|))))) (((|#2| |#2|) . T)) (|has| |#1| (-1109)) (|has| |#2| (-368)) @@ -1561,16 +1561,16 @@ (|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)) (($) -2740 (|has| |#1| (-458)) (|has| |#1| (-562)) (|has| |#1| (-916)))) -((($) -2740 (|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)) (($) -2892 (|has| |#1| (-458)) (|has| |#1| (-562)) (|has| |#1| (-916)))) +((($) -2892 (|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))) -((($) -2740 (|has| |#2| (-174)) (|has| |#2| (-854)) (|has| |#2| (-1058))) (((-570)) -2740 (|has| |#2| (-174)) (|has| |#2| (-368)) (|has| |#2| (-854)) (|has| |#2| (-1058))) ((|#2|) -2740 (|has| |#2| (-174)) (|has| |#2| (-368)) (|has| |#2| (-1058)))) +((($) -2892 (|has| |#2| (-174)) (|has| |#2| (-854)) (|has| |#2| (-1058))) (((-570)) -2892 (|has| |#2| (-174)) (|has| |#2| (-368)) (|has| |#2| (-854)) (|has| |#2| (-1058))) ((|#2|) -2892 (|has| |#2| (-174)) (|has| |#2| (-368)) (|has| |#2| (-1058)))) ((((-570) |#3|) . T)) ((((-570) (-145)) . T)) ((((-145)) . T)) @@ -1596,19 +1596,19 @@ (((|#1|) -12 (|has| |#1| (-313 |#1|)) (|has| |#1| (-1109)))) (((|#1| |#2|) . T)) ((((-570) (-145)) . 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T)) -(-2740 (|has| |#1| (-148)) (-12 (|has| |#1| (-368)) (|has| |#2| (-148)))) -(-2740 (|has| |#1| (-146)) (-12 (|has| |#1| (-368)) (|has| |#2| (-146)))) +(-2892 (|has| |#1| (-148)) (-12 (|has| |#1| (-368)) (|has| |#2| (-148)))) +(-2892 (|has| |#1| (-146)) (-12 (|has| |#1| (-368)) (|has| |#2| (-146)))) (((|#4|) . T)) (|has| |#1| (-146)) ((((-1168) |#1|) . T)) @@ -1622,24 +1622,24 @@ (((|#3|) . T)) ((((-1269 |#1| |#2| |#3|)) |has| |#1| (-368))) ((($) . T) (((-570)) . T) (((-413 (-570))) |has| |#1| (-38 (-413 (-570)))) ((|#1|) . T)) -((((-413 (-570))) -2740 (|has| |#1| (-38 (-413 (-570)))) (|has| |#1| (-368))) (((-1184 |#1| |#2| |#3|)) |has| |#1| (-368)) (((-570)) . T) (($) . T) ((|#1|) . T)) -(((|#1|) . T) (((-413 (-570))) -2740 (|has| |#1| (-38 (-413 (-570)))) (|has| |#1| (-368))) (((-570)) . T) (($) . T)) +((((-413 (-570))) -2892 (|has| |#1| (-38 (-413 (-570)))) (|has| |#1| (-368))) (((-1184 |#1| |#2| |#3|)) |has| |#1| (-368)) (((-570)) . T) (($) . T) ((|#1|) . T)) +(((|#1|) . 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T)) -(((|#4|) -2740 (|has| |#4| (-174)) (|has| |#4| (-368)))) -(((|#3|) -2740 (|has| |#3| (-174)) (|has| |#3| (-368)))) +(((|#4|) -2892 (|has| |#4| (-174)) (|has| |#4| (-368)))) +(((|#3|) -2892 (|has| |#3| (-174)) (|has| |#3| (-368)))) (|has| |#2| (-368)) (((|#1|) |has| |#1| (-174))) -(((|#4|) -2740 (|has| |#4| (-174)) (|has| |#4| (-368)) (|has| |#4| (-1058))) (($) |has| |#4| (-174))) -(((|#3|) -2740 (|has| |#3| (-174)) (|has| |#3| (-368)) (|has| |#3| (-1058))) (($) |has| |#3| (-174))) +(((|#4|) -2892 (|has| |#4| (-174)) (|has| |#4| (-368)) (|has| |#4| (-1058))) (($) |has| |#4| (-174))) +(((|#3|) -2892 (|has| |#3| (-174)) (|has| |#3| (-368)) (|has| |#3| (-1058))) (($) |has| |#3| (-174))) (((|#2|) |has| |#2| (-1058))) ((((-1168) |#1|) . T)) (((|#3| |#3|) -12 (|has| |#3| (-313 |#3|)) (|has| |#3| (-1109)))) @@ -1648,8 +1648,8 @@ ((($) . T) (((-570)) . T) (((-413 (-570))) |has| |#2| (-38 (-413 (-570)))) ((|#2|) . T)) ((((-394) (-1168)) . T)) ((($) |has| |#1| (-562)) ((|#1|) |has| |#1| (-174)) (((-413 (-570))) |has| |#1| (-38 (-413 (-570))))) -((((-868)) -2740 (|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 (|:| -2013 (-1168)) (|:| -2224 #0#))) . T)) +((((-868)) -2892 (|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 (|:| -2106 (-1168)) (|:| -2339 #0#))) . T)) (((|#1|) . T)) ((((-868)) . T)) (((|#2| |#2|) -12 (|has| |#2| (-313 |#2|)) (|has| |#2| (-1109)))) @@ -1658,7 +1658,7 @@ ((((-570)) . T)) (|has| |#2| (-148)) (|has| |#1| (-479)) -(-2740 (|has| |#1| (-479)) (|has| |#1| (-732)) (|has| |#1| (-907 (-1186))) (|has| |#1| (-1058))) +(-2892 (|has| |#1| (-479)) (|has| |#1| (-732)) (|has| |#1| (-907 (-1186))) (|has| |#1| (-1058))) (|has| |#1| (-368)) ((((-868)) . T)) (|has| |#1| (-38 (-413 (-570)))) @@ -1669,8 +1669,8 @@ (|has| |#1| (-854)) ((((-868)) . T)) (((|#2|) . T)) -((((-413 (-570))) -2740 (|has| |#1| (-38 (-413 (-570)))) (|has| |#1| (-368))) (($) -2740 (|has| |#1| (-368)) (|has| |#1| (-562))) (((-1269 |#1| |#2| |#3|)) |has| |#1| (-368)) ((|#1|) |has| |#1| (-174))) -(((|#1|) |has| |#1| (-174)) (((-413 (-570))) -2740 (|has| |#1| (-38 (-413 (-570)))) (|has| |#1| (-368))) (($) -2740 (|has| |#1| (-368)) (|has| |#1| (-562)))) +((((-413 (-570))) -2892 (|has| |#1| (-38 (-413 (-570)))) (|has| |#1| (-368))) (($) -2892 (|has| |#1| (-368)) (|has| |#1| (-562))) (((-1269 |#1| |#2| |#3|)) |has| |#1| (-368)) ((|#1|) |has| |#1| (-174))) +(((|#1|) |has| |#1| (-174)) (((-413 (-570))) -2892 (|has| |#1| (-38 (-413 (-570)))) (|has| |#1| (-368))) (($) -2892 (|has| |#1| (-368)) (|has| |#1| (-562)))) ((($) |has| |#1| (-562)) ((|#1|) |has| |#1| (-174)) (((-413 (-570))) |has| |#1| (-38 (-413 (-570))))) (((|#2|) . T) (((-570)) . T) (((-825 |#1|)) . T)) (((|#1| |#2|) . T)) @@ -1679,7 +1679,7 @@ ((((-868)) . T)) ((((-868)) . T)) (|has| |#1| (-1109)) -(((|#2| (-488 (-2426 |#1|) (-777)) (-870 |#1|)) . T)) +(((|#2| (-488 (-2569 |#1|) (-777)) (-870 |#1|)) . T)) ((((-413 (-570))) . #0=(|has| |#2| (-368))) (($) . #0#)) (((|#1| (-537 (-1186)) (-1186)) . T)) (((|#1|) . T)) @@ -1700,17 +1700,17 @@ (((|#2|) |has| |#2| (-174))) (((|#1|) . T)) (((|#2|) . T)) -(((|#1|) . T) (((-2 (|:| -2013 (-1168)) (|:| -2224 |#1|))) . T)) -((((-2 (|:| -2013 |#1|) (|:| -2224 |#2|))) . T)) +(((|#1|) . T) (((-2 (|:| -2106 (-1168)) (|:| -2339 |#1|))) . T)) +((((-2 (|:| -2106 |#1|) (|:| -2339 |#2|))) . T)) (((|#2|) . T)) -((((-2 (|:| -2013 (-1186)) (|:| -2224 (-52)))) . T)) +((((-2 (|:| -2106 (-1186)) (|:| -2339 (-52)))) . T)) ((((-1184 |#1| |#2| |#3|)) |has| |#1| (-368))) -((((-2 (|:| -2013 |#1|) (|:| -2224 |#2|))) . T)) +((((-2 (|:| -2106 |#1|) (|:| -2339 |#2|))) . T)) ((((-1186) (-52)) . T)) ((($ $) . T)) (((|#1| (-570)) . T)) ((((-917 |#1|)) . T)) -(((|#1|) -2740 (|has| |#1| (-174)) (|has| |#1| (-368)) (|has| |#1| (-1058))) (($) -2740 (|has| |#1| (-907 (-1186))) (|has| |#1| (-1058)))) +(((|#1|) -2892 (|has| |#1| (-174)) (|has| |#1| (-368)) (|has| |#1| (-1058))) (($) -2892 (|has| |#1| (-907 (-1186))) (|has| |#1| (-1058)))) (((|#1|) . T) (((-570)) |has| |#1| (-1047 (-570))) (((-413 (-570))) |has| |#1| (-1047 (-413 (-570))))) (|has| |#1| (-856)) (|has| |#1| (-856)) @@ -1728,13 +1728,13 @@ (((|#4| |#4|) -12 (|has| |#4| (-313 |#4|)) (|has| |#4| (-1109)))) (((|#1|) |has| |#1| (-174))) (((|#4| |#4|) -12 (|has| |#4| (-313 |#4|)) (|has| |#4| (-1109)))) -(((|#3|) -2740 (|has| |#3| (-174)) (|has| |#3| (-368)))) -((($) -2740 (|has| |#1| (-458)) (|has| |#1| (-562)) (|has| |#1| (-916))) ((|#1|) |has| |#1| (-174)) (((-413 (-570))) |has| |#1| (-38 (-413 (-570))))) -(-2740 (|has| |#2| (-368)) (|has| |#2| (-458)) (|has| |#2| (-916))) -((($) -2740 (|has| |#1| (-174)) (|has| |#1| (-458)) (|has| |#1| (-562)) (|has| |#1| (-916))) ((|#1|) . 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T)) -(-2740 (|has| |#1| (-311)) (|has| |#1| (-368)) (|has| |#1| (-354))) +(-2892 (|has| |#1| (-311)) (|has| |#1| (-368)) (|has| |#1| (-354))) (|has| |#1| (-854)) (|has| |#1| (-854)) (|has| |#1| (-854)) @@ -1752,14 +1752,14 @@ ((((-570)) . T) (($) . T) (((-413 (-570))) . T)) (|has| |#1| (-38 (-413 (-570)))) (|has| |#1| (-38 (-413 (-570)))) -(-2740 (|has| |#1| (-368)) (|has| |#1| (-354))) +(-2892 (|has| |#1| (-368)) (|has| |#1| (-354))) (|has| |#1| (-38 (-413 (-570)))) (|has| |#1| (-38 (-413 (-570)))) -((((-2 (|:| -2013 |#1|) (|:| -2224 |#2|))) . T)) +((((-2 (|:| -2106 |#1|) (|:| -2339 |#2|))) . T)) ((((-1186)) |has| |#1| (-907 (-1186))) (((-1091)) . T)) (((|#1|) . 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T)) ((((-570) |#1|) . T)) ((((-1186)) |has| (-413 |#2|) (-907 (-1186)))) -(((|#1|) . T) (($) -2740 (|has| |#1| (-294)) (|has| |#1| (-368))) (((-413 (-570))) |has| |#1| (-368))) +(((|#1|) . T) (($) -2892 (|has| |#1| (-294)) (|has| |#1| (-368))) (((-413 (-570))) |has| |#1| (-368))) ((((-542)) |has| |#2| (-620 (-542)))) ((((-695 |#2|)) . T) (((-868)) . T)) (((|#1|) . T)) @@ -2349,22 +2349,22 @@ (((|#4|) -12 (|has| |#4| (-313 |#4|)) (|has| |#4| (-1109)))) ((((-876 |#1|)) . T)) (((|#1|) |has| |#1| (-174))) -(-2740 (|has| |#4| (-799)) (|has| |#4| (-854))) -(-2740 (|has| |#3| (-799)) (|has| |#3| (-854))) +(-2892 (|has| |#4| (-799)) (|has| |#4| (-854))) +(-2892 (|has| |#3| (-799)) (|has| |#3| (-854))) (((|#1| |#1|) -12 (|has| |#1| (-313 |#1|)) (|has| |#1| (-1109)))) ((((-868)) . T)) ((((-868)) . T)) (((|#1|) . T)) ((($) . T) (((-570)) . T) ((|#2|) . T)) (((|#4|) -12 (|has| |#4| (-313 |#4|)) (|has| |#4| (-1109)))) -(((|#3|) -2740 (|has| |#3| (-174)) (|has| |#3| (-368)))) +(((|#3|) -2892 (|has| |#3| (-174)) (|has| |#3| (-368)))) (((|#2|) |has| |#2| (-1058))) (((|#3|) . T)) (((|#1|) . T)) ((((-413 |#2|)) . T)) -(((|#2|) -2740 (|has| |#2| (-174)) (|has| |#2| (-368)))) +(((|#2|) -2892 (|has| |#2| (-174)) (|has| |#2| (-368)))) (((|#1|) . T)) -(((|#2|) -2740 (|has| |#2| (-174)) (|has| |#2| (-368)) (|has| |#2| (-1058))) (($) |has| |#2| (-174))) +(((|#2|) -2892 (|has| |#2| (-174)) (|has| |#2| (-368)) (|has| |#2| (-1058))) (($) |has| |#2| (-174))) (((|#3|) -12 (|has| |#3| (-313 |#3|)) (|has| |#3| (-1109)))) ((((-570) |#1|) . T)) (((|#1|) . T)) @@ -2373,17 +2373,17 @@ ((((-413 (-570))) . T) (($) . T)) ((((-413 (-570))) . T) (($) . T)) ((((-413 (-570))) . T) (($) . T)) -(-2740 (|has| |#1| (-458)) (|has| |#1| (-1231))) +(-2892 (|has| |#1| (-458)) (|has| |#1| (-1231))) ((($) . 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T)) (|has| |#1| (-38 (-413 (-570)))) -((((-2 (|:| -2013 (-1168)) (|:| -2224 (-52)))) |has| (-2 (|:| -2013 (-1168)) (|:| -2224 (-52))) (-313 (-2 (|:| -2013 (-1168)) (|:| -2224 (-52)))))) +((((-2 (|:| -2106 (-1168)) (|:| -2339 (-52)))) |has| (-2 (|:| -2106 (-1168)) (|:| -2339 (-52))) (-313 (-2 (|:| -2106 (-1168)) (|:| -2339 (-52)))))) (((|#1|) -12 (|has| |#1| (-313 |#1|)) (|has| |#1| (-1109)))) (|has| |#1| (-854)) (|has| |#1| (-38 (-413 (-570)))) @@ -2407,48 +2407,48 @@ (|has| |#1| (-38 (-413 (-570)))) ((((-1168)) . T) (((-512)) . T) (((-227)) . T) (((-570)) . T)) ((((-868)) . T)) -(((|#2|) . T) (((-570)) . T) (($) -2740 (|has| |#1| (-368)) (|has| |#1| (-458)) (|has| |#1| (-562)) (|has| |#1| (-916))) (((-1091)) . T) ((|#1|) . T) (((-413 (-570))) -2740 (|has| |#1| (-38 (-413 (-570)))) (|has| |#1| (-1047 (-413 (-570)))))) +(((|#2|) . T) (((-570)) . T) (($) -2892 (|has| |#1| (-368)) (|has| |#1| (-458)) (|has| |#1| (-562)) (|has| |#1| (-916))) (((-1091)) . T) ((|#1|) . 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T)) @@ -2474,10 +2474,10 @@ ((((-868)) . T)) ((((-868)) . T)) ((((-542)) |has| |#1| (-620 (-542)))) -((((-2 (|:| -2013 |#1|) (|:| -2224 |#2|))) . T)) +((((-2 (|:| -2106 |#1|) (|:| -2339 |#2|))) . T)) ((((-570)) . T) (($) . T) (((-413 (-570))) . T)) ((((-1186) |#1|) |has| |#1| (-520 (-1186) |#1|)) ((|#1| |#1|) |has| |#1| (-313 |#1|))) -(((|#1|) -2740 (|has| |#1| (-174)) (|has| |#1| (-368)))) +(((|#1|) -2892 (|has| |#1| (-174)) (|has| |#1| (-368)))) (((|#1|) . T) (((-413 (-570))) . T) (($) . T)) ((((-570)) . T) (((-413 (-570))) . T) (($) . T)) (((|#1|) . T) (((-413 (-570))) . T) (($) . T)) @@ -2487,10 +2487,10 @@ (((|#1|) . T) (($) . T) (((-413 (-570))) . T)) (((|#1|) . T) (($) . T) (((-413 (-570))) . T)) (((|#2|) |has| |#2| (-368))) -((($) -2740 (|has| |#1| (-368)) (|has| |#1| (-354))) (((-413 (-570))) -2740 (|has| |#1| (-368)) (|has| |#1| (-354))) ((|#1|) . T)) +((($) -2892 (|has| |#1| (-368)) (|has| |#1| (-354))) (((-413 (-570))) -2892 (|has| |#1| (-368)) (|has| |#1| (-354))) ((|#1|) . T)) (((|#2|) . T)) ((((-413 (-570))) . T) (((-705)) . T) (($) . T)) -((($) . T) (((-413 (-570))) -2740 (|has| |#1| (-368)) (|has| |#1| (-354))) ((|#1|) . T)) +((($) . T) (((-413 (-570))) -2892 (|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) (($) . T)) @@ -2509,13 +2509,13 @@ (|has| |#1| (-146)) (|has| |#1| (-148)) ((($ $) . 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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)) (($) |has| |#1| (-562))) -((((-413 (-570))) -2740 (|has| |#1| (-38 (-413 (-570)))) (|has| |#1| (-368))) (($) -2740 (|has| |#1| (-174)) (|has| |#1| (-368)) (|has| |#1| (-562))) ((|#1|) . T)) +((((-413 (-570))) -2892 (|has| |#1| (-38 (-413 (-570)))) (|has| |#1| (-368))) (($) -2892 (|has| |#1| (-174)) (|has| |#1| (-368)) (|has| |#1| (-562))) ((|#1|) . T)) (|has| |#1| (-368)) -((($) |has| |#1| (-854)) (((-570)) -2740 (|has| |#1| (-21)) (|has| |#1| (-854)))) +((($) |has| |#1| (-854)) (((-570)) -2892 (|has| |#1| (-21)) (|has| |#1| (-854)))) (|has| |#1| (-146)) (|has| |#1| (-148)) (|has| |#1| (-148)) @@ -2576,17 +2576,17 @@ (((|#1|) . T)) (((|#2| |#2|) -12 (|has| |#2| (-313 |#2|)) (|has| |#2| (-1109)))) (((|#2| |#3|) . T)) -(-2740 (|has| |#2| (-368)) (|has| |#2| (-458)) (|has| |#2| (-562)) (|has| |#2| (-916))) +(-2892 (|has| |#2| (-368)) (|has| |#2| (-458)) (|has| |#2| (-562)) (|has| |#2| (-916))) (((|#1| (-537 |#2|)) . T)) (((|#1| (-777)) . T)) (((|#1| (-537 (-1097 (-1186)))) . T)) (((|#1|) |has| |#1| (-174))) (((|#1|) . T)) (|has| |#2| (-916)) -(-2740 (|has| |#2| (-799)) (|has| |#2| (-854))) +(-2892 (|has| |#2| (-799)) (|has| |#2| (-854))) ((((-868)) . T)) -(((|#2|) -2740 (|has| |#2| (-174)) (|has| |#2| (-368)))) -(((|#2|) -2740 (|has| |#2| (-174)) (|has| |#2| (-368)) (|has| |#2| (-1058))) (($) |has| |#2| (-174))) +(((|#2|) -2892 (|has| |#2| (-174)) (|has| |#2| (-368)))) +(((|#2|) -2892 (|has| |#2| (-174)) (|has| |#2| (-368)) (|has| |#2| (-1058))) (($) |has| |#2| (-174))) ((($ $) . T) ((#0=(-1262 |#2| |#3| |#4|) #0#) . T) ((#1=(-413 (-570)) #1#) |has| #0# (-38 (-413 (-570))))) ((((-917 |#1|)) . T)) (-12 (|has| |#1| (-368)) (|has| |#2| (-826))) @@ -2594,14 +2594,14 @@ ((((-868)) . T)) ((($) . T)) ((($) . T)) -(-2740 (|has| |#1| (-311)) (|has| |#1| (-368)) (|has| |#1| (-354)) (|has| |#1| (-562))) +(-2892 (|has| |#1| (-311)) (|has| |#1| (-368)) (|has| |#1| (-354)) (|has| |#1| (-562))) (|has| |#1| (-368)) (|has| |#1| (-368)) (((|#1| |#2|) . T)) ((($) . T) ((#0=(-1262 |#2| |#3| |#4|)) . T) (((-413 (-570))) |has| #0# (-38 (-413 (-570))))) ((((-1184 |#1| |#2| |#3|)) |has| |#1| (-368))) -(-2740 (-12 (|has| |#1| (-311)) (|has| |#1| (-916))) (|has| |#1| (-368)) (|has| |#1| (-354))) -(-2740 (|has| |#1| (-907 (-1186))) (|has| |#1| (-1058))) +(-2892 (-12 (|has| |#1| (-311)) (|has| |#1| (-916))) (|has| |#1| (-368)) (|has| |#1| (-354))) +(-2892 (|has| |#1| (-907 (-1186))) (|has| |#1| (-1058))) ((((-570)) |has| |#1| (-645 (-570))) ((|#1|) . T)) (((|#1| |#2|) . T)) ((((-868)) . T)) @@ -2646,28 +2646,28 @@ (((|#2|) . T)) (((|#4| |#4|) -12 (|has| |#4| (-313 |#4|)) (|has| |#4| (-1109)))) (((|#2|) . T)) -(((|#2|) -2740 (|has| |#2| (-6 (-4451 "*"))) (|has| |#2| (-174)))) -(-2740 (|has| |#2| (-458)) (|has| |#2| (-562)) (|has| |#2| (-916))) -(-2740 (|has| |#1| (-458)) (|has| |#1| (-562)) (|has| |#1| (-916))) +(((|#2|) -2892 (|has| |#2| (-6 (-4451 "*"))) (|has| |#2| (-174)))) +(-2892 (|has| |#2| (-458)) (|has| |#2| (-562)) (|has| |#2| (-916))) +(-2892 (|has| |#1| (-458)) (|has| |#1| (-562)) (|has| |#1| (-916))) (|has| |#2| (-916)) (|has| |#1| (-916)) (((|#2|) |has| |#2| (-174))) -((((-2 (|:| -2013 |#1|) (|:| -2224 |#2|))) . T)) +((((-2 (|:| -2106 |#1|) (|:| -2339 |#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)) ((($) . T) (((-570)) . T)) -((((-2 (|:| -2013 (-1168)) (|:| -2224 (-52)))) . T)) +((((-2 (|:| -2106 (-1168)) (|:| -2339 (-52)))) . T)) (((|#1|) . T)) -((((-2 (|:| -2013 |#1|) (|:| -2224 |#2|))) . T)) +((((-2 (|:| -2106 |#1|) (|:| -2339 |#2|))) . T)) ((((-868)) . T)) (((|#1| |#2|) . T)) ((($) . T) (((-570)) . T)) (((|#1| (-413 (-570))) . T)) (((|#1|) . T)) -(-2740 (|has| |#1| (-294)) (|has| |#1| (-368))) +(-2892 (|has| |#1| (-294)) (|has| |#1| (-368))) ((((-145)) . T)) ((((-413 |#2|)) . T) (((-413 (-570))) . T) (($) . T)) (|has| |#1| (-854)) @@ -2683,7 +2683,7 @@ ((((-868)) . T)) ((((-868)) . T)) ((((-189)) . T) (((-868)) . T)) -((((-2 (|:| -2013 |#1|) (|:| -2224 |#2|))) . T)) +((((-2 (|:| -2106 |#1|) (|:| -2339 |#2|))) . T)) (((|#2| |#2|) . T) ((|#1| |#1|) . T)) ((((-868)) . T)) ((((-868)) . T)) @@ -2696,7 +2696,7 @@ ((((-868)) . T)) ((((-1168)) . T)) ((((-1186) |#1|) |has| |#1| (-520 (-1186) |#1|)) ((|#1| |#1|) |has| |#1| (-313 |#1|))) -((((-2 (|:| -2013 (-1168)) (|:| -2224 |#1|))) . T)) +((((-2 (|:| -2106 (-1168)) (|:| -2339 |#1|))) . T)) (|has| |#1| (-856)) ((((-868)) . T)) ((((-542)) |has| |#1| (-620 (-542)))) @@ -2708,16 +2708,16 @@ (((|#2|) . T)) ((((-917 |#1|)) . T) (((-413 (-570))) . T) (($) . T)) ((($) . T) (((-570)) . T) (((-413 (-570))) . T) (((-618 $)) . T)) -(-2740 (|has| |#4| (-174)) (|has| |#4| (-732)) (|has| |#4| (-854)) (|has| |#4| (-1058))) -(-2740 (|has| |#3| (-174)) (|has| |#3| (-732)) (|has| |#3| (-854)) (|has| |#3| (-1058))) +(-2892 (|has| |#4| (-174)) (|has| |#4| (-732)) (|has| |#4| (-854)) (|has| |#4| (-1058))) +(-2892 (|has| |#3| (-174)) (|has| |#3| (-732)) (|has| |#3| (-854)) (|has| |#3| (-1058))) ((((-1186) (-52)) . T)) -(-2740 (|has| |#1| (-458)) (|has| |#1| (-562)) (|has| |#1| (-916))) -(-2740 (|has| |#1| (-368)) (|has| |#1| (-458)) (|has| |#1| (-562)) (|has| |#1| (-916))) +(-2892 (|has| |#1| (-458)) (|has| |#1| (-562)) (|has| |#1| (-916))) +(-2892 (|has| |#1| (-368)) (|has| |#1| (-458)) (|has| |#1| (-562)) (|has| |#1| (-916))) (((|#1|) . T)) (((|#1|) . T)) (((|#1|) . T)) -(-2740 (|has| |#2| (-25)) (|has| |#2| (-132)) (|has| |#2| (-174)) (|has| |#2| (-368)) (|has| |#2| (-799)) (|has| |#2| (-854)) (|has| |#2| (-1058))) -(-2740 (|has| |#2| (-174)) (|has| |#2| (-368)) (|has| |#2| (-854)) (|has| |#2| (-1058))) +(-2892 (|has| |#2| (-25)) (|has| |#2| (-132)) (|has| |#2| (-174)) (|has| |#2| (-368)) (|has| |#2| (-799)) (|has| |#2| (-854)) (|has| |#2| (-1058))) +(-2892 (|has| |#2| (-174)) (|has| |#2| (-368)) (|has| |#2| (-854)) (|has| |#2| (-1058))) (|has| |#1| (-916)) ((((-917 |#1|)) . T) (((-413 (-570))) . T) (($) . T) (((-570)) . T)) (|has| |#1| (-916)) @@ -2734,12 +2734,12 @@ (|has| |#1| (-38 (-413 (-570)))) (|has| |#1| (-38 (-413 (-570)))) (|has| |#1| (-38 (-413 (-570)))) -(-2740 (|has| |#1| (-368)) (|has| |#1| (-458)) (|has| |#1| (-562)) (|has| |#1| (-916))) +(-2892 (|has| |#1| (-368)) (|has| |#1| (-458)) (|has| |#1| (-562)) (|has| |#1| (-916))) (|has| |#1| (-826)) (((#0=(-917 |#1|) #0#) . T) (($ $) . T) ((#1=(-413 (-570)) #1#) . T)) ((((-413 |#2|)) . T)) (|has| |#1| (-854)) -((((-1213 |#1|)) . T) (((-868)) -2740 (|has| |#1| (-619 (-868))) (|has| |#1| (-1109)))) +((((-1213 |#1|)) . T) (((-868)) -2892 (|has| |#1| (-619 (-868))) (|has| |#1| (-1109)))) (((|#1| |#1|) . T) ((#0=(-413 (-570)) #0#) . T) ((#1=(-570) #1#) . T) (($ $) . T)) ((((-917 |#1|)) . T) (($) . T) (((-413 (-570))) . T)) (((|#2|) |has| |#2| (-1058)) (((-570)) -12 (|has| |#2| (-645 (-570))) (|has| |#2| (-1058)))) @@ -2755,28 +2755,28 @@ (((|#2|) |has| |#2| (-174))) (((|#1|) . T)) (((|#2|) . T)) -(-2740 (|has| |#1| (-146)) (|has| |#1| (-373))) -(-2740 (|has| |#1| (-146)) (|has| |#1| (-373))) -(-2740 (|has| |#1| (-146)) (|has| |#1| (-373))) -((((-2 (|:| -2013 (-1186)) (|:| -2224 (-52)))) . T)) -(((#0=(-52)) . T) (((-2 (|:| -2013 (-1186)) (|:| -2224 #0#))) . T)) +(-2892 (|has| |#1| (-146)) (|has| |#1| (-373))) +(-2892 (|has| |#1| (-146)) (|has| |#1| (-373))) +(-2892 (|has| |#1| (-146)) (|has| |#1| (-373))) +((((-2 (|:| -2106 (-1186)) (|:| -2339 (-52)))) . T)) +(((#0=(-52)) . T) (((-2 (|:| -2106 (-1186)) (|:| -2339 #0#))) . T)) (|has| |#1| (-354)) ((((-570)) . T)) ((((-868)) . T)) (((|#1|) . T)) (((#0=(-1263 |#1| |#2| |#3| |#4|) $) |has| #0# (-290 #0# #0#))) (|has| |#1| (-368)) -(((|#1|) -2740 (|has| |#1| (-174)) (|has| |#1| (-368)) (|has| |#1| (-1058))) (($) -2740 (|has| |#1| (-907 (-1186))) (|has| |#1| (-1058))) (((-570)) -2740 (|has| |#1| (-21)) (|has| |#1| (-174)) (|has| |#1| (-368)) (|has| |#1| (-907 (-1186))) (|has| |#1| (-1058)))) +(((|#1|) -2892 (|has| |#1| (-174)) (|has| |#1| (-368)) (|has| |#1| (-1058))) (($) -2892 (|has| |#1| (-907 (-1186))) (|has| |#1| (-1058))) (((-570)) -2892 (|has| |#1| (-21)) (|has| |#1| (-174)) (|has| |#1| (-368)) (|has| |#1| (-907 (-1186))) (|has| |#1| (-1058)))) (((#0=(-1091) |#1|) . T) ((#0# $) . T) (($ $) . T)) -(-2740 (|has| |#1| (-368)) (|has| |#1| (-354))) +(-2892 (|has| |#1| (-368)) (|has| |#1| (-354))) (((#0=(-413 (-570)) #0#) . T) ((#1=(-705) #1#) . T) (($ $) . T)) ((((-320 |#1|)) . T) (($) . T)) (((|#1|) . T) (((-413 (-570))) |has| |#1| (-368))) ((((-868)) . T)) (|has| |#1| (-1109)) (((|#1|) . T)) -(((|#1|) -2740 (|has| |#2| (-372 |#1|)) (|has| |#2| (-423 |#1|)))) -(((|#1|) -2740 (|has| |#2| (-372 |#1|)) (|has| |#2| (-423 |#1|)))) +(((|#1|) -2892 (|has| |#2| (-372 |#1|)) (|has| |#2| (-423 |#1|)))) +(((|#1|) -2892 (|has| |#2| (-372 |#1|)) (|has| |#2| (-423 |#1|)))) (((|#2|) . T)) ((((-413 (-570))) . T) (((-705)) . T) (($) . T)) ((((-585)) . T)) @@ -2801,7 +2801,7 @@ (((|#1|) . T)) ((((-570)) . T)) (((|#2|) . T) (((-413 (-570))) |has| |#1| (-1047 (-413 (-570)))) ((|#1|) . T) (($) . T) (((-570)) . T)) -(-2740 (|has| |#1| (-174)) (|has| |#1| (-368)) (|has| |#1| (-458)) (|has| |#1| (-562)) (|has| |#1| (-916))) +(-2892 (|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)) ((($) . T)) @@ -2845,7 +2845,7 @@ (|has| |#2| (-1031)) ((($) . T)) (|has| |#1| (-916)) -((((-2 (|:| -2013 |#1|) (|:| -2224 |#2|))) . T)) +((((-2 (|:| -2106 |#1|) (|:| -2339 |#2|))) . T)) ((($) . T)) (((|#2|) . T)) (((|#1|) . T)) @@ -2854,10 +2854,10 @@ (|has| |#1| (-368)) ((((-917 |#1|)) . T)) ((($) . T) (((-570)) . T) ((|#1|) . T) (((-413 (-570))) . T)) -((($) -2740 (|has| |#1| (-368)) (|has| |#1| (-458)) (|has| |#1| (-562)) (|has| |#1| (-916))) ((|#1|) |has| |#1| (-174)) (((-413 (-570))) |has| |#1| (-38 (-413 (-570))))) -((($) |has| |#1| (-854)) (((-570)) -2740 (|has| |#1| (-21)) (|has| |#1| (-854)))) +((($) -2892 (|has| |#1| (-368)) (|has| |#1| (-458)) (|has| |#1| (-562)) (|has| |#1| (-916))) ((|#1|) |has| |#1| (-174)) (((-413 (-570))) |has| |#1| (-38 (-413 (-570))))) +((($) |has| |#1| (-854)) (((-570)) -2892 (|has| |#1| (-21)) (|has| |#1| (-854)))) ((($ $) . T) ((#0=(-413 (-570)) #0#) . T)) -(-2740 (|has| |#1| (-373)) (|has| |#1| (-856))) +(-2892 (|has| |#1| (-373)) (|has| |#1| (-856))) (((|#1|) . T)) ((((-777)) . T)) ((((-868)) . T)) @@ -2868,17 +2868,17 @@ ((((-570)) . T) (($) . T)) ((((-570)) . T) (($) . T)) ((((-777) |#1|) . T)) -(((|#2| (-242 (-2426 |#1|) (-777))) . T)) +(((|#2| (-242 (-2569 |#1|) (-777))) . T)) (((|#1| (-537 |#3|)) . T)) ((((-413 (-570))) . T)) -(-2740 (|has| |#1| (-458)) (|has| |#1| (-562)) (|has| |#1| (-916))) +(-2892 (|has| |#1| (-458)) (|has| |#1| (-562)) (|has| |#1| (-916))) ((((-1168)) . T) (((-868)) . T)) -(((#0=(-2 (|:| -2013 (-1186)) (|:| -2224 (-52))) #0#) |has| (-2 (|:| -2013 (-1186)) (|:| -2224 (-52))) (-313 (-2 (|:| -2013 (-1186)) (|:| -2224 (-52)))))) +(((#0=(-2 (|:| -2106 (-1186)) (|:| -2339 (-52))) #0#) |has| (-2 (|:| -2106 (-1186)) (|:| -2339 (-52))) (-313 (-2 (|:| -2106 (-1186)) (|:| -2339 (-52)))))) ((((-1168)) . T)) (|has| |#1| (-916)) (|has| |#2| (-368)) (((|#1|) . T) (($) . T) (((-570)) . T)) -(-2740 (|has| |#2| (-132)) (|has| |#2| (-174)) (|has| |#2| (-368)) (|has| |#2| (-799)) (|has| |#2| (-854)) (|has| |#2| (-1058))) +(-2892 (|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)) @@ -2895,11 +2895,11 @@ (|has| |#1| (-38 (-413 (-570)))) (|has| |#1| (-38 (-413 (-570)))) (|has| |#1| (-38 (-413 (-570)))) -(-2740 (|has| |#1| (-311)) (|has| |#1| (-368)) (|has| |#1| (-354))) +(-2892 (|has| |#1| (-311)) (|has| |#1| (-368)) (|has| |#1| (-354))) (|has| |#1| (-38 (-413 (-570)))) (-12 (|has| |#1| (-551)) (|has| |#1| (-834))) ((((-868)) . T)) -((((-1186)) -2740 (-12 (|has| |#1| (-15 * (|#1| (-570) |#1|))) (|has| |#1| (-907 (-1186)))) (-12 (|has| |#1| (-368)) (|has| |#2| (-907 (-1186)))))) +((((-1186)) -2892 (-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)) @@ -2911,7 +2911,7 @@ (((|#2|) |has| |#1| (-368))) (((|#2|) |has| |#1| (-368))) ((((-570)) . T) (($) . T)) -((((-2 (|:| -2013 |#1|) (|:| -2224 |#2|))) . T)) +((((-2 (|:| -2106 |#1|) (|:| -2339 |#2|))) . T)) (((|#1|) . T)) (((|#1|) |has| |#1| (-174))) (((|#1|) . T)) @@ -2941,11 +2941,11 @@ (((|#2|) |has| |#1| (-368))) ((((-384)) -12 (|has| |#1| (-368)) (|has| |#2| (-893 (-384)))) (((-570)) -12 (|has| |#1| (-368)) (|has| |#2| (-893 (-570))))) (|has| |#1| (-368)) -(-2740 (|has| |#1| (-368)) (|has| |#1| (-562))) +(-2892 (|has| |#1| (-368)) (|has| |#1| (-562))) (|has| |#1| (-368)) (((|#1|) . T)) ((($) . T) (((-570)) . T) ((|#2|) . T)) -(-2740 (|has| |#1| (-368)) (|has| |#1| (-562))) +(-2892 (|has| |#1| (-368)) (|has| |#1| (-562))) (|has| |#1| (-368)) (((|#3|) . T)) ((((-1168)) . T) (((-512)) . T) (((-227)) . T) (((-570)) . T)) @@ -2953,23 +2953,23 @@ (|has| |#1| (-562)) (((|#4| |#4|) -12 (|has| |#4| (-313 |#4|)) (|has| |#4| (-1109)))) ((((-413 |#2|)) . T) (((-413 (-570))) . T) (($) . T) (((-570)) . T)) -(-2740 (|has| |#2| (-132)) (|has| |#2| (-174)) (|has| |#2| (-368)) (|has| |#2| (-799)) (|has| |#2| (-854)) (|has| |#2| (-1058))) +(-2892 (|has| |#2| (-132)) (|has| |#2| (-174)) (|has| |#2| (-368)) (|has| |#2| (-799)) (|has| |#2| (-854)) (|has| |#2| (-1058))) (((|#2|) . T)) (((|#2|) . T)) -(-2740 (|has| |#2| (-174)) (|has| |#2| (-732)) (|has| |#2| (-854)) (|has| |#2| (-1058))) -((((-2 (|:| -2013 |#1|) (|:| -2224 |#2|))) . T)) -((((-2 (|:| -2013 (-1168)) (|:| -2224 |#1|))) . T)) -((((-2 (|:| -2013 |#1|) (|:| -2224 |#2|))) . T)) +(-2892 (|has| |#2| (-174)) (|has| |#2| (-732)) (|has| |#2| (-854)) (|has| |#2| (-1058))) +((((-2 (|:| -2106 |#1|) (|:| -2339 |#2|))) . T)) +((((-2 (|:| -2106 (-1168)) (|:| -2339 |#1|))) . T)) +((((-2 (|:| -2106 |#1|) (|:| -2339 |#2|))) . T)) (|has| |#1| (-38 (-413 (-570)))) (((|#1| |#2|) . T)) (|has| |#1| (-38 (-413 (-570)))) -(-2740 (|has| |#1| (-146)) (|has| |#1| (-373))) +(-2892 (|has| |#1| (-146)) (|has| |#1| (-373))) ((($) . T)) ((((-1168) |#1|) . T)) (|has| |#1| (-148)) -(-2740 (|has| |#1| (-146)) (|has| |#1| (-373))) +(-2892 (|has| |#1| (-146)) (|has| |#1| (-373))) (|has| |#1| (-148)) -(-2740 (|has| |#1| (-146)) (|has| |#1| (-373))) +(-2892 (|has| |#1| (-146)) (|has| |#1| (-373))) ((($) . T)) (|has| |#1| (-148)) ((((-587 |#1|)) . T)) @@ -2983,7 +2983,7 @@ ((((-413 (-570))) |has| |#2| (-1047 (-570))) (((-570)) |has| |#2| (-1047 (-570))) (((-1186)) |has| |#2| (-1047 (-1186))) ((|#2|) . T)) (((#0=(-413 |#2|) #0#) . T) ((#1=(-413 (-570)) #1#) . T) (($ $) . T)) (((|#1|) . T)) -(-2740 (|has| |#1| (-146)) (|has| |#1| (-354))) +(-2892 (|has| |#1| (-146)) (|has| |#1| (-354))) (|has| |#1| (-148)) ((((-868)) . T)) ((($) . T)) @@ -3009,7 +3009,7 @@ ((((-917 |#1|)) . T) (((-413 (-570))) . T) (($) . T) (((-570)) . T)) ((((-868)) . T)) ((((-542)) |has| |#1| (-620 (-542)))) -((((-868)) -2740 (|has| |#1| (-619 (-868))) (|has| |#1| (-856)) (|has| |#1| (-1109)))) +((((-868)) -2892 (|has| |#1| (-619 (-868))) (|has| |#1| (-856)) (|has| |#1| (-1109)))) ((((-115)) . T) ((|#1|) . T)) (((|#1|) . T)) (((|#1|) . T)) @@ -3031,7 +3031,7 @@ ((((-570)) . T)) ((((-868)) . T)) ((((-570)) . T)) -(-2740 (|has| |#2| (-799)) (|has| |#2| (-854))) +(-2892 (|has| |#2| (-799)) (|has| |#2| (-854))) ((((-171 (-384))) . T) (((-227)) . T) (((-384)) . T)) ((((-868)) . T)) ((((-868)) . T)) @@ -3043,9 +3043,9 @@ (((|#1|) . T) (($) . T) (((-413 (-570))) . 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T)) -(((|#1|) -2740 (|has| |#1| (-174)) (|has| |#1| (-368)))) +(((|#1|) -2892 (|has| |#1| (-174)) (|has| |#1| (-368)))) (((|#1|) . T)) -(((|#1|) -2740 (|has| |#1| (-174)) (|has| |#1| (-368)) (|has| |#1| (-1058)))) +(((|#1|) -2892 (|has| |#1| (-174)) (|has| |#1| (-368)) (|has| |#1| (-1058)))) ((((-570)) . T) (((-413 (-570))) . T)) (((|#1|) . T)) (|has| |#1| (-562)) ((($) . T) (((-570)) . T) ((|#1|) . T) (((-413 (-570))) |has| |#1| (-368))) ((((-413 |#2|)) . T) (((-413 (-570))) . T) (($) . T)) -(-2740 (|has| |#1| (-368)) (|has| |#1| (-562))) +(-2892 (|has| |#1| (-368)) (|has| |#1| (-562))) ((((-384)) . T)) (((|#1|) . T)) (((|#1|) . T)) (|has| |#1| (-368)) -(-2740 (|has| |#1| (-368)) (|has| |#1| (-562))) +(-2892 (|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|))))) -(-2740 (|has| |#2| (-458)) (|has| |#2| (-562)) (|has| |#2| (-916))) +(-2892 (|has| |#2| (-458)) (|has| |#2| (-562)) (|has| |#2| (-916))) (((|#1|) . T)) (((|#2| |#3|) . T)) (((|#1|) . T)) @@ -3092,13 +3092,13 @@ (|has| |#2| (-368)) ((((-587 |#1|)) . T) (((-413 (-570))) . T) (($) . T) (((-570)) . T)) ((((-570)) . T) (((-413 (-570))) . T) (($) . T)) -((((-2 (|:| -2013 (-1168)) (|:| -2224 (-52)))) . T)) +((((-2 (|:| -2106 (-1168)) (|:| -2339 (-52)))) . T)) (((|#1|) . T)) (((|#1|) . T) (((-570)) . T)) (((|#1|) -12 (|has| |#1| (-313 |#1|)) (|has| |#1| (-1109)))) ((((-868)) . T)) ((((-868)) . T)) -(-2740 (|has| |#3| (-799)) (|has| |#3| (-854))) +(-2892 (|has| |#3| (-799)) (|has| |#3| (-854))) ((((-868)) . T)) ((((-1129)) . T) (((-868)) . T)) ((((-542)) . T) (((-868)) . T)) @@ -3109,12 +3109,12 @@ ((((-570)) . T)) (((|#3|) . T)) ((((-868)) . T)) -(-2740 (|has| |#1| (-311)) (|has| |#1| (-368)) (|has| |#1| (-354))) -((((-570)) . T) (((-413 (-570))) -2740 (|has| |#2| (-38 (-413 (-570)))) (|has| |#2| (-1047 (-413 (-570))))) ((|#2|) . T) (($) -2740 (|has| |#2| (-458)) (|has| |#2| (-562)) (|has| |#2| (-916))) (((-870 |#1|)) . T)) -((((-1134 |#1| |#2|)) . T) ((|#2|) . T) (($) -2740 (|has| |#1| (-458)) (|has| |#1| (-562)) (|has| |#1| (-916))) ((|#1|) . T) (((-413 (-570))) -2740 (|has| |#1| (-38 (-413 (-570)))) (|has| |#1| (-1047 (-413 (-570))))) (((-570)) . T)) -((((-1182 |#1|)) . T) (((-570)) . T) (($) -2740 (|has| |#1| (-368)) (|has| |#1| (-458)) (|has| |#1| (-562)) (|has| |#1| (-916))) (((-1091)) . T) ((|#1|) . 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T)) +((((-1182 |#1|)) . T) (((-570)) . T) (($) -2892 (|has| |#1| (-368)) (|has| |#1| (-458)) (|has| |#1| (-562)) (|has| |#1| (-916))) (((-1091)) . T) ((|#1|) . T) (((-413 (-570))) -2892 (|has| |#1| (-38 (-413 (-570)))) (|has| |#1| (-1047 (-413 (-570)))))) +(-2892 (|has| |#1| (-146)) (|has| |#1| (-148)) (|has| |#1| (-174)) (|has| |#1| (-562)) (|has| |#1| (-1058))) +((((-1134 |#1| (-1186))) . T) (((-570)) . T) (((-1097 (-1186))) . T) (($) -2892 (|has| |#1| (-458)) (|has| |#1| (-562)) (|has| |#1| (-916))) ((|#1|) . T) (((-413 (-570))) -2892 (|has| |#1| (-38 (-413 (-570)))) (|has| |#1| (-1047 (-413 (-570))))) (((-1186)) . T)) (((#0=(-587 |#1|) #0#) . T) (($ $) . T) ((#1=(-413 (-570)) #1#) . T)) ((($ $) . T) ((#0=(-413 (-570)) #0#) . T)) (((|#1|) |has| |#1| (-174))) @@ -3132,7 +3132,7 @@ (((|#1|) . T)) ((((-868)) . T)) ((((-298 |#3|)) . T)) -(((#0=(-413 (-570)) #0#) |has| |#2| (-38 (-413 (-570)))) ((|#2| |#2|) . T) (($ $) -2740 (|has| |#2| (-174)) (|has| |#2| (-458)) (|has| |#2| (-562)) (|has| |#2| (-916)))) +(((#0=(-413 (-570)) #0#) |has| |#2| (-38 (-413 (-570)))) ((|#2| |#2|) . T) (($ $) -2892 (|has| |#2| (-174)) (|has| |#2| (-458)) (|has| |#2| (-562)) (|has| |#2| (-916)))) (((|#2| |#2|) . T) ((|#6| |#6|) . T)) (((|#1|) . T)) ((($) . T) (((-413 (-570))) |has| |#2| (-38 (-413 (-570)))) ((|#2|) . T)) @@ -3140,21 +3140,21 @@ (((|#1|) . T) (((-413 (-570))) . T) (($) . T)) (((|#1|) . T) (((-413 (-570))) . T) (($) . T)) (((|#1|) . T) (((-413 (-570))) . T) (($) . T)) -((($ $) -2740 (|has| |#1| (-174)) (|has| |#1| (-458)) (|has| |#1| (-562)) (|has| |#1| (-916))) ((|#1| |#1|) . T) ((#0=(-413 (-570)) #0#) |has| |#1| (-38 (-413 (-570))))) -((($ $) -2740 (|has| |#1| (-174)) (|has| |#1| (-368)) (|has| |#1| (-458)) (|has| |#1| (-562)) (|has| |#1| (-916))) ((|#1| |#1|) . 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T)) (((|#1|) |has| |#1| (-174))) -(-2740 (|has| |#2| (-25)) (|has| |#2| (-132)) (|has| |#2| (-174)) (|has| |#2| (-368)) (|has| |#2| (-799)) (|has| |#2| (-854)) (|has| |#2| (-1058))) +(-2892 (|has| |#2| (-25)) (|has| |#2| (-132)) (|has| |#2| (-174)) (|has| |#2| (-368)) (|has| |#2| (-799)) (|has| |#2| (-854)) (|has| |#2| (-1058))) (((|#1|) . T)) (((|#1|) . T)) -(-2740 (|has| |#2| (-174)) (|has| |#2| (-368)) (|has| |#2| (-854)) (|has| |#2| (-1058))) +(-2892 (|has| |#2| (-174)) (|has| |#2| (-368)) (|has| |#2| (-854)) (|has| |#2| (-1058))) (((|#1|) . T)) ((((-413 (-570))) . T) (((-570)) . T) (($) . T)) ((((-542)) . T)) @@ -3195,14 +3195,14 @@ ((($ $) . T) ((#0=(-413 (-570)) #0#) . T)) ((((-1186)) |has| |#1| (-907 (-1186)))) ((((-917 |#1|)) . T) (((-413 (-570))) . T) (($) . T)) -((($) . T) (((-413 (-570))) -2740 (|has| |#1| (-38 (-413 (-570)))) (|has| |#1| (-368))) ((|#1|) . T)) -(((#0=(-413 (-570)) #0#) |has| |#1| (-38 (-413 (-570)))) ((|#1| |#1|) . 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T)) (|has| |#2| (-826)) (|has| |#2| (-826)) -((((-413 (-570))) -2740 (|has| |#1| (-38 (-413 (-570)))) (|has| |#1| (-368))) ((|#2|) |has| |#1| (-368)) (($) . T) ((|#1|) . T)) -(((|#1|) . T) (((-413 (-570))) -2740 (|has| |#1| (-38 (-413 (-570)))) (|has| |#1| (-368))) (($) . T)) +((((-413 (-570))) -2892 (|has| |#1| (-38 (-413 (-570)))) (|has| |#1| (-368))) ((|#2|) |has| |#1| (-368)) (($) . T) ((|#1|) . T)) +(((|#1|) . T) (((-413 (-570))) -2892 (|has| |#1| (-38 (-413 (-570)))) (|has| |#1| (-368))) (($) . T)) (((|#1| |#1|) -12 (|has| |#1| (-313 |#1|)) (|has| |#1| (-1109)))) (((|#1|) . T) (((-570)) |has| |#1| (-1047 (-570))) (((-413 (-570))) |has| |#1| (-1047 (-413 (-570))))) ((((-570)) |has| |#1| (-893 (-570))) (((-384)) |has| |#1| (-893 (-384)))) @@ -3239,7 +3239,7 @@ (((|#1|) . 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T)) -(-2740 (|has| |#2| (-799)) (|has| |#2| (-854))) -(-2740 (-12 (|has| |#1| (-799)) (|has| |#2| (-799))) (-12 (|has| |#1| (-856)) (|has| |#2| (-856)))) +(-2892 (|has| |#2| (-799)) (|has| |#2| (-854))) +(-2892 (-12 (|has| |#1| (-799)) (|has| |#2| (-799))) (-12 (|has| |#1| (-856)) (|has| |#2| (-856)))) ((((-876 |#1|)) . T)) (((|#1|) . T)) (|has| |#1| (-373)) @@ -3285,7 +3285,7 @@ (((|#1|) . T)) ((((-868)) . T)) (|has| |#2| (-916)) -((((-2 (|:| -2013 (-1186)) (|:| -2224 (-52)))) . T)) +((((-2 (|:| -2106 (-1186)) (|:| -2339 (-52)))) . T)) ((((-542)) |has| |#2| (-620 (-542))) (((-899 (-384))) |has| |#2| (-620 (-899 (-384)))) (((-899 (-570))) |has| |#2| (-620 (-899 (-570))))) ((((-868)) . T)) ((((-868)) . T)) @@ -3312,7 +3312,7 @@ ((((-1191)) . T)) ((((-650 |#1|)) . T)) ((($) . T) (((-570)) . T) (((-1263 |#1| |#2| |#3| |#4|)) . T) (((-413 (-570))) . 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T)) -((($) -2740 (|has| |#1| (-458)) (|has| |#1| (-562)) (|has| |#1| (-916))) ((|#1|) |has| |#1| (-174)) (((-413 (-570))) |has| |#1| (-38 (-413 (-570))))) +((($) -2892 (|has| |#1| (-458)) (|has| |#1| (-562)) (|has| |#1| (-916))) ((|#1|) |has| |#1| (-174)) (((-413 (-570))) |has| |#1| (-38 (-413 (-570))))) ((($ $) . T) (((-1186) $) . T)) ((((-1269 |#1| |#2| |#3|)) . T)) (|has| |#2| (-916)) @@ -3651,7 +3651,7 @@ (((|#1|) . T)) (((|#1| |#1|) |has| |#1| (-174))) ((((-705)) . T)) -((((-868)) -2740 (|has| |#1| (-619 (-868))) (|has| |#1| (-1109)))) +((((-868)) -2892 (|has| |#1| (-619 (-868))) (|has| |#1| (-1109)))) ((((-1191)) . T)) (((|#1|) |has| |#1| (-174))) ((((-1191)) . T)) @@ -3668,13 +3668,13 @@ ((((-1191)) . T)) ((((-1191)) . T)) ((((-1191)) . T)) -(-2740 (|has| |#1| (-368)) (|has| |#1| (-354))) -(-2740 (|has| |#1| (-368)) (|has| |#1| (-354))) +(-2892 (|has| |#1| (-368)) (|has| |#1| (-354))) +(-2892 (|has| |#1| (-368)) (|has| |#1| (-354))) ((((-1191)) . T)) ((((-1191)) . 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T)) ((((-570)) . T)) -((((-2 (|:| -2013 |#1|) (|:| -2224 |#2|))) . T)) +((((-2 (|:| -2106 |#1|) (|:| -2339 |#2|))) . T)) (((|#1| |#2|) . T)) (((|#1|) . T)) -(-2740 (|has| |#2| (-174)) (|has| |#2| (-732)) (|has| |#2| (-854)) (|has| |#2| (-1058))) +(-2892 (|has| |#2| (-174)) (|has| |#2| (-732)) (|has| |#2| (-854)) (|has| |#2| (-1058))) ((((-1186)) -12 (|has| |#2| (-907 (-1186))) (|has| |#2| (-1058)))) -(-2740 (-12 (|has| |#1| (-479)) (|has| |#2| (-479))) (-12 (|has| |#1| (-732)) (|has| |#2| (-732)))) +(-2892 (-12 (|has| |#1| (-479)) (|has| |#2| (-479))) (-12 (|has| |#1| (-732)) (|has| |#2| (-732)))) (|has| |#1| (-146)) (|has| |#1| (-148)) (|has| |#1| (-368)) @@ -3729,7 +3729,7 @@ (((|#1| |#2|) . T)) ((((-570)) . T) ((|#2|) |has| |#2| (-174))) ((((-115)) . T) ((|#1|) . T) (((-570)) . T)) -(-2740 (|has| |#1| (-354)) (|has| |#1| (-373))) +(-2892 (|has| |#1| (-354)) (|has| |#1| (-373))) (((|#1| |#2|) . T)) ((((-227)) . T)) ((((-413 (-570))) . T) (($) . T) (((-570)) . T)) @@ -3741,7 +3741,7 @@ (((|#1|) . T)) (((|#1|) . T)) ((((-542)) |has| |#1| (-620 (-542)))) -((((-868)) -2740 (|has| |#1| (-619 (-868))) (|has| |#1| (-856)) (|has| |#1| (-1109)))) +((((-868)) -2892 (|has| |#1| (-619 (-868))) (|has| |#1| (-856)) (|has| |#1| (-1109)))) ((($) . T) (((-413 (-570))) . T)) (|has| |#1| (-916)) (|has| |#1| (-916)) @@ -3752,14 +3752,14 @@ (((|#1| |#1|) |has| |#1| (-174))) (((|#1|) . T) (((-570)) . T)) ((((-1191)) . T)) -(-2740 (|has| |#1| (-368)) (|has| |#1| (-562))) -(-2740 (|has| |#1| (-21)) (|has| |#1| (-854))) +(-2892 (|has| |#1| (-368)) (|has| |#1| (-562))) +(-2892 (|has| |#1| (-21)) (|has| |#1| (-854))) (((|#2|) . T)) -(-2740 (|has| |#1| (-21)) (|has| |#1| (-854))) +(-2892 (|has| |#1| (-21)) (|has| |#1| (-854))) (((|#1|) |has| |#1| (-174))) (((|#1|) . T)) (((|#1|) . T)) -((((-868)) -2740 (-12 (|has| |#1| (-619 (-868))) (|has| |#2| (-619 (-868)))) (-12 (|has| |#1| (-1109)) (|has| |#2| (-1109))))) +((((-868)) -2892 (-12 (|has| |#1| (-619 (-868))) (|has| |#2| (-619 (-868)))) (-12 (|has| |#1| (-1109)) (|has| |#2| (-1109))))) ((((-413 |#2|) |#3|) . T)) ((((-413 (-570))) . T) (($) . T)) (|has| |#1| (-38 (-413 (-570)))) @@ -3773,19 +3773,19 @@ (((|#1|) . T) (((-413 (-570))) . T) (((-570)) . T) (($) . T)) (((#0=(-570) #0#) . T)) ((($) . T) (((-413 (-570))) . T)) -(-2740 (|has| |#4| (-174)) (|has| |#4| (-732)) (|has| |#4| (-854)) (|has| |#4| (-1058))) -(-2740 (|has| |#3| (-174)) (|has| |#3| (-732)) (|has| |#3| (-854)) (|has| |#3| (-1058))) +(-2892 (|has| |#4| (-174)) (|has| |#4| (-732)) (|has| |#4| (-854)) (|has| |#4| (-1058))) +(-2892 (|has| |#3| (-174)) (|has| |#3| (-732)) (|has| |#3| (-854)) (|has| |#3| (-1058))) ((((-868)) . T) (((-1191)) . T)) (|has| |#4| (-799)) -(-2740 (|has| |#4| (-799)) (|has| |#4| (-854))) +(-2892 (|has| |#4| (-799)) (|has| |#4| (-854))) (|has| |#4| (-854)) (|has| |#3| (-799)) ((((-1191)) . T)) -(-2740 (|has| |#3| (-799)) (|has| |#3| (-854))) +(-2892 (|has| |#3| (-799)) (|has| |#3| (-854))) (|has| |#3| (-854)) ((((-570)) . T)) (((|#2|) . T)) -((((-1186)) -2740 (-12 (|has| (-1184 |#1| |#2| |#3|) (-907 (-1186))) (|has| |#1| (-368))) (-12 (|has| |#1| (-15 * (|#1| (-570) |#1|))) (|has| |#1| (-907 (-1186)))))) +((((-1186)) -2892 (-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) (($ $) . T)) @@ -3800,11 +3800,11 @@ ((((-1184 |#1| |#2| |#3|)) |has| |#1| (-368))) ((((-1149 |#1| |#2|)) . T)) ((((-1184 |#1| |#2| |#3|)) |has| |#1| (-368))) -(((|#2|) . T) (((-2 (|:| -2013 |#1|) (|:| -2224 |#2|))) . T)) -((((-2 (|:| -2013 (-1186)) (|:| -2224 (-52)))) . T)) +(((|#2|) . T) (((-2 (|:| -2106 |#1|) (|:| -2339 |#2|))) . T)) +((((-2 (|:| -2106 (-1186)) (|:| -2339 (-52)))) . T)) ((($) . T)) (|has| |#1| (-1031)) -(((|#2|) . T) (((-2 (|:| -2013 |#1|) (|:| -2224 |#2|))) . T)) +(((|#2|) . T) (((-2 (|:| -2106 |#1|) (|:| -2339 |#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)) @@ -3821,15 +3821,15 @@ ((((-1184 |#1| |#2| |#3|)) . T)) ((((-1184 |#1| |#2| |#3|)) . T) (((-1177 |#1| |#2| |#3|)) . T)) ((((-868)) . T)) -((((-868)) -2740 (|has| |#1| (-619 (-868))) (|has| |#1| (-1109)))) +((((-868)) -2892 (|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) (($) -2740 (|has| |#4| (-174)) (|has| |#4| (-854)) (|has| |#4| (-1058))) ((|#4|) -2740 (|has| |#4| (-174)) (|has| |#4| (-368)) (|has| |#4| (-1058)))) -(((|#2|) . T) (($) -2740 (|has| |#3| (-174)) (|has| |#3| (-854)) (|has| |#3| (-1058))) ((|#3|) -2740 (|has| |#3| (-174)) (|has| |#3| (-368)) (|has| |#3| (-1058)))) +(((|#3|) . T) ((|#2|) . T) (($) -2892 (|has| |#4| (-174)) (|has| |#4| (-854)) (|has| |#4| (-1058))) ((|#4|) -2892 (|has| |#4| (-174)) (|has| |#4| (-368)) (|has| |#4| (-1058)))) +(((|#2|) . T) (($) -2892 (|has| |#3| (-174)) (|has| |#3| (-854)) (|has| |#3| (-1058))) ((|#3|) -2892 (|has| |#3| (-174)) (|has| |#3| (-368)) (|has| |#3| (-1058)))) (((|#1|) . T)) (((|#1|) . T)) (|has| |#1| (-368)) @@ -3844,7 +3844,7 @@ ((((-189)) . T) (((-868)) . T)) ((((-868)) . T)) (((|#1|) . T)) -((((-868)) -2740 (|has| |#1| (-619 (-868))) (|has| |#1| (-1109)))) +((((-868)) -2892 (|has| |#1| (-619 (-868))) (|has| |#1| (-1109)))) ((((-130)) . T) (((-868)) . T)) ((((-570) |#1|) . T)) ((((-130)) . T)) @@ -3853,13 +3853,13 @@ (((|#1|) . T)) (((|#2| $) -12 (|has| |#1| (-368)) (|has| |#2| (-290 |#2| |#2|))) (($ $) . T)) ((($ $) . T)) -(-2740 (|has| |#1| (-368)) (|has| |#1| (-458)) (|has| |#1| (-916))) -(-2740 (|has| |#1| (-856)) (|has| |#1| (-1109))) +(-2892 (|has| |#1| (-368)) (|has| |#1| (-458)) (|has| |#1| (-916))) +(-2892 (|has| |#1| (-856)) (|has| |#1| (-1109))) ((((-868)) . T)) ((((-868)) . T)) ((((-868)) . T)) (((|#1| (-537 |#2|)) . T)) -((((-2 (|:| -2013 (-1186)) (|:| -2224 (-52)))) . T)) +((((-2 (|:| -2106 (-1186)) (|:| -2339 (-52)))) . T)) ((((-570) (-130)) . T)) (((|#1| (-570)) . T)) (((|#1| (-413 (-570))) . T)) @@ -3874,8 +3874,8 @@ ((((-1191)) . T)) ((((-868)) . T) (((-1191)) . T)) ((((-868)) . T) (((-1191)) . T)) -(-2740 (|has| |#2| (-458)) (|has| |#2| (-562)) (|has| |#2| (-916))) -(-2740 (|has| |#1| (-458)) (|has| |#1| (-562)) (|has| |#1| (-916))) +(-2892 (|has| |#2| (-458)) (|has| |#2| (-562)) (|has| |#2| (-916))) +(-2892 (|has| |#1| (-458)) (|has| |#1| (-562)) (|has| |#1| (-916))) ((($) . T)) (((|#2| (-537 (-870 |#1|))) . T)) ((((-1191)) . T)) @@ -3890,13 +3890,13 @@ ((((-1191)) . T)) ((((-868)) . T) (((-1191)) . T)) ((((-1191)) . T)) -((((-868)) -2740 (|has| |#1| (-619 (-868))) (|has| |#1| (-1109)))) +((((-868)) -2892 (|has| |#1| (-619 (-868))) (|has| |#1| (-1109)))) (((|#1|) . T)) (((|#2| (-777)) . T)) (((|#1| |#2|) . T)) ((((-1168) |#1|) . T)) ((((-413 |#2|)) . T)) -((((-2 (|:| -2013 |#1|) (|:| -2224 |#2|))) . T)) +((((-2 (|:| -2106 |#1|) (|:| -2339 |#2|))) . T)) (|has| |#1| (-562)) (|has| |#1| (-562)) ((($) . T) ((|#2|) . T)) @@ -3907,14 +3907,14 @@ ((((-570)) . T) (($) . T)) (((|#2| $) |has| |#2| (-290 |#2| |#2|))) (((|#1| (-650 |#1|)) |has| |#1| (-854))) -(-2740 (|has| |#1| (-235)) (|has| |#1| (-354))) -(-2740 (|has| |#1| (-368)) (|has| |#1| (-354))) +(-2892 (|has| |#1| (-235)) (|has| |#1| (-354))) +(-2892 (|has| |#1| (-368)) (|has| |#1| (-354))) ((((-1273 |#1|)) . T) (((-570)) . T) ((|#2|) . T) (((-413 (-570))) |has| |#2| (-1047 (-413 (-570))))) (|has| |#1| (-1109)) (((|#1|) . T)) -((((-1273 |#1|)) . T) (((-570)) . T) (($) -2740 (|has| |#2| (-368)) (|has| |#2| (-458)) (|has| |#2| (-562)) (|has| |#2| (-916))) (((-1091)) . T) ((|#2|) . T) (((-413 (-570))) -2740 (|has| |#2| (-38 (-413 (-570)))) (|has| |#2| (-1047 (-413 (-570)))))) +((((-1273 |#1|)) . T) (((-570)) . T) (($) -2892 (|has| |#2| (-368)) (|has| |#2| (-458)) (|has| |#2| (-562)) (|has| |#2| (-916))) (((-1091)) . T) ((|#2|) . T) (((-413 (-570))) -2892 (|has| |#2| (-38 (-413 (-570)))) (|has| |#2| (-1047 (-413 (-570)))))) ((((-413 (-570))) . T) (($) . T)) -((((-1008 |#1|)) . T) ((|#1|) . T) (((-570)) -2740 (|has| (-1008 |#1|) (-1047 (-570))) (|has| |#1| (-1047 (-570)))) (((-413 (-570))) -2740 (|has| (-1008 |#1|) (-1047 (-413 (-570)))) (|has| |#1| (-1047 (-413 (-570)))))) +((((-1008 |#1|)) . T) ((|#1|) . T) (((-570)) -2892 (|has| (-1008 |#1|) (-1047 (-570))) (|has| |#1| (-1047 (-570)))) (((-413 (-570))) -2892 (|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)))) @@ -3930,10 +3930,10 @@ (((|#1| |#2| |#3| |#4|) . T)) (((#0=(-1149 |#1| |#2|) #0#) |has| (-1149 |#1| |#2|) (-313 (-1149 |#1| |#2|)))) (((|#1|) . 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176282) ((-487 . -916) 176261) ((-1241 . -1047) 176227) ((-1221 . -520) 176194) ((-1096 . -723) 176043) ((-1071 . -654) 176030) ((-959 . -654) 175955) ((-603 . -496) 175936) ((-591 . -496) 175917) ((-788 . -723) 175746) ((-603 . -619) 175712) ((-591 . -619) 175678) ((-542 . -619) 175660) ((-542 . -620) 175641) ((-786 . -723) 175490) ((-1086 . -102) T) ((-386 . -25) T) ((-629 . -652) 175462) ((-386 . -21) T) ((-487 . -654) 175387) ((-467 . -723) 175358) ((-460 . -723) 175207) ((-996 . -102) T) ((-1199 . -620) NIL) ((-1199 . -619) 175189) ((-1151 . -1132) 175134) ((-743 . -102) T) ((-118 . -652) 175064) ((-611 . -622) 175046) ((-1055 . -1220) 174975) ((-908 . -313) 174913) ((-537 . -25) T) ((-882 . -93) T) ((-720 . -622) 174867) ((-687 . -93) T) ((-651 . -496) 174848) ((-142 . -102) T) ((-44 . -132) T) ((-682 . -93) T) ((-670 . -619) 174830) ((-348 . -1067) T) ((-293 . -1121) T) ((-651 . -619) 174783) ((-484 . -93) T) ((-360 . -619) 174765) ((-357 . -619) 174747) ((-349 . -619) 174729) 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T) ((-570 . -1109) T) ((-501 . -1109) T) ((-247 . -292) 160931) ((-317 . -233) 160892) ((-1182 . -893) NIL) ((-55 . -1109) T) ((-1134 . -893) 160751) ((-130 . -856) T) ((-1182 . -1047) 160631) ((-1134 . -1047) 160514) ((-185 . -619) 160496) ((-860 . -1047) 160392) ((-788 . -290) 160319) ((-823 . -1121) T) ((-1043 . -732) T) ((-608 . -657) 160303) ((-1055 . -985) 160232) ((-1008 . -102) T) ((-823 . -23) T) ((-718 . -1161) 160210) ((-700 . -1067) T) ((-608 . -378) 160194) ((-356 . -458) T) ((-348 . -294) T) ((-1278 . -1109) T) ((-250 . -1109) T) ((-405 . -102) T) ((-293 . -21) T) ((-293 . -25) T) ((-366 . -732) T) ((-716 . -1109) T) ((-705 . -1109) T) ((-366 . -479) T) ((-1221 . -619) 160176) ((-1182 . -382) 160160) ((-1134 . -382) 160144) ((-1033 . -417) 160106) ((-142 . -231) 160088) ((-384 . -800) T) ((-384 . -797) T) ((-876 . -174) T) ((-384 . -732) T) ((-717 . -619) 160070) ((-718 . -38) 159899) ((-1277 . -1275) 159883) ((-356 . -408) T) ((-1277 . -1109) 159833) ((-1200 . -1109) T) 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. -1231) T) ((-1008 . -313) 158978) ((-882 . -622) 158959) ((-720 . -654) 158919) ((-219 . -1231) T) ((-687 . -622) 158900) ((-227 . -1047) 158860) ((-40 . -294) T) ((-682 . -622) 158841) ((-493 . -562) T) ((-484 . -622) 158822) ((-320 . -652) 158506) ((-317 . -652) 158420) ((-364 . -25) T) ((-364 . -21) T) ((-358 . -25) T) ((-219 . -562) T) ((-358 . -21) T) ((-350 . -25) T) ((-350 . -21) T) ((-247 . -622) 158397) ((-139 . -622) 158378) ((-138 . -622) 158359) ((-134 . -622) 158340) ((-108 . -25) T) ((-108 . -21) T) ((-48 . -1067) T) ((-586 . -174) T) ((-570 . -174) T) ((-501 . -174) T) ((-664 . -619) 158322) ((-743 . -742) 158306) ((-341 . -619) 158288) ((-68 . -388) T) ((-68 . -401) T) ((-1111 . -107) 158272) ((-1071 . -893) 158254) ((-959 . -893) 158179) ((-659 . -1121) T) ((-629 . -723) 158166) ((-487 . -893) NIL) ((-1155 . -102) T) ((-1103 . -624) 158150) ((-1071 . -1047) 158132) ((-97 . -619) 158114) ((-483 . -148) T) ((-959 . -1047) 157994) ((-118 . -723) 157939) ((-659 . -23) T) 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152751) ((-112 . -620) 152733) ((-724 . -479) T) ((-717 . -622) 152683) ((-1300 . -1060) 152667) ((-488 . -21) 152577) ((-128 . -495) 152561) ((-122 . -495) 152545) ((-488 . -25) 152396) ((-1300 . -646) 152366) ((-629 . -294) T) ((-592 . -1065) 152341) ((-443 . -1109) T) ((-1071 . -311) T) ((-118 . -294) T) ((-1113 . -102) T) ((-1012 . -102) T) ((-592 . -111) 152309) ((-1151 . -313) 152247) ((-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) 152157) ((-512 . -102) T) ((-508 . -102) T) ((-359 . -174) T) ((-348 . -619) 152139) ((-413 . -1060) 152091) ((-400 . -619) 152073) ((-1129 . -854) T) ((-480 . -732) T) ((-899 . -1047) 152041) ((-413 . -646) 151993) ((-108 . -856) T) ((-664 . -1065) 151977) ((-493 . -132) T) ((-1263 . -1067) T) ((-219 . -132) T) ((-1166 . -102) 151955) ((-99 . -1109) T) ((-247 . 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NIL) ((-741 . -1121) T) ((-721 . -1121) T) ((-664 . -622) 149822) ((-1277 . -495) 149806) ((-1151 . -38) 149766) ((-970 . -23) T) ((-917 . -654) 149731) ((-871 . -1109) T) ((-849 . -102) T) ((-823 . -21) T) ((-641 . -1060) 149715) ((-613 . -1060) 149699) ((-823 . -25) T) ((-741 . -23) T) ((-721 . -23) T) ((-641 . -646) 149683) ((-110 . -667) T) ((-613 . -646) 149667) ((-587 . -1065) 149632) ((-524 . -1065) 149577) ((-229 . -57) 149535) ((-459 . -23) T) ((-413 . -102) T) ((-266 . -102) T) ((-110 . -113) T) ((-700 . -294) T) ((-872 . -38) 149505) ((-587 . -111) 149461) ((-524 . -111) 149390) ((-1096 . -622) 149126) ((-424 . -1121) T) ((-320 . -1067) 149016) ((-317 . -1067) T) ((-129 . -1227) T) ((-788 . -622) 148764) ((-786 . -622) 148530) ((-664 . -1058) T) ((-1305 . -1109) T) ((-460 . -622) 148315) ((-171 . -311) 148246) ((-424 . -23) T) ((-40 . -619) 148228) ((-40 . -620) 148212) ((-108 . -1001) 148194) ((-117 . -875) 148178) ((-655 . -622) 148162) ((-48 . -520) 148128) ((-1213 . 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147292) ((-908 . -1109) 147270) ((-50 . -1058) T) ((-1289 . -21) T) ((-1289 . -25) T) ((-1184 . -562) 147249) ((-1183 . -1231) 147228) ((-1183 . -562) 147179) ((-587 . -1058) T) ((-524 . -1058) T) ((-1177 . -1231) 147158) ((-366 . -1047) 147142) ((-326 . -1047) 147126) ((-1033 . -294) T) ((-384 . -893) 147108) ((-1177 . -562) 147059) ((-1012 . -38) 147004) ((-1008 . -652) 146927) ((-805 . -1121) T) ((-917 . -732) T) ((-587 . -245) T) ((-587 . -235) T) ((-524 . -235) T) ((-524 . -245) T) ((-1135 . -562) 146906) ((-359 . -294) T) ((-653 . -701) 146890) ((-384 . -1047) 146850) ((-298 . -1060) 146771) ((-1129 . -1067) T) ((-103 . -126) 146755) ((-298 . -646) 146697) ((-805 . -23) T) ((-1299 . -1294) 146673) ((-1277 . -290) 146650) ((-413 . -313) 146615) ((-1297 . -1294) 146594) ((-1263 . -1109) T) ((-876 . -619) 146576) ((-842 . -1047) 146545) ((-205 . -793) T) ((-204 . -793) T) ((-203 . -793) T) ((-202 . -793) T) ((-201 . -793) T) ((-200 . -793) T) ((-199 . -793) T) ((-198 . -793) T) 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. -152) 144183) ((-348 . -235) T) ((-348 . -245) T) ((-40 . -1065) 144128) ((-878 . -891) 144112) ((-878 . -893) 144037) ((-718 . -1067) T) ((-700 . -1011) NIL) ((-1261 . -47) 144007) ((-1240 . -47) 143984) ((-1150 . -1019) 143955) ((-3 . |UnionCategory|) T) ((-1129 . -723) 143942) ((-1114 . -619) 143924) ((-1089 . -148) 143903) ((-1089 . -146) 143854) ((-973 . -622) 143838) ((-227 . -927) T) ((-40 . -111) 143767) ((-878 . -1047) 143631) ((-1013 . -368) T) ((-1012 . -233) 143608) ((-707 . -1060) 143595) ((-921 . -368) T) ((-707 . -646) 143582) ((-323 . -1215) 143548) ((-384 . -311) T) ((-323 . -1212) 143514) ((-320 . -174) 143493) ((-317 . -174) T) ((-587 . -1296) 143480) ((-524 . -1296) 143457) ((-364 . -148) 143436) ((-117 . -1060) 143423) ((-364 . -146) 143374) ((-358 . -148) 143353) ((-358 . -146) 143304) ((-350 . -148) 143283) ((-614 . -1203) 143259) ((-117 . -646) 143246) ((-350 . -146) 143197) ((-323 . -35) 143163) ((-481 . -1203) 143142) ((0 . |EnumerationCategory|) T) ((-323 . 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-313) 141927) ((-1013 . -1121) T) ((-142 . -520) NIL) ((-872 . -652) 141872) ((-1012 . -354) NIL) ((-980 . -23) T) ((-921 . -1121) T) ((-356 . -38) 141837) ((-921 . -23) T) ((-878 . -907) 141796) ((-82 . -619) 141778) ((-40 . -1058) T) ((-876 . -1065) 141765) ((-876 . -111) 141750) ((-707 . -102) T) ((-700 . -619) 141732) ((-608 . -1227) T) ((-602 . -562) 141711) ((-433 . -1121) T) ((-344 . -1060) 141695) ((-215 . -1109) T) ((-176 . -1060) 141627) ((-480 . -47) 141597) ((-135 . -102) T) ((-40 . -235) 141569) ((-40 . -245) T) ((-117 . -102) T) ((-601 . -562) 141548) ((-344 . -646) 141532) ((-700 . -620) 141440) ((-320 . -520) 141406) ((-176 . -646) 141338) ((-317 . -520) 141230) ((-1261 . -1047) 141214) ((-1240 . -1047) 141000) ((-1008 . -417) 140984) ((-433 . -23) T) ((-1129 . -174) T) ((-1263 . -294) T) ((-660 . -723) 140954) ((-145 . -1109) T) ((-48 . -1011) T) ((-413 . -233) 140938) ((-299 . -237) 140888) ((-877 . -927) T) ((-877 . -826) NIL) ((-876 . -622) 140860) ((-870 . -856) T) 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139764) ((-48 . -620) 139709) ((-242 . -132) 139579) ((-1300 . -652) 139538) ((-1250 . -927) 139517) ((-822 . -1231) 139496) ((-394 . -496) 139477) ((-1044 . -520) 139321) ((-394 . -619) 139287) ((-822 . -562) 139218) ((-592 . -654) 139193) ((-267 . -47) 139165) ((-249 . -47) 139122) ((-537 . -515) 139099) ((-586 . -622) 139071) ((-570 . -622) 139043) ((-501 . -622) 138976) ((-1083 . -1227) T) ((-1009 . -1227) T) ((-1269 . -23) T) ((-705 . -1065) 138941) ((-1269 . -1121) T) ((-1262 . -1121) T) ((-1262 . -23) T) ((-1241 . -1121) T) ((-1241 . -23) T) ((-1012 . -375) 138913) ((-112 . -373) T) ((-480 . -907) 138819) ((-1221 . -732) T) ((-911 . -619) 138801) ((-55 . -622) 138783) ((-91 . -107) 138767) ((-1129 . -294) T) ((-912 . -856) 138718) ((-707 . -1161) T) ((-705 . -111) 138674) ((-849 . -652) 138591) ((-602 . -1121) T) ((-601 . -1121) T) ((-718 . -723) 138420) ((-717 . -732) T) ((-1013 . -132) T) ((-980 . -132) T) ((-493 . -856) T) ((-921 . -132) T) ((-805 . -25) T) ((-805 . -21) T) 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NIL) ((-118 . -1065) 137482) ((-460 . -654) 137407) ((-670 . -1047) 137384) ((-629 . -111) 137369) ((-396 . -1060) 137353) ((-360 . -1047) 137337) ((-357 . -1047) 137321) ((-349 . -1047) 137305) ((-267 . -1047) 137149) ((-249 . -1047) 137025) ((-118 . -111) 136954) ((-59 . -1227) T) ((-396 . -646) 136938) ((-627 . -1060) 136922) ((-525 . -1227) T) ((-522 . -1227) T) ((-503 . -1227) T) ((-502 . -1227) T) ((-443 . -619) 136904) ((-440 . -619) 136886) ((-627 . -646) 136870) ((-3 . -102) T) ((-1036 . -1220) 136839) ((-839 . -102) T) ((-695 . -57) 136797) ((-705 . -1058) T) ((-641 . -652) 136766) ((-613 . -652) 136735) ((-50 . -654) 136709) ((-293 . -458) T) ((-482 . -1220) 136678) ((0 . -102) T) ((-587 . -654) 136643) ((-524 . -654) 136588) ((-49 . -102) T) ((-917 . -1047) 136575) ((-705 . -245) T) ((-1089 . -415) 136554) ((-737 . -645) 136502) ((-1008 . -1109) T) ((-718 . -174) 136393) ((-629 . -622) 136288) ((-493 . -1001) 136270) ((-267 . -382) 136254) ((-249 . -382) 136238) ((-405 . 