diff options
| author | dos-reis <gdr@axiomatics.org> | 2011-05-21 02:03:15 +0000 |
|---|---|---|
| committer | dos-reis <gdr@axiomatics.org> | 2011-05-21 02:03:15 +0000 |
| commit | 58dc9f8145468998071a2a69d3dbfb6c710eab39 (patch) | |
| tree | 55dc479b3854da39e13abd1281904e148e7f3f7e /src/share/algebra | |
| parent | 8887fe1d244a40fdc3980d87e30f445249ecdf2e (diff) | |
| download | open-axiom-58dc9f8145468998071a2a69d3dbfb6c710eab39.tar.gz | |
* interp/modemap.boot (augModemapsFromDomain): Don't add modemaps
for element types of Vector or List aggregates.
* algebrar/: Adjust algebras that depended on this behaviour.
Diffstat (limited to 'src/share/algebra')
| -rw-r--r-- | src/share/algebra/browse.daase | 636 | ||||
| -rw-r--r-- | src/share/algebra/category.daase | 1574 | ||||
| -rw-r--r-- | src/share/algebra/compress.daase | 1348 | ||||
| -rw-r--r-- | src/share/algebra/interp.daase | 9136 | ||||
| -rw-r--r-- | src/share/algebra/operation.daase | 26390 |
5 files changed, 19544 insertions, 19540 deletions
diff --git a/src/share/algebra/browse.daase b/src/share/algebra/browse.daase index 59c65b35..4669489b 100644 --- a/src/share/algebra/browse.daase +++ b/src/share/algebra/browse.daase @@ -1,5 +1,5 @@ -(2294555 . 3514823548) +(2294555 . 3514927622) (-18 A S) ((|constructor| (NIL "One-dimensional-array aggregates serves as models for one-dimensional arrays. Categorically,{} these aggregates are finite linear aggregates with the \\spadatt{shallowlyMutable} property,{} that is,{} any component of the array may be changed without affecting the identity of the overall array. Array data structures are typically represented by a fixed area in storage and therefore cannot efficiently grow or shrink on demand as can list structures (see however \\spadtype{FlexibleArray} for a data structure which is a cross between a list and an array). Iteration over,{} and access to,{} elements of arrays is extremely fast (and often can be optimized to open-code). Insertion and deletion however is generally slow since an entirely new data structure must be created for the result."))) NIL @@ -56,7 +56,7 @@ NIL ((|constructor| (NIL "This domain represents the syntax for an add-expression.")) (|body| (((|SpadAst|) $) "base(\\spad{d}) returns the actual body of the add-domain expression `d'.")) (|base| (((|SpadAst|) $) "\\spad{base(d)} returns the base domain(\\spad{s}) of the add-domain expression."))) NIL NIL -(-32 R -4164) +(-32 R -4140) ((|constructor| (NIL "This package provides algebraic functions over an integral domain.")) (|iroot| ((|#2| |#1| (|Integer|)) "\\spad{iroot(p, n)} should be a non-exported function.")) (|definingPolynomial| ((|#2| |#2|) "\\spad{definingPolynomial(f)} returns the defining polynomial of \\spad{f} as an element of \\spad{F}. Error: if \\spad{f} is not a kernel.")) (|minPoly| (((|SparseUnivariatePolynomial| |#2|) (|Kernel| |#2|)) "\\spad{minPoly(k)} returns the defining polynomial of \\spad{k}.")) (** ((|#2| |#2| (|Fraction| (|Integer|))) "\\spad{x ** q} is \\spad{x} raised to the rational power \\spad{q}.")) (|droot| (((|OutputForm|) (|List| |#2|)) "\\spad{droot(l)} should be a non-exported function.")) (|inrootof| ((|#2| (|SparseUnivariatePolynomial| |#2|) |#2|) "\\spad{inrootof(p, x)} should be a non-exported function.")) (|belong?| (((|Boolean|) (|BasicOperator|)) "\\spad{belong?(op)} is \\spad{true} if \\spad{op} is an algebraic operator,{} that is,{} an \\spad{n}th root or implicit algebraic operator.")) (|operator| (((|BasicOperator|) (|BasicOperator|)) "\\spad{operator(op)} returns a copy of \\spad{op} with the domain-dependent properties appropriate for \\spad{F}. Error: if \\spad{op} is not an algebraic operator,{} that is,{} an \\spad{n}th root or implicit algebraic operator.")) (|rootOf| ((|#2| (|SparseUnivariatePolynomial| |#2|) (|Symbol|)) "\\spad{rootOf(p, y)} returns \\spad{y} such that \\spad{p(y) = 0}. The object returned displays as \\spad{'y}."))) NIL ((|HasCategory| |#1| (|%list| (QUOTE -1070) (QUOTE (-560))))) @@ -88,11 +88,11 @@ NIL ((|constructor| (NIL "Factorization of univariate polynomials with coefficients in \\spadtype{AlgebraicNumber}.")) (|doublyTransitive?| (((|Boolean|) |#1|) "\\spad{doublyTransitive?(p)} is \\spad{true} if \\spad{p} is irreducible over over the field \\spad{K} generated by its coefficients,{} and if \\spad{p(X) / (X - a)} is irreducible over \\spad{K(a)} where \\spad{p(a) = 0}.")) (|split| (((|Factored| |#1|) |#1|) "\\spad{split(p)} returns a prime factorisation of \\spad{p} over its splitting field.")) (|factor| (((|Factored| |#1|) |#1|) "\\spad{factor(p)} returns a prime factorisation of \\spad{p} over the field generated by its coefficients.") (((|Factored| |#1|) |#1| (|List| (|AlgebraicNumber|))) "\\spad{factor(p, [a1,...,an])} returns a prime factorisation of \\spad{p} over the field generated by its coefficients and \\spad{a1},{}...,{}an."))) NIL NIL -(-40 -4164 UP UPUP -3871) +(-40 -4140 UP UPUP -3771) ((|constructor| (NIL "Function field defined by \\spad{f}(\\spad{x},{} \\spad{y}) = 0.")) (|knownInfBasis| (((|Void|) (|NonNegativeInteger|)) "\\spad{knownInfBasis(n)} \\undocumented{}"))) ((-4503 |has| (-421 |#2|) (-376)) (-4508 |has| (-421 |#2|) (-376)) (-4502 |has| (-421 |#2|) (-376)) ((-4512 "*") . T) (-4504 . T) (-4505 . T) (-4507 . T)) -((|HasCategory| (-421 |#2|) (QUOTE (-147))) (|HasCategory| (-421 |#2|) (QUOTE (-149))) (|HasCategory| (-421 |#2|) (QUOTE (-363))) (-4144 (|HasCategory| (-421 |#2|) (QUOTE (-376))) (|HasCategory| (-421 |#2|) (QUOTE (-363)))) (|HasCategory| (-421 |#2|) (QUOTE (-376))) (|HasCategory| (-421 |#2|) (QUOTE (-381))) (-4144 (-12 (|HasCategory| (-421 |#2|) (QUOTE (-240))) (|HasCategory| (-421 |#2|) (QUOTE (-376)))) (|HasCategory| (-421 |#2|) (QUOTE (-363)))) (-4144 (-12 (|HasCategory| (-421 |#2|) (QUOTE (-240))) (|HasCategory| (-421 |#2|) (QUOTE (-376)))) (-12 (|HasCategory| (-421 |#2|) (QUOTE (-239))) (|HasCategory| (-421 |#2|) (QUOTE (-376)))) (|HasCategory| (-421 |#2|) (QUOTE (-363)))) (-4144 (-12 (|HasCategory| (-421 |#2|) (|%list| (QUOTE -928) (QUOTE (-1209)))) (|HasCategory| (-421 |#2|) (QUOTE (-376)))) (-12 (|HasCategory| (-421 |#2|) (|%list| (QUOTE -928) (QUOTE (-1209)))) (|HasCategory| (-421 |#2|) (QUOTE (-363))))) (-4144 (-12 (|HasCategory| (-421 |#2|) (|%list| (QUOTE -928) (QUOTE (-1209)))) (|HasCategory| (-421 |#2|) (QUOTE (-376)))) (-12 (|HasCategory| (-421 |#2|) (|%list| (QUOTE -930) (QUOTE (-1209)))) (|HasCategory| (-421 |#2|) (QUOTE (-376))))) (|HasCategory| (-421 |#2|) (|%list| (QUOTE -660) (QUOTE (-560)))) (-4144 (|HasCategory| (-421 |#2|) (|%list| (QUOTE -1070) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| (-421 |#2|) (QUOTE (-376)))) (|HasCategory| (-421 |#2|) (|%list| (QUOTE -1070) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| (-421 |#2|) (|%list| (QUOTE -1070) (QUOTE (-560)))) (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (QUOTE (-381))) (-12 (|HasCategory| (-421 |#2|) (QUOTE (-239))) (|HasCategory| (-421 |#2|) (QUOTE (-376)))) (-12 (|HasCategory| (-421 |#2|) (|%list| (QUOTE -930) (QUOTE (-1209)))) (|HasCategory| (-421 |#2|) (QUOTE (-376)))) (-12 (|HasCategory| (-421 |#2|) (QUOTE (-240))) (|HasCategory| (-421 |#2|) (QUOTE (-376)))) (-12 (|HasCategory| (-421 |#2|) (|%list| (QUOTE -928) (QUOTE (-1209)))) (|HasCategory| (-421 |#2|) (QUOTE (-376))))) -(-41 R -4164) +((|HasCategory| (-421 |#2|) (QUOTE (-147))) (|HasCategory| (-421 |#2|) (QUOTE (-149))) (|HasCategory| (-421 |#2|) (QUOTE (-363))) (-4118 (|HasCategory| (-421 |#2|) (QUOTE (-376))) (|HasCategory| (-421 |#2|) (QUOTE (-363)))) (|HasCategory| (-421 |#2|) (QUOTE (-376))) (|HasCategory| (-421 |#2|) (QUOTE (-381))) (-4118 (-12 (|HasCategory| (-421 |#2|) (QUOTE (-240))) (|HasCategory| (-421 |#2|) (QUOTE (-376)))) (|HasCategory| (-421 |#2|) (QUOTE (-363)))) (-4118 (-12 (|HasCategory| (-421 |#2|) (QUOTE (-240))) (|HasCategory| (-421 |#2|) (QUOTE (-376)))) (-12 (|HasCategory| (-421 |#2|) (QUOTE (-239))) (|HasCategory| (-421 |#2|) (QUOTE (-376)))) (|HasCategory| (-421 |#2|) (QUOTE (-363)))) (-4118 (-12 (|HasCategory| (-421 |#2|) (|%list| (QUOTE -928) (QUOTE (-1209)))) (|HasCategory| (-421 |#2|) (QUOTE (-376)))) (-12 (|HasCategory| (-421 |#2|) (|%list| (QUOTE -928) (QUOTE (-1209)))) (|HasCategory| (-421 |#2|) (QUOTE (-363))))) (-4118 (-12 (|HasCategory| (-421 |#2|) (|%list| (QUOTE -928) (QUOTE (-1209)))) (|HasCategory| (-421 |#2|) (QUOTE (-376)))) (-12 (|HasCategory| (-421 |#2|) (|%list| (QUOTE -930) (QUOTE (-1209)))) (|HasCategory| (-421 |#2|) (QUOTE (-376))))) (|HasCategory| (-421 |#2|) (|%list| (QUOTE -660) (QUOTE (-560)))) (-4118 (|HasCategory| (-421 |#2|) (|%list| (QUOTE -1070) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| (-421 |#2|) (QUOTE (-376)))) (|HasCategory| (-421 |#2|) (|%list| (QUOTE -1070) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| (-421 |#2|) (|%list| (QUOTE -1070) (QUOTE (-560)))) (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (QUOTE (-381))) (-12 (|HasCategory| (-421 |#2|) (QUOTE (-239))) (|HasCategory| (-421 |#2|) (QUOTE (-376)))) (-12 (|HasCategory| (-421 |#2|) (|%list| (QUOTE -930) (QUOTE (-1209)))) (|HasCategory| (-421 |#2|) (QUOTE (-376)))) (-12 (|HasCategory| (-421 |#2|) (QUOTE (-240))) (|HasCategory| (-421 |#2|) (QUOTE (-376)))) (-12 (|HasCategory| (-421 |#2|) (|%list| (QUOTE -928) (QUOTE (-1209)))) (|HasCategory| (-421 |#2|) (QUOTE (-376))))) +(-41 R -4140) ((|constructor| (NIL "AlgebraicManipulations provides functions to simplify and expand expressions involving algebraic operators.")) (|rootKerSimp| ((|#2| (|BasicOperator|) |#2| (|NonNegativeInteger|)) "\\spad{rootKerSimp(op,f,n)} should be local but conditional.")) (|rootSimp| ((|#2| |#2|) "\\spad{rootSimp(f)} transforms every radical of the form \\spad{(a * b**(q*n+r))**(1/n)} appearing in \\spad{f} into \\spad{b**q * (a * b**r)**(1/n)}. This transformation is not in general valid for all complex numbers \\spad{b}.")) (|rootProduct| ((|#2| |#2|) "\\spad{rootProduct(f)} combines every product of the form \\spad{(a**(1/n))**m * (a**(1/s))**t} into a single power of a root of \\spad{a},{} and transforms every radical power of the form \\spad{(a**(1/n))**m} into a simpler form.")) (|rootPower| ((|#2| |#2|) "\\spad{rootPower(f)} transforms every radical power of the form \\spad{(a**(1/n))**m} into a simpler form if \\spad{m} and \\spad{n} have a common factor.")) (|ratPoly| (((|SparseUnivariatePolynomial| |#2|) |#2|) "\\spad{ratPoly(f)} returns a polynomial \\spad{p} such that \\spad{p} has no algebraic coefficients,{} and \\spad{p(f) = 0}.")) (|ratDenom| ((|#2| |#2| (|List| (|Kernel| |#2|))) "\\spad{ratDenom(f, [a1,...,an])} removes the \\spad{ai}'s which are algebraic from the denominators in \\spad{f}.") ((|#2| |#2| (|List| |#2|)) "\\spad{ratDenom(f, [a1,...,an])} removes the \\spad{ai}'s which are algebraic kernels from the denominators in \\spad{f}.") ((|#2| |#2| |#2|) "\\spad{ratDenom(f, a)} removes \\spad{a} from the denominators in \\spad{f} if \\spad{a} is an algebraic kernel.") ((|#2| |#2|) "\\spad{ratDenom(f)} rationalizes the denominators appearing in \\spad{f} by moving all the algebraic quantities into the numerators.")) (|rootSplit| ((|#2| |#2|) "\\spad{rootSplit(f)} transforms every radical of the form \\spad{(a/b)**(1/n)} appearing in \\spad{f} into \\spad{a**(1/n) / b**(1/n)}. This transformation is not in general valid for all complex numbers \\spad{a} and \\spad{b}.")) (|coerce| (($ (|SparseMultivariatePolynomial| |#1| (|Kernel| $))) "\\spad{coerce(x)} \\undocumented")) (|denom| (((|SparseMultivariatePolynomial| |#1| (|Kernel| $)) $) "\\spad{denom(x)} \\undocumented")) (|numer| (((|SparseMultivariatePolynomial| |#1| (|Kernel| $)) $) "\\spad{numer(x)} \\undocumented"))) NIL ((-12 (|HasCategory| |#1| (QUOTE (-466))) (|HasCategory| |#1| (|%list| (QUOTE -1070) (QUOTE (-560)))) (|HasCategory| |#2| (|%list| (QUOTE -435) (|devaluate| |#1|))))) @@ -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."))) ((-4510 . T) (-4511 . T)) -((-4144 (-12 (|HasCategory| (-2 (|:| -2118 |#1|) (|:| -3964 |#2|)) (QUOTE (-872))) (|HasCategory| (-2 (|:| -2118 |#1|) (|:| -3964 |#2|)) (|%list| (QUOTE -321) (|%list| (QUOTE -2) (|%list| (QUOTE |:|) (QUOTE -2118) (|devaluate| |#1|)) (|%list| (QUOTE |:|) (QUOTE -3964) (|devaluate| |#2|)))))) (-12 (|HasCategory| (-2 (|:| -2118 |#1|) (|:| -3964 |#2|)) (QUOTE (-1133))) (|HasCategory| (-2 (|:| -2118 |#1|) (|:| -3964 |#2|)) (|%list| (QUOTE -321) (|%list| (QUOTE -2) (|%list| (QUOTE |:|) (QUOTE -2118) (|devaluate| |#1|)) (|%list| (QUOTE |:|) (QUOTE -3964) (|devaluate| |#2|))))))) (-4144 (|HasCategory| (-2 (|:| -2118 |#1|) (|:| -3964 |#2|)) (QUOTE (-872))) (|HasCategory| (-2 (|:| -2118 |#1|) (|:| -3964 |#2|)) (QUOTE (-1133))) (|HasCategory| (-2 (|:| -2118 |#1|) (|:| -3964 |#2|)) (|%list| (QUOTE -632) (QUOTE (-888)))) (|HasCategory| |#2| (QUOTE (-1133))) (|HasCategory| |#2| (|%list| (QUOTE -632) (QUOTE (-888))))) (|HasCategory| (-2 (|:| -2118 |#1|) (|:| -3964 |#2|)) (|%list| (QUOTE -633) (QUOTE (-549)))) (-12 (|HasCategory| |#2| (QUOTE (-1133))) (|HasCategory| |#2| (|%list| (QUOTE -321) (|devaluate| |#2|)))) (-4144 (|HasCategory| (-2 (|:| -2118 |#1|) (|:| -3964 |#2|)) (QUOTE (-872))) (|HasCategory| (-2 (|:| -2118 |#1|) (|:| -3964 |#2|)) (QUOTE (-1133))) (|HasCategory| |#2| (QUOTE (-1133)))) (|HasCategory| (-2 (|:| -2118 |#1|) (|:| -3964 |#2|)) (QUOTE (-872))) (-4144 (|HasCategory| (-2 (|:| -2118 |#1|) (|:| -3964 |#2|)) (QUOTE (-102))) (|HasCategory| (-2 (|:| -2118 |#1|) (|:| -3964 |#2|)) (QUOTE (-872))) (|HasCategory| (-2 (|:| -2118 |#1|) (|:| -3964 |#2|)) (QUOTE (-1133))) (|HasCategory| |#2| (QUOTE (-102))) (|HasCategory| |#2| (QUOTE (-1133)))) (|HasCategory| |#1| (QUOTE (-872))) (|HasCategory| |#2| (QUOTE (-1133))) (|HasCategory| (-560) (QUOTE (-872))) (|HasCategory| (-2 (|:| -2118 |#1|) (|:| -3964 |#2|)) (QUOTE (-1133))) (-4144 (|HasCategory| (-2 (|:| -2118 |#1|) (|:| -3964 |#2|)) (QUOTE (-1133))) (|HasCategory| |#2| (QUOTE (-1133)))) (-4144 (|HasCategory| (-2 (|:| -2118 |#1|) (|:| -3964 |#2|)) (|%list| (QUOTE -632) (QUOTE (-888)))) (|HasCategory| |#2| (|%list| (QUOTE -632) (QUOTE (-888))))) (-4144 (|HasCategory| (-2 (|:| -2118 |#1|) (|:| -3964 |#2|)) (QUOTE (-102))) (|HasCategory| |#2| (QUOTE (-102)))) (|HasCategory| |#2| (QUOTE (-102))) (|HasCategory| |#2| (|%list| (QUOTE -632) (QUOTE (-888)))) (|HasCategory| (-2 (|:| -2118 |#1|) (|:| -3964 |#2|)) (|%list| (QUOTE -632) (QUOTE (-888)))) (|HasCategory| (-2 (|:| -2118 |#1|) (|:| -3964 |#2|)) (QUOTE (-102))) (-12 (|HasCategory| (-2 (|:| -2118 |#1|) (|:| -3964 |#2|)) (QUOTE (-1133))) (|HasCategory| (-2 (|:| -2118 |#1|) (|:| -3964 |#2|)) (|%list| (QUOTE -321) (|%list| (QUOTE -2) (|%list| (QUOTE |:|) (QUOTE -2118) (|devaluate| |#1|)) (|%list| (QUOTE |:|) (QUOTE -3964) (|devaluate| |#2|))))))) +((-4118 (-12 (|HasCategory| (-2 (|:| -2115 |#1|) (|:| -3934 |#2|)) (QUOTE (-872))) (|HasCategory| (-2 (|:| -2115 |#1|) (|:| -3934 |#2|)) (|%list| (QUOTE -321) (|%list| (QUOTE -2) (|%list| (QUOTE |:|) (QUOTE -2115) (|devaluate| |#1|)) (|%list| (QUOTE |:|) (QUOTE -3934) (|devaluate| |#2|)))))) (-12 (|HasCategory| (-2 (|:| -2115 |#1|) (|:| -3934 |#2|)) (QUOTE (-1133))) (|HasCategory| (-2 (|:| -2115 |#1|) (|:| -3934 |#2|)) (|%list| (QUOTE -321) (|%list| (QUOTE -2) (|%list| (QUOTE |:|) (QUOTE -2115) (|devaluate| |#1|)) (|%list| (QUOTE |:|) (QUOTE -3934) (|devaluate| |#2|))))))) (-4118 (|HasCategory| (-2 (|:| -2115 |#1|) (|:| -3934 |#2|)) (QUOTE (-872))) (|HasCategory| (-2 (|:| -2115 |#1|) (|:| -3934 |#2|)) (QUOTE (-1133))) (|HasCategory| (-2 (|:| -2115 |#1|) (|:| -3934 |#2|)) (|%list| (QUOTE -632) (QUOTE (-888)))) (|HasCategory| |#2| (QUOTE (-1133))) (|HasCategory| |#2| (|%list| (QUOTE -632) (QUOTE (-888))))) (|HasCategory| (-2 (|:| -2115 |#1|) (|:| -3934 |#2|)) (|%list| (QUOTE -633) (QUOTE (-549)))) (-12 (|HasCategory| |#2| (QUOTE (-1133))) (|HasCategory| |#2| (|%list| (QUOTE -321) (|devaluate| |#2|)))) (-4118 (|HasCategory| (-2 (|:| -2115 |#1|) (|:| -3934 |#2|)) (QUOTE (-872))) (|HasCategory| (-2 (|:| -2115 |#1|) (|:| -3934 |#2|)) (QUOTE (-1133))) (|HasCategory| |#2| (QUOTE (-1133)))) (|HasCategory| (-2 (|:| -2115 |#1|) (|:| -3934 |#2|)) (QUOTE (-872))) (-4118 (|HasCategory| (-2 (|:| -2115 |#1|) (|:| -3934 |#2|)) (QUOTE (-102))) (|HasCategory| (-2 (|:| -2115 |#1|) (|:| -3934 |#2|)) (QUOTE (-872))) (|HasCategory| (-2 (|:| -2115 |#1|) (|:| -3934 |#2|)) (QUOTE (-1133))) (|HasCategory| |#2| (QUOTE (-102))) (|HasCategory| |#2| (QUOTE (-1133)))) (|HasCategory| |#1| (QUOTE (-872))) (|HasCategory| |#2| (QUOTE (-1133))) (|HasCategory| (-560) (QUOTE (-872))) (|HasCategory| (-2 (|:| -2115 |#1|) (|:| -3934 |#2|)) (QUOTE (-1133))) (-4118 (|HasCategory| (-2 (|:| -2115 |#1|) (|:| -3934 |#2|)) (QUOTE (-1133))) (|HasCategory| |#2| (QUOTE (-1133)))) (-4118 (|HasCategory| (-2 (|:| -2115 |#1|) (|:| -3934 |#2|)) (|%list| (QUOTE -632) (QUOTE (-888)))) (|HasCategory| |#2| (|%list| (QUOTE -632) (QUOTE (-888))))) (-4118 (|HasCategory| (-2 (|:| -2115 |#1|) (|:| -3934 |#2|)) (QUOTE (-102))) (|HasCategory| |#2| (QUOTE (-102)))) (|HasCategory| |#2| (QUOTE (-102))) (|HasCategory| |#2| (|%list| (QUOTE -632) (QUOTE (-888)))) (|HasCategory| (-2 (|:| -2115 |#1|) (|:| -3934 |#2|)) (|%list| (QUOTE -632) (QUOTE (-888)))) (|HasCategory| (-2 (|:| -2115 |#1|) (|:| -3934 |#2|)) (QUOTE (-102))) (-12 (|HasCategory| (-2 (|:| -2115 |#1|) (|:| -3934 |#2|)) (QUOTE (-1133))) (|HasCategory| (-2 (|:| -2115 |#1|) (|:| -3934 |#2|)) (|%list| (QUOTE -321) (|%list| (QUOTE -2) (|%list| (QUOTE |:|) (QUOTE -2115) (|devaluate| |#1|)) (|%list| (QUOTE |:|) (QUOTE -3934) (|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| $) "\\spad{leadingCoefficient(p)} returns the coefficient highest degree term of \\spad{p}."))) NIL @@ -144,7 +144,7 @@ NIL ((|constructor| (NIL "\\spad{ApplyUnivariateSkewPolynomial} (internal) allows univariate skew polynomials to be applied to appropriate modules.")) (|apply| ((|#2| |#3| (|Mapping| |#2| |#2|) |#2|) "\\spad{apply(p, f, m)} returns \\spad{p(m)} where the action is given by \\spad{x m = f(m)}. \\spad{f} must be an \\spad{R}-pseudo linear map on \\spad{M}."))) NIL NIL -(-54 |Base| R -4164) +(-54 |Base| R -4140) ((|constructor| (NIL "This package apply rewrite rules to expressions,{} calling the pattern matcher.")) (|localUnquote| ((|#3| |#3| (|List| (|Symbol|))) "\\spad{localUnquote(f,ls)} is a local function.")) (|applyRules| ((|#3| (|List| (|RewriteRule| |#1| |#2| |#3|)) |#3| (|PositiveInteger|)) "\\spad{applyRules([r1,...,rn], expr, n)} applies the rules \\spad{r1},{}...,{}rn to \\spad{f} a most \\spad{n} times.") ((|#3| (|List| (|RewriteRule| |#1| |#2| |#3|)) |#3|) "\\spad{applyRules([r1,...,rn], expr)} applies the rules \\spad{r1},{}...,{}rn to \\spad{f} an unlimited number of times,{} \\spadignore{i.e.} until none of \\spad{r1},{}...,{}rn is applicable to the expression."))) NIL NIL @@ -163,7 +163,7 @@ NIL (-58 S) ((|constructor| (NIL "This is the domain of 1-based one dimensional arrays")) (|oneDimensionalArray| (($ (|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}"))) ((-4511 . T) (-4510 . T)) -((-4144 (-12 (|HasCategory| |#1| (QUOTE (-872))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|))))) (-4144 (-12 (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-888))))) (|HasCategory| |#1| (|%list| (QUOTE -633) (QUOTE (-549)))) (-4144 (|HasCategory| |#1| (QUOTE (-872))) (|HasCategory| |#1| (QUOTE (-1133)))) (|HasCategory| |#1| (QUOTE (-872))) (-4144 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-872))) (|HasCategory| |#1| (QUOTE (-1133)))) (|HasCategory| (-560) (QUOTE (-872))) (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-888)))) (|HasCategory| |#1| (QUOTE (-102))) (-12 (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|))))) +((-4118 (-12 (|HasCategory| |#1| (QUOTE (-872))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|))))) (-4118 (-12 (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-888))))) (|HasCategory| |#1| (|%list| (QUOTE -633) (QUOTE (-549)))) (-4118 (|HasCategory| |#1| (QUOTE (-872))) (|HasCategory| |#1| (QUOTE (-1133)))) (|HasCategory| |#1| (QUOTE (-872))) (-4118 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-872))) (|HasCategory| |#1| (QUOTE (-1133)))) (|HasCategory| (-560) (QUOTE (-872))) (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-888)))) (|HasCategory| |#1| (QUOTE (-102))) (-12 (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|))))) (-59 A B) ((|constructor| (NIL "\\indented{1}{This package provides tools for operating on one-dimensional arrays} with unary and binary functions involving different underlying types")) (|map| (((|OneDimensionalArray| |#2|) (|Mapping| |#2| |#1|) (|OneDimensionalArray| |#1|)) "\\spad{map(f,a)} applies function \\spad{f} to each member of one-dimensional array \\spad{a} resulting in a new one-dimensional array over a possibly different underlying domain.")) (|reduce| ((|#2| (|Mapping| |#2| |#1| |#2|) (|OneDimensionalArray| |#1|) |#2|) "\\spad{reduce(f,a,r)} applies function \\spad{f} to each successive element of the one-dimensional array \\spad{a} and an accumulant initialized to \\spad{r}. For example,{} \\spad{reduce(_+\\$Integer,[1,2,3],0)} does \\spad{3+(2+(1+0))}. Note: third argument \\spad{r} may be regarded as the identity element for the function \\spad{f}.")) (|scan| (((|OneDimensionalArray| |#2|) (|Mapping| |#2| |#1| |#2|) (|OneDimensionalArray| |#1|) |#2|) "\\spad{scan(f,a,r)} successively applies \\spad{reduce(f,x,r)} to more and more leading sub-arrays \\spad{x} of one-dimensional array \\spad{a}. More precisely,{} if \\spad{a} is \\spad{[a1,a2,...]},{} then \\spad{scan(f,a,r)} returns \\spad{[reduce(f,[a1],r),reduce(f,[a1,a2],r),...]}."))) NIL @@ -171,64 +171,64 @@ NIL (-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's."))) ((-4510 . T) (-4511 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1133))) (-4144 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-1133)))) (-4144 (-12 (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-888))))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-888)))) (|HasCategory| |#1| (QUOTE (-102)))) -(-61 -4401) +((-12 (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1133))) (-4118 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-1133)))) (-4118 (-12 (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-888))))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-888)))) (|HasCategory| |#1| (QUOTE (-102)))) +(-61 -4385) ((|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 -(-62 -4401) +(-62 -4385) ((|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 -(-63 -4401) +(-63 -4385) ((|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 -(-64 -4401) +(-64 -4385) ((|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 -(-65 -4401) +(-65 -4385) ((|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 -4401) +(-66 -4385) ((|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 -4401) +(-67 -4385) ((|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 -4401) +(-68 -4385) ((|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 -4401) +(-69 -4385) ((|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 -4401) +(-70 -4385) ((|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 -4401) +(-71 -4385) ((|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 -4401) +(-72 -4385) ((|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 -4401) +(-73 -4385) ((|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 -4401) +(-74 -4385) ((|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 -(-75 -4401) +(-75 -4385) ((|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 @@ -240,51 +240,51 @@ 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 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 -(-78 -4401) +(-78 -4385) ((|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 -(-79 -4401) +(-79 -4385) ((|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 -4401) +(-80 -4385) ((|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 -4401) +(-81 -4385) ((|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 -4401) +(-82 -4385) ((|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 -(-83 -4401) +(-83 -4385) ((|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 -(-84 -4401) +(-84 -4385) ((|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 -(-85 -4401) +(-85 -4385) ((|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 -(-86 -4401) +(-86 -4385) ((|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 -(-87 -4401) +(-87 -4385) ((|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 -(-88 -4401) +(-88 -4385) ((|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 -(-89 -4401) +(-89 -4385) ((|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}."))) ((-4510 . T) (-4511 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1133))) (-4144 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-1133)))) (-4144 (-12 (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-888))))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-888)))) (|HasCategory| |#1| (QUOTE (-102)))) +((-12 (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1133))) (-4118 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-1133)))) (-4118 (-12 (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-888))))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-888)))) (|HasCategory| |#1| (QUOTE (-102)))) (-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 pl and 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{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 ls.")) (|balancedBinaryTree| (($ (|NonNegativeInteger|) |#1|) "\\spad{balancedBinaryTree(n, s)} creates a balanced binary tree with \\spad{n} nodes each with value \\spad{s}."))) ((-4510 . T) (-4511 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1133))) (-4144 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-1133)))) (-4144 (-12 (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-888))))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-888)))) (|HasCategory| |#1| (QUOTE (-102)))) +((-12 (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1133))) (-4118 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-1133)))) (-4118 (-12 (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-888))))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-888)))) (|HasCategory| |#1| (QUOTE (-102)))) (-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."))) ((-4502 . T) (-4508 . T) (-4503 . T) ((-4512 "*") . T) (-4504 . T) (-4505 . T) (-4507 . T)) -((|HasCategory| (-560) (QUOTE (-940))) (|HasCategory| (-560) (|%list| (QUOTE -1070) (QUOTE (-1209)))) (|HasCategory| (-560) (QUOTE (-147))) (|HasCategory| (-560) (QUOTE (-149))) (|HasCategory| (-560) (|%list| (QUOTE -633) (QUOTE (-549)))) (|HasCategory| (-560) (QUOTE (-1052))) (|HasCategory| (-560) (QUOTE (-844))) (|HasCategory| (-560) (QUOTE (-872))) (-4144 (|HasCategory| (-560) (QUOTE (-844))) (|HasCategory| (-560) (QUOTE (-872)))) (|HasCategory| (-560) (|%list| (QUOTE -1070) (QUOTE (-560)))) (|HasCategory| (-560) (QUOTE (-1184))) (|HasCategory| (-560) (|%list| (QUOTE -912) (QUOTE (-391)))) (|HasCategory| (-560) (|%list| (QUOTE -912) (QUOTE (-560)))) (|HasCategory| (-560) (|%list| (QUOTE -633) (|%list| (QUOTE -916) (QUOTE (-391))))) (|HasCategory| (-560) (|%list| (QUOTE -633) (|%list| (QUOTE -916) (QUOTE (-560))))) (|HasCategory| (-560) (QUOTE (-239))) (|HasCategory| (-560) (|%list| (QUOTE -930) (QUOTE (-1209)))) (|HasCategory| (-560) (QUOTE (-240))) (|HasCategory| (-560) (|%list| (QUOTE -928) (QUOTE (-1209)))) (|HasCategory| (-560) (|%list| (QUOTE -528) (QUOTE (-1209)) (QUOTE (-560)))) (|HasCategory| (-560) (|%list| (QUOTE -321) (QUOTE (-560)))) (|HasCategory| (-560) (|%list| (QUOTE -298) (QUOTE (-560)) (QUOTE (-560)))) (|HasCategory| (-560) (QUOTE (-319))) (|HasCategory| (-560) (QUOTE (-559))) (|HasCategory| (-560) (|%list| (QUOTE -660) (QUOTE (-560)))) (-12 (|HasCategory| $ (QUOTE (-147))) (|HasCategory| (-560) (QUOTE (-940)))) (-4144 (-12 (|HasCategory| $ (QUOTE (-147))) (|HasCategory| (-560) (QUOTE (-940)))) (|HasCategory| (-560) (QUOTE (-147))))) +((|HasCategory| (-560) (QUOTE (-940))) (|HasCategory| (-560) (|%list| (QUOTE -1070) (QUOTE (-1209)))) (|HasCategory| (-560) (QUOTE (-147))) (|HasCategory| (-560) (QUOTE (-149))) (|HasCategory| (-560) (|%list| (QUOTE -633) (QUOTE (-549)))) (|HasCategory| (-560) (QUOTE (-1052))) (|HasCategory| (-560) (QUOTE (-844))) (|HasCategory| (-560) (QUOTE (-872))) (-4118 (|HasCategory| (-560) (QUOTE (-844))) (|HasCategory| (-560) (QUOTE (-872)))) (|HasCategory| (-560) (|%list| (QUOTE -1070) (QUOTE (-560)))) (|HasCategory| (-560) (QUOTE (-1184))) (|HasCategory| (-560) (|%list| (QUOTE -912) (QUOTE (-391)))) (|HasCategory| (-560) (|%list| (QUOTE -912) (QUOTE (-560)))) (|HasCategory| (-560) (|%list| (QUOTE -633) (|%list| (QUOTE -916) (QUOTE (-391))))) (|HasCategory| (-560) (|%list| (QUOTE -633) (|%list| (QUOTE -916) (QUOTE (-560))))) (|HasCategory| (-560) (QUOTE (-239))) (|HasCategory| (-560) (|%list| (QUOTE -930) (QUOTE (-1209)))) (|HasCategory| (-560) (QUOTE (-240))) (|HasCategory| (-560) (|%list| (QUOTE -928) (QUOTE (-1209)))) (|HasCategory| (-560) (|%list| (QUOTE -528) (QUOTE (-1209)) (QUOTE (-560)))) (|HasCategory| (-560) (|%list| (QUOTE -321) (QUOTE (-560)))) (|HasCategory| (-560) (|%list| (QUOTE -298) (QUOTE (-560)) (QUOTE (-560)))) (|HasCategory| (-560) (QUOTE (-319))) (|HasCategory| (-560) (QUOTE (-559))) (|HasCategory| (-560) (|%list| (QUOTE -660) (QUOTE (-560)))) (-12 (|HasCategory| $ (QUOTE (-147))) (|HasCategory| (-560) (QUOTE (-940)))) (-4118 (-12 (|HasCategory| $ (QUOTE (-147))) (|HasCategory| (-560) (QUOTE (-940)))) (|HasCategory| (-560) (QUOTE (-147))))) (-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 `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 @@ -396,7 +396,7 @@ NIL ((|constructor| (NIL "This package exports functions to set some commonly used properties of operators,{} including properties which contain functions.")) (|constantOpIfCan| (((|Union| |#1| "failed") (|BasicOperator|)) "\\spad{constantOpIfCan(op)} returns \\spad{a} if \\spad{op} is the constant nullary operator always returning \\spad{a},{} \"failed\" otherwise.")) (|constantOperator| (((|BasicOperator|) |#1|) "\\spad{constantOperator(a)} returns a nullary operator op such that \\spad{op()} always evaluate to \\spad{a}.")) (|derivative| (((|Union| (|List| (|Mapping| |#1| (|List| |#1|))) "failed") (|BasicOperator|)) "\\spad{derivative(op)} returns the value of the \"\\%diff\" property of \\spad{op} if it has one,{} and \"failed\" otherwise.") (((|BasicOperator|) (|BasicOperator|) (|Mapping| |#1| |#1|)) "\\spad{derivative(op, foo)} attaches foo as the \"\\%diff\" property of \\spad{op}. If \\spad{op} has an \"\\%diff\" property \\spad{f},{} then applying a derivation \\spad{D} to \\spad{op}(a) returns \\spad{f(a) * D(a)}. Argument \\spad{op} must be unary.") (((|BasicOperator|) (|BasicOperator|) (|List| (|Mapping| |#1| (|List| |#1|)))) "\\spad{derivative(op, [foo1,...,foon])} attaches [\\spad{foo1},{}...,{}foon] as the \"\\%diff\" property of \\spad{op}. If \\spad{op} has an \"\\%diff\" property \\spad{[f1,...,fn]} then applying a derivation \\spad{D} to \\spad{op(a1,...,an)} returns \\spad{f1(a1,...,an) * D(a1) + ... + fn(a1,...,an) * D(an)}.")) (|evaluate| (((|Union| (|Mapping| |#1| (|List| |#1|)) "failed") (|BasicOperator|)) "\\spad{evaluate(op)} returns the value of the \"\\%eval\" property of \\spad{op} if it has one,{} and \"failed\" otherwise.") (((|BasicOperator|) (|BasicOperator|) (|Mapping| |#1| |#1|)) "\\spad{evaluate(op, foo)} attaches foo as the \"\\%eval\" property of \\spad{op}. If \\spad{op} has an \"\\%eval\" property \\spad{f},{} then applying \\spad{op} to a returns the result of \\spad{f(a)}. Argument \\spad{op} must be unary.") (((|BasicOperator|) (|BasicOperator|) (|Mapping| |#1| (|List| |#1|))) "\\spad{evaluate(op, foo)} attaches foo as the \"\\%eval\" property of \\spad{op}. If \\spad{op} has an \"\\%eval\" property \\spad{f},{} then applying \\spad{op} to \\spad{(a1,...,an)} returns the result of \\spad{f(a1,...,an)}.") (((|Union| |#1| "failed") (|BasicOperator|) (|List| |#1|)) "\\spad{evaluate(op, [a1,...,an])} checks if \\spad{op} has an \"\\%eval\" property \\spad{f}. If it has,{} then \\spad{f(a1,...,an)} is returned,{} and \"failed\" otherwise."))) NIL NIL -(-117 -4164 UP) +(-117 -4140 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 @@ -407,7 +407,7 @@ NIL (-119 |p|) ((|constructor| (NIL "Stream-based implementation of Qp: numbers are represented as sum(\\spad{i} = \\spad{k}..,{} a[\\spad{i}] * p^i),{} where the a[\\spad{i}] lie in -(\\spad{p} - 1)\\spad{/2},{}...,{}(\\spad{p} - 1)\\spad{/2}."))) ((-4502 . T) (-4508 . T) (-4503 . T) ((-4512 "*") . T) (-4504 . T) (-4505 . T) (-4507 . T)) -((|HasCategory| (-118 |#1|) (QUOTE (-940))) (|HasCategory| (-118 |#1|) (|%list| (QUOTE -1070) (QUOTE (-1209)))) (|HasCategory| (-118 |#1|) (QUOTE (-147))) (|HasCategory| (-118 |#1|) (QUOTE (-149))) (|HasCategory| (-118 |#1|) (|%list| (QUOTE -633) (QUOTE (-549)))) (|HasCategory| (-118 |#1|) (QUOTE (-1052))) (|HasCategory| (-118 |#1|) (QUOTE (-844))) (|HasCategory| (-118 |#1|) (QUOTE (-872))) (-4144 (|HasCategory| (-118 |#1|) (QUOTE (-844))) (|HasCategory| (-118 |#1|) (QUOTE (-872)))) (|HasCategory| (-118 |#1|) (|%list| (QUOTE -1070) (QUOTE (-560)))) (|HasCategory| (-118 |#1|) (QUOTE (-1184))) (|HasCategory| (-118 |#1|) (|%list| (QUOTE -912) (QUOTE (-391)))) (|HasCategory| (-118 |#1|) (|%list| (QUOTE -912) (QUOTE (-560)))) (|HasCategory| (-118 |#1|) (|%list| (QUOTE -633) (|%list| (QUOTE -916) (QUOTE (-391))))) (|HasCategory| (-118 |#1|) (|%list| (QUOTE -633) (|%list| (QUOTE -916) (QUOTE (-560))))) (|HasCategory| (-118 |#1|) (|%list| (QUOTE -660) (QUOTE (-560)))) (|HasCategory| (-118 |#1|) (QUOTE (-239))) (|HasCategory| (-118 |#1|) (|%list| (QUOTE -930) (QUOTE (-1209)))) (|HasCategory| (-118 |#1|) (QUOTE (-240))) (|HasCategory| (-118 |#1|) (|%list| (QUOTE -928) (QUOTE (-1209)))) (|HasCategory| (-118 |#1|) (|%list| (QUOTE -528) (QUOTE (-1209)) (|%list| (QUOTE -118) (|devaluate| |#1|)))) (|HasCategory| (-118 |#1|) (|%list| (QUOTE -321) (|%list| (QUOTE -118) (|devaluate| |#1|)))) (|HasCategory| (-118 |#1|) (|%list| (QUOTE -298) (|%list| (QUOTE -118) (|devaluate| |#1|)) (|%list| (QUOTE -118) (|devaluate| |#1|)))) (|HasCategory| (-118 |#1|) (QUOTE (-319))) (|HasCategory| (-118 |#1|) (QUOTE (-559))) (-12 (|HasCategory| $ (QUOTE (-147))) (|HasCategory| (-118 |#1|) (QUOTE (-940)))) (-4144 (-12 (|HasCategory| $ (QUOTE (-147))) (|HasCategory| (-118 |#1|) (QUOTE (-940)))) (|HasCategory| (-118 |#1|) (QUOTE (-147))))) +((|HasCategory| (-118 |#1|) (QUOTE (-940))) (|HasCategory| (-118 |#1|) (|%list| (QUOTE -1070) (QUOTE (-1209)))) (|HasCategory| (-118 |#1|) (QUOTE (-147))) (|HasCategory| (-118 |#1|) (QUOTE (-149))) (|HasCategory| (-118 |#1|) (|%list| (QUOTE -633) (QUOTE (-549)))) (|HasCategory| (-118 |#1|) (QUOTE (-1052))) (|HasCategory| (-118 |#1|) (QUOTE (-844))) (|HasCategory| (-118 |#1|) (QUOTE (-872))) (-4118 (|HasCategory| (-118 |#1|) (QUOTE (-844))) (|HasCategory| (-118 |#1|) (QUOTE (-872)))) (|HasCategory| (-118 |#1|) (|%list| (QUOTE -1070) (QUOTE (-560)))) (|HasCategory| (-118 |#1|) (QUOTE (-1184))) (|HasCategory| (-118 |#1|) (|%list| (QUOTE -912) (QUOTE (-391)))) (|HasCategory| (-118 |#1|) (|%list| (QUOTE -912) (QUOTE (-560)))) (|HasCategory| (-118 |#1|) (|%list| (QUOTE -633) (|%list| (QUOTE -916) (QUOTE (-391))))) (|HasCategory| (-118 |#1|) (|%list| (QUOTE -633) (|%list| (QUOTE -916) (QUOTE (-560))))) (|HasCategory| (-118 |#1|) (|%list| (QUOTE -660) (QUOTE (-560)))) (|HasCategory| (-118 |#1|) (QUOTE (-239))) (|HasCategory| (-118 |#1|) (|%list| (QUOTE -930) (QUOTE (-1209)))) (|HasCategory| (-118 |#1|) (QUOTE (-240))) (|HasCategory| (-118 |#1|) (|%list| (QUOTE -928) (QUOTE (-1209)))) (|HasCategory| (-118 |#1|) (|%list| (QUOTE -528) (QUOTE (-1209)) (|%list| (QUOTE -118) (|devaluate| |#1|)))) (|HasCategory| (-118 |#1|) (|%list| (QUOTE -321) (|%list| (QUOTE -118) (|devaluate| |#1|)))) (|HasCategory| (-118 |#1|) (|%list| (QUOTE -298) (|%list| (QUOTE -118) (|devaluate| |#1|)) (|%list| (QUOTE -118) (|devaluate| |#1|)))) (|HasCategory| (-118 |#1|) (QUOTE (-319))) (|HasCategory| (-118 |#1|) (QUOTE (-559))) (-12 (|HasCategory| $ (QUOTE (-147))) (|HasCategory| (-118 |#1|) (QUOTE (-940)))) (-4118 (-12 (|HasCategory| $ (QUOTE (-147))) (|HasCategory| (-118 |#1|) (QUOTE (-940)))) (|HasCategory| (-118 |#1|) (QUOTE (-147))))) (-120 A S) ((|constructor| (NIL "A binary-recursive aggregate has 0,{} 1 or 2 children and serves as a model for a binary tree or a doubly-linked aggregate structure")) (|setright!| (($ $ $) "\\spad{setright!(a,x)} sets the right child of \\spad{t} to be \\spad{x}.")) (|setleft!| (($ $ $) "\\spad{setleft!(a,b)} sets the left child of \\axiom{a} to be \\spad{b}.")) (|setelt| (($ $ "right" $) "\\spad{setelt(a,\"right\",b)} (also written \\axiom{\\spad{b} . right := \\spad{b}}) is equivalent to \\axiom{setright!(a,{}\\spad{b})}.") (($ $ "left" $) "\\spad{setelt(a,\"left\",b)} (also written \\axiom{a . left := \\spad{b}}) is equivalent to \\axiom{setleft!(a,{}\\spad{b})}.")) (|right| (($ $) "\\spad{right(a)} returns the right child.")) (|elt| (($ $ "right") "\\spad{elt(a,\"right\")} (also written: \\axiom{a . right}) is equivalent to \\axiom{right(a)}.") (($ $ "left") "\\spad{elt(u,\"left\")} (also written: \\axiom{a . left}) is equivalent to \\axiom{left(a)}.")) (|left| (($ $) "\\spad{left(u)} returns the left child."))) NIL @@ -423,7 +423,7 @@ NIL (-123 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"))) ((-4510 . T) (-4511 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1133))) (-4144 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-1133)))) (-4144 (-12 (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-888))))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-888)))) (|HasCategory| |#1| (QUOTE (-102)))) +((-12 (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1133))) (-4118 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-1133)))) (-4118 (-12 (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-888))))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-888)))) (|HasCategory| |#1| (QUOTE (-102)))) (-124 S) ((|constructor| (NIL "The bit aggregate category models aggregates representing large quantities of Boolean data.")) (|xor| (($ $ $) "\\spad{xor(a,b)} returns the logical {\\em exclusive-or} of bit aggregates \\axiom{a} and \\axiom{\\spad{b}}.")) (|nor| (($ $ $) "\\spad{nor(a,b)} returns the logical {\\em nor} of bit aggregates \\axiom{a} and \\axiom{\\spad{b}}.")) (|nand| (($ $ $) "\\spad{nand(a,b)} returns the logical {\\em nand} of bit aggregates \\axiom{a} and \\axiom{\\spad{b}}."))) NIL @@ -443,11 +443,11 @@ NIL (-128 S) ((|constructor| (NIL "\\spadtype{BinaryTournament(S)} is the domain of binary trees where elements are ordered down the tree. A binary search tree is either empty or is a node containing a \\spadfun{value} of type \\spad{S},{} and a \\spadfun{right} and a \\spadfun{left} which are both \\spadtype{BinaryTree(S)}")) (|insert!| (($ |#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."))) ((-4510 . T) (-4511 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1133))) (-4144 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-1133)))) (-4144 (-12 (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-888))))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-888)))) (|HasCategory| |#1| (QUOTE (-102)))) +((-12 (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1133))) (-4118 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-1133)))) (-4118 (-12 (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-888))))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-888)))) (|HasCategory| |#1| (QUOTE (-102)))) (-129 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."))) ((-4510 . T) (-4511 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1133))) (-4144 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-1133)))) (-4144 (-12 (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-888))))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-888)))) (|HasCategory| |#1| (QUOTE (-102)))) +((-12 (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1133))) (-4118 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-1133)))) (-4118 (-12 (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-888))))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-888)))) (|HasCategory| |#1| (QUOTE (-102)))) (-130) ((|constructor| (NIL "Byte is the datatype of 8-bit sized unsigned integer values.")) (|sample| (($) "\\spad{sample} gives a sample datum of type Byte.")) (|bitior| (($ $ $) "bitor(\\spad{x},{}\\spad{y}) returns the bitwise `inclusive or' of `x' and `y'.")) (|bitand| (($ $ $) "\\spad{bitand(x,y)} returns the bitwise `and' of `x' and `y'.")) (|byte| (($ (|NonNegativeInteger|)) "\\spad{byte(x)} injects the unsigned integer value `v' into the Byte algebra. `v' must be non-negative and less than 256."))) NIL @@ -455,7 +455,7 @@ NIL (-131) ((|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 `n'. The array can then store up to `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 `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."))) ((-4511 . T) (-4510 . T)) -((-4144 (-12 (|HasCategory| (-130) (QUOTE (-872))) (|HasCategory| (-130) (|%list| (QUOTE -321) (QUOTE (-130))))) (-12 (|HasCategory| (-130) (QUOTE (-1133))) (|HasCategory| (-130) (|%list| (QUOTE -321) (QUOTE (-130)))))) (-4144 (-12 (|HasCategory| (-130) (QUOTE (-1133))) (|HasCategory| (-130) (|%list| (QUOTE -321) (QUOTE (-130))))) (|HasCategory| (-130) (|%list| (QUOTE -632) (QUOTE (-888))))) (|HasCategory| (-130) (|%list| (QUOTE -633) (QUOTE (-549)))) (-4144 (|HasCategory| (-130) (QUOTE (-872))) (|HasCategory| (-130) (QUOTE (-1133)))) (|HasCategory| (-130) (QUOTE (-872))) (-4144 (|HasCategory| (-130) (QUOTE (-102))) (|HasCategory| (-130) (QUOTE (-872))) (|HasCategory| (-130) (QUOTE (-1133)))) (|HasCategory| (-560) (QUOTE (-872))) (|HasCategory| (-130) (QUOTE (-1133))) (|HasCategory| (-130) (|%list| (QUOTE -632) (QUOTE (-888)))) (|HasCategory| (-130) (QUOTE (-102))) (-12 (|HasCategory| (-130) (QUOTE (-1133))) (|HasCategory| (-130) (|%list| (QUOTE -321) (QUOTE (-130)))))) +((-4118 (-12 (|HasCategory| (-130) (QUOTE (-872))) (|HasCategory| (-130) (|%list| (QUOTE -321) (QUOTE (-130))))) (-12 (|HasCategory| (-130) (QUOTE (-1133))) (|HasCategory| (-130) (|%list| (QUOTE -321) (QUOTE (-130)))))) (-4118 (-12 (|HasCategory| (-130) (QUOTE (-1133))) (|HasCategory| (-130) (|%list| (QUOTE -321) (QUOTE (-130))))) (|HasCategory| (-130) (|%list| (QUOTE -632) (QUOTE (-888))))) (|HasCategory| (-130) (|%list| (QUOTE -633) (QUOTE (-549)))) (-4118 (|HasCategory| (-130) (QUOTE (-872))) (|HasCategory| (-130) (QUOTE (-1133)))) (|HasCategory| (-130) (QUOTE (-872))) (-4118 (|HasCategory| (-130) (QUOTE (-102))) (|HasCategory| (-130) (QUOTE (-872))) (|HasCategory| (-130) (QUOTE (-1133)))) (|HasCategory| (-560) (QUOTE (-872))) (|HasCategory| (-130) (QUOTE (-1133))) (|HasCategory| (-130) (|%list| (QUOTE -632) (QUOTE (-888)))) (|HasCategory| (-130) (QUOTE (-102))) (-12 (|HasCategory| (-130) (QUOTE (-1133))) (|HasCategory| (-130) (|%list| (QUOTE -321) (QUOTE (-130)))))) (-132) ((|constructor| (NIL "This datatype describes byte order of machine values stored memory.")) (|unknownEndian| (($) "\\spad{unknownEndian} for none of the above.")) (|bigEndian| (($) "\\spad{bigEndian} describes big endian host")) (|littleEndian| (($) "\\spad{littleEndian} describes little endian host"))) NIL @@ -476,11 +476,11 @@ NIL ((|constructor| (NIL "Members of the domain CardinalNumber are values indicating the cardinality of sets,{} both finite and infinite. Arithmetic operations are defined on cardinal numbers as follows. \\blankline If \\spad{x = \\#X} and \\spad{y = \\#Y} then \\indented{2}{\\spad{x+y\\space{2}= \\#(X+Y)}\\space{3}\\tab{30}disjoint union} \\indented{2}{\\spad{x-y\\space{2}= \\#(X-Y)}\\space{3}\\tab{30}relative complement} \\indented{2}{\\spad{x*y\\space{2}= \\#(X*Y)}\\space{3}\\tab{30}cartesian product} \\indented{2}{\\spad{x**y = \\#(X**Y)}\\space{2}\\tab{30}\\spad{X**Y = \\{g| g:Y->X\\}}} \\blankline The non-negative integers have a natural construction as cardinals \\indented{2}{\\spad{0 = \\#\\{\\}},{} \\spad{1 = \\{0\\}},{} \\spad{2 = \\{0, 1\\}},{} ...,{} \\spad{n = \\{i| 0 <= i < n\\}}.} \\blankline That \\spad{0} acts as a zero for the multiplication of cardinals is equivalent to the axiom of choice. \\blankline The generalized continuum hypothesis asserts \\center{\\spad{2**Aleph i = Aleph(i+1)}} and is independent of the axioms of set theory [Goedel 1940]. \\blankline Three commonly encountered cardinal numbers are \\indented{3}{\\spad{a = \\#Z}\\space{7}\\tab{30}countable infinity} \\indented{3}{\\spad{c = \\#R}\\space{7}\\tab{30}the continuum} \\indented{3}{\\spad{f = \\#\\{g| g:[0,1]->R\\}}} \\blankline In this domain,{} these values are obtained using \\indented{3}{\\spad{a := Aleph 0},{} \\spad{c := 2**a},{} \\spad{f := 2**c}.} \\blankline")) (|generalizedContinuumHypothesisAssumed| (((|Boolean|) (|Boolean|)) "\\spad{generalizedContinuumHypothesisAssumed(bool)} is used to dictate whether the hypothesis is to be assumed.")) (|generalizedContinuumHypothesisAssumed?| (((|Boolean|)) "\\spad{generalizedContinuumHypothesisAssumed?()} tests if the hypothesis is currently assumed.")) (|countable?| (((|Boolean|) $) "\\spad{countable?(\\spad{a})} determines whether \\spad{a} is a countable cardinal,{} \\spadignore{i.e.} an integer or \\spad{Aleph 0}.")) (|finite?| (((|Boolean|) $) "\\spad{finite?(\\spad{a})} determines whether \\spad{a} is a finite cardinal,{} \\spadignore{i.e.} an integer.")) (|Aleph| (($ (|NonNegativeInteger|)) "\\spad{Aleph(n)} provides the named (infinite) cardinal number.")) (** (($ $ $) "\\spad{x**y} returns \\spad{\\#(X**Y)} where \\spad{X**Y} is defined \\indented{1}{as \\spad{\\{g| g:Y->X\\}}.}")) (- (((|Union| $ "failed") $ $) "\\spad{x - y} returns an element \\spad{z} such that \\spad{z+y=x} or \"failed\" if no such element exists.")) (|commutative| ((|attribute| "*") "a domain \\spad{D} has \\spad{commutative(\"*\")} if it has an operation \\spad{\"*\": (D,D) -> D} which is commutative."))) (((-4512 "*") . T)) NIL -(-137 |minix| -2127 R) +(-137 |minix| -2123 R) ((|constructor| (NIL "CartesianTensor(minix,{}dim,{}\\spad{R}) provides Cartesian tensors with components belonging to a commutative ring \\spad{R}. These tensors can have any number of indices. Each index takes values from \\spad{minix} to \\spad{minix + dim - 1}.")) (|sample| (($) "\\spad{sample()} returns an object of type \\%.")) (|unravel| (($ (|List| |#3|)) "\\spad{unravel(t)} produces a tensor from a list of components such that \\indented{2}{\\spad{unravel(ravel(t)) = t}.}")) (|ravel| (((|List| |#3|) $) "\\spad{ravel(t)} produces a list of components from a tensor such that \\indented{2}{\\spad{unravel(ravel(t)) = t}.}")) (|leviCivitaSymbol| (($) "\\spad{leviCivitaSymbol()} is the rank \\spad{dim} tensor defined by \\spad{leviCivitaSymbol()(i1,...idim) = +1/0/-1} if \\spad{i1,...,idim} is an even/is nota /is an odd permutation of \\spad{minix,...,minix+dim-1}.")) (|kroneckerDelta| (($) "\\spad{kroneckerDelta()} is the rank 2 tensor defined by \\indented{3}{\\spad{kroneckerDelta()(i,j)}} \\indented{6}{\\spad{= 1\\space{2}if i = j}} \\indented{6}{\\spad{= 0 if\\space{2}i \\~= j}}")) (|reindex| (($ $ (|List| (|Integer|))) "\\spad{reindex(t,[i1,...,idim])} permutes the indices of \\spad{t}. For example,{} if \\spad{r = reindex(t, [4,1,2,3])} for a rank 4 tensor \\spad{t},{} then \\spad{r} is the rank for tensor given by \\indented{4}{\\spad{r(i,j,k,l) = t(l,i,j,k)}.}")) (|transpose| (($ $ (|Integer|) (|Integer|)) "\\spad{transpose(t,i,j)} exchanges the \\spad{i}\\spad{-}th and \\spad{j}\\spad{-}th indices of \\spad{t}. For example,{} if \\spad{r = transpose(t,2,3)} for a rank 4 tensor \\spad{t},{} then \\spad{r} is the rank 4 tensor given by \\indented{4}{\\spad{r(i,j,k,l) = t(i,k,j,l)}.}") (($ $) "\\spad{transpose(t)} exchanges the first and last indices of \\spad{t}. For example,{} if \\spad{r = transpose(t)} for a rank 4 tensor \\spad{t},{} then \\spad{r} is the rank 4 tensor given by \\indented{4}{\\spad{r(i,j,k,l) = t(l,j,k,i)}.}")) (|contract| (($ $ (|Integer|) (|Integer|)) "\\spad{contract(t,i,j)} is the contraction of tensor \\spad{t} which sums along the \\spad{i}\\spad{-}th and \\spad{j}\\spad{-}th indices. For example,{} if \\spad{r = contract(t,1,3)} for a rank 4 tensor \\spad{t},{} then \\spad{r} is the rank 2 \\spad{(= 4 - 2)} tensor given by \\indented{4}{\\spad{r(i,j) = sum(h=1..dim,t(h,i,h,j))}.}") (($ $ (|Integer|) $ (|Integer|)) "\\spad{contract(t,i,s,j)} is the inner product of tenors \\spad{s} and \\spad{t} which sums along the \\spad{k1}\\spad{-}th index of \\spad{t} and the \\spad{k2}\\spad{-}th index of \\spad{s}. For example,{} if \\spad{r = contract(s,2,t,1)} for rank 3 tensors rank 3 tensors \\spad{s} and \\spad{t},{} then \\spad{r} is the rank 4 \\spad{(= 3 + 3 - 2)} tensor given by \\indented{4}{\\spad{r(i,j,k,l) = sum(h=1..dim,s(i,h,j)*t(h,k,l))}.}")) (* (($ $ $) "\\spad{s*t} is the inner product of the tensors \\spad{s} and \\spad{t} which contracts the last index of \\spad{s} with the first index of \\spad{t},{} \\spadignore{i.e.} \\indented{4}{\\spad{t*s = contract(t,rank t, s, 1)}} \\indented{4}{\\spad{t*s = sum(k=1..N, t[i1,..,iN,k]*s[k,j1,..,jM])}} This is compatible with the use of \\spad{M*v} to denote the matrix-vector inner product.")) (|product| (($ $ $) "\\spad{product(s,t)} is the outer product of the tensors \\spad{s} and \\spad{t}. For example,{} if \\spad{r = product(s,t)} for rank 2 tensors \\spad{s} and \\spad{t},{} then \\spad{r} is a rank 4 tensor given by \\indented{4}{\\spad{r(i,j,k,l) = s(i,j)*t(k,l)}.}")) (|elt| ((|#3| $ (|List| (|Integer|))) "\\spad{elt(t,[i1,...,iN])} gives a component of a rank \\spad{N} tensor.") ((|#3| $ (|Integer|) (|Integer|) (|Integer|) (|Integer|)) "\\spad{elt(t,i,j,k,l)} gives a component of a rank 4 tensor.") ((|#3| $ (|Integer|) (|Integer|) (|Integer|)) "\\spad{elt(t,i,j,k)} gives a component of a rank 3 tensor.") ((|#3| $ (|Integer|) (|Integer|)) "\\spad{elt(t,i,j)} gives a component of a rank 2 tensor.") ((|#3| $) "\\spad{elt(t)} gives the component of a rank 0 tensor.")) (|rank| (((|NonNegativeInteger|) $) "\\spad{rank(t)} returns the tensorial rank of \\spad{t} (that is,{} the number of indices). This is the same as the graded module degree.")) (|coerce| (($ (|List| $)) "\\spad{coerce([t_1,...,t_dim])} allows tensors to be constructed using lists.") (($ (|List| |#3|)) "\\spad{coerce([r_1,...,r_dim])} allows tensors to be constructed using lists.") (($ (|SquareMatrix| |#2| |#3|)) "\\spad{coerce(m)} views a matrix as a rank 2 tensor.") (($ (|DirectProduct| |#2| |#3|)) "\\spad{coerce(v)} views a vector as a rank 1 tensor."))) NIL NIL -(-138 |minix| -2127 S T$) +(-138 |minix| -2123 S T$) ((|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 @@ -503,7 +503,7 @@ NIL (-143) ((|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}."))) ((-4510 . T) (-4500 . T) (-4511 . T)) -((-4144 (-12 (|HasCategory| (-146) (QUOTE (-381))) (|HasCategory| (-146) (|%list| (QUOTE -321) (QUOTE (-146))))) (-12 (|HasCategory| (-146) (QUOTE (-1133))) (|HasCategory| (-146) (|%list| (QUOTE -321) (QUOTE (-146)))))) (|HasCategory| (-146) (|%list| (QUOTE -633) (QUOTE (-549)))) (|HasCategory| (-146) (QUOTE (-381))) (|HasCategory| (-146) (QUOTE (-872))) (|HasCategory| (-146) (QUOTE (-1133))) (|HasCategory| (-146) (|%list| (QUOTE -632) (QUOTE (-888)))) (|HasCategory| (-146) (QUOTE (-102))) (-12 (|HasCategory| (-146) (QUOTE (-1133))) (|HasCategory| (-146) (|%list| (QUOTE -321) (QUOTE (-146)))))) +((-4118 (-12 (|HasCategory| (-146) (QUOTE (-381))) (|HasCategory| (-146) (|%list| (QUOTE -321) (QUOTE (-146))))) (-12 (|HasCategory| (-146) (QUOTE (-1133))) (|HasCategory| (-146) (|%list| (QUOTE -321) (QUOTE (-146)))))) (|HasCategory| (-146) (|%list| (QUOTE -633) (QUOTE (-549)))) (|HasCategory| (-146) (QUOTE (-381))) (|HasCategory| (-146) (QUOTE (-872))) (|HasCategory| (-146) (QUOTE (-1133))) (|HasCategory| (-146) (|%list| (QUOTE -632) (QUOTE (-888)))) (|HasCategory| (-146) (QUOTE (-102))) (-12 (|HasCategory| (-146) (QUOTE (-1133))) (|HasCategory| (-146) (|%list| (QUOTE -321) (QUOTE (-146)))))) (-144 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}'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}'s.")) (|commonDenominator| ((|#1| |#3|) "\\spad{commonDenominator([q1,...,qn])} returns a common denominator \\spad{d} for \\spad{q1},{}...,{}qn."))) NIL @@ -528,7 +528,7 @@ NIL ((|constructor| (NIL "Rings of Characteristic Zero."))) ((-4507 . T)) NIL -(-150 -4164 UP UPUP) +(-150 -4140 UP UPUP) ((|constructor| (NIL "Tools to send a point to infinity on an algebraic curve.")) (|chvar| (((|Record| (|:| |func| |#3|) (|:| |poly| |#3|) (|:| |c1| (|Fraction| |#2|)) (|:| |c2| (|Fraction| |#2|)) (|:| |deg| (|NonNegativeInteger|))) |#3| |#3|) "\\spad{chvar(f(x,y), p(x,y))} returns \\spad{[g(z,t), q(z,t), c1(z), c2(z), n]} such that under the change of variable \\spad{x = c1(z)},{} \\spad{y = t * c2(z)},{} one gets \\spad{f(x,y) = g(z,t)}. The algebraic relation between \\spad{x} and \\spad{y} is \\spad{p(x, y) = 0}. The algebraic relation between \\spad{z} and \\spad{t} is \\spad{q(z, t) = 0}.")) (|eval| ((|#3| |#3| (|Fraction| |#2|) (|Fraction| |#2|)) "\\spad{eval(p(x,y), f(x), g(x))} returns \\spad{p(f(x), y * g(x))}.")) (|goodPoint| ((|#1| |#3| |#3|) "\\spad{goodPoint(p, q)} returns an integer a such that a is neither a pole of \\spad{p(x,y)} nor a branch point of \\spad{q(x,y) = 0}.")) (|rootPoly| (((|Record| (|:| |exponent| (|NonNegativeInteger|)) (|:| |coef| (|Fraction| |#2|)) (|:| |radicand| |#2|)) (|Fraction| |#2|) (|NonNegativeInteger|)) "\\spad{rootPoly(g, n)} returns \\spad{[m, c, P]} such that \\spad{c * g ** (1/n) = P ** (1/m)} thus if \\spad{y**n = g},{} then \\spad{z**m = P} where \\spad{z = c * y}.")) (|radPoly| (((|Union| (|Record| (|:| |radicand| (|Fraction| |#2|)) (|:| |deg| (|NonNegativeInteger|))) "failed") |#3|) "\\spad{radPoly(p(x, y))} returns \\spad{[c(x), n]} if \\spad{p} is of the form \\spad{y**n - c(x)},{} \"failed\" otherwise.")) (|mkIntegral| (((|Record| (|:| |coef| (|Fraction| |#2|)) (|:| |poly| |#3|)) |#3|) "\\spad{mkIntegral(p(x,y))} returns \\spad{[c(x), q(x,z)]} such that \\spad{z = c * y} is integral. The algebraic relation between \\spad{x} and \\spad{y} is \\spad{p(x, y) = 0}. The algebraic relation between \\spad{x} and \\spad{z} is \\spad{q(x, z) = 0}."))) NIL NIL @@ -568,7 +568,7 @@ NIL ((|constructor| (NIL "Color() specifies a domain of 27 colors provided in the \\Language{} system (the colors mix additively).")) (|color| (($ (|Integer|)) "\\spad{color(i)} returns a color of the indicated hue \\spad{i}.")) (|numberOfHues| (((|PositiveInteger|)) "\\spad{numberOfHues()} returns the number of total hues,{} set in totalHues.")) (|hue| (((|Integer|) $) "\\spad{hue(c)} returns the hue index of the indicated color \\spad{c}.")) (|blue| (($) "\\spad{blue()} returns the position of the blue hue from total hues.")) (|green| (($) "\\spad{green()} returns the position of the green hue from total hues.")) (|yellow| (($) "\\spad{yellow()} returns the position of the yellow hue from total hues.")) (|red| (($) "\\spad{red()} returns the position of the red hue from total hues.")) (+ (($ $ $) "\\spad{c1 + c2} additively mixes the two colors \\spad{c1} and \\spad{c2}.")) (* (($ (|DoubleFloat|) $) "\\spad{s * c},{} returns the color \\spad{c},{} whose weighted shade has been scaled by \\spad{s}.") (($ (|PositiveInteger|) $) "\\spad{s * c},{} returns the color \\spad{c},{} whose weighted shade has been scaled by \\spad{s}."))) NIL NIL -(-160 R -4164) +(-160 R -4140) ((|constructor| (NIL "Provides combinatorial functions over an integral domain.")) (|ipow| ((|#2| (|List| |#2|)) "\\spad{ipow(l)} should be local but conditional.")) (|iidprod| ((|#2| (|List| |#2|)) "\\spad{iidprod(l)} should be local but conditional.")) (|iidsum| ((|#2| (|List| |#2|)) "\\spad{iidsum(l)} should be local but conditional.")) (|iipow| ((|#2| (|List| |#2|)) "\\spad{iipow(l)} should be local but conditional.")) (|iiperm| ((|#2| (|List| |#2|)) "\\spad{iiperm(l)} should be local but conditional.")) (|iibinom| ((|#2| (|List| |#2|)) "\\spad{iibinom(l)} should be local but conditional.")) (|iifact| ((|#2| |#2|) "\\spad{iifact(x)} should be local but conditional.")) (|product| ((|#2| |#2| (|SegmentBinding| |#2|)) "\\spad{product(f(n), n = a..b)} returns \\spad{f}(a) * ... * \\spad{f}(\\spad{b}) as a formal product.") ((|#2| |#2| (|Symbol|)) "\\spad{product(f(n), n)} returns the formal product \\spad{P}(\\spad{n}) which verifies \\spad{P}(\\spad{n+1})/P(\\spad{n}) = \\spad{f}(\\spad{n}).")) (|summation| ((|#2| |#2| (|SegmentBinding| |#2|)) "\\spad{summation(f(n), n = a..b)} returns \\spad{f}(a) + ... + \\spad{f}(\\spad{b}) as a formal sum.") ((|#2| |#2| (|Symbol|)) "\\spad{summation(f(n), n)} returns the formal sum \\spad{S}(\\spad{n}) which verifies \\spad{S}(\\spad{n+1}) - \\spad{S}(\\spad{n}) = \\spad{f}(\\spad{n}).")) (|factorials| ((|#2| |#2| (|Symbol|)) "\\spad{factorials(f, x)} rewrites the permutations and binomials in \\spad{f} involving \\spad{x} in terms of factorials.") ((|#2| |#2|) "\\spad{factorials(f)} rewrites the permutations and binomials in \\spad{f} in terms of factorials.")) (|factorial| ((|#2| |#2|) "\\spad{factorial(n)} returns the factorial of \\spad{n},{} \\spadignore{i.e.} n!.")) (|permutation| ((|#2| |#2| |#2|) "\\spad{permutation(n, r)} returns the number of permutations of \\spad{n} objects taken \\spad{r} at a time,{} \\spadignore{i.e.} n!/(\\spad{n}-\\spad{r})!.")) (|binomial| ((|#2| |#2| |#2|) "\\spad{binomial(n, r)} returns the number of subsets of \\spad{r} objects taken among \\spad{n} objects,{} \\spadignore{i.e.} n!/(r! * (\\spad{n}-\\spad{r})!).")) (** ((|#2| |#2| |#2|) "\\spad{a ** b} is the formal exponential a**b.")) (|operator| (((|BasicOperator|) (|BasicOperator|)) "\\spad{operator(op)} returns a copy of \\spad{op} with the domain-dependent properties appropriate for \\spad{F}; error if \\spad{op} is not a combinatorial operator.")) (|belong?| (((|Boolean|) (|BasicOperator|)) "\\spad{belong?(op)} is \\spad{true} if \\spad{op} is a combinatorial operator."))) NIL NIL @@ -602,7 +602,7 @@ NIL ((|HasCategory| |#2| (QUOTE (-940))) (|HasCategory| |#2| (QUOTE (-559))) (|HasCategory| |#2| (QUOTE (-1034))) (|HasCategory| |#2| (QUOTE (-1235))) (|HasCategory| |#2| (QUOTE (-1092))) (|HasCategory| |#2| (QUOTE (-1052))) (|HasCategory| |#2| (QUOTE (-147))) (|HasCategory| |#2| (QUOTE (-149))) (|HasCategory| |#2| (|%list| (QUOTE -633) (QUOTE (-549)))) (|HasCategory| |#2| (QUOTE (-376))) (|HasAttribute| |#2| (QUOTE -4506)) (|HasAttribute| |#2| (QUOTE -4509)) (|HasCategory| |#2| (QUOTE (-319))) (|HasCategory| |#2| (QUOTE (-571)))) (-168 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})"))) -((-4503 -4144 (|has| |#1| (-571)) (-12 (|has| |#1| (-319)) (|has| |#1| (-940)))) (-4508 |has| |#1| (-376)) (-4502 |has| |#1| (-376)) (-4506 |has| |#1| (-6 -4506)) (-4509 |has| |#1| (-6 -4509)) (-2873 . T) ((-4512 "*") . T) (-4504 . T) (-4505 . T) (-4507 . T)) +((-4503 -4118 (|has| |#1| (-571)) (-12 (|has| |#1| (-319)) (|has| |#1| (-940)))) (-4508 |has| |#1| (-376)) (-4502 |has| |#1| (-376)) (-4506 |has| |#1| (-6 -4506)) (-4509 |has| |#1| (-6 -4509)) (-2864 . T) ((-4512 "*") . T) (-4504 . T) (-4505 . T) (-4507 . T)) NIL (-169 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}."))) -((-4503 -4144 (|has| |#1| (-571)) (-12 (|has| |#1| (-319)) (|has| |#1| (-940)))) (-4508 |has| |#1| (-376)) (-4502 |has| |#1| (-376)) (-4506 |has| |#1| (-6 -4506)) (-4509 |has| |#1| (-6 -4509)) (-2873 . T) ((-4512 "*") . T) (-4504 . T) (-4505 . T) (-4507 . 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(|map| (((|Complex| |#2|) (|Mapping| |#2| |#1|) (|Complex| |#1|)) "\\spad{map(f,u)} maps \\spad{f} onto real and imaginary parts of \\spad{u}."))) NIL @@ -692,7 +692,7 @@ NIL ((|constructor| (NIL "This domain enumerates the three kinds of constructors available in OpenAxiom: category constructors,{} domain constructors,{} and package constructors.")) (|package| (($) "`package' is the kind of package constructors.")) (|domain| (($) "`domain' is the kind of domain constructors")) (|category| (($) "`category' is the kind of category constructors"))) NIL NIL -(-191 R -4164) +(-191 R -4140) ((|constructor| (NIL "\\spadtype{ComplexTrigonometricManipulations} provides function that compute the real and imaginary parts of complex functions.")) (|complexForm| (((|Complex| (|Expression| |#1|)) |#2|) "\\spad{complexForm(f)} returns \\spad{[real f, imag f]}.")) (|trigs| ((|#2| |#2|) "\\spad{trigs(f)} rewrites all the complex logs and exponentials appearing in \\spad{f} in terms of trigonometric functions.")) (|real?| (((|Boolean|) |#2|) "\\spad{real?(f)} returns \\spad{true} if \\spad{f = real f}.")) (|imag| (((|Expression| |#1|) |#2|) "\\spad{imag(f)} returns the imaginary part of \\spad{f} where \\spad{f} is a complex function.")) (|real| (((|Expression| |#1|) |#2|) "\\spad{real(f)} returns the real part of \\spad{f} where \\spad{f} is a complex function.")) (|complexElementary| ((|#2| |#2| (|Symbol|)) "\\spad{complexElementary(f, x)} rewrites the kernels of \\spad{f} involving \\spad{x} in terms of the 2 fundamental complex transcendental elementary functions: \\spad{log, exp}.") ((|#2| |#2|) "\\spad{complexElementary(f)} rewrites \\spad{f} in terms of the 2 fundamental complex transcendental elementary functions: \\spad{log, exp}.")) (|complexNormalize| ((|#2| |#2| (|Symbol|)) "\\spad{complexNormalize(f, x)} rewrites \\spad{f} using the least possible number of complex independent kernels involving \\spad{x}.") ((|#2| |#2|) "\\spad{complexNormalize(f)} rewrites \\spad{f} using the least possible number of complex independent kernels."))) NIL NIL @@ -804,23 +804,23 @@ NIL ((|constructor| (NIL "\\indented{1}{Author: Gabriel Dos Reis} Date Created: July 2,{} 2010 Date Last Modified: July 2,{} 2010 Descrption: \\indented{2}{Representation of a dual vector space basis,{} given by symbols.}")) (|dual| (($ (|LinearBasis| |#1|)) "\\spad{dual x} constructs the dual vector of a linear element which is part of a basis."))) NIL NIL -(-219 -4164 UP UPUP R) +(-219 -4140 UP UPUP R) ((|constructor| (NIL "This package provides functions for computing the residues of a function on an algebraic curve.")) (|doubleResultant| ((|#2| |#4| (|Mapping| |#2| |#2|)) "\\spad{doubleResultant(f, ')} returns \\spad{p}(\\spad{x}) whose roots are rational multiples of the residues of \\spad{f} at all its finite poles. Argument ' is the derivation to use."))) NIL NIL -(-220 -4164 FP) +(-220 -4140 FP) ((|constructor| (NIL "Package for the factorization of a univariate polynomial with coefficients in a finite field. The algorithm used is the \"distinct degree\" algorithm of Cantor-Zassenhaus,{} modified to use trace instead of the norm and a table for computing Frobenius as suggested by Naudin and Quitte .")) (|irreducible?| (((|Boolean|) |#2|) "\\spad{irreducible?(p)} tests whether the polynomial \\spad{p} is irreducible.")) (|tracePowMod| ((|#2| |#2| (|NonNegativeInteger|) |#2|) "\\spad{tracePowMod(u,k,v)} produces the sum of \\spad{u**(q**i)} for \\spad{i} running and q= size \\spad{F}")) (|trace2PowMod| ((|#2| |#2| (|NonNegativeInteger|) |#2|) "\\spad{trace2PowMod(u,k,v)} produces the sum of \\spad{u**(2**i)} for \\spad{i} running from 1 to \\spad{k} all computed modulo the polynomial \\spad{v}.")) (|exptMod| ((|#2| |#2| (|NonNegativeInteger|) |#2|) "\\spad{exptMod(u,k,v)} raises the polynomial \\spad{u} to the \\spad{k}th power modulo the polynomial \\spad{v}.")) (|separateFactors| (((|List| |#2|) (|List| (|Record| (|:| |deg| (|NonNegativeInteger|)) (|:| |prod| |#2|)))) "\\spad{separateFactors(lfact)} takes the list produced by \\spadfunFrom{separateDegrees}{DistinctDegreeFactorization} and produces the complete list of factors.")) (|separateDegrees| (((|List| (|Record| (|:| |deg| (|NonNegativeInteger|)) (|:| |prod| |#2|))) |#2|) "\\spad{separateDegrees(p)} splits the square free polynomial \\spad{p} into factors each of which is a product of irreducibles of the same degree.")) (|distdfact| (((|Record| (|:| |cont| |#1|) (|:| |factors| (|List| (|Record| (|:| |irr| |#2|) (|:| |pow| (|Integer|)))))) |#2| (|Boolean|)) "\\spad{distdfact(p,sqfrflag)} produces the complete factorization of the polynomial \\spad{p} returning an internal data structure. If argument \\spad{sqfrflag} is \\spad{true},{} the polynomial is assumed square free.")) (|factorSquareFree| (((|Factored| |#2|) |#2|) "\\spad{factorSquareFree(p)} produces the complete factorization of the square free polynomial \\spad{p}.")) (|factor| (((|Factored| |#2|) |#2|) "\\spad{factor(p)} produces the complete factorization of the polynomial \\spad{p}."))) 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T)) -((|HasCategory| (-560) (QUOTE (-940))) (|HasCategory| (-560) (|%list| (QUOTE -1070) (QUOTE (-1209)))) (|HasCategory| (-560) (QUOTE (-147))) (|HasCategory| (-560) (QUOTE (-149))) (|HasCategory| (-560) (|%list| (QUOTE -633) (QUOTE (-549)))) (|HasCategory| (-560) (QUOTE (-1052))) (|HasCategory| (-560) (QUOTE (-844))) (|HasCategory| (-560) (QUOTE (-872))) (-4144 (|HasCategory| (-560) (QUOTE (-844))) (|HasCategory| (-560) (QUOTE (-872)))) (|HasCategory| (-560) (|%list| (QUOTE -1070) (QUOTE (-560)))) (|HasCategory| (-560) (QUOTE (-1184))) (|HasCategory| (-560) (|%list| (QUOTE -912) (QUOTE (-391)))) (|HasCategory| (-560) (|%list| (QUOTE -912) (QUOTE (-560)))) (|HasCategory| (-560) (|%list| (QUOTE -633) (|%list| (QUOTE -916) (QUOTE (-391))))) (|HasCategory| (-560) (|%list| (QUOTE -633) (|%list| (QUOTE -916) (QUOTE (-560))))) (|HasCategory| (-560) (QUOTE (-239))) (|HasCategory| (-560) (|%list| (QUOTE -930) (QUOTE (-1209)))) (|HasCategory| (-560) (QUOTE (-240))) (|HasCategory| (-560) (|%list| (QUOTE -928) (QUOTE (-1209)))) (|HasCategory| (-560) (|%list| (QUOTE -528) (QUOTE (-1209)) (QUOTE (-560)))) (|HasCategory| (-560) (|%list| (QUOTE -321) (QUOTE (-560)))) (|HasCategory| (-560) (|%list| (QUOTE -298) (QUOTE (-560)) (QUOTE (-560)))) (|HasCategory| (-560) (QUOTE (-319))) (|HasCategory| (-560) (QUOTE (-559))) (|HasCategory| (-560) (|%list| (QUOTE -660) (QUOTE (-560)))) (-12 (|HasCategory| $ (QUOTE (-147))) (|HasCategory| (-560) (QUOTE (-940)))) (-4144 (-12 (|HasCategory| $ (QUOTE (-147))) (|HasCategory| (-560) (QUOTE (-940)))) (|HasCategory| (-560) (QUOTE (-147))))) +((|HasCategory| (-560) (QUOTE (-940))) (|HasCategory| (-560) (|%list| (QUOTE -1070) (QUOTE (-1209)))) (|HasCategory| (-560) (QUOTE (-147))) (|HasCategory| (-560) (QUOTE (-149))) (|HasCategory| (-560) (|%list| (QUOTE -633) (QUOTE (-549)))) (|HasCategory| (-560) (QUOTE (-1052))) (|HasCategory| (-560) (QUOTE (-844))) (|HasCategory| (-560) (QUOTE (-872))) (-4118 (|HasCategory| (-560) (QUOTE (-844))) (|HasCategory| (-560) (QUOTE (-872)))) (|HasCategory| (-560) (|%list| (QUOTE -1070) (QUOTE (-560)))) (|HasCategory| (-560) (QUOTE (-1184))) (|HasCategory| (-560) (|%list| (QUOTE -912) (QUOTE (-391)))) (|HasCategory| (-560) (|%list| (QUOTE -912) (QUOTE (-560)))) (|HasCategory| (-560) (|%list| (QUOTE -633) (|%list| (QUOTE -916) (QUOTE (-391))))) (|HasCategory| (-560) (|%list| (QUOTE -633) (|%list| (QUOTE -916) (QUOTE (-560))))) (|HasCategory| (-560) (QUOTE (-239))) (|HasCategory| (-560) (|%list| (QUOTE -930) (QUOTE (-1209)))) (|HasCategory| (-560) (QUOTE (-240))) (|HasCategory| (-560) (|%list| (QUOTE -928) (QUOTE (-1209)))) (|HasCategory| (-560) (|%list| (QUOTE -528) (QUOTE (-1209)) (QUOTE (-560)))) (|HasCategory| (-560) (|%list| (QUOTE -321) (QUOTE (-560)))) (|HasCategory| (-560) (|%list| (QUOTE -298) (QUOTE (-560)) (QUOTE (-560)))) (|HasCategory| (-560) (QUOTE (-319))) (|HasCategory| (-560) (QUOTE (-559))) (|HasCategory| (-560) (|%list| (QUOTE -660) (QUOTE (-560)))) (-12 (|HasCategory| $ (QUOTE (-147))) (|HasCategory| (-560) (QUOTE (-940)))) (-4118 (-12 (|HasCategory| $ (QUOTE (-147))) (|HasCategory| (-560) (QUOTE (-940)))) (|HasCategory| (-560) (QUOTE (-147))))) (-222) ((|constructor| (NIL "This domain represents the syntax of a definition.")) (|body| (((|SpadAst|) $) "\\spad{body(d)} returns the right hand side of the definition `d'.")) (|signature| (((|Signature|) $) "\\spad{signature(d)} returns the signature of the operation being defined. Note that this list may be partial in that it contains only the types actually specified in the definition.")) (|head| (((|HeadAst|) $) "\\spad{head(d)} returns the head of the definition `d'. This is a list of identifiers starting with the name of the operation followed by the name of the parameters,{} if any."))) NIL NIL -(-223 R -4164) +(-223 R -4140) ((|constructor| (NIL "\\spadtype{ElementaryFunctionDefiniteIntegration} provides functions to compute definite integrals of elementary functions.")) (|innerint| (((|Union| (|:| |f1| (|OrderedCompletion| |#2|)) (|:| |f2| (|List| (|OrderedCompletion| |#2|))) (|:| |fail| "failed") (|:| |pole| "potentialPole")) |#2| (|Symbol|) (|OrderedCompletion| |#2|) (|OrderedCompletion| |#2|) (|Boolean|)) "\\spad{innerint(f, x, a, b, ignore?)} should be local but conditional")) (|integrate| (((|Union| (|:| |f1| (|OrderedCompletion| |#2|)) (|:| |f2| (|List| (|OrderedCompletion| |#2|))) (|:| |fail| "failed") (|:| |pole| "potentialPole")) |#2| (|SegmentBinding| (|OrderedCompletion| |#2|)) (|String|)) "\\spad{integrate(f, x = a..b, \"noPole\")} returns the integral of \\spad{f(x)dx} from a to \\spad{b}. If it is not possible to check whether \\spad{f} has a pole for \\spad{x} between a and \\spad{b} (because of parameters),{} then this function will assume that \\spad{f} has no such pole. Error: if \\spad{f} has a pole for \\spad{x} between a and \\spad{b} or if the last argument is not \"noPole\".") (((|Union| (|:| |f1| (|OrderedCompletion| |#2|)) (|:| |f2| (|List| (|OrderedCompletion| |#2|))) (|:| |fail| "failed") (|:| |pole| "potentialPole")) |#2| (|SegmentBinding| (|OrderedCompletion| |#2|))) "\\spad{integrate(f, x = a..b)} returns the integral of \\spad{f(x)dx} from a to \\spad{b}. Error: if \\spad{f} has a pole for \\spad{x} between a and \\spad{b}."))) NIL NIL @@ -835,18 +835,18 @@ NIL (-226 S) ((|constructor| (NIL "Linked list implementation of a Dequeue")) (|dequeue| (($ (|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}."))) ((-4510 . T) (-4511 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1133))) (-4144 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-1133)))) (-4144 (-12 (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-888))))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-888)))) (|HasCategory| |#1| (QUOTE (-102)))) +((-12 (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1133))) (-4118 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-1133)))) (-4118 (-12 (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-888))))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-888)))) (|HasCategory| |#1| (QUOTE (-102)))) (-227 |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}."))) ((-4507 . T)) NIL -(-228 R -4164) +(-228 R -4140) ((|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 (-229) ((|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}."))) -((-2862 . T) (-4502 . T) (-4508 . T) (-4503 . T) ((-4512 "*") . T) (-4504 . T) (-4505 . T) (-4507 . T)) +((-2853 . T) (-4502 . T) (-4508 . T) (-4503 . T) ((-4512 "*") . T) (-4504 . T) (-4505 . T) (-4507 . T)) NIL (-230) ((|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)}.}"))) @@ -855,7 +855,7 @@ NIL (-231 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}"))) ((-4510 . T) (-4511 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1133))) (-4144 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-1133)))) (-4144 (-12 (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-888))))) (|HasCategory| |#1| (QUOTE (-319))) (|HasCategory| |#1| (QUOTE (-571))) (|HasAttribute| |#1| (QUOTE (-4512 "*"))) (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-888)))) (|HasCategory| |#1| (QUOTE (-102)))) +((-12 (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1133))) (-4118 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-1133)))) (-4118 (-12 (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-888))))) (|HasCategory| |#1| (QUOTE (-319))) (|HasCategory| |#1| (QUOTE (-571))) (|HasAttribute| |#1| (QUOTE (-4512 "*"))) (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-888)))) (|HasCategory| |#1| (QUOTE (-102)))) (-232 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 @@ -904,19 +904,19 @@ NIL ((|constructor| (NIL "any solution of a homogeneous linear Diophantine equation can be represented as a sum of minimal solutions,{} which form a \"basis\" (a minimal solution cannot be represented as a nontrivial sum of solutions) in the case of an inhomogeneous linear Diophantine equation,{} each solution is the sum of a inhomogeneous solution and any number of homogeneous solutions therefore,{} it suffices to compute two sets: \\indented{3}{1. all minimal inhomogeneous solutions} \\indented{3}{2. all minimal homogeneous solutions} the algorithm implemented is a completion procedure,{} which enumerates all solutions in a recursive depth-first-search it can be seen as finding monotone paths in a graph for more details see Reference")) (|dioSolve| (((|Record| (|:| |varOrder| (|List| (|Symbol|))) (|:| |inhom| (|Union| (|List| (|Vector| (|NonNegativeInteger|))) "failed")) (|:| |hom| (|List| (|Vector| (|NonNegativeInteger|))))) (|Equation| (|Polynomial| (|Integer|)))) "\\spad{dioSolve(u)} computes a basis of all minimal solutions for linear homogeneous Diophantine equation \\spad{u},{} then all minimal solutions of inhomogeneous equation"))) NIL NIL -(-244 S -2127 R) +(-244 S -2123 R) ((|constructor| (NIL "\\indented{2}{This category represents a finite cartesian product of a given type.} Many categorical properties are preserved under this construction.")) (|dot| ((|#3| $ $) "\\spad{dot(x,y)} computes the inner product of the vectors \\spad{x} and \\spad{y}.")) (|unitVector| (($ (|PositiveInteger|)) "\\spad{unitVector(n)} produces a vector with 1 in position \\spad{n} and zero elsewhere.")) (|directProduct| (($ (|Vector| |#3|)) "\\spad{directProduct(v)} converts the vector \\spad{v} to become a direct product. Error: if the length of \\spad{v} is different from dim.")) (|finiteAggregate| ((|attribute|) "attribute to indicate an aggregate of finite size"))) NIL ((|HasCategory| |#3| (QUOTE (-376))) (|HasCategory| |#3| (QUOTE (-817))) (|HasCategory| |#3| (QUOTE (-872))) (|HasAttribute| |#3| (QUOTE -4507)) (|HasCategory| |#3| (QUOTE (-175))) (|HasCategory| |#3| (QUOTE (-381))) (|HasCategory| |#3| (QUOTE (-748))) (|HasCategory| |#3| (QUOTE (-21))) (|HasCategory| |#3| (QUOTE (-23))) (|HasCategory| |#3| (QUOTE (-133))) (|HasCategory| |#3| (QUOTE (-25))) (|HasCategory| |#3| (QUOTE (-1081))) (|HasCategory| |#3| (QUOTE (-1133)))) -(-245 -2127 R) +(-245 -2123 R) ((|constructor| (NIL "\\indented{2}{This category represents a finite cartesian product of a given type.} Many categorical properties are preserved under this construction.")) (|dot| ((|#2| $ $) "\\spad{dot(x,y)} computes the inner product of the vectors \\spad{x} and \\spad{y}.")) (|unitVector| (($ (|PositiveInteger|)) "\\spad{unitVector(n)} produces a vector with 1 in position \\spad{n} and zero elsewhere.")) (|directProduct| (($ (|Vector| |#2|)) "\\spad{directProduct(v)} converts the vector \\spad{v} to become a direct product. Error: if the length of \\spad{v} is different from dim.")) (|finiteAggregate| ((|attribute|) "attribute to indicate an aggregate of finite size"))) ((-4504 |has| |#2| (-1081)) (-4505 |has| |#2| (-1081)) (-4507 |has| |#2| (-6 -4507)) (-4510 . T)) NIL -(-246 -2127 R) +(-246 -2123 R) ((|constructor| (NIL "\\indented{2}{This type represents the finite direct or cartesian product of an} underlying component type. This contrasts with simple vectors in that the members can be viewed as having constant length. Thus many categorical properties can by lifted from the underlying component type. Component extraction operations are provided but no updating operations. Thus new direct product elements can either be created by converting vector elements using the \\spadfun{directProduct} function or by taking appropriate linear combinations of basis vectors provided by the \\spad{unitVector} operation."))) ((-4504 |has| |#2| (-1081)) (-4505 |has| |#2| (-1081)) (-4507 |has| |#2| (-6 -4507)) (-4510 . 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The operations all iterate over their vector argument and either return a value of type \\spad{B} or a direct product over \\spad{B}.")) (|map| (((|DirectProduct| |#1| |#3|) (|Mapping| |#3| |#2|) (|DirectProduct| |#1| |#2|)) "\\spad{map(f, v)} applies the function \\spad{f} to every element of the vector \\spad{v} producing a new vector containing the values.")) (|reduce| ((|#3| (|Mapping| |#3| |#2| |#3|) (|DirectProduct| |#1| |#2|) |#3|) "\\spad{reduce(func,vec,ident)} combines the elements in \\spad{vec} using the binary function \\spad{func}. Argument \\spad{ident} is returned if the vector is empty.")) (|scan| (((|DirectProduct| |#1| |#3|) (|Mapping| |#3| |#2| |#3|) (|DirectProduct| |#1| |#2|) |#3|) "\\spad{scan(func,vec,ident)} creates a new vector whose elements are the result of applying reduce to the binary function \\spad{func},{} increasing initial subsequences of the vector \\spad{vec},{} and the element \\spad{ident}."))) NIL NIL @@ -939,7 +939,7 @@ NIL (-252 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}"))) ((-4511 . T) (-4510 . 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(|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'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 @@ -951,7 +951,7 @@ NIL (-255 |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 `x'.")) (|constructor| (NIL "\\indented{1}{Author: Gabriel Dos Reis} Date Create: October 18,{} 2007. Date Last Updated: December 20,{} 2008. Basic Operations: coerce,{} reify Related Constructors: Type,{} Syntax,{} OutputForm Also See: Type,{} ConstructorCall") (((|DomainConstructor|) $) "\\spad{constructor(d)} returns the domain constructor that is instantiated to the domain object `d'."))) 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In addition,{} it implements defaults for the basic functions. The functions \\spadfun{order} and \\spadfun{weight} are extended from the set of derivatives of differential indeterminates to the set of differential polynomials. Other operations provided on differential polynomials are \\spadfun{leader},{} \\spadfun{initial},{} \\spadfun{separant},{} \\spadfun{differentialVariables},{} and \\spadfun{isobaric?}. Furthermore,{} if the ground ring is a differential ring,{} then evaluation (substitution of differential indeterminates by elements of the ground ring or by differential polynomials) is provided by \\spadfun{eval}. A convenient way of referencing derivatives is provided by the functions \\spadfun{makeVariable}. \\blankline To construct a domain using this constructor,{} one needs to provide a ground ring \\spad{R},{} an ordered set \\spad{S} of differential indeterminates,{} a ranking \\spad{V} on the set of derivatives of the differential indeterminates,{} and a set \\spad{E} of exponents in bijection with the set of differential monomials in the given differential indeterminates. \\blankline")) (|separant| (($ $) "\\spad{separant(p)} returns the partial derivative of the differential polynomial \\spad{p} with respect to its leader.")) (|initial| (($ $) "\\spad{initial(p)} returns the leading coefficient when the differential polynomial \\spad{p} is written as a univariate polynomial in its leader.")) (|leader| ((|#4| $) "\\spad{leader(p)} returns the derivative of the highest rank appearing in the differential polynomial \\spad{p} Note: an error occurs if \\spad{p} is in the ground ring.")) (|isobaric?| (((|Boolean|) $) "\\spad{isobaric?(p)} returns \\spad{true} if every differential monomial appearing in the differential polynomial \\spad{p} has same weight,{} and returns \\spad{false} otherwise.")) (|weight| (((|NonNegativeInteger|) $ |#3|) "\\spad{weight(p, s)} returns the maximum weight of all differential monomials appearing in the differential polynomial \\spad{p} when \\spad{p} is viewed as a differential polynomial in the differential indeterminate \\spad{s} alone.") (((|NonNegativeInteger|) $) "\\spad{weight(p)} returns the maximum weight of all differential monomials appearing in the differential polynomial \\spad{p}.")) (|weights| (((|List| (|NonNegativeInteger|)) $ |#3|) "\\spad{weights(p, s)} returns a list of weights of differential monomials appearing in the differential polynomial \\spad{p} when \\spad{p} is viewed as a differential polynomial in the differential indeterminate \\spad{s} alone.") (((|List| (|NonNegativeInteger|)) $) "\\spad{weights(p)} returns a list of weights of differential monomials appearing in differential polynomial \\spad{p}.")) (|degree| (((|NonNegativeInteger|) $ |#3|) "\\spad{degree(p, s)} returns the maximum degree of the differential polynomial \\spad{p} viewed as a differential polynomial in the differential indeterminate \\spad{s} alone.")) (|order| (((|NonNegativeInteger|) $) "\\spad{order(p)} returns the order of the differential polynomial \\spad{p},{} which is the maximum number of differentiations of a differential indeterminate,{} among all those appearing in \\spad{p}.") (((|NonNegativeInteger|) $ |#3|) "\\spad{order(p,s)} returns the order of the differential polynomial \\spad{p} in differential indeterminate \\spad{s}.")) (|differentialVariables| (((|List| |#3|) $) "\\spad{differentialVariables(p)} returns a list of differential indeterminates occurring in a differential polynomial \\spad{p}.")) (|makeVariable| (((|Mapping| $ (|NonNegativeInteger|)) $) "\\spad{makeVariable(p)} views \\spad{p} as an element of a differential ring,{} in such a way that the \\spad{n}-th derivative of \\spad{p} may be simply referenced as \\spad{z}.\\spad{n} where \\spad{z} := makeVariable(\\spad{p}). Note: In the interpreter,{} \\spad{z} is given as an internal map,{} which may be ignored.") (((|Mapping| $ (|NonNegativeInteger|)) |#3|) "\\spad{makeVariable(s)} views \\spad{s} as a differential indeterminate,{} in such a way that the \\spad{n}-th derivative of \\spad{s} may be simply referenced as \\spad{z}.\\spad{n} where \\spad{z} :=makeVariable(\\spad{s}). Note: In the interpreter,{} \\spad{z} is given as an internal map,{} which may be ignored."))) NIL @@ -1031,7 +1031,7 @@ NIL (-275 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"))) (((-4512 "*") |has| |#1| (-175)) (-4503 |has| |#1| (-571)) (-4508 |has| |#1| (-6 -4508)) (-4505 . T) (-4504 . T) (-4507 . 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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}.")) (|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 @@ -1076,11 +1076,11 @@ NIL ((|constructor| (NIL "A domain used in the construction of the exterior algebra on a set \\spad{X} over a ring \\spad{R}. This domain represents the set of all ordered subsets of the set \\spad{X},{} assumed to be in correspondance with {1,{}2,{}3,{} ...}. The ordered subsets are themselves ordered lexicographically and are in bijective correspondance with an ordered basis of the exterior algebra. In this domain we are dealing strictly with the exponents of basis elements which can only be 0 or 1. \\blankline The multiplicative identity element of the exterior algebra corresponds to the empty subset of \\spad{X}. A coerce from List Integer to an ordered basis element is provided to allow the convenient input of expressions. Another exported function forgets the ordered structure and simply returns the list corresponding to an ordered subset.")) (|Nul| (($ (|NonNegativeInteger|)) "\\spad{Nul()} gives the basis element 1 for the algebra generated by \\spad{n} generators.")) (|exponents| (((|List| (|Integer|)) $) "\\spad{exponents(x)} converts a domain element into a list of zeros and ones corresponding to the exponents in the basis element that \\spad{x} represents.")) (|degree| (((|NonNegativeInteger|) $) "\\spad{degree(x)} gives the numbers of 1's in \\spad{x},{} \\spadignore{i.e.} the number of non-zero exponents in the basis element that \\spad{x} represents.")) (|coerce| (($ (|List| (|Integer|))) "\\spad{coerce(l)} converts a list of 0's and 1's into a basis element,{} where 1 (respectively 0) designates that the variable of the corresponding index of \\spad{l} is (respectively,{} is not) present. Error: if an element of \\spad{l} is not 0 or 1."))) NIL NIL -(-287 R -4164) +(-287 R -4140) ((|constructor| (NIL "Provides elementary functions over an integral domain.")) (|localReal?| (((|Boolean|) |#2|) "\\spad{localReal?(x)} should be local but conditional")) (|specialTrigs| (((|Union| |#2| "failed") |#2| (|List| (|Record| (|:| |func| |#2|) (|:| |pole| (|Boolean|))))) "\\spad{specialTrigs(x,l)} should be local but conditional")) (|iiacsch| ((|#2| |#2|) "\\spad{iiacsch(x)} should be local but conditional")) (|iiasech| ((|#2| |#2|) "\\spad{iiasech(x)} should be local but conditional")) (|iiacoth| ((|#2| |#2|) "\\spad{iiacoth(x)} should be local but conditional")) (|iiatanh| ((|#2| |#2|) "\\spad{iiatanh(x)} should be local but conditional")) (|iiacosh| ((|#2| |#2|) "\\spad{iiacosh(x)} should be local but conditional")) (|iiasinh| ((|#2| |#2|) "\\spad{iiasinh(x)} should be local but conditional")) (|iicsch| ((|#2| |#2|) "\\spad{iicsch(x)} should be local but conditional")) (|iisech| ((|#2| |#2|) "\\spad{iisech(x)} should be local but conditional")) (|iicoth| ((|#2| |#2|) "\\spad{iicoth(x)} should be local but conditional")) (|iitanh| ((|#2| |#2|) "\\spad{iitanh(x)} should be local but conditional")) (|iicosh| ((|#2| |#2|) "\\spad{iicosh(x)} should be local but conditional")) (|iisinh| ((|#2| |#2|) "\\spad{iisinh(x)} should be local but conditional")) (|iiacsc| ((|#2| |#2|) "\\spad{iiacsc(x)} should be local but conditional")) (|iiasec| ((|#2| |#2|) "\\spad{iiasec(x)} should be local but conditional")) (|iiacot| ((|#2| |#2|) "\\spad{iiacot(x)} should be local but conditional")) (|iiatan| ((|#2| |#2|) "\\spad{iiatan(x)} should be local but conditional")) (|iiacos| ((|#2| |#2|) "\\spad{iiacos(x)} should be local but conditional")) (|iiasin| ((|#2| |#2|) "\\spad{iiasin(x)} should be local but conditional")) (|iicsc| ((|#2| |#2|) "\\spad{iicsc(x)} should be local but conditional")) (|iisec| ((|#2| |#2|) "\\spad{iisec(x)} should be local but conditional")) (|iicot| ((|#2| |#2|) "\\spad{iicot(x)} should be local but conditional")) (|iitan| ((|#2| |#2|) "\\spad{iitan(x)} should be local but conditional")) (|iicos| ((|#2| |#2|) "\\spad{iicos(x)} should be local but conditional")) (|iisin| ((|#2| |#2|) "\\spad{iisin(x)} should be local but conditional")) (|iilog| ((|#2| |#2|) "\\spad{iilog(x)} should be local but conditional")) (|iiexp| ((|#2| |#2|) "\\spad{iiexp(x)} should be local but conditional")) (|iisqrt3| ((|#2|) "\\spad{iisqrt3()} should be local but conditional")) (|iisqrt2| ((|#2|) "\\spad{iisqrt2()} should be local but conditional")) (|operator| (((|BasicOperator|) (|BasicOperator|)) "\\spad{operator(p)} returns an elementary operator with the same symbol as \\spad{p}")) (|belong?| (((|Boolean|) (|BasicOperator|)) "\\spad{belong?(p)} returns \\spad{true} if operator \\spad{p} is elementary")) (|pi| ((|#2|) "\\spad{pi()} returns the \\spad{pi} operator")) (|acsch| ((|#2| |#2|) "\\spad{acsch(x)} applies the inverse hyperbolic cosecant operator to \\spad{x}")) (|asech| ((|#2| |#2|) "\\spad{asech(x)} applies the inverse hyperbolic secant operator to \\spad{x}")) (|acoth| ((|#2| |#2|) "\\spad{acoth(x)} applies the inverse hyperbolic cotangent operator to \\spad{x}")) (|atanh| ((|#2| |#2|) "\\spad{atanh(x)} applies the inverse hyperbolic tangent operator to \\spad{x}")) (|acosh| ((|#2| |#2|) "\\spad{acosh(x)} applies the inverse hyperbolic cosine operator to \\spad{x}")) (|asinh| ((|#2| |#2|) "\\spad{asinh(x)} applies the inverse hyperbolic sine operator to \\spad{x}")) (|csch| ((|#2| |#2|) "\\spad{csch(x)} applies the hyperbolic cosecant operator to \\spad{x}")) (|sech| ((|#2| |#2|) "\\spad{sech(x)} applies the hyperbolic secant operator to \\spad{x}")) (|coth| ((|#2| |#2|) "\\spad{coth(x)} applies the hyperbolic cotangent operator to \\spad{x}")) (|tanh| ((|#2| |#2|) "\\spad{tanh(x)} applies the hyperbolic tangent operator to \\spad{x}")) (|cosh| ((|#2| |#2|) "\\spad{cosh(x)} applies the hyperbolic cosine operator to \\spad{x}")) (|sinh| ((|#2| |#2|) "\\spad{sinh(x)} applies the hyperbolic sine operator to \\spad{x}")) (|acsc| ((|#2| |#2|) "\\spad{acsc(x)} applies the inverse cosecant operator to \\spad{x}")) (|asec| ((|#2| |#2|) "\\spad{asec(x)} applies the inverse secant operator to \\spad{x}")) (|acot| ((|#2| |#2|) "\\spad{acot(x)} applies the inverse cotangent operator to \\spad{x}")) (|atan| ((|#2| |#2|) "\\spad{atan(x)} applies the inverse tangent operator to \\spad{x}")) (|acos| ((|#2| |#2|) "\\spad{acos(x)} applies the inverse cosine operator to \\spad{x}")) (|asin| ((|#2| |#2|) "\\spad{asin(x)} applies the inverse sine operator to \\spad{x}")) (|csc| ((|#2| |#2|) "\\spad{csc(x)} applies the cosecant operator to \\spad{x}")) (|sec| ((|#2| |#2|) "\\spad{sec(x)} applies the secant operator to \\spad{x}")) (|cot| ((|#2| |#2|) "\\spad{cot(x)} applies the cotangent operator to \\spad{x}")) (|tan| ((|#2| |#2|) "\\spad{tan(x)} applies the tangent operator to \\spad{x}")) (|cos| ((|#2| |#2|) "\\spad{cos(x)} applies the cosine operator to \\spad{x}")) (|sin| ((|#2| |#2|) "\\spad{sin(x)} applies the sine operator to \\spad{x}")) (|log| ((|#2| |#2|) "\\spad{log(x)} applies the logarithm operator to \\spad{x}")) (|exp| ((|#2| |#2|) "\\spad{exp(x)} applies the exponential operator to \\spad{x}"))) NIL NIL -(-288 R -4164) +(-288 R -4140) ((|constructor| (NIL "ElementaryFunctionStructurePackage provides functions to test the algebraic independence of various elementary functions,{} using the Risch structure theorem (real and complex versions). It also provides transformations on elementary functions which are not considered simplifications.")) (|tanQ| ((|#2| (|Fraction| (|Integer|)) |#2|) "\\spad{tanQ(q,a)} is a local function with a conditional implementation.")) (|rootNormalize| ((|#2| |#2| (|Kernel| |#2|)) "\\spad{rootNormalize(f, k)} returns \\spad{f} rewriting either \\spad{k} which must be an \\spad{n}th-root in terms of radicals already in \\spad{f},{} or some radicals in \\spad{f} in terms of \\spad{k}.")) (|validExponential| (((|Union| |#2| "failed") (|List| (|Kernel| |#2|)) |#2| (|Symbol|)) "\\spad{validExponential([k1,...,kn],f,x)} returns \\spad{g} if \\spad{exp(f)=g} and \\spad{g} involves only \\spad{k1...kn},{} and \"failed\" otherwise.")) (|realElementary| ((|#2| |#2| (|Symbol|)) "\\spad{realElementary(f,x)} rewrites the kernels of \\spad{f} involving \\spad{x} in terms of the 4 fundamental real transcendental elementary functions: \\spad{log, exp, tan, atan}.") ((|#2| |#2|) "\\spad{realElementary(f)} rewrites \\spad{f} in terms of the 4 fundamental real transcendental elementary functions: \\spad{log, exp, tan, atan}.")) (|rischNormalize| (((|Record| (|:| |func| |#2|) (|:| |kers| (|List| (|Kernel| |#2|))) (|:| |vals| (|List| |#2|))) |#2| (|Symbol|)) "\\spad{rischNormalize(f, x)} returns \\spad{[g, [k1,...,kn], [h1,...,hn]]} such that \\spad{g = normalize(f, x)} and each \\spad{ki} was rewritten as \\spad{hi} during the normalization.")) (|normalize| ((|#2| |#2| (|Symbol|)) "\\spad{normalize(f, x)} rewrites \\spad{f} using the least possible number of real algebraically independent kernels involving \\spad{x}.") ((|#2| |#2|) "\\spad{normalize(f)} rewrites \\spad{f} using the least possible number of real algebraically independent kernels."))) NIL NIL @@ -1132,7 +1132,7 @@ NIL ((|constructor| (NIL "An eltable aggregate is one which can be viewed as a function. For example,{} the list \\axiom{[1,{}7,{}4]} can applied to 0,{}1,{} and 2 respectively will return the integers 1,{}7,{} and 4; thus this list may be viewed as mapping 0 to 1,{} 1 to 7 and 2 to 4. In general,{} an aggregate can map members of a domain {\\em Dom} to an image domain {\\em Im}.")) (|qsetelt!| ((|#2| $ |#1| |#2|) "\\spad{qsetelt!(u,x,y)} sets the image of \\axiom{\\spad{x}} to be \\axiom{\\spad{y}} under \\axiom{\\spad{u}},{} without checking that \\axiom{\\spad{x}} is in the domain of \\axiom{\\spad{u}}. If such a check is required use the function \\axiom{setelt}.")) (|setelt| ((|#2| $ |#1| |#2|) "\\spad{setelt(u,x,y)} sets the image of \\spad{x} to be \\spad{y} under \\spad{u},{} assuming \\spad{x} is in the domain of \\spad{u}. Error: if \\spad{x} is not in the domain of \\spad{u}.")) (|qelt| ((|#2| $ |#1|) "\\spad{qelt(u, x)} applies \\axiom{\\spad{u}} to \\axiom{\\spad{x}} without checking whether \\axiom{\\spad{x}} is in the domain of \\axiom{\\spad{u}}. If \\axiom{\\spad{x}} is not in the domain of \\axiom{\\spad{u}} a memory-access violation may occur. If a check on whether \\axiom{\\spad{x}} is in the domain of \\axiom{\\spad{u}} is required,{} use the function \\axiom{elt}.")) (|elt| ((|#2| $ |#1| |#2|) "\\spad{elt(u, x, y)} applies \\spad{u} to \\spad{x} if \\spad{x} is in the domain of \\spad{u},{} and returns \\spad{y} otherwise. For example,{} if \\spad{u} is a polynomial in \\axiom{\\spad{x}} over the rationals,{} \\axiom{elt(\\spad{u},{}\\spad{n},{}0)} may define the coefficient of \\axiom{\\spad{x}} to the power \\spad{n},{} returning 0 when \\spad{n} is out of range."))) NIL NIL -(-301 S R |Mod| -2386 -2834 |exactQuo|) +(-301 S R |Mod| -4318 -3338 |exactQuo|) ((|constructor| (NIL "These domains are used for the factorization and gcds of univariate polynomials over the integers in order to work modulo different primes. See \\spadtype{ModularRing},{} \\spadtype{ModularField}")) (|inv| (($ $) "\\spad{inv(x)} \\undocumented")) (|recip| (((|Union| $ "failed") $) "\\spad{recip(x)} \\undocumented")) (|exQuo| (((|Union| $ "failed") $ $) "\\spad{exQuo(x,y)} \\undocumented")) (|reduce| (($ |#2| |#3|) "\\spad{reduce(r,m)} \\undocumented")) (|coerce| ((|#2| $) "\\spad{coerce(x)} \\undocumented")) (|modulus| ((|#3| $) "\\spad{modulus(x)} \\undocumented"))) ((-4503 . T) ((-4512 "*") . T) (-4504 . T) (-4505 . T) (-4507 . T)) NIL @@ -1150,8 +1150,8 @@ NIL NIL (-305 S) ((|constructor| (NIL "Equations as mathematical objects. All properties of the basis domain,{} \\spadignore{e.g.} being an abelian group are carried over the equation domain,{} by performing the structural operations on the left and on the right hand side.")) (|subst| (($ $ $) "\\spad{subst(eq1,eq2)} substitutes \\spad{eq2} into both sides of \\spad{eq1} the lhs of \\spad{eq2} should be a kernel")) (|inv| (($ $) "\\spad{inv(x)} returns the multiplicative inverse of \\spad{x}.")) (/ (($ $ $) "\\spad{e1/e2} produces a new equation by dividing the left and right hand sides of equations \\spad{e1} and \\spad{e2}.")) (|factorAndSplit| (((|List| $) $) "\\spad{factorAndSplit(eq)} make the right hand side 0 and factors the new left hand side. Each factor is equated to 0 and put into the resulting list without repetitions.")) (|rightOne| (((|Union| $ "failed") $) "\\spad{rightOne(eq)} divides by the right hand side.") (((|Union| $ "failed") $) "\\spad{rightOne(eq)} divides by the right hand side,{} if possible.")) (|leftOne| (((|Union| $ "failed") $) "\\spad{leftOne(eq)} divides by the left hand side.") (((|Union| $ "failed") $) "\\spad{leftOne(eq)} divides by the left hand side,{} if possible.")) (* (($ $ |#1|) "\\spad{eqn*x} produces a new equation by multiplying both sides of equation eqn by \\spad{x}.") (($ |#1| $) "\\spad{x*eqn} produces a new equation by multiplying both sides of equation eqn by \\spad{x}.")) (- (($ $ |#1|) "\\spad{eqn-x} produces a new equation by subtracting \\spad{x} from both sides of equation eqn.") (($ |#1| $) "\\spad{x-eqn} produces a new equation by subtracting both sides of equation eqn from \\spad{x}.")) (|rightZero| (($ $) "\\spad{rightZero(eq)} subtracts the right hand side.")) (|leftZero| (($ $) "\\spad{leftZero(eq)} subtracts the left hand side.")) (+ (($ $ |#1|) "\\spad{eqn+x} produces a new equation by adding \\spad{x} to both sides of equation eqn.") (($ |#1| $) "\\spad{x+eqn} produces a new equation by adding \\spad{x} to both sides of equation eqn.")) (|eval| (($ $ (|List| $)) "\\spad{eval(eqn, [x1=v1, ... xn=vn])} replaces \\spad{xi} by \\spad{vi} in equation \\spad{eqn}.") (($ $ $) "\\spad{eval(eqn, x=f)} replaces \\spad{x} by \\spad{f} in equation \\spad{eqn}.")) (|map| (($ (|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.")) (= (($ |#1| |#1|) "\\spad{a=b} creates an equation."))) -((-4507 -4144 (|has| |#1| (-1081)) (|has| |#1| (-487))) (-4504 |has| |#1| (-1081)) (-4505 |has| |#1| (-1081))) -((|HasCategory| |#1| (QUOTE (-376))) (-4144 (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (QUOTE (-1081)))) (-4144 (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-376)))) (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-1081))) (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (|%list| (QUOTE -928) (QUOTE (-1209)))) (-4144 (|HasCategory| |#1| (|%list| (QUOTE -928) (QUOTE (-1209)))) (|HasCategory| |#1| (QUOTE (-1081)))) (-4144 (|HasCategory| |#1| (|%list| (QUOTE -928) (QUOTE (-1209)))) (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-25))) (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (QUOTE (-1081)))) (-4144 (|HasCategory| |#1| (|%list| (QUOTE -928) (QUOTE (-1209)))) (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (QUOTE (-1081)))) (-4144 (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-1081)))) (-4144 (|HasCategory| |#1| (QUOTE (-487))) (|HasCategory| |#1| (QUOTE (-748)))) (|HasCategory| |#1| (QUOTE (-487))) (-4144 (|HasCategory| |#1| (|%list| (QUOTE -928) (QUOTE (-1209)))) (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-25))) (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (QUOTE (-487))) (|HasCategory| |#1| (QUOTE (-748))) (|HasCategory| |#1| (QUOTE (-1081))) (|HasCategory| |#1| (QUOTE (-1144))) (|HasCategory| |#1| (QUOTE (-1133)))) (-4144 (|HasCategory| |#1| (QUOTE (-487))) (|HasCategory| |#1| (QUOTE (-748))) (|HasCategory| |#1| (QUOTE (-1144)))) (|HasCategory| |#1| (|%list| (QUOTE -528) (QUOTE (-1209)) (|devaluate| |#1|))) (-12 (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-571))) (|HasCategory| |#1| (QUOTE (-310))) (-4144 (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (QUOTE (-487)))) (-4144 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-748)))) (-4144 (|HasCategory| |#1| (QUOTE (-487))) (|HasCategory| |#1| (QUOTE (-1081)))) (|HasCategory| |#1| (QUOTE (-25))) (|HasCategory| |#1| (QUOTE (-1144))) (|HasCategory| |#1| (QUOTE (-748)))) +((-4507 -4118 (|has| |#1| (-1081)) (|has| |#1| (-487))) (-4504 |has| |#1| (-1081)) (-4505 |has| |#1| (-1081))) +((|HasCategory| |#1| (QUOTE (-376))) (-4118 (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (QUOTE (-1081)))) (-4118 (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-376)))) (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-1081))) (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (|%list| (QUOTE -928) (QUOTE (-1209)))) (-4118 (|HasCategory| |#1| (|%list| (QUOTE -928) (QUOTE (-1209)))) (|HasCategory| |#1| (QUOTE (-1081)))) (-4118 (|HasCategory| |#1| (|%list| (QUOTE -928) (QUOTE (-1209)))) (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-25))) (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (QUOTE (-1081)))) (-4118 (|HasCategory| |#1| (|%list| (QUOTE -928) (QUOTE (-1209)))) (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (QUOTE (-1081)))) (-4118 (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-1081)))) (-4118 (|HasCategory| |#1| (QUOTE (-487))) (|HasCategory| |#1| (QUOTE (-748)))) (|HasCategory| |#1| (QUOTE (-487))) (-4118 (|HasCategory| |#1| (|%list| (QUOTE -928) (QUOTE (-1209)))) (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-25))) (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (QUOTE (-487))) (|HasCategory| |#1| (QUOTE (-748))) (|HasCategory| |#1| (QUOTE (-1081))) (|HasCategory| |#1| (QUOTE (-1144))) (|HasCategory| |#1| (QUOTE (-1133)))) (-4118 (|HasCategory| |#1| (QUOTE (-487))) (|HasCategory| |#1| (QUOTE (-748))) (|HasCategory| |#1| (QUOTE (-1144)))) (|HasCategory| |#1| (|%list| (QUOTE -528) (QUOTE (-1209)) (|devaluate| |#1|))) (-12 (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-571))) (|HasCategory| |#1| (QUOTE (-310))) (-4118 (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (QUOTE (-487)))) (-4118 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-748)))) (-4118 (|HasCategory| |#1| (QUOTE (-487))) (|HasCategory| |#1| (QUOTE (-1081)))) (|HasCategory| |#1| (QUOTE (-25))) (|HasCategory| |#1| (QUOTE (-1144))) (|HasCategory| |#1| (QUOTE (-748)))) (-306 S R) ((|constructor| (NIL "This package provides operations for mapping the sides of equations.")) (|map| (((|Equation| |#2|) (|Mapping| |#2| |#1|) (|Equation| |#1|)) "\\spad{map(f,eq)} returns an equation where \\spad{f} is applied to the sides of \\spad{eq}"))) NIL @@ -1159,7 +1159,7 @@ NIL (-307 |Key| |Entry|) ((|constructor| (NIL "This domain provides tables where the keys are compared using \\spadfun{eq?}. Thus keys are considered equal only if they are the same instance of a structure."))) ((-4510 . T) (-4511 . T)) -((-12 (|HasCategory| (-2 (|:| -2118 |#1|) (|:| -3964 |#2|)) (QUOTE (-1133))) (|HasCategory| (-2 (|:| -2118 |#1|) (|:| -3964 |#2|)) (|%list| (QUOTE -321) (|%list| (QUOTE -2) (|%list| (QUOTE |:|) (QUOTE -2118) (|devaluate| |#1|)) (|%list| (QUOTE |:|) (QUOTE -3964) (|devaluate| |#2|)))))) (-4144 (|HasCategory| (-2 (|:| -2118 |#1|) (|:| -3964 |#2|)) (QUOTE (-1133))) (|HasCategory| |#2| (QUOTE (-1133)))) (-4144 (|HasCategory| (-2 (|:| -2118 |#1|) (|:| -3964 |#2|)) (QUOTE (-102))) (|HasCategory| (-2 (|:| -2118 |#1|) (|:| -3964 |#2|)) (QUOTE (-1133))) (|HasCategory| |#2| (QUOTE (-102))) (|HasCategory| |#2| (QUOTE (-1133)))) (-4144 (|HasCategory| (-2 (|:| -2118 |#1|) (|:| -3964 |#2|)) (QUOTE (-1133))) (|HasCategory| (-2 (|:| -2118 |#1|) (|:| -3964 |#2|)) (|%list| (QUOTE -632) (QUOTE (-888)))) (|HasCategory| |#2| (QUOTE (-1133))) (|HasCategory| |#2| (|%list| (QUOTE -632) (QUOTE (-888))))) (|HasCategory| (-2 (|:| -2118 |#1|) (|:| -3964 |#2|)) (|%list| (QUOTE -633) (QUOTE (-549)))) (-12 (|HasCategory| |#2| (QUOTE (-1133))) (|HasCategory| |#2| (|%list| (QUOTE -321) (|devaluate| |#2|)))) (|HasCategory| (-2 (|:| -2118 |#1|) (|:| -3964 |#2|)) (QUOTE (-1133))) (|HasCategory| |#1| (QUOTE (-872))) (|HasCategory| |#2| (QUOTE (-1133))) (-4144 (|HasCategory| (-2 (|:| -2118 |#1|) (|:| -3964 |#2|)) (|%list| (QUOTE -632) (QUOTE (-888)))) (|HasCategory| |#2| (|%list| (QUOTE -632) (QUOTE (-888))))) (-4144 (|HasCategory| (-2 (|:| -2118 |#1|) (|:| -3964 |#2|)) (QUOTE (-102))) (|HasCategory| |#2| (QUOTE (-102)))) (|HasCategory| |#2| (QUOTE (-102))) (|HasCategory| |#2| (|%list| (QUOTE -632) (QUOTE (-888)))) (|HasCategory| (-2 (|:| -2118 |#1|) (|:| -3964 |#2|)) (|%list| (QUOTE -632) (QUOTE (-888)))) (|HasCategory| (-2 (|:| -2118 |#1|) (|:| -3964 |#2|)) (QUOTE (-102)))) +((-12 (|HasCategory| (-2 (|:| -2115 |#1|) (|:| -3934 |#2|)) (QUOTE (-1133))) (|HasCategory| (-2 (|:| -2115 |#1|) (|:| -3934 |#2|)) (|%list| (QUOTE -321) (|%list| (QUOTE -2) (|%list| (QUOTE |:|) (QUOTE -2115) (|devaluate| |#1|)) (|%list| (QUOTE |:|) (QUOTE -3934) (|devaluate| |#2|)))))) (-4118 (|HasCategory| (-2 (|:| -2115 |#1|) (|:| -3934 |#2|)) (QUOTE (-1133))) (|HasCategory| |#2| (QUOTE (-1133)))) (-4118 (|HasCategory| (-2 (|:| -2115 |#1|) (|:| -3934 |#2|)) (QUOTE (-102))) (|HasCategory| (-2 (|:| -2115 |#1|) (|:| -3934 |#2|)) (QUOTE (-1133))) (|HasCategory| |#2| (QUOTE (-102))) (|HasCategory| |#2| (QUOTE (-1133)))) (-4118 (|HasCategory| (-2 (|:| -2115 |#1|) (|:| -3934 |#2|)) (QUOTE (-1133))) (|HasCategory| (-2 (|:| -2115 |#1|) (|:| -3934 |#2|)) (|%list| (QUOTE -632) (QUOTE (-888)))) (|HasCategory| |#2| (QUOTE (-1133))) (|HasCategory| |#2| (|%list| (QUOTE -632) (QUOTE (-888))))) (|HasCategory| (-2 (|:| -2115 |#1|) (|:| -3934 |#2|)) (|%list| (QUOTE -633) (QUOTE (-549)))) (-12 (|HasCategory| |#2| (QUOTE (-1133))) (|HasCategory| |#2| (|%list| (QUOTE -321) (|devaluate| |#2|)))) (|HasCategory| (-2 (|:| -2115 |#1|) (|:| -3934 |#2|)) (QUOTE (-1133))) (|HasCategory| |#1| (QUOTE (-872))) (|HasCategory| |#2| (QUOTE (-1133))) (-4118 (|HasCategory| (-2 (|:| -2115 |#1|) (|:| -3934 |#2|)) (|%list| (QUOTE -632) (QUOTE (-888)))) (|HasCategory| |#2| (|%list| (QUOTE -632) (QUOTE (-888))))) (-4118 (|HasCategory| (-2 (|:| -2115 |#1|) (|:| -3934 |#2|)) (QUOTE (-102))) (|HasCategory| |#2| (QUOTE (-102)))) (|HasCategory| |#2| (QUOTE (-102))) (|HasCategory| |#2| (|%list| (QUOTE -632) (QUOTE (-888)))) (|HasCategory| (-2 (|:| -2115 |#1|) (|:| -3934 |#2|)) (|%list| (QUOTE -632) (QUOTE (-888)))) (|HasCategory| (-2 (|:| -2115 |#1|) (|:| -3934 |#2|)) (QUOTE (-102)))) (-308) ((|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 @@ -1172,11 +1172,11 @@ NIL ((|constructor| (NIL "An expression space is a set which is closed under certain operators.")) (|odd?| (((|Boolean|) $) "\\spad{odd? x} is \\spad{true} if \\spad{x} is an odd integer.")) (|even?| (((|Boolean|) $) "\\spad{even? x} is \\spad{true} if \\spad{x} is an even integer.")) (|definingPolynomial| (($ $) "\\spad{definingPolynomial(x)} returns an expression \\spad{p} such that \\spad{p(x) = 0}.")) (|minPoly| (((|SparseUnivariatePolynomial| $) (|Kernel| $)) "\\spad{minPoly(k)} returns \\spad{p} such that \\spad{p(k) = 0}.")) (|eval| (($ $ (|BasicOperator|) (|Mapping| $ $)) "\\spad{eval(x, s, f)} replaces every \\spad{s(a)} in \\spad{x} by \\spad{f(a)} for any \\spad{a}.") (($ $ (|BasicOperator|) (|Mapping| $ (|List| $))) "\\spad{eval(x, s, f)} replaces every \\spad{s(a1,..,am)} in \\spad{x} by \\spad{f(a1,..,am)} for any \\spad{a1},{}...,{}\\spad{am}.") (($ $ (|List| (|BasicOperator|)) (|List| (|Mapping| $ (|List| $)))) "\\spad{eval(x, [s1,...,sm], [f1,...,fm])} replaces every \\spad{si(a1,...,an)} in \\spad{x} by \\spad{fi(a1,...,an)} for any \\spad{a1},{}...,{}\\spad{an}.") (($ $ (|List| (|BasicOperator|)) (|List| (|Mapping| $ $))) "\\spad{eval(x, [s1,...,sm], [f1,...,fm])} replaces every \\spad{si(a)} in \\spad{x} by \\spad{fi(a)} for any \\spad{a}.") (($ $ (|Symbol|) (|Mapping| $ $)) "\\spad{eval(x, s, f)} replaces every \\spad{s(a)} in \\spad{x} by \\spad{f(a)} for any \\spad{a}.") (($ $ (|Symbol|) (|Mapping| $ (|List| $))) "\\spad{eval(x, s, f)} replaces every \\spad{s(a1,..,am)} in \\spad{x} by \\spad{f(a1,..,am)} for any \\spad{a1},{}...,{}\\spad{am}.") (($ $ (|List| (|Symbol|)) (|List| (|Mapping| $ (|List| $)))) "\\spad{eval(x, [s1,...,sm], [f1,...,fm])} replaces every \\spad{si(a1,...,an)} in \\spad{x} by \\spad{fi(a1,...,an)} for any \\spad{a1},{}...,{}\\spad{an}.") (($ $ (|List| (|Symbol|)) (|List| (|Mapping| $ $))) "\\spad{eval(x, [s1,...,sm], [f1,...,fm])} replaces every \\spad{si(a)} in \\spad{x} by \\spad{fi(a)} for any \\spad{a}.")) (|freeOf?| (((|Boolean|) $ (|Symbol|)) "\\spad{freeOf?(x, s)} tests if \\spad{x} does not contain any operator whose name is \\spad{s}.") (((|Boolean|) $ $) "\\spad{freeOf?(x, y)} tests if \\spad{x} does not contain any occurrence of \\spad{y},{} where \\spad{y} is a single kernel.")) (|map| (($ (|Mapping| $ $) (|Kernel| $)) "\\spad{map(f, k)} returns \\spad{op(f(x1),...,f(xn))} where \\spad{k = op(x1,...,xn)}.")) (|kernel| (($ (|BasicOperator|) (|List| $)) "\\spad{kernel(op, [f1,...,fn])} constructs \\spad{op(f1,...,fn)} without evaluating it.") (($ (|BasicOperator|) $) "\\spad{kernel(op, x)} constructs \\spad{op}(\\spad{x}) without evaluating it.")) (|is?| (((|Boolean|) $ (|Symbol|)) "\\spad{is?(x, s)} tests if \\spad{x} is a kernel and is the name of its operator is \\spad{s}.") (((|Boolean|) $ (|BasicOperator|)) "\\spad{is?(x, op)} tests if \\spad{x} is a kernel and is its operator is op.")) (|belong?| (((|Boolean|) (|BasicOperator|)) "\\spad{belong?(op)} tests if \\% accepts \\spad{op} as applicable to its elements.")) (|operator| (((|BasicOperator|) (|BasicOperator|)) "\\spad{operator(op)} returns a copy of \\spad{op} with the domain-dependent properties appropriate for \\%.")) (|operators| (((|List| (|BasicOperator|)) $) "\\spad{operators(f)} returns all the basic operators appearing in \\spad{f},{} no matter what their levels are.")) (|tower| (((|List| (|Kernel| $)) $) "\\spad{tower(f)} returns all the kernels appearing in \\spad{f},{} no matter what their levels are.")) (|kernels| (((|List| (|Kernel| $)) $) "\\spad{kernels(f)} returns the list of all the top-level kernels appearing in \\spad{f},{} but not the ones appearing in the arguments of the top-level kernels.")) (|mainKernel| (((|Union| (|Kernel| $) "failed") $) "\\spad{mainKernel(f)} returns a kernel of \\spad{f} with maximum nesting level,{} or if \\spad{f} has no kernels (\\spadignore{i.e.} \\spad{f} is a constant).")) (|height| (((|NonNegativeInteger|) $) "\\spad{height(f)} returns the highest nesting level appearing in \\spad{f}. Constants have height 0. Symbols have height 1. For any operator op and expressions \\spad{f1},{}...,{}fn,{} \\spad{op(f1,...,fn)} has height equal to \\spad{1 + max(height(f1),...,height(fn))}.")) (|distribute| (($ $ $) "\\spad{distribute(f, g)} expands all the kernels in \\spad{f} that contain \\spad{g} in their arguments and that are formally enclosed by a \\spadfunFrom{box}{ExpressionSpace} or a \\spadfunFrom{paren}{ExpressionSpace} expression.") (($ $) "\\spad{distribute(f)} expands all the kernels in \\spad{f} that are formally enclosed by a \\spadfunFrom{box}{ExpressionSpace} or \\spadfunFrom{paren}{ExpressionSpace} expression.")) (|paren| (($ (|List| $)) "\\spad{paren([f1,...,fn])} returns \\spad{(f1,...,fn)}. This prevents the \\spad{fi} from being evaluated when operators are applied to them,{} and makes them applicable to a unary operator. For example,{} \\spad{atan(paren [x, 2])} returns the formal kernel \\spad{atan((x, 2))}.") (($ $) "\\spad{paren(f)} returns (\\spad{f}). This prevents \\spad{f} from being evaluated when operators are applied to it. For example,{} \\spad{log(1)} returns 0,{} but \\spad{log(paren 1)} returns the formal kernel log((1)).")) (|box| (($ (|List| $)) "\\spad{box([f1,...,fn])} returns \\spad{(f1,...,fn)} with a 'box' around them that prevents the \\spad{fi} from being evaluated when operators are applied to them,{} and makes them applicable to a unary operator. For example,{} \\spad{atan(box [x, 2])} returns the formal kernel \\spad{atan(x, 2)}.") (($ $) "\\spad{box(f)} returns \\spad{f} with a 'box' around it that prevents \\spad{f} from being evaluated when operators are applied to it. For example,{} \\spad{log(1)} returns 0,{} but \\spad{log(box 1)} returns the formal kernel log(1).")) (|subst| (($ $ (|List| (|Kernel| $)) (|List| $)) "\\spad{subst(f, [k1...,kn], [g1,...,gn])} replaces the kernels \\spad{k1},{}...,{}kn by \\spad{g1},{}...,{}gn formally in \\spad{f}.") (($ $ (|List| (|Equation| $))) "\\spad{subst(f, [k1 = g1,...,kn = gn])} replaces the kernels \\spad{k1},{}...,{}kn by \\spad{g1},{}...,{}gn formally in \\spad{f}.") (($ $ (|Equation| $)) "\\spad{subst(f, k = g)} replaces the kernel \\spad{k} by \\spad{g} formally in \\spad{f}.")) (|elt| (($ (|BasicOperator|) (|List| $)) "\\spad{elt(op,[x1,...,xn])} or \\spad{op}([\\spad{x1},{}...,{}xn]) applies the \\spad{n}-ary operator \\spad{op} to \\spad{x1},{}...,{}xn.") (($ (|BasicOperator|) $ $ $ $) "\\spad{elt(op,x,y,z,t)} or \\spad{op}(\\spad{x},{} \\spad{y},{} \\spad{z},{} \\spad{t}) applies the 4-ary operator \\spad{op} to \\spad{x},{} \\spad{y},{} \\spad{z} and \\spad{t}.") (($ (|BasicOperator|) $ $ $) "\\spad{elt(op,x,y,z)} or \\spad{op}(\\spad{x},{} \\spad{y},{} \\spad{z}) applies the ternary operator \\spad{op} to \\spad{x},{} \\spad{y} and \\spad{z}.") (($ (|BasicOperator|) $ $) "\\spad{elt(op,x,y)} or \\spad{op}(\\spad{x},{} \\spad{y}) applies the binary operator \\spad{op} to \\spad{x} and \\spad{y}.") (($ (|BasicOperator|) $) "\\spad{elt(op,x)} or \\spad{op}(\\spad{x}) applies the unary operator \\spad{op} to \\spad{x}."))) NIL NIL -(-311 -4164 S) +(-311 -4140 S) ((|constructor| (NIL "This package allows a map from any expression space into any object to be lifted to a kernel over the expression set,{} using a given property of the operator of the kernel.")) (|map| ((|#2| (|Mapping| |#2| |#1|) (|String|) (|Kernel| |#1|)) "\\spad{map(f, p, k)} uses the property \\spad{p} of the operator of \\spad{k},{} in order to lift \\spad{f} and apply it to \\spad{k}."))) NIL NIL -(-312 E -4164) +(-312 E -4140) ((|constructor| (NIL "This package allows a mapping \\spad{E} -> \\spad{F} to be lifted to a kernel over \\spad{E}; This lifting can fail if the operator of the kernel cannot be applied in \\spad{F}; Do not use this package with \\spad{E} = \\spad{F},{} since this may drop some properties of the operators.")) (|map| ((|#2| (|Mapping| |#2| |#1|) (|Kernel| |#1|)) "\\spad{map(f, k)} returns \\spad{g = op(f(a1),...,f(an))} where \\spad{k = op(a1,...,an)}."))) NIL NIL @@ -1216,7 +1216,7 @@ NIL ((|constructor| (NIL "This category provides \\spadfun{eval} operations. A domain may belong to this category if it is possible to make ``evaluation'' substitutions.")) (|eval| (($ $ (|List| (|Equation| |#1|))) "\\spad{eval(f, [x1 = v1,...,xn = vn])} replaces \\spad{xi} by \\spad{vi} in \\spad{f}.") (($ $ (|Equation| |#1|)) "\\spad{eval(f,x = v)} replaces \\spad{x} by \\spad{v} in \\spad{f}."))) NIL NIL -(-322 -4164) +(-322 -4140) ((|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 @@ -1231,11 +1231,11 @@ NIL (-325 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))}."))) ((-4502 . T) (-4508 . T) (-4503 . T) ((-4512 "*") . T) (-4504 . T) (-4505 . T) (-4507 . T)) -((|HasCategory| (-1286 |#1| |#2| |#3| |#4|) (QUOTE (-940))) (|HasCategory| (-1286 |#1| |#2| |#3| |#4|) (|%list| (QUOTE -1070) (QUOTE (-1209)))) (|HasCategory| (-1286 |#1| |#2| |#3| |#4|) (QUOTE (-147))) (|HasCategory| (-1286 |#1| |#2| |#3| |#4|) (QUOTE (-149))) (|HasCategory| (-1286 |#1| |#2| |#3| |#4|) (|%list| (QUOTE -633) (QUOTE (-549)))) (|HasCategory| (-1286 |#1| |#2| |#3| |#4|) (QUOTE (-1052))) (|HasCategory| (-1286 |#1| |#2| |#3| |#4|) (QUOTE (-844))) (|HasCategory| (-1286 |#1| |#2| |#3| |#4|) (QUOTE (-872))) (-4144 (|HasCategory| (-1286 |#1| |#2| |#3| |#4|) (QUOTE (-844))) (|HasCategory| (-1286 |#1| |#2| |#3| |#4|) (QUOTE (-872)))) (|HasCategory| (-1286 |#1| |#2| |#3| |#4|) (|%list| (QUOTE -1070) (QUOTE (-560)))) (|HasCategory| (-1286 |#1| |#2| |#3| |#4|) (QUOTE (-1184))) (|HasCategory| (-1286 |#1| |#2| |#3| |#4|) (|%list| (QUOTE -912) (QUOTE (-391)))) (|HasCategory| (-1286 |#1| |#2| |#3| |#4|) (|%list| (QUOTE -912) (QUOTE (-560)))) (|HasCategory| (-1286 |#1| |#2| |#3| 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(|HasCategory| (-1286 |#1| |#2| |#3| |#4|) (|%list| (QUOTE -928) (QUOTE (-1209)))) (|HasCategory| (-1286 |#1| |#2| |#3| |#4|) (|%list| (QUOTE -528) (QUOTE (-1209)) (|%list| (QUOTE -1286) (|devaluate| |#1|) (|devaluate| |#2|) (|devaluate| |#3|) (|devaluate| |#4|)))) (|HasCategory| (-1286 |#1| |#2| |#3| |#4|) (|%list| (QUOTE -321) (|%list| (QUOTE -1286) (|devaluate| |#1|) (|devaluate| |#2|) (|devaluate| |#3|) (|devaluate| |#4|)))) (|HasCategory| (-1286 |#1| |#2| |#3| |#4|) (|%list| (QUOTE -298) (|%list| (QUOTE -1286) (|devaluate| |#1|) (|devaluate| |#2|) (|devaluate| |#3|) (|devaluate| |#4|)) (|%list| (QUOTE -1286) (|devaluate| |#1|) (|devaluate| |#2|) (|devaluate| |#3|) (|devaluate| |#4|)))) (|HasCategory| (-1286 |#1| |#2| |#3| |#4|) (QUOTE (-319))) (|HasCategory| (-1286 |#1| |#2| |#3| |#4|) (QUOTE (-559))) (-12 (|HasCategory| (-1286 |#1| |#2| |#3| |#4|) (QUOTE (-940))) (|HasCategory| $ (QUOTE (-147)))) (-4118 (|HasCategory| (-1286 |#1| |#2| |#3| |#4|) (QUOTE (-147))) (-12 (|HasCategory| (-1286 |#1| |#2| |#3| |#4|) (QUOTE (-940))) (|HasCategory| $ (QUOTE (-147)))))) (-326 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."))) -((-4507 -4144 (-12 (|has| |#1| (-571)) (-4144 (|has| |#1| (-1081)) (|has| |#1| (-487)))) (|has| |#1| (-1081)) (|has| |#1| (-487))) (-4505 |has| |#1| (-175)) (-4504 |has| |#1| (-175)) ((-4512 "*") |has| |#1| (-571)) (-4503 |has| |#1| (-571)) (-4508 |has| |#1| (-571)) (-4502 |has| |#1| (-571))) -((-4144 (|HasCategory| |#1| (|%list| (QUOTE -1070) (|%list| (QUOTE 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(|HasCategory| |#1| (QUOTE (-571))) (|HasCategory| |#1| (|%list| (QUOTE -1070) (QUOTE (-560))))) (-4118 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-25))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-149))) (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-571))) (|HasCategory| |#1| (QUOTE (-1081)))) (-4118 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-149))) (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-571))) (|HasCategory| |#1| (QUOTE (-1081)))) (-4118 (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-149))) (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-571))) (|HasCategory| |#1| (QUOTE (-1081)))) (-12 (|HasCategory| |#1| (QUOTE (-466))) (|HasCategory| |#1| (QUOTE (-571)))) (-4118 (|HasCategory| |#1| (QUOTE (-487))) (|HasCategory| |#1| (QUOTE (-571)))) (-12 (|HasCategory| |#1| (|%list| (QUOTE -660) (QUOTE (-560)))) (|HasCategory| |#1| (QUOTE (-1081)))) (-4118 (-12 (|HasCategory| |#1| (|%list| (QUOTE -660) (QUOTE (-560)))) (|HasCategory| |#1| (QUOTE (-1081)))) (|HasCategory| |#1| (QUOTE (-21)))) (-4118 (-12 (|HasCategory| |#1| (|%list| (QUOTE -660) (QUOTE (-560)))) (|HasCategory| |#1| (QUOTE (-1081)))) (|HasCategory| |#1| (QUOTE (-25))) (|HasCategory| |#1| (QUOTE (-1144)))) (-4118 (-12 (|HasCategory| |#1| (|%list| (QUOTE -660) (QUOTE (-560)))) (|HasCategory| |#1| (QUOTE (-1081)))) (|HasCategory| |#1| (QUOTE (-25)))) (-4118 (|HasCategory| |#1| (QUOTE (-487))) (|HasCategory| |#1| (QUOTE (-1081)))) (-4118 (-12 (|HasCategory| |#1| (|%list| (QUOTE -1070) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#1| (QUOTE (-571)))) (-12 (|HasCategory| |#1| (QUOTE (-571))) (|HasCategory| |#1| (|%list| (QUOTE -1070) (QUOTE (-560)))))) (|HasCategory| |#1| (QUOTE (-25))) (|HasCategory| |#1| (QUOTE (-1144))) (|HasCategory| |#1| (|%list| (QUOTE -1070) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| $ (QUOTE (-1081))) (|HasCategory| $ (|%list| (QUOTE -1070) (QUOTE (-560))))) (-327 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 @@ -1244,7 +1244,7 @@ NIL ((|constructor| (NIL "This package provides functions to convert functional expressions to power series.")) (|series| (((|Any|) |#2| (|Equation| |#2|) (|Fraction| (|Integer|))) "\\spad{series(f,x = a,n)} expands the expression \\spad{f} as a series in powers of (\\spad{x} - a); terms will be computed up to order at least \\spad{n}.") (((|Any|) |#2| (|Equation| |#2|)) "\\spad{series(f,x = a)} expands the expression \\spad{f} as a series in powers of (\\spad{x} - a).") (((|Any|) |#2| (|Fraction| (|Integer|))) "\\spad{series(f,n)} returns a series expansion of the expression \\spad{f}. Note: \\spad{f} should have only one variable; the series will be expanded in powers of that variable and terms will be computed up to order at least \\spad{n}.") (((|Any|) |#2|) "\\spad{series(f)} returns a series expansion of the expression \\spad{f}. Note: \\spad{f} should have only one variable; the series will be expanded in powers of that variable.") (((|Any|) (|Symbol|)) "\\spad{series(x)} returns \\spad{x} viewed as a series.")) (|puiseux| (((|Any|) |#2| (|Equation| |#2|) (|Fraction| (|Integer|))) "\\spad{puiseux(f,x = a,n)} expands the expression \\spad{f} as a Puiseux series in powers of \\spad{(x - a)}; terms will be computed up to order at least \\spad{n}.") (((|Any|) |#2| (|Equation| |#2|)) "\\spad{puiseux(f,x = a)} expands the expression \\spad{f} as a Puiseux series in powers of \\spad{(x - a)}.") (((|Any|) |#2| (|Fraction| (|Integer|))) "\\spad{puiseux(f,n)} returns a Puiseux expansion of the expression \\spad{f}. Note: \\spad{f} should have only one variable; the series will be expanded in powers of that variable and terms will be computed up to order at least \\spad{n}.") (((|Any|) |#2|) "\\spad{puiseux(f)} returns a Puiseux expansion of the expression \\spad{f}. Note: \\spad{f} should have only one variable; the series will be expanded in powers of that variable.") (((|Any|) (|Symbol|)) "\\spad{puiseux(x)} returns \\spad{x} viewed as a Puiseux series.")) (|laurent| (((|Any|) |#2| (|Equation| |#2|) (|Integer|)) "\\spad{laurent(f,x = a,n)} expands the expression \\spad{f} as a Laurent series in powers of \\spad{(x - a)}; terms will be computed up to order at least \\spad{n}.") (((|Any|) |#2| (|Equation| |#2|)) "\\spad{laurent(f,x = a)} expands the expression \\spad{f} as a Laurent series in powers of \\spad{(x - a)}.") (((|Any|) |#2| (|Integer|)) "\\spad{laurent(f,n)} returns a Laurent expansion of the expression \\spad{f}. Note: \\spad{f} should have only one variable; the series will be expanded in powers of that variable and terms will be computed up to order at least \\spad{n}.") (((|Any|) |#2|) "\\spad{laurent(f)} returns a Laurent expansion of the expression \\spad{f}. Note: \\spad{f} should have only one variable; the series will be expanded in powers of that variable.") (((|Any|) (|Symbol|)) "\\spad{laurent(x)} returns \\spad{x} viewed as a Laurent series.")) (|taylor| (((|Any|) |#2| (|Equation| |#2|) (|NonNegativeInteger|)) "\\spad{taylor(f,x = a)} expands the expression \\spad{f} as a Taylor series in powers of \\spad{(x - a)}; terms will be computed up to order at least \\spad{n}.") (((|Any|) |#2| (|Equation| |#2|)) "\\spad{taylor(f,x = a)} expands the expression \\spad{f} as a Taylor series in powers of \\spad{(x - a)}.") (((|Any|) |#2| (|NonNegativeInteger|)) "\\spad{taylor(f,n)} returns a Taylor expansion of the expression \\spad{f}. Note: \\spad{f} should have only one variable; the series will be expanded in powers of that variable and terms will be computed up to order at least \\spad{n}.") (((|Any|) |#2|) "\\spad{taylor(f)} returns a Taylor expansion of the expression \\spad{f}. Note: \\spad{f} should have only one variable; the series will be expanded in powers of that variable.") (((|Any|) (|Symbol|)) "\\spad{taylor(x)} returns \\spad{x} viewed as a Taylor series."))) NIL NIL -(-329 R -4164) +(-329 R -4140) ((|constructor| (NIL "Taylor series solutions of explicit ODE's.")) (|seriesSolve| (((|Any|) |#2| (|BasicOperator|) (|Equation| |#2|) (|List| |#2|)) "\\spad{seriesSolve(eq, y, x = a, [b0,...,bn])} is equivalent to \\spad{seriesSolve(eq = 0, y, x = a, [b0,...,b(n-1)])}.") (((|Any|) |#2| (|BasicOperator|) (|Equation| |#2|) (|Equation| |#2|)) "\\spad{seriesSolve(eq, y, x = a, y a = b)} is equivalent to \\spad{seriesSolve(eq=0, y, x=a, y a = b)}.") (((|Any|) |#2| (|BasicOperator|) (|Equation| |#2|) |#2|) "\\spad{seriesSolve(eq, y, x = a, b)} is equivalent to \\spad{seriesSolve(eq = 0, y, x = a, y a = b)}.") (((|Any|) (|Equation| |#2|) (|BasicOperator|) (|Equation| |#2|) |#2|) "\\spad{seriesSolve(eq,y, x=a, b)} is equivalent to \\spad{seriesSolve(eq, y, x=a, y a = b)}.") (((|Any|) (|List| |#2|) (|List| (|BasicOperator|)) (|Equation| |#2|) (|List| (|Equation| |#2|))) "\\spad{seriesSolve([eq1,...,eqn], [y1,...,yn], x = a,[y1 a = b1,..., yn a = bn])} is equivalent to \\spad{seriesSolve([eq1=0,...,eqn=0], [y1,...,yn], x = a, [y1 a = b1,..., yn a = bn])}.") (((|Any|) (|List| |#2|) (|List| (|BasicOperator|)) (|Equation| |#2|) (|List| |#2|)) "\\spad{seriesSolve([eq1,...,eqn], [y1,...,yn], x=a, [b1,...,bn])} is equivalent to \\spad{seriesSolve([eq1=0,...,eqn=0], [y1,...,yn], x=a, [b1,...,bn])}.") (((|Any|) (|List| (|Equation| |#2|)) (|List| (|BasicOperator|)) (|Equation| |#2|) (|List| |#2|)) "\\spad{seriesSolve([eq1,...,eqn], [y1,...,yn], x=a, [b1,...,bn])} is equivalent to \\spad{seriesSolve([eq1,...,eqn], [y1,...,yn], x = a, [y1 a = b1,..., yn a = bn])}.") (((|Any|) (|List| (|Equation| |#2|)) (|List| (|BasicOperator|)) (|Equation| |#2|) (|List| (|Equation| |#2|))) "\\spad{seriesSolve([eq1,...,eqn],[y1,...,yn],x = a,[y1 a = b1,...,yn a = bn])} returns a taylor series solution of \\spad{[eq1,...,eqn]} around \\spad{x = a} with initial conditions \\spad{yi(a) = bi}. Note: eqi must be of the form \\spad{fi(x, y1 x, y2 x,..., yn x) y1'(x) + gi(x, y1 x, y2 x,..., yn x) = h(x, y1 x, y2 x,..., yn x)}.") (((|Any|) (|Equation| |#2|) (|BasicOperator|) (|Equation| |#2|) (|List| |#2|)) "\\spad{seriesSolve(eq,y,x=a,[b0,...,b(n-1)])} returns a Taylor series solution of \\spad{eq} around \\spad{x = a} with initial conditions \\spad{y(a) = b0},{} \\spad{y'(a) = b1},{} \\spad{y''(a) = b2},{} ...,{}\\spad{y(n-1)(a) = b(n-1)} \\spad{eq} must be of the form \\spad{f(x, y x, y'(x),..., y(n-1)(x)) y(n)(x) + g(x,y x,y'(x),...,y(n-1)(x)) = h(x,y x, y'(x),..., y(n-1)(x))}.") (((|Any|) (|Equation| |#2|) (|BasicOperator|) (|Equation| |#2|) (|Equation| |#2|)) "\\spad{seriesSolve(eq,y,x=a, y a = b)} returns a Taylor series solution of \\spad{eq} around \\spad{x} = a with initial condition \\spad{y(a) = b}. Note: \\spad{eq} must be of the form \\spad{f(x, y x) y'(x) + g(x, y x) = h(x, y x)}."))) NIL NIL @@ -1255,7 +1255,7 @@ NIL (-331 FE |var| |cen|) ((|constructor| (NIL "ExponentialOfUnivariatePuiseuxSeries is a domain used to represent essential singularities of functions. An object in this domain is a function of the form \\spad{exp(f(x))},{} where \\spad{f(x)} is a Puiseux series with no terms of non-negative degree. Objects are ordered according to order of singularity,{} with functions which tend more rapidly to zero or infinity considered to be larger. Thus,{} if \\spad{order(f(x)) < order(g(x))},{} \\spadignore{i.e.} the first non-zero term of \\spad{f(x)} has lower degree than the first non-zero term of \\spad{g(x)},{} then \\spad{exp(f(x)) > exp(g(x))}. If \\spad{order(f(x)) = order(g(x))},{} then the ordering is essentially random. This domain is used in computing limits involving functions with essential singularities.")) (|exponentialOrder| (((|Fraction| (|Integer|)) $) "\\spad{exponentialOrder(exp(c * x **(-n) + ...))} returns \\spad{-n}. exponentialOrder(0) returns \\spad{0}.")) (|exponent| (((|UnivariatePuiseuxSeries| |#1| |#2| |#3|) $) "\\spad{exponent(exp(f(x)))} returns \\spad{f(x)}")) (|exponential| (($ (|UnivariatePuiseuxSeries| |#1| |#2| |#3|)) "\\spad{exponential(f(x))} returns \\spad{exp(f(x))}. Note: the function does NOT check that \\spad{f(x)} has no non-negative terms."))) (((-4512 "*") |has| |#1| (-175)) (-4503 |has| |#1| (-571)) (-4508 |has| |#1| (-376)) (-4502 |has| |#1| (-376)) (-4504 . T) (-4505 . T) (-4507 . 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(|log| (((|List| (|Record| (|:| |coef| (|NonNegativeInteger|)) (|:| |logand| |#1|))) (|Factored| |#1|)) "\\spad{log(f)} returns \\spad{[(a1,b1),...,(am,bm)]} such that the logarithm of \\spad{f} is equal to \\spad{a1*log(b1) + ... + am*log(bm)}.")) (|nthRoot| (((|Record| (|:| |exponent| (|NonNegativeInteger|)) (|:| |coef| |#1|) (|:| |radicand| (|List| |#1|))) (|Factored| |#1|) (|NonNegativeInteger|)) "\\spad{nthRoot(f, n)} returns \\spad{(p, r, [r1,...,rm])} such that the \\spad{n}th-root of \\spad{f} is equal to \\spad{r * \\spad{p}th-root(r1 * ... * rm)},{} where \\spad{r1},{}...,{}rm are distinct factors of \\spad{f},{} each of which has an exponent smaller than \\spad{p} in \\spad{f}."))) NIL @@ -1287,12 +1287,12 @@ NIL (-339 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."))) ((-4511 . T) (-4510 . T)) -((-4144 (-12 (|HasCategory| |#1| (QUOTE (-872))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|))))) (-4144 (-12 (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-888))))) (|HasCategory| |#1| (|%list| (QUOTE -633) (QUOTE (-549)))) (-4144 (|HasCategory| |#1| (QUOTE (-872))) (|HasCategory| |#1| (QUOTE (-1133)))) (|HasCategory| |#1| (QUOTE (-872))) (-4144 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-872))) (|HasCategory| |#1| (QUOTE (-1133)))) (|HasCategory| (-560) (QUOTE (-872))) (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-888)))) (|HasCategory| |#1| (QUOTE (-102))) (-12 (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|))))) -(-340 S -4164) +((-4118 (-12 (|HasCategory| |#1| (QUOTE (-872))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|))))) (-4118 (-12 (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-888))))) (|HasCategory| |#1| (|%list| (QUOTE -633) (QUOTE (-549)))) (-4118 (|HasCategory| |#1| (QUOTE (-872))) (|HasCategory| |#1| (QUOTE (-1133)))) (|HasCategory| |#1| (QUOTE (-872))) (-4118 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-872))) (|HasCategory| |#1| (QUOTE (-1133)))) (|HasCategory| (-560) (QUOTE (-872))) (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-888)))) (|HasCategory| |#1| (QUOTE (-102))) (-12 (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|))))) +(-340 S -4140) ((|constructor| (NIL "FiniteAlgebraicExtensionField {\\em F} is the category of fields which are finite algebraic extensions of the field {\\em F}. If {\\em F} is finite then any finite algebraic extension of {\\em F} is finite,{} too. Let {\\em K} be a finite algebraic extension of the finite field {\\em F}. The exponentiation of elements of {\\em K} defines a \\spad{Z}-module structure on the multiplicative group of {\\em K}. The additive group of {\\em K} becomes a module over the ring of polynomials over {\\em F} via the operation \\spadfun{linearAssociatedExp}(a:K,{}f:SparseUnivariatePolynomial \\spad{F}) which is linear over {\\em F},{} \\spadignore{i.e.} for elements {\\em a} from {\\em K},{} {\\em c,d} from {\\em F} and {\\em f,g} univariate polynomials over {\\em F} we have \\spadfun{linearAssociatedExp}(a,{}cf+dg) equals {\\em c} times \\spadfun{linearAssociatedExp}(a,{}\\spad{f}) plus {\\em d} times \\spadfun{linearAssociatedExp}(a,{}\\spad{g}). Therefore \\spadfun{linearAssociatedExp} is defined completely by its action on monomials from {\\em F[X]}: \\spadfun{linearAssociatedExp}(a,{}monomial(1,{}\\spad{k})\\$SUP(\\spad{F})) is defined to be \\spadfun{Frobenius}(a,{}\\spad{k}) which is {\\em a**(q**k)} where {\\em q=size()\\$F}. The operations order and discreteLog associated with the multiplicative exponentiation have additive analogues associated to the operation \\spadfun{linearAssociatedExp}. These are the functions \\spadfun{linearAssociatedOrder} and \\spadfun{linearAssociatedLog},{} respectively.")) (|linearAssociatedLog| (((|Union| (|SparseUnivariatePolynomial| |#2|) "failed") $ $) "\\spad{linearAssociatedLog(b,a)} returns a polynomial {\\em g},{} such that the \\spadfun{linearAssociatedExp}(\\spad{b},{}\\spad{g}) equals {\\em a}. If there is no such polynomial {\\em g},{} then \\spadfun{linearAssociatedLog} fails.") (((|SparseUnivariatePolynomial| |#2|) $) "\\spad{linearAssociatedLog(a)} returns a polynomial {\\em g},{} such that \\spadfun{linearAssociatedExp}(normalElement(),{}\\spad{g}) equals {\\em a}.")) (|linearAssociatedOrder| (((|SparseUnivariatePolynomial| |#2|) $) "\\spad{linearAssociatedOrder(a)} retruns the monic polynomial {\\em g} of least degree,{} such that \\spadfun{linearAssociatedExp}(a,{}\\spad{g}) is 0.")) (|linearAssociatedExp| (($ $ (|SparseUnivariatePolynomial| |#2|)) "\\spad{linearAssociatedExp(a,f)} is linear over {\\em F},{} \\spadignore{i.e.} for elements {\\em a} from {\\em \\$},{} {\\em c,d} form {\\em F} and {\\em f,g} univariate polynomials over {\\em F} we have \\spadfun{linearAssociatedExp}(a,{}cf+dg) equals {\\em c} times \\spadfun{linearAssociatedExp}(a,{}\\spad{f}) plus {\\em d} times \\spadfun{linearAssociatedExp}(a,{}\\spad{g}). Therefore \\spadfun{linearAssociatedExp} is defined completely by its action on monomials from {\\em F[X]}: \\spadfun{linearAssociatedExp}(a,{}monomial(1,{}\\spad{k})\\$SUP(\\spad{F})) is defined to be \\spadfun{Frobenius}(a,{}\\spad{k}) which is {\\em a**(q**k)},{} where {\\em q=size()\\$F}.")) (|generator| (($) "\\spad{generator()} returns a root of the defining polynomial. This element generates the field as an algebra over the ground field.")) (|normal?| (((|Boolean|) $) "\\spad{normal?(a)} tests whether the element \\spad{a} is normal over the ground field \\spad{F},{} \\spadignore{i.e.} \\spad{a**(q**i), 0 <= i <= extensionDegree()-1} is an \\spad{F}-basis,{} where \\spad{q = size()\\$F}. Implementation according to Lidl/Niederreiter: Theorem 2.39.")) (|normalElement| (($) "\\spad{normalElement()} returns a element,{} normal over the ground field \\spad{F},{} \\spadignore{i.e.} \\spad{a**(q**i), 0 <= i < extensionDegree()} is an \\spad{F}-basis,{} where \\spad{q = size()\\$F}. At the first call,{} the element is computed by \\spadfunFrom{createNormalElement}{FiniteAlgebraicExtensionField} then cached in a global variable. On subsequent calls,{} the element is retrieved by referencing the global variable.")) (|createNormalElement| (($) "\\spad{createNormalElement()} computes a normal element over the ground field \\spad{F},{} that is,{} \\spad{a**(q**i), 0 <= i < extensionDegree()} is an \\spad{F}-basis,{} where \\spad{q = size()\\$F}. Reference: Such an element exists Lidl/Niederreiter: Theorem 2.35.")) (|trace| (($ $ (|PositiveInteger|)) "\\spad{trace(a,d)} computes the trace of \\spad{a} with respect to the field of extension degree \\spad{d} over the ground field of size \\spad{q}. Error: if \\spad{d} does not divide the extension degree of \\spad{a}. Note: \\spad{trace(a,d) = reduce(+,[a**(q**(d*i)) for i in 0..n/d])}.") ((|#2| $) "\\spad{trace(a)} computes the trace of \\spad{a} with respect to the field considered as an algebra with 1 over the ground field \\spad{F}.")) (|norm| (($ $ (|PositiveInteger|)) "\\spad{norm(a,d)} computes the norm of \\spad{a} with respect to the field of extension degree \\spad{d} over the ground field of size. Error: if \\spad{d} does not divide the extension degree of \\spad{a}. Note: norm(a,{}\\spad{d}) = reduce(*,{}[a**(q**(d*i)) for \\spad{i} in 0..n/d])") ((|#2| $) "\\spad{norm(a)} computes the norm of \\spad{a} with respect to the field considered as an algebra with 1 over the ground field \\spad{F}.")) (|degree| (((|PositiveInteger|) $) "\\spad{degree(a)} returns the degree of the minimal polynomial of an element \\spad{a} over the ground field \\spad{F}.")) (|extensionDegree| (((|PositiveInteger|)) "\\spad{extensionDegree()} returns the degree of field extension.")) (|definingPolynomial| (((|SparseUnivariatePolynomial| |#2|)) "\\spad{definingPolynomial()} returns the polynomial used to define the field extension.")) (|minimalPolynomial| (((|SparseUnivariatePolynomial| $) $ (|PositiveInteger|)) "\\spad{minimalPolynomial(x,n)} computes the minimal polynomial of \\spad{x} over the field of extension degree \\spad{n} over the ground field \\spad{F}.") (((|SparseUnivariatePolynomial| |#2|) $) "\\spad{minimalPolynomial(a)} returns the minimal polynomial of an element \\spad{a} over the ground field \\spad{F}.")) (|represents| (($ (|Vector| |#2|)) "\\spad{represents([a1,..,an])} returns \\spad{a1*v1 + ... + an*vn},{} where \\spad{v1},{}...,{}vn are the elements of the fixed basis.")) (|coordinates| (((|Matrix| |#2|) (|Vector| $)) "\\spad{coordinates([v1,...,vm])} returns the coordinates of the \\spad{vi}'s with to the fixed basis. The coordinates of \\spad{vi} are contained in the \\spad{i}th row of the matrix returned by this function.") (((|Vector| |#2|) $) "\\spad{coordinates(a)} returns the coordinates of \\spad{a} with respect to the fixed \\spad{F}-vectorspace basis.")) (|basis| (((|Vector| $) (|PositiveInteger|)) "\\spad{basis(n)} returns a fixed basis of a subfield of \\$ as \\spad{F}-vectorspace.") (((|Vector| $)) "\\spad{basis()} returns a fixed basis of \\$ as \\spad{F}-vectorspace."))) NIL ((|HasCategory| |#2| (QUOTE (-381)))) -(-341 -4164) +(-341 -4140) ((|constructor| (NIL "FiniteAlgebraicExtensionField {\\em F} is the category of fields which are finite algebraic extensions of the field {\\em F}. If {\\em F} is finite then any finite algebraic extension of {\\em F} is finite,{} too. Let {\\em K} be a finite algebraic extension of the finite field {\\em F}. The exponentiation of elements of {\\em K} defines a \\spad{Z}-module structure on the multiplicative group of {\\em K}. The additive group of {\\em K} becomes a module over the ring of polynomials over {\\em F} via the operation \\spadfun{linearAssociatedExp}(a:K,{}f:SparseUnivariatePolynomial \\spad{F}) which is linear over {\\em F},{} \\spadignore{i.e.} for elements {\\em a} from {\\em K},{} {\\em c,d} from {\\em F} and {\\em f,g} univariate polynomials over {\\em F} we have \\spadfun{linearAssociatedExp}(a,{}cf+dg) equals {\\em c} times \\spadfun{linearAssociatedExp}(a,{}\\spad{f}) plus {\\em d} times \\spadfun{linearAssociatedExp}(a,{}\\spad{g}). Therefore \\spadfun{linearAssociatedExp} is defined completely by its action on monomials from {\\em F[X]}: \\spadfun{linearAssociatedExp}(a,{}monomial(1,{}\\spad{k})\\$SUP(\\spad{F})) is defined to be \\spadfun{Frobenius}(a,{}\\spad{k}) which is {\\em a**(q**k)} where {\\em q=size()\\$F}. The operations order and discreteLog associated with the multiplicative exponentiation have additive analogues associated to the operation \\spadfun{linearAssociatedExp}. These are the functions \\spadfun{linearAssociatedOrder} and \\spadfun{linearAssociatedLog},{} respectively.")) (|linearAssociatedLog| (((|Union| (|SparseUnivariatePolynomial| |#1|) "failed") $ $) "\\spad{linearAssociatedLog(b,a)} returns a polynomial {\\em g},{} such that the \\spadfun{linearAssociatedExp}(\\spad{b},{}\\spad{g}) equals {\\em a}. If there is no such polynomial {\\em g},{} then \\spadfun{linearAssociatedLog} fails.") (((|SparseUnivariatePolynomial| |#1|) $) "\\spad{linearAssociatedLog(a)} returns a polynomial {\\em g},{} such that \\spadfun{linearAssociatedExp}(normalElement(),{}\\spad{g}) equals {\\em a}.")) (|linearAssociatedOrder| (((|SparseUnivariatePolynomial| |#1|) $) "\\spad{linearAssociatedOrder(a)} retruns the monic polynomial {\\em g} of least degree,{} such that \\spadfun{linearAssociatedExp}(a,{}\\spad{g}) is 0.")) (|linearAssociatedExp| (($ $ (|SparseUnivariatePolynomial| |#1|)) "\\spad{linearAssociatedExp(a,f)} is linear over {\\em F},{} \\spadignore{i.e.} for elements {\\em a} from {\\em \\$},{} {\\em c,d} form {\\em F} and {\\em f,g} univariate polynomials over {\\em F} we have \\spadfun{linearAssociatedExp}(a,{}cf+dg) equals {\\em c} times \\spadfun{linearAssociatedExp}(a,{}\\spad{f}) plus {\\em d} times \\spadfun{linearAssociatedExp}(a,{}\\spad{g}). Therefore \\spadfun{linearAssociatedExp} is defined completely by its action on monomials from {\\em F[X]}: \\spadfun{linearAssociatedExp}(a,{}monomial(1,{}\\spad{k})\\$SUP(\\spad{F})) is defined to be \\spadfun{Frobenius}(a,{}\\spad{k}) which is {\\em a**(q**k)},{} where {\\em q=size()\\$F}.")) (|generator| (($) "\\spad{generator()} returns a root of the defining polynomial. This element generates the field as an algebra over the ground field.")) (|normal?| (((|Boolean|) $) "\\spad{normal?(a)} tests whether the element \\spad{a} is normal over the ground field \\spad{F},{} \\spadignore{i.e.} \\spad{a**(q**i), 0 <= i <= extensionDegree()-1} is an \\spad{F}-basis,{} where \\spad{q = size()\\$F}. Implementation according to Lidl/Niederreiter: Theorem 2.39.")) (|normalElement| (($) "\\spad{normalElement()} returns a element,{} normal over the ground field \\spad{F},{} \\spadignore{i.e.} \\spad{a**(q**i), 0 <= i < extensionDegree()} is an \\spad{F}-basis,{} where \\spad{q = size()\\$F}. At the first call,{} the element is computed by \\spadfunFrom{createNormalElement}{FiniteAlgebraicExtensionField} then cached in a global variable. On subsequent calls,{} the element is retrieved by referencing the global variable.")) (|createNormalElement| (($) "\\spad{createNormalElement()} computes a normal element over the ground field \\spad{F},{} that is,{} \\spad{a**(q**i), 0 <= i < extensionDegree()} is an \\spad{F}-basis,{} where \\spad{q = size()\\$F}. Reference: Such an element exists Lidl/Niederreiter: Theorem 2.35.")) (|trace| (($ $ (|PositiveInteger|)) "\\spad{trace(a,d)} computes the trace of \\spad{a} with respect to the field of extension degree \\spad{d} over the ground field of size \\spad{q}. Error: if \\spad{d} does not divide the extension degree of \\spad{a}. Note: \\spad{trace(a,d) = reduce(+,[a**(q**(d*i)) for i in 0..n/d])}.") ((|#1| $) "\\spad{trace(a)} computes the trace of \\spad{a} with respect to the field considered as an algebra with 1 over the ground field \\spad{F}.")) (|norm| (($ $ (|PositiveInteger|)) "\\spad{norm(a,d)} computes the norm of \\spad{a} with respect to the field of extension degree \\spad{d} over the ground field of size. Error: if \\spad{d} does not divide the extension degree of \\spad{a}. Note: norm(a,{}\\spad{d}) = reduce(*,{}[a**(q**(d*i)) for \\spad{i} in 0..n/d])") ((|#1| $) "\\spad{norm(a)} computes the norm of \\spad{a} with respect to the field considered as an algebra with 1 over the ground field \\spad{F}.")) (|degree| (((|PositiveInteger|) $) "\\spad{degree(a)} returns the degree of the minimal polynomial of an element \\spad{a} over the ground field \\spad{F}.")) (|extensionDegree| (((|PositiveInteger|)) "\\spad{extensionDegree()} returns the degree of field extension.")) (|definingPolynomial| (((|SparseUnivariatePolynomial| |#1|)) "\\spad{definingPolynomial()} returns the polynomial used to define the field extension.")) (|minimalPolynomial| (((|SparseUnivariatePolynomial| $) $ (|PositiveInteger|)) "\\spad{minimalPolynomial(x,n)} computes the minimal polynomial of \\spad{x} over the field of extension degree \\spad{n} over the ground field \\spad{F}.") (((|SparseUnivariatePolynomial| |#1|) $) "\\spad{minimalPolynomial(a)} returns the minimal polynomial of an element \\spad{a} over the ground field \\spad{F}.")) (|represents| (($ (|Vector| |#1|)) "\\spad{represents([a1,..,an])} returns \\spad{a1*v1 + ... + an*vn},{} where \\spad{v1},{}...,{}vn are the elements of the fixed basis.")) (|coordinates| (((|Matrix| |#1|) (|Vector| $)) "\\spad{coordinates([v1,...,vm])} returns the coordinates of the \\spad{vi}'s with to the fixed basis. The coordinates of \\spad{vi} are contained in the \\spad{i}th row of the matrix returned by this function.") (((|Vector| |#1|) $) "\\spad{coordinates(a)} returns the coordinates of \\spad{a} with respect to the fixed \\spad{F}-vectorspace basis.")) (|basis| (((|Vector| $) (|PositiveInteger|)) "\\spad{basis(n)} returns a fixed basis of a subfield of \\$ as \\spad{F}-vectorspace.") (((|Vector| $)) "\\spad{basis()} returns a fixed basis of \\$ as \\spad{F}-vectorspace."))) ((-4502 . T) (-4508 . T) (-4503 . T) ((-4512 "*") . T) (-4504 . T) (-4505 . T) (-4507 . T)) NIL @@ -1312,7 +1312,7 @@ NIL ((|constructor| (NIL "Represntation of data needed to instantiate a domain constructor.")) (|lookupFunction| (((|Identifier|) $) "\\spad{lookupFunction x} returns the name of the lookup function associated with the functor data \\spad{x}.")) (|categories| (((|PrimitiveArray| (|ConstructorCall| (|CategoryConstructor|))) $) "\\spad{categories x} returns the list of categories forms each domain object obtained from the domain data \\spad{x} belongs to.")) (|encodingDirectory| (((|PrimitiveArray| (|NonNegativeInteger|)) $) "\\spad{encodintDirectory x} returns the directory of domain-wide entity description.")) (|attributeData| (((|List| (|Pair| (|Syntax|) (|NonNegativeInteger|))) $) "\\spad{attributeData x} returns the list of attribute-predicate bit vector index pair associated with the functor data \\spad{x}.")) (|domainTemplate| (((|DomainTemplate|) $) "\\spad{domainTemplate x} returns the domain template vector associated with the functor data \\spad{x}."))) NIL NIL -(-346 -4164 UP UPUP R) +(-346 -4140 UP UPUP R) ((|constructor| (NIL "This domains implements finite rational divisors on a curve,{} that is finite formal sums SUM(\\spad{n} * \\spad{P}) where the \\spad{n}'s are integers and the \\spad{P}'s are finite rational points on the curve.")) (|lSpaceBasis| (((|Vector| |#4|) $) "\\spad{lSpaceBasis(d)} returns a basis for \\spad{L(d) = {f | (f) >= -d}} as a module over \\spad{K[x]}.")) (|finiteBasis| (((|Vector| |#4|) $) "\\spad{finiteBasis(d)} returns a basis for \\spad{d} as a module over {\\em K[x]}."))) NIL NIL @@ -1320,11 +1320,11 @@ NIL ((|constructor| (NIL "\\indented{1}{Lift a map to finite divisors.} Author: Manuel Bronstein Date Created: 1988 Date Last Updated: 19 May 1993")) (|map| (((|FiniteDivisor| |#5| |#6| |#7| |#8|) (|Mapping| |#5| |#1|) (|FiniteDivisor| |#1| |#2| |#3| |#4|)) "\\spad{map(f,d)} \\undocumented{}"))) NIL NIL -(-348 S -4164 UP UPUP R) +(-348 S -4140 UP UPUP R) ((|constructor| (NIL "This category describes finite rational divisors on a curve,{} that is finite formal sums SUM(\\spad{n} * \\spad{P}) where the \\spad{n}'s are integers and the \\spad{P}'s are finite rational points on the curve.")) (|generator| (((|Union| |#5| "failed") $) "\\spad{generator(d)} returns \\spad{f} if \\spad{(f) = d},{} \"failed\" if \\spad{d} is not principal.")) (|principal?| (((|Boolean|) $) "\\spad{principal?(D)} tests if the argument is the divisor of a function.")) (|reduce| (($ $) "\\spad{reduce(D)} converts \\spad{D} to some reduced form (the reduced forms can be differents in different implementations).")) (|decompose| (((|Record| (|:| |id| (|FractionalIdeal| |#3| (|Fraction| |#3|) |#4| |#5|)) (|:| |principalPart| |#5|)) $) "\\spad{decompose(d)} returns \\spad{[id, f]} where \\spad{d = (id) + div(f)}.")) (|divisor| (($ |#5| |#3| |#3| |#3| |#2|) "\\spad{divisor(h, d, d', g, r)} returns the sum of all the finite points where \\spad{h/d} has residue \\spad{r}. \\spad{h} must be integral. \\spad{d} must be squarefree. \\spad{d'} is some derivative of \\spad{d} (not necessarily dd/dx). \\spad{g = gcd(d,discriminant)} contains the ramified zeros of \\spad{d}") (($ |#2| |#2| (|Integer|)) "\\spad{divisor(a, b, n)} makes the divisor \\spad{nP} where P: \\spad{(x = a, y = b)}. \\spad{P} is allowed to be singular if \\spad{n} is a multiple of the rank.") (($ |#2| |#2|) "\\spad{divisor(a, b)} makes the divisor P: \\spad{(x = a, y = b)}. Error: if \\spad{P} is singular.") (($ |#5|) "\\spad{divisor(g)} returns the divisor of the function \\spad{g}.") (($ (|FractionalIdeal| |#3| (|Fraction| |#3|) |#4| |#5|)) "\\spad{divisor(I)} makes a divisor \\spad{D} from an ideal \\spad{I}.")) (|ideal| (((|FractionalIdeal| |#3| (|Fraction| |#3|) |#4| |#5|) $) "\\spad{ideal(D)} returns the ideal corresponding to a divisor \\spad{D}."))) NIL NIL -(-349 -4164 UP UPUP R) +(-349 -4140 UP UPUP R) ((|constructor| (NIL "This category describes finite rational divisors on a curve,{} that is finite formal sums SUM(\\spad{n} * \\spad{P}) where the \\spad{n}'s are integers and the \\spad{P}'s are finite rational points on the curve.")) (|generator| (((|Union| |#4| "failed") $) "\\spad{generator(d)} returns \\spad{f} if \\spad{(f) = d},{} \"failed\" if \\spad{d} is not principal.")) (|principal?| (((|Boolean|) $) "\\spad{principal?(D)} tests if the argument is the divisor of a function.")) (|reduce| (($ $) "\\spad{reduce(D)} converts \\spad{D} to some reduced form (the reduced forms can be differents in different implementations).")) (|decompose| (((|Record| (|:| |id| (|FractionalIdeal| |#2| (|Fraction| |#2|) |#3| |#4|)) (|:| |principalPart| |#4|)) $) "\\spad{decompose(d)} returns \\spad{[id, f]} where \\spad{d = (id) + div(f)}.")) (|divisor| (($ |#4| |#2| |#2| |#2| |#1|) "\\spad{divisor(h, d, d', g, r)} returns the sum of all the finite points where \\spad{h/d} has residue \\spad{r}. \\spad{h} must be integral. \\spad{d} must be squarefree. \\spad{d'} is some derivative of \\spad{d} (not necessarily dd/dx). \\spad{g = gcd(d,discriminant)} contains the ramified zeros of \\spad{d}") (($ |#1| |#1| (|Integer|)) "\\spad{divisor(a, b, n)} makes the divisor \\spad{nP} where P: \\spad{(x = a, y = b)}. \\spad{P} is allowed to be singular if \\spad{n} is a multiple of the rank.") (($ |#1| |#1|) "\\spad{divisor(a, b)} makes the divisor P: \\spad{(x = a, y = b)}. Error: if \\spad{P} is singular.") (($ |#4|) "\\spad{divisor(g)} returns the divisor of the function \\spad{g}.") (($ (|FractionalIdeal| |#2| (|Fraction| |#2|) |#3| |#4|)) "\\spad{divisor(I)} makes a divisor \\spad{D} from an ideal \\spad{I}.")) (|ideal| (((|FractionalIdeal| |#2| (|Fraction| |#2|) |#3| |#4|) $) "\\spad{ideal(D)} returns the ideal corresponding to a divisor \\spad{D}."))) NIL NIL @@ -1343,12 +1343,12 @@ NIL (-353 |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}."))) ((-4502 . T) (-4508 . T) (-4503 . T) ((-4512 "*") . T) (-4504 . T) (-4505 . T) (-4507 . T)) -((-4144 (|HasCategory| (-936 |#1|) (QUOTE (-147))) (|HasCategory| (-936 |#1|) (QUOTE (-381)))) (|HasCategory| (-936 |#1|) (QUOTE (-149))) (|HasCategory| (-936 |#1|) (QUOTE (-381))) (|HasCategory| (-936 |#1|) (QUOTE (-147)))) -(-354 S -4164 UP UPUP) +((-4118 (|HasCategory| (-936 |#1|) (QUOTE (-147))) (|HasCategory| (-936 |#1|) (QUOTE (-381)))) (|HasCategory| (-936 |#1|) (QUOTE (-149))) (|HasCategory| (-936 |#1|) (QUOTE (-381))) (|HasCategory| (-936 |#1|) (QUOTE (-147)))) +(-354 S -4140 UP UPUP) ((|constructor| (NIL "This category is a model for the function field of a plane algebraic curve.")) (|rationalPoints| (((|List| (|List| |#2|))) "\\spad{rationalPoints()} returns the list of all the affine rational points.")) (|nonSingularModel| (((|List| (|Polynomial| |#2|)) (|Symbol|)) "\\spad{nonSingularModel(u)} returns the equations in \\spad{u1},{}...,{}un of an affine non-singular model for the curve.")) (|algSplitSimple| (((|Record| (|:| |num| $) (|:| |den| |#3|) (|:| |derivden| |#3|) (|:| |gd| |#3|)) $ (|Mapping| |#3| |#3|)) "\\spad{algSplitSimple(f, D)} returns \\spad{[h,d,d',g]} such that \\spad{f=h/d},{} \\spad{h} is integral at all the normal places \\spad{w}.\\spad{r}.\\spad{t}. \\spad{D},{} \\spad{d' = Dd},{} \\spad{g = gcd(d, discriminant())} and \\spad{D} is the derivation to use. \\spad{f} must have at most simple finite poles.")) (|hyperelliptic| (((|Union| |#3| "failed")) "\\spad{hyperelliptic()} returns \\spad{p(x)} if the curve is the hyperelliptic defined by \\spad{y**2 = p(x)},{} \"failed\" otherwise.")) (|elliptic| (((|Union| |#3| "failed")) "\\spad{elliptic()} returns \\spad{p(x)} if the curve is the elliptic defined by \\spad{y**2 = p(x)},{} \"failed\" otherwise.")) (|elt| ((|#2| $ |#2| |#2|) "\\spad{elt(f,a,b)} or \\spad{f}(a,{} \\spad{b}) returns the value of \\spad{f} at the point \\spad{(x = a, y = b)} if it is not singular.")) (|primitivePart| (($ $) "\\spad{primitivePart(f)} removes the content of the denominator and the common content of the numerator of \\spad{f}.")) (|differentiate| (($ $ (|Mapping| |#3| |#3|)) "\\spad{differentiate(x, d)} extends the derivation \\spad{d} from UP to \\$ and applies it to \\spad{x}.")) (|integralDerivationMatrix| (((|Record| (|:| |num| (|Matrix| |#3|)) (|:| |den| |#3|)) (|Mapping| |#3| |#3|)) "\\spad{integralDerivationMatrix(d)} extends the derivation \\spad{d} from UP to \\$ and returns (\\spad{M},{} \\spad{Q}) such that the i^th row of \\spad{M} divided by \\spad{Q} form the coordinates of \\spad{d(wi)} with respect to \\spad{(w1,...,wn)} where \\spad{(w1,...,wn)} is the integral basis returned by integralBasis().")) (|integralRepresents| (($ (|Vector| |#3|) |#3|) "\\spad{integralRepresents([A1,...,An], D)} returns \\spad{(A1 w1+...+An wn)/D} where \\spad{(w1,...,wn)} is the integral basis of \\spad{integralBasis()}.")) (|integralCoordinates| (((|Record| (|:| |num| (|Vector| |#3|)) (|:| |den| |#3|)) $) "\\spad{integralCoordinates(f)} returns \\spad{[[A1,...,An], D]} such that \\spad{f = (A1 w1 +...+ An wn) / D} where \\spad{(w1,...,wn)} is the integral basis returned by \\spad{integralBasis()}.")) (|represents| (($ (|Vector| |#3|) |#3|) "\\spad{represents([A0,...,A(n-1)],D)} returns \\spad{(A0 + A1 y +...+ A(n-1)*y**(n-1))/D}.")) (|yCoordinates| (((|Record| (|:| |num| (|Vector| |#3|)) (|:| |den| |#3|)) $) "\\spad{yCoordinates(f)} returns \\spad{[[A1,...,An], D]} such that \\spad{f = (A1 + A2 y +...+ An y**(n-1)) / D}.")) (|inverseIntegralMatrixAtInfinity| (((|Matrix| (|Fraction| |#3|))) "\\spad{inverseIntegralMatrixAtInfinity()} returns \\spad{M} such that \\spad{M (v1,...,vn) = (1, y, ..., y**(n-1))} where \\spad{(v1,...,vn)} is the local integral basis at infinity returned by \\spad{infIntBasis()}.")) (|integralMatrixAtInfinity| (((|Matrix| (|Fraction| |#3|))) "\\spad{integralMatrixAtInfinity()} returns \\spad{M} such that \\spad{(v1,...,vn) = M (1, y, ..., y**(n-1))} where \\spad{(v1,...,vn)} is the local integral basis at infinity returned by \\spad{infIntBasis()}.")) (|inverseIntegralMatrix| (((|Matrix| (|Fraction| |#3|))) "\\spad{inverseIntegralMatrix()} returns \\spad{M} such that \\spad{M (w1,...,wn) = (1, y, ..., y**(n-1))} where \\spad{(w1,...,wn)} is the integral basis of \\spadfunFrom{integralBasis}{FunctionFieldCategory}.")) (|integralMatrix| (((|Matrix| (|Fraction| |#3|))) "\\spad{integralMatrix()} returns \\spad{M} such that \\spad{(w1,...,wn) = M (1, y, ..., y**(n-1))},{} where \\spad{(w1,...,wn)} is the integral basis of \\spadfunFrom{integralBasis}{FunctionFieldCategory}.")) (|reduceBasisAtInfinity| (((|Vector| $) (|Vector| $)) "\\spad{reduceBasisAtInfinity(b1,...,bn)} returns \\spad{(x**i * bj)} for all \\spad{i},{}\\spad{j} such that \\spad{x**i*bj} is locally integral at infinity.")) (|normalizeAtInfinity| (((|Vector| $) (|Vector| $)) "\\spad{normalizeAtInfinity(v)} makes \\spad{v} normal at infinity.")) (|complementaryBasis| (((|Vector| $) (|Vector| $)) "\\spad{complementaryBasis(b1,...,bn)} returns the complementary basis \\spad{(b1',...,bn')} of \\spad{(b1,...,bn)}.")) (|integral?| (((|Boolean|) $ |#3|) "\\spad{integral?(f, p)} tests whether \\spad{f} is locally integral at \\spad{p(x) = 0}.") (((|Boolean|) $ |#2|) "\\spad{integral?(f, a)} tests whether \\spad{f} is locally integral at \\spad{x = a}.") (((|Boolean|) $) "\\spad{integral?()} tests if \\spad{f} is integral over \\spad{k[x]}.")) (|integralAtInfinity?| (((|Boolean|) $) "\\spad{integralAtInfinity?()} tests if \\spad{f} is locally integral at infinity.")) (|integralBasisAtInfinity| (((|Vector| $)) "\\spad{integralBasisAtInfinity()} returns the local integral basis at infinity.")) (|integralBasis| (((|Vector| $)) "\\spad{integralBasis()} returns the integral basis for the curve.")) (|ramified?| (((|Boolean|) |#3|) "\\spad{ramified?(p)} tests whether \\spad{p(x) = 0} is ramified.") (((|Boolean|) |#2|) "\\spad{ramified?(a)} tests whether \\spad{x = a} is ramified.")) (|ramifiedAtInfinity?| (((|Boolean|)) "\\spad{ramifiedAtInfinity?()} tests if infinity is ramified.")) (|singular?| (((|Boolean|) |#3|) "\\spad{singular?(p)} tests whether \\spad{p(x) = 0} is singular.") (((|Boolean|) |#2|) "\\spad{singular?(a)} tests whether \\spad{x = a} is singular.")) (|singularAtInfinity?| (((|Boolean|)) "\\spad{singularAtInfinity?()} tests if there is a singularity at infinity.")) (|branchPoint?| (((|Boolean|) |#3|) "\\spad{branchPoint?(p)} tests whether \\spad{p(x) = 0} is a branch point.") (((|Boolean|) |#2|) "\\spad{branchPoint?(a)} tests whether \\spad{x = a} is a branch point.")) (|branchPointAtInfinity?| (((|Boolean|)) "\\spad{branchPointAtInfinity?()} tests if there is a branch point at infinity.")) (|rationalPoint?| (((|Boolean|) |#2| |#2|) "\\spad{rationalPoint?(a, b)} tests if \\spad{(x=a,y=b)} is on the curve.")) (|absolutelyIrreducible?| (((|Boolean|)) "\\spad{absolutelyIrreducible?()} tests if the curve absolutely irreducible?")) (|genus| (((|NonNegativeInteger|)) "\\spad{genus()} returns the genus of one absolutely irreducible component")) (|numberOfComponents| (((|NonNegativeInteger|)) "\\spad{numberOfComponents()} returns the number of absolutely irreducible components."))) NIL ((|HasCategory| |#2| (QUOTE (-381))) (|HasCategory| |#2| (QUOTE (-376)))) -(-355 -4164 UP UPUP) +(-355 -4140 UP UPUP) ((|constructor| (NIL "This category is a model for the function field of a plane algebraic curve.")) (|rationalPoints| (((|List| (|List| |#1|))) "\\spad{rationalPoints()} returns the list of all the affine rational points.")) (|nonSingularModel| (((|List| (|Polynomial| |#1|)) (|Symbol|)) "\\spad{nonSingularModel(u)} returns the equations in \\spad{u1},{}...,{}un of an affine non-singular model for the curve.")) (|algSplitSimple| (((|Record| (|:| |num| $) (|:| |den| |#2|) (|:| |derivden| |#2|) (|:| |gd| |#2|)) $ (|Mapping| |#2| |#2|)) "\\spad{algSplitSimple(f, D)} returns \\spad{[h,d,d',g]} such that \\spad{f=h/d},{} \\spad{h} is integral at all the normal places \\spad{w}.\\spad{r}.\\spad{t}. \\spad{D},{} \\spad{d' = Dd},{} \\spad{g = gcd(d, discriminant())} and \\spad{D} is the derivation to use. \\spad{f} must have at most simple finite poles.")) (|hyperelliptic| (((|Union| |#2| "failed")) "\\spad{hyperelliptic()} returns \\spad{p(x)} if the curve is the hyperelliptic defined by \\spad{y**2 = p(x)},{} \"failed\" otherwise.")) (|elliptic| (((|Union| |#2| "failed")) "\\spad{elliptic()} returns \\spad{p(x)} if the curve is the elliptic defined by \\spad{y**2 = p(x)},{} \"failed\" otherwise.")) (|elt| ((|#1| $ |#1| |#1|) "\\spad{elt(f,a,b)} or \\spad{f}(a,{} \\spad{b}) returns the value of \\spad{f} at the point \\spad{(x = a, y = b)} if it is not singular.")) (|primitivePart| (($ $) "\\spad{primitivePart(f)} removes the content of the denominator and the common content of the numerator of \\spad{f}.")) (|differentiate| (($ $ (|Mapping| |#2| |#2|)) "\\spad{differentiate(x, d)} extends the derivation \\spad{d} from UP to \\$ and applies it to \\spad{x}.")) (|integralDerivationMatrix| (((|Record| (|:| |num| (|Matrix| |#2|)) (|:| |den| |#2|)) (|Mapping| |#2| |#2|)) "\\spad{integralDerivationMatrix(d)} extends the derivation \\spad{d} from UP to \\$ and returns (\\spad{M},{} \\spad{Q}) such that the i^th row of \\spad{M} divided by \\spad{Q} form the coordinates of \\spad{d(wi)} with respect to \\spad{(w1,...,wn)} where \\spad{(w1,...,wn)} is the integral basis returned by integralBasis().")) (|integralRepresents| (($ (|Vector| |#2|) |#2|) "\\spad{integralRepresents([A1,...,An], D)} returns \\spad{(A1 w1+...+An wn)/D} where \\spad{(w1,...,wn)} is the integral basis of \\spad{integralBasis()}.")) (|integralCoordinates| (((|Record| (|:| |num| (|Vector| |#2|)) (|:| |den| |#2|)) $) "\\spad{integralCoordinates(f)} returns \\spad{[[A1,...,An], D]} such that \\spad{f = (A1 w1 +...+ An wn) / D} where \\spad{(w1,...,wn)} is the integral basis returned by \\spad{integralBasis()}.")) (|represents| (($ (|Vector| |#2|) |#2|) "\\spad{represents([A0,...,A(n-1)],D)} returns \\spad{(A0 + A1 y +...+ A(n-1)*y**(n-1))/D}.")) (|yCoordinates| (((|Record| (|:| |num| (|Vector| |#2|)) (|:| |den| |#2|)) $) "\\spad{yCoordinates(f)} returns \\spad{[[A1,...,An], D]} such that \\spad{f = (A1 + A2 y +...+ An y**(n-1)) / D}.")) (|inverseIntegralMatrixAtInfinity| (((|Matrix| (|Fraction| |#2|))) "\\spad{inverseIntegralMatrixAtInfinity()} returns \\spad{M} such that \\spad{M (v1,...,vn) = (1, y, ..., y**(n-1))} where \\spad{(v1,...,vn)} is the local integral basis at infinity returned by \\spad{infIntBasis()}.")) (|integralMatrixAtInfinity| (((|Matrix| (|Fraction| |#2|))) "\\spad{integralMatrixAtInfinity()} returns \\spad{M} such that \\spad{(v1,...,vn) = M (1, y, ..., y**(n-1))} where \\spad{(v1,...,vn)} is the local integral basis at infinity returned by \\spad{infIntBasis()}.")) (|inverseIntegralMatrix| (((|Matrix| (|Fraction| |#2|))) "\\spad{inverseIntegralMatrix()} returns \\spad{M} such that \\spad{M (w1,...,wn) = (1, y, ..., y**(n-1))} where \\spad{(w1,...,wn)} is the integral basis of \\spadfunFrom{integralBasis}{FunctionFieldCategory}.")) (|integralMatrix| (((|Matrix| (|Fraction| |#2|))) "\\spad{integralMatrix()} returns \\spad{M} such that \\spad{(w1,...,wn) = M (1, y, ..., y**(n-1))},{} where \\spad{(w1,...,wn)} is the integral basis of \\spadfunFrom{integralBasis}{FunctionFieldCategory}.")) (|reduceBasisAtInfinity| (((|Vector| $) (|Vector| $)) "\\spad{reduceBasisAtInfinity(b1,...,bn)} returns \\spad{(x**i * bj)} for all \\spad{i},{}\\spad{j} such that \\spad{x**i*bj} is locally integral at infinity.")) (|normalizeAtInfinity| (((|Vector| $) (|Vector| $)) "\\spad{normalizeAtInfinity(v)} makes \\spad{v} normal at infinity.")) (|complementaryBasis| (((|Vector| $) (|Vector| $)) "\\spad{complementaryBasis(b1,...,bn)} returns the complementary basis \\spad{(b1',...,bn')} of \\spad{(b1,...,bn)}.")) (|integral?| (((|Boolean|) $ |#2|) "\\spad{integral?(f, p)} tests whether \\spad{f} is locally integral at \\spad{p(x) = 0}.") (((|Boolean|) $ |#1|) "\\spad{integral?(f, a)} tests whether \\spad{f} is locally integral at \\spad{x = a}.") (((|Boolean|) $) "\\spad{integral?()} tests if \\spad{f} is integral over \\spad{k[x]}.")) (|integralAtInfinity?| (((|Boolean|) $) "\\spad{integralAtInfinity?()} tests if \\spad{f} is locally integral at infinity.")) (|integralBasisAtInfinity| (((|Vector| $)) "\\spad{integralBasisAtInfinity()} returns the local integral basis at infinity.")) (|integralBasis| (((|Vector| $)) "\\spad{integralBasis()} returns the integral basis for the curve.")) (|ramified?| (((|Boolean|) |#2|) "\\spad{ramified?(p)} tests whether \\spad{p(x) = 0} is ramified.") (((|Boolean|) |#1|) "\\spad{ramified?(a)} tests whether \\spad{x = a} is ramified.")) (|ramifiedAtInfinity?| (((|Boolean|)) "\\spad{ramifiedAtInfinity?()} tests if infinity is ramified.")) (|singular?| (((|Boolean|) |#2|) "\\spad{singular?