diff options
| author | dos-reis <gdr@axiomatics.org> | 2011-02-24 09:24:02 +0000 |
|---|---|---|
| committer | dos-reis <gdr@axiomatics.org> | 2011-02-24 09:24:02 +0000 |
| commit | 654d295a347b5d262f2fced49c4f010428ee207e (patch) | |
| tree | 7eae5d401441d205b1bd041d1f992990ad276753 /src/share/algebra | |
| parent | b297c03b5d2d5a6d88edc5e44548da67ee7c7082 (diff) | |
| download | open-axiom-654d295a347b5d262f2fced49c4f010428ee207e.tar.gz | |
more cleanups
Diffstat (limited to 'src/share/algebra')
| -rw-r--r-- | src/share/algebra/browse.daase | 632 | ||||
| -rw-r--r-- | src/share/algebra/category.daase | 1574 | ||||
| -rw-r--r-- | src/share/algebra/compress.daase | 1345 | ||||
| -rw-r--r-- | src/share/algebra/interp.daase | 9072 | ||||
| -rw-r--r-- | src/share/algebra/operation.daase | 27565 |
5 files changed, 20095 insertions, 20093 deletions
diff --git a/src/share/algebra/browse.daase b/src/share/algebra/browse.daase index 9bbdd68f..8f140e22 100644 --- a/src/share/algebra/browse.daase +++ b/src/share/algebra/browse.daase @@ -1,5 +1,5 @@ -(2294384 . 3507509287) +(2294384 . 3507527188) (-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 -1596) +(-32 R -1594) ((|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 -1069) (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 -1596 UP UPUP -2849) +(-40 -1594 UP UPUP -3988) ((|constructor| (NIL "Function field defined by \\spad{f}(\\spad{x},{} \\spad{y}) = 0.")) (|knownInfBasis| (((|Void|) (|NonNegativeInteger|)) "\\spad{knownInfBasis(n)} \\undocumented{}"))) ((-4501 |has| (-421 |#2|) (-376)) (-4506 |has| (-421 |#2|) (-376)) (-4500 |has| (-421 |#2|) (-376)) ((-4510 "*") . T) (-4502 . T) (-4503 . T) (-4505 . T)) -((|HasCategory| (-421 |#2|) (QUOTE (-147))) (|HasCategory| (-421 |#2|) (QUOTE (-149))) (|HasCategory| (-421 |#2|) (QUOTE (-363))) (-2181 (|HasCategory| (-421 |#2|) (QUOTE (-376))) (|HasCategory| (-421 |#2|) (QUOTE (-363)))) (|HasCategory| (-421 |#2|) (QUOTE (-376))) (|HasCategory| (-421 |#2|) (QUOTE (-381))) (-2181 (-12 (|HasCategory| (-421 |#2|) (QUOTE (-240))) (|HasCategory| (-421 |#2|) (QUOTE (-376)))) (|HasCategory| (-421 |#2|) (QUOTE (-363)))) (-2181 (-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)))) (-2181 (-12 (|HasCategory| (-421 |#2|) (|%list| (QUOTE -927) (QUOTE (-1207)))) (|HasCategory| (-421 |#2|) (QUOTE (-376)))) (-12 (|HasCategory| (-421 |#2|) (|%list| (QUOTE -927) (QUOTE (-1207)))) (|HasCategory| (-421 |#2|) (QUOTE (-363))))) (-2181 (-12 (|HasCategory| (-421 |#2|) (|%list| (QUOTE -927) (QUOTE (-1207)))) (|HasCategory| (-421 |#2|) (QUOTE (-376)))) (-12 (|HasCategory| (-421 |#2|) (|%list| (QUOTE -929) (QUOTE (-1207)))) (|HasCategory| (-421 |#2|) (QUOTE (-376))))) (|HasCategory| (-421 |#2|) (|%list| (QUOTE -660) (QUOTE (-560)))) (-2181 (|HasCategory| (-421 |#2|) (|%list| (QUOTE -1069) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| (-421 |#2|) (QUOTE (-376)))) (|HasCategory| (-421 |#2|) (|%list| (QUOTE -1069) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| (-421 |#2|) (|%list| (QUOTE -1069) (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 -929) (QUOTE (-1207)))) (|HasCategory| (-421 |#2|) (QUOTE (-376)))) (-12 (|HasCategory| (-421 |#2|) (QUOTE (-240))) (|HasCategory| (-421 |#2|) (QUOTE (-376)))) (-12 (|HasCategory| (-421 |#2|) (|%list| (QUOTE -927) (QUOTE (-1207)))) (|HasCategory| (-421 |#2|) (QUOTE (-376))))) -(-41 R -1596) +((|HasCategory| (-421 |#2|) (QUOTE (-147))) (|HasCategory| (-421 |#2|) (QUOTE (-149))) (|HasCategory| (-421 |#2|) (QUOTE (-363))) (-2173 (|HasCategory| (-421 |#2|) (QUOTE (-376))) (|HasCategory| (-421 |#2|) (QUOTE (-363)))) (|HasCategory| (-421 |#2|) (QUOTE (-376))) (|HasCategory| (-421 |#2|) (QUOTE (-381))) (-2173 (-12 (|HasCategory| (-421 |#2|) (QUOTE (-240))) (|HasCategory| (-421 |#2|) (QUOTE (-376)))) (|HasCategory| (-421 |#2|) (QUOTE (-363)))) (-2173 (-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)))) (-2173 (-12 (|HasCategory| (-421 |#2|) (|%list| (QUOTE -927) (QUOTE (-1207)))) (|HasCategory| (-421 |#2|) (QUOTE (-376)))) (-12 (|HasCategory| (-421 |#2|) (|%list| (QUOTE -927) (QUOTE (-1207)))) (|HasCategory| (-421 |#2|) (QUOTE (-363))))) (-2173 (-12 (|HasCategory| (-421 |#2|) (|%list| (QUOTE -927) (QUOTE (-1207)))) (|HasCategory| (-421 |#2|) (QUOTE (-376)))) (-12 (|HasCategory| (-421 |#2|) (|%list| (QUOTE -929) (QUOTE (-1207)))) (|HasCategory| (-421 |#2|) (QUOTE (-376))))) (|HasCategory| (-421 |#2|) (|%list| (QUOTE -660) (QUOTE (-560)))) (-2173 (|HasCategory| (-421 |#2|) (|%list| (QUOTE -1069) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| (-421 |#2|) (QUOTE (-376)))) (|HasCategory| (-421 |#2|) (|%list| (QUOTE -1069) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| (-421 |#2|) (|%list| (QUOTE -1069) (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 -929) (QUOTE (-1207)))) (|HasCategory| (-421 |#2|) (QUOTE (-376)))) (-12 (|HasCategory| (-421 |#2|) (QUOTE (-240))) (|HasCategory| (-421 |#2|) (QUOTE (-376)))) (-12 (|HasCategory| (-421 |#2|) (|%list| (QUOTE -927) (QUOTE (-1207)))) (|HasCategory| (-421 |#2|) (QUOTE (-376))))) +(-41 R -1594) ((|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 -1069) (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."))) ((-4508 . T) (-4509 . T)) -((-2181 (-12 (|HasCategory| (-2 (|:| -3819 |#1|) (|:| -2913 |#2|)) (QUOTE (-871))) (|HasCategory| (-2 (|:| -3819 |#1|) (|:| -2913 |#2|)) (|%list| (QUOTE -321) (|%list| (QUOTE -2) (|%list| (QUOTE |:|) (QUOTE -3819) (|devaluate| |#1|)) (|%list| (QUOTE |:|) (QUOTE -2913) (|devaluate| |#2|)))))) (-12 (|HasCategory| (-2 (|:| -3819 |#1|) (|:| -2913 |#2|)) (QUOTE (-1132))) (|HasCategory| (-2 (|:| -3819 |#1|) (|:| -2913 |#2|)) (|%list| (QUOTE -321) (|%list| (QUOTE -2) (|%list| (QUOTE |:|) (QUOTE -3819) (|devaluate| |#1|)) (|%list| (QUOTE |:|) (QUOTE -2913) (|devaluate| |#2|))))))) (-2181 (|HasCategory| (-2 (|:| -3819 |#1|) (|:| -2913 |#2|)) (QUOTE (-871))) (|HasCategory| (-2 (|:| -3819 |#1|) (|:| -2913 |#2|)) (QUOTE (-1132))) (|HasCategory| (-2 (|:| -3819 |#1|) (|:| -2913 |#2|)) (|%list| (QUOTE -632) (QUOTE (-887)))) (|HasCategory| |#2| (QUOTE (-1132))) (|HasCategory| |#2| (|%list| (QUOTE -632) (QUOTE (-887))))) (|HasCategory| (-2 (|:| -3819 |#1|) (|:| -2913 |#2|)) (|%list| (QUOTE -633) (QUOTE (-549)))) (-12 (|HasCategory| |#2| (QUOTE (-1132))) (|HasCategory| |#2| (|%list| (QUOTE -321) (|devaluate| |#2|)))) (-2181 (|HasCategory| (-2 (|:| -3819 |#1|) (|:| -2913 |#2|)) (QUOTE (-871))) (|HasCategory| (-2 (|:| -3819 |#1|) (|:| -2913 |#2|)) (QUOTE (-1132))) (|HasCategory| |#2| (QUOTE (-1132)))) (|HasCategory| (-2 (|:| -3819 |#1|) (|:| -2913 |#2|)) (QUOTE (-871))) (-2181 (|HasCategory| (-2 (|:| -3819 |#1|) (|:| -2913 |#2|)) (QUOTE (-102))) (|HasCategory| (-2 (|:| -3819 |#1|) (|:| -2913 |#2|)) (QUOTE (-871))) (|HasCategory| (-2 (|:| -3819 |#1|) (|:| -2913 |#2|)) (QUOTE (-1132))) (|HasCategory| |#2| (QUOTE (-102))) (|HasCategory| |#2| (QUOTE (-1132)))) (|HasCategory| |#1| (QUOTE (-871))) (|HasCategory| |#2| (QUOTE (-1132))) (|HasCategory| (-560) (QUOTE (-871))) (|HasCategory| (-2 (|:| -3819 |#1|) (|:| -2913 |#2|)) (QUOTE (-1132))) (-2181 (|HasCategory| (-2 (|:| -3819 |#1|) (|:| -2913 |#2|)) (QUOTE (-1132))) (|HasCategory| |#2| (QUOTE (-1132)))) (-2181 (|HasCategory| (-2 (|:| -3819 |#1|) (|:| -2913 |#2|)) (|%list| (QUOTE -632) (QUOTE (-887)))) (|HasCategory| |#2| (|%list| (QUOTE -632) (QUOTE (-887))))) (-2181 (|HasCategory| (-2 (|:| -3819 |#1|) (|:| -2913 |#2|)) (QUOTE (-102))) (|HasCategory| |#2| (QUOTE (-102)))) (|HasCategory| |#2| (QUOTE (-102))) (|HasCategory| |#2| (|%list| (QUOTE -632) (QUOTE (-887)))) (|HasCategory| (-2 (|:| -3819 |#1|) (|:| -2913 |#2|)) (|%list| (QUOTE -632) (QUOTE (-887)))) (|HasCategory| (-2 (|:| -3819 |#1|) (|:| -2913 |#2|)) (QUOTE (-102))) (-12 (|HasCategory| (-2 (|:| -3819 |#1|) (|:| -2913 |#2|)) (QUOTE (-1132))) (|HasCategory| (-2 (|:| -3819 |#1|) (|:| -2913 |#2|)) (|%list| (QUOTE -321) (|%list| (QUOTE -2) (|%list| (QUOTE |:|) (QUOTE -3819) (|devaluate| |#1|)) (|%list| (QUOTE |:|) (QUOTE -2913) (|devaluate| |#2|))))))) +((-2173 (-12 (|HasCategory| (-2 (|:| -3835 |#1|) (|:| -2923 |#2|)) (QUOTE (-871))) (|HasCategory| (-2 (|:| -3835 |#1|) (|:| -2923 |#2|)) (|%list| (QUOTE -321) (|%list| (QUOTE -2) (|%list| (QUOTE |:|) (QUOTE -3835) (|devaluate| |#1|)) (|%list| (QUOTE |:|) (QUOTE -2923) (|devaluate| |#2|)))))) (-12 (|HasCategory| (-2 (|:| -3835 |#1|) (|:| -2923 |#2|)) (QUOTE (-1132))) (|HasCategory| (-2 (|:| -3835 |#1|) (|:| -2923 |#2|)) (|%list| (QUOTE -321) (|%list| (QUOTE -2) (|%list| (QUOTE |:|) (QUOTE -3835) (|devaluate| |#1|)) (|%list| (QUOTE |:|) (QUOTE -2923) (|devaluate| |#2|))))))) (-2173 (|HasCategory| (-2 (|:| -3835 |#1|) (|:| -2923 |#2|)) (QUOTE (-871))) (|HasCategory| (-2 (|:| -3835 |#1|) (|:| -2923 |#2|)) (QUOTE (-1132))) (|HasCategory| (-2 (|:| -3835 |#1|) (|:| -2923 |#2|)) (|%list| (QUOTE -632) (QUOTE (-887)))) (|HasCategory| |#2| (QUOTE (-1132))) (|HasCategory| |#2| (|%list| (QUOTE -632) (QUOTE (-887))))) (|HasCategory| (-2 (|:| -3835 |#1|) (|:| -2923 |#2|)) (|%list| (QUOTE -633) (QUOTE (-549)))) (-12 (|HasCategory| |#2| (QUOTE (-1132))) (|HasCategory| |#2| (|%list| (QUOTE -321) (|devaluate| |#2|)))) (-2173 (|HasCategory| (-2 (|:| -3835 |#1|) (|:| -2923 |#2|)) (QUOTE (-871))) (|HasCategory| (-2 (|:| -3835 |#1|) (|:| -2923 |#2|)) (QUOTE (-1132))) (|HasCategory| |#2| (QUOTE (-1132)))) (|HasCategory| (-2 (|:| -3835 |#1|) (|:| -2923 |#2|)) (QUOTE (-871))) (-2173 (|HasCategory| (-2 (|:| -3835 |#1|) (|:| -2923 |#2|)) (QUOTE (-102))) (|HasCategory| (-2 (|:| -3835 |#1|) (|:| -2923 |#2|)) (QUOTE (-871))) (|HasCategory| (-2 (|:| -3835 |#1|) (|:| -2923 |#2|)) (QUOTE (-1132))) (|HasCategory| |#2| (QUOTE (-102))) (|HasCategory| |#2| (QUOTE (-1132)))) (|HasCategory| |#1| (QUOTE (-871))) (|HasCategory| |#2| (QUOTE (-1132))) (|HasCategory| (-560) (QUOTE (-871))) (|HasCategory| (-2 (|:| -3835 |#1|) (|:| -2923 |#2|)) (QUOTE (-1132))) (-2173 (|HasCategory| (-2 (|:| -3835 |#1|) (|:| -2923 |#2|)) (QUOTE (-1132))) (|HasCategory| |#2| (QUOTE (-1132)))) (-2173 (|HasCategory| (-2 (|:| -3835 |#1|) (|:| -2923 |#2|)) (|%list| (QUOTE -632) (QUOTE (-887)))) (|HasCategory| |#2| (|%list| (QUOTE -632) (QUOTE (-887))))) (-2173 (|HasCategory| (-2 (|:| -3835 |#1|) (|:| -2923 |#2|)) (QUOTE (-102))) (|HasCategory| |#2| (QUOTE (-102)))) (|HasCategory| |#2| (QUOTE (-102))) (|HasCategory| |#2| (|%list| (QUOTE -632) (QUOTE (-887)))) (|HasCategory| (-2 (|:| -3835 |#1|) (|:| -2923 |#2|)) (|%list| (QUOTE -632) (QUOTE (-887)))) (|HasCategory| (-2 (|:| -3835 |#1|) (|:| -2923 |#2|)) (QUOTE (-102))) (-12 (|HasCategory| (-2 (|:| -3835 |#1|) (|:| -2923 |#2|)) (QUOTE (-1132))) (|HasCategory| (-2 (|:| -3835 |#1|) (|:| -2923 |#2|)) (|%list| (QUOTE -321) (|%list| (QUOTE -2) (|%list| (QUOTE |:|) (QUOTE -3835) (|devaluate| |#1|)) (|%list| (QUOTE |:|) (QUOTE -2923) (|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| $) "\\spad{leadingCoefficient(p)} returns the coefficient highest degree term of \\spad{p}."))) NIL @@ -144,7 +144,7 @@ NIL ((|constructor| (NIL "\\spad{ApplyUnivariateSkewPolynomial} (internal) allows univariate skew polynomials to be applied to appropriate modules.")) (|apply| ((|#2| |#3| (|Mapping| |#2| |#2|) |#2|) "\\spad{apply(p, f, m)} returns \\spad{p(m)} where the action is given by \\spad{x m = f(m)}. \\spad{f} must be an \\spad{R}-pseudo linear map on \\spad{M}."))) NIL NIL -(-54 |Base| R -1596) +(-54 |Base| R -1594) ((|constructor| (NIL "This package apply rewrite rules to expressions,{} calling the pattern matcher.")) (|localUnquote| ((|#3| |#3| (|List| (|Symbol|))) "\\spad{localUnquote(f,ls)} is a local function.")) (|applyRules| ((|#3| (|List| (|RewriteRule| |#1| |#2| |#3|)) |#3| (|PositiveInteger|)) "\\spad{applyRules([r1,...,rn], expr, n)} applies the rules \\spad{r1},{}...,{}rn to \\spad{f} a most \\spad{n} times.") ((|#3| (|List| (|RewriteRule| |#1| |#2| |#3|)) |#3|) "\\spad{applyRules([r1,...,rn], expr)} applies the rules \\spad{r1},{}...,{}rn to \\spad{f} an unlimited number of times,{} \\spadignore{i.e.} until none of \\spad{r1},{}...,{}rn is applicable to the expression."))) NIL NIL @@ -163,7 +163,7 @@ NIL (-58 S) ((|constructor| (NIL "This is the domain of 1-based one dimensional arrays")) (|oneDimensionalArray| (($ (|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}"))) ((-4509 . T) (-4508 . T)) -((-2181 (-12 (|HasCategory| |#1| (QUOTE (-871))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1132))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|))))) (-2181 (-12 (|HasCategory| |#1| (QUOTE (-1132))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-887))))) (|HasCategory| |#1| (|%list| (QUOTE -633) (QUOTE (-549)))) (-2181 (|HasCategory| |#1| (QUOTE (-871))) (|HasCategory| |#1| (QUOTE (-1132)))) (|HasCategory| |#1| (QUOTE (-871))) (-2181 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-871))) (|HasCategory| |#1| (QUOTE (-1132)))) (|HasCategory| (-560) (QUOTE (-871))) (|HasCategory| |#1| (QUOTE (-1132))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-887)))) (|HasCategory| |#1| (QUOTE (-102))) (-12 (|HasCategory| |#1| (QUOTE (-1132))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|))))) +((-2173 (-12 (|HasCategory| |#1| (QUOTE (-871))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1132))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|))))) (-2173 (-12 (|HasCategory| |#1| (QUOTE (-1132))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-887))))) (|HasCategory| |#1| (|%list| (QUOTE -633) (QUOTE (-549)))) (-2173 (|HasCategory| |#1| (QUOTE (-871))) (|HasCategory| |#1| (QUOTE (-1132)))) (|HasCategory| |#1| (QUOTE (-871))) (-2173 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-871))) (|HasCategory| |#1| (QUOTE (-1132)))) (|HasCategory| (-560) (QUOTE (-871))) (|HasCategory| |#1| (QUOTE (-1132))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-887)))) (|HasCategory| |#1| (QUOTE (-102))) (-12 (|HasCategory| |#1| (QUOTE (-1132))) (|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."))) ((-4508 . T) (-4509 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1132))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1132))) (-2181 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-1132)))) (-2181 (-12 (|HasCategory| |#1| (QUOTE (-1132))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-887))))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-887)))) (|HasCategory| |#1| (QUOTE (-102)))) -(-61 -3949) +((-12 (|HasCategory| |#1| (QUOTE (-1132))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1132))) (-2173 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-1132)))) (-2173 (-12 (|HasCategory| |#1| (QUOTE (-1132))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-887))))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-887)))) (|HasCategory| |#1| (QUOTE (-102)))) +(-61 -3965) ((|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 -3949) +(-62 -3965) ((|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 -3949) +(-63 -3965) ((|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 -3949) +(-64 -3965) ((|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 -3949) +(-65 -3965) ((|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 -3949) +(-66 -3965) ((|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 -3949) +(-67 -3965) ((|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 -3949) +(-68 -3965) ((|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 -3949) +(-69 -3965) ((|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 -3949) +(-70 -3965) ((|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 -3949) +(-71 -3965) ((|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 -3949) +(-72 -3965) ((|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 -3949) +(-73 -3965) ((|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 -3949) +(-74 -3965) ((|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 -3949) +(-75 -3965) ((|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 -3949) +(-78 -3965) ((|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 -3949) +(-79 -3965) ((|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 -3949) +(-80 -3965) ((|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 -3949) +(-81 -3965) ((|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 -3949) +(-82 -3965) ((|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 -3949) +(-83 -3965) ((|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 -3949) +(-84 -3965) ((|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 -3949) +(-85 -3965) ((|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 -3949) +(-86 -3965) ((|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 -3949) +(-87 -3965) ((|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 -3949) +(-88 -3965) ((|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 -3949) +(-89 -3965) ((|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}."))) ((-4508 . T) (-4509 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1132))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1132))) (-2181 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-1132)))) (-2181 (-12 (|HasCategory| |#1| (QUOTE (-1132))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-887))))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-887)))) (|HasCategory| |#1| (QUOTE (-102)))) +((-12 (|HasCategory| |#1| (QUOTE (-1132))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1132))) (-2173 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-1132)))) (-2173 (-12 (|HasCategory| |#1| (QUOTE (-1132))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-887))))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-887)))) (|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}."))) ((-4508 . T) (-4509 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1132))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1132))) (-2181 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-1132)))) (-2181 (-12 (|HasCategory| |#1| (QUOTE (-1132))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-887))))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-887)))) (|HasCategory| |#1| (QUOTE (-102)))) +((-12 (|HasCategory| |#1| (QUOTE (-1132))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1132))) (-2173 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-1132)))) (-2173 (-12 (|HasCategory| |#1| (QUOTE (-1132))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-887))))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-887)))) (|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."))) ((-4500 . T) (-4506 . T) (-4501 . T) ((-4510 "*") . T) (-4502 . T) (-4503 . T) (-4505 . T)) -((|HasCategory| (-560) (QUOTE (-939))) (|HasCategory| (-560) (|%list| (QUOTE -1069) (QUOTE (-1207)))) (|HasCategory| (-560) (QUOTE (-147))) (|HasCategory| (-560) (QUOTE (-149))) (|HasCategory| (-560) (|%list| (QUOTE -633) (QUOTE (-549)))) (|HasCategory| (-560) (QUOTE (-1051))) (|HasCategory| (-560) (QUOTE (-842))) (|HasCategory| (-560) (QUOTE (-871))) (-2181 (|HasCategory| (-560) (QUOTE (-842))) (|HasCategory| (-560) (QUOTE (-871)))) (|HasCategory| (-560) (|%list| (QUOTE -1069) (QUOTE (-560)))) (|HasCategory| (-560) (QUOTE (-1182))) (|HasCategory| (-560) (|%list| (QUOTE -911) (QUOTE (-391)))) (|HasCategory| (-560) (|%list| (QUOTE -911) (QUOTE (-560)))) (|HasCategory| (-560) (|%list| (QUOTE -633) (|%list| (QUOTE -915) (QUOTE (-391))))) (|HasCategory| (-560) (|%list| (QUOTE -633) (|%list| (QUOTE -915) (QUOTE (-560))))) (|HasCategory| (-560) (QUOTE (-239))) (|HasCategory| (-560) (|%list| (QUOTE -929) (QUOTE (-1207)))) (|HasCategory| (-560) (QUOTE (-240))) (|HasCategory| (-560) (|%list| (QUOTE -927) (QUOTE (-1207)))) (|HasCategory| (-560) (|%list| (QUOTE -528) (QUOTE (-1207)) (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 (-939)))) (-2181 (-12 (|HasCategory| $ (QUOTE (-147))) (|HasCategory| (-560) (QUOTE (-939)))) (|HasCategory| (-560) (QUOTE (-147))))) +((|HasCategory| (-560) (QUOTE (-939))) (|HasCategory| (-560) (|%list| (QUOTE -1069) (QUOTE (-1207)))) (|HasCategory| (-560) (QUOTE (-147))) (|HasCategory| (-560) (QUOTE (-149))) (|HasCategory| (-560) (|%list| (QUOTE -633) (QUOTE (-549)))) (|HasCategory| (-560) (QUOTE (-1051))) (|HasCategory| (-560) (QUOTE (-842))) (|HasCategory| (-560) (QUOTE (-871))) (-2173 (|HasCategory| (-560) (QUOTE (-842))) (|HasCategory| (-560) (QUOTE (-871)))) (|HasCategory| (-560) (|%list| (QUOTE -1069) (QUOTE (-560)))) (|HasCategory| (-560) (QUOTE (-1182))) (|HasCategory| (-560) (|%list| (QUOTE -911) (QUOTE (-391)))) (|HasCategory| (-560) (|%list| (QUOTE -911) (QUOTE (-560)))) (|HasCategory| (-560) (|%list| (QUOTE -633) (|%list| (QUOTE -915) (QUOTE (-391))))) (|HasCategory| (-560) (|%list| (QUOTE -633) (|%list| (QUOTE -915) (QUOTE (-560))))) (|HasCategory| (-560) (QUOTE (-239))) (|HasCategory| (-560) (|%list| (QUOTE -929) (QUOTE (-1207)))) (|HasCategory| (-560) (QUOTE (-240))) (|HasCategory| (-560) (|%list| (QUOTE -927) (QUOTE (-1207)))) (|HasCategory| (-560) (|%list| (QUOTE -528) (QUOTE (-1207)) (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 (-939)))) (-2173 (-12 (|HasCategory| $ (QUOTE (-147))) (|HasCategory| (-560) (QUOTE (-939)))) (|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 -1596 UP) +(-117 -1594 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}."))) ((-4500 . T) (-4506 . T) (-4501 . T) ((-4510 "*") . T) (-4502 . T) (-4503 . T) (-4505 . T)) -((|HasCategory| (-118 |#1|) (QUOTE (-939))) (|HasCategory| (-118 |#1|) (|%list| (QUOTE -1069) (QUOTE (-1207)))) (|HasCategory| (-118 |#1|) (QUOTE (-147))) (|HasCategory| (-118 |#1|) (QUOTE (-149))) (|HasCategory| (-118 |#1|) (|%list| (QUOTE -633) (QUOTE (-549)))) (|HasCategory| (-118 |#1|) (QUOTE (-1051))) (|HasCategory| (-118 |#1|) (QUOTE (-842))) (|HasCategory| (-118 |#1|) (QUOTE (-871))) (-2181 (|HasCategory| (-118 |#1|) (QUOTE (-842))) (|HasCategory| (-118 |#1|) (QUOTE (-871)))) (|HasCategory| (-118 |#1|) (|%list| (QUOTE -1069) (QUOTE (-560)))) (|HasCategory| (-118 |#1|) (QUOTE (-1182))) (|HasCategory| (-118 |#1|) (|%list| (QUOTE -911) (QUOTE (-391)))) (|HasCategory| (-118 |#1|) (|%list| (QUOTE -911) (QUOTE (-560)))) (|HasCategory| (-118 |#1|) (|%list| (QUOTE -633) (|%list| (QUOTE -915) (QUOTE (-391))))) (|HasCategory| (-118 |#1|) (|%list| (QUOTE -633) (|%list| (QUOTE -915) (QUOTE (-560))))) (|HasCategory| (-118 |#1|) (|%list| (QUOTE -660) (QUOTE (-560)))) (|HasCategory| (-118 |#1|) (QUOTE (-239))) (|HasCategory| (-118 |#1|) (|%list| (QUOTE -929) (QUOTE (-1207)))) (|HasCategory| (-118 |#1|) (QUOTE (-240))) (|HasCategory| (-118 |#1|) (|%list| (QUOTE -927) (QUOTE (-1207)))) (|HasCategory| (-118 |#1|) (|%list| (QUOTE -528) (QUOTE (-1207)) (|%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 (-939)))) (-2181 (-12 (|HasCategory| $ (QUOTE (-147))) (|HasCategory| (-118 |#1|) (QUOTE (-939)))) (|HasCategory| (-118 |#1|) (QUOTE (-147))))) +((|HasCategory| (-118 |#1|) (QUOTE (-939))) (|HasCategory| (-118 |#1|) (|%list| (QUOTE -1069) (QUOTE (-1207)))) (|HasCategory| (-118 |#1|) (QUOTE (-147))) (|HasCategory| (-118 |#1|) (QUOTE (-149))) (|HasCategory| (-118 |#1|) (|%list| (QUOTE -633) (QUOTE (-549)))) (|HasCategory| (-118 |#1|) (QUOTE (-1051))) (|HasCategory| (-118 |#1|) (QUOTE (-842))) (|HasCategory| (-118 |#1|) (QUOTE (-871))) (-2173 (|HasCategory| (-118 |#1|) (QUOTE (-842))) (|HasCategory| (-118 |#1|) (QUOTE (-871)))) (|HasCategory| (-118 |#1|) (|%list| (QUOTE -1069) (QUOTE (-560)))) (|HasCategory| (-118 |#1|) (QUOTE (-1182))) (|HasCategory| (-118 |#1|) (|%list| (QUOTE -911) (QUOTE (-391)))) (|HasCategory| (-118 |#1|) (|%list| (QUOTE -911) (QUOTE (-560)))) (|HasCategory| (-118 |#1|) (|%list| (QUOTE -633) (|%list| (QUOTE -915) (QUOTE (-391))))) (|HasCategory| (-118 |#1|) (|%list| (QUOTE -633) (|%list| (QUOTE -915) (QUOTE (-560))))) (|HasCategory| (-118 |#1|) (|%list| (QUOTE -660) (QUOTE (-560)))) (|HasCategory| (-118 |#1|) (QUOTE (-239))) (|HasCategory| (-118 |#1|) (|%list| (QUOTE -929) (QUOTE (-1207)))) (|HasCategory| (-118 |#1|) (QUOTE (-240))) (|HasCategory| (-118 |#1|) (|%list| (QUOTE -927) (QUOTE (-1207)))) (|HasCategory| (-118 |#1|) (|%list| (QUOTE -528) (QUOTE (-1207)) (|%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 (-939)))) (-2173 (-12 (|HasCategory| $ (QUOTE (-147))) (|HasCategory| (-118 |#1|) (QUOTE (-939)))) (|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"))) ((-4508 . T) (-4509 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1132))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1132))) (-2181 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-1132)))) (-2181 (-12 (|HasCategory| |#1| (QUOTE (-1132))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-887))))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-887)))) (|HasCategory| |#1| (QUOTE (-102)))) +((-12 (|HasCategory| |#1| (QUOTE (-1132))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1132))) (-2173 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-1132)))) (-2173 (-12 (|HasCategory| |#1| (QUOTE (-1132))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-887))))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-887)))) (|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."))) ((-4508 . T) (-4509 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1132))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1132))) (-2181 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-1132)))) (-2181 (-12 (|HasCategory| |#1| (QUOTE (-1132))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-887))))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-887)))) (|HasCategory| |#1| (QUOTE (-102)))) +((-12 (|HasCategory| |#1| (QUOTE (-1132))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1132))) (-2173 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-1132)))) (-2173 (-12 (|HasCategory| |#1| (QUOTE (-1132))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-887))))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-887)))) (|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."))) ((-4508 . T) (-4509 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1132))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1132))) (-2181 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-1132)))) (-2181 (-12 (|HasCategory| |#1| (QUOTE (-1132))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-887))))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-887)))) (|HasCategory| |#1| (QUOTE (-102)))) +((-12 (|HasCategory| |#1| (QUOTE (-1132))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1132))) (-2173 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-1132)))) (-2173 (-12 (|HasCategory| |#1| (QUOTE (-1132))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-887))))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-887)))) (|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."))) ((-4509 . T) (-4508 . T)) -((-2181 (-12 (|HasCategory| (-130) (QUOTE (-871))) (|HasCategory| (-130) (|%list| (QUOTE -321) (QUOTE (-130))))) (-12 (|HasCategory| (-130) (QUOTE (-1132))) (|HasCategory| (-130) (|%list| (QUOTE -321) (QUOTE (-130)))))) (-2181 (-12 (|HasCategory| (-130) (QUOTE (-1132))) (|HasCategory| (-130) (|%list| (QUOTE -321) (QUOTE (-130))))) (|HasCategory| (-130) (|%list| (QUOTE -632) (QUOTE (-887))))) (|HasCategory| (-130) (|%list| (QUOTE -633) (QUOTE (-549)))) (-2181 (|HasCategory| (-130) (QUOTE (-871))) (|HasCategory| (-130) (QUOTE (-1132)))) (|HasCategory| (-130) (QUOTE (-871))) (-2181 (|HasCategory| (-130) (QUOTE (-102))) (|HasCategory| (-130) (QUOTE (-871))) (|HasCategory| (-130) (QUOTE (-1132)))) (|HasCategory| (-560) (QUOTE (-871))) (|HasCategory| (-130) (QUOTE (-1132))) (|HasCategory| (-130) (|%list| (QUOTE -632) (QUOTE (-887)))) (|HasCategory| (-130) (QUOTE (-102))) (-12 (|HasCategory| (-130) (QUOTE (-1132))) (|HasCategory| (-130) (|%list| (QUOTE -321) (QUOTE (-130)))))) +((-2173 (-12 (|HasCategory| (-130) (QUOTE (-871))) (|HasCategory| (-130) (|%list| (QUOTE -321) (QUOTE (-130))))) (-12 (|HasCategory| (-130) (QUOTE (-1132))) (|HasCategory| (-130) (|%list| (QUOTE -321) (QUOTE (-130)))))) (-2173 (-12 (|HasCategory| (-130) (QUOTE (-1132))) (|HasCategory| (-130) (|%list| (QUOTE -321) (QUOTE (-130))))) (|HasCategory| (-130) (|%list| (QUOTE -632) (QUOTE (-887))))) (|HasCategory| (-130) (|%list| (QUOTE -633) (QUOTE (-549)))) (-2173 (|HasCategory| (-130) (QUOTE (-871))) (|HasCategory| (-130) (QUOTE (-1132)))) (|HasCategory| (-130) (QUOTE (-871))) (-2173 (|HasCategory| (-130) (QUOTE (-102))) (|HasCategory| (-130) (QUOTE (-871))) (|HasCategory| (-130) (QUOTE (-1132)))) (|HasCategory| (-560) (QUOTE (-871))) (|HasCategory| (-130) (QUOTE (-1132))) (|HasCategory| (-130) (|%list| (QUOTE -632) (QUOTE (-887)))) (|HasCategory| (-130) (QUOTE (-102))) (-12 (|HasCategory| (-130) (QUOTE (-1132))) (|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") $ $) "\\spad{x - y} returns an element \\spad{z} such that \\spad{z+y=x} or \"failed\" if no such element exists.")) (|commutative| ((|attribute| "*") "a domain \\spad{D} has \\spad{commutative(\"*\")} if it has an operation \\spad{\"*\": (D,D) -> D} which is commutative."))) (((-4510 "*") . T)) NIL -(-137 |minix| -3370 R) +(-137 |minix| -3367 R) ((|constructor| (NIL "CartesianTensor(minix,{}dim,{}\\spad{R}) provides Cartesian tensors with components belonging to a commutative ring \\spad{R}. These tensors can have any number of indices. Each index takes values from \\spad{minix} to \\spad{minix + dim - 1}.")) (|sample| (($) "\\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| -3370 S T$) +(-138 |minix| -3367 S T$) ((|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}."))) ((-4508 . T) (-4498 . T) (-4509 . T)) -((-2181 (-12 (|HasCategory| (-146) (QUOTE (-381))) (|HasCategory| (-146) (|%list| (QUOTE -321) (QUOTE (-146))))) (-12 (|HasCategory| (-146) (QUOTE (-1132))) (|HasCategory| (-146) (|%list| (QUOTE -321) (QUOTE (-146)))))) (|HasCategory| (-146) (|%list| (QUOTE -633) (QUOTE (-549)))) (|HasCategory| (-146) (QUOTE (-381))) (|HasCategory| (-146) (QUOTE (-871))) (|HasCategory| (-146) (QUOTE (-1132))) (|HasCategory| (-146) (|%list| (QUOTE -632) (QUOTE (-887)))) (|HasCategory| (-146) (QUOTE (-102))) (-12 (|HasCategory| (-146) (QUOTE (-1132))) (|HasCategory| (-146) (|%list| (QUOTE -321) (QUOTE (-146)))))) +((-2173 (-12 (|HasCategory| (-146) (QUOTE (-381))) (|HasCategory| (-146) (|%list| (QUOTE -321) (QUOTE (-146))))) (-12 (|HasCategory| (-146) (QUOTE (-1132))) (|HasCategory| (-146) (|%list| (QUOTE -321) (QUOTE (-146)))))) (|HasCategory| (-146) (|%list| (QUOTE -633) (QUOTE (-549)))) (|HasCategory| (-146) (QUOTE (-381))) (|HasCategory| (-146) (QUOTE (-871))) (|HasCategory| (-146) (QUOTE (-1132))) (|HasCategory| (-146) (|%list| (QUOTE -632) (QUOTE (-887)))) (|HasCategory| (-146) (QUOTE (-102))) (-12 (|HasCategory| (-146) (QUOTE (-1132))) (|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."))) ((-4505 . T)) NIL -(-150 -1596 UP UPUP) +(-150 -1594 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 -1596) +(-160 R -1594) ((|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 (-939))) (|HasCategory| |#2| (QUOTE (-559))) (|HasCategory| |#2| (QUOTE (-1033))) (|HasCategory| |#2| (QUOTE (-1233))) (|HasCategory| |#2| (QUOTE (-1091))) (|HasCategory| |#2| (QUOTE (-1051))) (|HasCategory| |#2| (QUOTE (-147))) (|HasCategory| |#2| (QUOTE (-149))) (|HasCategory| |#2| (|%list| (QUOTE -633) (QUOTE (-549)))) (|HasCategory| |#2| (QUOTE (-376))) (|HasAttribute| |#2| (QUOTE -4504)) (|HasAttribute| |#2| (QUOTE -4507)) (|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})"))) -((-4501 -2181 (|has| |#1| (-571)) (-12 (|has| |#1| (-319)) (|has| |#1| (-939)))) (-4506 |has| |#1| (-376)) (-4500 |has| |#1| (-376)) (-4504 |has| |#1| (-6 -4504)) (-4507 |has| |#1| (-6 -4507)) (-2992 . T) ((-4510 "*") . T) (-4502 . T) (-4503 . T) (-4505 . T)) +((-4501 -2173 (|has| |#1| (-571)) (-12 (|has| |#1| (-319)) (|has| |#1| (-939)))) (-4506 |has| |#1| (-376)) (-4500 |has| |#1| (-376)) (-4504 |has| |#1| (-6 -4504)) (-4507 |has| |#1| (-6 -4507)) (-2993 . T) ((-4510 "*") . T) (-4502 . T) (-4503 . T) (-4505 . 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}."))) -((-4501 -2181 (|has| |#1| (-571)) (-12 (|has| |#1| (-319)) (|has| |#1| (-939)))) (-4506 |has| |#1| (-376)) (-4500 |has| |#1| (-376)) (-4504 |has| |#1| (-6 -4504)) (-4507 |has| |#1| (-6 -4507)) (-2992 . T) ((-4510 "*") . T) (-4502 . T) (-4503 . T) (-4505 . 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T) ((-4510 "*") . T) (-4502 . T) (-4503 . T) (-4505 . 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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| (($) "`category' is the kind of category constructors"))) NIL NIL -(-191 R -1596) +(-191 R -1594) ((|constructor| (NIL "\\spadtype{ComplexTrigonometricManipulations} provides function that compute the real and imaginary parts of complex functions.")) (|complexForm| (((|Complex| (|Expression| |#1|)) |#2|) "\\spad{complexForm(f)} returns \\spad{[real f, imag f]}.")) (|trigs| ((|#2| |#2|) "\\spad{trigs(f)} rewrites all the complex logs and exponentials appearing in \\spad{f} in terms of trigonometric functions.")) (|real?| (((|Boolean|) |#2|) "\\spad{real?(f)} returns \\spad{true} if \\spad{f = real f}.")) (|imag| (((|Expression| |#1|) |#2|) "\\spad{imag(f)} returns the imaginary part of \\spad{f} where \\spad{f} is a complex function.")) (|real| (((|Expression| |#1|) |#2|) "\\spad{real(f)} returns the real part of \\spad{f} where \\spad{f} is a complex function.")) (|complexElementary| ((|#2| |#2| (|Symbol|)) "\\spad{complexElementary(f, x)} rewrites the kernels of \\spad{f} involving \\spad{x} in terms of the 2 fundamental complex transcendental elementary functions: \\spad{log, exp}.") ((|#2| |#2|) "\\spad{complexElementary(f)} rewrites \\spad{f} in terms of the 2 fundamental complex transcendental elementary functions: \\spad{log, exp}.")) (|complexNormalize| ((|#2| |#2| (|Symbol|)) "\\spad{complexNormalize(f, x)} rewrites \\spad{f} using the least possible number of complex independent kernels involving \\spad{x}.") ((|#2| |#2|) "\\spad{complexNormalize(f)} rewrites \\spad{f} using the least possible number of complex independent kernels."))) NIL NIL @@ -804,23 +804,23 @@ NIL ((|constructor| (NIL "\\indented{1}{Author: Gabriel Dos Reis} Date Created: July 2,{} 2010 Date Last Modified: July 2,{} 2010 Descrption: \\indented{2}{Representation of a dual vector space basis,{} given by symbols.}")) (|dual| (($ (|LinearBasis| |#1|)) "\\spad{dual x} constructs the dual vector of a linear element which is part of a basis."))) NIL NIL -(-219 -1596 UP UPUP R) +(-219 -1594 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 -1596 FP) +(-220 -1594 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 (-939))) (|HasCategory| (-560) (|%list| (QUOTE -1069) (QUOTE (-1207)))) (|HasCategory| (-560) (QUOTE (-147))) (|HasCategory| (-560) (QUOTE (-149))) (|HasCategory| (-560) (|%list| (QUOTE -633) (QUOTE (-549)))) (|HasCategory| (-560) (QUOTE (-1051))) (|HasCategory| (-560) (QUOTE (-842))) (|HasCategory| (-560) (QUOTE (-871))) (-2181 (|HasCategory| (-560) (QUOTE (-842))) (|HasCategory| (-560) (QUOTE (-871)))) (|HasCategory| (-560) (|%list| (QUOTE -1069) (QUOTE (-560)))) (|HasCategory| (-560) (QUOTE (-1182))) (|HasCategory| (-560) (|%list| (QUOTE -911) (QUOTE (-391)))) (|HasCategory| (-560) (|%list| (QUOTE -911) (QUOTE (-560)))) (|HasCategory| (-560) (|%list| (QUOTE -633) (|%list| (QUOTE -915) (QUOTE (-391))))) (|HasCategory| (-560) (|%list| (QUOTE -633) (|%list| (QUOTE -915) (QUOTE (-560))))) (|HasCategory| (-560) (QUOTE (-239))) (|HasCategory| (-560) (|%list| (QUOTE -929) (QUOTE (-1207)))) (|HasCategory| (-560) (QUOTE (-240))) (|HasCategory| (-560) (|%list| (QUOTE -927) (QUOTE (-1207)))) (|HasCategory| (-560) (|%list| (QUOTE -528) (QUOTE (-1207)) (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 (-939)))) (-2181 (-12 (|HasCategory| $ (QUOTE (-147))) (|HasCategory| (-560) (QUOTE (-939)))) (|HasCategory| (-560) (QUOTE (-147))))) +((|HasCategory| (-560) (QUOTE (-939))) (|HasCategory| (-560) (|%list| (QUOTE -1069) (QUOTE (-1207)))) (|HasCategory| (-560) (QUOTE (-147))) (|HasCategory| (-560) (QUOTE (-149))) (|HasCategory| (-560) (|%list| (QUOTE -633) (QUOTE (-549)))) (|HasCategory| (-560) (QUOTE (-1051))) (|HasCategory| (-560) (QUOTE (-842))) (|HasCategory| (-560) (QUOTE (-871))) (-2173 (|HasCategory| (-560) (QUOTE (-842))) (|HasCategory| (-560) (QUOTE (-871)))) (|HasCategory| (-560) (|%list| (QUOTE -1069) (QUOTE (-560)))) (|HasCategory| (-560) (QUOTE (-1182))) (|HasCategory| (-560) (|%list| (QUOTE -911) (QUOTE (-391)))) (|HasCategory| (-560) (|%list| (QUOTE -911) (QUOTE (-560)))) (|HasCategory| (-560) (|%list| (QUOTE -633) (|%list| (QUOTE -915) (QUOTE (-391))))) (|HasCategory| (-560) (|%list| (QUOTE -633) (|%list| (QUOTE -915) (QUOTE (-560))))) (|HasCategory| (-560) (QUOTE (-239))) (|HasCategory| (-560) (|%list| (QUOTE -929) (QUOTE (-1207)))) (|HasCategory| (-560) (QUOTE (-240))) (|HasCategory| (-560) (|%list| (QUOTE -927) (QUOTE (-1207)))) (|HasCategory| (-560) (|%list| (QUOTE -528) (QUOTE (-1207)) (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 (-939)))) (-2173 (-12 (|HasCategory| $ (QUOTE (-147))) (|HasCategory| (-560) (QUOTE (-939)))) (|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|) $) "\\spad{head(d)} returns the head of the definition `d'. This is a list of identifiers starting with the name of the operation followed by the name of the parameters,{} if any."))) NIL NIL -(-223 R -1596) +(-223 R -1594) ((|constructor| (NIL "\\spadtype{ElementaryFunctionDefiniteIntegration} provides functions to compute definite integrals of elementary functions.")) (|innerint| (((|Union| (|:| |f1| (|OrderedCompletion| |#2|)) (|:| |f2| (|List| (|OrderedCompletion| |#2|))) (|:| |fail| "failed") (|:| |pole| "potentialPole")) |#2| (|Symbol|) (|OrderedCompletion| |#2|) (|OrderedCompletion| |#2|) (|Boolean|)) "\\spad{innerint(f, x, a, b, ignore?)} should be local but conditional")) (|integrate| (((|Union| (|:| |f1| (|OrderedCompletion| |#2|)) (|:| |f2| (|List| (|OrderedCompletion| |#2|))) (|:| |fail| "failed") (|:| |pole| "potentialPole")) |#2| (|SegmentBinding| (|OrderedCompletion| |#2|)) (|String|)) "\\spad{integrate(f, x = a..b, \"noPole\")} returns the integral of \\spad{f(x)dx} from a to \\spad{b}. If it is not possible to check whether \\spad{f} has a pole for \\spad{x} between a and \\spad{b} (because of parameters),{} then this function will assume that \\spad{f} has no such pole. Error: if \\spad{f} has a pole for \\spad{x} between a and \\spad{b} or if the last argument is not \"noPole\".") (((|Union| (|:| |f1| (|OrderedCompletion| |#2|)) (|:| |f2| (|List| (|OrderedCompletion| |#2|))) (|:| |fail| "failed") (|:| |pole| "potentialPole")) |#2| (|SegmentBinding| (|OrderedCompletion| |#2|))) "\\spad{integrate(f, x = a..b)} returns the integral of \\spad{f(x)dx} from a to \\spad{b}. Error: if \\spad{f} has a pole for \\spad{x} between a and \\spad{b}."))) NIL NIL @@ -835,18 +835,18 @@ NIL (-226 S) ((|constructor| (NIL "Linked list implementation of a Dequeue")) (|dequeue| (($ (|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}."))) ((-4508 . T) (-4509 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1132))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1132))) (-2181 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-1132)))) (-2181 (-12 (|HasCategory| |#1| (QUOTE (-1132))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-887))))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-887)))) (|HasCategory| |#1| (QUOTE (-102)))) +((-12 (|HasCategory| |#1| (QUOTE (-1132))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1132))) (-2173 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-1132)))) (-2173 (-12 (|HasCategory| |#1| (QUOTE (-1132))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-887))))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-887)))) (|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}."))) ((-4505 . T)) NIL -(-228 R -1596) +(-228 R -1594) ((|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}."))) -((-2980 . T) (-4500 . T) (-4506 . T) (-4501 . T) ((-4510 "*") . T) (-4502 . T) (-4503 . T) (-4505 . T)) +((-2981 . T) (-4500 . T) (-4506 . T) (-4501 . T) ((-4510 "*") . T) (-4502 . T) (-4503 . T) (-4505 . 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}"))) ((-4508 . T) (-4509 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1132))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1132))) (-2181 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-1132)))) (-2181 (-12 (|HasCategory| |#1| (QUOTE (-1132))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-887))))) (|HasCategory| |#1| (QUOTE (-319))) (|HasCategory| |#1| (QUOTE (-571))) (|HasAttribute| |#1| (QUOTE (-4510 "*"))) (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-887)))) (|HasCategory| |#1| (QUOTE (-102)))) +((-12 (|HasCategory| |#1| (QUOTE (-1132))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1132))) (-2173 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-1132)))) (-2173 (-12 (|HasCategory| |#1| (QUOTE (-1132))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-887))))) (|HasCategory| |#1| (QUOTE (-319))) (|HasCategory| |#1| (QUOTE (-571))) (|HasAttribute| |#1| (QUOTE (-4510 "*"))) (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-887)))) (|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 -3370 R) +(-244 S -3367 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 (-815))) (|HasCategory| |#3| (QUOTE (-871))) (|HasAttribute| |#3| (QUOTE -4505)) (|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 (-1080))) (|HasCategory| |#3| (QUOTE (-1132)))) -(-245 -3370 R) +(-245 -3367 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"))) ((-4502 |has| |#2| (-1080)) (-4503 |has| |#2| (-1080)) (-4505 |has| |#2| (-6 -4505)) (-4508 . T)) NIL -(-246 -3370 R) +(-246 -3367 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."))) ((-4502 |has| |#2| (-1080)) (-4503 |has| |#2| (-1080)) (-4505 |has| |#2| (-6 -4505)) (-4508 . 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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}"))) ((-4509 . T) (-4508 . 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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"))) (((-4510 "*") |has| |#1| (-175)) (-4501 |has| |#1| (-571)) (-4506 |has| |#1| (-6 -4506)) (-4503 . T) (-4502 . T) (-4505 . 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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 -1596) +(-287 R -1594) ((|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 -1596) +(-288 R -1594) ((|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| -4284 -2846 |exactQuo|) +(-301 S R |Mod| -2288 -3960 |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| $) "\\spad{modulus(x)} \\undocumented"))) ((-4501 . T) ((-4510 "*") . T) (-4502 . T) (-4503 . T) (-4505 . T)) NIL @@ -1150,8 +1150,8 @@ NIL NIL (-305 S) ((|constructor| (NIL "Equations as mathematical objects. All properties of the basis domain,{} \\spadignore{e.g.} being an abelian group are carried over the equation domain,{} by performing the structural operations on the left and on the right hand side.")) (|subst| (($ $ $) "\\spad{subst(eq1,eq2)} substitutes \\spad{eq2} into both sides of \\spad{eq1} the lhs of \\spad{eq2} should be a kernel")) (|inv| (($ $) "\\spad{inv(x)} returns the multiplicative inverse of \\spad{x}.")) (/ (($ $ $) "\\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."))) -((-4505 -2181 (|has| |#1| (-1080)) (|has| |#1| (-487))) (-4502 |has| |#1| (-1080)) (-4503 |has| |#1| (-1080))) -((|HasCategory| |#1| (QUOTE (-376))) (-2181 (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (QUOTE (-1080)))) (-2181 (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-376)))) (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-1080))) (|HasCategory| |#1| (QUOTE (-1132))) (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (|%list| (QUOTE -927) (QUOTE (-1207)))) (-2181 (|HasCategory| |#1| (|%list| (QUOTE -927) (QUOTE (-1207)))) (|HasCategory| |#1| (QUOTE (-1080)))) (-2181 (|HasCategory| |#1| (|%list| (QUOTE -927) (QUOTE (-1207)))) (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-25))) (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (QUOTE (-1080)))) (-2181 (|HasCategory| |#1| (|%list| (QUOTE -927) (QUOTE (-1207)))) (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (QUOTE (-1080)))) (-2181 (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-1080)))) (-2181 (|HasCategory| |#1| (QUOTE (-487))) (|HasCategory| |#1| (QUOTE (-748)))) (|HasCategory| |#1| (QUOTE (-487))) (-2181 (|HasCategory| |#1| (|%list| (QUOTE -927) (QUOTE (-1207)))) (|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 (-1080))) (|HasCategory| |#1| (QUOTE (-1143))) (|HasCategory| |#1| (QUOTE (-1132)))) (-2181 (|HasCategory| |#1| (QUOTE (-487))) (|HasCategory| |#1| (QUOTE (-748))) (|HasCategory| |#1| (QUOTE (-1143)))) (|HasCategory| |#1| (|%list| (QUOTE -528) (QUOTE (-1207)) (|devaluate| |#1|))) (-12 (|HasCategory| |#1| (QUOTE (-1132))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-571))) (|HasCategory| |#1| (QUOTE (-310))) (-2181 (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (QUOTE (-487)))) (-2181 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-748)))) (-2181 (|HasCategory| |#1| (QUOTE (-487))) (|HasCategory| |#1| (QUOTE (-1080)))) (|HasCategory| |#1| (QUOTE (-25))) (|HasCategory| |#1| (QUOTE (-1143))) (|HasCategory| |#1| (QUOTE (-748)))) +((-4505 -2173 (|has| |#1| (-1080)) (|has| |#1| (-487))) (-4502 |has| |#1| (-1080)) (-4503 |has| |#1| (-1080))) +((|HasCategory| |#1| (QUOTE (-376))) (-2173 (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (QUOTE (-1080)))) (-2173 (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-376)))) (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-1080))) (|HasCategory| |#1| (QUOTE (-1132))) (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (|%list| (QUOTE -927) (QUOTE (-1207)))) (-2173 (|HasCategory| |#1| (|%list| (QUOTE -927) (QUOTE (-1207)))) (|HasCategory| |#1| (QUOTE (-1080)))) (-2173 (|HasCategory| |#1| (|%list| (QUOTE -927) (QUOTE (-1207)))) (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-25))) (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (QUOTE (-1080)))) (-2173 (|HasCategory| |#1| (|%list| (QUOTE -927) (QUOTE (-1207)))) (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (QUOTE (-1080)))) (-2173 (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-1080)))) (-2173 (|HasCategory| |#1| (QUOTE (-487))) (|HasCategory| |#1| (QUOTE (-748)))) (|HasCategory| |#1| (QUOTE (-487))) (-2173 (|HasCategory| |#1| (|%list| (QUOTE -927) (QUOTE (-1207)))) (|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 (-1080))) (|HasCategory| |#1| (QUOTE (-1143))) (|HasCategory| |#1| (QUOTE (-1132)))) (-2173 (|HasCategory| |#1| (QUOTE (-487))) (|HasCategory| |#1| (QUOTE (-748))) (|HasCategory| |#1| (QUOTE (-1143)))) (|HasCategory| |#1| (|%list| (QUOTE -528) (QUOTE (-1207)) (|devaluate| |#1|))) (-12 (|HasCategory| |#1| (QUOTE (-1132))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-571))) (|HasCategory| |#1| (QUOTE (-310))) (-2173 (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (QUOTE (-487)))) (-2173 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-748)))) (-2173 (|HasCategory| |#1| (QUOTE (-487))) (|HasCategory| |#1| (QUOTE (-1080)))) (|HasCategory| |#1| (QUOTE (-25))) (|HasCategory| |#1| (QUOTE (-1143))) (|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."))) ((-4508 . T) (-4509 . T)) -((-12 (|HasCategory| (-2 (|:| -3819 |#1|) (|:| -2913 |#2|)) (QUOTE (-1132))) (|HasCategory| (-2 (|:| -3819 |#1|) (|:| -2913 |#2|)) (|%list| (QUOTE -321) (|%list| (QUOTE -2) (|%list| (QUOTE |:|) (QUOTE -3819) (|devaluate| |#1|)) (|%list| (QUOTE |:|) (QUOTE -2913) (|devaluate| |#2|)))))) (-2181 (|HasCategory| (-2 (|:| -3819 |#1|) (|:| -2913 |#2|)) (QUOTE (-1132))) (|HasCategory| |#2| (QUOTE (-1132)))) (-2181 (|HasCategory| (-2 (|:| -3819 |#1|) (|:| -2913 |#2|)) (QUOTE (-102))) (|HasCategory| (-2 (|:| -3819 |#1|) (|:| -2913 |#2|)) (QUOTE (-1132))) (|HasCategory| |#2| (QUOTE (-102))) (|HasCategory| |#2| (QUOTE (-1132)))) (-2181 (|HasCategory| (-2 (|:| -3819 |#1|) (|:| -2913 |#2|)) (QUOTE (-1132))) (|HasCategory| (-2 (|:| -3819 |#1|) (|:| -2913 |#2|)) (|%list| (QUOTE -632) (QUOTE (-887)))) (|HasCategory| |#2| (QUOTE (-1132))) (|HasCategory| |#2| (|%list| (QUOTE -632) (QUOTE (-887))))) (|HasCategory| (-2 (|:| -3819 |#1|) (|:| -2913 |#2|)) (|%list| (QUOTE -633) (QUOTE (-549)))) (-12 (|HasCategory| |#2| (QUOTE (-1132))) (|HasCategory| |#2| (|%list| (QUOTE -321) (|devaluate| |#2|)))) (|HasCategory| (-2 (|:| -3819 |#1|) (|:| -2913 |#2|)) (QUOTE (-1132))) (|HasCategory| |#1| (QUOTE (-871))) (|HasCategory| |#2| (QUOTE (-1132))) (-2181 (|HasCategory| (-2 (|:| -3819 |#1|) (|:| -2913 |#2|)) (|%list| (QUOTE -632) (QUOTE (-887)))) (|HasCategory| |#2| (|%list| (QUOTE -632) (QUOTE (-887))))) (-2181 (|HasCategory| (-2 (|:| -3819 |#1|) (|:| -2913 |#2|)) (QUOTE (-102))) (|HasCategory| |#2| (QUOTE (-102)))) (|HasCategory| |#2| (QUOTE (-102))) (|HasCategory| |#2| (|%list| (QUOTE -632) (QUOTE (-887)))) (|HasCategory| (-2 (|:| -3819 |#1|) (|:| -2913 |#2|)) (|%list| (QUOTE -632) (QUOTE (-887)))) (|HasCategory| (-2 (|:| -3819 |#1|) (|:| -2913 |#2|)) (QUOTE (-102)))) +((-12 (|HasCategory| (-2 (|:| -3835 |#1|) (|:| -2923 |#2|)) (QUOTE (-1132))) (|HasCategory| (-2 (|:| -3835 |#1|) (|:| -2923 |#2|)) (|%list| (QUOTE -321) (|%list| (QUOTE -2) (|%list| (QUOTE |:|) (QUOTE -3835) (|devaluate| |#1|)) (|%list| (QUOTE |:|) (QUOTE -2923) (|devaluate| |#2|)))))) (-2173 (|HasCategory| (-2 (|:| -3835 |#1|) (|:| -2923 |#2|)) (QUOTE (-1132))) (|HasCategory| |#2| (QUOTE (-1132)))) (-2173 (|HasCategory| (-2 (|:| -3835 |#1|) (|:| -2923 |#2|)) (QUOTE (-102))) (|HasCategory| (-2 (|:| -3835 |#1|) (|:| -2923 |#2|)) (QUOTE (-1132))) (|HasCategory| |#2| (QUOTE (-102))) (|HasCategory| |#2| (QUOTE (-1132)))) (-2173 (|HasCategory| (-2 (|:| -3835 |#1|) (|:| -2923 |#2|)) (QUOTE (-1132))) (|HasCategory| (-2 (|:| -3835 |#1|) (|:| -2923 |#2|)) (|%list| (QUOTE -632) (QUOTE (-887)))) (|HasCategory| |#2| (QUOTE (-1132))) (|HasCategory| |#2| (|%list| (QUOTE -632) (QUOTE (-887))))) (|HasCategory| (-2 (|:| -3835 |#1|) (|:| -2923 |#2|)) (|%list| (QUOTE -633) (QUOTE (-549)))) (-12 (|HasCategory| |#2| (QUOTE (-1132))) (|HasCategory| |#2| (|%list| (QUOTE -321) (|devaluate| |#2|)))) (|HasCategory| (-2 (|:| -3835 |#1|) (|:| -2923 |#2|)) (QUOTE (-1132))) (|HasCategory| |#1| (QUOTE (-871))) (|HasCategory| |#2| (QUOTE (-1132))) (-2173 (|HasCategory| (-2 (|:| -3835 |#1|) (|:| -2923 |#2|)) (|%list| (QUOTE -632) (QUOTE (-887)))) (|HasCategory| |#2| (|%list| (QUOTE -632) (QUOTE (-887))))) (-2173 (|HasCategory| (-2 (|:| -3835 |#1|) (|:| -2923 |#2|)) (QUOTE (-102))) (|HasCategory| |#2| (QUOTE (-102)))) (|HasCategory| |#2| (QUOTE (-102))) (|HasCategory| |#2| (|%list| (QUOTE -632) (QUOTE (-887)))) (|HasCategory| (-2 (|:| -3835 |#1|) (|:| -2923 |#2|)) (|%list| (QUOTE -632) (QUOTE (-887)))) (|HasCategory| (-2 (|:| -3835 |#1|) (|:| -2923 |#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|) $) "\\spad{elt(op,x)} or \\spad{op}(\\spad{x}) applies the unary operator \\spad{op} to \\spad{x}."))) NIL NIL -(-311 -1596 S) +(-311 -1594 S) ((|constructor| (NIL "This package allows a map from any expression space into any object to be lifted to a kernel over the expression set,{} using a given property of the operator of the kernel.")) (|map| ((|#2| (|Mapping| |#2| |#1|) (|String|) (|Kernel| |#1|)) "\\spad{map(f, p, k)} uses the property \\spad{p} of the operator of \\spad{k},{} in order to lift \\spad{f} and apply it to \\spad{k}."))) NIL NIL -(-312 E -1596) +(-312 E -1594) ((|constructor| (NIL "This package allows a mapping \\spad{E} -> \\spad{F} to be lifted to a kernel over \\spad{E}; This lifting can fail if the operator of the kernel cannot be applied in \\spad{F}; Do not use this package with \\spad{E} = \\spad{F},{} since this may drop some properties of the operators.")) (|map| ((|#2| (|Mapping| |#2| |#1|) (|Kernel| |#1|)) "\\spad{map(f, k)} returns \\spad{g = op(f(a1),...,f(an))} where \\spad{k = op(a1,...,an)}."))) NIL NIL @@ -1216,7 +1216,7 @@ NIL ((|constructor| (NIL "This category provides \\spadfun{eval} operations. A domain may belong to this category if it is possible to make ``evaluation'' substitutions.")) (|eval| (($ $ (|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 -1596) +(-322 -1594) ((|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))}."))) ((-4500 . T) (-4506 . T) (-4501 . T) ((-4510 "*") . T) (-4502 . T) (-4503 . T) (-4505 . T)) -((|HasCategory| (-1284 |#1| |#2| |#3| |#4|) (QUOTE (-939))) (|HasCategory| (-1284 |#1| |#2| |#3| |#4|) (|%list| (QUOTE -1069) (QUOTE (-1207)))) (|HasCategory| (-1284 |#1| |#2| |#3| |#4|) (QUOTE (-147))) (|HasCategory| (-1284 |#1| |#2| |#3| |#4|) (QUOTE (-149))) (|HasCategory| (-1284 |#1| |#2| |#3| |#4|) (|%list| (QUOTE -633) (QUOTE (-549)))) (|HasCategory| (-1284 |#1| |#2| |#3| |#4|) (QUOTE (-1051))) (|HasCategory| (-1284 |#1| |#2| |#3| |#4|) (QUOTE (-842))) (|HasCategory| (-1284 |#1| |#2| |#3| |#4|) (QUOTE (-871))) (-2181 (|HasCategory| (-1284 |#1| |#2| |#3| |#4|) (QUOTE (-842))) (|HasCategory| (-1284 |#1| |#2| |#3| |#4|) (QUOTE (-871)))) (|HasCategory| (-1284 |#1| |#2| |#3| |#4|) (|%list| (QUOTE -1069) (QUOTE (-560)))) (|HasCategory| (-1284 |#1| |#2| |#3| |#4|) (QUOTE (-1182))) (|HasCategory| (-1284 |#1| |#2| |#3| |#4|) (|%list| (QUOTE -911) (QUOTE (-391)))) (|HasCategory| (-1284 |#1| |#2| |#3| |#4|) (|%list| (QUOTE -911) (QUOTE (-560)))) (|HasCategory| (-1284 |#1| |#2| |#3| 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(|HasCategory| (-1284 |#1| |#2| |#3| |#4|) (|%list| (QUOTE -927) (QUOTE (-1207)))) (|HasCategory| (-1284 |#1| |#2| |#3| |#4|) (|%list| (QUOTE -528) (QUOTE (-1207)) (|%list| (QUOTE -1284) (|devaluate| |#1|) (|devaluate| |#2|) (|devaluate| |#3|) (|devaluate| |#4|)))) (|HasCategory| (-1284 |#1| |#2| |#3| |#4|) (|%list| (QUOTE -321) (|%list| (QUOTE -1284) (|devaluate| |#1|) (|devaluate| |#2|) (|devaluate| |#3|) (|devaluate| |#4|)))) (|HasCategory| (-1284 |#1| |#2| |#3| |#4|) (|%list| (QUOTE -298) (|%list| (QUOTE -1284) (|devaluate| |#1|) (|devaluate| |#2|) (|devaluate| |#3|) (|devaluate| |#4|)) (|%list| (QUOTE -1284) (|devaluate| |#1|) (|devaluate| |#2|) (|devaluate| |#3|) (|devaluate| |#4|)))) (|HasCategory| (-1284 |#1| |#2| |#3| |#4|) (QUOTE (-319))) (|HasCategory| (-1284 |#1| |#2| |#3| |#4|) (QUOTE (-559))) (-12 (|HasCategory| (-1284 |#1| |#2| |#3| |#4|) (QUOTE (-939))) (|HasCategory| $ (QUOTE (-147)))) (-2173 (|HasCategory| (-1284 |#1| |#2| |#3| |#4|) (QUOTE (-147))) (-12 (|HasCategory| (-1284 |#1| |#2| |#3| |#4|) (QUOTE (-939))) (|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."))) -((-4505 -2181 (-12 (|has| |#1| (-571)) (-2181 (|has| |#1| (-1080)) (|has| |#1| (-487)))) (|has| |#1| (-1080)) (|has| |#1| (-487))) (-4503 |has| |#1| (-175)) (-4502 |has| |#1| (-175)) ((-4510 "*") |has| |#1| (-571)) (-4501 |has| |#1| (-571)) (-4506 |has| |#1| (-571)) (-4500 |has| |#1| (-571))) -((-2181 (|HasCategory| |#1| (|%list| (QUOTE -1069) (|%list| (QUOTE 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|has| |#1| (-175)) (-4502 |has| |#1| (-175)) ((-4510 "*") |has| |#1| (-571)) (-4501 |has| |#1| (-571)) (-4506 |has| |#1| (-571)) (-4500 |has| |#1| (-571))) +((-2173 (|HasCategory| |#1| (|%list| (QUOTE -1069) (|%list| (QUOTE -421) (QUOTE (-560))))) (-12 (|HasCategory| |#1| (QUOTE (-571))) (|HasCategory| |#1| (|%list| (QUOTE -1069) (QUOTE (-560)))))) (|HasCategory| |#1| (QUOTE (-571))) (-2173 (|HasCategory| |#1| (QUOTE (-571))) (|HasCategory| |#1| (QUOTE (-1080)))) (|HasCategory| |#1| (QUOTE (-21))) (-2173 (|HasCategory| |#1| (|%list| (QUOTE -1069) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#1| (QUOTE (-571)))) (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-149))) (-2173 (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-1080)))) (|HasCategory| |#1| (QUOTE (-1080))) (-2173 (-12 (|HasCategory| |#1| (|%list| (QUOTE -660) (QUOTE (-560)))) (|HasCategory| |#1| (QUOTE (-147)))) (-12 (|HasCategory| |#1| (|%list| 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(|HasCategory| |#1| (QUOTE (-571))) (|HasCategory| |#1| (|%list| (QUOTE -1069) (QUOTE (-560))))) (-2173 (|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 (-1080)))) (-2173 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-149))) (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-571))) (|HasCategory| |#1| (QUOTE (-1080)))) (-2173 (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-149))) (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-571))) (|HasCategory| |#1| (QUOTE (-1080)))) (-12 (|HasCategory| |#1| (QUOTE (-466))) (|HasCategory| |#1| (QUOTE (-571)))) (-2173 (|HasCategory| |#1| (QUOTE (-487))) (|HasCategory| |#1| (QUOTE (-571)))) (-12 (|HasCategory| |#1| (|%list| (QUOTE -660) (QUOTE (-560)))) (|HasCategory| |#1| (QUOTE (-1080)))) (-2173 (-12 (|HasCategory| |#1| (|%list| (QUOTE -660) (QUOTE (-560)))) (|HasCategory| |#1| (QUOTE (-1080)))) (|HasCategory| |#1| (QUOTE (-21)))) (-2173 (-12 (|HasCategory| |#1| (|%list| (QUOTE -660) (QUOTE (-560)))) (|HasCategory| |#1| (QUOTE (-1080)))) (|HasCategory| |#1| (QUOTE (-25))) (|HasCategory| |#1| (QUOTE (-1143)))) (-2173 (-12 (|HasCategory| |#1| (|%list| (QUOTE -660) (QUOTE (-560)))) (|HasCategory| |#1| (QUOTE (-1080)))) (|HasCategory| |#1| (QUOTE (-25)))) (-2173 (|HasCategory| |#1| (QUOTE (-487))) (|HasCategory| |#1| (QUOTE (-1080)))) (-2173 (-12 (|HasCategory| |#1| (|%list| (QUOTE -1069) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#1| (QUOTE (-571)))) (-12 (|HasCategory| |#1| (QUOTE (-571))) (|HasCategory| |#1| (|%list| (QUOTE -1069) (QUOTE (-560)))))) (|HasCategory| |#1| (QUOTE (-25))) (|HasCategory| |#1| (QUOTE (-1143))) (|HasCategory| |#1| (|%list| (QUOTE -1069) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| $ (QUOTE (-1080))) (|HasCategory| $ (|%list| (QUOTE -1069) (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 -1596) +(-329 R -1594) ((|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."))) (((-4510 "*") |has| |#1| (-175)) (-4501 |has| |#1| (-571)) (-4506 |has| |#1| (-376)) (-4500 |has| |#1| (-376)) (-4502 . T) (-4503 . T) (-4505 . 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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."))) ((-4509 . T) (-4508 . T)) -((-2181 (-12 (|HasCategory| |#1| (QUOTE (-871))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1132))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|))))) (-2181 (-12 (|HasCategory| |#1| (QUOTE (-1132))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-887))))) (|HasCategory| |#1| (|%list| (QUOTE -633) (QUOTE (-549)))) (-2181 (|HasCategory| |#1| (QUOTE (-871))) (|HasCategory| |#1| (QUOTE (-1132)))) (|HasCategory| |#1| (QUOTE (-871))) (-2181 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-871))) (|HasCategory| |#1| (QUOTE (-1132)))) (|HasCategory| (-560) (QUOTE (-871))) (|HasCategory| |#1| (QUOTE (-1132))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-887)))) (|HasCategory| |#1| (QUOTE (-102))) (-12 (|HasCategory| |#1| (QUOTE (-1132))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|))))) -(-340 S -1596) +((-2173 (-12 (|HasCategory| |#1| (QUOTE (-871))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1132))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|))))) (-2173 (-12 (|HasCategory| |#1| (QUOTE (-1132))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-887))))) (|HasCategory| |#1| (|%list| (QUOTE -633) (QUOTE (-549)))) (-2173 (|HasCategory| |#1| (QUOTE (-871))) (|HasCategory| |#1| (QUOTE (-1132)))) (|HasCategory| |#1| (QUOTE (-871))) (-2173 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-871))) (|HasCategory| |#1| (QUOTE (-1132)))) (|HasCategory| (-560) (QUOTE (-871))) (|HasCategory| |#1| (QUOTE (-1132))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-887)))) (|HasCategory| |#1| (QUOTE (-102))) (-12 (|HasCategory| |#1| (QUOTE (-1132))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|))))) +(-340 S -1594) ((|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 -1596) +(-341 -1594) ((|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."))) ((-4500 . T) (-4506 . T) (-4501 . T) ((-4510 "*") . T) (-4502 . T) (-4503 . T) (-4505 . 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 -1596 UP UPUP R) +(-346 -1594 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 -1596 UP UPUP R) +(-348 S -1594 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 -1596 UP UPUP R) +(-349 -1594 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}."))) ((-4500 . T) (-4506 . T) (-4501 . T) ((-4510 "*") . T) (-4502 . T) (-4503 . T) (-4505 . T)) -((-2181 (|HasCategory| (-935 |#1|) (QUOTE (-147))) (|HasCategory| (-935 |#1|) (QUOTE (-381)))) (|HasCategory| (-935 |#1|) (QUOTE (-149))) (|HasCategory| (-935 |#1|) (QUOTE (-381))) (|HasCategory| (-935 |#1|) (QUOTE (-147)))) -(-354 S -1596 UP UPUP) +((-2173 (|HasCategory| (-935 |#1|) (QUOTE (-147))) (|HasCategory| (-935 |#1|) (QUOTE (-381)))) (|HasCategory| (-935 |#1|) (QUOTE (-149))) (|HasCategory| (-935 |#1|) (QUOTE (-381))) (|HasCategory| (-935 |#1|) (QUOTE (-147)))) +(-354 S -1594 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 -1596 UP UPUP) +(-355 -1594 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."))) ((-4501 |has| (-421 |#2|) (-376)) (-4506 |has| (-421 |#2|) (-376)) (-4500 |has| (-421 |#2|) (-376)) ((-4510 "*") . T) (-4502 . T) (-4503 . T) (-4505 . 