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. -619) 131954) ((-805 . -856) 131933) ((-1169 . -152) 131880) ((-1008 . -520) 131792) ((-359 . -235) T) ((-359 . -245) T) ((-394 . -622) 131773) ((-1013 . -25) T) ((-142 . -619) 131755) ((-142 . -620) 131714) ((-917 . -311) T) ((-1013 . -21) T) ((-980 . -25) T) ((-921 . -21) T) ((-921 . -25) T) ((-433 . -21) T) ((-433 . -25) T) ((-849 . -417) 131698) ((-48 . -1058) T) ((-1299 . -1291) 131682) ((-1297 . -1291) 131666) ((-1044 . -610) 131641) ((-320 . -620) 131502) ((-320 . -619) 131484) ((-317 . -620) NIL) ((-317 . -619) 131466) ((-48 . -245) T) ((-48 . -235) T) ((-660 . -290) 131427) ((-556 . -237) 131377) ((-140 . -619) 131344) ((-137 . -619) 131326) ((-115 . -619) 131308) ((-483 . -38) 131273) ((-1301 . -1298) 131252) ((-1292 . -132) T) ((-1300 . -1067) T) ((-1091 . -102) T) ((-88 . -1227) T) ((-506 . -313) NIL) ((-1009 . -107) 131236) ((-896 . -1109) T) ((-892 . -1109) T) ((-1277 . -657) 131220) ((-1277 . -378) 131204) ((-331 . -1227) T) ((-599 . -856) T) ((-1151 . -1109) T) 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. -23) T) ((-1160 . -1092) T) ((-1134 . -23) T) ((-860 . -23) T) ((-487 . -562) 130187) ((-1151 . -723) 130119) ((-676 . -1060) 130103) ((-1155 . -520) 130036) ((-676 . -646) 130020) ((-1044 . -620) NIL) ((-1044 . -619) 130002) ((-96 . -1092) T) ((-872 . -723) 129972) ((-1221 . -47) 129941) ((-254 . -132) T) ((-253 . -132) T) ((-1113 . -1109) T) ((-1012 . -1109) T) ((-62 . -619) 129923) ((-1177 . -856) NIL) ((-1033 . -798) T) ((-1033 . -801) T) ((-1305 . -1065) 129910) ((-1305 . -111) 129895) ((-1269 . -25) T) ((-1269 . -21) T) ((-876 . -654) 129882) ((-1262 . -21) T) ((-1262 . -25) T) ((-1241 . -21) T) ((-1241 . -25) T) ((-1036 . -152) 129866) ((-878 . -826) 129845) ((-878 . -927) T) ((-718 . -290) 129772) ((-602 . -21) T) ((-344 . -652) 129731) ((-602 . -25) T) ((-601 . -21) T) ((-176 . -652) 129648) ((-40 . -732) T) ((-224 . -520) 129581) ((-601 . -25) T) ((-482 . -152) 129565) ((-469 . -152) 129549) ((-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) 129533) ((-1297 . -1060) 129517) ((-1299 . -646) 129487) ((-1166 . -1109) 129465) ((-877 . -1231) T) ((-1297 . -646) 129435) ((-660 . -619) 129417) ((-877 . -562) T) ((-700 . -373) NIL) ((-44 . -1060) 129401) ((-1305 . -622) 129383) ((-1300 . -1109) T) ((-676 . -102) T) ((-364 . -1284) 129367) ((-358 . -1284) 129351) ((-44 . -646) 129335) ((-350 . -1284) 129319) ((-554 . -102) T) ((-526 . -856) 129298) ((-1055 . -1109) T) ((-823 . -458) 129277) ((-153 . -1060) 129261) ((-1055 . -1080) 129190) ((-1036 . -985) 129159) ((-825 . -1121) T) ((-1012 . -723) 129104) ((-153 . -646) 129088) ((-392 . -1121) T) ((-482 . -985) 129057) ((-469 . -985) 129026) ((-110 . -152) 129008) ((-73 . -619) 128990) ((-900 . -619) 128972) ((-1089 . -730) 128951) ((-1305 . -1058) T) ((-822 . -645) 128899) ((-298 . -1067) 128841) ((-171 . -1231) 128746) ((-227 . -1121) T) ((-328 . -23) T) ((-1177 . -1001) 128698) ((-849 . -1109) T) 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. -1121) T) ((-118 . -916) NIL) ((-1299 . -1298) 125888) ((-1297 . -1298) 125867) ((-788 . -893) NIL) ((-786 . -893) 125726) ((-1292 . -25) T) ((-1292 . -21) T) ((-1224 . -102) 125704) ((-1115 . -401) T) ((-629 . -654) 125691) ((-460 . -893) NIL) ((-681 . -102) 125669) ((-1096 . -1047) 125496) ((-877 . -23) T) ((-788 . -1047) 125355) ((-786 . -1047) 125212) ((-118 . -654) 125157) ((-460 . -1047) 125033) ((-320 . -622) 124597) ((-317 . -622) 124480) ((-396 . -652) 124449) ((-655 . -1047) 124433) ((-633 . -102) T) ((-224 . -495) 124417) ((-1277 . -34) T) ((-627 . -652) 124376) ((-293 . -1060) 124363) ((-137 . -622) 124347) ((-293 . -646) 124334) ((-641 . -723) 124318) ((-613 . -723) 124302) ((-676 . -38) 124262) ((-323 . -102) T) ((-85 . -619) 124244) ((-50 . -1047) 124228) ((-1129 . -1065) 124215) ((-1096 . -382) 124199) ((-788 . -382) 124183) ((-705 . -732) T) ((-705 . -800) T) ((-705 . -797) T) ((-587 . -1047) 124170) ((-524 . -1047) 124147) ((-60 . -57) 124109) ((-328 . -132) T) 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NIL) ((-118 . -732) T) ((-700 . -916) NIL) ((-1055 . -520) 122854) ((-487 . -132) T) ((-577 . -23) T) ((-681 . -313) 122792) ((-641 . -767) T) ((-613 . -767) T) ((-1241 . -856) NIL) ((-1089 . -1060) 122702) ((-1012 . -294) T) ((-700 . -654) 122652) ((-254 . -21) T) ((-356 . -1109) T) ((-254 . -25) T) ((-253 . -21) T) ((-253 . -25) T) ((-153 . -38) 122636) ((-2 . -102) T) ((-917 . -927) T) ((-1089 . -646) 122504) ((-488 . -1284) 122474) ((-1129 . -1058) T) ((-717 . -311) T) ((-364 . -1060) 122426) ((-358 . -1060) 122378) ((-350 . -1060) 122330) ((-364 . -646) 122282) ((-225 . -1047) 122259) ((-358 . -646) 122211) ((-108 . -1060) 122161) ((-350 . -646) 122113) ((-298 . -723) 122055) ((-707 . -1067) T) ((-493 . -458) T) ((-413 . -520) 121967) ((-108 . -646) 121917) ((-219 . -458) T) ((-1129 . -235) T) ((-299 . -152) 121867) ((-1008 . -620) 121828) ((-1008 . -619) 121810) ((-998 . -619) 121792) ((-117 . -1067) T) ((-660 . -1065) 121776) ((-227 . -499) T) ((-405 . -619) 121758) ((-405 . -620) 121735) ((-1063 . -1284) 121705) ((-660 . -111) 121684) ((-1151 . -495) 121668) ((-1301 . -652) 121627) ((-386 . -652) 121596) ((-821 . -38) 121566) ((-63 . -447) T) ((-63 . -401) T) ((-1169 . -102) T) ((-877 . -132) T) ((-490 . -102) 121544) ((-1305 . -373) T) ((-1089 . -102) T) ((-1070 . -102) T) ((-356 . -723) 121489) ((-737 . -148) 121468) ((-737 . -146) 121447) ((-660 . -622) 121365) ((-1033 . -654) 121302) ((-529 . -1109) 121280) ((-364 . -102) T) ((-358 . -102) T) ((-350 . -102) T) ((-108 . -102) T) ((-510 . -1109) T) ((-359 . -654) 121225) ((-1182 . -645) 121173) ((-1134 . -645) 121121) ((-390 . -515) 121100) ((-839 . -854) 121079) ((-384 . -1231) T) ((-700 . -732) T) ((-1241 . -1001) 121031) ((-344 . -1067) T) ((-112 . -1227) T) ((-176 . -1067) T) ((-103 . -619) 120963) ((-1184 . -146) 120942) ((-1184 . -148) 120921) ((-384 . -562) T) ((-1183 . -148) 120900) ((-1183 . -146) 120879) ((-1177 . -146) 120786) ((-413 . -294) T) ((-1177 . -148) 120693) ((-1135 . -148) 120672) 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-102) T) ((-272 . -102) T) ((-348 . -1047) 119508) ((-271 . -102) T) ((-214 . -102) T) ((-213 . -102) T) ((-211 . -102) T) ((-210 . -102) T) ((-209 . -102) T) ((-208 . -102) T) ((-205 . -102) T) ((-204 . -102) T) ((-203 . -102) T) ((-202 . -102) T) ((-201 . -102) T) ((-200 . -102) T) ((-199 . -102) T) ((-198 . -102) T) ((-197 . -102) T) ((-196 . -102) T) ((-195 . -102) T) ((-359 . -732) T) ((-718 . -111) 119317) ((-676 . -233) 119301) ((-587 . -311) T) ((-524 . -311) T) ((-298 . -520) 119250) ((-108 . -313) NIL) ((-72 . -401) T) ((-1122 . -102) 119040) ((-839 . -417) 119024) ((-1129 . -801) T) ((-1129 . -798) T) ((-707 . -1109) T) ((-584 . -619) 119006) ((-384 . -368) T) ((-171 . -499) 118984) ((-224 . -619) 118916) ((-135 . -1109) T) ((-117 . -1109) T) ((-973 . -1227) T) ((-48 . -732) T) ((-1055 . -495) 118881) ((-142 . -431) 118863) ((-142 . -373) T) ((-1036 . -102) T) ((-518 . -515) 118842) ((-718 . -622) 118598) ((-482 . -102) T) ((-469 . -102) T) ((-1043 . -1121) T) ((-1234 . -619) 118580) ((-1191 . -1047) 118516) ((-1184 . -35) 118482) ((-1184 . -95) 118448) ((-1184 . -1215) 118414) ((-1184 . -1212) 118380) ((-1168 . -313) NIL) ((-89 . -402) T) ((-89 . -401) T) ((-1089 . -1161) 118359) ((-1183 . -1212) 118325) ((-1183 . -1215) 118291) ((-1043 . -23) T) ((-1183 . -95) 118257) ((-577 . -499) T) ((-1183 . -35) 118223) ((-1177 . -1212) 118189) ((-1177 . -1215) 118155) ((-1177 . -95) 118121) ((-366 . -1121) T) ((-364 . -1161) 118100) ((-358 . -1161) 118079) ((-350 . -1161) 118058) ((-1177 . -35) 118024) ((-1135 . -35) 117990) ((-1135 . -95) 117956) ((-108 . -1161) T) ((-1135 . -1215) 117922) ((-839 . -1067) 117901) ((-653 . -313) 117839) ((-638 . -313) 117690) ((-1135 . -1212) 117656) ((-718 . -1058) T) ((-1071 . -645) 117638) ((-1089 . -38) 117506) ((-959 . -645) 117454) ((-1013 . -148) T) ((-1013 . -146) NIL) ((-384 . -1121) T) ((-328 . -25) T) ((-326 . -23) T) ((-950 . -856) 117433) ((-718 . -330) 117410) ((-487 . -645) 117358) ((-40 . -1047) 117246) ((-718 . -235) T) ((-707 . -723) 117233) ((-344 . -1109) T) ((-176 . -1109) T) ((-335 . -856) T) ((-424 . -458) 117183) ((-384 . -23) T) ((-364 . -38) 117148) ((-358 . -38) 117113) ((-350 . -38) 117078) ((-80 . -447) T) ((-80 . -401) T) ((-227 . -25) T) ((-227 . -21) T) ((-842 . -1121) T) ((-108 . -38) 117028) ((-833 . -1121) T) ((-780 . -1109) T) ((-117 . -723) 117015) ((-678 . -1047) 116999) ((-618 . -102) T) ((-842 . -23) T) ((-833 . -23) T) ((-1166 . -290) 116976) ((-1122 . -313) 116914) ((-488 . -1060) 116811) ((-1111 . -237) 116795) ((-64 . -402) T) ((-64 . -401) T) ((-1160 . -102) T) ((-110 . -102) T) ((-488 . -646) 116737) ((-40 . -382) 116714) ((-96 . -102) T) ((-659 . -858) 116698) ((-1144 . -1092) T) ((-1071 . -21) T) ((-1071 . -25) T) ((-1063 . -1060) 116682) ((-821 . -233) 116651) ((-959 . -25) T) ((-959 . -21) T) ((-1063 . -646) 116593) ((-627 . -1067) T) ((-1129 . -373) T) ((-1036 . -313) 116531) ((-676 . -652) 116490) ((-487 . -25) T) ((-487 . -21) T) ((-390 . -1060) 116474) 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. -148) 113964) ((-601 . -146) 113943) ((-501 . -1047) 113886) ((-1144 . -1146) T) ((-87 . -389) T) ((-87 . -401) T) ((-878 . -368) T) ((-842 . -132) T) ((-833 . -132) T) ((-971 . -652) 113830) ((-720 . -23) T) ((-512 . -619) 113796) ((-508 . -619) 113778) ((-821 . -652) 113528) ((-1301 . -1067) T) ((-384 . -1069) T) ((-1035 . -1109) 113506) ((-55 . -1047) 113488) ((-908 . -34) T) ((-488 . -313) 113426) ((-598 . -102) T) ((-1166 . -620) 113387) ((-1166 . -619) 113319) ((-1188 . -1060) 113202) ((-45 . -102) T) ((-823 . -102) T) ((-1188 . -646) 113099) ((-1250 . -25) T) ((-1250 . -21) T) ((-861 . -25) T) ((-44 . -372) 113083) ((-861 . -21) T) ((-737 . -458) 113034) ((-1300 . -619) 113016) ((-1289 . -1060) 112986) ((-1063 . -313) 112924) ((-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) 112894) ((-627 . -1109) T) ((-705 . -893) 112876) ((-1277 . -1227) T) 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. -1047) 111511) ((-650 . -856) 111490) ((-1289 . -102) T) ((-299 . -102) T) ((-718 . -373) 111469) ((-118 . -1047) 111446) ((-396 . -723) 111430) ((-627 . -723) 111414) ((-45 . -313) 111218) ((-822 . -146) 111197) ((-822 . -148) 111176) ((-293 . -652) 111148) ((-1300 . -387) 111127) ((-825 . -856) T) ((-1279 . -1109) T) ((-1169 . -231) 111074) ((-392 . -856) 111053) ((-1269 . -1215) 111019) ((-1269 . -1212) 110985) ((-1262 . -1212) 110951) ((-521 . -132) T) ((-1262 . -1215) 110917) ((-1241 . -1212) 110883) ((-1241 . -1215) 110849) ((-1269 . -35) 110815) ((-1269 . -95) 110781) ((-641 . -619) 110750) ((-613 . -619) 110719) ((-227 . -856) T) ((-1262 . -95) 110685) ((-1262 . -35) 110651) ((-1261 . -1121) T) ((-1129 . -654) 110638) ((-1241 . -95) 110604) ((-1240 . -1121) T) ((-599 . -152) 110586) ((-1089 . -354) 110565) ((-176 . -294) T) ((-118 . -382) 110542) ((-118 . -343) 110519) ((-1241 . -35) 110485) ((-876 . -311) T) ((-317 . -800) NIL) ((-317 . -797) NIL) ((-320 . -732) 110334) 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. -313) 92245) ((-1096 . -1121) T) ((-1300 . -654) 92219) ((-788 . -1121) T) ((-786 . -1121) T) ((-460 . -1121) T) ((-1071 . -458) T) ((-1160 . -1109) T) ((-959 . -458) 92170) ((-1124 . -1092) T) ((-110 . -1109) T) ((-1096 . -23) T) ((-823 . -1067) T) ((-788 . -23) T) ((-786 . -23) T) ((-487 . -458) 92121) ((-1169 . -520) 91904) ((-386 . -387) 91883) ((-1188 . -417) 91867) ((-467 . -23) T) ((-460 . -23) T) ((-96 . -1109) T) ((-490 . -520) 91800) ((-1269 . -1060) 91683) ((-1269 . -646) 91580) ((-1262 . -646) 91421) ((-1262 . -1060) 91256) ((-293 . -294) T) ((-1241 . -1060) 91046) ((-1091 . -619) 91028) ((-1091 . -620) 91009) ((-413 . -916) 90988) ((-1241 . -646) 90784) ((-50 . -1121) T) ((-1221 . -132) T) ((-1033 . -927) T) ((-1012 . -732) T) ((-849 . -654) 90757) ((-718 . -893) NIL) ((-602 . -1060) 90717) ((-587 . -1121) T) ((-524 . -1121) T) ((-601 . -1060) 90600) ((-1177 . -406) 90552) ((-1013 . -313) NIL) ((-821 . -495) 90536) ((-602 . -646) 90509) ((-359 . -927) T) ((-601 . -646) 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. -619) 78032) ((-358 . -619) 78014) ((-350 . -619) 77996) ((-66 . -402) T) ((-66 . -401) T) ((-108 . -620) 77926) ((-108 . -619) 77868) ((-213 . -902) T) ((-965 . -152) 77852) ((-777 . -132) T) ((-676 . -622) 77770) ((-135 . -732) T) ((-117 . -732) T) ((-1261 . -35) 77736) ((-1063 . -495) 77720) ((-586 . -23) T) ((-570 . -23) T) ((-501 . -23) T) ((-1240 . -95) 77686) ((-1240 . -35) 77652) ((-1182 . -102) T) ((-1134 . -102) T) ((-860 . -102) T) ((-229 . -495) 77636) ((-1299 . -111) 77615) ((-1297 . -111) 77594) ((-44 . -1065) 77578) ((-1299 . -622) 77524) ((-1250 . -1253) 77508) ((-861 . -858) 77492) ((-1299 . -1058) T) ((-1188 . -294) 77471) ((-110 . -290) 77446) ((-1297 . -622) 77375) ((-129 . -152) 77357) ((-1151 . -907) 77316) ((-44 . -111) 77295) ((-1232 . -1109) T) ((-1191 . -1272) T) ((-1176 . -496) 77276) ((-1176 . -619) 77242) ((-676 . -1058) T) ((-1168 . -620) NIL) ((-1168 . -619) 77224) ((-1072 . -616) 77199) ((-1072 . -1109) T) ((-1003 . -496) 77180) ((-74 . -447) T) ((-74 . -401) T) ((-1003 . -619) 77146) ((-153 . -1065) 77130) ((-676 . -235) 77109) ((-577 . -560) 77093) ((-360 . -148) 77072) ((-360 . -146) 77023) ((-357 . -148) 77002) ((-357 . -146) 76953) ((-349 . -148) 76932) ((-349 . -146) 76883) ((-267 . -146) 76862) ((-267 . -148) 76841) ((-254 . -38) 76811) ((-249 . -148) 76790) ((-118 . -368) T) ((-249 . -146) 76769) ((-253 . -38) 76739) ((-153 . -111) 76718) ((-1012 . -1047) 76606) ((-1177 . -854) NIL) ((-700 . -1231) T) ((-805 . -1067) T) ((-705 . -1121) T) ((-1297 . -1058) T) ((-1166 . -1227) T) ((-1012 . -382) 76583) ((-917 . -146) T) ((-917 . -148) 76565) ((-876 . -132) T) ((-821 . -1065) 76462) ((-705 . -23) T) ((-700 . -562) T) ((-227 . -1060) 76427) ((-653 . -619) 76359) ((-653 . -620) 76320) ((-638 . -620) NIL) ((-638 . -619) 76302) ((-493 . -174) T) ((-227 . -646) 76267) ((-225 . -21) T) ((-219 . -174) T) ((-225 . -25) T) ((-480 . -1215) 76233) ((-480 . -1212) 76199) ((-277 . -619) 76181) ((-276 . -619) 76163) ((-275 . -619) 76145) 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1786) ((-849 . -856) 1765) ((-570 . -1161) T) ((-480 . -294) 1716) ((-602 . -732) T) ((-366 . -619) 1698) ((-326 . -619) 1680) ((-424 . -1047) 1576) ((-601 . -732) T) ((-413 . -856) 1527) ((-171 . -111) 1423) ((-839 . -132) 1375) ((-743 . -152) 1359) ((-1277 . -313) 1297) ((-493 . -311) T) ((-384 . -619) 1264) ((-526 . -1019) 1248) ((-384 . -620) 1162) ((-219 . -311) T) ((-142 . -152) 1144) ((-720 . -290) 1123) ((-493 . -1031) T) ((-586 . -38) 1110) ((-570 . -38) 1097) ((-501 . -38) 1062) ((-219 . -1031) T) ((-877 . -1058) T) ((-842 . -619) 1044) ((-833 . -619) 1026) ((-831 . -619) 1008) ((-822 . -916) 987) ((-1301 . -1121) T) ((-1250 . -1065) 810) ((-861 . -1065) 794) ((-877 . -245) T) ((-877 . -235) NIL) ((-695 . -1227) T) ((-1301 . -23) T) ((-822 . -654) 719) ((-556 . -1227) T) ((-424 . -343) 703) ((-577 . -1065) 690) ((-1250 . -111) 499) ((-707 . -645) 481) ((-861 . -111) 460) ((-386 . -23) T) ((-171 . -622) 238) ((-1199 . -520) 30) ((-882 . -1109) T) ((-687 . -1109) T) ((-682 . -1109) T) ((-668 . -1109) T))
\ No newline at end of file diff --git a/src/share/algebra/compress.daase b/src/share/algebra/compress.daase index 3bb63ba0..2495bdd3 100644 --- a/src/share/algebra/compress.daase +++ b/src/share/algebra/compress.daase @@ -1,5 +1,5 @@ -(30 . 3480583730) +(30 . 3480761522) (4452 |Enumeration| |Mapping| |Record| |Union| |ofCategory| |isDomain| ATTRIBUTE |package| |domain| |category| CATEGORY |nobranch| AND |Join| |ofType| SIGNATURE "failed" "algebra" |OneDimensionalArrayAggregate&| @@ -484,665 +484,667 @@ |XPolynomial| |XPolynomialRing| |XRecursivePolynomial| |ParadoxicalCombinatorsForStreams| |ZeroDimensionalSolvePackage| |IntegerLinearDependence| |IntegerMod| |Enumeration| |Mapping| - |Record| |Union| |stosePrepareSubResAlgo| |voidMode| - |orthonormalBasis| |fixedPoints| |permutationRepresentation| |pi| - |writeByte!| |arbitrary| |increase| |polynomialZeros| |subscript| - |makeMulti| |quasiComponent| |quotedOperators| |lazyGintegrate| - |infinity| |bat1| |functionIsContinuousAtEndPoints| |e02agf| - |pascalTriangle| |diag| |bounds| |convergents| |cothIfCan| - |conditionsForIdempotents| |tan2trig| |cond| |aQuartic| |subMatrix| - |setMinPoints3D| |f07adf| |factorFraction| |decrease| |permutations| - |singularitiesOf| |unitCanonical| |cCsch| |generate| |log10| |d01bbf| - |e01bgf| |selectIntegrationRoutines| |map| |d01asf| |leftLcm| |e02bdf| - |stirling2| |algint| |sinhIfCan| |mainSquareFreePart| |bitand| - |kernel| |previous| |measure| |twist| |buildSyntax| |predicates| |abs| - |iisqrt2| |isQuotient| |incrementBy| |realEigenvalues| |unit?| - |OMgetEndApp| |nextSublist| |outerProduct| |bitior| |draw| - |squareFree| |qfactor| |OMgetInteger| |morphism| |iidsum| - |messagePrint| |deref| |solveRetract| |fmecg| |Beta| |expand| - |intensity| |superHeight| |stoseInvertible?reg| |setClipValue| - |rowEchLocal| |elliptic?| |currentEnv| |normalizedAssociate| |e01saf| - |root?| |removeRoughlyRedundantFactorsInPols| |filterWhile| - |fixedDivisor| |f04arf| |invertibleSet| |e02aef| |initTable!| - |multinomial| |fortranCharacter| |findCycle| |findBinding| - |nativeModuleExtension| |filterUntil| |symbol| |internalIntegrate0| - |polygamma| |evaluateInverse| |rename!| |convert| F2FG |simpsono| - |generalizedContinuumHypothesisAssumed| |getProperty| |endSubProgram| - |cSin| |points| |select| |expression| |makeObject| |isobaric?| - |iCompose| |writeInt8!| |untab| |minimumExponent| |e02ahf| |saturate| - |height| |OMReadError?| |decompose| |cCot| |OMclose| |OMputError| - |integer| |coef| |setleft!| |lastSubResultantElseSplit| |shrinkable| - |e04mbf| |listLoops| |constantCoefficientRicDE| |adjoint| - |selectOptimizationRoutines| |minrank| |numFunEvals3D| |makeCos| - |psolve| |oneDimensionalArray| |mergeDifference| |elaborate| - |fortranDoubleComplex| |ScanRoman| |leftRemainder| - |inputOutputBinaryFile| |rightExactQuotient| |resetVariableOrder| - |redPol| |corrPoly| |irVar| |f01mcf| |elem?| ** |fractRadix| - |monomials| |numberOfFractionalTerms| |basisOfCommutingElements| - |slex| |roughSubIdeal?| |getOperands| |rectangularMatrix| - |partialQuotients| |elColumn2!| |rootOf| |tanIfCan| |stoseInvertible?| - |associator| |separate| |iibinom| |internalAugment| |besselY| - |stiffnessAndStabilityFactor| |clikeUniv| |lighting| |conjug| - |separateDegrees| |jordanAdmissible?| |cAtanh| |makeRecord| |power| - |permutationGroup| |lo| |insertBottom!| |complexNumericIfCan| - |certainlySubVariety?| |iilog| |internalSubQuasiComponent?| - |nextColeman| |lazyVariations| |currentSubProgram| |initials| - |wholeRagits| |incr| |acsch| |setErrorBound| |label| |exists?| - |prologue| |solveLinear| |setOrder| |initial| |normalElement| - |sqfrFactor| |nilFactor| |definingInequation| |hasHi| |copyInto!| - |PDESolve| |bivariatePolynomials| |topFortranOutputStack| - |radicalEigenvectors| |lflimitedint| |splitLinear| |encodingDirectory| - |trace2PowMod| |subSet| |coordinates| |acscIfCan| |cycleLength| - |e01bhf| |clearDenominator| |e02ddf| |copy!| |qqq| |diff| - |complexElementary| |generalPosition| |reduceByQuasiMonic| |invmod| - |prepareDecompose| |asimpson| Y |Is| |components| |makeSUP| - |bezoutResultant| |maxrow| |d02bbf| |integralBasisAtInfinity| - |zeroSetSplit| |choosemon| |dual| |phiCoord| |minPoints| |move| - |OMgetApp| |connect| |sub| |nthFlag| |transcendenceDegree| - |completeEval| |pop!| |external?| |derivative| |df2ef| |setProperty| - |OMlistCDs| |tail| |OMencodingXML| |beauzamyBound| |elRow2!| |pureLex| - |OMsupportsCD?| |constructor| |monicModulo| |rules| - |euclideanNormalForm| |hessian| |csch2sinh| |more?| |symmetric?| - |squareFreePrim| |changeBase| |numberOfPrimitivePoly| - |LagrangeInterpolation| |totalDifferential| |realElementary| |nothing| - |roughBasicSet| |dihedral| |dioSolve| |f04qaf| |option| |power!| - |tubeRadius| |iterationVar| |assign| |eyeDistance| |showSummary| - |separateFactors| |numerator| |leastMonomial| |characteristic| - |csubst| |d01anf| |iicsch| |disjunction| |bumptab| |mkcomm| - |nthFractionalTerm| |systemSizeIF| |insertionSort!| |critBonD| - |fixedPointExquo| |f02ajf| |evaluate| |doubleResultant| |OMgetAtp| - |outputFixed| |showAttributes| |factorPolynomial| |sylvesterMatrix| - |lepol| |reducedContinuedFraction| |f01brf| |spherical| |unknown| - |cyclicSubmodule| |d01gaf| |atrapezoidal| |maxPoints3D| |macroExpand| - |clearTheIFTable| |noKaratsuba| |compactFraction| |pToHdmp| - |degreeSubResultantEuclidean| |rightTrim| |subNode?| |positiveSolve| - |escape| |s21bcf| |groebnerIdeal| |fortranLiteralLine| |leftTrim| - |legendre| |monicRightFactorIfCan| |clearTable!| |removeSinhSq| - |listConjugateBases| |minPoints3D| |linkToFortran| |mapBivariate| - |scalarTypeOf| |tanintegrate| |quoted?| |currentCategoryFrame| - |horizConcat| |s20adf| |logGamma| |unknownEndian| |constantIfCan| - |leftDivide| |iiabs| |say| |primintfldpoly| |makeUnit| F - |unrankImproperPartitions1| |f02abf| |dmpToP| |upperBound| |rightUnit| - |rombergo| |pushdown| |padecf| |genericRightMinimalPolynomial| - |integralDerivationMatrix| |s14baf| |iiasec| |selectFiniteRoutines| - |doublyTransitive?| |outputArgs| |factorAndSplit| |gcdPrimitive| - |implies| |An| |jacobiIdentity?| |setAdaptive3D| |df2fi| - |numberOfComponents| |partialDenominators| |viewZoomDefault| - |relerror| |insertMatch| |removeIrreducibleRedundantFactors| |remove| - |function| |multivariate| |numberOfIrreduciblePoly| |primlimitedint| - |oddlambert| |localAbs| |prod| |fortran| |OMsetEncoding| |variables| - |optional?| |OMputVariable| |wordInGenerators| |coleman| |result| - |s21bdf| |nextPrimitivePoly| |d01amf| |reciprocalPolynomial| - |startPolynomial| |integral?| |hconcat| |open| |reorder| |generators| - |last| |e02bcf| |eval| |reset| |dmpToHdmp| |lieAlgebra?| |totalLex| - |prinshINFO| |KrullNumber| |assoc| |even?| |clearTheFTable| |null| - |discriminantEuclidean| |column| |argumentList!| |xCoord| - |simplifyPower| |fullPartialFraction| |primintegrate| |lazyIntegrate| - |critB| |quasiRegular| |pattern| |not| |factorSFBRlcUnit| |baseRDEsys| - |insertTop!| |write| |ricDsolve| |rst| |polygon?| - |generalizedEigenvectors| |d01aqf| |pseudoQuotient| |torsion?| |and| - |isList| |primitivePart| |d02kef| |save| |credPol| |deepestTail| - |cyclicParents| |leadingTerm| |negative?| |operations| - |complementaryBasis| |solveid| |or| |setPredicates| |zoom| |taylor| - |lllp| |lifting| |cycleRagits| |style| |d02gaf| |f01qdf| |jacobian| - |viewpoint| |xor| |expandTrigProducts| |decreasePrecision| |laurent| - |low| |preprocess| |pointLists| |s18aff| |innerint| |e02daf| |message| - |lazyResidueClass| |closedCurve?| |case| |createMultiplicationTable| - |puiseux| |leftRegularRepresentation| |f04mbf| |OMputFloat| - |getBadValues| |initiallyReduced?| |bitTruth| |normFactors| - |degreeSubResultant| |Zero| |host| |hypergeometric0F1| - |removeRoughlyRedundantFactorsInContents| |shade| |hi| |monicDivide| - |iicot| |setAttributeButtonStep| |measure2Result| |One| - |exponentialOrder| |inv| |copies| |imagj| |extendedIntegrate| - |OMopenFile| |initiallyReduce| |variationOfParameters| |binaryTree| - |trigs2explogs| |ground?| |reducedSystem| |rightRemainder| |ref| - |inverseLaplace| |createRandomElement| |multisect| |collect| - |elaborateFile| |legendreP| |rroot| |ground| |lcm| |lookupFunction| - |mapUnivariate| |setRow!| |inverseColeman| |bottom!| - |trailingCoefficient| |edf2ef| |var1StepsDefault| |coord| - |leadingMonomial| |variable?| |leaf?| |in?| |pointData| |groebgen| - |append| |selectPDERoutines| |leadingCoefficient| - |rewriteIdealWithQuasiMonicGenerators| |resultantReduit| |delay| - |charClass| |LyndonWordsList1| |nonLinearPart| |primitiveMonomials| - |interReduce| |gcd| |constDsolve| |multiplyExponents| |elt| |output| - |mesh?| |mapUp!| |compound?| |rationalPoints| |leftTraceMatrix| - |safetyMargin| |eigenvector| |squareMatrix| |SFunction| - |hasPredicate?| |contours| |false| |reductum| |times!| |listexp| - |push| |rowEchelonLocal| |startTable!| RF2UTS |cfirst| - |reducedQPowers| |nextSubsetGray| |primeFrobenius| - |removeRoughlyRedundantFactorsInPol| |edf2efi| - |getMultiplicationMatrix| |mappingMode| |tableau| |approxSqrt| - |mappingAst| |unaryFunction| |ParCondList| |partition| |gcdcofactprim| - |indicialEquations| |meshPar2Var| |f01qcf| |primPartElseUnitCanonical| - |d01alf| |factorSquareFreeByRecursion| |swap| |headRemainder| - |ratPoly| |thetaCoord| |HermiteIntegrate| |s19aaf| |cCos| - |brillhartIrreducible?| |fractRagits| |adaptive| |moduloP| - |numberOfComputedEntries| |hostPlatform| |subQuasiComponent?| - |gcdcofact| |graphCurves| |magnitude| |showRegion| |cAsec| - |viewDefaults| |semiResultantEuclidean2| |mainForm| |operators| - |categories| |exprHasAlgebraicWeight| |viewport2D| - |parabolicCylindrical| |ranges| |fortranCarriageReturn| |sechIfCan| - |applyRules| |tanQ| |blankSeparate| |noLinearFactor?| - |OMconnOutDevice| |cAcosh| |isPlus| |unravel| |splitSquarefree| |odd?| - |selectfirst| |palgRDE0| |dominantTerm| |OMputApp| |ceiling| - |computeInt| |f02bbf| |externalList| |open?| |infieldint| |euler| - |lagrange| |resetAttributeButtons| |normal01| |genericLeftTraceForm| - |cTanh| |balancedFactorisation| |finite?| |removeSinSq| |build| - |realEigenvectors| |Nul| |f04maf| |plusInfinity| |coefficient| - |partialFraction| |meshFun2Var| |OMencodingBinary| |s17aef| - |accuracyIF| |fillPascalTriangle| |range| |row| |minusInfinity| |inf| - |OMconnInDevice| |cosIfCan| |addiag| |constantLeft| - |nextsousResultant2| |isAtom| |BumInSepFFE| |irreducibleFactor| - |iiacsc| |basis| |exponential| |equiv| |primitive?| |bivariate?| - |distribute| |romberg| |cot2trig| |Ei| |fixPredicate| |key| - |drawStyle| |algebraicDecompose| |absolutelyIrreducible?| - |removeSuperfluousQuasiComponents| |createLowComplexityTable| |aCubic| - |lfunc| |functorData| |denomRicDE| |diagonalProduct| |commutative?| - |partialNumerators| |invertIfCan| |logIfCan| |basicSet| - |alphanumeric?| |filename| |mainCoefficients| |irDef| |printStats!| - |bytes| |innerEigenvectors| |d02raf| |subResultantGcd| |shiftRight| - |permutation| |type| |zeroOf| |mat| |cTan| |iitanh| |multiEuclidean| - |symmetricGroup| |listOfMonoms| |algebraic?| |makeTerm| - |multiEuclideanTree| |stoseIntegralLastSubResultant| - |genericRightTraceForm| |parse| |tensorProduct| |minRowIndex| - |quadratic| |moduleSum| |viewThetaDefault| |lyndon?| |nary?| - |makeprod| |unexpand| |next| |printStatement| |minGbasis| - |shallowCopy| |gramschmidt| |lastSubResultant| |leftScalarTimes!| - |linearAssociatedLog| |algintegrate| |Vectorise| |heap| - |extendedEuclidean| |fractionFreeGauss!| |flexibleArray| - |UpTriBddDenomInv| |leftTrace| |e04ycf| |myDegree| |s18dcf| - |lfextlimint| |index?| |rowEch| |quasiAlgebraicSet| |LiePolyIfCan| - |checkPrecision| |OMunhandledSymbol| |quoByVar| |unitNormalize| - |bitCoef| |gcdPolynomial| |rationalFunction| |associatedEquations| - |numerators| |palgint0| |cyclicEntries| |overset?| EQ - |derivationCoordinates| |unit| |palgLODE| |setMaxPoints| - |musserTrials| |pmComplexintegrate| |supersub| |symbol?| - |triangularSystems| |parabolic| |showAll?| |internalZeroSetSplit| - |lhs| |less?| |hermiteH| |hdmpToDmp| |complexForm| |finiteBasis| - |dimensionsOf| |addPoint2| |rootSplit| |generalizedInverse| |indices| - |rhs| |basisOfRightNucleus| |represents| |fortranComplex| |e01bff| - |evenInfiniteProduct| |factorByRecursion| |constantRight| |weight| - |curve| |selectAndPolynomials| |ddFact| |besselI| |c06ecf| |s19abf| - |iiasin| |principal?| |read!| |Ci| |mapDown!| |badValues| |cosh2sech| - |iroot| |iiacosh| |getProperties| |rule| |mapmult| |nodes| |csc2sin| - |orbit| |children| |tubePointsDefault| |ef2edf| |createThreeSpace| - |kmax| |setPosition| |compose| |index| |internalLastSubResultant| - |pushuconst| |leviCivitaSymbol| |complexRoots| |e01sff| - |karatsubaDivide| |selectODEIVPRoutines| |extractIndex| - |nextNormalPrimitivePoly| |schema| |ScanFloatIgnoreSpaces| - |representationType| |companionBlocks| |SturmHabichtCoefficients| - |setTex!| |totalfract| |enumerate| |center| |biRank| - |nextLatticePermutation| |indicialEquationAtInfinity| |complexExpand| - |cAcsch| |flagFactor| |generalLambert| |recoverAfterFail| |has?| - |OMputEndAttr| |putColorInfo| |pair| |stoseInvertibleSet| |inspect| - |rk4qc| |stoseLastSubResultant| |c06frf| |value| |modularGcdPrimitive| - |comparison| |trueEqual| |totalDegree| |OMputObject| - |selectPolynomials| |eigenMatrix| |approxNthRoot| |lazyPseudoDivide| - |mapExponents| |strongGenerators| |alternative?| |s17agf| - |semiDiscriminantEuclidean| |transform| |whitePoint| |OMputEndBind| - |characteristicSet| |infiniteProduct| |OMputInteger| |e04naf| - |member?| |createGenericMatrix| |rational| |extractSplittingLeaf| - |max| |stoseInvertible?sqfreg| |entry| |generateIrredPoly| - |removeSuperfluousCases| |pow| |hitherPlane| |child| |setlast!| - |qualifier| |localUnquote| |bigEndian| |iipow| |iicosh| |polyRicDE| - |possiblyInfinite?| |raisePolynomial| |prefixRagits| |parametersOf| - |toseInvertible?| |printHeader| |elliptic| |setFieldInfo| - |currentScope| |returnTypeOf| |realZeros| |divisor| |sign| |s14aaf| - |printTypes| |useSingleFactorBound?| |rightDivide| |stFunc1| - |viewWriteDefault| |ratDenom| |sn| |clipParametric| |palginfieldint| - |readIfCan!| |reverse| |mindegTerm| |useEisensteinCriterion?| - |limitedIntegrate| |binding| |idealiser| |e04ucf| |problemPoints| - |makeResult| |critMTonD1| |cSinh| |replaceKthElement| |extractTop!| - |leftExtendedGcd| |call| |satisfy?| |pushNewContour| |central?| - |getOrder| |OMgetBVar| |areEquivalent?| |bumptab1| |leaves| |tree| - |superscript| |heapSort| |univariatePolynomials| |mkAnswer| |lllip| - |showAllElements| |cCsc| |numberOfMonomials| |setref| |lazyPrem| - |numericIfCan| |readLineIfCan!| |randomLC| |lazyEvaluate| |sinIfCan| - |f02bjf| |s18aef| |subResultantsChain| |structuralConstants| - |getButtonValue| |geometric| |exteriorDifferential| |lfintegrate| - |cycleTail| |OMputSymbol| |showScalarValues| |imagE| |algSplitSimple| - |OMUnknownSymbol?| |normInvertible?| |init| |mainMonomial| - |primlimintfrac| |lowerCase!| |exp1| |resultantReduitEuclidean| - |extendedResultant| |quatern| |removeConstantTerm| |imagK| |cAcot| - |nlde| |rewriteSetWithReduction| |nullary| |extendIfCan| |repeating| - |chebyshevU| |lookup| |setScreenResolution3D| |explicitEntries?| - |lieAdmissible?| |graphImage| |setRealSteps| |key?| |bandedHessian| - |generator| |bezoutMatrix| |laplace| |eulerE| |f07fdf| |cyclic?| - |bits| |reverse!| |hostByteOrder| |bfEntry| |numberOfNormalPoly| - |c06eaf| |rootOfIrreduciblePoly| |e04jaf| |component| |setchildren!| - |replace| |fixedPoint| |monicLeftDivide| |mindeg| |search| |zCoord| - |string?| |root| |iteratedInitials| |exprex| |randomR| |OMgetEndAtp| - |stack| |bombieriNorm| |f02awf| |determinant| |rem| |cycle| |getRef| - |continuedFraction| |roughBase?| |divideExponents| |curveColorPalette| - |e02def| |lprop| |singRicDE| |quo| |semiResultantReduitEuclidean| - |putProperty| |startStats!| |internalIntegrate| |condition| |iisqrt3| - |univariatePolynomialsGcds| |useSingleFactorBound| |roughUnitIdeal?| - |taylorRep| |OMsupportsSymbol?| |setPrologue!| - |getSyntaxFormsFromFile| |div| |routines| |symmetricDifference| - |minimalPolynomial| |OMgetObject| |sturmSequence| |cAcos| - |monomialIntegrate| |tan2cot| |nthRootIfCan| |exquo| - |solveLinearlyOverQ| |dim| |showIntensityFunctions| |bringDown| - |quasiRegular?| |lifting1| |c06gsf| |point?| |doubleRank| - |genericLeftDiscriminant| ~= |rightScalarTimes!| - |tryFunctionalDecomposition?| |frst| |setFormula!| |newLine| |tab| - |lastSubResultantEuclidean| |resize| |#| |matrix| |cycles| |dec| - 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|duplicates?| |optAttributes| |sin?| |ratDsolve| |OMencodingUnknown| - |stoseSquareFreePart| |weakBiRank| |rangeIsFinite| |iiacoth| |unary?| - |sort!| |polyPart| |setScreenResolution| |minIndex| |reshape| - |arguments| |sayLength| |var1Steps| |rationalPoint?| |setelt| |trunc| - |readLine!| |harmonic| |octon| |getGoodPrime| |double?| |e01baf| - |stopMusserTrials| |moreAlgebraic?| |badNum| |abelianGroup| - |colorFunction| |sequences| |kroneckerDelta| |patternMatchTimes| - |intChoose| |s17dlf| |identitySquareMatrix| |numericalOptimization| - |hue| |digamma| |copy| |tanh2coth| |OMputAtp| |iicsc| |integerIfCan| - |s17ajf| |aQuadratic| |union| |close!| |mapUnivariateIfCan| - |explimitedint| |primextintfrac| |rewriteIdealWithHeadRemainder| - |createPrimitiveElement| |writeLine!| |readUInt8!| |linear?| |rank| - |OMputEndAtp| |e02dcf| |gderiv| |triangulate| |isOr| |uniform| - |cartesian| |singularAtInfinity?| |cAsinh| |blue| |maxrank| |update| - |primaryDecomp| |npcoef| |roman| |primPartElseUnitCanonical!| - |autoCoerce| |maxdeg| |c06ekf| |freeOf?| |float?| |exQuo| |s18acf| - |nonQsign| |laurentRep| |imagJ| |tanAn| - |semiLastSubResultantEuclidean| |outputGeneral| |fortranLogical| - |complexNormalize| |janko2| |deleteRoutine!| |sizePascalTriangle| - |algebraicSort| |stiffnessAndStabilityOfODEIF| |iprint| - |totalGroebner| |crest| |tab1| |makeViewport2D| - |createIrreduciblePoly| |ideal| |hex| |showTheFTable| |top!| - |wronskianMatrix| |Lazard2| |screenResolution3D| |factorOfDegree| - |leftRecip| |asinhIfCan| |showTheSymbolTable| |ptFunc| |dequeue!| - |cscIfCan| |asechIfCan| |digit?| |maximumExponent| |denominators| - |cyclicCopy| |semiIndiceSubResultantEuclidean| |pseudoRemainder| - |exprHasWeightCosWXorSinWX| |position| |subNodeOf?| |ode1| - |makeVariable| |mkPrim| |internalInfRittWu?| |associative?| - |mergeFactors| |gbasis| |c06ebf| |match?| |lists| |torsionIfCan| - |rootRadius| |symmetricTensors| |groebner| |leftGcd| - |antiCommutative?| |monomial?| |binaryTournament| |exportedOperators| - |overlap| |dimensions| |createZechTable| |pastel| |chainSubResultants| - |univariate?| |interpretString| |genericLeftNorm| |alternating| - |coordinate| |isNot| |simplifyLog| |e01sbf| |mathieu11| - |relationsIdeal| |rquo| |bipolar| |associatedSystem| |prime?| - |categoryMode| |OMgetBind| |summation| |declare| |findConstructor| - |simpleBounds?| |linearAssociatedOrder| |f04asf| |ksec| |failed?| - |expt| |curve?| |lSpaceBasis| |univariateSolve| |delete!| - |viewPosDefault| |rootBound| |expIfCan| |ignore?| |printCode| - |conjugates| |multiplyCoefficients| |epilogue| |limitPlus| - |swapColumns!| |clearTheSymbolTable| |f01ref| |atoms| |bernoulliB| - |maxColIndex| |entry?| |numberOfImproperPartitions| |f01qef| - |normalized?| |arg1| |LazardQuotient| |clipSurface| |rk4a| |iFTable| - |setLegalFortranSourceExtensions| |unitsColorDefault| |leadingSupport| - |zeroDimensional?| |euclideanGroebner| |dot| |scopes| |traceMatrix| - |arg2| |factorSquareFreePolynomial| |sech| |mathieu12| |rightGcd| - |aromberg| |indicialEquation| |OMgetFloat| |edf2df| |physicalLength!| - |size?| |hcrf| |generalSqFr| |csch| |composite| - |createNormalPrimitivePoly| |f04axf| |extend| |contractSolve| |close| - |inputBinaryFile| |cAsech| |shanksDiscLogAlgorithm| |quadraticNorm| - |conditions| |expandLog| |nextNormalPoly| |asinh| |exprToUPS| - |outputForm| |createMultiplicationMatrix| |constant?| |sparsityIF| - |extensionDegree| |subtractIfCan| |redPo| |match| - |halfExtendedSubResultantGcd2| |acosh| |closed?| |zeroVector| |stop| - |fibonacci| |linGenPos| |bumprow| |ODESolve| |display| |radix| - |bright| |cylindrical| |clipPointsDefault| |supRittWu?| |atanh| - |leadingCoefficientRicDE| |leadingIdeal| |goodPoint| |algebraicOf| - |largest| |useNagFunctions| |c06gqf| |rootPoly| |li| |rationalIfCan| - |collectQuasiMonic| |genericLeftMinimalPolynomial| |acoth| |s17def| - |compBound| |reindex| |dimension| |complexSolve| |shuffle| |asech| - |arity| |pair?| |diagonals| |sts2stst| |controlPanel| |chvar| - |collectUnder| |subresultantSequence| |ldf2lst| - |initializeGroupForWordProblem| |cCoth| |middle| |rootsOf| |subHeight| - |completeHermite| |OMencodingSGML| |changeName| |rotatey| - |integerBound| |polarCoordinates| |multiple| |OMcloseConn| |presub| - |primitiveElement| |karatsuba| |e02dff| |infinityNorm| |nodeOf?| - |input| |e04gcf| |iisec| |setClosed| |setButtonValue| |rightNorm| - |box| |bat| |applyQuote| |stripCommentsAndBlanks| |simplify| |library| - |is?| |aspFilename| |scanOneDimSubspaces| |cycleElt| |var2Steps| - |deleteProperty!| |nand| |iifact| |HenselLift| |dequeue| - |unrankImproperPartitions0| |sumOfDivisors| |merge!| |frobenius| - |padicFraction| |bfKeys| |multMonom| |critT| |testDim| |pole?| |df2mf| - |leftDiscriminant| |explicitlyEmpty?| |virtualDegree| - |selectNonFiniteRoutines| |extract!| |setLabelValue| - |mainCharacterization| |multiset| |ruleset| |leftZero| - |basisOfMiddleNucleus| |repeatUntilLoop| |updatD| |patternMatch| - |prepareSubResAlgo| |curveColor| |rotate| |s17adf| |Hausdorff| - |f02aef| |pol| |bernoulli| |set| |getMultiplicationTable| |f02axf| - |outputFloating| |axesColorDefault| |imaginary| |setOfMinN| - |basisOfCenter| |expintfldpoly| |test| |countRealRootsMultiple| - |eisensteinIrreducible?| |matrixGcd| |id| |rightMinimalPolynomial| - |ListOfTerms| |decimal| |linearAssociatedExp| |exponential1| - |halfExtendedResultant1| |suchThat| |subTriSet?| |sincos| |split!| - |localIntegralBasis| |putProperties| |unmakeSUP| |latex| |integer?| - |expint| |setCondition!| |leftMinimalPolynomial| - |irreducibleRepresentation| |reify| |shellSort| |table| |inR?| - |linearMatrix| |selectMultiDimensionalRoutines| |constantOpIfCan| - |eulerPhi| |leftUnits| |OMgetString| |subst| |lazy?| |insert| |new| - |sqfree| |split| |setAdaptive| |smith| |calcRanges| |obj| - |OMParseError?| |splitDenominator| |nullSpace| |reducedForm| |isMult| - |moebiusMu| |outlineRender| |solve1| |eq| |palglimint0| |prefix| - |inverseIntegralMatrix| |cache| |makeYoungTableau| |closedCurve| - |f2st| |edf2fi| |iter| |ridHack1| |e04fdf| |adaptive?| |eigenvalues| - |d03faf| |besselK| |sin2csc| |zeroMatrix| |delete| |rowEchelon| |sh| - |signature| |hasTopPredicate?| |clip| |sizeMultiplication| - |radicalRoots| GF2FG |node?| |expintegrate| |order| |localReal?| - |rightPower| |rightFactorCandidate| |logical?| |front| - |var2StepsDefault| |f04jgf| |rightCharacteristicPolynomial| |one?| - |mathieu23| |modularFactor| |parent| |modifyPointData| |specialTrigs| - |scaleRoots| |lazyPseudoRemainder| |entries| |conjunction| |objects| - |useEisensteinCriterion| |exactQuotient| - |rewriteSetByReducingWithParticularGenerators| |oddInfiniteProduct| - |leftMult| |powerAssociative?| |tanhIfCan| |directory| |wholeRadix| - |base| |script| |rightAlternative?| |imports| |lowerCase?| |hasoln| - |pointColor| |pushucoef| |rischDEsys| |parseString| |attributeData| - |module| |s18adf| |rational?| |tryFunctionalDecomposition| - |singleFactorBound| |nor| |cPower| |divide| |retractIfCan| |cExp| - |leftQuotient| |isOp| |monicRightDivide| |selectSumOfSquaresRoutines| - |flatten| |limit| |viewSizeDefault| |exp| |deepestInitial| |shufflein| - |chiSquare1| |trim| |alphanumeric| |complexEigenvalues| |tex| - |cRationalPower| |nil?| |left| |numer| |finiteBound| |reduceLODE| - |cschIfCan| |OMgetEndError| |/\\| |whatInfinity| |s21bbf| - |boundOfCauchy| |chebyshevT| |rspace| |qroot| |right| |outputList| - |denom| |radicalOfLeftTraceForm| |isExpt| |isAnd| |rCoord| - |printingInfo?| |\\/| |e02akf| |e01sef| |coshIfCan| |debug3D| |green| - |subset?| |setPoly| |withPredicates| |denominator| |sorted?| |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| |gcdcofactprim| |trivialIdeal?| |antiCommutator| + |tanSum| |pi| |divide| |csch2sinh| |mapExponents| |f02aaf| F2FG + |indicialEquations| |ode2| |divisors| |content| |cExp| |infinity| + |cAsinh| |more?| |infix| |strongGenerators| |allRootsOf| |simpsono| + |reduction| |meshPar2Var| |numberOfFactors| |cotIfCan| |cond| + |leftQuotient| |generalizedContinuumHypothesisAssumed| |symmetric?| + |alternative?| |lazyPseudoQuotient| |blue| |setValue!| |factor1| + |d02gbf| |f01qcf| |lowerBound| |generate| |getProperty| |log10| + |squareFreePrim| |isOp| |s17agf| |dihedralGroup| |length| |map| + |maxrank| |linearlyDependentOverZ?| |inrootof| + |primPartElseUnitCanonical| |rotatez| |resetNew| |bitand| + |jordanAlgebra?| |kernel| |primaryDecomp| |changeBase| + |semiDiscriminantEuclidean| |scripts| |sturmVariationsOf| + |endSubProgram| |isQuotient| |gethi| |incrementBy| |d01alf| + |coerceListOfPairs| |symmetricProduct| |outerProduct| |matrixGcd| + |bitior| |draw| |numberOfPrimitivePoly| |cSin| |transform| |f07aef| + |npcoef| |SturmHabicht| |cup| |identityMatrix| + |factorSquareFreeByRecursion| |createNormalElement| |expand| + |rightMinimalPolynomial| |exprHasLogarithmicWeights| + |LagrangeInterpolation| |whitePoint| |pquo| |roman| |points| + |currentEnv| |swap| |particularSolution| |Frobenius| |filterWhile| + |weierstrass| |ListOfTerms| |totalDifferential| |isobaric?| + |nextPrimitiveNormalPoly| |OMputEndBind| |OMopenString| + |primPartElseUnitCanonical!| |genericRightTrace| |commutator| |zag| + |headRemainder| |filterUntil| |symbol| |decimal| |realElementary| + |iCompose| |LyndonWordsList| |findBinding| |characteristicSet| + |convert| |rationalPower| |maxdeg| |ratPoly| |previous| |e02ajf| + |tanNa| |upperCase| |select| |expression| |linearAssociatedExp| + |cyclic| |makeObject| |hMonic| |roughBasicSet| |c06ekf| + |infiniteProduct| |nativeModuleExtension| |writeInt8!| |height| + |e02adf| |s15adf| |thetaCoord| |solve| |integer| |exponential1| + |dihedral| |coef| |freeOf?| |internalIntegrate0| |OMputEndError| + |OMputInteger| |thenBranch| |untab| |HermiteIntegrate| + |radicalEigenvalues| |outputAsTex| |cycleEntry| + |halfExtendedResultant1| |dioSolve| |jokerMode| |commutativeEquality| + |minimumExponent| |e04naf| |float?| |polygamma| |s19aaf| |light| + |notelem| |pseudoDivide| |subTriSet?| |exptMod| |yRange| |f04qaf| + |atanhIfCan| |member?| ** |exQuo| |e02ahf| |cCos| |just| |palgint| + |isEquiv| |sincos| |zRange| |basisOfRightNucloid| |power!| + |createGenericMatrix| |numberOfVariables| |saturate| |s18acf| + |elliptic?| |brillhartIrreducible?| |drawComplex| |sumOfSquares| + |bit?| |split!| |map!| |tubeRadius| |flexible?| |rightExtendedGcd| + |rational| |nonQsign| |OMReadError?| |makeRecord| |e02bbf| + |normalizedAssociate| |roughEqualIdeals?| |fractRagits| |lo| + |setEmpty!| |localIntegralBasis| |qsetelt!| |prolateSpheroidal| + |iterationVar| |extractSplittingLeaf| |generalTwoFactor| |laurentRep| + |decompose| |rightRank| |cyclotomicFactorization| |adaptive| + |algDsolve| |incr| |putProperties| |universe| |assign| |label| + |readBytes!| |max| |cCot| |imagJ| |initial| |moduloP| + |rewriteIdealWithRemainder| |OMwrite| |froot| |unmakeSUP| |f02xef| + |eyeDistance| |writeBytes!| |stoseInvertible?sqfreg| |tanAn| |OMclose| + |linearDependence| |numberOfComputedEntries| |f04faf| |modulus| + |latex| |generateIrredPoly| |separateFactors| |vconcat| + |wordInStrongGenerators| |semiLastSubResultantEuclidean| |OMputError| + |hostPlatform| |removeZeroes| |square?| |setStatus!| |integer?| + |setleft!| |outputGeneral| |numerator| |removeSuperfluousCases| + |airyBi| |realSolve| Y |stosePrepareSubResAlgo| |subQuasiComponent?| + |transcendentalDecompose| |dictionary| |characteristicPolynomial| + |expint| |acsch| |fortranLogical| |leastMonomial| |palglimint| |pow| + |solveInField| |lastSubResultantElseSplit| |voidMode| |gcdcofact| + |cross| |moebius| |semicolonSeparate| |setCondition!| |shrinkable| + |characteristic| |stoseInternalLastSubResultant| |hitherPlane| + |OMreceive| |complexNormalize| |factorsOfDegree| |graphCurves| + |weights| |symFunc| |leftMinimalPolynomial| |tail| |constantKernel| + |csubst| |e04mbf| |child| |janko2| |adaptive3D?| |constructor| |rules| + |expressIdealMember| |magnitude| |UP2ifCan| |complete| + |irreducibleRepresentation| |curry| |d01anf| |d03edf| |setlast!| + |deleteRoutine!| |listLoops| |nothing| |SturmHabichtMultiple| + |showRegion| |irForm| |stFunc2| |reify| |option| |iicsch| + |domainTemplate| |extractPoint| |qualifier| |sizePascalTriangle| + |constantCoefficientRicDE| |showSummary| |cAsec| |diagonal| + |increasePrecision| |palgRDE| |shellSort| |disjunction| |localUnquote| + |commonDenominator| |pr2dmp| |algebraicSort| |empty| |viewDefaults| + |univcase| |stFuncN| |inR?| |permutationRepresentation| |bumptab| + |bigEndian| |recur| |stiffnessAndStabilityOfODEIF| |setVariableOrder| + |showAttributes| |semiResultantEuclidean2| |atanIfCan| |dualSignature| + |rightTraceMatrix| |linearMatrix| |unknown| |writeByte!| |mkcomm| + |basisOfLeftNucloid| |iipow| |separant| |iprint| |digit| |macroExpand| + |mainForm| |RemainderList| |critMonD1| |rightTrim| + |selectMultiDimensionalRoutines| |arbitrary| |nthFractionalTerm| + |iicosh| |primes| |totalGroebner| |setMaxPoints3D| |operators| + |att2Result| |OMserve| |euclideanSize| |leftTrim| |constantOpIfCan| + |increase| |systemSizeIF| |polyRicDE| |upperCase!| |iicos| |crest| + |exprHasAlgebraicWeight| |exponent| |packageCall| + |showTheRoutinesTable| |eulerPhi| |polynomialZeros| |insertionSort!| + |e01daf| |possiblyInfinite?| |btwFact| |tab1| |say| F |splitNodeOf!| + |viewport2D| |dfRange| |maxint| |leftUnits| |subscript| |critBonD| + |raisePolynomial| |enterInCache| |modularGcd| |makeViewport2D| + |parabolicCylindrical| |perfectSquare?| |cyclotomicDecomposition| + |f01rdf| |OMgetString| |makeMulti| |fixedPointExquo| + |genericLeftTrace| |prefixRagits| |createIrreduciblePoly| |eof?| + |ranges| |graphs| |rangePascalTriangle| |OMconnectTCP| |setImagSteps| + |lazy?| |ideal| |quasiComponent| |f02ajf| |parametersOf| |twoFactor| + |remove| |function| |multivariate| |fortranCarriageReturn| + |OMgetEndAttr| |nullary?| |recolor| |binomThmExpt| |sqfree| |fortran| + |quotedOperators| |hex| |evaluate| |variables| |toseInvertible?| + |slash| |result| |someBasis| |sechIfCan| |integralCoordinates| + |qinterval| |polar| |split| |doubleResultant| |lazyGintegrate| |open| + |nthr| |printHeader| |last| |showTheFTable| |eval| |reset| + |applyRules| |inconsistent?| |squareTop| |d01apf| |setAdaptive| + |assoc| |bat1| |elliptic| |OMgetAtp| |character?| |null| |top!| + |expextendedint| |tanQ| |elseBranch| |exponents| |numberOfCycles| + |smith| |functionIsContinuousAtEndPoints| |outputFixed| |setFieldInfo| + |pattern| |c06gbf| |not| |e01bef| |wronskianMatrix| |write| + |blankSeparate| |red| |ip4Address| |explogs2trigs| |calcRanges| + |e02agf| |factorPolynomial| |and| |crushedSet| |currentScope| + |rischNormalize| |Lazard2| |save| |noLinearFactor?| |leadingExponent| + |changeVar| |rotate!| |sylvesterMatrix| |OMParseError?| |operations| + |pascalTriangle| |taylor| |or| |returnTypeOf| |terms| + |screenResolution3D| |mainVariables| |ellipticCylindrical| + |OMconnOutDevice| |reduceBasisAtInfinity| |symmetricPower| + |splitDenominator| |factorOfDegree| |diag| |lepol| |probablyZeroDim?| + |realZeros| |xor| |laurent| |se2rfi| |cAcosh| |polyred| |secIfCan| + |nextsubResultant2| |reducedContinuedFraction| |nullSpace| |divisor| + |bounds| |leftRecip| |message| |symbolTableOf| |case| |puiseux| + |acotIfCan| |isPlus| |integral| |headAst| |purelyAlgebraic?| + |reducedForm| |convergents| |linSolve| |f01brf| |Zero| |sign| + |getStream| |asinhIfCan| |unravel| |number?| |changeMeasure| + |denomLODE| |hi| |isMult| |cothIfCan| |s14aaf| |inv| |One| + |getExplanations| |intersect| |showTheSymbolTable| |splitSquarefree| + |redmat| |sPol| |hspace| |moebiusMu| |conditionsForIdempotents| + |wholeRagits| |extractBottom!| |yCoordinates| |printTypes| |ground?| + |ptFunc| |fortranInteger| |odd?| |nthExpon| |pToDmp| |outlineRender| + |setErrorBound| |tan2trig| |outputMeasure| |ground| + |useSingleFactorBound?| |startTableInvSet!| |lcm| |dequeue!| + |orthonormalBasis| |s17acf| |selectfirst| |nthCoef| + |completeEchelonBasis| |solve1| |exists?| |aQuartic| |complex?| + |normal?| |rightDivide| |leadingMonomial| |cscIfCan| |fixedPoints| + |errorKind| |getCurve| |palglimint0| |subMatrix| |prologue| + |brillhartTrials| |lexTriangular| |append| |stFunc1| + |leadingCoefficient| |asechIfCan| |reducedSystem| |firstNumer| + |inverseIntegralMatrix| |randnum| |check| |solveLinear| + |maximumExponent| |s21baf| |setMinPoints3D| |primitiveMonomials| + |pade| |elt| |viewWriteDefault| |gcd| |output| |computeBasis| + |rightRemainder| |findCycle| |midpoints| |birth| |makeYoungTableau| + |f07adf| |setOrder| |ratDenom| |denominators| |rightTrace| |addMatch| + |false| |reductum| |semiDegreeSubResultantEuclidean| |ref| |droot| + |subscriptedVariables| |closedCurve| |normalElement| |factorFraction| + |cAcsc| |cyclicCopy| |normalDeriv| |inverseLaplace| |gcdprim| + |backOldPos| |f2st| |decrease| |sqfrFactor| |principal?| + |getPickedPoints| |lyndonIfCan| |semiIndiceSubResultantEuclidean| + |OMputBind| |createRandomElement| |element?| |cLog| |edf2fi| + |nilFactor| |permutations| |read!| |degree| |getMatch| + |pseudoRemainder| |solid?| |multisect| |bubbleSort!| |infLex?| + |ridHack1| |singularitiesOf| |definingInequation| |Ci| |d01fcf| + |rootSimp| |exprHasWeightCosWXorSinWX| |argument| |collect| |e04fdf| + |unitCanonical| |hasHi| |mapDown!| |resultantEuclidean| |ramified?| + |subNodeOf?| |elaborateFile| |c05nbf| |OMsend| |numberOfComposites| + |adaptive?| |copyInto!| |cCsch| |readUInt16!| |badValues| |categories| + |univariatePolynomial| |ode1| |generalizedContinuumHypothesisAssumed?| + |legendreP| |removeRedundantFactors| |graphStates| |eigenvalues| + |d01bbf| |PDESolve| |directSum| |cosh2sech| |makeVariable| + |lfextendedint| |rroot| |outputAsScript| |wreath| |leadingBasisTerm| + |d03faf| |e01bgf| |bivariatePolynomials| |iroot| |alphabetic?| + |lookupFunction| |ramifiedAtInfinity?| |imagI| |difference| |besselK| + |topFortranOutputStack| |selectIntegrationRoutines| |iiacosh| + |clearFortranOutputStack| |block| |stoseSquareFreePart| + |mapUnivariate| |screenResolution| |numericalIntegration| + |getOperator| |sin2csc| |d01asf| |radicalEigenvectors| |getProperties| + |rubiksGroup| |weakBiRank| |curryLeft| |setRow!| |distdfact| + |indiceSubResultant| |mvar| |plusInfinity| |zeroMatrix| |lflimitedint| + |leftLcm| |countRealRoots| |mapmult| |rangeIsFinite| |quotientByP| + |monic?| |inverseColeman| |c02aff| |subPolSet?| |minusInfinity| + |splitLinear| |e02bdf| |leftCharacteristicPolynomial| |nodes| + |iiacoth| |lex| |bottom!| |normalize| |principalIdeal| |nullity| + |rightNorm| |stirling2| |encodingDirectory| |linears| |csc2sin| + |unary?| |rename| |divideIfCan!| |trailingCoefficient| |singular?| + |presuper| |bat| |trace2PowMod| |algint| |s13aaf| |orbit| |key| + |sort!| |cyclotomic| |edf2ef| |minPol| |generic| |interpolate| + |stripCommentsAndBlanks| |subSet| |sinhIfCan| |high| |children| + |polyPart| |OMmakeConn| |unitNormal| |var1StepsDefault| |safeCeiling| + |infRittWu?| |simplify| |filename| |coordinates| |truncate| + |tubePointsDefault| |inRadical?| |setScreenResolution| |coord| + |extractClosed| |s17dhf| |removeZero| |type| |is?| |acscIfCan| + |ef2edf| |isConnected?| |minIndex| |divideIfCan| |variable?| + |coefChoose| |shiftRoots| |diophantineSystem| |aspFilename| + |wordsForStrongGenerators| |cycleLength| |parse| |createThreeSpace| + |sayLength| |hdmpToP| |d01ajf| |leaf?| |minPoly| |sdf2lst| + |scanOneDimSubspaces| |next| |e01bhf| |rightZero| |kmax| |var1Steps| + |iiacos| |in?| |removeCosSq| |safeFloor| |pushdterm| |cycleElt| + |clearDenominator| |setPosition| |inHallBasis?| |integralAtInfinity?| + |rationalPoint?| |ldf2vmf| |pointData| |s15aef| |OMputString| + |var2Steps| |e02ddf| |rightMult| |compose| |integralMatrixAtInfinity| + |trunc| |iiGamma| |groebgen| |explicitlyFinite?| |checkPrecision| + |scalarMatrix| |deleteProperty!| |copy!| |internalLastSubResultant| + |aLinear| |f07fef| |readLine!| |realRoots| |drawToScale| + |selectPDERoutines| |supDimElseRittWu?| EQ |nand| |qqq| |nthFactor| + |pushuconst| |harmonic| |reseed| |completeHensel| + |rewriteIdealWithQuasiMonicGenerators| |f02agf| |nextPrime| |iifact| + |leviCivitaSymbol| |diff| |B1solve| |lhs| |associates?| |octon| + |resultantReduit| |child?| |basisOfNucleus| |typeLists| |HenselLift| + |complexRoots| |complexElementary| |radicalEigenvector| |rhs| + |OMbindTCP| |getGoodPrime| |interval| |twist| |delay| |movedPoints| + |hermite| |dequeue| |generalPosition| |fprindINFO| |e01sff| |double?| + |startTableGcd!| |charClass| |ran| |powern| |push!| |buildSyntax| + |unrankImproperPartitions0| |reduceByQuasiMonic| |karatsubaDivide| + |pointSizeDefault| |basisOfCentroid| |e01baf| |associatorDependence| + |LyndonWordsList1| |iisin| |nextPartition| |sumOfDivisors| |rule| + |invmod| |selectODEIVPRoutines| |decomposeFunc| + |combineFeatureCompatibility| |stopMusserTrials| |nonLinearPart| + |isOpen?| |distFact| |revert| |merge!| |index| |prepareDecompose| + |antisymmetric?| |extractIndex| |cSech| |moreAlgebraic?| + |groebnerFactorize| |interReduce| |toScale| |coHeight| |frobenius| + |asimpson| |nextNormalPrimitivePoly| |squareFreePart| |innerSolve1| + |badNum| |constDsolve| |recip| |hexDigit| |viewDeltaXDefault| + |padicFraction| |Is| |center| |schema| |generalInfiniteProduct| + |fortranLinkerArgs| |abelianGroup| |squareFreeFactors| + |multiplyExponents| |zeroSquareMatrix| |getDatabase| |bfKeys| + |prinpolINFO| |components| |ScanFloatIgnoreSpaces| |pair| + |colorFunction| |removeCoshSq| |genericPosition| |mesh?| + |mightHaveRoots| |value| |nextItem| |multMonom| |makeSUP| + |representationType| |connectTo| |sequences| |setMinPoints| |mapUp!| + |radicalSolve| |intPatternMatch| |ratpart| |critT| |bezoutResultant| + |laguerreL| |companionBlocks| |kroneckerDelta| |complexZeros| + |OMreadFile| |compound?| |testModulus| |pointPlot| |testDim| |maxrow| + |OMgetAttr| |SturmHabichtCoefficients| |critM| |patternMatchTimes| + |rationalPoints| |scan| |divisorCascade| |topPredicate| |entry| + |pole?| |d02bbf| |resultantnaif| |setTex!| |bandedJacobian| + |intChoose| |leftTraceMatrix| |tRange| |zeroDim?| |minordet| |df2mf| + |integralBasisAtInfinity| |expenseOfEvaluation| |totalfract| + |complexLimit| |s17dlf| |safetyMargin| |contains?| |equality| LODO2FUN + |leftDiscriminant| |zeroSetSplit| |numberOfOperations| |enumerate| + |identitySquareMatrix| |trapezoidal| |eigenvector| |OMgetEndObject| + |matrixDimensions| |unvectorise| |explicitlyEmpty?| |choosemon| + |biRank| |splitConstant| |numericalOptimization| + |squareFreePolynomial| |bag| |atom?| |squareMatrix| |reverse| + |primitivePart!| |virtualDegree| |dual| |s17dgf| + |nextLatticePermutation| |wrregime| |hue| |SFunction| |polygon| + |makeFR| |f02akf| |selectNonFiniteRoutines| |call| |phiCoord| + |indicialEquationAtInfinity| |ode| |iiatan| |digamma| + |intermediateResultsIF| |hasPredicate?| |antiAssociative?| |conjugate| + |extract!| |leaves| |tree| |minPoints| |complexExpand| + |antisymmetricTensors| |dflist| |tanh2coth| |refine| |contours| + |schwerpunkt| |definingPolynomial| |setLabelValue| |move| |cAcsch| + |setfirst!| |mainKernel| |OMputAtp| |readInt32!| |times!| |zerosOf| + |plot| |mainCharacterization| |OMgetApp| |flagFactor| |makeEq| |iicsc| + |cSec| |listexp| |lazyPquo| |acosIfCan| |create| |multiset| |prem| + |connect| |generalLambert| |init| |createPrimitivePoly| |integerIfCan| + |push| |pointColorDefault| |linearPart| |iomode| |leftZero| |sub| + |recoverAfterFail| |drawCurves| |GospersMethod| |s17ajf| + |rowEchelonLocal| |e04dgf| |round| |rightLcm| |basisOfMiddleNucleus| + |nthFlag| |has?| |fortranLiteral| |belong?| |aQuadratic| |elaboration| + |startTable!| |coth2trigh| |perspective| |repeatUntilLoop| |generator| + |transcendenceDegree| |c05pbf| |OMputEndAttr| |close!| |color| + |leftFactor| RF2UTS |prime| |parametric?| |updatD| |completeEval| + |putColorInfo| |OMputEndObject| |mapUnivariateIfCan| |create3Space| + |branchPoint?| |cfirst| |iiasech| |position!| |patternMatch| |pop!| + |normalizeAtInfinity| |stoseInvertibleSet| |explimitedint| + |normDeriv2| |reducedQPowers| |closed| |matrixConcat3D| |search| + |lexico| |prepareSubResAlgo| |inspect| |find| |primextintfrac| + |rarrow| |stack| |nextSubsetGray| |OMgetEndBVar| |triangSolve| |rem| + |isPower| |curveColor| |adjoint| |rk4qc| |argscript| + |basisOfLeftAnnihilator| |rewriteIdealWithHeadRemainder| + |primeFrobenius| |f02aff| |floor| |quo| + |unprotectedRemoveRedundantFactors| |rotate| + |selectOptimizationRoutines| |deepExpand| |stoseLastSubResultant| + |createPrimitiveElement| |lazyIrreducibleFactors| |condition| + |removeRoughlyRedundantFactorsInPol| |rur| |factorials| |checkRur| + |s17adf| |minrank| |c06frf| |c06fuf| |oddintegers| |writeLine!| + |imagi| |div| |quasiMonicPolynomials| |Hausdorff| |numFunEvals3D| + |firstSubsetGray| |modularGcdPrimitive| |readUInt8!| |quote| |isList| + |setleaves!| |exprToXXP| |exquo| |f02aef| |dim| |makeCos| |comparison| + |incrementKthElement| |dmp2rfi| |linear?| |primitivePart| ~= |besselJ| + |cyclicEqual?