(p)} tests whether \\spad{p(x) = 0} is singular.") (((|Boolean|) |#1|) "\\spad{singular?(a)} tests whether \\spad{x = a} is singular.")) (|singularAtInfinity?| (((|Boolean|)) "\\spad{singularAtInfinity?()} tests if there is a singularity at infinity.")) (|branchPoint?| (((|Boolean|) |#2|) "\\spad{branchPoint?(p)} tests whether \\spad{p(x) = 0} is a branch point.") (((|Boolean|) |#1|) "\\spad{branchPoint?(a)} tests whether \\spad{x = a} is a branch point.")) (|branchPointAtInfinity?| (((|Boolean|)) "\\spad{branchPointAtInfinity?()} tests if there is a branch point at infinity.")) (|rationalPoint?| (((|Boolean|) |#1| |#1|) "\\spad{rationalPoint?(a, b)} tests if \\spad{(x=a,y=b)} is on the curve.")) (|absolutelyIrreducible?| (((|Boolean|)) "\\spad{absolutelyIrreducible?()} tests if the curve absolutely irreducible?")) (|genus| (((|NonNegativeInteger|)) "\\spad{genus()} returns the genus of one absolutely irreducible component")) (|numberOfComponents| (((|NonNegativeInteger|)) "\\spad{numberOfComponents()} returns the number of absolutely irreducible components."))) ((-4503 |has| (-421 |#2|) (-376)) (-4508 |has| (-421 |#2|) (-376)) (-4502 |has| (-421 |#2|) (-376)) ((-4512 "*") . T) (-4504 . T) (-4505 . T) (-4507 . T)) NIL @@ -1359,15 +1359,15 @@ NIL (-357 |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."))) ((-4502 . T) (-4508 . T) (-4503 . T) ((-4512 "*") . T) (-4504 . T) (-4505 . T) (-4507 . T)) -((-4144 (|HasCategory| (-936 |#1|) (QUOTE (-147))) (|HasCategory| (-936 |#1|) (QUOTE (-381)))) (|HasCategory| (-936 |#1|) (QUOTE (-149))) (|HasCategory| (-936 |#1|) (QUOTE (-381))) (|HasCategory| (-936 |#1|) (QUOTE (-147)))) +((-4118 (|HasCategory| (-936 |#1|) (QUOTE (-147))) (|HasCategory| (-936 |#1|) (QUOTE (-381)))) (|HasCategory| (-936 |#1|) (QUOTE (-149))) (|HasCategory| (-936 |#1|) (QUOTE (-381))) (|HasCategory| (-936 |#1|) (QUOTE (-147)))) (-358 GF |defpol|) ((|constructor| (NIL "FiniteFieldCyclicGroupExtensionByPolynomial(GF,{}defpol) implements a finite extension field of the ground field {\\em GF}. Its elements are represented by powers of a primitive element,{} \\spadignore{i.e.} a generator of the multiplicative (cyclic) group. As primitive element we choose the root of the extension polynomial {\\em defpol},{} which MUST be primitive (user responsibility). Zech logarithms are stored in a table of size half of the field size,{} and use \\spadtype{SingleInteger} for representing field elements,{} hence,{} there are restrictions on the size of the field.")) (|getZechTable| (((|PrimitiveArray| (|SingleInteger|))) "\\spad{getZechTable()} returns the zech logarithm table of the field it is used to perform additions in the field quickly."))) ((-4502 . T) (-4508 . T) (-4503 . T) ((-4512 "*") . T) (-4504 . T) (-4505 . T) (-4507 . T)) -((-4144 (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-381)))) (|HasCategory| |#1| (QUOTE (-149))) (|HasCategory| |#1| (QUOTE (-381))) (|HasCategory| |#1| (QUOTE (-147)))) +((-4118 (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-381)))) (|HasCategory| |#1| (QUOTE (-149))) (|HasCategory| |#1| (QUOTE (-381))) (|HasCategory| |#1| (QUOTE (-147)))) (-359 GF |extdeg|) ((|constructor| (NIL "FiniteFieldCyclicGroupExtension(GF,{}\\spad{n}) implements a extension of degree \\spad{n} over the ground field {\\em GF}. Its elements are represented by powers of a primitive element,{} \\spadignore{i.e.} a generator of the multiplicative (cyclic) group. As primitive element we choose the root of the extension polynomial,{} which is created by {\\em createPrimitivePoly} from \\spadtype{FiniteFieldPolynomialPackage}. Zech logarithms are stored in a table of size half of the field size,{} and use \\spadtype{SingleInteger} for representing field elements,{} hence,{} there are restrictions on the size of the field.")) (|getZechTable| (((|PrimitiveArray| (|SingleInteger|))) "\\spad{getZechTable()} returns the zech logarithm table of the field. This table is used to perform additions in the field quickly."))) ((-4502 . T) (-4508 . T) (-4503 . T) ((-4512 "*") . T) (-4504 . T) (-4505 . T) (-4507 . T)) -((-4144 (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-381)))) (|HasCategory| |#1| (QUOTE (-149))) (|HasCategory| |#1| (QUOTE (-381))) (|HasCategory| |#1| (QUOTE (-147)))) +((-4118 (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-381)))) (|HasCategory| |#1| (QUOTE (-149))) (|HasCategory| |#1| (QUOTE (-381))) (|HasCategory| |#1| (QUOTE (-147)))) (-360 GF) ((|constructor| (NIL "FiniteFieldFunctions(GF) is a package with functions concerning finite extension fields of the finite ground field {\\em GF},{} \\spadignore{e.g.} Zech logarithms.")) (|createLowComplexityNormalBasis| (((|Union| (|SparseUnivariatePolynomial| |#1|) (|Vector| (|List| (|Record| (|:| |value| |#1|) (|:| |index| (|SingleInteger|)))))) (|PositiveInteger|)) "\\spad{createLowComplexityNormalBasis(n)} tries to find a a low complexity normal basis of degree {\\em n} over {\\em GF} and returns its multiplication matrix If no low complexity basis is found it calls \\axiomFunFrom{createNormalPoly}{FiniteFieldPolynomialPackage}(\\spad{n}) to produce a normal polynomial of degree {\\em n} over {\\em GF}")) (|createLowComplexityTable| (((|Union| (|Vector| (|List| (|Record| (|:| |value| |#1|) (|:| |index| (|SingleInteger|))))) "failed") (|PositiveInteger|)) "\\spad{createLowComplexityTable(n)} tries to find a low complexity normal basis of degree {\\em n} over {\\em GF} and returns its multiplication matrix Fails,{} if it does not find a low complexity basis")) (|sizeMultiplication| (((|NonNegativeInteger|) (|Vector| (|List| (|Record| (|:| |value| |#1|) (|:| |index| (|SingleInteger|)))))) "\\spad{sizeMultiplication(m)} returns the number of entries of the multiplication table {\\em m}.")) (|createMultiplicationMatrix| (((|Matrix| |#1|) (|Vector| (|List| (|Record| (|:| |value| |#1|) (|:| |index| (|SingleInteger|)))))) "\\spad{createMultiplicationMatrix(m)} forms the multiplication table {\\em m} into a matrix over the ground field.")) (|createMultiplicationTable| (((|Vector| (|List| (|Record| (|:| |value| |#1|) (|:| |index| (|SingleInteger|))))) (|SparseUnivariatePolynomial| |#1|)) "\\spad{createMultiplicationTable(f)} generates a multiplication table for the normal basis of the field extension determined by {\\em f}. This is needed to perform multiplications between elements represented as coordinate vectors to this basis. See \\spadtype{FFNBP},{} \\spadtype{FFNBX}.")) (|createZechTable| (((|PrimitiveArray| (|SingleInteger|)) (|SparseUnivariatePolynomial| |#1|)) "\\spad{createZechTable(f)} generates a Zech logarithm table for the cyclic group representation of a extension of the ground field by the primitive polynomial {\\em f(x)},{} \\spadignore{i.e.} \\spad{Z(i)},{} defined by {\\em x**Z(i) = 1+x**i} is stored at index \\spad{i}. This is needed in particular to perform addition of field elements in finite fields represented in this way. See \\spadtype{FFCGP},{} \\spadtype{FFCGX}."))) NIL @@ -1384,42 +1384,42 @@ NIL ((|constructor| (NIL "FiniteFieldCategory is the category of finite fields")) (|representationType| (((|Union| "prime" "polynomial" "normal" "cyclic")) "\\spad{representationType()} returns the type of the representation,{} one of: \\spad{prime},{} \\spad{polynomial},{} \\spad{normal},{} or \\spad{cyclic}.")) (|order| (((|PositiveInteger|) $) "\\spad{order(b)} computes the order of an element \\spad{b} in the multiplicative group of the field. Error: if \\spad{b} equals 0.")) (|discreteLog| (((|NonNegativeInteger|) $) "\\spad{discreteLog(a)} computes the discrete logarithm of \\spad{a} with respect to \\spad{primitiveElement()} of the field.")) (|primitive?| (((|Boolean|) $) "\\spad{primitive?(b)} tests whether the element \\spad{b} is a generator of the (cyclic) multiplicative group of the field,{} \\spadignore{i.e.} is a primitive element. Implementation Note: see ch.IX.1.3,{} th.2 in \\spad{D}. Lipson.")) (|primitiveElement| (($) "\\spad{primitiveElement()} returns a primitive element stored in a global variable in the domain. At first call,{} the primitive element is computed by calling \\spadfun{createPrimitiveElement}.")) (|createPrimitiveElement| (($) "\\spad{createPrimitiveElement()} computes a generator of the (cyclic) multiplicative group of the field.")) (|tableForDiscreteLogarithm| (((|Table| (|PositiveInteger|) (|NonNegativeInteger|)) (|Integer|)) "\\spad{tableForDiscreteLogarithm(a,n)} returns a table of the discrete logarithms of \\spad{a**0} up to \\spad{a**(n-1)} which,{} called with key \\spad{lookup(a**i)} returns \\spad{i} for \\spad{i} in \\spad{0..n-1}. Error: if not called for prime divisors of order of \\indented{7}{multiplicative group.}")) (|factorsOfCyclicGroupSize| (((|List| (|Record| (|:| |factor| (|Integer|)) (|:| |exponent| (|Integer|))))) "\\spad{factorsOfCyclicGroupSize()} returns the factorization of size()\\spad{-1}")) (|conditionP| (((|Union| (|Vector| $) "failed") (|Matrix| $)) "\\spad{conditionP(mat)},{} given a matrix representing a homogeneous system of equations,{} returns a vector whose characteristic'th powers is a non-trivial solution,{} or \"failed\" if no such vector exists.")) (|charthRoot| (($ $) "\\spad{charthRoot(a)} takes the characteristic'th root of {\\em a}. Note: such a root is alway defined in finite fields."))) ((-4502 . T) (-4508 . T) (-4503 . T) ((-4512 "*") . T) (-4504 . T) (-4505 . T) (-4507 . T)) NIL -(-364 R UP -4164) +(-364 R UP -4140) ((|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 (-365 |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."))) ((-4502 . T) (-4508 . T) (-4503 . T) ((-4512 "*") . T) (-4504 . T) (-4505 . T) (-4507 . T)) -((-4144 (|HasCategory| (-936 |#1|) (QUOTE (-147))) (|HasCategory| (-936 |#1|) (QUOTE (-381)))) (|HasCategory| (-936 |#1|) (QUOTE (-149))) (|HasCategory| (-936 |#1|) (QUOTE (-381))) (|HasCategory| (-936 |#1|) (QUOTE (-147)))) +((-4118 (|HasCategory| (-936 |#1|) (QUOTE (-147))) (|HasCategory| (-936 |#1|) (QUOTE (-381)))) (|HasCategory| (-936 |#1|) (QUOTE (-149))) (|HasCategory| (-936 |#1|) (QUOTE (-381))) (|HasCategory| (-936 |#1|) (QUOTE (-147)))) (-366 GF |uni|) ((|constructor| (NIL "FiniteFieldNormalBasisExtensionByPolynomial(GF,{}uni) implements a finite extension of the ground field {\\em GF}. The elements are represented by coordinate vectors with respect to. a normal basis,{} \\spadignore{i.e.} a basis consisting of the conjugates (\\spad{q}-powers) of an element,{} in this case called normal element,{} where \\spad{q} is the size of {\\em GF}. The normal element is chosen as a root of the extension polynomial,{} which MUST be normal over {\\em GF} (user responsibility)")) (|sizeMultiplication| (((|NonNegativeInteger|)) "\\spad{sizeMultiplication()} returns the number of entries in the multiplication table of the field. Note: the time of multiplication of field elements depends on this size.")) (|getMultiplicationMatrix| (((|Matrix| |#1|)) "\\spad{getMultiplicationMatrix()} returns the multiplication table in form of a matrix.")) (|getMultiplicationTable| (((|Vector| (|List| (|Record| (|:| |value| |#1|) (|:| |index| (|SingleInteger|)))))) "\\spad{getMultiplicationTable()} returns the multiplication table for the normal basis of the field. This table is used to perform multiplications between field elements."))) ((-4502 . T) (-4508 . T) (-4503 . T) ((-4512 "*") . T) (-4504 . T) (-4505 . T) (-4507 . T)) -((-4144 (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-381)))) (|HasCategory| |#1| (QUOTE (-149))) (|HasCategory| |#1| (QUOTE (-381))) (|HasCategory| |#1| (QUOTE (-147)))) +((-4118 (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-381)))) (|HasCategory| |#1| (QUOTE (-149))) (|HasCategory| |#1| (QUOTE (-381))) (|HasCategory| |#1| (QUOTE (-147)))) (-367 GF |extdeg|) ((|constructor| (NIL "FiniteFieldNormalBasisExtensionByPolynomial(GF,{}\\spad{n}) implements a finite extension field of degree \\spad{n} over the ground field {\\em GF}. The elements are represented by coordinate vectors with respect to a normal basis,{} \\spadignore{i.e.} a basis consisting of the conjugates (\\spad{q}-powers) of an element,{} in this case called normal element. This is chosen as a root of the extension polynomial,{} created by {\\em createNormalPoly} from \\spadtype{FiniteFieldPolynomialPackage}")) (|sizeMultiplication| (((|NonNegativeInteger|)) "\\spad{sizeMultiplication()} returns the number of entries in the multiplication table of the field. Note: the time of multiplication of field elements depends on this size.")) (|getMultiplicationMatrix| (((|Matrix| |#1|)) "\\spad{getMultiplicationMatrix()} returns the multiplication table in form of a matrix.")) (|getMultiplicationTable| (((|Vector| (|List| (|Record| (|:| |value| |#1|) (|:| |index| (|SingleInteger|)))))) "\\spad{getMultiplicationTable()} returns the multiplication table for the normal basis of the field. This table is used to perform multiplications between field elements."))) ((-4502 . T) (-4508 . T) (-4503 . T) ((-4512 "*") . T) (-4504 . T) (-4505 . T) (-4507 . T)) -((-4144 (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-381)))) (|HasCategory| |#1| (QUOTE (-149))) (|HasCategory| |#1| (QUOTE (-381))) (|HasCategory| |#1| (QUOTE (-147)))) +((-4118 (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-381)))) (|HasCategory| |#1| (QUOTE (-149))) (|HasCategory| |#1| (QUOTE (-381))) (|HasCategory| |#1| (QUOTE (-147)))) (-368 GF |defpol|) ((|constructor| (NIL "FiniteFieldExtensionByPolynomial(GF,{} defpol) implements the extension of the finite field {\\em GF} generated by the extension polynomial {\\em defpol} which MUST be irreducible. Note: the user has the responsibility to ensure that {\\em defpol} is irreducible."))) ((-4502 . T) (-4508 . T) (-4503 . T) ((-4512 "*") . T) (-4504 . T) (-4505 . T) (-4507 . T)) -((-4144 (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-381)))) (|HasCategory| |#1| (QUOTE (-149))) (|HasCategory| |#1| (QUOTE (-381))) (|HasCategory| |#1| (QUOTE (-147)))) +((-4118 (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-381)))) (|HasCategory| |#1| (QUOTE (-149))) (|HasCategory| |#1| (QUOTE (-381))) (|HasCategory| |#1| (QUOTE (-147)))) (-369 GF) ((|constructor| (NIL "This package provides a number of functions for generating,{} counting and testing irreducible,{} normal,{} primitive,{} random polynomials over finite fields.")) (|reducedQPowers| (((|PrimitiveArray| (|SparseUnivariatePolynomial| |#1|)) (|SparseUnivariatePolynomial| |#1|)) "\\spad{reducedQPowers(f)} generates \\spad{[x,x**q,x**(q**2),...,x**(q**(n-1))]} reduced modulo \\spad{f} where \\spad{q = size()\\$GF} and \\spad{n = degree f}.")) (|leastAffineMultiple| (((|SparseUnivariatePolynomial| |#1|) (|SparseUnivariatePolynomial| |#1|)) "\\spad{leastAffineMultiple(f)} computes the least affine polynomial which is divisible by the polynomial \\spad{f} over the finite field {\\em GF},{} \\spadignore{i.e.} a polynomial whose exponents are 0 or a power of \\spad{q},{} the size of {\\em GF}.")) (|random| (((|SparseUnivariatePolynomial| |#1|) (|PositiveInteger|) (|PositiveInteger|)) "\\spad{random(m,n)}\\$FFPOLY(GF) generates a random monic polynomial of degree \\spad{d} over the finite field {\\em GF},{} \\spad{d} between \\spad{m} and \\spad{n}.") (((|SparseUnivariatePolynomial| |#1|) (|PositiveInteger|)) "\\spad{random(n)}\\$FFPOLY(GF) generates a random monic polynomial of degree \\spad{n} over the finite field {\\em GF}.")) (|nextPrimitiveNormalPoly| (((|Union| (|SparseUnivariatePolynomial| |#1|) "failed") (|SparseUnivariatePolynomial| |#1|)) "\\spad{nextPrimitiveNormalPoly(f)} yields the next primitive normal polynomial over a finite field {\\em GF} of the same degree as \\spad{f} in the following order,{} or \"failed\" if there are no greater ones. Error: if \\spad{f} has degree 0. Note: the input polynomial \\spad{f} is made monic. Also,{} \\spad{f < g} if the {\\em lookup} of the constant term of \\spad{f} is less than this number for \\spad{g} or,{} in case these numbers are equal,{} if the {\\em lookup} of the coefficient of the term of degree {\\em n-1} of \\spad{f} is less than this number for \\spad{g}. If these numbers are equals,{} \\spad{f < g} if the number of monomials of \\spad{f} is less than that for \\spad{g},{} or if the lists of exponents for \\spad{f} are lexicographically less than those for \\spad{g}. If these lists are also equal,{} the lists of coefficients are coefficients according to the lexicographic ordering induced by the ordering of the elements of {\\em GF} given by {\\em lookup}. This operation is equivalent to nextNormalPrimitivePoly(\\spad{f}).")) (|nextNormalPrimitivePoly| (((|Union| (|SparseUnivariatePolynomial| |#1|) "failed") (|SparseUnivariatePolynomial| |#1|)) "\\spad{nextNormalPrimitivePoly(f)} yields the next normal primitive polynomial over a finite field {\\em GF} of the same degree as \\spad{f} in the following order,{} or \"failed\" if there are no greater ones. Error: if \\spad{f} has degree 0. Note: the input polynomial \\spad{f} is made monic. Also,{} \\spad{f < g} if the {\\em lookup} of the constant term of \\spad{f} is less than this number for \\spad{g} or if {\\em lookup} of the coefficient of the term of degree {\\em n-1} of \\spad{f} is less than this number for \\spad{g}. Otherwise,{} \\spad{f < g} if the number of monomials of \\spad{f} is less than that for \\spad{g} or if the lists of exponents for \\spad{f} are lexicographically less than those for \\spad{g}. If these lists are also equal,{} the lists of coefficients are compared according to the lexicographic ordering induced by the ordering of the elements of {\\em GF} given by {\\em lookup}. This operation is equivalent to nextPrimitiveNormalPoly(\\spad{f}).")) (|nextNormalPoly| (((|Union| (|SparseUnivariatePolynomial| |#1|) "failed") (|SparseUnivariatePolynomial| |#1|)) "\\spad{nextNormalPoly(f)} yields the next normal polynomial over a finite field {\\em GF} of the same degree as \\spad{f} in the following order,{} or \"failed\" if there are no greater ones. Error: if \\spad{f} has degree 0. Note: the input polynomial \\spad{f} is made monic. Also,{} \\spad{f < g} if the {\\em lookup} of the coefficient of the term of degree {\\em n-1} of \\spad{f} is less than that for \\spad{g}. In case these numbers are equal,{} \\spad{f < g} if if the number of monomials of \\spad{f} is less that for \\spad{g} or if the list of exponents of \\spad{f} are lexicographically less than the corresponding list for \\spad{g}. If these lists are also equal,{} the lists of coefficients are compared according to the lexicographic ordering induced by the ordering of the elements of {\\em GF} given by {\\em lookup}.")) (|nextPrimitivePoly| (((|Union| (|SparseUnivariatePolynomial| |#1|) "failed") (|SparseUnivariatePolynomial| |#1|)) "\\spad{nextPrimitivePoly(f)} yields the next primitive polynomial over a finite field {\\em GF} of the same degree as \\spad{f} in the following order,{} or \"failed\" if there are no greater ones. Error: if \\spad{f} has degree 0. Note: the input polynomial \\spad{f} is made monic. Also,{} \\spad{f < g} if the {\\em lookup} of the constant term of \\spad{f} is less than this number for \\spad{g}. If these values are equal,{} then \\spad{f < g} if if the number of monomials of \\spad{f} is less than that for \\spad{g} or if the lists of exponents of \\spad{f} are lexicographically less than the corresponding list for \\spad{g}. If these lists are also equal,{} the lists of coefficients are compared according to the lexicographic ordering induced by the ordering of the elements of {\\em GF} given by {\\em lookup}.")) (|nextIrreduciblePoly| (((|Union| (|SparseUnivariatePolynomial| |#1|) "failed") (|SparseUnivariatePolynomial| |#1|)) "\\spad{nextIrreduciblePoly(f)} yields the next monic irreducible polynomial over a finite field {\\em GF} of the same degree as \\spad{f} in the following order,{} or \"failed\" if there are no greater ones. Error: if \\spad{f} has degree 0. Note: the input polynomial \\spad{f} is made monic. Also,{} \\spad{f < g} if the number of monomials of \\spad{f} is less than this number for \\spad{g}. If \\spad{f} and \\spad{g} have the same number of monomials,{} the lists of exponents are compared lexicographically. If these lists are also equal,{} the lists of coefficients are compared according to the lexicographic ordering induced by the ordering of the elements of {\\em GF} given by {\\em lookup}.")) (|createPrimitiveNormalPoly| (((|SparseUnivariatePolynomial| |#1|) (|PositiveInteger|)) "\\spad{createPrimitiveNormalPoly(n)}\\$FFPOLY(GF) generates a normal and primitive polynomial of degree \\spad{n} over the field {\\em GF}. polynomial of degree \\spad{n} over the field {\\em GF}.")) (|createNormalPrimitivePoly| (((|SparseUnivariatePolynomial| |#1|) (|PositiveInteger|)) "\\spad{createNormalPrimitivePoly(n)}\\$FFPOLY(GF) generates a normal and primitive polynomial of degree \\spad{n} over the field {\\em GF}. Note: this function is equivalent to createPrimitiveNormalPoly(\\spad{n})")) (|createNormalPoly| (((|SparseUnivariatePolynomial| |#1|) (|PositiveInteger|)) "\\spad{createNormalPoly(n)}\\$FFPOLY(GF) generates a normal polynomial of degree \\spad{n} over the finite field {\\em GF}.")) (|createPrimitivePoly| (((|SparseUnivariatePolynomial| |#1|) (|PositiveInteger|)) "\\spad{createPrimitivePoly(n)}\\$FFPOLY(GF) generates a primitive polynomial of degree \\spad{n} over the finite field {\\em GF}.")) (|createIrreduciblePoly| (((|SparseUnivariatePolynomial| |#1|) (|PositiveInteger|)) "\\spad{createIrreduciblePoly(n)}\\$FFPOLY(GF) generates a monic irreducible univariate polynomial of degree \\spad{n} over the finite field {\\em GF}.")) (|numberOfNormalPoly| (((|PositiveInteger|) (|PositiveInteger|)) "\\spad{numberOfNormalPoly(n)}\\$FFPOLY(GF) yields the number of normal polynomials of degree \\spad{n} over the finite field {\\em GF}.")) (|numberOfPrimitivePoly| (((|PositiveInteger|) (|PositiveInteger|)) "\\spad{numberOfPrimitivePoly(n)}\\$FFPOLY(GF) yields the number of primitive polynomials of degree \\spad{n} over the finite field {\\em GF}.")) (|numberOfIrreduciblePoly| (((|PositiveInteger|) (|PositiveInteger|)) "\\spad{numberOfIrreduciblePoly(n)}\\$FFPOLY(GF) yields the number of monic irreducible univariate polynomials of degree \\spad{n} over the finite field {\\em GF}.")) (|normal?| (((|Boolean|) (|SparseUnivariatePolynomial| |#1|)) "\\spad{normal?(f)} tests whether the polynomial \\spad{f} over a finite field is normal,{} \\spadignore{i.e.} its roots are linearly independent over the field.")) (|primitive?| (((|Boolean|) (|SparseUnivariatePolynomial| |#1|)) "\\spad{primitive?(f)} tests whether the polynomial \\spad{f} over a finite field is primitive,{} \\spadignore{i.e.} all its roots are primitive."))) NIL NIL -(-370 -4164 GF) +(-370 -4140 GF) ((|constructor| (NIL "\\spad{FiniteFieldPolynomialPackage2}(\\spad{F},{}GF) exports some functions concerning finite fields,{} which depend on a finite field {\\em GF} and an algebraic extension \\spad{F} of {\\em GF},{} \\spadignore{e.g.} a zero of a polynomial over {\\em GF} in \\spad{F}.")) (|rootOfIrreduciblePoly| ((|#1| (|SparseUnivariatePolynomial| |#2|)) "\\spad{rootOfIrreduciblePoly(f)} computes one root of the monic,{} irreducible polynomial \\spad{f},{} which degree must divide the extension degree of {\\em F} over {\\em GF},{} \\spadignore{i.e.} \\spad{f} splits into linear factors over {\\em F}.")) (|Frobenius| ((|#1| |#1|) "\\spad{Frobenius(x)} \\undocumented{}")) (|basis| (((|Vector| |#1|) (|PositiveInteger|)) "\\spad{basis(n)} \\undocumented{}")) (|lookup| (((|PositiveInteger|) |#1|) "\\spad{lookup(x)} \\undocumented{}")) (|coerce| ((|#1| |#2|) "\\spad{coerce(x)} \\undocumented{}"))) NIL NIL -(-371 -4164 FP FPP) +(-371 -4140 FP FPP) ((|constructor| (NIL "This package solves linear diophantine equations for Bivariate polynomials over finite fields")) (|solveLinearPolynomialEquation| (((|Union| (|List| |#3|) "failed") (|List| |#3|) |#3|) "\\spad{solveLinearPolynomialEquation([f1, ..., fn], g)} (where the \\spad{fi} are relatively prime to each other) returns a list of \\spad{ai} such that \\spad{g/prod fi = sum ai/fi} or returns \"failed\" if no such list of \\spad{ai}'s exists."))) NIL NIL (-372 GF |n|) ((|constructor| (NIL "FiniteFieldExtensionByPolynomial(GF,{} \\spad{n}) implements an extension of the finite field {\\em GF} of degree \\spad{n} generated by the extension polynomial constructed by \\spadfunFrom{createIrreduciblePoly}{FiniteFieldPolynomialPackage} from \\spadtype{FiniteFieldPolynomialPackage}."))) ((-4502 . T) (-4508 . T) (-4503 . T) ((-4512 "*") . T) (-4504 . T) (-4505 . T) (-4507 . T)) -((-4144 (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-381)))) (|HasCategory| |#1| (QUOTE (-149))) (|HasCategory| |#1| (QUOTE (-381))) (|HasCategory| |#1| (QUOTE (-147)))) +((-4118 (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-381)))) (|HasCategory| |#1| (QUOTE (-149))) (|HasCategory| |#1| (QUOTE (-381))) (|HasCategory| |#1| (QUOTE (-147)))) (-373 R |ls|) ((|constructor| (NIL "This is just an interface between several packages and domains. The goal is to compute lexicographical Groebner bases of sets of polynomial with type \\spadtype{Polynomial R} by the {\\em FGLM} algorithm if this is possible (\\spadignore{i.e.} if the input system generates a zero-dimensional ideal).")) (|groebner| (((|List| (|Polynomial| |#1|)) (|List| (|Polynomial| |#1|))) "\\axiom{groebner(\\spad{lq1})} returns the lexicographical Groebner basis of \\axiom{\\spad{lq1}}. If \\axiom{\\spad{lq1}} generates a zero-dimensional ideal then the {\\em FGLM} strategy is used,{} otherwise the {\\em Sugar} strategy is used.")) (|fglmIfCan| (((|Union| (|List| (|Polynomial| |#1|)) "failed") (|List| (|Polynomial| |#1|))) "\\axiom{fglmIfCan(\\spad{lq1})} returns the lexicographical Groebner basis of \\axiom{\\spad{lq1}} by using the {\\em FGLM} strategy,{} if \\axiom{zeroDimensional?(\\spad{lq1})} holds.")) (|zeroDimensional?| (((|Boolean|) (|List| (|Polynomial| |#1|))) "\\axiom{zeroDimensional?(\\spad{lq1})} returns \\spad{true} iff \\axiom{\\spad{lq1}} generates a zero-dimensional ideal \\spad{w}.\\spad{r}.\\spad{t}. the variables of \\axiom{ls}."))) NIL @@ -1494,7 +1494,7 @@ NIL NIL (-391) ((|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}."))) -((-4493 . T) (-4501 . T) (-2862 . T) (-4502 . T) (-4508 . T) (-4503 . T) ((-4512 "*") . T) (-4504 . T) (-4505 . T) (-4507 . T)) +((-4493 . T) (-4501 . T) (-2853 . T) (-4502 . T) (-4508 . T) (-4503 . T) ((-4512 "*") . T) (-4504 . T) (-4505 . T) (-4507 . T)) NIL (-392 |Par|) ((|constructor| (NIL "\\indented{3}{This is a package for the approximation of complex solutions for} systems of equations of rational functions with complex rational coefficients. The results are expressed as either complex rational numbers or complex floats depending on the type of the precision parameter which can be either a rational number or a floating point number.")) (|complexRoots| (((|List| (|List| (|Complex| |#1|))) (|List| (|Fraction| (|Polynomial| (|Complex| (|Integer|))))) (|List| (|Symbol|)) |#1|) "\\spad{complexRoots(lrf, lv, eps)} finds all the complex solutions of a list of rational functions with rational number coefficients with respect the the variables appearing in \\spad{lv}. Each solution is computed to precision eps and returned as list corresponding to the order of variables in \\spad{lv}.") (((|List| (|Complex| |#1|)) (|Fraction| (|Polynomial| (|Complex| (|Integer|)))) |#1|) "\\spad{complexRoots(rf, eps)} finds all the complex solutions of a univariate rational function with rational number coefficients. The solutions are computed to precision eps.")) (|complexSolve| (((|List| (|Equation| (|Polynomial| (|Complex| |#1|)))) (|Equation| (|Fraction| (|Polynomial| (|Complex| (|Integer|))))) |#1|) "\\spad{complexSolve(eq,eps)} finds all the complex solutions of the equation \\spad{eq} of rational functions with rational rational coefficients with respect to all the variables appearing in \\spad{eq},{} with precision \\spad{eps}.") (((|List| (|Equation| (|Polynomial| (|Complex| |#1|)))) (|Fraction| (|Polynomial| (|Complex| (|Integer|)))) |#1|) "\\spad{complexSolve(p,eps)} find all the complex solutions of the rational function \\spad{p} with complex rational coefficients with respect to all the variables appearing in \\spad{p},{} with precision \\spad{eps}.") (((|List| (|List| (|Equation| (|Polynomial| (|Complex| |#1|))))) (|List| (|Equation| (|Fraction| (|Polynomial| (|Complex| (|Integer|)))))) |#1|) "\\spad{complexSolve(leq,eps)} finds all the complex solutions to precision \\spad{eps} of the system \\spad{leq} of equations of rational functions over complex rationals with respect to all the variables appearing in lp.") (((|List| (|List| (|Equation| (|Polynomial| (|Complex| |#1|))))) (|List| (|Fraction| (|Polynomial| (|Complex| (|Integer|))))) |#1|) "\\spad{complexSolve(lp,eps)} finds all the complex solutions to precision \\spad{eps} of the system \\spad{lp} of rational functions over the complex rationals with respect to all the variables appearing in \\spad{lp}."))) @@ -1552,7 +1552,7 @@ NIL ((|constructor| (NIL "Code to manipulate Fortran Output Stack")) (|topFortranOutputStack| (((|String|)) "\\spad{topFortranOutputStack()} returns the top element of the Fortran output stack")) (|pushFortranOutputStack| (((|Void|) (|String|)) "\\spad{pushFortranOutputStack(f)} pushes \\spad{f} onto the Fortran output stack") (((|Void|) (|FileName|)) "\\spad{pushFortranOutputStack(f)} pushes \\spad{f} onto the Fortran output stack")) (|popFortranOutputStack| (((|Void|)) "\\spad{popFortranOutputStack()} pops the Fortran output stack")) (|showFortranOutputStack| (((|Stack| (|String|))) "\\spad{showFortranOutputStack()} returns the Fortran output stack")) (|clearFortranOutputStack| (((|Stack| (|String|))) "\\spad{clearFortranOutputStack()} clears the Fortran output stack"))) NIL NIL -(-406 -4164 UP UPUP R) +(-406 -4140 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 @@ -1576,11 +1576,11 @@ NIL ((|constructor| (NIL "\\axiomType{FortranFunctionCategory} is the category of arguments to NAG Library routines which return (sets of) function values.")) (|retractIfCan| (((|Union| $ "failed") (|Fraction| (|Polynomial| (|Integer|)))) "\\spad{retractIfCan(e)} tries to convert \\spad{e} into an ASP,{} checking that \\indented{1}{legal Fortran-77 is produced.}") (((|Union| $ "failed") (|Fraction| (|Polynomial| (|Float|)))) "\\spad{retractIfCan(e)} tries to convert \\spad{e} into an ASP,{} checking that \\indented{1}{legal Fortran-77 is produced.}") (((|Union| $ "failed") (|Polynomial| (|Integer|))) "\\spad{retractIfCan(e)} tries to convert \\spad{e} into an ASP,{} checking that \\indented{1}{legal Fortran-77 is produced.}") (((|Union| $ "failed") (|Polynomial| (|Float|))) "\\spad{retractIfCan(e)} tries to convert \\spad{e} into an ASP,{} checking that \\indented{1}{legal Fortran-77 is produced.}") (((|Union| $ "failed") (|Expression| (|Integer|))) "\\spad{retractIfCan(e)} tries to convert \\spad{e} into an ASP,{} checking that \\indented{1}{legal Fortran-77 is produced.}") (((|Union| $ "failed") (|Expression| (|Float|))) "\\spad{retractIfCan(e)} tries to convert \\spad{e} into an ASP,{} checking that \\indented{1}{legal Fortran-77 is produced.}")) (|retract| (($ (|Fraction| (|Polynomial| (|Integer|)))) "\\spad{retract(e)} tries to convert \\spad{e} into an ASP,{} checking that \\indented{1}{legal Fortran-77 is produced.}") (($ (|Fraction| (|Polynomial| (|Float|)))) "\\spad{retract(e)} tries to convert \\spad{e} into an ASP,{} checking that \\indented{1}{legal Fortran-77 is produced.}") (($ (|Polynomial| (|Integer|))) "\\spad{retract(e)} tries to convert \\spad{e} into an ASP,{} checking that \\indented{1}{legal Fortran-77 is produced.}") (($ (|Polynomial| (|Float|))) "\\spad{retract(e)} tries to convert \\spad{e} into an ASP,{} checking that \\indented{1}{legal Fortran-77 is produced.}") (($ (|Expression| (|Integer|))) "\\spad{retract(e)} tries to convert \\spad{e} into an ASP,{} checking that \\indented{1}{legal Fortran-77 is produced.}") (($ (|Expression| (|Float|))) "\\spad{retract(e)} tries to convert \\spad{e} into an ASP,{} checking that \\indented{1}{legal Fortran-77 is produced.}")) (|coerce| (($ (|Record| (|:| |localSymbols| (|SymbolTable|)) (|:| |code| (|List| (|FortranCode|))))) "\\spad{coerce(e)} takes the component of \\spad{e} from \\spadtype{List FortranCode} and uses it as the body of the ASP,{} making the declarations in the \\spadtype{SymbolTable} component.") (($ (|FortranCode|)) "\\spad{coerce(e)} takes an object from \\spadtype{FortranCode} and \\indented{1}{uses it as the body of an ASP.}") (($ (|List| (|FortranCode|))) "\\spad{coerce(e)} takes an object from \\spadtype{List FortranCode} and \\indented{1}{uses it as the body of an ASP.}"))) NIL NIL -(-412 -4401 |returnType| -1629 |symbols|) +(-412 -4385 |returnType| -1660 |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 -(-413 -4164 UP) +(-413 -4140 UP) ((|constructor| (NIL "\\indented{1}{Full partial fraction expansion of rational functions} Author: Manuel Bronstein Date Created: 9 December 1992 Date Last Updated: June 18,{} 2010 References: \\spad{M}.Bronstein & \\spad{B}.Salvy,{} \\indented{12}{Full Partial Fraction Decomposition of Rational Functions,{}} \\indented{12}{in Proceedings of \\spad{ISSAC'93},{} Kiev,{} ACM Press.}")) (|construct| (($ (|List| (|Record| (|:| |exponent| (|NonNegativeInteger|)) (|:| |center| |#2|) (|:| |num| |#2|)))) "\\spad{construct(l)} is the inverse of fracPart.")) (|fracPart| (((|List| (|Record| (|:| |exponent| (|NonNegativeInteger|)) (|:| |center| |#2|) (|:| |num| |#2|))) $) "\\spad{fracPart(f)} returns the list of summands of the fractional part of \\spad{f}.")) (|polyPart| ((|#2| $) "\\spad{polyPart(f)} returns the polynomial part of \\spad{f}.")) (|fullPartialFraction| (($ (|Fraction| |#2|)) "\\spad{fullPartialFraction(f)} returns \\spad{[p, [[j, Dj, Hj]...]]} such that \\spad{f = p(x) + \\sum_{[j,Dj,Hj] in l} \\sum_{Dj(a)=0} Hj(a)/(x - a)\\^j}.")) (+ (($ |#2| $) "\\spad{p + x} returns the sum of \\spad{p} and \\spad{x}"))) NIL NIL @@ -1602,12 +1602,12 @@ NIL ((|HasAttribute| |#1| (QUOTE -4493)) (|HasAttribute| |#1| (QUOTE -4501))) (-418) ((|constructor| (NIL "This category is intended as a model for floating point systems. A floating point system is a model for the real numbers. In fact,{} it is an approximation in the sense that not all real numbers are exactly representable by floating point numbers. A floating point system is characterized by the following: \\blankline \\indented{2}{1: \\spadfunFrom{base}{FloatingPointSystem} of the \\spadfunFrom{exponent}{FloatingPointSystem}.} \\indented{9}{(actual implemenations are usually binary or decimal)} \\indented{2}{2: \\spadfunFrom{precision}{FloatingPointSystem} of the \\spadfunFrom{mantissa}{FloatingPointSystem} (arbitrary or fixed)} \\indented{2}{3: rounding error for operations} \\blankline Because a Float is an approximation to the real numbers,{} even though it is defined to be a join of a Field and OrderedRing,{} some of the attributes do not hold. In particular associative(\"+\") does not hold. Algorithms defined over a field need special considerations when the field is a floating point system.")) (|max| (($) "\\spad{max()} returns the maximum floating point number.")) (|min| (($) "\\spad{min()} returns the minimum floating point number.")) (|decreasePrecision| (((|PositiveInteger|) (|Integer|)) "\\spad{decreasePrecision(n)} decreases the current \\spadfunFrom{precision}{FloatingPointSystem} precision by \\spad{n} decimal digits.")) (|increasePrecision| (((|PositiveInteger|) (|Integer|)) "\\spad{increasePrecision(n)} increases the current \\spadfunFrom{precision}{FloatingPointSystem} by \\spad{n} decimal digits.")) (|precision| (((|PositiveInteger|) (|PositiveInteger|)) "\\spad{precision(n)} set the precision in the base to \\spad{n} decimal digits.") (((|PositiveInteger|)) "\\spad{precision()} returns the precision in digits base.")) (|digits| (((|PositiveInteger|) (|PositiveInteger|)) "\\spad{digits(d)} set the \\spadfunFrom{precision}{FloatingPointSystem} to \\spad{d} digits.") (((|PositiveInteger|)) "\\spad{digits()} returns ceiling's precision in decimal digits.")) (|bits| (((|PositiveInteger|) (|PositiveInteger|)) "\\spad{bits(n)} set the \\spadfunFrom{precision}{FloatingPointSystem} to \\spad{n} bits.") (((|PositiveInteger|)) "\\spad{bits()} returns ceiling's precision in bits.")) (|mantissa| (((|Integer|) $) "\\spad{mantissa(x)} returns the mantissa part of \\spad{x}.")) (|exponent| (((|Integer|) $) "\\spad{exponent(x)} returns the \\spadfunFrom{exponent}{FloatingPointSystem} part of \\spad{x}.")) (|base| (((|PositiveInteger|)) "\\spad{base()} returns the base of the \\spadfunFrom{exponent}{FloatingPointSystem}.")) (|order| (((|Integer|) $) "\\spad{order x} is the order of magnitude of \\spad{x}. Note: \\spad{base ** order x <= |x| < base ** (1 + order x)}.")) (|float| (($ (|Integer|) (|Integer|) (|PositiveInteger|)) "\\spad{float(a,e,b)} returns \\spad{a * b ** e}.") (($ (|Integer|) (|Integer|)) "\\spad{float(a,e)} returns \\spad{a * base() ** e}.")) (|approximate| ((|attribute|) "\\spad{approximate} means \"is an approximation to the real numbers\"."))) -((-2862 . T) (-4502 . T) (-4508 . T) (-4503 . T) ((-4512 "*") . T) (-4504 . T) (-4505 . T) (-4507 . T)) +((-2853 . T) (-4502 . T) (-4508 . T) (-4503 . T) ((-4512 "*") . T) (-4504 . T) (-4505 . T) (-4507 . T)) NIL (-419 R) ((|constructor| (NIL "\\spadtype{Factored} creates a domain whose objects are kept in factored form as long as possible. Thus certain operations like multiplication and gcd are relatively easy to do. Others,{} like addition require somewhat more work,{} and unless the argument domain provides a factor function,{} the result may not be completely factored. Each object consists of a unit and a list of factors,{} where a factor has a member of \\spad{R} (the \"base\"),{} and exponent and a flag indicating what is known about the base. A flag may be one of \"nil\",{} \"sqfr\",{} \"irred\" or \"prime\",{} which respectively mean that nothing is known about the base,{} it is square-free,{} it is irreducible,{} or it is prime. The current restriction to integral domains allows simplification to be performed without worrying about multiplication order.")) (|rationalIfCan| (((|Union| (|Fraction| (|Integer|)) "failed") $) "\\spad{rationalIfCan(u)} returns a rational number if \\spad{u} really is one,{} and \"failed\" otherwise.")) (|rational| (((|Fraction| (|Integer|)) $) "\\spad{rational(u)} assumes spadvar{\\spad{u}} is actually a rational number and does the conversion to rational number (see \\spadtype{Fraction Integer}).")) (|rational?| (((|Boolean|) $) "\\spad{rational?(u)} tests if \\spadvar{\\spad{u}} is actually a rational number (see \\spadtype{Fraction Integer}).")) (|map| (($ (|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."))) ((-4503 . T) ((-4512 "*") . T) (-4504 . T) (-4505 . T) (-4507 . T)) -((|HasCategory| |#1| (|%list| (QUOTE -528) (QUOTE (-1209)) (QUOTE $))) (|HasCategory| |#1| (|%list| (QUOTE -321) (QUOTE $))) (|HasCategory| |#1| (|%list| (QUOTE -298) (QUOTE $) (QUOTE $))) (|HasCategory| |#1| (|%list| (QUOTE -633) (QUOTE (-549)))) (|HasCategory| |#1| (QUOTE (-1254))) (-4144 (|HasCategory| |#1| (QUOTE (-466))) (|HasCategory| |#1| (QUOTE (-1254)))) (|HasCategory| |#1| (QUOTE (-1052))) (|HasCategory| |#1| (|%list| (QUOTE -1070) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#1| (|%list| (QUOTE -1070) (QUOTE (-560)))) (|HasCategory| |#1| (|%list| (QUOTE -528) (QUOTE (-1209)) (|devaluate| |#1|))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|))) (|HasCategory| |#1| (|%list| (QUOTE -298) (|devaluate| |#1|) (|devaluate| |#1|))) (|HasCategory| |#1| (QUOTE (-239))) (|HasCategory| |#1| (|%list| (QUOTE -930) (QUOTE (-1209)))) (|HasCategory| |#1| (QUOTE (-240))) (|HasCategory| |#1| (|%list| (QUOTE -928) (QUOTE (-1209)))) (|HasCategory| |#1| (QUOTE (-559))) (|HasCategory| |#1| (QUOTE (-466)))) +((|HasCategory| |#1| (|%list| (QUOTE -528) (QUOTE (-1209)) (QUOTE $))) (|HasCategory| |#1| (|%list| (QUOTE -321) (QUOTE $))) (|HasCategory| |#1| (|%list| (QUOTE -298) (QUOTE $) (QUOTE $))) (|HasCategory| |#1| (|%list| (QUOTE -633) (QUOTE (-549)))) (|HasCategory| |#1| (QUOTE (-1254))) (-4118 (|HasCategory| |#1| (QUOTE (-466))) (|HasCategory| |#1| (QUOTE (-1254)))) (|HasCategory| |#1| (QUOTE (-1052))) (|HasCategory| |#1| (|%list| (QUOTE -1070) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#1| (|%list| (QUOTE -1070) (QUOTE (-560)))) (|HasCategory| |#1| (|%list| (QUOTE -528) (QUOTE (-1209)) (|devaluate| |#1|))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|))) (|HasCategory| |#1| (|%list| (QUOTE -298) (|devaluate| |#1|) (|devaluate| |#1|))) (|HasCategory| |#1| (QUOTE (-239))) (|HasCategory| |#1| (|%list| (QUOTE -930) (QUOTE (-1209)))) (|HasCategory| |#1| (QUOTE (-240))) (|HasCategory| |#1| (|%list| (QUOTE -928) (QUOTE (-1209)))) (|HasCategory| |#1| (QUOTE (-559))) (|HasCategory| |#1| (QUOTE (-466)))) (-420 R S) ((|constructor| (NIL "\\spadtype{FactoredFunctions2} contains functions that involve factored objects whose underlying domains may not be the same. For example,{} \\spadfun{map} might be used to coerce an object of type \\spadtype{Factored(Integer)} to \\spadtype{Factored(Complex(Integer))}.")) (|map| (((|Factored| |#2|) (|Mapping| |#2| |#1|) (|Factored| |#1|)) "\\spad{map(fn,u)} is used to apply the function \\userfun{\\spad{fn}} to every factor of \\spadvar{\\spad{u}}. The new factored object will have all its information flags set to \"nil\". This function is used,{} for example,{} to coerce every factor base to another type."))) NIL @@ -1615,7 +1615,7 @@ NIL (-421 S) ((|constructor| (NIL "Fraction takes an IntegralDomain \\spad{S} and produces the domain of Fractions with numerators and denominators from \\spad{S}. If \\spad{S} is also a GcdDomain,{} then gcd's between numerator and denominator will be cancelled during all operations.")) (|canonical| ((|attribute|) "\\spad{canonical} means that equal elements are in fact identical."))) ((-4497 -12 (|has| |#1| (-6 -4508)) (|has| |#1| (-466)) (|has| |#1| (-6 -4497))) (-4502 . T) (-4508 . T) (-4503 . T) ((-4512 "*") . T) (-4504 . T) (-4505 . T) (-4507 . T)) -((|HasCategory| |#1| (QUOTE (-940))) (|HasCategory| |#1| (|%list| (QUOTE -1070) (QUOTE (-1209)))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-149))) (-4144 (-12 (|HasCategory| |#1| (QUOTE (-559))) (|HasCategory| |#1| (QUOTE (-845)))) (|HasCategory| |#1| (|%list| (QUOTE -633) (QUOTE (-549))))) (|HasCategory| |#1| (QUOTE (-1052))) (|HasCategory| |#1| (QUOTE (-844))) (|HasCategory| |#1| (QUOTE (-872))) (-4144 (|HasCategory| |#1| (QUOTE (-844))) (|HasCategory| |#1| (QUOTE (-872)))) (-4144 (-12 (|HasCategory| |#1| (QUOTE (-559))) (|HasCategory| |#1| (QUOTE (-845)))) (|HasCategory| |#1| (|%list| (QUOTE -1070) (QUOTE (-560))))) (|HasCategory| |#1| (QUOTE (-1184))) (|HasCategory| |#1| (|%list| (QUOTE -912) (QUOTE (-391)))) (-4144 (-12 (|HasCategory| |#1| (QUOTE (-559))) (|HasCategory| |#1| (QUOTE (-845)))) (|HasCategory| |#1| (|%list| (QUOTE -912) (QUOTE (-560))))) (|HasCategory| |#1| (|%list| (QUOTE -633) (|%list| (QUOTE -916) (QUOTE (-391))))) (-4144 (|HasCategory| |#1| (|%list| (QUOTE -633) (|%list| (QUOTE -916) (QUOTE (-560))))) (-12 (|HasCategory| |#1| (QUOTE (-559))) (|HasCategory| |#1| (QUOTE (-845))))) (-4144 (|HasCategory| |#1| (|%list| (QUOTE -660) (QUOTE (-560)))) (-12 (|HasCategory| |#1| (QUOTE (-559))) (|HasCategory| |#1| (QUOTE (-845))))) (|HasCategory| |#1| (QUOTE (-239))) (|HasCategory| |#1| (|%list| (QUOTE -930) (QUOTE (-1209)))) (|HasCategory| |#1| (QUOTE (-240))) (|HasCategory| |#1| (|%list| (QUOTE -928) (QUOTE (-1209)))) (|HasCategory| |#1| (|%list| (QUOTE -528) (QUOTE (-1209)) (|devaluate| |#1|))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|))) (|HasCategory| |#1| (|%list| (QUOTE -298) (|devaluate| |#1|) (|devaluate| |#1|))) (-12 (|HasCategory| |#1| (QUOTE (-559))) (|HasCategory| |#1| (QUOTE (-845)))) (|HasCategory| |#1| (QUOTE (-319))) (|HasCategory| |#1| (QUOTE (-559))) (-12 (|HasAttribute| |#1| (QUOTE -4508)) (|HasAttribute| |#1| (QUOTE -4497)) (|HasCategory| |#1| (QUOTE (-466)))) (|HasCategory| |#1| (|%list| (QUOTE -633) (QUOTE (-549)))) (|HasCategory| |#1| (|%list| (QUOTE -1070) (QUOTE (-560)))) (|HasCategory| |#1| (|%list| (QUOTE -912) (QUOTE (-560)))) (|HasCategory| |#1| (|%list| (QUOTE -633) (|%list| (QUOTE -916) (QUOTE (-560))))) (|HasCategory| |#1| (|%list| (QUOTE -660) (QUOTE (-560)))) (-12 (|HasCategory| $ (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-940)))) (-4144 (-12 (|HasCategory| $ (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-940)))) (|HasCategory| |#1| (QUOTE (-147))))) +((|HasCategory| |#1| (QUOTE (-940))) (|HasCategory| |#1| (|%list| (QUOTE -1070) (QUOTE (-1209)))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-149))) (-4118 (-12 (|HasCategory| |#1| (QUOTE (-559))) (|HasCategory| |#1| (QUOTE (-845)))) (|HasCategory| |#1| (|%list| (QUOTE -633) (QUOTE (-549))))) (|HasCategory| |#1| (QUOTE (-1052))) (|HasCategory| |#1| (QUOTE (-844))) (|HasCategory| |#1| (QUOTE (-872))) (-4118 (|HasCategory| |#1| (QUOTE (-844))) (|HasCategory| |#1| (QUOTE (-872)))) (-4118 (-12 (|HasCategory| |#1| (QUOTE (-559))) (|HasCategory| |#1| (QUOTE (-845)))) (|HasCategory| |#1| (|%list| (QUOTE -1070) (QUOTE (-560))))) (|HasCategory| |#1| (QUOTE (-1184))) (|HasCategory| |#1| (|%list| (QUOTE -912) (QUOTE (-391)))) (-4118 (-12 (|HasCategory| |#1| (QUOTE (-559))) (|HasCategory| |#1| (QUOTE (-845)))) (|HasCategory| |#1| (|%list| (QUOTE -912) (QUOTE (-560))))) (|HasCategory| |#1| (|%list| (QUOTE -633) (|%list| (QUOTE -916) (QUOTE (-391))))) (-4118 (|HasCategory| |#1| (|%list| (QUOTE -633) (|%list| (QUOTE -916) (QUOTE (-560))))) (-12 (|HasCategory| |#1| (QUOTE (-559))) (|HasCategory| |#1| (QUOTE (-845))))) (-4118 (|HasCategory| |#1| (|%list| (QUOTE -660) (QUOTE (-560)))) (-12 (|HasCategory| |#1| (QUOTE (-559))) (|HasCategory| |#1| (QUOTE (-845))))) (|HasCategory| |#1| (QUOTE (-239))) (|HasCategory| |#1| (|%list| (QUOTE -930) (QUOTE (-1209)))) (|HasCategory| |#1| (QUOTE (-240))) (|HasCategory| |#1| (|%list| (QUOTE -928) (QUOTE (-1209)))) (|HasCategory| |#1| (|%list| (QUOTE -528) (QUOTE (-1209)) (|devaluate| |#1|))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|))) (|HasCategory| |#1| (|%list| (QUOTE -298) (|devaluate| |#1|) (|devaluate| |#1|))) (-12 (|HasCategory| |#1| (QUOTE (-559))) (|HasCategory| |#1| (QUOTE (-845)))) (|HasCategory| |#1| (QUOTE (-319))) (|HasCategory| |#1| (QUOTE (-559))) (-12 (|HasAttribute| |#1| (QUOTE -4508)) (|HasAttribute| |#1| (QUOTE -4497)) (|HasCategory| |#1| (QUOTE (-466)))) (|HasCategory| |#1| (|%list| (QUOTE -633) (QUOTE (-549)))) (|HasCategory| |#1| (|%list| (QUOTE -1070) (QUOTE (-560)))) (|HasCategory| |#1| (|%list| (QUOTE -912) (QUOTE (-560)))) (|HasCategory| |#1| (|%list| (QUOTE -633) (|%list| (QUOTE -916) (QUOTE (-560))))) (|HasCategory| |#1| (|%list| (QUOTE -660) (QUOTE (-560)))) (-12 (|HasCategory| $ (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-940)))) (-4118 (-12 (|HasCategory| $ (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-940)))) (|HasCategory| |#1| (QUOTE (-147))))) (-422 A B) ((|constructor| (NIL "This package extends a map between integral domains to a map between Fractions over those domains by applying the map to the numerators and denominators.")) (|map| (((|Fraction| |#2|) (|Mapping| |#2| |#1|) (|Fraction| |#1|)) "\\spad{map(func,frac)} applies the function \\spad{func} to the numerator and denominator of the fraction \\spad{frac}."))) NIL @@ -1636,7 +1636,7 @@ NIL ((|constructor| (NIL "\\indented{2}{A is fully retractable to \\spad{B} means that A is retractable to \\spad{B},{} and,{}} \\indented{2}{in addition,{} if \\spad{B} is retractable to the integers or rational} \\indented{2}{numbers then so is A.} \\indented{2}{In particular,{} what we are asserting is that there are no integers} \\indented{2}{(rationals) in A which don't retract into \\spad{B}.} Date Created: March 1990 Date Last Updated: 9 April 1991"))) NIL NIL -(-427 R -4164 UP A) +(-427 R -4140 UP A) ((|constructor| (NIL "Fractional ideals in a framed algebra.")) (|randomLC| ((|#4| (|NonNegativeInteger|) (|Vector| |#4|)) "\\spad{randomLC(n,x)} should be local but conditional.")) (|minimize| (($ $) "\\spad{minimize(I)} returns a reduced set of generators for \\spad{I}.")) (|denom| ((|#1| $) "\\spad{denom(1/d * (f1,...,fn))} returns \\spad{d}.")) (|numer| (((|Vector| |#4|) $) "\\spad{numer(1/d * (f1,...,fn))} = the vector \\spad{[f1,...,fn]}.")) (|norm| ((|#2| $) "\\spad{norm(I)} returns the norm of the ideal \\spad{I}.")) (|basis| (((|Vector| |#4|) $) "\\spad{basis((f1,...,fn))} returns the vector \\spad{[f1,...,fn]}.")) (|ideal| (($ (|Vector| |#4|)) "\\spad{ideal([f1,...,fn])} returns the ideal \\spad{(f1,...,fn)}."))) ((-4507 . T)) NIL @@ -1644,7 +1644,7 @@ NIL ((|constructor| (NIL "\\indented{1}{Lifting of morphisms to fractional ideals.} Author: Manuel Bronstein Date Created: 1 Feb 1989 Date Last Updated: 27 Feb 1990 Keywords: ideal,{} algebra,{} module.")) (|map| (((|FractionalIdeal| |#5| |#6| |#7| |#8|) (|Mapping| |#5| |#1|) (|FractionalIdeal| |#1| |#2| |#3| |#4|)) "\\spad{map(f,i)} \\undocumented{}"))) NIL NIL -(-429 R -4164 UP A |ibasis|) +(-429 R -4140 UP A |ibasis|) ((|constructor| (NIL "Module representation of fractional ideals.")) (|module| (($ (|FractionalIdeal| |#1| |#2| |#3| |#4|)) "\\spad{module(I)} returns \\spad{I} viewed has a module over \\spad{R}.") (($ (|Vector| |#4|)) "\\spad{module([f1,...,fn])} = the module generated by \\spad{(f1,...,fn)} over \\spad{R}.")) (|norm| ((|#2| $) "\\spad{norm(f)} returns the norm of the module \\spad{f}.")) (|basis| (((|Vector| |#4|) $) "\\spad{basis((f1,...,fn))} = the vector \\spad{[f1,...,fn]}."))) NIL ((|HasCategory| |#4| (|%list| (QUOTE -1070) (|devaluate| |#2|)))) @@ -1670,7 +1670,7 @@ NIL ((|HasCategory| |#2| (|%list| (QUOTE -1070) (QUOTE (-560)))) (|HasCategory| |#2| (QUOTE (-571))) (|HasCategory| |#2| (QUOTE (-175))) (|HasCategory| |#2| (QUOTE (-147))) (|HasCategory| |#2| (QUOTE (-149))) (|HasCategory| |#2| (QUOTE (-1081))) (|HasCategory| |#2| (QUOTE (-21))) (|HasCategory| |#2| (QUOTE (-25))) (|HasCategory| |#2| (QUOTE (-487))) (|HasCategory| |#2| (QUOTE (-1144))) (|HasCategory| |#2| (|%list| (QUOTE -633) (QUOTE (-549))))) (-435 R) ((|constructor| (NIL "A space of formal functions with arguments in an arbitrary ordered set.")) (|univariate| (((|Fraction| (|SparseUnivariatePolynomial| $)) $ (|Kernel| $)) "\\spad{univariate(f, k)} returns \\spad{f} viewed as a univariate fraction in \\spad{k}.")) (/ (($ (|SparseMultivariatePolynomial| |#1| (|Kernel| $)) (|SparseMultivariatePolynomial| |#1| (|Kernel| $))) "\\spad{p1/p2} returns the quotient of \\spad{p1} and \\spad{p2} as an element of \\%.")) (|denominator| (($ $) "\\spad{denominator(f)} returns the denominator of \\spad{f} converted to \\%.")) (|denom| (((|SparseMultivariatePolynomial| |#1| (|Kernel| $)) $) "\\spad{denom(f)} returns the denominator of \\spad{f} viewed as a polynomial in the kernels over \\spad{R}.")) (|convert| (($ (|Factored| $)) "\\spad{convert(f1\\^e1 ... fm\\^em)} returns \\spad{(f1)\\^e1 ... (fm)\\^em} as an element of \\%,{} using formal kernels created using a \\spadfunFrom{paren}{ExpressionSpace}.")) (|isPower| (((|Union| (|Record| (|:| |val| $) (|:| |exponent| (|Integer|))) "failed") $) "\\spad{isPower(p)} returns \\spad{[x, n]} if \\spad{p = x**n} and \\spad{n <> 0}.")) (|numerator| (($ $) "\\spad{numerator(f)} returns the numerator of \\spad{f} converted to \\%.")) (|numer| (((|SparseMultivariatePolynomial| |#1| (|Kernel| $)) $) "\\spad{numer(f)} returns the numerator of \\spad{f} viewed as a polynomial in the kernels over \\spad{R} if \\spad{R} is an integral domain. If not,{} then numer(\\spad{f}) = \\spad{f} viewed as a polynomial in the kernels over \\spad{R}.")) (|coerce| (($ (|Fraction| (|Polynomial| (|Fraction| |#1|)))) "\\spad{coerce(f)} returns \\spad{f} as an element of \\%.") (($ (|Polynomial| (|Fraction| |#1|))) "\\spad{coerce(p)} returns \\spad{p} as an element of \\%.") (($ (|Fraction| |#1|)) "\\spad{coerce(q)} returns \\spad{q} as an element of \\%.") (($ (|SparseMultivariatePolynomial| |#1| (|Kernel| $))) "\\spad{coerce(p)} returns \\spad{p} as an element of \\%.")) (|isMult| (((|Union| (|Record| (|:| |coef| (|Integer|)) (|:| |var| (|Kernel| $))) "failed") $) "\\spad{isMult(p)} returns \\spad{[n, x]} if \\spad{p = n * x} and \\spad{n <> 0}.")) (|isPlus| (((|Union| (|List| $) "failed") $) "\\spad{isPlus(p)} returns \\spad{[m1,...,mn]} if \\spad{p = m1 +...+ mn} and \\spad{n > 1}.")) (|isExpt| (((|Union| (|Record| (|:| |var| (|Kernel| $)) (|:| |exponent| (|Integer|))) "failed") $ (|Symbol|)) "\\spad{isExpt(p,f)} returns \\spad{[x, n]} if \\spad{p = x**n} and \\spad{n <> 0} and \\spad{x = f(a)}.") (((|Union| (|Record| (|:| |var| (|Kernel| $)) (|:| |exponent| (|Integer|))) "failed") $ (|BasicOperator|)) "\\spad{isExpt(p,op)} returns \\spad{[x, n]} if \\spad{p = x**n} and \\spad{n <> 0} and \\spad{x = op(a)}.") (((|Union| (|Record| (|:| |var| (|Kernel| $)) (|:| |exponent| (|Integer|))) "failed") $) "\\spad{isExpt(p)} returns \\spad{[x, n]} if \\spad{p = x**n} and \\spad{n <> 0}.")) (|isTimes| (((|Union| (|List| $) "failed") $) "\\spad{isTimes(p)} returns \\spad{[a1,...,an]} if \\spad{p = a1*...*an} and \\spad{n > 1}.")) (** (($ $ (|NonNegativeInteger|)) "\\spad{x**n} returns \\spad{x} * \\spad{x} * \\spad{x} * ... * \\spad{x} (\\spad{n} times).")) (|eval| (($ $ (|Symbol|) (|NonNegativeInteger|) (|Mapping| $ $)) "\\spad{eval(x, s, n, f)} replaces every \\spad{s(a)**n} in \\spad{x} by \\spad{f(a)} for any \\spad{a}.") (($ $ (|Symbol|) (|NonNegativeInteger|) (|Mapping| $ (|List| $))) "\\spad{eval(x, s, n, f)} replaces every \\spad{s(a1,...,am)**n} in \\spad{x} by \\spad{f(a1,...,am)} for any \\spad{a1},{}...,{}am.") (($ $ (|List| (|Symbol|)) (|List| (|NonNegativeInteger|)) (|List| (|Mapping| $ (|List| $)))) "\\spad{eval(x, [s1,...,sm], [n1,...,nm], [f1,...,fm])} replaces every \\spad{si(a1,...,an)**ni} in \\spad{x} by \\spad{fi(a1,...,an)} for any \\spad{a1},{}...,{}am.") (($ $ (|List| (|Symbol|)) (|List| (|NonNegativeInteger|)) (|List| (|Mapping| $ $))) "\\spad{eval(x, [s1,...,sm], [n1,...,nm], [f1,...,fm])} replaces every \\spad{si(a)**ni} in \\spad{x} by \\spad{fi(a)} for any \\spad{a}.") (($ $ (|List| (|BasicOperator|)) (|List| $) (|Symbol|)) "\\spad{eval(x, [s1,...,sm], [f1,...,fm], y)} replaces every \\spad{si(a)} in \\spad{x} by \\spad{fi(y)} with \\spad{y} replaced by \\spad{a} for any \\spad{a}.") (($ $ (|BasicOperator|) $ (|Symbol|)) "\\spad{eval(x, s, f, y)} replaces every \\spad{s(a)} in \\spad{x} by \\spad{f(y)} with \\spad{y} replaced by \\spad{a} for any \\spad{a}.") (($ $) "\\spad{eval(f)} unquotes all the quoted operators in \\spad{f}.") (($ $ (|List| (|Symbol|))) "\\spad{eval(f, [foo1,...,foon])} unquotes all the \\spad{fooi}'s in \\spad{f}.") (($ $ (|Symbol|)) "\\spad{eval(f, foo)} unquotes all the foo's in \\spad{f}.")) (|applyQuote| (($ (|Symbol|) (|List| $)) "\\spad{applyQuote(foo, [x1,...,xn])} returns \\spad{'foo(x1,...,xn)}.") (($ (|Symbol|) $ $ $ $) "\\spad{applyQuote(foo, x, y, z, t)} returns \\spad{'foo(x,y,z,t)}.") (($ (|Symbol|) $ $ $) "\\spad{applyQuote(foo, x, y, z)} returns \\spad{'foo(x,y,z)}.") (($ (|Symbol|) $ $) "\\spad{applyQuote(foo, x, y)} returns \\spad{'foo(x,y)}.") (($ (|Symbol|) $) "\\spad{applyQuote(foo, x)} returns \\spad{'foo(x)}.")) (|variables| (((|List| (|Symbol|)) $) "\\spad{variables(f)} returns the list of all the variables of \\spad{f}.")) (|ground| ((|#1| $) "\\spad{ground(f)} returns \\spad{f} as an element of \\spad{R}. An error occurs if \\spad{f} is not an element of \\spad{R}.")) (|ground?| (((|Boolean|) $) "\\spad{ground?(f)} tests if \\spad{f} is an element of \\spad{R}."))) -((-4507 -4144 (|has| |#1| (-1081)) (|has| |#1| (-487))) (-4505 |has| |#1| (-175)) (-4504 |has| |#1| (-175)) ((-4512 "*") |has| |#1| (-571)) (-4503 |has| |#1| (-571)) (-4508 |has| |#1| (-571)) (-4502 |has| |#1| (-571))) +((-4507 -4118 (|has| |#1| (-1081)) (|has| |#1| (-487))) (-4505 |has| |#1| (-175)) (-4504 |has| |#1| (-175)) ((-4512 "*") |has| |#1| (-571)) (-4503 |has| |#1| (-571)) (-4508 |has| |#1| (-571)) (-4502 |has| |#1| (-571))) NIL (-436 R A S B) ((|constructor| (NIL "This package allows a mapping \\spad{R} -> \\spad{S} to be lifted to a mapping from a function space over \\spad{R} to a function space over \\spad{S}.")) (|map| ((|#4| (|Mapping| |#3| |#1|) |#2|) "\\spad{map(f, a)} applies \\spad{f} to all the constants in \\spad{R} appearing in \\spad{a}."))) @@ -1696,7 +1696,7 @@ NIL ((|constructor| (NIL "\\spad{FiniteSetAggregateFunctions2} provides functions involving two finite set aggregates where the underlying domains might be different. An example of this is to create a set of rational numbers by mapping a function across a set of integers,{} where the function divides each integer by 1000.")) (|scan| ((|#4| (|Mapping| |#3| |#1| |#3|) |#2| |#3|) "\\spad{scan(f,a,r)} successively applies \\spad{reduce(f,x,r)} to more and more leading sub-aggregates \\spad{x} of aggregate \\spad{a}. More precisely,{} if \\spad{a} is \\spad{[a1,a2,...]},{} then \\spad{scan(f,a,r)} returns \\spad {[reduce(f,[a1],r),reduce(f,[a1,a2],r),...]}.")) (|reduce| ((|#3| (|Mapping| |#3| |#1| |#3|) |#2| |#3|) "\\spad{reduce(f,a,r)} applies function \\spad{f} to each successive element of the aggregate \\spad{a} and an accumulant initialised to \\spad{r}. For example,{} \\spad{reduce(_+\\$Integer,[1,2,3],0)} does a \\spad{3+(2+(1+0))}. Note: third argument \\spad{r} may be regarded as an identity element for the function.")) (|map| ((|#4| (|Mapping| |#3| |#1|) |#2|) "\\spad{map(f,a)} applies function \\spad{f} to each member of aggregate \\spad{a},{} creating a new aggregate with a possibly different underlying domain."))) NIL NIL -(-442 R -4164) +(-442 R -4140) ((|constructor| (NIL "\\spadtype{FunctionSpaceComplexIntegration} provides functions for the indefinite integration of complex-valued functions.")) (|complexIntegrate| ((|#2| |#2| (|Symbol|)) "\\spad{complexIntegrate(f, x)} returns the integral of \\spad{f(x)dx} where \\spad{x} is viewed as a complex variable.")) (|internalIntegrate0| (((|IntegrationResult| |#2|) |#2| (|Symbol|)) "\\spad{internalIntegrate0 should} be a local function,{} but is conditional.")) (|internalIntegrate| (((|IntegrationResult| |#2|) |#2| (|Symbol|)) "\\spad{internalIntegrate(f, x)} returns the integral of \\spad{f(x)dx} where \\spad{x} is viewed as a complex variable."))) NIL NIL @@ -1704,19 +1704,19 @@ NIL ((|constructor| (NIL "\\indented{1}{Author: James Davenport} Date Created: 17 April 1992 Date Last Updated: Basic Functions: Related Constructors: Also See: AMS Classifications: Keywords: References: Description:")) (|makeCos| (($ |#2| |#1|) "\\spad{makeCos(e,r)} makes a sin expression with given argument and coefficient")) (|makeSin| (($ |#2| |#1|) "\\spad{makeSin(e,r)} makes a sin expression with given argument and coefficient")) (|coerce| (($ (|FourierComponent| |#2|)) "\\spad{coerce(c)} converts sin/cos terms into Fourier Series") (($ |#1|) "\\spad{coerce(r)} converts coefficients into Fourier Series"))) ((-4497 -12 (|has| |#1| (-6 -4497)) (|has| |#2| (-6 -4497))) (-4504 . T) (-4505 . T) (-4507 . T)) ((-12 (|HasAttribute| |#1| (QUOTE -4497)) (|HasAttribute| |#2| (QUOTE -4497)))) -(-444 R -4164) +(-444 R -4140) ((|constructor| (NIL "\\spadtype{FunctionSpaceIntegration} provides functions for the indefinite integration of real-valued functions.")) (|integrate| (((|Union| |#2| (|List| |#2|)) |#2| (|Symbol|)) "\\spad{integrate(f, x)} returns the integral of \\spad{f(x)dx} where \\spad{x} is viewed as a real variable."))) NIL NIL -(-445 R -4164) +(-445 R -4140) ((|constructor| (NIL "Provides some special functions over an integral domain.")) (|iiabs| ((|#2| |#2|) "\\spad{iiabs(x)} should be local but conditional.")) (|iiGamma| ((|#2| |#2|) "\\spad{iiGamma(x)} should be local but conditional.")) (|airyBi| ((|#2| |#2|) "\\spad{airyBi(x)} returns the airybi function applied to \\spad{x}")) (|airyAi| ((|#2| |#2|) "\\spad{airyAi(x)} returns the airyai function applied to \\spad{x}")) (|besselK| ((|#2| |#2| |#2|) "\\spad{besselK(x,y)} returns the besselk function applied to \\spad{x} and \\spad{y}")) (|besselI| ((|#2| |#2| |#2|) "\\spad{besselI(x,y)} returns the besseli function applied to \\spad{x} and \\spad{y}")) (|besselY| ((|#2| |#2| |#2|) "\\spad{besselY(x,y)} returns the bessely function applied to \\spad{x} and \\spad{y}")) (|besselJ| ((|#2| |#2| |#2|) "\\spad{besselJ(x,y)} returns the besselj function applied to \\spad{x} and \\spad{y}")) (|polygamma| ((|#2| |#2| |#2|) "\\spad{polygamma(x,y)} returns the polygamma function applied to \\spad{x} and \\spad{y}")) (|digamma| ((|#2| |#2|) "\\spad{digamma(x)} returns the digamma function applied to \\spad{x}")) (|Beta| ((|#2| |#2| |#2|) "\\spad{Beta(x,y)} returns the beta function applied to \\spad{x} and \\spad{y}")) (|Gamma| ((|#2| |#2| |#2|) "\\spad{Gamma(a,x)} returns the incomplete Gamma function applied to a and \\spad{x}") ((|#2| |#2|) "\\spad{Gamma(f)} returns the formal Gamma function applied to \\spad{f}")) (|abs| ((|#2| |#2|) "\\spad{abs(f)} returns the absolute value operator applied to \\spad{f}")) (|operator| (((|BasicOperator|) (|BasicOperator|)) "\\spad{operator(op)} returns a copy of \\spad{op} with the domain-dependent properties appropriate for \\spad{F}; error if \\spad{op} is not a special function operator")) (|belong?| (((|Boolean|) (|BasicOperator|)) "\\spad{belong?(op)} is \\spad{true} if \\spad{op} is a special function operator."))) NIL NIL -(-446 R -4164) +(-446 R -4140) ((|constructor| (NIL "FunctionsSpacePrimitiveElement provides functions to compute primitive elements in functions spaces.")) (|primitiveElement| (((|Record| (|:| |primelt| |#2|) (|:| |pol1| (|SparseUnivariatePolynomial| |#2|)) (|:| |pol2| (|SparseUnivariatePolynomial| |#2|)) (|:| |prim| (|SparseUnivariatePolynomial| |#2|))) |#2| |#2|) "\\spad{primitiveElement(a1, a2)} returns \\spad{[a, q1, q2, q]} such that \\spad{k(a1, a2) = k(a)},{} \\spad{ai = qi(a)},{} and \\spad{q(a) = 0}. The minimal polynomial for \\spad{a2} may involve \\spad{a1},{} but the minimal polynomial for \\spad{a1} may not involve \\spad{a2}; This operations uses \\spadfun{resultant}.") (((|Record| (|:| |primelt| |#2|) (|:| |poly| (|List| (|SparseUnivariatePolynomial| |#2|))) (|:| |prim| (|SparseUnivariatePolynomial| |#2|))) (|List| |#2|)) "\\spad{primitiveElement([a1,...,an])} returns \\spad{[a, [q1,...,qn], q]} such that then \\spad{k(a1,...,an) = k(a)},{} \\spad{ai = qi(a)},{} and \\spad{q(a) = 0}. This operation uses the technique of \\spadglossSee{groebner bases}{Groebner basis}."))) NIL ((|HasCategory| |#2| (QUOTE (-27)))) -(-447 R -4164) +(-447 R -4140) ((|constructor| (NIL "This package provides function which replaces transcendental kernels in a function space by random integers. The correspondence between the kernels and the integers is fixed between calls to new().")) (|newReduc| (((|Void|)) "\\spad{newReduc()} \\undocumented")) (|bringDown| (((|SparseUnivariatePolynomial| (|Fraction| (|Integer|))) |#2| (|Kernel| |#2|)) "\\spad{bringDown(f,k)} \\undocumented") (((|Fraction| (|Integer|)) |#2|) "\\spad{bringDown(f)} \\undocumented"))) NIL NIL @@ -1724,7 +1724,7 @@ NIL ((|constructor| (NIL "Creates and manipulates objects which correspond to the basic FORTRAN data types: REAL,{} INTEGER,{} COMPLEX,{} LOGICAL and CHARACTER")) (= (((|Boolean|) $ $) "\\spad{x=y} tests for equality")) (|logical?| (((|Boolean|) $) "\\spad{logical?(t)} tests whether \\spad{t} is equivalent to the FORTRAN type LOGICAL.")) (|character?| (((|Boolean|) $) "\\spad{character?(t)} tests whether \\spad{t} is equivalent to the FORTRAN type CHARACTER.")) (|doubleComplex?| (((|Boolean|) $) "\\spad{doubleComplex?(t)} tests whether \\spad{t} is equivalent to the (non-standard) FORTRAN type DOUBLE COMPLEX.")) (|complex?| (((|Boolean|) $) "\\spad{complex?(t)} tests whether \\spad{t} is equivalent to the FORTRAN type COMPLEX.")) (|integer?| (((|Boolean|) $) "\\spad{integer?(t)} tests whether \\spad{t} is equivalent to the FORTRAN type INTEGER.")) (|double?| (((|Boolean|) $) "\\spad{double?(t)} tests whether \\spad{t} is equivalent to the FORTRAN type DOUBLE PRECISION")) (|real?| (((|Boolean|) $) "\\spad{real?(t)} tests whether \\spad{t} is equivalent to the FORTRAN type REAL.")) (|coerce| (((|SExpression|) $) "\\spad{coerce(x)} returns the \\spad{s}-expression associated with \\spad{x}") (((|Symbol|) $) "\\spad{coerce(x)} returns the symbol associated with \\spad{x}") (($ (|Symbol|)) "\\spad{coerce(s)} transforms the symbol \\spad{s} into an element of FortranScalarType provided \\spad{s} is one of real,{} complex,{}double precision,{} logical,{} integer,{} character,{} REAL,{} COMPLEX,{} LOGICAL,{} INTEGER,{} CHARACTER,{} DOUBLE PRECISION") (($ (|String|)) "\\spad{coerce(s)} transforms the string \\spad{s} into an element of FortranScalarType provided \\spad{s} is one of \"real\",{} \"double precision\",{} \"complex\",{} \"logical\",{} \"integer\",{} \"character\",{} \"REAL\",{} \"COMPLEX\",{} \"LOGICAL\",{} \"INTEGER\",{} \"CHARACTER\",{} \"DOUBLE PRECISION\""))) NIL NIL -(-449 R -4164 UP) +(-449 R -4140 UP) ((|constructor| (NIL "\\indented{1}{Used internally by IR2F} Author: Manuel Bronstein Date Created: 12 May 1988 Date Last Updated: 22 September 1993 Keywords: function,{} space,{} polynomial,{} factoring")) (|anfactor| (((|Union| (|Factored| (|SparseUnivariatePolynomial| (|AlgebraicNumber|))) "failed") |#3|) "\\spad{anfactor(p)} tries to factor \\spad{p} over algebraic numbers,{} returning \"failed\" if it cannot")) (|UP2ifCan| (((|Union| (|:| |overq| (|SparseUnivariatePolynomial| (|Fraction| (|Integer|)))) (|:| |overan| (|SparseUnivariatePolynomial| (|AlgebraicNumber|))) (|:| |failed| (|Boolean|))) |#3|) "\\spad{UP2ifCan(x)} should be local but conditional.")) (|qfactor| (((|Union| (|Factored| (|SparseUnivariatePolynomial| (|Fraction| (|Integer|)))) "failed") |#3|) "\\spad{qfactor(p)} tries to factor \\spad{p} over fractions of integers,{} returning \"failed\" if it cannot")) (|ffactor| (((|Factored| |#3|) |#3|) "\\spad{ffactor(p)} tries to factor a univariate polynomial \\spad{p} over \\spad{F}"))) NIL ((|HasCategory| |#2| (|%list| (QUOTE -1070) (QUOTE (-48))))) @@ -1756,7 +1756,7 @@ NIL ((|constructor| (NIL "\\spadtype{GaloisGroupFactorizer} provides functions to factor resolvents.")) (|btwFact| (((|Record| (|:| |contp| (|Integer|)) (|:| |factors| (|List| (|Record| (|:| |irr| |#1|) (|:| |pow| (|Integer|)))))) |#1| (|Boolean|) (|Set| (|NonNegativeInteger|)) (|NonNegativeInteger|)) "\\spad{btwFact(p,sqf,pd,r)} returns the factorization of \\spad{p},{} the result is a Record such that \\spad{contp=}content \\spad{p},{} \\spad{factors=}List of irreducible factors of \\spad{p} with exponent. If \\spad{sqf=true} the polynomial is assumed to be square free (\\spadignore{i.e.} without repeated factors). \\spad{pd} is the \\spadtype{Set} of possible degrees. \\spad{r} is a lower bound for the number of factors of \\spad{p}. Please do not use this function in your code because its design may change.")) (|henselFact| (((|Record| (|:| |contp| (|Integer|)) (|:| |factors| (|List| (|Record| (|:| |irr| |#1|) (|:| |pow| (|Integer|)))))) |#1| (|Boolean|)) "\\spad{henselFact(p,sqf)} returns the factorization of \\spad{p},{} the result is a Record such that \\spad{contp=}content \\spad{p},{} \\spad{factors=}List of irreducible factors of \\spad{p} with exponent. If \\spad{sqf=true} the polynomial is assumed to be square free (\\spadignore{i.e.} without repeated factors).")) (|factorOfDegree| (((|Union| |#1| "failed") (|PositiveInteger|) |#1| (|List| (|NonNegativeInteger|)) (|NonNegativeInteger|) (|Boolean|)) "\\spad{factorOfDegree(d,p,listOfDegrees,r,sqf)} returns a factor of \\spad{p} of degree \\spad{d} knowing that \\spad{p} has for possible splitting of its degree \\spad{listOfDegrees},{} and that \\spad{p} has at least \\spad{r} factors. If \\spad{sqf=true} the polynomial is assumed to be square free (\\spadignore{i.e.} without repeated factors).") (((|Union| |#1| "failed") (|PositiveInteger|) |#1| (|List| (|NonNegativeInteger|)) (|NonNegativeInteger|)) "\\spad{factorOfDegree(d,p,listOfDegrees,r)} returns a factor of \\spad{p} of degree \\spad{d} knowing that \\spad{p} has for possible splitting of its degree \\spad{listOfDegrees},{} and that \\spad{p} has at least \\spad{r} factors.") (((|Union| |#1| "failed") (|PositiveInteger|) |#1| (|List| (|NonNegativeInteger|))) "\\spad{factorOfDegree(d,p,listOfDegrees)} returns a factor of \\spad{p} of degree \\spad{d} knowing that \\spad{p} has for possible splitting of its degree \\spad{listOfDegrees}.") (((|Union| |#1| "failed") (|PositiveInteger|) |#1| (|NonNegativeInteger|)) "\\spad{factorOfDegree(d,p,r)} returns a factor of \\spad{p} of degree \\spad{d} knowing that \\spad{p} has at least \\spad{r} factors.") (((|Union| |#1| "failed") (|PositiveInteger|) |#1|) "\\spad{factorOfDegree(d,p)} returns a factor of \\spad{p} of degree \\spad{d}.")) (|factorSquareFree| (((|Factored| |#1|) |#1| (|NonNegativeInteger|) (|NonNegativeInteger|)) "\\spad{factorSquareFree(p,d,r)} factorizes the polynomial \\spad{p} using the single factor bound algorithm,{} knowing that \\spad{d} divides the degree of all factors of \\spad{p} and that \\spad{p} has at least \\spad{r} factors. \\spad{f} is supposed not having any repeated factor (this is not checked).") (((|Factored| |#1|) |#1| (|List| (|NonNegativeInteger|)) (|NonNegativeInteger|)) "\\spad{factorSquareFree(p,listOfDegrees,r)} factorizes the polynomial \\spad{p} using the single factor bound algorithm,{} knowing that \\spad{p} has for possible splitting of its degree \\spad{listOfDegrees} and that \\spad{p} has at least \\spad{r} factors. \\spad{f} is supposed not having any repeated factor (this is not checked).") (((|Factored| |#1|) |#1| (|List| (|NonNegativeInteger|))) "\\spad{factorSquareFree(p,listOfDegrees)} factorizes the polynomial \\spad{p} using the single factor bound algorithm and knowing that \\spad{p} has for possible splitting of its degree \\spad{listOfDegrees}. \\spad{f} is supposed not having any repeated factor (this is not checked).") (((|Factored| |#1|) |#1| (|NonNegativeInteger|)) "\\spad{factorSquareFree(p,r)} factorizes the polynomial \\spad{p} using the single factor bound algorithm and knowing that \\spad{p} has at least \\spad{r} factors. \\spad{f} is supposed not having any repeated factor (this is not checked).") (((|Factored| |#1|) |#1|) "\\spad{factorSquareFree(p)} returns the factorization of \\spad{p} which is supposed not having any repeated factor (this is not checked).")) (|factor| (((|Factored| |#1|) |#1| (|NonNegativeInteger|) (|NonNegativeInteger|)) "\\spad{factor(p,d,r)} factorizes the polynomial \\spad{p} using the single factor bound algorithm,{} knowing that \\spad{d} divides the degree of all factors of \\spad{p} and that \\spad{p} has at least \\spad{r} factors.") (((|Factored| |#1|) |#1| (|List| (|NonNegativeInteger|)) (|NonNegativeInteger|)) "\\spad{factor(p,listOfDegrees,r)} factorizes the polynomial \\spad{p} using the single factor bound algorithm,{} knowing that \\spad{p} has for possible splitting of its degree \\spad{listOfDegrees} and that \\spad{p} has at least \\spad{r} factors.") (((|Factored| |#1|) |#1| (|List| (|NonNegativeInteger|))) "\\spad{factor(p,listOfDegrees)} factorizes the polynomial \\spad{p} using the single factor bound algorithm and knowing that \\spad{p} has for possible splitting of its degree \\spad{listOfDegrees}.") (((|Factored| |#1|) |#1| (|NonNegativeInteger|)) "\\spad{factor(p,r)} factorizes the polynomial \\spad{p} using the single factor bound algorithm and knowing that \\spad{p} has at least \\spad{r} factors.") (((|Factored| |#1|) |#1|) "\\spad{factor(p)} returns the factorization of \\spad{p} over the integers.")) (|tryFunctionalDecomposition| (((|Boolean|) (|Boolean|)) "\\spad{tryFunctionalDecomposition(b)} chooses whether factorizers have to look for functional decomposition of polynomials (\\spad{true}) or not (\\spad{false}). Returns the previous value.")) (|tryFunctionalDecomposition?| (((|Boolean|)) "\\spad{tryFunctionalDecomposition?()} returns \\spad{true} if factorizers try functional decomposition of polynomials before factoring them.")) (|eisensteinIrreducible?| (((|Boolean|) |#1|) "\\spad{eisensteinIrreducible?(p)} returns \\spad{true} if \\spad{p} can be shown to be irreducible by Eisenstein's criterion,{} \\spad{false} is inconclusive.")) (|useEisensteinCriterion| (((|Boolean|) (|Boolean|)) "\\spad{useEisensteinCriterion(b)} chooses whether factorizers check Eisenstein's criterion before factoring: \\spad{true} for using it,{} \\spad{false} else. Returns the previous value.")) (|useEisensteinCriterion?| (((|Boolean|)) "\\spad{useEisensteinCriterion?()} returns \\spad{true} if factorizers check Eisenstein's criterion before factoring.")) (|useSingleFactorBound| (((|Boolean|) (|Boolean|)) "\\spad{useSingleFactorBound(b)} chooses the algorithm to be used by the factorizers: \\spad{true} for algorithm with single factor bound,{} \\spad{false} for algorithm with overall bound. Returns the previous value.")) (|useSingleFactorBound?| (((|Boolean|)) "\\spad{useSingleFactorBound?()} returns \\spad{true} if algorithm with single factor bound is used for factorization,{} \\spad{false} for algorithm with overall bound.")) (|modularFactor| (((|Record| (|:| |prime| (|Integer|)) (|:| |factors| (|List| |#1|))) |#1|) "\\spad{modularFactor(f)} chooses a \"good\" prime and returns the factorization of \\spad{f} modulo this prime in a form that may be used by \\spadfunFrom{completeHensel}{GeneralHenselPackage}. If prime is zero it means that \\spad{f} has been proved to be irreducible over the integers or that \\spad{f} is a unit (\\spadignore{i.e.} 1 or \\spad{-1}). \\spad{f} shall be primitive (\\spadignore{i.e.} content(\\spad{p})\\spad{=1}) and square free (\\spadignore{i.e.} without repeated factors).")) (|numberOfFactors| (((|NonNegativeInteger|) (|List| (|Record| (|:| |factor| |#1|) (|:| |degree| (|Integer|))))) "\\spad{numberOfFactors(ddfactorization)} returns the number of factors of the polynomial \\spad{f} modulo \\spad{p} where \\spad{ddfactorization} is the distinct degree factorization of \\spad{f} computed by \\spadfunFrom{ddFact}{ModularDistinctDegreeFactorizer} for some prime \\spad{p}.")) (|stopMusserTrials| (((|PositiveInteger|) (|PositiveInteger|)) "\\spad{stopMusserTrials(n)} sets to \\spad{n} the bound on the number of factors for which \\spadfun{modularFactor} stops to look for an other prime. You will have to remember that the step of recombining the extraneous factors may take up to \\spad{2**n} trials. Returns the previous value.") (((|PositiveInteger|)) "\\spad{stopMusserTrials()} returns the bound on the number of factors for which \\spadfun{modularFactor} stops to look for an other prime. You will have to remember that the step of recombining the extraneous factors may take up to \\spad{2**stopMusserTrials()} trials.")) (|musserTrials| (((|PositiveInteger|) (|PositiveInteger|)) "\\spad{musserTrials(n)} sets to \\spad{n} the number of primes to be tried in \\spadfun{modularFactor} and returns the previous value.") (((|PositiveInteger|)) "\\spad{musserTrials()} returns the number of primes that are tried in \\spadfun{modularFactor}.")) (|degreePartition| (((|Multiset| (|NonNegativeInteger|)) (|List| (|Record| (|:| |factor| |#1|) (|:| |degree| (|Integer|))))) "\\spad{degreePartition(ddfactorization)} returns the degree partition of the polynomial \\spad{f} modulo \\spad{p} where \\spad{ddfactorization} is the distinct degree factorization of \\spad{f} computed by \\spadfunFrom{ddFact}{ModularDistinctDegreeFactorizer} for some prime \\spad{p}.")) (|makeFR| (((|Factored| |#1|) (|Record| (|:| |contp| (|Integer|)) (|:| |factors| (|List| (|Record| (|:| |irr| |#1|) (|:| |pow| (|Integer|))))))) "\\spad{makeFR(flist)} turns the final factorization of henselFact into a \\spadtype{Factored} object."))) NIL NIL -(-457 R UP -4164) +(-457 R UP -4140) ((|constructor| (NIL "\\spadtype{GaloisGroupFactorizationUtilities} provides functions that will be used by the factorizer.")) (|length| ((|#3| |#2|) "\\spad{length(p)} returns the sum of the absolute values of the coefficients of the polynomial \\spad{p}.")) (|height| ((|#3| |#2|) "\\spad{height(p)} returns the maximal absolute value of the coefficients of the polynomial \\spad{p}.")) (|infinityNorm| ((|#3| |#2|) "\\spad{infinityNorm(f)} returns the maximal absolute value of the coefficients of the polynomial \\spad{f}.")) (|quadraticNorm| ((|#3| |#2|) "\\spad{quadraticNorm(f)} returns the \\spad{l2} norm of the polynomial \\spad{f}.")) (|norm| ((|#3| |#2| (|PositiveInteger|)) "\\spad{norm(f,p)} returns the lp norm of the polynomial \\spad{f}.")) (|singleFactorBound| (((|Integer|) |#2|) "\\spad{singleFactorBound(p,r)} returns a bound on the infinite norm of the factor of \\spad{p} with smallest Bombieri's norm. \\spad{p} shall be of degree higher or equal to 2.") (((|Integer|) |#2| (|NonNegativeInteger|)) "\\spad{singleFactorBound(p,r)} returns a bound on the infinite norm of the factor of \\spad{p} with smallest Bombieri's norm. \\spad{r} is a lower bound for the number of factors of \\spad{p}. \\spad{p} shall be of degree higher or equal to 2.")) (|rootBound| (((|Integer|) |#2|) "\\spad{rootBound(p)} returns a bound on the largest norm of the complex roots of \\spad{p}.")) (|bombieriNorm| ((|#3| |#2| (|PositiveInteger|)) "\\spad{bombieriNorm(p,n)} returns the \\spad{n}th Bombieri's norm of \\spad{p}.") ((|#3| |#2|) "\\spad{bombieriNorm(p)} returns quadratic Bombieri's norm of \\spad{p}.")) (|beauzamyBound| (((|Integer|) |#2|) "\\spad{beauzamyBound(p)} returns a bound on the larger coefficient of any factor of \\spad{p}."))) NIL NIL @@ -1803,7 +1803,7 @@ NIL (-468 |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"))) (((-4512 "*") |has| |#2| (-175)) (-4503 |has| |#2| (-571)) (-4508 |has| |#2| (-6 -4508)) (-4505 . T) (-4504 . T) (-4507 . T)) -((|HasCategory| |#2| (QUOTE (-940))) (-4144 (|HasCategory| |#2| (QUOTE (-175))) (|HasCategory| |#2| (QUOTE (-466))) (|HasCategory| |#2| (QUOTE (-571))) (|HasCategory| |#2| (QUOTE (-940)))) (-4144 (|HasCategory| |#2| (QUOTE (-466))) (|HasCategory| |#2| (QUOTE (-571))) (|HasCategory| |#2| (QUOTE (-940)))) (-4144 (|HasCategory| |#2| (QUOTE (-466))) (|HasCategory| |#2| (QUOTE (-940)))) (|HasCategory| |#2| (QUOTE (-571))) (|HasCategory| |#2| (QUOTE (-175))) (-4144 (|HasCategory| |#2| (QUOTE (-175))) (|HasCategory| |#2| (QUOTE (-571)))) (-12 (|HasCategory| (-889 |#1|) (|%list| (QUOTE -912) (QUOTE (-391)))) (|HasCategory| |#2| (|%list| (QUOTE -912) (QUOTE (-391))))) (-12 (|HasCategory| (-889 |#1|) (|%list| (QUOTE -912) (QUOTE (-560)))) (|HasCategory| |#2| (|%list| (QUOTE -912) (QUOTE (-560))))) (-12 (|HasCategory| (-889 |#1|) (|%list| (QUOTE -633) (|%list| (QUOTE -916) (QUOTE (-391))))) (|HasCategory| |#2| (|%list| (QUOTE -633) (|%list| (QUOTE -916) (QUOTE (-391)))))) (-12 (|HasCategory| (-889 |#1|) (|%list| (QUOTE -633) (|%list| (QUOTE -916) (QUOTE (-560))))) (|HasCategory| |#2| (|%list| (QUOTE -633) (|%list| (QUOTE -916) (QUOTE (-560)))))) (-12 (|HasCategory| (-889 |#1|) (|%list| (QUOTE -633) (QUOTE (-549)))) (|HasCategory| |#2| (|%list| (QUOTE -633) (QUOTE (-549))))) (|HasCategory| |#2| (|%list| (QUOTE -660) (QUOTE (-560)))) (|HasCategory| |#2| (QUOTE (-149))) (|HasCategory| |#2| (QUOTE (-147))) (|HasCategory| |#2| (|%list| (QUOTE -38) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#2| (|%list| (QUOTE -1070) (QUOTE (-560)))) (-4144 (|HasCategory| |#2| (|%list| (QUOTE -38) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#2| (|%list| (QUOTE -1070) (|%list| (QUOTE -421) (QUOTE (-560)))))) (|HasCategory| |#2| (|%list| (QUOTE -1070) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#2| (QUOTE (-376))) (|HasAttribute| |#2| (QUOTE -4508)) (|HasCategory| |#2| (QUOTE (-466))) (-12 (|HasCategory| $ (QUOTE (-147))) (|HasCategory| |#2| (QUOTE (-940)))) (-4144 (-12 (|HasCategory| $ (QUOTE (-147))) (|HasCategory| |#2| (QUOTE (-940)))) (|HasCategory| |#2| (QUOTE (-147))))) +((|HasCategory| |#2| (QUOTE (-940))) (-4118 (|HasCategory| |#2| (QUOTE (-175))) (|HasCategory| |#2| (QUOTE (-466))) (|HasCategory| |#2| (QUOTE (-571))) (|HasCategory| |#2| (QUOTE (-940)))) (-4118 (|HasCategory| |#2| (QUOTE (-466))) (|HasCategory| |#2| (QUOTE (-571))) (|HasCategory| |#2| (QUOTE (-940)))) (-4118 (|HasCategory| |#2| (QUOTE (-466))) (|HasCategory| |#2| (QUOTE (-940)))) (|HasCategory| |#2| (QUOTE (-571))) (|HasCategory| |#2| (QUOTE (-175))) (-4118 (|HasCategory| |#2| (QUOTE (-175))) (|HasCategory| |#2| (QUOTE (-571)))) (-12 (|HasCategory| (-889 |#1|) (|%list| (QUOTE -912) (QUOTE (-391)))) (|HasCategory| |#2| (|%list| (QUOTE -912) (QUOTE (-391))))) (-12 (|HasCategory| (-889 |#1|) (|%list| (QUOTE -912) (QUOTE (-560)))) (|HasCategory| |#2| (|%list| (QUOTE -912) (QUOTE (-560))))) (-12 (|HasCategory| (-889 |#1|) (|%list| (QUOTE -633) (|%list| (QUOTE -916) (QUOTE (-391))))) (|HasCategory| |#2| (|%list| (QUOTE -633) (|%list| (QUOTE -916) (QUOTE (-391)))))) (-12 (|HasCategory| (-889 |#1|) (|%list| (QUOTE -633) (|%list| (QUOTE -916) (QUOTE (-560))))) (|HasCategory| |#2| (|%list| (QUOTE -633) (|%list| (QUOTE -916) (QUOTE (-560)))))) (-12 (|HasCategory| (-889 |#1|) (|%list| (QUOTE -633) (QUOTE (-549)))) (|HasCategory| |#2| (|%list| (QUOTE -633) (QUOTE (-549))))) (|HasCategory| |#2| (|%list| (QUOTE -660) (QUOTE (-560)))) (|HasCategory| |#2| (QUOTE (-149))) (|HasCategory| |#2| (QUOTE (-147))) (|HasCategory| |#2| (|%list| (QUOTE -38) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#2| (|%list| (QUOTE -1070) (QUOTE (-560)))) (-4118 (|HasCategory| |#2| (|%list| (QUOTE -38) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#2| (|%list| (QUOTE -1070) (|%list| (QUOTE -421) (QUOTE (-560)))))) (|HasCategory| |#2| (|%list| (QUOTE -1070) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#2| (QUOTE (-376))) (|HasAttribute| |#2| (QUOTE -4508)) (|HasCategory| |#2| (QUOTE (-466))) (-12 (|HasCategory| $ (QUOTE (-147))) (|HasCategory| |#2| (QUOTE (-940)))) (-4118 (-12 (|HasCategory| $ (QUOTE (-147))) (|HasCategory| |#2| (QUOTE (-940)))) (|HasCategory| |#2| (QUOTE (-147))))) (-469 R BP) ((|constructor| (NIL "\\indented{1}{Author : \\spad{P}.Gianni.} January 1990 The equation \\spad{Af+Bg=h} and its generalization to \\spad{n} polynomials is solved for solutions over the \\spad{R},{} euclidean domain. A table containing the solutions of \\spad{Af+Bg=x**k} is used. The operations are performed modulus a prime which are in principle big enough,{} but the solutions are tested and,{} in case of failure,{} a hensel lifting process is used to get to the right solutions. It will be used in the factorization of multivariate polynomials over finite field,{} with \\spad{R=F[x]}.")) (|testModulus| (((|Boolean|) |#1| (|List| |#2|)) "\\spad{testModulus(p,lp)} returns \\spad{true} if the the prime \\spad{p} is valid for the list of polynomials \\spad{lp},{} \\spadignore{i.e.} preserves the degree and they remain relatively prime.")) (|solveid| (((|Union| (|List| |#2|) "failed") |#2| |#1| (|Vector| (|List| |#2|))) "\\spad{solveid(h,table)} computes the coefficients of the extended euclidean algorithm for a list of polynomials whose tablePow is \\spad{table} and with right side \\spad{h}.")) (|tablePow| (((|Union| (|Vector| (|List| |#2|)) "failed") (|NonNegativeInteger|) |#1| (|List| |#2|)) "\\spad{tablePow(maxdeg,prime,lpol)} constructs the table with the coefficients of the Extended Euclidean Algorithm for \\spad{lpol}. Here the right side is \\spad{x**k},{} for \\spad{k} less or equal to \\spad{maxdeg}. The operation returns \"failed\" when the elements are not coprime modulo \\spad{prime}.")) (|compBound| (((|NonNegativeInteger|) |#2| (|List| |#2|)) "\\spad{compBound(p,lp)} computes a bound for the coefficients of the solution polynomials. Given a polynomial right hand side \\spad{p},{} and a list \\spad{lp} of left hand side polynomials. Exported because it depends on the valuation.")) (|reduction| ((|#2| |#2| |#1|) "\\spad{reduction(p,prime)} reduces the polynomial \\spad{p} modulo \\spad{prime} of \\spad{R}. Note: this function is exported only because it's conditional."))) NIL @@ -1868,7 +1868,7 @@ NIL ((|constructor| (NIL "GradedModule(\\spad{R},{}\\spad{E}) denotes ``E-graded \\spad{R}-module'',{} \\spadignore{i.e.} collection of \\spad{R}-modules indexed by an abelian monoid \\spad{E}. An element \\spad{g} of \\spad{G[s]} for some specific \\spad{s} in \\spad{E} is said to be an element of \\spad{G} with {\\em degree} \\spad{s}. Sums are defined in each module \\spad{G[s]} so two elements of \\spad{G} have a sum if they have the same degree. \\blankline Morphisms can be defined and composed by degree to give the mathematical category of graded modules.")) (+ (($ $ $) "\\spad{g+h} is the sum of \\spad{g} and \\spad{h} in the module of elements of the same degree as \\spad{g} and \\spad{h}. Error: if \\spad{g} and \\spad{h} have different degrees.")) (- (($ $ $) "\\spad{g-h} is the difference of \\spad{g} and \\spad{h} in the module of elements of the same degree as \\spad{g} and \\spad{h}. Error: if \\spad{g} and \\spad{h} have different degrees.") (($ $) "\\spad{-g} is the additive inverse of \\spad{g} in the module of elements of the same grade as \\spad{g}.")) (* (($ $ |#1|) "\\spad{g*r} is right module multiplication.") (($ |#1| $) "\\spad{r*g} is left module multiplication.")) ((|Zero|) (($) "0 denotes the zero of degree 0.")) (|degree| ((|#2| $) "\\spad{degree(g)} names the degree of \\spad{g}. The set of all elements of a given degree form an \\spad{R}-module."))) NIL NIL -(-485 |lv| -4164 R) +(-485 |lv| -4140 R) ((|constructor| (NIL "\\indented{1}{Author : \\spad{P}.Gianni,{} Summer \\spad{'88},{} revised November \\spad{'89}} Solve systems of polynomial equations using Groebner bases Total order Groebner bases are computed and then converted to lex ones This package is mostly intended for internal use.")) (|genericPosition| (((|Record| (|:| |dpolys| (|List| (|DistributedMultivariatePolynomial| |#1| |#2|))) (|:| |coords| (|List| (|Integer|)))) (|List| (|DistributedMultivariatePolynomial| |#1| |#2|)) (|List| (|OrderedVariableList| |#1|))) "\\spad{genericPosition(lp,lv)} puts a radical zero dimensional ideal in general position,{} for system \\spad{lp} in variables \\spad{lv}.")) (|testDim| (((|Union| (|List| (|HomogeneousDistributedMultivariatePolynomial| |#1| |#2|)) "failed") (|List| (|HomogeneousDistributedMultivariatePolynomial| |#1| |#2|)) (|List| (|OrderedVariableList| |#1|))) "\\spad{testDim(lp,lv)} tests if the polynomial system \\spad{lp} in variables \\spad{lv} is zero dimensional.")) (|groebSolve| (((|List| (|List| (|DistributedMultivariatePolynomial| |#1| |#2|))) (|List| (|DistributedMultivariatePolynomial| |#1| |#2|)) (|List| (|OrderedVariableList| |#1|))) "\\spad{groebSolve(lp,lv)} reduces the polynomial system \\spad{lp} in variables \\spad{lv} to triangular form. Algorithm based on groebner bases algorithm with linear algebra for change of ordering. Preprocessing for the general solver. The polynomials in input are of type \\spadtype{DMP}."))) NIL NIL @@ -1883,11 +1883,11 @@ NIL (-488 |Coef| |var| |cen|) ((|constructor| (NIL "This is a category of univariate Puiseux series constructed from univariate Laurent series. A Puiseux series is represented by a pair \\spad{[r,f(x)]},{} where \\spad{r} is a positive rational number and \\spad{f(x)} is a Laurent series. This pair represents the Puiseux series \\spad{f(x\\^r)}.")) (|integrate| (($ $ (|Variable| |#2|)) "\\spad{integrate(f(x))} returns an anti-derivative of the power series \\spad{f(x)} with constant coefficient 0. We may integrate a series when we can divide coefficients by integers.")) (|coerce| (($ (|UnivariatePuiseuxSeries| |#1| |#2| |#3|)) "\\spad{coerce(f)} converts a Puiseux series to a general power series.") 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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)}"))) ((-4511 . T) (-4510 . T)) @@ -1903,7 +1903,7 @@ NIL (-493 |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."))) ((-4510 . T) (-4511 . 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Hall as given in Serre's book Lie Groups -- 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{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 @@ -1911,11 +1911,11 @@ NIL (-495 |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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(-1081)))) (-12 (|HasCategory| |#2| (QUOTE (-239))) (|HasCategory| |#2| (QUOTE (-1081)))) (-12 (|HasCategory| |#2| (QUOTE (-1081))) (|HasCategory| |#2| (|%list| (QUOTE -930) (QUOTE (-1209))))) (-4118 (|HasCategory| |#2| (QUOTE (-1081))) (-12 (|HasCategory| |#2| (QUOTE (-1133))) (|HasCategory| |#2| (|%list| (QUOTE -1070) (QUOTE (-560)))))) (-12 (|HasCategory| |#2| (QUOTE (-1133))) (|HasCategory| |#2| (|%list| (QUOTE -1070) (QUOTE (-560))))) (-12 (|HasCategory| |#2| (|%list| (QUOTE -1070) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#2| (QUOTE (-1133)))) (|HasAttribute| |#2| (QUOTE -4507)) (-12 (|HasCategory| |#2| (QUOTE (-240))) (|HasCategory| |#2| (QUOTE (-1081)))) (-12 (|HasCategory| |#2| (QUOTE (-1081))) (|HasCategory| |#2| (|%list| (QUOTE -928) (QUOTE (-1209))))) (|HasCategory| |#2| (QUOTE (-175))) (|HasCategory| |#2| (QUOTE (-23))) (|HasCategory| |#2| (QUOTE (-133))) (|HasCategory| |#2| (QUOTE (-25))) (|HasCategory| |#2| (|%list| (QUOTE -632) (QUOTE (-888)))) (|HasCategory| |#2| (QUOTE (-102))) (-12 (|HasCategory| |#2| (QUOTE (-1133))) (|HasCategory| |#2| (|%list| (QUOTE -321) (|devaluate| |#2|))))) (-497) ((|constructor| (NIL "This domain represents the header of a definition.")) (|parameters| (((|List| (|ParameterAst|)) $) "\\spad{parameters(h)} gives the parameters specified in the definition header `h'.")) (|name| (((|Identifier|) $) "\\spad{name(h)} returns the name of the operation defined defined.")) (|headAst| (($ (|Identifier|) (|List| (|ParameterAst|))) "\\spad{headAst(f,[x1,..,xn])} constructs a function definition header."))) NIL @@ -1923,8 +1923,8 @@ NIL (-498 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}."))) ((-4510 . T) (-4511 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1133))) (-4144 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-1133)))) (-4144 (-12 (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-888))))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-888)))) (|HasCategory| |#1| (QUOTE (-102)))) -(-499 -4164 UP UPUP R) +((-12 (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1133))) (-4118 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-1133)))) (-4118 (-12 (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-888))))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-888)))) (|HasCategory| |#1| (QUOTE (-102)))) +(-499 -4140 UP UPUP R) ((|constructor| (NIL "This domains implements finite rational divisors on an hyperelliptic curve,{} that is finite formal sums SUM(\\spad{n} * \\spad{P}) where the \\spad{n}'s are integers and the \\spad{P}'s are finite rational points on the curve. The equation of the curve must be \\spad{y^2} = \\spad{f}(\\spad{x}) and \\spad{f} must have odd degree."))) NIL NIL @@ -1935,7 +1935,7 @@ NIL (-501) ((|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."))) ((-4502 . T) (-4508 . T) (-4503 . T) ((-4512 "*") . T) (-4504 . T) (-4505 . T) (-4507 . T)) -((|HasCategory| (-560) (QUOTE (-940))) (|HasCategory| (-560) (|%list| (QUOTE -1070) (QUOTE (-1209)))) (|HasCategory| (-560) (QUOTE (-147))) (|HasCategory| (-560) (QUOTE (-149))) (|HasCategory| (-560) (|%list| (QUOTE -633) (QUOTE (-549)))) (|HasCategory| (-560) (QUOTE (-1052))) (|HasCategory| (-560) (QUOTE (-844))) (|HasCategory| (-560) (QUOTE (-872))) (-4144 (|HasCategory| (-560) (QUOTE (-844))) (|HasCategory| (-560) (QUOTE (-872)))) (|HasCategory| (-560) (|%list| (QUOTE -1070) (QUOTE (-560)))) (|HasCategory| (-560) (QUOTE (-1184))) (|HasCategory| (-560) (|%list| (QUOTE -912) (QUOTE (-391)))) (|HasCategory| (-560) (|%list| (QUOTE -912) (QUOTE (-560)))) (|HasCategory| (-560) (|%list| (QUOTE -633) (|%list| (QUOTE -916) (QUOTE (-391))))) (|HasCategory| (-560) (|%list| (QUOTE -633) (|%list| (QUOTE -916) (QUOTE (-560))))) (|HasCategory| (-560) (QUOTE (-239))) (|HasCategory| (-560) (|%list| (QUOTE -930) (QUOTE (-1209)))) (|HasCategory| (-560) (QUOTE (-240))) (|HasCategory| (-560) (|%list| (QUOTE -928) (QUOTE (-1209)))) (|HasCategory| (-560) (|%list| (QUOTE -528) (QUOTE (-1209)) (QUOTE (-560)))) (|HasCategory| (-560) (|%list| (QUOTE -321) (QUOTE (-560)))) (|HasCategory| (-560) (|%list| (QUOTE -298) (QUOTE (-560)) (QUOTE (-560)))) (|HasCategory| (-560) (QUOTE (-319))) (|HasCategory| (-560) (QUOTE (-559))) (|HasCategory| (-560) (|%list| (QUOTE -660) (QUOTE (-560)))) (-12 (|HasCategory| $ (QUOTE (-147))) (|HasCategory| (-560) (QUOTE (-940)))) (-4144 (-12 (|HasCategory| $ (QUOTE (-147))) (|HasCategory| (-560) (QUOTE (-940)))) (|HasCategory| (-560) (QUOTE (-147))))) +((|HasCategory| (-560) (QUOTE (-940))) (|HasCategory| (-560) (|%list| (QUOTE -1070) (QUOTE (-1209)))) (|HasCategory| (-560) (QUOTE (-147))) (|HasCategory| (-560) (QUOTE (-149))) (|HasCategory| (-560) (|%list| (QUOTE -633) (QUOTE (-549)))) (|HasCategory| (-560) (QUOTE (-1052))) (|HasCategory| (-560) (QUOTE (-844))) (|HasCategory| (-560) (QUOTE (-872))) (-4118 (|HasCategory| (-560) (QUOTE (-844))) (|HasCategory| (-560) (QUOTE (-872)))) (|HasCategory| (-560) (|%list| (QUOTE -1070) (QUOTE (-560)))) (|HasCategory| (-560) (QUOTE (-1184))) (|HasCategory| (-560) (|%list| (QUOTE -912) (QUOTE (-391)))) (|HasCategory| (-560) (|%list| (QUOTE -912) (QUOTE (-560)))) (|HasCategory| (-560) (|%list| (QUOTE -633) (|%list| (QUOTE -916) (QUOTE (-391))))) (|HasCategory| (-560) (|%list| (QUOTE -633) (|%list| (QUOTE -916) (QUOTE (-560))))) (|HasCategory| (-560) (QUOTE (-239))) (|HasCategory| (-560) (|%list| (QUOTE -930) (QUOTE (-1209)))) (|HasCategory| (-560) (QUOTE (-240))) (|HasCategory| (-560) (|%list| (QUOTE -928) (QUOTE (-1209)))) (|HasCategory| (-560) (|%list| (QUOTE -528) (QUOTE (-1209)) (QUOTE (-560)))) (|HasCategory| (-560) (|%list| (QUOTE -321) (QUOTE (-560)))) (|HasCategory| (-560) (|%list| (QUOTE -298) (QUOTE (-560)) (QUOTE (-560)))) (|HasCategory| (-560) (QUOTE (-319))) (|HasCategory| (-560) (QUOTE (-559))) (|HasCategory| (-560) (|%list| (QUOTE -660) (QUOTE (-560)))) (-12 (|HasCategory| $ (QUOTE (-147))) (|HasCategory| (-560) (QUOTE (-940)))) (-4118 (-12 (|HasCategory| $ (QUOTE (-147))) (|HasCategory| (-560) (QUOTE (-940)))) (|HasCategory| (-560) (QUOTE (-147))))) (-502 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|) $) "\\spad{map(f,u)} returns a copy of \\spad{u} with each element \\spad{x} replaced by \\spad{f}(\\spad{x}). For collections,{} \\axiom{map(\\spad{f},{}\\spad{u}) = [\\spad{f}(\\spad{x}) for \\spad{x} in \\spad{u}]}."))) NIL @@ -1960,7 +1960,7 @@ NIL ((|constructor| (NIL "Category for the hyperbolic trigonometric functions.")) (|tanh| (($ $) "\\spad{tanh(x)} returns the hyperbolic tangent of \\spad{x}.")) (|sinh| (($ $) "\\spad{sinh(x)} returns the hyperbolic sine of \\spad{x}.")) (|sech| (($ $) "\\spad{sech(x)} returns the hyperbolic secant of \\spad{x}.")) (|csch| (($ $) "\\spad{csch(x)} returns the hyperbolic cosecant of \\spad{x}.")) (|coth| (($ $) "\\spad{coth(x)} returns the hyperbolic cotangent of \\spad{x}.")) (|cosh| (($ $) "\\spad{cosh(x)} returns the hyperbolic cosine of \\spad{x}."))) NIL NIL -(-508 -4164 UP |AlExt| |AlPol|) +(-508 -4140 UP |AlExt| |AlPol|) ((|constructor| (NIL "Factorization of univariate polynomials with coefficients in an algebraic extension of a field over which we can factor UP's.")) (|factor| (((|Factored| |#4|) |#4| (|Mapping| (|Factored| |#2|) |#2|)) "\\spad{factor(p, f)} returns a prime factorisation of \\spad{p}; \\spad{f} is a factorisation map for elements of UP."))) NIL NIL @@ -1971,16 +1971,16 @@ NIL (-510 S |mn|) ((|constructor| (NIL "\\indented{1}{Author Micheal Monagan \\spad{Aug/87}} This is the basic one dimensional array data type."))) ((-4511 . T) (-4510 . T)) -((-4144 (-12 (|HasCategory| |#1| (QUOTE (-872))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|))))) (-4144 (-12 (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-888))))) (|HasCategory| |#1| (|%list| (QUOTE -633) (QUOTE (-549)))) (-4144 (|HasCategory| |#1| (QUOTE (-872))) (|HasCategory| |#1| (QUOTE (-1133)))) (|HasCategory| |#1| (QUOTE (-872))) (-4144 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-872))) (|HasCategory| |#1| (QUOTE (-1133)))) (|HasCategory| (-560) (QUOTE (-872))) (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-888)))) (|HasCategory| |#1| (QUOTE (-102))) (-12 (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|))))) +((-4118 (-12 (|HasCategory| |#1| (QUOTE (-872))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|))))) (-4118 (-12 (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-888))))) (|HasCategory| |#1| (|%list| (QUOTE -633) (QUOTE (-549)))) (-4118 (|HasCategory| |#1| (QUOTE (-872))) (|HasCategory| |#1| (QUOTE (-1133)))) (|HasCategory| |#1| (QUOTE (-872))) (-4118 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-872))) (|HasCategory| |#1| (QUOTE (-1133)))) (|HasCategory| (-560) (QUOTE (-872))) (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-888)))) (|HasCategory| |#1| (QUOTE (-102))) (-12 (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|))))) (-511 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'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."))) ((-4510 . T) (-4511 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1133))) (-4144 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-1133)))) (-4144 (-12 (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-888))))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-888)))) (|HasCategory| |#1| (QUOTE (-102)))) +((-12 (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1133))) (-4118 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-1133)))) (-4118 (-12 (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-888))))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-888)))) (|HasCategory| |#1| (QUOTE (-102)))) (-512 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 -(-513 R UP -4164) +(-513 R UP -4140) ((|constructor| (NIL "This package contains functions used in the packages FunctionFieldIntegralBasis and NumberFieldIntegralBasis.")) (|moduleSum| (((|Record| (|:| |basis| (|Matrix| |#1|)) (|:| |basisDen| |#1|) (|:| |basisInv| (|Matrix| |#1|))) (|Record| (|:| |basis| (|Matrix| |#1|)) (|:| |basisDen| |#1|) (|:| |basisInv| (|Matrix| |#1|))) (|Record| (|:| |basis| (|Matrix| |#1|)) (|:| |basisDen| |#1|) (|:| |basisInv| (|Matrix| |#1|)))) "\\spad{moduleSum(m1,m2)} returns the sum of two modules in the framed algebra \\spad{F}. Each module \\spad{mi} is represented as follows: \\spad{F} is a framed algebra with \\spad{R}-module basis \\spad{w1,w2,...,wn} and \\spad{mi} is a record \\spad{[basis,basisDen,basisInv]}. If \\spad{basis} is the matrix \\spad{(aij, i = 1..n, j = 1..n)},{} then a basis \\spad{v1,...,vn} for \\spad{mi} is given by \\spad{vi = (1/basisDen) * sum(aij * wj, j = 1..n)},{} \\spadignore{i.e.} the \\spad{i}th row of 'basis' contains the coordinates of the \\spad{i}th basis vector. Similarly,{} the \\spad{i}th row of the matrix \\spad{basisInv} contains the coordinates of \\spad{wi} with respect to the basis \\spad{v1,...,vn}: if \\spad{basisInv} is the matrix \\spad{(bij, i = 1..n, j = 1..n)},{} then \\spad{wi = sum(bij * vj, j = 1..n)}.")) (|idealiserMatrix| (((|Matrix| |#1|) (|Matrix| |#1|) (|Matrix| |#1|)) "\\spad{idealiserMatrix(m1, m2)} returns the matrix representing the linear conditions on the Ring associatied with an ideal defined by \\spad{m1} and \\spad{m2}.")) (|idealiser| (((|Matrix| |#1|) (|Matrix| |#1|) (|Matrix| |#1|) |#1|) "\\spad{idealiser(m1,m2,d)} computes the order of an ideal defined by \\spad{m1} and \\spad{m2} where \\spad{d} is the known part of the denominator") (((|Matrix| |#1|) (|Matrix| |#1|) (|Matrix| |#1|)) "\\spad{idealiser(m1,m2)} computes the order of an ideal defined by \\spad{m1} and \\spad{m2}")) (|leastPower| (((|NonNegativeInteger|) (|NonNegativeInteger|) (|NonNegativeInteger|)) "\\spad{leastPower(p,n)} returns \\spad{e},{} where \\spad{e} is the smallest integer such that \\spad{p **e >= n}")) (|divideIfCan!| ((|#1| (|Matrix| |#1|) (|Matrix| |#1|) |#1| (|Integer|)) "\\spad{divideIfCan!(matrix,matrixOut,prime,n)} attempts to divide the entries of \\spad{matrix} by \\spad{prime} and store the result in \\spad{matrixOut}. If it is successful,{} 1 is returned and if not,{} \\spad{prime} is returned. Here both \\spad{matrix} and \\spad{matrixOut} are \\spad{n}-by-\\spad{n} upper triangular matrices.")) (|matrixGcd| ((|#1| (|Matrix| |#1|) |#1| (|NonNegativeInteger|)) "\\spad{matrixGcd(mat,sing,n)} is \\spad{gcd(sing,g)} where \\spad{g} is the gcd of the entries of the \\spad{n}-by-\\spad{n} upper-triangular matrix \\spad{mat}.")) (|diagonalProduct| ((|#1| (|Matrix| |#1|)) "\\spad{diagonalProduct(m)} returns the product of the elements on the diagonal of the matrix \\spad{m}")) (|squareFree| (((|Factored| $) $) "\\spad{squareFree(x)} returns a square-free factorisation of \\spad{x}"))) NIL NIL @@ -2000,7 +2000,7 @@ NIL ((|constructor| (NIL "InnerCommonDenominator provides functions to compute the common denominator of a finite linear aggregate of elements of the quotient field of an integral domain.")) (|splitDenominator| (((|Record| (|:| |num| |#3|) (|:| |den| |#1|)) |#4|) "\\spad{splitDenominator([q1,...,qn])} returns \\spad{[[p1,...,pn], d]} such that \\spad{qi = pi/d} and \\spad{d} is a common denominator for the \\spad{qi}'s.")) (|clearDenominator| ((|#3| |#4|) "\\spad{clearDenominator([q1,...,qn])} returns \\spad{[p1,...,pn]} such that \\spad{qi = pi/d} where \\spad{d} is a common denominator for the \\spad{qi}'s.")) (|commonDenominator| ((|#1| |#4|) "\\spad{commonDenominator([q1,...,qn])} returns a common denominator \\spad{d} for \\spad{q1},{}...,{}qn."))) NIL NIL -(-518 -4164 |Expon| |VarSet| |DPoly|) +(-518 -4140 |Expon| |VarSet| |DPoly|) ((|constructor| (NIL "This domain represents polynomial ideals with coefficients in any field and supports the basic ideal operations,{} including intersection sum and quotient. An ideal is represented by a list of polynomials (the generators of the ideal) and a boolean that is \\spad{true} if the generators are a Groebner basis. The algorithms used are based on Groebner basis computations. The ordering is determined by the datatype of the input polynomials. Users may use refinements of total degree orderings.")) (|relationsIdeal| (((|SuchThat| (|List| (|Polynomial| |#1|)) (|List| (|Equation| (|Polynomial| |#1|)))) (|List| |#4|)) "\\spad{relationsIdeal(polyList)} returns the ideal of relations among the polynomials in \\spad{polyList}.")) (|saturate| (($ $ |#4| (|List| |#3|)) "\\spad{saturate(I,f,lvar)} is the saturation with respect to the prime principal ideal which is generated by \\spad{f} in the polynomial ring \\spad{F[lvar]}.") (($ $ |#4|) "\\spad{saturate(I,f)} is the saturation of the ideal \\spad{I} with respect to the multiplicative set generated by the polynomial \\spad{f}.")) (|coerce| (($ (|List| |#4|)) "\\spad{coerce(polyList)} converts the list of polynomials \\spad{polyList} to an ideal.")) (|generators| (((|List| |#4|) $) "\\spad{generators(I)} returns a list of generators for the ideal \\spad{I}.")) (|groebner?| (((|Boolean|) $) "\\spad{groebner?(I)} tests if the generators of the ideal \\spad{I} are a Groebner basis.")) (|groebnerIdeal| (($ (|List| |#4|)) "\\spad{groebnerIdeal(polyList)} constructs the ideal generated by the list of polynomials \\spad{polyList} which are assumed to be a Groebner basis. Note: this operation avoids a Groebner basis computation.")) (|ideal| (($ (|List| |#4|)) "\\spad{ideal(polyList)} constructs the ideal generated by the list of polynomials \\spad{polyList}.")) (|leadingIdeal| (($ $) "\\spad{leadingIdeal(I)} is the ideal generated by the leading terms of the elements of the ideal \\spad{I}.")) (|dimension| (((|Integer|) $) "\\spad{dimension(I)} gives the dimension of the ideal \\spad{I}. in the ring \\spad{F[lvar]},{} where lvar are the variables appearing in \\spad{I}") (((|Integer|) $ (|List| |#3|)) "\\spad{dimension(I,lvar)} gives the dimension of the ideal \\spad{I},{} in the ring \\spad{F[lvar]}")) (|backOldPos| (($ (|Record| (|:| |mval| (|Matrix| |#1|)) (|:| |invmval| (|Matrix| |#1|)) (|:| |genIdeal| $))) "\\spad{backOldPos(genPos)} takes the result produced by \\spadfunFrom{generalPosition}{PolynomialIdeals} and performs the inverse transformation,{} returning the original ideal \\spad{backOldPos(generalPosition(I,listvar))} = \\spad{I}.")) (|generalPosition| (((|Record| (|:| |mval| (|Matrix| |#1|)) (|:| |invmval| (|Matrix| |#1|)) (|:| |genIdeal| $)) $ (|List| |#3|)) "\\spad{generalPosition(I,listvar)} perform a random linear transformation on the variables in \\spad{listvar} and returns the transformed ideal along with the change of basis matrix.")) (|groebner| (($ $) "\\spad{groebner(I)} returns a set of generators of \\spad{I} that are a Groebner basis for \\spad{I}.")) (|quotient| (($ $ |#4|) "\\spad{quotient(I,f)} computes the quotient of the ideal \\spad{I} by the principal ideal generated by the polynomial \\spad{f},{} \\spad{(I:(f))}.") (($ $ $) "\\spad{quotient(I,J)} computes the quotient of the ideals \\spad{I} and \\spad{J},{} \\spad{(I:J)}.")) (|intersect| (($ (|List| $)) "\\spad{intersect(LI)} computes the intersection of the list of ideals \\spad{LI}.") (($ $ $) "\\spad{intersect(I,J)} computes the intersection of the ideals \\spad{I} and \\spad{J}.")) (|zeroDim?| (((|Boolean|) $) "\\spad{zeroDim?(I)} tests if the ideal \\spad{I} is zero dimensional,{} \\spadignore{i.e.} all its associated primes are maximal,{} in the ring \\spad{F[lvar]},{} where lvar are the variables appearing in \\spad{I}") (((|Boolean|) $ (|List| |#3|)) "\\spad{zeroDim?(I,lvar)} tests if the ideal \\spad{I} is zero dimensional,{} \\spadignore{i.e.} all its associated primes are maximal,{} in the ring \\spad{F[lvar]}")) (|inRadical?| (((|Boolean|) |#4| $) "\\spad{inRadical?(f,I)} tests if some power of the polynomial \\spad{f} belongs to the ideal \\spad{I}.")) (|in?| (((|Boolean|) $ $) "\\spad{in?(I,J)} tests if the ideal \\spad{I} is contained in the ideal \\spad{J}.")) (|element?| (((|Boolean|) |#4| $) "\\spad{element?(f,I)} tests whether the polynomial \\spad{f} belongs to the ideal \\spad{I}.")) (|zero?| (((|Boolean|) $) "\\spad{zero?(I)} tests whether the ideal \\spad{I} is the zero ideal")) (|one?| (((|Boolean|) $) "\\spad{one?(I)} tests whether the ideal \\spad{I} is the unit ideal,{} \\spadignore{i.e.} contains 1.")) (+ (($ $ $) "\\spad{I+J} computes the ideal generated by the union of \\spad{I} and \\spad{J}.")) (** (($ $ (|NonNegativeInteger|)) "\\spad{I**n} computes the \\spad{n}th power of the ideal \\spad{I}.")) (* (($ $ $) "\\spad{I*J} computes the product of the ideal \\spad{I} and \\spad{J}."))) NIL ((|HasCategory| |#3| (|%list| (QUOTE -633) (QUOTE (-1209))))) @@ -2051,7 +2051,7 @@ NIL (-530 S |mn|) ((|constructor| (NIL "\\indented{1}{Author: Michael Monagan \\spad{July/87},{} modified SMW \\spad{June/91}} A FlexibleArray is the notion of an array intended to allow for growth at the end only. Hence the following efficient operations \\indented{2}{\\spad{append(x,a)} meaning append item \\spad{x} at the end of the array \\spad{a}} \\indented{2}{\\spad{delete(a,n)} meaning delete the last item from the array \\spad{a}} Flexible arrays support the other operations inherited from \\spadtype{ExtensibleLinearAggregate}. However,{} these are not efficient. Flexible arrays combine the \\spad{O(1)} access time property of arrays with growing and shrinking at the end in \\spad{O(1)} (average) time. This is done by using an ordinary array which may have zero or more empty slots at the end. When the array becomes full it is copied into a new larger (50\\% larger) array. Conversely,{} when the array becomes less than 1/2 full,{} it is copied into a smaller array. Flexible arrays provide for an efficient implementation of many data structures in particular heaps,{} stacks and sets.")) (|shrinkable| (((|Boolean|) (|Boolean|)) "\\spad{shrinkable(b)} sets the shrinkable attribute of flexible arrays to \\spad{b} and returns the previous value")) (|physicalLength!| (($ $ (|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}"))) ((-4511 . T) (-4510 . T)) -((-4144 (-12 (|HasCategory| |#1| (QUOTE (-872))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|))))) (-4144 (-12 (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-888))))) (|HasCategory| |#1| (|%list| (QUOTE -633) (QUOTE (-549)))) (-4144 (|HasCategory| |#1| (QUOTE (-872))) (|HasCategory| |#1| (QUOTE (-1133)))) (|HasCategory| |#1| (QUOTE (-872))) (-4144 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-872))) (|HasCategory| |#1| (QUOTE (-1133)))) (|HasCategory| (-560) (QUOTE (-872))) (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-888)))) (|HasCategory| |#1| (QUOTE (-102))) (-12 (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|))))) +((-4118 (-12 (|HasCategory| |#1| (QUOTE (-872))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|))))) (-4118 (-12 (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-888))))) (|HasCategory| |#1| (|%list| (QUOTE -633) (QUOTE (-549)))) (-4118 (|HasCategory| |#1| (QUOTE (-872))) (|HasCategory| |#1| (QUOTE (-1133)))) (|HasCategory| |#1| (QUOTE (-872))) (-4118 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-872))) (|HasCategory| |#1| (QUOTE (-1133)))) (|HasCategory| (-560) (QUOTE (-872))) (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-888)))) (|HasCategory| |#1| (QUOTE (-102))) (-12 (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|))))) (-531) ((|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 @@ -2059,15 +2059,15 @@ NIL (-532 |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}."))) ((-4502 . T) (-4508 . T) (-4503 . T) ((-4512 "*") . T) (-4504 . T) (-4505 . T) (-4507 . T)) -((-4144 (|HasCategory| (-595 |#1|) (QUOTE (-147))) (|HasCategory| (-595 |#1|) (QUOTE (-381)))) (|HasCategory| (-595 |#1|) (QUOTE (-149))) (|HasCategory| (-595 |#1|) (QUOTE (-381))) (|HasCategory| (-595 |#1|) (QUOTE (-147)))) +((-4118 (|HasCategory| (-595 |#1|) (QUOTE (-147))) (|HasCategory| (-595 |#1|) (QUOTE (-381)))) (|HasCategory| (-595 |#1|) (QUOTE (-149))) (|HasCategory| (-595 |#1|) (QUOTE (-381))) (|HasCategory| (-595 |#1|) (QUOTE (-147)))) (-533 R |mnRow| |mnCol| |Row| |Col|) ((|constructor| (NIL "\\indented{1}{This is an internal type which provides an implementation of} 2-dimensional arrays as PrimitiveArray's of PrimitiveArray's."))) ((-4510 . T) (-4511 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1133))) (-4144 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-1133)))) (-4144 (-12 (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-888))))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-888)))) (|HasCategory| |#1| (QUOTE (-102)))) +((-12 (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1133))) (-4118 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-1133)))) (-4118 (-12 (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-888))))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-888)))) (|HasCategory| |#1| (QUOTE (-102)))) (-534 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."))) ((-4511 . T) (-4510 . T)) -((-4144 (-12 (|HasCategory| |#1| (QUOTE (-872))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|))))) (-4144 (-12 (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-888))))) (|HasCategory| |#1| (|%list| (QUOTE -633) (QUOTE (-549)))) (-4144 (|HasCategory| |#1| (QUOTE (-872))) (|HasCategory| |#1| (QUOTE (-1133)))) (|HasCategory| |#1| (QUOTE (-872))) (-4144 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-872))) (|HasCategory| |#1| (QUOTE (-1133)))) (|HasCategory| (-560) (QUOTE (-872))) (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-888)))) (|HasCategory| |#1| (QUOTE (-102))) (-12 (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|))))) +((-4118 (-12 (|HasCategory| |#1| (QUOTE (-872))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|))))) (-4118 (-12 (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-888))))) (|HasCategory| |#1| (|%list| (QUOTE -633) (QUOTE (-549)))) (-4118 (|HasCategory| |#1| (QUOTE (-872))) (|HasCategory| |#1| (QUOTE (-1133)))) (|HasCategory| |#1| (QUOTE (-872))) (-4118 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-872))) (|HasCategory| |#1| (QUOTE (-1133)))) (|HasCategory| (-560) (QUOTE (-872))) (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-888)))) (|HasCategory| |#1| (QUOTE (-102))) (-12 (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|))))) (-535 R |Row| |Col| M) ((|constructor| (NIL "\\spadtype{InnerMatrixLinearAlgebraFunctions} is an internal package which provides standard linear algebra functions on domains in \\spad{MatrixCategory}")) (|inverse| (((|Union| |#4| "failed") |#4|) "\\spad{inverse(m)} returns the inverse of the matrix \\spad{m}. If the matrix is not invertible,{} \"failed\" is returned. Error: if the matrix is not square.")) (|generalizedInverse| ((|#4| |#4|) "\\spad{generalizedInverse(m)} returns the generalized (Moore--Penrose) inverse of the matrix \\spad{m},{} \\spadignore{i.e.} the matrix \\spad{h} such that m*h*m=h,{} h*m*h=m,{} m*h and h*m are both symmetric matrices.")) (|determinant| ((|#1| |#4|) "\\spad{determinant(m)} returns the determinant of the matrix \\spad{m}. an error message is returned if the matrix is not square.")) (|nullSpace| (((|List| |#3|) |#4|) "\\spad{nullSpace(m)} returns a basis for the null space of the matrix \\spad{m}.")) (|nullity| (((|NonNegativeInteger|) |#4|) "\\spad{nullity(m)} returns the mullity of the matrix \\spad{m}. This is the dimension of the null space of the matrix \\spad{m}.")) (|rank| (((|NonNegativeInteger|) |#4|) "\\spad{rank(m)} returns the rank of the matrix \\spad{m}.")) (|rowEchelon| ((|#4| |#4|) "\\spad{rowEchelon(m)} returns the row echelon form of the matrix \\spad{m}."))) NIL @@ -2079,7 +2079,7 @@ NIL (-537 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."))) ((-4510 . T) (-4511 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1133))) (-4144 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-1133)))) (-4144 (-12 (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-888))))) (|HasCategory| |#1| (QUOTE (-319))) (|HasCategory| |#1| (QUOTE (-571))) (|HasAttribute| |#1| (QUOTE (-4512 "*"))) (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-888)))) (|HasCategory| |#1| (QUOTE (-102)))) +((-12 (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1133))) (-4118 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-1133)))) (-4118 (-12 (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-888))))) (|HasCategory| |#1| (QUOTE (-319))) (|HasCategory| |#1| (QUOTE (-571))) (|HasAttribute| |#1| (QUOTE (-4512 "*"))) (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-888)))) (|HasCategory| |#1| (QUOTE (-102)))) (-538) ((|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 @@ -2112,7 +2112,7 @@ NIL ((|constructor| (NIL "\\indented{2}{IndexedExponents of an ordered set of variables gives a representation} for the degree of polynomials in commuting variables. It gives an ordered pairing of non negative integer exponents with variables"))) NIL ((-12 (|HasCategory| (-793) (QUOTE (-1133))) (|HasCategory| |#1| (QUOTE (-1133))))) -(-546 K -4164 |Par|) +(-546 K -4140 |Par|) ((|constructor| (NIL "This package is the inner package to be used by NumericRealEigenPackage and NumericComplexEigenPackage for the computation of numeric eigenvalues and eigenvectors.")) (|innerEigenvectors| (((|List| (|Record| (|:| |outval| |#2|) (|:| |outmult| (|Integer|)) (|:| |outvect| (|List| (|Matrix| |#2|))))) (|Matrix| |#1|) |#3| (|Mapping| (|Factored| (|SparseUnivariatePolynomial| |#1|)) (|SparseUnivariatePolynomial| |#1|))) "\\spad{innerEigenvectors(m,eps,factor)} computes explicitly the eigenvalues and the correspondent eigenvectors of the matrix \\spad{m}. The parameter \\spad{eps} determines the type of the output,{} \\spad{factor} is the univariate factorizer to br used to reduce the characteristic polynomial into irreducible factors.")) (|solve1| (((|List| |#2|) (|SparseUnivariatePolynomial| |#1|) |#3|) "\\spad{solve1(pol, eps)} finds the roots of the univariate polynomial polynomial \\spad{pol} to precision eps. If \\spad{K} is \\spad{Fraction Integer} then only the real roots are returned,{} if \\spad{K} is \\spad{Complex Fraction Integer} then all roots are found.")) (|charpol| (((|SparseUnivariatePolynomial| |#1|) (|Matrix| |#1|)) "\\spad{charpol(m)} computes the characteristic polynomial of a matrix \\spad{m} with entries in \\spad{K}. This function returns a polynomial over \\spad{K},{} while the general one (that is in EiegenPackage) returns Fraction \\spad{P} \\spad{K}"))) NIL NIL @@ -2136,7 +2136,7 @@ NIL ((|constructor| (NIL "This package computes infinite products of univariate Taylor series over an integral domain of characteristic 0.")) (|generalInfiniteProduct| ((|#2| |#2| (|Integer|) (|Integer|)) "\\spad{generalInfiniteProduct(f(x),a,d)} computes \\spad{product(n=a,a+d,a+2*d,...,f(x**n))}. The series \\spad{f(x)} should have constant coefficient 1.")) (|oddInfiniteProduct| ((|#2| |#2|) "\\spad{oddInfiniteProduct(f(x))} computes \\spad{product(n=1,3,5...,f(x**n))}. The series \\spad{f(x)} should have constant coefficient 1.")) (|evenInfiniteProduct| ((|#2| |#2|) "\\spad{evenInfiniteProduct(f(x))} computes \\spad{product(n=2,4,6...,f(x**n))}. The series \\spad{f(x)} should have constant coefficient 1.")) (|infiniteProduct| ((|#2| |#2|) "\\spad{infiniteProduct(f(x))} computes \\spad{product(n=1,2,3...,f(x**n))}. The series \\spad{f(x)} should have constant coefficient 1."))) NIL NIL -(-552 K -4164 |Par|) +(-552 K -4140 |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 @@ -2191,12 +2191,12 @@ NIL (-565 |Key| |Entry| |addDom|) ((|constructor| (NIL "This domain is used to provide a conditional \"add\" domain for the implementation of \\spadtype{Table}."))) ((-4510 . T) (-4511 . T)) -((-12 (|HasCategory| (-2 (|:| -2118 |#1|) (|:| -3964 |#2|)) (QUOTE (-1133))) (|HasCategory| (-2 (|:| -2118 |#1|) (|:| -3964 |#2|)) (|%list| (QUOTE -321) (|%list| (QUOTE -2) (|%list| (QUOTE |:|) (QUOTE -2118) (|devaluate| |#1|)) (|%list| (QUOTE |:|) (QUOTE -3964) (|devaluate| |#2|)))))) (-4144 (|HasCategory| (-2 (|:| -2118 |#1|) (|:| -3964 |#2|)) (QUOTE (-1133))) (|HasCategory| |#2| (QUOTE (-1133)))) (-4144 (|HasCategory| (-2 (|:| -2118 |#1|) (|:| -3964 |#2|)) (QUOTE (-102))) (|HasCategory| (-2 (|:| -2118 |#1|) (|:| -3964 |#2|)) (QUOTE (-1133))) (|HasCategory| |#2| (QUOTE (-102))) (|HasCategory| |#2| (QUOTE (-1133)))) (-4144 (|HasCategory| (-2 (|:| -2118 |#1|) (|:| -3964 |#2|)) (QUOTE (-1133))) (|HasCategory| (-2 (|:| -2118 |#1|) (|:| -3964 |#2|)) (|%list| (QUOTE -632) (QUOTE (-888)))) (|HasCategory| |#2| (QUOTE (-1133))) (|HasCategory| |#2| (|%list| (QUOTE -632) (QUOTE (-888))))) (|HasCategory| (-2 (|:| -2118 |#1|) (|:| -3964 |#2|)) (|%list| (QUOTE -633) (QUOTE (-549)))) (-12 (|HasCategory| |#2| (QUOTE (-1133))) (|HasCategory| |#2| (|%list| (QUOTE -321) (|devaluate| |#2|)))) (|HasCategory| (-2 (|:| -2118 |#1|) (|:| -3964 |#2|)) (QUOTE (-1133))) (|HasCategory| |#1| (QUOTE (-872))) (|HasCategory| |#2| (QUOTE (-1133))) (-4144 (|HasCategory| (-2 (|:| -2118 |#1|) (|:| -3964 |#2|)) (|%list| (QUOTE -632) (QUOTE (-888)))) (|HasCategory| |#2| (|%list| (QUOTE -632) (QUOTE (-888))))) (-4144 (|HasCategory| (-2 (|:| -2118 |#1|) (|:| -3964 |#2|)) (QUOTE (-102))) (|HasCategory| |#2| (QUOTE (-102)))) (|HasCategory| |#2| (QUOTE (-102))) (|HasCategory| |#2| (|%list| (QUOTE -632) (QUOTE (-888)))) (|HasCategory| (-2 (|:| -2118 |#1|) (|:| -3964 |#2|)) (|%list| (QUOTE -632) (QUOTE (-888)))) (|HasCategory| (-2 (|:| -2118 |#1|) (|:| -3964 |#2|)) (QUOTE (-102)))) -(-566 R -4164) +((-12 (|HasCategory| (-2 (|:| -2115 |#1|) (|:| -3934 |#2|)) (QUOTE (-1133))) (|HasCategory| (-2 (|:| -2115 |#1|) (|:| -3934 |#2|)) (|%list| (QUOTE -321) (|%list| (QUOTE -2) (|%list| (QUOTE |:|) (QUOTE -2115) (|devaluate| |#1|)) (|%list| (QUOTE |:|) (QUOTE -3934) (|devaluate| |#2|)))))) (-4118 (|HasCategory| (-2 (|:| -2115 |#1|) (|:| -3934 |#2|)) (QUOTE (-1133))) (|HasCategory| |#2| (QUOTE (-1133)))) (-4118 (|HasCategory| (-2 (|:| -2115 |#1|) (|:| -3934 |#2|)) (QUOTE (-102))) (|HasCategory| (-2 (|:| -2115 |#1|) (|:| -3934 |#2|)) (QUOTE (-1133))) (|HasCategory| |#2| (QUOTE (-102))) (|HasCategory| |#2| (QUOTE (-1133)))) (-4118 (|HasCategory| (-2 (|:| -2115 |#1|) (|:| -3934 |#2|)) (QUOTE (-1133))) (|HasCategory| (-2 (|:| -2115 |#1|) (|:| -3934 |#2|)) (|%list| (QUOTE -632) (QUOTE (-888)))) (|HasCategory| |#2| (QUOTE (-1133))) (|HasCategory| |#2| (|%list| (QUOTE -632) (QUOTE (-888))))) (|HasCategory| (-2 (|:| -2115 |#1|) (|:| -3934 |#2|)) (|%list| (QUOTE -633) (QUOTE (-549)))) (-12 (|HasCategory| |#2| (QUOTE (-1133))) (|HasCategory| |#2| (|%list| (QUOTE -321) (|devaluate| |#2|)))) (|HasCategory| (-2 (|:| -2115 |#1|) (|:| -3934 |#2|)) (QUOTE (-1133))) (|HasCategory| |#1| (QUOTE (-872))) (|HasCategory| |#2| (QUOTE (-1133))) (-4118 (|HasCategory| (-2 (|:| -2115 |#1|) (|:| -3934 |#2|)) (|%list| (QUOTE -632) (QUOTE (-888)))) (|HasCategory| |#2| (|%list| (QUOTE -632) (QUOTE (-888))))) (-4118 (|HasCategory| (-2 (|:| -2115 |#1|) (|:| -3934 |#2|)) (QUOTE (-102))) (|HasCategory| |#2| (QUOTE (-102)))) (|HasCategory| |#2| (QUOTE (-102))) (|HasCategory| |#2| (|%list| (QUOTE -632) (QUOTE (-888)))) (|HasCategory| (-2 (|:| -2115 |#1|) (|:| -3934 |#2|)) (|%list| (QUOTE -632) (QUOTE (-888)))) (|HasCategory| (-2 (|:| -2115 |#1|) (|:| -3934 |#2|)) (QUOTE (-102)))) +(-566 R -4140) ((|constructor| (NIL "This package provides functions for the integration of algebraic integrands over transcendental functions.")) (|algint| (((|IntegrationResult| |#2|) |#2| (|Kernel| |#2|) (|Kernel| |#2|) (|Mapping| (|SparseUnivariatePolynomial| |#2|) (|SparseUnivariatePolynomial| |#2|))) "\\spad{algint(f, x, y, d)} returns the integral of \\spad{f(x,y)dx} where \\spad{y} is an algebraic function of \\spad{x}; \\spad{d} is the derivation to use on \\spad{k[x]}."))) NIL NIL -(-567 R0 -4164 UP UPUP R) +(-567 R0 -4140 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 @@ -2206,7 +2206,7 @@ NIL NIL (-569 R) ((|constructor| (NIL "\\indented{1}{+ Author: Mike Dewar} + Date Created: November 1996 + Date Last Updated: + Basic Functions: + Related Constructors: + Also See: + AMS Classifications: + Keywords: + References: + Description: + This category implements of interval arithmetic and transcendental + functions over intervals.")) (|contains?| (((|Boolean|) $ |#1|) "\\spad{contains?(i,f)} returns \\spad{true} if \\axiom{\\spad{f}} is contained within the interval \\axiom{\\spad{i}},{} \\spad{false} otherwise.")) (|negative?| (((|Boolean|) $) "\\spad{negative?(u)} returns \\axiom{\\spad{true}} if every element of \\spad{u} is negative,{} \\axiom{\\spad{false}} otherwise.")) (|positive?| (((|Boolean|) $) "\\spad{positive?(u)} returns \\axiom{\\spad{true}} if every element of \\spad{u} is positive,{} \\axiom{\\spad{false}} otherwise.")) (|width| ((|#1| $) "\\spad{width(u)} returns \\axiom{sup(\\spad{u}) - inf(\\spad{u})}.")) (|sup| ((|#1| $) "\\spad{sup(u)} returns the supremum of \\axiom{\\spad{u}}.")) (|inf| ((|#1| $) "\\spad{inf(u)} returns the infinum of \\axiom{\\spad{u}}.")) (|qinterval| (($ |#1| |#1|) "\\spad{qinterval(inf,sup)} creates a new interval \\axiom{[\\spad{inf},{}\\spad{sup}]},{} without checking the ordering on the elements.")) (|interval| (($ (|Fraction| (|Integer|))) "\\spad{interval(f)} creates a new interval around \\spad{f}.") (($ |#1|) "\\spad{interval(f)} creates a new interval around \\spad{f}.") (($ |#1| |#1|) "\\spad{interval(inf,sup)} creates a new interval,{} either \\axiom{[\\spad{inf},{}\\spad{sup}]} if \\axiom{\\spad{inf} <= \\spad{sup}} or \\axiom{[\\spad{sup},{}in]} otherwise."))) -((-2862 . T) (-4503 . T) ((-4512 "*") . T) (-4504 . T) (-4505 . T) (-4507 . T)) +((-2853 . T) (-4503 . T) ((-4512 "*") . T) (-4504 . T) (-4505 . T) (-4507 . T)) NIL (-570 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."))) @@ -2216,7 +2216,7 @@ NIL ((|constructor| (NIL "The category of commutative integral domains,{} \\spadignore{i.e.} commutative rings with no zero divisors. \\blankline Conditional attributes: \\indented{2}{canonicalUnitNormal\\tab{20}the canonical field is the same for all associates} \\indented{2}{canonicalsClosed\\tab{20}the product of two canonicals is itself canonical}")) (|unit?| (((|Boolean|) $) "\\spad{unit?(x)} tests whether \\spad{x} is a unit,{} \\spadignore{i.e.} is invertible.")) (|associates?| (((|Boolean|) $ $) "\\spad{associates?(x,y)} tests whether \\spad{x} and \\spad{y} are associates,{} \\spadignore{i.e.} differ by a unit factor.")) (|unitCanonical| (($ $) "\\spad{unitCanonical(x)} returns \\spad{unitNormal(x).canonical}.")) (|unitNormal| (((|Record| (|:| |unit| $) (|:| |canonical| $) (|:| |associate| $)) $) "\\spad{unitNormal(x)} tries to choose a canonical element from the associate class of \\spad{x}. The attribute canonicalUnitNormal,{} if asserted,{} means that the \"canonical\" element is the same across all associates of \\spad{x} if \\spad{unitNormal(x) = [u,c,a]} then \\spad{u*c = x},{} \\spad{a*u = 1}.")) (|exquo| (((|Union| $ "failed") $ $) "\\spad{exquo(a,b)} either returns an element \\spad{c} such that \\spad{c*b=a} or \"failed\" if no such element can be found."))) ((-4503 . T) ((-4512 "*") . T) (-4504 . T) (-4505 . T) (-4507 . T)) NIL -(-572 R -4164) +(-572 R -4140) ((|constructor| (NIL "This package provides functions for integration,{} limited integration,{} extended integration and the risch differential equation for elemntary functions.")) (|lfextlimint| (((|Union| (|Record| (|:| |ratpart| |#2|) (|:| |coeff| |#2|)) "failed") |#2| (|Symbol|) (|Kernel| |#2|) (|List| (|Kernel| |#2|))) "\\spad{lfextlimint(f,x,k,[k1,...,kn])} returns functions \\spad{[h, c]} such that \\spad{dh/dx = f - c dk/dx}. Value \\spad{h} is looked for in a field containing \\spad{f} and \\spad{k1},{}...,{}kn (the \\spad{ki}'s must be logs).")) (|lfintegrate| (((|IntegrationResult| |#2|) |#2| (|Symbol|)) "\\spad{lfintegrate(f, x)} = \\spad{g} such that \\spad{dg/dx = f}.")) (|lfinfieldint| (((|Union| |#2| "failed") |#2| (|Symbol|)) "\\spad{lfinfieldint(f, x)} returns a function \\spad{g} such that \\spad{dg/dx = f} if \\spad{g} exists,{} \"failed\" otherwise.")) (|lflimitedint| (((|Union| (|Record| (|:| |mainpart| |#2|) (|:| |limitedlogs| (|List| (|Record| (|:| |coeff| |#2|) (|:| |logand| |#2|))))) "failed") |#2| (|Symbol|) (|List| |#2|)) "\\spad{lflimitedint(f,x,[g1,...,gn])} returns functions \\spad{[h,[[ci, gi]]]} such that the \\spad{gi}'s are among \\spad{[g1,...,gn]},{} and \\spad{d(h+sum(ci log(gi)))/dx = f},{} if possible,{} \"failed\" otherwise.")) (|lfextendedint| (((|Union| (|Record| (|:| |ratpart| |#2|) (|:| |coeff| |#2|)) "failed") |#2| (|Symbol|) |#2|) "\\spad{lfextendedint(f, x, g)} returns functions \\spad{[h, c]} such that \\spad{dh/dx = f - cg},{} if (\\spad{h},{} \\spad{c}) exist,{} \"failed\" otherwise."))) NIL NIL @@ -2228,7 +2228,7 @@ NIL ((|constructor| (NIL "\\blankline")) (|entry| (((|Record| (|:| |endPointContinuity| (|Union| (|:| |continuous| "Continuous at the end points") (|:| |lowerSingular| "There is a singularity at the lower end point") (|:| |upperSingular| "There is a singularity at the upper end point") (|:| |bothSingular| "There are singularities at both end points") (|:| |notEvaluated| "End point continuity not yet evaluated"))) (|:| |singularitiesStream| (|Union| (|:| |str| (|Stream| (|DoubleFloat|))) (|:| |notEvaluated| "Internal singularities not yet evaluated"))) (|:| |range| (|Union| (|:| |finite| "The range is finite") (|:| |lowerInfinite| "The bottom of range is infinite") (|:| |upperInfinite| "The top of range is infinite") (|:| |bothInfinite| "Both top and bottom points are infinite") (|:| |notEvaluated| "Range not yet evaluated")))) (|Record| (|:| |var| (|Symbol|)) (|:| |fn| (|Expression| (|DoubleFloat|))) (|:| |range| (|Segment| (|OrderedCompletion| (|DoubleFloat|)))) (|:| |abserr| (|DoubleFloat|)) (|:| |relerr| (|DoubleFloat|)))) "\\spad{entry(n)} \\undocumented{}")) (|entries| (((|List| (|Record| (|:| |key| (|Record| (|:| |var| (|Symbol|)) (|:| |fn| (|Expression| (|DoubleFloat|))) (|:| |range| (|Segment| (|OrderedCompletion| (|DoubleFloat|)))) (|:| |abserr| (|DoubleFloat|)) (|:| |relerr| (|DoubleFloat|)))) (|:| |entry| (|Record| (|:| |endPointContinuity| (|Union| (|:| |continuous| "Continuous at the end points") (|:| |lowerSingular| "There is a singularity at the lower end point") (|:| |upperSingular| "There is a singularity at the upper end point") (|:| |bothSingular| "There are singularities at both end points") (|:| |notEvaluated| "End point continuity not yet evaluated"))) (|:| |singularitiesStream| (|Union| (|:| |str| (|Stream| (|DoubleFloat|))) (|:| |notEvaluated| "Internal singularities not yet evaluated"))) (|:| |range| (|Union| (|:| |finite| "The range is finite") (|:| |lowerInfinite| "The bottom of range is infinite") (|:| |upperInfinite| "The top of range is infinite") (|:| |bothInfinite| "Both top and bottom points are infinite") (|:| |notEvaluated| "Range not yet evaluated"))))))) $) "\\spad{entries(x)} \\undocumented{}")) (|showAttributes| (((|Union| (|Record| (|:| |endPointContinuity| (|Union| (|:| |continuous| "Continuous at the end points") (|:| |lowerSingular| "There is a singularity at the lower end point") (|:| |upperSingular| "There is a singularity at the upper end point") (|:| |bothSingular| "There are singularities at both end points") (|:| |notEvaluated| "End point continuity not yet evaluated"))) (|:| |singularitiesStream| (|Union| (|:| |str| (|Stream| (|DoubleFloat|))) (|:| |notEvaluated| "Internal singularities not yet evaluated"))) (|:| |range| (|Union| (|:| |finite| "The range is finite") (|:| |lowerInfinite| "The bottom of range is infinite") (|:| |upperInfinite| "The top of range is infinite") (|:| |bothInfinite| "Both top and bottom points are infinite") (|:| |notEvaluated| "Range not yet evaluated")))) "failed") (|Record| (|:| |var| (|Symbol|)) (|:| |fn| (|Expression| (|DoubleFloat|))) (|:| |range| (|Segment| (|OrderedCompletion| (|DoubleFloat|)))) (|:| |abserr| (|DoubleFloat|)) (|:| |relerr| (|DoubleFloat|)))) "\\spad{showAttributes(x)} \\undocumented{}")) (|insert!| (($ (|Record| (|:| |key| (|Record| (|:| |var| (|Symbol|)) (|:| |fn| (|Expression| (|DoubleFloat|))) (|:| |range| (|Segment| (|OrderedCompletion| (|DoubleFloat|)))) (|:| |abserr| (|DoubleFloat|)) (|:| |relerr| (|DoubleFloat|)))) (|:| |entry| (|Record| (|:| |endPointContinuity| (|Union| (|:| |continuous| "Continuous at the end points") (|:| |lowerSingular| "There is a singularity at the lower end point") (|:| |upperSingular| "There is a singularity at the upper end point") (|:| |bothSingular| "There are singularities at both end points") (|:| |notEvaluated| "End point continuity not yet evaluated"))) (|:| |singularitiesStream| (|Union| (|:| |str| (|Stream| (|DoubleFloat|))) (|:| |notEvaluated| "Internal singularities not yet evaluated"))) (|:| |range| (|Union| (|:| |finite| "The range is finite") (|:| |lowerInfinite| "The bottom of range is infinite") (|:| |upperInfinite| "The top of range is infinite") (|:| |bothInfinite| "Both top and bottom points are infinite") (|:| |notEvaluated| "Range not yet evaluated"))))))) "\\spad{insert!(r)} inserts an entry \\spad{r} into theIFTable")) (|fTable| (($ (|List| (|Record| (|:| |key| (|Record| (|:| |var| (|Symbol|)) (|:| |fn| (|Expression| (|DoubleFloat|))) (|:| |range| (|Segment| (|OrderedCompletion| (|DoubleFloat|)))) (|:| |abserr| (|DoubleFloat|)) (|:| |relerr| (|DoubleFloat|)))) (|:| |entry| (|Record| (|:| |endPointContinuity| (|Union| (|:| |continuous| "Continuous at the end points") (|:| |lowerSingular| "There is a singularity at the lower end point") (|:| |upperSingular| "There is a singularity at the upper end point") (|:| |bothSingular| "There are singularities at both end points") (|:| |notEvaluated| "End point continuity not yet evaluated"))) (|:| |singularitiesStream| (|Union| (|:| |str| (|Stream| (|DoubleFloat|))) (|:| |notEvaluated| "Internal singularities not yet evaluated"))) (|:| |range| (|Union| (|:| |finite| "The range is finite") (|:| |lowerInfinite| "The bottom of range is infinite") (|:| |upperInfinite| "The top of range is infinite") (|:| |bothInfinite| "Both top and bottom points are infinite") (|:| |notEvaluated| "Range not yet evaluated")))))))) "\\spad{fTable(l)} creates a functions table from the elements of \\spad{l}.")) (|keys| (((|List| (|Record| (|:| |var| (|Symbol|)) (|:| |fn| (|Expression| (|DoubleFloat|))) (|:| |range| (|Segment| (|OrderedCompletion| (|DoubleFloat|)))) (|:| |abserr| (|DoubleFloat|)) (|:| |relerr| (|DoubleFloat|)))) $) "\\spad{keys(f)} returns the list of keys of \\spad{f}")) (|clearTheFTable| (((|Void|)) "\\spad{clearTheFTable()} clears the current table of functions.")) (|showTheFTable| (($) "\\spad{showTheFTable()} returns the current table of functions."))) NIL NIL -(-575 R -4164 L) +(-575 R -4140 L) ((|constructor| (NIL "This internal package rationalises integrands on curves of the form: \\indented{2}{\\spad{y\\^2 = a x\\^2 + b x + c}} \\indented{2}{\\spad{y\\^2 = (a x + b) / (c x + d)}} \\indented{2}{\\spad{f(x, y) = 0} where \\spad{f} has degree 1 in \\spad{x}} The rationalization is done for integration,{} limited integration,{} extended integration and the risch differential equation.")) (|palgLODE0| (((|Record| (|:| |particular| (|Union| |#2| "failed")) (|:| |basis| (|List| |#2|))) |#3| |#2| (|Kernel| |#2|) (|Kernel| |#2|) (|Kernel| |#2|) |#2| (|Fraction| (|SparseUnivariatePolynomial| |#2|))) "\\spad{palgLODE0(op,g,x,y,z,t,c)} returns the solution of \\spad{op f = g} Argument \\spad{y} is an algebraic function of \\spad{x} satisfying \\spad{f(x,y)dx = c f(t,y) dy}; \\spad{c} and \\spad{t} are rational functions of \\spad{y}.") (((|Record| (|:| |particular| (|Union| |#2| "failed")) (|:| |basis| (|List| |#2|))) |#3| |#2| (|Kernel| |#2|) (|Kernel| |#2|) |#2| (|SparseUnivariatePolynomial| |#2|)) "\\spad{palgLODE0(op, g, x, y, d, p)} returns the solution of \\spad{op f = g}. Argument \\spad{y} is an algebraic function of \\spad{x} satisfying \\spad{d(x)\\^2y(x)\\^2 = P(x)}.")) (|lift| (((|SparseUnivariatePolynomial| (|Fraction| (|SparseUnivariatePolynomial| |#2|))) (|SparseUnivariatePolynomial| |#2|) (|Kernel| |#2|)) "\\spad{lift(u,k)} \\undocumented")) (|multivariate| ((|#2| (|SparseUnivariatePolynomial| (|Fraction| (|SparseUnivariatePolynomial| |#2|))) (|Kernel| |#2|) |#2|) "\\spad{multivariate(u,k,f)} \\undocumented")) (|univariate| (((|SparseUnivariatePolynomial| (|Fraction| (|SparseUnivariatePolynomial| |#2|))) |#2| (|Kernel| |#2|) (|Kernel| |#2|) (|SparseUnivariatePolynomial| |#2|)) "\\spad{univariate(f,k,k,p)} \\undocumented")) (|palgRDE0| (((|Union| |#2| "failed") |#2| |#2| (|Kernel| |#2|) (|Kernel| |#2|) (|Mapping| (|Union| |#2| "failed") |#2| |#2| (|Symbol|)) (|Kernel| |#2|) |#2| (|Fraction| (|SparseUnivariatePolynomial| |#2|))) "\\spad{palgRDE0(f, g, x, y, foo, t, c)} returns a function \\spad{z(x,y)} such that \\spad{dz/dx + n * df/dx z(x,y) = g(x,y)} if such a \\spad{z} exists,{} and \"failed\" otherwise. Argument \\spad{y} is an algebraic function of \\spad{x} satisfying \\spad{f(x,y)dx = c f(t,y) dy}; \\spad{c} and \\spad{t} are rational functions of \\spad{y}. Argument \\spad{foo},{} called by \\spad{foo(a, b, x)},{} is a function that solves \\spad{du/dx + n * da/dx u(x) = u(x)} for an unknown \\spad{u(x)} not involving \\spad{y}.") (((|Union| |#2| "failed") |#2| |#2| (|Kernel| |#2|) (|Kernel| |#2|) (|Mapping| (|Union| |#2| "failed") |#2| |#2| (|Symbol|)) |#2| (|SparseUnivariatePolynomial| |#2|)) "\\spad{palgRDE0(f, g, x, y, foo, d, p)} returns a function \\spad{z(x,y)} such that \\spad{dz/dx + n * df/dx z(x,y) = g(x,y)} if such a \\spad{z} exists,{} and \"failed\" otherwise. Argument \\spad{y} is an algebraic function of \\spad{x} satisfying \\spad{d(x)\\^2y(x)\\^2 = P(x)}. Argument \\spad{foo},{} called by \\spad{foo(a, b, x)},{} is a function that solves \\spad{du/dx + n * da/dx u(x) = u(x)} for an unknown \\spad{u(x)} not involving \\spad{y}.")) (|palglimint0| (((|Union| (|Record| (|:| |mainpart| |#2|) (|:| |limitedlogs| (|List| (|Record| (|:| |coeff| |#2|) (|:| |logand| |#2|))))) "failed") |#2| (|Kernel| |#2|) (|Kernel| |#2|) (|List| |#2|) (|Kernel| |#2|) |#2| (|Fraction| (|SparseUnivariatePolynomial| |#2|))) "\\spad{palglimint0(f, x, y, [u1,...,un], z, t, c)} returns functions \\spad{[h,[[ci, ui]]]} such that the \\spad{ui}'s are among \\spad{[u1,...,un]} and \\spad{d(h + sum(ci log(ui)))/dx = f(x,y)} if such functions exist,{} and \"failed\" otherwise. Argument \\spad{y} is an algebraic function of \\spad{x} satisfying \\spad{f(x,y)dx = c f(t,y) dy}; \\spad{c} and \\spad{t} are rational functions of \\spad{y}.") (((|Union| (|Record| (|:| |mainpart| |#2|) (|:| |limitedlogs| (|List| (|Record| (|:| |coeff| |#2|) (|:| |logand| |#2|))))) "failed") |#2| (|Kernel| |#2|) (|Kernel| |#2|) (|List| |#2|) |#2| (|SparseUnivariatePolynomial| |#2|)) "\\spad{palglimint0(f, x, y, [u1,...,un], d, p)} returns functions \\spad{[h,[[ci, ui]]]} such that the \\spad{ui}'s are among \\spad{[u1,...,un]} and \\spad{d(h + sum(ci log(ui)))/dx = f(x,y)} if such functions exist,{} and \"failed\" otherwise. Argument \\spad{y} is an algebraic function of \\spad{x} satisfying \\spad{d(x)\\^2y(x)\\^2 = P(x)}.")) (|palgextint0| (((|Union| (|Record| (|:| |ratpart| |#2|) (|:| |coeff| |#2|)) "failed") |#2| (|Kernel| |#2|) (|Kernel| |#2|) |#2| (|Kernel| |#2|) |#2| (|Fraction| (|SparseUnivariatePolynomial| |#2|))) "\\spad{palgextint0(f, x, y, g, z, t, c)} returns functions \\spad{[h, d]} such that \\spad{dh/dx = f(x,y) - d g},{} where \\spad{y} is an algebraic function of \\spad{x} satisfying \\spad{f(x,y)dx = c f(t,y) dy},{} and \\spad{c} and \\spad{t} are rational functions of \\spad{y}. Argument \\spad{z} is a dummy variable not appearing in \\spad{f(x,y)}. The operation returns \"failed\" if no such functions exist.") (((|Union| (|Record| (|:| |ratpart| |#2|) (|:| |coeff| |#2|)) "failed") |#2| (|Kernel| |#2|) (|Kernel| |#2|) |#2| |#2| (|SparseUnivariatePolynomial| |#2|)) "\\spad{palgextint0(f, x, y, g, d, p)} returns functions \\spad{[h, c]} such that \\spad{dh/dx = f(x,y) - c g},{} where \\spad{y} is an algebraic function of \\spad{x} satisfying \\spad{d(x)\\^2 y(x)\\^2 = P(x)},{} or \"failed\" if no such functions exist.")) (|palgint0| (((|IntegrationResult| |#2|) |#2| (|Kernel| |#2|) (|Kernel| |#2|) (|Kernel| |#2|) |#2| (|Fraction| (|SparseUnivariatePolynomial| |#2|))) "\\spad{palgint0(f, x, y, z, t, c)} returns the integral of \\spad{f(x,y)dx} where \\spad{y} is an algebraic function of \\spad{x} satisfying \\spad{f(x,y)dx = c f(t,y) dy}; \\spad{c} and \\spad{t} are rational functions of \\spad{y}. Argument \\spad{z} is a dummy variable not appearing in \\spad{f(x,y)}.") (((|IntegrationResult| |#2|) |#2| (|Kernel| |#2|) (|Kernel| |#2|) |#2| (|SparseUnivariatePolynomial| |#2|)) "\\spad{palgint0(f, x, y, d, p)} returns the integral of \\spad{f(x,y)dx} where \\spad{y} is an algebraic function of \\spad{x} satisfying \\spad{d(x)\\^2 y(x)\\^2 = P(x)}."))) NIL ((|HasCategory| |#3| (|%list| (QUOTE -680) (|devaluate| |#2|)))) @@ -2236,11 +2236,11 @@ NIL ((|constructor| (NIL "This package provides various number theoretic functions on the integers.")) (|sumOfKthPowerDivisors| (((|Integer|) (|Integer|) (|NonNegativeInteger|)) "\\spad{sumOfKthPowerDivisors(n,k)} returns the sum of the \\spad{k}th powers of the integers between 1 and \\spad{n} (inclusive) which divide \\spad{n}. the sum of the \\spad{k}th powers of the divisors of \\spad{n} is often denoted by \\spad{sigma_k(n)}.")) (|sumOfDivisors| (((|Integer|) (|Integer|)) "\\spad{sumOfDivisors(n)} returns the sum of the integers between 1 and \\spad{n} (inclusive) which divide \\spad{n}. The sum of the divisors of \\spad{n} is often denoted by \\spad{sigma(n)}.")) (|numberOfDivisors| (((|Integer|) (|Integer|)) "\\spad{numberOfDivisors(n)} returns the number of integers between 1 and \\spad{n} (inclusive) which divide \\spad{n}. The number of divisors of \\spad{n} is often denoted by \\spad{tau(n)}.")) (|moebiusMu| (((|Integer|) (|Integer|)) "\\spad{moebiusMu(n)} returns the Moebius function \\spad{mu(n)}. \\spad{mu(n)} is either \\spad{-1},{}0 or 1 as follows: \\spad{mu(n) = 0} if \\spad{n} is divisible by a square > 1,{} \\spad{mu(n) = (-1)^k} if \\spad{n} is square-free and has \\spad{k} distinct prime divisors.")) (|legendre| (((|Integer|) (|Integer|) (|Integer|)) "\\spad{legendre(a,p)} returns the Legendre symbol \\spad{L(a/p)}. \\spad{L(a/p) = (-1)**((p-1)/2) mod p} (\\spad{p} prime),{} which is 0 if \\spad{a} is 0,{} 1 if \\spad{a} is a quadratic residue \\spad{mod p} and \\spad{-1} otherwise. Note: because the primality test is expensive,{} if it is known that \\spad{p} is prime then use \\spad{jacobi(a,p)}.")) (|jacobi| (((|Integer|) (|Integer|) (|Integer|)) "\\spad{jacobi(a,b)} returns the Jacobi symbol \\spad{J(a/b)}. When \\spad{b} is odd,{} \\spad{J(a/b) = product(L(a/p) for p in factor b )}. Note: by convention,{} 0 is returned if \\spad{gcd(a,b) ~= 1}. Iterative \\spad{O(log(b)^2)} version coded by Michael Monagan June 1987.")) (|harmonic| (((|Fraction| (|Integer|)) (|Integer|)) "\\spad{harmonic(n)} returns the \\spad{n}th harmonic number. This is \\spad{H[n] = sum(1/k,k=1..n)}.")) (|fibonacci| (((|Integer|) (|Integer|)) "\\spad{fibonacci(n)} returns the \\spad{n}th Fibonacci number. the Fibonacci numbers \\spad{F[n]} are defined by \\spad{F[0] = F[1] = 1} and \\spad{F[n] = F[n-1] + F[n-2]}. The algorithm has running time \\spad{O(log(n)^3)}. Reference: Knuth,{} The Art of Computer Programming Vol 2,{} Semi-Numerical Algorithms.")) (|eulerPhi| (((|Integer|) (|Integer|)) "\\spad{eulerPhi(n)} returns the number of integers between 1 and \\spad{n} (including 1) which are relatively prime to \\spad{n}. This is the Euler phi function \\spad{\\phi(n)} is also called the totient function.")) (|euler| (((|Integer|) (|Integer|)) "\\spad{euler(n)} returns the \\spad{n}th Euler number. This is \\spad{2^n E(n,1/2)},{} where \\spad{E(n,x)} is the \\spad{n}th Euler polynomial.")) (|divisors| (((|List| (|Integer|)) (|Integer|)) "\\spad{divisors(n)} returns a list of the divisors of \\spad{n}.")) (|chineseRemainder| (((|Integer|) (|Integer|) (|Integer|) (|Integer|) (|Integer|)) "\\spad{chineseRemainder(x1,m1,x2,m2)} returns \\spad{w},{} where \\spad{w} is such that \\spad{w = x1 mod m1} and \\spad{w = x2 mod m2}. Note: \\spad{m1} and \\spad{m2} must be relatively prime.")) (|bernoulli| (((|Fraction| (|Integer|)) (|Integer|)) "\\spad{bernoulli(n)} returns the \\spad{n}th Bernoulli number. this is \\spad{B(n,0)},{} where \\spad{B(n,x)} is the \\spad{n}th Bernoulli polynomial."))) NIL NIL -(-577 -4164 UP UPUP R) +(-577 -4140 UP UPUP R) ((|constructor| (NIL "algebraic Hermite redution.")) (|HermiteIntegrate| (((|Record| (|:| |answer| |#4|) (|:| |logpart| |#4|)) |#4| (|Mapping| |#2| |#2|)) "\\spad{HermiteIntegrate(f, ')} returns \\spad{[g,h]} such that \\spad{f = g' + h} and \\spad{h} has a only simple finite normal poles."))) NIL NIL -(-578 -4164 UP) +(-578 -4140 UP) ((|constructor| (NIL "Hermite integration,{} transcendental case.")) (|HermiteIntegrate| (((|Record| (|:| |answer| (|Fraction| |#2|)) (|:| |logpart| (|Fraction| |#2|)) (|:| |specpart| (|Fraction| |#2|)) (|:| |polypart| |#2|)) (|Fraction| |#2|) (|Mapping| |#2| |#2|)) "\\spad{HermiteIntegrate(f, D)} returns \\spad{[g, h, s, p]} such that \\spad{f = Dg + h + s + p},{} \\spad{h} has a squarefree denominator normal \\spad{w}.\\spad{r}.\\spad{t}. \\spad{D},{} and all the squarefree factors of the denominator of \\spad{s} are special \\spad{w}.\\spad{r}.\\spad{t}. \\spad{D}. Furthermore,{} \\spad{h} and \\spad{s} have no polynomial parts. \\spad{D} is the derivation to use on \\spadtype{UP}."))) NIL NIL @@ -2248,15 +2248,15 @@ NIL ((|measure| (((|Record| (|:| |measure| (|Float|)) (|:| |name| (|String|)) (|:| |explanations| (|List| (|String|))) (|:| |extra| (|Result|))) (|NumericalIntegrationProblem|) (|RoutinesTable|)) "\\spad{measure(prob,R)} is a top level ANNA function for identifying the most appropriate numerical routine from those in the routines table provided for solving the numerical integration problem defined by \\axiom{\\spad{prob}}. \\blankline It calls each \\axiom{domain} listed in \\axiom{\\spad{R}} of \\axiom{category} \\axiomType{NumericalIntegrationCategory} in turn to calculate all measures and returns the best \\spadignore{i.e.} the name of the most appropriate domain and any other relevant information.") (((|Record| (|:| |measure| (|Float|)) (|:| |name| (|String|)) (|:| |explanations| (|List| (|String|))) (|:| |extra| (|Result|))) (|NumericalIntegrationProblem|)) "\\spad{measure(prob)} is a top level ANNA function for identifying the most appropriate numerical routine for solving the numerical integration problem defined by \\axiom{\\spad{prob}}. \\blankline It calls each \\axiom{domain} of \\axiom{category} \\axiomType{NumericalIntegrationCategory} in turn to calculate all measures and returns the best \\spadignore{i.e.} the name of the most appropriate domain and any other relevant information.")) (|integrate| (((|Union| (|Result|) "failed") (|Expression| (|Float|)) (|SegmentBinding| (|OrderedCompletion| (|Float|))) (|Symbol|)) "\\spad{integrate(exp, x = a..b, numerical)} is a top level ANNA function to integrate an expression,{} {\\tt \\spad{exp}},{} over a given range,{} {\\tt a} to {\\tt \\spad{b}}. \\blankline It iterates over the \\axiom{domains} of \\axiomType{NumericalIntegrationCategory} to get the name and other relevant information of the the (domain of the) numerical routine likely to be the most appropriate,{} \\spadignore{i.e.} have the best \\axiom{measure}. \\blankline It then performs the integration of the given expression on that \\axiom{domain}.\\newline \\blankline Default values for the absolute and relative error are used. \\blankline It is an error if the last argument is not {\\tt numerical}.") (((|Union| (|Result|) "failed") (|Expression| (|Float|)) (|SegmentBinding| (|OrderedCompletion| (|Float|))) (|String|)) "\\spad{integrate(exp, x = a..b, \"numerical\")} is a top level ANNA function to integrate an expression,{} {\\tt \\spad{exp}},{} over a given range,{} {\\tt a} to {\\tt \\spad{b}}. \\blankline It iterates over the \\axiom{domains} of \\axiomType{NumericalIntegrationCategory} to get the name and other relevant information of the the (domain of the) numerical routine likely to be the most appropriate,{} \\spadignore{i.e.} have the best \\axiom{measure}. \\blankline It then performs the integration of the given expression on that \\axiom{domain}.\\newline \\blankline Default values for the absolute and relative error are used. \\blankline It is an error of the last argument is not {\\tt \"numerical\"}.") (((|Result|) (|Expression| (|Float|)) (|List| (|Segment| (|OrderedCompletion| (|Float|)))) (|Float|) (|Float|) (|RoutinesTable|)) "\\spad{integrate(exp, [a..b,c..d,...], epsabs, epsrel, routines)} is a top level ANNA function to integrate a multivariate expression,{} {\\tt \\spad{exp}},{} over a given set of ranges to the required absolute and relative accuracy,{} using the routines available in the RoutinesTable provided. \\blankline It iterates over the \\axiom{domains} of \\axiomType{NumericalIntegrationCategory} to get the name and other relevant information of the the (domain of the) numerical routine likely to be the most appropriate,{} \\spadignore{i.e.} have the best \\axiom{measure}. \\blankline It then performs the integration of the given expression on that \\axiom{domain}.") (((|Result|) (|Expression| (|Float|)) (|List| (|Segment| (|OrderedCompletion| (|Float|)))) (|Float|) (|Float|)) "\\spad{integrate(exp, [a..b,c..d,...], epsabs, epsrel)} is a top level ANNA function to integrate a multivariate expression,{} {\\tt \\spad{exp}},{} over a given set of ranges to the required absolute and relative accuracy. \\blankline It iterates over the \\axiom{domains} of \\axiomType{NumericalIntegrationCategory} to get the name and other relevant information of the the (domain of the) numerical routine likely to be the most appropriate,{} \\spadignore{i.e.} have the best \\axiom{measure}. \\blankline It then performs the integration of the given expression on that \\axiom{domain}.") (((|Result|) (|Expression| (|Float|)) (|List| (|Segment| (|OrderedCompletion| (|Float|)))) (|Float|)) "\\spad{integrate(exp, [a..b,c..d,...], epsrel)} is a top level ANNA function to integrate a multivariate expression,{} {\\tt \\spad{exp}},{} over a given set of ranges to the required relative accuracy. \\blankline It iterates over the \\axiom{domains} of \\axiomType{NumericalIntegrationCategory} to get the name and other relevant information of the the (domain of the) numerical routine likely to be the most appropriate,{} \\spadignore{i.e.} have the best \\axiom{measure}. \\blankline It then performs the integration of the given expression on that \\axiom{domain}. \\blankline If epsrel = 0,{} a default absolute accuracy is used.") (((|Result|) (|Expression| (|Float|)) (|List| (|Segment| (|OrderedCompletion| (|Float|))))) "\\spad{integrate(exp, [a..b,c..d,...])} is a top level ANNA function to integrate a multivariate expression,{} {\\tt \\spad{exp}},{} over a given set of ranges. \\blankline It iterates over the \\axiom{domains} of \\axiomType{NumericalIntegrationCategory} to get the name and other relevant information of the the (domain of the) numerical routine likely to be the most appropriate,{} \\spadignore{i.e.} have the best \\axiom{measure}. \\blankline It then performs the integration of the given expression on that \\axiom{domain}. \\blankline Default values for the absolute and relative error are used.") (((|Result|) (|Expression| (|Float|)) (|Segment| (|OrderedCompletion| (|Float|)))) "\\spad{integrate(exp, a..b)} is a top level ANNA function to integrate an expression,{} {\\tt \\spad{exp}},{} over a given range {\\tt a} to {\\tt \\spad{b}}. \\blankline It iterates over the \\axiom{domains} of \\axiomType{NumericalIntegrationCategory} to get the name and other relevant information of the the (domain of the) numerical routine likely to be the most appropriate,{} \\spadignore{i.e.} have the best \\axiom{measure}. \\blankline It then performs the integration of the given expression on that \\axiom{domain}. \\blankline Default values for the absolute and relative error are used.") (((|Result|) (|Expression| (|Float|)) (|Segment| (|OrderedCompletion| (|Float|))) (|Float|)) "\\spad{integrate(exp, a..b, epsrel)} is a top level ANNA function to integrate an expression,{} {\\tt \\spad{exp}},{} over a given range {\\tt a} to {\\tt \\spad{b}} to the required relative accuracy. \\blankline It iterates over the \\axiom{domains} of \\axiomType{NumericalIntegrationCategory} to get the name and other relevant information of the the (domain of the) numerical routine likely to be the most appropriate,{} \\spadignore{i.e.} have the best \\axiom{measure}. \\blankline It then performs the integration of the given expression on that \\axiom{domain}. \\blankline If epsrel = 0,{} a default absolute accuracy is used.") (((|Result|) (|Expression| (|Float|)) (|Segment| (|OrderedCompletion| (|Float|))) (|Float|) (|Float|)) "\\spad{integrate(exp, a..b, epsabs, epsrel)} is a top level ANNA function to integrate an expression,{} {\\tt \\spad{exp}},{} over a given range {\\tt a} to {\\tt \\spad{b}} to the required absolute and relative accuracy. \\blankline It iterates over the \\axiom{domains} of \\axiomType{NumericalIntegrationCategory} to get the name and other relevant information of the the (domain of the) numerical routine likely to be the most appropriate,{} \\spadignore{i.e.} have the best \\axiom{measure}. \\blankline It then performs the integration of the given expression on that \\axiom{domain}.") (((|Result|) (|NumericalIntegrationProblem|)) "\\spad{integrate(IntegrationProblem)} is a top level ANNA function to integrate an expression over a given range or ranges to the required absolute and relative accuracy. \\blankline It iterates over the \\axiom{domains} of \\axiomType{NumericalIntegrationCategory} to get the name and other relevant information of the the (domain of the) numerical routine likely to be the most appropriate,{} \\spadignore{i.e.} have the best \\axiom{measure}. \\blankline It then performs the integration of the given expression on that \\axiom{domain}.") (((|Result|) (|Expression| (|Float|)) (|Segment| (|OrderedCompletion| (|Float|))) (|Float|) (|Float|) (|RoutinesTable|)) "\\spad{integrate(exp, a..b, epsrel, routines)} is a top level ANNA function to integrate an expression,{} {\\tt \\spad{exp}},{} over a given range {\\tt a} to {\\tt \\spad{b}} to the required absolute and relative accuracy using the routines available in the RoutinesTable provided. \\blankline It iterates over the \\axiom{domains} of \\axiomType{NumericalIntegrationCategory} to get the name and other relevant information of the the (domain of the) numerical routine likely to be the most appropriate,{} \\spadignore{i.e.} have the best \\axiom{measure}. \\blankline It then performs the integration of the given expression on that \\axiom{domain}."))) NIL NIL -(-580 R -4164 L) +(-580 R -4140 L) ((|constructor| (NIL "This package provides functions for integration,{} limited integration,{} extended integration and the risch differential equation for pure algebraic integrands.")) (|palgLODE| (((|Record| (|:| |particular| (|Union| |#2| "failed")) (|:| |basis| (|List| |#2|))) |#3| |#2| (|Kernel| |#2|) (|Kernel| |#2|) (|Symbol|)) "\\spad{palgLODE(op, g, kx, y, x)} returns the solution of \\spad{op f = g}. \\spad{y} is an algebraic function of \\spad{x}.")) (|palgRDE| (((|Union| |#2| "failed") |#2| |#2| |#2| (|Kernel| |#2|) (|Kernel| |#2|) (|Mapping| (|Union| |#2| "failed") |#2| |#2| (|Symbol|))) "\\spad{palgRDE(nfp, f, g, x, y, foo)} returns a function \\spad{z(x,y)} such that \\spad{dz/dx + n * df/dx z(x,y) = g(x,y)} if such a \\spad{z} exists,{} \"failed\" otherwise; \\spad{y} is an algebraic function of \\spad{x}; \\spad{foo(a, b, x)} is a function that solves \\spad{du/dx + n * da/dx u(x) = u(x)} for an unknown \\spad{u(x)} not involving \\spad{y}. \\spad{nfp} is \\spad{n * df/dx}.")) (|palglimint| (((|Union| (|Record| (|:| |mainpart| |#2|) (|:| |limitedlogs| (|List| (|Record| (|:| |coeff| |#2|) (|:| |logand| |#2|))))) "failed") |#2| (|Kernel| |#2|) (|Kernel| |#2|) (|List| |#2|)) "\\spad{palglimint(f, x, y, [u1,...,un])} returns functions \\spad{[h,[[ci, ui]]]} such that the \\spad{ui}'s are among \\spad{[u1,...,un]} and \\spad{d(h + sum(ci log(ui)))/dx = f(x,y)} if such functions exist,{} \"failed\" otherwise; \\spad{y} is an algebraic function of \\spad{x}.")) (|palgextint| (((|Union| (|Record| (|:| |ratpart| |#2|) (|:| |coeff| |#2|)) "failed") |#2| (|Kernel| |#2|) (|Kernel| |#2|) |#2|) "\\spad{palgextint(f, x, y, g)} returns functions \\spad{[h, c]} such that \\spad{dh/dx = f(x,y) - c g},{} where \\spad{y} is an algebraic function of \\spad{x}; returns \"failed\" if no such functions exist.")) (|palgint| (((|IntegrationResult| |#2|) |#2| (|Kernel| |#2|) (|Kernel| |#2|)) "\\spad{palgint(f, x, y)} returns the integral of \\spad{f(x,y)dx} where \\spad{y} is an algebraic function of \\spad{x}."))) NIL ((|HasCategory| |#3| (|%list| (QUOTE -680) (|devaluate| |#2|)))) -(-581 R -4164) +(-581 R -4140) ((|constructor| (NIL "\\spadtype{PatternMatchIntegration} provides functions that use the pattern matcher to find some indefinite and definite integrals involving special functions and found in the litterature.")) (|pmintegrate| (((|Union| |#2| "failed") |#2| (|Symbol|) (|OrderedCompletion| |#2|) (|OrderedCompletion| |#2|)) "\\spad{pmintegrate(f, x = a..b)} returns the integral of \\spad{f(x)dx} from a to \\spad{b} if it can be found by the built-in pattern matching rules.") (((|Union| (|Record| (|:| |special| |#2|) (|:| |integrand| |#2|)) "failed") |#2| (|Symbol|)) "\\spad{pmintegrate(f, x)} returns either \"failed\" or \\spad{[g,h]} such that \\spad{integrate(f,x) = g + integrate(h,x)}.")) (|pmComplexintegrate| (((|Union| (|Record| (|:| |special| |#2|) (|:| |integrand| |#2|)) "failed") |#2| (|Symbol|)) "\\spad{pmComplexintegrate(f, x)} returns either \"failed\" or \\spad{[g,h]} such that \\spad{integrate(f,x) = g + integrate(h,x)}. It only looks for special complex integrals that pmintegrate does not return.")) (|splitConstant| (((|Record| (|:| |const| |#2|) (|:| |nconst| |#2|)) |#2| (|Symbol|)) "\\spad{splitConstant(f, x)} returns \\spad{[c, g]} such that \\spad{f = c * g} and \\spad{c} does not involve \\spad{t}."))) NIL ((-12 (|HasCategory| |#1| (|%list| (QUOTE -633) (|%list| (QUOTE -916) (QUOTE (-560))))) (|HasCategory| |#1| (|%list| (QUOTE -912) (QUOTE (-560)))) (|HasCategory| |#2| (QUOTE (-1171)))) (-12 (|HasCategory| |#1| (|%list| (QUOTE -633) (|%list| (QUOTE -916) (QUOTE (-560))))) (|HasCategory| |#1| (|%list| (QUOTE -912) (QUOTE (-560)))) (|HasCategory| |#2| (QUOTE (-649))))) -(-582 -4164 UP) +(-582 -4140 UP) ((|constructor| (NIL "This package provides functions for the base case of the Risch algorithm.")) (|limitedint| (((|Union| (|Record| (|:| |mainpart| (|Fraction| |#2|)) (|:| |limitedlogs| (|List| (|Record| (|:| |coeff| (|Fraction| |#2|)) (|:| |logand| (|Fraction| |#2|)))))) "failed") (|Fraction| |#2|) (|List| (|Fraction| |#2|))) "\\spad{limitedint(f, [g1,...,gn])} returns fractions \\spad{[h,[[ci, gi]]]} such that the \\spad{gi}'s are among \\spad{[g1,...,gn]},{} \\spad{ci' = 0},{} and \\spad{(h+sum(ci log(gi)))' = f},{} if possible,{} \"failed\" otherwise.")) (|extendedint| (((|Union| (|Record| (|:| |ratpart| (|Fraction| |#2|)) (|:| |coeff| (|Fraction| |#2|))) "failed") (|Fraction| |#2|) (|Fraction| |#2|)) "\\spad{extendedint(f, g)} returns fractions \\spad{[h, c]} such that \\spad{c' = 0} and \\spad{h' = f - cg},{} if \\spad{(h, c)} exist,{} \"failed\" otherwise.")) (|infieldint| (((|Union| (|Fraction| |#2|) "failed") (|Fraction| |#2|)) "\\spad{infieldint(f)} returns \\spad{g} such that \\spad{g' = f} or \"failed\" if the integral of \\spad{f} is not a rational function.")) (|integrate| (((|IntegrationResult| (|Fraction| |#2|)) (|Fraction| |#2|)) "\\spad{integrate(f)} returns \\spad{g} such that \\spad{g' = f}."))) NIL NIL @@ -2264,27 +2264,27 @@ 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 -(-584 -4164) +(-584 -4140) ((|constructor| (NIL "This package provides functions for the integration of rational functions.")) (|extendedIntegrate| (((|Union| (|Record| (|:| |ratpart| (|Fraction| (|Polynomial| |#1|))) (|:| |coeff| (|Fraction| (|Polynomial| |#1|)))) "failed") (|Fraction| (|Polynomial| |#1|)) (|Symbol|) (|Fraction| (|Polynomial| |#1|))) "\\spad{extendedIntegrate(f, x, g)} returns fractions \\spad{[h, c]} such that \\spad{dc/dx = 0} and \\spad{dh/dx = f - cg},{} if \\spad{(h, c)} exist,{} \"failed\" otherwise.")) (|limitedIntegrate| (((|Union| (|Record| (|:| |mainpart| (|Fraction| (|Polynomial| |#1|))) (|:| |limitedlogs| (|List| (|Record| (|:| |coeff| (|Fraction| (|Polynomial| |#1|))) (|:| |logand| (|Fraction| (|Polynomial| |#1|))))))) "failed") (|Fraction| (|Polynomial| |#1|)) (|Symbol|) (|List| (|Fraction| (|Polynomial| |#1|)))) "\\spad{limitedIntegrate(f, x, [g1,...,gn])} returns fractions \\spad{[h, [[ci,gi]]]} such that the \\spad{gi}'s are among \\spad{[g1,...,gn]},{} \\spad{dci/dx = 0},{} and \\spad{d(h + sum(ci log(gi)))/dx = f} if possible,{} \"failed\" otherwise.")) (|infieldIntegrate| (((|Union| (|Fraction| (|Polynomial| |#1|)) "failed") (|Fraction| (|Polynomial| |#1|)) (|Symbol|)) "\\spad{infieldIntegrate(f, x)} returns a fraction \\spad{g} such that \\spad{dg/dx = f} if \\spad{g} exists,{} \"failed\" otherwise.")) (|internalIntegrate| (((|IntegrationResult| (|Fraction| (|Polynomial| |#1|))) (|Fraction| (|Polynomial| |#1|)) (|Symbol|)) "\\spad{internalIntegrate(f, x)} returns \\spad{g} such that \\spad{dg/dx = f}."))) NIL NIL (-585 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."))) -((-2862 . T) (-4503 . T) ((-4512 "*") . T) (-4504 . T) (-4505 . T) (-4507 . T)) +((-2853 . T) (-4503 . T) ((-4512 "*") . T) (-4504 . T) (-4505 . T) (-4507 . T)) NIL (-586) ((|constructor| (NIL "This package provides the implementation for the \\spadfun{solveLinearPolynomialEquation} operation over the integers. It uses a lifting technique from the package GenExEuclid")) (|solveLinearPolynomialEquation| (((|Union| (|List| (|SparseUnivariatePolynomial| (|Integer|))) "failed") (|List| (|SparseUnivariatePolynomial| (|Integer|))) (|SparseUnivariatePolynomial| (|Integer|))) "\\spad{solveLinearPolynomialEquation([f1, ..., fn], g)} (where the \\spad{fi} are relatively prime to each other) returns a list of \\spad{ai} such that \\spad{g/prod fi = sum ai/fi} or returns \"failed\" if no such list of \\spad{ai}'s exists."))) NIL NIL -(-587 R -4164) +(-587 R -4140) ((|constructor| (NIL "\\indented{1}{Tools for the integrator} Author: Manuel Bronstein Date Created: 25 April 1990 Date Last Updated: 9 June 1993 Keywords: elementary,{} function,{} integration.")) (|intPatternMatch| (((|IntegrationResult| |#2|) |#2| (|Symbol|) (|Mapping| (|IntegrationResult| |#2|) |#2| (|Symbol|)) (|Mapping| (|Union| (|Record| (|:| |special| |#2|) (|:| |integrand| |#2|)) "failed") |#2| (|Symbol|))) "\\spad{intPatternMatch(f, x, int, pmint)} tries to integrate \\spad{f} first by using the integration function \\spad{int},{} and then by using the pattern match intetgration function \\spad{pmint} on any remaining unintegrable part.")) (|mkPrim| ((|#2| |#2| (|Symbol|)) "\\spad{mkPrim(f, x)} makes the logs in \\spad{f} which are linear in \\spad{x} primitive with respect to \\spad{x}.")) (|removeConstantTerm| ((|#2| |#2| (|Symbol|)) "\\spad{removeConstantTerm(f, x)} returns \\spad{f} minus any additive constant with respect to \\spad{x}.")) (|vark| (((|List| (|Kernel| |#2|)) (|List| |#2|) (|Symbol|)) "\\spad{vark([f1,...,fn],x)} returns the set-theoretic union of \\spad{(varselect(f1,x),...,varselect(fn,x))}.")) (|union| (((|List| (|Kernel| |#2|)) (|List| (|Kernel| |#2|)) (|List| (|Kernel| |#2|))) "\\spad{union(l1, l2)} returns set-theoretic union of \\spad{l1} and \\spad{l2}.")) (|ksec| (((|Kernel| |#2|) (|Kernel| |#2|) (|List| (|Kernel| |#2|)) (|Symbol|)) "\\spad{ksec(k, [k1,...,kn], x)} returns the second top-level \\spad{ki} after \\spad{k} involving \\spad{x}.")) (|kmax| (((|Kernel| |#2|) (|List| (|Kernel| |#2|))) "\\spad{kmax([k1,...,kn])} returns the top-level \\spad{ki} for integration.")) (|varselect| (((|List| (|Kernel| |#2|)) (|List| (|Kernel| |#2|)) (|Symbol|)) "\\spad{varselect([k1,...,kn], x)} returns the \\spad{ki} which involve \\spad{x}."))) NIL ((-12 (|HasCategory| |#1| (|%list| (QUOTE -633) (|%list| (QUOTE -916) (QUOTE (-560))))) (|HasCategory| |#1| (QUOTE (-466))) (|HasCategory| |#1| (|%list| (QUOTE -912) (QUOTE (-560)))) (|HasCategory| |#2| (QUOTE (-296))) (|HasCategory| |#2| (QUOTE (-649))) (|HasCategory| |#2| (|%list| (QUOTE -1070) (QUOTE (-1209))))) (-12 (|HasCategory| |#1| (QUOTE (-466))) (|HasCategory| |#2| (QUOTE (-296)))) (|HasCategory| |#1| (QUOTE (-571)))) -(-588 -4164 UP) +(-588 -4140 UP) ((|constructor| (NIL "This package provides functions for the transcendental case of the Risch algorithm.")) (|monomialIntPoly| (((|Record| (|:| |answer| |#2|) (|:| |polypart| |#2|)) |#2| (|Mapping| |#2| |#2|)) "\\spad{monomialIntPoly(p, ')} returns [\\spad{q},{} \\spad{r}] such that \\spad{p = q' + r} and \\spad{degree(r) < degree(t')}. Error if \\spad{degree(t') < 2}.")) (|monomialIntegrate| (((|Record| (|:| |ir| (|IntegrationResult| (|Fraction| |#2|))) (|:| |specpart| (|Fraction| |#2|)) (|:| |polypart| |#2|)) (|Fraction| |#2|) (|Mapping| |#2| |#2|)) "\\spad{monomialIntegrate(f, ')} returns \\spad{[ir, s, p]} such that \\spad{f = ir' + s + p} and all the squarefree factors of the denominator of \\spad{s} are special \\spad{w}.