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."))) ((-4500 . T) (-4506 . T) (-4501 . T) ((-4510 "*") . T) (-4502 . T) (-4503 . T) (-4505 . T)) -((-2181 (|HasCategory| (-935 |#1|) (QUOTE (-147))) (|HasCategory| (-935 |#1|) (QUOTE (-381)))) (|HasCategory| (-935 |#1|) (QUOTE (-149))) (|HasCategory| (-935 |#1|) (QUOTE (-381))) (|HasCategory| (-935 |#1|) (QUOTE (-147)))) +((-2173 (|HasCategory| (-935 |#1|) (QUOTE (-147))) (|HasCategory| (-935 |#1|) (QUOTE (-381)))) (|HasCategory| (-935 |#1|) (QUOTE (-149))) (|HasCategory| (-935 |#1|) (QUOTE (-381))) (|HasCategory| (-935 |#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."))) ((-4500 . T) (-4506 . T) (-4501 . T) ((-4510 "*") . T) (-4502 . T) (-4503 . T) (-4505 . T)) -((-2181 (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-381)))) (|HasCategory| |#1| (QUOTE (-149))) (|HasCategory| |#1| (QUOTE (-381))) (|HasCategory| |#1| (QUOTE (-147)))) +((-2173 (|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."))) ((-4500 . T) (-4506 . T) (-4501 . T) ((-4510 "*") . T) (-4502 . T) (-4503 . T) (-4505 . T)) -((-2181 (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-381)))) (|HasCategory| |#1| (QUOTE (-149))) (|HasCategory| |#1| (QUOTE (-381))) (|HasCategory| |#1| (QUOTE (-147)))) +((-2173 (|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."))) ((-4500 . T) (-4506 . T) (-4501 . T) ((-4510 "*") . T) (-4502 . T) (-4503 . T) (-4505 . T)) NIL -(-364 R UP -1596) +(-364 R UP -1594) ((|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."))) ((-4500 . T) (-4506 . T) (-4501 . T) ((-4510 "*") . T) (-4502 . T) (-4503 . T) (-4505 . T)) -((-2181 (|HasCategory| (-935 |#1|) (QUOTE (-147))) (|HasCategory| (-935 |#1|) (QUOTE (-381)))) (|HasCategory| (-935 |#1|) (QUOTE (-149))) (|HasCategory| (-935 |#1|) (QUOTE (-381))) (|HasCategory| (-935 |#1|) (QUOTE (-147)))) +((-2173 (|HasCategory| (-935 |#1|) (QUOTE (-147))) (|HasCategory| (-935 |#1|) (QUOTE (-381)))) (|HasCategory| (-935 |#1|) (QUOTE (-149))) (|HasCategory| (-935 |#1|) (QUOTE (-381))) (|HasCategory| (-935 |#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."))) ((-4500 . T) (-4506 . T) (-4501 . T) ((-4510 "*") . T) (-4502 . T) (-4503 . T) (-4505 . T)) -((-2181 (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-381)))) (|HasCategory| |#1| (QUOTE (-149))) (|HasCategory| |#1| (QUOTE (-381))) (|HasCategory| |#1| (QUOTE (-147)))) +((-2173 (|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."))) ((-4500 . T) (-4506 . T) (-4501 . T) ((-4510 "*") . T) (-4502 . T) (-4503 . T) (-4505 . T)) -((-2181 (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-381)))) (|HasCategory| |#1| (QUOTE (-149))) (|HasCategory| |#1| (QUOTE (-381))) (|HasCategory| |#1| (QUOTE (-147)))) +((-2173 (|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."))) ((-4500 . T) (-4506 . T) (-4501 . T) ((-4510 "*") . T) (-4502 . T) (-4503 . T) (-4505 . T)) -((-2181 (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-381)))) (|HasCategory| |#1| (QUOTE (-149))) (|HasCategory| |#1| (QUOTE (-381))) (|HasCategory| |#1| (QUOTE (-147)))) +((-2173 (|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 -1596 GF) +(-370 -1594 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 -1596 FP FPP) +(-371 -1594 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}."))) ((-4500 . T) (-4506 . T) (-4501 . T) ((-4510 "*") . T) (-4502 . T) (-4503 . T) (-4505 . T)) -((-2181 (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-381)))) (|HasCategory| |#1| (QUOTE (-149))) (|HasCategory| |#1| (QUOTE (-381))) (|HasCategory| |#1| (QUOTE (-147)))) +((-2173 (|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}."))) -((-4491 . T) (-4499 . T) (-2980 . T) (-4500 . T) (-4506 . T) (-4501 . T) ((-4510 "*") . T) (-4502 . T) (-4503 . T) (-4505 . T)) +((-4491 . T) (-4499 . T) (-2981 . T) (-4500 . T) (-4506 . T) (-4501 . T) ((-4510 "*") . T) (-4502 . T) (-4503 . T) (-4505 . 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 -1596 UP UPUP R) +(-406 -1594 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 -3949 |returnType| -2800 |symbols|) +(-412 -3965 |returnType| -2797 |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 -1596 UP) +(-413 -1594 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| $) "\\spad{p + x} returns the sum of \\spad{p} and \\spad{x}"))) NIL NIL @@ -1602,12 +1602,12 @@ NIL ((|HasAttribute| |#1| (QUOTE -4491)) (|HasAttribute| |#1| (QUOTE -4499))) (-418) ((|constructor| (NIL "This category is intended as a model for floating point systems. A floating point system is a model for the real numbers. In fact,{} it is an approximation in the sense that not all real numbers are exactly representable by floating point numbers. A floating point system is characterized by the following: \\blankline \\indented{2}{1: \\spadfunFrom{base}{FloatingPointSystem} of the \\spadfunFrom{exponent}{FloatingPointSystem}.} \\indented{9}{(actual implemenations are usually binary or decimal)} \\indented{2}{2: \\spadfunFrom{precision}{FloatingPointSystem} of the \\spadfunFrom{mantissa}{FloatingPointSystem} (arbitrary or fixed)} \\indented{2}{3: rounding error for operations} \\blankline Because a Float is an approximation to the real numbers,{} even though it is defined to be a join of a Field and OrderedRing,{} some of the attributes do not hold. In particular associative(\"+\") does not hold. Algorithms defined over a field need special considerations when the field is a floating point system.")) (|max| (($) "\\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\"."))) -((-2980 . T) (-4500 . T) (-4506 . T) (-4501 . T) ((-4510 "*") . T) (-4502 . T) (-4503 . T) (-4505 . T)) +((-2981 . T) (-4500 . T) (-4506 . T) (-4501 . T) ((-4510 "*") . T) (-4502 . T) (-4503 . T) (-4505 . 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."))) ((-4501 . T) ((-4510 "*") . T) (-4502 . T) (-4503 . T) (-4505 . T)) -((|HasCategory| |#1| (|%list| (QUOTE -528) (QUOTE (-1207)) (QUOTE $))) (|HasCategory| |#1| (|%list| (QUOTE -321) (QUOTE $))) (|HasCategory| |#1| (|%list| (QUOTE -298) (QUOTE $) (QUOTE $))) (|HasCategory| |#1| (|%list| (QUOTE -633) (QUOTE (-549)))) (|HasCategory| |#1| (QUOTE (-1252))) (-2181 (|HasCategory| |#1| (QUOTE (-466))) (|HasCategory| |#1| (QUOTE (-1252)))) (|HasCategory| |#1| (QUOTE (-1051))) (|HasCategory| |#1| (|%list| (QUOTE -1069) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#1| (|%list| (QUOTE -1069) (QUOTE (-560)))) (|HasCategory| |#1| (|%list| (QUOTE -528) (QUOTE (-1207)) (|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 -929) (QUOTE (-1207)))) (|HasCategory| |#1| (QUOTE (-240))) (|HasCategory| |#1| (|%list| (QUOTE -927) (QUOTE (-1207)))) (|HasCategory| |#1| (QUOTE (-559))) (|HasCategory| |#1| (QUOTE (-466)))) +((|HasCategory| |#1| (|%list| (QUOTE -528) (QUOTE (-1207)) (QUOTE $))) (|HasCategory| |#1| (|%list| (QUOTE -321) (QUOTE $))) (|HasCategory| |#1| (|%list| (QUOTE -298) (QUOTE $) (QUOTE $))) (|HasCategory| |#1| (|%list| (QUOTE -633) (QUOTE (-549)))) (|HasCategory| |#1| (QUOTE (-1252))) (-2173 (|HasCategory| |#1| (QUOTE (-466))) (|HasCategory| |#1| (QUOTE (-1252)))) (|HasCategory| |#1| (QUOTE (-1051))) (|HasCategory| |#1| (|%list| (QUOTE -1069) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#1| (|%list| (QUOTE -1069) (QUOTE (-560)))) (|HasCategory| |#1| (|%list| (QUOTE -528) (QUOTE (-1207)) (|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 -929) (QUOTE (-1207)))) (|HasCategory| |#1| (QUOTE (-240))) (|HasCategory| |#1| (|%list| (QUOTE -927) (QUOTE (-1207)))) (|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."))) ((-4495 -12 (|has| |#1| (-6 -4506)) (|has| |#1| (-466)) (|has| |#1| (-6 -4495))) (-4500 . T) (-4506 . T) (-4501 . T) ((-4510 "*") . T) (-4502 . T) (-4503 . T) (-4505 . 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|#1| (|%list| (QUOTE -633) (|%list| (QUOTE -915) (QUOTE (-560))))) (-12 (|HasCategory| |#1| (QUOTE (-559))) (|HasCategory| |#1| (QUOTE (-843))))) (-2181 (|HasCategory| |#1| (|%list| (QUOTE -660) (QUOTE (-560)))) (-12 (|HasCategory| |#1| (QUOTE (-559))) (|HasCategory| |#1| (QUOTE (-843))))) (|HasCategory| |#1| (QUOTE (-239))) (|HasCategory| |#1| (|%list| (QUOTE -929) (QUOTE (-1207)))) (|HasCategory| |#1| (QUOTE (-240))) (|HasCategory| |#1| (|%list| (QUOTE -927) (QUOTE (-1207)))) (|HasCategory| |#1| (|%list| (QUOTE -528) (QUOTE (-1207)) (|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 (-843)))) (|HasCategory| |#1| (QUOTE (-319))) (|HasCategory| |#1| (QUOTE (-559))) (-12 (|HasAttribute| |#1| (QUOTE -4506)) (|HasAttribute| |#1| (QUOTE -4495)) (|HasCategory| |#1| (QUOTE (-466)))) (|HasCategory| |#1| (|%list| (QUOTE -633) (QUOTE (-549)))) (|HasCategory| |#1| (|%list| (QUOTE -1069) (QUOTE (-560)))) (|HasCategory| |#1| (|%list| (QUOTE -911) (QUOTE (-560)))) (|HasCategory| |#1| (|%list| (QUOTE -633) (|%list| (QUOTE -915) (QUOTE (-560))))) (|HasCategory| |#1| (|%list| (QUOTE -660) (QUOTE (-560)))) (-12 (|HasCategory| $ (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-939)))) (-2181 (-12 (|HasCategory| $ (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-939)))) (|HasCategory| |#1| (QUOTE (-147))))) +((|HasCategory| |#1| (QUOTE (-939))) (|HasCategory| |#1| (|%list| (QUOTE -1069) (QUOTE (-1207)))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-149))) (-2173 (-12 (|HasCategory| |#1| (QUOTE (-559))) (|HasCategory| |#1| (QUOTE (-843)))) (|HasCategory| |#1| (|%list| (QUOTE -633) (QUOTE (-549))))) (|HasCategory| |#1| (QUOTE (-1051))) (|HasCategory| |#1| (QUOTE (-842))) (|HasCategory| |#1| (QUOTE (-871))) (-2173 (|HasCategory| |#1| (QUOTE (-842))) (|HasCategory| |#1| (QUOTE (-871)))) (-2173 (-12 (|HasCategory| |#1| (QUOTE (-559))) (|HasCategory| |#1| (QUOTE (-843)))) (|HasCategory| |#1| (|%list| (QUOTE -1069) (QUOTE (-560))))) (|HasCategory| |#1| (QUOTE (-1182))) (|HasCategory| |#1| (|%list| (QUOTE -911) (QUOTE (-391)))) (-2173 (-12 (|HasCategory| |#1| (QUOTE (-559))) (|HasCategory| |#1| (QUOTE (-843)))) (|HasCategory| |#1| (|%list| (QUOTE -911) (QUOTE (-560))))) (|HasCategory| |#1| (|%list| (QUOTE -633) (|%list| (QUOTE -915) (QUOTE (-391))))) (-2173 (|HasCategory| |#1| (|%list| (QUOTE -633) (|%list| (QUOTE -915) (QUOTE (-560))))) (-12 (|HasCategory| |#1| (QUOTE (-559))) (|HasCategory| |#1| (QUOTE (-843))))) (-2173 (|HasCategory| |#1| (|%list| (QUOTE -660) (QUOTE (-560)))) (-12 (|HasCategory| |#1| (QUOTE (-559))) (|HasCategory| |#1| (QUOTE (-843))))) (|HasCategory| |#1| (QUOTE (-239))) (|HasCategory| |#1| (|%list| (QUOTE -929) (QUOTE (-1207)))) (|HasCategory| |#1| (QUOTE (-240))) (|HasCategory| |#1| (|%list| (QUOTE -927) (QUOTE (-1207)))) (|HasCategory| |#1| (|%list| (QUOTE -528) (QUOTE (-1207)) (|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 (-843)))) (|HasCategory| |#1| (QUOTE (-319))) (|HasCategory| |#1| (QUOTE (-559))) (-12 (|HasAttribute| |#1| (QUOTE -4506)) (|HasAttribute| |#1| (QUOTE -4495)) (|HasCategory| |#1| (QUOTE (-466)))) (|HasCategory| |#1| (|%list| (QUOTE -633) (QUOTE (-549)))) (|HasCategory| |#1| (|%list| (QUOTE -1069) (QUOTE (-560)))) (|HasCategory| |#1| (|%list| (QUOTE -911) (QUOTE (-560)))) (|HasCategory| |#1| (|%list| (QUOTE -633) (|%list| (QUOTE -915) (QUOTE (-560))))) (|HasCategory| |#1| (|%list| (QUOTE -660) (QUOTE (-560)))) (-12 (|HasCategory| $ (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-939)))) (-2173 (-12 (|HasCategory| $ (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-939)))) (|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 -1596 UP A) +(-427 R -1594 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)}."))) ((-4505 . 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 -1596 UP A |ibasis|) +(-429 R -1594 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 -1069) (|devaluate| |#2|)))) @@ -1670,7 +1670,7 @@ NIL ((|HasCategory| |#2| (|%list| (QUOTE -1069) (QUOTE (-560)))) (|HasCategory| |#2| (QUOTE (-571))) (|HasCategory| |#2| (QUOTE (-175))) (|HasCategory| |#2| (QUOTE (-147))) (|HasCategory| |#2| (QUOTE (-149))) (|HasCategory| |#2| (QUOTE (-1080))) (|HasCategory| |#2| (QUOTE (-21))) (|HasCategory| |#2| (QUOTE (-25))) (|HasCategory| |#2| (QUOTE (-487))) (|HasCategory| |#2| (QUOTE (-1143))) (|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|) $) "\\spad{ground?(f)} tests if \\spad{f} is an element of \\spad{R}."))) -((-4505 -2181 (|has| |#1| (-1080)) (|has| |#1| (-487))) (-4503 |has| |#1| (-175)) (-4502 |has| |#1| (-175)) ((-4510 "*") |has| |#1| (-571)) (-4501 |has| |#1| (-571)) (-4506 |has| |#1| (-571)) (-4500 |has| |#1| (-571))) +((-4505 -2173 (|has| |#1| (-1080)) (|has| |#1| (-487))) (-4503 |has| |#1| (-175)) (-4502 |has| |#1| (-175)) ((-4510 "*") |has| |#1| (-571)) (-4501 |has| |#1| (-571)) (-4506 |has| |#1| (-571)) (-4500 |has| |#1| (-571))) NIL (-436 R A S B) ((|constructor| (NIL "This package allows a mapping \\spad{R} -> \\spad{S} to be lifted to a mapping from a function space over \\spad{R} to a function space over \\spad{S}.")) (|map| ((|#4| (|Mapping| |#3| |#1|) |#2|) "\\spad{map(f, a)} applies \\spad{f} to all the constants in \\spad{R} appearing in \\spad{a}."))) @@ -1696,7 +1696,7 @@ NIL ((|constructor| (NIL "\\spad{FiniteSetAggregateFunctions2} provides functions involving two finite set aggregates where the underlying domains might be different. An example of this is to create a set of rational numbers by mapping a function across a set of integers,{} where the function divides each integer by 1000.")) (|scan| ((|#4| (|Mapping| |#3| |#1| |#3|) |#2| |#3|) "\\spad{scan(f,a,r)} successively applies \\spad{reduce(f,x,r)} to more and more leading sub-aggregates \\spad{x} of aggregate \\spad{a}. More precisely,{} if \\spad{a} is \\spad{[a1,a2,...]},{} then \\spad{scan(f,a,r)} returns \\spad {[reduce(f,[a1],r),reduce(f,[a1,a2],r),...]}.")) (|reduce| ((|#3| (|Mapping| |#3| |#1| |#3|) |#2| |#3|) "\\spad{reduce(f,a,r)} applies function \\spad{f} to each successive element of the aggregate \\spad{a} and an accumulant initialised to \\spad{r}. For example,{} \\spad{reduce(_+\\$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 -1596) +(-442 R -1594) ((|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"))) ((-4495 -12 (|has| |#1| (-6 -4495)) (|has| |#2| (-6 -4495))) (-4502 . T) (-4503 . T) (-4505 . T)) ((-12 (|HasAttribute| |#1| (QUOTE -4495)) (|HasAttribute| |#2| (QUOTE -4495)))) -(-444 R -1596) +(-444 R -1594) ((|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 -1596) +(-445 R -1594) ((|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 -1596) +(-446 R -1594) ((|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 -1596) +(-447 R -1594) ((|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 -1596 UP) +(-449 R -1594 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 -1069) (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 -1596) +(-457 R UP -1594) ((|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"))) (((-4510 "*") |has| |#2| (-175)) (-4501 |has| |#2| (-571)) (-4506 |has| |#2| (-6 -4506)) (-4503 . T) (-4502 . T) (-4505 . T)) -((|HasCategory| |#2| (QUOTE (-939))) (-2181 (|HasCategory| |#2| (QUOTE (-175))) (|HasCategory| |#2| (QUOTE (-466))) (|HasCategory| |#2| (QUOTE (-571))) (|HasCategory| |#2| (QUOTE (-939)))) (-2181 (|HasCategory| |#2| (QUOTE (-466))) (|HasCategory| |#2| (QUOTE (-571))) (|HasCategory| |#2| (QUOTE (-939)))) (-2181 (|HasCategory| |#2| (QUOTE (-466))) (|HasCategory| |#2| (QUOTE (-939)))) (|HasCategory| |#2| (QUOTE (-571))) (|HasCategory| |#2| (QUOTE (-175))) (-2181 (|HasCategory| |#2| (QUOTE (-175))) (|HasCategory| |#2| (QUOTE (-571)))) (-12 (|HasCategory| (-888 |#1|) (|%list| (QUOTE -911) (QUOTE (-391)))) (|HasCategory| |#2| (|%list| (QUOTE -911) (QUOTE (-391))))) (-12 (|HasCategory| (-888 |#1|) (|%list| (QUOTE -911) (QUOTE (-560)))) (|HasCategory| |#2| (|%list| (QUOTE -911) (QUOTE (-560))))) (-12 (|HasCategory| (-888 |#1|) (|%list| (QUOTE -633) (|%list| (QUOTE -915) (QUOTE (-391))))) (|HasCategory| |#2| (|%list| (QUOTE -633) (|%list| (QUOTE -915) (QUOTE (-391)))))) (-12 (|HasCategory| (-888 |#1|) (|%list| (QUOTE -633) (|%list| (QUOTE -915) (QUOTE (-560))))) (|HasCategory| |#2| (|%list| (QUOTE -633) (|%list| (QUOTE -915) (QUOTE (-560)))))) (-12 (|HasCategory| (-888 |#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 -1069) (QUOTE (-560)))) (-2181 (|HasCategory| |#2| (|%list| (QUOTE -38) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#2| (|%list| (QUOTE -1069) (|%list| (QUOTE -421) (QUOTE (-560)))))) (|HasCategory| |#2| (|%list| (QUOTE -1069) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#2| (QUOTE (-376))) (|HasAttribute| |#2| (QUOTE -4506)) (|HasCategory| |#2| (QUOTE (-466))) (-12 (|HasCategory| $ (QUOTE (-147))) (|HasCategory| |#2| (QUOTE (-939)))) (-2181 (-12 (|HasCategory| $ (QUOTE (-147))) (|HasCategory| |#2| (QUOTE (-939)))) (|HasCategory| |#2| (QUOTE (-147))))) +((|HasCategory| |#2| (QUOTE (-939))) (-2173 (|HasCategory| |#2| (QUOTE (-175))) (|HasCategory| |#2| (QUOTE (-466))) (|HasCategory| |#2| (QUOTE (-571))) (|HasCategory| |#2| (QUOTE (-939)))) (-2173 (|HasCategory| |#2| (QUOTE (-466))) (|HasCategory| |#2| (QUOTE (-571))) (|HasCategory| |#2| (QUOTE (-939)))) (-2173 (|HasCategory| |#2| (QUOTE (-466))) (|HasCategory| |#2| (QUOTE (-939)))) (|HasCategory| |#2| (QUOTE (-571))) (|HasCategory| |#2| (QUOTE (-175))) (-2173 (|HasCategory| |#2| (QUOTE (-175))) (|HasCategory| |#2| (QUOTE (-571)))) (-12 (|HasCategory| (-888 |#1|) (|%list| (QUOTE -911) (QUOTE (-391)))) (|HasCategory| |#2| (|%list| (QUOTE -911) (QUOTE (-391))))) (-12 (|HasCategory| (-888 |#1|) (|%list| (QUOTE -911) (QUOTE (-560)))) (|HasCategory| |#2| (|%list| (QUOTE -911) (QUOTE (-560))))) (-12 (|HasCategory| (-888 |#1|) (|%list| (QUOTE -633) (|%list| (QUOTE -915) (QUOTE (-391))))) (|HasCategory| |#2| (|%list| (QUOTE -633) (|%list| (QUOTE -915) (QUOTE (-391)))))) (-12 (|HasCategory| (-888 |#1|) (|%list| (QUOTE -633) (|%list| (QUOTE -915) (QUOTE (-560))))) (|HasCategory| |#2| (|%list| (QUOTE -633) (|%list| (QUOTE -915) (QUOTE (-560)))))) (-12 (|HasCategory| (-888 |#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 -1069) (QUOTE (-560)))) (-2173 (|HasCategory| |#2| (|%list| (QUOTE -38) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#2| (|%list| (QUOTE -1069) (|%list| (QUOTE -421) (QUOTE (-560)))))) (|HasCategory| |#2| (|%list| (QUOTE -1069) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#2| (QUOTE (-376))) (|HasAttribute| |#2| (QUOTE -4506)) (|HasCategory| |#2| (QUOTE (-466))) (-12 (|HasCategory| $ (QUOTE (-147))) (|HasCategory| |#2| (QUOTE (-939)))) (-2173 (-12 (|HasCategory| $ (QUOTE (-147))) (|HasCategory| |#2| (QUOTE (-939)))) (|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| -1596 R) +(-485 |lv| -1594 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)}"))) ((-4509 . T) (-4508 . 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."))) ((-4508 . T) (-4509 . 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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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(-1080)))) (-12 (|HasCategory| |#2| (QUOTE (-239))) (|HasCategory| |#2| (QUOTE (-1080)))) (-12 (|HasCategory| |#2| (QUOTE (-1080))) (|HasCategory| |#2| (|%list| (QUOTE -929) (QUOTE (-1207))))) (-2173 (|HasCategory| |#2| (QUOTE (-1080))) (-12 (|HasCategory| |#2| (QUOTE (-1132))) (|HasCategory| |#2| (|%list| (QUOTE -1069) (QUOTE (-560)))))) (-12 (|HasCategory| |#2| (QUOTE (-1132))) (|HasCategory| |#2| (|%list| (QUOTE -1069) (QUOTE (-560))))) (-12 (|HasCategory| |#2| (|%list| (QUOTE -1069) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#2| (QUOTE (-1132)))) (|HasAttribute| |#2| (QUOTE -4505)) (-12 (|HasCategory| |#2| (QUOTE (-240))) (|HasCategory| |#2| (QUOTE (-1080)))) (-12 (|HasCategory| |#2| (QUOTE (-1080))) (|HasCategory| |#2| (|%list| (QUOTE -927) (QUOTE (-1207))))) (|HasCategory| |#2| (QUOTE (-175))) (|HasCategory| |#2| (QUOTE (-23))) (|HasCategory| |#2| (QUOTE (-133))) (|HasCategory| |#2| (QUOTE (-25))) (|HasCategory| |#2| (|%list| (QUOTE -632) (QUOTE (-887)))) (|HasCategory| |#2| (QUOTE (-102))) (-12 (|HasCategory| |#2| (QUOTE (-1132))) (|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}."))) ((-4508 . T) (-4509 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1132))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1132))) (-2181 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-1132)))) (-2181 (-12 (|HasCategory| |#1| (QUOTE (-1132))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-887))))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-887)))) (|HasCategory| |#1| (QUOTE (-102)))) -(-499 -1596 UP UPUP R) +((-12 (|HasCategory| |#1| (QUOTE (-1132))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1132))) (-2173 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-1132)))) (-2173 (-12 (|HasCategory| |#1| (QUOTE (-1132))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-887))))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-887)))) (|HasCategory| |#1| (QUOTE (-102)))) +(-499 -1594 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."))) ((-4500 . T) (-4506 . T) (-4501 . T) ((-4510 "*") . T) (-4502 . T) (-4503 . T) (-4505 . T)) -((|HasCategory| (-560) (QUOTE (-939))) (|HasCategory| (-560) (|%list| (QUOTE -1069) (QUOTE (-1207)))) (|HasCategory| (-560) (QUOTE (-147))) (|HasCategory| (-560) (QUOTE (-149))) (|HasCategory| (-560) (|%list| (QUOTE -633) (QUOTE (-549)))) (|HasCategory| (-560) (QUOTE (-1051))) (|HasCategory| (-560) (QUOTE (-842))) (|HasCategory| (-560) (QUOTE (-871))) (-2181 (|HasCategory| (-560) (QUOTE (-842))) (|HasCategory| (-560) (QUOTE (-871)))) (|HasCategory| (-560) (|%list| (QUOTE -1069) (QUOTE (-560)))) (|HasCategory| (-560) (QUOTE (-1182))) (|HasCategory| (-560) (|%list| (QUOTE -911) (QUOTE (-391)))) (|HasCategory| (-560) (|%list| (QUOTE -911) (QUOTE (-560)))) (|HasCategory| (-560) (|%list| (QUOTE -633) (|%list| (QUOTE -915) (QUOTE (-391))))) (|HasCategory| (-560) (|%list| (QUOTE -633) (|%list| (QUOTE -915) (QUOTE (-560))))) (|HasCategory| (-560) (QUOTE (-239))) (|HasCategory| (-560) (|%list| (QUOTE -929) (QUOTE (-1207)))) (|HasCategory| (-560) (QUOTE (-240))) (|HasCategory| (-560) (|%list| (QUOTE -927) (QUOTE (-1207)))) (|HasCategory| (-560) (|%list| (QUOTE -528) (QUOTE (-1207)) (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 (-939)))) (-2181 (-12 (|HasCategory| $ (QUOTE (-147))) (|HasCategory| (-560) (QUOTE (-939)))) (|HasCategory| (-560) (QUOTE (-147))))) +((|HasCategory| (-560) (QUOTE (-939))) (|HasCategory| (-560) (|%list| (QUOTE -1069) (QUOTE (-1207)))) (|HasCategory| (-560) (QUOTE (-147))) (|HasCategory| (-560) (QUOTE (-149))) (|HasCategory| (-560) (|%list| (QUOTE -633) (QUOTE (-549)))) (|HasCategory| (-560) (QUOTE (-1051))) (|HasCategory| (-560) (QUOTE (-842))) (|HasCategory| (-560) (QUOTE (-871))) (-2173 (|HasCategory| (-560) (QUOTE (-842))) (|HasCategory| (-560) (QUOTE (-871)))) (|HasCategory| (-560) (|%list| (QUOTE -1069) (QUOTE (-560)))) (|HasCategory| (-560) (QUOTE (-1182))) (|HasCategory| (-560) (|%list| (QUOTE -911) (QUOTE (-391)))) (|HasCategory| (-560) (|%list| (QUOTE -911) (QUOTE (-560)))) (|HasCategory| (-560) (|%list| (QUOTE -633) (|%list| (QUOTE -915) (QUOTE (-391))))) (|HasCategory| (-560) (|%list| (QUOTE -633) (|%list| (QUOTE -915) (QUOTE (-560))))) (|HasCategory| (-560) (QUOTE (-239))) (|HasCategory| (-560) (|%list| (QUOTE -929) (QUOTE (-1207)))) (|HasCategory| (-560) (QUOTE (-240))) (|HasCategory| (-560) (|%list| (QUOTE -927) (QUOTE (-1207)))) (|HasCategory| (-560) (|%list| (QUOTE -528) (QUOTE (-1207)) (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 (-939)))) (-2173 (-12 (|HasCategory| $ (QUOTE (-147))) (|HasCategory| (-560) (QUOTE (-939)))) (|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 -1596 UP |AlExt| |AlPol|) +(-508 -1594 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."))) ((-4509 . T) (-4508 . T)) -((-2181 (-12 (|HasCategory| |#1| (QUOTE (-871))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1132))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|))))) (-2181 (-12 (|HasCategory| |#1| (QUOTE (-1132))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-887))))) (|HasCategory| |#1| (|%list| (QUOTE -633) (QUOTE (-549)))) (-2181 (|HasCategory| |#1| (QUOTE (-871))) (|HasCategory| |#1| (QUOTE (-1132)))) (|HasCategory| |#1| (QUOTE (-871))) (-2181 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-871))) (|HasCategory| |#1| (QUOTE (-1132)))) (|HasCategory| (-560) (QUOTE (-871))) (|HasCategory| |#1| (QUOTE (-1132))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-887)))) (|HasCategory| |#1| (QUOTE (-102))) (-12 (|HasCategory| |#1| (QUOTE (-1132))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|))))) +((-2173 (-12 (|HasCategory| |#1| (QUOTE (-871))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1132))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|))))) (-2173 (-12 (|HasCategory| |#1| (QUOTE (-1132))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-887))))) (|HasCategory| |#1| (|%list| (QUOTE -633) (QUOTE (-549)))) (-2173 (|HasCategory| |#1| (QUOTE (-871))) (|HasCategory| |#1| (QUOTE (-1132)))) (|HasCategory| |#1| (QUOTE (-871))) (-2173 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-871))) (|HasCategory| |#1| (QUOTE (-1132)))) (|HasCategory| (-560) (QUOTE (-871))) (|HasCategory| |#1| (QUOTE (-1132))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-887)))) (|HasCategory| |#1| (QUOTE (-102))) (-12 (|HasCategory| |#1| (QUOTE (-1132))) (|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."))) ((-4508 . T) (-4509 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1132))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1132))) (-2181 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-1132)))) (-2181 (-12 (|HasCategory| |#1| (QUOTE (-1132))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-887))))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-887)))) (|HasCategory| |#1| (QUOTE (-102)))) +((-12 (|HasCategory| |#1| (QUOTE (-1132))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1132))) (-2173 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-1132)))) (-2173 (-12 (|HasCategory| |#1| (QUOTE (-1132))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-887))))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-887)))) (|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 -1596) +(-513 R UP -1594) ((|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| $) $) "\\spad{squareFree(x)} returns a square-free factorisation of \\spad{x}"))) NIL NIL @@ -2000,7 +2000,7 @@ NIL ((|constructor| (NIL "InnerCommonDenominator provides functions to compute the common denominator of a finite linear aggregate of elements of the quotient field of an integral domain.")) (|splitDenominator| (((|Record| (|:| |num| |#3|) (|:| |den| |#1|)) |#4|) "\\spad{splitDenominator([q1,...,qn])} returns \\spad{[[p1,...,pn], d]} such that \\spad{qi = pi/d} and \\spad{d} is a common denominator for the \\spad{qi}'s.")) (|clearDenominator| ((|#3| |#4|) "\\spad{clearDenominator([q1,...,qn])} returns \\spad{[p1,...,pn]} such that \\spad{qi = pi/d} where \\spad{d} is a common denominator for the \\spad{qi}'s.")) (|commonDenominator| ((|#1| |#4|) "\\spad{commonDenominator([q1,...,qn])} returns a common denominator \\spad{d} for \\spad{q1},{}...,{}qn."))) NIL NIL -(-518 -1596 |Expon| |VarSet| |DPoly|) +(-518 -1594 |Expon| |VarSet| |DPoly|) ((|constructor| (NIL "This domain represents polynomial ideals with coefficients in any field and supports the basic ideal operations,{} including intersection sum and quotient. An ideal is represented by a list of polynomials (the generators of the ideal) and a boolean that is \\spad{true} if the generators are a Groebner basis. The algorithms used are based on Groebner basis computations. The ordering is determined by the datatype of the input polynomials. Users may use refinements of total degree orderings.")) (|relationsIdeal| (((|SuchThat| (|List| (|Polynomial| |#1|)) (|List| (|Equation| (|Polynomial| |#1|)))) (|List| |#4|)) "\\spad{relationsIdeal(polyList)} returns the ideal of relations among the polynomials in \\spad{polyList}.")) (|saturate| (($ $ |#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}.")) (* (($ $ $) "\\spad{I*J} computes the product of the ideal \\spad{I} and \\spad{J}."))) NIL ((|HasCategory| |#3| (|%list| (QUOTE -633) (QUOTE (-1207))))) @@ -2051,7 +2051,7 @@ NIL (-530 S |mn|) ((|constructor| (NIL "\\indented{1}{Author: Michael Monagan \\spad{July/87},{} modified SMW \\spad{June/91}} A FlexibleArray is the notion of an array intended to allow for growth at the end only. Hence the following efficient operations \\indented{2}{\\spad{append(x,a)} meaning append item \\spad{x} at the end of the array \\spad{a}} \\indented{2}{\\spad{delete(a,n)} meaning delete the last item from the array \\spad{a}} Flexible arrays support the other operations inherited from \\spadtype{ExtensibleLinearAggregate}. However,{} these are not efficient. Flexible arrays combine the \\spad{O(1)} access time property of arrays with growing and shrinking at the end in \\spad{O(1)} (average) time. This is done by using an ordinary array which may have zero or more empty slots at the end. When the array becomes full it is copied into a new larger (50\\% larger) array. Conversely,{} when the array becomes less than 1/2 full,{} it is copied into a smaller array. Flexible arrays provide for an efficient implementation of many data structures in particular heaps,{} stacks and sets.")) (|shrinkable| (((|Boolean|) (|Boolean|)) "\\spad{shrinkable(b)} sets the shrinkable attribute of flexible arrays to \\spad{b} and returns the previous value")) (|physicalLength!| (($ $ (|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}"))) ((-4509 . T) (-4508 . T)) -((-2181 (-12 (|HasCategory| |#1| (QUOTE (-871))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1132))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|))))) (-2181 (-12 (|HasCategory| |#1| (QUOTE (-1132))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-887))))) (|HasCategory| |#1| (|%list| (QUOTE -633) (QUOTE (-549)))) (-2181 (|HasCategory| |#1| (QUOTE (-871))) (|HasCategory| |#1| (QUOTE (-1132)))) (|HasCategory| |#1| (QUOTE (-871))) (-2181 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-871))) (|HasCategory| |#1| (QUOTE (-1132)))) (|HasCategory| (-560) (QUOTE (-871))) (|HasCategory| |#1| (QUOTE (-1132))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-887)))) (|HasCategory| |#1| (QUOTE (-102))) (-12 (|HasCategory| |#1| (QUOTE (-1132))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|))))) +((-2173 (-12 (|HasCategory| |#1| (QUOTE (-871))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1132))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|))))) (-2173 (-12 (|HasCategory| |#1| (QUOTE (-1132))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-887))))) (|HasCategory| |#1| (|%list| (QUOTE -633) (QUOTE (-549)))) (-2173 (|HasCategory| |#1| (QUOTE (-871))) (|HasCategory| |#1| (QUOTE (-1132)))) (|HasCategory| |#1| (QUOTE (-871))) (-2173 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-871))) (|HasCategory| |#1| (QUOTE (-1132)))) (|HasCategory| (-560) (QUOTE (-871))) (|HasCategory| |#1| (QUOTE (-1132))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-887)))) (|HasCategory| |#1| (QUOTE (-102))) (-12 (|HasCategory| |#1| (QUOTE (-1132))) (|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}."))) ((-4500 . T) (-4506 . T) (-4501 . T) ((-4510 "*") . T) (-4502 . T) (-4503 . T) (-4505 . T)) -((-2181 (|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)))) +((-2173 (|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."))) ((-4508 . T) (-4509 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1132))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1132))) (-2181 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-1132)))) (-2181 (-12 (|HasCategory| |#1| (QUOTE (-1132))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-887))))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-887)))) (|HasCategory| |#1| (QUOTE (-102)))) +((-12 (|HasCategory| |#1| (QUOTE (-1132))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1132))) (-2173 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-1132)))) (-2173 (-12 (|HasCategory| |#1| (QUOTE (-1132))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-887))))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-887)))) (|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."))) ((-4509 . T) (-4508 . T)) -((-2181 (-12 (|HasCategory| |#1| (QUOTE (-871))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1132))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|))))) (-2181 (-12 (|HasCategory| |#1| (QUOTE (-1132))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-887))))) (|HasCategory| |#1| (|%list| (QUOTE -633) (QUOTE (-549)))) (-2181 (|HasCategory| |#1| (QUOTE (-871))) (|HasCategory| |#1| (QUOTE (-1132)))) (|HasCategory| |#1| (QUOTE (-871))) (-2181 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-871))) (|HasCategory| |#1| (QUOTE (-1132)))) (|HasCategory| (-560) (QUOTE (-871))) (|HasCategory| |#1| (QUOTE (-1132))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-887)))) (|HasCategory| |#1| (QUOTE (-102))) (-12 (|HasCategory| |#1| (QUOTE (-1132))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|))))) +((-2173 (-12 (|HasCategory| |#1| (QUOTE (-871))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1132))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|))))) (-2173 (-12 (|HasCategory| |#1| (QUOTE (-1132))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-887))))) (|HasCategory| |#1| (|%list| (QUOTE -633) (QUOTE (-549)))) (-2173 (|HasCategory| |#1| (QUOTE (-871))) (|HasCategory| |#1| (QUOTE (-1132)))) (|HasCategory| |#1| (QUOTE (-871))) (-2173 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-871))) (|HasCategory| |#1| (QUOTE (-1132)))) (|HasCategory| (-560) (QUOTE (-871))) (|HasCategory| |#1| (QUOTE (-1132))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-887)))) (|HasCategory| |#1| (QUOTE (-102))) (-12 (|HasCategory| |#1| (QUOTE (-1132))) (|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."))) ((-4508 . T) (-4509 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1132))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1132))) (-2181 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-1132)))) (-2181 (-12 (|HasCategory| |#1| (QUOTE (-1132))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-887))))) (|HasCategory| |#1| (QUOTE (-319))) (|HasCategory| |#1| (QUOTE (-571))) (|HasAttribute| |#1| (QUOTE (-4510 "*"))) (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-887)))) (|HasCategory| |#1| (QUOTE (-102)))) +((-12 (|HasCategory| |#1| (QUOTE (-1132))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1132))) (-2173 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-1132)))) (-2173 (-12 (|HasCategory| |#1| (QUOTE (-1132))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-887))))) (|HasCategory| |#1| (QUOTE (-319))) (|HasCategory| |#1| (QUOTE (-571))) (|HasAttribute| |#1| (QUOTE (-4510 "*"))) (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-887)))) (|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 (-1132))) (|HasCategory| |#1| (QUOTE (-1132))))) -(-546 K -1596 |Par|) +(-546 K -1594 |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 -1596 |Par|) +(-552 K -1594 |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}."))) ((-4508 . T) (-4509 . T)) -((-12 (|HasCategory| (-2 (|:| -3819 |#1|) (|:| -2913 |#2|)) (QUOTE (-1132))) (|HasCategory| (-2 (|:| -3819 |#1|) (|:| -2913 |#2|)) (|%list| (QUOTE -321) (|%list| (QUOTE -2) (|%list| (QUOTE |:|) (QUOTE -3819) (|devaluate| |#1|)) (|%list| (QUOTE |:|) (QUOTE -2913) (|devaluate| |#2|)))))) (-2181 (|HasCategory| (-2 (|:| -3819 |#1|) (|:| -2913 |#2|)) (QUOTE (-1132))) (|HasCategory| |#2| (QUOTE (-1132)))) (-2181 (|HasCategory| (-2 (|:| -3819 |#1|) (|:| -2913 |#2|)) (QUOTE (-102))) (|HasCategory| (-2 (|:| -3819 |#1|) (|:| -2913 |#2|)) (QUOTE (-1132))) (|HasCategory| |#2| (QUOTE (-102))) (|HasCategory| |#2| (QUOTE (-1132)))) (-2181 (|HasCategory| (-2 (|:| -3819 |#1|) (|:| -2913 |#2|)) (QUOTE (-1132))) (|HasCategory| (-2 (|:| -3819 |#1|) (|:| -2913 |#2|)) (|%list| (QUOTE -632) (QUOTE (-887)))) (|HasCategory| |#2| (QUOTE (-1132))) (|HasCategory| |#2| (|%list| (QUOTE -632) (QUOTE (-887))))) (|HasCategory| (-2 (|:| -3819 |#1|) (|:| -2913 |#2|)) (|%list| (QUOTE -633) (QUOTE (-549)))) (-12 (|HasCategory| |#2| (QUOTE (-1132))) (|HasCategory| |#2| (|%list| (QUOTE -321) (|devaluate| |#2|)))) (|HasCategory| (-2 (|:| -3819 |#1|) (|:| -2913 |#2|)) (QUOTE (-1132))) (|HasCategory| |#1| (QUOTE (-871))) (|HasCategory| |#2| (QUOTE (-1132))) (-2181 (|HasCategory| (-2 (|:| -3819 |#1|) (|:| -2913 |#2|)) (|%list| (QUOTE -632) (QUOTE (-887)))) (|HasCategory| |#2| (|%list| (QUOTE -632) (QUOTE (-887))))) (-2181 (|HasCategory| (-2 (|:| -3819 |#1|) (|:| -2913 |#2|)) (QUOTE (-102))) (|HasCategory| |#2| (QUOTE (-102)))) (|HasCategory| |#2| (QUOTE (-102))) (|HasCategory| |#2| (|%list| (QUOTE -632) (QUOTE (-887)))) (|HasCategory| (-2 (|:| -3819 |#1|) (|:| -2913 |#2|)) (|%list| (QUOTE -632) (QUOTE (-887)))) (|HasCategory| (-2 (|:| -3819 |#1|) (|:| -2913 |#2|)) (QUOTE (-102)))) -(-566 R -1596) +((-12 (|HasCategory| (-2 (|:| -3835 |#1|) (|:| -2923 |#2|)) (QUOTE (-1132))) (|HasCategory| (-2 (|:| -3835 |#1|) (|:| -2923 |#2|)) (|%list| (QUOTE -321) (|%list| (QUOTE -2) (|%list| (QUOTE |:|) (QUOTE -3835) (|devaluate| |#1|)) (|%list| (QUOTE |:|) (QUOTE -2923) (|devaluate| |#2|)))))) (-2173 (|HasCategory| (-2 (|:| -3835 |#1|) (|:| -2923 |#2|)) (QUOTE (-1132))) (|HasCategory| |#2| (QUOTE (-1132)))) (-2173 (|HasCategory| (-2 (|:| -3835 |#1|) (|:| -2923 |#2|)) (QUOTE (-102))) (|HasCategory| (-2 (|:| -3835 |#1|) (|:| -2923 |#2|)) (QUOTE (-1132))) (|HasCategory| |#2| (QUOTE (-102))) (|HasCategory| |#2| (QUOTE (-1132)))) (-2173 (|HasCategory| (-2 (|:| -3835 |#1|) (|:| -2923 |#2|)) (QUOTE (-1132))) (|HasCategory| (-2 (|:| -3835 |#1|) (|:| -2923 |#2|)) (|%list| (QUOTE -632) (QUOTE (-887)))) (|HasCategory| |#2| (QUOTE (-1132))) (|HasCategory| |#2| (|%list| (QUOTE -632) (QUOTE (-887))))) (|HasCategory| (-2 (|:| -3835 |#1|) (|:| -2923 |#2|)) (|%list| (QUOTE -633) (QUOTE (-549)))) (-12 (|HasCategory| |#2| (QUOTE (-1132))) (|HasCategory| |#2| (|%list| (QUOTE -321) (|devaluate| |#2|)))) (|HasCategory| (-2 (|:| -3835 |#1|) (|:| -2923 |#2|)) (QUOTE (-1132))) (|HasCategory| |#1| (QUOTE (-871))) (|HasCategory| |#2| (QUOTE (-1132))) (-2173 (|HasCategory| (-2 (|:| -3835 |#1|) (|:| -2923 |#2|)) (|%list| (QUOTE -632) (QUOTE (-887)))) (|HasCategory| |#2| (|%list| (QUOTE -632) (QUOTE (-887))))) (-2173 (|HasCategory| (-2 (|:| -3835 |#1|) (|:| -2923 |#2|)) (QUOTE (-102))) (|HasCategory| |#2| (QUOTE (-102)))) (|HasCategory| |#2| (QUOTE (-102))) (|HasCategory| |#2| (|%list| (QUOTE -632) (QUOTE (-887)))) (|HasCategory| (-2 (|:| -3835 |#1|) (|:| -2923 |#2|)) (|%list| (QUOTE -632) (QUOTE (-887)))) (|HasCategory| (-2 (|:| -3835 |#1|) (|:| -2923 |#2|)) (QUOTE (-102)))) +(-566 R -1594) ((|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 -1596 UP UPUP R) +(-567 R0 -1594 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."))) -((-2980 . T) (-4501 . T) ((-4510 "*") . T) (-4502 . T) (-4503 . T) (-4505 . T)) +((-2981 . T) (-4501 . T) ((-4510 "*") . T) (-4502 . T) (-4503 . T) (-4505 . 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."))) ((-4501 . T) ((-4510 "*") . T) (-4502 . T) (-4503 . T) (-4505 . T)) NIL -(-572 R -1596) +(-572 R -1594) ((|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 -1596 L) +(-575 R -1594 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 -1596 UP UPUP R) +(-577 -1594 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 -1596 UP) +(-578 -1594 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 -1596 L) +(-580 R -1594 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 -1596) +(-581 R -1594) ((|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 -915) (QUOTE (-560))))) (|HasCategory| |#1| (|%list| (QUOTE -911) (QUOTE (-560)))) (|HasCategory| |#2| (QUOTE (-1170)))) (-12 (|HasCategory| |#1| (|%list| (QUOTE -633) (|%list| (QUOTE -915) (QUOTE (-560))))) (|HasCategory| |#1| (|%list| (QUOTE -911) (QUOTE (-560)))) (|HasCategory| |#2| (QUOTE (-649))))) -(-582 -1596 UP) +(-582 -1594 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 -1596) +(-584 -1594) ((|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."))) -((-2980 . T) (-4501 . T) ((-4510 "*") . T) (-4502 . T) (-4503 . T) (-4505 . T)) +((-2981 . T) (-4501 . T) ((-4510 "*") . T) (-4502 . T) (-4503 . T) (-4505 . 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 -1596) +(-587 R -1594) ((|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 -915) (QUOTE (-560))))) (|HasCategory| |#1| (QUOTE (-466))) (|HasCategory| |#1| (|%list| (QUOTE -911) (QUOTE (-560)))) (|HasCategory| |#2| (QUOTE (-296))) (|HasCategory| |#2| (QUOTE (-649))) (|HasCategory| |#2| (|%list| (QUOTE -1069) (QUOTE (-1207))))) (-12 (|HasCategory| |#1| (QUOTE (-466))) (|HasCategory| |#2| (QUOTE (-296)))) (|HasCategory| |#1| (QUOTE (-571)))) -(-588 -1596 UP) +(-588 -1594 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 -1596) +(-589 R -1594) ((|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 -1596) +(-597 -1594) ((|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}."))) ((-4503 . T) (-4502 . T)) ((|HasCategory| |#1| (|%list| (QUOTE -927) (QUOTE (-1207)))) (|HasCategory| |#1| (|%list| (QUOTE -1069) (QUOTE (-1207))))) -(-598 E -1596) +(-598 E -1594) ((|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 -1596) +(-599 R -1594) ((|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"))) ((-4509 . T) (-4508 . T)) -((-2181 (-12 (|HasCategory| (-146) (QUOTE (-871))) (|HasCategory| (-146) (|%list| (QUOTE -321) (QUOTE (-146))))) (-12 (|HasCategory| (-146) (QUOTE (-1132))) (|HasCategory| (-146) (|%list| (QUOTE -321) (QUOTE (-146)))))) (-2181 (|HasCategory| (-146) (|%list| (QUOTE -632) (QUOTE (-887)))) (-12 (|HasCategory| (-146) (QUOTE (-1132))) (|HasCategory| (-146) (|%list| (QUOTE -321) (QUOTE (-146)))))) (|HasCategory| (-146) (|%list| (QUOTE -633) (QUOTE (-549)))) (-2181 (|HasCategory| (-146) (QUOTE (-871))) (|HasCategory| (-146) (QUOTE (-1132)))) (|HasCategory| (-146) (QUOTE (-871))) (-2181 (|HasCategory| (-146) (QUOTE (-102))) (|HasCategory| (-146) (QUOTE (-871))) (|HasCategory| (-146) (QUOTE (-1132)))) (|HasCategory| (-560) (QUOTE (-871))) (|HasCategory| (-146) (QUOTE (-1132))) (|HasCategory| (-146) (|%list| (QUOTE -632) (QUOTE (-887)))) (|HasCategory| (-146) (QUOTE (-102))) (-12 (|HasCategory| (-146) (QUOTE (-1132))) (|HasCategory| (-146) (|%list| (QUOTE -321) (QUOTE (-146)))))) +((-2173 (-12 (|HasCategory| (-146) (QUOTE (-871))) (|HasCategory| (-146) (|%list| (QUOTE -321) (QUOTE (-146))))) (-12 (|HasCategory| (-146) (QUOTE (-1132))) (|HasCategory| (-146) (|%list| (QUOTE -321) (QUOTE (-146)))))) (-2173 (|HasCategory| (-146) (|%list| (QUOTE -632) (QUOTE (-887)))) (-12 (|HasCategory| (-146) (QUOTE (-1132))) (|HasCategory| (-146) (|%list| (QUOTE -321) (QUOTE (-146)))))) (|HasCategory| (-146) (|%list| (QUOTE -633) (QUOTE (-549)))) (-2173 (|HasCategory| (-146) (QUOTE (-871))) (|HasCategory| (-146) (QUOTE (-1132)))) (|HasCategory| (-146) (QUOTE (-871))) (-2173 (|HasCategory| (-146) (QUOTE (-102))) (|HasCategory| (-146) (QUOTE (-871))) (|HasCategory| (-146) (QUOTE (-1132)))) (|HasCategory| (-560) (QUOTE (-871))) (|HasCategory| (-146) (QUOTE (-1132))) (|HasCategory| (-146) (|%list| (QUOTE -632) (QUOTE (-887)))) (|HasCategory| (-146) (QUOTE (-102))) (-12 (|HasCategory| (-146) (QUOTE (-1132))) (|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}."))) (((-4510 "*") |has| |#1| (-175)) (-4501 |has| |#1| (-571)) (-4502 . T) (-4503 . T) (-4505 . T)) -((|HasCategory| |#1| (|%list| (QUOTE -38) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#1| (QUOTE (-571))) (-2181 (|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 -927) (QUOTE (-1207)))) (|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 (-1143))) (|HasCategory| |#1| (QUOTE (-376))) (-12 (|HasSignature| |#1| (|%list| (QUOTE **) (|%list| (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-560))))) (|HasSignature| |#1| (|%list| (QUOTE -4272) (|%list| (|devaluate| |#1|) (QUOTE (-1207)))))) (|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))) (-2173 (|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 -927) (QUOTE (-1207)))) (|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 (-1143))) (|HasCategory| |#1| (QUOTE (-376))) (-12 (|HasSignature| |#1| (|%list| (QUOTE **) (|%list| (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-560))))) (|HasSignature| |#1| (|%list| (QUOTE -2383) (|%list| (|devaluate| |#1|) (QUOTE (-1207)))))) (|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.}"))) (((-4510 "*") |has| |#1| (-571)) (-4501 |has| |#1| (-571)) (-4502 . T) (-4503 . T) (-4505 . 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 -1596 FG) +(-614 R -1594 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."))) ((-4509 . T) (-4508 . T)) -((-2181 (-12 (|HasCategory| |#1| (QUOTE (-871))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1132))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|))))) (-2181 (-12 (|HasCategory| |#1| (QUOTE (-1132))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-887))))) (|HasCategory| |#1| (|%list| (QUOTE -633) (QUOTE (-549)))) (-2181 (|HasCategory| |#1| (QUOTE (-871))) (|HasCategory| |#1| (QUOTE (-1132)))) (|HasCategory| |#1| (QUOTE (-871))) (-2181 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-871))) (|HasCategory| |#1| (QUOTE (-1132)))) (|HasCategory| (-560) (QUOTE (-871))) (|HasCategory| |#1| (QUOTE (-1132))) (|HasCategory| |#1| (QUOTE (-25))) (|HasCategory| |#1| (QUOTE (-23))) (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-748))) (|HasCategory| |#1| (QUOTE (-1080))) (-12 (|HasCategory| |#1| (QUOTE (-1033))) (|HasCategory| |#1| (QUOTE (-1080)))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-887)))) (|HasCategory| |#1| (QUOTE (-102))) (-12 (|HasCategory| |#1| (QUOTE (-1132))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|))))) +((-2173 (-12 (|HasCategory| |#1| (QUOTE (-871))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1132))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|))))) (-2173 (-12 (|HasCategory| |#1| (QUOTE (-1132))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-887))))) (|HasCategory| |#1| (|%list| (QUOTE -633) (QUOTE (-549)))) (-2173 (|HasCategory| |#1| (QUOTE (-871))) (|HasCategory| |#1| (QUOTE (-1132)))) (|HasCategory| |#1| (QUOTE (-871))) (-2173 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-871))) (|HasCategory| |#1| (QUOTE (-1132)))) (|HasCategory| (-560) (QUOTE (-871))) (|HasCategory| |#1| (QUOTE (-1132))) (|HasCategory| |#1| (QUOTE (-25))) (|HasCategory| |#1| (QUOTE (-23))) (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-748))) (|HasCategory| |#1| (QUOTE (-1080))) (-12 (|HasCategory| |#1| (QUOTE (-1033))) (|HasCategory| |#1| (QUOTE (-1080)))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-887)))) (|HasCategory| |#1| (QUOTE (-102))) (-12 (|HasCategory| |#1| (QUOTE (-1132))) (|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)."))) -((-4505 -2181 (-1376 (|has| |#2| (-380 |#1|)) (|has| |#1| (-571))) (-12 (|has| |#2| (-432 |#1|)) (|has| |#1| (-571)))) (-4503 . T) (-4502 . T)) -((-2181 (|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|)))) (-2181 (-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|)))) +((-4505 -2173 (-1376 (|has| |#2| (-380 |#1|)) (|has| |#1| (-571))) (-12 (|has| |#2| (-432 |#1|)) (|has| |#1| (-571)))) (-4503 . T) (-4502 . T)) +((-2173 (|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|)))) (-2173 (-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."))) ((-4508 . T) (-4509 . T)) -((-12 (|HasCategory| (-2 (|:| -3819 (-1189)) (|:| -2913 |#1|)) (QUOTE (-1132))) (|HasCategory| (-2 (|:| -3819 (-1189)) (|:| -2913 |#1|)) (|%list| (QUOTE -321) (|%list| (QUOTE -2) (|%list| (QUOTE |:|) (QUOTE -3819) (QUOTE (-1189))) (|%list| (QUOTE |:|) (QUOTE -2913) (|devaluate| |#1|)))))) (|HasCategory| (-2 (|:| -3819 (-1189)) (|:| -2913 |#1|)) (|%list| (QUOTE -633) (QUOTE (-549)))) (-12 (|HasCategory| |#1| (QUOTE (-1132))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1132))) (|HasCategory| (-1189) (QUOTE (-871))) (|HasCategory| (-2 (|:| -3819 (-1189)) (|:| -2913 |#1|)) (QUOTE (-1132))) (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-887)))) (|HasCategory| (-2 (|:| -3819 (-1189)) (|:| -2913 |#1|)) (|%list| (QUOTE -632) (QUOTE (-887)))) (|HasCategory| (-2 (|:| -3819 (-1189)) (|:| -2913 |#1|)) (QUOTE (-102)))) +((-12 (|HasCategory| (-2 (|:| -3835 (-1189)) (|:| -2923 |#1|)) (QUOTE (-1132))) (|HasCategory| (-2 (|:| -3835 (-1189)) (|:| -2923 |#1|)) (|%list| (QUOTE -321) (|%list| (QUOTE -2) (|%list| (QUOTE |:|) (QUOTE -3835) (QUOTE (-1189))) (|%list| (QUOTE |:|) (QUOTE -2923) (|devaluate| |#1|)))))) (|HasCategory| (-2 (|:| -3835 (-1189)) (|:| -2923 |#1|)) (|%list| (QUOTE -633) (QUOTE (-549)))) (-12 (|HasCategory| |#1| (QUOTE (-1132))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1132))) (|HasCategory| (-1189) (QUOTE (-871))) (|HasCategory| (-2 (|:| -3835 (-1189)) (|:| -2923 |#1|)) (QUOTE (-1132))) (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-887)))) (|HasCategory| (-2 (|:| -3835 (-1189)) (|:| -2923 |#1|)) (|%list| (QUOTE -632) (QUOTE (-887)))) (|HasCategory| (-2 (|:| -3835 (-1189)) (|:| -2923 |#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| $) "\\spad{convert(a)} transforms a into an element of \\spad{S}."))) NIL NIL -(-634 -1596 UP) +(-634 -1594 UP) ((|constructor| (NIL "\\spadtype{Kovacic} provides a modified Kovacic's algorithm for solving explicitely irreducible 2nd order linear ordinary differential equations.")) (|kovacic| (((|Union| (|SparseUnivariatePolynomial| (|Fraction| |#2|)) "failed") (|Fraction| |#2|) (|Fraction| |#2|) (|Fraction| |#2|) (|Mapping| (|Factored| |#2|) |#2|)) "\\spad{kovacic(a_0,a_1,a_2,ezfactor)} returns either \"failed\" or \\spad{P}(\\spad{u}) such that \\spad{\\$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."))) ((-4505 . T)) NIL -(-641 R -1596) +(-641 R -1594) ((|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 -1596) +(-648 R -1594) ((|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| -1596) +(-650 |lv| -1594) ((|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."))) ((-4509 . T)) -((-12 (|HasCategory| (-2 (|:| -3819 (-1189)) (|:| -2913 (-51))) (QUOTE (-1132))) (|HasCategory| (-2 (|:| -3819 (-1189)) (|:| -2913 (-51))) (|%list| (QUOTE -321) (|%list| (QUOTE -2) (|%list| (QUOTE |:|) (QUOTE -3819) (QUOTE (-1189))) (|%list| (QUOTE |:|) (QUOTE -2913) (QUOTE (-51))))))) (-2181 (|HasCategory| (-2 (|:| -3819 (-1189)) (|:| -2913 (-51))) (QUOTE (-1132))) (|HasCategory| (-51) (QUOTE (-1132)))) (-2181 (|HasCategory| (-2 (|:| -3819 (-1189)) (|:| -2913 (-51))) (QUOTE (-102))) (|HasCategory| (-2 (|:| -3819 (-1189)) (|:| -2913 (-51))) (QUOTE (-1132))) (|HasCategory| (-51) (QUOTE (-102))) (|HasCategory| (-51) (QUOTE (-1132)))) (-2181 (|HasCategory| (-2 (|:| -3819 (-1189)) (|:| -2913 (-51))) (QUOTE (-1132))) (|HasCategory| (-2 (|:| -3819 (-1189)) (|:| -2913 (-51))) (|%list| (QUOTE -632) (QUOTE (-887)))) (|HasCategory| (-51) (QUOTE (-1132))) (|HasCategory| (-51) (|%list| (QUOTE -632) (QUOTE (-887))))) (|HasCategory| (-2 (|:| -3819 (-1189)) (|:| -2913 (-51))) (|%list| (QUOTE -633) (QUOTE (-549)))) (-12 (|HasCategory| (-51) (QUOTE (-1132))) (|HasCategory| (-51) (|%list| (QUOTE -321) (QUOTE (-51))))) (|HasCategory| (-1189) (QUOTE (-871))) (-2181 (|HasCategory| (-2 (|:| -3819 (-1189)) (|:| -2913 (-51))) (|%list| (QUOTE -632) (QUOTE (-887)))) (|HasCategory| (-51) (|%list| (QUOTE -632) (QUOTE (-887))))) (-2181 (|HasCategory| (-2 (|:| -3819 (-1189)) (|:| -2913 (-51))) (QUOTE (-102))) (|HasCategory| (-51) (QUOTE (-102)))) (|HasCategory| (-51) (QUOTE (-1132))) (|HasCategory| (-51) (QUOTE (-102))) (|HasCategory| (-51) (|%list| (QUOTE -632) (QUOTE (-887)))) (|HasCategory| (-2 (|:| -3819 (-1189)) (|:| -2913 (-51))) (|%list| (QUOTE -632) (QUOTE (-887)))) (|HasCategory| (-2 (|:| -3819 (-1189)) (|:| -2913 (-51))) (QUOTE (-102))) (|HasCategory| (-2 (|:| -3819 (-1189)) (|:| -2913 (-51))) (QUOTE (-1132)))) +((-12 (|HasCategory| (-2 (|:| -3835 (-1189)) (|:| -2923 (-51))) (QUOTE (-1132))) (|HasCategory| (-2 (|:| -3835 (-1189)) (|:| -2923 (-51))) (|%list| (QUOTE -321) (|%list| (QUOTE -2) (|%list| (QUOTE |:|) (QUOTE -3835) (QUOTE (-1189))) (|%list| (QUOTE |:|) (QUOTE -2923) (QUOTE (-51))))))) (-2173 (|HasCategory| (-2 (|:| -3835 (-1189)) (|:| -2923 (-51))) (QUOTE (-1132))) (|HasCategory| (-51) (QUOTE (-1132)))) (-2173 (|HasCategory| (-2 (|:| -3835 (-1189)) (|:| -2923 (-51))) (QUOTE (-102))) (|HasCategory| (-2 (|:| -3835 (-1189)) (|:| -2923 (-51))) (QUOTE (-1132))) (|HasCategory| (-51) (QUOTE (-102))) (|HasCategory| (-51) (QUOTE (-1132)))) (-2173 (|HasCategory| (-2 (|:| -3835 (-1189)) (|:| -2923 (-51))) (QUOTE (-1132))) (|HasCategory| (-2 (|:| -3835 (-1189)) (|:| -2923 (-51))) (|%list| (QUOTE -632) (QUOTE (-887)))) (|HasCategory| (-51) (QUOTE (-1132))) (|HasCategory| (-51) (|%list| (QUOTE -632) (QUOTE (-887))))) (|HasCategory| (-2 (|:| -3835 (-1189)) (|:| -2923 (-51))) (|%list| (QUOTE -633) (QUOTE (-549)))) (-12 (|HasCategory| (-51) (QUOTE (-1132))) (|HasCategory| (-51) (|%list| (QUOTE -321) (QUOTE (-51))))) (|HasCategory| (-1189) (QUOTE (-871))) (-2173 (|HasCategory| (-2 (|:| -3835 (-1189)) (|:| -2923 (-51))) (|%list| (QUOTE -632) (QUOTE (-887)))) (|HasCategory| (-51) (|%list| (QUOTE -632) (QUOTE (-887))))) (-2173 (|HasCategory| (-2 (|:| -3835 (-1189)) (|:| -2923 (-51))) (QUOTE (-102))) (|HasCategory| (-51) (QUOTE (-102)))) (|HasCategory| (-51) (QUOTE (-1132))) (|HasCategory| (-51) (QUOTE (-102))) (|HasCategory| (-51) (|%list| (QUOTE -632) (QUOTE (-887)))) (|HasCategory| (-2 (|:| -3835 (-1189)) (|:| -2923 (-51))) (|%list| (QUOTE -632) (QUOTE (-887)))) (|HasCategory| (-2 (|:| -3835 (-1189)) (|:| -2923 (-51))) (QUOTE (-102))) (|HasCategory| (-2 (|:| -3835 (-1189)) (|:| -2923 (-51))) (QUOTE (-1132)))) (-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)."))) -((-4505 -2181 (-1376 (|has| |#2| (-380 |#1|)) (|has| |#1| (-571))) (-12 (|has| |#2| (-432 |#1|)) (|has| |#1| (-571)))) (-4503 . T) (-4502 . T)) -((-2181 (|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|)))) (-2181 (-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|)))) +((-4505 -2173 (-1376 (|has| |#2| (-380 |#1|)) (|has| |#1| (-571))) (-12 (|has| |#2| (-432 |#1|)) (|has| |#1| (-571)))) (-4503 . T) (-4502 . T)) +((-2173 (|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|)))) (-2173 (-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| (($ $ $) "\\axiom{construct(\\spad{x},{}\\spad{y})} returns the Lie bracket of \\axiom{\\spad{x}} and \\axiom{\\spad{y}}."))) NIL @@ -2583,7 +2583,7 @@ NIL (-663 S) ((|constructor| (NIL "\\spadtype{List} implements singly-linked lists that are addressable by indices; the index of the first element is 1. In addition to the operations provided by \\spadtype{IndexedList},{} this constructor provides some LISP-like functions such as \\spadfun{null} and \\spadfun{cons}.")) (|setDifference| (($ $ $) "\\spad{setDifference(u1,u2)} returns a list of the elements of \\spad{u1} that are not also in \\spad{u2}. The order of elements in the resulting list is unspecified.")) (|setIntersection| (($ $ $) "\\spad{setIntersection(u1,u2)} returns a list of the elements that lists \\spad{u1} and \\spad{u2} have in common. The order of elements in the resulting list is unspecified.")) (|setUnion| (($ $ $) "\\spad{setUnion(u1,u2)} appends the two lists \\spad{u1} and \\spad{u2},{} then removes all duplicates. The order of elements in the resulting list is unspecified.")) (|append| (($ $ $) "\\spad{append(u1,u2)} appends the elements of list \\spad{u1} onto the front of list \\spad{u2}. This new list and \\spad{u2} will share some structure.")) (|cons| (($ |#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."))) ((-4509 . T) (-4508 . T)) -((-2181 (-12 (|HasCategory| |#1| (QUOTE (-871))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1132))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|))))) (-2181 (-12 (|HasCategory| |#1| (QUOTE (-1132))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-887))))) (|HasCategory| |#1| (|%list| (QUOTE -633) (QUOTE (-549)))) (-2181 (|HasCategory| |#1| (QUOTE (-871))) (|HasCategory| |#1| (QUOTE (-1132)))) (|HasCategory| |#1| (QUOTE (-871))) (-2181 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-871))) (|HasCategory| |#1| (QUOTE (-1132)))) (|HasCategory| |#1| (QUOTE (-843))) (|HasCategory| (-560) (QUOTE (-871))) (|HasCategory| |#1| (QUOTE (-1132))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-887)))) (|HasCategory| |#1| (QUOTE (-102))) (-12 (|HasCategory| |#1| (QUOTE (-1132))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|))))) +((-2173 (-12 (|HasCategory| |#1| (QUOTE (-871))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1132))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|))))) (-2173 (-12 (|HasCategory| |#1| (QUOTE (-1132))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-887))))) (|HasCategory| |#1| (|%list| (QUOTE -633) (QUOTE (-549)))) (-2173 (|HasCategory| |#1| (QUOTE (-871))) (|HasCategory| |#1| (QUOTE (-1132)))) (|HasCategory| |#1| (QUOTE (-871))) (-2173 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-871))) (|HasCategory| |#1| (QUOTE (-1132)))) (|HasCategory| |#1| (QUOTE (-843))) (|HasCategory| (-560) (QUOTE (-871))) (|HasCategory| |#1| (QUOTE (-1132))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-887)))) (|HasCategory| |#1| (QUOTE (-102))) (-12 (|HasCategory| |#1| (QUOTE (-1132))) (|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."))) ((-4508 . T) (-4509 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1132))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1132))) (-2181 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-1132)))) (-2181 (-12 (|HasCategory| |#1| (QUOTE (-1132))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-887))))) (|HasCategory| |#1| (|%list| (QUOTE -633) (QUOTE (-549)))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-887)))) (|HasCategory| |#1| (QUOTE (-102)))) +((-12 (|HasCategory| |#1| (QUOTE (-1132))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1132))) (-2173 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-1132)))) (-2173 (-12 (|HasCategory| |#1| (QUOTE (-1132))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-887))))) (|HasCategory| |#1| (|%list| (QUOTE -633) (QUOTE (-549)))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-887)))) (|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}."))) ((-4503 . T) (-4502 . T)) ((|HasCategory| |#1| (QUOTE (-813)))) -(-675 R -1596 L) +(-675 R -1594 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 -3986) +(-676 A -2394) ((|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}}"))) ((-4502 . T) (-4503 . T) (-4505 . T)) ((|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (|%list| (QUOTE -1069) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#1| (|%list| (QUOTE -1069) (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}."))) ((-4502 . T) (-4503 . T) (-4505 . T)) NIL -(-681 -1596 UP) +(-681 -1594 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}."))) ((-4509 . T) (-4508 . T)) NIL -(-689 -1596 |Row| |Col| M) +(-689 -1594 |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 -1596) +(-690 -1594) ((|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."))) ((-4505 . T) (-4508 . T) (-4502 . T) (-4503 . T)) -((|HasCategory| |#2| (|%list| (QUOTE -927) (QUOTE (-1207)))) (|HasCategory| |#2| (|%list| (QUOTE -929) (QUOTE (-1207)))) (|HasCategory| |#2| (QUOTE (-240))) (|HasCategory| |#2| (QUOTE (-239))) (|HasAttribute| |#2| (QUOTE (-4510 "*"))) (|HasCategory| |#2| (|%list| (QUOTE -660) (QUOTE (-560)))) (|HasCategory| |#2| (|%list| (QUOTE -1069) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#2| (|%list| (QUOTE -1069) (QUOTE (-560)))) (-2181 (-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 (-1132))) (|HasCategory| |#2| (|%list| (QUOTE -321) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (|%list| (QUOTE -321) (|devaluate| |#2|))) (|HasCategory| |#2| (|%list| (QUOTE -927) (QUOTE (-1207)))))) (|HasCategory| |#2| (QUOTE (-319))) (|HasCategory| |#2| (QUOTE (-1132))) (|HasCategory| |#2| (QUOTE (-376))) (|HasCategory| |#2| (QUOTE (-571))) (-2181 (|HasAttribute| |#2| (QUOTE (-4510 "*"))) (|HasCategory| |#2| (|%list| (QUOTE -927) (QUOTE (-1207)))) (|HasCategory| |#2| (QUOTE (-240)))) (|HasCategory| |#2| (|%list| (QUOTE -632) (QUOTE (-887)))) (|HasCategory| |#2| (QUOTE (-102))) (-12 (|HasCategory| |#2| (QUOTE (-1132))) (|HasCategory| |#2| (|%list| (QUOTE -321) (|devaluate| |#2|)))) (|HasCategory| |#2| (QUOTE (-175)))) +((|HasCategory| |#2| (|%list| (QUOTE -927) (QUOTE (-1207)))) (|HasCategory| |#2| (|%list| (QUOTE -929) (QUOTE (-1207)))) (|HasCategory| |#2| (QUOTE (-240))) (|HasCategory| |#2| (QUOTE (-239))) (|HasAttribute| |#2| (QUOTE (-4510 "*"))) (|HasCategory| |#2| (|%list| (QUOTE -660) (QUOTE (-560)))) (|HasCategory| |#2| (|%list| (QUOTE -1069) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#2| (|%list| (QUOTE -1069) (QUOTE (-560)))) (-2173 (-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 (-1132))) (|HasCategory| |#2| (|%list| (QUOTE -321) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (|%list| (QUOTE -321) (|devaluate| |#2|))) (|HasCategory| |#2| (|%list| (QUOTE -927) (QUOTE (-1207)))))) (|HasCategory| |#2| (QUOTE (-319))) (|HasCategory| |#2| (QUOTE (-1132))) (|HasCategory| |#2| (QUOTE (-376))) (|HasCategory| |#2| (QUOTE (-571))) (-2173 (|HasAttribute| |#2| (QUOTE (-4510 "*"))) (|HasCategory| |#2| (|%list| (QUOTE -927) (QUOTE (-1207)))) (|HasCategory| |#2| (QUOTE (-240)))) (|HasCategory| |#2| (|%list| (QUOTE -632) (QUOTE (-887)))) (|HasCategory| |#2| (QUOTE (-102))) (-12 (|HasCategory| |#2| (QUOTE (-1132))) (|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 -((-2181 (-12 (|HasCategory| |#1| (QUOTE (-1080))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1132))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|))))) (|HasCategory| |#1| (QUOTE (-1132))) (-2181 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-1132)))) (-2181 (-12 (|HasCategory| |#1| (QUOTE (-1132))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-887))))) (|HasCategory| |#1| (QUOTE (-1080))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-887)))) (|HasCategory| |#1| (QUOTE (-102))) (-12 (|HasCategory| |#1| (QUOTE (-1132))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|))))) +((-2173 (-12 (|HasCategory| |#1| (QUOTE (-1080))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1132))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|))))) (|HasCategory| |#1| (QUOTE (-1132))) (-2173 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-1132)))) (-2173 (-12 (|HasCategory| |#1| (QUOTE (-1132))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-887))))) (|HasCategory| |#1| (QUOTE (-1080))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-887)))) (|HasCategory| |#1| (QUOTE (-102))) (-12 (|HasCategory| |#1| (QUOTE (-1132))) (|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."))) ((-4508 . T) (-4509 . T)) -((-2181 (-12 (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1132))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|))))) (|HasCategory| |#1| (QUOTE (-1132))) (-2181 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-1132)))) (-2181 (-12 (|HasCategory| |#1| (QUOTE (-1132))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-887))))) (|HasCategory| |#1| (|%list| (QUOTE -633) (QUOTE (-549)))) (|HasCategory| |#1| (QUOTE (-319))) (|HasCategory| |#1| (QUOTE (-571))) (|HasAttribute| |#1| (QUOTE (-4510 "*"))) (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-887)))) (|HasCategory| |#1| (QUOTE (-102))) (-12 (|HasCategory| |#1| (QUOTE (-1132))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|))))) +((-2173 (-12 (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1132))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|))))) (|HasCategory| |#1| (QUOTE (-1132))) (-2173 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-1132)))) (-2173 (-12 (|HasCategory| |#1| (QUOTE (-1132))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-887))))) (|HasCategory| |#1| (|%list| (QUOTE -633) (QUOTE (-549)))) (|HasCategory| |#1| (QUOTE (-319))) (|HasCategory| |#1| (QUOTE (-571))) (|HasAttribute| |#1| (QUOTE (-4510 "*"))) (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-887)))) (|HasCategory| |#1| (QUOTE (-102))) (-12 (|HasCategory| |#1| (QUOTE (-1132))) (|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 -1596 FLAF FLAS) +(-714 S -1594 FLAF FLAS) ((|constructor| (NIL "\\indented{1}{\\spadtype{MultiVariableCalculusFunctions} Package provides several} \\indented{1}{functions for multivariable calculus.