| |pol| |psolve| |trueEqual| |FormatArabic| |updatF| + |OMputEndAtp| |d02kef| |makeCrit| |chiSquare| |#| |bernoulli| |matrix| + |oneDimensionalArray| |dec| |e02dcf| |viewDeltaYDefault| |credPol| ~ + |paren| |pdct| |getMultiplicationTable| |discreteLog| + |mergeDifference| |e04ycf| |concat| |rightUnits| |gderiv| + |deepestTail| |halfExtendedResultant2| UTS2UP |f02axf| |elaborate| + |myDegree| |alternatingGroup| |triangulate| |dark| |cyclicParents| + |leftRankPolynomial| |addPointLast| |outputFloating| |printInfo| + |fortranDoubleComplex| |identification| |s18dcf| |insertRoot!| + |clearCache| |isOr| |leadingTerm| |level| |axesColorDefault| + |ScanRoman| |lfextlimint| |modifyPoint| |uniform| |mpsode| |negative?| + |e02def| |showClipRegion| |imaginary| |leftRemainder| |index?| + |s19adf| |cartesian| |polCase| |complementaryBasis| |lprop| + |repeating?| |substring?| |setOfMinN| |inputOutputBinaryFile| |rowEch| + |axes| |char| |singularAtInfinity?| |symmetricRemainder| |solveid| + |failed| |nonSingularModel| |singRicDE| |basisOfCenter| + |rightExactQuotient| |acoshIfCan| |quasiAlgebraicSet| |s17aff| + |setPredicates| |semiResultantReduitEuclidean| |suffix?| + |expintfldpoly| |resetVariableOrder| |jacobi| |LiePolyIfCan| |digits| + |generic?| |zoom| |putProperty| |queue| |countRealRootsMultiple| + |redPol| |meshPar1Var| |OMunhandledSymbol| |rdregime| |simplifyExp| + |compile| |hyperelliptic| |lllp| |startStats!| |prefix?| |status| + |eisensteinIrreducible?| |corrPoly| |swapRows!| |quoByVar| |df2st| + |stronglyReduced?| |lifting| |rightDiscriminant| |internalIntegrate| + |irVar| |computeCycleEntry| |unitNormalize| |powers| |leftFactorIfCan| + |cycleRagits| |setprevious!| |iisqrt3| |fibonacci| |second| + |fortranDouble| |f01mcf| |bitCoef| |yCoord| |erf| |viewPhiDefault| + |float| |style| |sequence| |univariatePolynomialsGcds| |linGenPos| + |third| |elem?| |functionIsFracPolynomial?| |gcdPolynomial| + |addBadValue| |fortranTypeOf| |d02gaf| |useSingleFactorBound| + |restorePrecision| |bumprow| |fractRadix| |lyndon| |rationalFunction| + |lfinfieldint| |nsqfree| |void| |f01qdf| |readUInt32!| + |roughUnitIdeal?| |ODESolve| |associatedEquations| |monomials| + |degreePartition| |dilog| |f01rcf| |s18def| |perfectSqrt| |jacobian| + |taylorRep| |infix?| |radix| |numerators| |numberOfFractionalTerms| + |writable?| |makeSeries| |sin| |polyRDE| |mask| |viewpoint| + |OMsupportsSymbol?| |semiSubResultantGcdEuclidean1| |cylindrical| + |basisOfCommutingElements| |palgint0| |cos| |inverse| |binomial| + |branchIfCan| |expandTrigProducts| |setPrologue!| |sinh2csch| + |clipPointsDefault| |coerceP| |isTimes| |slex| |cyclicEntries| |expr| + |tan| |stopTableInvSet!| |decreasePrecision| |charpol| + |getSyntaxFormsFromFile| |supRittWu?| |exprToGenUPS| |roughSubIdeal?| + |hasSolution?| |overset?| |cot| |remainder| |low| + |isAbsolutelyIrreducible?| |routines| |leadingCoefficientRicDE| + |rootKerSimp| |getOperands| |derivationCoordinates| |commaSeparate| + |physicalLength| |sec| GE |toroidal| |preprocess| |double| + |symmetricDifference| |leadingIdeal| |option?| |unit| + |rectangularMatrix| |selectsecond| |LazardQuotient2| |csc| |log| GT + |pointLists| |callForm?| |minimalPolynomial| |goodPoint| + |partialQuotients| |createPrimitiveNormalPoly| |palgextint| |palgLODE| + |variable| |merge| |asin| LE |s18aff| |OMgetObject| |writeUInt8!| + |algebraicOf| |createNormalPoly| |elColumn2!| |firstDenom| |iterators| + BY |setMaxPoints| |redpps| |acos| LT |innerint| |sturmSequence| + |LowTriBddDenomInv| |largest| |musserTrials| |rootOf| |minimumDegree| + |OMlistSymbols| |scripted?| |atan| |e02daf| |cAcos| + |lazyPremWithDefault| |useNagFunctions| |Aleph| |tanIfCan| + |pmComplexintegrate| |patternVariable| |repSq| |acot| + |lazyResidueClass| |monomialIntegrate| |printInfo!| |c06gqf| + |positiveRemainder| |stoseInvertible?| |supersub| |rdHack1| + |symmetricSquare| |asec| |closedCurve?| |clipWithRanges| |tan2cot| + |rootPoly| |whileLoop| |associator| |c06fpf| |symbol?| |baseRDE| + |acsc| |createMultiplicationTable| |nthRootIfCan| |declare!| + |karatsubaOnce| |rationalIfCan| |separate| |listBranches| |list?| + |triangularSystems| |invertibleElseSplit?| |sinh| + |leftRegularRepresentation| |cap| |solveLinearlyOverQ| + |collectQuasiMonic| |iibinom| |parabolic| |interactiveEnv| + |returnType!| |d02ejf| |cosh| |lowerPolynomial| |f04mbf| + |showIntensityFunctions| NOT |genericLeftMinimalPolynomial| |anfactor| + |internalAugment| |showAll?| |tube| |OMread| |tanh| |alphabetic| + |OMputFloat| |lists| |bringDown| OR |s17def| |critpOrder| |besselY| + |fTable| |internalZeroSetSplit| |trapezoidalo| |coth| + |constantOperator| |getBadValues| AND |quasiRegular?| |compBound| + |stiffnessAndStabilityFactor| |setsubMatrix!| |less?| |signAround| + |removeSquaresIfCan| |bindings| |initiallyReduced?| |lifting1| |keys| + |reindex| |rootPower| |clikeUniv| |hermiteH| |depth| |iidprod| + |linearPolynomials| |bitTruth| |c06gsf| |permanent| |dimension| + |lighting| |hdmpToDmp| |makingStats?| |compdegd| |rightFactorIfCan| + |LyndonBasis| |normFactors| |debug| |point?| |segment| |complexSolve| + |conjug| |changeThreshhold| |complexForm| |f01maf| |meatAxe| + |degreeSubResultant| D |doubleRank| |cot2tan| |shuffle| + |separateDegrees| |finiteBasis| |addPoint| |postfix| + |stoseInvertibleSetreg| |host| |genericLeftDiscriminant| |colorDef| + |arity| |jordanAdmissible?| |f02adf| |dimensionsOf| |OMputBVar| + |zero?| |hypergeometric0F1| |fill!| |rightScalarTimes!| |pair?| + |cAtanh| |functionIsOscillatory| |addPoint2| |e02gaf| |headReduced?| + |removeRoughlyRedundantFactorsInContents| + |tryFunctionalDecomposition?| |semiResultantEuclideannaif| |diagonals| + |power| |rootSplit| |imagk| |e02zaf| |normalise| |shade| |frst| + |divergence| |sts2stst| |permutationGroup| |dn| |generalizedInverse| + |listYoungTableaus| |expandPower| |setFormula!| |monicDivide| |orbits| + * |controlPanel| |insertBottom!| |indices| |quadraticForm| + |countable?| |defineProperty| |iicot| |newLine| + |indiceSubResultantEuclidean| |chvar| |complexNumericIfCan| + |basisOfRightNucleus| |members| |primextendedint| |changeWeightLevel| + |properties| |setAttributeButtonStep| |optimize| |setProperties| |tab| + |collectUnder| |certainlySubVariety?| |numberOfHues| |represents| + |factorsOfCyclicGroupSize| |makeFloatFunction| |translate| + |measure2Result| |lastSubResultantEuclidean| |typeList| = + |subresultantSequence| |iilog| |fortranComplex| |mapMatrixIfCan| + |vark| |f04mcf| |exponentialOrder| |print| |toseInvertibleSet| + |resize| |ldf2lst| |internalSubQuasiComponent?| |e01bff| |mix| + |showArrayValues| |maxRowIndex| |copies| |resolve| |cycles| + |taylorIfCan| |initializeGroupForWordProblem| < |nextColeman| + |prevPrime| |evenInfiniteProduct| |tableForDiscreteLogarithm| + |rightRecip| |imagj| |Gamma| |getVariableOrder| |cCoth| > + |lazyVariations| |factorByRecursion| |mesh| |leftRank| |setStatus| + |extendedIntegrate| |bsolve| |makeViewport3D| <= |middle| + |currentSubProgram| |socf2socdf| |constantRight| |OMUnknownCD?| + |viewport3D| |OMopenFile| |minimize| |fintegrate| |rootsOf| >= + |initials| |weight| |removeRedundantFactorsInPols| |iflist2Result| + |evenlambert| |initiallyReduce| |byteBuffer| |airyAi| |operation| + |subHeight| |pdf2df| |curve| |ScanArabic| |elements| + |variationOfParameters| |f02fjf| |traverse| |completeHermite| + |selectAndPolynomials| |extractProperty| |qPot| |monomRDEsys| + |interpret| |binaryTree| |mathieu24| |firstUncouplingMatrix| + |OMencodingSGML| + |ddFact| |distance| |concat!| |before?| |true| + |trigs2explogs| |iiperm| |updateStatus!| |changeName| - |cn| + |morphism| |neglist| |besselI| |maxPoints| |composites| |rotatey| + |d02bhf| |sech2cosh| |mantissa| / |iidsum| |c06ecf| |s13acf| |leftOne| + |head| |jacobiIdentity?| |upperCase?| |leftPower| |integerBound| + |ocf2ocdf| |s19abf| |increment| |tubeRadiusDefault| |category| + |setAdaptive3D| |nil| |OMreadStr| |acschIfCan| |polarCoordinates| + |iiasin| |enqueue!| |fortranReal| |stronglyReduce| |domain| |df2fi| + |vedf2vef| |fractionPart| |OMcloseConn| |triangular?| |usingTable?| + |package| |numberOfComponents| |regularRepresentation| |cAtan| + |presub| |aCubic| |transcendent?| |shift| |setLength!| |paraboloidal| + |iisqrt2| |partialDenominators| |readInt8!| |resetBadValues| + |approximate| |primitiveElement| |LiePoly| |lfunc| |duplicates?| + |norm| |realEigenvalues| |viewZoomDefault| |complex| |mapCoef| + |henselFact| |karatsuba| |varList| |functorData| |lambert| + |optAttributes| |factorset| |relerror| |e02dff| |simpson| |denomRicDE| + |show| |sin?| |factors| |exp1| |insertMatch| |submod| |property| + |infinityNorm| |getZechTable| |diagonalProduct| |Beta| |tracePowMod| + |ratDsolve| |removeIrreducibleRedundantFactors| |computeCycleLength| + |resultantReduitEuclidean| |nodeOf?| |commutative?| |surface| |trace| + |intensity| |drawComplexVectorField| |OMencodingUnknown| + |numberOfIrreduciblePoly| |sortConstraints| |extendedResultant| + |e04gcf| |partialNumerators| |retract| |subResultantChain| |leader| + |leastAffineMultiple| |primlimitedint| |quatern| |units| |iisec| + |invertIfCan| |delta| |cycleSplit!| |weighted| |reduced?| |oddlambert| + |removeConstantTerm| |ReduceOrder| |setClosed| |logIfCan| + |mainExpression| |mainVariable| |quasiMonic?| |localAbs| |figureUnits| + |imagK| |setButtonValue| |quickSort| |basicSet| + |differentialVariables| |integralRepresents| |prod| |hexDigit?| + |cAcot| |alphanumeric?| |sylvesterSequence| |conical| |lintgcd| + |OMsetEncoding| |hclf| |nlde| |limitPlus| |typeForm| |processTemplate| + |mainCoefficients| |plus!| |solveLinearPolynomialEquationByRecursion| + |code| |optional?| |uniform01| |rewriteSetWithReduction| + |swapColumns!| |groebSolve| |irDef| |LyndonCoordinates| |c02agf| + |OMputVariable| |nullary| |semiResultantEuclidean1| + |clearTheSymbolTable| |formula| |mainMonomials| |printStats!| + |graeffe| |setTopPredicate| |wordInGenerators| |duplicates| + |extendIfCan| |f01ref| |getCode| |lambda| |bytes| |balancedBinaryTree| + |genus| |monicRightDivide| |coleman| |normalizeIfCan| |repeating| + |atoms| |plus| |idealiserMatrix| |innerEigenvectors| |clipBoolean| + |inverseIntegralMatrixAtInfinity| |selectSumOfSquaresRoutines| + |s21bdf| |outputSpacing| |chebyshevU| |bernoulliB| |d02raf| + |wholePart| |anticoord| |possiblyNewVariety?| |limit| |dom| + |nextPrimitivePoly| |lookup| |invmultisect| |maxColIndex| + |homogeneous?| |zeroSetSplitIntoTriangularSystems| |nrows| + |subResultantGcd| |sample| |sum| |viewSizeDefault| |datalist| |d01amf| + |createLowComplexityNormalBasis| |setScreenResolution3D| |entry?| + |solveRetract| |ncols| |transpose| |shiftRight| |d01gbf| |monomRDE| + |deepestInitial| |reciprocalPolynomial| |explicitEntries?| |null?| + |numberOfImproperPartitions| |times| |permutation| + |listRepresentation| |readByte!| |extendedint| |shufflein| + |makeSketch| |startPolynomial| |lieAdmissible?| |symbolTable| |f01qef| + |linear| |zeroOf| |getGraph| |leastPower| + |removeRedundantFactorsInContents| |chiSquare1| |top| |integral?| + |solid| |graphImage| |normalized?| |lp| |systemCommand| |mat| + |tablePow| |curryRight| |s01eaf| |trim| |setRealSteps| + |pushFortranOutputStack| |hconcat| |complexEigenvectors| |title| + |comp| |LazardQuotient| |polynomial| |iisech| |mulmod| |cTan| + |nthRoot| |point| |alphanumeric| |popFortranOutputStack| |reorder| + |key?| |po| |clipSurface| |monom| |node| |options| |iitanh| |expPot| + |symbolIfCan| |deriv| |complexEigenvalues| |continue| |sort| + |solveLinearPolynomialEquationByFractions| |generators| + |bandedHessian| |outputAsFortran| |rk4a| |normal| |multiEuclidean| + |Si| |gradient| |retractable?| |nextSublist| |cRationalPower| + |bezoutMatrix| |e02bcf| |predicates| |e| |constantToUnaryFunction| + |iFTable| |showFortranOutputStack| |genericRightDiscriminant| + |superHeight| |symmetricGroup| |tanh2trigh| |squareFree| |series| + |nil?| |list| |dmpToHdmp| |abs| |laplace| |stopTableGcd!| + |setLegalFortranSourceExtensions| |common| |noValueMode| |string| + |listOfMonoms| |stoseInvertible?reg| |minus!| + |standardBasisOfCyclicSubmodule| |finiteBound| |unit?| |car| + |lieAlgebra?| |eulerE| |userOrdered?| |unitsColorDefault| |algebraic?| + |sup| |bezoutDiscriminant| |f01bsf| |reduceLODE| |OMgetEndApp| + |random| |cdr| |totalLex| |doubleComplex?| |f07fdf| |leadingSupport| + |log2| |makeTerm| |generalizedEigenvector| |poisson| |cschIfCan| + |setDifference| |prinshINFO| |complexIntegrate| |cyclic?| + |zeroDimensional?| |multiEuclideanTree| |bitLength| |charthRoot| + |totolex| |min| |OMgetEndError| |setIntersection| |KrullNumber| |bits| + |prinb| |euclideanGroebner| |iisinh| |stoseIntegralLastSubResultant| + |yellow| |monomialIntPoly| |whatInfinity| |setUnion| |even?| |iExquo| + |reverse!| |dot| |rightRegularRepresentation| |genericRightTraceForm| + |sumSquares| |mainContent| |s21bbf| |messagePrint| |apply| + |clearTheFTable| |optpair| |hostByteOrder| |scopes| + |reducedDiscriminant| |tensorProduct| |OMgetType| |outputBinaryFile| + |boundOfCauchy| |deref| |discriminantEuclidean| |bfEntry| + |rootDirectory| |traceMatrix| |zero| |select!| |minRowIndex| |omError| + |pile| |chebyshevT| |size| |column| |numberOfNormalPoly| |limitedint| + |factorSquareFreePolynomial| |rootProduct| |const| |quadratic| |width| + |SturmHabichtSequence| |rspace| |argumentList!| |c06eaf| + |idealSimplify| |mathieu12| |And| |write!| |moduleSum| + |monicCompleteDecompose| |equation| |llprop| |qroot| + |rootOfIrreduciblePoly| |xCoord| |toseLastSubResultant| |vector| + |rightGcd| |Or| |mkIntegral| |viewThetaDefault| |extension| |makeop| + |radicalOfLeftTraceForm| |first| |simplifyPower| |e04jaf| |youngGroup| + |differentiate| |aromberg| |Not| |lyndon?| |OMgetError| + |diagonalMatrix| |htrigs| |isExpt| |rest| |fullPartialFraction| + |component| |headReduce| |parents| |indicialEquation| |numeric| + |nary?| |pushup| |getMeasure| |quartic| |isAnd| |substitute| + |primintegrate| |primeFactor| |setchildren!| |OMgetFloat| |radical| + |cCosh| |makeprod| |radicalSimplify| |hash| |trigs| |rCoord| + |removeDuplicates| |lazyIntegrate| |replace| |lineColorDefault| + |edf2df| |tubePlot| |c06gcf| |unexpand| |count| |enterPointData| + |printingInfo?| |critB| |fixedPoint| |mr| |doubleFloatFormat| + |physicalLength!| |printStatement| |e02bef| |super| |f02wef| |name| + |overlabel| |optional| |e02akf| |quasiRegular| |monicLeftDivide| + |viewWriteAvailable| |size?| |mainSquareFreePart| |setright!| + |rotatex| |minGbasis| |lift| |body| |stoseInvertibleSetsqfreg| + |e01sef| |tubePoints| |factorSFBRlcUnit| |hcrf| |mindeg| |inc| + |measure| |sncndn| |integralMatrix| |shallowCopy| |leftNorm| |reduce| + |coshIfCan| |parts| |baseRDEsys| |f04atf| |zCoord| |generalSqFr| + |prindINFO| |gramschmidt| |taylorQuoByVar| |subspace| |debug3D| + |insertTop!| |infinite?| |string?| |composite| |lastSubResultant| + |product| |nthExponent| |makeSin| |green| |ricDsolve| |root| + |halfExtendedSubResultantGcd1| |createNormalPrimitivePoly| + |leftScalarTimes!| |lowerCase| |rationalApproximation| |fglmIfCan| + |subset?| |rst| |iiacot| |iteratedInitials| |f04axf| |setClipValue| + |linearAssociatedLog| |autoReduced?| |rightRankPolynomial| + |rightQuotient| |setPoly| |factorGroebnerBasis| |polygon?| |exprex| + SEGMENT |error| |extend| |ord| |rowEchLocal| |algintegrate| + |perfectNthPower?| |port| |unitVector| |fortranCharacter| + |withPredicates| |generalizedEigenvectors| |seriesSolve| |randomR| + |assert| |contractSolve| |tower| |Vectorise| |extractIfCan| |reopen!| + |laplacian| |denominator| |d01aqf| |OMgetEndAtp| |acothIfCan| + |inputBinaryFile| |pleskenSplit| |heap| |xn| |iiasinh| |t| |sorted?| + |pseudoQuotient| |bombieriNorm| |groebner?| |cAsech| + |extendedEuclidean| |e02baf| |every?| |mainPrimitivePart| + |loadNativeModule| |torsion?| |readInt16!| |f02awf| + |shanksDiscLogAlgorithm| |rightOne| |fractionFreeGauss!| + |littleEndian| |vspace| |elRow1!| |determinant| |quadraticNorm| + |complement| |flexibleArray| |mapSolve| |inGroundField?| |spherical| + |constant| |fi2df| |cycle| |expandLog| |complexNumeric| |newReduc| + |UpTriBddDenomInv| |fullDisplay| |putGraph| |cyclicSubmodule| |getRef| + |mapGen| |nextNormalPoly| |byte| |predicate| |leftTrace| + |leadingIndex| |environment| |plotPolar| |d01gaf| |pointColorPalette| + |continuedFraction| |exprToUPS| |kernels| |leftAlternative?| |d02cjf| + |atrapezoidal| |principalAncestors| |roughBase?| |outputForm| + |palgRDE0| |operator| |varselect| |cons| |makeGraphImage| + |numberOfChildren| |maxPoints3D| |perfectNthRoot| |divideExponents| + |createMultiplicationMatrix| |mapExpon| |dominantTerm| |qfactor| + |asecIfCan| |augment| |step| |clearTheIFTable| |expenseOfEvaluationIF| + |curveColorPalette| |constant?| |univariate| |OMputApp| |conditionP| + |OMgetInteger| |sizeLess?| |numberOfDivisors| |noKaratsuba| |comment| + |sparsityIF| |OMgetSymbol| |ceiling| |subResultantGcdEuclidean| + |characteristicSerie| |compactFraction| |clipParametric| |powerSum| + |extensionDegree| |computeInt| |cosSinInfo| |returns| |mathieu22| + |palginfieldint| |pToHdmp| |computePowers| |coerce| |subtractIfCan| + |factor| |f02bbf| |coercePreimagesImages| |getlo| |plenaryPower| + |fmecg| |int| |binary| |degreeSubResultantEuclidean| |construct| + |readIfCan!| |redPo| |sqrt| |source| |externalList| |listOfLists| + |subNode?| |fortranCompilerName| |mindegTerm| |qelt| + |halfExtendedSubResultantGcd2| |basisOfLeftNucleus| |real| + |parameters| |open?| |d01akf| |direction| |positiveSolve| + |useEisensteinCriterion?| |binaryFunction| |qsetelt| |closed?| |imag| + |ffactor| |infieldint| |contract| |solveLinearPolynomialEquation| + |escape| |limitedIntegrate| |s17dcf| |zeroVector| |xRange| + |directProduct| |powmod| |euler| |rk4| |mapdiv| |s21bcf| |binding| + |squareFreeLexTriangular| |deepCopy| |lagrange| |monicDecomposeIfCan| + |lquo| |e01saf| |groebnerIdeal| |idealiser| |medialSet| |mkPrim| + |resetAttributeButtons| |brace| |rk4f| |target| |ptree| |signatureAst| + |internalDecompose| |root?| |fortranLiteralLine| |e04ucf| |empty?| + |internalInfRittWu?| |destruct| |ParCond| |normal01| |initTable!| + |c06fqf| |newTypeLists| |legendre| |problemPoints| |laurentIfCan| + |associative?| |multinomial| |genericLeftTraceForm| + |purelyTranscendental?| |pack!| |OMputEndApp| |kind| + |monicRightFactorIfCan| |d03eef| |makeResult| |mergeFactors| + |highCommonTerms| |cTanh| |compiledFunction| |coerceL| |rowEchelon| + |op| |clearTable!| |critMTonD1| |seed| |gbasis| + |balancedFactorisation| |argumentListOf| |OMputEndBVar| + |upDateBranches| |sh| |removeSinhSq| |cSinh| |showTheIFTable| |c06ebf| + |ravel| |monomial| |pmintegrate| |finite?| |algebraicVariables| + |linearDependenceOverZ| |hasTopPredicate?| |listConjugateBases| + |multiple?| |replaceKthElement| |torsionIfCan| + |branchPointAtInfinity?| |overbar| |removeSinSq| |genericRightNorm| + |reshape| |clip| |arguments| |extractTop!| |minPoints3D| |over| + |setelt| |rootRadius| |build| |mdeg| |changeNameToObjf| |partitions| + |sizeMultiplication| |linkToFortran| |leftExtendedGcd| |mirror| + |symmetricTensors| |irreducible?| |realEigenvectors| |setColumn!| + |goodnessOfFit| |radicalRoots| |removeRoughlyRedundantFactorsInPols| + |shallowExpand| |mapBivariate| |satisfy?| |copy| |groebner| |Nul| + |newSubProgram| |iicoth| |region| GF2FG |union| |fixedDivisor| + |scalarTypeOf| FG2F |pushNewContour| |leftGcd| |f04maf| |setEpilogue!| + |minset| |rischDE| |node?| |tanintegrate| |modTree| |central?| + |antiCommutative?| |nextIrreduciblePoly| |coefficient| |vectorise| + |diagonal?| |update| |expintegrate| |definingEquations| |quoted?| + |autoCoerce| |getOrder| |monomial?| |sumOfKthPowerDivisors| + |partialFraction| |gensym| |unparse| |order| |currentCategoryFrame| + |validExponential| |OMgetBVar| |binaryTournament| |bothWays| + |meshFun2Var| |logpart| |factorSquareFree| |localReal?| |horizConcat| + |areEquivalent?| |cos2sec| |exportedOperators| |maxIndex| + |OMencodingBinary| |real?| |rank| |errorInfo| |rightPower| |s20adf| + |pomopo!| |bumptab1| |overlap| |s17aef| UP2UTS |categoryFrame| + |asinIfCan| |rightFactorCandidate| |logGamma| |superscript| + |resultant| |digit?| |dimensions| |radPoly| |accuracyIF| + |zeroDimPrime?| |positive?| |position| |logical?| |unknownEndian| + |f2df| |heapSort| |createZechTable| |quadratic?| |fillPascalTriangle| + |match?| |setnext!| |insert!| |front| |constantIfCan| |doubleDisc| + |univariatePolynomials| |pastel| |range| |relativeApprox| + |palgextint0| |integralBasis| |var2StepsDefault| |leftDivide| + |mkAnswer| |seriesToOutputForm| |chainSubResultants| |padicallyExpand| + |row| |palgLODE0| |RittWuCompare| |f04jgf| |iiabs| |forLoop| |lllip| + |univariate?| |declare| |inf| |setrest!| |OMgetVariable| + |internalSubPolSet?| |rightCharacteristicPolynomial| |primintfldpoly| + |eigenvectors| |showAllElements| |interpretString| |irCtor| + |OMconnInDevice| |BasicMethod| |setvalue!| |one?| |makeUnit| + |quotient| |cCsc| |genericLeftNorm| |cosIfCan| |completeSmith| + |fracPart| |mainValue| |mathieu23| |unrankImproperPartitions1| + |numberOfMonomials| |bivariateSLPEBR| |alternating| + |componentUpperBound| |addiag| |mainVariable?| |endOfFile?| + |modularFactor| |arg1| |f02abf| |setref| |stopTable!| |coordinate| + |constantLeft| |exactQuotient!| |checkForZero| |addmod| |parent| + |goto| |arg2| |dmpToP| |sech| |lazyPrem| |isNot| |factorial| + |nextsousResultant2| |zeroDimPrimary?| |setelt!| |modifyPointData| + |numericIfCan| |upperBound| |csch| |shiftLeft| |simplifyLog| + |normalizedDivide| |isAtom| |close| |reflect| |mainDefiningPolynomial| + |specialTrigs| |rightUnit| |leftUnit| |conditions| |asinh| + |readLineIfCan!| |e01sbf| |integralLastSubResultant| |BumInSepFFE| + |s17akf| |s19acf| |scaleRoots| |randomLC| |match| |rombergo| |s13adf| + |acosh| |mathieu11| |getIdentifier| |stop| |irreducibleFactor| + |midpoint| |display| |laguerre| |bright| |lazyPseudoRemainder| + |arrayStack| |precision| |pushdown| |lazyEvaluate| |atanh| + |relationsIdeal| |iiacsc| |remove!| |consnewpol| + |resultantEuclideannaif| |entries| |li| |oblateSpheroidal| |padecf| + |acoth| |sinIfCan| |rquo| |elementary| |basis| |ipow| + |bipolarCylindrical| |conjunction| |binarySearchTree| + |genericRightMinimalPolynomial| |f02bjf| |asech| |bipolar| + |basisOfRightAnnihilator| |exponential| |s20acf| |integers| + |useEisensteinCriterion| |integralDerivationMatrix| |s18aef| + |leftExactQuotient| |associatedSystem| |c05adf| |equiv| |vertConcat| + |isImplies| |exactQuotient| |s14baf| |subResultantsChain| |multiple| + |addMatchRestricted| |prime?| |primitive?| |input| + |toseSquareFreePart| |cAcoth| |integrate| + |rewriteSetByReducingWithParticularGenerators| |iiasec| |applyQuote| + |cyclicGroup| |structuralConstants| |sn| |categoryMode| |cAsin| + |library| |bivariate?| |iiexp| |innerSolve| |oddInfiniteProduct| + |selectFiniteRoutines| |getButtonValue| |infieldIntegrate| |OMgetBind| + |distribute| |intcompBasis| |coerceImages| |Lazard| |leftMult| + |doublyTransitive?| |geometric| |coefficients| |summation| |romberg| + |closeComponent| |eq?| |approximants| |powerAssociative?| + |exteriorDifferential| |outputArgs| |ruleset| |reverseLex| + |findConstructor| |bracket| |cot2trig| |pdf2ef| |swap!| |tanhIfCan| + |factorAndSplit| |box| |lfintegrate| |back| |simpleBounds?| |Ei| + |semiSubResultantGcdEuclidean2| |set| |readable?| |f04adf| + |wholeRadix| |gcdPrimitive| |collectUpper| |cycleTail| + |linearAssociatedOrder| |test| |capacity| |id| |fixPredicate| |s14abf| + |algebraicCoefficients?| |rightAlternative?| |stirling1| |implies| + |suchThat| |OMputSymbol| |f04asf| |dAndcExp| |drawStyle| + |knownInfBasis| |coth2tanh| |imports| |An| |iiacsch| + |showScalarValues| |ksec| |removeDuplicates!| |table| + |algebraicDecompose| |getConstant| |s17ahf| |lowerCase?| |any| |imagE| + |purelyAlgebraicLeadingMonomial?| |failed?| |absolutelyIrreducible?| + |insert| |new| |extendedSubResultantGcd| |space| |factorList| |hasoln| + |external?| |obj| |algSplitSimple| |loopPoints| |f04arf| |expt| + |OMgetEndBind| |removeSuperfluousQuasiComponents| |scale| |normalForm| + |eq| |pointColor| |derivative| |prefix| |cache| |OMUnknownSymbol?| + |tValues| |curve?| |iitan| |createLowComplexityTable| |graphState| + |iter| |coerceS| |pushucoef| |df2ef| + |dimensionOfIrreducibleRepresentation| |normInvertible?| |lSpaceBasis| + |invertibleSet| |uncouplingMatrices| |delete| |lexGroebner| + |signature| |rischDEsys| |setProperty| |normalDenom| |mainMonomial| + |e02aef| |univariateSolve| |subst| |edf2efi| |any?| |skewSFunction| + |noncommutativeJordanAlgebra?| |parseString| |OMlistCDs| + |primlimintfrac| |part?| |delete!| |getMultiplicationMatrix| + |numFunEvals| |irreducibleFactors| |cubic| |attributeData| + |OMencodingXML| |lowerCase!| |sec2cos| |viewPosDefault| |cardinality| + |mappingMode| |iiatanh| |FormatRoman| |module| |beauzamyBound| + |rootBound| |directory| |script| |UnVectorise| |tableau| |opeval| + |sinhcosh| |s18adf| |elRow2!| |totalDegree| |discriminant| |expIfCan| + |approxSqrt| |ScanFloatIgnoreSpacesIfCan| |rootNormalize| |kovacic| + |rational?| |OMputObject| |pureLex| |subresultantVector| + |retractIfCan| |ignore?| |chineseRemainder| |mappingAst| |flatten| + |PollardSmallFactor| |internal?| |exp| |tryFunctionalDecomposition| + |OMsupportsCD?| |OMputAttr| |selectPolynomials| |printCode| |objects| + |tex| |linearlyDependent?| |unaryFunction| |left| |singleFactorBound| + |numer| |monicModulo| |eigenMatrix| |minColIndex| |identity| + |conjugates| |appendPoint| |base| |ParCondList| |selectOrPolynomials| + |/\\| |right| |nor| |outputList| |denom| |euclideanNormalForm| + |palgintegrate| |approxNthRoot| |evaluateInverse| + |multiplyCoefficients| |\\/| |regime| |partition| |cyclePartition| + |invertible?| |cPower| |hessian| |lazyPseudoDivide| |subCase?| + |rename!| |epilogue| |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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(|has| |#2| (-799)) (|has| |#2| (-368)) (|has| |#2| (-174)) (|has| |#2| (-132)) (|has| |#2| (-25))) ((-34) . T) ((-38 |#2|) |has| |#2| (-174)) ((-102) -2740 (|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|) -2740 (|has| |#2| (-1058)) (|has| |#2| (-368)) (|has| |#2| (-174))) ((-111 $ $) |has| |#2| (-174)) ((-132) -2740 (|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)) -2740 (|has| |#2| (-1058)) (-12 (|has| |#2| (-1047 (-570))) (|has| |#2| (-1109))) (|has| |#2| (-854)) (|has| |#2| (-174))) ((-622 |#2|) -2740 (|has| |#2| (-1109)) (|has| |#2| (-174))) ((-619 (-868)) -2740 (|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)) -2740 (|has| |#2| (-1058)) (|has| |#2| (-854)) (|has| |#2| (-368)) (|has| |#2| (-174))) ((-652 |#2|) -2740 (|has| |#2| (-1058)) (|has| |#2| (-368)) (|has| |#2| (-174))) ((-652 $) -2740 (|has| |#2| (-1058)) (|has| |#2| (-854)) (|has| |#2| (-174))) ((-654 |#2|) -2740 (|has| |#2| (-1058)) (|has| |#2| (-368)) (|has| |#2| (-174))) ((-654 $) -2740 (|has| |#2| (-1058)) (|has| |#2| (-854)) (|has| |#2| (-174))) ((-646 |#2|) -2740 (|has| |#2| (-368)) (|has| |#2| (-174))) ((-645 (-570)) -12 (|has| |#2| (-645 (-570))) (|has| |#2| (-1058))) ((-645 |#2|) |has| |#2| (-1058)) ((-723 |#2|) -2740 (|has| |#2| (-368)) (|has| |#2| (-174))) ((-732) -2740 (|has| |#2| (-1058)) (|has| |#2| (-854)) (|has| |#2| (-732)) (|has| |#2| (-174))) ((-797) |has| |#2| (-854)) ((-798) -2740 (|has| |#2| (-854)) (|has| |#2| (-799))) ((-799) |has| |#2| (-799)) ((-800) -2740 (|has| |#2| (-854)) (|has| |#2| (-799))) ((-801) -2740 (|has| |#2| (-854)) (|has| |#2| (-799))) ((-854) |has| |#2| (-854)) ((-856) -2740 (|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|) -2740 (|has| |#2| (-1058)) (|has| |#2| (-368)) (|has| |#2| (-174))) ((-1060 $) |has| |#2| (-174)) ((-1065 |#2|) -2740 (|has| |#2| (-1058)) (|has| |#2| (-368)) (|has| |#2| (-174))) ((-1065 $) |has| |#2| (-174)) ((-1058) -2740 (|has| |#2| (-1058)) (|has| |#2| (-854)) (|has| |#2| (-174))) ((-1067) -2740 (|has| |#2| (-1058)) (|has| |#2| (-854)) (|has| |#2| (-174))) ((-1121) -2740 (|has| |#2| (-1058)) (|has| |#2| (-854)) (|has| |#2| (-732)) (|has| |#2| (-174))) ((-1109) -2740 (|has| |#2| (-1109)) (|has| |#2| (-1058)) (|has| |#2| (-854)) (|has| |#2| (-799)) (|has| |#2| (-732)) (|has| |#2| (-373)) (|has| |#2| (-368)) (|has| |#2| (-174)) (|has| |#2| (-132)) (|has| |#2| (-25))) ((-1227) . T) ((-1284 |#2|) |has| |#2| (-368))) -((-2942 (((-242 |#1| |#3|) (-1 |#3| |#2| |#3|) (-242 |#1| |#2|) |#3|) 21)) (-3529 ((|#3| (-1 |#3| |#2| |#3|) (-242 |#1| |#2|) |#3|) 23)) (-1352 (((-242 |#1| |#3|) (-1 |#3| |#2|) (-242 |#1| |#2|)) 18))) -(((-241 |#1| |#2| |#3|) (-10 -7 (-15 -2942 ((-242 |#1| |#3|) (-1 |#3| |#2| |#3|) (-242 |#1| |#2|) |#3|)) (-15 -3529 (|#3| (-1 |#3| |#2| |#3|) (-242 |#1| |#2|) |#3|)) (-15 -1352 ((-242 |#1| |#3|) (-1 |#3| |#2|) (-242 |#1| |#2|)))) (-777) (-1227) (-1227)) (T -241)) -((-1352 (*1 *2 *3 *4) (-12 (-5 *3 (-1 *7 *6)) (-5 *4 (-242 *5 *6)) (-14 *5 (-777)) (-4 *6 (-1227)) (-4 *7 (-1227)) (-5 *2 (-242 *5 *7)) (-5 *1 (-241 *5 *6 *7)))) (-3529 (*1 *2 *3 *4 *2) (-12 (-5 *3 (-1 *2 *6 *2)) (-5 *4 (-242 *5 *6)) (-14 *5 (-777)) (-4 *6 (-1227)) (-4 *2 (-1227)) (-5 *1 (-241 *5 *6 *2)))) (-2942 (*1 *2 *3 *4 *5) (-12 (-5 *3 (-1 *5 *7 *5)) (-5 *4 (-242 *6 *7)) (-14 *6 (-777)) (-4 *7 (-1227)) (-4 *5 (-1227)) (-5 *2 (-242 *6 *5)) (-5 *1 (-241 *6 *7 *5))))) -(-10 -7 (-15 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|%noBranch|) (IF (|has| |t#2| (-132)) (-6 (-132)) |%noBranch|) (IF (|has| |t#2| (-732)) (PROGN (-6 (-732)) (-15 * ($ |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 -4446)) (-6 -4446) |%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) -2892 (|has| |#2| (-1058)) (|has| |#2| (-854)) (|has| |#2| (-368)) (|has| |#2| (-174))) ((-23) -2892 (|has| |#2| (-1058)) (|has| |#2| (-854)) (|has| |#2| (-799)) (|has| |#2| (-368)) (|has| |#2| (-174)) (|has| |#2| (-132))) ((-25) -2892 (|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) -2892 (|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|) -2892 (|has| |#2| (-1058)) (|has| |#2| (-368)) (|has| |#2| (-174))) ((-111 $ $) |has| |#2| (-174)) ((-132) -2892 (|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)) -2892 (|has| |#2| (-1058)) (-12 (|has| |#2| (-1047 (-570))) (|has| |#2| (-1109))) (|has| |#2| (-854)) (|has| |#2| (-174))) ((-622 |#2|) -2892 (|has| |#2| (-1109)) (|has| |#2| (-174))) ((-619 (-868)) -2892 (|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)) -2892 (|has| |#2| (-1058)) (|has| |#2| (-854)) (|has| |#2| (-368)) (|has| |#2| (-174))) ((-652 |#2|) -2892 (|has| |#2| (-1058)) (|has| |#2| (-368)) (|has| |#2| (-174))) ((-652 $) -2892 (|has| |#2| (-1058)) (|has| |#2| (-854)) (|has| |#2| (-174))) ((-654 |#2|) -2892 (|has| |#2| (-1058)) (|has| |#2| (-368)) (|has| |#2| (-174))) ((-654 $) -2892 (|has| |#2| (-1058)) (|has| |#2| (-854)) (|has| |#2| (-174))) ((-646 |#2|) -2892 (|has| |#2| (-368)) (|has| |#2| (-174))) ((-645 (-570)) -12 (|has| |#2| (-645 (-570))) (|has| |#2| (-1058))) ((-645 |#2|) |has| |#2| (-1058)) ((-723 |#2|) -2892 (|has| |#2| (-368)) (|has| |#2| (-174))) ((-732) -2892 (|has| |#2| (-1058)) (|has| |#2| (-854)) (|has| |#2| (-732)) (|has| |#2| (-174))) ((-797) |has| |#2| (-854)) ((-798) -2892 (|has| |#2| (-854)) (|has| |#2| (-799))) ((-799) |has| |#2| (-799)) ((-800) -2892 (|has| |#2| (-854)) (|has| |#2| (-799))) ((-801) -2892 (|has| |#2| (-854)) (|has| |#2| (-799))) ((-854) |has| |#2| (-854)) ((-856) -2892 (|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|) -2892 (|has| |#2| (-1058)) (|has| |#2| (-368)) (|has| |#2| (-174))) ((-1060 $) |has| |#2| (-174)) ((-1065 |#2|) -2892 (|has| |#2| (-1058)) (|has| |#2| (-368)) (|has| |#2| (-174))) ((-1065 $) |has| |#2| (-174)) ((-1058) -2892 (|has| |#2| (-1058)) (|has| |#2| (-854)) (|has| |#2| (-174))) ((-1067) -2892 (|has| |#2| (-1058)) (|has| |#2| (-854)) (|has| |#2| (-174))) ((-1121) -2892 (|has| |#2| (-1058)) (|has| |#2| (-854)) (|has| |#2| (-732)) (|has| |#2| (-174))) ((-1109) -2892 (|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))) +((-2336 (((-242 |#1| |#3|) (-1 |#3| |#2| |#3|) (-242 |#1| |#2|) |#3|) 21)) (-3625 ((|#3| (-1 |#3| |#2| |#3|) (-242 |#1| |#2|) |#3|) 23)) (-1356 (((-242 |#1| |#3|) (-1 |#3| |#2|) (-242 |#1| |#2|)) 18))) +(((-241 |#1| |#2| |#3|) (-10 -7 (-15 -2336 ((-242 |#1| |#3|) (-1 |#3| |#2| |#3|) (-242 |#1| |#2|) |#3|)) (-15 -3625 (|#3| (-1 |#3| |#2| |#3|) (-242 |#1| |#2|) |#3|)) (-15 -1356 ((-242 |#1| |#3|) (-1 |#3| |#2|) (-242 |#1| |#2|)))) (-777) (-1227) (-1227)) (T -241)) +((-1356 (*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)))) (-3625 (*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)))) (-2336 (*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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T) ((-174) -2740 (|has| |#1| (-916)) (|has| |#1| (-562)) (|has| |#1| (-458)) (|has| |#1| (-174))) ((-620 (-542)) -12 (|has| |#1| (-620 (-542))) (|has| |#3| (-620 (-542)))) ((-620 (-899 (-384))) -12 (|has| |#1| (-620 (-899 (-384)))) (|has| |#3| (-620 (-899 (-384))))) ((-620 (-899 (-570))) -12 (|has| |#1| (-620 (-899 (-570)))) (|has| |#3| (-620 (-899 (-570))))) ((-233 |#1|) . T) ((-235) |has| |#1| (-235)) ((-294) -2740 (|has| |#1| (-916)) (|has| |#1| (-562)) (|has| |#1| (-458))) ((-313 $) . T) ((-330 |#1| |#4|) . T) ((-382 |#1|) . T) ((-417 |#1|) . T) ((-458) -2740 (|has| |#1| (-916)) (|has| |#1| (-458))) ((-520 |#2| |#1|) |has| |#1| (-235)) ((-520 |#2| $) |has| |#1| (-235)) ((-520 |#3| |#1|) . T) ((-520 |#3| $) . T) ((-520 $ $) . T) ((-562) -2740 (|has| |#1| (-916)) (|has| |#1| (-562)) (|has| |#1| (-458))) ((-652 #0#) |has| |#1| (-38 (-413 (-570)))) ((-652 (-570)) . T) ((-652 |#1|) . T) ((-652 $) . T) ((-654 #0#) |has| |#1| (-38 (-413 (-570)))) ((-654 |#1|) . T) ((-654 $) . T) ((-646 #0#) |has| |#1| (-38 (-413 (-570)))) ((-646 |#1|) |has| |#1| (-174)) ((-646 $) -2740 (|has| |#1| (-916)) (|has| |#1| (-562)) (|has| |#1| (-458))) ((-645 (-570)) |has| |#1| (-645 (-570))) ((-645 |#1|) . T) ((-723 #0#) |has| |#1| (-38 (-413 (-570)))) ((-723 |#1|) |has| |#1| (-174)) ((-723 $) -2740 (|has| |#1| (-916)) (|has| |#1| (-562)) (|has| |#1| (-458))) ((-732) . T) ((-907 (-1186)) |has| |#1| (-907 (-1186))) ((-907 |#3|) . T) ((-893 (-384)) -12 (|has| |#1| (-893 (-384))) (|has| |#3| (-893 (-384)))) ((-893 (-570)) -12 (|has| |#1| (-893 (-570))) (|has| |#3| (-893 (-570)))) ((-956 |#1| |#4| |#3|) . T) ((-916) |has| |#1| (-916)) ((-1047 (-413 (-570))) |has| |#1| (-1047 (-413 (-570)))) ((-1047 (-570)) |has| |#1| (-1047 (-570))) ((-1047 |#1|) . T) ((-1047 |#2|) . T) ((-1047 |#3|) . T) ((-1060 #0#) |has| |#1| (-38 (-413 (-570)))) ((-1060 |#1|) . T) ((-1060 $) -2740 (|has| |#1| (-916)) (|has| |#1| (-562)) (|has| |#1| (-458)) (|has| |#1| (-174))) ((-1065 #0#) |has| |#1| (-38 (-413 (-570)))) ((-1065 |#1|) . T) ((-1065 $) -2740 (|has| |#1| (-916)) (|has| |#1| (-562)) (|has| |#1| (-458)) (|has| |#1| (-174))) ((-1058) . T) ((-1067) . T) ((-1121) . T) ((-1109) . 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T) ((-23) . T) ((-47 |#1| |#4|) . T) ((-25) . T) ((-38 #0=(-413 (-570))) |has| |#1| (-38 (-413 (-570)))) ((-38 |#1|) |has| |#1| (-174)) ((-38 $) -2892 (|has| |#1| (-916)) (|has| |#1| (-562)) (|has| |#1| (-458))) ((-102) . T) ((-111 #0# #0#) |has| |#1| (-38 (-413 (-570)))) ((-111 |#1| |#1|) . T) ((-111 $ $) -2892 (|has| |#1| (-916)) (|has| |#1| (-562)) (|has| |#1| (-458)) (|has| |#1| (-174))) ((-132) . T) ((-146) |has| |#1| (-146)) ((-148) |has| |#1| (-148)) ((-622 #0#) -2892 (|has| |#1| (-1047 (-413 (-570)))) (|has| |#1| (-38 (-413 (-570))))) ((-622 (-570)) . T) ((-622 |#1|) . T) ((-622 |#2|) . T) ((-622 |#3|) . T) ((-622 $) -2892 (|has| |#1| (-916)) (|has| |#1| (-562)) (|has| |#1| (-458))) ((-619 (-868)) . T) ((-174) -2892 (|has| |#1| (-916)) (|has| |#1| (-562)) (|has| |#1| (-458)) (|has| |#1| (-174))) ((-620 (-542)) -12 (|has| |#1| (-620 (-542))) (|has| |#3| (-620 (-542)))) ((-620 (-899 (-384))) -12 (|has| |#1| (-620 (-899 (-384)))) (|has| |#3| (-620 (-899 (-384))))) ((-620 (-899 (-570))) -12 (|has| |#1| (-620 (-899 (-570)))) (|has| |#3| (-620 (-899 (-570))))) ((-233 |#1|) . T) ((-235) |has| |#1| (-235)) ((-294) -2892 (|has| |#1| (-916)) (|has| |#1| (-562)) (|has| |#1| (-458))) ((-313 $) . T) ((-330 |#1| |#4|) . T) ((-382 |#1|) . T) ((-417 |#1|) . T) ((-458) -2892 (|has| |#1| (-916)) (|has| |#1| (-458))) ((-520 |#2| |#1|) |has| |#1| (-235)) ((-520 |#2| $) |has| |#1| (-235)) ((-520 |#3| |#1|) . T) ((-520 |#3| $) . T) ((-520 $ $) . T) ((-562) -2892 (|has| |#1| (-916)) (|has| |#1| (-562)) (|has| |#1| (-458))) ((-652 #0#) |has| |#1| (-38 (-413 (-570)))) ((-652 (-570)) . T) ((-652 |#1|) . T) ((-652 $) . T) ((-654 #0#) |has| |#1| (-38 (-413 (-570)))) ((-654 |#1|) . T) ((-654 $) . T) ((-646 #0#) |has| |#1| (-38 (-413 (-570)))) ((-646 |#1|) |has| |#1| (-174)) ((-646 $) -2892 (|has| |#1| (-916)) (|has| |#1| (-562)) (|has| |#1| (-458))) ((-645 (-570)) |has| |#1| (-645 (-570))) ((-645 |#1|) . T) ((-723 #0#) |has| |#1| (-38 (-413 (-570)))) ((-723 |#1|) |has| |#1| (-174)) ((-723 $) -2892 (|has| |#1| (-916)) (|has| |#1| (-562)) (|has| |#1| (-458))) ((-732) . T) ((-907 (-1186)) |has| |#1| (-907 (-1186))) ((-907 |#3|) . T) ((-893 (-384)) -12 (|has| |#1| (-893 (-384))) (|has| |#3| (-893 (-384)))) ((-893 (-570)) -12 (|has| |#1| (-893 (-570))) (|has| |#3| (-893 (-570)))) ((-956 |#1| |#4| |#3|) . T) ((-916) |has| |#1| (-916)) ((-1047 (-413 (-570))) |has| |#1| (-1047 (-413 (-570)))) ((-1047 (-570)) |has| |#1| (-1047 (-570))) ((-1047 |#1|) . T) ((-1047 |#2|) . T) ((-1047 |#3|) . T) ((-1060 #0#) |has| |#1| (-38 (-413 (-570)))) ((-1060 |#1|) . T) ((-1060 $) -2892 (|has| |#1| (-916)) (|has| |#1| (-562)) (|has| |#1| (-458)) (|has| |#1| (-174))) ((-1065 #0#) |has| |#1| (-38 (-413 (-570)))) ((-1065 |#1|) . T) ((-1065 $) -2892 (|has| |#1| (-916)) (|has| |#1| (-562)) (|has| |#1| (-458)) (|has| |#1| (-174))) ((-1058) . T) ((-1067) . T) ((-1121) . T) ((-1109) . T) ((-1231) |has| |#1| (-916))) +((-2557 (((-112) $ $) 19 (|has| |#1| (-1109)))) (-1784 ((|#1| $) 55)) (-3353 ((|#1| $) 45)) (-3606 (((-112) $ (-777)) 8)) (-3317 (($) 7 T CONST)) (-1816 (($ $) 61)) (-3481 (($ $) 49)) (-2242 ((|#1| |#1| $) 47)) (-2487 ((|#1| $) 46)) (-3627 (((-650 |#1|) $) 31 (|has| $ (-6 -4449)))) (-1327 (((-112) $ (-777)) 9)) (-3003 (((-650 |#1|) $) 30 (|has| $ (-6 -4449)))) (-1480 (((-112) |#1| $) 28 (-12 (|has| |#1| (-1109)) (|has| $ (-6 -4449))))) (-1502 (($ (-1 |#1| |#1|) $) 35 (|has| $ (-6 -4450)))) (-1356 (($ (-1 |#1| |#1|) $) 36)) (-2907 (((-112) $ (-777)) 10)) (-1355 (((-777) $) 62)) (-1553 (((-1168) $) 22 (|has| |#1| (-1109)))) (-2498 ((|#1| $) 40)) (-3637 ((|#1| |#1| $) 53)) (-2992 ((|#1| |#1| $) 52)) (-4037 (($ |#1| $) 41)) (-1444 (((-777) $) 56)) (-3576 (((-1129) $) 21 (|has| |#1| (-1109)))) (-4038 ((|#1| $) 63)) (-3929 ((|#1| $) 51)) (-1886 ((|#1| $) 50)) (-2402 ((|#1| $) 42)) (-3706 (((-112) (-1 (-112) |#1|) $) 33 (|has| $ (-6 -4449)))) (-1771 (($ $ (-650 (-298 |#1|))) 27 (-12 (|has| |#1| (-313 |#1|)) (|has| |#1| (-1109)))) (($ $ (-298 |#1|)) 26 (-12 (|has| |#1| (-313 |#1|)) (|has| |#1| (-1109)))) (($ $ |#1| |#1|) 25 (-12 (|has| |#1| (-313 |#1|)) (|has| |#1| (-1109)))) (($ $ (-650 |#1|) (-650 |#1|)) 24 (-12 (|has| |#1| (-313 |#1|)) (|has| |#1| (-1109))))) (-4230 (((-112) $ $) 14)) (-3143 ((|#1| |#1| $) 59)) (-3870 (((-112) $) 11)) (-1646 (($) 12)) (-1903 ((|#1| $) 60)) (-2233 (($) 58) (($ (-650 |#1|)) 57)) (-2918 (((-777) $) 44)) (-3587 (((-777) (-1 (-112) |#1|) $) 32 (|has| $ (-6 -4449))) (((-777) |#1| $) 29 (-12 (|has| |#1| (-1109)) (|has| $ (-6 -4449))))) (-3952 (($ $) 13)) (-3799 (((-868) $) 18 (|has| |#1| (-619 (-868))))) (-2086 ((|#1| $) 54)) (-3105 (((-112) $ $) 23 (|has| |#1| (-1109)))) (-2376 (($ (-650 |#1|)) 43)) (-4246 ((|#1| $) 64)) (-4337 (((-112) (-1 (-112) |#1|) $) 34 (|has| $ (-6 -4449)))) (-3021 (((-112) $ $) 20 (|has| |#1| (-1109)))) (-2569 (((-777) $) 6 (|has| $ (-6 -4449))))) (((-257 |#1|) (-141) (-1227)) (T -257)) -((-4207 (*1 *1) (-12 (-4 *1 (-257 *2)) (-4 *2 (-1227)))) (-4207 (*1 *1 *2) (-12 (-5 *2 (-650 *3)) (-4 *3 (-1227)) (-4 *1 (-257 *3)))) (-1435 (*1 *2 *1) (-12 (-4 *1 (-257 *3)) (-4 *3 (-1227)) (-5 *2 (-777)))) (-3979 (*1 *2 *1) (-12 (-4 *1 (-257 *2)) (-4 *2 (-1227)))) (-1852 (*1 *2 *1) (-12 (-4 *1 (-257 *2)) (-4 *2 (-1227)))) (-1756 (*1 *2 *2 *1) (-12 (-4 *1 (-257 *2)) (-4 *2 (-1227)))) (-1499 (*1 *2 *2 *1) (-12 (-4 *1 (-257 *2)) (-4 *2 (-1227)))) (-2273 (*1 *2 *1) (-12 (-4 *1 (-257 *2)) (-4 *2 (-1227)))) (-2886 (*1 *2 *1) (-12 (-4 *1 (-257 *2)) (-4 *2 (-1227)))) (-2347 (*1 *1 *1) (-12 (-4 *1 (-257 *2)) (-4 *2 (-1227))))) -(-13 (-1130 |t#1|) (-1004 |t#1|) (-10 -8 (-15 -4207 ($)) (-15 -4207 ($ (-650 |t#1|))) (-15 -1435 ((-777) $)) (-15 -3979 (|t#1| $)) (-15 -1852 (|t#1| $)) (-15 -1756 (|t#1| |t#1| $)) (-15 -1499 (|t#1| |t#1| $)) (-15 -2273 (|t#1| $)) (-15 -2886 (|t#1| $)) (-15 -2347 ($ $)))) -(((-34) . 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|bothInfinite| "Both top and bottom points are infinite") (|:| |notEvaluated| "Range not yet evaluated"))))))) $) 36)) (-1740 (((-1282)) 11))) -(((-565) (-10 -8 (-15 -3978 ($)) (-15 -1740 ((-1282))) (-15 -2761 ((-650 (-2 (|:| |var| (-1186)) (|:| |fn| (-320 (-227))) (|:| -1990 (-1103 (-849 (-227)))) (|:| |abserr| (-227)) (|:| |relerr| (-227)))) $)) (-15 -3189 ($ (-650 (-2 (|:| -2013 (-2 (|:| |var| (-1186)) (|:| |fn| (-320 (-227))) (|:| -1990 (-1103 (-849 (-227)))) (|:| |abserr| (-227)) (|:| |relerr| (-227)))) (|:| -2224 (-2 (|:| |endPointContinuity| (-3 (|:| |continuous| "Continuous at the end points") (|:| |lowerSingular| "There is a singularity at the lower end point") (|:| |upperSingular| "There is a singularity at the upper end point") (|:| |bothSingular| "There are singularities at both end points") (|:| |notEvaluated| "End point continuity not yet evaluated"))) (|:| |singularitiesStream| (-3 (|:| |str| (-1166 (-227))) (|:| |notEvaluated| "Internal singularities not yet evaluated"))) (|:| -1990 (-3 (|:| |finite| "The range is finite") (|:| |lowerInfinite| "The bottom of range is infinite") (|:| |upperInfinite| "The top of range is infinite") (|:| |bothInfinite| "Both top and bottom points are infinite") (|:| |notEvaluated| "Range not yet evaluated"))))))))) (-15 -2599 ($ (-2 (|:| -2013 (-2 (|:| |var| (-1186)) (|:| |fn| (-320 (-227))) (|:| -1990 (-1103 (-849 (-227)))) (|:| |abserr| (-227)) (|:| |relerr| (-227)))) (|:| -2224 (-2 (|:| |endPointContinuity| (-3 (|:| |continuous| "Continuous at the end points") (|:| |lowerSingular| "There is a singularity at the lower end point") (|:| |upperSingular| "There is a singularity at the upper end point") (|:| |bothSingular| "There are singularities at both end points") (|:| |notEvaluated| "End point continuity not yet evaluated"))) (|:| |singularitiesStream| (-3 (|:| |str| (-1166 (-227))) (|:| |notEvaluated| "Internal singularities not yet evaluated"))) (|:| -1990 (-3 (|:| |finite| "The range is finite") (|:| 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|endPointContinuity| (-3 (|:| |continuous| "Continuous at the end points") (|:| |lowerSingular| "There is a singularity at the lower end point") (|:| |upperSingular| "There is a singularity at the upper end point") (|:| |bothSingular| "There are singularities at both end points") (|:| |notEvaluated| "End point continuity not yet evaluated"))) (|:| |singularitiesStream| (-3 (|:| |str| (-1166 (-227))) (|:| |notEvaluated| "Internal singularities not yet evaluated"))) (|:| -1990 (-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)))) (-2761 (*1 *2 *1) (-12 (-5 *2 (-650 (-2 (|:| |var| (-1186)) (|:| |fn| (-320 (-227))) (|:| -1990 (-1103 (-849 (-227)))) (|:| |abserr| (-227)) (|:| |relerr| (-227))))) (-5 *1 (-565)))) (-1740 (*1 *2) (-12 (-5 *2 (-1282)) (-5 *1 (-565)))) 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|upperInfinite| "The top of range is infinite") (|:| |bothInfinite| "Both top and bottom points are infinite") (|:| |notEvaluated| "Range not yet evaluated"))))))))) (-15 -2599 ($ (-2 (|:| -2013 (-2 (|:| |var| (-1186)) (|:| |fn| (-320 (-227))) (|:| -1990 (-1103 (-849 (-227)))) (|:| |abserr| (-227)) (|:| |relerr| (-227)))) (|:| -2224 (-2 (|:| |endPointContinuity| (-3 (|:| |continuous| "Continuous at the end points") (|:| |lowerSingular| "There is a singularity at the lower end point") (|:| |upperSingular| "There is a singularity at the upper end point") (|:| |bothSingular| "There are singularities at both end points") (|:| |notEvaluated| "End point continuity not yet evaluated"))) (|:| |singularitiesStream| (-3 (|:| |str| (-1166 (-227))) (|:| |notEvaluated| "Internal singularities not yet evaluated"))) (|:| -1990 (-3 (|:| |finite| "The range is finite") (|:| |lowerInfinite| "The bottom of range is infinite") (|:| |upperInfinite| "The top of range is infinite") (|:| |bothInfinite| "Both 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"Range not yet evaluated")))))))) 26)) (-2339 (((-2 (|:| |endPointContinuity| (-3 (|:| |continuous| "Continuous at the end points") (|:| |lowerSingular| "There is a singularity at the lower end point") (|:| |upperSingular| "There is a singularity at the upper end point") (|:| |bothSingular| "There are singularities at both end points") (|:| |notEvaluated| "End point continuity not yet evaluated"))) (|:| |singularitiesStream| (-3 (|:| |str| (-1166 (-227))) (|:| |notEvaluated| "Internal singularities not yet evaluated"))) (|:| -4043 (-3 (|:| |finite| "The range is finite") (|:| |lowerInfinite| "The bottom of range is infinite") (|:| |upperInfinite| "The top of range is infinite") (|:| |bothInfinite| "Both top and bottom points are infinite") (|:| |notEvaluated| "Range not yet evaluated")))) (-2 (|:| |var| (-1186)) (|:| |fn| (-320 (-227))) (|:| -4043 (-1103 (-849 (-227)))) (|:| |abserr| (-227)) (|:| |relerr| (-227)))) 38)) (-4161 (((-650 (-2 (|:| -2106 (-2 (|:| |var| (-1186)) (|:| |fn| 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T) ((-23) . T) ((-47 |#1| #0=(-570)) . T) ((-25) . T) ((-38 #1=(-413 (-570))) -2740 (|has| |#1| (-368)) (|has| |#1| (-38 (-413 (-570))))) ((-38 |#1|) |has| |#1| (-174)) ((-38 |#2|) |has| |#1| (-368)) ((-38 $) -2740 (|has| |#1| (-562)) (|has| |#1| (-368))) ((-35) |has| |#1| (-38 (-413 (-570)))) ((-95) |has| |#1| (-38 (-413 (-570)))) ((-102) . T) ((-111 #1# #1#) -2740 (|has| |#1| (-368)) (|has| |#1| (-38 (-413 (-570))))) ((-111 |#1| |#1|) . T) ((-111 |#2| |#2|) |has| |#1| (-368)) ((-111 $ $) -2740 (|has| |#1| (-562)) (|has| |#1| (-368)) (|has| |#1| (-174))) ((-132) . T) ((-146) -2740 (-12 (|has| |#1| (-368)) (|has| |#2| (-146))) (|has| |#1| (-146))) ((-148) -2740 (-12 (|has| |#1| (-368)) (|has| |#2| (-148))) (|has| |#1| (-148))) ((-622 #1#) -2740 (|has| |#1| (-368)) (|has| |#1| (-38 (-413 (-570))))) ((-622 (-570)) . T) ((-622 #2=(-1186)) -12 (|has| |#1| (-368)) (|has| |#2| (-1047 (-1186)))) ((-622 |#1|) |has| |#1| (-174)) ((-622 |#2|) . 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T) ((-652 |#1|) . T) ((-652 |#2|) |has| |#1| (-368)) ((-652 $) . T) ((-654 #1#) -2740 (|has| |#1| (-368)) (|has| |#1| (-38 (-413 (-570))))) ((-654 |#1|) . T) ((-654 |#2|) |has| |#1| (-368)) ((-654 $) . T) ((-646 #1#) -2740 (|has| |#1| (-368)) (|has| |#1| (-38 (-413 (-570))))) ((-646 |#1|) |has| |#1| (-174)) ((-646 |#2|) |has| |#1| (-368)) ((-646 $) -2740 (|has| |#1| (-562)) (|has| |#1| (-368))) ((-645 (-570)) -12 (|has| |#1| (-368)) (|has| |#2| (-645 (-570)))) ((-645 |#2|) |has| |#1| (-368)) ((-723 #1#) -2740 (|has| |#1| (-368)) (|has| |#1| (-38 (-413 (-570))))) ((-723 |#1|) |has| |#1| (-174)) ((-723 |#2|) |has| |#1| (-368)) ((-723 $) -2740 (|has| |#1| (-562)) (|has| |#1| (-368))) ((-732) . 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T) ((-652 |#1|) . T) ((-652 |#2|) |has| |#1| (-368)) ((-652 $) . T) ((-654 #1#) -2892 (|has| |#1| (-368)) (|has| |#1| (-38 (-413 (-570))))) ((-654 |#1|) . T) ((-654 |#2|) |has| |#1| (-368)) ((-654 $) . T) ((-646 #1#) -2892 (|has| |#1| (-368)) (|has| |#1| (-38 (-413 (-570))))) ((-646 |#1|) |has| |#1| (-174)) ((-646 |#2|) |has| |#1| (-368)) ((-646 $) -2892 (|has| |#1| (-562)) (|has| |#1| (-368))) ((-645 (-570)) -12 (|has| |#1| (-368)) (|has| |#2| (-645 (-570)))) ((-645 |#2|) |has| |#1| (-368)) ((-723 #1#) -2892 (|has| |#1| (-368)) (|has| |#1| (-38 (-413 (-570))))) ((-723 |#1|) |has| |#1| (-174)) ((-723 |#2|) |has| |#1| (-368)) ((-723 $) -2892 (|has| |#1| (-562)) (|has| |#1| (-368))) ((-732) . 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T) ((-1060 #1#) |has| |#1| (-38 (-413 (-570)))) ((-1060 |#1|) . T) ((-1060 $) -2892 (|has| |#1| (-916)) (|has| |#1| (-562)) (|has| |#1| (-458)) (|has| |#1| (-368)) (|has| |#1| (-174))) ((-1065 #1#) |has| |#1| (-38 (-413 (-570)))) ((-1065 |#1|) . T) ((-1065 $) -2892 (|has| |#1| (-916)) (|has| |#1| (-562)) (|has| |#1| (-458)) (|has| |#1| (-368)) (|has| |#1| (-174))) ((-1058) . T) ((-1067) . T) ((-1121) . T) ((-1109) . 