\\spad{r}.\\spad{t} the derivation '.")) (|expintfldpoly| (((|Union| (|LaurentPolynomial| |#1| |#2|) "failed") (|LaurentPolynomial| |#1| |#2|) (|Mapping| (|Record| (|:| |ans| |#1|) (|:| |right| |#1|) (|:| |sol?| (|Boolean|))) (|Integer|) |#1|)) "\\spad{expintfldpoly(p, foo)} returns \\spad{q} such that \\spad{p' = q} or \"failed\" if no such \\spad{q} exists. Argument foo is a Risch differential equation function on \\spad{F}.")) (|primintfldpoly| (((|Union| |#2| "failed") |#2| (|Mapping| (|Union| (|Record| (|:| |ratpart| |#1|) (|:| |coeff| |#1|)) "failed") |#1|) |#1|) "\\spad{primintfldpoly(p, ', t')} returns \\spad{q} such that \\spad{p' = q} or \"failed\" if no such \\spad{q} exists. Argument \\spad{t'} is the derivative of the primitive generating the extension.")) (|primlimintfrac| (((|Union| (|Record| (|:| |mainpart| (|Fraction| |#2|)) (|:| |limitedlogs| (|List| (|Record| (|:| |coeff| (|Fraction| |#2|)) (|:| |logand| (|Fraction| |#2|)))))) "failed") (|Fraction| |#2|) (|Mapping| |#2| |#2|) (|List| (|Fraction| |#2|))) "\\spad{primlimintfrac(f, ', [u1,...,un])} returns \\spad{[v, [c1,...,cn]]} such that \\spad{ci' = 0} and \\spad{f = v' + +/[ci * ui'/ui]}. Error: if \\spad{degree numer f >= degree denom f}.")) (|primextintfrac| (((|Union| (|Record| (|:| |ratpart| (|Fraction| |#2|)) (|:| |coeff| (|Fraction| |#2|))) "failed") (|Fraction| |#2|) (|Mapping| |#2| |#2|) (|Fraction| |#2|)) "\\spad{primextintfrac(f, ', g)} returns \\spad{[v, c]} such that \\spad{f = v' + c g} and \\spad{c' = 0}. Error: if \\spad{degree numer f >= degree denom f} or if \\spad{degree numer g >= degree denom g} or if \\spad{denom g} is not squarefree.")) (|explimitedint| (((|Union| (|Record| (|:| |answer| (|Record| (|:| |mainpart| (|Fraction| |#2|)) (|:| |limitedlogs| (|List| (|Record| (|:| |coeff| (|Fraction| |#2|)) (|:| |logand| (|Fraction| |#2|))))))) (|:| |a0| |#1|)) "failed") (|Fraction| |#2|) (|Mapping| |#2| |#2|) (|Mapping| (|Record| (|:| |ans| |#1|) (|:| |right| |#1|) (|:| |sol?| (|Boolean|))) (|Integer|) |#1|) (|List| (|Fraction| |#2|))) "\\spad{explimitedint(f, ', foo, [u1,...,un])} returns \\spad{[v, [c1,...,cn], a]} such that \\spad{ci' = 0},{} \\spad{f = v' + a + reduce(+,[ci * ui'/ui])},{} and \\spad{a = 0} or \\spad{a} has no integral in \\spad{F}. Returns \"failed\" if no such \\spad{v},{} \\spad{ci},{} a exist. Argument \\spad{foo} is a Risch differential equation function on \\spad{F}.")) (|primlimitedint| (((|Union| (|Record| (|:| |answer| (|Record| (|:| |mainpart| (|Fraction| |#2|)) (|:| |limitedlogs| (|List| (|Record| (|:| |coeff| (|Fraction| |#2|)) (|:| |logand| (|Fraction| |#2|))))))) (|:| |a0| |#1|)) "failed") (|Fraction| |#2|) (|Mapping| |#2| |#2|) (|Mapping| (|Union| (|Record| (|:| |ratpart| |#1|) (|:| |coeff| |#1|)) "failed") |#1|) (|List| (|Fraction| |#2|))) "\\spad{primlimitedint(f, ', foo, [u1,...,un])} returns \\spad{[v, [c1,...,cn], a]} such that \\spad{ci' = 0},{} \\spad{f = v' + a + reduce(+,[ci * ui'/ui])},{} and \\spad{a = 0} or \\spad{a} has no integral in UP. Returns \"failed\" if no such \\spad{v},{} \\spad{ci},{} a exist. Argument \\spad{foo} is an extended integration function on \\spad{F}.")) (|expextendedint| (((|Union| (|Record| (|:| |answer| (|Fraction| |#2|)) (|:| |a0| |#1|)) (|Record| (|:| |ratpart| (|Fraction| |#2|)) (|:| |coeff| (|Fraction| |#2|))) "failed") (|Fraction| |#2|) (|Mapping| |#2| |#2|) (|Mapping| (|Record| (|:| |ans| |#1|) (|:| |right| |#1|) (|:| |sol?| (|Boolean|))) (|Integer|) |#1|) (|Fraction| |#2|)) "\\spad{expextendedint(f, ', foo, g)} returns either \\spad{[v, c]} such that \\spad{f = v' + c g} and \\spad{c' = 0},{} or \\spad{[v, a]} such that \\spad{f = g' + a},{} and \\spad{a = 0} or \\spad{a} has no integral in \\spad{F}. Returns \"failed\" if neither case can hold. Argument \\spad{foo} is a Risch differential equation function on \\spad{F}.")) (|primextendedint| (((|Union| (|Record| (|:| |answer| (|Fraction| |#2|)) (|:| |a0| |#1|)) (|Record| (|:| |ratpart| (|Fraction| |#2|)) (|:| |coeff| (|Fraction| |#2|))) "failed") (|Fraction| |#2|) (|Mapping| |#2| |#2|) (|Mapping| (|Union| (|Record| (|:| |ratpart| |#1|) (|:| |coeff| |#1|)) "failed") |#1|) (|Fraction| |#2|)) "\\spad{primextendedint(f, ', foo, g)} returns either \\spad{[v, c]} such that \\spad{f = v' + c g} and \\spad{c' = 0},{} or \\spad{[v, a]} such that \\spad{f = g' + a},{} and \\spad{a = 0} or \\spad{a} has no integral in UP. Returns \"failed\" if neither case can hold. Argument \\spad{foo} is an extended integration function on \\spad{F}.")) (|tanintegrate| (((|Record| (|:| |answer| (|IntegrationResult| (|Fraction| |#2|))) (|:| |a0| |#1|)) (|Fraction| |#2|) (|Mapping| |#2| |#2|) (|Mapping| (|Union| (|List| |#1|) "failed") (|Integer|) |#1| |#1|)) "\\spad{tanintegrate(f, ', foo)} returns \\spad{[g, a]} such that \\spad{f = g' + a},{} and \\spad{a = 0} or \\spad{a} has no integral in \\spad{F}; Argument foo is a Risch differential system solver on \\spad{F}.")) (|expintegrate| (((|Record| (|:| |answer| (|IntegrationResult| (|Fraction| |#2|))) (|:| |a0| |#1|)) (|Fraction| |#2|) (|Mapping| |#2| |#2|) (|Mapping| (|Record| (|:| |ans| |#1|) (|:| |right| |#1|) (|:| |sol?| (|Boolean|))) (|Integer|) |#1|)) "\\spad{expintegrate(f, ', foo)} returns \\spad{[g, a]} such that \\spad{f = g' + a},{} and \\spad{a = 0} or \\spad{a} has no integral in \\spad{F}; Argument foo is a Risch differential equation solver on \\spad{F}.")) (|primintegrate| (((|Record| (|:| |answer| (|IntegrationResult| (|Fraction| |#2|))) (|:| |a0| |#1|)) (|Fraction| |#2|) (|Mapping| |#2| |#2|) (|Mapping| (|Union| (|Record| (|:| |ratpart| |#1|) (|:| |coeff| |#1|)) "failed") |#1|)) "\\spad{primintegrate(f, ', foo)} returns \\spad{[g, a]} such that \\spad{f = g' + a},{} and \\spad{a = 0} or \\spad{a} has no integral in UP. Argument foo is an extended integration function on \\spad{F}."))) NIL NIL -(-589 R -4164) +(-589 R -4140) ((|constructor| (NIL "This package computes the inverse Laplace Transform.")) (|inverseLaplace| (((|Union| |#2| "failed") |#2| (|Symbol|) (|Symbol|)) "\\spad{inverseLaplace(f, s, t)} returns the Inverse Laplace transform of \\spad{f(s)} using \\spad{t} as the new variable or \"failed\" if unable to find a closed form."))) NIL NIL @@ -2316,15 +2316,15 @@ NIL ((|constructor| (NIL "A package to print strings without line-feed nor carriage-return.")) (|iprint| (((|Void|) (|String|)) "\\axiom{iprint(\\spad{s})} prints \\axiom{\\spad{s}} at the current position of the cursor."))) NIL NIL -(-597 -4164) +(-597 -4140) ((|constructor| (NIL "If a function \\spad{f} has an elementary integral \\spad{g},{} then \\spad{g} can be written in the form \\spad{g = h + c1 log(u1) + c2 log(u2) + ... + cn log(un)} where \\spad{h},{} which is in the same field than \\spad{f},{} is called the rational part of the integral,{} and \\spad{c1 log(u1) + ... cn log(un)} is called the logarithmic part of the integral. This domain manipulates integrals represented in that form,{} by keeping both parts separately. The logs are not explicitly computed.")) (|differentiate| ((|#1| $ (|Symbol|)) "\\spad{differentiate(ir,x)} differentiates \\spad{ir} with respect to \\spad{x}") ((|#1| $ (|Mapping| |#1| |#1|)) "\\spad{differentiate(ir,D)} differentiates \\spad{ir} with respect to the derivation \\spad{D}.")) (|integral| (($ |#1| (|Symbol|)) "\\spad{integral(f,x)} returns the formal integral of \\spad{f} with respect to \\spad{x}") (($ |#1| |#1|) "\\spad{integral(f,x)} returns the formal integral of \\spad{f} with respect to \\spad{x}")) (|elem?| (((|Boolean|) $) "\\spad{elem?(ir)} tests if an integration result is elementary over F?")) (|notelem| (((|List| (|Record| (|:| |integrand| |#1|) (|:| |intvar| |#1|))) $) "\\spad{notelem(ir)} returns the non-elementary part of an integration result")) (|logpart| (((|List| (|Record| (|:| |scalar| (|Fraction| (|Integer|))) (|:| |coeff| (|SparseUnivariatePolynomial| |#1|)) (|:| |logand| (|SparseUnivariatePolynomial| |#1|)))) $) "\\spad{logpart(ir)} returns the logarithmic part of an integration result")) (|ratpart| ((|#1| $) "\\spad{ratpart(ir)} returns the rational part of an integration result")) (|mkAnswer| (($ |#1| (|List| (|Record| (|:| |scalar| (|Fraction| (|Integer|))) (|:| |coeff| (|SparseUnivariatePolynomial| |#1|)) (|:| |logand| (|SparseUnivariatePolynomial| |#1|)))) (|List| (|Record| (|:| |integrand| |#1|) (|:| |intvar| |#1|)))) "\\spad{mkAnswer(r,l,ne)} creates an integration result from a rational part \\spad{r},{} a logarithmic part \\spad{l},{} and a non-elementary part \\spad{ne}."))) ((-4505 . T) (-4504 . T)) ((|HasCategory| |#1| (|%list| (QUOTE -928) (QUOTE (-1209)))) (|HasCategory| |#1| (|%list| (QUOTE -1070) (QUOTE (-1209))))) -(-598 E -4164) +(-598 E -4140) ((|constructor| (NIL "\\indented{1}{Internally used by the integration packages} Author: Manuel Bronstein Date Created: 1987 Date Last Updated: 12 August 1992 Keywords: integration.")) (|map| (((|Union| (|Record| (|:| |mainpart| |#2|) (|:| |limitedlogs| (|List| (|Record| (|:| |coeff| |#2|) (|:| |logand| |#2|))))) "failed") (|Mapping| |#2| |#1|) (|Union| (|Record| (|:| |mainpart| |#1|) (|:| |limitedlogs| (|List| (|Record| (|:| |coeff| |#1|) (|:| |logand| |#1|))))) "failed")) "\\spad{map(f,ufe)} \\undocumented") (((|Union| |#2| "failed") (|Mapping| |#2| |#1|) (|Union| |#1| "failed")) "\\spad{map(f,ue)} \\undocumented") (((|Union| (|Record| (|:| |ratpart| |#2|) (|:| |coeff| |#2|)) "failed") (|Mapping| |#2| |#1|) (|Union| (|Record| (|:| |ratpart| |#1|) (|:| |coeff| |#1|)) "failed")) "\\spad{map(f,ure)} \\undocumented") (((|IntegrationResult| |#2|) (|Mapping| |#2| |#1|) (|IntegrationResult| |#1|)) "\\spad{map(f,ire)} \\undocumented"))) NIL NIL -(-599 R -4164) +(-599 R -4140) ((|constructor| (NIL "This package allows a sum of logs over the roots of a polynomial to be expressed as explicit logarithms and arc tangents,{} provided that the indexing polynomial can be factored into quadratics.")) (|complexExpand| ((|#2| (|IntegrationResult| |#2|)) "\\spad{complexExpand(i)} returns the expanded complex function corresponding to \\spad{i}.")) (|expand| (((|List| |#2|) (|IntegrationResult| |#2|)) "\\spad{expand(i)} returns the list of possible real functions corresponding to \\spad{i}.")) (|split| (((|IntegrationResult| |#2|) (|IntegrationResult| |#2|)) "\\spad{split(u(x) + sum_{P(a)=0} Q(a,x))} returns \\spad{u(x) + sum_{P1(a)=0} Q(a,x) + ... + sum_{Pn(a)=0} Q(a,x)} where \\spad{P1},{}...,{}Pn are the factors of \\spad{P}."))) NIL NIL @@ -2359,7 +2359,7 @@ NIL (-607 |mn|) ((|constructor| (NIL "This domain implements low-level strings"))) ((-4511 . T) (-4510 . T)) -((-4144 (-12 (|HasCategory| (-146) (QUOTE (-872))) (|HasCategory| (-146) (|%list| (QUOTE -321) (QUOTE (-146))))) (-12 (|HasCategory| (-146) (QUOTE (-1133))) (|HasCategory| (-146) (|%list| (QUOTE -321) (QUOTE (-146)))))) (-4144 (|HasCategory| (-146) (|%list| (QUOTE -632) (QUOTE (-888)))) (-12 (|HasCategory| (-146) (QUOTE (-1133))) (|HasCategory| (-146) (|%list| (QUOTE -321) (QUOTE (-146)))))) (|HasCategory| (-146) (|%list| (QUOTE -633) (QUOTE (-549)))) (-4144 (|HasCategory| (-146) (QUOTE (-872))) (|HasCategory| (-146) (QUOTE (-1133)))) (|HasCategory| (-146) (QUOTE (-872))) (-4144 (|HasCategory| (-146) (QUOTE (-102))) (|HasCategory| (-146) (QUOTE (-872))) (|HasCategory| (-146) (QUOTE (-1133)))) (|HasCategory| (-560) (QUOTE (-872))) (|HasCategory| (-146) (QUOTE (-1133))) (|HasCategory| (-146) (|%list| (QUOTE -632) (QUOTE (-888)))) (|HasCategory| (-146) (QUOTE (-102))) (-12 (|HasCategory| (-146) (QUOTE (-1133))) (|HasCategory| (-146) (|%list| (QUOTE -321) (QUOTE (-146)))))) +((-4118 (-12 (|HasCategory| (-146) (QUOTE (-872))) (|HasCategory| (-146) (|%list| (QUOTE -321) (QUOTE (-146))))) (-12 (|HasCategory| (-146) (QUOTE (-1133))) (|HasCategory| (-146) (|%list| (QUOTE -321) (QUOTE (-146)))))) (-4118 (|HasCategory| (-146) (|%list| (QUOTE -632) (QUOTE (-888)))) (-12 (|HasCategory| (-146) (QUOTE (-1133))) (|HasCategory| (-146) (|%list| (QUOTE -321) (QUOTE (-146)))))) (|HasCategory| (-146) (|%list| (QUOTE -633) (QUOTE (-549)))) (-4118 (|HasCategory| (-146) (QUOTE (-872))) (|HasCategory| (-146) (QUOTE (-1133)))) (|HasCategory| (-146) (QUOTE (-872))) (-4118 (|HasCategory| (-146) (QUOTE (-102))) (|HasCategory| (-146) (QUOTE (-872))) (|HasCategory| (-146) (QUOTE (-1133)))) (|HasCategory| (-560) (QUOTE (-872))) (|HasCategory| (-146) (QUOTE (-1133))) (|HasCategory| (-146) (|%list| (QUOTE -632) (QUOTE (-888)))) (|HasCategory| (-146) (QUOTE (-102))) (-12 (|HasCategory| (-146) (QUOTE (-1133))) (|HasCategory| (-146) (|%list| (QUOTE -321) (QUOTE (-146)))))) (-608 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 @@ -2367,7 +2367,7 @@ NIL (-609 |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}."))) (((-4512 "*") |has| |#1| (-175)) (-4503 |has| |#1| (-571)) (-4504 . T) (-4505 . T) (-4507 . T)) -((|HasCategory| |#1| (|%list| (QUOTE -38) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#1| (QUOTE (-571))) (-4144 (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-571)))) (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-149))) (-12 (|HasCategory| |#1| (|%list| (QUOTE -928) (QUOTE (-1209)))) (|HasSignature| |#1| (|%list| (QUOTE *) (|%list| (|devaluate| |#1|) (QUOTE (-560)) (|devaluate| |#1|))))) (|HasSignature| |#1| (|%list| (QUOTE *) (|%list| (|devaluate| |#1|) (QUOTE (-560)) (|devaluate| |#1|)))) (|HasCategory| (-560) (QUOTE (-1144))) (|HasCategory| |#1| (QUOTE (-376))) (-12 (|HasSignature| |#1| (|%list| (QUOTE **) (|%list| (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-560))))) (|HasSignature| |#1| (|%list| (QUOTE -3903) (|%list| (|devaluate| |#1|) (QUOTE (-1209)))))) (|HasSignature| |#1| (|%list| (QUOTE **) (|%list| (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-560)))))) +((|HasCategory| |#1| (|%list| (QUOTE -38) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#1| (QUOTE (-571))) (-4118 (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-571)))) (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-149))) (-12 (|HasCategory| |#1| (|%list| (QUOTE -928) (QUOTE (-1209)))) (|HasSignature| |#1| (|%list| (QUOTE *) (|%list| (|devaluate| |#1|) (QUOTE (-560)) (|devaluate| |#1|))))) (|HasSignature| |#1| (|%list| (QUOTE *) (|%list| (|devaluate| |#1|) (QUOTE (-560)) (|devaluate| |#1|)))) (|HasCategory| (-560) (QUOTE (-1144))) (|HasCategory| |#1| (QUOTE (-376))) (-12 (|HasSignature| |#1| (|%list| (QUOTE **) (|%list| (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-560))))) (|HasSignature| |#1| (|%list| (QUOTE -3866) (|%list| (|devaluate| |#1|) (QUOTE (-1209)))))) (|HasSignature| |#1| (|%list| (QUOTE **) (|%list| (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-560)))))) (-610 |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.}"))) (((-4512 "*") |has| |#1| (-571)) (-4503 |has| |#1| (-571)) (-4504 . T) (-4505 . T) (-4507 . T)) @@ -2384,7 +2384,7 @@ NIL ((|constructor| (NIL "Functions defined on streams with entries in two sets.")) (|map| (((|Stream| |#3|) (|Mapping| |#3| |#1| |#2|) (|InfiniteTuple| |#1|) (|Stream| |#2|)) "\\spad{map(f,a,b)} \\undocumented") (((|Stream| |#3|) (|Mapping| |#3| |#1| |#2|) (|Stream| |#1|) (|InfiniteTuple| |#2|)) "\\spad{map(f,a,b)} \\undocumented") (((|InfiniteTuple| |#3|) (|Mapping| |#3| |#1| |#2|) (|InfiniteTuple| |#1|) (|InfiniteTuple| |#2|)) "\\spad{map(f,a,b)} \\undocumented"))) NIL NIL -(-614 R -4164 FG) +(-614 R -4140 FG) ((|constructor| (NIL "This package provides transformations from trigonometric functions to exponentials and logarithms,{} and back. \\spad{F} and FG should be the same type of function space.")) (|trigs2explogs| ((|#3| |#3| (|List| (|Kernel| |#3|)) (|List| (|Symbol|))) "\\spad{trigs2explogs(f, [k1,...,kn], [x1,...,xm])} rewrites all the trigonometric functions appearing in \\spad{f} and involving one of the \\spad{xi's} in terms of complex logarithms and exponentials. A kernel of the form \\spad{tan(u)} is expressed using \\spad{exp(u)**2} if it is one of the \\spad{ki's},{} in terms of \\spad{exp(2*u)} otherwise.")) (|explogs2trigs| (((|Complex| |#2|) |#3|) "\\spad{explogs2trigs(f)} rewrites all the complex logs and exponentials appearing in \\spad{f} in terms of trigonometric functions.")) (F2FG ((|#3| |#2|) "\\spad{F2FG(a + sqrt(-1) b)} returns \\spad{a + i b}.")) (FG2F ((|#2| |#3|) "\\spad{FG2F(a + i b)} returns \\spad{a + sqrt(-1) b}.")) (GF2FG ((|#3| (|Complex| |#2|)) "\\spad{GF2FG(a + i b)} returns \\spad{a + i b} viewed as a function with the \\spad{i} pushed down into the coefficient domain."))) NIL NIL @@ -2395,7 +2395,7 @@ NIL (-616 R |mn|) ((|constructor| (NIL "\\indented{2}{This type represents vector like objects with varying lengths} and a user-specified initial index."))) ((-4511 . T) (-4510 . T)) -((-4144 (-12 (|HasCategory| |#1| (QUOTE (-872))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|))))) (-4144 (-12 (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-888))))) (|HasCategory| |#1| (|%list| (QUOTE -633) (QUOTE (-549)))) (-4144 (|HasCategory| |#1| (QUOTE (-872))) (|HasCategory| |#1| (QUOTE (-1133)))) (|HasCategory| |#1| (QUOTE (-872))) (-4144 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-872))) (|HasCategory| |#1| (QUOTE (-1133)))) (|HasCategory| (-560) (QUOTE (-872))) (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#1| (QUOTE (-25))) (|HasCategory| |#1| (QUOTE (-23))) (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-748))) (|HasCategory| |#1| (QUOTE (-1081))) (-12 (|HasCategory| |#1| (QUOTE (-1034))) (|HasCategory| |#1| (QUOTE (-1081)))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-888)))) (|HasCategory| |#1| (QUOTE (-102))) (-12 (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|))))) +((-4118 (-12 (|HasCategory| |#1| (QUOTE (-872))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|))))) (-4118 (-12 (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-888))))) (|HasCategory| |#1| (|%list| (QUOTE -633) (QUOTE (-549)))) (-4118 (|HasCategory| |#1| (QUOTE (-872))) (|HasCategory| |#1| (QUOTE (-1133)))) (|HasCategory| |#1| (QUOTE (-872))) (-4118 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-872))) (|HasCategory| |#1| (QUOTE (-1133)))) (|HasCategory| (-560) (QUOTE (-872))) (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#1| (QUOTE (-25))) (|HasCategory| |#1| (QUOTE (-23))) (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-748))) (|HasCategory| |#1| (QUOTE (-1081))) (-12 (|HasCategory| |#1| (QUOTE (-1034))) (|HasCategory| |#1| (QUOTE (-1081)))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-888)))) (|HasCategory| |#1| (QUOTE (-102))) (-12 (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|))))) (-617 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|) $) "\\spad{entries(u)} returns a list of all the entries of aggregate \\spad{u} in no assumed order."))) NIL @@ -2410,8 +2410,8 @@ NIL NIL (-620 R A) ((|constructor| (NIL "\\indented{1}{AssociatedJordanAlgebra takes an algebra \\spad{A} and uses \\spadfun{*\\$A}} \\indented{1}{to define the new multiplications \\spad{a*b := (a *\\$A b + b *\\$A a)/2}} \\indented{1}{(anticommutator).} \\indented{1}{The usual notation \\spad{{a,b}_+} cannot be used due to} \\indented{1}{restrictions in the current language.} \\indented{1}{This domain only gives a Jordan algebra if the} \\indented{1}{Jordan-identity \\spad{(a*b)*c + (b*c)*a + (c*a)*b = 0} holds} \\indented{1}{for all \\spad{a},{}\\spad{b},{}\\spad{c} in \\spad{A}.} \\indented{1}{This relation can be checked by} \\indented{1}{\\spadfun{jordanAdmissible?()\\$A}.} \\blankline If the underlying algebra is of type \\spadtype{FramedNonAssociativeAlgebra(R)} (\\spadignore{i.e.} a non associative algebra over \\spad{R} which is a free \\spad{R}-module of finite rank,{} together with a fixed \\spad{R}-module basis),{} then the same is \\spad{true} for the associated Jordan algebra. Moreover,{} if the underlying algebra is of type \\spadtype{FiniteRankNonAssociativeAlgebra(R)} (\\spadignore{i.e.} a non associative algebra over \\spad{R} which is a free \\spad{R}-module of finite rank),{} then the same \\spad{true} for the associated Jordan algebra.")) (|coerce| (($ |#2|) "\\spad{coerce(a)} coerces the element \\spad{a} of the algebra \\spad{A} to an element of the Jordan algebra \\spadtype{AssociatedJordanAlgebra}(\\spad{R},{}A)."))) -((-4507 -4144 (-2609 (|has| |#2| (-380 |#1|)) (|has| |#1| (-571))) (-12 (|has| |#2| (-432 |#1|)) (|has| |#1| (-571)))) (-4505 . T) (-4504 . T)) -((-4144 (|HasCategory| |#2| (|%list| (QUOTE -380) (|devaluate| |#1|))) (|HasCategory| |#2| (|%list| (QUOTE -432) (|devaluate| |#1|)))) (|HasCategory| |#2| (|%list| (QUOTE -432) (|devaluate| |#1|))) (-12 (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#2| (|%list| (QUOTE -432) (|devaluate| |#1|)))) (-4144 (-12 (|HasCategory| |#1| (QUOTE (-571))) (|HasCategory| |#2| (|%list| (QUOTE -380) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-571))) (|HasCategory| |#2| (|%list| (QUOTE -432) (|devaluate| |#1|))))) (|HasCategory| |#2| (|%list| (QUOTE -380) (|devaluate| |#1|)))) +((-4507 -4118 (-2596 (|has| |#2| (-380 |#1|)) (|has| |#1| (-571))) (-12 (|has| |#2| (-432 |#1|)) (|has| |#1| (-571)))) (-4505 . T) (-4504 . T)) +((-4118 (|HasCategory| |#2| (|%list| (QUOTE -380) (|devaluate| |#1|))) (|HasCategory| |#2| (|%list| (QUOTE -432) (|devaluate| |#1|)))) (|HasCategory| |#2| (|%list| (QUOTE -432) (|devaluate| |#1|))) (-12 (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#2| (|%list| (QUOTE -432) (|devaluate| |#1|)))) (-4118 (-12 (|HasCategory| |#1| (QUOTE (-571))) (|HasCategory| |#2| (|%list| (QUOTE -380) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-571))) (|HasCategory| |#2| (|%list| (QUOTE -432) (|devaluate| |#1|))))) (|HasCategory| |#2| (|%list| (QUOTE -380) (|devaluate| |#1|)))) (-621) ((|constructor| (NIL "This is the datatype for the JVM bytecodes."))) NIL @@ -2439,7 +2439,7 @@ NIL (-627 |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."))) ((-4510 . T) (-4511 . T)) -((-12 (|HasCategory| (-2 (|:| -2118 (-1191)) (|:| -3964 |#1|)) (QUOTE (-1133))) (|HasCategory| (-2 (|:| -2118 (-1191)) (|:| -3964 |#1|)) (|%list| (QUOTE -321) (|%list| (QUOTE -2) (|%list| (QUOTE |:|) (QUOTE -2118) (QUOTE (-1191))) (|%list| (QUOTE |:|) (QUOTE -3964) (|devaluate| |#1|)))))) (|HasCategory| (-2 (|:| -2118 (-1191)) (|:| -3964 |#1|)) (|%list| (QUOTE -633) (QUOTE (-549)))) (-12 (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| (-1191) (QUOTE (-872))) (|HasCategory| (-2 (|:| -2118 (-1191)) (|:| -3964 |#1|)) (QUOTE (-1133))) (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-888)))) (|HasCategory| (-2 (|:| -2118 (-1191)) (|:| -3964 |#1|)) (|%list| (QUOTE -632) (QUOTE (-888)))) (|HasCategory| (-2 (|:| -2118 (-1191)) (|:| -3964 |#1|)) (QUOTE (-102)))) +((-12 (|HasCategory| (-2 (|:| -2115 (-1191)) (|:| -3934 |#1|)) (QUOTE (-1133))) (|HasCategory| (-2 (|:| -2115 (-1191)) (|:| -3934 |#1|)) (|%list| (QUOTE -321) (|%list| (QUOTE -2) (|%list| (QUOTE |:|) (QUOTE -2115) (QUOTE (-1191))) (|%list| (QUOTE |:|) (QUOTE -3934) (|devaluate| |#1|)))))) (|HasCategory| (-2 (|:| -2115 (-1191)) (|:| -3934 |#1|)) (|%list| (QUOTE -633) (QUOTE (-549)))) (-12 (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| (-1191) (QUOTE (-872))) (|HasCategory| (-2 (|:| -2115 (-1191)) (|:| -3934 |#1|)) (QUOTE (-1133))) (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-888)))) (|HasCategory| (-2 (|:| -2115 (-1191)) (|:| -3934 |#1|)) (|%list| (QUOTE -632) (QUOTE (-888)))) (|HasCategory| (-2 (|:| -2115 (-1191)) (|:| -3934 |#1|)) (QUOTE (-102)))) (-628 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 @@ -2464,7 +2464,7 @@ NIL ((|constructor| (NIL "A is convertible to \\spad{B} means any element of A can be converted into an element of \\spad{B},{} but not automatically by the interpreter.")) (|convert| ((|#1| $) "\\spad{convert(a)} transforms a into an element of \\spad{S}."))) NIL NIL -(-634 -4164 UP) +(-634 -4140 UP) ((|constructor| (NIL "\\spadtype{Kovacic} provides a modified Kovacic's algorithm for solving explicitely irreducible 2nd order linear ordinary differential equations.")) (|kovacic| (((|Union| (|SparseUnivariatePolynomial| (|Fraction| |#2|)) "failed") (|Fraction| |#2|) (|Fraction| |#2|) (|Fraction| |#2|) (|Mapping| (|Factored| |#2|) |#2|)) "\\spad{kovacic(a_0,a_1,a_2,ezfactor)} returns either \"failed\" or \\spad{P}(\\spad{u}) such that \\spad{\\$e^{\\int(-a_1/2a_2)} e^{\\int u}\\$} is a solution of \\indented{5}{\\spad{\\$a_2 y'' + a_1 y' + a0 y = 0\\$}} whenever \\spad{u} is a solution of \\spad{P u = 0}. The equation must be already irreducible over the rational functions. Argument \\spad{ezfactor} is a factorisation in \\spad{UP},{} not necessarily into irreducibles.") (((|Union| (|SparseUnivariatePolynomial| (|Fraction| |#2|)) "failed") (|Fraction| |#2|) (|Fraction| |#2|) (|Fraction| |#2|)) "\\spad{kovacic(a_0,a_1,a_2)} returns either \"failed\" or \\spad{P}(\\spad{u}) such that \\spad{\\$e^{\\int(-a_1/2a_2)} e^{\\int u}\\$} is a solution of \\indented{5}{\\spad{a_2 y'' + a_1 y' + a0 y = 0}} whenever \\spad{u} is a solution of \\spad{P u = 0}. The equation must be already irreducible over the rational functions."))) NIL NIL @@ -2492,7 +2492,7 @@ NIL ((|constructor| (NIL "The category of all left algebras over an arbitrary ring.")) (|coerce| (($ |#1|) "\\spad{coerce(r)} returns \\spad{r} * 1 where 1 is the identity of the left algebra."))) ((-4507 . T)) NIL -(-641 R -4164) +(-641 R -4140) ((|constructor| (NIL "This package computes the forward Laplace Transform.")) (|laplace| ((|#2| |#2| (|Symbol|) (|Symbol|)) "\\spad{laplace(f, t, s)} returns the Laplace transform of \\spad{f(t)} using \\spad{s} as the new variable. This is \\spad{integral(exp(-s*t)*f(t), t = 0..\\%plusInfinity)}. Returns the formal object \\spad{laplace(f, t, s)} if it cannot compute the transform."))) NIL NIL @@ -2520,7 +2520,7 @@ NIL ((|constructor| (NIL "A package for solving polynomial systems with finitely many solutions. The decompositions are given by means of regular triangular sets. The computations use lexicographical Groebner bases. The main operations are \\axiomOpFrom{lexTriangular}{LexTriangularPackage} and \\axiomOpFrom{squareFreeLexTriangular}{LexTriangularPackage}. The second one provide decompositions by means of square-free regular triangular sets. Both are based on the {\\em lexTriangular} method described in [1]. They differ from the algorithm described in [2] by the fact that multiciplities of the roots are not kept. With the \\axiomOpFrom{squareFreeLexTriangular}{LexTriangularPackage} operation all multiciplities are removed. With the other operation some multiciplities may remain. Both operations admit an optional argument to produce normalized triangular sets. \\newline")) (|zeroSetSplit| (((|List| (|SquareFreeRegularTriangularSet| |#1| (|IndexedExponents| (|OrderedVariableList| |#2|)) (|OrderedVariableList| |#2|) (|NewSparseMultivariatePolynomial| |#1| (|OrderedVariableList| |#2|)))) (|List| (|NewSparseMultivariatePolynomial| |#1| (|OrderedVariableList| |#2|))) (|Boolean|)) "\\axiom{zeroSetSplit(lp,{} norm?)} decomposes the variety associated with \\axiom{lp} into square-free regular chains. Thus a point belongs to this variety iff it is a regular zero of a regular set in in the output. Note that \\axiom{lp} needs to generate a zero-dimensional ideal. If \\axiom{norm?} is \\axiom{\\spad{true}} then the regular sets are normalized.") (((|List| (|RegularChain| |#1| |#2|)) (|List| (|NewSparseMultivariatePolynomial| |#1| (|OrderedVariableList| |#2|))) (|Boolean|)) "\\axiom{zeroSetSplit(lp,{} norm?)} decomposes the variety associated with \\axiom{lp} into regular chains. Thus a point belongs to this variety iff it is a regular zero of a regular set in in the output. Note that \\axiom{lp} needs to generate a zero-dimensional ideal. If \\axiom{norm?} is \\axiom{\\spad{true}} then the regular sets are normalized.")) (|squareFreeLexTriangular| (((|List| (|SquareFreeRegularTriangularSet| |#1| (|IndexedExponents| (|OrderedVariableList| |#2|)) (|OrderedVariableList| |#2|) (|NewSparseMultivariatePolynomial| |#1| (|OrderedVariableList| |#2|)))) (|List| (|NewSparseMultivariatePolynomial| |#1| (|OrderedVariableList| |#2|))) (|Boolean|)) "\\axiom{squareFreeLexTriangular(base,{} norm?)} decomposes the variety associated with \\axiom{base} into square-free regular chains. Thus a point belongs to this variety iff it is a regular zero of a regular set in in the output. Note that \\axiom{base} needs to be a lexicographical Groebner basis of a zero-dimensional ideal. If \\axiom{norm?} is \\axiom{\\spad{true}} then the regular sets are normalized.")) (|lexTriangular| (((|List| (|RegularChain| |#1| |#2|)) (|List| (|NewSparseMultivariatePolynomial| |#1| (|OrderedVariableList| |#2|))) (|Boolean|)) "\\axiom{lexTriangular(base,{} norm?)} decomposes the variety associated with \\axiom{base} into regular chains. Thus a point belongs to this variety iff it is a regular zero of a regular set in in the output. Note that \\axiom{base} needs to be a lexicographical Groebner basis of a zero-dimensional ideal. If \\axiom{norm?} is \\axiom{\\spad{true}} then the regular sets are normalized.")) (|groebner| (((|List| (|NewSparseMultivariatePolynomial| |#1| (|OrderedVariableList| |#2|))) (|List| (|NewSparseMultivariatePolynomial| |#1| (|OrderedVariableList| |#2|)))) "\\axiom{groebner(lp)} returns the lexicographical Groebner basis of \\axiom{lp}. If \\axiom{lp} generates a zero-dimensional ideal then the {\\em FGLM} strategy is used,{} otherwise the {\\em Sugar} strategy is used.")) (|fglmIfCan| (((|Union| (|List| (|NewSparseMultivariatePolynomial| |#1| (|OrderedVariableList| |#2|))) "failed") (|List| (|NewSparseMultivariatePolynomial| |#1| (|OrderedVariableList| |#2|)))) "\\axiom{fglmIfCan(lp)} returns the lexicographical Groebner basis of \\axiom{lp} by using the {\\em FGLM} strategy,{} if \\axiom{zeroDimensional?(lp)} holds .")) (|zeroDimensional?| (((|Boolean|) (|List| (|NewSparseMultivariatePolynomial| |#1| (|OrderedVariableList| |#2|)))) "\\axiom{zeroDimensional?(lp)} returns \\spad{true} iff \\axiom{lp} generates a zero-dimensional ideal \\spad{w}.\\spad{r}.\\spad{t}. the variables involved in \\axiom{lp}."))) NIL NIL -(-648 R -4164) +(-648 R -4140) ((|constructor| (NIL "This package provides liouvillian functions over an integral domain.")) (|integral| ((|#2| |#2| (|SegmentBinding| |#2|)) "\\spad{integral(f,x = a..b)} denotes the definite integral of \\spad{f} with respect to \\spad{x} from \\spad{a} to \\spad{b}.") ((|#2| |#2| (|Symbol|)) "\\spad{integral(f,x)} indefinite integral of \\spad{f} with respect to \\spad{x}.")) (|dilog| ((|#2| |#2|) "\\spad{dilog(f)} denotes the dilogarithm")) (|erf| ((|#2| |#2|) "\\spad{erf(f)} denotes the error function")) (|li| ((|#2| |#2|) "\\spad{li(f)} denotes the logarithmic integral")) (|Ci| ((|#2| |#2|) "\\spad{Ci(f)} denotes the cosine integral")) (|Si| ((|#2| |#2|) "\\spad{Si(f)} denotes the sine integral")) (|Ei| ((|#2| |#2|) "\\spad{Ei(f)} denotes the exponential integral")) (|operator| (((|BasicOperator|) (|BasicOperator|)) "\\spad{operator(op)} returns the Liouvillian operator based on \\spad{op}")) (|belong?| (((|Boolean|) (|BasicOperator|)) "\\spad{belong?(op)} checks if \\spad{op} is Liouvillian"))) NIL NIL @@ -2528,18 +2528,18 @@ 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 -(-650 |lv| -4164) +(-650 |lv| -4140) ((|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 (-651) ((|constructor| (NIL "This domain provides a simple way to save values in files.")) (|setelt| (((|Any|) $ (|Symbol|) (|Any|)) "\\spad{lib.k := v} saves the value \\spad{v} in the library \\spad{lib}. It can later be extracted using the key \\spad{k}.")) (|pack!| (($ $) "\\spad{pack!(f)} reorganizes the file \\spad{f} on disk to recover unused space.")) (|library| (($ (|FileName|)) "\\spad{library(ln)} creates a new library file."))) ((-4511 . T)) -((-12 (|HasCategory| (-2 (|:| -2118 (-1191)) (|:| -3964 (-51))) (QUOTE (-1133))) (|HasCategory| (-2 (|:| -2118 (-1191)) (|:| -3964 (-51))) (|%list| (QUOTE -321) (|%list| (QUOTE -2) (|%list| (QUOTE |:|) (QUOTE -2118) (QUOTE (-1191))) (|%list| (QUOTE |:|) (QUOTE -3964) (QUOTE (-51))))))) (-4144 (|HasCategory| (-2 (|:| -2118 (-1191)) (|:| -3964 (-51))) (QUOTE (-1133))) (|HasCategory| (-51) (QUOTE (-1133)))) (-4144 (|HasCategory| (-2 (|:| -2118 (-1191)) (|:| -3964 (-51))) (QUOTE (-102))) (|HasCategory| (-2 (|:| -2118 (-1191)) (|:| -3964 (-51))) (QUOTE (-1133))) (|HasCategory| (-51) (QUOTE (-102))) (|HasCategory| (-51) (QUOTE (-1133)))) (-4144 (|HasCategory| (-2 (|:| -2118 (-1191)) (|:| -3964 (-51))) (QUOTE (-1133))) (|HasCategory| (-2 (|:| -2118 (-1191)) (|:| -3964 (-51))) (|%list| (QUOTE -632) (QUOTE (-888)))) (|HasCategory| (-51) (QUOTE (-1133))) (|HasCategory| (-51) (|%list| (QUOTE -632) (QUOTE (-888))))) (|HasCategory| (-2 (|:| -2118 (-1191)) (|:| -3964 (-51))) (|%list| (QUOTE -633) (QUOTE (-549)))) (-12 (|HasCategory| (-51) (QUOTE (-1133))) (|HasCategory| (-51) (|%list| (QUOTE -321) (QUOTE (-51))))) (|HasCategory| (-1191) (QUOTE (-872))) (-4144 (|HasCategory| (-2 (|:| -2118 (-1191)) (|:| -3964 (-51))) (|%list| (QUOTE -632) (QUOTE (-888)))) (|HasCategory| (-51) (|%list| (QUOTE -632) (QUOTE (-888))))) (-4144 (|HasCategory| (-2 (|:| -2118 (-1191)) (|:| -3964 (-51))) (QUOTE (-102))) (|HasCategory| (-51) (QUOTE (-102)))) (|HasCategory| (-51) (QUOTE (-1133))) (|HasCategory| (-51) (QUOTE (-102))) (|HasCategory| (-51) (|%list| (QUOTE -632) (QUOTE (-888)))) (|HasCategory| (-2 (|:| -2118 (-1191)) (|:| -3964 (-51))) (|%list| (QUOTE -632) (QUOTE (-888)))) (|HasCategory| (-2 (|:| -2118 (-1191)) (|:| -3964 (-51))) (QUOTE (-102))) (|HasCategory| (-2 (|:| -2118 (-1191)) (|:| -3964 (-51))) (QUOTE (-1133)))) +((-12 (|HasCategory| (-2 (|:| -2115 (-1191)) (|:| -3934 (-51))) (QUOTE (-1133))) (|HasCategory| (-2 (|:| -2115 (-1191)) (|:| -3934 (-51))) (|%list| (QUOTE -321) (|%list| (QUOTE -2) (|%list| (QUOTE |:|) (QUOTE -2115) (QUOTE (-1191))) (|%list| (QUOTE |:|) (QUOTE -3934) (QUOTE (-51))))))) (-4118 (|HasCategory| (-2 (|:| -2115 (-1191)) (|:| -3934 (-51))) (QUOTE (-1133))) (|HasCategory| (-51) (QUOTE (-1133)))) (-4118 (|HasCategory| (-2 (|:| -2115 (-1191)) (|:| -3934 (-51))) (QUOTE (-102))) (|HasCategory| (-2 (|:| -2115 (-1191)) (|:| -3934 (-51))) (QUOTE (-1133))) (|HasCategory| (-51) (QUOTE (-102))) (|HasCategory| (-51) (QUOTE (-1133)))) (-4118 (|HasCategory| (-2 (|:| -2115 (-1191)) (|:| -3934 (-51))) (QUOTE (-1133))) (|HasCategory| (-2 (|:| -2115 (-1191)) (|:| -3934 (-51))) (|%list| (QUOTE -632) (QUOTE (-888)))) (|HasCategory| (-51) (QUOTE (-1133))) (|HasCategory| (-51) (|%list| (QUOTE -632) (QUOTE (-888))))) (|HasCategory| (-2 (|:| -2115 (-1191)) (|:| -3934 (-51))) (|%list| (QUOTE -633) (QUOTE (-549)))) (-12 (|HasCategory| (-51) (QUOTE (-1133))) (|HasCategory| (-51) (|%list| (QUOTE -321) (QUOTE (-51))))) (|HasCategory| (-1191) (QUOTE (-872))) (-4118 (|HasCategory| (-2 (|:| -2115 (-1191)) (|:| -3934 (-51))) (|%list| (QUOTE -632) (QUOTE (-888)))) (|HasCategory| (-51) (|%list| (QUOTE -632) (QUOTE (-888))))) (-4118 (|HasCategory| (-2 (|:| -2115 (-1191)) (|:| -3934 (-51))) (QUOTE (-102))) (|HasCategory| (-51) (QUOTE (-102)))) (|HasCategory| (-51) (QUOTE (-1133))) (|HasCategory| (-51) (QUOTE (-102))) (|HasCategory| (-51) (|%list| (QUOTE -632) (QUOTE (-888)))) (|HasCategory| (-2 (|:| -2115 (-1191)) (|:| -3934 (-51))) (|%list| (QUOTE -632) (QUOTE (-888)))) (|HasCategory| (-2 (|:| -2115 (-1191)) (|:| -3934 (-51))) (QUOTE (-102))) (|HasCategory| (-2 (|:| -2115 (-1191)) (|:| -3934 (-51))) (QUOTE (-1133)))) (-652 R A) ((|constructor| (NIL "AssociatedLieAlgebra takes an algebra \\spad{A} and uses \\spadfun{*\\$A} to define the Lie bracket \\spad{a*b := (a *\\$A b - b *\\$A a)} (commutator). Note that the notation \\spad{[a,b]} cannot be used due to restrictions of the current compiler. This domain only gives a Lie algebra if the Jacobi-identity \\spad{(a*b)*c + (b*c)*a + (c*a)*b = 0} holds for all \\spad{a},{}\\spad{b},{}\\spad{c} in \\spad{A}. This relation can be checked by \\spad{lieAdmissible?()\\$A}. \\blankline If the underlying algebra is of type \\spadtype{FramedNonAssociativeAlgebra(R)} (\\spadignore{i.e.} a non associative algebra over \\spad{R} which is a free \\spad{R}-module of finite rank,{} together with a fixed \\spad{R}-module basis),{} then the same is \\spad{true} for the associated Lie algebra. Also,{} if the underlying algebra is of type \\spadtype{FiniteRankNonAssociativeAlgebra(R)} (\\spadignore{i.e.} a non associative algebra over \\spad{R} which is a free \\spad{R}-module of finite rank),{} then the same is \\spad{true} for the associated Lie algebra.")) (|coerce| (($ |#2|) "\\spad{coerce(a)} coerces the element \\spad{a} of the algebra \\spad{A} to an element of the Lie algebra \\spadtype{AssociatedLieAlgebra}(\\spad{R},{}A)."))) -((-4507 -4144 (-2609 (|has| |#2| (-380 |#1|)) (|has| |#1| (-571))) (-12 (|has| |#2| (-432 |#1|)) (|has| |#1| (-571)))) (-4505 . T) (-4504 . T)) -((-4144 (|HasCategory| |#2| (|%list| (QUOTE -380) (|devaluate| |#1|))) (|HasCategory| |#2| (|%list| (QUOTE -432) (|devaluate| |#1|)))) (|HasCategory| |#2| (|%list| (QUOTE -432) (|devaluate| |#1|))) (-12 (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#2| (|%list| (QUOTE -432) (|devaluate| |#1|)))) (-4144 (-12 (|HasCategory| |#1| (QUOTE (-571))) (|HasCategory| |#2| (|%list| (QUOTE -380) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-571))) (|HasCategory| |#2| (|%list| (QUOTE -432) (|devaluate| |#1|))))) (|HasCategory| |#2| (|%list| (QUOTE -380) (|devaluate| |#1|)))) +((-4507 -4118 (-2596 (|has| |#2| (-380 |#1|)) (|has| |#1| (-571))) (-12 (|has| |#2| (-432 |#1|)) (|has| |#1| (-571)))) (-4505 . T) (-4504 . T)) +((-4118 (|HasCategory| |#2| (|%list| (QUOTE -380) (|devaluate| |#1|))) (|HasCategory| |#2| (|%list| (QUOTE -432) (|devaluate| |#1|)))) (|HasCategory| |#2| (|%list| (QUOTE -432) (|devaluate| |#1|))) (-12 (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#2| (|%list| (QUOTE -432) (|devaluate| |#1|)))) (-4118 (-12 (|HasCategory| |#1| (QUOTE (-571))) (|HasCategory| |#2| (|%list| (QUOTE -380) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-571))) (|HasCategory| |#2| (|%list| (QUOTE -432) (|devaluate| |#1|))))) (|HasCategory| |#2| (|%list| (QUOTE -380) (|devaluate| |#1|)))) (-653 S R) ((|constructor| (NIL "\\axiom{JacobiIdentity} means that \\axiom{[\\spad{x},{}[\\spad{y},{}\\spad{z}]]+[\\spad{y},{}[\\spad{z},{}\\spad{x}]]+[\\spad{z},{}[\\spad{x},{}\\spad{y}]] = 0} holds.")) (/ (($ $ |#2|) "\\axiom{x/r} returns the division of \\axiom{\\spad{x}} by \\axiom{\\spad{r}}.")) (|construct| (($ $ $) "\\axiom{construct(\\spad{x},{}\\spad{y})} returns the Lie bracket of \\axiom{\\spad{x}} and \\axiom{\\spad{y}}."))) NIL @@ -2563,7 +2563,7 @@ NIL (-658 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}'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}'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}'s are 0,{} \"failed\" if the \\spad{vi}'s are linearly independent over \\spad{S}.")) (|linearlyDependent?| (((|Boolean|) (|Vector| |#2|)) "\\spad{linearlyDependent?([v1,...,vn])} returns \\spad{true} if the \\spad{vi}'s are linearly dependent over \\spad{S},{} \\spad{false} otherwise."))) NIL -((-2598 (|HasCategory| |#1| (QUOTE (-376)))) (|HasCategory| |#1| (QUOTE (-376)))) +((-2584 (|HasCategory| |#1| (QUOTE (-376)))) (|HasCategory| |#1| (QUOTE (-376)))) (-659 K B) ((|constructor| (NIL "A simple data structure for elements that form a vector space of finite dimension over a given field,{} with a given symbolic basis.")) (|coordinates| (((|Vector| |#1|) $) "\\spad{coordinates x} returns the coordinates of the linear element with respect to the basis \\spad{B}.")) (|linearElement| (($ (|List| |#1|)) "\\spad{linearElement [x1,..,xn]} returns a linear element \\indented{1}{with coordinates \\spad{[x1,..,xn]} with respect to} the basis elements \\spad{B}."))) ((-4505 . T) (-4504 . T)) @@ -2583,7 +2583,7 @@ NIL (-663 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."))) ((-4511 . T) (-4510 . T)) -((-4144 (-12 (|HasCategory| |#1| (QUOTE (-872))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|))))) (-4144 (-12 (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-888))))) (|HasCategory| |#1| (|%list| (QUOTE -633) (QUOTE (-549)))) (-4144 (|HasCategory| |#1| (QUOTE (-872))) (|HasCategory| |#1| (QUOTE (-1133)))) (|HasCategory| |#1| (QUOTE (-872))) (-4144 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-872))) (|HasCategory| |#1| (QUOTE (-1133)))) (|HasCategory| |#1| (QUOTE (-845))) (|HasCategory| (-560) (QUOTE (-872))) (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-888)))) (|HasCategory| |#1| (QUOTE (-102))) (-12 (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|))))) +((-4118 (-12 (|HasCategory| |#1| (QUOTE (-872))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|))))) (-4118 (-12 (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-888))))) (|HasCategory| |#1| (|%list| (QUOTE -633) (QUOTE (-549)))) (-4118 (|HasCategory| |#1| (QUOTE (-872))) (|HasCategory| |#1| (QUOTE (-1133)))) (|HasCategory| |#1| (QUOTE (-872))) (-4118 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-872))) (|HasCategory| |#1| (QUOTE (-1133)))) (|HasCategory| |#1| (QUOTE (-845))) (|HasCategory| (-560) (QUOTE (-872))) (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-888)))) (|HasCategory| |#1| (QUOTE (-102))) (-12 (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|))))) (-664 A B) ((|constructor| (NIL "\\spadtype{ListFunctions2} implements utility functions that operate on two kinds of lists,{} each with a possibly different type of element.")) (|map| (((|List| |#2|) (|Mapping| |#2| |#1|) (|List| |#1|)) "\\spad{map(fn,u)} applies \\spad{fn} to each element of list \\spad{u} and returns a new list with the results. For example \\spad{map(square,[1,2,3]) = [1,4,9]}.")) (|reduce| ((|#2| (|Mapping| |#2| |#1| |#2|) (|List| |#1|) |#2|) "\\spad{reduce(fn,u,ident)} successively uses the binary function \\spad{fn} on the elements of list \\spad{u} and the result of previous applications. \\spad{ident} is returned if the \\spad{u} is empty. Note the order of application in the following examples: \\spad{reduce(fn,[1,2,3],0) = fn(3,fn(2,fn(1,0)))} and \\spad{reduce(*,[2,3],1) = 3 * (2 * 1)}.")) (|scan| (((|List| |#2|) (|Mapping| |#2| |#1| |#2|) (|List| |#1|) |#2|) "\\spad{scan(fn,u,ident)} successively uses the binary function \\spad{fn} to reduce more and more of list \\spad{u}. \\spad{ident} is returned if the \\spad{u} is empty. The result is a list of the reductions at each step. See \\spadfun{reduce} for more information. Examples: \\spad{scan(fn,[1,2],0) = [fn(2,fn(1,0)),fn(1,0)]} and \\spad{scan(*,[2,3],1) = [2 * 1, 3 * (2 * 1)]}."))) NIL @@ -2607,7 +2607,7 @@ NIL (-669 S) ((|substitute| (($ |#1| |#1| $) "\\spad{substitute(x,y,d)} replace \\spad{x}'s with \\spad{y}'s in dictionary \\spad{d}.")) (|duplicates?| (((|Boolean|) $) "\\spad{duplicates?(d)} tests if dictionary \\spad{d} has duplicate entries."))) ((-4510 . T) (-4511 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1133))) (-4144 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-1133)))) (-4144 (-12 (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-888))))) (|HasCategory| |#1| (|%list| (QUOTE -633) (QUOTE (-549)))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-888)))) (|HasCategory| |#1| (QUOTE (-102)))) +((-12 (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1133))) (-4118 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-1133)))) (-4118 (-12 (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-888))))) (|HasCategory| |#1| (|%list| (QUOTE -633) (QUOTE (-549)))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-888)))) (|HasCategory| |#1| (QUOTE (-102)))) (-670 R) ((|constructor| (NIL "The category of left modules over an rng (ring not necessarily with unit). This is an abelian group which supports left multiplation by elements of the rng. \\blankline"))) NIL @@ -2628,11 +2628,11 @@ NIL ((|constructor| (NIL "Localize(\\spad{M},{}\\spad{R},{}\\spad{S}) produces fractions with numerators from an \\spad{R} module \\spad{M} and denominators from some multiplicative subset \\spad{D} of \\spad{R}.")) (|denom| ((|#3| $) "\\spad{denom x} returns the denominator of \\spad{x}.")) (|numer| ((|#1| $) "\\spad{numer x} returns the numerator of \\spad{x}.")) (/ (($ |#1| |#3|) "\\spad{m / d} divides the element \\spad{m} by \\spad{d}.") (($ $ |#3|) "\\spad{x / d} divides the element \\spad{x} by \\spad{d}."))) ((-4505 . T) (-4504 . T)) ((|HasCategory| |#1| (QUOTE (-814)))) -(-675 R -4164 L) +(-675 R -4140 L) ((|constructor| (NIL "\\spad{ElementaryFunctionLODESolver} provides the top-level functions for finding closed form solutions of linear ordinary differential equations and initial value problems.")) (|solve| (((|Union| |#2| "failed") |#3| |#2| (|Symbol|) |#2| (|List| |#2|)) "\\spad{solve(op, g, x, a, [y0,...,ym])} returns either the solution of the initial value problem \\spad{op y = g, y(a) = y0, y'(a) = y1,...} or \"failed\" if the solution cannot be found; \\spad{x} is the dependent variable.") (((|Union| (|Record| (|:| |particular| |#2|) (|:| |basis| (|List| |#2|))) "failed") |#3| |#2| (|Symbol|)) "\\spad{solve(op, g, x)} returns either a solution of the ordinary differential equation \\spad{op y = g} or \"failed\" if no non-trivial solution can be found; When found,{} the solution is returned in the form \\spad{[h, [b1,...,bm]]} where \\spad{h} is a particular solution and and \\spad{[b1,...bm]} are linearly independent solutions of the associated homogenuous equation \\spad{op y = 0}. A full basis for the solutions of the homogenuous equation is not always returned,{} only the solutions which were found; \\spad{x} is the dependent variable."))) NIL NIL -(-676 A -3297) +(-676 A -3467) ((|constructor| (NIL "\\spad{LinearOrdinaryDifferentialOperator} defines a ring of differential operators with coefficients in a ring A with a given derivation. Multiplication of operators corresponds to functional composition: \\indented{4}{\\spad{(L1 * L2).(f) = L1 L2 f}}"))) ((-4504 . T) (-4505 . T) (-4507 . T)) ((|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (|%list| (QUOTE -1070) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#1| (|%list| (QUOTE -1070) (QUOTE (-560)))) (|HasCategory| |#1| (QUOTE (-571))) (|HasCategory| |#1| (QUOTE (-466))) (|HasCategory| |#1| (QUOTE (-376)))) @@ -2652,7 +2652,7 @@ NIL ((|constructor| (NIL "\\spad{LinearOrdinaryDifferentialOperatorCategory} is the category of differential operators with coefficients in a ring A with a given derivation. Multiplication of operators corresponds to functional composition: \\indented{4}{\\spad{(L1 * L2).(f) = L1 L2 f}}")) (|directSum| (($ $ $) "\\spad{directSum(a,b)} computes an operator \\spad{c} of minimal order such that the nullspace of \\spad{c} is generated by all the sums of a solution of \\spad{a} by a solution of \\spad{b}.")) (|symmetricSquare| (($ $) "\\spad{symmetricSquare(a)} computes \\spad{symmetricProduct(a,a)} using a more efficient method.")) (|symmetricPower| (($ $ (|NonNegativeInteger|)) "\\spad{symmetricPower(a,n)} computes an operator \\spad{c} of minimal order such that the nullspace of \\spad{c} is generated by all the products of \\spad{n} solutions of \\spad{a}.")) (|symmetricProduct| (($ $ $) "\\spad{symmetricProduct(a,b)} computes an operator \\spad{c} of minimal order such that the nullspace of \\spad{c} is generated by all the products of a solution of \\spad{a} by a solution of \\spad{b}.")) (|adjoint| (($ $) "\\spad{adjoint(a)} returns the adjoint operator of a.")) (D (($) "\\spad{D()} provides the operator corresponding to a derivation in the ring \\spad{A}."))) ((-4504 . T) (-4505 . T) (-4507 . T)) NIL -(-681 -4164 UP) +(-681 -4140 UP) ((|constructor| (NIL "\\spadtype{LinearOrdinaryDifferentialOperatorFactorizer} provides a factorizer for linear ordinary differential operators whose coefficients are rational functions.")) (|factor1| (((|List| (|LinearOrdinaryDifferentialOperator1| (|Fraction| |#2|))) (|LinearOrdinaryDifferentialOperator1| (|Fraction| |#2|))) "\\spad{factor1(a)} returns the factorisation of a,{} assuming that a has no first-order right factor.")) (|factor| (((|List| (|LinearOrdinaryDifferentialOperator1| (|Fraction| |#2|))) (|LinearOrdinaryDifferentialOperator1| (|Fraction| |#2|))) "\\spad{factor(a)} returns the factorisation of a.") (((|List| (|LinearOrdinaryDifferentialOperator1| (|Fraction| |#2|))) (|LinearOrdinaryDifferentialOperator1| (|Fraction| |#2|)) (|Mapping| (|List| |#1|) |#2|)) "\\spad{factor(a, zeros)} returns the factorisation of a. \\spad{zeros} is a zero finder in \\spad{UP}."))) NIL ((|HasCategory| |#1| (QUOTE (-27)))) @@ -2684,11 +2684,11 @@ NIL ((|constructor| (NIL "A list aggregate is a model for a linked list data structure. A linked list is a versatile data structure. Insertion and deletion are efficient and searching is a linear operation.")) (|list| (($ |#1|) "\\spad{list(x)} returns the list of one element \\spad{x}."))) ((-4511 . T) (-4510 . T)) NIL -(-689 -4164 |Row| |Col| M) +(-689 -4140 |Row| |Col| M) ((|constructor| (NIL "This package solves linear system in the matrix form \\spad{AX = B}.")) (|rank| (((|NonNegativeInteger|) |#4| |#3|) "\\spad{rank(A,B)} computes the rank of the complete matrix \\spad{(A|B)} of the linear system \\spad{AX = B}.")) (|hasSolution?| (((|Boolean|) |#4| |#3|) "\\spad{hasSolution?(A,B)} tests if the linear system \\spad{AX = B} has a solution.")) (|particularSolution| (((|Union| |#3| "failed") |#4| |#3|) "\\spad{particularSolution(A,B)} finds a particular solution of the linear system \\spad{AX = B}.")) (|solve| (((|List| (|Record| (|:| |particular| (|Union| |#3| "failed")) (|:| |basis| (|List| |#3|)))) |#4| (|List| |#3|)) "\\spad{solve(A,LB)} finds a particular soln of the systems \\spad{AX = B} and a basis of the associated homogeneous systems \\spad{AX = 0} where \\spad{B} varies in the list of column vectors \\spad{LB}.") (((|Record| (|:| |particular| (|Union| |#3| "failed")) (|:| |basis| (|List| |#3|))) |#4| |#3|) "\\spad{solve(A,B)} finds a particular solution of the system \\spad{AX = B} and a basis of the associated homogeneous system \\spad{AX = 0}."))) NIL NIL -(-690 -4164) +(-690 -4140) ((|constructor| (NIL "This package solves linear system in the matrix form \\spad{AX = B}. It is essentially a particular instantiation of the package \\spadtype{LinearSystemMatrixPackage} for Matrix and Vector. This package's existence makes it easier to use \\spadfun{solve} in the AXIOM interpreter.")) (|rank| (((|NonNegativeInteger|) (|Matrix| |#1|) (|Vector| |#1|)) "\\spad{rank(A,B)} computes the rank of the complete matrix \\spad{(A|B)} of the linear system \\spad{AX = B}.")) (|hasSolution?| (((|Boolean|) (|Matrix| |#1|) (|Vector| |#1|)) "\\spad{hasSolution?(A,B)} tests if the linear system \\spad{AX = B} has a solution.")) (|particularSolution| (((|Union| (|Vector| |#1|) "failed") (|Matrix| |#1|) (|Vector| |#1|)) "\\spad{particularSolution(A,B)} finds a particular solution of the linear system \\spad{AX = B}.")) (|solve| (((|List| (|Record| (|:| |particular| (|Union| (|Vector| |#1|) "failed")) (|:| |basis| (|List| (|Vector| |#1|))))) (|List| (|List| |#1|)) (|List| (|Vector| |#1|))) "\\spad{solve(A,LB)} finds a particular soln of the systems \\spad{AX = B} and a basis of the associated homogeneous systems \\spad{AX = 0} where \\spad{B} varies in the list of column vectors \\spad{LB}.") (((|List| (|Record| (|:| |particular| (|Union| (|Vector| |#1|) "failed")) (|:| |basis| (|List| (|Vector| |#1|))))) (|Matrix| |#1|) (|List| (|Vector| |#1|))) "\\spad{solve(A,LB)} finds a particular soln of the systems \\spad{AX = B} and a basis of the associated homogeneous systems \\spad{AX = 0} where \\spad{B} varies in the list of column vectors \\spad{LB}.") (((|Record| (|:| |particular| (|Union| (|Vector| |#1|) "failed")) (|:| |basis| (|List| (|Vector| |#1|)))) (|List| (|List| |#1|)) (|Vector| |#1|)) "\\spad{solve(A,B)} finds a particular solution of the system \\spad{AX = B} and a basis of the associated homogeneous system \\spad{AX = 0}.") (((|Record| (|:| |particular| (|Union| (|Vector| |#1|) "failed")) (|:| |basis| (|List| (|Vector| |#1|)))) (|Matrix| |#1|) (|Vector| |#1|)) "\\spad{solve(A,B)} finds a particular solution of the system \\spad{AX = B} and a basis of the associated homogeneous system \\spad{AX = 0}."))) NIL NIL @@ -2699,7 +2699,7 @@ NIL (-692 |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."))) ((-4507 . T) (-4510 . T) (-4504 . T) (-4505 . T)) -((|HasCategory| |#2| (|%list| (QUOTE -928) (QUOTE (-1209)))) (|HasCategory| |#2| (|%list| (QUOTE -930) (QUOTE (-1209)))) (|HasCategory| |#2| (QUOTE (-240))) (|HasCategory| |#2| (QUOTE (-239))) (|HasAttribute| |#2| (QUOTE (-4512 "*"))) (|HasCategory| |#2| (|%list| (QUOTE -660) (QUOTE (-560)))) (|HasCategory| |#2| (|%list| (QUOTE -1070) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#2| (|%list| (QUOTE -1070) (QUOTE (-560)))) (-4144 (-12 (|HasCategory| |#2| (|%list| (QUOTE -660) (QUOTE (-560)))) (|HasCategory| |#2| (|%list| (QUOTE -321) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-240))) (|HasCategory| |#2| (|%list| (QUOTE -321) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-1133))) (|HasCategory| |#2| (|%list| (QUOTE -321) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (|%list| (QUOTE -321) (|devaluate| |#2|))) (|HasCategory| |#2| (|%list| (QUOTE -928) (QUOTE (-1209)))))) (|HasCategory| |#2| (QUOTE (-319))) (|HasCategory| |#2| (QUOTE (-1133))) (|HasCategory| |#2| (QUOTE (-376))) (|HasCategory| |#2| (QUOTE (-571))) (-4144 (|HasAttribute| |#2| (QUOTE (-4512 "*"))) (|HasCategory| |#2| (|%list| (QUOTE -928) (QUOTE (-1209)))) (|HasCategory| |#2| (QUOTE (-240)))) (|HasCategory| |#2| (|%list| (QUOTE -632) (QUOTE (-888)))) (|HasCategory| |#2| (QUOTE (-102))) (-12 (|HasCategory| |#2| (QUOTE (-1133))) (|HasCategory| |#2| (|%list| (QUOTE -321) (|devaluate| |#2|)))) (|HasCategory| |#2| (QUOTE (-175)))) +((|HasCategory| |#2| (|%list| (QUOTE -928) (QUOTE (-1209)))) (|HasCategory| |#2| (|%list| (QUOTE -930) (QUOTE (-1209)))) (|HasCategory| |#2| (QUOTE (-240))) (|HasCategory| |#2| (QUOTE (-239))) (|HasAttribute| |#2| (QUOTE (-4512 "*"))) (|HasCategory| |#2| (|%list| (QUOTE -660) (QUOTE (-560)))) (|HasCategory| |#2| (|%list| (QUOTE -1070) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#2| (|%list| (QUOTE -1070) (QUOTE (-560)))) (-4118 (-12 (|HasCategory| |#2| (|%list| (QUOTE -660) (QUOTE (-560)))) (|HasCategory| |#2| (|%list| (QUOTE -321) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-240))) (|HasCategory| |#2| (|%list| (QUOTE -321) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-1133))) (|HasCategory| |#2| (|%list| (QUOTE -321) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (|%list| (QUOTE -321) (|devaluate| |#2|))) (|HasCategory| |#2| (|%list| (QUOTE -928) (QUOTE (-1209)))))) (|HasCategory| |#2| (QUOTE (-319))) (|HasCategory| |#2| (QUOTE (-1133))) (|HasCategory| |#2| (QUOTE (-376))) (|HasCategory| |#2| (QUOTE (-571))) (-4118 (|HasAttribute| |#2| (QUOTE (-4512 "*"))) (|HasCategory| |#2| (|%list| (QUOTE -928) (QUOTE (-1209)))) (|HasCategory| |#2| (QUOTE (-240)))) (|HasCategory| |#2| (|%list| (QUOTE -632) (QUOTE (-888)))) (|HasCategory| |#2| (QUOTE (-102))) (-12 (|HasCategory| |#2| (QUOTE (-1133))) (|HasCategory| |#2| (|%list| (QUOTE -321) (|devaluate| |#2|)))) (|HasCategory| |#2| (QUOTE (-175)))) (-693) ((|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 @@ -2719,7 +2719,7 @@ NIL (-697 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 -((-4144 (-12 (|HasCategory| |#1| (QUOTE (-1081))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|))))) (|HasCategory| |#1| (QUOTE (-1133))) (-4144 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-1133)))) (-4144 (-12 (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-888))))) (|HasCategory| |#1| (QUOTE (-1081))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-888)))) (|HasCategory| |#1| (QUOTE (-102))) (-12 (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|))))) +((-4118 (-12 (|HasCategory| |#1| (QUOTE (-1081))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|))))) (|HasCategory| |#1| (QUOTE (-1133))) (-4118 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-1133)))) (-4118 (-12 (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-888))))) (|HasCategory| |#1| (QUOTE (-1081))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-888)))) (|HasCategory| |#1| (QUOTE (-102))) (-12 (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|))))) (-698) ((|constructor| (NIL "This domain represents the syntax of a macro definition.")) (|body| (((|SpadAst|) $) "\\spad{body(m)} returns the right hand side of the definition `m'.")) (|head| (((|HeadAst|) $) "\\spad{head(m)} returns the head of the macro definition `m'. This is a list of identifiers starting with the name of the macro followed by the name of the parameters,{} if any."))) NIL @@ -2775,7 +2775,7 @@ NIL (-711 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."))) ((-4510 . T) (-4511 . T)) -((-4144 (-12 (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|))))) (|HasCategory| |#1| (QUOTE (-1133))) (-4144 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-1133)))) (-4144 (-12 (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-888))))) (|HasCategory| |#1| (|%list| (QUOTE -633) (QUOTE (-549)))) (|HasCategory| |#1| (QUOTE (-319))) (|HasCategory| |#1| (QUOTE (-571))) (|HasAttribute| |#1| (QUOTE (-4512 "*"))) (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-888)))) (|HasCategory| |#1| (QUOTE (-102))) (-12 (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|))))) +((-4118 (-12 (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|))))) (|HasCategory| |#1| (QUOTE (-1133))) (-4118 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-1133)))) (-4118 (-12 (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-888))))) (|HasCategory| |#1| (|%list| (QUOTE -633) (QUOTE (-549)))) (|HasCategory| |#1| (QUOTE (-319))) (|HasCategory| |#1| (QUOTE (-571))) (|HasAttribute| |#1| (QUOTE (-4512 "*"))) (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-888)))) (|HasCategory| |#1| (QUOTE (-102))) (-12 (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|))))) (-712 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{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 @@ -2784,7 +2784,7 @@ NIL ((|constructor| (NIL "This domain implements the notion of optional value,{} where a computation may fail to produce expected value.")) (|nothing| (($) "\\spad{nothing} represents failure or absence of value.")) (|autoCoerce| ((|#1| $) "\\spad{autoCoerce} is a courtesy coercion function used by the compiler in case it knows that `x' really is a \\spadtype{T}.")) (|case| (((|Boolean|) $ (|[\|\|]| |nothing|)) "\\spad{x case nothing} holds if the value for \\spad{x} is missing.") (((|Boolean|) $ (|[\|\|]| |#1|)) "\\spad{x case T} returns \\spad{true} if \\spad{x} is actually a data of type \\spad{T}.")) (|just| (($ |#1|) "\\spad{just x} injects the value `x' into \\%."))) NIL NIL -(-714 S -4164 FLAF FLAS) +(-714 S -4140 FLAF FLAS) ((|constructor| (NIL "\\indented{1}{\\spadtype{MultiVariableCalculusFunctions} Package provides several} \\indented{1}{functions for multivariable calculus.} These include gradient,{} hessian and jacobian,{} divergence and laplacian. Various forms for banded and sparse storage of matrices are included.")) (|bandedJacobian| (((|Matrix| |#2|) |#3| |#4| (|NonNegativeInteger|) (|NonNegativeInteger|)) "\\spad{bandedJacobian(vf,xlist,kl,ku)} computes the jacobian,{} the matrix of first partial derivatives,{} of the vector field \\spad{vf},{} \\spad{vf} a vector function of the variables listed in \\spad{xlist},{} \\spad{kl} is the number of nonzero subdiagonals,{} \\spad{ku} is the number of nonzero superdiagonals,{} \\spad{kl+ku+1} being actual bandwidth. Stores the nonzero band in a matrix,{} dimensions \\spad{kl+ku+1} by \\#xlist. The upper triangle is in the top \\spad{ku} rows,{} the diagonal is in row \\spad{ku+1},{} the lower triangle in the last \\spad{kl} rows. Entries in a column in the band store correspond to entries in same column of full store. (The notation conforms to LAPACK/NAG-\\spad{F07} conventions.)")) (|jacobian| (((|Matrix| |#2|) |#3| |#4|) "\\spad{jacobian(vf,xlist)} computes the jacobian,{} the matrix of first partial derivatives,{} of the vector field \\spad{vf},{} \\spad{vf} a vector function of the variables listed in \\spad{xlist}.")) (|bandedHessian| (((|Matrix| |#2|) |#2| |#4| (|NonNegativeInteger|)) "\\spad{bandedHessian(v,xlist,k)} computes the hessian,{} the matrix of second partial derivatives,{} of the scalar field \\spad{v},{} \\spad{v} a function of the variables listed in \\spad{xlist},{} \\spad{k} is the semi-bandwidth,{} the number of nonzero subdiagonals,{} 2*k+1 being actual bandwidth. Stores the nonzero band in lower triangle in a matrix,{} dimensions \\spad{k+1} by \\#xlist,{} whose rows are the vectors formed by diagonal,{} subdiagonal,{} etc. of the real,{} full-matrix,{} hessian. (The notation conforms to LAPACK/NAG-\\spad{F07} conventions.)")) (|hessian| (((|Matrix| |#2|) |#2| |#4|) "\\spad{hessian(v,xlist)} computes the hessian,{} the matrix of second partial derivatives,{} of the scalar field \\spad{v},{} \\spad{v} a function of the variables listed in \\spad{xlist}.")) (|laplacian| ((|#2| |#2| |#4|) "\\spad{laplacian(v,xlist)} computes the laplacian of the scalar field \\spad{v},{} \\spad{v} a function of the variables listed in \\spad{xlist}.")) (|divergence| ((|#2| |#3| |#4|) "\\spad{divergence(vf,xlist)} computes the divergence of the vector field \\spad{vf},{} \\spad{vf} a vector function of the variables listed in \\spad{xlist}.")) (|gradient| (((|Vector| |#2|) |#2| |#4|) "\\spad{gradient(v,xlist)} computes the gradient,{} the vector of first partial derivatives,{} of the scalar field \\spad{v},{} \\spad{v} a function of the variables listed in \\spad{xlist}."))) 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T) (-4502 . T) (-4508 . T) (-4503 . T) ((-4512 "*") . T) (-4504 . T) (-4505 . T) (-4507 . T)) +((-2853 . T) (-4502 . T) (-4508 . T) (-4503 . T) ((-4512 "*") . T) (-4504 . T) (-4505 . T) (-4507 . T)) NIL (-722 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."))) @@ -2840,7 +2840,7 @@ NIL ((|constructor| (NIL "MakeRecord is used internally by the interpreter to create record types which are used for doing parallel iterations on streams.")) 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(|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (QUOTE (-466))) (|HasCategory| |#1| (QUOTE (-571))) (|HasCategory| |#1| (QUOTE (-940)))) (-4118 (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (QUOTE (-466))) (|HasCategory| |#1| (QUOTE (-571))) (|HasCategory| |#1| (QUOTE (-940)))) (-4118 (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (QUOTE (-466))) (|HasCategory| |#1| (QUOTE (-940)))) (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (QUOTE (-1184))) (|HasCategory| |#1| (|%list| (QUOTE -930) (QUOTE (-1209)))) (|HasCategory| |#1| (|%list| (QUOTE -928) (QUOTE (-1209)))) (|HasCategory| |#1| (QUOTE (-381))) (|HasCategory| |#1| (QUOTE (-363))) (|HasCategory| |#1| (QUOTE (-239))) (|HasCategory| |#1| (QUOTE (-240))) (|HasAttribute| |#1| (QUOTE -4508)) (|HasCategory| |#1| (QUOTE (-466))) (-12 (|HasCategory| $ (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-940)))) (-4118 (-12 (|HasCategory| $ (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-940)))) (|HasCategory| |#1| (QUOTE (-147))))) (-735 IS E |ff|) ((|constructor| (NIL "This package \\undocumented")) (|construct| (($ |#1| |#2|) "\\spad{construct(i,e)} \\undocumented")) (|index| ((|#1| $) "\\spad{index(x)} \\undocumented")) (|exponent| ((|#2| $) "\\spad{exponent(x)} \\undocumented"))) NIL @@ -2876,7 +2876,7 @@ NIL ((|constructor| (NIL "Algebra of ADDITIVE operators on a module.")) (|makeop| (($ |#1| (|FreeGroup| (|BasicOperator|))) "\\spad{makeop should} be local but conditional")) (|opeval| ((|#2| (|BasicOperator|) |#2|) "\\spad{opeval should} be local but conditional")) (** (($ $ (|Integer|)) "\\spad{op**n} \\undocumented") (($ (|BasicOperator|) (|Integer|)) "\\spad{op**n} \\undocumented")) (|evaluateInverse| (($ $ (|Mapping| |#2| |#2|)) "\\spad{evaluateInverse(x,f)} \\undocumented")) (|evaluate| (($ $ (|Mapping| |#2| |#2|)) "\\spad{evaluate(f, u +-> g u)} attaches the map \\spad{g} to \\spad{f}. \\spad{f} must be a basic operator \\spad{g} MUST be additive,{} \\spadignore{i.e.} \\spad{g(a + b) = g(a) + g(b)} for any \\spad{a},{} \\spad{b} in \\spad{M}. This implies that \\spad{g(n a) = n g(a)} for any \\spad{a} in \\spad{M} and integer \\spad{n > 0}.")) (|conjug| ((|#1| |#1|) "\\spad{conjug(x)}should be local but conditional")) (|adjoint| (($ $ $) "\\spad{adjoint(op1, op2)} sets the adjoint of \\spad{op1} to be \\spad{op2}. \\spad{op1} must be a basic operator") (($ $) "\\spad{adjoint(op)} returns the adjoint of the operator \\spad{op}."))) ((-4505 |has| |#1| (-175)) (-4504 |has| |#1| (-175)) (-4507 . T)) ((|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-149)))) -(-737 R |Mod| -2386 -2834 |exactQuo|) +(-737 R |Mod| -4318 -3338 |exactQuo|) ((|constructor| (NIL "These domains are used for the factorization and gcds of univariate polynomials over the integers in order to work modulo different primes. See \\spadtype{EuclideanModularRing} ,{}\\spadtype{ModularField}")) (|inv| (($ $) "\\spad{inv(x)} \\undocumented")) (|recip| (((|Union| $ "failed") $) "\\spad{recip(x)} \\undocumented")) (|exQuo| (((|Union| $ "failed") $ $) "\\spad{exQuo(x,y)} \\undocumented")) (|reduce| (($ |#1| |#2|) "\\spad{reduce(r,m)} \\undocumented")) (|coerce| ((|#1| $) "\\spad{coerce(x)} \\undocumented")) (|modulus| ((|#2| $) "\\spad{modulus(x)} \\undocumented"))) ((-4507 . T)) NIL @@ -2888,7 +2888,7 @@ NIL ((|constructor| (NIL "The category of modules over a commutative ring. \\blankline"))) ((-4505 . T) (-4504 . T)) NIL -(-740 -4164) +(-740 -4140) ((|constructor| (NIL "\\indented{1}{MoebiusTransform(\\spad{F}) is the domain of fractional linear (Moebius)} transformations over \\spad{F}.")) (|eval| (((|OnePointCompletion| |#1|) $ (|OnePointCompletion| |#1|)) "\\spad{eval(m,x)} returns \\spad{(a*x + b)/(c*x + d)} where \\spad{m = moebius(a,b,c,d)} (see \\spadfunFrom{moebius}{MoebiusTransform}).") ((|#1| $ |#1|) "\\spad{eval(m,x)} returns \\spad{(a*x + b)/(c*x + d)} where \\spad{m = moebius(a,b,c,d)} (see \\spadfunFrom{moebius}{MoebiusTransform}).")) (|recip| (($ $) "\\spad{recip(m)} = recip() * \\spad{m}") (($) "\\spad{recip()} returns \\spad{matrix [[0,1],[1,0]]} representing the map \\spad{x -> 1 / x}.")) (|scale| (($ $ |#1|) "\\spad{scale(m,h)} returns \\spad{scale(h) * m} (see \\spadfunFrom{shift}{MoebiusTransform}).") (($ |#1|) "\\spad{scale(k)} returns \\spad{matrix [[k,0],[0,1]]} representing the map \\spad{x -> k * x}.")) (|shift| (($ $ |#1|) "\\spad{shift(m,h)} returns \\spad{shift(h) * m} (see \\spadfunFrom{shift}{MoebiusTransform}).") (($ |#1|) "\\spad{shift(k)} returns \\spad{matrix [[1,k],[0,1]]} representing the map \\spad{x -> x + k}.")) (|moebius| (($ |#1| |#1| |#1| |#1|) "\\spad{moebius(a,b,c,d)} returns \\spad{matrix [[a,b],[c,d]]}."))) ((-4507 . T)) NIL @@ -2924,7 +2924,7 @@ NIL ((|constructor| (NIL "The class of multiplicative monoids,{} \\spadignore{i.e.} semigroups with a multiplicative identity element. \\blankline")) (|recip| (((|Union| $ "failed") $) "\\spad{recip(x)} tries to compute the multiplicative inverse for \\spad{x} or \"failed\" if it cannot find the inverse (see unitsKnown).")) (** (($ $ (|NonNegativeInteger|)) "\\spad{x**n} returns the repeated product of \\spad{x} \\spad{n} times,{} \\spadignore{i.e.} exponentiation.")) (|one?| (((|Boolean|) $) "\\spad{one?(x)} tests if \\spad{x} is equal to 1.")) (|sample| (($) "\\spad{sample yields} a value of type \\%")) ((|One|) (($) "1 is the multiplicative identity."))) NIL NIL -(-749 -4164 UP) +(-749 -4140 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 @@ -2943,7 +2943,7 @@ NIL (-753 |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."))) (((-4512 "*") |has| |#2| (-175)) (-4503 |has| |#2| (-571)) (-4508 |has| |#2| (-6 -4508)) (-4505 . T) (-4504 . T) (-4507 . T)) -((|HasCategory| |#2| (QUOTE (-940))) (-4144 (|HasCategory| |#2| (QUOTE (-175))) (|HasCategory| |#2| (QUOTE (-466))) (|HasCategory| |#2| (QUOTE (-571))) (|HasCategory| |#2| (QUOTE (-940)))) (-4144 (|HasCategory| |#2| (QUOTE (-466))) (|HasCategory| |#2| (QUOTE (-571))) (|HasCategory| |#2| (QUOTE (-940)))) (-4144 (|HasCategory| |#2| (QUOTE (-466))) (|HasCategory| |#2| (QUOTE (-940)))) (|HasCategory| |#2| (QUOTE (-571))) (|HasCategory| |#2| (QUOTE (-175))) (-4144 (|HasCategory| |#2| (QUOTE (-175))) (|HasCategory| |#2| (QUOTE (-571)))) (-12 (|HasCategory| (-889 |#1|) (|%list| (QUOTE -912) (QUOTE (-391)))) (|HasCategory| |#2| (|%list| (QUOTE -912) (QUOTE (-391))))) (-12 (|HasCategory| (-889 |#1|) (|%list| (QUOTE -912) (QUOTE (-560)))) (|HasCategory| |#2| (|%list| (QUOTE -912) (QUOTE (-560))))) (-12 (|HasCategory| (-889 |#1|) (|%list| (QUOTE -633) (|%list| (QUOTE -916) (QUOTE (-391))))) (|HasCategory| |#2| (|%list| (QUOTE -633) (|%list| (QUOTE -916) (QUOTE (-391)))))) (-12 (|HasCategory| (-889 |#1|) (|%list| (QUOTE -633) (|%list| (QUOTE -916) (QUOTE (-560))))) (|HasCategory| |#2| (|%list| (QUOTE -633) (|%list| (QUOTE -916) (QUOTE (-560)))))) (-12 (|HasCategory| (-889 |#1|) (|%list| (QUOTE -633) (QUOTE (-549)))) (|HasCategory| |#2| (|%list| (QUOTE -633) (QUOTE (-549))))) (|HasCategory| |#2| (|%list| (QUOTE -660) (QUOTE (-560)))) (|HasCategory| |#2| (QUOTE (-149))) (|HasCategory| |#2| (QUOTE (-147))) (|HasCategory| |#2| (|%list| (QUOTE -38) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#2| (|%list| (QUOTE -1070) (QUOTE (-560)))) (-4144 (|HasCategory| |#2| (|%list| (QUOTE -38) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#2| (|%list| (QUOTE -1070) (|%list| (QUOTE -421) (QUOTE (-560)))))) (|HasCategory| |#2| (|%list| (QUOTE -1070) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#2| (QUOTE (-376))) (|HasAttribute| |#2| (QUOTE -4508)) (|HasCategory| |#2| (QUOTE (-466))) (-12 (|HasCategory| $ (QUOTE (-147))) (|HasCategory| |#2| (QUOTE (-940)))) (-4144 (-12 (|HasCategory| $ (QUOTE (-147))) (|HasCategory| |#2| (QUOTE (-940)))) (|HasCategory| |#2| (QUOTE (-147))))) +((|HasCategory| |#2| (QUOTE (-940))) (-4118 (|HasCategory| |#2| (QUOTE (-175))) (|HasCategory| |#2| (QUOTE (-466))) (|HasCategory| |#2| (QUOTE (-571))) (|HasCategory| |#2| (QUOTE (-940)))) (-4118 (|HasCategory| |#2| (QUOTE (-466))) (|HasCategory| |#2| (QUOTE (-571))) (|HasCategory| |#2| (QUOTE (-940)))) (-4118 (|HasCategory| |#2| (QUOTE (-466))) (|HasCategory| |#2| (QUOTE (-940)))) (|HasCategory| |#2| (QUOTE (-571))) (|HasCategory| |#2| (QUOTE (-175))) (-4118 (|HasCategory| |#2| (QUOTE (-175))) (|HasCategory| |#2| (QUOTE (-571)))) (-12 (|HasCategory| (-889 |#1|) (|%list| (QUOTE -912) (QUOTE (-391)))) (|HasCategory| |#2| (|%list| (QUOTE -912) (QUOTE (-391))))) (-12 (|HasCategory| (-889 |#1|) (|%list| (QUOTE -912) (QUOTE (-560)))) (|HasCategory| |#2| (|%list| (QUOTE -912) (QUOTE (-560))))) (-12 (|HasCategory| (-889 |#1|) (|%list| (QUOTE -633) (|%list| (QUOTE -916) (QUOTE (-391))))) (|HasCategory| |#2| (|%list| (QUOTE -633) (|%list| (QUOTE -916) (QUOTE (-391)))))) (-12 (|HasCategory| (-889 |#1|) (|%list| (QUOTE -633) (|%list| (QUOTE -916) (QUOTE (-560))))) (|HasCategory| |#2| (|%list| (QUOTE -633) (|%list| (QUOTE -916) (QUOTE (-560)))))) (-12 (|HasCategory| (-889 |#1|) (|%list| (QUOTE -633) (QUOTE (-549)))) (|HasCategory| |#2| (|%list| (QUOTE -633) (QUOTE (-549))))) (|HasCategory| |#2| (|%list| (QUOTE -660) (QUOTE (-560)))) (|HasCategory| |#2| (QUOTE (-149))) (|HasCategory| |#2| (QUOTE (-147))) (|HasCategory| |#2| (|%list| (QUOTE -38) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#2| (|%list| (QUOTE -1070) (QUOTE (-560)))) (-4118 (|HasCategory| |#2| (|%list| (QUOTE -38) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#2| (|%list| (QUOTE -1070) (|%list| (QUOTE -421) (QUOTE (-560)))))) (|HasCategory| |#2| (|%list| (QUOTE -1070) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#2| (QUOTE (-376))) (|HasAttribute| |#2| (QUOTE -4508)) (|HasCategory| |#2| (QUOTE (-466))) (-12 (|HasCategory| $ (QUOTE (-147))) (|HasCategory| |#2| (QUOTE (-940)))) (-4118 (-12 (|HasCategory| $ (QUOTE (-147))) (|HasCategory| |#2| (QUOTE (-940)))) (|HasCategory| |#2| (QUOTE (-147))))) (-754 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 @@ -3076,11 +3076,11 @@ NIL ((|constructor| (NIL "This package computes explicitly eigenvalues and eigenvectors of matrices with entries over the complex rational numbers. The results are expressed either as complex floating numbers or as complex rational numbers depending on the type of the precision parameter.")) (|complexEigenvectors| (((|List| (|Record| (|:| |outval| (|Complex| |#1|)) (|:| |outmult| (|Integer|)) (|:| |outvect| (|List| (|Matrix| (|Complex| |#1|)))))) (|Matrix| (|Complex| (|Fraction| (|Integer|)))) |#1|) "\\spad{complexEigenvectors(m,eps)} returns a list of records each one containing a complex eigenvalue,{} its algebraic multiplicity,{} and a list of associated eigenvectors. All these results are computed to precision \\spad{eps} and are expressed as complex floats or complex rational numbers depending on the type of \\spad{eps} (float or rational).")) (|complexEigenvalues| (((|List| (|Complex| |#1|)) (|Matrix| (|Complex| (|Fraction| (|Integer|)))) |#1|) "\\spad{complexEigenvalues(m,eps)} computes the eigenvalues of the matrix \\spad{m} to precision \\spad{eps}. The eigenvalues are expressed as complex floats or complex rational numbers depending on the type of \\spad{eps} (float or rational).")) (|characteristicPolynomial| (((|Polynomial| (|Complex| (|Fraction| (|Integer|)))) (|Matrix| (|Complex| (|Fraction| (|Integer|)))) (|Symbol|)) "\\spad{characteristicPolynomial(m,x)} returns the characteristic polynomial of the matrix \\spad{m} expressed as polynomial over Complex Rationals with variable \\spad{x}.") (((|Polynomial| (|Complex| (|Fraction| (|Integer|)))) (|Matrix| (|Complex| (|Fraction| (|Integer|))))) "\\spad{characteristicPolynomial(m)} returns the characteristic polynomial of the matrix \\spad{m} expressed as polynomial over complex rationals with a new symbol as variable."))) NIL NIL -(-787 -4164) +(-787 -4140) ((|constructor| (NIL "\\spadtype{NumericContinuedFraction} provides functions \\indented{2}{for converting floating point numbers to continued fractions.}")) (|continuedFraction| (((|ContinuedFraction| (|Integer|)) |#1|) "\\spad{continuedFraction(f)} converts the floating point number \\spad{f} to a reduced continued fraction."))) NIL NIL -(-788 P -4164) +(-788 P -4140) ((|constructor| (NIL "This package provides a division and related operations for \\spadtype{MonogenicLinearOperator}\\spad{s} over a \\spadtype{Field}. Since the multiplication is in general non-commutative,{} these operations all have left- and right-hand versions. This package provides the operations based on left-division.")) (|leftLcm| ((|#1| |#1| |#1|) "\\spad{leftLcm(a,b)} computes the value \\spad{m} of lowest degree such that \\spad{m = a*aa = b*bb} for some values \\spad{aa} and \\spad{bb}. The value \\spad{m} is computed using left-division.")) (|leftGcd| ((|#1| |#1| |#1|) "\\spad{leftGcd(a,b)} computes the value \\spad{g} of highest degree such that \\indented{3}{\\spad{a = aa*g}} \\indented{3}{\\spad{b = bb*g}} for some values \\spad{aa} and \\spad{bb}. The value \\spad{g} is computed using left-division.")) (|leftExactQuotient| (((|Union| |#1| "failed") |#1| |#1|) "\\spad{leftExactQuotient(a,b)} computes the value \\spad{q},{} if it exists,{} \\indented{1}{such that \\spad{a = b*q}.}")) (|leftRemainder| ((|#1| |#1| |#1|) "\\spad{leftRemainder(a,b)} computes the pair \\spad{[q,r]} such that \\spad{a = b*q + r} and the degree of \\spad{r} is less than the degree of \\spad{b}. The value \\spad{r} is returned.")) (|leftQuotient| ((|#1| |#1| |#1|) "\\spad{leftQuotient(a,b)} computes the pair \\spad{[q,r]} such that \\spad{a = b*q + r} and the degree of \\spad{r} is less than the degree of \\spad{b}. The value \\spad{q} is returned.")) (|leftDivide| (((|Record| (|:| |quotient| |#1|) (|:| |remainder| |#1|)) |#1| |#1|) "\\spad{leftDivide(a,b)} returns the pair \\spad{[q,r]} such that \\spad{a = b*q + r} and the degree of \\spad{r} is less than the degree of \\spad{b}. This process is called ``left division''."))) NIL NIL @@ -3088,7 +3088,7 @@ NIL NIL NIL NIL -(-790 UP -4164) +(-790 UP -4140) ((|constructor| (NIL "In this package \\spad{F} is a framed algebra over the integers (typically \\spad{F = Z[a]} for some algebraic integer a). The package provides functions to compute the integral closure of \\spad{Z} in the quotient quotient field of \\spad{F}.")) (|localIntegralBasis| (((|Record| (|:| |basis| (|Matrix| (|Integer|))) (|:| |basisDen| (|Integer|)) (|:| |basisInv| (|Matrix| (|Integer|)))) (|Integer|)) "\\spad{integralBasis(p)} returns a record \\spad{[basis,basisDen,basisInv]} containing information regarding the local integral closure of \\spad{Z} at the prime \\spad{p} in the quotient field of \\spad{F},{} where \\spad{F} is a framed algebra with \\spad{Z}-module basis \\spad{w1,w2,...,wn}. If \\spad{basis} is the matrix \\spad{(aij, i = 1..n, j = 1..n)},{} then the \\spad{i}th element of the integral basis is \\spad{vi = (1/basisDen) * sum(aij * wj, j = 1..n)},{} \\spadignore{i.e.} the \\spad{i}th row of \\spad{basis} contains the coordinates of the \\spad{i}th basis vector. Similarly,{} the \\spad{i}th row of the matrix \\spad{basisInv} contains the coordinates of \\spad{wi} with respect to the basis \\spad{v1,...,vn}: if \\spad{basisInv} is the matrix \\spad{(bij, i = 1..n, j = 1..n)},{} then \\spad{wi = sum(bij * vj, j = 1..n)}.")) (|integralBasis| (((|Record| (|:| |basis| (|Matrix| (|Integer|))) (|:| |basisDen| (|Integer|)) (|:| |basisInv| (|Matrix| (|Integer|))))) "\\spad{integralBasis()} returns a record \\spad{[basis,basisDen,basisInv]} containing information regarding the integral closure of \\spad{Z} in the quotient field of \\spad{F},{} where \\spad{F} is a framed algebra with \\spad{Z}-module basis \\spad{w1,w2,...,wn}. If \\spad{basis} is the matrix \\spad{(aij, i = 1..n, j = 1..n)},{} then the \\spad{i}th element of the integral basis is \\spad{vi = (1/basisDen) * sum(aij * wj, j = 1..n)},{} \\spadignore{i.e.} the \\spad{i}th row of \\spad{basis} contains the coordinates of the \\spad{i}th basis vector. Similarly,{} the \\spad{i}th row of the matrix \\spad{basisInv} contains the coordinates of \\spad{wi} with respect to the basis \\spad{v1,...,vn}: if \\spad{basisInv} is the matrix \\spad{(bij, i = 1..n, j = 1..n)},{} then \\spad{wi = sum(bij * vj, j = 1..n)}.")) (|discriminant| (((|Integer|)) "\\spad{discriminant()} returns the discriminant of the integral closure of \\spad{Z} in the quotient field of the framed algebra \\spad{F}."))) NIL NIL @@ -3104,7 +3104,7 @@ NIL ((|constructor| (NIL "\\spadtype{NonNegativeInteger} provides functions for non \\indented{2}{negative integers.}")) (|commutative| ((|attribute| "*") "\\spad{commutative(\"*\")} means multiplication is commutative : \\spad{x*y = y*x}.")) (|random| (($ $) "\\spad{random(n)} returns a random integer from 0 to \\spad{n-1}.")) (|shift| (($ $ (|Integer|)) "\\spad{shift(a,i)} shift \\spad{a} by \\spad{i} bits.")) (|exquo| (((|Union| $ "failed") $ $) "\\spad{exquo(a,b)} returns the quotient of \\spad{a} and \\spad{b},{} or \"failed\" if \\spad{b} is zero or \\spad{a} rem \\spad{b} is zero.")) (|divide| (((|Record| (|:| |quotient| $) (|:| |remainder| $)) $ $) "\\spad{divide(a,b)} returns a record containing both remainder and quotient.")) (|gcd| (($ $ $) "\\spad{gcd(a,b)} computes the greatest common divisor of two non negative integers \\spad{a} and \\spad{b}.")) (|rem| (($ $ $) "\\spad{a rem b} returns the remainder of \\spad{a} and \\spad{b}.")) (|quo| (($ $ $) "\\spad{a quo b} returns the quotient of \\spad{a} and \\spad{b},{} forgetting the remainder."))) (((-4512 "*") . T)) NIL -(-794 R -4164) +(-794 R -4140) ((|constructor| (NIL "NonLinearFirstOrderODESolver provides a function for finding closed form first integrals of nonlinear ordinary differential equations of order 1.")) (|solve| (((|Union| |#2| "failed") |#2| |#2| (|BasicOperator|) (|Symbol|)) "\\spad{solve(M(x,y), N(x,y), y, x)} returns \\spad{F(x,y)} such that \\spad{F(x,y) = c} for a constant \\spad{c} is a first integral of the equation \\spad{M(x,y) dx + N(x,y) dy = 0},{} or \"failed\" if no first-integral can be found."))) NIL NIL @@ -3124,7 +3124,7 @@ NIL ((|constructor| (NIL "A package for computing normalized assocites of univariate polynomials with coefficients in a tower of simple extensions of a field.\\newline References : \\indented{1}{[1] \\spad{D}. LAZARD \"A new method for solving algebraic systems of} \\indented{5}{positive dimension\" Discr. App. Math. 33:147-160,{}1991} \\indented{1}{[2] \\spad{M}. MORENO MAZA and \\spad{R}. RIOBOO \"Computations of gcd over} \\indented{5}{algebraic towers of simple extensions\" In proceedings of \\spad{AAECC11}} \\indented{5}{Paris,{} 1995.} \\indented{1}{[3] \\spad{M}. MORENO MAZA \"Calculs de pgcd au-dessus des tours} \\indented{5}{d'extensions simples et resolution des systemes d'equations} \\indented{5}{algebriques\" These,{} Universite \\spad{P}.etM. Curie,{} Paris,{} 1997.}")) (|normInvertible?| (((|List| (|Record| (|:| |val| (|Boolean|)) (|:| |tower| |#5|))) |#4| |#5|) "\\axiom{normInvertible?(\\spad{p},{}ts)} is an internal subroutine,{} exported only for developement.")) (|outputArgs| (((|Void|) (|String|) (|String|) |#4| |#5|) "\\axiom{outputArgs(\\spad{s1},{}\\spad{s2},{}\\spad{p},{}ts)} is an internal subroutine,{} exported only for developement.")) (|normalize| (((|List| (|Record| (|:| |val| |#4|) (|:| |tower| |#5|))) |#4| |#5|) "\\axiom{normalize(\\spad{p},{}ts)} normalizes \\axiom{\\spad{p}} \\spad{w}.\\spad{r}.\\spad{t} \\spad{ts}.")) (|normalizedAssociate| ((|#4| |#4| |#5|) "\\axiom{normalizedAssociate(\\spad{p},{}ts)} returns a normalized polynomial \\axiom{\\spad{n}} \\spad{w}.\\spad{r}.\\spad{t}. \\spad{ts} such that \\axiom{\\spad{n}} and \\axiom{\\spad{p}} are associates \\spad{w}.\\spad{r}.\\spad{t} \\spad{ts} and assuming that \\axiom{\\spad{p}} is invertible \\spad{w}.\\spad{r}.\\spad{t} \\spad{ts}.")) (|recip| (((|Record| (|:| |num| |#4|) (|:| |den| |#4|)) |#4| |#5|) "\\axiom{recip(\\spad{p},{}ts)} returns the inverse of \\axiom{\\spad{p}} \\spad{w}.\\spad{r}.\\spad{t} \\spad{ts} assuming that \\axiom{\\spad{p}} is invertible \\spad{w}.\\spad{r}.\\spad{t} \\spad{ts}."))) NIL NIL -(-799 -4164 |ExtF| |SUEx| |ExtP| |n|) +(-799 -4140 |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 @@ -3139,11 +3139,11 @@ NIL (-802 R |VarSet|) ((|constructor| (NIL "A post-facto extension for \\axiomType{SMP} in order to speed up operations related to pseudo-division and gcd. This domain is based on the \\axiomType{NSUP} constructor which is itself a post-facto extension of the \\axiomType{SUP} constructor."))) (((-4512 "*") |has| |#1| (-175)) (-4503 |has| |#1| (-571)) (-4508 |has| |#1| (-6 -4508)) (-4505 . T) (-4504 . T) (-4507 . 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((|constructor| (NIL "A post-facto extension for \\axiomType{SUP} in order to speed up operations related to pseudo-division and gcd for both \\axiomType{SUP} and,{} consequently,{} \\axiomType{NSMP}.")) (|halfExtendedResultant2| (((|Record| (|:| |resultant| |#1|) (|:| |coef2| $)) $ $) "\\axiom{\\spad{halfExtendedResultant2}(a,{}\\spad{b})} returns \\axiom{[\\spad{r},{}ca]} such that \\axiom{extendedResultant(a,{}\\spad{b})} returns \\axiom{[\\spad{r},{}ca,{} cb]}")) (|halfExtendedResultant1| (((|Record| (|:| |resultant| |#1|) (|:| |coef1| $)) $ $) "\\axiom{\\spad{halfExtendedResultant1}(a,{}\\spad{b})} returns \\axiom{[\\spad{r},{}ca]} such that \\axiom{extendedResultant(a,{}\\spad{b})} returns \\axiom{[\\spad{r},{}ca,{} cb]}")) (|extendedResultant| (((|Record| (|:| |resultant| |#1|) (|:| |coef1| $) (|:| |coef2| $)) $ $) "\\axiom{extendedResultant(a,{}\\spad{b})} returns \\axiom{[\\spad{r},{}ca,{}cb]} such that \\axiom{\\spad{r}} is the resultant of \\axiom{a} and \\axiom{\\spad{b}} and \\axiom{\\spad{r} = ca * a + cb * \\spad{b}}")) (|halfExtendedSubResultantGcd2| (((|Record| (|:| |gcd| $) (|:| |coef2| $)) $ $) "\\axiom{\\spad{halfExtendedSubResultantGcd2}(a,{}\\spad{b})} returns \\axiom{[\\spad{g},{}cb]} such that \\axiom{extendedSubResultantGcd(a,{}\\spad{b})} returns \\axiom{[\\spad{g},{}ca,{} cb]}")) (|halfExtendedSubResultantGcd1| (((|Record| (|:| |gcd| $) (|:| |coef1| $)) $ $) "\\axiom{\\spad{halfExtendedSubResultantGcd1}(a,{}\\spad{b})} returns \\axiom{[\\spad{g},{}ca]} such that \\axiom{extendedSubResultantGcd(a,{}\\spad{b})} returns \\axiom{[\\spad{g},{}ca,{} cb]}")) (|extendedSubResultantGcd| (((|Record| (|:| |gcd| $) (|:| |coef1| $) (|:| |coef2| $)) $ $) "\\axiom{extendedSubResultantGcd(a,{}\\spad{b})} returns \\axiom{[\\spad{g},{}ca,{} cb]} such that \\axiom{\\spad{g}} is a gcd of \\axiom{a} and \\axiom{\\spad{b}} in \\axiom{R^(\\spad{-1}) \\spad{P}} and \\axiom{\\spad{g} = ca * a + cb * \\spad{b}}")) (|lastSubResultant| (($ $ $) "\\axiom{lastSubResultant(a,{}\\spad{b})} returns \\axiom{resultant(a,{}\\spad{b})} if \\axiom{a} and \\axiom{\\spad{b}} has no non-trivial gcd in \\axiom{R^(\\spad{-1}) \\spad{P}} otherwise the non-zero sub-resultant with smallest index.")) (|subResultantsChain| (((|List| $) $ $) "\\axiom{subResultantsChain(a,{}\\spad{b})} returns the list of the non-zero sub-resultants of \\axiom{a} and \\axiom{\\spad{b}} sorted by increasing degree.")) (|lazyPseudoQuotient| (($ $ $) "\\axiom{lazyPseudoQuotient(a,{}\\spad{b})} returns \\axiom{\\spad{q}} if \\axiom{lazyPseudoDivide(a,{}\\spad{b})} returns \\axiom{[\\spad{c},{}\\spad{g},{}\\spad{q},{}\\spad{r}]}")) (|lazyPseudoDivide| (((|Record| (|:| |coef| |#1|) (|:| |gap| (|NonNegativeInteger|)) (|:| |quotient| $) (|:| |remainder| $)) $ $) "\\axiom{lazyPseudoDivide(a,{}\\spad{b})} returns \\axiom{[\\spad{c},{}\\spad{g},{}\\spad{q},{}\\spad{r}]} such that \\axiom{c^n * a = q*b +r} and \\axiom{lazyResidueClass(a,{}\\spad{b})} returns \\axiom{[\\spad{r},{}\\spad{c},{}\\spad{n}]} where \\axiom{\\spad{n} + \\spad{g} = max(0,{} degree(\\spad{b}) - degree(a) + 1)}.")) (|lazyPseudoRemainder| (($ $ $) "\\axiom{lazyPseudoRemainder(a,{}\\spad{b})} returns \\axiom{\\spad{r}} if \\axiom{lazyResidueClass(a,{}\\spad{b})} returns \\axiom{[\\spad{r},{}\\spad{c},{}\\spad{n}]}. This lazy pseudo-remainder is computed by means of the \\axiomOpFrom{fmecg}{NewSparseUnivariatePolynomial} operation.")) (|lazyResidueClass| (((|Record| (|:| |polnum| $) (|:| |polden| |#1|) (|:| |power| (|NonNegativeInteger|))) $ $) "\\axiom{lazyResidueClass(a,{}\\spad{b})} returns \\axiom{[\\spad{r},{}\\spad{c},{}\\spad{n}]} such that \\axiom{\\spad{r}} is reduced \\spad{w}.\\spad{r}.\\spad{t}. \\axiom{\\spad{b}} and \\axiom{\\spad{b}} divides \\axiom{c^n * a - \\spad{r}} where \\axiom{\\spad{c}} is \\axiom{leadingCoefficient(\\spad{b})} and \\axiom{\\spad{n}} is as small as possible with the previous properties.")) (|monicModulo| (($ $ $) "\\axiom{monicModulo(a,{}\\spad{b})} returns \\axiom{\\spad{r}} such that \\axiom{\\spad{r}} is reduced \\spad{w}.\\spad{r}.\\spad{t}. \\axiom{\\spad{b}} and \\axiom{\\spad{b}} divides \\axiom{a -r} where \\axiom{\\spad{b}} is monic.")) (|fmecg| (($ $ (|NonNegativeInteger|) |#1| $) "\\axiom{fmecg(\\spad{p1},{}\\spad{e},{}\\spad{r},{}\\spad{p2})} returns \\axiom{\\spad{p1} - \\spad{r} * X**e * \\spad{p2}} where \\axiom{\\spad{X}} is \\axiom{monomial(1,{}1)}"))) (((-4512 "*") |has| |#1| (-175)) (-4503 |has| |#1| (-571)) (-4506 |has| |#1| (-376)) (-4508 |has| |#1| (-6 -4508)) (-4505 . T) (-4504 . T) (-4507 . 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(-466))) (|HasCategory| |#1| (QUOTE (-571))) (|HasCategory| |#1| (QUOTE (-940)))) (-4118 (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (QUOTE (-466))) (|HasCategory| |#1| (QUOTE (-571))) (|HasCategory| |#1| (QUOTE (-940)))) (-4118 (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (QUOTE (-466))) (|HasCategory| |#1| (QUOTE (-940)))) (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (QUOTE (-1184))) (|HasCategory| |#1| (|%list| (QUOTE -930) (QUOTE (-1209)))) (|HasCategory| |#1| (|%list| (QUOTE -928) (QUOTE (-1209)))) (|HasCategory| |#1| (QUOTE (-239))) (|HasCategory| |#1| (QUOTE (-240))) (|HasAttribute| |#1| (QUOTE -4508)) (|HasCategory| |#1| (QUOTE (-466))) (-12 (|HasCategory| $ (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-940)))) (-4118 (-12 (|HasCategory| $ (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-940)))) (|HasCategory| |#1| (QUOTE (-147))))) (-804 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 @@ -3219,8 +3219,8 @@ NIL (-822 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}."))) ((-4504 . T) (-4505 . T) (-4507 . T)) -((|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-149))) (|HasCategory| |#1| (|%list| (QUOTE -633) (QUOTE (-549)))) (|HasCategory| |#1| (QUOTE (-872))) (|HasCategory| |#1| (QUOTE (-381))) (|HasCategory| |#1| (|%list| (QUOTE -528) (QUOTE (-1209)) (|devaluate| |#1|))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|))) (|HasCategory| |#1| (|%list| (QUOTE -298) (|devaluate| |#1|) (|devaluate| |#1|))) (-4144 (|HasCategory| (-1028 |#1|) (|%list| (QUOTE -1070) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#1| (|%list| (QUOTE -1070) (|%list| (QUOTE -421) (QUOTE (-560)))))) (-4144 (|HasCategory| (-1028 |#1|) (|%list| (QUOTE -1070) (QUOTE (-560)))) (|HasCategory| |#1| (|%list| (QUOTE -1070) (QUOTE (-560))))) (|HasCategory| |#1| (QUOTE (-1092))) (|HasCategory| |#1| (QUOTE (-559))) (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| (-1028 |#1|) (|%list| (QUOTE -1070) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| (-1028 |#1|) (|%list| (QUOTE -1070) (QUOTE (-560)))) (|HasCategory| |#1| (|%list| (QUOTE -1070) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#1| (|%list| (QUOTE -1070) (QUOTE (-560))))) -(-823 -4144 R OS S) +((|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-149))) (|HasCategory| |#1| (|%list| (QUOTE -633) (QUOTE (-549)))) (|HasCategory| |#1| (QUOTE (-872))) (|HasCategory| |#1| (QUOTE (-381))) (|HasCategory| |#1| (|%list| (QUOTE -528) (QUOTE (-1209)) (|devaluate| |#1|))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|))) (|HasCategory| |#1| (|%list| (QUOTE -298) (|devaluate| |#1|) (|devaluate| |#1|))) (-4118 (|HasCategory| (-1028 |#1|) (|%list| (QUOTE -1070) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#1| (|%list| (QUOTE -1070) (|%list| (QUOTE -421) (QUOTE (-560)))))) (-4118 (|HasCategory| (-1028 |#1|) (|%list| (QUOTE -1070) (QUOTE (-560)))) (|HasCategory| |#1| (|%list| (QUOTE -1070) (QUOTE (-560))))) (|HasCategory| |#1| (QUOTE (-1092))) (|HasCategory| |#1| (QUOTE (-559))) (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| (-1028 |#1|) (|%list| (QUOTE -1070) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| (-1028 |#1|) (|%list| (QUOTE -1070) (QUOTE (-560)))) (|HasCategory| |#1| (|%list| (QUOTE -1070) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#1| (|%list| (QUOTE -1070) (QUOTE (-560))))) +(-823 -4118 R OS S) ((|constructor| (NIL "\\spad{OctonionCategoryFunctions2} implements functions between two octonion domains defined over different rings. The function map is used to coerce between octonion types.")) (|map| ((|#3| (|Mapping| |#4| |#2|) |#1|) "\\spad{map(f,u)} maps \\spad{f} onto the component parts of the octonion \\spad{u}."))) NIL NIL @@ -3228,11 +3228,11 @@ NIL ((|ODESolve| (((|Result|) (|Record| (|:| |xinit| (|DoubleFloat|)) (|:| |xend| (|DoubleFloat|)) (|:| |fn| (|Vector| (|Expression| (|DoubleFloat|)))) (|:| |yinit| (|List| (|DoubleFloat|))) (|:| |intvals| (|List| (|DoubleFloat|))) (|:| |g| (|Expression| (|DoubleFloat|))) (|:| |abserr| (|DoubleFloat|)) (|:| |relerr| (|DoubleFloat|)))) "\\spad{ODESolve(args)} performs the integration of the function given the strategy or method returned by \\axiomFun{measure}.")) (|measure| (((|Record| (|:| |measure| (|Float|)) (|:| |explanations| (|String|))) (|RoutinesTable|) (|Record| (|:| |xinit| (|DoubleFloat|)) (|:| |xend| (|DoubleFloat|)) (|:| |fn| (|Vector| (|Expression| (|DoubleFloat|)))) (|:| |yinit| (|List| (|DoubleFloat|))) (|:| |intvals| (|List| (|DoubleFloat|))) (|:| |g| (|Expression| (|DoubleFloat|))) (|:| |abserr| (|DoubleFloat|)) (|:| |relerr| (|DoubleFloat|)))) "\\spad{measure(R,args)} calculates an estimate of the ability of a particular method to solve a problem. \\blankline This method may be either a specific NAG routine or a strategy (such as transforming the function from one which is difficult to one which is easier to solve). \\blankline It will call whichever agents are needed to perform analysis on the problem in order to calculate the measure. There is a parameter,{} labelled \\axiom{sofar},{} which would contain the best compatibility found so far."))) NIL NIL -(-825 R -4164 L) +(-825 R -4140 L) ((|constructor| (NIL "Solution of linear ordinary differential equations,{} constant coefficient case.")) (|constDsolve| (((|Record| (|:| |particular| |#2|) (|:| |basis| (|List| |#2|))) |#3| |#2| (|Symbol|)) "\\spad{constDsolve(op, g, x)} returns \\spad{[f, [y1,...,ym]]} where \\spad{f} is a particular solution of the equation \\spad{op y = g},{} and the \\spad{yi}'s form a basis for the solutions of \\spad{op y = 0}."))) NIL NIL -(-826 R -4164) +(-826 R -4140) ((|constructor| (NIL "\\spad{ElementaryFunctionODESolver} provides the top-level functions for finding closed form solutions of ordinary differential equations and initial value problems.")) (|solve| (((|Union| |#2| "failed") |#2| (|BasicOperator|) (|Equation| |#2|) (|List| |#2|)) "\\spad{solve(eq, y, x = a, [y0,...,ym])} returns either the solution of the initial value problem \\spad{eq, y(a) = y0, y'(a) = y1,...} or \"failed\" if the solution cannot be found; error if the equation is not one linear ordinary or of the form \\spad{dy/dx = f(x,y)}.") (((|Union| |#2| "failed") (|Equation| |#2|) (|BasicOperator|) (|Equation| |#2|) (|List| |#2|)) "\\spad{solve(eq, y, x = a, [y0,...,ym])} returns either the solution of the initial value problem \\spad{eq, y(a) = y0, y'(a) = y1,...} or \"failed\" if the solution cannot be found; error if the equation is not one linear ordinary or of the form \\spad{dy/dx = f(x,y)}.") (((|Union| (|Record| (|:| |particular| |#2|) (|:| |basis| (|List| |#2|))) |#2| "failed") |#2| (|BasicOperator|) (|Symbol|)) "\\spad{solve(eq, y, x)} returns either a solution of the ordinary differential equation \\spad{eq} or \"failed\" if no non-trivial solution can be found; If the equation is linear ordinary,{} a solution is of the form \\spad{[h, [b1,...,bm]]} where \\spad{h} is a particular solution and and \\spad{[b1,...bm]} are linearly independent solutions of the associated homogenuous equation \\spad{f(x,y) = 0}; A full basis for the solutions of the homogenuous equation is not always returned,{} only the solutions which were found; If the equation is of the form {dy/dx = \\spad{f}(\\spad{x},{}\\spad{y})},{} a solution is of the form \\spad{h(x,y)} where \\spad{h(x,y) = c} is a first integral of the equation for any constant \\spad{c}.") (((|Union| (|Record| (|:| |particular| |#2|) (|:| |basis| (|List| |#2|))) |#2| "failed") (|Equation| |#2|) (|BasicOperator|) (|Symbol|)) "\\spad{solve(eq, y, x)} returns either a solution of the ordinary differential equation \\spad{eq} or \"failed\" if no non-trivial solution can be found; If the equation is linear ordinary,{} a solution is of the form \\spad{[h, [b1,...,bm]]} where \\spad{h} is a particular solution and \\spad{[b1,...bm]} are linearly independent solutions of the associated homogenuous equation \\spad{f(x,y) = 0}; A full basis for the solutions of the homogenuous equation is not always returned,{} only the solutions which were found; If the equation is of the form {dy/dx = \\spad{f}(\\spad{x},{}\\spad{y})},{} a solution is of the form \\spad{h(x,y)} where \\spad{h(x,y) = c} is a first integral of the equation for any constant \\spad{c}; error if the equation is not one of those 2 forms.") (((|Union| (|Record| (|:| |particular| (|Vector| |#2|)) (|:| |basis| (|List| (|Vector| |#2|)))) "failed") (|List| |#2|) (|List| (|BasicOperator|)) (|Symbol|)) "\\spad{solve([eq_1,...,eq_n], [y_1,...,y_n], x)} returns either \"failed\" or,{} if the equations form a fist order linear system,{} a solution of the form \\spad{[y_p, [b_1,...,b_n]]} where \\spad{h_p} is a particular solution and \\spad{[b_1,...b_m]} are linearly independent solutions of the associated homogenuous system. error if the equations do not form a first order linear system") (((|Union| (|Record| (|:| |particular| (|Vector| |#2|)) (|:| |basis| (|List| (|Vector| |#2|)))) "failed") (|List| (|Equation| |#2|)) (|List| (|BasicOperator|)) (|Symbol|)) "\\spad{solve([eq_1,...,eq_n], [y_1,...,y_n], x)} returns either \"failed\" or,{} if the equations form a fist order linear system,{} a solution of the form \\spad{[y_p, [b_1,...,b_n]]} where \\spad{h_p} is a particular solution and \\spad{[b_1,...b_m]} are linearly independent solutions of the associated homogenuous system. error if the equations do not form a first order linear system") (((|Union| (|List| (|Vector| |#2|)) "failed") (|Matrix| |#2|) (|Symbol|)) "\\spad{solve(m, x)} returns a basis for the solutions of \\spad{D y = m y}. \\spad{x} is the dependent variable.") (((|Union| (|Record| (|:| |particular| (|Vector| |#2|)) (|:| |basis| (|List| (|Vector| |#2|)))) "failed") (|Matrix| |#2|) (|Vector| |#2|) (|Symbol|)) "\\spad{solve(m, v, x)} returns \\spad{[v_p, [v_1,...,v_m]]} such that the solutions of the system \\spad{D y = m y + v} are \\spad{v_p + c_1 v_1 + ... + c_m v_m} where the \\spad{c_i's} are constants,{} and the \\spad{v_i's} form a basis for the solutions of \\spad{D y = m y}. \\spad{x} is the dependent variable."))) NIL NIL @@ -3240,7 +3240,7 @@ NIL ((|constructor| (NIL "\\axiom{ODEIntensityFunctionsTable()} provides a dynamic table and a set of functions to store details found out about sets of ODE's.")) (|showIntensityFunctions| (((|Union| (|Record| (|:| |stiffness| (|Float|)) (|:| |stability| (|Float|)) (|:| |expense| (|Float|)) (|:| |accuracy| (|Float|)) (|:| |intermediateResults| (|Float|))) "failed") (|Record| (|:| |xinit| (|DoubleFloat|)) (|:| |xend| (|DoubleFloat|)) (|:| |fn| (|Vector| (|Expression| (|DoubleFloat|)))) (|:| |yinit| (|List| (|DoubleFloat|))) (|:| |intvals| (|List| (|DoubleFloat|))) (|:| |g| (|Expression| (|DoubleFloat|))) (|:| |abserr| (|DoubleFloat|)) (|:| |relerr| (|DoubleFloat|)))) "\\spad{showIntensityFunctions(k)} returns the entries in the table of intensity functions \\spad{k}.")) (|insert!| (($ (|Record| (|:| |key| (|Record| (|:| |xinit| (|DoubleFloat|)) (|:| |xend| (|DoubleFloat|)) (|:| |fn| (|Vector| (|Expression| (|DoubleFloat|)))) (|:| |yinit| (|List| (|DoubleFloat|))) (|:| |intvals| (|List| (|DoubleFloat|))) (|:| |g| (|Expression| (|DoubleFloat|))) (|:| |abserr| (|DoubleFloat|)) (|:| |relerr| (|DoubleFloat|)))) (|:| |entry| (|Record| (|:| |stiffness| (|Float|)) (|:| |stability| (|Float|)) (|:| |expense| (|Float|)) (|:| |accuracy| (|Float|)) (|:| |intermediateResults| (|Float|)))))) "\\spad{insert!(r)} inserts an entry \\spad{r} into theIFTable")) (|iFTable| (($ (|List| (|Record| (|:| |key| (|Record| (|:| |xinit| (|DoubleFloat|)) (|:| |xend| (|DoubleFloat|)) (|:| |fn| (|Vector| (|Expression| (|DoubleFloat|)))) (|:| |yinit| (|List| (|DoubleFloat|))) (|:| |intvals| (|List| (|DoubleFloat|))) (|:| |g| (|Expression| (|DoubleFloat|))) (|:| |abserr| (|DoubleFloat|)) (|:| |relerr| (|DoubleFloat|)))) (|:| |entry| (|Record| (|:| |stiffness| (|Float|)) (|:| |stability| (|Float|)) (|:| |expense| (|Float|)) (|:| |accuracy| (|Float|)) (|:| |intermediateResults| (|Float|))))))) "\\spad{iFTable(l)} creates an intensity-functions table from the elements of \\spad{l}.")) (|keys| (((|List| (|Record| (|:| |xinit| (|DoubleFloat|)) (|:| |xend| (|DoubleFloat|)) (|:| |fn| (|Vector| (|Expression| (|DoubleFloat|)))) (|:| |yinit| (|List| (|DoubleFloat|))) (|:| |intvals| (|List| (|DoubleFloat|))) (|:| |g| (|Expression| (|DoubleFloat|))) (|:| |abserr| (|DoubleFloat|)) (|:| |relerr| (|DoubleFloat|)))) $) "\\spad{keys(tab)} returns the list of keys of \\spad{f}")) (|clearTheIFTable| (((|Void|)) "\\spad{clearTheIFTable()} clears the current table of intensity functions.")) (|showTheIFTable| (($) "\\spad{showTheIFTable()} returns the current table of intensity functions."))) NIL NIL -(-828 R -4164) +(-828 R -4140) ((|constructor| (NIL "\\spadtype{ODEIntegration} provides an interface to the integrator. This package is intended for use by the differential equations solver but not at top-level.")) (|diff| (((|Mapping| |#2| |#2|) (|Symbol|)) "\\spad{diff(x)} returns the derivation with respect to \\spad{x}.")) (|expint| ((|#2| |#2| (|Symbol|)) "\\spad{expint(f, x)} returns e^{the integral of \\spad{f} with respect to \\spad{x}}.")) (|int| ((|#2| |#2| (|Symbol|)) "\\spad{int(f, x)} returns the integral of \\spad{f} with respect to \\spad{x}."))) NIL NIL @@ -3248,11 +3248,11 @@ NIL ((|measure| (((|Record| (|:| |measure| (|Float|)) (|:| |name| (|String|)) (|:| |explanations| (|List| (|String|)))) (|NumericalODEProblem|) (|RoutinesTable|)) "\\spad{measure(prob,R)} is a top level ANNA function for identifying the most appropriate numerical routine from those in the routines table provided for solving the numerical ODE problem defined by \\axiom{\\spad{prob}}. \\blankline It calls each \\axiom{domain} listed in \\axiom{\\spad{R}} of \\axiom{category} \\axiomType{OrdinaryDifferentialEquationsSolverCategory} in turn to calculate all measures and returns the best \\spadignore{i.e.} the name of the most appropriate domain and any other relevant information. It predicts the likely most effective NAG numerical Library routine to solve the input set of ODEs by checking various attributes of the system of ODEs and calculating a measure of compatibility of each routine to these attributes.") (((|Record| (|:| |measure| (|Float|)) (|:| |name| (|String|)) (|:| |explanations| (|List| (|String|)))) (|NumericalODEProblem|)) "\\spad{measure(prob)} is a top level ANNA function for identifying the most appropriate numerical routine from those in the routines table provided for solving the numerical ODE problem defined by \\axiom{\\spad{prob}}. \\blankline It calls each \\axiom{domain} of \\axiom{category} \\axiomType{OrdinaryDifferentialEquationsSolverCategory} in turn to calculate all measures and returns the best \\spadignore{i.e.} the name of the most appropriate domain and any other relevant information. It predicts the likely most effective NAG numerical Library routine to solve the input set of ODEs by checking various attributes of the system of ODEs and calculating a measure of compatibility of each routine to these attributes.")) (|solve| (((|Result|) (|Vector| (|Expression| (|Float|))) (|Float|) (|Float|) (|List| (|Float|)) (|Expression| (|Float|)) (|List| (|Float|)) (|Float|) (|Float|)) "\\spad{solve(f,xStart,xEnd,yInitial,G,intVals,epsabs,epsrel)} is a top level ANNA function to solve numerically a system of ordinary differential equations,{} \\axiom{\\spad{f}},{} \\spadignore{i.e.} equations for the derivatives \\spad{Y}[1]'..\\spad{Y}[\\spad{n}]' defined in terms of \\spad{X},{}\\spad{Y}[1]..\\spad{Y}[\\spad{n}] from \\axiom{\\spad{xStart}} to \\axiom{\\spad{xEnd}} with the initial values for \\spad{Y}[1]..\\spad{Y}[\\spad{n}] (\\axiom{\\spad{yInitial}}) to an absolute error requirement \\axiom{\\spad{epsabs}} and relative error \\axiom{\\spad{epsrel}}. The values of \\spad{Y}[1]..\\spad{Y}[\\spad{n}] will be output for the values of \\spad{X} in \\axiom{\\spad{intVals}}. The calculation will stop if the function \\spad{G}(\\spad{X},{}\\spad{Y}[1],{}..,{}\\spad{Y}[\\spad{n}]) evaluates to zero before \\spad{X} = \\spad{xEnd}. \\blankline It iterates over the \\axiom{domains} of \\axiomType{OrdinaryDifferentialEquationsSolverCategory} contained in the table of routines \\axiom{\\spad{R}} to get the name and other relevant information of the the (domain of the) numerical routine likely to be the most appropriate,{} \\spadignore{i.e.} have the best \\axiom{measure}. \\blankline The method used to perform the numerical process will be one of the routines contained in the NAG numerical Library. The function predicts the likely most effective routine by checking various attributes of the system of ODE's and calculating a measure of compatibility of each routine to these attributes. \\blankline It then calls the resulting `best' routine.") (((|Result|) (|Vector| (|Expression| (|Float|))) (|Float|) (|Float|) (|List| (|Float|)) (|Expression| (|Float|)) (|List| (|Float|)) (|Float|)) "\\spad{solve(f,xStart,xEnd,yInitial,G,intVals,tol)} is a top level ANNA function to solve numerically a system of ordinary differential equations,{} \\axiom{\\spad{f}},{} \\spadignore{i.e.} equations for the derivatives \\spad{Y}[1]'..\\spad{Y}[\\spad{n}]' defined in terms of \\spad{X},{}\\spad{Y}[1]..\\spad{Y}[\\spad{n}] from \\axiom{\\spad{xStart}} to \\axiom{\\spad{xEnd}} with the initial values for \\spad{Y}[1]..\\spad{Y}[\\spad{n}] (\\axiom{\\spad{yInitial}}) to a tolerance \\axiom{\\spad{tol}}. The values of \\spad{Y}[1]..\\spad{Y}[\\spad{n}] will be output for the values of \\spad{X} in \\axiom{\\spad{intVals}}. The calculation will stop if the function \\spad{G}(\\spad{X},{}\\spad{Y}[1],{}..,{}\\spad{Y}[\\spad{n}]) evaluates to zero before \\spad{X} = \\spad{xEnd}. \\blankline It iterates over the \\axiom{domains} of \\axiomType{OrdinaryDifferentialEquationsSolverCategory} contained in the table of routines \\axiom{\\spad{R}} to get the name and other relevant information of the the (domain of the) numerical routine likely to be the most appropriate,{} \\spadignore{i.e.} have the best \\axiom{measure}. \\blankline The method used to perform the numerical process will be one of the routines contained in the NAG numerical Library. The function predicts the likely most effective routine by checking various attributes of the system of ODE's and calculating a measure of compatibility of each routine to these attributes. \\blankline It then calls the resulting `best' routine.") (((|Result|) (|Vector| (|Expression| (|Float|))) (|Float|) (|Float|) (|List| (|Float|)) (|List| (|Float|)) (|Float|)) "\\spad{solve(f,xStart,xEnd,yInitial,intVals,tol)} is a top level ANNA function to solve numerically a system of ordinary differential equations,{} \\axiom{\\spad{f}},{} \\spadignore{i.e.} equations for the derivatives \\spad{Y}[1]'..\\spad{Y}[\\spad{n}]' defined in terms of \\spad{X},{}\\spad{Y}[1]..\\spad{Y}[\\spad{n}] from \\axiom{\\spad{xStart}} to \\axiom{\\spad{xEnd}} with the initial values for \\spad{Y}[1]..\\spad{Y}[\\spad{n}] (\\axiom{\\spad{yInitial}}) to a tolerance \\axiom{\\spad{tol}}. The values of \\spad{Y}[1]..\\spad{Y}[\\spad{n}] will be output for the values of \\spad{X} in \\axiom{\\spad{intVals}}. \\blankline It iterates over the \\axiom{domains} of \\axiomType{OrdinaryDifferentialEquationsSolverCategory} contained in the table of routines \\axiom{\\spad{R}} to get the name and other relevant information of the the (domain of the) numerical routine likely to be the most appropriate,{} \\spadignore{i.e.} have the best \\axiom{measure}. \\blankline The method used to perform the numerical process will be one of the routines contained in the NAG numerical Library. The function predicts the likely most effective routine by checking various attributes of the system of ODE's and calculating a measure of compatibility of each routine to these attributes. \\blankline It then calls the resulting `best' routine.") (((|Result|) (|Vector| (|Expression| (|Float|))) (|Float|) (|Float|) (|List| (|Float|)) (|Expression| (|Float|)) (|Float|)) "\\spad{solve(f,xStart,xEnd,yInitial,G,tol)} is a top level ANNA function to solve numerically a system of ordinary differential equations,{} \\axiom{\\spad{f}},{} \\spadignore{i.e.} equations for the derivatives \\spad{Y}[1]'..\\spad{Y}[\\spad{n}]' defined in terms of \\spad{X},{}\\spad{Y}[1]..\\spad{Y}[\\spad{n}] from \\axiom{\\spad{xStart}} to \\axiom{\\spad{xEnd}} with the initial values for \\spad{Y}[1]..\\spad{Y}[\\spad{n}] (\\axiom{\\spad{yInitial}}) to a tolerance \\axiom{\\spad{tol}}. The calculation will stop if the function \\spad{G}(\\spad{X},{}\\spad{Y}[1],{}..,{}\\spad{Y}[\\spad{n}]) evaluates to zero before \\spad{X} = \\spad{xEnd}. \\blankline It iterates over the \\axiom{domains} of \\axiomType{OrdinaryDifferentialEquationsSolverCategory} contained in the table of routines \\axiom{\\spad{R}} to get the name and other relevant information of the the (domain of the) numerical routine likely to be the most appropriate,{} \\spadignore{i.e.} have the best \\axiom{measure}. \\blankline The method used to perform the numerical process will be one of the routines contained in the NAG numerical Library. The function predicts the likely most effective routine by checking various attributes of the system of ODE's and calculating a measure of compatibility of each routine to these attributes. \\blankline It then calls the resulting `best' routine.") (((|Result|) (|Vector| (|Expression| (|Float|))) (|Float|) (|Float|) (|List| (|Float|)) (|Float|)) "\\spad{solve(f,xStart,xEnd,yInitial,tol)} is a top level ANNA function to solve numerically a system of ordinary differential equations,{} \\axiom{\\spad{f}},{} \\spadignore{i.e.} equations for the derivatives \\spad{Y}[1]'..\\spad{Y}[\\spad{n}]' defined in terms of \\spad{X},{}\\spad{Y}[1]..\\spad{Y}[\\spad{n}] from \\axiom{\\spad{xStart}} to \\axiom{\\spad{xEnd}} with the initial values for \\spad{Y}[1]..\\spad{Y}[\\spad{n}] (\\axiom{\\spad{yInitial}}) to a tolerance \\axiom{\\spad{tol}}. \\blankline It iterates over the \\axiom{domains} of \\axiomType{OrdinaryDifferentialEquationsSolverCategory} contained in the table of routines \\axiom{\\spad{R}} to get the name and other relevant information of the the (domain of the) numerical routine likely to be the most appropriate,{} \\spadignore{i.e.} have the best \\axiom{measure}. \\blankline The method used to perform the numerical process will be one of the routines contained in the NAG numerical Library. The function predicts the likely most effective routine by checking various attributes of the system of ODE's and calculating a measure of compatibility of each routine to these attributes. \\blankline It then calls the resulting `best' routine.") (((|Result|) (|Vector| (|Expression| (|Float|))) (|Float|) (|Float|) (|List| (|Float|))) "\\spad{solve(f,xStart,xEnd,yInitial)} is a top level ANNA function to solve numerically a system of ordinary differential equations \\spadignore{i.e.} equations for the derivatives \\spad{Y}[1]'..\\spad{Y}[\\spad{n}]' defined in terms of \\spad{X},{}\\spad{Y}[1]..\\spad{Y}[\\spad{n}],{} together with a starting value for \\spad{X} and \\spad{Y}[1]..\\spad{Y}[\\spad{n}] (called the initial conditions) and a final value of \\spad{X}. A default value is used for the accuracy requirement. \\blankline It iterates over the \\axiom{domains} of \\axiomType{OrdinaryDifferentialEquationsSolverCategory} contained in the table of routines \\axiom{\\spad{R}} to get the name and other relevant information of the the (domain of the) numerical routine likely to be the most appropriate,{} \\spadignore{i.e.} have the best \\axiom{measure}. \\blankline The method used to perform the numerical process will be one of the routines contained in the NAG numerical Library. The function predicts the likely most effective routine by checking various attributes of the system of ODE's and calculating a measure of compatibility of each routine to these attributes. \\blankline It then calls the resulting `best' routine.") (((|Result|) (|NumericalODEProblem|) (|RoutinesTable|)) "\\spad{solve(odeProblem,R)} is a top level ANNA function to solve numerically a system of ordinary differential equations \\spadignore{i.e.} equations for the derivatives \\spad{Y}[1]'..\\spad{Y}[\\spad{n}]' defined in terms of \\spad{X},{}\\spad{Y}[1]..\\spad{Y}[\\spad{n}],{} together with starting values for \\spad{X} and \\spad{Y}[1]..\\spad{Y}[\\spad{n}] (called the initial conditions),{} a final value of \\spad{X},{} an accuracy requirement and any intermediate points at which the result is required. \\blankline It iterates over the \\axiom{domains} of \\axiomType{OrdinaryDifferentialEquationsSolverCategory} contained in the table of routines \\axiom{\\spad{R}} to get the name and other relevant information of the the (domain of the) numerical routine likely to be the most appropriate,{} \\spadignore{i.e.} have the best \\axiom{measure}. \\blankline The method used to perform the numerical process will be one of the routines contained in the NAG numerical Library. The function predicts the likely most effective routine by checking various attributes of the system of ODE's and calculating a measure of compatibility of each routine to these attributes. \\blankline It then calls the resulting `best' routine.") (((|Result|) (|NumericalODEProblem|)) "\\spad{solve(odeProblem)} is a top level ANNA function to solve numerically a system of ordinary differential equations \\spadignore{i.e.} equations for the derivatives \\spad{Y}[1]'..\\spad{Y}[\\spad{n}]' defined in terms of \\spad{X},{}\\spad{Y}[1]..\\spad{Y}[\\spad{n}],{} together with starting values for \\spad{X} and \\spad{Y}[1]..\\spad{Y}[\\spad{n}] (called the initial conditions),{} a final value of \\spad{X},{} an accuracy requirement and any intermediate points at which the result is required. \\blankline It iterates over the \\axiom{domains} of \\axiomType{OrdinaryDifferentialEquationsSolverCategory} to get the name and other relevant information of the the (domain of the) numerical routine likely to be the most appropriate,{} \\spadignore{i.e.} have the best \\axiom{measure}. \\blankline The method used to perform the numerical process will be one of the routines contained in the NAG numerical Library. The function predicts the likely most effective routine by checking various attributes of the system of ODE's and calculating a measure of compatibility of each routine to these attributes. \\blankline It then calls the resulting `best' routine."))) NIL NIL -(-830 -4164 UP UPUP R) +(-830 -4140 UP UPUP R) ((|constructor| (NIL "In-field solution of an linear ordinary differential equation,{} pure algebraic case.")) (|algDsolve| (((|Record| (|:| |particular| (|Union| |#4| "failed")) (|:| |basis| (|List| |#4|))) (|LinearOrdinaryDifferentialOperator1| |#4|) |#4|) "\\spad{algDsolve(op, g)} returns \\spad{[\"failed\", []]} if the equation \\spad{op y = g} has no solution in \\spad{R}. Otherwise,{} it returns \\spad{[f, [y1,...,ym]]} where \\spad{f} is a particular rational solution and the \\spad{y_i's} form a basis for the solutions in \\spad{R} of the homogeneous equation."))) NIL NIL -(-831 -4164 UP L LQ) +(-831 -4140 UP L LQ) ((|constructor| (NIL "\\spad{PrimitiveRatDE} provides functions for in-field solutions of linear \\indented{1}{ordinary differential equations,{} in the transcendental case.} \\indented{1}{The derivation to use is given by the parameter \\spad{L}.}")) (|splitDenominator| (((|Record| (|:| |eq| |#3|) (|:| |rh| (|List| (|Fraction| |#2|)))) |#4| (|List| (|Fraction| |#2|))) "\\spad{splitDenominator(op, [g1,...,gm])} returns \\spad{op0, [h1,...,hm]} such that the equations \\spad{op y = c1 g1 + ... + cm gm} and \\spad{op0 y = c1 h1 + ... + cm hm} have the same solutions.")) (|indicialEquation| ((|#2| |#4| |#1|) "\\spad{indicialEquation(op, a)} returns the indicial equation of \\spad{op} at \\spad{a}.") ((|#2| |#3| |#1|) "\\spad{indicialEquation(op, a)} returns the indicial equation of \\spad{op} at \\spad{a}.")) (|indicialEquations| (((|List| (|Record| (|:| |center| |#2|) (|:| |equation| |#2|))) |#4| |#2|) "\\spad{indicialEquations(op, p)} returns \\spad{[[d1,e1],...,[dq,eq]]} where the \\spad{d_i}'s are the affine singularities of \\spad{op} above the roots of \\spad{p},{} and the \\spad{e_i}'s are the indicial equations at each \\spad{d_i}.") (((|List| (|Record| (|:| |center| |#2|) (|:| |equation| |#2|))) |#4|) "\\spad{indicialEquations op} returns \\spad{[[d1,e1],...,[dq,eq]]} where the \\spad{d_i}'s are the affine singularities of \\spad{op},{} and the \\spad{e_i}'s are the indicial equations at each \\spad{d_i}.") (((|List| (|Record| (|:| |center| |#2|) (|:| |equation| |#2|))) |#3| |#2|) "\\spad{indicialEquations(op, p)} returns \\spad{[[d1,e1],...,[dq,eq]]} where the \\spad{d_i}'s are the affine singularities of \\spad{op} above the roots of \\spad{p},{} and the \\spad{e_i}'s are the indicial equations at each \\spad{d_i}.") (((|List| (|Record| (|:| |center| |#2|) (|:| |equation| |#2|))) |#3|) "\\spad{indicialEquations op} returns \\spad{[[d1,e1],...,[dq,eq]]} where the \\spad{d_i}'s are the affine singularities of \\spad{op},{} and the \\spad{e_i}'s are the indicial equations at each \\spad{d_i}.")) (|denomLODE| ((|#2| |#3| (|List| (|Fraction| |#2|))) "\\spad{denomLODE(op, [g1,...,gm])} returns a polynomial \\spad{d} such that any rational solution of \\spad{op y = c1 g1 + ... + cm gm} is of the form \\spad{p/d} for some polynomial \\spad{p}.") (((|Union| |#2| "failed") |#3| (|Fraction| |#2|)) "\\spad{denomLODE(op, g)} returns a polynomial \\spad{d} such that any rational solution of \\spad{op y = g} is of the form \\spad{p/d} for some polynomial \\spad{p},{} and \"failed\",{} if the equation has no rational solution."))) NIL NIL @@ -3260,38 +3260,38 @@ 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 -(-833 -4164 UP L LQ) +(-833 -4140 UP L LQ) ((|constructor| (NIL "In-field solution of Riccati equations,{} primitive case.")) (|changeVar| ((|#3| |#3| (|Fraction| |#2|)) "\\spad{changeVar(+/[ai D^i], a)} returns the operator \\spad{+/[ai (D+a)^i]}.") ((|#3| |#3| |#2|) "\\spad{changeVar(+/[ai D^i], a)} returns the operator \\spad{+/[ai (D+a)^i]}.")) (|singRicDE| (((|List| (|Record| (|:| |frac| (|Fraction| |#2|)) (|:| |eq| |#3|))) |#3| (|Mapping| (|List| |#2|) |#2| (|SparseUnivariatePolynomial| |#2|)) (|Mapping| (|Factored| |#2|) |#2|)) "\\spad{singRicDE(op, zeros, ezfactor)} returns \\spad{[[f1, L1], [f2, L2], ... , [fk, Lk]]} such that the singular part of any rational solution of the associated Riccati equation of \\spad{op y=0} must be one of the \\spad{fi}'s (up to the constant coefficient),{} in which case the equation for \\spad{z=y e^{-int p}} is \\spad{Li z=0}. \\spad{zeros(C(x),H(x,y))} returns all the \\spad{P_i(x)}'s such that \\spad{H(x,P_i(x)) = 0 modulo C(x)}. Argument \\spad{ezfactor} is a factorisation in \\spad{UP},{} not necessarily into irreducibles.")) (|polyRicDE| (((|List| (|Record| (|:| |poly| |#2|) (|:| |eq| |#3|))) |#3| (|Mapping| (|List| |#1|) |#2|)) "\\spad{polyRicDE(op, zeros)} returns \\spad{[[p1, L1], [p2, L2], ... , [pk, Lk]]} such that the polynomial part of any rational solution of the associated Riccati equation of \\spad{op y=0} must be one of the \\spad{pi}'s (up to the constant coefficient),{} in which case the equation for \\spad{z=y e^{-int p}} is \\spad{Li z =0}. \\spad{zeros} is a zero finder in \\spad{UP}.")) (|constantCoefficientRicDE| (((|List| (|Record| (|:| |constant| |#1|) (|:| |eq| |#3|))) |#3| (|Mapping| (|List| |#1|) |#2|)) "\\spad{constantCoefficientRicDE(op, ric)} returns \\spad{[[a1, L1], [a2, L2], ... , [ak, Lk]]} such that any rational solution with no polynomial part of the associated Riccati equation of \\spad{op y = 0} must be one of the \\spad{ai}'s in which case the equation for \\spad{z = y e^{-int ai}} is \\spad{Li z = 0}. \\spad{ric} is a Riccati equation solver over \\spad{F},{} whose input is the associated linear equation.")) (|leadingCoefficientRicDE| (((|List| (|Record| (|:| |deg| (|NonNegativeInteger|)) (|:| |eq| |#2|))) |#3|) "\\spad{leadingCoefficientRicDE(op)} returns \\spad{[[m1, p1], [m2, p2], ... , [mk, pk]]} such that the polynomial part of any rational solution of the associated Riccati equation of \\spad{op y = 0} must have degree mj for some \\spad{j},{} and its leading coefficient is then a zero of pj. In addition,{}\\spad{m1>m2> ... >mk}.")) (|denomRicDE| ((|#2| |#3|) "\\spad{denomRicDE(op)} returns a polynomial \\spad{d} such that any rational solution of the associated Riccati equation of \\spad{op y = 0} is of the form \\spad{p/d + q'/q + r} for some polynomials \\spad{p} and \\spad{q} and a reduced \\spad{r}. Also,{} \\spad{deg(p) < deg(d)} and {gcd(\\spad{d},{}\\spad{q}) = 1}."))) NIL NIL -(-834 -4164 UP) +(-834 -4140 UP) ((|constructor| (NIL "\\spad{RationalLODE} provides functions for in-field solutions of linear \\indented{1}{ordinary differential equations,{} in the rational case.}")) (|indicialEquationAtInfinity| ((|#2| (|LinearOrdinaryDifferentialOperator2| |#2| (|Fraction| |#2|))) "\\spad{indicialEquationAtInfinity op} returns the indicial equation of \\spad{op} at infinity.") ((|#2| (|LinearOrdinaryDifferentialOperator1| (|Fraction| |#2|))) "\\spad{indicialEquationAtInfinity op} returns the indicial equation of \\spad{op} at infinity.")) (|ratDsolve| (((|Record| (|:| |basis| (|List| (|Fraction| |#2|))) (|:| |mat| (|Matrix| |#1|))) (|LinearOrdinaryDifferentialOperator2| |#2| (|Fraction| |#2|)) (|List| (|Fraction| |#2|))) "\\spad{ratDsolve(op, [g1,...,gm])} returns \\spad{[[h1,...,hq], M]} such that any rational solution of \\spad{op y = c1 g1 + ... + cm gm} is of the form \\spad{d1 h1 + ... + dq hq} where \\spad{M [d1,...,dq,c1,...,cm] = 0}.") (((|Record| (|:| |particular| (|Union| (|Fraction| |#2|) "failed")) (|:| |basis| (|List| (|Fraction| |#2|)))) (|LinearOrdinaryDifferentialOperator2| |#2| (|Fraction| |#2|)) (|Fraction| |#2|)) "\\spad{ratDsolve(op, g)} returns \\spad{[\"failed\", []]} if the equation \\spad{op y = g} has no rational solution. Otherwise,{} it returns \\spad{[f, [y1,...,ym]]} where \\spad{f} is a particular rational solution and the \\spad{yi}'s form a basis for the rational solutions of the homogeneous equation.") (((|Record| (|:| |basis| (|List| (|Fraction| |#2|))) (|:| |mat| (|Matrix| |#1|))) (|LinearOrdinaryDifferentialOperator1| (|Fraction| |#2|)) (|List| (|Fraction| |#2|))) "\\spad{ratDsolve(op, [g1,...,gm])} returns \\spad{[[h1,...,hq], M]} such that any rational solution of \\spad{op y = c1 g1 + ... + cm gm} is of the form \\spad{d1 h1 + ... + dq hq} where \\spad{M [d1,...,dq,c1,...,cm] = 0}.") (((|Record| (|:| |particular| (|Union| (|Fraction| |#2|) "failed")) (|:| |basis| (|List| (|Fraction| |#2|)))) (|LinearOrdinaryDifferentialOperator1| (|Fraction| |#2|)) (|Fraction| |#2|)) "\\spad{ratDsolve(op, g)} returns \\spad{[\"failed\", []]} if the equation \\spad{op y = g} has no rational solution. Otherwise,{} it returns \\spad{[f, [y1,...,ym]]} where \\spad{f} is a particular rational solution and the \\spad{yi}'s form a basis for the rational solutions of the homogeneous equation."))) NIL NIL -(-835 -4164 L UP A LO) +(-835 -4140 L UP A LO) ((|constructor| (NIL "Elimination of an algebraic from the coefficentss of a linear ordinary differential equation.")) (|reduceLODE| (((|Record| (|:| |mat| (|Matrix| |#2|)) (|:| |vec| (|Vector| |#1|))) |#5| |#4|) "\\spad{reduceLODE(op, g)} returns \\spad{[m, v]} such that any solution in \\spad{A} of \\spad{op z = g} is of the form \\spad{z = (z_1,...,z_m) . (b_1,...,b_m)} where the \\spad{b_i's} are the basis of \\spad{A} over \\spad{F} returned by \\spadfun{basis}() from \\spad{A},{} and the \\spad{z_i's} satisfy the differential system \\spad{M.z = v}."))) NIL NIL -(-836 -4164 UP) +(-836 -4140 UP) ((|constructor| (NIL "In-field solution of Riccati equations,{} rational case.")) (|polyRicDE| (((|List| (|Record| (|:| |poly| |#2|) (|:| |eq| (|LinearOrdinaryDifferentialOperator2| |#2| (|Fraction| |#2|))))) (|LinearOrdinaryDifferentialOperator2| |#2| (|Fraction| |#2|)) (|Mapping| (|List| |#1|) |#2|)) "\\spad{polyRicDE(op, zeros)} returns \\spad{[[p1, L1], [p2, L2], ... , [pk,Lk]]} such that the polynomial part of any rational solution of the associated Riccati equation of \\spad{op y = 0} must be one of the \\spad{pi}'s (up to the constant coefficient),{} in which case the equation for \\spad{z = y e^{-int p}} is \\spad{Li z = 0}. \\spad{zeros} is a zero finder in \\spad{UP}.")) (|singRicDE| (((|List| (|Record| (|:| |frac| (|Fraction| |#2|)) (|:| |eq| (|LinearOrdinaryDifferentialOperator2| |#2| (|Fraction| |#2|))))) (|LinearOrdinaryDifferentialOperator2| |#2| (|Fraction| |#2|)) (|Mapping| (|Factored| |#2|) |#2|)) "\\spad{singRicDE(op, ezfactor)} returns \\spad{[[f1,L1], [f2,L2],..., [fk,Lk]]} such that the singular ++ part of any rational solution of the associated Riccati equation of \\spad{op y = 0} must be one of the \\spad{fi}'s (up to the constant coefficient),{} in which case the equation for \\spad{z = y e^{-int ai}} is \\spad{Li z = 0}. Argument \\spad{ezfactor} is a factorisation in \\spad{UP},{} not necessarily into irreducibles.")) (|ricDsolve| (((|List| (|Fraction| |#2|)) (|LinearOrdinaryDifferentialOperator2| |#2| (|Fraction| |#2|)) (|Mapping| (|Factored| |#2|) |#2|)) "\\spad{ricDsolve(op, ezfactor)} returns the rational solutions of the associated Riccati equation of \\spad{op y = 0}. Argument \\spad{ezfactor} is a factorisation in \\spad{UP},{} not necessarily into irreducibles.") (((|List| (|Fraction| |#2|)) (|LinearOrdinaryDifferentialOperator2| |#2| (|Fraction| |#2|))) "\\spad{ricDsolve(op)} returns the rational solutions of the associated Riccati equation of \\spad{op y = 0}.") (((|List| (|Fraction| |#2|)) (|LinearOrdinaryDifferentialOperator1| (|Fraction| |#2|)) (|Mapping| (|Factored| |#2|) |#2|)) "\\spad{ricDsolve(op, ezfactor)} returns the rational solutions of the associated Riccati equation of \\spad{op y = 0}. Argument \\spad{ezfactor} is a factorisation in \\spad{UP},{} not necessarily into irreducibles.") (((|List| (|Fraction| |#2|)) (|LinearOrdinaryDifferentialOperator1| (|Fraction| |#2|))) "\\spad{ricDsolve(op)} returns the rational solutions of the associated Riccati equation of \\spad{op y = 0}.") (((|List| (|Fraction| |#2|)) (|LinearOrdinaryDifferentialOperator2| |#2| (|Fraction| |#2|)) (|Mapping| (|List| |#1|) |#2|) (|Mapping| (|Factored| |#2|) |#2|)) "\\spad{ricDsolve(op, zeros, ezfactor)} returns the rational solutions of the associated Riccati equation of \\spad{op y = 0}. \\spad{zeros} is a zero finder in \\spad{UP}. Argument \\spad{ezfactor} is a factorisation in \\spad{UP},{} not necessarily into irreducibles.") (((|List| (|Fraction| |#2|)) (|LinearOrdinaryDifferentialOperator2| |#2| (|Fraction| |#2|)) (|Mapping| (|List| |#1|) |#2|)) "\\spad{ricDsolve(op, zeros)} returns the rational solutions of the associated Riccati equation of \\spad{op y = 0}. \\spad{zeros} is a zero finder in \\spad{UP}.") (((|List| (|Fraction| |#2|)) (|LinearOrdinaryDifferentialOperator1| (|Fraction| |#2|)) (|Mapping| (|List| |#1|) |#2|) (|Mapping| (|Factored| |#2|) |#2|)) "\\spad{ricDsolve(op, zeros, ezfactor)} returns the rational solutions of the associated Riccati equation of \\spad{op y = 0}. \\spad{zeros} is a zero finder in \\spad{UP}. Argument \\spad{ezfactor} is a factorisation in \\spad{UP},{} not necessarily into irreducibles.") (((|List| (|Fraction| |#2|)) (|LinearOrdinaryDifferentialOperator1| (|Fraction| |#2|)) (|Mapping| (|List| |#1|) |#2|)) "\\spad{ricDsolve(op, zeros)} returns the rational solutions of the associated Riccati equation of \\spad{op y = 0}. \\spad{zeros} is a zero finder in \\spad{UP}."))) NIL ((|HasCategory| |#1| (QUOTE (-27)))) -(-837 -4164 LO) +(-837 -4140 LO) ((|constructor| (NIL "SystemODESolver provides tools for triangulating and solving some systems of linear ordinary differential equations.")) (|solveInField| (((|Record| (|:| |particular| (|Union| (|Vector| |#1|) "failed")) (|:| |basis| (|List| (|Vector| |#1|)))) (|Matrix| |#2|) (|Vector| |#1|) (|Mapping| (|Record| (|:| |particular| (|Union| |#1| "failed")) (|:| |basis| (|List| |#1|))) |#2| |#1|)) "\\spad{solveInField(m, v, solve)} returns \\spad{[[v_1,...,v_m], v_p]} such that the solutions in \\spad{F} of the system \\spad{m x = v} are \\spad{v_p + c_1 v_1 + ... + c_m v_m} where the \\spad{c_i's} are constants,{} and the \\spad{v_i's} form a basis for the solutions of \\spad{m x = 0}. Argument \\spad{solve} is a function for solving a single linear ordinary differential equation in \\spad{F}.")) (|solve| (((|Union| (|Record| (|:| |particular| (|Vector| |#1|)) (|:| |basis| (|Matrix| |#1|))) "failed") (|Matrix| |#1|) (|Vector| |#1|) (|Mapping| (|Union| (|Record| (|:| |particular| |#1|) (|:| |basis| (|List| |#1|))) "failed") |#2| |#1|)) "\\spad{solve(m, v, solve)} returns \\spad{[[v_1,...,v_m], v_p]} such that the solutions in \\spad{F} of the system \\spad{D x = m x + v} are \\spad{v_p + c_1 v_1 + ... + c_m v_m} where the \\spad{c_i's} are constants,{} and the \\spad{v_i's} form a basis for the solutions of \\spad{D x = m x}. Argument \\spad{solve} is a function for solving a single linear ordinary differential equation in \\spad{F}.")) (|triangulate| (((|Record| (|:| |mat| (|Matrix| |#2|)) (|:| |vec| (|Vector| |#1|))) (|Matrix| |#2|) (|Vector| |#1|)) "\\spad{triangulate(m, v)} returns \\spad{[m_0, v_0]} such that \\spad{m_0} is upper triangular and the system \\spad{m_0 x = v_0} is equivalent to \\spad{m x = v}.") (((|Record| (|:| A (|Matrix| |#1|)) (|:| |eqs| (|List| (|Record| (|:| C (|Matrix| |#1|)) (|:| |g| (|Vector| |#1|)) (|:| |eq| |#2|) (|:| |rh| |#1|))))) (|Matrix| |#1|) (|Vector| |#1|)) "\\spad{triangulate(M,v)} returns \\spad{A,[[C_1,g_1,L_1,h_1],...,[C_k,g_k,L_k,h_k]]} such that under the change of variable \\spad{y = A z},{} the first order linear system \\spad{D y = M y + v} is uncoupled as \\spad{D z_i = C_i z_i + g_i} and each \\spad{C_i} is a companion matrix corresponding to the scalar equation \\spad{L_i z_j = h_i}."))) NIL NIL -(-838 -4164 LODO) +(-838 -4140 LODO) ((|constructor| (NIL "\\spad{ODETools} provides tools for the linear ODE solver.")) (|particularSolution| (((|Union| |#1| "failed") |#2| |#1| (|List| |#1|) (|Mapping| |#1| |#1|)) "\\spad{particularSolution(op, g, [f1,...,fm], I)} returns a particular solution \\spad{h} of the equation \\spad{op y = g} where \\spad{[f1,...,fm]} are linearly independent and \\spad{op(fi)=0}. The value \"failed\" is returned if no particular solution is found. Note: the method of variations of parameters is used.")) (|variationOfParameters| (((|Union| (|Vector| |#1|) "failed") |#2| |#1| (|List| |#1|)) "\\spad{variationOfParameters(op, g, [f1,...,fm])} returns \\spad{[u1,...,um]} such that a particular solution of the equation \\spad{op y = g} is \\spad{f1 int(u1) + ... + fm int(um)} where \\spad{[f1,...,fm]} are linearly independent and \\spad{op(fi)=0}. The value \"failed\" is returned if \\spad{m < n} and no particular solution is found.")) (|wronskianMatrix| (((|Matrix| |#1|) (|List| |#1|) (|NonNegativeInteger|)) "\\spad{wronskianMatrix([f1,...,fn], q, D)} returns the \\spad{q x n} matrix \\spad{m} whose i^th row is \\spad{[f1^(i-1),...,fn^(i-1)]}.") (((|Matrix| |#1|) (|List| |#1|)) "\\spad{wronskianMatrix([f1,...,fn])} returns the \\spad{n x n} matrix \\spad{m} whose i^th row is \\spad{[f1^(i-1),...,fn^(i-1)]}."))) 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(|HasCategory| |#2| (QUOTE (-102))) (-12 (|HasCategory| |#2| (QUOTE (-1133))) (|HasCategory| |#2| (|%list| (QUOTE -321) (|devaluate| |#2|))))) (-840 R) ((|constructor| (NIL "\\spadtype{OrderlyDifferentialPolynomial} implements an ordinary differential polynomial ring in arbitrary number of differential indeterminates,{} with coefficients in a ring. The ranking on the differential indeterminate is orderly. This is analogous to the domain \\spadtype{Polynomial}. \\blankline"))) (((-4512 "*") |has| |#1| (-175)) (-4503 |has| |#1| (-571)) (-4508 |has| |#1| (-6 -4508)) (-4505 . T) (-4504 . T) (-4507 . T)) -((|HasCategory| |#1| (QUOTE (-940))) (-4144 (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-466))) (|HasCategory| |#1| (QUOTE (-571))) (|HasCategory| |#1| (QUOTE (-940)))) (-4144 (|HasCategory| |#1| (QUOTE (-466))) (|HasCategory| |#1| (QUOTE (-571))) (|HasCategory| |#1| (QUOTE (-940)))) (-4144 (|HasCategory| |#1| (QUOTE (-466))) (|HasCategory| |#1| (QUOTE (-940)))) (|HasCategory| |#1| (QUOTE (-571))) (|HasCategory| |#1| (QUOTE (-175))) (-4144 (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-571)))) (-12 (|HasCategory| (-842 (-1209)) (|%list| (QUOTE -912) (QUOTE (-391)))) (|HasCategory| |#1| (|%list| (QUOTE -912) (QUOTE (-391))))) (-12 (|HasCategory| (-842 (-1209)) (|%list| (QUOTE -912) (QUOTE (-560)))) (|HasCategory| |#1| (|%list| (QUOTE -912) (QUOTE (-560))))) (-12 (|HasCategory| (-842 (-1209)) (|%list| (QUOTE -633) (|%list| (QUOTE -916) (QUOTE (-391))))) (|HasCategory| |#1| (|%list| (QUOTE -633) (|%list| (QUOTE -916) (QUOTE (-391)))))) (-12 (|HasCategory| (-842 (-1209)) (|%list| (QUOTE -633) (|%list| (QUOTE -916) (QUOTE (-560))))) (|HasCategory| |#1| (|%list| (QUOTE -633) (|%list| (QUOTE -916) (QUOTE (-560)))))) (-12 (|HasCategory| (-842 (-1209)) (|%list| (QUOTE -633) (QUOTE (-549)))) (|HasCategory| |#1| (|%list| (QUOTE -633) (QUOTE (-549))))) (|HasCategory| |#1| (|%list| (QUOTE -660) (QUOTE (-560)))) (|HasCategory| |#1| (QUOTE (-149))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (|%list| (QUOTE -38) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#1| (|%list| (QUOTE -1070) (QUOTE (-560)))) (-4144 (|HasCategory| |#1| (|%list| (QUOTE -38) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#1| (|%list| (QUOTE -1070) (|%list| (QUOTE -421) (QUOTE (-560)))))) (|HasCategory| |#1| (|%list| (QUOTE -1070) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#1| (QUOTE (-240))) (|HasCategory| |#1| (QUOTE (-239))) (|HasCategory| |#1| (|%list| (QUOTE -930) (QUOTE (-1209)))) (|HasCategory| |#1| (|%list| (QUOTE -928) (QUOTE (-1209)))) (|HasCategory| |#1| (QUOTE (-376))) (|HasAttribute| |#1| (QUOTE -4508)) (|HasCategory| |#1| (QUOTE (-466))) (-12 (|HasCategory| $ (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-940)))) (-4144 (-12 (|HasCategory| $ (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-940)))) (|HasCategory| |#1| (QUOTE (-147))))) +((|HasCategory| |#1| (QUOTE (-940))) (-4118 (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-466))) (|HasCategory| |#1| (QUOTE (-571))) (|HasCategory| |#1| (QUOTE (-940)))) (-4118 (|HasCategory| |#1| (QUOTE (-466))) (|HasCategory| |#1| (QUOTE (-571))) (|HasCategory| |#1| (QUOTE (-940)))) (-4118 (|HasCategory| |#1| (QUOTE (-466))) (|HasCategory| |#1| (QUOTE (-940)))) (|HasCategory| |#1| (QUOTE (-571))) (|HasCategory| |#1| (QUOTE (-175))) (-4118 (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-571)))) (-12 (|HasCategory| (-842 (-1209)) (|%list| (QUOTE -912) (QUOTE (-391)))) (|HasCategory| |#1| (|%list| (QUOTE -912) (QUOTE (-391))))) (-12 (|HasCategory| (-842 (-1209)) (|%list| (QUOTE -912) (QUOTE (-560)))) (|HasCategory| |#1| (|%list| (QUOTE -912) (QUOTE (-560))))) (-12 (|HasCategory| (-842 (-1209)) (|%list| (QUOTE -633) (|%list| (QUOTE -916) (QUOTE (-391))))) (|HasCategory| |#1| (|%list| (QUOTE -633) (|%list| (QUOTE -916) (QUOTE (-391)))))) (-12 (|HasCategory| (-842 (-1209)) (|%list| (QUOTE -633) (|%list| (QUOTE -916) (QUOTE (-560))))) (|HasCategory| |#1| (|%list| (QUOTE -633) (|%list| (QUOTE -916) (QUOTE (-560)))))) (-12 (|HasCategory| (-842 (-1209)) (|%list| (QUOTE -633) (QUOTE (-549)))) (|HasCategory| |#1| (|%list| (QUOTE -633) (QUOTE (-549))))) (|HasCategory| |#1| (|%list| (QUOTE -660) (QUOTE (-560)))) (|HasCategory| |#1| (QUOTE (-149))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (|%list| (QUOTE -38) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#1| (|%list| (QUOTE -1070) (QUOTE (-560)))) (-4118 (|HasCategory| |#1| (|%list| (QUOTE -38) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#1| (|%list| (QUOTE -1070) (|%list| (QUOTE -421) (QUOTE (-560)))))) (|HasCategory| |#1| (|%list| (QUOTE -1070) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#1| (QUOTE (-240))) (|HasCategory| |#1| (QUOTE (-239))) (|HasCategory| |#1| (|%list| (QUOTE -930) (QUOTE (-1209)))) (|HasCategory| |#1| (|%list| (QUOTE -928) (QUOTE (-1209)))) (|HasCategory| |#1| (QUOTE (-376))) (|HasAttribute| |#1| (QUOTE -4508)) (|HasCategory| |#1| (QUOTE (-466))) (-12 (|HasCategory| $ (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-940)))) (-4118 (-12 (|HasCategory| $ (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-940)))) (|HasCategory| |#1| (QUOTE (-147))))) (-841 |Kernels| R |var|) ((|constructor| (NIL "This constructor produces an ordinary differential ring from a partial differential ring by specifying a variable."))) (((-4512 "*") |has| |#2| (-376)) (-4503 |has| |#2| (-376)) (-4508 |has| |#2| (-376)) (-4502 |has| |#2| (-376)) (-4507 . T) (-4505 . T) (-4504 . T)) @@ -3355,7 +3355,7 @@ NIL (-856 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."))) ((-4507 |has| |#1| (-871))) -((|HasCategory| |#1| (QUOTE (-871))) (|HasCategory| |#1| (QUOTE (-21))) (-4144 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-871)))) (|HasCategory| |#1| (|%list| (QUOTE -1070) (|%list| (QUOTE -421) (QUOTE (-560))))) (-4144 (|HasCategory| |#1| (QUOTE (-871))) (|HasCategory| |#1| (|%list| (QUOTE -1070) (QUOTE (-560))))) (|HasCategory| |#1| (|%list| (QUOTE -1070) (QUOTE (-560)))) (|HasCategory| |#1| (QUOTE (-559)))) +((|HasCategory| |#1| (QUOTE (-871))) (|HasCategory| |#1| (QUOTE (-21))) (-4118 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-871)))) (|HasCategory| |#1| (|%list| (QUOTE -1070) (|%list| (QUOTE -421) (QUOTE (-560))))) (-4118 (|HasCategory| |#1| (QUOTE (-871))) (|HasCategory| |#1| (|%list| (QUOTE -1070) (QUOTE (-560))))) (|HasCategory| |#1| (|%list| (QUOTE -1070) (QUOTE (-560)))) (|HasCategory| |#1| (QUOTE (-559)))) (-857 R S) ((|constructor| (NIL "Lifting of maps to one-point completions. Date Created: 4 Oct 1989 Date Last Updated: 4 Oct 1989")) (|map| (((|OnePointCompletion| |#2|) (|Mapping| |#2| |#1|) (|OnePointCompletion| |#1|) (|OnePointCompletion| |#2|)) "\\spad{map(f, r, i)} lifts \\spad{f} and applies it to \\spad{r},{} assuming that \\spad{f}(infinity) = \\spad{i}.") (((|OnePointCompletion| |#2|) (|Mapping| |#2| |#1|) (|OnePointCompletion| |#1|)) "\\spad{map(f, r)} lifts \\spad{f} and applies it to \\spad{r},{} assuming that \\spad{f}(infinity) = infinity."))) NIL @@ -3395,7 +3395,7 @@ NIL (-866 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| (($) "\\spad{plusInfinity()} returns +infinity."))) ((-4507 |has| |#1| (-871))) -((|HasCategory| |#1| (QUOTE (-871))) (|HasCategory| |#1| (QUOTE (-21))) (-4144 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-871)))) (|HasCategory| |#1| (|%list| (QUOTE -1070) (|%list| (QUOTE -421) (QUOTE (-560))))) (-4144 (|HasCategory| |#1| (QUOTE (-871))) (|HasCategory| |#1| (|%list| (QUOTE -1070) (QUOTE (-560))))) (|HasCategory| |#1| (|%list| (QUOTE -1070) (QUOTE (-560)))) (|HasCategory| |#1| (QUOTE (-559)))) +((|HasCategory| |#1| (QUOTE (-871))) (|HasCategory| |#1| (QUOTE (-21))) (-4118 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-871)))) (|HasCategory| |#1| (|%list| (QUOTE -1070) (|%list| (QUOTE -421) (QUOTE (-560))))) (-4118 (|HasCategory| |#1| (QUOTE (-871))) (|HasCategory| |#1| (|%list| (QUOTE -1070) (QUOTE (-560))))) (|HasCategory| |#1| (|%list| (QUOTE -1070) (QUOTE (-560)))) (|HasCategory| |#1| (QUOTE (-559)))) (-867 R S) ((|constructor| (NIL "Lifting of maps to ordered completions. Date Created: 4 Oct 1989 Date Last Updated: 4 Oct 1989")) (|map| (((|OrderedCompletion| |#2|) (|Mapping| |#2| |#1|) (|OrderedCompletion| |#1|) (|OrderedCompletion| |#2|) (|OrderedCompletion| |#2|)) "\\spad{map(f, r, p, m)} lifts \\spad{f} and applies it to \\spad{r},{} assuming that \\spad{f}(plusInfinity) = \\spad{p} and that \\spad{f}(minusInfinity) = \\spad{m}.") (((|OrderedCompletion| |#2|) (|Mapping| |#2| |#1|) (|OrderedCompletion| |#1|)) "\\spad{map(f, r)} lifts \\spad{f} and applies it to \\spad{r},{} assuming that \\spad{f}(plusInfinity) = plusInfinity and that \\spad{f}(minusInfinity) = minusInfinity."))) NIL @@ -3404,7 +3404,7 @@ NIL ((|constructor| (NIL "Ordered finite sets.")) (|max| (($) "\\spad{max} is the maximum value of \\%.")) (|min| (($) "\\spad{min} is the minimum value of \\%."))) NIL NIL -(-869 -2127 S) +(-869 -2123 S) ((|constructor| (NIL "\\indented{3}{This package provides ordering functions on vectors which} are suitable parameters for OrderedDirectProduct.")) (|reverseLex| (((|Boolean|) (|Vector| |#2|) (|Vector| |#2|)) "\\spad{reverseLex(v1,v2)} return \\spad{true} if the vector \\spad{v1} is less than the vector \\spad{v2} in the ordering which is total degree refined by the reverse lexicographic ordering.")) (|totalLex| (((|Boolean|) (|Vector| |#2|) (|Vector| |#2|)) "\\spad{totalLex(v1,v2)} return \\spad{true} if the vector \\spad{v1} is less than the vector \\spad{v2} in the ordering which is total degree refined by lexicographic ordering.")) (|pureLex| (((|Boolean|) (|Vector| |#2|) (|Vector| |#2|)) "\\spad{pureLex(v1,v2)} return \\spad{true} if the vector \\spad{v1} is less than the vector \\spad{v2} in the lexicographic ordering."))) NIL NIL @@ -3444,11 +3444,11 @@ NIL ((|constructor| (NIL "\\spad{UnivariateSkewPolynomialCategoryOps} provides products and \\indented{1}{divisions of univariate skew polynomials.}")) (|rightDivide| (((|Record| (|:| |quotient| |#2|) (|:| |remainder| |#2|)) |#2| |#2| (|Automorphism| |#1|)) "\\spad{rightDivide(a, b, sigma)} returns the pair \\spad{[q,r]} such that \\spad{a = q*b + r} and the degree of \\spad{r} is less than the degree of \\spad{b}. This process is called ``right division''. \\spad{\\sigma} is the morphism to use.")) (|leftDivide| (((|Record| (|:| |quotient| |#2|) (|:| |remainder| |#2|)) |#2| |#2| (|Automorphism| |#1|)) "\\spad{leftDivide(a, b, sigma)} returns the pair \\spad{[q,r]} such that \\spad{a = b*q + r} and the degree of \\spad{r} is less than the degree of \\spad{b}. This process is called ``left division''. \\spad{\\sigma} is the morphism to use.")) (|monicRightDivide| (((|Record| (|:| |quotient| |#2|) (|:| |remainder| |#2|)) |#2| |#2| (|Automorphism| |#1|)) "\\spad{monicRightDivide(a, b, sigma)} returns the pair \\spad{[q,r]} such that \\spad{a = q*b + r} and the degree of \\spad{r} is less than the degree of \\spad{b}. \\spad{b} must be monic. This process is called ``right division''. \\spad{\\sigma} is the morphism to use.")) (|monicLeftDivide| (((|Record| (|:| |quotient| |#2|) (|:| |remainder| |#2|)) |#2| |#2| (|Automorphism| |#1|)) "\\spad{monicLeftDivide(a, b, sigma)} returns the pair \\spad{[q,r]} such that \\spad{a = b*q + r} and the degree of \\spad{r} is less than the degree of \\spad{b}. \\spad{b} must be monic. This process is called ``left division''. \\spad{\\sigma} is the morphism to use.")) (|apply| ((|#1| |#2| |#1| |#1| (|Automorphism| |#1|) (|Mapping| |#1| |#1|)) "\\spad{apply(p, c, m, sigma, delta)} returns \\spad{p(m)} where the action is given by \\spad{x m = c sigma(m) + delta(m)}.")) (|times| ((|#2| |#2| |#2| (|Automorphism| |#1|) (|Mapping| |#1| |#1|)) "\\spad{times(p, q, sigma, delta)} returns \\spad{p * q}. \\spad{\\sigma} and \\spad{\\delta} are the maps to use."))) NIL ((|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (QUOTE (-571)))) -(-879 R |sigma| -1337) +(-879 R |sigma| -3828) ((|constructor| (NIL "This is the domain of sparse univariate skew polynomials over an Ore coefficient field. The multiplication is given by \\spad{x a = \\sigma(a) x + \\delta a}.")) (|outputForm| (((|OutputForm|) $ (|OutputForm|)) "\\spad{outputForm(p, x)} returns the output form of \\spad{p} using \\spad{x} for the otherwise anonymous variable."))) ((-4504 . T) (-4505 . T) (-4507 . T)) ((|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (|%list| (QUOTE -1070) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#1| (|%list| (QUOTE -1070) (QUOTE (-560)))) (|HasCategory| |#1| (QUOTE (-571))) (|HasCategory| |#1| (QUOTE (-466))) (|HasCategory| |#1| (QUOTE (-376)))) -(-880 |x| R |sigma| -1337) +(-880 |x| R |sigma| -3828) ((|constructor| (NIL "This is the domain of univariate skew polynomials over an Ore coefficient field in a named variable. The multiplication is given by \\spad{x a = \\sigma(a) x + \\delta a}."))) ((-4504 . T) (-4505 . T) (-4507 . T)) ((|HasCategory| |#2| (QUOTE (-175))) (|HasCategory| |#2| (|%list| (QUOTE -1070) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#2| (|%list| (QUOTE -1070) (QUOTE (-560)))) (|HasCategory| |#2| (QUOTE (-571))) (|HasCategory| |#2| (QUOTE (-466))) (|HasCategory| |#2| (QUOTE (-376)))) @@ -3515,15 +3515,15 @@ NIL (-896 |p|) ((|constructor| (NIL "Stream-based implementation of Qp: numbers are represented as sum(\\spad{i} = \\spad{k}..,{} a[\\spad{i}] * p^i) where the a[\\spad{i}] lie in 0,{}1,{}...,{}(\\spad{p} - 1)."))) ((-4502 . T) (-4508 . T) (-4503 . T) ((-4512 "*") . T) (-4504 . T) (-4505 . T) (-4507 . T)) -((|HasCategory| (-894 |#1|) (QUOTE (-940))) (|HasCategory| (-894 |#1|) (|%list| (QUOTE -1070) (QUOTE (-1209)))) (|HasCategory| (-894 |#1|) (QUOTE (-147))) (|HasCategory| (-894 |#1|) (QUOTE (-149))) (|HasCategory| (-894 |#1|) (|%list| (QUOTE -633) (QUOTE (-549)))) (|HasCategory| (-894 |#1|) (QUOTE (-1052))) (|HasCategory| (-894 |#1|) (QUOTE (-844))) (|HasCategory| (-894 |#1|) (QUOTE (-872))) (-4144 (|HasCategory| (-894 |#1|) (QUOTE (-844))) (|HasCategory| (-894 |#1|) (QUOTE (-872)))) (|HasCategory| (-894 |#1|) (|%list| (QUOTE -1070) (QUOTE (-560)))) (|HasCategory| (-894 |#1|) (QUOTE (-1184))) (|HasCategory| (-894 |#1|) (|%list| (QUOTE -912) (QUOTE (-391)))) (|HasCategory| (-894 |#1|) (|%list| (QUOTE -912) (QUOTE (-560)))) (|HasCategory| (-894 |#1|) (|%list| (QUOTE -633) (|%list| (QUOTE -916) (QUOTE (-391))))) (|HasCategory| (-894 |#1|) (|%list| (QUOTE -633) (|%list| (QUOTE -916) (QUOTE (-560))))) (|HasCategory| (-894 |#1|) (|%list| (QUOTE -660) (QUOTE (-560)))) (|HasCategory| (-894 |#1|) (QUOTE (-239))) (|HasCategory| (-894 |#1|) (|%list| (QUOTE -930) (QUOTE (-1209)))) (|HasCategory| (-894 |#1|) (QUOTE (-240))) (|HasCategory| (-894 |#1|) (|%list| (QUOTE -928) (QUOTE (-1209)))) (|HasCategory| (-894 |#1|) (|%list| (QUOTE -528) (QUOTE (-1209)) (|%list| (QUOTE -894) (|devaluate| |#1|)))) (|HasCategory| (-894 |#1|) (|%list| (QUOTE -321) (|%list| (QUOTE -894) (|devaluate| |#1|)))) (|HasCategory| (-894 |#1|) (|%list| (QUOTE -298) (|%list| (QUOTE -894) (|devaluate| |#1|)) (|%list| (QUOTE -894) (|devaluate| |#1|)))) (|HasCategory| (-894 |#1|) (QUOTE (-319))) (|HasCategory| (-894 |#1|) (QUOTE (-559))) (-12 (|HasCategory| $ (QUOTE (-147))) (|HasCategory| (-894 |#1|) (QUOTE (-940)))) (-4144 (-12 (|HasCategory| $ (QUOTE (-147))) (|HasCategory| (-894 |#1|) (QUOTE (-940)))) (|HasCategory| (-894 |#1|) (QUOTE (-147))))) +((|HasCategory| (-894 |#1|) (QUOTE (-940))) (|HasCategory| (-894 |#1|) (|%list| (QUOTE -1070) (QUOTE (-1209)))) (|HasCategory| (-894 |#1|) (QUOTE (-147))) (|HasCategory| (-894 |#1|) (QUOTE (-149))) (|HasCategory| (-894 |#1|) (|%list| (QUOTE -633) (QUOTE (-549)))) (|HasCategory| (-894 |#1|) (QUOTE (-1052))) (|HasCategory| (-894 |#1|) (QUOTE (-844))) (|HasCategory| (-894 |#1|) (QUOTE (-872))) (-4118 (|HasCategory| (-894 |#1|) (QUOTE (-844))) (|HasCategory| (-894 |#1|) (QUOTE (-872)))) (|HasCategory| (-894 |#1|) (|%list| (QUOTE -1070) (QUOTE (-560)))) (|HasCategory| (-894 |#1|) (QUOTE (-1184))) (|HasCategory| (-894 |#1|) (|%list| (QUOTE -912) (QUOTE (-391)))) (|HasCategory| (-894 |#1|) (|%list| (QUOTE -912) (QUOTE (-560)))) (|HasCategory| (-894 |#1|) (|%list| (QUOTE -633) (|%list| (QUOTE -916) (QUOTE (-391))))) (|HasCategory| (-894 |#1|) (|%list| (QUOTE -633) (|%list| (QUOTE -916) (QUOTE (-560))))) (|HasCategory| (-894 |#1|) (|%list| (QUOTE -660) (QUOTE (-560)))) (|HasCategory| (-894 |#1|) (QUOTE (-239))) (|HasCategory| (-894 |#1|) (|%list| (QUOTE -930) (QUOTE (-1209)))) (|HasCategory| (-894 |#1|) (QUOTE (-240))) (|HasCategory| (-894 |#1|) (|%list| (QUOTE -928) (QUOTE (-1209)))) (|HasCategory| (-894 |#1|) (|%list| (QUOTE -528) (QUOTE (-1209)) (|%list| (QUOTE -894) (|devaluate| |#1|)))) (|HasCategory| (-894 |#1|) (|%list| (QUOTE -321) (|%list| (QUOTE -894) (|devaluate| |#1|)))) (|HasCategory| (-894 |#1|) (|%list| (QUOTE -298) (|%list| (QUOTE -894) (|devaluate| |#1|)) (|%list| (QUOTE -894) (|devaluate| |#1|)))) (|HasCategory| (-894 |#1|) (QUOTE (-319))) (|HasCategory| (-894 |#1|) (QUOTE (-559))) (-12 (|HasCategory| $ (QUOTE (-147))) (|HasCategory| (-894 |#1|) (QUOTE (-940)))) (-4118 (-12 (|HasCategory| $ (QUOTE (-147))) (|HasCategory| (-894 |#1|) (QUOTE (-940)))) (|HasCategory| (-894 |#1|) (QUOTE (-147))))) (-897 |p| PADIC) ((|constructor| (NIL "This is the category of stream-based representations of Qp.")) (|removeZeroes| (($ (|Integer|) $) "\\spad{removeZeroes(n,x)} removes up to \\spad{n} leading zeroes from the \\spad{p}-adic rational \\spad{x}.") (($ $) "\\spad{removeZeroes(x)} removes leading zeroes from the representation of the \\spad{p}-adic rational \\spad{x}. A \\spad{p}-adic rational is represented by (1) an exponent and (2) a \\spad{p}-adic integer which may have leading zero digits. When the \\spad{p}-adic integer has a leading zero digit,{} a 'leading zero' is removed from the \\spad{p}-adic rational as follows: the number is rewritten by increasing the exponent by 1 and dividing the \\spad{p}-adic integer by \\spad{p}. Note: \\spad{removeZeroes(f)} removes all leading zeroes from \\spad{f}.")) (|continuedFraction| (((|ContinuedFraction| (|Fraction| (|Integer|))) $) "\\spad{continuedFraction(x)} converts the \\spad{p}-adic rational number \\spad{x} to a continued fraction.")) (|approximate| (((|Fraction| (|Integer|)) $ (|Integer|)) "\\spad{approximate(x,n)} returns a rational number \\spad{y} such that \\spad{y = x (mod p^n)}."))) ((-4502 . T) (-4508 . T) (-4503 . T) ((-4512 "*") . T) (-4504 . T) (-4505 . T) (-4507 . T)) -((|HasCategory| |#2| (QUOTE (-940))) (|HasCategory| |#2| (|%list| (QUOTE -1070) (QUOTE (-1209)))) (|HasCategory| |#2| (QUOTE (-147))) (|HasCategory| |#2| (QUOTE (-149))) (|HasCategory| |#2| (|%list| (QUOTE -633) (QUOTE (-549)))) (|HasCategory| |#2| (QUOTE (-1052))) (|HasCategory| |#2| (QUOTE (-844))) (|HasCategory| |#2| (QUOTE (-872))) (-4144 (|HasCategory| |#2| (QUOTE (-844))) (|HasCategory| |#2| (QUOTE (-872)))) (|HasCategory| |#2| (|%list| (QUOTE -1070) (QUOTE (-560)))) (|HasCategory| |#2| (QUOTE (-1184))) (|HasCategory| |#2| (|%list| (QUOTE -912) (QUOTE (-391)))) (|HasCategory| |#2| (|%list| (QUOTE -912) (QUOTE (-560)))) (|HasCategory| |#2| (|%list| (QUOTE -633) (|%list| (QUOTE -916) (QUOTE (-391))))) (|HasCategory| |#2| (|%list| (QUOTE -633) (|%list| (QUOTE -916) (QUOTE (-560))))) (|HasCategory| |#2| (|%list| (QUOTE -660) (QUOTE (-560)))) (|HasCategory| |#2| (QUOTE (-239))) (|HasCategory| |#2| (|%list| (QUOTE -930) (QUOTE (-1209)))) (|HasCategory| |#2| (QUOTE (-240))) (|HasCategory| |#2| (|%list| (QUOTE -928) (QUOTE (-1209)))) (|HasCategory| |#2| (|%list| (QUOTE -528) (QUOTE (-1209)) (|devaluate| |#2|))) (|HasCategory| |#2| (|%list| (QUOTE -321) (|devaluate| |#2|))) (|HasCategory| |#2| (|%list| (QUOTE -298) (|devaluate| |#2|) (|devaluate| |#2|))) (|HasCategory| |#2| (QUOTE (-319))) (|HasCategory| |#2| (QUOTE (-559))) (-12 (|HasCategory| $ (QUOTE (-147))) (|HasCategory| |#2| (QUOTE (-940)))) (-4144 (-12 (|HasCategory| $ (QUOTE (-147))) (|HasCategory| |#2| (QUOTE (-940)))) (|HasCategory| |#2| (QUOTE (-147))))) +((|HasCategory| |#2| (QUOTE (-940))) (|HasCategory| |#2| (|%list| (QUOTE -1070) (QUOTE (-1209)))) (|HasCategory| |#2| (QUOTE (-147))) (|HasCategory| |#2| (QUOTE (-149))) (|HasCategory| |#2| (|%list| (QUOTE -633) (QUOTE (-549)))) (|HasCategory| |#2| (QUOTE (-1052))) (|HasCategory| |#2| (QUOTE (-844))) (|HasCategory| |#2| (QUOTE (-872))) (-4118 (|HasCategory| |#2| (QUOTE (-844))) (|HasCategory| |#2| (QUOTE (-872)))) (|HasCategory| |#2| (|%list| (QUOTE -1070) (QUOTE (-560)))) (|HasCategory| |#2| (QUOTE (-1184))) (|HasCategory| |#2| (|%list| (QUOTE -912) (QUOTE (-391)))) (|HasCategory| |#2| (|%list| (QUOTE -912) (QUOTE (-560)))) (|HasCategory| |#2| (|%list| (QUOTE -633) (|%list| (QUOTE -916) (QUOTE (-391))))) (|HasCategory| |#2| (|%list| (QUOTE -633) (|%list| (QUOTE -916) (QUOTE (-560))))) (|HasCategory| |#2| (|%list| (QUOTE -660) (QUOTE (-560)))) (|HasCategory| |#2| (QUOTE (-239))) (|HasCategory| |#2| (|%list| (QUOTE -930) (QUOTE (-1209)))) (|HasCategory| |#2| (QUOTE (-240))) (|HasCategory| |#2| (|%list| (QUOTE -928) (QUOTE (-1209)))) (|HasCategory| |#2| (|%list| (QUOTE -528) (QUOTE (-1209)) (|devaluate| |#2|))) (|HasCategory| |#2| (|%list| (QUOTE -321) (|devaluate| |#2|))) (|HasCategory| |#2| (|%list| (QUOTE -298) (|devaluate| |#2|) (|devaluate| |#2|))) (|HasCategory| |#2| (QUOTE (-319))) (|HasCategory| |#2| (QUOTE (-559))) (-12 (|HasCategory| $ (QUOTE (-147))) (|HasCategory| |#2| (QUOTE (-940)))) (-4118 (-12 (|HasCategory| $ (QUOTE (-147))) (|HasCategory| |#2| (QUOTE (-940)))) (|HasCategory| |#2| (QUOTE (-147))))) (-898 S T$) ((|constructor| (NIL "\\indented{1}{This domain provides a very simple representation} of the notion of `pair of objects'. It does not try to achieve all possible imaginable things.")) (|second| ((|#2| $) "\\spad{second(p)} extracts the second components of `p'.")) (|first| ((|#1| $) "\\spad{first(p)} extracts the first component of `p'.")) (|construct| (($ |#1| |#2|) "\\spad{construct(s,t)} is same as pair(\\spad{s},{}\\spad{t}),{} with syntactic sugar.")) (|pair| (($ |#1| |#2|) "\\spad{pair(s,t)} returns a pair object composed of `s' and `t'."))) NIL -((-12 (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#2| (QUOTE (-1133)))) (-4144 (-12 (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#2| (QUOTE (-1133)))) (-12 (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-888)))) (|HasCategory| |#2| (|%list| (QUOTE -632) (QUOTE (-888)))))) (-12 (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-888)))) (|HasCategory| |#2| (|%list| (QUOTE -632) (QUOTE (-888)))))) +((-12 (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#2| (QUOTE (-1133)))) (-4118 (-12 (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#2| (QUOTE (-1133)))) (-12 (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-888)))) (|HasCategory| |#2| (|%list| (QUOTE -632) (QUOTE (-888)))))) (-12 (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-888)))) (|HasCategory| |#2| (|%list| (QUOTE -632) (QUOTE (-888)))))) (-899) ((|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'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's lowest value."))) NIL @@ -3583,7 +3583,7 @@ NIL (-913 |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 (-2598 (|HasCategory| |#2| (QUOTE (-1081)))) (-2598 (|HasCategory| |#2| (|%list| (QUOTE -1070) (QUOTE (-1209)))))) (-12 (|HasCategory| |#2| (QUOTE (-1081))) (-2598 (|HasCategory| |#2| (|%list| (QUOTE -1070) (QUOTE (-1209)))))) (|HasCategory| |#2| (|%list| (QUOTE -1070) (QUOTE (-1209))))) +((-12 (-2584 (|HasCategory| |#2| (QUOTE (-1081)))) (-2584 (|HasCategory| |#2| (|%list| (QUOTE -1070) (QUOTE (-1209)))))) (-12 (|HasCategory| |#2| (QUOTE (-1081))) (-2584 (|HasCategory| |#2| (|%list| (QUOTE -1070) (QUOTE (-1209)))))) (|HasCategory| |#2| (|%list| (QUOTE -1070) (QUOTE (-1209))))) (-914 R S) ((|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'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},{}\\spad{e1}),{}...,{}(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 @@ -3596,7 +3596,7 @@ NIL ((|constructor| (NIL "Patterns for use by the pattern matcher.")) (|optpair| (((|Union| (|List| $) "failed") (|List| $)) "\\spad{optpair(l)} returns \\spad{l} has the form \\spad{[a, b]} and a is optional,{} and \"failed\" otherwise.")) (|variables| (((|List| $) $) "\\spad{variables(p)} returns the list of matching variables appearing in \\spad{p}.")) (|getBadValues| (((|List| (|Any|)) $) "\\spad{getBadValues(p)} returns the list of \"bad values\" for \\spad{p}. Note: \\spad{p} is not allowed to match any of its \"bad values\".")) (|addBadValue| (($ $ (|Any|)) "\\spad{addBadValue(p, v)} adds \\spad{v} to the list of \"bad values\" for \\spad{p}. Note: \\spad{p} is not allowed to match any of its \"bad values\".")) (|resetBadValues| (($ $) "\\spad{resetBadValues(p)} initializes the list of \"bad values\" for \\spad{p} to \\spad{[]}. Note: \\spad{p} is not allowed to match any of its \"bad values\".")) (|hasTopPredicate?| (((|Boolean|) $) "\\spad{hasTopPredicate?(p)} tests if \\spad{p} has a top-level predicate.")) (|topPredicate| (((|Record| (|:| |var| (|List| (|Symbol|))) (|:| |pred| (|Any|))) $) "\\spad{topPredicate(x)} returns \\spad{[[a1,...,an], f]} where the top-level predicate of \\spad{x} is \\spad{f(a1,...,an)}. Note: \\spad{n} is 0 if \\spad{x} has no top-level predicate.")) (|setTopPredicate| (($ $ (|List| (|Symbol|)) (|Any|)) "\\spad{setTopPredicate(x, [a1,...,an], f)} returns \\spad{x} with the top-level predicate set to \\spad{f(a1,...,an)}.")) (|patternVariable| (($ (|Symbol|) (|Boolean|) (|Boolean|) (|Boolean|)) "\\spad{patternVariable(x, c?, o?, m?)} creates a pattern variable \\spad{x},{} which is constant if \\spad{c? = true},{} optional if \\spad{o? = true},{} and multiple if \\spad{m? = true}.")) (|withPredicates| (($ $ (|List| (|Any|))) "\\spad{withPredicates(p, [p1,...,pn])} makes a copy of \\spad{p} and attaches the predicate \\spad{p1} and ... and pn to the copy,{} which is returned.")) (|setPredicates| (($ $ (|List| (|Any|))) "\\spad{setPredicates(p, [p1,...,pn])} attaches the predicate \\spad{p1} and ... and pn to \\spad{p}.")) (|predicates| (((|List| (|Any|)) $) "\\spad{predicates(p)} returns \\spad{[p1,...,pn]} such that the predicate attached to \\spad{p} is \\spad{p1} and ... and pn.")) (|hasPredicate?| (((|Boolean|) $) "\\spad{hasPredicate?(p)} tests if \\spad{p} has predicates attached to it.")) (|optional?| (((|Boolean|) $) "\\spad{optional?(p)} tests if \\spad{p} is a single matching variable which can match an identity.")) (|multiple?| (((|Boolean|) $) "\\spad{multiple?(p)} tests if \\spad{p} is a single matching variable allowing list matching or multiple term matching in a sum or product.")) (|generic?| (((|Boolean|) $) "\\spad{generic?(p)} tests if \\spad{p} is a single matching variable.")) (|constant?| (((|Boolean|) $) "\\spad{constant?(p)} tests if \\spad{p} contains no matching variables.")) (|symbol?