} These include gradient,{} hessian and jacobian,{} divergence and laplacian. Various forms for banded and sparse storage of matrices are included.")) (|bandedJacobian| (((|Matrix| |#2|) |#3| |#4| (|NonNegativeInteger|) (|NonNegativeInteger|)) "\\spad{bandedJacobian(vf,xlist,kl,ku)} computes the jacobian,{} the matrix of first partial derivatives,{} of the vector field \\spad{vf},{} \\spad{vf} a vector function of the variables listed in \\spad{xlist},{} \\spad{kl} is the number of nonzero subdiagonals,{} \\spad{ku} is the number of nonzero superdiagonals,{} \\spad{kl+ku+1} being actual bandwidth. Stores the nonzero band in a matrix,{} dimensions \\spad{kl+ku+1} by \\#xlist. The upper triangle is in the top \\spad{ku} rows,{} the diagonal is in row \\spad{ku+1},{} the lower triangle in the last \\spad{kl} rows. Entries in a column in the band store correspond to entries in same column of full store. (The notation conforms to LAPACK/NAG-\\spad{F07} conventions.)")) (|jacobian| (((|Matrix| |#2|) |#3| |#4|) "\\spad{jacobian(vf,xlist)} computes the jacobian,{} the matrix of first partial derivatives,{} of the vector field \\spad{vf},{} \\spad{vf} a vector function of the variables listed in \\spad{xlist}.")) (|bandedHessian| (((|Matrix| |#2|) |#2| |#4| (|NonNegativeInteger|)) "\\spad{bandedHessian(v,xlist,k)} computes the hessian,{} the matrix of second partial derivatives,{} of the scalar field \\spad{v},{} \\spad{v} a function of the variables listed in \\spad{xlist},{} \\spad{k} is the semi-bandwidth,{} the number of nonzero subdiagonals,{} 2*k+1 being actual bandwidth. Stores the nonzero band in lower triangle in a matrix,{} dimensions \\spad{k+1} by \\#xlist,{} whose rows are the vectors formed by diagonal,{} subdiagonal,{} etc. of the real,{} full-matrix,{} hessian. (The notation conforms to LAPACK/NAG-\\spad{F07} conventions.)")) (|hessian| (((|Matrix| |#2|) |#2| |#4|) "\\spad{hessian(v,xlist)} computes the hessian,{} the matrix of second partial derivatives,{} of the scalar field \\spad{v},{} \\spad{v} a function of the variables listed in \\spad{xlist}.")) (|laplacian| ((|#2| |#2| |#4|) "\\spad{laplacian(v,xlist)} computes the laplacian of the scalar field \\spad{v},{} \\spad{v} a function of the variables listed in \\spad{xlist}.")) (|divergence| ((|#2| |#3| |#4|) "\\spad{divergence(vf,xlist)} computes the divergence of the vector field \\spad{vf},{} \\spad{vf} a vector function of the variables listed in \\spad{xlist}.")) (|gradient| (((|Vector| |#2|) |#2| |#4|) "\\spad{gradient(v,xlist)} computes the gradient,{} the vector of first partial derivatives,{} of the scalar field \\spad{v},{} \\spad{v} a function of the variables listed in \\spad{xlist}."))) NIL NIL @@ -2794,8 +2794,8 @@ NIL NIL (-716) ((|constructor| (NIL "A domain which models the complex number representation used by machines in the AXIOM-NAG link.")) (|coerce| (((|Complex| (|Float|)) $) "\\spad{coerce(u)} transforms \\spad{u} into a COmplex Float") (($ (|Complex| (|MachineInteger|))) "\\spad{coerce(u)} transforms \\spad{u} into a MachineComplex") (($ (|Complex| (|MachineFloat|))) "\\spad{coerce(u)} transforms \\spad{u} into a MachineComplex") (($ (|Complex| (|Integer|))) "\\spad{coerce(u)} transforms \\spad{u} into a MachineComplex") (($ (|Complex| (|Float|))) "\\spad{coerce(u)} transforms \\spad{u} into a MachineComplex"))) -((-4501 . T) (-4506 |has| (-721) (-376)) (-4500 |has| (-721) (-376)) (-2992 . T) (-4507 |has| (-721) (-6 -4507)) (-4504 |has| (-721) (-6 -4504)) ((-4510 "*") . T) (-4502 . T) (-4503 . T) (-4505 . 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T) (-4500 . T) (-4506 . T) (-4501 . T) ((-4510 "*") . T) (-4502 . T) (-4503 . T) (-4505 . T)) +((-2981 . T) (-4500 . T) (-4506 . T) (-4501 . T) ((-4510 "*") . T) (-4502 . T) (-4503 . T) (-4505 . 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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(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| (($ $ $) "\\spad{adjoint(op1, op2)} sets the adjoint of \\spad{op1} to be \\spad{op2}. \\spad{op1} must be a basic operator") (($ $) "\\spad{adjoint(op)} returns the adjoint of the operator \\spad{op}."))) ((-4503 |has| |#1| (-175)) (-4502 |has| |#1| (-175)) (-4505 . T)) ((|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-149)))) -(-737 R |Mod| -4284 -2846 |exactQuo|) +(-737 R |Mod| -2288 -3960 |exactQuo|) ((|constructor| (NIL "These domains are used for the factorization and gcds of univariate polynomials over the integers in order to work modulo different primes. See \\spadtype{EuclideanModularRing} ,{}\\spadtype{ModularField}")) (|inv| (($ $) "\\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"))) ((-4505 . T)) NIL @@ -2888,7 +2888,7 @@ NIL ((|constructor| (NIL "The category of modules over a commutative ring. \\blankline"))) ((-4503 . T) (-4502 . T)) NIL -(-740 -1596) +(-740 -1594) ((|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]]}."))) ((-4505 . 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 -1596 UP) +(-749 -1594 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."))) (((-4510 "*") |has| |#2| (-175)) (-4501 |has| |#2| (-571)) (-4506 |has| |#2| (-6 -4506)) (-4503 . T) (-4502 . T) (-4505 . T)) -((|HasCategory| |#2| (QUOTE (-939))) (-2181 (|HasCategory| |#2| (QUOTE (-175))) (|HasCategory| |#2| (QUOTE (-466))) (|HasCategory| |#2| (QUOTE (-571))) (|HasCategory| |#2| (QUOTE (-939)))) (-2181 (|HasCategory| |#2| (QUOTE (-466))) (|HasCategory| |#2| (QUOTE (-571))) (|HasCategory| |#2| (QUOTE (-939)))) (-2181 (|HasCategory| |#2| (QUOTE (-466))) (|HasCategory| |#2| (QUOTE (-939)))) (|HasCategory| |#2| (QUOTE (-571))) (|HasCategory| |#2| (QUOTE (-175))) (-2181 (|HasCategory| |#2| (QUOTE (-175))) (|HasCategory| |#2| (QUOTE (-571)))) (-12 (|HasCategory| (-888 |#1|) (|%list| (QUOTE -911) (QUOTE (-391)))) (|HasCategory| |#2| (|%list| (QUOTE -911) (QUOTE (-391))))) (-12 (|HasCategory| (-888 |#1|) (|%list| (QUOTE -911) (QUOTE (-560)))) (|HasCategory| |#2| (|%list| (QUOTE -911) (QUOTE (-560))))) (-12 (|HasCategory| (-888 |#1|) (|%list| (QUOTE -633) (|%list| (QUOTE -915) (QUOTE (-391))))) (|HasCategory| |#2| (|%list| (QUOTE -633) (|%list| (QUOTE -915) (QUOTE (-391)))))) (-12 (|HasCategory| (-888 |#1|) (|%list| (QUOTE -633) (|%list| (QUOTE -915) (QUOTE (-560))))) (|HasCategory| |#2| (|%list| (QUOTE -633) (|%list| (QUOTE -915) (QUOTE (-560)))))) (-12 (|HasCategory| (-888 |#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 -1069) (QUOTE (-560)))) (-2181 (|HasCategory| |#2| (|%list| (QUOTE -38) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#2| (|%list| (QUOTE -1069) (|%list| (QUOTE -421) (QUOTE (-560)))))) (|HasCategory| |#2| (|%list| (QUOTE -1069) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#2| (QUOTE (-376))) (|HasAttribute| |#2| (QUOTE -4506)) (|HasCategory| |#2| (QUOTE (-466))) (-12 (|HasCategory| $ (QUOTE (-147))) (|HasCategory| |#2| (QUOTE (-939)))) (-2181 (-12 (|HasCategory| $ (QUOTE (-147))) (|HasCategory| |#2| (QUOTE (-939)))) (|HasCategory| |#2| (QUOTE (-147))))) +((|HasCategory| |#2| (QUOTE (-939))) (-2173 (|HasCategory| |#2| (QUOTE (-175))) (|HasCategory| |#2| (QUOTE (-466))) (|HasCategory| |#2| (QUOTE (-571))) (|HasCategory| |#2| (QUOTE (-939)))) (-2173 (|HasCategory| |#2| (QUOTE (-466))) (|HasCategory| |#2| (QUOTE (-571))) (|HasCategory| |#2| (QUOTE (-939)))) (-2173 (|HasCategory| |#2| (QUOTE (-466))) (|HasCategory| |#2| (QUOTE (-939)))) (|HasCategory| |#2| (QUOTE (-571))) (|HasCategory| |#2| (QUOTE (-175))) (-2173 (|HasCategory| |#2| (QUOTE (-175))) (|HasCategory| |#2| (QUOTE (-571)))) (-12 (|HasCategory| (-888 |#1|) (|%list| (QUOTE -911) (QUOTE (-391)))) (|HasCategory| |#2| (|%list| (QUOTE -911) (QUOTE (-391))))) (-12 (|HasCategory| (-888 |#1|) (|%list| (QUOTE -911) (QUOTE (-560)))) (|HasCategory| |#2| (|%list| (QUOTE -911) (QUOTE (-560))))) (-12 (|HasCategory| (-888 |#1|) (|%list| (QUOTE -633) (|%list| (QUOTE -915) (QUOTE (-391))))) (|HasCategory| |#2| (|%list| (QUOTE -633) (|%list| (QUOTE -915) (QUOTE (-391)))))) (-12 (|HasCategory| (-888 |#1|) (|%list| (QUOTE -633) (|%list| (QUOTE -915) (QUOTE (-560))))) (|HasCategory| |#2| (|%list| (QUOTE -633) (|%list| (QUOTE -915) (QUOTE (-560)))))) (-12 (|HasCategory| (-888 |#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 -1069) (QUOTE (-560)))) (-2173 (|HasCategory| |#2| (|%list| (QUOTE -38) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#2| (|%list| (QUOTE -1069) (|%list| (QUOTE -421) (QUOTE (-560)))))) (|HasCategory| |#2| (|%list| (QUOTE -1069) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#2| (QUOTE (-376))) (|HasAttribute| |#2| (QUOTE -4506)) (|HasCategory| |#2| (QUOTE (-466))) (-12 (|HasCategory| $ (QUOTE (-147))) (|HasCategory| |#2| (QUOTE (-939)))) (-2173 (-12 (|HasCategory| $ (QUOTE (-147))) (|HasCategory| |#2| (QUOTE (-939)))) (|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 -1596) +(-787 -1594) ((|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 -1596) +(-788 P -1594) ((|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 -1596) +(-790 UP -1594) ((|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."))) (((-4510 "*") . T)) NIL -(-794 R -1596) +(-794 R -1594) ((|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 -1596 |ExtF| |SUEx| |ExtP| |n|) +(-799 -1594 |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."))) (((-4510 "*") |has| |#1| (-175)) (-4501 |has| |#1| (-571)) (-4506 |has| |#1| (-6 -4506)) (-4503 . T) (-4502 . T) (-4505 . 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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)}"))) (((-4510 "*") |has| |#1| (-175)) (-4501 |has| |#1| (-571)) (-4504 |has| |#1| (-376)) (-4506 |has| |#1| (-6 -4506)) (-4503 . T) (-4502 . T) (-4505 . 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(|%list| (QUOTE -633) (|%list| (QUOTE -915) (QUOTE (-391)))))) (-12 (|HasCategory| (-1113) (|%list| (QUOTE -633) (|%list| (QUOTE -915) (QUOTE (-560))))) (|HasCategory| |#1| (|%list| (QUOTE -633) (|%list| (QUOTE -915) (QUOTE (-560)))))) (-12 (|HasCategory| (-1113) (|%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 -1069) (QUOTE (-560)))) (-2173 (|HasCategory| |#1| (|%list| (QUOTE -38) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#1| (|%list| (QUOTE -1069) (|%list| (QUOTE -421) (QUOTE (-560)))))) (|HasCategory| |#1| (|%list| (QUOTE -1069) (|%list| (QUOTE -421) (QUOTE (-560))))) (-2173 (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (QUOTE (-466))) (|HasCategory| |#1| (QUOTE (-571))) (|HasCategory| |#1| (QUOTE (-939)))) (-2173 (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (QUOTE (-466))) (|HasCategory| |#1| (QUOTE (-571))) (|HasCategory| |#1| (QUOTE (-939)))) (-2173 (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (QUOTE (-466))) (|HasCategory| |#1| (QUOTE (-939)))) (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (QUOTE (-1182))) (|HasCategory| |#1| (|%list| (QUOTE -929) (QUOTE (-1207)))) (|HasCategory| |#1| (|%list| (QUOTE -927) (QUOTE (-1207)))) (|HasCategory| |#1| (QUOTE (-239))) (|HasCategory| |#1| (QUOTE (-240))) (|HasAttribute| |#1| (QUOTE -4506)) (|HasCategory| |#1| (QUOTE (-466))) (-12 (|HasCategory| $ (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-939)))) (-2173 (-12 (|HasCategory| $ (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-939)))) (|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 @@ -3211,8 +3211,8 @@ NIL (-820 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}."))) ((-4502 . T) (-4503 . T) (-4505 . T)) -((|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-149))) (|HasCategory| |#1| (|%list| (QUOTE -633) (QUOTE (-549)))) (|HasCategory| |#1| (QUOTE (-871))) (|HasCategory| |#1| (QUOTE (-381))) (|HasCategory| |#1| (|%list| (QUOTE -528) (QUOTE (-1207)) (|devaluate| |#1|))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|))) (|HasCategory| |#1| (|%list| (QUOTE -298) (|devaluate| |#1|) (|devaluate| |#1|))) (-2181 (|HasCategory| (-1027 |#1|) (|%list| (QUOTE -1069) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#1| (|%list| (QUOTE -1069) (|%list| (QUOTE -421) (QUOTE (-560)))))) (-2181 (|HasCategory| (-1027 |#1|) (|%list| (QUOTE -1069) (QUOTE (-560)))) (|HasCategory| |#1| (|%list| (QUOTE -1069) (QUOTE (-560))))) (|HasCategory| |#1| (QUOTE (-1091))) (|HasCategory| |#1| (QUOTE (-559))) (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| (-1027 |#1|) (|%list| (QUOTE -1069) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| (-1027 |#1|) (|%list| (QUOTE -1069) (QUOTE (-560)))) (|HasCategory| |#1| (|%list| (QUOTE -1069) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#1| (|%list| (QUOTE -1069) (QUOTE (-560))))) -(-821 -2181 R OS S) +((|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-149))) (|HasCategory| |#1| (|%list| (QUOTE -633) (QUOTE (-549)))) (|HasCategory| |#1| (QUOTE (-871))) (|HasCategory| |#1| (QUOTE (-381))) (|HasCategory| |#1| (|%list| (QUOTE -528) (QUOTE (-1207)) (|devaluate| |#1|))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|))) (|HasCategory| |#1| (|%list| (QUOTE -298) (|devaluate| |#1|) (|devaluate| |#1|))) (-2173 (|HasCategory| (-1027 |#1|) (|%list| (QUOTE -1069) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#1| (|%list| (QUOTE -1069) (|%list| (QUOTE -421) (QUOTE (-560)))))) (-2173 (|HasCategory| (-1027 |#1|) (|%list| (QUOTE -1069) (QUOTE (-560)))) (|HasCategory| |#1| (|%list| (QUOTE -1069) (QUOTE (-560))))) (|HasCategory| |#1| (QUOTE (-1091))) (|HasCategory| |#1| (QUOTE (-559))) (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| (-1027 |#1|) (|%list| (QUOTE -1069) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| (-1027 |#1|) (|%list| (QUOTE -1069) (QUOTE (-560)))) (|HasCategory| |#1| (|%list| (QUOTE -1069) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#1| (|%list| (QUOTE -1069) (QUOTE (-560))))) +(-821 -2173 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 @@ -3220,11 +3220,11 @@ 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 -(-823 R -1596 L) +(-823 R -1594 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 -(-824 R -1596) +(-824 R -1594) ((|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 @@ -3232,7 +3232,7 @@ 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 -(-826 R -1596) +(-826 R -1594) ((|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 @@ -3240,11 +3240,11 @@ 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 -(-828 -1596 UP UPUP R) +(-828 -1594 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 -(-829 -1596 UP L LQ) +(-829 -1594 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 @@ -3252,38 +3252,38 @@ 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 -(-831 -1596 UP L LQ) +(-831 -1594 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 -(-832 -1596 UP) +(-832 -1594 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 -(-833 -1596 L UP A LO) +(-833 -1594 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 -(-834 -1596 UP) +(-834 -1594 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)))) -(-835 -1596 LO) +(-835 -1594 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 -(-836 -1596 LODO) +(-836 -1594 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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(-1080)))) (-12 (|HasCategory| |#2| (QUOTE (-239))) (|HasCategory| |#2| (QUOTE (-1080)))) (-12 (|HasCategory| |#2| (QUOTE (-1080))) (|HasCategory| |#2| (|%list| (QUOTE -929) (QUOTE (-1207))))) (-2173 (|HasCategory| |#2| (QUOTE (-1080))) (-12 (|HasCategory| |#2| (QUOTE (-1132))) (|HasCategory| |#2| (|%list| (QUOTE -1069) (QUOTE (-560)))))) (-12 (|HasCategory| |#2| (QUOTE (-1132))) (|HasCategory| |#2| (|%list| (QUOTE -1069) (QUOTE (-560))))) (-12 (|HasCategory| |#2| (|%list| (QUOTE -1069) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#2| (QUOTE (-1132)))) (|HasAttribute| |#2| (QUOTE -4505)) (-12 (|HasCategory| |#2| (QUOTE (-240))) (|HasCategory| |#2| (QUOTE (-1080)))) (-12 (|HasCategory| |#2| (QUOTE (-1080))) (|HasCategory| |#2| (|%list| (QUOTE -927) (QUOTE (-1207))))) (|HasCategory| |#2| (QUOTE (-175))) (|HasCategory| |#2| (QUOTE (-23))) (|HasCategory| |#2| (QUOTE (-133))) (|HasCategory| |#2| (QUOTE (-25))) (|HasCategory| |#2| (|%list| (QUOTE -632) (QUOTE (-887)))) (|HasCategory| |#2| (QUOTE (-102))) (-12 (|HasCategory| |#2| (QUOTE (-1132))) (|HasCategory| |#2| (|%list| (QUOTE -321) (|devaluate| |#2|))))) (-838 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"))) (((-4510 "*") |has| |#1| (-175)) (-4501 |has| |#1| (-571)) (-4506 |has| |#1| (-6 -4506)) (-4503 . T) (-4502 . T) (-4505 . T)) -((|HasCategory| |#1| (QUOTE (-939))) (-2181 (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-466))) (|HasCategory| |#1| (QUOTE (-571))) (|HasCategory| |#1| (QUOTE (-939)))) (-2181 (|HasCategory| |#1| (QUOTE (-466))) (|HasCategory| |#1| (QUOTE (-571))) (|HasCategory| |#1| (QUOTE (-939)))) (-2181 (|HasCategory| |#1| (QUOTE (-466))) (|HasCategory| |#1| (QUOTE (-939)))) (|HasCategory| |#1| (QUOTE (-571))) (|HasCategory| |#1| (QUOTE (-175))) (-2181 (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-571)))) (-12 (|HasCategory| (-840 (-1207)) (|%list| (QUOTE -911) (QUOTE (-391)))) (|HasCategory| |#1| (|%list| (QUOTE -911) (QUOTE (-391))))) (-12 (|HasCategory| (-840 (-1207)) (|%list| (QUOTE -911) (QUOTE (-560)))) (|HasCategory| |#1| (|%list| (QUOTE -911) (QUOTE (-560))))) (-12 (|HasCategory| (-840 (-1207)) (|%list| (QUOTE -633) (|%list| (QUOTE -915) (QUOTE (-391))))) (|HasCategory| |#1| (|%list| (QUOTE -633) (|%list| (QUOTE -915) (QUOTE (-391)))))) (-12 (|HasCategory| (-840 (-1207)) (|%list| (QUOTE -633) (|%list| (QUOTE -915) (QUOTE (-560))))) (|HasCategory| |#1| (|%list| (QUOTE -633) (|%list| (QUOTE -915) (QUOTE (-560)))))) (-12 (|HasCategory| (-840 (-1207)) (|%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 -1069) (QUOTE (-560)))) (-2181 (|HasCategory| |#1| (|%list| (QUOTE -38) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#1| (|%list| (QUOTE -1069) (|%list| (QUOTE -421) (QUOTE (-560)))))) (|HasCategory| |#1| (|%list| (QUOTE -1069) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#1| (QUOTE (-240))) (|HasCategory| |#1| (QUOTE (-239))) (|HasCategory| |#1| (|%list| (QUOTE -929) (QUOTE (-1207)))) (|HasCategory| |#1| (|%list| (QUOTE -927) (QUOTE (-1207)))) (|HasCategory| |#1| (QUOTE (-376))) (|HasAttribute| |#1| (QUOTE -4506)) (|HasCategory| |#1| (QUOTE (-466))) (-12 (|HasCategory| $ (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-939)))) (-2181 (-12 (|HasCategory| $ (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-939)))) (|HasCategory| |#1| (QUOTE (-147))))) +((|HasCategory| |#1| (QUOTE (-939))) (-2173 (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-466))) (|HasCategory| |#1| (QUOTE (-571))) (|HasCategory| |#1| (QUOTE (-939)))) (-2173 (|HasCategory| |#1| (QUOTE (-466))) (|HasCategory| |#1| (QUOTE (-571))) (|HasCategory| |#1| (QUOTE (-939)))) (-2173 (|HasCategory| |#1| (QUOTE (-466))) (|HasCategory| |#1| (QUOTE (-939)))) (|HasCategory| |#1| (QUOTE (-571))) (|HasCategory| |#1| (QUOTE (-175))) (-2173 (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-571)))) (-12 (|HasCategory| (-840 (-1207)) (|%list| (QUOTE -911) (QUOTE (-391)))) (|HasCategory| |#1| (|%list| (QUOTE -911) (QUOTE (-391))))) (-12 (|HasCategory| (-840 (-1207)) (|%list| (QUOTE -911) (QUOTE (-560)))) (|HasCategory| |#1| (|%list| (QUOTE -911) (QUOTE (-560))))) (-12 (|HasCategory| (-840 (-1207)) (|%list| (QUOTE -633) (|%list| (QUOTE -915) (QUOTE (-391))))) (|HasCategory| |#1| (|%list| (QUOTE -633) (|%list| (QUOTE -915) (QUOTE (-391)))))) (-12 (|HasCategory| (-840 (-1207)) (|%list| (QUOTE -633) (|%list| (QUOTE -915) (QUOTE (-560))))) (|HasCategory| |#1| (|%list| (QUOTE -633) (|%list| (QUOTE -915) (QUOTE (-560)))))) (-12 (|HasCategory| (-840 (-1207)) (|%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 -1069) (QUOTE (-560)))) (-2173 (|HasCategory| |#1| (|%list| (QUOTE -38) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#1| (|%list| (QUOTE -1069) (|%list| (QUOTE -421) (QUOTE (-560)))))) (|HasCategory| |#1| (|%list| (QUOTE -1069) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#1| (QUOTE (-240))) (|HasCategory| |#1| (QUOTE (-239))) (|HasCategory| |#1| (|%list| (QUOTE -929) (QUOTE (-1207)))) (|HasCategory| |#1| (|%list| (QUOTE -927) (QUOTE (-1207)))) (|HasCategory| |#1| (QUOTE (-376))) (|HasAttribute| |#1| (QUOTE -4506)) (|HasCategory| |#1| (QUOTE (-466))) (-12 (|HasCategory| $ (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-939)))) (-2173 (-12 (|HasCategory| $ (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-939)))) (|HasCategory| |#1| (QUOTE (-147))))) (-839 |Kernels| R |var|) ((|constructor| (NIL "This constructor produces an ordinary differential ring from a partial differential ring by specifying a variable."))) (((-4510 "*") |has| |#2| (-376)) (-4501 |has| |#2| (-376)) (-4506 |has| |#2| (-376)) (-4500 |has| |#2| (-376)) (-4505 . T) (-4503 . T) (-4502 . T)) @@ -3347,7 +3347,7 @@ NIL (-854 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."))) ((-4505 |has| |#1| (-870))) -((|HasCategory| |#1| (QUOTE (-870))) (|HasCategory| |#1| (QUOTE (-21))) (-2181 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-870)))) (|HasCategory| |#1| (|%list| (QUOTE -1069) (|%list| (QUOTE -421) (QUOTE (-560))))) (-2181 (|HasCategory| |#1| (QUOTE (-870))) (|HasCategory| |#1| (|%list| (QUOTE -1069) (QUOTE (-560))))) (|HasCategory| |#1| (|%list| (QUOTE -1069) (QUOTE (-560)))) (|HasCategory| |#1| (QUOTE (-559)))) +((|HasCategory| |#1| (QUOTE (-870))) (|HasCategory| |#1| (QUOTE (-21))) (-2173 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-870)))) (|HasCategory| |#1| (|%list| (QUOTE -1069) (|%list| (QUOTE -421) (QUOTE (-560))))) (-2173 (|HasCategory| |#1| (QUOTE (-870))) (|HasCategory| |#1| (|%list| (QUOTE -1069) (QUOTE (-560))))) (|HasCategory| |#1| (|%list| (QUOTE -1069) (QUOTE (-560)))) (|HasCategory| |#1| (QUOTE (-559)))) (-855 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 @@ -3387,7 +3387,7 @@ NIL (-864 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| (($) "\\spad{plusInfinity()} returns +infinity."))) ((-4505 |has| |#1| (-870))) -((|HasCategory| |#1| (QUOTE (-870))) (|HasCategory| |#1| (QUOTE (-21))) (-2181 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-870)))) (|HasCategory| |#1| (|%list| (QUOTE -1069) (|%list| (QUOTE -421) (QUOTE (-560))))) (-2181 (|HasCategory| |#1| (QUOTE (-870))) (|HasCategory| |#1| (|%list| (QUOTE -1069) (QUOTE (-560))))) (|HasCategory| |#1| (|%list| (QUOTE -1069) (QUOTE (-560)))) (|HasCategory| |#1| (QUOTE (-559)))) +((|HasCategory| |#1| (QUOTE (-870))) (|HasCategory| |#1| (QUOTE (-21))) (-2173 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-870)))) (|HasCategory| |#1| (|%list| (QUOTE -1069) (|%list| (QUOTE -421) (QUOTE (-560))))) (-2173 (|HasCategory| |#1| (QUOTE (-870))) (|HasCategory| |#1| (|%list| (QUOTE -1069) (QUOTE (-560))))) (|HasCategory| |#1| (|%list| (QUOTE -1069) (QUOTE (-560)))) (|HasCategory| |#1| (QUOTE (-559)))) (-865 R S) ((|constructor| (NIL "Lifting of maps to ordered completions. Date Created: 4 Oct 1989 Date Last Updated: 4 Oct 1989")) (|map| (((|OrderedCompletion| |#2|) (|Mapping| |#2| |#1|) (|OrderedCompletion| |#1|) (|OrderedCompletion| |#2|) (|OrderedCompletion| |#2|)) "\\spad{map(f, r, p, m)} lifts \\spad{f} and applies it to \\spad{r},{} assuming that \\spad{f}(plusInfinity) = \\spad{p} and that \\spad{f}(minusInfinity) = \\spad{m}.") (((|OrderedCompletion| |#2|) (|Mapping| |#2| |#1|) (|OrderedCompletion| |#1|)) "\\spad{map(f, r)} lifts \\spad{f} and applies it to \\spad{r},{} assuming that \\spad{f}(plusInfinity) = plusInfinity and that \\spad{f}(minusInfinity) = minusInfinity."))) NIL @@ -3396,7 +3396,7 @@ NIL ((|constructor| (NIL "Ordered finite sets.")) (|max| (($) "\\spad{max} is the maximum value of \\%.")) (|min| (($) "\\spad{min} is the minimum value of \\%."))) NIL NIL -(-867 -3370 S) +(-867 -3367 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 @@ -3440,11 +3440,11 @@ 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)))) -(-878 R |sigma| -2072) +(-878 R |sigma| -2726) ((|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."))) ((-4502 . T) (-4503 . T) (-4505 . T)) ((|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (|%list| (QUOTE -1069) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#1| (|%list| (QUOTE -1069) (QUOTE (-560)))) (|HasCategory| |#1| (QUOTE (-571))) (|HasCategory| |#1| (QUOTE (-466))) (|HasCategory| |#1| (QUOTE (-376)))) -(-879 |x| R |sigma| -2072) +(-879 |x| R |sigma| -2726) ((|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}."))) ((-4502 . T) (-4503 . T) (-4505 . T)) ((|HasCategory| |#2| (QUOTE (-175))) (|HasCategory| |#2| (|%list| (QUOTE -1069) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#2| (|%list| (QUOTE -1069) (QUOTE (-560)))) (|HasCategory| |#2| (QUOTE (-571))) (|HasCategory| |#2| (QUOTE (-466))) (|HasCategory| |#2| (QUOTE (-376)))) @@ -3511,15 +3511,15 @@ NIL (-895 |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)."))) ((-4500 . T) (-4506 . T) (-4501 . T) ((-4510 "*") . T) (-4502 . T) (-4503 . T) (-4505 . T)) -((|HasCategory| (-893 |#1|) (QUOTE (-939))) (|HasCategory| (-893 |#1|) (|%list| (QUOTE -1069) (QUOTE (-1207)))) (|HasCategory| (-893 |#1|) (QUOTE (-147))) (|HasCategory| (-893 |#1|) (QUOTE (-149))) (|HasCategory| (-893 |#1|) (|%list| (QUOTE -633) (QUOTE (-549)))) (|HasCategory| (-893 |#1|) (QUOTE (-1051))) (|HasCategory| (-893 |#1|) (QUOTE (-842))) (|HasCategory| (-893 |#1|) (QUOTE (-871))) (-2181 (|HasCategory| (-893 |#1|) (QUOTE (-842))) (|HasCategory| (-893 |#1|) (QUOTE (-871)))) (|HasCategory| (-893 |#1|) (|%list| (QUOTE -1069) (QUOTE (-560)))) (|HasCategory| (-893 |#1|) (QUOTE (-1182))) (|HasCategory| (-893 |#1|) (|%list| (QUOTE -911) (QUOTE (-391)))) (|HasCategory| (-893 |#1|) (|%list| (QUOTE -911) (QUOTE (-560)))) (|HasCategory| (-893 |#1|) (|%list| (QUOTE -633) (|%list| (QUOTE -915) (QUOTE (-391))))) (|HasCategory| (-893 |#1|) (|%list| (QUOTE -633) (|%list| (QUOTE -915) (QUOTE (-560))))) (|HasCategory| (-893 |#1|) (|%list| (QUOTE -660) (QUOTE (-560)))) (|HasCategory| (-893 |#1|) (QUOTE (-239))) (|HasCategory| (-893 |#1|) (|%list| (QUOTE -929) (QUOTE (-1207)))) (|HasCategory| (-893 |#1|) (QUOTE (-240))) (|HasCategory| (-893 |#1|) (|%list| (QUOTE -927) (QUOTE (-1207)))) (|HasCategory| (-893 |#1|) (|%list| (QUOTE -528) (QUOTE (-1207)) (|%list| (QUOTE -893) (|devaluate| |#1|)))) (|HasCategory| (-893 |#1|) (|%list| (QUOTE -321) (|%list| (QUOTE -893) (|devaluate| |#1|)))) (|HasCategory| (-893 |#1|) (|%list| (QUOTE -298) (|%list| (QUOTE -893) (|devaluate| |#1|)) (|%list| (QUOTE -893) (|devaluate| |#1|)))) (|HasCategory| (-893 |#1|) (QUOTE (-319))) (|HasCategory| (-893 |#1|) (QUOTE (-559))) (-12 (|HasCategory| $ (QUOTE (-147))) (|HasCategory| (-893 |#1|) (QUOTE (-939)))) (-2181 (-12 (|HasCategory| $ (QUOTE (-147))) (|HasCategory| (-893 |#1|) (QUOTE (-939)))) (|HasCategory| (-893 |#1|) (QUOTE (-147))))) +((|HasCategory| (-893 |#1|) (QUOTE (-939))) (|HasCategory| (-893 |#1|) (|%list| (QUOTE -1069) (QUOTE (-1207)))) (|HasCategory| (-893 |#1|) (QUOTE (-147))) (|HasCategory| (-893 |#1|) (QUOTE (-149))) (|HasCategory| (-893 |#1|) (|%list| (QUOTE -633) (QUOTE (-549)))) (|HasCategory| (-893 |#1|) (QUOTE (-1051))) (|HasCategory| (-893 |#1|) (QUOTE (-842))) (|HasCategory| (-893 |#1|) (QUOTE (-871))) (-2173 (|HasCategory| (-893 |#1|) (QUOTE (-842))) (|HasCategory| (-893 |#1|) (QUOTE (-871)))) (|HasCategory| (-893 |#1|) (|%list| (QUOTE -1069) (QUOTE (-560)))) (|HasCategory| (-893 |#1|) (QUOTE (-1182))) (|HasCategory| (-893 |#1|) (|%list| (QUOTE -911) (QUOTE (-391)))) (|HasCategory| (-893 |#1|) (|%list| (QUOTE -911) (QUOTE (-560)))) (|HasCategory| (-893 |#1|) (|%list| (QUOTE -633) (|%list| (QUOTE -915) (QUOTE (-391))))) (|HasCategory| (-893 |#1|) (|%list| (QUOTE -633) (|%list| (QUOTE -915) (QUOTE (-560))))) (|HasCategory| (-893 |#1|) (|%list| (QUOTE -660) (QUOTE (-560)))) (|HasCategory| (-893 |#1|) (QUOTE (-239))) (|HasCategory| (-893 |#1|) (|%list| (QUOTE -929) (QUOTE (-1207)))) (|HasCategory| (-893 |#1|) (QUOTE (-240))) (|HasCategory| (-893 |#1|) (|%list| (QUOTE -927) (QUOTE (-1207)))) (|HasCategory| (-893 |#1|) (|%list| (QUOTE -528) (QUOTE (-1207)) (|%list| (QUOTE -893) (|devaluate| |#1|)))) (|HasCategory| (-893 |#1|) (|%list| (QUOTE -321) (|%list| (QUOTE -893) (|devaluate| |#1|)))) (|HasCategory| (-893 |#1|) (|%list| (QUOTE -298) (|%list| (QUOTE -893) (|devaluate| |#1|)) (|%list| (QUOTE -893) (|devaluate| |#1|)))) (|HasCategory| (-893 |#1|) (QUOTE (-319))) (|HasCategory| (-893 |#1|) (QUOTE (-559))) (-12 (|HasCategory| $ (QUOTE (-147))) (|HasCategory| (-893 |#1|) (QUOTE (-939)))) (-2173 (-12 (|HasCategory| $ (QUOTE (-147))) (|HasCategory| (-893 |#1|) (QUOTE (-939)))) (|HasCategory| (-893 |#1|) (QUOTE (-147))))) (-896 |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)}."))) ((-4500 . T) (-4506 . T) (-4501 . T) ((-4510 "*") . T) (-4502 . T) (-4503 . T) (-4505 . T)) -((|HasCategory| |#2| (QUOTE (-939))) (|HasCategory| |#2| (|%list| (QUOTE -1069) (QUOTE (-1207)))) (|HasCategory| |#2| (QUOTE (-147))) (|HasCategory| |#2| (QUOTE (-149))) (|HasCategory| |#2| (|%list| (QUOTE -633) (QUOTE (-549)))) (|HasCategory| |#2| (QUOTE (-1051))) (|HasCategory| |#2| (QUOTE (-842))) (|HasCategory| |#2| (QUOTE (-871))) (-2181 (|HasCategory| |#2| (QUOTE (-842))) (|HasCategory| |#2| (QUOTE (-871)))) (|HasCategory| |#2| (|%list| (QUOTE -1069) (QUOTE (-560)))) (|HasCategory| |#2| (QUOTE (-1182))) (|HasCategory| |#2| (|%list| (QUOTE -911) (QUOTE (-391)))) (|HasCategory| |#2| (|%list| (QUOTE -911) (QUOTE (-560)))) (|HasCategory| |#2| (|%list| (QUOTE -633) (|%list| (QUOTE -915) (QUOTE (-391))))) (|HasCategory| |#2| (|%list| (QUOTE -633) (|%list| (QUOTE -915) (QUOTE (-560))))) (|HasCategory| |#2| (|%list| (QUOTE -660) (QUOTE (-560)))) (|HasCategory| |#2| (QUOTE (-239))) (|HasCategory| |#2| (|%list| (QUOTE -929) (QUOTE (-1207)))) (|HasCategory| |#2| (QUOTE (-240))) (|HasCategory| |#2| (|%list| (QUOTE -927) (QUOTE (-1207)))) (|HasCategory| |#2| (|%list| (QUOTE -528) (QUOTE (-1207)) (|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 (-939)))) (-2181 (-12 (|HasCategory| $ (QUOTE (-147))) (|HasCategory| |#2| (QUOTE (-939)))) (|HasCategory| |#2| (QUOTE (-147))))) +((|HasCategory| |#2| (QUOTE (-939))) (|HasCategory| |#2| (|%list| (QUOTE -1069) (QUOTE (-1207)))) (|HasCategory| |#2| (QUOTE (-147))) (|HasCategory| |#2| (QUOTE (-149))) (|HasCategory| |#2| (|%list| (QUOTE -633) (QUOTE (-549)))) (|HasCategory| |#2| (QUOTE (-1051))) (|HasCategory| |#2| (QUOTE (-842))) (|HasCategory| |#2| (QUOTE (-871))) (-2173 (|HasCategory| |#2| (QUOTE (-842))) (|HasCategory| |#2| (QUOTE (-871)))) (|HasCategory| |#2| (|%list| (QUOTE -1069) (QUOTE (-560)))) (|HasCategory| |#2| (QUOTE (-1182))) (|HasCategory| |#2| (|%list| (QUOTE -911) (QUOTE (-391)))) (|HasCategory| |#2| (|%list| (QUOTE -911) (QUOTE (-560)))) (|HasCategory| |#2| (|%list| (QUOTE -633) (|%list| (QUOTE -915) (QUOTE (-391))))) (|HasCategory| |#2| (|%list| (QUOTE -633) (|%list| (QUOTE -915) (QUOTE (-560))))) (|HasCategory| |#2| (|%list| (QUOTE -660) (QUOTE (-560)))) (|HasCategory| |#2| (QUOTE (-239))) (|HasCategory| |#2| (|%list| (QUOTE -929) (QUOTE (-1207)))) (|HasCategory| |#2| (QUOTE (-240))) (|HasCategory| |#2| (|%list| (QUOTE -927) (QUOTE (-1207)))) (|HasCategory| |#2| (|%list| (QUOTE -528) (QUOTE (-1207)) (|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 (-939)))) (-2173 (-12 (|HasCategory| $ (QUOTE (-147))) (|HasCategory| |#2| (QUOTE (-939)))) (|HasCategory| |#2| (QUOTE (-147))))) (-897 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 (-1132))) (|HasCategory| |#2| (QUOTE (-1132)))) (-2181 (-12 (|HasCategory| |#1| (QUOTE (-1132))) (|HasCategory| |#2| (QUOTE (-1132)))) (-12 (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-887)))) (|HasCategory| |#2| (|%list| (QUOTE -632) (QUOTE (-887)))))) (-12 (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-887)))) (|HasCategory| |#2| (|%list| (QUOTE -632) (QUOTE (-887)))))) +((-12 (|HasCategory| |#1| (QUOTE (-1132))) (|HasCategory| |#2| (QUOTE (-1132)))) (-2173 (-12 (|HasCategory| |#1| (QUOTE (-1132))) (|HasCategory| |#2| (QUOTE (-1132)))) (-12 (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-887)))) (|HasCategory| |#2| (|%list| (QUOTE -632) (QUOTE (-887)))))) (-12 (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-887)))) (|HasCategory| |#2| (|%list| (QUOTE -632) (QUOTE (-887)))))) (-898) ((|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 @@ -3592,7 +3592,7 @@ 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 -(-916 R -1796) +(-916 R -1806) ((|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 @@ -3620,7 +3620,7 @@ 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 -(-923 UP -1596) +(-923 UP -1594) ((|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 @@ -3651,11 +3651,11 @@ NIL (-930 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 (-1132))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1132))) (-2181 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-1132)))) (-2181 (-12 (|HasCategory| |#1| (QUOTE (-1132))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-887))))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-887)))) (|HasCategory| |#1| (QUOTE (-102)))) +((-12 (|HasCategory| |#1| (QUOTE (-1132))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1132))) (-2173 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-1132)))) (-2173 (-12 (|HasCategory| |#1| (QUOTE (-1132))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-887))))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-887)))) (|HasCategory| |#1| (QUOTE (-102)))) (-931 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|))) $) "\\spad{listRepresentation(p)} produces a representation {\\em rep} of the permutation \\spad{p} as a list of preimages and images,{} \\spad{i}.\\spad{e} \\spad{p} maps {\\em (rep.preimage).k} to {\\em (rep.image).k} for all indices \\spad{k}. Elements of \\spad{S} not in {\\em (rep.preimage).k} are fixed points,{} and these are the only fixed points of the permutation."))) ((-4505 . T)) -((-2181 (|HasCategory| |#1| (QUOTE (-381))) (|HasCategory| |#1| (QUOTE (-871)))) (|HasCategory| |#1| (QUOTE (-381))) (|HasCategory| |#1| (QUOTE (-871)))) +((-2173 (|HasCategory| |#1| (QUOTE (-381))) (|HasCategory| |#1| (QUOTE (-871)))) (|HasCategory| |#1| (QUOTE (-381))) (|HasCategory| |#1| (QUOTE (-871)))) (-932 |n| R) ((|constructor| (NIL "Permanent implements the functions {\\em permanent},{} the permanent for square matrices.")) (|permanent| ((|#2| (|SquareMatrix| |#1| |#2|)) "\\spad{permanent(x)} computes the permanent of a square matrix \\spad{x}. The {\\em permanent} is equivalent to the \\spadfun{determinant} except that coefficients have no change of sign. This function is much more difficult to compute than the {\\em determinant}. The formula used is by \\spad{H}.\\spad{J}. Ryser,{} improved by [Nijenhuis and Wilf,{} Ch. 19]. Note: permanent(\\spad{x}) choose one of three algorithms,{} depending on the underlying ring \\spad{R} and on \\spad{n},{} the number of rows (and columns) of x:\\begin{items} \\item 1. if 2 has an inverse in \\spad{R} we can use the algorithm of \\indented{3}{[Nijenhuis and Wilf,{} ch.19,{}\\spad{p}.158]; if 2 has no inverse,{}} \\indented{3}{some modifications are necessary:} \\item 2. if {\\em n > 6} and \\spad{R} is an integral domain with characteristic \\indented{3}{different from 2 (the algorithm works if and only 2 is not a} \\indented{3}{zero-divisor of \\spad{R} and {\\em characteristic()\\$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 @@ -3688,7 +3688,7 @@ 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| (((|Union| $ "failed") $) "\\spad{charthRoot(r)} returns the \\spad{p}\\spad{-}th root of \\spad{r},{} or \"failed\" 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}."))) ((-4501 . T) ((-4510 "*") . T) (-4502 . T) (-4503 . T) (-4505 . T)) NIL -(-940 R0 -1596 UP UPUP R) +(-940 R0 -1594 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 @@ -3716,7 +3716,7 @@ 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 -(-947 -1596) +(-947 -1594) ((|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 @@ -3732,11 +3732,11 @@ 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| (((|Union| (|List| $) "failed") (|List| $) $) "\\spad{expressIdealMember([f1,...,fn],h)} returns a representation of \\spad{h} as a linear combination of the \\spad{fi} or \"failed\" 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)}"))) ((-4501 . T) ((-4510 "*") . T) (-4502 . T) (-4503 . T) (-4505 . T)) NIL -(-951 |xx| -1596) +(-951 |xx| -1594) ((|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 -(-952 -1596 P) +(-952 -1594 P) ((|constructor| (NIL "This package exports interpolation algorithms")) (|LagrangeInterpolation| ((|#2| (|List| |#1|) (|List| |#1|)) "\\spad{LagrangeInterpolation(l1,l2)} \\undocumented"))) NIL NIL @@ -3764,7 +3764,7 @@ 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 -(-959 R -1596) +(-959 R -1594) ((|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 @@ -3772,7 +3772,7 @@ 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 -(-961 S R -1596) +(-961 S R -1594) ((|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 @@ -3792,11 +3792,11 @@ 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 -911) (|devaluate| |#1|)))) -(-966 -1796) +(-966 -1806) ((|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 -(-967 R -1596 -1796) +(-967 R -1594 -1806) ((|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 @@ -3819,7 +3819,7 @@ NIL (-972 R) ((|constructor| (NIL "This domain implements points in coordinate space"))) ((-4509 . T) (-4508 . T)) -((-2181 (-12 (|HasCategory| |#1| (QUOTE (-871))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1132))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|))))) (-2181 (-12 (|HasCategory| |#1| (QUOTE (-1132))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-887))))) (|HasCategory| |#1| (|%list| (QUOTE -633) (QUOTE (-549)))) (-2181 (|HasCategory| |#1| (QUOTE (-871))) (|HasCategory| |#1| (QUOTE (-1132)))) (|HasCategory| |#1| (QUOTE (-871))) (-2181 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-871))) (|HasCategory| |#1| (QUOTE (-1132)))) (|HasCategory| (-560) (QUOTE (-871))) (|HasCategory| |#1| (QUOTE (-1132))) (|HasCategory| |#1| (QUOTE (-25))) (|HasCategory| |#1| (QUOTE (-23))) (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-748))) (|HasCategory| |#1| (QUOTE (-1080))) (-12 (|HasCategory| |#1| (QUOTE (-1033))) (|HasCategory| |#1| (QUOTE (-1080)))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-887)))) (|HasCategory| |#1| (QUOTE (-102))) (-12 (|HasCategory| |#1| (QUOTE (-1132))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|))))) +((-2173 (-12 (|HasCategory| |#1| (QUOTE (-871))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1132))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|))))) (-2173 (-12 (|HasCategory| |#1| (QUOTE (-1132))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-887))))) (|HasCategory| |#1| (|%list| (QUOTE -633) (QUOTE (-549)))) (-2173 (|HasCategory| |#1| (QUOTE (-871))) (|HasCategory| |#1| (QUOTE (-1132)))) (|HasCategory| |#1| (QUOTE (-871))) (-2173 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-871))) (|HasCategory| |#1| (QUOTE (-1132)))) (|HasCategory| (-560) (QUOTE (-871))) (|HasCategory| |#1| (QUOTE (-1132))) (|HasCategory| |#1| (QUOTE (-25))) (|HasCategory| |#1| (QUOTE (-23))) (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-748))) (|HasCategory| |#1| (QUOTE (-1080))) (-12 (|HasCategory| |#1| (QUOTE (-1033))) (|HasCategory| |#1| (QUOTE (-1080)))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-887)))) (|HasCategory| |#1| (QUOTE (-102))) (-12 (|HasCategory| |#1| (QUOTE (-1132))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|))))) (-973 |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 @@ -3831,7 +3831,7 @@ NIL (-975 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}."))) (((-4510 "*") |has| |#1| (-175)) (-4501 |has| |#1| (-571)) (-4506 |has| |#1| (-6 -4506)) (-4503 . T) (-4502 . T) (-4505 . T)) -((|HasCategory| |#1| (QUOTE (-939))) (-2181 (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-466))) (|HasCategory| |#1| (QUOTE (-571))) (|HasCategory| |#1| (QUOTE (-939)))) (-2181 (|HasCategory| |#1| (QUOTE (-466))) (|HasCategory| |#1| (QUOTE (-571))) (|HasCategory| |#1| (QUOTE (-939)))) (-2181 (|HasCategory| |#1| (QUOTE (-466))) (|HasCategory| |#1| (QUOTE (-939)))) (|HasCategory| |#1| (QUOTE (-571))) (|HasCategory| |#1| (QUOTE (-175))) (-2181 (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-571)))) (-12 (|HasCategory| (-1207) (|%list| (QUOTE -911) (QUOTE (-391)))) (|HasCategory| |#1| (|%list| (QUOTE -911) (QUOTE (-391))))) (-12 (|HasCategory| (-1207) (|%list| (QUOTE -911) (QUOTE (-560)))) (|HasCategory| |#1| (|%list| (QUOTE -911) (QUOTE (-560))))) (-12 (|HasCategory| (-1207) (|%list| (QUOTE -633) (|%list| (QUOTE -915) (QUOTE (-391))))) (|HasCategory| |#1| (|%list| (QUOTE -633) (|%list| (QUOTE -915) (QUOTE (-391)))))) (-12 (|HasCategory| (-1207) (|%list| (QUOTE -633) (|%list| (QUOTE -915) (QUOTE (-560))))) (|HasCategory| |#1| (|%list| (QUOTE -633) (|%list| (QUOTE -915) (QUOTE (-560)))))) (-12 (|HasCategory| (-1207) (|%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 -1069) (QUOTE (-560)))) (-2181 (|HasCategory| |#1| (|%list| (QUOTE -38) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#1| (|%list| (QUOTE -1069) (|%list| (QUOTE -421) (QUOTE (-560)))))) (|HasCategory| |#1| (|%list| (QUOTE -1069) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#1| (QUOTE (-376))) (|HasAttribute| |#1| (QUOTE -4506)) (|HasCategory| |#1| (QUOTE (-466))) (-12 (|HasCategory| $ (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-939)))) (-2181 (-12 (|HasCategory| $ (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-939)))) (|HasCategory| |#1| (QUOTE (-147))))) +((|HasCategory| |#1| (QUOTE (-939))) (-2173 (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-466))) (|HasCategory| |#1| (QUOTE (-571))) (|HasCategory| |#1| (QUOTE (-939)))) (-2173 (|HasCategory| |#1| (QUOTE (-466))) (|HasCategory| |#1| (QUOTE (-571))) (|HasCategory| |#1| (QUOTE (-939)))) (-2173 (|HasCategory| |#1| (QUOTE (-466))) (|HasCategory| |#1| (QUOTE (-939)))) (|HasCategory| |#1| (QUOTE (-571))) (|HasCategory| |#1| (QUOTE (-175))) (-2173 (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-571)))) (-12 (|HasCategory| (-1207) (|%list| (QUOTE -911) (QUOTE (-391)))) (|HasCategory| |#1| (|%list| (QUOTE -911) (QUOTE (-391))))) (-12 (|HasCategory| (-1207) (|%list| (QUOTE -911) (QUOTE (-560)))) (|HasCategory| |#1| (|%list| (QUOTE -911) (QUOTE (-560))))) (-12 (|HasCategory| (-1207) (|%list| (QUOTE -633) (|%list| (QUOTE -915) (QUOTE (-391))))) (|HasCategory| |#1| (|%list| (QUOTE -633) (|%list| (QUOTE -915) (QUOTE (-391)))))) (-12 (|HasCategory| (-1207) (|%list| (QUOTE -633) (|%list| (QUOTE -915) (QUOTE (-560))))) (|HasCategory| |#1| (|%list| (QUOTE -633) (|%list| (QUOTE -915) (QUOTE (-560)))))) (-12 (|HasCategory| (-1207) (|%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 -1069) (QUOTE (-560)))) (-2173 (|HasCategory| |#1| (|%list| (QUOTE -38) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#1| (|%list| (QUOTE -1069) (|%list| (QUOTE -421) (QUOTE (-560)))))) (|HasCategory| |#1| (|%list| (QUOTE -1069) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#1| (QUOTE (-376))) (|HasAttribute| |#1| (QUOTE -4506)) (|HasCategory| |#1| (QUOTE (-466))) (-12 (|HasCategory| $ (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-939)))) (-2173 (-12 (|HasCategory| $ (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-939)))) (|HasCategory| |#1| (QUOTE (-147))))) (-976 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 @@ -3848,7 +3848,7 @@ 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}."))) (((-4510 "*") |has| |#1| (-175)) (-4501 |has| |#1| (-571)) (-4506 |has| |#1| (-6 -4506)) (-4503 . T) (-4502 . T) (-4505 . T)) NIL -(-980 E V R P -1596) +(-980 E V R P -1594) ((|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 @@ -3856,7 +3856,7 @@ 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 -(-982 E V R P -1596) +(-982 E V R P -1594) ((|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| $) "\\spad{numer(x)} \\undocumented"))) NIL ((|HasCategory| |#3| (QUOTE (-466)))) @@ -3871,7 +3871,7 @@ NIL (-985 R E) ((|constructor| (NIL "This domain represents generalized polynomials with coefficients (from a not necessarily commutative ring),{} and terms indexed by their exponents (from an arbitrary ordered abelian monoid). This type is used,{} for example,{} by the \\spadtype{DistributedMultivariatePolynomial} domain where the exponent domain is a direct product of non negative integers.")) (|canonicalUnitNormal| ((|attribute|) "canonicalUnitNormal guarantees that the function unitCanonical returns the same representative for all associates of any particular element.")) (|fmecg| (($ $ |#2| |#1| $) "\\spad{fmecg(p1,e,r,p2)} finds \\spad{X} : \\spad{p1} - \\spad{r} * X**e * \\spad{p2}"))) (((-4510 "*") |has| |#1| (-175)) (-4501 |has| |#1| (-571)) (-4506 |has| |#1| (-6 -4506)) (-4502 . T) (-4503 . T) (-4505 . T)) -((|HasCategory| |#1| (|%list| (QUOTE -38) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#1| (QUOTE (-571))) (-2181 (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-571)))) (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-149))) (-2181 (|HasCategory| |#1| (|%list| (QUOTE -38) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#1| (|%list| (QUOTE -1069) (|%list| (QUOTE -421) (QUOTE (-560)))))) (|HasCategory| |#1| (|%list| (QUOTE -1069) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#1| (|%list| (QUOTE -1069) (QUOTE (-560)))) (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (QUOTE (-466))) (-12 (|HasCategory| |#1| (QUOTE (-571))) (|HasCategory| |#2| (QUOTE (-133)))) (|HasAttribute| |#1| (QUOTE -4506))) +((|HasCategory| |#1| (|%list| (QUOTE -38) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#1| (QUOTE (-571))) (-2173 (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-571)))) (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-149))) (-2173 (|HasCategory| |#1| (|%list| (QUOTE -38) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#1| (|%list| (QUOTE -1069) (|%list| (QUOTE -421) (QUOTE (-560)))))) (|HasCategory| |#1| (|%list| (QUOTE -1069) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#1| (|%list| (QUOTE -1069) (QUOTE (-560)))) (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (QUOTE (-466))) (-12 (|HasCategory| |#1| (QUOTE (-571))) (|HasCategory| |#2| (QUOTE (-133)))) (|HasAttribute| |#1| (QUOTE -4506))) (-986 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 @@ -3879,7 +3879,7 @@ NIL (-987 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"))) ((-4509 . T) (-4508 . T)) -((-2181 (-12 (|HasCategory| |#1| (QUOTE (-871))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1132))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|))))) (-2181 (-12 (|HasCategory| |#1| (QUOTE (-1132))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-887))))) (|HasCategory| |#1| (|%list| (QUOTE -633) (QUOTE (-549)))) (-2181 (|HasCategory| |#1| (QUOTE (-871))) (|HasCategory| |#1| (QUOTE (-1132)))) (|HasCategory| |#1| (QUOTE (-871))) (-2181 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-871))) (|HasCategory| |#1| (QUOTE (-1132)))) (|HasCategory| (-560) (QUOTE (-871))) (|HasCategory| |#1| (QUOTE (-1132))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-887)))) (|HasCategory| |#1| (QUOTE (-102))) (-12 (|HasCategory| |#1| (QUOTE (-1132))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|))))) +((-2173 (-12 (|HasCategory| |#1| (QUOTE (-871))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1132))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|))))) (-2173 (-12 (|HasCategory| |#1| (QUOTE (-1132))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-887))))) (|HasCategory| |#1| (|%list| (QUOTE -633) (QUOTE (-549)))) (-2173 (|HasCategory| |#1| (QUOTE (-871))) (|HasCategory| |#1| (QUOTE (-1132)))) (|HasCategory| |#1| (QUOTE (-871))) (-2173 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-871))) (|HasCategory| |#1| (QUOTE (-1132)))) (|HasCategory| (-560) (QUOTE (-871))) (|HasCategory| |#1| (QUOTE (-1132))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-887)))) (|HasCategory| |#1| (QUOTE (-102))) (-12 (|HasCategory| |#1| (QUOTE (-1132))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|))))) (-988 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 @@ -3888,7 +3888,7 @@ 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 -(-990 -1596) +(-990 -1594) ((|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 @@ -3903,7 +3903,7 @@ NIL (-993 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"))) ((-4505 -12 (|has| |#2| (-487)) (|has| |#1| (-487)))) -((-2181 (-12 (|HasCategory| |#1| (QUOTE (-815))) (|HasCategory| |#2| (QUOTE (-815)))) (-12 (|HasCategory| |#1| (QUOTE (-871))) (|HasCategory| |#2| (QUOTE (-871))))) (-12 (|HasCategory| |#1| (QUOTE (-815))) (|HasCategory| |#2| (QUOTE (-815)))) (-2181 (-12 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#2| (QUOTE (-21)))) (-12 (|HasCategory| |#1| (QUOTE (-133))) (|HasCategory| |#2| (QUOTE (-133)))) (-12 (|HasCategory| |#1| (QUOTE (-815))) (|HasCategory| |#2| (QUOTE (-815))))) (-12 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#2| (QUOTE (-21)))) (-2181 (-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 (-815))) (|HasCategory| |#2| (QUOTE (-815))))) (-12 (|HasCategory| |#1| (QUOTE (-487))) (|HasCategory| |#2| (QUOTE (-487)))) (-2181 (-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)))) (-2181 (-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 (-815))) (|HasCategory| |#2| (QUOTE (-815))))) (-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 (-871))) (|HasCategory| |#2| (QUOTE (-871))))) +((-2173 (-12 (|HasCategory| |#1| (QUOTE (-815))) (|HasCategory| |#2| (QUOTE (-815)))) (-12 (|HasCategory| |#1| (QUOTE (-871))) (|HasCategory| |#2| (QUOTE (-871))))) (-12 (|HasCategory| |#1| (QUOTE (-815))) (|HasCategory| |#2| (QUOTE (-815)))) (-2173 (-12 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#2| (QUOTE (-21)))) (-12 (|HasCategory| |#1| (QUOTE (-133))) (|HasCategory| |#2| (QUOTE (-133)))) (-12 (|HasCategory| |#1| (QUOTE (-815))) (|HasCategory| |#2| (QUOTE (-815))))) (-12 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#2| (QUOTE (-21)))) (-2173 (-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 (-815))) (|HasCategory| |#2| (QUOTE (-815))))) (-12 (|HasCategory| |#1| (QUOTE (-487))) (|HasCategory| |#2| (QUOTE (-487)))) (-2173 (-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)))) (-2173 (-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 (-815))) (|HasCategory| |#2| (QUOTE (-815))))) (-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 (-871))) (|HasCategory| |#2| (QUOTE (-871))))) (-994) ((|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 @@ -3992,7 +3992,7 @@ 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 -(-1016 K R UP -1596) +(-1016 K R UP -1594) ((|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 @@ -4039,7 +4039,7 @@ NIL (-1027 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.}"))) ((-4501 |has| |#1| (-302)) (-4502 . T) (-4503 . T) (-4505 . T)) -((|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-149))) (|HasCategory| |#1| (|%list| (QUOTE -633) (QUOTE (-549)))) (|HasCategory| |#1| (QUOTE (-376))) (-2181 (|HasCategory| |#1| (QUOTE (-302))) (|HasCategory| |#1| (QUOTE (-376)))) (|HasCategory| |#1| (QUOTE (-302))) (|HasCategory| |#1| (QUOTE (-871))) (|HasCategory| |#1| (|%list| (QUOTE -660) (QUOTE (-560)))) (|HasCategory| |#1| (|%list| (QUOTE -528) (QUOTE (-1207)) (|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 -929) (QUOTE (-1207)))) (|HasCategory| |#1| (QUOTE (-240))) (|HasCategory| |#1| (|%list| (QUOTE -927) (QUOTE (-1207)))) (-2181 (|HasCategory| |#1| (|%list| (QUOTE -1069) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#1| (QUOTE (-376)))) (|HasCategory| |#1| (|%list| (QUOTE -1069) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#1| (|%list| (QUOTE -1069) (QUOTE (-560)))) (|HasCategory| |#1| (QUOTE (-1091))) (|HasCategory| |#1| (QUOTE (-559)))) +((|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-149))) (|HasCategory| |#1| (|%list| (QUOTE -633) (QUOTE (-549)))) (|HasCategory| |#1| (QUOTE (-376))) (-2173 (|HasCategory| |#1| (QUOTE (-302))) (|HasCategory| |#1| (QUOTE (-376)))) (|HasCategory| |#1| (QUOTE (-302))) (|HasCategory| |#1| (QUOTE (-871))) (|HasCategory| |#1| (|%list| (QUOTE -660) (QUOTE (-560)))) (|HasCategory| |#1| (|%list| (QUOTE -528) (QUOTE (-1207)) (|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 -929) (QUOTE (-1207)))) (|HasCategory| |#1| (QUOTE (-240))) (|HasCategory| |#1| (|%list| (QUOTE -927) (QUOTE (-1207)))) (-2173 (|HasCategory| |#1| (|%list| (QUOTE -1069) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#1| (QUOTE (-376)))) (|HasCategory| |#1| (|%list| (QUOTE -1069) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#1| (|%list| (QUOTE -1069) (QUOTE (-560)))) (|HasCategory| |#1| (QUOTE (-1091))) (|HasCategory| |#1| (QUOTE (-559)))) (-1028 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| $) "\\spad{imagI(q)} extracts the imaginary \\spad{i} part of quaternion \\spad{q}.")) (|conjugate| (($ $) "\\spad{conjugate(q)} negates the imaginary parts of quaternion \\spad{q}."))) NIL @@ -4055,7 +4055,7 @@ NIL (-1031 S) ((|constructor| (NIL "Linked List implementation of a Queue")) (|queue| (($ (|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}."))) ((-4508 . T) (-4509 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1132))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1132))) (-2181 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-1132)))) (-2181 (-12 (|HasCategory| |#1| (QUOTE (-1132))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-887))))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-887)))) (|HasCategory| |#1| (QUOTE (-102)))) +((-12 (|HasCategory| |#1| (QUOTE (-1132))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1132))) (-2173 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-1132)))) (-2173 (-12 (|HasCategory| |#1| (QUOTE (-1132))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-887))))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-887)))) (|HasCategory| |#1| (QUOTE (-102)))) (-1032 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| (($ $) "\\spad{sqrt(x)} returns the square root of \\spad{x}."))) NIL @@ -4064,14 +4064,14 @@ NIL ((|constructor| (NIL "The \\spad{RadicalCategory} is a model for the rational numbers.")) (** (($ $ (|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| (($ $) "\\spad{sqrt(x)} returns the square root of \\spad{x}."))) NIL NIL -(-1034 -1596 UP UPUP |radicnd| |n|) +(-1034 -1594 UP UPUP |radicnd| |n|) ((|constructor| (NIL "Function field defined by y**n = \\spad{f}(\\spad{x})."))) ((-4501 |has| (-421 |#2|) (-376)) (-4506 |has| (-421 |#2|) (-376)) (-4500 |has| (-421 |#2|) (-376)) ((-4510 "*") . 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(|fractRadix| (($ (|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."))) ((-4500 . T) (-4506 . T) (-4501 . T) ((-4510 "*") . T) (-4502 . T) (-4503 . T) (-4505 . T)) -((|HasCategory| (-560) (QUOTE (-939))) (|HasCategory| (-560) (|%list| (QUOTE -1069) (QUOTE (-1207)))) (|HasCategory| (-560) (QUOTE (-147))) (|HasCategory| (-560) (QUOTE (-149))) (|HasCategory| (-560) (|%list| (QUOTE -633) (QUOTE (-549)))) (|HasCategory| (-560) (QUOTE (-1051))) (|HasCategory| (-560) (QUOTE (-842))) (|HasCategory| (-560) (QUOTE (-871))) (-2181 (|HasCategory| (-560) (QUOTE (-842))) (|HasCategory| (-560) (QUOTE (-871)))) (|HasCategory| (-560) (|%list| (QUOTE -1069) (QUOTE (-560)))) (|HasCategory| (-560) (QUOTE (-1182))) (|HasCategory| (-560) (|%list| (QUOTE -911) (QUOTE (-391)))) (|HasCategory| (-560) (|%list| (QUOTE -911) (QUOTE (-560)))) (|HasCategory| (-560) (|%list| (QUOTE -633) (|%list| (QUOTE -915) (QUOTE (-391))))) (|HasCategory| (-560) (|%list| (QUOTE -633) (|%list| (QUOTE -915) (QUOTE (-560))))) (|HasCategory| (-560) (QUOTE (-239))) (|HasCategory| (-560) (|%list| (QUOTE -929) (QUOTE (-1207)))) (|HasCategory| (-560) (QUOTE (-240))) (|HasCategory| (-560) (|%list| (QUOTE -927) (QUOTE (-1207)))) (|HasCategory| (-560) (|%list| (QUOTE -528) (QUOTE (-1207)) (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 (-939)))) (-2181 (-12 (|HasCategory| $ (QUOTE (-147))) (|HasCategory| (-560) (QUOTE (-939)))) (|HasCategory| (-560) (QUOTE (-147))))) +((|HasCategory| (-560) (QUOTE (-939))) (|HasCategory| (-560) (|%list| (QUOTE -1069) (QUOTE (-1207)))) (|HasCategory| (-560) (QUOTE (-147))) (|HasCategory| (-560) (QUOTE (-149))) (|HasCategory| (-560) (|%list| (QUOTE -633) (QUOTE (-549)))) (|HasCategory| (-560) (QUOTE (-1051))) (|HasCategory| (-560) (QUOTE (-842))) (|HasCategory| (-560) (QUOTE (-871))) (-2173 (|HasCategory| (-560) (QUOTE (-842))) (|HasCategory| (-560) (QUOTE (-871)))) (|HasCategory| (-560) (|%list| (QUOTE -1069) (QUOTE (-560)))) (|HasCategory| (-560) (QUOTE (-1182))) (|HasCategory| (-560) (|%list| (QUOTE -911) (QUOTE (-391)))) (|HasCategory| (-560) (|%list| (QUOTE -911) (QUOTE (-560)))) (|HasCategory| (-560) (|%list| (QUOTE -633) (|%list| (QUOTE -915) (QUOTE (-391))))) (|HasCategory| (-560) (|%list| (QUOTE -633) (|%list| (QUOTE -915) (QUOTE (-560))))) (|HasCategory| (-560) (QUOTE (-239))) (|HasCategory| (-560) (|%list| (QUOTE -929) (QUOTE (-1207)))) (|HasCategory| (-560) (QUOTE (-240))) (|HasCategory| (-560) (|%list| (QUOTE -927) (QUOTE (-1207)))) (|HasCategory| (-560) (|%list| (QUOTE -528) (QUOTE (-1207)) (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 (-939)))) (-2173 (-12 (|HasCategory| $ (QUOTE (-147))) (|HasCategory| (-560) (QUOTE (-939)))) (|HasCategory| (-560) (QUOTE (-147))))) (-1036) ((|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 @@ -4104,19 +4104,19 @@ 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}}"))) ((-4501 . T) (-4506 . T) (-4500 . T) (-4503 . T) (-4502 . T) ((-4510 "*") . T) (-4505 . T)) NIL -(-1044 R -1596) +(-1044 R -1594) ((|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 -(-1045 R -1596) +(-1045 R -1594) ((|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 -(-1046 -1596 UP) +(-1046 -1594 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 -(-1047 -1596 UP) +(-1047 -1594 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 @@ -4151,8 +4151,8 @@ NIL (-1055 |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"))) ((-4501 . T) (-4506 . T) (-4500 . T) (-4503 . T) (-4502 . T) ((-4510 "*") . T) (-4505 . T)) -((-2181 (|HasCategory| (-421 (-560)) (|%list| (QUOTE -1069) (QUOTE (-560)))) (|HasCategory| |#1| (|%list| (QUOTE -1069) (QUOTE (-560))))) (|HasCategory| |#1| (|%list| (QUOTE -1069) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#1| (|%list| (QUOTE -1069) (QUOTE (-560)))) (|HasCategory| (-421 (-560)) (|%list| (QUOTE -1069) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| (-421 (-560)) (|%list| (QUOTE -1069) (QUOTE (-560))))) -(-1056 -1596 L) +((-2173 (|HasCategory| (-421 (-560)) (|%list| (QUOTE -1069) (QUOTE (-560)))) (|HasCategory| |#1| (|%list| (QUOTE -1069) (QUOTE (-560))))) (|HasCategory| |#1| (|%list| (QUOTE -1069) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#1| (|%list| (QUOTE -1069) (QUOTE (-560)))) (|HasCategory| (-421 (-560)) (|%list| (QUOTE -1069) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| (-421 (-560)) (|%list| (QUOTE -1069) (QUOTE (-560))))) +(-1056 -1594 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 @@ -4188,14 +4188,14 @@ 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 -(-1065 -1596 |Expon| |VarSet| |FPol| |LFPol|) +(-1065 -1594 |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"))) (((-4510 "*") . T) (-4502 . T) (-4503 . T) (-4505 . T)) NIL (-1066) ((|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.