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3209707 3211025 3211600 "XPR" 3212626 NIL XPR (NIL T T) -8 NIL NIL NIL) (-1299 3207428 3209038 3209242 "XPOLY" 3209538 NIL XPOLY (NIL T) -8 NIL NIL NIL) (-1298 3205081 3206449 3206504 "XPOLYC" 3206792 NIL XPOLYC (NIL T T) -9 NIL 3206905 NIL) (-1297 3201457 3203598 3203986 "XPBWPOLY" 3204739 NIL XPBWPOLY (NIL T T) -8 NIL NIL NIL) (-1296 3197152 3199447 3199489 "XF" 3200110 NIL XF (NIL T) -9 NIL 3200510 NIL) (-1295 3196773 3196861 3197030 "XF-" 3197035 NIL XF- (NIL T T) -8 NIL NIL NIL) (-1294 3191969 3193258 3193313 "XFALG" 3195485 NIL XFALG (NIL T T) -9 NIL 3196274 NIL) (-1293 3191102 3191206 3191411 "XEXPPKG" 3191861 NIL XEXPPKG (NIL T T T) -7 NIL NIL NIL) (-1292 3189211 3190952 3191048 "XDPOLY" 3191053 NIL XDPOLY (NIL T T) -8 NIL NIL NIL) (-1291 3188018 3188618 3188661 "XALG" 3188666 NIL XALG (NIL T) -9 NIL 3188777 NIL) (-1290 3181460 3185995 3186489 "WUTSET" 3187610 NIL WUTSET (NIL T T T T) -8 NIL NIL NIL) (-1289 3179716 3180512 3180835 "WP" 3181271 NIL WP (NIL T T T T NIL NIL NIL) -8 NIL NIL NIL) (-1288 3179318 3179538 3179608 "WHILEAST" 3179668 T WHILEAST (NIL) -8 NIL NIL NIL) (-1287 3178790 3179035 3179129 "WHEREAST" 3179246 T WHEREAST (NIL) -8 NIL NIL NIL) (-1286 3177676 3177874 3178169 "WFFINTBS" 3178587 NIL WFFINTBS (NIL T T T T) -7 NIL NIL NIL) (-1285 3175580 3176007 3176469 "WEIER" 3177248 NIL WEIER (NIL T) -7 NIL NIL NIL) (-1284 3174626 3175076 3175118 "VSPACE" 3175254 NIL VSPACE (NIL T) -9 NIL 3175328 NIL) (-1283 3174464 3174491 3174582 "VSPACE-" 3174587 NIL VSPACE- (NIL T T) -8 NIL NIL NIL) (-1282 3174273 3174315 3174383 "VOID" 3174418 T VOID (NIL) -8 NIL NIL NIL) (-1281 3172409 3172768 3173174 "VIEW" 3173889 T VIEW (NIL) -7 NIL NIL NIL) (-1280 3168833 3169472 3170209 "VIEWDEF" 3171694 T VIEWDEF (NIL) -7 NIL NIL NIL) (-1279 3158137 3160381 3162554 "VIEW3D" 3166682 T VIEW3D (NIL) -8 NIL NIL NIL) (-1278 3150388 3152048 3153627 "VIEW2D" 3156580 T VIEW2D (NIL) -8 NIL NIL NIL) (-1277 3145741 3150158 3150250 "VECTOR" 3150331 NIL VECTOR (NIL T) -8 NIL NIL NIL) (-1276 3144318 3144577 3144895 "VECTOR2" 3145471 NIL VECTOR2 (NIL T T) -7 NIL NIL NIL) (-1275 3137792 3142099 3142142 "VECTCAT" 3143137 NIL VECTCAT (NIL T) -9 NIL 3143724 NIL) (-1274 3136806 3137060 3137450 "VECTCAT-" 3137455 NIL VECTCAT- (NIL T T) -8 NIL NIL NIL) (-1273 3136260 3136457 3136577 "VARIABLE" 3136721 NIL VARIABLE (NIL NIL) -8 NIL NIL NIL) (-1272 3136193 3136198 3136228 "UTYPE" 3136233 T UTYPE (NIL) -9 NIL NIL NIL) (-1271 3135023 3135177 3135439 "UTSODETL" 3136019 NIL UTSODETL (NIL T T T T) -7 NIL NIL NIL) (-1270 3132463 3132923 3133447 "UTSODE" 3134564 NIL UTSODE (NIL T T) -7 NIL NIL NIL) (-1269 3124300 3130089 3130578 "UTS" 3132032 NIL UTS (NIL T NIL NIL) -8 NIL NIL NIL) (-1268 3115174 3120541 3120584 "UTSCAT" 3121696 NIL UTSCAT (NIL T) -9 NIL 3122454 NIL) (-1267 3112521 3113244 3114233 "UTSCAT-" 3114238 NIL UTSCAT- (NIL T T) -8 NIL NIL NIL) (-1266 3112148 3112191 3112324 "UTS2" 3112472 NIL UTS2 (NIL T T T T) -7 NIL NIL NIL) (-1265 3106374 3108986 3109029 "URAGG" 3111099 NIL URAGG (NIL T) -9 NIL 3111822 NIL) (-1264 3103313 3104176 3105299 "URAGG-" 3105304 NIL URAGG- (NIL T T) -8 NIL NIL NIL) (-1263 3099022 3101948 3102413 "UPXSSING" 3102977 NIL UPXSSING (NIL T T NIL NIL) -8 NIL NIL NIL) (-1262 3091088 3098269 3098542 "UPXS" 3098807 NIL UPXS (NIL T NIL NIL) -8 NIL NIL NIL) (-1261 3084161 3090992 3091064 "UPXSCONS" 3091069 NIL UPXSCONS (NIL T T) -8 NIL NIL NIL) (-1260 3073906 3080699 3080761 "UPXSCCA" 3081335 NIL UPXSCCA (NIL T T) -9 NIL 3081568 NIL) (-1259 3073544 3073629 3073803 "UPXSCCA-" 3073808 NIL UPXSCCA- (NIL T T T) -8 NIL NIL NIL) (-1258 3063141 3069707 3069750 "UPXSCAT" 3070398 NIL UPXSCAT (NIL T) -9 NIL 3071007 NIL) (-1257 3062571 3062650 3062829 "UPXS2" 3063056 NIL UPXS2 (NIL T T NIL NIL NIL NIL) -7 NIL NIL NIL) (-1256 3061225 3061478 3061829 "UPSQFREE" 3062314 NIL UPSQFREE (NIL T T) -7 NIL NIL NIL) (-1255 3054646 3057703 3057758 "UPSCAT" 3058919 NIL UPSCAT (NIL T T) -9 NIL 3059693 NIL) (-1254 3053850 3054057 3054384 "UPSCAT-" 3054389 NIL UPSCAT- (NIL T T T) -8 NIL NIL NIL) (-1253 3039505 3047273 3047316 "UPOLYC" 3049417 NIL UPOLYC (NIL T) -9 NIL 3050638 NIL) (-1252 3030833 3033259 3036406 "UPOLYC-" 3036411 NIL UPOLYC- (NIL T T) -8 NIL NIL NIL) (-1251 3030460 3030503 3030636 "UPOLYC2" 3030784 NIL UPOLYC2 (NIL T T T T) -7 NIL NIL NIL) (-1250 3022271 3030143 3030272 "UP" 3030379 NIL UP (NIL NIL T) -8 NIL NIL NIL) (-1249 3021610 3021717 3021881 "UPMP" 3022160 NIL UPMP (NIL T T) -7 NIL NIL NIL) (-1248 3021163 3021244 3021383 "UPDIVP" 3021523 NIL UPDIVP (NIL T T) -7 NIL NIL NIL) (-1247 3019731 3019980 3020296 "UPDECOMP" 3020912 NIL UPDECOMP (NIL T T) -7 NIL NIL NIL) (-1246 3018962 3019074 3019260 "UPCDEN" 3019615 NIL UPCDEN (NIL T T T) -7 NIL NIL NIL) (-1245 3018481 3018550 3018699 "UP2" 3018887 NIL UP2 (NIL NIL T NIL T) -7 NIL NIL NIL) (-1244 3016948 3017685 3017962 "UNISEG" 3018239 NIL UNISEG (NIL T) -8 NIL NIL NIL) (-1243 3016163 3016290 3016495 "UNISEG2" 3016791 NIL UNISEG2 (NIL T T) -7 NIL NIL NIL) (-1242 3015223 3015403 3015629 "UNIFACT" 3015979 NIL UNIFACT (NIL T) -7 NIL NIL NIL) (-1241 2999155 3014400 3014651 "ULS" 3015030 NIL ULS (NIL T NIL NIL) -8 NIL NIL NIL) (-1240 2987153 2999059 2999131 "ULSCONS" 2999136 NIL ULSCONS (NIL T T) -8 NIL NIL NIL) (-1239 2969170 2981155 2981217 "ULSCCAT" 2981855 NIL ULSCCAT (NIL T T) -9 NIL 2982144 NIL) (-1238 2968220 2968465 2968853 "ULSCCAT-" 2968858 NIL ULSCCAT- (NIL T T T) -8 NIL NIL NIL) (-1237 2957594 2964074 2964117 "ULSCAT" 2964980 NIL ULSCAT (NIL T) -9 NIL 2965711 NIL) (-1236 2957024 2957103 2957282 "ULS2" 2957509 NIL ULS2 (NIL T T NIL NIL NIL NIL) -7 NIL NIL NIL) (-1235 2956151 2956661 2956768 "UINT8" 2956879 T UINT8 (NIL) -8 NIL NIL 2956964) (-1234 2955277 2955787 2955894 "UINT64" 2956005 T UINT64 (NIL) -8 NIL NIL 2956090) (-1233 2954403 2954913 2955020 "UINT32" 2955131 T UINT32 (NIL) -8 NIL NIL 2955216) (-1232 2953529 2954039 2954146 "UINT16" 2954257 T UINT16 (NIL) -8 NIL NIL 2954342) (-1231 2951832 2952789 2952819 "UFD" 2953031 T UFD (NIL) -9 NIL 2953145 NIL) (-1230 2951626 2951672 2951767 "UFD-" 2951772 NIL UFD- (NIL T) -8 NIL NIL NIL) (-1229 2950708 2950891 2951107 "UDVO" 2951432 T UDVO (NIL) -7 NIL NIL NIL) (-1228 2948524 2948933 2949404 "UDPO" 2950272 NIL UDPO (NIL T) -7 NIL NIL NIL) (-1227 2948457 2948462 2948492 "TYPE" 2948497 T TYPE (NIL) -9 NIL NIL NIL) (-1226 2948217 2948412 2948443 "TYPEAST" 2948448 T TYPEAST (NIL) -8 NIL NIL NIL) (-1225 2947188 2947390 2947630 "TWOFACT" 2948011 NIL TWOFACT (NIL T) -7 NIL NIL NIL) (-1224 2946211 2946597 2946832 "TUPLE" 2946988 NIL TUPLE (NIL T) -8 NIL NIL NIL) (-1223 2943902 2944421 2944960 "TUBETOOL" 2945694 T TUBETOOL (NIL) -7 NIL NIL NIL) (-1222 2942751 2942956 2943197 "TUBE" 2943695 NIL TUBE (NIL T) -8 NIL NIL NIL) (-1221 2937480 2941723 2942006 "TS" 2942503 NIL TS (NIL T) -8 NIL NIL NIL) (-1220 2926120 2930239 2930336 "TSETCAT" 2935605 NIL TSETCAT (NIL T T T T) -9 NIL 2937136 NIL) (-1219 2920852 2922452 2924343 "TSETCAT-" 2924348 NIL TSETCAT- (NIL T T T T T) -8 NIL NIL NIL) (-1218 2915491 2916338 2917267 "TRMANIP" 2919988 NIL TRMANIP (NIL T T) -7 NIL NIL NIL) (-1217 2914932 2914995 2915158 "TRIMAT" 2915423 NIL TRIMAT (NIL T T T T) -7 NIL NIL NIL) (-1216 2912798 2913035 2913392 "TRIGMNIP" 2914681 NIL TRIGMNIP (NIL T T) -7 NIL NIL NIL) (-1215 2912318 2912431 2912461 "TRIGCAT" 2912674 T TRIGCAT (NIL) -9 NIL NIL NIL) (-1214 2911987 2912066 2912207 "TRIGCAT-" 2912212 NIL TRIGCAT- (NIL T) -8 NIL NIL NIL) (-1213 2908832 2910845 2911126 "TREE" 2911741 NIL TREE (NIL T) -8 NIL NIL NIL) (-1212 2908106 2908634 2908664 "TRANFUN" 2908699 T TRANFUN (NIL) -9 NIL 2908765 NIL) (-1211 2907385 2907576 2907856 "TRANFUN-" 2907861 NIL TRANFUN- (NIL T) -8 NIL NIL NIL) (-1210 2907189 2907221 2907282 "TOPSP" 2907346 T TOPSP (NIL) -7 NIL NIL NIL) (-1209 2906537 2906652 2906806 "TOOLSIGN" 2907070 NIL TOOLSIGN (NIL T) -7 NIL NIL NIL) (-1208 2905171 2905714 2905953 "TEXTFILE" 2906320 T TEXTFILE (NIL) -8 NIL NIL NIL) (-1207 2903083 2903624 2904053 "TEX" 2904764 T TEX (NIL) -8 NIL NIL NIL) (-1206 2902864 2902895 2902967 "TEX1" 2903046 NIL TEX1 (NIL T) -7 NIL NIL NIL) (-1205 2902512 2902575 2902665 "TEMUTL" 2902796 T TEMUTL (NIL) -7 NIL NIL NIL) (-1204 2900666 2900946 2901271 "TBCMPPK" 2902235 NIL TBCMPPK (NIL T T) -7 NIL NIL NIL) (-1203 2892443 2898826 2898882 "TBAGG" 2899282 NIL TBAGG (NIL T T) -9 NIL 2899493 NIL) (-1202 2887513 2889001 2890755 "TBAGG-" 2890760 NIL TBAGG- (NIL T T T) -8 NIL NIL NIL) (-1201 2886897 2887004 2887149 "TANEXP" 2887402 NIL TANEXP (NIL T) -7 NIL NIL NIL) (-1200 2886408 2886672 2886762 "TALGOP" 2886842 NIL TALGOP (NIL T) -8 NIL NIL NIL) (-1199 2879798 2886265 2886358 "TABLE" 2886363 NIL TABLE (NIL T T) -8 NIL NIL NIL) (-1198 2879210 2879309 2879447 "TABLEAU" 2879695 NIL TABLEAU (NIL T) -8 NIL NIL NIL) (-1197 2873818 2875038 2876286 "TABLBUMP" 2877996 NIL TABLBUMP (NIL T) -7 NIL NIL NIL) (-1196 2873040 2873187 2873368 "SYSTEM" 2873659 T SYSTEM (NIL) -8 NIL NIL NIL) (-1195 2869499 2870198 2870981 "SYSSOLP" 2872291 NIL SYSSOLP (NIL T) -7 NIL NIL NIL) (-1194 2869297 2869454 2869485 "SYSPTR" 2869490 T SYSPTR (NIL) -8 NIL NIL NIL) (-1193 2868341 2868846 2868965 "SYSNNI" 2869151 NIL SYSNNI (NIL NIL) -8 NIL NIL 2869236) (-1192 2867648 2868107 2868186 "SYSINT" 2868246 NIL SYSINT (NIL NIL) -8 NIL NIL 2868291) (-1191 2863980 2864926 2865636 "SYNTAX" 2866960 T SYNTAX (NIL) -8 NIL NIL NIL) (-1190 2861138 2861740 2862372 "SYMTAB" 2863370 T SYMTAB (NIL) -8 NIL NIL NIL) (-1189 2856387 2857289 2858272 "SYMS" 2860177 T SYMS (NIL) -8 NIL NIL NIL) (-1188 2853622 2855845 2856075 "SYMPOLY" 2856192 NIL SYMPOLY (NIL T) -8 NIL NIL NIL) (-1187 2853139 2853214 2853337 "SYMFUNC" 2853534 NIL SYMFUNC (NIL T) -7 NIL NIL NIL) (-1186 2849159 2850451 2851264 "SYMBOL" 2852348 T SYMBOL (NIL) -8 NIL NIL NIL) (-1185 2842698 2844387 2846107 "SWITCH" 2847461 T SWITCH (NIL) -8 NIL NIL NIL) (-1184 2835932 2841519 2841822 "SUTS" 2842453 NIL SUTS (NIL T NIL NIL) -8 NIL NIL NIL) (-1183 2827998 2835179 2835452 "SUPXS" 2835717 NIL SUPXS (NIL T NIL NIL) -8 NIL NIL NIL) (-1182 2819757 2827616 2827742 "SUP" 2827907 NIL SUP (NIL T) -8 NIL NIL NIL) (-1181 2818916 2819043 2819260 "SUPFRACF" 2819625 NIL SUPFRACF (NIL T T T T) -7 NIL NIL NIL) (-1180 2818537 2818596 2818709 "SUP2" 2818851 NIL SUP2 (NIL T T) -7 NIL NIL NIL) (-1179 2816985 2817259 2817615 "SUMRF" 2818236 NIL SUMRF (NIL T) -7 NIL NIL NIL) (-1178 2816320 2816386 2816578 "SUMFS" 2816906 NIL SUMFS (NIL T T) -7 NIL NIL NIL) (-1177 2800287 2815497 2815748 "SULS" 2816127 NIL SULS (NIL T NIL NIL) -8 NIL NIL NIL) (-1176 2799889 2800109 2800179 "SUCHTAST" 2800239 T SUCHTAST (NIL) -8 NIL NIL NIL) (-1175 2799184 2799414 2799554 "SUCH" 2799797 NIL SUCH (NIL T T) -8 NIL NIL NIL) (-1174 2793050 2794090 2795049 "SUBSPACE" 2798272 NIL SUBSPACE (NIL NIL T) -8 NIL NIL NIL) (-1173 2792480 2792570 2792734 "SUBRESP" 2792938 NIL SUBRESP (NIL T T) -7 NIL NIL NIL) (-1172 2785846 2787145 2788456 "STTF" 2791216 NIL STTF (NIL T) -7 NIL NIL NIL) (-1171 2780019 2781139 2782286 "STTFNC" 2784746 NIL STTFNC (NIL T) -7 NIL NIL NIL) (-1170 2771330 2773201 2774995 "STTAYLOR" 2778260 NIL STTAYLOR (NIL T) -7 NIL NIL NIL) (-1169 2764460 2771194 2771277 "STRTBL" 2771282 NIL STRTBL (NIL T) -8 NIL NIL NIL) (-1168 2759824 2764415 2764446 "STRING" 2764451 T STRING (NIL) -8 NIL NIL NIL) (-1167 2754685 2759197 2759227 "STRICAT" 2759286 T STRICAT (NIL) -9 NIL 2759348 NIL) (-1166 2747438 2752304 2752915 "STREAM" 2754109 NIL STREAM (NIL T) -8 NIL NIL NIL) (-1165 2746948 2747025 2747169 "STREAM3" 2747355 NIL STREAM3 (NIL T T T) -7 NIL NIL NIL) (-1164 2745930 2746113 2746348 "STREAM2" 2746761 NIL STREAM2 (NIL T T) -7 NIL NIL NIL) (-1163 2745618 2745670 2745763 "STREAM1" 2745872 NIL STREAM1 (NIL T) -7 NIL NIL NIL) (-1162 2744634 2744815 2745046 "STINPROD" 2745434 NIL STINPROD (NIL T) -7 NIL NIL NIL) (-1161 2744186 2744396 2744426 "STEP" 2744506 T STEP (NIL) -9 NIL 2744584 NIL) (-1160 2743373 2743675 2743823 "STEPAST" 2744060 T STEPAST (NIL) -8 NIL NIL NIL) (-1159 2736805 2743272 2743349 "STBL" 2743354 NIL STBL (NIL T T NIL) -8 NIL NIL NIL) (-1158 2731931 2736026 2736069 "STAGG" 2736222 NIL STAGG (NIL T) -9 NIL 2736311 NIL) (-1157 2729633 2730235 2731107 "STAGG-" 2731112 NIL STAGG- (NIL T T) -8 NIL NIL NIL) (-1156 2727780 2729403 2729495 "STACK" 2729576 NIL STACK (NIL T) -8 NIL NIL NIL) (-1155 2720475 2725921 2726377 "SREGSET" 2727410 NIL SREGSET (NIL T T T T) -8 NIL NIL NIL) (-1154 2712900 2714269 2715782 "SRDCMPK" 2719081 NIL SRDCMPK (NIL T T T T T) -7 NIL NIL NIL) (-1153 2705817 2710340 2710370 "SRAGG" 2711673 T SRAGG (NIL) -9 NIL 2712281 NIL) (-1152 2704834 2705089 2705468 "SRAGG-" 2705473 NIL SRAGG- (NIL T) -8 NIL NIL NIL) (-1151 2699294 2703781 2704202 "SQMATRIX" 2704460 NIL SQMATRIX (NIL NIL T) -8 NIL NIL NIL) (-1150 2692979 2696012 2696739 "SPLTREE" 2698639 NIL SPLTREE (NIL T T) -8 NIL NIL NIL) (-1149 2688942 2689635 2690281 "SPLNODE" 2692405 NIL SPLNODE (NIL T T) -8 NIL NIL NIL) (-1148 2687989 2688222 2688252 "SPFCAT" 2688696 T SPFCAT (NIL) -9 NIL NIL NIL) (-1147 2686726 2686936 2687200 "SPECOUT" 2687747 T SPECOUT (NIL) -7 NIL NIL NIL) (-1146 2677836 2679708 2679738 "SPADXPT" 2684414 T SPADXPT (NIL) -9 NIL 2686578 NIL) (-1145 2677597 2677637 2677706 "SPADPRSR" 2677789 T SPADPRSR (NIL) -7 NIL NIL NIL) (-1144 2675646 2677552 2677583 "SPADAST" 2677588 T SPADAST (NIL) -8 NIL NIL NIL) (-1143 2667591 2669364 2669407 "SPACEC" 2673780 NIL SPACEC (NIL T) -9 NIL 2675596 NIL) (-1142 2665721 2667523 2667572 "SPACE3" 2667577 NIL SPACE3 (NIL T) -8 NIL NIL NIL) (-1141 2664473 2664644 2664935 "SORTPAK" 2665526 NIL SORTPAK (NIL T T) -7 NIL NIL NIL) (-1140 2662565 2662868 2663280 "SOLVETRA" 2664137 NIL SOLVETRA (NIL T) -7 NIL NIL NIL) (-1139 2661615 2661837 2662098 "SOLVESER" 2662338 NIL SOLVESER (NIL T) -7 NIL NIL NIL) (-1138 2656919 2657807 2658802 "SOLVERAD" 2660667 NIL SOLVERAD (NIL T) -7 NIL NIL NIL) (-1137 2652734 2653343 2654072 "SOLVEFOR" 2656286 NIL SOLVEFOR (NIL T T) -7 NIL NIL NIL) (-1136 2647004 2652083 2652180 "SNTSCAT" 2652185 NIL SNTSCAT (NIL T T T T) -9 NIL 2652255 NIL) (-1135 2641110 2645327 2645718 "SMTS" 2646694 NIL SMTS (NIL T T T) -8 NIL NIL NIL) (-1134 2635795 2640998 2641075 "SMP" 2641080 NIL SMP (NIL T T) -8 NIL NIL NIL) (-1133 2633954 2634255 2634653 "SMITH" 2635492 NIL SMITH (NIL T T T T) -7 NIL NIL NIL) (-1132 2626667 2630863 2630966 "SMATCAT" 2632317 NIL SMATCAT (NIL NIL T T T) -9 NIL 2632867 NIL) (-1131 2623607 2624430 2625608 "SMATCAT-" 2625613 NIL SMATCAT- (NIL T NIL T T T) -8 NIL NIL NIL) (-1130 2621273 2622843 2622886 "SKAGG" 2623147 NIL SKAGG (NIL T) -9 NIL 2623282 NIL) (-1129 2617599 2620746 2620930 "SINT" 2621082 T SINT (NIL) -8 NIL NIL 2621244) (-1128 2617371 2617409 2617475 "SIMPAN" 2617555 T SIMPAN (NIL) -7 NIL NIL NIL) (-1127 2616650 2616906 2617046 "SIG" 2617253 T SIG (NIL) -8 NIL NIL NIL) (-1126 2615488 2615709 2615984 "SIGNRF" 2616409 NIL SIGNRF (NIL T) -7 NIL NIL NIL) (-1125 2614321 2614472 2614756 "SIGNEF" 2615317 NIL SIGNEF (NIL T T) -7 NIL NIL NIL) (-1124 2613627 2613904 2614028 "SIGAST" 2614219 T SIGAST (NIL) -8 NIL NIL NIL) (-1123 2611317 2611771 2612277 "SHP" 2613168 NIL SHP (NIL T NIL) -7 NIL NIL NIL) (-1122 2605169 2611218 2611294 "SHDP" 2611299 NIL SHDP (NIL NIL NIL T) -8 NIL NIL NIL) (-1121 2604742 2604934 2604964 "SGROUP" 2605057 T SGROUP (NIL) -9 NIL 2605119 NIL) (-1120 2604600 2604626 2604699 "SGROUP-" 2604704 NIL SGROUP- (NIL T) -8 NIL NIL NIL) (-1119 2601435 2602133 2602856 "SGCF" 2603899 T SGCF (NIL) -7 NIL NIL NIL) (-1118 2595803 2600882 2600979 "SFRTCAT" 2600984 NIL SFRTCAT (NIL T T T T) -9 NIL 2601023 NIL) (-1117 2589224 2590242 2591378 "SFRGCD" 2594786 NIL SFRGCD (NIL T T T T T) -7 NIL NIL NIL) (-1116 2582350 2583423 2584609 "SFQCMPK" 2588157 NIL SFQCMPK (NIL T T T T T) -7 NIL NIL NIL) (-1115 2581970 2582059 2582170 "SFORT" 2582291 NIL SFORT (NIL T T) -8 NIL NIL NIL) (-1114 2581088 2581810 2581931 "SEXOF" 2581936 NIL SEXOF (NIL T T T T T) -8 NIL NIL NIL) (-1113 2580195 2580969 2581037 "SEX" 2581042 T SEX (NIL) -8 NIL NIL NIL) (-1112 2575708 2576423 2576518 "SEXCAT" 2579455 NIL SEXCAT (NIL T T T T T) -9 NIL 2580033 NIL) (-1111 2572861 2575642 2575690 "SET" 2575695 NIL SET (NIL T) -8 NIL NIL NIL) (-1110 2571085 2571574 2571879 "SETMN" 2572602 NIL SETMN (NIL NIL NIL) -8 NIL NIL NIL) (-1109 2570581 2570733 2570763 "SETCAT" 2570939 T SETCAT (NIL) -9 NIL 2571049 NIL) (-1108 2570273 2570351 2570481 "SETCAT-" 2570486 NIL SETCAT- (NIL T) -8 NIL NIL NIL) (-1107 2566634 2568734 2568777 "SETAGG" 2569647 NIL SETAGG (NIL T) -9 NIL 2569987 NIL) (-1106 2566092 2566208 2566445 "SETAGG-" 2566450 NIL SETAGG- (NIL T T) -8 NIL NIL NIL) (-1105 2565535 2565788 2565889 "SEQAST" 2566013 T SEQAST (NIL) -8 NIL NIL NIL) (-1104 2564734 2565028 2565089 "SEGXCAT" 2565375 NIL SEGXCAT (NIL T T) -9 NIL 2565495 NIL) (-1103 2563740 2564400 2564582 "SEG" 2564587 NIL SEG (NIL T) -8 NIL NIL NIL) (-1102 2562719 2562933 2562976 "SEGCAT" 2563498 NIL SEGCAT (NIL T) -9 NIL 2563719 NIL) (-1101 2561651 2562082 2562290 "SEGBIND" 2562546 NIL SEGBIND (NIL T) -8 NIL NIL NIL) (-1100 2561272 2561331 2561444 "SEGBIND2" 2561586 NIL SEGBIND2 (NIL T T) -7 NIL NIL NIL) (-1099 2560845 2561073 2561150 "SEGAST" 2561217 T SEGAST (NIL) -8 NIL NIL NIL) (-1098 2560064 2560190 2560394 "SEG2" 2560689 NIL SEG2 (NIL T T) -7 NIL NIL NIL) (-1097 2559474 2559999 2560046 "SDVAR" 2560051 NIL SDVAR (NIL T) -8 NIL NIL NIL) (-1096 2552001 2559244 2559374 "SDPOL" 2559379 NIL SDPOL (NIL T) -8 NIL NIL NIL) (-1095 2550594 2550860 2551179 "SCPKG" 2551716 NIL SCPKG (NIL T) -7 NIL NIL NIL) (-1094 2549758 2549930 2550122 "SCOPE" 2550424 T SCOPE (NIL) -8 NIL NIL NIL) (-1093 2548978 2549112 2549291 "SCACHE" 2549613 NIL SCACHE (NIL T) -7 NIL NIL NIL) (-1092 2548624 2548810 2548840 "SASTCAT" 2548845 T SASTCAT (NIL) -9 NIL 2548858 NIL) (-1091 2548111 2548459 2548535 "SAOS" 2548570 T SAOS (NIL) -8 NIL NIL NIL) (-1090 2547676 2547711 2547884 "SAERFFC" 2548070 NIL SAERFFC (NIL T T T) -7 NIL NIL NIL) (-1089 2541615 2547573 2547653 "SAE" 2547658 NIL SAE (NIL T T NIL) -8 NIL NIL NIL) (-1088 2541208 2541243 2541402 "SAEFACT" 2541574 NIL SAEFACT (NIL T T T) -7 NIL NIL NIL) (-1087 2539529 2539843 2540244 "RURPK" 2540874 NIL RURPK (NIL T NIL) -7 NIL NIL NIL) (-1086 2538166 2538472 2538777 "RULESET" 2539363 NIL RULESET (NIL T T T) -8 NIL NIL NIL) (-1085 2535389 2535919 2536377 "RULE" 2537847 NIL RULE (NIL T T T) -8 NIL NIL NIL) (-1084 2535001 2535183 2535266 "RULECOLD" 2535341 NIL RULECOLD (NIL NIL) -8 NIL NIL NIL) (-1083 2534791 2534819 2534890 "RTVALUE" 2534952 T RTVALUE (NIL) -8 NIL NIL NIL) (-1082 2534262 2534508 2534602 "RSTRCAST" 2534719 T RSTRCAST (NIL) -8 NIL NIL NIL) (-1081 2529110 2529905 2530825 "RSETGCD" 2533461 NIL RSETGCD (NIL T T T T T) -7 NIL NIL NIL) (-1080 2518340 2523419 2523516 "RSETCAT" 2527635 NIL RSETCAT (NIL T T T T) -9 NIL 2528732 NIL) (-1079 2516267 2516806 2517630 "RSETCAT-" 2517635 NIL RSETCAT- (NIL T T T T T) -8 NIL NIL NIL) (-1078 2508653 2510029 2511549 "RSDCMPK" 2514866 NIL RSDCMPK (NIL T T T T T) -7 NIL NIL NIL) (-1077 2506632 2507099 2507173 "RRCC" 2508259 NIL RRCC (NIL T T) -9 NIL 2508603 NIL) (-1076 2505983 2506157 2506436 "RRCC-" 2506441 NIL RRCC- (NIL T T T) -8 NIL NIL NIL) (-1075 2505426 2505679 2505780 "RPTAST" 2505904 T RPTAST (NIL) -8 NIL NIL NIL) (-1074 2479272 2488631 2488698 "RPOLCAT" 2499364 NIL RPOLCAT (NIL T T T) -9 NIL 2502524 NIL) (-1073 2470770 2473110 2476232 "RPOLCAT-" 2476237 NIL RPOLCAT- (NIL T T T T) -8 NIL NIL NIL) (-1072 2461701 2468981 2469463 "ROUTINE" 2470310 T ROUTINE (NIL) -8 NIL NIL NIL) (-1071 2458499 2461327 2461467 "ROMAN" 2461583 T ROMAN (NIL) -8 NIL NIL NIL) (-1070 2456743 2457359 2457619 "ROIRC" 2458304 NIL ROIRC (NIL T T) -8 NIL NIL NIL) (-1069 2452975 2455259 2455289 "RNS" 2455593 T RNS (NIL) -9 NIL 2455867 NIL) (-1068 2451484 2451867 2452401 "RNS-" 2452476 NIL RNS- (NIL T) -8 NIL NIL NIL) (-1067 2450887 2451295 2451325 "RNG" 2451330 T RNG (NIL) -9 NIL 2451351 NIL) (-1066 2449890 2450252 2450454 "RNGBIND" 2450738 NIL RNGBIND (NIL T T) -8 NIL NIL NIL) (-1065 2449289 2449677 2449720 "RMODULE" 2449725 NIL RMODULE (NIL T) -9 NIL 2449752 NIL) (-1064 2448125 2448219 2448555 "RMCAT2" 2449190 NIL RMCAT2 (NIL NIL NIL T T T T T T T T) -7 NIL NIL NIL) (-1063 2444975 2447471 2447768 "RMATRIX" 2447887 NIL RMATRIX (NIL NIL NIL T) -8 NIL NIL NIL) (-1062 2437802 2440062 2440177 "RMATCAT" 2443536 NIL RMATCAT (NIL NIL NIL T T T) -9 NIL 2444518 NIL) (-1061 2437177 2437324 2437631 "RMATCAT-" 2437636 NIL RMATCAT- (NIL T NIL NIL T T T) -8 NIL NIL NIL) (-1060 2436578 2436799 2436842 "RLINSET" 2437036 NIL RLINSET (NIL T) -9 NIL 2437127 NIL) (-1059 2436145 2436220 2436348 "RINTERP" 2436497 NIL RINTERP (NIL NIL T) -7 NIL NIL NIL) (-1058 2435203 2435757 2435787 "RING" 2435843 T RING (NIL) -9 NIL 2435935 NIL) (-1057 2434995 2435039 2435136 "RING-" 2435141 NIL RING- (NIL T) -8 NIL NIL NIL) (-1056 2433836 2434073 2434331 "RIDIST" 2434759 T RIDIST (NIL) -7 NIL NIL NIL) (-1055 2425125 2433304 2433510 "RGCHAIN" 2433684 NIL RGCHAIN (NIL T NIL) -8 NIL NIL NIL) (-1054 2424475 2424881 2424922 "RGBCSPC" 2424980 NIL RGBCSPC (NIL T) -9 NIL 2425032 NIL) (-1053 2423633 2424014 2424055 "RGBCMDL" 2424287 NIL RGBCMDL (NIL T) -9 NIL 2424401 NIL) (-1052 2420627 2421241 2421911 "RF" 2422997 NIL RF (NIL T) -7 NIL NIL NIL) (-1051 2420273 2420336 2420439 "RFFACTOR" 2420558 NIL RFFACTOR (NIL T) -7 NIL NIL NIL) (-1050 2419998 2420033 2420130 "RFFACT" 2420232 NIL RFFACT (NIL T) -7 NIL NIL NIL) (-1049 2418115 2418479 2418861 "RFDIST" 2419638 T RFDIST (NIL) -7 NIL NIL NIL) (-1048 2417568 2417660 2417823 "RETSOL" 2418017 NIL RETSOL (NIL T T) -7 NIL NIL NIL) (-1047 2417204 2417284 2417327 "RETRACT" 2417460 NIL RETRACT (NIL T) -9 NIL 2417547 NIL) (-1046 2417053 2417078 2417165 "RETRACT-" 2417170 NIL RETRACT- (NIL T T) -8 NIL NIL NIL) (-1045 2416655 2416875 2416945 "RETAST" 2417005 T RETAST (NIL) -8 NIL NIL NIL) (-1044 2409393 2416308 2416435 "RESULT" 2416550 T RESULT (NIL) -8 NIL NIL NIL) (-1043 2407984 2408662 2408861 "RESRING" 2409296 NIL RESRING (NIL T T T T NIL) -8 NIL NIL NIL) (-1042 2407620 2407669 2407767 "RESLATC" 2407921 NIL RESLATC (NIL T) -7 NIL NIL NIL) (-1041 2407325 2407360 2407467 "REPSQ" 2407579 NIL REPSQ (NIL T) -7 NIL NIL NIL) (-1040 2404747 2405327 2405929 "REP" 2406745 T REP (NIL) -7 NIL NIL NIL) (-1039 2404444 2404479 2404590 "REPDB" 2404706 NIL REPDB (NIL T) -7 NIL NIL NIL) (-1038 2398344 2399733 2400956 "REP2" 2403256 NIL REP2 (NIL T) -7 NIL NIL NIL) (-1037 2394721 2395402 2396210 "REP1" 2397571 NIL REP1 (NIL T) -7 NIL NIL NIL) (-1036 2387417 2392862 2393318 "REGSET" 2394351 NIL REGSET (NIL T T T T) -8 NIL NIL NIL) (-1035 2386182 2386565 2386815 "REF" 2387202 NIL REF (NIL T) -8 NIL NIL NIL) (-1034 2385559 2385662 2385829 "REDORDER" 2386066 NIL REDORDER (NIL T T) -7 NIL NIL NIL) (-1033 2381527 2384772 2384999 "RECLOS" 2385387 NIL RECLOS (NIL T) -8 NIL NIL NIL) (-1032 2380579 2380760 2380975 "REALSOLV" 2381334 T REALSOLV (NIL) -7 NIL NIL NIL) (-1031 2380425 2380466 2380496 "REAL" 2380501 T REAL (NIL) -9 NIL 2380536 NIL) (-1030 2376908 2377710 2378594 "REAL0Q" 2379590 NIL REAL0Q (NIL T) -7 NIL NIL NIL) (-1029 2372509 2373497 2374558 "REAL0" 2375889 NIL REAL0 (NIL T) -7 NIL NIL NIL) (-1028 2371980 2372226 2372320 "RDUCEAST" 2372437 T RDUCEAST (NIL) -8 NIL NIL NIL) (-1027 2371385 2371457 2371664 "RDIV" 2371902 NIL RDIV (NIL T T T T T) -7 NIL NIL NIL) (-1026 2370453 2370627 2370840 "RDIST" 2371207 NIL RDIST (NIL T) -7 NIL NIL NIL) (-1025 2369050 2369337 2369709 "RDETRS" 2370161 NIL RDETRS (NIL T T) -7 NIL NIL NIL) (-1024 2366862 2367316 2367854 "RDETR" 2368592 NIL RDETR (NIL T T) -7 NIL NIL NIL) (-1023 2365487 2365765 2366162 "RDEEFS" 2366578 NIL RDEEFS (NIL T T) -7 NIL NIL NIL) (-1022 2363996 2364302 2364727 "RDEEF" 2365175 NIL RDEEF (NIL T T) -7 NIL NIL NIL) (-1021 2358057 2360977 2361007 "RCFIELD" 2362302 T RCFIELD (NIL) -9 NIL 2363033 NIL) (-1020 2356121 2356625 2357321 "RCFIELD-" 2357396 NIL RCFIELD- (NIL T) -8 NIL NIL NIL) (-1019 2352390 2354222 2354265 "RCAGG" 2355349 NIL RCAGG (NIL T) -9 NIL 2355814 NIL) (-1018 2352018 2352112 2352275 "RCAGG-" 2352280 NIL RCAGG- (NIL T T) -8 NIL NIL NIL) (-1017 2351353 2351465 2351630 "RATRET" 2351902 NIL RATRET (NIL T) -7 NIL NIL NIL) (-1016 2350906 2350973 2351094 "RATFACT" 2351281 NIL RATFACT (NIL T) -7 NIL NIL NIL) (-1015 2350214 2350334 2350486 "RANDSRC" 2350776 T RANDSRC (NIL) -7 NIL NIL NIL) (-1014 2349948 2349992 2350065 "RADUTIL" 2350163 T RADUTIL (NIL) -7 NIL NIL NIL) (-1013 2343062 2348779 2349090 "RADIX" 2349671 NIL RADIX (NIL NIL) -8 NIL NIL NIL) (-1012 2334681 2342904 2343034 "RADFF" 2343039 NIL RADFF (NIL T T T NIL NIL) -8 NIL NIL NIL) (-1011 2334328 2334403 2334433 "RADCAT" 2334593 T RADCAT (NIL) -9 NIL NIL NIL) (-1010 2334110 2334158 2334258 "RADCAT-" 2334263 NIL RADCAT- (NIL T) -8 NIL NIL NIL) (-1009 2332208 2333880 2333972 "QUEUE" 2334053 NIL QUEUE (NIL T) -8 NIL NIL NIL) (-1008 2328745 2332141 2332189 "QUAT" 2332194 NIL QUAT (NIL T) -8 NIL NIL NIL) (-1007 2328376 2328419 2328550 "QUATCT2" 2328696 NIL QUATCT2 (NIL T T T T) -7 NIL NIL NIL) (-1006 2321825 2325170 2325212 "QUATCAT" 2326003 NIL QUATCAT (NIL T) -9 NIL 2326769 NIL) (-1005 2317964 2319001 2320391 "QUATCAT-" 2320487 NIL QUATCAT- (NIL T T) -8 NIL NIL NIL) (-1004 2315429 2317040 2317083 "QUAGG" 2317464 NIL QUAGG (NIL T) -9 NIL 2317639 NIL) (-1003 2315031 2315251 2315321 "QQUTAST" 2315381 T QQUTAST (NIL) -8 NIL NIL NIL) (-1002 2313924 2314424 2314598 "QFORM" 2314903 NIL QFORM (NIL NIL T) -8 NIL NIL NIL) (-1001 2304917 2310156 2310198 "QFCAT" 2310866 NIL QFCAT (NIL T) -9 NIL 2311867 NIL) (-1000 2300484 2301685 2303279 "QFCAT-" 2303375 NIL QFCAT- (NIL T T) -8 NIL NIL NIL) (-999 2300118 2300161 2300290 "QFCAT2" 2300435 NIL QFCAT2 (NIL T T T T) -7 NIL NIL NIL) (-998 2299578 2299688 2299818 "QEQUAT" 2300008 T QEQUAT (NIL) -8 NIL NIL NIL) (-997 2292724 2293797 2294981 "QCMPACK" 2298511 NIL QCMPACK (NIL T T T T T) -7 NIL NIL NIL) (-996 2290273 2290721 2291149 "QALGSET" 2292379 NIL QALGSET (NIL T T T T) -8 NIL NIL NIL) (-995 2289518 2289692 2289924 "QALGSET2" 2290093 NIL QALGSET2 (NIL NIL NIL) -7 NIL NIL NIL) (-994 2288208 2288432 2288749 "PWFFINTB" 2289291 NIL PWFFINTB (NIL T T T T) -7 NIL NIL NIL) (-993 2286390 2286558 2286912 "PUSHVAR" 2288022 NIL PUSHVAR (NIL T T T T) -7 NIL NIL NIL) (-992 2282308 2283362 2283403 "PTRANFN" 2285287 NIL PTRANFN (NIL T) -9 NIL NIL NIL) (-991 2280710 2281001 2281323 "PTPACK" 2282019 NIL PTPACK (NIL T) -7 NIL NIL NIL) (-990 2280342 2280399 2280508 "PTFUNC2" 2280647 NIL PTFUNC2 (NIL T T) -7 NIL NIL NIL) (-989 2274819 2279214 2279255 "PTCAT" 2279551 NIL PTCAT (NIL T) -9 NIL 2279704 NIL) (-988 2274477 2274512 2274636 "PSQFR" 2274778 NIL PSQFR (NIL T T T T) -7 NIL NIL NIL) (-987 2273072 2273370 2273704 "PSEUDLIN" 2274175 NIL PSEUDLIN (NIL T) -7 NIL NIL NIL) (-986 2259835 2262206 2264530 "PSETPK" 2270832 NIL PSETPK (NIL T T T T) -7 NIL NIL NIL) (-985 2252853 2255593 2255689 "PSETCAT" 2258710 NIL PSETCAT (NIL T T T T) -9 NIL 2259524 NIL) (-984 2250689 2251323 2252144 "PSETCAT-" 2252149 NIL PSETCAT- (NIL T T T T T) -8 NIL NIL NIL) (-983 2250038 2250203 2250231 "PSCURVE" 2250499 T PSCURVE (NIL) -9 NIL 2250666 NIL) (-982 2246036 2247552 2247617 "PSCAT" 2248461 NIL PSCAT (NIL T T T) -9 NIL 2248701 NIL) (-981 2245099 2245315 2245715 "PSCAT-" 2245720 NIL PSCAT- (NIL T T T T) -8 NIL NIL NIL) (-980 2243835 2244489 2244689 "PRTITION" 2244919 T PRTITION (NIL) -8 NIL NIL NIL) (-979 2243310 2243556 2243648 "PRTDAST" 2243763 T PRTDAST (NIL) -8 NIL NIL NIL) (-978 2232400 2234614 2236802 "PRS" 2241172 NIL PRS (NIL T T) -7 NIL NIL NIL) (-977 2230211 2231750 2231790 "PRQAGG" 2231973 NIL PRQAGG (NIL T) -9 NIL 2232075 NIL) (-976 2229547 2229852 2229880 "PROPLOG" 2230019 T PROPLOG (NIL) -9 NIL 2230134 NIL) (-975 2229151 2229208 2229331 "PROPFUN2" 2229470 NIL PROPFUN2 (NIL T T) -8 NIL NIL NIL) (-974 2228466 2228587 2228759 "PROPFUN1" 2229012 NIL PROPFUN1 (NIL T) -8 NIL NIL NIL) (-973 2226647 2227213 2227510 "PROPFRML" 2228202 NIL PROPFRML (NIL T) -8 NIL NIL NIL) (-972 2226116 2226223 2226351 "PROPERTY" 2226539 T PROPERTY (NIL) -8 NIL NIL NIL) (-971 2220174 2224282 2225102 "PRODUCT" 2225342 NIL PRODUCT (NIL T T) -8 NIL NIL NIL) (-970 2217452 2219632 2219866 "PR" 2219985 NIL PR (NIL T T) -8 NIL NIL NIL) (-969 2217248 2217280 2217339 "PRINT" 2217413 T PRINT (NIL) -7 NIL NIL NIL) (-968 2216588 2216705 2216857 "PRIMES" 2217128 NIL PRIMES (NIL T) -7 NIL NIL NIL) (-967 2214653 2215054 2215520 "PRIMELT" 2216167 NIL PRIMELT (NIL T) -7 NIL NIL NIL) (-966 2214382 2214431 2214459 "PRIMCAT" 2214583 T PRIMCAT (NIL) -9 NIL NIL NIL) (-965 2210497 2214320 2214365 "PRIMARR" 2214370 NIL PRIMARR (NIL T) -8 NIL NIL NIL) (-964 2209504 2209682 2209910 "PRIMARR2" 2210315 NIL PRIMARR2 (NIL T T) -7 NIL NIL NIL) (-963 2209147 2209203 2209314 "PREASSOC" 2209442 NIL PREASSOC (NIL T T) -7 NIL NIL NIL) (-962 2208622 2208755 2208783 "PPCURVE" 2208988 T PPCURVE (NIL) -9 NIL 2209124 NIL) (-961 2208217 2208417 2208500 "PORTNUM" 2208559 T PORTNUM (NIL) -8 NIL NIL NIL) (-960 2205576 2205975 2206567 "POLYROOT" 2207798 NIL POLYROOT (NIL T T T T T) -7 NIL NIL NIL) (-959 2199758 2205180 2205340 "POLY" 2205449 NIL POLY (NIL T) -8 NIL NIL NIL) (-958 2199141 2199199 2199433 "POLYLIFT" 2199694 NIL POLYLIFT (NIL T T T T T) -7 NIL NIL NIL) (-957 2195416 2195865 2196494 "POLYCATQ" 2198686 NIL POLYCATQ (NIL T T T T T) -7 NIL NIL NIL) (-956 2182128 2187256 2187321 "POLYCAT" 2190835 NIL POLYCAT (NIL T T T) -9 NIL 2192713 NIL) (-955 2175577 2177439 2179823 "POLYCAT-" 2179828 NIL POLYCAT- (NIL T T T T) -8 NIL NIL NIL) (-954 2175164 2175232 2175352 "POLY2UP" 2175503 NIL POLY2UP (NIL NIL T) -7 NIL NIL NIL) (-953 2174796 2174853 2174962 "POLY2" 2175101 NIL POLY2 (NIL T T) -7 NIL NIL NIL) (-952 2173481 2173720 2173996 "POLUTIL" 2174570 NIL POLUTIL (NIL T T) -7 NIL NIL NIL) (-951 2171836 2172113 2172444 "POLTOPOL" 2173203 NIL POLTOPOL (NIL NIL T) -7 NIL NIL NIL) (-950 2167301 2171772 2171818 "POINT" 2171823 NIL POINT (NIL T) -8 NIL NIL NIL) (-949 2165488 2165845 2166220 "PNTHEORY" 2166946 T PNTHEORY (NIL) -7 NIL NIL NIL) (-948 2163946 2164243 2164642 "PMTOOLS" 2165186 NIL PMTOOLS (NIL T T T) -7 NIL NIL NIL) (-947 2163539 2163617 2163734 "PMSYM" 2163862 NIL PMSYM (NIL T) -7 NIL NIL NIL) (-946 2163047 2163116 2163291 "PMQFCAT" 2163464 NIL PMQFCAT (NIL T T T) -7 NIL NIL NIL) (-945 2162402 2162512 2162668 "PMPRED" 2162924 NIL PMPRED (NIL T) -7 NIL NIL NIL) (-944 2161795 2161881 2162043 "PMPREDFS" 2162303 NIL PMPREDFS (NIL T T T) -7 NIL NIL NIL) (-943 2160459 2160667 2161045 "PMPLCAT" 2161557 NIL PMPLCAT (NIL T T T T T) -7 NIL NIL NIL) (-942 2159991 2160070 2160222 "PMLSAGG" 2160374 NIL PMLSAGG (NIL T T T) -7 NIL NIL NIL) (-941 2159464 2159540 2159722 "PMKERNEL" 2159909 NIL PMKERNEL (NIL T T) -7 NIL NIL NIL) (-940 2159081 2159156 2159269 "PMINS" 2159383 NIL PMINS (NIL T) -7 NIL NIL NIL) (-939 2158523 2158592 2158801 "PMFS" 2159006 NIL PMFS (NIL T T T) -7 NIL NIL NIL) (-938 2157751 2157869 2158074 "PMDOWN" 2158400 NIL PMDOWN (NIL T T T) -7 NIL NIL NIL) (-937 2156918 2157076 2157257 "PMASS" 2157590 T PMASS (NIL) -7 NIL NIL NIL) (-936 2156191 2156301 2156464 "PMASSFS" 2156805 NIL PMASSFS (NIL T T) -7 NIL NIL NIL) (-935 2155846 2155914 2156008 "PLOTTOOL" 2156117 T PLOTTOOL (NIL) -7 NIL NIL NIL) (-934 2150453 2151657 2152805 "PLOT" 2154718 T PLOT (NIL) -8 NIL NIL NIL) (-933 2146257 2147301 2148222 "PLOT3D" 2149552 T PLOT3D (NIL) -8 NIL NIL NIL) (-932 2145169 2145346 2145581 "PLOT1" 2146061 NIL PLOT1 (NIL T) -7 NIL NIL NIL) (-931 2120558 2125235 2130086 "PLEQN" 2140435 NIL PLEQN (NIL T T T T) -7 NIL NIL NIL) (-930 2119876 2119998 2120178 "PINTERP" 2120423 NIL PINTERP (NIL NIL T) -7 NIL NIL NIL) (-929 2119569 2119616 2119719 "PINTERPA" 2119823 NIL PINTERPA (NIL T T) -7 NIL NIL NIL) (-928 2118790 2119338 2119425 "PI" 2119465 T PI (NIL) -8 NIL NIL 2119532) (-927 2117087 2118062 2118090 "PID" 2118272 T PID (NIL) -9 NIL 2118406 NIL) (-926 2116838 2116875 2116950 "PICOERCE" 2117044 NIL PICOERCE (NIL T) -7 NIL NIL NIL) (-925 2116158 2116297 2116473 "PGROEB" 2116694 NIL PGROEB (NIL T) -7 NIL NIL NIL) (-924 2111745 2112559 2113464 "PGE" 2115273 T PGE (NIL) -7 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(-767 1782960 1783485 1783513 "NARNG" 1783630 T NARNG (NIL) -9 NIL 1783721 NIL) (-766 1782652 1782719 1782853 "NARNG-" 1782858 NIL NARNG- (NIL T) -8 NIL NIL NIL) (-765 1781531 1781738 1781973 "NAGSP" 1782437 T NAGSP (NIL) -7 NIL NIL NIL) (-764 1772803 1774487 1776160 "NAGS" 1779878 T NAGS (NIL) -7 NIL NIL NIL) (-763 1771351 1771659 1771990 "NAGF07" 1772492 T NAGF07 (NIL) -7 NIL NIL NIL) (-762 1765889 1767180 1768487 "NAGF04" 1770064 T NAGF04 (NIL) -7 NIL NIL NIL) (-761 1758857 1760471 1762104 "NAGF02" 1764276 T NAGF02 (NIL) -7 NIL NIL NIL) (-760 1754081 1755181 1756298 "NAGF01" 1757760 T NAGF01 (NIL) -7 NIL NIL NIL) (-759 1747709 1749275 1750860 "NAGE04" 1752516 T NAGE04 (NIL) -7 NIL NIL NIL) (-758 1738878 1740999 1743129 "NAGE02" 1745599 T NAGE02 (NIL) -7 NIL NIL NIL) (-757 1734831 1735778 1736742 "NAGE01" 1737934 T NAGE01 (NIL) -7 NIL NIL NIL) (-756 1732626 1733160 1733718 "NAGD03" 1734293 T NAGD03 (NIL) -7 NIL NIL NIL) (-755 1724376 1726304 1728258 "NAGD02" 1730692 T NAGD02 (NIL) -7 NIL NIL NIL) (-754 1718187 1719612 1721052 "NAGD01" 1722956 T NAGD01 (NIL) -7 NIL NIL NIL) (-753 1714396 1715218 1716055 "NAGC06" 1717370 T NAGC06 (NIL) -7 NIL NIL NIL) (-752 1712861 1713193 1713549 "NAGC05" 1714060 T NAGC05 (NIL) -7 NIL NIL NIL) (-751 1712237 1712356 1712500 "NAGC02" 1712737 T NAGC02 (NIL) -7 NIL NIL NIL) (-750 1711196 1711779 1711819 "NAALG" 1711898 NIL NAALG (NIL T) -9 NIL 1711959 NIL) (-749 1711031 1711060 1711150 "NAALG-" 1711155 NIL NAALG- (NIL T T) -8 NIL NIL NIL) (-748 1704981 1706089 1707276 "MULTSQFR" 1709927 NIL MULTSQFR (NIL T T T T) -7 NIL NIL NIL) (-747 1704300 1704375 1704559 "MULTFACT" 1704893 NIL MULTFACT (NIL T T T T) -7 NIL NIL NIL) (-746 1697024 1700937 1700990 "MTSCAT" 1702060 NIL MTSCAT (NIL T T) -9 NIL 1702575 NIL) (-745 1696736 1696790 1696882 "MTHING" 1696964 NIL MTHING (NIL T) -7 NIL NIL NIL) (-744 1696528 1696561 1696621 "MSYSCMD" 1696696 T MSYSCMD (NIL) -7 NIL NIL NIL) (-743 1692610 1695283 1695603 "MSET" 1696241 NIL MSET (NIL T) -8 NIL NIL NIL) (-742 1689679 1692171 1692212 "MSETAGG" 1692217 NIL MSETAGG (NIL T) -9 NIL 1692251 NIL) (-741 1685520 1687058 1687803 "MRING" 1688979 NIL MRING (NIL T T) -8 NIL NIL NIL) (-740 1685086 1685153 1685284 "MRF2" 1685447 NIL MRF2 (NIL T T T) -7 NIL NIL NIL) (-739 1684704 1684739 1684883 "MRATFAC" 1685045 NIL MRATFAC (NIL T T T T) -7 NIL NIL NIL) (-738 1682316 1682611 1683042 "MPRFF" 1684409 NIL MPRFF (NIL T T T T) -7 NIL NIL NIL) (-737 1676613 1682170 1682267 "MPOLY" 1682272 NIL MPOLY (NIL NIL T) -8 NIL NIL NIL) (-736 1676103 1676138 1676346 "MPCPF" 1676572 NIL MPCPF (NIL T T T T) -7 NIL NIL NIL) (-735 1675617 1675660 1675844 "MPC3" 1676054 NIL MPC3 (NIL T T T T T T T) -7 NIL NIL NIL) (-734 1674812 1674893 1675114 "MPC2" 1675532 NIL MPC2 (NIL T T T T T T T) -7 NIL NIL NIL) (-733 1673113 1673450 1673840 "MONOTOOL" 1674472 NIL MONOTOOL (NIL T T) -7 NIL NIL NIL) (-732 1672338 1672655 1672683 "MONOID" 1672902 T MONOID (NIL) -9 NIL 1673049 NIL) (-731 1671884 1672003 1672184 "MONOID-" 1672189 NIL MONOID- (NIL T) -8 NIL NIL NIL) (-730 1662359 1668310 1668369 "MONOGEN" 1669043 NIL MONOGEN (NIL T T) -9 NIL 1669499 NIL) (-729 1659577 1660312 1661312 "MONOGEN-" 1661431 NIL MONOGEN- (NIL T T T) -8 NIL NIL NIL) (-728 1658410 1658856 1658884 "MONADWU" 1659276 T MONADWU (NIL) -9 NIL 1659514 NIL) (-727 1657782 1657941 1658189 "MONADWU-" 1658194 NIL MONADWU- (NIL T) -8 NIL NIL NIL) (-726 1657141 1657385 1657413 "MONAD" 1657620 T MONAD (NIL) -9 NIL 1657732 NIL) (-725 1656826 1656904 1657036 "MONAD-" 1657041 NIL MONAD- (NIL T) -8 NIL NIL NIL) (-724 1655115 1655739 1656018 "MOEBIUS" 1656579 NIL MOEBIUS (NIL T) -8 NIL NIL NIL) (-723 1654393 1654797 1654837 "MODULE" 1654842 NIL MODULE (NIL T) -9 NIL 1654881 NIL) (-722 1653961 1654057 1654247 "MODULE-" 1654252 NIL MODULE- (NIL T T) -8 NIL NIL NIL) (-721 1651641 1652325 1652652 "MODRING" 1653785 NIL MODRING (NIL T T NIL NIL NIL) -8 NIL NIL NIL) (-720 1648585 1649746 1650267 "MODOP" 1651170 NIL MODOP (NIL T T) -8 NIL NIL NIL) (-719 1647173 1647652 1647929 "MODMONOM" 1648448 NIL MODMONOM (NIL T T NIL) -8 NIL NIL NIL) (-718 1637215 1645464 1645878 "MODMON" 1646810 NIL MODMON (NIL T T) -8 NIL NIL NIL) (-717 1634371 1636059 1636335 "MODFIELD" 1637090 NIL MODFIELD (NIL T T NIL NIL NIL) -8 NIL NIL NIL) (-716 1633348 1633652 1633842 "MMLFORM" 1634201 T MMLFORM (NIL) -8 NIL NIL NIL) (-715 1632874 1632917 1633096 "MMAP" 1633299 NIL MMAP (NIL T T T T T T) -7 NIL NIL NIL) (-714 1630953 1631720 1631761 "MLO" 1632184 NIL MLO (NIL T) -9 NIL 1632426 NIL) (-713 1628319 1628835 1629437 "MLIFT" 1630434 NIL MLIFT (NIL T T T T) -7 NIL NIL NIL) (-712 1627710 1627794 1627948 "MKUCFUNC" 1628230 NIL MKUCFUNC (NIL T T T) -7 NIL NIL NIL) (-711 1627309 1627379 1627502 "MKRECORD" 1627633 NIL MKRECORD (NIL T T) -7 NIL NIL NIL) (-710 1626356 1626518 1626746 "MKFUNC" 1627120 NIL MKFUNC (NIL T) -7 NIL NIL NIL) (-709 1625744 1625848 1626004 "MKFLCFN" 1626239 NIL MKFLCFN (NIL T) -7 NIL NIL NIL) (-708 1625021 1625123 1625308 "MKBCFUNC" 1625637 NIL MKBCFUNC (NIL T T T T) -7 NIL NIL NIL) (-707 1621728 1624575 1624711 "MINT" 1624905 T MINT (NIL) -8 NIL NIL NIL) (-706 1620540 1620783 1621060 "MHROWRED" 1621483 NIL MHROWRED (NIL T) -7 NIL NIL NIL) (-705 1615920 1619075 1619480 "MFLOAT" 1620155 T MFLOAT (NIL) -8 NIL NIL NIL) (-704 1615277 1615353 1615524 "MFINFACT" 1615832 NIL MFINFACT (NIL T T T T) -7 NIL NIL NIL) (-703 1611592 1612440 1613324 "MESH" 1614413 T MESH (NIL) -7 NIL NIL NIL) (-702 1609982 1610294 1610647 "MDDFACT" 1611279 NIL MDDFACT (NIL T) -7 NIL NIL NIL) (-701 1606777 1609141 1609182 "MDAGG" 1609437 NIL MDAGG (NIL T) -9 NIL 1609580 NIL) (-700 1596517 1606070 1606277 "MCMPLX" 1606590 T MCMPLX (NIL) -8 NIL NIL NIL) (-699 1595654 1595800 1596001 "MCDEN" 1596366 NIL MCDEN (NIL T T) -7 NIL NIL NIL) (-698 1593544 1593814 1594194 "MCALCFN" 1595384 NIL MCALCFN (NIL T T T T) -7 NIL NIL NIL) (-697 1592469 1592709 1592942 "MAYBE" 1593350 NIL MAYBE (NIL T) -8 NIL NIL NIL) (-696 1590081 1590604 1591166 "MATSTOR" 1591940 NIL MATSTOR (NIL T) -7 NIL NIL NIL) (-695 1586038 1589453 1589701 "MATRIX" 1589866 NIL MATRIX (NIL T) -8 NIL NIL NIL) (-694 1581802 1582511 1583247 "MATLIN" 1585395 NIL MATLIN (NIL T T T T) -7 NIL NIL NIL) (-693 1571908 1575094 1575171 "MATCAT" 1580051 NIL MATCAT (NIL T T T) -9 NIL 1581468 NIL) (-692 1568264 1569285 1570641 "MATCAT-" 1570646 NIL MATCAT- (NIL T T T T) -8 NIL NIL NIL) (-691 1566858 1567011 1567344 "MATCAT2" 1568099 NIL MATCAT2 (NIL T T T T T T T T) -7 NIL NIL NIL) (-690 1564970 1565294 1565678 "MAPPKG3" 1566533 NIL MAPPKG3 (NIL T T T) -7 NIL NIL NIL) (-689 1563951 1564124 1564346 "MAPPKG2" 1564794 NIL MAPPKG2 (NIL T T) -7 NIL NIL NIL) (-688 1562450 1562734 1563061 "MAPPKG1" 1563657 NIL MAPPKG1 (NIL T) -7 NIL NIL NIL) (-687 1561529 1561856 1562033 "MAPPAST" 1562293 T MAPPAST (NIL) -8 NIL NIL NIL) (-686 1561140 1561198 1561321 "MAPHACK3" 1561465 NIL MAPHACK3 (NIL T T T) -7 NIL NIL NIL) (-685 1560732 1560793 1560907 "MAPHACK2" 1561072 NIL MAPHACK2 (NIL T T) -7 NIL NIL NIL) (-684 1560169 1560273 1560415 "MAPHACK1" 1560623 NIL MAPHACK1 (NIL T) -7 NIL NIL NIL) (-683 1558248 1558869 1559173 "MAGMA" 1559897 NIL MAGMA (NIL T) -8 NIL NIL NIL) (-682 1557727 1557972 1558063 "MACROAST" 1558177 T MACROAST (NIL) -8 NIL NIL NIL) (-681 1554145 1555966 1556427 "M3D" 1557299 NIL M3D (NIL T) -8 NIL NIL NIL) (-680 1548251 1552514 1552555 "LZSTAGG" 1553337 NIL LZSTAGG (NIL T) -9 NIL 1553632 NIL) (-679 1544208 1545382 1546839 "LZSTAGG-" 1546844 NIL LZSTAGG- (NIL T T) -8 NIL NIL NIL) (-678 1541295 1542099 1542586 "LWORD" 1543753 NIL LWORD (NIL T) -8 NIL NIL NIL) (-677 1540871 1541099 1541174 "LSTAST" 1541240 T LSTAST (NIL) -8 NIL NIL NIL) (-676 1534037 1540642 1540776 "LSQM" 1540781 NIL LSQM (NIL NIL T) -8 NIL NIL NIL) (-675 1533261 1533400 1533628 "LSPP" 1533892 NIL LSPP (NIL T T T T) -7 NIL NIL NIL) (-674 1531073 1531374 1531830 "LSMP" 1532950 NIL LSMP (NIL T T T T) -7 NIL NIL NIL) (-673 1527852 1528526 1529256 "LSMP1" 1530375 NIL LSMP1 (NIL T) -7 NIL NIL NIL) (-672 1521729 1527019 1527060 "LSAGG" 1527122 NIL LSAGG (NIL T) -9 NIL 1527200 NIL) (-671 1518424 1519348 1520561 "LSAGG-" 1520566 NIL LSAGG- (NIL T T) -8 NIL NIL NIL) (-670 1516023 1517568 1517817 "LPOLY" 1518219 NIL LPOLY (NIL T T) -8 NIL NIL NIL) (-669 1515605 1515690 1515813 "LPEFRAC" 1515932 NIL LPEFRAC (NIL T) -7 NIL NIL NIL) (-668 1513926 1514699 1514952 "LO" 1515437 NIL LO (NIL T T T) -8 NIL NIL NIL) (-667 1513578 1513690 1513718 "LOGIC" 1513829 T LOGIC (NIL) -9 NIL 1513910 NIL) (-666 1513440 1513463 1513534 "LOGIC-" 1513539 NIL LOGIC- (NIL T) -8 NIL NIL NIL) (-665 1512633 1512773 1512966 "LODOOPS" 1513296 NIL LODOOPS (NIL T T) -7 NIL NIL NIL) (-664 1510056 1512549 1512615 "LODO" 1512620 NIL LODO (NIL T NIL) -8 NIL NIL NIL) (-663 1508594 1508829 1509182 "LODOF" 1509803 NIL LODOF (NIL T T) -7 NIL NIL NIL) (-662 1504812 1507243 1507284 "LODOCAT" 1507722 NIL LODOCAT (NIL T) -9 NIL 1507933 NIL) (-661 1504545 1504603 1504730 "LODOCAT-" 1504735 NIL LODOCAT- (NIL T T) -8 NIL NIL NIL) (-660 1501865 1504386 1504504 "LODO2" 1504509 NIL LODO2 (NIL T T) -8 NIL NIL NIL) (-659 1499300 1501802 1501847 "LODO1" 1501852 NIL LODO1 (NIL T) -8 NIL NIL NIL) (-658 1498181 1498346 1498651 "LODEEF" 1499123 NIL LODEEF (NIL T T T) -7 NIL NIL NIL) (-657 1493420 1496311 1496352 "LNAGG" 1497299 NIL LNAGG (NIL T) -9 NIL 1497743 NIL) (-656 1492567 1492781 1493123 "LNAGG-" 1493128 NIL LNAGG- (NIL T T) -8 NIL NIL NIL) (-655 1488703 1489492 1490131 "LMOPS" 1491982 NIL LMOPS (NIL T T NIL) -8 NIL NIL NIL) (-654 1488106 1488494 1488535 "LMODULE" 1488540 NIL LMODULE (NIL T) -9 NIL 1488566 NIL) (-653 1485304 1487751 1487874 "LMDICT" 1488016 NIL LMDICT (NIL T) -8 NIL NIL NIL) (-652 1484710 1484931 1484972 "LLINSET" 1485163 NIL LLINSET (NIL T) -9 NIL 1485254 NIL) (-651 1484409 1484618 1484678 "LITERAL" 1484683 NIL LITERAL (NIL T) -8 NIL NIL NIL) (-650 1477572 1483343 1483647 "LIST" 1484138 NIL LIST (NIL T) -8 NIL NIL NIL) (-649 1477097 1477171 1477310 "LIST3" 1477492 NIL LIST3 (NIL T T T) -7 NIL NIL NIL) (-648 1476104 1476282 1476510 "LIST2" 1476915 NIL LIST2 (NIL T T) -7 NIL NIL NIL) (-647 1474238 1474550 1474949 "LIST2MAP" 1475751 NIL LIST2MAP (NIL T T) -7 NIL NIL NIL) (-646 1473834 1474071 1474112 "LINSET" 1474117 NIL LINSET (NIL T) -9 NIL 1474151 NIL) (-645 1472495 1473165 1473206 "LINEXP" 1473461 NIL LINEXP (NIL T) -9 NIL 1473610 NIL) (-644 1471142 1471402 1471699 "LINDEP" 1472247 NIL LINDEP (NIL T T) -7 NIL NIL NIL) (-643 1467909 1468628 1469405 "LIMITRF" 1470397 NIL LIMITRF (NIL T) -7 NIL NIL NIL) (-642 1466212 1466508 1466917 "LIMITPS" 1467604 NIL LIMITPS (NIL T T) -7 NIL NIL NIL) (-641 1460640 1465723 1465951 "LIE" 1466033 NIL LIE (NIL T T) -8 NIL NIL NIL) (-640 1459588 1460057 1460097 "LIECAT" 1460237 NIL LIECAT (NIL T) -9 NIL 1460388 NIL) (-639 1459429 1459456 1459544 "LIECAT-" 1459549 NIL LIECAT- (NIL T T) -8 NIL NIL NIL) (-638 1451925 1458878 1459043 "LIB" 1459284 T LIB (NIL) -8 NIL NIL NIL) (-637 1447560 1448443 1449378 "LGROBP" 1451042 NIL LGROBP (NIL NIL T) -7 NIL NIL NIL) (-636 1445558 1445832 1446182 "LF" 1447281 NIL LF (NIL T T) -7 NIL NIL NIL) (-635 1444398 1445090 1445118 "LFCAT" 1445325 T LFCAT (NIL) -9 NIL 1445464 NIL) (-634 1441300 1441930 1442618 "LEXTRIPK" 1443762 NIL LEXTRIPK (NIL T NIL) -7 NIL NIL NIL) (-633 1438044 1438870 1439373 "LEXP" 1440880 NIL LEXP (NIL T T NIL) -8 NIL NIL NIL) (-632 1437520 1437765 1437857 "LETAST" 1437972 T LETAST (NIL) -8 NIL NIL NIL) (-631 1435918 1436231 1436632 "LEADCDET" 1437202 NIL LEADCDET (NIL T T T T) -7 NIL NIL NIL) (-630 1435108 1435182 1435411 "LAZM3PK" 1435839 NIL LAZM3PK (NIL T T T T T T) -7 NIL NIL NIL) (-629 1430025 1433185 1433723 "LAUPOL" 1434620 NIL LAUPOL (NIL T T) -8 NIL NIL NIL) (-628 1429604 1429648 1429809 "LAPLACE" 1429975 NIL LAPLACE (NIL T T) -7 NIL NIL NIL) (-627 1427543 1428705 1428956 "LA" 1429437 NIL LA (NIL T T T) -8 NIL NIL NIL) (-626 1426537 1427121 1427162 "LALG" 1427224 NIL LALG (NIL T) -9 NIL 1427283 NIL) (-625 1426251 1426310 1426446 "LALG-" 1426451 NIL LALG- (NIL T T) -8 NIL NIL NIL) (-624 1426086 1426110 1426151 "KVTFROM" 1426213 NIL KVTFROM (NIL T) -9 NIL NIL NIL) (-623 1425009 1425453 1425638 "KTVLOGIC" 1425921 T KTVLOGIC (NIL) -8 NIL NIL NIL) (-622 1424844 1424868 1424909 "KRCFROM" 1424971 NIL KRCFROM (NIL T) -9 NIL NIL NIL) (-621 1423748 1423935 1424234 "KOVACIC" 1424644 NIL KOVACIC (NIL T T) -7 NIL NIL NIL) (-620 1423583 1423607 1423648 "KONVERT" 1423710 NIL KONVERT (NIL T) -9 NIL NIL NIL) (-619 1423418 1423442 1423483 "KOERCE" 1423545 NIL KOERCE (NIL T) -9 NIL NIL NIL) (-618 1421248 1422011 1422388 "KERNEL" 1423074 NIL KERNEL (NIL T) -8 NIL NIL NIL) (-617 1420744 1420825 1420957 "KERNEL2" 1421162 NIL KERNEL2 (NIL T T) -7 NIL NIL NIL) (-616 1414514 1419283 1419337 "KDAGG" 1419714 NIL KDAGG (NIL T T) -9 NIL 1419920 NIL) (-615 1414043 1414167 1414372 "KDAGG-" 1414377 NIL KDAGG- (NIL T T T) -8 NIL NIL NIL) (-614 1407191 1413704 1413859 "KAFILE" 1413921 NIL KAFILE (NIL T) -8 NIL NIL NIL) (-613 1401619 1406702 1406930 "JORDAN" 1407012 NIL JORDAN (NIL T T) -8 NIL NIL NIL) (-612 1400998 1401268 1401389 "JOINAST" 1401518 T JOINAST (NIL) -8 NIL NIL NIL) (-611 1400844 1400903 1400958 "JAVACODE" 1400963 T JAVACODE (NIL) -8 NIL NIL NIL) (-610 1397096 1399049 1399103 "IXAGG" 1400032 NIL IXAGG (NIL T T) -9 NIL 1400491 NIL) (-609 1396015 1396321 1396740 "IXAGG-" 1396745 NIL IXAGG- (NIL T T T) -8 NIL NIL NIL) (-608 1391545 1395937 1395996 "IVECTOR" 1396001 NIL IVECTOR (NIL T NIL) -8 NIL NIL NIL) (-607 1390311 1390548 1390814 "ITUPLE" 1391312 NIL ITUPLE (NIL T) -8 NIL NIL NIL) (-606 1388813 1388990 1389285 "ITRIGMNP" 1390133 NIL ITRIGMNP (NIL T T T) -7 NIL NIL NIL) (-605 1387558 1387762 1388045 "ITFUN3" 1388589 NIL ITFUN3 (NIL T T T) -7 NIL NIL NIL) (-604 1387190 1387247 1387356 "ITFUN2" 1387495 NIL ITFUN2 (NIL T T) -7 NIL NIL NIL) (-603 1386349 1386670 1386844 "ITFORM" 1387036 T ITFORM (NIL) -8 NIL NIL NIL) (-602 1384310 1385369 1385647 "ITAYLOR" 1386104 NIL ITAYLOR (NIL T) -8 NIL NIL NIL) (-601 1373255 1378447 1379610 "ISUPS" 1383180 NIL ISUPS (NIL T) -8 NIL NIL NIL) (-600 1372359 1372499 1372735 "ISUMP" 1373102 NIL ISUMP (NIL T T T T) -7 NIL NIL NIL) (-599 1367734 1372304 1372345 "ISTRING" 1372350 NIL ISTRING (NIL NIL) -8 NIL NIL NIL) (-598 1367210 1367455 1367547 "ISAST" 1367662 T ISAST (NIL) -8 NIL NIL NIL) (-597 1366419 1366501 1366717 "IRURPK" 1367124 NIL IRURPK (NIL T T T T T) -7 NIL NIL NIL) (-596 1365355 1365556 1365796 "IRSN" 1366199 T IRSN (NIL) -7 NIL NIL NIL) (-595 1363426 1363781 1364210 "IRRF2F" 1364993 NIL IRRF2F (NIL T) -7 NIL NIL NIL) (-594 1363173 1363211 1363287 "IRREDFFX" 1363382 NIL IRREDFFX (NIL T) -7 NIL NIL NIL) (-593 1361788 1362047 1362346 "IROOT" 1362906 NIL IROOT (NIL T) -7 NIL NIL NIL) (-592 1358392 1359472 1360164 "IR" 1361128 NIL IR (NIL T) -8 NIL NIL NIL) (-591 1357597 1357885 1358036 "IRFORM" 1358261 T IRFORM (NIL) -8 NIL NIL NIL) (-590 1355210 1355705 1356271 "IR2" 1357075 NIL IR2 (NIL T T) -7 NIL NIL NIL) (-589 1354310 1354423 1354637 "IR2F" 1355093 NIL IR2F (NIL T T) -7 NIL NIL NIL) (-588 1354101 1354135 1354195 "IPRNTPK" 1354270 T IPRNTPK (NIL) -7 NIL NIL NIL) (-587 1350682 1353990 1354059 "IPF" 1354064 NIL IPF (NIL NIL) -8 NIL NIL NIL) (-586 1349009 1350607 1350664 "IPADIC" 1350669 NIL IPADIC (NIL NIL NIL) -8 NIL NIL NIL) (-585 1348321 1348569 1348699 "IP4ADDR" 1348899 T IP4ADDR (NIL) -8 NIL NIL NIL) (-584 1347695 1347950 1348082 "IOMODE" 1348209 T IOMODE (NIL) -8 NIL NIL NIL) (-583 1346768 1347292 1347419 "IOBFILE" 1347588 T IOBFILE (NIL) -8 NIL NIL NIL) (-582 1346256 1346672 1346700 "IOBCON" 1346705 T IOBCON (NIL) -9 NIL 1346726 NIL) (-581 1345767 1345825 1346008 "INVLAPLA" 1346192 NIL INVLAPLA (NIL T T) -7 NIL NIL NIL) (-580 1335415 1337769 1340155 "INTTR" 1343431 NIL INTTR (NIL T T) -7 NIL NIL NIL) (-579 1331750 1332492 1333357 "INTTOOLS" 1334600 NIL INTTOOLS (NIL T T) -7 NIL NIL NIL) (-578 1331336 1331427 1331544 "INTSLPE" 1331653 T INTSLPE (NIL) -7 NIL NIL NIL) (-577 1329289 1331259 1331318 "INTRVL" 1331323 NIL INTRVL (NIL T) -8 NIL NIL NIL) (-576 1326891 1327403 1327978 "INTRF" 1328774 NIL INTRF (NIL T) -7 NIL NIL NIL) (-575 1326302 1326399 1326541 "INTRET" 1326789 NIL INTRET (NIL T) -7 NIL NIL NIL) (-574 1324299 1324688 1325158 "INTRAT" 1325910 NIL INTRAT (NIL T T) -7 NIL NIL NIL) (-573 1321562 1322145 1322764 "INTPM" 1323784 NIL INTPM (NIL T T) -7 NIL NIL NIL) (-572 1318307 1318906 1319644 "INTPAF" 1320948 NIL INTPAF (NIL T T T) -7 NIL NIL NIL) (-571 1313486 1314448 1315499 "INTPACK" 1317276 T INTPACK (NIL) -7 NIL NIL NIL) (-570 1310434 1313283 1313392 "INT" 1313397 T INT (NIL) -8 NIL NIL NIL) (-569 1309686 1309838 1310046 "INTHERTR" 1310276 NIL INTHERTR (NIL T T) -7 NIL NIL NIL) (-568 1309125 1309205 1309393 "INTHERAL" 1309600 NIL INTHERAL (NIL T T T T) -7 NIL NIL NIL) (-567 1306971 1307414 1307871 "INTHEORY" 1308688 T INTHEORY (NIL) -7 NIL NIL NIL) (-566 1298377 1299998 1301770 "INTG0" 1305323 NIL INTG0 (NIL T T T) -7 NIL NIL NIL) (-565 1278950 1283740 1288550 "INTFTBL" 1293587 T INTFTBL (NIL) -8 NIL NIL NIL) (-564 1278199 1278337 1278510 "INTFACT" 1278809 NIL INTFACT (NIL T) -7 NIL NIL NIL) (-563 1275626 1276072 1276629 "INTEF" 1277753 NIL INTEF (NIL T T) -7 NIL NIL NIL) (-562 1273993 1274732 1274760 "INTDOM" 1275061 T INTDOM (NIL) -9 NIL 1275268 NIL) (-561 1273362 1273536 1273778 "INTDOM-" 1273783 NIL INTDOM- (NIL T) -8 NIL NIL NIL) (-560 1269750 1271678 1271732 "INTCAT" 1272531 NIL INTCAT (NIL T) -9 NIL 1272852 NIL) (-559 1269222 1269325 1269453 "INTBIT" 1269642 T INTBIT (NIL) -7 NIL NIL NIL) (-558 1267921 1268075 1268382 "INTALG" 1269067 NIL INTALG (NIL T T T T T) -7 NIL NIL NIL) (-557 1267404 1267494 1267651 "INTAF" 1267825 NIL INTAF (NIL T T) -7 NIL NIL NIL) (-556 1260747 1267214 1267354 "INTABL" 1267359 NIL INTABL (NIL T T T) -8 NIL NIL NIL) (-555 1260088 1260554 1260619 "INT8" 1260653 T INT8 (NIL) -8 NIL NIL 1260698) (-554 1259428 1259894 1259959 "INT64" 1259993 T INT64 (NIL) -8 NIL NIL 1260038) (-553 1258768 1259234 1259299 "INT32" 1259333 T INT32 (NIL) -8 NIL NIL 1259378) (-552 1258108 1258574 1258639 "INT16" 1258673 T INT16 (NIL) -8 NIL NIL 1258718) (-551 1253018 1255731 1255759 "INS" 1256693 T INS (NIL) -9 NIL 1257358 NIL) (-550 1250258 1251029 1252003 "INS-" 1252076 NIL INS- (NIL T) -8 NIL NIL NIL) (-549 1249033 1249260 1249558 "INPSIGN" 1250011 NIL INPSIGN (NIL T T) -7 NIL NIL NIL) (-548 1248151 1248268 1248465 "INPRODPF" 1248913 NIL INPRODPF (NIL T T) -7 NIL NIL NIL) (-547 1247045 1247162 1247399 "INPRODFF" 1248031 NIL INPRODFF (NIL T T T T) -7 NIL NIL NIL) (-546 1246045 1246197 1246457 "INNMFACT" 1246881 NIL INNMFACT (NIL T T T T) -7 NIL NIL NIL) (-545 1245242 1245339 1245527 "INMODGCD" 1245944 NIL INMODGCD (NIL T T NIL NIL) -7 NIL NIL NIL) (-544 1243750 1243995 1244319 "INFSP" 1244987 NIL INFSP (NIL T T T) -7 NIL NIL NIL) (-543 1242934 1243051 1243234 "INFPROD0" 1243630 NIL INFPROD0 (NIL T T) -7 NIL NIL NIL) (-542 1239789 1240999 1241514 "INFORM" 1242427 T INFORM (NIL) -8 NIL NIL NIL) (-541 1239399 1239459 1239557 "INFORM1" 1239724 NIL INFORM1 (NIL T) -7 NIL NIL NIL) (-540 1238922 1239011 1239125 "INFINITY" 1239305 T INFINITY (NIL) -7 NIL NIL NIL) (-539 1238098 1238642 1238743 "INETCLTS" 1238841 T INETCLTS (NIL) -8 NIL NIL NIL) (-538 1236714 1236964 1237285 "INEP" 1237846 NIL INEP (NIL T T T) -7 NIL NIL NIL) (-537 1235963 1236611 1236676 "INDE" 1236681 NIL INDE (NIL T) -8 NIL NIL NIL) (-536 1235527 1235595 1235712 "INCRMAPS" 1235890 NIL INCRMAPS (NIL T) -7 NIL NIL NIL) (-535 1234345 1234796 1235002 "INBFILE" 1235341 T INBFILE (NIL) -8 NIL NIL NIL) (-534 1229645 1230581 1231525 "INBFF" 1233433 NIL INBFF (NIL T) -7 NIL NIL NIL) (-533 1228553 1228822 1228850 "INBCON" 1229363 T INBCON (NIL) -9 NIL 1229629 NIL) (-532 1227805 1228028 1228304 "INBCON-" 1228309 NIL INBCON- (NIL T) -8 NIL NIL NIL) (-531 1227284 1227529 1227620 "INAST" 1227734 T INAST (NIL) -8 NIL NIL NIL) (-530 1226711 1226963 1227069 "IMPTAST" 1227198 T IMPTAST (NIL) -8 NIL NIL NIL) (-529 1223157 1226555 1226659 "IMATRIX" 1226664 NIL IMATRIX (NIL T NIL NIL) -8 NIL NIL NIL) (-528 1221865 1221988 1222304 "IMATQF" 1223013 NIL IMATQF (NIL T T T T T T T T) -7 NIL NIL NIL) (-527 1220085 1220312 1220649 "IMATLIN" 1221621 NIL IMATLIN (NIL T T T T) -7 NIL NIL NIL) (-526 1214663 1220009 1220067 "ILIST" 1220072 NIL ILIST (NIL T NIL) -8 NIL NIL NIL) (-525 1212568 1214523 1214636 "IIARRAY2" 1214641 NIL IIARRAY2 (NIL T NIL NIL T T) -8 NIL NIL NIL) (-524 1207966 1212479 1212543 "IFF" 1212548 NIL IFF (NIL NIL NIL) -8 NIL NIL NIL) (-523 1207313 1207583 1207699 "IFAST" 1207870 T IFAST (NIL) -8 NIL NIL NIL) (-522 1202308 1206605 1206793 "IFARRAY" 1207170 NIL IFARRAY (NIL T NIL) -8 NIL NIL NIL) (-521 1201488 1202212 1202285 "IFAMON" 1202290 NIL IFAMON (NIL T T NIL) -8 NIL NIL NIL) (-520 1201072 1201137 1201191 "IEVALAB" 1201398 NIL IEVALAB (NIL T T) -9 NIL NIL NIL) (-519 1200747 1200815 1200975 "IEVALAB-" 1200980 NIL IEVALAB- (NIL T T T) -8 NIL NIL NIL) (-518 1200378 1200661 1200724 "IDPO" 1200729 NIL IDPO (NIL T T) -8 NIL NIL NIL) (-517 1199628 1200267 1200342 "IDPOAMS" 1200347 NIL IDPOAMS (NIL T T) -8 NIL NIL NIL) (-516 1198935 1199517 1199592 "IDPOAM" 1199597 NIL IDPOAM (NIL T T) -8 NIL NIL NIL) (-515 1197994 1198270 1198323 "IDPC" 1198736 NIL IDPC (NIL T T) -9 NIL 1198885 NIL) (-514 1197463 1197886 1197959 "IDPAM" 1197964 NIL IDPAM (NIL T T) -8 NIL NIL NIL) (-513 1196839 1197355 1197428 "IDPAG" 1197433 NIL IDPAG (NIL T T) -8 NIL NIL NIL) (-512 1196484 1196675 1196750 "IDENT" 1196784 T IDENT (NIL) -8 NIL NIL NIL) (-511 1192739 1193587 1194482 "IDECOMP" 1195641 NIL IDECOMP (NIL NIL NIL) -7 NIL NIL NIL) (-510 1185577 1186662 1187709 "IDEAL" 1191775 NIL IDEAL (NIL T T T T) -8 NIL NIL NIL) (-509 1184737 1184849 1185049 "ICDEN" 1185461 NIL ICDEN (NIL T T T T) -7 NIL NIL NIL) (-508 1183808 1184217 1184364 "ICARD" 1184610 T ICARD (NIL) -8 NIL NIL NIL) (-507 1181868 1182181 1182586 "IBPTOOLS" 1183485 NIL IBPTOOLS (NIL T T T T) -7 NIL NIL NIL) (-506 1177475 1181488 1181601 "IBITS" 1181787 NIL IBITS (NIL NIL) -8 NIL NIL NIL) (-505 1174198 1174774 1175469 "IBATOOL" 1176892 NIL IBATOOL (NIL T T T) -7 NIL NIL NIL) (-504 1171977 1172439 1172972 "IBACHIN" 1173733 NIL IBACHIN (NIL T T T) -7 NIL NIL NIL) (-503 1169806 1171823 1171926 "IARRAY2" 1171931 NIL IARRAY2 (NIL T NIL NIL) -8 NIL NIL NIL) (-502 1165912 1169732 1169789 "IARRAY1" 1169794 NIL IARRAY1 (NIL T NIL) -8 NIL NIL NIL) (-501 1160021 1164324 1164805 "IAN" 1165451 T IAN (NIL) -8 NIL NIL NIL) (-500 1159532 1159589 1159762 "IALGFACT" 1159958 NIL IALGFACT (NIL T T T T) -7 NIL NIL NIL) (-499 1159060 1159173 1159201 "HYPCAT" 1159408 T HYPCAT (NIL) -9 NIL NIL NIL) (-498 1158598 1158715 1158901 "HYPCAT-" 1158906 NIL HYPCAT- (NIL T) -8 NIL NIL NIL) (-497 1158193 1158393 1158476 "HOSTNAME" 1158535 T HOSTNAME (NIL) -8 NIL NIL NIL) (-496 1158038 1158075 1158116 "HOMOTOP" 1158121 NIL HOMOTOP (NIL T) -9 NIL 1158154 NIL) (-495 1154670 1156048 1156089 "HOAGG" 1157070 NIL HOAGG (NIL T) -9 NIL 1157749 NIL) (-494 1153264 1153663 1154189 "HOAGG-" 1154194 NIL HOAGG- (NIL T T) -8 NIL NIL NIL) (-493 1147266 1152857 1153007 "HEXADEC" 1153134 T HEXADEC (NIL) -8 NIL NIL NIL) (-492 1146014 1146236 1146499 "HEUGCD" 1147043 NIL HEUGCD (NIL T) -7 NIL NIL NIL) (-491 1145090 1145851 1145981 "HELLFDIV" 1145986 NIL HELLFDIV (NIL T T T T) -8 NIL NIL NIL) (-490 1143269 1144867 1144955 "HEAP" 1145034 NIL HEAP (NIL T) -8 NIL NIL NIL) (-489 1142532 1142821 1142955 "HEADAST" 1143155 T HEADAST (NIL) -8 NIL NIL NIL) (-488 1136398 1142447 1142509 "HDP" 1142514 NIL HDP (NIL NIL T) -8 NIL NIL NIL) (-487 1130386 1136033 1136185 "HDMP" 1136299 NIL HDMP (NIL NIL T) -8 NIL NIL NIL) (-486 1129710 1129850 1130014 "HB" 1130242 T HB (NIL) -7 NIL NIL NIL) (-485 1123096 1129556 1129660 "HASHTBL" 1129665 NIL HASHTBL (NIL T T NIL) -8 NIL NIL NIL) (-484 1122572 1122817 1122909 "HASAST" 1123024 T HASAST (NIL) -8 NIL NIL NIL) (-483 1120350 1122194 1122376 "HACKPI" 1122410 T HACKPI (NIL) -8 NIL NIL NIL) (-482 1116018 1120203 1120316 "GTSET" 1120321 NIL GTSET (NIL T T T T) -8 NIL NIL NIL) (-481 1109433 1115896 1115994 "GSTBL" 1115999 NIL GSTBL (NIL T T T NIL) -8 NIL NIL NIL) (-480 1101711 1108464 1108729 "GSERIES" 1109224 NIL GSERIES (NIL T NIL NIL) -8 NIL NIL NIL) (-479 1100852 1101269 1101297 "GROUP" 1101500 T GROUP (NIL) -9 NIL 1101634 NIL) (-478 1100218 1100377 1100628 "GROUP-" 1100633 NIL GROUP- (NIL T) -8 NIL NIL NIL) (-477 1098585 1098906 1099293 "GROEBSOL" 1099895 NIL GROEBSOL (NIL NIL T T) -7 NIL NIL NIL) (-476 1097499 1097787 1097838 "GRMOD" 1098367 NIL GRMOD (NIL T T) -9 NIL 1098535 NIL) (-475 1097267 1097303 1097431 "GRMOD-" 1097436 NIL GRMOD- (NIL T T T) -8 NIL NIL NIL) (-474 1092557 1093621 1094621 "GRIMAGE" 1096287 T GRIMAGE (NIL) -8 NIL NIL NIL) (-473 1091023 1091284 1091608 "GRDEF" 1092253 T GRDEF (NIL) -7 NIL NIL NIL) (-472 1090467 1090583 1090724 "GRAY" 1090902 T GRAY (NIL) -7 NIL NIL NIL) (-471 1089654 1090060 1090111 "GRALG" 1090264 NIL GRALG (NIL T T) -9 NIL 1090357 NIL) (-470 1089315 1089388 1089551 "GRALG-" 1089556 NIL GRALG- (NIL T T T) -8 NIL NIL NIL) (-469 1086092 1088900 1089078 "GPOLSET" 1089222 NIL GPOLSET (NIL T T T T) -8 NIL NIL NIL) (-468 1085446 1085503 1085761 "GOSPER" 1086029 NIL GOSPER (NIL T T T T T) -7 NIL NIL NIL) (-467 1081178 1081884 1082410 "GMODPOL" 1085145 NIL GMODPOL (NIL NIL T T T NIL T) -8 NIL NIL NIL) (-466 1080183 1080367 1080605 "GHENSEL" 1080990 NIL GHENSEL (NIL T T) -7 NIL NIL NIL) (-465 1074339 1075182 1076202 "GENUPS" 1079267 NIL GENUPS (NIL T T) -7 NIL NIL NIL) (-464 1074036 1074087 1074176 "GENUFACT" 1074282 NIL GENUFACT (NIL T) -7 NIL NIL NIL) (-463 1073448 1073525 1073690 "GENPGCD" 1073954 NIL GENPGCD (NIL T T T T) -7 NIL NIL NIL) (-462 1072922 1072957 1073170 "GENMFACT" 1073407 NIL GENMFACT (NIL T T T T T) -7 NIL NIL NIL) (-461 1071488 1071745 1072052 "GENEEZ" 1072665 NIL GENEEZ (NIL T T) -7 NIL NIL NIL) (-460 1065634 1071099 1071261 "GDMP" 1071411 NIL GDMP (NIL NIL T T) -8 NIL NIL NIL) (-459 1054976 1059405 1060511 "GCNAALG" 1064617 NIL GCNAALG (NIL T NIL NIL NIL) -8 NIL NIL NIL) (-458 1053303 1054165 1054193 "GCDDOM" 1054448 T GCDDOM (NIL) -9 NIL 1054605 NIL) (-457 1052773 1052900 1053115 "GCDDOM-" 1053120 NIL GCDDOM- (NIL T) -8 NIL NIL NIL) (-456 1051445 1051630 1051934 "GB" 1052552 NIL GB (NIL T T T T) -7 NIL NIL NIL) (-455 1040061 1042391 1044783 "GBINTERN" 1049136 NIL GBINTERN (NIL T T T T) -7 NIL NIL NIL) (-454 1037898 1038190 1038611 "GBF" 1039736 NIL GBF (NIL T T T T) -7 NIL NIL NIL) (-453 1036679 1036844 1037111 "GBEUCLID" 1037714 NIL GBEUCLID (NIL T T T T) -7 NIL NIL NIL) (-452 1036028 1036153 1036302 "GAUSSFAC" 1036550 T GAUSSFAC (NIL) -7 NIL NIL NIL) (-451 1034395 1034697 1035011 "GALUTIL" 1035747 NIL GALUTIL (NIL T) -7 NIL NIL NIL) (-450 1032703 1032977 1033301 "GALPOLYU" 1034122 NIL GALPOLYU (NIL T T) -7 NIL NIL NIL) (-449 1030068 1030358 1030765 "GALFACTU" 1032400 NIL GALFACTU (NIL T T T) -7 NIL NIL NIL) (-448 1021873 1023373 1024981 "GALFACT" 1028500 NIL GALFACT (NIL T) -7 NIL NIL NIL) (-447 1019261 1019919 1019947 "FVFUN" 1021103 T FVFUN (NIL) -9 NIL 1021823 NIL) (-446 1018527 1018709 1018737 "FVC" 1019028 T FVC (NIL) -9 NIL 1019211 NIL) (-445 1018170 1018352 1018420 "FUNDESC" 1018479 T FUNDESC (NIL) -8 NIL NIL NIL) (-444 1017785 1017967 1018048 "FUNCTION" 1018122 NIL FUNCTION (NIL NIL) -8 NIL NIL NIL) (-443 1015529 1016107 1016573 "FT" 1017339 T FT (NIL) -8 NIL NIL NIL) (-442 1014320 1014830 1015033 "FTEM" 1015346 T FTEM (NIL) -8 NIL NIL NIL) (-441 1012611 1012900 1013297 "FSUPFACT" 1014011 NIL FSUPFACT (NIL T T T) -7 NIL NIL NIL) (-440 1011008 1011297 1011629 "FST" 1012299 T FST (NIL) -8 NIL NIL NIL) (-439 1010207 1010313 1010501 "FSRED" 1010890 NIL FSRED (NIL T T) -7 NIL NIL NIL) (-438 1008906 1009162 1009509 "FSPRMELT" 1009922 NIL FSPRMELT (NIL T T) -7 NIL NIL NIL) (-437 1006212 1006650 1007136 "FSPECF" 1008469 NIL FSPECF (NIL T T) -7 NIL NIL NIL) (-436 987850 996181 996222 "FS" 1000106 NIL FS (NIL T) -9 NIL 1002395 NIL) (-435 976493 979486 983543 "FS-" 983843 NIL FS- (NIL T T) -8 NIL NIL NIL) (-434 976021 976075 976245 "FSINT" 976434 NIL FSINT (NIL T T) -7 NIL NIL NIL) (-433 974313 975014 975317 "FSERIES" 975800 NIL FSERIES (NIL T T) -8 NIL NIL NIL) (-432 973355 973471 973695 "FSCINT" 974193 NIL FSCINT (NIL T T) -7 NIL NIL NIL) (-431 969563 972299 972340 "FSAGG" 972710 NIL FSAGG (NIL T) -9 NIL 972969 NIL) (-430 967325 967926 968722 "FSAGG-" 968817 NIL FSAGG- (NIL T T) -8 NIL NIL NIL) (-429 966367 966510 966737 "FSAGG2" 967178 NIL FSAGG2 (NIL T T T T) -7 NIL NIL NIL) (-428 964049 964329 964876 "FS2UPS" 966085 NIL FS2UPS (NIL T T T T T NIL) -7 NIL NIL NIL) (-427 963683 963726 963855 "FS2" 964000 NIL FS2 (NIL T T T T) -7 NIL NIL NIL) (-426 962561 962732 963034 "FS2EXPXP" 963508 NIL FS2EXPXP (NIL T T NIL NIL) -7 NIL NIL NIL) (-425 961987 962102 962254 "FRUTIL" 962441 NIL FRUTIL (NIL T) -7 NIL NIL NIL) (-424 953400 957482 958840 "FR" 960661 NIL FR (NIL T) -8 NIL NIL NIL) (-423 948369 951043 951083 "FRNAALG" 952479 NIL FRNAALG (NIL T) -9 NIL 953086 NIL) (-422 944042 945118 946393 "FRNAALG-" 947143 NIL FRNAALG- (NIL T T) -8 NIL NIL NIL) (-421 943680 943723 943850 "FRNAAF2" 943993 NIL FRNAAF2 (NIL T T T T) -7 NIL NIL NIL) (-420 942055 942529 942825 "FRMOD" 943492 NIL FRMOD (NIL T T T T NIL) -8 NIL NIL NIL) (-419 939798 940430 940748 "FRIDEAL" 941846 NIL FRIDEAL (NIL T T T T) -8 NIL NIL NIL) (-418 938989 939076 939367 "FRIDEAL2" 939705 NIL FRIDEAL2 (NIL T T T T T T T T) -7 NIL NIL NIL) (-417 938122 938536 938577 "FRETRCT" 938582 NIL FRETRCT (NIL T) -9 NIL 938758 NIL) (-416 937234 937465 937816 "FRETRCT-" 937821 NIL FRETRCT- (NIL T T) -8 NIL NIL NIL) (-415 934322 935532 935591 "FRAMALG" 936473 NIL FRAMALG (NIL T T) -9 NIL 936765 NIL) (-414 932456 932911 933541 "FRAMALG-" 933764 NIL FRAMALG- (NIL T T T) -8 NIL NIL NIL) (-413 926375 931929 932206 "FRAC" 932211 NIL FRAC (NIL T) -8 NIL NIL NIL) (-412 926011 926068 926175 "FRAC2" 926312 NIL FRAC2 (NIL T T) -7 NIL NIL NIL) (-411 925647 925704 925811 "FR2" 925948 NIL FR2 (NIL T T) -7 NIL NIL NIL) (-410 920160 923053 923081 "FPS" 924200 T FPS (NIL) -9 NIL 924757 NIL) (-409 919609 919718 919882 "FPS-" 920028 NIL FPS- (NIL T) -8 NIL NIL NIL) (-408 916911 918580 918608 "FPC" 918833 T FPC (NIL) -9 NIL 918975 NIL) (-407 916704 916744 916841 "FPC-" 916846 NIL FPC- (NIL T) -8 NIL NIL NIL) (-406 915494 916192 916233 "FPATMAB" 916238 NIL FPATMAB (NIL T) -9 NIL 916390 NIL) (-405 913167 913670 914096 "FPARFRAC" 915131 NIL FPARFRAC (NIL T T) -8 NIL NIL NIL) (-404 908561 909059 