| (((|Boolean|) $) "\\spad{symbol?(p)} tests if \\spad{p} is a symbol.")) (|quoted?| (((|Boolean|) $) "\\spad{quoted?(p)} tests if \\spad{p} is of the form 's for a symbol \\spad{s}.")) (|inR?| (((|Boolean|) $) "\\spad{inR?(p)} tests if \\spad{p} is an atom (\\spadignore{i.e.} an element of \\spad{R}).")) (|copy| (($ $) "\\spad{copy(p)} returns a recursive copy of \\spad{p}.")) (|convert| (($ (|List| $)) "\\spad{convert([a1,...,an])} returns the pattern \\spad{[a1,...,an]}.")) (|depth| (((|NonNegativeInteger|) $) "\\spad{depth(p)} returns the nesting level of \\spad{p}.")) (/ (($ $ $) "\\spad{a / b} returns the pattern \\spad{a / b}.")) (** (($ $ $) "\\spad{a ** b} returns the pattern \\spad{a ** b}.") (($ $ (|NonNegativeInteger|)) "\\spad{a ** n} returns the pattern \\spad{a ** n}.")) (* (($ $ $) "\\spad{a * b} returns the pattern \\spad{a * b}.")) (+ (($ $ $) "\\spad{a + b} returns the pattern \\spad{a + b}.")) (|elt| (($ (|BasicOperator|) (|List| $)) "\\spad{elt(op, [a1,...,an])} returns \\spad{op(a1,...,an)}.")) (|isPower| (((|Union| (|Record| (|:| |val| $) (|:| |exponent| $)) "failed") $) "\\spad{isPower(p)} returns \\spad{[a, b]} if \\spad{p = a ** b},{} and \"failed\" otherwise.")) (|isList| (((|Union| (|List| $) "failed") $) "\\spad{isList(p)} returns \\spad{[a1,...,an]} if \\spad{p = [a1,...,an]},{} \"failed\" otherwise.")) (|isQuotient| (((|Union| (|Record| (|:| |num| $) (|:| |den| $)) "failed") $) "\\spad{isQuotient(p)} returns \\spad{[a, b]} if \\spad{p = a / b},{} and \"failed\" otherwise.")) (|isExpt| (((|Union| (|Record| (|:| |val| $) (|:| |exponent| (|NonNegativeInteger|))) "failed") $) "\\spad{isExpt(p)} returns \\spad{[q, n]} if \\spad{n > 0} and \\spad{p = q ** n},{} and \"failed\" otherwise.")) (|isOp| (((|Union| (|Record| (|:| |op| (|BasicOperator|)) (|:| |arg| (|List| $))) "failed") $) "\\spad{isOp(p)} returns \\spad{[op, [a1,...,an]]} if \\spad{p = op(a1,...,an)},{} and \"failed\" otherwise.") (((|Union| (|List| $) "failed") $ (|BasicOperator|)) "\\spad{isOp(p, op)} returns \\spad{[a1,...,an]} if \\spad{p = op(a1,...,an)},{} and \"failed\" otherwise.")) (|isTimes| (((|Union| (|List| $) "failed") $) "\\spad{isTimes(p)} returns \\spad{[a1,...,an]} if \\spad{n > 1} and \\spad{p = a1 * ... * an},{} and \"failed\" otherwise.")) (|isPlus| (((|Union| (|List| $) "failed") $) "\\spad{isPlus(p)} returns \\spad{[a1,...,an]} if \\spad{n > 1} \\indented{1}{and \\spad{p = a1 + ... + an},{}} and \"failed\" otherwise.")) ((|One|) (($) "1")) ((|Zero|) (($) "0"))) NIL NIL -(-917 R -4219) +(-917 R -4195) ((|constructor| (NIL "Tools for patterns.")) (|badValues| (((|List| |#2|) (|Pattern| |#1|)) "\\spad{badValues(p)} returns the list of \"bad values\" for \\spad{p}; \\spad{p} is not allowed to match any of its \"bad values\".")) (|addBadValue| (((|Pattern| |#1|) (|Pattern| |#1|) |#2|) "\\spad{addBadValue(p, v)} adds \\spad{v} to the list of \"bad values\" for \\spad{p}; \\spad{p} is not allowed to match any of its \"bad values\".")) (|satisfy?| (((|Boolean|) (|List| |#2|) (|Pattern| |#1|)) "\\spad{satisfy?([v1,...,vn], p)} returns \\spad{f(v1,...,vn)} where \\spad{f} is the top-level predicate attached to \\spad{p}.") (((|Boolean|) |#2| (|Pattern| |#1|)) "\\spad{satisfy?(v, p)} returns \\spad{f}(\\spad{v}) where \\spad{f} is the predicate attached to \\spad{p}.")) (|predicate| (((|Mapping| (|Boolean|) |#2|) (|Pattern| |#1|)) "\\spad{predicate(p)} returns the predicate attached to \\spad{p},{} the constant function \\spad{true} if \\spad{p} has no predicates attached to it.")) (|suchThat| (((|Pattern| |#1|) (|Pattern| |#1|) (|List| (|Symbol|)) (|Mapping| (|Boolean|) (|List| |#2|))) "\\spad{suchThat(p, [a1,...,an], f)} returns a copy of \\spad{p} with the top-level predicate set to \\spad{f(a1,...,an)}.") (((|Pattern| |#1|) (|Pattern| |#1|) (|List| (|Mapping| (|Boolean|) |#2|))) "\\spad{suchThat(p, [f1,...,fn])} makes a copy of \\spad{p} and adds the predicate \\spad{f1} and ... and fn to the copy,{} which is returned.") (((|Pattern| |#1|) (|Pattern| |#1|) (|Mapping| (|Boolean|) |#2|)) "\\spad{suchThat(p, f)} makes a copy of \\spad{p} and adds the predicate \\spad{f} to the copy,{} which is returned."))) NIL NIL @@ -3624,7 +3624,7 @@ NIL ((|PDESolve| (((|Result|) (|Record| (|:| |pde| (|List| (|Expression| (|DoubleFloat|)))) (|:| |constraints| (|List| (|Record| (|:| |start| (|DoubleFloat|)) (|:| |finish| (|DoubleFloat|)) (|:| |grid| (|NonNegativeInteger|)) (|:| |boundaryType| (|Integer|)) (|:| |dStart| (|Matrix| (|DoubleFloat|))) (|:| |dFinish| (|Matrix| (|DoubleFloat|)))))) (|:| |f| (|List| (|List| (|Expression| (|DoubleFloat|))))) (|:| |st| (|String|)) (|:| |tol| (|DoubleFloat|)))) "\\spad{PDESolve(args)} performs the integration of the function given the strategy or method returned by \\axiomFun{measure}.")) (|measure| (((|Record| (|:| |measure| (|Float|)) (|:| |explanations| (|String|))) (|RoutinesTable|) (|Record| (|:| |pde| (|List| (|Expression| (|DoubleFloat|)))) (|:| |constraints| (|List| (|Record| (|:| |start| (|DoubleFloat|)) (|:| |finish| (|DoubleFloat|)) (|:| |grid| (|NonNegativeInteger|)) (|:| |boundaryType| (|Integer|)) (|:| |dStart| (|Matrix| (|DoubleFloat|))) (|:| |dFinish| (|Matrix| (|DoubleFloat|)))))) (|:| |f| (|List| (|List| (|Expression| (|DoubleFloat|))))) (|:| |st| (|String|)) (|:| |tol| (|DoubleFloat|)))) "\\spad{measure(R,args)} calculates an estimate of the ability of a particular method to solve a problem. \\blankline This method may be either a specific NAG routine or a strategy (such as transforming the function from one which is difficult to one which is easier to solve). \\blankline It will call whichever agents are needed to perform analysis on the problem in order to calculate the measure. There is a parameter,{} labelled \\axiom{sofar},{} which would contain the best compatibility found so far."))) NIL NIL -(-924 UP -4164) +(-924 UP -4140) ((|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 @@ -3655,11 +3655,11 @@ NIL (-931 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})'s")) (|ptree| (($ $ $) "\\spad{ptree(x,y)} \\undocumented") (($ |#1|) "\\spad{ptree(s)} is a leaf? pendant tree"))) NIL -((-12 (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1133))) (-4144 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-1133)))) (-4144 (-12 (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-888))))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-888)))) (|HasCategory| |#1| (QUOTE (-102)))) +((-12 (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1133))) (-4118 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-1133)))) (-4118 (-12 (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-888))))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-888)))) (|HasCategory| |#1| (QUOTE (-102)))) (-932 S) ((|constructor| (NIL "Permutation(\\spad{S}) implements the group of all bijections \\indented{2}{on a set \\spad{S},{} which move only a finite number of points.} \\indented{2}{A permutation is considered as a map from \\spad{S} into \\spad{S}. In particular} \\indented{2}{multiplication is defined as composition of maps:} \\indented{2}{{\\em pi1 * pi2 = pi1 o pi2}.} \\indented{2}{The internal representation of permuatations are two lists} \\indented{2}{of equal length representing preimages and images.}")) (|coerceImages| (($ (|List| |#1|)) "\\spad{coerceImages(ls)} coerces the list {\\em ls} to a permutation whose image is given by {\\em ls} and the preimage is fixed to be {\\em [1,...,n]}. Note: {coerceImages(\\spad{ls})=coercePreimagesImages([1,{}...,{}\\spad{n}],{}\\spad{ls})}. We assume that both preimage and image do not contain repetitions.")) (|fixedPoints| (((|Set| |#1|) $) "\\spad{fixedPoints(p)} returns the points fixed by the permutation \\spad{p}.")) (|sort| (((|List| $) (|List| $)) "\\spad{sort(lp)} sorts a list of permutations {\\em lp} according to cycle structure first according to length of cycles,{} second,{} if \\spad{S} has \\spadtype{Finite} or \\spad{S} has \\spadtype{OrderedSet} according to lexicographical order of entries in cycles of equal length.")) (|odd?| (((|Boolean|) $) "\\spad{odd?(p)} returns \\spad{true} if and only if \\spad{p} is an odd permutation \\spadignore{i.e.} {\\em sign(p)} is {\\em -1}.")) (|even?| (((|Boolean|) $) "\\spad{even?(p)} returns \\spad{true} if and only if \\spad{p} is an even permutation,{} \\spadignore{i.e.} {\\em sign(p)} is 1.")) (|sign| (((|Integer|) $) "\\spad{sign(p)} returns the signum of the permutation \\spad{p},{} \\spad{+1} or \\spad{-1}.")) (|numberOfCycles| (((|NonNegativeInteger|) $) "\\spad{numberOfCycles(p)} returns the number of non-trivial cycles of the permutation \\spad{p}.")) (|order| (((|NonNegativeInteger|) $) "\\spad{order(p)} returns the order of a permutation \\spad{p} as a group element.")) (|cyclePartition| (((|Partition|) $) "\\spad{cyclePartition(p)} returns the cycle structure of a permutation \\spad{p} including cycles of length 1 only if \\spad{S} is finite.")) (|degree| (((|NonNegativeInteger|) $) "\\spad{degree(p)} retuns the number of points moved by the permutation \\spad{p}.")) (|coerceListOfPairs| (($ (|List| (|List| |#1|))) "\\spad{coerceListOfPairs(lls)} coerces a list of pairs {\\em lls} to a permutation. Error: if not consistent,{} \\spadignore{i.e.} the set of the first elements coincides with the set of second elements. coerce(\\spad{p}) generates output of the permutation \\spad{p} with domain OutputForm.")) (|coerce| (($ (|List| |#1|)) "\\spad{coerce(ls)} coerces a cycle {\\em ls},{} \\spadignore{i.e.} a list with not repetitions to a permutation,{} which maps {\\em ls.i} to {\\em ls.i+1},{} indices modulo the length of the list. Error: if repetitions occur.") (($ (|List| (|List| |#1|))) "\\spad{coerce(lls)} coerces a list of cycles {\\em lls} to a permutation,{} each cycle being a list with no repetitions,{} is coerced to the permutation,{} which maps {\\em ls.i} to {\\em ls.i+1},{} indices modulo the length of the list,{} then these permutations are mutiplied. Error: if repetitions occur in one cycle.")) (|coercePreimagesImages| (($ (|List| (|List| |#1|))) "\\spad{coercePreimagesImages(lls)} coerces the representation {\\em lls} of a permutation as a list of preimages and images to a permutation. We assume that both preimage and image do not contain repetitions.")) (|listRepresentation| (((|Record| (|:| |preimage| (|List| |#1|)) (|:| |image| (|List| |#1|))) $) "\\spad{listRepresentation(p)} produces a representation {\\em rep} of the permutation \\spad{p} as a list of preimages and images,{} \\spad{i}.\\spad{e} \\spad{p} maps {\\em (rep.preimage).k} to {\\em (rep.image).k} for all indices \\spad{k}. Elements of \\spad{S} not in {\\em (rep.preimage).k} are fixed points,{} and these are the only fixed points of the permutation."))) ((-4507 . T)) -((-4144 (|HasCategory| |#1| (QUOTE (-381))) (|HasCategory| |#1| (QUOTE (-872)))) (|HasCategory| |#1| (QUOTE (-381))) (|HasCategory| |#1| (QUOTE (-872)))) +((-4118 (|HasCategory| |#1| (QUOTE (-381))) (|HasCategory| |#1| (QUOTE (-872)))) (|HasCategory| |#1| (QUOTE (-381))) (|HasCategory| |#1| (QUOTE (-872)))) (-933 |n| R) ((|constructor| (NIL "Permanent implements the functions {\\em permanent},{} the permanent for square matrices.")) (|permanent| ((|#2| (|SquareMatrix| |#1| |#2|)) "\\spad{permanent(x)} computes the permanent of a square matrix \\spad{x}. The {\\em permanent} is equivalent to the \\spadfun{determinant} except that coefficients have no change of sign. This function is much more difficult to compute than the {\\em determinant}. The formula used is by \\spad{H}.\\spad{J}. Ryser,{} improved by [Nijenhuis and Wilf,{} Ch. 19]. Note: permanent(\\spad{x}) choose one of three algorithms,{} depending on the underlying ring \\spad{R} and on \\spad{n},{} the number of rows (and columns) of x:\\begin{items} \\item 1. if 2 has an inverse in \\spad{R} we can use the algorithm of \\indented{3}{[Nijenhuis and Wilf,{} ch.19,{}\\spad{p}.158]; if 2 has no inverse,{}} \\indented{3}{some modifications are necessary:} \\item 2. if {\\em n > 6} and \\spad{R} is an integral domain with characteristic \\indented{3}{different from 2 (the algorithm works if and only 2 is not a} \\indented{3}{zero-divisor of \\spad{R} and {\\em characteristic()\\$R ~= 2},{}} \\indented{3}{but how to check that for any given \\spad{R} ?),{}} \\indented{3}{the local function {\\em permanent2} is called;} \\item 3. else,{} the local function {\\em permanent3} is called \\indented{3}{(works for all commutative rings \\spad{R}).} \\end{items}"))) NIL @@ -3692,7 +3692,7 @@ NIL ((|constructor| (NIL "This is the category of domains that know \"enough\" about themselves in order to factor univariate polynomials over themselves. This will be used in future releases for supporting factorization over finitely generated coefficient fields,{} it is not yet available in the current release of axiom.")) (|charthRoot| (((|Maybe| $) $) "\\spad{charthRoot(r)} returns the \\spad{p}\\spad{-}th root of \\spad{r},{} or \\spad{nothing} if none exists in the domain.")) (|conditionP| (((|Union| (|Vector| $) "failed") (|Matrix| $)) "\\spad{conditionP(m)} returns a vector of elements,{} not all zero,{} whose \\spad{p}\\spad{-}th powers (\\spad{p} is the characteristic of the domain) are a solution of the homogenous linear system represented by \\spad{m},{} or \"failed\" is there is no such vector.")) (|solveLinearPolynomialEquation| (((|Union| (|List| (|SparseUnivariatePolynomial| $)) "failed") (|List| (|SparseUnivariatePolynomial| $)) (|SparseUnivariatePolynomial| $)) "\\spad{solveLinearPolynomialEquation([f1, ..., fn], g)} (where the \\spad{fi} are relatively prime to each other) returns a list of \\spad{ai} such that \\spad{g/prod fi = sum ai/fi} or returns \"failed\" if no such list of \\spad{ai}'s exists.")) (|gcdPolynomial| (((|SparseUnivariatePolynomial| $) (|SparseUnivariatePolynomial| $) (|SparseUnivariatePolynomial| $)) "\\spad{gcdPolynomial(p,q)} returns the gcd of the univariate polynomials \\spad{p} qnd \\spad{q}.")) (|factorSquareFreePolynomial| (((|Factored| (|SparseUnivariatePolynomial| $)) (|SparseUnivariatePolynomial| $)) "\\spad{factorSquareFreePolynomial(p)} factors the univariate polynomial \\spad{p} into irreducibles where \\spad{p} is known to be square free and primitive with respect to its main variable.")) (|factorPolynomial| (((|Factored| (|SparseUnivariatePolynomial| $)) (|SparseUnivariatePolynomial| $)) "\\spad{factorPolynomial(p)} returns the factorization into irreducibles of the univariate polynomial \\spad{p}.")) (|squareFreePolynomial| (((|Factored| (|SparseUnivariatePolynomial| $)) (|SparseUnivariatePolynomial| $)) "\\spad{squareFreePolynomial(p)} returns the square-free factorization of the univariate polynomial \\spad{p}."))) ((-4503 . T) ((-4512 "*") . T) (-4504 . T) (-4505 . T) (-4507 . T)) NIL -(-941 R0 -4164 UP UPUP R) +(-941 R0 -4140 UP UPUP R) ((|constructor| (NIL "This package provides function for testing whether a divisor on a curve is a torsion divisor.")) (|torsionIfCan| (((|Union| (|Record| (|:| |order| (|NonNegativeInteger|)) (|:| |function| |#5|)) "failed") (|FiniteDivisor| |#2| |#3| |#4| |#5|)) "\\spad{torsionIfCan(f)}\\\\ undocumented")) (|torsion?| (((|Boolean|) (|FiniteDivisor| |#2| |#3| |#4| |#5|)) "\\spad{torsion?(f)} \\undocumented")) (|order| (((|Union| (|NonNegativeInteger|) "failed") (|FiniteDivisor| |#2| |#3| |#4| |#5|)) "\\spad{order(f)} \\undocumented"))) NIL NIL @@ -3720,7 +3720,7 @@ NIL ((|constructor| (NIL "PermutationGroupExamples provides permutation groups for some classes of groups: symmetric,{} alternating,{} dihedral,{} cyclic,{} direct products of cyclic,{} which are in fact the finite abelian groups of symmetric groups called Young subgroups. Furthermore,{} Rubik's group as permutation group of 48 integers and a list of sporadic simple groups derived from the atlas of finite groups.")) (|youngGroup| (((|PermutationGroup| (|Integer|)) (|Partition|)) "\\spad{youngGroup(lambda)} constructs the direct product of the symmetric groups given by the parts of the partition {\\em lambda}.") (((|PermutationGroup| (|Integer|)) (|List| (|Integer|))) "\\spad{youngGroup([n1,...,nk])} constructs the direct product of the symmetric groups {\\em Sn1},{}...,{}{\\em Snk}.")) (|rubiksGroup| (((|PermutationGroup| (|Integer|))) "\\spad{rubiksGroup constructs} the permutation group representing Rubic's Cube acting on integers {\\em 10*i+j} for {\\em 1 <= i <= 6},{} {\\em 1 <= j <= 8}. The faces of Rubik's Cube are labelled in the obvious way Front,{} Right,{} Up,{} Down,{} Left,{} Back and numbered from 1 to 6 in this given ordering,{} the pieces on each face (except the unmoveable center piece) are clockwise numbered from 1 to 8 starting with the piece in the upper left corner. The moves of the cube are represented as permutations on these pieces,{} represented as a two digit integer {\\em ij} where \\spad{i} is the numer of theface (1 to 6) and \\spad{j} is the number of the piece on this face. The remaining ambiguities are resolved by looking at the 6 generators,{} which represent a 90 degree turns of the faces,{} or from the following pictorial description. Permutation group representing Rubic's Cube acting on integers 10*i+j for 1 <= \\spad{i} <= 6,{} 1 <= \\spad{j} \\spad{<=8}. \\blankline\\begin{verbatim}Rubik's Cube: +-----+ +-- B where: marks Side # : / U /|/ / / | F(ront) <-> 1 L --> +-----+ R| R(ight) <-> 2 | | + U(p) <-> 3 | F | / D(own) <-> 4 | |/ L(eft) <-> 5 +-----+ B(ack) <-> 6 ^ | DThe Cube's surface: The pieces on each side +---+ (except the unmoveable center |567| piece) are clockwise numbered |4U8| from 1 to 8 starting with the |321| piece in the upper left +---+---+---+ corner (see figure on the |781|123|345| left). The moves of the cube |6L2|8F4|2R6| are represented as |543|765|187| permutations on these pieces. +---+---+---+ Each of the pieces is |123| represented as a two digit |8D4| integer ij where i is the |765| # of the side ( 1 to 6 for +---+ F to B (see table above )) |567| and j is the # of the piece. |4B8| |321| +---+\\end{verbatim}")) (|janko2| (((|PermutationGroup| (|Integer|))) "\\spad{janko2 constructs} the janko group acting on the integers 1,{}...,{}100.") (((|PermutationGroup| (|Integer|)) (|List| (|Integer|))) "\\spad{janko2(li)} constructs the janko group acting on the 100 integers given in the list {\\em li}. Note: duplicates in the list will be removed. Error: if {\\em li} has less or more than 100 different entries")) (|mathieu24| (((|PermutationGroup| (|Integer|))) "\\spad{mathieu24 constructs} the mathieu group acting on the integers 1,{}...,{}24.") (((|PermutationGroup| (|Integer|)) (|List| (|Integer|))) "\\spad{mathieu24(li)} constructs the mathieu group acting on the 24 integers given in the list {\\em li}. Note: duplicates in the list will be removed. Error: if {\\em li} has less or more than 24 different entries.")) (|mathieu23| (((|PermutationGroup| (|Integer|))) "\\spad{mathieu23 constructs} the mathieu group acting on the integers 1,{}...,{}23.") (((|PermutationGroup| (|Integer|)) (|List| (|Integer|))) "\\spad{mathieu23(li)} constructs the mathieu group acting on the 23 integers given in the list {\\em li}. Note: duplicates in the list will be removed. Error: if {\\em li} has less or more than 23 different entries.")) (|mathieu22| (((|PermutationGroup| (|Integer|))) "\\spad{mathieu22 constructs} the mathieu group acting on the integers 1,{}...,{}22.") (((|PermutationGroup| (|Integer|)) (|List| (|Integer|))) "\\spad{mathieu22(li)} constructs the mathieu group acting on the 22 integers given in the list {\\em li}. Note: duplicates in the list will be removed. Error: if {\\em li} has less or more than 22 different entries.")) (|mathieu12| (((|PermutationGroup| (|Integer|))) "\\spad{mathieu12 constructs} the mathieu group acting on the integers 1,{}...,{}12.") (((|PermutationGroup| (|Integer|)) (|List| (|Integer|))) "\\spad{mathieu12(li)} constructs the mathieu group acting on the 12 integers given in the list {\\em li}. Note: duplicates in the list will be removed Error: if {\\em li} has less or more than 12 different entries.")) (|mathieu11| (((|PermutationGroup| (|Integer|))) "\\spad{mathieu11 constructs} the mathieu group acting on the integers 1,{}...,{}11.") (((|PermutationGroup| (|Integer|)) (|List| (|Integer|))) "\\spad{mathieu11(li)} constructs the mathieu group acting on the 11 integers given in the list {\\em li}. Note: duplicates in the list will be removed. error,{} if {\\em li} has less or more than 11 different entries.")) (|dihedralGroup| (((|PermutationGroup| (|Integer|)) (|List| (|Integer|))) "\\spad{dihedralGroup([i1,...,ik])} constructs the dihedral group of order 2k acting on the integers out of {\\em i1},{}...,{}{\\em ik}. Note: duplicates in the list will be removed.") (((|PermutationGroup| (|Integer|)) (|PositiveInteger|)) "\\spad{dihedralGroup(n)} constructs the dihedral group of order 2n acting on integers 1,{}...,{}\\spad{N}.")) (|cyclicGroup| (((|PermutationGroup| (|Integer|)) (|List| (|Integer|))) "\\spad{cyclicGroup([i1,...,ik])} constructs the cyclic group of order \\spad{k} acting on the integers {\\em i1},{}...,{}{\\em ik}. Note: duplicates in the list will be removed.") (((|PermutationGroup| (|Integer|)) (|PositiveInteger|)) "\\spad{cyclicGroup(n)} constructs the cyclic group of order \\spad{n} acting on the integers 1,{}...,{}\\spad{n}.")) (|abelianGroup| (((|PermutationGroup| (|Integer|)) (|List| (|PositiveInteger|))) "\\spad{abelianGroup([n1,...,nk])} constructs the abelian group that is the direct product of cyclic groups with order {\\em ni}.")) (|alternatingGroup| (((|PermutationGroup| (|Integer|)) (|List| (|Integer|))) "\\spad{alternatingGroup(li)} constructs the alternating group acting on the integers in the list {\\em li},{} generators are in general the {\\em n-2}-cycle {\\em (li.3,...,li.n)} and the 3-cycle {\\em (li.1,li.2,li.3)},{} if \\spad{n} is odd and product of the 2-cycle {\\em (li.1,li.2)} with {\\em n-2}-cycle {\\em (li.3,...,li.n)} and the 3-cycle {\\em (li.1,li.2,li.3)},{} if \\spad{n} is even. Note: duplicates in the list will be removed.") (((|PermutationGroup| (|Integer|)) (|PositiveInteger|)) "\\spad{alternatingGroup(n)} constructs the alternating group {\\em An} acting on the integers 1,{}...,{}\\spad{n},{} generators are in general the {\\em n-2}-cycle {\\em (3,...,n)} and the 3-cycle {\\em (1,2,3)} if \\spad{n} is odd and the product of the 2-cycle {\\em (1,2)} with {\\em n-2}-cycle {\\em (3,...,n)} and the 3-cycle {\\em (1,2,3)} if \\spad{n} is even.")) (|symmetricGroup| (((|PermutationGroup| (|Integer|)) (|List| (|Integer|))) "\\spad{symmetricGroup(li)} constructs the symmetric group acting on the integers in the list {\\em li},{} generators are the cycle given by {\\em li} and the 2-cycle {\\em (li.1,li.2)}. Note: duplicates in the list will be removed.") (((|PermutationGroup| (|Integer|)) (|PositiveInteger|)) "\\spad{symmetricGroup(n)} constructs the symmetric group {\\em Sn} acting on the integers 1,{}...,{}\\spad{n},{} generators are the {\\em n}-cycle {\\em (1,...,n)} and the 2-cycle {\\em (1,2)}."))) NIL NIL -(-948 -4164) +(-948 -4140) ((|constructor| (NIL "Groebner functions for \\spad{P} \\spad{F} \\indented{2}{This package is an interface package to the groebner basis} package which allows you to compute groebner bases for polynomials in either lexicographic ordering or total degree ordering refined by reverse lex. The input is the ordinary polynomial type which is internally converted to a type with the required ordering. The resulting grobner basis is converted back to ordinary polynomials. The ordering among the variables is controlled by an explicit list of variables which is passed as a second argument. The coefficient domain is allowed to be any gcd domain,{} but the groebner basis is computed as if the polynomials were over a field.")) (|totalGroebner| (((|List| (|Polynomial| |#1|)) (|List| (|Polynomial| |#1|)) (|List| (|Symbol|))) "\\spad{totalGroebner(lp,lv)} computes Groebner basis for the list of polynomials \\spad{lp} with the terms ordered first by total degree and then refined by reverse lexicographic ordering. The variables are ordered by their position in the list \\spad{lv}.")) (|lexGroebner| (((|List| (|Polynomial| |#1|)) (|List| (|Polynomial| |#1|)) (|List| (|Symbol|))) "\\spad{lexGroebner(lp,lv)} computes Groebner basis for the list of polynomials \\spad{lp} in lexicographic order. The variables are ordered by their position in the list \\spad{lv}."))) NIL NIL @@ -3736,11 +3736,11 @@ NIL ((|constructor| (NIL "The category of constructive principal ideal domains,{} \\spadignore{i.e.} where a single generator can be constructively found for any ideal given by a finite set of generators. Note that this constructive definition only implies that finitely generated ideals are principal. It is not clear what we would mean by an infinitely generated ideal.")) (|expressIdealMember| (((|Maybe| (|List| $)) (|List| $) $) "\\spad{expressIdealMember([f1,...,fn],h)} returns a representation of \\spad{h} as a linear combination of the \\spad{fi} or \\spad{nothing} if \\spad{h} is not in the ideal generated by the \\spad{fi}.")) (|principalIdeal| (((|Record| (|:| |coef| (|List| $)) (|:| |generator| $)) (|List| $)) "\\spad{principalIdeal([f1,...,fn])} returns a record whose generator component is a generator of the ideal generated by \\spad{[f1,...,fn]} whose coef component satisfies \\spad{generator = sum (input.i * coef.i)}"))) ((-4503 . T) ((-4512 "*") . T) (-4504 . T) (-4505 . T) (-4507 . T)) NIL -(-952 |xx| -4164) +(-952 |xx| -4140) ((|constructor| (NIL "This package exports interpolation algorithms")) (|interpolate| (((|SparseUnivariatePolynomial| |#2|) (|List| |#2|) (|List| |#2|)) "\\spad{interpolate(lf,lg)} \\undocumented") (((|UnivariatePolynomial| |#1| |#2|) (|UnivariatePolynomial| |#1| |#2|) (|List| |#2|) (|List| |#2|)) "\\spad{interpolate(u,lf,lg)} \\undocumented"))) NIL NIL -(-953 -4164 P) +(-953 -4140 P) ((|constructor| (NIL "This package exports interpolation algorithms")) (|LagrangeInterpolation| ((|#2| (|List| |#1|) (|List| |#1|)) "\\spad{LagrangeInterpolation(l1,l2)} \\undocumented"))) NIL NIL @@ -3768,7 +3768,7 @@ NIL ((|constructor| (NIL "Attaching assertions to symbols for pattern matching. Date Created: 21 Mar 1989 Date Last Updated: 23 May 1990")) (|multiple| (((|Expression| (|Integer|)) (|Symbol|)) "\\spad{multiple(x)} tells the pattern matcher that \\spad{x} should preferably match a multi-term quantity in a sum or product. For matching on lists,{} multiple(\\spad{x}) tells the pattern matcher that \\spad{x} should match a list instead of an element of a list.")) (|optional| (((|Expression| (|Integer|)) (|Symbol|)) "\\spad{optional(x)} tells the pattern matcher that \\spad{x} can match an identity (0 in a sum,{} 1 in a product or exponentiation)..")) (|constant| (((|Expression| (|Integer|)) (|Symbol|)) "\\spad{constant(x)} tells the pattern matcher that \\spad{x} should match only the symbol 'x and no other quantity.")) (|assert| (((|Expression| (|Integer|)) (|Symbol|) (|Identifier|)) "\\spad{assert(x, s)} makes the assertion \\spad{s} about \\spad{x}."))) NIL NIL -(-960 R -4164) +(-960 R -4140) ((|constructor| (NIL "Attaching assertions to symbols for pattern matching; Date Created: 21 Mar 1989 Date Last Updated: 23 May 1990")) (|multiple| ((|#2| |#2|) "\\spad{multiple(x)} tells the pattern matcher that \\spad{x} should preferably match a multi-term quantity in a sum or product. For matching on lists,{} multiple(\\spad{x}) tells the pattern matcher that \\spad{x} should match a list instead of an element of a list. Error: if \\spad{x} is not a symbol.")) (|optional| ((|#2| |#2|) "\\spad{optional(x)} tells the pattern matcher that \\spad{x} can match an identity (0 in a sum,{} 1 in a product or exponentiation). Error: if \\spad{x} is not a symbol.")) (|constant| ((|#2| |#2|) "\\spad{constant(x)} tells the pattern matcher that \\spad{x} should match only the symbol 'x and no other quantity. Error: if \\spad{x} is not a symbol.")) (|assert| ((|#2| |#2| (|Identifier|)) "\\spad{assert(x, s)} makes the assertion \\spad{s} about \\spad{x}. Error: if \\spad{x} is not a symbol."))) NIL NIL @@ -3776,7 +3776,7 @@ NIL ((|constructor| (NIL "This packages provides tools for matching recursively in type towers.")) (|patternMatch| (((|PatternMatchResult| |#1| |#3|) |#2| (|Pattern| |#1|) (|PatternMatchResult| |#1| |#3|)) "\\spad{patternMatch(expr, pat, res)} matches the pattern \\spad{pat} to the expression \\spad{expr}; res contains the variables of \\spad{pat} which are already matched and their matches. Note: this function handles type towers by changing the predicates and calling the matching function provided by \\spad{A}.")) (|fixPredicate| (((|Mapping| (|Boolean|) |#2|) (|Mapping| (|Boolean|) |#3|)) "\\spad{fixPredicate(f)} returns \\spad{g} defined by \\spad{g}(a) = \\spad{f}(a::B)."))) NIL NIL -(-962 S R -4164) +(-962 S R -4140) ((|constructor| (NIL "This package provides pattern matching functions on function spaces.")) (|patternMatch| (((|PatternMatchResult| |#1| |#3|) |#3| (|Pattern| |#1|) (|PatternMatchResult| |#1| |#3|)) "\\spad{patternMatch(expr, pat, res)} matches the pattern \\spad{pat} to the expression \\spad{expr}; res contains the variables of \\spad{pat} which are already matched and their matches."))) NIL NIL @@ -3796,11 +3796,11 @@ NIL ((|constructor| (NIL "This package provides pattern matching functions on polynomials.")) (|patternMatch| (((|PatternMatchResult| |#1| |#5|) |#5| (|Pattern| |#1|) (|PatternMatchResult| |#1| |#5|)) "\\spad{patternMatch(p, pat, res)} matches the pattern \\spad{pat} to the polynomial \\spad{p}; res contains the variables of \\spad{pat} which are already matched and their matches.") (((|PatternMatchResult| |#1| |#5|) |#5| (|Pattern| |#1|) (|PatternMatchResult| |#1| |#5|) (|Mapping| (|PatternMatchResult| |#1| |#5|) |#3| (|Pattern| |#1|) (|PatternMatchResult| |#1| |#5|))) "\\spad{patternMatch(p, pat, res, vmatch)} matches the pattern \\spad{pat} to the polynomial \\spad{p}. \\spad{res} contains the variables of \\spad{pat} which are already matched and their matches; vmatch is the matching function to use on the variables."))) NIL ((|HasCategory| |#3| (|%list| (QUOTE -912) (|devaluate| |#1|)))) -(-967 -4219) +(-967 -4195) ((|constructor| (NIL "Attaching predicates to symbols for pattern matching. Date Created: 21 Mar 1989 Date Last Updated: 23 May 1990")) (|suchThat| (((|Expression| (|Integer|)) (|Symbol|) (|List| (|Mapping| (|Boolean|) |#1|))) "\\spad{suchThat(x, [f1, f2, ..., fn])} attaches the predicate \\spad{f1} and \\spad{f2} and ... and fn to \\spad{x}.") (((|Expression| (|Integer|)) (|Symbol|) (|Mapping| (|Boolean|) |#1|)) "\\spad{suchThat(x, foo)} attaches the predicate foo to \\spad{x}."))) NIL NIL -(-968 R -4164 -4219) +(-968 R -4140 -4195) ((|constructor| (NIL "Attaching predicates to symbols for pattern matching. Date Created: 21 Mar 1989 Date Last Updated: 23 May 1990")) (|suchThat| ((|#2| |#2| (|List| (|Mapping| (|Boolean|) |#3|))) "\\spad{suchThat(x, [f1, f2, ..., fn])} attaches the predicate \\spad{f1} and \\spad{f2} and ... and fn to \\spad{x}. Error: if \\spad{x} is not a symbol.") ((|#2| |#2| (|Mapping| (|Boolean|) |#3|)) "\\spad{suchThat(x, foo)} attaches the predicate foo to \\spad{x}; error if \\spad{x} is not a symbol."))) NIL NIL @@ -3823,7 +3823,7 @@ NIL (-973 R) ((|constructor| (NIL "This domain implements points in coordinate space"))) ((-4511 . T) (-4510 . T)) -((-4144 (-12 (|HasCategory| |#1| (QUOTE (-872))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|))))) (-4144 (-12 (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-888))))) (|HasCategory| |#1| (|%list| (QUOTE -633) (QUOTE (-549)))) (-4144 (|HasCategory| |#1| (QUOTE (-872))) (|HasCategory| |#1| (QUOTE (-1133)))) (|HasCategory| |#1| (QUOTE (-872))) (-4144 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-872))) (|HasCategory| |#1| (QUOTE (-1133)))) (|HasCategory| (-560) (QUOTE (-872))) (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#1| (QUOTE (-25))) (|HasCategory| |#1| (QUOTE (-23))) (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-748))) (|HasCategory| |#1| (QUOTE (-1081))) (-12 (|HasCategory| |#1| (QUOTE (-1034))) (|HasCategory| |#1| (QUOTE (-1081)))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-888)))) (|HasCategory| |#1| (QUOTE (-102))) (-12 (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|))))) +((-4118 (-12 (|HasCategory| |#1| (QUOTE (-872))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|))))) (-4118 (-12 (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-888))))) (|HasCategory| |#1| (|%list| (QUOTE -633) (QUOTE (-549)))) (-4118 (|HasCategory| |#1| (QUOTE (-872))) (|HasCategory| |#1| (QUOTE (-1133)))) (|HasCategory| |#1| (QUOTE (-872))) (-4118 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-872))) (|HasCategory| |#1| (QUOTE (-1133)))) (|HasCategory| (-560) (QUOTE (-872))) (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#1| (QUOTE (-25))) (|HasCategory| |#1| (QUOTE (-23))) (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-748))) (|HasCategory| |#1| (QUOTE (-1081))) (-12 (|HasCategory| |#1| (QUOTE (-1034))) (|HasCategory| |#1| (QUOTE (-1081)))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-888)))) (|HasCategory| |#1| (QUOTE (-102))) (-12 (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|))))) (-974 |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 @@ -3835,7 +3835,7 @@ NIL (-976 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}."))) (((-4512 "*") |has| |#1| (-175)) (-4503 |has| |#1| (-571)) (-4508 |has| |#1| (-6 -4508)) (-4505 . T) (-4504 . T) (-4507 . T)) -((|HasCategory| |#1| (QUOTE (-940))) (-4144 (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-466))) (|HasCategory| |#1| (QUOTE (-571))) (|HasCategory| |#1| (QUOTE (-940)))) (-4144 (|HasCategory| |#1| (QUOTE (-466))) (|HasCategory| |#1| (QUOTE (-571))) (|HasCategory| |#1| (QUOTE (-940)))) (-4144 (|HasCategory| |#1| (QUOTE (-466))) (|HasCategory| |#1| (QUOTE (-940)))) (|HasCategory| |#1| (QUOTE (-571))) (|HasCategory| |#1| (QUOTE (-175))) (-4144 (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-571)))) (-12 (|HasCategory| (-1209) (|%list| (QUOTE -912) (QUOTE (-391)))) (|HasCategory| |#1| (|%list| (QUOTE -912) (QUOTE (-391))))) (-12 (|HasCategory| (-1209) (|%list| (QUOTE -912) (QUOTE (-560)))) (|HasCategory| |#1| (|%list| (QUOTE -912) (QUOTE (-560))))) (-12 (|HasCategory| (-1209) (|%list| (QUOTE -633) (|%list| (QUOTE -916) (QUOTE (-391))))) (|HasCategory| |#1| (|%list| (QUOTE -633) (|%list| (QUOTE -916) (QUOTE (-391)))))) (-12 (|HasCategory| (-1209) (|%list| (QUOTE -633) (|%list| (QUOTE -916) (QUOTE (-560))))) (|HasCategory| |#1| (|%list| (QUOTE -633) (|%list| (QUOTE -916) (QUOTE (-560)))))) (-12 (|HasCategory| (-1209) (|%list| (QUOTE -633) (QUOTE (-549)))) (|HasCategory| |#1| (|%list| (QUOTE -633) (QUOTE (-549))))) (|HasCategory| |#1| (|%list| (QUOTE -660) (QUOTE (-560)))) (|HasCategory| |#1| (QUOTE (-149))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (|%list| (QUOTE -38) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#1| (|%list| (QUOTE -1070) (QUOTE (-560)))) (-4144 (|HasCategory| |#1| (|%list| (QUOTE -38) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#1| (|%list| (QUOTE -1070) (|%list| (QUOTE -421) (QUOTE (-560)))))) (|HasCategory| |#1| (|%list| (QUOTE -1070) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#1| (QUOTE (-376))) (|HasAttribute| |#1| (QUOTE -4508)) (|HasCategory| |#1| (QUOTE (-466))) (-12 (|HasCategory| $ (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-940)))) (-4144 (-12 (|HasCategory| $ (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-940)))) (|HasCategory| |#1| (QUOTE (-147))))) +((|HasCategory| |#1| (QUOTE (-940))) (-4118 (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-466))) (|HasCategory| |#1| (QUOTE (-571))) (|HasCategory| |#1| (QUOTE (-940)))) (-4118 (|HasCategory| |#1| (QUOTE (-466))) (|HasCategory| |#1| (QUOTE (-571))) (|HasCategory| |#1| (QUOTE (-940)))) (-4118 (|HasCategory| |#1| (QUOTE (-466))) (|HasCategory| |#1| (QUOTE (-940)))) (|HasCategory| |#1| (QUOTE (-571))) (|HasCategory| |#1| (QUOTE (-175))) (-4118 (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-571)))) (-12 (|HasCategory| (-1209) (|%list| (QUOTE -912) (QUOTE (-391)))) (|HasCategory| |#1| (|%list| (QUOTE -912) (QUOTE (-391))))) (-12 (|HasCategory| (-1209) (|%list| (QUOTE -912) (QUOTE (-560)))) (|HasCategory| |#1| (|%list| (QUOTE -912) (QUOTE (-560))))) (-12 (|HasCategory| (-1209) (|%list| (QUOTE -633) (|%list| (QUOTE -916) (QUOTE (-391))))) (|HasCategory| |#1| (|%list| (QUOTE -633) (|%list| (QUOTE -916) (QUOTE (-391)))))) (-12 (|HasCategory| (-1209) (|%list| (QUOTE -633) (|%list| (QUOTE -916) (QUOTE (-560))))) (|HasCategory| |#1| (|%list| (QUOTE -633) (|%list| (QUOTE -916) (QUOTE (-560)))))) (-12 (|HasCategory| (-1209) (|%list| (QUOTE -633) (QUOTE (-549)))) (|HasCategory| |#1| (|%list| (QUOTE -633) (QUOTE (-549))))) (|HasCategory| |#1| (|%list| (QUOTE -660) (QUOTE (-560)))) (|HasCategory| |#1| (QUOTE (-149))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (|%list| (QUOTE -38) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#1| (|%list| (QUOTE -1070) (QUOTE (-560)))) (-4118 (|HasCategory| |#1| (|%list| (QUOTE -38) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#1| (|%list| (QUOTE -1070) (|%list| (QUOTE -421) (QUOTE (-560)))))) (|HasCategory| |#1| (|%list| (QUOTE -1070) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#1| (QUOTE (-376))) (|HasAttribute| |#1| (QUOTE -4508)) (|HasCategory| |#1| (QUOTE (-466))) (-12 (|HasCategory| $ (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-940)))) (-4118 (-12 (|HasCategory| $ (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-940)))) (|HasCategory| |#1| (QUOTE (-147))))) (-977 R S) ((|constructor| (NIL "\\indented{2}{This package takes a mapping between coefficient rings,{} and lifts} it to a mapping between polynomials over those rings.")) (|map| (((|Polynomial| |#2|) (|Mapping| |#2| |#1|) (|Polynomial| |#1|)) "\\spad{map(f, p)} produces a new polynomial as a result of applying the function \\spad{f} to every coefficient of the polynomial \\spad{p}."))) NIL @@ -3852,7 +3852,7 @@ NIL ((|constructor| (NIL "The category for general multi-variate polynomials over a ring \\spad{R},{} in variables from VarSet,{} with exponents from the \\spadtype{OrderedAbelianMonoidSup}.")) (|canonicalUnitNormal| ((|attribute|) "we can choose a unique representative for each associate class. This normalization is chosen to be normalization of leading coefficient (by default).")) (|squareFreePart| (($ $) "\\spad{squareFreePart(p)} returns product of all the irreducible factors of polynomial \\spad{p} each taken with multiplicity one.")) (|squareFree| (((|Factored| $) $) "\\spad{squareFree(p)} returns the square free factorization of the polynomial \\spad{p}.")) (|primitivePart| (($ $ |#3|) "\\spad{primitivePart(p,v)} returns the unitCanonical associate of the polynomial \\spad{p} with its content with respect to the variable \\spad{v} divided out.") (($ $) "\\spad{primitivePart(p)} returns the unitCanonical associate of the polynomial \\spad{p} with its content divided out.")) (|content| (($ $ |#3|) "\\spad{content(p,v)} is the gcd of the coefficients of the polynomial \\spad{p} when \\spad{p} is viewed as a univariate polynomial with respect to the variable \\spad{v}. Thus,{} for polynomial 7*x**2*y + 14*x*y**2,{} the gcd of the coefficients with respect to \\spad{x} is 7*y.")) (|discriminant| (($ $ |#3|) "\\spad{discriminant(p,v)} returns the disriminant of the polynomial \\spad{p} with respect to the variable \\spad{v}.")) (|resultant| (($ $ $ |#3|) "\\spad{resultant(p,q,v)} returns the resultant of the polynomials \\spad{p} and \\spad{q} with respect to the variable \\spad{v}.")) (|primitiveMonomials| (((|List| $) $) "\\spad{primitiveMonomials(p)} gives the list of monomials of the polynomial \\spad{p} with their coefficients removed. Note: \\spad{primitiveMonomials(sum(a_(i) X^(i))) = [X^(1),...,X^(n)]}.")) (|variables| (((|List| |#3|) $) "\\spad{variables(p)} returns the list of those variables actually appearing in the polynomial \\spad{p}.")) (|totalDegree| (((|NonNegativeInteger|) $ (|List| |#3|)) "\\spad{totalDegree(p, lv)} returns the maximum sum (over all monomials of polynomial \\spad{p}) of the variables in the list lv.") (((|NonNegativeInteger|) $) "\\spad{totalDegree(p)} returns the largest sum over all monomials of all exponents of a monomial.")) (|isExpt| (((|Union| (|Record| (|:| |var| |#3|) (|:| |exponent| (|NonNegativeInteger|))) "failed") $) "\\spad{isExpt(p)} returns \\spad{[x, n]} if polynomial \\spad{p} has the form \\spad{x**n} and \\spad{n > 0}.")) (|isTimes| (((|Union| (|List| $) "failed") $) "\\spad{isTimes(p)} returns \\spad{[a1,...,an]} if polynomial \\spad{p = a1 ... an} and \\spad{n >= 2},{} and,{} for each \\spad{i},{} \\spad{ai} is either a nontrivial constant in \\spad{R} or else of the form \\spad{x**e},{} where \\spad{e > 0} is an integer and \\spad{x} in a member of VarSet.")) (|isPlus| (((|Union| (|List| $) "failed") $) "\\spad{isPlus(p)} returns \\spad{[m1,...,mn]} if polynomial \\spad{p = m1 + ... + mn} and \\spad{n >= 2} and each \\spad{mi} is a nonzero monomial.")) (|multivariate| (($ (|SparseUnivariatePolynomial| $) |#3|) "\\spad{multivariate(sup,v)} converts an anonymous univariable polynomial \\spad{sup} to a polynomial in the variable \\spad{v}.") (($ (|SparseUnivariatePolynomial| |#1|) |#3|) "\\spad{multivariate(sup,v)} converts an anonymous univariable polynomial \\spad{sup} to a polynomial in the variable \\spad{v}.")) (|monomial| (($ $ (|List| |#3|) (|List| (|NonNegativeInteger|))) "\\spad{monomial(a,[v1..vn],[e1..en])} returns \\spad{a*prod(vi**ei)}.") (($ $ |#3| (|NonNegativeInteger|)) "\\spad{monomial(a,x,n)} creates the monomial \\spad{a*x**n} where \\spad{a} is a polynomial,{} \\spad{x} is a variable and \\spad{n} is a nonnegative integer.")) (|monicDivide| (((|Record| (|:| |quotient| $) (|:| |remainder| $)) $ $ |#3|) "\\spad{monicDivide(a,b,v)} divides the polynomial a by the polynomial \\spad{b},{} with each viewed as a univariate polynomial in \\spad{v} returning both the quotient and remainder. Error: if \\spad{b} is not monic with respect to \\spad{v}.")) (|minimumDegree| (((|List| (|NonNegativeInteger|)) $ (|List| |#3|)) "\\spad{minimumDegree(p, lv)} gives the list of minimum degrees of the polynomial \\spad{p} with respect to each of the variables in the list lv") (((|NonNegativeInteger|) $ |#3|) "\\spad{minimumDegree(p,v)} gives the minimum degree of polynomial \\spad{p} with respect to \\spad{v},{} \\spadignore{i.e.} viewed a univariate polynomial in \\spad{v}")) (|mainVariable| (((|Union| |#3| "failed") $) "\\spad{mainVariable(p)} returns the biggest variable which actually occurs in the polynomial \\spad{p},{} or \"failed\" if no variables are present. fails precisely if polynomial satisfies ground?")) (|univariate| (((|SparseUnivariatePolynomial| |#1|) $) "\\spad{univariate(p)} converts the multivariate polynomial \\spad{p},{} which should actually involve only one variable,{} into a univariate polynomial in that variable,{} whose coefficients are in the ground ring. Error: if polynomial is genuinely multivariate") (((|SparseUnivariatePolynomial| $) $ |#3|) "\\spad{univariate(p,v)} converts the multivariate polynomial \\spad{p} into a univariate polynomial in \\spad{v},{} whose coefficients are still multivariate polynomials (in all the other variables).")) (|monomials| (((|List| $) $) "\\spad{monomials(p)} returns the list of non-zero monomials of polynomial \\spad{p},{} \\spadignore{i.e.} \\spad{monomials(sum(a_(i) X^(i))) = [a_(1) X^(1),...,a_(n) X^(n)]}.")) (|coefficient| (($ $ (|List| |#3|) (|List| (|NonNegativeInteger|))) "\\spad{coefficient(p, lv, ln)} views the polynomial \\spad{p} as a polynomial in the variables of \\spad{lv} and returns the coefficient of the term \\spad{lv**ln},{} \\spadignore{i.e.} \\spad{prod(lv_i ** ln_i)}.") (($ $ |#3| (|NonNegativeInteger|)) "\\spad{coefficient(p,v,n)} views the polynomial \\spad{p} as a univariate polynomial in \\spad{v} and returns the coefficient of the \\spad{v**n} term.")) (|degree| (((|List| (|NonNegativeInteger|)) $ (|List| |#3|)) "\\spad{degree(p,lv)} gives the list of degrees of polynomial \\spad{p} with respect to each of the variables in the list \\spad{lv}.") (((|NonNegativeInteger|) $ |#3|) "\\spad{degree(p,v)} gives the degree of polynomial \\spad{p} with respect to the variable \\spad{v}."))) (((-4512 "*") |has| |#1| (-175)) (-4503 |has| |#1| (-571)) (-4508 |has| |#1| (-6 -4508)) (-4505 . T) (-4504 . T) (-4507 . T)) NIL -(-981 E V R P -4164) +(-981 E V R P -4140) ((|constructor| (NIL "This package transforms multivariate polynomials or fractions into univariate polynomials or fractions,{} and back.")) (|isPower| (((|Union| (|Record| (|:| |val| |#5|) (|:| |exponent| (|Integer|))) "failed") |#5|) "\\spad{isPower(p)} returns \\spad{[x, n]} if \\spad{p = x**n} and \\spad{n <> 0},{} \"failed\" otherwise.")) (|isExpt| (((|Union| (|Record| (|:| |var| |#2|) (|:| |exponent| (|Integer|))) "failed") |#5|) "\\spad{isExpt(p)} returns \\spad{[x, n]} if \\spad{p = x**n} and \\spad{n <> 0},{} \"failed\" otherwise.")) (|isTimes| (((|Union| (|List| |#5|) "failed") |#5|) "\\spad{isTimes(p)} returns \\spad{[a1,...,an]} if \\spad{p = a1 ... an} and \\spad{n > 1},{} \"failed\" otherwise.")) (|isPlus| (((|Union| (|List| |#5|) "failed") |#5|) "\\spad{isPlus(p)} returns [\\spad{m1},{}...,{}mn] if \\spad{p = m1 + ... + mn} and \\spad{n > 1},{} \"failed\" otherwise.")) (|multivariate| ((|#5| (|Fraction| (|SparseUnivariatePolynomial| |#5|)) |#2|) "\\spad{multivariate(f, v)} applies both the numerator and denominator of \\spad{f} to \\spad{v}.")) (|univariate| (((|SparseUnivariatePolynomial| |#5|) |#5| |#2| (|SparseUnivariatePolynomial| |#5|)) "\\spad{univariate(f, x, p)} returns \\spad{f} viewed as a univariate polynomial in \\spad{x},{} using the side-condition \\spad{p(x) = 0}.") (((|Fraction| (|SparseUnivariatePolynomial| |#5|)) |#5| |#2|) "\\spad{univariate(f, v)} returns \\spad{f} viewed as a univariate rational function in \\spad{v}.")) (|mainVariable| (((|Union| |#2| "failed") |#5|) "\\spad{mainVariable(f)} returns the highest variable appearing in the numerator or the denominator of \\spad{f},{} \"failed\" if \\spad{f} has no variables.")) (|variables| (((|List| |#2|) |#5|) "\\spad{variables(f)} returns the list of variables appearing in the numerator or the denominator of \\spad{f}."))) NIL NIL @@ -3860,7 +3860,7 @@ NIL ((|constructor| (NIL "This package provides a very general map function,{} which given a set \\spad{S} and polynomials over \\spad{R} with maps from the variables into \\spad{S} and the coefficients into \\spad{S},{} maps polynomials into \\spad{S}. \\spad{S} is assumed to support \\spad{+},{} \\spad{*} and \\spad{**}.")) (|map| ((|#5| (|Mapping| |#5| |#2|) (|Mapping| |#5| |#3|) |#4|) "\\spad{map(varmap, coefmap, p)} takes a \\spad{varmap},{} a mapping from the variables of polynomial \\spad{p} into \\spad{S},{} \\spad{coefmap},{} a mapping from coefficients of \\spad{p} into \\spad{S},{} and \\spad{p},{} and produces a member of \\spad{S} using the corresponding arithmetic. in \\spad{S}"))) NIL NIL -(-983 E V R P -4164) +(-983 E V R P -4140) ((|constructor| (NIL "computes \\spad{n}-th roots of quotients of multivariate polynomials")) (|nthr| (((|Record| (|:| |exponent| (|NonNegativeInteger|)) (|:| |coef| |#4|) (|:| |radicand| (|List| |#4|))) |#4| (|NonNegativeInteger|)) "\\spad{nthr(p,n)} should be local but conditional")) (|froot| (((|Record| (|:| |exponent| (|NonNegativeInteger|)) (|:| |coef| |#5|) (|:| |radicand| |#5|)) |#5| (|NonNegativeInteger|)) "\\spad{froot(f, n)} returns \\spad{[m,c,r]} such that \\spad{f**(1/n) = c * r**(1/m)}.")) (|qroot| (((|Record| (|:| |exponent| (|NonNegativeInteger|)) (|:| |coef| |#5|) (|:| |radicand| |#5|)) (|Fraction| (|Integer|)) (|NonNegativeInteger|)) "\\spad{qroot(f, n)} returns \\spad{[m,c,r]} such that \\spad{f**(1/n) = c * r**(1/m)}.")) (|rroot| (((|Record| (|:| |exponent| (|NonNegativeInteger|)) (|:| |coef| |#5|) (|:| |radicand| |#5|)) |#3| (|NonNegativeInteger|)) "\\spad{rroot(f, n)} returns \\spad{[m,c,r]} such that \\spad{f**(1/n) = c * r**(1/m)}.")) (|denom| ((|#4| $) "\\spad{denom(x)} \\undocumented")) (|numer| ((|#4| $) "\\spad{numer(x)} \\undocumented"))) NIL ((|HasCategory| |#3| (QUOTE (-466)))) @@ -3875,7 +3875,7 @@ NIL (-986 R E) ((|constructor| (NIL "This domain represents generalized polynomials with coefficients (from a not necessarily commutative ring),{} and terms indexed by their exponents (from an arbitrary ordered abelian monoid). This type is used,{} for example,{} by the \\spadtype{DistributedMultivariatePolynomial} domain where the exponent domain is a direct product of non negative integers.")) (|canonicalUnitNormal| ((|attribute|) "canonicalUnitNormal guarantees that the function unitCanonical returns the same representative for all associates of any particular element.")) (|fmecg| (($ $ |#2| |#1| $) "\\spad{fmecg(p1,e,r,p2)} finds \\spad{X} : \\spad{p1} - \\spad{r} * X**e * \\spad{p2}"))) (((-4512 "*") |has| |#1| (-175)) (-4503 |has| |#1| (-571)) (-4508 |has| |#1| (-6 -4508)) (-4504 . T) (-4505 . T) (-4507 . T)) -((|HasCategory| |#1| (|%list| (QUOTE -38) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#1| (QUOTE (-571))) (-4144 (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-571)))) (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-149))) (-4144 (|HasCategory| |#1| (|%list| (QUOTE -38) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#1| (|%list| (QUOTE -1070) (|%list| (QUOTE -421) (QUOTE (-560)))))) (|HasCategory| |#1| (|%list| (QUOTE -1070) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#1| (|%list| (QUOTE -1070) (QUOTE (-560)))) (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (QUOTE (-466))) (-12 (|HasCategory| |#1| (QUOTE (-571))) (|HasCategory| |#2| (QUOTE (-133)))) (|HasAttribute| |#1| (QUOTE -4508))) +((|HasCategory| |#1| (|%list| (QUOTE -38) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#1| (QUOTE (-571))) (-4118 (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-571)))) (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-149))) (-4118 (|HasCategory| |#1| (|%list| (QUOTE -38) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#1| (|%list| (QUOTE -1070) (|%list| (QUOTE -421) (QUOTE (-560)))))) (|HasCategory| |#1| (|%list| (QUOTE -1070) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#1| (|%list| (QUOTE -1070) (QUOTE (-560)))) (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (QUOTE (-466))) (-12 (|HasCategory| |#1| (QUOTE (-571))) (|HasCategory| |#2| (QUOTE (-133)))) (|HasAttribute| |#1| (QUOTE -4508))) (-987 R L) ((|constructor| (NIL "\\spadtype{PrecomputedAssociatedEquations} stores some generic precomputations which speed up the computations of the associated equations needed for factoring operators.")) (|firstUncouplingMatrix| (((|Union| (|Matrix| |#1|) "failed") |#2| (|PositiveInteger|)) "\\spad{firstUncouplingMatrix(op, m)} returns the matrix A such that \\spad{A w = (W',W'',...,W^N)} in the corresponding associated equations for right-factors of order \\spad{m} of \\spad{op}. Returns \"failed\" if the matrix A has not been precomputed for the particular combination \\spad{degree(L), m}."))) NIL @@ -3883,7 +3883,7 @@ NIL (-988 S) ((|constructor| (NIL "\\indented{1}{This provides a fast array type with no bound checking on elt's.} Minimum index is 0 in this type,{} cannot be changed"))) ((-4511 . T) (-4510 . T)) -((-4144 (-12 (|HasCategory| |#1| (QUOTE (-872))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|))))) (-4144 (-12 (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-888))))) (|HasCategory| |#1| (|%list| (QUOTE -633) (QUOTE (-549)))) (-4144 (|HasCategory| |#1| (QUOTE (-872))) (|HasCategory| |#1| (QUOTE (-1133)))) (|HasCategory| |#1| (QUOTE (-872))) (-4144 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-872))) (|HasCategory| |#1| (QUOTE (-1133)))) (|HasCategory| (-560) (QUOTE (-872))) (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-888)))) (|HasCategory| |#1| (QUOTE (-102))) (-12 (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|))))) +((-4118 (-12 (|HasCategory| |#1| (QUOTE (-872))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|))))) (-4118 (-12 (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-888))))) (|HasCategory| |#1| (|%list| (QUOTE -633) (QUOTE (-549)))) (-4118 (|HasCategory| |#1| (QUOTE (-872))) (|HasCategory| |#1| (QUOTE (-1133)))) (|HasCategory| |#1| (QUOTE (-872))) (-4118 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-872))) (|HasCategory| |#1| (QUOTE (-1133)))) (|HasCategory| (-560) (QUOTE (-872))) (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-888)))) (|HasCategory| |#1| (QUOTE (-102))) (-12 (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|))))) (-989 A B) ((|constructor| (NIL "\\indented{1}{This package provides tools for operating on primitive arrays} with unary and binary functions involving different underlying types")) (|map| (((|PrimitiveArray| |#2|) (|Mapping| |#2| |#1|) (|PrimitiveArray| |#1|)) "\\spad{map(f,a)} applies function \\spad{f} to each member of primitive array \\spad{a} resulting in a new primitive array over a possibly different underlying domain.")) (|reduce| ((|#2| (|Mapping| |#2| |#1| |#2|) (|PrimitiveArray| |#1|) |#2|) "\\spad{reduce(f,a,r)} applies function \\spad{f} to each successive element of the primitive array \\spad{a} and an accumulant initialized to \\spad{r}. For example,{} \\spad{reduce(_+\\$Integer,[1,2,3],0)} does \\spad{3+(2+(1+0))}. Note: third argument \\spad{r} may be regarded as the identity element for the function \\spad{f}.")) (|scan| (((|PrimitiveArray| |#2|) (|Mapping| |#2| |#1| |#2|) (|PrimitiveArray| |#1|) |#2|) "\\spad{scan(f,a,r)} successively applies \\spad{reduce(f,x,r)} to more and more leading sub-arrays \\spad{x} of primitive array \\spad{a}. More precisely,{} if \\spad{a} is \\spad{[a1,a2,...]},{} then \\spad{scan(f,a,r)} returns \\spad{[reduce(f,[a1],r),reduce(f,[a1,a2],r),...]}."))) NIL @@ -3892,7 +3892,7 @@ NIL ((|constructor| (NIL "Category for the functions defined by integrals.")) (|integral| (($ $ (|SegmentBinding| $)) "\\spad{integral(f, x = a..b)} returns the formal definite integral of \\spad{f} dx for \\spad{x} between \\spad{a} and \\spad{b}.") (($ $ (|Symbol|)) "\\spad{integral(f, x)} returns the formal integral of \\spad{f} dx."))) NIL NIL -(-991 -4164) +(-991 -4140) ((|constructor| (NIL "PrimitiveElement provides functions to compute primitive elements in algebraic extensions.")) (|primitiveElement| (((|Record| (|:| |coef| (|List| (|Integer|))) (|:| |poly| (|List| (|SparseUnivariatePolynomial| |#1|))) (|:| |prim| (|SparseUnivariatePolynomial| |#1|))) (|List| (|Polynomial| |#1|)) (|List| (|Symbol|)) (|Symbol|)) "\\spad{primitiveElement([p1,...,pn], [a1,...,an], a)} returns \\spad{[[c1,...,cn], [q1,...,qn], q]} such that then \\spad{k(a1,...,an) = k(a)},{} where \\spad{a = a1 c1 + ... + an cn},{} \\spad{ai = qi(a)},{} and \\spad{q(a) = 0}. The \\spad{pi}'s are the defining polynomials for the \\spad{ai}'s. This operation uses the technique of \\spadglossSee{groebner bases}{Groebner basis}.") (((|Record| (|:| |coef| (|List| (|Integer|))) (|:| |poly| (|List| (|SparseUnivariatePolynomial| |#1|))) (|:| |prim| (|SparseUnivariatePolynomial| |#1|))) (|List| (|Polynomial| |#1|)) (|List| (|Symbol|))) "\\spad{primitiveElement([p1,...,pn], [a1,...,an])} returns \\spad{[[c1,...,cn], [q1,...,qn], q]} such that then \\spad{k(a1,...,an) = k(a)},{} where \\spad{a = a1 c1 + ... + an cn},{} \\spad{ai = qi(a)},{} and \\spad{q(a) = 0}. The \\spad{pi}'s are the defining polynomials for the \\spad{ai}'s. This operation uses the technique of \\spadglossSee{groebner bases}{Groebner basis}.") (((|Record| (|:| |coef1| (|Integer|)) (|:| |coef2| (|Integer|)) (|:| |prim| (|SparseUnivariatePolynomial| |#1|))) (|Polynomial| |#1|) (|Symbol|) (|Polynomial| |#1|) (|Symbol|)) "\\spad{primitiveElement(p1, a1, p2, a2)} returns \\spad{[c1, c2, q]} such that \\spad{k(a1, a2) = k(a)} where \\spad{a = c1 a1 + c2 a2, and q(a) = 0}. The \\spad{pi}'s are the defining polynomials for the \\spad{ai}'s. The \\spad{p2} may involve \\spad{a1},{} but \\spad{p1} must not involve \\spad{a2}. This operation uses \\spadfun{resultant}."))) NIL NIL @@ -3907,7 +3907,7 @@ NIL (-994 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"))) ((-4507 -12 (|has| |#2| (-487)) (|has| |#1| (-487)))) -((-4144 (-12 (|HasCategory| |#1| (QUOTE (-817))) (|HasCategory| |#2| (QUOTE (-817)))) (-12 (|HasCategory| |#1| (QUOTE (-872))) (|HasCategory| |#2| (QUOTE (-872))))) (-12 (|HasCategory| |#1| (QUOTE (-817))) (|HasCategory| |#2| (QUOTE (-817)))) (-4144 (-12 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#2| (QUOTE (-21)))) (-12 (|HasCategory| |#1| (QUOTE (-133))) (|HasCategory| |#2| (QUOTE (-133)))) (-12 (|HasCategory| |#1| (QUOTE (-817))) (|HasCategory| |#2| (QUOTE (-817))))) (-12 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#2| (QUOTE (-21)))) (-4144 (-12 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#2| (QUOTE (-21)))) (-12 (|HasCategory| |#1| (QUOTE (-23))) (|HasCategory| |#2| (QUOTE (-23)))) (-12 (|HasCategory| |#1| (QUOTE (-133))) (|HasCategory| |#2| (QUOTE (-133)))) (-12 (|HasCategory| |#1| (QUOTE (-817))) (|HasCategory| |#2| (QUOTE (-817))))) (-12 (|HasCategory| |#1| (QUOTE (-487))) (|HasCategory| |#2| (QUOTE (-487)))) (-4144 (-12 (|HasCategory| |#1| (QUOTE (-487))) (|HasCategory| |#2| (QUOTE (-487)))) (-12 (|HasCategory| |#1| (QUOTE (-748))) (|HasCategory| |#2| (QUOTE (-748))))) (-12 (|HasCategory| |#1| (QUOTE (-381))) (|HasCategory| |#2| (QUOTE (-381)))) (-4144 (-12 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#2| (QUOTE (-21)))) (-12 (|HasCategory| |#1| (QUOTE (-23))) (|HasCategory| |#2| (QUOTE (-23)))) (-12 (|HasCategory| |#1| (QUOTE (-133))) (|HasCategory| |#2| (QUOTE (-133)))) (-12 (|HasCategory| |#1| (QUOTE (-487))) (|HasCategory| |#2| (QUOTE (-487)))) (-12 (|HasCategory| |#1| (QUOTE (-748))) (|HasCategory| |#2| (QUOTE (-748)))) (-12 (|HasCategory| |#1| (QUOTE (-817))) (|HasCategory| |#2| (QUOTE (-817))))) (-12 (|HasCategory| |#1| (QUOTE (-748))) (|HasCategory| |#2| (QUOTE (-748)))) (-12 (|HasCategory| |#1| (QUOTE (-23))) (|HasCategory| |#2| (QUOTE (-23)))) (-12 (|HasCategory| |#1| (QUOTE (-133))) (|HasCategory| |#2| (QUOTE (-133)))) (-12 (|HasCategory| |#1| (QUOTE (-872))) (|HasCategory| |#2| (QUOTE (-872))))) +((-4118 (-12 (|HasCategory| |#1| (QUOTE (-817))) (|HasCategory| |#2| (QUOTE (-817)))) (-12 (|HasCategory| |#1| (QUOTE (-872))) (|HasCategory| |#2| (QUOTE (-872))))) (-12 (|HasCategory| |#1| (QUOTE (-817))) (|HasCategory| |#2| (QUOTE (-817)))) (-4118 (-12 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#2| (QUOTE (-21)))) (-12 (|HasCategory| |#1| (QUOTE (-133))) (|HasCategory| |#2| (QUOTE (-133)))) (-12 (|HasCategory| |#1| (QUOTE (-817))) (|HasCategory| |#2| (QUOTE (-817))))) (-12 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#2| (QUOTE (-21)))) (-4118 (-12 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#2| (QUOTE (-21)))) (-12 (|HasCategory| |#1| (QUOTE (-23))) (|HasCategory| |#2| (QUOTE (-23)))) (-12 (|HasCategory| |#1| (QUOTE (-133))) (|HasCategory| |#2| (QUOTE (-133)))) (-12 (|HasCategory| |#1| (QUOTE (-817))) (|HasCategory| |#2| (QUOTE (-817))))) (-12 (|HasCategory| |#1| (QUOTE (-487))) (|HasCategory| |#2| (QUOTE (-487)))) (-4118 (-12 (|HasCategory| |#1| (QUOTE (-487))) (|HasCategory| |#2| (QUOTE (-487)))) (-12 (|HasCategory| |#1| (QUOTE (-748))) (|HasCategory| |#2| (QUOTE (-748))))) (-12 (|HasCategory| |#1| (QUOTE (-381))) (|HasCategory| |#2| (QUOTE (-381)))) (-4118 (-12 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#2| (QUOTE (-21)))) (-12 (|HasCategory| |#1| (QUOTE (-23))) (|HasCategory| |#2| (QUOTE (-23)))) (-12 (|HasCategory| |#1| (QUOTE (-133))) (|HasCategory| |#2| (QUOTE (-133)))) (-12 (|HasCategory| |#1| (QUOTE (-487))) (|HasCategory| |#2| (QUOTE (-487)))) (-12 (|HasCategory| |#1| (QUOTE (-748))) (|HasCategory| |#2| (QUOTE (-748)))) (-12 (|HasCategory| |#1| (QUOTE (-817))) (|HasCategory| |#2| (QUOTE (-817))))) (-12 (|HasCategory| |#1| (QUOTE (-748))) (|HasCategory| |#2| (QUOTE (-748)))) (-12 (|HasCategory| |#1| (QUOTE (-23))) (|HasCategory| |#2| (QUOTE (-23)))) (-12 (|HasCategory| |#1| (QUOTE (-133))) (|HasCategory| |#2| (QUOTE (-133)))) (-12 (|HasCategory| |#1| (QUOTE (-872))) (|HasCategory| |#2| (QUOTE (-872))))) (-995) ((|constructor| (NIL "\\indented{1}{Author: Gabriel Dos Reis} Date Created: October 24,{} 2007 Date Last Modified: January 18,{} 2008. An `Property' is a pair of name and value.")) (|property| (($ (|Identifier|) (|SExpression|)) "\\spad{property(n,val)} constructs a property with name `n' and value `val'.")) (|value| (((|SExpression|) $) "\\spad{value(p)} returns value of property \\spad{p}")) (|name| (((|Identifier|) $) "\\spad{name(p)} returns the name of property \\spad{p}"))) NIL @@ -3996,7 +3996,7 @@ NIL ((|constructor| (NIL "This package \\undocumented{}")) (|map| ((|#4| (|Mapping| |#4| (|Polynomial| |#1|)) |#4|) "\\spad{map(f,p)} \\undocumented{}")) (|pushup| ((|#4| |#4| (|List| |#3|)) "\\spad{pushup(p,lv)} \\undocumented{}") ((|#4| |#4| |#3|) "\\spad{pushup(p,v)} \\undocumented{}")) (|pushdown| ((|#4| |#4| (|List| |#3|)) "\\spad{pushdown(p,lv)} \\undocumented{}") ((|#4| |#4| |#3|) "\\spad{pushdown(p,v)} \\undocumented{}")) (|variable| (((|Union| $ "failed") (|Symbol|)) "\\spad{variable(s)} makes an element from symbol \\spad{s} or fails")) (|convert| (((|Symbol|) $) "\\spad{convert(x)} converts \\spad{x} to a symbol"))) NIL NIL -(-1017 K R UP -4164) +(-1017 K R UP -4140) ((|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 @@ -4043,7 +4043,7 @@ NIL (-1028 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.}"))) ((-4503 |has| |#1| (-302)) (-4504 . T) (-4505 . T) (-4507 . T)) -((|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-149))) (|HasCategory| |#1| (|%list| (QUOTE -633) (QUOTE (-549)))) (|HasCategory| |#1| (QUOTE (-376))) (-4144 (|HasCategory| |#1| (QUOTE (-302))) (|HasCategory| |#1| (QUOTE (-376)))) (|HasCategory| |#1| (QUOTE (-302))) (|HasCategory| |#1| (QUOTE (-872))) (|HasCategory| |#1| (|%list| (QUOTE -660) (QUOTE (-560)))) (|HasCategory| |#1| (|%list| (QUOTE -528) (QUOTE (-1209)) (|devaluate| |#1|))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|))) (|HasCategory| |#1| (|%list| (QUOTE -298) (|devaluate| |#1|) (|devaluate| |#1|))) (|HasCategory| |#1| (QUOTE (-239))) (|HasCategory| |#1| (|%list| (QUOTE -930) (QUOTE (-1209)))) (|HasCategory| |#1| (QUOTE (-240))) (|HasCategory| |#1| (|%list| (QUOTE -928) (QUOTE (-1209)))) (-4144 (|HasCategory| |#1| (|%list| (QUOTE -1070) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#1| (QUOTE (-376)))) (|HasCategory| |#1| (|%list| (QUOTE -1070) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#1| (|%list| (QUOTE -1070) (QUOTE (-560)))) (|HasCategory| |#1| (QUOTE (-1092))) (|HasCategory| |#1| (QUOTE (-559)))) +((|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-149))) (|HasCategory| |#1| (|%list| (QUOTE -633) (QUOTE (-549)))) (|HasCategory| |#1| (QUOTE (-376))) (-4118 (|HasCategory| |#1| (QUOTE (-302))) (|HasCategory| |#1| (QUOTE (-376)))) (|HasCategory| |#1| (QUOTE (-302))) (|HasCategory| |#1| (QUOTE (-872))) (|HasCategory| |#1| (|%list| (QUOTE -660) (QUOTE (-560)))) (|HasCategory| |#1| (|%list| (QUOTE -528) (QUOTE (-1209)) (|devaluate| |#1|))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|))) (|HasCategory| |#1| (|%list| (QUOTE -298) (|devaluate| |#1|) (|devaluate| |#1|))) (|HasCategory| |#1| (QUOTE (-239))) (|HasCategory| |#1| (|%list| (QUOTE -930) (QUOTE (-1209)))) (|HasCategory| |#1| (QUOTE (-240))) (|HasCategory| |#1| (|%list| (QUOTE -928) (QUOTE (-1209)))) (-4118 (|HasCategory| |#1| (|%list| (QUOTE -1070) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#1| (QUOTE (-376)))) (|HasCategory| |#1| (|%list| (QUOTE -1070) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#1| (|%list| (QUOTE -1070) (QUOTE (-560)))) (|HasCategory| |#1| (QUOTE (-1092))) (|HasCategory| |#1| (QUOTE (-559)))) (-1029 S R) ((|constructor| (NIL "\\spadtype{QuaternionCategory} describes the category of quaternions and implements functions that are not representation specific.")) (|rationalIfCan| (((|Union| (|Fraction| (|Integer|)) "failed") $) "\\spad{rationalIfCan(q)} returns \\spad{q} as a rational number,{} or \"failed\" if this is not possible. Note: if \\spad{rational?(q)} is \\spad{true},{} the conversion can be done and the rational number will be returned.")) (|rational| (((|Fraction| (|Integer|)) $) "\\spad{rational(q)} tries to convert \\spad{q} into a rational number. Error: if this is not possible. If \\spad{rational?(q)} is \\spad{true},{} the conversion will be done and the rational number returned.")) (|rational?| (((|Boolean|) $) "\\spad{rational?(q)} returns {\\it \\spad{true}} if all the imaginary parts of \\spad{q} are zero and the real part can be converted into a rational number,{} and {\\it \\spad{false}} otherwise.")) (|abs| ((|#2| $) "\\spad{abs(q)} computes the absolute value of quaternion \\spad{q} (sqrt of norm).")) (|real| ((|#2| $) "\\spad{real(q)} extracts the real part of quaternion \\spad{q}.")) (|quatern| (($ |#2| |#2| |#2| |#2|) "\\spad{quatern(r,i,j,k)} constructs a quaternion from scalars.")) (|norm| ((|#2| $) "\\spad{norm(q)} computes the norm of \\spad{q} (the sum of the squares of the components).")) (|imagK| ((|#2| $) "\\spad{imagK(q)} extracts the imaginary \\spad{k} part of quaternion \\spad{q}.")) (|imagJ| ((|#2| $) "\\spad{imagJ(q)} extracts the imaginary \\spad{j} part of quaternion \\spad{q}.")) (|imagI| ((|#2| $) "\\spad{imagI(q)} extracts the imaginary \\spad{i} part of quaternion \\spad{q}.")) (|conjugate| (($ $) "\\spad{conjugate(q)} negates the imaginary parts of quaternion \\spad{q}."))) NIL @@ -4059,7 +4059,7 @@ NIL (-1032 S) ((|constructor| (NIL "Linked List implementation of a Queue")) (|queue| (($ (|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}."))) ((-4510 . T) (-4511 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1133))) (-4144 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-1133)))) (-4144 (-12 (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-888))))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-888)))) (|HasCategory| |#1| (QUOTE (-102)))) +((-12 (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1133))) (-4118 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-1133)))) (-4118 (-12 (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-888))))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-888)))) (|HasCategory| |#1| (QUOTE (-102)))) (-1033 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| (($ $) "\\spad{sqrt(x)} returns the square root of \\spad{x}."))) NIL @@ -4068,14 +4068,14 @@ NIL ((|constructor| (NIL "The \\spad{RadicalCategory} is a model for the rational numbers.")) (** (($ $ (|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 -(-1035 -4164 UP UPUP |radicnd| |n|) +(-1035 -4140 UP UPUP |radicnd| |n|) ((|constructor| (NIL "Function field defined by y**n = \\spad{f}(\\spad{x})."))) ((-4503 |has| (-421 |#2|) (-376)) (-4508 |has| (-421 |#2|) (-376)) (-4502 |has| (-421 |#2|) (-376)) ((-4512 "*") . T) (-4504 . T) (-4505 . T) (-4507 . T)) -((|HasCategory| (-421 |#2|) (QUOTE (-147))) (|HasCategory| (-421 |#2|) (QUOTE (-149))) (|HasCategory| (-421 |#2|) (QUOTE (-363))) (-4144 (|HasCategory| (-421 |#2|) (QUOTE (-376))) (|HasCategory| (-421 |#2|) (QUOTE (-363)))) (|HasCategory| (-421 |#2|) (QUOTE (-376))) (|HasCategory| (-421 |#2|) (QUOTE (-381))) (-4144 (-12 (|HasCategory| (-421 |#2|) (QUOTE (-240))) (|HasCategory| (-421 |#2|) (QUOTE (-376)))) (|HasCategory| (-421 |#2|) (QUOTE (-363)))) (-4144 (-12 (|HasCategory| (-421 |#2|) (QUOTE (-240))) (|HasCategory| (-421 |#2|) (QUOTE (-376)))) (-12 (|HasCategory| (-421 |#2|) (QUOTE (-239))) (|HasCategory| (-421 |#2|) (QUOTE (-376)))) (|HasCategory| (-421 |#2|) (QUOTE (-363)))) (-4144 (-12 (|HasCategory| (-421 |#2|) (|%list| (QUOTE -928) (QUOTE (-1209)))) (|HasCategory| (-421 |#2|) (QUOTE (-376)))) (-12 (|HasCategory| (-421 |#2|) (|%list| (QUOTE -928) (QUOTE (-1209)))) (|HasCategory| (-421 |#2|) (QUOTE (-363))))) (-4144 (-12 (|HasCategory| (-421 |#2|) (|%list| (QUOTE -928) (QUOTE (-1209)))) (|HasCategory| (-421 |#2|) (QUOTE (-376)))) (-12 (|HasCategory| (-421 |#2|) (|%list| (QUOTE -930) (QUOTE (-1209)))) (|HasCategory| (-421 |#2|) (QUOTE (-376))))) (|HasCategory| (-421 |#2|) (|%list| (QUOTE -660) (QUOTE (-560)))) (-4144 (|HasCategory| (-421 |#2|) (|%list| (QUOTE -1070) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| (-421 |#2|) (QUOTE (-376)))) (|HasCategory| (-421 |#2|) (|%list| (QUOTE -1070) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| (-421 |#2|) (|%list| (QUOTE -1070) (QUOTE (-560)))) (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (QUOTE (-381))) (-12 (|HasCategory| (-421 |#2|) (QUOTE (-239))) (|HasCategory| (-421 |#2|) (QUOTE (-376)))) (-12 (|HasCategory| (-421 |#2|) (|%list| (QUOTE -930) (QUOTE (-1209)))) (|HasCategory| (-421 |#2|) (QUOTE (-376)))) (-12 (|HasCategory| (-421 |#2|) (QUOTE (-240))) (|HasCategory| (-421 |#2|) (QUOTE (-376)))) (-12 (|HasCategory| (-421 |#2|) (|%list| (QUOTE -928) (QUOTE (-1209)))) (|HasCategory| (-421 |#2|) (QUOTE (-376))))) +((|HasCategory| (-421 |#2|) (QUOTE (-147))) (|HasCategory| (-421 |#2|) (QUOTE (-149))) (|HasCategory| (-421 |#2|) (QUOTE (-363))) (-4118 (|HasCategory| (-421 |#2|) (QUOTE (-376))) (|HasCategory| (-421 |#2|) (QUOTE (-363)))) (|HasCategory| (-421 |#2|) (QUOTE (-376))) (|HasCategory| (-421 |#2|) (QUOTE (-381))) (-4118 (-12 (|HasCategory| (-421 |#2|) (QUOTE (-240))) (|HasCategory| (-421 |#2|) (QUOTE (-376)))) (|HasCategory| (-421 |#2|) (QUOTE (-363)))) (-4118 (-12 (|HasCategory| (-421 |#2|) (QUOTE (-240))) (|HasCategory| (-421 |#2|) (QUOTE (-376)))) (-12 (|HasCategory| (-421 |#2|) (QUOTE (-239))) (|HasCategory| (-421 |#2|) (QUOTE (-376)))) (|HasCategory| (-421 |#2|) (QUOTE (-363)))) (-4118 (-12 (|HasCategory| (-421 |#2|) (|%list| (QUOTE -928) (QUOTE (-1209)))) (|HasCategory| (-421 |#2|) (QUOTE (-376)))) (-12 (|HasCategory| (-421 |#2|) (|%list| (QUOTE -928) (QUOTE (-1209)))) (|HasCategory| (-421 |#2|) (QUOTE (-363))))) (-4118 (-12 (|HasCategory| (-421 |#2|) (|%list| (QUOTE -928) (QUOTE (-1209)))) (|HasCategory| (-421 |#2|) (QUOTE (-376)))) (-12 (|HasCategory| (-421 |#2|) (|%list| (QUOTE -930) (QUOTE (-1209)))) (|HasCategory| (-421 |#2|) (QUOTE (-376))))) (|HasCategory| (-421 |#2|) (|%list| (QUOTE -660) (QUOTE (-560)))) (-4118 (|HasCategory| (-421 |#2|) (|%list| (QUOTE -1070) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| (-421 |#2|) (QUOTE (-376)))) (|HasCategory| (-421 |#2|) (|%list| (QUOTE -1070) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| (-421 |#2|) (|%list| (QUOTE -1070) (QUOTE (-560)))) (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (QUOTE (-381))) (-12 (|HasCategory| (-421 |#2|) (QUOTE (-239))) (|HasCategory| (-421 |#2|) (QUOTE (-376)))) (-12 (|HasCategory| (-421 |#2|) (|%list| (QUOTE -930) (QUOTE (-1209)))) (|HasCategory| (-421 |#2|) (QUOTE (-376)))) (-12 (|HasCategory| (-421 |#2|) (QUOTE (-240))) (|HasCategory| (-421 |#2|) (QUOTE (-376)))) (-12 (|HasCategory| (-421 |#2|) (|%list| (QUOTE -928) (QUOTE (-1209)))) (|HasCategory| (-421 |#2|) (QUOTE (-376))))) (-1036 |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."))) ((-4502 . T) (-4508 . T) (-4503 . T) ((-4512 "*") . T) (-4504 . T) (-4505 . T) (-4507 . T)) -((|HasCategory| (-560) (QUOTE (-940))) (|HasCategory| (-560) (|%list| (QUOTE -1070) (QUOTE (-1209)))) (|HasCategory| (-560) (QUOTE (-147))) (|HasCategory| (-560) (QUOTE (-149))) (|HasCategory| (-560) (|%list| (QUOTE -633) (QUOTE (-549)))) (|HasCategory| (-560) (QUOTE (-1052))) (|HasCategory| (-560) (QUOTE (-844))) (|HasCategory| (-560) (QUOTE (-872))) (-4144 (|HasCategory| (-560) (QUOTE (-844))) (|HasCategory| (-560) (QUOTE (-872)))) (|HasCategory| (-560) (|%list| (QUOTE -1070) (QUOTE (-560)))) (|HasCategory| (-560) (QUOTE (-1184))) (|HasCategory| (-560) (|%list| (QUOTE -912) (QUOTE (-391)))) (|HasCategory| (-560) (|%list| (QUOTE -912) (QUOTE (-560)))) (|HasCategory| (-560) (|%list| (QUOTE -633) (|%list| (QUOTE -916) (QUOTE (-391))))) (|HasCategory| (-560) (|%list| (QUOTE -633) (|%list| (QUOTE -916) (QUOTE (-560))))) (|HasCategory| (-560) (QUOTE (-239))) (|HasCategory| (-560) (|%list| (QUOTE -930) (QUOTE (-1209)))) (|HasCategory| (-560) (QUOTE (-240))) (|HasCategory| (-560) (|%list| (QUOTE -928) (QUOTE (-1209)))) (|HasCategory| (-560) (|%list| (QUOTE -528) (QUOTE (-1209)) (QUOTE (-560)))) (|HasCategory| (-560) (|%list| (QUOTE -321) (QUOTE (-560)))) (|HasCategory| (-560) (|%list| (QUOTE -298) (QUOTE (-560)) (QUOTE (-560)))) (|HasCategory| (-560) (QUOTE (-319))) (|HasCategory| (-560) (QUOTE (-559))) (|HasCategory| (-560) (|%list| (QUOTE -660) (QUOTE (-560)))) (-12 (|HasCategory| $ (QUOTE (-147))) (|HasCategory| (-560) (QUOTE (-940)))) (-4144 (-12 (|HasCategory| $ (QUOTE (-147))) (|HasCategory| (-560) (QUOTE (-940)))) (|HasCategory| (-560) (QUOTE (-147))))) +((|HasCategory| (-560) (QUOTE (-940))) (|HasCategory| (-560) (|%list| (QUOTE -1070) (QUOTE (-1209)))) (|HasCategory| (-560) (QUOTE (-147))) (|HasCategory| (-560) (QUOTE (-149))) (|HasCategory| (-560) (|%list| (QUOTE -633) (QUOTE (-549)))) (|HasCategory| (-560) (QUOTE (-1052))) (|HasCategory| (-560) (QUOTE (-844))) (|HasCategory| (-560) (QUOTE (-872))) (-4118 (|HasCategory| (-560) (QUOTE (-844))) (|HasCategory| (-560) (QUOTE (-872)))) (|HasCategory| (-560) (|%list| (QUOTE -1070) (QUOTE (-560)))) (|HasCategory| (-560) (QUOTE (-1184))) (|HasCategory| (-560) (|%list| (QUOTE -912) (QUOTE (-391)))) (|HasCategory| (-560) (|%list| (QUOTE -912) (QUOTE (-560)))) (|HasCategory| (-560) (|%list| (QUOTE -633) (|%list| (QUOTE -916) (QUOTE (-391))))) (|HasCategory| (-560) (|%list| (QUOTE -633) (|%list| (QUOTE -916) (QUOTE (-560))))) (|HasCategory| (-560) (QUOTE (-239))) (|HasCategory| (-560) (|%list| (QUOTE -930) (QUOTE (-1209)))) (|HasCategory| (-560) (QUOTE (-240))) (|HasCategory| (-560) (|%list| (QUOTE -928) (QUOTE (-1209)))) (|HasCategory| (-560) (|%list| (QUOTE -528) (QUOTE (-1209)) (QUOTE (-560)))) (|HasCategory| (-560) (|%list| (QUOTE -321) (QUOTE (-560)))) (|HasCategory| (-560) (|%list| (QUOTE -298) (QUOTE (-560)) (QUOTE (-560)))) (|HasCategory| (-560) (QUOTE (-319))) (|HasCategory| (-560) (QUOTE (-559))) (|HasCategory| (-560) (|%list| (QUOTE -660) (QUOTE (-560)))) (-12 (|HasCategory| $ (QUOTE (-147))) (|HasCategory| (-560) (QUOTE (-940)))) (-4118 (-12 (|HasCategory| $ (QUOTE (-147))) (|HasCategory| (-560) (QUOTE (-940)))) (|HasCategory| (-560) (QUOTE (-147))))) (-1037) ((|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 @@ -4108,19 +4108,19 @@ NIL ((|constructor| (NIL "\\axiomType{RealClosedField} provides common acces functions for all real closed fields.")) (|approximate| (((|Fraction| (|Integer|)) $ $) "\\axiom{approximate(\\spad{n},{}\\spad{p})} gives an approximation of \\axiom{\\spad{n}} that has precision \\axiom{\\spad{p}}")) (|rename| (($ $ (|OutputForm|)) "\\axiom{rename(\\spad{x},{}name)} gives a new number that prints as name")) (|rename!| (($ $ (|OutputForm|)) "\\axiom{rename!(\\spad{x},{}name)} changes the way \\axiom{\\spad{x}} is printed")) (|sqrt| (($ (|Integer|)) "\\axiom{sqrt(\\spad{x})} is \\axiom{\\spad{x} ** (1/2)}") (($ (|Fraction| (|Integer|))) "\\axiom{sqrt(\\spad{x})} is \\axiom{\\spad{x} ** (1/2)}") (($ $) "\\axiom{sqrt(\\spad{x})} is \\axiom{\\spad{x} ** (1/2)}") (($ $ (|PositiveInteger|)) "\\axiom{sqrt(\\spad{x},{}\\spad{n})} is \\axiom{\\spad{x} ** (1/n)}")) (|allRootsOf| (((|List| $) (|Polynomial| (|Integer|))) "\\axiom{allRootsOf(pol)} creates all the roots of \\axiom{pol} naming each uniquely") (((|List| $) (|Polynomial| (|Fraction| (|Integer|)))) "\\axiom{allRootsOf(pol)} creates all the roots of \\axiom{pol} naming each uniquely") (((|List| $) (|Polynomial| $)) "\\axiom{allRootsOf(pol)} creates all the roots of \\axiom{pol} naming each uniquely") (((|List| $) (|SparseUnivariatePolynomial| (|Integer|))) "\\axiom{allRootsOf(pol)} creates all the roots of \\axiom{pol} naming each uniquely") (((|List| $) (|SparseUnivariatePolynomial| (|Fraction| (|Integer|)))) "\\axiom{allRootsOf(pol)} creates all the roots of \\axiom{pol} naming each uniquely") (((|List| $) (|SparseUnivariatePolynomial| $)) "\\axiom{allRootsOf(pol)} creates all the roots of \\axiom{pol} naming each uniquely")) (|rootOf| (((|Union| $ "failed") (|SparseUnivariatePolynomial| $) (|PositiveInteger|)) "\\axiom{rootOf(pol,{}\\spad{n})} creates the \\spad{n}th root for the order of \\axiom{pol} and gives it unique name") (((|Union| $ "failed") (|SparseUnivariatePolynomial| $) (|PositiveInteger|) (|OutputForm|)) "\\axiom{rootOf(pol,{}\\spad{n},{}name)} creates the \\spad{n}th root for the order of \\axiom{pol} and names it \\axiom{name}")) (|mainValue| (((|Union| (|SparseUnivariatePolynomial| $) "failed") $) "\\axiom{mainValue(\\spad{x})} is the expression of \\axiom{\\spad{x}} in terms of \\axiom{SparseUnivariatePolynomial(\\$)}")) (|mainDefiningPolynomial| (((|Union| (|SparseUnivariatePolynomial| $) "failed") $) "\\axiom{mainDefiningPolynomial(\\spad{x})} is the defining polynomial for the main algebraic quantity of \\axiom{\\spad{x}}")) (|mainForm| (((|Union| (|OutputForm|) "failed") $) "\\axiom{mainForm(\\spad{x})} is the main algebraic quantity name of \\axiom{\\spad{x}}"))) ((-4503 . T) (-4508 . T) (-4502 . T) (-4505 . T) (-4504 . T) ((-4512 "*") . T) (-4507 . T)) NIL -(-1045 R -4164) +(-1045 R -4140) ((|constructor| (NIL "\\indented{1}{Risch differential equation,{} elementary case.} Author: Manuel Bronstein Date Created: 1 February 1988 Date Last Updated: 2 November 1995 Keywords: elementary,{} function,{} integration.")) (|rischDE| (((|Record| (|:| |ans| |#2|) (|:| |right| |#2|) (|:| |sol?| (|Boolean|))) (|Integer|) |#2| |#2| (|Symbol|) (|Mapping| (|Union| (|Record| (|:| |mainpart| |#2|) (|:| |limitedlogs| (|List| (|Record| (|:| |coeff| |#2|) (|:| |logand| |#2|))))) "failed") |#2| (|List| |#2|)) (|Mapping| (|Union| (|Record| (|:| |ratpart| |#2|) (|:| |coeff| |#2|)) "failed") |#2| |#2|)) "\\spad{rischDE(n, f, g, x, lim, ext)} returns \\spad{[y, h, b]} such that \\spad{dy/dx + n df/dx y = h} and \\spad{b := h = g}. The equation \\spad{dy/dx + n df/dx y = g} has no solution if \\spad{h \\~~= g} (\\spad{y} is a partial solution in that case). Notes: \\spad{lim} is a limited integration function,{} and ext is an extended integration function."))) NIL NIL -(-1046 R -4164) +(-1046 R -4140) ((|constructor| (NIL "\\indented{1}{Risch differential equation,{} elementary case.} Author: Manuel Bronstein Date Created: 12 August 1992 Date Last Updated: 17 August 1992 Keywords: elementary,{} function,{} integration.")) (|rischDEsys| (((|Union| (|List| |#2|) "failed") (|Integer|) |#2| |#2| |#2| (|Symbol|) (|Mapping| (|Union| (|Record| (|:| |mainpart| |#2|) (|:| |limitedlogs| (|List| (|Record| (|:| |coeff| |#2|) (|:| |logand| |#2|))))) "failed") |#2| (|List| |#2|)) (|Mapping| (|Union| (|Record| (|:| |ratpart| |#2|) (|:| |coeff| |#2|)) "failed") |#2| |#2|)) "\\spad{rischDEsys(n, f, g_1, g_2, x,lim,ext)} returns \\spad{y_1.y_2} such that \\spad{(dy1/dx,dy2/dx) + ((0, - n df/dx),(n df/dx,0)) (y1,y2) = (g1,g2)} if \\spad{y_1,y_2} exist,{} \"failed\" otherwise. \\spad{lim} is a limited integration function,{} \\spad{ext} is an extended integration function."))) NIL NIL -(-1047 -4164 UP) +(-1047 -4140 UP) ((|constructor| (NIL "\\indented{1}{Risch differential equation,{} transcendental case.} Author: Manuel Bronstein Date Created: Jan 1988 Date Last Updated: 2 November 1995")) (|polyRDE| (((|Union| (|:| |ans| (|Record| (|:| |ans| |#2|) (|:| |nosol| (|Boolean|)))) (|:| |eq| (|Record| (|:| |b| |#2|) (|:| |c| |#2|) (|:| |m| (|Integer|)) (|:| |alpha| |#2|) (|:| |beta| |#2|)))) |#2| |#2| |#2| (|Integer|) (|Mapping| |#2| |#2|)) "\\spad{polyRDE(a, B, C, n, D)} returns either: 1. \\spad{[Q, b]} such that \\spad{degree(Q) <= n} and \\indented{3}{\\spad{a Q'+ B Q = C} if \\spad{b = true},{} \\spad{Q} is a partial solution} \\indented{3}{otherwise.} 2. \\spad{[B1, C1, m, \\alpha, \\beta]} such that any polynomial solution \\indented{3}{of degree at most \\spad{n} of \\spad{A Q' + BQ = C} must be of the form} \\indented{3}{\\spad{Q = \\alpha H + \\beta} where \\spad{degree(H) <= m} and} \\indented{3}{\\spad{H} satisfies \\spad{H' + B1 H = C1}.} \\spad{D} is the derivation to use.")) (|baseRDE| (((|Record| (|:| |ans| (|Fraction| |#2|)) (|:| |nosol| (|Boolean|))) (|Fraction| |#2|) (|Fraction| |#2|)) "\\spad{baseRDE(f, g)} returns a \\spad{[y, b]} such that \\spad{y' + fy = g} if \\spad{b = true},{} \\spad{y} is a partial solution otherwise (no solution in that case). \\spad{D} is the derivation to use.")) (|monomRDE| (((|Union| (|Record| (|:| |a| |#2|) (|:| |b| (|Fraction| |#2|)) (|:| |c| (|Fraction| |#2|)) (|:| |t| |#2|)) "failed") (|Fraction| |#2|) (|Fraction| |#2|) (|Mapping| |#2| |#2|)) "\\spad{monomRDE(f,g,D)} returns \\spad{[A, B, C, T]} such that \\spad{y' + f y = g} has a solution if and only if \\spad{y = Q / T},{} where \\spad{Q} satisfies \\spad{A Q' + B Q = C} and has no normal pole. A and \\spad{T} are polynomials and \\spad{B} and \\spad{C} have no normal poles. \\spad{D} is the derivation to use."))) NIL NIL -(-1048 -4164 UP) +(-1048 -4140 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 @@ -4155,8 +4155,8 @@ NIL (-1056 |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"))) ((-4503 . T) (-4508 . T) (-4502 . T) (-4505 . T) (-4504 . T) ((-4512 "*") . T) (-4507 . T)) -((-4144 (|HasCategory| (-421 (-560)) (|%list| (QUOTE -1070) (QUOTE (-560)))) (|HasCategory| |#1| (|%list| (QUOTE -1070) (QUOTE (-560))))) (|HasCategory| |#1| (|%list| (QUOTE -1070) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#1| (|%list| (QUOTE -1070) (QUOTE (-560)))) (|HasCategory| (-421 (-560)) (|%list| (QUOTE -1070) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| (-421 (-560)) (|%list| (QUOTE -1070) (QUOTE (-560))))) -(-1057 -4164 L) +((-4118 (|HasCategory| (-421 (-560)) (|%list| (QUOTE -1070) (QUOTE (-560)))) (|HasCategory| |#1| (|%list| (QUOTE -1070) (QUOTE (-560))))) (|HasCategory| |#1| (|%list| (QUOTE -1070) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#1| (|%list| (QUOTE -1070) (QUOTE (-560)))) (|HasCategory| (-421 (-560)) (|%list| (QUOTE -1070) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| (-421 (-560)) (|%list| (QUOTE -1070) (QUOTE (-560))))) +(-1057 -4140 L) ((|constructor| (NIL "\\spadtype{ReductionOfOrder} provides functions for reducing the order of linear ordinary differential equations once some solutions are known.")) (|ReduceOrder| (((|Record| (|:| |eq| |#2|) (|:| |op| (|List| |#1|))) |#2| (|List| |#1|)) "\\spad{ReduceOrder(op, [f1,...,fk])} returns \\spad{[op1,[g1,...,gk]]} such that for any solution \\spad{z} of \\spad{op1 z = 0},{} \\spad{y = gk \\int(g_{k-1} \\int(... \\int(g1 \\int z)...)} is a solution of \\spad{op y = 0}. Each \\spad{fi} must satisfy \\spad{op fi = 0}.") ((|#2| |#2| |#1|) "\\spad{ReduceOrder(op, s)} returns \\spad{op1} such that for any solution \\spad{z} of \\spad{op1 z = 0},{} \\spad{y = s \\int z} is a solution of \\spad{op y = 0}. \\spad{s} must satisfy \\spad{op s = 0}."))) NIL NIL @@ -4192,14 +4192,14 @@ 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 -(-1066 -4164 |Expon| |VarSet| |FPol| |LFPol|) +(-1066 -4140 |Expon| |VarSet| |FPol| |LFPol|) ((|constructor| (NIL "ResidueRing is the quotient of a polynomial ring by an ideal. The ideal is given as a list of generators. The elements of the domain are equivalence classes expressed in terms of reduced elements")) (|lift| ((|#4| $) "\\spad{lift(x)} return the canonical representative of the equivalence class \\spad{x}")) (|coerce| (($ |#4|) "\\spad{coerce(f)} produces the equivalence class of \\spad{f} in the residue ring")) (|reduce| (($ |#4|) "\\spad{reduce(f)} produces the equivalence class of \\spad{f} in the residue ring"))) (((-4512 "*") . T) (-4504 . T) (-4505 . T) (-4507 . T)) NIL (-1067) ((|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.}"))) ((-4510 . T) (-4511 . T)) -((-12 (|HasCategory| (-2 (|:| -2118 (-1209)) (|:| -3964 (-51))) (QUOTE (-1133))) (|HasCategory| (-2 (|:| -2118 (-1209)) (|:| -3964 (-51))) (|%list| (QUOTE -321) (|%list| (QUOTE -2) (|%list| (QUOTE |:|) (QUOTE -2118) (QUOTE (-1209))) (|%list| (QUOTE |:|) (QUOTE -3964) (QUOTE (-51))))))) (-4144 (|HasCategory| (-2 (|:| -2118 (-1209)) (|:| -3964 (-51))) (QUOTE (-1133))) (|HasCategory| (-51) (QUOTE (-1133)))) (-4144 (|HasCategory| (-2 (|:| -2118 (-1209)) (|:| -3964 (-51))) (QUOTE (-102))) (|HasCategory| (-2 (|:| -2118 (-1209)) (|:| -3964 (-51))) (QUOTE (-1133))) (|HasCategory| (-51) (QUOTE (-102))) (|HasCategory| (-51) (QUOTE (-1133)))) (-4144 (|HasCategory| (-2 (|:| -2118 (-1209)) (|:| -3964 (-51))) (QUOTE (-1133))) (|HasCategory| (-2 (|:| -2118 (-1209)) (|:| -3964 (-51))) (|%list| (QUOTE -632) (QUOTE (-888)))) (|HasCategory| (-51) (QUOTE (-1133))) (|HasCategory| (-51) (|%list| (QUOTE -632) (QUOTE (-888))))) (|HasCategory| (-2 (|:| -2118 (-1209)) (|:| -3964 (-51))) (|%list| (QUOTE -633) (QUOTE (-549)))) (-12 (|HasCategory| (-51) (QUOTE (-1133))) (|HasCategory| (-51) (|%list| (QUOTE -321) (QUOTE (-51))))) (|HasCategory| (-2 (|:| -2118 (-1209)) (|:| -3964 (-51))) (QUOTE (-1133))) (|HasCategory| (-1209) (QUOTE (-872))) (|HasCategory| (-51) (QUOTE (-1133))) (-4144 (|HasCategory| (-2 (|:| -2118 (-1209)) (|:| -3964 (-51))) (|%list| (QUOTE -632) (QUOTE (-888)))) (|HasCategory| (-51) (|%list| (QUOTE -632) (QUOTE (-888))))) (-4144 (|HasCategory| (-2 (|:| -2118 (-1209)) (|:| -3964 (-51))) (QUOTE (-102))) (|HasCategory| (-51) (QUOTE (-102)))) (|HasCategory| (-51) (QUOTE (-102))) (|HasCategory| (-51) (|%list| (QUOTE -632) (QUOTE (-888)))) (|HasCategory| (-2 (|:| -2118 (-1209)) (|:| -3964 (-51))) (|%list| (QUOTE -632) (QUOTE (-888)))) (|HasCategory| (-2 (|:| -2118 (-1209)) (|:| -3964 (-51))) (QUOTE (-102)))) +((-12 (|HasCategory| (-2 (|:| -2115 (-1209)) (|:| -3934 (-51))) (QUOTE (-1133))) (|HasCategory| (-2 (|:| -2115 (-1209)) (|:| -3934 (-51))) (|%list| (QUOTE -321) (|%list| (QUOTE -2) (|%list| (QUOTE |:|) (QUOTE -2115) (QUOTE (-1209))) (|%list| (QUOTE |:|) (QUOTE -3934) (QUOTE (-51))))))) (-4118 (|HasCategory| (-2 (|:| -2115 (-1209)) (|:| -3934 (-51))) (QUOTE (-1133))) (|HasCategory| (-51) (QUOTE (-1133)))) (-4118 (|HasCategory| (-2 (|:| -2115 (-1209)) (|:| -3934 (-51))) (QUOTE (-102))) (|HasCategory| (-2 (|:| -2115 (-1209)) (|:| -3934 (-51))) (QUOTE (-1133))) (|HasCategory| (-51) (QUOTE (-102))) (|HasCategory| (-51) (QUOTE (-1133)))) (-4118 (|HasCategory| (-2 (|:| -2115 (-1209)) (|:| -3934 (-51))) (QUOTE (-1133))) (|HasCategory| (-2 (|:| -2115 (-1209)) (|:| -3934 (-51))) (|%list| (QUOTE -632) (QUOTE (-888)))) (|HasCategory| (-51) (QUOTE (-1133))) (|HasCategory| (-51) (|%list| (QUOTE -632) (QUOTE (-888))))) (|HasCategory| (-2 (|:| -2115 (-1209)) (|:| -3934 (-51))) (|%list| (QUOTE -633) (QUOTE (-549)))) (-12 (|HasCategory| (-51) (QUOTE (-1133))) (|HasCategory| (-51) (|%list| (QUOTE -321) (QUOTE (-51))))) (|HasCategory| (-2 (|:| -2115 (-1209)) (|:| -3934 (-51))) (QUOTE (-1133))) (|HasCategory| (-1209) (QUOTE (-872))) (|HasCategory| (-51) (QUOTE (-1133))) (-4118 (|HasCategory| (-2 (|:| -2115 (-1209)) (|:| -3934 (-51))) (|%list| (QUOTE -632) (QUOTE (-888)))) (|HasCategory| (-51) (|%list| (QUOTE -632) (QUOTE (-888))))) (-4118 (|HasCategory| (-2 (|:| -2115 (-1209)) (|:| -3934 (-51))) (QUOTE (-102))) (|HasCategory| (-51) (QUOTE (-102)))) (|HasCategory| (-51) (QUOTE (-102))) (|HasCategory| (-51) (|%list| (QUOTE -632) (QUOTE (-888)))) (|HasCategory| (-2 (|:| -2115 (-1209)) (|:| -3934 (-51))) (|%list| (QUOTE -632) (QUOTE (-888)))) (|HasCategory| (-2 (|:| -2115 (-1209)) (|:| -3934 (-51))) (QUOTE (-102)))) (-1068) ((|constructor| (NIL "This domain represents `return' expressions.")) (|expression| (((|SpadAst|) $) "\\spad{expression(e)} returns the expression returned by `e'."))) NIL @@ -4256,7 +4256,7 @@ NIL ((|constructor| (NIL "The category of rings with unity,{} always associative,{} but not necessarily commutative.")) (|unitsKnown| ((|attribute|) "recip truly yields reciprocal or \"failed\" if not a unit. Note: \\spad{recip(0) = \"failed\"}.")) (|characteristic| (((|NonNegativeInteger|)) "\\spad{characteristic()} returns the characteristic of the ring this is the smallest positive integer \\spad{n} such that \\spad{n*x=0} for all \\spad{x} in the ring,{} or zero if no such \\spad{n} exists."))) ((-4507 . T)) NIL -(-1082 |xx| -4164) +(-1082 |xx| -4140) ((|constructor| (NIL "This package exports rational interpolation algorithms"))) NIL NIL @@ -4275,7 +4275,7 @@ NIL (-1086 |m| |n| R) ((|constructor| (NIL "\\spadtype{RectangularMatrix} is a matrix domain where the number of rows and the number of columns are parameters of the domain.")) (|rectangularMatrix| (($ (|Matrix| |#3|)) "\\spad{rectangularMatrix(m)} converts a matrix of type \\spadtype{Matrix} to a matrix of type \\spad{RectangularMatrix}."))) ((-4510 . T) (-4505 . T) (-4504 . T)) -((|HasCategory| |#3| (QUOTE (-175))) (-4144 (-12 (|HasCategory| |#3| (QUOTE (-175))) (|HasCategory| |#3| (|%list| (QUOTE -321) (|devaluate| |#3|)))) (-12 (|HasCategory| |#3| (QUOTE (-376))) (|HasCategory| |#3| (|%list| (QUOTE -321) (|devaluate| |#3|)))) (-12 (|HasCategory| |#3| (QUOTE (-1133))) (|HasCategory| |#3| (|%list| (QUOTE -321) (|devaluate| |#3|))))) (|HasCategory| |#3| (|%list| (QUOTE -633) (QUOTE (-549)))) (-4144 (|HasCategory| |#3| (QUOTE (-175))) (|HasCategory| |#3| (QUOTE (-376)))) (|HasCategory| |#3| (QUOTE (-376))) (|HasCategory| |#3| (QUOTE (-1133))) (|HasCategory| |#3| (QUOTE (-319))) (|HasCategory| |#3| (QUOTE (-571))) (-12 (|HasCategory| |#3| (QUOTE (-1133))) (|HasCategory| |#3| (|%list| (QUOTE -321) (|devaluate| |#3|)))) (|HasCategory| |#3| (QUOTE (-102))) (|HasCategory| |#3| (|%list| (QUOTE -632) (QUOTE (-888))))) +((|HasCategory| |#3| (QUOTE (-175))) (-4118 (-12 (|HasCategory| |#3| (QUOTE (-175))) (|HasCategory| |#3| (|%list| (QUOTE -321) (|devaluate| |#3|)))) (-12 (|HasCategory| |#3| (QUOTE (-376))) (|HasCategory| |#3| (|%list| (QUOTE -321) (|devaluate| |#3|)))) (-12 (|HasCategory| |#3| (QUOTE (-1133))) (|HasCategory| |#3| (|%list| (QUOTE -321) (|devaluate| |#3|))))) (|HasCategory| |#3| (|%list| (QUOTE -633) (QUOTE (-549)))) (-4118 (|HasCategory| |#3| (QUOTE (-175))) (|HasCategory| |#3| (QUOTE (-376)))) (|HasCategory| |#3| (QUOTE (-376))) (|HasCategory| |#3| (QUOTE (-1133))) (|HasCategory| |#3| (QUOTE (-319))) (|HasCategory| |#3| (QUOTE (-571))) (-12 (|HasCategory| |#3| (QUOTE (-1133))) (|HasCategory| |#3| (|%list| (QUOTE -321) (|devaluate| |#3|)))) (|HasCategory| |#3| (QUOTE (-102))) (|HasCategory| |#3| (|%list| (QUOTE -632) (QUOTE (-888))))) (-1087 |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 @@ -4311,7 +4311,7 @@ NIL (-1095) ((|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| (($ $) "\\spad{selectMultiDimensionalRoutines(R)} chooses only those routines from the database which are designed for use with multi-dimensional expressions")) (|selectNonFiniteRoutines| (($ $) "\\spad{selectNonFiniteRoutines(R)} chooses only those routines from the database which are designed for use with non-finite expressions.")) (|selectSumOfSquaresRoutines| (($ $) "\\spad{selectSumOfSquaresRoutines(R)} chooses only those routines from the database which are designed for use with sums of squares")) (|selectFiniteRoutines| (($ $) "\\spad{selectFiniteRoutines(R)} chooses only those routines from the database which are designed for use with finite expressions")) (|selectODEIVPRoutines| (($ $) "\\spad{selectODEIVPRoutines(R)} chooses only those routines from the database which are for the solution of ODE's")) (|selectPDERoutines| (($ $) "\\spad{selectPDERoutines(R)} chooses only those routines from the database which are for the solution of PDE's")) (|selectOptimizationRoutines| (($ $) "\\spad{selectOptimizationRoutines(R)} chooses only those routines from the database which are for integration")) (|selectIntegrationRoutines| (($ $) "\\spad{selectIntegrationRoutines(R)} chooses only those routines from the database which are for integration")) (|routines| (($) "\\spad{routines()} initialises a database of known NAG routines")) (|concat| (($ $ $) "\\spad{concat(x,y)} merges two tables \\spad{x} and \\spad{y}"))) ((-4510 . T) (-4511 . T)) -((-12 (|HasCategory| (-2 (|:| -2118 (-1209)) (|:| -3964 (-51))) (QUOTE (-1133))) (|HasCategory| (-2 (|:| -2118 (-1209)) (|:| -3964 (-51))) (|%list| (QUOTE -321) (|%list| (QUOTE -2) (|%list| (QUOTE |:|) (QUOTE -2118) (QUOTE (-1209))) (|%list| (QUOTE |:|) (QUOTE -3964) (QUOTE (-51))))))) (-4144 (|HasCategory| (-2 (|:| -2118 (-1209)) (|:| -3964 (-51))) (QUOTE (-1133))) (|HasCategory| (-51) (QUOTE (-1133)))) (-4144 (|HasCategory| (-2 (|:| -2118 (-1209)) (|:| -3964 (-51))) (QUOTE (-102))) (|HasCategory| (-2 (|:| -2118 (-1209)) (|:| -3964 (-51))) (QUOTE (-1133))) (|HasCategory| (-51) (QUOTE (-102))) (|HasCategory| (-51) (QUOTE (-1133)))) (-4144 (|HasCategory| (-2 (|:| -2118 (-1209)) (|:| -3964 (-51))) (QUOTE (-1133))) (|HasCategory| (-2 (|:| -2118 (-1209)) (|:| -3964 (-51))) (|%list| (QUOTE -632) (QUOTE (-888)))) (|HasCategory| (-51) (QUOTE (-1133))) (|HasCategory| (-51) (|%list| (QUOTE -632) (QUOTE (-888))))) (|HasCategory| (-2 (|:| -2118 (-1209)) (|:| -3964 (-51))) (|%list| (QUOTE -633) (QUOTE (-549)))) (-12 (|HasCategory| (-51) (QUOTE (-1133))) (|HasCategory| (-51) (|%list| (QUOTE -321) (QUOTE (-51))))) (|HasCategory| (-2 (|:| -2118 (-1209)) (|:| -3964 (-51))) (QUOTE (-1133))) (|HasCategory| (-1209) (QUOTE (-872))) (|HasCategory| (-51) (QUOTE (-1133))) (-4144 (|HasCategory| (-2 (|:| -2118 (-1209)) (|:| -3964 (-51))) (|%list| (QUOTE -632) (QUOTE (-888)))) (|HasCategory| (-51) (|%list| (QUOTE -632) (QUOTE (-888))))) (-4144 (|HasCategory| (-2 (|:| -2118 (-1209)) (|:| -3964 (-51))) (QUOTE (-102))) (|HasCategory| (-51) (QUOTE (-102)))) (|HasCategory| (-51) (QUOTE (-102))) (|HasCategory| (-51) (|%list| (QUOTE -632) (QUOTE (-888)))) (|HasCategory| (-2 (|:| -2118 (-1209)) (|:| -3964 (-51))) (|%list| (QUOTE -632) (QUOTE (-888)))) (|HasCategory| (-2 (|:| -2118 (-1209)) (|:| -3964 (-51))) (QUOTE (-102)))) +((-12 (|HasCategory| (-2 (|:| -2115 (-1209)) (|:| -3934 (-51))) (QUOTE (-1133))) (|HasCategory| (-2 (|:| -2115 (-1209)) (|:| -3934 (-51))) (|%list| (QUOTE -321) (|%list| (QUOTE -2) (|%list| (QUOTE |:|) (QUOTE -2115) (QUOTE (-1209))) (|%list| (QUOTE |:|) (QUOTE -3934) (QUOTE (-51))))))) (-4118 (|HasCategory| (-2 (|:| -2115 (-1209)) (|:| -3934 (-51))) (QUOTE (-1133))) (|HasCategory| (-51) (QUOTE (-1133)))) (-4118 (|HasCategory| (-2 (|:| -2115 (-1209)) (|:| -3934 (-51))) (QUOTE (-102))) (|HasCategory| (-2 (|:| -2115 (-1209)) (|:| -3934 (-51))) (QUOTE (-1133))) (|HasCategory| (-51) (QUOTE (-102))) (|HasCategory| (-51) (QUOTE (-1133)))) (-4118 (|HasCategory| (-2 (|:| -2115 (-1209)) (|:| -3934 (-51))) (QUOTE (-1133))) (|HasCategory| (-2 (|:| -2115 (-1209)) (|:| -3934 (-51))) (|%list| (QUOTE -632) (QUOTE (-888)))) (|HasCategory| (-51) (QUOTE (-1133))) (|HasCategory| (-51) (|%list| (QUOTE -632) (QUOTE (-888))))) (|HasCategory| (-2 (|:| -2115 (-1209)) (|:| -3934 (-51))) (|%list| (QUOTE -633) (QUOTE (-549)))) (-12 (|HasCategory| (-51) (QUOTE (-1133))) (|HasCategory| (-51) (|%list| (QUOTE -321) (QUOTE (-51))))) (|HasCategory| (-2 (|:| -2115 (-1209)) (|:| -3934 (-51))) (QUOTE (-1133))) (|HasCategory| (-1209) (QUOTE (-872))) (|HasCategory| (-51) (QUOTE (-1133))) (-4118 (|HasCategory| (-2 (|:| -2115 (-1209)) (|:| -3934 (-51))) (|%list| (QUOTE -632) (QUOTE (-888)))) (|HasCategory| (-51) (|%list| (QUOTE -632) (QUOTE (-888))))) (-4118 (|HasCategory| (-2 (|:| -2115 (-1209)) (|:| -3934 (-51))) (QUOTE (-102))) (|HasCategory| (-51) (QUOTE (-102)))) (|HasCategory| (-51) (QUOTE (-102))) (|HasCategory| (-51) (|%list| (QUOTE -632) (QUOTE (-888)))) (|HasCategory| (-2 (|:| -2115 (-1209)) (|:| -3934 (-51))) (|%list| (QUOTE -632) (QUOTE (-888)))) (|HasCategory| (-2 (|:| -2115 (-1209)) (|:| -3934 (-51))) (QUOTE (-102)))) (-1096 S R E V) ((|constructor| (NIL "A category for general multi-variate polynomials with coefficients in a ring,{} variables in an ordered set,{} and exponents from an ordered abelian monoid,{} with a \\axiomOp{sup} operation. When not constant,{} such a polynomial is viewed as a univariate polynomial in its main variable \\spad{w}. \\spad{r}. \\spad{t}. to the total ordering on the elements in the ordered set,{} so that some operations usually defined for univariate polynomials make sense here.")) (|mainSquareFreePart| (($ $) "\\axiom{mainSquareFreePart(\\spad{p})} returns the square free part of \\axiom{\\spad{p}} viewed as a univariate polynomial in its main variable and with coefficients in the polynomial ring generated by its other variables over \\axiom{\\spad{R}}.")) (|mainPrimitivePart| (($ $) "\\axiom{mainPrimitivePart(\\spad{p})} returns the primitive part of \\axiom{\\spad{p}} viewed as a univariate polynomial in its main variable and with coefficients in the polynomial ring generated by its other variables over \\axiom{\\spad{R}}.")) (|mainContent| (($ $) "\\axiom{mainContent(\\spad{p})} returns the content of \\axiom{\\spad{p}} viewed as a univariate polynomial in its main variable and with coefficients in the polynomial ring generated by its other variables over \\axiom{\\spad{R}}.")) (|primitivePart!| (($ $) "\\axiom{primitivePart!(\\spad{p})} replaces \\axiom{\\spad{p}} by its primitive part.")) (|gcd| ((|#2| |#2| $) "\\axiom{gcd(\\spad{r},{}\\spad{p})} returns the gcd of \\axiom{\\spad{r}} and the content of \\axiom{\\spad{p}}.")) (|nextsubResultant2| (($ $ $ $ $) "\\axiom{\\spad{nextsubResultant2}(\\spad{p},{}\\spad{q},{}\\spad{z},{}\\spad{s})} is the multivariate version of the operation \\axiomOpFrom{\\spad{next_sousResultant2}}{PseudoRemainderSequence} from the \\axiomType{PseudoRemainderSequence} constructor.")) (|LazardQuotient2| (($ $ $ $ (|NonNegativeInteger|)) "\\axiom{\\spad{LazardQuotient2}(\\spad{p},{}a,{}\\spad{b},{}\\spad{n})} returns \\axiom{(a**(\\spad{n}-1) * \\spad{p}) exquo b**(\\spad{n}-1)} assuming that this quotient does not fail.")) (|LazardQuotient| (($ $ $ (|NonNegativeInteger|)) "\\axiom{LazardQuotient(a,{}\\spad{b},{}\\spad{n})} returns \\axiom{a**n exquo b**(\\spad{n}-1)} assuming that this quotient does not fail.")) (|lastSubResultant| (($ $ $) "\\axiom{lastSubResultant(a,{}\\spad{b})} returns the last non-zero subresultant of \\axiom{a} and \\axiom{\\spad{b}} where \\axiom{a} and \\axiom{\\spad{b}} are assumed to have the same main variable \\axiom{\\spad{v}} and are viewed as univariate polynomials in \\axiom{\\spad{v}}.")) (|subResultantChain| (((|List| $) $ $) "\\axiom{subResultantChain(a,{}\\spad{b})},{} where \\axiom{a} and \\axiom{\\spad{b}} are not contant polynomials with the same main variable,{} returns the subresultant chain of \\axiom{a} and \\axiom{\\spad{b}}.")) (|resultant| (($ $ $) "\\axiom{resultant(a,{}\\spad{b})} computes the resultant of \\axiom{a} and \\axiom{\\spad{b}} where \\axiom{a} and \\axiom{\\spad{b}} are assumed to have the same main variable \\axiom{\\spad{v}} and are viewed as univariate polynomials in \\axiom{\\spad{v}}.")) (|halfExtendedSubResultantGcd2| (((|Record| (|:| |gcd| $) (|:| |coef2| $)) $ $) "\\axiom{\\spad{halfExtendedSubResultantGcd2}(a,{}\\spad{b})} returns \\axiom{[\\spad{g},{}cb]} if \\axiom{extendedSubResultantGcd(a,{}\\spad{b})} returns \\axiom{[\\spad{g},{}ca,{}cb]} otherwise produces an error.")) (|halfExtendedSubResultantGcd1| (((|Record| (|:| |gcd| $) (|:| |coef1| $)) $ $) "\\axiom{\\spad{halfExtendedSubResultantGcd1}(a,{}\\spad{b})} returns \\axiom{[\\spad{g},{}ca]} if \\axiom{extendedSubResultantGcd(a,{}\\spad{b})} returns \\axiom{[\\spad{g},{}ca,{}cb]} otherwise produces an error.")) (|extendedSubResultantGcd| (((|Record| (|:| |gcd| $) (|:| |coef1| $) (|:| |coef2| $)) $ $) "\\axiom{extendedSubResultantGcd(a,{}\\spad{b})} returns \\axiom{[ca,{}cb,{}\\spad{r}]} such that \\axiom{\\spad{r}} is \\axiom{subResultantGcd(a,{}\\spad{b})} and we have \\axiom{ca * a + cb * cb = \\spad{r}} .")) (|subResultantGcd| (($ $ $) "\\axiom{subResultantGcd(a,{}\\spad{b})} computes a gcd of \\axiom{a} and \\axiom{\\spad{b}} where \\axiom{a} and \\axiom{\\spad{b}} are assumed to have the same main variable \\axiom{\\spad{v}} and are viewed as univariate polynomials in \\axiom{\\spad{v}} with coefficients in the fraction field of the polynomial ring generated by their other variables over \\axiom{\\spad{R}}.")) (|exactQuotient!| (($ $ $) "\\axiom{exactQuotient!(a,{}\\spad{b})} replaces \\axiom{a} by \\axiom{exactQuotient(a,{}\\spad{b})}") (($ $ |#2|) "\\axiom{exactQuotient!(\\spad{p},{}\\spad{r})} replaces \\axiom{\\spad{p}} by \\axiom{exactQuotient(\\spad{p},{}\\spad{r})}.")) (|exactQuotient| (($ $ $) "\\axiom{exactQuotient(a,{}\\spad{b})} computes the exact quotient of \\axiom{a} by \\axiom{\\spad{b}},{} which is assumed to be a divisor of \\axiom{a}. No error is returned if this exact quotient fails!") (($ $ |#2|) "\\axiom{exactQuotient(\\spad{p},{}\\spad{r})} computes the exact quotient of \\axiom{\\spad{p}} by \\axiom{\\spad{r}},{} which is assumed to be a divisor of \\axiom{\\spad{p}}. No error is returned if this exact quotient fails!")) (|primPartElseUnitCanonical!| (($ $) "\\axiom{primPartElseUnitCanonical!(\\spad{p})} replaces \\axiom{\\spad{p}} by \\axiom{primPartElseUnitCanonical(\\spad{p})}.")) (|primPartElseUnitCanonical| (($ $) "\\axiom{primPartElseUnitCanonical(\\spad{p})} returns \\axiom{primitivePart(\\spad{p})} if \\axiom{\\spad{R}} is a gcd-domain,{} otherwise \\axiom{unitCanonical(\\spad{p})}.")) (|convert| (($ (|Polynomial| |#2|)) "\\axiom{convert(\\spad{p})} returns \\axiom{\\spad{p}} as an element of the current domain if all its variables belong to \\axiom{\\spad{V}},{} otherwise an error is produced.") (($ (|Polynomial| (|Integer|))) "\\axiom{convert(\\spad{p})} returns the same as \\axiom{retract(\\spad{p})}.") (($ (|Polynomial| (|Integer|))) "\\axiom{convert(\\spad{p})} returns the same as \\axiom{retract(\\spad{p})}") (($ (|Polynomial| (|Fraction| (|Integer|)))) "\\axiom{convert(\\spad{p})} returns the same as \\axiom{retract(\\spad{p})}.")) (|retract| (($ (|Polynomial| |#2|)) "\\axiom{retract(\\spad{p})} returns \\axiom{\\spad{p}} as an element of the current domain if \\axiom{retractIfCan(\\spad{p})} does not return \"failed\",{} otherwise an error is produced.") (($ (|Polynomial| |#2|)) "\\axiom{retract(\\spad{p})} returns \\axiom{\\spad{p}} as an element of the current domain if \\axiom{retractIfCan(\\spad{p})} does not return \"failed\",{} otherwise an error is produced.") (($ (|Polynomial| (|Integer|))) "\\axiom{retract(\\spad{p})} returns \\axiom{\\spad{p}} as an element of the current domain if \\axiom{retractIfCan(\\spad{p})} does not return \"failed\",{} otherwise an error is produced.") (($ (|Polynomial| |#2|)) "\\axiom{retract(\\spad{p})} returns \\axiom{\\spad{p}} as an element of the current domain if \\axiom{retractIfCan(\\spad{p})} does not return \"failed\",{} otherwise an error is produced.") (($ (|Polynomial| (|Integer|))) "\\axiom{retract(\\spad{p})} returns \\axiom{\\spad{p}} as an element of the current domain if \\axiom{retractIfCan(\\spad{p})} does not return \"failed\",{} otherwise an error is produced.") (($ (|Polynomial| (|Fraction| (|Integer|)))) "\\axiom{retract(\\spad{p})} returns \\axiom{\\spad{p}} as an element of the current domain if \\axiom{retractIfCan(\\spad{p})} does not return \"failed\",{} otherwise an error is produced.")) (|retractIfCan| (((|Union| $ "failed") (|Polynomial| |#2|)) "\\axiom{retractIfCan(\\spad{p})} returns \\axiom{\\spad{p}} as an element of the current domain if all its variables belong to \\axiom{\\spad{V}}.") (((|Union| $ "failed") (|Polynomial| |#2|)) "\\axiom{retractIfCan(\\spad{p})} returns \\axiom{\\spad{p}} as an element of the current domain if all its variables belong to \\axiom{\\spad{V}}.") (((|Union| $ "failed") (|Polynomial| (|Integer|))) "\\axiom{retractIfCan(\\spad{p})} returns \\axiom{\\spad{p}} as an element of the current domain if all its variables belong to \\axiom{\\spad{V}}.") (((|Union| $ "failed") (|Polynomial| |#2|)) "\\axiom{retractIfCan(\\spad{p})} returns \\axiom{\\spad{p}} as an element of the current domain if all its variables belong to \\axiom{\\spad{V}}.") (((|Union| $ "failed") (|Polynomial| (|Integer|))) "\\axiom{retractIfCan(\\spad{p})} returns \\axiom{\\spad{p}} as an element of the current domain if all its variables belong to \\axiom{\\spad{V}}.") (((|Union| $ "failed") (|Polynomial| (|Fraction| (|Integer|)))) "\\axiom{retractIfCan(\\spad{p})} returns \\axiom{\\spad{p}} as an element of the current domain if all its variables belong to \\axiom{\\spad{V}}.")) (|initiallyReduce| (($ $ $) "\\axiom{initiallyReduce(a,{}\\spad{b})} returns a polynomial \\axiom{\\spad{r}} such that \\axiom{initiallyReduced?(\\spad{r},{}\\spad{b})} holds and there exists an integer \\axiom{\\spad{e}} such that \\axiom{init(\\spad{b})^e a - \\spad{r}} is zero modulo \\axiom{\\spad{b}}.")) (|headReduce| (($ $ $) "\\axiom{headReduce(a,{}\\spad{b})} returns a polynomial \\axiom{\\spad{r}} such that \\axiom{headReduced?(\\spad{r},{}\\spad{b})} holds and there exists an integer \\axiom{\\spad{e}} such that \\axiom{init(\\spad{b})^e a - \\spad{r}} is zero modulo \\axiom{\\spad{b}}.")) (|lazyResidueClass| (((|Record| (|:| |polnum| $) (|:| |polden| $) (|:| |power| (|NonNegativeInteger|))) $ $) "\\axiom{lazyResidueClass(a,{}\\spad{b})} returns \\axiom{[\\spad{p},{}\\spad{q},{}\\spad{n}]} where \\axiom{\\spad{p} / q**n} represents the residue class of \\axiom{a} modulo \\axiom{\\spad{b}} and \\axiom{\\spad{p}} is reduced \\spad{w}.\\spad{r}.\\spad{t}. \\axiom{\\spad{b}} and \\axiom{\\spad{q}} is \\axiom{init(\\spad{b})}.")) (|monicModulo| (($ $ $) "\\axiom{monicModulo(a,{}\\spad{b})} computes \\axiom{a mod \\spad{b}},{} if \\axiom{\\spad{b}} is monic as univariate polynomial in its main variable.")) (|pseudoDivide| (((|Record| (|:| |quotient| $) (|:| |remainder| $)) $ $) "\\axiom{pseudoDivide(a,{}\\spad{b})} computes \\axiom{[pquo(a,{}\\spad{b}),{}prem(a,{}\\spad{b})]},{} both polynomials viewed as univariate polynomials in the main variable of \\axiom{\\spad{b}},{} if \\axiom{\\spad{b}} is not a constant polynomial.")) (|lazyPseudoDivide| (((|Record| (|:| |coef| $) (|:| |gap| (|NonNegativeInteger|)) (|:| |quotient| $) (|:| |remainder| $)) $ $ |#4|) "\\axiom{lazyPseudoDivide(a,{}\\spad{b},{}\\spad{v})} returns \\axiom{[\\spad{c},{}\\spad{g},{}\\spad{q},{}\\spad{r}]} such that \\axiom{\\spad{r} = lazyPrem(a,{}\\spad{b},{}\\spad{v})},{} \\axiom{(c**g)*r = prem(a,{}\\spad{b},{}\\spad{v})} and \\axiom{\\spad{q}} is the pseudo-quotient computed in this lazy pseudo-division.") (((|Record| (|:| |coef| $) (|:| |gap| (|NonNegativeInteger|)) (|:| |quotient| $) (|:| |remainder| $)) $ $) "\\axiom{lazyPseudoDivide(a,{}\\spad{b})} returns \\axiom{[\\spad{c},{}\\spad{g},{}\\spad{q},{}\\spad{r}]} such that \\axiom{[\\spad{c},{}\\spad{g},{}\\spad{r}] = lazyPremWithDefault(a,{}\\spad{b})} and \\axiom{\\spad{q}} is the pseudo-quotient computed in this lazy pseudo-division.")) (|lazyPremWithDefault| (((|Record| (|:| |coef| $) (|:| |gap| (|NonNegativeInteger|)) (|:| |remainder| $)) $ $ |#4|) "\\axiom{lazyPremWithDefault(a,{}\\spad{b},{}\\spad{v})} returns \\axiom{[\\spad{c},{}\\spad{g},{}\\spad{r}]} such that \\axiom{\\spad{r} = lazyPrem(a,{}\\spad{b},{}\\spad{v})} and \\axiom{(c**g)*r = prem(a,{}\\spad{b},{}\\spad{v})}.") (((|Record| (|:| |coef| $) (|:| |gap| (|NonNegativeInteger|)) (|:| |remainder| $)) $ $) "\\axiom{lazyPremWithDefault(a,{}\\spad{b})} returns \\axiom{[\\spad{c},{}\\spad{g},{}\\spad{r}]} such that \\axiom{\\spad{r} = lazyPrem(a,{}\\spad{b})} and \\axiom{(c**g)*r = prem(a,{}\\spad{b})}.")) (|lazyPquo| (($ $ $ |#4|) "\\axiom{lazyPquo(a,{}\\spad{b},{}\\spad{v})} returns the polynomial \\axiom{\\spad{q}} such that \\axiom{lazyPseudoDivide(a,{}\\spad{b},{}\\spad{v})} returns \\axiom{[\\spad{c},{}\\spad{g},{}\\spad{q},{}\\spad{r}]}.") (($ $ $) "\\axiom{lazyPquo(a,{}\\spad{b})} returns the polynomial \\axiom{\\spad{q}} such that \\axiom{lazyPseudoDivide(a,{}\\spad{b})} returns \\axiom{[\\spad{c},{}\\spad{g},{}\\spad{q},{}\\spad{r}]}.")) (|lazyPrem| (($ $ $ |#4|) "\\axiom{lazyPrem(a,{}\\spad{b},{}\\spad{v})} returns the polynomial \\axiom{\\spad{r}} reduced \\spad{w}.\\spad{r}.\\spad{t}. \\axiom{\\spad{b}} viewed as univariate polynomials in the variable \\axiom{\\spad{v}} such that \\axiom{\\spad{b}} divides \\axiom{init(\\spad{b})^e a - \\spad{r}} where \\axiom{\\spad{e}} is the number of steps of this pseudo-division.") (($ $ $) "\\axiom{lazyPrem(a,{}\\spad{b})} returns the polynomial \\axiom{\\spad{r}} reduced \\spad{w}.\\spad{r}.\\spad{t}. \\axiom{\\spad{b}} and such that \\axiom{\\spad{b}} divides \\axiom{init(\\spad{b})^e a - \\spad{r}} where \\axiom{\\spad{e}} is the number of steps of this pseudo-division.")) (|pquo| (($ $ $ |#4|) "\\axiom{pquo(a,{}\\spad{b},{}\\spad{v})} computes the pseudo-quotient of \\axiom{a} by \\axiom{\\spad{b}},{} both viewed as univariate polynomials in \\axiom{\\spad{v}}.") (($ $ $) "\\axiom{pquo(a,{}\\spad{b})} computes the pseudo-quotient of \\axiom{a} by \\axiom{\\spad{b}},{} both viewed as univariate polynomials in the main variable of \\axiom{\\spad{b}}.")) (|prem| (($ $ $ |#4|) "\\axiom{prem(a,{}\\spad{b},{}\\spad{v})} computes the pseudo-remainder of \\axiom{a} by \\axiom{\\spad{b}},{} both viewed as univariate polynomials in \\axiom{\\spad{v}}.") (($ $ $) "\\axiom{prem(a,{}\\spad{b})} computes the pseudo-remainder of \\axiom{a} by \\axiom{\\spad{b}},{} both viewed as univariate polynomials in the main variable of \\axiom{\\spad{b}}.")) (|normalized?| (((|Boolean|) $ (|List| $)) "\\axiom{normalized?(\\spad{q},{}lp)} returns \\spad{true} iff \\axiom{normalized?(\\spad{q},{}\\spad{p})} holds for every \\axiom{\\spad{p}} in \\axiom{lp}.") (((|Boolean|) $ $) "\\axiom{normalized?(a,{}\\spad{b})} returns \\spad{true} iff \\axiom{a} and its iterated initials have degree zero \\spad{w}.\\spad{r}.\\spad{t}. the main variable of \\axiom{\\spad{b}}")) (|initiallyReduced?| (((|Boolean|) $ (|List| $)) "\\axiom{initiallyReduced?(\\spad{q},{}lp)} returns \\spad{true} iff \\axiom{initiallyReduced?(\\spad{q},{}\\spad{p})} holds for every \\axiom{\\spad{p}} in \\axiom{lp}.") (((|Boolean|) $ $) "\\axiom{initiallyReduced?(a,{}\\spad{b})} returns \\spad{false} iff there exists an iterated initial of \\axiom{a} which is not reduced \\spad{w}.\\spad{r}.\\spad{t} \\axiom{\\spad{b}}.")) (|headReduced?| (((|Boolean|) $ (|List| $)) "\\axiom{headReduced?(\\spad{q},{}lp)} returns \\spad{true} iff \\axiom{headReduced?(\\spad{q},{}\\spad{p})} holds for every \\axiom{\\spad{p}} in \\axiom{lp}.") (((|Boolean|) $ $) "\\axiom{headReduced?(a,{}\\spad{b})} returns \\spad{true} iff \\axiom{degree(head(a),{}mvar(\\spad{b})) < mdeg(\\spad{b})}.")) (|reduced?| (((|Boolean|) $ (|List| $)) "\\axiom{reduced?(\\spad{q},{}lp)} returns \\spad{true} iff \\axiom{reduced?(\\spad{q},{}\\spad{p})} holds for every \\axiom{\\spad{p}} in \\axiom{lp}.") (((|Boolean|) $ $) "\\axiom{reduced?(a,{}\\spad{b})} returns \\spad{true} iff \\axiom{degree(a,{}mvar(\\spad{b})) < mdeg(\\spad{b})}.")) (|supRittWu?| (((|Boolean|) $ $) "\\axiom{supRittWu?(a,{}\\spad{b})} returns \\spad{true} if \\axiom{a} is greater than \\axiom{\\spad{b}} \\spad{w}.\\spad{r}.\\spad{t}. the Ritt and Wu Wen Tsun ordering using the refinement of Lazard.")) (|infRittWu?| (((|Boolean|) $ $) "\\axiom{infRittWu?(a,{}\\spad{b})} returns \\spad{true} if \\axiom{a} is less than \\axiom{\\spad{b}} \\spad{w}.\\spad{r}.\\spad{t}. the Ritt and Wu Wen Tsun ordering using the refinement of Lazard.")) (|RittWuCompare| (((|Union| (|Boolean|) "failed") $ $) "\\axiom{RittWuCompare(a,{}\\spad{b})} returns \\axiom{\"failed\"} if \\axiom{a} and \\axiom{\\spad{b}} have same rank \\spad{w}.\\spad{r}.\\spad{t}. Ritt and Wu Wen Tsun ordering using the refinement of Lazard,{} otherwise returns \\axiom{infRittWu?(a,{}\\spad{b})}.")) (|mainMonomials| (((|List| $) $) "\\axiom{mainMonomials(\\spad{p})} returns an error if \\axiom{\\spad{p}} is \\axiom{\\spad{O}},{} otherwise,{} if \\axiom{\\spad{p}} belongs to \\axiom{\\spad{R}} returns [1],{} otherwise returns the list of the monomials of \\axiom{\\spad{p}},{} where \\axiom{\\spad{p}} is viewed as a univariate polynomial in its main variable.")) (|mainCoefficients| (((|List| $) $) "\\axiom{mainCoefficients(\\spad{p})} returns an error if \\axiom{\\spad{p}} is \\axiom{\\spad{O}},{} otherwise,{} if \\axiom{\\spad{p}} belongs to \\axiom{\\spad{R}} returns [\\spad{p}],{} otherwise returns the list of the coefficients of \\axiom{\\spad{p}},{} where \\axiom{\\spad{p}} is viewed as a univariate polynomial in its main variable.")) (|leastMonomial| (($ $) "\\axiom{leastMonomial(\\spad{p})} returns an error if \\axiom{\\spad{p}} is \\axiom{\\spad{O}},{} otherwise,{} if \\axiom{\\spad{p}} belongs to \\axiom{\\spad{R}} returns \\axiom{1},{} otherwise,{} the monomial of \\axiom{\\spad{p}} with lowest degree,{} where \\axiom{\\spad{p}} is viewed as a univariate polynomial in its main variable.")) (|mainMonomial| (($ $) "\\axiom{mainMonomial(\\spad{p})} returns an error if \\axiom{\\spad{p}} is \\axiom{\\spad{O}},{} otherwise,{} if \\axiom{\\spad{p}} belongs to \\axiom{\\spad{R}} returns \\axiom{1},{} otherwise,{} \\axiom{mvar(\\spad{p})} raised to the power \\axiom{mdeg(\\spad{p})}.")) (|quasiMonic?| (((|Boolean|) $) "\\axiom{quasiMonic?(\\spad{p})} returns \\spad{false} if \\axiom{\\spad{p}} belongs to \\axiom{\\spad{R}},{} otherwise returns \\spad{true} iff the initial of \\axiom{\\spad{p}} lies in the base ring \\axiom{\\spad{R}}.")) (|monic?| (((|Boolean|) $) "\\axiom{monic?(\\spad{p})} returns \\spad{false} if \\axiom{\\spad{p}} belongs to \\axiom{\\spad{R}},{} otherwise returns \\spad{true} iff \\axiom{\\spad{p}} is monic as a univariate polynomial in its main variable.")) (|reductum| (($ $ |#4|) "\\axiom{reductum(\\spad{p},{}\\spad{v})} returns the reductum of \\axiom{\\spad{p}},{} where \\axiom{\\spad{p}} is viewed as a univariate polynomial in \\axiom{\\spad{v}}.")) (|leadingCoefficient| (($ $ |#4|) "\\axiom{leadingCoefficient(\\spad{p},{}\\spad{v})} returns the leading coefficient of \\axiom{\\spad{p}},{} where \\axiom{\\spad{p}} is viewed as A univariate polynomial in \\axiom{\\spad{v}}.")) (|deepestInitial| (($ $) "\\axiom{deepestInitial(\\spad{p})} returns an error if \\axiom{\\spad{p}} belongs to \\axiom{\\spad{R}},{} otherwise returns the last term of \\axiom{iteratedInitials(\\spad{p})}.")) (|iteratedInitials| (((|List| $) $) "\\axiom{iteratedInitials(\\spad{p})} returns \\axiom{[]} if \\axiom{\\spad{p}} belongs to \\axiom{\\spad{R}},{} otherwise returns the list of the iterated initials of \\axiom{\\spad{p}}.")) (|deepestTail| (($ $) "\\axiom{deepestTail(\\spad{p})} returns \\axiom{0} if \\axiom{\\spad{p}} belongs to \\axiom{\\spad{R}},{} otherwise returns tail(\\spad{p}),{} if \\axiom{tail(\\spad{p})} belongs to \\axiom{\\spad{R}} or \\axiom{mvar(tail(\\spad{p})) < mvar(\\spad{p})},{} otherwise returns \\axiom{deepestTail(tail(\\spad{p}))}.")) (|tail| (($ $) "\\axiom{tail(\\spad{p})} returns its reductum,{} where \\axiom{\\spad{p}} is viewed as a univariate polynomial in its main variable.")) (|head| (($ $) "\\axiom{head(\\spad{p})} returns \\axiom{\\spad{p}} if \\axiom{\\spad{p}} belongs to \\axiom{\\spad{R}},{} otherwise returns its leading term (monomial in the AXIOM sense),{} where \\axiom{\\spad{p}} is viewed as a univariate polynomial in its main variable.")) (|init| (($ $) "\\axiom{init(\\spad{p})} returns an error if \\axiom{\\spad{p}} belongs to \\axiom{\\spad{R}},{} otherwise returns its leading coefficient,{} where \\axiom{\\spad{p}} is viewed as a univariate polynomial in its main variable.")) (|mdeg| (((|NonNegativeInteger|) $) "\\axiom{mdeg(\\spad{p})} returns an error if \\axiom{\\spad{p}} is \\axiom{0},{} otherwise,{} if \\axiom{\\spad{p}} belongs to \\axiom{\\spad{R}} returns \\axiom{0},{} otherwise,{} returns the degree of \\axiom{\\spad{p}} in its main variable.")) (|mvar| ((|#4| $) "\\axiom{mvar(\\spad{p})} returns an error if \\axiom{\\spad{p}} belongs to \\axiom{\\spad{R}},{} otherwise returns its main variable \\spad{w}. \\spad{r}. \\spad{t}. to the total ordering on the elements in \\axiom{\\spad{V}}."))) NIL @@ -4356,7 +4356,7 @@ NIL ((|constructor| (NIL "This is the datatype of OpenAxiom runtime values. It exists solely for internal purposes.")) (|eq| (((|Boolean|) $ $) "\\spad{eq(x,y)} holds if both values \\spad{x} and \\spad{y} resides at the same address in memory."))) NIL NIL -(-1107 |Base| R -4164) +(-1107 |Base| R -4140) ((|constructor| (NIL "\\indented{1}{Rules for the pattern matcher} Author: Manuel Bronstein Date Created: 24 Oct 1988 Date Last Updated: 26 October 1993 Keywords: pattern,{} matching,{} rule.")) (|quotedOperators| (((|List| (|Symbol|)) $) "\\spad{quotedOperators(r)} returns the list of operators on the right hand side of \\spad{r} that are considered quoted,{} that is they are not evaluated during any rewrite,{} but just applied formally to their arguments.")) (|elt| ((|#3| $ |#3| (|PositiveInteger|)) "\\spad{elt(r,f,n)} or \\spad{r}(\\spad{f},{} \\spad{n}) applies the rule \\spad{r} to \\spad{f} at most \\spad{n} times.")) (|rhs| ((|#3| $) "\\spad{rhs(r)} returns the right hand side of the rule \\spad{r}.")) (|lhs| ((|#3| $) "\\spad{lhs(r)} returns the left hand side of the rule \\spad{r}.")) (|pattern| (((|Pattern| |#1|) $) "\\spad{pattern(r)} returns the pattern corresponding to the left hand side of the rule \\spad{r}.")) (|suchThat| (($ $ (|List| (|Symbol|)) (|Mapping| (|Boolean|) (|List| |#3|))) "\\spad{suchThat(r, [a1,...,an], f)} returns the rewrite rule \\spad{r} with the predicate \\spad{f(a1,...,an)} attached to it.")) (|rule| (($ |#3| |#3| (|List| (|Symbol|))) "\\spad{rule(f, g, [f1,...,fn])} creates the rewrite rule \\spad{f == eval(eval(g, g is f), [f1,...,fn])},{} that is a rule with left-hand side \\spad{f} and right-hand side \\spad{g}; The symbols \\spad{f1},{}...,{}fn are the operators that are considered quoted,{} that is they are not evaluated during any rewrite,{} but just applied formally to their arguments.") (($ |#3| |#3|) "\\spad{rule(f, g)} creates the rewrite rule: \\spad{f == eval(g, g is f)},{} with left-hand side \\spad{f} and right-hand side \\spad{g}."))) NIL NIL @@ -4364,7 +4364,7 @@ NIL ((|constructor| (NIL "This domain implements named rules")) (|name| (((|Symbol|) $) "\\spad{name(x)} returns the symbol"))) NIL NIL -(-1109 |Base| R -4164) +(-1109 |Base| R -4140) ((|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 @@ -4375,7 +4375,7 @@ NIL (-1111 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."))) ((-4503 |has| |#1| (-376)) (-4508 |has| |#1| (-376)) (-4502 |has| |#1| (-376)) ((-4512 "*") . T) (-4504 . T) (-4505 . T) (-4507 . T)) -((|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-149))) (|HasCategory| |#1| (QUOTE (-363))) (-4144 (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (QUOTE (-363)))) (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (QUOTE (-381))) (-4144 (-12 (|HasCategory| |#1| (QUOTE (-240))) (|HasCategory| |#1| (QUOTE (-376)))) (|HasCategory| |#1| (QUOTE (-363)))) (-4144 (-12 (|HasCategory| |#1| (QUOTE (-240))) (|HasCategory| |#1| (QUOTE (-376)))) (-12 (|HasCategory| |#1| (QUOTE (-239))) (|HasCategory| |#1| (QUOTE (-376)))) (|HasCategory| |#1| (QUOTE (-363)))) (-4144 (-12 (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (|%list| (QUOTE -928) (QUOTE (-1209))))) (-12 (|HasCategory| |#1| (QUOTE (-363))) (|HasCategory| |#1| (|%list| (QUOTE -928) (QUOTE (-1209)))))) (-4144 (-12 (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (|%list| (QUOTE -928) (QUOTE (-1209))))) (-12 (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (|%list| (QUOTE -930) (QUOTE (-1209)))))) (|HasCategory| |#1| (|%list| (QUOTE -660) (QUOTE (-560)))) (-4144 (|HasCategory| |#1| (|%list| (QUOTE -1070) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#1| (QUOTE (-376)))) (|HasCategory| |#1| (|%list| (QUOTE -1070) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#1| (|%list| (QUOTE -1070) (QUOTE (-560)))) (-4144 (-12 (|HasCategory| |#1| (QUOTE (-239))) (|HasCategory| |#1| (QUOTE (-376)))) (|HasCategory| |#1| (QUOTE (-363)))) (-12 (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (|%list| (QUOTE -930) (QUOTE (-1209))))) (-12 (|HasCategory| |#1| (QUOTE (-239))) (|HasCategory| |#1| (QUOTE (-376)))) (-12 (|HasCategory| |#1| (QUOTE (-240))) (|HasCategory| |#1| (QUOTE (-376)))) (-12 (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (|%list| (QUOTE -928) (QUOTE (-1209)))))) +((|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-149))) (|HasCategory| |#1| (QUOTE (-363))) (-4118 (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (QUOTE (-363)))) (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (QUOTE (-381))) (-4118 (-12 (|HasCategory| |#1| (QUOTE (-240))) (|HasCategory| |#1| (QUOTE (-376)))) (|HasCategory| |#1| (QUOTE (-363)))) (-4118 (-12 (|HasCategory| |#1| (QUOTE (-240))) (|HasCategory| |#1| (QUOTE (-376)))) (-12 (|HasCategory| |#1| (QUOTE (-239))) (|HasCategory| |#1| (QUOTE (-376)))) (|HasCategory| |#1| (QUOTE (-363)))) (-4118 (-12 (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (|%list| (QUOTE -928) (QUOTE (-1209))))) (-12 (|HasCategory| |#1| (QUOTE (-363))) (|HasCategory| |#1| (|%list| (QUOTE -928) (QUOTE (-1209)))))) (-4118 (-12 (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (|%list| (QUOTE -928) (QUOTE (-1209))))) (-12 (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (|%list| (QUOTE -930) (QUOTE (-1209)))))) (|HasCategory| |#1| (|%list| (QUOTE -660) (QUOTE (-560)))) (-4118 (|HasCategory| |#1| (|%list| (QUOTE -1070) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#1| (QUOTE (-376)))) (|HasCategory| |#1| (|%list| (QUOTE -1070) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#1| (|%list| (QUOTE -1070) (QUOTE (-560)))) (-4118 (-12 (|HasCategory| |#1| (QUOTE (-239))) (|HasCategory| |#1| (QUOTE (-376)))) (|HasCategory| |#1| (QUOTE (-363)))) (-12 (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (|%list| (QUOTE -930) (QUOTE (-1209))))) (-12 (|HasCategory| |#1| (QUOTE (-239))) (|HasCategory| |#1| (QUOTE (-376)))) (-12 (|HasCategory| |#1| (QUOTE (-240))) (|HasCategory| |#1| (QUOTE (-376)))) (-12 (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (|%list| (QUOTE -928) (QUOTE (-1209)))))) (-1112 UP SAE UPA) ((|constructor| (NIL "Factorization of univariate polynomials with coefficients in an algebraic extension of the rational numbers (\\spadtype{Fraction Integer}).")) (|factor| (((|Factored| |#3|) |#3|) "\\spad{factor(p)} returns a prime factorisation of \\spad{p}."))) NIL @@ -4407,7 +4407,7 @@ NIL (-1119 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"))) (((-4512 "*") |has| |#1| (-175)) (-4503 |has| |#1| (-571)) (-4508 |has| |#1| (-6 -4508)) (-4505 . T) (-4504 . T) (-4507 . T)) -((|HasCategory| |#1| (QUOTE (-940))) (-4144 (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-466))) (|HasCategory| |#1| (QUOTE (-571))) (|HasCategory| |#1| (QUOTE (-940)))) (-4144 (|HasCategory| |#1| (QUOTE (-466))) (|HasCategory| |#1| (QUOTE (-571))) (|HasCategory| |#1| (QUOTE (-940)))) (-4144 (|HasCategory| |#1| (QUOTE (-466))) (|HasCategory| |#1| (QUOTE (-940)))) (|HasCategory| |#1| (QUOTE (-571))) (|HasCategory| |#1| (QUOTE (-175))) (-4144 (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-571)))) (-12 (|HasCategory| (-1120 (-1209)) (|%list| (QUOTE -912) (QUOTE (-391)))) (|HasCategory| |#1| (|%list| (QUOTE -912) (QUOTE (-391))))) (-12 (|HasCategory| (-1120 (-1209)) (|%list| (QUOTE -912) (QUOTE (-560)))) (|HasCategory| |#1| (|%list| (QUOTE -912) (QUOTE (-560))))) (-12 (|HasCategory| (-1120 (-1209)) (|%list| (QUOTE -633) (|%list| (QUOTE -916) (QUOTE (-391))))) (|HasCategory| |#1| (|%list| (QUOTE -633) (|%list| (QUOTE -916) (QUOTE (-391)))))) (-12 (|HasCategory| (-1120 (-1209)) (|%list| (QUOTE -633) (|%list| (QUOTE -916) (QUOTE (-560))))) (|HasCategory| |#1| (|%list| (QUOTE -633) (|%list| (QUOTE -916) (QUOTE (-560)))))) (-12 (|HasCategory| (-1120 (-1209)) (|%list| (QUOTE -633) (QUOTE (-549)))) (|HasCategory| |#1| (|%list| (QUOTE -633) (QUOTE (-549))))) (|HasCategory| |#1| (|%list| (QUOTE -660) (QUOTE (-560)))) (|HasCategory| |#1| (QUOTE (-149))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (|%list| (QUOTE -38) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#1| (|%list| (QUOTE -1070) (QUOTE (-560)))) (-4144 (|HasCategory| |#1| (|%list| (QUOTE -38) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#1| (|%list| (QUOTE -1070) (|%list| (QUOTE -421) (QUOTE (-560)))))) (|HasCategory| |#1| (|%list| (QUOTE -1070) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#1| (QUOTE (-240))) (|HasCategory| |#1| (QUOTE (-239))) (|HasCategory| |#1| (|%list| (QUOTE -930) (QUOTE (-1209)))) (|HasCategory| |#1| (|%list| (QUOTE -928) (QUOTE (-1209)))) (|HasCategory| |#1| (QUOTE (-376))) (|HasAttribute| |#1| (QUOTE -4508)) (|HasCategory| |#1| (QUOTE (-466))) (-12 (|HasCategory| $ (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-940)))) (-4144 (-12 (|HasCategory| $ (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-940)))) (|HasCategory| |#1| (QUOTE (-147))))) +((|HasCategory| |#1| (QUOTE (-940))) (-4118 (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-466))) (|HasCategory| |#1| (QUOTE (-571))) (|HasCategory| |#1| (QUOTE (-940)))) (-4118 (|HasCategory| |#1| (QUOTE (-466))) (|HasCategory| |#1| (QUOTE (-571))) (|HasCategory| |#1| (QUOTE (-940)))) (-4118 (|HasCategory| |#1| (QUOTE (-466))) (|HasCategory| |#1| (QUOTE (-940)))) (|HasCategory| |#1| (QUOTE (-571))) (|HasCategory| |#1| (QUOTE (-175))) (-4118 (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-571)))) (-12 (|HasCategory| (-1120 (-1209)) (|%list| (QUOTE -912) (QUOTE (-391)))) (|HasCategory| |#1| (|%list| (QUOTE -912) (QUOTE (-391))))) (-12 (|HasCategory| (-1120 (-1209)) (|%list| (QUOTE -912) (QUOTE (-560)))) (|HasCategory| |#1| (|%list| (QUOTE -912) (QUOTE (-560))))) (-12 (|HasCategory| (-1120 (-1209)) (|%list| (QUOTE -633) (|%list| (QUOTE -916) (QUOTE (-391))))) (|HasCategory| |#1| (|%list| (QUOTE -633) (|%list| (QUOTE -916) (QUOTE (-391)))))) (-12 (|HasCategory| (-1120 (-1209)) (|%list| (QUOTE -633) (|%list| (QUOTE -916) (QUOTE (-560))))) (|HasCategory| |#1| (|%list| (QUOTE -633) (|%list| (QUOTE -916) (QUOTE (-560)))))) (-12 (|HasCategory| (-1120 (-1209)) (|%list| (QUOTE -633) (QUOTE (-549)))) (|HasCategory| |#1| (|%list| (QUOTE -633) (QUOTE (-549))))) (|HasCategory| |#1| (|%list| (QUOTE -660) (QUOTE (-560)))) (|HasCategory| |#1| (QUOTE (-149))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (|%list| (QUOTE -38) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#1| (|%list| (QUOTE -1070) (QUOTE (-560)))) (-4118 (|HasCategory| |#1| (|%list| (QUOTE -38) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#1| (|%list| (QUOTE -1070) (|%list| (QUOTE -421) (QUOTE (-560)))))) (|HasCategory| |#1| (|%list| (QUOTE -1070) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#1| (QUOTE (-240))) (|HasCategory| |#1| (QUOTE (-239))) (|HasCategory| |#1| (|%list| (QUOTE -930) (QUOTE (-1209)))) (|HasCategory| |#1| (|%list| (QUOTE -928) (QUOTE (-1209)))) (|HasCategory| |#1| (QUOTE (-376))) (|HasAttribute| |#1| (QUOTE -4508)) (|HasCategory| |#1| (QUOTE (-466))) (-12 (|HasCategory| $ (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-940)))) (-4118 (-12 (|HasCategory| $ (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-940)))) (|HasCategory| |#1| (QUOTE (-147))))) (-1120 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 @@ -4447,7 +4447,7 @@ NIL (-1129 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)}}"))) ((-4510 . T) (-4500 . T) (-4511 . T)) -((-4144 (-12 (|HasCategory| |#1| (QUOTE (-381))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|))))) (|HasCategory| |#1| (|%list| (QUOTE -633) (QUOTE (-549)))) (|HasCategory| |#1| (QUOTE (-381))) (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#1| (QUOTE (-872))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-888)))) (|HasCategory| |#1| (QUOTE (-102))) (-12 (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|))))) +((-4118 (-12 (|HasCategory| |#1| (QUOTE (-381))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|))))) (|HasCategory| |#1| (|%list| (QUOTE -633) (QUOTE (-549)))) (|HasCategory| |#1| (QUOTE (-381))) (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#1| (QUOTE (-872))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-888)))) (|HasCategory| |#1| (QUOTE (-102))) (-12 (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|))))) (-1130 A S) ((|constructor| (NIL "A set category lists a collection of set-theoretic operations useful for both finite sets and multisets. Note however that finite sets are distinct from multisets. Although the operations defined for set categories are common to both,{} the relationship between the two cannot be described by inclusion or inheritance.")) (|union| (($ |#2| $) "\\spad{union(x,u)} returns the set aggregate \\spad{u} with the element \\spad{x} added. If \\spad{u} already contains \\spad{x},{} \\axiom{union(\\spad{x},{}\\spad{u})} returns a copy of \\spad{u}.") (($ $ |#2|) "\\spad{union(u,x)} returns the set aggregate \\spad{u} with the element \\spad{x} added. If \\spad{u} already contains \\spad{x},{} \\axiom{union(\\spad{u},{}\\spad{x})} returns a copy of \\spad{u}.") (($ $ $) "\\spad{union(u,v)} returns the set aggregate of elements which are members of either set aggregate \\spad{u} or \\spad{v}.")) (|subset?| (((|Boolean|) $ $) "\\spad{subset?(u,v)} tests if \\spad{u} is a subset of \\spad{v}. Note: equivalent to \\axiom{reduce(and,{}{member?(\\spad{x},{}\\spad{v}) for \\spad{x} in \\spad{u}},{}\\spad{true},{}\\spad{false})}.")) (|symmetricDifference| (($ $ $) "\\spad{symmetricDifference(u,v)} returns the set aggregate of elements \\spad{x} which are members of set aggregate \\spad{u} or set aggregate \\spad{v} but not both. If \\spad{u} and \\spad{v} have no elements in common,{} \\axiom{symmetricDifference(\\spad{u},{}\\spad{v})} returns a copy of \\spad{u}. Note: \\axiom{symmetricDifference(\\spad{u},{}\\spad{v}) = union(difference(\\spad{u},{}\\spad{v}),{}difference(\\spad{v},{}\\spad{u}))}")) (|difference| (($ $ |#2|) "\\spad{difference(u,x)} returns the set aggregate \\spad{u} with element \\spad{x} removed. If \\spad{u} does not contain \\spad{x},{} a copy of \\spad{u} is returned. Note: \\axiom{difference(\\spad{s},{} \\spad{x}) = difference(\\spad{s},{} {\\spad{x}})}.") (($ $ $) "\\spad{difference(u,v)} returns the set aggregate \\spad{w} consisting of elements in set aggregate \\spad{u} but not in set aggregate \\spad{v}. If \\spad{u} and \\spad{v} have no elements in common,{} \\axiom{difference(\\spad{u},{}\\spad{v})} returns a copy of \\spad{u}. Note: equivalent to the notation (not currently supported) \\axiom{{\\spad{x} for \\spad{x} in \\spad{u} | not member?(\\spad{x},{}\\spad{v})}}.")) (|intersect| (($ $ $) "\\spad{intersect(u,v)} returns the set aggregate \\spad{w} consisting of elements common to both set aggregates \\spad{u} and \\spad{v}. Note: equivalent to the notation (not currently supported) {\\spad{x} for \\spad{x} in \\spad{u} | member?(\\spad{x},{}\\spad{v})}.")) (|set| (($ (|List| |#2|)) "\\spad{set([x,y,...,z])} creates a set aggregate containing items \\spad{x},{}\\spad{y},{}...,{}\\spad{z}.") (($) "\\spad{set()}\\$\\spad{D} creates an empty set aggregate of type \\spad{D}.")) (|brace| (($ (|List| |#2|)) "\\spad{brace([x,y,...,z])} creates a set aggregate containing items \\spad{x},{}\\spad{y},{}...,{}\\spad{z}. This form is considered obsolete. Use \\axiomFun{set} instead.") (($) "\\spad{brace()}\\$\\spad{D} (otherwise written {}\\$\\spad{D}) creates an empty set aggregate of type \\spad{D}. This form is considered obsolete. Use \\axiomFun{set} instead.")) (|part?| (((|Boolean|) $ $) "\\spad{s} < \\spad{t} returns \\spad{true} if all elements of set aggregate \\spad{s} are also elements of set aggregate \\spad{t}."))) NIL @@ -4511,7 +4511,7 @@ NIL (-1145 |dimtot| |dim1| S) ((|constructor| (NIL "\\indented{2}{This type represents the finite direct or cartesian product of an} underlying ordered component type. The vectors are ordered as if they were split into two blocks. The \\spad{dim1} parameter specifies the length of the first block. The ordering is lexicographic between the blocks but acts like \\spadtype{HomogeneousDirectProduct} within each block. This type is a suitable third argument for \\spadtype{GeneralDistributedMultivariatePolynomial}."))) ((-4504 |has| |#3| (-1081)) (-4505 |has| |#3| (-1081)) (-4507 |has| |#3| (-6 -4507)) (-4510 . 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(|HasCategory| |#3| (QUOTE (-102))) (-12 (|HasCategory| |#3| (QUOTE (-1133))) (|HasCategory| |#3| (|%list| (QUOTE -321) (|devaluate| |#3|))))) (-1146 R |x|) ((|constructor| (NIL "This package produces functions for counting etc. real roots of univariate polynomials in \\spad{x} over \\spad{R},{} which must be an OrderedIntegralDomain")) (|countRealRootsMultiple| (((|Integer|) (|UnivariatePolynomial| |#2| |#1|)) "\\spad{countRealRootsMultiple(p)} says how many real roots \\spad{p} has,{} counted with multiplicity")) (|SturmHabichtMultiple| (((|Integer|) (|UnivariatePolynomial| |#2| |#1|) (|UnivariatePolynomial| |#2| |#1|)) "\\spad{SturmHabichtMultiple(p1,p2)} computes c_{+}-c_{-} where c_{+} is the number of real roots of \\spad{p1} with \\spad{p2>0} and c_{-} is the number of real roots of \\spad{p1} with \\spad{p2<0}. If \\spad{p2=1} what you get is the number of real roots of \\spad{p1}.")) (|countRealRoots| (((|Integer|) (|UnivariatePolynomial| |#2| |#1|)) "\\spad{countRealRoots(p)} says how many real roots \\spad{p} has")) (|SturmHabicht| (((|Integer|) (|UnivariatePolynomial| |#2| |#1|) (|UnivariatePolynomial| |#2| |#1|)) "\\spad{SturmHabicht(p1,p2)} computes c_{+}-c_{-} where c_{+} is the number of real roots of \\spad{p1} with \\spad{p2>0} and c_{-} is the number of real roots of \\spad{p1} with \\spad{p2<0}. If \\spad{p2=1} what you get is the number of real roots of \\spad{p1}.")) (|SturmHabichtCoefficients| (((|List| |#1|) (|UnivariatePolynomial| |#2| |#1|) (|UnivariatePolynomial| |#2| |#1|)) "\\spad{SturmHabichtCoefficients(p1,p2)} computes the principal Sturm-Habicht coefficients of \\spad{p1} and \\spad{p2}")) (|SturmHabichtSequence| (((|List| (|UnivariatePolynomial| |#2| |#1|)) (|UnivariatePolynomial| |#2| |#1|) (|UnivariatePolynomial| |#2| |#1|)) "\\spad{SturmHabichtSequence(p1,p2)} computes the Sturm-Habicht sequence of \\spad{p1} and \\spad{p2}")) (|subresultantSequence| (((|List| (|UnivariatePolynomial| |#2| |#1|)) (|UnivariatePolynomial| |#2| |#1|) (|UnivariatePolynomial| |#2| |#1|)) "\\spad{subresultantSequence(p1,p2)} computes the (standard) subresultant sequence of \\spad{p1} and \\spad{p2}"))) NIL @@ -4524,7 +4524,7 @@ NIL ((|constructor| (NIL "This domain represents a signature AST. A signature AST \\indented{2}{is a description of an exported operation,{} \\spadignore{e.g.} its name,{} result} \\indented{2}{type,{} and the list of its argument types.}")) (|signature| (((|Signature|) $) "\\spad{signature(s)} returns AST of the declared signature for `s'.")) (|name| (((|Identifier|) $) "\\spad{name(s)} returns the name of the signature `s'.")) (|signatureAst| (($ (|Identifier|) (|Signature|)) "\\spad{signatureAst(n,s,t)} builds the signature AST n: \\spad{s} -> \\spad{t}"))) NIL NIL -(-1149 R -4164) +(-1149 R -4140) ((|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 @@ -4559,16 +4559,16 @@ NIL (-1157 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."))) (((-4512 "*") |has| |#1| (-175)) (-4503 |has| |#1| (-571)) (-4508 |has| |#1| (-6 -4508)) (-4505 . T) (-4504 . T) (-4507 . 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A Taylor series is represented by a stream of polynomials from the polynomial domain SMP. The \\spad{n}th element of the stream is a form of degree \\spad{n}. SMTS is an internal domain.")) (|fintegrate| (($ (|Mapping| $) |#2| |#1|) "\\spad{fintegrate(f,v,c)} is the integral of \\spad{f()} with respect \\indented{1}{to \\spad{v} and having \\spad{c} as the constant of integration.} \\indented{1}{The evaluation of \\spad{f()} is delayed.}")) (|integrate| (($ $ |#2| |#1|) "\\spad{integrate(s,v,c)} is the integral of \\spad{s} with respect \\indented{1}{to \\spad{v} and having \\spad{c} as the constant of integration.}")) (|csubst| (((|Mapping| (|Stream| |#3|) |#3|) (|List| |#2|) (|List| (|Stream| |#3|))) "\\spad{csubst(a,b)} is for internal use only")) (* (($ |#3| $) "\\spad{smp*ts} multiplies a TaylorSeries by a monomial SMP.")) (|coerce| (($ |#3|) "\\spad{coerce(poly)} regroups the terms by total degree and forms a series.") (($ |#2|) "\\spad{coerce(var)} converts a variable to a Taylor series")) (|coefficient| ((|#3| $ (|NonNegativeInteger|)) "\\spad{coefficient(s, n)} gives the terms of total degree \\spad{n}."))) (((-4512 "*") |has| |#1| (-175)) (-4503 |has| |#1| (-571)) (-4505 . T) (-4504 . T) (-4507 . T)) -((|HasCategory| |#1| (|%list| (QUOTE -38) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-149))) (|HasCategory| |#1| (QUOTE (-147))) (-4144 (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-571)))) (|HasCategory| |#1| (QUOTE (-571))) (|HasCategory| |#1| (QUOTE (-376)))) +((|HasCategory| |#1| (|%list| (QUOTE -38) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-149))) (|HasCategory| |#1| (QUOTE (-147))) (-4118 (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-571)))) (|HasCategory| |#1| (QUOTE (-571))) (|HasCategory| |#1| (QUOTE (-376)))) (-1159 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}"))) ((-4511 . T) (-4510 . T)) NIL -(-1160 UP -4164) +(-1160 UP -4140) ((|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 @@ -4623,11 +4623,11 @@ NIL (-1173 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,{}ls,{}sub?)} returns \\axiom{a} where the children list of \\axiom{\\spad{l}} has been set to \\axiom{[[\\spad{s}]\\$\\% for \\spad{s} in 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,{}ls)} returns \\axiom{a} where the children list of \\axiom{\\spad{l}} has been set to \\axiom{[[\\spad{s}]\\$\\% for \\spad{s} in 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|))) $) "\\axiom{result(a)} where \\axiom{ls} is the leaves list of \\axiom{a} returns \\axiom{[[value(\\spad{s}),{}condition(\\spad{s})]\\$VT for \\spad{s} in 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},{}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 ls]}.") (($ |#1| |#2| (|List| (|SplittingNode| |#1| |#2|))) "\\axiom{construct(\\spad{v},{}\\spad{t},{}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 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."))) ((-4510 . T) (-4511 . T)) -((-12 (|HasCategory| (-1172 |#1| |#2|) (|%list| (QUOTE -321) (|%list| (QUOTE -1172) (|devaluate| |#1|) (|devaluate| |#2|)))) (|HasCategory| (-1172 |#1| |#2|) (QUOTE (-1133)))) (|HasCategory| (-1172 |#1| |#2|) (QUOTE (-1133))) (-4144 (|HasCategory| (-1172 |#1| |#2|) (QUOTE (-102))) (|HasCategory| (-1172 |#1| |#2|) (QUOTE (-1133)))) (-4144 (|HasCategory| (-1172 |#1| |#2|) (|%list| (QUOTE -632) (QUOTE (-888)))) (-12 (|HasCategory| (-1172 |#1| |#2|) (|%list| (QUOTE -321) (|%list| (QUOTE -1172) (|devaluate| |#1|) (|devaluate| |#2|)))) (|HasCategory| (-1172 |#1| |#2|) (QUOTE (-1133))))) (|HasCategory| (-1172 |#1| |#2|) (|%list| (QUOTE -632) (QUOTE (-888)))) (|HasCategory| (-1172 |#1| |#2|) (QUOTE (-102)))) +((-12 (|HasCategory| (-1172 |#1| |#2|) (|%list| (QUOTE -321) (|%list| (QUOTE -1172) (|devaluate| |#1|) (|devaluate| |#2|)))) (|HasCategory| (-1172 |#1| |#2|) (QUOTE (-1133)))) (|HasCategory| (-1172 |#1| |#2|) (QUOTE (-1133))) (-4118 (|HasCategory| (-1172 |#1| |#2|) (QUOTE (-102))) (|HasCategory| (-1172 |#1| |#2|) (QUOTE (-1133)))) (-4118 (|HasCategory| (-1172 |#1| |#2|) (|%list| (QUOTE -632) (QUOTE (-888)))) (-12 (|HasCategory| (-1172 |#1| |#2|) (|%list| (QUOTE -321) (|%list| (QUOTE -1172) (|devaluate| |#1|) (|devaluate| |#2|)))) (|HasCategory| (-1172 |#1| |#2|) (QUOTE (-1133))))) (|HasCategory| (-1172 |#1| |#2|) (|%list| (QUOTE -632) (QUOTE (-888)))) (|HasCategory| (-1172 |#1| |#2|) (QUOTE (-102)))) (-1174 |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}."))) ((-4507 . T) (-4499 |has| |#2| (-6 (-4512 "*"))) (-4510 . T) (-4504 . T) (-4505 . T)) -((|HasCategory| |#2| (|%list| (QUOTE -928) (QUOTE (-1209)))) (|HasCategory| |#2| (|%list| (QUOTE -930) (QUOTE (-1209)))) (|HasCategory| |#2| (QUOTE (-240))) (|HasCategory| |#2| (QUOTE (-239))) (|HasAttribute| |#2| (QUOTE (-4512 "*"))) (|HasCategory| |#2| (|%list| (QUOTE -660) (QUOTE (-560)))) (|HasCategory| |#2| (|%list| (QUOTE -1070) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#2| (|%list| (QUOTE -1070) (QUOTE (-560)))) (-4144 (-12 (|HasCategory| |#2| (|%list| (QUOTE -660) (QUOTE (-560)))) (|HasCategory| |#2| (|%list| (QUOTE -321) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-240))) (|HasCategory| |#2| (|%list| (QUOTE -321) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-1133))) (|HasCategory| |#2| (|%list| (QUOTE -321) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (|%list| (QUOTE -321) (|devaluate| |#2|))) (|HasCategory| |#2| (|%list| (QUOTE -928) (QUOTE (-1209)))))) (|HasCategory| |#2| (|%list| (QUOTE -633) (QUOTE (-549)))) (|HasCategory| |#2| (QUOTE (-319))) (|HasCategory| |#2| (QUOTE (-571))) (|HasCategory| |#2| (QUOTE (-1133))) (|HasCategory| |#2| (QUOTE (-376))) (-4144 (|HasAttribute| |#2| (QUOTE (-4512 "*"))) (|HasCategory| |#2| (|%list| (QUOTE -928) (QUOTE (-1209)))) (|HasCategory| |#2| (QUOTE (-240)))) (|HasCategory| |#2| (|%list| (QUOTE -632) (QUOTE (-888)))) (|HasCategory| |#2| (QUOTE (-102))) (-12 (|HasCategory| |#2| (QUOTE (-1133))) (|HasCategory| |#2| (|%list| (QUOTE -321) (|devaluate| |#2|)))) (|HasCategory| |#2| (QUOTE (-175)))) +((|HasCategory| |#2| (|%list| (QUOTE -928) (QUOTE (-1209)))) (|HasCategory| |#2| (|%list| (QUOTE -930) (QUOTE (-1209)))) (|HasCategory| |#2| (QUOTE (-240))) (|HasCategory| |#2| (QUOTE (-239))) (|HasAttribute| |#2| (QUOTE (-4512 "*"))) (|HasCategory| |#2| (|%list| (QUOTE -660) (QUOTE (-560)))) (|HasCategory| |#2| (|%list| (QUOTE -1070) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#2| (|%list| (QUOTE -1070) (QUOTE (-560)))) (-4118 (-12 (|HasCategory| |#2| (|%list| (QUOTE -660) (QUOTE (-560)))) (|HasCategory| |#2| (|%list| (QUOTE -321) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-240))) (|HasCategory| |#2| (|%list| (QUOTE -321) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-1133))) (|HasCategory| |#2| (|%list| (QUOTE -321) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (|%list| (QUOTE -321) (|devaluate| |#2|))) (|HasCategory| |#2| (|%list| (QUOTE -928) (QUOTE (-1209)))))) (|HasCategory| |#2| (|%list| (QUOTE -633) (QUOTE (-549)))) (|HasCategory| |#2| (QUOTE (-319))) (|HasCategory| |#2| (QUOTE (-571))) (|HasCategory| |#2| (QUOTE (-1133))) (|HasCategory| |#2| (QUOTE (-376))) (-4118 (|HasAttribute| |#2| (QUOTE (-4512 "*"))) (|HasCategory| |#2| (|%list| (QUOTE -928) (QUOTE (-1209)))) (|HasCategory| |#2| (QUOTE (-240)))) (|HasCategory| |#2| (|%list| (QUOTE -632) (QUOTE (-888)))) (|HasCategory| |#2| (QUOTE (-102))) (-12 (|HasCategory| |#2| (QUOTE (-1133))) (|HasCategory| |#2| (|%list| (QUOTE -321) (|devaluate| |#2|)))) (|HasCategory| |#2| (QUOTE (-175)))) (-1175 S) ((|constructor| (NIL "A string aggregate is a category for strings,{} that is,{} one dimensional arrays of characters.")) (|elt| (($ $ $) "\\spad{elt(s,t)} returns the concatenation of \\spad{s} and \\spad{t}. It is provided to allow juxtaposition of strings to work as concatenation. For example,{} \\axiom{\"smoo\" \"shed\"} returns \\axiom{\"smooshed\"}.")) (|rightTrim| (($ $ (|CharacterClass|)) "\\spad{rightTrim(s,cc)} returns \\spad{s} with all trailing occurences of characters in \\spad{cc} deleted. For example,{} \\axiom{rightTrim(\"(abc)\",{} charClass \"()\")} returns \\axiom{\"(abc\"}.") (($ $ (|Character|)) "\\spad{rightTrim(s,c)} returns \\spad{s} with all trailing occurrences of \\spad{c} deleted. For example,{} \\axiom{rightTrim(\" abc \",{} char \" \")} returns \\axiom{\" abc\"}.")) (|leftTrim| (($ $ (|CharacterClass|)) "\\spad{leftTrim(s,cc)} returns \\spad{s} with all leading characters in \\spad{cc} deleted. For example,{} \\axiom{leftTrim(\"(abc)\",{} charClass \"()\")} returns \\axiom{\"abc)\"}.") (($ $ (|Character|)) "\\spad{leftTrim(s,c)} returns \\spad{s} with all leading characters \\spad{c} deleted. For example,{} \\axiom{leftTrim(\" abc \",{} char \" \")} returns \\axiom{\"abc \"}.")) (|trim| (($ $ (|CharacterClass|)) "\\spad{trim(s,cc)} returns \\spad{s} with all characters in \\spad{cc} deleted from right and left ends. For example,{} \\axiom{trim(\"(abc)\",{} charClass \"()\")} returns \\axiom{\"abc\"}.") (($ $ (|Character|)) "\\spad{trim(s,c)} returns \\spad{s} with all characters \\spad{c} deleted from right and left ends. For example,{} \\axiom{trim(\" abc \",{} char \" \")} returns \\axiom{\"abc\"}.")) (|split| (((|List| $) $ (|CharacterClass|)) "\\spad{split(s,cc)} returns a list of substrings delimited by characters in \\spad{cc}.") (((|List| $) $ (|Character|)) "\\spad{split(s,c)} returns a list of substrings delimited by character \\spad{c}.")) (|coerce| (($ (|Character|)) "\\spad{coerce(c)} returns \\spad{c} as a string \\spad{s} with the character \\spad{c}.")) (|position| (((|Integer|) (|CharacterClass|) $ (|Integer|)) "\\spad{position(cc,t,i)} returns the position \\axiom{\\spad{j} >= \\spad{i}} in \\spad{t} of the first character belonging to \\spad{cc}.") (((|Integer|) $ $ (|Integer|)) "\\spad{position(s,t,i)} returns the position \\spad{j} of the substring \\spad{s} in string \\spad{t},{} where \\axiom{\\spad{j} >= \\spad{i}} is required.")) (|replace| (($ $ (|UniversalSegment| (|Integer|)) $) "\\spad{replace(s,i..j,t)} replaces the substring \\axiom{\\spad{s}(\\spad{i}..\\spad{j})} of \\spad{s} by string \\spad{t}.")) (|match?| (((|Boolean|) $ $ (|Character|)) "\\spad{match?(s,t,c)} tests if \\spad{s} matches \\spad{t} except perhaps for multiple and consecutive occurrences of character \\spad{c}. Typically \\spad{c} is the blank character.")) (|match| (((|NonNegativeInteger|) $ $ (|Character|)) "\\spad{match(p,s,wc)} tests if pattern \\axiom{\\spad{p}} matches subject \\axiom{\\spad{s}} where \\axiom{\\spad{wc}} is a wild card character. If no match occurs,{} the index \\axiom{0} is returned; otheriwse,{} the value returned is the first index of the first character in the subject matching the subject (excluding that matched by an initial wild-card). For example,{} \\axiom{match(\"*to*\",{}\"yorktown\",{}\"*\")} returns \\axiom{5} indicating a successful match starting at index \\axiom{5} of \\axiom{\"yorktown\"}.")) (|substring?| (((|Boolean|) $ $ (|Integer|)) "\\spad{substring?(s,t,i)} tests if \\spad{s} is a substring of \\spad{t} beginning at index \\spad{i}. Note: \\axiom{substring?(\\spad{s},{}\\spad{t},{}0) = prefix?(\\spad{s},{}\\spad{t})}.")) (|suffix?| (((|Boolean|) $ $) "\\spad{suffix?(s,t)} tests if the string \\spad{s} is the final substring of \\spad{t}. Note: \\axiom{suffix?(\\spad{s},{}\\spad{t}) == reduce(and,{}[\\spad{s}.\\spad{i} = \\spad{t}.(\\spad{n} - \\spad{m} + \\spad{i}) for \\spad{i} in 0..maxIndex \\spad{s}])} where \\spad{m} and \\spad{n} denote the maxIndex of \\spad{s} and \\spad{t} respectively.")) (|prefix?| (((|Boolean|) $ $) "\\spad{prefix?(s,t)} tests if the string \\spad{s} is the initial substring of \\spad{t}. Note: \\axiom{prefix?(\\spad{s},{}\\spad{t}) == reduce(and,{}[\\spad{s}.\\spad{i} = \\spad{t}.\\spad{i} for \\spad{i} in 0..maxIndex \\spad{s}])}.")) (|upperCase!| (($ $) "\\spad{upperCase!(s)} destructively replaces the alphabetic characters in \\spad{s} by upper case characters.")) (|upperCase| (($ $) "\\spad{upperCase(s)} returns the string with all characters in upper case.")) (|lowerCase!| (($ $) "\\spad{lowerCase!(s)} destructively replaces the alphabetic characters in \\spad{s} by lower case.")) (|lowerCase| (($ $) "\\spad{lowerCase(s)} returns the string with all characters in lower case."))) NIL @@ -4651,7 +4651,7 @@ NIL (-1180 S) ((|constructor| (NIL "Linked List implementation of a Stack")) (|stack| (($ (|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}."))) ((-4510 . T) (-4511 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1133))) (-4144 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-1133)))) (-4144 (-12 (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-888))))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-888)))) (|HasCategory| |#1| (QUOTE (-102)))) +((-12 (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1133))) (-4118 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-1133)))) (-4118 (-12 (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-888))))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-888)))) (|HasCategory| |#1| (QUOTE (-102)))) (-1181 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}.")) (|size?| (((|Boolean|) $ (|NonNegativeInteger|)) "\\spad{size?(u,n)} tests if \\spad{u} has exactly \\spad{n} elements.")) (|more?| (((|Boolean|) $ (|NonNegativeInteger|)) "\\spad{more?(u,n)} tests if \\spad{u} has greater than \\spad{n} elements.")) (|less?| (((|Boolean|) $ (|NonNegativeInteger|)) "\\spad{less?(u,n)} tests if \\spad{u} has less than \\spad{n} elements.")) (|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 @@ -4663,7 +4663,7 @@ NIL (-1183 |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."))) ((-4511 . T)) -((-12 (|HasCategory| (-2 (|:| -2118 |#1|) (|:| -3964 |#2|)) (QUOTE (-1133))) (|HasCategory| (-2 (|:| -2118 |#1|) (|:| -3964 |#2|)) (|%list| (QUOTE -321) (|%list| (QUOTE -2) (|%list| (QUOTE |:|) (QUOTE -2118) (|devaluate| |#1|)) (|%list| (QUOTE |:|) (QUOTE -3964) (|devaluate| |#2|)))))) (-4144 (|HasCategory| (-2 (|:| -2118 |#1|) (|:| -3964 |#2|)) (QUOTE (-1133))) (|HasCategory| |#2| (QUOTE (-1133)))) (-4144 (|HasCategory| (-2 (|:| -2118 |#1|) (|:| -3964 |#2|)) (QUOTE (-102))) (|HasCategory| (-2 (|:| -2118 |#1|) (|:| -3964 |#2|)) (QUOTE (-1133))) (|HasCategory| |#2| (QUOTE (-102))) (|HasCategory| |#2| (QUOTE (-1133)))) (-4144 (|HasCategory| (-2 (|:| -2118 |#1|) (|:| -3964 |#2|)) (QUOTE (-1133))) (|HasCategory| (-2 (|:| -2118 |#1|) (|:| -3964 |#2|)) (|%list| (QUOTE -632) (QUOTE (-888)))) (|HasCategory| |#2| (QUOTE (-1133))) (|HasCategory| |#2| (|%list| (QUOTE -632) (QUOTE (-888))))) (|HasCategory| (-2 (|:| -2118 |#1|) (|:| -3964 |#2|)) (|%list| (QUOTE -633) (QUOTE (-549)))) (-12 (|HasCategory| |#2| (QUOTE (-1133))) (|HasCategory| |#2| (|%list| (QUOTE -321) (|devaluate| |#2|)))) (|HasCategory| |#1| (QUOTE (-872))) (-4144 (|HasCategory| (-2 (|:| -2118 |#1|) (|:| -3964 |#2|)) (QUOTE (-102))) (|HasCategory| |#2| (QUOTE (-102)))) (-4144 (|HasCategory| (-2 (|:| -2118 |#1|) (|:| -3964 |#2|)) (|%list| (QUOTE -632) (QUOTE (-888)))) (|HasCategory| |#2| (|%list| (QUOTE -632) (QUOTE (-888))))) (|HasCategory| |#2| (QUOTE (-1133))) (|HasCategory| |#2| (QUOTE (-102))) (|HasCategory| |#2| (|%list| (QUOTE -632) (QUOTE (-888)))) (|HasCategory| (-2 (|:| -2118 |#1|) (|:| -3964 |#2|)) (|%list| (QUOTE -632) (QUOTE (-888)))) (|HasCategory| (-2 (|:| -2118 |#1|) (|:| -3964 |#2|)) (QUOTE (-102))) (|HasCategory| (-2 (|:| -2118 |#1|) (|:| -3964 |#2|)) (QUOTE (-1133)))) +((-12 (|HasCategory| (-2 (|:| -2115 |#1|) (|:| -3934 |#2|)) (QUOTE (-1133))) (|HasCategory| (-2 (|:| -2115 |#1|) (|:| -3934 |#2|)) (|%list| (QUOTE -321) (|%list| (QUOTE -2) (|%list| (QUOTE |:|) (QUOTE -2115) (|devaluate| |#1|)) (|%list| (QUOTE |:|) (QUOTE -3934) (|devaluate| |#2|)))))) (-4118 (|HasCategory| (-2 (|:| -2115 |#1|) (|:| -3934 |#2|)) (QUOTE (-1133))) (|HasCategory| |#2| (QUOTE (-1133)))) (-4118 (|HasCategory| (-2 (|:| -2115 |#1|) (|:| -3934 |#2|)) (QUOTE (-102))) (|HasCategory| (-2 (|:| -2115 |#1|) (|:| -3934 |#2|)) (QUOTE (-1133))) (|HasCategory| |#2| (QUOTE (-102))) (|HasCategory| |#2| (QUOTE (-1133)))) (-4118 (|HasCategory| (-2 (|:| -2115 |#1|) (|:| -3934 |#2|)) (QUOTE (-1133))) (|HasCategory| (-2 (|:| -2115 |#1|) (|:| -3934 |#2|)) (|%list| (QUOTE -632) (QUOTE (-888)))) (|HasCategory| |#2| (QUOTE (-1133))) (|HasCategory| |#2| (|%list| (QUOTE -632) (QUOTE (-888))))) (|HasCategory| (-2 (|:| -2115 |#1|) (|:| -3934 |#2|)) (|%list| (QUOTE -633) (QUOTE (-549)))) (-12 (|HasCategory| |#2| (QUOTE (-1133))) (|HasCategory| |#2| (|%list| (QUOTE -321) (|devaluate| |#2|)))) (|HasCategory| |#1| (QUOTE (-872))) (-4118 (|HasCategory| (-2 (|:| -2115 |#1|) (|:| -3934 |#2|)) (QUOTE (-102))) (|HasCategory| |#2| (QUOTE (-102)))) (-4118 (|HasCategory| (-2 (|:| -2115 |#1|) (|:| -3934 |#2|)) (|%list| (QUOTE -632) (QUOTE (-888)))) (|HasCategory| |#2| (|%list| (QUOTE -632) (QUOTE (-888))))) (|HasCategory| |#2| (QUOTE (-1133))) (|HasCategory| |#2| (QUOTE (-102))) (|HasCategory| |#2| (|%list| (QUOTE -632) (QUOTE (-888)))) (|HasCategory| (-2 (|:| -2115 |#1|) (|:| -3934 |#2|)) (|%list| (QUOTE -632) (QUOTE (-888)))) (|HasCategory| (-2 (|:| -2115 |#1|) (|:| -3934 |#2|)) (QUOTE (-102))) (|HasCategory| (-2 (|:| -2115 |#1|) (|:| -3934 |#2|)) (QUOTE (-1133)))) (-1184) ((|constructor| (NIL "A class of objects which can be 'stepped through'. Repeated applications of \\spadfun{nextItem} is guaranteed never to return duplicate items and only return \"failed\" after exhausting all elements of the domain. This assumes that the sequence starts with \\spad{init()}. For infinite domains,{} repeated application of \\spadfun{nextItem} is not required to reach all possible domain elements starting from any initial element. \\blankline Conditional attributes: \\indented{2}{infinite\\tab{15}repeated \\spad{nextItem}'s are never \\spad{nothing}.}")) (|nextItem| (((|Maybe| $) $) "\\spad{nextItem(x)} returns the next item,{} or \\spad{failed} if domain is exhausted.")) (|init| (($) "\\spad{init()} chooses an initial object for stepping."))) NIL @@ -4679,7 +4679,7 @@ NIL (-1187 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."))) ((-4511 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1133))) (-4144 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-1133)))) (-4144 (-12 (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-888))))) (|HasCategory| |#1| (|%list| (QUOTE -633) (QUOTE (-549)))) (|HasCategory| (-560) (QUOTE (-872))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-888)))) (|HasCategory| |#1| (QUOTE (-102)))) +((-12 (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1133))) (-4118 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-1133)))) (-4118 (-12 (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-888))))) (|HasCategory| |#1| (|%list| (QUOTE -633) (QUOTE (-549)))) (|HasCategory| (-560) (QUOTE (-872))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-888)))) (|HasCategory| |#1| (QUOTE (-102)))) (-1188 S) ((|constructor| (NIL "Functions defined on streams with entries in one set.")) (|concat| (((|Stream| |#1|) (|Stream| (|Stream| |#1|))) "\\spad{concat(u)} returns the left-to-right concatentation of the streams in \\spad{u}. Note: \\spad{concat(u) = reduce(concat,u)}."))) NIL @@ -4695,11 +4695,11 @@ NIL (-1191) ((|string| (($ (|DoubleFloat|)) "\\spad{string f} returns the decimal representation of \\spad{f} in a string") (($ (|Integer|)) "\\spad{string i} returns the decimal representation of \\spad{i} in a string"))) ((-4511 . T) (-4510 . T)) -((-4144 (-12 (|HasCategory| (-146) (QUOTE (-872))) (|HasCategory| (-146) (|%list| (QUOTE -321) (QUOTE (-146))))) (-12 (|HasCategory| (-146) (QUOTE (-1133))) (|HasCategory| (-146) (|%list| (QUOTE -321) (QUOTE (-146)))))) (-4144 (|HasCategory| (-146) (|%list| (QUOTE -632) (QUOTE (-888)))) (-12 (|HasCategory| (-146) (QUOTE (-1133))) (|HasCategory| (-146) (|%list| (QUOTE -321) (QUOTE (-146)))))) (|HasCategory| (-146) (|%list| (QUOTE -633) (QUOTE (-549)))) (-4144 (|HasCategory| (-146) (QUOTE (-872))) (|HasCategory| (-146) (QUOTE (-1133)))) (|HasCategory| (-146) (QUOTE (-872))) (-4144 (|HasCategory| (-146) (QUOTE (-102))) (|HasCategory| (-146) (QUOTE (-872))) (|HasCategory| (-146) (QUOTE (-1133)))) (|HasCategory| (-560) (QUOTE (-872))) (|HasCategory| (-146) (QUOTE (-1133))) (|HasCategory| (-146) (|%list| (QUOTE -632) (QUOTE (-888)))) (|HasCategory| (-146) (QUOTE (-102))) (-12 (|HasCategory| (-146) (QUOTE (-1133))) (|HasCategory| (-146) (|%list| (QUOTE -321) (QUOTE (-146)))))) +((-4118 (-12 (|HasCategory| (-146) (QUOTE (-872))) (|HasCategory| (-146) (|%list| (QUOTE -321) (QUOTE (-146))))) (-12 (|HasCategory| (-146) (QUOTE (-1133))) (|HasCategory| (-146) (|%list| (QUOTE -321) (QUOTE (-146)))))) (-4118 (|HasCategory| (-146) (|%list| (QUOTE -632) (QUOTE (-888)))) (-12 (|HasCategory| (-146) (QUOTE (-1133))) (|HasCategory| (-146) (|%list| (QUOTE -321) (QUOTE (-146)))))) (|HasCategory| (-146) (|%list| (QUOTE -633) (QUOTE (-549)))) (-4118 (|HasCategory| (-146) (QUOTE (-872))) (|HasCategory| (-146) (QUOTE (-1133)))) (|HasCategory| (-146) (QUOTE (-872))) (-4118 (|HasCategory| (-146) (QUOTE (-102))) (|HasCategory| (-146) (QUOTE (-872))) (|HasCategory| (-146) (QUOTE (-1133)))) (|HasCategory| (-560) (QUOTE (-872))) (|HasCategory| (-146) (QUOTE (-1133))) (|HasCategory| (-146) (|%list| (QUOTE -632) (QUOTE (-888)))) (|HasCategory| (-146) (QUOTE (-102))) (-12 (|HasCategory| (-146) (QUOTE (-1133))) (|HasCategory| (-146) (|%list| (QUOTE -321) (QUOTE (-146)))))) (-1192 |Entry|) ((|constructor| (NIL "This domain provides tables where the keys are strings. A specialized hash function for strings is used."))) ((-4510 . T) (-4511 . T)) -((-12 (|HasCategory| (-2 (|:| -2118 (-1191)) (|:| -3964 |#1|)) (QUOTE (-1133))) (|HasCategory| (-2 (|:| -2118 (-1191)) (|:| -3964 |#1|)) (|%list| (QUOTE -321) (|%list| (QUOTE -2) (|%list| (QUOTE |:|) (QUOTE -2118) (QUOTE (-1191))) (|%list| (QUOTE |:|) (QUOTE -3964) (|devaluate| |#1|)))))) (-4144 (|HasCategory| (-2 (|:| -2118 (-1191)) (|:| -3964 |#1|)) (QUOTE (-1133))) (|HasCategory| |#1| (QUOTE (-1133)))) (-4144 (|HasCategory| (-2 (|:| -2118 (-1191)) (|:| -3964 |#1|)) (QUOTE (-102))) (|HasCategory| (-2 (|:| -2118 (-1191)) (|:| -3964 |#1|)) (QUOTE (-1133))) (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-1133)))) (-4144 (|HasCategory| (-2 (|:| -2118 (-1191)) (|:| -3964 |#1|)) (QUOTE (-1133))) (|HasCategory| (-2 (|:| -2118 (-1191)) (|:| -3964 |#1|)) (|%list| (QUOTE -632) (QUOTE (-888)))) (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-888))))) (|HasCategory| (-2 (|:| -2118 (-1191)) (|:| -3964 |#1|)) (|%list| (QUOTE -633) (QUOTE (-549)))) (-12 (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| (-2 (|:| -2118 (-1191)) (|:| -3964 |#1|)) (QUOTE (-1133))) (|HasCategory| (-1191) (QUOTE (-872))) (|HasCategory| |#1| (QUOTE (-1133))) (-4144 (|HasCategory| (-2 (|:| -2118 (-1191)) (|:| -3964 |#1|)) (|%list| (QUOTE -632) (QUOTE (-888)))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-888))))) (-4144 (|HasCategory| (-2 (|:| -2118 (-1191)) (|:| -3964 |#1|)) (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-102)))) (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-888)))) (|HasCategory| (-2 (|:| -2118 (-1191)) (|:| -3964 |#1|)) (|%list| (QUOTE -632) (QUOTE (-888)))) (|HasCategory| (-2 (|:| -2118 (-1191)) (|:| -3964 |#1|)) (QUOTE (-102)))) +((-12 (|HasCategory| (-2 (|:| -2115 (-1191)) (|:| -3934 |#1|)) (QUOTE (-1133))) (|HasCategory| (-2 (|:| -2115 (-1191)) (|:| -3934 |#1|)) (|%list| (QUOTE -321) (|%list| (QUOTE -2) (|%list| (QUOTE |:|) (QUOTE -2115) (QUOTE (-1191))) (|%list| (QUOTE |:|) (QUOTE -3934) (|devaluate| |#1|)))))) (-4118 (|HasCategory| (-2 (|:| -2115 (-1191)) (|:| -3934 |#1|)) (QUOTE (-1133))) (|HasCategory| |#1| (QUOTE (-1133)))) (-4118 (|HasCategory| (-2 (|:| -2115 (-1191)) (|:| -3934 |#1|)) (QUOTE (-102))) (|HasCategory| (-2 (|:| -2115 (-1191)) (|:| -3934 |#1|)) (QUOTE (-1133))) (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-1133)))) (-4118 (|HasCategory| (-2 (|:| -2115 (-1191)) (|:| -3934 |#1|)) (QUOTE (-1133))) (|HasCategory| (-2 (|:| -2115 (-1191)) (|:| -3934 |#1|)) (|%list| (QUOTE -632) (QUOTE (-888)))) (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-888))))) (|HasCategory| (-2 (|:| -2115 (-1191)) (|:| -3934 |#1|)) (|%list| (QUOTE -633) (QUOTE (-549)))) (-12 (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| (-2 (|:| -2115 (-1191)) (|:| -3934 |#1|)) (QUOTE (-1133))) (|HasCategory| (-1191) (QUOTE (-872))) (|HasCategory| |#1| (QUOTE (-1133))) (-4118 (|HasCategory| (-2 (|:| -2115 (-1191)) (|:| -3934 |#1|)) (|%list| (QUOTE -632) (QUOTE (-888)))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-888))))) (-4118 (|HasCategory| (-2 (|:| -2115 (-1191)) (|:| -3934 |#1|)) (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-102)))) (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-888)))) (|HasCategory| (-2 (|:| -2115 (-1191)) (|:| -3934 |#1|)) (|%list| (QUOTE -632) (QUOTE (-888)))) (|HasCategory| (-2 (|:| -2115 (-1191)) (|:| -3934 |#1|)) (QUOTE (-102)))) (-1193 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 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 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 @@ -4730,9 +4730,9 @@ NIL NIL (-1200 |Coef| |var| |cen|) ((|constructor| (NIL "Sparse Laurent series in one variable \\indented{2}{\\spadtype{SparseUnivariateLaurentSeries} is a domain representing Laurent} \\indented{2}{series in one variable with coefficients in an arbitrary ring.