}"))) ((-4508 . T) (-4509 . T)) -((-12 (|HasCategory| (-2 (|:| -3819 (-1207)) (|:| -2913 (-51))) (QUOTE (-1132))) (|HasCategory| (-2 (|:| -3819 (-1207)) (|:| -2913 (-51))) (|%list| (QUOTE -321) (|%list| (QUOTE -2) (|%list| (QUOTE |:|) (QUOTE -3819) (QUOTE (-1207))) (|%list| (QUOTE |:|) (QUOTE -2913) (QUOTE (-51))))))) (-2181 (|HasCategory| (-2 (|:| -3819 (-1207)) (|:| -2913 (-51))) (QUOTE (-1132))) (|HasCategory| (-51) (QUOTE (-1132)))) (-2181 (|HasCategory| (-2 (|:| -3819 (-1207)) (|:| -2913 (-51))) (QUOTE (-102))) (|HasCategory| (-2 (|:| -3819 (-1207)) (|:| -2913 (-51))) (QUOTE (-1132))) (|HasCategory| (-51) (QUOTE (-102))) (|HasCategory| (-51) (QUOTE (-1132)))) (-2181 (|HasCategory| (-2 (|:| -3819 (-1207)) (|:| -2913 (-51))) (QUOTE (-1132))) (|HasCategory| (-2 (|:| -3819 (-1207)) (|:| -2913 (-51))) (|%list| (QUOTE -632) (QUOTE (-887)))) (|HasCategory| (-51) (QUOTE (-1132))) (|HasCategory| (-51) (|%list| (QUOTE -632) (QUOTE (-887))))) (|HasCategory| (-2 (|:| -3819 (-1207)) (|:| -2913 (-51))) (|%list| (QUOTE -633) (QUOTE (-549)))) (-12 (|HasCategory| (-51) (QUOTE (-1132))) (|HasCategory| (-51) (|%list| (QUOTE -321) (QUOTE (-51))))) (|HasCategory| (-2 (|:| -3819 (-1207)) (|:| -2913 (-51))) (QUOTE (-1132))) (|HasCategory| (-1207) (QUOTE (-871))) (|HasCategory| (-51) (QUOTE (-1132))) (-2181 (|HasCategory| (-2 (|:| -3819 (-1207)) (|:| -2913 (-51))) (|%list| (QUOTE -632) (QUOTE (-887)))) (|HasCategory| (-51) (|%list| (QUOTE -632) (QUOTE (-887))))) (-2181 (|HasCategory| (-2 (|:| -3819 (-1207)) (|:| -2913 (-51))) (QUOTE (-102))) (|HasCategory| (-51) (QUOTE (-102)))) (|HasCategory| (-51) (QUOTE (-102))) (|HasCategory| (-51) (|%list| (QUOTE -632) (QUOTE (-887)))) (|HasCategory| (-2 (|:| -3819 (-1207)) (|:| -2913 (-51))) (|%list| (QUOTE -632) (QUOTE (-887)))) (|HasCategory| (-2 (|:| -3819 (-1207)) (|:| -2913 (-51))) (QUOTE (-102)))) +((-12 (|HasCategory| (-2 (|:| -3835 (-1207)) (|:| -2923 (-51))) (QUOTE (-1132))) (|HasCategory| (-2 (|:| -3835 (-1207)) (|:| -2923 (-51))) (|%list| (QUOTE -321) (|%list| (QUOTE -2) (|%list| (QUOTE |:|) (QUOTE -3835) (QUOTE (-1207))) (|%list| (QUOTE |:|) (QUOTE -2923) (QUOTE (-51))))))) (-2173 (|HasCategory| (-2 (|:| -3835 (-1207)) (|:| -2923 (-51))) (QUOTE (-1132))) (|HasCategory| (-51) (QUOTE (-1132)))) (-2173 (|HasCategory| (-2 (|:| -3835 (-1207)) (|:| -2923 (-51))) (QUOTE (-102))) (|HasCategory| (-2 (|:| -3835 (-1207)) (|:| -2923 (-51))) (QUOTE (-1132))) (|HasCategory| (-51) (QUOTE (-102))) (|HasCategory| (-51) (QUOTE (-1132)))) (-2173 (|HasCategory| (-2 (|:| -3835 (-1207)) (|:| -2923 (-51))) (QUOTE (-1132))) (|HasCategory| (-2 (|:| -3835 (-1207)) (|:| -2923 (-51))) (|%list| (QUOTE -632) (QUOTE (-887)))) (|HasCategory| (-51) (QUOTE (-1132))) (|HasCategory| (-51) (|%list| (QUOTE -632) (QUOTE (-887))))) (|HasCategory| (-2 (|:| -3835 (-1207)) (|:| -2923 (-51))) (|%list| (QUOTE -633) (QUOTE (-549)))) (-12 (|HasCategory| (-51) (QUOTE (-1132))) (|HasCategory| (-51) (|%list| (QUOTE -321) (QUOTE (-51))))) (|HasCategory| (-2 (|:| -3835 (-1207)) (|:| -2923 (-51))) (QUOTE (-1132))) (|HasCategory| (-1207) (QUOTE (-871))) (|HasCategory| (-51) (QUOTE (-1132))) (-2173 (|HasCategory| (-2 (|:| -3835 (-1207)) (|:| -2923 (-51))) (|%list| (QUOTE -632) (QUOTE (-887)))) (|HasCategory| (-51) (|%list| (QUOTE -632) (QUOTE (-887))))) (-2173 (|HasCategory| (-2 (|:| -3835 (-1207)) (|:| -2923 (-51))) (QUOTE (-102))) (|HasCategory| (-51) (QUOTE (-102)))) (|HasCategory| (-51) (QUOTE (-102))) (|HasCategory| (-51) (|%list| (QUOTE -632) (QUOTE (-887)))) (|HasCategory| (-2 (|:| -3835 (-1207)) (|:| -2923 (-51))) (|%list| (QUOTE -632) (QUOTE (-887)))) (|HasCategory| (-2 (|:| -3835 (-1207)) (|:| -2923 (-51))) (QUOTE (-102)))) (-1067) ((|constructor| (NIL "This domain represents `return' expressions.")) (|expression| (((|SpadAst|) $) "\\spad{expression(e)} returns the expression returned by `e'."))) NIL @@ -4252,7 +4252,7 @@ NIL ((|constructor| (NIL "The category of rings with unity,{} always associative,{} but not necessarily commutative.")) (|unitsKnown| ((|attribute|) "recip truly yields reciprocal or \"failed\" if not a unit. Note: \\spad{recip(0) = \"failed\"}.")) (|characteristic| (((|NonNegativeInteger|)) "\\spad{characteristic()} returns the characteristic of the ring this is the smallest positive integer \\spad{n} such that \\spad{n*x=0} for all \\spad{x} in the ring,{} or zero if no such \\spad{n} exists."))) ((-4505 . T)) NIL -(-1081 |xx| -1596) +(-1081 |xx| -1594) ((|constructor| (NIL "This package exports rational interpolation algorithms"))) NIL NIL @@ -4271,7 +4271,7 @@ NIL (-1085 |m| |n| R) ((|constructor| (NIL "\\spadtype{RectangularMatrix} is a matrix domain where the number of rows and the number of columns are parameters of the domain.")) (|rectangularMatrix| (($ (|Matrix| |#3|)) "\\spad{rectangularMatrix(m)} converts a matrix of type \\spadtype{Matrix} to a matrix of type \\spad{RectangularMatrix}."))) ((-4508 . T) (-4503 . T) (-4502 . T)) -((|HasCategory| |#3| (QUOTE (-175))) (-2181 (-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 (-1132))) (|HasCategory| |#3| (|%list| (QUOTE -321) (|devaluate| |#3|))))) (|HasCategory| |#3| (|%list| (QUOTE -633) (QUOTE (-549)))) (-2181 (|HasCategory| |#3| (QUOTE (-175))) (|HasCategory| |#3| (QUOTE (-376)))) (|HasCategory| |#3| (QUOTE (-376))) (|HasCategory| |#3| (QUOTE (-1132))) (|HasCategory| |#3| (QUOTE (-319))) (|HasCategory| |#3| (QUOTE (-571))) (-12 (|HasCategory| |#3| (QUOTE (-1132))) (|HasCategory| |#3| (|%list| (QUOTE -321) (|devaluate| |#3|)))) (|HasCategory| |#3| (QUOTE (-102))) (|HasCategory| |#3| (|%list| (QUOTE -632) (QUOTE (-887))))) +((|HasCategory| |#3| (QUOTE (-175))) (-2173 (-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 (-1132))) (|HasCategory| |#3| (|%list| (QUOTE -321) (|devaluate| |#3|))))) (|HasCategory| |#3| (|%list| (QUOTE -633) (QUOTE (-549)))) (-2173 (|HasCategory| |#3| (QUOTE (-175))) (|HasCategory| |#3| (QUOTE (-376)))) (|HasCategory| |#3| (QUOTE (-376))) (|HasCategory| |#3| (QUOTE (-1132))) (|HasCategory| |#3| (QUOTE (-319))) (|HasCategory| |#3| (QUOTE (-571))) (-12 (|HasCategory| |#3| (QUOTE (-1132))) (|HasCategory| |#3| (|%list| (QUOTE -321) (|devaluate| |#3|)))) (|HasCategory| |#3| (QUOTE (-102))) (|HasCategory| |#3| (|%list| (QUOTE -632) (QUOTE (-887))))) (-1086 |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 @@ -4307,7 +4307,7 @@ NIL (-1094) ((|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}"))) ((-4508 . T) (-4509 . T)) -((-12 (|HasCategory| (-2 (|:| -3819 (-1207)) (|:| -2913 (-51))) (QUOTE (-1132))) (|HasCategory| (-2 (|:| -3819 (-1207)) (|:| -2913 (-51))) (|%list| (QUOTE -321) (|%list| (QUOTE -2) (|%list| (QUOTE |:|) (QUOTE -3819) (QUOTE (-1207))) (|%list| (QUOTE |:|) (QUOTE -2913) (QUOTE (-51))))))) (-2181 (|HasCategory| (-2 (|:| -3819 (-1207)) (|:| -2913 (-51))) (QUOTE (-1132))) (|HasCategory| (-51) (QUOTE (-1132)))) (-2181 (|HasCategory| (-2 (|:| -3819 (-1207)) (|:| -2913 (-51))) (QUOTE (-102))) (|HasCategory| (-2 (|:| -3819 (-1207)) (|:| -2913 (-51))) (QUOTE (-1132))) (|HasCategory| (-51) (QUOTE (-102))) (|HasCategory| (-51) (QUOTE (-1132)))) (-2181 (|HasCategory| (-2 (|:| -3819 (-1207)) (|:| -2913 (-51))) (QUOTE (-1132))) (|HasCategory| (-2 (|:| -3819 (-1207)) (|:| -2913 (-51))) (|%list| (QUOTE -632) (QUOTE (-887)))) (|HasCategory| (-51) (QUOTE (-1132))) (|HasCategory| (-51) (|%list| (QUOTE -632) (QUOTE (-887))))) (|HasCategory| (-2 (|:| -3819 (-1207)) (|:| -2913 (-51))) (|%list| (QUOTE -633) (QUOTE (-549)))) (-12 (|HasCategory| (-51) (QUOTE (-1132))) (|HasCategory| (-51) (|%list| (QUOTE -321) (QUOTE (-51))))) (|HasCategory| (-2 (|:| -3819 (-1207)) (|:| -2913 (-51))) (QUOTE (-1132))) (|HasCategory| (-1207) (QUOTE (-871))) (|HasCategory| (-51) (QUOTE (-1132))) (-2181 (|HasCategory| (-2 (|:| -3819 (-1207)) (|:| -2913 (-51))) (|%list| (QUOTE -632) (QUOTE (-887)))) (|HasCategory| (-51) (|%list| (QUOTE -632) (QUOTE (-887))))) (-2181 (|HasCategory| (-2 (|:| -3819 (-1207)) (|:| -2913 (-51))) (QUOTE (-102))) (|HasCategory| (-51) (QUOTE (-102)))) (|HasCategory| (-51) (QUOTE (-102))) (|HasCategory| (-51) (|%list| (QUOTE -632) (QUOTE (-887)))) (|HasCategory| (-2 (|:| -3819 (-1207)) (|:| -2913 (-51))) (|%list| (QUOTE -632) (QUOTE (-887)))) (|HasCategory| (-2 (|:| -3819 (-1207)) (|:| -2913 (-51))) (QUOTE (-102)))) +((-12 (|HasCategory| (-2 (|:| -3835 (-1207)) (|:| -2923 (-51))) (QUOTE (-1132))) (|HasCategory| (-2 (|:| -3835 (-1207)) (|:| -2923 (-51))) (|%list| (QUOTE -321) (|%list| (QUOTE -2) (|%list| (QUOTE |:|) (QUOTE -3835) (QUOTE (-1207))) (|%list| (QUOTE |:|) (QUOTE -2923) (QUOTE (-51))))))) (-2173 (|HasCategory| (-2 (|:| -3835 (-1207)) (|:| -2923 (-51))) (QUOTE (-1132))) (|HasCategory| (-51) (QUOTE (-1132)))) (-2173 (|HasCategory| (-2 (|:| -3835 (-1207)) (|:| -2923 (-51))) (QUOTE (-102))) (|HasCategory| (-2 (|:| -3835 (-1207)) (|:| -2923 (-51))) (QUOTE (-1132))) (|HasCategory| (-51) (QUOTE (-102))) (|HasCategory| (-51) (QUOTE (-1132)))) (-2173 (|HasCategory| (-2 (|:| -3835 (-1207)) (|:| -2923 (-51))) (QUOTE (-1132))) (|HasCategory| (-2 (|:| -3835 (-1207)) (|:| -2923 (-51))) (|%list| (QUOTE -632) (QUOTE (-887)))) (|HasCategory| (-51) (QUOTE (-1132))) (|HasCategory| (-51) (|%list| (QUOTE -632) (QUOTE (-887))))) (|HasCategory| (-2 (|:| -3835 (-1207)) (|:| -2923 (-51))) (|%list| (QUOTE -633) (QUOTE (-549)))) (-12 (|HasCategory| (-51) (QUOTE (-1132))) (|HasCategory| (-51) (|%list| (QUOTE -321) (QUOTE (-51))))) (|HasCategory| (-2 (|:| -3835 (-1207)) (|:| -2923 (-51))) (QUOTE (-1132))) (|HasCategory| (-1207) (QUOTE (-871))) (|HasCategory| (-51) (QUOTE (-1132))) (-2173 (|HasCategory| (-2 (|:| -3835 (-1207)) (|:| -2923 (-51))) (|%list| (QUOTE -632) (QUOTE (-887)))) (|HasCategory| (-51) (|%list| (QUOTE -632) (QUOTE (-887))))) (-2173 (|HasCategory| (-2 (|:| -3835 (-1207)) (|:| -2923 (-51))) (QUOTE (-102))) (|HasCategory| (-51) (QUOTE (-102)))) (|HasCategory| (-51) (QUOTE (-102))) (|HasCategory| (-51) (|%list| (QUOTE -632) (QUOTE (-887)))) (|HasCategory| (-2 (|:| -3835 (-1207)) (|:| -2923 (-51))) (|%list| (QUOTE -632) (QUOTE (-887)))) (|HasCategory| (-2 (|:| -3835 (-1207)) (|:| -2923 (-51))) (QUOTE (-102)))) (-1095 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 @@ -4352,7 +4352,7 @@ 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 -(-1106 |Base| R -1596) +(-1106 |Base| R -1594) ((|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 @@ -4360,7 +4360,7 @@ NIL ((|constructor| (NIL "This domain implements named rules")) (|name| (((|Symbol|) $) "\\spad{name(x)} returns the symbol"))) NIL NIL -(-1108 |Base| R -1596) +(-1108 |Base| R -1594) ((|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 @@ -4371,7 +4371,7 @@ NIL (-1110 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."))) ((-4501 |has| |#1| (-376)) (-4506 |has| |#1| (-376)) (-4500 |has| |#1| (-376)) ((-4510 "*") . T) (-4502 . T) (-4503 . T) (-4505 . T)) -((|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-149))) (|HasCategory| |#1| (QUOTE (-363))) (-2181 (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (QUOTE (-363)))) (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (QUOTE (-381))) (-2181 (-12 (|HasCategory| |#1| (QUOTE (-240))) (|HasCategory| |#1| (QUOTE (-376)))) (|HasCategory| |#1| (QUOTE (-363)))) (-2181 (-12 (|HasCategory| |#1| (QUOTE (-240))) (|HasCategory| |#1| (QUOTE (-376)))) (-12 (|HasCategory| |#1| (QUOTE (-239))) (|HasCategory| |#1| (QUOTE (-376)))) (|HasCategory| |#1| (QUOTE (-363)))) (-2181 (-12 (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (|%list| (QUOTE -927) (QUOTE (-1207))))) (-12 (|HasCategory| |#1| (QUOTE (-363))) (|HasCategory| |#1| (|%list| (QUOTE -927) (QUOTE (-1207)))))) (-2181 (-12 (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (|%list| (QUOTE -927) (QUOTE (-1207))))) (-12 (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (|%list| (QUOTE -929) (QUOTE (-1207)))))) (|HasCategory| |#1| (|%list| (QUOTE -660) (QUOTE (-560)))) (-2181 (|HasCategory| |#1| (|%list| (QUOTE -1069) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#1| (QUOTE (-376)))) (|HasCategory| |#1| (|%list| (QUOTE -1069) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#1| (|%list| (QUOTE -1069) (QUOTE (-560)))) (-2181 (-12 (|HasCategory| |#1| (QUOTE (-239))) (|HasCategory| |#1| (QUOTE (-376)))) (|HasCategory| |#1| (QUOTE (-363)))) (-12 (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (|%list| (QUOTE -929) (QUOTE (-1207))))) (-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 -927) (QUOTE (-1207)))))) +((|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-149))) (|HasCategory| |#1| (QUOTE (-363))) (-2173 (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (QUOTE (-363)))) (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (QUOTE (-381))) (-2173 (-12 (|HasCategory| |#1| (QUOTE (-240))) (|HasCategory| |#1| (QUOTE (-376)))) (|HasCategory| |#1| (QUOTE (-363)))) (-2173 (-12 (|HasCategory| |#1| (QUOTE (-240))) (|HasCategory| |#1| (QUOTE (-376)))) (-12 (|HasCategory| |#1| (QUOTE (-239))) (|HasCategory| |#1| (QUOTE (-376)))) (|HasCategory| |#1| (QUOTE (-363)))) (-2173 (-12 (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (|%list| (QUOTE -927) (QUOTE (-1207))))) (-12 (|HasCategory| |#1| (QUOTE (-363))) (|HasCategory| |#1| (|%list| (QUOTE -927) (QUOTE (-1207)))))) (-2173 (-12 (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (|%list| (QUOTE -927) (QUOTE (-1207))))) (-12 (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (|%list| (QUOTE -929) (QUOTE (-1207)))))) (|HasCategory| |#1| (|%list| (QUOTE -660) (QUOTE (-560)))) (-2173 (|HasCategory| |#1| (|%list| (QUOTE -1069) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#1| (QUOTE (-376)))) (|HasCategory| |#1| (|%list| (QUOTE -1069) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#1| (|%list| (QUOTE -1069) (QUOTE (-560)))) (-2173 (-12 (|HasCategory| |#1| (QUOTE (-239))) (|HasCategory| |#1| (QUOTE (-376)))) (|HasCategory| |#1| (QUOTE (-363)))) (-12 (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (|%list| (QUOTE -929) (QUOTE (-1207))))) (-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 -927) (QUOTE (-1207)))))) (-1111 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 @@ -4403,7 +4403,7 @@ NIL (-1118 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"))) (((-4510 "*") |has| |#1| (-175)) (-4501 |has| |#1| (-571)) (-4506 |has| |#1| (-6 -4506)) (-4503 . T) (-4502 . T) (-4505 . 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A sequential ranking is a ranking \\spadfun{<} of the derivatives with the property that for any derivative \\spad{v},{} there are only a finite number of derivatives \\spad{u} with \\spad{u} \\spadfun{<} \\spad{v}. This domain belongs to \\spadtype{DifferentialVariableCategory}. It defines \\spadfun{weight} to be just \\spadfun{order},{} and it defines a sequential ranking \\spadfun{<} on derivatives \\spad{u} by the lexicographic order on the pair (\\spadfun{variable}(\\spad{u}),{} \\spadfun{order}(\\spad{u}))."))) NIL @@ -4443,7 +4443,7 @@ NIL (-1128 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)}}"))) ((-4508 . T) (-4498 . T) (-4509 . 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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 @@ -4507,7 +4507,7 @@ NIL (-1144 |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. 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|#3| (|%list| (QUOTE -1069) (QUOTE (-560))))) (-12 (|HasCategory| |#3| (QUOTE (-240))) (|HasCategory| |#3| (|%list| (QUOTE -1069) (QUOTE (-560))))) (-12 (|HasCategory| |#3| (QUOTE (-376))) (|HasCategory| |#3| (|%list| (QUOTE -1069) (QUOTE (-560))))) (-12 (|HasCategory| |#3| (QUOTE (-381))) (|HasCategory| |#3| (|%list| (QUOTE -1069) (QUOTE (-560))))) (-12 (|HasCategory| |#3| (QUOTE (-748))) (|HasCategory| |#3| (|%list| (QUOTE -1069) (QUOTE (-560))))) (-12 (|HasCategory| |#3| (QUOTE (-815))) (|HasCategory| |#3| (|%list| (QUOTE -1069) (QUOTE (-560))))) (-12 (|HasCategory| |#3| (QUOTE (-871))) (|HasCategory| |#3| (|%list| (QUOTE -1069) (QUOTE (-560))))) (-12 (|HasCategory| |#3| (QUOTE (-1080))) (|HasCategory| |#3| (|%list| (QUOTE -1069) (QUOTE (-560))))) (-12 (|HasCategory| |#3| (QUOTE (-1132))) (|HasCategory| |#3| (|%list| (QUOTE -1069) (QUOTE (-560)))))) (|HasCategory| (-560) (QUOTE (-871))) (-12 (|HasCategory| |#3| (|%list| (QUOTE -660) (QUOTE (-560)))) (|HasCategory| |#3| (QUOTE (-1080)))) (-12 (|HasCategory| |#3| (QUOTE (-239))) (|HasCategory| |#3| (QUOTE (-1080)))) (-12 (|HasCategory| |#3| (QUOTE (-1080))) (|HasCategory| |#3| (|%list| (QUOTE -929) (QUOTE (-1207))))) (-2173 (|HasCategory| |#3| (QUOTE (-1080))) (-12 (|HasCategory| |#3| (QUOTE (-1132))) (|HasCategory| |#3| (|%list| (QUOTE -1069) (QUOTE (-560)))))) (-12 (|HasCategory| |#3| (QUOTE (-1132))) (|HasCategory| |#3| (|%list| (QUOTE -1069) (QUOTE (-560))))) (-12 (|HasCategory| |#3| (|%list| (QUOTE -1069) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#3| (QUOTE (-1132)))) (|HasAttribute| |#3| (QUOTE -4505)) (-12 (|HasCategory| |#3| (QUOTE (-240))) (|HasCategory| |#3| (QUOTE (-1080)))) (-12 (|HasCategory| |#3| (QUOTE (-1080))) (|HasCategory| |#3| (|%list| (QUOTE -927) (QUOTE (-1207))))) (|HasCategory| |#3| (QUOTE (-175))) (|HasCategory| |#3| (QUOTE (-23))) (|HasCategory| |#3| (QUOTE (-133))) (|HasCategory| |#3| (QUOTE (-25))) (|HasCategory| |#3| (|%list| (QUOTE -632) (QUOTE (-887)))) (|HasCategory| |#3| (QUOTE (-102))) (-12 (|HasCategory| |#3| (QUOTE (-1132))) (|HasCategory| |#3| (|%list| (QUOTE -321) (|devaluate| |#3|))))) (-1145 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 @@ -4520,7 +4520,7 @@ 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 -(-1148 R -1596) +(-1148 R -1594) ((|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 @@ -4555,16 +4555,16 @@ NIL (-1156 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."))) (((-4510 "*") |has| |#1| (-175)) (-4501 |has| |#1| (-571)) (-4506 |has| |#1| (-6 -4506)) (-4503 . T) (-4502 . T) (-4505 . T)) -((|HasCategory| |#1| (QUOTE (-939))) (-2181 (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-466))) (|HasCategory| |#1| (QUOTE (-571))) (|HasCategory| |#1| (QUOTE (-939)))) (-2181 (|HasCategory| |#1| (QUOTE (-466))) (|HasCategory| |#1| (QUOTE (-571))) (|HasCategory| |#1| (QUOTE (-939)))) (-2181 (|HasCategory| |#1| (QUOTE (-466))) (|HasCategory| |#1| (QUOTE (-939)))) (|HasCategory| |#1| (QUOTE (-571))) (|HasCategory| |#1| (QUOTE (-175))) (-2181 (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-571)))) (-12 (|HasCategory| |#1| (|%list| (QUOTE -911) (QUOTE (-391)))) (|HasCategory| |#2| (|%list| (QUOTE -911) (QUOTE (-391))))) (-12 (|HasCategory| |#1| (|%list| (QUOTE -911) (QUOTE (-560)))) (|HasCategory| |#2| (|%list| (QUOTE -911) (QUOTE (-560))))) (-12 (|HasCategory| |#1| (|%list| (QUOTE -633) (|%list| (QUOTE -915) (QUOTE (-391))))) (|HasCategory| |#2| (|%list| (QUOTE -633) (|%list| (QUOTE -915) (QUOTE (-391)))))) (-12 (|HasCategory| |#1| (|%list| (QUOTE -633) (|%list| (QUOTE -915) (QUOTE (-560))))) (|HasCategory| |#2| (|%list| (QUOTE -633) (|%list| (QUOTE -915) (QUOTE (-560)))))) (-12 (|HasCategory| |#1| (|%list| (QUOTE -633) (QUOTE (-549)))) (|HasCategory| |#2| (|%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 -1069) (QUOTE (-560)))) (-2181 (|HasCategory| |#1| (|%list| (QUOTE -38) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#1| (|%list| (QUOTE -1069) (|%list| (QUOTE -421) (QUOTE (-560)))))) (|HasCategory| |#1| (|%list| (QUOTE -1069) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#1| (QUOTE (-376))) (|HasAttribute| |#1| (QUOTE -4506)) (|HasCategory| |#1| (QUOTE (-466))) (-12 (|HasCategory| $ (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-939)))) (-2181 (-12 (|HasCategory| $ (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-939)))) (|HasCategory| |#1| (QUOTE (-147))))) +((|HasCategory| |#1| (QUOTE (-939))) (-2173 (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-466))) (|HasCategory| |#1| (QUOTE (-571))) (|HasCategory| |#1| (QUOTE (-939)))) (-2173 (|HasCategory| |#1| (QUOTE (-466))) (|HasCategory| |#1| (QUOTE (-571))) (|HasCategory| |#1| (QUOTE (-939)))) (-2173 (|HasCategory| |#1| (QUOTE (-466))) (|HasCategory| |#1| (QUOTE (-939)))) (|HasCategory| |#1| (QUOTE (-571))) (|HasCategory| |#1| (QUOTE (-175))) (-2173 (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-571)))) (-12 (|HasCategory| |#1| (|%list| (QUOTE -911) (QUOTE (-391)))) (|HasCategory| |#2| (|%list| (QUOTE -911) (QUOTE (-391))))) (-12 (|HasCategory| |#1| (|%list| (QUOTE -911) (QUOTE (-560)))) (|HasCategory| |#2| (|%list| (QUOTE -911) (QUOTE (-560))))) (-12 (|HasCategory| |#1| (|%list| (QUOTE -633) (|%list| (QUOTE -915) (QUOTE (-391))))) (|HasCategory| |#2| (|%list| (QUOTE -633) (|%list| (QUOTE -915) (QUOTE (-391)))))) (-12 (|HasCategory| |#1| (|%list| (QUOTE -633) (|%list| (QUOTE -915) (QUOTE (-560))))) (|HasCategory| |#2| (|%list| (QUOTE -633) (|%list| (QUOTE -915) (QUOTE (-560)))))) (-12 (|HasCategory| |#1| (|%list| (QUOTE -633) (QUOTE (-549)))) (|HasCategory| |#2| (|%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 -1069) (QUOTE (-560)))) (-2173 (|HasCategory| |#1| (|%list| (QUOTE -38) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#1| (|%list| (QUOTE -1069) (|%list| (QUOTE -421) (QUOTE (-560)))))) (|HasCategory| |#1| (|%list| (QUOTE -1069) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#1| (QUOTE (-376))) (|HasAttribute| |#1| (QUOTE -4506)) (|HasCategory| |#1| (QUOTE (-466))) (-12 (|HasCategory| $ (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-939)))) (-2173 (-12 (|HasCategory| $ (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-939)))) (|HasCategory| |#1| (QUOTE (-147))))) (-1157 |Coef| |Var| SMP) ((|constructor| (NIL "This domain provides multivariate Taylor series with variables from an arbitrary ordered set. A Taylor series is represented by a stream of polynomials from the polynomial domain SMP. The \\spad{n}th element of the stream is a form of degree \\spad{n}. SMTS is an internal domain.")) (|fintegrate| (($ (|Mapping| $) |#2| |#1|) "\\spad{fintegrate(f,v,c)} is the integral of \\spad{f()} with respect \\indented{1}{to \\spad{v} and having \\spad{c} as the constant of integration.} \\indented{1}{The evaluation of \\spad{f()} is delayed.}")) (|integrate| (($ $ |#2| |#1|) "\\spad{integrate(s,v,c)} is the integral of \\spad{s} with respect \\indented{1}{to \\spad{v} and having \\spad{c} as the constant of integration.}")) (|csubst| (((|Mapping| (|Stream| |#3|) |#3|) (|List| |#2|) (|List| (|Stream| |#3|))) "\\spad{csubst(a,b)} is for internal use only")) (* (($ |#3| $) "\\spad{smp*ts} multiplies a TaylorSeries by a monomial SMP.")) (|coerce| (($ |#3|) "\\spad{coerce(poly)} regroups the terms by total degree and forms a series.") (($ |#2|) "\\spad{coerce(var)} converts a variable to a Taylor series")) (|coefficient| ((|#3| $ (|NonNegativeInteger|)) "\\spad{coefficient(s, n)} gives the terms of total degree \\spad{n}."))) (((-4510 "*") |has| |#1| (-175)) (-4501 |has| |#1| (-571)) (-4503 . T) (-4502 . T) (-4505 . T)) -((|HasCategory| |#1| (|%list| (QUOTE -38) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-149))) (|HasCategory| |#1| (QUOTE (-147))) (-2181 (|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))) (-2173 (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-571)))) (|HasCategory| |#1| (QUOTE (-571))) (|HasCategory| |#1| (QUOTE (-376)))) (-1158 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}"))) ((-4509 . T) (-4508 . T)) NIL -(-1159 UP -1596) +(-1159 UP -1594) ((|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 @@ -4619,11 +4619,11 @@ NIL (-1172 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."))) ((-4508 . T) (-4509 . T)) -((-12 (|HasCategory| (-1171 |#1| |#2|) (|%list| (QUOTE -321) (|%list| (QUOTE -1171) (|devaluate| |#1|) (|devaluate| |#2|)))) (|HasCategory| (-1171 |#1| |#2|) (QUOTE (-1132)))) (|HasCategory| (-1171 |#1| |#2|) (QUOTE (-1132))) (-2181 (|HasCategory| (-1171 |#1| |#2|) (QUOTE (-102))) (|HasCategory| (-1171 |#1| |#2|) (QUOTE (-1132)))) (-2181 (|HasCategory| (-1171 |#1| |#2|) (|%list| (QUOTE -632) (QUOTE (-887)))) (-12 (|HasCategory| (-1171 |#1| |#2|) (|%list| (QUOTE -321) (|%list| (QUOTE -1171) (|devaluate| |#1|) (|devaluate| |#2|)))) (|HasCategory| (-1171 |#1| |#2|) (QUOTE (-1132))))) (|HasCategory| (-1171 |#1| |#2|) (|%list| (QUOTE -632) (QUOTE (-887)))) (|HasCategory| (-1171 |#1| |#2|) (QUOTE (-102)))) +((-12 (|HasCategory| (-1171 |#1| |#2|) (|%list| (QUOTE -321) (|%list| (QUOTE -1171) (|devaluate| |#1|) (|devaluate| |#2|)))) (|HasCategory| (-1171 |#1| |#2|) (QUOTE (-1132)))) (|HasCategory| (-1171 |#1| |#2|) (QUOTE (-1132))) (-2173 (|HasCategory| (-1171 |#1| |#2|) (QUOTE (-102))) (|HasCategory| (-1171 |#1| |#2|) (QUOTE (-1132)))) (-2173 (|HasCategory| (-1171 |#1| |#2|) (|%list| (QUOTE -632) (QUOTE (-887)))) (-12 (|HasCategory| (-1171 |#1| |#2|) (|%list| (QUOTE -321) (|%list| (QUOTE -1171) (|devaluate| |#1|) (|devaluate| |#2|)))) (|HasCategory| (-1171 |#1| |#2|) (QUOTE (-1132))))) (|HasCategory| (-1171 |#1| |#2|) (|%list| (QUOTE -632) (QUOTE (-887)))) (|HasCategory| (-1171 |#1| |#2|) (QUOTE (-102)))) (-1173 |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}."))) ((-4505 . T) (-4497 |has| |#2| (-6 (-4510 "*"))) (-4508 . T) (-4502 . T) (-4503 . T)) -((|HasCategory| |#2| (|%list| (QUOTE -927) (QUOTE (-1207)))) (|HasCategory| |#2| (|%list| (QUOTE -929) (QUOTE (-1207)))) (|HasCategory| |#2| (QUOTE (-240))) (|HasCategory| |#2| (QUOTE (-239))) (|HasAttribute| |#2| (QUOTE (-4510 "*"))) (|HasCategory| |#2| (|%list| (QUOTE -660) (QUOTE (-560)))) (|HasCategory| |#2| (|%list| (QUOTE -1069) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#2| (|%list| (QUOTE -1069) (QUOTE (-560)))) (-2181 (-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 (-1132))) (|HasCategory| |#2| (|%list| (QUOTE -321) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (|%list| (QUOTE -321) (|devaluate| |#2|))) (|HasCategory| |#2| (|%list| (QUOTE -927) (QUOTE (-1207)))))) (|HasCategory| |#2| (|%list| (QUOTE -633) (QUOTE (-549)))) (|HasCategory| |#2| (QUOTE (-319))) (|HasCategory| |#2| (QUOTE (-571))) (|HasCategory| |#2| (QUOTE (-1132))) (|HasCategory| |#2| (QUOTE (-376))) (-2181 (|HasAttribute| |#2| (QUOTE (-4510 "*"))) (|HasCategory| |#2| (|%list| (QUOTE -927) (QUOTE (-1207)))) (|HasCategory| |#2| (QUOTE (-240)))) (|HasCategory| |#2| (|%list| (QUOTE -632) (QUOTE (-887)))) (|HasCategory| |#2| (QUOTE (-102))) (-12 (|HasCategory| |#2| (QUOTE (-1132))) (|HasCategory| |#2| (|%list| (QUOTE -321) (|devaluate| |#2|)))) (|HasCategory| |#2| (QUOTE (-175)))) +((|HasCategory| |#2| (|%list| (QUOTE -927) (QUOTE (-1207)))) (|HasCategory| |#2| (|%list| (QUOTE -929) (QUOTE (-1207)))) (|HasCategory| |#2| (QUOTE (-240))) (|HasCategory| |#2| (QUOTE (-239))) (|HasAttribute| |#2| (QUOTE (-4510 "*"))) (|HasCategory| |#2| (|%list| (QUOTE -660) (QUOTE (-560)))) (|HasCategory| |#2| (|%list| (QUOTE -1069) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#2| (|%list| (QUOTE -1069) (QUOTE (-560)))) (-2173 (-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 (-1132))) (|HasCategory| |#2| (|%list| (QUOTE -321) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (|%list| (QUOTE -321) (|devaluate| |#2|))) (|HasCategory| |#2| (|%list| (QUOTE -927) (QUOTE (-1207)))))) (|HasCategory| |#2| (|%list| (QUOTE -633) (QUOTE (-549)))) (|HasCategory| |#2| (QUOTE (-319))) (|HasCategory| |#2| (QUOTE (-571))) (|HasCategory| |#2| (QUOTE (-1132))) (|HasCategory| |#2| (QUOTE (-376))) (-2173 (|HasAttribute| |#2| (QUOTE (-4510 "*"))) (|HasCategory| |#2| (|%list| (QUOTE -927) (QUOTE (-1207)))) (|HasCategory| |#2| (QUOTE (-240)))) (|HasCategory| |#2| (|%list| (QUOTE -632) (QUOTE (-887)))) (|HasCategory| |#2| (QUOTE (-102))) (-12 (|HasCategory| |#2| (QUOTE (-1132))) (|HasCategory| |#2| (|%list| (QUOTE -321) (|devaluate| |#2|)))) (|HasCategory| |#2| (QUOTE (-175)))) (-1174 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|) $ $) "\\spad{prefix?(s,t)} tests if the string \\spad{s} is the initial substring of \\spad{t}. Note: \\axiom{prefix?(\\spad{s},{}\\spad{t}) == reduce(and,{}[\\spad{s}.\\spad{i} = \\spad{t}.\\spad{i} for \\spad{i} in 0..maxIndex \\spad{s}])}.")) (|upperCase!| (($ $) "\\spad{upperCase!(s)} destructively replaces the alphabetic characters in \\spad{s} by upper case characters.")) (|upperCase| (($ $) "\\spad{upperCase(s)} returns the string with all characters in upper case.")) (|lowerCase!| (($ $) "\\spad{lowerCase!(s)} destructively replaces the alphabetic characters in \\spad{s} by lower case.")) (|lowerCase| (($ $) "\\spad{lowerCase(s)} returns the string with all characters in lower case."))) NIL @@ -4643,7 +4643,7 @@ NIL (-1178 S) ((|constructor| (NIL "Linked List implementation of a Stack")) (|stack| (($ (|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}."))) ((-4508 . T) (-4509 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1132))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1132))) (-2181 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-1132)))) (-2181 (-12 (|HasCategory| |#1| (QUOTE (-1132))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-887))))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-887)))) (|HasCategory| |#1| (QUOTE (-102)))) +((-12 (|HasCategory| |#1| (QUOTE (-1132))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1132))) (-2173 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-1132)))) (-2173 (-12 (|HasCategory| |#1| (QUOTE (-1132))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-887))))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-887)))) (|HasCategory| |#1| (QUOTE (-102)))) (-1179 A S) ((|constructor| (NIL "A stream aggregate is a linear aggregate which possibly has an infinite number of elements. A basic domain constructor which builds stream aggregates is \\spadtype{Stream}. From streams,{} a number of infinite structures such power series can be built. A stream aggregate may also be infinite since it may be cyclic. For example,{} see \\spadtype{DecimalExpansion}.")) (|possiblyInfinite?| (((|Boolean|) $) "\\spad{possiblyInfinite?(s)} tests if the stream \\spad{s} could possibly have an infinite number of elements. Note: for many datatypes,{} \\axiom{possiblyInfinite?(\\spad{s}) = not explictlyFinite?(\\spad{s})}.")) (|explicitlyFinite?| (((|Boolean|) $) "\\spad{explicitlyFinite?(s)} tests if the stream has a finite number of elements,{} and \\spad{false} otherwise. Note: for many datatypes,{} \\axiom{explicitlyFinite?(\\spad{s}) = not possiblyInfinite?(\\spad{s})}."))) NIL @@ -4655,7 +4655,7 @@ NIL (-1181 |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."))) ((-4509 . T)) -((-12 (|HasCategory| (-2 (|:| -3819 |#1|) (|:| -2913 |#2|)) (QUOTE (-1132))) (|HasCategory| (-2 (|:| -3819 |#1|) (|:| -2913 |#2|)) (|%list| (QUOTE -321) (|%list| (QUOTE -2) (|%list| (QUOTE |:|) (QUOTE -3819) (|devaluate| |#1|)) (|%list| (QUOTE |:|) (QUOTE -2913) (|devaluate| |#2|)))))) (-2181 (|HasCategory| (-2 (|:| -3819 |#1|) (|:| -2913 |#2|)) (QUOTE (-1132))) (|HasCategory| |#2| (QUOTE (-1132)))) (-2181 (|HasCategory| (-2 (|:| -3819 |#1|) (|:| -2913 |#2|)) (QUOTE (-102))) (|HasCategory| (-2 (|:| -3819 |#1|) (|:| -2913 |#2|)) (QUOTE (-1132))) (|HasCategory| |#2| (QUOTE (-102))) (|HasCategory| |#2| (QUOTE (-1132)))) (-2181 (|HasCategory| (-2 (|:| -3819 |#1|) (|:| -2913 |#2|)) (QUOTE (-1132))) (|HasCategory| (-2 (|:| -3819 |#1|) (|:| -2913 |#2|)) (|%list| (QUOTE -632) (QUOTE (-887)))) (|HasCategory| |#2| (QUOTE (-1132))) (|HasCategory| |#2| (|%list| (QUOTE -632) (QUOTE (-887))))) (|HasCategory| (-2 (|:| -3819 |#1|) (|:| -2913 |#2|)) (|%list| (QUOTE -633) (QUOTE (-549)))) (-12 (|HasCategory| |#2| (QUOTE (-1132))) (|HasCategory| |#2| (|%list| (QUOTE -321) (|devaluate| |#2|)))) (|HasCategory| |#1| (QUOTE (-871))) (-2181 (|HasCategory| (-2 (|:| -3819 |#1|) (|:| -2913 |#2|)) (QUOTE (-102))) (|HasCategory| |#2| (QUOTE (-102)))) (-2181 (|HasCategory| (-2 (|:| -3819 |#1|) (|:| -2913 |#2|)) (|%list| (QUOTE -632) (QUOTE (-887)))) (|HasCategory| |#2| (|%list| (QUOTE -632) (QUOTE (-887))))) (|HasCategory| |#2| (QUOTE (-1132))) (|HasCategory| |#2| (QUOTE (-102))) (|HasCategory| |#2| (|%list| (QUOTE -632) (QUOTE (-887)))) (|HasCategory| (-2 (|:| -3819 |#1|) (|:| -2913 |#2|)) (|%list| (QUOTE -632) (QUOTE (-887)))) (|HasCategory| (-2 (|:| -3819 |#1|) (|:| -2913 |#2|)) (QUOTE (-102))) (|HasCategory| (-2 (|:| -3819 |#1|) (|:| -2913 |#2|)) (QUOTE (-1132)))) +((-12 (|HasCategory| (-2 (|:| -3835 |#1|) (|:| -2923 |#2|)) (QUOTE (-1132))) (|HasCategory| (-2 (|:| -3835 |#1|) (|:| -2923 |#2|)) (|%list| (QUOTE -321) (|%list| (QUOTE -2) (|%list| (QUOTE |:|) (QUOTE -3835) (|devaluate| |#1|)) (|%list| (QUOTE |:|) (QUOTE -2923) (|devaluate| |#2|)))))) (-2173 (|HasCategory| (-2 (|:| -3835 |#1|) (|:| -2923 |#2|)) (QUOTE (-1132))) (|HasCategory| |#2| (QUOTE (-1132)))) (-2173 (|HasCategory| (-2 (|:| -3835 |#1|) (|:| -2923 |#2|)) (QUOTE (-102))) (|HasCategory| (-2 (|:| -3835 |#1|) (|:| -2923 |#2|)) (QUOTE (-1132))) (|HasCategory| |#2| (QUOTE (-102))) (|HasCategory| |#2| (QUOTE (-1132)))) (-2173 (|HasCategory| (-2 (|:| -3835 |#1|) (|:| -2923 |#2|)) (QUOTE (-1132))) (|HasCategory| (-2 (|:| -3835 |#1|) (|:| -2923 |#2|)) (|%list| (QUOTE -632) (QUOTE (-887)))) (|HasCategory| |#2| (QUOTE (-1132))) (|HasCategory| |#2| (|%list| (QUOTE -632) (QUOTE (-887))))) (|HasCategory| (-2 (|:| -3835 |#1|) (|:| -2923 |#2|)) (|%list| (QUOTE -633) (QUOTE (-549)))) (-12 (|HasCategory| |#2| (QUOTE (-1132))) (|HasCategory| |#2| (|%list| (QUOTE -321) (|devaluate| |#2|)))) (|HasCategory| |#1| (QUOTE (-871))) (-2173 (|HasCategory| (-2 (|:| -3835 |#1|) (|:| -2923 |#2|)) (QUOTE (-102))) (|HasCategory| |#2| (QUOTE (-102)))) (-2173 (|HasCategory| (-2 (|:| -3835 |#1|) (|:| -2923 |#2|)) (|%list| (QUOTE -632) (QUOTE (-887)))) (|HasCategory| |#2| (|%list| (QUOTE -632) (QUOTE (-887))))) (|HasCategory| |#2| (QUOTE (-1132))) (|HasCategory| |#2| (QUOTE (-102))) (|HasCategory| |#2| (|%list| (QUOTE -632) (QUOTE (-887)))) (|HasCategory| (-2 (|:| -3835 |#1|) (|:| -2923 |#2|)) (|%list| (QUOTE -632) (QUOTE (-887)))) (|HasCategory| (-2 (|:| -3835 |#1|) (|:| -2923 |#2|)) (QUOTE (-102))) (|HasCategory| (-2 (|:| -3835 |#1|) (|:| -2923 |#2|)) (QUOTE (-1132)))) (-1182) ((|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 \"failed\".}")) (|nextItem| (((|Union| $ "failed") $) "\\spad{nextItem(x)} returns the next item,{} or \"failed\" if domain is exhausted.")) (|init| (($) "\\spad{init()} chooses an initial object for stepping."))) NIL @@ -4671,7 +4671,7 @@ NIL (-1185 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."))) ((-4509 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1132))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1132))) (-2181 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-1132)))) (-2181 (-12 (|HasCategory| |#1| (QUOTE (-1132))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-887))))) (|HasCategory| |#1| (|%list| (QUOTE -633) (QUOTE (-549)))) (|HasCategory| (-560) (QUOTE (-871))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-887)))) (|HasCategory| |#1| (QUOTE (-102)))) +((-12 (|HasCategory| |#1| (QUOTE (-1132))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1132))) (-2173 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-1132)))) (-2173 (-12 (|HasCategory| |#1| (QUOTE (-1132))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-887))))) (|HasCategory| |#1| (|%list| (QUOTE -633) (QUOTE (-549)))) (|HasCategory| (-560) (QUOTE (-871))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-887)))) (|HasCategory| |#1| (QUOTE (-102)))) (-1186 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 @@ -4687,11 +4687,11 @@ NIL (-1189) ((|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"))) ((-4509 . T) (-4508 . T)) -((-2181 (-12 (|HasCategory| (-146) (QUOTE (-871))) (|HasCategory| (-146) (|%list| (QUOTE -321) (QUOTE (-146))))) (-12 (|HasCategory| (-146) (QUOTE (-1132))) (|HasCategory| (-146) (|%list| (QUOTE -321) (QUOTE (-146)))))) (-2181 (|HasCategory| (-146) (|%list| (QUOTE -632) (QUOTE (-887)))) (-12 (|HasCategory| (-146) (QUOTE (-1132))) (|HasCategory| (-146) (|%list| (QUOTE -321) (QUOTE (-146)))))) (|HasCategory| (-146) (|%list| (QUOTE -633) (QUOTE (-549)))) (-2181 (|HasCategory| (-146) (QUOTE (-871))) (|HasCategory| (-146) (QUOTE (-1132)))) (|HasCategory| (-146) (QUOTE (-871))) (-2181 (|HasCategory| (-146) (QUOTE (-102))) (|HasCategory| (-146) (QUOTE (-871))) (|HasCategory| (-146) (QUOTE (-1132)))) (|HasCategory| (-560) (QUOTE (-871))) (|HasCategory| (-146) (QUOTE (-1132))) (|HasCategory| (-146) (|%list| (QUOTE -632) (QUOTE (-887)))) (|HasCategory| (-146) (QUOTE (-102))) (-12 (|HasCategory| (-146) (QUOTE (-1132))) (|HasCategory| (-146) (|%list| (QUOTE -321) (QUOTE (-146)))))) +((-2173 (-12 (|HasCategory| (-146) (QUOTE (-871))) (|HasCategory| (-146) (|%list| (QUOTE -321) (QUOTE (-146))))) (-12 (|HasCategory| (-146) (QUOTE (-1132))) (|HasCategory| (-146) (|%list| (QUOTE -321) (QUOTE (-146)))))) (-2173 (|HasCategory| (-146) (|%list| (QUOTE -632) (QUOTE (-887)))) (-12 (|HasCategory| (-146) (QUOTE (-1132))) (|HasCategory| (-146) (|%list| (QUOTE -321) (QUOTE (-146)))))) (|HasCategory| (-146) (|%list| (QUOTE -633) (QUOTE (-549)))) (-2173 (|HasCategory| (-146) (QUOTE (-871))) (|HasCategory| (-146) (QUOTE (-1132)))) (|HasCategory| (-146) (QUOTE (-871))) (-2173 (|HasCategory| (-146) (QUOTE (-102))) (|HasCategory| (-146) (QUOTE (-871))) (|HasCategory| (-146) (QUOTE (-1132)))) (|HasCategory| (-560) (QUOTE (-871))) (|HasCategory| (-146) (QUOTE (-1132))) (|HasCategory| (-146) (|%list| (QUOTE -632) (QUOTE (-887)))) (|HasCategory| (-146) (QUOTE (-102))) (-12 (|HasCategory| (-146) (QUOTE (-1132))) (|HasCategory| (-146) (|%list| (QUOTE -321) (QUOTE (-146)))))) (-1190 |Entry|) ((|constructor| (NIL "This domain provides tables where the keys are strings. A specialized hash function for strings is used."))) ((-4508 . T) (-4509 . T)) -((-12 (|HasCategory| (-2 (|:| -3819 (-1189)) (|:| -2913 |#1|)) (QUOTE (-1132))) (|HasCategory| (-2 (|:| -3819 (-1189)) (|:| -2913 |#1|)) (|%list| (QUOTE -321) (|%list| (QUOTE -2) (|%list| (QUOTE |:|) (QUOTE -3819) (QUOTE (-1189))) (|%list| (QUOTE |:|) (QUOTE -2913) (|devaluate| |#1|)))))) (-2181 (|HasCategory| (-2 (|:| -3819 (-1189)) (|:| -2913 |#1|)) (QUOTE (-1132))) (|HasCategory| |#1| (QUOTE (-1132)))) (-2181 (|HasCategory| (-2 (|:| -3819 (-1189)) (|:| -2913 |#1|)) (QUOTE (-102))) (|HasCategory| (-2 (|:| -3819 (-1189)) (|:| -2913 |#1|)) (QUOTE (-1132))) (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-1132)))) (-2181 (|HasCategory| (-2 (|:| -3819 (-1189)) (|:| -2913 |#1|)) (QUOTE (-1132))) (|HasCategory| (-2 (|:| -3819 (-1189)) (|:| -2913 |#1|)) (|%list| (QUOTE -632) (QUOTE (-887)))) (|HasCategory| |#1| (QUOTE (-1132))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-887))))) (|HasCategory| (-2 (|:| -3819 (-1189)) (|:| -2913 |#1|)) (|%list| (QUOTE -633) (QUOTE (-549)))) (-12 (|HasCategory| |#1| (QUOTE (-1132))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| (-2 (|:| -3819 (-1189)) (|:| -2913 |#1|)) (QUOTE (-1132))) (|HasCategory| (-1189) (QUOTE (-871))) (|HasCategory| |#1| (QUOTE (-1132))) (-2181 (|HasCategory| (-2 (|:| -3819 (-1189)) (|:| -2913 |#1|)) (|%list| (QUOTE -632) (QUOTE (-887)))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-887))))) (-2181 (|HasCategory| (-2 (|:| -3819 (-1189)) (|:| -2913 |#1|)) (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-102)))) (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-887)))) (|HasCategory| (-2 (|:| -3819 (-1189)) (|:| -2913 |#1|)) (|%list| (QUOTE -632) (QUOTE (-887)))) (|HasCategory| (-2 (|:| -3819 (-1189)) (|:| -2913 |#1|)) (QUOTE (-102)))) +((-12 (|HasCategory| (-2 (|:| -3835 (-1189)) (|:| -2923 |#1|)) (QUOTE (-1132))) (|HasCategory| (-2 (|:| -3835 (-1189)) (|:| -2923 |#1|)) (|%list| (QUOTE -321) (|%list| (QUOTE -2) (|%list| (QUOTE |:|) (QUOTE -3835) (QUOTE (-1189))) (|%list| (QUOTE |:|) (QUOTE -2923) (|devaluate| |#1|)))))) (-2173 (|HasCategory| (-2 (|:| -3835 (-1189)) (|:| -2923 |#1|)) (QUOTE (-1132))) (|HasCategory| |#1| (QUOTE (-1132)))) (-2173 (|HasCategory| (-2 (|:| -3835 (-1189)) (|:| -2923 |#1|)) (QUOTE (-102))) (|HasCategory| (-2 (|:| -3835 (-1189)) (|:| -2923 |#1|)) (QUOTE (-1132))) (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-1132)))) (-2173 (|HasCategory| (-2 (|:| -3835 (-1189)) (|:| -2923 |#1|)) (QUOTE (-1132))) (|HasCategory| (-2 (|:| -3835 (-1189)) (|:| -2923 |#1|)) (|%list| (QUOTE -632) (QUOTE (-887)))) (|HasCategory| |#1| (QUOTE (-1132))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-887))))) (|HasCategory| (-2 (|:| -3835 (-1189)) (|:| -2923 |#1|)) (|%list| (QUOTE -633) (QUOTE (-549)))) (-12 (|HasCategory| |#1| (QUOTE (-1132))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| (-2 (|:| -3835 (-1189)) (|:| -2923 |#1|)) (QUOTE (-1132))) (|HasCategory| (-1189) (QUOTE (-871))) (|HasCategory| |#1| (QUOTE (-1132))) (-2173 (|HasCategory| (-2 (|:| -3835 (-1189)) (|:| -2923 |#1|)) (|%list| (QUOTE -632) (QUOTE (-887)))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-887))))) (-2173 (|HasCategory| (-2 (|:| -3835 (-1189)) (|:| -2923 |#1|)) (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-102)))) (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-887)))) (|HasCategory| (-2 (|:| -3835 (-1189)) (|:| -2923 |#1|)) (|%list| (QUOTE -632) (QUOTE (-887)))) (|HasCategory| (-2 (|:| -3835 (-1189)) (|:| -2923 |#1|)) (QUOTE (-102)))) (-1191 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 @@ -4722,9 +4722,9 @@ NIL NIL (-1198 |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 @@ -4735,7 +4735,7 @@ NIL (-1201 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 @@ -4747,11 +4747,11 @@ NIL (-1204 |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."))) (((-4510 "*") |has| |#1| (-175)) (-4501 |has| |#1| (-571)) (-4506 |has| |#1| (-376)) (-4500 |has| |#1| (-376)) (-4502 . T) (-4503 . T) (-4505 . T)) -((|HasCategory| |#1| (|%list| (QUOTE -38) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#1| (QUOTE (-571))) (|HasCategory| |#1| (QUOTE (-175))) (-2181 (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-571)))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-149))) (-12 (|HasCategory| |#1| (|%list| (QUOTE -927) (QUOTE (-1207)))) (|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 (-1143))) (|HasCategory| |#1| (QUOTE (-376))) (-2181 (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (QUOTE (-571)))) (-2181 (|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 -4272) (|%list| (|devaluate| |#1|) (QUOTE (-1207)))))) (|HasSignature| |#1| (|%list| (QUOTE **) (|%list| (|devaluate| |#1|) (|devaluate| |#1|) (|%list| (QUOTE -421) (QUOTE (-560)))))) (-2181 (-12 (|HasCategory| |#1| (|%list| (QUOTE -29) (QUOTE (-560)))) (|HasCategory| |#1| (|%list| (QUOTE -38) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#1| (QUOTE (-989))) (|HasCategory| |#1| (QUOTE (-1233)))) (-12 (|HasCategory| |#1| (|%list| (QUOTE -38) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasSignature| |#1| (|%list| (QUOTE -2891) (|%list| (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1207))))) (|HasSignature| |#1| (|%list| (QUOTE -2646) (|%list| (|%list| (QUOTE -663) (QUOTE (-1207))) (|devaluate| |#1|))))))) +((|HasCategory| |#1| (|%list| (QUOTE -38) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#1| (QUOTE (-571))) (|HasCategory| |#1| (QUOTE (-175))) (-2173 (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-571)))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-149))) (-12 (|HasCategory| |#1| (|%list| (QUOTE -927) (QUOTE (-1207)))) (|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 (-1143))) (|HasCategory| |#1| (QUOTE (-376))) (-2173 (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (QUOTE (-571)))) (-2173 (|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 -2383) (|%list| (|devaluate| |#1|) (QUOTE (-1207)))))) (|HasSignature| |#1| (|%list| (QUOTE **) (|%list| (|devaluate| |#1|) (|devaluate| |#1|) (|%list| (QUOTE -421) (QUOTE (-560)))))) (-2173 (-12 (|HasCategory| |#1| (|%list| (QUOTE -29) (QUOTE (-560)))) (|HasCategory| |#1| (|%list| (QUOTE -38) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#1| (QUOTE (-989))) (|HasCategory| |#1| (QUOTE (-1233)))) (-12 (|HasCategory| |#1| (|%list| (QUOTE -38) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasSignature| |#1| (|%list| (QUOTE -3146) (|%list| (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1207))))) (|HasSignature| |#1| (|%list| (QUOTE -2637) (|%list| (|%list| (QUOTE -663) (QUOTE (-1207))) (|devaluate| |#1|))))))) (-1205 |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}."))) (((-4510 "*") |has| |#1| (-175)) (-4501 |has| |#1| (-571)) (-4502 . T) (-4503 . T) (-4505 . T)) -((|HasCategory| |#1| (|%list| (QUOTE -38) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#1| (QUOTE (-571))) (-2181 (|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 -927) (QUOTE (-1207)))) (|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 (-1143))) (-12 (|HasSignature| |#1| (|%list| (QUOTE **) (|%list| (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-793))))) (|HasSignature| |#1| (|%list| (QUOTE -4272) (|%list| (|devaluate| |#1|) (QUOTE (-1207)))))) (|HasSignature| |#1| (|%list| (QUOTE **) (|%list| (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-793))))) (|HasCategory| |#1| (QUOTE (-376))) (-2181 (-12 (|HasCategory| |#1| (|%list| (QUOTE -29) (QUOTE (-560)))) (|HasCategory| |#1| (|%list| (QUOTE -38) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#1| (QUOTE (-989))) (|HasCategory| |#1| (QUOTE (-1233)))) (-12 (|HasCategory| |#1| (|%list| (QUOTE -38) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasSignature| |#1| (|%list| (QUOTE -2891) (|%list| (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1207))))) (|HasSignature| |#1| (|%list| (QUOTE -2646) (|%list| (|%list| (QUOTE -663) (QUOTE (-1207))) (|devaluate| |#1|))))))) +((|HasCategory| |#1| (|%list| (QUOTE -38) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#1| (QUOTE (-571))) (-2173 (|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 -927) (QUOTE (-1207)))) (|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 (-1143))) (-12 (|HasSignature| |#1| (|%list| (QUOTE **) (|%list| (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-793))))) (|HasSignature| |#1| (|%list| (QUOTE -2383) (|%list| (|devaluate| |#1|) (QUOTE (-1207)))))) (|HasSignature| |#1| (|%list| (QUOTE **) (|%list| (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-793))))) (|HasCategory| |#1| (QUOTE (-376))) (-2173 (-12 (|HasCategory| |#1| (|%list| (QUOTE -29) (QUOTE (-560)))) (|HasCategory| |#1| (|%list| (QUOTE -38) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#1| (QUOTE (-989))) (|HasCategory| |#1| (QUOTE (-1233)))) (-12 (|HasCategory| |#1| (|%list| (QUOTE -38) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasSignature| |#1| (|%list| (QUOTE -3146) (|%list| (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1207))))) (|HasSignature| |#1| (|%list| (QUOTE -2637) (|%list| (|%list| (QUOTE -663) (QUOTE (-1207))) (|devaluate| |#1|))))))) (-1206) ((|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 @@ -4767,7 +4767,7 @@ NIL (-1209 R) ((|constructor| (NIL "This domain implements symmetric polynomial"))) (((-4510 "*") |has| |#1| (-175)) (-4501 |has| |#1| (-571)) (-4506 |has| |#1| (-6 -4506)) (-4502 . T) (-4503 . T) (-4505 . T)) -((|HasCategory| |#1| (|%list| (QUOTE -38) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#1| (QUOTE (-571))) (-2181 (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-571)))) (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-149))) (-2181 (|HasCategory| |#1| (|%list| (QUOTE -38) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#1| (|%list| (QUOTE -1069) (|%list| (QUOTE -421) (QUOTE (-560)))))) (|HasCategory| |#1| (|%list| (QUOTE -1069) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#1| (|%list| (QUOTE -1069) (QUOTE (-560)))) (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (QUOTE (-466))) (-12 (|HasCategory| (-1002) (QUOTE (-133))) (|HasCategory| |#1| (QUOTE (-571)))) (|HasAttribute| |#1| (QUOTE -4506))) +((|HasCategory| |#1| (|%list| (QUOTE -38) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#1| (QUOTE (-571))) (-2173 (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-571)))) (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-149))) (-2173 (|HasCategory| |#1| (|%list| (QUOTE -38) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#1| (|%list| (QUOTE -1069) (|%list| (QUOTE -421) (QUOTE (-560)))))) (|HasCategory| |#1| (|%list| (QUOTE -1069) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#1| (|%list| (QUOTE -1069) (QUOTE (-560)))) (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (QUOTE (-466))) (-12 (|HasCategory| (-1002) (QUOTE (-133))) (|HasCategory| |#1| (QUOTE (-571)))) (|HasAttribute| |#1| (QUOTE -4506))) (-1210) ((|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 @@ -4807,7 +4807,7 @@ NIL (-1219 |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}"))) ((-4508 . T) (-4509 . T)) -((-12 (|HasCategory| (-2 (|:| -3819 |#1|) (|:| -2913 |#2|)) (QUOTE (-1132))) (|HasCategory| (-2 (|:| -3819 |#1|) (|:| -2913 |#2|)) (|%list| (QUOTE -321) (|%list| (QUOTE -2) (|%list| (QUOTE |:|) (QUOTE -3819) (|devaluate| |#1|)) (|%list| (QUOTE |:|) (QUOTE -2913) (|devaluate| |#2|)))))) (-2181 (|HasCategory| (-2 (|:| -3819 |#1|) (|:| -2913 |#2|)) (QUOTE (-1132))) (|HasCategory| |#2| (QUOTE (-1132)))) (-2181 (|HasCategory| (-2 (|:| -3819 |#1|) (|:| -2913 |#2|)) (QUOTE (-102))) (|HasCategory| (-2 (|:| -3819 |#1|) (|:| -2913 |#2|)) (QUOTE (-1132))) (|HasCategory| |#2| (QUOTE (-102))) (|HasCategory| |#2| (QUOTE (-1132)))) (-2181 (|HasCategory| (-2 (|:| -3819 |#1|) (|:| -2913 |#2|)) (QUOTE (-1132))) (|HasCategory| (-2 (|:| -3819 |#1|) (|:| -2913 |#2|)) (|%list| (QUOTE -632) (QUOTE (-887)))) (|HasCategory| |#2| (QUOTE (-1132))) (|HasCategory| |#2| (|%list| (QUOTE -632) (QUOTE (-887))))) (|HasCategory| (-2 (|:| -3819 |#1|) (|:| -2913 |#2|)) (|%list| (QUOTE -633) (QUOTE (-549)))) (-12 (|HasCategory| |#2| (QUOTE (-1132))) (|HasCategory| |#2| (|%list| (QUOTE -321) (|devaluate| |#2|)))) (|HasCategory| (-2 (|:| -3819 |#1|) (|:| -2913 |#2|)) (QUOTE (-1132))) (|HasCategory| |#1| (QUOTE (-871))) (|HasCategory| |#2| (QUOTE (-1132))) (-2181 (|HasCategory| (-2 (|:| -3819 |#1|) (|:| -2913 |#2|)) (|%list| (QUOTE -632) (QUOTE (-887)))) (|HasCategory| |#2| (|%list| (QUOTE -632) (QUOTE (-887))))) (-2181 (|HasCategory| (-2 (|:| -3819 |#1|) (|:| -2913 |#2|)) (QUOTE (-102))) (|HasCategory| |#2| (QUOTE (-102)))) (|HasCategory| |#2| (QUOTE (-102))) (|HasCategory| |#2| (|%list| (QUOTE -632) (QUOTE (-887)))) (|HasCategory| (-2 (|:| -3819 |#1|) (|:| -2913 |#2|)) (|%list| (QUOTE -632) (QUOTE (-887)))) (|HasCategory| (-2 (|:| -3819 |#1|) (|:| -2913 |#2|)) (QUOTE (-102)))) +((-12 (|HasCategory| (-2 (|:| -3835 |#1|) (|:| -2923 |#2|)) (QUOTE (-1132))) (|HasCategory| (-2 (|:| -3835 |#1|) (|:| -2923 |#2|)) (|%list| (QUOTE -321) (|%list| (QUOTE -2) (|%list| (QUOTE |:|) (QUOTE -3835) (|devaluate| |#1|)) (|%list| (QUOTE |:|) (QUOTE -2923) (|devaluate| |#2|)))))) (-2173 (|HasCategory| (-2 (|:| -3835 |#1|) (|:| -2923 |#2|)) (QUOTE (-1132))) (|HasCategory| |#2| (QUOTE (-1132)))) (-2173 (|HasCategory| (-2 (|:| -3835 |#1|) (|:| -2923 |#2|)) (QUOTE (-102))) (|HasCategory| (-2 (|:| -3835 |#1|) (|:| -2923 |#2|)) (QUOTE (-1132))) (|HasCategory| |#2| (QUOTE (-102))) (|HasCategory| |#2| (QUOTE (-1132)))) (-2173 (|HasCategory| (-2 (|:| -3835 |#1|) (|:| -2923 |#2|)) (QUOTE (-1132))) (|HasCategory| (-2 (|:| -3835 |#1|) (|:| -2923 |#2|)) (|%list| (QUOTE -632) (QUOTE (-887)))) (|HasCategory| |#2| (QUOTE (-1132))) (|HasCategory| |#2| (|%list| (QUOTE -632) (QUOTE (-887))))) (|HasCategory| (-2 (|:| -3835 |#1|) (|:| -2923 |#2|)) (|%list| (QUOTE -633) (QUOTE (-549)))) (-12 (|HasCategory| |#2| (QUOTE (-1132))) (|HasCategory| |#2| (|%list| (QUOTE -321) (|devaluate| |#2|)))) (|HasCategory| (-2 (|:| -3835 |#1|) (|:| -2923 |#2|)) (QUOTE (-1132))) (|HasCategory| |#1| (QUOTE (-871))) (|HasCategory| |#2| (QUOTE (-1132))) (-2173 (|HasCategory| (-2 (|:| -3835 |#1|) (|:| -2923 |#2|)) (|%list| (QUOTE -632) (QUOTE (-887)))) (|HasCategory| |#2| (|%list| (QUOTE -632) (QUOTE (-887))))) (-2173 (|HasCategory| (-2 (|:| -3835 |#1|) (|:| -2923 |#2|)) (QUOTE (-102))) (|HasCategory| |#2| (QUOTE (-102)))) (|HasCategory| |#2| (QUOTE (-102))) (|HasCategory| |#2| (|%list| (QUOTE -632) (QUOTE (-887)))) (|HasCategory| (-2 (|:| -3835 |#1|) (|:| -2923 |#2|)) (|%list| (QUOTE -632) (QUOTE (-887)))) (|HasCategory| (-2 (|:| -3835 |#1|) (|:| -2923 |#2|)) (QUOTE (-102)))) (-1220 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 @@ -4867,7 +4867,7 @@ NIL (-1234 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| $)) "\\spad{tree(nd,ls)} creates a tree with value \\spad{nd},{} and children \\spad{ls}."))) ((-4509 . T) (-4508 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1132))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1132))) (-2181 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-1132)))) (-2181 (-12 (|HasCategory| |#1| (QUOTE (-1132))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-887))))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-887)))) (|HasCategory| |#1| (QUOTE (-102)))) +((-12 (|HasCategory| |#1| (QUOTE (-1132))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1132))) (-2173 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-1132)))) (-2173 (-12 (|HasCategory| |#1| (QUOTE (-1132))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-887))))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-887)))) (|HasCategory| |#1| (QUOTE (-102)))) (-1235 S) ((|constructor| (NIL "Category for the trigonometric functions.")) (|tan| (($ $) "\\spad{tan(x)} returns the tangent of \\spad{x}.")) (|sin| (($ $) "\\spad{sin(x)} returns the sine of \\spad{x}.")) (|sec| (($ $) "\\spad{sec(x)} returns the secant of \\spad{x}.")) (|csc| (($ $) "\\spad{csc(x)} returns the cosecant of \\spad{x}.")) (|cot| (($ $) "\\spad{cot(x)} returns the cotangent of \\spad{x}.")) (|cos| (($ $) "\\spad{cos(x)} returns the cosine of \\spad{x}."))) NIL @@ -4876,7 +4876,7 @@ NIL ((|constructor| (NIL "Category for the trigonometric functions.")) (|tan| (($ $) "\\spad{tan(x)} returns the tangent of \\spad{x}.")) (|sin| (($ $) "\\spad{sin(x)} returns the sine of \\spad{x}.")) (|sec| (($ $) "\\spad{sec(x)} returns the secant of \\spad{x}.")) (|csc| (($ $) "\\spad{csc(x)} returns the cosecant of \\spad{x}.")) (|cot| (($ $) "\\spad{cot(x)} returns the cotangent of \\spad{x}.")) (|cos| (($ $) "\\spad{cos(x)} returns the cosine of \\spad{x}."))) NIL NIL -(-1237 R -1596) +(-1237 R -1594) ((|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 @@ -4884,14 +4884,14 @@ 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 -(-1239 R -1596) +(-1239 R -1594) ((|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 -915) (|devaluate| |#1|)))) (|HasCategory| |#1| (|%list| (QUOTE -911) (|devaluate| |#1|))) (|HasCategory| |#2| (|%list| (QUOTE -633) (|%list| (QUOTE -915) (|devaluate| |#1|)))) (|HasCategory| |#2| (|%list| (QUOTE -911) (|devaluate| |#1|))))) (-1240 |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}."))) (((-4510 "*") |has| |#1| (-175)) (-4501 |has| |#1| (-571)) (-4503 . T) (-4502 . T) (-4505 . T)) -((|HasCategory| |#1| (|%list| (QUOTE -38) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-149))) (|HasCategory| |#1| (QUOTE (-147))) (-2181 (|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))) (-2173 (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-571)))) (|HasCategory| |#1| (QUOTE (-571))) (|HasCategory| |#1| (QUOTE (-376)))) (-1241 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 @@ -4912,7 +4912,7 @@ 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 (-1132))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-887))))) -(-1246 -1596) +(-1246 -1594) ((|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 @@ -4958,8 +4958,8 @@ NIL NIL (-1257 |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 @@ -4995,7 +4995,7 @@ NIL (-1266 |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}"))) (((-4510 "*") |has| |#2| (-175)) (-4501 |has| |#2| (-571)) (-4504 |has| |#2| (-376)) (-4506 |has| |#2| (-6 -4506)) (-4503 . T) (-4502 . T) (-4505 . T)) -((|HasCategory| |#2| (QUOTE (-939))) (|HasCategory| |#2| (QUOTE (-571))) (|HasCategory| |#2| (QUOTE (-175))) (-2181 (|HasCategory| |#2| (QUOTE (-175))) (|HasCategory| |#2| (QUOTE (-571)))) (-12 (|HasCategory| (-1113) (|%list| (QUOTE -911) (QUOTE (-391)))) (|HasCategory| |#2| (|%list| (QUOTE -911) (QUOTE (-391))))) (-12 (|HasCategory| (-1113) (|%list| (QUOTE -911) (QUOTE (-560)))) (|HasCategory| |#2| (|%list| (QUOTE -911) (QUOTE (-560))))) (-12 (|HasCategory| (-1113) (|%list| (QUOTE -633) (|%list| (QUOTE -915) (QUOTE (-391))))) (|HasCategory| |#2| (|%list| (QUOTE -633) (|%list| (QUOTE -915) (QUOTE (-391)))))) (-12 (|HasCategory| (-1113) (|%list| (QUOTE -633) (|%list| (QUOTE -915) (QUOTE (-560))))) (|HasCategory| |#2| (|%list| (QUOTE -633) (|%list| (QUOTE -915) (QUOTE (-560)))))) (-12 (|HasCategory| (-1113) (|%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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(|%list| (QUOTE -633) (|%list| (QUOTE -915) (QUOTE (-391)))))) (-12 (|HasCategory| (-1113) (|%list| (QUOTE -633) (|%list| (QUOTE -915) (QUOTE (-560))))) (|HasCategory| |#2| (|%list| (QUOTE -633) (|%list| (QUOTE -915) (QUOTE (-560)))))) (-12 (|HasCategory| (-1113) (|%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 -1069) (QUOTE (-560)))) (-2173 (|HasCategory| |#2| (|%list| (QUOTE -38) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#2| (|%list| (QUOTE -1069) (|%list| (QUOTE -421) (QUOTE (-560)))))) (|HasCategory| |#2| (|%list| (QUOTE -1069) (|%list| (QUOTE -421) (QUOTE (-560))))) (-2173 (|HasCategory| |#2| (QUOTE (-175))) (|HasCategory| |#2| (QUOTE (-376))) (|HasCategory| |#2| (QUOTE (-466))) (|HasCategory| |#2| (QUOTE (-571))) (|HasCategory| |#2| (QUOTE (-939)))) (-2173 (|HasCategory| |#2| (QUOTE (-376))) (|HasCategory| |#2| (QUOTE (-466))) (|HasCategory| |#2| (QUOTE (-571))) (|HasCategory| |#2| (QUOTE (-939)))) (-2173 (|HasCategory| |#2| (QUOTE (-376))) (|HasCategory| |#2| (QUOTE (-466))) (|HasCategory| |#2| (QUOTE (-939)))) (|HasCategory| |#2| (QUOTE (-376))) (|HasCategory| |#2| (QUOTE (-1182))) (|HasCategory| |#2| (|%list| (QUOTE -929) (QUOTE (-1207)))) (|HasCategory| |#2| (|%list| (QUOTE -927) (QUOTE (-1207)))) (|HasCategory| |#2| (QUOTE (-239))) (|HasCategory| |#2| (QUOTE (-240))) (|HasAttribute| |#2| (QUOTE -4506)) (|HasCategory| |#2| (QUOTE (-466))) (-12 (|HasCategory| $ (QUOTE (-147))) (|HasCategory| |#2| (QUOTE (-939)))) (-2173 (-12 (|HasCategory| $ (QUOTE (-147))) (|HasCategory| |#2| (QUOTE (-939)))) (|HasCategory| |#2| (QUOTE (-147))))) (-1267 |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 @@ -5031,7 +5031,7 @@ NIL (-1275 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 -927) (QUOTE (-1207)))) (|HasSignature| |#2| (|%list| (QUOTE *) (|%list| (|devaluate| |#2|) (|devaluate| |#3|) (|devaluate| |#2|)))) (|HasCategory| |#3| (QUOTE (-1143))) (|HasSignature| |#2| (|%list| (QUOTE **) (|%list| (|devaluate| |#2|) (|devaluate| |#2|) (|devaluate| |#3|)))) (|HasSignature| |#2| (|%list| (QUOTE -4272) (|%list| (|devaluate| |#2|) (QUOTE (-1207)))))) +((|HasCategory| |#2| (|%list| (QUOTE -927) (QUOTE (-1207)))) (|HasSignature| |#2| (|%list| (QUOTE *) (|%list| (|devaluate| |#2|) (|devaluate| |#3|) (|devaluate| |#2|)))) (|HasCategory| |#3| (QUOTE (-1143))) (|HasSignature| |#2| (|%list| (QUOTE **) (|%list| (|devaluate| |#2|) (|devaluate| |#2|) (|devaluate| |#3|)))) (|HasSignature| |#2| (|%list| (QUOTE -2383) (|%list| (|devaluate| |#2|) (QUOTE (-1207)))))) (-1276 |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|))) $) "\\spad{terms(f(x))} returns a stream of non-zero terms,{} where a a term is an exponent-coefficient pair. The terms in the stream are ordered by increasing order of exponents."))) (((-4510 "*") |has| |#1| (-175)) (-4501 |has| |#1| (-571)) (-4502 . T) (-4503 . T) (-4505 . T)) @@ -5043,7 +5043,7 @@ NIL (-1278 |Coef| |var| |cen|) ((|constructor| (NIL "Dense Puiseux series in one variable \\indented{2}{\\spadtype{UnivariatePuiseuxSeries} is a domain representing Puiseux} \\indented{2}{series in one variable with coefficients in an arbitrary ring.\\space{2}The} \\indented{2}{parameters of the type specify the coefficient ring,{} the power series} \\indented{2}{variable,{} and the center of the power series expansion.\\space{2}For example,{}} \\indented{2}{\\spad{UnivariatePuiseuxSeries(Integer,x,3)} represents Puiseux series in} \\indented{2}{\\spad{(x - 3)} with \\spadtype{Integer} coefficients.