909741 "FORTRAN" 912599 NIL FORTRAN (NIL NIL NIL NIL NIL) -8 NIL NIL NIL) (-403 906277 906777 907316 "FORT" 908042 T FORT (NIL) -7 NIL NIL NIL) (-402 903953 904515 904543 "FORTFN" 905603 T FORTFN (NIL) -9 NIL 906227 NIL) (-401 903717 903767 903795 "FORTCAT" 903854 T FORTCAT (NIL) -9 NIL 903916 NIL) (-400 901823 902333 902723 "FORMULA" 903347 T FORMULA (NIL) -8 NIL NIL NIL) (-399 901611 901641 901710 "FORMULA1" 901787 NIL FORMULA1 (NIL T) -7 NIL NIL NIL) (-398 901134 901186 901359 "FORDER" 901553 NIL FORDER (NIL T T T T) -7 NIL NIL NIL) (-397 900230 900394 900587 "FOP" 900961 T FOP (NIL) -7 NIL NIL NIL) (-396 898811 899510 899684 "FNLA" 900112 NIL FNLA (NIL NIL NIL T) -8 NIL NIL NIL) (-395 897540 897955 897983 "FNCAT" 898443 T FNCAT (NIL) -9 NIL 898703 NIL) (-394 897079 897499 897527 "FNAME" 897532 T FNAME (NIL) -8 NIL NIL NIL) (-393 895642 896605 896633 "FMTC" 896638 T FMTC (NIL) -9 NIL 896674 NIL) (-392 894388 895578 895624 "FMONOID" 895629 NIL FMONOID (NIL T) -8 NIL NIL NIL) (-391 891216 892384 892425 "FMONCAT" 893642 NIL FMONCAT (NIL T) -9 NIL 894247 NIL) (-390 890408 890958 891107 "FM" 891112 NIL FM (NIL T T) -8 NIL NIL NIL) (-389 887832 888478 888506 "FMFUN" 889650 T FMFUN (NIL) -9 NIL 890358 NIL) (-388 887101 887282 887310 "FMC" 887600 T FMC (NIL) -9 NIL 887782 NIL) (-387 884180 885040 885094 "FMCAT" 886289 NIL FMCAT (NIL T T) -9 NIL 886784 NIL) (-386 883046 883946 884046 "FM1" 884125 NIL FM1 (NIL T T) -8 NIL NIL NIL) (-385 880820 881236 881730 "FLOATRP" 882597 NIL FLOATRP (NIL T) -7 NIL NIL NIL) (-384 874394 878549 879170 "FLOAT" 880219 T FLOAT (NIL) -8 NIL NIL NIL) (-383 871832 872332 872910 "FLOATCP" 873861 NIL FLOATCP (NIL T) -7 NIL NIL NIL) (-382 870572 871410 871451 "FLINEXP" 871456 NIL FLINEXP (NIL T) -9 NIL 871549 NIL) (-381 869726 869961 870289 "FLINEXP-" 870294 NIL FLINEXP- (NIL T T) -8 NIL NIL NIL) (-380 868802 868946 869170 "FLASORT" 869578 NIL FLASORT (NIL T T) -7 NIL NIL NIL) (-379 865918 866786 866838 "FLALG" 868065 NIL FLALG (NIL T T) -9 NIL 868532 NIL) (-378 859654 863404 863445 "FLAGG" 864707 NIL FLAGG (NIL T) -9 NIL 865359 NIL) (-377 858380 858719 859209 "FLAGG-" 859214 NIL FLAGG- (NIL T T) -8 NIL NIL NIL) (-376 857422 857565 857792 "FLAGG2" 858233 NIL FLAGG2 (NIL T T T T) -7 NIL NIL NIL) (-375 854273 855281 855340 "FINRALG" 856468 NIL FINRALG (NIL T T) -9 NIL 856976 NIL) (-374 853433 853662 854001 "FINRALG-" 854006 NIL FINRALG- (NIL T T T) -8 NIL NIL NIL) (-373 852813 853052 853080 "FINITE" 853276 T FINITE (NIL) -9 NIL 853383 NIL) (-372 845170 847357 847397 "FINAALG" 851064 NIL FINAALG (NIL T) -9 NIL 852517 NIL) (-371 840502 841552 842696 "FINAALG-" 844075 NIL FINAALG- (NIL T T) -8 NIL NIL NIL) (-370 839870 840257 840360 "FILE" 840432 NIL FILE (NIL T) -8 NIL NIL NIL) (-369 838528 838866 838920 "FILECAT" 839604 NIL FILECAT (NIL T T) -9 NIL 839820 NIL) (-368 836244 837772 837800 "FIELD" 837840 T FIELD (NIL) -9 NIL 837920 NIL) (-367 834864 835249 835760 "FIELD-" 835765 NIL FIELD- (NIL T) -8 NIL NIL NIL) (-366 832714 833499 833846 "FGROUP" 834550 NIL FGROUP (NIL T) -8 NIL NIL NIL) (-365 831804 831968 832188 "FGLMICPK" 832546 NIL FGLMICPK (NIL T NIL) -7 NIL NIL NIL) (-364 827636 831729 831786 "FFX" 831791 NIL FFX (NIL T NIL) -8 NIL NIL NIL) (-363 827237 827298 827433 "FFSLPE" 827569 NIL FFSLPE (NIL T T T) -7 NIL NIL NIL) (-362 823227 824009 824805 "FFPOLY" 826473 NIL FFPOLY (NIL T) -7 NIL NIL NIL) (-361 822731 822767 822976 "FFPOLY2" 823185 NIL FFPOLY2 (NIL T T) -7 NIL NIL NIL) (-360 818575 822650 822713 "FFP" 822718 NIL FFP (NIL T NIL) -8 NIL NIL NIL) (-359 813973 818486 818550 "FF" 818555 NIL FF (NIL NIL NIL) -8 NIL NIL NIL) (-358 809099 813316 813506 "FFNBX" 813827 NIL FFNBX (NIL T NIL) -8 NIL NIL NIL) (-357 804027 808234 808492 "FFNBP" 808953 NIL FFNBP (NIL T NIL) -8 NIL NIL NIL) (-356 798660 803311 803522 "FFNB" 803860 NIL FFNB (NIL NIL NIL) -8 NIL NIL NIL) (-355 797492 797690 798005 "FFINTBAS" 798457 NIL FFINTBAS (NIL T T T) -7 NIL NIL NIL) (-354 793561 795781 795809 "FFIELDC" 796429 T FFIELDC (NIL) -9 NIL 796805 NIL) (-353 792223 792594 793091 "FFIELDC-" 793096 NIL FFIELDC- (NIL T) -8 NIL NIL NIL) (-352 791792 791838 791962 "FFHOM" 792165 NIL FFHOM (NIL T T T) -7 NIL NIL NIL) (-351 789487 789974 790491 "FFF" 791307 NIL FFF (NIL T) -7 NIL NIL NIL) (-350 785105 789229 789330 "FFCGX" 789430 NIL FFCGX (NIL T NIL) -8 NIL NIL NIL) (-349 780727 784837 784944 "FFCGP" 785048 NIL FFCGP (NIL T NIL) -8 NIL NIL NIL) (-348 775910 780454 780562 "FFCG" 780663 NIL FFCG (NIL NIL NIL) -8 NIL NIL NIL) (-347 757306 766387 766473 "FFCAT" 771638 NIL FFCAT (NIL T T T) -9 NIL 773089 NIL) (-346 752503 753551 754865 "FFCAT-" 756095 NIL FFCAT- (NIL T T T T) -8 NIL NIL NIL) (-345 751914 751957 752192 "FFCAT2" 752454 NIL FFCAT2 (NIL T T T T T T T T) -7 NIL NIL NIL) (-344 741237 744886 746106 "FEXPR" 750766 NIL FEXPR (NIL NIL NIL T) -8 NIL NIL NIL) (-343 740237 740672 740713 "FEVALAB" 740797 NIL FEVALAB (NIL T) -9 NIL 741058 NIL) (-342 739396 739606 739944 "FEVALAB-" 739949 NIL FEVALAB- (NIL T T) -8 NIL NIL NIL) (-341 737962 738779 738982 "FDIV" 739295 NIL FDIV (NIL T T T T) -8 NIL NIL NIL) (-340 734982 735723 735838 "FDIVCAT" 737406 NIL FDIVCAT (NIL T T T T) -9 NIL 737843 NIL) (-339 734744 734771 734941 "FDIVCAT-" 734946 NIL FDIVCAT- (NIL T T T T T) -8 NIL NIL NIL) (-338 733964 734051 734328 "FDIV2" 734651 NIL FDIV2 (NIL T T T T T T T T) -7 NIL NIL NIL) (-337 732938 733259 733461 "FCTRDATA" 733782 T FCTRDATA (NIL) -8 NIL NIL NIL) (-336 731624 731883 732172 "FCPAK1" 732669 T FCPAK1 (NIL) -7 NIL NIL NIL) (-335 730723 731124 731265 "FCOMP" 731515 NIL FCOMP (NIL T) -8 NIL NIL NIL) (-334 714428 717873 721411 "FC" 727205 T FC (NIL) -8 NIL NIL NIL) (-333 706791 710819 710859 "FAXF" 712661 NIL FAXF (NIL T) -9 NIL 713353 NIL) (-332 704067 704725 705550 "FAXF-" 706015 NIL FAXF- (NIL T T) -8 NIL NIL NIL) (-331 699119 703443 703619 "FARRAY" 703924 NIL FARRAY (NIL T) -8 NIL NIL NIL) (-330 694013 696080 696133 "FAMR" 697156 NIL FAMR (NIL T T) -9 NIL 697616 NIL) (-329 692903 693205 693640 "FAMR-" 693645 NIL FAMR- (NIL T T T) -8 NIL NIL NIL) (-328 692072 692825 692878 "FAMONOID" 692883 NIL FAMONOID (NIL T) -8 NIL NIL NIL) (-327 689858 690568 690621 "FAMONC" 691562 NIL FAMONC (NIL T T) -9 NIL 691948 NIL) (-326 688522 689612 689749 "FAGROUP" 689754 NIL FAGROUP (NIL T) -8 NIL NIL NIL) (-325 686317 686636 687039 "FACUTIL" 688203 NIL FACUTIL (NIL T T T T) -7 NIL NIL NIL) (-324 685416 685601 685823 "FACTFUNC" 686127 NIL FACTFUNC (NIL T) -7 NIL NIL NIL) (-323 677838 684719 684918 "EXPUPXS" 685272 NIL EXPUPXS (NIL T NIL NIL) -8 NIL NIL NIL) (-322 675321 675861 676447 "EXPRTUBE" 677272 T EXPRTUBE (NIL) -7 NIL NIL NIL) (-321 671592 672184 672914 "EXPRODE" 674660 NIL EXPRODE (NIL T T) -7 NIL NIL NIL) (-320 657077 670241 670670 "EXPR" 671196 NIL EXPR (NIL T) -8 NIL NIL NIL) (-319 651631 652218 653024 "EXPR2UPS" 656375 NIL EXPR2UPS (NIL T T) -7 NIL NIL NIL) (-318 651263 651320 651429 "EXPR2" 651568 NIL EXPR2 (NIL T T) -7 NIL NIL NIL) (-317 642651 650414 650705 "EXPEXPAN" 651099 NIL EXPEXPAN (NIL T T NIL NIL) -8 NIL NIL NIL) (-316 642451 642608 642637 "EXIT" 642642 T EXIT (NIL) -8 NIL NIL NIL) (-315 641931 642175 642266 "EXITAST" 642380 T EXITAST (NIL) -8 NIL NIL NIL) (-314 641558 641620 641733 "EVALCYC" 641863 NIL EVALCYC (NIL T) -7 NIL NIL NIL) (-313 641099 641217 641258 "EVALAB" 641428 NIL EVALAB (NIL T) -9 NIL 641532 NIL) (-312 640580 640702 640923 "EVALAB-" 640928 NIL EVALAB- (NIL T T) -8 NIL NIL NIL) (-311 637948 639250 639278 "EUCDOM" 639833 T EUCDOM (NIL) -9 NIL 640183 NIL) (-310 636353 636795 637385 "EUCDOM-" 637390 NIL EUCDOM- (NIL T) -8 NIL NIL NIL) (-309 623891 626651 629401 "ESTOOLS" 633623 T ESTOOLS (NIL) -7 NIL NIL NIL) (-308 623523 623580 623689 "ESTOOLS2" 623828 NIL ESTOOLS2 (NIL T T) -7 NIL NIL NIL) (-307 623274 623316 623396 "ESTOOLS1" 623475 NIL ESTOOLS1 (NIL T) -7 NIL NIL NIL) (-306 617311 618919 618947 "ES" 621715 T ES (NIL) -9 NIL 623125 NIL) (-305 612258 613545 615362 "ES-" 615526 NIL ES- (NIL T) -8 NIL NIL NIL) (-304 608632 609393 610173 "ESCONT" 611498 T ESCONT (NIL) -7 NIL NIL NIL) (-303 608377 608409 608491 "ESCONT1" 608594 NIL ESCONT1 (NIL NIL NIL) -7 NIL NIL NIL) (-302 608052 608102 608202 "ES2" 608321 NIL ES2 (NIL T T) -7 NIL NIL NIL) (-301 607682 607740 607849 "ES1" 607988 NIL ES1 (NIL T T) -7 NIL NIL NIL) (-300 606898 607027 607203 "ERROR" 607526 T ERROR (NIL) -7 NIL NIL NIL) (-299 600290 606757 606848 "EQTBL" 606853 NIL EQTBL (NIL T T) -8 NIL NIL NIL) (-298 592793 595604 597053 "EQ" 598874 NIL -2099 (NIL T) -8 NIL NIL NIL) (-297 592425 592482 592591 "EQ2" 592730 NIL EQ2 (NIL T T) -7 NIL NIL NIL) (-296 587715 588763 589856 "EP" 591364 NIL EP (NIL T) -7 NIL NIL NIL) (-295 586315 586606 586912 "ENV" 587429 T ENV (NIL) -8 NIL NIL NIL) (-294 585409 585963 585991 "ENTIRER" 585996 T ENTIRER (NIL) -9 NIL 586042 NIL) (-293 581876 583364 583734 "EMR" 585208 NIL EMR (NIL T T T NIL NIL NIL) -8 NIL NIL NIL) (-292 581020 581205 581259 "ELTAGG" 581639 NIL ELTAGG (NIL T T) -9 NIL 581850 NIL) (-291 580739 580801 580942 "ELTAGG-" 580947 NIL ELTAGG- (NIL T T T) -8 NIL NIL NIL) (-290 580528 580557 580611 "ELTAB" 580695 NIL ELTAB (NIL T T) -9 NIL NIL NIL) (-289 579654 579800 579999 "ELFUTS" 580379 NIL ELFUTS (NIL T T) -7 NIL NIL NIL) (-288 579396 579452 579480 "ELEMFUN" 579585 T ELEMFUN (NIL) -9 NIL NIL NIL) (-287 579266 579287 579355 "ELEMFUN-" 579360 NIL ELEMFUN- (NIL T) -8 NIL NIL NIL) (-286 574110 577366 577407 "ELAGG" 578347 NIL ELAGG (NIL T) -9 NIL 578810 NIL) (-285 572395 572829 573492 "ELAGG-" 573497 NIL ELAGG- (NIL T T) -8 NIL NIL NIL) (-284 571707 571844 572000 "ELABOR" 572259 T ELABOR (NIL) -8 NIL NIL NIL) (-283 570368 570647 570941 "ELABEXPR" 571433 T ELABEXPR (NIL) -8 NIL NIL NIL) (-282 563232 565035 565862 "EFUPXS" 569644 NIL EFUPXS (NIL T T T T) -8 NIL NIL NIL) (-281 556682 558483 559293 "EFULS" 562508 NIL EFULS (NIL T T T) -8 NIL NIL NIL) (-280 554167 554525 554997 "EFSTRUC" 556314 NIL EFSTRUC (NIL T T) -7 NIL NIL NIL) (-279 543958 545524 547072 "EF" 552682 NIL EF (NIL T T) -7 NIL NIL NIL) (-278 543032 543443 543592 "EAB" 543829 T EAB (NIL) -8 NIL NIL NIL) (-277 542214 542991 543019 "E04UCFA" 543024 T E04UCFA (NIL) -8 NIL NIL NIL) (-276 541396 542173 542201 "E04NAFA" 542206 T E04NAFA (NIL) -8 NIL NIL NIL) (-275 540578 541355 541383 "E04MBFA" 541388 T E04MBFA (NIL) -8 NIL NIL NIL) (-274 539760 540537 540565 "E04JAFA" 540570 T E04JAFA (NIL) -8 NIL NIL NIL) (-273 538944 539719 539747 "E04GCFA" 539752 T E04GCFA (NIL) -8 NIL NIL NIL) (-272 538128 538903 538931 "E04FDFA" 538936 T E04FDFA (NIL) -8 NIL NIL NIL) (-271 537310 538087 538115 "E04DGFA" 538120 T E04DGFA (NIL) -8 NIL NIL NIL) (-270 531483 532835 534199 "E04AGNT" 535966 T E04AGNT (NIL) -7 NIL NIL NIL) (-269 530163 530669 530709 "DVARCAT" 531184 NIL DVARCAT (NIL T) -9 NIL 531383 NIL) (-268 529367 529579 529893 "DVARCAT-" 529898 NIL DVARCAT- (NIL T T) -8 NIL NIL NIL) (-267 522504 529166 529295 "DSMP" 529300 NIL DSMP (NIL T T T) -8 NIL NIL NIL) (-266 517285 518449 519517 "DROPT" 521456 T DROPT (NIL) -8 NIL NIL NIL) (-265 516950 517009 517107 "DROPT1" 517220 NIL DROPT1 (NIL T) -7 NIL NIL NIL) (-264 512065 513191 514328 "DROPT0" 515833 T DROPT0 (NIL) -7 NIL NIL NIL) (-263 510410 510735 511121 "DRAWPT" 511699 T DRAWPT (NIL) -7 NIL NIL NIL) (-262 504997 505920 506999 "DRAW" 509384 NIL DRAW (NIL T) -7 NIL NIL NIL) (-261 504630 504683 504801 "DRAWHACK" 504938 NIL DRAWHACK (NIL T) -7 NIL NIL NIL) (-260 503361 503630 503921 "DRAWCX" 504359 T DRAWCX (NIL) -7 NIL NIL NIL) (-259 502876 502945 503096 "DRAWCURV" 503287 NIL DRAWCURV (NIL T T) -7 NIL NIL NIL) (-258 493344 495306 497421 "DRAWCFUN" 500781 T DRAWCFUN (NIL) -7 NIL NIL NIL) (-257 490108 492037 492078 "DQAGG" 492707 NIL DQAGG (NIL T) -9 NIL 492981 NIL) (-256 478232 484701 484784 "DPOLCAT" 486636 NIL DPOLCAT (NIL T T T T) -9 NIL 487181 NIL) (-255 473068 474417 476375 "DPOLCAT-" 476380 NIL DPOLCAT- (NIL T T T T T) -8 NIL NIL NIL) (-254 466190 472929 473027 "DPMO" 473032 NIL DPMO (NIL NIL T T) -8 NIL NIL NIL) (-253 459215 465970 466137 "DPMM" 466142 NIL DPMM (NIL NIL T T T) -8 NIL NIL NIL) (-252 458693 458907 459005 "DOMTMPLT" 459137 T DOMTMPLT (NIL) -8 NIL NIL NIL) (-251 458126 458495 458575 "DOMCTOR" 458633 T DOMCTOR (NIL) -8 NIL NIL NIL) (-250 457338 457606 457757 "DOMAIN" 457995 T DOMAIN (NIL) -8 NIL NIL NIL) (-249 451326 456973 457125 "DMP" 457239 NIL DMP (NIL NIL T) -8 NIL NIL NIL) (-248 450926 450982 451126 "DLP" 451264 NIL DLP (NIL T) -7 NIL NIL NIL) (-247 444748 450253 450443 "DLIST" 450768 NIL DLIST (NIL T) -8 NIL NIL NIL) (-246 441545 443601 443642 "DLAGG" 444192 NIL DLAGG (NIL T) -9 NIL 444422 NIL) (-245 440221 440885 440913 "DIVRING" 441005 T DIVRING (NIL) -9 NIL 441088 NIL) (-244 439458 439648 439948 "DIVRING-" 439953 NIL DIVRING- (NIL T) -8 NIL NIL NIL) (-243 437560 437917 438323 "DISPLAY" 439072 T DISPLAY (NIL) -7 NIL NIL NIL) (-242 431448 437474 437537 "DIRPROD" 437542 NIL DIRPROD (NIL NIL T) -8 NIL NIL NIL) (-241 430296 430499 430764 "DIRPROD2" 431241 NIL DIRPROD2 (NIL NIL T T) -7 NIL NIL NIL) (-240 419071 425077 425130 "DIRPCAT" 425540 NIL DIRPCAT (NIL NIL T) -9 NIL 426380 NIL) (-239 416397 417039 417920 "DIRPCAT-" 418257 NIL DIRPCAT- (NIL T NIL T) -8 NIL NIL NIL) (-238 415684 415844 416030 "DIOSP" 416231 T DIOSP (NIL) -7 NIL NIL NIL) (-237 412339 414596 414637 "DIOPS" 415071 NIL DIOPS (NIL T) -9 NIL 415300 NIL) (-236 411888 412002 412193 "DIOPS-" 412198 NIL DIOPS- (NIL T T) -8 NIL NIL NIL) (-235 410711 411339 411367 "DIFRING" 411554 T DIFRING (NIL) -9 NIL 411664 NIL) (-234 410357 410434 410586 "DIFRING-" 410591 NIL DIFRING- (NIL T) -8 NIL NIL NIL) (-233 408093 409365 409406 "DIFEXT" 409769 NIL DIFEXT (NIL T) -9 NIL 410063 NIL) (-232 406378 406806 407472 "DIFEXT-" 407477 NIL DIFEXT- (NIL T T) -8 NIL NIL NIL) (-231 403653 405910 405951 "DIAGG" 405956 NIL DIAGG (NIL T) -9 NIL 405976 NIL) (-230 403037 403194 403446 "DIAGG-" 403451 NIL DIAGG- (NIL T T) -8 NIL NIL NIL) (-229 398454 401996 402273 "DHMATRIX" 402806 NIL DHMATRIX (NIL T) -8 NIL NIL NIL) (-228 394066 394975 395985 "DFSFUN" 397464 T DFSFUN (NIL) -7 NIL NIL NIL) (-227 389145 392997 393309 "DFLOAT" 393774 T DFLOAT (NIL) -8 NIL NIL NIL) (-226 387408 387689 388078 "DFINTTLS" 388853 NIL DFINTTLS (NIL T T) -7 NIL NIL NIL) (-225 384437 385429 385829 "DERHAM" 387074 NIL DERHAM (NIL T NIL) -8 NIL NIL NIL) (-224 382238 384212 384301 "DEQUEUE" 384381 NIL DEQUEUE (NIL T) -8 NIL NIL NIL) (-223 381492 381625 381808 "DEGRED" 382100 NIL DEGRED (NIL T T) -7 NIL NIL NIL) (-222 377922 378667 379513 "DEFINTRF" 380720 NIL DEFINTRF (NIL T) -7 NIL NIL NIL) (-221 375477 375946 376538 "DEFINTEF" 377441 NIL DEFINTEF (NIL T T) -7 NIL NIL NIL) (-220 374827 375097 375212 "DEFAST" 375382 T DEFAST (NIL) -8 NIL NIL NIL) (-219 368829 374420 374570 "DECIMAL" 374697 T DECIMAL (NIL) -8 NIL NIL NIL) (-218 366341 366799 367305 "DDFACT" 368373 NIL DDFACT (NIL T T) -7 NIL NIL NIL) (-217 365937 365980 366131 "DBLRESP" 366292 NIL DBLRESP (NIL T T T T) -7 NIL NIL NIL) (-216 363809 364170 364530 "DBASE" 365704 NIL DBASE (NIL T) -8 NIL NIL NIL) (-215 363051 363289 363435 "DATAARY" 363708 NIL DATAARY (NIL NIL T) -8 NIL NIL NIL) (-214 362157 363010 363038 "D03FAFA" 363043 T D03FAFA (NIL) -8 NIL NIL NIL) (-213 361264 362116 362144 "D03EEFA" 362149 T D03EEFA (NIL) -8 NIL NIL NIL) (-212 359214 359680 360169 "D03AGNT" 360795 T D03AGNT (NIL) -7 NIL NIL NIL) (-211 358503 359173 359201 "D02EJFA" 359206 T D02EJFA (NIL) -8 NIL NIL NIL) (-210 357792 358462 358490 "D02CJFA" 358495 T D02CJFA (NIL) -8 NIL NIL NIL) (-209 357081 357751 357779 "D02BHFA" 357784 T D02BHFA (NIL) -8 NIL NIL NIL) (-208 356370 357040 357068 "D02BBFA" 357073 T D02BBFA (NIL) -8 NIL NIL NIL) (-207 349567 351156 352762 "D02AGNT" 354784 T D02AGNT (NIL) -7 NIL NIL NIL) (-206 347335 347858 348404 "D01WGTS" 349041 T D01WGTS (NIL) -7 NIL NIL NIL) (-205 346402 347294 347322 "D01TRNS" 347327 T D01TRNS (NIL) -8 NIL NIL NIL) (-204 345470 346361 346389 "D01GBFA" 346394 T D01GBFA (NIL) -8 NIL NIL NIL) (-203 344538 345429 345457 "D01FCFA" 345462 T D01FCFA (NIL) -8 NIL NIL NIL) (-202 343606 344497 344525 "D01ASFA" 344530 T D01ASFA (NIL) -8 NIL NIL NIL) (-201 342674 343565 343593 "D01AQFA" 343598 T D01AQFA (NIL) -8 NIL NIL NIL) (-200 341742 342633 342661 "D01APFA" 342666 T D01APFA (NIL) -8 NIL NIL NIL) (-199 340810 341701 341729 "D01ANFA" 341734 T D01ANFA (NIL) -8 NIL NIL NIL) (-198 339878 340769 340797 "D01AMFA" 340802 T D01AMFA (NIL) -8 NIL NIL NIL) (-197 338946 339837 339865 "D01ALFA" 339870 T D01ALFA (NIL) -8 NIL NIL NIL) (-196 338014 338905 338933 "D01AKFA" 338938 T D01AKFA (NIL) -8 NIL NIL NIL) (-195 337082 337973 338001 "D01AJFA" 338006 T D01AJFA (NIL) -8 NIL NIL NIL) (-194 330377 331930 333491 "D01AGNT" 335541 T D01AGNT (NIL) -7 NIL NIL NIL) (-193 329714 329842 329994 "CYCLOTOM" 330245 T CYCLOTOM (NIL) -7 NIL NIL NIL) (-192 326448 327162 327889 "CYCLES" 329007 T CYCLES (NIL) -7 NIL NIL NIL) (-191 325760 325894 326065 "CVMP" 326309 NIL CVMP (NIL T) -7 NIL NIL NIL) (-190 323601 323859 324228 "CTRIGMNP" 325488 NIL CTRIGMNP (NIL T T) -7 NIL NIL NIL) (-189 323037 323395 323468 "CTOR" 323548 T CTOR (NIL) -8 NIL NIL NIL) (-188 322546 322768 322869 "CTORKIND" 322956 T CTORKIND (NIL) -8 NIL NIL NIL) (-187 321837 322153 322181 "CTORCAT" 322363 T CTORCAT (NIL) -9 NIL 322476 NIL) (-186 321435 321546 321705 "CTORCAT-" 321710 NIL CTORCAT- (NIL T) -8 NIL NIL NIL) (-185 320897 321109 321217 "CTORCALL" 321359 NIL CTORCALL (NIL T) -8 NIL NIL NIL) (-184 320271 320370 320523 "CSTTOOLS" 320794 NIL CSTTOOLS (NIL T T) -7 NIL NIL NIL) (-183 316070 316727 317485 "CRFP" 319583 NIL CRFP (NIL T T) -7 NIL NIL NIL) (-182 315545 315791 315883 "CRCEAST" 315998 T CRCEAST (NIL) -8 NIL NIL NIL) (-181 314592 314777 315005 "CRAPACK" 315349 NIL CRAPACK (NIL T) -7 NIL NIL NIL) (-180 313976 314077 314281 "CPMATCH" 314468 NIL CPMATCH (NIL T T T) -7 NIL NIL NIL) (-179 313701 313729 313835 "CPIMA" 313942 NIL CPIMA (NIL T T T) -7 NIL NIL NIL) (-178 310049 310721 311440 "COORDSYS" 313036 NIL COORDSYS (NIL T) -7 NIL NIL NIL) (-177 309461 309582 309724 "CONTOUR" 309927 T CONTOUR (NIL) -8 NIL NIL NIL) (-176 305352 307464 307956 "CONTFRAC" 309001 NIL CONTFRAC (NIL T) -8 NIL NIL NIL) (-175 305232 305253 305281 "CONDUIT" 305318 T CONDUIT (NIL) -9 NIL NIL NIL) (-174 304320 304874 304902 "COMRING" 304907 T COMRING (NIL) -9 NIL 304959 NIL) (-173 303374 303678 303862 "COMPPROP" 304156 T COMPPROP (NIL) -8 NIL NIL NIL) (-172 303035 303070 303198 "COMPLPAT" 303333 NIL COMPLPAT (NIL T T T) -7 NIL NIL NIL) (-171 293326 302844 302953 "COMPLEX" 302958 NIL COMPLEX (NIL T) -8 NIL NIL NIL) (-170 292962 293019 293126 "COMPLEX2" 293263 NIL COMPLEX2 (NIL T T) -7 NIL NIL NIL) (-169 292301 292422 292582 "COMPILER" 292822 T COMPILER (NIL) -8 NIL NIL NIL) (-168 292019 292054 292152 "COMPFACT" 292260 NIL COMPFACT (NIL T T) -7 NIL NIL NIL) (-167 276099 286093 286133 "COMPCAT" 287137 NIL COMPCAT (NIL T) -9 NIL 288485 NIL) (-166 265611 268538 272165 "COMPCAT-" 272521 NIL COMPCAT- (NIL T T) -8 NIL NIL NIL) (-165 265340 265368 265471 "COMMUPC" 265577 NIL COMMUPC (NIL T T T) -7 NIL NIL NIL) (-164 265134 265168 265227 "COMMONOP" 265301 T COMMONOP (NIL) -7 NIL NIL NIL) (-163 264690 264885 264972 "COMM" 265067 T COMM (NIL) -8 NIL NIL NIL) (-162 264266 264494 264569 "COMMAAST" 264635 T COMMAAST (NIL) -8 NIL NIL NIL) (-161 263515 263709 263737 "COMBOPC" 264075 T COMBOPC (NIL) -9 NIL 264250 NIL) (-160 262411 262621 262863 "COMBINAT" 263305 NIL COMBINAT (NIL T) -7 NIL NIL NIL) (-159 258868 259442 260069 "COMBF" 261833 NIL COMBF (NIL T T) -7 NIL NIL NIL) (-158 257626 257984 258219 "COLOR" 258653 T COLOR (NIL) -8 NIL NIL NIL) (-157 257102 257347 257439 "COLONAST" 257554 T COLONAST (NIL) -8 NIL NIL NIL) (-156 256742 256789 256914 "CMPLXRT" 257049 NIL CMPLXRT (NIL T T) -7 NIL NIL NIL) (-155 256190 256442 256541 "CLLCTAST" 256663 T CLLCTAST (NIL) -8 NIL NIL NIL) (-154 251689 252720 253800 "CLIP" 255130 T CLIP (NIL) -7 NIL NIL NIL) (-153 250030 250790 251030 "CLIF" 251516 NIL CLIF (NIL NIL T NIL) -8 NIL NIL NIL) (-152 246205 248176 248217 "CLAGG" 249146 NIL CLAGG (NIL T) -9 NIL 249682 NIL) (-151 244627 245084 245667 "CLAGG-" 245672 NIL CLAGG- (NIL T T) -8 NIL NIL NIL) (-150 244171 244256 244396 "CINTSLPE" 244536 NIL CINTSLPE (NIL T T) -7 NIL NIL NIL) (-149 241672 242143 242691 "CHVAR" 243699 NIL CHVAR (NIL T T T) -7 NIL NIL NIL) (-148 240846 241400 241428 "CHARZ" 241433 T CHARZ (NIL) -9 NIL 241448 NIL) (-147 240600 240640 240718 "CHARPOL" 240800 NIL CHARPOL (NIL T) -7 NIL NIL NIL) (-146 239658 240245 240273 "CHARNZ" 240320 T CHARNZ (NIL) -9 NIL 240376 NIL) (-145 237564 238312 238665 "CHAR" 239325 T CHAR (NIL) -8 NIL NIL NIL) (-144 237290 237351 237379 "CFCAT" 237490 T CFCAT (NIL) -9 NIL NIL NIL) (-143 236531 236642 236825 "CDEN" 237174 NIL CDEN (NIL T T T) -7 NIL NIL NIL) (-142 232496 235684 235964 "CCLASS" 236271 T CCLASS (NIL) -8 NIL NIL NIL) (-141 231747 231904 232081 "CATEGORY" 232339 T -10 (NIL) -8 NIL NIL NIL) (-140 231320 231666 231714 "CATCTOR" 231719 T CATCTOR (NIL) -8 NIL NIL NIL) (-139 230771 231023 231121 "CATAST" 231242 T CATAST (NIL) -8 NIL NIL NIL) (-138 230247 230492 230584 "CASEAST" 230699 T CASEAST (NIL) -8 NIL NIL NIL) (-137 225256 226276 227029 "CARTEN" 229550 NIL CARTEN (NIL NIL NIL T) -8 NIL NIL NIL) (-136 224364 224512 224733 "CARTEN2" 225103 NIL CARTEN2 (NIL NIL NIL T T) -7 NIL NIL NIL) (-135 222680 223514 223771 "CARD" 224127 T CARD (NIL) -8 NIL NIL NIL) (-134 222256 222484 222559 "CAPSLAST" 222625 T CAPSLAST (NIL) -8 NIL NIL NIL) (-133 221760 221968 221996 "CACHSET" 222128 T CACHSET (NIL) -9 NIL 222206 NIL) (-132 221230 221552 221580 "CABMON" 221630 T CABMON (NIL) -9 NIL 221686 NIL) (-131 220703 220934 221044 "BYTEORD" 221140 T BYTEORD (NIL) -8 NIL NIL NIL) (-130 219685 220237 220379 "BYTE" 220542 T BYTE (NIL) -8 NIL NIL 220664) (-129 215035 219190 219362 "BYTEBUF" 219533 T BYTEBUF (NIL) -8 NIL NIL NIL) (-128 212544 214727 214834 "BTREE" 214961 NIL BTREE (NIL T) -8 NIL NIL NIL) (-127 209993 212192 212314 "BTOURN" 212454 NIL BTOURN (NIL T) -8 NIL NIL NIL) (-126 207363 209463 209504 "BTCAT" 209572 NIL BTCAT (NIL T) -9 NIL 209649 NIL) (-125 207030 207110 207259 "BTCAT-" 207264 NIL BTCAT- (NIL T T) -8 NIL NIL NIL) (-124 202440 206319 206347 "BTAGG" 206461 T BTAGG (NIL) -9 NIL 206571 NIL) (-123 201930 202055 202261 "BTAGG-" 202266 NIL BTAGG- (NIL T) -8 NIL NIL NIL) (-122 198925 201208 201423 "BSTREE" 201747 NIL BSTREE (NIL T) -8 NIL NIL NIL) (-121 198063 198189 198373 "BRILL" 198781 NIL BRILL (NIL T) -7 NIL NIL NIL) (-120 194715 196789 196830 "BRAGG" 197479 NIL BRAGG (NIL T) -9 NIL 197737 NIL) (-119 193244 193650 194205 "BRAGG-" 194210 NIL BRAGG- (NIL T T) -8 NIL NIL NIL) (-118 186471 192588 192773 "BPADICRT" 193091 NIL BPADICRT (NIL NIL) -8 NIL NIL NIL) (-117 184786 186408 186453 "BPADIC" 186458 NIL BPADIC (NIL NIL) -8 NIL NIL NIL) (-116 184484 184514 184628 "BOUNDZRO" 184750 NIL BOUNDZRO (NIL T T) -7 NIL NIL NIL) (-115 179712 180910 181822 "BOP" 183592 T BOP (NIL) -8 NIL NIL NIL) (-114 177493 177897 178372 "BOP1" 179270 NIL BOP1 (NIL T) -7 NIL NIL NIL) (-113 177194 177255 177283 "BOOLE" 177394 T BOOLE (NIL) -9 NIL 177476 NIL) (-112 176019 176768 176917 "BOOLEAN" 177065 T BOOLEAN (NIL) -8 NIL NIL NIL) (-111 175298 175702 175756 "BMODULE" 175761 NIL BMODULE (NIL T T) -9 NIL 175826 NIL) (-110 171099 175096 175169 "BITS" 175245 T BITS (NIL) -8 NIL NIL NIL) (-109 170520 170639 170779 "BINDING" 170979 T BINDING (NIL) -8 NIL NIL NIL) (-108 164525 170115 170264 "BINARY" 170391 T BINARY (NIL) -8 NIL NIL NIL) (-107 162305 163780 163821 "BGAGG" 164081 NIL BGAGG (NIL T) -9 NIL 164218 NIL) (-106 162136 162168 162259 "BGAGG-" 162264 NIL BGAGG- (NIL T T) -8 NIL NIL NIL) (-105 161207 161520 161725 "BFUNCT" 161951 T BFUNCT (NIL) -8 NIL NIL NIL) (-104 159897 160075 160363 "BEZOUT" 161031 NIL BEZOUT (NIL T T T T T) -7 NIL NIL NIL) (-103 156366 158749 159079 "BBTREE" 159600 NIL BBTREE (NIL T) -8 NIL NIL NIL) (-102 156100 156153 156181 "BASTYPE" 156300 T BASTYPE (NIL) -9 NIL NIL NIL) (-101 155952 155981 156054 "BASTYPE-" 156059 NIL BASTYPE- (NIL T) -8 NIL NIL NIL) (-100 155386 155462 155614 "BALFACT" 155863 NIL BALFACT (NIL T T) -7 NIL NIL NIL) (-99 154242 154801 154987 "AUTOMOR" 155231 NIL AUTOMOR (NIL T) -8 NIL NIL NIL) (-98 153968 153973 153999 "ATTREG" 154004 T ATTREG (NIL) -9 NIL NIL NIL) (-97 152220 152665 153017 "ATTRBUT" 153634 T ATTRBUT (NIL) -8 NIL NIL NIL) (-96 151828 152048 152114 "ATTRAST" 152172 T ATTRAST (NIL) -8 NIL NIL NIL) (-95 151364 151477 151503 "ATRIG" 151704 T ATRIG (NIL) -9 NIL NIL NIL) (-94 151173 151214 151301 "ATRIG-" 151306 NIL ATRIG- (NIL T) -8 NIL NIL NIL) (-93 150818 151004 151030 "ASTCAT" 151035 T ASTCAT (NIL) -9 NIL 151065 NIL) (-92 150545 150604 150723 "ASTCAT-" 150728 NIL ASTCAT- (NIL T) -8 NIL NIL NIL) (-91 148694 150321 150409 "ASTACK" 150488 NIL ASTACK (NIL T) -8 NIL NIL NIL) (-90 147199 147496 147861 "ASSOCEQ" 148376 NIL ASSOCEQ (NIL T T) -7 NIL NIL NIL) (-89 146231 146858 146982 "ASP9" 147106 NIL ASP9 (NIL NIL) -8 NIL NIL NIL) (-88 145994 146179 146218 "ASP8" 146223 NIL ASP8 (NIL NIL) -8 NIL NIL NIL) (-87 144862 145599 145741 "ASP80" 145883 NIL ASP80 (NIL NIL) -8 NIL NIL NIL) (-86 143760 144497 144629 "ASP7" 144761 NIL ASP7 (NIL NIL) -8 NIL NIL NIL) (-85 142714 143437 143555 "ASP78" 143673 NIL ASP78 (NIL NIL) -8 NIL NIL NIL) (-84 141683 142394 142511 "ASP77" 142628 NIL ASP77 (NIL NIL) -8 NIL NIL NIL) (-83 140595 141321 141452 "ASP74" 141583 NIL ASP74 (NIL NIL) -8 NIL NIL NIL) (-82 139495 140230 140362 "ASP73" 140494 NIL ASP73 (NIL NIL) -8 NIL NIL NIL) (-81 138599 139321 139421 "ASP6" 139426 NIL ASP6 (NIL NIL) -8 NIL NIL NIL) (-80 137544 138276 138394 "ASP55" 138512 NIL ASP55 (NIL NIL) -8 NIL NIL NIL) (-79 136493 137218 137337 "ASP50" 137456 NIL ASP50 (NIL NIL) -8 NIL NIL NIL) (-78 135581 136194 136304 "ASP4" 136414 NIL ASP4 (NIL NIL) -8 NIL NIL NIL) (-77 134669 135282 135392 "ASP49" 135502 NIL ASP49 (NIL NIL) -8 NIL NIL NIL) (-76 133453 134208 134376 "ASP42" 134558 NIL ASP42 (NIL NIL NIL NIL) -8 NIL NIL NIL) (-75 132229 132986 133156 "ASP41" 133340 NIL ASP41 (NIL NIL NIL NIL) -8 NIL NIL NIL) (-74 131179 131906 132024 "ASP35" 132142 NIL ASP35 (NIL NIL) -8 NIL NIL NIL) (-73 130944 131127 131166 "ASP34" 131171 NIL ASP34 (NIL NIL) -8 NIL NIL NIL) (-72 130681 130748 130824 "ASP33" 130899 NIL ASP33 (NIL NIL) -8 NIL NIL NIL) (-71 129574 130316 130448 "ASP31" 130580 NIL ASP31 (NIL NIL) -8 NIL NIL NIL) (-70 129339 129522 129561 "ASP30" 129566 NIL ASP30 (NIL NIL) -8 NIL NIL NIL) (-69 129074 129143 129219 "ASP29" 129294 NIL ASP29 (NIL NIL) -8 NIL NIL NIL) (-68 128839 129022 129061 "ASP28" 129066 NIL ASP28 (NIL NIL) -8 NIL NIL NIL) (-67 128604 128787 128826 "ASP27" 128831 NIL ASP27 (NIL NIL) -8 NIL NIL NIL) (-66 127688 128302 128413 "ASP24" 128524 NIL ASP24 (NIL NIL) -8 NIL NIL NIL) (-65 126764 127490 127602 "ASP20" 127607 NIL ASP20 (NIL NIL) -8 NIL NIL NIL) (-64 125852 126465 126575 "ASP1" 126685 NIL ASP1 (NIL NIL) -8 NIL NIL NIL) (-63 124794 125526 125645 "ASP19" 125764 NIL ASP19 (NIL NIL) -8 NIL NIL NIL) (-62 124531 124598 124674 "ASP12" 124749 NIL ASP12 (NIL NIL) -8 NIL NIL NIL) (-61 123383 124130 124274 "ASP10" 124418 NIL ASP10 (NIL NIL) -8 NIL NIL NIL) (-60 121234 123227 123318 "ARRAY2" 123323 NIL ARRAY2 (NIL T) -8 NIL NIL NIL) (-59 116999 120882 120996 "ARRAY1" 121151 NIL ARRAY1 (NIL T) -8 NIL NIL NIL) (-58 116031 116204 116425 "ARRAY12" 116822 NIL ARRAY12 (NIL T T) -7 NIL NIL NIL) (-57 110343 112261 112336 "ARR2CAT" 114966 NIL ARR2CAT (NIL T T T) -9 NIL 115724 NIL) (-56 107777 108521 109475 "ARR2CAT-" 109480 NIL ARR2CAT- (NIL T T T T) -8 NIL NIL NIL) (-55 107094 107404 107529 "ARITY" 107670 T ARITY (NIL) -8 NIL NIL NIL) (-54 105870 106022 106321 "APPRULE" 106930 NIL APPRULE (NIL T T T) -7 NIL NIL NIL) (-53 105521 105569 105688 "APPLYORE" 105816 NIL APPLYORE (NIL T T T) -7 NIL NIL NIL) (-52 104875 105114 105234 "ANY" 105419 T ANY (NIL) -8 NIL NIL NIL) (-51 104153 104276 104433 "ANY1" 104749 NIL ANY1 (NIL T) -7 NIL NIL NIL) (-50 101683 102590 102917 "ANTISYM" 103877 NIL ANTISYM (NIL T NIL) -8 NIL NIL NIL) (-49 101175 101390 101486 "ANON" 101605 T ANON (NIL) -8 NIL NIL NIL) (-48 95424 99714 100168 "AN" 100739 T AN (NIL) -8 NIL NIL NIL) (-47 91322 92710 92761 "AMR" 93509 NIL AMR (NIL T T) -9 NIL 94109 NIL) (-46 90434 90655 91018 "AMR-" 91023 NIL AMR- (NIL T T T) -8 NIL NIL NIL) (-45 74873 90351 90412 "ALIST" 90417 NIL ALIST (NIL T T) -8 NIL NIL NIL) (-44 71676 74467 74636 "ALGSC" 74791 NIL ALGSC (NIL T NIL NIL NIL) -8 NIL NIL NIL) (-43 68231 68786 69393 "ALGPKG" 71116 NIL ALGPKG (NIL T T) -7 NIL NIL NIL) (-42 67508 67609 67793 "ALGMFACT" 68117 NIL ALGMFACT (NIL T T T) -7 NIL NIL NIL) (-41 63543 64122 64716 "ALGMANIP" 67092 NIL ALGMANIP (NIL T T) -7 NIL NIL NIL) (-40 54913 63169 63319 "ALGFF" 63476 NIL ALGFF (NIL T T T NIL) -8 NIL NIL NIL) (-39 54109 54240 54419 "ALGFACT" 54771 NIL ALGFACT (NIL T) -7 NIL NIL NIL) (-38 53050 53650 53688 "ALGEBRA" 53693 NIL ALGEBRA (NIL T) -9 NIL 53734 NIL) (-37 52768 52827 52959 "ALGEBRA-" 52964 NIL ALGEBRA- (NIL T T) -8 NIL NIL NIL) (-36 34861 50770 50822 "ALAGG" 50958 NIL ALAGG (NIL T T) -9 NIL 51119 NIL) (-35 34397 34510 34536 "AHYP" 34737 T AHYP (NIL) -9 NIL NIL NIL) (-34 33328 33576 33602 "AGG" 34101 T AGG (NIL) -9 NIL 34380 NIL) (-33 32762 32924 33138 "AGG-" 33143 NIL AGG- (NIL T) -8 NIL NIL NIL) (-32 30568 30991 31396 "AF" 32404 NIL AF (NIL T T) -7 NIL NIL NIL) (-31 30048 30293 30383 "ADDAST" 30496 T ADDAST (NIL) -8 NIL NIL NIL) (-30 29316 29575 29731 "ACPLOT" 29910 T ACPLOT (NIL) -8 NIL NIL NIL) (-29 18639 26443 26481 "ACFS" 27088 NIL ACFS (NIL T) -9 NIL 27327 NIL) (-28 16666 17156 17918 "ACFS-" 17923 NIL ACFS- (NIL T T) -8 NIL NIL NIL) (-27 12784 14713 14739 "ACF" 15618 T ACF (NIL) -9 NIL 16031 NIL) (-26 11488 11822 12315 "ACF-" 12320 NIL ACF- (NIL T) -8 NIL NIL NIL) (-25 11060 11255 11281 "ABELSG" 11373 T ABELSG (NIL) -9 NIL 11438 NIL) (-24 10927 10952 11018 "ABELSG-" 11023 NIL ABELSG- (NIL T) -8 NIL NIL NIL) (-23 10270 10557 10583 "ABELMON" 10753 T ABELMON (NIL) -9 NIL 10865 NIL) (-22 9934 10018 10156 "ABELMON-" 10161 NIL ABELMON- (NIL T) -8 NIL NIL NIL) (-21 9282 9654 9680 "ABELGRP" 9752 T ABELGRP (NIL) -9 NIL 9827 NIL) (-20 8745 8874 9090 "ABELGRP-" 9095 NIL ABELGRP- (NIL T) -8 NIL NIL NIL) (-19 4334 8084 8123 "A1AGG" 8128 NIL A1AGG (NIL T) -9 NIL 8168 NIL) (-18 30 1252 2814 "A1AGG-" 2819 NIL A1AGG- (NIL T T) -8 NIL NIL NIL))
\ No newline at end of file +((-3 3228581 3228586 3228591 NIL NIL NIL NIL (NIL) -8 NIL NIL NIL) (-2 3228566 3228571 3228576 NIL NIL NIL NIL (NIL) -8 NIL NIL NIL) (-1 3228551 3228556 3228561 NIL NIL NIL NIL (NIL) -8 NIL NIL NIL) (0 3228536 3228541 3228546 NIL NIL NIL NIL (NIL) -8 NIL NIL NIL) (-1305 3227679 3228411 3228488 "ZMOD" 3228493 NIL ZMOD (NIL NIL) -8 NIL NIL NIL) (-1304 3226789 3226953 3227162 "ZLINDEP" 3227511 NIL ZLINDEP (NIL T) -7 NIL NIL NIL) (-1303 3216089 3217857 3219829 "ZDSOLVE" 3224919 NIL ZDSOLVE (NIL T NIL NIL) -7 NIL NIL NIL) (-1302 3215335 3215476 3215665 "YSTREAM" 3215935 NIL YSTREAM (NIL T) -7 NIL NIL NIL) (-1301 3213109 3214636 3214840 "XRPOLY" 3215178 NIL XRPOLY (NIL T T) -8 NIL NIL NIL) (-1300 3209662 3210980 3211555 "XPR" 3212581 NIL XPR (NIL T T) -8 NIL NIL NIL) (-1299 3207383 3208993 3209197 "XPOLY" 3209493 NIL XPOLY (NIL T) -8 NIL NIL NIL) (-1298 3205036 3206404 3206459 "XPOLYC" 3206747 NIL XPOLYC (NIL T T) -9 NIL 3206860 NIL) (-1297 3201412 3203553 3203941 "XPBWPOLY" 3204694 NIL XPBWPOLY (NIL T T) -8 NIL NIL NIL) (-1296 3197107 3199402 3199444 "XF" 3200065 NIL XF (NIL T) -9 NIL 3200465 NIL) (-1295 3196728 3196816 3196985 "XF-" 3196990 NIL XF- (NIL T T) -8 NIL NIL NIL) (-1294 3191924 3193213 3193268 "XFALG" 3195440 NIL XFALG (NIL T T) -9 NIL 3196229 NIL) (-1293 3191057 3191161 3191366 "XEXPPKG" 3191816 NIL XEXPPKG (NIL T T T) -7 NIL NIL NIL) (-1292 3189166 3190907 3191003 "XDPOLY" 3191008 NIL XDPOLY (NIL T T) -8 NIL NIL NIL) (-1291 3187973 3188573 3188616 "XALG" 3188621 NIL XALG (NIL T) -9 NIL 3188732 NIL) (-1290 3181415 3185950 3186444 "WUTSET" 3187565 NIL WUTSET (NIL T T T T) -8 NIL NIL NIL) (-1289 3179671 3180467 3180790 "WP" 3181226 NIL WP (NIL T T T T NIL NIL NIL) -8 NIL NIL NIL) (-1288 3179273 3179493 3179563 "WHILEAST" 3179623 T WHILEAST (NIL) -8 NIL NIL NIL) (-1287 3178745 3178990 3179084 "WHEREAST" 3179201 T WHEREAST (NIL) -8 NIL NIL NIL) (-1286 3177631 3177829 3178124 "WFFINTBS" 3178542 NIL WFFINTBS (NIL T T T T) -7 NIL NIL NIL) (-1285 3175535 3175962 3176424 "WEIER" 3177203 NIL WEIER (NIL T) -7 NIL NIL NIL) (-1284 3174581 3175031 3175073 "VSPACE" 3175209 NIL VSPACE (NIL T) -9 NIL 3175283 NIL) (-1283 3174419 3174446 3174537 "VSPACE-" 3174542 NIL VSPACE- (NIL T T) -8 NIL NIL NIL) (-1282 3174228 3174270 3174338 "VOID" 3174373 T VOID (NIL) -8 NIL NIL NIL) (-1281 3172364 3172723 3173129 "VIEW" 3173844 T VIEW (NIL) -7 NIL NIL NIL) (-1280 3168788 3169427 3170164 "VIEWDEF" 3171649 T VIEWDEF (NIL) -7 NIL NIL NIL) (-1279 3158092 3160336 3162509 "VIEW3D" 3166637 T VIEW3D (NIL) -8 NIL NIL NIL) (-1278 3150343 3152003 3153582 "VIEW2D" 3156535 T VIEW2D (NIL) -8 NIL NIL NIL) (-1277 3145696 3150113 3150205 "VECTOR" 3150286 NIL VECTOR (NIL T) -8 NIL NIL NIL) (-1276 3144273 3144532 3144850 "VECTOR2" 3145426 NIL VECTOR2 (NIL T T) -7 NIL NIL NIL) (-1275 3137747 3142054 3142097 "VECTCAT" 3143092 NIL VECTCAT (NIL T) -9 NIL 3143679 NIL) (-1274 3136761 3137015 3137405 "VECTCAT-" 3137410 NIL VECTCAT- (NIL T T) -8 NIL NIL NIL) (-1273 3136215 3136412 3136532 "VARIABLE" 3136676 NIL VARIABLE (NIL NIL) -8 NIL NIL NIL) (-1272 3136148 3136153 3136183 "UTYPE" 3136188 T UTYPE (NIL) -9 NIL NIL NIL) (-1271 3134978 3135132 3135394 "UTSODETL" 3135974 NIL UTSODETL (NIL T T T T) -7 NIL NIL NIL) (-1270 3132418 3132878 3133402 "UTSODE" 3134519 NIL UTSODE (NIL T T) -7 NIL NIL NIL) (-1269 3124256 3130044 3130533 "UTS" 3131987 NIL UTS (NIL T NIL NIL) -8 NIL NIL NIL) (-1268 3115130 3120497 3120540 "UTSCAT" 3121652 NIL UTSCAT (NIL T) -9 NIL 3122410 NIL) (-1267 3112478 3113200 3114189 "UTSCAT-" 3114194 NIL UTSCAT- (NIL T T) -8 NIL NIL NIL) (-1266 3112105 3112148 3112281 "UTS2" 3112429 NIL UTS2 (NIL T T T T) -7 NIL NIL NIL) (-1265 3106331 3108943 3108986 "URAGG" 3111056 NIL URAGG (NIL T) -9 NIL 3111779 NIL) (-1264 3103270 3104133 3105256 "URAGG-" 3105261 NIL URAGG- (NIL T T) -8 NIL NIL NIL) (-1263 3098979 3101905 3102370 "UPXSSING" 3102934 NIL UPXSSING (NIL T T NIL NIL) -8 NIL NIL NIL) (-1262 3091045 3098226 3098499 "UPXS" 3098764 NIL UPXS (NIL T NIL NIL) -8 NIL NIL NIL) (-1261 3084118 3090949 3091021 "UPXSCONS" 3091026 NIL UPXSCONS (NIL T T) -8 NIL NIL NIL) (-1260 3073863 3080656 3080718 "UPXSCCA" 3081292 NIL UPXSCCA (NIL T T) -9 NIL 3081525 NIL) (-1259 3073501 3073586 3073760 "UPXSCCA-" 3073765 NIL UPXSCCA- (NIL T T T) -8 NIL NIL NIL) (-1258 3063098 3069664 3069707 "UPXSCAT" 3070355 NIL UPXSCAT (NIL T) -9 NIL 3070964 NIL) (-1257 3062528 3062607 3062786 "UPXS2" 3063013 NIL UPXS2 (NIL T T NIL NIL NIL NIL) -7 NIL NIL NIL) (-1256 3061182 3061435 3061786 "UPSQFREE" 3062271 NIL UPSQFREE (NIL T T) -7 NIL NIL NIL) (-1255 3054603 3057660 3057715 "UPSCAT" 3058876 NIL UPSCAT (NIL T T) -9 NIL 3059650 NIL) (-1254 3053807 3054014 3054341 "UPSCAT-" 3054346 NIL UPSCAT- (NIL T T T) -8 NIL NIL NIL) (-1253 3039462 3047230 3047273 "UPOLYC" 3049374 NIL UPOLYC (NIL T) -9 NIL 3050595 NIL) (-1252 3030790 3033216 3036363 "UPOLYC-" 3036368 NIL UPOLYC- (NIL T T) -8 NIL NIL NIL) (-1251 3030417 3030460 3030593 "UPOLYC2" 3030741 NIL UPOLYC2 (NIL T T T T) -7 NIL NIL NIL) (-1250 3022228 3030100 3030229 "UP" 3030336 NIL UP (NIL NIL T) -8 NIL NIL NIL) (-1249 3021567 3021674 3021838 "UPMP" 3022117 NIL UPMP (NIL T T) -7 NIL NIL NIL) (-1248 3021120 3021201 3021340 "UPDIVP" 3021480 NIL UPDIVP (NIL T T) -7 NIL NIL NIL) (-1247 3019688 3019937 3020253 "UPDECOMP" 3020869 NIL UPDECOMP (NIL T T) -7 NIL NIL NIL) (-1246 3018919 3019031 3019217 "UPCDEN" 3019572 NIL UPCDEN (NIL T T T) -7 NIL NIL NIL) (-1245 3018438 3018507 3018656 "UP2" 3018844 NIL UP2 (NIL NIL T NIL T) -7 NIL NIL NIL) (-1244 3016905 3017642 3017919 "UNISEG" 3018196 NIL UNISEG (NIL T) -8 NIL NIL NIL) (-1243 3016120 3016247 3016452 "UNISEG2" 3016748 NIL UNISEG2 (NIL T T) -7 NIL NIL NIL) (-1242 3015180 3015360 3015586 "UNIFACT" 3015936 NIL UNIFACT (NIL T) -7 NIL NIL NIL) (-1241 2999112 3014357 3014608 "ULS" 3014987 NIL ULS (NIL T NIL NIL) -8 NIL NIL NIL) (-1240 2987110 2999016 2999088 "ULSCONS" 2999093 NIL ULSCONS (NIL T T) -8 NIL NIL NIL) (-1239 2969127 2981112 2981174 "ULSCCAT" 2981812 NIL ULSCCAT (NIL T T) -9 NIL 2982101 NIL) (-1238 2968177 2968422 2968810 "ULSCCAT-" 2968815 NIL ULSCCAT- (NIL T T T) -8 NIL NIL NIL) (-1237 2957551 2964031 2964074 "ULSCAT" 2964937 NIL ULSCAT (NIL T) -9 NIL 2965668 NIL) (-1236 2956981 2957060 2957239 "ULS2" 2957466 NIL ULS2 (NIL T T NIL NIL NIL NIL) -7 NIL NIL NIL) (-1235 2956108 2956618 2956725 "UINT8" 2956836 T UINT8 (NIL) -8 NIL NIL 2956921) (-1234 2955234 2955744 2955851 "UINT64" 2955962 T UINT64 (NIL) -8 NIL NIL 2956047) (-1233 2954360 2954870 2954977 "UINT32" 2955088 T UINT32 (NIL) -8 NIL NIL 2955173) (-1232 2953486 2953996 2954103 "UINT16" 2954214 T UINT16 (NIL) -8 NIL NIL 2954299) (-1231 2951789 2952746 2952776 "UFD" 2952988 T UFD (NIL) -9 NIL 2953102 NIL) (-1230 2951583 2951629 2951724 "UFD-" 2951729 NIL UFD- (NIL T) -8 NIL NIL NIL) (-1229 2950665 2950848 2951064 "UDVO" 2951389 T UDVO (NIL) -7 NIL NIL NIL) (-1228 2948481 2948890 2949361 "UDPO" 2950229 NIL UDPO (NIL T) -7 NIL NIL NIL) (-1227 2948414 2948419 2948449 "TYPE" 2948454 T TYPE (NIL) -9 NIL NIL NIL) (-1226 2948174 2948369 2948400 "TYPEAST" 2948405 T TYPEAST (NIL) -8 NIL NIL NIL) (-1225 2947145 2947347 2947587 "TWOFACT" 2947968 NIL TWOFACT (NIL T) -7 NIL NIL NIL) (-1224 2946168 2946554 2946789 "TUPLE" 2946945 NIL TUPLE (NIL T) -8 NIL NIL NIL) (-1223 2943859 2944378 2944917 "TUBETOOL" 2945651 T TUBETOOL (NIL) -7 NIL NIL NIL) (-1222 2942708 2942913 2943154 "TUBE" 2943652 NIL TUBE (NIL T) -8 NIL NIL NIL) (-1221 2937437 2941680 2941963 "TS" 2942460 NIL TS (NIL T) -8 NIL NIL NIL) (-1220 2926077 2930196 2930293 "TSETCAT" 2935562 NIL TSETCAT (NIL T T T T) -9 NIL 2937093 NIL) (-1219 2920809 2922409 2924300 "TSETCAT-" 2924305 NIL TSETCAT- (NIL T T T T T) -8 NIL NIL NIL) (-1218 2915448 2916295 2917224 "TRMANIP" 2919945 NIL TRMANIP (NIL T T) -7 NIL NIL NIL) (-1217 2914889 2914952 2915115 "TRIMAT" 2915380 NIL TRIMAT (NIL T T T T) -7 NIL NIL NIL) (-1216 2912755 2912992 2913349 "TRIGMNIP" 2914638 NIL TRIGMNIP (NIL T T) -7 NIL NIL NIL) (-1215 2912275 2912388 2912418 "TRIGCAT" 2912631 T TRIGCAT (NIL) -9 NIL NIL NIL) (-1214 2911944 2912023 2912164 "TRIGCAT-" 2912169 NIL TRIGCAT- (NIL T) -8 NIL NIL NIL) (-1213 2908789 2910802 2911083 "TREE" 2911698 NIL TREE (NIL T) -8 NIL NIL NIL) (-1212 2908063 2908591 2908621 "TRANFUN" 2908656 T TRANFUN (NIL) -9 NIL 2908722 NIL) (-1211 2907342 2907533 2907813 "TRANFUN-" 2907818 NIL TRANFUN- (NIL T) -8 NIL NIL NIL) (-1210 2907146 2907178 2907239 "TOPSP" 2907303 T TOPSP (NIL) -7 NIL NIL NIL) (-1209 2906494 2906609 2906763 "TOOLSIGN" 2907027 NIL TOOLSIGN (NIL T) -7 NIL NIL NIL) (-1208 2905128 2905671 2905910 "TEXTFILE" 2906277 T TEXTFILE (NIL) -8 NIL NIL NIL) (-1207 2903040 2903581 2904010 "TEX" 2904721 T TEX (NIL) -8 NIL NIL NIL) (-1206 2902821 2902852 2902924 "TEX1" 2903003 NIL TEX1 (NIL T) -7 NIL NIL NIL) (-1205 2902469 2902532 2902622 "TEMUTL" 2902753 T TEMUTL (NIL) -7 NIL NIL NIL) (-1204 2900623 2900903 2901228 "TBCMPPK" 2902192 NIL TBCMPPK (NIL T T) -7 NIL NIL NIL) (-1203 2892400 2898783 2898839 "TBAGG" 2899239 NIL TBAGG (NIL T T) -9 NIL 2899450 NIL) (-1202 2887470 2888958 2890712 "TBAGG-" 2890717 NIL TBAGG- (NIL T T T) -8 NIL NIL NIL) (-1201 2886854 2886961 2887106 "TANEXP" 2887359 NIL TANEXP (NIL T) -7 NIL NIL NIL) (-1200 2886365 2886629 2886719 "TALGOP" 2886799 NIL TALGOP (NIL T) -8 NIL NIL NIL) (-1199 2879755 2886222 2886315 "TABLE" 2886320 NIL TABLE (NIL T T) -8 NIL NIL NIL) (-1198 2879167 2879266 2879404 "TABLEAU" 2879652 NIL TABLEAU (NIL T) -8 NIL NIL NIL) (-1197 2873775 2874995 2876243 "TABLBUMP" 2877953 NIL TABLBUMP (NIL T) -7 NIL NIL NIL) (-1196 2872997 2873144 2873325 "SYSTEM" 2873616 T SYSTEM (NIL) -8 NIL NIL NIL) (-1195 2869456 2870155 2870938 "SYSSOLP" 2872248 NIL SYSSOLP (NIL T) -7 NIL NIL NIL) (-1194 2869254 2869411 2869442 "SYSPTR" 2869447 T SYSPTR (NIL) -8 NIL NIL NIL) (-1193 2868298 2868803 2868922 "SYSNNI" 2869108 NIL SYSNNI (NIL NIL) -8 NIL NIL 2869193) (-1192 2867605 2868064 2868143 "SYSINT" 2868203 NIL SYSINT (NIL NIL) -8 NIL NIL 2868248) (-1191 2863937 2864883 2865593 "SYNTAX" 2866917 T SYNTAX (NIL) -8 NIL NIL NIL) (-1190 2861095 2861697 2862329 "SYMTAB" 2863327 T SYMTAB (NIL) -8 NIL NIL NIL) (-1189 2856344 2857246 2858229 "SYMS" 2860134 T SYMS (NIL) -8 NIL NIL NIL) (-1188 2853579 2855802 2856032 "SYMPOLY" 2856149 NIL SYMPOLY (NIL T) -8 NIL NIL NIL) (-1187 2853096 2853171 2853294 "SYMFUNC" 2853491 NIL SYMFUNC (NIL T) -7 NIL NIL NIL) (-1186 2849116 2850408 2851221 "SYMBOL" 2852305 T SYMBOL (NIL) -8 NIL NIL NIL) (-1185 2842655 2844344 2846064 "SWITCH" 2847418 T SWITCH (NIL) -8 NIL NIL NIL) (-1184 2835889 2841476 2841779 "SUTS" 2842410 NIL SUTS (NIL T NIL NIL) -8 NIL NIL NIL) (-1183 2827955 2835136 2835409 "SUPXS" 2835674 NIL SUPXS (NIL T NIL NIL) -8 NIL NIL NIL) (-1182 2819714 2827573 2827699 "SUP" 2827864 NIL SUP (NIL T) -8 NIL NIL NIL) (-1181 2818873 2819000 2819217 "SUPFRACF" 2819582 NIL SUPFRACF (NIL T T T T) -7 NIL NIL NIL) (-1180 2818494 2818553 2818666 "SUP2" 2818808 NIL SUP2 (NIL T T) -7 NIL NIL NIL) (-1179 2816942 2817216 2817572 "SUMRF" 2818193 NIL SUMRF (NIL T) -7 NIL NIL NIL) (-1178 2816277 2816343 2816535 "SUMFS" 2816863 NIL SUMFS (NIL T T) -7 NIL NIL NIL) (-1177 2800244 2815454 2815705 "SULS" 2816084 NIL SULS (NIL T NIL NIL) -8 NIL NIL NIL) (-1176 2799846 2800066 2800136 "SUCHTAST" 2800196 T SUCHTAST (NIL) -8 NIL NIL NIL) (-1175 2799141 2799371 2799511 "SUCH" 2799754 NIL SUCH (NIL T T) -8 NIL NIL NIL) (-1174 2793008 2794047 2795006 "SUBSPACE" 2798229 NIL SUBSPACE (NIL NIL T) -8 NIL NIL NIL) (-1173 2792438 2792528 2792692 "SUBRESP" 2792896 NIL SUBRESP (NIL T T) -7 NIL NIL NIL) (-1172 2785806 2787103 2788414 "STTF" 2791174 NIL STTF (NIL T) -7 NIL NIL NIL) (-1171 2779979 2781099 2782246 "STTFNC" 2784706 NIL STTFNC (NIL T) -7 NIL NIL NIL) (-1170 2771292 2773161 2774955 "STTAYLOR" 2778220 NIL STTAYLOR (NIL T) -7 NIL NIL NIL) (-1169 2764422 2771156 2771239 "STRTBL" 2771244 NIL STRTBL (NIL T) -8 NIL NIL NIL) (-1168 2759786 2764377 2764408 "STRING" 2764413 T STRING (NIL) -8 NIL NIL NIL) (-1167 2754647 2759159 2759189 "STRICAT" 2759248 T STRICAT (NIL) -9 NIL 2759310 NIL) (-1166 2747400 2752266 2752877 "STREAM" 2754071 NIL STREAM (NIL T) -8 NIL NIL NIL) (-1165 2746910 2746987 2747131 "STREAM3" 2747317 NIL STREAM3 (NIL T T T) -7 NIL NIL NIL) (-1164 2745892 2746075 2746310 "STREAM2" 2746723 NIL STREAM2 (NIL T T) -7 NIL NIL NIL) (-1163 2745580 2745632 2745725 "STREAM1" 2745834 NIL STREAM1 (NIL T) -7 NIL NIL NIL) (-1162 2744596 2744777 2745008 "STINPROD" 2745396 NIL STINPROD (NIL T) -7 NIL NIL NIL) (-1161 2744148 2744358 2744388 "STEP" 2744468 T STEP (NIL) -9 NIL 2744546 NIL) (-1160 2743335 2743637 2743785 "STEPAST" 2744022 T STEPAST (NIL) -8 NIL NIL NIL) (-1159 2736767 2743234 2743311 "STBL" 2743316 NIL STBL (NIL T T NIL) -8 NIL NIL NIL) (-1158 2731893 2735988 2736031 "STAGG" 2736184 NIL STAGG (NIL T) -9 NIL 2736273 NIL) (-1157 2729595 2730197 2731069 "STAGG-" 2731074 NIL STAGG- (NIL T T) -8 NIL NIL NIL) (-1156 2727742 2729365 2729457 "STACK" 2729538 NIL STACK (NIL T) -8 NIL NIL NIL) (-1155 2720437 2725883 2726339 "SREGSET" 2727372 NIL SREGSET (NIL T T T T) -8 NIL NIL NIL) (-1154 2712862 2714231 2715744 "SRDCMPK" 2719043 NIL SRDCMPK (NIL T T T T T) -7 NIL NIL NIL) (-1153 2705779 2710302 2710332 "SRAGG" 2711635 T SRAGG (NIL) -9 NIL 2712243 NIL) (-1152 2704796 2705051 2705430 "SRAGG-" 2705435 NIL SRAGG- (NIL T) -8 NIL NIL NIL) (-1151 2699256 2703743 2704164 "SQMATRIX" 2704422 NIL SQMATRIX (NIL NIL T) -8 NIL NIL NIL) (-1150 2692941 2695974 2696701 "SPLTREE" 2698601 NIL SPLTREE (NIL T T) -8 NIL NIL NIL) (-1149 2688904 2689597 2690243 "SPLNODE" 2692367 NIL SPLNODE (NIL T T) -8 NIL NIL NIL) (-1148 2687951 2688184 2688214 "SPFCAT" 2688658 T SPFCAT (NIL) -9 NIL NIL NIL) (-1147 2686688 2686898 2687162 "SPECOUT" 2687709 T SPECOUT (NIL) -7 NIL NIL NIL) (-1146 2677798 2679670 2679700 "SPADXPT" 2684376 T SPADXPT (NIL) -9 NIL 2686540 NIL) (-1145 2677559 2677599 2677668 "SPADPRSR" 2677751 T SPADPRSR (NIL) -7 NIL NIL NIL) (-1144 2675608 2677514 2677545 "SPADAST" 2677550 T SPADAST (NIL) -8 NIL NIL NIL) (-1143 2667553 2669326 2669369 "SPACEC" 2673742 NIL SPACEC (NIL T) -9 NIL 2675558 NIL) (-1142 2665683 2667485 2667534 "SPACE3" 2667539 NIL SPACE3 (NIL T) -8 NIL NIL NIL) (-1141 2664435 2664606 2664897 "SORTPAK" 2665488 NIL SORTPAK (NIL T T) -7 NIL NIL NIL) (-1140 2662527 2662830 2663242 "SOLVETRA" 2664099 NIL SOLVETRA (NIL T) -7 NIL NIL NIL) (-1139 2661577 2661799 2662060 "SOLVESER" 2662300 NIL SOLVESER (NIL T) -7 NIL NIL NIL) (-1138 2656881 2657769 2658764 "SOLVERAD" 2660629 NIL SOLVERAD (NIL T) -7 NIL NIL NIL) (-1137 2652696 2653305 2654034 "SOLVEFOR" 2656248 NIL SOLVEFOR (NIL T T) -7 NIL NIL NIL) (-1136 2646966 2652045 2652142 "SNTSCAT" 2652147 NIL SNTSCAT (NIL T T T T) -9 NIL 2652217 NIL) (-1135 2641072 2645289 2645680 "SMTS" 2646656 NIL SMTS (NIL T T T) -8 NIL NIL NIL) (-1134 2635757 2640960 2641037 "SMP" 2641042 NIL SMP (NIL T T) -8 NIL NIL NIL) (-1133 2633916 2634217 2634615 "SMITH" 2635454 NIL SMITH (NIL T T T T) -7 NIL NIL NIL) (-1132 2626629 2630825 2630928 "SMATCAT" 2632279 NIL SMATCAT (NIL NIL T T T) -9 NIL 2632829 NIL) (-1131 2623569 2624392 2625570 "SMATCAT-" 2625575 NIL SMATCAT- (NIL T NIL T T T) -8 NIL NIL NIL) (-1130 2621235 2622805 2622848 "SKAGG" 2623109 NIL SKAGG (NIL T) -9 NIL 2623244 NIL) (-1129 2617561 2620708 2620892 "SINT" 2621044 T SINT (NIL) -8 NIL NIL 2621206) (-1128 2617333 2617371 2617437 "SIMPAN" 2617517 T SIMPAN (NIL) -7 NIL NIL NIL) (-1127 2616612 2616868 2617008 "SIG" 2617215 T SIG (NIL) -8 NIL NIL NIL) (-1126 2615450 2615671 2615946 "SIGNRF" 2616371 NIL SIGNRF (NIL T) -7 NIL NIL NIL) (-1125 2614283 2614434 2614718 "SIGNEF" 2615279 NIL SIGNEF (NIL T T) -7 NIL NIL NIL) (-1124 2613589 2613866 2613990 "SIGAST" 2614181 T SIGAST (NIL) -8 NIL NIL NIL) (-1123 2611279 2611733 2612239 "SHP" 2613130 NIL SHP (NIL T NIL) -7 NIL NIL NIL) (-1122 2605131 2611180 2611256 "SHDP" 2611261 NIL SHDP (NIL NIL NIL T) -8 NIL NIL NIL) (-1121 2604704 2604896 2604926 "SGROUP" 2605019 T SGROUP (NIL) -9 NIL 2605081 NIL) (-1120 2604562 2604588 2604661 "SGROUP-" 2604666 NIL SGROUP- (NIL T) -8 NIL NIL NIL) (-1119 2601397 2602095 2602818 "SGCF" 2603861 T SGCF (NIL) -7 NIL NIL NIL) (-1118 2595765 2600844 2600941 "SFRTCAT" 2600946 NIL SFRTCAT (NIL T T T T) -9 NIL 2600985 NIL) (-1117 2589186 2590204 2591340 "SFRGCD" 2594748 NIL SFRGCD (NIL T T T T T) -7 NIL NIL NIL) (-1116 2582312 2583385 2584571 "SFQCMPK" 2588119 NIL SFQCMPK (NIL T T T T T) -7 NIL NIL NIL) (-1115 2581932 2582021 2582132 "SFORT" 2582253 NIL SFORT (NIL T T) -8 NIL NIL NIL) (-1114 2581050 2581772 2581893 "SEXOF" 2581898 NIL SEXOF (NIL T T T T T) -8 NIL NIL NIL) (-1113 2580157 2580931 2580999 "SEX" 2581004 T SEX (NIL) -8 NIL NIL NIL) (-1112 2575670 2576385 2576480 "SEXCAT" 2579417 NIL SEXCAT (NIL T T T T T) -9 NIL 2579995 NIL) (-1111 2572823 2575604 2575652 "SET" 2575657 NIL SET (NIL T) -8 NIL NIL NIL) (-1110 2571047 2571536 2571841 "SETMN" 2572564 NIL SETMN (NIL NIL NIL) -8 NIL NIL NIL) (-1109 2570543 2570695 2570725 "SETCAT" 2570901 T SETCAT (NIL) -9 NIL 2571011 NIL) (-1108 2570235 2570313 2570443 "SETCAT-" 2570448 NIL SETCAT- (NIL T) -8 NIL NIL NIL) (-1107 2566596 2568696 2568739 "SETAGG" 2569609 NIL SETAGG (NIL T) -9 NIL 2569949 NIL) (-1106 2566054 2566170 2566407 "SETAGG-" 2566412 NIL SETAGG- (NIL T T) -8 NIL NIL NIL) (-1105 2565497 2565750 2565851 "SEQAST" 2565975 T SEQAST (NIL) -8 NIL NIL NIL) (-1104 2564696 2564990 2565051 "SEGXCAT" 2565337 NIL SEGXCAT (NIL T T) -9 NIL 2565457 NIL) (-1103 2563702 2564362 2564544 "SEG" 2564549 NIL SEG (NIL T) -8 NIL NIL NIL) (-1102 2562681 2562895 2562938 "SEGCAT" 2563460 NIL SEGCAT (NIL T) -9 NIL 2563681 NIL) (-1101 2561613 2562044 2562252 "SEGBIND" 2562508 NIL SEGBIND (NIL T) -8 NIL NIL NIL) (-1100 2561234 2561293 2561406 "SEGBIND2" 2561548 NIL SEGBIND2 (NIL T T) -7 NIL NIL NIL) (-1099 2560807 2561035 2561112 "SEGAST" 2561179 T SEGAST (NIL) -8 NIL NIL NIL) (-1098 2560026 2560152 2560356 "SEG2" 2560651 NIL SEG2 (NIL T T) -7 NIL NIL NIL) (-1097 2559436 2559961 2560008 "SDVAR" 2560013 NIL SDVAR (NIL T) -8 NIL NIL NIL) (-1096 2551963 2559206 2559336 "SDPOL" 2559341 NIL SDPOL (NIL T) -8 NIL NIL NIL) (-1095 2550556 2550822 2551141 "SCPKG" 2551678 NIL SCPKG (NIL T) -7 NIL NIL NIL) (-1094 2549720 2549892 2550084 "SCOPE" 2550386 T SCOPE (NIL) -8 NIL NIL NIL) (-1093 2548940 2549074 2549253 "SCACHE" 2549575 NIL SCACHE (NIL T) -7 NIL NIL NIL) (-1092 2548586 2548772 2548802 "SASTCAT" 2548807 T SASTCAT (NIL) -9 NIL 2548820 NIL) (-1091 2548073 2548421 2548497 "SAOS" 2548532 T SAOS (NIL) -8 NIL NIL NIL) (-1090 2547638 2547673 2547846 "SAERFFC" 2548032 NIL SAERFFC (NIL T T T) -7 NIL NIL NIL) (-1089 2541577 2547535 2547615 "SAE" 2547620 NIL SAE (NIL T T NIL) -8 NIL NIL NIL) (-1088 2541170 2541205 2541364 "SAEFACT" 2541536 NIL SAEFACT (NIL T T T) -7 NIL NIL NIL) (-1087 2539491 2539805 2540206 "RURPK" 2540836 NIL RURPK (NIL T NIL) -7 NIL NIL NIL) (-1086 2538128 2538434 2538739 "RULESET" 2539325 NIL RULESET (NIL T T T) -8 NIL NIL NIL) (-1085 2535351 2535881 2536339 "RULE" 2537809 NIL RULE (NIL T T T) -8 NIL NIL NIL) (-1084 2534963 2535145 2535228 "RULECOLD" 2535303 NIL RULECOLD (NIL NIL) -8 NIL NIL NIL) (-1083 2534753 2534781 2534852 "RTVALUE" 2534914 T RTVALUE (NIL) -8 NIL NIL NIL) (-1082 2534224 2534470 2534564 "RSTRCAST" 2534681 T RSTRCAST (NIL) -8 NIL NIL NIL) (-1081 2529072 2529867 2530787 "RSETGCD" 2533423 NIL RSETGCD (NIL T T T T T) -7 NIL NIL NIL) (-1080 2518302 2523381 2523478 "RSETCAT" 2527597 NIL RSETCAT (NIL T T T T) -9 NIL 2528694 NIL) (-1079 2516229 2516768 2517592 "RSETCAT-" 2517597 NIL RSETCAT- (NIL T T T T T) -8 NIL NIL NIL) (-1078 2508615 2509991 2511511 "RSDCMPK" 2514828 NIL RSDCMPK (NIL T T T T T) -7 NIL NIL NIL) (-1077 2506594 2507061 2507135 "RRCC" 2508221 NIL RRCC (NIL T T) -9 NIL 2508565 NIL) (-1076 2505945 2506119 2506398 "RRCC-" 2506403 NIL RRCC- (NIL T T T) -8 NIL NIL NIL) (-1075 2505388 2505641 2505742 "RPTAST" 2505866 T RPTAST (NIL) -8 NIL NIL NIL) (-1074 2479234 2488593 2488660 "RPOLCAT" 2499326 NIL RPOLCAT (NIL T T T) -9 NIL 2502486 NIL) (-1073 2470732 2473072 2476194 "RPOLCAT-" 2476199 NIL RPOLCAT- (NIL T T T T) -8 NIL NIL NIL) (-1072 2461663 2468943 2469425 "ROUTINE" 2470272 T ROUTINE (NIL) -8 NIL NIL NIL) (-1071 2458461 2461289 2461429 "ROMAN" 2461545 T ROMAN (NIL) -8 NIL NIL NIL) (-1070 2456705 2457321 2457581 "ROIRC" 2458266 NIL ROIRC (NIL T T) -8 NIL NIL NIL) (-1069 2452937 2455221 2455251 "RNS" 2455555 T RNS (NIL) -9 NIL 2455829 NIL) (-1068 2451446 2451829 2452363 "RNS-" 2452438 NIL RNS- (NIL T) -8 NIL NIL NIL) (-1067 2450849 2451257 2451287 "RNG" 2451292 T RNG (NIL) -9 NIL 2451313 NIL) (-1066 2449852 2450214 2450416 "RNGBIND" 2450700 NIL RNGBIND (NIL T T) -8 NIL NIL NIL) (-1065 2449251 2449639 2449682 "RMODULE" 2449687 NIL RMODULE (NIL T) -9 NIL 2449714 NIL) (-1064 2448087 2448181 2448517 "RMCAT2" 2449152 NIL RMCAT2 (NIL NIL NIL T T T T T T T T) -7 NIL NIL NIL) (-1063 2444937 2447433 2447730 "RMATRIX" 2447849 NIL RMATRIX (NIL NIL NIL T) -8 NIL NIL NIL) (-1062 2437764 2440024 2440139 "RMATCAT" 2443498 NIL RMATCAT (NIL NIL NIL T T T) -9 NIL 2444480 NIL) (-1061 2437139 2437286 2437593 "RMATCAT-" 2437598 NIL RMATCAT- (NIL T NIL NIL T T T) -8 NIL NIL NIL) (-1060 2436540 2436761 2436804 "RLINSET" 2436998 NIL RLINSET (NIL T) -9 NIL 2437089 NIL) (-1059 2436107 2436182 2436310 "RINTERP" 2436459 NIL RINTERP (NIL NIL T) -7 NIL NIL NIL) (-1058 2435165 2435719 2435749 "RING" 2435805 T RING (NIL) -9 NIL 2435897 NIL) (-1057 2434957 2435001 2435098 "RING-" 2435103 NIL RING- (NIL T) -8 NIL NIL NIL) (-1056 2433798 2434035 2434293 "RIDIST" 2434721 T RIDIST (NIL) -7 NIL NIL NIL) (-1055 2425087 2433266 2433472 "RGCHAIN" 2433646 NIL RGCHAIN (NIL T NIL) -8 NIL NIL NIL) (-1054 2424437 2424843 2424884 "RGBCSPC" 2424942 NIL RGBCSPC (NIL T) -9 NIL 2424994 NIL) (-1053 2423595 2423976 2424017 "RGBCMDL" 2424249 NIL RGBCMDL (NIL T) -9 NIL 2424363 NIL) (-1052 2420589 2421203 2421873 "RF" 2422959 NIL RF (NIL T) -7 NIL NIL NIL) (-1051 2420235 2420298 2420401 "RFFACTOR" 2420520 NIL RFFACTOR (NIL T) -7 NIL NIL NIL) (-1050 2419960 2419995 2420092 "RFFACT" 2420194 NIL RFFACT (NIL T) -7 NIL NIL NIL) (-1049 2418077 2418441 2418823 "RFDIST" 2419600 T RFDIST (NIL) -7 NIL NIL NIL) (-1048 2417530 2417622 2417785 "RETSOL" 2417979 NIL RETSOL (NIL T T) -7 NIL NIL NIL) (-1047 2417166 2417246 2417289 "RETRACT" 2417422 NIL RETRACT (NIL T) -9 NIL 2417509 NIL) (-1046 2417015 2417040 2417127 "RETRACT-" 2417132 NIL RETRACT- (NIL T T) -8 NIL NIL NIL) (-1045 2416617 2416837 2416907 "RETAST" 2416967 T RETAST (NIL) -8 NIL NIL NIL) (-1044 2409355 2416270 2416397 "RESULT" 2416512 T RESULT (NIL) -8 NIL NIL NIL) (-1043 2407946 2408624 2408823 "RESRING" 2409258 NIL RESRING (NIL T T T T NIL) -8 NIL NIL NIL) (-1042 2407582 2407631 2407729 "RESLATC" 2407883 NIL RESLATC (NIL T) -7 NIL NIL NIL) (-1041 2407287 2407322 2407429 "REPSQ" 2407541 NIL REPSQ (NIL T) -7 NIL NIL NIL) (-1040 2404709 2405289 2405891 "REP" 2406707 T REP (NIL) -7 NIL NIL NIL) (-1039 2404406 2404441 2404552 "REPDB" 2404668 NIL REPDB (NIL T) -7 NIL NIL NIL) (-1038 2398306 2399695 2400918 "REP2" 2403218 NIL REP2 (NIL T) -7 NIL NIL NIL) (-1037 2394683 2395364 2396172 "REP1" 2397533 NIL REP1 (NIL T) -7 NIL NIL NIL) (-1036 2387379 2392824 2393280 "REGSET" 2394313 NIL REGSET (NIL T T T T) -8 NIL NIL NIL) (-1035 2386144 2386527 2386777 "REF" 2387164 NIL REF (NIL T) -8 NIL NIL NIL) (-1034 2385521 2385624 2385791 "REDORDER" 2386028 NIL REDORDER (NIL T T) -7 NIL NIL NIL) (-1033 2381489 2384734 2384961 "RECLOS" 2385349 NIL RECLOS (NIL T) -8 NIL NIL NIL) (-1032 2380541 2380722 2380937 "REALSOLV" 2381296 T REALSOLV (NIL) -7 NIL NIL NIL) (-1031 2380387 2380428 2380458 "REAL" 2380463 T REAL (NIL) -9 NIL 2380498 NIL) (-1030 2376870 2377672 2378556 "REAL0Q" 2379552 NIL REAL0Q (NIL T) -7 NIL NIL NIL) (-1029 2372471 2373459 2374520 "REAL0" 2375851 NIL REAL0 (NIL T) -7 NIL NIL NIL) (-1028 2371942 2372188 2372282 "RDUCEAST" 2372399 T RDUCEAST (NIL) -8 NIL NIL NIL) (-1027 2371347 2371419 2371626 "RDIV" 2371864 NIL RDIV (NIL T T T T T) -7 NIL NIL NIL) (-1026 2370415 2370589 2370802 "RDIST" 2371169 NIL RDIST (NIL T) -7 NIL NIL NIL) (-1025 2369012 2369299 2369671 "RDETRS" 2370123 NIL RDETRS (NIL T T) -7 NIL NIL NIL) (-1024 2366824 2367278 2367816 "RDETR" 2368554 NIL RDETR (NIL T T) -7 NIL NIL NIL) (-1023 2365449 2365727 2366124 "RDEEFS" 2366540 NIL RDEEFS (NIL T T) -7 NIL NIL NIL) (-1022 2363958 2364264 2364689 "RDEEF" 2365137 NIL RDEEF (NIL T T) -7 NIL NIL NIL) (-1021 2358019 2360939 2360969 "RCFIELD" 2362264 T RCFIELD (NIL) -9 NIL 2362995 NIL) (-1020 2356083 2356587 2357283 "RCFIELD-" 2357358 NIL RCFIELD- (NIL T) -8 NIL NIL NIL) (-1019 2352352 2354184 2354227 "RCAGG" 2355311 NIL RCAGG (NIL T) -9 NIL 2355776 NIL) (-1018 2351980 2352074 2352237 "RCAGG-" 2352242 NIL RCAGG- (NIL T T) -8 NIL NIL NIL) (-1017 2351315 2351427 2351592 "RATRET" 2351864 NIL RATRET (NIL T) -7 NIL NIL NIL) (-1016 2350868 2350935 2351056 "RATFACT" 2351243 NIL RATFACT (NIL T) -7 NIL NIL NIL) (-1015 2350176 2350296 2350448 "RANDSRC" 2350738 T RANDSRC (NIL) -7 NIL NIL NIL) (-1014 2349910 2349954 2350027 "RADUTIL" 2350125 T RADUTIL (NIL) -7 NIL NIL NIL) (-1013 2343024 2348741 2349052 "RADIX" 2349633 NIL RADIX (NIL NIL) -8 NIL NIL NIL) (-1012 2334643 2342866 2342996 "RADFF" 2343001 NIL RADFF (NIL T T T NIL NIL) -8 NIL NIL NIL) (-1011 2334290 