\\space{2}The} \\indented{2}{parameters of the type specify the coefficient ring,{} the power series} \\indented{2}{variable,{} and the center of the power series expansion.\\space{2}For example,{}} \\indented{2}{\\spad{SparseUnivariateLaurentSeries(Integer,x,3)} represents Laurent} \\indented{2}{series in \\spad{(x - 3)} with integer coefficients.}")) (|integrate| (($ $ (|Variable| |#2|)) "\\spad{integrate(f(x))} returns an anti-derivative of the power series \\spad{f(x)} with constant coefficient 0. 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(|sum| ((|#2| |#2| (|SegmentBinding| |#2|)) "\\spad{sum(f(n), n = a..b)} returns \\spad{f}(a) + \\spad{f}(\\spad{a+1}) + ... + \\spad{f}(\\spad{b}).") ((|#2| |#2| (|Symbol|)) "\\spad{sum(a(n), n)} returns A(\\spad{n}) such that A(\\spad{n+1}) - A(\\spad{n}) = a(\\spad{n})."))) NIL NIL @@ -4743,7 +4743,7 @@ NIL (-1203 R) ((|constructor| (NIL "This domain represents univariate polynomials over arbitrary (not necessarily commutative) coefficient rings. The variable is unspecified so that the variable displays as \\spad{?} on output. If it is necessary to specify the variable name,{} use type \\spadtype{UnivariatePolynomial}. The representation is sparse in the sense that only non-zero terms are represented.")) 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mapping from sparse univariate polynomial over \\spad{R} to a sparse univariate polynomial over \\spad{S}. Note that the mapping is assumed to send zero to zero,{} since it will only be applied to the non-zero coefficients of the polynomial.")) (|map| (((|SparseUnivariatePolynomial| |#2|) (|Mapping| |#2| |#1|) (|SparseUnivariatePolynomial| |#1|)) "\\spad{map(func, poly)} creates a new polynomial by applying \\spad{func} to every non-zero coefficient of the polynomial poly."))) NIL @@ -4755,11 +4755,11 @@ NIL (-1206 |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."))) (((-4512 "*") |has| |#1| (-175)) (-4503 |has| |#1| (-571)) (-4508 |has| |#1| (-376)) (-4502 |has| |#1| (-376)) (-4504 . T) (-4505 . T) (-4507 . T)) -((|HasCategory| |#1| (|%list| (QUOTE -38) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#1| (QUOTE (-571))) (|HasCategory| |#1| (QUOTE (-175))) (-4144 (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-571)))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-149))) (-12 (|HasCategory| |#1| (|%list| (QUOTE -928) (QUOTE (-1209)))) (|HasSignature| |#1| (|%list| (QUOTE *) (|%list| (|devaluate| |#1|) (|%list| (QUOTE -421) (QUOTE (-560))) (|devaluate| |#1|))))) (|HasSignature| |#1| (|%list| (QUOTE *) (|%list| (|devaluate| |#1|) (|%list| (QUOTE -421) (QUOTE (-560))) (|devaluate| |#1|)))) (|HasCategory| (-421 (-560)) (QUOTE (-1144))) (|HasCategory| |#1| (QUOTE (-376))) (-4144 (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (QUOTE (-571)))) (-4144 (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (QUOTE (-571)))) (-12 (|HasSignature| |#1| (|%list| (QUOTE **) (|%list| (|devaluate| |#1|) (|devaluate| |#1|) (|%list| (QUOTE -421) (QUOTE (-560)))))) (|HasSignature| |#1| (|%list| (QUOTE -3903) (|%list| (|devaluate| |#1|) (QUOTE (-1209)))))) (|HasSignature| |#1| (|%list| (QUOTE **) (|%list| (|devaluate| |#1|) (|devaluate| |#1|) (|%list| (QUOTE -421) (QUOTE (-560)))))) (-4144 (-12 (|HasCategory| |#1| (|%list| (QUOTE -29) (QUOTE (-560)))) (|HasCategory| |#1| (|%list| (QUOTE -38) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#1| (QUOTE (-990))) (|HasCategory| |#1| (QUOTE (-1235)))) (-12 (|HasCategory| |#1| (|%list| (QUOTE -38) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasSignature| |#1| (|%list| (QUOTE -2884) (|%list| (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1209))))) (|HasSignature| |#1| (|%list| (QUOTE -3648) (|%list| (|%list| (QUOTE -663) (QUOTE (-1209))) (|devaluate| |#1|))))))) +((|HasCategory| |#1| (|%list| (QUOTE -38) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#1| (QUOTE (-571))) (|HasCategory| |#1| (QUOTE (-175))) (-4118 (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-571)))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-149))) (-12 (|HasCategory| |#1| (|%list| (QUOTE -928) (QUOTE (-1209)))) (|HasSignature| |#1| (|%list| (QUOTE *) (|%list| (|devaluate| |#1|) (|%list| (QUOTE -421) (QUOTE (-560))) (|devaluate| |#1|))))) (|HasSignature| |#1| (|%list| (QUOTE *) (|%list| (|devaluate| |#1|) (|%list| (QUOTE -421) (QUOTE (-560))) (|devaluate| |#1|)))) (|HasCategory| (-421 (-560)) (QUOTE (-1144))) (|HasCategory| |#1| (QUOTE (-376))) (-4118 (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (QUOTE (-571)))) (-4118 (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (QUOTE (-571)))) (-12 (|HasSignature| |#1| (|%list| (QUOTE **) (|%list| (|devaluate| |#1|) (|devaluate| |#1|) (|%list| (QUOTE -421) (QUOTE (-560)))))) (|HasSignature| |#1| (|%list| (QUOTE -3866) (|%list| (|devaluate| |#1|) (QUOTE (-1209)))))) (|HasSignature| |#1| (|%list| (QUOTE **) (|%list| (|devaluate| |#1|) (|devaluate| |#1|) (|%list| (QUOTE -421) (QUOTE (-560)))))) (-4118 (-12 (|HasCategory| |#1| (|%list| (QUOTE -29) (QUOTE (-560)))) (|HasCategory| |#1| (|%list| (QUOTE -38) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#1| (QUOTE (-990))) (|HasCategory| |#1| (QUOTE (-1235)))) (-12 (|HasCategory| |#1| (|%list| (QUOTE -38) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasSignature| |#1| (|%list| (QUOTE -2554) (|%list| (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1209))))) (|HasSignature| |#1| (|%list| (QUOTE -3615) (|%list| (|%list| (QUOTE -663) (QUOTE (-1209))) (|devaluate| |#1|))))))) (-1207 |Coef| |var| |cen|) ((|constructor| (NIL "Sparse Taylor series in one variable \\indented{2}{\\spadtype{SparseUnivariateTaylorSeries} is a domain representing Taylor} \\indented{2}{series in one variable with coefficients in an arbitrary ring.\\space{2}The} \\indented{2}{parameters of the type specify the coefficient ring,{} the power series} \\indented{2}{variable,{} and the center of the power series expansion.\\space{2}For example,{}} \\indented{2}{\\spadtype{SparseUnivariateTaylorSeries}(Integer,{}\\spad{x},{}3) represents Taylor} \\indented{2}{series in \\spad{(x - 3)} with \\spadtype{Integer} coefficients.}")) (|integrate| (($ $ (|Variable| |#2|)) "\\spad{integrate(f(x),x)} returns an anti-derivative of the power series \\spad{f(x)} with constant coefficient 0. We may integrate a series when we can divide coefficients by integers.")) (|univariatePolynomial| (((|UnivariatePolynomial| |#2| |#1|) $ (|NonNegativeInteger|)) "\\spad{univariatePolynomial(f,k)} returns a univariate polynomial \\indented{1}{consisting of the sum of all terms of \\spad{f} of degree \\spad{<= k}.}")) (|coerce| (($ (|Variable| |#2|)) "\\spad{coerce(var)} converts the series variable \\spad{var} into a \\indented{1}{Taylor series.}") (($ (|UnivariatePolynomial| |#2| |#1|)) "\\spad{coerce(p)} converts a univariate polynomial \\spad{p} in the variable \\spad{var} to a univariate Taylor series in \\spad{var}."))) (((-4512 "*") |has| |#1| (-175)) (-4503 |has| |#1| (-571)) (-4504 . T) (-4505 . T) (-4507 . T)) -((|HasCategory| |#1| (|%list| (QUOTE -38) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#1| (QUOTE (-571))) (-4144 (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-571)))) (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-149))) (-12 (|HasCategory| |#1| (|%list| (QUOTE -928) (QUOTE (-1209)))) (|HasSignature| |#1| (|%list| (QUOTE *) (|%list| (|devaluate| |#1|) (QUOTE (-793)) (|devaluate| |#1|))))) (|HasSignature| |#1| (|%list| (QUOTE *) (|%list| (|devaluate| |#1|) (QUOTE (-793)) (|devaluate| |#1|)))) (|HasCategory| (-793) (QUOTE (-1144))) (-12 (|HasSignature| |#1| (|%list| (QUOTE **) (|%list| (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-793))))) (|HasSignature| |#1| (|%list| (QUOTE -3903) (|%list| (|devaluate| |#1|) (QUOTE (-1209)))))) (|HasSignature| |#1| (|%list| (QUOTE **) (|%list| (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-793))))) (|HasCategory| |#1| (QUOTE (-376))) (-4144 (-12 (|HasCategory| |#1| (|%list| (QUOTE -29) (QUOTE (-560)))) (|HasCategory| |#1| (|%list| (QUOTE -38) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#1| (QUOTE (-990))) (|HasCategory| |#1| (QUOTE (-1235)))) (-12 (|HasCategory| |#1| (|%list| (QUOTE -38) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasSignature| |#1| (|%list| (QUOTE -2884) (|%list| (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1209))))) (|HasSignature| |#1| (|%list| (QUOTE -3648) (|%list| (|%list| (QUOTE -663) (QUOTE (-1209))) (|devaluate| |#1|))))))) +((|HasCategory| |#1| (|%list| (QUOTE -38) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#1| (QUOTE (-571))) (-4118 (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-571)))) (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-149))) (-12 (|HasCategory| |#1| (|%list| (QUOTE -928) (QUOTE (-1209)))) (|HasSignature| |#1| (|%list| (QUOTE *) (|%list| (|devaluate| |#1|) (QUOTE (-793)) (|devaluate| |#1|))))) (|HasSignature| |#1| (|%list| (QUOTE *) (|%list| (|devaluate| |#1|) (QUOTE (-793)) (|devaluate| |#1|)))) (|HasCategory| (-793) (QUOTE (-1144))) (-12 (|HasSignature| |#1| (|%list| (QUOTE **) (|%list| (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-793))))) (|HasSignature| |#1| (|%list| (QUOTE -3866) (|%list| (|devaluate| |#1|) (QUOTE (-1209)))))) (|HasSignature| |#1| (|%list| (QUOTE **) (|%list| (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-793))))) (|HasCategory| |#1| (QUOTE (-376))) (-4118 (-12 (|HasCategory| |#1| (|%list| (QUOTE -29) (QUOTE (-560)))) (|HasCategory| |#1| (|%list| (QUOTE -38) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#1| (QUOTE (-990))) (|HasCategory| |#1| (QUOTE (-1235)))) (-12 (|HasCategory| |#1| (|%list| (QUOTE -38) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasSignature| |#1| (|%list| (QUOTE -2554) (|%list| (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1209))))) (|HasSignature| |#1| (|%list| (QUOTE -3615) (|%list| (|%list| (QUOTE -663) (QUOTE (-1209))) (|devaluate| |#1|))))))) (-1208) ((|constructor| (NIL "This domain builds representations of boolean expressions for use with the \\axiomType{FortranCode} domain.")) (NOT (($ $) "\\spad{NOT(x)} returns the \\axiomType{Switch} expression representing \\spad{\\~~x}.") (($ (|Union| (|:| I (|Expression| (|Integer|))) (|:| F (|Expression| (|Float|))) (|:| CF (|Expression| (|Complex| (|Float|)))) (|:| |switch| $))) "\\spad{NOT(x)} returns the \\axiomType{Switch} expression representing \\spad{\\~~x}.")) (AND (($ (|Union| (|:| I (|Expression| (|Integer|))) (|:| F (|Expression| (|Float|))) (|:| CF (|Expression| (|Complex| (|Float|)))) (|:| |switch| $)) (|Union| (|:| I (|Expression| (|Integer|))) (|:| F (|Expression| (|Float|))) (|:| CF (|Expression| (|Complex| (|Float|)))) (|:| |switch| $))) "\\spad{AND(x,y)} returns the \\axiomType{Switch} expression representing \\spad{x and y}.")) (EQ (($ (|Union| (|:| I (|Expression| (|Integer|))) (|:| F (|Expression| (|Float|))) (|:| CF (|Expression| (|Complex| (|Float|)))) (|:| |switch| $)) (|Union| (|:| I (|Expression| (|Integer|))) (|:| F (|Expression| (|Float|))) (|:| CF (|Expression| (|Complex| (|Float|)))) (|:| |switch| $))) "\\spad{EQ(x,y)} returns the \\axiomType{Switch} expression representing \\spad{x = y}.")) (OR (($ (|Union| (|:| I (|Expression| (|Integer|))) (|:| F (|Expression| (|Float|))) (|:| CF (|Expression| (|Complex| (|Float|)))) (|:| |switch| $)) (|Union| (|:| I (|Expression| (|Integer|))) (|:| F (|Expression| (|Float|))) (|:| CF (|Expression| (|Complex| (|Float|)))) (|:| |switch| $))) "\\spad{OR(x,y)} returns the \\axiomType{Switch} expression representing \\spad{x or y}.")) (GE (($ (|Union| (|:| I (|Expression| (|Integer|))) (|:| F (|Expression| (|Float|))) (|:| CF (|Expression| (|Complex| (|Float|)))) (|:| |switch| $)) (|Union| (|:| I (|Expression| (|Integer|))) (|:| F (|Expression| (|Float|))) (|:| CF (|Expression| (|Complex| (|Float|)))) (|:| |switch| $))) "\\spad{GE(x,y)} returns the \\axiomType{Switch} expression representing \\spad{x>=y}.")) (LE (($ (|Union| (|:| I (|Expression| (|Integer|))) (|:| F (|Expression| (|Float|))) (|:| CF (|Expression| (|Complex| (|Float|)))) (|:| |switch| $)) (|Union| (|:| I (|Expression| (|Integer|))) (|:| F (|Expression| (|Float|))) (|:| CF (|Expression| (|Complex| (|Float|)))) (|:| |switch| $))) "\\spad{LE(x,y)} returns the \\axiomType{Switch} expression representing \\spad{x<=y}.")) (GT (($ (|Union| (|:| I (|Expression| (|Integer|))) (|:| F (|Expression| (|Float|))) (|:| CF (|Expression| (|Complex| (|Float|)))) (|:| |switch| $)) (|Union| (|:| I (|Expression| (|Integer|))) (|:| F (|Expression| (|Float|))) (|:| CF (|Expression| (|Complex| (|Float|)))) (|:| |switch| $))) "\\spad{GT(x,y)} returns the \\axiomType{Switch} expression representing \\spad{x>y}.")) (LT (($ (|Union| (|:| I (|Expression| (|Integer|))) (|:| F (|Expression| (|Float|))) (|:| CF (|Expression| (|Complex| (|Float|)))) (|:| |switch| $)) (|Union| (|:| I (|Expression| (|Integer|))) (|:| F (|Expression| (|Float|))) (|:| CF (|Expression| (|Complex| (|Float|)))) (|:| |switch| $))) "\\spad{LT(x,y)} returns the \\axiomType{Switch} expression representing \\spad{x<y}.")) (|coerce| (($ (|Symbol|)) "\\spad{coerce(s)} \\undocumented{}"))) NIL @@ -4775,7 +4775,7 @@ NIL (-1211 R) ((|constructor| (NIL "This domain implements symmetric polynomial"))) (((-4512 "*") |has| |#1| (-175)) (-4503 |has| |#1| (-571)) (-4508 |has| |#1| (-6 -4508)) (-4504 . T) (-4505 . T) (-4507 . T)) -((|HasCategory| |#1| (|%list| (QUOTE -38) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#1| (QUOTE (-571))) (-4144 (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-571)))) (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-149))) (-4144 (|HasCategory| |#1| (|%list| (QUOTE -38) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#1| (|%list| (QUOTE -1070) (|%list| (QUOTE -421) (QUOTE (-560)))))) (|HasCategory| |#1| (|%list| (QUOTE -1070) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#1| (|%list| (QUOTE -1070) (QUOTE (-560)))) (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (QUOTE (-466))) (-12 (|HasCategory| (-1003) (QUOTE (-133))) (|HasCategory| |#1| (QUOTE (-571)))) (|HasAttribute| |#1| (QUOTE -4508))) +((|HasCategory| |#1| (|%list| (QUOTE -38) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#1| (QUOTE (-571))) (-4118 (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-571)))) (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-149))) (-4118 (|HasCategory| |#1| (|%list| (QUOTE -38) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#1| (|%list| (QUOTE -1070) (|%list| (QUOTE -421) (QUOTE (-560)))))) (|HasCategory| |#1| (|%list| (QUOTE -1070) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#1| (|%list| (QUOTE -1070) (QUOTE (-560)))) (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (QUOTE (-466))) (-12 (|HasCategory| (-1003) (QUOTE (-133))) (|HasCategory| |#1| (QUOTE (-571)))) (|HasAttribute| |#1| (QUOTE -4508))) (-1212) ((|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 @@ -4815,7 +4815,7 @@ NIL (-1221 |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}"))) ((-4510 . T) (-4511 . T)) -((-12 (|HasCategory| (-2 (|:| -2118 |#1|) (|:| -3964 |#2|)) (QUOTE (-1133))) (|HasCategory| (-2 (|:| -2118 |#1|) (|:| -3964 |#2|)) (|%list| (QUOTE -321) (|%list| (QUOTE -2) (|%list| (QUOTE |:|) (QUOTE -2118) (|devaluate| |#1|)) (|%list| (QUOTE |:|) (QUOTE -3964) (|devaluate| |#2|)))))) (-4144 (|HasCategory| (-2 (|:| -2118 |#1|) (|:| -3964 |#2|)) (QUOTE (-1133))) (|HasCategory| |#2| (QUOTE (-1133)))) (-4144 (|HasCategory| (-2 (|:| -2118 |#1|) (|:| -3964 |#2|)) (QUOTE (-102))) (|HasCategory| (-2 (|:| -2118 |#1|) (|:| -3964 |#2|)) (QUOTE (-1133))) (|HasCategory| |#2| (QUOTE (-102))) (|HasCategory| |#2| (QUOTE (-1133)))) (-4144 (|HasCategory| (-2 (|:| -2118 |#1|) (|:| -3964 |#2|)) (QUOTE (-1133))) (|HasCategory| (-2 (|:| -2118 |#1|) (|:| -3964 |#2|)) (|%list| (QUOTE -632) (QUOTE (-888)))) (|HasCategory| |#2| (QUOTE (-1133))) (|HasCategory| |#2| (|%list| (QUOTE -632) (QUOTE (-888))))) (|HasCategory| (-2 (|:| -2118 |#1|) (|:| -3964 |#2|)) (|%list| (QUOTE -633) (QUOTE (-549)))) (-12 (|HasCategory| |#2| (QUOTE (-1133))) (|HasCategory| |#2| (|%list| (QUOTE -321) (|devaluate| |#2|)))) (|HasCategory| (-2 (|:| -2118 |#1|) (|:| -3964 |#2|)) (QUOTE (-1133))) (|HasCategory| |#1| (QUOTE (-872))) (|HasCategory| |#2| (QUOTE (-1133))) (-4144 (|HasCategory| (-2 (|:| -2118 |#1|) (|:| -3964 |#2|)) (|%list| (QUOTE -632) (QUOTE (-888)))) (|HasCategory| |#2| (|%list| (QUOTE -632) (QUOTE (-888))))) (-4144 (|HasCategory| (-2 (|:| -2118 |#1|) (|:| -3964 |#2|)) (QUOTE (-102))) (|HasCategory| |#2| (QUOTE (-102)))) (|HasCategory| |#2| (QUOTE (-102))) (|HasCategory| |#2| (|%list| (QUOTE -632) (QUOTE (-888)))) (|HasCategory| (-2 (|:| -2118 |#1|) (|:| -3964 |#2|)) (|%list| (QUOTE -632) (QUOTE (-888)))) (|HasCategory| (-2 (|:| -2118 |#1|) (|:| -3964 |#2|)) (QUOTE (-102)))) +((-12 (|HasCategory| (-2 (|:| -2115 |#1|) (|:| -3934 |#2|)) (QUOTE (-1133))) (|HasCategory| (-2 (|:| -2115 |#1|) (|:| -3934 |#2|)) (|%list| (QUOTE -321) (|%list| (QUOTE -2) (|%list| (QUOTE |:|) (QUOTE -2115) (|devaluate| |#1|)) (|%list| (QUOTE |:|) (QUOTE -3934) (|devaluate| |#2|)))))) (-4118 (|HasCategory| (-2 (|:| -2115 |#1|) (|:| -3934 |#2|)) (QUOTE (-1133))) (|HasCategory| |#2| (QUOTE (-1133)))) (-4118 (|HasCategory| (-2 (|:| -2115 |#1|) (|:| -3934 |#2|)) (QUOTE (-102))) (|HasCategory| (-2 (|:| -2115 |#1|) (|:| -3934 |#2|)) (QUOTE (-1133))) (|HasCategory| |#2| (QUOTE (-102))) (|HasCategory| |#2| (QUOTE (-1133)))) (-4118 (|HasCategory| (-2 (|:| -2115 |#1|) (|:| -3934 |#2|)) (QUOTE (-1133))) (|HasCategory| (-2 (|:| -2115 |#1|) (|:| -3934 |#2|)) (|%list| (QUOTE -632) (QUOTE (-888)))) (|HasCategory| |#2| (QUOTE (-1133))) (|HasCategory| |#2| (|%list| (QUOTE -632) (QUOTE (-888))))) (|HasCategory| (-2 (|:| -2115 |#1|) (|:| -3934 |#2|)) (|%list| (QUOTE -633) (QUOTE (-549)))) (-12 (|HasCategory| |#2| (QUOTE (-1133))) (|HasCategory| |#2| (|%list| (QUOTE -321) (|devaluate| |#2|)))) (|HasCategory| (-2 (|:| -2115 |#1|) (|:| -3934 |#2|)) (QUOTE (-1133))) (|HasCategory| |#1| (QUOTE (-872))) (|HasCategory| |#2| (QUOTE (-1133))) (-4118 (|HasCategory| (-2 (|:| -2115 |#1|) (|:| -3934 |#2|)) (|%list| (QUOTE -632) (QUOTE (-888)))) (|HasCategory| |#2| (|%list| (QUOTE -632) (QUOTE (-888))))) (-4118 (|HasCategory| (-2 (|:| -2115 |#1|) (|:| -3934 |#2|)) (QUOTE (-102))) (|HasCategory| |#2| (QUOTE (-102)))) (|HasCategory| |#2| (QUOTE (-102))) (|HasCategory| |#2| (|%list| (QUOTE -632) (QUOTE (-888)))) (|HasCategory| (-2 (|:| -2115 |#1|) (|:| -3934 |#2|)) (|%list| (QUOTE -632) (QUOTE (-888)))) (|HasCategory| (-2 (|:| -2115 |#1|) (|:| -3934 |#2|)) (QUOTE (-102)))) (-1222 S) ((|constructor| (NIL "\\indented{1}{The tableau domain is for printing Young tableaux,{} and} coercions to and from List List \\spad{S} where \\spad{S} is a set.")) (|coerce| (((|OutputForm|) $) "\\spad{coerce(t)} converts a tableau \\spad{t} to an output form.")) (|listOfLists| (((|List| (|List| |#1|)) $) "\\spad{listOfLists t} converts a tableau \\spad{t} to a list of lists.")) (|tableau| (($ (|List| (|List| |#1|))) "\\spad{tableau(ll)} converts a list of lists \\spad{ll} to a tableau."))) NIL @@ -4875,7 +4875,7 @@ NIL (-1236 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| $)) "\\spad{tree(nd,ls)} creates a tree with value \\spad{nd},{} and children \\spad{ls}."))) ((-4511 . T) (-4510 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1133))) (-4144 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-1133)))) (-4144 (-12 (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-888))))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-888)))) (|HasCategory| |#1| (QUOTE (-102)))) +((-12 (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1133))) (-4118 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-1133)))) (-4118 (-12 (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-888))))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-888)))) (|HasCategory| |#1| (QUOTE (-102)))) (-1237 S) ((|constructor| (NIL "Category for the trigonometric functions.")) (|tan| (($ $) "\\spad{tan(x)} returns the tangent of \\spad{x}.")) (|sin| (($ $) "\\spad{sin(x)} returns the sine of \\spad{x}.")) (|sec| (($ $) "\\spad{sec(x)} returns the secant of \\spad{x}.")) (|csc| (($ $) "\\spad{csc(x)} returns the cosecant of \\spad{x}.")) (|cot| (($ $) "\\spad{cot(x)} returns the cotangent of \\spad{x}.")) (|cos| (($ $) "\\spad{cos(x)} returns the cosine of \\spad{x}."))) NIL @@ -4884,7 +4884,7 @@ NIL ((|constructor| (NIL "Category for the trigonometric functions.")) (|tan| (($ $) "\\spad{tan(x)} returns the tangent of \\spad{x}.")) (|sin| (($ $) "\\spad{sin(x)} returns the sine of \\spad{x}.")) (|sec| (($ $) "\\spad{sec(x)} returns the secant of \\spad{x}.")) (|csc| (($ $) "\\spad{csc(x)} returns the cosecant of \\spad{x}.")) (|cot| (($ $) "\\spad{cot(x)} returns the cotangent of \\spad{x}.")) (|cos| (($ $) "\\spad{cos(x)} returns the cosine of \\spad{x}."))) NIL NIL -(-1239 R -4164) +(-1239 R -4140) ((|constructor| (NIL "\\spadtype{TrigonometricManipulations} provides transformations from trigonometric functions to complex exponentials and logarithms,{} and back.")) (|complexForm| (((|Complex| |#2|) |#2|) "\\spad{complexForm(f)} returns \\spad{[real f, imag f]}.")) (|real?| (((|Boolean|) |#2|) "\\spad{real?(f)} returns \\spad{true} if \\spad{f = real f}.")) (|imag| ((|#2| |#2|) "\\spad{imag(f)} returns the imaginary part of \\spad{f} where \\spad{f} is a complex function.")) (|real| ((|#2| |#2|) "\\spad{real(f)} returns the real part of \\spad{f} where \\spad{f} is a complex function.")) (|trigs| ((|#2| |#2|) "\\spad{trigs(f)} rewrites all the complex logs and exponentials appearing in \\spad{f} in terms of trigonometric functions.")) (|complexElementary| ((|#2| |#2| (|Symbol|)) "\\spad{complexElementary(f, x)} rewrites the kernels of \\spad{f} involving \\spad{x} in terms of the 2 fundamental complex transcendental elementary functions: \\spad{log, exp}.") ((|#2| |#2|) "\\spad{complexElementary(f)} rewrites \\spad{f} in terms of the 2 fundamental complex transcendental elementary functions: \\spad{log, exp}.")) (|complexNormalize| ((|#2| |#2| (|Symbol|)) "\\spad{complexNormalize(f, x)} rewrites \\spad{f} using the least possible number of complex independent kernels involving \\spad{x}.") ((|#2| |#2|) "\\spad{complexNormalize(f)} rewrites \\spad{f} using the least possible number of complex independent kernels."))) NIL NIL @@ -4892,14 +4892,14 @@ NIL ((|constructor| (NIL "This package provides functions that compute \"fraction-free\" inverses of upper and lower triangular matrices over a integral domain. By \"fraction-free inverses\" we mean the following: given a matrix \\spad{B} with entries in \\spad{R} and an element \\spad{d} of \\spad{R} such that \\spad{d} * inv(\\spad{B}) also has entries in \\spad{R},{} we return \\spad{d} * inv(\\spad{B}). Thus,{} it is not necessary to pass to the quotient field in any of our computations.")) (|LowTriBddDenomInv| ((|#4| |#4| |#1|) "\\spad{LowTriBddDenomInv(B,d)} returns \\spad{M},{} where \\spad{B} is a non-singular lower triangular matrix and \\spad{d} is an element of \\spad{R} such that \\spad{M = d * inv(B)} has entries in \\spad{R}.")) (|UpTriBddDenomInv| ((|#4| |#4| |#1|) "\\spad{UpTriBddDenomInv(B,d)} returns \\spad{M},{} where \\spad{B} is a non-singular upper triangular matrix and \\spad{d} is an element of \\spad{R} such that \\spad{M = d * inv(B)} has entries in \\spad{R}."))) NIL NIL -(-1241 R -4164) +(-1241 R -4140) ((|constructor| (NIL "TranscendentalManipulations provides functions to simplify and expand expressions involving transcendental operators.")) (|expandTrigProducts| ((|#2| |#2|) "\\spad{expandTrigProducts(e)} replaces \\axiom{sin(\\spad{x})*sin(\\spad{y})} by \\spad{(cos(x-y)-cos(x+y))/2},{} \\axiom{cos(\\spad{x})*cos(\\spad{y})} by \\spad{(cos(x-y)+cos(x+y))/2},{} and \\axiom{sin(\\spad{x})*cos(\\spad{y})} by \\spad{(sin(x-y)+sin(x+y))/2}. Note that this operation uses the pattern matcher and so is relatively expensive. To avoid getting into an infinite loop the transformations are applied at most ten times.")) (|removeSinhSq| ((|#2| |#2|) "\\spad{removeSinhSq(f)} converts every \\spad{sinh(u)**2} appearing in \\spad{f} into \\spad{1 - cosh(x)**2},{} and also reduces higher powers of \\spad{sinh(u)} with that formula.")) (|removeCoshSq| ((|#2| |#2|) "\\spad{removeCoshSq(f)} converts every \\spad{cosh(u)**2} appearing in \\spad{f} into \\spad{1 - sinh(x)**2},{} and also reduces higher powers of \\spad{cosh(u)} with that formula.")) (|removeSinSq| ((|#2| |#2|) "\\spad{removeSinSq(f)} converts every \\spad{sin(u)**2} appearing in \\spad{f} into \\spad{1 - cos(x)**2},{} and also reduces higher powers of \\spad{sin(u)} with that formula.")) (|removeCosSq| ((|#2| |#2|) "\\spad{removeCosSq(f)} converts every \\spad{cos(u)**2} appearing in \\spad{f} into \\spad{1 - sin(x)**2},{} and also reduces higher powers of \\spad{cos(u)} with that formula.")) (|coth2tanh| ((|#2| |#2|) "\\spad{coth2tanh(f)} converts every \\spad{coth(u)} appearing in \\spad{f} into \\spad{1/tanh(u)}.")) (|cot2tan| ((|#2| |#2|) "\\spad{cot2tan(f)} converts every \\spad{cot(u)} appearing in \\spad{f} into \\spad{1/tan(u)}.")) (|tanh2coth| ((|#2| |#2|) "\\spad{tanh2coth(f)} converts every \\spad{tanh(u)} appearing in \\spad{f} into \\spad{1/coth(u)}.")) (|tan2cot| ((|#2| |#2|) "\\spad{tan2cot(f)} converts every \\spad{tan(u)} appearing in \\spad{f} into \\spad{1/cot(u)}.")) (|tanh2trigh| ((|#2| |#2|) "\\spad{tanh2trigh(f)} converts every \\spad{tanh(u)} appearing in \\spad{f} into \\spad{sinh(u)/cosh(u)}.")) (|tan2trig| ((|#2| |#2|) "\\spad{tan2trig(f)} converts every \\spad{tan(u)} appearing in \\spad{f} into \\spad{sin(u)/cos(u)}.")) (|sinh2csch| ((|#2| |#2|) "\\spad{sinh2csch(f)} converts every \\spad{sinh(u)} appearing in \\spad{f} into \\spad{1/csch(u)}.")) (|sin2csc| ((|#2| |#2|) "\\spad{sin2csc(f)} converts every \\spad{sin(u)} appearing in \\spad{f} into \\spad{1/csc(u)}.")) (|sech2cosh| ((|#2| |#2|) "\\spad{sech2cosh(f)} converts every \\spad{sech(u)} appearing in \\spad{f} into \\spad{1/cosh(u)}.")) (|sec2cos| ((|#2| |#2|) "\\spad{sec2cos(f)} converts every \\spad{sec(u)} appearing in \\spad{f} into \\spad{1/cos(u)}.")) (|csch2sinh| ((|#2| |#2|) "\\spad{csch2sinh(f)} converts every \\spad{csch(u)} appearing in \\spad{f} into \\spad{1/sinh(u)}.")) (|csc2sin| ((|#2| |#2|) "\\spad{csc2sin(f)} converts every \\spad{csc(u)} appearing in \\spad{f} into \\spad{1/sin(u)}.")) (|coth2trigh| ((|#2| |#2|) "\\spad{coth2trigh(f)} converts every \\spad{coth(u)} appearing in \\spad{f} into \\spad{cosh(u)/sinh(u)}.")) (|cot2trig| ((|#2| |#2|) "\\spad{cot2trig(f)} converts every \\spad{cot(u)} appearing in \\spad{f} into \\spad{cos(u)/sin(u)}.")) (|cosh2sech| ((|#2| |#2|) "\\spad{cosh2sech(f)} converts every \\spad{cosh(u)} appearing in \\spad{f} into \\spad{1/sech(u)}.")) (|cos2sec| ((|#2| |#2|) "\\spad{cos2sec(f)} converts every \\spad{cos(u)} appearing in \\spad{f} into \\spad{1/sec(u)}.")) (|expandLog| ((|#2| |#2|) "\\spad{expandLog(f)} converts every \\spad{log(a/b)} appearing in \\spad{f} into \\spad{log(a) - log(b)},{} and every \\spad{log(a*b)} into \\spad{log(a) + log(b)}..")) (|expandPower| ((|#2| |#2|) "\\spad{expandPower(f)} converts every power \\spad{(a/b)**c} appearing in \\spad{f} into \\spad{a**c * b**(-c)}.")) (|simplifyLog| ((|#2| |#2|) "\\spad{simplifyLog(f)} converts every \\spad{log(a) - log(b)} appearing in \\spad{f} into \\spad{log(a/b)},{} every \\spad{log(a) + log(b)} into \\spad{log(a*b)} and every \\spad{n*log(a)} into \\spad{log(a^n)}.")) (|simplifyExp| ((|#2| |#2|) "\\spad{simplifyExp(f)} converts every product \\spad{exp(a)*exp(b)} appearing in \\spad{f} into \\spad{exp(a+b)}.")) (|htrigs| ((|#2| |#2|) "\\spad{htrigs(f)} converts all the exponentials in \\spad{f} into hyperbolic sines and cosines.")) (|simplify| ((|#2| |#2|) "\\spad{simplify(f)} performs the following simplifications on f:\\begin{items} \\item 1. rewrites trigs and hyperbolic trigs in terms of \\spad{sin} ,{}\\spad{cos},{} \\spad{sinh},{} \\spad{cosh}. \\item 2. rewrites \\spad{sin**2} and \\spad{sinh**2} in terms of \\spad{cos} and \\spad{cosh},{} \\item 3. rewrites \\spad{exp(a)*exp(b)} as \\spad{exp(a+b)}. \\item 4. rewrites \\spad{(a**(1/n))**m * (a**(1/s))**t} as a single power of a single radical of \\spad{a}. \\end{items}")) (|expand| ((|#2| |#2|) "\\spad{expand(f)} performs the following expansions on f:\\begin{items} \\item 1. logs of products are expanded into sums of logs,{} \\item 2. trigonometric and hyperbolic trigonometric functions of sums are expanded into sums of products of trigonometric and hyperbolic trigonometric functions. \\item 3. formal powers of the form \\spad{(a/b)**c} are expanded into \\spad{a**c * b**(-c)}. \\end{items}"))) NIL ((-12 (|HasCategory| |#1| (|%list| (QUOTE -633) (|%list| (QUOTE -916) (|devaluate| |#1|)))) (|HasCategory| |#1| (|%list| (QUOTE -912) (|devaluate| |#1|))) (|HasCategory| |#2| (|%list| (QUOTE -633) (|%list| (QUOTE -916) (|devaluate| |#1|)))) (|HasCategory| |#2| (|%list| (QUOTE -912) (|devaluate| |#1|))))) (-1242 |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}."))) (((-4512 "*") |has| |#1| (-175)) (-4503 |has| |#1| (-571)) (-4505 . T) (-4504 . T) (-4507 . T)) -((|HasCategory| |#1| (|%list| (QUOTE -38) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-149))) (|HasCategory| |#1| (QUOTE (-147))) (-4144 (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-571)))) (|HasCategory| |#1| (QUOTE (-571))) (|HasCategory| |#1| (QUOTE (-376)))) +((|HasCategory| |#1| (|%list| (QUOTE -38) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-149))) (|HasCategory| |#1| (QUOTE (-147))) (-4118 (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-571)))) (|HasCategory| |#1| (QUOTE (-571))) (|HasCategory| |#1| (QUOTE (-376)))) (-1243 S R E V P) ((|constructor| (NIL "The category of triangular sets of multivariate polynomials with coefficients in an integral domain. Let \\axiom{\\spad{R}} be an integral domain and \\axiom{\\spad{V}} a finite ordered set of variables,{} say \\axiom{\\spad{X1} < \\spad{X2} < ... < Xn}. A set \\axiom{\\spad{S}} of polynomials in \\axiom{\\spad{R}[\\spad{X1},{}\\spad{X2},{}...,{}Xn]} is triangular if no elements of \\axiom{\\spad{S}} lies in \\axiom{\\spad{R}},{} and if two distinct elements of \\axiom{\\spad{S}} have distinct main variables. Note that the empty set is a triangular set. A triangular set is not necessarily a (lexicographical) Groebner basis and the notion of reduction related to triangular sets is based on the recursive view of polynomials. We recall this notion here and refer to [1] for more details. A polynomial \\axiom{\\spad{P}} is reduced \\spad{w}.\\spad{r}.\\spad{t} a non-constant polynomial \\axiom{\\spad{Q}} if the degree of \\axiom{\\spad{P}} in the main variable of \\axiom{\\spad{Q}} is less than the main degree of \\axiom{\\spad{Q}}. A polynomial \\axiom{\\spad{P}} is reduced \\spad{w}.\\spad{r}.\\spad{t} a triangular set \\axiom{\\spad{T}} if it is reduced \\spad{w}.\\spad{r}.\\spad{t}. every polynomial of \\axiom{\\spad{T}}. \\newline References : \\indented{1}{[1] \\spad{P}. AUBRY,{} \\spad{D}. LAZARD and \\spad{M}. MORENO MAZA \"On the Theories} \\indented{5}{of Triangular Sets\" Journal of Symbol. Comp. (to appear)}")) (|coHeight| (((|NonNegativeInteger|) $) "\\axiom{coHeight(ts)} returns \\axiom{size()\\$\\spad{V}} minus \\axiom{\\#ts}.")) (|extend| (($ $ |#5|) "\\axiom{extend(ts,{}\\spad{p})} returns a triangular set which encodes the simple extension by \\axiom{\\spad{p}} of the extension of the base field defined by \\axiom{ts},{} according to the properties of triangular sets of the current category If the required properties do not hold an error is returned.")) (|extendIfCan| (((|Union| $ "failed") $ |#5|) "\\axiom{extendIfCan(ts,{}\\spad{p})} returns a triangular set which encodes the simple extension by \\axiom{\\spad{p}} of the extension of the base field defined by \\axiom{ts},{} according to the properties of triangular sets of the current domain. If the required properties do not hold then \"failed\" is returned. This operation encodes in some sense the properties of the triangular sets of the current category. Is is used to implement the \\axiom{construct} operation to guarantee that every triangular set build from a list of polynomials has the required properties.")) (|select| (((|Union| |#5| "failed") $ |#4|) "\\axiom{select(ts,{}\\spad{v})} returns the polynomial of \\axiom{ts} with \\axiom{\\spad{v}} as main variable,{} if any.")) (|algebraic?| (((|Boolean|) |#4| $) "\\axiom{algebraic?(\\spad{v},{}ts)} returns \\spad{true} iff \\axiom{\\spad{v}} is the main variable of some polynomial in \\axiom{ts}.")) (|algebraicVariables| (((|List| |#4|) $) "\\axiom{algebraicVariables(ts)} returns the decreasingly sorted list of the main variables of the polynomials of \\axiom{ts}.")) (|rest| (((|Union| $ "failed") $) "\\axiom{rest(ts)} returns the polynomials of \\axiom{ts} with smaller main variable than \\axiom{mvar(ts)} if \\axiom{ts} is not empty,{} otherwise returns \"failed\"")) (|last| (((|Union| |#5| "failed") $) "\\axiom{last(ts)} returns the polynomial of \\axiom{ts} with smallest main variable if \\axiom{ts} is not empty,{} otherwise returns \\axiom{\"failed\"}.")) (|first| (((|Union| |#5| "failed") $) "\\axiom{first(ts)} returns the polynomial of \\axiom{ts} with greatest main variable if \\axiom{ts} is not empty,{} otherwise returns \\axiom{\"failed\"}.")) (|zeroSetSplitIntoTriangularSystems| (((|List| (|Record| (|:| |close| $) (|:| |open| (|List| |#5|)))) (|List| |#5|)) "\\axiom{zeroSetSplitIntoTriangularSystems(lp)} returns a list of triangular systems \\axiom{[[\\spad{ts1},{}\\spad{qs1}],{}...,{}[tsn,{}qsn]]} such that the zero set of \\axiom{lp} is the union of the closures of the \\axiom{W_i} where \\axiom{W_i} consists of the zeros of \\axiom{ts} which do not cancel any polynomial in \\axiom{qsi}.")) (|zeroSetSplit| (((|List| $) (|List| |#5|)) "\\axiom{zeroSetSplit(lp)} returns a list \\axiom{lts} of triangular sets such that the zero set of \\axiom{lp} is the union of the closures of the regular zero sets of the members of \\axiom{lts}.")) (|reduceByQuasiMonic| ((|#5| |#5| $) "\\axiom{reduceByQuasiMonic(\\spad{p},{}ts)} returns the same as \\axiom{remainder(\\spad{p},{}collectQuasiMonic(ts)).polnum}.")) (|collectQuasiMonic| (($ $) "\\axiom{collectQuasiMonic(ts)} returns the subset of \\axiom{ts} consisting of the polynomials with initial in \\axiom{\\spad{R}}.")) (|removeZero| ((|#5| |#5| $) "\\axiom{removeZero(\\spad{p},{}ts)} returns \\axiom{0} if \\axiom{\\spad{p}} reduces to \\axiom{0} by pseudo-division \\spad{w}.\\spad{r}.\\spad{t} \\axiom{ts} otherwise returns a polynomial \\axiom{\\spad{q}} computed from \\axiom{\\spad{p}} by removing any coefficient in \\axiom{\\spad{p}} reducing to \\axiom{0}.")) (|initiallyReduce| ((|#5| |#5| $) "\\axiom{initiallyReduce(\\spad{p},{}ts)} returns a polynomial \\axiom{\\spad{r}} such that \\axiom{initiallyReduced?(\\spad{r},{}ts)} holds and there exists some product \\axiom{\\spad{h}} of \\axiom{initials(ts)} such that \\axiom{h*p - \\spad{r}} lies in the ideal generated by \\axiom{ts}.")) (|headReduce| ((|#5| |#5| $) "\\axiom{headReduce(\\spad{p},{}ts)} returns a polynomial \\axiom{\\spad{r}} such that \\axiom{headReduce?(\\spad{r},{}ts)} holds and there exists some product \\axiom{\\spad{h}} of \\axiom{initials(ts)} such that \\axiom{h*p - \\spad{r}} lies in the ideal generated by \\axiom{ts}.")) (|stronglyReduce| ((|#5| |#5| $) "\\axiom{stronglyReduce(\\spad{p},{}ts)} returns a polynomial \\axiom{\\spad{r}} such that \\axiom{stronglyReduced?(\\spad{r},{}ts)} holds and there exists some product \\axiom{\\spad{h}} of \\axiom{initials(ts)} such that \\axiom{h*p - \\spad{r}} lies in the ideal generated by \\axiom{ts}.")) (|rewriteSetWithReduction| (((|List| |#5|) (|List| |#5|) $ (|Mapping| |#5| |#5| |#5|) (|Mapping| (|Boolean|) |#5| |#5|)) "\\axiom{rewriteSetWithReduction(lp,{}ts,{}redOp,{}redOp?)} returns a list \\axiom{lq} of polynomials such that \\axiom{[reduce(\\spad{p},{}ts,{}redOp,{}redOp?) for \\spad{p} in lp]} and \\axiom{lp} have the same zeros inside the regular zero set of \\axiom{ts}. Moreover,{} for every polynomial \\axiom{\\spad{q}} in \\axiom{lq} and every polynomial \\axiom{\\spad{t}} in \\axiom{ts} \\axiom{redOp?(\\spad{q},{}\\spad{t})} holds and there exists a polynomial \\axiom{\\spad{p}} in the ideal generated by \\axiom{lp} and a product \\axiom{\\spad{h}} of \\axiom{initials(ts)} such that \\axiom{h*p - \\spad{r}} lies in the ideal generated by \\axiom{ts}. The operation \\axiom{redOp} must satisfy the following conditions. For every \\axiom{\\spad{p}} and \\axiom{\\spad{q}} we have \\axiom{redOp?(redOp(\\spad{p},{}\\spad{q}),{}\\spad{q})} and there exists an integer \\axiom{\\spad{e}} and a polynomial \\axiom{\\spad{f}} such that \\axiom{init(\\spad{q})^e*p = f*q + redOp(\\spad{p},{}\\spad{q})}.")) (|reduce| ((|#5| |#5| $ (|Mapping| |#5| |#5| |#5|) (|Mapping| (|Boolean|) |#5| |#5|)) "\\axiom{reduce(\\spad{p},{}ts,{}redOp,{}redOp?)} returns a polynomial \\axiom{\\spad{r}} such that \\axiom{redOp?(\\spad{r},{}\\spad{p})} holds for every \\axiom{\\spad{p}} of \\axiom{ts} and there exists some product \\axiom{\\spad{h}} of the initials of the members of \\axiom{ts} such that \\axiom{h*p - \\spad{r}} lies in the ideal generated by \\axiom{ts}. The operation \\axiom{redOp} must satisfy the following conditions. For every \\axiom{\\spad{p}} and \\axiom{\\spad{q}} we have \\axiom{redOp?(redOp(\\spad{p},{}\\spad{q}),{}\\spad{q})} and there exists an integer \\axiom{\\spad{e}} and a polynomial \\axiom{\\spad{f}} such that \\axiom{init(\\spad{q})^e*p = f*q + redOp(\\spad{p},{}\\spad{q})}.")) (|autoReduced?| (((|Boolean|) $ (|Mapping| (|Boolean|) |#5| (|List| |#5|))) "\\axiom{autoReduced?(ts,{}redOp?)} returns \\spad{true} iff every element of \\axiom{ts} is reduced \\spad{w}.\\spad{r}.\\spad{t} to every other in the sense of \\axiom{redOp?}")) (|initiallyReduced?| (((|Boolean|) $) "\\spad{initiallyReduced?(ts)} returns \\spad{true} iff for every element \\axiom{\\spad{p}} of \\axiom{\\spad{ts}} \\axiom{\\spad{p}} and all its iterated initials are reduced \\spad{w}.\\spad{r}.\\spad{t}. to the other elements of \\axiom{\\spad{ts}} with the same main variable.") (((|Boolean|) |#5| $) "\\axiom{initiallyReduced?(\\spad{p},{}ts)} returns \\spad{true} iff \\axiom{\\spad{p}} and all its iterated initials are reduced \\spad{w}.\\spad{r}.\\spad{t}. to the elements of \\axiom{ts} with the same main variable.")) (|headReduced?| (((|Boolean|) $) "\\spad{headReduced?(ts)} returns \\spad{true} iff the head of every element of \\axiom{\\spad{ts}} is reduced \\spad{w}.\\spad{r}.\\spad{t} to any other element of \\axiom{\\spad{ts}}.") (((|Boolean|) |#5| $) "\\axiom{headReduced?(\\spad{p},{}ts)} returns \\spad{true} iff the head of \\axiom{\\spad{p}} is reduced \\spad{w}.\\spad{r}.\\spad{t}. \\axiom{ts}.")) (|stronglyReduced?| (((|Boolean|) $) "\\axiom{stronglyReduced?(ts)} returns \\spad{true} iff every element of \\axiom{ts} is reduced \\spad{w}.\\spad{r}.\\spad{t} to any other element of \\axiom{ts}.") (((|Boolean|) |#5| $) "\\axiom{stronglyReduced?(\\spad{p},{}ts)} returns \\spad{true} iff \\axiom{\\spad{p}} is reduced \\spad{w}.\\spad{r}.\\spad{t}. \\axiom{ts}.")) (|reduced?| (((|Boolean|) |#5| $ (|Mapping| (|Boolean|) |#5| |#5|)) "\\axiom{reduced?(\\spad{p},{}ts,{}redOp?)} returns \\spad{true} iff \\axiom{\\spad{p}} is reduced \\spad{w}.\\spad{r}.\\spad{t}. in the sense of the operation \\axiom{redOp?},{} that is if for every \\axiom{\\spad{t}} in \\axiom{ts} \\axiom{redOp?(\\spad{p},{}\\spad{t})} holds.")) (|normalized?| (((|Boolean|) $) "\\axiom{normalized?(ts)} returns \\spad{true} iff for every axiom{\\spad{p}} in axiom{ts} we have \\axiom{normalized?(\\spad{p},{}us)} where \\axiom{us} is \\axiom{collectUnder(ts,{}mvar(\\spad{p}))}.") (((|Boolean|) |#5| $) "\\axiom{normalized?(\\spad{p},{}ts)} returns \\spad{true} iff \\axiom{\\spad{p}} and all its iterated initials have degree zero \\spad{w}.\\spad{r}.\\spad{t}. the main variables of the polynomials of \\axiom{ts}")) (|quasiComponent| (((|Record| (|:| |close| (|List| |#5|)) (|:| |open| (|List| |#5|))) $) "\\axiom{quasiComponent(ts)} returns \\axiom{[lp,{}lq]} where \\axiom{lp} is the list of the members of \\axiom{ts} and \\axiom{lq}is \\axiom{initials(ts)}.")) (|degree| (((|NonNegativeInteger|) $) "\\axiom{degree(ts)} returns the product of main degrees of the members of \\axiom{ts}.")) (|initials| (((|List| |#5|) $) "\\axiom{initials(ts)} returns the list of the non-constant initials of the members of \\axiom{ts}.")) (|basicSet| (((|Union| (|Record| (|:| |bas| $) (|:| |top| (|List| |#5|))) "failed") (|List| |#5|) (|Mapping| (|Boolean|) |#5|) (|Mapping| (|Boolean|) |#5| |#5|)) "\\axiom{basicSet(ps,{}pred?,{}redOp?)} returns the same as \\axiom{basicSet(qs,{}redOp?)} where \\axiom{qs} consists of the polynomials of \\axiom{ps} satisfying property \\axiom{pred?}.") (((|Union| (|Record| (|:| |bas| $) (|:| |top| (|List| |#5|))) "failed") (|List| |#5|) (|Mapping| (|Boolean|) |#5| |#5|)) "\\axiom{basicSet(ps,{}redOp?)} returns \\axiom{[bs,{}ts]} where \\axiom{concat(bs,{}ts)} is \\axiom{ps} and \\axiom{bs} is a basic set in Wu Wen Tsun sense of \\axiom{ps} \\spad{w}.\\spad{r}.\\spad{t} the reduction-test \\axiom{redOp?},{} if no non-zero constant polynomial lie in \\axiom{ps},{} otherwise \\axiom{\"failed\"} is returned.")) (|infRittWu?| (((|Boolean|) $ $) "\\axiom{infRittWu?(\\spad{ts1},{}\\spad{ts2})} returns \\spad{true} iff \\axiom{\\spad{ts2}} has higher rank than \\axiom{\\spad{ts1}} in Wu Wen Tsun sense."))) NIL @@ -4920,7 +4920,7 @@ NIL ((|constructor| (NIL "\\indented{1}{This domain is used to interface with the interpreter's notion} of comma-delimited sequences of values.")) (|length| (((|NonNegativeInteger|) $) "\\spad{length(x)} returns the number of elements in tuple \\spad{x}")) (|select| ((|#1| $ (|NonNegativeInteger|)) "\\spad{select(x,n)} returns the \\spad{n}-th element of tuple \\spad{x}. tuples are 0-based"))) NIL ((|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-888))))) -(-1248 -4164) +(-1248 -4140) ((|constructor| (NIL "A basic package for the factorization of bivariate polynomials over a finite field. The functions here represent the base step for the multivariate factorizer.")) (|twoFactor| (((|Factored| (|SparseUnivariatePolynomial| (|SparseUnivariatePolynomial| |#1|))) (|SparseUnivariatePolynomial| (|SparseUnivariatePolynomial| |#1|)) (|Integer|)) "\\spad{twoFactor(p,n)} returns the factorisation of polynomial \\spad{p},{} a sparse univariate polynomial (sup) over a sup over \\spad{F}. Also,{} \\spad{p} is assumed primitive and square-free and \\spad{n} is the degree of the inner variable of \\spad{p} (maximum of the degrees of the coefficients of \\spad{p}).")) (|generalSqFr| (((|Factored| (|SparseUnivariatePolynomial| (|SparseUnivariatePolynomial| |#1|))) (|SparseUnivariatePolynomial| (|SparseUnivariatePolynomial| |#1|))) "\\spad{generalSqFr(p)} returns the square-free factorisation of polynomial \\spad{p},{} a sparse univariate polynomial (sup) over a sup over \\spad{F}.")) (|generalTwoFactor| (((|Factored| (|SparseUnivariatePolynomial| (|SparseUnivariatePolynomial| |#1|))) (|SparseUnivariatePolynomial| (|SparseUnivariatePolynomial| |#1|))) "\\spad{generalTwoFactor(p)} returns the factorisation of polynomial \\spad{p},{} a sparse univariate polynomial (sup) over a sup over \\spad{F}."))) NIL NIL @@ -4966,8 +4966,8 @@ NIL NIL (-1259 |Coef| |var| |cen|) ((|constructor| (NIL "Dense Laurent series in one variable \\indented{2}{\\spadtype{UnivariateLaurentSeries} is a domain representing Laurent} \\indented{2}{series in one variable with coefficients in an arbitrary ring.\\space{2}The} \\indented{2}{parameters of the type specify the coefficient ring,{} the power series} \\indented{2}{variable,{} and the center of the power series expansion.\\space{2}For example,{}} \\indented{2}{\\spad{UnivariateLaurentSeries(Integer,x,3)} represents Laurent series in} \\indented{2}{\\spad{(x - 3)} with integer coefficients.}")) (|integrate| (($ $ (|Variable| |#2|)) "\\spad{integrate(f(x))} returns an anti-derivative of the power series \\spad{f(x)} with constant coefficient 0. We may integrate a series when we can divide coefficients by integers.")) 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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 @@ -5003,7 +5003,7 @@ NIL (-1268 |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}"))) (((-4512 "*") |has| |#2| (-175)) (-4503 |has| |#2| (-571)) (-4506 |has| |#2| (-376)) (-4508 |has| |#2| (-6 -4508)) (-4505 . T) (-4504 . T) (-4507 . T)) -((|HasCategory| |#2| (QUOTE (-940))) (|HasCategory| |#2| (QUOTE (-571))) (|HasCategory| |#2| (QUOTE (-175))) (-4144 (|HasCategory| |#2| (QUOTE (-175))) (|HasCategory| |#2| (QUOTE (-571)))) (-12 (|HasCategory| (-1114) (|%list| (QUOTE -912) (QUOTE (-391)))) (|HasCategory| |#2| (|%list| (QUOTE -912) (QUOTE (-391))))) (-12 (|HasCategory| (-1114) (|%list| (QUOTE -912) (QUOTE (-560)))) (|HasCategory| |#2| (|%list| (QUOTE -912) (QUOTE (-560))))) (-12 (|HasCategory| (-1114) (|%list| (QUOTE -633) (|%list| (QUOTE -916) (QUOTE (-391))))) (|HasCategory| |#2| (|%list| (QUOTE -633) (|%list| (QUOTE -916) (QUOTE (-391)))))) (-12 (|HasCategory| (-1114) (|%list| (QUOTE -633) (|%list| (QUOTE -916) (QUOTE (-560))))) (|HasCategory| |#2| (|%list| (QUOTE -633) (|%list| (QUOTE -916) (QUOTE (-560)))))) (-12 (|HasCategory| (-1114) (|%list| (QUOTE -633) (QUOTE (-549)))) (|HasCategory| |#2| (|%list| (QUOTE -633) (QUOTE (-549))))) (|HasCategory| |#2| (|%list| (QUOTE -660) (QUOTE (-560)))) (|HasCategory| |#2| 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(-466))) (|HasCategory| |#2| (QUOTE (-571))) (|HasCategory| |#2| (QUOTE (-940)))) (-4118 (|HasCategory| |#2| (QUOTE (-376))) (|HasCategory| |#2| (QUOTE (-466))) (|HasCategory| |#2| (QUOTE (-571))) (|HasCategory| |#2| (QUOTE (-940)))) (-4118 (|HasCategory| |#2| (QUOTE (-376))) (|HasCategory| |#2| (QUOTE (-466))) (|HasCategory| |#2| (QUOTE (-940)))) (|HasCategory| |#2| (QUOTE (-376))) (|HasCategory| |#2| (QUOTE (-1184))) (|HasCategory| |#2| (|%list| (QUOTE -930) (QUOTE (-1209)))) (|HasCategory| |#2| (|%list| (QUOTE -928) (QUOTE (-1209)))) (|HasCategory| |#2| (QUOTE (-239))) (|HasCategory| |#2| (QUOTE (-240))) (|HasAttribute| |#2| (QUOTE -4508)) (|HasCategory| |#2| (QUOTE (-466))) (-12 (|HasCategory| $ (QUOTE (-147))) (|HasCategory| |#2| (QUOTE (-940)))) (-4118 (-12 (|HasCategory| $ (QUOTE (-147))) (|HasCategory| |#2| (QUOTE (-940)))) (|HasCategory| |#2| (QUOTE (-147))))) (-1269 |x| R |y| S) ((|constructor| (NIL "This package lifts a mapping from coefficient rings \\spad{R} to \\spad{S} to a mapping from \\spadtype{UnivariatePolynomial}(\\spad{x},{}\\spad{R}) to \\spadtype{UnivariatePolynomial}(\\spad{y},{}\\spad{S}). Note that the mapping is assumed to send zero to zero,{} since it will only be applied to the non-zero coefficients of the polynomial.")) (|map| (((|UnivariatePolynomial| |#3| |#4|) (|Mapping| |#4| |#2|) (|UnivariatePolynomial| |#1| |#2|)) "\\spad{map(func, poly)} creates a new polynomial by applying \\spad{func} to every non-zero coefficient of the polynomial poly."))) NIL @@ -5039,7 +5039,7 @@ NIL (-1277 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{n} to be computed.")) (|approximate| ((|#2| $ |#3|) "\\spad{approximate(f)} returns a truncated power series with the series variable viewed as an element of the coefficient domain.")) (|truncate| (($ $ |#3| |#3|) "\\spad{truncate(f,k1,k2)} returns a (finite) power series consisting of the sum of all terms of \\spad{f} of degree \\spad{d} with \\spad{k1 <= d <= k2}.") (($ $ |#3|) "\\spad{truncate(f,k)} returns a (finite) power series consisting of the sum of all terms of \\spad{f} of degree \\spad{<= k}.")) (|order| ((|#3| $ |#3|) "\\spad{order(f,n) = min(m,n)},{} where \\spad{m} is the degree of the lowest order non-zero term in \\spad{f}.") ((|#3| $) "\\spad{order(f)} is the degree of the lowest order non-zero term in \\spad{f}. This will result in an infinite loop if \\spad{f} has no non-zero terms.")) (|multiplyExponents| (($ $ (|PositiveInteger|)) "\\spad{multiplyExponents(f,n)} multiplies all exponents of the power series \\spad{f} by the positive integer \\spad{n}.")) (|center| ((|#2| $) "\\spad{center(f)} returns the point about which the series \\spad{f} is expanded.")) (|variable| (((|Symbol|) $) "\\spad{variable(f)} returns the (unique) power series variable of the power series \\spad{f}.")) (|terms| (((|Stream| (|Record| (|:| |k| |#3|) (|:| |c| |#2|))) $) "\\spad{terms(f(x))} returns a stream of non-zero terms,{} where a a term is an exponent-coefficient pair. The terms in the stream are ordered by increasing order of exponents."))) NIL -((|HasCategory| |#2| (|%list| (QUOTE -928) (QUOTE (-1209)))) (|HasSignature| |#2| (|%list| (QUOTE *) (|%list| (|devaluate| |#2|) (|devaluate| |#3|) (|devaluate| |#2|)))) (|HasCategory| |#3| (QUOTE (-1144))) (|HasSignature| |#2| (|%list| (QUOTE **) (|%list| (|devaluate| |#2|) (|devaluate| |#2|) (|devaluate| |#3|)))) (|HasSignature| |#2| (|%list| (QUOTE -3903) (|%list| (|devaluate| |#2|) (QUOTE (-1209)))))) +((|HasCategory| |#2| (|%list| (QUOTE -928) (QUOTE (-1209)))) (|HasSignature| |#2| (|%list| (QUOTE *) (|%list| (|devaluate| |#2|) (|devaluate| |#3|) (|devaluate| |#2|)))) (|HasCategory| |#3| (QUOTE (-1144))) (|HasSignature| |#2| (|%list| (QUOTE **) (|%list| (|devaluate| |#2|) (|devaluate| |#2|) (|devaluate| |#3|)))) (|HasSignature| |#2| (|%list| (QUOTE -3866) (|%list| (|devaluate| |#2|) (QUOTE (-1209)))))) (-1278 |Coef| |Expon|) ((|constructor| (NIL "\\spadtype{UnivariatePowerSeriesCategory} is the most general univariate power series category with exponents in an ordered abelian monoid. Note: this category exports a substitution function if it is possible to multiply exponents. Note: this category exports a derivative operation if it is possible to multiply coefficients by exponents.")) (|eval| (((|Stream| |#1|) $ |#1|) "\\spad{eval(f,a)} evaluates a power series at a value in the ground ring by returning a stream of partial sums.")) (|extend| (($ $ |#2|) "\\spad{extend(f,n)} causes all terms of \\spad{f} of degree <= \\spad{n} to be computed.")) (|approximate| ((|#1| $ |#2|) "\\spad{approximate(f)} returns a truncated power series with the series variable viewed as an element of the coefficient domain.")) (|truncate| (($ $ |#2| |#2|) "\\spad{truncate(f,k1,k2)} returns a (finite) power series consisting of the sum of all terms of \\spad{f} of degree \\spad{d} with \\spad{k1 <= d <= k2}.") (($ $ |#2|) "\\spad{truncate(f,k)} returns a (finite) power series consisting of the sum of all terms of \\spad{f} of degree \\spad{<= k}.")) (|order| ((|#2| $ |#2|) "\\spad{order(f,n) = min(m,n)},{} where \\spad{m} is the degree of the lowest order non-zero term in \\spad{f}.") ((|#2| $) "\\spad{order(f)} is the degree of the lowest order non-zero term in \\spad{f}. This will result in an infinite loop if \\spad{f} has no non-zero terms.")) (|multiplyExponents| (($ $ (|PositiveInteger|)) "\\spad{multiplyExponents(f,n)} multiplies all exponents of the power series \\spad{f} by the positive integer \\spad{n}.")) (|center| ((|#1| $) "\\spad{center(f)} returns the point about which the series \\spad{f} is expanded.")) (|variable| (((|Symbol|) $) "\\spad{variable(f)} returns the (unique) power series variable of the power series \\spad{f}.")) (|terms| (((|Stream| (|Record| (|:| |k| |#2|) (|:| |c| |#1|))) $) "\\spad{terms(f(x))} returns a stream of non-zero terms,{} where a a term is an exponent-coefficient pair. The terms in the stream are ordered by increasing order of exponents."))) (((-4512 "*") |has| |#1| (-175)) (-4503 |has| |#1| (-571)) (-4504 . T) (-4505 . T) (-4507 . T)) @@ -5051,7 +5051,7 @@ NIL (-1280 |Coef| |var| |cen|) ((|constructor| (NIL "Dense Puiseux series in one variable \\indented{2}{\\spadtype{UnivariatePuiseuxSeries} is a domain representing Puiseux} \\indented{2}{series in one variable with coefficients in an arbitrary ring.\\space{2}The} \\indented{2}{parameters of the type specify the coefficient ring,{} the power series} \\indented{2}{variable,{} and the center of the power series expansion.\\space{2}For example,{}} \\indented{2}{\\spad{UnivariatePuiseuxSeries(Integer,x,3)} represents Puiseux series in} \\indented{2}{\\spad{(x - 3)} with \\spadtype{Integer} coefficients.}")) (|integrate| (($ $ (|Variable| |#2|)) "\\spad{integrate(f(x))} returns an anti-derivative of the power series \\spad{f(x)} with constant coefficient 0. We may integrate a series when we can divide coefficients by integers."))) (((-4512 "*") |has| |#1| (-175)) (-4503 |has| |#1| (-571)) (-4508 |has| |#1| (-376)) (-4502 |has| |#1| (-376)) (-4504 . T) (-4505 . T) (-4507 . T)) -((|HasCategory| |#1| (|%list| (QUOTE -38) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#1| (QUOTE (-571))) (|HasCategory| |#1| (QUOTE (-175))) (-4144 (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-571)))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-149))) (-12 (|HasCategory| |#1| (|%list| (QUOTE -928) (QUOTE (-1209)))) (|HasSignature| |#1| (|%list| (QUOTE *) (|%list| (|devaluate| |#1|) (|%list| (QUOTE -421) (QUOTE (-560))) (|devaluate| |#1|))))) (|HasSignature| |#1| (|%list| (QUOTE *) (|%list| (|devaluate| |#1|) (|%list| (QUOTE -421) (QUOTE (-560))) (|devaluate| |#1|)))) (|HasCategory| (-421 (-560)) (QUOTE (-1144))) (|HasCategory| |#1| (QUOTE (-376))) (-4144 (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (QUOTE (-571)))) (-4144 (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (QUOTE (-571)))) (-12 (|HasSignature| |#1| (|%list| (QUOTE **) (|%list| (|devaluate| |#1|) (|devaluate| |#1|) (|%list| (QUOTE -421) (QUOTE (-560)))))) (|HasSignature| |#1| (|%list| (QUOTE -3903) (|%list| (|devaluate| |#1|) (QUOTE (-1209)))))) (|HasSignature| |#1| (|%list| (QUOTE **) (|%list| (|devaluate| |#1|) (|devaluate| |#1|) (|%list| (QUOTE -421) (QUOTE (-560)))))) (-4144 (-12 (|HasCategory| |#1| (|%list| (QUOTE -29) (QUOTE (-560)))) (|HasCategory| |#1| (|%list| (QUOTE -38) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#1| (QUOTE (-990))) (|HasCategory| |#1| (QUOTE (-1235)))) (-12 (|HasCategory| |#1| (|%list| (QUOTE -38) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasSignature| |#1| (|%list| (QUOTE -2884) (|%list| (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1209))))) (|HasSignature| |#1| (|%list| (QUOTE -3648) (|%list| (|%list| (QUOTE -663) (QUOTE (-1209))) (|devaluate| |#1|))))))) +((|HasCategory| |#1| (|%list| (QUOTE -38) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#1| (QUOTE (-571))) (|HasCategory| |#1| (QUOTE (-175))) (-4118 (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-571)))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-149))) (-12 (|HasCategory| |#1| (|%list| (QUOTE -928) (QUOTE (-1209)))) (|HasSignature| |#1| (|%list| (QUOTE *) (|%list| (|devaluate| |#1|) (|%list| (QUOTE -421) (QUOTE (-560))) (|devaluate| |#1|))))) (|HasSignature| |#1| (|%list| (QUOTE *) (|%list| (|devaluate| |#1|) (|%list| (QUOTE -421) (QUOTE (-560))) (|devaluate| |#1|)))) (|HasCategory| (-421 (-560)) (QUOTE (-1144))) (|HasCategory| |#1| (QUOTE (-376))) (-4118 (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (QUOTE (-571)))) (-4118 (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (QUOTE (-571)))) (-12 (|HasSignature| |#1| (|%list| (QUOTE **) (|%list| (|devaluate| |#1|) (|devaluate| |#1|) (|%list| (QUOTE -421) (QUOTE (-560)))))) (|HasSignature| |#1| (|%list| (QUOTE -3866) (|%list| (|devaluate| |#1|) (QUOTE (-1209)))))) (|HasSignature| |#1| (|%list| (QUOTE **) (|%list| (|devaluate| |#1|) (|devaluate| |#1|) (|%list| (QUOTE -421) (QUOTE (-560)))))) (-4118 (-12 (|HasCategory| |#1| (|%list| (QUOTE -29) (QUOTE (-560)))) (|HasCategory| |#1| (|%list| (QUOTE -38) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#1| (QUOTE (-990))) (|HasCategory| |#1| (QUOTE (-1235)))) (-12 (|HasCategory| |#1| (|%list| (QUOTE -38) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasSignature| |#1| (|%list| (QUOTE -2554) (|%list| (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1209))))) (|HasSignature| |#1| (|%list| (QUOTE -3615) (|%list| (|%list| (QUOTE -663) (QUOTE (-1209))) (|devaluate| |#1|))))))) (-1281 |Coef1| |Coef2| |var1| |var2| |cen1| |cen2|) ((|constructor| (NIL "Mapping package for univariate Puiseux series. This package allows one to apply a function to the coefficients of a univariate Puiseux series.")) (|map| (((|UnivariatePuiseuxSeries| |#2| |#4| |#6|) (|Mapping| |#2| |#1|) (|UnivariatePuiseuxSeries| |#1| |#3| |#5|)) "\\spad{map(f,g(x))} applies the map \\spad{f} to the coefficients of the Puiseux series \\spad{g(x)}."))) NIL @@ -5071,11 +5071,11 @@ NIL (-1285 |Coef| ULS) ((|constructor| (NIL "This package enables one to construct a univariate Puiseux series domain from a univariate Laurent series domain. Univariate Puiseux series are represented by a pair \\spad{[r,f(x)]},{} where \\spad{r} is a positive rational number and \\spad{f(x)} is a Laurent series. This pair represents the Puiseux series \\spad{f(x^r)}."))) (((-4512 "*") |has| |#1| (-175)) (-4503 |has| |#1| (-571)) (-4508 |has| |#1| (-376)) (-4502 |has| |#1| (-376)) (-4504 . T) (-4505 . T) (-4507 . T)) -((|HasCategory| |#1| (QUOTE (-571))) (|HasCategory| |#1| (QUOTE (-175))) (-4144 (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-571)))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-149))) (-12 (|HasCategory| |#1| (|%list| (QUOTE -928) (QUOTE (-1209)))) (|HasSignature| |#1| (|%list| (QUOTE *) (|%list| (|devaluate| |#1|) (|%list| (QUOTE -421) (QUOTE (-560))) (|devaluate| |#1|))))) (|HasSignature| |#1| (|%list| (QUOTE *) (|%list| (|devaluate| |#1|) (|%list| (QUOTE -421) (QUOTE (-560))) (|devaluate| |#1|)))) (|HasCategory| (-421 (-560)) (QUOTE (-1144))) (|HasCategory| |#1| (QUOTE (-376))) (-4144 (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (QUOTE (-571)))) (-4144 (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (QUOTE (-571)))) (-12 (|HasSignature| |#1| (|%list| (QUOTE **) (|%list| (|devaluate| |#1|) (|devaluate| |#1|) (|%list| (QUOTE -421) (QUOTE (-560)))))) (|HasSignature| |#1| (|%list| (QUOTE -3903) (|%list| (|devaluate| |#1|) (QUOTE (-1209)))))) (|HasSignature| |#1| (|%list| (QUOTE **) (|%list| (|devaluate| |#1|) (|devaluate| |#1|) (|%list| (QUOTE -421) (QUOTE (-560)))))) (-4144 (-12 (|HasCategory| |#1| (|%list| (QUOTE -29) (QUOTE (-560)))) (|HasCategory| |#1| (|%list| (QUOTE -38) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#1| (QUOTE (-990))) (|HasCategory| |#1| (QUOTE (-1235)))) (-12 (|HasCategory| |#1| (|%list| (QUOTE -38) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasSignature| |#1| (|%list| (QUOTE -2884) (|%list| (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1209))))) (|HasSignature| |#1| (|%list| (QUOTE -3648) (|%list| (|%list| (QUOTE -663) (QUOTE (-1209))) (|devaluate| |#1|)))))) (|HasCategory| |#1| (|%list| (QUOTE -38) (|%list| (QUOTE -421) (QUOTE (-560)))))) +((|HasCategory| |#1| (QUOTE (-571))) (|HasCategory| |#1| (QUOTE (-175))) (-4118 (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-571)))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-149))) (-12 (|HasCategory| |#1| (|%list| (QUOTE -928) (QUOTE (-1209)))) (|HasSignature| |#1| (|%list| (QUOTE *) (|%list| (|devaluate| |#1|) (|%list| (QUOTE -421) (QUOTE (-560))) (|devaluate| |#1|))))) (|HasSignature| |#1| (|%list| (QUOTE *) (|%list| (|devaluate| |#1|) (|%list| (QUOTE -421) (QUOTE (-560))) (|devaluate| |#1|)))) (|HasCategory| (-421 (-560)) (QUOTE (-1144))) (|HasCategory| |#1| (QUOTE (-376))) (-4118 (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (QUOTE (-571)))) (-4118 (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (QUOTE (-571)))) (-12 (|HasSignature| |#1| (|%list| (QUOTE **) (|%list| (|devaluate| |#1|) (|devaluate| |#1|) (|%list| (QUOTE -421) (QUOTE (-560)))))) (|HasSignature| |#1| (|%list| (QUOTE -3866) (|%list| (|devaluate| |#1|) (QUOTE (-1209)))))) (|HasSignature| |#1| (|%list| (QUOTE **) (|%list| (|devaluate| |#1|) (|devaluate| |#1|) (|%list| (QUOTE -421) (QUOTE (-560)))))) (-4118 (-12 (|HasCategory| |#1| (|%list| (QUOTE -29) (QUOTE (-560)))) (|HasCategory| |#1| (|%list| (QUOTE -38) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#1| (QUOTE (-990))) (|HasCategory| |#1| (QUOTE (-1235)))) (-12 (|HasCategory| |#1| (|%list| (QUOTE -38) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasSignature| |#1| (|%list| (QUOTE -2554) (|%list| (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1209))))) (|HasSignature| |#1| (|%list| (QUOTE -3615) (|%list| (|%list| (QUOTE -663) (QUOTE (-1209))) (|devaluate| |#1|)))))) (|HasCategory| |#1| (|%list| (QUOTE -38) (|%list| (QUOTE -421) (QUOTE (-560)))))) (-1286 R FE |var| |cen|) ((|constructor| (NIL "UnivariatePuiseuxSeriesWithExponentialSingularity is a domain used to represent functions with essential singularities. Objects in this domain are sums,{} where each term in the sum is a univariate Puiseux series times the exponential of a univariate Puiseux series. Thus,{} the elements of this domain are sums of expressions of the form \\spad{g(x) * exp(f(x))},{} where \\spad{g}(\\spad{x}) is a univariate Puiseux series and \\spad{f}(\\spad{x}) is a univariate Puiseux series with no terms of non-negative degree.")) (|dominantTerm| (((|Union| (|Record| (|:| |%term| (|Record| (|:| |%coef| (|UnivariatePuiseuxSeries| |#2| |#3| |#4|)) (|:| |%expon| (|ExponentialOfUnivariatePuiseuxSeries| |#2| |#3| |#4|)) (|:| |%expTerms| (|List| (|Record| (|:| |k| (|Fraction| (|Integer|))) (|:| |c| |#2|)))))) (|:| |%type| (|String|))) "failed") $) "\\spad{dominantTerm(f(var))} returns the term that dominates the limiting behavior of \\spad{f(var)} as \\spad{var -> cen+} together with a \\spadtype{String} which briefly describes that behavior. The value of the \\spadtype{String} will be \\spad{\"zero\"} (resp. \\spad{\"infinity\"}) if the term tends to zero (resp. infinity) exponentially and will \\spad{\"series\"} if the term is a Puiseux series.")) (|limitPlus| (((|Union| (|OrderedCompletion| |#2|) "failed") $) "\\spad{limitPlus(f(var))} returns \\spad{limit(var -> cen+,f(var))}."))) (((-4512 "*") |has| (-1280 |#2| |#3| |#4|) (-175)) (-4503 |has| (-1280 |#2| |#3| |#4|) (-571)) (-4504 . T) (-4505 . T) (-4507 . T)) -((|HasCategory| (-1280 |#2| |#3| |#4|) (|%list| (QUOTE -38) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| (-1280 |#2| |#3| |#4|) (QUOTE (-147))) (|HasCategory| (-1280 |#2| |#3| |#4|) (QUOTE (-149))) (|HasCategory| (-1280 |#2| |#3| |#4|) (QUOTE (-175))) (-4144 (|HasCategory| (-1280 |#2| |#3| |#4|) (|%list| (QUOTE -38) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| (-1280 |#2| |#3| |#4|) (|%list| (QUOTE -1070) (|%list| (QUOTE -421) (QUOTE (-560)))))) (|HasCategory| (-1280 |#2| |#3| |#4|) (|%list| (QUOTE -1070) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| (-1280 |#2| |#3| |#4|) (|%list| (QUOTE -1070) (QUOTE (-560)))) (|HasCategory| (-1280 |#2| |#3| |#4|) (QUOTE (-376))) (|HasCategory| (-1280 |#2| |#3| |#4|) (QUOTE (-466))) (|HasCategory| (-1280 |#2| |#3| |#4|) (QUOTE (-571)))) +((|HasCategory| (-1280 |#2| |#3| |#4|) (|%list| (QUOTE -38) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| (-1280 |#2| |#3| |#4|) (QUOTE (-147))) (|HasCategory| (-1280 |#2| |#3| |#4|) (QUOTE (-149))) (|HasCategory| (-1280 |#2| |#3| |#4|) (QUOTE (-175))) (-4118 (|HasCategory| (-1280 |#2| |#3| |#4|) (|%list| (QUOTE -38) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| (-1280 |#2| |#3| |#4|) (|%list| (QUOTE -1070) (|%list| (QUOTE -421) (QUOTE (-560)))))) (|HasCategory| (-1280 |#2| |#3| |#4|) (|%list| (QUOTE -1070) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| (-1280 |#2| |#3| |#4|) (|%list| (QUOTE -1070) (QUOTE (-560)))) (|HasCategory| (-1280 |#2| |#3| |#4|) (QUOTE (-376))) (|HasCategory| (-1280 |#2| |#3| |#4|) (QUOTE (-466))) (|HasCategory| (-1280 |#2| |#3| |#4|) (QUOTE (-571)))) (-1287 A S) ((|constructor| (NIL "A unary-recursive aggregate is a one where nodes may have either 0 or 1 children. This aggregate models,{} though not precisely,{} a linked list possibly with a single cycle. A node with one children models a non-empty list,{} with the \\spadfun{value} of the list designating the head,{} or \\spadfun{first},{} of the list,{} and the child designating the tail,{} or \\spadfun{rest},{} of the list. A node with no child then designates the empty list. Since these aggregates are recursive aggregates,{} they may be cyclic.")) (|split!| (($ $ (|Integer|)) "\\spad{split!(u,n)} splits \\spad{u} into two aggregates: \\axiom{\\spad{v} = rest(\\spad{u},{}\\spad{n})} and \\axiom{\\spad{w} = first(\\spad{u},{}\\spad{n})},{} returning \\axiom{\\spad{v}}. Note: afterwards \\axiom{rest(\\spad{u},{}\\spad{n})} returns \\axiom{empty()}.")) (|setlast!| ((|#2| $ |#2|) "\\spad{setlast!(u,x)} destructively changes the last element of \\spad{u} to \\spad{x}.")) (|setrest!| (($ $ $) "\\spad{setrest!(u,v)} destructively changes the rest of \\spad{u} to \\spad{v}.")) (|setelt| ((|#2| $ "last" |#2|) "\\spad{setelt(u,\"last\",x)} (also written: \\axiom{\\spad{u}.last := \\spad{b}}) is equivalent to \\axiom{setlast!(\\spad{u},{}\\spad{v})}.") (($ $ "rest" $) "\\spad{setelt(u,\"rest\",v)} (also written: \\axiom{\\spad{u}.rest := \\spad{v}}) is equivalent to \\axiom{setrest!(\\spad{u},{}\\spad{v})}.") ((|#2| $ "first" |#2|) "\\spad{setelt(u,\"first\",x)} (also written: \\axiom{\\spad{u}.first := \\spad{x}}) is equivalent to \\axiom{setfirst!(\\spad{u},{}\\spad{x})}.")) (|setfirst!| ((|#2| $ |#2|) "\\spad{setfirst!(u,x)} destructively changes the first element of a to \\spad{x}.")) (|cycleSplit!| (($ $) "\\spad{cycleSplit!(u)} splits the aggregate by dropping off the cycle. The value returned is the cycle entry,{} or nil if none exists. For example,{} if \\axiom{\\spad{w} = concat(\\spad{u},{}\\spad{v})} is the cyclic list where \\spad{v} is the head of the cycle,{} \\axiom{cycleSplit!(\\spad{w})} will drop \\spad{v} off \\spad{w} thus destructively changing \\spad{w} to \\spad{u},{} and returning \\spad{v}.")) (|concat!| (($ $ |#2|) "\\spad{concat!(u,x)} destructively adds element \\spad{x} to the end of \\spad{u}. Note: \\axiom{concat!(a,{}\\spad{x}) = setlast!(a,{}[\\spad{x}])}.") (($ $ $) "\\spad{concat!(u,v)} destructively concatenates \\spad{v} to the end of \\spad{u}. Note: \\axiom{concat!(\\spad{u},{}\\spad{v}) = setlast!(\\spad{u},{}\\spad{v})}.")) (|cycleTail| (($ $) "\\spad{cycleTail(u)} returns the last node in the cycle,{} or empty if none exists.")) (|cycleLength| (((|NonNegativeInteger|) $) "\\spad{cycleLength(u)} returns the length of a top-level cycle contained in aggregate \\spad{u},{} or 0 is \\spad{u} has no such cycle.")) (|cycleEntry| (($ $) "\\spad{cycleEntry(u)} returns the head of a top-level cycle contained in aggregate \\spad{u},{} or \\axiom{empty()} if none exists.")) (|third| ((|#2| $) "\\spad{third(u)} returns the third element of \\spad{u}. Note: \\axiom{third(\\spad{u}) = first(rest(rest(\\spad{u})))}.")) (|second| ((|#2| $) "\\spad{second(u)} returns the second element of \\spad{u}. Note: \\axiom{second(\\spad{u}) = first(rest(\\spad{u}))}.")) (|tail| (($ $) "\\spad{tail(u)} returns the last node of \\spad{u}. Note: if \\spad{u} is \\axiom{shallowlyMutable},{} \\axiom{setrest(tail(\\spad{u}),{}\\spad{v}) = concat(\\spad{u},{}\\spad{v})}.")) (|last| (($ $ (|NonNegativeInteger|)) "\\spad{last(u,n)} returns a copy of the last \\spad{n} (\\axiom{\\spad{n} >= 0}) nodes of \\spad{u}. Note: \\axiom{last(\\spad{u},{}\\spad{n})} is a list of \\spad{n} elements.") ((|#2| $) "\\spad{last(u)} resturn the last element of \\spad{u}. Note: for lists,{} \\axiom{last(\\spad{u}) = \\spad{u} . (maxIndex \\spad{u}) = \\spad{u} . (\\# \\spad{u} - 1)}.")) (|rest| (($ $ (|NonNegativeInteger|)) "\\spad{rest(u,n)} returns the \\axiom{\\spad{n}}th (\\spad{n} >= 0) node of \\spad{u}. Note: \\axiom{rest(\\spad{u},{}0) = \\spad{u}}.") (($ $) "\\spad{rest(u)} returns an aggregate consisting of all but the first element of \\spad{u} (equivalently,{} the next node of \\spad{u}).")) (|elt| ((|#2| $ "last") "\\spad{elt(u,\"last\")} (also written: \\axiom{\\spad{u} . last}) is equivalent to last \\spad{u}.") (($ $ "rest") "\\spad{elt(\\%,\"rest\")} (also written: \\axiom{\\spad{u}.rest}) is equivalent to \\axiom{rest \\spad{u}}.") ((|#2| $ "first") "\\spad{elt(u,\"first\")} (also written: \\axiom{\\spad{u} . first}) is equivalent to first \\spad{u}.")) (|first| (($ $ (|NonNegativeInteger|)) "\\spad{first(u,n)} returns a copy of the first \\spad{n} (\\axiom{\\spad{n} >= 0}) elements of \\spad{u}.") ((|#2| $) "\\spad{first(u)} returns the first element of \\spad{u} (equivalently,{} the value at the current node).")) (|concat| (($ |#2| $) "\\spad{concat(x,u)} returns aggregate consisting of \\spad{x} followed by the elements of \\spad{u}. Note: if \\axiom{\\spad{v} = concat(\\spad{x},{}\\spad{u})} then \\axiom{\\spad{x} = first \\spad{v}} and \\axiom{\\spad{u} = rest \\spad{v}}.") (($ $ $) "\\spad{concat(u,v)} returns an aggregate \\spad{w} consisting of the elements of \\spad{u} followed by the elements of \\spad{v}. Note: \\axiom{\\spad{v} = rest(\\spad{w},{}\\#a)}."))) NIL @@ -5087,7 +5087,7 @@ NIL (-1289 |Coef| |var| |cen|) ((|constructor| (NIL "Dense Taylor series in one variable \\spadtype{UnivariateTaylorSeries} is a domain representing Taylor series in one variable with coefficients in an arbitrary ring. The parameters of the type specify the coefficient ring,{} the power series variable,{} and the center of the power series expansion. For example,{} \\spadtype{UnivariateTaylorSeries}(Integer,{}\\spad{x},{}3) represents Taylor series in \\spad{(x - 3)} with \\spadtype{Integer} coefficients.")) (|integrate| (($ $ (|Variable| |#2|)) "\\spad{integrate(f(x),x)} returns an anti-derivative of the power series \\spad{f(x)} with constant coefficient 0. We may integrate a series when we can divide coefficients by integers.")) (|invmultisect| (($ (|Integer|) (|Integer|) $) "\\spad{invmultisect(a,b,f(x))} substitutes \\spad{x^((a+b)*n)} \\indented{1}{for \\spad{x^n} and multiples by \\spad{x^b}.}")) (|multisect| (($ (|Integer|) (|Integer|) $) "\\spad{multisect(a,b,f(x))} selects the coefficients of \\indented{1}{\\spad{x^((a+b)*n+a)},{} and changes this monomial to \\spad{x^n}.}")) (|revert| (($ $) "\\spad{revert(f(x))} returns a Taylor series \\spad{g(x)} such that \\spad{f(g(x)) = g(f(x)) = x}. Series \\spad{f(x)} should have constant coefficient 0 and invertible 1st order coefficient.")) (|generalLambert| (($ $ (|Integer|) (|Integer|)) "\\spad{generalLambert(f(x),a,d)} returns \\spad{f(x^a) + f(x^(a + d)) + \\indented{1}{f(x^(a + 2 d)) + ... }. \\spad{f(x)} should have zero constant} \\indented{1}{coefficient and \\spad{a} and \\spad{d} should be positive.}")) (|evenlambert| (($ $) "\\spad{evenlambert(f(x))} returns \\spad{f(x^2) + f(x^4) + f(x^6) + ...}. \\indented{1}{\\spad{f(x)} should have a zero constant coefficient.} \\indented{1}{This function is used for computing infinite products.} \\indented{1}{If \\spad{f(x)} is a Taylor series with constant term 1,{} then} \\indented{1}{\\spad{product(n=1..infinity,f(x^(2*n))) = exp(log(evenlambert(f(x))))}.}")) (|oddlambert| (($ $) "\\spad{oddlambert(f(x))} returns \\spad{f(x) + f(x^3) + f(x^5) + ...}. \\indented{1}{\\spad{f(x)} should have a zero constant coefficient.} \\indented{1}{This function is used for computing infinite products.} \\indented{1}{If \\spad{f(x)} is a Taylor series with constant term 1,{} then} \\indented{1}{\\spad{product(n=1..infinity,f(x^(2*n-1)))=exp(log(oddlambert(f(x))))}.}")) (|lambert| (($ $) "\\spad{lambert(f(x))} returns \\spad{f(x) + f(x^2) + f(x^3) + ...}. \\indented{1}{This function is used for computing infinite products.} \\indented{1}{\\spad{f(x)} should have zero constant coefficient.} \\indented{1}{If \\spad{f(x)} is a Taylor series with constant term 1,{} then} \\indented{1}{\\spad{product(n = 1..infinity,f(x^n)) = exp(log(lambert(f(x))))}.}")) (|lagrange| (($ $) "\\spad{lagrange(g(x))} produces the Taylor series for \\spad{f(x)} \\indented{1}{where \\spad{f(x)} is implicitly defined as \\spad{f(x) = x*g(f(x))}.}")) (|univariatePolynomial| (((|UnivariatePolynomial| |#2| |#1|) $ (|NonNegativeInteger|)) "\\spad{univariatePolynomial(f,k)} returns a univariate polynomial \\indented{1}{consisting of the sum of all terms of \\spad{f} of degree \\spad{<= k}.}")) (|coerce| (($ (|Variable| |#2|)) "\\spad{coerce(var)} converts the series variable \\spad{var} into a \\indented{1}{Taylor series.}") (($ (|UnivariatePolynomial| |#2| |#1|)) "\\spad{coerce(p)} converts a univariate polynomial \\spad{p} in the variable \\spad{var} to a univariate Taylor series in \\spad{var}."))) (((-4512 "*") |has| |#1| (-175)) (-4503 |has| |#1| (-571)) (-4504 . T) (-4505 . T) (-4507 . T)) -((|HasCategory| |#1| (|%list| (QUOTE -38) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#1| (QUOTE (-571))) (-4144 (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-571)))) (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-149))) (-12 (|HasCategory| |#1| (|%list| (QUOTE -928) (QUOTE (-1209)))) (|HasSignature| |#1| (|%list| (QUOTE *) (|%list| (|devaluate| |#1|) (QUOTE (-793)) (|devaluate| |#1|))))) (|HasSignature| |#1| (|%list| (QUOTE *) (|%list| (|devaluate| |#1|) (QUOTE (-793)) (|devaluate| |#1|)))) (|HasCategory| (-793) (QUOTE (-1144))) (-12 (|HasSignature| |#1| (|%list| (QUOTE **) (|%list| (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-793))))) (|HasSignature| |#1| (|%list| (QUOTE -3903) (|%list| (|devaluate| |#1|) (QUOTE (-1209)))))) (|HasSignature| |#1| (|%list| (QUOTE **) (|%list| (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-793))))) (|HasCategory| |#1| (QUOTE (-376))) (-4144 (-12 (|HasCategory| |#1| (|%list| (QUOTE -29) (QUOTE (-560)))) (|HasCategory| |#1| (|%list| (QUOTE -38) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#1| (QUOTE (-990))) (|HasCategory| |#1| (QUOTE (-1235)))) (-12 (|HasCategory| |#1| (|%list| (QUOTE -38) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasSignature| |#1| (|%list| (QUOTE -2884) (|%list| (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1209))))) (|HasSignature| |#1| (|%list| (QUOTE -3648) (|%list| (|%list| (QUOTE -663) (QUOTE (-1209))) (|devaluate| |#1|))))))) +((|HasCategory| |#1| (|%list| (QUOTE -38) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#1| (QUOTE (-571))) (-4118 (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-571)))) (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-149))) (-12 (|HasCategory| |#1| (|%list| (QUOTE -928) (QUOTE (-1209)))) (|HasSignature| |#1| (|%list| (QUOTE *) (|%list| (|devaluate| |#1|) (QUOTE (-793)) (|devaluate| |#1|))))) (|HasSignature| |#1| (|%list| (QUOTE *) (|%list| (|devaluate| |#1|) (QUOTE (-793)) (|devaluate| |#1|)))) (|HasCategory| (-793) (QUOTE (-1144))) (-12 (|HasSignature| |#1| (|%list| (QUOTE **) (|%list| (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-793))))) (|HasSignature| |#1| (|%list| (QUOTE -3866) (|%list| (|devaluate| |#1|) (QUOTE (-1209)))))) (|HasSignature| |#1| (|%list| (QUOTE **) (|%list| (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-793))))) (|HasCategory| |#1| (QUOTE (-376))) (-4118 (-12 (|HasCategory| |#1| (|%list| (QUOTE -29) (QUOTE (-560)))) (|HasCategory| |#1| (|%list| (QUOTE -38) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#1| (QUOTE (-990))) (|HasCategory| |#1| (QUOTE (-1235)))) (-12 (|HasCategory| |#1| (|%list| (QUOTE -38) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasSignature| |#1| (|%list| (QUOTE -2554) (|%list| (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1209))))) (|HasSignature| |#1| (|%list| (QUOTE -3615) (|%list| (|%list| (QUOTE -663) (QUOTE (-1209))) (|devaluate| |#1|))))))) (-1290 |Coef1| |Coef2| UTS1 UTS2) ((|constructor| (NIL "Mapping package for univariate Taylor series. \\indented{2}{This package allows one to apply a function to the coefficients of} \\indented{2}{a univariate Taylor series.}")) (|map| ((|#4| (|Mapping| |#2| |#1|) |#3|) "\\spad{map(f,g(x))} applies the map \\spad{f} to the coefficients of \\indented{1}{the Taylor series \\spad{g(x)}.}"))) NIL @@ -5095,7 +5095,7 @@ NIL (-1291 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 (-560)))) (|HasCategory| |#2| (QUOTE (-990))) (|HasCategory| |#2| (QUOTE (-1235))) (|HasSignature| |#2| (|%list| (QUOTE -3648) (|%list| (|%list| (QUOTE -663) (QUOTE (-1209))) (|devaluate| |#2|)))) (|HasSignature| |#2| (|%list| (QUOTE -2884) (|%list| (|devaluate| |#2|) (|devaluate| |#2|) (QUOTE (-1209))))) (|HasCategory| |#2| (|%list| (QUOTE -38) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#2| (QUOTE (-376)))) +((|HasCategory| |#2| (|%list| (QUOTE -29) (QUOTE (-560)))) (|HasCategory| |#2| (QUOTE (-990))) (|HasCategory| |#2| (QUOTE (-1235))) (|HasSignature| |#2| (|%list| (QUOTE -3615) (|%list| (|%list| (QUOTE -663) (QUOTE (-1209))) (|devaluate| |#2|)))) (|HasSignature| |#2| (|%list| (QUOTE -2554) (|%list| (|devaluate| |#2|) (|devaluate| |#2|) (QUOTE (-1209))))) (|HasCategory| |#2| (|%list| (QUOTE -38) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#2| (QUOTE (-376)))) (-1292 |Coef|) ((|constructor| (NIL "\\spadtype{UnivariateTaylorSeriesCategory} is the category of Taylor series in one variable.")) (|integrate| (($ $ (|Symbol|)) "\\spad{integrate(f(x),y)} returns an anti-derivative of the power series \\spad{f(x)} with respect to the variable \\spad{y}.") (($ $ (|Symbol|)) "\\spad{integrate(f(x),y)} returns an anti-derivative of the power series \\spad{f(x)} with respect to the variable \\spad{y}.") (($ $) "\\spad{integrate(f(x))} returns an anti-derivative of the power series \\spad{f(x)} with constant coefficient 0. We may integrate a series when we can divide coefficients by integers.")) (** (($ $ |#1|) "\\spad{f(x) ** a} computes a power of a power series. When the coefficient ring is a field,{} we may raise a series to an exponent from the coefficient ring provided that the constant coefficient of the series is 1.")) (|polynomial| (((|Polynomial| |#1|) $ (|NonNegativeInteger|) (|NonNegativeInteger|)) "\\spad{polynomial(f,k1,k2)} returns a polynomial consisting of the sum of all terms of \\spad{f} of degree \\spad{d} with \\spad{k1 <= d <= k2}.") (((|Polynomial| |#1|) $ (|NonNegativeInteger|)) "\\spad{polynomial(f,k)} returns a polynomial consisting of the sum of all terms of \\spad{f} of degree \\spad{<= k}.")) (|multiplyCoefficients| (($ (|Mapping| |#1| (|Integer|)) $) "\\spad{multiplyCoefficients(f,sum(n = 0..infinity,a[n] * x**n))} returns \\spad{sum(n = 0..infinity,f(n) * a[n] * x**n)}. This function is used when Laurent series are represented by a Taylor series and an order.")) (|quoByVar| (($ $) "\\spad{quoByVar(a0 + a1 x + a2 x**2 + ...)} returns \\spad{a1 + a2 x + a3 x**2 + ...} Thus,{} this function substracts the constant term and divides by the series variable. This function is used when Laurent series are represented by a Taylor series and an order.")) (|coefficients| (((|Stream| |#1|) $) "\\spad{coefficients(a0 + a1 x + a2 x**2 + ...)} returns a stream of coefficients: \\spad{[a0,a1,a2,...]}. The entries of the stream may be zero.")) (|series| (($ (|Stream| |#1|)) "\\spad{series([a0,a1,a2,...])} is the Taylor series \\spad{a0 + a1 x + a2 x**2 + ...}.") (($ (|Stream| (|Record| (|:| |k| (|NonNegativeInteger|)) (|:| |c| |#1|)))) "\\spad{series(st)} creates a series from a stream of non-zero terms,{} where a term is an exponent-coefficient pair. The terms in the stream should be ordered by increasing order of exponents."))) (((-4512 "*") |has| |#1| (-175)) (-4503 |has| |#1| (-571)) (-4504 . T) (-4505 . T) (-4507 . T)) @@ -5104,7 +5104,7 @@ NIL ((|constructor| (NIL "\\indented{1}{This package provides Taylor series solutions to regular} linear or non-linear ordinary differential equations of arbitrary order.")) (|mpsode| (((|List| |#2|) (|List| |#1|) (|List| (|Mapping| |#2| (|List| |#2|)))) "\\spad{mpsode(r,f)} solves the system of differential equations \\spad{dy[i]/dx =f[i] [x,y[1],y[2],...,y[n]]},{} \\spad{y[i](a) = r[i]} for \\spad{i} in 1..\\spad{n}.")) (|ode| ((|#2| (|Mapping| |#2| (|List| |#2|)) (|List| |#1|)) "\\spad{ode(f,cl)} is the solution to \\spad{y<n>=f(y,y',..,y<n-1>)} such that \\spad{y<i>(a) = cl.i} for \\spad{i} in 1..\\spad{n}.")) (|ode2| ((|#2| (|Mapping| |#2| |#2| |#2|) |#1| |#1|) "\\spad{ode2(f,c0,c1)} is the solution to \\spad{y'' = f(y,y')} such that \\spad{y(a) = c0} and \\spad{y'(a) = c1}.")) (|ode1| ((|#2| (|Mapping| |#2| |#2|) |#1|) "\\spad{ode1(f,c)} is the solution to \\spad{y' = f(y)} such that \\spad{y(a) = c}.")) (|fixedPointExquo| ((|#2| |#2| |#2|) "\\spad{fixedPointExquo(f,g)} computes the exact quotient of \\spad{f} and \\spad{g} using a fixed point computation.")) (|stFuncN| (((|Mapping| (|Stream| |#1|) (|List| (|Stream| |#1|))) (|Mapping| |#2| (|List| |#2|))) "\\spad{stFuncN(f)} is a local function xported due to compiler problem. This function is of no interest to the top-level user.")) (|stFunc2| (((|Mapping| (|Stream| |#1|) (|Stream| |#1|) (|Stream| |#1|)) (|Mapping| |#2| |#2| |#2|)) "\\spad{stFunc2(f)} is a local function exported due to compiler problem. This function is of no interest to the top-level user.")) (|stFunc1| (((|Mapping| (|Stream| |#1|) (|Stream| |#1|)) (|Mapping| |#2| |#2|)) "\\spad{stFunc1(f)} is a local function exported due to compiler problem. This function is of no interest to the top-level user."))) NIL NIL -(-1294 -4164 UP L UTS) +(-1294 -4140 UP L UTS) ((|constructor| (NIL "\\spad{RUTSodetools} provides tools to interface with the series \\indented{1}{ODE solver when presented with linear ODEs.}")) (RF2UTS ((|#4| (|Fraction| |#2|)) "\\spad{RF2UTS(f)} converts \\spad{f} to a Taylor series.")) (LODO2FUN (((|Mapping| |#4| (|List| |#4|)) |#3|) "\\spad{LODO2FUN(op)} returns the function to pass to the series ODE solver in order to solve \\spad{op y = 0}.")) (UTS2UP ((|#2| |#4| (|NonNegativeInteger|)) "\\spad{UTS2UP(s, n)} converts the first \\spad{n} terms of \\spad{s} to a univariate polynomial.")) (UP2UTS ((|#4| |#2|) "\\spad{UP2UTS(p)} converts \\spad{p} to a Taylor series."))) NIL ((|HasCategory| |#1| (QUOTE (-571)))) @@ -5127,7 +5127,7 @@ NIL (-1299 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."))) ((-4511 . T) (-4510 . T)) -((-4144 (-12 (|HasCategory| |#1| (QUOTE (-872))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|))))) (-4144 (-12 (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-888))))) (|HasCategory| |#1| (|%list| (QUOTE -633) (QUOTE (-549)))) (-4144 (|HasCategory| |#1| (QUOTE (-872))) (|HasCategory| |#1| (QUOTE (-1133)))) (|HasCategory| |#1| (QUOTE (-872))) (-4144 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-872))) (|HasCategory| |#1| (QUOTE (-1133)))) (|HasCategory| (-560) (QUOTE (-872))) (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#1| (QUOTE (-25))) (|HasCategory| |#1| (QUOTE (-23))) (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-748))) (|HasCategory| |#1| (QUOTE (-1081))) (-12 (|HasCategory| |#1| (QUOTE (-1034))) (|HasCategory| |#1| (QUOTE (-1081)))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-888)))) (|HasCategory| |#1| (QUOTE (-102))) (-12 (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|))))) +((-4118 (-12 (|HasCategory| |#1| (QUOTE (-872))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|))))) (-4118 (-12 (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-888))))) (|HasCategory| |#1| (|%list| (QUOTE -633) (QUOTE (-549)))) (-4118 (|HasCategory| |#1| (QUOTE (-872))) (|HasCategory| |#1| (QUOTE (-1133)))) (|HasCategory| |#1| (QUOTE (-872))) (-4118 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-872))) (|HasCategory| |#1| (QUOTE (-1133)))) (|HasCategory| (-560) (QUOTE (-872))) (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#1| (QUOTE (-25))) (|HasCategory| |#1| (QUOTE (-23))) (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-748))) (|HasCategory| |#1| (QUOTE (-1081))) (-12 (|HasCategory| |#1| (QUOTE (-1034))) (|HasCategory| |#1| (QUOTE (-1081)))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-888)))) (|HasCategory| |#1| (QUOTE (-102))) (-12 (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|))))) (-1300 A B) ((|constructor| (NIL "\\indented{2}{This package provides operations which all take as arguments} vectors of elements of some type \\spad{A} and functions from \\spad{A} to another of type \\spad{B}. The operations all iterate over their vector argument and either return a value of type \\spad{B} or a vector over \\spad{B}.")) (|map| (((|Union| (|Vector| |#2|) "failed") (|Mapping| (|Union| |#2| "failed") |#1|) (|Vector| |#1|)) "\\spad{map(f, v)} applies the function \\spad{f} to every element of the vector \\spad{v} producing a new vector containing the values or \\spad{\"failed\"}.") (((|Vector| |#2|) (|Mapping| |#2| |#1|) (|Vector| |#1|)) "\\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| ((|#2| (|Mapping| |#2| |#1| |#2|) (|Vector| |#1|) |#2|) "\\spad{reduce(func,vec,ident)} combines the elements in \\spad{vec} using the binary function \\spad{func}. Argument \\spad{ident} is returned if \\spad{vec} is empty.")) (|scan| (((|Vector| |#2|) (|Mapping| |#2| |#1| |#2|) (|Vector| |#1|) |#2|) "\\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 @@ -5164,7 +5164,7 @@ NIL ((|constructor| (NIL "This package implements the Weierstrass preparation theorem \\spad{f} or multivariate power series. weierstrass(\\spad{v},{}\\spad{p}) where \\spad{v} is a variable,{} and \\spad{p} is a TaylorSeries(\\spad{R}) in which the terms of lowest degree \\spad{s} must include c*v**s where \\spad{c} is a constant,{}\\spad{s>0},{} is a list of TaylorSeries coefficients A[\\spad{i}] of the equivalent polynomial A = A[0] + A[1]*v + A[2]\\spad{*v**2} + ... + A[\\spad{s}-1]*v**(\\spad{s}-1) + v**s such that p=A*B ,{} \\spad{B} being a TaylorSeries of minimum degree 0")) (|qqq| (((|Mapping| (|Stream| (|TaylorSeries| |#1|)) (|Stream| (|TaylorSeries| |#1|))) (|NonNegativeInteger|) (|TaylorSeries| |#1|) (|Stream| (|TaylorSeries| |#1|))) "\\spad{qqq(n,s,st)} is used internally.")) (|weierstrass| (((|List| (|TaylorSeries| |#1|)) (|Symbol|) (|TaylorSeries| |#1|)) "\\spad{weierstrass(v,ts)} where \\spad{v} is a variable and \\spad{ts} is \\indented{1}{a TaylorSeries,{} impements the Weierstrass Preparation} \\indented{1}{Theorem. The result is a list of TaylorSeries that} \\indented{1}{are the coefficients of the equivalent series.}")) (|clikeUniv| (((|Mapping| (|SparseUnivariatePolynomial| (|Polynomial| |#1|)) (|Polynomial| |#1|)) (|Symbol|)) "\\spad{clikeUniv(v)} is used internally.")) (|sts2stst| (((|Stream| (|Stream| (|Polynomial| |#1|))) (|Symbol|) (|Stream| (|Polynomial| |#1|))) "\\spad{sts2stst(v,s)} is used internally.")) (|cfirst| (((|Mapping| (|Stream| (|Polynomial| |#1|)) (|Stream| (|Polynomial| |#1|))) (|NonNegativeInteger|)) "\\spad{cfirst n} is used internally.")) (|crest| (((|Mapping| (|Stream| (|Polynomial| |#1|)) (|Stream| (|Polynomial| |#1|))) (|NonNegativeInteger|)) "\\spad{crest n} is used internally."))) NIL NIL -(-1309 K R UP -4164) +(-1309 K R UP -4140) ((|constructor| (NIL "In this package \\spad{K} is a finite field,{} \\spad{R} is a ring of univariate polynomials over \\spad{K},{} and \\spad{F} is a framed algebra over \\spad{R}. The package provides a function to compute the integral closure of \\spad{R} in the quotient field of \\spad{F} as well as a function to compute a \"local integral basis\" at a specific prime.")) (|localIntegralBasis| (((|Record| (|:| |basis| (|Matrix| |#2|)) (|:| |basisDen| |#2|) (|:| |basisInv| (|Matrix| |#2|))) |#2|) "\\spad{integralBasis(p)} returns a record \\spad{[basis,basisDen,basisInv]} containing information regarding the local integral closure of \\spad{R} at the prime \\spad{p} in the quotient field of \\spad{F},{} where \\spad{F} is a framed algebra with \\spad{R}-module basis \\spad{w1,w2,...,wn}. If \\spad{basis} is the matrix \\spad{(aij, i = 1..n, j = 1..n)},{} then the \\spad{i}th element of the local integral basis is \\spad{vi = (1/basisDen) * sum(aij * wj, j = 1..n)},{} \\spadignore{i.e.} the \\spad{i}th row of \\spad{basis} contains the coordinates of the \\spad{i}th basis vector. Similarly,{} the \\spad{i}th row of the matrix \\spad{basisInv} contains the coordinates of \\spad{wi} with respect to the basis \\spad{v1,...,vn}: if \\spad{basisInv} is the matrix \\spad{(bij, i = 1..n, j = 1..n)},{} then \\spad{wi = sum(bij * vj, j = 1..n)}.")) (|integralBasis| (((|Record| (|:| |basis| (|Matrix| |#2|)) (|:| |basisDen| |#2|) (|:| |basisInv| (|Matrix| |#2|)))) "\\spad{integralBasis()} returns a record \\spad{[basis,basisDen,basisInv]} containing information regarding the integral closure of \\spad{R} in the quotient field of \\spad{F},{} where \\spad{F} is a framed algebra with \\spad{R}-module basis \\spad{w1,w2,...,wn}. If \\spad{basis} is the matrix \\spad{(aij, i = 1..n, j = 1..n)},{} then the \\spad{i}th element of the integral basis is \\spad{vi = (1/basisDen) * sum(aij * wj, j = 1..n)},{} \\spadignore{i.e.} the \\spad{i}th row of \\spad{basis} contains the coordinates of the \\spad{i}th basis vector. Similarly,{} the \\spad{i}th row of the matrix \\spad{basisInv} contains the coordinates of \\spad{wi} with respect to the basis \\spad{v1,...,vn}: if \\spad{basisInv} is the matrix \\spad{(bij, i = 1..n, j = 1..n)},{} then \\spad{wi = sum(bij * vj, j = 1..n)}."))) NIL NIL @@ -5196,11 +5196,11 @@ NIL ((|constructor| (NIL "This package provides computations of logarithms and exponentials for polynomials in non-commutative variables. \\newline Author: Michel Petitot (petitot@lifl.fr).")) (|Hausdorff| ((|#3| |#3| |#3| (|NonNegativeInteger|)) "\\axiom{Hausdorff(a,{}\\spad{b},{}\\spad{n})} returns log(exp(a)*exp(\\spad{b})) truncated at order \\axiom{\\spad{n}}.")) (|log| ((|#3| |#3| (|NonNegativeInteger|)) "\\axiom{log(\\spad{p},{} \\spad{n})} returns the logarithm of \\axiom{\\spad{p}} truncated at order \\axiom{\\spad{n}}.")) (|exp| ((|#3| |#3| (|NonNegativeInteger|)) "\\axiom{exp(\\spad{p},{} \\spad{n})} returns the exponential of \\axiom{\\spad{p}} truncated at order \\axiom{\\spad{n}}."))) NIL NIL -(-1317 S -4164) +(-1317 S -4140) ((|constructor| (NIL "ExtensionField {\\em F} is the category of fields which extend the field \\spad{F}")) (|Frobenius| (($ $ (|NonNegativeInteger|)) "\\spad{Frobenius(a,s)} returns \\spad{a**(q**s)} where \\spad{q} is the size()\\$\\spad{F}.") (($ $) "\\spad{Frobenius(a)} returns \\spad{a ** q} where \\spad{q} is the \\spad{size()\\$F}.")) (|transcendenceDegree| (((|NonNegativeInteger|)) "\\spad{transcendenceDegree()} returns the transcendence degree of the field extension,{} 0 if the extension is algebraic.")) (|extensionDegree| (((|OnePointCompletion| (|PositiveInteger|))) "\\spad{extensionDegree()} returns the degree of the field extension if the extension is algebraic,{} and \\spad{infinity} if it is not.")) (|degree| (((|OnePointCompletion| (|PositiveInteger|)) $) "\\spad{degree(a)} returns the degree of minimal polynomial of an element \\spad{a} if \\spad{a} is algebraic with respect to the ground field \\spad{F},{} and \\spad{infinity} otherwise.")) (|inGroundField?| (((|Boolean|) $) "\\spad{inGroundField?(a)} tests whether an element \\spad{a} is already in the ground field \\spad{F}.")) (|transcendent?| (((|Boolean|) $) "\\spad{transcendent?(a)} tests whether an element \\spad{a} is transcendent with respect to the ground field \\spad{F}.")) (|algebraic?| (((|Boolean|) $) "\\spad{algebraic?(a)} tests whether an element \\spad{a} is algebraic with respect to the ground field \\spad{F}."))) NIL ((|HasCategory| |#2| (QUOTE (-381))) (|HasCategory| |#2| (QUOTE (-147))) (|HasCategory| |#2| (QUOTE (-149)))) -(-1318 -4164) +(-1318 -4140) ((|constructor| (NIL "ExtensionField {\\em F} is the category of fields which extend the field \\spad{F}")) (|Frobenius| (($ $ (|NonNegativeInteger|)) "\\spad{Frobenius(a,s)} returns \\spad{a**(q**s)} where \\spad{q} is the size()\\$\\spad{F}.") (($ $) "\\spad{Frobenius(a)} returns \\spad{a ** q} where \\spad{q} is the \\spad{size()\\$F}.")) (|transcendenceDegree| (((|NonNegativeInteger|)) "\\spad{transcendenceDegree()} returns the transcendence degree of the field extension,{} 0 if the extension is algebraic.")) (|extensionDegree| (((|OnePointCompletion| (|PositiveInteger|))) "\\spad{extensionDegree()} returns the degree of the field extension if the extension is algebraic,{} and \\spad{infinity} if it is not.")) (|degree| (((|OnePointCompletion| (|PositiveInteger|)) $) "\\spad{degree(a)} returns the degree of minimal polynomial of an element \\spad{a} if \\spad{a} is algebraic with respect to the ground field \\spad{F},{} and \\spad{infinity} otherwise.")) (|inGroundField?| (((|Boolean|) $) "\\spad{inGroundField?(a)} tests whether an element \\spad{a} is already in the ground field \\spad{F}.")) (|transcendent?| (((|Boolean|) $) "\\spad{transcendent?(a)} tests whether an element \\spad{a} is transcendent with respect to the ground field \\spad{F}.")) (|algebraic?| (((|Boolean|) $) "\\spad{algebraic?(a)} tests whether an element \\spad{a} is algebraic with respect to the ground field \\spad{F}."))) ((-4502 . T) (-4508 . T) (-4503 . T) ((-4512 "*") . T) (-4504 . T) (-4505 . T) (-4507 . T)) NIL diff --git a/src/share/algebra/category.daase b/src/share/algebra/category.daase index 14f75789..bddbff88 100644 --- a/src/share/algebra/category.daase +++ b/src/share/algebra/category.daase @@ -1,15 +1,15 @@ -(205700 . 3514823553) -(((|#2| |#2|) -12 (|has| |#2| (-321 |#2|)) (|has| |#2| (-1133))) ((#0=(-2 (|:| -2118 |#1|) (|:| -3964 |#2|)) #0#) |has| (-2 (|:| -2118 |#1|) (|:| -3964 |#2|)) (-321 (-2 (|:| -2118 |#1|) (|:| -3964 |#2|))))) -((((-560)) . T) (($) -4144 (|has| |#1| (-319)) (|has| |#1| (-376)) (|has| |#1| (-363)) (|has| |#1| (-571))) (((-421 (-560))) -4144 (|has| |#1| (-376)) (|has| |#1| (-363)) (|has| |#1| (-1070 (-421 (-560))))) ((|#1|) . T)) +(205700 . 3514927628) +(((|#2| |#2|) -12 (|has| |#2| (-321 |#2|)) (|has| |#2| (-1133))) ((#0=(-2 (|:| -2115 |#1|) (|:| -3934 |#2|)) #0#) |has| (-2 (|:| -2115 |#1|) (|:| -3934 |#2|)) (-321 (-2 (|:| -2115 |#1|) (|:| -3934 |#2|))))) +((((-560)) . T) (($) -4118 (|has| |#1| (-319)) (|has| |#1| (-376)) (|has| |#1| (-363)) (|has| |#1| (-571))) (((-421 (-560))) -4118 (|has| |#1| (-376)) (|has| |#1| (-363)) (|has| |#1| (-1070 (-421 (-560))))) ((|#1|) . T)) (((|#2| |#2|) . T)) ((((-560)) . T)) -((($ $) -4144 (|has| |#2| (-175)) (|has| |#2| (-376)) (|has| |#2| (-466)) (|has| |#2| (-571)) (|has| |#2| (-940))) ((|#2| |#2|) . T) ((#0=(-421 (-560)) #0#) |has| |#2| (-38 (-421 (-560))))) +((($ $) -4118 (|has| |#2| (-175)) (|has| |#2| (-376)) (|has| |#2| (-466)) (|has| |#2| (-571)) (|has| |#2| (-940))) ((|#2| |#2|) . T) ((#0=(-421 (-560)) #0#) |has| |#2| (-38 (-421 (-560))))) ((($) . T)) (((|#1|) . T)) ((($) . T) (((-560)) |has| |#1| (-660 (-560))) ((|#1|) . T) (((-421 (-560))) |has| |#1| (-38 (-421 (-560))))) (((|#2|) . T)) -((($) -4144 (|has| |#2| (-175)) (|has| |#2| (-376)) (|has| |#2| (-466)) (|has| |#2| (-571)) (|has| |#2| (-940))) ((|#2|) . T) (((-421 (-560))) |has| |#2| (-38 (-421 (-560))))) +((($) -4118 (|has| |#2| (-175)) (|has| |#2| (-376)) (|has| |#2| (-466)) (|has| |#2| (-571)) (|has| |#2| (-940))) ((|#2|) . T) (((-421 (-560))) |has| |#2| (-38 (-421 (-560))))) (|has| |#1| (-940)) ((((-888)) . T)) ((((-888)) . T)) @@ -23,23 +23,23 @@ ((((-549)) . T) (((-1191)) . T) (((-229)) . T) (((-391)) . T) (((-916 (-391))) . T)) (((|#1|) . T)) ((((-229)) . T) (((-888)) . T)) -(-4144 (|has| |#2| (-817)) (|has| |#2| (-872))) -(-4144 (-12 (|has| |#1| (-817)) (|has| |#2| (-817))) (-12 (|has| |#1| (-872)) (|has| |#2| (-872)))) +(-4118 (|has| |#2| (-817)) (|has| |#2| (-872))) +(-4118 (-12 (|has| |#1| (-817)) (|has| |#2| (-817))) (-12 (|has| |#1| (-872)) (|has| |#2| (-872)))) (((|#1|) . T)) (((|#1|) -12 (|has| |#1| (-321 |#1|)) (|has| |#1| (-1133)))) -(-4144 (|has| |#1| (-21)) (|has| |#1| (-871))) -((($ $) . T) ((#0=(-421 (-560)) #0#) -4144 (|has| |#1| (-376)) (|has| |#1| (-363))) ((|#1| |#1|) . T)) -(-4144 (|has| |#1| (-844)) (|has| |#1| (-872))) +(-4118 (|has| |#1| (-21)) (|has| |#1| (-871))) +((($ $) . T) ((#0=(-421 (-560)) #0#) -4118 (|has| |#1| (-376)) (|has| |#1| (-363))) ((|#1| |#1|) . T)) +(-4118 (|has| |#1| (-844)) (|has| |#1| (-872))) ((((-421 (-560))) |has| |#1| (-1070 (-421 (-560)))) (((-560)) |has| |#1| (-1070 (-560))) ((|#1|) . T)) ((((-888)) . T)) ((((-888)) . T)) -(-4144 (|has| |#1| (-376)) (|has| |#1| (-571))) +(-4118 (|has| |#1| (-376)) (|has| |#1| (-571))) (|has| |#1| (-871)) (((|#1| |#1|) -12 (|has| |#1| (-321 |#1|)) (|has| |#1| (-1133)))) ((((-326 |#1|)) . T) (((-560)) . T) (($) . T)) (((|#1| |#2| |#3|) . T)) ((((-560)) . T) (((-894 |#1|)) . T) (($) . T) (((-421 (-560))) . T)) -((($) . T) (((-421 (-560))) -4144 (|has| |#1| (-376)) (|has| |#1| (-363))) ((|#1|) . T)) +((($) . T) (((-421 (-560))) -4118 (|has| |#1| (-376)) (|has| |#1| (-363))) ((|#1|) . T)) ((((-421 (-560))) . T) (((-721)) . T) (($) . T)) ((((-888)) . T)) ((((-1214)) . T)) @@ -52,14 +52,14 @@ (((|#1|) . T) ((|#2|) . T)) ((((-1214)) . T)) (((|#1|) . T) (((-560)) |has| |#1| (-1070 (-560))) (((-421 (-560))) |has| |#1| (-1070 (-421 (-560))))) -(-4144 (|has| |#2| (-175)) (|has| |#2| (-466)) (|has| |#2| (-571)) (|has| |#2| (-940))) -(-4144 (|has| |#1| (-175)) (|has| |#1| (-466)) (|has| |#1| (-571)) (|has| |#1| (-940))) -(((|#2| (-496 (-2236 |#1|) (-793))) . T)) -((((-1209)) -4144 (|has| (-421 |#2|) (-928 (-1209))) (|has| (-421 |#2|) (-930 (-1209))))) +(-4118 (|has| |#2| (-175)) (|has| |#2| (-466)) (|has| |#2| (-571)) (|has| |#2| (-940))) +(-4118 (|has| |#1| (-175)) (|has| |#1| (-466)) (|has| |#1| (-571)) (|has| |#1| (-940))) +(((|#2| (-496 (-2223 |#1|) (-793))) . T)) +((((-1209)) -4118 (|has| (-421 |#2|) (-928 (-1209))) (|has| (-421 |#2|) (-930 (-1209))))) (((|#1| (-545 (-1209))) . T)) ((((-1191)) . T) (((-988 (-130))) . T) (((-888)) . T)) ((((-888)) . T)) -((((-2 (|:| -2118 |#1|) (|:| -3964 |#2|))) . T)) +((((-2 (|:| -2115 |#1|) (|:| -3934 |#2|))) . T)) (((#0=(-894 |#1|) #0#) . T) ((#1=(-421 (-560)) #1#) . T) (($ $) . T)) (|has| |#4| (-381)) (|has| |#3| (-381)) @@ -75,14 +75,14 @@ (|has| |#1| (-147)) (|has| |#1| (-149)) (|has| |#1| (-571)) -((((-560)) . T) (((-421 (-560))) -4144 (|has| |#2| (-38 (-421 (-560)))) (|has| |#2| (-1070 (-421 (-560))))) ((|#2|) . T) (($) -4144 (|has| |#2| (-466)) (|has| |#2| (-571)) (|has| |#2| (-940))) (((-889 |#1|)) . T)) -(-4144 (|has| |#1| (-376)) (|has| |#1| (-571))) -(-4144 (|has| |#1| (-376)) (|has| |#1| (-571))) -((((-2 (|:| -2183 |#1|) (|:| -4067 |#2|))) . T)) +((((-560)) . T) (((-421 (-560))) -4118 (|has| |#2| (-38 (-421 (-560)))) (|has| |#2| (-1070 (-421 (-560))))) ((|#2|) . T) (($) -4118 (|has| |#2| (-466)) (|has| |#2| (-571)) (|has| |#2| (-940))) (((-889 |#1|)) . T)) +(-4118 (|has| |#1| (-376)) (|has| |#1| (-571))) +(-4118 (|has| |#1| (-376)) (|has| |#1| (-571))) +((((-2 (|:| -2175 |#1|) (|:| -1946 |#2|))) . T)) ((($) . T)) ((((-888)) |has| |#1| (-632 (-888))) ((|#1|) . T)) -((((-560)) . T) (((-421 (-560))) -4144 (|has| |#1| (-38 (-421 (-560)))) (|has| |#1| (-1070 (-421 (-560))))) ((|#1|) . T) (($) -4144 (|has| |#1| (-466)) (|has| |#1| (-571)) (|has| |#1| (-940))) (((-1209)) . T)) -((((-888)) -4144 (|has| |#1| (-632 (-888))) (|has| |#1| (-872)) (|has| |#1| (-1133)))) +((((-560)) . T) (((-421 (-560))) -4118 (|has| |#1| (-38 (-421 (-560)))) (|has| |#1| (-1070 (-421 (-560))))) ((|#1|) . T) (($) -4118 (|has| |#1| (-466)) (|has| |#1| (-571)) (|has| |#1| (-940))) (((-1209)) . T)) +((((-888)) -4118 (|has| |#1| (-632 (-888))) (|has| |#1| (-872)) (|has| |#1| (-1133)))) ((((-549)) |has| |#1| (-633 (-549)))) ((((-1209)) . T)) (((|#1|) . T)) @@ -103,12 +103,12 @@ ((((-888)) . T)) (((|#1| |#2|) . T)) (((|#1|) . T)) -(((#0=(-421 (-560)) #0#) |has| |#2| (-38 (-421 (-560)))) ((|#2| |#2|) . T) (($ $) -4144 (|has| |#2| (-175)) (|has| |#2| (-466)) (|has| |#2| (-571)) (|has| |#2| (-940)))) +(((#0=(-421 (-560)) #0#) |has| |#2| (-38 (-421 (-560)))) ((|#2| |#2|) . T) (($ $) -4118 (|has| |#2| (-175)) (|has| |#2| (-466)) (|has| |#2| (-571)) (|has| |#2| (-940)))) (|has| |#1| (-1133)) (((|#1|) . T)) ((((-118 |#1|)) . T) (($) . T) (((-421 (-560))) . T)) -((((-421 (-560))) |has| |#2| (-38 (-421 (-560)))) ((|#2|) |has| |#2| (-175)) (($) -4144 (|has| |#2| (-466)) (|has| |#2| (-571)) (|has| |#2| (-940)))) -((($) -4144 (|has| |#1| (-466)) (|has| |#1| (-571)) (|has| |#1| (-940))) ((|#1|) |has| |#1| (-175)) (((-421 (-560))) |has| |#1| (-38 (-421 (-560))))) +((((-421 (-560))) |has| |#2| (-38 (-421 (-560)))) ((|#2|) |has| |#2| (-175)) (($) -4118 (|has| |#2| (-466)) (|has| |#2| (-571)) (|has| |#2| (-940)))) +((($) -4118 (|has| |#1| (-466)) (|has| |#1| (-571)) (|has| |#1| (-940))) ((|#1|) |has| |#1| (-175)) (((-421 (-560))) |has| |#1| (-38 (-421 (-560))))) (((|#1|) . T) (((-421 (-560))) . T) (($) . T)) ((((-118 |#1|)) . T) (((-421 (-560))) . T) (($) . T)) (((|#1|) . T) (((-421 (-560))) . T) (($) . T)) @@ -116,14 +116,14 @@ ((((-421 (-560))) . T) (($) . T) (((-560)) . T)) ((($) . T) (((-560)) . T) (((-421 (-560))) |has| |#2| (-38 (-421 (-560)))) ((|#2|) . T)) (((|#2|) . T) (((-560)) . T) ((|#6|) . T)) -((((-421 (-560))) |has| |#2| (-38 (-421 (-560)))) ((|#2|) . T) (($) -4144 (|has| |#2| (-175)) (|has| |#2| (-466)) (|has| |#2| (-571)) (|has| |#2| (-940)))) +((((-421 (-560))) |has| |#2| (-38 (-421 (-560)))) ((|#2|) . T) (($) -4118 (|has| |#2| (-175)) (|has| |#2| (-466)) (|has| |#2| (-571)) (|has| |#2| (-940)))) ((($) . T)) ((($) . T)) (((|#2|) . T)) (((|#1|) . T) (((-421 (-560))) |has| |#1| (-38 (-421 (-560)))) (((-560)) . T) (($) . T)) ((((-560)) . T) (($) . T) ((|#1|) . T) (((-421 (-560))) |has| |#1| (-38 (-421 (-560))))) -((((-421 (-560))) |has| |#1| (-38 (-421 (-560)))) ((|#1|) . T) (($) -4144 (|has| |#1| (-175)) (|has| |#1| (-466)) (|has| |#1| (-571)) (|has| |#1| (-940)))) -(((#0=(-421 (-560)) #0#) |has| |#1| (-38 (-421 (-560)))) ((|#1| |#1|) . 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T)) (((|#1| (-1003)) . T)) ((((-560)) . T) ((|#2|) . T)) @@ -369,7 +369,7 @@ (((|#1|) . T)) (((|#2| |#2|) . T)) (|has| |#1| (-1184)) -((((-2 (|:| -2118 (-1191)) (|:| -3964 |#1|))) . T)) +((((-2 (|:| -2115 (-1191)) (|:| -3934 |#1|))) . T)) (|has| (-1286 |#1| |#2| |#3| |#4|) (-147)) (|has| (-1286 |#1| |#2| |#3| |#4|) (-149)) (|has| |#1| (-147)) @@ -381,28 +381,28 @@ (((|#2|) . T)) (((|#1|) . T)) (((|#2|) . T) (((-560)) |has| |#2| (-660 (-560)))) -((((-1157 |#1| (-1209))) . T) (((-560)) . T) (((-842 (-1209))) . T) (($) -4144 (|has| |#1| (-466)) (|has| |#1| (-571)) (|has| |#1| (-940))) ((|#1|) . T) (((-421 (-560))) -4144 (|has| |#1| (-38 (-421 (-560)))) (|has| |#1| (-1070 (-421 (-560))))) (((-1209)) . T)) +((((-1157 |#1| (-1209))) . T) (((-560)) . T) (((-842 (-1209))) . T) (($) -4118 (|has| |#1| (-466)) (|has| |#1| (-571)) (|has| |#1| (-940))) ((|#1|) . T) (((-421 (-560))) -4118 (|has| |#1| (-38 (-421 (-560)))) (|has| |#1| (-1070 (-421 (-560))))) (((-1209)) . 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T) (((-421 (-560))) -4144 (|has| |#1| (-38 (-421 (-560)))) (|has| |#1| (-376))) ((|#1|) . T)) +((($) . T) (((-421 (-560))) -4118 (|has| |#1| (-38 (-421 (-560)))) (|has| |#1| (-376))) ((|#1|) . T)) (|has| |#1| (-845)) ((((-421 (-560))) |has| |#1| (-1070 (-421 (-560)))) (((-560)) |has| |#1| (-1070 (-560))) ((|#1|) . T)) -(-4144 (|has| |#1| (-102)) (|has| |#1| (-1133))) +(-4118 (|has| |#1| (-102)) (|has| |#1| (-1133))) (((|#1| $) |has| |#1| (-298 |#1| |#1|))) ((((-421 (-560))) |has| |#1| (-38 (-421 (-560)))) ((|#1|) |has| |#1| (-175)) (($) |has| |#1| (-571))) ((($) |has| |#1| (-571))) @@ -1065,49 +1065,49 @@ (((|#4|) |has| |#4| (-1133))) (((|#3|) |has| |#3| (-1133))) (|has| |#3| (-381)) -((($) |has| |#1| (-571)) ((|#1|) . T) (((-421 (-560))) -4144 (|has| |#1| (-38 (-421 (-560)))) (|has| |#1| (-1070 (-421 (-560))))) (((-560)) . T)) +((($) |has| |#1| (-571)) ((|#1|) . T) (((-421 (-560))) -4118 (|has| |#1| (-38 (-421 (-560)))) (|has| |#1| (-1070 (-421 (-560))))) (((-560)) . T)) ((((-888)) . 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T)) -(-4144 (|has| |#1| (-21)) (|has| |#1| (-25)) (|has| |#1| (-147)) (|has| |#1| (-149)) (|has| |#1| (-175)) (|has| |#1| (-571)) (|has| |#1| (-1081))) +(-4118 (|has| |#1| (-21)) (|has| |#1| (-25)) (|has| |#1| (-147)) (|has| |#1| (-149)) (|has| |#1| (-175)) (|has| |#1| (-571)) (|has| |#1| (-1081))) (((|#1|) |has| |#1| (-175))) (|has| $ (-149)) (|has| $ (-149)) ((((-1214)) . T)) (((|#1|) |has| |#1| (-175))) -(-4144 (|has| |#1| (-102)) (|has| |#1| (-1133))) +(-4118 (|has| |#1| (-102)) (|has| |#1| (-1133))) ((((-888)) . T)) (|has| |#1| (-38 (-421 (-560)))) (|has| |#1| (-38 (-421 (-560)))) -(-4144 (|has| |#1| (-147)) (|has| |#1| (-149)) (|has| |#1| (-175)) (|has| |#1| (-487)) (|has| |#1| (-571)) (|has| |#1| (-1081)) (|has| |#1| (-1144))) +(-4118 (|has| |#1| (-147)) (|has| |#1| (-149)) (|has| |#1| (-175)) (|has| |#1| (-487)) (|has| |#1| (-571)) (|has| |#1| (-1081)) (|has| |#1| (-1144))) ((($ $) |has| |#1| (-298 $ $)) ((|#1| $) |has| |#1| (-298 |#1| |#1|))) (((|#1| (-421 (-560))) . T)) (((|#1|) . T)) @@ -1116,8 +1116,8 @@ (((|#1|) . T)) ((((-1209)) . T)) (|has| |#1| (-571)) -(-4144 (|has| |#1| (-376)) (|has| |#1| (-571))) -(-4144 (|has| |#1| (-376)) (|has| |#1| (-571))) +(-4118 (|has| |#1| (-376)) (|has| |#1| (-571))) +(-4118 (|has| |#1| (-376)) (|has| |#1| (-571))) (|has| |#1| (-571)) (|has| |#1| (-38 (-421 (-560)))) (|has| |#1| (-38 (-421 (-560)))) @@ -1129,7 +1129,7 @@ (|has| |#1| (-149)) (|has| |#1| (-147)) (|has| |#1| (-149)) -(((|#2| (-246 (-2236 |#1|) (-793)) (-889 |#1|)) . T)) +(((|#2| (-246 (-2223 |#1|) (-793)) (-889 |#1|)) . T)) (((|#1| (-545 |#3|) |#3|) . T)) (|has| |#1| (-147)) (((#0=(-421 (-560)) #0#) |has| |#2| (-376)) (($ $) . T)) @@ -1143,12 +1143,12 @@ (|has| |#1| (-147)) ((((-421 (-560))) |has| |#2| (-376)) (($) . T)) (((|#1| |#1|) -12 (|has| |#1| (-321 |#1|)) (|has| |#1| (-1133)))) -(-4144 (|has| |#2| (-466)) (|has| |#2| (-571)) (|has| |#2| (-940))) -(-4144 (|has| |#1| (-363)) (|has| |#1| (-381))) +(-4118 (|has| |#2| (-466)) (|has| |#2| (-571)) (|has| |#2| (-940))) +(-4118 (|has| |#1| (-363)) (|has| |#1| (-381))) ((((-1174 |#2| |#1|)) . T) ((|#1|) . T)) (((|#1| |#2|) . T)) (-12 (|has| |#2| (-240)) (|has| |#2| (-1081))) -(((|#2|) . T) (((-2 (|:| -2118 |#1|) (|:| -3964 |#2|))) . T)) +(((|#2|) . T) (((-2 (|:| -2115 |#1|) (|:| -3934 |#2|))) . T)) (|has| |#3| (-817)) (|has| |#3| (-817)) ((((-888)) . T)) @@ -1176,18 +1176,18 @@ ((((-888)) . T)) ((((-888)) . T)) (((|#1| |#2|) . T)) -((((-1209)) -4144 (|has| |#2| (-928 (-1209))) (|has| |#2| (-930 (-1209)))) (((-1114)) . T)) +((((-1209)) -4118 (|has| |#2| (-928 (-1209))) (|has| |#2| (-930 (-1209)))) (((-1114)) . T)) (((|#1|) . T)) (((|#3|) . T) (((-630 $)) . T)) (((|#1| (-421 (-560))) . T)) -((((-2 (|:| -2118 |#1|) (|:| -3964 |#2|))) . T)) +((((-2 (|:| -2115 |#1|) (|:| -3934 |#2|))) . T)) (((|#1| |#2|) . T)) (((|#1|) . T) (($) . T)) (((|#1|) . T)) (((|#1|) -12 (|has| |#1| (-321 |#1|)) (|has| |#1| (-1133)))) ((($ (-1296 |#2|)) . T) (($ (-1209)) -12 (|has| |#1| (-15 * (|#1| (-421 (-560)) |#1|))) (|has| |#1| (-928 (-1209))))) -((((-2 (|:| -2118 |#1|) (|:| -3964 |#2|))) . T)) -((((-560)) -4144 (-12 (|has| |#2| (-1070 (-560))) (|has| |#2| (-1133))) (|has| |#2| (-1081))) ((|#2|) |has| |#2| (-1133)) (((-421 (-560))) -12 (|has| |#2| (-1070 (-421 (-560)))) (|has| |#2| (-1133)))) +((((-2 (|:| -2115 |#1|) (|:| -3934 |#2|))) . T)) +((((-560)) -4118 (-12 (|has| |#2| (-1070 (-560))) (|has| |#2| (-1133))) (|has| |#2| (-1081))) ((|#2|) |has| |#2| (-1133)) (((-421 (-560))) -12 (|has| |#2| (-1070 (-421 (-560)))) (|has| |#2| (-1133)))) (((|#1|) . T) (((-421 (-560))) . T) (($) . T)) ((($ $) . T) ((|#2| $) . T)) ((((-560)) . T) (($) . T) (((-421 (-560))) . T)) @@ -1195,15 +1195,15 @@ ((((-888)) . T)) ((((-888)) . T)) (((|#1| |#1|) . T)) -(((|#2|) -12 (|has| |#2| (-321 |#2|)) (|has| |#2| (-1133))) (((-2 (|:| -2118 |#1|) (|:| -3964 |#2|))) |has| (-2 (|:| -2118 |#1|) (|:| -3964 |#2|)) (-321 (-2 (|:| -2118 |#1|) (|:| -3964 |#2|))))) -(((|#1|) -12 (|has| |#1| (-321 |#1|)) (|has| |#1| (-1133))) (((-2 (|:| -2118 (-1191)) (|:| -3964 |#1|))) |has| (-2 (|:| -2118 (-1191)) (|:| -3964 |#1|)) (-321 (-2 (|:| -2118 (-1191)) (|:| -3964 |#1|))))) +(((|#2|) -12 (|has| |#2| (-321 |#2|)) (|has| |#2| (-1133))) (((-2 (|:| -2115 |#1|) (|:| -3934 |#2|))) |has| (-2 (|:| -2115 |#1|) (|:| -3934 |#2|)) (-321 (-2 (|:| -2115 |#1|) (|:| -3934 |#2|))))) +(((|#1|) -12 (|has| |#1| (-321 |#1|)) (|has| |#1| (-1133))) (((-2 (|:| -2115 (-1191)) (|:| -3934 |#1|))) |has| (-2 (|:| -2115 (-1191)) (|:| -3934 |#1|)) (-321 (-2 (|:| -2115 (-1191)) (|:| -3934 |#1|))))) ((((-888)) . T)) (((|#1|) . T)) (((|#3| |#3|) . T)) (((|#1|) . T)) ((($) . T) ((|#2|) . T) (((-560)) |has| |#2| (-660 (-560)))) ((((-1209) (-51)) . T)) -((((-1209)) -4144 (|has| |#1| (-928 (-1209))) (|has| |#1| (-930 (-1209))))) +((((-1209)) -4118 (|has| |#1| (-928 (-1209))) (|has| |#1| (-930 (-1209))))) (((|#3|) . T)) ((($ $) . T) ((#0=(-889 |#1|) $) . T) ((#0# |#2|) . T)) (|has| |#1| (-845)) @@ -1211,10 +1211,10 @@ ((($) . T) (((-560)) . T) (((-421 (-560))) |has| |#1| (-38 (-421 (-560)))) ((|#1|) . T)) ((((-560)) . T) (($) . T) ((|#1|) . T) (((-421 (-560))) |has| |#1| (-38 (-421 (-560))))) (|has| (-1121 |#1|) (-1133)) -(((|#2| |#2|) -4144 (|has| |#2| (-175)) (|has| |#2| (-376)) (|has| |#2| (-1081)))) -(((|#2|) -4144 (|has| |#2| (-175)) (|has| |#2| (-376)))) -((((-560) (-2 (|:| -2118 |#1|) (|:| -3964 |#2|))) . T) ((|#1| |#2|) . T)) -(((|#2|) -4144 (|has| |#2| (-175)) (|has| |#2| (-376)) (|has| |#2| (-1081)))) +(((|#2| |#2|) -4118 (|has| |#2| (-175)) (|has| |#2| (-376)) (|has| |#2| (-1081)))) +(((|#2|) -4118 (|has| |#2| (-175)) (|has| |#2| (-376)))) +((((-560) (-2 (|:| -2115 |#1|) (|:| -3934 |#2|))) . T) ((|#1| |#2|) . T)) +(((|#2|) -4118 (|has| |#2| (-175)) (|has| |#2| (-376)) (|has| |#2| (-1081)))) ((((-560)) . T)) ((((-1214)) . T)) ((((-793)) . T)) @@ -1233,34 +1233,34 @@ (((|#1|) . T)) ((((-421 (-560))) . T) (($) . T)) ((($) . T) (((-421 (-560))) . T)) -(-4144 (|has| |#1| (-175)) (|has| |#1| (-571))) +(-4118 (|has| |#1| (-175)) (|has| |#1| (-571))) ((((-1214)) . T)) -(-4144 (|has| |#1| (-175)) (|has| |#1| (-376)) (|has| |#1| (-571))) -(-4144 (|has| |#1| (-175)) (|has| |#1| (-376)) (|has| |#1| (-571))) +(-4118 (|has| |#1| (-175)) (|has| |#1| (-376)) (|has| |#1| (-571))) +(-4118 (|has| |#1| (-175)) (|has| |#1| (-376)) (|has| |#1| (-571))) ((((-560)) . T)) -(-4144 (|has| |#1| (-175)) (|has| |#1| (-571))) +(-4118 (|has| |#1| (-175)) (|has| |#1| (-571))) (|has| |#1| (-147)) ((((-560)) . 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T)) -(-4144 (|has| |#2| (-175)) (|has| |#2| (-466)) (|has| |#2| (-571)) (|has| |#2| (-940))) +(-4118 (|has| |#2| (-175)) (|has| |#2| (-466)) (|has| |#2| (-571)) (|has| |#2| (-940))) (((|#1|) . T) (($) . T)) (((|#2|) |has| |#2| (-175))) -((($) -4144 (|has| |#2| (-376)) (|has| |#2| (-466)) (|has| |#2| (-571)) (|has| |#2| (-940))) ((|#2|) |has| |#2| (-175)) (((-421 (-560))) |has| |#2| (-38 (-421 (-560))))) +((($) -4118 (|has| |#2| (-376)) (|has| |#2| (-466)) (|has| |#2| (-571)) (|has| |#2| (-940))) ((|#2|) |has| |#2| (-175)) (((-421 (-560))) |has| |#2| (-38 (-421 (-560))))) ((((-894 |#1|)) . T)) -(-4144 (|has| |#2| (-21)) (|has| |#2| (-23)) (|has| |#2| (-25)) (|has| |#2| (-133)) (|has| |#2| (-175)) (|has| |#2| (-376)) (|has| |#2| (-381)) (|has| |#2| (-748)) (|has| |#2| (-817)) (|has| |#2| (-872)) (|has| |#2| (-1081)) (|has| |#2| (-1133))) +(-4118 (|has| |#2| (-21)) (|has| |#2| (-23)) (|has| |#2| (-25)) (|has| |#2| (-133)) (|has| |#2| (-175)) (|has| |#2| (-376)) (|has| |#2| (-381)) (|has| |#2| (-748)) (|has| |#2| (-817)) (|has| |#2| (-872)) (|has| |#2| (-1081)) (|has| |#2| (-1133))) (-12 (|has| |#3| (-240)) (|has| |#3| (-1081))) (|has| |#2| (-1184)) -(((#0=(-51)) . T) (((-2 (|:| -2118 (-1209)) (|:| -3964 #0#))) . T)) +(((#0=(-51)) . T) (((-2 (|:| -2115 (-1209)) (|:| -3934 #0#))) . T)) (((|#1| |#2|) . T)) (((|#1| (-657 |#2|)) . T)) (|has| |#3| (-1081)) @@ -1269,10 +1269,10 @@ (((|#1| (-560) (-1114)) . T)) (((|#1| (-421 (-560)) (-1114)) . T)) ((((-1209)) . T)) -((($) -4144 (|has| |#1| (-319)) (|has| |#1| (-376)) (|has| |#1| (-363)) (|has| |#1| (-571))) (((-421 (-560))) -4144 (|has| |#1| (-376)) (|has| |#1| (-363))) ((|#1|) . T)) -((($) -4144 (|has| (-421 |#2|) (-240)) (|has| (-421 |#2|) (-239)))) +((($) -4118 (|has| |#1| (-319)) (|has| |#1| (-376)) (|has| |#1| (-363)) (|has| |#1| (-571))) (((-421 (-560))) -4118 (|has| |#1| (-376)) (|has| |#1| (-363))) ((|#1|) . T)) +((($) -4118 (|has| (-421 |#2|) (-240)) (|has| (-421 |#2|) (-239)))) ((((-560) |#2|) . T)) -((($ (-1209)) -4144 (|has| |#2| (-928 (-1209))) (|has| |#2| (-930 (-1209))))) +((($ (-1209)) -4118 (|has| |#2| (-928 (-1209))) (|has| |#2| (-930 (-1209))))) (((|#1| |#2|) . T)) (((|#1| |#2|) . T)) (|has| |#2| (-381)) @@ -1280,46 +1280,46 @@ ((((-888)) . 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T)) (((|#1|) |has| |#1| (-321 |#1|))) @@ -1329,21 +1329,21 @@ (|has| |#1| (-381)) ((((-1209) $) |has| |#1| (-528 (-1209) $)) (($ $) |has| |#1| (-321 $)) ((|#1| |#1|) |has| |#1| (-321 |#1|)) (((-1209) |#1|) |has| |#1| (-528 (-1209) |#1|))) ((((-1209)) |has| |#1| (-928 (-1209)))) -(-4144 (-12 (|has| |#1| (-240)) (|has| |#1| (-376))) (|has| |#1| (-363))) +(-4118 (-12 (|has| |#1| (-240)) (|has| |#1| (-376))) (|has| |#1| (-363))) (((|#1| |#4|) . T)) (((|#1| |#3|) . T)) ((($) . T)) ((((-402) |#1|) . T)) -(-4144 (|has| |#1| (-376)) (|has| |#1| (-363))) -(-4144 (|has| |#1| (-102)) (|has| |#1| (-1133))) +(-4118 (|has| |#1| (-376)) (|has| |#1| (-363))) +(-4118 (|has| |#1| (-102)) (|has| |#1| (-1133))) (((|#2|) . T) (((-888)) . T)) ((((-888)) . T)) (((|#2|) . T)) ((((-936 |#1|)) . T)) ((((-888)) . T) (((-1214)) . T)) ((((-1214)) . T)) -((((-421 (-560))) |has| |#2| (-38 (-421 (-560)))) ((|#2|) |has| |#2| (-175)) (($) -4144 (|has| |#2| (-466)) (|has| |#2| (-571)) (|has| |#2| (-940)))) -((((-421 (-560))) |has| |#1| (-38 (-421 (-560)))) ((|#1|) |has| |#1| (-175)) (($) -4144 (|has| |#1| (-466)) (|has| |#1| (-571)) (|has| |#1| (-940)))) +((((-421 (-560))) |has| |#2| (-38 (-421 (-560)))) ((|#2|) |has| |#2| (-175)) (($) -4118 (|has| |#2| (-466)) (|has| |#2| (-571)) (|has| |#2| (-940)))) +((((-421 (-560))) |has| |#1| (-38 (-421 (-560)))) ((|#1|) |has| |#1| (-175)) (($) -4118 (|has| |#1| (-466)) (|has| |#1| (-571)) (|has| |#1| (-940)))) (((|#1| |#2|) . T)) ((($) . T)) ((((-560)) . T) (($) . T) (((-421 (-560))) . T)) @@ -1352,7 +1352,7 @@ (((|#1|) . T) (((-421 (-560))) . T) (($) . T) (((-560)) . T)) (((|#1| |#1|) . T)) (((#0=(-894 |#1|)) |has| #0# (-321 #0#))) -((((-560)) . T) (($) -4144 (|has| |#1| (-376)) (|has| |#1| (-363))) (((-421 (-560))) -4144 (|has| |#1| (-376)) (|has| |#1| (-363)) (|has| |#1| (-1070 (-421 (-560))))) ((|#1|) . T)) +((((-560)) . T) (($) -4118 (|has| |#1| (-376)) (|has| |#1| (-363))) (((-421 (-560))) -4118 (|has| |#1| (-376)) (|has| |#1| (-363)) (|has| |#1| (-1070 (-421 (-560))))) ((|#1|) . T)) (((|#1| |#2|) . T)) (|has| |#2| (-817)) (|has| |#2| (-817)) @@ -1361,7 +1361,7 @@ (-12 (|has| |#1| (-817)) (|has| |#2| (-817))) (|has| |#2| (-1081)) ((($) . T) (((-560)) . T) ((|#2|) . T)) -(((|#2|) . T) (((-2 (|:| -2118 |#1|) (|:| -3964 |#2|))) . T)) +(((|#2|) . T) (((-2 (|:| -2115 |#1|) (|:| -3934 |#2|))) . T)) (((|#2|) . T) (($) . T)) (|has| |#1| (-1235)) (((#0=(-560) #0#) . T) ((#1=(-421 (-560)) #1#) . T) (($ $) . T)) @@ -1375,7 +1375,7 @@ (((|#1| |#1|) . T) (($ $) . T) ((#0=(-421 (-560)) #0#) . T)) (|has| |#1| (-376)) ((((-560)) . T) (((-421 (-560))) . T) (($) . 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T) (((-421 (-560))) |has| |#2| (-38 (-421 (-560))))) +((($) -4118 (|has| |#2| (-175)) (|has| |#2| (-376)) (|has| |#2| (-466)) (|has| |#2| (-571)) (|has| |#2| (-940))) ((|#2|) . T) (((-421 (-560))) |has| |#2| (-38 (-421 (-560))))) ((((-560)) |has| #0=(-421 |#2|) (-660 (-560))) ((#0#) . T)) ((($) . T) (((-560)) . T)) ((((-560) (-146)) . T)) -((((-560) (-2 (|:| -2118 |#1|) (|:| -3964 |#2|))) . T) ((|#1| |#2|) . T)) +((((-560) (-2 (|:| -2115 |#1|) (|:| -3934 |#2|))) . T) ((|#1| |#2|) . T)) ((((-421 (-560))) . T) (($) . T)) (((|#1|) . T)) -((((-2 (|:| -2118 |#1|) (|:| -3964 |#2|))) . T)) +((((-2 (|:| -2115 |#1|) (|:| -3934 |#2|))) . T)) ((((-888)) . T)) ((((-936 |#1|)) . T)) (|has| |#1| (-376)) @@ -1423,11 +1423,11 @@ (|has| |#1| (-376)) (|has| |#1| (-15 * (|#1| (-421 (-560)) |#1|))) (|has| |#1| (-871)) -((($) -4144 (|has| |#1| (-319)) (|has| |#1| (-376)) (|has| |#1| (-363)) (|has| |#1| (-571))) (((-421 (-560))) -4144 (|has| |#1| (-376)) (|has| |#1| (-363))) ((|#1|) . T)) +((($) -4118 (|has| |#1| (-319)) (|has| |#1| (-376)) (|has| |#1| (-363)) (|has| |#1| (-571))) (((-421 (-560))) -4118 (|has| |#1| (-376)) (|has| |#1| (-363))) ((|#1|) . T)) (|has| |#1| (-376)) (((|#1|) . T) (($) . T)) (|has| |#1| (-871)) -((($) . T) (((-421 (-560))) -4144 (|has| |#1| (-376)) (|has| |#1| (-363))) ((|#1|) . T)) +((($) . T) (((-421 (-560))) -4118 (|has| |#1| (-376)) (|has| |#1| (-363))) ((|#1|) . T)) ((((-1209)) |has| |#1| (-928 (-1209)))) (|has| |#1| (-871)) ((((-520)) . T)) @@ -1443,7 +1443,7 @@ ((((-549)) . T)) ((((-888)) . T)) ((($) . T)) -((((-560) (-2 (|:| -2118 |#1|) (|:| -3964 |#2|))) . T) (((-1266 (-560)) $) . T) ((|#1| |#2|) . T)) +((((-560) (-2 (|:| -2115 |#1|) (|:| -3934 |#2|))) . T) (((-1266 (-560)) $) . T) ((|#1| |#2|) . T)) (((|#1|) . T)) (((|#2|) . T) (($) . T)) (((|#1|) |has| |#1| (-175))) @@ -1453,22 +1453,22 @@ (((|#1|) -12 (|has| |#1| (-321 |#1|)) (|has| |#1| (-1133)))) (((|#3|) . 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T)) -(((|#2|) -4144 (|has| |#2| (-175)) (|has| |#2| (-376)) (|has| |#2| (-1081)))) +(((|#2|) -4118 (|has| |#2| (-175)) (|has| |#2| (-376)) (|has| |#2| (-1081)))) (|has| $ (-149)) ((((-421 |#2|)) . T)) ((((-421 (-560))) |has| #0=(-421 |#2|) (-1070 (-421 (-560)))) (((-560)) |has| #0# (-1070 (-560))) ((#0#) . T)) @@ -1570,11 +1570,11 @@ (|has| |#2| (-149)) (|has| |#1| (-149)) (|has| |#1| (-147)) -(-4144 (|has| |#1| (-147)) (|has| |#1| (-381))) +(-4118 (|has| |#1| (-147)) (|has| |#1| (-381))) (|has| |#1| (-149)) -(-4144 (|has| |#1| (-147)) (|has| |#1| (-381))) +(-4118 (|has| |#1| (-147)) (|has| |#1| (-381))) (|has| |#1| (-149)) -(-4144 (|has| |#1| (-147)) (|has| |#1| (-381))) +(-4118 (|has| |#1| (-147)) (|has| |#1| (-381))) (|has| |#1| (-149)) (((|#1|) . T)) (|has| |#2| (-240)) @@ -1611,9 +1611,9 @@ ((((-888)) . T)) ((((-888)) . T)) ((((-1028 |#1|)) . T) ((|#1|) . T)) -((((-1209)) -4144 (|has| |#1| (-928 (-1209))) (|has| |#1| (-930 (-1209)))) (((-842 (-1209))) . 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T)) (((|#1| |#2|) . T)) ((((-1209)) -12 (|has| |#1| (-15 * (|#1| (-560) |#1|))) (|has| |#1| (-928 (-1209))))) (|has| |#1| (-814)) -(-4144 (|has| |#1| (-175)) (|has| |#1| (-571))) -((((-1209)) -4144 (-12 (|has| (-1289 |#1| |#2| |#3|) (-928 (-1209))) (|has| |#1| (-376))) (-12 (|has| (-1289 |#1| |#2| |#3|) (-930 (-1209))) (|has| |#1| (-376))) (-12 (|has| |#1| (-15 * (|#1| (-560) |#1|))) (|has| |#1| (-928 (-1209)))))) +(-4118 (|has| |#1| (-175)) (|has| |#1| (-571))) +((((-1209)) -4118 (-12 (|has| (-1289 |#1| |#2| |#3|) (-928 (-1209))) (|has| |#1| (-376))) (-12 (|has| (-1289 |#1| |#2| |#3|) (-930 (-1209))) (|has| |#1| (-376))) (-12 (|has| |#1| (-15 * (|#1| (-560) |#1|))) (|has| |#1| (-928 (-1209)))))) ((((-1209)) -12 (|has| |#1| (-15 * (|#1| (-421 (-560)) |#1|))) (|has| |#1| (-928 (-1209))))) ((((-1209)) -12 (|has| |#1| (-15 * (|#1| (-793) |#1|))) (|has| |#1| (-928 (-1209))))) (((|#1|) |has| |#1| (-175))) (((|#4|) . T)) (((|#4|) . T)) (((|#1| |#2|) . T)) -(-4144 (|has| |#1| (-149)) (-12 (|has| |#1| (-376)) (|has| |#2| (-149)))) +(-4118 (|has| |#1| (-149)) (-12 (|has| |#1| (-376)) (|has| |#2| (-149)))) (((|#4|) . T)) -(-4144 (|has| |#1| (-147)) (-12 (|has| |#1| (-376)) (|has| |#2| (-147)))) +(-4118 (|has| |#1| (-147)) (-12 (|has| |#1| (-376)) (|has| |#2| (-147)))) ((((-1191) |#1|) . T)) (|has| |#1| (-147)) (|has| |#1| (-149)) @@ -1718,24 +1718,24 @@ (((|#3|) . T)) ((((-1289 |#1| |#2| |#3|)) |has| |#1| (-376))) ((($) . T) (((-560)) . T) (((-421 (-560))) |has| |#1| (-38 (-421 (-560)))) ((|#1|) . T)) -((((-421 (-560))) -4144 (|has| |#1| (-38 (-421 (-560)))) (|has| |#1| (-376))) (((-1207 |#1| |#2| |#3|)) |has| |#1| (-376)) (((-560)) . T) (($) . T) ((|#1|) . T)) -(((|#1|) . T) (((-421 (-560))) -4144 (|has| |#1| (-38 (-421 (-560)))) (|has| |#1| (-376))) (((-560)) . T) (($) . T)) +((((-421 (-560))) -4118 (|has| |#1| (-38 (-421 (-560)))) (|has| |#1| (-376))) (((-1207 |#1| |#2| |#3|)) |has| |#1| (-376)) (((-560)) . T) (($) . T) ((|#1|) . T)) +(((|#1|) . T) (((-421 (-560))) -4118 (|has| |#1| (-38 (-421 (-560)))) (|has| |#1| (-376))) (((-560)) . T) (($) . T)) ((((-888)) . T)) -(-4144 (|has| |#1| (-102)) (|has| |#1| (-872)) (|has| |#1| (-1133))) +(-4118 (|has| |#1| (-102)) (|has| |#1| (-872)) (|has| |#1| (-1133))) (((|#1|) . T)) (((|#1|) . T) (((-421 (-560))) |has| |#1| (-38 (-421 (-560)))) (((-560)) . T) (($) . T)) -((((-888)) -4144 (|has| |#1| (-632 (-888))) (|has| |#1| (-1133)))) -((((-888)) -4144 (|has| |#1| (-632 (-888))) (|has| |#1| (-1133))) (((-988 |#1|)) . T)) +((((-888)) -4118 (|has| |#1| (-632 (-888))) (|has| |#1| (-1133)))) +((((-888)) -4118 (|has| |#1| (-632 (-888))) (|has| |#1| (-1133))) (((-988 |#1|)) . T)) (|has| |#1| (-871)) (|has| |#1| (-871)) (((|#1| |#1|) -12 (|has| |#1| (-321 |#1|)) (|has| |#1| (-1133)))) ((((-988 |#1|)) . T)) -(((|#4|) -4144 (|has| |#4| (-175)) (|has| |#4| (-376)) (|has| |#4| (-748)))) -(((|#3|) -4144 (|has| |#3| (-175)) (|has| |#3| (-376)) (|has| |#3| (-748)))) +(((|#4|) -4118 (|has| |#4| (-175)) (|has| |#4| (-376)) (|has| |#4| (-748)))) +(((|#3|) -4118 (|has| |#3| (-175)) (|has| |#3| (-376)) (|has| |#3| (-748)))) (|has| |#2| (-376)) (((|#1|) |has| |#1| (-175))) -(((|#4|) -4144 (|has| |#4| (-175)) (|has| |#4| (-376)) (|has| |#4| (-748)) (|has| |#4| (-1081)))) -(((|#3|) -4144 (|has| |#3| (-175)) (|has| |#3| (-376)) (|has| |#3| (-748)) (|has| |#3| (-1081)))) +(((|#4|) -4118 (|has| |#4| (-175)) (|has| |#4| (-376)) (|has| |#4| (-748)) (|has| |#4| (-1081)))) +(((|#3|) -4118 (|has| |#3| (-175)) (|has| |#3| (-376)) (|has| |#3| (-748)) (|has| |#3| (-1081)))) (((|#2|) |has| |#2| (-1081))) (((|#2|) |has| |#2| (-1081))) ((((-1191) |#1|) . T)) @@ -1747,8 +1747,8 @@ ((((-402) (-1191)) . T)) ((($ (-1209)) . T)) ((($) |has| |#1| (-571)) ((|#1|) |has| |#1| (-175)) (((-421 (-560))) |has| |#1| (-38 (-421 (-560))))) -((((-888)) -4144 (|has| |#2| (-21)) (|has| |#2| (-23)) (|has| |#2| (-25)) (|has| |#2| (-133)) (|has| |#2| (-632 (-888))) (|has| |#2| (-175)) (|has| |#2| (-376)) (|has| |#2| (-381)) (|has| |#2| (-748)) (|has| |#2| (-817)) (|has| |#2| (-872)) (|has| |#2| (-1081)) (|has| |#2| (-1133))) (((-1299 |#2|)) . T)) -(((#0=(-51)) . T) (((-2 (|:| -2118 (-1191)) (|:| -3964 #0#))) . T)) +((((-888)) -4118 (|has| |#2| (-21)) (|has| |#2| (-23)) (|has| |#2| (-25)) (|has| |#2| (-133)) (|has| |#2| (-632 (-888))) (|has| |#2| (-175)) (|has| |#2| (-376)) (|has| |#2| (-381)) (|has| |#2| (-748)) (|has| |#2| (-817)) (|has| |#2| (-872)) (|has| |#2| (-1081)) (|has| |#2| (-1133))) (((-1299 |#2|)) . T)) +(((#0=(-51)) . T) (((-2 (|:| -2115 (-1191)) (|:| -3934 #0#))) . T)) (((|#1|) . T)) ((((-888)) . T)) (((|#2| |#2|) -12 (|has| |#2| (-321 |#2|)) (|has| |#2| (-1133)))) @@ -1757,7 +1757,7 @@ ((((-560)) . T)) (|has| |#2| (-149)) (|has| |#1| (-487)) -(-4144 (|has| |#1| (-487)) (|has| |#1| (-748)) (|has| |#1| (-928 (-1209))) (|has| |#1| (-1081))) +(-4118 (|has| |#1| (-487)) (|has| |#1| (-748)) (|has| |#1| (-928 (-1209))) (|has| |#1| (-1081))) (|has| |#1| (-376)) ((((-888)) . T)) (|has| |#1| (-38 (-421 (-560)))) @@ -1768,8 +1768,8 @@ (|has| |#1| (-871)) ((((-888)) . T)) (((|#2|) . T)) -((((-421 (-560))) -4144 (|has| |#1| (-38 (-421 (-560)))) (|has| |#1| (-376))) (($) -4144 (|has| |#1| (-376)) (|has| |#1| (-571))) (((-1289 |#1| |#2| |#3|)) |has| |#1| (-376)) ((|#1|) |has| |#1| (-175))) -(((|#1|) |has| |#1| (-175)) (((-421 (-560))) -4144 (|has| |#1| (-38 (-421 (-560)))) (|has| |#1| (-376))) (($) -4144 (|has| |#1| (-376)) (|has| |#1| (-571)))) +((((-421 (-560))) -4118 (|has| |#1| (-38 (-421 (-560)))) (|has| |#1| (-376))) (($) -4118 (|has| |#1| (-376)) (|has| |#1| (-571))) (((-1289 |#1| |#2| |#3|)) |has| |#1| (-376)) ((|#1|) |has| |#1| (-175))) +(((|#1|) |has| |#1| (-175)) (((-421 (-560))) -4118 (|has| |#1| (-38 (-421 (-560)))) (|has| |#1| (-376))) (($) -4118 (|has| |#1| (-376)) (|has| |#1| (-571)))) ((($) |has| |#1| (-571)) ((|#1|) |has| |#1| (-175)) (((-421 (-560))) |has| |#1| (-38 (-421 (-560))))) (((|#2|) . T) (((-560)) . T) (((-843 |#1|)) . T)) (((|#1| |#2|) . T)) @@ -1778,8 +1778,8 @@ ((((-936 |#1|)) . T) (((-421 (-560))) . T) (($) . T)) ((((-888)) . T)) ((((-888)) . T)) -(-4144 (|has| |#1| (-102)) (|has| |#1| (-1133))) -(((|#2| (-496 (-2236 |#1|) (-793)) (-889 |#1|)) . T)) +(-4118 (|has| |#1| (-102)) (|has| |#1| (-1133))) +(((|#2| (-496 (-2223 |#1|) (-793)) (-889 |#1|)) . T)) ((((-421 (-560))) . #0=(|has| |#2| (-376))) (($) . #0#)) (((|#1| (-545 (-1209)) (-1209)) . T)) (((|#1|) . T)) @@ -1800,19 +1800,19 @@ (((|#2|) |has| |#2| (-175))) (((|#1|) . T)) (((|#2|) . T)) -(((|#1|) . T) (((-2 (|:| -2118 (-1191)) (|:| -3964 |#1|))) . T)) -((((-2 (|:| -2118 |#1|) (|:| -3964 |#2|))) . T)) +(((|#1|) . T) (((-2 (|:| -2115 (-1191)) (|:| -3934 |#1|))) . T)) +((((-2 (|:| -2115 |#1|) (|:| -3934 |#2|))) . T)) (((|#2|) . T)) -((((-2 (|:| -2118 (-1209)) (|:| -3964 (-51)))) . T)) +((((-2 (|:| -2115 (-1209)) (|:| -3934 (-51)))) . T)) ((((-1207 |#1| |#2| |#3|)) |has| |#1| (-376))) ((((-1207 |#1| |#2| |#3|)) |has| |#1| (-376))) -((((-2 (|:| -2118 |#1|) (|:| -3964 |#2|))) . T)) +((((-2 (|:| -2115 |#1|) (|:| -3934 |#2|))) . T)) ((((-1209) (-51)) . T)) ((((-421 (-560)) |#1|) . T) (($ $) . T)) (((|#1| (-560)) . T)) ((((-936 |#1|)) . T)) -(((|#1|) -4144 (|has| |#1| (-175)) (|has| |#1| (-376)) (|has| |#1| (-1081))) (($) -4144 (|has| |#1| (-928 (-1209))) (|has| |#1| (-1081)))) -((((-1209)) -4144 (-12 (|has| |#2| (-928 (-1209))) (|has| |#2| (-1081))) (-12 (|has| |#2| (-930 (-1209))) (|has| |#2| (-1081))))) +(((|#1|) -4118 (|has| |#1| (-175)) (|has| |#1| (-376)) (|has| |#1| (-1081))) (($) -4118 (|has| |#1| (-928 (-1209))) (|has| |#1| (-1081)))) +((((-1209)) -4118 (-12 (|has| |#2| (-928 (-1209))) (|has| |#2| (-1081))) (-12 (|has| |#2| (-930 (-1209))) (|has| |#2| (-1081))))) (((|#1|) . T) (((-560)) |has| |#1| (-1070 (-560))) (((-421 (-560))) |has| |#1| (-1070 (-421 (-560))))) (|has| |#1| (-872)) (|has| |#1| (-872)) @@ -1833,15 +1833,15 @@ (((|#4| |#4|) -12 (|has| |#4| (-321 |#4|)) (|has| |#4| (-1133)))) (((|#1|) |has| |#1| (-175))) (((|#4| |#4|) -12 (|has| |#4| (-321 |#4|)) (|has| |#4| (-1133)))) -(((|#3|) -4144 (|has| |#3| (-175)) (|has| |#3| (-376)))) -((($) -4144 (|has| |#1| (-466)) (|has| |#1| (-571)) (|has| |#1| (-940))) ((|#1|) |has| |#1| (-175)) (((-421 (-560))) |has| |#1| (-38 (-421 (-560))))) -(-4144 (|has| |#2| (-376)) (|has| |#2| (-466)) (|has| |#2| (-940))) -((($) -4144 (|has| |#1| (-175)) (|has| |#1| (-466)) (|has| |#1| (-571)) (|has| |#1| (-940))) ((|#1|) . 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T)) @@ -1850,7 +1850,7 @@ (|has| |#1| (-844)) (|has| |#1| (-844)) (((|#1|) . T)) -(-4144 (|has| |#1| (-319)) (|has| |#1| (-376)) (|has| |#1| (-363))) +(-4118 (|has| |#1| (-319)) (|has| |#1| (-376)) (|has| |#1| (-363))) (|has| |#1| (-871)) (|has| |#1| (-871)) (|has| |#1| (-871)) @@ -1859,14 +1859,14 @@ ((((-560)) . T) (($) . T) (((-421 (-560))) . T)) (|has| |#1| (-38 (-421 (-560)))) (|has| |#1| (-38 (-421 (-560)))) -(-4144 (|has| |#1| (-376)) (|has| |#1| (-363))) +(-4118 (|has| |#1| (-376)) (|has| |#1| (-363))) (|has| |#1| (-38 (-421 (-560)))) (|has| |#1| (-38 (-421 (-560)))) -((((-2 (|:| -2118 |#1|) (|:| -3964 |#2|))) . T)) +((((-2 (|:| -2115 |#1|) (|:| -3934 |#2|))) . T)) ((((-1209)) |has| |#1| (-928 (-1209))) (((-1114)) . T)) (((|#1|) . T)) (|has| |#1| (-871)) -(((#0=(-2 (|:| -2118 (-1191)) (|:| -3964 (-51))) #0#) |has| (-2 (|:| -2118 (-1191)) (|:| -3964 (-51))) (-321 (-2 (|:| -2118 (-1191)) (|:| -3964 (-51)))))) +(((#0=(-2 (|:| -2115 (-1191)) (|:| -3934 (-51))) #0#) |has| (-2 (|:| -2115 (-1191)) (|:| -3934 (-51))) (-321 (-2 (|:| -2115 (-1191)) (|:| -3934 (-51)))))) (((|#1| |#1|) -12 (|has| |#1| (-321 |#1|)) (|has| |#1| (-1133)))) (|has| |#1| (-1133)) ((((-888)) . T) (((-1214)) . T)) @@ -1889,14 +1889,14 @@ (((|#1| (-545 |#2|) |#2|) . T)) (((|#3|) . T)) (((|#1| (-793) (-1114)) . T)) -((((-421 (-560))) |has| |#1| (-1070 (-421 (-560)))) (((-560)) -4144 (|has| |#1| (-871)) (|has| |#1| (-1070 (-560)))) ((|#1|) . T)) +((((-421 (-560))) |has| |#1| (-1070 (-421 (-560)))) (((-560)) -4118 (|has| |#1| (-871)) (|has| |#1| (-1070 (-560)))) ((|#1|) . T)) (((|#1|) . T)) (((|#2|) . T)) ((((-146)) . 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T)) (((|#3|) |has| |#3| (-1081))) @@ -2360,7 +2360,7 @@ ((((-1209)) |has| |#2| (-928 (-1209)))) (|has| |#1| (-872)) ((((-888)) . T)) -((((-2 (|:| -2118 |#1|) (|:| -3964 |#2|))) . T)) +((((-2 (|:| -2115 |#1|) (|:| -3934 |#2|))) . T)) (|has| |#1| (-814)) ((((-421 (-560))) . T) (($) . T)) (|has| |#1| (-487)) @@ -2368,8 +2368,8 @@ (|has| |#1| (-381)) (|has| |#1| (-381)) (|has| |#1| (-376)) -(-4144 (|has| |#1| (-147)) (|has| |#1| (-149)) (|has| |#1| (-175)) (|has| |#1| (-487)) (|has| |#1| (-571)) (|has| |#1| (-1081)) (|has| |#1| (-1144))) -((($) -4144 (|has| |#1| (-240)) (|has| |#1| (-239)) (|has| |#1| (-363)))) +(-4118 (|has| |#1| (-147)) (|has| |#1| (-149)) (|has| |#1| (-175)) (|has| |#1| (-487)) (|has| |#1| (-571)) (|has| |#1| (-1081)) (|has| |#1| (-1144))) +((($) -4118 (|has| |#1| (-240)) (|has| |#1| (-239)) (|has| |#1| (-363)))) ((((-118 |#1|)) . T)) ((((-118 |#1|)) . T)) (|has| |#1| (-363)) @@ -2381,7 +2381,7 @@ (|has| |#1| (-38 (-421 (-560)))) (((|#2|) . T) (((-888)) . T)) (((|#2|) . T) (((-888)) . T)) -((($ (-1209)) -4144 (|has| |#1| (-928 (-1209))) (|has| |#1| (-930 (-1209))))) +((($ (-1209)) -4118 (|has| |#1| (-928 (-1209))) (|has| |#1| (-930 (-1209))))) (|has| |#1| (-38 (-421 (-560)))) (|has| |#1| (-38 (-421 (-560)))) (|has| |#1| (-38 (-421 (-560)))) @@ -2391,18 +2391,18 @@ (|has| |#1| (-38 (-421 (-560)))) (|has| |#1| (-38 (-421 (-560)))) (|has| |#1| (-872)) -((((-2 (|:| -2118 (-1191)) (|:| -3964 |#1|))) . T)) +((((-2 (|:| -2115 (-1191)) (|:| -3934 |#1|))) . T)) (((|#1| |#2|) . T)) ((($) . T) (((-560)) . T)) (|has| |#1| (-149)) (|has| |#1| (-147)) -((((-2 (|:| -2118 |#1|) (|:| -3964 |#2|))) |has| (-2 (|:| -2118 |#1|) (|:| -3964 |#2|)) (-321 (-2 (|:| -2118 |#1|) (|:| -3964 |#2|)))) ((|#2|) -12 (|has| |#2| (-321 |#2|)) (|has| |#2| (-1133)))) +((((-2 (|:| -2115 |#1|) (|:| -3934 |#2|))) |has| (-2 (|:| -2115 |#1|) (|:| -3934 |#2|)) (-321 (-2 (|:| -2115 |#1|) (|:| -3934 |#2|)))) ((|#2|) -12 (|has| |#2| (-321 |#2|)) (|has| |#2| (-1133)))) (((|#2|) . T)) (|has| |#1| (-15 * (|#1| (-560) |#1|))) (((|#3|) . T)) ((((-118 |#1|)) . T)) (|has| |#1| (-381)) -(-4144 (-12 (|has| (-1289 |#1| |#2| |#3|) (-240)) (|has| |#1| (-376))) (-12 (|has| (-1289 |#1| |#2| |#3|) (-239)) (|has| |#1| (-376))) (|has| |#1| (-15 * (|#1| (-560) |#1|)))) +(-4118 (-12 (|has| (-1289 |#1| |#2| |#3|) (-240)) (|has| |#1| (-376))) (-12 (|has| (-1289 |#1| |#2| |#3|) (-239)) (|has| |#1| (-376))) (|has| |#1| (-15 * (|#1| (-560) |#1|)))) (|has| |#1| (-15 * (|#1| (-421 (-560)) |#1|))) (|has| |#1| (-872)) (((|#2|) . T) (((-421 (-560))) |has| |#1| (-1070 (-421 (-560)))) (((-560)) |has| |#1| (-1070 (-560))) ((|#1|) . T)) @@ -2421,17 +2421,17 @@ (((|#1|) |has| |#1| (-376))) (((|#1|) |has| |#1| (-376))) ((((-888)) . T)) -((((-2 (|:| -2118 |#1|) (|:| -3964 |#2|))) . T)) +((((-2 (|:| -2115 |#1|) (|:| -3934 |#2|))) . T)) ((($ $) . T) (((-630 $) $) . T)) -(-4144 (|has| |#1| (-376)) (|has| |#1| (-571))) +(-4118 (|has| |#1| (-376)) (|has| |#1| (-571))) ((($) . 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T)) ((((-560)) -12 (|has| |#1| (-21)) (|has| |#2| (-21)))) @@ -2458,13 +2458,13 @@ (|has| |#1| (-147)) (|has| |#1| (-149)) ((((-560)) . T)) -(-4144 (|has| |#1| (-376)) (|has| |#1| (-571))) -(-4144 (|has| |#1| (-376)) (|has| |#1| (-571))) +(-4118 (|has| |#1| (-376)) (|has| |#1| (-571))) +(-4118 (|has| |#1| (-376)) (|has| |#1| (-571))) (((#0=(-1280 |#2| |#3| |#4|)) . T) (((-421 (-560))) |has| #0# (-38 (-421 (-560)))) (($) . T)) ((((-560)) . T)) ((($) . 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T)) @@ -2640,13 +2640,13 @@ ((((-421 (-560))) |has| |#1| (-1070 (-421 (-560)))) ((|#1|) . T) (((-560)) . T)) (|has| |#2| (-147)) (|has| |#2| (-149)) -(-4144 (|has| |#2| (-844)) (|has| |#2| (-872))) +(-4118 (|has| |#2| (-844)) (|has| |#2| (-872))) ((((-936 |#1|)) . T) (((-421 (-560))) . T) (($) . T)) -(-4144 (|has| |#1| (-102)) (|has| |#1| (-1133))) +(-4118 (|has| |#1| (-102)) (|has| |#1| (-1133))) ((((-560)) . T) ((|#1|) . T)) (((|#2|) . T) (($) . T) (((-560)) . T)) (((|#2|) . T)) -((((-1209)) -4144 (|has| |#2| (-928 (-1209))) (|has| |#2| (-930 (-1209))))) +((((-1209)) -4118 (|has| |#2| (-928 (-1209))) (|has| |#2| (-930 (-1209))))) (((|#1| |#1|) . T)) (((|#3|) |has| |#3| (-376))) ((((-421 |#2|)) . T)) @@ -2655,10 +2655,10 @@ ((((-888)) . T)) ((((-888)) . T)) ((((-549)) |has| |#1| (-633 (-549)))) -((((-2 (|:| -2118 |#1|) (|:| -3964 |#2|))) . T)) +((((-2 (|:| -2115 |#1|) (|:| -3934 |#2|))) . T)) ((((-560)) . T) (($) . T) (((-421 (-560))) . 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T) (((-560)) . T)) -((((-2 (|:| -2118 (-1191)) (|:| -3964 (-51)))) . T)) +((((-2 (|:| -2115 (-1191)) (|:| -3934 (-51)))) . T)) (((|#1|) . T)) -((((-2 (|:| -2118 |#1|) (|:| -3964 |#2|))) . T)) +((((-2 (|:| -2115 |#1|) (|:| -3934 |#2|))) . T)) ((((-888)) . T)) (((|#1| |#2|) . T)) ((($) . T) (((-560)) . T)) (((|#1| (-421 (-560))) . T)) (((|#1|) . T)) -(-4144 (|has| |#1| (-302)) (|has| |#1| (-376))) +(-4118 (|has| |#1| (-302)) (|has| |#1| (-376))) ((((-146)) . T)) ((((-560)) |has| #0=(-421 |#2|) (-660 (-560))) ((#0#) . T) (((-421 (-560))) . T) (($) . T)) (|has| |#1| (-871)) @@ -2878,7 +2878,7 @@ ((((-888)) . T)) ((((-888)) . T)) ((((-186)) . T) (((-888)) . T)) -((((-2 (|:| -2118 |#1|) (|:| -3964 |#2|))) . T)) +((((-2 (|:| -2115 |#1|) (|:| -3934 |#2|))) . T)) (((|#2| |#2|) . T) ((|#1| |#1|) . T)) ((((-888)) . T)) ((((-888)) . T)) @@ -2895,8 +2895,8 @@ (|has| |#1| (-872)) ((((-888)) . T)) ((((-549)) |has| |#1| (-633 (-549)))) -((((-2 (|:| -2118 (-1191)) (|:| -3964 |#1|))) . 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T) (($ $) . T)) ((((-560)) . T)) (((|#1|) . T)) @@ -2935,12 +2935,12 @@ (|has| |#1| (-38 (-421 (-560)))) (|has| |#1| (-38 (-421 (-560)))) (|has| |#1| (-38 (-421 (-560)))) -(-4144 (|has| |#1| (-376)) (|has| |#1| (-466)) (|has| |#1| (-571)) (|has| |#1| (-940))) +(-4118 (|has| |#1| (-376)) (|has| |#1| (-466)) (|has| |#1| (-571)) (|has| |#1| (-940))) (|has| |#1| (-844)) (((#0=(-936 |#1|) #0#) . T) (($ $) . T) ((#1=(-421 (-560)) #1#) . T)) ((((-421 |#2|)) . T)) (|has| |#1| (-871)) -((((-1236 |#1|)) . T) (((-888)) -4144 (|has| |#1| (-632 (-888))) (|has| |#1| (-1133)))) +((((-1236 |#1|)) . T) (((-888)) -4118 (|has| |#1| (-632 (-888))) (|has| |#1| (-1133)))) (((|#1| |#1|) . T) ((#0=(-421 (-560)) #0#) . T) ((#1=(-560) #1#) . T) (($ $) . T)) ((((-936 |#1|)) . T) (($) . T) (((-421 (-560))) . T)) (((|#2|) |has| |#2| (-1081)) (((-560)) -12 (|has| |#2| (-660 (-560))) (|has| |#2| (-1081)))) @@ -2959,36 +2959,36 @@ (((|#2|) |has| |#2| (-175))) (((|#1|) . T)) (((|#2|) . 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T)) -((($) -4144 (|has| |#1| (-240)) (|has| |#1| (-239)))) +((($) -4118 (|has| |#1| (-240)) (|has| |#1| (-239)))) ((((-560)) . T)) (((|#2|) . T) (((-421 (-560))) |has| |#1| (-1070 (-421 (-560)))) ((|#1|) . T) (($) . T) (((-560)) . T)) -(-4144 (|has| |#1| (-175)) (|has| |#1| (-376)) (|has| |#1| (-466)) (|has| |#1| (-571)) (|has| |#1| (-940))) +(-4118 (|has| |#1| (-175)) (|has| |#1| (-376)) (|has| |#1| (-466)) (|has| |#1| (-571)) (|has| |#1| (-940))) (((|#2|) . T) (((-560)) |has| |#2| (-660 (-560)))) (((|#1| |#2|) . T)) ((($) . T)) @@ -3055,7 +3055,7 @@ (|has| |#2| (-1052)) ((($) . T)) (|has| |#1| (-940)) -((((-2 (|:| -2118 |#1|) (|:| -3964 |#2|))) . T)) +((((-2 (|:| -2115 |#1|) (|:| -3934 |#2|))) . T)) (((|#4|) . T)) ((($) . T)) (((|#2|) . T)) @@ -3065,32 +3065,32 @@ (|has| |#1| (-376)) ((((-936 |#1|)) . T)) ((($) . T) (((-560)) . T) ((|#1|) . T) (((-421 (-560))) . 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T)) -(-4144 (-12 (|has| |#3| (-240)) (|has| |#3| (-1081))) (-12 (|has| |#3| (-239)) (|has| |#3| (-1081)))) +(-4118 (-12 (|has| |#3| (-240)) (|has| |#3| (-1081))) (-12 (|has| |#3| (-239)) (|has| |#3| (-1081)))) ((($) . T) (((-421 (-560))) . T)) ((($) . T) (((-560)) . T) (((-421 (-560))) . T) (((-630 $)) . T)) ((((-560)) . T) (($) . T)) ((((-560)) . T) (($) . T)) ((((-793) |#1|) . T)) -(((|#2| (-246 (-2236 |#1|) (-793))) . T)) +(((|#2| (-246 (-2223 |#1|) (-793))) . T)) (((|#1| (-545 |#3|)) . T)) ((((-421 (-560))) . T)) -(-4144 (|has| |#1| (-466)) (|has| |#1| (-571)) (|has| |#1| (-940))) +(-4118 (|has| |#1| (-466)) (|has| |#1| (-571)) (|has| |#1| (-940))) ((((-1191)) . T) (((-888)) . T)) -(((#0=(-2 (|:| -2118 (-1209)) (|:| -3964 (-51))) #0#) |has| (-2 (|:| -2118 (-1209)) (|:| -3964 (-51))) (-321 (-2 (|:| -2118 (-1209)) (|:| -3964 (-51)))))) +(((#0=(-2 (|:| -2115 (-1209)) (|:| -3934 (-51))) #0#) |has| (-2 (|:| -2115 (-1209)) (|:| -3934 (-51))) (-321 (-2 (|:| -2115 (-1209)) (|:| -3934 (-51)))))) ((((-1191)) . T)) (|has| |#1| (-940)) (|has| |#2| (-376)) (((|#1|) . T) (($) . T) (((-560)) . T)) -(-4144 (|has| |#2| (-21)) (|has| |#2| (-133)) (|has| |#2| (-175)) (|has| |#2| (-376)) (|has| |#2| (-817)) (|has| |#2| (-1081))) +(-4118 (|has| |#2| (-21)) (|has| |#2| (-133)) (|has| |#2| (-175)) (|has| |#2| (-376)) (|has| |#2| (-817)) (|has| |#2| (-1081))) ((((-171 (-391))) . T) (((-229)) . T) (((-391)) . T)) ((((-888)) . T)) (((|#1|) . T)) @@ -3107,12 +3107,12 @@ (|has| |#1| (-38 (-421 (-560)))) (|has| |#1| (-38 (-421 (-560)))) (|has| |#1| (-38 (-421 (-560)))) -(-4144 (|has| |#1| (-319)) (|has| |#1| (-376)) (|has| |#1| (-363))) +(-4118 (|has| |#1| (-319)) (|has| |#1| (-376)) (|has| |#1| (-363))) (|has| |#1| (-38 (-421 (-560)))) (-12 (|has| |#1| (-559)) (|has| |#1| (-845))) ((((-888)) . T)) (|has| |#1| (-376)) -((((-1209)) -4144 (-12 (|has| |#1| (-15 * (|#1| (-560) |#1|))) (|has| |#1| (-928 (-1209)))) (-12 (|has| |#1| (-376)) (|has| |#2| (-928 (-1209)))))) +((((-1209)) -4118 (-12 (|has| |#1| (-15 * (|#1| (-560) |#1|))) (|has| |#1| (-928 (-1209)))) (-12 (|has| |#1| (-376)) (|has| |#2| (-928 (-1209)))))) (|has| |#1| (-376)) ((((-1209)) -12 (|has| |#1| (-15 * (|#1| (-421 (-560)) |#1|))) (|has| |#1| (-928 (-1209))))) ((((-421 (-560))) . T) (($) . T)) @@ -3124,13 +3124,13 @@ ((((-560) |#1|) . T)) ((((-1209)) |has| |#1| (-928 (-1209)))) (((|#1|) . T)) -(-4144 (-12 (|has| |#1| (-240)) (|has| |#1| (-376))) (-12 (|has| |#1| (-239)) (|has| |#1| (-376))) (|has| |#1| (-363))) +(-4118 (-12 (|has| |#1| (-240)) (|has| |#1| (-376))) (-12 (|has| |#1| (-239)) (|has| |#1| (-376))) (|has| |#1| (-363))) (((|#2|) |has| |#1| (-376))) (((|#2|) |has| |#1| (-376))) -(-4144 (|has| |#4| (-817)) (|has| |#4| (-872))) -(-4144 (|has| |#3| (-817)) (|has| |#3| (-872))) +(-4118 (|has| |#4| (-817)) (|has| |#4| (-872))) +(-4118 (|has| |#3| (-817)) (|has| |#3| (-872))) ((((-560)) . T) (($) . T)) -((((-2 (|:| -2118 |#1|) (|:| -3964 |#2|))) . T)) +((((-2 (|:| -2115 |#1|) (|:| -3934 |#2|))) . T)) (((|#1|) . T)) (((|#1|) . T)) (((|#1|) |has| |#1| (-175))) @@ -3165,7 +3165,7 @@ (|has| |#1| (-872)) ((((-888)) . T)) (((|#1| |#1|) -12 (|has| |#1| (-321 |#1|)) (|has| |#1| (-1133)))) -(-4144 (|has| |#1| (-376)) (|has| |#1| (-571))) +(-4118 (|has| |#1| (-376)) (|has| |#1| (-571))) (|has| |#1| (-376)) (((|#1|) . T)) ((($) . T) (((-560)) . T) ((|#2|) . T)) @@ -3174,27 +3174,27 @@ (((|#3|) . T)) ((((-1191)) . T) (((-520)) . T) (((-229)) . T) (((-560)) . T)) (((|#1|) . T)) -(-4144 (|has| |#1| (-376)) (|has| |#1| (-571))) +(-4118 (|has| |#1| (-376)) (|has| |#1| (-571))) (|has| |#1| (-376)) (|has| |#1| (-571)) (((|#4| |#4|) -12 (|has| |#4| (-321 |#4|)) (|has| |#4| (-1133)))) ((((-421 |#2|)) . T) (((-421 (-560))) . T) (($) . T) (((-560)) . T)) -(-4144 (|has| |#2| (-21)) (|has| |#2| (-23)) (|has| |#2| (-133)) (|has| |#2| (-175)) (|has| |#2| (-376)) (|has| |#2| (-817)) (|has| |#2| (-1081))) +(-4118 (|has| |#2| (-21)) (|has| |#2| (-23)) (|has| |#2| (-133)) (|has| |#2| (-175)) (|has| |#2| (-376)) (|has| |#2| (-817)) (|has| |#2| (-1081))) (((|#2|) . T)) (((|#2|) . T)) (|has| |#2| (-1081)) -((((-2 (|:| -2118 |#1|) (|:| -3964 |#2|))) . T)) -((((-2 (|:| -2118 (-1191)) (|:| -3964 |#1|))) . T)) -((((-2 (|:| -2118 |#1|) (|:| -3964 |#2|))) . T)) +((((-2 (|:| -2115 |#1|) (|:| -3934 |#2|))) . T)) +((((-2 (|:| -2115 (-1191)) (|:| -3934 |#1|))) . T)) +((((-2 (|:| -2115 |#1|) (|:| -3934 |#2|))) . T)) (|has| |#1| (-38 (-421 (-560)))) (((|#1| |#2|) . T)) (|has| |#1| (-38 (-421 (-560)))) -(-4144 (|has| |#1| (-147)) (|has| |#1| (-381))) +(-4118 (|has| |#1| (-147)) (|has| |#1| (-381))) ((($) . T)) (|has| |#1| (-149)) -(-4144 (|has| |#1| (-147)) (|has| |#1| (-381))) +(-4118 (|has| |#1| (-147)) (|has| |#1| (-381))) (|has| |#1| (-149)) -(-4144 (|has| |#1| (-147)) (|has| |#1| (-381))) +(-4118 (|has| |#1| (-147)) (|has| |#1| (-381))) (|has| |#1| (-149)) ((($) . T)) ((((-595 |#1|)) . T)) @@ -3210,7 +3210,7 @@ ((((-421 (-560))) |has| |#2| . #0=((-1070 (-560)))) (((-560)) |has| |#2| . #0#) (((-1209)) |has| |#2| (-1070 (-1209))) ((|#2|) . T)) (((#0=(-421 |#2|) #0#) . T) ((#1=(-421 (-560)) #1#) . T) (($ $) . T)) (((|#1|) . T)) -(-4144 (|has| |#1| (-147)) (|has| |#1| (-363))) +(-4118 (|has| |#1| (-147)) (|has| |#1| (-363))) (|has| |#1| (-149)) ((((-888)) . T)) ((($) . T)) @@ -3230,15 +3230,15 @@ ((((-421 |#2|)) . T)) ((((-888)) . T)) (((|#1|) . T)) -((((-1209)) -4144 (|has| |#1| (-928 (-1209))) (|has| |#1| (-930 (-1209))))) -(-4144 (|has| |#1| (-102)) (|has| |#1| (-1133))) +((((-1209)) -4118 (|has| |#1| (-928 (-1209))) (|has| |#1| (-930 (-1209))))) +(-4118 (|has| |#1| (-102)) (|has| |#1| (-1133))) (|has| |#1| (-814)) (|has| |#1| (-814)) ((((-888)) . T)) ((((-936 |#1|)) . T) (((-421 (-560))) . T) (($) . T) (((-560)) . T)) ((((-888)) . T)) ((((-549)) |has| |#1| (-633 (-549)))) -((((-888)) -4144 (|has| |#1| (-632 (-888))) (|has| |#1| (-872)) (|has| |#1| (-1133)))) +((((-888)) -4118 (|has| |#1| (-632 (-888))) (|has| |#1| (-872)) (|has| |#1| (-1133)))) ((((-115)) . T) ((|#1|) . T)) (((|#1|) . T)) (((|#1|) . T)) @@ -3248,7 +3248,7 @@ (((|#1|) |has| |#1| (-175)) (($) |has| |#1| (-571)) (((-421 (-560))) |has| |#1| (-571))) ((((-888)) . T)) ((((-888)) . T)) -(-4144 (-12 (|has| |#2| (-240)) (|has| |#2| (-1081))) (-12 (|has| |#2| (-239)) (|has| |#2| (-1081)))) +(-4118 (-12 (|has| |#2| (-240)) (|has| |#2| (-1081))) (-12 (|has| |#2| (-239)) (|has| |#2| (-1081)))) (((#0=(-936 |#1|) #0#) . T) (($ $) . T) ((#1=(-421 (-560)) #1#) . T)) (((|#2|) . T)) (((|#1|) . T)) @@ -3260,10 +3260,10 @@ ((((-888)) . T)) (((|#2|) . T)) ((((-560)) . T)) -((((-1209)) -4144 (|has| (-421 |#2|) (-928 (-1209))) (|has| (-421 |#2|) (-930 (-1209))))) +((((-1209)) -4118 (|has| (-421 |#2|) (-928 (-1209))) (|has| (-421 |#2|) (-930 (-1209))))) ((((-888)) . T)) ((((-560)) . T)) -(-4144 (|has| |#2| (-817)) (|has| |#2| (-872))) +(-4118 (|has| |#2| (-817)) (|has| |#2| (-872))) ((((-171 (-391))) . T) (((-229)) . T) (((-391)) . T)) ((((-888)) . T)) ((((-888)) . T)) @@ -3275,11 +3275,11 @@ (((|#1|) . T) (($) . T) (((-421 (-560))) . T)) (|has| |#1| (-376)) (|has| |#1| (-376)) -((((-888)) -4144 (|has| |#1| (-632 (-888))) (|has| |#1| (-1133)))) -((((-888)) -4144 (|has| |#1| (-632 (-888))) (|has| |#1| (-1133)))) +((((-888)) -4118 (|has| |#1| (-632 (-888))) (|has| |#1| (-1133)))) +((((-888)) -4118 (|has| |#1| (-632 (-888))) (|has| |#1| (-1133)))) ((((-888)) . T)) ((((-560) $) . T) (((-663 (-560)) $) . T)) -(-4144 (|has| |#1| (-21)) (|has| |#1| (-25)) (|has| |#1| (-175)) (|has| |#1| (-376)) (|has| |#1| (-487)) (|has| |#1| (-748)) (|has| |#1| (-928 (-1209))) (|has| |#1| (-1081)) (|has| |#1| (-1144)) (|has| |#1| (-1133))) +(-4118 (|has| |#1| (-21)) (|has| |#1| (-25)) (|has| |#1| (-175)) (|has| |#1| (-376)) (|has| |#1| (-487)) (|has| |#1| (-748)) (|has| |#1| (-928 (-1209))) (|has| |#1| (-1081)) (|has| |#1| (-1144)) (|has| |#1| (-1133))) (|has| |#1| (-1184)) ((((-936 |#1|)) . T) (((-421 (-560))) . T) (($) . T)) ((($) . T)) @@ -3289,22 +3289,22 @@ (((#0=(-118 |#1|) $) |has| #0# (-298 #0# #0#))) (((|#1|) |has| |#1| (-175))) ((((-326 |#1|)) . T) (((-560)) . T)) -(-4144 (|has| |#2| (-240)) (|has| |#2| (-239))) +(-4118 (|has| |#2| (-240)) (|has| |#2| (-239))) (((|#1|) . T)) (((|#1| |#1|) . T)) ((((-888)) . T)) (((|#1|) . T)) ((((-115)) . T) ((|#1|) . T)) ((((-888)) . T)) -((((-1209)) -4144 (|has| |#2| (-928 (-1209))) (|has| |#2| (-930 (-1209))))) +((((-1209)) -4118 (|has| |#2| (-928 (-1209))) (|has| |#2| (-930 (-1209))))) (((|#1|) |has| |#1| (-321 |#1|))) ((((-560) |#1|) . T) (((-1266 (-560)) $) . T)) (((|#1| |#2|) . T)) ((((-1209) |#1|) . T)) -(((|#1|) -4144 (|has| |#1| (-175)) (|has| |#1| (-376)))) +(((|#1|) -4118 (|has| |#1| (-175)) (|has| |#1| (-376)))) (((|#1|) . T)) ((($ (-1209)) . T)) -(((|#1|) -4144 (|has| |#1| (-175)) (|has| |#1| (-376)) (|has| |#1| (-1081)))) +(((|#1|) -4118 (|has| |#1| (-175)) (|has| |#1| (-376)) (|has| |#1| (-1081)))) ((((-560)) . T) (((-421 (-560))) . T)) (((|#1|) . T)) (|has| |#1| (-571)) @@ -3313,15 +3313,15 @@ (((|#1|) . T)) (((|#1|) . T)) ((((-421 |#2|)) . T) (((-421 (-560))) . T) (($) . T)) -(-4144 (|has| |#1| (-376)) (|has| |#1| (-571))) +(-4118 (|has| |#1| (-376)) (|has| |#1| (-571))) (|has| |#1| (-376)) -(-4144 (|has| |#1| (-376)) (|has| |#1| (-571))) +(-4118 (|has| |#1| (-376)) (|has| |#1| (-571))) (|has| |#1| (-376)) (|has| |#1| (-571)) ((($) . T)) (|has| |#1| (-1133)) ((((-802 |#1| (-889 |#2|))) |has| (-802 |#1| (-889 |#2|)) (-321 (-802 |#1| (-889 |#2|))))) -(-4144 (|has| |#2| (-466)) (|has| |#2| (-571)) (|has| |#2| (-940))) +(-4118 (|has| |#2| (-466)) (|has| |#2| (-571)) (|has| |#2| (-940))) (((|#1|) . T)) (((|#2| |#3|) . T)) (((|#1|) . T)) @@ -3330,17 +3330,17 @@ (((|#1| (-793)) . T)) (|has| |#1| (-240)) (((|#1| (-545 (-1120 (-1209)))) . 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T) (((-421 (-560))) -4144 (|has| |#1| (-38 (-421 (-560)))) (|has| |#1| (-1070 (-421 (-560))))) (((-1209)) . T)) +((((-1157 |#1| (-1209))) . T) (((-560)) . T) (((-1120 (-1209))) . T) (($) -4118 (|has| |#1| (-466)) (|has| |#1| (-571)) (|has| |#1| (-940))) ((|#1|) . T) (((-421 (-560))) -4118 (|has| |#1| (-38 (-421 (-560)))) (|has| |#1| (-1070 (-421 (-560))))) (((-1209)) . T)) (((|#1|) |has| |#1| (-175))) (((|#1| (-1299 |#1|) (-1299 |#1|)) . T)) ((((-595 |#1|)) . T) (($) . T) (((-421 (-560))) . T)) @@ -3373,7 +3373,7 @@ ((((-421 (-560))) |has| |#1| (-1070 (-421 (-560)))) ((|#1|) . T) (((-560)) . T)) (((|#1|) . T)) ((((-888)) . T)) -(((#0=(-421 (-560)) #0#) |has| |#2| (-38 (-421 (-560)))) ((|#2| |#2|) . T) (($ $) -4144 (|has| |#2| (-175)) (|has| |#2| (-466)) (|has| |#2| (-571)) (|has| |#2| (-940)))) +(((#0=(-421 (-560)) #0#) |has| |#2| (-38 (-421 (-560)))) ((|#2| |#2|) . T) (($ $) -4118 (|has| |#2| (-175)) (|has| |#2| (-466)) (|has| |#2| (-571)) (|has| |#2| (-940)))) (((|#2| |#2|) . T) ((|#6| |#6|) . T)) ((((-305 |#3|)) . T)) (((|#1|) . T)) @@ -3382,30 +3382,30 @@ (((|#1|) . T) (((-421 (-560))) . T) (($) . T)) (((|#1|) . T) (((-421 (-560))) . T) (($) . T)) (((|#1|) . T) (((-421 (-560))) . T) (($) . T)) -((($ $) -4144 (|has| |#1| (-175)) (|has| |#1| (-466)) (|has| |#1| (-571)) (|has| |#1| (-940))) ((|#1| |#1|) . T) ((#0=(-421 (-560)) #0#) |has| |#1| (-38 (-421 (-560))))) -((($ $) -4144 (|has| |#1| (-175)) (|has| |#1| (-376)) (|has| |#1| (-466)) (|has| |#1| (-571)) (|has| |#1| (-940))) ((|#1| |#1|) . T) ((#0=(-421 (-560)) #0#) |has| |#1| (-38 (-421 (-560))))) +((($ $) -4118 (|has| |#1| (-175)) (|has| |#1| (-466)) (|has| |#1| (-571)) (|has| |#1| (-940))) ((|#1| |#1|) . T) ((#0=(-421 (-560)) #0#) |has| |#1| (-38 (-421 (-560))))) +((($ $) -4118 (|has| |#1| (-175)) (|has| |#1| (-376)) (|has| |#1| (-466)) (|has| |#1| (-571)) (|has| |#1| (-940))) ((|#1| |#1|) . T) ((#0=(-421 (-560)) #0#) |has| |#1| (-38 (-421 (-560))))) (((|#2|) . 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T)) -(-4144 (|has| |#2| (-817)) (|has| |#2| (-872))) -(-4144 (|has| |#1| (-102)) (|has| |#1| (-1133))) +(-4118 (|has| |#2| (-817)) (|has| |#2| (-872))) +(-4118 (|has| |#1| (-102)) (|has| |#1| (-1133))) (((|#1|) . T)) (((|#1|) . T) (($) . T) (((-421 (-560))) . T)) ((((-1209)) . T) ((|#1|) . T)) @@ -3417,15 +3417,15 @@ (((#0=(-421 (-560)) #0#) . T)) ((((-421 (-560))) . T)) (((|#1|) |has| |#1| (-175))) -(-4144 (|has| |#2| (-21)) (|has| |#2| (-175)) (|has| |#2| (-376)) (|has| |#2| (-1081))) +(-4118 (|has| |#2| (-21)) (|has| |#2| (-175)) (|has| |#2| (-376)) (|has| |#2| (-1081))) (((|#1|) . T)) (((|#1|) . T)) -(-4144 (|has| |#2| (-21)) (|has| |#2| (-23)) (|has| |#2| (-25)) (|has| |#2| (-133)) (|has| |#2| (-175)) (|has| |#2| (-376)) (|has| |#2| (-817)) (|has| |#2| (-1081))) +(-4118 (|has| |#2| (-21)) (|has| |#2| (-23)) (|has| |#2| (-25)) (|has| |#2| (-133)) (|has| |#2| (-175)) (|has| |#2| (-376)) (|has| |#2| (-817)) (|has| |#2| (-1081))) (((|#1|) . T)) ((((-421 (-560))) . T) (((-560)) . 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T) (((-560)) |has| |#2| (-1070 (-560))) (((-421 (-560))) |has| |#2| (-1070 (-421 (-560))))) ((((-1114)) . T) ((|#2|) . T) (((-560)) |has| |#2| (-1070 (-560))) (((-421 (-560))) |has| |#2| (-1070 (-421 (-560))))) (((|#1|) . T)) @@ -3475,11 +3475,11 @@ ((($) |has| |#1| (-381))) (|has| |#2| (-844)) (|has| |#2| (-844)) -((((-560)) -12 (|has| |#1| (-376)) (|has| |#2| (-660 (-560)))) (((-421 (-560))) -4144 (|has| |#1| (-38 (-421 (-560)))) (|has| |#1| (-376))) ((|#2|) |has| |#1| (-376)) (($) . T) ((|#1|) . T)) +((((-560)) -12 (|has| |#1| (-376)) (|has| |#2| (-660 (-560)))) (((-421 (-560))) -4118 (|has| |#1| (-38 (-421 (-560)))) (|has| |#1| (-376))) ((|#2|) |has| |#1| (-376)) (($) . T) ((|#1|) . T)) ((($ (-1209)) |has| |#1| (-928 (-1209)))) (((|#1|) . T) (((-560)) |has| |#1| (-1070 (-560))) (((-421 (-560))) |has| |#1| (-1070 (-421 (-560))))) -((($) -4144 (-12 (|has| |#1| (-240)) (|has| |#1| (-376))) (-12 (|has| |#1| (-239)) (|has| |#1| (-376))) (|has| |#1| (-363)))) -(((|#1|) . T) (((-421 (-560))) -4144 (|has| |#1| (-38 (-421 (-560)))) (|has| |#1| (-376))) (($) . T)) +((($) -4118 (-12 (|has| |#1| (-240)) (|has| |#1| (-376))) (-12 (|has| |#1| (-239)) (|has| |#1| (-376))) (|has| |#1| (-363)))) +(((|#1|) . T) (((-421 (-560))) -4118 (|has| |#1| (-38 (-421 (-560)))) (|has| |#1| (-376))) (($) . T)) (((|#1| |#1|) -12 (|has| |#1| (-321 |#1|)) (|has| |#1| (-1133)))) ((((-560)) |has| |#1| (-912 (-560))) (((-391)) |has| |#1| (-912 (-391)))) (((|#1|) . T)) @@ -3494,7 +3494,7 @@ (-12 (|has| |#1| (-376)) (|has| |#2| (-940))) (|has| |#1| (-376)) (((|#4|) -12 (|has| |#4| (-321 |#4|)) (|has| |#4| (-1133)))) -(((|#2|) -4144 (|has| |#2| (-6 (-4512 "*"))) (|has| |#2| (-175)))) +(((|#2|) -4118 (|has| |#2| (-6 (-4512 "*"))) (|has| |#2| (-175)))) (((|#2|) . T)) (|has| |#1| (-376)) (((|#2|) . T)) @@ -3508,12 +3508,12 @@ (((|#2| (-793)) . T)) ((((-1209)) . T)) ((((-894 |#1|)) . 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T)) (((|#2| |#2|) . T) ((#0=(-421 (-560)) #0#) . T) (($ $) . T)) (((|#2|) . T) (((-421 (-560))) . T) (($) . T)) @@ -3884,7 +3884,7 @@ ((((-888)) . T)) ((((-888)) . T)) ((((-888)) . T)) -(-4144 (|has| |#1| (-240)) (|has| |#1| (-239))) +(-4118 (|has| |#1| (-240)) (|has| |#1| (-239))) (((|#1|) . T) (((-888)) . T) (((-1214)) . T)) ((((-1214)) . T)) ((((-888)) . T)) @@ -3893,21 +3893,21 @@ ((((-657 |#2|)) . T)) (((|#1|) -12 (|has| |#1| (-321 |#1|)) (|has| |#1| (-1133)))) (((|#1| (-545 (-889 |#2|)) (-889 |#2|) (-802 |#1| (-889 |#2|))) . T)) -((((-421 (-560))) |has| |#2| (-38 (-421 (-560)))) ((|#2|) |has| |#2| (-175)) (($) -4144 (|has| |#2| (-466)) (|has| |#2| (-571)) (|has| |#2| (-940)))) +((((-421 (-560))) |has| |#2| (-38 (-421 (-560)))) ((|#2|) |has| |#2| (-175)) (($) -4118 (|has| |#2| (-466)) (|has| |#2| (-571)) (|has| |#2| (-940)))) (((|#2|) . T) ((|#6|) . T)) ((($) . T) (((-421 (-560))) |has| |#2| (-38 (-421 (-560)))) ((|#2|) . T) (((-560)) |has| |#2| (-660 (-560)))) ((($) . 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T)) -((($) -4144 (|has| |#1| (-466)) (|has| |#1| (-571)) (|has| |#1| (-940))) ((|#1|) |has| |#1| (-175)) (((-421 (-560))) |has| |#1| (-38 (-421 (-560))))) +((($) -4118 (|has| |#1| (-466)) (|has| |#1| (-571)) (|has| |#1| (-940))) ((|#1|) |has| |#1| (-175)) (((-421 (-560))) |has| |#1| (-38 (-421 (-560))))) (|has| |#2| (-940)) (((|#1| |#2| (-246 |#1| |#2|) (-246 |#1| |#2|)) . T)) ((((-888)) . T)) @@ -3923,9 +3923,9 @@ (((|#1| |#1|) |has| |#1| (-175))) ((((-721)) . T)) ((((-721)) . T)) -((((-888)) -4144 (|has| |#1| (-632 (-888))) (|has| |#1| (-1133)))) +((((-888)) -4118 (|has| |#1| (-632 (-888))) (|has| |#1| (-1133)))) ((((-1214)) . T)) -(-4144 (|has| |#2| (-817)) (|has| |#2| (-872))) +(-4118 (|has| |#2| (-817)) (|has| |#2| (-872))) (((|#1|) |has| |#1| (-175))) ((((-1214)) . T)) (((|#1| |#1|) . T)) @@ -3938,19 +3938,19 @@ (((|#1| (-560)) . T)) (((|#1|) . T)) ((((-421 (-560))) . T) (((-560)) . T) (($) . 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T)) ((((-1209)) -12 (|has| |#2| (-928 (-1209))) (|has| |#2| (-1081)))) (|has| |#2| (-1081)) -(-4144 (-12 (|has| |#1| (-487)) (|has| |#2| (-487))) (-12 (|has| |#1| (-748)) (|has| |#2| (-748)))) +(-4118 (-12 (|has| |#1| (-487)) (|has| |#2| (-487))) (-12 (|has| |#1| (-748)) (|has| |#2| (-748)))) (|has| |#1| (-147)) (|has| |#1| (-149)) (|has| |#1| (-376)) @@ -4008,7 +4008,7 @@ (((|#1| |#2|) . T)) ((((-560)) . T) ((|#2|) |has| |#2| (-175))) ((((-115)) . T) ((|#1|) . T) (((-560)) . T)) -(-4144 (|has| |#1| (-363)) (|has| |#1| (-381))) +(-4118 (|has| |#1| (-363)) (|has| |#1| (-381))) (((|#1| |#2|) . T)) ((((-229)) . T)) ((((-421 (-560))) . T) (($) . T) (((-560)) . T)) @@ -4017,11 +4017,11 @@ ((($) . T) (((-421 (-560))) |has| |#1| (-38 (-421 (-560)))) ((|#1|) . T) (((-560)) |has| |#1| (-660 (-560)))) ((($) . T) (((-560)) |has| |#1| (-660 (-560))) ((|#1|) . T) (((-421 (-560))) |has| |#1| (-38 (-421 (-560))))) (((|#2|) |has| |#2| (-1133)) (((-560)) -12 (|has| |#2| (-1070 (-560))) (|has| |#2| (-1133))) (((-421 (-560))) -12 (|has| |#2| (-1070 (-421 (-560)))) (|has| |#2| (-1133)))) -(-4144 (|has| |#2| (-240)) (|has| |#2| (-239))) +(-4118 (|has| |#2| (-240)) (|has| |#2| (-239))) (((|#1|) . T)) (((|#1|) . T)) ((((-549)) |has| |#1| (-633 (-549)))) -((((-888)) -4144 (|has| |#1| (-632 (-888))) (|has| |#1| (-872)) (|has| |#1| (-1133)))) +((((-888)) -4118 (|has| |#1| (-632 (-888))) (|has| |#1| (-872)) (|has| |#1| (-1133)))) ((((-560) $) . T) (((-663 (-560)) $) . T)) ((($) . T) (((-421 (-560))) . T)) (|has| |#1| (-940)) @@ -4033,14 +4033,14 @@ (((|#1| |#1|) |has| |#1| (-175))) (((|#1|) . T) (((-560)) . T)) ((((-1214)) . T)) -(-4144 (|has| |#1| (-376)) (|has| |#1| (-571))) -(-4144 (|has| |#1| (-21)) (|has| |#1| (-871))) +(-4118 (|has| |#1| (-376)) (|has| |#1| (-571))) +(-4118 (|has| |#1| (-21)) (|has| |#1| (-871))) (((|#2|) . T)) -(-4144 (|has| |#1| (-21)) (|has| |#1| (-871))) +(-4118 (|has| |#1| (-21)) (|has| |#1| (-871))) (((|#1|) |has| |#1| (-175))) (((|#1|) . T)) (((|#1|) . T)) -((((-888)) -4144 (-12 (|has| |#1| (-632 (-888))) (|has| |#2| (-632 (-888)))) (-12 (|has| |#1| (-1133)) (|has| |#2| (-1133))))) +((((-888)) -4118 (-12 (|has| |#1| (-632 (-888))) (|has| |#2| (-632 (-888)))) (-12 (|has| |#1| (-1133)) (|has| |#2| (-1133))))) ((((-421 |#2|) |#3|) . T)) ((((-421 (-560))) . T) (($) . T)) (|has| |#1| (-38 (-421 (-560)))) @@ -4049,7 +4049,7 @@ ((($) . T) (((-560)) . T)) (|has| (-421 |#2|) (-149)) (|has| (-421 |#2|) (-147)) -(-4144 (|has| |#3| (-817)) (|has| |#3| (-872))) +(-4118 (|has| |#3| (-817)) (|has| |#3| (-872))) ((($) . T)) ((((-721)) . T)) (((|#1|) . T) (((-421 (-560))) . T) (((-560)) . T) (($) . T)) @@ -4065,7 +4065,7 @@ ((((-1214)) . T)) ((((-560)) . T)) (((|#2|) . T)) -((((-1209)) -4144 (-12 (|has| (-1207 |#1| |#2| |#3|) (-928 (-1209))) (|has| |#1| (-376))) (-12 (|has| |#1| (-15 * (|#1| (-560) |#1|))) (|has| |#1| (-928 (-1209)))))) +((((-1209)) -4118 (-12 (|has| (-1207 |#1| |#2| |#3|) (-928 (-1209))) (|has| |#1| (-376))) (-12 (|has| |#1| (-15 * (|#1| (-560) |#1|))) (|has| |#1| (-928 (-1209)))))) ((((-1209)) -12 (|has| |#1| (-15 * (|#1| (-421 (-560)) |#1|))) (|has| |#1| (-928 (-1209))))) ((((-1209)) -12 (|has| |#1| (-15 * (|#1| (-793) |#1|))) (|has| |#1| (-928 (-1209))))) (((|#1| |#1|) . T) (($ $) . T)) @@ -4081,11 +4081,11 @@ ((((-1207 |#1| |#2| |#3|)) |has| |#1| (-376))) ((((-1172 |#1| |#2|)) . T)) ((((-1207 |#1| |#2| |#3|)) |has| |#1| (-376))) -(((|#2|) . T) (((-2 (|:| -2118 |#1|) (|:| -3964 |#2|))) . T)) -((((-2 (|:| -2118 (-1209)) (|:| -3964 (-51)))) . T)) +(((|#2|) . T) (((-2 (|:| -2115 |#1|) (|:| -3934 |#2|))) . T)) +((((-2 (|:| -2115 (-1209)) (|:| -3934 (-51)))) . T)) ((($) . T)) (|has| |#1| (-1052)) -(((|#2|) . T) (((-2 (|:| -2118 |#1|) (|:| -3964 |#2|))) . T)) +(((|#2|) . T) (((-2 (|:| -2115 |#1|) (|:| -3934 |#2|))) . T)) ((($) . T)) ((((-888)) . T)) ((((-549)) |has| |#2| (-633 (-549))) (((-916 (-560))) |has| |#2| (-633 (-916 (-560)))) (((-916 (-391))) |has| |#2| (-633 (-916 (-391)))) (((-391)) . #0=(|has| |#2| (-1052))) (((-229)) . #0#)) @@ -4094,7 +4094,7 @@ (((|#1|) . T)) (|has| |#1| (-38 (-421 (-560)))) (|has| |#1| (-38 (-421 (-560)))) -((((-1209)) -4144 (|has| |#2| (-928 (-1209))) (|has| |#2| (-930 (-1209))))) +((((-1209)) -4118 (|has| |#2| (-928 (-1209))) (|has| |#2| (-930 (-1209))))) ((((-888)) . T)) (((|#2|) . T)) ((((-888)) . T)) @@ -4104,15 +4104,15 @@ ((((-1207 |#1| |#2| |#3|)) . T)) ((((-1207 |#1| |#2| |#3|)) . T) (((-1200 |#1| |#2| |#3|)) . T)) ((((-888)) . T)) -((((-888)) -4144 (|has| |#1| (-632 (-888))) (|has| |#1| (-1133)))) +((((-888)) -4118 (|has| |#1| (-632 (-888))) (|has| |#1| (-1133)))) ((((-560) |#1|) . T)) ((((-1207 |#1| |#2| |#3|)) |has| |#1| (-376))) (((|#1| |#2| |#3| |#4|) . T)) (((|#1|) . T)) (((|#2|) . T)) (|has| |#2| (-376)) -(((|#3|) . T) ((|#2|) . T) ((|#4|) -4144 (|has| |#4| (-175)) (|has| |#4| (-376)) (|has| |#4| (-1081))) (($) |has| |#4| (-1081)) (((-560)) -12 (|has| |#4| (-660 (-560))) (|has| |#4| (-1081)))) -(((|#2|) . T) ((|#3|) -4144 (|has| |#3| (-175)) (|has| |#3| (-376)) (|has| |#3| (-1081))) (($) |has| |#3| (-1081)) (((-560)) -12 (|has| |#3| (-660 (-560))) (|has| |#3| (-1081)))) +(((|#3|) . T) ((|#2|) . T) ((|#4|) -4118 (|has| |#4| (-175)) (|has| |#4| (-376)) (|has| |#4| (-1081))) (($) |has| |#4| (-1081)) (((-560)) -12 (|has| |#4| (-660 (-560))) (|has| |#4| (-1081)))) +(((|#2|) . T) ((|#3|) -4118 (|has| |#3| (-175)) (|has| |#3| (-376)) (|has| |#3| (-1081))) (($) |has| |#3| (-1081)) (((-560)) -12 (|has| |#3| (-660 (-560))) (|has| |#3| (-1081)))) (((|#1|) . T)) (((|#1|) . T)) ((((-118 |#1|)) . T)) @@ -4126,7 +4126,7 @@ ((((-186)) . T) (((-888)) . T)) ((((-888)) . T)) (((|#1|) . T)) -((((-888)) -4144 (|has| |#1| (-632 (-888))) (|has| |#1| (-1133)))) +((((-888)) -4118 (|has| |#1| (-632 (-888))) (|has| |#1| (-1133)))) ((((-560) |#1|) . T) (((-1266 (-560)) $) . T)) ((((-888)) . T)) (((|#1|) . T)) @@ -4134,14 +4134,14 @@ (((|#1|) . T)) (((|#2| $) -12 (|has| |#1| (-376)) (|has| |#2| (-298 |#2| |#2|))) (($ $) . T) (((-560) |#1|) . T)) ((($ $) . T) (((-421 (-560)) |#1|) . T)) -(-4144 (|has| |#1| (-376)) (|has| |#1| (-466)) (|has| |#1| (-940))) +(-4118 (|has| |#1| (-376)) (|has| |#1| (-466)) (|has| |#1| (-940))) ((($ (-1209)) |has| |#1| (-1081))) -(-4144 (|has| |#1| (-872)) (|has| |#1| (-1133))) +(-4118 (|has| |#1| (-872)) (|has| |#1| (-1133))) ((((-888)) . T)) ((((-888)) . T)) ((((-888)) . T)) (((|#1| (-545 |#2|)) . T)) -((((-2 (|:| -2118 (-1209)) (|:| -3964 (-51)))) . T)) +((((-2 (|:| -2115 (-1209)) (|:| -3934 (-51)))) . T)) ((((-560) (-130)) . T)) (((|#1| (-560)) . T)) (((|#1| (-421 (-560))) . T)) @@ -4156,8 +4156,8 @@ ((((-1214)) . T)) ((((-888)) . T) (((-1214)) . T)) ((((-888)) . T) (((-1214)) . T)) -(-4144 (|has| |#2| (-466)) (|has| |#2| (-571)) (|has| |#2| (-940))) -(-4144 (|has| |#1| (-466)) (|has| |#1| (-571)) (|has| |#1| (-940))) +(-4118 (|has| |#2| (-466)) (|has| |#2| (-571)) (|has| |#2| (-940))) +(-4118 (|has| |#1| (-466)) (|has| |#1| (-571)) (|has| |#1| (-940))) ((($) . T)) (((|#2| (-545 (-889 |#1|))) . T)) ((((-1214)) . T)) @@ -4172,7 +4172,7 @@ ((((-1214)) . T)) ((((-888)) . T) (((-1214)) . T)) ((((-1214)) . T)) -((((-888)) -4144 (|has| |#1| (-632 (-888))) (|has| |#1| (-1133)))) +((((-888)) -4118 (|has| |#1| (-632 (-888))) (|has| |#1| (-1133)))) (((|#1| |#2|) . T)) (((|#1|) . T)) ((((-1191) |#1|) . T)) @@ -4180,7 +4180,7 @@ ((((-421 |#2|)) . T)) (|has| |#1| (-571)) (|has| |#1| (-571)) -((((-2 (|:| -2118 |#1|) (|:| -3964 |#2|))) . T)) +((((-2 (|:| -2115 |#1|) (|:| -3934 |#2|))) . T)) (((|#2| (-793)) . T)) ((($) . T) ((|#2|) . T)) ((($) . T) (((-421 (-560))) . T)) @@ -4190,14 +4190,14 @@ ((((-560)) . T) (($) . T)) (((|#2| $) |has| |#2| (-298 |#2| |#2|))) (((|#1| (-663 |#1|)) |has| |#1| (-871))) -(-4144 (|has| |#1| (-240)) (|has| |#1| (-363))) -(-4144 (|has| |#1| (-376)) (|has| |#1| (-363))) +(-4118 (|has| |#1| (-240)) (|has| |#1| (-363))) +(-4118 (|has| |#1| (-376)) (|has| |#1| (-363))) ((((-1296 |#1|)) . T) (((-560)) . T) ((|#2|) . T) (((-421 (-560))) |has| |#2| (-1070 (-421 (-560))))) (|has| |#1| (-1133)) (((|#1|) . T)) ((((-421 (-560))) . T) (($) . T)) -((((-1296 |#1|)) . T) (((-560)) . T) (($) -4144 (|has| |#2| (-376)) (|has| |#2| (-466)) (|has| |#2| (-571)) (|has| |#2| (-940))) (((-1114)) . T) ((|#2|) . T) (((-421 (-560))) -4144 (|has| |#2| (-38 (-421 (-560)))) (|has| |#2| (-1070 (-421 (-560)))))) -((((-1028 |#1|)) . T) ((|#1|) . T) (((-560)) -4144 (|has| (-1028 |#1|) (-1070 (-560))) (|has| |#1| (-1070 (-560)))) (((-421 (-560))) -4144 (|has| (-1028 |#1|) (-1070 (-421 (-560)))) (|has| |#1| (-1070 (-421 (-560)))))) +((((-1296 |#1|)) . T) (((-560)) . T) (($) -4118 (|has| |#2| (-376)) (|has| |#2| (-466)) (|has| |#2| (-571)) (|has| |#2| (-940))) (((-1114)) . T) ((|#2|) . T) (((-421 (-560))) -4118 (|has| |#2| (-38 (-421 (-560)))) (|has| |#2| (-1070 (-421 (-560)))))) +((((-1028 |#1|)) . T) ((|#1|) . T) (((-560)) -4118 (|has| (-1028 |#1|) (-1070 (-560))) (|has| |#1| (-1070 (-560)))) (((-421 (-560))) -4118 (|has| (-1028 |#1|) (-1070 (-421 (-560)))) (|has| |#1| (-1070 (-421 (-560)))))) ((((-936 |#1|)) . T) (((-421 (-560))) . T) (($) . T)) (((|#1| |#1|) -12 (|has| |#1| (-321 |#1|)) (|has| |#1| (-1133)))) (((|#1| |#1|) -12 (|has| |#1| (-321 |#1|)) (|has| |#1| (-1133)))) @@ -4214,11 +4214,11 @@ (((|#1| |#2| |#3| |#4|) . T)) (((#0=(-1172 |#1| |#2|) #0#) |has| (-1172 |#1| |#2|) (-321 (-1172 |#1| |#2|)))) (((|#1|) . 