}")) (|integrate| (($ $ (|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."))) (((-4510 "*") |has| |#1| (-175)) (-4501 |has| |#1| (-571)) (-4506 |has| |#1| (-376)) (-4500 |has| |#1| (-376)) (-4502 . T) (-4503 . T) (-4505 . T)) -((|HasCategory| |#1| (|%list| (QUOTE -38) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#1| (QUOTE (-571))) (|HasCategory| |#1| (QUOTE (-175))) (-2181 (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-571)))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-149))) (-12 (|HasCategory| |#1| (|%list| (QUOTE -927) (QUOTE (-1207)))) (|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 (-1143))) (|HasCategory| |#1| (QUOTE (-376))) (-2181 (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (QUOTE (-571)))) (-2181 (|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 -4272) (|%list| (|devaluate| |#1|) (QUOTE (-1207)))))) (|HasSignature| |#1| (|%list| (QUOTE **) (|%list| (|devaluate| |#1|) (|devaluate| |#1|) (|%list| (QUOTE -421) (QUOTE (-560)))))) (-2181 (-12 (|HasCategory| |#1| (|%list| (QUOTE -29) (QUOTE (-560)))) (|HasCategory| |#1| (|%list| (QUOTE -38) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#1| (QUOTE (-989))) (|HasCategory| |#1| (QUOTE (-1233)))) (-12 (|HasCategory| |#1| (|%list| (QUOTE -38) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasSignature| |#1| (|%list| (QUOTE -2891) (|%list| (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1207))))) (|HasSignature| |#1| (|%list| (QUOTE -2646) (|%list| (|%list| (QUOTE -663) (QUOTE (-1207))) (|devaluate| |#1|))))))) +((|HasCategory| |#1| (|%list| (QUOTE -38) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#1| (QUOTE (-571))) (|HasCategory| |#1| (QUOTE (-175))) (-2173 (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-571)))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-149))) (-12 (|HasCategory| |#1| (|%list| (QUOTE -927) (QUOTE (-1207)))) (|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 (-1143))) (|HasCategory| |#1| (QUOTE (-376))) (-2173 (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (QUOTE (-571)))) (-2173 (|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 -2383) (|%list| (|devaluate| |#1|) (QUOTE (-1207)))))) (|HasSignature| |#1| (|%list| (QUOTE **) (|%list| (|devaluate| |#1|) (|devaluate| |#1|) (|%list| (QUOTE -421) (QUOTE (-560)))))) (-2173 (-12 (|HasCategory| |#1| (|%list| (QUOTE -29) (QUOTE (-560)))) (|HasCategory| |#1| (|%list| (QUOTE -38) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#1| (QUOTE (-989))) (|HasCategory| |#1| (QUOTE (-1233)))) (-12 (|HasCategory| |#1| (|%list| (QUOTE -38) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasSignature| |#1| (|%list| (QUOTE -3146) (|%list| (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1207))))) (|HasSignature| |#1| (|%list| (QUOTE -2637) (|%list| (|%list| (QUOTE -663) (QUOTE (-1207))) (|devaluate| |#1|))))))) (-1279 |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 @@ -5063,11 +5063,11 @@ NIL (-1283 |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)}."))) (((-4510 "*") |has| |#1| (-175)) (-4501 |has| |#1| (-571)) (-4506 |has| |#1| (-376)) (-4500 |has| |#1| (-376)) (-4502 . T) (-4503 . T) (-4505 . T)) -((|HasCategory| |#1| (QUOTE (-571))) (|HasCategory| |#1| (QUOTE (-175))) (-2181 (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-571)))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-149))) (-12 (|HasCategory| |#1| (|%list| (QUOTE -927) (QUOTE (-1207)))) (|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 (-1143))) (|HasCategory| |#1| (QUOTE (-376))) (-2181 (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (QUOTE (-571)))) (-2181 (|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 -4272) (|%list| (|devaluate| |#1|) (QUOTE (-1207)))))) (|HasSignature| |#1| (|%list| (QUOTE **) (|%list| (|devaluate| |#1|) (|devaluate| |#1|) (|%list| (QUOTE -421) (QUOTE (-560)))))) (-2181 (-12 (|HasCategory| |#1| (|%list| (QUOTE -29) (QUOTE (-560)))) (|HasCategory| |#1| (|%list| (QUOTE -38) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#1| (QUOTE (-989))) (|HasCategory| |#1| (QUOTE (-1233)))) (-12 (|HasCategory| |#1| (|%list| (QUOTE -38) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasSignature| |#1| (|%list| (QUOTE -2891) (|%list| (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1207))))) (|HasSignature| |#1| (|%list| (QUOTE -2646) (|%list| (|%list| (QUOTE -663) (QUOTE (-1207))) (|devaluate| |#1|)))))) (|HasCategory| |#1| (|%list| (QUOTE -38) (|%list| (QUOTE -421) (QUOTE (-560)))))) +((|HasCategory| |#1| (QUOTE (-571))) (|HasCategory| |#1| (QUOTE (-175))) (-2173 (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-571)))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-149))) (-12 (|HasCategory| |#1| (|%list| (QUOTE -927) (QUOTE (-1207)))) (|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 (-1143))) (|HasCategory| |#1| (QUOTE (-376))) (-2173 (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (QUOTE (-571)))) (-2173 (|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 -2383) (|%list| (|devaluate| |#1|) (QUOTE (-1207)))))) (|HasSignature| |#1| (|%list| (QUOTE **) (|%list| (|devaluate| |#1|) (|devaluate| |#1|) (|%list| (QUOTE -421) (QUOTE (-560)))))) (-2173 (-12 (|HasCategory| |#1| (|%list| (QUOTE -29) (QUOTE (-560)))) (|HasCategory| |#1| (|%list| (QUOTE -38) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#1| (QUOTE (-989))) (|HasCategory| |#1| (QUOTE (-1233)))) (-12 (|HasCategory| |#1| (|%list| (QUOTE -38) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasSignature| |#1| (|%list| (QUOTE -3146) (|%list| (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1207))))) (|HasSignature| |#1| (|%list| (QUOTE -2637) (|%list| (|%list| (QUOTE -663) (QUOTE (-1207))) (|devaluate| |#1|)))))) (|HasCategory| |#1| (|%list| (QUOTE -38) (|%list| (QUOTE -421) (QUOTE (-560)))))) (-1284 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))}."))) (((-4510 "*") |has| (-1278 |#2| |#3| |#4|) (-175)) (-4501 |has| (-1278 |#2| |#3| |#4|) (-571)) (-4502 . T) (-4503 . T) (-4505 . T)) -((|HasCategory| (-1278 |#2| |#3| |#4|) (|%list| (QUOTE -38) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| (-1278 |#2| |#3| |#4|) (QUOTE (-147))) (|HasCategory| (-1278 |#2| |#3| |#4|) (QUOTE (-149))) (|HasCategory| (-1278 |#2| |#3| |#4|) (QUOTE (-175))) (-2181 (|HasCategory| (-1278 |#2| |#3| |#4|) (|%list| (QUOTE -38) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| (-1278 |#2| |#3| |#4|) (|%list| (QUOTE -1069) (|%list| (QUOTE -421) (QUOTE (-560)))))) (|HasCategory| (-1278 |#2| |#3| |#4|) (|%list| (QUOTE -1069) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| (-1278 |#2| |#3| |#4|) (|%list| (QUOTE -1069) (QUOTE (-560)))) (|HasCategory| (-1278 |#2| |#3| |#4|) (QUOTE (-376))) (|HasCategory| (-1278 |#2| |#3| |#4|) (QUOTE (-466))) (|HasCategory| (-1278 |#2| |#3| |#4|) (QUOTE (-571)))) +((|HasCategory| (-1278 |#2| |#3| |#4|) (|%list| (QUOTE -38) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| (-1278 |#2| |#3| |#4|) (QUOTE (-147))) (|HasCategory| (-1278 |#2| |#3| |#4|) (QUOTE (-149))) (|HasCategory| (-1278 |#2| |#3| |#4|) (QUOTE (-175))) (-2173 (|HasCategory| (-1278 |#2| |#3| |#4|) (|%list| (QUOTE -38) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| (-1278 |#2| |#3| |#4|) (|%list| (QUOTE -1069) (|%list| (QUOTE -421) (QUOTE (-560)))))) (|HasCategory| (-1278 |#2| |#3| |#4|) (|%list| (QUOTE -1069) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| (-1278 |#2| |#3| |#4|) (|%list| (QUOTE -1069) (QUOTE (-560)))) (|HasCategory| (-1278 |#2| |#3| |#4|) (QUOTE (-376))) (|HasCategory| (-1278 |#2| |#3| |#4|) (QUOTE (-466))) (|HasCategory| (-1278 |#2| |#3| |#4|) (QUOTE (-571)))) (-1285 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| $) "\\spad{concat(x,u)} returns aggregate consisting of \\spad{x} followed by the elements of \\spad{u}. Note: if \\axiom{\\spad{v} = concat(\\spad{x},{}\\spad{u})} then \\axiom{\\spad{x} = first \\spad{v}} and \\axiom{\\spad{u} = rest \\spad{v}}.") (($ $ $) "\\spad{concat(u,v)} returns an aggregate \\spad{w} consisting of the elements of \\spad{u} followed by the elements of \\spad{v}. Note: \\axiom{\\spad{v} = rest(\\spad{w},{}\\#a)}."))) NIL @@ -5079,7 +5079,7 @@ NIL (-1287 |Coef| |var| |cen|) ((|constructor| (NIL "Dense Taylor series in one variable \\spadtype{UnivariateTaylorSeries} is a domain representing Taylor series in one variable with coefficients in an arbitrary ring. The parameters of the type specify the coefficient ring,{} the power series variable,{} and the center of the power series expansion. For example,{} \\spadtype{UnivariateTaylorSeries}(Integer,{}\\spad{x},{}3) represents Taylor series in \\spad{(x - 3)} with \\spadtype{Integer} coefficients.")) (|integrate| (($ $ (|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}."))) (((-4510 "*") |has| |#1| (-175)) (-4501 |has| |#1| (-571)) (-4502 . T) (-4503 . T) (-4505 . T)) -((|HasCategory| |#1| (|%list| (QUOTE -38) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#1| (QUOTE (-571))) (-2181 (|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 -927) (QUOTE (-1207)))) (|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 (-1143))) (-12 (|HasSignature| |#1| (|%list| (QUOTE **) (|%list| (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-793))))) (|HasSignature| |#1| (|%list| (QUOTE -4272) (|%list| (|devaluate| |#1|) (QUOTE (-1207)))))) (|HasSignature| |#1| (|%list| (QUOTE **) (|%list| (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-793))))) (|HasCategory| |#1| (QUOTE (-376))) (-2181 (-12 (|HasCategory| |#1| (|%list| (QUOTE -29) (QUOTE (-560)))) (|HasCategory| |#1| (|%list| (QUOTE -38) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#1| (QUOTE (-989))) (|HasCategory| |#1| (QUOTE (-1233)))) (-12 (|HasCategory| |#1| (|%list| (QUOTE -38) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasSignature| |#1| (|%list| (QUOTE -2891) (|%list| (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1207))))) (|HasSignature| |#1| (|%list| (QUOTE -2646) (|%list| (|%list| (QUOTE -663) (QUOTE (-1207))) (|devaluate| |#1|))))))) +((|HasCategory| |#1| (|%list| (QUOTE -38) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#1| (QUOTE (-571))) (-2173 (|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 -927) (QUOTE (-1207)))) (|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 (-1143))) (-12 (|HasSignature| |#1| (|%list| (QUOTE **) (|%list| (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-793))))) (|HasSignature| |#1| (|%list| (QUOTE -2383) (|%list| (|devaluate| |#1|) (QUOTE (-1207)))))) (|HasSignature| |#1| (|%list| (QUOTE **) (|%list| (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-793))))) (|HasCategory| |#1| (QUOTE (-376))) (-2173 (-12 (|HasCategory| |#1| (|%list| (QUOTE -29) (QUOTE (-560)))) (|HasCategory| |#1| (|%list| (QUOTE -38) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#1| (QUOTE (-989))) (|HasCategory| |#1| (QUOTE (-1233)))) (-12 (|HasCategory| |#1| (|%list| (QUOTE -38) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasSignature| |#1| (|%list| (QUOTE -3146) (|%list| (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1207))))) (|HasSignature| |#1| (|%list| (QUOTE -2637) (|%list| (|%list| (QUOTE -663) (QUOTE (-1207))) (|devaluate| |#1|))))))) (-1288 |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 @@ -5087,7 +5087,7 @@ NIL (-1289 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 (-989))) (|HasCategory| |#2| (QUOTE (-1233))) (|HasSignature| |#2| (|%list| (QUOTE -2646) (|%list| (|%list| (QUOTE -663) (QUOTE (-1207))) (|devaluate| |#2|)))) (|HasSignature| |#2| (|%list| (QUOTE -2891) (|%list| (|devaluate| |#2|) (|devaluate| |#2|) (QUOTE (-1207))))) (|HasCategory| |#2| (|%list| (QUOTE -38) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#2| (QUOTE (-376)))) +((|HasCategory| |#2| (|%list| (QUOTE -29) (QUOTE (-560)))) (|HasCategory| |#2| (QUOTE (-989))) (|HasCategory| |#2| (QUOTE (-1233))) (|HasSignature| |#2| (|%list| (QUOTE -2637) (|%list| (|%list| (QUOTE -663) (QUOTE (-1207))) (|devaluate| |#2|)))) (|HasSignature| |#2| (|%list| (QUOTE -3146) (|%list| (|devaluate| |#2|) (|devaluate| |#2|) (QUOTE (-1207))))) (|HasCategory| |#2| (|%list| (QUOTE -38) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#2| (QUOTE (-376)))) (-1290 |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."))) (((-4510 "*") |has| |#1| (-175)) (-4501 |has| |#1| (-571)) (-4502 . T) (-4503 . T) (-4505 . T)) @@ -5096,7 +5096,7 @@ 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 -(-1292 -1596 UP L UTS) +(-1292 -1594 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)))) @@ -5119,7 +5119,7 @@ NIL (-1297 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."))) ((-4509 . T) (-4508 . T)) -((-2181 (-12 (|HasCategory| |#1| (QUOTE (-871))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1132))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|))))) (-2181 (-12 (|HasCategory| |#1| (QUOTE (-1132))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-887))))) (|HasCategory| |#1| (|%list| (QUOTE -633) (QUOTE (-549)))) (-2181 (|HasCategory| |#1| (QUOTE (-871))) (|HasCategory| |#1| (QUOTE (-1132)))) (|HasCategory| |#1| (QUOTE (-871))) (-2181 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-871))) (|HasCategory| |#1| (QUOTE (-1132)))) (|HasCategory| (-560) (QUOTE (-871))) (|HasCategory| |#1| (QUOTE (-1132))) (|HasCategory| |#1| (QUOTE (-25))) (|HasCategory| |#1| (QUOTE (-23))) (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-748))) (|HasCategory| |#1| (QUOTE (-1080))) (-12 (|HasCategory| |#1| (QUOTE (-1033))) (|HasCategory| |#1| (QUOTE (-1080)))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-887)))) (|HasCategory| |#1| (QUOTE (-102))) (-12 (|HasCategory| |#1| (QUOTE (-1132))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|))))) +((-2173 (-12 (|HasCategory| |#1| (QUOTE (-871))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1132))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|))))) (-2173 (-12 (|HasCategory| |#1| (QUOTE (-1132))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-887))))) (|HasCategory| |#1| (|%list| (QUOTE -633) (QUOTE (-549)))) (-2173 (|HasCategory| |#1| (QUOTE (-871))) (|HasCategory| |#1| (QUOTE (-1132)))) (|HasCategory| |#1| (QUOTE (-871))) (-2173 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-871))) (|HasCategory| |#1| (QUOTE (-1132)))) (|HasCategory| (-560) (QUOTE (-871))) (|HasCategory| |#1| (QUOTE (-1132))) (|HasCategory| |#1| (QUOTE (-25))) (|HasCategory| |#1| (QUOTE (-23))) (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-748))) (|HasCategory| |#1| (QUOTE (-1080))) (-12 (|HasCategory| |#1| (QUOTE (-1033))) (|HasCategory| |#1| (QUOTE (-1080)))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-887)))) (|HasCategory| |#1| (QUOTE (-102))) (-12 (|HasCategory| |#1| (QUOTE (-1132))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|))))) (-1298 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 @@ -5156,7 +5156,7 @@ 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 -(-1307 K R UP -1596) +(-1307 K R UP -1594) ((|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 @@ -5188,11 +5188,11 @@ 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 -(-1315 S -1596) +(-1315 S -1594) ((|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|) $) "\\spad{algebraic?(a)} tests whether an element \\spad{a} is algebraic with respect to the ground field \\spad{F}."))) NIL ((|HasCategory| |#2| (QUOTE (-381))) (|HasCategory| |#2| (QUOTE (-147))) (|HasCategory| |#2| (QUOTE (-149)))) -(-1316 -1596) +(-1316 -1594) ((|constructor| (NIL "ExtensionField {\\em F} is the category of fields which extend the field \\spad{F}")) (|Frobenius| (($ $ (|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|) $) "\\spad{algebraic?(a)} tests whether an element \\spad{a} is algebraic with respect to the ground field \\spad{F}."))) ((-4500 . T) (-4506 . T) (-4501 . T) ((-4510 "*") . T) (-4502 . T) (-4503 . T) (-4505 . T)) NIL diff --git a/src/share/algebra/category.daase b/src/share/algebra/category.daase index b75e3df2..2b06fb48 100644 --- a/src/share/algebra/category.daase +++ b/src/share/algebra/category.daase @@ -1,15 +1,15 @@ -(205732 . 3507509292) -(((|#2| |#2|) -12 (|has| |#2| (-321 |#2|)) (|has| |#2| (-1132))) ((#0=(-2 (|:| -3819 |#1|) (|:| -2913 |#2|)) #0#) |has| (-2 (|:| -3819 |#1|) (|:| -2913 |#2|)) (-321 (-2 (|:| -3819 |#1|) (|:| -2913 |#2|))))) -((((-560)) . T) (($) -2181 (|has| |#1| (-319)) (|has| |#1| (-376)) (|has| |#1| (-363)) (|has| |#1| (-571))) (((-421 (-560))) -2181 (|has| |#1| (-376)) (|has| |#1| (-363)) (|has| |#1| (-1069 (-421 (-560))))) ((|#1|) . T)) +(205732 . 3507527193) +(((|#2| |#2|) -12 (|has| |#2| (-321 |#2|)) (|has| |#2| (-1132))) ((#0=(-2 (|:| -3835 |#1|) (|:| -2923 |#2|)) #0#) |has| (-2 (|:| -3835 |#1|) (|:| -2923 |#2|)) (-321 (-2 (|:| -3835 |#1|) (|:| -2923 |#2|))))) +((((-560)) . T) (($) -2173 (|has| |#1| (-319)) (|has| |#1| (-376)) (|has| |#1| (-363)) (|has| |#1| (-571))) (((-421 (-560))) -2173 (|has| |#1| (-376)) (|has| |#1| (-363)) (|has| |#1| (-1069 (-421 (-560))))) ((|#1|) . T)) (((|#2| |#2|) . T)) ((((-560)) . T)) -((($ $) -2181 (|has| |#2| (-175)) (|has| |#2| (-376)) (|has| |#2| (-466)) (|has| |#2| (-571)) (|has| |#2| (-939))) ((|#2| |#2|) . T) ((#0=(-421 (-560)) #0#) |has| |#2| (-38 (-421 (-560))))) +((($ $) -2173 (|has| |#2| (-175)) (|has| |#2| (-376)) (|has| |#2| (-466)) (|has| |#2| (-571)) (|has| |#2| (-939))) ((|#2| |#2|) . T) ((#0=(-421 (-560)) #0#) |has| |#2| (-38 (-421 (-560))))) ((($) . T)) (((|#1|) . T)) ((($) . T) (((-560)) |has| |#1| (-660 (-560))) ((|#1|) . T) (((-421 (-560))) |has| |#1| (-38 (-421 (-560))))) (((|#2|) . T)) -((($) -2181 (|has| |#2| (-175)) (|has| |#2| (-376)) (|has| |#2| (-466)) (|has| |#2| (-571)) (|has| |#2| (-939))) ((|#2|) . T) (((-421 (-560))) |has| |#2| (-38 (-421 (-560))))) +((($) -2173 (|has| |#2| (-175)) (|has| |#2| (-376)) (|has| |#2| (-466)) (|has| |#2| (-571)) (|has| |#2| (-939))) ((|#2|) . T) (((-421 (-560))) |has| |#2| (-38 (-421 (-560))))) (|has| |#1| (-939)) ((((-887)) . T)) ((((-887)) . T)) @@ -23,23 +23,23 @@ ((((-549)) . T) (((-1189)) . T) (((-229)) . T) (((-391)) . T) (((-915 (-391))) . T)) (((|#1|) . T)) ((((-229)) . T) (((-887)) . T)) -(-2181 (|has| |#2| (-815)) (|has| |#2| (-871))) -(-2181 (-12 (|has| |#1| (-815)) (|has| |#2| (-815))) (-12 (|has| |#1| (-871)) (|has| |#2| (-871)))) +(-2173 (|has| |#2| (-815)) (|has| |#2| (-871))) +(-2173 (-12 (|has| |#1| (-815)) (|has| |#2| (-815))) (-12 (|has| |#1| (-871)) (|has| |#2| (-871)))) (((|#1|) . T)) (((|#1|) -12 (|has| |#1| (-321 |#1|)) (|has| |#1| (-1132)))) -(-2181 (|has| |#1| (-21)) (|has| |#1| (-870))) -((($ $) . T) ((#0=(-421 (-560)) #0#) -2181 (|has| |#1| (-376)) (|has| |#1| (-363))) ((|#1| |#1|) . T)) -(-2181 (|has| |#1| (-842)) (|has| |#1| (-871))) +(-2173 (|has| |#1| (-21)) (|has| |#1| (-870))) +((($ $) . T) ((#0=(-421 (-560)) #0#) -2173 (|has| |#1| (-376)) (|has| |#1| (-363))) ((|#1| |#1|) . T)) +(-2173 (|has| |#1| (-842)) (|has| |#1| (-871))) ((((-421 (-560))) |has| |#1| (-1069 (-421 (-560)))) (((-560)) |has| |#1| (-1069 (-560))) ((|#1|) . T)) ((((-887)) . T)) ((((-887)) . T)) -(-2181 (|has| |#1| (-376)) (|has| |#1| (-571))) +(-2173 (|has| |#1| (-376)) (|has| |#1| (-571))) (|has| |#1| (-870)) (((|#1| |#1|) -12 (|has| |#1| (-321 |#1|)) (|has| |#1| (-1132)))) ((((-326 |#1|)) . T) (((-560)) . T) (($) . T)) (((|#1| |#2| |#3|) . T)) ((((-560)) . T) (((-893 |#1|)) . T) (($) . T) (((-421 (-560))) . T)) -((($) . T) (((-421 (-560))) -2181 (|has| |#1| (-376)) (|has| |#1| (-363))) ((|#1|) . T)) +((($) . T) (((-421 (-560))) -2173 (|has| |#1| (-376)) (|has| |#1| (-363))) ((|#1|) . T)) ((((-421 (-560))) . T) (((-721)) . T) (($) . T)) ((((-887)) . T)) ((((-1212)) . T)) @@ -52,14 +52,14 @@ (((|#1|) . T) ((|#2|) . T)) ((((-1212)) . T)) (((|#1|) . T) (((-560)) |has| |#1| (-1069 (-560))) (((-421 (-560))) |has| |#1| (-1069 (-421 (-560))))) -(-2181 (|has| |#2| (-175)) (|has| |#2| (-466)) (|has| |#2| (-571)) (|has| |#2| (-939))) -(-2181 (|has| |#1| (-175)) (|has| |#1| (-466)) (|has| |#1| (-571)) (|has| |#1| (-939))) -(((|#2| (-496 (-2305 |#1|) (-793))) . T)) -((((-1207)) -2181 (|has| (-421 |#2|) (-927 (-1207))) (|has| (-421 |#2|) (-929 (-1207))))) +(-2173 (|has| |#2| (-175)) (|has| |#2| (-466)) (|has| |#2| (-571)) (|has| |#2| (-939))) +(-2173 (|has| |#1| (-175)) (|has| |#1| (-466)) (|has| |#1| (-571)) (|has| |#1| (-939))) +(((|#2| (-496 (-2292 |#1|) (-793))) . T)) +((((-1207)) -2173 (|has| (-421 |#2|) (-927 (-1207))) (|has| (-421 |#2|) (-929 (-1207))))) (((|#1| (-545 (-1207))) . T)) ((((-1189)) . T) (((-987 (-130))) . T) (((-887)) . T)) ((((-887)) . T)) -((((-2 (|:| -3819 |#1|) (|:| -2913 |#2|))) . T)) +((((-2 (|:| -3835 |#1|) (|:| -2923 |#2|))) . T)) (((#0=(-893 |#1|) #0#) . T) ((#1=(-421 (-560)) #1#) . T) (($ $) . T)) (|has| |#4| (-381)) (|has| |#3| (-381)) @@ -75,14 +75,14 @@ (|has| |#1| (-147)) (|has| |#1| (-149)) (|has| |#1| (-571)) -((((-560)) . T) (((-421 (-560))) -2181 (|has| |#2| (-38 (-421 (-560)))) (|has| |#2| (-1069 (-421 (-560))))) ((|#2|) . T) (($) -2181 (|has| |#2| (-466)) (|has| |#2| (-571)) (|has| |#2| (-939))) (((-888 |#1|)) . T)) -(-2181 (|has| |#1| (-376)) (|has| |#1| (-571))) -(-2181 (|has| |#1| (-376)) (|has| |#1| (-571))) -((((-2 (|:| -3989 |#1|) (|:| -3210 |#2|))) . T)) +((((-560)) . T) (((-421 (-560))) -2173 (|has| |#2| (-38 (-421 (-560)))) (|has| |#2| (-1069 (-421 (-560))))) ((|#2|) . T) (($) -2173 (|has| |#2| (-466)) (|has| |#2| (-571)) (|has| |#2| (-939))) (((-888 |#1|)) . T)) +(-2173 (|has| |#1| (-376)) (|has| |#1| (-571))) +(-2173 (|has| |#1| (-376)) (|has| |#1| (-571))) +((((-2 (|:| -3998 |#1|) (|:| -4417 |#2|))) . T)) ((($) . T)) ((((-887)) |has| |#1| (-632 (-887))) ((|#1|) . T)) -((((-560)) . T) (((-421 (-560))) -2181 (|has| |#1| (-38 (-421 (-560)))) (|has| |#1| (-1069 (-421 (-560))))) ((|#1|) . T) (($) -2181 (|has| |#1| (-466)) (|has| |#1| (-571)) (|has| |#1| (-939))) (((-1207)) . T)) -((((-887)) -2181 (|has| |#1| (-632 (-887))) (|has| |#1| (-871)) (|has| |#1| (-1132)))) +((((-560)) . T) (((-421 (-560))) -2173 (|has| |#1| (-38 (-421 (-560)))) (|has| |#1| (-1069 (-421 (-560))))) ((|#1|) . T) (($) -2173 (|has| |#1| (-466)) (|has| |#1| (-571)) (|has| |#1| (-939))) (((-1207)) . T)) +((((-887)) -2173 (|has| |#1| (-632 (-887))) (|has| |#1| (-871)) (|has| |#1| (-1132)))) ((((-549)) |has| |#1| (-633 (-549)))) ((((-1207)) . T)) (((|#1|) . T)) @@ -103,12 +103,12 @@ ((((-887)) . T)) (((|#1| |#2|) . T)) (((|#1|) . T)) -(((#0=(-421 (-560)) #0#) |has| |#2| (-38 (-421 (-560)))) ((|#2| |#2|) . T) (($ $) -2181 (|has| |#2| (-175)) (|has| |#2| (-466)) (|has| |#2| (-571)) (|has| |#2| (-939)))) +(((#0=(-421 (-560)) #0#) |has| |#2| (-38 (-421 (-560)))) ((|#2| |#2|) . T) (($ $) -2173 (|has| |#2| (-175)) (|has| |#2| (-466)) (|has| |#2| (-571)) (|has| |#2| (-939)))) (|has| |#1| (-1132)) (((|#1|) . T)) ((((-118 |#1|)) . T) (($) . T) (((-421 (-560))) . T)) -((((-421 (-560))) |has| |#2| (-38 (-421 (-560)))) ((|#2|) |has| |#2| (-175)) (($) -2181 (|has| |#2| (-466)) (|has| |#2| (-571)) (|has| |#2| (-939)))) -((($) -2181 (|has| |#1| (-466)) (|has| |#1| (-571)) (|has| |#1| (-939))) ((|#1|) |has| |#1| (-175)) (((-421 (-560))) |has| |#1| (-38 (-421 (-560))))) +((((-421 (-560))) |has| |#2| (-38 (-421 (-560)))) ((|#2|) |has| |#2| (-175)) (($) -2173 (|has| |#2| (-466)) (|has| |#2| (-571)) (|has| |#2| (-939)))) +((($) -2173 (|has| |#1| (-466)) (|has| |#1| (-571)) (|has| |#1| (-939))) ((|#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)) ((($) . T) (((-560)) . T) (((-421 (-560))) |has| |#2| (-38 (-421 (-560)))) ((|#2|) . T)) (((|#2|) . T) (((-560)) . T) ((|#6|) . T)) -((((-421 (-560))) |has| |#2| (-38 (-421 (-560)))) ((|#2|) . T) (($) -2181 (|has| |#2| (-175)) (|has| |#2| (-466)) (|has| |#2| (-571)) (|has| |#2| (-939)))) +((((-421 (-560))) |has| |#2| (-38 (-421 (-560)))) ((|#2|) . T) (($) -2173 (|has| |#2| (-175)) (|has| |#2| (-466)) (|has| |#2| (-571)) (|has| |#2| (-939)))) ((($) . T)) ((($) . T)) (((|#2|) . T)) (((|#1|) . T) (((-421 (-560))) |has| |#1| (-38 (-421 (-560)))) (((-560)) . T) (($) . T)) ((((-560)) . T) (($) . T) ((|#1|) . T) (((-421 (-560))) |has| |#1| (-38 (-421 (-560))))) -((((-421 (-560))) |has| |#1| (-38 (-421 (-560)))) ((|#1|) . T) (($) -2181 (|has| |#1| (-175)) (|has| |#1| (-466)) (|has| |#1| (-571)) (|has| |#1| (-939)))) -(((#0=(-421 (-560)) #0#) |has| |#1| (-38 (-421 (-560)))) ((|#1| |#1|) . 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T)) ((((-421 (-560))) . T) (($) . T)) @@ -228,7 +228,7 @@ (((|#1|) . T)) (|has| |#2| (-376)) ((((-1264 (-560)) $) . T) (((-560) |#1|) . T)) -((($) -2181 (|has| (-421 |#2|) (-240)) (|has| (-421 |#2|) (-239)))) +((($) -2173 (|has| (-421 |#2|) (-240)) (|has| (-421 |#2|) (-239)))) ((($) . T) (((-560)) . T) (((-421 (-560))) . T)) (((|#1| |#2|) . T)) ((((-887)) . T)) @@ -241,13 +241,13 @@ ((((-887)) . T)) ((((-887)) . T)) (((|#1| |#1|) . T)) -(((#0=(-421 (-560)) #0#) |has| |#1| (-38 (-421 (-560)))) ((|#1| |#1|) . T) (($ $) -2181 (|has| |#1| (-175)) (|has| |#1| (-466)) (|has| |#1| (-571)) (|has| |#1| (-939)))) -((($ $) -2181 (|has| |#1| (-175)) (|has| |#1| (-376)) (|has| |#1| (-466)) (|has| |#1| (-571)) (|has| |#1| (-939))) ((|#1| |#1|) . T) ((#0=(-421 (-560)) #0#) |has| |#1| (-38 (-421 (-560))))) +(((#0=(-421 (-560)) #0#) |has| |#1| (-38 (-421 (-560)))) ((|#1| |#1|) . 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T) (((-421 (-560))) -2181 (|has| |#1| (-38 (-421 (-560)))) (|has| |#1| (-376))) ((|#1|) . T)) +((($) . T) (((-421 (-560))) -2173 (|has| |#1| (-38 (-421 (-560)))) (|has| |#1| (-376))) ((|#1|) . T)) (|has| |#1| (-843)) ((((-421 (-560))) |has| |#1| (-1069 (-421 (-560)))) (((-560)) |has| |#1| (-1069 (-560))) ((|#1|) . T)) -(-2181 (|has| |#1| (-102)) (|has| |#1| (-1132))) +(-2173 (|has| |#1| (-102)) (|has| |#1| (-1132))) (((|#1| $) |has| |#1| (-298 |#1| |#1|))) ((((-421 (-560))) |has| |#1| (-38 (-421 (-560)))) ((|#1|) |has| |#1| (-175)) (($) |has| |#1| (-571))) ((($) |has| |#1| (-571))) @@ -1065,49 +1065,49 @@ (((|#4|) |has| |#4| (-1132))) (((|#3|) |has| |#3| (-1132))) (|has| |#3| (-381)) -((($) |has| |#1| (-571)) ((|#1|) . T) (((-421 (-560))) -2181 (|has| |#1| (-38 (-421 (-560)))) (|has| |#1| (-1069 (-421 (-560))))) (((-560)) . T)) +((($) |has| |#1| (-571)) ((|#1|) . T) (((-421 (-560))) -2173 (|has| |#1| (-38 (-421 (-560)))) (|has| |#1| (-1069 (-421 (-560))))) (((-560)) . T)) ((((-887)) . 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T)) -(-2181 (|has| |#1| (-21)) (|has| |#1| (-25)) (|has| |#1| (-147)) (|has| |#1| (-149)) (|has| |#1| (-175)) (|has| |#1| (-571)) (|has| |#1| (-1080))) +(-2173 (|has| |#1| (-21)) (|has| |#1| (-25)) (|has| |#1| (-147)) (|has| |#1| (-149)) (|has| |#1| (-175)) (|has| |#1| (-571)) (|has| |#1| (-1080))) (((|#1|) |has| |#1| (-175))) (|has| $ (-149)) (|has| $ (-149)) ((((-1212)) . T)) (((|#1|) |has| |#1| (-175))) -(-2181 (|has| |#1| (-102)) (|has| |#1| (-1132))) +(-2173 (|has| |#1| (-102)) (|has| |#1| (-1132))) ((((-887)) . T)) (|has| |#1| (-38 (-421 (-560)))) (|has| |#1| (-38 (-421 (-560)))) -(-2181 (|has| |#1| (-147)) (|has| |#1| (-149)) (|has| |#1| (-175)) (|has| |#1| (-487)) (|has| |#1| (-571)) (|has| |#1| (-1080)) (|has| |#1| (-1143))) +(-2173 (|has| |#1| (-147)) (|has| |#1| (-149)) (|has| |#1| (-175)) (|has| |#1| (-487)) (|has| |#1| (-571)) (|has| |#1| (-1080)) (|has| |#1| (-1143))) ((($ $) |has| |#1| (-298 $ $)) ((|#1| $) |has| |#1| (-298 |#1| |#1|))) (((|#1| (-421 (-560))) . T)) (((|#1|) . T)) @@ -1116,8 +1116,8 @@ (((|#1|) . T)) ((((-1207)) . T)) (|has| |#1| (-571)) -(-2181 (|has| |#1| (-376)) (|has| |#1| (-571))) -(-2181 (|has| |#1| (-376)) (|has| |#1| (-571))) +(-2173 (|has| |#1| (-376)) (|has| |#1| (-571))) +(-2173 (|has| |#1| (-376)) (|has| |#1| (-571))) (|has| |#1| (-571)) (|has| |#1| (-38 (-421 (-560)))) (|has| |#1| (-38 (-421 (-560)))) @@ -1129,7 +1129,7 @@ (|has| |#1| (-149)) (|has| |#1| (-147)) (|has| |#1| (-149)) -(((|#2| (-246 (-2305 |#1|) (-793)) (-888 |#1|)) . T)) +(((|#2| (-246 (-2292 |#1|) (-793)) (-888 |#1|)) . T)) (((|#1| (-545 |#3|) |#3|) . T)) (|has| |#1| (-147)) (((#0=(-421 (-560)) #0#) |has| |#2| (-376)) (($ $) . T)) @@ -1143,12 +1143,12 @@ (|has| |#1| (-147)) ((((-421 (-560))) |has| |#2| (-376)) (($) . T)) (((|#1| |#1|) -12 (|has| |#1| (-321 |#1|)) (|has| |#1| (-1132)))) -(-2181 (|has| |#2| (-466)) (|has| |#2| (-571)) (|has| |#2| (-939))) -(-2181 (|has| |#1| (-363)) (|has| |#1| (-381))) +(-2173 (|has| |#2| (-466)) (|has| |#2| (-571)) (|has| |#2| (-939))) +(-2173 (|has| |#1| (-363)) (|has| |#1| (-381))) ((((-1173 |#2| |#1|)) . T) ((|#1|) . T)) (((|#1| |#2|) . T)) (-12 (|has| |#2| (-240)) (|has| |#2| (-1080))) -(((|#2|) . T) (((-2 (|:| -3819 |#1|) (|:| -2913 |#2|))) . T)) +(((|#2|) . T) (((-2 (|:| -3835 |#1|) (|:| -2923 |#2|))) . T)) (|has| |#3| (-815)) (|has| |#3| (-815)) ((((-887)) . T)) @@ -1176,18 +1176,18 @@ ((((-887)) . T)) ((((-887)) . T)) (((|#1| |#2|) . T)) -((((-1207)) -2181 (|has| |#2| (-927 (-1207))) (|has| |#2| (-929 (-1207)))) (((-1113)) . T)) +((((-1207)) -2173 (|has| |#2| (-927 (-1207))) (|has| |#2| (-929 (-1207)))) (((-1113)) . T)) (((|#1|) . T)) (((|#3|) . T) (((-630 $)) . T)) (((|#1| (-421 (-560))) . T)) -((((-2 (|:| -3819 |#1|) (|:| -2913 |#2|))) . 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T)) -((((-1207)) -2181 (|has| |#1| (-927 (-1207))) (|has| |#1| (-929 (-1207))))) +((((-1207)) -2173 (|has| |#1| (-927 (-1207))) (|has| |#1| (-929 (-1207))))) (((|#3|) . T)) ((($ $) . T) ((#0=(-888 |#1|) $) . T) ((#0# |#2|) . T)) (|has| |#1| (-843)) @@ -1211,10 +1211,10 @@ ((($) . T) (((-560)) . T) (((-421 (-560))) |has| |#1| (-38 (-421 (-560)))) ((|#1|) . T)) ((((-560)) . T) (($) . T) ((|#1|) . T) (((-421 (-560))) |has| |#1| (-38 (-421 (-560))))) (|has| (-1120 |#1|) (-1132)) -(((|#2| |#2|) -2181 (|has| |#2| (-175)) (|has| |#2| (-376)) (|has| |#2| (-1080)))) -(((|#2|) -2181 (|has| |#2| (-175)) (|has| |#2| (-376)))) -((((-560) (-2 (|:| -3819 |#1|) (|:| -2913 |#2|))) . T) ((|#1| |#2|) . T)) -(((|#2|) -2181 (|has| |#2| (-175)) (|has| |#2| (-376)) (|has| |#2| (-1080)))) +(((|#2| |#2|) -2173 (|has| |#2| (-175)) (|has| |#2| (-376)) (|has| |#2| (-1080)))) +(((|#2|) -2173 (|has| |#2| (-175)) (|has| |#2| (-376)))) +((((-560) (-2 (|:| -3835 |#1|) (|:| -2923 |#2|))) . T) ((|#1| |#2|) . T)) +(((|#2|) -2173 (|has| |#2| (-175)) (|has| |#2| (-376)) (|has| |#2| (-1080)))) ((((-560)) . T)) ((((-1212)) . T)) ((((-793)) . T)) @@ -1233,34 +1233,34 @@ (((|#1|) . T)) ((((-421 (-560))) . T) (($) . T)) ((($) . T) (((-421 (-560))) . T)) -(-2181 (|has| |#1| (-175)) (|has| |#1| (-571))) +(-2173 (|has| |#1| (-175)) (|has| |#1| (-571))) ((((-1212)) . T)) -(-2181 (|has| |#1| (-175)) (|has| |#1| (-376)) (|has| |#1| (-571))) -(-2181 (|has| |#1| (-175)) (|has| |#1| (-376)) (|has| |#1| (-571))) +(-2173 (|has| |#1| (-175)) (|has| |#1| (-376)) (|has| |#1| (-571))) +(-2173 (|has| |#1| (-175)) (|has| |#1| (-376)) (|has| |#1| (-571))) ((((-560)) . T)) -(-2181 (|has| |#1| (-175)) (|has| |#1| (-571))) +(-2173 (|has| |#1| (-175)) (|has| |#1| (-571))) (|has| |#1| (-147)) ((((-560)) . 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T)) -((($) -2181 (|has| |#1| (-319)) (|has| |#1| (-376)) (|has| |#1| (-363)) (|has| |#1| (-571))) (((-421 (-560))) -2181 (|has| |#1| (-376)) (|has| |#1| (-363))) ((|#1|) . T)) -((($) -2181 (|has| (-421 |#2|) (-240)) (|has| (-421 |#2|) (-239)))) +((($) -2173 (|has| |#1| (-319)) (|has| |#1| (-376)) (|has| |#1| (-363)) (|has| |#1| (-571))) (((-421 (-560))) -2173 (|has| |#1| (-376)) (|has| |#1| (-363))) ((|#1|) . T)) +((($) -2173 (|has| (-421 |#2|) (-240)) (|has| (-421 |#2|) (-239)))) ((((-560) |#2|) . T)) -((($ (-1207)) -2181 (|has| |#2| (-927 (-1207))) (|has| |#2| (-929 (-1207))))) +((($ (-1207)) -2173 (|has| |#2| (-927 (-1207))) (|has| |#2| (-929 (-1207))))) (((|#1| |#2|) . T)) (((|#1| |#2|) . T)) (|has| |#2| (-381)) @@ -1280,46 +1280,46 @@ ((((-887)) . 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T)) (((|#1|) |has| |#1| (-321 |#1|))) @@ -1329,21 +1329,21 @@ (|has| |#1| (-381)) ((((-1207) $) |has| |#1| (-528 (-1207) $)) (($ $) |has| |#1| (-321 $)) ((|#1| |#1|) |has| |#1| (-321 |#1|)) (((-1207) |#1|) |has| |#1| (-528 (-1207) |#1|))) ((((-1207)) |has| |#1| (-927 (-1207)))) -(-2181 (-12 (|has| |#1| (-240)) (|has| |#1| (-376))) (|has| |#1| (-363))) +(-2173 (-12 (|has| |#1| (-240)) (|has| |#1| (-376))) (|has| |#1| (-363))) (((|#1| |#4|) . T)) (((|#1| |#3|) . T)) ((($) . T)) ((((-402) |#1|) . T)) -(-2181 (|has| |#1| (-376)) (|has| |#1| (-363))) -(-2181 (|has| |#1| (-102)) (|has| |#1| (-1132))) +(-2173 (|has| |#1| (-376)) (|has| |#1| (-363))) +(-2173 (|has| |#1| (-102)) (|has| |#1| (-1132))) (((|#2|) . T) (((-887)) . T)) ((((-887)) . T)) (((|#2|) . T)) ((((-935 |#1|)) . T)) ((((-887)) . T) (((-1212)) . T)) ((((-1212)) . T)) -((((-421 (-560))) |has| |#2| (-38 (-421 (-560)))) ((|#2|) |has| |#2| (-175)) (($) -2181 (|has| |#2| (-466)) (|has| |#2| (-571)) (|has| |#2| (-939)))) -((((-421 (-560))) |has| |#1| (-38 (-421 (-560)))) ((|#1|) |has| |#1| (-175)) (($) -2181 (|has| |#1| (-466)) (|has| |#1| (-571)) (|has| |#1| (-939)))) +((((-421 (-560))) |has| |#2| (-38 (-421 (-560)))) ((|#2|) |has| |#2| (-175)) (($) -2173 (|has| |#2| (-466)) (|has| |#2| (-571)) (|has| |#2| (-939)))) +((((-421 (-560))) |has| |#1| (-38 (-421 (-560)))) ((|#1|) |has| |#1| (-175)) (($) -2173 (|has| |#1| (-466)) (|has| |#1| (-571)) (|has| |#1| (-939)))) (((|#1| |#2|) . T)) ((($) . T)) ((((-560)) . T) (($) . T) (((-421 (-560))) . T)) @@ -1352,7 +1352,7 @@ (((|#1|) . T) (((-421 (-560))) . T) (($) . T) (((-560)) . T)) (((|#1| |#1|) . T)) (((#0=(-893 |#1|)) |has| #0# (-321 #0#))) -((((-560)) . T) (($) -2181 (|has| |#1| (-376)) (|has| |#1| (-363))) (((-421 (-560))) -2181 (|has| |#1| (-376)) (|has| |#1| (-363)) (|has| |#1| (-1069 (-421 (-560))))) ((|#1|) . T)) +((((-560)) . T) (($) -2173 (|has| |#1| (-376)) (|has| |#1| (-363))) (((-421 (-560))) -2173 (|has| |#1| (-376)) (|has| |#1| (-363)) (|has| |#1| (-1069 (-421 (-560))))) ((|#1|) . T)) (((|#1| |#2|) . T)) (|has| |#2| (-815)) (|has| |#2| (-815)) @@ -1361,7 +1361,7 @@ (-12 (|has| |#1| (-815)) (|has| |#2| (-815))) (|has| |#2| (-1080)) ((($) . T) (((-560)) . T) ((|#2|) . T)) -(((|#2|) . T) (((-2 (|:| -3819 |#1|) (|:| -2913 |#2|))) . T)) +(((|#2|) . T) (((-2 (|:| -3835 |#1|) (|:| -2923 |#2|))) . T)) (((|#2|) . T) (($) . T)) (|has| |#1| (-1233)) (((#0=(-560) #0#) . T) ((#1=(-421 (-560)) #1#) . T) (($ $) . T)) @@ -1375,7 +1375,7 @@ (((|#1| |#1|) . T) (($ $) . T) ((#0=(-421 (-560)) #0#) . T)) (|has| |#1| (-376)) ((((-560)) . T) (((-421 (-560))) . T) (($) . 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T) (((-421 (-560))) |has| |#2| (-38 (-421 (-560))))) +((($) -2173 (|has| |#2| (-175)) (|has| |#2| (-376)) (|has| |#2| (-466)) (|has| |#2| (-571)) (|has| |#2| (-939))) ((|#2|) . T) (((-421 (-560))) |has| |#2| (-38 (-421 (-560))))) ((((-560)) |has| #0=(-421 |#2|) (-660 (-560))) ((#0#) . T)) ((($) . T) (((-560)) . T)) ((((-560) (-146)) . T)) -((((-560) (-2 (|:| -3819 |#1|) (|:| -2913 |#2|))) . T) ((|#1| |#2|) . T)) +((((-560) (-2 (|:| -3835 |#1|) (|:| -2923 |#2|))) . T) ((|#1| |#2|) . T)) ((((-421 (-560))) . T) (($) . T)) (((|#1|) . T)) -((((-2 (|:| -3819 |#1|) (|:| -2913 |#2|))) . T)) +((((-2 (|:| -3835 |#1|) (|:| -2923 |#2|))) . T)) ((((-887)) . T)) ((((-935 |#1|)) . T)) (|has| |#1| (-376)) @@ -1423,11 +1423,11 @@ (|has| |#1| (-376)) (|has| |#1| (-15 * (|#1| (-421 (-560)) |#1|))) (|has| |#1| (-870)) -((($) -2181 (|has| |#1| (-319)) (|has| |#1| (-376)) (|has| |#1| (-363)) (|has| |#1| (-571))) (((-421 (-560))) -2181 (|has| |#1| (-376)) (|has| |#1| (-363))) ((|#1|) . 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T)) -(((|#2|) -2181 (|has| |#2| (-175)) (|has| |#2| (-376)) (|has| |#2| (-1080)))) +(((|#2|) -2173 (|has| |#2| (-175)) (|has| |#2| (-376)) (|has| |#2| (-1080)))) (|has| $ (-149)) ((((-421 |#2|)) . T)) ((((-421 (-560))) |has| #0=(-421 |#2|) (-1069 (-421 (-560)))) (((-560)) |has| #0# (-1069 (-560))) ((#0#) . T)) @@ -1570,11 +1570,11 @@ (|has| |#2| (-149)) (|has| |#1| (-149)) (|has| |#1| (-147)) -(-2181 (|has| |#1| (-147)) (|has| |#1| (-381))) +(-2173 (|has| |#1| (-147)) (|has| |#1| (-381))) (|has| |#1| (-149)) -(-2181 (|has| |#1| (-147)) (|has| |#1| (-381))) +(-2173 (|has| |#1| (-147)) (|has| |#1| (-381))) (|has| |#1| (-149)) -(-2181 (|has| |#1| (-147)) (|has| |#1| (-381))) +(-2173 (|has| |#1| (-147)) (|has| |#1| (-381))) (|has| |#1| (-149)) (((|#1|) . T)) (|has| |#2| (-240)) @@ -1611,9 +1611,9 @@ ((((-887)) . T)) ((((-887)) . T)) ((((-1027 |#1|)) . T) ((|#1|) . T)) -((((-1207)) -2181 (|has| |#1| (-927 (-1207))) (|has| |#1| (-929 (-1207)))) (((-840 (-1207))) . 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T)) -(-2181 (|has| |#1| (-149)) (-12 (|has| |#1| (-376)) (|has| |#2| (-149)))) +(-2173 (|has| |#1| (-149)) (-12 (|has| |#1| (-376)) (|has| |#2| (-149)))) (((|#4|) . T)) -(-2181 (|has| |#1| (-147)) (-12 (|has| |#1| (-376)) (|has| |#2| (-147)))) +(-2173 (|has| |#1| (-147)) (-12 (|has| |#1| (-376)) (|has| |#2| (-147)))) ((((-1189) |#1|) . T)) (|has| |#1| (-147)) (|has| |#1| (-149)) @@ -1719,24 +1719,24 @@ (((|#3|) . T)) ((((-1287 |#1| |#2| |#3|)) |has| |#1| (-376))) ((($) . T) (((-560)) . T) (((-421 (-560))) |has| |#1| (-38 (-421 (-560)))) ((|#1|) . T)) -((((-421 (-560))) -2181 (|has| |#1| (-38 (-421 (-560)))) (|has| |#1| (-376))) (((-1205 |#1| |#2| |#3|)) |has| |#1| (-376)) (((-560)) . T) (($) . T) ((|#1|) . T)) -(((|#1|) . T) (((-421 (-560))) -2181 (|has| |#1| (-38 (-421 (-560)))) (|has| |#1| (-376))) (((-560)) . T) (($) . T)) +((((-421 (-560))) -2173 (|has| |#1| (-38 (-421 (-560)))) (|has| |#1| (-376))) (((-1205 |#1| |#2| |#3|)) |has| |#1| (-376)) (((-560)) . T) (($) . T) ((|#1|) . T)) +(((|#1|) . T) (((-421 (-560))) -2173 (|has| |#1| (-38 (-421 (-560)))) (|has| |#1| (-376))) (((-560)) . T) (($) . T)) ((((-887)) . T)) -(-2181 (|has| |#1| (-102)) (|has| |#1| (-871)) (|has| |#1| (-1132))) +(-2173 (|has| |#1| (-102)) (|has| |#1| (-871)) (|has| |#1| (-1132))) (((|#1|) . T)) (((|#1|) . T) (((-421 (-560))) |has| |#1| (-38 (-421 (-560)))) (((-560)) . T) (($) . T)) -((((-887)) -2181 (|has| |#1| (-632 (-887))) (|has| |#1| (-1132)))) -((((-887)) -2181 (|has| |#1| (-632 (-887))) (|has| |#1| (-1132))) (((-987 |#1|)) . T)) +((((-887)) -2173 (|has| |#1| (-632 (-887))) (|has| |#1| (-1132)))) +((((-887)) -2173 (|has| |#1| (-632 (-887))) (|has| |#1| (-1132))) (((-987 |#1|)) . T)) (|has| |#1| (-870)) (|has| |#1| (-870)) (((|#1| |#1|) -12 (|has| |#1| (-321 |#1|)) (|has| |#1| (-1132)))) ((((-987 |#1|)) . T)) -(((|#4|) -2181 (|has| |#4| (-175)) (|has| |#4| (-376)) (|has| |#4| (-748)))) -(((|#3|) -2181 (|has| |#3| (-175)) (|has| |#3| (-376)) (|has| |#3| (-748)))) +(((|#4|) -2173 (|has| |#4| (-175)) (|has| |#4| (-376)) (|has| |#4| (-748)))) +(((|#3|) -2173 (|has| |#3| (-175)) (|has| |#3| (-376)) (|has| |#3| (-748)))) (|has| |#2| (-376)) (((|#1|) |has| |#1| (-175))) -(((|#4|) -2181 (|has| |#4| (-175)) (|has| |#4| (-376)) (|has| |#4| (-748)) (|has| |#4| (-1080)))) -(((|#3|) -2181 (|has| |#3| (-175)) (|has| |#3| (-376)) (|has| |#3| (-748)) (|has| |#3| (-1080)))) +(((|#4|) -2173 (|has| |#4| (-175)) (|has| |#4| (-376)) (|has| |#4| (-748)) (|has| |#4| (-1080)))) +(((|#3|) -2173 (|has| |#3| (-175)) (|has| |#3| (-376)) (|has| |#3| (-748)) (|has| |#3| (-1080)))) (((|#2|) |has| |#2| (-1080))) (((|#2|) |has| |#2| (-1080))) ((((-1189) |#1|) . T)) @@ -1748,8 +1748,8 @@ ((((-402) (-1189)) . T)) ((($ (-1207)) . T)) ((($) |has| |#1| (-571)) ((|#1|) |has| |#1| (-175)) (((-421 (-560))) |has| |#1| (-38 (-421 (-560))))) -((((-887)) -2181 (|has| |#2| (-21)) (|has| |#2| (-23)) (|has| |#2| (-25)) (|has| |#2| (-133)) (|has| |#2| (-632 (-887))) (|has| |#2| (-175)) (|has| |#2| (-376)) (|has| |#2| (-381)) (|has| |#2| (-748)) (|has| |#2| (-815)) (|has| |#2| (-871)) (|has| |#2| (-1080)) (|has| |#2| (-1132))) (((-1297 |#2|)) . T)) -(((#0=(-51)) . T) (((-2 (|:| -3819 (-1189)) (|:| -2913 #0#))) . T)) +((((-887)) -2173 (|has| |#2| (-21)) (|has| |#2| (-23)) (|has| |#2| (-25)) (|has| |#2| (-133)) (|has| |#2| (-632 (-887))) (|has| |#2| (-175)) (|has| |#2| (-376)) (|has| |#2| (-381)) (|has| |#2| (-748)) (|has| |#2| (-815)) (|has| |#2| (-871)) (|has| |#2| (-1080)) (|has| |#2| (-1132))) (((-1297 |#2|)) . T)) +(((#0=(-51)) . T) (((-2 (|:| -3835 (-1189)) (|:| -2923 #0#))) . T)) (((|#1|) . T)) ((((-887)) . T)) (((|#2| |#2|) -12 (|has| |#2| (-321 |#2|)) (|has| |#2| (-1132)))) @@ -1758,7 +1758,7 @@ ((((-560)) . T)) (|has| |#2| (-149)) (|has| |#1| (-487)) -(-2181 (|has| |#1| (-487)) (|has| |#1| (-748)) (|has| |#1| (-927 (-1207))) (|has| |#1| (-1080))) +(-2173 (|has| |#1| (-487)) (|has| |#1| (-748)) (|has| |#1| (-927 (-1207))) (|has| |#1| (-1080))) (|has| |#1| (-376)) ((((-887)) . T)) (|has| |#1| (-38 (-421 (-560)))) @@ -1769,8 +1769,8 @@ (|has| |#1| (-870)) ((((-887)) . T)) (((|#2|) . T)) -((((-421 (-560))) -2181 (|has| |#1| (-38 (-421 (-560)))) (|has| |#1| (-376))) (($) -2181 (|has| |#1| (-376)) (|has| |#1| (-571))) (((-1287 |#1| |#2| |#3|)) |has| |#1| (-376)) ((|#1|) |has| |#1| (-175))) -(((|#1|) |has| |#1| (-175)) (((-421 (-560))) -2181 (|has| |#1| (-38 (-421 (-560)))) (|has| |#1| (-376))) (($) -2181 (|has| |#1| (-376)) (|has| |#1| (-571)))) +((((-421 (-560))) -2173 (|has| |#1| (-38 (-421 (-560)))) (|has| |#1| (-376))) (($) -2173 (|has| |#1| (-376)) (|has| |#1| (-571))) (((-1287 |#1| |#2| |#3|)) |has| |#1| (-376)) ((|#1|) |has| |#1| (-175))) +(((|#1|) |has| |#1| (-175)) (((-421 (-560))) -2173 (|has| |#1| (-38 (-421 (-560)))) (|has| |#1| (-376))) (($) -2173 (|has| |#1| (-376)) (|has| |#1| (-571)))) ((($) |has| |#1| (-571)) ((|#1|) |has| |#1| (-175)) (((-421 (-560))) |has| |#1| (-38 (-421 (-560))))) (((|#2|) . T) (((-560)) . T) (((-841 |#1|)) . T)) (((|#1| |#2|) . T)) @@ -1779,8 +1779,8 @@ ((((-935 |#1|)) . T) (((-421 (-560))) . T) (($) . T)) ((((-887)) . T)) ((((-887)) . T)) -(-2181 (|has| |#1| (-102)) (|has| |#1| (-1132))) -(((|#2| (-496 (-2305 |#1|) (-793)) (-888 |#1|)) . T)) +(-2173 (|has| |#1| (-102)) (|has| |#1| (-1132))) +(((|#2| (-496 (-2292 |#1|) (-793)) (-888 |#1|)) . T)) ((((-421 (-560))) . #0=(|has| |#2| (-376))) (($) . #0#)) (((|#1| (-545 (-1207)) (-1207)) . T)) (((|#1|) . T)) @@ -1801,19 +1801,19 @@ (((|#2|) |has| |#2| (-175))) (((|#1|) . T)) (((|#2|) . T)) -(((|#1|) . T) (((-2 (|:| -3819 (-1189)) (|:| -2913 |#1|))) . T)) -((((-2 (|:| -3819 |#1|) (|:| -2913 |#2|))) . T)) +(((|#1|) . T) (((-2 (|:| -3835 (-1189)) (|:| -2923 |#1|))) . T)) +((((-2 (|:| -3835 |#1|) (|:| -2923 |#2|))) . T)) (((|#2|) . T)) -((((-2 (|:| -3819 (-1207)) (|:| -2913 (-51)))) . T)) +((((-2 (|:| -3835 (-1207)) (|:| -2923 (-51)))) . T)) ((((-1205 |#1| |#2| |#3|)) |has| |#1| (-376))) ((((-1205 |#1| |#2| |#3|)) |has| |#1| (-376))) -((((-2 (|:| -3819 |#1|) (|:| -2913 |#2|))) . T)) +((((-2 (|:| -3835 |#1|) (|:| -2923 |#2|))) . T)) ((((-1207) (-51)) . T)) ((((-421 (-560)) |#1|) . T) (($ $) . T)) (((|#1| (-560)) . T)) ((((-935 |#1|)) . T)) -(((|#1|) -2181 (|has| |#1| (-175)) (|has| |#1| (-376)) (|has| |#1| (-1080))) (($) -2181 (|has| |#1| (-927 (-1207))) (|has| |#1| (-1080)))) -((((-1207)) -2181 (-12 (|has| |#2| (-927 (-1207))) (|has| |#2| (-1080))) (-12 (|has| |#2| (-929 (-1207))) (|has| |#2| (-1080))))) +(((|#1|) -2173 (|has| |#1| (-175)) (|has| |#1| (-376)) (|has| |#1| (-1080))) (($) -2173 (|has| |#1| (-927 (-1207))) (|has| |#1| (-1080)))) +((((-1207)) -2173 (-12 (|has| |#2| (-927 (-1207))) (|has| |#2| (-1080))) (-12 (|has| |#2| (-929 (-1207))) (|has| |#2| (-1080))))) (((|#1|) . T) (((-560)) |has| |#1| (-1069 (-560))) (((-421 (-560))) |has| |#1| (-1069 (-421 (-560))))) (|has| |#1| (-871)) (|has| |#1| (-871)) @@ -1834,15 +1834,15 @@ (((|#4| |#4|) -12 (|has| |#4| (-321 |#4|)) (|has| |#4| (-1132)))) (((|#1|) |has| |#1| (-175))) (((|#4| |#4|) -12 (|has| |#4| (-321 |#4|)) (|has| |#4| (-1132)))) -(((|#3|) -2181 (|has| |#3| (-175)) (|has| |#3| (-376)))) -((($) -2181 (|has| |#1| (-466)) (|has| |#1| (-571)) (|has| |#1| (-939))) ((|#1|) |has| |#1| (-175)) (((-421 (-560))) |has| |#1| (-38 (-421 (-560))))) -(-2181 (|has| |#2| (-376)) (|has| |#2| (-466)) (|has| |#2| (-939))) -((($) -2181 (|has| |#1| (-175)) (|has| |#1| (-466)) (|has| |#1| (-571)) (|has| |#1| (-939))) ((|#1|) . T) (((-421 (-560))) |has| |#1| (-38 (-421 (-560))))) +(((|#3|) -2173 (|has| |#3| (-175)) (|has| |#3| (-376)))) +((($) -2173 (|has| |#1| (-466)) (|has| |#1| (-571)) (|has| |#1| (-939))) ((|#1|) |has| |#1| (-175)) (((-421 (-560))) |has| |#1| (-38 (-421 (-560))))) +(-2173 (|has| |#2| (-376)) (|has| |#2| (-466)) (|has| |#2| (-939))) +((($) -2173 (|has| |#1| (-175)) (|has| |#1| (-466)) (|has| |#1| (-571)) (|has| |#1| (-939))) ((|#1|) . T) (((-421 (-560))) |has| |#1| (-38 (-421 (-560))))) ((($ |#2|) . T)) -((($ (-1207)) -2181 (|has| |#1| (-927 (-1207))) (|has| |#1| (-929 (-1207)))) (($ (-1113)) . T)) +((($ (-1207)) -2173 (|has| |#1| (-927 (-1207))) (|has| |#1| (-929 (-1207)))) (($ (-1113)) . T)) ((($ $) . T) ((#0=(-421 (-560)) #0#) . T)) ((((-560) |#2|) . T)) -(((|#2|) -2181 (|has| |#2| (-175)) (|has| |#2| (-376)))) +(((|#2|) -2173 (|has| |#2| (-175)) (|has| |#2| (-376)))) (|has| |#1| (-363)) (((|#3| |#3|) -12 (|has| |#3| (-321 |#3|)) (|has| |#3| (-1132)))) (((|#2|) . T) (((-560)) . T)) @@ -1851,7 +1851,7 @@ (|has| |#1| (-842)) (|has| |#1| (-842)) (((|#1|) . T)) -(-2181 (|has| |#1| (-319)) (|has| |#1| (-376)) (|has| |#1| (-363))) +(-2173 (|has| |#1| (-319)) (|has| |#1| (-376)) (|has| |#1| (-363))) (|has| |#1| (-870)) (|has| |#1| (-870)) (|has| |#1| (-870)) @@ -1860,14 +1860,14 @@ ((((-560)) . T) (($) . T) (((-421 (-560))) . T)) (|has| |#1| (-38 (-421 (-560)))) (|has| |#1| (-38 (-421 (-560)))) -(-2181 (|has| |#1| (-376)) (|has| |#1| (-363))) +(-2173 (|has| |#1| (-376)) (|has| |#1| (-363))) (|has| |#1| (-38 (-421 (-560)))) (|has| |#1| (-38 (-421 (-560)))) -((((-2 (|:| -3819 |#1|) (|:| -2913 |#2|))) . T)) +((((-2 (|:| -3835 |#1|) (|:| -2923 |#2|))) . T)) ((((-1207)) |has| |#1| (-927 (-1207))) (((-1113)) . T)) (((|#1|) . T)) (|has| |#1| (-870)) -(((#0=(-2 (|:| -3819 (-1189)) (|:| -2913 (-51))) #0#) |has| (-2 (|:| -3819 (-1189)) (|:| -2913 (-51))) (-321 (-2 (|:| -3819 (-1189)) (|:| -2913 (-51)))))) +(((#0=(-2 (|:| -3835 (-1189)) (|:| -2923 (-51))) #0#) |has| (-2 (|:| -3835 (-1189)) (|:| -2923 (-51))) (-321 (-2 (|:| -3835 (-1189)) (|:| -2923 (-51)))))) (((|#1| |#1|) -12 (|has| |#1| (-321 |#1|)) (|has| |#1| (-1132)))) (|has| |#1| (-1132)) ((((-887)) . T) (((-1212)) . T)) @@ -1891,14 +1891,14 @@ (((|#3|) . T)) (((|#1| (-793) (-1113)) . T)) ((((-146)) . T)) -((((-421 (-560))) |has| |#1| (-1069 (-421 (-560)))) (((-560)) -2181 (|has| |#1| (-870)) (|has| |#1| (-1069 (-560)))) ((|#1|) . T)) +((((-421 (-560))) |has| |#1| (-1069 (-421 (-560)))) (((-560)) -2173 (|has| |#1| (-870)) (|has| |#1| (-1069 (-560)))) ((|#1|) . T)) (((|#1|) . T)) (((|#2|) . T)) ((((-146)) . 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T)) +((($) -2173 (|has| |#1| (-15 * (|#1| (-560) |#1|))) (-12 (|has| |#1| (-376)) (|has| |#2| (-240))) (-12 (|has| |#1| (-376)) (|has| |#2| (-239))))) ((($) |has| |#1| (-15 * (|#1| (-421 (-560)) |#1|)))) ((((-1002)) . T)) ((((-1002)) . T) (((-887)) . T)) @@ -2058,7 +2058,7 @@ ((($) . T)) (((|#1|) . T)) ((((-114)) . T)) -(-2181 (|has| |#1| (-175)) (|has| |#1| (-376)) (|has| |#1| (-571))) +(-2173 (|has| |#1| (-175)) (|has| |#1| (-376)) (|has| |#1| (-571))) ((((-560)) . T)) (((|#1| (-560)) . T)) ((($) . T)) @@ -2081,7 +2081,7 @@ (((|#1| (-1257 |#1| |#2| |#3|)) . T)) ((((-887)) . T)) (|has| |#1| (-1132)) -((((-2 (|:| -3819 |#1|) (|:| -2913 |#2|))) . T)) +((((-2 (|:| -3835 |#1|) (|:| -2923 |#2|))) . T)) (((|#1| (-793)) . T)) ((((-1189) |#1|) . T)) (((|#1|) . T)) @@ -2102,20 +2102,20 @@ ((((-560)) . T)) ((((-560)) . T)) ((((-887)) . T)) -(-2181 (|has| |#1| (-147)) (|has| |#1| (-363))) +(-2173 (|has| |#1| (-147)) (|has| |#1| (-363))) ((((-887)) . T)) (|has| |#1| (-149)) (((|#3|) . 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T)) (((|#3|) |has| |#3| (-1080))) @@ -2362,7 +2362,7 @@ ((((-1207)) |has| |#2| (-927 (-1207)))) (|has| |#1| (-871)) ((((-887)) . T)) -((((-2 (|:| -3819 |#1|) (|:| -2913 |#2|))) . T)) +((((-2 (|:| -3835 |#1|) (|:| -2923 |#2|))) . T)) (|has| |#1| (-813)) ((((-421 (-560))) . T) (($) . T)) (|has| |#1| (-487)) @@ -2370,8 +2370,8 @@ (|has| |#1| (-381)) (|has| |#1| (-381)) (|has| |#1| (-376)) -(-2181 (|has| |#1| (-147)) (|has| |#1| (-149)) (|has| |#1| (-175)) (|has| |#1| (-487)) (|has| |#1| (-571)) (|has| |#1| (-1080)) (|has| |#1| (-1143))) -((($) -2181 (|has| |#1| (-240)) (|has| |#1| (-239)) (|has| |#1| (-363)))) +(-2173 (|has| |#1| (-147)) (|has| |#1| (-149)) (|has| |#1| (-175)) (|has| |#1| (-487)) (|has| |#1| (-571)) (|has| |#1| (-1080)) (|has| |#1| (-1143))) +((($) -2173 (|has| |#1| (-240)) (|has| |#1| (-239)) (|has| |#1| (-363)))) ((((-118 |#1|)) . T)) ((((-118 |#1|)) . T)) (|has| |#1| (-363)) @@ -2383,7 +2383,7 @@ (|has| |#1| (-38 (-421 (-560)))) (((|#2|) . T) (((-887)) . T)) (((|#2|) . T) (((-887)) . T)) -((($ (-1207)) -2181 (|has| |#1| (-927 (-1207))) (|has| |#1| (-929 (-1207))))) +((($ (-1207)) -2173 (|has| |#1| (-927 (-1207))) (|has| |#1| (-929 (-1207))))) (|has| |#1| (-38 (-421 (-560)))) (|has| |#1| (-38 (-421 (-560)))) (|has| |#1| (-38 (-421 (-560)))) @@ -2393,18 +2393,18 @@ (|has| |#1| (-38 (-421 (-560)))) (|has| |#1| (-38 (-421 (-560)))) (|has| |#1| (-871)) -((((-2 (|:| -3819 (-1189)) (|:| -2913 |#1|))) . T)) +((((-2 (|:| -3835 (-1189)) (|:| -2923 |#1|))) . T)) (((|#1| |#2|) . T)) ((($) . T) (((-560)) . T)) (|has| |#1| (-149)) (|has| |#1| (-147)) -((((-2 (|:| -3819 |#1|) (|:| -2913 |#2|))) |has| (-2 (|:| -3819 |#1|) (|:| -2913 |#2|)) (-321 (-2 (|:| -3819 |#1|) (|:| -2913 |#2|)))) ((|#2|) -12 (|has| |#2| (-321 |#2|)) (|has| |#2| (-1132)))) +((((-2 (|:| -3835 |#1|) (|:| -2923 |#2|))) |has| (-2 (|:| -3835 |#1|) (|:| -2923 |#2|)) (-321 (-2 (|:| -3835 |#1|) (|:| -2923 |#2|)))) ((|#2|) -12 (|has| |#2| (-321 |#2|)) (|has| |#2| (-1132)))) (((|#2|) . T)) (|has| |#1| (-15 * (|#1| (-560) |#1|))) (((|#3|) . T)) ((((-118 |#1|)) . T)) (|has| |#1| (-381)) -(-2181 (-12 (|has| (-1287 |#1| |#2| |#3|) (-240)) (|has| |#1| (-376))) (-12 (|has| (-1287 |#1| |#2| |#3|) (-239)) (|has| |#1| (-376))) (|has| |#1| (-15 * (|#1| (-560) |#1|)))) +(-2173 (-12 (|has| (-1287 |#1| |#2| |#3|) (-240)) (|has| |#1| (-376))) (-12 (|has| (-1287 |#1| |#2| |#3|) (-239)) (|has| |#1| (-376))) (|has| |#1| (-15 * (|#1| (-560) |#1|)))) (|has| |#1| (-15 * (|#1| (-421 (-560)) |#1|))) (|has| |#1| (-871)) (((|#2|) . T) (((-421 (-560))) |has| |#1| (-1069 (-421 (-560)))) (((-560)) |has| |#1| (-1069 (-560))) ((|#1|) . T)) @@ -2423,17 +2423,17 @@ (((|#1|) |has| |#1| (-376))) (((|#1|) |has| |#1| (-376))) ((((-887)) . T)) -((((-2 (|:| -3819 |#1|) (|:| -2913 |#2|))) . T)) +((((-2 (|:| -3835 |#1|) (|:| -2923 |#2|))) . T)) ((($ $) . T) (((-630 $) $) . T)) -(-2181 (|has| |#1| (-376)) (|has| |#1| (-571))) +(-2173 (|has| |#1| (-376)) (|has| |#1| (-571))) ((($) . 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T)) -((((-1207)) -2181 (-12 (|has| |#3| (-927 (-1207))) (|has| |#3| (-1080))) (-12 (|has| |#3| (-929 (-1207))) (|has| |#3| (-1080))))) +((((-1207)) -2173 (-12 (|has| |#3| (-927 (-1207))) (|has| |#3| (-1080))) (-12 (|has| |#3| (-929 (-1207))) (|has| |#3| (-1080))))) ((((-663 (-802 |#1| (-888 |#2|)))) . T) (((-887)) . T)) ((((-549)) |has| (-802 |#1| (-888 |#2|)) (-633 (-549)))) (((|#1|) -12 (|has| |#1| (-321 |#1|)) (|has| |#1| (-1132)))) @@ -2442,17 +2442,17 @@ (((|#3|) -12 (|has| |#3| (-321 |#3|)) (|has| |#3| (-1132)))) (((|#1|) |has| |#1| (-175))) ((((-887)) . T)) -(-2181 (|has| |#2| (-466)) (|has| |#2| (-939))) +(-2173 (|has| |#2| (-466)) (|has| |#2| (-939))) (((|#1|) . T)) ((($) . T)) ((($) |has| |#1| (-571)) ((|#1|) |has| |#1| (-175)) (((-421 (-560))) |has| |#1| (-38 (-421 (-560))))) -((($) -2181 (|has| |#1| (-175)) (|has| |#1| (-571))) ((|#1|) . 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T)) ((((-560)) -12 (|has| |#1| (-21)) (|has| |#2| (-21)))) @@ -2460,13 +2460,13 @@ (|has| |#1| (-147)) (|has| |#1| (-149)) ((((-560)) . T)) -(-2181 (|has| |#1| (-376)) (|has| |#1| (-571))) -(-2181 (|has| |#1| (-376)) (|has| |#1| (-571))) +(-2173 (|has| |#1| (-376)) (|has| |#1| (-571))) +(-2173 (|has| |#1| (-376)) (|has| |#1| (-571))) (((#0=(-1278 |#2| |#3| |#4|)) . T) (((-421 (-560))) |has| #0# (-38 (-421 (-560)))) (($) . T)) ((((-560)) . T)) ((($) . 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T) (($ $) -2181 (|has| |#1| (-302)) (|has| |#1| (-376))) ((#0=(-421 (-560)) #0#) |has| |#1| (-376))) +(((|#1| |#1|) . T) (($ $) -2173 (|has| |#1| (-302)) (|has| |#1| (-376))) ((#0=(-421 (-560)) #0#) |has| |#1| (-376))) ((((-975 |#1|)) . T)) -((((-2 (|:| -3819 (-1207)) (|:| -2913 (-51)))) . T)) +((((-2 (|:| -3835 (-1207)) (|:| -2923 (-51)))) . T)) ((($) . T)) ((((-560) |#1|) . T)) ((((-1207)) |has| (-421 |#2|) (-927 (-1207)))) -(((|#1|) . T) (($) -2181 (|has| |#1| (-302)) (|has| |#1| (-376))) (((-421 (-560))) |has| |#1| (-376))) +(((|#1|) . T) (($) -2173 (|has| |#1| (-302)) (|has| |#1| (-376))) (((-421 (-560))) |has| |#1| (-376))) ((((-549)) |has| |#2| (-633 (-549)))) ((((-711 |#2|)) . T) (((-887)) . T)) (((|#1|) . T)) @@ -2518,24 +2518,24 @@ (((|#4|) -12 (|has| |#4| (-321 |#4|)) (|has| |#4| (-1132)))) ((((-893 |#1|)) . 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T)) @@ -2642,13 +2642,13 @@ ((((-421 (-560))) |has| |#1| (-1069 (-421 (-560)))) ((|#1|) . T) (((-560)) . T)) (|has| |#2| (-147)) (|has| |#2| (-149)) -(-2181 (|has| |#2| (-842)) (|has| |#2| (-871))) +(-2173 (|has| |#2| (-842)) (|has| |#2| (-871))) ((((-935 |#1|)) . T) (((-421 (-560))) . T) (($) . T)) -(-2181 (|has| |#1| (-102)) (|has| |#1| (-1132))) +(-2173 (|has| |#1| (-102)) (|has| |#1| (-1132))) ((((-560)) . T) ((|#1|) . T)) (((|#2|) . T) (($) . T) (((-560)) . T)) (((|#2|) . T)) -((((-1207)) -2181 (|has| |#2| (-927 (-1207))) (|has| |#2| (-929 (-1207))))) +((((-1207)) -2173 (|has| |#2| (-927 (-1207))) (|has| |#2| (-929 (-1207))))) (((|#1| |#1|) . T)) (((|#3|) |has| |#3| (-376))) ((((-421 |#2|)) . T)) @@ -2657,10 +2657,10 @@ ((((-887)) . T)) ((((-887)) . T)) ((((-549)) |has| |#1| (-633 (-549)))) -((((-2 (|:| -3819 |#1|) (|:| -2913 |#2|))) . T)) +((((-2 (|:| -3835 |#1|) (|:| -2923 |#2|))) . T)) ((((-560)) . T) (($) . T) (((-421 (-560))) . 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T) (((-560)) . T)) -((((-2 (|:| -3819 (-1189)) (|:| -2913 (-51)))) . T)) +((((-2 (|:| -3835 (-1189)) (|:| -2923 (-51)))) . T)) (((|#1|) . T)) -((((-2 (|:| -3819 |#1|) (|:| -2913 |#2|))) . T)) +((((-2 (|:| -3835 |#1|) (|:| -2923 |#2|))) . T)) ((((-887)) . T)) (((|#1| |#2|) . T)) ((($) . T) (((-560)) . T)) (((|#1| (-421 (-560))) . T)) (((|#1|) . T)) -(-2181 (|has| |#1| (-302)) (|has| |#1| (-376))) +(-2173 (|has| |#1| (-302)) (|has| |#1| (-376))) ((((-146)) . T)) ((((-560)) |has| #0=(-421 |#2|) (-660 (-560))) ((#0#) . T) (((-421 (-560))) . T) (($) . T)) (|has| |#1| (-870)) @@ -2880,7 +2880,7 @@ ((((-887)) . T)) ((((-887)) . T)) ((((-186)) . T) (((-887)) . T)) -((((-2 (|:| -3819 |#1|) (|:| -2913 |#2|))) . T)) +((((-2 (|:| -3835 |#1|) (|:| -2923 |#2|))) . T)) (((|#2| |#2|) . T) ((|#1| |#1|) . T)) ((((-887)) . T)) ((((-887)) . T)) @@ -2897,8 +2897,8 @@ (|has| |#1| (-871)) ((((-887)) . T)) ((((-549)) |has| |#1| (-633 (-549)))) -((((-2 (|:| -3819 (-1189)) (|:| -2913 |#1|))) . 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T) (($ $) . T)) ((((-560)) . T)) (((|#1|) . T)) @@ -2937,12 +2937,12 @@ (|has| |#1| (-38 (-421 (-560)))) (|has| |#1| (-38 (-421 (-560)))) (|has| |#1| (-38 (-421 (-560)))) -(-2181 (|has| |#1| (-376)) (|has| |#1| (-466)) (|has| |#1| (-571)) (|has| |#1| (-939))) +(-2173 (|has| |#1| (-376)) (|has| |#1| (-466)) (|has| |#1| (-571)) (|has| |#1| (-939))) (|has| |#1| (-842)) (((#0=(-935 |#1|) #0#) . T) (($ $) . T) ((#1=(-421 (-560)) #1#) . T)) ((((-421 |#2|)) . T)) (|has| |#1| (-870)) -((((-1234 |#1|)) . T) (((-887)) -2181 (|has| |#1| (-632 (-887))) (|has| |#1| (-1132)))) +((((-1234 |#1|)) . T) (((-887)) -2173 (|has| |#1| (-632 (-887))) (|has| |#1| (-1132)))) (((|#1| |#1|) . T) ((#0=(-421 (-560)) #0#) . T) ((#1=(-560) #1#) . T) (($ $) . T)) ((((-935 |#1|)) . T) (($) . T) (((-421 (-560))) . T)) (((|#2|) |has| |#2| (-1080)) (((-560)) -12 (|has| |#2| (-660 (-560))) (|has| |#2| (-1080)))) @@ -2961,36 +2961,36 @@ (((|#2|) |has| |#2| (-175))) (((|#1|) . T)) (((|#2|) . 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T)) -((($) -2181 (|has| |#1| (-240)) (|has| |#1| (-239)))) +((($) -2173 (|has| |#1| (-240)) (|has| |#1| (-239)))) ((((-560)) . T)) (((|#2|) . T) (((-421 (-560))) |has| |#1| (-1069 (-421 (-560)))) ((|#1|) . T) (($) . T) (((-560)) . T)) -(-2181 (|has| |#1| (-175)) (|has| |#1| (-376)) (|has| |#1| (-466)) (|has| |#1| (-571)) (|has| |#1| (-939))) +(-2173 (|has| |#1| (-175)) (|has| |#1| (-376)) (|has| |#1| (-466)) (|has| |#1| (-571)) (|has| |#1| (-939))) (((|#2|) . T) (((-560)) |has| |#2| (-660 (-560)))) (((|#1| |#2|) . T)) ((($) . T)) @@ -3057,7 +3057,7 @@ (|has| |#2| (-1051)) ((($) . T)) (|has| |#1| (-939)) -((((-2 (|:| -3819 |#1|) (|:| -2913 |#2|))) . T)) +((((-2 (|:| -3835 |#1|) (|:| -2923 |#2|))) . T)) (((|#4|) . T)) ((($) . T)) (((|#2|) . T)) @@ -3067,32 +3067,32 @@ (|has| |#1| (-376)) ((((-935 |#1|)) . T)) ((($) . T) (((-560)) . T) ((|#1|) . T) (((-421 (-560))) . 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T)) -(-2181 (-12 (|has| |#3| (-240)) (|has| |#3| (-1080))) (-12 (|has| |#3| (-239)) (|has| |#3| (-1080)))) +(-2173 (-12 (|has| |#3| (-240)) (|has| |#3| (-1080))) (-12 (|has| |#3| (-239)) (|has| |#3| (-1080)))) ((($) . T) (((-421 (-560))) . T)) ((($) . T) (((-560)) . T) (((-421 (-560))) . T) (((-630 $)) . T)) ((((-560)) . T) (($) . T)) ((((-560)) . T) (($) . T)) ((((-793) |#1|) . T)) -(((|#2| (-246 (-2305 |#1|) (-793))) . T)) +(((|#2| (-246 (-2292 |#1|) (-793))) . T)) (((|#1| (-545 |#3|)) . T)) ((((-421 (-560))) . T)) -(-2181 (|has| |#1| (-466)) (|has| |#1| (-571)) (|has| |#1| (-939))) +(-2173 (|has| |#1| (-466)) (|has| |#1| (-571)) (|has| |#1| (-939))) ((((-1189)) . T) (((-887)) . T)) -(((#0=(-2 (|:| -3819 (-1207)) (|:| -2913 (-51))) #0#) |has| (-2 (|:| -3819 (-1207)) (|:| -2913 (-51))) (-321 (-2 (|:| -3819 (-1207)) (|:| -2913 (-51)))))) +(((#0=(-2 (|:| -3835 (-1207)) (|:| -2923 (-51))) #0#) |has| (-2 (|:| -3835 (-1207)) (|:| -2923 (-51))) (-321 (-2 (|:| -3835 (-1207)) (|:| -2923 (-51)))))) ((((-1189)) . T)) (|has| |#1| (-939)) (|has| |#2| (-376)) (((|#1|) . T) (($) . T) (((-560)) . T)) -(-2181 (|has| |#2| (-21)) (|has| |#2| (-133)) (|has| |#2| (-175)) (|has| |#2| (-376)) (|has| |#2| (-815)) (|has| |#2| (-1080))) +(-2173 (|has| |#2| (-21)) (|has| |#2| (-133)) (|has| |#2| (-175)) (|has| |#2| (-376)) (|has| |#2| (-815)) (|has| |#2| (-1080))) ((((-171 (-391))) . T) (((-229)) . T) (((-391)) . T)) ((((-887)) . T)) (((|#1|) . T)) @@ -3109,12 +3109,12 @@ (|has| |#1| (-38 (-421 (-560)))) (|has| |#1| (-38 (-421 (-560)))) (|has| |#1| (-38 (-421 (-560)))) -(-2181 (|has| |#1| (-319)) (|has| |#1| (-376)) (|has| |#1| (-363))) +(-2173 (|has| |#1| (-319)) (|has| |#1| (-376)) (|has| |#1| (-363))) (|has| |#1| (-38 (-421 (-560)))) (-12 (|has| |#1| (-559)) (|has| |#1| (-843))) ((((-887)) . T)) (|has| |#1| (-376)) -((((-1207)) -2181 (-12 (|has| |#1| (-15 * (|#1| (-560) |#1|))) (|has| |#1| (-927 (-1207)))) (-12 (|has| |#1| (-376)) (|has| |#2| (-927 (-1207)))))) +((((-1207)) -2173 (-12 (|has| |#1| (-15 * (|#1| (-560) |#1|))) (|has| |#1| (-927 (-1207)))) (-12 (|has| |#1| (-376)) (|has| |#2| (-927 (-1207)))))) (|has| |#1| (-376)) ((((-1207)) -12 (|has| |#1| (-15 * (|#1| (-421 (-560)) |#1|))) (|has| |#1| (-927 (-1207))))) ((((-421 (-560))) . T) (($) . T)) @@ -3126,13 +3126,13 @@ ((((-560) |#1|) . T)) ((((-1207)) |has| |#1| (-927 (-1207)))) (((|#1|) . T)) -(-2181 (-12 (|has| |#1| (-240)) (|has| |#1| (-376))) (-12 (|has| |#1| (-239)) (|has| |#1| (-376))) (|has| |#1| (-363))) +(-2173 (-12 (|has| |#1| (-240)) (|has| |#1| (-376))) (-12 (|has| |#1| (-239)) (|has| |#1| (-376))) (|has| |#1| (-363))) (((|#2|) |has| |#1| (-376))) (((|#2|) |has| |#1| (-376))) -(-2181 (|has| |#4| (-815)) (|has| |#4| (-871))) -(-2181 (|has| |#3| (-815)) (|has| |#3| (-871))) +(-2173 (|has| |#4| (-815)) (|has| |#4| (-871))) +(-2173 (|has| |#3| (-815)) (|has| |#3| (-871))) ((((-560)) . T) (($) . T)) -((((-2 (|:| -3819 |#1|) (|:| -2913 |#2|))) . T)) +((((-2 (|:| -3835 |#1|) (|:| -2923 |#2|))) . T)) (((|#1|) . T)) (((|#1|) . T)) (((|#1|) |has| |#1| (-175))) @@ -3167,7 +3167,7 @@ (|has| |#1| (-871)) ((((-887)) . T)) (((|#1| |#1|) -12 (|has| |#1| (-321 |#1|)) (|has| |#1| (-1132)))) -(-2181 (|has| |#1| (-376)) (|has| |#1| (-571))) +(-2173 (|has| |#1| (-376)) (|has| |#1| (-571))) (|has| |#1| (-376)) (((|#1|) . T)) ((($) . T) (((-560)) . T) ((|#2|) . T)) @@ -3176,27 +3176,27 @@ (((|#3|) . T)) ((((-1189)) . T) (((-520)) . T) (((-229)) . T) (((-560)) . T)) (((|#1|) . T)) -(-2181 (|has| |#1| (-376)) (|has| |#1| (-571))) +(-2173 (|has| |#1| (-376)) (|has| |#1| (-571))) (|has| |#1| (-376)) (|has| |#1| (-571)) (((|#4| |#4|) -12 (|has| |#4| (-321 |#4|)) (|has| |#4| (-1132)))) ((((-421 |#2|)) . T) (((-421 (-560))) . T) (($) . T) (((-560)) . T)) -(-2181 (|has| |#2| (-21)) (|has| |#2| (-23)) (|has| |#2| (-133)) (|has| |#2| (-175)) (|has| |#2| (-376)) (|has| |#2| (-815)) (|has| |#2| (-1080))) +(-2173 (|has| |#2| (-21)) (|has| |#2| (-23)) (|has| |#2| (-133)) (|has| |#2| (-175)) (|has| |#2| (-376)) (|has| |#2| (-815)) (|has| |#2| (-1080))) (((|#2|) . T)) (((|#2|) . T)) (|has| |#2| (-1080)) -((((-2 (|:| -3819 |#1|) (|:| -2913 |#2|))) . T)) -((((-2 (|:| -3819 (-1189)) (|:| -2913 |#1|))) . T)) -((((-2 (|:| -3819 |#1|) (|:| -2913 |#2|))) . T)) +((((-2 (|:| -3835 |#1|) (|:| -2923 |#2|))) . T)) +((((-2 (|:| -3835 (-1189)) (|:| -2923 |#1|))) . T)) +((((-2 (|:| -3835 |#1|) (|:| -2923 |#2|))) . T)) (|has| |#1| (-38 (-421 (-560)))) (((|#1| |#2|) . T)) (|has| |#1| (-38 (-421 (-560)))) -(-2181 (|has| |#1| (-147)) (|has| |#1| (-381))) +(-2173 (|has| |#1| (-147)) (|has| |#1| (-381))) ((($) . T)) (|has| |#1| (-149)) -(-2181 (|has| |#1| (-147)) (|has| |#1| (-381))) +(-2173 (|has| |#1| (-147)) (|has| |#1| (-381))) (|has| |#1| (-149)) -(-2181 (|has| |#1| (-147)) (|has| |#1| (-381))) +(-2173 (|has| |#1| (-147)) (|has| |#1| (-381))) (|has| |#1| (-149)) ((($) . T)) ((((-595 |#1|)) . T)) @@ -3212,7 +3212,7 @@ ((((-421 (-560))) |has| |#2| (-1069 (-560))) (((-560)) |has| |#2| (-1069 (-560))) (((-1207)) |has| |#2| (-1069 (-1207))) ((|#2|) . T)) (((#0=(-421 |#2|) #0#) . T) ((#1=(-421 (-560)) #1#) . T) (($ $) . T)) (((|#1|) . T)) -(-2181 (|has| |#1| (-147)) (|has| |#1| (-363))) +(-2173 (|has| |#1| (-147)) (|has| |#1| (-363))) (|has| |#1| (-149)) ((((-887)) . T)) ((($) . T)) @@ -3232,15 +3232,15 @@ ((((-421 |#2|)) . T)) ((((-887)) . T)) (((|#1|) . T)) -((((-1207)) -2181 (|has| |#1| (-927 (-1207))) (|has| |#1| (-929 (-1207))))) -(-2181 (|has| |#1| (-102)) (|has| |#1| (-1132))) +((((-1207)) -2173 (|has| |#1| (-927 (-1207))) (|has| |#1| (-929 (-1207))))) +(-2173 (|has| |#1| (-102)) (|has| |#1| (-1132))) (|has| |#1| (-813)) (|has| |#1| (-813)) ((((-887)) . T)) ((((-935 |#1|)) . T) (((-421 (-560))) . T) (($) . T) (((-560)) . T)) ((((-887)) . T)) ((((-549)) |has| |#1| (-633 (-549)))) -((((-887)) -2181 (|has| |#1| (-632 (-887))) (|has| |#1| (-871)) (|has| |#1| (-1132)))) +((((-887)) -2173 (|has| |#1| (-632 (-887))) (|has| |#1| (-871)) (|has| |#1| (-1132)))) ((((-115)) . T) ((|#1|) . T)) (((|#1|) . T)) (((|#1|) . T)) @@ -3250,7 +3250,7 @@ (((|#1|) |has| |#1| (-175)) (($) |has| |#1| (-571)) (((-421 (-560))) |has| |#1| (-571))) ((((-887)) . T)) ((((-887)) . T)) -(-2181 (-12 (|has| |#2| (-240)) (|has| |#2| (-1080))) (-12 (|has| |#2| (-239)) (|has| |#2| (-1080)))) +(-2173 (-12 (|has| |#2| (-240)) (|has| |#2| (-1080))) (-12 (|has| |#2| (-239)) (|has| |#2| (-1080)))) (((#0=(-935 |#1|) #0#) . T) (($ $) . T) ((#1=(-421 (-560)) #1#) . T)) (((|#2|) . T)) (((|#1|) . T)) @@ -3262,10 +3262,10 @@ ((((-887)) . T)) (((|#2|) . T)) ((((-560)) . T)) -((((-1207)) -2181 (|has| (-421 |#2|) (-927 (-1207))) (|has| (-421 |#2|) (-929 (-1207))))) +((((-1207)) -2173 (|has| (-421 |#2|) (-927 (-1207))) (|has| (-421 |#2|) (-929 (-1207))))) ((((-887)) . T)) ((((-560)) . T)) -(-2181 (|has| |#2| (-815)) (|has| |#2| (-871))) +(-2173 (|has| |#2| (-815)) (|has| |#2| (-871))) ((((-171 (-391))) . T) (((-229)) . T) (((-391)) . T)) ((((-887)) . T)) ((((-887)) . T)) @@ -3277,11 +3277,11 @@ (((|#1|) . T) (($) . T) (((-421 (-560))) . T)) (|has| |#1| (-376)) (|has| |#1| (-376)) -((((-887)) -2181 (|has| |#1| (-632 (-887))) (|has| |#1| (-1132)))) -((((-887)) -2181 (|has| |#1| (-632 (-887))) (|has| |#1| (-1132)))) +((((-887)) -2173 (|has| |#1| (-632 (-887))) (|has| |#1| (-1132)))) +((((-887)) -2173 (|has| |#1| (-632 (-887))) (|has| |#1| (-1132)))) ((((-887)) . T)) ((((-560) $) . T) (((-663 (-560)) $) . T)) -(-2181 (|has| |#1| (-21)) (|has| |#1| (-25)) (|has| |#1| (-175)) (|has| |#1| (-376)) (|has| |#1| (-487)) (|has| |#1| (-748)) (|has| |#1| (-927 (-1207))) (|has| |#1| (-1080)) (|has| |#1| (-1143)) (|has| |#1| (-1132))) +(-2173 (|has| |#1| (-21)) (|has| |#1| (-25)) (|has| |#1| (-175)) (|has| |#1| (-376)) (|has| |#1| (-487)) (|has| |#1| (-748)) (|has| |#1| (-927 (-1207))) (|has| |#1| (-1080)) (|has| |#1| (-1143)) (|has| |#1| (-1132))) (|has| |#1| (-1182)) ((((-935 |#1|)) . T) (((-421 (-560))) . T) (($) . T)) ((($) . T)) @@ -3291,22 +3291,22 @@ (((#0=(-118 |#1|) $) |has| #0# (-298 #0# #0#))) (((|#1|) |has| |#1| (-175))) ((((-326 |#1|)) . T) (((-560)) . T)) -(-2181 (|has| |#2| (-240)) (|has| |#2| (-239))) +(-2173 (|has| |#2| (-240)) (|has| |#2| (-239))) (((|#1|) . T)) (((|#1| |#1|) . T)) ((((-887)) . T)) (((|#1|) . T)) ((((-115)) . T) ((|#1|) . T)) ((((-887)) . T)) -((((-1207)) -2181 (|has| |#2| (-927 (-1207))) (|has| |#2| (-929 (-1207))))) +((((-1207)) -2173 (|has| |#2| (-927 (-1207))) (|has| |#2| (-929 (-1207))))) (((|#1|) |has| |#1| (-321 |#1|))) ((((-560) |#1|) . T) (((-1264 (-560)) $) . T)) (((|#1| |#2|) . T)) ((((-1207) |#1|) . T)) -(((|#1|) -2181 (|has| |#1| (-175)) (|has| |#1| (-376)))) +(((|#1|) -2173 (|has| |#1| (-175)) (|has| |#1| (-376)))) (((|#1|) . T)) ((($ (-1207)) . T)) -(((|#1|) -2181 (|has| |#1| (-175)) (|has| |#1| (-376)) (|has| |#1| (-1080)))) +(((|#1|) -2173 (|has| |#1| (-175)) (|has| |#1| (-376)) (|has| |#1| (-1080)))) ((((-560)) . T) (((-421 (-560))) . T)) (((|#1|) . T)) (|has| |#1| (-571)) @@ -3315,15 +3315,15 @@ (((|#1|) . T)) (((|#1|) . T)) ((((-421 |#2|)) . T) (((-421 (-560))) . T) (($) . T)) -(-2181 (|has| |#1| (-376)) (|has| |#1| (-571))) +(-2173 (|has| |#1| (-376)) (|has| |#1| (-571))) (|has| |#1| (-376)) -(-2181 (|has| |#1| (-376)) (|has| |#1| (-571))) +(-2173 (|has| |#1| (-376)) (|has| |#1| (-571))) (|has| |#1| (-376)) (|has| |#1| (-571)) ((($) . T)) (|has| |#1| (-1132)) ((((-802 |#1| (-888 |#2|))) |has| (-802 |#1| (-888 |#2|)) (-321 (-802 |#1| (-888 |#2|))))) -(-2181 (|has| |#2| (-466)) (|has| |#2| (-571)) (|has| |#2| (-939))) +(-2173 (|has| |#2| (-466)) (|has| |#2| (-571)) (|has| |#2| (-939))) (((|#1|) . T)) (((|#2| |#3|) . T)) (((|#1|) . T)) @@ -3332,17 +3332,17 @@ (((|#1| (-793)) . T)) (|has| |#1| (-240)) (((|#1| (-545 (-1119 (-1207)))) . 