2334365 2334395 "RADCAT" 2334555 T RADCAT (NIL) -9 NIL NIL NIL) (-1010 2334072 2334120 2334220 "RADCAT-" 2334225 NIL RADCAT- (NIL T) -8 NIL NIL NIL) (-1009 2332170 2333842 2333934 "QUEUE" 2334015 NIL QUEUE (NIL T) -8 NIL NIL NIL) (-1008 2328707 2332103 2332151 "QUAT" 2332156 NIL QUAT (NIL T) -8 NIL NIL NIL) (-1007 2328338 2328381 2328512 "QUATCT2" 2328658 NIL QUATCT2 (NIL T T T T) -7 NIL NIL NIL) (-1006 2321787 2325132 2325174 "QUATCAT" 2325965 NIL QUATCAT (NIL T) -9 NIL 2326731 NIL) (-1005 2317926 2318963 2320353 "QUATCAT-" 2320449 NIL QUATCAT- (NIL T T) -8 NIL NIL NIL) (-1004 2315391 2317002 2317045 "QUAGG" 2317426 NIL QUAGG (NIL T) -9 NIL 2317601 NIL) (-1003 2314993 2315213 2315283 "QQUTAST" 2315343 T QQUTAST (NIL) -8 NIL NIL NIL) (-1002 2313886 2314386 2314560 "QFORM" 2314865 NIL QFORM (NIL NIL T) -8 NIL NIL NIL) (-1001 2304879 2310118 2310160 "QFCAT" 2310828 NIL QFCAT (NIL T) -9 NIL 2311829 NIL) (-1000 2300446 2301647 2303241 "QFCAT-" 2303337 NIL QFCAT- (NIL T T) -8 NIL NIL NIL) (-999 2300080 2300123 2300252 "QFCAT2" 2300397 NIL QFCAT2 (NIL T T T T) -7 NIL NIL NIL) (-998 2299540 2299650 2299780 "QEQUAT" 2299970 T QEQUAT (NIL) -8 NIL NIL NIL) (-997 2292686 2293759 2294943 "QCMPACK" 2298473 NIL QCMPACK (NIL T T T T T) -7 NIL NIL NIL) (-996 2290235 2290683 2291111 "QALGSET" 2292341 NIL QALGSET (NIL T T T T) -8 NIL NIL NIL) (-995 2289480 2289654 2289886 "QALGSET2" 2290055 NIL QALGSET2 (NIL NIL NIL) -7 NIL NIL NIL) (-994 2288170 2288394 2288711 "PWFFINTB" 2289253 NIL PWFFINTB (NIL T T T T) -7 NIL NIL NIL) (-993 2286352 2286520 2286874 "PUSHVAR" 2287984 NIL PUSHVAR (NIL T T T T) -7 NIL NIL NIL) (-992 2282270 2283324 2283365 "PTRANFN" 2285249 NIL PTRANFN (NIL T) -9 NIL NIL NIL) (-991 2280672 2280963 2281285 "PTPACK" 2281981 NIL PTPACK (NIL T) -7 NIL NIL NIL) (-990 2280304 2280361 2280470 "PTFUNC2" 2280609 NIL PTFUNC2 (NIL T T) -7 NIL NIL NIL) (-989 2274781 2279176 2279217 "PTCAT" 2279513 NIL PTCAT (NIL T) -9 NIL 2279666 NIL) (-988 2274439 2274474 2274598 "PSQFR" 2274740 NIL PSQFR (NIL T T T T) -7 NIL NIL NIL) (-987 2273034 2273332 2273666 "PSEUDLIN" 2274137 NIL PSEUDLIN (NIL T) -7 NIL NIL NIL) (-986 2259797 2262168 2264492 "PSETPK" 2270794 NIL PSETPK (NIL T T T T) -7 NIL NIL NIL) (-985 2252815 2255555 2255651 "PSETCAT" 2258672 NIL PSETCAT (NIL T T T T) -9 NIL 2259486 NIL) (-984 2250651 2251285 2252106 "PSETCAT-" 2252111 NIL PSETCAT- (NIL T T T T T) -8 NIL NIL NIL) (-983 2250000 2250165 2250193 "PSCURVE" 2250461 T PSCURVE (NIL) -9 NIL 2250628 NIL) (-982 2245998 2247514 2247579 "PSCAT" 2248423 NIL PSCAT (NIL T T T) -9 NIL 2248663 NIL) (-981 2245061 2245277 2245677 "PSCAT-" 2245682 NIL PSCAT- (NIL T T T T) -8 NIL NIL NIL) (-980 2243797 2244451 2244651 "PRTITION" 2244881 T PRTITION (NIL) -8 NIL NIL NIL) (-979 2243272 2243518 2243610 "PRTDAST" 2243725 T PRTDAST (NIL) -8 NIL NIL NIL) (-978 2232362 2234576 2236764 "PRS" 2241134 NIL PRS (NIL T T) -7 NIL NIL NIL) (-977 2230173 2231712 2231752 "PRQAGG" 2231935 NIL PRQAGG (NIL T) -9 NIL 2232037 NIL) (-976 2229509 2229814 2229842 "PROPLOG" 2229981 T PROPLOG (NIL) -9 NIL 2230096 NIL) (-975 2229113 2229170 2229293 "PROPFUN2" 2229432 NIL PROPFUN2 (NIL T T) -8 NIL NIL NIL) (-974 2228428 2228549 2228721 "PROPFUN1" 2228974 NIL PROPFUN1 (NIL T) -8 NIL NIL NIL) (-973 2226609 2227175 2227472 "PROPFRML" 2228164 NIL PROPFRML (NIL T) -8 NIL NIL NIL) (-972 2226078 2226185 2226313 "PROPERTY" 2226501 T PROPERTY (NIL) -8 NIL NIL NIL) (-971 2220136 2224244 2225064 "PRODUCT" 2225304 NIL PRODUCT (NIL T T) -8 NIL NIL NIL) (-970 2217414 2219594 2219828 "PR" 2219947 NIL PR (NIL T T) -8 NIL NIL NIL) (-969 2217210 2217242 2217301 "PRINT" 2217375 T PRINT (NIL) -7 NIL NIL NIL) (-968 2216550 2216667 2216819 "PRIMES" 2217090 NIL PRIMES (NIL T) -7 NIL NIL NIL) (-967 2214615 2215016 2215482 "PRIMELT" 2216129 NIL PRIMELT (NIL T) -7 NIL NIL NIL) (-966 2214344 2214393 2214421 "PRIMCAT" 2214545 T PRIMCAT (NIL) -9 NIL NIL NIL) (-965 2210459 2214282 2214327 "PRIMARR" 2214332 NIL PRIMARR (NIL T) -8 NIL NIL NIL) (-964 2209466 2209644 2209872 "PRIMARR2" 2210277 NIL PRIMARR2 (NIL T T) -7 NIL NIL NIL) (-963 2209109 2209165 2209276 "PREASSOC" 2209404 NIL PREASSOC (NIL T T) -7 NIL NIL NIL) (-962 2208584 2208717 2208745 "PPCURVE" 2208950 T PPCURVE (NIL) -9 NIL 2209086 NIL) (-961 2208179 2208379 2208462 "PORTNUM" 2208521 T PORTNUM (NIL) -8 NIL NIL NIL) (-960 2205538 2205937 2206529 "POLYROOT" 2207760 NIL POLYROOT (NIL T T T T T) -7 NIL NIL NIL) (-959 2199720 2205142 2205302 "POLY" 2205411 NIL POLY (NIL T) -8 NIL NIL NIL) (-958 2199103 2199161 2199395 "POLYLIFT" 2199656 NIL POLYLIFT (NIL T T T T T) -7 NIL NIL NIL) (-957 2195378 2195827 2196456 "POLYCATQ" 2198648 NIL POLYCATQ (NIL T T T T T) -7 NIL NIL NIL) (-956 2182090 2187218 2187283 "POLYCAT" 2190797 NIL POLYCAT (NIL T T T) -9 NIL 2192675 NIL) (-955 2175539 2177401 2179785 "POLYCAT-" 2179790 NIL POLYCAT- (NIL T T T T) -8 NIL NIL NIL) (-954 2175126 2175194 2175314 "POLY2UP" 2175465 NIL POLY2UP (NIL NIL T) -7 NIL NIL NIL) (-953 2174758 2174815 2174924 "POLY2" 2175063 NIL POLY2 (NIL T T) -7 NIL NIL NIL) (-952 2173443 2173682 2173958 "POLUTIL" 2174532 NIL POLUTIL (NIL T T) -7 NIL NIL NIL) (-951 2171798 2172075 2172406 "POLTOPOL" 2173165 NIL POLTOPOL (NIL NIL T) -7 NIL NIL NIL) (-950 2167263 2171734 2171780 "POINT" 2171785 NIL POINT (NIL T) -8 NIL NIL NIL) (-949 2165450 2165807 2166182 "PNTHEORY" 2166908 T PNTHEORY (NIL) -7 NIL NIL NIL) (-948 2163908 2164205 2164604 "PMTOOLS" 2165148 NIL PMTOOLS (NIL T T T) -7 NIL NIL NIL) (-947 2163501 2163579 2163696 "PMSYM" 2163824 NIL PMSYM (NIL T) -7 NIL NIL NIL) (-946 2163009 2163078 2163253 "PMQFCAT" 2163426 NIL PMQFCAT (NIL T T T) -7 NIL NIL NIL) (-945 2162364 2162474 2162630 "PMPRED" 2162886 NIL PMPRED (NIL T) -7 NIL NIL NIL) (-944 2161757 2161843 2162005 "PMPREDFS" 2162265 NIL PMPREDFS (NIL T T T) -7 NIL NIL NIL) (-943 2160421 2160629 2161007 "PMPLCAT" 2161519 NIL PMPLCAT (NIL T T T T T) -7 NIL NIL NIL) (-942 2159953 2160032 2160184 "PMLSAGG" 2160336 NIL PMLSAGG (NIL T T T) -7 NIL NIL NIL) (-941 2159426 2159502 2159684 "PMKERNEL" 2159871 NIL PMKERNEL (NIL T T) -7 NIL NIL NIL) (-940 2159043 2159118 2159231 "PMINS" 2159345 NIL PMINS (NIL T) -7 NIL NIL NIL) (-939 2158485 2158554 2158763 "PMFS" 2158968 NIL PMFS (NIL T T T) -7 NIL NIL NIL) (-938 2157713 2157831 2158036 "PMDOWN" 2158362 NIL PMDOWN (NIL T T T) -7 NIL NIL NIL) (-937 2156880 2157038 2157219 "PMASS" 2157552 T PMASS (NIL) -7 NIL NIL NIL) (-936 2156153 2156263 2156426 "PMASSFS" 2156767 NIL PMASSFS (NIL T T) -7 NIL NIL NIL) (-935 2155808 2155876 2155970 "PLOTTOOL" 2156079 T PLOTTOOL (NIL) -7 NIL NIL NIL) (-934 2150415 2151619 2152767 "PLOT" 2154680 T PLOT (NIL) -8 NIL NIL NIL) (-933 2146219 2147263 2148184 "PLOT3D" 2149514 T PLOT3D (NIL) -8 NIL NIL NIL) (-932 2145131 2145308 2145543 "PLOT1" 2146023 NIL PLOT1 (NIL T) -7 NIL NIL NIL) (-931 2120522 2125197 2130048 "PLEQN" 2140397 NIL PLEQN (NIL T T T T) -7 NIL NIL NIL) (-930 2119840 2119962 2120142 "PINTERP" 2120387 NIL PINTERP (NIL NIL T) -7 NIL NIL NIL) (-929 2119533 2119580 2119683 "PINTERPA" 2119787 NIL PINTERPA (NIL T T) -7 NIL NIL NIL) (-928 2118754 2119302 2119389 "PI" 2119429 T PI (NIL) -8 NIL NIL 2119496) (-927 2117051 2118026 2118054 "PID" 2118236 T PID (NIL) -9 NIL 2118370 NIL) (-926 2116802 2116839 2116914 "PICOERCE" 2117008 NIL PICOERCE (NIL T) -7 NIL NIL NIL) (-925 2116122 2116261 2116437 "PGROEB" 2116658 NIL PGROEB (NIL T) -7 NIL NIL NIL) (-924 2111709 2112523 2113428 "PGE" 2115237 T PGE (NIL) -7 NIL NIL NIL) (-923 2109832 2110079 2110445 "PGCD" 2111426 NIL PGCD (NIL T T T T) -7 NIL NIL NIL) (-922 2109170 2109273 2109434 "PFRPAC" 2109716 NIL PFRPAC (NIL T) -7 NIL NIL NIL) (-921 2105810 2107718 2108071 "PFR" 2108849 NIL PFR (NIL T) -8 NIL NIL NIL) (-920 2104199 2104443 2104768 "PFOTOOLS" 2105557 NIL PFOTOOLS (NIL T T) -7 NIL NIL NIL) (-919 2102732 2102971 2103322 "PFOQ" 2103956 NIL PFOQ (NIL T T T) -7 NIL NIL NIL) (-918 2101233 2101445 2101801 "PFO" 2102516 NIL PFO (NIL T T T T T) -7 NIL NIL NIL) (-917 2097786 2101122 2101191 "PF" 2101196 NIL PF (NIL NIL) -8 NIL NIL NIL) (-916 2095120 2096391 2096419 "PFECAT" 2097004 T PFECAT (NIL) -9 NIL 2097388 NIL) (-915 2094565 2094719 2094933 "PFECAT-" 2094938 NIL PFECAT- (NIL T) -8 NIL NIL NIL) (-914 2093168 2093420 2093721 "PFBRU" 2094314 NIL PFBRU (NIL T T) -7 NIL NIL NIL) (-913 2091034 2091386 2091818 "PFBR" 2092819 NIL PFBR (NIL T T T T) -7 NIL NIL NIL) (-912 2086916 2088410 2089086 "PERM" 2090391 NIL PERM (NIL T) -8 NIL NIL NIL) (-911 2082150 2083123 2083993 "PERMGRP" 2086079 NIL PERMGRP (NIL T) -8 NIL NIL NIL) (-910 2080256 2081213 2081254 "PERMCAT" 2081700 NIL PERMCAT (NIL T) -9 NIL 2082005 NIL) (-909 2079909 2079950 2080074 "PERMAN" 2080209 NIL PERMAN (NIL NIL T) -7 NIL NIL NIL) (-908 2077397 2079574 2079696 "PENDTREE" 2079820 NIL PENDTREE (NIL T) -8 NIL NIL NIL) (-907 2075421 2076189 2076230 "PDRING" 2076887 NIL PDRING (NIL T) -9 NIL 2077173 NIL) (-906 2074524 2074742 2075104 "PDRING-" 2075109 NIL PDRING- (NIL T T) -8 NIL NIL NIL) (-905 2071739 2072517 2073185 "PDEPROB" 2073876 T PDEPROB (NIL) -8 NIL NIL NIL) (-904 2069284 2069788 2070343 "PDEPACK" 2071204 T PDEPACK (NIL) -7 NIL NIL NIL) (-903 2068196 2068386 2068637 "PDECOMP" 2069083 NIL PDECOMP (NIL T T) -7 NIL NIL NIL) (-902 2065775 2066618 2066646 "PDECAT" 2067433 T PDECAT (NIL) -9 NIL 2068146 NIL) (-901 2065526 2065559 2065649 "PCOMP" 2065736 NIL PCOMP (NIL T T) -7 NIL NIL NIL) (-900 2063704 2064327 2064624 "PBWLB" 2065255 NIL PBWLB (NIL T) -8 NIL NIL NIL) (-899 2056177 2057777 2059115 "PATTERN" 2062387 NIL PATTERN (NIL T) -8 NIL NIL NIL) (-898 2055809 2055866 2055975 "PATTERN2" 2056114 NIL PATTERN2 (NIL T T) -7 NIL NIL NIL) (-897 2053566 2053954 2054411 "PATTERN1" 2055398 NIL PATTERN1 (NIL T T) -7 NIL NIL NIL) (-896 2050934 2051515 2051996 "PATRES" 2053131 NIL PATRES (NIL T T) -8 NIL NIL NIL) (-895 2050498 2050565 2050697 "PATRES2" 2050861 NIL PATRES2 (NIL T T T) -7 NIL NIL NIL) (-894 2048381 2048786 2049193 "PATMATCH" 2050165 NIL PATMATCH (NIL T T T) -7 NIL NIL NIL) (-893 2047891 2048100 2048141 "PATMAB" 2048248 NIL PATMAB (NIL T) -9 NIL 2048331 NIL) (-892 2046409 2046745 2047003 "PATLRES" 2047696 NIL PATLRES (NIL T T T) -8 NIL NIL NIL) (-891 2045955 2046078 2046119 "PATAB" 2046124 NIL PATAB (NIL T) -9 NIL 2046296 NIL) (-890 2043436 2043968 2044541 "PARTPERM" 2045402 T PARTPERM (NIL) -7 NIL NIL NIL) (-889 2043057 2043120 2043222 "PARSURF" 2043367 NIL PARSURF (NIL T) -8 NIL NIL NIL) (-888 2042689 2042746 2042855 "PARSU2" 2042994 NIL PARSU2 (NIL T T) -7 NIL NIL NIL) (-887 2042453 2042493 2042560 "PARSER" 2042642 T PARSER (NIL) -7 NIL NIL NIL) (-886 2042074 2042137 2042239 "PARSCURV" 2042384 NIL PARSCURV (NIL T) -8 NIL NIL NIL) (-885 2041706 2041763 2041872 "PARSC2" 2042011 NIL PARSC2 (NIL T T) -7 NIL NIL NIL) (-884 2041345 2041403 2041500 "PARPCURV" 2041642 NIL PARPCURV (NIL T) -8 NIL NIL NIL) (-883 2040977 2041034 2041143 "PARPC2" 2041282 NIL PARPC2 (NIL T T) -7 NIL NIL NIL) (-882 2040038 2040350 2040532 "PARAMAST" 2040815 T PARAMAST (NIL) -8 NIL NIL NIL) (-881 2039558 2039644 2039763 "PAN2EXPR" 2039939 T PAN2EXPR (NIL) -7 NIL NIL NIL) (-880 2038335 2038679 2038907 "PALETTE" 2039350 T PALETTE (NIL) -8 NIL NIL NIL) (-879 2036728 2037340 2037700 "PAIR" 2038021 NIL PAIR (NIL T T) -8 NIL NIL NIL) (-878 2030596 2035985 2036180 "PADICRC" 2036582 NIL PADICRC (NIL NIL T) -8 NIL NIL NIL) (-877 2023823 2029940 2030125 "PADICRAT" 2030443 NIL PADICRAT (NIL NIL) -8 NIL NIL NIL) (-876 2022138 2023760 2023805 "PADIC" 2023810 NIL PADIC (NIL NIL) -8 NIL NIL NIL) (-875 2019248 2020812 2020852 "PADICCT" 2021433 NIL PADICCT (NIL NIL) -9 NIL 2021715 NIL) (-874 2018205 2018405 2018673 "PADEPAC" 2019035 NIL PADEPAC (NIL T NIL NIL) -7 NIL NIL NIL) (-873 2017417 2017550 2017756 "PADE" 2018067 NIL PADE (NIL T T T) -7 NIL NIL NIL) (-872 2015804 2016625 2016905 "OWP" 2017221 NIL OWP (NIL T NIL NIL NIL) -8 NIL NIL NIL) (-871 2015297 2015510 2015607 "OVERSET" 2015727 T OVERSET (NIL) -8 NIL NIL NIL) (-870 2014343 2014902 2015074 "OVAR" 2015165 NIL OVAR (NIL NIL) -8 NIL NIL NIL) (-869 2013607 2013728 2013889 "OUT" 2014202 T OUT (NIL) -7 NIL NIL NIL) (-868 2002479 2004716 2006916 "OUTFORM" 2011427 T OUTFORM (NIL) -8 NIL NIL NIL) (-867 2001815 2002076 2002203 "OUTBFILE" 2002372 T OUTBFILE (NIL) -8 NIL NIL NIL) (-866 2001122 2001287 2001315 "OUTBCON" 2001633 T OUTBCON (NIL) -9 NIL 2001799 NIL) (-865 2000723 2000835 2000992 "OUTBCON-" 2000997 NIL OUTBCON- (NIL T) -8 NIL NIL NIL) (-864 2000103 2000452 2000541 "OSI" 2000654 T OSI (NIL) -8 NIL NIL NIL) (-863 1999633 1999971 1999999 "OSGROUP" 2000004 T OSGROUP (NIL) -9 NIL 2000026 NIL) (-862 1998378 1998605 1998890 "ORTHPOL" 1999380 NIL ORTHPOL (NIL T) -7 NIL NIL NIL) (-861 1995929 1998213 1998334 "OREUP" 1998339 NIL OREUP (NIL NIL T NIL NIL) -8 NIL NIL NIL) (-860 1993332 1995620 1995747 "ORESUP" 1995871 NIL ORESUP (NIL T NIL NIL) -8 NIL NIL NIL) (-859 1990860 1991360 1991921 "OREPCTO" 1992821 NIL OREPCTO (NIL T T) -7 NIL NIL NIL) (-858 1984546 1986747 1986788 "OREPCAT" 1989136 NIL OREPCAT (NIL T) -9 NIL 1990240 NIL) (-857 1981693 1982475 1983533 "OREPCAT-" 1983538 NIL OREPCAT- (NIL T T) -8 NIL NIL NIL) (-856 1980844 1981142 1981170 "ORDSET" 1981479 T ORDSET (NIL) -9 NIL 1981643 NIL) (-855 1980275 1980423 1980647 "ORDSET-" 1980652 NIL ORDSET- (NIL T) -8 NIL NIL NIL) (-854 1978840 1979631 1979659 "ORDRING" 1979861 T ORDRING (NIL) -9 NIL 1979986 NIL) (-853 1978485 1978579 1978723 "ORDRING-" 1978728 NIL ORDRING- (NIL T) -8 NIL NIL NIL) (-852 1977865 1978328 1978356 "ORDMON" 1978361 T ORDMON (NIL) -9 NIL 1978382 NIL) (-851 1977027 1977174 1977369 "ORDFUNS" 1977714 NIL ORDFUNS (NIL NIL T) -7 NIL NIL NIL) (-850 1976365 1976784 1976812 "ORDFIN" 1976877 T ORDFIN (NIL) -9 NIL 1976951 NIL) (-849 1972924 1974951 1975360 "ORDCOMP" 1975989 NIL ORDCOMP (NIL T) -8 NIL NIL NIL) (-848 1972190 1972317 1972503 "ORDCOMP2" 1972784 NIL ORDCOMP2 (NIL T T) -7 NIL NIL NIL) (-847 1968771 1969681 1970495 "OPTPROB" 1971396 T OPTPROB (NIL) -8 NIL NIL NIL) (-846 1965573 1966212 1966916 "OPTPACK" 1968087 T OPTPACK (NIL) -7 NIL NIL NIL) (-845 1963260 1964026 1964054 "OPTCAT" 1964873 T OPTCAT (NIL) -9 NIL 1965523 NIL) (-844 1962644 1962937 1963042 "OPSIG" 1963175 T OPSIG (NIL) -8 NIL NIL NIL) (-843 1962412 1962451 1962517 "OPQUERY" 1962598 T OPQUERY (NIL) -7 NIL NIL NIL) (-842 1959543 1960723 1961227 "OP" 1961941 NIL OP (NIL T) -8 NIL NIL NIL) (-841 1958917 1959143 1959184 "OPERCAT" 1959396 NIL OPERCAT (NIL T) -9 NIL 1959493 NIL) (-840 1958672 1958728 1958845 "OPERCAT-" 1958850 NIL OPERCAT- (NIL T T) -8 NIL NIL NIL) (-839 1955485 1957469 1957838 "ONECOMP" 1958336 NIL ONECOMP (NIL T) -8 NIL NIL NIL) (-838 1954790 1954905 1955079 "ONECOMP2" 1955357 NIL ONECOMP2 (NIL T T) -7 NIL NIL NIL) (-837 1954209 1954315 1954445 "OMSERVER" 1954680 T OMSERVER (NIL) -7 NIL NIL NIL) (-836 1951071 1953649 1953689 "OMSAGG" 1953750 NIL OMSAGG (NIL T) -9 NIL 1953814 NIL) (-835 1949694 1949957 1950239 "OMPKG" 1950809 T OMPKG (NIL) -7 NIL NIL NIL) (-834 1949124 1949227 1949255 "OM" 1949554 T OM (NIL) -9 NIL NIL NIL) (-833 1947671 1948673 1948842 "OMLO" 1949005 NIL OMLO (NIL T T) -8 NIL NIL NIL) (-832 1946631 1946778 1946998 "OMEXPR" 1947497 NIL OMEXPR (NIL T) -7 NIL NIL NIL) (-831 1945922 1946177 1946313 "OMERR" 1946515 T OMERR (NIL) -8 NIL NIL NIL) (-830 1945073 1945343 1945503 "OMERRK" 1945782 T OMERRK (NIL) -8 NIL NIL NIL) (-829 1944524 1944750 1944858 "OMENC" 1944985 T OMENC (NIL) -8 NIL NIL NIL) (-828 1938419 1939604 1940775 "OMDEV" 1943373 T OMDEV (NIL) -8 NIL NIL NIL) (-827 1937488 1937659 1937853 "OMCONN" 1938245 T OMCONN (NIL) -8 NIL NIL NIL) (-826 1936009 1936985 1937013 "OINTDOM" 1937018 T OINTDOM (NIL) -9 NIL 1937039 NIL) (-825 1933347 1934697 1935034 "OFMONOID" 1935704 NIL OFMONOID (NIL T) -8 NIL NIL NIL) (-824 1932758 1933284 1933329 "ODVAR" 1933334 NIL ODVAR (NIL T) -8 NIL NIL NIL) (-823 1930181 1932503 1932658 "ODR" 1932663 NIL ODR (NIL T T NIL) -8 NIL NIL NIL) (-822 1922762 1929957 1930083 "ODPOL" 1930088 NIL ODPOL (NIL T) -8 NIL NIL NIL) (-821 1916584 1922634 1922739 "ODP" 1922744 NIL ODP (NIL NIL T NIL) -8 NIL NIL NIL) (-820 1915350 1915565 1915840 "ODETOOLS" 1916358 NIL ODETOOLS (NIL T T) -7 NIL NIL NIL) (-819 1912317 1912975 1913691 "ODESYS" 1914683 NIL ODESYS (NIL T T) -7 NIL NIL NIL) (-818 1907199 1908107 1909132 "ODERTRIC" 1911392 NIL ODERTRIC (NIL T T) -7 NIL NIL NIL) (-817 1906625 1906707 1906901 "ODERED" 1907111 NIL ODERED (NIL T T T T T) -7 NIL NIL NIL) (-816 1903513 1904061 1904738 "ODERAT" 1906048 NIL ODERAT (NIL T T) -7 NIL NIL NIL) (-815 1900472 1900937 1901534 "ODEPRRIC" 1903042 NIL ODEPRRIC (NIL T T T T) -7 NIL NIL NIL) (-814 1898415 1899011 1899497 "ODEPROB" 1900006 T ODEPROB (NIL) -8 NIL NIL NIL) (-813 1894935 1895420 1896067 "ODEPRIM" 1897894 NIL ODEPRIM (NIL T T T T) -7 NIL NIL NIL) (-812 1894184 1894286 1894546 "ODEPAL" 1894827 NIL ODEPAL (NIL T T T T) -7 NIL NIL NIL) (-811 1890346 1891137 1892001 "ODEPACK" 1893340 T ODEPACK (NIL) -7 NIL NIL NIL) (-810 1889407 1889514 1889736 "ODEINT" 1890235 NIL ODEINT (NIL T T) -7 NIL NIL NIL) (-809 1883508 1884933 1886380 "ODEIFTBL" 1887980 T ODEIFTBL (NIL) -8 NIL NIL NIL) (-808 1878906 1879692 1880644 "ODEEF" 1882667 NIL ODEEF (NIL T T) -7 NIL NIL NIL) (-807 1878255 1878344 1878567 "ODECONST" 1878811 NIL ODECONST (NIL T T T) -7 NIL NIL NIL) (-806 1876380 1877041 1877069 "ODECAT" 1877674 T ODECAT (NIL) -9 NIL 1878205 NIL) (-805 1873235 1876085 1876207 "OCT" 1876290 NIL OCT (NIL T) -8 NIL NIL NIL) (-804 1872873 1872916 1873043 "OCTCT2" 1873186 NIL OCTCT2 (NIL T T T T) -7 NIL NIL NIL) (-803 1867522 1869957 1869997 "OC" 1871094 NIL OC (NIL T) -9 NIL 1871952 NIL) (-802 1864749 1865497 1866487 "OC-" 1866581 NIL OC- (NIL T T) -8 NIL NIL NIL) (-801 1864101 1864569 1864597 "OCAMON" 1864602 T OCAMON (NIL) -9 NIL 1864623 NIL) (-800 1863632 1863973 1864001 "OASGP" 1864006 T OASGP (NIL) -9 NIL 1864026 NIL) (-799 1862893 1863382 1863410 "OAMONS" 1863450 T OAMONS (NIL) -9 NIL 1863493 NIL) (-798 1862307 1862740 1862768 "OAMON" 1862773 T OAMON (NIL) -9 NIL 1862793 NIL) (-797 1861565 1862083 1862111 "OAGROUP" 1862116 T OAGROUP (NIL) -9 NIL 1862136 NIL) (-796 1861255 1861305 1861393 "NUMTUBE" 1861509 NIL NUMTUBE (NIL T) -7 NIL NIL NIL) (-795 1854828 1856346 1857882 "NUMQUAD" 1859739 T NUMQUAD (NIL) -7 NIL NIL NIL) (-794 1850584 1851572 1852597 "NUMODE" 1853823 T NUMODE (NIL) -7 NIL NIL NIL) (-793 1847939 1848819 1848847 "NUMINT" 1849770 T NUMINT (NIL) -9 NIL 1850534 NIL) (-792 1846887 1847084 1847302 "NUMFMT" 1847741 T NUMFMT (NIL) -7 NIL NIL NIL) (-791 1833246 1836191 1838723 "NUMERIC" 1844394 NIL NUMERIC (NIL T) -7 NIL NIL NIL) (-790 1827616 1832695 1832790 "NTSCAT" 1832795 NIL NTSCAT (NIL T T T T) -9 NIL 1832834 NIL) (-789 1826810 1826975 1827168 "NTPOLFN" 1827455 NIL NTPOLFN (NIL T) -7 NIL NIL NIL) (-788 1814887 1823635 1824447 "NSUP" 1826031 NIL NSUP (NIL T) -8 NIL NIL NIL) (-787 1814519 1814576 1814685 "NSUP2" 1814824 NIL NSUP2 (NIL T T) -7 NIL NIL NIL) (-786 1804745 1814293 1814426 "NSMP" 1814431 NIL NSMP (NIL T T) -8 NIL NIL NIL) (-785 1803177 1803478 1803835 "NREP" 1804433 NIL NREP (NIL T) -7 NIL NIL NIL) (-784 1801768 1802020 1802378 "NPCOEF" 1802920 NIL NPCOEF (NIL T T T T T) -7 NIL NIL NIL) (-783 1800834 1800949 1801165 "NORMRETR" 1801649 NIL NORMRETR (NIL T T T T NIL) -7 NIL NIL NIL) (-782 1798875 1799165 1799574 "NORMPK" 1800542 NIL NORMPK (NIL T T T T T) -7 NIL NIL NIL) (-781 1798560 1798588 1798712 "NORMMA" 1798841 NIL NORMMA (NIL T T T T) -7 NIL NIL NIL) (-780 1798360 1798517 1798546 "NONE" 1798551 T NONE (NIL) -8 NIL NIL NIL) (-779 1798149 1798178 1798247 "NONE1" 1798324 NIL NONE1 (NIL T) -7 NIL NIL NIL) (-778 1797646 1797708 1797887 "NODE1" 1798081 NIL NODE1 (NIL T T) -7 NIL NIL NIL) (-777 1795931 1796782 1797037 "NNI" 1797384 T NNI (NIL) -8 NIL NIL 1797619) (-776 1794351 1794664 1795028 "NLINSOL" 1795599 NIL NLINSOL (NIL T) -7 NIL NIL NIL) (-775 1790592 1791587 1792486 "NIPROB" 1793472 T NIPROB (NIL) -8 NIL NIL NIL) (-774 1789349 1789583 1789885 "NFINTBAS" 1790354 NIL NFINTBAS (NIL T T) -7 NIL NIL NIL) (-773 1788523 1788999 1789040 "NETCLT" 1789212 NIL NETCLT (NIL T) -9 NIL 1789294 NIL) (-772 1787231 1787462 1787743 "NCODIV" 1788291 NIL NCODIV (NIL T T) -7 NIL NIL NIL) (-771 1786993 1787030 1787105 "NCNTFRAC" 1787188 NIL NCNTFRAC (NIL T) -7 NIL NIL NIL) (-770 1785173 1785537 1785957 "NCEP" 1786618 NIL NCEP (NIL T) -7 NIL NIL NIL) (-769 1784024 1784797 1784825 "NASRING" 1784935 T NASRING (NIL) -9 NIL 1785015 NIL) (-768 1783819 1783863 1783957 "NASRING-" 1783962 NIL NASRING- (NIL T) -8 NIL NIL NIL) (-767 1782926 1783451 1783479 "NARNG" 1783596 T NARNG (NIL) -9 NIL 1783687 NIL) (-766 1782618 1782685 1782819 "NARNG-" 1782824 NIL NARNG- (NIL T) -8 NIL NIL NIL) (-765 1781497 1781704 1781939 "NAGSP" 1782403 T NAGSP (NIL) -7 NIL NIL NIL) (-764 1772769 1774453 1776126 "NAGS" 1779844 T NAGS (NIL) -7 NIL NIL NIL) (-763 1771317 1771625 1771956 "NAGF07" 1772458 T NAGF07 (NIL) -7 NIL NIL NIL) (-762 1765855 1767146 1768453 "NAGF04" 1770030 T NAGF04 (NIL) -7 NIL NIL NIL) (-761 1758823 1760437 1762070 "NAGF02" 1764242 T NAGF02 (NIL) -7 NIL NIL NIL) (-760 1754047 1755147 1756264 "NAGF01" 1757726 T NAGF01 (NIL) -7 NIL NIL NIL) (-759 1747675 1749241 1750826 "NAGE04" 1752482 T NAGE04 (NIL) -7 NIL NIL NIL) (-758 1738844 1740965 1743095 "NAGE02" 1745565 T NAGE02 (NIL) -7 NIL NIL NIL) (-757 1734797 1735744 1736708 "NAGE01" 1737900 T NAGE01 (NIL) -7 NIL NIL NIL) (-756 1732592 1733126 1733684 "NAGD03" 1734259 T NAGD03 (NIL) -7 NIL NIL NIL) (-755 1724342 1726270 1728224 "NAGD02" 1730658 T NAGD02 (NIL) -7 NIL NIL NIL) (-754 1718153 1719578 1721018 "NAGD01" 1722922 T NAGD01 (NIL) -7 NIL NIL NIL) (-753 1714362 1715184 1716021 "NAGC06" 1717336 T NAGC06 (NIL) -7 NIL NIL NIL) (-752 1712827 1713159 1713515 "NAGC05" 1714026 T NAGC05 (NIL) -7 NIL NIL NIL) (-751 1712203 1712322 1712466 "NAGC02" 1712703 T NAGC02 (NIL) -7 NIL NIL NIL) (-750 1711162 1711745 1711785 "NAALG" 1711864 NIL NAALG (NIL T) -9 NIL 1711925 NIL) (-749 1710997 1711026 1711116 "NAALG-" 1711121 NIL NAALG- (NIL T T) -8 NIL NIL NIL) (-748 1704947 1706055 1707242 "MULTSQFR" 1709893 NIL MULTSQFR (NIL T T T T) -7 NIL NIL NIL) (-747 1704266 1704341 1704525 "MULTFACT" 1704859 NIL MULTFACT (NIL T T T T) -7 NIL NIL NIL) (-746 1696990 1700903 1700956 "MTSCAT" 1702026 NIL MTSCAT (NIL T T) -9 NIL 1702541 NIL) (-745 1696702 1696756 1696848 "MTHING" 1696930 NIL MTHING (NIL T) -7 NIL NIL NIL) (-744 1696494 1696527 1696587 "MSYSCMD" 1696662 T MSYSCMD (NIL) -7 NIL NIL NIL) (-743 1692576 1695249 1695569 "MSET" 1696207 NIL MSET (NIL T) -8 NIL NIL NIL) (-742 1689645 1692137 1692178 "MSETAGG" 1692183 NIL MSETAGG (NIL T) -9 NIL 1692217 NIL) (-741 1685487 1687024 1687769 "MRING" 1688945 NIL MRING (NIL T T) -8 NIL NIL NIL) (-740 1685053 1685120 1685251 "MRF2" 1685414 NIL MRF2 (NIL T T T) -7 NIL NIL NIL) (-739 1684671 1684706 1684850 "MRATFAC" 1685012 NIL MRATFAC (NIL T T T T) -7 NIL NIL NIL) (-738 1682283 1682578 1683009 "MPRFF" 1684376 NIL MPRFF (NIL T T T T) -7 NIL NIL NIL) (-737 1676580 1682137 1682234 "MPOLY" 1682239 NIL MPOLY (NIL NIL T) -8 NIL NIL NIL) (-736 1676070 1676105 1676313 "MPCPF" 1676539 NIL MPCPF (NIL T T T T) -7 NIL NIL NIL) (-735 1675584 1675627 1675811 "MPC3" 1676021 NIL MPC3 (NIL T T T T T T T) -7 NIL NIL NIL) (-734 1674779 1674860 1675081 "MPC2" 1675499 NIL MPC2 (NIL T T T T T T T) -7 NIL NIL NIL) (-733 1673080 1673417 1673807 "MONOTOOL" 1674439 NIL MONOTOOL (NIL T T) -7 NIL NIL NIL) (-732 1672305 1672622 1672650 "MONOID" 1672869 T MONOID (NIL) -9 NIL 1673016 NIL) (-731 1671851 1671970 1672151 "MONOID-" 1672156 NIL MONOID- (NIL T) -8 NIL NIL NIL) (-730 1662326 1668277 1668336 "MONOGEN" 1669010 NIL MONOGEN (NIL T T) -9 NIL 1669466 NIL) (-729 1659544 1660279 1661279 "MONOGEN-" 1661398 NIL MONOGEN- (NIL T T T) -8 NIL NIL NIL) (-728 1658377 1658823 1658851 "MONADWU" 1659243 T MONADWU (NIL) -9 NIL 1659481 NIL) (-727 1657749 1657908 1658156 "MONADWU-" 1658161 NIL MONADWU- (NIL T) -8 NIL NIL NIL) (-726 1657108 1657352 1657380 "MONAD" 1657587 T MONAD (NIL) -9 NIL 1657699 NIL) (-725 1656793 1656871 1657003 "MONAD-" 1657008 NIL MONAD- (NIL T) -8 NIL NIL NIL) (-724 1655082 1655706 1655985 "MOEBIUS" 1656546 NIL MOEBIUS (NIL T) -8 NIL NIL NIL) (-723 1654360 1654764 1654804 "MODULE" 1654809 NIL MODULE (NIL T) -9 NIL 1654848 NIL) (-722 1653928 1654024 1654214 "MODULE-" 1654219 NIL MODULE- (NIL T T) -8 NIL NIL NIL) (-721 1651608 1652292 1652619 "MODRING" 1653752 NIL MODRING (NIL T T NIL NIL NIL) -8 NIL NIL NIL) (-720 1648552 1649713 1650234 "MODOP" 1651137 NIL MODOP (NIL T T) -8 NIL NIL NIL) (-719 1647140 1647619 1647896 "MODMONOM" 1648415 NIL MODMONOM (NIL T T NIL) -8 NIL NIL NIL) (-718 1637184 1645431 1645845 "MODMON" 1646777 NIL MODMON (NIL T T) -8 NIL NIL NIL) (-717 1634340 1636028 1636304 "MODFIELD" 1637059 NIL MODFIELD (NIL T T NIL NIL NIL) -8 NIL NIL NIL) (-716 1633317 1633621 1633811 "MMLFORM" 1634170 T MMLFORM (NIL) -8 NIL NIL NIL) (-715 1632843 1632886 1633065 "MMAP" 1633268 NIL MMAP (NIL T T T T T T) -7 NIL NIL NIL) (-714 1630922 1631689 1631730 "MLO" 1632153 NIL MLO (NIL T) -9 NIL 1632395 NIL) (-713 1628288 1628804 1629406 "MLIFT" 1630403 NIL MLIFT (NIL T T T T) -7 NIL NIL NIL) (-712 1627679 1627763 1627917 "MKUCFUNC" 1628199 NIL MKUCFUNC (NIL T T T) -7 NIL NIL NIL) (-711 1627278 1627348 1627471 "MKRECORD" 1627602 NIL MKRECORD (NIL T T) -7 NIL NIL NIL) (-710 1626325 1626487 1626715 "MKFUNC" 1627089 NIL MKFUNC (NIL T) -7 NIL NIL NIL) (-709 1625713 1625817 1625973 "MKFLCFN" 1626208 NIL MKFLCFN (NIL T) -7 NIL NIL NIL) (-708 1624990 1625092 1625277 "MKBCFUNC" 1625606 NIL MKBCFUNC (NIL T T T T) -7 NIL NIL NIL) (-707 1621697 1624544 1624680 "MINT" 1624874 T MINT (NIL) -8 NIL NIL NIL) (-706 1620509 1620752 1621029 "MHROWRED" 1621452 NIL MHROWRED (NIL T) -7 NIL NIL NIL) (-705 1615889 1619044 1619449 "MFLOAT" 1620124 T MFLOAT (NIL) -8 NIL NIL NIL) (-704 1615246 1615322 1615493 "MFINFACT" 1615801 NIL MFINFACT (NIL T T T T) -7 NIL NIL NIL) (-703 1611561 1612409 1613293 "MESH" 1614382 T MESH (NIL) -7 NIL NIL NIL) (-702 1609951 1610263 1610616 "MDDFACT" 1611248 NIL MDDFACT (NIL T) -7 NIL NIL NIL) (-701 1606746 1609110 1609151 "MDAGG" 1609406 NIL MDAGG (NIL T) -9 NIL 1609549 NIL) (-700 1596486 1606039 1606246 "MCMPLX" 1606559 T MCMPLX (NIL) -8 NIL NIL NIL) (-699 1595623 1595769 1595970 "MCDEN" 1596335 NIL MCDEN (NIL T T) -7 NIL NIL NIL) (-698 1593513 1593783 1594163 "MCALCFN" 1595353 NIL MCALCFN (NIL T T T T) -7 NIL NIL NIL) (-697 1592438 1592678 1592911 "MAYBE" 1593319 NIL MAYBE (NIL T) -8 NIL NIL NIL) (-696 1590050 1590573 1591135 "MATSTOR" 1591909 NIL MATSTOR (NIL T) -7 NIL NIL NIL) (-695 1586007 1589422 1589670 "MATRIX" 1589835 NIL MATRIX (NIL T) -8 NIL NIL NIL) (-694 1581773 1582480 1583216 "MATLIN" 1585364 NIL MATLIN (NIL T T T T) -7 NIL NIL NIL) (-693 1571879 1575065 1575142 "MATCAT" 1580022 NIL MATCAT (NIL T T T) -9 NIL 1581439 NIL) (-692 1568235 1569256 1570612 "MATCAT-" 1570617 NIL MATCAT- (NIL T T T T) -8 NIL NIL NIL) (-691 1566829 1566982 1567315 "MATCAT2" 1568070 NIL MATCAT2 (NIL T T T T T T T T) -7 NIL NIL NIL) (-690 1564941 1565265 1565649 "MAPPKG3" 1566504 NIL MAPPKG3 (NIL T T T) -7 NIL NIL NIL) (-689 1563922 1564095 1564317 "MAPPKG2" 1564765 NIL MAPPKG2 (NIL T T) -7 NIL NIL NIL) (-688 1562421 1562705 1563032 "MAPPKG1" 1563628 NIL MAPPKG1 (NIL T) -7 NIL NIL NIL) (-687 1561500 1561827 1562004 "MAPPAST" 1562264 T MAPPAST (NIL) -8 NIL NIL NIL) (-686 1561111 1561169 1561292 "MAPHACK3" 1561436 NIL MAPHACK3 (NIL T T T) -7 NIL NIL NIL) (-685 1560703 1560764 1560878 "MAPHACK2" 1561043 NIL MAPHACK2 (NIL T T) -7 NIL NIL NIL) (-684 1560141 1560244 1560386 "MAPHACK1" 1560594 NIL MAPHACK1 (NIL T) -7 NIL NIL NIL) (-683 1558220 1558841 1559145 "MAGMA" 1559869 NIL MAGMA (NIL T) -8 NIL NIL NIL) (-682 1557699 1557944 1558035 "MACROAST" 1558149 T MACROAST (NIL) -8 NIL NIL NIL) (-681 1554117 1555938 1556399 "M3D" 1557271 NIL M3D (NIL T) -8 NIL NIL NIL) (-680 1548223 1552486 1552527 "LZSTAGG" 1553309 NIL LZSTAGG (NIL T) -9 NIL 1553604 NIL) (-679 1544181 1545354 1546811 "LZSTAGG-" 1546816 NIL LZSTAGG- (NIL T T) -8 NIL NIL NIL) (-678 1541268 1542072 1542559 "LWORD" 1543726 NIL LWORD (NIL T) -8 NIL NIL NIL) (-677 1540844 1541072 1541147 "LSTAST" 1541213 T LSTAST (NIL) -8 NIL NIL NIL) (-676 1534010 1540615 1540749 "LSQM" 1540754 NIL LSQM (NIL NIL T) -8 NIL NIL NIL) (-675 1533234 1533373 1533601 "LSPP" 1533865 NIL LSPP (NIL T T T T) -7 NIL NIL NIL) (-674 1531046 1531347 1531803 "LSMP" 1532923 NIL LSMP (NIL T T T T) -7 NIL NIL NIL) (-673 1527825 1528499 1529229 "LSMP1" 1530348 NIL LSMP1 (NIL T) -7 NIL NIL NIL) (-672 1521702 1526992 1527033 "LSAGG" 1527095 NIL LSAGG (NIL T) -9 NIL 1527173 NIL) (-671 1518397 1519321 1520534 "LSAGG-" 1520539 NIL LSAGG- (NIL T T) -8 NIL NIL NIL) (-670 1515996 1517541 1517790 "LPOLY" 1518192 NIL LPOLY (NIL T T) -8 NIL NIL NIL) (-669 1515578 1515663 1515786 "LPEFRAC" 1515905 NIL LPEFRAC (NIL T) -7 NIL NIL NIL) (-668 1513899 1514672 1514925 "LO" 1515410 NIL LO (NIL T T T) -8 NIL NIL NIL) (-667 1513551 1513663 1513691 "LOGIC" 1513802 T LOGIC (NIL) -9 NIL 1513883 NIL) (-666 1513413 1513436 1513507 "LOGIC-" 1513512 NIL LOGIC- (NIL T) -8 NIL NIL NIL) (-665 1512606 1512746 1512939 "LODOOPS" 1513269 NIL LODOOPS (NIL T T) -7 NIL NIL NIL) (-664 1510029 1512522 1512588 "LODO" 1512593 NIL LODO (NIL T NIL) -8 NIL NIL NIL) (-663 1508567 1508802 1509155 "LODOF" 1509776 NIL LODOF (NIL T T) -7 NIL NIL NIL) (-662 1504785 1507216 1507257 "LODOCAT" 1507695 NIL LODOCAT (NIL T) -9 NIL 1507906 NIL) (-661 1504518 1504576 1504703 "LODOCAT-" 1504708 NIL LODOCAT- (NIL T T) -8 NIL NIL NIL) (-660 1501838 1504359 1504477 "LODO2" 1504482 NIL LODO2 (NIL T T) -8 NIL NIL NIL) (-659 1499273 1501775 1501820 "LODO1" 1501825 NIL LODO1 (NIL T) -8 NIL NIL NIL) (-658 1498154 1498319 1498624 "LODEEF" 1499096 NIL LODEEF (NIL T T T) -7 NIL NIL NIL) (-657 1493393 1496284 1496325 "LNAGG" 1497272 NIL LNAGG (NIL T) -9 NIL 1497716 NIL) (-656 1492540 1492754 1493096 "LNAGG-" 1493101 NIL LNAGG- (NIL T T) -8 NIL NIL NIL) (-655 1488676 1489465 1490104 "LMOPS" 1491955 NIL LMOPS (NIL T T NIL) -8 NIL NIL NIL) (-654 1488079 1488467 1488508 "LMODULE" 1488513 NIL LMODULE (NIL T) -9 NIL 1488539 NIL) (-653 1485277 1487724 1487847 "LMDICT" 1487989 NIL LMDICT (NIL T) -8 NIL NIL NIL) (-652 1484683 1484904 1484945 "LLINSET" 1485136 NIL LLINSET (NIL T) -9 NIL 1485227 NIL) (-651 1484382 1484591 1484651 "LITERAL" 1484656 NIL LITERAL (NIL T) -8 NIL NIL NIL) (-650 1477545 1483316 1483620 "LIST" 1484111 NIL LIST (NIL T) -8 NIL NIL NIL) (-649 1477070 1477144 1477283 "LIST3" 1477465 NIL LIST3 (NIL T T T) -7 NIL NIL NIL) (-648 1476077 1476255 1476483 "LIST2" 1476888 NIL LIST2 (NIL T T) -7 NIL NIL NIL) (-647 1474211 1474523 1474922 "LIST2MAP" 1475724 NIL LIST2MAP (NIL T T) -7 NIL NIL NIL) (-646 1473807 1474044 1474085 "LINSET" 1474090 NIL LINSET (NIL T) -9 NIL 1474124 NIL) (-645 1472468 1473138 1473179 "LINEXP" 1473434 NIL LINEXP (NIL T) -9 NIL 1473583 NIL) (-644 1471115 1471375 1471672 "LINDEP" 1472220 NIL LINDEP (NIL T T) -7 NIL NIL NIL) (-643 1467882 1468601 1469378 "LIMITRF" 1470370 NIL LIMITRF (NIL T) -7 NIL NIL NIL) (-642 1466185 1466481 1466890 "LIMITPS" 1467577 NIL LIMITPS (NIL T T) -7 NIL NIL NIL) (-641 1460613 1465696 1465924 "LIE" 1466006 NIL LIE (NIL T T) -8 NIL NIL NIL) (-640 1459561 1460030 1460070 "LIECAT" 1460210 NIL LIECAT (NIL T) -9 NIL 1460361 NIL) (-639 1459402 1459429 1459517 "LIECAT-" 1459522 NIL LIECAT- (NIL T T) -8 NIL NIL NIL) (-638 1451898 1458851 1459016 "LIB" 1459257 T LIB (NIL) -8 NIL NIL NIL) (-637 1447533 1448416 1449351 "LGROBP" 1451015 NIL LGROBP (NIL NIL T) -7 NIL NIL NIL) (-636 1445531 1445805 1446155 "LF" 1447254 NIL LF (NIL T T) -7 NIL NIL NIL) (-635 1444371 1445063 1445091 "LFCAT" 1445298 T LFCAT (NIL) -9 NIL 1445437 NIL) (-634 1441273 1441903 1442591 "LEXTRIPK" 1443735 NIL LEXTRIPK (NIL T NIL) -7 NIL NIL NIL) (-633 1438017 1438843 1439346 "LEXP" 1440853 NIL LEXP (NIL T T NIL) -8 NIL NIL NIL) (-632 1437493 1437738 1437830 "LETAST" 1437945 T LETAST (NIL) -8 NIL NIL NIL) (-631 1435891 1436204 1436605 "LEADCDET" 1437175 NIL LEADCDET (NIL T T T T) -7 NIL NIL NIL) (-630 1435081 1435155 1435384 "LAZM3PK" 1435812 NIL LAZM3PK (NIL T T T T T T) -7 NIL NIL NIL) (-629 1429998 1433158 1433696 "LAUPOL" 1434593 NIL LAUPOL (NIL T T) -8 NIL NIL NIL) (-628 1429577 1429621 1429782 "LAPLACE" 1429948 NIL LAPLACE (NIL T T) -7 NIL NIL NIL) (-627 1427516 1428678 1428929 "LA" 1429410 NIL LA (NIL T T T) -8 NIL NIL NIL) (-626 1426510 1427094 1427135 "LALG" 1427197 NIL LALG (NIL T) -9 NIL 1427256 NIL) (-625 1426224 1426283 1426419 "LALG-" 1426424 NIL LALG- (NIL T T) -8 NIL NIL NIL) (-624 1426059 1426083 1426124 "KVTFROM" 1426186 NIL KVTFROM (NIL T) -9 NIL NIL NIL) (-623 1424982 1425426 1425611 "KTVLOGIC" 1425894 T KTVLOGIC (NIL) -8 NIL NIL NIL) (-622 1424817 1424841 1424882 "KRCFROM" 1424944 NIL KRCFROM (NIL T) -9 NIL NIL NIL) (-621 1423721 1423908 1424207 "KOVACIC" 1424617 NIL KOVACIC (NIL T T) -7 NIL NIL NIL) (-620 1423556 1423580 1423621 "KONVERT" 1423683 NIL KONVERT (NIL T) -9 NIL NIL NIL) (-619 1423391 1423415 1423456 "KOERCE" 1423518 NIL KOERCE (NIL T) -9 NIL NIL NIL) (-618 1421221 1421984 1422361 "KERNEL" 1423047 NIL KERNEL (NIL T) -8 NIL NIL NIL) (-617 1420717 1420798 1420930 "KERNEL2" 1421135 NIL KERNEL2 (NIL T T) -7 NIL NIL NIL) (-616 1414487 1419256 1419310 "KDAGG" 1419687 NIL KDAGG (NIL T T) -9 NIL 1419893 NIL) (-615 1414016 1414140 1414345 "KDAGG-" 1414350 NIL KDAGG- (NIL T T T) -8 NIL NIL NIL) (-614 1407164 1413677 1413832 "KAFILE" 1413894 NIL KAFILE (NIL T) -8 NIL NIL NIL) (-613 1401592 1406675 1406903 "JORDAN" 1406985 NIL JORDAN (NIL T T) -8 NIL NIL NIL) (-612 1400971 1401241 1401362 "JOINAST" 1401491 T JOINAST (NIL) -8 NIL NIL NIL) (-611 1400817 1400876 1400931 "JAVACODE" 1400936 T JAVACODE (NIL) -8 NIL NIL NIL) (-610 1397069 1399022 1399076 "IXAGG" 1400005 NIL IXAGG (NIL T T) -9 NIL 1400464 NIL) (-609 1395988 1396294 1396713 "IXAGG-" 1396718 NIL IXAGG- (NIL T T T) -8 NIL NIL NIL) (-608 1391518 1395910 1395969 "IVECTOR" 1395974 NIL IVECTOR (NIL T NIL) -8 NIL NIL NIL) (-607 1390284 1390521 1390787 "ITUPLE" 1391285 NIL ITUPLE (NIL T) -8 NIL NIL NIL) (-606 1388786 1388963 1389258 "ITRIGMNP" 1390106 NIL ITRIGMNP (NIL T T T) -7 NIL NIL NIL) (-605 1387531 1387735 1388018 "ITFUN3" 1388562 NIL ITFUN3 (NIL T T T) -7 NIL NIL NIL) (-604 1387163 1387220 1387329 "ITFUN2" 1387468 NIL ITFUN2 (NIL T T) -7 NIL NIL NIL) (-603 1386322 1386643 1386817 "ITFORM" 1387009 T ITFORM (NIL) -8 NIL NIL NIL) (-602 1384283 1385342 1385620 "ITAYLOR" 1386077 NIL ITAYLOR (NIL T) -8 NIL NIL NIL) (-601 1373228 1378420 1379583 "ISUPS" 1383153 NIL ISUPS (NIL T) -8 NIL NIL NIL) (-600 1372332 1372472 1372708 "ISUMP" 1373075 NIL ISUMP (NIL T T T T) -7 NIL NIL NIL) (-599 1367707 1372277 1372318 "ISTRING" 1372323 NIL ISTRING (NIL NIL) -8 NIL NIL NIL) (-598 1367183 1367428 1367520 "ISAST" 1367635 T ISAST (NIL) -8 NIL NIL NIL) (-597 1366392 1366474 1366690 "IRURPK" 1367097 NIL IRURPK (NIL T T T T T) -7 NIL NIL NIL) (-596 1365328 1365529 1365769 "IRSN" 1366172 T IRSN (NIL) -7 NIL NIL NIL) (-595 1363399 1363754 1364183 "IRRF2F" 1364966 NIL IRRF2F (NIL T) -7 NIL NIL NIL) (-594 1363146 1363184 1363260 "IRREDFFX" 1363355 NIL IRREDFFX (NIL T) -7 NIL NIL NIL) (-593 1361761 1362020 1362319 "IROOT" 1362879 NIL IROOT (NIL T) -7 NIL NIL NIL) (-592 1358365 1359445 1360137 "IR" 1361101 NIL IR (NIL T) -8 NIL NIL NIL) (-591 1357570 1357858 1358009 "IRFORM" 1358234 T IRFORM (NIL) -8 NIL NIL NIL) (-590 1355183 1355678 1356244 "IR2" 1357048 NIL IR2 (NIL T T) -7 NIL NIL NIL) (-589 1354283 1354396 1354610 "IR2F" 1355066 NIL IR2F (NIL T T) -7 NIL NIL NIL) (-588 1354074 1354108 1354168 "IPRNTPK" 1354243 T IPRNTPK (NIL) -7 NIL NIL NIL) (-587 1350655 1353963 1354032 "IPF" 1354037 NIL IPF (NIL NIL) -8 NIL NIL NIL) (-586 1348982 1350580 1350637 "IPADIC" 1350642 NIL IPADIC (NIL NIL NIL) -8 NIL NIL NIL) (-585 1348294 1348542 1348672 "IP4ADDR" 1348872 T IP4ADDR (NIL) -8 NIL NIL NIL) (-584 1347668 1347923 1348055 "IOMODE" 1348182 T IOMODE (NIL) -8 NIL NIL NIL) (-583 1346741 1347265 1347392 "IOBFILE" 1347561 T IOBFILE (NIL) -8 NIL NIL NIL) (-582 1346229 1346645 1346673 "IOBCON" 1346678 T IOBCON (NIL) -9 NIL 1346699 NIL) (-581 1345740 1345798 1345981 "INVLAPLA" 1346165 NIL INVLAPLA (NIL T T) -7 NIL NIL NIL) (-580 1335388 1337742 1340128 "INTTR" 1343404 NIL INTTR (NIL T T) -7 NIL NIL NIL) (-579 1331723 1332465 1333330 "INTTOOLS" 1334573 NIL INTTOOLS (NIL T T) -7 NIL NIL NIL) (-578 1331309 1331400 1331517 "INTSLPE" 1331626 T INTSLPE (NIL) -7 NIL NIL NIL) (-577 1329262 1331232 1331291 "INTRVL" 1331296 NIL INTRVL (NIL T) -8 NIL NIL NIL) (-576 1326864 1327376 1327951 "INTRF" 1328747 NIL INTRF (NIL T) -7 NIL NIL NIL) (-575 1326275 1326372 1326514 "INTRET" 1326762 NIL INTRET (NIL T) -7 NIL NIL NIL) (-574 1324272 1324661 1325131 "INTRAT" 1325883 NIL INTRAT (NIL T T) -7 NIL NIL NIL) (-573 1321535 1322118 1322737 "INTPM" 1323757 NIL INTPM (NIL T T) -7 NIL NIL NIL) (-572 1318280 1318879 1319617 "INTPAF" 1320921 NIL INTPAF (NIL T T T) -7 NIL NIL NIL) (-571 1313459 1314421 1315472 "INTPACK" 1317249 T INTPACK (NIL) -7 NIL NIL NIL) (-570 1310407 1313256 1313365 "INT" 1313370 T INT (NIL) -8 NIL NIL NIL) (-569 1309659 1309811 1310019 "INTHERTR" 1310249 NIL INTHERTR (NIL T T) -7 NIL NIL NIL) (-568 1309098 1309178 1309366 "INTHERAL" 1309573 NIL INTHERAL (NIL T T T T) -7 NIL NIL NIL) (-567 1306944 1307387 1307844 "INTHEORY" 1308661 T INTHEORY (NIL) -7 NIL NIL NIL) (-566 1298350 1299971 1301743 "INTG0" 1305296 NIL INTG0 (NIL T T T) -7 NIL NIL NIL) (-565 1278923 1283713 1288523 "INTFTBL" 1293560 T INTFTBL (NIL) -8 NIL NIL NIL) (-564 1278172 1278310 1278483 "INTFACT" 1278782 NIL INTFACT (NIL T) -7 NIL NIL NIL) (-563 1275599 1276045 1276602 "INTEF" 1277726 NIL INTEF (NIL T T) -7 NIL NIL NIL) (-562 1273966 1274705 1274733 "INTDOM" 1275034 T INTDOM (NIL) -9 NIL 1275241 NIL) (-561 1273335 1273509 1273751 "INTDOM-" 1273756 NIL INTDOM- (NIL T) -8 NIL NIL NIL) (-560 1269723 1271651 1271705 "INTCAT" 1272504 NIL INTCAT (NIL T) -9 NIL 1272825 NIL) (-559 1269195 1269298 1269426 "INTBIT" 1269615 T INTBIT (NIL) -7 NIL NIL NIL) (-558 1267894 1268048 1268355 "INTALG" 1269040 NIL INTALG (NIL T T T T T) -7 NIL NIL NIL) (-557 1267377 1267467 1267624 "INTAF" 1267798 NIL INTAF (NIL T T) -7 NIL NIL NIL) (-556 1260720 1267187 1267327 "INTABL" 1267332 NIL INTABL (NIL T T T) -8 NIL NIL NIL) (-555 1260061 1260527 1260592 "INT8" 1260626 T INT8 (NIL) -8 NIL NIL 1260671) (-554 1259401 1259867 1259932 "INT64" 1259966 T INT64 (NIL) -8 NIL NIL 1260011) (-553 1258741 1259207 1259272 "INT32" 1259306 T INT32 (NIL) -8 NIL NIL 1259351) (-552 1258081 1258547 1258612 "INT16" 1258646 T INT16 (NIL) -8 NIL NIL 1258691) (-551 1252991 1255704 1255732 "INS" 1256666 T INS (NIL) -9 NIL 1257331 NIL) (-550 1250231 1251002 1251976 "INS-" 1252049 NIL INS- (NIL T) -8 NIL NIL NIL) (-549 1249006 1249233 1249531 "INPSIGN" 1249984 NIL INPSIGN (NIL T T) -7 NIL NIL NIL) (-548 1248124 1248241 1248438 "INPRODPF" 1248886 NIL INPRODPF (NIL T T) -7 NIL NIL NIL) (-547 1247018 1247135 1247372 "INPRODFF" 1248004 NIL INPRODFF (NIL T T T T) -7 NIL NIL NIL) (-546 1246018 1246170 1246430 "INNMFACT" 1246854 NIL INNMFACT (NIL T T T T) -7 NIL NIL NIL) (-545 1245215 1245312 1245500 "INMODGCD" 1245917 NIL INMODGCD (NIL T T NIL NIL) -7 NIL NIL NIL) (-544 1243723 1243968 1244292 "INFSP" 1244960 NIL INFSP (NIL T T T) -7 NIL NIL NIL) (-543 1242907 1243024 1243207 "INFPROD0" 1243603 NIL INFPROD0 (NIL T T) -7 NIL NIL NIL) (-542 1239762 1240972 1241487 "INFORM" 1242400 T INFORM (NIL) -8 NIL NIL NIL) (-541 1239372 1239432 1239530 "INFORM1" 1239697 NIL INFORM1 (NIL T) -7 NIL NIL NIL) (-540 1238895 1238984 1239098 "INFINITY" 1239278 T INFINITY (NIL) -7 NIL NIL NIL) (-539 1238071 1238615 1238716 "INETCLTS" 1238814 T INETCLTS (NIL) -8 NIL NIL NIL) (-538 1236687 1236937 1237258 "INEP" 1237819 NIL INEP (NIL T T T) -7 NIL NIL NIL) (-537 1235936 1236584 1236649 "INDE" 1236654 NIL INDE (NIL T) -8 NIL NIL NIL) (-536 1235500 1235568 1235685 "INCRMAPS" 1235863 NIL INCRMAPS (NIL T) -7 NIL NIL NIL) (-535 1234318 1234769 1234975 "INBFILE" 1235314 T INBFILE (NIL) -8 NIL NIL NIL) (-534 1229617 1230554 1231498 "INBFF" 1233406 NIL INBFF (NIL T) -7 NIL NIL NIL) (-533 1228525 1228794 1228822 "INBCON" 1229335 T INBCON (NIL) -9 NIL 1229601 NIL) (-532 1227777 1228000 1228276 "INBCON-" 1228281 NIL INBCON- (NIL T) -8 NIL NIL NIL) (-531 1227256 1227501 1227592 "INAST" 1227706 T INAST (NIL) -8 NIL NIL NIL) (-530 1226683 1226935 1227041 "IMPTAST" 1227170 T IMPTAST (NIL) -8 NIL NIL NIL) (-529 1223129 1226527 1226631 "IMATRIX" 1226636 NIL IMATRIX (NIL T NIL NIL) -8 NIL NIL NIL) (-528 1221837 1221960 1222276 "IMATQF" 1222985 NIL IMATQF (NIL T T T T T T T T) -7 NIL NIL NIL) (-527 1220057 1220284 1220621 "IMATLIN" 1221593 NIL IMATLIN (NIL T T T T) -7 NIL NIL NIL) (-526 1214635 1219981 1220039 "ILIST" 1220044 NIL ILIST (NIL T NIL) -8 NIL NIL NIL) (-525 1212540 1214495 1214608 "IIARRAY2" 1214613 NIL IIARRAY2 (NIL T NIL NIL T T) -8 NIL NIL NIL) (-524 1207938 1212451 1212515 "IFF" 1212520 NIL IFF (NIL NIL NIL) -8 NIL NIL NIL) (-523 1207285 1207555 1207671 "IFAST" 1207842 T IFAST (NIL) -8 NIL NIL NIL) (-522 1202280 1206577 1206765 "IFARRAY" 1207142 NIL IFARRAY (NIL T NIL) -8 NIL NIL NIL) (-521 1201460 1202184 1202257 "IFAMON" 1202262 NIL IFAMON (NIL T T NIL) -8 NIL NIL NIL) (-520 1201044 1201109 1201163 "IEVALAB" 1201370 NIL IEVALAB (NIL T T) -9 NIL NIL NIL) (-519 1200719 1200787 1200947 "IEVALAB-" 1200952 NIL IEVALAB- (NIL T T T) -8 NIL NIL NIL) (-518 1200350 1200633 1200696 "IDPO" 1200701 NIL IDPO (NIL T T) -8 NIL NIL NIL) (-517 1199600 1200239 1200314 "IDPOAMS" 1200319 NIL IDPOAMS (NIL T T) -8 NIL NIL NIL) (-516 1198907 1199489 1199564 "IDPOAM" 1199569 NIL IDPOAM (NIL T T) -8 NIL NIL NIL) (-515 1197966 1198242 1198295 "IDPC" 1198708 NIL IDPC (NIL T T) -9 NIL 1198857 NIL) (-514 1197435 1197858 1197931 "IDPAM" 1197936 NIL IDPAM (NIL T T) -8 NIL NIL NIL) (-513 1196811 1197327 1197400 "IDPAG" 1197405 NIL IDPAG (NIL T T) -8 NIL NIL NIL) (-512 1196456 1196647 1196722 "IDENT" 1196756 T IDENT (NIL) -8 NIL NIL NIL) (-511 1192711 1193559 1194454 "IDECOMP" 1195613 NIL IDECOMP (NIL NIL NIL) -7 NIL NIL NIL) (-510 1185549 1186634 1187681 "IDEAL" 1191747 NIL IDEAL (NIL T T T T) -8 NIL NIL NIL) (-509 1184709 1184821 1185021 "ICDEN" 1185433 NIL ICDEN (NIL T T T T) -7 NIL NIL NIL) (-508 1183780 1184189 1184336 "ICARD" 1184582 T ICARD (NIL) -8 NIL NIL NIL) (-507 1181840 1182153 1182558 "IBPTOOLS" 1183457 NIL IBPTOOLS (NIL T T T T) -7 NIL NIL NIL) (-506 1177447 1181460 1181573 "IBITS" 1181759 NIL IBITS (NIL NIL) -8 NIL NIL NIL) (-505 1174170 1174746 1175441 "IBATOOL" 1176864 NIL IBATOOL (NIL T T T) -7 NIL NIL NIL) (-504 1171949 1172411 1172944 "IBACHIN" 1173705 NIL IBACHIN (NIL T T T) -7 NIL NIL NIL) (-503 1169778 1171795 1171898 "IARRAY2" 1171903 NIL IARRAY2 (NIL T NIL NIL) -8 NIL NIL NIL) (-502 1165884 1169704 1169761 "IARRAY1" 1169766 NIL IARRAY1 (NIL T NIL) -8 NIL NIL NIL) (-501 1159993 1164296 1164777 "IAN" 1165423 T IAN (NIL) -8 NIL NIL NIL) (-500 1159504 1159561 1159734 "IALGFACT" 1159930 NIL IALGFACT (NIL T T T T) -7 NIL NIL NIL) (-499 1159032 1159145 1159173 "HYPCAT" 1159380 T HYPCAT (NIL) -9 NIL NIL NIL) (-498 1158570 1158687 1158873 "HYPCAT-" 1158878 NIL HYPCAT- (NIL T) -8 NIL NIL NIL) (-497 1158165 1158365 1158448 "HOSTNAME" 1158507 T HOSTNAME (NIL) -8 NIL NIL NIL) (-496 1158010 1158047 1158088 "HOMOTOP" 1158093 NIL HOMOTOP (NIL T) -9 NIL 1158126 NIL) (-495 1154642 1156020 1156061 "HOAGG" 1157042 NIL HOAGG (NIL T) -9 NIL 1157721 NIL) (-494 1153236 1153635 1154161 "HOAGG-" 1154166 NIL HOAGG- (NIL T T) -8 NIL NIL NIL) (-493 1147238 1152829 1152979 "HEXADEC" 1153106 T HEXADEC (NIL) -8 NIL NIL NIL) (-492 1145986 1146208 1146471 "HEUGCD" 1147015 NIL HEUGCD (NIL T) -7 NIL NIL NIL) (-491 1145062 1145823 1145953 "HELLFDIV" 1145958 NIL HELLFDIV (NIL T T T T) -8 NIL NIL NIL) (-490 1143241 1144839 1144927 "HEAP" 1145006 NIL HEAP (NIL T) -8 NIL NIL NIL) (-489 1142504 1142793 1142927 "HEADAST" 1143127 T HEADAST (NIL) -8 NIL NIL NIL) (-488 1136370 1142419 1142481 "HDP" 1142486 NIL HDP (NIL NIL T) -8 NIL NIL NIL) (-487 1130358 1136005 1136157 "HDMP" 1136271 NIL HDMP (NIL NIL T) -8 NIL NIL NIL) (-486 1129682 1129822 1129986 "HB" 1130214 T HB (NIL) -7 NIL NIL NIL) (-485 1123068 1129528 1129632 "HASHTBL" 1129637 NIL HASHTBL (NIL T T NIL) -8 NIL NIL NIL) (-484 1122544 1122789 1122881 "HASAST" 1122996 T HASAST (NIL) -8 NIL NIL NIL) (-483 1120322 1122166 1122348 "HACKPI" 1122382 T HACKPI (NIL) -8 NIL NIL NIL) (-482 1115990 1120175 1120288 "GTSET" 1120293 NIL GTSET (NIL T T T T) -8 NIL NIL NIL) (-481 1109405 1115868 1115966 "GSTBL" 1115971 NIL GSTBL (NIL T T T NIL) -8 NIL NIL NIL) (-480 1101683 1108436 1108701 "GSERIES" 1109196 NIL GSERIES (NIL T NIL NIL) -8 NIL NIL NIL) (-479 1100824 1101241 1101269 "GROUP" 1101472 T GROUP (NIL) -9 NIL 1101606 NIL) (-478 1100190 1100349 1100600 "GROUP-" 1100605 NIL GROUP- (NIL T) -8 NIL NIL NIL) (-477 1098557 1098878 1099265 "GROEBSOL" 1099867 NIL GROEBSOL (NIL NIL T T) -7 NIL NIL NIL) (-476 1097471 1097759 1097810 "GRMOD" 1098339 NIL GRMOD (NIL T T) -9 NIL 1098507 NIL) (-475 1097239 1097275 1097403 "GRMOD-" 1097408 NIL GRMOD- (NIL T T T) -8 NIL NIL NIL) (-474 1092529 1093593 1094593 "GRIMAGE" 1096259 T GRIMAGE (NIL) -8 NIL NIL NIL) (-473 1090995 1091256 1091580 "GRDEF" 1092225 T GRDEF (NIL) -7 NIL NIL NIL) (-472 1090439 1090555 1090696 "GRAY" 1090874 T GRAY (NIL) -7 NIL NIL NIL) (-471 1089626 1090032 1090083 "GRALG" 1090236 NIL GRALG (NIL T T) -9 NIL 1090329 NIL) (-470 1089287 1089360 1089523 "GRALG-" 1089528 NIL GRALG- (NIL T T T) -8 NIL NIL NIL) (-469 1086064 1088872 1089050 "GPOLSET" 1089194 NIL GPOLSET (NIL T T T T) -8 NIL NIL NIL) (-468 1085418 1085475 1085733 "GOSPER" 1086001 NIL GOSPER (NIL T T T T T) -7 NIL NIL NIL) (-467 1081150 1081856 1082382 "GMODPOL" 1085117 NIL GMODPOL (NIL NIL T T T NIL T) -8 NIL NIL NIL) (-466 1080155 1080339 1080577 "GHENSEL" 1080962 NIL GHENSEL (NIL T T) -7 NIL NIL NIL) (-465 1074311 1075154 1076174 "GENUPS" 1079239 NIL GENUPS (NIL T T) -7 NIL NIL NIL) (-464 1074008 1074059 1074148 "GENUFACT" 1074254 NIL GENUFACT (NIL T) -7 NIL NIL NIL) (-463 1073420 1073497 1073662 "GENPGCD" 1073926 NIL GENPGCD (NIL T T T T) -7 NIL NIL NIL) (-462 1072894 1072929 1073142 "GENMFACT" 1073379 NIL GENMFACT (NIL T T T T T) -7 NIL NIL NIL) (-461 1071460 1071717 1072024 "GENEEZ" 1072637 NIL GENEEZ (NIL T T) -7 NIL NIL NIL) (-460 1065608 1071071 1071233 "GDMP" 1071383 NIL GDMP (NIL NIL T T) -8 NIL NIL NIL) (-459 1054951 1059379 1060485 "GCNAALG" 1064591 NIL GCNAALG (NIL T NIL NIL NIL) -8 NIL NIL NIL) (-458 1053278 1054140 1054168 "GCDDOM" 1054423 T GCDDOM (NIL) -9 NIL 1054580 NIL) (-457 1052748 1052875 1053090 "GCDDOM-" 1053095 NIL GCDDOM- (NIL T) -8 NIL NIL NIL) (-456 1051420 1051605 1051909 "GB" 1052527 NIL GB (NIL T T T T) -7 NIL NIL NIL) (-455 1040036 1042366 1044758 "GBINTERN" 1049111 NIL GBINTERN (NIL T T T T) -7 NIL NIL NIL) (-454 1037873 1038165 1038586 "GBF" 1039711 NIL GBF (NIL T T T T) -7 NIL NIL NIL) (-453 1036654 1036819 1037086 "GBEUCLID" 1037689 NIL GBEUCLID (NIL T T T T) -7 NIL NIL NIL) (-452 1036003 1036128 1036277 "GAUSSFAC" 1036525 T GAUSSFAC (NIL) -7 NIL NIL NIL) (-451 1034370 1034672 1034986 "GALUTIL" 1035722 NIL GALUTIL (NIL T) -7 NIL NIL NIL) (-450 1032678 1032952 1033276 "GALPOLYU" 1034097 NIL GALPOLYU (NIL T T) -7 NIL NIL NIL) (-449 1030043 1030333 1030740 "GALFACTU" 1032375 NIL GALFACTU (NIL T T T) -7 NIL NIL NIL) (-448 1021849 1023348 1024956 "GALFACT" 1028475 NIL GALFACT (NIL T) -7 NIL NIL NIL) (-447 1019237 1019895 1019923 "FVFUN" 1021079 T FVFUN (NIL) -9 NIL 1021799 NIL) (-446 1018503 1018685 1018713 "FVC" 1019004 T FVC (NIL) -9 NIL 1019187 NIL) (-445 1018146 1018328 1018396 "FUNDESC" 1018455 T FUNDESC (NIL) -8 NIL NIL NIL) (-444 1017761 1017943 1018024 "FUNCTION" 1018098 NIL FUNCTION (NIL NIL) -8 NIL NIL NIL) (-443 1015505 1016083 1016549 "FT" 1017315 T FT (NIL) -8 NIL NIL NIL) (-442 1014296 1014806 1015009 "FTEM" 1015322 T FTEM (NIL) -8 NIL NIL NIL) (-441 1012587 1012876 1013273 "FSUPFACT" 1013987 NIL FSUPFACT (NIL T T T) -7 NIL NIL NIL) (-440 1010984 1011273 1011605 "FST" 1012275 T FST (NIL) -8 NIL NIL NIL) (-439 1010183 1010289 1010477 "FSRED" 1010866 NIL FSRED (NIL T T) -7 NIL NIL NIL) (-438 1008882 1009138 1009485 "FSPRMELT" 1009898 NIL FSPRMELT (NIL T T) -7 NIL NIL NIL) (-437 1006188 1006626 1007112 "FSPECF" 1008445 NIL FSPECF (NIL T T) -7 NIL NIL NIL) (-436 987826 996157 996198 "FS" 1000082 NIL FS (NIL T) -9 NIL 1002371 NIL) (-435 976469 979462 983519 "FS-" 983819 NIL FS- (NIL T T) -8 NIL NIL NIL) (-434 975997 976051 976221 "FSINT" 976410 NIL FSINT (NIL T T) -7 NIL NIL NIL) (-433 974289 974990 975293 "FSERIES" 975776 NIL FSERIES (NIL T T) -8 NIL NIL NIL) (-432 973331 973447 973671 "FSCINT" 974169 NIL FSCINT (NIL T T) -7 NIL NIL NIL) (-431 969539 972275 972316 "FSAGG" 972686 NIL FSAGG (NIL T) -9 NIL 972945 NIL) (-430 967301 967902 968698 "FSAGG-" 968793 NIL FSAGG- (NIL T T) -8 NIL NIL NIL) (-429 966343 966486 966713 "FSAGG2" 967154 NIL FSAGG2 (NIL T T T T) -7 NIL NIL NIL) (-428 964025 964305 964852 "FS2UPS" 966061 NIL FS2UPS (NIL T T T T T NIL) -7 NIL NIL NIL) (-427 963659 963702 963831 "FS2" 963976 NIL FS2 (NIL T T T T) -7 NIL NIL NIL) (-426 962537 962708 963010 "FS2EXPXP" 963484 NIL FS2EXPXP (NIL T T NIL NIL) -7 NIL NIL NIL) (-425 961963 962078 962230 "FRUTIL" 962417 NIL FRUTIL (NIL T) -7 NIL NIL NIL) (-424 953376 957458 958816 "FR" 960637 NIL FR (NIL T) -8 NIL NIL NIL) (-423 948345 951019 951059 "FRNAALG" 952455 NIL FRNAALG (NIL T) -9 NIL 953062 NIL) (-422 944018 945094 946369 "FRNAALG-" 947119 NIL FRNAALG- (NIL T T) -8 NIL NIL NIL) (-421 943656 943699 943826 "FRNAAF2" 943969 NIL FRNAAF2 (NIL T T T T) -7 NIL NIL NIL) (-420 942031 942505 942801 "FRMOD" 943468 NIL FRMOD (NIL T T T T NIL) -8 NIL NIL NIL) (-419 939774 940406 940724 "FRIDEAL" 941822 NIL FRIDEAL (NIL T T T T) -8 NIL NIL NIL) (-418 938965 939052 939343 "FRIDEAL2" 939681 NIL FRIDEAL2 (NIL T T T T T T T T) -7 NIL NIL NIL) (-417 938098 938512 938553 "FRETRCT" 938558 NIL FRETRCT (NIL T) -9 NIL 938734 NIL) (-416 937210 937441 937792 "FRETRCT-" 937797 NIL FRETRCT- (NIL T T) -8 NIL NIL NIL) (-415 934298 935508 935567 "FRAMALG" 936449 NIL FRAMALG (NIL T T) -9 NIL 936741 NIL) (-414 932432 932887 933517 "FRAMALG-" 933740 NIL FRAMALG- (NIL T T T) -8 NIL NIL NIL) (-413 926351 931905 932182 "FRAC" 932187 NIL FRAC (NIL T) -8 NIL NIL NIL) (-412 925987 926044 926151 "FRAC2" 926288 NIL FRAC2 (NIL T T) -7 NIL NIL NIL) (-411 925623 925680 925787 "FR2" 925924 NIL FR2 (NIL T T) -7 NIL NIL NIL) (-410 920136 923029 923057 "FPS" 924176 T FPS (NIL) -9 NIL 924733 NIL) (-409 919585 919694 919858 "FPS-" 920004 NIL FPS- (NIL T) -8 NIL NIL NIL) (-408 916887 918556 918584 "FPC" 918809 T FPC (NIL) -9 NIL 918951 NIL) (-407 916680 916720 916817 "FPC-" 916822 NIL FPC- (NIL T) -8 NIL NIL NIL) (-406 915470 916168 916209 "FPATMAB" 916214 NIL FPATMAB (NIL T) -9 NIL 916366 NIL) (-405 913143 913646 914072 "FPARFRAC" 915107 NIL FPARFRAC (NIL T T) -8 NIL NIL NIL) (-404 908537 909035 909717 "FORTRAN" 912575 NIL FORTRAN (NIL NIL NIL NIL NIL) -8 NIL NIL NIL) (-403 906253 906753 907292 "FORT" 908018 T FORT (NIL) -7 NIL NIL NIL) (-402 903929 904491 904519 "FORTFN" 905579 T FORTFN (NIL) -9 NIL 906203 NIL) (-401 903693 903743 903771 "FORTCAT" 903830 T FORTCAT (NIL) -9 NIL 903892 NIL) (-400 901799 902309 902699 "FORMULA" 903323 T FORMULA (NIL) -8 NIL NIL NIL) (-399 901587 901617 901686 "FORMULA1" 901763 NIL FORMULA1 (NIL T) -7 NIL NIL NIL) (-398 901110 901162 901335 "FORDER" 901529 NIL FORDER (NIL T T T T) -7 NIL NIL NIL) (-397 900206 900370 900563 "FOP" 900937 T FOP (NIL) -7 NIL NIL NIL) (-396 898787 899486 899660 "FNLA" 900088 NIL FNLA (NIL NIL NIL T) -8 NIL NIL NIL) (-395 897516 897931 897959 "FNCAT" 898419 T FNCAT (NIL) -9 NIL 898679 NIL) (-394 897055 897475 897503 "FNAME" 897508 T FNAME (NIL) -8 NIL NIL NIL) (-393 895618 896581 896609 "FMTC" 896614 T FMTC (NIL) -9 NIL 896650 NIL) (-392 894364 895554 895600 "FMONOID" 895605 NIL FMONOID (NIL T) -8 NIL NIL NIL) (-391 891192 892360 892401 "FMONCAT" 893618 NIL FMONCAT (NIL T) -9 NIL 894223 NIL) (-390 890384 890934 891083 "FM" 891088 NIL FM (NIL T T) -8 NIL NIL NIL) (-389 887808 888454 888482 "FMFUN" 889626 T FMFUN (NIL) -9 NIL 890334 NIL) (-388 887077 887258 887286 "FMC" 887576 T FMC (NIL) -9 NIL 887758 NIL) (-387 884156 885016 885070 "FMCAT" 886265 NIL FMCAT (NIL T T) -9 NIL 886760 NIL) (-386 883022 883922 884022 "FM1" 884101 NIL FM1 (NIL T T) -8 NIL NIL NIL) (-385 880796 881212 881706 "FLOATRP" 882573 NIL FLOATRP (NIL T) -7 NIL NIL NIL) (-384 874374 878525 879146 "FLOAT" 880195 T FLOAT (NIL) -8 NIL NIL NIL) (-383 871812 872312 872890 "FLOATCP" 873841 NIL FLOATCP (NIL T) -7 NIL NIL NIL) (-382 870552 871390 871431 "FLINEXP" 871436 NIL FLINEXP (NIL T) -9 NIL 871529 NIL) (-381 869706 869941 870269 "FLINEXP-" 870274 NIL FLINEXP- (NIL T T) -8 NIL NIL NIL) (-380 868782 868926 869150 "FLASORT" 869558 NIL FLASORT (NIL T T) -7 NIL NIL NIL) (-379 865898 866766 866818 "FLALG" 868045 NIL FLALG (NIL T T) -9 NIL 868512 NIL) (-378 859634 863384 863425 "FLAGG" 864687 NIL FLAGG (NIL T) -9 NIL 865339 NIL) (-377 858360 858699 859189 "FLAGG-" 859194 NIL FLAGG- (NIL T T) -8 NIL NIL NIL) (-376 857402 857545 857772 "FLAGG2" 858213 NIL FLAGG2 (NIL T T T T) -7 NIL NIL NIL) (-375 854253 855261 855320 "FINRALG" 856448 NIL FINRALG (NIL T T) -9 NIL 856956 NIL) (-374 853413 853642 853981 "FINRALG-" 853986 NIL FINRALG- (NIL T T T) -8 NIL NIL NIL) (-373 852793 853032 853060 "FINITE" 853256 T FINITE (NIL) -9 NIL 853363 NIL) (-372 845150 847337 847377 "FINAALG" 851044 NIL FINAALG (NIL T) -9 NIL 852497 NIL) (-371 840482 841532 842676 "FINAALG-" 844055 NIL FINAALG- (NIL T T) -8 NIL NIL NIL) (-370 839850 840237 840340 "FILE" 840412 NIL FILE (NIL T) -8 NIL NIL NIL) (-369 838508 838846 838900 "FILECAT" 839584 NIL FILECAT (NIL T T) -9 NIL 839800 NIL) (-368 836224 837752 837780 "FIELD" 837820 T FIELD (NIL) -9 NIL 837900 NIL) (-367 834844 835229 835740 "FIELD-" 835745 NIL FIELD- (NIL T) -8 NIL NIL NIL) (-366 832694 833479 833826 "FGROUP" 834530 NIL FGROUP (NIL T) -8 NIL NIL NIL) (-365 831784 831948 832168 "FGLMICPK" 832526 NIL FGLMICPK (NIL T NIL) -7 NIL NIL NIL) (-364 827616 831709 831766 "FFX" 831771 NIL FFX (NIL T NIL) -8 NIL NIL NIL) (-363 827217 827278 827413 "FFSLPE" 827549 NIL FFSLPE (NIL T T T) -7 NIL NIL NIL) (-362 823207 823989 824785 "FFPOLY" 826453 NIL FFPOLY (NIL T) -7 NIL NIL NIL) (-361 822711 822747 822956 "FFPOLY2" 823165 NIL FFPOLY2 (NIL T T) -7 NIL NIL NIL) (-360 818557 822630 822693 "FFP" 822698 NIL FFP (NIL T NIL) -8 NIL NIL NIL) (-359 813955 818468 818532 "FF" 818537 NIL FF (NIL NIL NIL) -8 NIL NIL NIL) (-358 809081 813298 813488 "FFNBX" 813809 NIL FFNBX (NIL T NIL) -8 NIL NIL NIL) (-357 804009 808216 808474 "FFNBP" 808935 NIL FFNBP (NIL T NIL) -8 NIL NIL NIL) (-356 798642 803293 803504 "FFNB" 803842 NIL FFNB (NIL NIL NIL) -8 NIL NIL NIL) (-355 797474 797672 797987 "FFINTBAS" 798439 NIL FFINTBAS (NIL T T T) -7 NIL NIL NIL) (-354 793543 795763 795791 "FFIELDC" 796411 T FFIELDC (NIL) -9 NIL 796787 NIL) (-353 792205 792576 793073 "FFIELDC-" 793078 NIL FFIELDC- (NIL T) -8 NIL NIL NIL) (-352 791774 791820 791944 "FFHOM" 792147 NIL FFHOM (NIL T T T) -7 NIL NIL NIL) (-351 789469 789956 790473 "FFF" 791289 NIL FFF (NIL T) -7 NIL NIL NIL) (-350 785087 789211 789312 "FFCGX" 789412 NIL FFCGX (NIL T NIL) -8 NIL NIL NIL) (-349 780709 784819 784926 "FFCGP" 785030 NIL FFCGP (NIL T NIL) -8 NIL NIL NIL) (-348 775892 780436 780544 "FFCG" 780645 NIL FFCG (NIL NIL NIL) -8 NIL NIL NIL) (-347 757288 766369 766455 "FFCAT" 771620 NIL FFCAT (NIL T T T) -9 NIL 773071 NIL) (-346 752485 753533 754847 "FFCAT-" 756077 NIL FFCAT- (NIL T T T T) -8 NIL NIL