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. -1070) 196875) ((-1203 . -670) 196764) ((-1157 . -670) 196653) ((-879 . -670) 196627) ((-740 . -632) 196609) ((-561 . -381) T) ((-1321 . -23) T) ((-716 . -930) NIL) ((-1320 . -23) T) ((-505 . -1133) T) ((-391 . -635) 196559) ((-391 . -637) 196541) ((-1066 . -1081) T) ((-890 . -102) T) ((-1221 . -298) 196520) ((-171 . -381) 196471) ((-1036 . -1249) T) ((-1003 . -1249) T) ((-944 . -1249) T) ((-858 . -635) 196425) ((-852 . -635) 196380) ((-44 . -23) T) ((-1329 . -102) T) ((-493 . -298) 196359) ((-597 . -1133) T) ((-1178 . -1141) 196328) ((-443 . -1249) T) ((-1135 . -1136) 196280) ((-404 . -21) T) ((-404 . -25) T) ((-154 . -1144) T) ((-1242 . -739) 196177) ((-1229 . -1133) T) ((-1036 . -910) 196159) ((-1036 . -912) 196141) ((-642 . -234) 196125) ((-642 . -274) 196109) ((-638 . -21) T) ((-301 . -571) T) ((-638 . -25) T) ((-1036 . -1070) 196069) ((-733 . -739) 196034) ((-246 . -390) 196003) ((-391 . -1081) T) ((-227 . -1089) T) ((-119 . -274) 195980) ((-119 . -234) 195957) ((-58 . -298) 195909) ((-154 . -23) T) ((-530 . -298) 195861) ((-339 . -528) 195794) ((-510 . -298) 195746) ((-391 . -250) T) ((-391 . -240) T) ((-858 . -1081) T) ((-852 . -1081) T) ((-734 . -980) 195715) ((-723 . -872) T) ((-630 . -875) T) ((-488 . -632) 195697) ((-1286 . -1083) 195602) ((-594 . -668) 195574) ((-560 . -668) 195546) ((-509 . -668) 195496) ((-852 . -240) 195475) ((-136 . -872) T) ((-1286 . -662) 195367) ((-676 . -1133) T) ((-1221 . -618) 195346) ((-565 . -1226) 195325) ((-346 . -1133) T) ((-331 . -376) 195304) ((-421 . -149) 195283) ((-421 . -147) 195262) ((-994 . -1144) 195161) ((-839 . -1144) 195139) ((-246 . -928) 195071) ((-678 . -877) 195055) ((-493 . -618) 195034) ((-110 . -875) T) ((-538 . -1249) T) ((-565 . -107) 194984) ((-1036 . -390) 194966) ((-1036 . -351) 194948) ((-1209 . -632) 194930) ((-97 . -1133) T) ((-994 . -23) 194741) ((-491 . -21) T) ((-491 . -25) T) ((-839 . -23) 194593) ((-1209 . -633) 194515) ((-58 . -19) 194499) ((-1203 . -748) T) ((-1157 . -748) T) ((-1119 . -1133) T) ((-530 . -19) 194483) ((-510 . -19) 194467) ((-58 . -618) 194444) ((-1035 . -239) 194381) ((-931 . -102) 194331) ((-879 . -748) T) ((-803 . -1133) T) ((-530 . -618) 194308) ((-510 . -618) 194285) ((-802 . -1133) T) ((-802 . -1097) 194252) ((-475 . -1133) T) ((-468 . -1133) T) ((-597 . -739) 194227) ((-671 . -1133) T) ((-1289 . -47) 194204) ((-1286 . -102) T) ((-1280 . -47) 194174) ((-1259 . -47) 194151) ((-1242 . -175) 194102) ((-1206 . -319) 194081) ((-1200 . -319) 194060) ((-1128 . -635) 194041) ((-1123 . -635) 194022) ((-1111 . -571) 193973) ((-1111 . -1254) 193924) ((-1105 . -635) 193905) ((-1036 . -928) NIL) ((-1098 . -635) 193886) ((-692 . -133) T) ((-646 . -1144) T) ((-1068 . -635) 193867) ((-1051 . -635) 193848) ((-736 . -1088) 193818) ((-734 . -922) 193721) ((-721 . -668) 193671) ((-286 . -1133) T) ((-86 . -455) T) ((-86 . -410) T) ((-733 . -175) T) ((-659 . -1088) 193655) ((-50 . -1133) T) ((-609 . -47) 193632) ((-229 . -670) 193597) ((-595 . -1133) T) ((-532 . -1133) T) ((-501 . -844) T) ((-501 . -951) T) ((-372 . -1254) T) ((-367 . -1254) T) ((-359 . -1254) T) ((-331 . -1144) T) ((-326 . -1083) 193507) ((-325 . -1083) 193436) ((-108 . -1254) T) ((-645 . -635) 193417) ((-372 . -571) T) ((-221 . -951) T) ((-221 . -844) T) ((-326 . -662) 193327) ((-325 . -662) 193256) ((-367 . -571) T) ((-359 . -571) T) ((-659 . -111) 193235) ((-497 . -635) 193216) ((-108 . -571) T) ((-1200 . -1052) NIL) ((-676 . -739) 193186) ((-496 . -875) 193137) ((-222 . -635) 193118) ((-331 . -23) T) ((-67 . -1249) T) ((-1032 . -632) 193050) ((-1329 . -1184) T) ((-716 . -274) 193032) ((-716 . -234) 193014) ((-1324 . -21) T) ((-736 . -111) 192979) ((-1324 . -25) T) ((-663 . -34) T) ((-252 . -503) 192963) ((-1321 . -133) T) ((-1320 . -133) T) ((-1313 . -102) T) ((-1296 . -632) 192929) ((-1129 . -1131) 192913) ((-174 . -1133) T) ((-1289 . -1249) T) ((-1280 . -1249) T) ((-1280 . -1070) 192848) ((-1259 . -1249) T) ((-1259 . -912) NIL) ((-976 . -940) 192827) ((-1259 . -910) 192779) ((-1259 . -1070) 192745) ((-1242 . -528) 192712) ((-529 . -635) 192696) ((-1221 . -633) NIL) ((-1221 . -632) 192678) ((-1174 . -1155) 192623) ((-495 . -940) 192602) ((-1119 . -739) 192451) ((-1094 . -670) 192423) ((-976 . -670) 192312) ((-842 . -875) T) ((-803 . -739) 192141) ((-611 . -504) 192122) ((-600 . -504) 192103) ((-611 . -632) 192069) ((-600 . -632) 192035) ((-549 . -632) 192017) ((-593 . -1249) T) ((-549 . -633) 191998) ((-802 . -739) 191847) ((-1109 . -102) T) ((-642 . -668) 191819) ((-395 . -25) T) ((-395 . -21) T) ((-495 . -670) 191708) ((-475 . -739) 191679) ((-468 . -739) 191528) ((-1018 . -102) T) ((-1078 . -1244) 191457) ((-931 . -321) 191395) ((-758 . -102) T) ((-659 . -635) 191372) ((-119 . -668) 191302) ((-901 . -93) T) ((-736 . -635) 191256) ((-703 . -93) T) ((-545 . -25) T) ((-698 . -93) T) ((-686 . -632) 191238) ((-667 . -504) 191219) ((-667 . -632) 191172) ((-143 . -102) T) ((-44 . -133) T) ((-610 . -1249) T) ((-609 . -1249) T) ((-357 . -1089) T) ((-301 . -1144) T) ((-492 . -93) T) ((-421 . -239) 191123) ((-368 . -632) 191105) ((-366 . -632) 191087) ((-358 . -632) 191069) ((-275 . -633) 190817) ((-275 . -632) 190799) ((-255 . -632) 190781) ((-255 . -633) 190642) ((-140 . -93) T) ((-139 . -93) T) ((-135 . -93) T) ((-1173 . -632) 190624) ((-1152 . -662) 190611) ((-1152 . -1083) 190598) ((-843 . -748) T) ((-843 . -882) T) ((-616 . -300) 190575) ((-595 . -739) 190540) ((-493 . -633) NIL) ((-493 . -632) 190522) ((-532 . -739) 190467) ((-326 . -102) T) ((-325 . -102) T) ((-301 . -23) T) ((-154 . -133) T) ((-936 . -632) 190449) ((-936 . -633) 190431) ((-400 . -748) T) ((-897 . -1088) 190383) ((-897 . -111) 190321) ((-736 . -1081) T) ((-734 . -1275) 190305) ((-716 . -363) NIL) ((-115 . -102) T) ((-141 . -102) T) ((-137 . -102) T) ((-533 . -632) 190237) ((-391 . -821) T) ((-170 . -1249) T) ((-227 . -1133) T) ((-391 . -816) T) ((-58 . -633) 190198) ((-229 . -818) T) ((-229 . -814) T) ((-58 . -632) 190110) ((-229 . -748) T) ((-530 . -633) 190071) ((-530 . -632) 189983) ((-511 . -632) 189915) ((-510 . -633) 189876) ((-510 . -632) 189788) ((-1111 . -376) 189739) ((-40 . -426) 189716) ((-78 . -1249) T) ((-896 . -940) NIL) ((-372 . -341) 189700) ((-372 . -376) T) ((-367 . -341) 189684) ((-367 . -376) T) ((-359 . -341) 189668) ((-359 . -376) T) ((-326 . -296) 189647) ((-108 . -376) T) ((-70 . -1249) T) ((-661 . -1133) T) ((-1259 . -351) 189599) ((-896 . -670) 189544) ((-1259 . -390) 189496) ((-994 . -133) 189351) ((-839 . -133) 189222) ((-45 . -875) NIL) ((-988 . -673) 189206) ((-1258 . -684) T) ((-1119 . -175) 189117) ((-988 . -385) 189101) ((-1094 . -818) T) ((-1094 . -814) T) ((-897 . -635) 188999) ((-803 . -175) 188890) ((-802 . -175) 188801) ((-840 . -47) 188763) ((-1094 . -748) T) ((-339 . -503) 188747) ((-976 . -748) T) ((-1313 . -321) 188685) ((-1289 . -928) 188598) ((-468 . -175) 188509) ((-252 . -298) 188461) ((-1285 . -1088) 188296) ((-1280 . -928) 188202) ((-1264 . -1088) 188010) ((-495 . -748) T) ((-1259 . -928) 187843) ((-1242 . -302) 187822) ((-1219 . -1249) T) ((-1216 . -381) T) ((-1215 . -381) T) ((-1178 . -153) 187806) ((-1152 . -102) T) ((-1147 . -1133) T) ((-1111 . -23) T) ((-1111 . -1144) T) ((-1108 . -102) T) ((-1090 . -632) 187773) ((-1035 . -424) 187745) ((-955 . -985) T) ((-758 . -321) 187683) ((-76 . -1249) T) ((-686 . -397) 187655) ((-171 . -940) 187608) ((-30 . -985) T) ((-114 . -868) T) ((-1 . -632) 187590) ((-1028 . -922) 187511) ((-131 . -673) 187493) ((-50 . -640) 187477) ((-716 . -668) 187412) ((-609 . -928) 187325) ((-452 . -102) T) ((-143 . -321) NIL) ((-131 . -385) 187307) ((-897 . -1081) T) ((-856 . -872) 187286) ((-81 . -1249) T) ((-733 . -302) T) ((-40 . -1089) T) ((-595 . -175) T) ((-532 . -175) T) ((-526 . -632) 187268) ((-171 . -670) 187142) ((-521 . -632) 187124) ((-365 . -149) 187106) ((-365 . -147) T) ((-372 . -1144) T) ((-367 . -1144) T) ((-359 . -1144) T) ((-1036 . -319) T) ((-944 . -319) T) ((-897 . -250) T) ((-108 . -1144) T) ((-897 . -240) 187085) ((-1285 . -111) 186906) ((-1264 . -111) 186695) ((-252 . -1288) 186679) ((-560 . -871) T) ((-372 . -23) T) ((-353 . -363) T) ((-326 . -321) 186666) ((-325 . -321) 186607) ((-367 . -23) T) ((-331 . -133) T) ((-359 . -23) T) ((-1036 . -1052) T) ((-31 . -635) 186588) ((-108 . -23) T) ((-678 . -1083) 186572) ((-252 . -618) 186549) ((-661 . -739) 186533) ((-345 . -1133) T) ((-678 . -662) 186503) ((-1286 . -38) 186395) ((-1268 . -940) 186374) ((-114 . -1133) T) ((-840 . -1249) T) ((-427 . -1249) T) ((-1067 . -102) T) ((-1268 . -670) 186263) ((-896 . -818) NIL) ((-880 . -670) 186237) ((-896 . -814) NIL) ((-840 . -912) NIL) ((-896 . -748) T) ((-1119 . -528) 186104) ((-803 . -528) 186051) ((-802 . -528) 186003) ((-585 . -670) 185990) ((-840 . -1070) 185818) ((-468 . -528) 185761) ((-402 . -403) T) ((-1285 . -635) 185574) ((-1264 . -635) 185322) ((-60 . -1249) T) ((-638 . -872) 185301) ((-514 . -684) T) ((-1178 . -1008) 185270) ((-1056 . -668) 185207) ((-1035 . -466) T) ((-721 . -871) T) ((-525 . -816) T) 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-1133) T) ((-919 . -102) T) ((-803 . -302) 183524) ((-339 . -19) 183508) ((-58 . -300) 183485) ((-802 . -302) 183416) ((-880 . -748) T) ((-119 . -871) NIL) ((-530 . -300) 183393) ((-339 . -618) 183370) ((-510 . -300) 183347) ((-468 . -302) 183278) ((-1067 . -321) 183129) ((-901 . -504) 183110) ((-901 . -632) 183076) ((-703 . -504) 183057) ((-585 . -748) T) ((-698 . -504) 183038) ((-703 . -632) 182988) ((-698 . -632) 182954) ((-674 . -632) 182936) ((-492 . -504) 182917) ((-492 . -632) 182883) ((-252 . -633) 182844) ((-252 . -504) 182821) ((-140 . -504) 182802) ((-139 . -504) 182783) ((-135 . -504) 182764) ((-252 . -632) 182656) ((-216 . -102) T) ((-140 . -632) 182622) ((-139 . -632) 182588) ((-135 . -632) 182554) ((-1180 . -34) T) ((-973 . -1249) T) ((-357 . -739) 182499) ((-692 . -25) T) ((-692 . -21) T) ((-1209 . -635) 182480) ((-343 . -1249) T) ((-488 . -1081) T) ((-652 . -432) 182445) ((-620 . -432) 182410) ((-1152 . -1184) T) ((-1280 . -319) 182389) ((-734 . -1083) 182212) ((-595 . -302) T) ((-532 . -302) T) ((-1259 . -319) 182191) ((-488 . -240) 182143) ((-488 . -250) 182122) ((-453 . -1249) T) ((-734 . -662) 181951) ((-1259 . -1052) NIL) ((-1111 . -133) T) ((-897 . -821) 181930) ((-146 . -102) T) ((-40 . -1133) T) ((-897 . -816) 181909) ((-663 . -1042) 181893) ((-594 . -1089) T) ((-560 . -1089) T) ((-509 . -1089) T) ((-421 . -466) T) ((-372 . -133) T) ((-326 . -414) 181877) ((-325 . -414) 181838) ((-367 . -133) T) ((-359 . -133) T) ((-1214 . -1133) T) ((-1152 . -38) 181825) ((-1121 . -632) 181792) ((-108 . -133) T) ((-984 . -1133) T) ((-949 . -1133) T) ((-793 . -1133) T) ((-694 . -1133) T) ((-723 . -149) T) ((-623 . -102) T) ((-118 . -149) T) ((-1321 . -21) T) ((-1321 . -25) T) ((-1320 . -21) T) ((-1320 . -25) T) ((-686 . -1088) 181776) ((-545 . -872) T) ((-514 . -872) T) ((-377 . -1249) T) ((-368 . -1088) 181728) ((-366 . -1088) 181680) ((-358 . -1088) 181632) ((-260 . -1249) T) ((-259 . -1249) T) ((-275 . -1088) 181475) ((-255 . -1088) 181318) ((-686 . -111) 181297) ((-841 . -1254) 181276) ((-562 . -868) T) ((-326 . -930) 181242) ((-368 . -111) 181180) ((-366 . -111) 181118) ((-358 . -111) 181056) ((-275 . -111) 180885) ((-255 . -111) 180714) ((-325 . -930) NIL) ((-642 . -426) 180698) ((-44 . -21) T) ((-44 . -25) T) ((-932 . -875) 180649) ((-130 . -684) T) ((-839 . -660) 180555) ((-841 . -571) 180534) ((-501 . -875) T) ((-260 . -1070) 180361) ((-259 . -1070) 180188) ((-128 . -121) 180172) ((-221 . -875) T) ((-936 . -1088) 180137) ((-734 . -102) T) ((-721 . -1089) T) ((-611 . -635) 180118) ((-600 . -635) 180099) ((-549 . -637) 180002) ((-357 . -175) T) ((-154 . -21) T) ((-154 . -25) T) ((-87 . -632) 179984) ((-936 . -111) 179940) ((-40 . -739) 179885) ((-894 . -1133) T) ((-686 . -635) 179862) ((-667 . -635) 179843) ((-368 . -635) 179780) ((-366 . -635) 179717) ((-358 . -635) 179654) ((-562 . -1133) T) ((-339 . -633) 179615) ((-339 . -632) 179527) ((-275 . -635) 179280) ((-255 . -635) 179065) ((-190 . -1249) T) ((-1264 . -816) 179018) ((-1264 . -821) 178971) ((-260 . -390) 178940) ((-259 . -390) 178909) ((-564 . -875) T) ((-678 . -38) 178879) ((-627 . -34) T) ((-496 . -1144) 178857) ((-489 . -34) T) ((-1145 . -133) 178728) ((-994 . -25) 178539) ((-936 . -635) 178489) ((-899 . -632) 178471) ((-218 . -868) T) ((-994 . -21) 178426) ((-839 . -25) 178259) ((-839 . -21) 178170) ((-1256 . -381) T) ((-642 . -1089) T) ((-1211 . -571) 178149) ((-1203 . -47) 178126) ((-368 . -1081) T) ((-366 . -1081) T) ((-496 . -23) 177978) ((-358 . -1081) T) ((-275 . -1081) T) ((-255 . -1081) T) ((-1157 . -47) 177950) ((-119 . -1089) T) ((-1066 . -670) 177924) ((-988 . -34) T) ((-368 . -240) 177903) ((-368 . -250) T) ((-366 . -240) 177882) ((-366 . -250) T) ((-358 . -240) 177861) ((-358 . -250) T) ((-275 . -338) 177833) ((-255 . -338) 177790) ((-275 . -240) 177769) ((-1187 . -153) 177753) ((-260 . -928) 177685) ((-259 . -928) 177617) ((-1174 . -922) 177538) ((-1114 . -872) T) ((-1266 . -1249) 177516) ((-429 . -1144) T) ((-1242 . -1034) 177482) ((-1086 . -23) T) ((-1056 . -871) T) ((-936 . -1081) T) ((-334 . -670) 177464) ((-723 . -239) T) ((-692 . -236) 177409) ((-1206 . -951) 177388) ((-1200 . -951) 177367) ((-1200 . -844) NIL) ((-1028 . -1083) 177263) ((-997 . -1249) T) ((-936 . -250) T) ((-841 . -376) 177242) ((-218 . -1133) T) ((-394 . -23) T) ((-129 . -1133) 177220) ((-123 . -1133) 177198) ((-936 . -240) T) ((-131 . -34) T) ((-391 . -670) 177163) ((-1028 . -662) 177111) ((-894 . -739) 177098) ((-1329 . -668) 177070) ((-1078 . -153) 177035) ((-1025 . -1249) T) ((-888 . -1249) T) ((-40 . -175) T) ((-716 . -426) 177017) ((-734 . -321) 177004) ((-858 . -670) 176964) ((-852 . -670) 176938) ((-331 . -25) T) ((-331 . -21) T) ((-676 . -298) 176917) ((-594 . -1133) T) ((-560 . -1133) T) ((-509 . -1133) T) ((-1203 . -1249) T) ((-252 . -300) 176894) ((-1157 . -1249) T) ((-879 . -1249) T) ((-325 . -274) 176855) ((-325 . -234) 176816) ((-1255 . -875) T) ((-1203 . -912) NIL) ((-55 . -1133) T) ((-1157 . -912) 176675) ((-130 . -872) T) ((-1203 . -1070) 176555) ((-1157 . -1070) 176438) ((-187 . -632) 176420) ((-879 . -1070) 176316) ((-803 . -298) 176243) ((-841 . -1144) T) ((-1066 . -748) T) ((-1078 . -1008) 176172) ((-616 . -673) 176156) ((-1035 . -922) 176063) ((-1028 . -102) T) ((-841 . -23) T) ((-734 . -1184) 176041) ((-716 . -1089) T) ((-616 . -385) 176025) ((-365 . -466) T) ((-357 . -302) T) ((-1302 . -1133) T) ((-256 . -1133) T) ((-413 . -102) T) ((-301 . -21) T) ((-301 . -25) T) ((-374 . -748) T) ((-732 . -1133) T) ((-721 . -1133) T) ((-374 . -487) T) ((-1242 . -632) 176007) ((-1203 . -390) 175991) ((-1157 . -390) 175975) ((-1056 . -426) 175937) ((-143 . -233) 175919) ((-391 . -818) T) ((-391 . -814) T) ((-894 . -175) T) ((-391 . -748) T) ((-733 . -632) 175901) ((-734 . -38) 175730) ((-1299 . -1298) 175714) ((-365 . -416) T) ((-1299 . -1133) 175664) ((-1223 . -1133) T) ((-594 . -739) 175651) ((-560 . -739) 175638) ((-509 . -739) 175603) ((-1286 . -668) 175493) ((-326 . -649) 175472) ((-858 . -748) T) ((-852 . -748) T) ((-1148 . -1249) T) ((-663 . -1249) T) ((-1111 . -660) 175420) ((-1203 . -928) 175363) ((-1157 . -928) 175347) ((-839 . -236) 175238) ((-674 . -1088) 175222) ((-108 . -660) 175204) ((-496 . -133) 175075) ((-1211 . -1144) T) ((-843 . -1249) T) ((-976 . -47) 175044) ((-642 . -1133) T) ((-674 . -111) 175023) ((-505 . -632) 174989) ((-339 . -300) 174966) ((-400 . -1249) T) ((-336 . -1249) T) ((-495 . -47) 174923) ((-1211 . -23) T) ((-119 . -1133) T) ((-103 . -102) 174873) ((-1312 . -1144) T) ((-563 . -872) T) ((-229 . -1249) T) ((-1086 . -133) T) ((-1056 . -1089) T) ((-1312 . -23) T) ((-1229 . -632) 174855) ((-843 . -1070) 174839) ((-1152 . -845) T) ((-1035 . -746) 174811) ((-1137 . -1133) T) ((-721 . -739) 174776) ((-597 . -632) 174758) ((-400 . -1070) 174742) ((-353 . -1089) T) ((-394 . -133) T) ((-336 . -1070) 174726) ((-1111 . -21) T) ((-1111 . -25) T) ((-1036 . -844) T) ((-229 . -912) 174708) ((-1036 . -951) T) ((-91 . -34) T) ((-1028 . -321) 174673) ((-944 . -951) T) ((-901 . -635) 174654) ((-736 . -670) 174614) ((-501 . -1254) T) ((-703 . -635) 174595) ((-698 . -635) 174576) ((-659 . -670) 174560) ((-221 . -1254) T) ((-421 . -922) 174481) ((-229 . -1070) 174441) ((-40 . -302) T) ((-501 . -571) T) ((-492 . -635) 174422) ((-372 . -25) T) ((-326 . -668) 174077) ((-325 . -668) 173991) ((-372 . -21) T) ((-367 . -25) T) ((-367 . -21) T) ((-221 . -571) T) ((-359 . -25) T) ((-359 . -21) T) ((-331 . -236) 173937) ((-252 . -635) 173914) ((-140 . -635) 173895) ((-139 . -635) 173876) ((-135 . -635) 173857) ((-108 . -25) T) ((-108 . -21) T) ((-48 . -1089) T) ((-594 . -175) T) ((-560 . -175) T) ((-509 . -175) T) ((-1094 . -1249) T) ((-976 . -1249) T) ((-735 . -1249) T) ((-661 . -298) 173824) ((-676 . -632) 173806) ((-495 . -1249) T) ((-758 . -759) 173790) ((-346 . -632) 173772) ((-68 . -396) T) ((-68 . -410) T) ((-1129 . -107) 173756) ((-1094 . -912) 173738) ((-976 . -912) 173663) ((-677 . -1144) T) ((-642 . -739) 173650) ((-495 . -912) NIL) ((-1178 . -102) T) ((-1121 . -637) 173634) ((-1094 . -1070) 173616) ((-97 . -632) 173598) ((-491 . -149) T) ((-976 . -1070) 173478) ((-119 . -739) 173423) ((-734 . -930) 173330) ((-677 . -23) T) ((-495 . -1070) 173206) ((-1119 . -633) NIL) ((-1119 . -632) 173188) ((-803 . -633) NIL) ((-803 . -632) 173149) ((-802 . -633) 172783) ((-802 . -632) 172697) ((-1145 . -660) 172603) ((-822 . -875) 172582) ((-475 . -632) 172564) ((-468 . -632) 172546) ((-468 . -633) 172407) ((-1067 . -233) 172353) ((-897 . -940) 172332) ((-128 . -34) T) ((-841 . -133) T) ((-671 . -632) 172314) ((-592 . -102) T) ((-368 . -1318) 172298) ((-366 . -1318) 172282) ((-358 . -1318) 172266) ((-123 . -528) 172199) ((-129 . -528) 172132) ((-526 . -816) T) ((-526 . -821) T) ((-525 . -818) T) ((-103 . -321) 172070) ((-226 . -102) 172020) ((-721 . -175) T) ((-716 . -1133) T) ((-897 . -670) 171936) ((-65 . -398) T) ((-286 . -632) 171918) ((-65 . -410) T) ((-976 . -390) 171902) ((-894 . -302) T) ((-50 . -632) 171884) ((-1152 . -668) 171856) ((-1028 . -38) 171804) ((-626 . -1133) T) ((-621 . -1133) T) ((-595 . -632) 171786) ((-495 . -390) 171770) ((-595 . -633) 171752) ((-532 . -632) 171734) ((-936 . -1318) 171721) ((-896 . -1249) T) ((-723 . -466) T) ((-509 . -528) 171687) ((-1311 . -1249) T) ((-1310 . -1249) T) ((-501 . -376) T) ((-368 . -381) 171666) ((-366 . -381) 171645) ((-358 . -381) 171624) ((-736 . -748) T) ((-221 . -376) T) ((-118 . -466) T) ((-1323 . -1314) 171608) ((-896 . -910) 171585) ((-896 . -912) NIL) ((-994 . -872) 171484) ((-839 . -872) 171435) ((-1257 . -102) T) ((-678 . -680) 171419) ((-1236 . -34) T) ((-174 . -632) 171401) ((-1145 . -25) 171234) ((-1145 . -21) 171145) ((-896 . -1070) 171122) ((-976 . -928) 171103) ((-1268 . -47) 171080) ((-936 . -381) T) ((-607 . -875) T) ((-58 . -673) 171064) ((-530 . -673) 171048) ((-495 . -928) 171025) ((-71 . -455) T) ((-71 . -410) T) ((-510 . -673) 171009) ((-58 . -385) 170993) ((-642 . -175) T) ((-530 . -385) 170977) ((-510 . -385) 170961) ((-561 . -1249) T) 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169678) ((-359 . -236) 169651) ((-177 . -466) T) ((-82 . -455) T) ((-226 . -321) 169589) ((-82 . -410) T) ((-227 . -632) 169571) ((-108 . -236) 169558) ((-221 . -23) T) ((-1324 . -1319) 169537) ((-699 . -1070) 169521) ((-594 . -302) T) ((-560 . -302) T) ((-509 . -302) T) ((-1268 . -1249) T) ((-137 . -484) 169476) ((-880 . -1249) T) ((-678 . -668) 169435) ((-48 . -1133) T) ((-734 . -274) 169419) ((-734 . -234) 169403) ((-896 . -928) NIL) ((-585 . -1249) T) ((-1268 . -912) NIL) ((-914 . -102) T) ((-911 . -102) T) ((-661 . -632) 169385) ((-402 . -1133) T) ((-171 . -390) 169369) ((-171 . -351) 169353) ((-1268 . -1070) 169233) ((-880 . -1070) 169129) ((-1174 . -102) T) ((-1028 . -930) 169052) ((-677 . -133) T) ((-674 . -816) 169031) ((-674 . -821) 169010) ((-119 . -528) 168918) ((-585 . -1070) 168900) ((-305 . -1307) 168870) ((-1200 . -875) NIL) ((-891 . -102) T) ((-986 . -571) 168849) ((-1242 . -1088) 168732) ((-1035 . -1083) 168677) ((-496 . -660) 168583) ((-935 . -1133) T) ((-1056 . -739) 168520) ((-733 . -1088) 168485) ((-1035 . -662) 168430) ((-636 . -102) T) ((-616 . -34) T) ((-1180 . -1249) T) ((-1242 . -111) 168299) ((-488 . -670) 168196) ((-353 . -739) 168141) ((-171 . -928) 168100) ((-721 . -302) T) ((-716 . -175) T) ((-733 . -111) 168056) ((-1329 . -1089) T) ((-1268 . -390) 168040) ((-419 . -1254) 168018) ((-1147 . -632) 168000) ((-325 . -871) NIL) ((-419 . -571) T) ((-229 . -319) T) ((-1264 . -814) 167953) ((-1264 . -818) 167906) ((-1285 . -748) T) ((-1264 . -748) T) ((-48 . -739) 167871) ((-229 . -1052) T) ((-1286 . -426) 167837) ((-1268 . -928) 167780) ((-365 . -1307) 167757) ((-1242 . -635) 167639) ((-740 . -748) T) ((-345 . -632) 167621) ((-534 . -875) 167600) ((-1145 . -236) 167491) ((-114 . -632) 167473) ((-114 . -633) 167455) ((-740 . -487) T) ((-733 . -635) 167405) ((-1323 . -1083) 167389) ((-496 . -25) 167222) ((-129 . -503) 167206) ((-123 . -503) 167190) ((-496 . -21) 167101) ((-1323 . -662) 167071) ((-642 . -302) T) ((-597 . -1088) 167046) ((-450 . -1133) T) ((-1094 . -319) T) ((-119 . -302) T) ((-1135 . -102) T) ((-1035 . -102) T) ((-597 . -111) 167014) ((-1242 . -1081) T) ((-1174 . -321) 166952) ((-1094 . -1052) T) ((-1086 . -25) T) ((-66 . -1249) T) ((-916 . -1249) T) ((-1086 . -21) T) ((-733 . -1081) T) ((-394 . -21) T) ((-394 . -25) T) ((-716 . -528) NIL) ((-1056 . -175) T) ((-733 . -250) T) ((-1094 . -559) T) ((-734 . -668) 166862) ((-520 . -102) T) ((-516 . -102) T) ((-357 . -632) 166844) ((-353 . -175) T) ((-421 . -1083) 166796) ((-407 . -632) 166778) ((-1152 . -871) T) ((-488 . -748) T) ((-916 . -1070) 166746) ((-421 . -662) 166698) ((-108 . -872) T) ((-676 . -1088) 166682) ((-501 . -133) T) ((-1286 . -1089) T) ((-221 . -133) T) ((-1187 . -102) 166632) ((-99 . -1133) T) ((-246 . -875) 166583) ((-252 . -688) 166567) ((-252 . -673) 166551) ((-676 . -111) 166530) ((-597 . -635) 166514) ((-326 . -426) 166498) ((-252 . -385) 166482) ((-1192 . -242) 166429) ((-1028 . -274) 166413) ((-1028 . -234) 166397) ((-74 . -1249) T) ((-48 . -175) T) ((-723 . -401) T) ((-723 . -145) T) ((-1323 . -102) T) ((-1231 . -1249) T) ((-1229 . -635) 166379) ((-1120 . -1249) T) ((-1119 . -1088) 166222) ((-1107 . -1249) T) ((-275 . -940) 166201) ((-255 . -940) 166180) ((-803 . -1088) 166003) ((-802 . -1088) 165846) ((-627 . -1249) T) ((-1197 . -632) 165828) ((-1119 . -111) 165657) ((-1078 . -102) T) ((-489 . -1249) T) ((-475 . -1088) 165628) ((-468 . -1088) 165471) ((-686 . -670) 165455) ((-896 . -319) T) ((-803 . -111) 165264) ((-802 . -111) 165093) ((-368 . -670) 165045) ((-366 . -670) 164997) ((-358 . -670) 164949) ((-275 . -670) 164838) ((-255 . -670) 164727) ((-1191 . -872) T) ((-1120 . -1070) 164711) ((-1107 . -1070) 164688) ((-1036 . -875) T) ((-1032 . -34) T) ((-475 . -111) 164649) ((-468 . -111) 164478) ((-1003 . -875) T) ((-996 . -632) 164460) ((-988 . -1249) T) ((-986 . -1144) T) ((-128 . -1042) 164444) ((-873 . -1249) T) ((-896 . -1052) NIL) ((-757 . -1144) T) ((-737 . -1144) T) ((-676 . -635) 164362) ((-1299 . -503) 164346) ((-1217 . -1249) T) ((-1216 . -1249) T) ((-1174 . -38) 164306) ((-986 . -23) T) ((-936 . -670) 164271) ((-890 . -1133) T) ((-866 . -102) T) ((-841 . -21) T) ((-652 . -1083) 164255) ((-620 . -1083) 164239) ((-841 . -25) T) ((-757 . -23) T) ((-737 . -23) T) ((-652 . -662) 164223) ((-110 . -684) T) ((-620 . -662) 164207) ((-595 . -1088) 164172) ((-532 . -1088) 164117) ((-231 . -57) 164075) ((-467 . -23) T) ((-421 . -102) T) ((-1215 . -1249) T) ((-270 . -102) T) ((-110 . -113) T) ((-716 . -302) T) ((-891 . -38) 164045) ((-1119 . -635) 163781) ((-595 . -111) 163737) ((-532 . -111) 163666) ((-419 . -1144) T) ((-326 . -1089) 163556) ((-325 . -1089) T) ((-132 . -1249) T) ((-131 . -1249) T) ((-803 . -635) 163304) ((-802 . -635) 163070) ((-676 . -1081) T) ((-1329 . -1133) T) ((-468 . -635) 162855) ((-171 . -319) 162786) ((-419 . -23) T) ((-40 . -632) 162768) ((-40 . -633) 162752) ((-108 . -1023) 162734) ((-118 . -895) 162718) ((-671 . -635) 162702) ((-48 . -528) 162668) ((-1236 . -1042) 162652) ((-1214 . -632) 162619) ((-1221 . -34) T) ((-984 . -632) 162585) ((-949 . -632) 162567) ((-1145 . -872) 162518) ((-793 . -632) 162500) ((-694 . -632) 162482) ((-531 . -1249) T) ((-1268 . -319) 162461) ((-1187 . -321) 162399) ((-1173 . -34) T) ((-493 . -34) T) ((-1124 . -1249) T) ((-491 . -466) T) ((-1066 . -1249) T) ((-1119 . -1081) T) ((-50 . -635) 162368) ((-803 . -1081) T) ((-802 . -1081) T) ((-669 . -242) 162352) ((-651 . -242) 162298) ((-1211 . -21) T) ((-595 . -635) 162248) ((-532 . -635) 162178) ((-496 . -236) 162069) ((-1211 . -25) T) ((-1119 . -338) 162030) ((-468 . -1081) T) ((-1119 . -240) 162009) ((-803 . -338) 161986) ((-803 . -240) T) ((-802 . -338) 161958) ((-753 . -1254) 161937) ((-533 . -34) T) ((-339 . -673) 161921) ((-530 . -34) T) ((-58 . -34) T) ((-511 . -34) T) ((-510 . -34) T) ((-468 . -338) 161900) ((-339 . -385) 161884) ((-374 . -1249) T) ((-334 . -1249) T) ((-1035 . -1184) NIL) ((-753 . -571) 161815) ((-652 . -102) T) ((-620 . -102) T) ((-368 . -748) T) ((-366 . -748) T) ((-358 . -748) T) ((-275 . -748) T) ((-255 . -748) T) ((-391 . -1249) T) ((-1312 . -21) T) ((-1078 . -321) 161723) ((-1312 . -25) T) ((-931 . -1133) 161701) ((-842 . -236) 161688) ((-50 . -1081) T) ((-1207 . -571) 161667) ((-1206 . -1254) 161646) ((-1206 . -571) 161597) ((-1200 . -1254) 161576) ((-1200 . -571) 161527) ((-1056 . -302) T) ((-595 . -1081) T) ((-532 . -1081) T) ((-1035 . -38) 161472) ((-374 . -1070) 161456) ((-334 . -1070) 161440) ((-1028 . -668) 161363) ((-391 . -912) 161345) ((-858 . -1249) T) ((-852 . -1249) T) ((-849 . -1249) T) ((-822 . -1144) T) ((-936 . -748) T) ((-595 . -250) T) ((-595 . -240) T) ((-532 . -240) T) ((-532 . -250) T) ((-1158 . -571) 161324) ((-353 . -302) T) ((-669 . -717) 161308) ((-391 . -1070) 161268) ((-305 . -1083) 161189) ((-352 . -922) 161168) ((-1152 . -1089) T) ((-103 . -127) 161152) ((-305 . -662) 161094) ((-822 . -23) T) ((-1321 . -1319) 161070) ((-1320 . -1319) 161049) ((-1299 . -298) 161001) ((-1286 . -1133) T) ((-421 . -321) 160966) ((-1174 . -930) 160889) ((-894 . -632) 160871) ((-858 . -1070) 160840) ((-661 . -1088) 160824) ((-206 . -809) T) ((-205 . -809) T) ((-204 . -809) T) ((-203 . -809) T) ((-202 . -809) T) ((-201 . -809) T) ((-200 . -809) T) ((-199 . -809) T) ((-198 . -809) T) ((-197 . -809) T) ((-562 . -632) 160806) ((-509 . -1034) T) ((-285 . -863) T) ((-284 . -863) T) ((-283 . -863) T) ((-282 . -863) T) ((-48 . -302) T) ((-281 . -863) T) ((-280 . -863) T) ((-279 . -863) T) ((-196 . -809) T) ((-661 . -111) 160785) ((-630 . -872) T) ((-678 . -426) 160769) ((-692 . -239) 160720) ((-227 . -635) 160682) ((-110 . -872) T) ((-677 . -21) T) ((-677 . -25) T) ((-1323 . -38) 160652) ((-119 . -298) 160603) ((-1299 . -19) 160587) ((-1259 . -875) NIL) ((-1299 . -618) 160564) ((-1313 . -1133) T) ((-365 . -1083) 160509) ((-1109 . -1133) T) ((-1018 . -1133) T) ((-986 . -133) T) ((-841 . -236) 160496) ((-758 . -1133) T) ((-365 . -662) 160441) ((-757 . -133) T) ((-737 . -133) T) ((-526 . -817) T) ((-526 . -818) T) ((-467 . -133) T) ((-421 . -1184) 160419) ((-227 . -1081) T) ((-305 . -102) 160201) ((-143 . -1133) T) ((-721 . -1034) T) ((-1137 . -298) 160157) ((-91 . -1249) T) ((-218 . -632) 160139) ((-129 . -632) 160071) ((-123 . -632) 160003) ((-1329 . -175) T) ((-1206 . -376) 159982) ((-1200 . -376) 159961) ((-326 . -1133) T) ((-419 . -133) T) ((-325 . -1133) T) ((-421 . -38) 159913) ((-1165 . -102) T) ((-1286 . -739) 159805) ((-1167 . -1295) T) ((-1128 . -1249) T) ((-1123 . -1249) T) ((-678 . -1089) T) ((-1105 . -1249) T) ((-1098 . -1249) T) ((-1068 . -1249) T) ((-1051 . -1249) T) ((-331 . -147) 159784) ((-331 . -149) 159763) ((-141 . -1133) T) ((-137 . -1133) T) ((-115 . -1133) T) ((-883 . -102) T) ((-645 . -1249) T) ((-497 . -1249) T) ((-594 . -632) 159745) ((-560 . -633) 159644) ((-560 . -632) 159626) ((-509 . -632) 159608) ((-509 . -633) 159553) ((-499 . -23) T) ((-222 . -1249) T) ((-496 . -872) 159504) ((-501 . -660) 159486) ((-995 . -632) 159468) ((-1035 . -930) 159377) ((-221 . -660) 159359) ((-229 . -418) T) ((-674 . -670) 159343) ((-55 . -632) 159325) ((-1203 . -951) 159304) ((-753 . -1144) T) ((-657 . -102) T) ((-529 . -1249) T) ((-525 . -1249) T) ((-522 . -1249) T) ((-365 . -102) T) ((-1250 . -1115) T) ((-1152 . -868) T) ((-842 . -872) T) ((-753 . -23) T) ((-357 . -1088) 159249) ((-1180 . -107) 159233) ((-1302 . -632) 159215) ((-1207 . -23) T) ((-1207 . -1144) T) ((-1206 . -1144) T) ((-659 . -1249) T) ((-1206 . -23) T) ((-1200 . -1144) T) ((-1200 . -23) T) ((-1174 . -274) 159199) ((-529 . -1070) 159183) ((-1174 . -234) 159167) ((-1158 . -1144) T) ((-357 . -111) 159096) ((-1036 . -1254) T) ((-128 . -1249) T) ((-944 . -1254) T) ((-1158 . -23) T) ((-1108 . -1133) T) ((-716 . -298) NIL) ((-736 . -1249) T) ((-1036 . -571) T) ((-944 . -571) T) ((-839 . -239) 158993) ((-625 . -684) T) ((-624 . -684) T) ((-257 . -1249) T) ((-186 . -1249) T) ((-163 . -1249) T) ((-159 . -1249) T) ((-256 . -632) 158975) ((-622 . -684) T) ((-822 . -133) T) 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-1133) 145971) ((-1257 . -868) T) ((-331 . -1005) 145933) ((-105 . -102) T) ((-48 . -1088) 145898) ((-896 . -875) NIL) ((-1324 . -102) T) ((-395 . -102) T) ((-1286 . -632) 145880) ((-1165 . -1166) 145864) ((-1036 . -660) 145846) ((-901 . -1249) T) ((-48 . -111) 145802) ((-703 . -1249) T) ((-698 . -1249) T) ((-674 . -1249) T) ((-839 . -922) 145669) ((-492 . -1249) T) ((-252 . -1249) T) ((-545 . -102) T) ((-514 . -102) T) ((-154 . -1307) 145653) ((-140 . -1249) T) ((-139 . -1249) T) ((-135 . -1249) T) ((-1250 . -102) T) ((-1056 . -635) 145590) ((-841 . -239) T) ((-1203 . -1254) 145569) ((-218 . -381) T) ((-353 . -635) 145499) ((-1157 . -1254) 145478) ((-246 . -25) 145311) ((-246 . -21) 145222) ((-129 . -121) 145206) ((-123 . -121) 145190) ((-44 . -766) 145174) ((-1203 . -571) 145085) ((-1157 . -571) 145016) ((-1257 . -1133) T) ((-561 . -875) T) ((-1067 . -298) 144991) ((-1199 . -1115) T) ((-1026 . -1115) T) ((-840 . -133) T) ((-119 . -821) NIL) ((-119 . -816) NIL) ((-368 . -319) T) 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143000) ((-1221 . -107) 142950) ((-669 . -153) 142934) ((-651 . -153) 142880) ((-118 . -668) 142852) ((-493 . -1226) 142831) ((-501 . -149) T) ((-501 . -147) NIL) ((-1152 . -633) 142746) ((-452 . -632) 142728) ((-221 . -149) T) ((-221 . -147) NIL) ((-1152 . -632) 142710) ((-130 . -102) T) ((-51 . -102) T) ((-1259 . -660) 142662) ((-493 . -107) 142612) ((-1025 . -23) T) ((-1324 . -38) 142582) ((-1203 . -1144) T) ((-1157 . -1144) T) ((-1094 . -1254) T) ((-246 . -236) 142473) ((-324 . -102) T) ((-879 . -1144) T) ((-976 . -1254) 142452) ((-495 . -1254) 142431) ((-1094 . -571) T) ((-976 . -571) 142362) ((-1203 . -23) T) ((-1185 . -1115) T) ((-1157 . -23) T) ((-879 . -23) T) ((-495 . -571) 142293) ((-1174 . -739) 142225) ((-692 . -1083) 142209) ((-1178 . -528) 142142) ((-692 . -662) 142126) ((-1067 . -633) NIL) ((-1067 . -632) 142108) ((-96 . -1115) T) ((-1329 . -1088) 142095) ((-891 . -739) 142065) ((-1329 . -111) 142050) ((-1242 . -47) 142019) ((-1200 . -872) NIL) ((-260 . -133) T) ((-259 . -133) T) ((-1135 . -1133) T) ((-1035 . -1133) T) ((-63 . -632) 142001) ((-1111 . -922) 141870) ((-1056 . -816) T) ((-1056 . -821) T) ((-1289 . -25) T) ((-1289 . -21) T) ((-1280 . -21) T) ((-1280 . -25) T) ((-894 . -670) 141857) ((-1259 . -21) T) ((-1259 . -25) T) ((-1059 . -153) 141841) ((-1036 . -236) 141828) ((-897 . -844) 141807) ((-897 . -951) T) ((-734 . -298) 141734) ((-610 . -21) T) ((-352 . -668) 141693) ((-108 . -922) NIL) ((-610 . -25) T) ((-609 . -21) T) ((-177 . -668) 141610) ((-40 . -748) T) ((-226 . -528) 141543) ((-609 . -25) T) ((-490 . -153) 141527) ((-477 . -153) 141511) ((-187 . -1249) T) ((-949 . -818) T) ((-949 . -748) T) ((-793 . -817) T) ((-793 . -818) T) ((-520 . -1133) T) ((-516 . -1133) T) ((-793 . -748) T) ((-229 . -376) T) ((-1321 . -1083) 141495) ((-1320 . -1083) 141479) ((-1321 . -662) 141449) ((-1187 . -1133) 141427) ((-896 . -1254) T) ((-1320 . -662) 141397) ((-1120 . -875) T) ((-678 . -632) 141379) ((-896 . -571) T) ((-716 . -381) NIL) ((-44 . -1083) 141363) ((-1329 . -635) 141345) ((-1323 . -1133) T) ((-692 . -102) T) ((-372 . -1307) 141329) ((-367 . -1307) 141313) ((-44 . -662) 141297) ((-359 . -1307) 141281) ((-563 . -102) T) ((-1242 . -1249) T) ((-534 . -872) 141260) ((-733 . -1249) T) ((-988 . -875) 141239) ((-873 . -875) T) ((-501 . -239) T) ((-221 . -239) T) ((-1078 . -1133) T) ((-841 . -466) 141218) ((-154 . -1083) 141202) ((-1078 . -1103) 141131) ((-1059 . -1008) 141100) ((-843 . -1144) T) ((-1035 . -739) 141045) ((-154 . -662) 141029) ((-400 . -1144) T) ((-490 . -1008) 140998) ((-477 . -1008) 140967) ((-1216 . -875) T) ((-110 . -153) 140949) ((-73 . -632) 140931) ((-919 . -632) 140913) ((-1215 . -875) T) ((-1111 . -746) 140892) ((-1329 . -1081) T) ((-840 . -660) 140840) ((-305 . -1089) 140782) ((-171 . -1254) 140687) ((-229 . -1144) T) ((-336 . -23) T) ((-1200 . -1023) 140639) ((-1286 . -1088) 140544) ((-866 . -1133) T) ((-131 . -875) T) ((-1158 . -762) 140523) ((-1285 . -951) 140502) ((-1264 . -951) 140481) ((-894 . -748) T) ((-171 . -571) 140392) ((-594 . -670) 140379) ((-560 . -670) 140351) ((-421 . -1133) T) ((-270 . -1133) T) ((-216 . -632) 140333) ((-509 . -670) 140283) ((-229 . -23) T) ((-1264 . -844) 140236) ((-1321 . -102) T) ((-505 . -1249) T) ((-353 . -1318) 140213) ((-1320 . -102) T) ((-1286 . -111) 140105) ((-1145 . -922) 139972) ((-839 . -1083) 139873) ((-839 . -662) 139795) ((-146 . -632) 139777) ((-1025 . -133) T) ((-44 . -102) T) ((-246 . -872) 139728) ((-597 . -1249) T) ((-1268 . -1254) 139707) ((-103 . -503) 139691) ((-1323 . -739) 139661) ((-1119 . -47) 139622) ((-1094 . -1144) T) ((-976 . -1144) T) ((-129 . -34) T) ((-123 . -34) T) ((-1268 . -571) 139533) ((-803 . -47) 139510) ((-802 . -47) 139482) ((-1229 . -1249) T) ((-1203 . -133) T) ((-353 . -381) T) ((-495 . -1144) T) ((-1157 . -133) T) ((-896 . -376) T) ((-468 . -47) 139461) ((-879 . -133) T) ((-334 . -875) 139440) ((-154 . -102) T) ((-1094 . -23) T) ((-976 . -23) T) ((-585 . -571) T) ((-840 . -25) T) ((-840 . -21) T) 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137321) ((-1119 . -1249) T) ((-1067 . -300) 137296) ((-594 . -748) T) ((-560 . -818) T) ((-171 . -376) 137247) ((-560 . -814) T) ((-560 . -748) T) ((-509 . -748) T) ((-803 . -1249) T) ((-802 . -1249) T) ((-1178 . -503) 137231) ((-475 . -1249) T) ((-468 . -1249) T) ((-1321 . -1322) 137207) ((-1119 . -912) NIL) ((-896 . -1144) T) ((-119 . -940) NIL) ((-1320 . -1322) 137186) ((-671 . -1249) T) ((-803 . -912) NIL) ((-802 . -912) 137045) ((-1315 . -25) T) ((-1315 . -21) T) ((-1247 . -102) 137023) ((-1138 . -410) T) ((-642 . -670) 137010) ((-468 . -912) NIL) ((-697 . -102) 136960) ((-1119 . -1070) 136787) ((-896 . -23) T) ((-803 . -1070) 136646) ((-802 . -1070) 136503) ((-119 . -670) 136448) ((-468 . -1070) 136324) ((-286 . -1249) T) ((-326 . -635) 135888) ((-325 . -635) 135771) ((-50 . -1249) T) ((-404 . -668) 135740) ((-671 . -1070) 135724) ((-646 . -102) T) ((-595 . -1249) T) ((-532 . -1249) T) ((-226 . -503) 135708) ((-1299 . -34) T) ((-638 . -668) 135667) ((-301 . -1083) 135654) ((-137 . -635) 135638) ((-301 . -662) 135625) ((-652 . -739) 135609) ((-620 . -739) 135593) ((-692 . -38) 135553) ((-331 . -102) T) ((-1152 . -1088) 135540) ((-86 . -632) 135522) ((-50 . -1070) 135506) ((-1119 . -390) 135490) ((-803 . -390) 135474) ((-721 . -748) T) ((-721 . -818) T) ((-721 . -814) T) ((-60 . -57) 135436) ((-595 . -1070) 135423) ((-532 . -1070) 135400) ((-174 . -1249) T) ((-336 . -133) T) ((-326 . -1081) 135290) ((-325 . -1081) T) ((-171 . -1144) T) ((-802 . -390) 135274) ((-45 . -153) 135224) ((-1036 . -1023) 135206) ((-468 . -390) 135190) ((-421 . -175) T) ((-326 . -250) 135169) ((-325 . -250) T) ((-325 . -240) NIL) ((-305 . -1133) 134951) ((-229 . -133) T) ((-1152 . -111) 134936) ((-171 . -23) T) ((-822 . -149) 134915) ((-822 . -147) 134894) ((-260 . -660) 134800) ((-259 . -660) 134706) ((-331 . -296) 134672) ((-1187 . -528) 134605) ((-491 . -668) 134555) ((-657 . -868) T) ((-496 . -922) 134422) ((-1165 . -1133) T) ((-229 . -1092) T) ((-839 . -321) 134360) ((-1119 . -928) 134295) ((-803 . -928) 134238) ((-802 . -928) 134222) ((-1321 . -38) 134192) ((-1320 . -38) 134162) ((-1268 . -1144) T) ((-880 . -1144) T) ((-468 . -928) 134139) ((-883 . -1133) T) ((-1268 . -23) T) ((-1152 . -635) 134111) ((-1094 . -133) T) ((-880 . -23) T) ((-585 . -1144) T) ((-642 . -748) T) ((-525 . -875) T) ((-368 . -951) T) ((-366 . -951) T) ((-301 . -102) T) ((-358 . -951) T) ((-1002 . -1115) T) ((-976 . -133) T) ((-840 . -236) 134056) ((-119 . -818) NIL) ((-119 . -814) NIL) ((-119 . -748) T) ((-1078 . -528) 133957) ((-716 . -940) NIL) ((-585 . -23) T) ((-495 . -133) T) ((-419 . -239) 133908) ((-697 . -321) 133846) ((-227 . -1249) T) ((-657 . -1133) T) ((-652 . -783) T) ((-620 . -783) T) ((-1259 . -872) NIL) ((-1111 . -1083) 133756) ((-1035 . -302) T) ((-716 . -670) 133706) ((-260 . -25) T) ((-365 . -1133) T) ((-260 . -21) T) ((-259 . -25) T) ((-259 . -21) T) ((-154 . -38) 133690) ((-2 . -102) T) ((-936 . -951) T) ((-1111 . -662) 133558) ((-496 . -1307) 133528) ((-1152 . -1081) T) ((-733 . -319) T) ((-723 . -1089) T) ((-372 . -1083) 133480) ((-367 . -1083) 133432) ((-359 . -1083) 133384) ((-372 . -662) 133336) ((-227 . -1070) 133313) ((-367 . -662) 133265) ((-108 . -1083) 133215) ((-359 . -662) 133167) ((-305 . -739) 133109) ((-661 . -1249) T) ((-501 . -466) T) ((-421 . -528) 133021) ((-108 . -662) 132971) ((-221 . -466) T) ((-1152 . -240) T) ((-307 . -153) 132921) ((-1028 . -633) 132882) ((-1028 . -632) 132864) ((-1021 . -632) 132846) ((-118 . -1089) T) ((-678 . -1088) 132830) ((-229 . -507) T) ((-413 . -632) 132812) ((-413 . -633) 132789) ((-1086 . -1307) 132759) ((-678 . -111) 132738) ((-692 . -930) 132661) ((-1174 . -503) 132645) ((-1324 . -668) 132604) ((-395 . -668) 132573) ((-64 . -455) T) ((-64 . -410) T) ((-1192 . -102) T) ((-896 . -133) T) ((-498 . -102) 132523) ((-1147 . -1249) T) ((-1256 . -875) T) ((-1329 . -381) T) ((-1111 . -102) T) ((-1093 . -102) T) ((-365 . -739) 132468) ((-897 . -875) 132419) ((-753 . -149) 132398) ((-753 . -147) 132377) ((-678 . -635) 132295) ((-1056 . -670) 132232) ((-537 . -1133) 132210) ((-372 . -102) T) ((-367 . -102) T) ((-359 . -102) T) ((-108 . -102) T) ((-518 . -1133) T) ((-353 . -670) 132155) ((-1203 . -660) 132103) ((-1157 . -660) 132051) ((-394 . -523) 132030) ((-856 . -871) 132009) ((-716 . -748) T) ((-391 . -1254) T) ((-345 . -1249) T) ((-1259 . -1023) 131961) ((-352 . -1089) T) ((-114 . -1249) T) ((-177 . -1089) T) ((-103 . -632) 131893) ((-1207 . -147) 131872) ((-1207 . -149) 131851) ((-391 . -571) T) ((-1206 . -149) 131830) ((-1206 . -147) 131809) ((-1200 . -147) 131716) ((-421 . -302) T) ((-1200 . -149) 131623) ((-1158 . -149) 131602) ((-1158 . -147) 131581) ((-331 . -38) 131422) ((-171 . -133) T) ((-325 . -821) NIL) ((-325 . -816) NIL) ((-678 . -1081) T) ((-48 . -670) 131372) ((-1145 . -1083) 131273) ((-919 . -635) 131250) ((-1145 . -662) 131172) ((-1199 . -102) T) ((-1026 . -102) T) ((-1025 . -21) T) ((-129 . -1042) 131156) ((-123 . -1042) 131140) ((-1025 . -25) T) ((-931 . -121) 131124) ((-1191 . -102) T) ((-1268 . -133) T) ((-1264 . -875) 131023) ((-1203 . -25) T) ((-1203 . -21) T) ((-1192 . -321) 130818) ((-357 . -1249) T) ((-1157 . -25) T) ((-880 . -133) T) ((-407 . -1249) T) ((-1157 . -21) T) ((-879 . -25) T) ((-879 . -21) T) ((-803 . -319) 130797) ((-1187 . -503) 130781) ((-1183 . -153) 130731) ((-1178 . -632) 130693) ((-669 . -102) 130643) ((-651 . -102) T) ((-1178 . -633) 130604) ((-585 . -133) T) ((-638 . -871) 130583) ((-1056 . -814) T) ((-1056 . -818) T) ((-1056 . -748) T) ((-839 . -930) 130452) ((-734 . -1088) 130275) ((-616 . -875) 130254) ((-498 . -321) 130192) ((-467 . -432) 130162) ((-365 . -175) T) ((-301 . -38) 130149) ((-260 . -236) 130040) ((-259 . -236) 129931) ((-285 . -102) T) ((-284 . -102) T) ((-283 . -102) T) ((-282 . -102) T) ((-281 . -102) T) ((-280 . -102) T) ((-357 . -1070) 129908) ((-279 . -102) T) ((-215 . -102) T) ((-214 . -102) T) ((-212 . -102) T) ((-211 . -102) T) ((-210 . -102) T) ((-209 . -102) T) ((-206 . -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) ((-734 . -111) 129717) ((-353 . -748) T) ((-692 . -274) 129701) ((-692 . -234) 129685) ((-595 . -319) T) ((-532 . -319) T) ((-305 . -528) 129634) ((-1197 . -1249) T) ((-108 . -321) NIL) ((-72 . -410) T) ((-1145 . -102) 129366) ((-856 . -426) 129350) ((-1152 . -821) T) ((-1152 . -816) T) ((-723 . -1133) T) ((-592 . -632) 129332) ((-391 . -376) T) ((-171 . -507) 129310) ((-226 . -632) 129242) ((-136 . -1133) T) ((-118 . -1133) T) ((-996 . -1249) T) ((-48 . -748) T) ((-1078 . -503) 129207) ((-143 . -440) 129189) ((-143 . -381) T) ((-1059 . -102) T) ((-524 . -523) 129168) ((-734 . -635) 128924) ((-1257 . -632) 128906) ((-1214 . -1249) T) ((-1214 . -1070) 128842) ((-1207 . -239) 128801) ((-490 . -102) T) ((-477 . -102) T) ((-1206 . -239) 128753) ((-1200 . -239) 128576) ((-1066 . -1144) T) ((-331 . -930) 128482) ((-1209 . -875) T) ((-1207 . -35) 128448) ((-1207 . -95) 128414) ((-1207 . -1238) 128380) ((-1207 . -1235) 128346) ((-1206 . -1235) 128312) ((-1206 . -1238) 128278) ((-1206 . -95) 128244) ((-1206 . -35) 128210) ((-1200 . -1235) 128176) ((-1200 . -1238) 128142) ((-1191 . -321) NIL) ((-89 . -411) T) ((-89 . -410) T) ((-1111 . -1184) 128121) ((-40 . -1249) T) ((-1200 . -95) 128087) ((-1066 . -23) T) ((-1200 . -35) 128053) ((-585 . -507) T) ((-1158 . -35) 128019) ((-1158 . -95) 127985) ((-1158 . -1238) 127951) ((-1158 . -1235) 127917) ((-374 . -1144) T) ((-372 . -1184) 127896) ((-367 . -1184) 127875) ((-359 . -1184) 127854) ((-1135 . -298) 127810) ((-984 . -1249) T) ((-949 . -1249) T) ((-108 . -1184) T) ((-856 . -1089) 127789) ((-793 . -1249) T) ((-669 . -321) 127727) ((-651 . -321) 127578) ((-694 . -1249) T) ((-734 . -1081) T) ((-1094 . -660) 127560) ((-1111 . -38) 127428) ((-976 . -660) 127376) ((-1036 . -149) T) ((-1036 . -147) NIL) ((-391 . -1144) T) ((-336 . -25) T) ((-334 . -23) T) ((-973 . -872) 127355) ((-734 . -338) 127332) ((-495 . -660) 127280) ((-40 . -1070) 127168) ((-734 . -240) T) ((-723 . -739) 127155) ((-352 . -1133) T) ((-177 . -1133) T) ((-343 . -872) T) ((-419 . -466) 127105) ((-391 . -23) T) ((-372 . -38) 127070) ((-367 . -38) 127035) ((-359 . -38) 127000) ((-80 . -455) T) ((-80 . -410) T) ((-229 . -25) T) ((-229 . -21) T) ((-858 . -1144) T) ((-108 . -38) 126950) ((-852 . -1144) T) ((-795 . -1133) T) ((-118 . -739) 126937) ((-694 . -1070) 126921) ((-630 . -102) T) ((-858 . -23) T) ((-852 . -23) T) ((-1187 . -298) 126873) ((-1145 . -321) 126811) ((-496 . -1083) 126712) ((-1129 . -242) 126696) ((-61 . -411) T) ((-61 . -410) T) ((-1185 . -102) T) ((-110 . -102) T) ((-496 . -662) 126618) ((-40 . -390) 126595) ((-96 . -102) T) ((-677 . -877) 126579) ((-1203 . -236) 126566) ((-1167 . -1115) T) ((-1094 . -21) T) ((-1094 . -25) T) ((-1086 . -1083) 126550) ((-839 . -274) 126519) ((-839 . -234) 126488) ((-976 . -25) T) ((-976 . -21) T) ((-1152 . -381) T) ((-1086 . -662) 126430) ((-638 . -1089) T) ((-1059 . -321) 126368) ((-914 . -632) 126350) ((-692 . -668) 126309) ((-495 . -25) T) ((-495 . -21) T) ((-394 . -1083) 126293) ((-911 . -632) 126275) ((-894 . -1249) T) ((-537 . -528) 126208) ((-260 . -872) 126159) ((-259 . -872) 126110) ((-394 . -662) 126080) ((-896 . -660) 126057) ((-490 . -321) 125995) ((-562 . -1249) T) ((-477 . -321) 125933) ((-365 . -302) T) ((-1187 . -1288) 125917) ((-1174 . -632) 125879) ((-1174 . -633) 125840) ((-1172 . -102) T) ((-1028 . -1088) 125736) ((-40 . -928) 125688) ((-1187 . -618) 125665) ((-1329 . -670) 125652) ((-1095 . -153) 125598) ((-501 . -922) NIL) ((-891 . -504) 125575) ((-1028 . -111) 125457) ((-897 . -1254) T) ((-221 . -922) NIL) ((-352 . -739) 125441) ((-891 . -632) 125403) ((-177 . -739) 125335) ((-897 . -571) T) ((-421 . -298) 125293) ((-246 . -239) 125190) ((-108 . -414) 125172) ((-85 . -398) T) ((-85 . -410) T) ((-723 . -175) T) ((-636 . -632) 125154) ((-99 . -748) T) ((-496 . -102) 124886) ((-99 . 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123928) ((-1028 . -240) 123907) ((-1289 . -149) 123886) ((-1285 . -1254) 123865) ((-856 . -1133) T) ((-1280 . -149) 123844) ((-1280 . -147) 123823) ((-1264 . -1254) 123802) ((-1259 . -147) 123709) ((-1259 . -149) 123616) ((-391 . -133) T) ((-229 . -236) 123603) ((-177 . -175) T) ((-560 . -912) 123585) ((0 . -1133) T) ((-171 . -21) T) ((-171 . -25) T) ((-55 . -1249) T) ((-49 . -1133) T) ((-1286 . -670) 123490) ((-1285 . -571) 123441) ((-1264 . -571) 123392) ((-736 . -1144) T) ((-659 . -23) T) ((-560 . -1070) 123374) ((-609 . -149) 123353) ((-609 . -147) 123332) ((-509 . -1070) 123275) ((-1167 . -1169) T) ((-88 . -398) T) ((-88 . -410) T) ((-897 . -376) T) ((-858 . -133) T) ((-852 . -133) T) ((-994 . -668) 123219) ((-736 . -23) T) ((-520 . -632) 123169) ((-516 . -632) 123151) ((-839 . -668) 122930) ((-1324 . -1089) T) ((-391 . -1092) T) ((-1058 . -1133) 122908) ((-55 . -1070) 122890) ((-931 . -34) T) ((-496 . -321) 122828) ((-606 . -102) T) ((-1187 . -633) 122789) ((-1187 . -632) 122721) 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-670) 121450) ((-325 . -670) 121379) ((-488 . -571) 121330) ((-352 . -528) 121296) ((-565 . -153) 121246) ((-40 . -319) T) ((-866 . -632) 121228) ((-723 . -302) T) ((-897 . -23) T) ((-391 . -507) T) ((-1111 . -274) 121198) ((-1111 . -234) 121168) ((-524 . -102) T) ((-421 . -633) 120975) ((-421 . -632) 120957) ((-270 . -632) 120939) ((-118 . -302) T) ((-1286 . -748) T) ((-642 . -1249) T) ((-1325 . -1133) T) ((-1285 . -376) 120918) ((-1264 . -376) 120897) ((-1313 . -34) T) ((-1258 . -1133) T) ((-119 . -1249) T) ((-108 . -274) 120879) ((-108 . -234) 120861) ((-1211 . -102) T) ((-491 . -1133) T) ((-537 . -503) 120845) ((-758 . -34) T) ((-677 . -1083) 120829) ((-677 . -662) 120799) ((-896 . -236) NIL) ((-143 . -34) T) ((-119 . -910) 120776) ((-119 . -912) NIL) ((-1312 . -102) T) ((-1289 . -239) 120735) ((-642 . -1070) 120618) ((-625 . -102) T) ((-624 . -102) T) ((-622 . -102) T) ((-663 . -872) 120597) ((-1280 . -239) 120549) ((-1259 . -239) 120372) ((-307 . -102) T) ((-734 . -381) 120351) 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. -319) T) ((-560 . -319) T) ((-509 . -319) T) ((-1324 . -739) 116675) ((-716 . -390) 116657) ((-716 . -351) 116639) ((-491 . -175) T) ((-395 . -739) 116609) ((-891 . -635) 116544) ((-896 . -872) NIL) ((-560 . -1052) T) ((-509 . -1052) T) ((-1165 . -632) 116526) ((-1145 . -245) 116505) ((-217 . -102) T) ((-1183 . -102) T) ((-71 . -632) 116487) ((-1056 . -1249) T) ((-1174 . -1081) T) ((-1211 . -38) 116384) ((-883 . -632) 116366) ((-560 . -559) T) ((-692 . -1089) T) ((-753 . -980) 116319) ((-1174 . -240) 116298) ((-353 . -1249) T) ((-1114 . -1133) T) ((-1066 . -25) T) ((-1066 . -21) T) ((-1035 . -1088) 116243) ((-339 . -875) 116222) ((-932 . -102) T) ((-891 . -1081) T) ((-716 . -928) NIL) ((-368 . -341) 116206) ((-368 . -376) T) ((-366 . -341) 116190) ((-366 . -376) T) ((-358 . -341) 116174) ((-358 . -376) T) ((-501 . -102) T) ((-1312 . -38) 116144) ((-561 . -872) T) ((-537 . -708) 116094) ((-221 . -102) T) ((-1056 . -1070) 115974) ((-1035 . -111) 115903) ((-657 . -632) 115885) ((-1207 . 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112348) ((-1200 . -1261) 112332) ((-529 . -25) T) ((-509 . -310) T) ((-526 . -23) T) ((-525 . -25) T) ((-522 . -25) T) ((-521 . -23) T) ((-421 . -1081) T) ((-419 . -1083) 112306) ((-331 . -1089) T) ((-716 . -319) T) ((-419 . -662) 112280) ((-108 . -871) T) ((-734 . -748) T) ((-421 . -250) T) ((-421 . -240) 112259) ((-391 . -236) 112246) ((-501 . -38) 112196) ((-221 . -38) 112146) ((-488 . -507) 112112) ((-659 . -21) T) ((-659 . -25) T) ((-1257 . -381) T) ((-1191 . -1176) T) ((-1134 . -102) T) ((-852 . -236) 112085) ((-723 . -632) 112067) ((-723 . -633) 111982) ((-736 . -21) T) ((-736 . -25) T) ((-1167 . -102) T) ((-496 . -668) 111761) ((-246 . -922) 111628) ((-136 . -632) 111610) ((-118 . -632) 111592) ((-159 . -25) T) ((-1321 . -1133) T) ((-897 . -660) 111540) ((-1320 . -1133) T) ((-890 . -1249) T) ((-986 . -102) T) ((-757 . -102) T) ((-737 . -102) T) ((-467 . -102) T) ((-840 . -466) 111491) ((-44 . -1133) T) ((-1120 . -872) T) ((-1095 . -321) 111342) ((-686 . -133) T) ((-1086 . -668) 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-410) T) ((-108 . -633) 81339) ((-108 . -632) 81281) ((-214 . -923) T) ((-988 . -153) 81265) ((-793 . -133) T) ((-692 . -635) 81183) ((-136 . -748) T) ((-118 . -748) T) ((-1285 . -35) 81149) ((-1086 . -503) 81133) ((-594 . -23) T) ((-560 . -23) T) ((-509 . -23) T) ((-1264 . -95) 81099) ((-1264 . -35) 81065) ((-1203 . -102) T) ((-1157 . -102) T) ((-879 . -102) T) ((-231 . -503) 81049) ((-1321 . -111) 81028) ((-1320 . -111) 81007) ((-44 . -1088) 80991) ((-1323 . -1249) T) ((-1321 . -635) 80937) ((-1321 . -1081) T) ((-1320 . -635) 80866) ((-1320 . -1081) T) ((-1268 . -1275) 80850) ((-880 . -877) 80834) ((-1211 . -302) 80813) ((-1135 . -1249) T) ((-110 . -298) 80763) ((-1035 . -1249) T) ((-131 . -153) 80745) ((-1174 . -928) 80704) ((-44 . -111) 80683) ((-1255 . -1133) T) ((-1214 . -1295) T) ((-1200 . -871) NIL) ((-1199 . -504) 80664) ((-692 . -1081) T) ((-1199 . -632) 80630) ((-1191 . -632) 80612) ((-488 . -239) 80564) ((-1095 . -629) 80539) ((-1026 . -504) 80520) ((-74 . -455) T) ((-74 . -410) T) ((-1095 . -1133) T) ((-154 . -1088) 80504) ((-1026 . -632) 80470) ((-692 . -240) 80449) ((-585 . -569) 80433) ((-368 . -149) 80412) ((-368 . -147) 80363) ((-366 . -149) 80342) ((-366 . -147) 80293) ((-358 . -149) 80272) ((-358 . -147) 80223) ((-275 . -147) 80202) ((-275 . -149) 80181) ((-255 . -149) 80160) ((-119 . -376) T) ((-255 . -147) 80139) ((-1191 . -633) NIL) ((-154 . -111) 80118) ((-1035 . -1070) 80006) ((-1187 . -1249) T) ((-716 . -1254) T) ((-822 . -1089) T) ((-721 . -1144) T) ((-1035 . -390) 79983) ((-520 . -1249) T) ((-516 . -1249) T) ((-936 . -147) T) ((-936 . -149) 79965) ((-894 . -133) T) ((-839 . -1088) 79886) ((-721 . -23) T) ((-716 . -571) T) ((-229 . -1083) 79851) ((-669 . -632) 79783) ((-669 . -633) 79744) ((-651 . -633) NIL) ((-651 . -632) 79726) ((-501 . -175) T) ((-229 . -662) 79691) ((-221 . -175) T) ((-227 . -21) T) ((-227 . -25) T) ((-488 . -1238) 79657) ((-488 . -1235) 79623) ((-285 . -632) 79605) ((-284 . -632) 79587) ((-283 . -632) 79569) ((-282 . 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-662) 74903) ((-495 . -102) T) ((-753 . -1089) T) ((-630 . -632) 74885) ((-630 . -633) 74746) ((-421 . -390) 74730) ((-421 . -351) 74714) ((-1203 . -38) 74543) ((-1157 . -38) 74392) ((-331 . -635) 74218) ((-936 . -239) T) ((-652 . -1249) T) ((-620 . -1249) T) ((-879 . -38) 74188) ((-404 . -670) 74172) ((-663 . -321) 74110) ((-1185 . -504) 74091) ((-1185 . -632) 74057) ((-986 . -739) 73954) ((-757 . -739) 73924) ((-638 . -670) 73898) ((-226 . -107) 73882) ((-45 . -298) 73782) ((-323 . -1133) T) ((-301 . -1088) 73769) ((-110 . -632) 73751) ((-110 . -633) 73733) ((-467 . -739) 73703) ((-840 . -262) 73642) ((-711 . -1133) 73620) ((-565 . -1133) T) ((-1207 . -1089) T) ((-1206 . -1089) T) ((-96 . -504) 73601) ((-1200 . -1089) T) ((-301 . -111) 73586) ((-1158 . -1089) T) ((-565 . -629) 73565) ((-96 . -632) 73531) ((-1036 . -871) T) ((-231 . -708) 73489) ((-716 . -1144) T) ((-1242 . -762) 73465) ((-1056 . -376) T) ((-862 . -860) 73447) ((-856 . -818) 73426) ((-421 . -928) 73385) ((-331 . 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-321) 71608) ((-585 . -662) 71595) ((-65 . -1249) T) ((-1165 . -1249) T) ((-1157 . -930) 71579) ((-1145 . -300) 71556) ((-1095 . -528) 71400) ((-693 . -1133) T) ((-642 . -133) T) ((-619 . -1133) T) ((-495 . -321) 71387) ((-561 . -102) T) ((-119 . -133) T) ((-301 . -1081) T) ((-183 . -1133) T) ((-164 . -1133) T) ((-158 . -1133) T) ((-156 . -1133) T) ((-467 . -783) T) ((-31 . -1115) T) ((-986 . -175) 71338) ((-1129 . -233) 71322) ((-1002 . -93) T) ((-1111 . -1088) 71232) ((-1086 . -632) 71194) ((-638 . -748) T) ((-638 . -818) 71173) ((-607 . -1133) T) ((-638 . -814) 71152) ((-307 . -298) 71131) ((-305 . -1249) T) ((-1086 . -633) 71092) ((-1056 . -1144) T) ((-325 . -875) NIL) ((-171 . -102) T) ((-286 . -872) T) ((-1111 . -111) 70988) ((-842 . -632) 70970) ((-1056 . -23) T) ((-1035 . -319) T) ((-926 . -102) T) ((-822 . -739) 70954) ((-372 . -1088) 70906) ((-367 . -1088) 70858) ((-353 . -1144) T) ((-429 . -632) 70840) ((-394 . -632) 70822) ((-359 . -1088) 70774) ((-231 . -632) 70706) ((-865 . -102) T) ((-832 . -102) T) ((-108 . -1088) 70656) ((-791 . -102) T) ((-699 . -102) T) ((-115 . -875) T) ((-488 . -466) 70635) ((-419 . -175) T) ((-372 . -111) 70573) ((-367 . -111) 70511) ((-359 . -111) 70449) ((-260 . -274) 70418) ((-260 . -234) 70387) ((-259 . -274) 70356) ((-259 . -234) 70325) ((-353 . -23) T) ((-71 . -1249) T) ((-229 . -38) 70290) ((-108 . -111) 70224) ((-40 . -25) T) ((-40 . -21) T) ((-692 . -742) T) ((-171 . -296) 70202) ((-48 . -1144) T) ((-883 . -1249) T) ((-949 . -25) T) ((-793 . -25) T) ((-1324 . -670) 70176) ((-1183 . -503) 70113) ((-499 . -1133) T) ((-1315 . -668) 70072) ((-1268 . -102) T) ((-1094 . -1184) T) ((-880 . -102) T) ((-246 . -1089) 70050) ((-994 . -816) 70003) ((-994 . -821) 69956) ((-395 . -670) 69940) ((-48 . -23) T) ((-839 . -821) 69919) ((-839 . -816) 69898) ((-563 . -381) T) ((-307 . -618) 69877) ((-491 . -748) T) ((-585 . -102) T) ((-1111 . -635) 69695) ((-257 . -189) T) ((-186 . -189) T) ((-896 . -321) 69652) ((-677 . -298) 69631) ((-657 . -1249) T) ((-114 . -684) T) ((-365 . -1249) T) ((-372 . -635) 69568) ((-367 . -635) 69505) ((-359 . -635) 69442) ((-77 . -1249) T) ((-108 . -635) 69392) ((-114 . -113) T) ((-1094 . -38) 69379) ((-686 . -387) 69358) ((-976 . -38) 69207) ((-753 . -1133) T) ((-495 . -38) 69056) ((-82 . -1249) T) ((-606 . -504) 69037) ((-1259 . -871) NIL) ((-1207 . -1133) T) ((-585 . -296) T) ((-1206 . -1133) T) ((-606 . -632) 69003) ((-1200 . -1133) T) ((-1152 . -875) T) ((-1111 . -1081) T) ((-365 . -1070) 68980) ((-841 . -504) 68964) ((-1036 . -1089) T) ((-45 . -632) 68946) ((-45 . -633) NIL) ((-944 . -1089) T) ((-841 . -632) 68915) ((-1180 . -102) 68865) ((-1111 . -250) 68816) ((-443 . -1089) T) ((-372 . -1081) T) ((-367 . -1081) T) ((-377 . -378) 68793) ((-359 . -1081) T) ((-357 . -236) 68780) ((-260 . -245) 68759) ((-259 . -245) 68738) ((-1111 . -240) 68663) ((-1158 . -1133) T) ((-305 . -928) 68622) ((-108 . -1081) T) ((-716 . -133) T) ((-419 . -528) 68464) ((-372 . -240) 68443) ((-372 . -250) T) 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\ No newline at end of file diff --git a/src/share/algebra/compress.daase b/src/share/algebra/compress.daase index dab21f9b..2d2adb95 100644 --- a/src/share/algebra/compress.daase +++ b/src/share/algebra/compress.daase @@ -1,5 +1,5 @@ -(30 . 3514823547) +(30 . 3514927621) (4513 |Enumeration| |Mapping| |Record| |Union| |ofCategory| |isDomain| ATTRIBUTE |package| |domain| |category| CATEGORY |nobranch| AND |Join| |ofType| SIGNATURE "failed" "algebra" |OneDimensionalArrayAggregate&| @@ -489,674 +489,678 @@ |XPolynomialsCat| |XPolynomialRing| |XRecursivePolynomial| |YoungDiagram| |ParadoxicalCombinatorsForStreams| |ZeroDimensionalSolvePackage| |IntegerLinearDependence| |IntegerMod| - |Enumeration| |Mapping| |Record| |Union| |eof?| |roughSubIdeal?| - |mulmod| |delta| |port| |integerBound| |sinIfCan| |setStatus| - |showRegion| |asimpson| |optional?| |putColorInfo| |OMUnknownCD?| - |cycles| |OMopenString| |setsubMatrix!| |gcdprim| |nthRoot| |capacity| - |systemSizeIF| |leaves| |matrix| |limit| |modTree| |mapMatrixIfCan| - |intermediateResultsIF| |rationalPoints| |nextLatticePermutation| - |writable?| |subSet| |makeResult| |setTopPredicate| |ODESolve| - |e02ajf| |roughEqualIdeals?| |eigenvalues| - |jvmInterfaceMethodConstantTag| |recur| |complexNumeric| |aQuartic| - |euler| |box| |setleft!| |algintegrate| |c05adf| |s15aef| - |mainVariables| |algebraic?| |alphanumeric| |solveInField| - |semiSubResultantGcdEuclidean1| |lex| |zag| |minimumDegree| - |prindINFO| |indicialEquations| |combineFeatureCompatibility| - |subPolSet?| |e02dff| |goto| |or| |balancedFactorisation| |OMreadStr| - |ipow| |outputMeasure| |lineColorDefault| |prepareDecompose| - |ratDenom| |strongGenerators| |OMencodingBinary| |iicsc| |xor| - |horizontalTab| |cPower| |factorials| |lowerPolynomial| - |lazyIntegrate| |biRank| |previous| |d01apf| |eyeDistance| |lambda| - |halfExtendedSubResultantGcd2| |postfix| |case| |f04faf| - |mainCharacterization| |constantToUnaryFunction| |cCosh| |declare| - |setImagSteps| |cons| |iiGamma| |numberOfDivisors| |d03eef| |f02ajf| - |Zero| |f04arf| |imagi| |realRoots| |tanSum| |apply| |nthExpon| - |s18acf| |minimize| |totolex| |create| |dark| |One| - |exportedOperators| |representationType| |adaptive| |minset| |first| - |OMgetBVar| |distribute| |clearFortranOutputStack| |normalDeriv| - |addMatch| |pToHdmp| |roman| |binomial| |clearDenominator| |rest| - |linear| |purelyAlgebraicLeadingMonomial?| |directSum| |debug3D| - |cardinality| |nthFlag| |lookup| |cSinh| |cTanh| |firstDenom| - |stirling2| |f02adf| |source| |binomThmExpt| |s19aaf| |setMinPoints3D| - |point| |repeating?| |traceMatrix| |thetaCoord| |qPot| |cyclicGroup| - |firstSubsetGray| |polynomial| |rewriteIdealWithQuasiMonicGenerators| - |jvmFloatConstantTag| |rombergo| |functionIsFracPolynomial?| - |sqfrFactor| |invertIfCan| |traverse| |subMatrix| |conjunction| - |toScale| |testDim| |elliptic| |cubic| |iiexp| |readIfCan!| |elt| - |meshPar1Var| |plenaryPower| |totalDifferential| |shrinkable| |target| - |resize| |rightDivide| |sinhIfCan| |ffactor| |series| |mathieu23| |mr| - |legendre| |lazyPrem| |branchPointAtInfinity?| |fortranLogical| - |genericLeftTraceForm| |readInt32!| |prem| |OMbindTCP| |dmpToHdmp| - |isobaric?| |triangSolve| |rationalPoint?| |OMputObject| |mesh| - |integerIfCan| |tValues| |cyclicEntries| |signAround| |cAcosh| - |rewriteSetWithReduction| |associates?| |toseSquareFreePart| - |infieldIntegrate| |leftRank| |setVariableOrder| |rootPower| - |homogeneous?| |rk4a| |sortConstraints| |chineseRemainder| - |FormatRoman| |sinhcosh| |OMencodingSGML| |primPartElseUnitCanonical!| - |definingPolynomial| |jvmPublic| |inGroundField?| |min| |extractPoint| - |integralRepresents| |particularSolution| |bigEndian| - |semiIndiceSubResultantEuclidean| |flatten| |union| |overbar| - |rotate!| |invertibleElseSplit?| |iicos| |changeWeightLevel| |iFTable| - |sylvesterMatrix| |dn| |copies| |lagrange| |drawComplexVectorField| - |moebiusMu| |besselI| |updatD| |coefChoose| |logpart| |intersect| - |root| |moduloP| |precision| |upperCase| |heap| - |factorSquareFreePolynomial| |showClipRegion| - |basisOfRightAnnihilator| |knownInfBasis| |resultantReduitEuclidean| - |clipBoolean| |partitions| |linearForm| |OMputBVar| |iteratedInitials| - |fractRagits| |stiffnessAndStabilityOfODEIF| |bits| |primitivePart| - |imagI| |sin2csc| |pquo| |SFunction| |iiasech| |getZechTable| - |scaleRoots| |conditionsForIdempotents| |stopTableGcd!| |trace2PowMod| - |ode2| |rootBound| |rational| |shiftLeft| |interpretString| - |changeMeasure| |primlimintfrac| |e02dcf| |bringDown| - |numberOfFractionalTerms| |removeIrreducibleRedundantFactors| |iiasec| - |simpsono| |alternative?| |packageCall| |coshIfCan| |rootOf| - |normInvertible?| |asinIfCan| |prinpolINFO| |jvmNative| - |selectNonFiniteRoutines| |functionIsContinuousAtEndPoints| - |pointColorPalette| |ldf2vmf| |entry?| |showTheFTable| |dimensions| - |arguments| |OMputApp| |cyclotomicFactorization| |factors| |iiacos| - |bumprow| |exists?| |enterPointData| |numberOfOperations| |s17akf| - |numeric| |real?| |seriesToOutputForm| |superscript| |OMopenFile| - |OMgetEndApp| |mainCoefficients| |numberOfChildren| |loopPoints| - |prefix| |radical| |quotientByP| |graphImage| |interReduce| - |OMconnOutDevice| |lookupFunction| |viewport3D| |getCode| |d02bbf| - |match?| |internalDecompose| |palginfieldint| |mindegTerm| - |setClipValue| |key?| |rightQuotient| |useEisensteinCriterion?| - |matrixGcd| |outerProduct| |parabolicCylindrical| |perfectNthPower?| - |recoverAfterFail| |freeOf?| |matrixConcat3D| |monicCompleteDecompose| - |bernoulli| |tanh2coth| |stopTable!| |Gamma| |isAtom| |palgintegrate| - |limitedint| |cAtan| |chiSquare1| |karatsubaDivide| |HenselLift| - |extendIfCan| |henselFact| |charthRoot| |realElementary| |curryLeft| - |rightMult| |characteristic| |weakBiRank| |any| |internalIntegrate| - |c06gqf| |exp1| |mapCoef| |iiabs| |f02agf| |groebnerFactorize| |cExp| - |multiplyCoefficients| |basisOfCentroid| |tanhIfCan| |getConstant| - |sup| |idealiserMatrix| |rename| |d02raf| |makeGraphImage| |kmax| - |e02daf| |log2| |OMsetEncoding| |stronglyReduced?| |imaginary| - |monomialIntPoly| |split!| |compile| |iilog| |jvmIntegerConstantTag| - |extendedIntegrate| |nthFactor| |rowEchLocal| |normal01| - |setchildren!| |node?| |revert| |unitCanonical| |OMgetError| - |reducedForm| |totalfract| |multMonom| |prevPrime| |constDsolve| - |cycle| |factorSquareFreeByRecursion| |internalLastSubResultant| - |scalarMatrix| |readUInt8!| |monicRightFactorIfCan| |poisson| |lllp| - |shiftRight| |iCompose| |nextsubResultant2| |fortranDoubleComplex| - |rightNorm| |gradient| |zero?| |laplacian| |intensity| |imagK| |ode| - |rquo| |relationsIdeal| |bright| |makeprod| |dmpToP| |rdHack1| - |predicates| |cyclicParents| |quoByVar| |verticalTab| |youngDiagram| - |weierstrass| |head| |littleEndian| |radicalSimplify| |functorData| - |OMputBind| |mainSquareFreePart| |s17ajf| |f02aaf| |e01sff| |routines| - |extendedSubResultantGcd| |endOfFile?| |irVar| |PollardSmallFactor| - |sinh2csch| |writeByte!| |subTriSet?| |f01bsf| |perspective| - |rationalApproximation| |scale| |patternVariable| |primextendedint| - |removeCosSq| |quadraticNorm| |center| |listOfLists| |central?| - |localReal?| |nonLinearPart| |simplifyLog| |opeval| |cCoth| - |decompose| |singularitiesOf| |numberOfFactors| - |eisensteinIrreducible?| |physicalLength| |modularGcdPrimitive| - |getDatabase| |irDef| |getPickedPoints| |elementary| - |leftReducedSystem| |fractionFreeGauss!| |iiasinh| - |stoseInvertible?reg| |OMgetApp| |positive?| |less?| |zeroMatrix| - |s13aaf| |normalDenom| |qroot| |elColumn2!| |dflist| |hitherPlane| - |kovacic| |OMgetType| |brillhartTrials| |linefeed| |close| - |primitiveElement| |nodeOf?| |currentCategoryFrame| |composites| - |remove!| |iiacsch| |coefficients| |createZechTable| |checkRur| |po| - |script| |basisOfCenter| |expenseOfEvaluation| |bitCoef| |e02gaf| - |enterInCache| |dominantTerm| |loadNativeModule| |table| |extractTop!| - |critpOrder| |purelyTranscendental?| |reflect| |outputAsTex| - |basisOfRightNucleus| |factorial| |initial| |ldf2lst| |display| - |leftUnits| |length| |select!| |inverseIntegralMatrixAtInfinity| |cap| - |integralMatrix| |rk4qc| |support| |elaborate| |commutator| - |lowerCase?| |f07aef| |scripts| |superHeight| |overlap| - |rightTraceMatrix| |irreducibleFactor| |ksec| |torsionIfCan| - |whatInfinity| |solve| |setMaxPoints| |tex| |varList| |rotatey| - |sumOfDivisors| |complexIntegrate| |integers| |environment| |new| - |antisymmetricTensors| |iisinh| |removeRoughlyRedundantFactorsInPols| - |screenResolution3D| |aLinear| |weight| |pushuconst| - |squareFreeFactors| |square?| |minordet| - |standardBasisOfCyclicSubmodule| |yellow| |hasoln| |jvmTransient| - |constant?| |coerceListOfPairs| |harmonic| |setOfMinN| |mathieu11| - |showTheSymbolTable| |identity| |complex?| - |removeRoughlyRedundantFactorsInContents| |lhs| |e01saf| |remainder| - |input| |lexTriangular| |mergeDifference| |chainSubResultants| - |deepCopy| |factorFraction| |stoseInvertibleSetreg| |reducedQPowers| - |outputFloating| |f01qef| |rhs| |sdf2lst| |readBytes!| |plus| - |sparsityIF| |pointPlot| |backOldPos| |semiResultantReduitEuclidean| - |whitePoint| |generalTwoFactor| |e| |FormatArabic| |lazy?| - |returnType!| |supersub| |newTypeLists| - |generalizedContinuumHypothesisAssumed?| |graeffe| |mainKernel| - |polyred| |getExplanations| |setlast!| |sign| |pmintegrate| - |trapezoidal| |quasiMonic?| |empty?| |pointLists| |times| |unit| - |iisec| |wholeRagits| |formula| |intPatternMatch| |f04mbf| - |triangularSystems| |newline| |subResultantGcdEuclidean| - |moreAlgebraic?| |UP2ifCan| |disjunction| |irreducibleFactors| - |connectTo| |indicialEquation| |addMatchRestricted| |pushup| - |basisOfLeftNucleus| |palgint0| |degreeSubResultantEuclidean| - |acothIfCan| |diagonal| |antiCommutator| |baseRDEsys| |gbasis| - |message| |Lazard| |bipolarCylindrical| |mathieu24| |isMult| - |exactQuotient!| |dimensionOfIrreducibleRepresentation| |left| - |linearlyDependentOverZ?| |leftScalarTimes!| |e02bcf| |getButtonValue| - |OMclose| |nsqfree| |OMgetVariable| |cot2tan| |var1StepsDefault| |mix| - |right| |nullary| |groebnerIdeal| |compactFraction| |extractBottom!| - |power!| |monom| |level| |mapDown!| |froot| |messagePrint| - |pointColorDefault| |alphabetic?| |nrows| |cosh2sech| |scripted?| - |reducedDiscriminant| |fortranComplex| |colorDef| - |ellipticCylindrical| |elRow2!| |toroidal| |hspace| |minPoints3D| - |ncols| |generalizedEigenvector| |filename| |width| - |indiceSubResultantEuclidean| |subresultantVector| |c06fqf| |f01mcf| - |lp| |selectsecond| |orbit| |alternatingGroup| |iroot| - |shanksDiscLogAlgorithm| |headReduce| |LyndonWordsList| |KrullNumber| - |iicot| |string?| |common| |moebius| |clipParametric| |complexRoots| - |innerint| |fixedPoint| |stack| |style| |squareFree| |sechIfCan| - |parse| |createMultiplicationMatrix| |denomRicDE| |expandPower| - |readByte!| |removeSquaresIfCan| |useNagFunctions| |mkAnswer| - |leftTrace| |nextPrimitivePoly| |d01bbf| |BasicMethod| |fractionPart| - |createGenericMatrix| |critMTonD1| |entries| |binary| |mirror| - |denominator| |rootsOf| |qqq| |copy!| |plotPolar| |separateDegrees| - |toseInvertibleSet| |outputArgs| |triangulate| |wreath| - |nextSubsetGray| |basisOfLeftNucloid| |jvmSynchronized| |is?| - |generateIrredPoly| |jvmProtected| |hyperelliptic| - |useSingleFactorBound| |eq| |someBasis| |autoReduced?| |calcRanges| - |hdmpToDmp| |cyclePartition| |structuralConstants| |optional| |pToDmp| - |commutative?| |tan2cot| |binaryTree| |solveLinear| - |solveLinearPolynomialEquationByFractions| |iter| |property| - |charClass| |generalizedInverse| |changeName| |f01rdf| |arg1| - |monicDivide| |satisfy?| |startTable!| |regularRepresentation| - |makeYoungTableau| |newLine| |divide| |linearMatrix| - |mainPrimitivePart| |genericPosition| |totalLex| |gcdPolynomial| |key| - |log10| |fortran| |sumOfSquares| |arg2| |companionBlocks| |size?| - |octon| |goodnessOfFit| |dim| |problemPoints| |typeLists| |atoms| - |mapExponents| |integralBasisAtInfinity| |oddInfiniteProduct| |htrigs| - |bitand| |An| |shift| |edf2fi| |topFortranOutputStack| - |rangePascalTriangle| |OMgetFloat| |setFormula!| |hessian| - |represents| |coth2trigh| |fortranDouble| |clearTheFTable| |symbol| - |sec2cos| |bitior| |jordanAdmissible?| |conditions| |OMwrite| |cdr| - |allRootsOf| |maxdeg| |permutation| |polarCoordinates| |s13acf| |rem| - |idealSimplify| |quotient| |mapSolve| |expression| |expr| |e04gcf| - |match| |paraboloidal| |dequeue| |integral?| |zeroDimPrime?| - |stiffnessAndStabilityFactor| |createMultiplicationTable| |gensym| - |quo| |isQuotient| |fortranCompilerName| |repeating| |integer| - |decomposeFunc| |duplicates| |listLoops| |index| - |removeRoughlyRedundantFactorsInPol| |internalIntegrate0| |d01akf| - |middle| |antiCommutative?| |f01rcf| |processTemplate| - |setMaxPoints3D| |createRandomElement| |setleaves!| |lfextendedint| - |d02kef| |algebraicOf| |interpret| |div| |expint| |algint| |s17dgf| - |univariate?| |augment| |symFunc| |closed| |parametersOf| - |alternating| |exQuo| |rule| |exquo| |primitivePart!| |compound?| - |getOperator| |makeFR| |mpsode| |stoseInvertible?| |irreducible?| - |cot2trig| |virtualDegree| |birth| |quadratic?| |hcrf| ~= |s17agf| - |checkPrecision| |rischDEsys| |member?| |unary?| |fortranReal| - |fillPascalTriangle| |startTableInvSet!| |cothIfCan| |child?| - |leftCharacteristicPolynomial| |height| |#| |cCos| |paren| |returns| - |associatorDependence| |squareTop| |substring?| |children| |tanIfCan| - |bubbleSort!| |outputList| |nativeModuleExtension| |fracPart| ~ |Ci| - |Beta| |commutativeEquality| |compiledFunction| |putProperties| - |baseRDE| |fortranTypeOf| |sub| |noKaratsuba| |primintegrate| - |jvmSuper| |axesColorDefault| |cCsc| |bsolve| |suffix?| |infLex?| - |lfextlimint| |lyndon?| |irForm| |crushedSet| |size| - |setScreenResolution| |normFactors| |characteristicPolynomial| - |coleman| |createThreeSpace| |e04ycf| |ptFunc| |realEigenvalues| - |ScanRoman| |conjug| |/\\| |wholePart| |c05nbf| |tan2trig| - |basisOfRightNucloid| |prinb| |prefix?| |byteBuffer| |subResultantGcd| - |OMputEndObject| |prime| |distdfact| |\\/| |result| |s14aaf| - |stoseSquareFreePart| |jvmStatic| |s14baf| |increasePrecision| - |completeHensel| |OMserve| |nextPrime| |simpleBounds?| |separant| - |generic?| |createNormalElement| |rightPower| |imagE| |cyclic?| - |escape| |rotatex| |iiatan| |localAbs| |more?| |separateFactors| - |c06gcf| |LiePoly| |returnTypeOf| |s14abf| |wrregime| - |leadingExponent| |car| |yCoordinates| |makeViewport2D| |safetyMargin| - |f04mcf| |radPoly| |genericLeftMinimalPolynomial| |macroExpand| - |tensorProduct| |nullary?| |lintgcd| |s18adf| |writeLine!| |component| - |selectPolynomials| |coordinate| |monomial?| |OMputEndError| - |modularGcd| |abs| |addPoint| |constantRight| |plus!| |infix?| - |d02gbf| |lazyPseudoRemainder| |explogs2trigs| |acotIfCan| |imagk| - |pascalTriangle| |true| |solveLinearPolynomialEquation| |direction| - |uniform01| |delay| |mask| |rename!| |stosePrepareSubResAlgo| |node| - |splitNodeOf!| |swapColumns!| |removeZeroes| |leftFactorIfCan| - |option?| |leftTraceMatrix| |s18def| |setEpilogue!| |digit| |df2mf| - |fibonacci| |rootRadius| |splitLinear| |s17adf| |commaSeparate| - |pdf2df| |f02awf| |tail| |sPol| |expintfldpoly| |f2st| |associative?| - |computeBasis| |pleskenSplit| |tanintegrate| |reduction| |d01ajf| - |pile| |maxPoints| |iomode| |fortranInteger| |exptMod| |setPosition| - |moduleSum| |weighted| |insert!| |cyclicCopy| |jvmVolatile| - |linearElement| |setelt!| |omError| |buildSyntax| |quasiComponent| - |padicFraction| |boundOfCauchy| |genericRightNorm| |resetBadValues| - |removeRedundantFactorsInPols| |outputGeneral| |doubleFloatFormat| - |radicalOfLeftTraceForm| |pmComplexintegrate| |zeroOf| |transpose| - |goodPoint| |inputBinaryFile| |e01bef| |jvmMethodrefConstantTag| - |title| |computeCycleLength| |composite| |lazyResidueClass| |position| - |argscript| |logGamma| |f04jgf| |outputBinaryFile| - |complexNumericIfCan| |twoFactor| |minrank| |printInfo!| - |associatedSystem| |insert| |resultant| |retractIfCan| |e01bgf| - |selectMultiDimensionalRoutines| |doubleResultant| |squareFreePrim| - |OMread| |implies| |comp| |integralLastSubResultant| |elements| - |partialDenominators| |finite?| |cartesian| |vectorise| |powerSum| - |cfirst| |laurentRep| |medialSet| |rightDiscriminant| |isList| - |comment| |f02axf| |null?| |inrootof| |internalZeroSetSplit| |log| - |logIfCan| |tanQ| |c02agf| |OMcloseConn| |upperBound| |categoryFrame| - |resetVariableOrder| |mainForm| |explimitedint| - |derivationCoordinates| |firstUncouplingMatrix| |var2StepsDefault| - |generalPosition| |fortranLinkerArgs| |factorSFBRlcUnit| |mathieu22| - |countable?| |set| |normalizedAssociate| |realEigenvectors| - |solveLinearPolynomialEquationByRecursion| |usingTable?| |e01bhf| - |coerceImages| |trigs2explogs| |negative?| |space| |equation| |Aleph| - |addPoint2| |constantOperator| |c06gbf| |clip| |expPot| |cyclotomic| - |powers| |scanOneDimSubspaces| |options| |contract| |romberg| |pop!| - |internalSubPolSet?| |simplify| |algSplitSimple| |iiacoth| - |selectFiniteRoutines| |setAdaptive| |expIfCan| |computePowers| - |mainContent| |genericLeftTrace| |primes| |elliptic?| |regime| - |coerceP| |upperCase!| |selectfirst| |map| |purelyAlgebraic?| - |cos2sec| |cond| |mapExpon| |string| |getIdentifier| - |sumOfKthPowerDivisors| |categories| |viewport2D| |putProperty| - |list?| |jvmInterface| |deepestTail| |lieAlgebra?| |unaryFunction| - |mainExpression| |rootProduct| |writeInt8!| |coercePreimagesImages| - |cAsinh| |userOrdered?| |kroneckerDelta| |pureLex| |d02cjf| - |errorKind| |nthRootIfCan| |halfExtendedResultant1| |c06ekf| |makeSUP| - |bothWays| |red| |sumSquares| |continuedFraction| |lexGroebner| - |setEmpty!| |oddintegers| |discreteLog| |OMsupportsCD?| |nullity| - |drawComplex| |att2Result| |init| |underscore| |mat| |makeSketch| - |bitLength| |bumptab1| |primextintfrac| |ignore?| |linGenPos| - |nthCoef| |s20adf| |iisqrt3| |rst| |getSyntaxFormsFromFile| |convert| - |evaluateInverse| |ptree| |subHeight| |setProperties| |polCase| - |monicModulo| |SturmHabichtCoefficients| |normalizeIfCan| - |getVariableOrder| |reducedContinuedFraction| |nthExponent| |null| - |hasSolution?| |partialFraction| |inR?| |eigenvector| |shufflein| - |solve1| |compose| |constantCoefficientRicDE| |asechIfCan| - |setLegalFortranSourceExtensions| - |rewriteSetByReducingWithParticularGenerators| |not| |startPolynomial| - |rewriteIdealWithRemainder| |setTex!| |palgextint| |credPol| - |chebyshevU| |c06ebf| |internalSubQuasiComponent?| |s19abf| |pastel| - |and| |newReduc| |OMgetAttr| |vertConcat| |unparse| - |SturmHabichtSequence| |epilogue| |pointColor| |iitan| |nary?| - |s21bdf| |fi2df| |removeSinSq| |push!| |monomRDE| |refine| |karatsuba| - |iprint| |semiDegreeSubResultantEuclidean| |number?| |extend| - |palgRDE| RF2UTS |btwFact| |last| |pseudoRemainder| |OMgetAtp| - |setOrder| |polynomialZeros| |janko2| |unitVector| |fmecg| - |linearAssociatedOrder| |ricDsolve| |assoc| |numberOfComposites| - |ScanArabic| |degreePartition| |transcendent?| |splitConstant| |dot| - |has?| |approxSqrt| |exponents| |Lazard2| |extendedEuclidean| - |cycleElt| |close!| |mainMonomial| |back| |tubeRadiusDefault| - |alphanumeric?| |deleteRoutine!| |f01maf| |crest| |viewPhiDefault| - |rowEch| |ratPoly| |cylindrical| |comparison| |taylorRep| |deref| - |removeZero| |measure| |sqfree| |twist| |failed| |sizePascalTriangle| - |f07fef| |coordinates| |dualSignature| |variable?| |rur| |csc2sin| - |resultantnaif| |mvar| |setScreenResolution3D| |dihedralGroup| |pole?| - |rationalPower| |collect| |pseudoDivide| |tryFunctionalDecomposition?| - |infRittWu?| |repSq| |e02akf| |outlineRender| |trigs| |bat| - |csch2sinh| |s17aef| |normalize| |divisor| |fprindINFO| |eval| - |doubleComplex?| |contains?| |bezoutMatrix| |lieAdmissible?| - |leftZero| |graphs| |generalizedContinuumHypothesisAssumed| |makeUnit| - |powmod| |initializeGroupForWordProblem| |constantLeft| - |toseLastSubResultant| |solid?| |laurentIfCan| |elaboration| - |topPredicate| |isOpen?| |ListOfTerms| |monic?| |recip| |qualifier| - |prod| |recolor| |e02aef| |attributeData| |Ei| |pow| |listexp| - |integralAtInfinity?| |f02wef| |cyclic| |cCsch| |cAsin| |f02bjf| - |showTheRoutinesTable| |leftGcd| |variable| |high| |status| |cn| ** - |getStream| |presub| |distFact| |row| |musserTrials| - |createNormalPoly| |coerceS| |iterators| |possiblyInfinite?| - |dictionary| |rightUnit| |neglist| |shallowCopy| |exprToXXP| |c06fpf| - |complexElementary| |euclideanGroebner| |determinant| |GospersMethod| - |lists| |innerEigenvectors| |printHeader| |pair| |heapSort| |mkPrim| - |isOr| |lastSubResultantElseSplit| |resetAttributeButtons| |s18dcf| - |s19acf| |nextItem| |myDegree| |tube| |oneDimensionalArray| - |leastPower| |latex| |lprop| |tanNa| |factorAndSplit| |polyRDE| - |outputSpacing| |viewDeltaXDefault| |keys| |univariatePolynomials| - |argument| |c02aff| |badNum| |graphCurves| |ode1| |isConnected?| - |lazyVariations| |minColIndex| |coord| |numberOfCycles| |f02fjf| - |B1solve| |createPrimitivePoly| |fixPredicate| - |showIntensityFunctions| |rightUnits| |iidprod| |setIntersection| - |ef2edf| |quasiMonicPolynomials| |s18aef| |radicalSolve| |yCoord| - |getOrder| |scopes| |trivialIdeal?| |elseBranch| |multiset| |increase| - |extractIfCan| |e02agf| |viewThetaDefault| |multiEuclideanTree| - |connect| |overlabel| |reducedSystem| |nil| |conical| |quatern| - |divisorCascade| |aromberg| |padecf| |lazyPquo| |increment| - |extendedResultant| |merge| |properties| |whileLoop| |fixedPoints| - |linearDependence| |probablyZeroDim?| |sech2cosh| |numer| - |genericLeftNorm| |jvmDoubleConstantTag| |internalInfRittWu?| - 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|leftRegularRepresentation| |aspFilename| |e01sbf| |readUInt32!| - |reverse| |complexForm| |torsion?| |invertible?| |curveColorPalette| - UP2UTS |redPol| |createLowComplexityNormalBasis| |firstNumer| - |getBadValues| |bytes| |reverse!| |phiCoord| |leftRecip| |monomials| - |factorsOfDegree| |dimension| |f07adf| |idealiser| |tableau| - |stopTableInvSet!| NOT |youngGroup| |chebyshevT| |showAllElements| - |rightTrace| |f04axf| |readable?| |eulerPhi| |parametric?| |sorted?| - |append| OR |mantissa| |extractSplittingLeaf| |constantOpIfCan| - |setLabelValue| |iiacosh| |front| |s17aff| |clipWithRanges| |terms| - |SturmHabicht| AND |morphism| |divideIfCan!| |leftExtendedGcd| |infix| - |explicitlyFinite?| |resultantReduit| |e02bdf| |collectUnder| F - |completeHermite| |nextIrreduciblePoly| |groebner?| - |LowTriBddDenomInv| |permanent| |radicalEigenvectors| |cycleEntry| - |bipolar| |floor| |inf| |reduceByQuasiMonic| |lyndonIfCan| |solveid| - |mapUnivariate| |substitute| |rewriteIdealWithHeadRemainder| - 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|generalizedEigenvectors| |bezoutResultant| |d01amf| |taylorQuoByVar| - |diagonalMatrix| |genericRightDiscriminant| |trailingCoefficient| - |d01gaf| |reseed| |complement| |binaryTournament| |showTheIFTable| - |category| |expandTrigProducts| |subscriptedVariables| - |tryFunctionalDecomposition| |part?| |linearlyDependent?| |in?| - |radix| |domain| |closedCurve| |compBound| |stripCommentsAndBlanks| - |psolve| = |mapUnivariateIfCan| |acosIfCan| |ParCond| |tree| |binding| - |infinite?| |package| |highCommonTerms| |clearCache| |collectUpper| - |zCoord| |extractClosed| |screenResolution| |areEquivalent?| - |bindings| |operation| |symmetricGroup| |d02gaf| |unmakeSUP| - |diagonalProduct| |hclf| |jvmFieldrefConstantTag| |hostByteOrder| < - |iiasin| |e04naf| |nonSingularModel| |cAcot| - |irreducibleRepresentation| |point?| |setUnion| > |unitNormal| - |symmetricDifference| |lquo| |e04ucf| |expt| |iifact| |sncndn| |t| - |inRadical?| |argumentList!| |symmetricProduct| <= |polyPart| - |bracket| |edf2ef| |numerators| |multisect| |sizeLess?| |d01aqf| - |curry| |collectQuasiMonic| |cTan| >= |ref| |invertibleSet| - |constructor| |trueEqual| |choosemon| |viewWriteDefault| - |inverseLaplace| |unrankImproperPartitions0| |fixedDivisor| - |permutations| |upDateBranches| |OMgetString| |callForm?| |vspace| - |restorePrecision| |pack!| |closedCurve?| |mappingMode| |nextColeman| - |primeFrobenius| |mainVariable?| |sturmVariationsOf| |upperCase?| - |order| |quoted?| |prime?| |createLowComplexityTable| |legendreP| - |tanAn| + |rightRankPolynomial| |stronglyReduce| |RittWuCompare| - |insertBottom!| |matrixDimensions| |hasPredicate?| |shiftRoots| - |OMgetObject| |untab| |setValue!| - |setPredicates| |unvectorise| - |fullDisplay| |rightZero| |lighting| |absolutelyIrreducible?| - |subset?| |points| / |LazardQuotient2| |graphState| |subst| |every?| - |arbitrary| |summation| |components| |name| |minimalPolynomial| - |measure2Result| |dimensionsOf| |c06eaf| |adaptive?| |updateStatus!| - |construct| |cLog| |LyndonWordsList1| |coerceL| |body| |s17ahf| - |splitSquarefree| |OMUnknownSymbol?| |writeBytes!| |rectangularMatrix| - |overset?| |mapUp!| |minPoly| |expextendedint| |hue| |conjugates| - |gcdPrimitive| |doublyTransitive?| |rootSimp| |multiple?| |f04asf| - |diophantineSystem| |jvmNameAndTypeConstantTag| |f2df| |modularFactor| - |merge!| |imagJ| |hexDigit| |polar| |conjugate| |objects| - |blankSeparate| |numFunEvals3D| |max| |sn| |leadingIndex| - |semiDiscriminantEuclidean| |nodes| |quotedOperators| |laguerre| - |ReduceOrder| |kind| |base| |isPower| SEGMENT |Vectorise| |enumerate| - |nextPartition| |indices| |concat!| |c06ecf| LODO2FUN |socf2socdf| - |quasiRegular?| |exteriorDifferential| |laguerreL| |green| - |genericRightTrace| |tower| |s13adf| |jacobiIdentity?| |changeBase| - |resultantEuclideannaif| |showScalarValues| |lazyIrreducibleFactors| - |inputOutputBinaryFile| |transform| |simplifyExp| |symmetricTensors| - |formfeed| |setClosed| |setAttributeButtonStep| |argumentListOf| - |sizeMultiplication| |makeSin| |isOp| |getMultiplicationMatrix| - |create3Space| |iipow| |divergence| |df2fi| |quickSort| |preprocess| - |nil| |infinite| |arbitraryExponent| |approximate| |complex| - |shallowMutable| |canonical| |noetherian| |central| - |partiallyOrderedSet| |arbitraryPrecision| |canonicalsClosed| - |noZeroDivisors| |rightUnitary| |leftUnitary| |additiveValuation| - |unitsKnown| |canonicalUnitNormal| |multiplicativeValuation| - |finiteAggregate| |shallowlyMutable| |commutative|)
\ No newline at end of file + |Enumeration| |Mapping| |Record| |Union| |omError| |content| + |youngGroup| |normalise| |port| |rk4a| |leftDiscriminant| |is?| + |doubleComplex?| |scan| |indices| |OMputBind| |leftFactor| + |buildSyntax| |rightRank| |chebyshevT| |sortConstraints| |charpol| + |generateIrredPoly| |createIrreduciblePoly| |contains?| |concat!| + |lowerPolynomial| |matrix| |mainSquareFreePart| |edf2df| + |quasiComponent| |showAllElements| |axes| |chineseRemainder| + |oblateSpheroidal| |jvmProtected| |bezoutMatrix| |realZeros| |c06ecf| + |lazyIntegrate| |s17ajf| |padicFraction| |leastMonomial| |rightTrace| + |positiveSolve| |hyperelliptic| |FormatRoman| |complexNumeric| + |generators| |lieAdmissible?| |subscript| LODO2FUN |biRank| + |numberOfDivisors| |f02aaf| |boundOfCauchy| + |primPartElseUnitCanonical| |basisOfNucleus| |f04axf| |sinhcosh| + |useSingleFactorBound| |leftDivide| |leftZero| |tab1| |socf2socdf| + |d03eef| |e01sff| |genericRightNorm| |Hausdorff| |readable?| + |withPredicates| |OMencodingSGML| |or| |someBasis| |cyclicSubmodule| + |makeEq| |graphs| |quasiRegular?| |f02ajf| |routines| |resetBadValues| + |linear?| |innerSolve1| |eulerPhi| |primPartElseUnitCanonical!| |xor| + |Is| |autoReduced?| |generalizedContinuumHypothesisAssumed| |ord| + |exteriorDifferential| |extendedSubResultantGcd| |d03faf| + |removeRedundantFactorsInPols| |parametric?| |schema| + |definingPolynomial| |case| |atrapezoidal| |calcRanges| |makeUnit| + |OMgetSymbol| |laguerreL| |declare| |cons| |endOfFile?| + |outputGeneral| |infiniteProduct| |sorted?| + |removeRedundantFactorsInContents| |jvmPublic| |Zero| |critT| + |hdmpToDmp| |powmod| |possiblyNewVariety?| |green| |apply| |irVar| + |getMultiplicationTable| |doubleFloatFormat| |float?| + |extractSplittingLeaf| |inGroundField?| |One| |cSec| |cyclePartition| + |initializeGroupForWordProblem| |mindeg| |genericRightTrace| |first| + |PollardSmallFactor| |radicalOfLeftTraceForm| |interactiveEnv| + |constantOpIfCan| |dmp2rfi| |extractPoint| |iExquo| + |structuralConstants| |operators| |constantLeft| |s13adf| |rest| + |sinh2csch| |pmComplexintegrate| |f01qcf| |setLabelValue| + |rationalIfCan| |integralRepresents| |pToDmp| |triangular?| |digits| + |toseLastSubResultant| |jacobiIdentity?| |writeByte!| |source| + |zeroOf| |airyBi| |computeInt| |iiacosh| |particularSolution| + |integralCoordinates| |commutative?| |solid?| |dfRange| |changeBase| + |d01apf| |subTriSet?| |tRange| |transpose| |front| |hostPlatform| + |bigEndian| |jvmAbstract| |tan2cot| |setvalue!| |laurentIfCan| + |resultantEuclideannaif| |eyeDistance| |f01bsf| |goodPoint| |curve| + |s17aff| |wordsForStrongGenerators| |semiIndiceSubResultantEuclidean| + |elt| |binaryTree| |retractable?| |elaboration| |OMputFloat| + |showScalarValues| |halfExtendedSubResultantGcd2| |target| + |perspective| |differentialVariables| |e01bef| |clipWithRanges| + |linears| |solveLinear| |overbar| |numericIfCan| |mr| |build| + |topPredicate| |lazyIrreducibleFactors| |rationalApproximation| + |jvmMethodrefConstantTag| |region| |xCoord| |terms| |rotate!| + |solveLinearPolynomialEquationByFractions| |removeCoshSq| |irCtor| + |isOpen?| |inputOutputBinaryFile| |scale| |computeCycleLength| + |updatF| |rischDE| |SturmHabicht| |invertibleElseSplit?| |OMlistCDs| + |property| |ListOfTerms| |curve?| |transform| |morphism| + |patternVariable| |composite| |univariateSolve| |unravel| + |setMinPoints3D| |iicos| |charClass| |limitPlus| |rangeIsFinite| + |monic?| |simplifyExp| |safeFloor| |primextendedint| |curryRight| + |lazyResidueClass| |divideIfCan!| |repeating?| |changeWeightLevel| + |generalizedInverse| |cSech| |midpoints| |recip| |flatten| + |symmetricTensors| |leftUnit| |union| |removeCosSq| |traceMatrix| + |argscript| |jvmUTF8ConstantTag| |leftExtendedGcd| |iFTable| + |changeName| |f02xef| |ridHack1| |qualifier| |formfeed| + |quadraticNorm| |logGamma| |rightAlternative?| |infix| + |localIntegralBasis| |sylvesterMatrix| |f01rdf| |OMsupportsSymbol?| + |uncouplingMatrices| |prod| |setClosed| |listOfLists| |iisqrt2| + |f04jgf| |e01baf| |explicitlyFinite?| |dn| |monicDivide| |graphStates| + |recolor| |printStatement| |setAttributeButtonStep| |central?| + |complexNumericIfCan| |normalForm| |perfectSquare?| |resultantReduit| + |copies| |gcdcofact| |satisfy?| |e02aef| |slash| |argumentListOf| + |localReal?| |leadingBasisTerm| |twoFactor| |e02bdf| |truncate| + |lagrange| |surface| |startTable!| |tubeRadius| |attributeData| + |sizeMultiplication| |nonLinearPart| |minrank| |setCondition!| + |collectUnder| |expandLog| |drawComplexVectorField| + |regularRepresentation| |leadingCoefficientRicDE| |linearPart| |Ei| + |makeSin| |simplifyLog| |printInfo!| |getGraph| |reciprocalPolynomial| + |completeHermite| |moebiusMu| |permutationGroup| |makeYoungTableau| + |pow| |extensionDegree| |arguments| |isOp| |opeval| |associatedSystem| + |gethi| |nextIrreduciblePoly| |groebgen| |besselI| |newLine| + |rootNormalize| |mkIntegral| |listexp| |getMultiplicationMatrix| + |cCoth| |OMgetEndBVar| |resultant| |exponentialOrder| |groebner?| + |updatD| |divide| |setrest!| |integralAtInfinity?| |e01bff| + |create3Space| |decompose| |d01anf| |e01bgf| |LowTriBddDenomInv| + |controlPanel| |linearMatrix| |lazyPremWithDefault| |f02bbf| |f02wef| + |iipow| |prefix| |singularitiesOf| |selectMultiDimensionalRoutines| + |algebraicSort| |iisech| |permanent| |mainPrimitivePart| |deriv| + |cyclic| |getRef| |divergence| |numberOfFactors| |match?| + |doubleResultant| |primaryDecomp| |radicalEigenvectors| |csubst| + |stirling1| |genericPosition| |cCsch| |check| |df2fi| |outerProduct| + |eisensteinIrreducible?| |squareFreePrim| |subNodeOf?| |primitive?| + |cycleEntry| |totalLex| |equiv| |inverseIntegralMatrix| |cAsin| + |quickSort| |positiveRemainder| |OMread| |bipolar| |nextNormalPoly| + |gcdPolynomial| |findBinding| |f02bjf| |plot| |preprocess| + |realElementary| |bitTruth| |strongGenerators| |implies| |palgLODE| + |floor| |sumOfSquares| |subCase?| |showTheRoutinesTable| |typeList| + |curryLeft| |OMencodingBinary| |integralLastSubResultant| |lambert| + |inf| |d02ejf| |ranges| |companionBlocks| |finiteBound| |leftGcd| + |rightMult| |iicsc| |divisors| |elements| |zeroVector| + |reduceByQuasiMonic| |high| |besselK| |characteristic| + |partialDenominators| |schwerpunkt| |lyndonIfCan| |mappingAst| + |cot2tan| |innerSolve| |status| |weakBiRank| |compile| |finite?| + |permutationRepresentation| |solveid| |cAtanh| |var1StepsDefault| + |getStream| |rightLcm| |internalIntegrate| |cartesian| + |noncommutativeJordanAlgebra?| |mapUnivariate| |completeEchelonBasis| + |mix| |fglmIfCan| |presub| |c06gqf| |swap!| + |rewriteIdealWithHeadRemainder| |nullary| |distFact| |mdeg| |exp1| + |yCoordinates| |monicDecomposeIfCan| |linSolve| |integralBasis| + |groebnerIdeal| |nor| |row| |mapCoef| |redPo| |makeViewport2D| + |normDeriv2| |trapezoidalo| |bright| |compactFraction| |musserTrials| + |UpTriBddDenomInv| |iiabs| |safetyMargin| |s19adf| + |semiResultantEuclidean2| |smith| |extractBottom!| |f02agf| |minus!| + |f04mcf| |approxNthRoot| |randnum| |power!| |repeatUntilLoop| RF2UTS + |groebnerFactorize| |radPoly| |modifyPoint| |sin?| |makeop| |mapDown!| + |btwFact| |maxRowIndex| |cExp| |genericLeftMinimalPolynomial| |d01asf| + |badValues| |linearPolynomials| |center| |froot| |rotatez| + |pseudoRemainder| |multiplyCoefficients| |OMputEndBVar| + |tensorProduct| |messagePrint| |frobenius| |OMgetAtp| + |basisOfCentroid| |nullary?| |convergents| |listOfMonoms| + |semiLastSubResultantEuclidean| |pointColorDefault| + |principalAncestors| |setOrder| |tanhIfCan| |cup| |lintgcd| |s21baf| + |removeRedundantFactors| |algintegrate| |alphabetic?| + |polynomialZeros| |expintegrate| |getConstant| |close| + |genericRightTraceForm| |s18adf| |arity| |incrementKthElement| + |remove!| |c05adf| |janko2| |cosh2sech| |interpolate| |script| + |setLength!| |figureUnits| |sup| |OMgetEndObject| |writeLine!| + |loadNativeModule| |table| |s15aef| |scripted?| |resetNew| + |unitVector| |setValue!| |initial| |idealiserMatrix| |display| + |component| |empty| |one?| |printTypes| |reducedDiscriminant| + |evenInfiniteProduct| |fmecg| |setPredicates| |rename| + |selectPolynomials| |root?| |tableForDiscreteLogarithm| |polygamma| + |linearAssociatedOrder| |fortranComplex| |decreasePrecision| |tex| + |varList| |unvectorise| |showFortranOutputStack| |d02raf| |coordinate| + |readLineIfCan!| |child| |new| |colorDef| |gcdcofactprim| |ricDsolve| + |fullDisplay| |makeGraphImage| |jvmFinal| |monomial?| |d03edf| + |minRowIndex| |ellipticCylindrical| |numberOfComposites| |power| + |rightZero| |kmax| |pushdterm| |OMputEndError| |OMputAtp| + |coefficient| |elRow2!| |lhs| |fortranLiteralLine| |ScanArabic| + |lighting| |modularGcd| |input| |e02daf| |makeSeries| |s15adf| + |exponent| |thetaCoord| |toroidal| |rhs| |degreePartition| + |difference| |absolutelyIrreducible?| |plus| |log2| |qPot| |abs| + |quasiRegular| |degreeSubResultant| |discriminantEuclidean| |e| + |hspace| |tanh2trigh| |transcendent?| |subset?| |OMsetEncoding| + |OMputEndApp| |split| |addPoint| |cyclicGroup| |deepestInitial| + |minPoints3D| |splitConstant| |s17dlf| |times| |points| + |stronglyReduced?| |constantRight| |drawStyle| |replace| |mapdiv| + |generalizedEigenvector| |LazardQuotient| |dot| |LazardQuotient2| + |imaginary| |plus!| |maxrank| |read!| |tab| + |indiceSubResultantEuclidean| |has?| |prolateSpheroidal| |graphState| + |message| |basisOfCommutingElements| |monomialIntPoly| |bit?| |d02gbf| + |rischNormalize| |left| |subresultantVector| |approxSqrt| |intChoose| + |every?| |groebner| |split!| |lazyPseudoRemainder| |karatsubaOnce| + |right| |sample| |arbitrary| |c06fqf| |exponents| |isExpt| |monom| + |level| |iilog| |hex| |explogs2trigs| |rightRegularRepresentation| + |dAndcExp| |f01mcf| |raisePolynomial| |Lazard2| |summation| + |jvmIntegerConstantTag| |iicsch| |acotIfCan| + |factorsOfCyclicGroupSize| |OMconnInDevice| |filename| |width| + |selectsecond| |extendedEuclidean| |just| |components| + |extendedIntegrate| |lp| |imagk| |quadraticForm| |chvar| |notelem| + |orbit| |cycleElt| |listConjugateBases| |common| |minimalPolynomial| + |nthFactor| |pascalTriangle| |rspace| |rowEchelon| |symbolTableOf| + |stack| |alternatingGroup| |parse| |close!| |parent| |measure2Result| + |rowEchLocal| |solveLinearPolynomialEquation| |selectPDERoutines| + |applyRules| |duplicates?| |iroot| |OMputEndAtp| |mainMonomial| + |dimensionsOf| |normal01| |generic| |direction| |cscIfCan| + |stoseInvertible?sqfreg| |shanksDiscLogAlgorithm| |back| |cycleLength| + |c06eaf| |rombergo| |setchildren!| |rightFactorCandidate| |uniform01| + |zeroSetSplit| |stFunc2| |headReduce| |coHeight| |tubeRadiusDefault| + |adaptive?| |eq| |node?| |delay| |trunc| |singRicDE| |getMatch| + |LyndonWordsList| |optional| |alphanumeric?| + |indicialEquationAtInfinity| |updateStatus!| + |functionIsFracPolynomial?| |iter| |revert| |maximumExponent| + |rename!| |isAnd| |generalSqFr| |arg1| |KrullNumber| |deleteRoutine!| + |subResultantChain| |cLog| |var2Steps| |unitCanonical| |iiacot| + |stosePrepareSubResAlgo| |llprop| |key| |log10| |fortran| |arg2| + |iicot| |f01maf| |changeVar| |LyndonWordsList1| |dim| + |integralMatrixAtInfinity| |f04arf| |sqfrFactor| |OMgetError| |lists| + |splitNodeOf!| |symmetricRemainder| |s21bbf| |bitand| |shift| + |string?| |primeFactor| |crest| |coerceL| |reducedForm| |imagi| + |swapColumns!| |invertIfCan| |ScanFloatIgnoreSpaces| |pushNewContour| + |symbol| |evenlambert| |bitior| |conditions| |moebius| |geometric| + |viewPhiDefault| |realRoots| |s17ahf| |laplace| |totalfract| + |complexEigenvalues| |rem| |redpps| |removeZeroes| |expression| |expr| + |match| |clipParametric| |stopMusserTrials| |rowEch| |splitSquarefree| + |iflist2Result| |multMonom| |quo| |isQuotient| |integer| + |leftFactorIfCan| |integer?| |symbol?| |complexRoots| |index| + |ratPoly| |monomRDEsys| |OMUnknownSymbol?| |prevPrime| |option?| + |ocf2ocdf| |tubePoints| |stFuncN| |innerint| |cylindrical| |e04fdf| + |writeBytes!| |interpret| |div| |constDsolve| |shellSort| + |leftTraceMatrix| |linearAssociatedLog| |listBranches| |fixedPoint| + |comparison| |lifting1| |rectangularMatrix| |rule| |exquo| |cycle| + |infinityNorm| |s18def| |cyclotomicDecomposition| |complexExpand| + |style| |bivariateSLPEBR| |taylorRep| |overset?| |identityMatrix| ~= + |factorSquareFreeByRecursion| |checkPrecision| |setEpilogue!| |mapGen| + |maxint| |resize| |squareFree| |leftRankPolynomial| |deref| |mapUp!| + |height| |#| |internalLastSubResultant| |digit| |assign| + |singleFactorBound| |radicalEigenvector| |substring?| |e02bef| + |sechIfCan| |outputList| |removeZero| |minPoly| ~ |scalarMatrix| + |df2mf| |write!| |bfKeys| |corrPoly| |createMultiplicationMatrix| + |e02bbf| |measure| |expextendedint| |readUInt8!| |fibonacci| + |makeMulti| |digit?| |complementaryBasis| |suffix?| |denomRicDE| + |f01ref| |sqfree| |hue| |size| |monicRightFactorIfCan| |rootRadius| + |conditionP| |saturate| |besselY| |expandPower| |constantKernel| + |twist| |conjugates| |/\\| |poisson| |splitLinear| GF2FG + |algebraicCoefficients?| |supDimElseRittWu?| |prefix?| |readByte!| + |sizePascalTriangle| |s21bcf| |gcdPrimitive| |\\/| |result| |lllp| + |hMonic| |s17adf| |dioSolve| |unprotectedRemoveRedundantFactors| + |removeSquaresIfCan| |f07fef| |OMReadError?| |doublyTransitive?| + |shiftRight| |beauzamyBound| |commaSeparate| |const| |OMputEndBind| + |useNagFunctions| |c06fuf| |coordinates| |rootSimp| |iCompose| + |pdf2df| |initiallyReduced?| |selectSumOfSquaresRoutines| + |mainMonomials| |mkAnswer| |dualSignature| |contractSolve| |multiple?| + |macroExpand| |critM| |f02awf| |simplifyPower| + |leftRegularRepresentation| |leftTrace| |variable?| |stFunc1| |f04asf| + |entry?| |sPol| |s01eaf| |aspFilename| |definingEquations| + |nextPrimitivePoly| |mapBivariate| |rur| |diophantineSystem| + |showTheFTable| |expintfldpoly| |polygon| |pushucoef| |e01sbf| + |infix?| |d01bbf| |bandedHessian| |csc2sin| + |jvmNameAndTypeConstantTag| |dimensions| |true| |f2st| + |patternMatchTimes| |readUInt32!| |acschIfCan| |mask| |f02akf| + |resultantnaif| |f2df| |node| |OMputApp| |associative?| |rroot| + |sequences| |complexForm| |whitePoint| |wordInStrongGenerators| |mvar| + |modularFactor| |cyclotomicFactorization| |computeBasis| |cycleSplit!| + |makeCos| |torsion?| |generalTwoFactor| |tail| |setScreenResolution3D| + |nullSpace| |merge!| |factors| |binarySearchTree| |pleskenSplit| + |leadingSupport| |invertible?| |FormatArabic| |dihedralGroup| + |partition| |imagJ| |iiacos| |curveColorPalette| |presuper| |lazy?| + |pole?| |fixedPointExquo| |hexDigit| |bumprow| |largest| + |axesColorDefault| |selectIntegrationRoutines| UP2UTS |returnType!| + |minGbasis| |rationalPower| |polar| |exists?| |cCsc| |initiallyReduce| + |redPol| |setStatus!| |supersub| |setColumn!| |collect| + |normalElement| |conjugate| |inputBinaryFile| |enterPointData| + |bsolve| |title| |leftOne| |createLowComplexityNormalBasis| |position| + |newTypeLists| |numberOfOperations| |blankSeparate| |nthFlag| + |outputBinaryFile| |infLex?| |rationalFunction| |bombieriNorm| + |firstNumer| |generalizedContinuumHypothesisAssumed?| |insert| + |retractIfCan| |lSpaceBasis| |s20adf| |numFunEvals3D| |lookup| + |s17akf| |lfextlimint| |leaf?| |imports| |comp| |getBadValues| + |graeffe| |setright!| |iisqrt3| |subSet| |max| |cSinh| |real?| + |lyndon?| |airyAi| |bytes| |stoseInvertibleSet| |comment| |mainKernel| + |rst| |numberOfImproperPartitions| |log| |leadingIndex| |makeResult| + |seriesToOutputForm| |irForm| |closeComponent| |polyred| |appendPoint| + |getSyntaxFormsFromFile| |setTopPredicate| |semiDiscriminantEuclidean| + |superscript| |setAdaptive3D| |crushedSet| |frst| + |removeSuperfluousCases| |solveInField| |getExplanations| + |evaluateInverse| |radicalRoots| |nodes| |OMopenFile| |set| + |setScreenResolution| |isImplies| |skewSFunction| |move| + |semiSubResultantGcdEuclidean1| |setlast!| |subHeight| |isTimes| + |quotedOperators| |OMgetEndApp| |equation| |f07fdf| |normFactors| + |critMonD1| |genericLeftDiscriminant| |lex| |setProperties| |sign| + |datalist| |removeSuperfluousQuasiComponents| |options| + |mainCoefficients| |characteristicPolynomial| |factorPolynomial| + |primintfldpoly| |OMgetBind| |pmintegrate| |polCase| |discriminant| + |symmetricDifference| |numberOfChildren| |exprHasAlgebraicWeight| + |coleman| |cycleRagits| |currentScope| |trapezoidal| |map| + |optAttributes| |monicModulo| |cond| |lquo| |string| |deepExpand| + |loopPoints| |categories| |createThreeSpace| |diagonal?| + |lastSubResultant| |quasiMonic?| |fTable| |SturmHabichtCoefficients| + |e04ucf| |eof?| |quotientByP| |testModulus| |e04ycf| |jvmStrict| + |lifting| |empty?| |normalizeIfCan| |leftLcm| |expt| |graphImage| + |roughSubIdeal?| |ptFunc| |low| |minPol| |trim| |pointLists| |slex| + |getVariableOrder| |iifact| |mulmod| |interReduce| |numberOfHues| + |realEigenvalues| |delete!| |unrankImproperPartitions1| |init| |unit| + |reducedContinuedFraction| |rightRecip| |sncndn| |integerBound| + |OMconnOutDevice| |leaves| |ScanRoman| |addiag| |headRemainder| + |integrate| |iisec| |eigenvalues| |nthExponent| |convert| |ptree| + |subresultantSequence| |inRadical?| |equality| |lookupFunction| + |sinIfCan| |conjug| |traverse| |inspect| |dihedral| + |jvmInterfaceMethodConstantTag| |null| |wholeRagits| |hasSolution?| + |algebraicDecompose| |argumentList!| |jvmLongConstantTag| |setStatus| + |viewport3D| |subMatrix| |wholePart| |antiAssociative?| |divideIfCan| + |spherical| |intPatternMatch| |not| |recur| |partialFraction| + |typeForm| |symmetricProduct| |getCode| |showRegion| |c05nbf| + |solveRetract| |varselect| |f04qaf| |f04mbf| |and| |prinshINFO| |inR?| + |polyPart| |d02bbf| |asimpson| |tan2trig| |divideExponents| + |reduceBasisAtInfinity| |d01alf| |triangularSystems| |eigenvector| + |cycleTail| |bracket| |optional?| |internalDecompose| + |basisOfRightNucloid| |singularAtInfinity?| |maxColIndex| |besselJ| + |newline| |index?| |shufflein| |edf2ef| |last| |putColorInfo| + |palginfieldint| |rootKerSimp| |prinb| |squareFreeLexTriangular| + |fintegrate| |subResultantGcdEuclidean| |extension| |solve1| |assoc| + |numerators| |OMUnknownCD?| |mindegTerm| |byteBuffer| |asecIfCan| + |binaryFunction| |readLine!| |moreAlgebraic?| |qfactor| |compose| + |multisect| |setClipValue| |cycles| |evaluate| |subResultantGcd| + |cAcoth| |coth2tanh| |UP2ifCan| |hypergeometric0F1| + |constantCoefficientRicDE| |sizeLess?| |key?| |OMopenString| |belong?| + |OMputEndObject| |f01qdf| |variationOfParameters| |disjunction| + |hdmpToP| |asechIfCan| |d01aqf| |failed| |setsubMatrix!| + |rightQuotient| |prime| |drawCurves| |reify| |pol| + |irreducibleFactors| |domainTemplate| + |setLegalFortranSourceExtensions| |curry| |useEisensteinCriterion?| + |gcdprim| |functionIsOscillatory| |distdfact| |padicallyExpand| + |outputAsScript| |connectTo| |setnext!| + |rewriteSetByReducingWithParticularGenerators| |collectQuasiMonic| + |qelt| |matrixGcd| |nthRoot| |s14aaf| |subResultantsChain| + |rowEchelonLocal| |viewDeltaYDefault| |eval| |indicialEquation| + |startPolynomial| |e02baf| |cTan| |qsetelt| |capacity| + |parabolicCylindrical| |elaborateFile| |stoseSquareFreePart| + |balancedBinaryTree| |rightRemainder| |addMatchRestricted| |cCot| + |rewriteIdealWithRemainder| |ref| |xRange| |systemSizeIF| + |perfectNthPower?| |jvmStatic| |queue| |pr2dmp| |nil?| |pushup| + |selectOptimizationRoutines| |setTex!| |invertibleSet| |yRange| + |limit| |recoverAfterFail| |invmod| |s14baf| |nand| |lfunc| + |basisOfLeftNucleus| |modTree| |zeroSquareMatrix| |palgextint| + |trueEqual| |mainVariables| |accuracyIF| |zRange| |freeOf?| + |increasePrecision| |critB| |variable| |cn| |leadingTerm| |rank| ** + |palgint0| |credPol| |fractRadix| |choosemon| |algebraic?| + |completeHensel| |map!| |mapMatrixIfCan| |matrixConcat3D| |iterators| + |defineProperty| |lfinfieldint| |semiResultantEuclidean1| + |degreeSubResultantEuclidean| |setMinPoints| |chebyshevU| + |alphanumeric| |viewWriteDefault| |qsetelt!| |intermediateResultsIF| + |monicCompleteDecompose| |OMserve| |uniform| |exponential1| + |aQuadratic| |pair| |acothIfCan| |logical?| |c06ebf| |inverseLaplace| + |bernoulli| |getProperty| |nextPrime| |LyndonCoordinates| + |roughUnitIdeal?| |diagonal| |OMputError| |internalSubQuasiComponent?| + |unrankImproperPartitions0| |simpleBounds?| |tanh2coth| |factor1| + |OMreceive| |keys| |tubePointsDefault| |antiCommutator| |s19abf| + |oddlambert| |fixedDivisor| |stopTable!| |separant| + |fortranCarriageReturn| |headAst| |UnVectorise| |baseRDEsys| + |ramifiedAtInfinity?| |pastel| |permutations| |Gamma| |OMputEndAttr| + |generic?| |symmetricPower| |insertMatch| |gbasis| |derivative| + |newReduc| |upDateBranches| |acsch| |isAtom| |createNormalElement| + |showArrayValues| |ip4Address| |addPointLast| |Lazard| |find| + |OMgetAttr| |OMgetString| |palgintegrate| |nil| |rightPower| + |branchIfCan| |var1Steps| |symmetricSquare| |bipolarCylindrical| + |vertConcat| |eulerE| |callForm?| |properties| |limitedint| + |monomialIntegrate| |imagE| |OMsend| |writeUInt8!| |numer| |unparse| + |mathieu24| |addMatch| |internal?| |vspace| |setProperty| |cAtan| + |translate| |cyclic?| |meatAxe| |countRealRoots| |denom| |curveColor| + |isMult| |pToHdmp| |SturmHabichtSequence| |restorePrecision| |escape| + |chiSquare1| |approximate| |subspace| |odd?| |sh| |lift| |doubleDisc| + |exactQuotient!| |roman| |epilogue| |pack!| |alphabetic| |complex| + |rotatex| |karatsubaDivide| |e04dgf| |orbits| |pi| |reduce| |inc| + |dimensionOfIrreducibleRepresentation| |pointColor| |getOperands| + |closedCurve?| |iiatan| |HenselLift| |cTanh| |e04jaf| |errorInfo| + |pushdown| |infinity| |linearlyDependentOverZ?| |iitan| |complexSolve| + |mappingMode| |rationalPoints| |localAbs| |extendIfCan| + |listRepresentation| |firstDenom| |specialTrigs| |times!| + |leftScalarTimes!| |nary?| |setFieldInfo| |nextColeman| |stirling2| + |nextLatticePermutation| |henselFact| |partialQuotients| |more?| + |bernoulliB| |mainDefiningPolynomial| |e02bcf| |s21bdf| + |wordInGenerators| |primeFrobenius| |swap| |writable?| |charthRoot| + |separateFactors| |completeSmith| |any?| |kernel| |getButtonValue| + |fi2df| |rdregime| |mainVariable?| |pdf2ef| |adaptive| |intcompBasis| + |c06gcf| |exactQuotient| |list| |OMclose| |setRow!| |removeSinSq| + |sturmVariationsOf| |coefChoose| |extract!| |mkcomm| |LiePoly| + |pseudoQuotient| |draw| |minset| |nsqfree| |flexibleArray| |push!| + |upperCase?| |currentEnv| |logpart| |carriageReturn| |rootPoly| + |returnTypeOf| |leastAffineMultiple| |OMgetBVar| |ffactor| + |OMgetVariable| |s18aff| |monomRDE| |order| |intersect| |finiteBasis| + |s14abf| |deleteProperty!| |hermite| |droot| |binomial| |refine| + |mathieu23| |quoted?| |root| |insertTop!| |wrregime| |seriesSolve| + |lepol| |lowerCase?| |selectOrPolynomials| |clearDenominator| + |karatsuba| |legendre| |prime?| |moduloP| |makeObject| + |leadingExponent| |categoryMode| |tubePlot| |jvmPrivate| |f07aef| + |bag| |iprint| |purelyAlgebraicLeadingMonomial?| + |createLowComplexityTable| |upperCase| |relativeApprox| |car| + |semiSubResultantGcdEuclidean2| |clearTheSymbolTable| |coef| |call| + |superHeight| |drawToScale| |semiDegreeSubResultantEuclidean| + |legendreP| |heap| |forLoop| |infieldint| |overlap| |number?| + |perfectSqrt| |tanAn| |factorSquareFreePolynomial| |lfextendedint| + |dequeue!| |byte| |lllip| |numberOfComponents| |rightTraceMatrix| + |lowerCase| |extend| |rightRankPolynomial| |showClipRegion| |d02kef| + |findCycle| |c05pbf| |nthFractionalTerm| |irreducibleFactor| + |parabolic| |palgRDE| |stronglyReduce| |basisOfRightAnnihilator| + |algebraicOf| |lazyGintegrate| |selectAndPolynomials| + |componentUpperBound| |ksec| |RittWuCompare| |knownInfBasis| |expint| + |viewSizeDefault| |exprHasWeightCosWXorSinWX| + |genericRightMinimalPolynomial| |computePowers| |torsionIfCan| + |rightTrim| |print| |viewDefaults| |insertBottom!| + |resultantReduitEuclidean| |algint| |lfintegrate| |genus| |cAsec| + |complexZeros| |whatInfinity| |leftTrim| |resolve| |mainContent| + |matrixDimensions| |clipBoolean| |optimize| |s17dgf| |OMgetEndAttr| + |push| |external?| |genericLeftTrace| |solve| |tablePow| + |systemCommand| |hasPredicate?| |partitions| |univariate?| |hasHi| + |super| |setMaxPoints| |e04mbf| |primes| |shiftRoots| |linearForm| + |cotIfCan| |augment| |radicalSolve| |transcendentalDecompose| |int| + |elliptic?| |rotatey| |jacobi| |normal| |OMgetObject| |OMputBVar| + |rightDivide| |groebSolve| |symFunc| |limitedIntegrate| |yCoord| + |sumOfDivisors| |sum| |iiacsc| |regime| |generator| |untab| + |sinhIfCan| |iteratedInitials| |closed| |setref| |numberOfMonomials| + |getOrder| |complexIntegrate| |coerceP| |removeConstantTerm| + |fractRagits| |jokerMode| |parametersOf| |eq?| |scopes| |integers| + |SturmHabichtMultiple| |upperCase!| |commonDenominator| |rules| + |stiffnessAndStabilityOfODEIF| |alternating| |zoom| |ratDsolve| + |trivialIdeal?| |environment| |physicalLength!| |selectfirst| + |position!| |OMreadStr| |bits| |exQuo| |modifyPointData| |elseBranch| + |reverseLex| |antisymmetricTensors| |midpoint| |purelyAlgebraic?| + |ipow| |e02def| |primitivePart| |primitivePart!| |product| |exprToUPS| + |multiset| |toScale| |iisinh| |normalizeAtInfinity| |cos2sec| + |outputMeasure| |rk4f| |imagI| |printInfo| |perfectNthRoot| + |compound?| |increase| |nonQsign| + |removeRoughlyRedundantFactorsInPols| |mapExpon| |minimumExponent| + |abelianGroup| |condition| |sin2csc| |output| |rightExactQuotient| + |getOperator| |explicitEntries?| |extractIfCan| |unknown| |testDim| + |screenResolution3D| |getIdentifier| |squareMatrix| |fortranLiteral| + |test| |pquo| |makeFR| |blue| |e02agf| |initials| |elliptic| |aLinear| + |sumOfKthPowerDivisors| |viewPosDefault| |mesh?| |SFunction| + |gramschmidt| |mpsode| |e02adf| |viewThetaDefault| |erf| |weight| + |iitanh| |cubic| |aQuartic| |delete| |viewport2D| + |generalizedEigenvectors| |expand| |iiasech| |universe| + |stoseInvertible?| |multiEuclideanTree| |jvmClassConstantTag| + |pushuconst| |euler| |iibinom| |putProperty| |bezoutResultant| |incr| + |filterWhile| |irreducible?| |getZechTable| |zeroDimensional?| + |rCoord| |li| |connect| |predicate| |setleft!| |squareFreeFactors| + |makeCrit| |list?| |d01amf| |hi| |filterUntil| |scaleRoots| |bottom!| + |cot2trig| |wronskianMatrix| |overlabel| |dilog| |square?| + |jvmInterface| |headReduced?| |taylorQuoByVar| |select| + |conditionsForIdempotents| |virtualDegree| |ceiling| |reducedSystem| + |mightHaveRoots| |sin| |formula| |minordet| |deepestTail| |nlde| + |diagonalMatrix| |constant| |stopTableGcd!| |setErrorBound| |birth| + |conical| |rightExtendedGcd| |cos| |lieAlgebra?| + |standardBasisOfCyclicSubmodule| |flexible?| |units| + |genericRightDiscriminant| |trace2PowMod| |quadratic?| |nthr| + |ParCondList| |quatern| |tan| |yellow| |zero| |normalizedDivide| + |unaryFunction| |trailingCoefficient| |ode2| |hcrf| + |complexEigenvectors| |divisorCascade| |numberOfComputedEntries| |cot| + |iiexp| |hasoln| |e02ahf| |mainExpression| |d01gaf| |rootBound| + |s17agf| |OMputInteger| |aromberg| |getMeasure| |sec| |jvmTransient| + |And| |readIfCan!| |rootProduct| |cAcsch| |reseed| |nrows| |rational| + |monicRightDivide| |rischDEsys| |e02ddf| |padecf| |csc| |meshPar1Var| + |Or| |constant?| |fortranCharacter| |writeInt8!| |complement| |ncols| + |makeRecord| |shiftLeft| |member?| |initTable!| + |lastSubResultantEuclidean| |lazyPquo| |asin| |code| + |coerceListOfPairs| |Not| |clipPointsDefault| |coercePreimagesImages| + |binaryTournament| |unary?| |interpretString| |next| |lexico| + |increment| |realSolve| |acos| |parameters| |harmonic| |cAsinh| + |enqueue!| |showTheIFTable| |assert| |changeMeasure| |arrayStack| + |fortranReal| |extendedResultant| |lazyPseudoDivide| |atan| + |setOfMinN| |inverse| |userOrdered?| |expandTrigProducts| + |primlimintfrac| |fillPascalTriangle| |aCubic| |merge| |magnitude| + |acot| |mathieu11| |kroneckerDelta| |associator| + |subscriptedVariables| |e02dcf| |hconcat| |startTableInvSet!| + |whileLoop| |setfirst!| |continue| |asec| |showTheSymbolTable| + |sayLength| |pureLex| |tryFunctionalDecomposition| |generate| + |bringDown| |cothIfCan| |pointData| |nextNormalPrimitivePoly| + |fixedPoints| |acsc| |identity| |palglimint| |d02cjf| |part?| |say| + |numberOfFractionalTerms| |quote| |child?| |linearDependence| |e01sef| + |dark| |sinh| |cCosh| |complex?| |incrementBy| |errorKind| + |rightFactorIfCan| |linearlyDependent?| |lineColorDefault| + |removeIrreducibleRedundantFactors| |leftCharacteristicPolynomial| + |bat1| |minPoints| |probablyZeroDim?| |exportedOperators| |cosh| + |setImagSteps| |removeRoughlyRedundantFactorsInContents| + |clearTheIFTable| |nthRootIfCan| |in?| |prepareDecompose| EQ |iiasec| + |setprevious!| |cCos| |sech2cosh| |rotate| |representationType| |tanh| + |iiGamma| |e01saf| |iisin| |halfExtendedResultant1| |ratDenom| |radix| + |simpsono| |paren| |lowerCase!| |genericLeftNorm| |complexLimit| + |coth| |kernels| |remainder| |factorList| |c06ekf| |parents| + |closedCurve| |alternative?| |returns| |f01brf| |jvmDoubleConstantTag| + |univariatePolynomial| |sech| |eigenvectors| |lexTriangular| + |operator| |makeSUP| |compBound| |packageCall| |associatorDependence| + |squareFreePart| |cAcsc| |internalInfRittWu?| |csch| |bothWays| + |mergeDifference| |univariate| |OMlistSymbols| + |stripCommentsAndBlanks| |ramified?| |coshIfCan| |squareTop| + |indicialEquations| |ratpart| |squareFreePolynomial| |asinh| + |chainSubResultants| |HermiteIntegrate| |red| |psolve| + |combineFeatureCompatibility| |rootOf| |iiatanh| |children| + |OMencodingUnknown| |radicalEigenvalues| |acosh| |deepCopy| + |outputFixed| |sumSquares| |mapUnivariateIfCan| |normInvertible?| + |subPolSet?| |diff| |tanIfCan| |cAcos| |c06gsf| |atanh| |f02abf| + |factorFraction| |factor| |continuedFraction| |acosIfCan| |asinIfCan| + |maxPoints3D| |bubbleSort!| |weights| |jordanAlgebra?| |acoth| + |stoseInvertibleSetreg| |sqrt| |lexGroebner| |viewZoomDefault| + |ParCond| |prinpolINFO| |integral| |nativeModuleExtension| + |readUInt16!| |atanIfCan| |asech| |reducedQPowers| |nothing| |real| + |setEmpty!| |BumInSepFFE| |binding| |showSummary| |jvmNative| + |fracPart| |e01daf| |isEquiv| |numberOfVariables| |outputFloating| + |imag| |pair?| |oddintegers| |infinite?| |leader| + |selectNonFiniteRoutines| |Ci| |OMgetEndBind| |d02bhf| |mapmult| + |multiple| |directProduct| |f01qef| |concat| |discreteLog| + |transcendenceDegree| |highCommonTerms| + |functionIsContinuousAtEndPoints| |showAttributes| |id| |OMconnectTCP| + |Beta| |rightMinimalPolynomial| |replaceKthElement| |applyQuote| + |ravel| |sdf2lst| |numericalIntegration| |OMsupportsCD?| + |collectUpper| |pointColorPalette| |commutativeEquality| |lo| + |stoseInvertibleSetsqfreg| |before?| F2FG |readBytes!| |reshape| + |brace| |nullity| |halfExtendedSubResultantGcd1| |zCoord| |ldf2vmf| + |compiledFunction| |f02aef| |step| |df2ef| |swapRows!| |sparsityIF| + |drawComplex| |destruct| |nextSublist| |extractClosed| |putProperties| + |internalAugment| |useEisensteinCriterion| |indiceSubResultant| + |ruleset| |pointPlot| |att2Result| |numberOfPrimitivePoly| + |screenResolution| |baseRDE| |norm| |completeEval| + |solveLinearlyOverQ| |symbolTable| |backOldPos| |underscore| + |useSingleFactorBound?| |areEquivalent?| |semicolonSeparate| + |fortranTypeOf| |leftQuotient| |newSubProgram| + |semiResultantReduitEuclidean| |basisOfLeftAnnihilator| |mat| + |symmetricGroup| |second| |parts| |sub| |toseInvertible?| |asinhIfCan| + |viewpoint| |pushFortranOutputStack| |suchThat| |makeSketch| + |monomial| |subQuasiComponent?| |d02gaf| |setRealSteps| |s17def| + |noKaratsuba| |third| |clipSurface| |popFortranOutputStack| + |physicalLength| |bitLength| |multivariate| |hasTopPredicate?| + |unmakeSUP| |primintegrate| |totalDegree| |integralDerivationMatrix| + |nextPrimitiveNormalPoly| |outputAsFortran| |modularGcdPrimitive| + |variables| |sort| |quasiAlgebraicSet| |bumptab1| |diagonalProduct| + |factorGroebnerBasis| |jvmSuper| |LagrangeInterpolation| + |viewWriteAvailable| |getDatabase| |primextintfrac| |exprex| |char| + |hclf| |directory| |top!| |linkToFortran| |irDef| |ignore?| + |jvmStringConstantTag| |random| |jvmFieldrefConstantTag| |signature| + |adaptive3D?| |size?| |iicosh| |elem?| |operation| |value| + |getPickedPoints| |linGenPos| |multiplyExponents| |hostByteOrder| + |octon| |secIfCan| |subtractIfCan| |f04adf| |elementary| + |colorFunction| |nthCoef| |iiasin| |leviCivitaSymbol| |goodnessOfFit| + |explicitlyEmpty?| |bandedJacobian| |leftReducedSystem| |taylor| + |e04naf| |float| |problemPoints| |degree| |dom| |s17dhf| |rubiksGroup| + |fractionFreeGauss!| |symmetric?| |vectorise| |laurent| + |nonSingularModel| |antisymmetric?| |typeLists| |obj| |rootSplit| + |edf2efi| |iiasinh| |powerSum| |addmod| |puiseux| |cAcot| |atoms| + |closed?| |branchPoint?| |diag| |stoseInvertible?reg| |unit?| |cfirst| + |zag| |irreducibleRepresentation| |decimal| |mapExponents| |op| + |OMgetApp| |ddFact| |laurentRep| |inv| |minimumDegree| |point?| + |integralBasisAtInfinity| |shallowExpand| |localUnquote| + |createNormalPoly| |vector| |positive?| |reduced?| |medialSet| + |ground?| |prindINFO| |setUnion| |compdegd| |oddInfiniteProduct| + |vedf2vef| |coerceS| |differentiate| |less?| |rightDiscriminant| + |bumptab| |ground| |unitNormal| |s17acf| |htrigs| |cSin| + |possiblyInfinite?| |subst| |zeroMatrix| |bfEntry| |isList| + |leadingMonomial| |An| |s20acf| |dictionary| |printCode| + |expenseOfEvaluationIF| |s13aaf| |f02axf| + |zeroSetSplitIntoTriangularSystems| |npcoef| |leadingCoefficient| GE + |edf2fi| |cAsech| |rightUnit| |hermiteH| |denominators| |normalDenom| + |numberOfNormalPoly| |null?| |OMunhandledSymbol| |primitiveMonomials| + GT |distribute| |topFortranOutputStack| |conjunction| |mainVariable| + |neglist| |quadratic| |inrootof| |qroot| |fullPartialFraction| |over| + |diagonals| |reductum| LE |clearFortranOutputStack| |label| + |rangePascalTriangle| |iterationVar| |modulus| |shallowCopy| + |elColumn2!| |objects| |mainValue| |internalZeroSetSplit| |reorder| + |stoseIntegralLastSubResultant| LT |basisOfMiddleNucleus| |sn| + |normalDeriv| |OMgetFloat| |exprToXXP| |Frobenius| |dflist| |base| + |PDESolve| |logIfCan| |cRationalPower| |prologue| |leftAlternative?| + |setFormula!| |leftNorm| |c06fpf| |hitherPlane| |tanQ| |meshPar2Var| + |palgint| |d01gbf| |zeroDimPrimary?| |hessian| |light| + |complexElementary| |kovacic| |c02agf| |patternMatch| |rarrow| UTS2UP + |represents| |definingInequation| |createPrimitiveNormalPoly| + |euclideanGroebner| |OMgetType| |OMcloseConn| |OMreadFile| + |makeVariable| |OMgetInteger| |setPoly| |coth2trigh| |minIndex| + |determinant| |brillhartTrials| |tracePowMod| |univcase| |upperBound| + |f04atf| |delta| |option| |fortranDouble| |postfix| |redmat| + |GospersMethod| |lazyEvaluate| |linefeed| |categoryFrame| |error| + |leftMult| |iicoth| |polygon?| |clearTheFTable| |consnewpol| + |getProperties| |innerEigenvectors| |primitiveElement| + |stoseLastSubResultant| |resetVariableOrder| |symbolIfCan| |f02aff| + |f04faf| |isPlus| |sec2cos| |removeDuplicates!| |printHeader| + |ODESolve| |library| |nodeOf?| |OMputVariable| |mainForm| |backspace| + |roughBase?| |jordanAdmissible?| |heapSort| |sylvesterSequence| + |mainCharacterization| |coerce| |box| |hash| |cyclicEqual?| |e02ajf| + |search| |currentCategoryFrame| |explimitedint| |LiePolyIfCan| + |bivariatePolynomials| |clearTable!| |decrease| + |constantToUnaryFunction| |count| |OMwrite| |mkPrim| |noValueMode| + |roughEqualIdeals?| |bezoutDiscriminant| |composites| + |derivationCoordinates| |expressIdealMember| |sort!| |f02adf| + |OMgetEndAtp| |cdr| |isOr| |showAll?| |retract| |iiacsch| + |binomThmExpt| |polyRicDE| |firstUncouplingMatrix| |d01fcf| + |stoseInternalLastSubResultant| |function| |OMParseError?| + |allRootsOf| |multinomial| |lastSubResultantElseSplit| |previous| + |rightOne| |unitNormalize| |coefficients| |prepareSubResAlgo| + |var2StepsDefault| |lambda| |s19aaf| |plenaryPower| |exprToGenUPS| + |maxdeg| |resetAttributeButtons| |leftPower| |createZechTable| + |generalPosition| |clikeUniv| |ran| |isNot| |totalDifferential| + |permutation| |makeFloatFunction| |approximants| |s18dcf| |checkRur| + |euclideanNormalForm| |fortranLinkerArgs| |identification| + |sturmSequence| |entry| |pattern| |polarCoordinates| |findConstructor| + |linearAssociatedExp| |s19acf| |cache| |po| |makeTerm| + |factorSFBRlcUnit| |countRealRootsMultiple| |shape| |hexDigit?| + |s13acf| |nextItem| |linearDependenceOverZ| |basisOfCenter| |linear| + |shuffle| |mathieu22| |vark| |horizConcat| |idealSimplify| + |complexNormalize| |myDegree| |gderiv| |horizontalTab| + |expenseOfEvaluation| |reset| |countable?| |optpair| |elRow1!| + |denomLODE| |point| |shrinkable| |anfactor| |quotient| |column| |tube| + |plusInfinity| |bitCoef| |cPower| |polynomial| |normalizedAssociate| + |insertionSort!| |principal?| |anticoord| |palglimint0| |mapSolve| + |setelt| |oneDimensionalArray| |externalList| |minusInfinity| + |factorials| |e02gaf| |write| |realEigenvectors| |startStats!| + |factorByRecursion| |semiResultantEuclideannaif| |zerosOf| |e04gcf| + |copy| |changeNameToObjf| |leastPower| |save| |enterInCache| + |noLinearFactor?| |solveLinearPolynomialEquationByRecursion| + |startTableGcd!| |sts2stst| |series| |doubleRank| |paraboloidal| + |autoCoerce| |latex| |open?| |show| |directSum| |dominantTerm| + |rootDirectory| |usingTable?| |palgLODE0| |unexpand| |dequeue| + |numFunEvals| |lprop| |pointSizeDefault| |extractTop!| |e01bhf| + |OMputAttr| |debug3D| |createNormalPrimitivePoly| |complete| |lcm| + |integral?| |lazyPseudoQuotient| |identitySquareMatrix| |tanNa| BY + |trace| |createPrimitiveElement| |critpOrder| |cardinality| + |coerceImages| |critBonD| |makeViewport3D| |dec| |top| |zeroDimPrime?| + |resultantEuclidean| |factorAndSplit| |powern| |type| + |purelyTranscendental?| |block| |trigs2explogs| |Si| |bivariate?| + |gcd| |min| |stiffnessAndStabilityFactor| |checkForZero| |polyRDE| + |eigenMatrix| |exp| |reflect| |ScanFloatIgnoreSpacesIfCan| |negative?| + |generalInfiniteProduct| |maxrow| |false| |iiperm| + |createMultiplicationTable| |safeCeiling| |outputSpacing| |depth| + |outputAsTex| |space| |even?| |euclideanSize| |imagj| |gensym| + |update| |double| |generalLambert| |leadingIdeal| |viewDeltaXDefault| + |basisOfRightNucleus| |precision| |Aleph| |sequence| + |rootOfIrreduciblePoly| |vconcat| |reverse| |fortranCompilerName| + |rational?| |jacobian| |univariatePolynomials| |factorial| |addPoint2| + |currentSubProgram| |computeCycleEntry| |shade| |reverse!| |repeating| + |cross| |argument| |getGoodPrime| |ldf2lst| |constantOperator| + |factorSquareFree| |nextsousResultant2| |printingInfo?| NOT FG2F + |decomposeFunc| |c02aff| |orthonormalBasis| |leftUnits| + |exprHasLogarithmicWeights| |c06gbf| |rightCharacteristicPolynomial| + |e02zaf| OR |append| |mantissa| |setButtonValue| |duplicates| + |halfExtendedResultant2| |badNum| |select!| |clip| |readInt16!| + |cosIfCan| |signatureAst| AND |removeDuplicates| |listLoops| |normal?| + |graphCurves| |unknownEndian| |inverseIntegralMatrixAtInfinity| + |expPot| |supRittWu?| |element?| F |firstSubsetGray| |monicLeftDivide| + |removeRoughlyRedundantFactorsInPol| |numerator| |ode1| |cap| + |numberOfIrreduciblePoly| |cyclotomic| |validExponential| |submod| + |internalIntegrate0| |substitute| |isConnected?| |atanhIfCan| + |declare!| |rewriteIdealWithQuasiMonicGenerators| |color| + |integralMatrix| |numeric| |mergeFactors| |powers| |maxIndex| + |univariatePolynomialsGcds| |encodingDirectory| |d01akf| + |inconsistent?| |jvmFloatConstantTag| |lazyVariations| |radical| + |rk4qc| |wholeRadix| |scanOneDimSubspaces| |s17dcf| |RemainderList| + |setDifference| |middle| |normalized?| |rightScalarTimes!| + |minColIndex| |associatedEquations| |contract| |support| |debug| + |lazyPrem| |constantIfCan| |prefixRagits| |open| |antiCommutative?| + |characteristicSerie| |coord| |randomR| |elaborate| + |branchPointAtInfinity?| |romberg| D |splitDenominator| |getlo| + |principalIdeal| |reindex| |f01rcf| |numberOfCycles| |outputForm| + |copyInto!| |fortranLogical| |commutator| |basis| |pop!| |fill!| + |void| |stop| |processTemplate| |listYoungTableaus| |f02fjf| + |acscIfCan| |multiEuclidean| |genericLeftTraceForm| + |internalSubPolSet?| |OMmakeConn| |putGraph| |OMputString| |remove| + |setMaxPoints3D| Y |B1solve| |distance| |nextsubResultant2| |any| + |reduceLODE| |simplify| |palgextint0| |simpson| * |operations| |rk4| + |createRandomElement| |segment| |range| |createPrimitivePoly| + |fortranDoubleComplex| |insertRoot!| |algSplitSimple| + |changeThreshhold| |extractProperty| |readInt32!| |setleaves!| + |chiSquare| |fixPredicate| |basicSet| |rightNorm| |category| |iiacoth| + |setPrologue!| |df2st| |thenBranch| |prem| |showIntensityFunctions| + |pade| |gradient| |domain| |module| |selectFiniteRoutines| |singular?| + |cosSinInfo| |BasicMethod| |OMbindTCP| |exponential| = |rightUnits| + |getCurve| |zero?| |tree| |package| |lyndon| |setAdaptive| |host| + |taylorIfCan| |clearCache| |dmpToHdmp| |fractionPart| |removeSinhSq| + |iidprod| |endSubProgram| |bindings| |laplacian| |LyndonBasis| + |expIfCan| |lowerBound| |separate| |iidsum| |isobaric?| + |createGenericMatrix| < |setIntersection| |OMgetEndError| |intensity| + |leftMinimalPolynomial| |unitsColorDefault| |critMTonD1| |triangSolve| + |OMencodingXML| > |ef2edf| |invmultisect| |imagK| |extendedint| + |tanintegrate| |rationalPoint?| |parseString| |t| |digamma| |entries| + |tanSum| |bounds| <= |leftExactQuotient| |quasiMonicPolynomials| |ode| + |reduction| |certainlySubVariety?| |binary| |round| |inverseColeman| + |nthExpon| |OMputObject| |OMputSymbol| >= |s18aef| |roughBasicSet| + |constructor| |rquo| |lflimitedint| |d01ajf| |palgRDE0| |se2rfi| + |s18acf| |mesh| |isAbsolutelyIrreducible?| |mirror| |relationsIdeal| + |algDsolve| |pile| |contours| |sincos| |integerIfCan| + |brillhartIrreducible?| |denominator| |inHallBasis?| |pseudoDivide| + |makeprod| |partialNumerators| |maxPoints| |qinterval| + |algebraicVariables| |rootsOf| |tValues| |c06frf| + + |tryFunctionalDecomposition?| |interval| |dmpToP| |iomode| + |flagFactor| |reopen!| |readInt8!| |ideal| |cyclicEntries| |qqq| - + |pomopo!| |infRittWu?| |rdHack1| |fortranInteger| |f04maf| + |signAround| |copy!| |addBadValue| / |repSq| |characteristicSet| + |predicates| |Nul| |exptMod| |double?| |phiCoord| |name| |cAcosh| + |numericalOptimization| |plotPolar| |meshFun2Var| |e02akf| |construct| + |cyclicParents| |setPosition| |character?| |leftRecip| |leftRemainder| + |body| |rewriteSetWithReduction| |separateDegrees| |acoshIfCan| + |selectODEIVPRoutines| |outlineRender| |quoByVar| |moduleSum| + |primlimitedint| |failed?| |monomials| |associates?| + |toseInvertibleSet| |subNode?| |adjoint| |trigs| |verticalTab| |pdct| + |weighted| |length| |factorsOfDegree| |seed| |minimize| |e02dff| + |toseSquareFreePart| |relerror| |outputArgs| |factorset| |bat| + |laguerre| |totalGroebner| |youngDiagram| |insert!| |scripts| + |randomLC| |dimension| |goto| |infieldIntegrate| |totolex| + |triangulate| |mathieu12| |factorOfDegree| |csch2sinh| |ReduceOrder| + |kind| SEGMENT |weierstrass| |extractIndex| |cyclicCopy| |xn| |f07adf| + |leftRank| |balancedFactorisation| |create| |wreath| |nilFactor| + |voidMode| |s17aef| |isPower| |head| |jvmVolatile| |rightGcd| + |idealiser| |printStats!| |tower| |setVariableOrder| |nextSubsetGray| + |dual| |normalize| |cschIfCan| |Vectorise| |littleEndian| + |powerAssociative?| |linearElement| |members| |tableau| |rootPower| + |basisOfLeftNucloid| |zeroDim?| |divisor| |makingStats?| |enumerate| + |radicalSimplify| |scalarTypeOf| |setelt!| |stopTableInvSet!| + |quartic| |homogeneous?| |jvmSynchronized| |atom?| |solid| + |fprindINFO| |nextPartition| |functorData| |nil| |infinite| + |arbitraryExponent| |approximate| |complex| |shallowMutable| + |canonical| |noetherian| |central| |partiallyOrderedSet| + |arbitraryPrecision| |canonicalsClosed| |noZeroDivisors| + |rightUnitary| |leftUnitary| |additiveValuation| |unitsKnown| + |canonicalUnitNormal| |multiplicativeValuation| |finiteAggregate| + |shallowlyMutable| |commutative|)
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|t#1| |t#1| |t#1|) $ $ |t#1|)))) +(((-34) . 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T) ((-23) . T) ((-25) . T) ((-38 #0=(-421 (-560))) -4144 (|has| |#1| (-363)) (|has| |#1| (-376))) ((-38 |#1|) . T) ((-38 $) -4144 (|has| |#1| (-571)) (|has| |#1| (-363)) (|has| |#1| (-376)) (|has| |#1| (-319))) ((-35) |has| |#1| (-1235)) ((-95) |has| |#1| (-1235)) ((-102) . T) ((-111 #0# #0#) -4144 (|has| |#1| (-363)) (|has| |#1| (-376))) ((-111 |#1| |#1|) . T) ((-111 $ $) . T) ((-133) . T) ((-147) -4144 (|has| |#1| (-363)) (|has| |#1| (-147))) ((-149) |has| |#1| (-149)) ((-635 #0#) -4144 (|has| |#1| (-1070 (-421 (-560)))) (|has| |#1| (-363)) (|has| |#1| (-376))) ((-635 (-560)) . T) ((-635 |#1|) . T) ((-635 $) -4144 (|has| |#1| (-571)) (|has| |#1| (-363)) (|has| |#1| (-376)) (|has| |#1| (-319))) ((-632 (-888)) . T) ((-175) . T) ((-633 (-171 (-229))) |has| |#1| (-1052)) ((-633 (-171 (-391))) |has| |#1| (-1052)) ((-633 (-549)) |has| |#1| (-633 (-549))) ((-633 (-916 (-391))) |has| |#1| (-633 (-916 (-391)))) ((-633 (-916 (-560))) |has| |#1| (-633 (-916 (-560)))) ((-633 #1=(-1203 |#1|)) . 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T) ((-23) . T) ((-25) . T) ((-38 #0=(-421 (-560))) -4118 (|has| |#1| (-363)) (|has| |#1| (-376))) ((-38 |#1|) . T) ((-38 $) -4118 (|has| |#1| (-571)) (|has| |#1| (-363)) (|has| |#1| (-376)) (|has| |#1| (-319))) ((-35) |has| |#1| (-1235)) ((-95) |has| |#1| (-1235)) ((-102) . T) ((-111 #0# #0#) -4118 (|has| |#1| (-363)) (|has| |#1| (-376))) ((-111 |#1| |#1|) . T) ((-111 $ $) . T) ((-133) . T) ((-147) -4118 (|has| |#1| (-363)) (|has| |#1| (-147))) ((-149) |has| |#1| (-149)) ((-635 #0#) -4118 (|has| |#1| (-1070 (-421 (-560)))) (|has| |#1| (-363)) (|has| |#1| (-376))) ((-635 (-560)) . T) ((-635 |#1|) . T) ((-635 $) -4118 (|has| |#1| (-571)) (|has| |#1| (-363)) (|has| |#1| (-376)) (|has| |#1| (-319))) ((-632 (-888)) . T) ((-175) . T) ((-633 (-171 (-229))) |has| |#1| (-1052)) ((-633 (-171 (-391))) |has| |#1| (-1052)) ((-633 (-549)) |has| |#1| (-633 (-549))) ((-633 (-916 (-391))) |has| |#1| (-633 (-916 (-391)))) ((-633 (-916 (-560))) |has| |#1| (-633 (-916 (-560)))) ((-633 #1=(-1203 |#1|)) . T) ((-236 $) -4118 (|has| |#1| (-363)) (|has| |#1| (-239)) (|has| |#1| (-240))) ((-234 |#1|) . T) ((-240) -4118 (|has| |#1| (-363)) (|has| |#1| (-240))) ((-239) -4118 (|has| |#1| (-363)) (|has| |#1| (-239)) (|has| |#1| (-240))) ((-274 |#1|) . T) ((-250) -4118 (|has| |#1| (-363)) (|has| |#1| (-376))) ((-296) |has| |#1| (-1235)) ((-298 |#1| $) |has| |#1| (-298 |#1| |#1|)) ((-302) -4118 (|has| |#1| (-571)) (|has| |#1| (-363)) (|has| |#1| (-376)) (|has| |#1| (-319))) ((-319) -4118 (|has| |#1| (-363)) (|has| |#1| (-376)) (|has| |#1| (-319))) ((-321 |#1|) |has| |#1| (-321 |#1|)) ((-376) -4118 (|has| |#1| (-363)) (|has| |#1| (-376))) ((-416) |has| |#1| (-363)) ((-381) -4118 (|has| |#1| (-381)) (|has| |#1| (-363))) ((-363) |has| |#1| (-363)) ((-383 |#1| #1#) . T) ((-424 |#1| #1#) . T) ((-351 |#1|) . T) ((-390 |#1|) . T) ((-414 |#1|) . T) ((-426 |#1|) . T) ((-466) -4118 (|has| |#1| (-363)) (|has| |#1| (-376)) (|has| |#1| (-319))) ((-507) |has| |#1| (-1235)) ((-528 (-1209) |#1|) |has| |#1| (-528 (-1209) |#1|)) ((-528 |#1| |#1|) |has| |#1| (-321 |#1|)) ((-571) -4118 (|has| |#1| (-571)) (|has| |#1| (-363)) (|has| |#1| (-376)) (|has| |#1| (-319))) ((-668 #0#) -4118 (|has| |#1| (-363)) (|has| |#1| (-376))) ((-668 (-560)) . T) ((-668 |#1|) . T) ((-668 $) . T) ((-670 #0#) -4118 (|has| |#1| (-363)) (|has| |#1| (-376))) ((-670 #2=(-560)) |has| |#1| (-660 (-560))) ((-670 |#1|) . T) ((-670 $) . T) ((-662 #0#) -4118 (|has| |#1| (-363)) (|has| |#1| (-376))) ((-662 |#1|) . T) ((-662 $) -4118 (|has| |#1| (-571)) (|has| |#1| (-363)) (|has| |#1| (-376)) (|has| |#1| (-319))) ((-660 #2#) |has| |#1| (-660 (-560))) ((-660 |#1|) . T) ((-739 #0#) -4118 (|has| |#1| (-363)) (|has| |#1| (-376))) ((-739 |#1|) . T) ((-739 $) -4118 (|has| |#1| (-571)) (|has| |#1| (-363)) (|has| |#1| (-376)) (|has| |#1| (-319))) ((-746 |#1| #1#) . T) ((-748) . T) ((-922 $ #3=(-1209)) -4118 (|has| |#1| (-930 (-1209))) (|has| |#1| (-928 (-1209)))) ((-928 (-1209)) |has| |#1| (-928 (-1209))) ((-930 #3#) -4118 (|has| |#1| (-930 (-1209))) (|has| |#1| (-928 (-1209)))) ((-912 (-391)) |has| |#1| (-912 (-391))) ((-912 (-560)) |has| |#1| (-912 (-560))) ((-910 |#1|) . T) ((-940) -12 (|has| |#1| (-319)) (|has| |#1| (-940))) ((-951) -4118 (|has| |#1| (-363)) (|has| |#1| (-376)) (|has| |#1| (-319))) ((-1034) -12 (|has| |#1| (-1034)) (|has| |#1| (-1235))) ((-1070 (-421 (-560))) |has| |#1| (-1070 (-421 (-560)))) ((-1070 (-560)) |has| |#1| (-1070 (-560))) ((-1070 |#1|) . T) ((-1083 #0#) -4118 (|has| |#1| (-363)) (|has| |#1| (-376))) ((-1083 |#1|) . T) ((-1083 $) . T) ((-1088 #0#) -4118 (|has| |#1| (-363)) (|has| |#1| (-376))) ((-1088 |#1|) . T) ((-1088 $) . T) ((-1081) . T) ((-1089) . T) ((-1144) . T) ((-1133) . T) ((-1184) |has| |#1| (-363)) ((-1235) |has| |#1| (-1235)) ((-1238) |has| |#1| (-1235)) ((-1249) . 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(|has| |#2| (-23)) (|has| |#2| (-21))) ((-34) . T) ((-102) -4118 (|has| |#2| (-1133)) (|has| |#2| (-1081)) (|has| |#2| (-872)) (|has| |#2| (-817)) (|has| |#2| (-748)) (|has| |#2| (-381)) (|has| |#2| (-376)) (|has| |#2| (-175)) (|has| |#2| (-133)) (|has| |#2| (-102)) (|has| |#2| (-25)) (|has| |#2| (-23)) (|has| |#2| (-21))) ((-111 |#2| |#2|) -4118 (|has| |#2| (-1081)) (|has| |#2| (-376)) (|has| |#2| (-175))) ((-133) -4118 (|has| |#2| (-1081)) (|has| |#2| (-817)) (|has| |#2| (-376)) (|has| |#2| (-175)) (|has| |#2| (-133)) (|has| |#2| (-21))) ((-635 #0=(-421 (-560))) -12 (|has| |#2| (-1070 (-421 (-560)))) (|has| |#2| (-1133))) ((-635 (-560)) -4118 (|has| |#2| (-1081)) (-12 (|has| |#2| (-1070 (-560))) (|has| |#2| (-1133)))) ((-635 |#2|) |has| |#2| (-1133)) ((-632 (-888)) -4118 (|has| |#2| (-1133)) (|has| |#2| (-1081)) (|has| |#2| (-872)) (|has| |#2| (-817)) (|has| |#2| (-748)) (|has| |#2| (-381)) (|has| |#2| (-376)) (|has| |#2| (-175)) (|has| |#2| (-632 (-888))) (|has| |#2| (-133)) (|has| |#2| (-25)) (|has| |#2| (-23)) (|has| |#2| (-21))) ((-632 (-1299 |#2|)) . T) ((-236 $) -4118 (-12 (|has| |#2| (-239)) (|has| |#2| (-1081))) (-12 (|has| |#2| (-240)) (|has| |#2| (-1081)))) ((-234 |#2|) |has| |#2| (-1081)) ((-240) -12 (|has| |#2| (-240)) (|has| |#2| (-1081))) ((-239) -4118 (-12 (|has| |#2| (-239)) (|has| |#2| (-1081))) (-12 (|has| |#2| (-240)) (|has| |#2| (-1081)))) ((-274 |#2|) |has| |#2| (-1081)) ((-298 #1=(-560) |#2|) . T) ((-300 #1# |#2|) . T) ((-321 |#2|) -12 (|has| |#2| (-321 |#2|)) (|has| |#2| (-1133))) ((-381) |has| |#2| (-381)) ((-390 |#2|) |has| |#2| (-1081)) ((-426 |#2|) |has| |#2| (-1133)) ((-503 |#2|) . T) ((-618 #1# |#2|) . T) ((-528 |#2| |#2|) -12 (|has| |#2| (-321 |#2|)) (|has| |#2| (-1133))) ((-668 (-560)) -4118 (|has| |#2| (-1081)) (|has| |#2| (-376)) (|has| |#2| (-175)) (|has| |#2| (-21))) ((-668 |#2|) -4118 (|has| |#2| (-1081)) (|has| |#2| (-748)) (|has| |#2| (-376)) (|has| |#2| (-175))) ((-668 $) |has| |#2| (-1081)) ((-670 #2=(-560)) -12 (|has| |#2| (-660 (-560))) (|has| |#2| (-1081))) ((-670 |#2|) -4118 (|has| |#2| (-1081)) (|has| |#2| (-376)) (|has| |#2| (-175))) ((-670 $) |has| |#2| (-1081)) ((-662 |#2|) -4118 (|has| |#2| (-748)) (|has| |#2| (-376)) (|has| |#2| (-175))) ((-660 #2#) -12 (|has| |#2| (-660 (-560))) (|has| |#2| (-1081))) ((-660 |#2|) |has| |#2| (-1081)) ((-739 |#2|) -4118 (|has| |#2| (-376)) (|has| |#2| (-175))) ((-748) |has| |#2| (-1081)) ((-816) |has| |#2| (-817)) ((-817) |has| |#2| (-817)) ((-818) |has| |#2| (-817)) ((-821) |has| |#2| (-817)) ((-872) -4118 (|has| |#2| (-872)) (|has| |#2| (-817))) ((-875) -4118 (|has| |#2| (-872)) (|has| |#2| (-817))) ((-922 $ #3=(-1209)) -4118 (-12 (|has| |#2| (-930 (-1209))) (|has| |#2| (-1081))) (-12 (|has| |#2| (-928 (-1209))) (|has| |#2| (-1081)))) ((-928 (-1209)) -12 (|has| |#2| (-928 (-1209))) (|has| |#2| (-1081))) ((-930 #3#) -4118 (-12 (|has| |#2| (-930 (-1209))) (|has| |#2| (-1081))) (-12 (|has| |#2| (-928 (-1209))) (|has| |#2| (-1081)))) ((-1070 #0#) -12 (|has| |#2| (-1070 (-421 (-560)))) (|has| |#2| (-1133))) ((-1070 (-560)) -12 (|has| |#2| (-1070 (-560))) (|has| |#2| (-1133))) ((-1070 |#2|) |has| |#2| (-1133)) ((-1083 |#2|) -4118 (|has| |#2| (-1081)) (|has| |#2| (-748)) (|has| |#2| (-376)) (|has| |#2| (-175))) ((-1088 |#2|) -4118 (|has| |#2| (-1081)) (|has| |#2| (-376)) (|has| |#2| (-175))) ((-1081) |has| |#2| (-1081)) ((-1089) |has| |#2| (-1081)) ((-1144) |has| |#2| (-1081)) ((-1133) -4118 (|has| |#2| (-1133)) (|has| |#2| (-1081)) (|has| |#2| (-872)) (|has| |#2| (-817)) (|has| |#2| (-748)) (|has| |#2| (-381)) (|has| |#2| (-376)) (|has| |#2| (-175)) (|has| |#2| (-133)) (|has| |#2| (-25)) (|has| |#2| (-23)) (|has| |#2| (-21))) ((-1249) . T) ((-1307 |#2|) |has| |#2| (-376))) +((-2211 (((-114) $ $) NIL (|has| |#2| (-102)) ELT)) (-4270 (((-114) $) NIL (|has| |#2| (-23)) ELT)) (-1888 (($ (-949)) 63 (|has| |#2| (-1081)) ELT)) (-1790 (((-1305) $ (-560) (-560)) NIL (|has| $ (-6 -4511)) ELT)) (-1880 (($ $ $) 69 (|has| |#2| (-817)) ELT)) (-3650 (((-3 $ "failed") $ $) 54 (|has| |#2| (-133)) ELT)) (-2255 (((-793)) NIL (|has| |#2| (-381)) ELT)) (-3983 ((|#2| $ (-560) |#2|) NIL (|has| $ (-6 -4511)) ELT)) (-2010 (($) NIL T CONST)) (-2416 (((-3 (-560) "failed") $) NIL (-12 (|has| |#2| (-1070 (-560))) (|has| |#2| (-1133))) ELT) (((-3 (-421 (-560)) "failed") $) NIL (-12 (|has| |#2| (-1070 (-421 (-560)))) (|has| |#2| (-1133))) ELT) (((-3 |#2| "failed") $) 31 (|has| |#2| (-1133)) ELT)) (-3894 (((-560) $) NIL (-12 (|has| |#2| (-1070 (-560))) (|has| |#2| (-1133))) ELT) (((-421 (-560)) $) NIL (-12 (|has| |#2| (-1070 (-421 (-560)))) (|has| |#2| (-1133))) ELT) ((|#2| $) 29 (|has| |#2| (-1133)) ELT)) (-3231 (((-711 (-560)) (-711 $)) NIL (-12 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T) ((-23) . T) ((-47 |#1| |#4|) . T) ((-25) . T) ((-38 #0=(-421 (-560))) |has| |#1| (-38 (-421 (-560)))) ((-38 |#1|) |has| |#1| (-175)) ((-38 $) -4144 (|has| |#1| (-940)) (|has| |#1| (-571)) (|has| |#1| (-466))) ((-102) . T) ((-111 #0# #0#) |has| |#1| (-38 (-421 (-560)))) ((-111 |#1| |#1|) . T) ((-111 $ $) -4144 (|has| |#1| (-940)) (|has| |#1| (-571)) (|has| |#1| (-466)) (|has| |#1| (-175))) ((-133) . T) ((-147) |has| |#1| (-147)) ((-149) |has| |#1| (-149)) ((-635 #0#) -4144 (|has| |#1| (-1070 (-421 (-560)))) (|has| |#1| (-38 (-421 (-560))))) ((-635 (-560)) . T) ((-635 |#1|) . T) ((-635 |#2|) . T) ((-635 |#3|) . T) ((-635 $) -4144 (|has| |#1| (-940)) (|has| |#1| (-571)) (|has| |#1| (-466))) ((-632 (-888)) . T) ((-175) -4144 (|has| |#1| (-940)) (|has| |#1| (-571)) (|has| |#1| (-466)) (|has| |#1| (-175))) ((-633 (-549)) -12 (|has| |#1| (-633 (-549))) (|has| |#3| (-633 (-549)))) ((-633 (-916 (-391))) -12 (|has| |#1| (-633 (-916 (-391)))) (|has| |#3| (-633 (-916 (-391))))) ((-633 (-916 (-560))) -12 (|has| |#1| (-633 (-916 (-560)))) (|has| |#3| (-633 (-916 (-560))))) ((-236 $) -4144 (|has| |#1| (-239)) (|has| |#1| (-240))) ((-234 |#1|) . T) ((-240) |has| |#1| (-240)) ((-239) -4144 (|has| |#1| (-239)) (|has| |#1| (-240))) ((-274 |#1|) . T) ((-302) -4144 (|has| |#1| (-940)) (|has| |#1| (-571)) (|has| |#1| (-466))) ((-321 $) . T) ((-338 |#1| |#4|) . T) ((-390 |#1|) . T) ((-426 |#1|) . T) ((-466) -4144 (|has| |#1| (-940)) (|has| |#1| (-466))) ((-528 |#2| |#1|) |has| |#1| (-240)) ((-528 |#2| $) |has| |#1| (-240)) ((-528 |#3| |#1|) . T) ((-528 |#3| $) . T) ((-528 $ $) . T) ((-571) -4144 (|has| |#1| (-940)) (|has| |#1| (-571)) (|has| |#1| (-466))) ((-668 #0#) |has| |#1| (-38 (-421 (-560)))) ((-668 (-560)) . T) ((-668 |#1|) . T) ((-668 $) . T) ((-670 #0#) |has| |#1| (-38 (-421 (-560)))) ((-670 #1=(-560)) |has| |#1| (-660 (-560))) ((-670 |#1|) . T) ((-670 $) . T) ((-662 #0#) |has| |#1| (-38 (-421 (-560)))) ((-662 |#1|) |has| |#1| (-175)) ((-662 $) -4144 (|has| |#1| (-940)) (|has| |#1| (-571)) (|has| |#1| (-466))) ((-660 #1#) |has| |#1| (-660 (-560))) ((-660 |#1|) . T) ((-739 #0#) |has| |#1| (-38 (-421 (-560)))) ((-739 |#1|) |has| |#1| (-175)) ((-739 $) -4144 (|has| |#1| (-940)) (|has| |#1| (-571)) (|has| |#1| (-466))) ((-748) . T) ((-922 $ #2=(-1209)) -4144 (|has| |#1| (-930 (-1209))) (|has| |#1| (-928 (-1209)))) ((-922 $ |#3|) . T) ((-928 (-1209)) |has| |#1| (-928 (-1209))) ((-928 |#3|) . T) ((-930 #2#) -4144 (|has| |#1| (-930 (-1209))) (|has| |#1| (-928 (-1209)))) ((-930 |#3|) . T) ((-912 (-391)) -12 (|has| |#1| (-912 (-391))) (|has| |#3| (-912 (-391)))) ((-912 (-560)) -12 (|has| |#1| (-912 (-560))) (|has| |#3| (-912 (-560)))) ((-980 |#1| |#4| |#3|) . T) ((-940) |has| |#1| (-940)) ((-1070 (-421 (-560))) |has| |#1| (-1070 (-421 (-560)))) ((-1070 (-560)) |has| |#1| (-1070 (-560))) ((-1070 |#1|) . T) ((-1070 |#2|) . T) ((-1070 |#3|) . T) ((-1083 #0#) |has| |#1| (-38 (-421 (-560)))) ((-1083 |#1|) . T) ((-1083 $) -4144 (|has| |#1| (-940)) (|has| |#1| (-571)) (|has| |#1| (-466)) (|has| |#1| (-175))) ((-1088 #0#) |has| |#1| (-38 (-421 (-560)))) ((-1088 |#1|) . T) ((-1088 $) -4144 (|has| |#1| (-940)) (|has| |#1| (-571)) (|has| |#1| (-466)) (|has| |#1| (-175))) ((-1081) . T) ((-1089) . T) ((-1144) . T) ((-1133) . T) ((-1249) . T) ((-1254) |has| |#1| (-940))) -((-2223 (((-114) $ $) 19 (|has| |#1| (-102)) ELT)) (-2865 ((|#1| $) 58 T ELT)) (-4065 ((|#1| $) 48 T ELT)) (-2950 (($) 7 T CONST)) (-1556 (($ $) 64 T ELT)) (-4123 (($ $) 52 T ELT)) (-2622 ((|#1| |#1| $) 50 T ELT)) (-2501 ((|#1| $) 49 T ELT)) (-4245 (((-663 |#1|) $) 30 (|has| $ (-6 -4510)) ELT)) (-3000 (((-663 |#1|) $) 29 (|has| $ (-6 -4510)) ELT)) (-2227 (((-114) |#1| $) 27 (-12 (|has| |#1| (-1133)) (|has| $ (-6 -4510))) ELT)) (-3405 (($ (-1 |#1| |#1|) $) 34 (|has| $ (-6 -4511)) ELT)) (-2518 (($ (-1 |#1| |#1|) $) 35 T ELT)) (-1859 (((-793) $) 65 T ELT)) (-2780 (((-1191) $) 22 (|has| |#1| (-1133)) ELT)) (-3999 ((|#1| $) 43 T ELT)) (-3385 ((|#1| |#1| $) 56 T ELT)) (-4377 ((|#1| |#1| $) 55 T ELT)) (-2396 (($ |#1| $) 44 T ELT)) (-2235 (((-793) $) 59 T ELT)) (-3904 (((-1152) $) 21 (|has| |#1| (-1133)) ELT)) (-4150 ((|#1| $) 66 T ELT)) (-1848 ((|#1| $) 54 T ELT)) (-2000 ((|#1| $) 53 T ELT)) (-4040 ((|#1| $) 45 T ELT)) (-4397 (((-114) (-1 (-114) |#1|) $) 32 (|has| $ (-6 -4510)) ELT)) (-2703 (($ $ (-663 (-305 |#1|))) 26 (-12 (|has| |#1| (-321 |#1|)) (|has| |#1| (-1133))) ELT) (($ $ (-305 |#1|)) 25 (-12 (|has| |#1| (-321 |#1|)) (|has| |#1| (-1133))) ELT) (($ $ |#1| |#1|) 24 (-12 (|has| |#1| (-321 |#1|)) (|has| |#1| (-1133))) ELT) (($ $ (-663 |#1|) (-663 |#1|)) 23 (-12 (|has| |#1| (-321 |#1|)) (|has| |#1| (-1133))) ELT)) (-3931 (((-114) $ $) 11 T ELT)) (-3631 ((|#1| |#1| $) 62 T ELT)) (-1950 (((-114) $) 8 T ELT)) (-3404 (($) 9 T ELT)) (-3249 ((|#1| $) 63 T ELT)) (-2169 (($) 61 T ELT) (($ (-663 |#1|)) 60 T ELT)) (-4093 (((-793) $) 47 T ELT)) (-3915 (((-793) (-1 (-114) |#1|) $) 31 (|has| $ (-6 -4510)) ELT) (((-793) |#1| $) 28 (-12 (|has| |#1| (-1133)) (|has| $ (-6 -4510))) ELT)) (-4021 (($ $) 10 T ELT)) (-3903 (((-888) $) 17 (|has| |#1| (-632 (-888))) ELT)) (-3273 ((|#1| $) 57 T ELT)) (-2855 (((-114) $ $) 20 (|has| |#1| (-102)) ELT)) (-3730 (($ (-663 |#1|)) 46 T ELT)) (-2658 ((|#1| $) 67 T ELT)) (-4038 (((-114) (-1 (-114) |#1|) $) 33 (|has| $ (-6 -4510)) ELT)) (-4288 (((-114) $ $) 18 (|has| |#1| (-102)) ELT)) (-2236 (((-793) $) 6 (|has| $ (-6 -4510)) ELT))) +((-3817 (*1 *2 *3) (-12 (-4 *4 (-1081)) (-4 *3 (-872)) (-4 *5 (-277 *3)) (-4 *6 (-817)) (-5 *2 (-1 *1 (-793))) (-4 *1 (-262 *4 *3 *5 *6)))) (-1524 (*1 *2 *1) (-12 (-4 *1 (-262 *3 *4 *5 *6)) (-4 *3 (-1081)) (-4 *4 (-872)) (-4 *5 (-277 *4)) (-4 *6 (-817)) (-5 *2 (-663 *4)))) (-2952 (*1 *2 *1 *3) (-12 (-4 *1 (-262 *4 *3 *5 *6)) (-4 *4 (-1081)) (-4 *3 (-872)) (-4 *5 (-277 *3)) (-4 *6 (-817)) (-5 *2 (-793)))) (-2952 (*1 *2 *1) (-12 (-4 *1 (-262 *3 *4 *5 *6)) (-4 *3 (-1081)) (-4 *4 (-872)) (-4 *5 (-277 *4)) (-4 *6 (-817)) (-5 *2 (-793)))) (-3665 (*1 *2 *1 *3) (-12 (-4 *1 (-262 *4 *3 *5 *6)) (-4 *4 (-1081)) (-4 *3 (-872)) (-4 *5 (-277 *3)) (-4 *6 (-817)) (-5 *2 (-793)))) (-3480 (*1 *2 *1) (-12 (-4 *1 (-262 *3 *4 *5 *6)) (-4 *3 (-1081)) (-4 *4 (-872)) (-4 *5 (-277 *4)) (-4 *6 (-817)) (-5 *2 (-663 (-793))))) (-3183 (*1 *2 *1) (-12 (-4 *1 (-262 *3 *4 *5 *6)) (-4 *3 (-1081)) (-4 *4 (-872)) (-4 *5 (-277 *4)) (-4 *6 (-817)) (-5 *2 (-793)))) (-3480 (*1 *2 *1 *3) (-12 (-4 *1 (-262 *4 *3 *5 *6)) (-4 *4 (-1081)) (-4 *3 (-872)) (-4 *5 (-277 *3)) (-4 *6 (-817)) (-5 *2 (-663 (-793))))) (-3183 (*1 *2 *1 *3) (-12 (-4 *1 (-262 *4 *3 *5 *6)) (-4 *4 (-1081)) (-4 *3 (-872)) (-4 *5 (-277 *3)) (-4 *6 (-817)) (-5 *2 (-793)))) (-4290 (*1 *2 *1) (-12 (-4 *1 (-262 *3 *4 *5 *6)) (-4 *3 (-1081)) (-4 *4 (-872)) (-4 *5 (-277 *4)) (-4 *6 (-817)) (-5 *2 (-114)))) (-3511 (*1 *2 *1) (-12 (-4 *1 (-262 *3 *4 *2 *5)) (-4 *3 (-1081)) (-4 *4 (-872)) (-4 *5 (-817)) (-4 *2 (-277 *4)))) (-1890 (*1 *1 *1) (-12 (-4 *1 (-262 *2 *3 *4 *5)) (-4 *2 (-1081)) (-4 *3 (-872)) (-4 *4 (-277 *3)) (-4 *5 (-817)))) (-2790 (*1 *1 *1) (-12 (-4 *1 (-262 *2 *3 *4 *5)) (-4 *2 (-1081)) (-4 *3 (-872)) (-4 *4 (-277 *3)) (-4 *5 (-817)))) (-3817 (*1 *2 *1) (-12 (-4 *3 (-240)) (-4 *3 (-1081)) (-4 *4 (-872)) (-4 *5 (-277 *4)) (-4 *6 (-817)) (-5 *2 (-1 *1 (-793))) (-4 *1 (-262 *3 *4 *5 *6))))) +(-13 (-980 |t#1| |t#4| |t#3|) (-234 |t#1|) (-1070 |t#2|) (-10 -8 (-15 -3817 ((-1 $ (-793)) |t#2|)) (-15 -1524 ((-663 |t#2|) $)) (-15 -2952 ((-793) $ |t#2|)) (-15 -2952 ((-793) $)) (-15 -3665 ((-793) $ |t#2|)) (-15 -3480 ((-663 (-793)) $)) (-15 -3183 ((-793) $)) (-15 -3480 ((-663 (-793)) $ |t#2|)) (-15 -3183 ((-793) $ |t#2|)) (-15 -4290 ((-114) $)) (-15 -3511 (|t#3| $)) (-15 -1890 ($ $)) (-15 -2790 ($ $)) (IF (|has| |t#1| (-240)) (PROGN (-6 (-528 |t#2| |t#1|)) (-6 (-528 |t#2| $)) (-6 (-321 $)) (-15 -3817 ((-1 $ (-793)) $))) |%noBranch|))) +(((-21) . T) ((-23) . T) ((-47 |#1| |#4|) . T) ((-25) . T) ((-38 #0=(-421 (-560))) |has| |#1| (-38 (-421 (-560)))) ((-38 |#1|) |has| |#1| (-175)) ((-38 $) -4118 (|has| |#1| (-940)) (|has| |#1| (-571)) (|has| |#1| (-466))) ((-102) . T) ((-111 #0# #0#) |has| |#1| (-38 (-421 (-560)))) ((-111 |#1| |#1|) . T) ((-111 $ $) -4118 (|has| |#1| (-940)) (|has| |#1| (-571)) (|has| |#1| (-466)) (|has| |#1| (-175))) ((-133) . T) ((-147) |has| |#1| (-147)) ((-149) |has| |#1| (-149)) ((-635 #0#) -4118 (|has| |#1| (-1070 (-421 (-560)))) (|has| |#1| (-38 (-421 (-560))))) ((-635 (-560)) . T) ((-635 |#1|) . T) ((-635 |#2|) . T) ((-635 |#3|) . T) ((-635 $) -4118 (|has| |#1| (-940)) (|has| |#1| (-571)) (|has| |#1| (-466))) ((-632 (-888)) . T) ((-175) -4118 (|has| |#1| (-940)) (|has| |#1| (-571)) (|has| |#1| (-466)) (|has| |#1| (-175))) ((-633 (-549)) -12 (|has| |#1| (-633 (-549))) (|has| |#3| (-633 (-549)))) ((-633 (-916 (-391))) -12 (|has| |#1| (-633 (-916 (-391)))) (|has| |#3| (-633 (-916 (-391))))) ((-633 (-916 (-560))) -12 (|has| |#1| (-633 (-916 (-560)))) (|has| |#3| (-633 (-916 (-560))))) ((-236 $) -4118 (|has| |#1| (-239)) (|has| |#1| (-240))) ((-234 |#1|) . T) ((-240) |has| |#1| (-240)) ((-239) -4118 (|has| |#1| (-239)) (|has| |#1| (-240))) ((-274 |#1|) . T) ((-302) -4118 (|has| |#1| (-940)) (|has| |#1| (-571)) (|has| |#1| (-466))) ((-321 $) . T) ((-338 |#1| |#4|) . T) ((-390 |#1|) . T) ((-426 |#1|) . T) ((-466) -4118 (|has| |#1| (-940)) (|has| |#1| (-466))) ((-528 |#2| |#1|) |has| |#1| (-240)) ((-528 |#2| $) |has| |#1| (-240)) ((-528 |#3| |#1|) . T) ((-528 |#3| $) . T) ((-528 $ $) . T) ((-571) -4118 (|has| |#1| (-940)) (|has| |#1| (-571)) (|has| |#1| (-466))) ((-668 #0#) |has| |#1| (-38 (-421 (-560)))) ((-668 (-560)) . T) ((-668 |#1|) . T) ((-668 $) . T) ((-670 #0#) |has| |#1| (-38 (-421 (-560)))) ((-670 #1=(-560)) |has| |#1| (-660 (-560))) ((-670 |#1|) . T) ((-670 $) . T) ((-662 #0#) |has| |#1| (-38 (-421 (-560)))) ((-662 |#1|) |has| |#1| (-175)) ((-662 $) -4118 (|has| |#1| (-940)) (|has| |#1| (-571)) (|has| |#1| (-466))) ((-660 #1#) |has| |#1| (-660 (-560))) ((-660 |#1|) . T) ((-739 #0#) |has| |#1| (-38 (-421 (-560)))) ((-739 |#1|) |has| |#1| (-175)) ((-739 $) -4118 (|has| |#1| (-940)) (|has| |#1| (-571)) (|has| |#1| (-466))) ((-748) . T) ((-922 $ #2=(-1209)) -4118 (|has| |#1| (-930 (-1209))) (|has| |#1| (-928 (-1209)))) ((-922 $ |#3|) . T) ((-928 (-1209)) |has| |#1| (-928 (-1209))) ((-928 |#3|) . T) ((-930 #2#) -4118 (|has| |#1| (-930 (-1209))) (|has| |#1| (-928 (-1209)))) ((-930 |#3|) . T) ((-912 (-391)) -12 (|has| |#1| (-912 (-391))) (|has| |#3| (-912 (-391)))) ((-912 (-560)) -12 (|has| |#1| (-912 (-560))) (|has| |#3| (-912 (-560)))) ((-980 |#1| |#4| |#3|) . T) ((-940) |has| |#1| (-940)) ((-1070 (-421 (-560))) |has| |#1| (-1070 (-421 (-560)))) ((-1070 (-560)) |has| |#1| (-1070 (-560))) ((-1070 |#1|) . T) ((-1070 |#2|) . T) ((-1070 |#3|) . T) ((-1083 #0#) |has| |#1| (-38 (-421 (-560)))) ((-1083 |#1|) . T) ((-1083 $) -4118 (|has| |#1| (-940)) (|has| |#1| (-571)) (|has| |#1| (-466)) (|has| |#1| (-175))) ((-1088 #0#) |has| |#1| (-38 (-421 (-560)))) ((-1088 |#1|) . T) ((-1088 $) -4118 (|has| |#1| (-940)) (|has| |#1| (-571)) (|has| |#1| (-466)) (|has| |#1| (-175))) ((-1081) . T) ((-1089) . T) ((-1144) . T) ((-1133) . T) ((-1249) . 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T) ((-310) . T) ((-376) |has| |#1| (-571)) ((-390 |#1|) |has| |#1| (-1081)) ((-414 |#1|) . T) ((-426 |#1|) . T) ((-466) |has| |#1| (-571)) ((-487) |has| |#1| (-487)) ((-528 (-630 $) $) . T) ((-528 $ $) . 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T) ((-951) |has| |#1| (-571)) ((-1070 (-421 (-560))) -4144 (|has| |#1| (-1070 (-421 (-560)))) (-12 (|has| |#1| (-571)) (|has| |#1| (-1070 (-560))))) ((-1070 #1#) |has| |#1| (-571)) ((-1070 (-560)) |has| |#1| (-1070 (-560))) ((-1070 #2#) . T) ((-1070 #3#) |has| |#1| (-1081)) ((-1070 #4#) . T) ((-1070 |#1|) . T) ((-1083 #0#) |has| |#1| (-571)) ((-1083 |#1|) |has| |#1| (-175)) ((-1083 $) |has| |#1| (-571)) ((-1088 #0#) |has| |#1| (-571)) ((-1088 |#1|) |has| |#1| (-175)) ((-1088 $) |has| |#1| (-571)) ((-1081) -4144 (|has| |#1| (-1081)) (|has| |#1| (-571)) (|has| |#1| (-175)) (|has| |#1| (-149)) (|has| |#1| (-147))) ((-1089) -4144 (|has| |#1| (-1081)) (|has| |#1| (-571)) (|has| |#1| (-175)) (|has| |#1| (-149)) (|has| |#1| (-147))) ((-1144) -4144 (|has| |#1| (-1144)) (|has| |#1| (-1081)) (|has| |#1| (-571)) (|has| |#1| (-487)) (|has| |#1| (-175)) (|has| |#1| (-149)) (|has| |#1| (-147))) ((-1133) . T) ((-1249) . 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T) ((-951) |has| |#1| (-571)) ((-1070 (-421 (-560))) -4118 (|has| |#1| (-1070 (-421 (-560)))) (-12 (|has| |#1| (-571)) (|has| |#1| (-1070 (-560))))) ((-1070 #1#) |has| |#1| (-571)) ((-1070 (-560)) |has| |#1| (-1070 (-560))) ((-1070 #2#) . T) ((-1070 #3#) |has| |#1| (-1081)) ((-1070 #4#) . T) ((-1070 |#1|) . T) ((-1083 #0#) |has| |#1| (-571)) ((-1083 |#1|) |has| |#1| (-175)) ((-1083 $) |has| |#1| (-571)) ((-1088 #0#) |has| |#1| (-571)) ((-1088 |#1|) |has| |#1| (-175)) ((-1088 $) |has| |#1| (-571)) ((-1081) -4118 (|has| |#1| (-1081)) (|has| |#1| (-571)) (|has| |#1| (-175)) (|has| |#1| (-149)) (|has| |#1| (-147))) ((-1089) -4118 (|has| |#1| (-1081)) (|has| |#1| (-571)) (|has| |#1| (-175)) (|has| |#1| (-149)) (|has| |#1| (-147))) ((-1144) -4118 (|has| |#1| (-1144)) (|has| |#1| (-1081)) (|has| |#1| (-571)) (|has| |#1| (-487)) (|has| |#1| (-175)) (|has| |#1| (-149)) (|has| |#1| (-147))) ((-1133) . T) ((-1249) . 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(|:| -3934 (-2 (|:| |endPointContinuity| (-3 (|:| |continuous| "Continuous at the end points") (|:| |lowerSingular| "There is a singularity at the lower end point") (|:| |upperSingular| "There is a singularity at the upper end point") (|:| |bothSingular| "There are singularities at both end points") (|:| |notEvaluated| "End point continuity not yet evaluated"))) (|:| |singularitiesStream| (-3 (|:| |str| (-1187 (-229))) (|:| |notEvaluated| "Internal singularities not yet evaluated"))) (|:| -4237 (-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 -3525 ((-3 (-2 (|:| |endPointContinuity| (-3 (|:| |continuous| "Continuous at the end points") (|:| |lowerSingular| "There is a singularity at the lower end point") (|:| |upperSingular| "There is a singularity at the upper end 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T) ((-23) . T) ((-25) . T) ((-38 #0=(-421 (-560))) -4118 (|has| |#1| (-363)) (|has| |#1| (-376))) ((-38 |#1|) . T) ((-38 $) -4118 (|has| |#1| (-363)) (|has| |#1| (-376))) ((-102) . T) ((-111 #0# #0#) -4118 (|has| |#1| (-363)) (|has| |#1| (-376))) ((-111 |#1| |#1|) . T) ((-111 $ $) . T) ((-133) . T) ((-147) -4118 (|has| |#1| (-363)) (|has| |#1| (-147))) ((-149) |has| |#1| (-149)) ((-635 #0#) -4118 (|has| |#1| (-1070 (-421 (-560)))) (|has| |#1| (-363)) (|has| |#1| (-376))) ((-635 (-560)) . T) ((-635 |#1|) . T) ((-635 $) -4118 (|has| |#1| (-363)) (|has| |#1| (-376))) ((-632 (-888)) . T) ((-175) . T) ((-633 |#2|) . T) ((-236 $) -4118 (|has| |#1| (-363)) (-12 (|has| |#1| (-239)) (|has| |#1| (-376))) (-12 (|has| |#1| (-240)) (|has| |#1| (-376)))) ((-234 |#1|) |has| |#1| (-376)) ((-240) -4118 (|has| |#1| (-363)) (-12 (|has| |#1| (-240)) (|has| |#1| (-376)))) ((-239) -4118 (|has| |#1| (-363)) (-12 (|has| |#1| (-239)) (|has| |#1| (-376))) (-12 (|has| |#1| (-240)) (|has| |#1| (-376)))) ((-274 |#1|) |has| |#1| (-376)) ((-250) -4118 (|has| |#1| (-363)) (|has| |#1| (-376))) ((-302) -4118 (|has| |#1| (-363)) (|has| |#1| (-376))) ((-319) -4118 (|has| |#1| (-363)) (|has| |#1| (-376))) ((-376) -4118 (|has| |#1| (-363)) (|has| |#1| (-376))) ((-416) |has| |#1| (-363)) ((-381) -4118 (|has| |#1| (-381)) (|has| |#1| (-363))) ((-363) |has| |#1| (-363)) ((-383 |#1| |#2|) . T) ((-424 |#1| |#2|) . T) ((-390 |#1|) . T) ((-426 |#1|) . T) ((-466) -4118 (|has| |#1| (-363)) (|has| |#1| (-376))) ((-571) -4118 (|has| |#1| (-363)) (|has| |#1| (-376))) ((-668 #0#) -4118 (|has| |#1| (-363)) (|has| |#1| (-376))) ((-668 (-560)) . T) ((-668 |#1|) . T) ((-668 $) . T) ((-670 #0#) -4118 (|has| |#1| (-363)) (|has| |#1| (-376))) ((-670 #1=(-560)) |has| |#1| (-660 (-560))) ((-670 |#1|) . T) ((-670 $) . T) ((-662 #0#) -4118 (|has| |#1| (-363)) (|has| |#1| (-376))) ((-662 |#1|) . T) ((-662 $) -4118 (|has| |#1| (-363)) (|has| |#1| (-376))) ((-660 #1#) |has| |#1| (-660 (-560))) ((-660 |#1|) . T) ((-739 #0#) -4118 (|has| |#1| (-363)) (|has| |#1| (-376))) ((-739 |#1|) . T) ((-739 $) -4118 (|has| |#1| (-363)) (|has| |#1| (-376))) ((-748) . T) ((-922 $ #2=(-1209)) -4118 (-12 (|has| |#1| (-376)) (|has| |#1| (-930 (-1209)))) (-12 (|has| |#1| (-376)) (|has| |#1| (-928 (-1209))))) ((-928 (-1209)) -12 (|has| |#1| (-376)) (|has| |#1| (-928 (-1209)))) ((-930 #2#) -4118 (-12 (|has| |#1| (-376)) (|has| |#1| (-930 (-1209)))) (-12 (|has| |#1| (-376)) (|has| |#1| (-928 (-1209))))) ((-951) -4118 (|has| |#1| (-363)) (|has| |#1| (-376))) ((-1070 (-421 (-560))) |has| |#1| (-1070 (-421 (-560)))) ((-1070 (-560)) |has| |#1| (-1070 (-560))) ((-1070 |#1|) . T) ((-1083 #0#) -4118 (|has| |#1| (-363)) (|has| |#1| (-376))) ((-1083 |#1|) . T) ((-1083 $) . T) ((-1088 #0#) -4118 (|has| |#1| (-363)) (|has| |#1| (-376))) ((-1088 |#1|) . T) ((-1088 $) . T) ((-1081) . T) ((-1089) . T) ((-1144) . T) ((-1133) . T) ((-1184) |has| |#1| (-363)) ((-1249) . 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T) ((-23) . T) ((-47 |#1| #0=(-560)) . T) ((-25) . T) ((-38 #1=(-421 (-560))) -4144 (|has| |#1| (-376)) (|has| |#1| (-38 (-421 (-560))))) ((-38 |#1|) |has| |#1| (-175)) ((-38 $) -4144 (|has| |#1| (-571)) (|has| |#1| (-376))) ((-35) |has| |#1| (-38 (-421 (-560)))) ((-95) |has| |#1| (-38 (-421 (-560)))) ((-102) . T) ((-111 #1# #1#) -4144 (|has| |#1| (-376)) (|has| |#1| (-38 (-421 (-560))))) ((-111 |#1| |#1|) . T) ((-111 $ $) -4144 (|has| |#1| (-571)) (|has| |#1| (-376)) (|has| |#1| (-175))) ((-133) . T) ((-147) |has| |#1| (-147)) ((-149) |has| |#1| (-149)) ((-635 #1#) -4144 (|has| |#1| (-376)) (|has| |#1| (-38 (-421 (-560))))) ((-635 (-560)) . T) ((-635 |#1|) |has| |#1| (-175)) ((-635 $) -4144 (|has| |#1| (-571)) (|has| |#1| (-376))) ((-632 (-888)) . 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T) ((-23) . T) ((-47 |#1| #0=(-560)) . T) ((-25) . T) ((-38 #1=(-421 (-560))) -4144 (|has| |#1| (-376)) (|has| |#1| (-38 (-421 (-560))))) ((-38 |#1|) |has| |#1| (-175)) ((-38 |#2|) |has| |#1| (-376)) ((-38 $) -4144 (|has| |#1| (-571)) (|has| |#1| (-376))) ((-35) |has| |#1| (-38 (-421 (-560)))) ((-95) |has| |#1| (-38 (-421 (-560)))) ((-102) . T) ((-111 #1# #1#) -4144 (|has| |#1| (-376)) (|has| |#1| (-38 (-421 (-560))))) ((-111 |#1| |#1|) . T) ((-111 |#2| |#2|) |has| |#1| (-376)) ((-111 $ $) -4144 (|has| |#1| (-571)) (|has| |#1| (-376)) (|has| |#1| (-175))) ((-133) . T) ((-147) -4144 (-12 (|has| |#1| (-376)) (|has| |#2| (-147))) (|has| |#1| (-147))) ((-149) -4144 (-12 (|has| |#1| (-376)) (|has| |#2| (-149))) (|has| |#1| (-149))) ((-635 #1#) -4144 (|has| |#1| (-376)) (|has| |#1| (-38 (-421 (-560))))) ((-635 (-560)) . T) ((-635 #2=(-1209)) -12 (|has| |#1| (-376)) (|has| |#2| (-1070 (-1209)))) ((-635 |#1|) |has| |#1| (-175)) ((-635 |#2|) . T) ((-635 $) -4144 (|has| |#1| (-571)) (|has| |#1| (-376))) ((-632 (-888)) . T) ((-175) -4144 (|has| |#1| (-571)) (|has| |#1| (-376)) (|has| |#1| (-175))) ((-633 (-229)) -12 (|has| |#1| (-376)) (|has| |#2| (-1052))) ((-633 (-391)) -12 (|has| |#1| (-376)) (|has| |#2| (-1052))) ((-633 (-549)) -12 (|has| |#1| (-376)) (|has| |#2| (-633 (-549)))) ((-633 (-916 (-391))) -12 (|has| |#1| (-376)) (|has| |#2| (-633 (-916 (-391))))) ((-633 (-916 (-560))) -12 (|has| |#1| (-376)) (|has| |#2| (-633 (-916 (-560))))) ((-236 $) -4144 (-12 (|has| |#1| (-376)) (|has| |#2| (-239))) (-12 (|has| |#1| (-376)) (|has| |#2| (-240))) (|has| |#1| (-15 * (|#1| (-560) |#1|)))) ((-234 |#2|) |has| |#1| (-376)) ((-240) -4144 (-12 (|has| |#1| (-376)) (|has| |#2| (-240))) (|has| |#1| (-15 * (|#1| (-560) |#1|)))) ((-239) -4144 (-12 (|has| |#1| (-376)) (|has| |#2| (-239))) (-12 (|has| |#1| (-376)) (|has| |#2| (-240))) (|has| |#1| (-15 * (|#1| (-560) |#1|)))) ((-274 |#2|) |has| |#1| (-376)) ((-250) |has| |#1| (-376)) ((-296) |has| |#1| (-38 (-421 (-560)))) ((-298 #0# |#1|) . T) ((-298 |#2| $) -12 (|has| |#1| (-376)) (|has| |#2| (-298 |#2| |#2|))) ((-298 $ $) |has| (-560) (-1144)) ((-302) -4144 (|has| |#1| (-571)) (|has| |#1| (-376))) ((-319) |has| |#1| (-376)) ((-321 |#2|) -12 (|has| |#1| (-376)) (|has| |#2| (-321 |#2|))) ((-376) |has| |#1| (-376)) ((-351 |#2|) |has| |#1| (-376)) ((-390 |#2|) |has| |#1| (-376)) ((-414 |#2|) |has| |#1| (-376)) ((-466) |has| |#1| (-376)) ((-507) |has| |#1| (-38 (-421 (-560)))) ((-528 (-1209) |#2|) -12 (|has| |#1| (-376)) (|has| |#2| (-528 (-1209) |#2|))) ((-528 |#2| |#2|) -12 (|has| |#1| (-376)) (|has| |#2| (-321 |#2|))) ((-571) -4144 (|has| |#1| (-571)) (|has| |#1| (-376))) ((-668 #1#) -4144 (|has| |#1| (-376)) (|has| |#1| (-38 (-421 (-560))))) ((-668 (-560)) . T) ((-668 |#1|) . T) ((-668 |#2|) |has| |#1| (-376)) ((-668 $) . T) ((-670 #1#) -4144 (|has| |#1| (-376)) (|has| |#1| (-38 (-421 (-560))))) ((-670 #3=(-560)) -12 (|has| |#1| (-376)) (|has| |#2| (-660 (-560)))) ((-670 |#1|) . T) ((-670 |#2|) |has| |#1| (-376)) ((-670 $) . T) ((-662 #1#) -4144 (|has| |#1| (-376)) (|has| |#1| (-38 (-421 (-560))))) ((-662 |#1|) |has| |#1| (-175)) ((-662 |#2|) |has| |#1| (-376)) ((-662 $) -4144 (|has| |#1| (-571)) (|has| |#1| (-376))) ((-660 #3#) -12 (|has| |#1| (-376)) (|has| |#2| (-660 (-560)))) ((-660 |#2|) |has| |#1| (-376)) ((-739 #1#) -4144 (|has| |#1| (-376)) (|has| |#1| (-38 (-421 (-560))))) ((-739 |#1|) |has| |#1| (-175)) ((-739 |#2|) |has| |#1| (-376)) ((-739 $) -4144 (|has| |#1| (-571)) (|has| |#1| (-376))) ((-748) . T) ((-814) -12 (|has| |#1| (-376)) (|has| |#2| (-844))) ((-816) -12 (|has| |#1| (-376)) (|has| |#2| (-844))) ((-818) -12 (|has| |#1| (-376)) (|has| |#2| (-844))) ((-821) -12 (|has| |#1| (-376)) (|has| |#2| (-844))) ((-844) -12 (|has| |#1| (-376)) (|has| |#2| (-844))) ((-871) -12 (|has| |#1| (-376)) (|has| |#2| (-844))) ((-872) -4144 (-12 (|has| |#1| (-376)) (|has| |#2| (-872))) (-12 (|has| |#1| (-376)) (|has| |#2| (-844)))) ((-875) -4144 (-12 (|has| |#1| (-376)) (|has| |#2| (-872))) (-12 (|has| |#1| (-376)) (|has| |#2| (-844)))) ((-922 $ #4=(-1209)) -4144 (-12 (|has| |#1| (-376)) (|has| |#2| (-930 (-1209)))) (-12 (|has| |#1| (-376)) (|has| |#2| (-928 (-1209)))) (-12 (|has| |#1| (-15 * (|#1| (-560) |#1|))) (|has| |#1| (-928 (-1209))))) ((-928 (-1209)) -4144 (-12 (|has| |#1| (-376)) (|has| |#2| (-928 (-1209)))) (-12 (|has| |#1| (-15 * (|#1| (-560) |#1|))) (|has| |#1| (-928 (-1209))))) ((-930 #4#) -4144 (-12 (|has| |#1| (-376)) (|has| |#2| (-930 (-1209)))) (-12 (|has| |#1| (-376)) (|has| |#2| (-928 (-1209)))) (-12 (|has| |#1| (-15 * (|#1| (-560) |#1|))) (|has| |#1| (-928 (-1209))))) ((-912 (-391)) -12 (|has| |#1| (-376)) (|has| |#2| (-912 (-391)))) ((-912 (-560)) -12 (|has| |#1| (-376)) (|has| |#2| (-912 (-560)))) ((-910 |#2|) |has| |#1| (-376)) ((-940) -12 (|has| |#1| (-376)) (|has| |#2| (-940))) ((-1005 |#1| #0# (-1114)) . T) ((-951) |has| |#1| (-376)) ((-1023 |#2|) |has| |#1| (-376)) ((-1034) |has| |#1| (-38 (-421 (-560)))) ((-1052) -12 (|has| |#1| (-376)) (|has| |#2| (-1052))) ((-1070 (-421 (-560))) -12 (|has| |#1| (-376)) (|has| |#2| (-1070 (-560)))) ((-1070 (-560)) -12 (|has| |#1| (-376)) (|has| |#2| (-1070 (-560)))) ((-1070 #2#) -12 (|has| |#1| (-376)) (|has| |#2| (-1070 (-1209)))) ((-1070 |#2|) . T) ((-1083 #1#) -4144 (|has| |#1| (-376)) (|has| |#1| (-38 (-421 (-560))))) ((-1083 |#1|) . T) ((-1083 |#2|) |has| |#1| (-376)) ((-1083 $) -4144 (|has| |#1| (-571)) (|has| |#1| (-376)) (|has| |#1| (-175))) ((-1088 #1#) -4144 (|has| |#1| (-376)) (|has| |#1| (-38 (-421 (-560))))) ((-1088 |#1|) . T) ((-1088 |#2|) |has| |#1| (-376)) ((-1088 $) -4144 (|has| |#1| (-571)) (|has| |#1| (-376)) (|has| |#1| (-175))) ((-1081) . T) ((-1089) . T) ((-1144) . T) ((-1133) . T) ((-1184) -12 (|has| |#1| (-376)) (|has| |#2| (-1184))) ((-1235) |has| |#1| (-38 (-421 (-560)))) ((-1238) |has| |#1| (-38 (-421 (-560)))) ((-1249) . T) ((-1254) |has| |#1| (-376)) ((-1261 |#1|) . T) ((-1278 |#1| #0#) . 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T) ((-298 |#2| $) -12 (|has| |#1| (-376)) (|has| |#2| (-298 |#2| |#2|))) ((-298 $ $) |has| (-560) (-1144)) ((-302) -4118 (|has| |#1| (-571)) (|has| |#1| (-376))) ((-319) |has| |#1| (-376)) ((-321 |#2|) -12 (|has| |#1| (-376)) (|has| |#2| (-321 |#2|))) ((-376) |has| |#1| (-376)) ((-351 |#2|) |has| |#1| (-376)) ((-390 |#2|) |has| |#1| (-376)) ((-414 |#2|) |has| |#1| (-376)) ((-466) |has| |#1| (-376)) ((-507) |has| |#1| (-38 (-421 (-560)))) ((-528 (-1209) |#2|) -12 (|has| |#1| (-376)) (|has| |#2| (-528 (-1209) |#2|))) ((-528 |#2| |#2|) -12 (|has| |#1| (-376)) (|has| |#2| (-321 |#2|))) ((-571) -4118 (|has| |#1| (-571)) (|has| |#1| (-376))) ((-668 #1#) -4118 (|has| |#1| (-376)) (|has| |#1| (-38 (-421 (-560))))) ((-668 (-560)) . T) ((-668 |#1|) . T) ((-668 |#2|) |has| |#1| (-376)) ((-668 $) . T) ((-670 #1#) -4118 (|has| |#1| (-376)) (|has| |#1| (-38 (-421 (-560))))) ((-670 #3=(-560)) -12 (|has| |#1| (-376)) (|has| |#2| (-660 (-560)))) ((-670 |#1|) . T) ((-670 |#2|) |has| |#1| (-376)) ((-670 $) . T) ((-662 #1#) -4118 (|has| |#1| (-376)) (|has| |#1| (-38 (-421 (-560))))) ((-662 |#1|) |has| |#1| (-175)) ((-662 |#2|) |has| |#1| (-376)) ((-662 $) -4118 (|has| |#1| (-571)) (|has| |#1| (-376))) ((-660 #3#) -12 (|has| |#1| (-376)) (|has| |#2| (-660 (-560)))) ((-660 |#2|) |has| |#1| (-376)) ((-739 #1#) -4118 (|has| |#1| (-376)) (|has| |#1| (-38 (-421 (-560))))) ((-739 |#1|) |has| |#1| (-175)) ((-739 |#2|) |has| |#1| (-376)) ((-739 $) -4118 (|has| |#1| (-571)) (|has| |#1| (-376))) ((-748) . T) ((-814) -12 (|has| |#1| (-376)) (|has| |#2| (-844))) ((-816) -12 (|has| |#1| (-376)) (|has| |#2| (-844))) ((-818) -12 (|has| |#1| (-376)) (|has| |#2| (-844))) ((-821) -12 (|has| |#1| (-376)) (|has| |#2| (-844))) ((-844) -12 (|has| |#1| (-376)) (|has| |#2| (-844))) ((-871) -12 (|has| |#1| (-376)) (|has| |#2| (-844))) ((-872) -4118 (-12 (|has| |#1| (-376)) (|has| |#2| (-872))) (-12 (|has| |#1| (-376)) (|has| |#2| (-844)))) ((-875) -4118 (-12 (|has| |#1| (-376)) (|has| |#2| (-872))) (-12 (|has| |#1| (-376)) (|has| |#2| (-844)))) ((-922 $ #4=(-1209)) -4118 (-12 (|has| |#1| (-376)) (|has| |#2| (-930 (-1209)))) (-12 (|has| |#1| (-376)) (|has| |#2| (-928 (-1209)))) (-12 (|has| |#1| (-15 * (|#1| (-560) |#1|))) (|has| |#1| (-928 (-1209))))) ((-928 (-1209)) -4118 (-12 (|has| |#1| (-376)) (|has| |#2| (-928 (-1209)))) (-12 (|has| |#1| (-15 * (|#1| (-560) |#1|))) (|has| |#1| (-928 (-1209))))) ((-930 #4#) -4118 (-12 (|has| |#1| (-376)) (|has| |#2| (-930 (-1209)))) (-12 (|has| |#1| (-376)) (|has| |#2| (-928 (-1209)))) (-12 (|has| |#1| (-15 * (|#1| (-560) |#1|))) (|has| |#1| (-928 (-1209))))) ((-912 (-391)) -12 (|has| |#1| (-376)) (|has| |#2| (-912 (-391)))) ((-912 (-560)) -12 (|has| |#1| (-376)) (|has| |#2| (-912 (-560)))) ((-910 |#2|) |has| |#1| (-376)) ((-940) -12 (|has| |#1| (-376)) (|has| |#2| (-940))) ((-1005 |#1| #0# (-1114)) . T) ((-951) |has| |#1| (-376)) ((-1023 |#2|) |has| |#1| (-376)) ((-1034) |has| |#1| (-38 (-421 (-560)))) ((-1052) -12 (|has| |#1| (-376)) (|has| |#2| (-1052))) ((-1070 (-421 (-560))) -12 (|has| |#1| (-376)) (|has| |#2| (-1070 (-560)))) ((-1070 (-560)) -12 (|has| |#1| (-376)) (|has| |#2| (-1070 (-560)))) ((-1070 #2#) -12 (|has| |#1| (-376)) (|has| |#2| (-1070 (-1209)))) ((-1070 |#2|) . T) ((-1083 #1#) -4118 (|has| |#1| (-376)) (|has| |#1| (-38 (-421 (-560))))) ((-1083 |#1|) . T) ((-1083 |#2|) |has| |#1| (-376)) ((-1083 $) -4118 (|has| |#1| (-571)) (|has| |#1| (-376)) (|has| |#1| (-175))) ((-1088 #1#) -4118 (|has| |#1| (-376)) (|has| |#1| (-38 (-421 (-560))))) ((-1088 |#1|) . T) ((-1088 |#2|) |has| |#1| (-376)) ((-1088 $) -4118 (|has| |#1| (-571)) (|has| |#1| (-376)) (|has| |#1| (-175))) ((-1081) . T) ((-1089) . T) ((-1144) . T) ((-1133) . T) ((-1184) -12 (|has| |#1| (-376)) (|has| |#2| (-1184))) ((-1235) |has| |#1| (-38 (-421 (-560)))) ((-1238) |has| |#1| (-38 (-421 (-560)))) ((-1249) . T) ((-1254) |has| |#1| (-376)) ((-1261 |#1|) . T) ((-1278 |#1| #0#) . 