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T) (((-421 (-560))) -2181 (|has| |#1| (-38 (-421 (-560)))) (|has| |#1| (-1069 (-421 (-560))))) (((-1207)) . T)) +((((-1156 |#1| (-1207))) . T) (((-560)) . T) (((-1119 (-1207))) . T) (($) -2173 (|has| |#1| (-466)) (|has| |#1| (-571)) (|has| |#1| (-939))) ((|#1|) . T) (((-421 (-560))) -2173 (|has| |#1| (-38 (-421 (-560)))) (|has| |#1| (-1069 (-421 (-560))))) (((-1207)) . T)) (((|#1|) |has| |#1| (-175))) (((|#1| (-1297 |#1|) (-1297 |#1|)) . T)) ((((-595 |#1|)) . T) (($) . T) (((-421 (-560))) . T)) @@ -3375,7 +3375,7 @@ ((((-421 (-560))) |has| |#1| (-1069 (-421 (-560)))) ((|#1|) . T) (((-560)) . T)) (((|#1|) . T)) ((((-887)) . T)) -(((#0=(-421 (-560)) #0#) |has| |#2| (-38 (-421 (-560)))) ((|#2| |#2|) . T) (($ $) -2181 (|has| |#2| (-175)) (|has| |#2| (-466)) (|has| |#2| (-571)) (|has| |#2| (-939)))) +(((#0=(-421 (-560)) #0#) |has| |#2| (-38 (-421 (-560)))) ((|#2| |#2|) . T) (($ $) -2173 (|has| |#2| (-175)) (|has| |#2| (-466)) (|has| |#2| (-571)) (|has| |#2| (-939)))) (((|#2| |#2|) . T) ((|#6| |#6|) . T)) ((((-305 |#3|)) . T)) (((|#1|) . T)) @@ -3384,30 +3384,30 @@ (((|#1|) . T) (((-421 (-560))) . T) (($) . T)) (((|#1|) . T) (((-421 (-560))) . T) (($) . T)) (((|#1|) . T) (((-421 (-560))) . T) (($) . T)) -((($ $) -2181 (|has| |#1| (-175)) (|has| |#1| (-466)) (|has| |#1| (-571)) (|has| |#1| (-939))) ((|#1| |#1|) . T) ((#0=(-421 (-560)) #0#) |has| |#1| (-38 (-421 (-560))))) -((($ $) -2181 (|has| |#1| (-175)) (|has| |#1| (-376)) (|has| |#1| (-466)) (|has| |#1| (-571)) (|has| |#1| (-939))) ((|#1| |#1|) . T) ((#0=(-421 (-560)) #0#) |has| |#1| (-38 (-421 (-560))))) +((($ $) -2173 (|has| |#1| (-175)) (|has| |#1| (-466)) (|has| |#1| (-571)) (|has| |#1| (-939))) ((|#1| |#1|) . T) ((#0=(-421 (-560)) #0#) |has| |#1| (-38 (-421 (-560))))) +((($ $) -2173 (|has| |#1| (-175)) (|has| |#1| (-376)) (|has| |#1| (-466)) (|has| |#1| (-571)) (|has| |#1| (-939))) ((|#1| |#1|) . T) ((#0=(-421 (-560)) #0#) |has| |#1| (-38 (-421 (-560))))) (((|#2|) . 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T)) -(-2181 (|has| |#2| (-815)) (|has| |#2| (-871))) -(-2181 (|has| |#1| (-102)) (|has| |#1| (-1132))) +(-2173 (|has| |#2| (-815)) (|has| |#2| (-871))) +(-2173 (|has| |#1| (-102)) (|has| |#1| (-1132))) (((|#1|) . T)) (((|#1|) . T) (($) . T) (((-421 (-560))) . T)) ((((-1207)) . T) ((|#1|) . T)) @@ -3419,15 +3419,15 @@ (((#0=(-421 (-560)) #0#) . T)) ((((-421 (-560))) . T)) (((|#1|) |has| |#1| (-175))) -(-2181 (|has| |#2| (-21)) (|has| |#2| (-175)) (|has| |#2| (-376)) (|has| |#2| (-1080))) +(-2173 (|has| |#2| (-21)) (|has| |#2| (-175)) (|has| |#2| (-376)) (|has| |#2| (-1080))) (((|#1|) . T)) (((|#1|) . T)) -(-2181 (|has| |#2| (-21)) (|has| |#2| (-23)) (|has| |#2| (-25)) (|has| |#2| (-133)) (|has| |#2| (-175)) (|has| |#2| (-376)) (|has| |#2| (-815)) (|has| |#2| (-1080))) +(-2173 (|has| |#2| (-21)) (|has| |#2| (-23)) (|has| |#2| (-25)) (|has| |#2| (-133)) (|has| |#2| (-175)) (|has| |#2| (-376)) (|has| |#2| (-815)) (|has| |#2| (-1080))) (((|#1|) . T)) ((((-421 (-560))) . T) (((-560)) . 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T) (((-421 (-560))) -2181 (|has| |#1| (-38 (-421 (-560)))) (|has| |#1| (-376))) (($) . T)) +((($) -2173 (-12 (|has| |#1| (-240)) (|has| |#1| (-376))) (-12 (|has| |#1| (-239)) (|has| |#1| (-376))) (|has| |#1| (-363)))) +(((|#1|) . T) (((-421 (-560))) -2173 (|has| |#1| (-38 (-421 (-560)))) (|has| |#1| (-376))) (($) . T)) (((|#1| |#1|) -12 (|has| |#1| (-321 |#1|)) (|has| |#1| (-1132)))) ((((-560)) |has| |#1| (-911 (-560))) (((-391)) |has| |#1| (-911 (-391)))) (((|#1|) . T)) @@ -3496,7 +3496,7 @@ (-12 (|has| |#1| (-376)) (|has| |#2| (-939))) (|has| |#1| (-376)) (((|#4|) -12 (|has| |#4| (-321 |#4|)) (|has| |#4| (-1132)))) -(((|#2|) -2181 (|has| |#2| (-6 (-4510 "*"))) (|has| |#2| (-175)))) +(((|#2|) -2173 (|has| |#2| (-6 (-4510 "*"))) (|has| |#2| (-175)))) (((|#2|) . T)) (|has| |#1| (-376)) (((|#2|) . T)) @@ -3510,12 +3510,12 @@ (((|#2| (-793)) . T)) ((((-1207)) . T)) ((((-893 |#1|)) . 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T) (((-421 (-560))) . T) (((-560)) |has| |#2| (-660 (-560)))) -(-2181 (|has| |#1| (-102)) (|has| |#1| (-1132))) +(-2173 (|has| |#1| (-102)) (|has| |#1| (-1132))) (((|#1|) -12 (|has| |#1| (-321 |#1|)) (|has| |#1| (-1132)))) (((|#1| |#1|) -12 (|has| |#1| (-321 |#1|)) (|has| |#1| (-1132)))) (((|#1| |#1|) -12 (|has| |#1| (-321 |#1|)) (|has| |#1| (-1132)))) @@ -3542,7 +3542,7 @@ (((|#1|) . T)) ((((-887)) . T)) (|has| |#2| (-939)) -((((-2 (|:| -3819 (-1207)) (|:| -2913 (-51)))) . T)) +((((-2 (|:| -3835 (-1207)) (|:| -2923 (-51)))) . T)) ((((-549)) |has| |#2| (-633 (-549))) (((-915 (-391))) |has| |#2| (-633 (-915 (-391)))) (((-915 (-560))) |has| |#2| (-633 (-915 (-560))))) ((((-887)) . T)) ((((-887)) . T)) @@ -3553,7 +3553,7 @@ ((((-1201 |#1|)) . T) (((-887)) . T)) ((((-887)) . T)) ((((-421 (-560))) |has| |#2| (-1069 (-421 (-560)))) (((-560)) |has| |#2| (-1069 (-560))) ((|#2|) . T) (((-888 |#1|)) . T)) -((((-1207)) -2181 (|has| |#1| (-927 (-1207))) (|has| |#1| (-929 (-1207)))) (((-1113)) . 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T) (((-421 (-560))) |has| |#1| (-38 (-421 (-560))))) (((|#2|) |has| |#2| (-1132)) (((-560)) -12 (|has| |#2| (-1069 (-560))) (|has| |#2| (-1132))) (((-421 (-560))) -12 (|has| |#2| (-1069 (-421 (-560)))) (|has| |#2| (-1132)))) -(-2181 (|has| |#2| (-240)) (|has| |#2| (-239))) +(-2173 (|has| |#2| (-240)) (|has| |#2| (-239))) (((|#1|) . T)) (((|#1|) . T)) ((((-549)) |has| |#1| (-633 (-549)))) -((((-887)) -2181 (|has| |#1| (-632 (-887))) (|has| |#1| (-871)) (|has| |#1| (-1132)))) +((((-887)) -2173 (|has| |#1| (-632 (-887))) (|has| |#1| (-871)) (|has| |#1| (-1132)))) ((((-560) $) . T) (((-663 (-560)) $) . T)) ((($) . T) (((-421 (-560))) . T)) (|has| |#1| (-939)) @@ -4035,14 +4035,14 @@ (((|#1| |#1|) |has| |#1| (-175))) (((|#1|) . T) (((-560)) . T)) ((((-1212)) . T)) -(-2181 (|has| |#1| (-376)) (|has| |#1| (-571))) -(-2181 (|has| |#1| (-21)) (|has| |#1| (-870))) +(-2173 (|has| |#1| (-376)) (|has| |#1| (-571))) +(-2173 (|has| |#1| (-21)) (|has| |#1| (-870))) (((|#2|) . T)) -(-2181 (|has| |#1| (-21)) (|has| |#1| (-870))) +(-2173 (|has| |#1| (-21)) (|has| |#1| (-870))) (((|#1|) |has| |#1| (-175))) (((|#1|) . T)) (((|#1|) . T)) -((((-887)) -2181 (-12 (|has| |#1| (-632 (-887))) (|has| |#2| (-632 (-887)))) (-12 (|has| |#1| (-1132)) (|has| |#2| (-1132))))) +((((-887)) -2173 (-12 (|has| |#1| (-632 (-887))) (|has| |#2| (-632 (-887)))) (-12 (|has| |#1| (-1132)) (|has| |#2| (-1132))))) ((((-421 |#2|) |#3|) . T)) ((((-421 (-560))) . T) (($) . T)) (|has| |#1| (-38 (-421 (-560)))) @@ -4051,7 +4051,7 @@ ((($) . T) (((-560)) . T)) (|has| (-421 |#2|) (-149)) (|has| (-421 |#2|) (-147)) -(-2181 (|has| |#3| (-815)) (|has| |#3| (-871))) +(-2173 (|has| |#3| (-815)) (|has| |#3| (-871))) ((($) . T)) ((((-721)) . T)) (((|#1|) . T) (((-421 (-560))) . T) (((-560)) . T) (($) . T)) @@ -4067,7 +4067,7 @@ ((((-1212)) . T)) ((((-560)) . T)) (((|#2|) . T)) -((((-1207)) -2181 (-12 (|has| (-1205 |#1| |#2| |#3|) (-927 (-1207))) (|has| |#1| (-376))) (-12 (|has| |#1| (-15 * (|#1| (-560) |#1|))) (|has| |#1| (-927 (-1207)))))) +((((-1207)) -2173 (-12 (|has| (-1205 |#1| |#2| |#3|) (-927 (-1207))) (|has| |#1| (-376))) (-12 (|has| |#1| (-15 * (|#1| (-560) |#1|))) (|has| |#1| (-927 (-1207)))))) ((((-1207)) -12 (|has| |#1| (-15 * (|#1| (-421 (-560)) |#1|))) (|has| |#1| (-927 (-1207))))) ((((-1207)) -12 (|has| |#1| (-15 * (|#1| (-793) |#1|))) (|has| |#1| (-927 (-1207))))) (((|#1| |#1|) . T) (($ $) . T)) @@ -4083,11 +4083,11 @@ ((((-1205 |#1| |#2| |#3|)) |has| |#1| (-376))) ((((-1171 |#1| |#2|)) . T)) ((((-1205 |#1| |#2| |#3|)) |has| |#1| (-376))) -(((|#2|) . T) (((-2 (|:| -3819 |#1|) (|:| -2913 |#2|))) . T)) -((((-2 (|:| -3819 (-1207)) (|:| -2913 (-51)))) . T)) +(((|#2|) . T) (((-2 (|:| -3835 |#1|) (|:| -2923 |#2|))) . T)) +((((-2 (|:| -3835 (-1207)) (|:| -2923 (-51)))) . T)) ((($) . T)) (|has| |#1| (-1051)) -(((|#2|) . T) (((-2 (|:| -3819 |#1|) (|:| -2913 |#2|))) . T)) +(((|#2|) . T) (((-2 (|:| -3835 |#1|) (|:| -2923 |#2|))) . T)) ((($) . T)) ((((-887)) . T)) ((((-549)) |has| |#2| (-633 (-549))) (((-915 (-560))) |has| |#2| (-633 (-915 (-560)))) (((-915 (-391))) |has| |#2| (-633 (-915 (-391)))) (((-391)) . #0=(|has| |#2| (-1051))) (((-229)) . #0#)) @@ -4096,7 +4096,7 @@ (((|#1|) . T)) (|has| |#1| (-38 (-421 (-560)))) (|has| |#1| (-38 (-421 (-560)))) -((((-1207)) -2181 (|has| |#2| (-927 (-1207))) (|has| |#2| (-929 (-1207))))) +((((-1207)) -2173 (|has| |#2| (-927 (-1207))) (|has| |#2| (-929 (-1207))))) ((((-887)) . T)) (((|#2|) . T)) ((((-887)) . T)) @@ -4106,15 +4106,15 @@ ((((-1205 |#1| |#2| |#3|)) . T)) ((((-1205 |#1| |#2| |#3|)) . T) (((-1198 |#1| |#2| |#3|)) . T)) ((((-887)) . T)) -((((-887)) -2181 (|has| |#1| (-632 (-887))) (|has| |#1| (-1132)))) +((((-887)) -2173 (|has| |#1| (-632 (-887))) (|has| |#1| (-1132)))) ((((-560) |#1|) . T)) ((((-1205 |#1| |#2| |#3|)) |has| |#1| (-376))) (((|#1| |#2| |#3| |#4|) . T)) (((|#1|) . T)) (((|#2|) . T)) (|has| |#2| (-376)) -(((|#3|) . T) ((|#2|) . T) ((|#4|) -2181 (|has| |#4| (-175)) (|has| |#4| (-376)) (|has| |#4| (-1080))) (($) |has| |#4| (-1080)) (((-560)) -12 (|has| |#4| (-660 (-560))) (|has| |#4| (-1080)))) -(((|#2|) . T) ((|#3|) -2181 (|has| |#3| (-175)) (|has| |#3| (-376)) (|has| |#3| (-1080))) (($) |has| |#3| (-1080)) (((-560)) -12 (|has| |#3| (-660 (-560))) (|has| |#3| (-1080)))) +(((|#3|) . T) ((|#2|) . T) ((|#4|) -2173 (|has| |#4| (-175)) (|has| |#4| (-376)) (|has| |#4| (-1080))) (($) |has| |#4| (-1080)) (((-560)) -12 (|has| |#4| (-660 (-560))) (|has| |#4| (-1080)))) +(((|#2|) . T) ((|#3|) -2173 (|has| |#3| (-175)) (|has| |#3| (-376)) (|has| |#3| (-1080))) (($) |has| |#3| (-1080)) (((-560)) -12 (|has| |#3| (-660 (-560))) (|has| |#3| (-1080)))) (((|#1|) . T)) (((|#1|) . T)) ((((-118 |#1|)) . T)) @@ -4128,7 +4128,7 @@ ((((-186)) . T) (((-887)) . T)) ((((-887)) . T)) (((|#1|) . T)) -((((-887)) -2181 (|has| |#1| (-632 (-887))) (|has| |#1| (-1132)))) +((((-887)) -2173 (|has| |#1| (-632 (-887))) (|has| |#1| (-1132)))) ((((-560) |#1|) . T) (((-1264 (-560)) $) . T)) ((((-887)) . T)) (((|#1|) . T)) @@ -4136,14 +4136,14 @@ (((|#1|) . T)) (((|#2| $) -12 (|has| |#1| (-376)) (|has| |#2| (-298 |#2| |#2|))) (($ $) . T) (((-560) |#1|) . T)) ((($ $) . T) (((-421 (-560)) |#1|) . T)) -(-2181 (|has| |#1| (-376)) (|has| |#1| (-466)) (|has| |#1| (-939))) +(-2173 (|has| |#1| (-376)) (|has| |#1| (-466)) (|has| |#1| (-939))) ((($ (-1207)) |has| |#1| (-1080))) -(-2181 (|has| |#1| (-871)) (|has| |#1| (-1132))) +(-2173 (|has| |#1| (-871)) (|has| |#1| (-1132))) ((((-887)) . T)) ((((-887)) . T)) ((((-887)) . T)) (((|#1| (-545 |#2|)) . T)) -((((-2 (|:| -3819 (-1207)) (|:| -2913 (-51)))) . T)) +((((-2 (|:| -3835 (-1207)) (|:| -2923 (-51)))) . T)) ((((-560) (-130)) . T)) (((|#1| (-560)) . T)) (((|#1| (-421 (-560))) . T)) @@ -4158,8 +4158,8 @@ ((((-1212)) . T)) ((((-887)) . T) (((-1212)) . T)) ((((-887)) . T) (((-1212)) . T)) -(-2181 (|has| |#2| (-466)) (|has| |#2| (-571)) (|has| |#2| (-939))) -(-2181 (|has| |#1| (-466)) (|has| |#1| (-571)) (|has| |#1| (-939))) +(-2173 (|has| |#2| (-466)) (|has| |#2| (-571)) (|has| |#2| (-939))) +(-2173 (|has| |#1| (-466)) (|has| |#1| (-571)) (|has| |#1| (-939))) ((($) . T)) (((|#2| (-545 (-888 |#1|))) . T)) ((((-1212)) . T)) @@ -4174,7 +4174,7 @@ ((((-1212)) . T)) ((((-887)) . T) (((-1212)) . T)) ((((-1212)) . T)) -((((-887)) -2181 (|has| |#1| (-632 (-887))) (|has| |#1| (-1132)))) +((((-887)) -2173 (|has| |#1| (-632 (-887))) (|has| |#1| (-1132)))) (((|#1| |#2|) . T)) (((|#1|) . T)) ((((-1189) |#1|) . T)) @@ -4182,7 +4182,7 @@ ((((-421 |#2|)) . T)) (|has| |#1| (-571)) (|has| |#1| (-571)) -((((-2 (|:| -3819 |#1|) (|:| -2913 |#2|))) . T)) +((((-2 (|:| -3835 |#1|) (|:| -2923 |#2|))) . T)) (((|#2| (-793)) . T)) ((($) . T) ((|#2|) . T)) ((($) . T) (((-421 (-560))) . T)) @@ -4192,14 +4192,14 @@ ((((-560)) . T) (($) . 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T) (($) -2173 (|has| |#2| (-376)) (|has| |#2| (-466)) (|has| |#2| (-571)) (|has| |#2| (-939))) (((-1113)) . T) ((|#2|) . T) (((-421 (-560))) -2173 (|has| |#2| (-38 (-421 (-560)))) (|has| |#2| (-1069 (-421 (-560)))))) +((((-1027 |#1|)) . T) ((|#1|) . T) (((-560)) -2173 (|has| (-1027 |#1|) (-1069 (-560))) (|has| |#1| (-1069 (-560)))) (((-421 (-560))) -2173 (|has| (-1027 |#1|) (-1069 (-421 (-560)))) (|has| |#1| (-1069 (-421 (-560)))))) ((((-935 |#1|)) . T) (((-421 (-560))) . T) (($) . T)) (((|#1| |#1|) -12 (|has| |#1| (-321 |#1|)) (|has| |#1| (-1132)))) (((|#1| |#1|) -12 (|has| |#1| (-321 |#1|)) (|has| |#1| (-1132)))) @@ -4216,11 +4216,11 @@ (((|#1| |#2| |#3| |#4|) . T)) (((#0=(-1171 |#1| |#2|) #0#) |has| (-1171 |#1| |#2|) (-321 (-1171 |#1| |#2|)))) (((|#1|) . 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196913) ((-1201 . -670) 196802) ((-1156 . -670) 196691) ((-878 . -670) 196665) ((-740 . -632) 196647) ((-561 . -381) T) ((-1319 . -23) T) ((-716 . -929) NIL) ((-1318 . -23) T) ((-505 . -1132) T) ((-391 . -635) 196597) ((-391 . -637) 196579) ((-1065 . -1080) T) ((-889 . -102) T) ((-1219 . -298) 196558) ((-171 . -381) 196509) ((-1035 . -1247) T) ((-1002 . -1247) T) ((-943 . -1247) T) ((-856 . -635) 196463) ((-850 . -635) 196418) ((-44 . -23) T) ((-1327 . -102) T) ((-493 . -298) 196397) ((-597 . -1132) T) ((-1177 . -1140) 196366) ((-443 . -1247) T) ((-1134 . -1135) 196318) ((-404 . -21) T) ((-404 . -25) T) ((-154 . -1143) T) ((-1240 . -739) 196215) ((-1227 . -1132) T) ((-1035 . -909) 196197) ((-1035 . -911) 196179) ((-642 . -234) 196163) ((-642 . -274) 196147) ((-638 . -21) T) ((-301 . -571) T) ((-638 . -25) T) ((-1035 . -1069) 196107) ((-733 . -739) 196072) ((-246 . -390) 196041) ((-391 . -1080) T) ((-227 . -1088) T) ((-119 . -274) 196018) ((-119 . -234) 195995) ((-58 . -298) 195947) 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T) ((-530 . -19) 194521) ((-510 . -19) 194505) ((-58 . -618) 194482) ((-1034 . -239) 194419) ((-930 . -102) 194369) ((-878 . -748) T) ((-803 . -1132) T) ((-530 . -618) 194346) ((-510 . -618) 194323) ((-802 . -1132) T) ((-802 . -1096) 194290) ((-475 . -1132) T) ((-468 . -1132) T) ((-597 . -739) 194265) ((-671 . -1132) T) ((-1287 . -47) 194242) ((-1284 . -102) T) ((-1278 . -47) 194212) ((-1257 . -47) 194189) ((-1240 . -175) 194140) ((-1204 . -319) 194119) ((-1198 . -319) 194098) ((-1127 . -635) 194079) ((-1122 . -635) 194060) ((-1110 . -571) 194011) ((-1110 . -1252) 193962) ((-1104 . -635) 193943) ((-1035 . -927) NIL) ((-1097 . -635) 193924) ((-692 . -133) T) ((-646 . -1143) T) ((-1067 . -635) 193905) ((-1050 . -635) 193886) ((-736 . -1087) 193856) ((-734 . -921) 193759) ((-721 . -668) 193709) ((-286 . -1132) T) ((-86 . -455) T) ((-86 . -410) T) ((-733 . -175) T) ((-659 . -1087) 193693) ((-50 . -1132) T) ((-609 . -47) 193670) ((-229 . -670) 193635) ((-595 . -1132) T) ((-532 . -1132) T) 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T) ((-492 . -93) T) ((-421 . -239) 191161) ((-368 . -632) 191143) ((-366 . -632) 191125) ((-358 . -632) 191107) ((-275 . -633) 190855) ((-275 . -632) 190837) ((-255 . -632) 190819) ((-255 . -633) 190680) ((-140 . -93) T) ((-139 . -93) T) ((-135 . -93) T) ((-1172 . -632) 190662) ((-1151 . -662) 190649) ((-1151 . -1082) 190636) ((-841 . -748) T) ((-841 . -881) T) ((-616 . -300) 190613) ((-595 . -739) 190578) ((-493 . -633) NIL) ((-493 . -632) 190560) ((-532 . -739) 190505) ((-326 . -102) T) ((-325 . -102) T) ((-301 . -23) T) ((-154 . -133) T) ((-935 . -632) 190487) ((-935 . -633) 190469) ((-400 . -748) T) ((-896 . -1087) 190421) ((-896 . -111) 190359) ((-736 . -1080) T) ((-734 . -1273) 190343) ((-716 . -363) NIL) ((-115 . -102) T) ((-141 . -102) T) ((-137 . -102) T) ((-533 . -632) 190275) ((-391 . -819) T) ((-170 . -1247) T) ((-227 . -1132) T) ((-391 . -814) T) ((-58 . -633) 190236) ((-229 . -816) T) ((-229 . -813) T) ((-58 . -632) 190148) ((-229 . -748) T) ((-530 . -633) 190109) ((-530 . -632) 190021) ((-511 . -632) 189953) ((-510 . -633) 189914) ((-510 . -632) 189826) ((-1110 . -376) 189777) ((-40 . -426) 189754) ((-78 . -1247) T) ((-895 . -939) NIL) ((-372 . -341) 189738) ((-372 . -376) T) ((-367 . -341) 189722) ((-367 . -376) T) ((-359 . -341) 189706) ((-359 . -376) T) ((-326 . -296) 189685) ((-108 . -376) T) ((-70 . -1247) T) ((-661 . -1132) T) ((-1257 . -351) 189637) ((-895 . -670) 189582) ((-1257 . -390) 189534) ((-993 . -133) 189389) ((-837 . -133) 189260) ((-45 . -874) NIL) ((-987 . -673) 189244) ((-1256 . -684) T) ((-1118 . -175) 189155) ((-987 . -385) 189139) ((-1093 . -816) T) ((-1093 . -813) T) ((-896 . -635) 189037) ((-803 . -175) 188928) ((-802 . -175) 188839) ((-838 . -47) 188801) ((-1093 . -748) T) ((-339 . -503) 188785) ((-975 . -748) T) ((-1311 . -321) 188723) ((-1287 . -927) 188636) ((-468 . -175) 188547) ((-252 . -298) 188499) ((-1283 . -1087) 188334) ((-1278 . -927) 188240) ((-1262 . -1087) 188048) ((-495 . -748) T) ((-1257 . -927) 187881) ((-1240 . -302) 187860) ((-1217 . -1247) T) ((-1214 . -381) T) ((-1213 . -381) T) ((-1177 . -153) 187844) ((-1151 . -102) T) ((-1146 . -1132) T) ((-1110 . -23) T) ((-1110 . -1143) T) ((-1107 . -102) T) ((-1089 . -632) 187811) ((-1034 . -424) 187783) ((-954 . -984) T) ((-758 . -321) 187721) ((-76 . -1247) T) ((-686 . -397) 187693) ((-171 . -939) 187646) ((-30 . -984) T) ((-114 . -866) T) ((-1 . -632) 187628) ((-1027 . -921) 187549) ((-131 . -673) 187531) ((-50 . -640) 187515) ((-716 . -668) 187450) ((-609 . -927) 187363) ((-452 . -102) T) ((-143 . -321) NIL) ((-131 . -385) 187345) ((-896 . -1080) T) ((-854 . -871) 187324) ((-81 . -1247) T) ((-733 . -302) T) ((-40 . -1088) T) ((-595 . -175) T) ((-532 . -175) T) ((-526 . -632) 187306) ((-171 . -670) 187180) ((-521 . -632) 187162) ((-365 . -149) 187144) ((-365 . -147) T) ((-372 . -1143) T) ((-367 . -1143) T) ((-359 . -1143) T) ((-1035 . -319) T) ((-943 . -319) T) ((-896 . -250) T) ((-108 . -1143) T) ((-896 . -240) 187123) ((-1283 . -111) 186944) ((-1262 . -111) 186733) ((-252 . -1286) 186717) ((-560 . -870) T) ((-372 . -23) T) ((-353 . -363) T) ((-326 . -321) 186704) ((-325 . -321) 186645) ((-367 . -23) T) ((-331 . -133) T) ((-359 . -23) T) ((-1035 . -1051) T) ((-31 . -635) 186626) ((-108 . -23) T) ((-678 . -1082) 186610) ((-252 . -618) 186587) ((-661 . -739) 186571) ((-345 . -1132) T) ((-678 . -662) 186541) ((-1284 . -38) 186433) ((-1266 . -939) 186412) ((-114 . -1132) T) ((-838 . -1247) T) ((-427 . -1247) T) ((-1066 . -102) T) ((-1266 . -670) 186301) ((-895 . -816) NIL) ((-879 . -670) 186275) ((-895 . -813) NIL) ((-838 . -911) NIL) ((-895 . -748) T) ((-1118 . -528) 186148) ((-803 . -528) 186095) ((-802 . -528) 186047) ((-585 . -670) 186034) ((-838 . -1069) 185862) ((-468 . -528) 185805) ((-402 . -403) T) ((-1283 . -635) 185618) ((-1262 . -635) 185366) ((-60 . -1247) T) ((-638 . -871) 185345) ((-514 . -684) T) ((-1177 . -1007) 185314) ((-1055 . -668) 185251) ((-1034 . -466) T) ((-721 . -870) T) ((-525 . -814) T) 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-1132) T) ((-918 . -102) T) ((-803 . -302) 183568) ((-339 . -19) 183552) ((-58 . -300) 183529) ((-802 . -302) 183460) ((-879 . -748) T) ((-119 . -870) NIL) ((-530 . -300) 183437) ((-339 . -618) 183414) ((-510 . -300) 183391) ((-468 . -302) 183322) ((-1066 . -321) 183173) ((-900 . -504) 183154) ((-900 . -632) 183120) ((-703 . -504) 183101) ((-585 . -748) T) ((-698 . -504) 183082) ((-703 . -632) 183032) ((-698 . -632) 182998) ((-674 . -632) 182980) ((-492 . -504) 182961) ((-492 . -632) 182927) ((-252 . -633) 182888) ((-252 . -504) 182865) ((-140 . -504) 182846) ((-139 . -504) 182827) ((-135 . -504) 182808) ((-252 . -632) 182700) ((-216 . -102) T) ((-140 . -632) 182666) ((-139 . -632) 182632) ((-135 . -632) 182598) ((-1178 . -34) T) ((-972 . -1247) T) ((-357 . -739) 182543) ((-692 . -25) T) ((-692 . -21) T) ((-1207 . -635) 182524) ((-343 . -1247) T) ((-488 . -1080) T) ((-652 . -432) 182489) ((-620 . -432) 182454) ((-1151 . -1182) T) ((-1278 . -319) 182433) ((-734 . -1082) 182256) ((-595 . -302) T) ((-532 . -302) T) ((-1257 . -319) 182235) ((-488 . -240) 182187) ((-488 . -250) 182166) ((-453 . -1247) T) ((-734 . -662) 181995) ((-1257 . -1051) NIL) ((-1110 . -133) T) ((-896 . -819) 181974) ((-146 . -102) T) ((-40 . -1132) T) ((-896 . -814) 181953) ((-663 . -1041) 181937) ((-594 . -1088) T) ((-560 . -1088) T) ((-509 . -1088) T) ((-421 . -466) T) ((-372 . -133) T) ((-326 . -414) 181921) ((-325 . -414) 181882) ((-367 . -133) T) ((-359 . -133) T) ((-1212 . -1132) T) ((-1151 . -38) 181869) ((-1120 . -632) 181836) ((-108 . -133) T) ((-983 . -1132) T) ((-948 . -1132) T) ((-793 . -1132) T) ((-694 . -1132) T) ((-723 . -149) T) ((-623 . -102) T) ((-118 . -149) T) ((-1319 . -21) T) ((-1319 . -25) T) ((-1318 . -21) T) ((-1318 . -25) T) ((-686 . -1087) 181820) ((-545 . -871) T) ((-514 . -871) T) ((-377 . -1247) T) ((-368 . -1087) 181772) ((-366 . -1087) 181724) ((-358 . -1087) 181676) ((-260 . -1247) T) ((-259 . -1247) T) ((-275 . -1087) 181519) ((-255 . -1087) 181362) ((-686 . -111) 181341) ((-839 . -1252) 181320) ((-562 . -866) T) ((-326 . -929) 181286) ((-368 . -111) 181224) ((-366 . -111) 181162) ((-358 . -111) 181100) ((-275 . -111) 180929) ((-255 . -111) 180758) ((-325 . -929) NIL) ((-642 . -426) 180742) ((-44 . -21) T) ((-44 . -25) T) ((-931 . -874) 180693) ((-130 . -684) T) ((-837 . -660) 180599) ((-839 . -571) 180578) ((-501 . -874) T) ((-260 . -1069) 180405) ((-259 . -1069) 180232) ((-128 . -121) 180216) ((-221 . -874) T) ((-935 . -1087) 180181) ((-734 . -102) T) ((-721 . -1088) T) ((-611 . -635) 180162) ((-600 . -635) 180143) ((-549 . -637) 180046) ((-357 . -175) T) ((-154 . -21) T) ((-154 . -25) T) ((-87 . -632) 180028) ((-935 . -111) 179984) ((-40 . -739) 179929) ((-893 . -1132) T) ((-686 . -635) 179906) ((-667 . -635) 179887) ((-368 . -635) 179824) ((-366 . -635) 179761) ((-358 . -635) 179698) ((-562 . -1132) T) ((-339 . -633) 179659) ((-339 . -632) 179571) ((-275 . -635) 179324) ((-255 . -635) 179109) ((-190 . -1247) T) ((-1262 . -814) 179062) 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177526) ((-1085 . -23) T) ((-1055 . -870) T) ((-935 . -1080) T) ((-334 . -670) 177508) ((-723 . -239) T) ((-692 . -236) 177453) ((-1204 . -950) 177432) ((-1198 . -950) 177411) ((-1198 . -842) NIL) ((-1027 . -1082) 177307) ((-996 . -1247) T) ((-935 . -250) T) ((-839 . -376) 177286) ((-218 . -1132) T) ((-394 . -23) T) ((-129 . -1132) 177264) ((-123 . -1132) 177242) ((-935 . -240) T) ((-131 . -34) T) ((-391 . -670) 177207) ((-1027 . -662) 177155) ((-893 . -739) 177142) ((-1327 . -668) 177114) ((-1077 . -153) 177079) ((-1024 . -1247) T) ((-887 . -1247) T) ((-40 . -175) T) ((-716 . -426) 177061) ((-734 . -321) 177048) ((-856 . -670) 177008) ((-850 . -670) 176982) ((-331 . -25) T) ((-331 . -21) T) ((-676 . -298) 176961) ((-594 . -1132) T) ((-560 . -1132) T) ((-509 . -1132) T) ((-1201 . -1247) T) ((-252 . -300) 176938) ((-1156 . -1247) T) ((-878 . -1247) T) ((-325 . -274) 176899) ((-325 . -234) 176860) ((-1253 . -874) T) ((-1201 . -911) NIL) ((-55 . -1132) T) ((-1156 . -911) 176719) ((-130 . -871) T) ((-1201 . -1069) 176599) ((-1156 . -1069) 176482) ((-187 . -632) 176464) ((-878 . -1069) 176360) ((-803 . -298) 176287) ((-839 . -1143) T) ((-1065 . -748) T) ((-1077 . -1007) 176216) ((-616 . -673) 176200) ((-1034 . -921) 176107) ((-1027 . -102) T) ((-839 . -23) T) ((-734 . -1182) 176085) ((-716 . -1088) T) ((-616 . -385) 176069) ((-365 . -466) T) ((-357 . -302) T) ((-1300 . -1132) T) ((-256 . -1132) T) ((-413 . -102) T) ((-301 . -21) T) ((-301 . -25) T) ((-374 . -748) T) ((-732 . -1132) T) ((-721 . -1132) T) ((-374 . -487) T) ((-1240 . -632) 176051) ((-1201 . -390) 176035) ((-1156 . -390) 176019) ((-1055 . -426) 175981) ((-143 . -233) 175963) ((-391 . -816) T) ((-391 . -813) T) ((-893 . -175) T) ((-391 . -748) T) ((-733 . -632) 175945) ((-734 . -38) 175774) ((-1297 . -1296) 175758) ((-365 . -416) T) ((-1297 . -1132) 175708) ((-1221 . -1132) T) ((-594 . -739) 175695) ((-560 . -739) 175682) ((-509 . -739) 175647) ((-1284 . -668) 175537) ((-326 . -649) 175516) ((-856 . -748) T) 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T) ((-900 . -635) 174698) ((-736 . -670) 174658) ((-501 . -1252) T) ((-703 . -635) 174639) ((-698 . -635) 174620) ((-659 . -670) 174604) ((-221 . -1252) T) ((-421 . -921) 174525) ((-229 . -1069) 174485) ((-40 . -302) T) ((-501 . -571) T) ((-492 . -635) 174466) ((-372 . -25) T) ((-326 . -668) 174121) ((-325 . -668) 174035) ((-372 . -21) T) ((-367 . -25) T) ((-367 . -21) T) ((-221 . -571) T) ((-359 . -25) T) ((-359 . -21) T) ((-331 . -236) 173981) ((-252 . -635) 173958) ((-140 . -635) 173939) ((-139 . -635) 173920) ((-135 . -635) 173901) ((-108 . -25) T) ((-108 . -21) T) ((-48 . -1088) T) ((-594 . -175) T) ((-560 . -175) T) ((-509 . -175) T) ((-1093 . -1247) T) ((-975 . -1247) T) ((-735 . -1247) T) ((-661 . -298) 173868) ((-676 . -632) 173850) ((-495 . -1247) T) ((-758 . -759) 173834) ((-346 . -632) 173816) ((-68 . -396) T) ((-68 . -410) T) ((-1128 . -107) 173800) ((-1093 . -911) 173782) ((-975 . -911) 173707) ((-677 . -1143) T) ((-642 . -739) 173694) ((-495 . -911) NIL) ((-1177 . -102) T) ((-1120 . -637) 173678) ((-1093 . -1069) 173660) ((-97 . -632) 173642) ((-491 . -149) T) ((-975 . -1069) 173522) ((-119 . -739) 173467) ((-734 . -929) 173374) ((-677 . -23) T) ((-495 . -1069) 173250) ((-1118 . -633) NIL) ((-1118 . -632) 173232) ((-803 . -633) NIL) ((-803 . -632) 173193) ((-802 . -633) 172827) ((-802 . -632) 172741) ((-1144 . -660) 172647) ((-820 . -874) 172626) ((-475 . -632) 172608) ((-468 . -632) 172590) ((-468 . -633) 172451) ((-1066 . -233) 172397) ((-896 . -939) 172376) ((-128 . -34) T) ((-839 . -133) T) ((-671 . -632) 172358) ((-592 . -102) T) ((-368 . -1316) 172342) ((-366 . -1316) 172326) ((-358 . -1316) 172310) ((-123 . -528) 172243) ((-129 . -528) 172176) ((-526 . -814) T) ((-526 . -819) T) ((-525 . -816) T) ((-103 . -321) 172114) ((-226 . -102) 172064) ((-721 . -175) T) ((-716 . -1132) T) ((-896 . -670) 171980) ((-65 . -398) T) ((-286 . -632) 171962) ((-65 . -410) T) ((-975 . -390) 171946) ((-893 . -302) T) ((-50 . -632) 171928) ((-1151 . -668) 171900) 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169722) ((-359 . -236) 169695) ((-177 . -466) T) ((-82 . -455) T) ((-226 . -321) 169633) ((-82 . -410) T) ((-227 . -632) 169615) ((-108 . -236) 169602) ((-221 . -23) T) ((-1322 . -1317) 169581) ((-699 . -1069) 169565) ((-594 . -302) T) ((-560 . -302) T) ((-509 . -302) T) ((-1266 . -1247) T) ((-137 . -484) 169520) ((-879 . -1247) T) ((-678 . -668) 169479) ((-48 . -1132) T) ((-734 . -274) 169463) ((-734 . -234) 169447) ((-895 . -927) NIL) ((-585 . -1247) T) ((-1266 . -911) NIL) ((-913 . -102) T) ((-910 . -102) T) ((-661 . -632) 169429) ((-402 . -1132) T) ((-171 . -390) 169413) ((-171 . -351) 169397) ((-1266 . -1069) 169277) ((-879 . -1069) 169173) ((-1173 . -102) T) ((-1027 . -929) 169096) ((-677 . -133) T) ((-674 . -814) 169075) ((-674 . -819) 169054) ((-119 . -528) 168962) ((-585 . -1069) 168944) ((-305 . -1305) 168914) ((-1198 . -874) NIL) ((-890 . -102) T) ((-985 . -571) 168893) ((-1240 . -1087) 168776) ((-1034 . -1082) 168721) ((-496 . -660) 168627) ((-934 . -1132) T) ((-1055 . -739) 168564) ((-733 . -1087) 168529) ((-1034 . -662) 168474) ((-636 . -102) T) ((-616 . -34) T) ((-1178 . -1247) T) ((-1240 . -111) 168343) ((-488 . -670) 168240) ((-353 . -739) 168185) ((-171 . -927) 168144) ((-721 . -302) T) ((-716 . -175) T) ((-733 . -111) 168100) ((-1327 . -1088) T) ((-1266 . -390) 168084) ((-419 . -1252) 168062) ((-1146 . -632) 168044) ((-325 . -870) NIL) ((-419 . -571) T) ((-229 . -319) T) ((-1262 . -813) 167997) ((-1262 . -816) 167950) ((-1283 . -748) T) ((-1262 . -748) T) ((-48 . -739) 167915) ((-229 . -1051) T) ((-1284 . -426) 167881) ((-1266 . -927) 167824) ((-365 . -1305) 167801) ((-1240 . -635) 167683) ((-740 . -748) T) ((-345 . -632) 167665) ((-534 . -874) 167644) ((-1144 . -236) 167535) ((-114 . -632) 167517) ((-114 . -633) 167499) ((-740 . -487) T) ((-733 . -635) 167449) ((-1321 . -1082) 167433) ((-496 . -25) 167266) ((-129 . -503) 167250) ((-123 . -503) 167234) ((-496 . -21) 167145) ((-1321 . -662) 167115) ((-642 . -302) T) ((-597 . -1087) 167090) 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-1247) T) ((-48 . -175) T) ((-723 . -401) T) ((-723 . -145) T) ((-1321 . -102) T) ((-1229 . -1247) T) ((-1227 . -635) 166423) ((-1119 . -1247) T) ((-1118 . -1087) 166266) ((-1106 . -1247) T) ((-275 . -939) 166245) ((-255 . -939) 166224) ((-803 . -1087) 166047) ((-802 . -1087) 165890) ((-627 . -1247) T) ((-1195 . -632) 165872) ((-1118 . -111) 165701) ((-1077 . -102) T) ((-489 . -1247) T) ((-475 . -1087) 165672) ((-468 . -1087) 165515) ((-686 . -670) 165499) ((-895 . -319) T) ((-803 . -111) 165308) ((-802 . -111) 165137) ((-368 . -670) 165089) ((-366 . -670) 165041) ((-358 . -670) 164993) ((-275 . -670) 164882) ((-255 . -670) 164771) ((-1189 . -871) T) ((-1119 . -1069) 164755) ((-1106 . -1069) 164732) ((-1035 . -874) T) ((-1031 . -34) T) ((-475 . -111) 164693) ((-468 . -111) 164522) ((-1002 . -874) T) ((-995 . -632) 164504) ((-987 . -1247) T) ((-985 . -1143) T) ((-128 . -1041) 164488) ((-872 . -1247) T) ((-895 . -1051) NIL) ((-757 . -1143) T) ((-737 . -1143) T) ((-676 . -635) 164406) ((-1297 . -503) 164390) ((-1215 . -1247) T) ((-1214 . -1247) T) ((-1173 . -38) 164350) ((-985 . -23) T) ((-935 . -670) 164315) ((-889 . -1132) T) ((-864 . -102) T) ((-839 . -21) T) ((-652 . -1082) 164299) ((-620 . -1082) 164283) ((-839 . -25) T) ((-757 . -23) T) ((-737 . -23) T) ((-652 . -662) 164267) ((-110 . -684) T) ((-620 . -662) 164251) ((-595 . -1087) 164216) ((-532 . -1087) 164161) ((-231 . -57) 164119) ((-467 . -23) T) ((-421 . -102) T) ((-1213 . -1247) T) ((-270 . -102) T) ((-110 . -113) T) ((-716 . -302) T) ((-890 . -38) 164089) ((-1118 . -635) 163825) ((-595 . -111) 163781) ((-532 . -111) 163710) ((-419 . -1143) T) ((-326 . -1088) 163600) ((-325 . -1088) T) ((-132 . -1247) T) ((-131 . -1247) T) ((-803 . -635) 163348) ((-802 . -635) 163114) ((-676 . -1080) T) ((-1327 . -1132) T) ((-468 . -635) 162899) ((-171 . -319) 162830) ((-419 . -23) T) ((-40 . -632) 162812) ((-40 . -633) 162796) ((-108 . -1022) 162778) ((-118 . -894) 162762) ((-671 . -635) 162746) ((-48 . -528) 162712) 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-1132) T) ((-421 . -321) 161010) ((-1173 . -929) 160933) ((-893 . -632) 160915) ((-856 . -1069) 160884) ((-661 . -1087) 160868) ((-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) 160850) ((-509 . -1033) T) ((-285 . -861) T) ((-284 . -861) T) ((-283 . -861) T) ((-282 . -861) T) ((-48 . -302) T) ((-281 . -861) T) ((-280 . -861) T) ((-279 . -861) T) ((-196 . -809) T) ((-661 . -111) 160829) ((-630 . -871) T) ((-678 . -426) 160813) ((-692 . -239) 160764) ((-227 . -635) 160726) ((-110 . -871) T) ((-677 . -21) T) ((-677 . -25) T) ((-1321 . -38) 160696) ((-119 . -298) 160647) ((-1297 . -19) 160631) ((-1257 . -874) NIL) ((-1297 . -618) 160608) ((-1311 . -1132) T) ((-365 . -1082) 160553) ((-1108 . -1132) T) ((-1017 . -1132) T) ((-985 . -133) T) ((-839 . -236) 160540) ((-758 . -1132) T) ((-365 . -662) 160485) ((-757 . -133) T) ((-737 . -133) T) ((-526 . -815) T) ((-526 . -816) T) ((-467 . -133) T) ((-421 . -1182) 160463) ((-227 . -1080) T) ((-305 . -102) 160245) ((-143 . -1132) T) ((-721 . -1033) T) ((-1136 . -298) 160201) ((-91 . -1247) T) ((-218 . -632) 160183) ((-129 . -632) 160115) ((-123 . -632) 160047) ((-1327 . -175) T) ((-1204 . -376) 160026) ((-1198 . -376) 160005) ((-326 . -1132) T) ((-419 . -133) T) ((-325 . -1132) T) ((-421 . -38) 159957) ((-1164 . -102) T) ((-1284 . -739) 159849) ((-1166 . -1293) T) ((-1127 . -1247) T) ((-1122 . -1247) T) ((-678 . -1088) T) ((-1104 . -1247) T) ((-1097 . -1247) T) ((-1067 . -1247) T) ((-1050 . -1247) T) ((-331 . -147) 159828) ((-331 . -149) 159807) ((-141 . -1132) T) ((-137 . -1132) T) ((-115 . -1132) T) ((-882 . -102) T) ((-645 . -1247) T) ((-497 . -1247) T) ((-594 . -632) 159789) ((-560 . -633) 159688) ((-560 . -632) 159670) ((-509 . -632) 159652) ((-509 . -633) 159597) ((-499 . -23) T) ((-222 . -1247) T) ((-496 . -871) 159548) ((-501 . -660) 159530) ((-994 . -632) 159512) ((-1034 . 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-1132) 146013) ((-1255 . -866) T) ((-331 . -1004) 145975) ((-105 . -102) T) ((-48 . -1087) 145940) ((-895 . -874) NIL) ((-1322 . -102) T) ((-395 . -102) T) ((-1284 . -632) 145922) ((-1164 . -1165) 145906) ((-1035 . -660) 145888) ((-900 . -1247) T) ((-48 . -111) 145844) ((-703 . -1247) T) ((-698 . -1247) T) ((-674 . -1247) T) ((-837 . -921) 145711) ((-492 . -1247) T) ((-252 . -1247) T) ((-545 . -102) T) ((-514 . -102) T) ((-154 . -1305) 145695) ((-140 . -1247) T) ((-139 . -1247) T) ((-135 . -1247) T) ((-1248 . -102) T) ((-1055 . -635) 145632) ((-839 . -239) T) ((-1201 . -1252) 145611) ((-218 . -381) T) ((-353 . -635) 145541) ((-1156 . -1252) 145520) ((-246 . -25) 145353) ((-246 . -21) 145264) ((-129 . -121) 145248) ((-123 . -121) 145232) ((-44 . -766) 145216) ((-1201 . -571) 145127) ((-1156 . -571) 145058) ((-1255 . -1132) T) ((-561 . -874) T) ((-1066 . -298) 145033) ((-1197 . -1114) T) ((-1025 . -1114) T) ((-838 . -133) T) ((-119 . -819) NIL) ((-119 . -814) NIL) ((-368 . -319) T) 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143042) ((-1219 . -107) 142992) ((-669 . -153) 142976) ((-651 . -153) 142922) ((-118 . -668) 142894) ((-493 . -1224) 142873) ((-501 . -149) T) ((-501 . -147) NIL) ((-1151 . -633) 142788) ((-452 . -632) 142770) ((-221 . -149) T) ((-221 . -147) NIL) ((-1151 . -632) 142752) ((-130 . -102) T) ((-51 . -102) T) ((-1257 . -660) 142704) ((-493 . -107) 142654) ((-1024 . -23) T) ((-1322 . -38) 142624) ((-1201 . -1143) T) ((-1156 . -1143) T) ((-1093 . -1252) T) ((-246 . -236) 142515) ((-324 . -102) T) ((-878 . -1143) T) ((-975 . -1252) 142494) ((-495 . -1252) 142473) ((-1093 . -571) T) ((-975 . -571) 142404) ((-1201 . -23) T) ((-1183 . -1114) T) ((-1156 . -23) T) ((-878 . -23) T) ((-495 . -571) 142335) ((-1173 . -739) 142267) ((-692 . -1082) 142251) ((-1177 . -528) 142184) ((-692 . -662) 142168) ((-1066 . -633) NIL) ((-1066 . -632) 142150) ((-96 . -1114) T) ((-1327 . -1087) 142137) ((-890 . -739) 142107) ((-1327 . -111) 142092) ((-1240 . -47) 142061) ((-1198 . -871) NIL) ((-260 . -133) T) ((-259 . -133) T) ((-1134 . -1132) T) ((-1034 . -1132) T) ((-63 . -632) 142043) ((-1110 . -921) 141912) ((-1055 . -814) T) ((-1055 . -819) T) ((-1287 . -25) T) ((-1287 . -21) T) ((-1278 . -21) T) ((-1278 . -25) T) ((-893 . -670) 141899) ((-1257 . -21) T) ((-1257 . -25) T) ((-1058 . -153) 141883) ((-1035 . -236) 141870) ((-896 . -842) 141849) ((-896 . -950) T) ((-734 . -298) 141776) ((-610 . -21) T) ((-352 . -668) 141735) ((-108 . -921) NIL) ((-610 . -25) T) ((-609 . -21) T) ((-177 . -668) 141652) ((-40 . -748) T) ((-226 . -528) 141585) ((-609 . -25) T) ((-490 . -153) 141569) ((-477 . -153) 141553) ((-187 . -1247) T) ((-948 . -816) T) ((-948 . -748) T) ((-793 . -815) T) ((-793 . -816) T) ((-520 . -1132) T) ((-516 . -1132) T) ((-793 . -748) T) ((-229 . -376) T) ((-1319 . -1082) 141537) ((-1318 . -1082) 141521) ((-1319 . -662) 141491) ((-1185 . -1132) 141469) ((-895 . -1252) T) ((-1318 . -662) 141439) ((-1119 . -874) T) ((-678 . -632) 141421) ((-895 . -571) T) ((-716 . -381) NIL) ((-44 . -1082) 141405) ((-1327 . -635) 141387) ((-1321 . -1132) T) ((-692 . -102) T) ((-372 . -1305) 141371) ((-367 . -1305) 141355) ((-44 . -662) 141339) ((-359 . -1305) 141323) ((-563 . -102) T) ((-1240 . -1247) T) ((-534 . -871) 141302) ((-733 . -1247) T) ((-987 . -874) 141281) ((-872 . -874) T) ((-501 . -239) T) ((-221 . -239) T) ((-1077 . -1132) T) ((-839 . -466) 141260) ((-154 . -1082) 141244) ((-1077 . -1102) 141173) ((-1058 . -1007) 141142) ((-841 . -1143) T) ((-1034 . -739) 141087) ((-154 . -662) 141071) ((-400 . -1143) T) ((-490 . -1007) 141040) ((-477 . -1007) 141009) ((-1214 . -874) T) ((-110 . -153) 140991) ((-73 . -632) 140973) ((-918 . -632) 140955) ((-1213 . -874) T) ((-1110 . -746) 140934) ((-1327 . -1080) T) ((-838 . -660) 140882) ((-305 . -1088) 140824) ((-171 . -1252) 140729) ((-229 . -1143) T) ((-336 . -23) T) ((-1198 . -1022) 140681) ((-1284 . -1087) 140586) ((-864 . -1132) T) ((-131 . -874) T) ((-1157 . -762) 140565) ((-1283 . -950) 140544) ((-1262 . -950) 140523) ((-893 . -748) T) ((-171 . -571) 140434) ((-594 . -670) 140421) ((-560 . -670) 140393) ((-421 . -1132) T) ((-270 . -1132) T) ((-216 . -632) 140375) ((-509 . -670) 140325) ((-229 . -23) T) ((-1262 . -842) 140278) ((-1319 . -102) T) ((-505 . -1247) T) ((-353 . -1316) 140255) ((-1318 . -102) T) ((-1284 . -111) 140147) ((-1144 . -921) 140014) ((-837 . -1082) 139915) ((-837 . -662) 139837) ((-146 . -632) 139819) ((-1024 . -133) T) ((-44 . -102) T) ((-246 . -871) 139770) ((-597 . -1247) T) ((-1266 . -1252) 139749) ((-103 . -503) 139733) ((-1321 . -739) 139703) ((-1118 . -47) 139664) ((-1093 . -1143) T) ((-975 . -1143) T) ((-129 . -34) T) ((-123 . -34) T) ((-1266 . -571) 139575) ((-803 . -47) 139552) ((-802 . -47) 139524) ((-1227 . -1247) T) ((-1201 . -133) T) ((-353 . -381) T) ((-495 . -1143) T) ((-1156 . -133) T) ((-895 . -376) T) ((-468 . -47) 139503) ((-878 . -133) T) ((-334 . -874) 139482) ((-154 . -102) T) ((-1093 . -23) T) ((-975 . -23) T) ((-585 . -571) T) ((-838 . -25) T) ((-838 . -21) T) 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137363) ((-1118 . -1247) T) ((-1066 . -300) 137338) ((-594 . -748) T) ((-560 . -816) T) ((-171 . -376) 137289) ((-560 . -813) T) ((-560 . -748) T) ((-509 . -748) T) ((-803 . -1247) T) ((-802 . -1247) T) ((-1177 . -503) 137273) ((-475 . -1247) T) ((-468 . -1247) T) ((-1319 . -1320) 137249) ((-1118 . -911) NIL) ((-895 . -1143) T) ((-119 . -939) NIL) ((-1318 . -1320) 137228) ((-671 . -1247) T) ((-803 . -911) NIL) ((-802 . -911) 137087) ((-1313 . -25) T) ((-1313 . -21) T) ((-1245 . -102) 137065) ((-1137 . -410) T) ((-642 . -670) 137052) ((-468 . -911) NIL) ((-697 . -102) 137002) ((-1118 . -1069) 136829) ((-895 . -23) T) ((-803 . -1069) 136688) ((-802 . -1069) 136545) ((-119 . -670) 136490) ((-468 . -1069) 136366) ((-286 . -1247) T) ((-326 . -635) 135930) ((-325 . -635) 135813) ((-50 . -1247) T) ((-404 . -668) 135782) ((-671 . -1069) 135766) ((-646 . -102) T) ((-595 . -1247) T) ((-532 . -1247) T) ((-226 . -503) 135750) ((-1297 . -34) T) ((-638 . -668) 135709) ((-301 . -1082) 135696) ((-137 . -635) 135680) ((-301 . -662) 135667) ((-652 . -739) 135651) ((-620 . -739) 135635) ((-692 . -38) 135595) ((-331 . -102) T) ((-1151 . -1087) 135582) ((-86 . -632) 135564) ((-50 . -1069) 135548) ((-1118 . -390) 135532) ((-803 . -390) 135516) ((-721 . -748) T) ((-721 . -816) T) ((-721 . -813) T) ((-60 . -57) 135478) ((-595 . -1069) 135465) ((-532 . -1069) 135442) ((-174 . -1247) T) ((-336 . -133) T) ((-326 . -1080) 135332) ((-325 . -1080) T) ((-171 . -1143) T) ((-802 . -390) 135316) ((-45 . -153) 135266) ((-1035 . -1022) 135248) ((-468 . -390) 135232) ((-421 . -175) T) ((-326 . -250) 135211) ((-325 . -250) T) ((-325 . -240) NIL) ((-305 . -1132) 134993) ((-229 . -133) T) ((-1151 . -111) 134978) ((-171 . -23) T) ((-820 . -149) 134957) ((-820 . -147) 134936) ((-260 . -660) 134842) ((-259 . -660) 134748) ((-331 . -296) 134714) ((-1185 . -528) 134647) ((-491 . -668) 134597) ((-657 . -866) T) ((-496 . -921) 134464) ((-1164 . -1132) T) ((-229 . -1091) T) ((-837 . -321) 134402) ((-1118 . -927) 134337) ((-803 . -927) 134280) ((-802 . -927) 134264) ((-1319 . -38) 134234) ((-1318 . -38) 134204) ((-1266 . -1143) T) ((-879 . -1143) T) ((-468 . -927) 134181) ((-882 . -1132) T) ((-1266 . -23) T) ((-1151 . -635) 134153) ((-1093 . -133) T) ((-879 . -23) T) ((-585 . -1143) T) ((-642 . -748) T) ((-525 . -874) T) ((-368 . -950) T) ((-366 . -950) T) ((-301 . -102) T) ((-358 . -950) T) ((-1001 . -1114) T) ((-975 . -133) T) ((-838 . -236) 134098) ((-119 . -816) NIL) ((-119 . -813) NIL) ((-119 . -748) T) ((-1077 . -528) 133999) ((-716 . -939) NIL) ((-585 . -23) T) ((-495 . -133) T) ((-419 . -239) 133950) ((-697 . -321) 133888) ((-227 . -1247) T) ((-657 . -1132) T) ((-652 . -783) T) ((-620 . -783) T) ((-1257 . -871) NIL) ((-1110 . -1082) 133798) ((-1034 . -302) T) ((-716 . -670) 133748) ((-260 . -25) T) ((-365 . -1132) T) ((-260 . -21) T) ((-259 . -25) T) ((-259 . -21) T) ((-154 . -38) 133732) ((-2 . -102) T) ((-935 . -950) T) ((-1110 . -662) 133600) ((-496 . -1305) 133570) ((-1151 . -1080) T) ((-733 . -319) T) ((-723 . -1088) T) ((-372 . -1082) 133522) ((-367 . -1082) 133474) ((-359 . -1082) 133426) ((-372 . -662) 133378) ((-227 . -1069) 133355) ((-367 . -662) 133307) ((-108 . -1082) 133257) ((-359 . -662) 133209) ((-305 . -739) 133151) ((-661 . -1247) T) ((-501 . -466) T) ((-421 . -528) 133063) ((-108 . -662) 133013) ((-221 . -466) T) ((-1151 . -240) T) ((-307 . -153) 132963) ((-1027 . -633) 132924) ((-1027 . -632) 132906) ((-1020 . -632) 132888) ((-118 . -1088) T) ((-678 . -1087) 132872) ((-229 . -507) T) ((-413 . -632) 132854) ((-413 . -633) 132831) ((-1085 . -1305) 132801) ((-678 . -111) 132780) ((-692 . -929) 132703) ((-1173 . -503) 132687) ((-1322 . -668) 132646) ((-395 . -668) 132615) ((-64 . -455) T) ((-64 . -410) T) ((-1190 . -102) T) ((-895 . -133) T) ((-498 . -102) 132565) ((-1146 . -1247) T) ((-1254 . -874) T) ((-1327 . -381) T) ((-1110 . -102) T) ((-1092 . -102) T) ((-365 . -739) 132510) ((-896 . -874) 132461) ((-753 . -149) 132440) ((-753 . -147) 132419) 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131166) ((-1189 . -102) T) ((-1266 . -133) T) ((-1262 . -874) 131065) ((-1201 . -25) T) ((-1201 . -21) T) ((-1190 . -321) 130860) ((-357 . -1247) T) ((-1156 . -25) T) ((-879 . -133) T) ((-407 . -1247) T) ((-1156 . -21) T) ((-878 . -25) T) ((-878 . -21) T) ((-803 . -319) 130839) ((-1185 . -503) 130823) ((-1181 . -153) 130773) ((-1177 . -632) 130735) ((-669 . -102) 130685) ((-651 . -102) T) ((-1177 . -633) 130646) ((-585 . -133) T) ((-638 . -870) 130625) ((-1055 . -813) T) ((-1055 . -816) T) ((-1055 . -748) T) ((-837 . -929) 130494) ((-734 . -1087) 130317) ((-616 . -874) 130296) ((-498 . -321) 130234) ((-467 . -432) 130204) ((-365 . -175) T) ((-301 . -38) 130191) ((-260 . -236) 130082) ((-259 . -236) 129973) ((-285 . -102) T) ((-284 . -102) T) ((-283 . -102) T) ((-282 . -102) T) ((-281 . -102) T) ((-280 . -102) T) ((-357 . -1069) 129950) ((-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 . 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-874) T) ((-1205 . -35) 128490) ((-1205 . -95) 128456) ((-1205 . -1236) 128422) ((-1205 . -1233) 128388) ((-1204 . -1233) 128354) ((-1204 . -1236) 128320) ((-1204 . -95) 128286) ((-1204 . -35) 128252) ((-1198 . -1233) 128218) ((-1198 . -1236) 128184) ((-1189 . -321) NIL) ((-89 . -411) T) ((-89 . -410) T) ((-1110 . -1182) 128163) ((-40 . -1247) T) ((-1198 . -95) 128129) ((-1065 . -23) T) ((-1198 . -35) 128095) ((-585 . -507) T) ((-1157 . -35) 128061) ((-1157 . -95) 128027) ((-1157 . -1236) 127993) ((-1157 . -1233) 127959) ((-374 . -1143) T) ((-372 . -1182) 127938) ((-367 . -1182) 127917) ((-359 . -1182) 127896) ((-1134 . -298) 127852) ((-983 . -1247) T) ((-948 . -1247) T) ((-108 . -1182) T) ((-854 . -1088) 127831) ((-793 . -1247) T) ((-669 . -321) 127769) ((-651 . -321) 127620) ((-694 . -1247) T) ((-734 . -1080) T) ((-1093 . -660) 127602) ((-1110 . -38) 127470) ((-975 . -660) 127418) ((-1035 . -149) T) ((-1035 . -147) NIL) ((-391 . -1143) T) ((-336 . -25) T) ((-334 . -23) T) ((-972 . -871) 127397) ((-734 . -338) 127374) ((-495 . -660) 127322) ((-40 . -1069) 127210) ((-734 . -240) T) ((-723 . -739) 127197) ((-352 . -1132) T) ((-177 . -1132) T) ((-343 . -871) T) ((-419 . -466) 127147) ((-391 . -23) T) ((-372 . -38) 127112) ((-367 . -38) 127077) ((-359 . -38) 127042) ((-80 . -455) T) ((-80 . -410) T) ((-229 . -25) T) ((-229 . -21) T) ((-856 . -1143) T) ((-108 . -38) 126992) ((-850 . -1143) T) ((-795 . -1132) T) ((-118 . -739) 126979) ((-694 . -1069) 126963) ((-630 . -102) T) ((-856 . -23) T) ((-850 . -23) T) ((-1185 . -298) 126915) ((-1144 . -321) 126853) ((-496 . -1082) 126754) ((-1128 . -242) 126738) ((-61 . -411) T) ((-61 . -410) T) ((-1183 . -102) T) ((-110 . -102) T) ((-496 . -662) 126660) ((-40 . -390) 126637) ((-96 . -102) T) ((-677 . -876) 126621) ((-1201 . -236) 126608) ((-1166 . -1114) T) ((-1093 . -21) T) ((-1093 . -25) T) ((-1085 . -1082) 126592) ((-837 . -274) 126561) ((-837 . -234) 126530) ((-975 . -25) T) ((-975 . -21) T) ((-1151 . -381) T) ((-1085 . -662) 126472) ((-638 . -1088) T) ((-1058 . -321) 126410) ((-913 . -632) 126392) ((-692 . -668) 126351) ((-495 . -25) T) ((-495 . -21) T) ((-394 . -1082) 126335) ((-910 . -632) 126317) ((-893 . -1247) T) ((-537 . -528) 126250) ((-260 . -871) 126201) ((-259 . -871) 126152) ((-394 . -662) 126122) ((-895 . -660) 126099) ((-490 . -321) 126037) ((-562 . -1247) T) ((-477 . -321) 125975) ((-365 . -302) T) ((-1185 . -1286) 125959) ((-1173 . -632) 125921) ((-1173 . -633) 125882) ((-1171 . -102) T) ((-1027 . -1087) 125778) ((-40 . -927) 125730) ((-1185 . -618) 125707) ((-1327 . -670) 125694) ((-1094 . -153) 125640) ((-501 . -921) NIL) ((-890 . -504) 125617) ((-1027 . -111) 125499) ((-896 . -1252) T) ((-221 . -921) NIL) ((-352 . -739) 125483) ((-890 . -632) 125445) ((-177 . -739) 125377) ((-896 . -571) T) ((-421 . -298) 125335) ((-246 . -239) 125232) ((-108 . -414) 125214) ((-85 . -398) T) ((-85 . -410) T) ((-723 . -175) T) ((-636 . -632) 125196) ((-99 . -748) T) ((-496 . -102) 124928) ((-99 . 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-1233) 84069) ((-1283 . -1236) 84035) ((-1266 . -921) 83938) ((-1201 . -1082) 83761) ((-1173 . -1247) T) ((-1156 . -1082) 83604) ((-878 . -1082) 83588) ((-651 . -618) 83563) ((-1283 . -95) 83529) ((-1283 . -239) 83481) ((-1264 . -102) 83459) ((-1201 . -662) 83288) ((-1156 . -662) 83137) ((-878 . -662) 83107) ((-1262 . -1233) 83073) ((-1118 . -25) T) ((-564 . -1132) T) ((-1118 . -21) T) ((-985 . -1088) T) ((-545 . -814) T) ((-545 . -819) T) ((-119 . -1252) T) ((-890 . -1247) T) ((-642 . -571) T) ((-803 . -25) T) ((-803 . -21) T) ((-802 . -21) T) ((-802 . -25) T) ((-757 . -1088) T) ((-737 . -1088) T) ((-692 . -1087) 83057) ((-531 . -1114) T) ((-475 . -25) T) ((-119 . -571) T) ((-475 . -21) T) ((-468 . -25) T) ((-468 . -21) T) ((-1262 . -1236) 83023) ((-1183 . -93) T) ((-1173 . -1069) 82919) ((-839 . -302) 82898) ((-1262 . -239) 82757) ((-846 . -1132) T) ((-995 . -998) T) ((-692 . -111) 82736) ((-636 . -1247) T) ((-307 . -528) 82528) ((-1257 . -234) 82480) ((-1257 . -274) 82432) ((-1256 . -381) T) ((-260 . -321) 82370) ((-259 . -321) 82308) ((-1253 . -866) T) ((-1190 . -633) NIL) ((-1190 . -632) 82290) ((-1173 . -390) 82274) ((-1151 . -842) T) ((-1151 . -950) T) ((-96 . -93) T) ((-1144 . -618) 82251) ((-1110 . -633) 82235) ((-1110 . -632) 82217) ((-1035 . -668) 82167) ((-943 . -668) 82104) ((-837 . -300) 82081) ((-498 . -632) 82013) ((-627 . -153) 81960) ((-501 . -739) 81910) ((-419 . -1088) T) ((-496 . -503) 81894) ((-443 . -668) 81853) ((-339 . -871) 81832) ((-352 . -670) 81806) ((-50 . -21) T) ((-50 . -25) T) ((-221 . -739) 81756) ((-171 . -746) 81727) ((-177 . -670) 81659) ((-595 . -21) T) ((-595 . -25) T) ((-532 . -25) T) ((-532 . -21) T) ((-489 . -153) 81609) ((-1092 . -632) 81591) ((-1024 . -102) T) ((-887 . -102) T) ((-838 . -929) 81491) ((-820 . -426) 81454) ((-40 . -133) T) ((-721 . -376) T) ((-723 . -748) T) ((-723 . -816) T) ((-723 . -813) T) ((-215 . -922) T) ((-594 . -1143) T) ((-560 . -1143) T) ((-509 . -1143) T) ((-372 . -632) 81436) ((-367 . -632) 81418) ((-359 . -632) 81400) ((-66 . -411) T) ((-66 . -410) T) ((-108 . -633) 81330) ((-108 . -632) 81272) ((-214 . -922) T) ((-987 . -153) 81256) ((-793 . -133) T) ((-692 . -635) 81174) ((-136 . -748) T) ((-118 . -748) T) ((-1283 . -35) 81140) ((-1085 . -503) 81124) ((-594 . -23) T) ((-560 . -23) T) ((-509 . -23) T) ((-1262 . -95) 81090) ((-1262 . -35) 81056) ((-1201 . -102) T) ((-1156 . -102) T) ((-878 . -102) T) ((-231 . -503) 81040) ((-1319 . -111) 81019) ((-1318 . -111) 80998) ((-44 . -1087) 80982) ((-1321 . -1247) T) ((-1319 . -635) 80928) ((-1319 . -1080) T) ((-1318 . -635) 80857) ((-1318 . -1080) T) ((-1266 . -1273) 80841) ((-879 . -876) 80825) ((-1209 . -302) 80804) ((-1134 . -1247) T) ((-110 . -298) 80754) ((-1034 . -1247) T) ((-131 . -153) 80736) ((-1173 . -927) 80695) ((-44 . -111) 80674) ((-1253 . -1132) T) ((-1212 . -1293) T) ((-1198 . -870) NIL) ((-1197 . -504) 80655) ((-692 . -1080) T) ((-1197 . -632) 80621) ((-1189 . -632) 80603) ((-488 . -239) 80555) ((-1094 . -629) 80530) ((-1025 . -504) 80511) ((-74 . -455) T) ((-74 . -410) T) ((-1094 . -1132) T) ((-154 . -1087) 80495) ((-1025 . -632) 80461) ((-692 . -240) 80440) ((-585 . -569) 80424) ((-368 . -149) 80403) ((-368 . -147) 80354) ((-366 . -149) 80333) ((-366 . -147) 80284) ((-358 . -149) 80263) ((-358 . -147) 80214) ((-275 . -147) 80193) ((-275 . -149) 80172) ((-255 . -149) 80151) ((-119 . -376) T) ((-255 . -147) 80130) ((-1189 . -633) NIL) ((-154 . -111) 80109) ((-1034 . -1069) 79997) ((-1185 . -1247) T) ((-716 . -1252) T) ((-820 . -1088) T) ((-721 . -1143) T) ((-1034 . -390) 79974) ((-520 . -1247) T) ((-516 . -1247) T) ((-935 . -147) T) ((-935 . -149) 79956) ((-893 . -133) T) ((-837 . -1087) 79877) ((-721 . -23) T) ((-716 . -571) T) ((-229 . -1082) 79842) ((-669 . -632) 79774) ((-669 . -633) 79735) ((-651 . -633) NIL) ((-651 . -632) 79717) ((-501 . -175) T) ((-229 . -662) 79682) ((-221 . -175) T) ((-227 . -21) T) ((-227 . -25) T) ((-488 . -1236) 79648) ((-488 . -1233) 79614) ((-285 . -632) 79596) ((-284 . -632) 79578) ((-283 . -632) 79560) ((-282 . -632) 79542) ((-281 . -632) 79524) ((-514 . -673) 79506) ((-280 . -632) 79488) ((-352 . -748) T) ((-279 . -632) 79470) ((-110 . -19) 79452) ((-177 . -748) T) ((-514 . -385) 79434) ((-215 . -632) 79416) ((-534 . -1180) 79400) ((-514 . -125) T) ((-110 . -618) 79375) ((-214 . -632) 79357) ((-488 . -35) 79323) ((-488 . -95) 79289) ((-212 . -632) 79271) ((-211 . -632) 79253) ((-210 . -632) 79235) ((-209 . -632) 79217) ((-206 . -632) 79199) ((-205 . -632) 79181) ((-204 . -632) 79163) ((-203 . -632) 79145) ((-202 . -632) 79127) ((-201 . -632) 79109) ((-200 . -632) 79091) ((-549 . -1135) 79043) ((-199 . -632) 79025) ((-198 . -632) 79007) ((-45 . -503) 78944) ((-197 . -632) 78926) ((-196 . -632) 78908) ((-154 . -635) 78877) ((-1147 . -102) T) ((-837 . -111) 78793) ((-663 . -102) 78723) ((-661 . -21) T) ((-661 . -25) T) ((-496 . -298) 78700) ((-1321 . -1069) 78684) ((-1144 . -632) 78377) ((-1133 . -1132) T) ((-1077 . -1247) T) ((-1201 . -321) 78364) ((-1093 . -1082) 78351) ((-1166 . -1132) T) ((-975 . -1082) 78194) ((-1156 . -321) 78181) ((-1127 . -1114) T) ((-642 . -1143) T) ((-1093 . -662) 78168) ((-1122 . -1114) T) ((-975 . -662) 78017) ((-1118 . -236) 77962) ((-495 . -1082) 77805) ((-1104 . -1114) T) ((-1097 . -1114) T) ((-1067 . -1114) T) ((-1050 . -1114) T) ((-119 . -1143) T) ((-495 . -662) 77654) ((-803 . -236) 77641) ((-841 . -102) T) ((-645 . -1114) T) ((-642 . -23) T) ((-1181 . -528) 77433) ((-497 . -1114) T) ((-985 . -1132) T) ((-400 . -102) T) ((-336 . -102) T) ((-222 . -1114) T) ((-864 . -1247) T) ((-154 . -1080) T) ((-753 . -426) 77417) ((-119 . -23) T) ((-1034 . -927) 77369) ((-757 . -1132) T) ((-737 . -1132) T) ((-1287 . -668) 77279) ((-1278 . -668) 77161) ((-467 . -1132) T) ((-421 . -1247) T) ((-326 . -435) 77145) ((-606 . -93) T) ((-1058 . -633) 77106) ((-270 . -1247) T) ((-1055 . -1252) T) ((-229 . -102) T) ((-1058 . -632) 77068) ((-838 . -274) 77052) ((-838 . -234) 77036) ((-837 . -635) 76834) 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75010) ((-735 . -102) T) ((-307 . -503) 74947) ((-895 . -662) 74892) ((-495 . -102) T) ((-753 . -1088) T) ((-630 . -632) 74874) ((-630 . -633) 74735) ((-421 . -390) 74719) ((-421 . -351) 74703) ((-1201 . -38) 74532) ((-1156 . -38) 74381) ((-331 . -635) 74207) ((-935 . -239) T) ((-652 . -1247) T) ((-620 . -1247) T) ((-878 . -38) 74177) ((-404 . -670) 74161) ((-663 . -321) 74099) ((-1183 . -504) 74080) ((-1183 . -632) 74046) ((-985 . -739) 73943) ((-757 . -739) 73913) ((-638 . -670) 73887) ((-226 . -107) 73871) ((-45 . -298) 73771) ((-323 . -1132) T) ((-301 . -1087) 73758) ((-110 . -632) 73740) ((-110 . -633) 73722) ((-467 . -739) 73692) ((-838 . -262) 73631) ((-711 . -1132) 73609) ((-565 . -1132) T) ((-1205 . -1088) T) ((-1204 . -1088) T) ((-96 . -504) 73590) ((-1198 . -1088) T) ((-301 . -111) 73575) ((-1157 . -1088) T) ((-565 . -629) 73554) ((-96 . -632) 73520) ((-1035 . -870) T) ((-231 . -708) 73478) ((-716 . -1143) T) ((-1240 . -762) 73454) ((-1055 . -376) T) ((-860 . -858) 73436) 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T) ((-895 . -321) 69641) ((-677 . -298) 69620) ((-657 . -1247) T) ((-114 . -684) T) ((-365 . -1247) T) ((-372 . -635) 69557) ((-367 . -635) 69494) ((-359 . -635) 69431) ((-77 . -1247) T) ((-108 . -635) 69381) ((-114 . -113) T) ((-1093 . -38) 69368) ((-686 . -387) 69347) ((-975 . -38) 69196) ((-753 . -1132) T) ((-495 . -38) 69045) ((-82 . -1247) T) ((-606 . -504) 69026) ((-1257 . -870) NIL) ((-1205 . -1132) T) ((-585 . -296) T) ((-1204 . -1132) T) ((-606 . -632) 68992) ((-1198 . -1132) T) ((-1151 . -874) T) ((-1110 . -1080) T) ((-365 . -1069) 68969) ((-839 . -504) 68953) ((-1035 . -1088) T) ((-45 . -632) 68935) ((-45 . -633) NIL) ((-943 . -1088) T) ((-839 . -632) 68904) ((-1178 . -102) 68854) ((-1110 . -250) 68805) ((-443 . -1088) T) ((-372 . -1080) T) ((-367 . -1080) T) ((-377 . -378) 68782) ((-359 . -1080) T) ((-357 . -236) 68769) ((-260 . -245) 68748) ((-259 . -245) 68727) ((-1110 . -240) 68652) ((-1157 . -1132) T) ((-305 . -927) 68611) ((-108 . -1080) T) ((-716 . -133) T) ((-419 . -528) 68453) ((-372 . -240) 68432) ((-372 . -250) T) ((-44 . -742) T) ((-367 . -240) 68411) ((-367 . -250) T) ((-359 . -240) 68390) ((-359 . -250) T) ((-1197 . -635) 68371) ((-171 . -321) 68336) ((-108 . -250) T) ((-108 . -240) T) ((-1025 . -635) 68317) ((-331 . -814) T) ((-893 . -21) T) ((-893 . -25) T) ((-421 . -319) T) ((-514 . -34) T) ((-110 . -300) 68292) ((-1144 . -1087) 68213) ((-895 . -1182) NIL) ((-342 . -632) 68195) ((-421 . -1051) 68173) ((-1144 . -111) 68089) ((-713 . -1293) T) ((-451 . -1132) T) ((-258 . -1132) T) ((-1322 . -748) T) ((-64 . -632) 68071) ((-895 . -38) 68016) ((-616 . -153) 68000) ((-537 . -1247) T) ((-524 . -632) 67940) ((-1266 . -321) 67927) ((-753 . -739) 67776) ((-545 . -815) T) ((-545 . -816) T) ((-560 . -660) 67758) ((-509 . -660) 67718) ((-518 . -1247) T) ((-659 . -1305) 67702) ((-368 . -466) T) ((-366 . -466) T) ((-358 . -466) T) ((-275 . -466) 67653) ((-539 . -1132) T) ((-534 . -1132) 67603) ((-255 . -466) 67554) ((-1181 . -298) 67533) ((-1209 . 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. -1088) T) ((-1240 . -149) 63676) ((-334 . -1082) 63658) ((-1240 . -147) 63637) ((-1215 . -102) T) ((-1214 . -102) T) ((-1213 . -102) T) ((-1205 . -175) 63588) ((-334 . -662) 63570) ((-723 . -1247) T) ((-1204 . -175) 63501) ((-1198 . -175) 63432) ((-1183 . -635) 63413) ((-1157 . -175) 63364) ((-610 . -1088) T) ((-609 . -1088) T) ((-1035 . -1132) T) ((-1002 . -1132) T) ((-391 . -1082) 63329) ((-136 . -1247) T) ((-118 . -1247) T) ((-943 . -1132) T) ((-895 . -929) NIL) ((-391 . -662) 63294) ((-146 . -874) T) ((-820 . -818) 63278) ((-721 . -25) T) ((-721 . -21) T) ((-119 . -660) 63255) ((-723 . -911) 63237) ((-443 . -1132) T) ((-326 . -1252) 63216) ((-325 . -1252) T) ((-171 . -414) 63200) ((-856 . -1082) 63170) ((-488 . -1004) 63132) ((-72 . -632) 63114) ((-132 . -102) T) ((-131 . -102) T) ((-850 . -1082) 63098) ((-108 . -819) T) ((-108 . -814) T) ((-723 . -1069) 63080) ((-326 . -571) 63059) ((-325 . -571) T) ((-856 . -662) 63029) ((-850 . -662) 62999) ((-1327 . -23) T) ((-136 . -1069) 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. -921) 60880) ((-987 . -321) 60818) ((-856 . -102) T) ((-443 . -739) 60802) ((-229 . -843) T) ((-850 . -102) T) ((-847 . -102) T) ((-1319 . -670) 60776) ((-1283 . -1282) 60755) ((-493 . -153) 60705) ((-1283 . -1276) 60675) ((-1151 . -1252) T) ((-352 . -1069) 60642) ((-1283 . -1280) 60626) ((-1266 . -929) 60533) ((-1262 . -1261) 60512) ((-80 . -632) 60494) ((-931 . -632) 60476) ((-1262 . -1276) 60453) ((-1151 . -571) T) ((-948 . -871) T) ((-793 . -871) T) ((-694 . -871) T) ((-501 . -633) 60383) ((-501 . -632) 60324) ((-391 . -296) T) ((-1262 . -1259) 60308) ((-1284 . -1143) T) ((-221 . -633) 60238) ((-221 . -632) 60179) ((-1094 . -618) 60154) ((-840 . -635) 60138) ((-560 . -236) 60125) ((-530 . -153) 60109) ((-58 . -153) 60093) ((-510 . -153) 60077) ((-509 . -236) 60064) ((-372 . -1316) 60048) ((-367 . -1316) 60032) ((-359 . -1316) 60016) ((-326 . -376) 59995) ((-325 . -376) T) ((-496 . -1080) 59973) ((-716 . -660) 59955) ((-1318 . -670) 59929) ((-131 . -321) NIL) ((-1284 . -23) T) 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|null| |log2| |removeConstantTerm| |hconcat| |cTan| - |subResultantsChain| |disjunction| |freeOf?| |equation| - |stosePrepareSubResAlgo| |intcompBasis| - |stoseIntegralLastSubResultant| |dequeue| |operation| |not| |cAcsch| - |nullary| |qfactor| |selectfirst| |graphImage| |cSec| |jvmStrict| - |iiexp| |showTheFTable| |iExquo| |and| |rootBound| |selectsecond| - |LyndonCoordinates| |terms| |redPol| |doublyTransitive?| |unit?| - |OMsetEncoding| |tubePoints| |or| |stirling2| |critT| |startStats!| - |loopPoints| |pointSizeDefault| |weakBiRank| |primitive?| - |showAllElements| |leftRank| |xor| |c06ekf| |compactFraction| |value| - |measure| |elaborate| |factorByRecursion| - |semiDegreeSubResultantEuclidean| |primlimintfrac| |heap| |cAcoth| - |rightNorm| |case| |createPrimitivePoly| |gcdPrimitive| |ldf2vmf| - |f02aef| |traceMatrix| |relerror| |radPoly| |nsqfree| |readUInt8!| - |Zero| |subst| |lintgcd| |explicitlyFinite?| |polyPart| |resize| - |basisOfRightNucloid| |sqfrFactor| |stopMusserTrials| |One| |notelem| - |OMreadStr| |contains?| |OMputEndAttr| |discriminant| |Lazard| - |besselJ| |argumentListOf| |graphState| |mainDefiningPolynomial| - |createGenericMatrix| |asecIfCan| |halfExtendedSubResultantGcd2| - |composites| |genericRightNorm| |sorted?| |s13aaf| - |useEisensteinCriterion?| |uniform01| |optional?| |factors| |c06gsf| - |viewport2D| |Vectorise| |euler| |solveInField| |f04mcf| |orbit| - |basisOfCentroid| |generalizedContinuumHypothesisAssumed?| - |subResultantChain| |messagePrint| |reducedDiscriminant| |objects| - |regularRepresentation| |testModulus| |perfectNthPower?| - |stoseInvertible?| |symmetricPower| |separant| |rarrow| - |changeMeasure| |rootOf| |base| |fixedPoint| |linearAssociatedOrder| - |aromberg| |OMParseError?| |f07fdf| |elt| |ricDsolve| |dominantTerm| - |insertBottom!| |fortranLogical| |readUInt16!| |gcdcofact| - |unknownEndian| |linearPart| |cSin| |functionIsFracPolynomial?| - |diophantineSystem| |leftOne| EQ |internalLastSubResultant| |bytes| - |setvalue!| |flatten| |clearTheSymbolTable| |tanh2coth| |totolex| - 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|fractionFreeGauss!| |An| |cothIfCan| |isAnd| |infLex?| |iiacos| - |OMputSymbol| |polynomialZeros| |mantissa| |s19adf| |changeThreshhold| - |axesColorDefault| |superHeight| |epilogue| |complexSolve| |overlap| - |f04asf| |removeRedundantFactors| |bitTruth| |numeric| |iiacsc| - |ridHack1| |relativeApprox| |uniform| |extractSplittingLeaf| |say| - |polyred| |cot2tan| |completeEchelonBasis| |controlPanel| |radical| - |pole?| |toScale| |mix| |resultantEuclideannaif| |UpTriBddDenomInv| - |basicSet| |iroot| |oneDimensionalArray| |doubleRank| |quickSort| - |coord| |optimize| |bumptab| |setMinPoints3D| |csch2sinh| |dfRange| - |outputBinaryFile| |leftMult| |f07aef| |factorList| |e02def| |qroot| - |getMultiplicationTable| |trace2PowMod| |bivariatePolynomials| - |s13adf| |merge!| |seed| |regime| |complexElementary| |listBranches| - |quartic| |rootProduct| |ravel| |setVariableOrder| |safetyMargin| - |mapdiv| |resetAttributeButtons| |components| |parts| |primaryDecomp| - |corrPoly| |tensorProduct| |setLegalFortranSourceExtensions| - 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|pointColor| |unitNormal| |retractIfCan| |OMconnInDevice| |step| - |viewWriteDefault| |basisOfLeftNucleus| |permutationRepresentation| - |makeMulti| |leftFactor| |rCoord| |arbitrary| |minPoly| |redPo| - |leftQuotient| |degreeSubResultantEuclidean| |low| - |jvmClassConstantTag| |Hausdorff| |inverse| |bitCoef| |extendedint| - |exptMod| |f04faf| |taylorRep| |log10| |concat!| |HermiteIntegrate| - |rootOfIrreduciblePoly| |fortranLiteralLine| |completeHensel| - |addPointLast| |s17aff| |updatF| |tablePow| |presuper| |eulerPhi| - |cyclicCopy| |explicitEntries?| |bitand| |putProperties| |ocf2ocdf| - |totalfract| |OMputObject| |tower| |showIntensityFunctions| - |interpolate| |showSummary| |euclideanNormalForm| |OMgetInteger| - |atanhIfCan| |prologue| |purelyTranscendental?| - |wordInStrongGenerators| |bitior| |lieAlgebra?| |equality| |linGenPos| - |OMsend| |principalIdeal| |finite?| |legendre| |printingInfo?| - |realEigenvalues| |areEquivalent?| |perfectSquare?| |reducedForm| - |printInfo| |supRittWu?| |polygon| |beauzamyBound| |internalIntegrate| - 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|viewpoint| |setFieldInfo| |invertible?| |fortranCarriageReturn| - |physicalLength!