NIL) (-345 751896 751939 752174 "FFCAT2" 752436 NIL FFCAT2 (NIL T T T T T T T T) -7 NIL NIL NIL) (-344 741219 744868 746088 "FEXPR" 750748 NIL FEXPR (NIL NIL NIL T) -8 NIL NIL NIL) (-343 740219 740654 740695 "FEVALAB" 740779 NIL FEVALAB (NIL T) -9 NIL 741040 NIL) (-342 739378 739588 739926 "FEVALAB-" 739931 NIL FEVALAB- (NIL T T) -8 NIL NIL NIL) (-341 737944 738761 738964 "FDIV" 739277 NIL FDIV (NIL T T T T) -8 NIL NIL NIL) (-340 734964 735705 735820 "FDIVCAT" 737388 NIL FDIVCAT (NIL T T T T) -9 NIL 737825 NIL) (-339 734726 734753 734923 "FDIVCAT-" 734928 NIL FDIVCAT- (NIL T T T T T) -8 NIL NIL NIL) (-338 733946 734033 734310 "FDIV2" 734633 NIL FDIV2 (NIL T T T T T T T T) -7 NIL NIL NIL) (-337 732920 733241 733443 "FCTRDATA" 733764 T FCTRDATA (NIL) -8 NIL NIL NIL) (-336 731606 731865 732154 "FCPAK1" 732651 T FCPAK1 (NIL) -7 NIL NIL NIL) (-335 730705 731106 731247 "FCOMP" 731497 NIL FCOMP (NIL T) -8 NIL NIL NIL) (-334 714410 717855 721393 "FC" 727187 T FC (NIL) -8 NIL NIL NIL) (-333 706773 710801 710841 "FAXF" 712643 NIL FAXF (NIL T) -9 NIL 713335 NIL) (-332 704050 704707 705532 "FAXF-" 705997 NIL FAXF- (NIL T T) -8 NIL NIL NIL) (-331 699102 703426 703602 "FARRAY" 703907 NIL FARRAY (NIL T) -8 NIL NIL NIL) (-330 693996 696063 696116 "FAMR" 697139 NIL FAMR (NIL T T) -9 NIL 697599 NIL) (-329 692886 693188 693623 "FAMR-" 693628 NIL FAMR- (NIL T T T) -8 NIL NIL NIL) (-328 692055 692808 692861 "FAMONOID" 692866 NIL FAMONOID (NIL T) -8 NIL NIL NIL) (-327 689841 690551 690604 "FAMONC" 691545 NIL FAMONC (NIL T T) -9 NIL 691931 NIL) (-326 688505 689595 689732 "FAGROUP" 689737 NIL FAGROUP (NIL T) -8 NIL NIL NIL) (-325 686300 686619 687022 "FACUTIL" 688186 NIL FACUTIL (NIL T T T T) -7 NIL NIL NIL) (-324 685399 685584 685806 "FACTFUNC" 686110 NIL FACTFUNC (NIL T) -7 NIL NIL NIL) (-323 677821 684702 684901 "EXPUPXS" 685255 NIL EXPUPXS (NIL T NIL NIL) -8 NIL NIL NIL) (-322 675304 675844 676430 "EXPRTUBE" 677255 T EXPRTUBE (NIL) -7 NIL NIL NIL) (-321 671575 672167 672897 "EXPRODE" 674643 NIL EXPRODE (NIL T T) -7 NIL NIL NIL) (-320 657060 670224 670653 "EXPR" 671179 NIL EXPR (NIL T) -8 NIL NIL NIL) (-319 651614 652201 653007 "EXPR2UPS" 656358 NIL EXPR2UPS (NIL T T) -7 NIL NIL NIL) (-318 651246 651303 651412 "EXPR2" 651551 NIL EXPR2 (NIL T T) -7 NIL NIL NIL) (-317 642634 650397 650688 "EXPEXPAN" 651082 NIL EXPEXPAN (NIL T T NIL NIL) -8 NIL NIL NIL) (-316 642434 642591 642620 "EXIT" 642625 T EXIT (NIL) -8 NIL NIL NIL) (-315 641914 642158 642249 "EXITAST" 642363 T EXITAST (NIL) -8 NIL NIL NIL) (-314 641541 641603 641716 "EVALCYC" 641846 NIL EVALCYC (NIL T) -7 NIL NIL NIL) (-313 641082 641200 641241 "EVALAB" 641411 NIL EVALAB (NIL T) -9 NIL 641515 NIL) (-312 640563 640685 640906 "EVALAB-" 640911 NIL EVALAB- (NIL T T) -8 NIL NIL NIL) (-311 637931 639233 639261 "EUCDOM" 639816 T EUCDOM (NIL) -9 NIL 640166 NIL) (-310 636336 636778 637368 "EUCDOM-" 637373 NIL EUCDOM- (NIL T) -8 NIL NIL NIL) (-309 623875 626634 629384 "ESTOOLS" 633606 T ESTOOLS (NIL) -7 NIL NIL NIL) (-308 623507 623564 623673 "ESTOOLS2" 623812 NIL ESTOOLS2 (NIL T T) -7 NIL NIL NIL) (-307 623258 623300 623380 "ESTOOLS1" 623459 NIL ESTOOLS1 (NIL T) -7 NIL NIL NIL) (-306 617295 618903 618931 "ES" 621699 T ES (NIL) -9 NIL 623109 NIL) (-305 612242 613529 615346 "ES-" 615510 NIL ES- (NIL T) -8 NIL NIL NIL) (-304 608616 609377 610157 "ESCONT" 611482 T ESCONT (NIL) -7 NIL NIL NIL) (-303 608361 608393 608475 "ESCONT1" 608578 NIL ESCONT1 (NIL NIL NIL) -7 NIL NIL NIL) (-302 608036 608086 608186 "ES2" 608305 NIL ES2 (NIL T T) -7 NIL NIL NIL) (-301 607666 607724 607833 "ES1" 607972 NIL ES1 (NIL T T) -7 NIL NIL NIL) (-300 606882 607011 607187 "ERROR" 607510 T ERROR (NIL) -7 NIL NIL NIL) (-299 600274 606741 606832 "EQTBL" 606837 NIL EQTBL (NIL T T) -8 NIL NIL NIL) (-298 592777 595588 597037 "EQ" 598858 NIL -2199 (NIL T) -8 NIL NIL NIL) (-297 592409 592466 592575 "EQ2" 592714 NIL EQ2 (NIL T T) -7 NIL NIL NIL) (-296 587700 588747 589840 "EP" 591348 NIL EP (NIL T) -7 NIL NIL NIL) (-295 586300 586591 586897 "ENV" 587414 T ENV (NIL) -8 NIL NIL NIL) (-294 585394 585948 585976 "ENTIRER" 585981 T ENTIRER (NIL) -9 NIL 586027 NIL) (-293 581861 583349 583719 "EMR" 585193 NIL EMR (NIL T T T NIL NIL NIL) -8 NIL NIL NIL) (-292 581005 581190 581244 "ELTAGG" 581624 NIL ELTAGG (NIL T T) -9 NIL 581835 NIL) (-291 580724 580786 580927 "ELTAGG-" 580932 NIL ELTAGG- (NIL T T T) -8 NIL NIL NIL) (-290 580513 580542 580596 "ELTAB" 580680 NIL ELTAB (NIL T T) -9 NIL NIL NIL) (-289 579639 579785 579984 "ELFUTS" 580364 NIL ELFUTS (NIL T T) -7 NIL NIL NIL) (-288 579381 579437 579465 "ELEMFUN" 579570 T ELEMFUN (NIL) -9 NIL NIL NIL) (-287 579251 579272 579340 "ELEMFUN-" 579345 NIL ELEMFUN- (NIL T) -8 NIL NIL NIL) (-286 574095 577351 577392 "ELAGG" 578332 NIL ELAGG (NIL T) -9 NIL 578795 NIL) (-285 572380 572814 573477 "ELAGG-" 573482 NIL ELAGG- (NIL T T) -8 NIL NIL NIL) (-284 571692 571829 571985 "ELABOR" 572244 T ELABOR (NIL) -8 NIL NIL NIL) (-283 570353 570632 570926 "ELABEXPR" 571418 T ELABEXPR (NIL) -8 NIL NIL NIL) (-282 563217 565020 565847 "EFUPXS" 569629 NIL EFUPXS (NIL T T T T) -8 NIL NIL NIL) (-281 556667 558468 559278 "EFULS" 562493 NIL EFULS (NIL T T T) -8 NIL NIL NIL) (-280 554152 554510 554982 "EFSTRUC" 556299 NIL EFSTRUC (NIL T T) -7 NIL NIL NIL) (-279 543943 545509 547057 "EF" 552667 NIL EF (NIL T T) -7 NIL NIL NIL) (-278 543017 543428 543577 "EAB" 543814 T EAB (NIL) -8 NIL NIL NIL) (-277 542199 542976 543004 "E04UCFA" 543009 T E04UCFA (NIL) -8 NIL NIL NIL) (-276 541381 542158 542186 "E04NAFA" 542191 T E04NAFA (NIL) -8 NIL NIL NIL) (-275 540563 541340 541368 "E04MBFA" 541373 T E04MBFA (NIL) -8 NIL NIL NIL) (-274 539745 540522 540550 "E04JAFA" 540555 T E04JAFA (NIL) -8 NIL NIL NIL) (-273 538929 539704 539732 "E04GCFA" 539737 T E04GCFA (NIL) -8 NIL NIL NIL) (-272 538113 538888 538916 "E04FDFA" 538921 T E04FDFA (NIL) -8 NIL NIL NIL) (-271 537295 538072 538100 "E04DGFA" 538105 T E04DGFA (NIL) -8 NIL NIL NIL) (-270 531468 532820 534184 "E04AGNT" 535951 T E04AGNT (NIL) -7 NIL NIL NIL) (-269 530148 530654 530694 "DVARCAT" 531169 NIL DVARCAT (NIL T) -9 NIL 531368 NIL) (-268 529352 529564 529878 "DVARCAT-" 529883 NIL DVARCAT- (NIL T T) -8 NIL NIL NIL) (-267 522489 529151 529280 "DSMP" 529285 NIL DSMP (NIL T T T) -8 NIL NIL NIL) (-266 517270 518434 519502 "DROPT" 521441 T DROPT (NIL) -8 NIL NIL NIL) (-265 516935 516994 517092 "DROPT1" 517205 NIL DROPT1 (NIL T) -7 NIL NIL NIL) (-264 512050 513176 514313 "DROPT0" 515818 T DROPT0 (NIL) -7 NIL NIL NIL) (-263 510395 510720 511106 "DRAWPT" 511684 T DRAWPT (NIL) -7 NIL NIL NIL) (-262 504982 505905 506984 "DRAW" 509369 NIL DRAW (NIL T) -7 NIL NIL NIL) (-261 504615 504668 504786 "DRAWHACK" 504923 NIL DRAWHACK (NIL T) -7 NIL NIL NIL) (-260 503346 503615 503906 "DRAWCX" 504344 T DRAWCX (NIL) -7 NIL NIL NIL) (-259 502861 502930 503081 "DRAWCURV" 503272 NIL DRAWCURV (NIL T T) -7 NIL NIL NIL) (-258 493329 495291 497406 "DRAWCFUN" 500766 T DRAWCFUN (NIL) -7 NIL NIL NIL) (-257 490093 492022 492063 "DQAGG" 492692 NIL DQAGG (NIL T) -9 NIL 492966 NIL) (-256 478217 484686 484769 "DPOLCAT" 486621 NIL DPOLCAT (NIL T T T T) -9 NIL 487166 NIL) (-255 473054 474402 476360 "DPOLCAT-" 476365 NIL DPOLCAT- (NIL T T T T T) -8 NIL NIL NIL) (-254 466176 472915 473013 "DPMO" 473018 NIL DPMO (NIL NIL T T) -8 NIL NIL NIL) (-253 459201 465956 466123 "DPMM" 466128 NIL DPMM (NIL NIL T T T) -8 NIL NIL NIL) (-252 458679 458893 458991 "DOMTMPLT" 459123 T DOMTMPLT (NIL) -8 NIL NIL NIL) (-251 458112 458481 458561 "DOMCTOR" 458619 T DOMCTOR (NIL) -8 NIL NIL NIL) (-250 457324 457592 457743 "DOMAIN" 457981 T DOMAIN (NIL) -8 NIL NIL NIL) (-249 451312 456959 457111 "DMP" 457225 NIL DMP (NIL NIL T) -8 NIL NIL NIL) (-248 450912 450968 451112 "DLP" 451250 NIL DLP (NIL T) -7 NIL NIL NIL) (-247 444734 450239 450429 "DLIST" 450754 NIL DLIST (NIL T) -8 NIL NIL NIL) (-246 441531 443587 443628 "DLAGG" 444178 NIL DLAGG (NIL T) -9 NIL 444408 NIL) (-245 440207 440871 440899 "DIVRING" 440991 T DIVRING (NIL) -9 NIL 441074 NIL) (-244 439444 439634 439934 "DIVRING-" 439939 NIL DIVRING- (NIL T) -8 NIL NIL NIL) (-243 437546 437903 438309 "DISPLAY" 439058 T DISPLAY (NIL) -7 NIL NIL NIL) (-242 431434 437460 437523 "DIRPROD" 437528 NIL DIRPROD (NIL NIL T) -8 NIL NIL NIL) (-241 430282 430485 430750 "DIRPROD2" 431227 NIL DIRPROD2 (NIL NIL T T) -7 NIL NIL NIL) (-240 419057 425063 425116 "DIRPCAT" 425526 NIL DIRPCAT (NIL NIL T) -9 NIL 426366 NIL) (-239 416383 417025 417906 "DIRPCAT-" 418243 NIL DIRPCAT- (NIL T NIL T) -8 NIL NIL NIL) (-238 415670 415830 416016 "DIOSP" 416217 T DIOSP (NIL) -7 NIL NIL NIL) (-237 412325 414582 414623 "DIOPS" 415057 NIL DIOPS (NIL T) -9 NIL 415286 NIL) (-236 411874 411988 412179 "DIOPS-" 412184 NIL DIOPS- (NIL T T) -8 NIL NIL NIL) (-235 410697 411325 411353 "DIFRING" 411540 T DIFRING (NIL) -9 NIL 411650 NIL) (-234 410343 410420 410572 "DIFRING-" 410577 NIL DIFRING- (NIL T) -8 NIL NIL NIL) (-233 408079 409351 409392 "DIFEXT" 409755 NIL DIFEXT (NIL T) -9 NIL 410049 NIL) (-232 406364 406792 407458 "DIFEXT-" 407463 NIL DIFEXT- (NIL T T) -8 NIL NIL NIL) (-231 403639 405896 405937 "DIAGG" 405942 NIL DIAGG (NIL T) -9 NIL 405962 NIL) (-230 403023 403180 403432 "DIAGG-" 403437 NIL DIAGG- (NIL T T) -8 NIL NIL NIL) (-229 398440 401982 402259 "DHMATRIX" 402792 NIL DHMATRIX (NIL T) -8 NIL NIL NIL) (-228 394052 394961 395971 "DFSFUN" 397450 T DFSFUN (NIL) -7 NIL NIL NIL) (-227 389131 392983 393295 "DFLOAT" 393760 T DFLOAT (NIL) -8 NIL NIL NIL) (-226 387394 387675 388064 "DFINTTLS" 388839 NIL DFINTTLS (NIL T T) -7 NIL NIL NIL) (-225 384423 385415 385815 "DERHAM" 387060 NIL DERHAM (NIL T NIL) -8 NIL NIL NIL) (-224 382224 384198 384287 "DEQUEUE" 384367 NIL DEQUEUE (NIL T) -8 NIL NIL NIL) (-223 381478 381611 381794 "DEGRED" 382086 NIL DEGRED (NIL T T) -7 NIL NIL NIL) (-222 377908 378653 379499 "DEFINTRF" 380706 NIL DEFINTRF (NIL T) -7 NIL NIL NIL) (-221 375463 375932 376524 "DEFINTEF" 377427 NIL DEFINTEF (NIL T T) -7 NIL NIL NIL) (-220 374813 375083 375198 "DEFAST" 375368 T DEFAST (NIL) -8 NIL NIL NIL) (-219 368815 374406 374556 "DECIMAL" 374683 T DECIMAL (NIL) -8 NIL NIL NIL) (-218 366327 366785 367291 "DDFACT" 368359 NIL DDFACT (NIL T T) -7 NIL NIL NIL) (-217 365923 365966 366117 "DBLRESP" 366278 NIL DBLRESP (NIL T T T T) -7 NIL NIL NIL) (-216 363795 364156 364516 "DBASE" 365690 NIL DBASE (NIL T) -8 NIL NIL NIL) (-215 363037 363275 363421 "DATAARY" 363694 NIL DATAARY (NIL NIL T) -8 NIL NIL NIL) (-214 362143 362996 363024 "D03FAFA" 363029 T D03FAFA (NIL) -8 NIL NIL NIL) (-213 361250 362102 362130 "D03EEFA" 362135 T D03EEFA (NIL) -8 NIL NIL NIL) (-212 359200 359666 360155 "D03AGNT" 360781 T D03AGNT (NIL) -7 NIL NIL NIL) (-211 358489 359159 359187 "D02EJFA" 359192 T D02EJFA (NIL) -8 NIL NIL NIL) (-210 357778 358448 358476 "D02CJFA" 358481 T D02CJFA (NIL) -8 NIL NIL NIL) (-209 357067 357737 357765 "D02BHFA" 357770 T D02BHFA (NIL) -8 NIL NIL NIL) (-208 356356 357026 357054 "D02BBFA" 357059 T D02BBFA (NIL) -8 NIL NIL NIL) (-207 349553 351142 352748 "D02AGNT" 354770 T D02AGNT (NIL) -7 NIL NIL NIL) (-206 347321 347844 348390 "D01WGTS" 349027 T D01WGTS (NIL) -7 NIL NIL NIL) (-205 346388 347280 347308 "D01TRNS" 347313 T D01TRNS (NIL) -8 NIL NIL NIL) (-204 345456 346347 346375 "D01GBFA" 346380 T D01GBFA (NIL) -8 NIL NIL NIL) (-203 344524 345415 345443 "D01FCFA" 345448 T D01FCFA (NIL) -8 NIL NIL NIL) (-202 343592 344483 344511 "D01ASFA" 344516 T D01ASFA (NIL) -8 NIL NIL NIL) (-201 342660 343551 343579 "D01AQFA" 343584 T D01AQFA (NIL) -8 NIL NIL NIL) (-200 341728 342619 342647 "D01APFA" 342652 T D01APFA (NIL) -8 NIL NIL NIL) (-199 340796 341687 341715 "D01ANFA" 341720 T D01ANFA (NIL) -8 NIL NIL NIL) (-198 339864 340755 340783 "D01AMFA" 340788 T D01AMFA (NIL) -8 NIL NIL NIL) (-197 338932 339823 339851 "D01ALFA" 339856 T D01ALFA (NIL) -8 NIL NIL NIL) (-196 338000 338891 338919 "D01AKFA" 338924 T D01AKFA (NIL) -8 NIL NIL NIL) (-195 337068 337959 337987 "D01AJFA" 337992 T D01AJFA (NIL) -8 NIL NIL NIL) (-194 330363 331916 333477 "D01AGNT" 335527 T D01AGNT (NIL) -7 NIL NIL NIL) (-193 329700 329828 329980 "CYCLOTOM" 330231 T CYCLOTOM (NIL) -7 NIL NIL NIL) (-192 326434 327148 327875 "CYCLES" 328993 T CYCLES (NIL) -7 NIL NIL NIL) (-191 325746 325880 326051 "CVMP" 326295 NIL CVMP (NIL T) -7 NIL NIL NIL) (-190 323587 323845 324214 "CTRIGMNP" 325474 NIL CTRIGMNP (NIL T T) -7 NIL NIL NIL) (-189 323023 323381 323454 "CTOR" 323534 T CTOR (NIL) -8 NIL NIL NIL) (-188 322532 322754 322855 "CTORKIND" 322942 T CTORKIND (NIL) -8 NIL NIL NIL) (-187 321823 322139 322167 "CTORCAT" 322349 T CTORCAT (NIL) -9 NIL 322462 NIL) (-186 321421 321532 321691 "CTORCAT-" 321696 NIL CTORCAT- (NIL T) -8 NIL NIL NIL) (-185 320883 321095 321203 "CTORCALL" 321345 NIL CTORCALL (NIL T) -8 NIL NIL NIL) (-184 320257 320356 320509 "CSTTOOLS" 320780 NIL CSTTOOLS (NIL T T) -7 NIL NIL NIL) (-183 316056 316713 317471 "CRFP" 319569 NIL CRFP (NIL T T) -7 NIL NIL NIL) (-182 315531 315777 315869 "CRCEAST" 315984 T CRCEAST (NIL) -8 NIL NIL NIL) (-181 314578 314763 314991 "CRAPACK" 315335 NIL CRAPACK (NIL T) -7 NIL NIL NIL) (-180 313962 314063 314267 "CPMATCH" 314454 NIL CPMATCH (NIL T T T) -7 NIL NIL NIL) (-179 313687 313715 313821 "CPIMA" 313928 NIL CPIMA (NIL T T T) -7 NIL NIL NIL) (-178 310035 310707 311426 "COORDSYS" 313022 NIL COORDSYS (NIL T) -7 NIL NIL NIL) (-177 309447 309568 309710 "CONTOUR" 309913 T CONTOUR (NIL) -8 NIL NIL NIL) (-176 305338 307450 307942 "CONTFRAC" 308987 NIL CONTFRAC (NIL T) -8 NIL NIL NIL) (-175 305218 305239 305267 "CONDUIT" 305304 T CONDUIT (NIL) -9 NIL NIL NIL) (-174 304306 304860 304888 "COMRING" 304893 T COMRING (NIL) -9 NIL 304945 NIL) (-173 303360 303664 303848 "COMPPROP" 304142 T COMPPROP (NIL) -8 NIL NIL NIL) (-172 303021 303056 303184 "COMPLPAT" 303319 NIL COMPLPAT (NIL T T T) -7 NIL NIL NIL) (-171 293312 302830 302939 "COMPLEX" 302944 NIL COMPLEX (NIL T) -8 NIL NIL NIL) (-170 292948 293005 293112 "COMPLEX2" 293249 NIL COMPLEX2 (NIL T T) -7 NIL NIL NIL) (-169 292287 292408 292568 "COMPILER" 292808 T COMPILER (NIL) -8 NIL NIL NIL) (-168 292005 292040 292138 "COMPFACT" 292246 NIL COMPFACT (NIL T T) -7 NIL NIL NIL) (-167 276085 286079 286119 "COMPCAT" 287123 NIL COMPCAT (NIL T) -9 NIL 288471 NIL) (-166 265597 268524 272151 "COMPCAT-" 272507 NIL COMPCAT- (NIL T T) -8 NIL NIL NIL) (-165 265326 265354 265457 "COMMUPC" 265563 NIL COMMUPC (NIL T T T) -7 NIL NIL NIL) (-164 265120 265154 265213 "COMMONOP" 265287 T COMMONOP (NIL) -7 NIL NIL NIL) (-163 264676 264871 264958 "COMM" 265053 T COMM (NIL) -8 NIL NIL NIL) (-162 264252 264480 264555 "COMMAAST" 264621 T COMMAAST (NIL) -8 NIL NIL NIL) (-161 263501 263695 263723 "COMBOPC" 264061 T COMBOPC (NIL) -9 NIL 264236 NIL) (-160 262397 262607 262849 "COMBINAT" 263291 NIL COMBINAT (NIL T) -7 NIL NIL NIL) (-159 258854 259428 260055 "COMBF" 261819 NIL COMBF (NIL T T) -7 NIL NIL NIL) (-158 257612 257970 258205 "COLOR" 258639 T COLOR (NIL) -8 NIL NIL NIL) (-157 257088 257333 257425 "COLONAST" 257540 T COLONAST (NIL) -8 NIL NIL NIL) (-156 256728 256775 256900 "CMPLXRT" 257035 NIL CMPLXRT (NIL T T) -7 NIL NIL NIL) (-155 256176 256428 256527 "CLLCTAST" 256649 T CLLCTAST (NIL) -8 NIL NIL NIL) (-154 251678 252706 253786 "CLIP" 255116 T CLIP (NIL) -7 NIL NIL NIL) (-153 250019 250779 251019 "CLIF" 251505 NIL CLIF (NIL NIL T NIL) -8 NIL NIL NIL) (-152 246194 248165 248206 "CLAGG" 249135 NIL CLAGG (NIL T) -9 NIL 249671 NIL) (-151 244616 245073 245656 "CLAGG-" 245661 NIL CLAGG- (NIL T T) -8 NIL NIL NIL) (-150 244160 244245 244385 "CINTSLPE" 244525 NIL CINTSLPE (NIL T T) -7 NIL NIL NIL) (-149 241661 242132 242680 "CHVAR" 243688 NIL CHVAR (NIL T T T) -7 NIL NIL NIL) (-148 240835 241389 241417 "CHARZ" 241422 T CHARZ (NIL) -9 NIL 241437 NIL) (-147 240589 240629 240707 "CHARPOL" 240789 NIL CHARPOL (NIL T) -7 NIL NIL NIL) (-146 239647 240234 240262 "CHARNZ" 240309 T CHARNZ (NIL) -9 NIL 240365 NIL) (-145 237553 238301 238654 "CHAR" 239314 T CHAR (NIL) -8 NIL NIL NIL) (-144 237279 237340 237368 "CFCAT" 237479 T CFCAT (NIL) -9 NIL NIL NIL) (-143 236520 236631 236814 "CDEN" 237163 NIL CDEN (NIL T T T) -7 NIL NIL NIL) (-142 232485 235673 235953 "CCLASS" 236260 T CCLASS (NIL) -8 NIL NIL NIL) (-141 231736 231893 232070 "CATEGORY" 232328 T -10 (NIL) -8 NIL NIL NIL) (-140 231309 231655 231703 "CATCTOR" 231708 T CATCTOR (NIL) -8 NIL NIL NIL) (-139 230760 231012 231110 "CATAST" 231231 T CATAST (NIL) -8 NIL NIL NIL) (-138 230236 230481 230573 "CASEAST" 230688 T CASEAST (NIL) -8 NIL NIL NIL) (-137 225246 226265 227018 "CARTEN" 229539 NIL CARTEN (NIL NIL NIL T) -8 NIL NIL NIL) (-136 224354 224502 224723 "CARTEN2" 225093 NIL CARTEN2 (NIL NIL NIL T T) -7 NIL NIL NIL) (-135 222670 223504 223761 "CARD" 224117 T CARD (NIL) -8 NIL NIL NIL) (-134 222246 222474 222549 "CAPSLAST" 222615 T CAPSLAST (NIL) -8 NIL NIL NIL) (-133 221750 221958 221986 "CACHSET" 222118 T CACHSET (NIL) -9 NIL 222196 NIL) (-132 221220 221542 221570 "CABMON" 221620 T CABMON (NIL) -9 NIL 221676 NIL) (-131 220693 220924 221034 "BYTEORD" 221130 T BYTEORD (NIL) -8 NIL NIL NIL) (-130 219675 220227 220369 "BYTE" 220532 T BYTE (NIL) -8 NIL NIL 220654) (-129 215025 219180 219352 "BYTEBUF" 219523 T BYTEBUF (NIL) -8 NIL NIL NIL) (-128 212534 214717 214824 "BTREE" 214951 NIL BTREE (NIL T) -8 NIL NIL NIL) (-127 209983 212182 212304 "BTOURN" 212444 NIL BTOURN (NIL T) -8 NIL NIL NIL) (-126 207353 209453 209494 "BTCAT" 209562 NIL BTCAT (NIL T) -9 NIL 209639 NIL) (-125 207020 207100 207249 "BTCAT-" 207254 NIL BTCAT- (NIL T T) -8 NIL NIL NIL) (-124 202430 206309 206337 "BTAGG" 206451 T BTAGG (NIL) -9 NIL 206561 NIL) (-123 201920 202045 202251 "BTAGG-" 202256 NIL BTAGG- (NIL T) -8 NIL NIL NIL) (-122 198915 201198 201413 "BSTREE" 201737 NIL BSTREE (NIL T) -8 NIL NIL NIL) (-121 198053 198179 198363 "BRILL" 198771 NIL BRILL (NIL T) -7 NIL NIL NIL) (-120 194705 196779 196820 "BRAGG" 197469 NIL BRAGG (NIL T) -9 NIL 197727 NIL) (-119 193234 193640 194195 "BRAGG-" 194200 NIL BRAGG- (NIL T T) -8 NIL NIL NIL) (-118 186461 192578 192763 "BPADICRT" 193081 NIL BPADICRT (NIL NIL) -8 NIL NIL NIL) (-117 184776 186398 186443 "BPADIC" 186448 NIL BPADIC (NIL NIL) -8 NIL NIL NIL) (-116 184474 184504 184618 "BOUNDZRO" 184740 NIL BOUNDZRO (NIL T T) -7 NIL NIL NIL) (-115 179702 180900 181812 "BOP" 183582 T BOP (NIL) -8 NIL NIL NIL) (-114 177483 177887 178362 "BOP1" 179260 NIL BOP1 (NIL T) -7 NIL NIL NIL) (-113 177184 177245 177273 "BOOLE" 177384 T BOOLE (NIL) -9 NIL 177466 NIL) (-112 176009 176758 176907 "BOOLEAN" 177055 T BOOLEAN (NIL) -8 NIL NIL NIL) (-111 175288 175692 175746 "BMODULE" 175751 NIL BMODULE (NIL T T) -9 NIL 175816 NIL) (-110 171089 175086 175159 "BITS" 175235 T BITS (NIL) -8 NIL NIL NIL) (-109 170510 170629 170769 "BINDING" 170969 T BINDING (NIL) -8 NIL NIL NIL) (-108 164515 170105 170254 "BINARY" 170381 T BINARY (NIL) -8 NIL NIL NIL) (-107 162295 163770 163811 "BGAGG" 164071 NIL BGAGG (NIL T) -9 NIL 164208 NIL) (-106 162126 162158 162249 "BGAGG-" 162254 NIL BGAGG- (NIL T T) -8 NIL NIL NIL) (-105 161197 161510 161715 "BFUNCT" 161941 T BFUNCT (NIL) -8 NIL NIL NIL) (-104 159887 160065 160353 "BEZOUT" 161021 NIL BEZOUT (NIL T T T T T) -7 NIL NIL NIL) (-103 156356 158739 159069 "BBTREE" 159590 NIL BBTREE (NIL T) -8 NIL NIL NIL) (-102 156090 156143 156171 "BASTYPE" 156290 T BASTYPE (NIL) -9 NIL NIL NIL) (-101 155942 155971 156044 "BASTYPE-" 156049 NIL BASTYPE- (NIL T) -8 NIL NIL NIL) (-100 155376 155452 155604 "BALFACT" 155853 NIL BALFACT (NIL T T) -7 NIL NIL NIL) (-99 154232 154791 154977 "AUTOMOR" 155221 NIL AUTOMOR (NIL T) -8 NIL NIL NIL) (-98 153958 153963 153989 "ATTREG" 153994 T ATTREG (NIL) -9 NIL NIL NIL) (-97 152210 152655 153007 "ATTRBUT" 153624 T ATTRBUT (NIL) -8 NIL NIL NIL) (-96 151818 152038 152104 "ATTRAST" 152162 T ATTRAST (NIL) -8 NIL NIL NIL) (-95 151354 151467 151493 "ATRIG" 151694 T ATRIG (NIL) -9 NIL NIL NIL) (-94 151163 151204 151291 "ATRIG-" 151296 NIL ATRIG- (NIL T) -8 NIL NIL NIL) (-93 150808 150994 151020 "ASTCAT" 151025 T ASTCAT (NIL) -9 NIL 151055 NIL) (-92 150535 150594 150713 "ASTCAT-" 150718 NIL ASTCAT- (NIL T) -8 NIL NIL NIL) (-91 148684 150311 150399 "ASTACK" 150478 NIL ASTACK (NIL T) -8 NIL NIL NIL) (-90 147189 147486 147851 "ASSOCEQ" 148366 NIL ASSOCEQ (NIL T T) -7 NIL NIL NIL) (-89 146221 146848 146972 "ASP9" 147096 NIL ASP9 (NIL NIL) -8 NIL NIL NIL) (-88 145984 146169 146208 "ASP8" 146213 NIL ASP8 (NIL NIL) -8 NIL NIL NIL) (-87 144852 145589 145731 "ASP80" 145873 NIL ASP80 (NIL NIL) -8 NIL NIL NIL) (-86 143750 144487 144619 "ASP7" 144751 NIL ASP7 (NIL NIL) -8 NIL NIL NIL) (-85 142704 143427 143545 "ASP78" 143663 NIL ASP78 (NIL NIL) -8 NIL NIL NIL) (-84 141673 142384 142501 "ASP77" 142618 NIL ASP77 (NIL NIL) -8 NIL NIL NIL) (-83 140585 141311 141442 "ASP74" 141573 NIL ASP74 (NIL NIL) -8 NIL NIL NIL) (-82 139485 140220 140352 "ASP73" 140484 NIL ASP73 (NIL NIL) -8 NIL NIL NIL) (-81 138589 139311 139411 "ASP6" 139416 NIL ASP6 (NIL NIL) -8 NIL NIL NIL) (-80 137536 138266 138384 "ASP55" 138502 NIL ASP55 (NIL NIL) -8 NIL NIL NIL) (-79 136485 137210 137329 "ASP50" 137448 NIL ASP50 (NIL NIL) -8 NIL NIL NIL) (-78 135573 136186 136296 "ASP4" 136406 NIL ASP4 (NIL NIL) -8 NIL NIL NIL) (-77 134661 135274 135384 "ASP49" 135494 NIL ASP49 (NIL NIL) -8 NIL NIL NIL) (-76 133445 134200 134368 "ASP42" 134550 NIL ASP42 (NIL NIL NIL NIL) -8 NIL NIL NIL) (-75 132222 132978 133148 "ASP41" 133332 NIL ASP41 (NIL NIL NIL NIL) -8 NIL NIL NIL) (-74 131172 131899 132017 "ASP35" 132135 NIL ASP35 (NIL NIL) -8 NIL NIL NIL) (-73 130937 131120 131159 "ASP34" 131164 NIL ASP34 (NIL NIL) -8 NIL NIL NIL) (-72 130674 130741 130817 "ASP33" 130892 NIL ASP33 (NIL NIL) -8 NIL NIL NIL) (-71 129568 130309 130441 "ASP31" 130573 NIL ASP31 (NIL NIL) -8 NIL NIL NIL) (-70 129333 129516 129555 "ASP30" 129560 NIL ASP30 (NIL NIL) -8 NIL NIL NIL) (-69 129068 129137 129213 "ASP29" 129288 NIL ASP29 (NIL NIL) -8 NIL NIL NIL) (-68 128833 129016 129055 "ASP28" 129060 NIL ASP28 (NIL NIL) -8 NIL NIL NIL) (-67 128598 128781 128820 "ASP27" 128825 NIL ASP27 (NIL NIL) -8 NIL NIL NIL) (-66 127682 128296 128407 "ASP24" 128518 NIL ASP24 (NIL NIL) -8 NIL NIL NIL) (-65 126759 127484 127596 "ASP20" 127601 NIL ASP20 (NIL NIL) -8 NIL NIL NIL) (-64 125847 126460 126570 "ASP1" 126680 NIL ASP1 (NIL NIL) -8 NIL NIL NIL) (-63 124790 125521 125640 "ASP19" 125759 NIL ASP19 (NIL NIL) -8 NIL NIL NIL) (-62 124527 124594 124670 "ASP12" 124745 NIL ASP12 (NIL NIL) -8 NIL NIL NIL) (-61 123379 124126 124270 "ASP10" 124414 NIL ASP10 (NIL NIL) -8 NIL NIL NIL) (-60 121230 123223 123314 "ARRAY2" 123319 NIL ARRAY2 (NIL T) -8 NIL NIL NIL) (-59 116995 120878 120992 "ARRAY1" 121147 NIL ARRAY1 (NIL T) -8 NIL NIL NIL) (-58 116027 116200 116421 "ARRAY12" 116818 NIL ARRAY12 (NIL T T) -7 NIL NIL NIL) (-57 110339 112257 112332 "ARR2CAT" 114962 NIL ARR2CAT (NIL T T T) -9 NIL 115720 NIL) (-56 107773 108517 109471 "ARR2CAT-" 109476 NIL ARR2CAT- (NIL T T T T) -8 NIL NIL NIL) (-55 107090 107400 107525 "ARITY" 107666 T ARITY (NIL) -8 NIL NIL NIL) (-54 105866 106018 106317 "APPRULE" 106926 NIL APPRULE (NIL T T T) -7 NIL NIL NIL) (-53 105517 105565 105684 "APPLYORE" 105812 NIL APPLYORE (NIL T T T) -7 NIL NIL NIL) (-52 104871 105110 105230 "ANY" 105415 T ANY (NIL) -8 NIL NIL NIL) (-51 104149 104272 104429 "ANY1" 104745 NIL ANY1 (NIL T) -7 NIL NIL NIL) (-50 101679 102586 102913 "ANTISYM" 103873 NIL ANTISYM (NIL T NIL) -8 NIL NIL NIL) (-49 101171 101386 101482 "ANON" 101601 T ANON (NIL) -8 NIL NIL NIL) (-48 95420 99710 100164 "AN" 100735 T AN (NIL) -8 NIL NIL NIL) (-47 91318 92706 92757 "AMR" 93505 NIL AMR (NIL T T) -9 NIL 94105 NIL) (-46 90430 90651 91014 "AMR-" 91019 NIL AMR- (NIL T T T) -8 NIL NIL NIL) (-45 74869 90347 90408 "ALIST" 90413 NIL ALIST (NIL T T) -8 NIL NIL NIL) (-44 71674 74463 74632 "ALGSC" 74787 NIL ALGSC (NIL T NIL NIL NIL) -8 NIL NIL NIL) (-43 68230 68784 69391 "ALGPKG" 71114 NIL ALGPKG (NIL T T) -7 NIL NIL NIL) (-42 67507 67608 67792 "ALGMFACT" 68116 NIL ALGMFACT (NIL T T T) -7 NIL NIL NIL) (-41 63542 64121 64715 "ALGMANIP" 67091 NIL ALGMANIP (NIL T T) -7 NIL NIL NIL) (-40 54912 63168 63318 "ALGFF" 63475 NIL ALGFF (NIL T T T NIL) -8 NIL NIL NIL) (-39 54108 54239 54418 "ALGFACT" 54770 NIL ALGFACT (NIL T) -7 NIL NIL NIL) (-38 53049 53649 53687 "ALGEBRA" 53692 NIL ALGEBRA (NIL T) -9 NIL 53733 NIL) (-37 52767 52826 52958 "ALGEBRA-" 52963 NIL ALGEBRA- (NIL T T) -8 NIL NIL NIL) (-36 34860 50769 50821 "ALAGG" 50957 NIL ALAGG (NIL T T) -9 NIL 51118 NIL) (-35 34396 34509 34535 "AHYP" 34736 T AHYP (NIL) -9 NIL NIL NIL) (-34 33327 33575 33601 "AGG" 34100 T AGG (NIL) -9 NIL 34379 NIL) (-33 32761 32923 33137 "AGG-" 33142 NIL AGG- (NIL T) -8 NIL NIL NIL) (-32 30567 30990 31395 "AF" 32403 NIL AF (NIL T T) -7 NIL NIL NIL) (-31 30047 30292 30382 "ADDAST" 30495 T ADDAST (NIL) -8 NIL NIL NIL) (-30 29315 29574 29730 "ACPLOT" 29909 T ACPLOT (NIL) -8 NIL NIL NIL) (-29 18638 26442 26480 "ACFS" 27087 NIL ACFS (NIL T) -9 NIL 27326 NIL) (-28 16665 17155 17917 "ACFS-" 17922 NIL ACFS- (NIL T T) -8 NIL NIL NIL) (-27 12783 14712 14738 "ACF" 15617 T ACF (NIL) -9 NIL 16030 NIL) (-26 11487 11821 12314 "ACF-" 12319 NIL ACF- (NIL T) -8 NIL NIL NIL) (-25 11059 11254 11280 "ABELSG" 11372 T ABELSG (NIL) -9 NIL 11437 NIL) (-24 10926 10951 11017 "ABELSG-" 11022 NIL ABELSG- (NIL T) -8 NIL NIL NIL) (-23 10269 10556 10582 "ABELMON" 10752 T ABELMON (NIL) -9 NIL 10864 NIL) (-22 9933 10017 10155 "ABELMON-" 10160 NIL ABELMON- (NIL T) -8 NIL NIL NIL) (-21 9281 9653 9679 "ABELGRP" 9751 T ABELGRP (NIL) -9 NIL 9826 NIL) (-20 8744 8873 9089 "ABELGRP-" 9094 NIL ABELGRP- (NIL T) -8 NIL NIL NIL) (-19 4333 8083 8122 "A1AGG" 8127 NIL A1AGG (NIL T) -9 NIL 8167 NIL) (-18 30 1251 2813 "A1AGG-" 2818 NIL A1AGG- (NIL T T) -8 NIL NIL NIL))
\ No newline at end of file diff --git a/src/share/algebra/operation.daase b/src/share/algebra/operation.daase index 7923c5c4..3ef76f94 100644 --- a/src/share/algebra/operation.daase +++ b/src/share/algebra/operation.daase @@ -1,66 +1,90 @@ -(733547 . 3480583734) -(((*1 *2 *1) - (-12 (-4 *1 (-378 *3)) (-4 *3 (-1227)) (-4 *3 (-856)) (-5 *2 (-112)))) - ((*1 *2 *3 *1) - (-12 (-5 *3 (-1 (-112) *4 *4)) (-4 *1 (-378 *4)) (-4 *4 (-1227)) - (-5 *2 (-112))))) -(((*1 *1 *1) (-12 (-4 *1 (-436 *2)) (-4 *2 (-1109)) (-4 *2 (-562)))) - ((*1 *1 *1) (-12 (-4 *1 (-1001 *2)) (-4 *2 (-562))))) -(((*1 *1 *1 *2) - (-12 (-5 *2 (-650 (-52))) (-5 *1 (-899 *3)) (-4 *3 (-1109))))) -(((*1 *2 *2) - (-12 (-4 *3 (-1058)) (-5 *1 (-718 *3 *2)) (-4 *2 (-1253 *3))))) +(733547 . 3480761526) +(((*1 *2 *1) (-12 (-5 *2 (-650 (-1168))) (-5 *1 (-400)))) + ((*1 *2 *1) (-12 (-5 *2 (-650 (-1168))) (-5 *1 (-1207))))) +(((*1 *1 *1 *2) (-12 (-4 *1 (-1021)) (-5 *2 (-868))))) +(((*1 *2 *3 *3) + (-12 (-5 *3 (-2 (|:| |val| (-650 *7)) (|:| -3684 *8))) + (-4 *7 (-1074 *4 *5 *6)) (-4 *8 (-1080 *4 *5 *6 *7)) (-4 *4 (-458)) + (-4 *5 (-799)) (-4 *6 (-856)) (-5 *2 (-112)) + (-5 *1 (-997 *4 *5 *6 *7 *8)))) + ((*1 *2 *3 *3) + (-12 (-5 *3 (-2 (|:| |val| (-650 *7)) (|:| -3684 *8))) + (-4 *7 (-1074 *4 *5 *6)) (-4 *8 (-1080 *4 *5 *6 *7)) (-4 *4 (-458)) + (-4 *5 (-799)) (-4 *6 (-856)) (-5 *2 (-112)) + (-5 *1 (-1116 *4 *5 *6 *7 *8))))) (((*1 *2 *1 *1) - (-12 (-4 *1 (-1107 *3)) (-4 *3 (-1109)) (-5 *2 (-112))))) -(((*1 *1) (-5 *1 (-158))) - ((*1 *2 *1) (-12 (-4 *1 (-1053 *2)) (-4 *2 (-23))))) -(((*1 *2 *2) (-12 (-5 *2 (-112)) (-5 *1 (-933))))) -(((*1 *2 *2) (|partial| -12 (-4 *1 (-992 *2)) (-4 *2 (-1212))))) -(((*1 *2 *3 *4 *4 *4 *3 *3 *5 *5 *3) - (-12 (-5 *3 (-570)) (-5 *4 (-695 (-227))) (-5 *5 (-227)) - (-5 *2 (-1044)) (-5 *1 (-757))))) -(((*1 *2 *3 *4 *4 *5 *3 *3 *4 *3) - (-12 (-5 *3 (-570)) (-5 *5 (-695 (-227))) (-5 *4 (-227)) - (-5 *2 (-1044)) (-5 *1 (-758))))) + (-12 + (-5 *2 + (-2 (|:| -1452 *3) (|:| |gap| (-777)) (|:| -4077 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(-4 *1 (-1080 *4 *5 *6 *3))))) +(((*1 *2 *1) (-12 (-5 *2 (-980)) (-5 *1 (-912 *3)) (-4 *3 (-1109))))) +(((*1 *2 *2) (-12 (-5 *1 (-160 *2)) (-4 *2 (-551)))) + ((*1 *1 *2) (-12 (-5 *2 (-650 (-570))) (-5 *1 (-980))))) +(((*1 *2 *3 *4 *5 *6 *7 *7 *8) + (-12 + (-5 *3 + (-2 (|:| |det| *12) (|:| |rows| (-650 (-570))) + (|:| |cols| (-650 (-570))))) + (-5 *4 (-695 *12)) (-5 *5 (-650 (-413 (-959 *9)))) + (-5 *6 (-650 (-650 *12))) (-5 *7 (-777)) (-5 *8 (-570)) + (-4 *9 (-13 (-311) (-148))) (-4 *12 (-956 *9 *11 *10)) + (-4 *10 (-13 (-856) (-620 (-1186)))) (-4 *11 (-799)) + (-5 *2 + (-2 (|:| |eqzro| (-650 *12)) (|:| |neqzro| (-650 *12)) + (|:| |wcond| (-650 (-959 *9))) + (|:| |bsoln| + (-2 (|:| |partsol| (-1277 (-413 (-959 *9)))) + (|:| -4169 (-650 (-1277 (-413 (-959 *9))))))))) + (-5 *1 (-931 *9 *10 *11 *12))))) (((*1 *1 *1 *1) (-4 *1 (-667)))) -(((*1 *2) - (-12 (-5 *2 (-112)) (-5 *1 (-1204 *3 *4)) (-4 *3 (-1109)) - (-4 *4 (-1109))))) -(((*1 *2 *3) (-12 (-5 *3 (-950 *2)) (-5 *1 (-991 *2)) (-4 *2 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- (-5 *1 (-957 *4 *5 *6 *7 *3)) - (-4 *3 - (-13 (-368) - (-10 -8 (-15 -3735 ($ *7)) (-15 -4399 (*7 $)) - (-15 -4413 (*7 $)))))))) -(((*1 *2) - (-12 (-4 *3 (-562)) (-5 *2 (-650 *4)) (-5 *1 (-43 *3 *4)) - (-4 *4 (-423 *3))))) +(((*1 *1 *2 *1) + (-12 (-5 *2 (-1 *3 (-570))) (-4 *3 (-1058)) (-5 *1 (-601 *3)))) + ((*1 *1 *2 *1) + (-12 (-5 *2 (-1 *3 (-570))) (-4 *1 (-1237 *3)) (-4 *3 (-1058)))) + ((*1 *1 *2 *1) + (-12 (-5 *2 (-1 *3 (-570))) (-4 *1 (-1268 *3)) (-4 *3 (-1058))))) +(((*1 *1 *1 *2) + (-12 (-5 *2 (-1 *4 *4)) (-4 *4 (-654 *3)) (-4 *3 (-1058)) + (-5 *1 (-720 *3 *4)))) + ((*1 *1 *1 *2) + (-12 (-5 *2 (-1 *3 *3)) (-4 *3 (-1058)) (-5 *1 (-842 *3))))) +(((*1 *2 *2 *3) (-12 (-5 *3 (-777)) (-5 *1 (-593 *2)) (-4 *2 (-551))))) +(((*1 *2 *3 *4) + (-12 (-5 *4 (-1 *7 *7)) (-4 *7 (-1253 *6)) + (-4 *6 (-13 (-27) (-436 *5))) (-4 *5 (-13 (-562) (-1047 (-570)))) + (-4 *8 (-1253 (-413 *7))) (-5 *2 (-592 *3)) + (-5 *1 (-558 *5 *6 *7 *8 *3)) (-4 *3 (-347 *6 *7 *8))))) +(((*1 *2 *2 *3) + (-12 (-5 *3 (-650 *2)) (-4 *2 (-956 *4 *5 *6)) (-4 *4 (-311)) + (-4 *5 (-799)) (-4 *6 (-856)) (-5 *1 (-453 *4 *5 *6 *2))))) (((*1 *2 *1) (-12 (-5 *2 (-1134 (-570) (-618 (-48)))) (-5 *1 (-48)))) ((*1 *2 *1) (-12 (-4 *3 (-1001 *2)) (-4 *4 (-1253 *3)) (-4 *2 (-311)) @@ -77,6 +101,7 @@ (-5 *1 (-668 *3 *4 *2)) (-4 *3 (-723 *4)))) ((*1 *2 *1) (-12 (-4 *1 (-1001 *2)) (-4 *2 (-562))))) (((*1 *2 *3) (-12 (-5 *3 (-650 (-52))) (-5 *2 (-1282)) (-5 *1 (-869))))) +(((*1 *1 *1 *1) (-5 *1 (-112))) ((*1 *1 *1 *1) (-4 *1 (-124)))) (((*1 *1 *1) (-12 (-4 *1 (-120 *2)) (-4 *2 (-1227)))) ((*1 *1 *1) (-12 (-5 *1 (-678 *2)) (-4 *2 (-856)))) ((*1 *1 *1) (-12 (-5 *1 (-683 *2)) (-4 *2 (-856)))) @@ -85,34 +110,46 @@ ((*1 *2 *1) (-12 (-4 *2 (-13 (-854) (-368))) (-5 *1 (-1070 *2 *3)) (-4 *3 (-1253 *2))))) -(((*1 *2 *3 *4) - (-12 (-5 *3 (-413 (-570))) (-4 *5 (-799)) (-4 *6 (-856)) - (-4 *7 (-562)) (-4 *8 (-956 *7 *5 *6)) - (-5 *2 (-2 (|:| -3011 (-777)) (|:| -1442 *9) (|:| |radicand| *9))) - (-5 *1 (-960 *5 *6 *7 *8 *9)) (-5 *4 (-777)) - (-4 *9 - (-13 (-368) - (-10 -8 (-15 -3735 ($ *8)) (-15 -4399 (*8 $)) (-15 -4413 (*8 $)))))))) -(((*1 *1 *2 *2) (-12 (-5 *2 (-570)) (-5 *1 (-868))))) -(((*1 *2 *3 *2) (-12 (-5 *3 (-777)) (-5 *1 (-862 *2)) (-4 *2 (-174)))) - ((*1 *2 *3) - (-12 (-5 *2 (-1182 (-570))) (-5 *1 (-949)) (-5 *3 (-570))))) -(((*1 *2 *3) - (-12 (-4 *2 (-368)) (-4 *2 (-854)) (-5 *1 (-952 *2 *3)) - (-4 *3 (-1253 *2))))) -(((*1 *2 *3 *3 *3 *4) - (-12 (-5 *3 (-227)) (-5 *4 (-570)) (-5 *2 (-1044)) (-5 *1 (-764))))) -(((*1 *2 *1) (-12 (-5 *2 (-1129)) (-5 *1 (-849 *3)) (-4 *3 (-1109))))) (((*1 *1 *1 *1) (-4 *1 (-667)))) -(((*1 *2 *1) (-12 (-5 *2 (-1282)) (-5 *1 (-828))))) -(((*1 *2 *2) (|partial| -12 (-4 *1 (-992 *2)) (-4 *2 (-1212))))) (((*1 *2 *3 *4) - (-12 (-4 *5 (-368)) (-4 *7 (-1253 *5)) (-4 *4 (-730 *5 *7)) - (-5 *2 (-2 (|:| -2042 (-695 *6)) (|:| |vec| (-1277 *5)))) - (-5 *1 (-817 *5 *6 *7 *4 *3)) (-4 *6 (-662 *5)) (-4 *3 (-662 *4))))) + (-12 (-5 *3 (-650 (-1 (-112) *8))) (-4 *8 (-1074 *5 *6 *7)) + (-4 *5 (-562)) (-4 *6 (-799)) (-4 *7 (-856)) + (-5 *2 (-2 (|:| |goodPols| (-650 *8)) (|:| |badPols| (-650 *8)))) + (-5 *1 (-986 *5 *6 *7 *8)) (-5 *4 (-650 *8))))) (((*1 *2 *3 *4) - (-12 (-5 *3 (-650 (-849 (-227)))) (-5 *4 (-227)) (-5 *2 (-650 *4)) - (-5 *1 (-270))))) + (-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 (|:| -4006 (-777)) + (|:| |eqns| + (-650 + (-2 (|:| |det| *8) (|:| |rows| (-650 (-570))) + (|:| |cols| (-650 (-570)))))) + (|:| |fgb| (-650 *8))))) + (-5 *1 (-931 *5 *6 *7 *8)) (-5 *4 (-777))))) +(((*1 *2 *1) (-12 (-5 *2 (-1144)) (-5 *1 (-31)))) + ((*1 *2) (-12 (-4 *1 (-410)) (-5 *2 (-928)))) ((*1 *1) (-4 *1 (-551))) + ((*1 *2 *2) (-12 (-5 *2 (-928)) (-5 *1 (-705)))) + ((*1 *2 *1) (-12 (-5 *2 (-650 *3)) (-5 *1 (-911 *3)) (-4 *3 (-1109))))) +(((*1 *2 *1 *3) + (-12 (-5 *3 (-950 (-227))) (-5 *2 (-1282)) (-5 *1 (-474))))) +(((*1 *2 *2) (-12 (-5 *2 (-1166 (-650 (-570)))) (-5 *1 (-890))))) +(((*1 *1) (-12 (-5 *1 (-229 *2)) (-4 *2 (-13 (-368) (-1212)))))) +(((*1 *2 *1) + (-12 (-4 *1 (-57 *3 *4 *5)) (-4 *3 (-1227)) (-4 *4 (-378 *3)) + (-4 *5 (-378 *3)) (-5 *2 (-570)))) + ((*1 *2 *1) + (-12 (-4 *1 (-1062 *3 *4 *5 *6 *7)) (-4 *5 (-1058)) + (-4 *6 (-240 *4 *5)) (-4 *7 (-240 *3 *5)) (-5 *2 (-570))))) +(((*1 *2 *3) + (|partial| -12 (-5 *3 (-695 (-413 (-959 (-570))))) + (-5 *2 (-695 (-320 (-570)))) (-5 *1 (-1040))))) +(((*1 *1 *1 *1) (-12 (-5 *1 (-788 *2)) (-4 *2 (-1058)))) + ((*1 *1 *1 *1) + (-12 (-4 *1 (-1074 *2 *3 *4)) (-4 *2 (-1058)) (-4 *3 (-799)) + (-4 *4 (-856))))) (((*1 *2 *1) (-12 (-5 *2 (-1134 (-570) (-618 (-48)))) (-5 *1 (-48)))) ((*1 *2 *1) (-12 (-4 *3 (-311)) (-4 *4 (-1001 *3)) (-4 *5 (-1253 *4)) @@ -129,6 +166,14 @@ (-12 (-4 *3 (-174)) (-4 *2 (-723 *3)) (-5 *1 (-668 *2 *3 *4)) (-4 *4 (|SubsetCategory| (-732) *3)))) ((*1 *2 *1) (-12 (-4 *1 (-1001 *2)) (-4 *2 (-562))))) +(((*1 *2 *3 *4) + (-12 (-5 *4 (-777)) (-4 *5 (-1058)) (-5 *2 (-570)) + (-5 *1 (-449 *5 *3 *6)) (-4 *3 (-1253 *5)) + (-4 *6 (-13 (-410) (-1047 *5) (-368) (-1212) (-288))))) + ((*1 *2 *3) + (-12 (-4 *4 (-1058)) (-5 *2 (-570)) (-5 *1 (-449 *4 *3 *5)) + (-4 *3 (-1253 *4)) + (-4 *5 (-13 (-410) (-1047 *4) (-368) (-1212) (-288)))))) (((*1 *1 *1) (-12 (-4 *1 (-120 *2)) (-4 *2 (-1227)))) ((*1 *1 *1) (-12 (-5 *1 (-678 *2)) (-4 *2 (-856)))) ((*1 *1 *1) (-12 (-5 *1 (-683 *2)) (-4 *2 (-856)))) @@ -137,24 +182,28 @@ ((*1 *2 *1) (-12 (-4 *2 (-13 (-854) (-368))) (-5 *1 (-1070 *2 *3)) (-4 *3 (-1253 *2))))) -(((*1 *2 *1) (-12 (-5 *2 (-112)) (-5 *1 (-1191))))) -(((*1 *1 *1 *2) - (-12 (-5 *2 (-413 (-570))) (-5 *1 (-601 *3)) (-4 *3 (-38 *2)) - (-4 *3 (-1058))))) +(((*1 *2 *3) + (-12 (-5 *3 (-1186)) (-5 *2 (-1 *6 *5)) (-5 *1 (-712 *4 *5 *6)) + (-4 *4 (-620 (-542))) (-4 *5 (-1227)) (-4 *6 (-1227))))) +(((*1 *2 *3) + (-12 (-5 *3 (-1277 *5)) (-4 *5 (-645 *4)) (-4 *4 (-562)) + (-5 *2 (-112)) (-5 *1 (-644 *4 *5))))) (((*1 *2 *1) (-12 (-5 *2 (-650 (-1168))) (-5 *1 (-1207))))) +(((*1 *2 *1) + (-12 (-4 *1 (-1143 *3)) (-4 *3 (-1058)) + (-5 *2 + (-2 (|:| -1399 (-777)) (|:| |curves| (-777)) + (|:| |polygons| (-777)) (|:| |constructs| (-777))))))) +(((*1 *2 *1) (-12 (-5 *2 (-1282)) (-5 *1 (-334))))) (((*1 *2 *3 *4) - (-12 (-5 *3 (-695 (-171 (-413 (-570))))) (-5 *2 (-650 (-171 *4))) - (-5 *1 (-770 *4)) (-4 *4 (-13 (-368) (-854)))))) -(((*1 *1) (-5 *1 (-142)))) -(((*1 *1 *1 *2) (-12 (-4 *1 (-1153)) (-5 *2 (-142)))) - ((*1 *1 *1 *2) (-12 (-4 *1 (-1153)) (-5 *2 (-145))))) -(((*1 *2 *3) (-12 (-5 *3 (-777)) (-5 *2 (-384)) (-5 *1 (-1049))))) -(((*1 *2 *3 *2) - (-12 (-5 *2 (-1166 (-650 (-570)))) (-5 *3 (-650 (-570))) - (-5 *1 (-890))))) -(((*1 *1 *1) - (-12 (-4 *1 (-1074 *2 *3 *4)) (-4 *2 (-1058)) (-4 *3 (-799)) - (-4 *4 (-856))))) + (-12 (-5 *3 (-1 (-112) *8)) (-4 *8 (-1074 *5 *6 *7)) (-4 *5 (-562)) + (-4 *6 (-799)) (-4 *7 (-856)) + (-5 *2 (-2 (|:| |goodPols| (-650 *8)) (|:| |badPols| (-650 *8)))) + (-5 *1 (-986 *5 *6 *7 *8)) (-5 *4 (-650 *8))))) +(((*1 *2 *1) (-12 (-5 *2 (-1282)) (-5 *1 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((*1 *2 *3) - (|partial| -12 (-5 *2 (-413 (-570))) (-5 *1 (-1017 *3)) - (-4 *3 (-1047 *2))))) +(((*1 *2 *3 *3 *4 *4) + (|partial| -12 (-5 *3 (-777)) (-4 *5 (-368)) (-5 *2 (-176 *6)) + (-5 *1 (-873 *5 *4 *6)) (-4 *4 (-1268 *5)) (-4 *6 (-1253 *5))))) +(((*1 *2 *3) + (-12 (-5 *2 (-1 (-950 *3) (-950 *3))) (-5 *1 (-178 *3)) + (-4 *3 (-13 (-368) (-1212) (-1011)))))) (((*1 *1 *1) (-4 *1 (-635))) ((*1 *2 *2) (-12 (-4 *3 (-562)) (-5 *1 (-636 *3 *2)) (-4 *2 (-13 (-436 *3) (-1011) (-1212)))))) -(((*1 *2 *3 *4) - (-12 (-5 *3 (-413 *6)) (-4 *5 (-1231)) (-4 *6 (-1253 *5)) - (-5 *2 (-2 (|:| -3011 (-777)) (|:| -1442 *3) (|:| |radicand| *6))) - (-5 *1 (-149 *5 *6 *7)) (-5 *4 (-777)) (-4 *7 (-1253 *3))))) -(((*1 *2 *3 *3 *4 *3) - (-12 (-5 *3 (-570)) (-5 *4 (-695 (-227))) (-5 *2 (-1044)) - (-5 *1 (-753))))) -(((*1 *2 *2) - (-12 (-5 *2 (-112)) (-5 *1 (-344 *3 *4 *5)) (-14 *3 (-650 (-1186))) - (-14 *4 (-650 (-1186))) (-4 *5 (-393)))) - ((*1 *2) - (-12 (-5 *2 (-112)) (-5 *1 (-344 *3 *4 *5)) (-14 *3 (-650 (-1186))) - (-14 *4 (-650 (-1186))) (-4 *5 (-393))))) -(((*1 *2 *3 *4) - (-12 (-5 *3 (-650 *2)) (-5 *4 (-1 (-112) *2 *2)) (-5 *1 (-1228 *2)) - (-4 *2 (-1109)))) - ((*1 *2 *3) - (-12 (-5 *3 (-650 *2)) (-4 *2 (-1109)) (-4 *2 (-856)) - (-5 *1 (-1228 *2))))) -(((*1 *1 *2 *3) - (-12 (-5 *2 (-1070 (-1033 *4) (-1182 (-1033 *4)))) (-5 *3 (-868)) - (-5 *1 (-1033 *4)) (-4 *4 (-13 (-854) (-368) (-1031)))))) +(((*1 *2 *1) + (-12 + (-5 *2 + (-650 + (-2 + (|:| -2106 + (-2 (|:| |var| (-1186)) (|:| |fn| (-320 (-227))) + (|:| -4043 (-1103 (-849 (-227)))) (|:| |abserr| (-227)) + (|:| |relerr| (-227)))) + (|:| -2339 + (-2 + (|:| |endPointContinuity| + (-3 (|:| |continuous| "Continuous at the end points") + (|:| |lowerSingular| + "There is a singularity at the lower end point") + (|:| |upperSingular| + "There is a singularity at the upper end point") + (|:| |bothSingular| + "There are singularities at both end points") + (|:| |notEvaluated| + "End point continuity not yet evaluated"))) + (|:| |singularitiesStream| + (-3 (|:| |str| (-1166 (-227))) + (|:| |notEvaluated| + "Internal singularities not yet evaluated"))) + (|:| -4043 + (-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) + (-12 (-4 *1 (-610 *3 *4)) (-4 *3 (-1109)) (-4 *4 (-1227)) + (-5 *2 (-650 *4))))) (((*1 *2 *3 *3) - (-12 (-4 *4 (-1253 *2)) (-4 *2 (-1231)) (-5 *1 (-149 *2 *4 *3)) - (-4 *3 (-1253 (-413 *4)))))) -(((*1 *1 *1) - (-12 (-4 *2 (-368)) (-4 *3 (-799)) (-4 *4 (-856)) - (-5 *1 (-510 *2 *3 *4 *5)) (-4 *5 (-956 *2 *3 *4))))) + (-12 (-4 *4 (-562)) + (-5 *2 (-2 (|:| |coef1| *3) (|:| |coef2| *3) (|:| -4020 *4))) + (-5 *1 (-978 *4 *3)) (-4 *3 (-1253 *4))))) +(((*1 *2 *3 *4 *5) + (-12 (-5 *5 (-570)) (-4 *6 (-799)) (-4 *7 (-856)) (-4 *8 (-311)) + (-4 *9 (-956 *8 *6 *7)) + (-5 *2 (-2 (|:| -2560 (-1182 *9)) (|:| |polval| (-1182 *8)))) + (-5 *1 (-748 *6 *7 *8 *9)) (-5 *3 (-1182 *9)) (-5 *4 (-1182 *8))))) +(((*1 *1 *2 *1) + (-12 (-5 *2 (-1 (-112) *3)) (|has| *1 (-6 -4449)) (-4 *1 (-237 *3)) + (-4 *3 (-1109)))) + ((*1 *1 *2 *1) + (-12 (|has| *1 (-6 -4449)) (-4 *1 (-237 *2)) (-4 *2 (-1109)))) + ((*1 *1 *2 *1) + (-12 (-4 *1 (-286 *2)) (-4 *2 (-1227)) (-4 *2 (-1109)))) + ((*1 *1 *2 *1) + (-12 (-5 *2 (-1 (-112) *3)) (-4 *1 (-286 *3)) (-4 *3 (-1227)))) + ((*1 *2 *3 *1) + (|partial| -12 (-4 *1 (-616 *3 *2)) (-4 *3 (-1109)) (-4 *2 (-1109)))) + ((*1 *1 *2 *1 *3) + (-12 (-5 *2 (-1 (-112) *4)) (-5 *3 (-570)) (-4 *4 (-1109)) + (-5 *1 (-743 *4)))) + ((*1 *1 *2 *1 *3) + (-12 (-5 *3 (-570)) (-5 *1 (-743 *2)) (-4 *2 (-1109)))) + ((*1 *1 *2 *1) + (-12 (-5 *2 (-1149 *3 *4)) (-4 *3 (-13 (-1109) (-34))) + (-4 *4 (-13 (-1109) (-34))) (-5 *1 (-1150 *3 *4))))) +(((*1 *2 *2) + (-12 (-4 *3 (-562)) (-5 *1 (-279 *3 *2)) + (-4 *2 (-13 (-436 *3) (-1011)))))) (((*1 *2 *3) - (-12 (-4 *4 (-13 (-368) (-148) (-1047 (-413 (-570))))) - (-4 *5 (-1253 *4)) - (-5 *2 (-650 (-2 (|:| |deg| (-777)) (|:| -4302 *5)))) - (-5 *1 (-815 *4 *5 *3 *6)) (-4 *3 (-662 *5)) - (-4 *6 (-662 (-413 *5)))))) + (-12 (-5 *3 (-650 *7)) (-4 *7 (-956 *4 *5 *6)) (-4 *6 (-620 (-1186))) + (-4 *4 (-368)) (-4 *5 (-799)) (-4 *6 (-856)) + (-5 *2 (-1175 (-650 (-959 *4)) (-650 (-298 (-959 *4))))) + (-5 *1 (-510 *4 *5 *6 *7))))) (((*1 *1 *1) (-4 *1 (-35))) ((*1 *2 *2) (-12 (-4 *3 (-562)) (-5 *1 (-279 *3 *2)) @@ -1591,21 +1498,38 @@ ((*1 *2 *2) (-12 (-5 *2 (-1166 *3)) (-4 *3 (-38 (-413 (-570)))) (-5 *1 (-1172 *3))))) -(((*1 *2 *1 *1) - (-12 (-4 *1 (-1074 *3 *4 *5)) (-4 *3 (-1058)) (-4 *4 (-799)) - (-4 *5 (-856)) (-5 *2 (-112))))) -(((*1 *2) (-12 (-5 *2 (-112)) (-5 *1 (-473)))) - ((*1 *2 *2) (-12 (-5 *2 (-112)) (-5 *1 (-473))))) -(((*1 *2 *2) - (-12 (-5 *2 (-950 *3)) (-4 *3 (-13 (-368) (-1212) (-1011))) - (-5 *1 (-178 *3))))) +(((*1 *1 *1) (-12 (-4 *1 (-680 *2)) (-4 *2 (-1227))))) +(((*1 *2 *2 *3) + (-12 (-4 *4 (-799)) + (-4 *3 (-13 (-856) (-10 -8 (-15 -1425 ((-1186) $))))) (-4 *5 (-562)) + (-5 *1 (-738 *4 *3 *5 *2)) (-4 *2 (-956 (-413 (-959 *5)) *4 *3)))) + ((*1 *2 *2 *3) + (-12 (-4 *4 (-1058)) (-4 *5 (-799)) + (-4 *3 + (-13 (-856) + (-10 -8 (-15 -1425 ((-1186) $)) + (-15 -2799 ((-3 $ "failed") (-1186)))))) + (-5 *1 (-993 *4 *5 *3 *2)) (-4 *2 (-956 (-959 *4) *5 *3)))) + ((*1 *2 *2 *3) + (-12 (-5 *3 (-650 *6)) + (-4 *6 + (-13 (-856) + (-10 -8 (-15 -1425 ((-1186) $)) + (-15 -2799 ((-3 $ "failed") (-1186)))))) + (-4 *4 (-1058)) (-4 *5 (-799)) (-5 *1 (-993 *4 *5 *6 *2)) + (-4 *2 (-956 (-959 *4) *5 *6))))) +(((*1 *2 *2) (-12 (-5 *2 (-928)) (|has| *1 (-6 -4440)) (-4 *1 (-410)))) + ((*1 *2) (-12 (-4 *1 (-410)) (-5 *2 (-928)))) + ((*1 *2 *2) (-12 (-5 *2 (-928)) (-5 *1 (-705)))) + ((*1 *2) (-12 (-5 *2 (-928)) (-5 *1 (-705))))) +(((*1 *1 *2) (-12 (-5 *2 (-650 *3)) (-4 *3 (-1109)) (-5 *1 (-91 *3))))) +(((*1 *1 *1 *1) (-12 (-5 *1 (-788 *2)) (-4 *2 (-1058))))) (((*1 *2 *3) (-12 (-5 *2 (-650 (-1168))) (-5 *1 (-243)) (-5 *3 (-1168)))) ((*1 *2 *2) (-12 (-5 *2 (-650 (-1168))) (-5 *1 (-243)))) ((*1 *1 *2) (-12 (-5 *2 (-158)) (-5 *1 (-880))))) -(((*1 *2 *3 *4) - (-12 (-5 *3 (-413 (-570))) (-5 *4 (-570)) (-5 *2 (-52)) - (-5 *1 (-1014))))) +(((*1 *2 *3) + (-12 (-5 *2 (-1182 (-570))) (-5 *1 (-949)) (-5 *3 (-570))))) (((*1 *1 *1 *2) (-12 (-5 *2 (-1 (-868) (-868))) (-5 *1 (-115)))) ((*1 *1 *1 *2) (-12 (-5 *2 (-1 (-868) (-650 (-868)))) (-5 *1 (-115)))) ((*1 *2 *1) @@ -1614,8 +1538,8 @@ (-12 (-5 *2 (-1282)) (-5 *1 (-216 *3)) (-4 *3 (-13 (-856) - (-10 -8 (-15 -1877 ((-1168) $ (-1186))) (-15 -4131 (*2 $)) - (-15 -3807 (*2 $))))))) + (-10 -8 (-15 -1940 ((-1168) $ (-1186))) (-15 -4147 (*2 $)) + (-15 -3732 (*2 $))))))) ((*1 *2 *1) (-12 (-5 *2 (-1282)) (-5 *1 (-400)))) ((*1 *2 *1 *3) (-12 (-5 *3 (-570)) (-5 *2 (-1282)) (-5 *1 (-400)))) ((*1 *2 *1) (-12 (-5 *2 (-1282)) (-5 *1 (-508)))) @@ -1623,31 +1547,14 @@ ((*1 *2 *1) (-12 (-5 *2 (-1282)) (-5 *1 (-1207)))) ((*1 *2 *1 *3) (-12 (-5 *3 (-570)) (-5 *2 (-1282)) (-5 *1 (-1207))))) (((*1 *2 *3) - (-12 (-4 *1 (-806)) - (-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 (-1044))))) -(((*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 *3) - (-12 (-5 *3 (-650 (-487 *4 *5))) (-14 *4 (-650 (-1186))) - (-4 *5 (-458)) - (-5 *2 - (-2 (|:| |gblist| (-650 (-249 *4 *5))) - (|:| |gvlist| (-650 (-570))))) - (-5 *1 (-637 *4 *5))))) -(((*1 *2 *2) (-12 (-5 *2 (-570)) (-5 *1 (-567))))) + (-12 (-5 *3 (-2 (|:| -4397 (-413 (-570))) (|:| -4410 (-413 (-570))))) + (-5 *2 (-413 (-570))) (-5 *1 (-1029 *4)) (-4 *4 (-1253 (-570)))))) +(((*1 *1 *2 *3) (-12 (-5 *3 (-570)) (-5 *1 (-424 *2)) (-4 *2 (-562))))) (((*1 *1) (-5 *1 (-334)))) -(((*1 *2 *3 *4) - (-12 (-5 *3 (-1186)) (-5 *4 (-959 (-570))) (-5 *2 (-334)) - (-5 *1 (-336))))) -(((*1 *2 *1) (-12 (-5 *2 (-112)) (-5 *1 (-173)))) - ((*1 *2 *1) (-12 (-5 *2 (-112)) (-5 *1 (-1222 *3)) (-4 *3 (-983))))) +(((*1 *2 *1) (|partial| -12 (-5 *2 (-512)) (-5 *1 (-283))))) +(((*1 *2 *3) + (-12 (-5 *3 (-650 (-570))) (-5 *2 (-911 (-570))) (-5 *1 (-924)))) + ((*1 *2) (-12 (-5 *2 (-911 (-570))) (-5 *1 (-924))))) (((*1 *1 *1) (-4 *1 (-35))) ((*1 *2 *2) (-12 (-4 *3 (-562)) (-5 *1 (-279 *3 *2)) @@ -1664,13 +1571,14 @@ ((*1 *2 *2) (-12 (-5 *2 (-1166 *3)) (-4 *3 (-38 (-413 (-570)))) (-5 *1 (-1172 *3))))) -(((*1 *2 *1 *1) - (-12 (-5 *2 (-2 (|:| -1874 (-788 *3)) (|:| |coef2| (-788 *3)))) - (-5 *1 (-788 *3)) (-4 *3 (-562)) (-4 *3 (-1058)))) - ((*1 *2 *1 *1) - (-12 (-4 *3 (-562)) (-4 *3 (-1058)) (-4 *4 (-799)) (-4 *5 (-856)) - (-5 *2 (-2 (|:| -1874 *1) (|:| |coef2| *1))) - (-4 *1 (-1074 *3 *4 *5))))) +(((*1 *2 *3 *4) + (-12 (-5 *3 (-227)) (-5 *4 (-570)) (-5 *2 (-1044)) (-5 *1 (-764))))) +(((*1 *2 *3 *4 *4 *4 *4 *5 *5) + (-12 (-5 *3 (-1 (-384) (-384))) (-5 *4 (-384)) + (-5 *2 + (-2 (|:| -2307 *4) (|:| -3669 *4) (|:| |totalpts| (-570)) + (|:| |success| (-112)))) + (-5 *1 (-795)) (-5 *5 (-570))))) (((*1 *2 *3 *4) (-12 (-5 *3 (-650 *5)) (-5 *4 (-650 *6)) (-4 *5 (-1109)) (-4 *6 (-1227)) (-5 *2 (-1 *6 *5)) (-5 *1 (-647 *5 *6)))) @@ -1691,57 +1599,31 @@ (-4 *5 (-1109)) (-4 *2 (-1227)) (-5 *1 (-647 *5 *2)))) ((*1 *2 *1 *1 *3) (-12 (-4 *1 (-1153)) (-5 *3 (-145)) (-5 *2 (-777))))) (((*1 *2 *3 *4) - (-12 (-5 *4 (-650 *3)) (-4 *3 (-956 *5 *6 *7)) (-4 *5 (-458)) - (-4 *6 (-799)) (-4 *7 (-856)) - (-5 *2 (-2 (|:| |poly| *3) (|:| |mult| *5))) - (-5 *1 (-455 *5 *6 *7 *3))))) -(((*1 *1 *1 *1) (|partial| -4 *1 (-132)))) -(((*1 *2) - (-12 (-4 *4 (-368)) (-5 *2 (-928)) (-5 *1 (-332 *3 *4)) - (-4 *3 (-333 *4)))) - ((*1 *2) - (-12 (-4 *4 (-368)) (-5 *2 (-839 (-928))) (-5 *1 (-332 *3 *4)) - (-4 *3 (-333 *4)))) - ((*1 *2) (-12 (-4 *1 (-333 *3)) (-4 *3 (-368)) (-5 *2 (-928)))) - ((*1 *2) - (-12 (-4 *1 (-1296 *3)) (-4 *3 (-368)) (-5 *2 (-839 (-928)))))) -(((*1 *2 *3) - (-12 (-5 *3 (-695 (-320 (-227)))) (-5 *2 (-384)) (-5 *1 (-207))))) -(((*1 *2 *1) (-12 (-5 *2 (-112)) (-5 *1 (-283)))) - ((*1 *2 *1) (-12 (-5 *2 (-112)) (-5 *1 (-899 *3)) (-4 *3 (-1109)))) - ((*1 *2 *1) - (-12 (-4 *1 (-1294 *3 *4)) (-4 *3 (-856)) (-4 *4 (-1058)) - (-5 *2 (-112)))) - ((*1 *2 *1) - (-12 (-5 *2 (-112)) (-5 *1 (-1300 *3 *4)) (-4 *3 (-1058)) - (-4 *4 (-852))))) -(((*1 *2 *3) - (-12 (-5 *3 (-1277 (-650 (-2 (|:| -2196 *4) (|:| -2160 (-1129)))))) - (-4 *4 (-354)) (-5 *2 (-695 *4)) (-5 *1 (-351 *4))))) -(((*1 *2 *1 *3 *3 *4) - (-12 (-5 *3 (-1 (-868) (-868) (-868))) (-5 *4 (-570)) (-5 *2 (-868)) - (-5 *1 (-655 *5 *6 *7)) (-4 *5 (-1109)) (-4 *6 (-23)) (-14 *7 *6))) - ((*1 *2 *1 *2) - (-12 (-5 *2 (-868)) (-5 *1 (-860 *3 *4 *5)) (-4 *3 (-1058)) - (-14 *4 (-99 *3)) (-14 *5 (-1 *3 *3)))) - ((*1 *1 *2) (-12 (-5 *2 (-227)) (-5 *1 (-868)))) - ((*1 *1 *2) (-12 (-5 *2 (-1168)) (-5 *1 (-868)))) - ((*1 *1 *2) (-12 (-5 *2 (-1186)) (-5 *1 (-868)))) - ((*1 *1 *2) (-12 (-5 *2 (-570)) (-5 *1 (-868)))) - ((*1 *2 *1 *2) - (-12 (-5 *2 (-868)) (-5 *1 (-1182 *3)) (-4 *3 (-1058))))) -(((*1 *2 *3 *4 *5) - (-12 (-5 *4 (-112)) (-4 *6 (-13 (-458) (-1047 (-570)) (-645 (-570)))) - (-4 *3 (-13 (-27) (-1212) (-436 *6) (-10 -8 (-15 -3735 ($ *7))))) - (-4 *7 (-854)) - (-4 *8 - (-13 (-1255 *3 *7) (-368) (-1212) - (-10 -8 (-15 -3447 ($ $)) (-15 -3722 ($ $))))) + (-12 (-5 *3 (-777)) (-5 *4 (-1277 *2)) (-4 *5 (-311)) + (-4 *6 (-1001 *5)) (-4 *2 (-13 (-415 *6 *7) (-1047 *6))) + (-5 *1 (-419 *5 *6 *7 *2)) (-4 *7 (-1253 *6))))) +(((*1 *2 *2 *3) + (-12 (-4 *3 (-1058)) (-5 *1 (-450 *3 *2)) (-4 *2 (-1253 *3))))) +(((*1 *2 *3 *4) + (-12 (-5 *3 (-227)) (-5 *4 (-570)) (-5 *2 (-1044)) (-5 *1 (-764))))) +(((*1 *2 *3 *4) + (-12 (-5 *3 (-227)) (-5 *4 (-570)) (-5 *2 (-1044)) (-5 *1 (-764))))) +(((*1 *2 *2) + (-12 (-5 *2 - (-3 (|:| |%series| *8) - (|:| |%problem| (-2 (|:| |func| (-1168)) (|:| |prob| (-1168)))))) - (-5 *1 (-428 *6 *3 *7 *8 *9 *10)) (-5 *5 (-1168)) (-4 *9 (-992 *8)) - (-14 *10 (-1186))))) + (-2 (|:| |flg| (-3 "nil" "sqfr" "irred" "prime")) (|:| |fctr| *4) + (|:| |xpnt| (-570)))) + (-4 *4 (-13 (-1253 *3) (-562) (-10 -8 (-15 -1942 ($ $ $))))) + (-4 *3 (-562)) (-5 *1 (-1256 *3 *4))))) +(((*1 *2 *3 *3 *4) + (-12 (-4 *5 (-458)) (-4 *6 (-799)) (-4 *7 (-856)) + (-4 *3 (-1074 *5 *6 *7)) + (-5 *2 (-650 (-2 (|:| |val| *3) (|:| -3684 *4)))) + (-5 *1 (-1081 *5 *6 *7 *3 *4)) (-4 *4 (-1080 *5 *6 *7 *3))))) +(((*1 *2 *3 *4 *4 *4 *5 *4 *6 *6 *3) + (-12 (-5 *4 (-695 (-227))) (-5 *5 (-695 (-570))) (-5 *6 (-227)) + (-5 *3 (-570)) (-5 *2 (-1044)) (-5 *1 (-757))))) +(((*1 *2 *1) (|partial| -12 (-5 *2 (-1168)) (-5 *1 (-1208))))) (((*1 *1 *1) (-4 *1 (-35))) ((*1 *2 *2) (-12 (-4 *3 (-562)) (-5 *1 (-279 *3 *2)) @@ -1758,80 +1640,36 @@ ((*1 *2 *2) (-12 (-5 *2 (-1166 *3)) (-4 *3 (-38 (-413 (-570)))) (-5 *1 (-1172 *3))))) -(((*1 *2 *2) - (|partial| -12 (-5 *2 (-1182 *3)) (-4 *3 (-354)) (-5 *1 (-362 *3))))) -(((*1 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*6)) + (-5 *2 (-2 (|:| |goodPols| (-650 *7)) (|:| |badPols| (-650 *7)))) + (-5 *1 (-986 *4 *5 *6 *7)) (-5 *3 (-650 *7))))) +(((*1 *2 *3) + (-12 (-4 *4 (-1253 (-413 *2))) (-5 *2 (-570)) (-5 *1 (-920 *4 *3)) + (-4 *3 (-1253 (-413 *4)))))) +(((*1 *2 *3) + (|partial| -12 (-5 *3 (-618 *4)) (-4 *4 (-1109)) (-4 *2 (-1109)) + (-5 *1 (-617 *2 *4))))) +(((*1 *2 *1) (-12 (-4 *1 (-1004 *2)) (-4 *2 (-1227))))) +(((*1 *1 *2 *1) (-12 (-4 *1 (-107 *2)) (-4 *2 (-1227)))) + ((*1 *1 *2 *1) (-12 (-5 *1 (-122 *2)) (-4 *2 (-856)))) + ((*1 *1 *2 *1) (-12 (-5 *1 (-127 *2)) (-4 *2 (-856)))) + ((*1 *1 *1 *1 *2) + (-12 (-5 *2 (-570)) (-4 *1 (-286 *3)) (-4 *3 (-1227)))) + ((*1 *1 *2 *1 *3) + (-12 (-5 *3 (-570)) (-4 *1 (-286 *2)) (-4 *2 (-1227)))) + ((*1 *1 *2) + (-12 + (-5 *2 + (-2 + (|:| -2106 + (-2 (|:| |var| (-1186)) (|:| |fn| (-320 (-227))) + (|:| -4043 (-1103 (-849 (-227)))) (|:| |abserr| (-227)) + (|:| |relerr| (-227)))) + (|:| -2339 + (-2 + (|:| |endPointContinuity| + (-3 (|:| |continuous| "Continuous at the end points") + (|:| |lowerSingular| + "There is a singularity at the lower end point") + (|:| |upperSingular| + "There is a singularity at the upper end point") + (|:| |bothSingular| + "There are singularities at both end points") + (|:| |notEvaluated| + "End point continuity not yet evaluated"))) + (|:| |singularitiesStream| + (-3 (|:| |str| (-1166 (-227))) + (|:| |notEvaluated| + "Internal singularities not yet evaluated"))) + (|:| -4043 + (-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 *1 *2 *1 *3) + (-12 (-5 *3 (-777)) (-4 *1 (-701 *2)) (-4 *2 (-1109)))) + ((*1 *1 *2) + (-12 + (-5 *2 + (-2 + (|:| -2106 + (-2 (|:| |xinit| (-227)) (|:| |xend| (-227)) + (|:| |fn| (-1277 (-320 (-227)))) (|:| |yinit| (-650 (-227))) + (|:| |intvals| (-650 (-227))) (|:| |g| (-320 (-227))) + (|:| |abserr| (-227)) (|:| |relerr| (-227)))) + (|:| -2339 + (-2 (|:| |stiffness| (-384)) (|:| |stability| (-384)) + (|:| |expense| (-384)) (|:| |accuracy| (-384)) + (|:| |intermediateResults| (-384)))))) + (-5 *1 (-809)))) + ((*1 *2 *3 *4) + (-12 (-5 *2 (-1282)) (-5 *1 (-1204 *3 *4)) (-4 *3 (-1109)) + (-4 *4 (-1109))))) +(((*1 *1 *1 *1) + (-12 (|has| *1 (-6 -4450)) (-4 *1 (-246 *2)) (-4 *2 (-1227))))) +(((*1 *2 *1 *1 *3) (-12 (-4 *1 (-1153)) (-5 *3 (-145)) (-5 *2 (-112))))) +(((*1 *2) (-12 (-5 *2 (-1282)) (-5 *1 (-451 *3)) (-4 *3 (-1058))))) +(((*1 *2 *3) (-12 (-5 *3 (-320 (-227))) (-5 *2 (-112)) (-5 *1 (-270))))) +(((*1 *2 *3) + (-12 (-5 *3 (-1182 *4)) (-4 *4 (-354)) (-5 *2 (-965 (-1129))) + (-5 *1 (-351 *4))))) +(((*1 *2 *3 *2) + (-12 (-5 *3 (-1 (-112) *4 *4)) (-4 *4 (-1227)) (-5 *1 (-380 *4 *2)) + (-4 *2 (-13 (-378 *4) (-10 -7 (-6 -4450))))))) +(((*1 *2 *3) (-12 (-5 *3 (-384)) (-5 *2 (-227)) (-5 *1 (-309))))) +(((*1 *1) (-5 *1 (-131)))) +(((*1 *2 *1) (-12 (-5 *2 (-112)) (-5 *1 (-440))))) (((*1 *2 *1) (-12 (-4 *1 (-133)) (-5 *2 (-777)))) ((*1 *2 *3 *1 *2) (-12 (-5 *2 (-570)) (-4 *1 (-378 *3)) (-4 *3 (-1227)) @@ -2302,93 +2115,19 @@ ((*1 *2 *1) (-12 (-5 *2 (-1129)) (-5 *1 (-535)))) ((*1 *2 *3 *1 *2) (-12 (-4 *1 (-1153)) (-5 *2 (-570)) (-5 *3 (-142)))) ((*1 *2 *1 *1 *2) (-12 (-4 *1 (-1153)) (-5 *2 (-570))))) -(((*1 *2 *3) - (|partial| -12 - (-5 *3 - (-2 (|:| |var| (-1186)) (|:| |fn| (-320 (-227))) - (|:| -1990 (-1103 (-849 (-227)))) (|:| |abserr| (-227)) - (|:| |relerr| (-227)))) - (-5 *2 (-2 (|:| -3854 (-115)) (|:| |w| (-227)))) (-5 *1 (-206))))) -(((*1 *1 *1 *1) (-12 (-4 *1 (-1253 *2)) (-4 *2 (-1058))))) -(((*1 *2 *3 *3 *4) - (-12 (-5 *4 (-777)) (-4 *5 (-562)) - (-5 *2 (-2 (|:| |coef2| *3) (|:| |subResultant| *3))) - (-5 *1 (-978 *5 *3)) (-4 *3 (-1253 *5))))) -(((*1 *1 *1) (-12 (-5 *1 (-1213 *2)) (-4 *2 (-1109))))) -(((*1 *2 *1) (-12 (-5 *2 (-1166 *3)) (-5 *1 (-176 *3)) (-4 *3 (-311))))) -(((*1 *2) (-12 (-5 *2 (-570)) (-5 *1 (-705)))) - ((*1 *2 *2) (-12 (-5 *2 (-570)) (-5 *1 (-705))))) -(((*1 *2 *1) (-12 (-5 *2 (-112)) (-5 *1 (-145))))) -(((*1 *2 *2) (|partial| -12 (-4 *1 (-992 *2)) (-4 *2 (-1212))))) -(((*1 *2 *2) (|partial| -12 (-4 *1 (-992 *2)) (-4 *2 (-1212))))) -(((*1 *2 *1) (-12 (-4 *1 (-1004 *2)) (-4 *2 (-1227))))) -(((*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 *1) (-5 *1 (-1189)))) -(((*1 *2 *2) (|partial| -12 (-4 *1 (-992 *2)) (-4 *2 (-1212))))) -(((*1 *1 *1) - (|partial| -12 (-4 *1 (-372 *2)) (-4 *2 (-174)) (-4 *2 (-562)))) - ((*1 *1 *1) (|partial| -4 *1 (-728)))) -(((*1 *2 *3 *2) - (|partial| -12 (-5 *3 (-928)) (-5 *1 (-448 *2)) - (-4 *2 (-1253 (-570))))) - ((*1 *2 *3 *2 *4) - (|partial| -12 (-5 *3 (-928)) (-5 *4 (-777)) (-5 *1 (-448 *2)) - (-4 *2 (-1253 (-570))))) - ((*1 *2 *3 *2 *4) - (|partial| -12 (-5 *3 (-928)) (-5 *4 (-650 (-777))) (-5 *1 (-448 *2)) - (-4 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*1 (-340 *3 *4 *5 *6)) (-4 *3 (-368)) (-4 *4 (-1253 *3)) - (-4 *5 (-1253 (-413 *4))) (-4 *6 (-347 *3 *4 *5)) - (-5 *2 (-419 *4 (-413 *4) *5 *6)))) - ((*1 *1 *2) - (-12 (-5 *2 (-1277 *6)) (-4 *6 (-13 (-415 *4 *5) (-1047 *4))) - (-4 *4 (-1001 *3)) (-4 *5 (-1253 *4)) (-4 *3 (-311)) - (-5 *1 (-419 *3 *4 *5 *6)))) - ((*1 *1 *2) - (-12 (-5 *2 (-650 *6)) (-4 *6 (-956 *3 *4 *5)) (-4 *3 (-368)) - (-4 *4 (-799)) (-4 *5 (-856)) (-5 *1 (-510 *3 *4 *5 *6))))) -(((*1 *2 *3) - (-12 (-5 *3 (-928)) (-5 *2 (-1182 *4)) (-5 *1 (-362 *4)) - (-4 *4 (-354))))) -(((*1 *1 *2 *3) - (-12 (-5 *2 (-474)) (-5 *3 (-650 (-266))) (-5 *1 (-1278)))) - ((*1 *1 *1) (-5 *1 (-1278)))) -(((*1 *2 *3) - (-12 (-4 *4 (-856)) (-5 *2 (-650 (-650 (-650 *4)))) - (-5 *1 (-1197 *4)) (-5 *3 (-650 (-650 *4)))))) + (-12 (-4 *1 (-560 *3)) (-4 *3 (-13 (-410) (-1212))) (-5 *2 (-112)))) + ((*1 *2 *1) (-12 (-4 *1 (-854)) (-5 *2 (-112)))) + ((*1 *2 *3 *1) + (-12 (-4 *1 (-1077 *4 *3)) (-4 *4 (-13 (-854) (-368))) + (-4 *3 (-1253 *4)) (-5 *2 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(-4 *1 (-369 *3 *2)) (-4 *3 (-1109)) (-4 *2 (-1109))))) -(((*1 *2 *3 *3) - (-12 (-4 *4 (-826)) (-14 *5 (-1186)) (-5 *2 (-650 (-1250 *5 *4))) - (-5 *1 (-1123 *4 *5)) (-5 *3 (-1250 *5 *4))))) -(((*1 *1 *2) (-12 (-5 *2 (-650 (-868))) (-5 *1 (-868))))) -(((*1 *2 *1) (-12 (-5 *2 (-1186)) (-5 *1 (-828))))) -(((*1 *2 *3) (-12 (-5 *2 (-650 (-570))) (-5 *1 (-452)) (-5 *3 (-570))))) + (-12 (-4 *4 (-13 (-562) (-1047 (-570)))) (-4 *5 (-436 *4)) + (-5 *2 (-424 *3)) (-5 *1 (-441 *4 *5 *3)) (-4 *3 (-1253 *5))))) (((*1 *2 *1) (-12 (-4 *1 (-167 *2)) (-4 *2 (-174)))) ((*1 *2 *3) (-12 (-4 *4 (-13 (-562) (-1047 (-570)))) (-5 *2 (-320 *4)) @@ -3382,49 +3246,46 @@ ((*1 *2 *2) (-12 (-4 *3 (-13 (-458) (-1047 (-570)) (-645 (-570)))) (-5 *1 (-1216 *3 *2)) (-4 *2 (-13 (-27) (-1212) (-436 *3)))))) -(((*1 *1) (-5 *1 (-158)))) -(((*1 *2 *2) (-12 (-5 *2 (-570)) (-5 *1 (-559))))) -(((*1 *1 *2 *1) - (-12 (-5 *2 (-1 *3 *3)) (-4 *1 (-57 *3 *4 *5)) (-4 *3 (-1227)) - (-4 *4 (-378 *3)) (-4 *5 (-378 *3)))) - ((*1 *1 *2 *1) 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(-5 *2 (-570)) (-5 *1 (-1209 *4)) + (-4 *4 (-1058))))) +(((*1 *2 *3 *3 *3 *3 *4 *4 *4 *5) + (-12 (-5 *3 (-227)) (-5 *4 (-570)) + (-5 *5 (-3 (|:| |fn| (-394)) (|:| |fp| (-64 -1707)))) + (-5 *2 (-1044)) (-5 *1 (-754))))) +(((*1 *2 *1) (-12 (-5 *2 (-112)) (-5 *1 (-1222 *3)) (-4 *3 (-983))))) +(((*1 *2 *1) (-12 (-5 *2 (-650 (-512))) (-5 *1 (-49)))) + ((*1 *2 *1) (-12 (-5 *2 (-650 (-882))) (-5 *1 (-489))))) (((*1 *2 *1) (-12 (-4 *1 (-167 *2)) (-4 *2 (-174)))) ((*1 *2 *3) (-12 (-4 *4 (-13 (-562) (-1047 (-570)))) (-5 *2 (-320 *4)) @@ -3434,44 +3295,45 @@ ((*1 *2 *2) (-12 (-4 *3 (-13 (-458) (-1047 (-570)) (-645 (-570)))) (-5 *1 (-1216 *3 *2)) (-4 *2 (-13 (-27) (-1212) (-436 *3)))))) -(((*1 *2 *1) (-12 (-4 *1 (-533)) (-5 *2 (-697 (-130)))))) -(((*1 *2 *3 *3 *4) - (|partial| -12 (-5 *4 (-1 *6 *6)) (-4 *6 (-1253 *5)) - (-4 *5 (-13 (-368) (-148) (-1047 (-570)))) - (-5 *2 - (-2 (|:| |a| *6) (|:| |b| (-413 *6)) (|:| |c| (-413 *6)) - (|:| -3608 *6))) - (-5 *1 (-1024 *5 *6)) (-5 *3 (-413 *6))))) 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(-4 *3 (-856)) (-4 *4 (-1058)) + (-5 *2 (-2 (|:| |k| (-825 *3)) (|:| |c| *4)))))) +(((*1 *2) (-12 (-5 *2 (-1168)) (-5 *1 (-765))))) +(((*1 *2 *1 *1 *3) + (-12 (-5 *3 (-1 (-112) *5 *5)) (-4 *5 (-13 (-1109) (-34))) + (-5 *2 (-112)) (-5 *1 (-1149 *4 *5)) (-4 *4 (-13 (-1109) (-34)))))) +(((*1 *2 *1) + (-12 (-4 *1 (-693 *3 *4 *5)) (-4 *3 (-1058)) (-4 *4 (-378 *3)) + (-4 *5 (-378 *3)) (-5 *2 (-650 (-650 *3))))) + ((*1 *2 *1) + (-12 (-4 *1 (-1062 *3 *4 *5 *6 *7)) (-4 *5 (-1058)) + (-4 *6 (-240 *4 *5)) (-4 *7 (-240 *3 *5)) (-5 *2 (-650 (-650 *5))))) + ((*1 *2 *1) + (-12 (-5 *2 (-650 (-650 *3))) (-5 *1 (-1198 *3)) (-4 *3 (-1109))))) +(((*1 *2 *1) (-12 (-5 *2 (-650 (-1186))) (-5 *1 (-1190))))) (((*1 *2 *1) (-12 (-5 *2 (-650 (-1226))) (-5 *1 (-687)))) ((*1 *2 *1) (-12 (-5 *2 (-650 (-1191))) (-5 *1 (-1127))))) -(((*1 *2 *1) - (-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 *1 *1) (-12 (-5 *1 (-344 *2 *3 *4)) (-14 *2 (-650 (-1186))) (-14 *3 (-650 (-1186))) (-4 *4 (-393)))) @@ -3481,26 +3343,23 @@ ((*1 *1 *2) (-12 (-5 *2 (-413 (-570))) (-4 *1 (-1021)))) ((*1 *1 *1 *2) (-12 (-4 *1 (-1021)) (-5 *2 (-928)))) ((*1 *1 *1) (-4 *1 (-1021)))) -(((*1 *2 *2 *2 *2) - (-12 (-5 *2 (-695 *3)) (-4 *3 (-1058)) (-5 *1 (-696 *3))))) -(((*1 *2 *1) (-12 (-4 *1 (-962)) (-5 *2 (-1103 (-227))))) - ((*1 *2 *1) (-12 (-4 *1 (-983)) (-5 *2 (-1103 (-227)))))) -(((*1 *2 *3) - (-12 (-5 *3 (-650 (-570))) (-5 *2 (-570)) (-5 *1 (-492 *4)) - (-4 *4 (-1253 *2))))) -(((*1 *2 *1) - (-12 (-4 *1 (-256 *3 *4 *5 *6)) (-4 *3 (-1058)) (-4 *4 (-856)) - (-4 *5 (-269 *4)) (-4 *6 (-799)) (-5 *2 (-650 *4))))) +(((*1 *2 *3 *4) + (-12 (-5 *4 (-650 *3)) (-4 *3 (-956 *5 *6 *7)) (-4 *5 (-458)) + (-4 *6 (-799)) (-4 *7 (-856)) + (-5 *2 (-2 (|:| |poly| *3) (|:| |mult| *5))) + (-5 *1 (-455 *5 *6 *7 *3))))) +(((*1 *2 *1) (|partial| -12 (-5 *1 (-370 *2)) (-4 *2 (-1109)))) + ((*1 *2 *1) (|partial| -12 (-5 *2 (-1168)) (-5 *1 (-1208))))) (((*1 *1 *2) (-12 (-5 *2 (-650 *3)) (-4 *3 (-1227)) (-4 *1 (-152 *3)))) ((*1 *1 *2) (-12 - (-5 *2 (-650 (-2 (|:| -3011 (-777)) (|:| -2178 *4) (|:| |num| *4)))) + (-5 *2 (-650 (-2 (|:| -1696 (-777)) (|:| -2288 *4) (|:| |num| *4)))) (-4 *4 (-1253 *3)) (-4 *3 (-13 (-368) (-148))) (-5 *1 (-405 *3 *4)))) ((*1 *1 *2 *3 *4) - (-12 (-5 *2 (-3 (|:| |fst| (-440)) (|:| -2559 "void"))) + (-12 (-5 *2 (-3 (|:| |fst| (-440)) (|:| -2713 "void"))) (-5 *3 (-650 (-959 (-570)))) (-5 *4 (-112)) (-5 *1 (-443)))) ((*1 *1 *2 *3 *4) - (-12 (-5 *2 (-3 (|:| |fst| (-440)) (|:| -2559 "void"))) + (-12 (-5 *2 (-3 (|:| |fst| (-440)) (|:| -2713 "void"))) (-5 *3 (-650 (-1186))) (-5 *4 (-112)) (-5 *1 (-443)))) ((*1 *2 *1) (-12 (-5 *2 (-1166 *3)) (-5 *1 (-607 *3)) (-4 *3 (-1227)))) @@ -3520,24 +3379,24 @@ ((*1 *1 *2 *3) (-12 (-5 *1 (-719 *2 *3 *4)) (-4 *2 (-856)) (-4 *3 (-1109)) (-14 *4 - (-1 (-112) (-2 (|:| -2160 *2) (|:| -3011 *3)) - (-2 (|:| -2160 *2) (|:| -3011 *3)))))) + (-1 (-112) (-2 (|:| -2266 *2) (|:| -1696 *3)) + (-2 (|:| -2266 *2) (|:| -1696 *3)))))) ((*1 *1 *2 *3) (-12 (-5 *2 (-512)) (-5 *3 (-1127)) (-5 *1 (-844)))) ((*1 *1 *2 *3) (-12 (-5 *1 (-879 *2 *3)) (-4 *2 (-1227)) (-4 *3 (-1227)))) ((*1 *1 *2) - (-12 (-5 *2 (-650 (-2 (|:| -2013 (-1186)) (|:| -2224 *4)))) + (-12 (-5 *2 (-650 (-2 (|:| -2106 (-1186)) (|:| -2339 *4)))) (-4 *4 (-1109)) (-5 *1 (-896 *3 *4)) (-4 *3 (-1109)))) ((*1 *2 *3 *4) (-12 (-5 *4 (-650 *5)) (-4 *5 (-13 (-1109) (-34))) (-5 *2 (-650 (-1149 *3 *5))) (-5 *1 (-1149 *3 *5)) (-4 *3 (-13 (-1109) (-34))))) ((*1 *2 *3) - (-12 (-5 *3 (-650 (-2 (|:| |val| *4) (|:| -3593 *5)))) + (-12 (-5 *3 (-650 (-2 (|:| |val| *4) (|:| -3684 *5)))) (-4 *4 (-13 (-1109) (-34))) (-4 *5 (-13 (-1109) (-34))) (-5 *2 (-650 (-1149 *4 *5))) (-5 *1 (-1149 *4 *5)))) ((*1 *1 *2) - (-12 (-5 *2 (-2 (|:| |val| *3) (|:| -3593 *4))) + (-12 (-5 *2 (-2 (|:| |val| *3) (|:| -3684 *4))) (-4 *3 (-13 (-1109) (-34))) (-4 *4 (-13 (-1109) (-34))) (-5 *1 (-1149 *3 *4)))) ((*1 *1 *2 *3) @@ -3560,26 +3419,13 @@ (-4 *4 (-13 (-1109) (-34))) (-5 *1 (-1150 *3 *4)))) ((*1 *1 *2 *3) (-12 (-5 *1 (-1175 *2 *3)) (-4 *2 (-1109)) (-4 *3 (-1109))))) -(((*1 *2 *1) - (-12 (-4 *1 (-1074 *3 *4 *5)) (-4 *3 (-1058)) (-4 *4 (-799)) - (-4 *5 (-856)) (-5 *2 (-112))))) -(((*1 *2 *1 *3) - (-12 (-5 *3 (-650 *1)) (-4 *1 (-1074 *4 *5 *6)) (-4 *4 (-1058)) - (-4 *5 (-799)) (-4 *6 (-856)) (-5 *2 (-112)))) - ((*1 *2 *1 *1) - (-12 (-4 *1 (-1074 *3 *4 *5)) (-4 *3 (-1058)) (-4 *4 (-799)) - (-4 *5 (-856)) (-5 *2 (-112)))) - ((*1 *2 *3 *1 *4) - (-12 (-5 *4 (-1 (-112) *3 *3)) (-4 *1 (-1220 *5 *6 *7 *3)) - (-4 *5 (-562)) (-4 *6 (-799)) (-4 *7 (-856)) - (-4 *3 (-1074 *5 *6 *7)) (-5 *2 (-112))))) -(((*1 *2 *1) - (-12 (-5 *2 (-112)) (-5 *1 (-1174 *3 *4)) (-14 *3 (-928)) - (-4 *4 (-1058))))) -(((*1 *2 *2 *3) - (-12 (-5 *3 (-618 *2)) (-4 *2 (-13 (-27) (-1212) (-436 *4))) - (-4 *4 (-13 (-562) (-1047 (-570)) (-645 (-570)))) - (-5 *1 (-280 *4 *2))))) +(((*1 *2 *3 *3 *4) + (-12 (-5 *4 (-777)) (-4 *5 (-562)) + (-5 *2 + (-2 (|:| |coef1| *3) (|:| |coef2| *3) (|:| |subResultant| *3))) + (-5 *1 (-978 *5 *3)) (-4 *3 (-1253 *5))))) +(((*1 *1 *2) (-12 (-5 *2 (-413 (-570))) (-5 *1 (-108)))) + ((*1 *1 *1 *2) (-12 (-5 *2 (-650 (-542))) (-5 *1 (-542))))) (((*1 *2 *2 *3) (-12 (-5 *3 (-1186)) (-4 *4 (-13 (-311) (-1047 (-570)) (-645 (-570)) (-148))) @@ -3588,20 +3434,31 @@ ((*1 *1 *1) (-5 *1 (-868))) ((*1 *2 *3) (-12 (-5 *2 (-1166 *3)) (-5 *1 (-1170 *3)) (-4 *3 (-1058))))) +(((*1 *1 *1 *2 *3 *1) + (-12 (-5 *2 (-777)) (-5 *1 (-788 *3)) (-4 *3 (-1058)))) + ((*1 *1 *1 *2 *3 *1) + (-12 (-5 *1 (-970 *3 *2)) (-4 *2 (-132)) (-4 *3 (-562)) + (-4 *3 (-1058)) (-4 *2 (-798)))) + ((*1 *1 *1 *2 *3 *1) + (-12 (-5 *2 (-777)) (-5 *1 (-1182 *3)) (-4 *3 (-1058)))) + ((*1 *1 *1 *2 *3 *1) + (-12 (-5 *2 (-980)) (-4 *2 (-132)) (-5 *1 (-1188 *3)) (-4 *3 (-562)) + (-4 *3 (-1058)))) + ((*1 *1 *1 *2 *3 *1) + (-12 (-5 *2 (-777)) (-5 *1 (-1250 *4 *3)) (-14 *4 (-1186)) + (-4 *3 (-1058))))) +(((*1 *1 *1 *2) (-12 (-5 *2 (-928)) (-4 *1 (-750 *3)) (-4 *3 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((*1 *1 *2) (-12 (-5 *2 (-334)) (-5 *1 (-404 *3 *4 *5 *6)) (-14 *3 (-1186)) - (-14 *4 (-3 (|:| |fst| (-440)) (|:| -2559 "void"))) + (-14 *4 (-3 (|:| |fst| (-440)) (|:| -2713 "void"))) (-14 *5 (-650 (-1186))) (-14 *6 (-1190)))) ((*1 *1 *2) (-12 (-5 *2 (-335 *4)) (-4 *4 (-13 (-856) (-21))) @@ -3968,14 +3818,14 @@ ((*1 *1 *2) (-12 (-5 *2 (-440)) (-5 *1 (-443)))) ((*1 *1 *2) (-12 - (-5 *2 (-2 (|:| |localSymbols| (-1190)) (|:| -3136 (-650 (-334))))) + (-5 *2 (-2 (|:| |localSymbols| (-1190)) (|:| -3261 (-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)) (|:| -3136 (-650 (-334))))) + (-5 *2 (-2 (|:| |localSymbols| (-1190)) (|:| -3261 (-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)))) @@ -4044,7 +3894,7 @@ 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+ (|:| |a0| *7))) + (-5 *1 (-580 *7 *8))))) +(((*1 *2 *2) (-12 (-5 *2 (-1182 *3)) (-4 *3 (-354)) (-5 *1 (-362 *3))))) (((*1 *2 *1) (-12 (-4 *1 (-256 *3 *4 *2 *5)) (-4 *3 (-1058)) (-4 *4 (-856)) (-4 *5 (-799)) (-4 *2 (-269 *4))))) -(((*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| *3) (|:| -3593 *4)))) - (-5 *1 (-1081 *5 *6 *7 *3 *4)) (-4 *4 (-1080 *5 *6 *7 *3))))) +(((*1 *2 *1 *1) + (-12 (-4 *3 (-562)) (-4 *3 (-1058)) (-4 *4 (-799)) (-4 *5 (-856)) + (-5 *2 (-650 *1)) (-4 *1 (-1074 *3 *4 *5))))) (((*1 *2 *3) (-12 (-5 *3 (-52)) (-5 *1 (-51 *2)) (-4 *2 (-1227)))) ((*1 *1 *2) (-12 (-5 *2 (-959 (-384))) (-5 *1 (-344 *3 *4 *5)) @@ -7630,11 +7025,11 @@ (-3 (|:| |nia| (-2 (|:| |var| (-1186)) (|:| |fn| (-320 (-227))) - (|:| -1990 (-1103 (-849 (-227)))) (|:| |abserr| (-227)) + (|:| -4043 (-1103 (-849 (-227)))) (|:| |abserr| (-227)) (|:| |relerr| (-227)))) (|:| |mdnia| (-2 (|:| |fn| (-320 (-227))) - (|:| -1990 (-650 (-1103 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*2 (-1268 *3))))) (((*1 *1 *1 *1) (-4 *1 (-21))) ((*1 *1 *1) (-4 *1 (-21))) @@ -8263,8 +7599,8 @@ (-12 (-5 *1 (-216 *2)) (-4 *2 (-13 (-856) - (-10 -8 (-15 -1877 ((-1168) $ (-1186))) (-15 -4131 ((-1282) $)) - (-15 -3807 ((-1282) $))))))) + (-10 -8 (-15 -1940 ((-1168) $ (-1186))) (-15 -4147 ((-1282) $)) + (-15 -3732 ((-1282) $))))))) ((*1 *1 *1 *2) (-12 (-5 *1 (-298 *2)) (-4 *2 (-21)) (-4 *2 (-1227)))) ((*1 *1 *2 *1) (-12 (-5 *1 (-298 *2)) (-4 *2 (-21)) (-4 *2 (-1227)))) ((*1 *1 *1 *1) @@ -8284,75 +7620,40 @@ ((*1 *2 *2 *2) (-12 (-5 *2 (-950 (-227))) (-5 *1 (-1223)))) ((*1 *1 *1 *1) (-12 (-4 *1 (-1275 *2)) (-4 *2 (-1227)) (-4 *2 (-21)))) ((*1 *1 *1) (-12 (-4 *1 (-1275 *2)) (-4 *2 (-1227)) (-4 *2 (-21))))) -(((*1 *2 *3 *1) - (-12 (-5 *3 (-1 (-112) *4)) (|has| *1 (-6 -4449)) (-4 *1 (-495 *4)) - (-4 *4 (-1227)) (-5 *2 (-112))))) -(((*1 *2 *3 *4) - (-12 (-5 *4 (-112)) (-4 *5 (-13 (-311) (-148))) (-4 *6 (-799)) - (-4 *7 (-856)) (-4 *8 (-1074 *5 *6 *7)) (-5 *2 (-650 *3)) - (-5 *1 (-597 *5 *6 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+ (-5 *1 (-1285 *4)) (-4 *4 (-368))))) +(((*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 -4399 ((-1134 *3 (-618 $)) $)) + (-15 -4413 ((-1134 *3 (-618 $)) $)) + (-15 -3799 ($ (-1134 *3 (-618 $)))))))))) +(((*1 *1 *1 *2) + (-12 (-5 *2 (-650 (-570))) (-5 *1 (-137 *3 *4 *5)) (-14 *3 (-570)) + (-14 *4 (-777)) (-4 *5 (-174))))) (((*1 *2 *1) (-12 (-5 *2 (-650 (-2 (|:| |var| (-1186)) (|:| |fn| (-320 (-227))) - (|:| -1990 (-1103 (-849 (-227)))) (|:| |abserr| (-227)) + (|:| -4043 (-1103 (-849 (-227)))) (|:| |abserr| (-227)) (|:| |relerr| (-227))))) (-5 *1 (-565)))) ((*1 *2 *1) @@ -9428,60 +8630,70 @@ (|:| |intvals| (-650 (-227))) (|:| |g| (-320 (-227))) (|:| |abserr| (-227)) (|:| |relerr| (-227))))) (-5 *1 (-809))))) -(((*1 *2 *3) (-12 (-5 *3 (-1168)) (-5 *2 (-928)) (-5 *1 (-792))))) +(((*1 *2 *3 *4 *2 *5 *6 *7 *8 *9 *10) + (|partial| -12 (-5 *2 (-650 (-1182 *13))) (-5 *3 (-1182 *13)) + (-5 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*2 (-112)) + (-5 *1 (-1228 *3))))) +(((*1 *1 *1 *2 *2 *1) + (-12 (-5 *2 (-570)) (-4 *1 (-693 *3 *4 *5)) (-4 *3 (-1058)) + (-4 *4 (-378 *3)) (-4 *5 (-378 *3))))) (((*1 *2 *3) - (-12 (-4 *1 (-354)) (-5 *3 (-570)) (-5 *2 (-1199 (-928) (-777)))))) + (-12 (-5 *3 (-695 (-320 (-227)))) + (-5 *2 + (-2 (|:| |stiffnessFactor| (-384)) (|:| |stabilityFactor| (-384)))) + (-5 *1 (-207))))) +(((*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 *1) - (-12 (-4 *1 (-57 *3 *4 *5)) (-4 *3 (-1227)) (-4 *4 (-378 *3)) - (-4 *5 (-378 *3)) (-5 *2 (-570)))) + (-12 (-4 *1 (-1294 *3 *4)) (-4 *3 (-856)) (-4 *4 (-1058)) + (-5 *2 (-112)))) ((*1 *2 *1) - (-12 (-4 *1 (-1062 *3 *4 *5 *6 *7)) (-4 *5 (-1058)) - (-4 *6 (-240 *4 *5)) (-4 *7 (-240 *3 *5)) (-5 *2 (-570))))) -(((*1 *2 *3 *4 *3 *4 *5 *3 *4 *3 *3 *3 *3) - (-12 (-5 *4 (-695 (-227))) (-5 *5 (-695 (-570))) (-5 *3 (-570)) - (-5 *2 (-1044)) (-5 *1 (-762))))) -(((*1 *2 *3 *4) - (-12 (-5 *4 (-1186)) (-5 *2 (-1 (-227) (-227))) (-5 *1 (-709 *3)) - (-4 *3 (-620 (-542))))) - ((*1 *2 *3 *4 *4) - (-12 (-5 *4 (-1186)) (-5 *2 (-1 (-227) (-227) (-227))) - (-5 *1 (-709 *3)) (-4 *3 (-620 (-542)))))) -(((*1 *2 *3) - (-12 (-5 *3 (-777)) (-5 *2 (-1282)) (-5 *1 (-872 *4 *5 *6 *7)) - (-4 *4 (-1058)) (-14 *5 (-650 (-1186))) (-14 *6 (-650 *3)) - (-14 *7 *3))) - ((*1 *2 *3) - (-12 (-5 *3 (-777)) (-4 *4 (-1058)) (-4 *5 (-856)) (-4 *6 (-799)) - (-14 *8 (-650 *5)) (-5 *2 (-1282)) - (-5 *1 (-1289 *4 *5 *6 *7 *8 *9 *10)) (-4 *7 (-956 *4 *6 *5)) - (-14 *9 (-650 *3)) (-14 *10 *3)))) + (-12 (-5 *2 (-112)) (-5 *1 (-1300 *3 *4)) (-4 *3 (-1058)) + (-4 *4 (-852))))) (((*1 *1 *2 *2) (-12 (-5 *2 - (-3 (|:| I (-320 (-570))) (|:| -1674 (-320 (-384))) + (-3 (|:| I (-320 (-570))) (|:| -1707 (-320 (-384))) (|:| CF (-320 (-171 (-384)))) (|:| |switch| (-1185)))) (-5 *1 (-1185))))) -(((*1 *1 *1 *2 *3) - (-12 (-5 *2 (-650 (-777))) (-5 *3 (-173)) (-5 *1 (-1174 *4 *5)) - (-14 *4 (-928)) (-4 *5 (-1058))))) -(((*1 *2 *3) - (-12 (-5 *3 (-650 (-570))) (-5 *2 (-650 (-695 (-570)))) - (-5 *1 (-1119))))) -(((*1 *2 *3 *3 *4 *4 *3 *4 *4 *3 *3 *3) - (-12 (-5 *3 (-570)) (-5 *4 (-695 (-227))) (-5 *2 (-1044)) - (-5 *1 (-758))))) -(((*1 *2 *3 *3 *3 *4 *5 *5 *3) - (-12 (-5 *3 (-570)) (-5 *5 (-695 (-227))) (-5 *4 (-227)) - (-5 *2 (-1044)) (-5 *1 (-758))))) +(((*1 *2 *1) + (-12 (-5 *2 (-650 (-52))) (-5 *1 (-899 *3)) (-4 *3 (-1109))))) +(((*1 *2 *3) (-12 (-5 *2 (-115)) (-5 *1 (-114 *3)) (-4 *3 (-1109))))) (((*1 *2 *2) (-12 (-4 *3 (-562)) (-5 *1 (-279 *3 *2)) (-4 *2 (-13 (-436 *3) (-1011))))) @@ -9498,52 +8710,87 @@ ((*1 *2 *2) (-12 (-5 *2 (-1166 *3)) (-4 *3 (-38 (-413 (-570)))) (-5 *1 (-1172 *3))))) -(((*1 *2 *1) (-12 (-4 *1 (-23)) (-5 *2 (-112)))) - ((*1 *2 *1) (-12 (-5 *2 (-112)) (-5 *1 (-55)))) - ((*1 *2 *1) - (-12 (-4 *3 (-368)) (-4 *4 (-799)) (-4 *5 (-856)) (-5 *2 (-112)) - (-5 *1 (-510 *3 *4 *5 *6)) (-4 *6 (-956 *3 *4 *5)))) - ((*1 *2 *1) (-12 (-4 *1 (-652 *3)) (-4 *3 (-1067)) (-5 *2 (-112)))) - ((*1 *2 *1) (-12 (-4 *1 (-1060 *3)) (-4 *3 (-1067)) (-5 *2 (-112)))) - ((*1 *2 *3 *1) - (-12 (-4 *1 (-1077 *4 *3)) (-4 *4 (-13 (-854) (-368))) - (-4 *3 (-1253 *4)) (-5 *2 (-112))))) -(((*1 *1 *1 *1) (-5 *1 (-868)))) -(((*1 *2 *3 *3 *3 *3 *4 *5 *6 *6 *7 *7 *3) - (-12 (-5 *4 (-650 (-112))) (-5 *5 (-695 (-227))) - (-5 *6 (-695 (-570))) (-5 *7 (-227)) (-5 *3 (-570)) (-5 *2 (-1044)) - (-5 *1 (-760))))) -(((*1 *2 *2 *3 *4) - (|partial| -12 (-5 *3 (-777)) (-4 *4 (-13 (-562) (-148))) - (-5 *1 (-1247 *4 *2)) (-4 *2 (-1253 *4))))) -(((*1 *2 *3) - (-12 (-4 *4 (-562)) (-4 *5 (-799)) (-4 *6 (-856)) - (-4 *7 (-1074 *4 *5 *6)) - (-5 *2 (-2 (|:| |goodPols| (-650 *7)) (|:| |badPols| (-650 *7)))) - (-5 *1 (-986 *4 *5 *6 *7)) (-5 *3 (-650 *7))))) -(((*1 *1 *2 *2) - (-12 - (-5 *2 - (-3 (|:| I (-320 (-570))) (|:| -1674 (-320 (-384))) - (|:| CF (-320 (-171 (-384)))) (|:| |switch| (-1185)))) - (-5 *1 (-1185))))) -(((*1 *2 *2) - (-12 (-5 *2 (-650 *6)) (-4 *6 (-1074 *3 *4 *5)) (-4 *3 (-562)) - (-4 *4 (-799)) (-4 *5 (-856)) (-5 *1 (-986 *3 *4 *5 *6))))) (((*1 *2 *3 *4 *4 *4 *4 *5 *5) (-12 (-5 *3 (-1 (-384) (-384))) (-5 *4 (-384)) (-5 *2 - (-2 (|:| -2196 *4) (|:| -3577 *4) (|:| |totalpts| (-570)) + (-2 (|:| -2307 *4) (|:| -3669 *4) (|:| |totalpts| (-570)) (|:| |success| (-112)))) (-5 *1 (-795)) (-5 *5 (-570))))) -(((*1 *2 *3) (-12 (-5 *3 (-828)) (-5 *2 (-52)) (-5 *1 (-835))))) -(((*1 *2 *3 *4 *4 *5 *4 *3 *6 *3 *4 *7 *8 *9 *10) - (-12 (-5 *4 (-570)) (-5 *5 (-1168)) (-5 *6 (-695 (-227))) - (-5 *7 (-3 (|:| |fn| (-394)) (|:| |fp| (-89 G)))) - (-5 *8 (-3 (|:| |fn| (-394)) (|:| |fp| (-86 FCN)))) - (-5 *9 (-3 (|:| |fn| (-394)) (|:| |fp| (-71 PEDERV)))) - (-5 *10 (-3 (|:| |fn| (-394)) (|:| |fp| (-88 OUTPUT)))) - (-5 *3 (-227)) (-5 *2 (-1044)) (-5 *1 (-755))))) +(((*1 *2 *3 *4 *4 *4) + (-12 (-5 *3 (-650 *8)) (-5 *4 (-112)) (-4 *8 (-1074 *5 *6 *7)) + (-4 *5 (-458)) (-4 *6 (-799)) (-4 *7 (-856)) + (-5 *2 (-650 (-1036 *5 *6 *7 *8))) (-5 *1 (-1036 *5 *6 *7 *8)))) + ((*1 *2 *3 *4 *4 *4) + (-12 (-5 *3 (-650 *8)) (-5 *4 (-112)) (-4 *8 (-1074 *5 *6 *7)) + (-4 *5 (-458)) (-4 *6 (-799)) (-4 *7 (-856)) + (-5 *2 (-650 (-1155 *5 *6 *7 *8))) (-5 *1 (-1155 *5 *6 *7 *8))))) +(((*1 *1 *2) + (-12 + (-5 *2 + (-650 + (-2 + (|:| -2106 + (-2 (|:| |var| (-1186)) (|:| |fn| (-320 (-227))) + (|:| -4043 (-1103 (-849 (-227)))) (|:| |abserr| (-227)) + (|:| |relerr| (-227)))) + (|:| -2339 + (-2 + (|:| |endPointContinuity| + (-3 (|:| |continuous| "Continuous at the end points") + (|:| |lowerSingular| + "There is a singularity at the lower end point") + (|:| |upperSingular| + "There is a singularity at the upper end point") + (|:| |bothSingular| + "There are singularities at both end points") + (|:| |notEvaluated| + "End point continuity not yet evaluated"))) + (|:| |singularitiesStream| + (-3 (|:| |str| (-1166 (-227))) + (|:| |notEvaluated| + "Internal singularities not yet evaluated"))) + (|:| -4043 + (-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 *2 *2) (-12 (-5 *2 (-227)) (-5 *1 (-228)))) + ((*1 *2 *2 *2) (-12 (-5 *2 (-171 (-227))) (-5 *1 (-228)))) + ((*1 *2 *2 *2) + (-12 (-4 *3 (-562)) (-5 *1 (-437 *3 *2)) (-4 *2 (-436 *3)))) + ((*1 *1 *1 *1) (-4 *1 (-1148)))) +(((*1 *2 *3 *3) + (-12 + (-5 *3 + (-2 (|:| |lcmfij| *5) (|:| |totdeg| (-777)) (|:| |poli| *7) + (|:| |polj| *7))) + (-4 *5 (-799)) (-4 *7 (-956 *4 *5 *6)) (-4 *4 (-458)) (-4 *6 (-856)) + (-5 *2 (-112)) (-5 *1 (-455 *4 *5 *6 *7))))) +(((*1 *2 *3 *4 *5 *6 *5) + (-12 (-5 *4 (-171 (-227))) (-5 *5 (-570)) (-5 *6 (-1168)) + (-5 *3 (-227)) (-5 *2 (-1044)) (-5 *1 (-764))))) +(((*1 *1 *2 *2) + (-12 + (-5 *2 + (-3 (|:| I (-320 (-570))) (|:| -1707 (-320 (-384))) + (|:| CF (-320 (-171 (-384)))) (|:| |switch| (-1185)))) + (-5 *1 (-1185))))) +(((*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 *1) + (-12 (-4 *4 (-1109)) (-5 *2 (-896 *3 *5)) (-5 *1 (-892 *3 *4 *5)) + (-4 *3 (-1109)) (-4 *5 (-672 *4))))) +(((*1 *2 *1 *3) (-12 (-5 *3 (-227)) (-5 *2 (-1282)) (-5 *1 (-828))))) +(((*1 *1) (-5 *1 (-142)))) (((*1 *2 *2) (-12 (-4 *3 (-562)) (-5 *1 (-279 *3 *2)) (-4 *2 (-13 (-436 *3) (-1011))))) @@ -9563,62 +8810,67 @@ ((*1 *2 *2) (-12 (-5 *2 (-1166 *3)) (-4 *3 (-38 (-413 (-570)))) (-5 *1 (-1172 *3))))) -(((*1 *2 *1) (-12 (-4 *1 (-962)) (-5 *2 (-650 (-650 (-950 (-227))))))) - ((*1 *2 *1) (-12 (-4 *1 (-983)) (-5 *2 (-650 (-650 (-950 (-227)))))))) -(((*1 *2 *3 *3) - (-12 (-4 *4 (-13 (-368) (-148) (-1047 (-570)))) (-4 *5 (-1253 *4)) - (-5 *2 (-2 (|:| |ans| (-413 *5)) (|:| |nosol| (-112)))) - (-5 *1 (-1024 *4 *5)) (-5 *3 (-413 *5))))) -(((*1 *1 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(-12 (-5 *4 (-112)) (-4 *5 (-458)) (-4 *6 (-799)) (-4 *7 (-856)) + (-5 *2 (-650 (-1036 *5 *6 *7 *3))) (-5 *1 (-1036 *5 *6 *7 *3)) + (-4 *3 (-1074 *5 *6 *7)))) + ((*1 *1 *2 *1) + (-12 (-5 *2 (-650 *6)) (-4 *1 (-1080 *3 *4 *5 *6)) (-4 *3 (-458)) + (-4 *4 (-799)) (-4 *5 (-856)) (-4 *6 (-1074 *3 *4 *5)))) + ((*1 *1 *2 *1) + (-12 (-4 *1 (-1080 *3 *4 *5 *2)) (-4 *3 (-458)) (-4 *4 (-799)) + (-4 *5 (-856)) (-4 *2 (-1074 *3 *4 *5)))) + ((*1 *2 *3 *1 *4 *4 *4 *4 *4) + (-12 (-5 *4 (-112)) (-4 *5 (-458)) (-4 *6 (-799)) (-4 *7 (-856)) + (-5 *2 (-650 (-1155 *5 *6 *7 *3))) (-5 *1 (-1155 *5 *6 *7 *3)) + (-4 *3 (-1074 *5 *6 *7))))) +(((*1 *2 *3) + (|partial| -12 (-4 *5 (-1047 (-48))) + (-4 *4 (-13 (-562) (-1047 (-570)))) (-4 *5 (-436 *4)) + (-5 *2 (-424 (-1182 (-48)))) (-5 *1 (-441 *4 *5 *3)) + (-4 *3 (-1253 *5))))) +(((*1 *2 *1) + (-12 (-5 *2 (-1182 (-413 (-959 *3)))) (-5 *1 (-459 *3 *4 *5 *6)) + (-4 *3 (-562)) (-4 *3 (-174)) (-14 *4 (-928)) + (-14 *5 (-650 (-1186))) (-14 *6 (-1277 (-695 *3)))))) (((*1 *1 *1) (-5 *1 (-1185))) ((*1 *1 *2) (-12 (-5 *2 - (-3 (|:| I (-320 (-570))) (|:| -1674 (-320 (-384))) + (-3 (|:| I (-320 (-570))) (|:| -1707 (-320 (-384))) (|:| CF (-320 (-171 (-384)))) (|:| |switch| (-1185)))) (-5 *1 (-1185))))) -(((*1 *2 *1) (-12 (-5 *2 (-424 *3)) (-5 *1 (-921 *3)) (-4 *3 (-311))))) -(((*1 *1 *1 *1) (-12 (-4 *1 (-378 *2)) (-4 *2 (-1227)) (-4 *2 (-856)))) - ((*1 *1 *2 *1 *1) - (-12 (-5 *2 (-1 (-112) *3 *3)) (-4 *1 (-378 *3)) (-4 *3 (-1227)))) - ((*1 *1 *1 *1) (-12 (-4 *1 (-977 *2)) (-4 *2 (-856)))) - ((*1 *1 *1 *1) (-12 (-4 *1 (-1143 *2)) (-4 *2 (-1058)))) - ((*1 *1 *2) - (-12 (-5 *2 (-650 *1)) (-4 *1 (-1143 *3)) (-4 *3 (-1058)))) - ((*1 *1 *2) - (-12 (-5 *2 (-650 (-1174 *3 *4))) (-5 *1 (-1174 *3 *4)) - (-14 *3 (-928)) (-4 *4 (-1058)))) - ((*1 *1 *1 *1) - (-12 (-5 *1 (-1174 *2 *3)) (-14 *2 (-928)) (-4 *3 (-1058))))) -(((*1 *1 *1 *1 *1 *2) - (-12 (-5 *2 (-777)) (-4 *1 (-1074 *3 *4 *5)) (-4 *3 (-1058)) - (-4 *4 (-799)) (-4 *5 (-856)) (-4 *3 (-562))))) -(((*1 *2 *1) (-12 (-5 *2 (-777)) (-5 *1 (-331 *3)) (-4 *3 (-1227)))) - ((*1 *2 *1) - (-12 (-5 *2 (-777)) (-5 *1 (-522 *3 *4)) (-4 *3 (-1227)) - (-14 *4 (-570))))) -(((*1 *2 *3 *4 *5) - (-12 (-5 *4 (-112)) (-4 *6 (-13 (-458) (-1047 (-570)) (-645 (-570)))) - (-4 *3 (-13 (-27) (-1212) (-436 *6) (-10 -8 (-15 -3735 ($ *7))))) - (-4 *7 (-854)) - (-4 *8 - (-13 (-1255 *3 *7) (-368) (-1212) - (-10 -8 (-15 -3447 ($ $)) (-15 -3722 ($ $))))) - (-5 *2 - (-3 (|:| |%series| *8) - (|:| |%problem| (-2 (|:| |func| (-1168)) (|:| |prob| (-1168)))))) - (-5 *1 (-428 *6 *3 *7 *8 *9 *10)) (-5 *5 (-1168)) (-4 *9 (-992 *8)) - (-14 *10 (-1186))))) +(((*1 *2 *3) + (|partial| -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 + (-2 (|:| |stiffness| (-384)) (|:| |stability| (-384)) + (|:| |expense| (-384)) (|:| |accuracy| (-384)) + (|:| |intermediateResults| (-384)))) + (-5 *1 (-809))))) +(((*1 *2 *3 *4 *5 *6 *3 *3 *3 *3 *6 *3 *7 *8) + (-12 (-5 *3 (-570)) (-5 *4 (-695 (-227))) (-5 *5 (-112)) + (-5 *6 (-227)) (-5 *7 (-3 (|:| |fn| (-394)) (|:| |fp| (-68 APROD)))) + (-5 *8 (-3 (|:| |fn| (-394)) (|:| |fp| (-73 MSOLVE)))) + (-5 *2 (-1044)) (-5 *1 (-762))))) +(((*1 *2 *3) + (-12 (-5 *3 (-1182 *7)) (-4 *7 (-956 *6 *4 *5)) (-4 *4 (-799)) + (-4 *5 (-856)) (-4 *6 (-1058)) (-5 *2 (-1182 *6)) + (-5 *1 (-325 *4 *5 *6 *7))))) (((*1 *2 *2) (-12 (-4 *3 (-562)) (-5 *1 (-279 *3 *2)) (-4 *2 (-13 (-436 *3) (-1011))))) @@ -9638,62 +8890,44 @@ ((*1 *2 *2) (-12 (-5 *2 (-1166 *3)) (-4 *3 (-38 (-413 (-570)))) (-5 *1 (-1172 *3))))) -(((*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 *4 *3 *5 *5 *5 *5 *5) - (|partial| -12 (-5 *5 (-112)) (-4 *6 (-458)) (-4 *7 (-799)) - (-4 *8 (-856)) (-4 *9 (-1074 *6 *7 *8)) - (-5 *2 - (-2 (|:| -4302 (-650 *9)) (|:| -3593 *4) (|:| |ineq| (-650 *9)))) - (-5 *1 (-997 *6 *7 *8 *9 *4)) (-5 *3 (-650 *9)) - (-4 *4 (-1080 *6 *7 *8 *9)))) - ((*1 *2 *3 *4 *3 *5 *5 *5 *5 *5) - (|partial| -12 (-5 *5 (-112)) (-4 *6 (-458)) (-4 *7 (-799)) - (-4 *8 (-856)) (-4 *9 (-1074 *6 *7 *8)) - (-5 *2 - (-2 (|:| -4302 (-650 *9)) (|:| -3593 *4) (|:| |ineq| (-650 *9)))) - (-5 *1 (-1116 *6 *7 *8 *9 *4)) (-5 *3 (-650 *9)) - (-4 *4 (-1080 *6 *7 *8 *9))))) -(((*1 *2 *1) (-12 (-4 *1 (-395)) (-5 *2 (-112))))) -(((*1 *2 *3 *3 *3 *4 *3) - (-12 (-5 *3 (-570)) (-5 *4 (-695 (-171 (-227)))) (-5 *2 (-1044)) - (-5 *1 (-760))))) -(((*1 *2 *3 *4 *5) - (-12 (-5 *4 (-650 *7)) (-5 *5 (-650 (-650 *8))) (-4 *7 (-856)) - (-4 *8 (-311)) (-4 *6 (-799)) (-4 *9 (-956 *8 *6 *7)) - (-5 *2 - (-2 (|:| |unitPart| *9) - (|:| |suPart| - (-650 (-2 (|:| -3739 (-1182 *9)) (|:| -3011 (-570))))))) - (-5 *1 (-748 *6 *7 *8 *9)) (-5 *3 (-1182 *9))))) -(((*1 *2 *2 *3) - (-12 (-5 *2 (-899 *4)) (-4 *4 (-1109)) (-5 *1 (-897 *4 *3)) - (-4 *3 (-1227)))) - ((*1 *1 *1 *2) (-12 (-5 *2 (-52)) (-5 *1 (-899 *3)) (-4 *3 (-1109))))) -(((*1 *1) (-5 *1 (-443)))) -(((*1 *2 *2 *2) - (|partial| -12 (-4 *3 (-13 (-562) (-148))) (-5 *1 (-1247 *3 *2)) - (-4 *2 (-1253 *3))))) -(((*1 *2 *3) (-12 (-5 *3 (-227)) (-5 *2 (-1168)) (-5 *1 (-194)))) - ((*1 *2 *3) (-12 (-5 *3 (-227)) (-5 *2 (-1168)) (-5 *1 (-304)))) - ((*1 *2 *3) (-12 (-5 *3 (-227)) (-5 *2 (-1168)) (-5 *1 (-309))))) +(((*1 *2 *3 *4 *4 *5 *4 *3 *6 *3 *4 *7 *8 *9 *10) + (-12 (-5 *4 (-570)) (-5 *5 (-1168)) (-5 *6 (-695 (-227))) + (-5 *7 (-3 (|:| |fn| (-394)) (|:| |fp| (-89 G)))) + (-5 *8 (-3 (|:| |fn| (-394)) (|:| |fp| (-86 FCN)))) + (-5 *9 (-3 (|:| |fn| (-394)) (|:| |fp| (-71 PEDERV)))) + (-5 *10 (-3 (|:| |fn| (-394)) (|:| |fp| (-88 OUTPUT)))) + (-5 *3 (-227)) (-5 *2 (-1044)) (-5 *1 (-755))))) (((*1 *2 *3) - (-12 (-5 *3 (-1168)) (-4 *4 (-13 (-311) (-148))) - (-4 *5 (-13 (-856) (-620 (-1186)))) (-4 *6 (-799)) - (-5 *2 - (-650 - (-2 (|:| |eqzro| (-650 *7)) (|:| |neqzro| (-650 *7)) - (|:| |wcond| (-650 (-959 *4))) - (|:| |bsoln| - (-2 (|:| |partsol| (-1277 (-413 (-959 *4)))) - (|:| -2003 (-650 (-1277 (-413 (-959 *4)))))))))) - (-5 *1 (-931 *4 *5 *6 *7)) (-4 *7 (-956 *4 *6 *5))))) + (-12 (-5 *3 (-3 (|:| |fst| (-440)) (|:| -2713 "void"))) + (-5 *2 (-1282)) (-5 *1 (-1189)))) + ((*1 *2 *3 *4) + (-12 (-5 *3 (-1186)) + (-5 *4 (-3 (|:| |fst| (-440)) (|:| -2713 "void"))) (-5 *2 (-1282)) + (-5 *1 (-1189)))) + ((*1 *2 *3 *4 *1) + (-12 (-5 *3 (-1186)) + (-5 *4 (-3 (|:| |fst| (-440)) (|:| -2713 "void"))) (-5 *2 (-1282)) + (-5 *1 (-1189))))) +(((*1 *1) (-5 *1 (-295)))) +(((*1 *2 *2) + (-12 (-5 *2 (-950 *3)) (-4 *3 (-13 (-368) (-1212) (-1011))) + (-5 *1 (-178 *3))))) +(((*1 *2 *3) + (-12 (-5 *3 (-650 *2)) (-4 *2 (-436 *4)) (-5 *1 (-159 *4 *2)) + (-4 *4 (-562))))) +(((*1 *1 *1) + (-12 (-4 *1 (-1220 *2 *3 *4 *5)) (-4 *2 (-562)) (-4 *3 (-799)) + (-4 *4 (-856)) (-4 *5 (-1074 *2 *3 *4))))) +(((*1 *2 *3 *4) + (|partial| -12 (-5 *3 (-1277 *4)) (-4 *4 (-645 (-570))) + (-5 *2 (-1277 (-413 (-570)))) (-5 *1 (-1304 *4))))) +(((*1 *2 *3 *3) + (-12 (-5 *3 (-1188 (-413 (-570)))) (-5 *2 (-413 (-570))) + (-5 *1 (-192))))) +(((*1 *2 *1 *3) + (-12 (-5 *3 (-1277 *1)) (-4 *1 (-372 *4)) (-4 *4 (-174)) + (-5 *2 (-695 *4)))) + ((*1 *2 *1) (-12 (-4 *1 (-423 *3)) (-4 *3 (-174)) (-5 *2 (-695 *3))))) (((*1 *2 *2) (-12 (-4 *3 (-562)) (-5 *1 (-279 *3 *2)) (-4 *2 (-13 (-436 *3) (-1011))))) @@ -9713,25 +8947,53 @@ ((*1 *2 *2) (-12 (-5 *2 (-1166 *3)) (-4 *3 (-38 (-413 (-570)))) (-5 *1 (-1172 *3))))) -(((*1 *2 *1) (-12 (-5 *2 (-112)) (-5 *1 (-899 *3)) (-4 *3 (-1109))))) -(((*1 *1 *1 *2) (-12 (-5 *2 (-928)) (-4 *1 (-750 *3)) (-4 *3 (-174))))) -(((*1 *1 *2) (-12 (-5 *2 (-320 (-171 (-384)))) (-5 *1 (-334)))) - ((*1 *1 *2) (-12 (-5 *2 (-320 (-570))) (-5 *1 (-334)))) - ((*1 *1 *2) (-12 (-5 *2 (-320 (-384))) (-5 *1 (-334)))) - ((*1 *1 *2) (-12 (-5 *2 (-320 (-700))) (-5 *1 (-334)))) - ((*1 *1 *2) (-12 (-5 *2 (-320 (-707))) (-5 *1 (-334)))) - ((*1 *1 *2) (-12 (-5 *2 (-320 (-705))) (-5 *1 (-334)))) - ((*1 *1) (-5 *1 (-334)))) +(((*1 *2 *3 *1) + (-12 (-4 *4 (-458)) (-4 *5 (-799)) (-4 *6 (-856)) + (-4 *3 (-1074 *4 *5 *6)) (-5 *2 (-3 (-112) (-650 *1))) + (-4 *1 (-1080 *4 *5 *6 *3))))) +(((*1 *2 *3 *4) + (-12 (-5 *3 (-650 (-413 (-959 *5)))) (-5 *4 (-650 (-1186))) + (-4 *5 (-562)) (-5 *2 (-650 (-650 (-959 *5)))) (-5 *1 (-1195 *5))))) +(((*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 *1) (-12 (-4 *1 (-962)) (-5 *2 (-650 (-650 (-950 (-227))))))) + ((*1 *2 *1) (-12 (-4 *1 (-983)) (-5 *2 (-650 (-650 (-950 (-227)))))))) (((*1 *2 *3) - (-12 (-5 *3 (-650 *7)) (-4 *7 (-1074 *4 *5 *6)) (-4 *4 (-562)) - (-4 *5 (-799)) (-4 *6 (-856)) (-5 *2 (-650 (-1290 *4 *5 *6 *7))) - (-5 *1 (-1290 *4 *5 *6 *7)))) - ((*1 *2 *3 *4 *5) - (-12 (-5 *3 (-650 *9)) (-5 *4 (-1 (-112) *9 *9)) - (-5 *5 (-1 *9 *9 *9)) (-4 *9 (-1074 *6 *7 *8)) (-4 *6 (-562)) - (-4 *7 (-799)) (-4 *8 (-856)) (-5 *2 (-650 (-1290 *6 *7 *8 *9))) - (-5 *1 (-1290 *6 *7 *8 *9))))) -(((*1 *2 *1 *1) (-12 (-4 *1 (-311)) (-5 *2 (-112))))) + (-12 (-4 *4 (-368)) (-4 *4 (-562)) (-4 *5 (-1253 *4)) + (-5 *2 (-2 (|:| -2118 (-629 *4 *5)) (|:| -4082 (-413 *5)))) + (-5 *1 (-629 *4 *5)) (-5 *3 (-413 *5)))) + ((*1 *2 *1) + (-12 (-5 *2 (-650 (-1174 *3 *4))) (-5 *1 (-1174 *3 *4)) + (-14 *3 (-928)) (-4 *4 (-1058)))) + ((*1 *2 *1 *1) + (-12 (-4 *3 (-458)) (-4 *3 (-1058)) + (-5 *2 (-2 (|:| |primePart| *1) (|:| |commonPart| *1))) + (-4 *1 (-1253 *3))))) +(((*1 *2 *1) + (|partial| -12 (-4 *1 (-167 *3)) (-4 *3 (-174)) (-4 *3 (-551)) + (-5 *2 (-413 (-570))))) + ((*1 *2 *1) + (|partial| -12 (-5 *2 (-413 (-570))) (-5 *1 (-424 *3)) (-4 *3 (-551)) + (-4 *3 (-562)))) + ((*1 *2 *1) (|partial| -12 (-4 *1 (-551)) (-5 *2 (-413 (-570))))) + ((*1 *2 *1) + (|partial| -12 (-4 *1 (-803 *3)) (-4 *3 (-174)) (-4 *3 (-551)) + (-5 *2 (-413 (-570))))) + ((*1 *2 *1) + (|partial| -12 (-5 *2 (-413 (-570))) (-5 *1 (-839 *3)) (-4 *3 (-551)) + (-4 *3 (-1109)))) + ((*1 *2 *1) + (|partial| -12 (-5 *2 (-413 (-570))) (-5 *1 (-849 *3)) (-4 *3 (-551)) + (-4 *3 (-1109)))) + ((*1 *2 *1) + (|partial| -12 (-4 *1 (-1006 *3)) (-4 *3 (-174)) (-4 *3 (-551)) + (-5 *2 (-413 (-570))))) + ((*1 *2 *3) + (|partial| -12 (-5 *2 (-413 (-570))) (-5 *1 (-1017 *3)) + (-4 *3 (-1047 *2))))) +(((*1 *2 *2 *2) + (-12 (-4 *3 (-1058)) (-5 *1 (-1249 *3 *2)) (-4 *2 (-1253 *3))))) (((*1 *2 *3 *2 *3) (-12 (-5 *2 (-443)) (-5 *3 (-1186)) (-5 *1 (-1189)))) ((*1 *2 *3 *2) (-12 (-5 *2 (-443)) (-5 *3 (-1186)) (-5 *1 (-1189)))) @@ -9744,17 +9006,12 @@ (-12 (-5 *2 (-443)) (-5 *3 (-1186)) (-5 *1 (-1190)))) ((*1 *2 *3 *2 *1) (-12 (-5 *2 (-443)) (-5 *3 (-650 (-1186))) (-5 *1 (-1190))))) -(((*1 *2 *2) (|partial| -12 (-4 *1 (-992 *2)) (-4 *2 (-1212))))) -(((*1 *2 *1) - (-12 (-5 *2 (-777)) (-5 *1 (-1174 *3 *4)) (-14 *3 (-928)) - (-4 *4 (-1058))))) -(((*1 *2 *3 *4 *4 *3 *5 *3 *6 *4 *7 *8 *9) - (-12 (-5 *4 (-570)) (-5 *5 (-1168)) (-5 *6 (-695 (-227))) - (-5 *7 (-3 (|:| |fn| (-394)) (|:| |fp| (-89 G)))) - (-5 *8 (-3 (|:| |fn| (-394)) (|:| |fp| (-86 FCN)))) - (-5 *9 (-3 (|:| |fn| (-394)) (|:| |fp| (-88 OUTPUT)))) - (-5 *3 (-227)) (-5 *2 (-1044)) (-5 *1 (-755))))) -(((*1 *2 *1) (-12 (-5 *2 (-295)) (-5 *1 (-284))))) +(((*1 *2 *2 *3) + (|partial| -12 (-5 *3 (-777)) (-4 *1 (-992 *2)) (-4 *2 (-1212))))) +(((*1 *2 *3) + (-12 (-5 *3 (-1182 *4)) (-4 *4 (-354)) + (-5 *2 (-1277 (-650 (-2 (|:| -2307 *4) (|:| -2266 (-1129)))))) + (-5 *1 (-351 *4))))) (((*1 *1 *1) (-4 *1 (-95))) ((*1 *2 *2) (-12 (-4 *3 (-562)) (-5 *1 (-279 *3 *2)) @@ -9771,38 +9028,33 @@ ((*1 *2 *2) (-12 (-5 *2 (-1166 *3)) (-4 *3 (-38 (-413 (-570)))) (-5 *1 (-1172 *3))))) -(((*1 *2 *1 *3 *4) - (-12 (-5 *3 (-474)) (-5 *4 (-928)) (-5 *2 (-1282)) (-5 *1 (-1278))))) -(((*1 *2 *1) (-12 (-4 *1 (-1296 *3)) (-4 *3 (-368)) (-5 *2 (-112))))) -(((*1 *1 *2) (-12 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*2 - (-3 (|:| I (-320 (-570))) (|:| -1674 (-320 (-384))) + (-3 (|:| I (-320 (-570))) (|:| -1707 (-320 (-384))) (|:| CF (-320 (-171 (-384)))) (|:| |switch| (-1185)))) (-5 *1 (-1185))))) (((*1 *1 *1) (-4 *1 (-95))) @@ -9975,52 +9254,39 @@ ((*1 *2 *2) (-12 (-5 *2 (-1166 *3)) (-4 *3 (-38 (-413 (-570)))) (-5 *1 (-1172 *3))))) -(((*1 *2 *3 *4 *4 *3 *5 *3 *3 *4 *3 *6) - (-12 (-5 *3 (-570)) (-5 *4 (-695 (-227))) (-5 *5 (-227)) - (-5 *6 (-3 (|:| |fn| (-394)) (|:| |fp| (-78 FUNCTN)))) - (-5 *2 (-1044)) (-5 *1 (-754))))) -(((*1 *2 *3) - (-12 (-4 *4 (-562)) (-4 *5 (-799)) (-4 *6 (-856)) - (-4 *7 (-1074 *4 *5 *6)) - (-5 *2 (-650 (-2 (|:| -4104 *1) (|:| -1726 (-650 *7))))) - (-5 *3 (-650 *7)) (-4 *1 (-1220 *4 *5 *6 *7))))) +(((*1 *2 *2 *3) + (-12 + (-5 *2 + (-2 (|:| |partsol| (-1277 (-413 (-959 *4)))) + (|:| -4169 (-650 (-1277 (-413 (-959 *4))))))) + (-5 *3 (-650 *7)) (-4 *4 (-13 (-311) (-148))) + (-4 *7 (-956 *4 *6 *5)) (-4 *5 (-13 (-856) (-620 (-1186)))) + (-4 *6 (-799)) (-5 *1 (-931 *4 *5 *6 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- (-12 (-5 *2 (-1 (-950 *3) (-950 *3))) (-5 *1 (-178 *3)) - (-4 *3 (-13 (-368) (-1212) (-1011)))))) + (-12 (-5 *3 (-227)) (-5 *4 (-570)) (-5 *2 (-1044)) (-5 *1 (-764))))) (((*1 *1 *2 *2) (-12 (-5 *2 - (-3 (|:| I (-320 (-570))) (|:| -1674 (-320 (-384))) + (-3 (|:| I (-320 (-570))) (|:| -1707 (-320 (-384))) (|:| CF (-320 (-171 (-384)))) (|:| |switch| (-1185)))) (-5 *1 (-1185))))) (((*1 *1 *1) (-4 *1 (-95))) @@ -10042,25 +9308,18 @@ ((*1 *2 *2) (-12 (-5 *2 (-1166 *3)) (-4 *3 (-38 (-413 (-570)))) (-5 *1 (-1172 *3))))) -(((*1 *1 *2 *3) - (-12 (-5 *2 (-1277 *3)) (-4 *3 (-1253 *4)) (-4 *4 (-1231)) - (-4 *1 (-347 *4 *3 *5)) (-4 *5 (-1253 (-413 *3)))))) -(((*1 *2 *1) - (|partial| -12 (-4 *1 (-956 *3 *4 *2)) (-4 *3 (-1058)) (-4 *4 (-799)) - (-4 *2 (-856)))) - ((*1 *2 *3) - (|partial| -12 (-4 *4 (-799)) (-4 *5 (-1058)) (-4 *6 (-956 *5 *4 *2)) - (-4 *2 (-856)) (-5 *1 (-957 *4 *2 *5 *6 *3)) - (-4 *3 - (-13 (-368) - (-10 -8 (-15 -3735 ($ *6)) (-15 -4399 (*6 $)) - (-15 -4413 (*6 $))))))) - ((*1 *2 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*3) + (-12 (-5 *3 (-928)) (-4 *4 (-373)) (-4 *4 (-368)) (-5 *2 (-1182 *1)) + (-4 *1 (-333 *4)))) + ((*1 *2 *1) (-12 (-4 *1 (-333 *3)) (-4 *3 (-368)) (-5 *2 (-1182 *3)))) + ((*1 *2 *1) + (-12 (-4 *1 (-375 *3 *2)) (-4 *3 (-174)) (-4 *3 (-368)) + (-4 *2 (-1253 *3)))) + ((*1 *2 *3) + (-12 (-5 *3 (-1277 *4)) (-4 *4 (-354)) (-5 *2 (-1182 *4)) + (-5 *1 (-534 *4))))) +(((*1 *2 *1) (-12 (-5 *2 (-112)) (-5 *1 (-283))))) +(((*1 *2 *1) (-12 (-5 *2 (-650 (-650 (-950 (-227))))) (-5 *1 (-474))))) (((*1 *1 *2 *2) (-12 (-5 *2 - (-3 (|:| I (-320 (-570))) (|:| -1674 (-320 (-384))) + (-3 (|:| I (-320 (-570))) (|:| -1707 (-320 (-384))) (|:| CF (-320 (-171 (-384)))) (|:| |switch| (-1185)))) (-5 *1 (-1185))))) (((*1 *2 *2) @@ -10116,7 +9382,7 @@ ((*1 *1 *1) (-4 *1 (-288))) ((*1 *2 *3) (-12 (-5 *3 (-424 *4)) (-4 *4 (-562)) - (-5 *2 (-650 (-2 (|:| -1442 (-777)) (|:| |logand| *4)))) + (-5 *2 (-650 (-2 (|:| -1452 (-777)) (|:| |logand| *4)))) (-5 *1 (-324 *4)))) ((*1 *1 *1) (-12 (-5 *1 (-344 *2 *3 *4)) (-14 *2 (-650 (-1186))) @@ -10152,43 +9418,49 @@ (-12 (-5 *2 (-1166 *3)) (-4 *3 (-38 (-413 (-570)))) (-5 *1 (-1172 *3)))) ((*1 *1 *1) (-4 *1 (-1215)))) -(((*1 *2 *2 *3) - (-12 (-5 *2 (-650 (-959 *4))) (-5 *3 (-650 (-1186))) (-4 *4 (-458)) - (-5 *1 (-925 *4))))) -(((*1 *2 *3) (-12 (-5 *3 (-868)) (-5 *2 (-1168)) (-5 *1 (-716))))) -(((*1 *2 *2 *3) - (-12 (-5 *3 (-650 *2)) (-4 *2 (-956 *4 *5 *6)) (-4 *4 (-368)) - (-4 *4 (-458)) (-4 *5 (-799)) (-4 *6 (-856)) - (-5 *1 (-456 *4 *5 *6 *2)))) - ((*1 *2 *3 *4 *5) - (-12 (-5 *4 (-99 *6)) (-5 *5 (-1 *6 *6)) (-4 *6 (-368)) - (-5 *2 - (-2 (|:| R (-695 *6)) (|:| A (-695 *6)) (|:| |Ainv| (-695 *6)))) - (-5 *1 (-987 *6)) (-5 *3 (-695 *6))))) -(((*1 *1) (-5 *1 (-145))) - ((*1 *2 *3) - (-12 (-5 *3 (-650 (-266))) (-5 *2 (-1142 (-227))) (-5 *1 (-264)))) - ((*1 *1 *2) (-12 (-5 *2 (-1142 (-227))) (-5 *1 (-266))))) +(((*1 *1 *1 *1 *1 *2) + (-12 (-5 *2 (-777)) (-4 *1 (-1074 *3 *4 *5)) (-4 *3 (-1058)) + (-4 *4 (-799)) (-4 *5 (-856)) (-4 *3 (-562))))) +(((*1 *2 *1) + 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(-384))) + (-3 (|:| I (-320 (-570))) (|:| -1707 (-320 (-384))) (|:| CF (-320 (-171 (-384)))) (|:| |switch| (-1185)))) (-5 *1 (-1185))))) (((*1 *2 *2) @@ -10207,29 +9479,46 @@ (-12 (-5 *2 (-1166 *3)) (-4 *3 (-38 (-413 (-570)))) (-5 *1 (-1172 *3)))) ((*1 *1 *1) (-4 *1 (-1215)))) -(((*1 *2 *1 *1) (-12 (-4 *1 (-34)) (-5 *2 (-112))))) -(((*1 *1 *2) (-12 (-5 *2 (-650 *3)) (-4 *3 (-1109)) (-5 *1 (-912 *3))))) -(((*1 *2 *3 *3 *4 *5) - (-12 (-5 *3 (-650 (-959 *6))) (-5 *4 (-650 (-1186))) (-4 *6 (-458)) - (-5 *2 (-650 (-650 *7))) (-5 *1 (-544 *6 *7 *5)) (-4 *7 (-368)) - (-4 *5 (-13 (-368) (-854)))))) -(((*1 *1 *1) - (-12 (-5 *1 (-601 *2)) (-4 *2 (-38 (-413 (-570)))) (-4 *2 (-1058))))) -(((*1 *1 *1 *1) - (-12 (-4 *1 (-693 *2 *3 *4)) (-4 *2 (-1058)) (-4 *3 (-378 *2)) - (-4 *4 (-378 *2))))) +(((*1 *2 *1) (-12 (-5 *2 (-777)) (-5 *1 (-331 *3)) (-4 *3 (-1227)))) + ((*1 *2 *1) + (-12 (-5 *2 (-777)) (-5 *1 (-522 *3 *4)) (-4 *3 (-1227)) + (-14 *4 (-570))))) (((*1 *2 *3) - (-12 (-5 *2 (-1166 (-570))) (-5 *1 (-1170 *4)) (-4 *4 (-1058)) - (-5 *3 (-570))))) + (-12 (-5 *3 (-650 (-1168))) (-5 *2 (-1168)) (-5 *1 (-194)))) + ((*1 *1 *2) (-12 (-5 *2 (-650 (-868))) (-5 *1 (-868))))) +(((*1 *2 *3 *4) + (-12 (-5 *3 (-1277 *1)) (-5 *4 (-1 *5 *5)) (-4 *5 (-368)) + (-4 *1 (-730 *5 *6)) (-4 *5 (-174)) (-4 *6 (-1253 *5)) + (-5 *2 (-695 *5))))) +(((*1 *2 *1) (|partial| -12 (-5 *2 (-650 (-283))) (-5 *1 (-283)))) + ((*1 *2 *1) (-12 (-5 *2 (-650 (-1191))) (-5 *1 (-1191))))) +(((*1 *2 *3 *2 *4) + (-12 (-5 *3 (-115)) (-5 *4 (-777)) + (-4 *5 (-13 (-458) (-1047 (-570)))) (-4 *5 (-562)) + (-5 *1 (-41 *5 *2)) (-4 *2 (-436 *5)) + (-4 *2 + (-13 (-368) (-306) + (-10 -8 (-15 -4399 ((-1134 *5 (-618 $)) $)) + (-15 -4413 ((-1134 *5 (-618 $)) $)) + (-15 -3799 ($ (-1134 *5 (-618 $)))))))))) (((*1 *2 *3) - (-12 (-5 *2 (-1 (-950 *3) (-950 *3))) (-5 *1 (-178 *3)) - (-4 *3 (-13 (-368) (-1212) (-1011)))))) -(((*1 *2 *3 *4 *5) - (-12 (-5 *5 (-570)) (-4 *6 (-799)) (-4 *7 (-856)) (-4 *8 (-311)) - (-4 *9 (-956 *8 *6 *7)) - (-5 *2 (-2 (|:| -4239 (-1182 *9)) (|:| |polval| (-1182 *8)))) - (-5 *1 (-748 *6 *7 *8 *9)) (-5 *3 (-1182 *9)) (-5 *4 (-1182 *8))))) -(((*1 *2 *1) (|partial| -12 (-5 *2 (-512)) (-5 *1 (-283))))) + (-12 (-4 *4 (-13 (-368) (-148) (-1047 (-413 (-570))))) + (-4 *5 (-1253 *4)) + (-5 *2 (-650 (-2 (|:| |deg| (-777)) (|:| -4306 *5)))) + (-5 *1 (-815 *4 *5 *3 *6)) (-4 *3 (-662 *5)) + (-4 *6 (-662 (-413 *5)))))) +(((*1 *1) (-5 *1 (-1072)))) +(((*1 *2 *3 *4) + (-12 (-5 *3 (-650 (-695 *5))) (-5 *4 (-570)) (-4 *5 (-368)) + (-4 *5 (-1058)) (-5 *2 (-112)) (-5 *1 (-1038 *5)))) + ((*1 *2 *3) + (-12 (-5 *3 (-650 (-695 *4))) (-4 *4 (-368)) (-4 *4 (-1058)) + (-5 *2 (-112)) (-5 *1 (-1038 *4))))) +(((*1 *2 *1) (-12 (-4 *1 (-1102 *2)) (-4 *2 (-1227))))) +(((*1 *2 *3 *1) + (-12 (-4 *1 (-985 *4 *5 *6 *3)) (-4 *4 (-1058)) (-4 *5 (-799)) + (-4 *6 (-856)) (-4 *3 (-1074 *4 *5 *6)) (-4 *4 (-562)) + (-5 *2 (-2 (|:| |rnum| *4) (|:| |polnum| *3) (|:| |den| *4)))))) (((*1 *2 *2) (-12 (-4 *3 (-562)) (-5 *1 (-279 *3 *2)) (-4 *2 (-13 (-436 *3) (-1011))))) @@ -10247,25 +9536,52 @@ (-5 *1 (-1172 *3)))) ((*1 *1 *1) (-4 *1 (-1215)))) (((*1 *2 *3 *4) - (-12 (-5 *3 (-227)) (-5 *4 (-570)) (-5 *2 (-1044)) (-5 *1 (-764))))) -(((*1 *2 *1) (|partial| -12 (-5 *2 (-1182 *1)) (-4 *1 (-1021))))) -(((*1 *2 *1 *3 *3 *3 *2) - (-12 (-5 *3 (-777)) (-5 *1 (-681 *2)) (-4 *2 (-1109))))) -(((*1 *1 *1 *1 *1) (-4 *1 (-551)))) -(((*1 *2 *1) (-12 (-5 *2 (-112)) (-5 *1 (-1208))))) -(((*1 *2 *1) (|partial| -12 (-5 *2 (-1182 *1)) (-4 *1 (-1021))))) -(((*1 *2 *3) (-12 (-5 *2 (-424 *3)) (-5 *1 (-564 *3)) (-4 *3 (-551))))) -(((*1 *2 *3 *3) - (-12 (-5 *3 (-650 *7)) (-4 *7 (-1074 *4 *5 *6)) (-4 *4 (-458)) - (-4 *5 (-799)) (-4 *6 (-856)) (-5 *2 (-112)) - (-5 *1 (-997 *4 *5 *6 *7 *8)) (-4 *8 (-1080 *4 *5 *6 *7)))) - ((*1 *2 *3 *3) - (-12 (-5 *3 (-650 *7)) (-4 *7 (-1074 *4 *5 *6)) (-4 *4 (-458)) - (-4 *5 (-799)) (-4 *6 (-856)) (-5 *2 (-112)) - (-5 *1 (-1116 *4 *5 *6 *7 *8)) (-4 *8 (-1080 *4 *5 *6 *7))))) + (-12 (-5 *4 (-650 (-650 *8))) (-5 *3 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-4201 ($ $))))) + (-5 *2 + (-3 (|:| |%series| *8) + (|:| |%problem| (-2 (|:| |func| (-1168)) (|:| |prob| (-1168)))))) + (-5 *1 (-428 *6 *3 *7 *8 *9 *10)) (-5 *5 (-1168)) (-4 *9 (-992 *8)) + (-14 *10 (-1186))))) +(((*1 *2 *1 *1) + (-12 (-4 *1 (-1074 *3 *4 *5)) (-4 *3 (-1058)) (-4 *4 (-799)) + (-4 *5 (-856)) (-5 *2 (-112))))) +(((*1 *2 *3) + (-12 (-5 *3 (-1168)) (-5 *2 (-650 (-1191))) (-5 *1 (-887))))) +(((*1 *2 *3) + (-12 (-5 *3 (-695 *4)) (-4 *4 (-368)) (-5 *2 (-1182 *4)) + (-5 *1 (-538 *4 *5 *6)) (-4 *5 (-368)) (-4 *6 (-13 (-368) (-854)))))) +(((*1 *2 *3) + (-12 (-5 *3 (-570)) (|has| *1 (-6 -4440)) (-4 *1 (-410)) + (-5 *2 (-928))))) +(((*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 *2) (-12 (-4 *3 (-562)) (-5 *1 (-279 *3 *2)) (-4 *2 (-13 (-436 *3) (-1011))))) @@ -10285,126 +9601,88 @@ (-12 (-5 *2 (-1166 *3)) (-4 *3 (-38 (-413 (-570)))) (-5 *1 (-1172 *3)))) ((*1 *1 *1) (-4 *1 (-1215)))) -(((*1 *2 *3 *4 *4 *3 *3 *5) - (|partial| -12 (-5 *4 (-618 *3)) (-5 *5 (-1182 *3)) - (-4 *3 (-13 (-436 *6) (-27) (-1212))) - (-4 *6 (-13 (-458) (-1047 (-570)) (-148) (-645 (-570)))) - (-5 *2 (-2 (|:| -3585 *3) (|:| |coeff| *3))) - (-5 *1 (-566 *6 *3 *7)) (-4 *7 (-1109)))) - ((*1 *2 *3 *4 *4 *3 *4 *3 *5) - (|partial| -12 (-5 *4 (-618 *3)) (-5 *5 (-413 (-1182 *3))) - (-4 *3 (-13 (-436 *6) (-27) (-1212))) - (-4 *6 (-13 (-458) (-1047 (-570)) (-148) (-645 (-570)))) - (-5 *2 (-2 (|:| -3585 *3) (|:| |coeff| *3))) - (-5 *1 (-566 *6 *3 *7)) (-4 *7 (-1109))))) (((*1 *2 *1) (-12 (-4 *1 (-1112 *3 *4 *5 *6 *2)) (-4 *3 (-1109)) (-4 *4 (-1109)) (-4 *5 (-1109)) (-4 *6 (-1109)) (-4 *2 (-1109))))) -(((*1 *1 *2 *1) (-12 (-4 *1 (-107 *2)) (-4 *2 (-1227)))) - ((*1 *1 *2 *1) (-12 (-5 *1 (-122 *2)) (-4 *2 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|lowerInfinite| - "The bottom of range is infinite") - (|:| |upperInfinite| "The top of range is infinite") - (|:| |bothInfinite| - "Both top and bottom points are infinite") - (|:| |notEvaluated| "Range not yet evaluated"))))))) - (-5 *1 (-565)))) - ((*1 *1 *2 *1 *3) - (-12 (-5 *3 (-777)) (-4 *1 (-701 *2)) (-4 *2 (-1109)))) - ((*1 *1 *2) - (-12 - (-5 *2 - (-2 - (|:| -2013 - (-2 (|:| |xinit| (-227)) (|:| |xend| (-227)) - (|:| |fn| (-1277 (-320 (-227)))) (|:| |yinit| (-650 (-227))) - (|:| |intvals| (-650 (-227))) (|:| |g| (-320 (-227))) - (|:| |abserr| (-227)) (|:| |relerr| (-227)))) - (|:| -2224 - (-2 (|:| |stiffness| (-384)) (|:| |stability| (-384)) - (|:| |expense| (-384)) (|:| |accuracy| (-384)) - (|:| |intermediateResults| (-384)))))) - (-5 *1 (-809)))) - ((*1 *2 *3 *4) - (-12 (-5 *2 (-1282)) (-5 *1 (-1204 *3 *4)) (-4 *3 (-1109)) - (-4 *4 (-1109))))) -(((*1 *2 *3) - (-12 - (-5 *3 - (-510 (-413 (-570)) (-242 *5 (-777)) (-870 *4) - (-249 *4 (-413 (-570))))) - (-14 *4 (-650 (-1186))) 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(-650 *9)) (|:| -3684 *4) (|:| |ineq| (-650 *9)))) + (-5 *1 (-997 *6 *7 *8 *9 *4)) (-5 *3 (-650 *9)) + (-4 *4 (-1080 *6 *7 *8 *9)))) + ((*1 *2 *3 *4 *3 *5 *5 *5 *5 *5) + (|partial| -12 (-5 *5 (-112)) (-4 *6 (-458)) (-4 *7 (-799)) + (-4 *8 (-856)) (-4 *9 (-1074 *6 *7 *8)) + (-5 *2 + (-2 (|:| -4306 (-650 *9)) (|:| -3684 *4) (|:| |ineq| (-650 *9)))) + (-5 *1 (-1116 *6 *7 *8 *9 *4)) (-5 *3 (-650 *9)) + (-4 *4 (-1080 *6 *7 *8 *9))))) +(((*1 *1 *1 *1) (-4 *1 (-144))) + ((*1 *2 *2 *2) + (-12 (-4 *3 (-562)) (-5 *1 (-159 *3 *2)) (-4 *2 (-436 *3)))) + ((*1 *2 *2 *2) (-12 (-5 *1 (-160 *2)) (-4 *2 (-551)))) + ((*1 *1 *1 *1) (-5 *1 (-868))) + ((*1 *2 *3 *4) + (-12 (-5 *4 |RationalNumber|) (-5 *2 (-1 (-570))) (-5 *1 (-1056)) + (-5 *3 (-570))))) +(((*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 *2 *2) (-12 (-4 *3 (-562)) (-5 *1 (-279 *3 *2)) (-4 *2 (-13 (-436 *3) (-1011))))) @@ -10425,45 +9703,72 @@ (-12 (-5 *2 (-1166 *3)) (-4 *3 (-38 (-413 (-570)))) (-5 *1 (-1172 *3)))) ((*1 *1 *1) (-4 *1 (-1215)))) -(((*1 *2 *3) (-12 (-5 *3 (-847)) (-5 *2 (-1044)) (-5 *1 (-846)))) - ((*1 *2 *3 *4) - (-12 (-5 *3 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(-5 *1 (-43 *3 *4)) + (-4 *4 (-423 *3))))) +(((*1 *2 *2) + (-12 (-5 *2 (-950 *3)) (-4 *3 (-13 (-368) (-1212) (-1011))) + (-5 *1 (-178 *3))))) +(((*1 *2 *3 *3) + (-12 (-4 *4 (-562)) (-5 *2 (-2 (|:| |coef1| *3) (|:| -1942 *3))) + (-5 *1 (-978 *4 *3)) (-4 *3 (-1253 *4))))) +(((*1 *2 *3 *3) (-12 (-5 *3 (-1168)) (-5 *2 (-112)) (-5 *1 (-835))))) +(((*1 *2 *3 *2) (-12 - (-5 *5 - (-2 (|:| |done| (-650 *11)) - (|:| |todo| (-650 (-2 (|:| |val| *3) (|:| -3593 *11)))))) - (-5 *6 (-777)) - (-5 *2 (-650 (-2 (|:| |val| (-650 *10)) (|:| -3593 *11)))) - (-5 *3 (-650 *10)) (-5 *4 (-650 *11)) (-4 *10 (-1074 *7 *8 *9)) - (-4 *11 (-1080 *7 *8 *9 *10)) (-4 *7 (-458)) (-4 *8 (-799)) - (-4 *9 (-856)) (-5 *1 (-1078 *7 *8 *9 *10 *11)))) - ((*1 *2 *3 *4 *2 *5 *6) + (-5 *2 + (-2 (|:| |theta| (-227)) (|:| |phi| (-227)) (|:| -4304 (-227)) + (|:| |scaleX| (-227)) (|:| |scaleY| (-227)) (|:| |scaleZ| (-227)) + (|:| |deltaX| (-227)) (|:| |deltaY| (-227)))) + (-5 *3 (-650 (-266))) (-5 *1 (-264)))) + ((*1 *1 *2) (-12 - 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(-12 (-5 *3 (-570)) (-5 *4 (-384)) (-5 *2 (-1282)) (-5 *1 (-1279)))) + ((*1 *2 *1 *3) + (-12 + (-5 *3 + (-2 (|:| |theta| (-227)) (|:| |phi| (-227)) (|:| -4304 (-227)) + (|:| |scaleX| (-227)) (|:| |scaleY| (-227)) (|:| |scaleZ| (-227)) + (|:| |deltaX| (-227)) (|:| |deltaY| (-227)))) + (-5 *2 (-1282)) (-5 *1 (-1279)))) + ((*1 *2 *1) + (-12 + (-5 *2 + (-2 (|:| |theta| (-227)) (|:| |phi| (-227)) (|:| -4304 (-227)) + (|:| |scaleX| (-227)) (|:| |scaleY| (-227)) (|:| |scaleZ| (-227)) + (|:| |deltaX| (-227)) (|:| |deltaY| (-227)))) + (-5 *1 (-1279)))) + ((*1 *2 *1 *3 *3 *3 *3 *3) + (-12 (-5 *3 (-384)) (-5 *2 (-1282)) (-5 *1 (-1279))))) (((*1 *1 *1) (-4 *1 (-551)))) -(((*1 *1 *2 *3) (-12 (-5 *2 (-512)) (-5 *3 (-1127)) (-5 *1 (-1124))))) +(((*1 *2 *3 *3 *3 *4 *5) + (-12 (-5 *5 (-1 *3 *3)) (-4 *3 (-1253 *6)) + (-4 *6 (-13 (-368) (-148) (-1047 *4))) (-5 *4 (-570)) + (-5 *2 + (-3 (|:| |ans| (-2 (|:| |ans| *3) (|:| |nosol| (-112)))) + (|:| -4306 + (-2 (|:| |b| *3) (|:| |c| *3) (|:| |m| *4) (|:| 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*3 (-174)) - (-4 *5 (-240 (-2426 *2) (-777))) + (-4 *5 (-240 (-2569 *2) (-777))) (-14 *6 - (-1 (-112) (-2 (|:| -2160 *4) (|:| -3011 *5)) - (-2 (|:| -2160 *4) (|:| -3011 *5)))) + (-1 (-112) (-2 (|:| -2266 *4) (|:| -1696 *5)) + (-2 (|:| -2266 *4) (|:| -1696 *5)))) (-5 *1 (-467 *2 *3 *4 *5 *6 *7)) (-4 *4 (-856)) (-4 *7 (-956 *3 *5 (-870 *2))))) ((*1 *1 *1) (-12 (-4 *1 (-515 *2 *3)) (-4 *2 (-1109)) (-4 *3 (-856)))) @@ -13681,42 +13258,69 @@ ((*1 *1 *1) (-12 (-5 *1 (-1300 *2 *3)) (-4 *2 (-1058)) (-4 *3 (-852))))) (((*1 *1) (-4 *1 (-976)))) -(((*1 *2 *1) (-12 (-5 *2 (-650 (-177))) (-5 *1 (-1094))))) -(((*1 *2 *1) (-12 (-5 *2 (-112)) (-5 *1 (-899 *3)) (-4 *3 (-1109))))) -(((*1 *2 *3) - (-12 (-5 *3 (-650 (-570))) (-5 *2 (-1188 (-413 (-570)))) - (-5 *1 (-192))))) -(((*1 *1 *2) - (-12 (-5 *2 (-695 *4)) (-4 *4 (-1058)) (-5 *1 (-1151 *3 *4)) - (-14 *3 (-777))))) -(((*1 *2 *3 *4) - (-12 (-5 *3 (-3 (-413 (-959 *5)) (-1175 (-1186) (-959 *5)))) - (-4 *5 (-458)) (-5 *2 (-650 (-695 (-413 (-959 *5))))) - 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(-777))))) +(((*1 *1 *1 *1) (-12 (-4 *1 (-858 *2)) (-4 *2 (-1058)) (-4 *2 (-368))))) +(((*1 *2 *2) + (-12 (-5 *2 (-650 (-487 *3 *4))) (-14 *3 (-650 (-1186))) + (-4 *4 (-458)) (-5 *1 (-637 *3 *4))))) (((*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)))) @@ -13725,6 +13329,36 @@ ((*1 *2 *3 *1) (-12 (-5 *3 (-570)) (-5 *2 (-1282)) (-5 *1 (-1166 *4)) (-4 *4 (-1109)) (-4 *4 (-1227))))) +(((*1 *1 *2) (-12 (-5 *2 (-650 *1)) (-4 *1 (-458)))) + ((*1 *1 *1 *1) (-4 *1 (-458))) + ((*1 *2 *3) + (-12 (-5 *3 (-650 *2)) (-5 *1 (-492 *2)) (-4 *2 (-1253 (-570))))) + ((*1 *2 *2 *2 *3) + (-12 (-5 *3 (-570)) (-5 *1 (-702 *2)) (-4 *2 (-1253 *3)))) + ((*1 *1 *1 *1) (-5 *1 (-777))) + ((*1 *2 *2 *2) + (-12 (-4 *3 (-799)) (-4 *4 (-856)) (-4 *5 (-311)) + (-5 *1 (-923 *3 *4 *5 *2)) (-4 *2 (-956 *5 *3 *4)))) + ((*1 *2 *3) + (-12 (-5 *3 (-650 *2)) (-4 *2 (-956 *6 *4 *5)) + (-5 *1 (-923 *4 *5 *6 *2)) (-4 *4 (-799)) (-4 *5 (-856)) + (-4 *6 (-311)))) + ((*1 *2 *2 *2) + (-12 (-5 *2 (-1182 *6)) (-4 *6 (-956 *5 *3 *4)) (-4 *3 (-799)) + (-4 *4 (-856)) (-4 *5 (-311)) (-5 *1 (-923 *3 *4 *5 *6)))) + ((*1 *2 *3) + (-12 (-5 *3 (-650 (-1182 *7))) (-4 *4 (-799)) (-4 *5 (-856)) + (-4 *6 (-311)) (-5 *2 (-1182 *7)) (-5 *1 (-923 *4 *5 *6 *7)) + (-4 *7 (-956 *6 *4 *5)))) + ((*1 *1 *1 *1) (-5 *1 (-928))) + ((*1 *2 *2 *2) + (-12 (-4 *3 (-458)) (-4 *3 (-562)) (-5 *1 (-978 *3 *2)) + (-4 *2 (-1253 *3)))) + ((*1 *2 *2 *1) + (-12 (-4 *1 (-1074 *2 *3 *4)) (-4 *2 (-1058)) (-4 *3 (-799)) + (-4 *4 (-856)) (-4 *2 (-458))))) +(((*1 *2) (-12 (-5 *2 (-650 (-1168))) (-5 *1 (-1280)))) + ((*1 *2 *2) (-12 (-5 *2 (-650 (-1168))) (-5 *1 (-1280))))) (((*1 *2 *1 *3 *3 *2) (-12 (-5 *3 (-570)) (-4 *1 (-57 *2 *4 *5)) (-4 *2 (-1227)) (-4 *4 (-378 *2)) (-4 *5 (-378 *2)))) @@ -13756,14 +13390,14 @@ (-12 (-5 *3 (-1186)) (-5 *2 (-247 (-1168))) (-5 *1 (-216 *4)) (-4 *4 (-13 (-856) - (-10 -8 (-15 -1877 ((-1168) $ *3)) (-15 -4131 ((-1282) $)) - 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(-1047 (-570)) (-1047 (-413 (-570))))) - (-5 *2 (-650 (-413 *6))) (-5 *1 (-818 *5 *6))))) + (-12 (-5 *3 (-650 (-650 (-950 (-227))))) + (-5 *2 (-650 (-1103 (-227)))) (-5 *1 (-935))))) +(((*1 *2 *3) + (-12 (-4 *4 (-562)) (-5 *2 (-171 *5)) (-5 *1 (-606 *4 *5 *3)) + (-4 *5 (-13 (-436 *4) (-1011) (-1212))) + (-4 *3 (-13 (-436 (-171 *4)) (-1011) (-1212)))))) +(((*1 *1 *2) (-12 (-5 *2 (-1168)) (-5 *1 (-585))))) +(((*1 *1) (-5 *1 (-158))) + ((*1 *2 *1) (-12 (-4 *1 (-1053 *2)) (-4 *2 (-23))))) +(((*1 *1 *2) (-12 (-5 *2 (-650 (-868))) (-5 *1 (-868))))) (((*1 *2 *1 *2 *3) (-12 (-5 *3 (-650 (-1168))) (-5 *2 (-1168)) (-5 *1 (-1278)))) ((*1 *2 *1 *2 *2) (-12 (-5 *2 (-1168)) (-5 *1 (-1278)))) @@ -14627,93 +14352,109 @@ (-12 (-5 *3 (-650 (-1168))) (-5 *2 (-1168)) (-5 *1 (-1279)))) ((*1 *2 *1 *2 *2) (-12 (-5 *2 (-1168)) (-5 *1 (-1279)))) ((*1 *2 *1 *2) (-12 (-5 *2 (-1168)) (-5 *1 (-1279))))) -(((*1 *2 *2 *1) (-12 (-4 *1 (-257 *2)) (-4 *2 (-1227))))) -(((*1 *2 *3 *3 *3) - (|partial| -12 (-4 *4 (-13 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|continuous| "Continuous at the end points") + (|:| |lowerSingular| + "There is a singularity at the lower end point") + (|:| |upperSingular| + "There is a singularity at the upper end point") + (|:| |bothSingular| "There are singularities at both end points") + (|:| |notEvaluated| "End point continuity not yet evaluated"))) + (-5 *1 (-194))))) +(((*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 *1) (-12 (-5 *2 (-777)) (-5 *1 (-912 *3)) (-4 *3 (-1109))))) +(((*1 *2 *1) (-12 (-5 *2 (-650 (-570))) (-5 *1 (-278))))) +(((*1 *2 *1) (-12 (-5 *2 (-1144)) (-5 *1 (-523))))) +(((*1 *2 *3 *2) + (-12 (-5 *3 (-413 (-570))) + (-4 *4 (-13 (-562) (-1047 (-570)) (-645 (-570)))) + (-5 *1 (-280 *4 *2)) (-4 *2 (-13 (-27) (-1212) (-436 *4)))))) +(((*1 *2 *3 *4 *5 *3) (-12 (-5 *4 (-1 *7 *7)) - (-5 *5 (-1 (-3 (-2 (|:| -3585 *6) (|:| |coeff| *6)) "failed") *6)) + (-5 *5 + (-1 (-2 (|:| |ans| *6) (|:| -4410 *6) (|:| |sol?| 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(-1186)))) (-4 *6 (-799)) (-5 *2 (-112)) + (-5 *1 (-931 *4 *5 *6 *7)) (-4 *7 (-956 *4 *6 *5))))) +(((*1 *2 *3 *2) + (-12 (-5 *3 (-650 (-1085 *4 *5 *2))) (-4 *4 (-1109)) + (-4 *5 (-13 (-1058) (-893 *4) (-620 (-899 *4)))) + (-4 *2 (-13 (-436 *5) (-893 *4) (-620 (-899 *4)))) + (-5 *1 (-54 *4 *5 *2)))) + ((*1 *2 *3 *2 *4) + (-12 (-5 *3 (-650 (-1085 *5 *6 *2))) (-5 *4 (-928)) (-4 *5 (-1109)) + (-4 *6 (-13 (-1058) (-893 *5) (-620 (-899 *5)))) + (-4 *2 (-13 (-436 *6) (-893 *5) (-620 (-899 *5)))) + (-5 *1 (-54 *5 *6 *2))))) (((*1 *2 *1) (-12 (-5 *2 (-1282)) (-5 *1 (-1278)))) ((*1 *2 *1) (-12 (-5 *2 (-1282)) (-5 *1 (-1279))))) (((*1 *2 *2 *3 *3) @@ -14815,9 +14556,7 @@ ((*1 *2 *1 *3) (-12 (-4 *1 (-1255 *3 *4)) (-4 *3 (-1058)) (-4 *4 (-798)) (|has| *3 (-15 ** (*3 *3 *4))) (-5 *2 (-1166 *3))))) -(((*1 *2 *3 *4 *4 *5 *3 *3) - (-12 (-5 *3 (-570)) (-5 *4 (-695 (-227))) (-5 *5 (-227)) - (-5 *2 (-1044)) (-5 *1 (-758))))) +(((*1 *1) (-5 *1 (-565)))) (((*1 *2 *1) (-12 (-4 *1 (-246 *2)) (-4 *2 (-1227)))) ((*1 *2 *1) (-12 (-5 *2 (-1144)) (-5 *1 (-1105)))) ((*1 *2 *1) @@ -14826,67 +14565,83 @@ ((*1 *1 *1 *2) (-12 (-5 *2 (-777)) (-4 *1 (-1265 *3)) (-4 *3 (-1227)))) ((*1 *2 *1) (-12 (-4 *1 (-1265 *2)) (-4 *2 (-1227))))) -(((*1 *2 *1) - (-12 (-4 *3 (-368)) (-4 *4 (-799)) (-4 *5 (-856)) (-5 *2 (-650 *6)) - (-5 *1 (-510 *3 *4 *5 *6)) (-4 *6 (-956 *3 *4 *5)))) - ((*1 *2 *1) - (-12 (-5 *2 (-650 (-912 *3))) (-5 *1 (-911 *3)) (-4 *3 (-1109))))) -(((*1 *1 *1 *2) - (-12 (-5 *2 (-650 (-570))) (-5 *1 (-249 *3 *4)) - (-14 *3 (-650 (-1186))) (-4 *4 (-1058)))) - ((*1 *1 *1 *2) - (-12 (-5 *2 (-650 (-570))) (-14 *3 (-650 (-1186))) - (-5 *1 (-460 *3 *4 *5)) (-4 *4 (-1058)) - (-4 *5 (-240 (-2426 *3) (-777))))) - ((*1 *1 *1 *2) - (-12 (-5 *2 (-650 (-570))) (-5 *1 (-487 *3 *4)) - (-14 *3 (-650 (-1186))) (-4 *4 (-1058))))) +(((*1 *2) (-12 (-5 *2 (-1282)) (-5 *1 (-1189)))) + ((*1 *2 *3) (-12 (-5 *3 (-1186)) (-5 *2 (-1282)) (-5 *1 (-1189)))) + ((*1 *2 *3 *1) (-12 (-5 *3 (-1186)) (-5 *2 (-1282)) (-5 *1 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+(((*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)) (|:| -3684 *4)))) + (-5 *1 (-1081 *5 *6 *7 *3 *4)) (-4 *4 (-1080 *5 *6 *7 *3))))) (((*1 *2 *3) (-12 (-5 *3 - (-2 (|:| |lfn| (-650 (-320 (-227)))) (|:| -2315 (-650 (-227))))) + (-2 (|:| |lfn| (-650 (-320 (-227)))) (|:| -2438 (-650 (-227))))) (-5 *2 (-650 (-1186))) (-5 *1 (-270)))) ((*1 *2 *3) (-12 (-5 *3 (-1182 *7)) (-4 *7 (-956 *6 *4 *5)) (-4 *4 (-799)) @@ -14908,7 +14663,7 @@ (-5 *1 (-957 *4 *5 *6 *7 *3)) (-4 *3 (-13 (-368) - (-10 -8 (-15 -3735 ($ *7)) (-15 -4399 (*7 $)) (-15 -4413 (*7 $))))))) + (-10 -8 (-15 -3799 ($ *7)) (-15 -4399 (*7 $)) (-15 -4413 (*7 $))))))) ((*1 *2 *1) (-12 (-4 *1 (-982 *3 *4 *5)) (-4 *3 (-1058)) (-4 *4 (-798)) (-4 *5 (-856)) (-5 *2 (-650 *5)))) @@ -14918,44 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(-15 -3799 ($ (-1134 *4 (-618 $)))))))))) +(((*1 *2 *1) + (-12 (-4 *1 (-1298 *3 *4)) (-4 *3 (-856)) (-4 *4 (-1058)) + (-5 *2 (-825 *3)))) + ((*1 *2 *1) + (-12 (-4 *2 (-852)) (-5 *1 (-1300 *3 *2)) (-4 *3 (-1058))))) +(((*1 *2 *1) + (-12 (-4 *1 (-1260 *3 *4)) (-4 *3 (-1058)) (-4 *4 (-1237 *3)) + (-5 *2 (-413 (-570)))))) (((*1 *2 *3) (-12 (-4 *5 (-13 (-620 *2) (-174))) (-5 *2 (-899 *4)) (-5 *1 (-172 *4 *5 *3)) (-4 *4 (-1109)) (-4 *3 (-167 *5)))) @@ -16561,9 +16594,9 @@ (-12 (-5 *2 (-959 *3)) (-4 *3 (-1058)) (-4 *1 (-1074 *3 *4 *5)) (-4 *5 (-620 (-1186))) (-4 *4 (-799)) (-4 *5 (-856)))) ((*1 *1 *2) - (-2740 + (-2892 (-12 (-5 *2 (-959 (-570))) (-4 *1 (-1074 *3 *4 *5)) - (-12 (-1753 (-4 *3 (-38 (-413 (-570))))) (-4 *3 (-38 (-570))) + (-12 (-1796 (-4 *3 (-38 (-413 (-570))))) (-4 *3 (-38 (-570))) (-4 *5 (-620 (-1186)))) (-4 *3 (-1058)) (-4 *4 (-799)) (-4 *5 (-856))) (-12 (-5 *2 (-959 (-570))) (-4 *1 (-1074 *3 *4 *5)) @@ -16574,12 +16607,12 @@ (-4 *3 (-38 (-413 (-570)))) (-4 *5 (-620 (-1186))) (-4 *3 (-1058)) (-4 *4 (-799)) (-4 *5 (-856)))) ((*1 *2 *3) - (-12 (-5 *3 (-2 (|:| |val| (-650 *7)) (|:| -3593 *8))) + (-12 (-5 *3 (-2 (|:| |val| (-650 *7)) (|:| -3684 *8))) (-4 *7 (-1074 *4 *5 *6)) (-4 *8 (-1080 *4 *5 *6 *7)) (-4 *4 (-458)) (-4 *5 (-799)) (-4 *6 (-856)) (-5 *2 (-1168)) (-5 *1 (-1078 *4 *5 *6 *7 *8)))) ((*1 *2 *3) - (-12 (-5 *3 (-2 (|:| |val| (-650 *7)) (|:| -3593 *8))) + (-12 (-5 *3 (-2 (|:| |val| (-650 *7)) (|:| -3684 *8))) (-4 *7 (-1074 *4 *5 *6)) (-4 *8 (-1118 *4 *5 *6 *7)) (-4 *4 (-458)) (-4 *5 (-799)) (-4 *6 (-856)) (-5 *2 (-1168)) (-5 *1 (-1154 *4 *5 *6 *7 *8)))) @@ -16611,23 +16644,30 @@ (-4 *4 (-13 (-854) (-311) (-148) (-1031))) (-14 *6 (-650 (-1186))) (-5 *2 (-650 (-786 *4 (-870 *6)))) (-5 *1 (-1303 *4 *5 *6)) (-14 *5 (-650 (-1186)))))) -(((*1 *1 *1 *2) (-12 (-4 *1 (-1021)) (-5 *2 (-868))))) -(((*1 *1 *1 *2) - (-12 (-5 *2 (-1 *4 *4)) (-4 *4 (-654 *3)) (-4 *3 (-1058)) - (-5 *1 (-720 *3 *4)))) - ((*1 *1 *1 *2) - (-12 (-5 *2 (-1 *3 *3)) (-4 *3 (-1058)) (-5 *1 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41983) + (-4218 . 41930) (-4219 . 41868) (-4220 . 41729) (-4221 . 41655) + (-4222 . 41552) (-4223 . 41456) (-4224 . 41378) (-4225 . 41293) + (-4226 . 40782) (-4227 . 40470) (-4228 . 40251) (-4229 . 40127) + (-4230 . 40073) (-4231 . 39990) (-4232 . 39923) (-4233 . 39822) + (-4234 . 39623) (-4235 . 39417) (-4236 . 39301) (-4237 . 39227) + (-4238 . 39139) (-4239 . 39043) (-4240 . 38960) (-4241 . 38836) + (-4242 . 38770) (-4243 . 38669) (-4244 . 38557) (-4245 . 38371) + (-4246 . 38314) (-4247 . 38231) (-4248 . 38099) (-4249 . 37969) + (-4250 . 37840) (-4251 . 37788) (-4252 . 37665) (-4253 . 37584) + (-4254 . 37173) (-4255 . 37045) (-4256 . 36988) (-4257 . 36894) + (-4258 . 36863) (-4259 . 36811) (-4260 . 36755) (-4261 . 36588) + (-4262 . 36500) (-4263 . 36357) (-4264 . 36199) (-4265 . 36141) + (-4266 . 36107) (-4267 . 34955) (-4268 . 34878) (-4269 . 34771) + (-4270 . 34655) (-4271 . 34582) (-4272 . 34426) (-4273 . 34330) + (-4274 . 34270) (-4275 . 34168) (-4276 . 34073) (-4277 . 34020) + 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22255) (-4339 . 22097) (-4340 . 22044) (-4341 . 21987) + (-4342 . 21684) (-4343 . 21607) (-4344 . 21451) (-4345 . 21092) + (-4346 . 21043) (-4347 . 20868) (-4348 . 20571) (-4349 . 20497) + (-4350 . 20469) (-4351 . 20437) (-4352 . 20341) (-4353 . 20226) + (-4354 . 20155) (-4355 . 20093) (-4356 . 19998) (-4357 . 19930) + (-4358 . 19567) (-4359 . 19409) (-4360 . 19251) (-4361 . 19198) + (-4362 . 18920) (-4363 . 18818) (-4364 . 18734) (-4365 . 18562) + (-4366 . 18407) (-4367 . 18319) (-4368 . 18163) (-4369 . 17920) + (-4370 . 17217) (-4371 . 17151) (-4372 . 17096) (-4373 . 17016) + (-4374 . 16856) (-4375 . 16423) (-4376 . 15772) (-4377 . 15719) + (-4378 . 15603) (-4379 . 15499) (-4380 . 10956) (-4381 . 10793) + (-4382 . 10207) (-4383 . 10126) (-4384 . 10095) (-4385 . 10030) + (-4386 . 9934) (-4387 . 8734) (-4388 . 8654) (-4389 . 8586) + (-4390 . 8533) (-4391 . 8293) (-4392 . 8240) (-4393 . 8065) + (-4394 . 8004) (-4395 . 7889) (-4396 . 7749) (-4397 . 7411) + (-4398 . 7079) (-4399 . 6375) 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