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T) ((-23) . T) ((-47 |#1| #0=(-793)) . T) ((-25) . T) ((-38 #1=(-421 (-560))) |has| |#1| (-38 (-421 (-560)))) ((-38 |#1|) |has| |#1| (-175)) ((-38 $) -4144 (|has| |#1| (-940)) (|has| |#1| (-571)) (|has| |#1| (-466)) (|has| |#1| (-376))) ((-102) . T) ((-111 #1# #1#) |has| |#1| (-38 (-421 (-560)))) ((-111 |#1| |#1|) . T) ((-111 $ $) -4144 (|has| |#1| (-940)) (|has| |#1| (-571)) (|has| |#1| (-466)) (|has| |#1| (-376)) (|has| |#1| (-175))) ((-133) . T) ((-147) |has| |#1| (-147)) ((-149) |has| |#1| (-149)) ((-635 #1#) -4144 (|has| |#1| (-1070 (-421 (-560)))) (|has| |#1| (-38 (-421 (-560))))) ((-635 (-560)) . T) ((-635 #2=(-1114)) . T) ((-635 |#1|) . T) ((-635 $) -4144 (|has| |#1| (-940)) (|has| |#1| (-571)) (|has| |#1| (-466)) (|has| |#1| (-376))) ((-632 (-888)) . T) ((-175) -4144 (|has| |#1| (-940)) (|has| |#1| (-571)) (|has| |#1| (-466)) (|has| |#1| (-376)) (|has| |#1| (-175))) ((-633 (-549)) -12 (|has| (-1114) (-633 (-549))) (|has| |#1| (-633 (-549)))) ((-633 (-916 (-391))) -12 (|has| (-1114) (-633 (-916 (-391)))) (|has| |#1| (-633 (-916 (-391))))) ((-633 (-916 (-560))) -12 (|has| (-1114) (-633 (-916 (-560)))) (|has| |#1| (-633 (-916 (-560))))) ((-236 $) . T) ((-234 |#1|) . T) ((-240) . T) ((-239) . T) ((-274 |#1|) . T) ((-298 (-421 $) (-421 $)) |has| |#1| (-571)) ((-298 |#1| |#1|) . T) ((-298 $ $) . T) ((-302) -4144 (|has| |#1| (-940)) (|has| |#1| (-571)) (|has| |#1| (-466)) (|has| |#1| (-376))) ((-319) |has| |#1| (-376)) ((-321 $) . T) ((-338 |#1| #0#) . T) ((-390 |#1|) . T) ((-426 |#1|) . T) ((-466) -4144 (|has| |#1| (-940)) (|has| |#1| (-466)) (|has| |#1| (-376))) ((-528 #2# |#1|) . T) ((-528 #2# $) . T) ((-528 $ $) . T) ((-571) -4144 (|has| |#1| (-940)) (|has| |#1| (-571)) (|has| |#1| (-466)) (|has| |#1| (-376))) ((-668 #1#) |has| |#1| (-38 (-421 (-560)))) ((-668 (-560)) . T) ((-668 |#1|) . T) ((-668 $) . T) ((-670 #1#) |has| |#1| (-38 (-421 (-560)))) ((-670 #3=(-560)) |has| |#1| (-660 (-560))) ((-670 |#1|) . T) ((-670 $) . T) ((-662 #1#) |has| |#1| (-38 (-421 (-560)))) ((-662 |#1|) |has| |#1| (-175)) ((-662 $) -4144 (|has| |#1| (-940)) (|has| |#1| (-571)) (|has| |#1| (-466)) (|has| |#1| (-376))) ((-660 #3#) |has| |#1| (-660 (-560))) ((-660 |#1|) . T) ((-739 #1#) |has| |#1| (-38 (-421 (-560)))) ((-739 |#1|) |has| |#1| (-175)) ((-739 $) -4144 (|has| |#1| (-940)) (|has| |#1| (-571)) (|has| |#1| (-466)) (|has| |#1| (-376))) ((-748) . T) ((-922 $ #2#) . T) ((-922 $ #4=(-1209)) -4144 (|has| |#1| (-930 (-1209))) (|has| |#1| (-928 (-1209)))) ((-928 #2#) . T) ((-928 (-1209)) |has| |#1| (-928 (-1209))) ((-930 #2#) . 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$)) |%noBranch|))) +(((-21) . T) ((-23) . T) ((-47 |#1| #0=(-793)) . T) ((-25) . T) ((-38 #1=(-421 (-560))) |has| |#1| (-38 (-421 (-560)))) ((-38 |#1|) |has| |#1| (-175)) ((-38 $) -4118 (|has| |#1| (-940)) (|has| |#1| (-571)) (|has| |#1| (-466)) (|has| |#1| (-376))) ((-102) . T) ((-111 #1# #1#) |has| |#1| (-38 (-421 (-560)))) ((-111 |#1| |#1|) . T) ((-111 $ $) -4118 (|has| |#1| (-940)) (|has| |#1| (-571)) (|has| |#1| (-466)) (|has| |#1| (-376)) (|has| |#1| (-175))) ((-133) . T) ((-147) |has| |#1| (-147)) ((-149) |has| |#1| (-149)) ((-635 #1#) -4118 (|has| |#1| (-1070 (-421 (-560)))) (|has| |#1| (-38 (-421 (-560))))) ((-635 (-560)) . T) ((-635 #2=(-1114)) . T) ((-635 |#1|) . T) ((-635 $) -4118 (|has| |#1| (-940)) (|has| |#1| (-571)) (|has| |#1| (-466)) (|has| |#1| (-376))) ((-632 (-888)) . T) ((-175) -4118 (|has| |#1| (-940)) (|has| |#1| (-571)) (|has| |#1| (-466)) (|has| |#1| (-376)) (|has| |#1| (-175))) ((-633 (-549)) -12 (|has| (-1114) (-633 (-549))) (|has| |#1| (-633 (-549)))) ((-633 (-916 (-391))) -12 (|has| (-1114) (-633 (-916 (-391)))) (|has| |#1| (-633 (-916 (-391))))) ((-633 (-916 (-560))) -12 (|has| (-1114) (-633 (-916 (-560)))) (|has| |#1| (-633 (-916 (-560))))) ((-236 $) . T) ((-234 |#1|) . T) ((-240) . T) ((-239) . T) ((-274 |#1|) . T) ((-298 (-421 $) (-421 $)) |has| |#1| (-571)) ((-298 |#1| |#1|) . T) ((-298 $ $) . T) ((-302) -4118 (|has| |#1| (-940)) (|has| |#1| (-571)) (|has| |#1| (-466)) (|has| |#1| (-376))) ((-319) |has| |#1| (-376)) ((-321 $) . T) ((-338 |#1| #0#) . T) ((-390 |#1|) . T) ((-426 |#1|) . T) ((-466) -4118 (|has| |#1| (-940)) (|has| |#1| (-466)) (|has| |#1| (-376))) ((-528 #2# |#1|) . T) ((-528 #2# $) . T) ((-528 $ $) . T) ((-571) -4118 (|has| |#1| (-940)) (|has| |#1| (-571)) (|has| |#1| (-466)) (|has| |#1| (-376))) ((-668 #1#) |has| |#1| (-38 (-421 (-560)))) ((-668 (-560)) . T) ((-668 |#1|) . T) ((-668 $) . T) ((-670 #1#) |has| |#1| (-38 (-421 (-560)))) ((-670 #3=(-560)) |has| |#1| (-660 (-560))) ((-670 |#1|) . T) ((-670 $) . T) ((-662 #1#) |has| |#1| (-38 (-421 (-560)))) ((-662 |#1|) |has| |#1| (-175)) ((-662 $) -4118 (|has| |#1| (-940)) (|has| |#1| (-571)) (|has| |#1| (-466)) (|has| |#1| (-376))) ((-660 #3#) |has| |#1| (-660 (-560))) ((-660 |#1|) . T) ((-739 #1#) |has| |#1| (-38 (-421 (-560)))) ((-739 |#1|) |has| |#1| (-175)) ((-739 $) -4118 (|has| |#1| (-940)) (|has| |#1| (-571)) (|has| |#1| (-466)) (|has| |#1| (-376))) ((-748) . T) ((-922 $ #2#) . T) ((-922 $ #4=(-1209)) -4118 (|has| |#1| (-930 (-1209))) (|has| |#1| (-928 (-1209)))) ((-928 #2#) . T) ((-928 (-1209)) |has| |#1| (-928 (-1209))) ((-930 #2#) . T) ((-930 #4#) -4118 (|has| |#1| (-930 (-1209))) (|has| |#1| (-928 (-1209)))) ((-912 (-391)) -12 (|has| (-1114) (-912 (-391))) (|has| |#1| (-912 (-391)))) ((-912 (-560)) -12 (|has| (-1114) (-912 (-560))) (|has| |#1| (-912 (-560)))) ((-980 |#1| #0# #2#) . T) ((-940) |has| |#1| (-940)) ((-951) |has| |#1| (-376)) ((-1070 (-421 (-560))) |has| |#1| (-1070 (-421 (-560)))) ((-1070 (-560)) |has| |#1| (-1070 (-560))) ((-1070 #2#) . T) ((-1070 |#1|) . T) ((-1083 #1#) |has| |#1| (-38 (-421 (-560)))) ((-1083 |#1|) . T) ((-1083 $) -4118 (|has| |#1| (-940)) (|has| |#1| (-571)) (|has| |#1| (-466)) (|has| |#1| (-376)) (|has| |#1| (-175))) ((-1088 #1#) |has| |#1| (-38 (-421 (-560)))) ((-1088 |#1|) . T) ((-1088 $) -4118 (|has| |#1| (-940)) (|has| |#1| (-571)) (|has| |#1| (-466)) (|has| |#1| (-376)) (|has| |#1| (-175))) ((-1081) . T) ((-1089) . T) ((-1144) . T) ((-1133) . T) ((-1184) |has| |#1| (-1184)) ((-1249) . 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T) ((-23) . T) ((-47 |#1| #0=(-421 (-560))) . T) ((-25) . T) ((-38 #1=(-421 (-560))) -4144 (|has| |#1| (-376)) (|has| |#1| (-38 (-421 (-560))))) ((-38 |#1|) |has| |#1| (-175)) ((-38 $) -4144 (|has| |#1| (-571)) (|has| |#1| (-376))) ((-35) |has| |#1| (-38 (-421 (-560)))) ((-95) |has| |#1| (-38 (-421 (-560)))) ((-102) . T) ((-111 #1# #1#) -4144 (|has| |#1| (-376)) (|has| |#1| (-38 (-421 (-560))))) ((-111 |#1| |#1|) . T) ((-111 $ $) -4144 (|has| |#1| (-571)) (|has| |#1| (-376)) (|has| |#1| (-175))) ((-133) . T) ((-147) |has| |#1| (-147)) ((-149) |has| |#1| (-149)) ((-635 #1#) -4144 (|has| |#1| (-376)) (|has| |#1| (-38 (-421 (-560))))) ((-635 (-560)) . T) ((-635 |#1|) |has| |#1| (-175)) ((-635 |#2|) . T) ((-635 $) -4144 (|has| |#1| (-571)) (|has| |#1| (-376))) ((-632 (-888)) . 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T) ((-662 #1#) -4144 (|has| |#1| (-376)) (|has| |#1| (-38 (-421 (-560))))) ((-662 |#1|) |has| |#1| (-175)) ((-662 $) -4144 (|has| |#1| (-571)) (|has| |#1| (-376))) ((-739 #1#) -4144 (|has| |#1| (-376)) (|has| |#1| (-38 (-421 (-560))))) ((-739 |#1|) |has| |#1| (-175)) ((-739 $) -4144 (|has| |#1| (-571)) (|has| |#1| (-376))) ((-748) . T) ((-922 $ #2=(-1209)) -12 (|has| |#1| (-15 * (|#1| (-421 (-560)) |#1|))) (|has| |#1| (-928 (-1209)))) ((-928 #2#) -12 (|has| |#1| (-15 * (|#1| (-421 (-560)) |#1|))) (|has| |#1| (-928 (-1209)))) ((-930 #2#) -12 (|has| |#1| (-15 * (|#1| (-421 (-560)) |#1|))) (|has| |#1| (-928 (-1209)))) ((-1005 |#1| #0# (-1114)) . T) ((-951) |has| |#1| (-376)) ((-1034) |has| |#1| (-38 (-421 (-560)))) ((-1070 |#2|) . T) ((-1083 #1#) -4144 (|has| |#1| (-376)) (|has| |#1| (-38 (-421 (-560))))) ((-1083 |#1|) . T) ((-1083 $) -4144 (|has| |#1| (-571)) (|has| |#1| (-376)) (|has| |#1| (-175))) ((-1088 #1#) -4144 (|has| |#1| (-376)) (|has| |#1| (-38 (-421 (-560))))) ((-1088 |#1|) . T) ((-1088 $) -4144 (|has| |#1| (-571)) (|has| |#1| (-376)) (|has| |#1| (-175))) ((-1081) . T) ((-1089) . T) ((-1144) . T) ((-1133) . T) ((-1235) |has| |#1| (-38 (-421 (-560)))) ((-1238) |has| |#1| (-38 (-421 (-560)))) ((-1249) . T) ((-1254) |has| |#1| (-376)) ((-1278 |#1| #0#) . T) ((-1282 |#1|) . 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T) ((-23) . T) ((-47 |#1| #0=(-421 (-560))) . T) ((-25) . T) ((-38 #1=(-421 (-560))) -4118 (|has| |#1| (-376)) (|has| |#1| (-38 (-421 (-560))))) ((-38 |#1|) |has| |#1| (-175)) ((-38 $) -4118 (|has| |#1| (-571)) (|has| |#1| (-376))) ((-35) |has| |#1| (-38 (-421 (-560)))) ((-95) |has| |#1| (-38 (-421 (-560)))) ((-102) . T) ((-111 #1# #1#) -4118 (|has| |#1| (-376)) (|has| |#1| (-38 (-421 (-560))))) ((-111 |#1| |#1|) . T) ((-111 $ $) -4118 (|has| |#1| (-571)) (|has| |#1| (-376)) (|has| |#1| (-175))) ((-133) . T) ((-147) |has| |#1| (-147)) ((-149) |has| |#1| (-149)) ((-635 #1#) -4118 (|has| |#1| (-376)) (|has| |#1| (-38 (-421 (-560))))) ((-635 (-560)) . T) ((-635 |#1|) |has| |#1| (-175)) ((-635 |#2|) . T) ((-635 $) -4118 (|has| |#1| (-571)) (|has| |#1| (-376))) ((-632 (-888)) . T) ((-175) -4118 (|has| |#1| (-571)) (|has| |#1| (-376)) (|has| |#1| (-175))) ((-236 $) |has| |#1| (-15 * (|#1| (-421 (-560)) |#1|))) ((-240) |has| |#1| (-15 * (|#1| (-421 (-560)) |#1|))) ((-239) |has| |#1| (-15 * (|#1| (-421 (-560)) |#1|))) ((-250) |has| |#1| (-376)) ((-296) |has| |#1| (-38 (-421 (-560)))) ((-298 #0# |#1|) . T) ((-298 $ $) |has| (-421 (-560)) (-1144)) ((-302) -4118 (|has| |#1| (-571)) (|has| |#1| (-376))) ((-319) |has| |#1| (-376)) ((-376) |has| |#1| (-376)) ((-466) |has| |#1| (-376)) ((-507) |has| |#1| (-38 (-421 (-560)))) ((-571) -4118 (|has| |#1| (-571)) (|has| |#1| (-376))) ((-668 #1#) -4118 (|has| |#1| (-376)) (|has| |#1| (-38 (-421 (-560))))) ((-668 (-560)) . T) ((-668 |#1|) . T) ((-668 $) . T) ((-670 #1#) -4118 (|has| |#1| (-376)) (|has| |#1| (-38 (-421 (-560))))) ((-670 |#1|) . T) ((-670 $) . T) ((-662 #1#) -4118 (|has| |#1| (-376)) (|has| |#1| (-38 (-421 (-560))))) ((-662 |#1|) |has| |#1| (-175)) ((-662 $) -4118 (|has| |#1| (-571)) (|has| |#1| (-376))) ((-739 #1#) -4118 (|has| |#1| (-376)) (|has| |#1| (-38 (-421 (-560))))) ((-739 |#1|) |has| |#1| (-175)) ((-739 $) -4118 (|has| |#1| (-571)) (|has| |#1| (-376))) ((-748) . T) ((-922 $ #2=(-1209)) -12 (|has| |#1| (-15 * (|#1| (-421 (-560)) |#1|))) (|has| |#1| (-928 (-1209)))) ((-928 #2#) -12 (|has| |#1| (-15 * (|#1| (-421 (-560)) |#1|))) (|has| |#1| (-928 (-1209)))) ((-930 #2#) -12 (|has| |#1| (-15 * (|#1| (-421 (-560)) |#1|))) (|has| |#1| (-928 (-1209)))) ((-1005 |#1| #0# (-1114)) . T) ((-951) |has| |#1| (-376)) ((-1034) |has| |#1| (-38 (-421 (-560)))) ((-1070 |#2|) . T) ((-1083 #1#) -4118 (|has| |#1| (-376)) (|has| |#1| (-38 (-421 (-560))))) ((-1083 |#1|) . T) ((-1083 $) -4118 (|has| |#1| (-571)) (|has| |#1| (-376)) (|has| |#1| (-175))) ((-1088 #1#) -4118 (|has| |#1| (-376)) (|has| |#1| (-38 (-421 (-560))))) ((-1088 |#1|) . T) ((-1088 $) -4118 (|has| |#1| (-571)) (|has| |#1| (-376)) (|has| |#1| (-175))) ((-1081) . T) ((-1089) . T) ((-1144) . T) ((-1133) . T) ((-1235) |has| |#1| (-38 (-421 (-560)))) ((-1238) |has| |#1| (-38 (-421 (-560)))) ((-1249) . T) ((-1254) |has| |#1| (-376)) ((-1278 |#1| #0#) . T) ((-1282 |#1|) . 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NIL NIL NIL NIL (NIL) -8 NIL NIL NIL) (-2 3460141 3460146 3460151 NIL NIL NIL NIL (NIL) -8 NIL NIL NIL) (-1 3460126 3460131 3460136 NIL NIL NIL NIL (NIL) -8 NIL NIL NIL) (0 3460111 3460116 3460121 NIL NIL NIL NIL (NIL) -8 NIL NIL NIL) (-1329 3459104 3459986 3460063 "ZMOD" 3460068 NIL ZMOD (NIL NIL) -8 NIL NIL NIL) (-1328 3458140 3458322 3458545 "ZLINDEP" 3458936 NIL ZLINDEP (NIL T) -7 NIL NIL NIL) (-1327 3447302 3449208 3451180 "ZDSOLVE" 3456270 NIL ZDSOLVE (NIL T NIL NIL) -7 NIL NIL NIL) (-1326 3446536 3446689 3446878 "YSTREAM" 3447148 NIL YSTREAM (NIL T) -7 NIL NIL NIL) (-1325 3445896 3446205 3446320 "YDIAGRAM" 3446443 T YDIAGRAM (NIL) -8 NIL NIL NIL) (-1324 3443344 3445197 3445401 "XRPOLY" 3445739 NIL XRPOLY (NIL T T) -8 NIL NIL NIL) (-1323 3439611 3441215 3441790 "XPR" 3442816 NIL XPR (NIL T T) -8 NIL NIL NIL) (-1322 3436942 3438618 3438673 "XPOLYC" 3438961 NIL XPOLYC (NIL T T) -9 NIL 3439074 NIL) (-1321 3434337 3436273 3436477 "XPOLY" 3436773 NIL XPOLY (NIL T) -8 NIL NIL NIL) (-1320 3430283 3432854 3433242 "XPBWPOLY" 3433995 NIL XPBWPOLY (NIL T T) -8 NIL NIL NIL) (-1319 3425175 3426754 3426809 "XFALG" 3428981 NIL XFALG (NIL T T) -9 NIL 3429770 NIL) (-1318 3420451 3423151 3423193 "XF" 3423814 NIL XF (NIL T) -9 NIL 3424214 NIL) (-1317 3420048 3420160 3420329 "XF-" 3420334 NIL XF- (NIL T T) -8 NIL NIL NIL) (-1316 3419163 3419285 3419490 "XEXPPKG" 3419940 NIL XEXPPKG (NIL T T T) -7 NIL NIL NIL) (-1315 3416904 3419013 3419109 "XDPOLY" 3419114 NIL XDPOLY (NIL T T) -8 NIL NIL NIL) (-1314 3415559 3416297 3416340 "XALG" 3416345 NIL XALG (NIL T) -9 NIL 3416456 NIL) (-1313 3408583 3413536 3414030 "WUTSET" 3415151 NIL WUTSET (NIL T T T T) -8 NIL NIL NIL) (-1312 3406685 3407635 3407958 "WP" 3408394 NIL WP (NIL T T T T NIL NIL NIL) -8 NIL NIL NIL) (-1311 3406233 3406507 3406577 "WHILEAST" 3406637 T WHILEAST (NIL) -8 NIL NIL NIL) (-1310 3405645 3405950 3406044 "WHEREAST" 3406161 T WHEREAST (NIL) -8 NIL NIL NIL) (-1309 3404519 3404729 3405024 "WFFINTBS" 3405442 NIL WFFINTBS (NIL T T T T) -7 NIL NIL NIL) (-1308 3402387 3402850 3403312 "WEIER" 3404091 NIL WEIER (NIL T) -7 NIL NIL NIL) (-1307 3401311 3401869 3401911 "VSPACE" 3402047 NIL VSPACE (NIL T) -9 NIL 3402121 NIL) (-1306 3401143 3401176 3401267 "VSPACE-" 3401272 NIL VSPACE- (NIL T T) -8 NIL NIL NIL) (-1305 3400940 3400994 3401062 "VOID" 3401097 T VOID (NIL) -8 NIL NIL NIL) (-1304 3397208 3398003 3398740 "VIEWDEF" 3400225 T VIEWDEF (NIL) -7 NIL NIL NIL) (-1303 3386152 3388756 3390929 "VIEW3D" 3395057 T VIEW3D (NIL) -8 NIL NIL NIL) (-1302 3378169 3380063 3381642 "VIEW2D" 3384595 T VIEW2D (NIL) -8 NIL NIL NIL) (-1301 3376269 3376664 3377070 "VIEW" 3377785 T VIEW (NIL) -7 NIL NIL NIL) (-1300 3374822 3375105 3375423 "VECTOR2" 3375999 NIL VECTOR2 (NIL T T) -7 NIL NIL NIL) (-1299 3369842 3374592 3374684 "VECTOR" 3374765 NIL VECTOR (NIL T) -8 NIL NIL NIL) (-1298 3362901 3367546 3367589 "VECTCAT" 3368584 NIL VECTCAT (NIL T) -9 NIL 3369171 NIL) (-1297 3361843 3362169 3362559 "VECTCAT-" 3362564 NIL VECTCAT- (NIL T T) -8 NIL NIL NIL) (-1296 3361249 3361494 3361614 "VARIABLE" 3361758 NIL VARIABLE (NIL NIL) -8 NIL NIL NIL) (-1295 3361182 3361187 3361217 "UTYPE" 3361222 T UTYPE (NIL) -9 NIL NIL NIL) (-1294 3359990 3360166 3360428 "UTSODETL" 3361008 NIL UTSODETL (NIL T T T T) -7 NIL NIL NIL) (-1293 3357382 3357890 3358414 "UTSODE" 3359531 NIL UTSODE (NIL T T) -7 NIL NIL NIL) (-1292 3347392 3353315 3353358 "UTSCAT" 3354470 NIL UTSCAT (NIL T) -9 NIL 3355228 NIL) (-1291 3344518 3345462 3346451 "UTSCAT-" 3346456 NIL UTSCAT- (NIL T T) -8 NIL NIL NIL) (-1290 3344139 3344188 3344321 "UTS2" 3344469 NIL UTS2 (NIL T T T T) -7 NIL NIL NIL) (-1289 3335456 3341900 3342380 "UTS" 3343717 NIL UTS (NIL T NIL NIL) -8 NIL NIL NIL) (-1288 3329434 3332266 3332309 "URAGG" 3334379 NIL URAGG (NIL T) -9 NIL 3335102 NIL) (-1287 3326466 3327434 3328458 "URAGG-" 3328463 NIL URAGG- (NIL T T) -8 NIL NIL NIL) (-1286 3321842 3325101 3325566 "UPXSSING" 3326130 NIL UPXSSING (NIL T T NIL NIL) -8 NIL NIL NIL) (-1285 3314271 3321746 3321818 "UPXSCONS" 3321823 NIL UPXSCONS (NIL T T) -8 NIL NIL NIL) (-1284 3303029 3310473 3310535 "UPXSCCA" 3311109 NIL UPXSCCA (NIL T T) -9 NIL 3311342 NIL) (-1283 3302649 3302752 3302926 "UPXSCCA-" 3302931 NIL UPXSCCA- (NIL T T T) -8 NIL NIL NIL) (-1282 3291307 3298476 3298519 "UPXSCAT" 3299167 NIL UPXSCAT (NIL T) -9 NIL 3299776 NIL) (-1281 3290731 3290816 3290995 "UPXS2" 3291222 NIL UPXS2 (NIL T T NIL NIL NIL NIL) -7 NIL NIL NIL) (-1280 3282223 3290113 3290377 "UPXS" 3290525 NIL UPXS (NIL T NIL NIL) -8 NIL NIL NIL) (-1279 3280859 3281130 3281481 "UPSQFREE" 3281966 NIL UPSQFREE (NIL T T) -7 NIL NIL NIL) (-1278 3273690 3277125 3277180 "UPSCAT" 3278260 NIL UPSCAT (NIL T T) -9 NIL 3279026 NIL) (-1277 3272846 3273101 3273428 "UPSCAT-" 3273433 NIL UPSCAT- (NIL T T T) -8 NIL NIL NIL) (-1276 3272467 3272516 3272649 "UPOLYC2" 3272797 NIL UPOLYC2 (NIL T T T T) -7 NIL NIL NIL) (-1275 3256615 3265594 3265637 "UPOLYC" 3267738 NIL UPOLYC (NIL T) -9 NIL 3268959 NIL) (-1274 3247484 3250383 3253523 "UPOLYC-" 3253528 NIL UPOLYC- (NIL T T) -8 NIL NIL NIL) (-1273 3246805 3246930 3247094 "UPMP" 3247373 NIL UPMP (NIL T T) -7 NIL NIL NIL) (-1272 3246352 3246439 3246578 "UPDIVP" 3246718 NIL UPDIVP (NIL T T) -7 NIL NIL NIL) (-1271 3244890 3245169 3245485 "UPDECOMP" 3246101 NIL UPDECOMP (NIL T T) -7 NIL NIL NIL) (-1270 3244103 3244233 3244419 "UPCDEN" 3244774 NIL UPCDEN (NIL T T T) -7 NIL NIL NIL) (-1269 3243616 3243691 3243840 "UP2" 3244028 NIL UP2 (NIL NIL T NIL T) -7 NIL NIL NIL) (-1268 3234212 3243299 3243428 "UP" 3243535 NIL UP (NIL NIL T) -8 NIL NIL NIL) (-1267 3233417 3233554 3233759 "UNISEG2" 3234055 NIL UNISEG2 (NIL T T) -7 NIL NIL NIL) (-1266 3231770 3232621 3232898 "UNISEG" 3233175 NIL UNISEG (NIL T) -8 NIL NIL NIL) (-1265 3230812 3231010 3231236 "UNIFACT" 3231586 NIL UNIFACT (NIL T) -7 NIL NIL NIL) (-1264 3217543 3230716 3230788 "ULSCONS" 3230793 NIL ULSCONS (NIL T T) -8 NIL NIL NIL) (-1263 3197360 3210623 3210685 "ULSCCAT" 3211323 NIL ULSCCAT (NIL T T) -9 NIL 3211612 NIL) (-1262 3196356 3196655 3197043 "ULSCCAT-" 3197048 NIL ULSCCAT- (NIL T T T) -8 NIL NIL NIL) (-1261 3184811 3191902 3191945 "ULSCAT" 3192808 NIL ULSCAT (NIL T) -9 NIL 3193539 NIL) (-1260 3184235 3184320 3184499 "ULS2" 3184726 NIL ULS2 (NIL T T NIL NIL NIL NIL) -7 NIL NIL NIL) (-1259 3166066 3183547 3183789 "ULS" 3184051 NIL ULS (NIL T NIL NIL) -8 NIL NIL NIL) (-1258 3164985 3165685 3165799 "UINT8" 3165910 T UINT8 (NIL) -8 NIL NIL 3166002) (-1257 3163903 3164603 3164717 "UINT64" 3164828 T UINT64 (NIL) -8 NIL NIL 3164920) (-1256 3162821 3163521 3163635 "UINT32" 3163746 T UINT32 (NIL) -8 NIL NIL 3163838) (-1255 3161739 3162439 3162553 "UINT16" 3162664 T UINT16 (NIL) -8 NIL NIL 3162756) (-1254 3159818 3160985 3161015 "UFD" 3161227 T UFD (NIL) -9 NIL 3161341 NIL) (-1253 3159600 3159658 3159753 "UFD-" 3159758 NIL UFD- (NIL T) -8 NIL NIL NIL) (-1252 3158658 3158865 3159081 "UDVO" 3159406 T UDVO (NIL) -7 NIL NIL NIL) (-1251 3156424 3156883 3157354 "UDPO" 3158222 NIL UDPO (NIL T) -7 NIL NIL NIL) (-1250 3156136 3156379 3156410 "TYPEAST" 3156415 T TYPEAST (NIL) -8 NIL NIL NIL) (-1249 3156069 3156074 3156104 "TYPE" 3156109 T TYPE (NIL) -9 NIL NIL NIL) (-1248 3155022 3155242 3155482 "TWOFACT" 3155863 NIL TWOFACT (NIL T) -7 NIL NIL NIL) (-1247 3153997 3154431 3154666 "TUPLE" 3154822 NIL TUPLE (NIL T) -8 NIL NIL NIL) (-1246 3151634 3152207 3152746 "TUBETOOL" 3153480 T TUBETOOL (NIL) -7 NIL NIL NIL) (-1245 3150440 3150681 3150923 "TUBE" 3151427 NIL TUBE (NIL T) -8 NIL NIL NIL) (-1244 3138689 3143197 3143294 "TSETCAT" 3148563 NIL TSETCAT (NIL T T T T) -9 NIL 3150095 NIL) (-1243 3133157 3135021 3136912 "TSETCAT-" 3136917 NIL TSETCAT- (NIL T T T T T) -8 NIL NIL NIL) (-1242 3127343 3132129 3132412 "TS" 3132909 NIL TS (NIL T) -8 NIL NIL NIL) (-1241 3121816 3122829 3123758 "TRMANIP" 3126479 NIL TRMANIP (NIL T T) -7 NIL NIL NIL) (-1240 3121245 3121320 3121483 "TRIMAT" 3121748 NIL TRIMAT (NIL T T T T) -7 NIL NIL NIL) (-1239 3119057 3119348 3119705 "TRIGMNIP" 3120994 NIL TRIGMNIP (NIL T T) -7 NIL NIL NIL) (-1238 3118541 3118690 3118720 "TRIGCAT" 3118933 T TRIGCAT (NIL) -9 NIL NIL NIL) (-1237 3118186 3118289 3118430 "TRIGCAT-" 3118435 NIL TRIGCAT- (NIL T) -8 NIL NIL NIL) (-1236 3114911 3117044 3117325 "TREE" 3117940 NIL TREE (NIL T) -8 NIL NIL NIL) (-1235 3114017 3114713 3114743 "TRANFUN" 3114778 T TRANFUN (NIL) -9 NIL 3114844 NIL) (-1234 3113236 3113487 3113767 "TRANFUN-" 3113772 NIL TRANFUN- (NIL T) -8 NIL NIL NIL) (-1233 3113034 3113072 3113133 "TOPSP" 3113197 T TOPSP (NIL) -7 NIL NIL NIL) (-1232 3112364 3112497 3112651 "TOOLSIGN" 3112915 NIL TOOLSIGN (NIL T) -7 NIL NIL NIL) (-1231 3110878 3111541 3111780 "TEXTFILE" 3112147 T TEXTFILE (NIL) -8 NIL NIL NIL) (-1230 3110653 3110690 3110762 "TEX1" 3110841 NIL TEX1 (NIL T) -7 NIL NIL NIL) (-1229 3108457 3109106 3109535 "TEX" 3110246 T TEX (NIL) -8 NIL NIL NIL) (-1228 3108093 3108168 3108258 "TEMUTL" 3108389 T TEMUTL (NIL) -7 NIL NIL NIL) (-1227 3106187 3106527 3106852 "TBCMPPK" 3107816 NIL TBCMPPK (NIL T T) -7 NIL NIL NIL) (-1226 3097621 3104273 3104329 "TBAGG" 3104729 NIL TBAGG (NIL T T) -9 NIL 3104940 NIL) (-1225 3092505 3094179 3095933 "TBAGG-" 3095938 NIL TBAGG- (NIL T T T) -8 NIL NIL NIL) (-1224 3091871 3091996 3092141 "TANEXP" 3092394 NIL TANEXP (NIL T) -7 NIL NIL NIL) (-1223 3091322 3091646 3091736 "TALGOP" 3091816 NIL TALGOP (NIL T) -8 NIL NIL NIL) (-1222 3090716 3090833 3090971 "TABLEAU" 3091219 NIL TABLEAU (NIL T) -8 NIL NIL NIL) (-1221 3083844 3090573 3090666 "TABLE" 3090671 NIL TABLE (NIL T T) -8 NIL NIL NIL) (-1220 3078374 3079672 3080920 "TABLBUMP" 3082630 NIL TABLBUMP (NIL T) -7 NIL NIL NIL) (-1219 3077584 3077743 3077924 "SYSTEM" 3078215 T SYSTEM (NIL) -8 NIL NIL NIL) (-1218 3073989 3074742 3075525 "SYSSOLP" 3076835 NIL SYSSOLP (NIL T) -7 NIL NIL NIL) (-1217 3073751 3073944 3073975 "SYSPTR" 3073980 T SYSPTR (NIL) -8 NIL NIL NIL) (-1216 3072590 3073282 3073408 "SYSNNI" 3073594 NIL SYSNNI (NIL NIL) -8 NIL NIL 3073686) (-1215 3071797 3072352 3072431 "SYSINT" 3072491 NIL SYSINT (NIL NIL) -8 NIL NIL 3072536) (-1214 3067895 3069075 3069785 "SYNTAX" 3071109 T SYNTAX (NIL) -8 NIL NIL NIL) (-1213 3064975 3065655 3066287 "SYMTAB" 3067285 T SYMTAB (NIL) -8 NIL NIL NIL) (-1212 3060074 3061126 3062109 "SYMS" 3064014 T SYMS (NIL) -8 NIL NIL NIL) (-1211 3056980 3059525 3059758 "SYMPOLY" 3059876 NIL SYMPOLY (NIL T) -8 NIL NIL NIL) (-1210 3056485 3056572 3056695 "SYMFUNC" 3056892 NIL SYMFUNC (NIL T) -7 NIL NIL NIL) (-1209 3052283 3053797 3054610 "SYMBOL" 3055694 T SYMBOL (NIL) -8 NIL NIL NIL) (-1208 3045756 3047511 3049231 "SWITCH" 3050585 T SWITCH (NIL) -8 NIL NIL NIL) (-1207 3038517 3044712 3045006 "SUTS" 3045520 NIL SUTS (NIL T NIL NIL) -8 NIL NIL NIL) (-1206 3030009 3037899 3038163 "SUPXS" 3038311 NIL SUPXS (NIL T NIL NIL) -8 NIL NIL NIL) (-1205 3029156 3029295 3029512 "SUPFRACF" 3029877 NIL SUPFRACF (NIL T T T T) -7 NIL NIL NIL) (-1204 3028771 3028836 3028949 "SUP2" 3029091 NIL SUP2 (NIL T T) -7 NIL NIL NIL) (-1203 3019315 3028389 3028515 "SUP" 3028680 NIL SUP (NIL T) -8 NIL NIL NIL) (-1202 3017739 3018037 3018393 "SUMRF" 3019014 NIL SUMRF (NIL T) -7 NIL NIL NIL) (-1201 3017062 3017140 3017332 "SUMFS" 3017660 NIL SUMFS (NIL T T) -7 NIL NIL NIL) (-1200 2998928 3016374 3016616 "SULS" 3016878 NIL SULS (NIL T NIL NIL) -8 NIL NIL NIL) (-1199 2998476 2998750 2998820 "SUCHTAST" 2998880 T SUCHTAST (NIL) -8 NIL NIL NIL) (-1198 2997717 2998001 2998141 "SUCH" 2998384 NIL SUCH (NIL T T) -8 NIL NIL NIL) (-1197 2991356 2992623 2993582 "SUBSPACE" 2996805 NIL SUBSPACE (NIL NIL T) -8 NIL NIL NIL) (-1196 2990776 2990876 2991040 "SUBRESP" 2991244 NIL SUBRESP (NIL T T) -7 NIL NIL NIL) (-1195 2984787 2986069 2987216 "STTFNC" 2989676 NIL STTFNC (NIL T) -7 NIL NIL NIL) (-1194 2977981 2979452 2980763 "STTF" 2983523 NIL STTF (NIL T) -7 NIL NIL NIL) (-1193 2969097 2971163 2972957 "STTAYLOR" 2976222 NIL STTAYLOR (NIL T) -7 NIL NIL NIL) (-1192 2961965 2968961 2969044 "STRTBL" 2969049 NIL STRTBL (NIL T) -8 NIL NIL NIL) (-1191 2956476 2961674 2961773 "STRING" 2961888 T STRING (NIL) -8 NIL NIL NIL) (-1190 2955980 2956063 2956207 "STREAM3" 2956393 NIL STREAM3 (NIL T T T) -7 NIL NIL NIL) (-1189 2954944 2955145 2955380 "STREAM2" 2955793 NIL STREAM2 (NIL T T) -7 NIL NIL NIL) (-1188 2954626 2954684 2954777 "STREAM1" 2954886 NIL STREAM1 (NIL T) -7 NIL NIL NIL) (-1187 2946740 2952245 2952856 "STREAM" 2954050 NIL STREAM (NIL T) -8 NIL NIL NIL) (-1186 2945732 2945937 2946168 "STINPROD" 2946556 NIL STINPROD (NIL T) -7 NIL NIL NIL) (-1185 2944847 2945221 2945369 "STEPAST" 2945606 T STEPAST (NIL) -8 NIL NIL NIL) (-1184 2944343 2944588 2944618 "STEP" 2944712 T STEP (NIL) -9 NIL 2944783 NIL) (-1183 2937513 2944242 2944319 "STBL" 2944324 NIL STBL (NIL T T NIL) -8 NIL NIL NIL) (-1182 2931694 2936307 2936350 "STAGG" 2936782 NIL STAGG (NIL T) -9 NIL 2936961 NIL) (-1181 2929246 2929998 2930870 "STAGG-" 2930875 NIL STAGG- (NIL T T) -8 NIL NIL NIL) (-1180 2927332 2929016 2929108 "STACK" 2929189 NIL STACK (NIL T) -8 NIL NIL NIL) (-1179 2926649 2927162 2927192 "SRING" 2927197 T SRING (NIL) -9 NIL 2927217 NIL) (-1178 2918771 2924790 2925246 "SREGSET" 2926279 NIL SREGSET (NIL T T T T) -8 NIL NIL NIL) (-1177 2911118 2912565 2914078 "SRDCMPK" 2917377 NIL SRDCMPK (NIL T T T T T) -7 NIL NIL NIL) (-1176 2903532 2908477 2908507 "SRAGG" 2909810 T SRAGG (NIL) -9 NIL 2910418 NIL) (-1175 2902483 2902804 2903183 "SRAGG-" 2903188 NIL SRAGG- (NIL T) -8 NIL NIL NIL) (-1174 2896181 2901430 2901851 "SQMATRIX" 2902109 NIL SQMATRIX (NIL NIL T) -8 NIL NIL NIL) (-1173 2889707 2892899 2893626 "SPLTREE" 2895526 NIL SPLTREE (NIL T T) -8 NIL NIL NIL) (-1172 2885532 2886363 2887009 "SPLNODE" 2889133 NIL SPLNODE (NIL T T) -8 NIL NIL NIL) (-1171 2884507 2884812 2884842 "SPFCAT" 2885286 T SPFCAT (NIL) -9 NIL NIL NIL) (-1170 2883202 2883454 2883718 "SPECOUT" 2884265 T SPECOUT (NIL) -7 NIL NIL NIL) (-1169 2873848 2876166 2876196 "SPADXPT" 2880874 T SPADXPT (NIL) -9 NIL 2883040 NIL) (-1168 2873603 2873649 2873718 "SPADPRSR" 2873801 T SPADPRSR (NIL) -7 NIL NIL NIL) (-1167 2871206 2873558 2873589 "SPADAST" 2873594 T SPADAST (NIL) -8 NIL NIL NIL) (-1166 2862807 2864910 2864953 "SPACEC" 2869326 NIL SPACEC (NIL T) -9 NIL 2871142 NIL) (-1165 2860607 2862739 2862788 "SPACE3" 2862793 NIL SPACE3 (NIL T) -8 NIL NIL NIL) (-1164 2859339 2859530 2859821 "SORTPAK" 2860412 NIL SORTPAK (NIL T T) -7 NIL NIL NIL) (-1163 2857401 2857734 2858146 "SOLVETRA" 2859003 NIL SOLVETRA (NIL T) -7 NIL NIL NIL) (-1162 2856439 2856673 2856934 "SOLVESER" 2857174 NIL SOLVESER (NIL T) -7 NIL NIL NIL) (-1161 2851671 2852631 2853626 "SOLVERAD" 2855491 NIL SOLVERAD (NIL T) -7 NIL NIL NIL) (-1160 2847396 2848095 2848824 "SOLVEFOR" 2851038 NIL SOLVEFOR (NIL T T) -7 NIL NIL NIL) (-1159 2841114 2846744 2846841 "SNTSCAT" 2846846 NIL SNTSCAT (NIL T T T T) -9 NIL 2846916 NIL) (-1158 2834665 2839437 2839828 "SMTS" 2840804 NIL SMTS (NIL T T T) -8 NIL NIL NIL) (-1157 2828387 2834553 2834630 "SMP" 2834635 NIL SMP (NIL T T) -8 NIL NIL NIL) (-1156 2826516 2826847 2827245 "SMITH" 2828084 NIL SMITH (NIL T T T T) -7 NIL NIL NIL) (-1155 2818155 2823095 2823198 "SMATCAT" 2824549 NIL SMATCAT (NIL NIL T T T) -9 NIL 2825099 NIL) (-1154 2814927 2815918 2817096 "SMATCAT-" 2817101 NIL SMATCAT- (NIL T NIL T T T) -8 NIL NIL NIL) (-1153 2812507 2814135 2814178 "SKAGG" 2814439 NIL SKAGG (NIL T) -9 NIL 2814574 NIL) (-1152 2808027 2811990 2812167 "SINT" 2812319 T SINT (NIL) -8 NIL NIL 2812474) (-1151 2807793 2807837 2807903 "SIMPAN" 2807983 T SIMPAN (NIL) -7 NIL NIL NIL) (-1150 2806613 2806852 2807127 "SIGNRF" 2807552 NIL SIGNRF (NIL T) -7 NIL NIL NIL) (-1149 2805428 2805597 2805881 "SIGNEF" 2806442 NIL SIGNEF (NIL T T) -7 NIL NIL NIL) (-1148 2804668 2805011 2805135 "SIGAST" 2805326 T SIGAST (NIL) -8 NIL NIL NIL) (-1147 2803893 2804203 2804343 "SIG" 2804550 T SIG (NIL) -8 NIL NIL NIL) (-1146 2801545 2802037 2802543 "SHP" 2803434 NIL SHP (NIL T NIL) -7 NIL NIL NIL) (-1145 2794983 2801446 2801522 "SHDP" 2801527 NIL SHDP (NIL NIL NIL T) -8 NIL NIL NIL) (-1144 2794494 2794734 2794764 "SGROUP" 2794857 T SGROUP (NIL) -9 NIL 2794919 NIL) (-1143 2794346 2794378 2794451 "SGROUP-" 2794456 NIL SGROUP- (NIL T) -8 NIL NIL NIL) (-1142 2791065 2791835 2792558 "SGCF" 2793645 T SGCF (NIL) -7 NIL NIL NIL) (-1141 2784881 2790511 2790608 "SFRTCAT" 2790613 NIL SFRTCAT (NIL T T T T) -9 NIL 2790652 NIL) (-1140 2778200 2779320 2780456 "SFRGCD" 2783864 NIL SFRGCD (NIL T T T T T) -7 NIL NIL NIL) (-1139 2771218 2772399 2773585 "SFQCMPK" 2777133 NIL SFQCMPK (NIL T T T T T) -7 NIL NIL NIL) (-1138 2770820 2770927 2771038 "SFORT" 2771159 NIL SFORT (NIL T T) -8 NIL NIL NIL) (-1137 2769746 2770660 2770781 "SEXOF" 2770786 NIL SEXOF (NIL T T T T T) -8 NIL NIL NIL) (-1136 2765335 2766242 2766337 "SEXCAT" 2768959 NIL SEXCAT (NIL T T T T T) -9 NIL 2769519 NIL) (-1135 2764250 2765216 2765284 "SEX" 2765289 T SEX (NIL) -8 NIL NIL NIL) (-1134 2762372 2762963 2763268 "SETMN" 2763991 NIL SETMN (NIL NIL NIL) -8 NIL NIL NIL) (-1133 2761902 2762090 2762120 "SETCAT" 2762237 T SETCAT (NIL) -9 NIL 2762322 NIL) (-1132 2761670 2761734 2761833 "SETCAT-" 2761838 NIL SETCAT- (NIL T) -8 NIL NIL NIL) (-1131 2757884 2760131 2760174 "SETAGG" 2761044 NIL SETAGG (NIL T) -9 NIL 2761384 NIL) (-1130 2757306 2757458 2757695 "SETAGG-" 2757700 NIL SETAGG- (NIL T T) -8 NIL NIL NIL) (-1129 2754229 2757240 2757288 "SET" 2757293 NIL SET (NIL T) -8 NIL NIL NIL) (-1128 2753612 2753925 2754026 "SEQAST" 2754150 T SEQAST (NIL) -8 NIL NIL NIL) (-1127 2752739 2753105 2753166 "SEGXCAT" 2753452 NIL SEGXCAT (NIL T T) -9 NIL 2753572 NIL) (-1126 2751664 2751932 2751975 "SEGCAT" 2752497 NIL SEGCAT (NIL T) -9 NIL 2752718 NIL) (-1125 2751279 2751344 2751457 "SEGBIND2" 2751599 NIL SEGBIND2 (NIL T T) -7 NIL NIL NIL) (-1124 2750169 2750642 2750850 "SEGBIND" 2751106 NIL SEGBIND (NIL T) -8 NIL NIL NIL) (-1123 2749688 2749970 2750047 "SEGAST" 2750114 T SEGAST (NIL) -8 NIL NIL NIL) (-1122 2748897 2749033 2749237 "SEG2" 2749532 NIL SEG2 (NIL T T) -7 NIL NIL NIL) (-1121 2747813 2748563 2748745 "SEG" 2748750 NIL SEG (NIL T) -8 NIL NIL NIL) (-1120 2747046 2747748 2747795 "SDVAR" 2747800 NIL SDVAR (NIL T) -8 NIL NIL NIL) (-1119 2738404 2746816 2746946 "SDPOL" 2746951 NIL SDPOL (NIL T) -8 NIL NIL NIL) (-1118 2736973 2737263 2737582 "SCPKG" 2738119 NIL SCPKG (NIL T) -7 NIL NIL NIL) (-1117 2736095 2736309 2736501 "SCOPE" 2736803 T SCOPE (NIL) -8 NIL NIL NIL) (-1116 2735291 2735449 2735628 "SCACHE" 2735950 NIL SCACHE (NIL T) -7 NIL NIL NIL) (-1115 2734875 2735109 2735139 "SASTCAT" 2735144 T SASTCAT (NIL) -9 NIL 2735157 NIL) (-1114 2734278 2734710 2734786 "SAOS" 2734821 T SAOS (NIL) -8 NIL NIL NIL) (-1113 2733837 2733878 2734051 "SAERFFC" 2734237 NIL SAERFFC (NIL T T T) -7 NIL NIL NIL) (-1112 2733424 2733465 2733624 "SAEFACT" 2733796 NIL SAEFACT (NIL T T T) -7 NIL NIL NIL) (-1111 2726472 2733321 2733401 "SAE" 2733406 NIL SAE (NIL T T NIL) -8 NIL NIL NIL) (-1110 2724775 2725107 2725508 "RURPK" 2726138 NIL RURPK (NIL T NIL) -7 NIL NIL NIL) (-1109 2723352 2723718 2724023 "RULESET" 2724609 NIL RULESET (NIL T T T) -8 NIL NIL NIL) (-1108 2722922 2723146 2723229 "RULECOLD" 2723304 NIL RULECOLD (NIL NIL) -8 NIL NIL NIL) (-1107 2720037 2720675 2721133 "RULE" 2722603 NIL RULE (NIL T T T) -8 NIL NIL NIL) (-1106 2719821 2719855 2719926 "RTVALUE" 2719988 T RTVALUE (NIL) -8 NIL NIL NIL) (-1105 2719232 2719538 2719632 "RSTRCAST" 2719749 T RSTRCAST (NIL) -8 NIL NIL NIL) (-1104 2714002 2714875 2715795 "RSETGCD" 2718431 NIL RSETGCD (NIL T T T T T) -7 NIL NIL NIL) (-1103 2702680 2708310 2708407 "RSETCAT" 2712526 NIL RSETCAT (NIL T T T T) -9 NIL 2713623 NIL) (-1102 2700499 2701146 2701970 "RSETCAT-" 2701975 NIL RSETCAT- (NIL T T T T T) -8 NIL NIL NIL) (-1101 2692807 2694261 2695781 "RSDCMPK" 2699098 NIL RSDCMPK (NIL T T T T T) -7 NIL NIL NIL) (-1100 2690676 2691239 2691313 "RRCC" 2692399 NIL RRCC (NIL T T) -9 NIL 2692743 NIL) (-1099 2689997 2690201 2690480 "RRCC-" 2690485 NIL RRCC- (NIL T T T) -8 NIL NIL NIL) (-1098 2689380 2689693 2689794 "RPTAST" 2689918 T RPTAST (NIL) -8 NIL NIL NIL) (-1097 2661766 2672492 2672559 "RPOLCAT" 2683225 NIL RPOLCAT (NIL T T T) -9 NIL 2686385 NIL) (-1096 2652736 2655604 2658726 "RPOLCAT-" 2658731 NIL RPOLCAT- (NIL T T T T) -8 NIL NIL NIL) (-1095 2643303 2650947 2651429 "ROUTINE" 2652276 T ROUTINE (NIL) -8 NIL NIL NIL) (-1094 2639366 2642929 2643069 "ROMAN" 2643185 T ROMAN (NIL) -8 NIL NIL NIL) (-1093 2637478 2638226 2638486 "ROIRC" 2639171 NIL ROIRC (NIL T T) -8 NIL NIL NIL) (-1092 2633251 2636020 2636050 "RNS" 2636319 T RNS (NIL) -9 NIL 2636575 NIL) (-1091 2631658 2632143 2632677 "RNS-" 2632752 NIL RNS- (NIL T) -8 NIL NIL NIL) (-1090 2630619 2631023 2631225 "RNGBIND" 2631509 NIL RNGBIND (NIL T T) -8 NIL NIL NIL) (-1089 2629912 2630416 2630446 "RNG" 2630451 T RNG (NIL) -9 NIL 2630472 NIL) (-1088 2629207 2629685 2629728 "RMODULE" 2629733 NIL RMODULE (NIL T) -9 NIL 2629760 NIL) (-1087 2628031 2628137 2628473 "RMCAT2" 2629108 NIL RMCAT2 (NIL NIL NIL T T T T T T T T) -7 NIL NIL NIL) (-1086 2624647 2627377 2627674 "RMATRIX" 2627793 NIL RMATRIX (NIL NIL NIL T) -8 NIL NIL NIL) (-1085 2617257 2619734 2619849 "RMATCAT" 2623208 NIL RMATCAT (NIL NIL NIL T T T) -9 NIL 2624190 NIL) (-1084 2616596 2616779 2617086 "RMATCAT-" 2617091 NIL RMATCAT- (NIL T NIL NIL T T T) -8 NIL NIL NIL) (-1083 2616169 2616383 2616426 "RLINSET" 2616488 NIL RLINSET (NIL T) -9 NIL 2616532 NIL) (-1082 2615730 2615811 2615939 "RINTERP" 2616088 NIL RINTERP (NIL NIL T) -7 NIL NIL NIL) (-1081 2614654 2615328 2615358 "RING" 2615414 T RING (NIL) -9 NIL 2615506 NIL) (-1080 2614434 2614490 2614587 "RING-" 2614592 NIL RING- (NIL T) -8 NIL NIL NIL) (-1079 2613245 2613512 2613770 "RIDIST" 2614198 T RIDIST (NIL) -7 NIL NIL NIL) (-1078 2603984 2612713 2612919 "RGCHAIN" 2613093 NIL RGCHAIN (NIL T NIL) -8 NIL NIL NIL) (-1077 2603242 2603726 2603767 "RGBCSPC" 2603825 NIL RGBCSPC (NIL T) -9 NIL 2603877 NIL) (-1076 2602308 2602767 2602808 "RGBCMDL" 2603040 NIL RGBCMDL (NIL T) -9 NIL 2603154 NIL) (-1075 2601948 2602017 2602120 "RFFACTOR" 2602239 NIL RFFACTOR (NIL T) -7 NIL NIL NIL) (-1074 2601667 2601708 2601805 "RFFACT" 2601907 NIL RFFACT (NIL T) -7 NIL NIL NIL) (-1073 2599718 2600148 2600530 "RFDIST" 2601307 T RFDIST (NIL) -7 NIL NIL NIL) (-1072 2596658 2597326 2597996 "RF" 2599082 NIL RF (NIL T) -7 NIL NIL NIL) (-1071 2596105 2596203 2596366 "RETSOL" 2596560 NIL RETSOL (NIL T T) -7 NIL NIL NIL) (-1070 2595723 2595821 2595864 "RETRACT" 2595997 NIL RETRACT (NIL T) -9 NIL 2596084 NIL) (-1069 2595566 2595597 2595684 "RETRACT-" 2595689 NIL RETRACT- (NIL T T) -8 NIL NIL NIL) (-1068 2595114 2595388 2595458 "RETAST" 2595518 T RETAST (NIL) -8 NIL NIL NIL) (-1067 2587578 2594767 2594894 "RESULT" 2595009 T RESULT (NIL) -8 NIL NIL NIL) (-1066 2586013 2586847 2587046 "RESRING" 2587481 NIL RESRING (NIL T T T T NIL) -8 NIL NIL NIL) (-1065 2585637 2585698 2585796 "RESLATC" 2585950 NIL RESLATC (NIL T) -7 NIL NIL NIL) (-1064 2585336 2585377 2585484 "REPSQ" 2585596 NIL REPSQ (NIL T) -7 NIL NIL NIL) (-1063 2585027 2585068 2585179 "REPDB" 2585295 NIL REPDB (NIL T) -7 NIL NIL NIL) (-1062 2578859 2580316 2581539 "REP2" 2583839 NIL REP2 (NIL T) -7 NIL NIL NIL) (-1061 2575162 2575917 2576725 "REP1" 2578086 NIL REP1 (NIL T) -7 NIL NIL NIL) (-1060 2572542 2573164 2573766 "REP" 2574582 T REP (NIL) -7 NIL NIL NIL) (-1059 2564664 2570683 2571139 "REGSET" 2572172 NIL REGSET (NIL T T T T) -8 NIL NIL NIL) (-1058 2563373 2563812 2564062 "REF" 2564449 NIL REF (NIL T) -8 NIL NIL NIL) (-1057 2562738 2562853 2563020 "REDORDER" 2563257 NIL REDORDER (NIL T T) -7 NIL NIL NIL) (-1056 2558109 2561951 2562178 "RECLOS" 2562566 NIL RECLOS (NIL T) -8 NIL NIL NIL) (-1055 2557143 2557342 2557557 "REALSOLV" 2557916 T REALSOLV (NIL) -7 NIL NIL NIL) (-1054 2553590 2554428 2555312 "REAL0Q" 2556308 NIL REAL0Q (NIL T) -7 NIL NIL NIL) (-1053 2549143 2550179 2551240 "REAL0" 2552571 NIL REAL0 (NIL T) -7 NIL NIL NIL) (-1052 2548977 2549030 2549060 "REAL" 2549065 T REAL (NIL) -9 NIL 2549100 NIL) (-1051 2548388 2548694 2548788 "RDUCEAST" 2548905 T RDUCEAST (NIL) -8 NIL NIL NIL) (-1050 2547787 2547865 2548072 "RDIV" 2548310 NIL RDIV (NIL T T T T T) -7 NIL NIL NIL) (-1049 2546837 2547029 2547242 "RDIST" 2547609 NIL RDIST (NIL T) -7 NIL NIL NIL) (-1048 2545422 2545721 2546093 "RDETRS" 2546545 NIL RDETRS (NIL T T) -7 NIL NIL NIL) (-1047 2543216 2543688 2544226 "RDETR" 2544964 NIL RDETR (NIL T T) -7 NIL NIL NIL) (-1046 2541835 2542119 2542516 "RDEEFS" 2542932 NIL RDEEFS (NIL T T) -7 NIL NIL NIL) (-1045 2540338 2540650 2541075 "RDEEF" 2541523 NIL RDEEF (NIL T T) -7 NIL NIL NIL) (-1044 2533817 2537292 2537322 "RCFIELD" 2538617 T RCFIELD (NIL) -9 NIL 2539348 NIL) (-1043 2531773 2532385 2533081 "RCFIELD-" 2533156 NIL RCFIELD- (NIL T) -8 NIL NIL NIL) (-1042 2527936 2529846 2529889 "RCAGG" 2530973 NIL RCAGG (NIL T) -9 NIL 2531438 NIL) (-1041 2527546 2527658 2527821 "RCAGG-" 2527826 NIL RCAGG- (NIL T T) -8 NIL NIL NIL) (-1040 2526863 2526993 2527158 "RATRET" 2527430 NIL RATRET (NIL T) -7 NIL NIL NIL) (-1039 2526404 2526483 2526604 "RATFACT" 2526791 NIL RATFACT (NIL T) -7 NIL NIL NIL) (-1038 2525682 2525832 2525984 "RANDSRC" 2526274 T RANDSRC (NIL) -7 NIL NIL NIL) (-1037 2525410 2525460 2525533 "RADUTIL" 2525631 T RADUTIL (NIL) -7 NIL NIL NIL) (-1036 2517555 2524241 2524552 "RADIX" 2525133 NIL RADIX (NIL NIL) -8 NIL NIL NIL) (-1035 2507170 2517397 2517527 "RADFF" 2517532 NIL RADFF (NIL T T T NIL NIL) -8 NIL NIL NIL) (-1034 2506799 2506892 2506922 "RADCAT" 2507082 T RADCAT (NIL) -9 NIL NIL NIL) (-1033 2506569 2506629 2506729 "RADCAT-" 2506734 NIL RADCAT- (NIL T) -8 NIL NIL NIL) (-1032 2504594 2506339 2506431 "QUEUE" 2506512 NIL QUEUE (NIL T) -8 NIL NIL NIL) (-1031 2504219 2504268 2504399 "QUATCT2" 2504545 NIL QUATCT2 (NIL T T T T) -7 NIL NIL NIL) (-1030 2496597 2500642 2500684 "QUATCAT" 2501475 NIL QUATCAT (NIL T) -9 NIL 2502241 NIL) (-1029 2492478 2493773 2495163 "QUATCAT-" 2495259 NIL QUATCAT- (NIL T T) -8 NIL NIL NIL) (-1028 2488324 2492411 2492459 "QUAT" 2492464 NIL QUAT (NIL T) -8 NIL NIL NIL) (-1027 2485691 2487372 2487415 "QUAGG" 2487796 NIL QUAGG (NIL T) -9 NIL 2487971 NIL) (-1026 2485239 2485513 2485583 "QQUTAST" 2485643 T QQUTAST (NIL) -8 NIL NIL NIL) (-1025 2484150 2484752 2484917 "QFORM" 2485120 NIL QFORM (NIL NIL T) -8 NIL NIL NIL) (-1024 2483775 2483824 2483955 "QFCAT2" 2484101 NIL QFCAT2 (NIL T T T T) -7 NIL NIL NIL) (-1023 2473472 2479622 2479664 "QFCAT" 2480332 NIL QFCAT (NIL T) -9 NIL 2481333 NIL) (-1022 2468806 2470254 2471841 "QFCAT-" 2471937 NIL QFCAT- (NIL T T) -8 NIL NIL NIL) (-1021 2468237 2468371 2468503 "QEQUAT" 2468696 T QEQUAT (NIL) -8 NIL NIL NIL) (-1020 2461255 2462436 2463622 "QCMPACK" 2467170 NIL QCMPACK (NIL T T T T T) -7 NIL NIL NIL) (-1019 2460484 2460666 2460902 "QALGSET2" 2461073 NIL QALGSET2 (NIL NIL NIL) -7 NIL NIL NIL) (-1018 2457934 2458470 2458900 "QALGSET" 2460139 NIL QALGSET (NIL T T T T) -8 NIL NIL NIL) (-1017 2456601 2456843 2457162 "PWFFINTB" 2457707 NIL PWFFINTB (NIL T T T T) -7 NIL NIL NIL) (-1016 2454746 2454944 2455300 "PUSHVAR" 2456415 NIL PUSHVAR (NIL T T T T) -7 NIL NIL NIL) (-1015 2450473 2451689 2451732 "PTRANFN" 2453643 NIL PTRANFN (NIL T) -9 NIL NIL NIL) (-1014 2448810 2449155 2449479 "PTPACK" 2450184 NIL PTPACK (NIL T) -7 NIL NIL NIL) (-1013 2448433 2448496 2448607 "PTFUNC2" 2448747 NIL PTFUNC2 (NIL T T) -7 NIL NIL NIL) (-1012 2442463 2447222 2447265 "PTCAT" 2447565 NIL PTCAT (NIL T) -9 NIL 2447718 NIL) (-1011 2442112 2442153 2442279 "PSQFR" 2442422 NIL PSQFR (NIL T T T T) -7 NIL NIL NIL) (-1010 2440684 2441000 2441336 "PSEUDLIN" 2441810 NIL PSEUDLIN (NIL T) -7 NIL NIL NIL) (-1009 2427204 2429779 2432105 "PSETPK" 2438444 NIL PSETPK (NIL T T T T) -7 NIL NIL NIL) (-1008 2420023 2422940 2423038 "PSETCAT" 2426079 NIL PSETCAT (NIL T T T T) -9 NIL 2426893 NIL) (-1007 2417748 2418490 2419314 "PSETCAT-" 2419319 NIL PSETCAT- (NIL T T T T T) -8 NIL NIL NIL) (-1006 2417061 2417256 2417286 "PSCURVE" 2417558 T PSCURVE (NIL) -9 NIL 2417725 NIL) (-1005 2412784 2414551 2414618 "PSCAT" 2415470 NIL PSCAT (NIL T T T) -9 NIL 2415710 NIL) (-1004 2411778 2412060 2412463 "PSCAT-" 2412468 NIL PSCAT- (NIL T T T T) -8 NIL NIL NIL) (-1003 2409946 2410837 2411102 "PRTITION" 2411535 T PRTITION (NIL) -8 NIL NIL NIL) (-1002 2409357 2409663 2409757 "PRTDAST" 2409874 T PRTDAST (NIL) -8 NIL NIL NIL) (-1001 2398201 2400623 2402813 "PRS" 2407219 NIL PRS (NIL T T) -7 NIL NIL NIL) (-1000 2395927 2397518 2397560 "PRQAGG" 2397746 NIL PRQAGG (NIL T) -9 NIL 2397848 NIL) (-999 2395106 2395555 2395583 "PROPLOG" 2395722 T PROPLOG (NIL) -9 NIL 2395837 NIL) (-998 2394704 2394767 2394890 "PROPFUN2" 2395029 NIL PROPFUN2 (NIL T T) -8 NIL NIL NIL) (-997 2394001 2394140 2394312 "PROPFUN1" 2394565 NIL PROPFUN1 (NIL T) -8 NIL NIL NIL) (-996 2391982 2392748 2393045 "PROPFRML" 2393737 NIL PROPFRML (NIL T) -8 NIL NIL NIL) (-995 2391427 2391558 2391686 "PROPERTY" 2391874 T PROPERTY (NIL) -8 NIL NIL NIL) (-994 2385240 2389593 2390413 "PRODUCT" 2390653 NIL PRODUCT (NIL T T) -8 NIL NIL NIL) (-993 2385030 2385068 2385127 "PRINT" 2385201 T PRINT (NIL) -7 NIL NIL NIL) (-992 2384346 2384487 2384639 "PRIMES" 2384910 NIL PRIMES (NIL T) -7 NIL NIL NIL) (-991 2382393 2382812 2383278 "PRIMELT" 2383925 NIL PRIMELT (NIL T) -7 NIL NIL NIL) (-990 2382110 2382171 2382199 "PRIMCAT" 2382323 T PRIMCAT (NIL) -9 NIL NIL NIL) (-989 2381099 2381295 2381523 "PRIMARR2" 2381928 NIL PRIMARR2 (NIL T T) -7 NIL NIL NIL) (-988 2376935 2381037 2381082 "PRIMARR" 2381087 NIL PRIMARR (NIL T) -8 NIL NIL NIL) (-987 2376572 2376634 2376745 "PREASSOC" 2376873 NIL PREASSOC (NIL T T) -7 NIL NIL NIL) (-986 2373537 2376030 2376264 "PR" 2376383 NIL PR (NIL T T) -8 NIL NIL NIL) (-985 2372988 2373145 2373173 "PPCURVE" 2373378 T PPCURVE (NIL) -9 NIL 2373514 NIL) (-984 2372535 2372783 2372866 "PORTNUM" 2372925 T PORTNUM (NIL) -8 NIL NIL NIL) (-983 2369872 2370293 2370885 "POLYROOT" 2372116 NIL POLYROOT (NIL T T T T T) -7 NIL NIL NIL) (-982 2369249 2369313 2369547 "POLYLIFT" 2369808 NIL POLYLIFT (NIL T T T T T) -7 NIL NIL NIL) (-981 2365470 2365973 2366602 "POLYCATQ" 2368794 NIL POLYCATQ (NIL T T T T T) -7 NIL NIL NIL) (-980 2351118 2357217 2357282 "POLYCAT" 2360796 NIL POLYCAT (NIL T T T) -9 NIL 2362674 NIL) (-979 2344258 2346443 2348820 "POLYCAT-" 2348825 NIL POLYCAT- (NIL T T T T) -8 NIL NIL NIL) (-978 2343839 2343913 2344033 "POLY2UP" 2344184 NIL POLY2UP (NIL NIL T) -7 NIL NIL NIL) (-977 2343465 2343528 2343637 "POLY2" 2343776 NIL POLY2 (NIL T T) -7 NIL NIL NIL) (-976 2336680 2343069 2343229 "POLY" 2343338 NIL POLY (NIL T) -8 NIL NIL NIL) (-975 2335341 2335604 2335880 "POLUTIL" 2336454 NIL POLUTIL (NIL T T) -7 NIL NIL NIL) (-974 2333660 2333973 2334304 "POLTOPOL" 2335063 NIL POLTOPOL (NIL NIL T) -7 NIL NIL NIL) (-973 2328770 2333594 2333641 "POINT" 2333646 NIL POINT (NIL T) -8 NIL NIL NIL) (-972 2326903 2327314 2327689 "PNTHEORY" 2328415 T PNTHEORY (NIL) -7 NIL NIL NIL) (-971 2325349 2325658 2326057 "PMTOOLS" 2326601 NIL PMTOOLS (NIL T T T) -7 NIL NIL NIL) (-970 2324936 2325020 2325137 "PMSYM" 2325265 NIL PMSYM (NIL T) -7 NIL NIL NIL) (-969 2324438 2324513 2324688 "PMQFCAT" 2324861 NIL PMQFCAT (NIL T T T) -7 NIL NIL NIL) (-968 2323819 2323917 2324079 "PMPREDFS" 2324339 NIL PMPREDFS (NIL T T T) -7 NIL NIL NIL) (-967 2323162 2323284 2323440 "PMPRED" 2323696 NIL PMPRED (NIL T) -7 NIL NIL NIL) (-966 2321816 2322034 2322412 "PMPLCAT" 2322924 NIL PMPLCAT (NIL T T T T T) -7 NIL NIL NIL) (-965 2321342 2321427 2321579 "PMLSAGG" 2321731 NIL PMLSAGG (NIL T T T) -7 NIL NIL NIL) (-964 2320809 2320891 2321073 "PMKERNEL" 2321260 NIL PMKERNEL (NIL T T) -7 NIL NIL NIL) (-963 2320420 2320501 2320614 "PMINS" 2320728 NIL PMINS (NIL T) -7 NIL NIL NIL) (-962 2319856 2319931 2320140 "PMFS" 2320345 NIL PMFS (NIL T T T) -7 NIL NIL NIL) (-961 2319072 2319202 2319407 "PMDOWN" 2319733 NIL PMDOWN (NIL T T T) -7 NIL NIL NIL) (-960 2318321 2318455 2318618 "PMASSFS" 2318959 NIL PMASSFS (NIL T T) -7 NIL NIL NIL) (-959 2317464 2317646 2317827 "PMASS" 2318160 T PMASS (NIL) -7 NIL NIL NIL) (-958 2317113 2317187 2317281 "PLOTTOOL" 2317390 T PLOTTOOL (NIL) -7 NIL NIL NIL) (-957 2312765 2313959 2314881 "PLOT3D" 2316211 T PLOT3D (NIL) -8 NIL NIL NIL) (-956 2311653 2311854 2312089 "PLOT1" 2312569 NIL PLOT1 (NIL T) -7 NIL NIL NIL) (-955 2306074 2307464 2308612 "PLOT" 2310525 T PLOT (NIL) -8 NIL NIL NIL) (-954 2281249 2286140 2290991 "PLEQN" 2301340 NIL PLEQN (NIL T T T T) -7 NIL NIL NIL) (-953 2280936 2280989 2281092 "PINTERPA" 2281196 NIL PINTERPA (NIL T T) -7 NIL NIL NIL) (-952 2280242 2280376 2280556 "PINTERP" 2280801 NIL PINTERP (NIL NIL T) -7 NIL NIL NIL) (-951 2278326 2279492 2279520 "PID" 2279717 T PID (NIL) -9 NIL 2279844 NIL) (-950 2278071 2278114 2278189 "PICOERCE" 2278283 NIL PICOERCE (NIL T) -7 NIL NIL NIL) (-949 2277167 2277835 2277922 "PI" 2277962 T PI (NIL) -8 NIL NIL 2278029) (-948 2276475 2276626 2276802 "PGROEB" 2277023 NIL PGROEB (NIL T) -7 NIL NIL NIL) (-947 2271914 2272873 2273779 "PGE" 2275589 T PGE (NIL) -7 NIL NIL NIL) (-946 2269995 2270284 2270650 "PGCD" 2271631 NIL PGCD (NIL T T T T) -7 NIL NIL NIL) (-945 2269321 2269436 2269597 "PFRPAC" 2269879 NIL PFRPAC (NIL T) -7 NIL NIL NIL) (-944 2265579 2267869 2268222 "PFR" 2269000 NIL PFR (NIL T) -8 NIL NIL NIL) (-943 2263932 2264212 2264537 "PFOTOOLS" 2265326 NIL PFOTOOLS (NIL T T) -7 NIL NIL NIL) (-942 2262447 2262704 2263055 "PFOQ" 2263689 NIL PFOQ (NIL T T T) -7 NIL NIL NIL) (-941 2260930 2261160 2261516 "PFO" 2262231 NIL PFO (NIL T T T T T) -7 NIL NIL NIL) (-940 2258014 2259520 2259548 "PFECAT" 2260141 T PFECAT (NIL) -9 NIL 2260518 NIL) (-939 2257462 2257627 2257834 "PFECAT-" 2257839 NIL PFECAT- (NIL T) -8 NIL NIL NIL) (-938 2256035 2256317 2256618 "PFBRU" 2257211 NIL PFBRU (NIL T T) -7 NIL NIL NIL) (-937 2253864 2254253 2254685 "PFBR" 2255686 NIL PFBR (NIL T T T T) -7 NIL NIL NIL) (-936 2249810 2253753 2253822 "PF" 2253827 NIL PF (NIL NIL) -8 NIL NIL NIL) (-935 2244864 2246017 2246887 "PERMGRP" 2248973 NIL PERMGRP (NIL T) -8 NIL NIL NIL) (-934 2242776 2243888 2243929 "PERMCAT" 2244329 NIL PERMCAT (NIL T) -9 NIL 2244627 NIL) (-933 2242423 2242470 2242594 "PERMAN" 2242729 NIL PERMAN (NIL NIL T) -7 NIL NIL NIL) (-932 2238225 2239932 2240580 "PERM" 2241808 NIL PERM (NIL T) -8 NIL NIL NIL) (-931 2235580 2237890 2238012 "PENDTREE" 2238136 NIL PENDTREE (NIL T) -8 NIL NIL NIL) (-930 2234461 2234724 2234765 "PDSPC" 2235298 NIL PDSPC (NIL T) -9 NIL 2235543 NIL) (-929 2233516 2233782 2234144 "PDSPC-" 2234149 NIL PDSPC- (NIL T T) -8 NIL NIL NIL) (-928 2232230 2233166 2233207 "PDRING" 2233212 NIL PDRING (NIL T) -9 NIL 2233240 NIL) (-927 2230973 2231735 2231789 "PDMOD" 2231794 NIL PDMOD (NIL T T) -9 NIL 2231898 NIL) (-926 2228140 2228966 2229634 "PDEPROB" 2230325 T PDEPROB (NIL) -8 NIL NIL NIL) (-925 2225649 2226189 2226744 "PDEPACK" 2227605 T PDEPACK (NIL) -7 NIL NIL NIL) (-924 2224537 2224751 2225002 "PDECOMP" 2225448 NIL PDECOMP (NIL T T) -7 NIL NIL NIL) (-923 2222054 2222945 2222973 "PDECAT" 2223760 T PDECAT (NIL) -9 NIL 2224473 NIL) (-922 2221671 2221738 2221792 "PDDOM" 2221957 NIL PDDOM (NIL T T) -9 NIL 2222037 NIL) (-921 2221484 2221520 2221627 "PDDOM-" 2221632 NIL PDDOM- (NIL T T T) -8 NIL NIL NIL) (-920 2221229 2221268 2221358 "PCOMP" 2221445 NIL PCOMP (NIL T T) -7 NIL NIL NIL) (-919 2219269 2220030 2220327 "PBWLB" 2220958 NIL PBWLB (NIL T) -8 NIL NIL NIL) (-918 2218895 2218958 2219067 "PATTERN2" 2219206 NIL PATTERN2 (NIL T T) -7 NIL NIL NIL) (-917 2216604 2217040 2217497 "PATTERN1" 2218484 NIL PATTERN1 (NIL T T) -7 NIL NIL NIL) (-916 2208783 2210677 2212015 "PATTERN" 2215287 NIL PATTERN (NIL T) -8 NIL NIL NIL) (-915 2208341 2208414 2208546 "PATRES2" 2208710 NIL PATRES2 (NIL T T T) -7 NIL NIL NIL) (-914 2205607 2206290 2206771 "PATRES" 2207906 NIL PATRES (NIL T T) -8 NIL NIL NIL) (-913 2203460 2203895 2204302 "PATMATCH" 2205274 NIL PATMATCH (NIL T T T) -7 NIL NIL NIL) (-912 2202914 2203165 2203206 "PATMAB" 2203313 NIL PATMAB (NIL T) -9 NIL 2203396 NIL) (-911 2201360 2201768 2202026 "PATLRES" 2202719 NIL PATLRES (NIL T T T) -8 NIL NIL NIL) (-910 2200898 2201029 2201070 "PATAB" 2201075 NIL PATAB (NIL T) -9 NIL 2201247 NIL) (-909 2199038 2199475 2199898 "PARTPERM" 2200495 T PARTPERM (NIL) -7 NIL NIL NIL) (-908 2198647 2198722 2198824 "PARSURF" 2198969 NIL PARSURF (NIL T) -8 NIL NIL NIL) (-907 2198273 2198336 2198445 "PARSU2" 2198584 NIL PARSU2 (NIL T T) -7 NIL NIL NIL) (-906 2198031 2198077 2198144 "PARSER" 2198226 T PARSER (NIL) -7 NIL NIL NIL) (-905 2197640 2197715 2197817 "PARSCURV" 2197962 NIL PARSCURV (NIL T) -8 NIL NIL NIL) (-904 2197266 2197329 2197438 "PARSC2" 2197577 NIL PARSC2 (NIL T T) -7 NIL NIL NIL) (-903 2196893 2196963 2197060 "PARPCURV" 2197202 NIL PARPCURV (NIL T) -8 NIL NIL NIL) (-902 2196519 2196582 2196691 "PARPC2" 2196830 NIL PARPC2 (NIL T T) -7 NIL NIL NIL) (-901 2195508 2195892 2196074 "PARAMAST" 2196357 T PARAMAST (NIL) -8 NIL NIL NIL) (-900 2195016 2195114 2195233 "PAN2EXPR" 2195409 T PAN2EXPR (NIL) -7 NIL NIL NIL) (-899 2193709 2194137 2194365 "PALETTE" 2194808 T PALETTE (NIL) -8 NIL NIL NIL) (-898 2192054 2192714 2193074 "PAIR" 2193395 NIL PAIR (NIL T T) -8 NIL NIL NIL) (-897 2184987 2191311 2191506 "PADICRC" 2191908 NIL PADICRC (NIL NIL T) -8 NIL NIL NIL) (-896 2177244 2184331 2184516 "PADICRAT" 2184834 NIL PADICRAT (NIL NIL) -8 NIL NIL NIL) (-895 2174041 2175904 2175944 "PADICCT" 2176525 NIL PADICCT (NIL NIL) -9 NIL 2176807 NIL) (-894 2172057 2173978 2174023 "PADIC" 2174028 NIL PADIC (NIL NIL) -8 NIL NIL NIL) (-893 2171002 2171214 2171482 "PADEPAC" 2171844 NIL PADEPAC (NIL T NIL NIL) -7 NIL NIL NIL) (-892 2170202 2170347 2170553 "PADE" 2170864 NIL PADE (NIL T T T) -7 NIL NIL NIL) (-891 2168435 2169410 2169690 "OWP" 2170006 NIL OWP (NIL T NIL NIL NIL) -8 NIL NIL NIL) (-890 2167880 2168141 2168238 "OVERSET" 2168358 T OVERSET (NIL) -8 NIL NIL NIL) (-889 2166800 2167485 2167657 "OVAR" 2167748 NIL OVAR (NIL NIL) -8 NIL NIL NIL) (-888 2155036 2157909 2160109 "OUTFORM" 2164620 T OUTFORM (NIL) -8 NIL NIL NIL) (-887 2154318 2154633 2154760 "OUTBFILE" 2154929 T OUTBFILE (NIL) -8 NIL NIL NIL) (-886 2153595 2153790 2153818 "OUTBCON" 2154136 T OUTBCON (NIL) -9 NIL 2154302 NIL) (-885 2153178 2153308 2153465 "OUTBCON-" 2153470 NIL OUTBCON- (NIL T) -8 NIL NIL NIL) (-884 2152418 2152563 2152724 "OUT" 2153037 T OUT (NIL) -7 NIL NIL NIL) (-883 2151714 2152147 2152236 "OSI" 2152349 T OSI (NIL) -8 NIL NIL NIL) (-882 2151133 2151555 2151583 "OSGROUP" 2151588 T OSGROUP (NIL) -9 NIL 2151610 NIL) (-881 2149844 2150105 2150390 "ORTHPOL" 2150880 NIL ORTHPOL (NIL T) -7 NIL NIL NIL) (-880 2147095 2149679 2149800 "OREUP" 2149805 NIL OREUP (NIL NIL T NIL NIL) -8 NIL NIL NIL) (-879 2144198 2146786 2146913 "ORESUP" 2147037 NIL ORESUP (NIL T NIL NIL) -8 NIL NIL NIL) (-878 2141698 2142226 2142787 "OREPCTO" 2143687 NIL OREPCTO (NIL T T) -7 NIL NIL NIL) (-877 2135076 2137571 2137612 "OREPCAT" 2139960 NIL OREPCAT (NIL T) -9 NIL 2141064 NIL) (-876 2132049 2133005 2134063 "OREPCAT-" 2134068 NIL OREPCAT- (NIL T T) -8 NIL NIL NIL) (-875 2131241 2131519 2131547 "ORDTYPE" 2131856 T ORDTYPE (NIL) -9 NIL 2132019 NIL) (-874 2130542 2130758 2131013 "ORDTYPE-" 2131018 NIL ORDTYPE- (NIL T) -8 NIL NIL NIL) (-873 2129898 2130281 2130439 "ORDSTRCT" 2130444 NIL ORDSTRCT (NIL T NIL) -8 NIL NIL NIL) (-872 2129396 2129766 2129794 "ORDSET" 2129799 T ORDSET (NIL) -9 NIL 2129821 NIL) (-871 2128047 2129018 2129046 "ORDRING" 2129051 T ORDRING (NIL) -9 NIL 2129080 NIL) (-870 2127298 2127863 2127891 "ORDMON" 2127896 T ORDMON (NIL) -9 NIL 2127917 NIL) (-869 2126442 2126607 2126802 "ORDFUNS" 2127147 NIL ORDFUNS (NIL NIL T) -7 NIL NIL NIL) (-868 2125657 2126172 2126200 "ORDFIN" 2126265 T ORDFIN (NIL) -9 NIL 2126339 NIL) (-867 2124911 2125050 2125236 "ORDCOMP2" 2125517 NIL ORDCOMP2 (NIL T T) -7 NIL NIL NIL) (-866 2121258 2123497 2123906 "ORDCOMP" 2124535 NIL ORDCOMP (NIL T) -8 NIL NIL NIL) (-865 2117779 2118749 2119563 "OPTPROB" 2120464 T OPTPROB (NIL) -8 NIL NIL NIL) (-864 2114521 2115220 2115924 "OPTPACK" 2117095 T OPTPACK (NIL) -7 NIL NIL NIL) (-863 2112134 2112960 2112988 "OPTCAT" 2113807 T OPTCAT (NIL) -9 NIL 2114457 NIL) (-862 2111452 2111811 2111916 "OPSIG" 2112049 T OPSIG (NIL) -8 NIL NIL NIL) (-861 2111214 2111259 2111325 "OPQUERY" 2111406 T OPQUERY (NIL) -7 NIL NIL NIL) (-860 2110520 2110800 2110841 "OPERCAT" 2111053 NIL OPERCAT (NIL T) -9 NIL 2111150 NIL) (-859 2110263 2110331 2110448 "OPERCAT-" 2110453 NIL OPERCAT- (NIL T T) -8 NIL NIL NIL) (-858 2107179 2108574 2109078 "OP" 2109792 NIL OP (NIL T) -8 NIL NIL NIL) (-857 2106472 2106599 2106773 "ONECOMP2" 2107051 NIL ONECOMP2 (NIL T T) -7 NIL NIL NIL) (-856 2103085 2105269 2105638 "ONECOMP" 2106136 NIL ONECOMP (NIL T) -8 NIL NIL NIL) (-855 2102486 2102610 2102740 "OMSERVER" 2102975 T OMSERVER (NIL) -7 NIL NIL NIL) (-854 2099109 2101924 2101964 "OMSAGG" 2102025 NIL OMSAGG (NIL T) -9 NIL 2102090 NIL) (-853 2097684 2097995 2098277 "OMPKG" 2098847 T OMPKG (NIL) -7 NIL NIL NIL) (-852 2096031 2097233 2097402 "OMLO" 2097565 NIL OMLO (NIL T T) -8 NIL NIL NIL) (-851 2094967 2095138 2095358 "OMEXPR" 2095857 NIL OMEXPR (NIL T) -7 NIL NIL NIL) (-850 2094052 2094388 2094548 "OMERRK" 2094827 T OMERRK (NIL) -8 NIL NIL NIL) (-849 2093289 2093598 2093734 "OMERR" 2093936 T OMERR (NIL) -8 NIL NIL NIL) (-848 2092680 2092966 2093074 "OMENC" 2093201 T OMENC (NIL) -8 NIL NIL NIL) (-847 2086317 2087760 2088931 "OMDEV" 2091529 T OMDEV (NIL) -8 NIL NIL NIL) (-846 2085350 2085557 2085751 "OMCONN" 2086143 T OMCONN (NIL) -8 NIL NIL NIL) (-845 2084756 2084883 2084911 "OM" 2085210 T OM (NIL) -9 NIL NIL NIL) (-844 2083034 2084226 2084254 "OINTDOM" 2084259 T OINTDOM (NIL) -9 NIL 2084280 NIL) (-843 2080109 2081722 2082059 "OFMONOID" 2082729 NIL OFMONOID (NIL T) -8 NIL NIL NIL) (-842 2079343 2080046 2080091 "ODVAR" 2080096 NIL ODVAR (NIL T) -8 NIL NIL NIL) (-841 2076487 2079088 2079243 "ODR" 2079248 NIL ODR (NIL T T NIL) -8 NIL NIL NIL) (-840 2067899 2076263 2076389 "ODPOL" 2076394 NIL ODPOL (NIL T) -8 NIL NIL NIL) (-839 2061307 2067771 2067876 "ODP" 2067881 NIL ODP (NIL NIL T NIL) -8 NIL NIL NIL) (-838 2060049 2060288 2060563 "ODETOOLS" 2061081 NIL ODETOOLS (NIL T T) -7 NIL NIL NIL) (-837 2056992 2057674 2058390 "ODESYS" 2059382 NIL ODESYS (NIL T T) -7 NIL NIL NIL) (-836 2051822 2052782 2053807 "ODERTRIC" 2056067 NIL ODERTRIC (NIL T T) -7 NIL NIL NIL) (-835 2051242 2051330 2051524 "ODERED" 2051734 NIL ODERED (NIL T T T T T) -7 NIL NIL NIL) (-834 2048094 2048678 2049355 "ODERAT" 2050665 NIL ODERAT (NIL T T) -7 NIL NIL NIL) (-833 2045010 2045518 2046115 "ODEPRRIC" 2047623 NIL ODEPRRIC (NIL T T T T) -7 NIL NIL NIL) (-832 2042905 2043549 2044035 "ODEPROB" 2044544 T ODEPROB (NIL) -8 NIL NIL NIL) (-831 2039371 2039910 2040557 "ODEPRIM" 2042384 NIL ODEPRIM (NIL T T T T) -7 NIL NIL NIL) (-830 2038614 2038722 2038982 "ODEPAL" 2039263 NIL ODEPAL (NIL T T T T) -7 NIL NIL NIL) (-829 2034716 2035567 2036431 "ODEPACK" 2037770 T ODEPACK (NIL) -7 NIL NIL NIL) (-828 2033759 2033884 2034106 "ODEINT" 2034605 NIL ODEINT (NIL T T) -7 NIL NIL NIL) (-827 2027824 2029285 2030732 "ODEIFTBL" 2032332 T ODEIFTBL (NIL) -8 NIL NIL NIL) (-826 2023174 2024008 2024960 "ODEEF" 2026983 NIL ODEEF (NIL T T) -7 NIL NIL NIL) (-825 2022517 2022612 2022835 "ODECONST" 2023079 NIL ODECONST (NIL T T T) -7 NIL NIL NIL) (-824 2020580 2021289 2021317 "ODECAT" 2021922 T ODECAT (NIL) -9 NIL 2022453 NIL) (-823 2020212 2020261 2020388 "OCTCT2" 2020531 NIL OCTCT2 (NIL T T T T) -7 NIL NIL NIL) (-822 2016712 2019917 2020039 "OCT" 2020122 NIL OCT (NIL T) -8 NIL NIL NIL) (-821 2015905 2016505 2016533 "OCAMON" 2016538 T OCAMON (NIL) -9 NIL 2016559 NIL) (-820 2010176 2012948 2012988 "OC" 2014085 NIL OC (NIL T) -9 NIL 2014943 NIL) (-819 2007211 2008151 2009141 "OC-" 2009235 NIL OC- (NIL T T) -8 NIL NIL NIL) (-818 2006631 2007056 2007084 "OASGP" 2007089 T OASGP (NIL) -9 NIL 2007109 NIL) (-817 2005727 2006354 2006382 "OAMONS" 2006422 T OAMONS (NIL) -9 NIL 2006465 NIL) (-816 2004903 2005462 2005490 "OAMON" 2005548 T OAMON (NIL) -9 NIL 2005600 NIL) (-815 2004761 2004794 2004862 "OAMON-" 2004867 NIL OAMON- (NIL T) -8 NIL NIL NIL) (-814 2003542 2004295 2004323 "OAGROUP" 2004470 T OAGROUP (NIL) -9 NIL 2004563 NIL) (-813 2003245 2003333 2003451 "OAGROUP-" 2003456 NIL OAGROUP- (NIL T) -8 NIL NIL NIL) (-812 2002927 2002983 2003072 "NUMTUBE" 2003189 NIL NUMTUBE (NIL T) -7 NIL NIL NIL) (-811 1996446 1998018 1999554 "NUMQUAD" 2001411 T NUMQUAD (NIL) -7 NIL NIL NIL) (-810 1992126 1993160 1994195 "NUMODE" 1995431 T NUMODE (NIL) -7 NIL NIL NIL) (-809 1989407 1990347 1990375 "NUMINT" 1991298 T NUMINT (NIL) -9 NIL 1992062 NIL) (-808 1988319 1988552 1988770 "NUMFMT" 1989209 T NUMFMT (NIL) -7 NIL NIL NIL) (-807 1974502 1977623 1980155 "NUMERIC" 1985826 NIL NUMERIC (NIL T) -7 NIL NIL NIL) (-806 1968320 1973950 1974045 "NTSCAT" 1974050 NIL NTSCAT (NIL T T T T) -9 NIL 1974089 NIL) (-805 1967500 1967679 1967872 "NTPOLFN" 1968159 NIL NTPOLFN (NIL T) -7 NIL NIL NIL) (-804 1967126 1967189 1967298 "NSUP2" 1967437 NIL NSUP2 (NIL T T) -7 NIL NIL NIL) (-803 1953908 1963951 1964763 "NSUP" 1966347 NIL NSUP (NIL T) -8 NIL NIL NIL) (-802 1942751 1953682 1953815 "NSMP" 1953820 NIL NSMP (NIL T T) -8 NIL NIL NIL) (-801 1941159 1941484 1941841 "NREP" 1942439 NIL NREP (NIL T) -7 NIL NIL NIL) (-800 1939738 1940002 1940360 "NPCOEF" 1940902 NIL NPCOEF (NIL T T T T T) -7 NIL NIL NIL) (-799 1938786 1938919 1939135 "NORMRETR" 1939619 NIL NORMRETR (NIL T T T T NIL) -7 NIL NIL NIL) (-798 1936797 1937117 1937526 "NORMPK" 1938494 NIL NORMPK (NIL T T T T T) -7 NIL NIL NIL) (-797 1936476 1936510 1936634 "NORMMA" 1936763 NIL NORMMA (NIL T T T T) -7 NIL NIL NIL) (-796 1936259 1936294 1936363 "NONE1" 1936440 NIL NONE1 (NIL T) -7 NIL NIL NIL) (-795 1936023 1936216 1936245 "NONE" 1936250 T NONE (NIL) -8 NIL NIL NIL) (-794 1935514 1935582 1935761 "NODE1" 1935955 NIL NODE1 (NIL T T) -7 NIL NIL NIL) (-793 1933575 1934637 1934892 "NNI" 1935239 T NNI (NIL) -8 NIL NIL 1935474) (-792 1931971 1932308 1932672 "NLINSOL" 1933243 NIL NLINSOL (NIL T) -7 NIL NIL NIL) (-791 1928152 1929207 1930106 "NIPROB" 1931092 T NIPROB (NIL) -8 NIL NIL NIL) (-790 1926891 1927143 1927445 "NFINTBAS" 1927914 NIL NFINTBAS (NIL T T) -7 NIL NIL NIL) (-789 1925975 1926541 1926582 "NETCLT" 1926754 NIL NETCLT (NIL T) -9 NIL 1926836 NIL) (-788 1924647 1924914 1925195 "NCODIV" 1925743 NIL NCODIV (NIL T T) -7 NIL NIL NIL) (-787 1924403 1924446 1924521 "NCNTFRAC" 1924604 NIL NCNTFRAC (NIL T) -7 NIL NIL NIL) (-786 1922559 1922947 1923367 "NCEP" 1924028 NIL NCEP (NIL T) -7 NIL NIL NIL) (-785 1921222 1922169 1922197 "NASRING" 1922307 T NASRING (NIL) -9 NIL 1922387 NIL) (-784 1921005 1921061 1921155 "NASRING-" 1921160 NIL NASRING- (NIL T) -8 NIL NIL NIL) (-783 1919972 1920623 1920651 "NARNG" 1920768 T NARNG (NIL) -9 NIL 1920859 NIL) (-782 1919646 1919731 1919865 "NARNG-" 1919870 NIL NARNG- (NIL T) -8 NIL NIL NIL) (-781 1918483 1918732 1918967 "NAGSP" 1919431 T NAGSP (NIL) -7 NIL NIL NIL) (-780 1909527 1911439 1913112 "NAGS" 1916830 T NAGS (NIL) -7 NIL NIL NIL) (-779 1908051 1908383 1908714 "NAGF07" 1909216 T NAGF07 (NIL) -7 NIL NIL NIL) (-778 1902523 1903880 1905187 "NAGF04" 1906764 T NAGF04 (NIL) -7 NIL NIL NIL) (-777 1895395 1897105 1898738 "NAGF02" 1900910 T NAGF02 (NIL) -7 NIL NIL NIL) (-776 1890559 1891719 1892836 "NAGF01" 1894298 T NAGF01 (NIL) -7 NIL NIL NIL) (-775 1884139 1885753 1887338 "NAGE04" 1888994 T NAGE04 (NIL) -7 NIL NIL NIL) (-774 1875200 1877429 1879559 "NAGE02" 1882029 T NAGE02 (NIL) -7 NIL NIL NIL) (-773 1871093 1872100 1873064 "NAGE01" 1874256 T NAGE01 (NIL) -7 NIL NIL NIL) (-772 1868870 1869422 1869980 "NAGD03" 1870555 T NAGD03 (NIL) -7 NIL NIL NIL) (-771 1860566 1862548 1864502 "NAGD02" 1866936 T NAGD02 (NIL) -7 NIL NIL NIL) (-770 1854305 1855802 1857242 "NAGD01" 1859146 T NAGD01 (NIL) -7 NIL NIL NIL) (-769 1850442 1851336 1852173 "NAGC06" 1853488 T NAGC06 (NIL) -7 NIL NIL NIL) (-768 1848889 1849239 1849595 "NAGC05" 1850106 T NAGC05 (NIL) -7 NIL NIL NIL) (-767 1848253 1848384 1848528 "NAGC02" 1848765 T NAGC02 (NIL) -7 NIL NIL NIL) (-766 1847054 1847781 1847821 "NAALG" 1847900 NIL NAALG (NIL T) -9 NIL 1847961 NIL) (-765 1846883 1846918 1847008 "NAALG-" 1847013 NIL NAALG- (NIL T T) -8 NIL NIL NIL) (-764 1840755 1841941 1843128 "MULTSQFR" 1845779 NIL MULTSQFR (NIL T T T T) -7 NIL NIL NIL) (-763 1840062 1840149 1840333 "MULTFACT" 1840667 NIL MULTFACT (NIL T T T T) -7 NIL NIL NIL) (-762 1832207 1836645 1836698 "MTSCAT" 1837768 NIL MTSCAT (NIL T T) -9 NIL 1838284 NIL) (-761 1831913 1831973 1832065 "MTHING" 1832147 NIL MTHING (NIL T) -7 NIL NIL NIL) (-760 1831699 1831738 1831798 "MSYSCMD" 1831873 T MSYSCMD (NIL) -7 NIL NIL NIL) (-759 1828555 1831260 1831301 "MSETAGG" 1831306 NIL MSETAGG (NIL T) -9 NIL 1831340 NIL) (-758 1824383 1827310 1827630 "MSET" 1828268 NIL MSET (NIL T) -8 NIL NIL NIL) (-757 1819985 1821762 1822507 "MRING" 1823683 NIL MRING (NIL T T) -8 NIL NIL NIL) (-756 1819545 1819618 1819749 "MRF2" 1819912 NIL MRF2 (NIL T T T) -7 NIL NIL NIL) (-755 1819157 1819198 1819342 "MRATFAC" 1819504 NIL MRATFAC (NIL T T T T) -7 NIL NIL NIL) (-754 1816727 1817064 1817495 "MPRFF" 1818862 NIL MPRFF (NIL T T T T) -7 NIL NIL NIL) (-753 1810061 1816581 1816678 "MPOLY" 1816683 NIL MPOLY (NIL NIL T) -8 NIL NIL NIL) (-752 1809545 1809586 1809794 "MPCPF" 1810020 NIL MPCPF (NIL T T T T) -7 NIL NIL NIL) (-751 1809053 1809102 1809286 "MPC3" 1809496 NIL MPC3 (NIL T T T T T T T) -7 NIL NIL NIL) (-750 1808236 1808329 1808550 "MPC2" 1808968 NIL MPC2 (NIL T T T T T T T) -7 NIL NIL NIL) (-749 1806513 1806874 1807264 "MONOTOOL" 1807896 NIL MONOTOOL (NIL T T) -7 NIL NIL NIL) (-748 1805658 1806041 1806069 "MONOID" 1806288 T MONOID (NIL) -9 NIL 1806435 NIL) (-747 1805174 1805323 1805504 "MONOID-" 1805509 NIL MONOID- (NIL T) -8 NIL NIL NIL) (-746 1794147 1800994 1801053 "MONOGEN" 1801727 NIL MONOGEN (NIL T T) -9 NIL 1802183 NIL) (-745 1791197 1792100 1793100 "MONOGEN-" 1793219 NIL MONOGEN- (NIL T T T) -8 NIL NIL NIL) (-744 1789914 1790462 1790490 "MONADWU" 1790882 T MONADWU (NIL) -9 NIL 1791120 NIL) (-743 1789244 1789445 1789693 "MONADWU-" 1789698 NIL MONADWU- (NIL T) -8 NIL NIL NIL) (-742 1788529 1788833 1788861 "MONAD" 1789068 T MONAD (NIL) -9 NIL 1789180 NIL) (-741 1788196 1788292 1788424 "MONAD-" 1788429 NIL MONAD- (NIL T) -8 NIL NIL NIL) (-740 1786335 1787109 1787388 "MOEBIUS" 1787949 NIL MOEBIUS (NIL T) -8 NIL NIL NIL) (-739 1785503 1786003 1786043 "MODULE" 1786048 NIL MODULE (NIL T) -9 NIL 1786087 NIL) (-738 1785041 1785167 1785357 "MODULE-" 1785362 NIL MODULE- (NIL T T) -8 NIL NIL NIL) (-737 1782571 1783405 1783732 "MODRING" 1784865 NIL MODRING (NIL T T NIL NIL NIL) -8 NIL NIL NIL) (-736 1779300 1780676 1781197 "MODOP" 1782100 NIL MODOP (NIL T T) -8 NIL NIL NIL) (-735 1777786 1778367 1778644 "MODMONOM" 1779163 NIL MODMONOM (NIL T T NIL) -8 NIL NIL NIL) (-734 1766546 1776077 1776491 "MODMON" 1777423 NIL MODMON (NIL T T) -8 NIL NIL NIL) (-733 1763379 1765390 1765666 "MODFIELD" 1766421 NIL MODFIELD (NIL T T NIL NIL NIL) -8 NIL NIL NIL) (-732 1762290 1762660 1762850 "MMLFORM" 1763209 T MMLFORM (NIL) -8 NIL NIL NIL) (-731 1761810 1761859 1762038 "MMAP" 1762241 NIL MMAP (NIL T T T T T T) -7 NIL NIL NIL) (-730 1759703 1760642 1760683 "MLO" 1761106 NIL MLO (NIL T) -9 NIL 1761348 NIL) (-729 1757051 1757585 1758187 "MLIFT" 1759184 NIL MLIFT (NIL T T T T) -7 NIL NIL NIL) (-728 1756430 1756526 1756680 "MKUCFUNC" 1756962 NIL MKUCFUNC (NIL T T T) -7 NIL NIL NIL) (-727 1756023 1756099 1756222 "MKRECORD" 1756353 NIL MKRECORD (NIL T T) -7 NIL NIL NIL) (-726 1755046 1755232 1755460 "MKFUNC" 1755834 NIL MKFUNC (NIL T) -7 NIL NIL NIL) (-725 1754422 1754538 1754694 "MKFLCFN" 1754929 NIL MKFLCFN (NIL T) -7 NIL NIL NIL) (-724 1753687 1753801 1753986 "MKBCFUNC" 1754315 NIL MKBCFUNC (NIL T T T T) -7 NIL NIL NIL) (-723 1749684 1753241 1753377 "MINT" 1753571 T MINT (NIL) -8 NIL NIL NIL) (-722 1748466 1748739 1749016 "MHROWRED" 1749439 NIL MHROWRED (NIL T) -7 NIL NIL NIL) (-721 1743217 1747001 1747406 "MFLOAT" 1748081 T MFLOAT (NIL) -8 NIL NIL NIL) (-720 1742562 1742650 1742821 "MFINFACT" 1743129 NIL MFINFACT (NIL T T T T) -7 NIL NIL NIL) (-719 1738841 1739725 1740609 "MESH" 1741698 T MESH (NIL) -7 NIL NIL NIL) (-718 1737195 1737543 1737896 "MDDFACT" 1738528 NIL MDDFACT (NIL T) -7 NIL NIL NIL) (-717 1733842 1736326 1736367 "MDAGG" 1736622 NIL MDAGG (NIL T) -9 NIL 1736765 NIL) (-716 1721565 1733135 1733342 "MCMPLX" 1733655 T MCMPLX (NIL) -8 NIL NIL NIL) (-715 1720684 1720848 1721049 "MCDEN" 1721414 NIL MCDEN (NIL T T) -7 NIL NIL NIL) (-714 1718532 1718844 1719224 "MCALCFN" 1720414 NIL MCALCFN (NIL T T T T) -7 NIL NIL NIL) (-713 1717409 1717697 1717930 "MAYBE" 1718338 NIL MAYBE (NIL T) -8 NIL NIL NIL) (-712 1714967 1715544 1716106 "MATSTOR" 1716880 NIL MATSTOR (NIL T) -7 NIL NIL NIL) (-711 1710503 1714339 1714587 "MATRIX" 1714752 NIL MATRIX (NIL T) -8 NIL NIL NIL) (-710 1706203 1706976 1707712 "MATLIN" 1709860 NIL MATLIN (NIL T T T T) -7 NIL NIL NIL) (-709 1704779 1704950 1705283 "MATCAT2" 1706038 NIL MATCAT2 (NIL T T T T T T T T) -7 NIL NIL NIL) (-708 1694232 1697836 1697913 "MATCAT" 1702945 NIL MATCAT (NIL T T T) -9 NIL 1704417 NIL) (-707 1690185 1691495 1692908 "MATCAT-" 1692913 NIL MATCAT- (NIL T T T T) -8 NIL NIL NIL) (-706 1688261 1688621 1689005 "MAPPKG3" 1689860 NIL MAPPKG3 (NIL T T T) -7 NIL NIL NIL) (-705 1687218 1687415 1687637 "MAPPKG2" 1688085 NIL MAPPKG2 (NIL T T) -7 NIL NIL NIL) (-704 1685675 1686001 1686328 "MAPPKG1" 1686924 NIL MAPPKG1 (NIL T) -7 NIL NIL NIL) (-703 1684676 1685081 1685258 "MAPPAST" 1685518 T MAPPAST (NIL) -8 NIL NIL NIL) (-702 1684281 1684345 1684468 "MAPHACK3" 1684612 NIL MAPHACK3 (NIL T T T) -7 NIL NIL NIL) (-701 1683861 1683934 1684048 "MAPHACK2" 1684213 NIL MAPHACK2 (NIL T T) -7 NIL NIL NIL) (-700 1683287 1683402 1683544 "MAPHACK1" 1683752 NIL MAPHACK1 (NIL T) -7 NIL NIL NIL) (-699 1681210 1681987 1682291 "MAGMA" 1683015 NIL MAGMA (NIL T) -8 NIL NIL NIL) (-698 1680629 1680934 1681025 "MACROAST" 1681139 T MACROAST (NIL) -8 NIL NIL NIL) (-697 1676986 1678868 1679329 "M3D" 1680201 NIL M3D (NIL T) -8 NIL NIL NIL) (-696 1670458 1675297 1675338 "LZSTAGG" 1676120 NIL LZSTAGG (NIL T) -9 NIL 1676415 NIL) (-695 1666140 1667589 1669046 "LZSTAGG-" 1669051 NIL LZSTAGG- (NIL T T) -8 NIL NIL NIL) (-694 1663053 1664031 1664518 "LWORD" 1665685 NIL LWORD (NIL T) -8 NIL NIL NIL) (-693 1662575 1662857 1662932 "LSTAST" 1662998 T LSTAST (NIL) -8 NIL NIL NIL) (-692 1654617 1662346 1662480 "LSQM" 1662485 NIL LSQM (NIL NIL T) -8 NIL NIL NIL) (-691 1653835 1653980 1654208 "LSPP" 1654472 NIL LSPP (NIL T T T T) -7 NIL NIL NIL) (-690 1650572 1651288 1652018 "LSMP1" 1653137 NIL LSMP1 (NIL T) -7 NIL NIL NIL) (-689 1648354 1648685 1649141 "LSMP" 1650261 NIL LSMP (NIL T T T T) -7 NIL NIL NIL) (-688 1641482 1647444 1647485 "LSAGG" 1647547 NIL LSAGG (NIL T) -9 NIL 1647625 NIL) (-687 1637991 1639101 1640314 "LSAGG-" 1640319 NIL LSAGG- (NIL T T) -8 NIL NIL NIL) (-686 1635286 1637135 1637384 "LPOLY" 1637786 NIL LPOLY (NIL T T) -8 NIL NIL NIL) (-685 1634862 1634953 1635076 "LPEFRAC" 1635195 NIL LPEFRAC (NIL T) -7 NIL NIL NIL) (-684 1634545 1634624 1634652 "LOGIC" 1634763 T LOGIC (NIL) -9 NIL 1634845 NIL) (-683 1634401 1634430 1634501 "LOGIC-" 1634506 NIL LOGIC- (NIL T) -8 NIL NIL NIL) (-682 1633576 1633734 1633927 "LODOOPS" 1634257 NIL LODOOPS (NIL T T) -7 NIL NIL NIL) (-681 1632100 1632349 1632702 "LODOF" 1633323 NIL LODOF (NIL T T) -7 NIL NIL NIL) (-680 1627976 1630735 1630776 "LODOCAT" 1631214 NIL LODOCAT (NIL T) -9 NIL 1631425 NIL) (-679 1627691 1627767 1627894 "LODOCAT-" 1627899 NIL LODOCAT- (NIL T T) -8 NIL NIL NIL) (-678 1624677 1627532 1627650 "LODO2" 1627655 NIL LODO2 (NIL T T) -8 NIL NIL NIL) (-677 1621784 1624614 1624659 "LODO1" 1624664 NIL LODO1 (NIL T) -8 NIL NIL NIL) (-676 1618879 1621700 1621766 "LODO" 1621771 NIL LODO (NIL T NIL) -8 NIL NIL NIL) (-675 1617748 1617925 1618230 "LODEEF" 1618702 NIL LODEEF (NIL T T T) -7 NIL NIL NIL) (-674 1615734 1616842 1617095 "LO" 1617580 NIL LO (NIL T T T) -8 NIL NIL NIL) (-673 1610817 1613900 1613941 "LNAGG" 1614803 NIL LNAGG (NIL T) -9 NIL 1615238 NIL) (-672 1609910 1610178 1610520 "LNAGG-" 1610525 NIL LNAGG- (NIL T T) -8 NIL NIL NIL) (-671 1605890 1606835 1607474 "LMOPS" 1609325 NIL LMOPS (NIL T T NIL) -8 NIL NIL NIL) (-670 1605189 1605667 1605708 "LMODULE" 1605713 NIL LMODULE (NIL T) -9 NIL 1605739 NIL) (-669 1602258 1604834 1604957 "LMDICT" 1605099 NIL LMDICT (NIL T) -8 NIL NIL NIL) (-668 1601834 1602048 1602089 "LLINSET" 1602150 NIL LLINSET (NIL T) -9 NIL 1602194 NIL) (-667 1601479 1601742 1601802 "LITERAL" 1601807 NIL LITERAL (NIL T) -8 NIL NIL NIL) (-666 1600998 1601078 1601217 "LIST3" 1601399 NIL LIST3 (NIL T T T) -7 NIL NIL NIL) (-665 1599096 1599444 1599843 "LIST2MAP" 1600645 NIL LIST2MAP (NIL T T) -7 NIL NIL NIL) (-664 1598085 1598281 1598509 "LIST2" 1598914 NIL LIST2 (NIL T T) -7 NIL NIL NIL) (-663 1590539 1597019 1597323 "LIST" 1597814 NIL LIST (NIL T) -8 NIL NIL NIL) (-662 1590122 1590358 1590399 "LINSET" 1590404 NIL LINSET (NIL T) -9 NIL 1590438 NIL) (-661 1588936 1589630 1589797 "LINFORM" 1590007 NIL LINFORM (NIL T NIL) -8 NIL NIL NIL) (-660 1587235 1587963 1588004 "LINEXP" 1588494 NIL LINEXP (NIL T) -9 NIL 1588767 NIL) (-659 1585811 1586715 1586896 "LINELT" 1587106 NIL LINELT (NIL T NIL) -8 NIL NIL NIL) (-658 1584368 1584648 1584959 "LINDEP" 1585563 NIL LINDEP (NIL T T) -7 NIL NIL NIL) (-657 1583504 1584100 1584210 "LINBASIS" 1584298 NIL LINBASIS (NIL NIL) -8 NIL NIL NIL) (-656 1580241 1580990 1581767 "LIMITRF" 1582759 NIL LIMITRF (NIL T) -7 NIL NIL NIL) (-655 1578526 1578840 1579249 "LIMITPS" 1579936 NIL LIMITPS (NIL T T) -7 NIL NIL NIL) (-654 1577354 1577929 1577969 "LIECAT" 1578109 NIL LIECAT (NIL T) -9 NIL 1578260 NIL) (-653 1577189 1577222 1577310 "LIECAT-" 1577315 NIL LIECAT- (NIL T T) -8 NIL NIL NIL) (-652 1571209 1576700 1576928 "LIE" 1577010 NIL LIE (NIL T T) -8 NIL NIL NIL) (-651 1563508 1570749 1570905 "LIB" 1571073 T LIB (NIL) -8 NIL NIL NIL) (-650 1559077 1560026 1560961 "LGROBP" 1562625 NIL LGROBP (NIL NIL T) -7 NIL NIL NIL) (-649 1557701 1558609 1558637 "LFCAT" 1558844 T LFCAT (NIL) -9 NIL 1558983 NIL) (-648 1555639 1555973 1556323 "LF" 1557422 NIL LF (NIL T T) -7 NIL NIL NIL) (-647 1552499 1553171 1553859 "LEXTRIPK" 1555003 NIL LEXTRIPK (NIL T NIL) -7 NIL NIL NIL) (-646 1549087 1550069 1550572 "LEXP" 1552079 NIL LEXP (NIL T T NIL) -8 NIL NIL NIL) (-645 1548503 1548808 1548900 "LETAST" 1549015 T LETAST (NIL) -8 NIL NIL NIL) (-644 1546889 1547214 1547615 "LEADCDET" 1548185 NIL LEADCDET (NIL T T T T) -7 NIL NIL NIL) (-643 1546067 1546153 1546382 "LAZM3PK" 1546810 NIL LAZM3PK (NIL T T T T T T) -7 NIL NIL NIL) (-642 1540592 1544144 1544682 "LAUPOL" 1545579 NIL LAUPOL (NIL T T) -8 NIL NIL NIL) (-641 1540165 1540215 1540376 "LAPLACE" 1540542 NIL LAPLACE (NIL T T) -7 NIL NIL NIL) (-640 1539013 1539729 1539770 "LALG" 1539832 NIL LALG (NIL T) -9 NIL 1539891 NIL) (-639 1538709 1538786 1538922 "LALG-" 1538927 NIL LALG- (NIL T T) -8 NIL NIL NIL) (-638 1536446 1537810 1538061 "LA" 1538542 NIL LA (NIL T T T) -8 NIL NIL NIL) (-637 1536275 1536305 1536346 "KVTFROM" 1536408 NIL KVTFROM (NIL T) -9 NIL NIL NIL) (-636 1535032 1535642 1535827 "KTVLOGIC" 1536110 T KTVLOGIC (NIL) -8 NIL NIL NIL) (-635 1534861 1534891 1534932 "KRCFROM" 1534994 NIL KRCFROM (NIL T) -9 NIL NIL NIL) (-634 1533753 1533952 1534251 "KOVACIC" 1534661 NIL KOVACIC (NIL T T) -7 NIL NIL NIL) (-633 1533582 1533612 1533653 "KONVERT" 1533715 NIL KONVERT (NIL T) -9 NIL NIL NIL) (-632 1533411 1533441 1533482 "KOERCE" 1533544 NIL KOERCE (NIL T) -9 NIL NIL NIL) (-631 1532895 1532988 1533120 "KERNEL2" 1533325 NIL KERNEL2 (NIL T T) -7 NIL NIL NIL) (-630 1530582 1531488 1531865 "KERNEL" 1532551 NIL KERNEL (NIL T) -8 NIL NIL NIL) (-629 1524164 1529059 1529113 "KDAGG" 1529490 NIL KDAGG (NIL T T) -9 NIL 1529696 NIL) (-628 1523675 1523817 1524022 "KDAGG-" 1524027 NIL KDAGG- (NIL T T T) -8 NIL NIL NIL) (-627 1516489 1523336 1523491 "KAFILE" 1523553 NIL KAFILE (NIL T) -8 NIL NIL NIL) (-626 1516093 1516378 1516441 "JVMOP" 1516446 T JVMOP (NIL) -8 NIL NIL NIL) (-625 1514829 1515333 1515582 "JVMMDACC" 1515864 T JVMMDACC (NIL) -8 NIL NIL NIL) (-624 1513765 1514219 1514424 "JVMFDACC" 1514644 T JVMFDACC (NIL) -8 NIL NIL NIL) (-623 1512346 1512841 1513141 "JVMCSTTG" 1513485 T JVMCSTTG (NIL) -8 NIL NIL NIL) (-622 1511482 1511886 1512047 "JVMCFACC" 1512205 T JVMCFACC (NIL) -8 NIL NIL NIL) (-621 1511160 1511399 1511448 "JVMBCODE" 1511453 T JVMBCODE (NIL) -8 NIL NIL NIL) (-620 1505179 1510671 1510899 "JORDAN" 1510981 NIL JORDAN (NIL T T) -8 NIL NIL NIL) (-619 1504492 1504828 1504949 "JOINAST" 1505078 T JOINAST (NIL) -8 NIL NIL NIL) (-618 1500638 1502669 1502723 "IXAGG" 1503652 NIL IXAGG (NIL T T) -9 NIL 1504111 NIL) (-617 1499491 1499863 1500282 "IXAGG-" 1500287 NIL IXAGG- (NIL T T T) -8 NIL NIL NIL) (-616 1494694 1499413 1499472 "IVECTOR" 1499477 NIL IVECTOR (NIL T NIL) -8 NIL NIL NIL) (-615 1493419 1493697 1493963 "ITUPLE" 1494461 NIL ITUPLE (NIL T) -8 NIL NIL NIL) (-614 1491891 1492098 1492393 "ITRIGMNP" 1493241 NIL ITRIGMNP (NIL T T T) -7 NIL NIL NIL) (-613 1490618 1490840 1491123 "ITFUN3" 1491667 NIL ITFUN3 (NIL T T T) -7 NIL NIL NIL) (-612 1490216 1490279 1490402 "ITFUN2" 1490541 NIL ITFUN2 (NIL T T) -8 NIL NIL NIL) (-611 1489321 1489696 1489870 "ITFORM" 1490062 T ITFORM (NIL) -8 NIL NIL NIL) (-610 1487090 1488341 1488619 "ITAYLOR" 1489076 NIL ITAYLOR (NIL T) -8 NIL NIL NIL) (-609 1475494 1481227 1482390 "ISUPS" 1485960 NIL ISUPS (NIL T) -8 NIL NIL NIL) (-608 1474586 1474738 1474974 "ISUMP" 1475341 NIL ISUMP (NIL T T T T) -7 NIL NIL NIL) (-607 1469550 1474531 1474572 "ISTRING" 1474577 NIL ISTRING (NIL NIL) -8 NIL NIL NIL) (-606 1468966 1469271 1469363 "ISAST" 1469478 T ISAST (NIL) -8 NIL NIL NIL) (-605 1468164 1468257 1468473 "IRURPK" 1468880 NIL IRURPK (NIL T T T T T) -7 NIL NIL NIL) (-604 1467076 1467301 1467541 "IRSN" 1467944 T IRSN (NIL) -7 NIL NIL NIL) (-603 1465121 1465502 1465931 "IRRF2F" 1466714 NIL IRRF2F (NIL T) -7 NIL NIL NIL) (-602 1464862 1464906 1464982 "IRREDFFX" 1465077 NIL IRREDFFX (NIL T) -7 NIL NIL NIL) (-601 1463435 1463736 1464035 "IROOT" 1464595 NIL IROOT (NIL T) -7 NIL NIL NIL) (-600 1462574 1462928 1463079 "IRFORM" 1463304 T IRFORM (NIL) -8 NIL NIL NIL) (-599 1461656 1461787 1462001 "IR2F" 1462457 NIL IR2F (NIL T T) -7 NIL NIL NIL) (-598 1459245 1459764 1460330 "IR2" 1461134 NIL IR2 (NIL T T) -7 NIL NIL NIL) (-597 1455685 1456929 1457621 "IR" 1458585 NIL IR (NIL T) -8 NIL NIL NIL) (-596 1455470 1455510 1455570 "IPRNTPK" 1455645 T IPRNTPK (NIL) -7 NIL NIL NIL) (-595 1451444 1455359 1455428 "IPF" 1455433 NIL IPF (NIL NIL) -8 NIL NIL NIL) (-594 1449472 1451369 1451426 "IPADIC" 1451431 NIL IPADIC (NIL NIL NIL) -8 NIL NIL NIL) (-593 1448730 1449032 1449162 "IP4ADDR" 1449362 T IP4ADDR (NIL) -8 NIL NIL NIL) (-592 1448068 1448359 1448491 "IOMODE" 1448618 T IOMODE (NIL) -8 NIL NIL NIL) (-591 1447039 1447665 1447792 "IOBFILE" 1447961 T IOBFILE (NIL) -8 NIL NIL NIL) (-590 1446449 1446943 1446971 "IOBCON" 1446976 T IOBCON (NIL) -9 NIL 1446997 NIL) (-589 1445954 1446018 1446201 "INVLAPLA" 1446385 NIL INVLAPLA (NIL T T) -7 NIL NIL NIL) (-588 1435524 1437956 1440342 "INTTR" 1443618 NIL INTTR (NIL T T) -7 NIL NIL NIL) (-587 1431817 1432601 1433466 "INTTOOLS" 1434709 NIL INTTOOLS (NIL T T) -7 NIL NIL NIL) (-586 1431397 1431494 1431611 "INTSLPE" 1431720 T INTSLPE (NIL) -7 NIL NIL NIL) (-585 1428864 1431320 1431379 "INTRVL" 1431384 NIL INTRVL (NIL T) -8 NIL NIL NIL) (-584 1426442 1426978 1427553 "INTRF" 1428349 NIL INTRF (NIL T) -7 NIL NIL NIL) (-583 1425835 1425950 1426092 "INTRET" 1426340 NIL INTRET (NIL T) -7 NIL NIL NIL) (-582 1423808 1424221 1424691 "INTRAT" 1425443 NIL INTRAT (NIL T T) -7 NIL NIL NIL) (-581 1421053 1421654 1422273 "INTPM" 1423293 NIL INTPM (NIL T T) -7 NIL NIL NIL) (-580 1417770 1418397 1419135 "INTPAF" 1420439 NIL INTPAF (NIL T T T) -7 NIL NIL NIL) (-579 1412871 1413911 1414962 "INTPACK" 1416739 T INTPACK (NIL) -7 NIL NIL NIL) (-578 1412117 1412275 1412483 "INTHERTR" 1412713 NIL INTHERTR (NIL T T) -7 NIL NIL NIL) (-577 1411550 1411636 1411824 "INTHERAL" 1412031 NIL INTHERAL (NIL T T T T) -7 NIL NIL NIL) (-576 1409318 1409839 1410296 "INTHEORY" 1411113 T INTHEORY (NIL) -7 NIL NIL NIL) (-575 1400650 1402345 1404117 "INTG0" 1407670 NIL INTG0 (NIL T T T) -7 NIL NIL NIL) (-574 1381175 1386013 1390823 "INTFTBL" 1395860 T INTFTBL (NIL) -8 NIL NIL NIL) (-573 1380400 1380562 1380735 "INTFACT" 1381034 NIL INTFACT (NIL T) -7 NIL NIL NIL) (-572 1377797 1378273 1378830 "INTEF" 1379954 NIL INTEF (NIL T T) -7 NIL NIL NIL) (-571 1375994 1376889 1376917 "INTDOM" 1377218 T INTDOM (NIL) -9 NIL 1377425 NIL) (-570 1375333 1375537 1375779 "INTDOM-" 1375784 NIL INTDOM- (NIL T) -8 NIL NIL NIL) (-569 1371201 1373622 1373676 "INTCAT" 1374475 NIL INTCAT (NIL T) -9 NIL 1374796 NIL) (-568 1370655 1370776 1370904 "INTBIT" 1371093 T INTBIT (NIL) -7 NIL NIL NIL) (-567 1369336 1369508 1369815 "INTALG" 1370500 NIL INTALG (NIL T T T T T) -7 NIL NIL NIL) (-566 1368813 1368909 1369066 "INTAF" 1369240 NIL INTAF (NIL T T) -7 NIL NIL NIL) (-565 1361894 1368623 1368763 "INTABL" 1368768 NIL INTABL (NIL T T T) -8 NIL NIL NIL) (-564 1361135 1361697 1361762 "INT8" 1361796 T INT8 (NIL) -8 NIL NIL 1361841) (-563 1360375 1360937 1361002 "INT64" 1361036 T INT64 (NIL) -8 NIL NIL 1361081) (-562 1359615 1360177 1360242 "INT32" 1360276 T INT32 (NIL) -8 NIL NIL 1360321) (-561 1358855 1359417 1359482 "INT16" 1359516 T INT16 (NIL) -8 NIL NIL 1359561) (-560 1355059 1358652 1358761 "INT" 1358766 T INT (NIL) -8 NIL NIL NIL) (-559 1349168 1352607 1352635 "INS" 1353569 T INS (NIL) -9 NIL 1354234 NIL) (-558 1346325 1347245 1348186 "INS-" 1348259 NIL INS- (NIL T) -8 NIL NIL NIL) (-557 1345082 1345327 1345625 "INPSIGN" 1346078 NIL INPSIGN (NIL T T) -7 NIL NIL NIL) (-556 1344176 1344317 1344514 "INPRODPF" 1344962 NIL INPRODPF (NIL T T) -7 NIL NIL NIL) (-555 1343046 1343187 1343424 "INPRODFF" 1344056 NIL INPRODFF (NIL T T T T) -7 NIL NIL NIL) (-554 1342034 1342198 1342458 "INNMFACT" 1342882 NIL INNMFACT (NIL T T T T) -7 NIL NIL NIL) (-553 1341213 1341328 1341516 "INMODGCD" 1341933 NIL INMODGCD (NIL T T NIL NIL) -7 NIL NIL NIL) (-552 1339697 1339966 1340290 "INFSP" 1340958 NIL INFSP (NIL T T T) -7 NIL NIL NIL) (-551 1338857 1338998 1339181 "INFPROD0" 1339577 NIL INFPROD0 (NIL T T) -7 NIL NIL NIL) (-550 1338455 1338527 1338625 "INFORM1" 1338792 NIL INFORM1 (NIL T) -7 NIL NIL NIL) (-549 1335022 1336520 1337035 "INFORM" 1337948 T INFORM (NIL) -8 NIL NIL NIL) (-548 1334527 1334634 1334748 "INFINITY" 1334928 T INFINITY (NIL) -7 NIL NIL NIL) (-547 1333601 1334247 1334348 "INETCLTS" 1334446 T INETCLTS (NIL) -8 NIL NIL NIL) (-546 1332199 1332467 1332788 "INEP" 1333349 NIL INEP (NIL T T T) -7 NIL NIL NIL) (-545 1331229 1332096 1332161 "INDE" 1332166 NIL INDE (NIL T) -8 NIL NIL NIL) (-544 1330781 1330861 1330978 "INCRMAPS" 1331156 NIL INCRMAPS (NIL T) -7 NIL NIL NIL) (-543 1329503 1330050 1330256 "INBFILE" 1330595 T INBFILE (NIL) -8 NIL NIL NIL) (-542 1324683 1325739 1326683 "INBFF" 1328591 NIL INBFF (NIL T) -7 NIL NIL NIL) (-541 1323537 1323860 1323888 "INBCON" 1324401 T INBCON (NIL) -9 NIL 1324667 NIL) (-540 1322747 1323012 1323288 "INBCON-" 1323293 NIL INBCON- (NIL T) -8 NIL NIL NIL) (-539 1322166 1322471 1322562 "INAST" 1322676 T INAST (NIL) -8 NIL NIL NIL) (-538 1321533 1321845 1321951 "IMPTAST" 1322080 T IMPTAST (NIL) -8 NIL NIL NIL) (-537 1317568 1321377 1321481 "IMATRIX" 1321486 NIL IMATRIX (NIL T NIL NIL) -8 NIL NIL NIL) (-536 1316260 1316399 1316715 "IMATQF" 1317424 NIL IMATQF (NIL T T T T T T T T) -7 NIL NIL NIL) (-535 1314440 1314707 1315044 "IMATLIN" 1316016 NIL IMATLIN (NIL T T T T) -7 NIL NIL NIL) (-534 1308355 1314364 1314422 "ILIST" 1314427 NIL ILIST (NIL T NIL) -8 NIL NIL NIL) (-533 1306135 1308215 1308328 "IIARRAY2" 1308333 NIL IIARRAY2 (NIL T NIL NIL T T) -8 NIL NIL NIL) (-532 1300956 1306046 1306110 "IFF" 1306115 NIL IFF (NIL NIL NIL) -8 NIL NIL NIL) (-531 1300237 1300573 1300689 "IFAST" 1300860 T IFAST (NIL) -8 NIL NIL NIL) (-530 1294863 1299529 1299717 "IFARRAY" 1300094 NIL IFARRAY (NIL T NIL) -8 NIL NIL NIL) (-529 1293901 1294767 1294840 "IFAMON" 1294845 NIL IFAMON (NIL T T NIL) -8 NIL NIL NIL) (-528 1293473 1293550 1293604 "IEVALAB" 1293811 NIL IEVALAB (NIL T T) -9 NIL NIL NIL) (-527 1293136 1293216 1293376 "IEVALAB-" 1293381 NIL IEVALAB- (NIL T T T) -8 NIL NIL NIL) (-526 1292169 1293025 1293100 "IDPOAMS" 1293105 NIL IDPOAMS (NIL T T) -8 NIL NIL NIL) (-525 1291271 1292058 1292133 "IDPOAM" 1292138 NIL IDPOAM (NIL T T) -8 NIL NIL NIL) (-524 1290652 1291186 1291248 "IDPO" 1291253 NIL IDPO (NIL T T) -8 NIL NIL NIL) (-523 1289132 1289659 1289711 "IDPC" 1290223 NIL IDPC (NIL T T) -9 NIL 1290504 NIL) (-522 1288464 1289024 1289097 "IDPAM" 1289102 NIL IDPAM (NIL T T) -8 NIL NIL NIL) (-521 1287679 1288356 1288429 "IDPAG" 1288434 NIL IDPAG (NIL T T) -8 NIL NIL NIL) (-520 1287223 1287485 1287575 "IDENT" 1287609 T IDENT (NIL) -8 NIL NIL NIL) (-519 1283442 1284326 1285221 "IDECOMP" 1286380 NIL IDECOMP (NIL NIL NIL) -7 NIL NIL NIL) (-518 1276077 1277365 1278412 "IDEAL" 1282478 NIL IDEAL (NIL T T T T) -8 NIL NIL NIL) (-517 1275219 1275349 1275549 "ICDEN" 1275961 NIL ICDEN (NIL T T T T) -7 NIL NIL NIL) (-516 1274194 1274699 1274846 "ICARD" 1275092 T ICARD (NIL) -8 NIL NIL NIL) (-515 1272224 1272567 1272972 "IBPTOOLS" 1273871 NIL IBPTOOLS (NIL T T T T) -7 NIL NIL NIL) (-514 1267453 1271844 1271957 "IBITS" 1272143 NIL IBITS (NIL NIL) -8 NIL NIL NIL) (-513 1264128 1264752 1265447 "IBATOOL" 1266870 NIL IBATOOL (NIL T T T) -7 NIL NIL NIL) (-512 1261889 1262369 1262902 "IBACHIN" 1263663 NIL IBACHIN (NIL T T T) -7 NIL NIL NIL) (-511 1259593 1261735 1261838 "IARRAY2" 1261843 NIL IARRAY2 (NIL T NIL NIL) -8 NIL NIL NIL) (-510 1255420 1259519 1259576 "IARRAY1" 1259581 NIL IARRAY1 (NIL T NIL) -8 NIL NIL NIL) (-509 1248437 1253832 1254313 "IAN" 1254959 T IAN (NIL) -8 NIL NIL NIL) (-508 1247942 1248005 1248178 "IALGFACT" 1248374 NIL IALGFACT (NIL T T T T) -7 NIL NIL NIL) (-507 1247434 1247583 1247611 "HYPCAT" 1247818 T HYPCAT (NIL) -9 NIL NIL NIL) (-506 1246936 1247089 1247275 "HYPCAT-" 1247280 NIL HYPCAT- (NIL T) -8 NIL NIL NIL) (-505 1246483 1246731 1246814 "HOSTNAME" 1246873 T HOSTNAME (NIL) -8 NIL NIL NIL) (-504 1246316 1246365 1246406 "HOMOTOP" 1246411 NIL HOMOTOP (NIL T) -9 NIL 1246444 NIL) (-503 1242860 1244248 1244289 "HOAGG" 1245270 NIL HOAGG (NIL T) -9 NIL 1245999 NIL) (-502 1241376 1241853 1242379 "HOAGG-" 1242384 NIL HOAGG- (NIL T T) -8 NIL NIL NIL) (-501 1234433 1240969 1241119 "HEXADEC" 1241246 T HEXADEC (NIL) -8 NIL NIL NIL) (-500 1233145 1233403 1233666 "HEUGCD" 1234210 NIL HEUGCD (NIL T) -7 NIL NIL NIL) (-499 1232077 1232982 1233112 "HELLFDIV" 1233117 NIL HELLFDIV (NIL T T T T) -8 NIL NIL NIL) (-498 1230199 1231852 1231941 "HEAP" 1232020 NIL HEAP (NIL T) -8 NIL NIL NIL) (-497 1229396 1229751 1229885 "HEADAST" 1230085 T HEADAST (NIL) -8 NIL NIL NIL) (-496 1222848 1229311 1229373 "HDP" 1229378 NIL HDP (NIL NIL T) -8 NIL NIL NIL) (-495 1215867 1222483 1222635 "HDMP" 1222749 NIL HDMP (NIL NIL T) -8 NIL NIL NIL) (-494 1215173 1215331 1215495 "HB" 1215723 T HB (NIL) -7 NIL NIL NIL) (-493 1208297 1215019 1215123 "HASHTBL" 1215128 NIL HASHTBL (NIL T T NIL) -8 NIL NIL NIL) (-492 1207713 1208018 1208110 "HASAST" 1208225 T HASAST (NIL) -8 NIL NIL NIL) (-491 1205126 1207335 1207517 "HACKPI" 1207551 T HACKPI (NIL) -8 NIL NIL NIL) (-490 1200412 1204979 1205092 "GTSET" 1205097 NIL GTSET (NIL T T T T) -8 NIL NIL NIL) (-489 1193565 1200290 1200388 "GSTBL" 1200393 NIL GSTBL (NIL T T T NIL) -8 NIL NIL NIL) (-488 1185328 1192730 1192986 "GSERIES" 1193365 NIL GSERIES (NIL T NIL NIL) -8 NIL NIL NIL) (-487 1184359 1184872 1184900 "GROUP" 1185103 T GROUP (NIL) -9 NIL 1185237 NIL) (-486 1183683 1183884 1184135 "GROUP-" 1184140 NIL GROUP- (NIL T) -8 NIL NIL NIL) (-485 1182032 1182371 1182758 "GROEBSOL" 1183360 NIL GROEBSOL (NIL NIL T T) -7 NIL NIL NIL) (-484 1180860 1181220 1181271 "GRMOD" 1181800 NIL GRMOD (NIL T T) -9 NIL 1181968 NIL) (-483 1180616 1180664 1180792 "GRMOD-" 1180797 NIL GRMOD- (NIL T T T) -8 NIL NIL NIL) (-482 1175756 1176970 1177970 "GRIMAGE" 1179636 T GRIMAGE (NIL) -8 NIL NIL NIL) (-481 1174150 1174483 1174807 "GRDEF" 1175452 T GRDEF (NIL) -7 NIL NIL NIL) (-480 1173582 1173710 1173851 "GRAY" 1174029 T GRAY (NIL) -7 NIL NIL NIL) (-479 1172659 1173161 1173212 "GRALG" 1173365 NIL GRALG (NIL T T) -9 NIL 1173458 NIL) (-478 1172296 1172393 1172556 "GRALG-" 1172561 NIL GRALG- (NIL T T T) -8 NIL NIL NIL) (-477 1168891 1171879 1172058 "GPOLSET" 1172202 NIL GPOLSET (NIL T T T T) -8 NIL NIL NIL) (-476 1168239 1168302 1168560 "GOSPER" 1168828 NIL GOSPER (NIL T T T T T) -7 NIL NIL NIL) (-475 1163809 1164677 1165203 "GMODPOL" 1167938 NIL GMODPOL (NIL NIL T T T NIL T) -8 NIL NIL NIL) (-474 1162796 1162998 1163236 "GHENSEL" 1163621 NIL GHENSEL (NIL T T) -7 NIL NIL NIL) (-473 1156868 1157795 1158815 "GENUPS" 1161880 NIL GENUPS (NIL T T) -7 NIL NIL NIL) (-472 1156559 1156616 1156705 "GENUFACT" 1156811 NIL GENUFACT (NIL T) -7 NIL NIL NIL) (-471 1155959 1156048 1156213 "GENPGCD" 1156477 NIL GENPGCD (NIL T T T T) -7 NIL NIL NIL) (-470 1155427 1155468 1155681 "GENMFACT" 1155918 NIL GENMFACT (NIL T T T T T) -7 NIL NIL NIL) (-469 1153964 1154250 1154557 "GENEEZ" 1155170 NIL GENEEZ (NIL T T) -7 NIL NIL NIL) (-468 1147142 1153575 1153737 "GDMP" 1153887 NIL GDMP (NIL NIL T T) -8 NIL NIL NIL) (-467 1135880 1140913 1142019 "GCNAALG" 1146125 NIL GCNAALG (NIL T NIL NIL NIL) -8 NIL NIL NIL) (-466 1134007 1135055 1135083 "GCDDOM" 1135338 T GCDDOM (NIL) -9 NIL 1135495 NIL) (-465 1133447 1133604 1133819 "GCDDOM-" 1133824 NIL GCDDOM- (NIL T) -8 NIL NIL NIL) (-464 1121919 1124393 1126785 "GBINTERN" 1131138 NIL GBINTERN (NIL T T T T) -7 NIL NIL NIL) (-463 1119720 1120048 1120469 "GBF" 1121594 NIL GBF (NIL T T T T) -7 NIL NIL NIL) (-462 1118477 1118666 1118933 "GBEUCLID" 1119536 NIL GBEUCLID (NIL T T T T) -7 NIL NIL NIL) (-461 1117127 1117334 1117638 "GB" 1118256 NIL GB (NIL T T T T) -7 NIL NIL NIL) (-460 1116458 1116601 1116750 "GAUSSFAC" 1116998 T GAUSSFAC (NIL) -7 NIL NIL NIL) (-459 1114779 1115127 1115441 "GALUTIL" 1116177 NIL GALUTIL (NIL T) -7 NIL NIL NIL) (-458 1113039 1113361 1113685 "GALPOLYU" 1114506 NIL GALPOLYU (NIL T T) -7 NIL NIL NIL) (-457 1110338 1110694 1111101 "GALFACTU" 1112736 NIL GALFACTU (NIL T T T) -7 NIL NIL NIL) (-456 1101952 1103643 1105251 "GALFACT" 1108770 NIL GALFACT (NIL T) -7 NIL NIL NIL) (-455 1099238 1099998 1100026 "FVFUN" 1101182 T FVFUN (NIL) -9 NIL 1101902 NIL) (-454 1098468 1098686 1098714 "FVC" 1099005 T FVC (NIL) -9 NIL 1099188 NIL) (-453 1098069 1098293 1098361 "FUNDESC" 1098420 T FUNDESC (NIL) -8 NIL NIL NIL) (-452 1097642 1097866 1097947 "FUNCTION" 1098021 NIL FUNCTION (NIL NIL) -8 NIL NIL NIL) (-451 1096319 1096943 1097146 "FTEM" 1097459 T FTEM (NIL) -8 NIL NIL NIL) (-450 1093949 1094641 1095107 "FT" 1095873 T FT (NIL) -8 NIL NIL NIL) (-449 1092218 1092529 1092926 "FSUPFACT" 1093640 NIL FSUPFACT (NIL T T T) -7 NIL NIL NIL) (-448 1090537 1090904 1091236 "FST" 1091906 T FST (NIL) -8 NIL NIL NIL) (-447 1089718 1089842 1090030 "FSRED" 1090419 NIL FSRED (NIL T T) -7 NIL NIL NIL) (-446 1088407 1088673 1089020 "FSPRMELT" 1089433 NIL FSPRMELT (NIL T T) -7 NIL NIL NIL) (-445 1085617 1086151 1086637 "FSPECF" 1087970 NIL FSPECF (NIL T T) -7 NIL NIL NIL) (-444 1085139 1085199 1085369 "FSINT" 1085558 NIL FSINT (NIL T T) -7 NIL NIL NIL) (-443 1083275 1084132 1084435 "FSERIES" 1084918 NIL FSERIES (NIL T T) -8 NIL NIL NIL) (-442 1082299 1082433 1082657 "FSCINT" 1083155 NIL FSCINT (NIL T T) -7 NIL NIL NIL) (-441 1081323 1081484 1081711 "FSAGG2" 1082152 NIL FSAGG2 (NIL T T T T) -7 NIL NIL NIL) (-440 1077298 1080267 1080308 "FSAGG" 1080678 NIL FSAGG (NIL T) -9 NIL 1080937 NIL) (-439 1074898 1075661 1076457 "FSAGG-" 1076552 NIL FSAGG- (NIL T T) -8 NIL NIL NIL) (-438 1072558 1072856 1073404 "FS2UPS" 1074616 NIL FS2UPS (NIL T T T T T NIL) -7 NIL NIL NIL) (-437 1071424 1071607 1071909 "FS2EXPXP" 1072383 NIL FS2EXPXP (NIL T T NIL NIL) -7 NIL NIL NIL) (-436 1071052 1071101 1071230 "FS2" 1071375 NIL FS2 (NIL T T T T) -7 NIL NIL NIL) (-435 1051290 1060826 1060867 "FS" 1064751 NIL FS (NIL T) -9 NIL 1067040 NIL) (-434 1039351 1042926 1046983 "FS-" 1047283 NIL FS- (NIL T T) -8 NIL NIL NIL) (-433 1038765 1038892 1039044 "FRUTIL" 1039231 NIL FRUTIL (NIL T) -7 NIL NIL NIL) (-432 1033276 1036454 1036494 "FRNAALG" 1037814 NIL FRNAALG (NIL T) -9 NIL 1038412 NIL) (-431 1028757 1030025 1031300 "FRNAALG-" 1032050 NIL FRNAALG- (NIL T T) -8 NIL NIL NIL) (-430 1028389 1028438 1028565 "FRNAAF2" 1028708 NIL FRNAAF2 (NIL T T T T) -7 NIL NIL NIL) (-429 1026676 1027238 1027534 "FRMOD" 1028201 NIL FRMOD (NIL T T T T NIL) -8 NIL NIL NIL) (-428 1025861 1025954 1026245 "FRIDEAL2" 1026583 NIL FRIDEAL2 (NIL T T T T T T T T) -7 NIL NIL NIL) (-427 1023466 1024236 1024554 "FRIDEAL" 1025652 NIL FRIDEAL (NIL T T T T) -8 NIL NIL NIL) (-426 1022557 1023013 1023054 "FRETRCT" 1023059 NIL FRETRCT (NIL T) -9 NIL 1023235 NIL) (-425 1021615 1021900 1022251 "FRETRCT-" 1022256 NIL FRETRCT- (NIL T T) -8 NIL NIL NIL) (-424 1018436 1019899 1019958 "FRAMALG" 1020840 NIL FRAMALG (NIL T T) -9 NIL 1021132 NIL) (-423 1016474 1017025 1017655 "FRAMALG-" 1017878 NIL FRAMALG- (NIL T T T) -8 NIL NIL NIL) (-422 1016104 1016167 1016274 "FRAC2" 1016411 NIL FRAC2 (NIL T T) -7 NIL NIL NIL) (-421 1009097 1015577 1015854 "FRAC" 1015859 NIL FRAC (NIL T) -8 NIL NIL NIL) (-420 1008727 1008790 1008897 "FR2" 1009034 NIL FR2 (NIL T T) -7 NIL NIL NIL) (-419 999644 1004222 1005580 "FR" 1007401 NIL FR (NIL T) -8 NIL NIL NIL) (-418 993563 997023 997051 "FPS" 998170 T FPS (NIL) -9 NIL 998727 NIL) (-417 992988 993121 993285 "FPS-" 993431 NIL FPS- (NIL T) -8 NIL NIL NIL) (-416 989954 991945 991973 "FPC" 992198 T FPC (NIL) -9 NIL 992340 NIL) (-415 989735 989787 989884 "FPC-" 989889 NIL FPC- (NIL T) -8 NIL NIL NIL) (-414 988493 989223 989264 "FPATMAB" 989269 NIL FPATMAB (NIL T) -9 NIL 989421 NIL) (-413 986636 987235 987582 "FPARFRAC" 988209 NIL FPARFRAC (NIL T T) -8 NIL NIL NIL) (-412 981928 982528 983210 "FORTRAN" 986068 NIL FORTRAN (NIL NIL NIL NIL NIL) -8 NIL NIL NIL) (-411 979502 980166 980194 "FORTFN" 981254 T FORTFN (NIL) -9 NIL 981878 NIL) (-410 979254 979316 979344 "FORTCAT" 979403 T FORTCAT (NIL) -9 NIL 979465 NIL) (-409 976940 977470 978009 "FORT" 978735 T FORT (NIL) -7 NIL NIL NIL) (-408 976722 976758 976827 "FORMULA1" 976904 NIL FORMULA1 (NIL T) -7 NIL NIL NIL) (-407 974726 975338 975728 "FORMULA" 976352 T FORMULA (NIL) -8 NIL NIL NIL) (-406 974243 974301 974474 "FORDER" 974668 NIL FORDER (NIL T T T T) -7 NIL NIL NIL) (-405 973303 973503 973696 "FOP" 974070 T FOP (NIL) -7 NIL NIL NIL) (-404 971716 972583 972757 "FNLA" 973185 NIL FNLA (NIL NIL NIL T) -8 NIL NIL NIL) (-403 970335 970846 970874 "FNCAT" 971334 T FNCAT (NIL) -9 NIL 971594 NIL) (-402 969778 970294 970322 "FNAME" 970327 T FNAME (NIL) -8 NIL NIL NIL) (-401 968104 969277 969305 "FMTC" 969310 T FMTC (NIL) -9 NIL 969346 NIL) (-400 966653 968040 968086 "FMONOID" 968091 NIL FMONOID (NIL T) -8 NIL NIL NIL) (-399 963242 964608 964649 "FMONCAT" 965866 NIL FMONCAT (NIL T) -9 NIL 966471 NIL) (-398 960564 961312 961340 "FMFUN" 962484 T FMFUN (NIL) -9 NIL 963192 NIL) (-397 957437 958489 958543 "FMCAT" 959738 NIL FMCAT (NIL T T) -9 NIL 960233 NIL) (-396 956670 956887 956915 "FMC" 957205 T FMC (NIL) -9 NIL 957387 NIL) (-395 955338 956436 956536 "FM1" 956615 NIL FM1 (NIL T T) -8 NIL NIL NIL) (-394 954356 955080 955229 "FM" 955234 NIL FM (NIL T T) -8 NIL NIL NIL) (-393 952094 952546 953040 "FLOATRP" 953907 NIL FLOATRP (NIL T) -7 NIL NIL NIL) (-392 949496 950032 950610 "FLOATCP" 951561 NIL FLOATCP (NIL T) -7 NIL NIL NIL) (-391 942159 947225 947846 "FLOAT" 948895 T FLOAT (NIL) -8 NIL NIL NIL) (-390 940677 941751 941792 "FLINEXP" 941797 NIL FLINEXP (NIL T) -9 NIL 941890 NIL) (-389 939807 940066 940394 "FLINEXP-" 940399 NIL FLINEXP- (NIL T T) -8 NIL NIL NIL) (-388 938865 939027 939251 "FLASORT" 939659 NIL FLASORT (NIL T T) -7 NIL NIL NIL) (-387 935783 936835 936887 "FLALG" 938114 NIL FLALG (NIL T T) -9 NIL 938581 NIL) (-386 934807 934968 935195 "FLAGG2" 935636 NIL FLAGG2 (NIL T T T T) -7 NIL NIL NIL) (-385 928176 932216 932257 "FLAGG" 933519 NIL FLAGG (NIL T) -9 NIL 934171 NIL) (-384 926830 927241 927731 "FLAGG-" 927736 NIL FLAGG- (NIL T T) -8 NIL NIL NIL) (-383 923468 924675 924734 "FINRALG" 925862 NIL FINRALG (NIL T T) -9 NIL 926370 NIL) (-382 922592 922857 923196 "FINRALG-" 923201 NIL FINRALG- (NIL T T T) -8 NIL NIL NIL) (-381 921898 922197 922225 "FINITE" 922421 T FINITE (NIL) -9 NIL 922528 NIL) (-380 913849 916428 916468 "FINAALG" 920135 NIL FINAALG (NIL T) -9 NIL 921588 NIL) (-379 908965 910231 911375 "FINAALG-" 912754 NIL FINAALG- (NIL T T) -8 NIL NIL NIL) (-378 907525 907947 908001 "FILECAT" 908685 NIL FILECAT (NIL T T) -9 NIL 908901 NIL) (-377 906803 907280 907383 "FILE" 907455 NIL FILE (NIL T) -8 NIL NIL NIL) (-376 904206 906033 906061 "FIELD" 906101 T FIELD (NIL) -9 NIL 906181 NIL) (-375 902748 903211 903722 "FIELD-" 903727 NIL FIELD- (NIL T) -8 NIL NIL NIL) (-374 900431 901383 901730 "FGROUP" 902434 NIL FGROUP (NIL T) -8 NIL NIL NIL) (-373 899503 899685 899905 "FGLMICPK" 900263 NIL FGLMICPK (NIL T NIL) -7 NIL NIL NIL) (-372 894758 899428 899485 "FFX" 899490 NIL FFX (NIL T NIL) -8 NIL NIL NIL) (-371 894353 894420 894555 "FFSLPE" 894691 NIL FFSLPE (NIL T T T) -7 NIL NIL NIL) (-370 893851 893893 894102 "FFPOLY2" 894311 NIL FFPOLY2 (NIL T T) -7 NIL NIL NIL) (-369 889727 890623 891419 "FFPOLY" 893087 NIL FFPOLY (NIL T) -7 NIL NIL NIL) (-368 884996 889646 889709 "FFP" 889714 NIL FFP (NIL T NIL) -8 NIL NIL NIL) (-367 879527 884339 884529 "FFNBX" 884850 NIL FFNBX (NIL T NIL) -8 NIL NIL NIL) (-366 873860 878662 878920 "FFNBP" 879381 NIL FFNBP (NIL T NIL) -8 NIL NIL NIL) (-365 867898 873144 873355 "FFNB" 873693 NIL FFNB (NIL NIL NIL) -8 NIL NIL NIL) (-364 866718 866928 867243 "FFINTBAS" 867695 NIL FFINTBAS (NIL T T T) -7 NIL NIL NIL) (-363 862311 864965 864993 "FFIELDC" 865613 T FFIELDC (NIL) -9 NIL 865989 NIL) (-362 860931 861372 861855 "FFIELDC-" 861860 NIL FFIELDC- (NIL T) -8 NIL NIL NIL) (-361 860488 860546 860670 "FFHOM" 860873 NIL FFHOM (NIL T T T) -7 NIL NIL NIL) (-360 858147 858670 859187 "FFF" 860003 NIL FFF (NIL T) -7 NIL NIL NIL) (-359 853182 857889 857990 "FFCGX" 858090 NIL FFCGX (NIL T NIL) -8 NIL NIL NIL) (-358 848221 852914 853021 "FFCGP" 853125 NIL FFCGP (NIL T NIL) -8 NIL NIL NIL) (-357 842821 847948 848056 "FFCG" 848157 NIL FFCG (NIL NIL NIL) -8 NIL NIL NIL) (-356 842226 842275 842510 "FFCAT2" 842772 NIL FFCAT2 (NIL T T T T T T T T) -7 NIL NIL NIL) (-355 820908 831958 832044 "FFCAT" 837209 NIL FFCAT (NIL T T T) -9 NIL 838660 NIL) (-354 815919 817153 818467 "FFCAT-" 819697 NIL FFCAT- (NIL T T T T) -8 NIL NIL NIL) (-353 810740 815830 815894 "FF" 815899 NIL FF (NIL NIL NIL) -8 NIL NIL NIL) (-352 799393 803712 804932 "FEXPR" 809592 NIL FEXPR (NIL NIL NIL T) -8 NIL NIL NIL) (-351 798321 798790 798831 "FEVALAB" 798915 NIL FEVALAB (NIL T) -9 NIL 799176 NIL) (-350 797438 797690 798028 "FEVALAB-" 798033 NIL FEVALAB- (NIL T T) -8 NIL NIL NIL) (-349 794300 795185 795300 "FDIVCAT" 796868 NIL FDIVCAT (NIL T T T T) -9 NIL 797305 NIL) (-348 794056 794089 794259 "FDIVCAT-" 794264 NIL FDIVCAT- (NIL T T T T T) -8 NIL NIL NIL) (-347 793270 793363 793640 "FDIV2" 793963 NIL FDIV2 (NIL T T T T T T T T) -7 NIL NIL NIL) (-346 791680 792653 792856 "FDIV" 793169 NIL FDIV (NIL T T T T) -8 NIL NIL NIL) (-345 790588 790975 791177 "FCTRDATA" 791498 T FCTRDATA (NIL) -8 NIL NIL NIL) (-344 789244 789533 789822 "FCPAK1" 790319 T FCPAK1 (NIL) -7 NIL NIL NIL) (-343 788247 788744 788885 "FCOMP" 789135 NIL FCOMP (NIL T) -8 NIL NIL NIL) (-342 771561 775397 778935 "FC" 784729 T FC (NIL) -8 NIL NIL NIL) (-341 763270 767882 767922 "FAXF" 769724 NIL FAXF (NIL T) -9 NIL 770416 NIL) (-340 760411 761218 762036 "FAXF-" 762501 NIL FAXF- (NIL T T) -8 NIL NIL NIL) (-339 755094 759787 759963 "FARRAY" 760268 NIL FARRAY (NIL T) -8 NIL NIL NIL) (-338 749659 752041 752094 "FAMR" 753117 NIL FAMR (NIL T T) -9 NIL 753577 NIL) (-337 748483 748851 749286 "FAMR-" 749291 NIL FAMR- (NIL T T T) -8 NIL NIL NIL) (-336 747510 748405 748458 "FAMONOID" 748463 NIL FAMONOID (NIL T) -8 NIL NIL NIL) (-335 745140 745992 746045 "FAMONC" 746986 NIL FAMONC (NIL T T) -9 NIL 747372 NIL) (-334 743614 744894 745031 "FAGROUP" 745036 NIL FAGROUP (NIL T) -8 NIL NIL NIL) (-333 741367 741728 742131 "FACUTIL" 743295 NIL FACUTIL (NIL T T T T) -7 NIL NIL NIL) (-332 740454 740651 740873 "FACTFUNC" 741177 NIL FACTFUNC (NIL T) -7 NIL NIL NIL) (-331 732195 739757 739956 "EXPUPXS" 740310 NIL EXPUPXS (NIL T NIL NIL) -8 NIL NIL NIL) (-330 729648 730218 730804 "EXPRTUBE" 731629 T EXPRTUBE (NIL) -7 NIL NIL NIL) (-329 725859 726511 727241 "EXPRODE" 728987 NIL EXPRODE (NIL T T) -7 NIL NIL NIL) (-328 720293 721000 721806 "EXPR2UPS" 725157 NIL EXPR2UPS (NIL T T) -7 NIL NIL NIL) (-327 719919 719982 720091 "EXPR2" 720230 NIL EXPR2 (NIL T T) -7 NIL NIL NIL) (-326 704227 718568 718997 "EXPR" 719523 NIL EXPR (NIL T) -8 NIL NIL NIL) (-325 694565 703378 703669 "EXPEXPAN" 704063 NIL EXPEXPAN (NIL T T NIL NIL) -8 NIL NIL NIL) (-324 693985 694289 694380 "EXITAST" 694494 T EXITAST (NIL) -8 NIL NIL NIL) (-323 693749 693942 693971 "EXIT" 693976 T EXIT (NIL) -8 NIL NIL NIL) (-322 693370 693438 693551 "EVALCYC" 693681 NIL EVALCYC (NIL T) -7 NIL NIL NIL) (-321 692887 693029 693070 "EVALAB" 693240 NIL EVALAB (NIL T) -9 NIL 693344 NIL) (-320 692344 692490 692711 "EVALAB-" 692716 NIL EVALAB- (NIL T T) -8 NIL NIL NIL) (-319 689459 691000 691028 "EUCDOM" 691583 T EUCDOM (NIL) -9 NIL 691933 NIL) (-318 687819 688320 688903 "EUCDOM-" 688908 NIL EUCDOM- (NIL T) -8 NIL NIL NIL) (-317 687445 687508 687617 "ESTOOLS2" 687756 NIL ESTOOLS2 (NIL T T) -7 NIL NIL NIL) (-316 687190 687238 687318 "ESTOOLS1" 687397 NIL ESTOOLS1 (NIL T) -7 NIL NIL NIL) (-315 674507 677488 680238 "ESTOOLS" 684460 T ESTOOLS (NIL) -7 NIL NIL NIL) (-314 674246 674284 674366 "ESCONT1" 674469 NIL ESCONT1 (NIL NIL NIL) -7 NIL NIL NIL) (-313 670554 671381 672161 "ESCONT" 673486 T ESCONT (NIL) -7 NIL NIL NIL) (-312 670223 670279 670379 "ES2" 670498 NIL ES2 (NIL T T) -7 NIL NIL NIL) (-311 669847 669911 670020 "ES1" 670159 NIL ES1 (NIL T T) -7 NIL NIL NIL) (-310 663548 665478 665506 "ES" 668274 T ES (NIL) -9 NIL 669684 NIL) (-309 658225 659782 661599 "ES-" 661763 NIL ES- (NIL T) -8 NIL NIL NIL) (-308 657417 657570 657746 "ERROR" 658069 T ERROR (NIL) -7 NIL NIL NIL) (-307 650547 657276 657367 "EQTBL" 657372 NIL EQTBL (NIL T T) -8 NIL NIL NIL) (-306 650173 650236 650345 "EQ2" 650484 NIL EQ2 (NIL T T) -7 NIL NIL NIL) (-305 642432 645487 646936 "EQ" 648757 NIL -3420 (NIL T) -8 NIL NIL NIL) (-304 637674 638770 639863 "EP" 641371 NIL EP (NIL T) -7 NIL NIL NIL) (-303 636214 636565 636871 "ENV" 637388 T ENV (NIL) -8 NIL NIL NIL) (-302 635174 635848 635876 "ENTIRER" 635881 T ENTIRER (NIL) -9 NIL 635927 NIL) (-301 631593 633356 633717 "EMR" 634982 NIL EMR (NIL T T T NIL NIL NIL) -8 NIL NIL NIL) (-300 630697 630908 630962 "ELTAGG" 631342 NIL ELTAGG (NIL T T) -9 NIL 631553 NIL) (-299 630404 630478 630619 "ELTAGG-" 630624 NIL ELTAGG- (NIL T T T) -8 NIL NIL NIL) (-298 630162 630197 630251 "ELTAB" 630335 NIL ELTAB (NIL T T) -9 NIL 630387 NIL) (-297 629264 629434 629633 "ELFUTS" 630013 NIL ELFUTS (NIL T T) -7 NIL NIL NIL) (-296 628988 629062 629090 "ELEMFUN" 629195 T ELEMFUN (NIL) -9 NIL NIL NIL) (-295 628852 628879 628947 "ELEMFUN-" 628952 NIL ELEMFUN- (NIL T) -8 NIL NIL NIL) (-294 623377 626894 626935 "ELAGG" 627875 NIL ELAGG (NIL T) -9 NIL 628338 NIL) (-293 621554 622096 622759 "ELAGG-" 622764 NIL ELAGG- (NIL T T) -8 NIL NIL NIL) (-292 620836 621003 621159 "ELABOR" 621418 T ELABOR (NIL) -8 NIL NIL NIL) (-291 619442 619776 620070 "ELABEXPR" 620562 T ELABEXPR (NIL) -8 NIL NIL NIL) (-290 611954 614079 614908 "EFUPXS" 618717 NIL EFUPXS (NIL T T T T) -8 NIL NIL NIL) (-289 605080 607203 608014 "EFULS" 611229 NIL EFULS (NIL T T T) -8 NIL NIL NIL) (-288 602517 602923 603395 "EFSTRUC" 604712 NIL EFSTRUC (NIL T T) -7 NIL NIL NIL) (-287 591955 593874 595422 "EF" 601032 NIL EF (NIL T T) -7 NIL NIL NIL) (-286 590933 591440 591589 "EAB" 591826 T EAB (NIL) -8 NIL NIL NIL) (-285 590055 590892 590920 "E04UCFA" 590925 T E04UCFA (NIL) -8 NIL NIL NIL) (-284 589177 590014 590042 "E04NAFA" 590047 T E04NAFA (NIL) -8 NIL NIL NIL) (-283 588299 589136 589164 "E04MBFA" 589169 T E04MBFA (NIL) -8 NIL NIL NIL) (-282 587421 588258 588286 "E04JAFA" 588291 T E04JAFA (NIL) -8 NIL NIL NIL) (-281 586545 587380 587408 "E04GCFA" 587413 T E04GCFA (NIL) -8 NIL NIL NIL) (-280 585669 586504 586532 "E04FDFA" 586537 T E04FDFA (NIL) -8 NIL NIL NIL) (-279 584791 585628 585656 "E04DGFA" 585661 T E04DGFA (NIL) -8 NIL NIL NIL) (-278 578868 580316 581680 "E04AGNT" 583447 T E04AGNT (NIL) -7 NIL NIL NIL) (-277 577488 578169 578209 "DVARCAT" 578550 NIL DVARCAT (NIL T) -9 NIL 578713 NIL) (-276 576638 576904 577218 "DVARCAT-" 577223 NIL DVARCAT- (NIL T T) -8 NIL NIL NIL) (-275 568606 576437 576566 "DSMP" 576571 NIL DSMP (NIL T T T) -8 NIL NIL NIL) (-274 566957 567748 567789 "DSEXT" 568152 NIL DSEXT (NIL T) -9 NIL 568446 NIL) (-273 565146 565670 566336 "DSEXT-" 566341 NIL DSEXT- (NIL T T) -8 NIL NIL NIL) (-272 564805 564870 564968 "DROPT1" 565081 NIL DROPT1 (NIL T) -7 NIL NIL NIL) (-271 559824 561046 562183 "DROPT0" 563688 T DROPT0 (NIL) -7 NIL NIL NIL) (-270 554407 555769 556837 "DROPT" 558776 T DROPT (NIL) -8 NIL NIL NIL) (-269 552716 553077 553463 "DRAWPT" 554041 T DRAWPT (NIL) -7 NIL NIL NIL) (-268 552343 552402 552520 "DRAWHACK" 552657 NIL DRAWHACK (NIL T) -7 NIL NIL NIL) (-267 551044 551343 551634 "DRAWCX" 552072 T DRAWCX (NIL) -7 NIL NIL NIL) (-266 550553 550628 550779 "DRAWCURV" 550970 NIL DRAWCURV (NIL T T) -7 NIL NIL NIL) (-265 540871 542983 545098 "DRAWCFUN" 548458 T DRAWCFUN (NIL) -7 NIL NIL NIL) (-264 535362 536381 537460 "DRAW" 539845 NIL DRAW (NIL T) -7 NIL NIL NIL) (-263 531944 534027 534068 "DQAGG" 534697 NIL DQAGG (NIL T) -9 NIL 534971 NIL) (-262 518527 526155 526238 "DPOLCAT" 528090 NIL DPOLCAT (NIL T T T T) -9 NIL 528635 NIL) (-261 513046 514712 516670 "DPOLCAT-" 516675 NIL DPOLCAT- (NIL T T T T T) -8 NIL NIL NIL) (-260 505968 512907 513005 "DPMO" 513010 NIL DPMO (NIL NIL T T) -8 NIL NIL NIL) (-259 498787 505748 505915 "DPMM" 505920 NIL DPMM (NIL NIL T T T) -8 NIL NIL NIL) (-258 498309 498571 498660 "DOMTMPLT" 498718 T DOMTMPLT (NIL) -8 NIL NIL NIL) (-257 497658 498111 498191 "DOMCTOR" 498249 T DOMCTOR (NIL) -8 NIL NIL NIL) (-256 496810 497138 497289 "DOMAIN" 497527 T DOMAIN (NIL) -8 NIL NIL NIL) (-255 489829 496445 496597 "DMP" 496711 NIL DMP (NIL NIL T) -8 NIL NIL NIL) (-254 487606 488896 488937 "DMEXT" 488942 NIL DMEXT (NIL T) -9 NIL 489118 NIL) (-253 487200 487262 487406 "DLP" 487544 NIL DLP (NIL T) -7 NIL NIL NIL) (-252 480323 486527 486717 "DLIST" 487042 NIL DLIST (NIL T) -8 NIL NIL NIL) (-251 476972 479148 479189 "DLAGG" 479739 NIL DLAGG (NIL T) -9 NIL 479969 NIL) (-250 475484 476298 476326 "DIVRING" 476418 T DIVRING (NIL) -9 NIL 476501 NIL) (-249 474667 474911 475211 "DIVRING-" 475216 NIL DIVRING- (NIL T) -8 NIL NIL NIL) (-248 472709 473126 473532 "DISPLAY" 474281 T DISPLAY (NIL) -7 NIL NIL NIL) (-247 471539 471760 472025 "DIRPROD2" 472502 NIL DIRPROD2 (NIL NIL T T) -7 NIL NIL NIL) (-246 465011 471453 471516 "DIRPROD" 471521 NIL DIRPROD (NIL NIL T) -8 NIL NIL NIL) (-245 453288 459722 459775 "DIRPCAT" 460033 NIL DIRPCAT (NIL NIL T) -9 NIL 460908 NIL) (-244 450488 451256 452137 "DIRPCAT-" 452474 NIL DIRPCAT- (NIL T NIL T) -8 NIL NIL NIL) (-243 449769 449935 450121 "DIOSP" 450322 T DIOSP (NIL) -7 NIL NIL NIL) (-242 446294 448653 448694 "DIOPS" 449128 NIL DIOPS (NIL T) -9 NIL 449357 NIL) (-241 445813 445957 446148 "DIOPS-" 446153 NIL DIOPS- (NIL T T) -8 NIL NIL NIL) (-240 444720 445492 445520 "DIFRING" 445525 T DIFRING (NIL) -9 NIL 445547 NIL) (-239 444368 444466 444494 "DIFFSPC" 444613 T DIFFSPC (NIL) -9 NIL 444688 NIL) (-238 443989 444091 444243 "DIFFSPC-" 444248 NIL DIFFSPC- (NIL T) -8 NIL NIL NIL) (-237 442925 443523 443564 "DIFFMOD" 443569 NIL DIFFMOD (NIL T) -9 NIL 443667 NIL) (-236 442621 442678 442719 "DIFFDOM" 442840 NIL DIFFDOM (NIL T) -9 NIL 442908 NIL) (-235 442468 442498 442582 "DIFFDOM-" 442587 NIL DIFFDOM- (NIL T T) -8 NIL NIL NIL) (-234 440208 441672 441713 "DIFEXT" 441718 NIL DIFEXT (NIL T) -9 NIL 441871 NIL) (-233 437353 439712 439753 "DIAGG" 439758 NIL DIAGG (NIL T) -9 NIL 439778 NIL) (-232 436701 436894 437146 "DIAGG-" 437151 NIL DIAGG- (NIL T T) -8 NIL NIL NIL) (-231 431665 435660 435937 "DHMATRIX" 436470 NIL DHMATRIX (NIL T) -8 NIL NIL NIL) (-230 427133 428186 429196 "DFSFUN" 430675 T DFSFUN (NIL) -7 NIL NIL NIL) (-229 421374 426064 426376 "DFLOAT" 426841 T DFLOAT (NIL) -8 NIL NIL NIL) (-228 419613 419918 420307 "DFINTTLS" 421082 NIL DFINTTLS (NIL T T) -7 NIL NIL NIL) (-227 416432 417634 418034 "DERHAM" 419279 NIL DERHAM (NIL T NIL) -8 NIL NIL NIL) (-226 414082 416207 416296 "DEQUEUE" 416376 NIL DEQUEUE (NIL T) -8 NIL NIL NIL) (-225 413324 413469 413652 "DEGRED" 413944 NIL DEGRED (NIL T T) -7 NIL NIL NIL) (-224 409730 410499 411345 "DEFINTRF" 412552 NIL DEFINTRF (NIL T) -7 NIL NIL NIL) (-223 407267 407754 408346 "DEFINTEF" 409249 NIL DEFINTEF (NIL T T) -7 NIL NIL NIL) (-222 406551 406887 407002 "DEFAST" 407172 T DEFAST (NIL) -8 NIL NIL NIL) (-221 399608 406144 406294 "DECIMAL" 406421 T DECIMAL (NIL) -8 NIL NIL NIL) (-220 397066 397578 398084 "DDFACT" 399152 NIL DDFACT (NIL T T) -7 NIL NIL NIL) (-219 396656 396705 396856 "DBLRESP" 397017 NIL DBLRESP (NIL T T T T) -7 NIL NIL NIL) (-218 395857 396426 396517 "DBASIS" 396605 NIL DBASIS (NIL NIL) -8 NIL NIL NIL) (-217 393641 394087 394448 "DBASE" 395623 NIL DBASE (NIL T) -8 NIL NIL NIL) (-216 392829 393121 393267 "DATAARY" 393540 NIL DATAARY (NIL NIL T) -8 NIL NIL NIL) (-215 391887 392788 392816 "D03FAFA" 392821 T D03FAFA (NIL) -8 NIL NIL NIL) (-214 390946 391846 391874 "D03EEFA" 391879 T D03EEFA (NIL) -8 NIL NIL NIL) (-213 388872 389362 389851 "D03AGNT" 390477 T D03AGNT (NIL) -7 NIL NIL NIL) (-212 388113 388831 388859 "D02EJFA" 388864 T D02EJFA (NIL) -8 NIL NIL NIL) (-211 387354 388072 388100 "D02CJFA" 388105 T D02CJFA (NIL) -8 NIL NIL NIL) (-210 386595 387313 387341 "D02BHFA" 387346 T D02BHFA (NIL) -8 NIL NIL NIL) (-209 385836 386554 386582 "D02BBFA" 386587 T D02BBFA (NIL) -8 NIL NIL NIL) (-208 378967 380622 382228 "D02AGNT" 384250 T D02AGNT (NIL) -7 NIL NIL NIL) (-207 376717 377258 377804 "D01WGTS" 378441 T D01WGTS (NIL) -7 NIL NIL NIL) (-206 375724 376676 376704 "D01TRNS" 376709 T D01TRNS (NIL) -8 NIL NIL NIL) (-205 374732 375683 375711 "D01GBFA" 375716 T D01GBFA (NIL) -8 NIL NIL NIL) (-204 373740 374691 374719 "D01FCFA" 374724 T D01FCFA (NIL) -8 NIL NIL NIL) (-203 372748 373699 373727 "D01ASFA" 373732 T D01ASFA (NIL) -8 NIL NIL NIL) (-202 371756 372707 372735 "D01AQFA" 372740 T D01AQFA (NIL) -8 NIL NIL NIL) (-201 370764 371715 371743 "D01APFA" 371748 T D01APFA (NIL) -8 NIL NIL NIL) (-200 369772 370723 370751 "D01ANFA" 370756 T D01ANFA (NIL) -8 NIL NIL NIL) (-199 368780 369731 369759 "D01AMFA" 369764 T D01AMFA (NIL) -8 NIL NIL NIL) (-198 367788 368739 368767 "D01ALFA" 368772 T D01ALFA (NIL) -8 NIL NIL NIL) (-197 366796 367747 367775 "D01AKFA" 367780 T D01AKFA (NIL) -8 NIL NIL NIL) (-196 365804 366755 366783 "D01AJFA" 366788 T D01AJFA (NIL) -8 NIL NIL NIL) (-195 359027 360652 362213 "D01AGNT" 364263 T D01AGNT (NIL) -7 NIL NIL NIL) (-194 358346 358492 358644 "CYCLOTOM" 358895 T CYCLOTOM (NIL) -7 NIL NIL NIL) (-193 355001 355794 356521 "CYCLES" 357639 T CYCLES (NIL) -7 NIL NIL NIL) (-192 354301 354447 354618 "CVMP" 354862 NIL CVMP (NIL T) -7 NIL NIL NIL) (-191 352088 352400 352769 "CTRIGMNP" 354029 NIL CTRIGMNP (NIL T T) -7 NIL NIL NIL) (-190 351561 351819 351920 "CTORKIND" 352007 T CTORKIND (NIL) -8 NIL NIL NIL) (-189 350766 351154 351182 "CTORCAT" 351364 T CTORCAT (NIL) -9 NIL 351477 NIL) (-188 350340 350475 350634 "CTORCAT-" 350639 NIL CTORCAT- (NIL T) -8 NIL NIL NIL) (-187 349754 350014 350122 "CTORCALL" 350264 NIL CTORCALL (NIL T) -8 NIL NIL NIL) (-186 349112 349548 349621 "CTOR" 349701 T CTOR (NIL) -8 NIL NIL NIL) (-185 348468 348585 348738 "CSTTOOLS" 349009 NIL CSTTOOLS (NIL T T) -7 NIL NIL NIL) (-184 344165 344924 345682 "CRFP" 347780 NIL CRFP (NIL T T) -7 NIL NIL NIL) (-183 343580 343886 343978 "CRCEAST" 344093 T CRCEAST (NIL) -8 NIL NIL NIL) (-182 342603 342812 343040 "CRAPACK" 343384 NIL CRAPACK (NIL T) -7 NIL NIL NIL) (-181 341983 342088 342292 "CPMATCH" 342479 NIL CPMATCH (NIL T T T) -7 NIL NIL NIL) (-180 341702 341736 341842 "CPIMA" 341949 NIL CPIMA (NIL T T T) -7 NIL NIL NIL) (-179 337960 338722 339441 "COORDSYS" 341037 NIL COORDSYS (NIL T) -7 NIL NIL NIL) (-178 337348 337493 337635 "CONTOUR" 337838 T CONTOUR (NIL) -8 NIL NIL NIL) (-177 332819 335351 335843 "CONTFRAC" 336888 NIL CONTFRAC (NIL T) -8 NIL NIL NIL) (-176 332693 332720 332748 "CONDUIT" 332785 T CONDUIT (NIL) -9 NIL NIL NIL) (-175 331647 332321 332349 "COMRING" 332354 T COMRING (NIL) -9 NIL 332406 NIL) (-174 330629 331005 331189 "COMPPROP" 331483 T COMPPROP (NIL) -8 NIL NIL NIL) (-173 330284 330325 330453 "COMPLPAT" 330588 NIL COMPLPAT (NIL T T T) -7 NIL NIL NIL) (-172 329914 329977 330084 "COMPLEX2" 330221 NIL COMPLEX2 (NIL T T) -7 NIL NIL NIL) (-171 318318 329723 329832 "COMPLEX" 329837 NIL COMPLEX (NIL T) -8 NIL NIL NIL) (-170 317639 317778 317938 "COMPILER" 318178 T COMPILER (NIL) -8 NIL NIL NIL) (-169 317351 317392 317490 "COMPFACT" 317598 NIL COMPFACT (NIL T T) -7 NIL NIL NIL) (-168 298745 311055 311095 "COMPCAT" 312099 NIL COMPCAT (NIL T) -9 NIL 313447 NIL) (-167 287633 291184 294811 "COMPCAT-" 295167 NIL COMPCAT- (NIL T T) -8 NIL NIL NIL) (-166 287356 287390 287493 "COMMUPC" 287599 NIL COMMUPC (NIL T T T) -7 NIL NIL NIL) (-165 287144 287184 287243 "COMMONOP" 287317 T COMMONOP (NIL) -7 NIL NIL NIL) (-164 286666 286948 287023 "COMMAAST" 287089 T COMMAAST (NIL) -8 NIL NIL NIL) (-163 286173 286417 286504 "COMM" 286599 T COMM (NIL) -8 NIL NIL NIL) (-162 285368 285616 285644 "COMBOPC" 285982 T COMBOPC (NIL) -9 NIL 286157 NIL) (-161 284222 284474 284716 "COMBINAT" 285158 NIL COMBINAT (NIL T) -7 NIL NIL NIL) (-160 280565 281253 281880 "COMBF" 283644 NIL COMBF (NIL T T) -7 NIL NIL NIL) (-159 279227 279681 279916 "COLOR" 280350 T COLOR (NIL) -8 NIL NIL NIL) (-158 278643 278948 279040 "COLONAST" 279155 T COLONAST (NIL) -8 NIL NIL NIL) (-157 278277 278330 278455 "CMPLXRT" 278590 NIL CMPLXRT (NIL T T) -7 NIL NIL NIL) (-156 277665 277977 278076 "CLLCTAST" 278198 T CLLCTAST (NIL) -8 NIL NIL NIL) (-155 273125 274195 275275 "CLIP" 276605 T CLIP (NIL) -7 NIL NIL NIL) (-154 271298 272226 272466 "CLIF" 272952 NIL CLIF (NIL NIL T NIL) -8 NIL NIL NIL) (-153 267391 269416 269457 "CLAGG" 270386 NIL CLAGG (NIL T) -9 NIL 270922 NIL) (-152 265735 266270 266853 "CLAGG-" 266858 NIL CLAGG- (NIL T T) -8 NIL NIL NIL) (-151 265273 265364 265504 "CINTSLPE" 265644 NIL CINTSLPE (NIL T T) -7 NIL NIL NIL) (-150 262738 263245 263793 "CHVAR" 264801 NIL CHVAR (NIL T T T) -7 NIL NIL NIL) (-149 261778 262452 262480 "CHARZ" 262485 T CHARZ (NIL) -9 NIL 262500 NIL) (-148 261526 261572 261650 "CHARPOL" 261732 NIL CHARPOL (NIL T) -7 NIL NIL NIL) (-147 260444 261150 261178 "CHARNZ" 261239 T CHARNZ (NIL) -9 NIL 261288 NIL) (-146 257388 258498 259027 "CHAR" 259935 T CHAR (NIL) -8 NIL NIL NIL) (-145 257096 257175 257203 "CFCAT" 257314 T CFCAT (NIL) -9 NIL NIL NIL) (-144 256319 256448 256631 "CDEN" 256980 NIL CDEN (NIL T T T) -7 NIL NIL NIL) (-143 252030 255472 255752 "CCLASS" 256059 T CCLASS (NIL) -8 NIL NIL NIL) (-142 251251 251438 251615 "CATEGORY" 251873 T -10 (NIL) -8 NIL NIL NIL) (-141 250746 251170 251218 "CATCTOR" 251223 T CATCTOR (NIL) -8 NIL NIL NIL) (-140 250137 250449 250547 "CATAST" 250668 T CATAST (NIL) -8 NIL NIL NIL) (-139 249553 249858 249950 "CASEAST" 250065 T CASEAST (NIL) -8 NIL NIL NIL) (-138 248649 248809 249030 "CARTEN2" 249400 NIL CARTEN2 (NIL NIL NIL T T) -7 NIL NIL NIL) (-137 243546 244806 245550 "CARTEN" 247961 NIL CARTEN (NIL NIL NIL T) -8 NIL NIL NIL) (-136 241676 242696 242953 "CARD" 243309 T CARD (NIL) -8 NIL NIL NIL) (-135 241198 241480 241555 "CAPSLAST" 241621 T CAPSLAST (NIL) -8 NIL NIL NIL) (-134 240640 240896 240924 "CACHSET" 241056 T CACHSET (NIL) -9 NIL 241134 NIL) (-133 240030 240418 240446 "CABMON" 240496 T CABMON (NIL) -9 NIL 240552 NIL) (-132 239467 239734 239844 "BYTEORD" 239940 T BYTEORD (NIL) -8 NIL NIL NIL) (-131 234508 238972 239144 "BYTEBUF" 239315 T BYTEBUF (NIL) -8 NIL NIL NIL) (-130 233339 234051 234186 "BYTE" 234349 T BYTE (NIL) -8 NIL NIL 234464) (-129 230715 233031 233138 "BTREE" 233265 NIL BTREE (NIL T) -8 NIL NIL NIL) (-128 228031 230363 230485 "BTOURN" 230625 NIL BTOURN (NIL T) -8 NIL NIL NIL) (-127 225249 227473 227514 "BTCAT" 227582 NIL BTCAT (NIL T) -9 NIL 227659 NIL) (-126 224898 224996 225145 "BTCAT-" 225150 NIL BTCAT- (NIL T T) -8 NIL NIL NIL) (-125 219901 224144 224172 "BTAGG" 224286 T BTAGG (NIL) -9 NIL 224396 NIL) (-124 219355 219516 219722 "BTAGG-" 219727 NIL BTAGG- (NIL T) -8 NIL NIL NIL) (-123 216205 218633 218848 "BSTREE" 219172 NIL BSTREE (NIL T) -8 NIL NIL NIL) (-122 215313 215469 215653 "BRILL" 216061 NIL BRILL (NIL T) -7 NIL NIL NIL) (-121 211819 214011 214052 "BRAGG" 214701 NIL BRAGG (NIL T) -9 NIL 214959 NIL) (-120 210252 210754 211309 "BRAGG-" 211314 NIL BRAGG- (NIL T T) -8 NIL NIL NIL) (-119 202509 209596 209781 "BPADICRT" 210099 NIL BPADICRT (NIL NIL) -8 NIL NIL NIL) (-118 200525 202446 202491 "BPADIC" 202496 NIL BPADIC (NIL NIL) -8 NIL NIL NIL) (-117 200217 200253 200367 "BOUNDZRO" 200489 NIL BOUNDZRO (NIL T T) -7 NIL NIL NIL) (-116 197944 198402 198877 "BOP1" 199775 NIL BOP1 (NIL T) -7 NIL NIL NIL) (-115 192974 194404 195302 "BOP" 197066 T BOP (NIL) -8 NIL NIL NIL) (-114 191639 192562 192704 "BOOLEAN" 192852 T BOOLEAN (NIL) -8 NIL NIL NIL) (-113 191232 191389 191417 "BOOLE" 191528 T BOOLE (NIL) -9 NIL 191609 NIL) (-112 191100 191127 191193 "BOOLE-" 191198 NIL BOOLE- (NIL T) -8 NIL NIL NIL) (-111 190269 190769 190823 "BMODULE" 190828 NIL BMODULE (NIL T T) -9 NIL 190893 NIL) (-110 185704 190067 190140 "BITS" 190216 T BITS (NIL) -8 NIL NIL NIL) (-109 185101 185244 185384 "BINDING" 185584 T BINDING (NIL) -8 NIL NIL NIL) (-108 178161 184696 184845 "BINARY" 184972 T BINARY (NIL) -8 NIL NIL NIL) (-107 175879 177388 177429 "BGAGG" 177689 NIL BGAGG (NIL T) -9 NIL 177826 NIL) (-106 175704 175742 175833 "BGAGG-" 175838 NIL BGAGG- (NIL T T) -8 NIL NIL NIL) (-105 174727 175088 175293 "BFUNCT" 175519 T BFUNCT (NIL) -8 NIL NIL NIL) (-104 173397 173595 173883 "BEZOUT" 174551 NIL BEZOUT (NIL T T T T T) -7 NIL NIL NIL) (-103 169709 172249 172579 "BBTREE" 173100 NIL BBTREE (NIL T) -8 NIL NIL NIL) (-102 169292 169388 169416 "BASTYPE" 169593 T BASTYPE (NIL) -9 NIL 169692 NIL) (-101 168950 169049 169184 "BASTYPE-" 169189 NIL BASTYPE- (NIL T) -8 NIL NIL NIL) (-100 168372 168460 168612 "BALFACT" 168861 NIL BALFACT (NIL T T) -7 NIL NIL NIL) (-99 167108 167787 167973 "AUTOMOR" 168217 NIL AUTOMOR (NIL T) -8 NIL NIL NIL) (-98 166834 166839 166865 "ATTREG" 166870 T ATTREG (NIL) -9 NIL NIL NIL) (-97 164996 165531 165883 "ATTRBUT" 166500 T ATTRBUT (NIL) -8 NIL NIL NIL) (-96 164550 164824 164890 "ATTRAST" 164948 T ATTRAST (NIL) -8 NIL NIL NIL) (-95 164050 164199 164225 "ATRIG" 164426 T ATRIG (NIL) -9 NIL NIL NIL) (-94 163847 163900 163987 "ATRIG-" 163992 NIL ATRIG- (NIL T) -8 NIL NIL NIL) (-93 163430 163664 163690 "ASTCAT" 163695 T ASTCAT (NIL) -9 NIL 163725 NIL) (-92 163139 163216 163335 "ASTCAT-" 163340 NIL ASTCAT- (NIL T) -8 NIL NIL NIL) (-91 161227 162915 163003 "ASTACK" 163082 NIL ASTACK (NIL T) -8 NIL NIL NIL) (-90 159716 160029 160394 "ASSOCEQ" 160909 NIL ASSOCEQ (NIL T T) -7 NIL NIL NIL) (-89 158640 159375 159499 "ASP9" 159623 NIL ASP9 (NIL NIL) -8 NIL NIL NIL) (-88 157400 158245 158387 "ASP80" 158529 NIL ASP80 (NIL NIL) -8 NIL NIL NIL) (-87 157127 157348 157387 "ASP8" 157392 NIL ASP8 (NIL NIL) -8 NIL NIL NIL) (-86 155973 156804 156922 "ASP78" 157040 NIL ASP78 (NIL NIL) -8 NIL NIL NIL) (-85 154834 155653 155770 "ASP77" 155887 NIL ASP77 (NIL NIL) -8 NIL NIL NIL) (-84 153638 154472 154603 "ASP74" 154734 NIL ASP74 (NIL NIL) -8 NIL NIL NIL) (-83 152430 153273 153405 "ASP73" 153537 NIL ASP73 (NIL NIL) -8 NIL NIL NIL) (-82 151220 152065 152197 "ASP7" 152329 NIL ASP7 (NIL NIL) -8 NIL NIL NIL) (-81 150216 151046 151146 "ASP6" 151151 NIL ASP6 (NIL NIL) -8 NIL NIL NIL) (-80 149055 149893 150011 "ASP55" 150129 NIL ASP55 (NIL NIL) -8 NIL NIL NIL) (-79 147896 148729 148848 "ASP50" 148967 NIL ASP50 (NIL NIL) -8 NIL NIL NIL) (-78 146876 147597 147707 "ASP49" 147817 NIL ASP49 (NIL NIL) -8 NIL NIL NIL) (-77 145552 146415 146583 "ASP42" 146765 NIL ASP42 (NIL NIL NIL NIL) -8 NIL NIL NIL) (-76 144221 145085 145255 "ASP41" 145439 NIL ASP41 (NIL NIL NIL NIL) -8 NIL NIL NIL) (-75 143201 143922 144032 "ASP4" 144142 NIL ASP4 (NIL NIL) -8 NIL NIL NIL) (-74 142043 142878 142996 "ASP35" 143114 NIL ASP35 (NIL NIL) -8 NIL NIL NIL) (-73 141772 141991 142030 "ASP34" 142035 NIL ASP34 (NIL NIL) -8 NIL NIL NIL) (-72 141491 141576 141652 "ASP33" 141727 NIL ASP33 (NIL NIL) -8 NIL NIL NIL) (-71 140277 141126 141258 "ASP31" 141390 NIL ASP31 (NIL NIL) -8 NIL NIL NIL) (-70 140006 140225 140264 "ASP30" 140269 NIL ASP30 (NIL NIL) -8 NIL NIL NIL) (-69 139723 139810 139886 "ASP29" 139961 NIL ASP29 (NIL NIL) -8 NIL NIL NIL) (-68 139452 139671 139710 "ASP28" 139715 NIL ASP28 (NIL NIL) -8 NIL NIL NIL) (-67 139181 139400 139439 "ASP27" 139444 NIL ASP27 (NIL NIL) -8 NIL NIL NIL) (-66 138157 138879 138990 "ASP24" 139101 NIL ASP24 (NIL NIL) -8 NIL NIL NIL) (-65 137126 137959 138071 "ASP20" 138076 NIL ASP20 (NIL NIL) -8 NIL NIL NIL) (-64 135961 136800 136919 "ASP19" 137038 NIL ASP19 (NIL NIL) -8 NIL NIL NIL) (-63 135680 135765 135841 "ASP12" 135916 NIL ASP12 (NIL NIL) -8 NIL NIL NIL) (-62 134424 135279 135423 "ASP10" 135567 NIL ASP10 (NIL NIL) -8 NIL NIL NIL) (-61 133404 134125 134235 "ASP1" 134345 NIL ASP1 (NIL NIL) -8 NIL NIL NIL) (-60 131130 133248 133339 "ARRAY2" 133344 NIL ARRAY2 (NIL T) -8 NIL NIL NIL) (-59 130144 130335 130556 "ARRAY12" 130953 NIL ARRAY12 (NIL T T) -7 NIL NIL NIL) (-58 125618 129792 129906 "ARRAY1" 130061 NIL ARRAY1 (NIL T) -8 NIL NIL NIL) (-57 119774 121820 121895 "ARR2CAT" 124525 NIL ARR2CAT (NIL T T T) -9 NIL 125283 NIL) (-56 117373 118150 119005 "ARR2CAT-" 119010 NIL ARR2CAT- (NIL T T T T) -8 NIL NIL NIL) (-55 116624 117000 117125 "ARITY" 117266 T ARITY (NIL) -8 NIL NIL NIL) (-54 115382 115552 115851 "APPRULE" 116460 NIL APPRULE (NIL T T T) -7 NIL NIL NIL) (-53 115027 115081 115200 "APPLYORE" 115328 NIL APPLYORE (NIL T T T) -7 NIL NIL NIL) (-52 114281 114428 114585 "ANY1" 114901 NIL ANY1 (NIL T) -7 NIL NIL NIL) (-51 113581 113874 113994 "ANY" 114179 T ANY (NIL) -8 NIL NIL NIL) (-50 110907 112018 112345 "ANTISYM" 113305 NIL ANTISYM (NIL T NIL) -8 NIL NIL NIL) (-49 110351 110614 110710 "ANON" 110829 T ANON (NIL) -8 NIL NIL NIL) (-48 103514 108890 109344 "AN" 109915 T AN (NIL) -8 NIL NIL NIL) (-47 99177 100786 100837 "AMR" 101585 NIL AMR (NIL T T) -9 NIL 102185 NIL) (-46 98229 98510 98873 "AMR-" 98878 NIL AMR- (NIL T T T) -8 NIL NIL NIL) (-45 81698 98146 98207 "ALIST" 98212 NIL ALIST (NIL T T) -8 NIL NIL NIL) (-44 77995 81292 81461 "ALGSC" 81616 NIL ALGSC (NIL T NIL NIL NIL) -8 NIL NIL NIL) (-43 74445 75105 75712 "ALGPKG" 77435 NIL ALGPKG (NIL T T) -7 NIL NIL NIL) (-42 73710 73823 74007 "ALGMFACT" 74331 NIL ALGMFACT (NIL T T T) -7 NIL NIL NIL) (-41 69693 70324 70918 "ALGMANIP" 73294 NIL ALGMANIP (NIL T T) -7 NIL NIL NIL) (-40 59053 69319 69469 "ALGFF" 69626 NIL ALGFF (NIL T T T NIL) -8 NIL NIL NIL) (-39 58225 58380 58559 "ALGFACT" 58911 NIL ALGFACT (NIL T) -7 NIL NIL NIL) (-38 57014 57752 57790 "ALGEBRA" 57795 NIL ALGEBRA (NIL T) -9 NIL 57836 NIL) (-37 56714 56791 56923 "ALGEBRA-" 56928 NIL ALGEBRA- (NIL T T) -8 NIL NIL NIL) (-36 37668 54551 54603 "ALAGG" 54739 NIL ALAGG (NIL T T) -9 NIL 54900 NIL) (-35 37168 37317 37343 "AHYP" 37544 T AHYP (NIL) -9 NIL NIL NIL) (-34 36470 36653 36679 "AGG" 36962 T AGG (NIL) -9 NIL 37151 NIL) (-33 36177 36264 36379 "AGG-" 36384 NIL AGG- (NIL T) -8 NIL NIL NIL) (-32 33937 34406 34811 "AF" 35819 NIL AF (NIL T T) -7 NIL NIL NIL) (-31 33357 33662 33752 "ADDAST" 33865 T ADDAST (NIL) -8 NIL NIL NIL) (-30 32589 32884 33040 "ACPLOT" 33219 T ACPLOT (NIL) -8 NIL NIL NIL) (-29 20153 29521 29559 "ACFS" 30166 NIL ACFS (NIL T) -9 NIL 30405 NIL) (-28 18060 18670 19432 "ACFS-" 19437 NIL ACFS- (NIL T T) -8 NIL NIL NIL) (-27 13768 16093 16119 "ACF" 16998 T ACF (NIL) -9 NIL 17411 NIL) (-26 12400 12806 13299 "ACF-" 13304 NIL ACF- (NIL T) -8 NIL NIL NIL) (-25 11910 12153 12179 "ABELSG" 12271 T ABELSG (NIL) -9 NIL 12336 NIL) (-24 11771 11802 11868 "ABELSG-" 11873 NIL ABELSG- (NIL T) -8 NIL NIL NIL) (-23 11040 11387 11413 "ABELMON" 11583 T ABELMON (NIL) -9 NIL 11695 NIL) (-22 10680 10788 10926 "ABELMON-" 10931 NIL ABELMON- (NIL T) -8 NIL NIL NIL) (-21 9930 10386 10412 "ABELGRP" 10484 T ABELGRP (NIL) -9 NIL 10559 NIL) (-20 9357 9522 9738 "ABELGRP-" 9743 NIL ABELGRP- (NIL T) -8 NIL NIL NIL) (-19 4579 8619 8658 "A1AGG" 8663 NIL A1AGG (NIL T) -9 NIL 8703 NIL) (-18 30 1497 3059 "A1AGG-" 3064 NIL A1AGG- (NIL T T) -8 NIL NIL NIL))
\ No newline at end of file +((-3 3460155 3460160 3460165 NIL NIL NIL NIL (NIL) -8 NIL NIL NIL) (-2 3460140 3460145 3460150 NIL NIL NIL NIL (NIL) -8 NIL NIL NIL) (-1 3460125 3460130 3460135 NIL NIL NIL NIL (NIL) -8 NIL NIL NIL) (0 3460110 3460115 3460120 NIL NIL NIL NIL (NIL) -8 NIL NIL NIL) (-1329 3459103 3459985 3460062 "ZMOD" 3460067 NIL ZMOD (NIL NIL) -8 NIL NIL NIL) (-1328 3458139 3458321 3458544 "ZLINDEP" 3458935 NIL ZLINDEP (NIL T) -7 NIL NIL NIL) (-1327 3447301 3449207 3451179 "ZDSOLVE" 3456269 NIL ZDSOLVE (NIL T NIL NIL) -7 NIL NIL NIL) (-1326 3446535 3446688 3446877 "YSTREAM" 3447147 NIL YSTREAM (NIL T) -7 NIL NIL NIL) (-1325 3445895 3446204 3446319 "YDIAGRAM" 3446442 T YDIAGRAM (NIL) -8 NIL NIL NIL) (-1324 3443343 3445196 3445400 "XRPOLY" 3445738 NIL XRPOLY (NIL T T) -8 NIL NIL NIL) (-1323 3439610 3441214 3441789 "XPR" 3442815 NIL XPR (NIL T T) -8 NIL NIL NIL) (-1322 3436941 3438617 3438672 "XPOLYC" 3438960 NIL XPOLYC (NIL T T) -9 NIL 3439073 NIL) (-1321 3434336 3436272 3436476 "XPOLY" 3436772 NIL XPOLY (NIL T) -8 NIL NIL NIL) (-1320 3430282 3432853 3433241 "XPBWPOLY" 3433994 NIL XPBWPOLY (NIL T T) -8 NIL NIL NIL) (-1319 3425174 3426753 3426808 "XFALG" 3428980 NIL XFALG (NIL T T) -9 NIL 3429769 NIL) (-1318 3420450 3423150 3423192 "XF" 3423813 NIL XF (NIL T) -9 NIL 3424213 NIL) (-1317 3420047 3420159 3420328 "XF-" 3420333 NIL XF- (NIL T T) -8 NIL NIL NIL) (-1316 3419162 3419284 3419489 "XEXPPKG" 3419939 NIL XEXPPKG (NIL T T T) -7 NIL NIL NIL) (-1315 3416903 3419012 3419108 "XDPOLY" 3419113 NIL XDPOLY (NIL T T) -8 NIL NIL NIL) (-1314 3415558 3416296 3416339 "XALG" 3416344 NIL XALG (NIL T) -9 NIL 3416455 NIL) (-1313 3408582 3413535 3414029 "WUTSET" 3415150 NIL WUTSET (NIL T T T T) -8 NIL NIL NIL) (-1312 3406684 3407634 3407957 "WP" 3408393 NIL WP (NIL T T T T NIL NIL NIL) -8 NIL NIL NIL) (-1311 3406232 3406506 3406576 "WHILEAST" 3406636 T WHILEAST (NIL) -8 NIL NIL NIL) (-1310 3405644 3405949 3406043 "WHEREAST" 3406160 T WHEREAST (NIL) -8 NIL NIL NIL) (-1309 3404518 3404728 3405023 "WFFINTBS" 3405441 NIL WFFINTBS (NIL T T T T) -7 NIL NIL NIL) (-1308 3402386 3402849 3403311 "WEIER" 3404090 NIL WEIER (NIL T) -7 NIL NIL NIL) (-1307 3401310 3401868 3401910 "VSPACE" 3402046 NIL VSPACE (NIL T) -9 NIL 3402120 NIL) (-1306 3401142 3401175 3401266 "VSPACE-" 3401271 NIL VSPACE- (NIL T T) -8 NIL NIL NIL) (-1305 3400939 3400993 3401061 "VOID" 3401096 T VOID (NIL) -8 NIL NIL NIL) (-1304 3397207 3398002 3398739 "VIEWDEF" 3400224 T VIEWDEF (NIL) -7 NIL NIL NIL) (-1303 3386151 3388755 3390928 "VIEW3D" 3395056 T VIEW3D (NIL) -8 NIL NIL NIL) (-1302 3378168 3380062 3381641 "VIEW2D" 3384594 T VIEW2D (NIL) -8 NIL NIL NIL) (-1301 3376268 3376663 3377069 "VIEW" 3377784 T VIEW (NIL) -7 NIL NIL NIL) (-1300 3374821 3375104 3375422 "VECTOR2" 3375998 NIL VECTOR2 (NIL T T) -7 NIL NIL NIL) (-1299 3369841 3374591 3374683 "VECTOR" 3374764 NIL VECTOR (NIL T) -8 NIL NIL NIL) (-1298 3362900 3367545 3367588 "VECTCAT" 3368583 NIL VECTCAT (NIL T) -9 NIL 3369170 NIL) (-1297 3361842 3362168 3362558 "VECTCAT-" 3362563 NIL VECTCAT- (NIL T T) -8 NIL NIL NIL) (-1296 3361248 3361493 3361613 "VARIABLE" 3361757 NIL VARIABLE (NIL NIL) -8 NIL NIL NIL) (-1295 3361181 3361186 3361216 "UTYPE" 3361221 T UTYPE (NIL) -9 NIL NIL NIL) (-1294 3359989 3360165 3360427 "UTSODETL" 3361007 NIL UTSODETL (NIL T T T T) -7 NIL NIL NIL) (-1293 3357381 3357889 3358413 "UTSODE" 3359530 NIL UTSODE (NIL T T) -7 NIL NIL NIL) (-1292 3347391 3353314 3353357 "UTSCAT" 3354469 NIL UTSCAT (NIL T) -9 NIL 3355227 NIL) (-1291 3344517 3345461 3346450 "UTSCAT-" 3346455 NIL UTSCAT- (NIL T T) -8 NIL NIL NIL) (-1290 3344138 3344187 3344320 "UTS2" 3344468 NIL UTS2 (NIL T T T T) -7 NIL NIL NIL) (-1289 3335455 3341899 3342379 "UTS" 3343716 NIL UTS (NIL T NIL NIL) -8 NIL NIL NIL) (-1288 3329433 3332265 3332308 "URAGG" 3334378 NIL URAGG (NIL T) -9 NIL 3335101 NIL) (-1287 3326465 3327433 3328457 "URAGG-" 3328462 NIL URAGG- (NIL T T) -8 NIL NIL NIL) (-1286 3321841 3325100 3325565 "UPXSSING" 3326129 NIL UPXSSING (NIL T T NIL NIL) -8 NIL NIL NIL) (-1285 3314270 3321745 3321817 "UPXSCONS" 3321822 NIL UPXSCONS (NIL T T) -8 NIL NIL NIL) (-1284 3303028 3310472 3310534 "UPXSCCA" 3311108 NIL UPXSCCA (NIL T T) -9 NIL 3311341 NIL) (-1283 3302648 3302751 3302925 "UPXSCCA-" 3302930 NIL UPXSCCA- (NIL T T T) -8 NIL NIL NIL) (-1282 3291306 3298475 3298518 "UPXSCAT" 3299166 NIL UPXSCAT (NIL T) -9 NIL 3299775 NIL) (-1281 3290730 3290815 3290994 "UPXS2" 3291221 NIL UPXS2 (NIL T T NIL NIL NIL NIL) -7 NIL NIL NIL) (-1280 3282222 3290112 3290376 "UPXS" 3290524 NIL UPXS (NIL T NIL NIL) -8 NIL NIL NIL) (-1279 3280858 3281129 3281480 "UPSQFREE" 3281965 NIL UPSQFREE (NIL T T) -7 NIL NIL NIL) (-1278 3273689 3277124 3277179 "UPSCAT" 3278259 NIL UPSCAT (NIL T T) -9 NIL 3279025 NIL) (-1277 3272845 3273100 3273427 "UPSCAT-" 3273432 NIL UPSCAT- (NIL T T T) -8 NIL NIL NIL) (-1276 3272466 3272515 3272648 "UPOLYC2" 3272796 NIL UPOLYC2 (NIL T T T T) -7 NIL NIL NIL) (-1275 3256614 3265593 3265636 "UPOLYC" 3267737 NIL UPOLYC (NIL T) -9 NIL 3268958 NIL) (-1274 3247483 3250382 3253522 "UPOLYC-" 3253527 NIL UPOLYC- (NIL T T) -8 NIL NIL NIL) (-1273 3246804 3246929 3247093 "UPMP" 3247372 NIL UPMP (NIL T T) -7 NIL NIL NIL) (-1272 3246351 3246438 3246577 "UPDIVP" 3246717 NIL UPDIVP (NIL T T) -7 NIL NIL NIL) (-1271 3244889 3245168 3245484 "UPDECOMP" 3246100 NIL UPDECOMP (NIL T T) -7 NIL NIL NIL) (-1270 3244102 3244232 3244418 "UPCDEN" 3244773 NIL UPCDEN (NIL T T T) -7 NIL NIL NIL) (-1269 3243615 3243690 3243839 "UP2" 3244027 NIL UP2 (NIL NIL T NIL T) -7 NIL NIL NIL) (-1268 3234211 3243298 3243427 "UP" 3243534 NIL UP (NIL NIL T) -8 NIL NIL NIL) (-1267 3233416 3233553 3233758 "UNISEG2" 3234054 NIL UNISEG2 (NIL T T) -7 NIL NIL NIL) (-1266 3231769 3232620 3232897 "UNISEG" 3233174 NIL UNISEG (NIL T) -8 NIL NIL NIL) (-1265 3230811 3231009 3231235 "UNIFACT" 3231585 NIL UNIFACT (NIL T) -7 NIL NIL NIL) (-1264 3217542 3230715 3230787 "ULSCONS" 3230792 NIL ULSCONS (NIL T T) -8 NIL NIL NIL) (-1263 3197359 3210622 3210684 "ULSCCAT" 3211322 NIL ULSCCAT (NIL T T) -9 NIL 3211611 NIL) (-1262 3196355 3196654 3197042 "ULSCCAT-" 3197047 NIL ULSCCAT- (NIL T T T) -8 NIL NIL NIL) (-1261 3184810 3191901 3191944 "ULSCAT" 3192807 NIL ULSCAT (NIL T) -9 NIL 3193538 NIL) (-1260 3184234 3184319 3184498 "ULS2" 3184725 NIL ULS2 (NIL T T NIL NIL NIL NIL) -7 NIL NIL NIL) (-1259 3166065 3183546 3183788 "ULS" 3184050 NIL ULS (NIL T NIL NIL) -8 NIL NIL NIL) (-1258 3164984 3165684 3165798 "UINT8" 3165909 T UINT8 (NIL) -8 NIL NIL 3166001) (-1257 3163902 3164602 3164716 "UINT64" 3164827 T UINT64 (NIL) -8 NIL NIL 3164919) (-1256 3162820 3163520 3163634 "UINT32" 3163745 T UINT32 (NIL) -8 NIL NIL 3163837) (-1255 3161738 3162438 3162552 "UINT16" 3162663 T UINT16 (NIL) -8 NIL NIL 3162755) (-1254 3159817 3160984 3161014 "UFD" 3161226 T UFD (NIL) -9 NIL 3161340 NIL) (-1253 3159599 3159657 3159752 "UFD-" 3159757 NIL UFD- (NIL T) -8 NIL NIL NIL) (-1252 3158657 3158864 3159080 "UDVO" 3159405 T UDVO (NIL) -7 NIL NIL NIL) (-1251 3156423 3156882 3157353 "UDPO" 3158221 NIL UDPO (NIL T) -7 NIL NIL NIL) (-1250 3156135 3156378 3156409 "TYPEAST" 3156414 T TYPEAST (NIL) -8 NIL NIL NIL) (-1249 3156068 3156073 3156103 "TYPE" 3156108 T TYPE (NIL) -9 NIL NIL NIL) (-1248 3155021 3155241 3155481 "TWOFACT" 3155862 NIL TWOFACT (NIL T) -7 NIL NIL NIL) (-1247 3153996 3154430 3154665 "TUPLE" 3154821 NIL TUPLE (NIL T) -8 NIL NIL NIL) (-1246 3151633 3152206 3152745 "TUBETOOL" 3153479 T TUBETOOL (NIL) -7 NIL NIL NIL) (-1245 3150439 3150680 3150922 "TUBE" 3151426 NIL TUBE (NIL T) -8 NIL NIL NIL) (-1244 3138688 3143196 3143293 "TSETCAT" 3148562 NIL TSETCAT (NIL T T T T) -9 NIL 3150094 NIL) (-1243 3133156 3135020 3136911 "TSETCAT-" 3136916 NIL TSETCAT- (NIL T T T T T) -8 NIL NIL NIL) (-1242 3127342 3132128 3132411 "TS" 3132908 NIL TS (NIL T) -8 NIL NIL NIL) (-1241 3121815 3122828 3123757 "TRMANIP" 3126478 NIL TRMANIP (NIL T T) -7 NIL NIL NIL) (-1240 3121244 3121319 3121482 "TRIMAT" 3121747 NIL TRIMAT (NIL T T T T) -7 NIL NIL NIL) (-1239 3119056 3119347 3119704 "TRIGMNIP" 3120993 NIL TRIGMNIP (NIL T T) -7 NIL NIL NIL) (-1238 3118540 3118689 3118719 "TRIGCAT" 3118932 T TRIGCAT (NIL) -9 NIL NIL NIL) (-1237 3118185 3118288 3118429 "TRIGCAT-" 3118434 NIL TRIGCAT- (NIL T) -8 NIL NIL NIL) (-1236 3114910 3117043 3117324 "TREE" 3117939 NIL TREE (NIL T) -8 NIL NIL NIL) (-1235 3114016 3114712 3114742 "TRANFUN" 3114777 T TRANFUN (NIL) -9 NIL 3114843 NIL) (-1234 3113235 3113486 3113766 "TRANFUN-" 3113771 NIL TRANFUN- (NIL T) -8 NIL NIL NIL) (-1233 3113033 3113071 3113132 "TOPSP" 3113196 T TOPSP (NIL) -7 NIL NIL NIL) (-1232 3112363 3112496 3112650 "TOOLSIGN" 3112914 NIL TOOLSIGN (NIL T) -7 NIL NIL NIL) (-1231 3110877 3111540 3111779 "TEXTFILE" 3112146 T TEXTFILE (NIL) -8 NIL NIL NIL) (-1230 3110652 3110689 3110761 "TEX1" 3110840 NIL TEX1 (NIL T) -7 NIL NIL NIL) (-1229 3108456 3109105 3109534 "TEX" 3110245 T TEX (NIL) -8 NIL NIL NIL) (-1228 3108092 3108167 3108257 "TEMUTL" 3108388 T TEMUTL (NIL) -7 NIL NIL NIL) (-1227 3106186 3106526 3106851 "TBCMPPK" 3107815 NIL TBCMPPK (NIL T T) -7 NIL NIL NIL) (-1226 3097620 3104272 3104328 "TBAGG" 3104728 NIL TBAGG (NIL T T) -9 NIL 3104939 NIL) (-1225 3092504 3094178 3095932 "TBAGG-" 3095937 NIL TBAGG- (NIL T T T) -8 NIL NIL NIL) (-1224 3091870 3091995 3092140 "TANEXP" 3092393 NIL TANEXP (NIL T) -7 NIL NIL NIL) (-1223 3091321 3091645 3091735 "TALGOP" 3091815 NIL TALGOP (NIL T) -8 NIL NIL NIL) (-1222 3090715 3090832 3090970 "TABLEAU" 3091218 NIL TABLEAU (NIL T) -8 NIL NIL NIL) (-1221 3083843 3090572 3090665 "TABLE" 3090670 NIL TABLE (NIL T T) -8 NIL NIL NIL) (-1220 3078373 3079671 3080919 "TABLBUMP" 3082629 NIL TABLBUMP (NIL T) -7 NIL NIL NIL) (-1219 3077583 3077742 3077923 "SYSTEM" 3078214 T SYSTEM (NIL) -8 NIL NIL NIL) (-1218 3073988 3074741 3075524 "SYSSOLP" 3076834 NIL SYSSOLP (NIL T) -7 NIL NIL NIL) (-1217 3073750 3073943 3073974 "SYSPTR" 3073979 T SYSPTR (NIL) -8 NIL NIL NIL) (-1216 3072589 3073281 3073407 "SYSNNI" 3073593 NIL SYSNNI (NIL NIL) -8 NIL NIL 3073685) (-1215 3071796 3072351 3072430 "SYSINT" 3072490 NIL SYSINT (NIL NIL) -8 NIL NIL 3072535) (-1214 3067894 3069074 3069784 "SYNTAX" 3071108 T SYNTAX (NIL) -8 NIL NIL NIL) (-1213 3064974 3065654 3066286 "SYMTAB" 3067284 T SYMTAB (NIL) -8 NIL NIL NIL) (-1212 3060073 3061125 3062108 "SYMS" 3064013 T SYMS (NIL) -8 NIL NIL NIL) (-1211 3056979 3059524 3059757 "SYMPOLY" 3059875 NIL SYMPOLY (NIL T) -8 NIL NIL NIL) (-1210 3056484 3056571 3056694 "SYMFUNC" 3056891 NIL SYMFUNC (NIL T) -7 NIL NIL NIL) (-1209 3052282 3053796 3054609 "SYMBOL" 3055693 T SYMBOL (NIL) -8 NIL NIL NIL) (-1208 3045755 3047510 3049230 "SWITCH" 3050584 T SWITCH (NIL) -8 NIL NIL NIL) (-1207 3038516 3044711 3045005 "SUTS" 3045519 NIL SUTS (NIL T NIL NIL) -8 NIL NIL NIL) (-1206 3030008 3037898 3038162 "SUPXS" 3038310 NIL SUPXS (NIL T NIL NIL) -8 NIL NIL NIL) (-1205 3029155 3029294 3029511 "SUPFRACF" 3029876 NIL SUPFRACF (NIL T T T T) -7 NIL NIL NIL) (-1204 3028770 3028835 3028948 "SUP2" 3029090 NIL SUP2 (NIL T T) -7 NIL NIL NIL) (-1203 3019314 3028388 3028514 "SUP" 3028679 NIL SUP (NIL T) -8 NIL NIL NIL) (-1202 3017738 3018036 3018392 "SUMRF" 3019013 NIL SUMRF (NIL T) -7 NIL NIL NIL) (-1201 3017061 3017139 3017331 "SUMFS" 3017659 NIL SUMFS (NIL T T) -7 NIL NIL NIL) (-1200 2998927 3016373 3016615 "SULS" 3016877 NIL SULS (NIL T NIL NIL) -8 NIL NIL NIL) (-1199 2998475 2998749 2998819 "SUCHTAST" 2998879 T SUCHTAST (NIL) -8 NIL NIL NIL) (-1198 2997716 2998000 2998140 "SUCH" 2998383 NIL SUCH (NIL T T) -8 NIL NIL NIL) (-1197 2991355 2992622 2993581 "SUBSPACE" 2996804 NIL SUBSPACE (NIL NIL T) -8 NIL NIL NIL) (-1196 2990775 2990875 2991039 "SUBRESP" 2991243 NIL SUBRESP (NIL T T) -7 NIL NIL NIL) (-1195 2984786 2986068 2987215 "STTFNC" 2989675 NIL STTFNC (NIL T) -7 NIL NIL NIL) (-1194 2977980 2979451 2980762 "STTF" 2983522 NIL STTF (NIL T) -7 NIL NIL NIL) (-1193 2969096 2971162 2972956 "STTAYLOR" 2976221 NIL STTAYLOR (NIL T) -7 NIL NIL NIL) (-1192 2961964 2968960 2969043 "STRTBL" 2969048 NIL STRTBL (NIL T) -8 NIL NIL NIL) (-1191 2956475 2961673 2961772 "STRING" 2961887 T STRING (NIL) -8 NIL NIL NIL) (-1190 2955979 2956062 2956206 "STREAM3" 2956392 NIL STREAM3 (NIL T T T) -7 NIL NIL NIL) (-1189 2954943 2955144 2955379 "STREAM2" 2955792 NIL STREAM2 (NIL T T) -7 NIL NIL NIL) (-1188 2954625 2954683 2954776 "STREAM1" 2954885 NIL STREAM1 (NIL T) -7 NIL NIL NIL) (-1187 2946739 2952244 2952855 "STREAM" 2954049 NIL STREAM (NIL T) -8 NIL NIL NIL) (-1186 2945731 2945936 2946167 "STINPROD" 2946555 NIL STINPROD (NIL T) -7 NIL NIL NIL) (-1185 2944846 2945220 2945368 "STEPAST" 2945605 T STEPAST (NIL) -8 NIL NIL NIL) (-1184 2944342 2944587 2944617 "STEP" 2944711 T STEP (NIL) -9 NIL 2944782 NIL) (-1183 2937512 2944241 2944318 "STBL" 2944323 NIL STBL (NIL T T NIL) -8 NIL NIL NIL) (-1182 2931693 2936306 2936349 "STAGG" 2936781 NIL STAGG (NIL T) -9 NIL 2936960 NIL) (-1181 2929245 2929997 2930869 "STAGG-" 2930874 NIL STAGG- (NIL T T) -8 NIL NIL NIL) (-1180 2927331 2929015 2929107 "STACK" 2929188 NIL STACK (NIL T) -8 NIL NIL NIL) (-1179 2926648 2927161 2927191 "SRING" 2927196 T SRING (NIL) -9 NIL 2927216 NIL) (-1178 2918770 2924789 2925245 "SREGSET" 2926278 NIL SREGSET (NIL T T T T) -8 NIL NIL NIL) (-1177 2911117 2912564 2914077 "SRDCMPK" 2917376 NIL SRDCMPK (NIL T T T T T) -7 NIL NIL NIL) (-1176 2903531 2908476 2908506 "SRAGG" 2909809 T SRAGG (NIL) -9 NIL 2910417 NIL) (-1175 2902482 2902803 2903182 "SRAGG-" 2903187 NIL SRAGG- (NIL T) -8 NIL NIL NIL) (-1174 2896180 2901429 2901850 "SQMATRIX" 2902108 NIL SQMATRIX (NIL NIL T) -8 NIL NIL NIL) (-1173 2889706 2892898 2893625 "SPLTREE" 2895525 NIL SPLTREE (NIL T T) -8 NIL NIL NIL) (-1172 2885531 2886362 2887008 "SPLNODE" 2889132 NIL SPLNODE (NIL T T) -8 NIL NIL NIL) (-1171 2884506 2884811 2884841 "SPFCAT" 2885285 T SPFCAT (NIL) -9 NIL NIL NIL) (-1170 2883201 2883453 2883717 "SPECOUT" 2884264 T SPECOUT (NIL) -7 NIL NIL NIL) (-1169 2873847 2876165 2876195 "SPADXPT" 2880873 T SPADXPT (NIL) -9 NIL 2883039 NIL) (-1168 2873602 2873648 2873717 "SPADPRSR" 2873800 T SPADPRSR (NIL) -7 NIL NIL NIL) (-1167 2871205 2873557 2873588 "SPADAST" 2873593 T SPADAST (NIL) -8 NIL NIL NIL) (-1166 2862806 2864909 2864952 "SPACEC" 2869325 NIL SPACEC (NIL T) -9 NIL 2871141 NIL) (-1165 2860606 2862738 2862787 "SPACE3" 2862792 NIL SPACE3 (NIL T) -8 NIL NIL NIL) (-1164 2859338 2859529 2859820 "SORTPAK" 2860411 NIL SORTPAK (NIL T T) -7 NIL NIL NIL) (-1163 2857400 2857733 2858145 "SOLVETRA" 2859002 NIL SOLVETRA (NIL T) -7 NIL NIL NIL) (-1162 2856438 2856672 2856933 "SOLVESER" 2857173 NIL SOLVESER (NIL T) -7 NIL NIL NIL) (-1161 2851670 2852630 2853625 "SOLVERAD" 2855490 NIL SOLVERAD (NIL T) -7 NIL NIL NIL) (-1160 2847395 2848094 2848823 "SOLVEFOR" 2851037 NIL SOLVEFOR (NIL T T) -7 NIL NIL NIL) (-1159 2841113 2846743 2846840 "SNTSCAT" 2846845 NIL SNTSCAT (NIL T T T T) -9 NIL 2846915 NIL) (-1158 2834664 2839436 2839827 "SMTS" 2840803 NIL SMTS (NIL T T T) -8 NIL NIL NIL) (-1157 2828386 2834552 2834629 "SMP" 2834634 NIL SMP (NIL T T) -8 NIL NIL NIL) (-1156 2826515 2826846 2827244 "SMITH" 2828083 NIL SMITH (NIL T T T T) -7 NIL NIL NIL) (-1155 2818154 2823094 2823197 "SMATCAT" 2824548 NIL SMATCAT (NIL NIL T T T) -9 NIL 2825098 NIL) (-1154 2814926 2815917 2817095 "SMATCAT-" 2817100 NIL SMATCAT- (NIL T NIL T T T) -8 NIL NIL NIL) (-1153 2812506 2814134 2814177 "SKAGG" 2814438 NIL SKAGG (NIL T) -9 NIL 2814573 NIL) (-1152 2808026 2811989 2812166 "SINT" 2812318 T SINT (NIL) -8 NIL NIL 2812473) (-1151 2807792 2807836 2807902 "SIMPAN" 2807982 T SIMPAN (NIL) -7 NIL NIL NIL) (-1150 2806612 2806851 2807126 "SIGNRF" 2807551 NIL SIGNRF (NIL T) -7 NIL NIL NIL) (-1149 2805427 2805596 2805880 "SIGNEF" 2806441 NIL SIGNEF (NIL T T) -7 NIL NIL NIL) (-1148 2804667 2805010 2805134 "SIGAST" 2805325 T SIGAST (NIL) -8 NIL NIL NIL) (-1147 2803892 2804202 2804342 "SIG" 2804549 T SIG (NIL) -8 NIL NIL NIL) (-1146 2801544 2802036 2802542 "SHP" 2803433 NIL SHP (NIL T NIL) -7 NIL NIL NIL) (-1145 2794982 2801445 2801521 "SHDP" 2801526 NIL SHDP (NIL NIL NIL T) -8 NIL NIL NIL) (-1144 2794493 2794733 2794763 "SGROUP" 2794856 T SGROUP (NIL) -9 NIL 2794918 NIL) (-1143 2794345 2794377 2794450 "SGROUP-" 2794455 NIL SGROUP- (NIL T) -8 NIL NIL NIL) (-1142 2791064 2791834 2792557 "SGCF" 2793644 T SGCF (NIL) -7 NIL NIL NIL) (-1141 2784880 2790510 2790607 "SFRTCAT" 2790612 NIL SFRTCAT (NIL T T T T) -9 NIL 2790651 NIL) (-1140 2778199 2779319 2780455 "SFRGCD" 2783863 NIL SFRGCD (NIL T T T T T) -7 NIL NIL NIL) (-1139 2771217 2772398 2773584 "SFQCMPK" 2777132 NIL SFQCMPK (NIL T T T T T) -7 NIL NIL NIL) (-1138 2770819 2770926 2771037 "SFORT" 2771158 NIL SFORT (NIL T T) -8 NIL NIL NIL) (-1137 2769745 2770659 2770780 "SEXOF" 2770785 NIL SEXOF (NIL T T T T T) -8 NIL NIL NIL) (-1136 2765334 2766241 2766336 "SEXCAT" 2768958 NIL SEXCAT (NIL T T T T T) -9 NIL 2769518 NIL) (-1135 2764249 2765215 2765283 "SEX" 2765288 T SEX (NIL) -8 NIL NIL NIL) (-1134 2762371 2762962 2763267 "SETMN" 2763990 NIL SETMN (NIL NIL NIL) -8 NIL NIL NIL) (-1133 2761901 2762089 2762119 "SETCAT" 2762236 T SETCAT (NIL) -9 NIL 2762321 NIL) (-1132 2761669 2761733 2761832 "SETCAT-" 2761837 NIL SETCAT- (NIL T) -8 NIL NIL NIL) (-1131 2757883 2760130 2760173 "SETAGG" 2761043 NIL SETAGG (NIL T) -9 NIL 2761383 NIL) (-1130 2757305 2757457 2757694 "SETAGG-" 2757699 NIL SETAGG- (NIL T T) -8 NIL NIL NIL) (-1129 2754228 2757239 2757287 "SET" 2757292 NIL SET (NIL T) -8 NIL NIL NIL) (-1128 2753611 2753924 2754025 "SEQAST" 2754149 T SEQAST (NIL) -8 NIL NIL NIL) (-1127 2752738 2753104 2753165 "SEGXCAT" 2753451 NIL SEGXCAT (NIL T T) -9 NIL 2753571 NIL) (-1126 2751663 2751931 2751974 "SEGCAT" 2752496 NIL SEGCAT (NIL T) -9 NIL 2752717 NIL) (-1125 2751278 2751343 2751456 "SEGBIND2" 2751598 NIL SEGBIND2 (NIL T T) -7 NIL NIL NIL) (-1124 2750168 2750641 2750849 "SEGBIND" 2751105 NIL SEGBIND (NIL T) -8 NIL NIL NIL) (-1123 2749687 2749969 2750046 "SEGAST" 2750113 T SEGAST (NIL) -8 NIL NIL NIL) (-1122 2748896 2749032 2749236 "SEG2" 2749531 NIL SEG2 (NIL T T) -7 NIL NIL NIL) (-1121 2747812 2748562 2748744 "SEG" 2748749 NIL SEG (NIL T) -8 NIL NIL NIL) (-1120 2747045 2747747 2747794 "SDVAR" 2747799 NIL SDVAR (NIL T) -8 NIL NIL NIL) (-1119 2738403 2746815 2746945 "SDPOL" 2746950 NIL SDPOL (NIL T) -8 NIL NIL NIL) (-1118 2736972 2737262 2737581 "SCPKG" 2738118 NIL SCPKG (NIL T) -7 NIL NIL NIL) (-1117 2736094 2736308 2736500 "SCOPE" 2736802 T SCOPE (NIL) -8 NIL NIL NIL) (-1116 2735290 2735448 2735627 "SCACHE" 2735949 NIL SCACHE (NIL T) -7 NIL NIL NIL) (-1115 2734874 2735108 2735138 "SASTCAT" 2735143 T SASTCAT (NIL) -9 NIL 2735156 NIL) (-1114 2734277 2734709 2734785 "SAOS" 2734820 T SAOS (NIL) -8 NIL NIL NIL) (-1113 2733836 2733877 2734050 "SAERFFC" 2734236 NIL SAERFFC (NIL T T T) -7 NIL NIL NIL) (-1112 2733423 2733464 2733623 "SAEFACT" 2733795 NIL SAEFACT (NIL T T T) -7 NIL NIL NIL) (-1111 2726471 2733320 2733400 "SAE" 2733405 NIL SAE (NIL T T NIL) -8 NIL NIL NIL) (-1110 2724774 2725106 2725507 "RURPK" 2726137 NIL RURPK (NIL T NIL) -7 NIL NIL NIL) (-1109 2723351 2723717 2724022 "RULESET" 2724608 NIL RULESET (NIL T T T) -8 NIL NIL NIL) (-1108 2722921 2723145 2723228 "RULECOLD" 2723303 NIL RULECOLD (NIL NIL) -8 NIL NIL NIL) (-1107 2720036 2720674 2721132 "RULE" 2722602 NIL RULE (NIL T T T) -8 NIL NIL NIL) (-1106 2719820 2719854 2719925 "RTVALUE" 2719987 T RTVALUE (NIL) -8 NIL NIL NIL) (-1105 2719231 2719537 2719631 "RSTRCAST" 2719748 T RSTRCAST (NIL) -8 NIL NIL NIL) (-1104 2714001 2714874 2715794 "RSETGCD" 2718430 NIL RSETGCD (NIL T T T T T) -7 NIL NIL NIL) (-1103 2702679 2708309 2708406 "RSETCAT" 2712525 NIL RSETCAT (NIL T T T T) -9 NIL 2713622 NIL) (-1102 2700498 2701145 2701969 "RSETCAT-" 2701974 NIL RSETCAT- (NIL T T T T T) -8 NIL NIL NIL) (-1101 2692806 2694260 2695780 "RSDCMPK" 2699097 NIL RSDCMPK (NIL T T T T T) -7 NIL NIL NIL) (-1100 2690675 2691238 2691312 "RRCC" 2692398 NIL RRCC (NIL T T) -9 NIL 2692742 NIL) (-1099 2689996 2690200 2690479 "RRCC-" 2690484 NIL RRCC- (NIL T T T) -8 NIL NIL NIL) (-1098 2689379 2689692 2689793 "RPTAST" 2689917 T RPTAST (NIL) -8 NIL NIL NIL) (-1097 2661765 2672491 2672558 "RPOLCAT" 2683224 NIL RPOLCAT (NIL T T T) -9 NIL 2686384 NIL) (-1096 2652735 2655603 2658725 "RPOLCAT-" 2658730 NIL RPOLCAT- (NIL T T T T) -8 NIL NIL NIL) (-1095 2643302 2650946 2651428 "ROUTINE" 2652275 T ROUTINE (NIL) -8 NIL NIL NIL) (-1094 2639365 2642928 2643068 "ROMAN" 2643184 T ROMAN (NIL) -8 NIL NIL NIL) (-1093 2637477 2638225 2638485 "ROIRC" 2639170 NIL ROIRC (NIL T T) -8 NIL NIL NIL) (-1092 2633250 2636019 2636049 "RNS" 2636318 T RNS (NIL) -9 NIL 2636574 NIL) (-1091 2631657 2632142 2632676 "RNS-" 2632751 NIL RNS- (NIL T) -8 NIL NIL NIL) (-1090 2630618 2631022 2631224 "RNGBIND" 2631508 NIL RNGBIND (NIL T T) -8 NIL NIL NIL) (-1089 2629911 2630415 2630445 "RNG" 2630450 T RNG (NIL) -9 NIL 2630471 NIL) (-1088 2629206 2629684 2629727 "RMODULE" 2629732 NIL RMODULE (NIL T) -9 NIL 2629759 NIL) (-1087 2628030 2628136 2628472 "RMCAT2" 2629107 NIL RMCAT2 (NIL NIL NIL T T T T T T T T) -7 NIL NIL NIL) (-1086 2624646 2627376 2627673 "RMATRIX" 2627792 NIL RMATRIX (NIL NIL NIL T) -8 NIL NIL NIL) (-1085 2617256 2619733 2619848 "RMATCAT" 2623207 NIL RMATCAT (NIL NIL NIL T T T) -9 NIL 2624189 NIL) (-1084 2616595 2616778 2617085 "RMATCAT-" 2617090 NIL RMATCAT- (NIL T NIL NIL T T T) -8 NIL NIL NIL) (-1083 2616168 2616382 2616425 "RLINSET" 2616487 NIL RLINSET (NIL T) -9 NIL 2616531 NIL) (-1082 2615729 2615810 2615938 "RINTERP" 2616087 NIL RINTERP (NIL NIL T) -7 NIL NIL NIL) (-1081 2614653 2615327 2615357 "RING" 2615413 T RING (NIL) -9 NIL 2615505 NIL) (-1080 2614433 2614489 2614586 "RING-" 2614591 NIL RING- (NIL T) -8 NIL NIL NIL) (-1079 2613244 2613511 2613769 "RIDIST" 2614197 T RIDIST (NIL) -7 NIL NIL NIL) (-1078 2603983 2612712 2612918 "RGCHAIN" 2613092 NIL RGCHAIN (NIL T NIL) -8 NIL NIL NIL) (-1077 2603241 2603725 2603766 "RGBCSPC" 2603824 NIL RGBCSPC (NIL T) -9 NIL 2603876 NIL) (-1076 2602307 2602766 2602807 "RGBCMDL" 2603039 NIL RGBCMDL (NIL T) -9 NIL 2603153 NIL) (-1075 2601947 2602016 2602119 "RFFACTOR" 2602238 NIL RFFACTOR (NIL T) -7 NIL NIL NIL) (-1074 2601666 2601707 2601804 "RFFACT" 2601906 NIL RFFACT (NIL T) -7 NIL NIL NIL) (-1073 2599717 2600147 2600529 "RFDIST" 2601306 T RFDIST (NIL) -7 NIL NIL NIL) (-1072 2596657 2597325 2597995 "RF" 2599081 NIL RF (NIL T) -7 NIL NIL NIL) (-1071 2596104 2596202 2596365 "RETSOL" 2596559 NIL RETSOL (NIL T T) -7 NIL NIL NIL) (-1070 2595722 2595820 2595863 "RETRACT" 2595996 NIL RETRACT (NIL T) -9 NIL 2596083 NIL) (-1069 2595565 2595596 2595683 "RETRACT-" 2595688 NIL RETRACT- (NIL T T) -8 NIL NIL NIL) (-1068 2595113 2595387 2595457 "RETAST" 2595517 T RETAST (NIL) -8 NIL NIL NIL) (-1067 2587577 2594766 2594893 "RESULT" 2595008 T RESULT (NIL) -8 NIL NIL NIL) (-1066 2586012 2586846 2587045 "RESRING" 2587480 NIL RESRING (NIL T T T T NIL) -8 NIL NIL NIL) (-1065 2585636 2585697 2585795 "RESLATC" 2585949 NIL RESLATC (NIL T) -7 NIL NIL NIL) (-1064 2585335 2585376 2585483 "REPSQ" 2585595 NIL REPSQ (NIL T) -7 NIL NIL NIL) (-1063 2585026 2585067 2585178 "REPDB" 2585294 NIL REPDB (NIL T) -7 NIL NIL NIL) (-1062 2578858 2580315 2581538 "REP2" 2583838 NIL REP2 (NIL T) -7 NIL NIL NIL) (-1061 2575161 2575916 2576724 "REP1" 2578085 NIL REP1 (NIL T) -7 NIL NIL NIL) (-1060 2572541 2573163 2573765 "REP" 2574581 T REP (NIL) -7 NIL NIL NIL) (-1059 2564663 2570682 2571138 "REGSET" 2572171 NIL REGSET (NIL T T T T) -8 NIL NIL NIL) (-1058 2563372 2563811 2564061 "REF" 2564448 NIL REF (NIL T) -8 NIL NIL NIL) (-1057 2562737 2562852 2563019 "REDORDER" 2563256 NIL REDORDER (NIL T T) -7 NIL NIL NIL) (-1056 2558108 2561950 2562177 "RECLOS" 2562565 NIL RECLOS (NIL T) -8 NIL NIL NIL) (-1055 2557142 2557341 2557556 "REALSOLV" 2557915 T REALSOLV (NIL) -7 NIL NIL NIL) (-1054 2553589 2554427 2555311 "REAL0Q" 2556307 NIL REAL0Q (NIL T) -7 NIL NIL NIL) (-1053 2549142 2550178 2551239 "REAL0" 2552570 NIL REAL0 (NIL T) -7 NIL NIL NIL) (-1052 2548976 2549029 2549059 "REAL" 2549064 T REAL (NIL) -9 NIL 2549099 NIL) (-1051 2548387 2548693 2548787 "RDUCEAST" 2548904 T RDUCEAST (NIL) -8 NIL NIL NIL) (-1050 2547786 2547864 2548071 "RDIV" 2548309 NIL RDIV (NIL T T T T T) -7 NIL NIL NIL) (-1049 2546836 2547028 2547241 "RDIST" 2547608 NIL RDIST (NIL T) -7 NIL NIL NIL) (-1048 2545421 2545720 2546092 "RDETRS" 2546544 NIL RDETRS (NIL T T) -7 NIL NIL NIL) (-1047 2543215 2543687 2544225 "RDETR" 2544963 NIL RDETR (NIL T T) -7 NIL NIL NIL) (-1046 2541834 2542118 2542515 "RDEEFS" 2542931 NIL RDEEFS (NIL T T) -7 NIL NIL NIL) (-1045 2540337 2540649 2541074 "RDEEF" 2541522 NIL RDEEF (NIL T T) -7 NIL NIL NIL) (-1044 2533816 2537291 2537321 "RCFIELD" 2538616 T RCFIELD (NIL) -9 NIL 2539347 NIL) (-1043 2531772 2532384 2533080 "RCFIELD-" 2533155 NIL RCFIELD- (NIL T) -8 NIL NIL NIL) (-1042 2527935 2529845 2529888 "RCAGG" 2530972 NIL RCAGG (NIL T) -9 NIL 2531437 NIL) (-1041 2527545 2527657 2527820 "RCAGG-" 2527825 NIL RCAGG- (NIL T T) -8 NIL NIL NIL) (-1040 2526862 2526992 2527157 "RATRET" 2527429 NIL RATRET (NIL T) -7 NIL NIL NIL) (-1039 2526403 2526482 2526603 "RATFACT" 2526790 NIL RATFACT (NIL T) -7 NIL NIL NIL) (-1038 2525681 2525831 2525983 "RANDSRC" 2526273 T RANDSRC (NIL) -7 NIL NIL NIL) (-1037 2525409 2525459 2525532 "RADUTIL" 2525630 T RADUTIL (NIL) -7 NIL NIL NIL) (-1036 2517554 2524240 2524551 "RADIX" 2525132 NIL RADIX (NIL NIL) -8 NIL NIL NIL) (-1035 2507169 2517396 2517526 "RADFF" 2517531 NIL RADFF (NIL T T T NIL NIL) -8 NIL NIL NIL) (-1034 2506798 2506891 2506921 "RADCAT" 2507081 T RADCAT (NIL) -9 NIL NIL NIL) (-1033 2506568 2506628 2506728 "RADCAT-" 2506733 NIL RADCAT- (NIL T) -8 NIL NIL NIL) (-1032 2504593 2506338 2506430 "QUEUE" 2506511 NIL QUEUE (NIL T) -8 NIL NIL NIL) (-1031 2504218 2504267 2504398 "QUATCT2" 2504544 NIL QUATCT2 (NIL T T T T) -7 NIL NIL NIL) (-1030 2496596 2500641 2500683 "QUATCAT" 2501474 NIL QUATCAT (NIL T) -9 NIL 2502240 NIL) (-1029 2492477 2493772 2495162 "QUATCAT-" 2495258 NIL QUATCAT- (NIL T T) -8 NIL NIL NIL) (-1028 2488323 2492410 2492458 "QUAT" 2492463 NIL QUAT (NIL T) -8 NIL NIL NIL) (-1027 2485690 2487371 2487414 "QUAGG" 2487795 NIL QUAGG (NIL T) -9 NIL 2487970 NIL) (-1026 2485238 2485512 2485582 "QQUTAST" 2485642 T QQUTAST (NIL) -8 NIL NIL NIL) (-1025 2484149 2484751 2484916 "QFORM" 2485119 NIL QFORM (NIL NIL T) -8 NIL NIL NIL) (-1024 2483774 2483823 2483954 "QFCAT2" 2484100 NIL QFCAT2 (NIL T T T T) -7 NIL NIL NIL) (-1023 2473471 2479621 2479663 "QFCAT" 2480331 NIL QFCAT (NIL T) -9 NIL 2481332 NIL) (-1022 2468805 2470253 2471840 "QFCAT-" 2471936 NIL QFCAT- (NIL T T) -8 NIL NIL NIL) (-1021 2468236 2468370 2468502 "QEQUAT" 2468695 T QEQUAT (NIL) -8 NIL NIL NIL) (-1020 2461254 2462435 2463621 "QCMPACK" 2467169 NIL QCMPACK (NIL T T T T T) -7 NIL NIL NIL) (-1019 2460483 2460665 2460901 "QALGSET2" 2461072 NIL QALGSET2 (NIL NIL NIL) -7 NIL NIL NIL) (-1018 2457933 2458469 2458899 "QALGSET" 2460138 NIL QALGSET (NIL T T T T) -8 NIL NIL NIL) (-1017 2456600 2456842 2457161 "PWFFINTB" 2457706 NIL PWFFINTB (NIL T T T T) -7 NIL NIL NIL) (-1016 2454745 2454943 2455299 "PUSHVAR" 2456414 NIL PUSHVAR (NIL T T T T) -7 NIL NIL NIL) (-1015 2450472 2451688 2451731 "PTRANFN" 2453642 NIL PTRANFN (NIL T) -9 NIL NIL NIL) (-1014 2448809 2449154 2449478 "PTPACK" 2450183 NIL PTPACK (NIL T) -7 NIL NIL NIL) (-1013 2448432 2448495 2448606 "PTFUNC2" 2448746 NIL PTFUNC2 (NIL T T) -7 NIL NIL NIL) (-1012 2442462 2447221 2447264 "PTCAT" 2447564 NIL PTCAT (NIL T) -9 NIL 2447717 NIL) (-1011 2442111 2442152 2442278 "PSQFR" 2442421 NIL PSQFR (NIL T T T T) -7 NIL NIL NIL) (-1010 2440683 2440999 2441335 "PSEUDLIN" 2441809 NIL PSEUDLIN (NIL T) -7 NIL NIL NIL) (-1009 2427203 2429778 2432104 "PSETPK" 2438443 NIL PSETPK (NIL T T T T) -7 NIL NIL NIL) (-1008 2420022 2422939 2423037 "PSETCAT" 2426078 NIL PSETCAT (NIL T T T T) -9 NIL 2426892 NIL) (-1007 2417747 2418489 2419313 "PSETCAT-" 2419318 NIL PSETCAT- (NIL T T T T T) -8 NIL NIL NIL) (-1006 2417060 2417255 2417285 "PSCURVE" 2417557 T PSCURVE (NIL) -9 NIL 2417724 NIL) (-1005 2412783 2414550 2414617 "PSCAT" 2415469 NIL PSCAT (NIL T T T) -9 NIL 2415709 NIL) (-1004 2411777 2412059 2412462 "PSCAT-" 2412467 NIL PSCAT- (NIL T T T T) -8 NIL NIL NIL) (-1003 2409945 2410836 2411101 "PRTITION" 2411534 T PRTITION (NIL) -8 NIL NIL NIL) (-1002 2409356 2409662 2409756 "PRTDAST" 2409873 T PRTDAST (NIL) -8 NIL NIL NIL) (-1001 2398200 2400622 2402812 "PRS" 2407218 NIL PRS (NIL T T) -7 NIL NIL NIL) (-1000 2395926 2397517 2397559 "PRQAGG" 2397745 NIL PRQAGG (NIL T) -9 NIL 2397847 NIL) (-999 2395105 2395554 2395582 "PROPLOG" 2395721 T PROPLOG (NIL) -9 NIL 2395836 NIL) (-998 2394703 2394766 2394889 "PROPFUN2" 2395028 NIL PROPFUN2 (NIL T T) -8 NIL NIL NIL) (-997 2394000 2394139 2394311 "PROPFUN1" 2394564 NIL PROPFUN1 (NIL T) -8 NIL NIL NIL) (-996 2391981 2392747 2393044 "PROPFRML" 2393736 NIL PROPFRML (NIL T) -8 NIL NIL NIL) (-995 2391426 2391557 2391685 "PROPERTY" 2391873 T PROPERTY (NIL) -8 NIL NIL NIL) (-994 2385239 2389592 2390412 "PRODUCT" 2390652 NIL PRODUCT (NIL T T) -8 NIL NIL NIL) (-993 2385029 2385067 2385126 "PRINT" 2385200 T PRINT (NIL) -7 NIL NIL NIL) (-992 2384345 2384486 2384638 "PRIMES" 2384909 NIL PRIMES (NIL T) -7 NIL NIL NIL) (-991 2382392 2382811 2383277 "PRIMELT" 2383924 NIL PRIMELT (NIL T) -7 NIL NIL NIL) (-990 2382109 2382170 2382198 "PRIMCAT" 2382322 T PRIMCAT (NIL) -9 NIL NIL NIL) (-989 2381098 2381294 2381522 "PRIMARR2" 2381927 NIL PRIMARR2 (NIL T T) -7 NIL NIL NIL) (-988 2376934 2381036 2381081 "PRIMARR" 2381086 NIL PRIMARR (NIL T) -8 NIL NIL NIL) (-987 2376571 2376633 2376744 "PREASSOC" 2376872 NIL PREASSOC (NIL T T) -7 NIL NIL NIL) (-986 2373536 2376029 2376263 "PR" 2376382 NIL PR (NIL T T) -8 NIL NIL NIL) (-985 2372987 2373144 2373172 "PPCURVE" 2373377 T PPCURVE (NIL) -9 NIL 2373513 NIL) (-984 2372534 2372782 2372865 "PORTNUM" 2372924 T PORTNUM (NIL) -8 NIL NIL NIL) (-983 2369871 2370292 2370884 "POLYROOT" 2372115 NIL POLYROOT (NIL T T T T T) -7 NIL NIL NIL) (-982 2369248 2369312 2369546 "POLYLIFT" 2369807 NIL POLYLIFT (NIL T T T T T) -7 NIL NIL NIL) (-981 2365469 2365972 2366601 "POLYCATQ" 2368793 NIL POLYCATQ (NIL T T T T T) -7 NIL NIL NIL) (-980 2351117 2357216 2357281 "POLYCAT" 2360795 NIL POLYCAT (NIL T T T) -9 NIL 2362673 NIL) (-979 2344257 2346442 2348819 "POLYCAT-" 2348824 NIL POLYCAT- (NIL T T T T) -8 NIL NIL NIL) (-978 2343838 2343912 2344032 "POLY2UP" 2344183 NIL POLY2UP (NIL NIL T) -7 NIL NIL NIL) (-977 2343464 2343527 2343636 "POLY2" 2343775 NIL POLY2 (NIL T T) -7 NIL NIL NIL) (-976 2336679 2343068 2343228 "POLY" 2343337 NIL POLY (NIL T) -8 NIL NIL NIL) (-975 2335340 2335603 2335879 "POLUTIL" 2336453 NIL POLUTIL (NIL T T) -7 NIL NIL NIL) (-974 2333659 2333972 2334303 "POLTOPOL" 2335062 NIL POLTOPOL (NIL NIL T) -7 NIL NIL NIL) (-973 2328769 2333593 2333640 "POINT" 2333645 NIL POINT (NIL T) -8 NIL NIL NIL) (-972 2326902 2327313 2327688 "PNTHEORY" 2328414 T PNTHEORY (NIL) -7 NIL NIL NIL) (-971 2325348 2325657 2326056 "PMTOOLS" 2326600 NIL PMTOOLS (NIL T T T) -7 NIL NIL NIL) (-970 2324935 2325019 2325136 "PMSYM" 2325264 NIL PMSYM (NIL T) -7 NIL NIL NIL) (-969 2324437 2324512 2324687 "PMQFCAT" 2324860 NIL PMQFCAT (NIL T T T) -7 NIL NIL NIL) (-968 2323818 2323916 2324078 "PMPREDFS" 2324338 NIL PMPREDFS (NIL T T T) -7 NIL NIL NIL) (-967 2323161 2323283 2323439 "PMPRED" 2323695 NIL PMPRED (NIL T) -7 NIL NIL NIL) (-966 2321815 2322033 2322411 "PMPLCAT" 2322923 NIL PMPLCAT (NIL T T T T T) -7 NIL NIL NIL) (-965 2321341 2321426 2321578 "PMLSAGG" 2321730 NIL PMLSAGG (NIL T T T) -7 NIL NIL NIL) (-964 2320808 2320890 2321072 "PMKERNEL" 2321259 NIL PMKERNEL (NIL T T) -7 NIL NIL NIL) (-963 2320419 2320500 2320613 "PMINS" 2320727 NIL PMINS (NIL T) -7 NIL NIL NIL) (-962 2319855 2319930 2320139 "PMFS" 2320344 NIL PMFS (NIL T T T) -7 NIL NIL NIL) (-961 2319071 2319201 2319406 "PMDOWN" 2319732 NIL PMDOWN (NIL T T T) -7 NIL NIL NIL) (-960 2318320 2318454 2318617 "PMASSFS" 2318958 NIL PMASSFS (NIL T T) -7 NIL NIL NIL) (-959 2317463 2317645 2317826 "PMASS" 2318159 T PMASS (NIL) -7 NIL NIL NIL) (-958 2317112 2317186 2317280 "PLOTTOOL" 2317389 T PLOTTOOL (NIL) -7 NIL NIL NIL) (-957 2312764 2313958 2314880 "PLOT3D" 2316210 T PLOT3D (NIL) -8 NIL NIL NIL) (-956 2311652 2311853 2312088 "PLOT1" 2312568 NIL PLOT1 (NIL T) -7 NIL NIL NIL) (-955 2306073 2307463 2308611 "PLOT" 2310524 T PLOT (NIL) -8 NIL NIL NIL) (-954 2281248 2286139 2290990 "PLEQN" 2301339 NIL PLEQN (NIL T T T T) -7 NIL NIL NIL) (-953 2280935 2280988 2281091 "PINTERPA" 2281195 NIL PINTERPA (NIL T T) -7 NIL NIL NIL) (-952 2280241 2280375 2280555 "PINTERP" 2280800 NIL PINTERP (NIL NIL T) -7 NIL NIL NIL) (-951 2278325 2279491 2279519 "PID" 2279716 T PID (NIL) -9 NIL 2279843 NIL) (-950 2278070 2278113 2278188 "PICOERCE" 2278282 NIL PICOERCE (NIL T) -7 NIL NIL NIL) (-949 2277166 2277834 2277921 "PI" 2277961 T PI (NIL) -8 NIL NIL 2278028) (-948 2276474 2276625 2276801 "PGROEB" 2277022 NIL PGROEB (NIL T) -7 NIL NIL NIL) (-947 2271913 2272872 2273778 "PGE" 2275588 T PGE (NIL) -7 NIL NIL NIL) (-946 2269994 2270283 2270649 "PGCD" 2271630 NIL PGCD (NIL T T T T) -7 NIL NIL NIL) (-945 2269320 2269435 2269596 "PFRPAC" 2269878 NIL PFRPAC (NIL T) -7 NIL NIL NIL) (-944 2265578 2267868 2268221 "PFR" 2268999 NIL PFR (NIL T) -8 NIL NIL NIL) (-943 2263931 2264211 2264536 "PFOTOOLS" 2265325 NIL PFOTOOLS (NIL T T) -7 NIL NIL NIL) (-942 2262446 2262703 2263054 "PFOQ" 2263688 NIL PFOQ (NIL T T T) -7 NIL NIL NIL) (-941 2260929 2261159 2261515 "PFO" 2262230 NIL PFO (NIL T T T T T) -7 NIL NIL NIL) (-940 2258013 2259519 2259547 "PFECAT" 2260140 T PFECAT (NIL) -9 NIL 2260517 NIL) (-939 2257461 2257626 2257833 "PFECAT-" 2257838 NIL PFECAT- (NIL T) -8 NIL NIL NIL) (-938 2256034 2256316 2256617 "PFBRU" 2257210 NIL PFBRU (NIL T T) -7 NIL NIL NIL) (-937 2253863 2254252 2254684 "PFBR" 2255685 NIL PFBR (NIL T T T T) -7 NIL NIL NIL) (-936 2249809 2253752 2253821 "PF" 2253826 NIL PF (NIL NIL) -8 NIL NIL NIL) (-935 2244863 2246016 2246886 "PERMGRP" 2248972 NIL PERMGRP (NIL T) -8 NIL NIL NIL) (-934 2242775 2243887 2243928 "PERMCAT" 2244328 NIL PERMCAT (NIL T) -9 NIL 2244626 NIL) (-933 2242422 2242469 2242593 "PERMAN" 2242728 NIL PERMAN (NIL NIL T) -7 NIL NIL NIL) (-932 2238224 2239931 2240579 "PERM" 2241807 NIL PERM (NIL T) -8 NIL NIL NIL) (-931 2235579 2237889 2238011 "PENDTREE" 2238135 NIL PENDTREE (NIL T) -8 NIL NIL NIL) (-930 2234460 2234723 2234764 "PDSPC" 2235297 NIL PDSPC (NIL T) -9 NIL 2235542 NIL) (-929 2233515 2233781 2234143 "PDSPC-" 2234148 NIL PDSPC- (NIL T T) -8 NIL NIL NIL) (-928 2232229 2233165 2233206 "PDRING" 2233211 NIL PDRING (NIL T) -9 NIL 2233239 NIL) (-927 2230972 2231734 2231788 "PDMOD" 2231793 NIL PDMOD (NIL T T) -9 NIL 2231897 NIL) (-926 2228139 2228965 2229633 "PDEPROB" 2230324 T PDEPROB (NIL) -8 NIL NIL NIL) (-925 2225648 2226188 2226743 "PDEPACK" 2227604 T PDEPACK (NIL) -7 NIL NIL NIL) (-924 2224536 2224750 2225001 "PDECOMP" 2225447 NIL PDECOMP (NIL T T) -7 NIL NIL NIL) (-923 2222053 2222944 2222972 "PDECAT" 2223759 T PDECAT (NIL) -9 NIL 2224472 NIL) (-922 2221670 2221737 2221791 "PDDOM" 2221956 NIL PDDOM (NIL T T) -9 NIL 2222036 NIL) (-921 2221483 2221519 2221626 "PDDOM-" 2221631 NIL PDDOM- (NIL T T T) -8 NIL NIL NIL) (-920 2221228 2221267 2221357 "PCOMP" 2221444 NIL PCOMP (NIL T T) -7 NIL NIL NIL) (-919 2219268 2220029 2220326 "PBWLB" 2220957 NIL PBWLB (NIL T) -8 NIL NIL NIL) (-918 2218894 2218957 2219066 "PATTERN2" 2219205 NIL PATTERN2 (NIL T T) -7 NIL NIL NIL) (-917 2216603 2217039 2217496 "PATTERN1" 2218483 NIL PATTERN1 (NIL T T) -7 NIL NIL NIL) (-916 2208782 2210676 2212014 "PATTERN" 2215286 NIL PATTERN (NIL T) -8 NIL NIL NIL) (-915 2208340 2208413 2208545 "PATRES2" 2208709 NIL PATRES2 (NIL T T T) -7 NIL NIL NIL) (-914 2205606 2206289 2206770 "PATRES" 2207905 NIL PATRES (NIL T T) -8 NIL NIL NIL) (-913 2203459 2203894 2204301 "PATMATCH" 2205273 NIL PATMATCH (NIL T T T) -7 NIL NIL NIL) (-912 2202913 2203164 2203205 "PATMAB" 2203312 NIL PATMAB (NIL T) -9 NIL 2203395 NIL) (-911 2201359 2201767 2202025 "PATLRES" 2202718 NIL PATLRES (NIL T T T) -8 NIL NIL NIL) (-910 2200897 2201028 2201069 "PATAB" 2201074 NIL PATAB (NIL T) -9 NIL 2201246 NIL) (-909 2199037 2199474 2199897 "PARTPERM" 2200494 T PARTPERM (NIL) -7 NIL NIL NIL) (-908 2198646 2198721 2198823 "PARSURF" 2198968 NIL PARSURF (NIL T) -8 NIL NIL NIL) (-907 2198272 2198335 2198444 "PARSU2" 2198583 NIL PARSU2 (NIL T T) -7 NIL NIL NIL) (-906 2198030 2198076 2198143 "PARSER" 2198225 T PARSER (NIL) -7 NIL NIL NIL) (-905 2197639 2197714 2197816 "PARSCURV" 2197961 NIL PARSCURV (NIL T) -8 NIL NIL NIL) (-904 2197265 2197328 2197437 "PARSC2" 2197576 NIL PARSC2 (NIL T T) -7 NIL NIL NIL) (-903 2196892 2196962 2197059 "PARPCURV" 2197201 NIL PARPCURV (NIL T) -8 NIL NIL NIL) (-902 2196518 2196581 2196690 "PARPC2" 2196829 NIL PARPC2 (NIL T T) -7 NIL NIL NIL) (-901 2195507 2195891 2196073 "PARAMAST" 2196356 T PARAMAST (NIL) -8 NIL NIL NIL) (-900 2195015 2195113 2195232 "PAN2EXPR" 2195408 T PAN2EXPR (NIL) -7 NIL NIL NIL) (-899 2193708 2194136 2194364 "PALETTE" 2194807 T PALETTE (NIL) -8 NIL NIL NIL) (-898 2192053 2192713 2193073 "PAIR" 2193394 NIL PAIR (NIL T T) -8 NIL NIL NIL) (-897 2184986 2191310 2191505 "PADICRC" 2191907 NIL PADICRC (NIL NIL T) -8 NIL NIL NIL) (-896 2177243 2184330 2184515 "PADICRAT" 2184833 NIL PADICRAT (NIL NIL) -8 NIL NIL NIL) (-895 2174040 2175903 2175943 "PADICCT" 2176524 NIL PADICCT (NIL NIL) -9 NIL 2176806 NIL) (-894 2172056 2173977 2174022 "PADIC" 2174027 NIL PADIC (NIL NIL) -8 NIL NIL NIL) (-893 2171001 2171213 2171481 "PADEPAC" 2171843 NIL PADEPAC (NIL T NIL NIL) -7 NIL NIL NIL) (-892 2170201 2170346 2170552 "PADE" 2170863 NIL PADE (NIL T T T) -7 NIL NIL NIL) (-891 2168434 2169409 2169689 "OWP" 2170005 NIL OWP (NIL T NIL NIL NIL) -8 NIL NIL NIL) (-890 2167879 2168140 2168237 "OVERSET" 2168357 T OVERSET (NIL) -8 NIL NIL NIL) (-889 2166799 2167484 2167656 "OVAR" 2167747 NIL OVAR (NIL NIL) -8 NIL NIL NIL) (-888 2155035 2157908 2160108 "OUTFORM" 2164619 T OUTFORM (NIL) -8 NIL NIL NIL) (-887 2154317 2154632 2154759 "OUTBFILE" 2154928 T OUTBFILE (NIL) -8 NIL NIL NIL) (-886 2153594 2153789 2153817 "OUTBCON" 2154135 T OUTBCON (NIL) -9 NIL 2154301 NIL) (-885 2153177 2153307 2153464 "OUTBCON-" 2153469 NIL OUTBCON- (NIL T) -8 NIL NIL NIL) (-884 2152417 2152562 2152723 "OUT" 2153036 T OUT (NIL) -7 NIL NIL NIL) (-883 2151713 2152146 2152235 "OSI" 2152348 T OSI (NIL) -8 NIL NIL NIL) (-882 2151132 2151554 2151582 "OSGROUP" 2151587 T OSGROUP (NIL) -9 NIL 2151609 NIL) (-881 2149843 2150104 2150389 "ORTHPOL" 2150879 NIL ORTHPOL (NIL T) -7 NIL NIL NIL) (-880 2147094 2149678 2149799 "OREUP" 2149804 NIL OREUP (NIL NIL T NIL NIL) -8 NIL NIL NIL) (-879 2144197 2146785 2146912 "ORESUP" 2147036 NIL ORESUP (NIL T NIL NIL) -8 NIL NIL NIL) (-878 2141697 2142225 2142786 "OREPCTO" 2143686 NIL OREPCTO (NIL T T) -7 NIL NIL NIL) (-877 2135075 2137570 2137611 "OREPCAT" 2139959 NIL OREPCAT (NIL T) -9 NIL 2141063 NIL) (-876 2132048 2133004 2134062 "OREPCAT-" 2134067 NIL OREPCAT- (NIL T T) -8 NIL NIL NIL) (-875 2131240 2131518 2131546 "ORDTYPE" 2131855 T ORDTYPE (NIL) -9 NIL 2132018 NIL) (-874 2130541 2130757 2131012 "ORDTYPE-" 2131017 NIL ORDTYPE- (NIL T) -8 NIL NIL NIL) (-873 2129897 2130280 2130438 "ORDSTRCT" 2130443 NIL ORDSTRCT (NIL T NIL) -8 NIL NIL NIL) (-872 2129395 2129765 2129793 "ORDSET" 2129798 T ORDSET (NIL) -9 NIL 2129820 NIL) (-871 2128046 2129017 2129045 "ORDRING" 2129050 T ORDRING (NIL) -9 NIL 2129079 NIL) (-870 2127297 2127862 2127890 "ORDMON" 2127895 T ORDMON (NIL) -9 NIL 2127916 NIL) (-869 2126441 2126606 2126801 "ORDFUNS" 2127146 NIL ORDFUNS (NIL NIL T) -7 NIL NIL NIL) (-868 2125656 2126171 2126199 "ORDFIN" 2126264 T ORDFIN (NIL) -9 NIL 2126338 NIL) (-867 2124910 2125049 2125235 "ORDCOMP2" 2125516 NIL ORDCOMP2 (NIL T T) -7 NIL NIL NIL) (-866 2121257 2123496 2123905 "ORDCOMP" 2124534 NIL ORDCOMP (NIL T) -8 NIL NIL NIL) (-865 2117778 2118748 2119562 "OPTPROB" 2120463 T OPTPROB (NIL) -8 NIL NIL NIL) (-864 2114520 2115219 2115923 "OPTPACK" 2117094 T OPTPACK (NIL) -7 NIL NIL NIL) (-863 2112133 2112959 2112987 "OPTCAT" 2113806 T OPTCAT (NIL) -9 NIL 2114456 NIL) (-862 2111451 2111810 2111915 "OPSIG" 2112048 T OPSIG (NIL) -8 NIL NIL NIL) (-861 2111213 2111258 2111324 "OPQUERY" 2111405 T OPQUERY (NIL) -7 NIL NIL NIL) (-860 2110519 2110799 2110840 "OPERCAT" 2111052 NIL OPERCAT (NIL T) -9 NIL 2111149 NIL) (-859 2110262 2110330 2110447 "OPERCAT-" 2110452 NIL OPERCAT- (NIL T T) -8 NIL NIL NIL) (-858 2107178 2108573 2109077 "OP" 2109791 NIL OP (NIL T) -8 NIL NIL NIL) (-857 2106471 2106598 2106772 "ONECOMP2" 2107050 NIL ONECOMP2 (NIL T T) -7 NIL NIL NIL) (-856 2103084 2105268 2105637 "ONECOMP" 2106135 NIL ONECOMP (NIL T) -8 NIL NIL NIL) (-855 2102485 2102609 2102739 "OMSERVER" 2102974 T OMSERVER (NIL) -7 