| |doubleDisc| |unitCanonical| |tanNa| |commutative?| - |complexLimit| |semiSubResultantGcdEuclidean2| |listYoungTableaus| - |sin?| |autoReduced?| |gensym| |isOp| |curve?| |f02axf| - |selectPDERoutines| |key| |setleft!| |lfinfieldint| - |sumOfKthPowerDivisors| |f02adf| |d03faf| |bernoulli| |traverse| - |mpsode| |s18dcf| |jvmProtected| |var2StepsDefault| |OMopenString| - |subresultantSequence| |e02bef| |aCubic| |normal01| |interpretString| - |diagonal| |mindegTerm| |oddintegers| |setAttributeButtonStep| - |tubeRadius| |filename| |showTheIFTable| |lazyResidueClass| |iCompose| - |curryRight| |iisech| |clearDenominator| |SFunction| |FormatArabic| - |inconsistent?| |sinhIfCan| |nodeOf?| |rischNormalize| - |pmComplexintegrate| |padicFraction| |differentialVariables| - |exprHasLogarithmicWeights| |LiePoly| |digit| |isPower| |children| - |createIrreduciblePoly| |close!| |parse| |cAsin| |maximumExponent| - |degreeSubResultant| |printStatement| |df2st| |OMgetType| - 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|iitan| |genericLeftMinimalPolynomial| |port| |recur| |totalDegree| - |flexibleArray| |endSubProgram| |makeCrit| |rowEch| |OMgetString| - |universe| |maxrank| ** |bits| |elColumn2!| |numericIfCan| |mapUp!| - |superscript| |numericalOptimization| |select!| |unexpand| |rdHack1| - |leftDivide| |showScalarValues| |mathieu23| |fixPredicate| |cross| - |s17dgf| |imagi| |high| |f04qaf| |t| |elRow2!| |blankSeparate| - |firstSubsetGray| |show| |nor| |kind| |makeSketch| |ListOfTerms| - |iiacosh| |mainContent| |head| |distdfact| |gbasis| |any| |frst| - |setProperties| |adaptive?| |removeIrreducibleRedundantFactors| - |leftScalarTimes!| |generic?| |jvmIntegerConstantTag| |mainExpression| - |trace| |arrayStack| |s17dcf| |sinhcosh| |OMopenFile| |solve1| |sh| - |sequence| |lazyIntegrate| |functionIsContinuousAtEndPoints| - |bandedHessian| |queue| |showAll?| |compose| |jacobiIdentity?| |rk4qc| - |stFunc1| |OMputError| |nextLatticePermutation| |createZechTable| - |palgint0| |univariatePolynomialsGcds| |zeroOf| |leftGcd| |linSolve| - |mightHaveRoots| |evaluate| |matrix| |decompose| |varList| |bindings| - |pol| |enqueue!| |typeList| |clearTable!| |trapezoidalo| |simplifyLog| - |coefficient| |nonSingularModel| |checkPrecision| |spherical| - |getMeasure| |safeCeiling| |e02ddf| |predicate| |sizeLess?| - |numberOfComputedEntries| |minrank| |invertibleSet| |e02dcf| - |rewriteIdealWithHeadRemainder| |OMencodingBinary| |padicallyExpand| - |coleman| |deepCopy| |e02zaf| |rquo| |direction| |ord| - |stiffnessAndStabilityOfODEIF| |quoByVar| |outputArgs| |setPredicates| - |copyInto!| |binaryTree| |setAdaptive| |lineColorDefault| |setLength!| - |mapExponents| |insert!| |viewDefaults| |gcdprim| |lookup| |stirling1| - |OMputEndBVar| |xn| |s14aaf| |innerSolve| |hex| |reducedSystem| - |f04arf| |rightExtendedGcd| |denomLODE| |jvmNative| |decomposeFunc| - |totalLex| |quotientByP| |failed?| |limitedint| |generateIrredPoly| - |qqq| |patternVariable| |firstUncouplingMatrix| |presub| - |upDateBranches| |removeDuplicates| |nthCoef| |coercePreimagesImages| - |inspect| |cCsc| |reduceLODE| |weierstrass| |just| |fortranComplex| - |getCode| |sturmVariationsOf| |plusInfinity| |upperBound| |size?| - |f02aff| |algSplitSimple| |ScanRoman| RF2UTS |OMreadFile| |top!| - |domainTemplate| |cCot| |minusInfinity| |nextNormalPrimitivePoly| - |readInt16!| |internalSubQuasiComponent?| |acotIfCan| - |divideExponents| |returns| |chebyshevU| |exprToXXP| |hasHi| |plus| - |c06eaf| |setUnion| |singularAtInfinity?| |rightExactQuotient| - |OMbindTCP| |cfirst| |parameters| |upperCase!| |deriv| - |createMultiplicationMatrix| |tanIfCan| |initTable!| |jvmPrivate| - |linearAssociatedExp| |UP2ifCan| |atanIfCan| |mainCoefficients| - |integralBasis| |refine| |gramschmidt| |union| |d01alf| |unitVector| - |writeByte!| |rootSplit| |rightMinimalPolynomial| - |genericRightDiscriminant| |next| |OMgetError| |polyRDE| |variable| - |const| |OMputString| |endOfFile?| |length| |subCase?| |times| |dec| - |palglimint0| |jvmLongConstantTag| |rspace| |shuffle| |conical| - |iterators| |e01daf| |symmetricTensors| |region| |scripts| - 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|resultantEuclidean| |cAtanh| |viewPosDefault| |coth2tanh| - |squareFreePart| |mulmod| |airyAi| |chebyshevT| |randnum| |unravel| - |mainVariable| |f2st| |printInfo!| |logical?| |find| |constantLeft| - |nextColeman| |isTimes| |upperCase?| |primeFactor| |wholePart| - |binarySearchTree| |maxPoints| |solveRetract| |lp| |extractBottom!| - |dihedral| |useSingleFactorBound?| |palgextint0| |recolor| - |monicRightDivide| |pToDmp| |pushdown| |setDifference| |jvmInterface| - |arity| |coshIfCan| |retractable?| |arg1| |vspace| |signatureAst| - |clipBoolean| |extend| |drawComplexVectorField| |node| |permutation| - |deleteRoutine!| |diagonals| |multiset| |arg2| |getMatch| |revert| - |iiabs| |isImplies| |discriminantEuclidean| |putProperty| |countable?| - |sumOfDivisors| |Gamma| |inf| |jokerMode| |cLog| |setrest!| - |factorSFBRlcUnit| |lexGroebner| |hclf| |resultant| |rotatey| |module| - |conditions| |karatsuba| |alphanumeric| |every?| |structuralConstants| - |B1solve| |triangular?| |newSubProgram| |rowEchelonLocal| - |linearlyDependent?| |s18acf| |match| |anticoord| |consnewpol| |nil?| - |partialNumerators| |convergents| |integerIfCan| |minColIndex| - |trueEqual| |reducedQPowers| |jordanAdmissible?| |factor1| - |standardBasisOfCyclicSubmodule| |printCode| |drawComplex| |edf2efi| - |splitSquarefree| |subNodeOf?| |resetNew| |algintegrate| |plot| - |discreteLog| |extractProperty| |yCoordinates| |polarCoordinates| - |getProperty| |cCoth| |slex| |cAcsc| |ran| |univariatePolynomials| - |constantKernel| |fixedDivisor| |extendedIntegrate| |OMputAttr| - |critMTonD1| |xCoord| |power| |sort| |quatern| - |stripCommentsAndBlanks| |leastPower| |numberOfImproperPartitions| - |binomial| |trim| |lazyVariations| |transcendentalDecompose| - |goodnessOfFit| |bright| |iicosh| |s17acf| |cap| |asimpson| |forLoop| - |saturate| |appendPoint| |root?| |interReduce| |random| - |updateStatus!| |makeViewport2D| |closedCurve| |initials| - |pseudoRemainder| |numberOfVariables| |approximants| |completeSmith| - |mainKernel| |limit| |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| |lfextlimint| |medialSet| + |expextendedint| |f02axf| |factor1| |redmat| |constantToUnaryFunction| + |exponentialOrder| |safeCeiling| |useEisensteinCriterion?| + |systemSizeIF| |OMputInteger| |selectPDERoutines| |member?| + |standardBasisOfCyclicSubmodule| |complete| |mathieu12| |rename| + |operation| |e02ddf| |null| |uniform01| |cCosh| + |rewriteSetByReducingWithParticularGenerators| |setleft!| + |fullDisplay| |printCode| |aromberg| |equation| |subQuasiComponent?| + |selectNonFiniteRoutines| |lowerCase!| |sizeLess?| |not| |isOr| + |multiplyExponents| |lfinfieldint| |removeRedundantFactorsInContents| + |drawComplex| |f01brf| |OMParseError?| |goto| |cycleEntry| + |numberOfComputedEntries| |and| |basisOfLeftAnnihilator| |operations| + |factorFraction| |sumOfKthPowerDivisors| |antisymmetric?| |edf2efi| + |f07fdf| |squareFreePolynomial| |unprotectedRemoveRedundantFactors| + |minrank| |or| |df2fi| |collectUnder| |checkRur| |f02adf| + |splitSquarefree| |particularSolution| |integralMatrixAtInfinity| + |GospersMethod| |invertibleSet| |xor| |symmetricPower| |ptFunc| + |permutationGroup| |d03faf| |cos2sec| |subNodeOf?| + |semiResultantEuclideannaif| |tryFunctionalDecomposition?| |inR?| + |e02dcf| |case| |subst| |nthExponent| |chainSubResultants| + |principal?| |bernoulli| |resetNew| |primPartElseUnitCanonical| + |cycleElt| |zeroSetSplit| |rewriteIdealWithHeadRemainder| |Zero| + |value| |SturmHabichtCoefficients| |traverse| |algintegrate| + |coefChoose| |OMputEndApp| |lambert| |OMencodingBinary| |One| + |quickSort| |univariate?| |exponential1| |mpsode| |plot| + |irreducible?| |categories| |nextNormalPoly| |commaSeparate| + |padicallyExpand| |coord| |radicalSolve| |optional?| |s18dcf| + |var1StepsDefault| |discreteLog| |mathieu24| |univariateSolve| + |polyRicDE| |more?| |coleman| |factors| |doubleComplex?| |bumptab| + |nextIrreduciblePoly| |jvmProtected| |objects| |extractProperty| + |s14abf| |deepCopy| |c06gsf| |conjugates| |setMinPoints3D| |copies| + |var2StepsDefault| |base| |yCoordinates| |logIfCan| |associator| + |OMputEndBind| |e02zaf| |inRadical?| |csch2sinh| |reopen!| + |OMopenString| |polarCoordinates| |upperCase| |leftDiscriminant| + |exprToUPS| |rquo| |elt| |dfRange| |scalarTypeOf| |f04atf| + |subresultantSequence| |getProperty| |quasiMonic?| |tanintegrate| + |meshPar2Var| |direction| |outputBinaryFile| |headReduce| |cCoth| EQ + |e04gcf| |setvalue!| |denomRicDE| |green| |ord| |leftMult| + |OMgetEndError| |shallowExpand| |OMclose| |slex| |optpair| |yCoord| + |recoverAfterFail| |stiffnessAndStabilityOfODEIF| |f07aef| |over| + |jvmTransient| |prepareSubResAlgo| |cAcsc| |droot| + |toseLastSubResultant| |truncate| |quoByVar| |iipow| |factorList| + |leftUnits| |whitePoint| |ran| |degree| |split!| |evenlambert| + |outputGeneral| |e02def| |computePowers| + |solveLinearPolynomialEquation| |univariatePolynomials| |light| + |OMputApp| |getGraph| |zeroDim?| |OMgetEndBVar| |qroot| |sncndn| + |OMserve| |irDef| |constantKernel| |pushuconst| |clearTheSymbolTable| + |implies| |apply| |nullity| |typeForm| |getMultiplicationTable| + |getExplanations| |rightFactorCandidate| |points| |fixedDivisor| + |multMonom| |partitions| |toseInvertibleSet| |first| + |prepareDecompose| |trace2PowMod| |determinant| |zeroVector| + |idealiserMatrix| |increasePrecision| |cExp| |OMputBVar| |rest| |red| + |directory| |resultantReduit| |bivariatePolynomials| + |inverseIntegralMatrixAtInfinity| |poisson| |multiEuclideanTree| + |previous| |null?| |coerceImages| |printStats!| |inrootof| |s13adf| + |badValues| |modularGcd| |OMgetVariable| |makeop| + |numberOfPrimitivePoly| |bfKeys| |univariatePolynomial| |setprevious!| + |eq?| |dAndcExp| |merge!| |integerBound| |predicates| + |generalTwoFactor| |mainPrimitivePart| |approxSqrt| |rur| + |duplicates?| F |block| |seed| |exponential| |solveLinear| + |algebraic?| |s21bcf| |tanh2coth| |listRepresentation| |iicsc| + |leftRecip| |repeating?| |And| |leviCivitaSymbol| |symbolIfCan| + |lyndon?| |regime| |search| |semiResultantReduitEuclidean| |jvmPublic| + |totolex| |OMReadError?| |figureUnits| |inGroundField?| |elliptic| + |Or| |bernoulliB| |complexElementary| |rightTraceMatrix| |sts2stst| + |nsqfree| |resultantEuclidean| |OMmakeConn| |cyclicEqual?| + |conjunction| |secIfCan| |iitan| |Not| |listBranches| |lllip| |max| + |RemainderList| |readUInt8!| |cAtanh| |tanQ| |leadingBasisTerm| + |fortranLinkerArgs| |genericLeftMinimalPolynomial| |quartic| + |realSolve| |symmetricSquare| |string?| |lintgcd| |viewPosDefault| + |headAst| |pointColorPalette| |normalDeriv| |sechIfCan| |recur| + |rootProduct| |brillhartIrreducible?| |c05nbf| |mesh?| |coth2tanh| + |delay| |makeYoungTableau| LODO2FUN |totalDegree| |f01qcf| + |setVariableOrder| |numberOfMonomials| |rdregime| |squareFreePart| + |critM| |bigEndian| |multiEuclidean| |flexibleArray| |bringDown| + |safetyMargin| |setCondition!| |removeSquaresIfCan| |startStats!| + |mulmod| |diagonalMatrix| |enumerate| |birth| |endSubProgram| |digit?| + |next| |collectUpper| |mapdiv| |contractSolve| |loopPoints| |airyAi| + |nonLinearPart| |parametric?| |qualifier| |makeCrit| + |resetAttributeButtons| |denominators| |subresultantVector| + |viewport3D| |pointSizeDefault| |chebyshevT| |PDESolve| |rootPoly| + |abs| |rowEch| |doubleResultant| |components| |complexEigenvectors| + |abelianGroup| |randnum| |goodPoint| |constantCoefficientRicDE| + |polCase| |outputList| |fortranLogical| |OMgetString| |primaryDecomp| + |ratpart| |dictionary| |monomRDE| |unravel| |stFunc2| |argumentListOf| + |maxIndex| |changeVar| |universe| |readUInt16!| |corrPoly| + |numberOfFractionalTerms| |primitivePart!| |sum| |solveLinearlyOverQ| + |mainVariable| |comment| |bit?| |graphState| |f07adf| |moduloP| + |gcdcofact| |maxrank| |ODESolve| |tensorProduct| + |eisensteinIrreducible?| |firstNumer| |f2st| |addMatch| |realRoots| + |readLineIfCan!| |bits| |setLegalFortranSourceExtensions| |tanSum| + |d02gbf| |compound?| |printInfo!| |stronglyReduced?| |squareTop| + |compiledFunction| |elColumn2!| |divisors| |roughSubIdeal?| |e04naf| + |bounds| |logical?| |assert| |bottom!| |innerSolve1| |rk4| + |numericIfCan| |top| |ratPoly| |reduceByQuasiMonic| |gethi| + |factorOfDegree| |find| |randomLC| F2FG |remove!| |mapUp!| |continue| + |factorAndSplit| |rename!| |any?| |opeval| |constantLeft| |palgextint| + |jacobi| |exQuo| |superscript| |bombieriNorm| |internalSubPolSet?| + |nextPrimitiveNormalPoly| |orthonormalBasis| |nextColeman| + |rangeIsFinite| |encodingDirectory| |dihedralGroup| + |numericalOptimization| |debug| |setErrorBound| + |extendedSubResultantGcd| |acoshIfCan| |extractIndex| |isTimes| |comp| + |mapMatrixIfCan| |tableForDiscreteLogarithm| |lighting| |select!| + |condition| D |sylvesterMatrix| |tubeRadiusDefault| |checkForZero| + |swap| |upperCase?| |point?| |anfactor| |s17def| |unexpand| |sup| + |weighted| |e01saf| |OMgetAtp| |primeFactor| |stop| |setTopPredicate| + |setPoly| |besselK| |rdHack1| |removeSinSq| |nthFractionalTerm| + |lagrange| |coHeight| |log| |wholePart| |jvmSuper| + |cyclotomicDecomposition| |createPrimitiveElement| |leftDivide| + |capacity| |squareFreePrim| |mainVariables| |csc2sin| + |binarySearchTree| |unknownEndian| |closeComponent| |delete!| + |modularGcdPrimitive| |showScalarValues| |mapGen| + |rewriteIdealWithQuasiMonicGenerators| |createNormalPoly| + |modifyPointData| |maxPoints| |close| |linearPart| |RittWuCompare| + |vertConcat| |s17aef| |mathieu23| |showArrayValues| |laurentRep| + |gradient| |cycleLength| |solveRetract| |hypergeometric0F1| + |expandTrigProducts| |cSin| |Is| |fixPredicate| |subMatrix| + |factorPolynomial| |var1Steps| |floor| |extractBottom!| |display| + |macroExpand| |zCoord| |surface| |simplify| |cross| |writeUInt8!| + |prefixRagits| |ceiling| |buildSyntax| |dihedral| |ode| |specialTrigs| + |isEquiv| |s17dgf| |represents| |algebraicCoefficients?| + |numberOfComposites| |multiplyCoefficients| |useSingleFactorBound?| + |changeWeightLevel| |scopes| |nthRootIfCan| |imagi| |applyRules| + |print| |fglmIfCan| |title| |rightMult| |hasTopPredicate?| + |palgextint0| |exprHasWeightCosWXorSinWX| |dark| |returnTypeOf| |high| + |resolve| |linkToFortran| |imagk| |rootDirectory| |vectorise| + |recolor| |setlast!| |quasiComponent| |setOrder| |f04qaf| |lift| + |byteBuffer| |stoseSquareFreePart| |fortran| |integral| |expIfCan| + |monicRightDivide| |exprToGenUPS| |outputFloating| |LyndonBasis| + |elRow2!| |reduce| |e| |primes| |numberOfComponents| |ratDenom| + |LyndonWordsList| |pToDmp| |output| |antiCommutator| |vark| + |dimensionsOf| |blankSeparate| |elementary| |cschIfCan| |expPot| + |dimensions| |test| |pushdown| |padecf| |rationalPoint?| + |topPredicate| |firstSubsetGray| |restorePrecision| |OMreceive| + |dioSolve| |hasoln| |setDifference| |primitiveElement| |var2Steps| + |highCommonTerms| |nor| |compile| |readBytes!| |cAcosh| + |virtualDegree| |difference| |jvmInterface| |integralCoordinates| + |generalLambert| |makeSketch| |symmetricProduct| |quadraticForm| + |minPol| |pseudoDivide| |arity| |compBound| |physicalLength| + |acothIfCan| |ListOfTerms| |categoryFrame| |integralRepresents| + |besselI| |hue| |init| |coshIfCan| |message| |minus!| |edf2ef| + |factorsOfDegree| |iiacosh| |loadNativeModule| |pdf2ef| |clearCache| + |intPatternMatch| |stronglyReduce| |partition| |remove| |retractable?| + |cAcoth| |cdr| |groebner?| |taylorIfCan| |mainContent| + |fillPascalTriangle| |back| |vspace| |linearAssociatedLog| |rightNorm| + |underscore| |duplicates| |head| |formfeed| |rationalPoints| + |derivative| |prinshINFO| |last| |doublyTransitive?| |signatureAst| + |range| |createPrimitivePoly| |lifting1| |OMputEndObject| |distdfact| + |rightCharacteristicPolynomial| |f02ajf| |assoc| |primintfldpoly| + |empty| |clipBoolean| |unit?| |semiSubResultantGcdEuclidean1| + |diagonal?| |characteristicSerie| |gbasis| |genericRightTrace| + |f04jgf| |harmonic| |laurentIfCan| |extend| |OMsetEncoding| + |firstDenom| |frst| |modTree| |tracePowMod| |script| |shiftRoots| + |OMputVariable| |drawComplexVectorField| GF2FG |pushup| |contours| + |setProperties| |closed| |normInvertible?| |bandedJacobian| + |evaluateInverse| |permutation| |Aleph| |mkPrim| |semicolonSeparate| + |byte| |adaptive?| |changeNameToObjf| |getlo| |label| |binaryFunction| + |c06gqf| |deleteRoutine!| |iiatanh| + |removeRoughlyRedundantFactorsInPol| |irreducibleFactors| + |removeIrreducibleRedundantFactors| |patternMatchTimes| |acosIfCan| + |tex| |diagonals| |clearFortranOutputStack| |normDeriv2| |flatten| + |clearTheIFTable| |leftScalarTimes!| |shanksDiscLogAlgorithm| |s20acf| + |monomials| |minordet| |multiset| |sincos| |imaginary| |quote| + |generic?| BY |sayLength| |meshPar1Var| |sortConstraints| |pushdterm| + |getMatch| |formula| UTS2UP |generalizedEigenvectors| |removeZeroes| + |jvmIntegerConstantTag| |initial| |df2ef| |outputFixed| + |matrixDimensions| |e04ucf| |revert| |patternMatch| |convert| |ef2edf| + |alternative?| |functionIsFracPolynomial?| |readInt32!| |s19acf| + |reverseLex| |hasPredicate?| |iiabs| |realEigenvectors| |leftNorm| + |splitNodeOf!| |pascalTriangle| |diophantineSystem| |plenaryPower| + |shift| |OMgetBind| |callForm?| |partialFraction| |isImplies| |clip| + |elaboration| |sizePascalTriangle| |leaves| |leftOne| |safeFloor| + |int| |option| |s19aaf| |debug3D| |pointLists| |karatsubaDivide| + |discriminantEuclidean| |submod| |nrows| |genericLeftTrace| |is?| + |times!| |multinomial| |row| |cTanh| |coerceS| |yellow| |ncols| + |f07fef| |sinh2csch| |jvmSynchronized| |c06ecf| |sign| + |positiveRemainder| |viewSizeDefault| |s20adf| |numer| NOT |exprex| + |mainDefiningPolynomial| |rowEchelon| |BumInSepFFE| |ref| |neglist| + |raisePolynomial| |collectQuasiMonic| |genericLeftNorm| |makeprod| + |d01apf| |denom| |s17ajf| OR |createGenericMatrix| + |quasiMonicPolynomials| |mr| |outerProduct| |computeCycleLength| + |viewPhiDefault| |sumOfSquares| |latex| |mainMonomials| |simplifyExp| + SEGMENT |normalize| AND |directSum| |rroot| |asecIfCan| |status| + |getZechTable| |rightUnit| |extendedEuclidean| |s21bdf| |makeEq| + |monomial?| |mapCoef| |pi| |euclideanSize| |unit| |rational| + |monicCompleteDecompose| |iisec| |e02adf| |d02kef| |trapezoidal| + |linearElement| |infinity| |sn| |credPol| |lfextendedint| |f04axf| + |point| |reindex| |leftTrace| |elem?| |primPartElseUnitCanonical!| + |infRittWu?| |expintfldpoly| |leftRegularRepresentation| |rem| + |findCycle| UP2UTS |e02gaf| |bitLength| |fractionFreeGauss!| + |aspFilename| |rewriteSetWithReduction| |declare| |nlde| |quo| |ptree| + |gcdPrimitive| |plotPolar| |genericLeftTraceForm| |content| |nthExpon| + |An| |roughUnitIdeal?| |graphCurves| |putGraph| |kernel| + |idealSimplify| |ldf2vmf| |cCos| |sqfree| |hostByteOrder| |series| + |rightPower| |cothIfCan| |stoseInternalLastSubResultant| + |ScanFloatIgnoreSpacesIfCan| |mesh| |smith| |list| |associates?| + |f02aef| |div| |graeffe| |normalizeAtInfinity| |heapSort| + |swapColumns!| |isAnd| |escape| |transcendent?| |draw| |showRegion| + |mainMonomial| |exquo| |expint| |badNum| |symmetricRemainder| + |currentEnv| |atrapezoidal| |infLex?| |scanOneDimSubspaces| + |findBinding| |extractClosed| |fortranDoubleComplex| ~= |llprop| + |complexNormalize| |swap!| |iiacos| |OMputAtp| |clearTheFTable| |mvar| + |reduction| |moebiusMu| * |Si| |#| |min| |cyclePartition| + |associatedSystem| |OMputSymbol| |selectODEIVPRoutines| + |explimitedint| |f04adf| |create| |infieldIntegrate| ~ |argscript| + |notelem| |leftExtendedGcd| |OMlistCDs| |properties| |makeObject| + |polynomialZeros| |lastSubResultantElseSplit| |primintegrate| + |singRicDE| |function| |atoms| |tubePoints| |mindeg| |lazyEvaluate| + |horizConcat| |jordanAlgebra?| |translate| |s19adf| |OMUnknownSymbol?| + |setEmpty!| |getOrder| |tab| |coef| |verticalTab| |stirling2| |c06fuf| + = |entry?| |OMreadStr| |eof?| |generator| |changeThreshhold| + |clipSurface| |OMsupportsSymbol?| |bivariateSLPEBR| |rightGcd| + |groebnerFactorize| |critT| |/\\| |OMencodingSGML| |contains?| + |jvmFieldrefConstantTag| |roughBasicSet| |substring?| + |inputBinaryFile| |axesColorDefault| |setImagSteps| |rombergo| + |baseRDE| |\\/| |OMputEndAttr| < |tValues| |closedCurve?| |stFuncN| + |createPrimitiveNormalPoly| |s14baf| |superHeight| |normalDenom| + |wordsForStrongGenerators| |norm| |numberOfIrreduciblePoly| > |s17agf| + |cycle| |belong?| |suffix?| |constantOperator| |epilogue| |c02aff| + |constDsolve| |jvmAbstract| |rightRegularRepresentation| <= + |primitivePart| |graphs| |choosemon| |complexSolve| |box| |coerce| + |cosIfCan| |littleEndian| |unitNormalize| |erf| |leftPower| + |perfectNthRoot| |cons| >= |aQuadratic| |integers| |diff| |overlap| + |prefix?| |fill!| |construct| |rightDiscriminant| |palgRDE0| + |nonQsign| |matrixConcat3D| |true| |hdmpToDmp| |drawCurves| + |branchIfCan| |f04asf| |mapSolve| |dmp2rfi| |fortranTypeOf| + |mkIntegral| |kernels| |minset| |argument| |elements| |rightDivide| + |createNormalElement| |removeRedundantFactors| |increase| |ideal| + |insertTop!| |dilog| |lifting| |positive?| + |getPickedPoints| + |operator| |rootKerSimp| |lowerCase?| |bitTruth| |OMread| |redpps| + |exists?| |sin| |linearDependence| |internalDecompose| - |rst| + |univariate| |critMonD1| |incr| |basisOfRightAnnihilator| |iiacsc| + |lazyGintegrate| |clipWithRanges| |lcm| |f02abf| |cos| |identity| + |source| / |minIndex| |whatInfinity| |randomR| |hi| |quoted?| + |ridHack1| |alphabetic?| |perfectSqrt| |lepol| |tan| |cyclicGroup| + |call| |withPredicates| |entries| |rules| |ffactor| |infix?| + |relativeApprox| |trunc| |append| |f02agf| |rubiksGroup| |cot| + |algDsolve| |viewZoomDefault| |OMconnectTCP| |factor| |printHeader| + |eigenvector| |mask| |expintegrate| |uniform| |exp1| |gcd| + |enterInCache| |sec| |rootPower| |set| |halfExtendedResultant2| + |target| |equiv| |sqrt| |OMputFloat| |iiasec| |extractSplittingLeaf| + |preprocess| |false| |nextSublist| |changeBase| |csc| |midpoint| + |indiceSubResultant| |numberOfChildren| |real| |viewDeltaXDefault| + |sumSquares| |backOldPos| |polyred| |eq| |rightRemainder| |asin| + |removeZero| |parabolicCylindrical| |postfix| |noKaratsuba| |imag| + |replace| |iter| |cot2tan| |linearlyDependentOverZ?| + |removeRoughlyRedundantFactorsInPols| |factorSquareFree| |acos| + |cyclicEntries| |directProduct| |pointColorDefault| + |numberOfNormalPoly| |s18def| |iisqrt2| |tree| |completeEchelonBasis| + |bumptab1| |newTypeLists| |squareFree| |decimal| |atan| |expt| + |numerator| |algebraicDecompose| |normalizedDivide| |hyperelliptic| + |controlPanel| |Nul| |lexTriangular| |tryFunctionalDecomposition| + |acot| |weights| |zeroDimPrime?| |LowTriBddDenomInv| |brace| + |multisect| |pole?| |countRealRootsMultiple| |s15aef| |OMencodingXML| + |distFact| |asec| |d01bbf| |e02ahf| |colorDef| |destruct| |depth| + |parents| |leftMinimalPolynomial| |toScale| |setelt| |coordinate| + |tube| |makeViewport3D| |froot| |acsc| |leftRank| |bezoutResultant| + 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|functorData| |curryLeft| |asinh| |qsetelt| + |unaryFunction| |f01qef| |width| |e02baf| |filterUntil| |iisinh| + |csubst| |acosh| |constant?| |xRange| |frobenius| |LazardQuotient| + |commutator| |select| |hasSolution?| |continuedFraction| |flagFactor| + |nthRoot| |d01fcf| |atanh| |yRange| |table| |aLinear| + |unitsColorDefault| |calcRanges| |createLowComplexityTable| + |quotedOperators| |hexDigit| |heap| |removeCosSq| |toseInvertible?| + |acoth| |zRange| |new| |element?| |match?| |getStream| |taylor| + |mapUnivariate| |iidprod| |SturmHabichtMultiple| |readable?| |d02raf| + |janko2| |failed| |asech| |map!| |laurent| |doubleFloatFormat| + |divideIfCan!| |create3Space| |startPolynomial| |setelt!| |supersub| + |qsetelt!| |dflist| |dimension| |puiseux| |generic| |stack| |divide| + |conjugate| |lSpaceBasis| |iExquo| |f01ref| |solid?| |multiple| + |delta| |trailingCoefficient| |c06fqf| |partialQuotients| |whileLoop| + |coordinates| |subtractIfCan| |rootBound| |setScreenResolution| + |applyQuote| |f04maf| |systemCommand| |iterationVar| |open?| |inv| + |optional| |makeRecord| |fractRagits| |schwerpunkt| |error| |getCurve| + |selectsecond| |blue| |socf2socdf| |symFunc| |ground?| + |euclideanGroebner| |e04dgf| |transcendenceDegree| + |expenseOfEvaluationIF| |degreeSubResultantEuclidean| |logGamma| + |normal| |modularFactor| |pushNewContour| |ground| |hspace| + |separateFactors| |overset?| |iiacsch| |low| |simpson| |ruleset| + |acsch| |lazyIrreducibleFactors| |cycleSplit!| |leadingMonomial| + |factorials| |iiacot| |setsubMatrix!| |jvmClassConstantTag| |psolve| + |f01qdf| |repeatUntilLoop| |toseSquareFreePart| |leadingCoefficient| + |mapUnivariateIfCan| |ratDsolve| |ldf2lst| |Hausdorff| |normalized?| + |iiperm| |left| |leadingIndex| |semiResultantEuclidean1| |invmod| + |primitiveMonomials| |vedf2vef| |move| |minimalPolynomial| |inverse| + |arguments| |nthFlag| |suchThat| |tan2trig| |lambda| |right| + |dimensionOfIrreducibleRepresentation| |s17ahf| |reductum| + |screenResolution| |fortranLiteral| |prindINFO| |bitCoef| |Frobenius| + |extendedResultant| |explogs2trigs| |alternatingGroup| |numFunEvals3D| + |nodes| |double| |pow| |complexNumericIfCan| |divisorCascade| + |extendedint| |minimumDegree| |lazyPseudoDivide| |unvectorise| + |intensity| |nullary?| |satisfy?| |eval| |exptMod| |univcase| + |readInt16!| |semiDegreeSubResultantEuclidean| |df2mf| + |leftReducedSystem| |numFunEvals| |extendIfCan| |tail| |readUInt32!| + |groebgen| |f04faf| |twoFactor| |primlimintfrac| + |internalSubQuasiComponent?| |shrinkable| |indices| |property| + |addPoint2| |mainForm| |round| |insertionSort!| |taylorRep| + |acotIfCan| |integralBasisAtInfinity| |FormatRoman| + |leftExactQuotient| |rightZero| |OMconnOutDevice| |genericPosition| + |returnType!| |cAsech| |concat!| |linear| |divideExponents| |sub| + |signAround| |internalInfRittWu?| |f01bsf| |lex| |e04mbf| |s19abf| + |HermiteIntegrate| |key?| |cn| |returns| |newline| |iiasinh| + |inverseIntegralMatrix| |triangulate| |wrregime| |OMputEndError| + |incrementKthElement| |principalAncestors| |rootOfIrreduciblePoly| + |chebyshevU| |polynomial| |infinityNorm| |limitPlus| |position!| + |integer?| |declare!| |hitherPlane| |setright!| |stoseInvertibleSet| + |fortranLiteralLine| |showTheSymbolTable| |exprToXXP| |ignore?| + |makeTerm| |getBadValues| |exportedOperators| |genericRightTraceForm| + |roughEqualIdeals?| |userOrdered?| |completeHensel| |positiveSolve| + |hasHi| |s01eaf| |radicalEigenvector| |subscript| |charClass| + |leftRemainder| |leadingTerm| |parent| |rootSimp| |addPointLast| + |c06eaf| |getIdentifier| |symbol| |leftRankPolynomial| |conditionP| + |linefeed| |members| |external?| |entry| |li| |youngGroup| |signature| + |s17aff| |initiallyReduce| |setUnion| |infinite?| |expression| + |createMultiplicationTable| |groebSolve| + |noncommutativeJordanAlgebra?| |infieldint| |bivariate?| + |deepestInitial| |updatF| |SturmHabichtSequence| |singularAtInfinity?| + |interactiveEnv| |nil| |integer| |hcrf| |augment| |rotatez| + |outputMeasure| |void| |viewport2D| |npcoef| |car| |tablePow| |e04ycf| + |rightExactQuotient| |f02xef| |nthr| |coth2trigh| |read!| |lexico| + |Vectorise| |bracket| |viewDeltaYDefault| |ranges| |presuper| + |OMbindTCP| |factorial| |iiatan| |ramifiedAtInfinity?| |insert| + |currentSubProgram| |segment| |scale| |measure| |euler| + |definingEquations| |stoseInvertibleSetreg| |eulerPhi| |constantRight| + |cfirst| |normalizeIfCan| |approximate| |ddFact| |rotate!| + |basisOfNucleus| |decreasePrecision| |elaborate| |skewSFunction| + |possiblyNewVariety?| |cyclicCopy| |characteristicSet| |upperCase!| + |dom| |complex| |matrixGcd| |complementaryBasis| |permutations| + |critpOrder| |reverse!| |factorByRecursion| |reverse| |distance| + |localIntegralBasis| |explicitEntries?| |radicalEigenvalues| |deriv| + |obj| |stoseInvertible?sqfreg| |selectMultiDimensionalRoutines| + |magnitude| |palglimint| |setMinPoints| |fortranCompilerName| + |makeSUP| |putProperties| |split| |createMultiplicationMatrix| + |finiteBasis| |symmetricDifference| |f01rcf| |extractPoint| |inc| + |moebius| |product| |knownInfBasis| |unrankImproperPartitions1| + |ocf2ocdf| |zeroSquareMatrix| |tanIfCan| |clipPointsDefault| |op| + |dual| |selectPolynomials| |solveid| |color| |localReal?| |kovacic| + |selectIntegrationRoutines| |binary| |totalfract| |initTable!| + |writable?| |e01sbf| |startTable!| |leftUnit| |singleFactorBound| + |fintegrate| |bfEntry| |stiffnessAndStabilityFactor| |OMputObject| + |nextItem| |jvmPrivate| |jvmNameAndTypeConstantTag| |setProperty| + |ReduceOrder| |OMwrite| |maxPoints3D| |OMgetEndBind| |expandPower| + |showIntensityFunctions| |triangSolve| |linearAssociatedExp| |e01bef| + |setStatus| |chiSquare| |someBasis| |slash| |elliptic?| |cond| + |normalise| |exprHasAlgebraicWeight| |interpolate| |UP2ifCan| + |numeric| |log2| |mainValue| |meatAxe| |lyndonIfCan| |allRootsOf| + |mkcomm| |chiSquare1| |euclideanNormalForm| |ParCondList| |radical| + |atanIfCan| |removeConstantTerm| |colorFunction| |rotate| + |fixedPoints| |mainSquareFreePart| |say| |pmintegrate| |d03eef| + |OMgetInteger| |denominator| |mainCoefficients| |hconcat| |qinterval| + |irVar| |binomThmExpt| |d03edf| |connectTo| |torsion?| |atanhIfCan| + |midpoints| |integralBasis| |optimize| |cTan| |functionIsOscillatory| + |pureLex| |tanhIfCan| |cubic| |lazy?| |maxrow| |intersect| |prologue| + |refine| |subResultantsChain| |s17dhf| |mdeg| |insertMatch| + |currentCategoryFrame| |parts| |separant| |simpleBounds?| + |removeRedundantFactorsInPols| |purelyTranscendental?| |subspace| + |gramschmidt| |traceMatrix| |disjunction| |alphanumeric?| + |leftFactorIfCan| |rightFactorIfCan| |LiePolyIfCan| + |removeDuplicates!| |rarrow| |pair?| |branchPoint?| + |wordInStrongGenerators| |d01alf| |relerror| |freeOf?| + |oblateSpheroidal| |thetaCoord| |variable?| |integrate| |cartesian| + |symbolTable| |changeMeasure| |removeCoshSq| |lieAlgebra?| |e02bbf| + |unitVector| |radPoly| |ravel| |stosePrepareSubResAlgo| |polar| + |jvmMethodrefConstantTag| |environment| |e01sef| |rightOne| + |indicialEquationAtInfinity| |equality| |setValue!| |writeByte!| + |listConjugateBases| |intcompBasis| |reshape| |headRemainder| |f02bjf| + |trigs| |pushFortranOutputStack| |lowerPolynomial| |se2rfi| + |idealiser| |linGenPos| |rootSplit| |stoseIntegralLastSubResultant| + |integral?| |cAcos| |rangePascalTriangle| |mathieu22| + |popFortranOutputStack| |comparison| |seriesToOutputForm| |OMsend| + |readLine!| |rightMinimalPolynomial| |dequeue| |d01gaf| |cycles| + |host| |digamma| |numberOfDivisors| |outputAsFortran| |lazyPrem| + |diagonalProduct| |internalLastSubResultant| |principalIdeal| + |genericRightDiscriminant| |cAcsch| |relationsIdeal| |cscIfCan| + |double?| |generators| |createLowComplexityNormalBasis| |bytes| |zoom| + |d01asf| |finite?| |OMgetError| |nullary| |e02aef| |hash| + |rationalFunction| |lastSubResultantEuclidean| |radicalRoots| |nary?| + |fractionPart| |legendre| |divideIfCan| |polyRDE| |qfactor| |count| + |qPot| |gderiv| |scaleRoots| |substitute| |rationalPower| |cycleTail| + |printingInfo?| |removeSinhSq| |const| |selectfirst| |dn| + |leadingExponent| |middle| |karatsubaOnce| |minGbasis| |s17adf| + |varselect| |realEigenvalues| |category| |OMputString| |graphImage| + |critBonD| |polygamma| |multiple?| |float?| |geometric| |aQuartic| + |semiDiscriminantEuclidean| |areEquivalent?| |domain| |endOfFile?| + |cSec| |cup| |cAcot| |zeroDimPrimary?| |KrullNumber| |e02ajf| + |henselFact| |perfectSquare?| |diag| |package| |subCase?| |position| + |rischDE| |part?| |wreath| |imagE| |OMencodingUnknown| + |supDimElseRittWu?| |reducedForm| |c05adf| |palglimint0| |cyclic| + |shade| |intChoose| |isList| |cAsinh| |odd?| |supRittWu?| + |invmultisect| |char| |jvmLongConstantTag| |simpsono| |square?| + |carriageReturn| |iicot| |datalist| |f01rdf| |mapmult| + |jvmFloatConstantTag| |polygon| |rspace| |s21baf| |cosh2sech| + |getOperator| |setTex!| |vector| |beauzamyBound| + |selectOptimizationRoutines| |shuffle| |rightUnits| |increment| + |reflect| |integralDerivationMatrix| |nextSubsetGray| |differentiate| + |monicModulo| |antiAssociative?| |internalIntegrate| |conical| + |selectSumOfSquaresRoutines| |maxdeg| |cyclotomicFactorization| + |lookupFunction| |iisin| |generalizedEigenvector| |copy!| + |fixedPointExquo| |e01daf| |float| |extension| |c06gcf| |rightRank| + |addmod| |representationType| |mergeFactors| |complexRoots| + |removeRoughlyRedundantFactorsInContents| |symmetricTensors| |s17dlf| + |eyeDistance| |makeGraphImage| |crest| |leadingSupport| + |OMunhandledSymbol| |region| |linear?| |composite| |ipow| |one?| + |sdf2lst| |ode1| |degreePartition| |coerceListOfPairs| + |basisOfCommutingElements| |getRef| |jvmFinal| |prime| |listOfLists| + |nextsousResultant2| |linearDependenceOverZ| |LyndonCoordinates| + |getButtonValue| |palgint| |jvmInterfaceMethodConstantTag| |groebner| + |getSyntaxFormsFromFile| |d01ajf| |countRealRoots| + |associatedEquations| |subscriptedVariables| |terms| |dim| + |viewWriteAvailable| |e04fdf| |iitanh| |romberg| |characteristic| + |scan| |rationalApproximation| |redPol| |vconcat| |voidMode| + |commutativeEquality| |iidsum| |isNot| |paren| |dot| |build| |pack!| + |radicalOfLeftTraceForm| |sparsityIF| |options| |elaborateFile| + |tubePointsDefault| |headReduced?| |balancedFactorisation| + |noLinearFactor?| |constructor| |maxint| |factorSquareFreePolynomial| + |indiceSubResultantEuclidean| |certainlySubVariety?| + |selectFiniteRoutines| |nextPrimitivePoly| |createRandomElement| + |hdmpToP| GE |jvmDoubleConstantTag| |kroneckerDelta| |showClipRegion| + |setRow!| |fullPartialFraction| |d02bbf| |string| |complex?| + |explicitlyFinite?| |setnext!| GT |LazardQuotient2| |character?| + |addPoint| |e02bef| |tRange| |leftAlternative?| |polyPart| |d01akf| + |e02bcf| |argumentList!| |retract| |OMlistSymbols| LE |reseed| + |cylindrical| |jvmStringConstantTag| |findConstructor| |aCubic| + |eigenvectors| |dequeue!| |radix| |OMgetAttr| |resize| + |invertibleElseSplit?| LT |bezoutMatrix| |jvmStatic| + |addMatchRestricted| |cache| |minPoints| |normal01| + |associatorDependence| |maxRowIndex| |semiResultantEuclidean2| + |tan2cot| |exactQuotient| |identityMatrix| |typeLists| |fortranDouble| + |interpretString| |limitedIntegrate| |quasiAlgebraicSet| + |iteratedInitials| |tab1| |delete| |outputArgs| |ScanArabic| + |cyclicParents| |digits| |constant| |lazyPquo| |diagonal| |setref| + |cPower| |push!| |iicos| |showTheRoutinesTable| |setPredicates| + |ricDsolve| |lazyPremWithDefault| |setLabelValue| |pquo| + |monicDecomposeIfCan| |mindegTerm| |completeHermite| |horizontalTab| + |monomialIntegrate| |moduleSum| |removeSuperfluousCases| |copyInto!| + |dominantTerm| |shiftRight| |biRank| |hermiteH| |numberOfHues| + |oddintegers| |rightAlternative?| |interval| |LyndonWordsList1| + |stoseInvertibleSetsqfreg| |binaryTree| |insertBottom!| |e02dff| + |getGoodPrime| |laguerre| |setAttributeButtonStep| + |complexEigenvalues| |extendedIntegrate| |swapRows!| |crushedSet| + |factorGroebnerBasis| |deepestTail| |setAdaptive| |subNode?| |space| + |rightLcm| |tubeRadius| |probablyZeroDim?| |OMputAttr| |laplacian| + |solve| |bag| |cyclic?| |lineColorDefault| |expenseOfEvaluation| + |LagrangeInterpolation| |negative?| |showTheIFTable| |outputAsScript| + |critMTonD1| |basisOfRightNucloid| |mappingMode| |e01bff| |less?| + |pile| |bsolve| |setLength!| |flexible?| |option?| |makeCos| + |mergeDifference| |lazyResidueClass| |xCoord| + |combineFeatureCompatibility| |weight| |sqfrFactor| + |antisymmetricTensors| |acscIfCan| |airyBi| |mapExponents| |second| + |integralMatrix| |dualSignature| |powern| |iCompose| |f02awf| |power| + |leftTraceMatrix| |stopMusserTrials| |sPol| |makeSeries| |c06frf| + |asechIfCan| |insert!| |third| |fractRadix| |innerint| |real?| + |curryRight| |OMgetEndObject| |quatern| |genericLeftDiscriminant| + |solveLinearPolynomialEquationByFractions| |c05pbf| |isExpt| + |extensionDegree| |viewDefaults| |setClipValue| |fibonacci| + |mappingAst| |id| |retractIfCan| |iisech| + |semiLastSubResultantEuclidean| |stripCommentsAndBlanks| |testDim| + |cAtan| |palgLODE| |OMsupportsCD?| |gcdprim| |prinb| |assign| + |mainCharacterization| |lo| |validExponential| |clearDenominator| + |leastPower| |cRationalPower| |transpose| |sech2cosh| |hermite| + |rootOf| |lookup| |setRealSteps| |rational?| |step| |coefficients| + |SFunction| |iiGamma| |numberOfImproperPartitions| |write!| |map| + |readInt8!| |fixedPoint| |selectOrPolynomials| |check| |stirling1| + |tower| |modifyPoint| |groebnerIdeal| |cSinh| + |squareFreeLexTriangular| |FormatArabic| |binomial| |tubePlot| + |linearAssociatedOrder| |mirror| |remainder| |subResultantGcd| |log10| + |OMputEndBVar| |eigenvalues| |curveColorPalette| |setEpilogue!| + |power!| |inconsistent?| |trim| |divisor| |quasiRegular| |shellSort| + |generalInfiniteProduct| |xn| |bitand| |printInfo| |fmecg| |zerosOf| + |categoryMode| |fortranCharacter| |sinhIfCan| |lazyVariations| + |showSummary| |balancedBinaryTree| |constantOpIfCan| |squareMatrix| + |shape| |s14aaf| |bitior| |c02agf| |OMgetApp| |Beta| + |intermediateResultsIF| |nodeOf?| |transcendentalDecompose| + |primextintfrac| |pseudoQuotient| |push| |subResultantGcdEuclidean| + |innerSolve| |reset| |powerAssociative?| |iprint| |usingTable?| + |rischNormalize| |po| |goodnessOfFit| |showAttributes| |changeName| + |f04mbf| |rightRecip| |makingStats?| |hex| |update| |adaptive3D?| + |derivationCoordinates| |monic?| |computeCycleEntry| + |pmComplexintegrate| |iicosh| |in?| |hostPlatform| + |useSingleFactorBound| |tanh2trigh| |reducedSystem| |write| + |basisOfCenter| |linears| |irForm| |complexNumeric| |padicFraction| + |splitDenominator| |s17acf| |numberOfFactors| |monomRDEsys| + |numericalIntegration| |charthRoot| |f04arf| |save| |iilog| |e02bdf| + |bumprow| |differentialVariables| |f2df| |cap| |makeFR| |prevPrime| + |iiacoth| |setAdaptive3D| |rightExtendedGcd| + |halfExtendedSubResultantGcd2| |semiIndiceSubResultantEuclidean| + |isAbsolutelyIrreducible?| |resetVariableOrder| + |exprHasLogarithmicWeights| |overlabel| |asimpson| |normalElement| + |ksec| |setFormula!| |subSet| |denomLODE| |composites| |outlineRender| + |identification| |leaf?| |LiePoly| |factorset| |forLoop| |kmax| + |initiallyReduced?| |sort!| |leastMonomial| |jvmNative| |mantissa| + |genericRightNorm| |d02cjf| |index?| |c06gbf| |digit| |shallowCopy| + |saturate| |parabolic| |tanAn| |pleskenSplit| |rightRankPolynomial| + |decomposeFunc| |mainVariable?| |stoseInvertible?reg| |parametersOf| + |elRow1!| |isPower| |appendPoint| |getMultiplicationMatrix| |adaptive| + |internalIntegrate0| |symbol?| |totalLex| |definingPolynomial| + |lfintegrate| |recip| |s18aff| |children| |root?| |unparse| + |zeroMatrix| |fortranInteger| |bubbleSort!| |quotientByP| + |triangularSystems| |untab| |unmakeSUP| |createIrreduciblePoly| + |imports| |interReduce| |reciprocalPolynomial| |UnVectorise| + |readByte!| |moreAlgebraic?| |failed?| |connect| |splitConstant| + |quasiRegular?| |close!| |exactQuotient!| |updateStatus!| |compdegd| + |sylvesterSequence| |makeUnit| |setfirst!| |limitedint| |e01bhf| + |d02gaf| |boundOfCauchy| |conditionsForIdempotents| |cAsin| + |makeViewport2D| |inputOutputBinaryFile| |getVariableOrder| |palgRDE| + |characteristicPolynomial| |generateIrredPoly| |partialDenominators| + |primeFrobenius| |Ci| |oddInfiniteProduct| |maximumExponent| Y + |closedCurve| |extract!| |scalarMatrix| |localAbs| |imagj| |qqq| + |bipolarCylindrical| |singularitiesOf| |rk4f| + |factorsOfCyclicGroupSize| |degreeSubResultant| |initials| + |iflist2Result| |algint| |complexExpand| |besselY| |patternVariable| + |accuracyIF| |nthFactor| |normalizedAssociate| |printStatement| + |mapBivariate| |pseudoRemainder| |musserTrials| |generalizedInverse| + |key| |identitySquareMatrix| |btwFact| |firstUncouplingMatrix| + |OMcloseConn| |newReduc| |s17akf| |df2st| |tableau| + |numberOfVariables| |rootNormalize| |radicalEigenvectors| + |useEisensteinCriterion| |e01bgf| |presub| |totalDifferential| + |collect| |oddlambert| |f01maf| |OMgetType| |approximants| |coerceP| + |filename| |makeResult| |s13acf| |column| |upDateBranches| + |inverseLaplace| |basisOfRightNucleus| |HenselLift| |linearForm| + |selectAndPolynomials| |completeSmith| |iiasin| |hMonic| + |constantIfCan| |symbolTableOf| |keys| |removeDuplicates| |conjug| + |ramified?| |empty?| |acschIfCan| |nativeModuleExtension| |mainKernel| + |parse| |purelyAlgebraicLeadingMonomial?| |expandLog| |rightTrace| + |indicialEquation| |nthCoef| |backspace| |htrigs| |curve| |lquo| + |finiteBound| |unknown| |limit| |f02bbf| |integralLastSubResultant| + |pointColor| |phiCoord| |coercePreimagesImages| |createThreeSpace| + |isobaric?| |invertIfCan| |deepExpand| |legendreP| + |generalizedContinuumHypothesisAssumed| |gcdcofactprim| |myDegree| + |unitNormal| |isQuotient| |inspect| |has?| |topFortranOutputStack| + |irCtor| |parseString| |list?| |normFactors| |companionBlocks| + |morphism| |OMconnInDevice| |cCsc| |d01amf| |radicalSimplify| |level| + |computeBasis| |addiag| |input| |complexZeros| |explicitlyEmpty?| + |leadingIdeal| |viewWriteDefault| |reduceLODE| |weakBiRank| + |basisOfCentroid| |primlimitedint| |writeInt8!| |twist| |roughBase?| + |library| |precision| |indicialEquations| |deref| |basisOfLeftNucleus| + |stopTable!| |weierstrass| |generalizedContinuumHypothesisAssumed?| + |primitive?| |iifact| |listexp| |central?| |startTableGcd!| |bothWays| + |minPoints3D| |problemPoints| |permutationRepresentation| |just| + |center| |exteriorDifferential| |showAllElements| |root| + |subResultantChain| |seriesSolve| |merge| |cardinality| |makeMulti| + |height| |fortranComplex| |name| |rule| |localUnquote| |edf2fi| + |sinIfCan| |algebraicVariables| |isOpen?| |pade| |leftFactor| + |getCode| |body| |packageCall| |resultantnaif| |prinpolINFO| |child| + |support| |rCoord| |stoseLastSubResultant| |sturmVariationsOf| + |branchPointAtInfinity?| |complexIntegrate| |rightTrim| + |deleteProperty!| |modulus| |laplace| |arbitrary| |nextsubResultant2| + |upperBound| |super| |leftTrim| |OMputEndAtp| |inverseColeman| + |bipolar| |index| |minPoly| |integralAtInfinity?| |size?| |curry| + |lprop| |getDatabase| |quadratic| |leftZero| |redPo| |trigs2explogs| + |f02aff| |setButtonValue| |minimumExponent| |cCsch| |addBadValue| + |component| |pair| |leftQuotient| |enterPointData| |solveInField| + |algSplitSimple| |d01gbf| |unrankImproperPartitions0| |rationalIfCan| + |sample| |imagJ| |f04mcf| |ScanRoman| |halfExtendedSubResultantGcd1| + |writeLine!| |paraboloidal| |distribute| |before?| |getConstant| + |f02aaf| |orbit| ** RF2UTS |linearMatrix| |monicDivide| |messagePrint| + |putColorInfo| |writeBytes!| |summation| |decrease| |youngDiagram| + |OMreadFile| |port| |basisOfLeftNucloid| |s18adf| + |reducedDiscriminant| |totalGroebner| |listLoops| + |initializeGroupForWordProblem| |f02wef| |overbar| |top!| + |jvmUTF8ConstantTag| |monicRightFactorIfCan| |regularRepresentation| + |any| |show| |kind| |wordInGenerators| |numerators| |sec2cos| + |domainTemplate| |alternating| |pr2dmp| |infix| |separate| + |outputAsTex| |e01baf| |prod| |cCot| |t| |zero| |Ei| |outputForm| + |squareFreeFactors| |definingInequation| |trace| |nand| |symmetric?| + |prem| |nextNormalPrimitivePoly| |units| |separateDegrees| + |computeInt| |iicsch| |generalSqFr| |realElementary| |pdf2df| |atom?| + |att2Result| |nextPrime| |style| |shufflein| |pdct| + |lazyPseudoQuotient| |internalZeroSetSplit| |mainExpression| |chvar| + |setOfMinN| |basisOfMiddleNucleus| |sin2csc| |minimize| |e02akf| + |matrix| |graphStates| |arrayStack| |varList| |bindings| |OMgetEndApp| + |zag| |d01anf| |adjoint| |stopTableGcd!| |reify| |Lazard2| |s17dcf| + |checkPrecision| |setColumn!| |lastSubResultant| + |solveLinearPolynomialEquationByRecursion| |subPolSet?| |predicate| + |sequences| |exponents| |maxColIndex| |sinhcosh| |code| |insertRoot!| + |makeFloatFunction| |ParCond| |roman| |putProperty| |extractTop!| + |noValueMode| |componentUpperBound| |OMopenFile| |quadratic?| + |transform| |isAtom| |inHallBasis?| |e01sff| |countable?| + |setMaxPoints3D| |newLine| |antiCommutative?| |solve1| |testModulus| + |imagI| |commonDenominator| |errorInfo| |bat| |sumOfDivisors| FG2F + |basis| |cyclicSubmodule| |sh| |critB| |lfunc| |elseBranch| + |perfectNthPower?| |prime?| |Gamma| |defineProperty| + |irreducibleFactor| |irreducibleRepresentation| |sequence| + |stoseInvertible?| |OMgetBVar| |largest| |rank| |expressIdealMember| + |linearPolynomials| |inf| |makeSin| |meshFun2Var| |dmpToHdmp| + |lazyIntegrate| |quotient| |s18aef| |pToHdmp| |reduced?| |jokerMode| + |optAttributes| |numberOfOperations| |mathieu11| + |functionIsContinuousAtEndPoints| |jvmStrict| |powers| |externalList| + |alphabetic| |eulerE| |cLog| |pastel| |lazyPseudoRemainder| + |setchildren!| |bandedHessian| |iiexp| |mat| |number?| + |reduceBasisAtInfinity| |currentScope| |setrest!| |expr| + |monomialIntPoly| |permanent| |plus| |setPrologue!| |plusInfinity| + |queue| |showTheFTable| |completeEval| |isConnected?| |OMgetObject| + |cotIfCan| |parameters| |factorSFBRlcUnit| |child?| + |uncouplingMatrices| |screenResolution3D| |minusInfinity| |showAll?| + |binaryTournament| |sorted?| |infiniteProduct| |palgLODE0| + |extractIfCan| |lexGroebner| |listOfMonoms| |OMgetSymbol| |union| + |internal?| |length| |compose| |octon| |OMUnknownCD?| |nilFactor| + |scripted?| |hclf| |makeVariable| |wholeRagits| |subset?| |scripts| + |jacobiIdentity?| |times| |dec| |createNormalPrimitivePoly| + |OMgetFloat| |routines| |pointData| |resultant| |variable| |powerSum| + |even?| |pop!| |rk4qc| |pattern| |s15adf| |leftLcm| |contract| |lllp| + |rotatey| |iterators| |showFortranOutputStack| |e04jaf| |setMaxPoints| + |stFunc1| |iisqrt3| |getProperties| |setPosition| |zeroDimensional?| + |module| |discriminant| |rk4a| |iFTable| |nullSpace| |type| + |OMputError| |rotatex| |attributeData| |unary?| |charpol| |karatsuba| + |Lazard| |e02agf| |size| |fortranReal| |evenInfiniteProduct| + |nextLatticePermutation| |monom| |outputSpacing| |printTypes| + |reducedContinuedFraction| |subTriSet?| |alphanumeric| |besselJ| + |innerEigenvectors| |lists| |algebraicOf| + |zeroSetSplitIntoTriangularSystems| |createZechTable| |leader| + |coerceL| |lowerCase| |simplifyPower| |rischDEsys| |every?| + |genericRightMinimalPolynomial| |concat| |binding| |cyclotomic| + |palgint0| |quadraticNorm| |cot2trig| |order| |thenBranch| |viewpoint| + |structuralConstants| |schema| |omError| |resetBadValues| |common| + |univariatePolynomialsGcds| |nothing| |leastAffineMultiple| + |asinIfCan| |setFieldInfo| |front| |B1solve| |pomopo!| |fi2df| + |pointPlot| |zeroOf| |algebraicSort| |measure2Result| + |removeSuperfluousQuasiComponents| |complement| |invertible?| + |triangular?| |ip4Address| |associative?| |d02bhf| |leftGcd| + |polygon?| |logpart| |shiftLeft| |fortranCarriageReturn| |node?| + |newSubProgram| |result| |solid| |iicoth| |complexForm| |linSolve| + |gcdPolynomial| |absolutelyIrreducible?| |f02fjf| |physicalLength!| + |subHeight| |rowEchelonLocal| |lp| |repeating| |generalPosition| + |PollardSmallFactor| |mightHaveRoots| |brillhartTrials| + |useNagFunctions| |doubleDisc| |lowerBound| |linearlyDependent?| + |setScreenResolution3D| |rootsOf| |perspective| |evaluate| |normal?| + |taylorQuoByVar| |arg1| |edf2df| |unitCanonical| |s18acf| |node| + |clikeUniv| |iibinom| |rowEchLocal| |decompose| |rootRadius| + |drawToScale| |arg2| |hessian| |tanNa| |anticoord| |e02daf| |plus!| + |halfExtendedResultant1| |pol| |lieAdmissible?| |mapExpon| + |commutative?| |startTableInvSet!| |consnewpol| |sturmSequence| + |numberOfCycles| |normalForm| |enqueue!| |reorder| |conditions| + |torsionIfCan| |complexLimit| |monicLeftDivide| |nil?| |curveColor| + |cAsec| |resultantReduitEuclidean| |typeList| |exponent| |match| + |closed?| |semiSubResultantGcdEuclidean2| |internalAugment| + |partialNumerators| |isPlus| |iomode| |d02ejf| |clearTable!| + |replaceKthElement| |mkAnswer| |bat1| |approxNthRoot| + |listYoungTableaus| |convergents| |setIntersection| + |rewriteIdealWithRemainder| |purelyAlgebraic?| |trapezoidalo| + |baseRDEsys| |ellipticCylindrical| |primextendedint| |sin?| + |leadingCoefficientRicDE| |integerIfCan| |drawStyle| |iiasech| + |palginfieldint| |simplifyLog| |viewThetaDefault| |updatD| |errorKind| + |strongGenerators| |autoReduced?| |minColIndex| |cosSinInfo| + |prolateSpheroidal| |ScanFloatIgnoreSpaces| |coefficient| |toroidal| + |singular?| |sort| |gensym| |symmetricGroup| |trueEqual| + |palgintegrate| |wronskianMatrix| |variationOfParameters| + |nonSingularModel| |repSq| |lflimitedint| |isOp| |readIfCan!| + |reducedQPowers| |possiblyInfinite?| |c06fpf| |imagK| |spherical| + |s21bbf| |random| |stopTableInvSet!| |sizeMultiplication| |curve?| + |jordanAdmissible?| |leftCharacteristicPolynomial| |OMgetEndAtp| + |cycleRagits| |bright| |getMeasure| |open| |s13aaf| |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) ((-107 #0=(-2 (|:| -3819 |#1|) (|:| -2913 |#2|))) . T) ((-102) -2181 (|has| |#2| (-1132)) (|has| |#2| (-102)) (|has| (-2 (|:| -3819 |#1|) (|:| -2913 |#2|)) (-1132)) (|has| (-2 (|:| -3819 |#1|) (|:| -2913 |#2|)) (-871)) (|has| (-2 (|:| -3819 |#1|) (|:| -2913 |#2|)) (-102))) ((-632 (-887)) -2181 (|has| |#2| (-1132)) (|has| |#2| (-632 (-887))) (|has| (-2 (|:| -3819 |#1|) (|:| -2913 |#2|)) (-1132)) (|has| (-2 (|:| -3819 |#1|) (|:| -2913 |#2|)) (-871)) (|has| (-2 (|:| -3819 |#1|) (|:| -2913 |#2|)) (-632 (-887)))) ((-153 #1=(-2 (|:| -3819 |#1|) (|:| -2913 |#2|))) . T) ((-633 (-549)) |has| (-2 (|:| -3819 |#1|) (|:| -2913 |#2|)) (-633 (-549))) ((-233 #0#) . T) ((-242 #0#) . T) ((-298 #2=(-560) #1#) . T) ((-298 (-1264 (-560)) $) . T) ((-298 |#1| |#2|) . T) ((-300 #2# #1#) . T) ((-300 |#1| |#2|) . T) ((-321 #1#) -12 (|has| (-2 (|:| -3819 |#1|) (|:| -2913 |#2|)) (-321 (-2 (|:| -3819 |#1|) (|:| -2913 |#2|)))) (|has| (-2 (|:| -3819 |#1|) (|:| -2913 |#2|)) (-1132))) ((-321 |#2|) -12 (|has| |#2| (-321 |#2|)) (|has| |#2| (-1132))) ((-294 #1#) . T) ((-385 #1#) . T) ((-503 #1#) . T) ((-503 |#2|) . T) ((-618 #2# #1#) . T) ((-618 |#1| |#2|) . T) ((-528 #1# #1#) -12 (|has| (-2 (|:| -3819 |#1|) (|:| -2913 |#2|)) (-321 (-2 (|:| -3819 |#1|) (|:| -2913 |#2|)))) (|has| (-2 (|:| -3819 |#1|) (|:| -2913 |#2|)) (-1132))) ((-528 |#2| |#2|) -12 (|has| |#2| (-321 |#2|)) (|has| |#2| (-1132))) ((-629 |#1| |#2|) . T) ((-673 #1#) . T) ((-688 #1#) . T) ((-871) |has| (-2 (|:| -3819 |#1|) (|:| -2913 |#2|)) (-871)) ((-874) |has| (-2 (|:| -3819 |#1|) (|:| -2913 |#2|)) (-871)) ((-1041 #1#) . T) ((-1132) -2181 (|has| |#2| (-1132)) (|has| (-2 (|:| -3819 |#1|) (|:| -2913 |#2|)) (-1132)) (|has| (-2 (|:| -3819 |#1|) (|:| -2913 |#2|)) (-871))) ((-1180 #1#) . T) ((-1224 |#1| |#2|) . T) ((-1247) . T) ((-1286 #1#) . 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T) ((-107 #0=(-2 (|:| -3835 |#1|) (|:| -2923 |#2|))) . T) ((-102) -2173 (|has| |#2| (-1132)) (|has| |#2| (-102)) (|has| (-2 (|:| -3835 |#1|) (|:| -2923 |#2|)) (-1132)) (|has| (-2 (|:| -3835 |#1|) (|:| -2923 |#2|)) (-871)) (|has| (-2 (|:| -3835 |#1|) (|:| -2923 |#2|)) (-102))) ((-632 (-887)) -2173 (|has| |#2| (-1132)) (|has| |#2| (-632 (-887))) (|has| (-2 (|:| -3835 |#1|) (|:| -2923 |#2|)) (-1132)) (|has| (-2 (|:| -3835 |#1|) (|:| -2923 |#2|)) (-871)) (|has| (-2 (|:| -3835 |#1|) (|:| -2923 |#2|)) (-632 (-887)))) ((-153 #1=(-2 (|:| -3835 |#1|) (|:| -2923 |#2|))) . T) ((-633 (-549)) |has| (-2 (|:| -3835 |#1|) (|:| -2923 |#2|)) (-633 (-549))) ((-233 #0#) . T) ((-242 #0#) . T) ((-298 #2=(-560) #1#) . T) ((-298 (-1264 (-560)) $) . T) ((-298 |#1| |#2|) . T) ((-300 #2# #1#) . T) ((-300 |#1| |#2|) . 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T) ((-23) . T) ((-25) . T) ((-38 #0=(-421 (-560))) -2181 (|has| |#1| (-363)) (|has| |#1| (-376))) ((-38 |#1|) . T) ((-38 $) -2181 (|has| |#1| (-571)) (|has| |#1| (-363)) (|has| |#1| (-376)) (|has| |#1| (-319))) ((-35) |has| |#1| (-1233)) ((-95) |has| |#1| (-1233)) ((-102) . T) ((-111 #0# #0#) -2181 (|has| |#1| (-363)) (|has| |#1| (-376))) ((-111 |#1| |#1|) . T) ((-111 $ $) . T) ((-133) . T) ((-147) -2181 (|has| |#1| (-363)) (|has| |#1| (-147))) ((-149) |has| |#1| (-149)) ((-635 #0#) -2181 (|has| |#1| (-1069 (-421 (-560)))) (|has| |#1| (-363)) (|has| |#1| (-376))) ((-635 (-560)) . T) ((-635 |#1|) . T) ((-635 $) -2181 (|has| |#1| (-571)) (|has| |#1| (-363)) (|has| |#1| (-376)) (|has| |#1| (-319))) ((-632 (-887)) . T) ((-175) . T) ((-633 (-171 (-229))) |has| |#1| (-1051)) ((-633 (-171 (-391))) |has| |#1| (-1051)) ((-633 (-549)) |has| |#1| (-633 (-549))) ((-633 (-915 (-391))) |has| |#1| (-633 (-915 (-391)))) ((-633 (-915 (-560))) |has| |#1| (-633 (-915 (-560)))) ((-633 #1=(-1201 |#1|)) . 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T) ((-23) . T) ((-25) . T) ((-38 #0=(-421 (-560))) -2173 (|has| |#1| (-363)) (|has| |#1| (-376))) ((-38 |#1|) . T) ((-38 $) -2173 (|has| |#1| (-571)) (|has| |#1| (-363)) (|has| |#1| (-376)) (|has| |#1| (-319))) ((-35) |has| |#1| (-1233)) ((-95) |has| |#1| (-1233)) ((-102) . T) ((-111 #0# #0#) -2173 (|has| |#1| (-363)) (|has| |#1| (-376))) ((-111 |#1| |#1|) . T) ((-111 $ $) . T) ((-133) . T) ((-147) -2173 (|has| |#1| (-363)) (|has| |#1| (-147))) ((-149) |has| |#1| (-149)) ((-635 #0#) -2173 (|has| |#1| (-1069 (-421 (-560)))) (|has| |#1| (-363)) (|has| |#1| (-376))) ((-635 (-560)) . T) ((-635 |#1|) . T) ((-635 $) -2173 (|has| |#1| (-571)) (|has| |#1| (-363)) (|has| |#1| (-376)) (|has| |#1| (-319))) ((-632 (-887)) . T) ((-175) . T) ((-633 (-171 (-229))) |has| |#1| (-1051)) ((-633 (-171 (-391))) |has| |#1| (-1051)) ((-633 (-549)) |has| |#1| (-633 (-549))) ((-633 (-915 (-391))) |has| |#1| (-633 (-915 (-391)))) ((-633 (-915 (-560))) |has| |#1| (-633 (-915 (-560)))) ((-633 #1=(-1201 |#1|)) . 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T) ((-466) -2173 (|has| |#1| (-363)) (|has| |#1| (-376)) (|has| |#1| (-319))) ((-507) |has| |#1| (-1233)) ((-528 (-1207) |#1|) |has| |#1| (-528 (-1207) |#1|)) ((-528 |#1| |#1|) |has| |#1| (-321 |#1|)) ((-571) -2173 (|has| |#1| (-571)) (|has| |#1| (-363)) (|has| |#1| (-376)) (|has| |#1| (-319))) ((-668 #0#) -2173 (|has| |#1| (-363)) (|has| |#1| (-376))) ((-668 (-560)) . T) ((-668 |#1|) . T) ((-668 $) . T) ((-670 #0#) -2173 (|has| |#1| (-363)) (|has| |#1| (-376))) ((-670 #2=(-560)) |has| |#1| (-660 (-560))) ((-670 |#1|) . T) ((-670 $) . T) ((-662 #0#) -2173 (|has| |#1| (-363)) (|has| |#1| (-376))) ((-662 |#1|) . T) ((-662 $) -2173 (|has| |#1| (-571)) (|has| |#1| (-363)) (|has| |#1| (-376)) (|has| |#1| (-319))) ((-660 #2#) |has| |#1| (-660 (-560))) ((-660 |#1|) . T) ((-739 #0#) -2173 (|has| |#1| (-363)) (|has| |#1| (-376))) ((-739 |#1|) . T) ((-739 $) -2173 (|has| |#1| (-571)) (|has| |#1| (-363)) (|has| |#1| (-376)) (|has| |#1| (-319))) ((-746 |#1| #1#) . T) ((-748) . 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T) ((-236 $) -2181 (-12 (|has| |#2| (-239)) (|has| |#2| (-1080))) (-12 (|has| |#2| (-240)) (|has| |#2| (-1080)))) ((-234 |#2|) |has| |#2| (-1080)) ((-240) -12 (|has| |#2| (-240)) (|has| |#2| (-1080))) ((-239) -2181 (-12 (|has| |#2| (-239)) (|has| |#2| (-1080))) (-12 (|has| |#2| (-240)) (|has| |#2| (-1080)))) ((-274 |#2|) |has| |#2| (-1080)) ((-298 #1=(-560) |#2|) . T) ((-300 #1# |#2|) . T) ((-321 |#2|) -12 (|has| |#2| (-321 |#2|)) (|has| |#2| (-1132))) ((-381) |has| |#2| (-381)) ((-390 |#2|) |has| |#2| (-1080)) ((-426 |#2|) |has| |#2| (-1132)) ((-503 |#2|) . T) ((-618 #1# |#2|) . 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T) ((-1305 |#2|) |has| |#2| (-376))) -((-2293 (((-114) $ $) NIL (|has| |#2| (-102)) ELT)) (-3401 (((-114) $) NIL (|has| |#2| (-23)) ELT)) (-4236 (($ (-948)) 62 (|has| |#2| (-1080)) ELT)) (-3975 (((-1303) $ (-560) (-560)) NIL (|has| $ (-6 -4509)) ELT)) (-1983 (($ $ $) 68 (|has| |#2| (-815)) ELT)) (-3715 (((-3 $ "failed") $ $) 53 (|has| |#2| (-133)) ELT)) (-4194 (((-114) $ (-793)) NIL T ELT)) (-4290 (((-793)) NIL (|has| |#2| (-381)) ELT)) (-2555 ((|#2| $ (-560) |#2|) NIL (|has| $ (-6 -4509)) ELT)) (-2853 (($) NIL T CONST)) (-3580 (((-3 (-560) "failed") $) NIL (-12 (|has| |#2| (-1069 (-560))) (|has| |#2| (-1132))) ELT) (((-3 (-421 (-560)) "failed") $) NIL (-12 (|has| |#2| (-1069 (-421 (-560)))) (|has| |#2| (-1132))) ELT) (((-3 |#2| "failed") $) 30 (|has| |#2| (-1132)) ELT)) (-3429 (((-560) $) NIL (-12 (|has| |#2| (-1069 (-560))) (|has| |#2| (-1132))) ELT) (((-421 (-560)) $) NIL (-12 (|has| |#2| (-1069 (-421 (-560)))) (|has| |#2| (-1132))) ELT) ((|#2| $) 28 (|has| |#2| (-1132)) ELT)) 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T) ((-102) -2173 (|has| |#2| (-1132)) (|has| |#2| (-1080)) (|has| |#2| (-871)) (|has| |#2| (-815)) (|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|) -2173 (|has| |#2| (-1080)) (|has| |#2| (-376)) (|has| |#2| (-175))) ((-133) -2173 (|has| |#2| (-1080)) (|has| |#2| (-815)) (|has| |#2| (-376)) (|has| |#2| (-175)) (|has| |#2| (-133)) (|has| |#2| (-21))) ((-635 #0=(-421 (-560))) -12 (|has| |#2| (-1069 (-421 (-560)))) (|has| |#2| (-1132))) ((-635 (-560)) -2173 (|has| |#2| (-1080)) (-12 (|has| |#2| (-1069 (-560))) (|has| |#2| (-1132)))) ((-635 |#2|) |has| |#2| (-1132)) ((-632 (-887)) -2173 (|has| |#2| (-1132)) (|has| |#2| (-1080)) (|has| |#2| (-871)) (|has| |#2| (-815)) (|has| |#2| (-748)) (|has| |#2| (-381)) (|has| |#2| (-376)) (|has| |#2| (-175)) (|has| |#2| (-632 (-887))) (|has| |#2| (-133)) (|has| |#2| (-25)) (|has| |#2| (-23)) (|has| |#2| (-21))) ((-632 (-1297 |#2|)) . T) ((-236 $) -2173 (-12 (|has| |#2| (-239)) (|has| |#2| (-1080))) (-12 (|has| |#2| (-240)) (|has| |#2| (-1080)))) ((-234 |#2|) |has| |#2| (-1080)) ((-240) -12 (|has| |#2| (-240)) (|has| |#2| (-1080))) ((-239) -2173 (-12 (|has| |#2| (-239)) (|has| |#2| (-1080))) (-12 (|has| |#2| (-240)) (|has| |#2| (-1080)))) ((-274 |#2|) |has| |#2| (-1080)) ((-298 #1=(-560) |#2|) . T) ((-300 #1# |#2|) . T) ((-321 |#2|) -12 (|has| |#2| (-321 |#2|)) (|has| |#2| (-1132))) ((-381) |has| |#2| (-381)) ((-390 |#2|) |has| |#2| (-1080)) ((-426 |#2|) |has| |#2| (-1132)) ((-503 |#2|) . T) ((-618 #1# |#2|) . T) ((-528 |#2| |#2|) -12 (|has| |#2| (-321 |#2|)) (|has| |#2| (-1132))) ((-668 (-560)) -2173 (|has| |#2| (-1080)) (|has| |#2| (-376)) (|has| |#2| (-175)) (|has| |#2| (-21))) ((-668 |#2|) -2173 (|has| |#2| (-1080)) (|has| |#2| (-748)) (|has| |#2| (-376)) (|has| |#2| (-175))) ((-668 $) |has| |#2| (-1080)) ((-670 #2=(-560)) -12 (|has| |#2| (-660 (-560))) (|has| |#2| (-1080))) ((-670 |#2|) -2173 (|has| |#2| (-1080)) (|has| |#2| (-376)) (|has| |#2| (-175))) ((-670 $) |has| |#2| (-1080)) ((-662 |#2|) -2173 (|has| |#2| (-748)) (|has| |#2| (-376)) (|has| |#2| (-175))) ((-660 #2#) -12 (|has| |#2| (-660 (-560))) (|has| |#2| (-1080))) ((-660 |#2|) |has| |#2| (-1080)) ((-739 |#2|) -2173 (|has| |#2| (-376)) (|has| |#2| (-175))) ((-748) |has| |#2| (-1080)) ((-814) |has| |#2| (-815)) ((-815) |has| |#2| (-815)) ((-816) |has| |#2| (-815)) ((-819) |has| |#2| (-815)) ((-871) -2173 (|has| |#2| (-871)) (|has| |#2| (-815))) ((-874) -2173 (|has| |#2| (-871)) (|has| |#2| (-815))) ((-921 $ #3=(-1207)) -2173 (-12 (|has| |#2| (-929 (-1207))) (|has| |#2| (-1080))) (-12 (|has| |#2| (-927 (-1207))) (|has| |#2| (-1080)))) ((-927 (-1207)) -12 (|has| |#2| (-927 (-1207))) (|has| |#2| (-1080))) ((-929 #3#) -2173 (-12 (|has| |#2| (-929 (-1207))) (|has| |#2| (-1080))) (-12 (|has| |#2| (-927 (-1207))) (|has| |#2| (-1080)))) ((-1069 #0#) -12 (|has| |#2| (-1069 (-421 (-560)))) (|has| |#2| (-1132))) ((-1069 (-560)) -12 (|has| |#2| (-1069 (-560))) (|has| |#2| (-1132))) ((-1069 |#2|) |has| |#2| (-1132)) ((-1082 |#2|) -2173 (|has| |#2| (-1080)) (|has| |#2| (-748)) (|has| |#2| (-376)) (|has| |#2| (-175))) ((-1087 |#2|) -2173 (|has| |#2| (-1080)) (|has| |#2| (-376)) (|has| |#2| (-175))) ((-1080) |has| |#2| (-1080)) ((-1088) |has| |#2| (-1080)) ((-1143) |has| |#2| (-1080)) ((-1132) -2173 (|has| |#2| (-1132)) (|has| |#2| (-1080)) (|has| |#2| (-871)) (|has| |#2| (-815)) (|has| |#2| (-748)) (|has| |#2| (-381)) (|has| |#2| (-376)) (|has| |#2| (-175)) (|has| |#2| (-133)) (|has| |#2| (-25)) (|has| |#2| (-23)) (|has| |#2| (-21))) ((-1247) . 