NIL NIL NIL) (-854 2099108 2101923 2101963 "OMSAGG" 2102024 NIL OMSAGG (NIL T) -9 NIL 2102089 NIL) (-853 2097683 2097994 2098276 "OMPKG" 2098846 T OMPKG (NIL) -7 NIL NIL NIL) (-852 2096030 2097232 2097401 "OMLO" 2097564 NIL OMLO (NIL T T) -8 NIL NIL NIL) (-851 2094966 2095137 2095357 "OMEXPR" 2095856 NIL OMEXPR (NIL T) -7 NIL NIL NIL) (-850 2094051 2094387 2094547 "OMERRK" 2094826 T OMERRK (NIL) -8 NIL NIL NIL) (-849 2093288 2093597 2093733 "OMERR" 2093935 T OMERR (NIL) -8 NIL NIL NIL) (-848 2092679 2092965 2093073 "OMENC" 2093200 T OMENC (NIL) -8 NIL NIL NIL) (-847 2086316 2087759 2088930 "OMDEV" 2091528 T OMDEV (NIL) -8 NIL NIL NIL) (-846 2085349 2085556 2085750 "OMCONN" 2086142 T OMCONN (NIL) -8 NIL NIL NIL) (-845 2084755 2084882 2084910 "OM" 2085209 T OM (NIL) -9 NIL NIL NIL) (-844 2083033 2084225 2084253 "OINTDOM" 2084258 T OINTDOM (NIL) -9 NIL 2084279 NIL) (-843 2080108 2081721 2082058 "OFMONOID" 2082728 NIL OFMONOID (NIL T) -8 NIL NIL NIL) (-842 2079342 2080045 2080090 "ODVAR" 2080095 NIL ODVAR (NIL T) -8 NIL NIL NIL) (-841 2076486 2079087 2079242 "ODR" 2079247 NIL ODR (NIL T T NIL) -8 NIL NIL NIL) (-840 2067898 2076262 2076388 "ODPOL" 2076393 NIL ODPOL (NIL T) -8 NIL NIL NIL) (-839 2061306 2067770 2067875 "ODP" 2067880 NIL ODP (NIL NIL T NIL) -8 NIL NIL NIL) (-838 2060048 2060287 2060562 "ODETOOLS" 2061080 NIL ODETOOLS (NIL T T) -7 NIL NIL NIL) (-837 2056991 2057673 2058389 "ODESYS" 2059381 NIL ODESYS (NIL T T) -7 NIL NIL NIL) (-836 2051821 2052781 2053806 "ODERTRIC" 2056066 NIL ODERTRIC (NIL T T) -7 NIL NIL NIL) (-835 2051241 2051329 2051523 "ODERED" 2051733 NIL ODERED (NIL T T T T T) -7 NIL NIL NIL) (-834 2048093 2048677 2049354 "ODERAT" 2050664 NIL ODERAT (NIL T T) -7 NIL NIL NIL) (-833 2045009 2045517 2046114 "ODEPRRIC" 2047622 NIL ODEPRRIC (NIL T T T T) -7 NIL NIL NIL) (-832 2042904 2043548 2044034 "ODEPROB" 2044543 T ODEPROB (NIL) -8 NIL NIL NIL) (-831 2039370 2039909 2040556 "ODEPRIM" 2042383 NIL ODEPRIM (NIL T T T T) -7 NIL NIL NIL) (-830 2038613 2038721 2038981 "ODEPAL" 2039262 NIL ODEPAL (NIL T T T T) -7 NIL NIL NIL) (-829 2034715 2035566 2036430 "ODEPACK" 2037769 T ODEPACK (NIL) -7 NIL NIL NIL) (-828 2033758 2033883 2034105 "ODEINT" 2034604 NIL ODEINT (NIL T T) -7 NIL NIL NIL) (-827 2027823 2029284 2030731 "ODEIFTBL" 2032331 T ODEIFTBL (NIL) -8 NIL NIL NIL) (-826 2023173 2024007 2024959 "ODEEF" 2026982 NIL ODEEF (NIL T T) -7 NIL NIL NIL) (-825 2022516 2022611 2022834 "ODECONST" 2023078 NIL ODECONST (NIL T T T) -7 NIL NIL NIL) (-824 2020579 2021288 2021316 "ODECAT" 2021921 T ODECAT (NIL) -9 NIL 2022452 NIL) (-823 2020211 2020260 2020387 "OCTCT2" 2020530 NIL OCTCT2 (NIL T T T T) -7 NIL NIL NIL) (-822 2016711 2019916 2020038 "OCT" 2020121 NIL OCT (NIL T) -8 NIL NIL NIL) (-821 2015904 2016504 2016532 "OCAMON" 2016537 T OCAMON (NIL) -9 NIL 2016558 NIL) (-820 2010175 2012947 2012987 "OC" 2014084 NIL OC (NIL T) -9 NIL 2014942 NIL) (-819 2007210 2008150 2009140 "OC-" 2009234 NIL OC- (NIL T T) -8 NIL NIL NIL) (-818 2006630 2007055 2007083 "OASGP" 2007088 T OASGP (NIL) -9 NIL 2007108 NIL) (-817 2005726 2006353 2006381 "OAMONS" 2006421 T OAMONS (NIL) -9 NIL 2006464 NIL) (-816 2004902 2005461 2005489 "OAMON" 2005547 T OAMON (NIL) -9 NIL 2005599 NIL) (-815 2004760 2004793 2004861 "OAMON-" 2004866 NIL OAMON- (NIL T) -8 NIL NIL NIL) (-814 2003541 2004294 2004322 "OAGROUP" 2004469 T OAGROUP (NIL) -9 NIL 2004562 NIL) (-813 2003244 2003332 2003450 "OAGROUP-" 2003455 NIL OAGROUP- (NIL T) -8 NIL NIL NIL) (-812 2002926 2002982 2003071 "NUMTUBE" 2003188 NIL NUMTUBE (NIL T) -7 NIL NIL NIL) (-811 1996445 1998017 1999553 "NUMQUAD" 2001410 T NUMQUAD (NIL) -7 NIL NIL NIL) (-810 1992125 1993159 1994194 "NUMODE" 1995430 T NUMODE (NIL) -7 NIL NIL NIL) (-809 1989406 1990346 1990374 "NUMINT" 1991297 T NUMINT (NIL) -9 NIL 1992061 NIL) (-808 1988318 1988551 1988769 "NUMFMT" 1989208 T NUMFMT (NIL) -7 NIL NIL NIL) (-807 1974501 1977622 1980154 "NUMERIC" 1985825 NIL NUMERIC (NIL T) -7 NIL NIL NIL) (-806 1968319 1973949 1974044 "NTSCAT" 1974049 NIL NTSCAT (NIL T T T T) -9 NIL 1974088 NIL) (-805 1967499 1967678 1967871 "NTPOLFN" 1968158 NIL NTPOLFN (NIL T) -7 NIL NIL NIL) (-804 1967125 1967188 1967297 "NSUP2" 1967436 NIL NSUP2 (NIL T T) -7 NIL NIL NIL) (-803 1953907 1963950 1964762 "NSUP" 1966346 NIL NSUP (NIL T) -8 NIL NIL NIL) (-802 1942750 1953681 1953814 "NSMP" 1953819 NIL NSMP (NIL T T) -8 NIL NIL NIL) (-801 1941158 1941483 1941840 "NREP" 1942438 NIL NREP (NIL T) -7 NIL NIL NIL) (-800 1939737 1940001 1940359 "NPCOEF" 1940901 NIL NPCOEF (NIL T T T T T) -7 NIL NIL NIL) (-799 1938785 1938918 1939134 "NORMRETR" 1939618 NIL NORMRETR (NIL T T T T NIL) -7 NIL NIL NIL) (-798 1936796 1937116 1937525 "NORMPK" 1938493 NIL NORMPK (NIL T T T T T) -7 NIL NIL NIL) (-797 1936475 1936509 1936633 "NORMMA" 1936762 NIL NORMMA (NIL T T T T) -7 NIL NIL NIL) (-796 1936258 1936293 1936362 "NONE1" 1936439 NIL NONE1 (NIL T) -7 NIL NIL NIL) (-795 1936022 1936215 1936244 "NONE" 1936249 T NONE (NIL) -8 NIL NIL NIL) (-794 1935513 1935581 1935760 "NODE1" 1935954 NIL NODE1 (NIL T T) -7 NIL NIL NIL) (-793 1933574 1934636 1934891 "NNI" 1935238 T NNI (NIL) -8 NIL NIL 1935473) (-792 1931970 1932307 1932671 "NLINSOL" 1933242 NIL NLINSOL (NIL T) -7 NIL NIL NIL) (-791 1928151 1929206 1930105 "NIPROB" 1931091 T NIPROB (NIL) -8 NIL NIL NIL) (-790 1926890 1927142 1927444 "NFINTBAS" 1927913 NIL NFINTBAS (NIL T T) -7 NIL NIL NIL) (-789 1925974 1926540 1926581 "NETCLT" 1926753 NIL NETCLT (NIL T) -9 NIL 1926835 NIL) (-788 1924646 1924913 1925194 "NCODIV" 1925742 NIL NCODIV (NIL T T) -7 NIL NIL NIL) (-787 1924402 1924445 1924520 "NCNTFRAC" 1924603 NIL NCNTFRAC (NIL T) -7 NIL NIL NIL) (-786 1922558 1922946 1923366 "NCEP" 1924027 NIL NCEP (NIL T) -7 NIL NIL NIL) (-785 1921221 1922168 1922196 "NASRING" 1922306 T NASRING (NIL) -9 NIL 1922386 NIL) (-784 1921004 1921060 1921154 "NASRING-" 1921159 NIL NASRING- (NIL T) -8 NIL NIL NIL) (-783 1919971 1920622 1920650 "NARNG" 1920767 T NARNG (NIL) -9 NIL 1920858 NIL) (-782 1919645 1919730 1919864 "NARNG-" 1919869 NIL NARNG- (NIL T) -8 NIL NIL NIL) (-781 1918482 1918731 1918966 "NAGSP" 1919430 T NAGSP (NIL) -7 NIL NIL NIL) (-780 1909526 1911438 1913111 "NAGS" 1916829 T NAGS (NIL) -7 NIL NIL NIL) (-779 1908050 1908382 1908713 "NAGF07" 1909215 T NAGF07 (NIL) -7 NIL NIL NIL) (-778 1902522 1903879 1905186 "NAGF04" 1906763 T NAGF04 (NIL) -7 NIL NIL NIL) (-777 1895394 1897104 1898737 "NAGF02" 1900909 T NAGF02 (NIL) -7 NIL NIL NIL) (-776 1890558 1891718 1892835 "NAGF01" 1894297 T NAGF01 (NIL) -7 NIL NIL NIL) (-775 1884138 1885752 1887337 "NAGE04" 1888993 T NAGE04 (NIL) -7 NIL NIL NIL) (-774 1875199 1877428 1879558 "NAGE02" 1882028 T NAGE02 (NIL) -7 NIL NIL NIL) (-773 1871092 1872099 1873063 "NAGE01" 1874255 T NAGE01 (NIL) -7 NIL NIL NIL) (-772 1868869 1869421 1869979 "NAGD03" 1870554 T NAGD03 (NIL) -7 NIL NIL NIL) (-771 1860565 1862547 1864501 "NAGD02" 1866935 T NAGD02 (NIL) -7 NIL NIL NIL) (-770 1854304 1855801 1857241 "NAGD01" 1859145 T NAGD01 (NIL) -7 NIL NIL NIL) (-769 1850441 1851335 1852172 "NAGC06" 1853487 T NAGC06 (NIL) -7 NIL NIL NIL) (-768 1848888 1849238 1849594 "NAGC05" 1850105 T NAGC05 (NIL) -7 NIL NIL NIL) (-767 1848252 1848383 1848527 "NAGC02" 1848764 T NAGC02 (NIL) -7 NIL NIL NIL) (-766 1847053 1847780 1847820 "NAALG" 1847899 NIL NAALG (NIL T) -9 NIL 1847960 NIL) (-765 1846882 1846917 1847007 "NAALG-" 1847012 NIL NAALG- (NIL T T) -8 NIL NIL NIL) (-764 1840754 1841940 1843127 "MULTSQFR" 1845778 NIL MULTSQFR (NIL T T T T) -7 NIL NIL NIL) (-763 1840061 1840148 1840332 "MULTFACT" 1840666 NIL MULTFACT (NIL T T T T) -7 NIL NIL NIL) (-762 1832206 1836644 1836697 "MTSCAT" 1837767 NIL MTSCAT (NIL T T) -9 NIL 1838283 NIL) (-761 1831912 1831972 1832064 "MTHING" 1832146 NIL MTHING (NIL T) -7 NIL NIL NIL) (-760 1831698 1831737 1831797 "MSYSCMD" 1831872 T MSYSCMD (NIL) -7 NIL NIL NIL) (-759 1828554 1831259 1831300 "MSETAGG" 1831305 NIL MSETAGG (NIL T) -9 NIL 1831339 NIL) (-758 1824382 1827309 1827629 "MSET" 1828267 NIL MSET (NIL T) -8 NIL NIL NIL) (-757 1819984 1821761 1822506 "MRING" 1823682 NIL MRING (NIL T T) -8 NIL NIL NIL) (-756 1819544 1819617 1819748 "MRF2" 1819911 NIL MRF2 (NIL T T T) -7 NIL NIL NIL) (-755 1819156 1819197 1819341 "MRATFAC" 1819503 NIL MRATFAC (NIL T T T T) -7 NIL NIL NIL) (-754 1816726 1817063 1817494 "MPRFF" 1818861 NIL MPRFF (NIL T T T T) -7 NIL NIL NIL) (-753 1810060 1816580 1816677 "MPOLY" 1816682 NIL MPOLY (NIL NIL T) -8 NIL NIL NIL) (-752 1809544 1809585 1809793 "MPCPF" 1810019 NIL MPCPF (NIL T T T T) -7 NIL NIL NIL) (-751 1809052 1809101 1809285 "MPC3" 1809495 NIL MPC3 (NIL T T T T T T T) -7 NIL NIL NIL) (-750 1808235 1808328 1808549 "MPC2" 1808967 NIL MPC2 (NIL T T T T T T T) -7 NIL NIL NIL) (-749 1806512 1806873 1807263 "MONOTOOL" 1807895 NIL MONOTOOL (NIL T T) -7 NIL NIL NIL) (-748 1805657 1806040 1806068 "MONOID" 1806287 T MONOID (NIL) -9 NIL 1806434 NIL) (-747 1805173 1805322 1805503 "MONOID-" 1805508 NIL MONOID- (NIL T) -8 NIL NIL NIL) (-746 1794146 1800993 1801052 "MONOGEN" 1801726 NIL MONOGEN (NIL T T) -9 NIL 1802182 NIL) (-745 1791196 1792099 1793099 "MONOGEN-" 1793218 NIL MONOGEN- (NIL T T T) -8 NIL NIL NIL) (-744 1789913 1790461 1790489 "MONADWU" 1790881 T MONADWU (NIL) -9 NIL 1791119 NIL) (-743 1789243 1789444 1789692 "MONADWU-" 1789697 NIL MONADWU- (NIL T) -8 NIL NIL NIL) (-742 1788528 1788832 1788860 "MONAD" 1789067 T MONAD (NIL) -9 NIL 1789179 NIL) (-741 1788195 1788291 1788423 "MONAD-" 1788428 NIL MONAD- (NIL T) -8 NIL NIL NIL) (-740 1786334 1787108 1787387 "MOEBIUS" 1787948 NIL MOEBIUS (NIL T) -8 NIL NIL NIL) (-739 1785502 1786002 1786042 "MODULE" 1786047 NIL MODULE (NIL T) -9 NIL 1786086 NIL) (-738 1785040 1785166 1785356 "MODULE-" 1785361 NIL MODULE- (NIL T T) -8 NIL NIL NIL) (-737 1782570 1783404 1783731 "MODRING" 1784864 NIL MODRING (NIL T T NIL NIL NIL) -8 NIL NIL NIL) (-736 1779299 1780675 1781196 "MODOP" 1782099 NIL MODOP (NIL T T) -8 NIL NIL NIL) (-735 1777785 1778366 1778643 "MODMONOM" 1779162 NIL MODMONOM (NIL T T NIL) -8 NIL NIL NIL) (-734 1766545 1776076 1776490 "MODMON" 1777422 NIL MODMON (NIL T T) -8 NIL NIL NIL) (-733 1763378 1765389 1765665 "MODFIELD" 1766420 NIL MODFIELD (NIL T T NIL NIL NIL) -8 NIL NIL NIL) (-732 1762289 1762659 1762849 "MMLFORM" 1763208 T MMLFORM (NIL) -8 NIL NIL NIL) (-731 1761809 1761858 1762037 "MMAP" 1762240 NIL MMAP (NIL T T T T T T) -7 NIL NIL NIL) (-730 1759702 1760641 1760682 "MLO" 1761105 NIL MLO (NIL T) -9 NIL 1761347 NIL) (-729 1757050 1757584 1758186 "MLIFT" 1759183 NIL MLIFT (NIL T T T T) -7 NIL NIL NIL) (-728 1756429 1756525 1756679 "MKUCFUNC" 1756961 NIL MKUCFUNC (NIL T T T) -7 NIL NIL NIL) (-727 1756022 1756098 1756221 "MKRECORD" 1756352 NIL MKRECORD (NIL T T) -7 NIL NIL NIL) (-726 1755045 1755231 1755459 "MKFUNC" 1755833 NIL MKFUNC (NIL T) -7 NIL NIL NIL) (-725 1754421 1754537 1754693 "MKFLCFN" 1754928 NIL MKFLCFN (NIL T) -7 NIL NIL NIL) (-724 1753686 1753800 1753985 "MKBCFUNC" 1754314 NIL MKBCFUNC (NIL T T T T) -7 NIL NIL NIL) (-723 1749683 1753240 1753376 "MINT" 1753570 T MINT (NIL) -8 NIL NIL NIL) (-722 1748465 1748738 1749015 "MHROWRED" 1749438 NIL MHROWRED (NIL T) -7 NIL NIL NIL) (-721 1743216 1747000 1747405 "MFLOAT" 1748080 T MFLOAT (NIL) -8 NIL NIL NIL) (-720 1742561 1742649 1742820 "MFINFACT" 1743128 NIL MFINFACT (NIL T T T T) -7 NIL NIL NIL) (-719 1738840 1739724 1740608 "MESH" 1741697 T MESH (NIL) -7 NIL NIL NIL) (-718 1737194 1737542 1737895 "MDDFACT" 1738527 NIL MDDFACT (NIL T) -7 NIL NIL NIL) (-717 1733841 1736325 1736366 "MDAGG" 1736621 NIL MDAGG (NIL T) -9 NIL 1736764 NIL) (-716 1721564 1733134 1733341 "MCMPLX" 1733654 T MCMPLX (NIL) -8 NIL NIL NIL) (-715 1720683 1720847 1721048 "MCDEN" 1721413 NIL MCDEN (NIL T T) -7 NIL NIL NIL) (-714 1718531 1718843 1719223 "MCALCFN" 1720413 NIL MCALCFN (NIL T T T T) -7 NIL NIL NIL) (-713 1717408 1717696 1717929 "MAYBE" 1718337 NIL MAYBE (NIL T) -8 NIL NIL NIL) (-712 1714966 1715543 1716105 "MATSTOR" 1716879 NIL MATSTOR (NIL T) -7 NIL NIL NIL) (-711 1710502 1714338 1714586 "MATRIX" 1714751 NIL MATRIX (NIL T) -8 NIL NIL NIL) (-710 1706202 1706975 1707711 "MATLIN" 1709859 NIL MATLIN (NIL T T T T) -7 NIL NIL NIL) (-709 1704778 1704949 1705282 "MATCAT2" 1706037 NIL MATCAT2 (NIL T T T T T T T T) -7 NIL NIL NIL) (-708 1694231 1697835 1697912 "MATCAT" 1702944 NIL MATCAT (NIL T T T) -9 NIL 1704416 NIL) (-707 1690184 1691494 1692907 "MATCAT-" 1692912 NIL MATCAT- (NIL T T T T) -8 NIL NIL NIL) (-706 1688260 1688620 1689004 "MAPPKG3" 1689859 NIL MAPPKG3 (NIL T T T) -7 NIL NIL NIL) (-705 1687217 1687414 1687636 "MAPPKG2" 1688084 NIL MAPPKG2 (NIL T T) -7 NIL NIL NIL) (-704 1685674 1686000 1686327 "MAPPKG1" 1686923 NIL MAPPKG1 (NIL T) -7 NIL NIL NIL) (-703 1684675 1685080 1685257 "MAPPAST" 1685517 T MAPPAST (NIL) -8 NIL NIL NIL) (-702 1684280 1684344 1684467 "MAPHACK3" 1684611 NIL MAPHACK3 (NIL T T T) -7 NIL NIL NIL) (-701 1683860 1683933 1684047 "MAPHACK2" 1684212 NIL MAPHACK2 (NIL T T) -7 NIL NIL NIL) (-700 1683286 1683401 1683543 "MAPHACK1" 1683751 NIL MAPHACK1 (NIL T) -7 NIL NIL NIL) (-699 1681209 1681986 1682290 "MAGMA" 1683014 NIL MAGMA (NIL T) -8 NIL NIL NIL) (-698 1680628 1680933 1681024 "MACROAST" 1681138 T MACROAST (NIL) -8 NIL NIL NIL) (-697 1676985 1678867 1679328 "M3D" 1680200 NIL M3D (NIL T) -8 NIL NIL NIL) (-696 1670457 1675296 1675337 "LZSTAGG" 1676119 NIL LZSTAGG (NIL T) -9 NIL 1676414 NIL) (-695 1666139 1667588 1669045 "LZSTAGG-" 1669050 NIL LZSTAGG- (NIL T T) -8 NIL NIL NIL) (-694 1663052 1664030 1664517 "LWORD" 1665684 NIL LWORD (NIL T) -8 NIL NIL NIL) (-693 1662574 1662856 1662931 "LSTAST" 1662997 T LSTAST (NIL) -8 NIL NIL NIL) (-692 1654616 1662345 1662479 "LSQM" 1662484 NIL LSQM (NIL NIL T) -8 NIL NIL NIL) (-691 1653834 1653979 1654207 "LSPP" 1654471 NIL LSPP (NIL T T T T) -7 NIL NIL NIL) (-690 1650571 1651287 1652017 "LSMP1" 1653136 NIL LSMP1 (NIL T) -7 NIL NIL NIL) (-689 1648353 1648684 1649140 "LSMP" 1650260 NIL LSMP (NIL T T T T) -7 NIL NIL NIL) (-688 1641481 1647443 1647484 "LSAGG" 1647546 NIL LSAGG (NIL T) -9 NIL 1647624 NIL) (-687 1637990 1639100 1640313 "LSAGG-" 1640318 NIL LSAGG- (NIL T T) -8 NIL NIL NIL) (-686 1635285 1637134 1637383 "LPOLY" 1637785 NIL LPOLY (NIL T T) -8 NIL NIL NIL) (-685 1634861 1634952 1635075 "LPEFRAC" 1635194 NIL LPEFRAC (NIL T) -7 NIL NIL NIL) (-684 1634544 1634623 1634651 "LOGIC" 1634762 T LOGIC (NIL) -9 NIL 1634844 NIL) (-683 1634400 1634429 1634500 "LOGIC-" 1634505 NIL LOGIC- (NIL T) -8 NIL NIL NIL) (-682 1633575 1633733 1633926 "LODOOPS" 1634256 NIL LODOOPS (NIL T T) -7 NIL NIL NIL) (-681 1632099 1632348 1632701 "LODOF" 1633322 NIL LODOF (NIL T T) -7 NIL NIL NIL) (-680 1627975 1630734 1630775 "LODOCAT" 1631213 NIL LODOCAT (NIL T) -9 NIL 1631424 NIL) (-679 1627690 1627766 1627893 "LODOCAT-" 1627898 NIL LODOCAT- (NIL T T) -8 NIL NIL NIL) (-678 1624676 1627531 1627649 "LODO2" 1627654 NIL LODO2 (NIL T T) -8 NIL NIL NIL) (-677 1621783 1624613 1624658 "LODO1" 1624663 NIL LODO1 (NIL T) -8 NIL NIL NIL) (-676 1618878 1621699 1621765 "LODO" 1621770 NIL LODO (NIL T NIL) -8 NIL NIL NIL) (-675 1617747 1617924 1618229 "LODEEF" 1618701 NIL LODEEF (NIL T T T) -7 NIL NIL NIL) (-674 1615733 1616841 1617094 "LO" 1617579 NIL LO (NIL T T T) -8 NIL NIL NIL) (-673 1610816 1613899 1613940 "LNAGG" 1614802 NIL LNAGG (NIL T) -9 NIL 1615237 NIL) (-672 1609909 1610177 1610519 "LNAGG-" 1610524 NIL LNAGG- (NIL T T) -8 NIL NIL NIL) (-671 1605889 1606834 1607473 "LMOPS" 1609324 NIL LMOPS (NIL T T NIL) -8 NIL NIL NIL) (-670 1605188 1605666 1605707 "LMODULE" 1605712 NIL LMODULE (NIL T) -9 NIL 1605738 NIL) (-669 1602257 1604833 1604956 "LMDICT" 1605098 NIL LMDICT (NIL T) -8 NIL NIL NIL) (-668 1601833 1602047 1602088 "LLINSET" 1602149 NIL LLINSET (NIL T) -9 NIL 1602193 NIL) (-667 1601478 1601741 1601801 "LITERAL" 1601806 NIL LITERAL (NIL T) -8 NIL NIL NIL) (-666 1600997 1601077 1601216 "LIST3" 1601398 NIL LIST3 (NIL T T T) -7 NIL NIL NIL) (-665 1599095 1599443 1599842 "LIST2MAP" 1600644 NIL LIST2MAP (NIL T T) -7 NIL NIL NIL) (-664 1598084 1598280 1598508 "LIST2" 1598913 NIL LIST2 (NIL T T) -7 NIL NIL NIL) (-663 1590538 1597018 1597322 "LIST" 1597813 NIL LIST (NIL T) -8 NIL NIL NIL) (-662 1590121 1590357 1590398 "LINSET" 1590403 NIL LINSET (NIL T) -9 NIL 1590437 NIL) (-661 1588935 1589629 1589796 "LINFORM" 1590006 NIL LINFORM (NIL T NIL) -8 NIL NIL NIL) (-660 1587234 1587962 1588003 "LINEXP" 1588493 NIL LINEXP (NIL T) -9 NIL 1588766 NIL) (-659 1585810 1586714 1586895 "LINELT" 1587105 NIL LINELT (NIL T NIL) -8 NIL NIL NIL) (-658 1584367 1584647 1584958 "LINDEP" 1585562 NIL LINDEP (NIL T T) -7 NIL NIL NIL) (-657 1583503 1584099 1584209 "LINBASIS" 1584297 NIL LINBASIS (NIL NIL) -8 NIL NIL NIL) (-656 1580240 1580989 1581766 "LIMITRF" 1582758 NIL LIMITRF (NIL T) -7 NIL NIL NIL) (-655 1578525 1578839 1579248 "LIMITPS" 1579935 NIL LIMITPS (NIL T T) -7 NIL NIL NIL) (-654 1577353 1577928 1577968 "LIECAT" 1578108 NIL LIECAT (NIL T) -9 NIL 1578259 NIL) (-653 1577188 1577221 1577309 "LIECAT-" 1577314 NIL LIECAT- (NIL T T) -8 NIL NIL NIL) (-652 1571208 1576699 1576927 "LIE" 1577009 NIL LIE (NIL T T) -8 NIL NIL NIL) (-651 1563507 1570748 1570904 "LIB" 1571072 T LIB (NIL) -8 NIL NIL NIL) (-650 1559076 1560025 1560960 "LGROBP" 1562624 NIL LGROBP (NIL NIL T) -7 NIL NIL NIL) (-649 1557700 1558608 1558636 "LFCAT" 1558843 T LFCAT (NIL) -9 NIL 1558982 NIL) (-648 1555638 1555972 1556322 "LF" 1557421 NIL LF (NIL T T) -7 NIL NIL NIL) (-647 1552498 1553170 1553858 "LEXTRIPK" 1555002 NIL LEXTRIPK (NIL T NIL) -7 NIL NIL NIL) (-646 1549086 1550068 1550571 "LEXP" 1552078 NIL LEXP (NIL T T NIL) -8 NIL NIL NIL) (-645 1548502 1548807 1548899 "LETAST" 1549014 T LETAST (NIL) -8 NIL NIL NIL) (-644 1546888 1547213 1547614 "LEADCDET" 1548184 NIL LEADCDET (NIL T T T T) -7 NIL NIL NIL) (-643 1546066 1546152 1546381 "LAZM3PK" 1546809 NIL LAZM3PK (NIL T T T T T T) -7 NIL NIL NIL) (-642 1540591 1544143 1544681 "LAUPOL" 1545578 NIL LAUPOL (NIL T T) -8 NIL NIL NIL) (-641 1540164 1540214 1540375 "LAPLACE" 1540541 NIL LAPLACE (NIL T T) -7 NIL NIL NIL) (-640 1539012 1539728 1539769 "LALG" 1539831 NIL LALG (NIL T) -9 NIL 1539890 NIL) (-639 1538708 1538785 1538921 "LALG-" 1538926 NIL LALG- (NIL T T) -8 NIL NIL NIL) (-638 1536445 1537809 1538060 "LA" 1538541 NIL LA (NIL T T T) -8 NIL NIL NIL) (-637 1536274 1536304 1536345 "KVTFROM" 1536407 NIL KVTFROM (NIL T) -9 NIL NIL NIL) (-636 1535031 1535641 1535826 "KTVLOGIC" 1536109 T KTVLOGIC (NIL) -8 NIL NIL NIL) (-635 1534860 1534890 1534931 "KRCFROM" 1534993 NIL KRCFROM (NIL T) -9 NIL NIL NIL) (-634 1533752 1533951 1534250 "KOVACIC" 1534660 NIL KOVACIC (NIL T T) -7 NIL NIL NIL) (-633 1533581 1533611 1533652 "KONVERT" 1533714 NIL KONVERT (NIL T) -9 NIL NIL NIL) (-632 1533410 1533440 1533481 "KOERCE" 1533543 NIL KOERCE (NIL T) -9 NIL NIL NIL) (-631 1532894 1532987 1533119 "KERNEL2" 1533324 NIL KERNEL2 (NIL T T) -7 NIL NIL NIL) (-630 1530581 1531487 1531864 "KERNEL" 1532550 NIL KERNEL (NIL T) -8 NIL NIL NIL) (-629 1524163 1529058 1529112 "KDAGG" 1529489 NIL KDAGG (NIL T T) -9 NIL 1529695 NIL) (-628 1523674 1523816 1524021 "KDAGG-" 1524026 NIL KDAGG- (NIL T T T) -8 NIL NIL NIL) (-627 1516488 1523335 1523490 "KAFILE" 1523552 NIL KAFILE (NIL T) -8 NIL NIL NIL) (-626 1516092 1516377 1516440 "JVMOP" 1516445 T JVMOP (NIL) -8 NIL NIL NIL) (-625 1514828 1515332 1515581 "JVMMDACC" 1515863 T JVMMDACC (NIL) -8 NIL NIL NIL) (-624 1513764 1514218 1514423 "JVMFDACC" 1514643 T JVMFDACC (NIL) -8 NIL NIL NIL) (-623 1512345 1512840 1513140 "JVMCSTTG" 1513484 T JVMCSTTG (NIL) -8 NIL NIL NIL) (-622 1511481 1511885 1512046 "JVMCFACC" 1512204 T JVMCFACC (NIL) -8 NIL NIL NIL) (-621 1511159 1511398 1511447 "JVMBCODE" 1511452 T JVMBCODE (NIL) -8 NIL NIL NIL) (-620 1505178 1510670 1510898 "JORDAN" 1510980 NIL JORDAN (NIL T T) -8 NIL NIL NIL) (-619 1504491 1504827 1504948 "JOINAST" 1505077 T JOINAST (NIL) -8 NIL NIL NIL) (-618 1500637 1502668 1502722 "IXAGG" 1503651 NIL IXAGG (NIL T T) -9 NIL 1504110 NIL) (-617 1499490 1499862 1500281 "IXAGG-" 1500286 NIL IXAGG- (NIL T T T) -8 NIL NIL NIL) (-616 1494693 1499412 1499471 "IVECTOR" 1499476 NIL IVECTOR (NIL T NIL) -8 NIL NIL NIL) (-615 1493418 1493696 1493962 "ITUPLE" 1494460 NIL ITUPLE (NIL T) -8 NIL NIL NIL) (-614 1491890 1492097 1492392 "ITRIGMNP" 1493240 NIL ITRIGMNP (NIL T T T) -7 NIL NIL NIL) (-613 1490617 1490839 1491122 "ITFUN3" 1491666 NIL ITFUN3 (NIL T T T) -7 NIL NIL NIL) (-612 1490215 1490278 1490401 "ITFUN2" 1490540 NIL ITFUN2 (NIL T T) -8 NIL NIL NIL) (-611 1489320 1489695 1489869 "ITFORM" 1490061 T ITFORM (NIL) -8 NIL NIL NIL) (-610 1487089 1488340 1488618 "ITAYLOR" 1489075 NIL ITAYLOR (NIL T) -8 NIL NIL NIL) (-609 1475493 1481226 1482389 "ISUPS" 1485959 NIL ISUPS (NIL T) -8 NIL NIL NIL) (-608 1474585 1474737 1474973 "ISUMP" 1475340 NIL ISUMP (NIL T T T T) -7 NIL NIL NIL) (-607 1469549 1474530 1474571 "ISTRING" 1474576 NIL ISTRING (NIL NIL) -8 NIL NIL NIL) (-606 1468965 1469270 1469362 "ISAST" 1469477 T ISAST (NIL) -8 NIL NIL NIL) (-605 1468163 1468256 1468472 "IRURPK" 1468879 NIL IRURPK (NIL T T T T T) -7 NIL NIL NIL) (-604 1467075 1467300 1467540 "IRSN" 1467943 T IRSN (NIL) -7 NIL NIL NIL) (-603 1465120 1465501 1465930 "IRRF2F" 1466713 NIL IRRF2F (NIL T) -7 NIL NIL NIL) (-602 1464861 1464905 1464981 "IRREDFFX" 1465076 NIL IRREDFFX (NIL T) -7 NIL NIL NIL) (-601 1463434 1463735 1464034 "IROOT" 1464594 NIL IROOT (NIL T) -7 NIL NIL NIL) (-600 1462573 1462927 1463078 "IRFORM" 1463303 T IRFORM (NIL) -8 NIL NIL NIL) (-599 1461655 1461786 1462000 "IR2F" 1462456 NIL IR2F (NIL T T) -7 NIL NIL NIL) (-598 1459244 1459763 1460329 "IR2" 1461133 NIL IR2 (NIL T T) -7 NIL NIL NIL) (-597 1455684 1456928 1457620 "IR" 1458584 NIL IR (NIL T) -8 NIL NIL NIL) (-596 1455469 1455509 1455569 "IPRNTPK" 1455644 T IPRNTPK (NIL) -7 NIL NIL NIL) (-595 1451443 1455358 1455427 "IPF" 1455432 NIL IPF (NIL NIL) -8 NIL NIL NIL) (-594 1449471 1451368 1451425 "IPADIC" 1451430 NIL IPADIC (NIL NIL NIL) -8 NIL NIL NIL) (-593 1448729 1449031 1449161 "IP4ADDR" 1449361 T IP4ADDR (NIL) -8 NIL NIL NIL) (-592 1448067 1448358 1448490 "IOMODE" 1448617 T IOMODE (NIL) -8 NIL NIL NIL) (-591 1447038 1447664 1447791 "IOBFILE" 1447960 T IOBFILE (NIL) -8 NIL NIL NIL) (-590 1446448 1446942 1446970 "IOBCON" 1446975 T IOBCON (NIL) -9 NIL 1446996 NIL) (-589 1445953 1446017 1446200 "INVLAPLA" 1446384 NIL INVLAPLA (NIL T T) -7 NIL NIL NIL) (-588 1435523 1437955 1440341 "INTTR" 1443617 NIL INTTR (NIL T T) -7 NIL NIL NIL) (-587 1431816 1432600 1433465 "INTTOOLS" 1434708 NIL INTTOOLS (NIL T T) -7 NIL NIL NIL) (-586 1431396 1431493 1431610 "INTSLPE" 1431719 T INTSLPE (NIL) -7 NIL NIL NIL) (-585 1428863 1431319 1431378 "INTRVL" 1431383 NIL INTRVL (NIL T) -8 NIL NIL NIL) (-584 1426441 1426977 1427552 "INTRF" 1428348 NIL INTRF (NIL T) -7 NIL NIL NIL) (-583 1425834 1425949 1426091 "INTRET" 1426339 NIL INTRET (NIL T) -7 NIL NIL NIL) (-582 1423807 1424220 1424690 "INTRAT" 1425442 NIL INTRAT (NIL T T) -7 NIL NIL NIL) (-581 1421052 1421653 1422272 "INTPM" 1423292 NIL INTPM (NIL T T) -7 NIL NIL NIL) (-580 1417769 1418396 1419134 "INTPAF" 1420438 NIL INTPAF (NIL T T T) -7 NIL NIL NIL) (-579 1412870 1413910 1414961 "INTPACK" 1416738 T INTPACK (NIL) -7 NIL NIL NIL) (-578 1412116 1412274 1412482 "INTHERTR" 1412712 NIL INTHERTR (NIL T T) -7 NIL NIL NIL) (-577 1411549 1411635 1411823 "INTHERAL" 1412030 NIL INTHERAL (NIL T T T T) -7 NIL NIL NIL) (-576 1409317 1409838 1410295 "INTHEORY" 1411112 T INTHEORY (NIL) -7 NIL NIL NIL) (-575 1400649 1402344 1404116 "INTG0" 1407669 NIL INTG0 (NIL T T T) -7 NIL NIL NIL) (-574 1381174 1386012 1390822 "INTFTBL" 1395859 T INTFTBL (NIL) -8 NIL NIL NIL) (-573 1380399 1380561 1380734 "INTFACT" 1381033 NIL INTFACT (NIL T) -7 NIL NIL NIL) (-572 1377796 1378272 1378829 "INTEF" 1379953 NIL INTEF (NIL T T) -7 NIL NIL NIL) (-571 1375993 1376888 1376916 "INTDOM" 1377217 T INTDOM (NIL) -9 NIL 1377424 NIL) (-570 1375332 1375536 1375778 "INTDOM-" 1375783 NIL INTDOM- (NIL T) -8 NIL NIL NIL) (-569 1371200 1373621 1373675 "INTCAT" 1374474 NIL INTCAT (NIL T) -9 NIL 1374795 NIL) (-568 1370654 1370775 1370903 "INTBIT" 1371092 T INTBIT (NIL) -7 NIL NIL NIL) (-567 1369335 1369507 1369814 "INTALG" 1370499 NIL INTALG (NIL T T T T T) -7 NIL NIL NIL) (-566 1368812 1368908 1369065 "INTAF" 1369239 NIL INTAF (NIL T T) -7 NIL NIL NIL) (-565 1361893 1368622 1368762 "INTABL" 1368767 NIL INTABL (NIL T T T) -8 NIL NIL NIL) (-564 1361134 1361696 1361761 "INT8" 1361795 T INT8 (NIL) -8 NIL NIL 1361840) (-563 1360374 1360936 1361001 "INT64" 1361035 T INT64 (NIL) -8 NIL NIL 1361080) (-562 1359614 1360176 1360241 "INT32" 1360275 T INT32 (NIL) -8 NIL NIL 1360320) (-561 1358854 1359416 1359481 "INT16" 1359515 T INT16 (NIL) -8 NIL NIL 1359560) (-560 1355058 1358651 1358760 "INT" 1358765 T INT (NIL) -8 NIL NIL NIL) (-559 1349167 1352606 1352634 "INS" 1353568 T INS (NIL) -9 NIL 1354233 NIL) (-558 1346324 1347244 1348185 "INS-" 1348258 NIL INS- (NIL T) -8 NIL NIL NIL) (-557 1345081 1345326 1345624 "INPSIGN" 1346077 NIL INPSIGN (NIL T T) -7 NIL NIL NIL) (-556 1344175 1344316 1344513 "INPRODPF" 1344961 NIL INPRODPF (NIL T T) -7 NIL NIL NIL) (-555 1343045 1343186 1343423 "INPRODFF" 1344055 NIL INPRODFF (NIL T T T T) -7 NIL NIL NIL) (-554 1342033 1342197 1342457 "INNMFACT" 1342881 NIL INNMFACT (NIL T T T T) -7 NIL NIL NIL) (-553 1341212 1341327 1341515 "INMODGCD" 1341932 NIL INMODGCD (NIL T T NIL NIL) -7 NIL NIL NIL) (-552 1339696 1339965 1340289 "INFSP" 1340957 NIL INFSP (NIL T T T) -7 NIL NIL NIL) (-551 1338856 1338997 1339180 "INFPROD0" 1339576 NIL INFPROD0 (NIL T T) -7 NIL NIL NIL) (-550 1338454 1338526 1338624 "INFORM1" 1338791 NIL INFORM1 (NIL T) -7 NIL NIL NIL) (-549 1335021 1336519 1337034 "INFORM" 1337947 T INFORM (NIL) -8 NIL NIL NIL) (-548 1334526 1334633 1334747 "INFINITY" 1334927 T INFINITY (NIL) -7 NIL NIL NIL) (-547 1333600 1334246 1334347 "INETCLTS" 1334445 T INETCLTS (NIL) -8 NIL NIL NIL) (-546 1332198 1332466 1332787 "INEP" 1333348 NIL INEP (NIL T T T) -7 NIL NIL NIL) (-545 1331228 1332095 1332160 "INDE" 1332165 NIL INDE (NIL T) -8 NIL NIL NIL) (-544 1330780 1330860 1330977 "INCRMAPS" 1331155 NIL INCRMAPS (NIL T) -7 NIL NIL NIL) (-543 1329502 1330049 1330255 "INBFILE" 1330594 T INBFILE (NIL) -8 NIL NIL NIL) (-542 1324682 1325738 1326682 "INBFF" 1328590 NIL INBFF (NIL T) -7 NIL NIL NIL) (-541 1323536 1323859 1323887 "INBCON" 1324400 T INBCON (NIL) -9 NIL 1324666 NIL) (-540 1322746 1323011 1323287 "INBCON-" 1323292 NIL INBCON- (NIL T) -8 NIL NIL NIL) (-539 1322165 1322470 1322561 "INAST" 1322675 T INAST (NIL) -8 NIL NIL NIL) (-538 1321532 1321844 1321950 "IMPTAST" 1322079 T IMPTAST (NIL) -8 NIL NIL NIL) (-537 1317567 1321376 1321480 "IMATRIX" 1321485 NIL IMATRIX (NIL T NIL NIL) -8 NIL NIL NIL) (-536 1316259 1316398 1316714 "IMATQF" 1317423 NIL IMATQF (NIL T T T T T T T T) -7 NIL NIL NIL) (-535 1314439 1314706 1315043 "IMATLIN" 1316015 NIL IMATLIN (NIL T T T T) -7 NIL NIL NIL) (-534 1308354 1314363 1314421 "ILIST" 1314426 NIL ILIST (NIL T NIL) -8 NIL NIL NIL) (-533 1306134 1308214 1308327 "IIARRAY2" 1308332 NIL IIARRAY2 (NIL T NIL NIL T T) -8 NIL NIL NIL) (-532 1300955 1306045 1306109 "IFF" 1306114 NIL IFF (NIL NIL NIL) -8 NIL NIL NIL) (-531 1300236 1300572 1300688 "IFAST" 1300859 T IFAST (NIL) -8 NIL NIL NIL) (-530 1294862 1299528 1299716 "IFARRAY" 1300093 NIL IFARRAY (NIL T NIL) -8 NIL NIL NIL) (-529 1293900 1294766 1294839 "IFAMON" 1294844 NIL IFAMON (NIL T T NIL) -8 NIL NIL NIL) (-528 1293472 1293549 1293603 "IEVALAB" 1293810 NIL IEVALAB (NIL T T) -9 NIL NIL NIL) (-527 1293135 1293215 1293375 "IEVALAB-" 1293380 NIL IEVALAB- (NIL T T T) -8 NIL NIL NIL) (-526 1292168 1293024 1293099 "IDPOAMS" 1293104 NIL IDPOAMS (NIL T T) -8 NIL NIL NIL) (-525 1291270 1292057 1292132 "IDPOAM" 1292137 NIL IDPOAM (NIL T T) -8 NIL NIL NIL) (-524 1290651 1291185 1291247 "IDPO" 1291252 NIL IDPO (NIL T T) -8 NIL NIL NIL) (-523 1289131 1289658 1289710 "IDPC" 1290222 NIL IDPC (NIL T T) -9 NIL 1290503 NIL) (-522 1288463 1289023 1289096 "IDPAM" 1289101 NIL IDPAM (NIL T T) -8 NIL NIL NIL) (-521 1287678 1288355 1288428 "IDPAG" 1288433 NIL IDPAG (NIL T T) -8 NIL NIL NIL) (-520 1287222 1287484 1287574 "IDENT" 1287608 T IDENT (NIL) -8 NIL NIL NIL) (-519 1283441 1284325 1285220 "IDECOMP" 1286379 NIL IDECOMP (NIL NIL NIL) -7 NIL NIL NIL) (-518 1276076 1277364 1278411 "IDEAL" 1282477 NIL IDEAL (NIL T T T T) -8 NIL NIL NIL) (-517 1275218 1275348 1275548 "ICDEN" 1275960 NIL ICDEN (NIL T T T T) -7 NIL NIL NIL) (-516 1274193 1274698 1274845 "ICARD" 1275091 T ICARD (NIL) -8 NIL NIL NIL) (-515 1272223 1272566 1272971 "IBPTOOLS" 1273870 NIL IBPTOOLS (NIL T T T T) -7 NIL NIL NIL) (-514 1267452 1271843 1271956 "IBITS" 1272142 NIL IBITS (NIL NIL) -8 NIL NIL NIL) (-513 1264127 1264751 1265446 "IBATOOL" 1266869 NIL IBATOOL (NIL T T T) -7 NIL NIL NIL) (-512 1261888 1262368 1262901 "IBACHIN" 1263662 NIL IBACHIN (NIL T T T) -7 NIL NIL NIL) (-511 1259592 1261734 1261837 "IARRAY2" 1261842 NIL IARRAY2 (NIL T NIL NIL) -8 NIL NIL NIL) (-510 1255419 1259518 1259575 "IARRAY1" 1259580 NIL IARRAY1 (NIL T NIL) -8 NIL NIL NIL) (-509 1248436 1253831 1254312 "IAN" 1254958 T IAN (NIL) -8 NIL NIL NIL) (-508 1247941 1248004 1248177 "IALGFACT" 1248373 NIL IALGFACT (NIL T T T T) -7 NIL NIL NIL) (-507 1247433 1247582 1247610 "HYPCAT" 1247817 T HYPCAT (NIL) -9 NIL NIL NIL) (-506 1246935 1247088 1247274 "HYPCAT-" 1247279 NIL HYPCAT- (NIL T) -8 NIL NIL NIL) (-505 1246482 1246730 1246813 "HOSTNAME" 1246872 T HOSTNAME (NIL) -8 NIL NIL NIL) (-504 1246315 1246364 1246405 "HOMOTOP" 1246410 NIL HOMOTOP (NIL T) -9 NIL 1246443 NIL) (-503 1242859 1244247 1244288 "HOAGG" 1245269 NIL HOAGG (NIL T) -9 NIL 1245998 NIL) (-502 1241375 1241852 1242378 "HOAGG-" 1242383 NIL HOAGG- (NIL T T) -8 NIL NIL NIL) (-501 1234432 1240968 1241118 "HEXADEC" 1241245 T HEXADEC (NIL) -8 NIL NIL NIL) (-500 1233144 1233402 1233665 "HEUGCD" 1234209 NIL HEUGCD (NIL T) -7 NIL NIL NIL) (-499 1232076 1232981 1233111 "HELLFDIV" 1233116 NIL HELLFDIV (NIL T T T T) -8 NIL NIL NIL) (-498 1230198 1231851 1231940 "HEAP" 1232019 NIL HEAP (NIL T) -8 NIL NIL NIL) (-497 1229395 1229750 1229884 "HEADAST" 1230084 T HEADAST (NIL) -8 NIL NIL NIL) (-496 1222847 1229310 1229372 "HDP" 1229377 NIL HDP (NIL NIL T) -8 NIL NIL NIL) (-495 1215866 1222482 1222634 "HDMP" 1222748 NIL HDMP (NIL NIL T) -8 NIL NIL NIL) (-494 1215172 1215330 1215494 "HB" 1215722 T HB (NIL) -7 NIL NIL NIL) (-493 1208296 1215018 1215122 "HASHTBL" 1215127 NIL HASHTBL (NIL T T NIL) -8 NIL NIL NIL) (-492 1207712 1208017 1208109 "HASAST" 1208224 T HASAST (NIL) -8 NIL NIL NIL) (-491 1205125 1207334 1207516 "HACKPI" 1207550 T HACKPI (NIL) -8 NIL NIL NIL) (-490 1200411 1204978 1205091 "GTSET" 1205096 NIL GTSET (NIL T T T T) -8 NIL NIL NIL) (-489 1193564 1200289 1200387 "GSTBL" 1200392 NIL GSTBL (NIL T T T NIL) -8 NIL NIL NIL) (-488 1185327 1192729 1192985 "GSERIES" 1193364 NIL GSERIES (NIL T NIL NIL) -8 NIL NIL NIL) (-487 1184358 1184871 1184899 "GROUP" 1185102 T GROUP (NIL) -9 NIL 1185236 NIL) (-486 1183682 1183883 1184134 "GROUP-" 1184139 NIL GROUP- (NIL T) -8 NIL NIL NIL) (-485 1182031 1182370 1182757 "GROEBSOL" 1183359 NIL GROEBSOL (NIL NIL T T) -7 NIL NIL NIL) (-484 1180859 1181219 1181270 "GRMOD" 1181799 NIL GRMOD (NIL T T) -9 NIL 1181967 NIL) (-483 1180615 1180663 1180791 "GRMOD-" 1180796 NIL GRMOD- (NIL T T T) -8 NIL NIL NIL) (-482 1175755 1176969 1177969 "GRIMAGE" 1179635 T GRIMAGE (NIL) -8 NIL NIL NIL) (-481 1174149 1174482 1174806 "GRDEF" 1175451 T GRDEF (NIL) -7 NIL NIL NIL) (-480 1173581 1173709 1173850 "GRAY" 1174028 T GRAY (NIL) -7 NIL NIL NIL) (-479 1172658 1173160 1173211 "GRALG" 1173364 NIL GRALG (NIL T T) -9 NIL 1173457 NIL) (-478 1172295 1172392 1172555 "GRALG-" 1172560 NIL GRALG- (NIL T T T) -8 NIL NIL NIL) (-477 1168890 1171878 1172057 "GPOLSET" 1172201 NIL GPOLSET (NIL T T T T) -8 NIL NIL NIL) (-476 1168238 1168301 1168559 "GOSPER" 1168827 NIL GOSPER (NIL T T T T T) -7 NIL NIL NIL) (-475 1163808 1164676 1165202 "GMODPOL" 1167937 NIL GMODPOL (NIL NIL T T T NIL T) -8 NIL NIL NIL) (-474 1162795 1162997 1163235 "GHENSEL" 1163620 NIL GHENSEL (NIL T T) -7 NIL NIL NIL) (-473 1156867 1157794 1158814 "GENUPS" 1161879 NIL GENUPS (NIL T T) -7 NIL NIL NIL) (-472 1156558 1156615 1156704 "GENUFACT" 1156810 NIL GENUFACT (NIL T) -7 NIL NIL NIL) (-471 1155958 1156047 1156212 "GENPGCD" 1156476 NIL GENPGCD (NIL T T T T) -7 NIL NIL NIL) (-470 1155426 1155467 1155680 "GENMFACT" 1155917 NIL GENMFACT (NIL T T T T T) -7 NIL NIL NIL) (-469 1153963 1154249 1154556 "GENEEZ" 1155169 NIL GENEEZ (NIL T T) -7 NIL NIL NIL) (-468 1147141 1153574 1153736 "GDMP" 1153886 NIL GDMP (NIL NIL T T) -8 NIL NIL NIL) (-467 1135879 1140912 1142018 "GCNAALG" 1146124 NIL GCNAALG (NIL T NIL NIL NIL) -8 NIL NIL NIL) (-466 1134006 1135054 1135082 "GCDDOM" 1135337 T GCDDOM (NIL) -9 NIL 1135494 NIL) (-465 1133446 1133603 1133818 "GCDDOM-" 1133823 NIL GCDDOM- (NIL T) -8 NIL NIL NIL) (-464 1121918 1124392 1126784 "GBINTERN" 1131137 NIL GBINTERN (NIL T T T T) -7 NIL NIL NIL) (-463 1119719 1120047 1120468 "GBF" 1121593 NIL GBF (NIL T T T T) -7 NIL NIL NIL) (-462 1118476 1118665 1118932 "GBEUCLID" 1119535 NIL GBEUCLID (NIL T T T T) -7 NIL NIL NIL) (-461 1117126 1117333 1117637 "GB" 1118255 NIL GB (NIL T T T T) -7 NIL NIL NIL) (-460 1116457 1116600 1116749 "GAUSSFAC" 1116997 T GAUSSFAC (NIL) -7 NIL NIL NIL) (-459 1114778 1115126 1115440 "GALUTIL" 1116176 NIL GALUTIL (NIL T) -7 NIL NIL NIL) (-458 1113038 1113360 1113684 "GALPOLYU" 1114505 NIL GALPOLYU (NIL T T) -7 NIL NIL NIL) (-457 1110337 1110693 1111100 "GALFACTU" 1112735 NIL GALFACTU (NIL T T T) -7 NIL NIL NIL) (-456 1101951 1103642 1105250 "GALFACT" 1108769 NIL GALFACT (NIL T) -7 NIL NIL NIL) (-455 1099237 1099997 1100025 "FVFUN" 1101181 T FVFUN (NIL) -9 NIL 1101901 NIL) (-454 1098467 1098685 1098713 "FVC" 1099004 T FVC (NIL) -9 NIL 1099187 NIL) (-453 1098068 1098292 1098360 "FUNDESC" 1098419 T FUNDESC (NIL) -8 NIL NIL NIL) (-452 1097641 1097865 1097946 "FUNCTION" 1098020 NIL FUNCTION (NIL NIL) -8 NIL NIL NIL) (-451 1096318 1096942 1097145 "FTEM" 1097458 T FTEM (NIL) -8 NIL NIL NIL) (-450 1093948 1094640 1095106 "FT" 1095872 T FT (NIL) -8 NIL NIL NIL) (-449 1092217 1092528 1092925 "FSUPFACT" 1093639 NIL FSUPFACT (NIL T T T) -7 NIL NIL NIL) (-448 1090536 1090903 1091235 "FST" 1091905 T FST (NIL) -8 NIL NIL NIL) (-447 1089717 1089841 1090029 "FSRED" 1090418 NIL FSRED (NIL T T) -7 NIL NIL NIL) (-446 1088406 1088672 1089019 "FSPRMELT" 1089432 NIL FSPRMELT (NIL T T) -7 NIL NIL NIL) (-445 1085616 1086150 1086636 "FSPECF" 1087969 NIL FSPECF (NIL T T) -7 NIL NIL NIL) (-444 1085138 1085198 1085368 "FSINT" 1085557 NIL FSINT (NIL T T) -7 NIL NIL NIL) (-443 1083274 1084131 1084434 "FSERIES" 1084917 NIL FSERIES (NIL T T) -8 NIL NIL NIL) (-442 1082298 1082432 1082656 "FSCINT" 1083154 NIL FSCINT (NIL T T) -7 NIL NIL NIL) (-441 1081322 1081483 1081710 "FSAGG2" 1082151 NIL FSAGG2 (NIL T T T T) -7 NIL NIL NIL) (-440 1077297 1080266 1080307 "FSAGG" 1080677 NIL FSAGG (NIL T) -9 NIL 1080936 NIL) (-439 1074897 1075660 1076456 "FSAGG-" 1076551 NIL FSAGG- (NIL T T) -8 NIL NIL NIL) (-438 1072557 1072855 1073403 "FS2UPS" 1074615 NIL FS2UPS (NIL T T T T T NIL) -7 NIL NIL NIL) (-437 1071423 1071606 1071908 "FS2EXPXP" 1072382 NIL FS2EXPXP (NIL T T NIL NIL) -7 NIL NIL NIL) (-436 1071051 1071100 1071229 "FS2" 1071374 NIL FS2 (NIL T T T T) -7 NIL NIL NIL) (-435 1051289 1060825 1060866 "FS" 1064750 NIL FS (NIL T) -9 NIL 1067039 NIL) (-434 1039350 1042925 1046982 "FS-" 1047282 NIL FS- (NIL T T) -8 NIL NIL NIL) (-433 1038764 1038891 1039043 "FRUTIL" 1039230 NIL FRUTIL (NIL T) -7 NIL NIL NIL) (-432 1033275 1036453 1036493 "FRNAALG" 1037813 NIL FRNAALG (NIL T) -9 NIL 1038411 NIL) (-431 1028756 1030024 1031299 "FRNAALG-" 1032049 NIL FRNAALG- (NIL T T) -8 NIL NIL NIL) (-430 1028388 1028437 1028564 "FRNAAF2" 1028707 NIL FRNAAF2 (NIL T T T T) -7 NIL NIL NIL) (-429 1026675 1027237 1027533 "FRMOD" 1028200 NIL FRMOD (NIL T T T T NIL) -8 NIL NIL NIL) (-428 1025860 1025953 1026244 "FRIDEAL2" 1026582 NIL FRIDEAL2 (NIL T T T T T T T T) -7 NIL NIL NIL) (-427 1023465 1024235 1024553 "FRIDEAL" 1025651 NIL FRIDEAL (NIL T T T T) -8 NIL NIL NIL) (-426 1022556 1023012 1023053 "FRETRCT" 1023058 NIL FRETRCT (NIL T) -9 NIL 1023234 NIL) (-425 1021614 1021899 1022250 "FRETRCT-" 1022255 NIL FRETRCT- (NIL T T) -8 NIL NIL NIL) (-424 1018435 1019898 1019957 "FRAMALG" 1020839 NIL FRAMALG (NIL T T) -9 NIL 1021131 NIL) (-423 1016473 1017024 1017654 "FRAMALG-" 1017877 NIL FRAMALG- (NIL T T T) -8 NIL NIL NIL) (-422 1016103 1016166 1016273 "FRAC2" 1016410 NIL FRAC2 (NIL T T) -7 NIL NIL NIL) (-421 1009096 1015576 1015853 "FRAC" 1015858 NIL FRAC (NIL T) -8 NIL NIL NIL) (-420 1008726 1008789 1008896 "FR2" 1009033 NIL FR2 (NIL T T) -7 NIL NIL NIL) (-419 999643 1004221 1005579 "FR" 1007400 NIL FR (NIL T) -8 NIL NIL NIL) (-418 993562 997022 997050 "FPS" 998169 T FPS (NIL) -9 NIL 998726 NIL) (-417 992987 993120 993284 "FPS-" 993430 NIL FPS- (NIL T) -8 NIL NIL NIL) (-416 989953 991944 991972 "FPC" 992197 T FPC (NIL) -9 NIL 992339 NIL) (-415 989734 989786 989883 "FPC-" 989888 NIL FPC- (NIL T) -8 NIL NIL NIL) (-414 988492 989222 989263 "FPATMAB" 989268 NIL FPATMAB (NIL T) -9 NIL 989420 NIL) (-413 986635 987234 987581 "FPARFRAC" 988208 NIL FPARFRAC (NIL T T) -8 NIL NIL NIL) (-412 981927 982527 983209 "FORTRAN" 986067 NIL FORTRAN (NIL NIL NIL NIL NIL) -8 NIL NIL NIL) (-411 979501 980165 980193 "FORTFN" 981253 T FORTFN (NIL) -9 NIL 981877 NIL) (-410 979253 979315 979343 "FORTCAT" 979402 T FORTCAT (NIL) -9 NIL 979464 NIL) (-409 976939 977469 978008 "FORT" 978734 T FORT (NIL) -7 NIL NIL NIL) (-408 976721 976757 976826 "FORMULA1" 976903 NIL FORMULA1 (NIL T) -7 NIL NIL NIL) (-407 974725 975337 975727 "FORMULA" 976351 T FORMULA (NIL) -8 NIL NIL NIL) (-406 974242 974300 974473 "FORDER" 974667 NIL FORDER (NIL T T T T) -7 NIL NIL NIL) (-405 973302 973502 973695 "FOP" 974069 T FOP (NIL) -7 NIL NIL NIL) (-404 971715 972582 972756 "FNLA" 973184 NIL FNLA (NIL NIL NIL T) -8 NIL NIL NIL) (-403 970334 970845 970873 "FNCAT" 971333 T FNCAT (NIL) -9 NIL 971593 NIL) (-402 969777 970293 970321 "FNAME" 970326 T FNAME (NIL) -8 NIL NIL NIL) (-401 968103 969276 969304 "FMTC" 969309 T FMTC (NIL) -9 NIL 969345 NIL) (-400 966652 968039 968085 "FMONOID" 968090 NIL FMONOID (NIL T) -8 NIL NIL NIL) (-399 963241 964607 964648 "FMONCAT" 965865 NIL FMONCAT (NIL T) -9 NIL 966470 NIL) (-398 960563 961311 961339 "FMFUN" 962483 T FMFUN (NIL) -9 NIL 963191 NIL) (-397 957436 958488 958542 "FMCAT" 959737 NIL FMCAT (NIL T T) -9 NIL 960232 NIL) (-396 956669 956886 956914 "FMC" 957204 T FMC (NIL) -9 NIL 957386 NIL) (-395 955337 956435 956535 "FM1" 956614 NIL FM1 (NIL T T) -8 NIL NIL NIL) (-394 954355 955079 955228 "FM" 955233 NIL FM (NIL T T) -8 NIL NIL NIL) (-393 952093 952545 953039 "FLOATRP" 953906 NIL FLOATRP (NIL T) -7 NIL NIL NIL) (-392 949495 950031 950609 "FLOATCP" 951560 NIL FLOATCP (NIL T) -7 NIL NIL NIL) (-391 942158 947224 947845 "FLOAT" 948894 T FLOAT (NIL) -8 NIL NIL NIL) (-390 940676 941750 941791 "FLINEXP" 941796 NIL FLINEXP (NIL T) -9 NIL 941889 NIL) (-389 939806 940065 940393 "FLINEXP-" 940398 NIL FLINEXP- (NIL T T) -8 NIL NIL NIL) (-388 938864 939026 939250 "FLASORT" 939658 NIL FLASORT (NIL T T) -7 NIL NIL NIL) (-387 935782 936834 936886 "FLALG" 938113 NIL FLALG (NIL T T) -9 NIL 938580 NIL) (-386 934806 934967 935194 "FLAGG2" 935635 NIL FLAGG2 (NIL T T T T) -7 NIL NIL NIL) (-385 928175 932215 932256 "FLAGG" 933518 NIL FLAGG (NIL T) -9 NIL 934170 NIL) (-384 926829 927240 927730 "FLAGG-" 927735 NIL FLAGG- (NIL T T) -8 NIL NIL NIL) (-383 923467 924674 924733 "FINRALG" 925861 NIL FINRALG (NIL T T) -9 NIL 926369 NIL) (-382 922591 922856 923195 "FINRALG-" 923200 NIL FINRALG- (NIL T T T) -8 NIL NIL NIL) (-381 921897 922196 922224 "FINITE" 922420 T FINITE (NIL) -9 NIL 922527 NIL) (-380 913848 916427 916467 "FINAALG" 920134 NIL FINAALG (NIL T) -9 NIL 921587 NIL) (-379 908964 910230 911374 "FINAALG-" 912753 NIL FINAALG- (NIL T T) -8 NIL NIL NIL) (-378 907524 907946 908000 "FILECAT" 908684 NIL FILECAT (NIL T T) -9 NIL 908900 NIL) (-377 906802 907279 907382 "FILE" 907454 NIL FILE (NIL T) -8 NIL NIL NIL) (-376 904205 906032 906060 "FIELD" 906100 T FIELD (NIL) -9 NIL 906180 NIL) (-375 902747 903210 903721 "FIELD-" 903726 NIL FIELD- (NIL T) -8 NIL NIL NIL) (-374 900430 901382 901729 "FGROUP" 902433 NIL FGROUP (NIL T) -8 NIL NIL NIL) (-373 899502 899684 899904 "FGLMICPK" 900262 NIL FGLMICPK (NIL T NIL) -7 NIL NIL NIL) (-372 894757 899427 899484 "FFX" 899489 NIL FFX (NIL T NIL) -8 NIL NIL NIL) (-371 894352 894419 894554 "FFSLPE" 894690 NIL FFSLPE (NIL T T T) -7 NIL NIL NIL) (-370 893850 893892 894101 "FFPOLY2" 894310 NIL FFPOLY2 (NIL T T) -7 NIL NIL NIL) (-369 889726 890622 891418 "FFPOLY" 893086 NIL FFPOLY (NIL T) -7 NIL NIL NIL) (-368 884995 889645 889708 "FFP" 889713 NIL FFP (NIL T NIL) -8 NIL NIL NIL) (-367 879526 884338 884528 "FFNBX" 884849 NIL FFNBX (NIL T NIL) -8 NIL NIL NIL) (-366 873859 878661 878919 "FFNBP" 879380 NIL FFNBP (NIL T NIL) -8 NIL NIL NIL) (-365 867897 873143 873354 "FFNB" 873692 NIL FFNB (NIL NIL NIL) -8 NIL NIL NIL) (-364 866717 866927 867242 "FFINTBAS" 867694 NIL FFINTBAS (NIL T T T) -7 NIL NIL NIL) (-363 862310 864964 864992 "FFIELDC" 865612 T FFIELDC (NIL) -9 NIL 865988 NIL) (-362 860930 861371 861854 "FFIELDC-" 861859 NIL FFIELDC- (NIL T) -8 NIL NIL NIL) (-361 860487 860545 860669 "FFHOM" 860872 NIL FFHOM (NIL T T T) -7 NIL NIL NIL) (-360 858146 858669 859186 "FFF" 860002 NIL FFF (NIL T) -7 NIL NIL NIL) (-359 853181 857888 857989 "FFCGX" 858089 NIL FFCGX (NIL T NIL) -8 NIL NIL NIL) (-358 848220 852913 853020 "FFCGP" 853124 NIL FFCGP (NIL T NIL) -8 NIL NIL NIL) (-357 842820 847947 848055 "FFCG" 848156 NIL FFCG (NIL NIL NIL) -8 NIL NIL NIL) (-356 842225 842274 842509 "FFCAT2" 842771 NIL FFCAT2 (NIL T T T T T T T T) -7 NIL NIL NIL) (-355 820907 831957 832043 "FFCAT" 837208 NIL FFCAT (NIL T T T) -9 NIL 838659 NIL) (-354 815918 817152 818466 "FFCAT-" 819696 NIL FFCAT- (NIL T T T T) -8 NIL NIL NIL) (-353 810739 815829 815893 "FF" 815898 NIL FF (NIL NIL NIL) -8 NIL NIL NIL) (-352 799392 803711 804931 "FEXPR" 809591 NIL FEXPR (NIL NIL NIL T) -8 NIL NIL NIL) (-351 798320 798789 798830 "FEVALAB" 798914 NIL FEVALAB (NIL T) -9 NIL 799175 NIL) (-350 797437 797689 798027 "FEVALAB-" 798032 NIL FEVALAB- (NIL T T) -8 NIL NIL NIL) (-349 794299 795184 795299 "FDIVCAT" 796867 NIL FDIVCAT (NIL T T T T) -9 NIL 797304 NIL) (-348 794055 794088 794258 "FDIVCAT-" 794263 NIL FDIVCAT- (NIL T T T T T) -8 NIL NIL NIL) (-347 793269 793362 793639 "FDIV2" 793962 NIL FDIV2 (NIL T T T T T T T T) -7 NIL NIL NIL) (-346 791679 792652 792855 "FDIV" 793168 NIL FDIV (NIL T T T T) -8 NIL NIL NIL) (-345 790587 790974 791176 "FCTRDATA" 791497 T FCTRDATA (NIL) -8 NIL NIL NIL) (-344 789243 789532 789821 "FCPAK1" 790318 T FCPAK1 (NIL) -7 NIL NIL NIL) (-343 788246 788743 788884 "FCOMP" 789134 NIL FCOMP (NIL T) -8 NIL NIL NIL) (-342 771560 775396 778934 "FC" 784728 T FC (NIL) -8 NIL NIL NIL) (-341 763269 767881 767921 "FAXF" 769723 NIL FAXF (NIL T) -9 NIL 770415 NIL) (-340 760410 761217 762035 "FAXF-" 762500 NIL FAXF- (NIL T T) -8 NIL NIL NIL) (-339 755093 759786 759962 "FARRAY" 760267 NIL FARRAY (NIL T) -8 NIL NIL NIL) (-338 749658 752040 752093 "FAMR" 753116 NIL FAMR (NIL T T) -9 NIL 753576 NIL) (-337 748482 748850 749285 "FAMR-" 749290 NIL FAMR- (NIL T T T) -8 NIL NIL NIL) (-336 747509 748404 748457 "FAMONOID" 748462 NIL FAMONOID (NIL T) -8 NIL NIL NIL) (-335 745139 745991 746044 "FAMONC" 746985 NIL FAMONC (NIL T T) -9 NIL 747371 NIL) (-334 743613 744893 745030 "FAGROUP" 745035 NIL FAGROUP (NIL T) -8 NIL NIL NIL) (-333 741366 741727 742130 "FACUTIL" 743294 NIL FACUTIL (NIL T T T T) -7 NIL NIL NIL) (-332 740453 740650 740872 "FACTFUNC" 741176 NIL FACTFUNC (NIL T) -7 NIL NIL NIL) (-331 732194 739756 739955 "EXPUPXS" 740309 NIL EXPUPXS (NIL T NIL NIL) -8 NIL NIL NIL) (-330 729647 730217 730803 "EXPRTUBE" 731628 T EXPRTUBE (NIL) -7 NIL NIL NIL) (-329 725858 726510 727240 "EXPRODE" 728986 NIL EXPRODE (NIL T T) -7 NIL NIL NIL) (-328 720292 720999 721805 "EXPR2UPS" 725156 NIL EXPR2UPS (NIL T T) -7 NIL NIL NIL) (-327 719918 719981 720090 "EXPR2" 720229 NIL EXPR2 (NIL T T) -7 NIL NIL NIL) (-326 704226 718567 718996 "EXPR" 719522 NIL EXPR (NIL T) -8 NIL NIL NIL) (-325 694564 703377 703668 "EXPEXPAN" 704062 NIL EXPEXPAN (NIL T T NIL NIL) -8 NIL NIL NIL) (-324 693984 694288 694379 "EXITAST" 694493 T EXITAST (NIL) -8 NIL NIL NIL) (-323 693748 693941 693970 "EXIT" 693975 T EXIT (NIL) -8 NIL NIL NIL) (-322 693369 693437 693550 "EVALCYC" 693680 NIL EVALCYC (NIL T) -7 NIL NIL NIL) (-321 692886 693028 693069 "EVALAB" 693239 NIL EVALAB (NIL T) -9 NIL 693343 NIL) (-320 692343 692489 692710 "EVALAB-" 692715 NIL EVALAB- (NIL T T) -8 NIL NIL NIL) (-319 689458 690999 691027 "EUCDOM" 691582 T EUCDOM (NIL) -9 NIL 691932 NIL) (-318 687818 688319 688902 "EUCDOM-" 688907 NIL EUCDOM- (NIL T) -8 NIL NIL NIL) (-317 687444 687507 687616 "ESTOOLS2" 687755 NIL ESTOOLS2 (NIL T T) -7 NIL NIL NIL) (-316 687189 687237 687317 "ESTOOLS1" 687396 NIL ESTOOLS1 (NIL T) -7 NIL NIL NIL) (-315 674506 677487 680237 "ESTOOLS" 684459 T ESTOOLS (NIL) -7 NIL NIL NIL) (-314 674245 674283 674365 "ESCONT1" 674468 NIL ESCONT1 (NIL NIL NIL) -7 NIL NIL NIL) (-313 670553 671380 672160 "ESCONT" 673485 T ESCONT (NIL) -7 NIL NIL NIL) (-312 670222 670278 670378 "ES2" 670497 NIL ES2 (NIL T T) -7 NIL NIL NIL) (-311 669846 669910 670019 "ES1" 670158 NIL ES1 (NIL T T) -7 NIL NIL NIL) (-310 663547 665477 665505 "ES" 668273 T ES (NIL) -9 NIL 669683 NIL) (-309 658224 659781 661598 "ES-" 661762 NIL ES- (NIL T) -8 NIL NIL NIL) (-308 657416 657569 657745 "ERROR" 658068 T ERROR (NIL) -7 NIL NIL NIL) (-307 650546 657275 657366 "EQTBL" 657371 NIL EQTBL (NIL T T) -8 NIL NIL NIL) (-306 650172 650235 650344 "EQ2" 650483 NIL EQ2 (NIL T T) -7 NIL NIL NIL) (-305 642431 645486 646935 "EQ" 648756 NIL -3395 (NIL T) -8 NIL NIL NIL) (-304 637673 638769 639862 "EP" 641370 NIL EP (NIL T) -7 NIL NIL NIL) (-303 636213 636564 636870 "ENV" 637387 T ENV (NIL) -8 NIL NIL NIL) (-302 635173 635847 635875 "ENTIRER" 635880 T ENTIRER (NIL) -9 NIL 635926 NIL) (-301 631592 633355 633716 "EMR" 634981 NIL EMR (NIL T T T NIL NIL NIL) -8 NIL NIL NIL) (-300 630696 630907 630961 "ELTAGG" 631341 NIL ELTAGG (NIL T T) -9 NIL 631552 NIL) (-299 630403 630477 630618 "ELTAGG-" 630623 NIL ELTAGG- (NIL T T T) -8 NIL NIL NIL) (-298 630161 630196 630250 "ELTAB" 630334 NIL ELTAB (NIL T T) -9 NIL 630386 NIL) (-297 629263 629433 629632 "ELFUTS" 630012 NIL ELFUTS (NIL T T) -7 NIL NIL NIL) (-296 628987 629061 629089 "ELEMFUN" 629194 T ELEMFUN (NIL) -9 NIL NIL NIL) (-295 628851 628878 628946 "ELEMFUN-" 628951 NIL ELEMFUN- (NIL T) -8 NIL NIL NIL) (-294 623376 626893 626934 "ELAGG" 627874 NIL ELAGG (NIL T) -9 NIL 628337 NIL) (-293 621553 622095 622758 "ELAGG-" 622763 NIL ELAGG- (NIL T T) -8 NIL NIL NIL) (-292 620835 621002 621158 "ELABOR" 621417 T ELABOR (NIL) -8 NIL NIL NIL) (-291 619441 619775 620069 "ELABEXPR" 620561 T ELABEXPR (NIL) -8 NIL NIL NIL) (-290 611953 614078 614907 "EFUPXS" 618716 NIL EFUPXS (NIL T T T T) -8 NIL NIL NIL) (-289 605079 607202 608013 "EFULS" 611228 NIL EFULS (NIL T T T) -8 NIL NIL NIL) (-288 602516 602922 603394 "EFSTRUC" 604711 NIL EFSTRUC (NIL T T) -7 NIL NIL NIL) (-287 591954 593873 595421 "EF" 601031 NIL EF (NIL T T) -7 NIL NIL NIL) (-286 590932 591439 591588 "EAB" 591825 T EAB (NIL) -8 NIL NIL NIL) (-285 590054 590891 590919 "E04UCFA" 590924 T E04UCFA (NIL) -8 NIL NIL NIL) (-284 589176 590013 590041 "E04NAFA" 590046 T E04NAFA (NIL) -8 NIL NIL NIL) (-283 588298 589135 589163 "E04MBFA" 589168 T E04MBFA (NIL) -8 NIL NIL NIL) (-282 587420 588257 588285 "E04JAFA" 588290 T E04JAFA (NIL) -8 NIL NIL NIL) (-281 586544 587379 587407 "E04GCFA" 587412 T E04GCFA (NIL) -8 NIL NIL NIL) (-280 585668 586503 586531 "E04FDFA" 586536 T E04FDFA (NIL) -8 NIL NIL NIL) (-279 584790 585627 585655 "E04DGFA" 585660 T E04DGFA (NIL) -8 NIL NIL NIL) (-278 578867 580315 581679 "E04AGNT" 583446 T E04AGNT (NIL) -7 NIL NIL NIL) (-277 577487 578168 578208 "DVARCAT" 578549 NIL DVARCAT (NIL T) -9 NIL 578712 NIL) (-276 576637 576903 577217 "DVARCAT-" 577222 NIL DVARCAT- (NIL T T) -8 NIL NIL NIL) (-275 568605 576436 576565 "DSMP" 576570 NIL DSMP (NIL T T T) -8 NIL NIL NIL) (-274 566956 567747 567788 "DSEXT" 568151 NIL DSEXT (NIL T) -9 NIL 568445 NIL) (-273 565145 565669 566335 "DSEXT-" 566340 NIL DSEXT- (NIL T T) -8 NIL NIL NIL) (-272 564804 564869 564967 "DROPT1" 565080 NIL DROPT1 (NIL T) -7 NIL NIL NIL) (-271 559823 561045 562182 "DROPT0" 563687 T DROPT0 (NIL) -7 NIL NIL NIL) (-270 554406 555768 556836 "DROPT" 558775 T DROPT (NIL) -8 NIL NIL NIL) (-269 552715 553076 553462 "DRAWPT" 554040 T DRAWPT (NIL) -7 NIL NIL NIL) (-268 552342 552401 552519 "DRAWHACK" 552656 NIL DRAWHACK (NIL T) -7 NIL NIL NIL) (-267 551043 551342 551633 "DRAWCX" 552071 T DRAWCX (NIL) -7 NIL NIL NIL) (-266 550552 550627 550778 "DRAWCURV" 550969 NIL DRAWCURV (NIL T T) -7 NIL NIL NIL) (-265 540870 542982 545097 "DRAWCFUN" 548457 T DRAWCFUN (NIL) -7 NIL NIL NIL) (-264 535361 536380 537459 "DRAW" 539844 NIL DRAW (NIL T) -7 NIL NIL NIL) (-263 531943 534026 534067 "DQAGG" 534696 NIL DQAGG (NIL T) -9 NIL 534970 NIL) (-262 518526 526154 526237 "DPOLCAT" 528089 NIL DPOLCAT (NIL T T T T) -9 NIL 528634 NIL) (-261 513045 514711 516669 "DPOLCAT-" 516674 NIL DPOLCAT- (NIL T T T T T) -8 NIL NIL NIL) (-260 505967 512906 513004 "DPMO" 513009 NIL DPMO (NIL NIL T T) -8 NIL NIL NIL) (-259 498786 505747 505914 "DPMM" 505919 NIL DPMM (NIL NIL T T T) -8 NIL NIL NIL) (-258 498308 498570 498659 "DOMTMPLT" 498717 T DOMTMPLT (NIL) -8 NIL NIL NIL) (-257 497657 498110 498190 "DOMCTOR" 498248 T DOMCTOR (NIL) -8 NIL NIL NIL) (-256 496809 497137 497288 "DOMAIN" 497526 T DOMAIN (NIL) -8 NIL NIL NIL) (-255 489828 496444 496596 "DMP" 496710 NIL DMP (NIL NIL T) -8 NIL NIL NIL) (-254 487605 488895 488936 "DMEXT" 488941 NIL DMEXT (NIL T) -9 NIL 489117 NIL) (-253 487199 487261 487405 "DLP" 487543 NIL DLP (NIL T) -7 NIL NIL NIL) (-252 480322 486526 486716 "DLIST" 487041 NIL DLIST (NIL T) -8 NIL NIL NIL) (-251 476971 479147 479188 "DLAGG" 479738 NIL DLAGG (NIL T) -9 NIL 479968 NIL) (-250 475483 476297 476325 "DIVRING" 476417 T DIVRING (NIL) -9 NIL 476500 NIL) (-249 474666 474910 475210 "DIVRING-" 475215 NIL DIVRING- (NIL T) -8 NIL NIL NIL) (-248 472708 473125 473531 "DISPLAY" 474280 T DISPLAY (NIL) -7 NIL NIL NIL) (-247 471538 471759 472024 "DIRPROD2" 472501 NIL DIRPROD2 (NIL NIL T T) -7 NIL NIL NIL) (-246 465010 471452 471515 "DIRPROD" 471520 NIL DIRPROD (NIL NIL T) -8 NIL NIL NIL) (-245 453287 459721 459774 "DIRPCAT" 460032 NIL DIRPCAT (NIL NIL T) -9 NIL 460907 NIL) (-244 450487 451255 452136 "DIRPCAT-" 452473 NIL DIRPCAT- (NIL T NIL T) -8 NIL NIL NIL) (-243 449768 449934 450120 "DIOSP" 450321 T DIOSP (NIL) -7 NIL NIL NIL) (-242 446293 448652 448693 "DIOPS" 449127 NIL DIOPS (NIL T) -9 NIL 449356 NIL) (-241 445812 445956 446147 "DIOPS-" 446152 NIL DIOPS- (NIL T T) -8 NIL NIL NIL) (-240 444719 445491 445519 "DIFRING" 445524 T DIFRING (NIL) -9 NIL 445546 NIL) (-239 444367 444465 444493 "DIFFSPC" 444612 T DIFFSPC (NIL) -9 NIL 444687 NIL) (-238 443988 444090 444242 "DIFFSPC-" 444247 NIL DIFFSPC- (NIL T) -8 NIL NIL NIL) (-237 442924 443522 443563 "DIFFMOD" 443568 NIL DIFFMOD (NIL T) -9 NIL 443666 NIL) (-236 442620 442677 442718 "DIFFDOM" 442839 NIL DIFFDOM (NIL T) -9 NIL 442907 NIL) (-235 442467 442497 442581 "DIFFDOM-" 442586 NIL DIFFDOM- (NIL T T) -8 NIL NIL NIL) (-234 440207 441671 441712 "DIFEXT" 441717 NIL DIFEXT (NIL T) -9 NIL 441870 NIL) (-233 437352 439711 439752 "DIAGG" 439757 NIL DIAGG (NIL T) -9 NIL 439777 NIL) (-232 436700 436893 437145 "DIAGG-" 437150 NIL DIAGG- (NIL T T) -8 NIL NIL NIL) (-231 431664 435659 435936 "DHMATRIX" 436469 NIL DHMATRIX (NIL T) -8 NIL NIL NIL) (-230 427132 428185 429195 "DFSFUN" 430674 T DFSFUN (NIL) -7 NIL NIL NIL) (-229 421373 426063 426375 "DFLOAT" 426840 T DFLOAT (NIL) -8 NIL NIL NIL) (-228 419612 419917 420306 "DFINTTLS" 421081 NIL DFINTTLS (NIL T T) -7 NIL NIL NIL) (-227 416431 417633 418033 "DERHAM" 419278 NIL DERHAM (NIL T NIL) -8 NIL NIL NIL) (-226 414081 416206 416295 "DEQUEUE" 416375 NIL DEQUEUE (NIL T) -8 NIL NIL NIL) (-225 413323 413468 413651 "DEGRED" 413943 NIL DEGRED (NIL T T) -7 NIL NIL NIL) (-224 409729 410498 411344 "DEFINTRF" 412551 NIL DEFINTRF (NIL T) -7 NIL NIL NIL) (-223 407266 407753 408345 "DEFINTEF" 409248 NIL DEFINTEF (NIL T T) -7 NIL NIL NIL) (-222 406550 406886 407001 "DEFAST" 407171 T DEFAST (NIL) -8 NIL NIL NIL) (-221 399607 406143 406293 "DECIMAL" 406420 T DECIMAL (NIL) -8 NIL NIL NIL) (-220 397065 397577 398083 "DDFACT" 399151 NIL DDFACT (NIL T T) -7 NIL NIL NIL) (-219 396655 396704 396855 "DBLRESP" 397016 NIL DBLRESP (NIL T T T T) -7 NIL NIL NIL) (-218 395856 396425 396516 "DBASIS" 396604 NIL DBASIS (NIL NIL) -8 NIL NIL NIL) (-217 393640 394086 394447 "DBASE" 395622 NIL DBASE (NIL T) -8 NIL NIL NIL) (-216 392828 393120 393266 "DATAARY" 393539 NIL DATAARY (NIL NIL T) -8 NIL NIL NIL) (-215 391886 392787 392815 "D03FAFA" 392820 T D03FAFA (NIL) -8 NIL NIL NIL) (-214 390945 391845 391873 "D03EEFA" 391878 T D03EEFA (NIL) -8 NIL NIL NIL) (-213 388871 389361 389850 "D03AGNT" 390476 T D03AGNT (NIL) -7 NIL NIL NIL) (-212 388112 388830 388858 "D02EJFA" 388863 T D02EJFA (NIL) -8 NIL NIL NIL) (-211 387353 388071 388099 "D02CJFA" 388104 T D02CJFA (NIL) -8 NIL NIL NIL) (-210 386594 387312 387340 "D02BHFA" 387345 T D02BHFA (NIL) -8 NIL NIL NIL) (-209 385835 386553 386581 "D02BBFA" 386586 T D02BBFA (NIL) -8 NIL NIL NIL) (-208 378966 380621 382227 "D02AGNT" 384249 T D02AGNT (NIL) -7 NIL NIL NIL) (-207 376716 377257 377803 "D01WGTS" 378440 T D01WGTS (NIL) -7 NIL NIL NIL) (-206 375723 376675 376703 "D01TRNS" 376708 T D01TRNS (NIL) -8 NIL NIL NIL) (-205 374731 375682 375710 "D01GBFA" 375715 T D01GBFA (NIL) -8 NIL NIL NIL) (-204 373739 374690 374718 "D01FCFA" 374723 T D01FCFA (NIL) -8 NIL NIL NIL) (-203 372747 373698 373726 "D01ASFA" 373731 T D01ASFA (NIL) -8 NIL NIL NIL) (-202 371755 372706 372734 "D01AQFA" 372739 T D01AQFA (NIL) -8 NIL NIL NIL) (-201 370763 371714 371742 "D01APFA" 371747 T D01APFA (NIL) -8 NIL NIL NIL) (-200 369771 370722 370750 "D01ANFA" 370755 T D01ANFA (NIL) -8 NIL NIL NIL) (-199 368779 369730 369758 "D01AMFA" 369763 T D01AMFA (NIL) -8 NIL NIL NIL) (-198 367787 368738 368766 "D01ALFA" 368771 T D01ALFA (NIL) -8 NIL NIL NIL) (-197 366795 367746 367774 "D01AKFA" 367779 T D01AKFA (NIL) -8 NIL NIL NIL) (-196 365803 366754 366782 "D01AJFA" 366787 T D01AJFA (NIL) -8 NIL NIL NIL) (-195 359026 360651 362212 "D01AGNT" 364262 T D01AGNT (NIL) -7 NIL NIL NIL) (-194 358345 358491 358643 "CYCLOTOM" 358894 T CYCLOTOM (NIL) -7 NIL NIL NIL) (-193 355000 355793 356520 "CYCLES" 357638 T CYCLES (NIL) -7 NIL NIL NIL) (-192 354300 354446 354617 "CVMP" 354861 NIL CVMP (NIL T) -7 NIL NIL NIL) (-191 352087 352399 352768 "CTRIGMNP" 354028 NIL CTRIGMNP (NIL T T) -7 NIL NIL NIL) (-190 351560 351818 351919 "CTORKIND" 352006 T CTORKIND (NIL) -8 NIL NIL NIL) (-189 350765 351153 351181 "CTORCAT" 351363 T CTORCAT (NIL) -9 NIL 351476 NIL) (-188 350339 350474 350633 "CTORCAT-" 350638 NIL CTORCAT- (NIL T) -8 NIL NIL NIL) (-187 349753 350013 350121 "CTORCALL" 350263 NIL CTORCALL (NIL T) -8 NIL NIL NIL) (-186 349111 349547 349620 "CTOR" 349700 T CTOR (NIL) -8 NIL NIL NIL) (-185 348467 348584 348737 "CSTTOOLS" 349008 NIL CSTTOOLS (NIL T T) -7 NIL NIL NIL) (-184 344164 344923 345681 "CRFP" 347779 NIL CRFP (NIL T T) -7 NIL NIL NIL) (-183 343579 343885 343977 "CRCEAST" 344092 T CRCEAST (NIL) -8 NIL NIL NIL) (-182 342602 342811 343039 "CRAPACK" 343383 NIL CRAPACK (NIL T) -7 NIL NIL NIL) (-181 341982 342087 342291 "CPMATCH" 342478 NIL CPMATCH (NIL T T T) -7 NIL NIL NIL) (-180 341701 341735 341841 "CPIMA" 341948 NIL CPIMA (NIL T T T) -7 NIL NIL NIL) (-179 337959 338721 339440 "COORDSYS" 341036 NIL COORDSYS (NIL T) -7 NIL NIL NIL) (-178 337347 337492 337634 "CONTOUR" 337837 T CONTOUR (NIL) -8 NIL NIL NIL) (-177 332818 335350 335842 "CONTFRAC" 336887 NIL CONTFRAC (NIL T) -8 NIL NIL NIL) (-176 332692 332719 332747 "CONDUIT" 332784 T CONDUIT (NIL) -9 NIL NIL NIL) (-175 331646 332320 332348 "COMRING" 332353 T COMRING (NIL) -9 NIL 332405 NIL) (-174 330628 331004 331188 "COMPPROP" 331482 T COMPPROP (NIL) -8 NIL NIL NIL) (-173 330283 330324 330452 "COMPLPAT" 330587 NIL COMPLPAT (NIL T T T) -7 NIL NIL NIL) (-172 329913 329976 330083 "COMPLEX2" 330220 NIL COMPLEX2 (NIL T T) -7 NIL NIL NIL) (-171 318317 329722 329831 "COMPLEX" 329836 NIL COMPLEX (NIL T) -8 NIL NIL NIL) (-170 317638 317777 317937 "COMPILER" 318177 T COMPILER (NIL) -8 NIL NIL NIL) (-169 317350 317391 317489 "COMPFACT" 317597 NIL COMPFACT (NIL T T) -7 NIL NIL NIL) (-168 298744 311054 311094 "COMPCAT" 312098 NIL COMPCAT (NIL T) -9 NIL 313446 NIL) (-167 287632 291183 294810 "COMPCAT-" 295166 NIL COMPCAT- (NIL T T) -8 NIL NIL NIL) (-166 287355 287389 287492 "COMMUPC" 287598 NIL COMMUPC (NIL T T T) -7 NIL NIL NIL) (-165 287143 287183 287242 "COMMONOP" 287316 T COMMONOP (NIL) -7 NIL NIL NIL) (-164 286665 286947 287022 "COMMAAST" 287088 T COMMAAST (NIL) -8 NIL NIL NIL) (-163 286172 286416 286503 "COMM" 286598 T COMM (NIL) -8 NIL NIL NIL) (-162 285367 285615 285643 "COMBOPC" 285981 T COMBOPC (NIL) -9 NIL 286156 NIL) (-161 284221 284473 284715 "COMBINAT" 285157 NIL COMBINAT (NIL T) -7 NIL NIL NIL) (-160 280564 281252 281879 "COMBF" 283643 NIL COMBF (NIL T T) -7 NIL NIL NIL) (-159 279226 279680 279915 "COLOR" 280349 T COLOR (NIL) -8 NIL NIL NIL) (-158 278642 278947 279039 "COLONAST" 279154 T COLONAST (NIL) -8 NIL NIL NIL) (-157 278276 278329 278454 "CMPLXRT" 278589 NIL CMPLXRT (NIL T T) -7 NIL NIL NIL) (-156 277664 277976 278075 "CLLCTAST" 278197 T CLLCTAST (NIL) -8 NIL NIL NIL) (-155 273124 274194 275274 "CLIP" 276604 T CLIP (NIL) -7 NIL NIL NIL) (-154 271297 272225 272465 "CLIF" 272951 NIL CLIF (NIL NIL T NIL) -8 NIL NIL NIL) (-153 267390 269415 269456 "CLAGG" 270385 NIL CLAGG (NIL T) -9 NIL 270921 NIL) (-152 265734 266269 266852 "CLAGG-" 266857 NIL CLAGG- (NIL T T) -8 NIL NIL NIL) (-151 265272 265363 265503 "CINTSLPE" 265643 NIL CINTSLPE (NIL T T) -7 NIL NIL NIL) (-150 262737 263244 263792 "CHVAR" 264800 NIL CHVAR (NIL T T T) -7 NIL NIL NIL) (-149 261777 262451 262479 "CHARZ" 262484 T CHARZ (NIL) -9 NIL 262499 NIL) (-148 261525 261571 261649 "CHARPOL" 261731 NIL CHARPOL (NIL T) -7 NIL NIL NIL) (-147 260443 261149 261177 "CHARNZ" 261238 T CHARNZ (NIL) -9 NIL 261287 NIL) (-146 257387 258497 259026 "CHAR" 259934 T CHAR (NIL) -8 NIL NIL NIL) (-145 257095 257174 257202 "CFCAT" 257313 T CFCAT (NIL) -9 NIL NIL NIL) (-144 256318 256447 256630 "CDEN" 256979 NIL CDEN (NIL T T T) -7 NIL NIL NIL) (-143 252029 255471 255751 "CCLASS" 256058 T CCLASS (NIL) -8 NIL NIL NIL) (-142 251250 251437 251614 "CATEGORY" 251872 T -10 (NIL) -8 NIL NIL NIL) (-141 250745 251169 251217 "CATCTOR" 251222 T CATCTOR (NIL) -8 NIL NIL NIL) (-140 250136 250448 250546 "CATAST" 250667 T CATAST (NIL) -8 NIL NIL NIL) (-139 249552 249857 249949 "CASEAST" 250064 T CASEAST (NIL) -8 NIL NIL NIL) (-138 248648 248808 249029 "CARTEN2" 249399 NIL CARTEN2 (NIL NIL NIL T T) -7 NIL NIL NIL) (-137 243545 244805 245549 "CARTEN" 247960 NIL CARTEN (NIL NIL NIL T) -8 NIL NIL NIL) (-136 241675 242695 242952 "CARD" 243308 T CARD (NIL) -8 NIL NIL NIL) (-135 241197 241479 241554 "CAPSLAST" 241620 T CAPSLAST (NIL) -8 NIL NIL NIL) (-134 240639 240895 240923 "CACHSET" 241055 T CACHSET (NIL) -9 NIL 241133 NIL) (-133 240029 240417 240445 "CABMON" 240495 T CABMON (NIL) -9 NIL 240551 NIL) (-132 239466 239733 239843 "BYTEORD" 239939 T BYTEORD (NIL) -8 NIL NIL NIL) (-131 234507 238971 239143 "BYTEBUF" 239314 T BYTEBUF (NIL) -8 NIL NIL NIL) (-130 233338 234050 234185 "BYTE" 234348 T BYTE (NIL) -8 NIL NIL 234463) (-129 230714 233030 233137 "BTREE" 233264 NIL BTREE (NIL T) -8 NIL NIL NIL) (-128 228030 230362 230484 "BTOURN" 230624 NIL BTOURN (NIL T) -8 NIL NIL NIL) (-127 225248 227472 227513 "BTCAT" 227581 NIL BTCAT (NIL T) -9 NIL 227658 NIL) (-126 224897 224995 225144 "BTCAT-" 225149 NIL BTCAT- (NIL T T) -8 NIL NIL NIL) (-125 219900 224143 224171 "BTAGG" 224285 T BTAGG (NIL) -9 NIL 224395 NIL) (-124 219354 219515 219721 "BTAGG-" 219726 NIL BTAGG- (NIL T) -8 NIL NIL NIL) (-123 216204 218632 218847 "BSTREE" 219171 NIL BSTREE (NIL T) -8 NIL NIL NIL) (-122 215312 215468 215652 "BRILL" 216060 NIL BRILL (NIL T) -7 NIL NIL NIL) (-121 211818 214010 214051 "BRAGG" 214700 NIL BRAGG (NIL T) -9 NIL 214958 NIL) (-120 210251 210753 211308 "BRAGG-" 211313 NIL BRAGG- (NIL T T) -8 NIL NIL NIL) (-119 202508 209595 209780 "BPADICRT" 210098 NIL BPADICRT (NIL NIL) -8 NIL NIL NIL) (-118 200524 202445 202490 "BPADIC" 202495 NIL BPADIC (NIL NIL) -8 NIL NIL NIL) (-117 200216 200252 200366 "BOUNDZRO" 200488 NIL BOUNDZRO (NIL T T) -7 NIL NIL NIL) (-116 197943 198401 198876 "BOP1" 199774 NIL BOP1 (NIL T) -7 NIL NIL NIL) (-115 192973 194403 195301 "BOP" 197065 T BOP (NIL) -8 NIL NIL NIL) (-114 191638 192561 192703 "BOOLEAN" 192851 T BOOLEAN (NIL) -8 NIL NIL NIL) (-113 191231 191388 191416 "BOOLE" 191527 T BOOLE (NIL) -9 NIL 191608 NIL) (-112 191099 191126 191192 "BOOLE-" 191197 NIL BOOLE- (NIL T) -8 NIL NIL NIL) (-111 190268 190768 190822 "BMODULE" 190827 NIL BMODULE (NIL T T) -9 NIL 190892 NIL) (-110 185703 190066 190139 "BITS" 190215 T BITS (NIL) -8 NIL NIL NIL) (-109 185100 185243 185383 "BINDING" 185583 T BINDING (NIL) -8 NIL NIL NIL) (-108 178160 184695 184844 "BINARY" 184971 T BINARY (NIL) -8 NIL NIL NIL) (-107 175878 177387 177428 "BGAGG" 177688 NIL BGAGG (NIL T) -9 NIL 177825 NIL) (-106 175703 175741 175832 "BGAGG-" 175837 NIL BGAGG- (NIL T T) -8 NIL NIL NIL) (-105 174726 175087 175292 "BFUNCT" 175518 T BFUNCT (NIL) -8 NIL NIL NIL) (-104 173396 173594 173882 "BEZOUT" 174550 NIL BEZOUT (NIL T T T T T) -7 NIL NIL NIL) (-103 169708 172248 172578 "BBTREE" 173099 NIL BBTREE (NIL T) -8 NIL NIL NIL) (-102 169291 169387 169415 "BASTYPE" 169592 T BASTYPE (NIL) -9 NIL 169691 NIL) (-101 168949 169048 169183 "BASTYPE-" 169188 NIL BASTYPE- (NIL T) -8 NIL NIL NIL) (-100 168371 168459 168611 "BALFACT" 168860 NIL BALFACT (NIL T T) -7 NIL NIL NIL) (-99 167107 167786 167972 "AUTOMOR" 168216 NIL AUTOMOR (NIL T) -8 NIL NIL NIL) (-98 166833 166838 166864 "ATTREG" 166869 T ATTREG (NIL) -9 NIL NIL NIL) (-97 164995 165530 165882 "ATTRBUT" 166499 T ATTRBUT (NIL) -8 NIL NIL NIL) (-96 164549 164823 164889 "ATTRAST" 164947 T ATTRAST (NIL) -8 NIL NIL NIL) (-95 164049 164198 164224 "ATRIG" 164425 T ATRIG (NIL) -9 NIL NIL NIL) (-94 163846 163899 163986 "ATRIG-" 163991 NIL ATRIG- (NIL T) -8 NIL NIL NIL) (-93 163429 163663 163689 "ASTCAT" 163694 T ASTCAT (NIL) -9 NIL 163724 NIL) (-92 163138 163215 163334 "ASTCAT-" 163339 NIL ASTCAT- (NIL T) -8 NIL NIL NIL) (-91 161226 162914 163002 "ASTACK" 163081 NIL ASTACK (NIL T) -8 NIL NIL NIL) (-90 159715 160028 160393 "ASSOCEQ" 160908 NIL ASSOCEQ (NIL T T) -7 NIL NIL NIL) (-89 158639 159374 159498 "ASP9" 159622 NIL ASP9 (NIL NIL) -8 NIL NIL NIL) (-88 157399 158244 158386 "ASP80" 158528 NIL ASP80 (NIL NIL) -8 NIL NIL NIL) (-87 157127 157347 157386 "ASP8" 157391 NIL ASP8 (NIL NIL) -8 NIL NIL NIL) (-86 155973 156804 156922 "ASP78" 157040 NIL ASP78 (NIL NIL) -8 NIL NIL NIL) (-85 154834 155653 155770 "ASP77" 155887 NIL ASP77 (NIL NIL) -8 NIL NIL NIL) (-84 153638 154472 154603 "ASP74" 154734 NIL ASP74 (NIL NIL) -8 NIL NIL NIL) (-83 152430 153273 153405 "ASP73" 153537 NIL ASP73 (NIL NIL) -8 NIL NIL NIL) (-82 151220 152065 152197 "ASP7" 152329 NIL ASP7 (NIL NIL) -8 NIL NIL NIL) (-81 150216 151046 151146 "ASP6" 151151 NIL ASP6 (NIL NIL) -8 NIL NIL NIL) (-80 149055 149893 150011 "ASP55" 150129 NIL ASP55 (NIL NIL) -8 NIL NIL NIL) (-79 147896 148729 148848 "ASP50" 148967 NIL ASP50 (NIL NIL) -8 NIL NIL NIL) (-78 146876 147597 147707 "ASP49" 147817 NIL ASP49 (NIL NIL) -8 NIL NIL NIL) (-77 145552 146415 146583 "ASP42" 146765 NIL ASP42 (NIL NIL NIL NIL) -8 NIL NIL NIL) (-76 144221 145085 145255 "ASP41" 145439 NIL ASP41 (NIL NIL NIL NIL) -8 NIL NIL NIL) (-75 143201 143922 144032 "ASP4" 144142 NIL ASP4 (NIL NIL) -8 NIL NIL NIL) (-74 142043 142878 142996 "ASP35" 143114 NIL ASP35 (NIL NIL) -8 NIL NIL NIL) (-73 141772 141991 142030 "ASP34" 142035 NIL ASP34 (NIL NIL) -8 NIL NIL NIL) (-72 141491 141576 141652 "ASP33" 141727 NIL ASP33 (NIL NIL) -8 NIL NIL NIL) (-71 140277 141126 141258 "ASP31" 141390 NIL ASP31 (NIL NIL) -8 NIL NIL NIL) (-70 140006 140225 140264 "ASP30" 140269 NIL ASP30 (NIL NIL) -8 NIL NIL NIL) (-69 139723 139810 139886 "ASP29" 139961 NIL ASP29 (NIL NIL) -8 NIL NIL NIL) (-68 139452 139671 139710 "ASP28" 139715 NIL ASP28 (NIL NIL) -8 NIL NIL NIL) (-67 139181 139400 139439 "ASP27" 139444 NIL ASP27 (NIL NIL) -8 NIL NIL NIL) (-66 138157 138879 138990 "ASP24" 139101 NIL ASP24 (NIL NIL) -8 NIL NIL NIL) (-65 137126 137959 138071 "ASP20" 138076 NIL ASP20 (NIL NIL) -8 NIL NIL NIL) (-64 135961 136800 136919 "ASP19" 137038 NIL ASP19 (NIL NIL) -8 NIL NIL NIL) (-63 135680 135765 135841 "ASP12" 135916 NIL ASP12 (NIL NIL) -8 NIL NIL NIL) (-62 134424 135279 135423 "ASP10" 135567 NIL ASP10 (NIL NIL) -8 NIL NIL NIL) (-61 133404 134125 134235 "ASP1" 134345 NIL ASP1 (NIL NIL) -8 NIL NIL NIL) (-60 131130 133248 133339 "ARRAY2" 133344 NIL ARRAY2 (NIL T) -8 NIL NIL NIL) (-59 130144 130335 130556 "ARRAY12" 130953 NIL ARRAY12 (NIL T T) -7 NIL NIL NIL) (-58 125618 129792 129906 "ARRAY1" 130061 NIL ARRAY1 (NIL T) -8 NIL NIL NIL) (-57 119774 121820 121895 "ARR2CAT" 124525 NIL ARR2CAT (NIL T T T) -9 NIL 125283 NIL) (-56 117373 118150 119005 "ARR2CAT-" 119010 NIL ARR2CAT- (NIL T T T T) -8 NIL NIL NIL) (-55 116624 117000 117125 "ARITY" 117266 T ARITY (NIL) -8 NIL NIL NIL) (-54 115382 115552 115851 "APPRULE" 116460 NIL APPRULE (NIL T T T) -7 NIL NIL NIL) (-53 115027 115081 115200 "APPLYORE" 115328 NIL APPLYORE (NIL T T T) -7 NIL NIL NIL) (-52 114281 114428 114585 "ANY1" 114901 NIL ANY1 (NIL T) -7 NIL NIL NIL) (-51 113581 113874 113994 "ANY" 114179 T ANY (NIL) -8 NIL NIL NIL) (-50 110907 112018 112345 "ANTISYM" 113305 NIL ANTISYM (NIL T NIL) -8 NIL NIL NIL) (-49 110351 110614 110710 "ANON" 110829 T ANON (NIL) -8 NIL NIL NIL) (-48 103514 108890 109344 "AN" 109915 T AN (NIL) -8 NIL NIL NIL) (-47 99177 100786 100837 "AMR" 101585 NIL AMR (NIL T T) -9 NIL 102185 NIL) (-46 98229 98510 98873 "AMR-" 98878 NIL AMR- (NIL T T T) -8 NIL NIL NIL) (-45 81698 98146 98207 "ALIST" 98212 NIL ALIST (NIL T T) -8 NIL NIL NIL) (-44 77995 81292 81461 "ALGSC" 81616 NIL ALGSC (NIL T NIL NIL NIL) -8 NIL NIL NIL) (-43 74445 75105 75712 "ALGPKG" 77435 NIL ALGPKG (NIL T T) -7 NIL NIL NIL) (-42 73710 73823 74007 "ALGMFACT" 74331 NIL ALGMFACT (NIL T T T) -7 NIL NIL NIL) (-41 69693 70324 70918 "ALGMANIP" 73294 NIL ALGMANIP (NIL T T) -7 NIL NIL NIL) (-40 59053 69319 69469 "ALGFF" 69626 NIL ALGFF (NIL T T T NIL) -8 NIL NIL NIL) (-39 58225 58380 58559 "ALGFACT" 58911 NIL ALGFACT (NIL T) -7 NIL NIL NIL) (-38 57014 57752 57790 "ALGEBRA" 57795 NIL ALGEBRA (NIL T) -9 NIL 57836 NIL) (-37 56714 56791 56923 "ALGEBRA-" 56928 NIL ALGEBRA- (NIL T T) -8 NIL NIL NIL) (-36 37668 54551 54603 "ALAGG" 54739 NIL ALAGG (NIL T T) -9 NIL 54900 NIL) (-35 37168 37317 37343 "AHYP" 37544 T AHYP (NIL) -9 NIL NIL NIL) (-34 36470 36653 36679 "AGG" 36962 T AGG (NIL) -9 NIL 37151 NIL) (-33 36177 36264 36379 "AGG-" 36384 NIL AGG- (NIL T) -8 NIL NIL NIL) (-32 33937 34406 34811 "AF" 35819 NIL AF (NIL T T) -7 NIL NIL NIL) (-31 33357 33662 33752 "ADDAST" 33865 T ADDAST (NIL) -8 NIL NIL NIL) (-30 32589 32884 33040 "ACPLOT" 33219 T ACPLOT (NIL) -8 NIL NIL NIL) (-29 20153 29521 29559 "ACFS" 30166 NIL ACFS (NIL T) -9 NIL 30405 NIL) (-28 18060 18670 19432 "ACFS-" 19437 NIL ACFS- (NIL T T) -8 NIL NIL NIL) (-27 13768 16093 16119 "ACF" 16998 T ACF (NIL) -9 NIL 17411 NIL) (-26 12400 12806 13299 "ACF-" 13304 NIL ACF- (NIL T) -8 NIL NIL NIL) (-25 11910 12153 12179 "ABELSG" 12271 T ABELSG (NIL) -9 NIL 12336 NIL) (-24 11771 11802 11868 "ABELSG-" 11873 NIL ABELSG- (NIL T) -8 NIL NIL NIL) (-23 11040 11387 11413 "ABELMON" 11583 T ABELMON (NIL) -9 NIL 11695 NIL) (-22 10680 10788 10926 "ABELMON-" 10931 NIL ABELMON- (NIL T) -8 NIL NIL NIL) (-21 9930 10386 10412 "ABELGRP" 10484 T ABELGRP (NIL) -9 NIL 10559 NIL) (-20 9357 9522 9738 "ABELGRP-" 9743 NIL ABELGRP- (NIL T) -8 NIL NIL NIL) (-19 4579 8619 8658 "A1AGG" 8663 NIL A1AGG (NIL T) -9 NIL 8703 NIL) (-18 30 1497 3059 "A1AGG-" 3064 NIL A1AGG- (NIL T T) -8 NIL NIL NIL))
\ No newline at end of file diff --git a/src/share/algebra/operation.daase b/src/share/algebra/operation.daase index 5480399c..48c8d5de 100644 --- a/src/share/algebra/operation.daase +++ b/src/share/algebra/operation.daase @@ -1,311 +1,468 @@ -(733460 . 3514823550) -(((*1 *2 *3 *4 *4) - (-12 (-5 *4 (-114)) (-4 *5 (-466)) (-4 *6 (-817)) (-4 *7 (-872)) - (-4 *8 (-1097 *5 *6 *7)) - (-5 *2 - (-2 (|:| |val| (-663 *8)) - (|:| |towers| (-663 (-1059 *5 *6 *7 *8))))) - (-5 *1 (-1059 *5 *6 *7 *8)) (-5 *3 (-663 *8)))) - ((*1 *2 *3 *4 *4) - (-12 (-5 *4 (-114)) (-4 *5 (-466)) (-4 *6 (-817)) (-4 *7 (-872)) - (-4 *8 (-1097 *5 *6 *7)) - (-5 *2 - (-2 (|:| |val| (-663 *8)) - (|:| |towers| (-663 (-1178 *5 *6 *7 *8))))) - (-5 *1 (-1178 *5 *6 *7 *8)) (-5 *3 (-663 *8))))) -(((*1 *2 *3 *2) - (-12 (-5 *3 (-1 (-114) *4 *4)) (-4 *4 (-1249)) (-5 *1 (-388 *4 *2)) - (-4 *2 (-13 (-385 *4) (-10 -7 (-6 -4511))))))) -(((*1 *2 *3) (-12 (-5 *3 (-229)) (-5 *2 (-421 (-560))) (-5 *1 (-315))))) -(((*1 *2 *3 *4) - (-12 (-4 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(-12 (-4 *3 (-466)) (-5 *1 (-1241 *3 *2)) - (-4 *2 (-13 (-435 *3) (-1235)))))) -(((*1 *2 *3) - (-12 (-5 *3 (-255 *4 *5)) (-14 *4 (-663 (-1209))) (-4 *5 (-466)) - (-5 *2 (-495 *4 *5)) (-5 *1 (-650 *4 *5))))) -(((*1 *1 *2) (-12 (-5 *2 (-1191)) (-5 *1 (-591)))) - ((*1 *1 *2) (-12 (-5 *2 (-402)) (-5 *1 (-591))))) -(((*1 *2 *2) - (-12 (-5 *2 (-663 *6)) (-4 *6 (-1097 *3 *4 *5)) (-4 *3 (-149)) - (-4 *3 (-319)) (-4 *3 (-571)) (-4 *4 (-817)) (-4 *5 (-872)) - (-5 *1 (-1009 *3 *4 *5 *6))))) -(((*1 *2 *2) (-12 (-5 *2 (-114)) (-5 *1 (-1067))))) -(((*1 *2 *3 *3) - (-12 (-4 *4 (-571)) - (-5 *2 (-2 (|:| |coef1| *3) (|:| |coef2| *3) (|:| -2434 *4))) - (-5 *1 (-1001 *4 *3)) (-4 *3 (-1275 *4))))) -(((*1 *1 *2 *2 *3) (-12 (-5 *2 (-560)) (-5 *3 (-949)) (-5 *1 (-721)))) - ((*1 *2 *2 *2 *3 *4) - (-12 (-5 *2 (-711 *5)) (-5 *3 (-99 *5)) (-5 *4 (-1 *5 *5)) - (-4 *5 (-376)) (-5 *1 (-1010 *5))))) -(((*1 *2) - (-12 (-4 *4 (-175)) (-5 *2 (-114)) (-5 *1 (-379 *3 *4)) - (-4 *3 (-380 *4)))) - ((*1 *2) (-12 (-4 *1 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(-5 *1 (-850))))) -(((*1 *2 *3 *4) - (-12 (-5 *4 (-1 *3 *3)) (-4 *3 (-1275 *5)) (-4 *5 (-376)) - (-5 *2 (-2 (|:| -3082 (-419 *3)) (|:| |special| (-419 *3)))) - (-5 *1 (-749 *5 *3))))) + (-12 (-4 *4 (-571)) (-4 *4 (-175)) (-4 *5 (-385 *4)) + (-4 *6 (-385 *4)) (-5 *2 (-2 (|:| |adjMat| *3) (|:| |detMat| *4))) + (-5 *1 (-710 *4 *5 *6 *3)) (-4 *3 (-708 *4 *5 *6)))) + ((*1 *1 *1 *1) + (-12 (-4 *2 (-175)) (-4 *2 (-1081)) (-5 *1 (-736 *2 *3)) + (-4 *3 (-670 *2)))) + ((*1 *1 *1) + (-12 (-4 *2 (-175)) (-4 *2 (-1081)) (-5 *1 (-736 *2 *3)) + (-4 *3 (-670 *2)))) + ((*1 *1 *1 *1) (-12 (-5 *1 (-858 *2)) (-4 *2 (-175)) (-4 *2 (-1081)))) + ((*1 *1 *1) (-12 (-5 *1 (-858 *2)) (-4 *2 (-175)) (-4 *2 (-1081))))) +(((*1 *2 *1 *1 *3) + (-12 (-5 *3 (-1 (-114) *5 *5)) (-4 *5 (-13 (-1133) (-34))) + (-5 *2 (-114)) (-5 *1 (-1172 *4 *5)) (-4 *4 (-13 (-1133) (-34)))))) (((*1 *2 *3 *4) - (-12 (-5 *3 (-229)) (-5 *4 (-560)) (-5 *2 (-1067)) (-5 *1 (-780))))) + (-12 (-4 *5 (-466)) (-4 *6 (-817)) (-4 *7 (-872)) + (-4 *3 (-1097 *5 *6 *7)) (-5 *2 (-663 *4)) + (-5 *1 (-1104 *5 *6 *7 *3 *4)) (-4 *4 (-1103 *5 *6 *7 *3))))) +(((*1 *2 *1 *1) (-12 (-4 *1 (-571)) (-5 *2 (-114))))) +(((*1 *2 *1) + (-12 (-4 *3 (-1081)) (-4 *4 (-1133)) (-5 *2 (-663 *1)) + (-4 *1 (-397 *3 *4)))) + ((*1 *2 *1) + (-12 (-5 *2 (-663 (-757 *3 *4))) (-5 *1 (-757 *3 *4)) (-4 *3 (-1081)) + (-4 *4 (-748)))) + ((*1 *2 *1) + (-12 (-4 *3 (-1081)) (-4 *4 (-817)) (-4 *5 (-872)) (-5 *2 (-663 *1)) + (-4 *1 (-980 *3 *4 *5))))) +(((*1 *2 *1) + (-12 (-4 *4 (-1133)) (-5 *2 (-114)) (-5 *1 (-911 *3 *4 *5)) + (-4 *3 (-1133)) (-4 *5 (-688 *4)))) + ((*1 *2 *1) + (-12 (-5 *2 (-114)) (-5 *1 (-914 *3 *4)) (-4 *3 (-1133)) + (-4 *4 (-1133))))) +(((*1 *2 *3 *4 *5 *6) + (|partial| -12 (-5 *4 (-1 *8 *8)) + (-5 *5 + (-1 (-3 (-2 (|:| -3447 *7) (|:| |coeff| *7)) "failed") *7)) + (-5 *6 (-663 (-421 *8))) (-4 *7 (-376)) (-4 *8 (-1275 *7)) + (-5 *3 (-421 *8)) + (-5 *2 + (-2 + (|:| |answer| + (-2 (|:| |mainpart| *3) + (|:| |limitedlogs| + (-663 (-2 (|:| |coeff| *3) (|:| |logand| *3)))))) + (|:| |a0| *7))) + (-5 *1 (-588 *7 *8))))) +(((*1 *2 *2 *2) + (-12 + (-5 *2 + (-2 (|:| -4206 (-711 *3)) (|:| |basisDen| *3) + (|:| |basisInv| (-711 *3)))) + (-4 *3 (-13 (-319) (-10 -8 (-15 -2218 ((-419 $) $))))) + (-4 *4 (-1275 *3)) (-5 *1 (-513 *3 *4 *5)) (-4 *5 (-424 *3 *4))))) +(((*1 *1 *1) (-12 (-4 *1 (-1292 *2)) (-4 *2 (-1081))))) +(((*1 *2 *1 *3) (-12 (-5 *3 (-1191)) (-5 *2 (-1305)) (-5 *1 (-1303))))) +(((*1 *1 *1) (-5 *1 (-1095)))) +(((*1 *2 *2) (|partial| -12 (-4 *1 (-1015 *2)) (-4 *2 (-1235))))) +(((*1 *2 *3) + (-12 (-4 *4 (-363)) + (-5 *2 (-663 (-2 (|:| |deg| (-793)) (|:| -1604 *3)))) + (-5 *1 (-220 *4 *3)) (-4 *3 (-1275 *4))))) +(((*1 *2 *2 *1 *3 *4) + (-12 (-5 *2 (-663 *8)) (-5 *3 (-1 *8 *8 *8)) + (-5 *4 (-1 (-114) *8 *8)) (-4 *1 (-1244 *5 *6 *7 *8)) (-4 *5 (-571)) + (-4 *6 (-817)) (-4 *7 (-872)) (-4 *8 (-1097 *5 *6 *7))))) (((*1 *2 *1) (-12 (-5 *2 (-1167)) (-5 *1 (-31)))) ((*1 *2 *1) (-12 (-5 *2 (-1214)) (-5 *1 (-49)))) ((*1 *2 *1) (-12 (-5 *2 (-663 (-1167))) (-5 *1 (-135)))) @@ -317,22 +474,26 @@ ((*1 *2 *1) (-12 (-5 *2 (-1167)) (-5 *1 (-1051)))) ((*1 *2 *1) (-12 (-5 *2 (-1167)) (-5 *1 (-1098)))) ((*1 *2 *1) (-12 (-5 *2 (-663 (-1167))) (-5 *1 (-1128))))) -(((*1 *2 *3) (-12 (-5 *3 (-888)) (-5 *2 (-1191)) (-5 *1 (-732))))) -(((*1 *2 *3 *4) - (-12 (-5 *3 (-663 *5)) (-5 *4 (-949)) (-4 *5 (-872)) - (-5 *2 (-58 (-663 (-694 *5)))) (-5 *1 (-694 *5))))) +(((*1 *2 *2 *2) + (-12 (-4 *3 (-376)) (-5 *1 (-788 *2 *3)) (-4 *2 (-730 *3)))) + ((*1 *1 *1 *1) (-12 (-4 *1 (-877 *2)) (-4 *2 (-1081)) (-4 *2 (-376))))) (((*1 *1 *1) - (-12 (-5 *1 (-609 *2)) (-4 *2 (-38 (-421 (-560)))) (-4 *2 (-1081))))) + (|partial| -12 (-4 *1 (-380 *2)) (-4 *2 (-175)) (-4 *2 (-571)))) + ((*1 *1 *1) (|partial| -4 *1 (-744)))) +(((*1 *2 *1) (-12 (-5 *2 (-114)) (-5 *1 (-448))))) +(((*1 *2 *1 *3) (-12 (-4 *1 (-134)) (-5 *3 (-793)) (-5 *2 (-1305))))) +(((*1 *2 *1) + (-12 (-5 *2 (-663 (-1236 *3))) (-5 *1 (-1236 *3)) (-4 *3 (-1133))))) (((*1 *1 *2) (-12 (-5 *2 (-663 *3)) (-4 *3 (-1249)) (-4 *1 (-153 *3)))) ((*1 *1 *2) (-12 - (-5 *2 (-663 (-2 (|:| -4067 (-793)) (|:| -1792 *4) (|:| |num| *4)))) + (-5 *2 (-663 (-2 (|:| -1946 (-793)) (|:| -1839 *4) (|:| |num| *4)))) (-4 *4 (-1275 *3)) (-4 *3 (-13 (-376) (-149))) (-5 *1 (-413 *3 *4)))) ((*1 *1 *2 *3 *4) - (-12 (-5 *2 (-3 (|:| |fst| (-448)) (|:| -4231 "void"))) + (-12 (-5 *2 (-3 (|:| |fst| (-448)) (|:| -4209 "void"))) (-5 *3 (-663 (-976 (-560)))) (-5 *4 (-114)) (-5 *1 (-450)))) ((*1 *1 *2 *3 *4) - (-12 (-5 *2 (-3 (|:| |fst| (-448)) (|:| -4231 "void"))) + (-12 (-5 *2 (-3 (|:| |fst| (-448)) (|:| -4209 "void"))) (-5 *3 (-663 (-1209))) (-5 *4 (-114)) (-5 *1 (-450)))) ((*1 *2 *1) (-12 (-5 *2 (-1187 *3)) (-5 *1 (-615 *3)) (-4 *3 (-1249)))) @@ -352,24 +513,24 @@ ((*1 *1 *2 *3) (-12 (-5 *1 (-735 *2 *3 *4)) (-4 *2 (-872)) (-4 *3 (-1133)) (-14 *4 - (-1 (-114) (-2 (|:| -2183 *2) (|:| -4067 *3)) - (-2 (|:| -2183 *2) (|:| -4067 *3)))))) + (-1 (-114) (-2 (|:| -2175 *2) (|:| -1946 *3)) + (-2 (|:| -2175 *2) (|:| -1946 *3)))))) ((*1 *1 *2 *3) (-12 (-5 *2 (-520)) (-5 *3 (-1147)) (-5 *1 (-862)))) ((*1 *1 *2 *3) (-12 (-5 *1 (-898 *2 *3)) (-4 *2 (-1249)) (-4 *3 (-1249)))) ((*1 *1 *2) - (-12 (-5 *2 (-663 (-2 (|:| -2118 (-1209)) (|:| -3964 *4)))) + (-12 (-5 *2 (-663 (-2 (|:| -2115 (-1209)) (|:| -3934 *4)))) (-4 *4 (-1133)) (-5 *1 (-914 *3 *4)) (-4 *3 (-1133)))) ((*1 *2 *3 *4) (-12 (-5 *4 (-663 *5)) (-4 *5 (-13 (-1133) (-34))) (-5 *2 (-663 (-1172 *3 *5))) (-5 *1 (-1172 *3 *5)) (-4 *3 (-13 (-1133) (-34))))) ((*1 *2 *3) - (-12 (-5 *3 (-663 (-2 (|:| |val| *4) (|:| -4466 *5)))) + (-12 (-5 *3 (-663 (-2 (|:| |val| *4) (|:| -4461 *5)))) (-4 *4 (-13 (-1133) (-34))) (-4 *5 (-13 (-1133) (-34))) (-5 *2 (-663 (-1172 *4 *5))) (-5 *1 (-1172 *4 *5)))) ((*1 *1 *2) - (-12 (-5 *2 (-2 (|:| |val| *3) (|:| -4466 *4))) + (-12 (-5 *2 (-2 (|:| |val| *3) (|:| -4461 *4))) (-4 *3 (-13 (-1133) (-34))) (-4 *4 (-13 (-1133) (-34))) (-5 *1 (-1172 *3 *4)))) ((*1 *1 *2 *3) @@ -392,42 +553,38 @@ (-4 *4 (-13 (-1133) (-34))) (-5 *1 (-1173 *3 *4)))) ((*1 *1 *2 *3) (-12 (-5 *1 (-1198 *2 *3)) (-4 *2 (-1133)) (-4 *3 (-1133))))) -(((*1 *1 *1) - (-12 (-5 *1 (-1173 *2 *3)) (-4 *2 (-13 (-1133) (-34))) - (-4 *3 (-13 (-1133) (-34)))))) -(((*1 *2) (-12 (-5 *2 (-114)) (-5 *1 (-955))))) -(((*1 *2 *3 *4 *3) - (-12 (-5 *3 (-560)) (-5 *4 (-711 (-229))) (-5 *2 (-1067)) - (-5 *1 (-769))))) -(((*1 *2 *1) (-12 (-5 *2 (-663 (-976 (-560)))) (-5 *1 (-450)))) - ((*1 *2 *3 *4) - (-12 (-5 *3 (-1209)) (-5 *4 (-711 (-229))) (-5 *2 (-1135)) - (-5 *1 (-781)))) +(((*1 *2 *3 *4 *4 *5 *3 *3 *4 *3) + (-12 (-5 *3 (-560)) (-5 *5 (-711 (-229))) (-5 *4 (-229)) + (-5 *2 (-1067)) (-5 *1 (-774))))) +(((*1 *2 *3 *4 *5 *5 *6) + (-12 (-5 *3 (-1 (-229) (-229) (-229))) + (-5 *4 (-3 (-1 (-229) (-229) (-229) (-229)) "undefined")) + (-5 *5 (-1121 (-229))) (-5 *6 (-663 (-270))) (-5 *2 (-1165 (-229))) + (-5 *1 (-719))))) +(((*1 *1 *2) (-12 (-5 *2 (-1 (-229) (-229))) (-5 *1 (-955)))) + ((*1 *1 *2 *3) + (-12 (-5 *2 (-1 (-229) (-229))) (-5 *3 (-1121 (-229))) + (-5 *1 (-955)))) + ((*1 *2 *3 *4 *5) + (-12 (-5 *4 (-1209)) (-5 *5 (-1121 (-229))) (-5 *2 (-955)) + (-5 *1 (-956 *3)) (-4 *3 (-633 (-549))))) ((*1 *2 *3 *4) - (-12 (-5 *3 (-1209)) (-5 *4 (-711 (-560))) (-5 *2 (-1135)) - (-5 *1 (-781))))) + (-12 (-5 *4 (-1209)) (-5 *2 (-955)) (-5 *1 (-956 *3)) + (-4 *3 (-633 (-549)))))) (((*1 *2 *3) - (-12 + (-12 (-4 *1 (-863)) (-5 *3 - (-2 (|:| -2672 (-391)) (|:| -4401 (-1191)) - (|:| |explanations| (-663 (-1191))))) - (-5 *2 (-1067)) (-5 *1 (-315)))) + (-2 (|:| |fn| (-326 (-229))) (|:| -2543 (-663 (-229))) + (|:| |lb| (-663 (-866 (-229)))) (|:| |cf| (-663 (-326 (-229)))) + (|:| |ub| (-663 (-866 (-229)))))) + (-5 *2 (-1067)))) ((*1 *2 *3) - (-12 + (-12 (-4 *1 (-863)) (-5 *3 - (-2 (|:| -2672 (-391)) (|:| -4401 (-1191)) - (|:| |explanations| (-663 (-1191))) (|:| |extra| (-1067)))) - (-5 *2 (-1067)) (-5 *1 (-315))))) -(((*1 *2 *1 *3) - (-12 (-5 *3 (-949)) (-4 *4 (-381)) (-4 *4 (-376)) (-5 *2 (-1203 *1)) - (-4 *1 (-341 *4)))) - ((*1 *2 *1) (-12 (-4 *1 (-341 *3)) (-4 *3 (-376)) (-5 *2 (-1203 *3)))) - ((*1 *2 *1) - (-12 (-4 *1 (-383 *3 *2)) (-4 *3 (-175)) (-4 *3 (-376)) - (-4 *2 (-1275 *3)))) - ((*1 *2 *3) - (-12 (-5 *3 (-1299 *4)) (-4 *4 (-363)) (-5 *2 (-1203 *4)) - (-5 *1 (-542 *4))))) + (-2 (|:| |lfn| (-663 (-326 (-229)))) (|:| -2543 (-663 (-229))))) + (-5 *2 (-1067))))) +(((*1 *1 *1) + (-12 (-5 *1 (-609 *2)) (-4 *2 (-38 (-421 (-560)))) (-4 *2 (-1081))))) (((*1 *2 *1) (-12 (-5 *2 (-1167)) (-5 *1 (-96)))) ((*1 *2 *1) (-12 (-5 *2 (-520)) (-5 *1 (-109)))) ((*1 *2 *1) @@ -441,37 +598,34 @@ ((*1 *2 *1) (-12 (-5 *2 (-1209)) (-5 *1 (-1108 *3)) (-14 *3 *2))) ((*1 *2 *1) (-12 (-5 *2 (-520)) (-5 *1 (-1148)))) ((*1 *1 *1) (-5 *1 (-1209)))) +(((*1 *2 *3) + (-12 (-5 *3 (-973 *2)) (-5 *1 (-1014 *2)) (-4 *2 (-1081))))) +(((*1 *2 *1) (-12 (-5 *2 (-114)) (-5 *1 (-448))))) +(((*1 *2 *2 *3 *2) + (-12 (-5 *3 (-793)) (-4 *4 (-363)) (-5 *1 (-220 *4 *2)) + (-4 *2 (-1275 *4)))) + ((*1 *2 *2 *3 *2 *3) + (-12 (-5 *3 (-560)) (-5 *1 (-718 *2)) (-4 *2 (-1275 *3))))) +(((*1 *1 *2) (-12 (-5 *2 (-793)) (-5 *1 (-286))))) (((*1 *2 *1) - (-12 (-4 *3 (-1081)) (-5 *2 (-663 *1)) (-4 *1 (-1166 *3))))) + (-12 (-5 *2 (-663 (-51))) (-5 *1 (-916 *3)) (-4 *3 (-1133))))) +(((*1 *1 *2) + (|partial| -12 (-5 *2 (-663 *6)) (-4 *6 (-1097 *3 *4 *5)) + (-4 *3 (-571)) (-4 *4 (-817)) (-4 *5 (-872)) + (-5 *1 (-1313 *3 *4 *5 *6)))) + ((*1 *1 *2 *3 *4) + (|partial| -12 (-5 *2 (-663 *8)) (-5 *3 (-1 (-114) *8 *8)) + (-5 *4 (-1 *8 *8 *8)) (-4 *8 (-1097 *5 *6 *7)) (-4 *5 (-571)) + (-4 *6 (-817)) (-4 *7 (-872)) (-5 *1 (-1313 *5 *6 *7 *8))))) (((*1 *2 *2 *3) - (-12 (-5 *3 (-1209)) (-4 *4 (-571)) (-5 *1 (-160 *4 *2)) - (-4 *2 (-435 *4)))) - ((*1 *2 *2 *3) - (-12 (-5 *3 (-1124 *2)) (-4 *2 (-435 *4)) (-4 *4 (-571)) - (-5 *1 (-160 *4 *2)))) - ((*1 *1 *1 *2) (-12 (-5 *2 (-1124 *1)) (-4 *1 (-162)))) - ((*1 *1 *1 *2) (-12 (-4 *1 (-162)) (-5 *2 (-1209))))) -(((*1 *1) (-5 *1 (-55)))) -(((*1 *2 *3 *1) - (-12 (-5 *3 (-1 (-114) *4)) (|has| *1 (-6 -4510)) (-4 *1 (-503 *4)) - (-4 *4 (-1249)) (-5 *2 (-114))))) -(((*1 *1 *1 *1) (-12 (-5 *1 (-305 *2)) (-4 *2 (-310)) (-4 *2 (-1249)))) - ((*1 *1 *1 *2 *3) - (-12 (-5 *2 (-663 (-630 *1))) (-5 *3 (-663 *1)) (-4 *1 (-310)))) - ((*1 *1 *1 *2) (-12 (-5 *2 (-663 (-305 *1))) (-4 *1 (-310)))) - ((*1 *1 *1 *2) (-12 (-5 *2 (-305 *1)) (-4 *1 (-310))))) -(((*1 *2 *1 *3 *4 *4 *4 *4 *5 *5 *5 *5 *6 *5 *6 *5) - (-12 (-5 *3 (-949)) (-5 *4 (-229)) (-5 *5 (-560)) (-5 *6 (-899)) - (-5 *2 (-1305)) (-5 *1 (-1302))))) -(((*1 *1 *1 *1 *1 *2) - (-12 (-5 *2 (-793)) (-4 *1 (-1097 *3 *4 *5)) (-4 *3 (-1081)) - (-4 *4 (-817)) (-4 *5 (-872)) (-4 *3 (-571))))) + (-12 (-5 *2 (-1299 *4)) (-5 *3 (-793)) (-4 *4 (-363)) + (-5 *1 (-542 *4))))) (((*1 *1 *1 *2) (-12 (-4 *1 (-47 *2 *3)) (-4 *2 (-1081)) (-4 *3 (-816)) (-4 *2 (-376)))) ((*1 *1 *1 *2) (-12 (-5 *2 (-560)) (-5 *1 (-229)))) ((*1 *1 *1 *1) - (-4144 (-12 (-5 *1 (-305 *2)) (-4 *2 (-376)) (-4 *2 (-1249))) + (-4118 (-12 (-5 *1 (-305 *2)) (-4 *2 (-376)) (-4 *2 (-1249))) (-12 (-5 *1 (-305 *2)) (-4 *2 (-487)) (-4 *2 (-1249))))) ((*1 *1 *1 *1) (-4 *1 (-376))) ((*1 *1 *1 *2) (-12 (-5 *2 (-560)) (-5 *1 (-391)))) @@ -519,48 +673,52 @@ ((*1 *1 *1 *2) (-12 (-5 *1 (-1323 *2 *3)) (-4 *2 (-376)) (-4 *2 (-1081)) (-4 *3 (-870))))) -(((*1 *2 *1 *3 *4) - (-12 (-5 *3 (-949)) (-5 *4 (-1191)) (-5 *2 (-1305)) (-5 *1 (-1302))))) -(((*1 *2 *1 *1) - (-12 (-4 *1 (-1131 *3)) (-4 *3 (-1133)) (-5 *2 (-114))))) -(((*1 *2) - (-12 (-4 *4 (-1254)) (-4 *5 (-1275 *4)) (-4 *6 (-1275 (-421 *5))) - (-5 *2 (-114)) (-5 *1 (-354 *3 *4 *5 *6)) (-4 *3 (-355 *4 *5 *6)))) - ((*1 *2) - (-12 (-4 *1 (-355 *3 *4 *5)) (-4 *3 (-1254)) (-4 *4 (-1275 *3)) - (-4 *5 (-1275 (-421 *4))) (-5 *2 (-114))))) -(((*1 *2 *1 *3 *3 *3) - (-12 (-5 *3 (-391)) (-5 *2 (-1305)) (-5 *1 (-1303))))) -(((*1 *1 *1) (-12 (-5 *1 (-305 *2)) (-4 *2 (-21)) (-4 *2 (-1249))))) -(((*1 *2 *1 *3 *3) - (-12 (-5 *3 (-949)) (-5 *2 (-1305)) (-5 *1 (-217 *4)) - (-4 *4 - (-13 (-872) - (-10 -8 (-15 -1497 ((-1191) $ (-1209))) (-15 -1857 (*2 $)) - (-15 -4387 (*2 $))))))) - ((*1 *2 *1) - (-12 (-5 *2 (-1305)) (-5 *1 (-217 *3)) - (-4 *3 - (-13 (-872) - (-10 -8 (-15 -1497 ((-1191) $ (-1209))) (-15 -1857 (*2 $)) - (-15 -4387 (*2 $))))))) - ((*1 *2 *1) (-12 (-5 *2 (-1305)) (-5 *1 (-516))))) -(((*1 *2 *3) - (-12 (-5 *3 (-1299 *4)) (-4 *4 (-1081)) (-4 *2 (-1275 *4)) - (-5 *1 (-458 *4 *2)))) - ((*1 *2 *3 *2 *4) - (-12 (-5 *2 (-421 (-1203 (-326 *5)))) (-5 *3 (-1299 (-326 *5))) - (-5 *4 (-560)) (-4 *5 (-571)) (-5 *1 (-1162 *5))))) -(((*1 *1 *1 *2) - (-12 (-5 *2 (-663 (-51))) (-5 *1 (-916 *3)) (-4 *3 (-1133))))) +(((*1 *1 *1 *2) (-12 (-5 *2 (-51)) (-5 *1 (-916 *3)) (-4 *3 (-1133)))) + ((*1 *2 *2 *3) + (-12 (-5 *2 (-916 *4)) (-4 *4 (-1133)) (-5 *1 (-917 *4 *3)) + (-4 *3 (-1249))))) +(((*1 *2 *2 *2) + (-12 (-5 *2 (-711 *3)) (-4 *3 (-1081)) (-5 *1 (-712 *3))))) +(((*1 *2 *3 *2 *4) + (|partial| -12 (-5 *4 (-1 (-3 (-560) "failed") *5)) (-4 *5 (-1081)) + (-5 *2 (-560)) (-5 *1 (-557 *5 *3)) (-4 *3 (-1275 *5)))) + ((*1 *2 *3 *4 *2 *5) + (|partial| -12 (-5 *5 (-1 (-3 (-560) "failed") 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(-1139 *4 *5 *6 *7 *8)) (-4 *8 (-1103 *4 *5 *6 *7)))) + ((*1 *2 *1 *1) + (-12 (-4 *1 (-1244 *3 *4 *5 *6)) (-4 *3 (-571)) (-4 *4 (-817)) + (-4 *5 (-872)) (-4 *6 (-1097 *3 *4 *5)) (-5 *2 (-114))))) +(((*1 *1 *1 *2 *3 *1) + (-12 (-4 *1 (-338 *2 *3)) (-4 *2 (-1081)) (-4 *3 (-816))))) (((*1 *1 *1 *1) (-4 *1 (-21))) ((*1 *1 *1) (-4 *1 (-21))) ((*1 *1 *1 *1) (|partial| -5 *1 (-136))) ((*1 *1 *1 *1) (-12 (-5 *1 (-217 *2)) (-4 *2 (-13 (-872) - (-10 -8 (-15 -1497 ((-1191) $ (-1209))) (-15 -1857 ((-1305) $)) - (-15 -4387 ((-1305) $))))))) + (-10 -8 (-15 -1515 ((-1191) $ (-1209))) (-15 -1892 ((-1305) $)) + (-15 -1921 ((-1305) $))))))) ((*1 *1 *1 *2) (-12 (-5 *1 (-305 *2)) (-4 *2 (-21)) (-4 *2 (-1249)))) ((*1 *1 *2 *1) (-12 (-5 *1 (-305 *2)) (-4 *2 (-21)) (-4 *2 (-1249)))) ((*1 *1 *1 *1) @@ -580,42 +738,50 @@ ((*1 *2 *2 *2) (-12 (-5 *2 (-973 (-229))) (-5 *1 (-1246)))) ((*1 *1 *1 *1) (-12 (-4 *1 (-1298 *2)) (-4 *2 (-1249)) (-4 *2 (-21)))) ((*1 *1 *1) (-12 (-4 *1 (-1298 *2)) (-4 *2 (-1249)) (-4 *2 (-21))))) +(((*1 *2 *3 *4 *5) + (-12 (-5 *3 (-793)) (-4 *6 (-376)) (-5 *4 (-1242 *6)) + (-5 *2 (-1 (-1187 *4) (-1187 *4))) (-5 *1 (-1308 *6)) + (-5 *5 (-1187 *4))))) +(((*1 *2 *1) + (-12 (-5 *2 (-663 (-1236 *3))) (-5 *1 (-1236 *3)) (-4 *3 (-1133))))) +(((*1 *2 *1) + (-12 (-4 *1 (-349 *3 *4 *5 *6)) (-4 *3 (-376)) (-4 *4 (-1275 *3)) + (-4 *5 (-1275 (-421 *4))) (-4 *6 (-355 *3 *4 *5)) + (-5 *2 (-427 *4 (-421 *4) *5 *6)))) + ((*1 *1 *2) + (-12 (-5 *2 (-1299 *6)) (-4 *6 (-13 (-424 *4 *5) (-1070 *4))) + (-4 *4 (-1023 *3)) (-4 *5 (-1275 *4)) (-4 *3 (-319)) + (-5 *1 (-427 *3 *4 *5 *6)))) + ((*1 *1 *2) + (-12 (-5 *2 (-663 *6)) (-4 *6 (-980 *3 *4 *5)) (-4 *3 (-376)) + (-4 *4 (-817)) (-4 *5 (-872)) (-5 *1 (-518 *3 *4 *5 *6))))) +(((*1 *2 *1) (-12 (-4 *1 (-541)) (-5 *2 (-713 (-564)))))) (((*1 *1 *1 *2) - (-12 (-5 *1 (-1172 *2 *3)) (-4 *2 (-13 (-1133) (-34))) - (-4 *3 (-13 (-1133) (-34)))))) -(((*1 *2 *2 *3) - (-12 (-5 *3 (-663 (-663 (-663 *4)))) (-5 *2 (-663 (-663 *4))) - (-4 *4 (-872)) (-5 *1 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(-5 *1 (-974 *4 *5))))) +(((*1 *1 *2) + (-12 (-5 *2 (-421 (-560))) (-4 *1 (-569 *3)) + (-4 *3 (-13 (-418) (-1235))))) + ((*1 *1 *2) (-12 (-4 *1 (-569 *2)) (-4 *2 (-13 (-418) (-1235))))) + ((*1 *1 *2 *2) (-12 (-4 *1 (-569 *2)) (-4 *2 (-13 (-418) (-1235)))))) (((*1 *2) - (-12 (-4 *4 (-175)) (-5 *2 (-1203 (-976 *4))) (-5 *1 (-431 *3 *4)) - (-4 *3 (-432 *4)))) - ((*1 *2) - (-12 (-4 *1 (-432 *3)) (-4 *3 (-175)) (-4 *3 (-376)) - (-5 *2 (-1203 (-976 *3))))) - ((*1 *2) - (-12 (-5 *2 (-1203 (-421 (-976 *3)))) (-5 *1 (-467 *3 *4 *5 *6)) - (-4 *3 (-571)) (-4 *3 (-175)) (-14 *4 (-949)) - (-14 *5 (-663 (-1209))) (-14 *6 (-1299 (-711 *3)))))) + (-12 (-5 *2 (-114)) (-5 *1 (-456 *3)) (-4 *3 (-1275 (-560)))))) (((*1 *1 *1 *1) (-4 *1 (-25))) ((*1 *1 *1 *1) (-5 *1 (-159))) ((*1 *1 *1 *1) (-12 (-5 *1 (-217 *2)) (-4 *2 (-13 (-872) - (-10 -8 (-15 -1497 ((-1191) $ (-1209))) (-15 -1857 ((-1305) $)) - (-15 -4387 ((-1305) $))))))) + (-10 -8 (-15 -1515 ((-1191) $ (-1209))) (-15 -1892 ((-1305) $)) + (-15 -1921 ((-1305) $))))))) ((*1 *1 *1 *2) (-12 (-5 *1 (-305 *2)) (-4 *2 (-25)) (-4 *2 (-1249)))) ((*1 *1 *2 *1) (-12 (-5 *1 (-305 *2)) (-4 *2 (-25)) (-4 *2 (-1249)))) ((*1 *1 *2 *1) @@ -638,205 +804,135 @@ (-12 (-5 *2 (-1187 *3)) (-4 *3 (-1081)) (-5 *1 (-1193 *3)))) ((*1 *2 *2 *2) (-12 (-5 *2 (-973 (-229))) (-5 *1 (-1246)))) ((*1 *1 *1 *1) (-12 (-4 *1 (-1298 *2)) (-4 *2 (-1249)) (-4 *2 (-25))))) +(((*1 *2 *3 *3 *4 *5 *5 *5 *3) + (-12 (-5 *3 (-560)) (-5 *4 (-1191)) (-5 *5 (-711 (-229))) + (-5 *2 (-1067)) (-5 *1 (-769))))) +(((*1 *2 *1) (-12 (-5 *2 (-663 (-663 (-229)))) (-5 *1 (-957))))) (((*1 *2 *3 *4) - (-12 (-5 *4 (-949)) (-5 *2 (-1203 *3)) (-5 *1 (-1224 *3)) - (-4 *3 (-376))))) -(((*1 *2 *3 *2) - (-12 (-5 *3 (-793)) (-5 *1 (-881 *2)) (-4 *2 (-38 (-421 (-560)))) - (-4 *2 (-175))))) -(((*1 *2 *3) - (|partial| -12 (-5 *3 (-949)) - (-5 *2 (-1299 (-663 (-2 (|:| -3677 *4) (|:| -2183 (-1152)))))) - (-5 *1 (-360 *4)) (-4 *4 (-363))))) -(((*1 *2 *3) (-12 (-5 *3 (-171 (-560))) (-5 *2 (-114)) (-5 *1 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(-1121 (-866 (-229)))) (|:| |abserr| (-229)) (|:| |relerr| (-229)))) (|:| |mdnia| (-2 (|:| |fn| (-326 (-229))) - (|:| -3918 (-663 (-1121 (-866 (-229))))) + (|:| -4237 (-663 (-1121 (-866 (-229))))) (|:| |abserr| (-229)) (|:| |relerr| (-229)))))) (-5 *1 (-791)))) ((*1 *2 *1) @@ -2904,13 +3193,13 @@ (-5 *2 (-3 (|:| |noa| - (-2 (|:| |fn| (-326 (-229))) (|:| -2560 (-663 (-229))) + (-2 (|:| |fn| (-326 (-229))) (|:| -2543 (-663 (-229))) (|:| |lb| (-663 (-866 (-229)))) (|:| |cf| (-663 (-326 (-229)))) (|:| |ub| (-663 (-866 (-229)))))) (|:| |lsa| (-2 (|:| |lfn| (-663 (-326 (-229)))) - (|:| -2560 (-663 (-229))))))) + (|:| -2543 (-663 (-229))))))) (-5 *1 (-865)))) ((*1 *2 *1) (-12 @@ -2929,26 +3218,26 @@ (-4 *4 (-817)) (-4 *5 (-872)) (-4 *1 (-1008 *3 *4 *5 *6)))) ((*1 *2 *1) (-12 (-4 *1 (-1070 *2)) (-4 *2 (-1249)))) ((*1 *1 *2) - (-4144 + (-4118 (-12 (-5 *2 (-976 *3)) - (-12 (-2598 (-4 *3 (-38 (-421 (-560))))) - (-2598 (-4 *3 (-38 (-560)))) (-4 *5 (-633 (-1209)))) + (-12 (-2584 (-4 *3 (-38 (-421 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+ (-5 *2 (-2 (|:| |localSymbols| (-1213)) (|:| -3306 (-663 (-342))))) (-4 *1 (-454)))) ((*1 *1 *2) (-12 (-5 *2 (-342)) (-4 *1 (-454)))) ((*1 *1 *2) (-12 (-5 *2 (-663 (-342))) (-4 *1 (-454)))) ((*1 *1 *2) (-12 (-5 *2 (-1299 (-721))) (-4 *1 (-454)))) ((*1 *1 *2) (-12 - (-5 *2 (-2 (|:| |localSymbols| (-1213)) (|:| -3317 (-663 (-342))))) + (-5 *2 (-2 (|:| |localSymbols| (-1213)) (|:| -3306 (-663 (-342))))) (-4 *1 (-455)))) ((*1 *1 *2) (-12 (-5 *2 (-342)) (-4 *1 (-455)))) ((*1 *1 *2) (-12 (-5 *2 (-663 (-342))) (-4 *1 (-455)))) @@ -3346,7 +3647,7 @@ (-14 *4 (-1 *2 *2 *3)) (-14 *5 (-1 (-3 *3 "failed") *3 *3)) (-14 *6 (-1 (-3 *2 "failed") *2 *2 *3)))) ((*1 *1 *2) - (-12 (-5 *2 (-663 (-2 (|:| -3002 *3) (|:| -2002 *4)))) + (-12 (-5 *2 (-663 (-2 (|:| -2990 *3) (|:| -2015 *4)))) (-4 *3 (-1081)) (-4 *4 (-748)) (-5 *1 (-757 *3 *4)))) ((*1 *1 *2) (-12 (-5 *2 (-560)) (-4 *1 (-785)))) ((*1 *1 *2) @@ -3355,25 +3656,25 @@ (-3 (|:| |nia| (-2 (|:| |var| (-1209)) (|:| |fn| (-326 (-229))) - (|:| -3918 (-1121 (-866 (-229)))) (|:| |abserr| (-229)) + (|:| -4237 (-1121 (-866 (-229)))) (|:| |abserr| (-229)) (|:| |relerr| (-229)))) (|:| |mdnia| (-2 (|:| |fn| (-326 (-229))) - (|:| -3918 (-663 (-1121 (-866 (-229))))) + (|:| -4237 (-663 (-1121 (-866 (-229))))) (|:| |abserr| (-229)) (|:| |relerr| (-229)))))) (-5 *1 (-791)))) ((*1 *1 *2) (-12 (-5 *2 (-2 (|:| |fn| (-326 (-229))) - (|:| -3918 (-663 (-1121 (-866 (-229))))) (|:| |abserr| (-229)) + (|:| -4237 (-663 (-1121 (-866 (-229))))) (|:| |abserr| (-229)) (|:| |relerr| (-229)))) (-5 *1 (-791)))) ((*1 *1 *2) (-12 (-5 *2 (-2 (|:| |var| (-1209)) (|:| |fn| (-326 (-229))) - (|:| -3918 (-1121 (-866 (-229)))) (|:| |abserr| (-229)) + (|:| -4237 (-1121 (-866 (-229)))) (|:| |abserr| (-229)) (|:| |relerr| (-229)))) (-5 *1 (-791)))) ((*1 *2 *3) (-12 (-5 *2 (-795)) (-5 *1 (-796 *3)) (-4 *3 (-1249)))) @@ -3391,23 +3692,23 @@ (-5 *2 (-3 (|:| |noa| - (-2 (|:| |fn| (-326 (-229))) (|:| -2560 (-663 (-229))) + (-2 (|:| |fn| (-326 (-229))) (|:| -2543 (-663 (-229))) (|:| 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(-5 *4 (-1203 *8))))) +(((*1 *2) (-12 (-5 *2 (-1305)) (-5 *1 (-574))))) +(((*1 *2 *1) (-12 (-4 *1 (-1166 *3)) (-4 *3 (-1081)) (-5 *2 (-114))))) +(((*1 *2 *2) + (-12 (-4 *3 (-571)) (-5 *1 (-287 *3 *2)) + (-4 *2 (-13 (-435 *3) (-1034)))))) +(((*1 *1 *2 *1) + (-12 (-5 *1 (-671 *2 *3 *4)) (-4 *2 (-1133)) (-4 *3 (-23)) + (-14 *4 *3)))) (((*1 *2 *3) (-12 (-5 *3 (-1191)) (-5 *2 (-323)) (-5 *1 (-308)))) ((*1 *2 *3) (-12 (-5 *3 (-663 (-1191))) (-5 *2 (-323)) (-5 *1 (-308)))) @@ -3586,353 +3943,351 @@ ((*1 *2 *3 *4) (-12 (-5 *4 (-663 (-1191))) (-5 *3 (-1191)) (-5 *2 (-323)) (-5 *1 (-308))))) -(((*1 *2 *2) - (-12 (-4 *3 (-363)) (-4 *4 (-341 *3)) (-4 *5 (-1275 *4)) - (-5 *1 (-799 *3 *4 *5 *2 *6)) (-4 *2 (-1275 *5)) (-14 *6 (-949)))) - ((*1 *1 *1 *2) - (-12 (-5 *2 (-793)) (-4 *1 (-1318 *3)) (-4 *3 (-376)) (-4 *3 (-381)))) - ((*1 *1 *1) (-12 (-4 *1 (-1318 *2)) (-4 *2 (-376)) (-4 *2 (-381))))) -(((*1 *2 *1) - (-12 (-4 *3 (-175)) (-4 *2 (-23)) (-5 *1 (-301 *3 *4 *2 *5 *6 *7)) - (-4 *4 (-1275 *3)) (-14 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-(((*1 *1 *1) - (|partial| -12 (-4 *1 (-380 *2)) (-4 *2 (-175)) (-4 *2 (-571)))) - ((*1 *1 *1) (|partial| -4 *1 (-744)))) -(((*1 *1 *2) (-12 (-5 *2 (-793)) (-5 *1 (-130))))) -(((*1 *2 *3) - (-12 (-4 *4 (-872)) (-5 *2 (-663 (-663 *4))) (-5 *1 (-1220 *4)) - (-5 *3 (-663 *4))))) -(((*1 *2 *2 *2) - (-12 (-4 *3 (-376)) (-5 *1 (-788 *2 *3)) (-4 *2 (-730 *3)))) - ((*1 *1 *1 *1) (-12 (-4 *1 (-877 *2)) (-4 *2 (-1081)) (-4 *2 (-376))))) + (-12 (-5 *3 (-663 (-326 (-391)))) (-5 *4 (-663 (-391))) + (-5 *2 (-1067)) (-5 *1 (-864))))) +(((*1 *1) + (-12 (-5 *1 (-137 *2 *3 *4)) (-14 *2 (-560)) (-14 *3 (-793)) + (-4 *4 (-175))))) +(((*1 *2 *2) + (-12 (-4 *3 (-571)) (-5 *1 (-287 *3 *2)) + (-4 *2 (-13 (-435 *3) (-1034)))))) +(((*1 *2 *1 *3) + (-12 (-5 *3 (-560)) (-4 *1 (-335 *4 *2)) (-4 *4 (-1133)) + (-4 *2 (-133))))) (((*1 *1 *2) - (-12 - (-5 *2 - (-663 - (-2 - (|:| -2118 - (-2 (|:| |var| (-1209)) (|:| |fn| (-326 (-229))) - (|:| -3918 (-1121 (-866 (-229)))) (|:| |abserr| (-229)) - (|:| |relerr| (-229)))) - (|:| -3964 - (-2 - (|:| |endPointContinuity| - (-3 (|:| |continuous| "Continuous at the end points") - (|:| |lowerSingular| - "There is a singularity at the lower end point") - (|:| |upperSingular| - "There is a singularity at the upper end point") - (|:| |bothSingular| - "There are singularities at both end points") - (|:| |notEvaluated| - "End point continuity not yet evaluated"))) - (|:| |singularitiesStream| - (-3 (|:| |str| (-1187 (-229))) - (|:| |notEvaluated| - "Internal singularities not yet evaluated"))) - (|:| -3918 - (-3 (|:| |finite| "The range is finite") - (|:| |lowerInfinite| - "The bottom of range is infinite") - (|:| |upperInfinite| "The top of range is infinite") - (|:| |bothInfinite| - "Both top and bottom points are infinite") - (|:| |notEvaluated| "Range not yet evaluated")))))))) - (-5 *1 (-574))))) + (-12 (-5 *2 (-1 (-229) (-229) (-229) (-229))) (-5 *1 (-270)))) + ((*1 *1 *2) (-12 (-5 *2 (-1 (-229) (-229) (-229))) (-5 *1 (-270)))) + ((*1 *1 *2) (-12 (-5 *2 (-1 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|Common| "common") (|:| |Print| "print"))) + (-5 *1 (-342))))) +(((*1 *2 *1) (-12 (-5 *2 (-114)) (-5 *1 (-597 *3)) (-4 *3 (-376))))) +(((*1 *2 *2) + (-12 (-4 *3 (-571)) (-5 *1 (-287 *3 *2)) + (-4 *2 (-13 (-435 *3) (-1034)))))) (((*1 *2 *1 *3) - (-12 (-5 *3 (-973 (-229))) (-5 *2 (-1305)) (-5 *1 (-482))))) -(((*1 *2 *2 *2) (-12 (-5 *2 (-560)) (-5 *1 (-1142))))) -(((*1 *1 *1 *1) - (-12 (|has| *1 (-6 -4511)) (-4 *1 (-121 *2)) (-4 *2 (-1249))))) -(((*1 *2 *1) - (-12 (-4 *3 (-376)) (-4 *4 (-1275 *3)) (-4 *5 (-1275 (-421 *4))) - (-5 *2 (-1299 *6)) (-5 *1 (-346 *3 *4 *5 *6)) - (-4 *6 (-355 *3 *4 *5))))) + (-12 (-5 *3 (-793)) (-4 *1 (-1182 *4)) (-4 *4 (-1249)) + (-5 *2 (-114))))) +(((*1 *2) (-12 (-5 *2 (-114)) (-5 *1 (-957))))) (((*1 *2 *1) (-12 (-5 *2 (-1147)) (-5 *1 (-222)))) ((*1 *2 *1) (-12 (-5 *2 (-1147)) (-5 *1 (-453)))) ((*1 *2 *1) (-12 (-5 *2 (-1147)) (-5 *1 (-862)))) ((*1 *1 *2 *3) (-12 (-5 *2 (-663 (-1214))) (-5 *3 (-1214)) (-5 *1 (-1147)))) ((*1 *2 *1) (-12 (-5 *2 (-1147)) (-5 *1 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(-376)) + (-5 *2 (-2 (|:| -3447 (-421 *6)) (|:| |coeff| (-421 *6)))) + (-5 *1 (-588 *5 *6)) (-5 *3 (-421 *6))))) (((*1 *2 *3) - (-12 (-4 *4 (-571)) (-5 *2 (-663 *3)) (-5 *1 (-43 *4 *3)) - (-4 *3 (-432 *4))))) -(((*1 *2) - (-12 (-5 *2 (-114)) (-5 *1 (-456 *3)) (-4 *3 (-1275 (-560)))))) -(((*1 *2 *2) (-12 (-5 *2 (-949)) (-5 *1 (-369 *3)) (-4 *3 (-363))))) + (-12 (-5 *3 (-1191)) (-5 *2 (-217 (-516))) (-5 *1 (-861))))) +(((*1 *2) (-12 (-5 *2 (-663 (-1191))) (-5 *1 (-1304))))) (((*1 *2 *3 *3) - (-12 (-4 *4 (-13 (-319) (-149))) (-4 *5 (-13 (-872) (-633 (-1209)))) - (-4 *6 (-817)) (-5 *2 (-663 (-663 (-560)))) - (-5 *1 (-954 *4 *5 *6 *7)) (-5 *3 (-560)) (-4 *7 (-980 *4 *6 *5))))) -(((*1 *2 *1 *1) - (-12 (-5 *2 (-2 (|:| -4077 (-803 *3)) (|:| |coef1| (-803 *3)))) - (-5 *1 (-803 *3)) (-4 *3 (-571)) (-4 *3 (-1081)))) - ((*1 *2 *1 *1) - (-12 (-4 *3 (-571)) (-4 *3 (-1081)) (-4 *4 (-817)) (-4 *5 (-872)) - (-5 *2 (-2 (|:| -4077 *1) (|:| |coef1| *1))) - (-4 *1 (-1097 *3 *4 *5))))) + (-12 (-5 *3 (-663 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(-2 (|:| |var| (-1209)) (|:| |fn| (-326 (-229))) - (|:| -3918 (-1121 (-866 (-229)))) (|:| |abserr| (-229)) - (|:| |relerr| (-229))))))) -(((*1 *2) - (-12 (-4 *4 (-376)) (-5 *2 (-793)) (-5 *1 (-340 *3 *4)) - (-4 *3 (-341 *4)))) - ((*1 *2) (-12 (-4 *1 (-1318 *3)) (-4 *3 (-376)) (-5 *2 (-793))))) -(((*1 *2 *1) - (-12 (-4 *1 (-1136 *3 *4 *5 *6 *7)) (-4 *3 (-1133)) (-4 *4 (-1133)) - (-4 *5 (-1133)) (-4 *6 (-1133)) (-4 *7 (-1133)) (-5 *2 (-114))))) -(((*1 *2 *2) - (-12 - (-5 *2 - (-2 (|:| |flg| (-3 "nil" "sqfr" "irred" "prime")) (|:| |fctr| *4) - (|:| |xpnt| (-560)))) - (-4 *4 (-13 (-1275 *3) (-571) (-10 -8 (-15 -4077 ($ $ $))))) - (-4 *3 (-571)) (-5 *1 (-1279 *3 *4))))) -(((*1 *2 *2) (-12 (-5 *2 (-391)) (-5 *1 (-1303)))) - ((*1 *2) (-12 (-5 *2 (-391)) (-5 *1 (-1303))))) + (-12 (-5 *2 (-663 (-663 (-663 *4)))) (-5 *3 (-663 *4)) (-4 *4 (-872)) + (-5 *1 (-1220 *4))))) +(((*1 *1 *2 *3) + (-12 (-5 *2 (-663 *3)) (-4 *3 (-980 *4 *6 *5)) (-4 *4 (-466)) + (-4 *5 (-872)) (-4 *6 (-817)) (-5 *1 (-1018 *4 *5 *6 *3))))) (((*1 *1 *1) (-12 (-4 *1 (-385 *2)) (-4 *2 (-1249)) (-4 *2 (-872)))) ((*1 *1 *2 *1) (-12 (-5 *2 (-1 (-114) *3 *3)) (-4 *1 (-385 *3)) (-4 *3 (-1249)))) @@ -4883,12 +5099,12 @@ ((*1 *2 *1 *3) (-12 (-4 *4 (-1081)) (-4 *5 (-817)) (-4 *3 (-872)) (-4 *6 (-1097 *4 *5 *3)) - (-5 *2 (-2 (|:| |under| *1) (|:| -4173 *1) (|:| |upper| *1))) + (-5 *2 (-2 (|:| |under| *1) (|:| -1741 *1) (|:| |upper| *1))) (-4 *1 (-1008 *4 *5 *3 *6))))) (((*1 *2 *3) (-12 (-5 *3 - (-2 (|:| |lfn| (-663 (-326 (-229)))) (|:| -2560 (-663 (-229))))) + (-2 (|:| |lfn| (-663 (-326 (-229)))) (|:| -2543 (-663 (-229))))) (-5 *2 (-663 (-1209))) (-5 *1 (-278)))) ((*1 *2 *3) (-12 (-5 *3 (-1203 *7)) (-4 *7 (-980 *6 *4 *5)) (-4 *4 (-817)) @@ -4910,7 +5126,7 @@ (-5 *1 (-981 *4 *5 *6 *7 *3)) (-4 *3 (-13 (-376) - (-10 -8 (-15 -3903 ($ *7)) (-15 -2841 (*7 $)) (-15 -2854 (*7 $))))))) + (-10 -8 (-15 -3866 ($ *7)) (-15 -2833 (*7 $)) (-15 -2845 (*7 $))))))) ((*1 *2 *1) (-12 (-4 *1 (-1005 *3 *4 *5)) (-4 *3 (-1081)) (-4 *4 (-816)) (-4 *5 (-872)) (-5 *2 (-663 *5)))) @@ -4920,22 +5136,9 @@ ((*1 *2 *3) (-12 (-5 *3 (-421 (-976 *4))) (-4 *4 (-571)) (-5 *2 (-663 (-1209))) (-5 *1 (-1072 *4))))) -(((*1 *2 *3 *4 *4 *4 *4) - (-12 (-5 *3 (-711 (-229))) (-5 *4 (-560)) (-5 *2 (-1067)) - (-5 *1 (-777))))) -(((*1 *2 *3) (-12 (-5 *3 (-793)) (-5 *2 (-1305)) (-5 *1 (-391)))) - ((*1 *2) (-12 (-5 *2 (-1305)) (-5 *1 (-391))))) -(((*1 *2 *3 *4) - (-12 (-5 *4 (-1 *6 *6)) (-4 *6 (-1275 *5)) (-4 *5 (-376)) - (-4 *7 (-1275 (-421 *6))) - (-5 *2 (-2 (|:| |answer| *3) (|:| -1570 *3))) - (-5 *1 (-577 *5 *6 *7 *3)) (-4 *3 (-355 *5 *6 *7)))) - ((*1 *2 *3 *4) - (-12 (-5 *4 (-1 *6 *6)) (-4 *6 (-1275 *5)) (-4 *5 (-376)) - (-5 *2 - (-2 (|:| |answer| (-421 *6)) (|:| -1570 (-421 *6)) - (|:| |specpart| (-421 *6)) (|:| |polypart| *6))) - (-5 *1 (-578 *5 *6)) (-5 *3 (-421 *6))))) +(((*1 *2 *3) + (-12 (-5 *3 (-663 *2)) (-4 *2 (-1275 *4)) (-5 *1 (-553 *4 *2 *5 *6)) + (-4 *4 (-319)) (-14 *5 *4) (-14 *6 (-1 *4 *4 (-793)))))) (((*1 *2) (-12 (-5 *2 (-1305)) (-5 *1 (-63 *3)) (-14 *3 (-1209)))) ((*1 *2) (-12 (-5 *2 (-1305)) (-5 *1 (-69 *3)) (-14 *3 (-1209)))) ((*1 *2) (-12 (-5 *2 (-1305)) (-5 *1 (-72 *3)) (-14 *3 (-1209)))) @@ -4946,34 +5149,27 @@ ((*1 *2 *3) (-12 (-5 *3 (-888)) (-5 *2 (-1305)) (-5 *1 (-1170)))) ((*1 *2 *3) (-12 (-5 *3 (-663 (-888))) (-5 *2 (-1305)) (-5 *1 (-1170))))) -(((*1 *2 *3) - (-12 (-5 *2 (-663 (-1191))) (-5 *1 (-853)) (-5 *3 (-1191))))) -(((*1 *2 *3) - (-12 (-4 *4 (-466)) - (-5 *2 - (-663 - (-2 (|:| |eigval| (-3 (-421 (-976 *4)) (-1198 (-1209) (-976 *4)))) - (|:| |eigmult| (-793)) - (|:| |eigvec| (-663 (-711 (-421 (-976 *4)))))))) - (-5 *1 (-304 *4)) (-5 *3 (-711 (-421 (-976 *4))))))) -(((*1 *2 *1) - (-12 - (-5 *2 - (-663 - (-2 (|:| |flg| (-3 "nil" "sqfr" "irred" "prime")) (|:| |fctr| *3) - (|:| |xpnt| (-560))))) - (-5 *1 (-419 *3)) (-4 *3 (-571)))) - ((*1 *2 *3 *4 *4 *4) - (-12 (-5 *4 (-793)) (-4 *3 (-363)) (-4 *5 (-1275 *3)) - (-5 *2 (-663 (-1203 *3))) (-5 *1 (-512 *3 *5 *6)) - (-4 *6 (-1275 *5))))) (((*1 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(-1047 *4 *5)) (-5 *3 (-421 *5))))) +(((*1 *2) (-12 (-5 *2 (-560)) (-5 *1 (-481)))) + ((*1 *2 *2) (-12 (-5 *2 (-560)) (-5 *1 (-481)))) + ((*1 *2) (-12 (-5 *2 (-560)) (-5 *1 (-955))))) +(((*1 *2 *2) (-12 (-5 *2 (-949)) (-5 *1 (-369 *3)) (-4 *3 (-363))))) (((*1 *2 *3) - (-12 (-5 *3 (-663 *4)) (-4 *4 (-872)) (-5 *2 (-663 (-686 *4 *5))) - (-5 *1 (-646 *4 *5 *6)) (-4 *5 (-13 (-175) (-739 (-421 (-560))))) - (-14 *6 (-949))))) -(((*1 *1 *2) (-12 (-5 *2 (-843 *3)) (-4 *3 (-872)) (-5 *1 (-694 *3))))) -(((*1 *1 *2) - (-12 (-5 *2 (-427 *3 *4 *5 *6)) (-4 *6 (-1070 *4)) (-4 *3 (-319)) - (-4 *4 (-1023 *3)) (-4 *5 (-1275 *4)) (-4 *6 (-424 *4 *5)) - (-14 *7 (-1299 *6)) (-5 *1 (-429 *3 *4 *5 *6 *7)))) - ((*1 *1 *2) - (-12 (-5 *2 (-1299 *6)) (-4 *6 (-424 *4 *5)) (-4 *4 (-1023 *3)) - (-4 *5 (-1275 *4)) (-4 *3 (-319)) (-5 *1 (-429 *3 *4 *5 *6 *7)) - (-14 *7 *2)))) -(((*1 *2 *1 *2) (-12 (-5 *2 (-663 (-1191))) (-5 *1 (-407)))) - ((*1 *2 *1 *2) (-12 (-5 *2 (-663 (-1191))) (-5 *1 (-1229))))) -(((*1 *1 *2 *1) (-12 (-5 *1 (-123 *2)) (-4 *2 (-872))))) -(((*1 *2 *3 *4) - (-12 (-4 *5 (-376)) (-4 *7 (-1275 *5)) (-4 *4 (-746 *5 *7)) - (-5 *2 (-2 (|:| -2562 (-711 *6)) (|:| |vec| (-1299 *5)))) - (-5 *1 (-835 *5 *6 *7 *4 *3)) (-4 *6 (-680 *5)) (-4 *3 (-680 *4))))) -(((*1 *2 *2 *1) (|partial| -12 (-5 *2 (-663 *1)) (-4 *1 (-319))))) -(((*1 *1 *1 *1 *2) - (-12 (-5 *2 (-560)) (|has| *1 (-6 -4511)) (-4 *1 (-385 *3)) - (-4 *3 (-1249))))) + (-12 + (-5 *3 + (-2 + (|:| |endPointContinuity| + (-3 (|:| |continuous| "Continuous at the end points") + (|:| |lowerSingular| + "There is a singularity at the lower end point") + (|:| |upperSingular| + "There is a singularity at the upper end point") + (|:| |bothSingular| + "There are singularities at both end points") + (|:| |notEvaluated| + "End point continuity not yet evaluated"))) + (|:| |singularitiesStream| + (-3 (|:| |str| (-1187 (-229))) + (|:| |notEvaluated| + "Internal singularities not yet evaluated"))) + (|:| -4237 + (-3 (|:| |finite| "The range is finite") + (|:| |lowerInfinite| "The bottom of range is infinite") + (|:| |upperInfinite| "The top of range is infinite") + (|:| |bothInfinite| + "Both top and bottom points are infinite") + (|:| |notEvaluated| "Range not yet evaluated"))))) + (-5 *2 (-1067)) (-5 *1 (-315))))) +(((*1 *1 *2 *3 *3 *3) + (-12 (-5 *2 (-1 (-973 (-229)) (-229))) (-5 *3 (-1121 (-229))) + (-5 *1 (-955)))) + ((*1 *1 *2 *3) + (-12 (-5 *2 (-1 (-973 (-229)) (-229))) (-5 *3 (-1121 (-229))) + (-5 *1 (-955)))) + ((*1 *1 *2 *3 *3 *3 *3) + (-12 (-5 *2 (-1 (-973 (-229)) (-229))) (-5 *3 (-1121 (-229))) + (-5 *1 (-957)))) + ((*1 *1 *2 *3) + (-12 (-5 *2 (-1 (-973 (-229)) (-229))) (-5 *3 (-1121 (-229))) + (-5 *1 (-957))))) (((*1 *1 *2) (-12 (-5 *2 (-663 (-1107 *3 *4 *5))) (-4 *3 (-1133)) (-4 *4 (-13 (-1081) (-912 *3) (-633 (-916 *3)))) (-4 *5 (-13 (-435 *4) (-912 *3) (-633 (-916 *3)))) (-5 *1 (-1109 *3 *4 *5))))) -(((*1 *2 *3) - (-12 (-4 *4 (-571)) (-4 *5 (-1023 *4)) - (-5 *2 (-2 (|:| |num| *3) (|:| |den| *4))) (-5 *1 (-144 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((*1 *2 *3 *4) + (-12 (-5 *4 (-1209)) (-5 *2 (-1 *6 *5)) (-5 *1 (-728 *3 *5 *6)) + (-4 *3 (-633 (-549))) (-4 *5 (-1249)) (-4 *6 (-1249))))) (((*1 *2 *3) - (|partial| -12 (-5 *3 (-1191)) (-5 *2 (-391)) (-5 *1 (-808))))) -(((*1 *1 *2) (-12 (-5 *2 (-663 (-342))) (-5 *1 (-342))))) -(((*1 *1) (-4 *1 (-363)))) -(((*1 *2 *1) (-12 (-5 *2 (-1305)) (-5 *1 (-847))))) + (-12 (-5 *3 (-663 (-229))) (-5 *2 (-1299 (-721))) (-5 *1 (-315))))) +(((*1 *2 *3) + (-12 (-5 *3 (-973 *2)) (-5 *1 (-1014 *2)) (-4 *2 (-1081))))) +(((*1 *2 *1 *1) + (-12 (-5 *2 (-2 (|:| -4053 (-803 *3)) (|:| |coef1| (-803 *3)))) + (-5 *1 (-803 *3)) (-4 *3 (-571)) (-4 *3 (-1081)))) + ((*1 *2 *1 *1) + (-12 (-4 *3 (-571)) (-4 *3 (-1081)) (-4 *4 (-817)) (-4 *5 (-872)) + (-5 *2 (-2 (|:| -4053 *1) (|:| |coef1| *1))) + (-4 *1 (-1097 *3 *4 *5))))) +(((*1 *2 *3) + (-12 (-4 *4 (-376)) (-4 *5 (-385 *4)) (-4 *6 (-385 *4)) + (-5 *2 (-793)) (-5 *1 (-535 *4 *5 *6 *3)) (-4 *3 (-708 *4 *5 *6)))) + ((*1 *2 *1) + (-12 (-4 *1 (-708 *3 *4 *5)) (-4 *3 (-1081)) (-4 *4 (-385 *3)) + (-4 *5 (-385 *3)) (-4 *3 (-571)) (-5 *2 (-793)))) + ((*1 *2 *3) + (-12 (-4 *4 (-571)) (-4 *4 (-175)) (-4 *5 (-385 *4)) + (-4 *6 (-385 *4)) (-5 *2 (-793)) (-5 *1 (-710 *4 *5 *6 *3)) + (-4 *3 (-708 *4 *5 *6)))) + ((*1 *2 *1) + (-12 (-4 *1 (-1085 *3 *4 *5 *6 *7)) (-4 *5 (-1081)) + (-4 *6 (-245 *4 *5)) (-4 *7 (-245 *3 *5)) (-4 *5 (-571)) + (-5 *2 (-793))))) (((*1 *1 *2) (-12 (-5 *2 (-663 (-888))) (-5 *1 (-888)))) ((*1 *1 *1) (-5 *1 (-888))) ((*1 *1 *2) (-12 (-5 *2 (-663 *3)) (-4 *3 (-1133)) (-4 *1 (-1131 *3)))) ((*1 *1) (-12 (-4 *1 (-1131 *2)) (-4 *2 (-1133))))) -(((*1 *2) (-12 (-5 *2 (-1191)) (-5 *1 (-1219))))) (((*1 *2 *3 *4) (-12 (-5 *3 (-663 *8)) (-5 *4 (-137 *5 *6 *7)) (-14 *5 (-560)) (-14 *6 (-793)) (-4 *7 (-175)) (-4 *8 (-175)) @@ -5324,52 +5588,43 @@ (-4 *8 (-1081)) (-4 *2 (-980 *9 *7 *5)) (-5 *1 (-750 *5 *6 *7 *8 *9 *4 *2)) (-4 *7 (-817)) (-4 *4 (-980 *8 *6 *5))))) +(((*1 *2 *1 *3) (-12 (-4 *1 (-541)) (-5 *3 (-131)) (-5 *2 (-793))))) (((*1 *2 *3) - (-12 (-5 *2 (-114)) (-5 *1 (-122 *3)) (-4 *3 (-1275 (-560)))))) -(((*1 *2 *3) - (-12 (-5 *3 (-1191)) (-5 *2 (-1305)) (-5 *1 (-1227 *4 *5)) - (-4 *4 (-1133)) (-4 *5 (-1133))))) -(((*1 *2 *2 *3) - (-12 (-5 *3 (-1 (-114) *4 *4)) (-4 *4 (-1249)) (-5 *1 (-1164 *4 *2)) - (-4 *2 (-13 (-618 (-560) *4) (-10 -7 (-6 -4510) (-6 -4511)))))) - ((*1 *2 *2) - (-12 (-4 *3 (-872)) (-4 *3 (-1249)) (-5 *1 (-1164 *3 *2)) - (-4 *2 (-13 (-618 (-560) *3) (-10 -7 (-6 -4510) (-6 -4511))))))) -(((*1 *2 *2) - (|partial| -12 (-5 *2 (-663 (-916 *3))) (-5 *1 (-916 *3)) - (-4 *3 (-1133))))) + (-12 (-4 *4 (-571)) (-4 *2 (-13 (-435 (-171 *4)) (-1034) (-1235))) + (-5 *1 (-614 *4 *3 *2)) (-4 *3 (-13 (-435 *4) (-1034) (-1235)))))) +(((*1 *2 *1 *1) (-12 (-4 *1 (-102)) (-5 *2 (-114))))) +(((*1 *2 *3 *4) + (-12 (-4 *5 (-466)) (-4 *6 (-817)) (-4 *7 (-872)) + (-4 *3 (-1097 *5 *6 *7)) (-5 *2 (-663 *4)) + (-5 *1 (-1140 *5 *6 *7 *3 *4)) (-4 *4 (-1103 *5 *6 *7 *3))))) (((*1 *2 *1) (-12 (-4 *1 (-1126 *2)) (-4 *2 (-1249))))) -(((*1 *2 *3 *3) - (-12 (-5 *2 (-1187 (-663 (-560)))) (-5 *1 (-909)) - (-5 *3 (-663 (-560)))))) -(((*1 *1 *2 *3) - (-12 (-5 *1 (-671 *2 *3 *4)) (-4 *2 (-1133)) (-4 *3 (-23)) - (-14 *4 *3)))) -(((*1 *2 *2 *3) - (-12 (-5 *3 (-663 *2)) (-4 *2 (-980 *4 *5 *6)) (-4 *4 (-319)) - (-4 *5 (-817)) (-4 *6 (-872)) (-5 *1 (-462 *4 *5 *6 *2))))) +(((*1 *2 *1 *1) + (-12 (-5 *2 (-114)) (-5 *1 (-671 *3 *4 *5)) (-4 *3 (-1133)) + (-4 *4 (-23)) (-14 *5 *4)))) +(((*1 *2 *3 *2) + (-12 (-5 *2 (-899)) (-5 *3 (-663 (-270))) (-5 *1 (-271))))) +(((*1 *1 *1 *2) + (-12 (-4 *1 (-1008 *3 *4 *2 *5)) (-4 *3 (-1081)) (-4 *4 (-817)) + (-4 *2 (-872)) (-4 *5 (-1097 *3 *4 *2))))) +(((*1 *2 *3) (-12 (-5 *3 (-1191)) (-5 *2 (-114)) (-5 *1 (-853))))) +(((*1 *2 *3 *2) + (-12 (-4 *1 (-809)) (-5 *2 (-1067)) + (-5 *3 + (-2 (|:| |fn| (-326 (-229))) + (|:| -4237 (-663 (-1121 (-866 (-229))))) (|:| |abserr| (-229)) + (|:| |relerr| (-229)))))) + ((*1 *2 *3 *2) + (-12 (-4 *1 (-809)) (-5 *2 (-1067)) + (-5 *3 + (-2 (|:| |var| (-1209)) (|:| |fn| (-326 (-229))) + (|:| -4237 (-1121 (-866 (-229)))) (|:| |abserr| (-229)) + (|:| |relerr| (-229))))))) (((*1 *2 *3) - (-12 (-5 *3 (-1209)) (-5 *2 (-1 (-1203 (-976 *4)) (-976 *4))) - (-5 *1 (-1308 *4)) (-4 *4 (-376))))) -(((*1 *2 *3 *3 *4) - (-12 (-4 *5 (-466)) (-4 *6 (-817)) (-4 *7 (-872)) - (-4 *3 (-1097 *5 *6 *7)) - (-5 *2 (-663 (-2 (|:| |val| (-663 *3)) (|:| -4466 *4)))) - (-5 *1 (-1104 *5 *6 *7 *3 *4)) (-4 *4 (-1103 *5 *6 *7 *3))))) -(((*1 *2 *3 *4) - (-12 (-5 *4 (-1 (-663 *5) *6)) - (-4 *5 (-13 (-376) (-149) (-1070 (-421 (-560))))) (-4 *6 (-1275 *5)) - (-5 *2 (-663 (-2 (|:| |poly| *6) (|:| -2085 *3)))) - (-5 *1 (-833 *5 *6 *3 *7)) (-4 *3 (-680 *6)) - (-4 *7 (-680 (-421 *6))))) - ((*1 *2 *3 *4) - (-12 (-5 *4 (-1 (-663 *5) *6)) - (-4 *5 (-13 (-376) (-149) (-1070 (-560)) (-1070 (-421 (-560))))) - (-4 *6 (-1275 *5)) - (-5 *2 (-663 (-2 (|:| |poly| *6) (|:| -2085 (-678 *6 (-421 *6)))))) - (-5 *1 (-836 *5 *6)) (-5 *3 (-678 *6 (-421 *6)))))) -(((*1 *2 *3 *1) - (-12 (-4 *1 (-951)) (-5 *2 (-713 (-663 *1))) (-5 *3 (-663 *1))))) + (-12 (-5 *3 (-1187 (-229))) (-5 *2 (-663 (-1191))) (-5 *1 (-195)))) + ((*1 *2 *3) + (-12 (-5 *3 (-1187 (-229))) (-5 *2 (-663 (-1191))) (-5 *1 (-313)))) + ((*1 *2 *3) + (-12 (-5 *3 (-1187 (-229))) (-5 *2 (-663 (-1191))) (-5 *1 (-315))))) (((*1 *2 *1) (-12 (-5 *2 (-663 *5)) (-5 *1 (-137 *3 *4 *5)) (-14 *3 (-560)) (-14 *4 (-793)) (-4 *5 (-175))))) @@ -5384,27 +5639,28 @@ (-12 (-5 *2 (-1209)) (-4 *1 (-435 *3)) (-4 *3 (-1133)))) ((*1 *1 *2 *1) (-12 (-5 *2 (-1209)) (-4 *1 (-435 *3)) (-4 *3 (-1133))))) -(((*1 *1 *2) - (|partial| -12 (-5 *2 (-1315 *3 *4)) (-4 *3 (-872)) (-4 *4 (-175)) - (-5 *1 (-686 *3 *4)))) - ((*1 *2 *1) - (|partial| -12 (-5 *2 (-686 *3 *4)) (-5 *1 (-1320 *3 *4)) - (-4 *3 (-872)) (-4 *4 (-175))))) -(((*1 *2 *1 *3) (-12 (-5 *3 (-1209)) (-5 *2 (-1305)) (-5 *1 (-847))))) -(((*1 *2 *3 *3 *4) - (-12 (-4 *5 (-466)) (-4 *6 (-817)) (-4 *7 (-872)) - (-4 *3 (-1097 *5 *6 *7)) - (-5 *2 (-663 (-2 (|:| |val| *3) (|:| -4466 *4)))) - (-5 *1 (-1140 *5 *6 *7 *3 *4)) (-4 *4 (-1103 *5 *6 *7 *3))))) +(((*1 *1 *1 *2 *2) + (|partial| -12 (-5 *2 (-949)) (-5 *1 (-1134 *3 *4)) (-14 *3 *2) + (-14 *4 *2)))) +(((*1 *2 *1) + (-12 (-4 *1 (-380 *3)) (-4 *3 (-175)) (-4 *3 (-571)) + (-5 *2 (-1203 *3))))) +(((*1 *1 *1 *1) (-5 *1 (-229))) + ((*1 *2 *2 *2) (-12 (-5 *2 (-229)) (-5 *1 (-230)))) + ((*1 *2 *2 *2) (-12 (-5 *2 (-171 (-229))) (-5 *1 (-230)))) + ((*1 *2 *2 *2) + (-12 (-4 *3 (-571)) (-5 *1 (-445 *3 *2)) (-4 *2 (-435 *3)))) + ((*1 *2 *3 *3) + (-12 (-5 *3 (-793)) (-5 *2 (-1 (-391))) (-5 *1 (-1073)))) + ((*1 *1 *1 *1) (-4 *1 (-1171)))) +(((*1 *2 *1 *3 *4) + (-12 (-5 *3 (-1191)) (-5 *4 (-1152)) (-5 *2 (-114)) (-5 *1 (-846))))) (((*1 *2 *2) (-12 (-5 *1 (-704 *2)) (-4 *2 (-1133))))) -(((*1 *1 *2 *1) - (-12 (-5 *1 (-671 *2 *3 *4)) (-4 *2 (-1133)) (-4 *3 (-23)) - (-14 *4 *3)))) (((*1 *2 *3) (|partial| -12 (-5 *3 (-2 (|:| |var| (-1209)) (|:| |fn| (-326 (-229))) - (|:| -3918 (-1121 (-866 (-229)))) (|:| |abserr| (-229)) + (|:| -4237 (-1121 (-866 (-229)))) (|:| |abserr| (-229)) (|:| |relerr| (-229)))) (-5 *2 (-2 @@ -5422,7 +5678,7 @@ (-3 (|:| |str| (-1187 (-229))) (|:| |notEvaluated| "Internal singularities not yet evaluated"))) - (|:| -3918 + (|:| -4237 (-3 (|:| |finite| "The range is finite") (|:| |lowerInfinite| "The bottom of range is infinite") (|:| |upperInfinite| "The top of range is infinite") @@ -5430,71 +5686,30 @@ "Both top and bottom points are infinite") (|:| |notEvaluated| "Range not yet evaluated"))))) (-5 *1 (-574))))) -(((*1 *2 *2 *3 *2) - (-12 (-5 *3 (-793)) (-4 *4 (-363)) (-5 *1 (-220 *4 *2)) - (-4 *2 (-1275 *4))))) -(((*1 *2 *3) (-12 (-5 *3 (-1191)) (-5 *2 (-51)) (-5 *1 (-853))))) -(((*1 *2 *3 *4 *2) - (-12 (-5 *2 (-914 *5 *3)) (-5 *4 (-916 *5)) (-4 *5 (-1133)) - (-4 *3 (-168 *6)) (-4 (-976 *6) (-912 *5)) - (-4 *6 (-13 (-912 *5) (-175))) (-5 *1 (-181 *5 *6 *3)))) - ((*1 *2 *1 *3 *2) - (-12 (-5 *2 (-914 *4 *1)) (-5 *3 (-916 *4)) (-4 *1 (-912 *4)) - (-4 *4 (-1133)))) - ((*1 *2 *3 *4 *2) - (-12 (-5 *2 (-914 *5 *6)) (-5 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"undefined")) - (-5 *5 (-1121 (-229))) (-5 *6 (-663 (-270))) (-5 *2 (-1165 (-229))) - (-5 *1 (-719)))) - ((*1 *2 *3 *4 *4 *5) - (-12 (-5 *3 (-1 (-973 (-229)) (-229) (-229))) (-5 *4 (-1121 (-229))) - (-5 *5 (-663 (-270))) (-5 *2 (-1165 (-229))) (-5 *1 (-719)))) - ((*1 *2 *2 *3 *4 *4 *5) - (-12 (-5 *2 (-1165 (-229))) (-5 *3 (-1 (-973 (-229)) (-229) (-229))) - (-5 *4 (-1121 (-229))) (-5 *5 (-663 (-270))) (-5 *1 (-719))))) +(((*1 *2 *3) + (-12 + (-5 *3 + (-2 (|:| |var| (-1209)) (|:| |fn| (-326 (-229))) + (|:| -4237 (-1121 (-866 (-229)))) (|:| |abserr| (-229)) + (|:| |relerr| (-229)))) + (-5 *2 + (-3 (|:| |continuous| "Continuous at the end points") + (|:| |lowerSingular| + "There is a singularity at the lower end point") + (|:| |upperSingular| + "There is a singularity at the upper end point") + (|:| |bothSingular| "There are singularities at both end points") + (|:| |notEvaluated| "End point continuity not yet evaluated"))) + (-5 *1 (-195))))) +(((*1 *1 *1 *1) + (-12 (-4 *1 (-335 *2 *3)) (-4 *2 (-1133)) (-4 *3 (-133)) + (-4 *3 (-816))))) +(((*1 *2) + (-12 (-4 *4 (-376)) (-5 *2 (-793)) (-5 *1 (-340 *3 *4)) + (-4 *3 (-341 *4)))) + ((*1 *2) (-12 (-4 *1 (-1318 *3)) (-4 *3 (-376)) (-5 *2 (-793))))) +(((*1 *2 *1) (-12 (-4 *1 (-363)) (-5 *2 (-793)))) + ((*1 *2 *1 *1) (|partial| -12 (-4 *1 (-416)) (-5 *2 (-793))))) (((*1 *2 *2 *2) (-12 (-5 *2 (-1067)) (-5 *1 (-315)))) ((*1 *2 *3) (-12 (-5 *3 (-663 (-1067))) (-5 *2 (-1067)) (-5 *1 (-315)))) @@ -5508,136 +5723,39 @@ (-4 *4 (-1249)))) ((*1 *1 *2 *1) (-12 (-4 *1 (-1288 *2)) (-4 *2 (-1249)))) ((*1 *1 *1 *1) (-12 (-4 *1 (-1288 *2)) (-4 *2 (-1249))))) -(((*1 *2 *3) - (-12 (-4 *1 (-923)) - (-5 *3 - (-2 (|:| |pde| (-663 (-326 (-229)))) - (|:| |constraints| - (-663 - (-2 (|:| |start| (-229)) (|:| |finish| (-229)) - (|:| |grid| (-793)) (|:| |boundaryType| (-560)) - (|:| |dStart| (-711 (-229))) (|:| |dFinish| (-711 (-229)))))) - (|:| |f| (-663 (-663 (-326 (-229))))) (|:| |st| (-1191)) - (|:| |tol| (-229)))) - (-5 *2 (-1067))))) +(((*1 *2 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(-114)) (-5 *1 (-856 *3)) (-4 *3 (-1133)))) + ((*1 *2 *1) (-12 (-5 *2 (-114)) (-5 *1 (-866 *3)) (-4 *3 (-1133))))) (((*1 *2 *3) - (-12 (-5 *3 (-1209)) - (-5 *2 - (-2 (|:| |zeros| (-1187 (-229))) (|:| |ones| (-1187 (-229))) - (|:| |singularities| (-1187 (-229))))) - (-5 *1 (-105))))) -(((*1 *2 *3 *4 *2) - (-12 (-5 *2 (-663 (-663 (-663 *5)))) (-5 *3 (-1 (-114) *5 *5)) - (-5 *4 (-663 *5)) (-4 *5 (-872)) (-5 *1 (-1220 *5))))) -(((*1 *2 *1 *3) - (-12 (-5 *3 (-663 *1)) (-4 *1 (-1097 *4 *5 *6)) (-4 *4 (-1081)) - (-4 *5 (-817)) (-4 *6 (-872)) (-5 *2 (-114)))) - ((*1 *2 *1 *1) - (-12 (-4 *1 (-1097 *3 *4 *5)) (-4 *3 (-1081)) (-4 *4 (-817)) - (-4 *5 (-872)) (-5 *2 (-114)))) - ((*1 *2 *3 *1 *4) - (-12 (-5 *4 (-1 (-114) *3 *3)) (-4 *1 (-1244 *5 *6 *7 *3)) - (-4 *5 (-571)) (-4 *6 (-817)) (-4 *7 (-872)) - (-4 *3 (-1097 *5 *6 *7)) (-5 *2 (-114))))) + (-12 (-5 *2 (-1187 (-560))) (-5 *1 (-1193 *4)) (-4 *4 (-1081)) + (-5 *3 (-560))))) +(((*1 *2 *1) + (-12 (-4 *1 (-1136 *3 *4 *5 *6 *7)) (-4 *3 (-1133)) (-4 *4 (-1133)) + (-4 *5 (-1133)) (-4 *6 (-1133)) (-4 *7 (-1133)) (-5 *2 (-114))))) (((*1 *2 *1) (-12 (-4 *1 (-168 *2)) (-4 *2 (-175)))) ((*1 *2 *3) (-12 (-4 *4 (-13 (-571) (-1070 (-560)))) (-5 *2 (-326 *4)) @@ -5645,61 +5763,40 @@ ((*1 *2 *2) (-12 (-4 *3 (-13 (-466) (-1070 (-560)) (-660 (-560)))) (-5 *1 (-1239 *3 *2)) (-4 *2 (-13 (-27) (-1235) (-435 *3)))))) +(((*1 *2 *3) (-12 (-5 *3 (-793)) (-5 *2 (-1305)) (-5 *1 (-391)))) + ((*1 *2) (-12 (-5 *2 (-1305)) (-5 *1 (-391))))) (((*1 *2 *3 *4) - (-12 (-5 *4 (-560)) (-5 *2 (-663 (-2 (|:| -3498 *3) (|:| -3182 *4)))) - (-5 *1 (-718 *3)) (-4 *3 (-1275 *4))))) -(((*1 *2 *1) (-12 (-4 *1 (-571)) (-5 *2 (-114))))) -(((*1 *2 *3 *4) - (-12 (-5 *4 (-630 *6)) (-4 *6 (-13 (-435 *5) (-27) (-1235))) - (-4 *5 (-13 (-466) (-1070 (-560)) (-149) (-660 (-560)))) - (-5 *2 (-1203 (-421 (-1203 *6)))) (-5 *1 (-575 *5 *6 *7)) - (-5 *3 (-1203 *6)) (-4 *7 (-1133)))) - ((*1 *2 *1) - (-12 (-4 *2 (-1275 *3)) (-5 *1 (-734 *3 *2)) (-4 *3 (-1081)))) - ((*1 *2 *1) - (-12 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(-711 *4)) - (-5 *1 (-1061 *5)) (-4 *5 (-1081)))) - ((*1 *2 *3) - (-12 (-5 *3 (-663 (-560))) (-5 *2 (-711 (-560))) (-5 *1 (-1061 *4)) - (-4 *4 (-1081)))) + (-12 (-5 *3 (-663 *8)) (-5 *4 (-663 *9)) (-4 *8 (-1097 *5 *6 *7)) + (-4 *9 (-1103 *5 *6 *7 *8)) (-4 *5 (-466)) (-4 *6 (-817)) + (-4 *7 (-872)) (-5 *2 (-793)) (-5 *1 (-1101 *5 *6 *7 *8 *9)))) ((*1 *2 *3 *4) - (-12 (-5 *3 (-663 (-932 (-560)))) (-5 *4 (-560)) - (-5 *2 (-663 (-711 *4))) (-5 *1 (-1061 *5)) (-4 *5 (-1081)))) - ((*1 *2 *3) - (-12 (-5 *3 (-663 (-663 (-560)))) (-5 *2 (-663 (-711 (-560)))) - (-5 *1 (-1061 *4)) (-4 *4 (-1081))))) + (-12 (-5 *3 (-663 *8)) (-5 *4 (-663 *9)) (-4 *8 (-1097 *5 *6 *7)) + (-4 *9 (-1141 *5 *6 *7 *8)) (-4 *5 (-466)) (-4 *6 (-817)) + (-4 *7 (-872)) (-5 *2 (-793)) (-5 *1 (-1177 *5 *6 *7 *8 *9))))) +(((*1 *2 *1) + (-12 (-5 *2 (-713 (-898 (-996 *3) (-996 *3)))) (-5 *1 (-996 *3)) + (-4 *3 (-1133))))) +(((*1 *2 *3 *3 *4 *4 *4 *3) + (-12 (-5 *3 (-560)) (-5 *4 (-711 (-229))) (-5 *2 (-1067)) + (-5 *1 (-773))))) +(((*1 *2 *1) + (-12 (-4 *3 (-13 (-376) (-149))) + (-5 *2 (-663 (-2 (|:| -1946 (-793)) (|:| -1839 *4) (|:| |num| *4)))) + (-5 *1 (-413 *3 *4)) (-4 *4 (-1275 *3))))) +(((*1 *1) (-5 *1 (-625)))) (((*1 *2 *1) (-12 (-5 *2 (-1305)) (-5 *1 (-256))))) -(((*1 *2 *3) - (-12 (-5 *2 (-171 *4)) (-5 *1 (-184 *4 *3)) - (-4 *4 (-13 (-376) (-871))) (-4 *3 (-1275 *2))))) -(((*1 *2 *3) (-12 (-5 *2 (-663 (-560))) (-5 *1 (-576)) (-5 *3 (-560))))) +(((*1 *1 *2 *3) + (-12 (-5 *2 (-520)) (-5 *3 (-663 (-995))) (-5 *1 (-109))))) (((*1 *2 *2) - (-12 (-5 *2 (-1187 *3)) (-4 *3 (-1081)) (-5 *1 (-1193 *3)))) - ((*1 *1 *1) - (-12 (-5 *1 (-1289 *2 *3 *4)) (-4 *2 (-1081)) (-14 *3 (-1209)) - (-14 *4 *2)))) + (-12 + (-5 *2 + (-2 (|:| |flg| (-3 "nil" "sqfr" "irred" "prime")) (|:| |fctr| *4) + (|:| |xpnt| (-560)))) + (-4 *4 (-13 (-1275 *3) (-571) (-10 -8 (-15 -4053 ($ $ $))))) + (-4 *3 (-571)) (-5 *1 (-1279 *3 *4))))) +(((*1 *1 *1) + (-12 (-5 *1 (-1172 *2 *3)) (-4 *2 (-13 (-1133) (-34))) + (-4 *3 (-13 (-1133) (-34)))))) (((*1 *2 *1) (-12 (-4 *1 (-168 *2)) (-4 *2 (-175)))) ((*1 *2 *3) (-12 (-4 *4 (-13 (-571) (-1070 (-560)))) (-5 *2 (-326 *4)) @@ -5710,8 +5807,9 @@ (-12 (-4 *3 (-13 (-466) (-1070 (-560)) (-660 (-560)))) (-5 *1 (-1239 *3 *2)) (-4 *2 (-13 (-27) (-1235) (-435 *3)))))) (((*1 *1) (-12 (-5 *1 (-713 *2)) (-4 *2 (-632 (-888)))))) -(((*1 *2 *3 *3) (-12 (-5 *3 (-560)) (-5 *2 (-114)) (-5 *1 (-568))))) -(((*1 *1 *1 *1) (-4 *1 (-559)))) +(((*1 *2 *3) + (-12 (-4 *4 (-363)) (-5 *2 (-988 (-1203 *4))) (-5 *1 (-369 *4)) + (-5 *3 (-1203 *4))))) (((*1 *1 *1) (-4 *1 (-35))) ((*1 *2 *2) (-12 (-4 *3 (-571)) (-5 *1 (-287 *3 *2)) @@ -5728,43 +5826,39 @@ ((*1 *2 *2) (-12 (-5 *2 (-1187 *3)) (-4 *3 (-38 (-421 (-560)))) (-5 *1 (-1195 *3))))) -(((*1 *2 *3 *1 *4) - (-12 (-5 *3 (-1172 *5 *6)) (-5 *4 (-1 (-114) *6 *6)) - (-4 *5 (-13 (-1133) (-34))) (-4 *6 (-13 (-1133) (-34))) - (-5 *2 (-114)) (-5 *1 (-1173 *5 *6))))) +(((*1 *2 *2) (|partial| -12 (-4 *1 (-1015 *2)) (-4 *2 (-1235))))) +(((*1 *2 *1) (-12 (-4 *1 (-541)) (-5 *2 (-713 (-1255)))))) +(((*1 *2) (-12 (-5 *2 (-1191)) (-5 *1 (-1219))))) +(((*1 *1 *2 *3) + (-12 (-5 *3 (-1209)) (-5 *1 (-597 *2)) (-4 *2 (-1070 *3)) + (-4 *2 (-376)))) + ((*1 *1 *2 *2) (-12 (-5 *1 (-597 *2)) (-4 *2 (-376)))) + ((*1 *2 *2 *3) + (-12 (-5 *3 (-1209)) (-4 *4 (-571)) (-5 *1 (-648 *4 *2)) + (-4 *2 (-13 (-435 *4) (-1034) (-1235))))) + ((*1 *2 *2 *3) + (-12 (-5 *3 (-1124 *2)) (-4 *2 (-13 (-435 *4) (-1034) (-1235))) + (-4 *4 (-571)) (-5 *1 (-648 *4 *2)))) + ((*1 *1 *1 *2) (-12 (-4 *1 (-990)) (-5 *2 (-1209)))) + ((*1 *1 *1 *2) (-12 (-5 *2 (-1124 *1)) (-4 *1 (-990))))) (((*1 *2 *3) - (-12 (-14 *4 (-663 (-1209))) (-14 *5 (-793)) + (-12 (-5 *3 (-663 *7)) (-4 *7 (-980 *4 *5 *6)) (-4 *4 (-466)) + (-4 *5 (-817)) (-4 *6 (-872)) (-5 *2 (-1305)) + (-5 *1 (-464 *4 *5 *6 *7))))) +(((*1 *2 *3 *4) + (-12 (-5 *3 (-711 *8)) (-5 *4 (-793)) (-4 *8 (-980 *5 *7 *6)) + (-4 *5 (-13 (-319) (-149))) (-4 *6 (-13 (-872) (-633 (-1209)))) + (-4 *7 (-817)) (-5 *2 (-663 - (-518 (-421 (-560)) (-246 *5 (-793)) (-889 *4) - (-255 *4 (-421 (-560)))))) - (-5 *1 (-519 *4 *5)) - (-5 *3 - (-518 (-421 (-560)) (-246 *5 (-793)) (-889 *4) - (-255 *4 (-421 (-560)))))))) -(((*1 *2 *2) - (-12 (-5 *2 (-663 *7)) (-4 *7 (-1103 *3 *4 *5 *6)) (-4 *3 (-466)) - (-4 *4 (-817)) (-4 *5 (-872)) (-4 *6 (-1097 *3 *4 *5)) - (-5 *1 (-1020 *3 *4 *5 *6 *7)))) - ((*1 *2 *2) - (-12 (-5 *2 (-663 *7)) (-4 *7 (-1103 *3 *4 *5 *6)) (-4 *3 (-466)) - (-4 *4 (-817)) (-4 *5 (-872)) (-4 *6 (-1097 *3 *4 *5)) - (-5 *1 (-1139 *3 *4 *5 *6 *7))))) -(((*1 *2 *3 *3 *3 *4 *3 *3 *4 *4 *4 *5) - (-12 (-5 *3 (-229)) (-5 *4 (-560)) - (-5 *5 (-3 (|:| |fn| (-402)) (|:| |fp| (-61 G)))) (-5 *2 (-1067)) - (-5 *1 (-770))))) -(((*1 *2 *1) (-12 (-5 *2 (-1305)) (-5 *1 (-847))))) -(((*1 *2 *3) - (-12 (-5 *3 (-1121 (-866 (-229)))) (-5 *2 (-229)) (-5 *1 (-195)))) - ((*1 *2 *3) - (-12 (-5 *3 (-1121 (-866 (-229)))) (-5 *2 (-229)) (-5 *1 (-313)))) - ((*1 *2 *3) - (-12 (-5 *3 (-1121 (-866 (-229)))) (-5 *2 (-229)) (-5 *1 (-315))))) -(((*1 *2 *1 *3) (-12 (-5 *3 (-949)) (-5 *2 (-482)) (-5 *1 (-1302))))) -(((*1 *1 *1 *2) - (-12 (-5 *1 (-1172 *3 *2)) (-4 *3 (-13 (-1133) (-34))) - (-4 *2 (-13 (-1133) (-34)))))) + (-2 (|:| |det| *8) (|:| |rows| (-663 (-560))) + (|:| |cols| (-663 (-560)))))) + (-5 *1 (-954 *5 *6 *7 *8))))) +(((*1 *2 *2) (-12 (-5 *2 (-391)) (-5 *1 (-1303)))) + ((*1 *2) (-12 (-5 *2 (-391)) (-5 *1 (-1303))))) +(((*1 *2 *2 *3) + (-12 (-5 *2 (-663 (-976 *4))) (-5 *3 (-663 (-1209))) (-4 *4 (-466)) + (-5 *1 (-948 *4))))) (((*1 *1 *1) (-12 (-5 *1 (-352 *2 *3 *4)) (-14 *2 (-663 (-1209))) (-14 *3 (-663 (-1209))) (-4 *4 (-401)))) @@ -5774,11 +5868,10 @@ ((*1 *1 *2) (-12 (-5 *2 (-421 (-560))) (-4 *1 (-1044)))) ((*1 *1 *1 *2) (-12 (-4 *1 (-1044)) (-5 *2 (-949)))) ((*1 *1 *1) (-4 *1 (-1044)))) -(((*1 *1 *1) - (-12 (-5 *1 (-50 *2 *3)) (-4 *2 (-1081)) (-14 *3 (-663 (-1209))))) - ((*1 *1 *1) - (-12 (-5 *1 (-227 *2 *3)) (-4 *2 (-13 (-1081) (-872))) - (-14 *3 (-663 (-1209)))))) +(((*1 *2 *3 *4) + (-12 (-4 *5 (-466)) (-4 *6 (-817)) (-4 *7 (-872)) + (-4 *3 (-1097 *5 *6 *7)) (-5 *2 (-663 *4)) + (-5 *1 (-1140 *5 *6 *7 *3 *4)) (-4 *4 (-1103 *5 *6 *7 *3))))) (((*1 *1 *1) (-4 *1 (-35))) ((*1 *2 *2) (-12 (-4 *3 (-571)) (-5 *1 (-287 *3 *2)) @@ -5795,57 +5888,37 @@ ((*1 *2 *2) (-12 (-5 *2 (-1187 *3)) (-4 *3 (-38 (-421 (-560)))) (-5 *1 (-1195 *3))))) -(((*1 *2 *2 *3) - (-12 (-5 *3 (-663 *2)) (-4 *2 (-980 *4 *5 *6)) (-4 *4 (-376)) - (-4 *4 (-466)) (-4 *5 (-817)) (-4 *6 (-872)) - (-5 *1 (-461 *4 *5 *6 *2)))) - ((*1 *2 *3 *4 *5) - (-12 (-5 *4 (-99 *6)) (-5 *5 (-1 *6 *6)) (-4 *6 (-376)) - (-5 *2 - (-2 (|:| R (-711 *6)) (|:| A (-711 *6)) (|:| |Ainv| (-711 *6)))) - (-5 *1 (-1010 *6)) (-5 *3 (-711 *6))))) -(((*1 *2) - (-12 (-4 *2 (-13 (-435 *3) (-1034))) (-5 *1 (-287 *3 *2)) - (-4 *3 (-571))))) (((*1 *2) (-12 (-4 *4 (-175)) (-5 *2 (-114)) (-5 *1 (-379 *3 *4)) (-4 *3 (-380 *4)))) ((*1 *2) (-12 (-4 *1 (-380 *3)) (-4 *3 (-175)) (-5 *2 (-114))))) -(((*1 *1) - (|partial| -12 (-4 *1 (-380 *2)) (-4 *2 (-571)) (-4 *2 (-175))))) -(((*1 *2 *3 *4) - (-12 (-5 *3 (-1 *6 *5 *4)) (-4 *5 (-1133)) (-4 *4 (-1133)) - (-4 *6 (-1133)) (-5 *2 (-1 *6 *5)) (-5 *1 (-706 *5 *4 *6))))) -(((*1 *2 *3) - (-12 (-5 *3 (-1078 *4 *5)) (-4 *4 (-13 (-871) (-319) (-149) (-1052))) - (-14 *5 (-663 (-1209))) - (-5 *2 - (-663 (-2 (|:| -2042 (-1203 *4)) (|:| -2678 (-663 (-976 *4)))))) - (-5 *1 (-1327 *4 *5 *6)) (-14 *6 (-663 (-1209))))) - ((*1 *2 *3 *4 *4 *4) - (-12 (-5 *4 (-114)) (-4 *5 (-13 (-871) (-319) (-149) (-1052))) - (-5 *2 - (-663 (-2 (|:| -2042 (-1203 *5)) (|:| -2678 (-663 (-976 *5)))))) - (-5 *1 (-1327 *5 *6 *7)) (-5 *3 (-663 (-976 *5))) - (-14 *6 (-663 (-1209))) (-14 *7 (-663 (-1209))))) - ((*1 *2 *3 *4 *4) - (-12 (-5 *4 (-114)) (-4 *5 (-13 (-871) (-319) (-149) (-1052))) - (-5 *2 - (-663 (-2 (|:| -2042 (-1203 *5)) (|:| -2678 (-663 (-976 *5)))))) - (-5 *1 (-1327 *5 *6 *7)) (-5 *3 (-663 (-976 *5))) - (-14 *6 (-663 (-1209))) (-14 *7 (-663 (-1209))))) - ((*1 *2 *3 *4) - (-12 (-5 *4 (-114)) (-4 *5 (-13 (-871) (-319) (-149) (-1052))) - (-5 *2 - (-663 (-2 (|:| -2042 (-1203 *5)) (|:| -2678 (-663 (-976 *5)))))) - (-5 *1 (-1327 *5 *6 *7)) (-5 *3 (-663 (-976 *5))) - (-14 *6 (-663 (-1209))) (-14 *7 (-663 (-1209))))) +(((*1 *2 *1 *3) + (-12 (-4 *1 (-262 *4 *3 *5 *6)) (-4 *4 (-1081)) (-4 *3 (-872)) + (-4 *5 (-277 *3)) (-4 *6 (-817)) (-5 *2 (-663 (-793))))) + ((*1 *2 *1) + (-12 (-4 *1 (-262 *3 *4 *5 *6)) (-4 *3 (-1081)) (-4 *4 (-872)) + (-4 *5 (-277 *4)) (-4 *6 (-817)) (-5 *2 (-663 (-793)))))) +(((*1 *2 *2 *3) + (-12 (-5 *3 (-1 (-114) *4 *4)) (-4 *4 (-1249)) (-5 *1 (-1164 *4 *2)) + (-4 *2 (-13 (-618 (-560) *4) (-10 -7 (-6 -4510) (-6 -4511)))))) + ((*1 *2 *2) + (-12 (-4 *3 (-872)) (-4 *3 (-1249)) (-5 *1 (-1164 *3 *2)) + (-4 *2 (-13 (-618 (-560) *3) (-10 -7 (-6 -4510) (-6 -4511))))))) +(((*1 *2) (-12 (-5 *2 (-560)) (-5 *1 (-957))))) +(((*1 *2 *2) (|partial| -12 (-4 *1 (-1015 *2)) (-4 *2 (-1235))))) +(((*1 *2 *2) (|partial| -12 (-4 *1 (-1015 *2)) (-4 *2 (-1235))))) +(((*1 *2 *1) + (-12 (-5 *2 (-177 (-421 (-560)))) (-5 *1 (-119 *3)) (-14 *3 (-560)))) + ((*1 *1 *2 *3 *3) + (-12 (-5 *3 (-1187 *2)) (-4 *2 (-319)) (-5 *1 (-177 *2)))) + ((*1 *1 *2) (-12 (-5 *2 (-421 *3)) (-4 *3 (-319)) (-5 *1 (-177 *3)))) ((*1 *2 *3) - (-12 (-4 *4 (-13 (-871) (-319) (-149) (-1052))) - (-5 *2 - (-663 (-2 (|:| -2042 (-1203 *4)) (|:| -2678 (-663 (-976 *4)))))) - (-5 *1 (-1327 *4 *5 *6)) (-5 *3 (-663 (-976 *4))) - (-14 *5 (-663 (-1209))) (-14 *6 (-663 (-1209)))))) + (-12 (-5 *2 (-177 (-560))) (-5 *1 (-787 *3)) (-4 *3 (-418)))) + ((*1 *2 *1) + (-12 (-5 *2 (-177 (-421 (-560)))) (-5 *1 (-896 *3)) (-14 *3 (-560)))) + ((*1 *2 *1) + (-12 (-14 *3 (-560)) (-5 *2 (-177 (-421 (-560)))) + (-5 *1 (-897 *3 *4)) (-4 *4 (-895 *3))))) (((*1 *2 *3 *4) (-12 (-5 *4 (-663 (-48))) (-5 *2 (-419 *3)) (-5 *1 (-39 *3)) (-4 *3 (-1275 (-48))))) @@ -5894,8 +5967,8 @@ (-12 (-4 *4 (-13 (-872) - (-10 -8 (-15 -2574 ((-1209) $)) - (-15 -2740 ((-3 $ "failed") (-1209)))))) + (-10 -8 (-15 -2558 ((-1209) $)) + (-15 -2735 ((-3 $ "failed") (-1209)))))) (-4 *5 (-817)) (-4 *7 (-571)) (-5 *2 (-419 *3)) (-5 *1 (-470 *4 *5 *6 *7 *3)) (-4 *6 (-571)) (-4 *3 (-980 *7 *5 *4)))) @@ -5944,13 +6017,13 @@ (-12 (-4 *4 (-817)) (-4 *5 (-13 (-872) - (-10 -8 (-15 -2574 ((-1209) $)) - (-15 -2740 ((-3 $ "failed") (-1209)))))) + (-10 -8 (-15 -2558 ((-1209) $)) + (-15 -2735 ((-3 $ "failed") (-1209)))))) (-4 *6 (-319)) (-5 *2 (-419 *3)) (-5 *1 (-752 *4 *5 *6 *3)) (-4 *3 (-980 (-976 *6) *4 *5)))) ((*1 *2 *3) (-12 (-4 *4 (-817)) - (-4 *5 (-13 (-872) (-10 -8 (-15 -2574 ((-1209) $))))) (-4 *6 (-571)) + (-4 *5 (-13 (-872) (-10 -8 (-15 -2558 ((-1209) $))))) (-4 *6 (-571)) (-5 *2 (-419 *3)) (-5 *1 (-754 *4 *5 *6 *3)) (-4 *3 (-980 (-421 (-976 *6)) *4 *5)))) ((*1 *2 *3) @@ -5986,85 +6059,12 @@ ((*1 *2 *1) (-12 (-5 *2 (-419 *1)) (-4 *1 (-1254)))) ((*1 *2 *3) (-12 (-5 *2 (-419 *3)) (-5 *1 (-1265 *3)) (-4 *3 (-1275 (-560)))))) -(((*1 *2 *3 *4 *2) - (-12 (-5 *2 (-663 (-2 (|:| |totdeg| (-793)) (|:| -2895 *3)))) - (-5 *4 (-793)) (-4 *3 (-980 *5 *6 *7)) (-4 *5 (-466)) (-4 *6 (-817)) - (-4 *7 (-872)) (-5 *1 (-464 *5 *6 *7 *3))))) -(((*1 *2 *1 *3 *4) - (-12 (-5 *3 (-949)) (-5 *4 (-1191)) (-5 *2 (-1305)) (-5 *1 (-1302))))) -(((*1 *2 *1) - (-12 (-4 *1 (-262 *3 *4 *5 *6)) (-4 *3 (-1081)) (-4 *4 (-872)) - (-4 *5 (-277 *4)) (-4 *6 (-817)) (-5 *2 (-663 *4))))) -(((*1 *1 *1) (-4 *1 (-35))) - ((*1 *2 *2) - (-12 (-4 *3 (-571)) (-5 *1 (-287 *3 *2)) - (-4 *2 (-13 (-435 *3) (-1034))))) - ((*1 *2 *2) - (-12 (-4 *3 (-38 (-421 (-560)))) (-4 *4 (-1292 *3)) - (-5 *1 (-289 *3 *4 *2)) (-4 *2 (-1263 *3 *4)))) - ((*1 *2 *2) - (-12 (-4 *3 (-38 (-421 (-560)))) (-4 *4 (-1261 *3)) - (-5 *1 (-290 *3 *4 *2 *5)) (-4 *2 (-1284 *3 *4)) (-4 *5 (-1015 *4)))) - ((*1 *2 *2) - (-12 (-5 *2 (-1187 *3)) (-4 *3 (-38 (-421 (-560)))) - (-5 *1 (-1194 *3)))) - ((*1 *2 *2) - (-12 (-5 *2 (-1187 *3)) (-4 *3 (-38 (-421 (-560)))) - (-5 *1 (-1195 *3))))) -(((*1 *1 *2 *2) (-12 (-5 *1 (-903 *2)) (-4 *2 (-1249)))) - ((*1 *1 *2 *2 *2) (-12 (-5 *1 (-905 *2)) (-4 *2 (-1249)))) - ((*1 *2 *1) - (-12 (-4 *1 (-1166 *3)) (-4 *3 (-1081)) (-5 *2 (-663 (-973 *3))))) - ((*1 *1 *2) - (-12 (-5 *2 (-663 (-973 *3))) (-4 *3 (-1081)) (-4 *1 (-1166 *3)))) - ((*1 *1 *1 *2) - (-12 (-5 *2 (-663 (-663 *3))) (-4 *1 (-1166 *3)) (-4 *3 (-1081)))) - ((*1 *1 *1 *2) - (-12 (-5 *2 (-663 (-973 *3))) (-4 *1 (-1166 *3)) (-4 *3 (-1081))))) -(((*1 *2 *1) (-12 (-5 *2 (-1121 (-229))) (-5 *1 (-955)))) - ((*1 *2 *1) (-12 (-5 *2 (-1121 (-229))) (-5 *1 (-957))))) -(((*1 *2 *2) (-12 (-5 *2 (-229)) (-5 *1 (-230)))) - ((*1 *2 *2) (-12 (-5 *2 (-171 (-229))) (-5 *1 (-230)))) - ((*1 *2 *2) - (-12 (-4 *3 (-571)) (-5 *1 (-445 *3 *2)) (-4 *2 (-435 *3)))) - ((*1 *1 *1) (-4 *1 (-1171)))) -(((*1 *2 *3 *3 *3 *4 *3) - (-12 (-5 *3 (-560)) (-5 *4 (-711 (-229))) (-5 *2 (-1067)) - (-5 *1 (-776))))) -(((*1 *1) (-5 *1 (-303)))) -(((*1 *2) - (-12 - (-5 *2 - (-1299 (-663 (-2 (|:| -3677 (-936 *3)) (|:| -2183 (-1152)))))) - (-5 *1 (-365 *3 *4)) (-14 *3 (-949)) (-14 *4 (-949)))) - ((*1 *2) - (-12 (-5 *2 (-1299 (-663 (-2 (|:| -3677 *3) (|:| -2183 (-1152)))))) - (-5 *1 (-366 *3 *4)) (-4 *3 (-363)) (-14 *4 (-3 (-1203 *3) *2)))) - ((*1 *2) - (-12 (-5 *2 (-1299 (-663 (-2 (|:| -3677 *3) (|:| -2183 (-1152)))))) - (-5 *1 (-367 *3 *4)) (-4 *3 (-363)) (-14 *4 (-949))))) -(((*1 *2 *2) - (-12 (-4 *3 (-13 (-571) (-149))) (-5 *1 (-551 *3 *2)) - (-4 *2 (-1292 *3)))) - ((*1 *2 *2) - (-12 (-4 *3 (-13 (-376) (-381) (-633 (-560)))) (-4 *4 (-1275 *3)) - (-4 *5 (-746 *3 *4)) (-5 *1 (-555 *3 *4 *5 *2)) (-4 *2 (-1292 *5)))) - ((*1 *2 *2) - (-12 (-4 *3 (-13 (-376) (-381) (-633 (-560)))) (-5 *1 (-556 *3 *2)) - (-4 *2 (-1292 *3)))) - ((*1 *2 *2) - (-12 (-5 *2 (-1187 *3)) (-4 *3 (-13 (-571) (-149))) - (-5 *1 (-1186 *3))))) -(((*1 *2 *3 *3 *4 *4 *5 *5 *3 *3 *4 *4 *5 *5 *3 *3 *4 *4 *5 *5 *3 *4 *4 - *4 *6 *4) - (-12 (-5 *4 (-560)) (-5 *5 (-711 (-229))) (-5 *6 (-697 (-229))) - (-5 *3 (-229)) (-5 *2 (-1067)) (-5 *1 (-772))))) (((*1 *2 *3) - (-12 (-5 *3 (-663 (-326 (-229)))) (-5 *2 (-114)) (-5 *1 (-278)))) - ((*1 *2 *3) (-12 (-5 *3 (-326 (-229))) (-5 *2 (-114)) (-5 *1 (-278)))) - ((*1 *2 *3) - (-12 (-4 *4 (-571)) (-4 *5 (-817)) (-4 *6 (-872)) (-5 *2 (-114)) - (-5 *1 (-1009 *4 *5 *6 *3)) (-4 *3 (-1097 *4 *5 *6))))) + (-12 (-5 *3 (-421 (-976 *4))) (-4 *4 (-319)) + (-5 *2 (-421 (-419 (-976 *4)))) (-5 *1 (-1075 *4))))) +(((*1 *2 *3 *4 *4 *4 *4) + (-12 (-5 *3 (-711 (-229))) (-5 *4 (-560)) (-5 *2 (-1067)) + (-5 *1 (-777))))) (((*1 *1 *1) (-4 *1 (-35))) ((*1 *2 *2) (-12 (-4 *3 (-571)) (-5 *1 (-287 *3 *2)) @@ -6081,19 +6081,39 @@ ((*1 *2 *2) (-12 (-5 *2 (-1187 *3)) (-4 *3 (-38 (-421 (-560)))) (-5 *1 (-1195 *3))))) -(((*1 *2 *2 *2 *3) - (-12 (-5 *3 (-793)) (-4 *4 (-13 (-1081) (-739 (-421 (-560))))) - (-4 *5 (-872)) (-5 *1 (-1316 *4 *5 *2)) (-4 *2 (-1322 *5 *4))))) +(((*1 *2 *3 *3 *4 *3) + (-12 (-5 *3 (-560)) (-5 *4 (-711 (-229))) (-5 *2 (-1067)) + (-5 *1 (-769))))) (((*1 *1 *1) - (-12 (-4 *1 (-1097 *2 *3 *4)) (-4 *2 (-1081)) (-4 *3 (-817)) - (-4 *4 (-872)) (-4 *2 (-571))))) + (-12 (-5 *1 (-609 *2)) (-4 *2 (-38 (-421 (-560)))) (-4 *2 (-1081))))) +(((*1 *2 *2) (|partial| -12 (-4 *1 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(-10 -8 (-15 -3903 ($ *7)) (-15 -2841 (*7 $)) (-15 -2854 (*7 $))))))) + (-10 -8 (-15 -3866 ($ *7)) (-15 -2833 (*7 $)) (-15 -2845 (*7 $))))))) ((*1 *2 *3 *4 *2) (-12 (-5 *2 (-1203 *3)) (-4 *3 (-13 (-376) - (-10 -8 (-15 -3903 ($ *7)) (-15 -2841 (*7 $)) (-15 -2854 (*7 $))))) + (-10 -8 (-15 -3866 ($ *7)) (-15 -2833 (*7 $)) (-15 -2845 (*7 $))))) (-4 *7 (-980 *6 *5 *4)) (-4 *5 (-817)) (-4 *4 (-872)) (-4 *6 (-1081)) (-5 *1 (-981 *5 *4 *6 *7 *3)))) ((*1 *2 *3 *4) (-12 (-5 *4 (-1209)) (-4 *5 (-571)) (-5 *2 (-421 (-1203 (-421 (-976 *5))))) (-5 *1 (-1072 *5)) (-5 *3 (-421 (-976 *5)))))) -(((*1 *2 *3 *3 *4 *3 *5 *3 *5 *4 *5 *5 *4 *4 *5 *3) - (-12 (-5 *4 (-711 (-229))) (-5 *5 (-711 (-560))) (-5 *3 (-560)) - (-5 *2 (-1067)) (-5 *1 (-778))))) -(((*1 *1 *2 *3 *4) - (-12 (-5 *3 (-560)) (-5 *4 (-3 "nil" "sqfr" "irred" "prime")) - (-5 *1 (-419 *2)) (-4 *2 (-571))))) -(((*1 *2 *1) (-12 (-5 *2 (-1187 *3)) (-5 *1 (-177 *3)) (-4 *3 (-319))))) +(((*1 *2 *2 *2) + (-12 (-5 *2 (-663 *3)) (-4 *3 (-872)) (-5 *1 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(-445 *3 *2)) (-4 *2 (-435 *3))))) (((*1 *2 *2) (-12 (-4 *3 (-571)) (-5 *1 (-287 *3 *2)) (-4 *2 (-13 (-435 *3) (-1034))))) @@ -6497,69 +6634,62 @@ ((*1 *2 *2) (-12 (-5 *2 (-1187 *3)) (-4 *3 (-38 (-421 (-560)))) (-5 *1 (-1195 *3))))) -(((*1 *2 *2 *3) - (-12 (-5 *3 (-793)) (-4 *4 (-376)) (-5 *1 (-924 *2 *4)) - (-4 *2 (-1275 *4))))) -(((*1 *1 *2 *3) - (-12 (-5 *2 (-1299 (-1209))) (-5 *3 (-1299 (-467 *4 *5 *6 *7))) - (-5 *1 (-467 *4 *5 *6 *7)) (-4 *4 (-175)) (-14 *5 (-949)) - (-14 *6 (-663 (-1209))) (-14 *7 (-1299 (-711 *4))))) - ((*1 *1 *2 *3) - (-12 (-5 *2 (-1209)) (-5 *3 (-1299 (-467 *4 *5 *6 *7))) - (-5 *1 (-467 *4 *5 *6 *7)) (-4 *4 (-175)) (-14 *5 (-949)) - (-14 *6 (-663 *2)) (-14 *7 (-1299 (-711 *4))))) - ((*1 *1 *2) - (-12 (-5 *2 (-1299 (-467 *3 *4 *5 *6))) (-5 *1 (-467 *3 *4 *5 *6)) - (-4 *3 (-175)) (-14 *4 (-949)) (-14 *5 (-663 (-1209))) - (-14 *6 (-1299 (-711 *3))))) - ((*1 *1 *2) - (-12 (-5 *2 (-1299 (-1209))) (-5 *1 (-467 *3 *4 *5 *6)) - (-4 *3 (-175)) (-14 *4 (-949)) (-14 *5 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(-663 - (-2 (|:| |det| *7) (|:| |rows| (-663 (-560))) - (|:| |cols| (-663 (-560)))))) - (|:| |fgb| (-663 *7))))) - (-4 *7 (-980 *4 *6 *5)) (-4 *4 (-13 (-319) (-149))) - (-4 *5 (-13 (-872) (-633 (-1209)))) (-4 *6 (-817)) (-5 *2 (-793)) - (-5 *1 (-954 *4 *5 *6 *7))))) -(((*1 *2 *1 *3) (-12 (-5 *3 (-1191)) (-5 *2 (-1305)) (-5 *1 (-1303))))) + (-2 (|:| -2087 (-663 *9)) (|:| -4461 *10) (|:| |ineq| (-663 *9))))) + (-5 *1 (-1020 *6 *7 *8 *9 *10)) (-5 *3 (-663 *9)))) + ((*1 *2 *3 *4 *5 *5) + (-12 (-5 *4 (-663 *10)) (-5 *5 (-114)) (-4 *10 (-1103 *6 *7 *8 *9)) + (-4 *6 (-466)) (-4 *7 (-817)) (-4 *8 (-872)) + (-4 *9 (-1097 *6 *7 *8)) + (-5 *2 + (-663 + (-2 (|:| -2087 (-663 *9)) (|:| -4461 *10) (|:| |ineq| (-663 *9))))) + (-5 *1 (-1139 *6 *7 *8 *9 *10)) (-5 *3 (-663 *9))))) +(((*1 *2 *3) + (-12 (-5 *3 (-229)) (-5 *2 (-114)) (-5 *1 (-314 *4 *5)) (-14 *4 *3) + (-14 *5 *3))) + ((*1 *2 *3 *4) + (-12 (-5 *4 (-1121 (-866 (-229)))) (-5 *3 (-229)) (-5 *2 (-114)) + (-5 *1 (-315)))) + ((*1 *2 *1 *1) + (-12 (-4 *3 (-376)) (-4 *4 (-817)) (-4 *5 (-872)) (-5 *2 (-114)) + (-5 *1 (-518 *3 *4 *5 *6)) (-4 *6 (-980 *3 *4 *5))))) +(((*1 *2 *2 *3) + (|partial| -12 (-5 *3 (-793)) (-4 *1 (-1015 *2)) (-4 *2 (-1235))))) +(((*1 *2) (-12 (-5 *2 (-1305)) (-5 *1 (-827))))) +(((*1 *2 *2 *2) + (-12 (-5 *2 (-663 *6)) (-4 *6 (-1097 *3 *4 *5)) (-4 *3 (-466)) + (-4 *3 (-571)) (-4 *4 (-817)) (-4 *5 (-872)) + (-5 *1 (-1009 *3 *4 *5 *6))))) +(((*1 *2 *2) (-12 (-5 *2 (-560)) (-5 *1 (-267))))) (((*1 *2 *2) (-12 (-4 *3 (-571)) (-5 *1 (-287 *3 *2)) (-4 *2 (-13 (-435 *3) (-1034))))) @@ -6579,107 +6709,36 @@ ((*1 *2 *2) (-12 (-5 *2 (-1187 *3)) (-4 *3 (-38 (-421 (-560)))) (-5 *1 (-1195 *3))))) +(((*1 *2 *1) (-12 (-5 *2 (-663 (-862))) (-5 *1 (-142))))) (((*1 *2 *3) - (-12 (-5 *2 (-419 *3)) (-5 *1 (-39 *3)) (-4 *3 (-1275 (-48))))) - ((*1 *2 *3 *1) - (-12 (-5 *2 (-2 (|:| |less| (-123 *3)) (|:| |greater| (-123 *3)))) - (-5 *1 (-123 *3)) (-4 *3 (-872)))) - ((*1 *2 *2) - (-12 (-5 *2 (-597 *4)) (-4 *4 (-13 (-29 *3) (-1235))) - 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(-5 *2 (-793)) - (-5 *1 (-689 *5 *6 *4 *3)) (-4 *3 (-708 *5 *6 *4)))) - ((*1 *2 *3 *4) - (-12 (-5 *3 (-711 *5)) (-5 *4 (-1299 *5)) (-4 *5 (-376)) - (-5 *2 (-793)) (-5 *1 (-690 *5)))) - ((*1 *2 *1) - (-12 (-4 *1 (-708 *3 *4 *5)) (-4 *3 (-1081)) (-4 *4 (-385 *3)) - (-4 *5 (-385 *3)) (-4 *3 (-571)) (-5 *2 (-793)))) - ((*1 *2 *3) - (-12 (-4 *4 (-571)) (-4 *4 (-175)) (-4 *5 (-385 *4)) - (-4 *6 (-385 *4)) (-5 *2 (-793)) (-5 *1 (-710 *4 *5 *6 *3)) - (-4 *3 (-708 *4 *5 *6)))) - ((*1 *2 *1) - (-12 (-4 *1 (-1085 *3 *4 *5 *6 *7)) (-4 *5 (-1081)) - (-4 *6 (-245 *4 *5)) (-4 *7 (-245 *3 *5)) (-4 *5 (-571)) - (-5 *2 (-793))))) + (-12 (-5 *3 (-1299 *5)) (-4 *5 (-13 (-1081) (-660 *4))) + (-4 *4 (-571)) (-5 *2 (-114)) (-5 *1 (-658 *4 *5))))) +(((*1 *2 *2 *3 *4) + (|partial| -12 (-5 *3 (-793)) (-4 *4 (-13 (-571) (-149))) + (-5 *1 (-1271 *4 *2)) (-4 *2 (-1275 *4))))) +(((*1 *2 *1) (-12 (-5 *2 (-850)) (-5 *1 (-849))))) +(((*1 *2 *3) + (-12 (-5 *2 (-1 *3 *3)) (-5 *1 (-544 *3)) (-4 *3 (-13 (-748) (-25)))))) +(((*1 *2 *1) (-12 (-5 *2 (-114)) (-5 *1 (-448))))) +(((*1 *1 *1) + (-12 (-5 *1 (-609 *2)) (-4 *2 (-38 (-421 (-560)))) (-4 *2 (-1081))))) (((*1 *2 *2) (-12 (-4 *3 (-571)) (-5 *1 (-287 *3 *2)) (-4 *2 (-13 (-435 *3) (-1034))))) @@ -6699,55 +6758,39 @@ ((*1 *2 *2) (-12 (-5 *2 (-1187 *3)) (-4 *3 (-38 (-421 (-560)))) (-5 *1 (-1195 *3))))) -(((*1 *2 *1) (-12 (-5 *2 (-1305)) (-5 *1 (-847))))) -(((*1 *2 *3 *3 *4 *3 *4 *4 *4 *4 *5) - (-12 (-5 *3 (-229)) (-5 *4 (-560)) - (-5 *5 (-3 (|:| |fn| (-402)) (|:| |fp| (-61 G)))) (-5 *2 (-1067)) - (-5 *1 (-770))))) -(((*1 *1 *1 *2 *3) - (-12 (-5 *2 (-793)) (-5 *3 (-973 *5)) (-4 *5 (-1081)) - (-5 *1 (-1197 *4 *5)) (-14 *4 (-949)))) - ((*1 *1 *1 *2 *3) - (-12 (-5 *2 (-663 (-793))) (-5 *3 (-793)) (-5 *1 (-1197 *4 *5)) - (-14 *4 (-949)) (-4 *5 (-1081)))) - ((*1 *1 *1 *2 *3) - (-12 (-5 *2 (-663 (-793))) (-5 *3 (-973 *5)) (-4 *5 (-1081)) - (-5 *1 (-1197 *4 *5)) (-14 *4 (-949))))) -(((*1 *2 *2 *2) - (-12 (-5 *2 (-711 *3)) (-4 *3 (-1081)) (-5 *1 (-712 *3)))) - ((*1 *2 *2 *2 *2) - (-12 (-5 *2 (-711 *3)) (-4 *3 (-1081)) (-5 *1 (-712 *3))))) -(((*1 *2 *3 *4) - (-12 (-5 *3 (-229)) (-5 *4 (-560)) (-5 *2 (-1067)) (-5 *1 (-780))))) -(((*1 *2 *3 *4) - (-12 (-5 *4 (-663 *3)) (-4 *3 (-980 *5 *6 *7)) (-4 *5 (-466)) - (-4 *6 (-817)) (-4 *7 (-872)) - (-5 *2 (-2 (|:| |poly| *3) (|:| |mult| *5))) - (-5 *1 (-464 *5 *6 *7 *3))))) -(((*1 *2 *1) (-12 (-4 *1 (-1006)) (-5 *2 (-1121 (-229)))))) +(((*1 *1 *2) (-12 (-5 *2 (-159)) (-5 *1 (-899))))) +(((*1 *2 *3 *4 *4 *4 *3 *3 *5 *5 *3) + (-12 (-5 *3 (-560)) (-5 *4 (-711 (-229))) (-5 *5 (-229)) + (-5 *2 (-1067)) (-5 *1 (-773))))) +(((*1 *2 *3) + (|partial| -12 (-5 *3 (-1299 *5)) (-4 *5 (-13 (-1081) (-660 *4))) + (-4 *4 (-571)) (-5 *2 (-1299 *4)) (-5 *1 (-658 *4 *5))))) +(((*1 *2 *1 *1) + (-12 (-4 *1 (-1042 *3)) (-4 *3 (-1249)) (-4 *3 (-1133)) + (-5 *2 (-114))))) +(((*1 *1) (-5 *1 (-146))) ((*1 *1 *1) (-5 *1 (-888)))) +(((*1 *2 *1) (-12 (-5 *2 (-560)) (-5 *1 (-944 *3)) (-4 *3 (-319))))) (((*1 *2 *3) (-12 (-5 *3 (-1191)) (-5 *2 (-1305)) (-5 *1 (-248)))) ((*1 *2 *3) (-12 (-5 *3 (-663 (-1191))) (-5 *2 (-1305)) (-5 *1 (-248))))) -(((*1 *2 *3) - (|partial| -12 (-4 *4 (-13 (-571) (-149))) - (-5 *2 (-2 (|:| -1985 *3) (|:| -1996 *3))) (-5 *1 (-1271 *4 *3)) - (-4 *3 (-1275 *4))))) (((*1 *2 *1 *1) - (-12 (-5 *2 (-421 (-560))) (-5 *1 (-1056 *3)) - (-4 *3 (-13 (-871) (-376) (-1052))))) - ((*1 *2 *3 *1 *2) - (-12 (-4 *2 (-13 (-871) (-376))) (-5 *1 (-1093 *2 *3)) - (-4 *3 (-1275 *2)))) - ((*1 *2 *3 *1 *2) - (-12 (-4 *1 (-1100 *2 *3)) (-4 *2 (-13 (-871) (-376))) - (-4 *3 (-1275 *2))))) -(((*1 *1) (-5 *1 (-611)))) -(((*1 *2 *2 *1) (-12 (-4 *1 (-263 *2)) (-4 *2 (-1249))))) -(((*1 *2 *1) - (-12 (-4 *3 (-376)) (-4 *4 (-1275 *3)) (-4 *5 (-1275 (-421 *4))) - (-5 *2 (-1299 *6)) (-5 *1 (-346 *3 *4 *5 *6)) - (-4 *6 (-355 *3 *4 *5))))) -(((*1 *1) (-5 *1 (-146)))) + (-12 (-4 *1 (-1131 *3)) (-4 *3 (-1133)) (-5 *2 (-114))))) +(((*1 *2 *3 *4 *4 *3 *5 *3 *6 *4 *7 *8 *9) + (-12 (-5 *4 (-560)) (-5 *5 (-1191)) (-5 *6 (-711 (-229))) + (-5 *7 (-3 (|:| |fn| (-402)) (|:| |fp| (-89 G)))) + (-5 *8 (-3 (|:| |fn| (-402)) (|:| |fp| (-82 FCN)))) + (-5 *9 (-3 (|:| |fn| (-402)) (|:| |fp| (-87 OUTPUT)))) + (-5 *3 (-229)) (-5 *2 (-1067)) (-5 *1 (-771))))) +(((*1 *2 *3 *4 *4 *5) + (|partial| -12 (-5 *4 (-630 *3)) (-5 *5 (-663 *3)) + (-4 *3 (-13 (-435 *6) (-27) (-1235))) + (-4 *6 (-13 (-466) (-1070 (-560)) (-149) (-660 (-560)))) + (-5 *2 + (-2 (|:| |mainpart| *3) + (|:| |limitedlogs| + (-663 (-2 (|:| |coeff| *3) (|:| |logand| *3)))))) + (-5 *1 (-580 *6 *3 *7)) (-4 *7 (-1133))))) +(((*1 *1) (-12 (-5 *1 (-231 *2)) (-4 *2 (-13 (-376) (-1235)))))) (((*1 *1 *1) (-4 *1 (-95))) ((*1 *2 *2) (-12 (-4 *3 (-571)) (-5 *1 (-287 *3 *2)) @@ -6764,28 +6807,22 @@ ((*1 *2 *2) (-12 (-5 *2 (-1187 *3)) (-4 *3 (-38 (-421 (-560)))) (-5 *1 (-1195 *3))))) -(((*1 *1 *1 *1) - (-12 (-4 *1 (-1275 *2)) (-4 *2 (-1081)) (-4 *2 (-571))))) -(((*1 *2 *3 *2 *2) - (-12 (-5 *2 (-663 (-495 *4 *5))) (-5 *3 (-889 *4)) - (-14 *4 (-663 (-1209))) (-4 *5 (-466)) (-5 *1 (-650 *4 *5))))) -(((*1 *2 *3) - (-12 (-4 *4 (-319)) (-4 *5 (-385 *4)) (-4 *6 (-385 *4)) - (-5 *2 - (-2 (|:| |Smith| *3) (|:| |leftEqMat| *3) (|:| |rightEqMat| *3))) - (-5 *1 (-1156 *4 *5 *6 *3)) (-4 *3 (-708 *4 *5 *6))))) -(((*1 *2 *1) (-12 (-5 *2 (-1187 *3)) (-5 *1 (-177 *3)) (-4 *3 (-319))))) (((*1 *2 *1) - (-12 (-5 *2 (-2 (|:| |preimage| (-663 *3)) (|:| |image| (-663 *3)))) - (-5 *1 (-932 *3)) (-4 *3 (-1133))))) -(((*1 *2 *3 *3 *3 *3 *4 *4 *4 *3 *5) - (-12 (-5 *3 (-560)) (-5 *4 (-711 (-229))) - (-5 *5 (-3 (|:| |fn| (-402)) (|:| |fp| (-66 FUNCT1)))) - (-5 *2 (-1067)) (-5 *1 (-775))))) -(((*1 *2 *1) (-12 (-4 *1 (-985)) (-5 *2 (-1121 (-229))))) - ((*1 *2 *1) (-12 (-4 *1 (-1006)) (-5 *2 (-1121 (-229)))))) + (-12 (-5 *2 (-1129 *3)) (-5 *1 (-932 *3)) (-4 *3 (-381)) + (-4 *3 (-1133))))) +(((*1 *2 *2) + (|partial| -12 (-5 *2 (-1203 *3)) (-4 *3 (-363)) (-5 *1 (-369 *3))))) (((*1 *2 *1) - (-12 (-5 *2 (-1129 (-1129 *3))) (-5 *1 (-935 *3)) (-4 *3 (-1133))))) + (-12 (-5 *2 (-663 (-973 *4))) (-5 *1 (-1197 *3 *4)) (-14 *3 (-949)) + (-4 *4 (-1081))))) +(((*1 *2 *2) (|partial| -12 (-4 *1 (-1015 *2)) (-4 *2 (-1235))))) +(((*1 *2 *3) + (-12 (-4 *4 (-13 (-571) (-1070 (-560)))) (-5 *2 (-421 (-560))) + (-5 *1 (-447 *4 *3)) (-4 *3 (-435 *4)))) + ((*1 *2 *3 *4) + (-12 (-5 *4 (-630 *3)) (-4 *3 (-435 *5)) + (-4 *5 (-13 (-571) (-1070 (-560)))) (-5 *2 (-1203 (-421 (-560)))) + (-5 *1 (-447 *5 *3))))) (((*1 *2 *3 *3) (-12 (-5 *3 (-793)) (-5 *2 (-1299 (-663 (-560)))) (-5 *1 (-494)))) ((*1 *1 *2 *3) @@ -6793,19 +6830,15 @@ ((*1 *1 *2 *3) (-12 (-5 *2 (-1 *3 *3)) (-4 *3 (-1249)) (-5 *1 (-1187 *3)))) ((*1 *1 *2) (-12 (-5 *2 (-1 *3)) (-4 *3 (-1249)) (-5 *1 (-1187 *3))))) -(((*1 *2 *1) - (-12 (-4 *1 (-1166 *3)) (-4 *3 (-1081)) (-5 *2 (-1197 3 *3)))) - ((*1 *1) (-12 (-5 *1 (-1197 *2 *3)) (-14 *2 (-949)) (-4 *3 (-1081)))) - ((*1 *1 *1 *2) (-12 (-5 *2 (-1165 (-229))) (-5 *1 (-1303)))) - ((*1 *2 *1) (-12 (-5 *2 (-1165 (-229))) (-5 *1 (-1303))))) -(((*1 *1 *1 *2 *3) (-12 (-5 *2 (-520)) (-5 *3 (-795)) (-5 *1 (-115)))) - ((*1 *1 *1 *2 *3) (-12 (-5 *2 (-1191)) (-5 *3 (-795)) (-5 *1 (-115))))) -(((*1 *2 *3 *4) - (-12 (-5 *4 (-1 *6 *6)) (-4 *6 (-1275 *5)) (-4 *5 (-376)) - (-5 *2 - (-2 (|:| |ir| (-597 (-421 *6))) (|:| |specpart| (-421 *6)) - (|:| |polypart| *6))) - (-5 *1 (-588 *5 *6)) (-5 *3 (-421 *6))))) +(((*1 *2 *2) + (-12 (-5 *2 (-114)) (-5 *1 (-456 *3)) (-4 *3 (-1275 (-560)))))) +(((*1 *2 *3 *3) + (-12 (-5 *3 (-1299 *5)) (-4 *5 (-816)) (-5 *2 (-114)) + (-5 *1 (-869 *4 *5)) (-14 *4 (-793))))) +(((*1 *2 *3) (-12 (-5 *3 (-1191)) (-5 *2 (-560)) (-5 *1 (-248)))) + ((*1 *2 *3) + (-12 (-5 *3 (-663 (-1191))) (-5 *2 (-560)) (-5 *1 (-248))))) +(((*1 *1) (-5 *1 (-1212)))) (((*1 *1 *1) (-4 *1 (-95))) ((*1 *2 *2) (-12 (-4 *3 (-571)) (-5 *1 (-287 *3 *2)) @@ -6823,42 +6856,30 @@ (-12 (-5 *2 (-1187 *3)) (-4 *3 (-38 (-421 (-560)))) (-5 *1 (-1195 *3))))) (((*1 *1 *2) (-12 (-5 *2 (-1152)) (-5 *1 (-342))))) -(((*1 *2 *3 *4 *3 *5 *5 *5 *5 *5) - (|partial| -12 (-5 *5 (-114)) (-4 *6 (-466)) (-4 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(-1133)) (-5 *2 (-1 *4)) - (-5 *1 (-1049 *4)))) - ((*1 *2 *3 *3) - (-12 (-5 *2 (-1 (-391))) (-5 *1 (-1073)) (-5 *3 (-391)))) - ((*1 *2 *3) - (-12 (-5 *3 (-1121 (-560))) (-5 *2 (-1 (-560))) (-5 *1 (-1079))))) -(((*1 *1 *1 *2 *3) - (-12 (-5 *2 (-663 (-793))) (-5 *3 (-174)) (-5 *1 (-1197 *4 *5)) - (-14 *4 (-949)) (-4 *5 (-1081))))) -(((*1 *2 *3 *3 *3 *3) - (-12 (-4 *4 (-466)) (-4 *3 (-817)) (-4 *5 (-872)) (-5 *2 (-114)) - (-5 *1 (-464 *4 *3 *5 *6)) (-4 *6 (-980 *4 *3 *5))))) -(((*1 *1 *1 *1) (-4 *1 (-559)))) + (-12 (-5 *3 (-663 (-560))) (-5 *2 (-935 (-560))) (-5 *1 (-947)))) + ((*1 *2) (-12 (-5 *2 (-935 (-560))) (-5 *1 (-947))))) (((*1 *1 *1) (-4 *1 (-95))) ((*1 *2 *2) (-12 (-4 *3 (-571)) (-5 *1 (-287 *3 *2)) @@ -6875,83 +6896,62 @@ ((*1 *2 *2) (-12 (-5 *2 (-1187 *3)) (-4 *3 (-38 (-421 (-560)))) (-5 *1 (-1195 *3))))) -(((*1 *1 *2) - (-12 (-5 *2 (-663 *3)) (-4 *3 (-1133)) (-5 *1 (-1032 *3))))) -(((*1 *2 *3) - (-12 (-5 *3 (-1191)) (-5 *2 (-663 (-713 (-292)))) (-5 *1 (-170))))) -(((*1 *2 *1 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(-1220 *3))))) +(((*1 *1 *2) + (-12 (-5 *2 (-663 (-949))) (-5 *1 (-1134 *3 *4)) (-14 *3 (-949)) + (-14 *4 (-949))))) (((*1 *1 *1) (-4 *1 (-95))) ((*1 *1 *1 *1) (-5 *1 (-229))) ((*1 *2 *2) (-12 (-4 *3 (-571)) (-5 *1 (-287 *3 *2)) @@ -6972,29 +6972,33 @@ ((*1 *2 *2) (-12 (-5 *2 (-1187 *3)) (-4 *3 (-38 (-421 (-560)))) (-5 *1 (-1195 *3))))) -(((*1 *1 *1 *2) - (|partial| -12 (-5 *2 (-793)) (-4 *1 (-1275 *3)) (-4 *3 (-1081))))) -(((*1 *2 *3 *4) - (-12 (-5 *3 (-663 (-976 *6))) (-5 *4 (-663 (-1209))) - (-4 *6 (-13 (-571) (-1070 *5))) (-4 *5 (-571)) - (-5 *2 (-663 (-663 (-305 (-421 (-976 *6)))))) (-5 *1 (-1071 *5 *6))))) -(((*1 *1) (-5 *1 (-623)))) -(((*1 *1 *1 *2) (-12 (-5 *2 (-1 (-114) (-115) (-115))) (-5 *1 (-115))))) -(((*1 *2 *3) - (-12 (-5 *3 (-1187 (-1187 *4))) (-5 *2 (-1187 *4)) (-5 *1 (-1193 *4)) - (-4 *4 (-1081))))) -(((*1 *2) (-12 (-5 *2 (-949)) (-5 *1 (-159))))) -(((*1 *2 *1 *3 *3) - (-12 (-5 *3 (-560)) (-4 *1 (-57 *2 *4 *5)) (-4 *4 (-385 *2)) - (-4 *5 (-385 *2)) (-4 *2 (-1249)))) - ((*1 *2 *1 *3) - (-12 (-5 *3 (-793)) (-4 *2 (-1133)) (-5 *1 (-216 *4 *2)) - (-14 *4 (-949)))) - ((*1 *2 *1 *3) - (-12 (-4 *1 (-300 *3 *2)) (-4 *3 (-1133)) (-4 *2 (-1249)))) - ((*1 *2 *1 *3 *3) - (-12 (-5 *3 (-560)) (-4 *1 (-1085 *4 *5 *2 *6 *7)) - (-4 *6 (-245 *5 *2)) (-4 *7 (-245 *4 *2)) (-4 *2 (-1081))))) +(((*1 *2 *1 *1) + (-12 + (-5 *2 + (-2 (|:| -2990 *3) (|:| |gap| (-793)) (|:| -3970 (-803 *3)) + (|:| -3416 (-803 *3)))) + (-5 *1 (-803 *3)) (-4 *3 (-1081)))) + ((*1 *2 *1 *1 *3) + (-12 (-4 *4 (-1081)) (-4 *5 (-817)) (-4 *3 (-872)) + (-5 *2 + (-2 (|:| -2990 *1) (|:| |gap| (-793)) (|:| -3970 *1) + (|:| -3416 *1))) + (-4 *1 (-1097 *4 *5 *3)))) + ((*1 *2 *1 *1) + (-12 (-4 *3 (-1081)) (-4 *4 (-817)) (-4 *5 (-872)) + (-5 *2 + (-2 (|:| -2990 *1) (|:| |gap| (-793)) (|:| -3970 *1) + (|:| -3416 *1))) + (-4 *1 (-1097 *3 *4 *5))))) +(((*1 *2 *1 *1) + (-12 + (-5 *2 + (-2 (|:| -1675 *3) (|:| |coef1| (-803 *3)) (|:| |coef2| (-803 *3)))) + (-5 *1 (-803 *3)) (-4 *3 (-571)) (-4 *3 (-1081))))) +(((*1 *1) (-5 *1 (-450)))) +(((*1 *1 *2) (-12 (-5 *2 (-663 *3)) (-4 *3 (-1133)) (-5 *1 (-91 *3))))) +(((*1 *1 *1 *2 *3) + (-12 (-5 *2 (-1209)) (-5 *3 (-391)) (-5 *1 (-1095))))) (((*1 *1 *1 *2) (-12 (-5 *2 (-520)) (-5 *1 (-115)))) ((*1 *2 *3 *4) (-12 (-5 *3 (-1209)) (-5 *4 (-520)) (-5 *2 (-326 (-560))) @@ -7002,20 +7006,13 @@ ((*1 *2 *2 *3) (-12 (-5 *3 (-520)) (-4 *4 (-1133)) (-5 *1 (-960 *4 *2)) (-4 *2 (-435 *4))))) -(((*1 *2 *1) (-12 (-4 *1 (-1126 *2)) (-4 *2 (-1249))))) -(((*1 *2 *3 *4) - (-12 (-5 *4 (-663 *5)) (-4 *5 (-1275 *3)) (-4 *3 (-319)) - (-5 *2 (-114)) (-5 *1 (-469 *3 *5))))) -(((*1 *2 *1) - (-12 (-5 *2 (-888)) (-5 *1 (-404 *3 *4 *5)) (-14 *3 (-793)) - (-14 *4 (-793)) (-4 *5 (-175))))) -(((*1 *2 *3) - (|partial| -12 - (-5 *3 - (-2 (|:| |var| (-1209)) (|:| |fn| (-326 (-229))) - (|:| -3918 (-1121 (-866 (-229)))) (|:| |abserr| (-229)) - (|:| |relerr| (-229)))) - (-5 *2 (-663 (-229))) (-5 *1 (-207))))) +(((*1 *1) (-5 *1 (-827)))) +(((*1 *2 *2 *1) (-12 (-4 *1 (-1027 *2)) (-4 *2 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(-229)) + (-5 *2 (-1067)) (-5 *1 (-774))))) +(((*1 *2 *3 *3) + (-12 (-4 *4 (-13 (-319) (-149))) (-4 *5 (-13 (-872) (-633 (-1209)))) + (-4 *6 (-817)) (-4 *7 (-980 *4 *6 *5)) (-5 *2 - (-663 - (-2 (|:| |outval| (-171 *4)) (|:| |outmult| (-560)) - (|:| |outvect| (-663 (-711 (-171 *4))))))) - (-5 *1 (-786 *4)) (-4 *4 (-13 (-376) (-871)))))) + (-2 (|:| |sysok| (-114)) (|:| |z0| (-663 *7)) (|:| |n0| (-663 *7)))) + (-5 *1 (-954 *4 *5 *6 *7)) (-5 *3 (-663 *7))))) +(((*1 *2 *2) + (-12 (-4 *3 (-571)) (-5 *1 (-287 *3 *2)) + (-4 *2 (-13 (-435 *3) (-1034)))))) (((*1 *2 *2) (-12 (-4 *3 (-571)) (-5 *1 (-287 *3 *2)) (-4 *2 (-13 (-435 *3) (-1034))))) @@ -7362,39 +7326,44 @@ (-12 (-5 *2 (-1187 *3)) (-4 *3 (-38 (-421 (-560)))) (-5 *1 (-1195 *3)))) ((*1 *1 *1) (-4 *1 (-1238)))) +(((*1 *2 *1) (-12 (-4 *1 (-696 *3)) (-4 *3 (-1249)) (-5 *2 (-793))))) +(((*1 *2 *3 *3 *4) + (-12 (-5 *4 (-114)) (-4 *5 (-13 (-376) (-871))) + (-5 *2 (-663 (-2 (|:| -2363 (-663 *3)) (|:| -3837 *5)))) + (-5 *1 (-184 *5 *3)) (-4 *3 (-1275 (-171 *5))))) + ((*1 *2 *3 *3) + (-12 (-4 *4 (-13 (-376) (-871))) + (-5 *2 (-663 (-2 (|:| -2363 (-663 *3)) (|:| -3837 *4)))) + (-5 *1 (-184 *4 *3)) (-4 *3 (-1275 (-171 *4)))))) (((*1 *2 *3 *4) - (-12 (-4 *5 (-817)) (-4 *6 (-872)) (-4 *7 (-571)) - (-4 *3 (-980 *7 *5 *6)) + (-12 (-5 *3 (-711 (-171 (-421 (-560))))) (-5 *2 - (-2 (|:| -4067 (-793)) (|:| -3002 *3) (|:| |radicand| (-663 *3)))) - (-5 *1 (-983 *5 *6 *7 *3 *8)) (-5 *4 (-793)) - (-4 *8 - (-13 (-376) - (-10 -8 (-15 -3903 ($ *3)) (-15 -2841 (*3 $)) (-15 -2854 (*3 $)))))))) -(((*1 *2 *2) - (-12 (-4 *2 (-13 (-376) (-871))) (-5 *1 (-184 *2 *3)) - (-4 *3 (-1275 (-171 *2)))))) -(((*1 *2 *1) (-12 (-4 *1 (-1023 *2)) (-4 *2 (-571)) (-4 *2 (-559)))) - ((*1 *1 *1) (-4 *1 (-1092)))) -(((*1 *2 *1) (-12 (-4 *1 (-263 *2)) (-4 *2 (-1249))))) + (-663 + (-2 (|:| |outval| (-171 *4)) (|:| |outmult| (-560)) + (|:| |outvect| (-663 (-711 (-171 *4))))))) + (-5 *1 (-786 *4)) (-4 *4 (-13 (-376) (-871)))))) +(((*1 *1 *1 *1) (-12 (-4 *1 (-399 *2)) (-4 *2 (-1133))))) +(((*1 *2 *3 *4 *4) + (-12 (-5 *3 (-1 *2 *2 *2)) (-4 *2 (-1292 *4)) (-5 *1 (-1293 *4 *2)) + (-4 *4 (-38 (-421 (-560))))))) +(((*1 *2 *1) + (-12 (-4 *2 (-571)) (-5 *1 (-642 *2 *3)) (-4 *3 (-1275 *2))))) (((*1 *2 *3) - (-12 (-5 *3 (-973 *2)) (-5 *1 (-1014 *2)) (-4 *2 (-1081))))) -(((*1 *1) (-12 (-4 *1 (-440 *2)) (-4 *2 (-381)) (-4 *2 (-1133))))) -(((*1 *2 *2) (-12 (-5 *2 (-663 (-711 (-326 (-560))))) (-5 *1 (-1060))))) -(((*1 *1) (-5 *1 (-159))) - ((*1 *2 *1) (-12 (-4 *1 (-1076 *2)) (-4 *2 (-23))))) -(((*1 *1 *1 *1) - (|partial| -12 (-4 *1 (-877 *2)) (-4 *2 (-1081)) (-4 *2 (-376))))) + (-12 (-5 *3 (-1209)) (-5 *2 (-1 *6 *5)) (-5 *1 (-728 *4 *5 *6)) + (-4 *4 (-633 (-549))) (-4 *5 (-1249)) (-4 *6 (-1249))))) +(((*1 *2 *3 *3) + (-12 (-4 *3 (-319)) (-4 *3 (-175)) (-4 *4 (-385 *3)) + (-4 *5 (-385 *3)) (-5 *2 (-2 (|:| -3970 *3) (|:| -3416 *3))) + (-5 *1 (-710 *3 *4 *5 *6)) (-4 *6 (-708 *3 *4 *5)))) + ((*1 *2 *3 *3) + (-12 (-5 *2 (-2 (|:| -3970 *3) (|:| -3416 *3))) (-5 *1 (-722 *3)) + (-4 *3 (-319))))) (((*1 *1 *2 *2) (-12 (-5 *2 (-793)) (-4 *3 (-1081)) (-4 *1 (-708 *3 *4 *5)) (-4 *4 (-385 *3)) (-4 *5 (-385 *3)))) ((*1 *1 *2) (-12 (-5 *2 (-793)) (-4 *1 (-1298 *3)) (-4 *3 (-23)) (-4 *3 (-1249))))) -(((*1 *2 *2 *3) - (|partial| -12 (-5 *3 (-793)) (-5 *1 (-601 *2)) (-4 *2 (-559)))) - ((*1 *2 *3) - (-12 (-5 *2 (-2 (|:| -4450 *3) (|:| -4067 (-793)))) (-5 *1 (-601 *3)) - (-4 *3 (-559))))) +(((*1 *1) (-5 *1 (-159)))) (((*1 *2 *2) (-12 (-4 *3 (-571)) (-5 *1 (-287 *3 *2)) (-4 *2 (-13 (-435 *3) (-1034))))) @@ -7414,41 +7383,37 @@ (-12 (-5 *2 (-1187 *3)) (-4 *3 (-38 (-421 (-560)))) (-5 *1 (-1195 *3)))) ((*1 *1 *1) (-4 *1 (-1238)))) -(((*1 *1 *1 *1) - (-12 (-5 *1 (-137 *2 *3 *4)) (-14 *2 (-560)) (-14 *3 (-793)) - (-4 *4 (-175)))) - ((*1 *2 *2 *3) - (-12 (-5 *3 (-1209)) (-4 *4 (-571)) (-5 *1 (-160 *4 *2)) - (-4 *2 (-435 *4)))) - ((*1 *2 *2 *3) - (-12 (-5 *3 (-1124 *2)) (-4 *2 (-435 *4)) (-4 *4 (-571)) - (-5 *1 (-160 *4 *2)))) - ((*1 *1 *1 *2) (-12 (-5 *2 (-1124 *1)) (-4 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(-663 (-1209))) (-4 *6 (-466)) - (-5 *2 (-663 (-663 (-255 *5 *6)))) (-5 *1 (-485 *5 *6 *7)) - (-5 *3 (-663 (-255 *5 *6))) (-4 *7 (-466))))) -(((*1 *2 *2) (|partial| -12 (-4 *1 (-1015 *2)) (-4 *2 (-1235))))) + (-12 (-5 *3 (-711 *8)) (-4 *8 (-980 *5 *7 *6)) + (-4 *5 (-13 (-319) (-149))) (-4 *6 (-13 (-872) (-633 (-1209)))) + (-4 *7 (-817)) + (-5 *2 + (-663 + (-2 (|:| -2738 (-793)) + (|:| |eqns| + (-663 + (-2 (|:| |det| *8) (|:| |rows| (-663 (-560))) + (|:| |cols| (-663 (-560)))))) + (|:| |fgb| (-663 *8))))) + (-5 *1 (-954 *5 *6 *7 *8)) (-5 *4 (-793))))) +(((*1 *2 *3 *4) + (-12 (-4 *5 (-817)) (-4 *6 (-872)) (-4 *7 (-571)) + (-4 *3 (-980 *7 *5 *6)) + (-5 *2 + (-2 (|:| -1946 (-793)) (|:| -2990 *3) (|:| |radicand| (-663 *3)))) + (-5 *1 (-983 *5 *6 *7 *3 *8)) (-5 *4 (-793)) + (-4 *8 + (-13 (-376) + (-10 -8 (-15 -3866 ($ *3)) (-15 -2833 (*3 $)) (-15 -2845 (*3 $)))))))) +(((*1 *2 *3) (-12 (-5 *3 (-326 (-229))) (-5 *2 (-114)) (-5 *1 (-278))))) +(((*1 *2 *2 *3 *2) + (-12 (-5 *3 (-793)) (-4 *4 (-363)) (-5 *1 (-220 *4 *2)) + (-4 *2 (-1275 *4))))) +(((*1 *2) + (-12 (-5 *2 (-421 (-976 *3))) (-5 *1 (-467 *3 *4 *5 *6)) + (-4 *3 (-571)) (-4 *3 (-175)) (-14 *4 (-949)) + (-14 *5 (-663 (-1209))) (-14 *6 (-1299 (-711 *3)))))) (((*1 *2 *3 *2) (-12 (-5 *2 (-663 (-391))) (-5 *3 (-663 (-270))) (-5 *1 (-271)))) ((*1 *2 *1 *2) (-12 (-5 *2 (-663 (-391))) (-5 *1 (-482)))) @@ -7457,13 +7422,17 @@ (-12 (-5 *3 (-949)) (-5 *4 (-899)) (-5 *2 (-1305)) (-5 *1 (-1302)))) ((*1 *2 *1 *3 *4) (-12 (-5 *3 (-949)) (-5 *4 (-1191)) (-5 *2 (-1305)) (-5 *1 (-1302))))) -(((*1 *2 *1) (-12 (-5 *2 (-114)) (-5 *1 (-1266 *3)) (-4 *3 (-1249))))) -(((*1 *2 *1) (-12 (-5 *2 (-1305)) (-5 *1 (-847))))) +(((*1 *2) + (-12 (-4 *4 (-175)) (-5 *2 (-114)) (-5 *1 (-379 *3 *4)) + (-4 *3 (-380 *4)))) + ((*1 *2) (-12 (-4 *1 (-380 *3)) (-4 *3 (-175)) (-5 *2 (-114))))) (((*1 *2 *3 *4) - (-12 (-5 *4 (-1209)) - (-4 *5 (-13 (-466) (-149) (-1070 (-560)) (-660 (-560)))) - (-5 *2 (-597 *3)) (-5 *1 (-572 *5 *3)) - (-4 *3 (-13 (-27) (-1235) (-435 *5)))))) + (-12 (-5 *3 (-663 (-711 *5))) (-5 *4 (-1299 *5)) (-4 *5 (-319)) + (-4 *5 (-1081)) (-5 *2 (-711 *5)) (-5 *1 (-1062 *5))))) +(((*1 *2) + (-12 (-4 *4 (-175)) (-5 *2 (-114)) (-5 *1 (-379 *3 *4)) + (-4 *3 (-380 *4)))) + ((*1 *2) (-12 (-4 *1 (-380 *3)) (-4 *3 (-175)) (-5 *2 (-114))))) (((*1 *2 *2) (-12 (-4 *3 (-571)) (-5 *1 (-287 *3 *2)) (-4 *2 (-13 (-435 *3) (-1034))))) @@ -7484,26 +7453,26 @@ (-12 (-5 *2 (-1187 *3)) (-4 *3 (-38 (-421 (-560)))) (-5 *1 (-1195 *3)))) ((*1 *1 *1) (-4 *1 (-1238)))) -(((*1 *2) (-12 (-5 *2 (-663 (-949))) (-5 *1 (-1304)))) - ((*1 *2 *2) (-12 (-5 *2 (-663 (-949))) (-5 *1 (-1304))))) -(((*1 *2 *3 *4 *5) - (-12 (-5 *3 (-1 *4 (-560))) (-5 *5 (-1 (-1187 *4))) (-4 *4 (-376)) - (-4 *4 (-1081)) (-5 *2 (-1187 *4)) (-5 *1 (-1193 *4))))) -(((*1 *2 *3 *1) - (-12 - (-5 *2 - (-2 (|:| |cycle?| (-114)) (|:| -1648 (-793)) (|:| |period| (-793)))) - (-5 *1 (-1187 *4)) (-4 *4 (-1249)) (-5 *3 (-793))))) -(((*1 *2 *1) (-12 (-4 *1 (-1027 *2)) (-4 *2 (-1249))))) -(((*1 *2 *3) (-12 (-5 *3 (-793)) (-5 *2 (-1 (-391))) (-5 *1 (-1073))))) -(((*1 *2 *3 *4 *5 *5 *6) - (-12 (-5 *4 (-560)) (-5 *6 (-1 (-1305) (-1299 *5) (-1299 *5) (-391))) - (-5 *3 (-1299 (-391))) (-5 *5 (-391)) (-5 *2 (-1305)) - (-5 *1 (-810)))) - ((*1 *2 *3 *4 *5 *5 *6 *3 *3 *3 *3) - (-12 (-5 *4 (-560)) (-5 *6 (-1 (-1305) (-1299 *5) (-1299 *5) (-391))) - (-5 *3 (-1299 (-391))) (-5 *5 (-391)) (-5 *2 (-1305)) - (-5 *1 (-810))))) +(((*1 *2 *1 *1) + (-12 (-4 *3 (-376)) (-4 *3 (-1081)) + (-5 *2 (-2 (|:| |coef1| *1) (|:| |coef2| *1) (|:| -3091 *1))) + (-4 *1 (-877 *3))))) +(((*1 *2 *3 *3) + (-12 (-5 *2 (-1 (-973 *3) (-973 *3))) (-5 *1 (-179 *3)) + (-4 *3 (-13 (-376) (-1235) (-1034)))))) +(((*1 *1 *1) + (-12 (-5 *1 (-1197 *2 *3)) (-14 *2 (-949)) (-4 *3 (-1081))))) +(((*1 *2 *2) + (-12 (-4 *2 (-13 (-376) (-871))) (-5 *1 (-184 *2 *3)) + (-4 *3 (-1275 (-171 *2)))))) +(((*1 *2) + (-12 (-4 *3 (-466)) (-4 *4 (-817)) (-4 *5 (-872)) + (-4 *6 (-1097 *3 *4 *5)) (-5 *2 (-1305)) + (-5 *1 (-1104 *3 *4 *5 *6 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+ (-3 (|:| |continuous| "Continuous at the end points") + (|:| |lowerSingular| + "There is a singularity at the lower end point") + (|:| |upperSingular| + "There is a singularity at the upper end point") + (|:| |bothSingular| + "There are singularities at both end points") + (|:| |notEvaluated| + "End point continuity not yet evaluated"))) + (|:| |singularitiesStream| + (-3 (|:| |str| (-1187 (-229))) + (|:| |notEvaluated| + "Internal singularities not yet evaluated"))) + (|:| -4237 + (-3 (|:| |finite| "The range is finite") + (|:| |lowerInfinite| + "The bottom of range is infinite") + (|:| |upperInfinite| "The top of range is infinite") + (|:| |bothInfinite| + "Both top and bottom points are infinite") + (|:| |notEvaluated| "Range not yet evaluated")))))))) + (-5 *1 (-574))))) +(((*1 *2 *1) + (-12 (-4 *1 (-1097 *3 *4 *5)) (-4 *3 (-1081)) (-4 *4 (-817)) + (-4 *5 (-872)) (-5 *2 (-114))))) +(((*1 *1 *1 *1) (-12 (-5 *1 (-803 *2)) (-4 *2 (-571)) (-4 *2 (-1081)))) + ((*1 *2 *2 *2) + (-12 (-4 *3 (-571)) (-5 *1 (-1001 *3 *2)) (-4 *2 (-1275 *3)))) + ((*1 *1 *1 *1) (-12 (-4 *1 (-1097 *2 *3 *4)) (-4 *2 (-1081)) (-4 *3 (-817)) - (-4 *4 (-872))))) -(((*1 *1) (-5 *1 (-622)))) + (-4 *4 (-872)) (-4 *2 (-571)))) + ((*1 *2 *3 *3 *1) + (-12 (-4 *4 (-466)) (-4 *5 (-817)) (-4 *6 (-872)) + (-4 *3 (-1097 *4 *5 *6)) + (-5 *2 (-663 (-2 (|:| |val| *3) (|:| -4461 *1)))) + (-4 *1 (-1103 *4 *5 *6 *3))))) (((*1 *2 *1) - (-12 (-4 *1 (-1136 *3 *4 *5 *6 *7)) (-4 *3 (-1133)) (-4 *4 (-1133)) - (-4 *5 (-1133)) (-4 *6 (-1133)) (-4 *7 (-1133)) (-5 *2 (-114))))) -(((*1 *1 *2 *2 *3 *1) - (-12 (-5 *2 (-520)) (-5 *3 (-1135)) (-5 *1 (-303))))) -(((*1 *1) (-5 *1 (-1302)))) + (-12 (-4 *1 (-708 *3 *4 *5)) (-4 *3 (-1081)) (-4 *4 (-385 *3)) + (-4 *5 (-385 *3)) (-5 *2 (-114)))) + ((*1 *2 *1) + (-12 (-4 *1 (-1085 *3 *4 *5 *6 *7)) (-4 *5 (-1081)) + (-4 *6 (-245 *4 *5)) (-4 *7 (-245 *3 *5)) (-5 *2 (-114))))) +(((*1 *2) (-12 (-5 *2 (-1165 (-229))) (-5 *1 (-1233))))) (((*1 *2 *1) (-12 (-5 *2 (-988 (-187 (-141)))) (-5 *1 (-345)))) ((*1 *2 *1) (-12 (-5 *2 (-663 (-1250))) (-5 *1 (-619))))) -(((*1 *2 *2 *3) (-12 (-5 *2 (-560)) (-5 *3 (-793)) (-5 *1 (-576))))) -(((*1 *2 *1) (|partial| -12 (-5 *2 (-520)) (-5 *1 (-291))))) +(((*1 *2 *3 *3 *3 *4 *5) + (-12 (-5 *5 (-663 (-663 (-229)))) (-5 *4 (-229)) + (-5 *2 (-663 (-973 *4))) (-5 *1 (-1246)) (-5 *3 (-973 *4))))) +(((*1 *2 *1) + (-12 (-5 *2 (-888)) (-5 *1 (-404 *3 *4 *5)) (-14 *3 (-793)) + (-14 *4 (-793)) (-4 *5 (-175))))) (((*1 *1 *1) (-5 *1 (-888))) ((*1 *2 *1) (-12 (-4 *1 (-1136 *2 *3 *4 *5 *6)) (-4 *3 (-1133)) (-4 *4 (-1133)) @@ -11426,24 +11475,37 @@ ((*1 *1 *2) (-12 (-5 *2 (-229)) (-5 *1 (-1191)))) ((*1 *1 *2) (-12 (-5 *2 (-560)) (-5 *1 (-1191)))) ((*1 *2 *1) (-12 (-5 *2 (-1191)) (-5 *1 (-1209))))) -(((*1 *1 *2 *1) - (-12 (-5 *2 (-1 (-560) (-560))) (-5 *1 (-374 *3)) (-4 *3 (-1133)))) - ((*1 *1 *2 *1) - (-12 (-5 *2 (-1 (-793) (-793))) (-4 *1 (-399 *3)) (-4 *3 (-1133)))) - ((*1 *1 *2 *1) - (-12 (-5 *2 (-1 *4 *4)) (-4 *4 (-23)) (-14 *5 *4) - (-5 *1 (-671 *3 *4 *5)) (-4 *3 (-1133))))) +(((*1 *2 *2 *1) + (-12 (-5 *2 (-1324 *3 *4)) (-4 *1 (-387 *3 *4)) (-4 *3 (-872)) + (-4 *4 (-175)))) + ((*1 *1 *1 *1) (|partial| -12 (-4 *1 (-399 *2)) (-4 *2 (-1133)))) + ((*1 *1 *1 *2) (|partial| -12 (-5 *1 (-843 *2)) (-4 *2 (-872)))) + ((*1 *1 *1 *1) + (-12 (-4 *1 (-1319 *2 *3)) (-4 *2 (-872)) (-4 *3 (-1081)))) + ((*1 *1 *1 *2) + (-12 (-5 *2 (-843 *3)) (-4 *1 (-1319 *3 *4)) (-4 *3 (-872)) + (-4 *4 (-1081)))) + ((*1 *1 *1 *2) + (-12 (-4 *1 (-1319 *2 *3)) (-4 *2 (-872)) (-4 *3 (-1081))))) (((*1 *1 *2 *1 *1) (-12 (-5 *2 (-1208)) (-5 *1 (-342)))) ((*1 *1 *2 *1) (-12 (-5 *2 (-1208)) (-5 *1 (-342))))) -(((*1 *2 *2) - (-12 (-4 *3 (-466)) (-5 *1 (-1241 *3 *2)) - (-4 *2 (-13 (-435 *3) (-1235)))))) -(((*1 *2 *1) - (-12 (-4 *1 (-1103 *3 *4 *5 *6)) (-4 *3 (-466)) (-4 *4 (-817)) - (-4 *5 (-872)) (-4 *6 (-1097 *3 *4 *5)) (-5 *2 (-114)))) - ((*1 *2 *3 *1) - (-12 (-4 *1 (-1103 *4 *5 *6 *3)) (-4 *4 (-466)) (-4 *5 (-817)) - (-4 *6 (-872)) (-4 *3 (-1097 *4 *5 *6)) (-5 *2 (-114))))) +(((*1 *1 *1 *1) (-12 (-5 *1 (-803 *2)) (-4 *2 (-1081)))) + ((*1 *1 *1 *1) + (-12 (-4 *1 (-1097 *2 *3 *4)) (-4 *2 (-1081)) (-4 *3 (-817)) + (-4 *4 (-872))))) +(((*1 *2 *3) + (-12 + (-5 *3 + (-3 + (|:| |noa| + (-2 (|:| |fn| (-326 (-229))) (|:| -2543 (-663 (-229))) + (|:| |lb| (-663 (-866 (-229)))) + (|:| |cf| (-663 (-326 (-229)))) + (|:| |ub| (-663 (-866 (-229)))))) + (|:| |lsa| + (-2 (|:| |lfn| (-663 (-326 (-229)))) + (|:| -2543 (-663 (-229))))))) + (-5 *2 (-663 (-1191))) (-5 *1 (-278))))) (((*1 *1 *2 *1) (-12 (-5 *2 (-1 *3 *3)) (-4 *1 (-47 *3 *4)) (-4 *3 (-1081)) (-4 *4 (-816)))) @@ -11550,9 +11612,9 @@ (-4 *6 (-376)) (-5 *2 (-597 *6)) (-5 *1 (-598 *5 *6)))) ((*1 *2 *3 *4) (|partial| -12 (-5 *3 (-1 *6 *5)) - (-5 *4 (-3 (-2 (|:| -3961 *5) (|:| |coeff| *5)) "failed")) + (-5 *4 (-3 (-2 (|:| -3447 *5) (|:| |coeff| *5)) "failed")) (-4 *5 (-376)) (-4 *6 (-376)) - (-5 *2 (-2 (|:| -3961 *6) (|:| |coeff| *6))) + (-5 *2 (-2 (|:| -3447 *6) (|:| |coeff| *6))) (-5 *1 (-598 *5 *6)))) ((*1 *2 *3 *4) (|partial| -12 (-5 *3 (-1 *2 *5)) (-5 *4 (-3 *5 "failed")) @@ -11671,7 +11733,7 @@ (-4 *8 (-1081)) (-4 *6 (-817)) (-4 *2 (-13 (-1133) - (-10 -8 (-15 -4373 ($ $ $)) (-15 * ($ $ $)) (-15 ** ($ $ (-793)))))) + (-10 -8 (-15 -4357 ($ $ $)) (-15 * ($ $ $)) (-15 ** ($ $ (-793)))))) (-5 *1 (-982 *6 *7 *8 *5 *2)) (-4 *5 (-980 *8 *6 *7)))) ((*1 *2 *3 *4) (-12 (-5 *3 (-1 *6 *5)) (-5 *4 (-988 *5)) (-4 *5 (-1249)) @@ -11687,8 +11749,8 @@ (-4 *2 (-980 (-976 *4) *5 *6)) (-4 *5 (-817)) (-4 *6 (-13 (-872) - (-10 -8 (-15 -2574 ((-1209) $)) - (-15 -2740 ((-3 $ "failed") (-1209)))))) + (-10 -8 (-15 -2558 ((-1209) $)) + (-15 -2735 ((-3 $ "failed") (-1209)))))) (-5 *1 (-1016 *4 *5 *6 *2)))) ((*1 *2 *3 *4) (-12 (-5 *3 (-1 *6 *5)) (-4 *5 (-571)) (-4 *6 (-571)) @@ -11775,151 +11837,169 @@ ((*1 *1 *2 *1) (-12 (-5 *2 (-1 *3 *3)) (-4 *3 (-1081)) (-5 *1 (-1323 *3 *4)) (-4 *4 (-870))))) -(((*1 *2 *1) - (-12 (-4 *2 (-1133)) (-5 *1 (-994 *2 *3)) (-4 *3 (-1133))))) -(((*1 *1 *1) (-4 *1 (-1176)))) -(((*1 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((*1 *2) + (-12 (-5 *2 (-1299 (-663 (-2 (|:| -3643 *3) (|:| -2175 (-1152)))))) + (-5 *1 (-367 *3 *4)) (-4 *3 (-363)) (-14 *4 (-949))))) +(((*1 *1 *2 *3) (-12 (-5 *2 (-520)) (-5 *3 (-611)) (-5 *1 (-600))))) (((*1 *2 *3 *4 *2) (-12 (-5 *4 (-1 *2 *2)) (-4 *2 (-670 *5)) (-4 *5 (-1081)) (-5 *1 (-53 *5 *2 *3)) (-4 *3 (-877 *5)))) @@ -17030,56 +16951,83 @@ ((*1 *2 *3 *2 *2 *4 *5) (-12 (-5 *4 (-99 *2)) (-5 *5 (-1 *2 *2)) (-4 *2 (-1081)) (-5 *1 (-878 *2 *3)) (-4 *3 (-877 *2))))) -(((*1 *2 *3) (-12 (-5 *3 (-663 *2)) (-5 *1 (-1224 *2)) (-4 *2 (-376))))) -(((*1 *2 *3 *4 *5) - (-12 (-5 *3 (-663 (-421 (-976 (-560))))) (-5 *4 (-663 (-1209))) - (-5 *2 (-663 (-663 *5))) (-5 *1 (-393 *5)) - (-4 *5 (-13 (-871) (-376))))) - ((*1 *2 *3 *4) - (-12 (-5 *3 (-421 (-976 (-560)))) (-5 *2 (-663 *4)) (-5 *1 (-393 *4)) - (-4 *4 (-13 (-871) (-376)))))) -(((*1 *2 *1) (-12 (-4 *1 (-820 *2)) (-4 *2 (-175))))) -(((*1 *2 *3 *4 *3 *4 *3) - (-12 (-5 *3 (-560)) (-5 *4 (-711 (-229))) (-5 *2 (-1067)) - (-5 *1 (-778))))) 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. 6176) (-4456 . 5924) (-4457 . 5896) + (-4458 . 5822) (-4459 . 5481) (-4460 . 5387) (-4461 . 5325) + (-4462 . 5166) (-4463 . 5078) (-4464 . 4840) (-4465 . 4307) + (-4466 . 4240) (-4467 . 4138) (-4468 . 4110) (-4469 . 4043) + (-4470 . 3938) (-4471 . 3708) (-4472 . 3624) (-4473 . 3339) + (-4474 . 3237) (-4475 . 2942) (-4476 . 2184) (-4477 . 2091) + (-4478 . 1983) (-4479 . 1801) (-4480 . 1708) (-4481 . 1623) + (-4482 . 1281) (-4483 . 981) (-4484 . 765) (-4485 . 737) (-4486 . 584) + (-4487 . 529) (-4488 . 273) (-4489 . 82) (-4490 . 30))
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