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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 $) -2181 (|has| |#1| (-939)) (|has| |#1| (-571)) (|has| |#1| (-466))) ((-102) . T) ((-111 #0# #0#) |has| |#1| (-38 (-421 (-560)))) ((-111 |#1| |#1|) . T) ((-111 $ $) -2181 (|has| |#1| (-939)) (|has| |#1| (-571)) (|has| |#1| (-466)) (|has| |#1| (-175))) ((-133) . T) ((-147) |has| |#1| (-147)) ((-149) |has| |#1| (-149)) ((-635 #0#) -2181 (|has| |#1| (-1069 (-421 (-560)))) (|has| |#1| (-38 (-421 (-560))))) ((-635 (-560)) . T) ((-635 |#1|) . T) ((-635 |#2|) . T) ((-635 |#3|) . T) ((-635 $) -2181 (|has| |#1| (-939)) (|has| |#1| (-571)) (|has| |#1| (-466))) ((-632 (-887)) . T) ((-175) -2181 (|has| |#1| (-939)) (|has| |#1| (-571)) (|has| |#1| (-466)) (|has| |#1| (-175))) ((-633 (-549)) -12 (|has| |#1| (-633 (-549))) (|has| |#3| (-633 (-549)))) ((-633 (-915 (-391))) -12 (|has| |#1| (-633 (-915 (-391)))) (|has| |#3| (-633 (-915 (-391))))) ((-633 (-915 (-560))) -12 (|has| |#1| (-633 (-915 (-560)))) (|has| |#3| (-633 (-915 (-560))))) ((-236 $) -2181 (|has| |#1| (-239)) (|has| |#1| (-240))) ((-234 |#1|) . T) ((-240) |has| |#1| (-240)) ((-239) -2181 (|has| |#1| (-239)) (|has| |#1| (-240))) ((-274 |#1|) . T) ((-302) -2181 (|has| |#1| (-939)) (|has| |#1| (-571)) (|has| |#1| (-466))) ((-321 $) . T) ((-338 |#1| |#4|) . T) ((-390 |#1|) . T) ((-426 |#1|) . T) ((-466) -2181 (|has| |#1| (-939)) (|has| |#1| (-466))) ((-528 |#2| |#1|) |has| |#1| (-240)) ((-528 |#2| $) |has| |#1| (-240)) ((-528 |#3| |#1|) . T) ((-528 |#3| $) . T) ((-528 $ $) . T) ((-571) -2181 (|has| |#1| (-939)) (|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 $) -2181 (|has| |#1| (-939)) (|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 $) -2181 (|has| |#1| (-939)) (|has| |#1| (-571)) (|has| |#1| (-466))) ((-748) . T) ((-921 $ #2=(-1207)) -2181 (|has| |#1| (-929 (-1207))) (|has| |#1| (-927 (-1207)))) ((-921 $ |#3|) . T) ((-927 (-1207)) |has| |#1| (-927 (-1207))) ((-927 |#3|) . T) ((-929 #2#) -2181 (|has| |#1| (-929 (-1207))) (|has| |#1| (-927 (-1207)))) ((-929 |#3|) . T) ((-911 (-391)) -12 (|has| |#1| (-911 (-391))) (|has| |#3| (-911 (-391)))) ((-911 (-560)) -12 (|has| |#1| (-911 (-560))) (|has| |#3| (-911 (-560)))) ((-979 |#1| |#4| |#3|) . T) ((-939) |has| |#1| (-939)) ((-1069 (-421 (-560))) |has| |#1| (-1069 (-421 (-560)))) ((-1069 (-560)) |has| |#1| (-1069 (-560))) ((-1069 |#1|) . T) ((-1069 |#2|) . T) ((-1069 |#3|) . T) ((-1082 #0#) |has| |#1| (-38 (-421 (-560)))) ((-1082 |#1|) . T) ((-1082 $) -2181 (|has| |#1| (-939)) (|has| |#1| (-571)) (|has| |#1| (-466)) (|has| |#1| (-175))) ((-1087 #0#) |has| |#1| (-38 (-421 (-560)))) ((-1087 |#1|) . T) ((-1087 $) -2181 (|has| |#1| (-939)) (|has| |#1| (-571)) (|has| |#1| (-466)) (|has| |#1| (-175))) ((-1080) . T) ((-1088) . T) ((-1143) . T) ((-1132) . T) ((-1247) . T) ((-1252) |has| |#1| (-939))) -((-2293 (((-114) $ $) 22 (|has| |#1| (-102)) ELT)) (-4200 ((|#1| $) 61 T ELT)) (-1755 ((|#1| $) 51 T ELT)) (-4194 (((-114) $ (-793)) 8 T ELT)) (-2853 (($) 7 T CONST)) (-3315 (($ $) 67 T ELT)) (-3912 (($ $) 55 T ELT)) (-2934 ((|#1| |#1| $) 53 T ELT)) (-2372 ((|#1| $) 52 T ELT)) (-3133 (((-663 |#1|) $) 33 (|has| $ (-6 -4508)) ELT)) (-3529 (((-114) $ (-793)) 9 T ELT)) (-3905 (((-663 |#1|) $) 32 (|has| $ (-6 -4508)) ELT)) (-2778 (((-114) |#1| $) 30 (-12 (|has| |#1| (-1132)) (|has| $ (-6 -4508))) ELT)) (-2717 (($ (-1 |#1| |#1|) $) 37 (|has| $ (-6 -4509)) ELT)) (-3748 (($ (-1 |#1| |#1|) $) 38 T ELT)) (-2939 (((-114) $ (-793)) 10 T ELT)) (-4248 (((-793) $) 68 T ELT)) (-3059 (((-1189) $) 25 (|has| |#1| (-1132)) ELT)) (-4184 ((|#1| $) 46 T ELT)) (-4298 ((|#1| |#1| $) 59 T ELT)) (-1480 ((|#1| |#1| $) 58 T ELT)) (-4155 (($ |#1| $) 47 T ELT)) (-3971 (((-793) $) 62 T ELT)) (-3191 (((-1151) $) 24 (|has| |#1| (-1132)) ELT)) (-2757 ((|#1| $) 69 T ELT)) (-1712 ((|#1| $) 57 T ELT)) (-4365 ((|#1| $) 56 T ELT)) (-2966 ((|#1| $) 48 T ELT)) (-4412 (((-114) (-1 (-114) |#1|) $) 35 (|has| $ (-6 -4508)) ELT)) (-2828 (($ $ (-663 (-305 |#1|))) 29 (-12 (|has| |#1| (-321 |#1|)) (|has| |#1| (-1132))) ELT) (($ $ (-305 |#1|)) 28 (-12 (|has| |#1| (-321 |#1|)) (|has| |#1| (-1132))) ELT) (($ $ |#1| |#1|) 27 (-12 (|has| |#1| (-321 |#1|)) (|has| |#1| (-1132))) ELT) (($ $ (-663 |#1|) (-663 |#1|)) 26 (-12 (|has| |#1| (-321 |#1|)) (|has| |#1| (-1132))) ELT)) (-1511 (((-114) $ $) 14 T ELT)) (-4118 ((|#1| |#1| $) 65 T ELT)) (-3276 (((-114) $) 11 T ELT)) (-3770 (($) 12 T ELT)) (-1767 ((|#1| $) 66 T ELT)) (-1363 (($) 64 T ELT) (($ (-663 |#1|)) 63 T ELT)) (-2576 (((-793) $) 50 T ELT)) (-3203 (((-793) (-1 (-114) |#1|) $) 34 (|has| $ (-6 -4508)) ELT) (((-793) |#1| $) 31 (-12 (|has| |#1| (-1132)) (|has| $ (-6 -4508))) ELT)) (-2579 (($ $) 13 T ELT)) (-4272 (((-887) $) 20 (|has| |#1| (-632 (-887))) ELT)) (-1673 ((|#1| $) 60 T ELT)) (-1700 (((-114) $ $) 23 (|has| |#1| (-102)) ELT)) (-2429 (($ (-663 |#1|)) 49 T ELT)) (-3768 ((|#1| $) 70 T ELT)) (-3744 (((-114) (-1 (-114) |#1|) $) 36 (|has| $ (-6 -4508)) ELT)) (-2342 (((-114) $ $) 21 (|has| |#1| (-102)) ELT)) (-2305 (((-793) $) 6 (|has| $ (-6 -4508)) ELT))) +((-4242 (*1 *2 *3) (-12 (-4 *4 (-1080)) (-4 *3 (-871)) (-4 *5 (-277 *3)) (-4 *6 (-815)) (-5 *2 (-1 *1 (-793))) (-4 *1 (-262 *4 *3 *5 *6)))) (-3704 (*1 *2 *1) (-12 (-4 *1 (-262 *3 *4 *5 *6)) (-4 *3 (-1080)) (-4 *4 (-871)) (-4 *5 (-277 *4)) (-4 *6 (-815)) (-5 *2 (-663 *4)))) (-4317 (*1 *2 *1 *3) (-12 (-4 *1 (-262 *4 *3 *5 *6)) (-4 *4 (-1080)) (-4 *3 (-871)) (-4 *5 (-277 *3)) (-4 *6 (-815)) (-5 *2 (-793)))) (-4317 (*1 *2 *1) (-12 (-4 *1 (-262 *3 *4 *5 *6)) (-4 *3 (-1080)) (-4 *4 (-871)) (-4 *5 (-277 *4)) (-4 *6 (-815)) (-5 *2 (-793)))) (-1521 (*1 *2 *1 *3) (-12 (-4 *1 (-262 *4 *3 *5 *6)) (-4 *4 (-1080)) (-4 *3 (-871)) (-4 *5 (-277 *3)) (-4 *6 (-815)) (-5 *2 (-793)))) (-2548 (*1 *2 *1) (-12 (-4 *1 (-262 *3 *4 *5 *6)) (-4 *3 (-1080)) (-4 *4 (-871)) (-4 *5 (-277 *4)) (-4 *6 (-815)) (-5 *2 (-663 (-793))))) (-3538 (*1 *2 *1) (-12 (-4 *1 (-262 *3 *4 *5 *6)) (-4 *3 (-1080)) (-4 *4 (-871)) (-4 *5 (-277 *4)) (-4 *6 (-815)) (-5 *2 (-793)))) (-2548 (*1 *2 *1 *3) (-12 (-4 *1 (-262 *4 *3 *5 *6)) (-4 *4 (-1080)) (-4 *3 (-871)) (-4 *5 (-277 *3)) (-4 *6 (-815)) (-5 *2 (-663 (-793))))) (-3538 (*1 *2 *1 *3) (-12 (-4 *1 (-262 *4 *3 *5 *6)) (-4 *4 (-1080)) (-4 *3 (-871)) (-4 *5 (-277 *3)) (-4 *6 (-815)) (-5 *2 (-793)))) (-3899 (*1 *2 *1) (-12 (-4 *1 (-262 *3 *4 *5 *6)) (-4 *3 (-1080)) (-4 *4 (-871)) (-4 *5 (-277 *4)) (-4 *6 (-815)) (-5 *2 (-114)))) (-4304 (*1 *2 *1) (-12 (-4 *1 (-262 *3 *4 *2 *5)) (-4 *3 (-1080)) (-4 *4 (-871)) (-4 *5 (-815)) (-4 *2 (-277 *4)))) (-2099 (*1 *1 *1) (-12 (-4 *1 (-262 *2 *3 *4 *5)) (-4 *2 (-1080)) (-4 *3 (-871)) (-4 *4 (-277 *3)) (-4 *5 (-815)))) (-3123 (*1 *1 *1) (-12 (-4 *1 (-262 *2 *3 *4 *5)) (-4 *2 (-1080)) (-4 *3 (-871)) (-4 *4 (-277 *3)) (-4 *5 (-815)))) (-4242 (*1 *2 *1) (-12 (-4 *3 (-240)) (-4 *3 (-1080)) (-4 *4 (-871)) (-4 *5 (-277 *4)) (-4 *6 (-815)) (-5 *2 (-1 *1 (-793))) (-4 *1 (-262 *3 *4 *5 *6))))) +(-13 (-979 |t#1| |t#4| |t#3|) (-234 |t#1|) (-1069 |t#2|) (-10 -8 (-15 -4242 ((-1 $ (-793)) |t#2|)) (-15 -3704 ((-663 |t#2|) $)) (-15 -4317 ((-793) $ |t#2|)) (-15 -4317 ((-793) $)) (-15 -1521 ((-793) $ |t#2|)) (-15 -2548 ((-663 (-793)) $)) (-15 -3538 ((-793) $)) (-15 -2548 ((-663 (-793)) $ |t#2|)) (-15 -3538 ((-793) $ |t#2|)) (-15 -3899 ((-114) $)) (-15 -4304 (|t#3| $)) (-15 -2099 ($ $)) (-15 -3123 ($ $)) (IF (|has| |t#1| (-240)) (PROGN (-6 (-528 |t#2| |t#1|)) (-6 (-528 |t#2| $)) (-6 (-321 $)) (-15 -4242 ((-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 $) -2173 (|has| |#1| (-939)) (|has| |#1| (-571)) (|has| |#1| (-466))) ((-102) . T) ((-111 #0# #0#) |has| |#1| (-38 (-421 (-560)))) ((-111 |#1| |#1|) . T) ((-111 $ $) -2173 (|has| |#1| (-939)) (|has| |#1| (-571)) (|has| |#1| (-466)) (|has| |#1| (-175))) ((-133) . T) ((-147) |has| |#1| (-147)) ((-149) |has| |#1| (-149)) ((-635 #0#) -2173 (|has| |#1| (-1069 (-421 (-560)))) (|has| |#1| (-38 (-421 (-560))))) ((-635 (-560)) . T) ((-635 |#1|) . T) ((-635 |#2|) . T) ((-635 |#3|) . T) ((-635 $) -2173 (|has| |#1| (-939)) (|has| |#1| (-571)) (|has| |#1| (-466))) ((-632 (-887)) . T) ((-175) -2173 (|has| |#1| (-939)) (|has| |#1| (-571)) (|has| |#1| (-466)) (|has| |#1| (-175))) ((-633 (-549)) -12 (|has| |#1| (-633 (-549))) (|has| |#3| (-633 (-549)))) ((-633 (-915 (-391))) -12 (|has| |#1| (-633 (-915 (-391)))) (|has| |#3| (-633 (-915 (-391))))) ((-633 (-915 (-560))) -12 (|has| |#1| (-633 (-915 (-560)))) (|has| |#3| (-633 (-915 (-560))))) ((-236 $) -2173 (|has| |#1| (-239)) (|has| |#1| (-240))) ((-234 |#1|) . T) ((-240) |has| |#1| (-240)) ((-239) -2173 (|has| |#1| (-239)) (|has| |#1| (-240))) ((-274 |#1|) . T) ((-302) -2173 (|has| |#1| (-939)) (|has| |#1| (-571)) (|has| |#1| (-466))) ((-321 $) . T) ((-338 |#1| |#4|) . T) ((-390 |#1|) . T) ((-426 |#1|) . T) ((-466) -2173 (|has| |#1| (-939)) (|has| |#1| (-466))) ((-528 |#2| |#1|) |has| |#1| (-240)) ((-528 |#2| $) |has| |#1| (-240)) ((-528 |#3| |#1|) . T) ((-528 |#3| $) . T) ((-528 $ $) . T) ((-571) -2173 (|has| |#1| (-939)) (|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 $) -2173 (|has| |#1| (-939)) (|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 $) -2173 (|has| |#1| (-939)) (|has| |#1| (-571)) (|has| |#1| (-466))) ((-748) . T) ((-921 $ #2=(-1207)) -2173 (|has| |#1| (-929 (-1207))) (|has| |#1| (-927 (-1207)))) ((-921 $ |#3|) . T) ((-927 (-1207)) |has| |#1| (-927 (-1207))) ((-927 |#3|) . T) ((-929 #2#) -2173 (|has| |#1| (-929 (-1207))) (|has| |#1| (-927 (-1207)))) ((-929 |#3|) . T) ((-911 (-391)) -12 (|has| |#1| (-911 (-391))) (|has| |#3| (-911 (-391)))) ((-911 (-560)) -12 (|has| |#1| (-911 (-560))) (|has| |#3| (-911 (-560)))) ((-979 |#1| |#4| |#3|) . T) ((-939) |has| |#1| (-939)) ((-1069 (-421 (-560))) |has| |#1| (-1069 (-421 (-560)))) ((-1069 (-560)) |has| |#1| (-1069 (-560))) ((-1069 |#1|) . T) ((-1069 |#2|) . T) ((-1069 |#3|) . T) ((-1082 #0#) |has| |#1| (-38 (-421 (-560)))) ((-1082 |#1|) . T) ((-1082 $) -2173 (|has| |#1| (-939)) (|has| |#1| (-571)) (|has| |#1| (-466)) (|has| |#1| (-175))) ((-1087 #0#) |has| |#1| (-38 (-421 (-560)))) ((-1087 |#1|) . T) ((-1087 $) -2173 (|has| |#1| (-939)) (|has| |#1| (-571)) (|has| |#1| (-466)) (|has| |#1| (-175))) ((-1080) . T) ((-1088) . T) ((-1143) . T) ((-1132) . T) ((-1247) . T) ((-1252) |has| |#1| (-939))) +((-2280 (((-114) $ $) 22 (|has| |#1| (-102)) ELT)) (-4055 ((|#1| $) 61 T ELT)) (-1765 ((|#1| $) 51 T ELT)) (-4001 (((-114) $ (-793)) 8 T ELT)) (-4023 (($) 7 T CONST)) (-2983 (($ $) 67 T ELT)) (-2998 (($ $) 55 T ELT)) (-3468 ((|#1| |#1| $) 53 T ELT)) (-4257 ((|#1| $) 52 T ELT)) (-3122 (((-663 |#1|) $) 33 (|has| $ (-6 -4508)) ELT)) (-1448 (((-114) $ (-793)) 9 T ELT)) (-2921 (((-663 |#1|) $) 32 (|has| $ (-6 -4508)) ELT)) (-1345 (((-114) |#1| $) 30 (-12 (|has| |#1| (-1132)) (|has| $ (-6 -4508))) ELT)) (-2705 (($ (-1 |#1| |#1|) $) 37 (|has| $ (-6 -4509)) ELT)) (-3605 (($ (-1 |#1| |#1|) $) 38 T ELT)) (-3527 (((-114) $ (-793)) 10 T ELT)) (-4235 (((-793) $) 68 T ELT)) (-2181 (((-1189) $) 25 (|has| |#1| (-1132)) ELT)) (-3908 ((|#1| $) 46 T ELT)) (-2421 ((|#1| |#1| $) 59 T ELT)) (-3495 ((|#1| |#1| $) 58 T ELT)) (-3557 (($ |#1| $) 47 T ELT)) (-3963 (((-793) $) 62 T ELT)) (-3214 (((-1151) $) 24 (|has| |#1| (-1132)) ELT)) (-4330 ((|#1| $) 69 T ELT)) (-4136 ((|#1| $) 57 T ELT)) (-1871 ((|#1| $) 56 T ELT)) (-3811 ((|#1| $) 48 T ELT)) (-4309 (((-114) (-1 (-114) |#1|) $) 35 (|has| $ (-6 -4508)) ELT)) (-2827 (($ $ (-663 (-305 |#1|))) 29 (-12 (|has| |#1| (-321 |#1|)) (|has| |#1| (-1132))) ELT) (($ $ (-305 |#1|)) 28 (-12 (|has| |#1| (-321 |#1|)) (|has| |#1| (-1132))) ELT) (($ $ |#1| |#1|) 27 (-12 (|has| |#1| (-321 |#1|)) (|has| |#1| (-1132))) ELT) (($ $ (-663 |#1|) (-663 |#1|)) 26 (-12 (|has| |#1| (-321 |#1|)) (|has| |#1| (-1132))) ELT)) (-1584 (((-114) $ $) 14 T ELT)) (-4406 ((|#1| |#1| $) 65 T ELT)) (-3876 (((-114) $) 11 T ELT)) (-2025 (($) 12 T ELT)) (-3433 ((|#1| $) 66 T ELT)) (-3189 (($) 64 T ELT) (($ (-663 |#1|)) 63 T ELT)) (-2563 (((-793) $) 50 T ELT)) (-3224 (((-793) (-1 (-114) |#1|) $) 34 (|has| $ (-6 -4508)) ELT) (((-793) |#1| $) 31 (-12 (|has| |#1| (-1132)) (|has| $ (-6 -4508))) ELT)) (-2593 (($ $) 13 T ELT)) (-2383 (((-887) $) 20 (|has| |#1| (-632 (-887))) ELT)) (-1761 ((|#1| $) 60 T ELT)) (-4031 (((-114) $ $) 23 (|has| |#1| (-102)) ELT)) (-3515 (($ (-663 |#1|)) 49 T ELT)) (-2002 ((|#1| $) 70 T ELT)) (-1778 (((-114) (-1 (-114) |#1|) $) 36 (|has| $ (-6 -4508)) ELT)) (-2330 (((-114) $ $) 21 (|has| |#1| (-102)) ELT)) (-2292 (((-793) $) 6 (|has| $ (-6 -4508)) ELT))) (((-263 |#1|) (-142) (-1247)) (T -263)) -((-1363 (*1 *1) (-12 (-4 *1 (-263 *2)) (-4 *2 (-1247)))) (-1363 (*1 *1 *2) (-12 (-5 *2 (-663 *3)) (-4 *3 (-1247)) (-4 *1 (-263 *3)))) (-3971 (*1 *2 *1) (-12 (-4 *1 (-263 *3)) (-4 *3 (-1247)) (-5 *2 (-793)))) (-4200 (*1 *2 *1) (-12 (-4 *1 (-263 *2)) (-4 *2 (-1247)))) (-1673 (*1 *2 *1) (-12 (-4 *1 (-263 *2)) (-4 *2 (-1247)))) (-4298 (*1 *2 *2 *1) (-12 (-4 *1 (-263 *2)) (-4 *2 (-1247)))) (-1480 (*1 *2 *2 *1) (-12 (-4 *1 (-263 *2)) (-4 *2 (-1247)))) (-1712 (*1 *2 *1) (-12 (-4 *1 (-263 *2)) (-4 *2 (-1247)))) (-4365 (*1 *2 *1) (-12 (-4 *1 (-263 *2)) (-4 *2 (-1247)))) (-3912 (*1 *1 *1) (-12 (-4 *1 (-263 *2)) (-4 *2 (-1247))))) -(-13 (-1152 |t#1|) (-1026 |t#1|) (-10 -8 (-15 -1363 ($)) (-15 -1363 ($ (-663 |t#1|))) (-15 -3971 ((-793) $)) (-15 -4200 (|t#1| $)) (-15 -1673 (|t#1| $)) (-15 -4298 (|t#1| |t#1| $)) (-15 -1480 (|t#1| |t#1| $)) (-15 -1712 (|t#1| $)) (-15 -4365 (|t#1| $)) (-15 -3912 ($ $)))) -(((-34) . 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T) ((-310) . T) ((-376) |has| |#1| (-571)) ((-390 |#1|) |has| |#1| (-1080)) ((-414 |#1|) . T) ((-426 |#1|) . T) ((-466) |has| |#1| (-571)) ((-487) |has| |#1| (-487)) ((-528 (-630 $) $) . T) ((-528 $ $) . 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T) ((-950) |has| |#1| (-571)) ((-1069 (-421 (-560))) -2173 (|has| |#1| (-1069 (-421 (-560)))) (-12 (|has| |#1| (-571)) (|has| |#1| (-1069 (-560))))) ((-1069 #1#) |has| |#1| (-571)) ((-1069 (-560)) |has| |#1| (-1069 (-560))) ((-1069 #2#) . T) ((-1069 #3#) |has| |#1| (-1080)) ((-1069 #4#) . T) ((-1069 |#1|) . T) ((-1082 #0#) |has| |#1| (-571)) ((-1082 |#1|) |has| |#1| (-175)) ((-1082 $) |has| |#1| (-571)) ((-1087 #0#) |has| |#1| (-571)) ((-1087 |#1|) |has| |#1| (-175)) ((-1087 $) |has| |#1| (-571)) ((-1080) -2173 (|has| |#1| (-1080)) (|has| |#1| (-571)) (|has| |#1| (-175)) (|has| |#1| (-149)) (|has| |#1| (-147))) ((-1088) -2173 (|has| |#1| (-1080)) (|has| |#1| (-571)) (|has| |#1| (-175)) (|has| |#1| (-149)) (|has| |#1| (-147))) ((-1143) -2173 (|has| |#1| (-1143)) (|has| |#1| (-1080)) (|has| |#1| (-571)) (|has| |#1| (-487)) (|has| |#1| (-175)) (|has| |#1| (-149)) (|has| |#1| (-147))) ((-1132) . T) ((-1247) . 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|bothSingular| "There are singularities at both end points") (|:| |notEvaluated| "End point continuity not yet evaluated"))) (|:| |singularitiesStream| (-3 (|:| |str| (-1185 (-229))) (|:| |notEvaluated| "Internal singularities not yet evaluated"))) (|:| -2016 (-3 (|:| |finite| "The range is finite") (|:| |lowerInfinite| "The bottom of range is infinite") (|:| |upperInfinite| "The top of range is infinite") (|:| |bothInfinite| "Both top and bottom points are infinite") (|:| |notEvaluated| "Range not yet evaluated")))) (-2 (|:| |var| (-1207)) (|:| |fn| (-326 (-229))) (|:| -2016 (-1120 (-864 (-229)))) (|:| |abserr| (-229)) (|:| |relerr| (-229))))))) (T -574)) +((-2923 (*1 *2 *3) (-12 (-5 *3 (-2 (|:| |var| (-1207)) (|:| |fn| (-326 (-229))) (|:| -2016 (-1120 (-864 (-229)))) (|:| |abserr| (-229)) (|:| |relerr| (-229)))) (-5 *2 (-2 (|:| |endPointContinuity| (-3 (|:| |continuous| "Continuous at the end points") (|:| |lowerSingular| "There is a singularity at the lower end point") (|:| 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|notEvaluated| "End point continuity not yet evaluated"))) (|:| |singularitiesStream| (-3 (|:| |str| (-1185 (-229))) (|:| |notEvaluated| "Internal singularities not yet evaluated"))) (|:| -2016 (-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)))) (-2632 (*1 *1 *2) (-12 (-5 *2 (-663 (-2 (|:| -3835 (-2 (|:| |var| (-1207)) (|:| |fn| (-326 (-229))) (|:| -2016 (-1120 (-864 (-229)))) (|:| |abserr| (-229)) (|:| |relerr| (-229)))) (|:| -2923 (-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 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T) ((-23) . T) ((-25) . T) ((-38 #0=(-421 (-560))) . T) ((-38 |#1|) . T) ((-38 $) . T) ((-102) . T) ((-111 #0# #0#) . T) ((-111 |#1| |#1|) . T) ((-111 $ $) . T) ((-133) . T) ((-147) |has| |#1| (-147)) ((-149) |has| |#1| (-149)) ((-635 #0#) . T) ((-635 (-560)) . T) ((-635 #1=(-1207)) |has| |#1| (-1069 (-1207))) ((-635 |#1|) . T) ((-635 $) . T) ((-632 (-887)) . T) ((-175) . T) ((-633 (-229)) |has| |#1| (-1051)) ((-633 (-391)) |has| |#1| (-1051)) ((-633 (-549)) |has| |#1| (-633 (-549))) ((-633 (-915 (-391))) |has| |#1| (-633 (-915 (-391)))) ((-633 (-915 (-560))) |has| |#1| (-633 (-915 (-560)))) ((-236 $) -2173 (|has| |#1| (-239)) (|has| |#1| (-240))) ((-234 |#1|) . T) ((-240) |has| |#1| (-240)) ((-239) -2173 (|has| |#1| (-239)) (|has| |#1| (-240))) ((-274 |#1|) . T) ((-250) . T) ((-298 |#1| $) |has| |#1| (-298 |#1| |#1|)) ((-302) . T) ((-319) . T) ((-321 |#1|) |has| |#1| (-321 |#1|)) ((-376) . T) ((-351 |#1|) . T) ((-390 |#1|) . T) ((-414 |#1|) . T) ((-466) . T) ((-528 (-1207) |#1|) |has| |#1| (-528 (-1207) |#1|)) ((-528 |#1| |#1|) |has| |#1| (-321 |#1|)) ((-571) . T) ((-668 #0#) . T) ((-668 (-560)) . T) ((-668 |#1|) . T) ((-668 $) . T) ((-670 #0#) . T) ((-670 #2=(-560)) |has| |#1| (-660 (-560))) ((-670 |#1|) . T) ((-670 $) . T) ((-662 #0#) . T) ((-662 |#1|) . T) ((-662 $) . T) ((-660 #2#) |has| |#1| (-660 (-560))) ((-660 |#1|) . T) ((-739 #0#) . T) ((-739 |#1|) . T) ((-739 $) . T) ((-748) . T) ((-813) |has| |#1| (-842)) ((-814) |has| |#1| (-842)) ((-816) |has| |#1| (-842)) ((-819) |has| |#1| (-842)) ((-842) |has| |#1| (-842)) ((-870) |has| |#1| (-842)) ((-871) -2173 (|has| |#1| (-871)) (|has| |#1| (-842))) ((-874) -2173 (|has| |#1| (-871)) (|has| |#1| (-842))) ((-921 $ #3=(-1207)) -2173 (|has| |#1| (-929 (-1207))) (|has| |#1| (-927 (-1207)))) ((-927 (-1207)) |has| |#1| (-927 (-1207))) ((-929 #3#) -2173 (|has| |#1| (-929 (-1207))) (|has| |#1| (-927 (-1207)))) ((-911 (-391)) |has| |#1| (-911 (-391))) ((-911 (-560)) |has| |#1| (-911 (-560))) ((-909 |#1|) . T) ((-939) |has| |#1| (-939)) ((-950) . T) ((-1051) |has| |#1| (-1051)) ((-1069 (-421 (-560))) |has| |#1| (-1069 (-560))) ((-1069 (-560)) |has| |#1| (-1069 (-560))) ((-1069 #1#) |has| |#1| (-1069 (-1207))) ((-1069 |#1|) . T) ((-1082 #0#) . T) ((-1082 |#1|) . T) ((-1082 $) . T) ((-1087 #0#) . T) ((-1087 |#1|) . T) ((-1087 $) . T) ((-1080) . T) ((-1088) . T) ((-1143) . T) ((-1132) . 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T) ((-662 #1#) -2173 (|has| |#1| (-376)) (|has| |#1| (-38 (-421 (-560))))) ((-662 |#1|) |has| |#1| (-175)) ((-662 $) -2173 (|has| |#1| (-571)) (|has| |#1| (-376))) ((-739 #1#) -2173 (|has| |#1| (-376)) (|has| |#1| (-38 (-421 (-560))))) ((-739 |#1|) |has| |#1| (-175)) ((-739 $) -2173 (|has| |#1| (-571)) (|has| |#1| (-376))) ((-748) . T) ((-921 $ #2=(-1207)) -12 (|has| |#1| (-15 * (|#1| (-560) |#1|))) (|has| |#1| (-927 (-1207)))) ((-927 #2#) -12 (|has| |#1| (-15 * (|#1| (-560) |#1|))) (|has| |#1| (-927 (-1207)))) ((-929 #2#) -12 (|has| |#1| (-15 * (|#1| (-560) |#1|))) (|has| |#1| (-927 (-1207)))) ((-1004 |#1| #0# (-1113)) . T) ((-950) |has| |#1| (-376)) ((-1033) |has| |#1| (-38 (-421 (-560)))) ((-1082 #1#) -2173 (|has| |#1| (-376)) (|has| |#1| (-38 (-421 (-560))))) ((-1082 |#1|) . T) ((-1082 $) -2173 (|has| |#1| (-571)) (|has| |#1| (-376)) (|has| |#1| (-175))) ((-1087 #1#) -2173 (|has| |#1| (-376)) (|has| |#1| (-38 (-421 (-560))))) ((-1087 |#1|) . T) ((-1087 $) -2173 (|has| |#1| (-571)) (|has| |#1| (-376)) (|has| |#1| (-175))) ((-1080) . T) ((-1088) . T) ((-1143) . T) ((-1132) . T) ((-1233) |has| |#1| (-38 (-421 (-560)))) ((-1236) |has| |#1| (-38 (-421 (-560)))) ((-1247) . T) ((-1252) |has| |#1| (-376)) ((-1276 |#1| #0#) . 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T) ((-23) . T) ((-47 |#1| #0=(-560)) . T) ((-25) . T) ((-38 #1=(-421 (-560))) -2181 (|has| |#1| (-376)) (|has| |#1| (-38 (-421 (-560))))) ((-38 |#1|) |has| |#1| (-175)) ((-38 |#2|) |has| |#1| (-376)) ((-38 $) -2181 (|has| |#1| (-571)) (|has| |#1| (-376))) ((-35) |has| |#1| (-38 (-421 (-560)))) ((-95) |has| |#1| (-38 (-421 (-560)))) ((-102) . T) ((-111 #1# #1#) -2181 (|has| |#1| (-376)) (|has| |#1| (-38 (-421 (-560))))) ((-111 |#1| |#1|) . T) ((-111 |#2| |#2|) |has| |#1| (-376)) ((-111 $ $) -2181 (|has| |#1| (-571)) (|has| |#1| (-376)) (|has| |#1| (-175))) ((-133) . T) ((-147) -2181 (-12 (|has| |#1| (-376)) (|has| |#2| (-147))) (|has| |#1| (-147))) ((-149) -2181 (-12 (|has| |#1| (-376)) (|has| |#2| (-149))) (|has| |#1| (-149))) ((-635 #1#) -2181 (|has| |#1| (-376)) (|has| |#1| (-38 (-421 (-560))))) ((-635 (-560)) . T) ((-635 #2=(-1207)) -12 (|has| |#1| (-376)) (|has| |#2| (-1069 (-1207)))) ((-635 |#1|) |has| |#1| (-175)) ((-635 |#2|) . T) ((-635 $) -2181 (|has| |#1| (-571)) (|has| |#1| (-376))) ((-632 (-887)) . T) ((-175) -2181 (|has| |#1| (-571)) (|has| |#1| (-376)) (|has| |#1| (-175))) ((-633 (-229)) -12 (|has| |#1| (-376)) (|has| |#2| (-1051))) ((-633 (-391)) -12 (|has| |#1| (-376)) (|has| |#2| (-1051))) ((-633 (-549)) -12 (|has| |#1| (-376)) (|has| |#2| (-633 (-549)))) ((-633 (-915 (-391))) -12 (|has| |#1| (-376)) (|has| |#2| (-633 (-915 (-391))))) ((-633 (-915 (-560))) -12 (|has| |#1| (-376)) (|has| |#2| (-633 (-915 (-560))))) ((-236 $) -2181 (-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) -2181 (-12 (|has| |#1| (-376)) (|has| |#2| (-240))) (|has| |#1| (-15 * (|#1| (-560) |#1|)))) ((-239) -2181 (-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) (-1143)) ((-302) -2181 (|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 (-1207) |#2|) -12 (|has| |#1| (-376)) (|has| |#2| (-528 (-1207) |#2|))) ((-528 |#2| |#2|) -12 (|has| |#1| (-376)) (|has| |#2| (-321 |#2|))) ((-571) -2181 (|has| |#1| (-571)) (|has| |#1| (-376))) ((-668 #1#) -2181 (|has| |#1| (-376)) (|has| |#1| (-38 (-421 (-560))))) ((-668 (-560)) . T) ((-668 |#1|) . T) ((-668 |#2|) |has| |#1| (-376)) ((-668 $) . T) ((-670 #1#) -2181 (|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#) -2181 (|has| |#1| (-376)) (|has| |#1| (-38 (-421 (-560))))) ((-662 |#1|) |has| |#1| (-175)) ((-662 |#2|) |has| |#1| (-376)) ((-662 $) -2181 (|has| |#1| (-571)) (|has| |#1| (-376))) ((-660 #3#) -12 (|has| |#1| (-376)) (|has| |#2| (-660 (-560)))) ((-660 |#2|) |has| |#1| (-376)) ((-739 #1#) -2181 (|has| |#1| (-376)) (|has| |#1| (-38 (-421 (-560))))) ((-739 |#1|) |has| |#1| (-175)) ((-739 |#2|) |has| |#1| (-376)) ((-739 $) -2181 (|has| |#1| (-571)) (|has| |#1| (-376))) ((-748) . 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T) ((-950) |has| |#1| (-376)) ((-1022 |#2|) |has| |#1| (-376)) ((-1033) |has| |#1| (-38 (-421 (-560)))) ((-1051) -12 (|has| |#1| (-376)) (|has| |#2| (-1051))) ((-1069 (-421 (-560))) -12 (|has| |#1| (-376)) (|has| |#2| (-1069 (-560)))) ((-1069 (-560)) -12 (|has| |#1| (-376)) (|has| |#2| (-1069 (-560)))) ((-1069 #2#) -12 (|has| |#1| (-376)) (|has| |#2| (-1069 (-1207)))) ((-1069 |#2|) . T) ((-1082 #1#) -2181 (|has| |#1| (-376)) (|has| |#1| (-38 (-421 (-560))))) ((-1082 |#1|) . T) ((-1082 |#2|) |has| |#1| (-376)) ((-1082 $) -2181 (|has| |#1| (-571)) (|has| |#1| (-376)) (|has| |#1| (-175))) ((-1087 #1#) -2181 (|has| |#1| (-376)) (|has| |#1| (-38 (-421 (-560))))) ((-1087 |#1|) . T) ((-1087 |#2|) |has| |#1| (-376)) ((-1087 $) -2181 (|has| |#1| (-571)) (|has| |#1| (-376)) (|has| |#1| (-175))) ((-1080) . T) ((-1088) . T) ((-1143) . T) ((-1132) . T) ((-1182) -12 (|has| |#1| (-376)) (|has| |#2| (-1182))) ((-1233) |has| |#1| (-38 (-421 (-560)))) ((-1236) |has| |#1| (-38 (-421 (-560)))) ((-1247) . 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T) ((-23) . T) ((-47 |#1| #0=(-560)) . T) ((-25) . T) ((-38 #1=(-421 (-560))) -2173 (|has| |#1| (-376)) (|has| |#1| (-38 (-421 (-560))))) ((-38 |#1|) |has| |#1| (-175)) ((-38 |#2|) |has| |#1| (-376)) ((-38 $) -2173 (|has| |#1| (-571)) (|has| |#1| (-376))) ((-35) |has| |#1| (-38 (-421 (-560)))) ((-95) |has| |#1| (-38 (-421 (-560)))) ((-102) . T) ((-111 #1# #1#) -2173 (|has| |#1| (-376)) (|has| |#1| (-38 (-421 (-560))))) ((-111 |#1| |#1|) . T) ((-111 |#2| |#2|) |has| |#1| (-376)) ((-111 $ $) -2173 (|has| |#1| (-571)) (|has| |#1| (-376)) (|has| |#1| (-175))) ((-133) . T) ((-147) -2173 (-12 (|has| |#1| (-376)) (|has| |#2| (-147))) (|has| |#1| (-147))) ((-149) -2173 (-12 (|has| |#1| (-376)) (|has| |#2| (-149))) (|has| |#1| (-149))) ((-635 #1#) -2173 (|has| |#1| (-376)) (|has| |#1| (-38 (-421 (-560))))) ((-635 (-560)) . T) ((-635 #2=(-1207)) -12 (|has| |#1| (-376)) (|has| |#2| (-1069 (-1207)))) ((-635 |#1|) |has| |#1| (-175)) ((-635 |#2|) . T) ((-635 $) -2173 (|has| |#1| (-571)) (|has| |#1| (-376))) ((-632 (-887)) . T) ((-175) -2173 (|has| |#1| (-571)) (|has| |#1| (-376)) (|has| |#1| (-175))) ((-633 (-229)) -12 (|has| |#1| (-376)) (|has| |#2| (-1051))) ((-633 (-391)) -12 (|has| |#1| (-376)) (|has| |#2| (-1051))) ((-633 (-549)) -12 (|has| |#1| (-376)) (|has| |#2| (-633 (-549)))) ((-633 (-915 (-391))) -12 (|has| |#1| (-376)) (|has| |#2| (-633 (-915 (-391))))) ((-633 (-915 (-560))) -12 (|has| |#1| (-376)) (|has| |#2| (-633 (-915 (-560))))) ((-236 $) -2173 (-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) -2173 (-12 (|has| |#1| (-376)) (|has| |#2| (-240))) (|has| |#1| (-15 * (|#1| (-560) |#1|)))) ((-239) -2173 (-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) (-1143)) ((-302) -2173 (|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 (-1207) |#2|) -12 (|has| |#1| (-376)) (|has| |#2| (-528 (-1207) |#2|))) ((-528 |#2| |#2|) -12 (|has| |#1| (-376)) (|has| |#2| (-321 |#2|))) ((-571) -2173 (|has| |#1| (-571)) (|has| |#1| (-376))) ((-668 #1#) -2173 (|has| |#1| (-376)) (|has| |#1| (-38 (-421 (-560))))) ((-668 (-560)) . T) ((-668 |#1|) . T) ((-668 |#2|) |has| |#1| (-376)) ((-668 $) . T) ((-670 #1#) -2173 (|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#) -2173 (|has| |#1| (-376)) (|has| |#1| (-38 (-421 (-560))))) ((-662 |#1|) |has| |#1| (-175)) ((-662 |#2|) |has| |#1| (-376)) ((-662 $) -2173 (|has| |#1| (-571)) (|has| |#1| (-376))) ((-660 #3#) -12 (|has| |#1| (-376)) (|has| |#2| (-660 (-560)))) ((-660 |#2|) |has| |#1| (-376)) ((-739 #1#) -2173 (|has| |#1| (-376)) (|has| |#1| (-38 (-421 (-560))))) ((-739 |#1|) |has| |#1| (-175)) ((-739 |#2|) |has| |#1| (-376)) ((-739 $) -2173 (|has| |#1| (-571)) (|has| |#1| (-376))) ((-748) . T) ((-813) -12 (|has| |#1| (-376)) (|has| |#2| (-842))) ((-814) -12 (|has| |#1| (-376)) (|has| |#2| (-842))) ((-816) -12 (|has| |#1| (-376)) (|has| |#2| (-842))) ((-819) -12 (|has| |#1| (-376)) (|has| |#2| (-842))) ((-842) -12 (|has| |#1| (-376)) (|has| |#2| (-842))) ((-870) -12 (|has| |#1| (-376)) (|has| |#2| (-842))) ((-871) -2173 (-12 (|has| |#1| (-376)) (|has| |#2| (-871))) (-12 (|has| |#1| (-376)) (|has| |#2| (-842)))) ((-874) -2173 (-12 (|has| |#1| (-376)) (|has| |#2| (-871))) (-12 (|has| |#1| (-376)) (|has| |#2| (-842)))) ((-921 $ #4=(-1207)) -2173 (-12 (|has| |#1| (-376)) (|has| |#2| (-929 (-1207)))) (-12 (|has| |#1| (-376)) (|has| |#2| (-927 (-1207)))) (-12 (|has| |#1| (-15 * (|#1| (-560) |#1|))) (|has| |#1| (-927 (-1207))))) ((-927 (-1207)) -2173 (-12 (|has| |#1| (-376)) (|has| |#2| (-927 (-1207)))) (-12 (|has| |#1| (-15 * (|#1| (-560) |#1|))) (|has| |#1| (-927 (-1207))))) ((-929 #4#) -2173 (-12 (|has| |#1| (-376)) (|has| |#2| (-929 (-1207)))) (-12 (|has| |#1| (-376)) (|has| |#2| (-927 (-1207)))) (-12 (|has| |#1| (-15 * (|#1| (-560) |#1|))) (|has| |#1| (-927 (-1207))))) ((-911 (-391)) -12 (|has| |#1| (-376)) (|has| |#2| (-911 (-391)))) ((-911 (-560)) -12 (|has| |#1| (-376)) (|has| |#2| (-911 (-560)))) ((-909 |#2|) |has| |#1| (-376)) ((-939) -12 (|has| |#1| (-376)) (|has| |#2| (-939))) ((-1004 |#1| #0# (-1113)) . T) ((-950) |has| |#1| (-376)) ((-1022 |#2|) |has| |#1| (-376)) ((-1033) |has| |#1| (-38 (-421 (-560)))) ((-1051) -12 (|has| |#1| (-376)) (|has| |#2| (-1051))) ((-1069 (-421 (-560))) -12 (|has| |#1| (-376)) (|has| |#2| (-1069 (-560)))) ((-1069 (-560)) -12 (|has| |#1| (-376)) (|has| |#2| (-1069 (-560)))) ((-1069 #2#) -12 (|has| |#1| (-376)) (|has| |#2| (-1069 (-1207)))) ((-1069 |#2|) . T) ((-1082 #1#) -2173 (|has| |#1| (-376)) (|has| |#1| (-38 (-421 (-560))))) ((-1082 |#1|) . T) ((-1082 |#2|) |has| |#1| (-376)) ((-1082 $) -2173 (|has| |#1| (-571)) (|has| |#1| (-376)) (|has| |#1| (-175))) ((-1087 #1#) -2173 (|has| |#1| (-376)) (|has| |#1| (-38 (-421 (-560))))) ((-1087 |#1|) . T) ((-1087 |#2|) |has| |#1| (-376)) ((-1087 $) -2173 (|has| |#1| (-571)) (|has| |#1| (-376)) (|has| |#1| (-175))) ((-1080) . T) ((-1088) . T) ((-1143) . T) ((-1132) . T) ((-1182) -12 (|has| |#1| (-376)) (|has| |#2| (-1182))) ((-1233) |has| |#1| (-38 (-421 (-560)))) ((-1236) |has| |#1| (-38 (-421 (-560)))) ((-1247) . T) ((-1252) |has| |#1| (-376)) ((-1259 |#1|) . T) ((-1276 |#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 $) -2181 (|has| |#1| (-939)) (|has| |#1| (-571)) (|has| |#1| (-466)) (|has| |#1| (-376))) ((-102) . T) ((-111 #1# #1#) |has| |#1| (-38 (-421 (-560)))) ((-111 |#1| |#1|) . T) ((-111 $ $) -2181 (|has| |#1| (-939)) (|has| |#1| (-571)) (|has| |#1| (-466)) (|has| |#1| (-376)) (|has| |#1| (-175))) ((-133) . T) ((-147) |has| |#1| (-147)) ((-149) |has| |#1| (-149)) ((-635 #1#) -2181 (|has| |#1| (-1069 (-421 (-560)))) (|has| |#1| (-38 (-421 (-560))))) ((-635 (-560)) . T) ((-635 #2=(-1113)) . T) ((-635 |#1|) . T) ((-635 $) -2181 (|has| |#1| (-939)) (|has| |#1| (-571)) (|has| |#1| (-466)) (|has| |#1| (-376))) ((-632 (-887)) . T) ((-175) -2181 (|has| |#1| (-939)) (|has| |#1| (-571)) (|has| |#1| (-466)) (|has| |#1| (-376)) (|has| |#1| (-175))) ((-633 (-549)) -12 (|has| (-1113) (-633 (-549))) (|has| |#1| (-633 (-549)))) ((-633 (-915 (-391))) -12 (|has| (-1113) (-633 (-915 (-391)))) (|has| |#1| (-633 (-915 (-391))))) ((-633 (-915 (-560))) -12 (|has| (-1113) (-633 (-915 (-560)))) (|has| |#1| (-633 (-915 (-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) -2181 (|has| |#1| (-939)) (|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) -2181 (|has| |#1| (-939)) (|has| |#1| (-466)) (|has| |#1| (-376))) ((-528 #2# |#1|) . T) ((-528 #2# $) . T) ((-528 $ $) . T) ((-571) -2181 (|has| |#1| (-939)) (|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 $) -2181 (|has| |#1| (-939)) (|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 $) -2181 (|has| |#1| (-939)) (|has| |#1| (-571)) (|has| |#1| (-466)) (|has| |#1| (-376))) ((-748) . T) ((-921 $ #2#) . T) ((-921 $ #4=(-1207)) -2181 (|has| |#1| (-929 (-1207))) (|has| |#1| (-927 (-1207)))) ((-927 #2#) . T) ((-927 (-1207)) |has| |#1| (-927 (-1207))) ((-929 #2#) . T) ((-929 #4#) -2181 (|has| |#1| (-929 (-1207))) (|has| |#1| (-927 (-1207)))) ((-911 (-391)) -12 (|has| (-1113) (-911 (-391))) (|has| |#1| (-911 (-391)))) ((-911 (-560)) -12 (|has| (-1113) (-911 (-560))) (|has| |#1| (-911 (-560)))) ((-979 |#1| #0# #2#) . T) ((-939) |has| |#1| (-939)) ((-950) |has| |#1| (-376)) ((-1069 (-421 (-560))) |has| |#1| (-1069 (-421 (-560)))) ((-1069 (-560)) |has| |#1| (-1069 (-560))) ((-1069 #2#) . T) ((-1069 |#1|) . T) ((-1082 #1#) |has| |#1| (-38 (-421 (-560)))) ((-1082 |#1|) . T) ((-1082 $) -2181 (|has| |#1| (-939)) (|has| |#1| (-571)) (|has| |#1| (-466)) (|has| |#1| (-376)) (|has| |#1| (-175))) ((-1087 #1#) |has| |#1| (-38 (-421 (-560)))) ((-1087 |#1|) . T) ((-1087 $) -2181 (|has| |#1| (-939)) (|has| |#1| (-571)) (|has| |#1| (-466)) (|has| |#1| (-376)) (|has| |#1| (-175))) ((-1080) . T) ((-1088) . T) ((-1143) . T) ((-1132) . T) ((-1182) |has| |#1| (-1182)) ((-1247) . 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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 $) -2173 (|has| |#1| (-939)) (|has| |#1| (-571)) (|has| |#1| (-466)) (|has| |#1| (-376))) ((-102) . T) ((-111 #1# #1#) |has| |#1| (-38 (-421 (-560)))) ((-111 |#1| |#1|) . T) ((-111 $ $) -2173 (|has| |#1| (-939)) (|has| |#1| (-571)) (|has| |#1| (-466)) (|has| |#1| (-376)) (|has| |#1| (-175))) ((-133) . T) ((-147) |has| |#1| (-147)) ((-149) |has| |#1| (-149)) ((-635 #1#) -2173 (|has| |#1| (-1069 (-421 (-560)))) (|has| |#1| (-38 (-421 (-560))))) ((-635 (-560)) . T) ((-635 #2=(-1113)) . T) ((-635 |#1|) . T) ((-635 $) -2173 (|has| |#1| (-939)) (|has| |#1| (-571)) (|has| |#1| (-466)) (|has| |#1| (-376))) ((-632 (-887)) . T) ((-175) -2173 (|has| |#1| (-939)) (|has| |#1| (-571)) (|has| |#1| (-466)) (|has| |#1| (-376)) (|has| |#1| (-175))) ((-633 (-549)) -12 (|has| (-1113) (-633 (-549))) (|has| |#1| (-633 (-549)))) ((-633 (-915 (-391))) -12 (|has| (-1113) (-633 (-915 (-391)))) (|has| |#1| (-633 (-915 (-391))))) ((-633 (-915 (-560))) -12 (|has| (-1113) (-633 (-915 (-560)))) (|has| |#1| (-633 (-915 (-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) -2173 (|has| |#1| (-939)) (|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) -2173 (|has| |#1| (-939)) (|has| |#1| (-466)) (|has| |#1| (-376))) ((-528 #2# |#1|) . T) ((-528 #2# $) . T) ((-528 $ $) . T) ((-571) -2173 (|has| |#1| (-939)) (|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 $) -2173 (|has| |#1| (-939)) (|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 $) -2173 (|has| |#1| (-939)) (|has| |#1| (-571)) (|has| |#1| (-466)) (|has| |#1| (-376))) ((-748) . T) ((-921 $ #2#) . T) ((-921 $ #4=(-1207)) -2173 (|has| |#1| (-929 (-1207))) (|has| |#1| (-927 (-1207)))) ((-927 #2#) . T) ((-927 (-1207)) |has| |#1| (-927 (-1207))) ((-929 #2#) . T) ((-929 #4#) -2173 (|has| |#1| (-929 (-1207))) (|has| |#1| (-927 (-1207)))) ((-911 (-391)) -12 (|has| (-1113) (-911 (-391))) (|has| |#1| (-911 (-391)))) ((-911 (-560)) -12 (|has| (-1113) (-911 (-560))) (|has| |#1| (-911 (-560)))) ((-979 |#1| #0# #2#) . T) ((-939) |has| |#1| (-939)) ((-950) |has| |#1| (-376)) ((-1069 (-421 (-560))) |has| |#1| (-1069 (-421 (-560)))) ((-1069 (-560)) |has| |#1| (-1069 (-560))) ((-1069 #2#) . T) ((-1069 |#1|) . T) ((-1082 #1#) |has| |#1| (-38 (-421 (-560)))) ((-1082 |#1|) . T) ((-1082 $) -2173 (|has| |#1| (-939)) (|has| |#1| (-571)) (|has| |#1| (-466)) (|has| |#1| (-376)) (|has| |#1| (-175))) ((-1087 #1#) |has| |#1| (-38 (-421 (-560)))) ((-1087 |#1|) . T) ((-1087 $) -2173 (|has| |#1| (-939)) (|has| |#1| (-571)) (|has| |#1| (-466)) (|has| |#1| (-376)) (|has| |#1| (-175))) ((-1080) . T) ((-1088) . T) ((-1143) . T) ((-1132) . T) ((-1182) |has| |#1| (-1182)) ((-1247) . 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T) ((-662 #1#) -2173 (|has| |#1| (-376)) (|has| |#1| (-38 (-421 (-560))))) ((-662 |#1|) |has| |#1| (-175)) ((-662 $) -2173 (|has| |#1| (-571)) (|has| |#1| (-376))) ((-739 #1#) -2173 (|has| |#1| (-376)) (|has| |#1| (-38 (-421 (-560))))) ((-739 |#1|) |has| |#1| (-175)) ((-739 $) -2173 (|has| |#1| (-571)) (|has| |#1| (-376))) ((-748) . T) ((-921 $ #2=(-1207)) -12 (|has| |#1| (-15 * (|#1| (-421 (-560)) |#1|))) (|has| |#1| (-927 (-1207)))) ((-927 #2#) -12 (|has| |#1| (-15 * (|#1| (-421 (-560)) |#1|))) (|has| |#1| (-927 (-1207)))) ((-929 #2#) -12 (|has| |#1| (-15 * (|#1| (-421 (-560)) |#1|))) (|has| |#1| (-927 (-1207)))) ((-1004 |#1| #0# (-1113)) . T) ((-950) |has| |#1| (-376)) ((-1033) |has| |#1| (-38 (-421 (-560)))) ((-1082 #1#) -2173 (|has| |#1| (-376)) (|has| |#1| (-38 (-421 (-560))))) ((-1082 |#1|) . T) ((-1082 $) -2173 (|has| |#1| (-571)) (|has| |#1| (-376)) (|has| |#1| (-175))) ((-1087 #1#) -2173 (|has| |#1| (-376)) (|has| |#1| (-38 (-421 (-560))))) ((-1087 |#1|) . 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T) ((-23) . T) ((-47 |#1| #0=(-421 (-560))) . T) ((-25) . T) ((-38 #1=(-421 (-560))) -2181 (|has| |#1| (-376)) (|has| |#1| (-38 (-421 (-560))))) ((-38 |#1|) |has| |#1| (-175)) ((-38 $) -2181 (|has| |#1| (-571)) (|has| |#1| (-376))) ((-35) |has| |#1| (-38 (-421 (-560)))) ((-95) |has| |#1| (-38 (-421 (-560)))) ((-102) . T) ((-111 #1# #1#) -2181 (|has| |#1| (-376)) (|has| |#1| (-38 (-421 (-560))))) ((-111 |#1| |#1|) . T) ((-111 $ $) -2181 (|has| |#1| (-571)) (|has| |#1| (-376)) (|has| |#1| (-175))) ((-133) . T) ((-147) |has| |#1| (-147)) ((-149) |has| |#1| (-149)) ((-635 #1#) -2181 (|has| |#1| (-376)) (|has| |#1| (-38 (-421 (-560))))) ((-635 (-560)) . T) ((-635 |#1|) |has| |#1| (-175)) ((-635 |#2|) . T) ((-635 $) -2181 (|has| |#1| (-571)) (|has| |#1| (-376))) ((-632 (-887)) . T) ((-175) -2181 (|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)) (-1143)) ((-302) -2181 (|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) -2181 (|has| |#1| (-571)) (|has| |#1| (-376))) ((-668 #1#) -2181 (|has| |#1| (-376)) (|has| |#1| (-38 (-421 (-560))))) ((-668 (-560)) . T) ((-668 |#1|) . T) ((-668 $) . T) ((-670 #1#) -2181 (|has| |#1| (-376)) (|has| |#1| (-38 (-421 (-560))))) ((-670 |#1|) . T) ((-670 $) . T) ((-662 #1#) -2181 (|has| |#1| (-376)) (|has| |#1| (-38 (-421 (-560))))) ((-662 |#1|) |has| |#1| (-175)) ((-662 $) -2181 (|has| |#1| (-571)) (|has| |#1| (-376))) ((-739 #1#) -2181 (|has| |#1| (-376)) (|has| |#1| (-38 (-421 (-560))))) ((-739 |#1|) |has| |#1| (-175)) ((-739 $) -2181 (|has| |#1| (-571)) (|has| |#1| (-376))) ((-748) . T) ((-921 $ #2=(-1207)) -12 (|has| |#1| (-15 * (|#1| (-421 (-560)) |#1|))) (|has| |#1| (-927 (-1207)))) ((-927 #2#) -12 (|has| |#1| (-15 * (|#1| (-421 (-560)) |#1|))) (|has| |#1| (-927 (-1207)))) ((-929 #2#) -12 (|has| |#1| (-15 * (|#1| (-421 (-560)) |#1|))) (|has| |#1| (-927 (-1207)))) ((-1004 |#1| #0# (-1113)) . T) ((-950) |has| |#1| (-376)) ((-1033) |has| |#1| (-38 (-421 (-560)))) ((-1069 |#2|) . T) ((-1082 #1#) -2181 (|has| |#1| (-376)) (|has| |#1| (-38 (-421 (-560))))) ((-1082 |#1|) . T) ((-1082 $) -2181 (|has| |#1| (-571)) (|has| |#1| (-376)) (|has| |#1| (-175))) ((-1087 #1#) -2181 (|has| |#1| (-376)) (|has| |#1| (-38 (-421 (-560))))) ((-1087 |#1|) . T) ((-1087 $) -2181 (|has| |#1| (-571)) (|has| |#1| (-376)) (|has| |#1| (-175))) ((-1080) . T) ((-1088) . T) ((-1143) . T) ((-1132) . T) ((-1233) |has| |#1| (-38 (-421 (-560)))) ((-1236) |has| |#1| (-38 (-421 (-560)))) ((-1247) . T) ((-1252) |has| |#1| (-376)) ((-1276 |#1| #0#) . T) ((-1280 |#1|) . 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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 $) |has| |#1| (-571)) ((-35) |has| |#1| (-38 (-421 (-560)))) ((-95) |has| |#1| (-38 (-421 (-560)))) ((-102) . T) ((-111 #1# #1#) |has| |#1| (-38 (-421 (-560)))) ((-111 |#1| |#1|) . T) ((-111 $ $) -2181 (|has| |#1| (-571)) (|has| |#1| (-175))) ((-133) . T) ((-147) |has| |#1| (-147)) ((-149) |has| |#1| (-149)) ((-635 #1#) |has| |#1| (-38 (-421 (-560)))) ((-635 (-560)) . T) ((-635 |#1|) |has| |#1| (-175)) ((-635 $) |has| |#1| (-571)) ((-632 (-887)) . T) ((-175) -2181 (|has| |#1| (-571)) (|has| |#1| (-175))) ((-236 $) |has| |#1| (-15 * (|#1| (-793) |#1|))) ((-240) |has| |#1| (-15 * (|#1| (-793) |#1|))) ((-239) |has| |#1| (-15 * (|#1| (-793) |#1|))) ((-296) |has| |#1| (-38 (-421 (-560)))) ((-298 #0# |#1|) . 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T) ((-1082 $) -2181 (|has| |#1| (-571)) (|has| |#1| (-175))) ((-1087 #1#) |has| |#1| (-38 (-421 (-560)))) ((-1087 |#1|) . T) ((-1087 $) -2181 (|has| |#1| (-571)) (|has| |#1| (-175))) ((-1080) . T) ((-1088) . T) ((-1143) . T) ((-1132) . T) ((-1233) |has| |#1| (-38 (-421 (-560)))) ((-1236) |has| |#1| (-38 (-421 (-560)))) ((-1247) . T) ((-1276 |#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 $) |has| |#1| (-571)) ((-35) |has| |#1| (-38 (-421 (-560)))) ((-95) |has| |#1| (-38 (-421 (-560)))) ((-102) . T) ((-111 #1# #1#) |has| |#1| (-38 (-421 (-560)))) ((-111 |#1| |#1|) . T) ((-111 $ $) -2173 (|has| |#1| (-571)) (|has| |#1| (-175))) ((-133) . T) ((-147) |has| |#1| (-147)) ((-149) |has| |#1| (-149)) ((-635 #1#) |has| |#1| (-38 (-421 (-560)))) ((-635 (-560)) . T) ((-635 |#1|) |has| |#1| (-175)) ((-635 $) |has| |#1| (-571)) ((-632 (-887)) . T) ((-175) -2173 (|has| |#1| (-571)) (|has| |#1| (-175))) ((-236 $) |has| |#1| (-15 * (|#1| (-793) |#1|))) ((-240) |has| |#1| (-15 * (|#1| (-793) |#1|))) ((-239) |has| |#1| (-15 * (|#1| (-793) |#1|))) ((-296) |has| |#1| (-38 (-421 (-560)))) ((-298 #0# |#1|) . 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T) ((-1082 $) -2173 (|has| |#1| (-571)) (|has| |#1| (-175))) ((-1087 #1#) |has| |#1| (-38 (-421 (-560)))) ((-1087 |#1|) . T) ((-1087 $) -2173 (|has| |#1| (-571)) (|has| |#1| (-175))) ((-1080) . T) ((-1088) . T) ((-1143) . T) ((-1132) . T) ((-1233) |has| |#1| (-38 (-421 (-560)))) ((-1236) |has| |#1| (-38 (-421 (-560)))) ((-1247) . T) ((-1276 |#1| #0#) . 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3473048 NIL NIL NIL NIL (NIL) -8 NIL NIL NIL) (-2 3473023 3473028 3473033 NIL NIL NIL NIL (NIL) -8 NIL NIL NIL) (-1 3473008 3473013 3473018 NIL NIL NIL NIL (NIL) -8 NIL NIL NIL) (0 3472993 3472998 3473003 NIL NIL NIL NIL (NIL) -8 NIL NIL NIL) (-1327 3471980 3472868 3472945 "ZMOD" 3472950 NIL ZMOD (NIL NIL) -8 NIL NIL NIL) (-1326 3471016 3471198 3471421 "ZLINDEP" 3471812 NIL ZLINDEP (NIL T) -7 NIL NIL NIL) (-1325 3460178 3462084 3464056 "ZDSOLVE" 3469146 NIL ZDSOLVE (NIL T NIL NIL) -7 NIL NIL NIL) (-1324 3459412 3459565 3459754 "YSTREAM" 3460024 NIL YSTREAM (NIL T) -7 NIL NIL NIL) (-1323 3458772 3459081 3459196 "YDIAGRAM" 3459319 T YDIAGRAM (NIL) -8 NIL NIL NIL) (-1322 3456220 3458073 3458277 "XRPOLY" 3458615 NIL XRPOLY (NIL T T) -8 NIL NIL NIL) (-1321 3452487 3454091 3454666 "XPR" 3455692 NIL XPR (NIL T T) -8 NIL NIL NIL) (-1320 3449818 3451494 3451549 "XPOLYC" 3451837 NIL XPOLYC (NIL T T) -9 NIL 3451950 NIL) (-1319 3447213 3449149 3449353 "XPOLY" 3449649 NIL XPOLY (NIL T) -8 NIL NIL NIL) (-1318 3443159 3445730 3446118 "XPBWPOLY" 3446871 NIL XPBWPOLY (NIL T T) -8 NIL NIL NIL) (-1317 3438051 3439630 3439685 "XFALG" 3441857 NIL XFALG (NIL T T) -9 NIL 3442646 NIL) (-1316 3433314 3436027 3436069 "XF" 3436690 NIL XF (NIL T) -9 NIL 3437090 NIL) (-1315 3432911 3433023 3433192 "XF-" 3433197 NIL XF- (NIL T T) -8 NIL NIL NIL) (-1314 3432026 3432148 3432353 "XEXPPKG" 3432803 NIL XEXPPKG (NIL T T T) -7 NIL NIL NIL) (-1313 3429767 3431876 3431972 "XDPOLY" 3431977 NIL XDPOLY (NIL T T) -8 NIL NIL NIL) (-1312 3428422 3429160 3429203 "XALG" 3429208 NIL XALG (NIL T) -9 NIL 3429319 NIL) (-1311 3421332 3426399 3426893 "WUTSET" 3428014 NIL WUTSET (NIL T T T T) -8 NIL NIL NIL) (-1310 3419434 3420384 3420707 "WP" 3421143 NIL WP (NIL T T T T NIL NIL NIL) -8 NIL NIL NIL) (-1309 3418982 3419256 3419326 "WHILEAST" 3419386 T WHILEAST (NIL) -8 NIL NIL NIL) (-1308 3418394 3418699 3418793 "WHEREAST" 3418910 T WHEREAST (NIL) -8 NIL NIL NIL) (-1307 3417268 3417478 3417773 "WFFINTBS" 3418191 NIL WFFINTBS (NIL T T T T) -7 NIL NIL NIL) (-1306 3415136 3415599 3416061 "WEIER" 3416840 NIL WEIER (NIL T) -7 NIL NIL NIL) (-1305 3414060 3414618 3414660 "VSPACE" 3414796 NIL VSPACE (NIL T) -9 NIL 3414870 NIL) (-1304 3413892 3413925 3414016 "VSPACE-" 3414021 NIL VSPACE- (NIL T T) -8 NIL NIL NIL) (-1303 3413689 3413743 3413811 "VOID" 3413846 T VOID (NIL) -8 NIL NIL NIL) (-1302 3409957 3410752 3411489 "VIEWDEF" 3412974 T VIEWDEF (NIL) -7 NIL NIL NIL) (-1301 3398901 3401505 3403678 "VIEW3D" 3407806 T VIEW3D (NIL) -8 NIL NIL NIL) (-1300 3390918 3392812 3394391 "VIEW2D" 3397344 T VIEW2D (NIL) -8 NIL NIL NIL) (-1299 3389018 3389413 3389819 "VIEW" 3390534 T VIEW (NIL) -7 NIL NIL NIL) (-1298 3387571 3387854 3388172 "VECTOR2" 3388748 NIL VECTOR2 (NIL T T) -7 NIL NIL NIL) (-1297 3382477 3387341 3387433 "VECTOR" 3387514 NIL VECTOR (NIL T) -8 NIL NIL NIL) (-1296 3375422 3380181 3380224 "VECTCAT" 3381219 NIL VECTCAT (NIL T) -9 NIL 3381806 NIL) (-1295 3374364 3374690 3375080 "VECTCAT-" 3375085 NIL VECTCAT- (NIL T T) -8 NIL NIL NIL) (-1294 3373770 3374015 3374135 "VARIABLE" 3374279 NIL VARIABLE (NIL NIL) -8 NIL NIL NIL) (-1293 3373703 3373708 3373738 "UTYPE" 3373743 T UTYPE (NIL) -9 NIL NIL NIL) (-1292 3372511 3372687 3372949 "UTSODETL" 3373529 NIL UTSODETL (NIL T T T T) -7 NIL NIL NIL) (-1291 3369903 3370411 3370935 "UTSODE" 3372052 NIL UTSODE (NIL T T) -7 NIL NIL NIL) (-1290 3359906 3365836 3365879 "UTSCAT" 3366991 NIL UTSCAT (NIL T) -9 NIL 3367749 NIL) (-1289 3357032 3357976 3358965 "UTSCAT-" 3358970 NIL UTSCAT- (NIL T T) -8 NIL NIL NIL) (-1288 3356653 3356702 3356835 "UTS2" 3356983 NIL UTS2 (NIL T T T T) -7 NIL NIL NIL) (-1287 3347963 3354414 3354894 "UTS" 3356231 NIL UTS (NIL T NIL NIL) -8 NIL NIL NIL) (-1286 3341830 3344773 3344816 "URAGG" 3346886 NIL URAGG (NIL T) -9 NIL 3347609 NIL) (-1285 3338553 3339632 3340755 "URAGG-" 3340760 NIL URAGG- (NIL T T) -8 NIL NIL NIL) (-1284 3333922 3337188 3337653 "UPXSSING" 3338217 NIL UPXSSING (NIL T T NIL NIL) -8 NIL NIL NIL) (-1283 3326337 3333826 3333898 "UPXSCONS" 3333903 NIL UPXSCONS (NIL T T) -8 NIL NIL NIL) (-1282 3315081 3322539 3322601 "UPXSCCA" 3323175 NIL UPXSCCA (NIL T T) -9 NIL 3323408 NIL) (-1281 3314701 3314804 3314978 "UPXSCCA-" 3314983 NIL UPXSCCA- (NIL T T T) -8 NIL NIL NIL) (-1280 3303345 3310528 3310571 "UPXSCAT" 3311219 NIL UPXSCAT (NIL T) -9 NIL 3311828 NIL) (-1279 3302769 3302854 3303033 "UPXS2" 3303260 NIL UPXS2 (NIL T T NIL NIL NIL NIL) -7 NIL NIL NIL) (-1278 3294247 3302151 3302415 "UPXS" 3302563 NIL UPXS (NIL T NIL NIL) -8 NIL NIL NIL) (-1277 3292883 3293154 3293505 "UPSQFREE" 3293990 NIL UPSQFREE (NIL T T) -7 NIL NIL NIL) (-1276 3285707 3289149 3289204 "UPSCAT" 3290284 NIL UPSCAT (NIL T T) -9 NIL 3291050 NIL) (-1275 3284863 3285118 3285445 "UPSCAT-" 3285450 NIL UPSCAT- (NIL T T T) -8 NIL NIL NIL) (-1274 3284484 3284533 3284666 "UPOLYC2" 3284814 NIL UPOLYC2 (NIL T T T T) -7 NIL NIL NIL) (-1273 3268611 3277611 3277654 "UPOLYC" 3279755 NIL UPOLYC (NIL T) -9 NIL 3280976 NIL) (-1272 3259459 3262365 3265512 "UPOLYC-" 3265517 NIL UPOLYC- (NIL T T) -8 NIL NIL NIL) (-1271 3258780 3258905 3259069 "UPMP" 3259348 NIL UPMP (NIL T T) -7 NIL NIL NIL) (-1270 3258327 3258414 3258553 "UPDIVP" 3258693 NIL UPDIVP (NIL T T) -7 NIL NIL NIL) (-1269 3256865 3257144 3257460 "UPDECOMP" 3258076 NIL UPDECOMP (NIL T T) -7 NIL NIL NIL) (-1268 3256078 3256208 3256394 "UPCDEN" 3256749 NIL UPCDEN (NIL T T T) -7 NIL NIL NIL) (-1267 3255591 3255666 3255815 "UP2" 3256003 NIL UP2 (NIL NIL T NIL T) -7 NIL NIL NIL) (-1266 3246166 3255274 3255403 "UP" 3255510 NIL UP (NIL NIL T) -8 NIL NIL NIL) (-1265 3245371 3245508 3245713 "UNISEG2" 3246009 NIL UNISEG2 (NIL T T) -7 NIL NIL NIL) (-1264 3243724 3244575 3244852 "UNISEG" 3245129 NIL UNISEG (NIL T) -8 NIL NIL NIL) (-1263 3242766 3242964 3243190 "UNIFACT" 3243540 NIL UNIFACT (NIL T) -7 NIL NIL NIL) (-1262 3229476 3242670 3242742 "ULSCONS" 3242747 NIL ULSCONS (NIL T T) -8 NIL NIL NIL) (-1261 3209272 3222556 3222618 "ULSCCAT" 3223256 NIL ULSCCAT (NIL T T) -9 NIL 3223545 NIL) (-1260 3208268 3208567 3208955 "ULSCCAT-" 3208960 NIL ULSCCAT- (NIL T T T) -8 NIL NIL NIL) (-1259 3196709 3203814 3203857 "ULSCAT" 3204720 NIL ULSCAT (NIL T) -9 NIL 3205451 NIL) (-1258 3196133 3196218 3196397 "ULS2" 3196624 NIL ULS2 (NIL T T NIL NIL NIL NIL) -7 NIL NIL NIL) (-1257 3177943 3195445 3195687 "ULS" 3195949 NIL ULS (NIL T NIL NIL) -8 NIL NIL NIL) (-1256 3176862 3177562 3177676 "UINT8" 3177787 T UINT8 (NIL) -8 NIL NIL 3177879) (-1255 3175780 3176480 3176594 "UINT64" 3176705 T UINT64 (NIL) -8 NIL NIL 3176797) (-1254 3174698 3175398 3175512 "UINT32" 3175623 T UINT32 (NIL) -8 NIL NIL 3175715) (-1253 3173616 3174316 3174430 "UINT16" 3174541 T UINT16 (NIL) -8 NIL NIL 3174633) (-1252 3171695 3172862 3172892 "UFD" 3173104 T UFD (NIL) -9 NIL 3173218 NIL) (-1251 3171477 3171535 3171630 "UFD-" 3171635 NIL UFD- (NIL T) -8 NIL NIL NIL) (-1250 3170535 3170742 3170958 "UDVO" 3171283 T UDVO (NIL) -7 NIL NIL NIL) (-1249 3168301 3168760 3169231 "UDPO" 3170099 NIL UDPO (NIL T) -7 NIL NIL NIL) (-1248 3168013 3168256 3168287 "TYPEAST" 3168292 T TYPEAST (NIL) -8 NIL NIL NIL) (-1247 3167946 3167951 3167981 "TYPE" 3167986 T TYPE (NIL) -9 NIL NIL NIL) (-1246 3166899 3167119 3167359 "TWOFACT" 3167740 NIL TWOFACT (NIL T) -7 NIL NIL NIL) (-1245 3165874 3166308 3166543 "TUPLE" 3166699 NIL TUPLE (NIL T) -8 NIL NIL NIL) (-1244 3163511 3164084 3164623 "TUBETOOL" 3165357 T TUBETOOL (NIL) -7 NIL NIL NIL) (-1243 3162317 3162558 3162800 "TUBE" 3163304 NIL TUBE (NIL T) -8 NIL NIL NIL) (-1242 3150452 3155074 3155171 "TSETCAT" 3160440 NIL TSETCAT (NIL T T T T) -9 NIL 3161972 NIL) (-1241 3144920 3146784 3148675 "TSETCAT-" 3148680 NIL TSETCAT- (NIL T T T T T) -8 NIL NIL NIL) (-1240 3139099 3143892 3144175 "TS" 3144672 NIL TS (NIL T) -8 NIL NIL NIL) (-1239 3133572 3134585 3135514 "TRMANIP" 3138235 NIL TRMANIP (NIL T T) -7 NIL NIL NIL) (-1238 3133001 3133076 3133239 "TRIMAT" 3133504 NIL TRIMAT (NIL T T T T) -7 NIL NIL NIL) (-1237 3130813 3131104 3131461 "TRIGMNIP" 3132750 NIL TRIGMNIP (NIL T T) -7 NIL NIL NIL) (-1236 3130297 3130446 3130476 "TRIGCAT" 3130689 T TRIGCAT (NIL) -9 NIL NIL NIL) (-1235 3129942 3130045 3130186 "TRIGCAT-" 3130191 NIL TRIGCAT- (NIL T) -8 NIL NIL NIL) (-1234 3126556 3128800 3129081 "TREE" 3129696 NIL TREE (NIL T) -8 NIL NIL NIL) (-1233 3125662 3126358 3126388 "TRANFUN" 3126423 T TRANFUN (NIL) -9 NIL 3126489 NIL) (-1232 3124881 3125132 3125412 "TRANFUN-" 3125417 NIL TRANFUN- (NIL T) -8 NIL NIL NIL) (-1231 3124679 3124717 3124778 "TOPSP" 3124842 T TOPSP (NIL) -7 NIL NIL NIL) (-1230 3124009 3124142 3124296 "TOOLSIGN" 3124560 NIL TOOLSIGN (NIL T) -7 NIL NIL NIL) (-1229 3122523 3123186 3123425 "TEXTFILE" 3123792 T TEXTFILE (NIL) -8 NIL NIL NIL) (-1228 3122298 3122335 3122407 "TEX1" 3122486 NIL TEX1 (NIL T) -7 NIL NIL NIL) (-1227 3120102 3120751 3121180 "TEX" 3121891 T TEX (NIL) -8 NIL NIL NIL) (-1226 3119738 3119813 3119903 "TEMUTL" 3120034 T TEMUTL (NIL) -7 NIL NIL NIL) (-1225 3117832 3118172 3118497 "TBCMPPK" 3119461 NIL TBCMPPK (NIL T T) -7 NIL NIL NIL) (-1224 3109152 3115918 3115974 "TBAGG" 3116374 NIL TBAGG (NIL T T) -9 NIL 3116585 NIL) (-1223 3104036 3105710 3107464 "TBAGG-" 3107469 NIL TBAGG- (NIL T T T) -8 NIL NIL NIL) (-1222 3103402 3103527 3103672 "TANEXP" 3103925 NIL TANEXP (NIL T) -7 NIL NIL NIL) (-1221 3102853 3103177 3103267 "TALGOP" 3103347 NIL TALGOP (NIL T) -8 NIL NIL NIL) (-1220 3102247 3102364 3102502 "TABLEAU" 3102750 NIL TABLEAU (NIL T) -8 NIL NIL NIL) (-1219 3095261 3102104 3102197 "TABLE" 3102202 NIL TABLE (NIL T T) -8 NIL NIL NIL) (-1218 3089791 3091089 3092337 "TABLBUMP" 3094047 NIL TABLBUMP (NIL T) -7 NIL NIL NIL) (-1217 3089001 3089160 3089341 "SYSTEM" 3089632 T SYSTEM (NIL) -8 NIL NIL NIL) (-1216 3085406 3086159 3086942 "SYSSOLP" 3088252 NIL SYSSOLP (NIL T) -7 NIL NIL NIL) (-1215 3085168 3085361 3085392 "SYSPTR" 3085397 T SYSPTR (NIL) -8 NIL NIL NIL) (-1214 3084007 3084699 3084825 "SYSNNI" 3085011 NIL SYSNNI (NIL NIL) -8 NIL NIL 3085103) (-1213 3083214 3083769 3083848 "SYSINT" 3083908 NIL SYSINT (NIL NIL) -8 NIL NIL 3083953) (-1212 3079312 3080492 3081202 "SYNTAX" 3082526 T SYNTAX (NIL) -8 NIL NIL NIL) (-1211 3076392 3077072 3077704 "SYMTAB" 3078702 T SYMTAB (NIL) -8 NIL NIL NIL) (-1210 3071491 3072543 3073526 "SYMS" 3075431 T SYMS (NIL) -8 NIL NIL NIL) (-1209 3068390 3070942 3071175 "SYMPOLY" 3071293 NIL SYMPOLY (NIL T) -8 NIL NIL NIL) (-1208 3067895 3067982 3068105 "SYMFUNC" 3068302 NIL SYMFUNC (NIL T) -7 NIL NIL NIL) (-1207 3063693 3065207 3066020 "SYMBOL" 3067104 T SYMBOL (NIL) -8 NIL NIL NIL) (-1206 3057166 3058921 3060641 "SWITCH" 3061995 T SWITCH (NIL) -8 NIL NIL NIL) (-1205 3049920 3056122 3056416 "SUTS" 3056930 NIL SUTS (NIL T NIL NIL) -8 NIL NIL NIL) (-1204 3041398 3049302 3049566 "SUPXS" 3049714 NIL SUPXS (NIL T NIL NIL) -8 NIL NIL NIL) (-1203 3040545 3040684 3040901 "SUPFRACF" 3041266 NIL SUPFRACF (NIL T T T T) -7 NIL NIL NIL) (-1202 3040160 3040225 3040338 "SUP2" 3040480 NIL SUP2 (NIL T T) -7 NIL NIL NIL) (-1201 3030683 3039778 3039904 "SUP" 3040069 NIL SUP (NIL T) -8 NIL NIL NIL) (-1200 3029107 3029405 3029761 "SUMRF" 3030382 NIL SUMRF (NIL T) -7 NIL NIL NIL) (-1199 3028430 3028508 3028700 "SUMFS" 3029028 NIL SUMFS (NIL T T) -7 NIL NIL NIL) (-1198 3010275 3027742 3027984 "SULS" 3028246 NIL SULS (NIL T NIL NIL) -8 NIL NIL NIL) (-1197 3009823 3010097 3010167 "SUCHTAST" 3010227 T SUCHTAST (NIL) -8 NIL NIL NIL) (-1196 3009064 3009348 3009488 "SUCH" 3009731 NIL SUCH (NIL T T) -8 NIL NIL NIL) (-1195 3002703 3003970 3004929 "SUBSPACE" 3008152 NIL SUBSPACE (NIL NIL T) -8 NIL NIL NIL) (-1194 3002123 3002223 3002387 "SUBRESP" 3002591 NIL SUBRESP (NIL T T) -7 NIL NIL NIL) (-1193 2996134 2997416 2998563 "STTFNC" 3001023 NIL STTFNC (NIL T) -7 NIL NIL NIL) (-1192 2989328 2990799 2992110 "STTF" 2994870 NIL STTF (NIL T) -7 NIL NIL NIL) (-1191 2980445 2982510 2984304 "STTAYLOR" 2987569 NIL STTAYLOR (NIL T) -7 NIL NIL NIL) (-1190 2973199 2980309 2980392 "STRTBL" 2980397 NIL STRTBL (NIL T) -8 NIL NIL NIL) (-1189 2967596 2972908 2973007 "STRING" 2973122 T STRING (NIL) -8 NIL NIL NIL) (-1188 2967100 2967183 2967327 "STREAM3" 2967513 NIL STREAM3 (NIL T T T) -7 NIL NIL NIL) (-1187 2966064 2966265 2966500 "STREAM2" 2966913 NIL STREAM2 (NIL T T) -7 NIL NIL NIL) (-1186 2965746 2965804 2965897 "STREAM1" 2966006 NIL STREAM1 (NIL T) -7 NIL NIL NIL) (-1185 2957860 2963365 2963976 "STREAM" 2965170 NIL STREAM (NIL T) -8 NIL NIL NIL) (-1184 2956852 2957057 2957288 "STINPROD" 2957676 NIL STINPROD (NIL T) -7 NIL NIL NIL) (-1183 2955967 2956341 2956489 "STEPAST" 2956726 T STEPAST (NIL) -8 NIL NIL NIL) (-1182 2955463 2955715 2955745 "STEP" 2955825 T STEP (NIL) -9 NIL 2955903 NIL) (-1181 2948519 2955362 2955439 "STBL" 2955444 NIL STBL (NIL T T NIL) -8 NIL NIL NIL) (-1180 2943069 2947682 2947725 "STAGG" 2947878 NIL STAGG (NIL T) -9 NIL 2947967 NIL) (-1179 2940621 2941373 2942245 "STAGG-" 2942250 NIL STAGG- (NIL T T) -8 NIL NIL NIL) (-1178 2938593 2940391 2940483 "STACK" 2940564 NIL STACK (NIL T) -8 NIL NIL NIL) (-1177 2930600 2936734 2937190 "SREGSET" 2938223 NIL SREGSET (NIL T T T T) -8 NIL NIL NIL) (-1176 2922947 2924394 2925907 "SRDCMPK" 2929206 NIL SRDCMPK (NIL T T T T T) -7 NIL NIL NIL) (-1175 2915247 2920306 2920336 "SRAGG" 2921639 T SRAGG (NIL) -9 NIL 2922247 NIL) (-1174 2914198 2914519 2914898 "SRAGG-" 2914903 NIL SRAGG- (NIL T) -8 NIL NIL NIL) (-1173 2907782 2913145 2913566 "SQMATRIX" 2913824 NIL SQMATRIX (NIL NIL T) -8 NIL NIL NIL) (-1172 2901194 2904500 2905227 "SPLTREE" 2907127 NIL SPLTREE (NIL T T) -8 NIL NIL NIL) (-1171 2897019 2897850 2898496 "SPLNODE" 2900620 NIL SPLNODE (NIL T T) -8 NIL NIL NIL) (-1170 2895994 2896299 2896329 "SPFCAT" 2896773 T SPFCAT (NIL) -9 NIL NIL NIL) (-1169 2894689 2894941 2895205 "SPECOUT" 2895752 T SPECOUT (NIL) -7 NIL NIL NIL) (-1168 2885335 2887653 2887683 "SPADXPT" 2892361 T SPADXPT (NIL) -9 NIL 2894527 NIL) (-1167 2885090 2885136 2885205 "SPADPRSR" 2885288 T SPADPRSR (NIL) -7 NIL NIL NIL) (-1166 2882693 2885045 2885076 "SPADAST" 2885081 T SPADAST (NIL) -8 NIL NIL NIL) (-1165 2874294 2876397 2876440 "SPACEC" 2880813 NIL SPACEC (NIL T) -9 NIL 2882629 NIL) (-1164 2872094 2874226 2874275 "SPACE3" 2874280 NIL SPACE3 (NIL T) -8 NIL NIL NIL) (-1163 2870826 2871017 2871308 "SORTPAK" 2871899 NIL SORTPAK (NIL T T) -7 NIL NIL NIL) (-1162 2868888 2869221 2869633 "SOLVETRA" 2870490 NIL SOLVETRA (NIL T) -7 NIL NIL NIL) (-1161 2867926 2868160 2868421 "SOLVESER" 2868661 NIL SOLVESER (NIL T) -7 NIL NIL NIL) (-1160 2863158 2864118 2865113 "SOLVERAD" 2866978 NIL SOLVERAD (NIL T) -7 NIL NIL NIL) (-1159 2858883 2859582 2860311 "SOLVEFOR" 2862525 NIL SOLVEFOR (NIL T T) -7 NIL NIL NIL) (-1158 2852487 2858231 2858328 "SNTSCAT" 2858333 NIL SNTSCAT (NIL T T T T) -9 NIL 2858403 NIL) (-1157 2846031 2850810 2851201 "SMTS" 2852177 NIL SMTS (NIL T T T) -8 NIL NIL NIL) (-1156 2839746 2845919 2845996 "SMP" 2846001 NIL SMP (NIL T T) -8 NIL NIL NIL) (-1155 2837875 2838206 2838604 "SMITH" 2839443 NIL SMITH (NIL T T T T) -7 NIL NIL NIL) (-1154 2829400 2834454 2834557 "SMATCAT" 2835908 NIL SMATCAT (NIL NIL T T T) -9 NIL 2836458 NIL) (-1153 2826172 2827163 2828341 "SMATCAT-" 2828346 NIL SMATCAT- (NIL T NIL T T T) -8 NIL NIL NIL) (-1152 2823641 2825380 2825423 "SKAGG" 2825684 NIL SKAGG (NIL T) -9 NIL 2825819 NIL) (-1151 2819131 2823110 2823294 "SINT" 2823446 T SINT (NIL) -8 NIL NIL 2823608) (-1150 2818897 2818941 2819007 "SIMPAN" 2819087 T SIMPAN (NIL) -7 NIL NIL NIL) (-1149 2817717 2817956 2818231 "SIGNRF" 2818656 NIL SIGNRF (NIL T) -7 NIL NIL NIL) (-1148 2816532 2816701 2816985 "SIGNEF" 2817546 NIL SIGNEF (NIL T T) -7 NIL NIL NIL) (-1147 2815772 2816115 2816239 "SIGAST" 2816430 T SIGAST (NIL) -8 NIL NIL NIL) (-1146 2814997 2815307 2815447 "SIG" 2815654 T SIG (NIL) -8 NIL NIL NIL) (-1145 2812649 2813141 2813647 "SHP" 2814538 NIL SHP (NIL T NIL) -7 NIL NIL NIL) (-1144 2806022 2812550 2812626 "SHDP" 2812631 NIL SHDP (NIL NIL NIL T) -8 NIL NIL NIL) (-1143 2805533 2805773 2805803 "SGROUP" 2805896 T SGROUP (NIL) -9 NIL 2805958 NIL) (-1142 2805385 2805417 2805490 "SGROUP-" 2805495 NIL SGROUP- (NIL T) -8 NIL NIL NIL) (-1141 2802104 2802874 2803597 "SGCF" 2804684 T SGCF (NIL) -7 NIL NIL NIL) (-1140 2795806 2801550 2801647 "SFRTCAT" 2801652 NIL SFRTCAT (NIL T T T T) -9 NIL 2801691 NIL) (-1139 2789125 2790245 2791381 "SFRGCD" 2794789 NIL SFRGCD (NIL T T T T T) -7 NIL NIL NIL) (-1138 2782143 2783324 2784510 "SFQCMPK" 2788058 NIL SFQCMPK (NIL T T T T T) -7 NIL NIL NIL) (-1137 2781745 2781852 2781963 "SFORT" 2782084 NIL SFORT (NIL T T) -8 NIL NIL NIL) (-1136 2780671 2781585 2781706 "SEXOF" 2781711 NIL SEXOF (NIL T T T T T) -8 NIL NIL NIL) (-1135 2776260 2777167 2777262 "SEXCAT" 2779884 NIL SEXCAT (NIL T T T T T) -9 NIL 2780444 NIL) (-1134 2775175 2776141 2776209 "SEX" 2776214 T SEX (NIL) -8 NIL NIL NIL) (-1133 2773297 2773888 2774193 "SETMN" 2774916 NIL SETMN (NIL NIL NIL) -8 NIL NIL NIL) (-1132 2772827 2773015 2773045 "SETCAT" 2773162 T SETCAT (NIL) -9 NIL 2773247 NIL) (-1131 2772595 2772659 2772758 "SETCAT-" 2772763 NIL SETCAT- (NIL T) -8 NIL NIL NIL) (-1130 2768698 2771056 2771099 "SETAGG" 2771969 NIL SETAGG (NIL T) -9 NIL 2772309 NIL) (-1129 2768120 2768272 2768509 "SETAGG-" 2768514 NIL SETAGG- (NIL T T) -8 NIL NIL NIL) (-1128 2764929 2768054 2768102 "SET" 2768107 NIL SET (NIL T) -8 NIL NIL NIL) (-1127 2764312 2764625 2764726 "SEQAST" 2764850 T SEQAST (NIL) -8 NIL NIL NIL) (-1126 2763439 2763805 2763866 "SEGXCAT" 2764152 NIL SEGXCAT (NIL T T) -9 NIL 2764272 NIL) (-1125 2762364 2762632 2762675 "SEGCAT" 2763197 NIL SEGCAT (NIL T) -9 NIL 2763418 NIL) (-1124 2761979 2762044 2762157 "SEGBIND2" 2762299 NIL SEGBIND2 (NIL T T) -7 NIL NIL NIL) (-1123 2760869 2761342 2761550 "SEGBIND" 2761806 NIL SEGBIND (NIL T) -8 NIL NIL NIL) (-1122 2760388 2760670 2760747 "SEGAST" 2760814 T SEGAST (NIL) -8 NIL NIL NIL) (-1121 2759597 2759733 2759937 "SEG2" 2760232 NIL SEG2 (NIL T T) -7 NIL NIL NIL) (-1120 2758513 2759263 2759445 "SEG" 2759450 NIL SEG (NIL T) -8 NIL NIL NIL) (-1119 2757746 2758448 2758495 "SDVAR" 2758500 NIL SDVAR (NIL T) -8 NIL NIL NIL) (-1118 2749097 2757516 2757646 "SDPOL" 2757651 NIL SDPOL (NIL T) -8 NIL NIL NIL) (-1117 2747666 2747956 2748275 "SCPKG" 2748812 NIL SCPKG (NIL T) -7 NIL NIL NIL) (-1116 2746788 2747002 2747194 "SCOPE" 2747496 T SCOPE (NIL) -8 NIL NIL NIL) (-1115 2745984 2746142 2746321 "SCACHE" 2746643 NIL SCACHE (NIL T) -7 NIL NIL NIL) (-1114 2745568 2745802 2745832 "SASTCAT" 2745837 T SASTCAT (NIL) -9 NIL 2745850 NIL) (-1113 2744971 2745403 2745479 "SAOS" 2745514 T SAOS (NIL) -8 NIL NIL NIL) (-1112 2744530 2744571 2744744 "SAERFFC" 2744930 NIL SAERFFC (NIL T T T) -7 NIL NIL NIL) (-1111 2744117 2744158 2744317 "SAEFACT" 2744489 NIL SAEFACT (NIL T T T) -7 NIL NIL NIL) (-1110 2737144 2744014 2744094 "SAE" 2744099 NIL SAE (NIL T T NIL) -8 NIL NIL NIL) (-1109 2735447 2735779 2736180 "RURPK" 2736810 NIL RURPK (NIL T NIL) -7 NIL NIL NIL) (-1108 2734024 2734390 2734695 "RULESET" 2735281 NIL RULESET (NIL T T T) -8 NIL NIL NIL) (-1107 2733594 2733818 2733901 "RULECOLD" 2733976 NIL RULECOLD (NIL NIL) -8 NIL NIL NIL) (-1106 2730709 2731347 2731805 "RULE" 2733275 NIL RULE (NIL T T T) -8 NIL NIL NIL) (-1105 2730493 2730527 2730598 "RTVALUE" 2730660 T RTVALUE (NIL) -8 NIL NIL NIL) (-1104 2729904 2730210 2730304 "RSTRCAST" 2730421 T RSTRCAST (NIL) -8 NIL NIL NIL) (-1103 2724674 2725547 2726467 "RSETGCD" 2729103 NIL RSETGCD (NIL T T T T T) -7 NIL NIL NIL) (-1102 2713238 2718982 2719079 "RSETCAT" 2723198 NIL RSETCAT (NIL T T T T) -9 NIL 2724295 NIL) (-1101 2711057 2711704 2712528 "RSETCAT-" 2712533 NIL RSETCAT- (NIL T T T T T) -8 NIL NIL NIL) (-1100 2703365 2704819 2706339 "RSDCMPK" 2709656 NIL RSDCMPK (NIL T T T T T) -7 NIL NIL NIL) (-1099 2701234 2701797 2701871 "RRCC" 2702957 NIL RRCC (NIL T T) -9 NIL 2703301 NIL) (-1098 2700555 2700759 2701038 "RRCC-" 2701043 NIL RRCC- (NIL T T T) -8 NIL NIL NIL) (-1097 2699938 2700251 2700352 "RPTAST" 2700476 T RPTAST (NIL) -8 NIL NIL NIL) (-1096 2672317 2683050 2683117 "RPOLCAT" 2693783 NIL RPOLCAT (NIL T T T) -9 NIL 2696943 NIL) (-1095 2663287 2666155 2669277 "RPOLCAT-" 2669282 NIL RPOLCAT- (NIL T T T T) -8 NIL NIL NIL) (-1094 2653740 2661498 2661980 "ROUTINE" 2662827 T ROUTINE (NIL) -8 NIL NIL NIL) (-1093 2649789 2653366 2653506 "ROMAN" 2653622 T ROMAN (NIL) -8 NIL NIL NIL) (-1092 2647901 2648649 2648909 "ROIRC" 2649594 NIL ROIRC (NIL T T) -8 NIL NIL NIL) (-1091 2643614 2646390 2646420 "RNS" 2646724 T RNS (NIL) -9 NIL 2646998 NIL) (-1090 2642021 2642506 2643040 "RNS-" 2643115 NIL RNS- (NIL T) -8 NIL NIL NIL) (-1089 2640982 2641386 2641588 "RNGBIND" 2641872 NIL RNGBIND (NIL T T) -8 NIL NIL NIL) (-1088 2640275 2640779 2640809 "RNG" 2640814 T RNG (NIL) -9 NIL 2640835 NIL) (-1087 2639570 2640048 2640091 "RMODULE" 2640096 NIL RMODULE (NIL T) -9 NIL 2640123 NIL) (-1086 2638394 2638500 2638836 "RMCAT2" 2639471 NIL RMCAT2 (NIL NIL NIL T T T T T T T T) -7 NIL NIL NIL) (-1085 2634896 2637740 2638037 "RMATRIX" 2638156 NIL RMATRIX (NIL NIL NIL T) -8 NIL NIL NIL) (-1084 2627395 2629983 2630098 "RMATCAT" 2633457 NIL RMATCAT (NIL NIL NIL T T T) -9 NIL 2634439 NIL) (-1083 2626734 2626917 2627224 "RMATCAT-" 2627229 NIL RMATCAT- (NIL T NIL NIL T T T) -8 NIL NIL NIL) (-1082 2626307 2626521 2626564 "RLINSET" 2626626 NIL RLINSET (NIL T) -9 NIL 2626670 NIL) (-1081 2625868 2625949 2626077 "RINTERP" 2626226 NIL RINTERP (NIL NIL T) -7 NIL NIL NIL) (-1080 2624792 2625466 2625496 "RING" 2625552 T RING (NIL) -9 NIL 2625644 NIL) (-1079 2624572 2624628 2624725 "RING-" 2624730 NIL RING- (NIL T) -8 NIL NIL NIL) (-1078 2623383 2623650 2623908 "RIDIST" 2624336 T RIDIST (NIL) -7 NIL NIL NIL) (-1077 2614008 2622851 2623057 "RGCHAIN" 2623231 NIL RGCHAIN (NIL T NIL) -8 NIL NIL NIL) (-1076 2613266 2613750 2613791 "RGBCSPC" 2613849 NIL RGBCSPC (NIL T) -9 NIL 2613901 NIL) (-1075 2612332 2612791 2612832 "RGBCMDL" 2613064 NIL RGBCMDL (NIL T) -9 NIL 2613178 NIL) (-1074 2611972 2612041 2612144 "RFFACTOR" 2612263 NIL RFFACTOR (NIL T) -7 NIL NIL NIL) (-1073 2611691 2611732 2611829 "RFFACT" 2611931 NIL RFFACT (NIL T) -7 NIL NIL NIL) (-1072 2609742 2610172 2610554 "RFDIST" 2611331 T RFDIST (NIL) -7 NIL NIL NIL) (-1071 2606682 2607350 2608020 "RF" 2609106 NIL RF (NIL T) -7 NIL NIL NIL) (-1070 2606129 2606227 2606390 "RETSOL" 2606584 NIL RETSOL (NIL T T) -7 NIL NIL NIL) (-1069 2605747 2605845 2605888 "RETRACT" 2606021 NIL RETRACT (NIL T) -9 NIL 2606108 NIL) (-1068 2605590 2605621 2605708 "RETRACT-" 2605713 NIL RETRACT- (NIL T T) -8 NIL NIL NIL) (-1067 2605138 2605412 2605482 "RETAST" 2605542 T RETAST (NIL) -8 NIL NIL NIL) (-1066 2597488 2604791 2604918 "RESULT" 2605033 T RESULT (NIL) -8 NIL NIL NIL) (-1065 2595923 2596757 2596956 "RESRING" 2597391 NIL RESRING (NIL T T T T NIL) -8 NIL NIL NIL) (-1064 2595547 2595608 2595706 "RESLATC" 2595860 NIL RESLATC (NIL T) -7 NIL NIL NIL) (-1063 2595246 2595287 2595394 "REPSQ" 2595506 NIL REPSQ (NIL T) -7 NIL NIL NIL) (-1062 2594937 2594978 2595089 "REPDB" 2595205 NIL REPDB (NIL T) -7 NIL NIL NIL) (-1061 2588769 2590226 2591449 "REP2" 2593749 NIL REP2 (NIL T) -7 NIL NIL NIL) (-1060 2585072 2585827 2586635 "REP1" 2587996 NIL REP1 (NIL T) -7 NIL NIL NIL) (-1059 2582452 2583074 2583676 "REP" 2584492 T REP (NIL) -7 NIL NIL NIL) (-1058 2574460 2580593 2581049 "REGSET" 2582082 NIL REGSET (NIL T T T T) -8 NIL NIL NIL) (-1057 2573169 2573608 2573858 "REF" 2574245 NIL REF (NIL T) -8 NIL NIL NIL) (-1056 2572534 2572649 2572816 "REDORDER" 2573053 NIL REDORDER (NIL T T) -7 NIL NIL NIL) (-1055 2567898 2571747 2571974 "RECLOS" 2572362 NIL RECLOS (NIL T) -8 NIL NIL NIL) (-1054 2566932 2567131 2567346 "REALSOLV" 2567705 T REALSOLV (NIL) -7 NIL NIL NIL) (-1053 2563379 2564217 2565101 "REAL0Q" 2566097 NIL REAL0Q (NIL T) -7 NIL NIL NIL) (-1052 2558932 2559968 2561029 "REAL0" 2562360 NIL REAL0 (NIL T) -7 NIL NIL NIL) (-1051 2558766 2558819 2558849 "REAL" 2558854 T REAL (NIL) -9 NIL 2558889 NIL) (-1050 2558177 2558483 2558577 "RDUCEAST" 2558694 T RDUCEAST (NIL) -8 NIL NIL NIL) (-1049 2557576 2557654 2557861 "RDIV" 2558099 NIL RDIV (NIL T T T T T) -7 NIL NIL NIL) (-1048 2556626 2556818 2557031 "RDIST" 2557398 NIL RDIST (NIL T) -7 NIL NIL NIL) (-1047 2555211 2555510 2555882 "RDETRS" 2556334 NIL RDETRS (NIL T T) -7 NIL NIL NIL) (-1046 2553005 2553477 2554015 "RDETR" 2554753 NIL RDETR (NIL T T) -7 NIL NIL NIL) (-1045 2551624 2551908 2552305 "RDEEFS" 2552721 NIL RDEEFS (NIL T T) -7 NIL NIL NIL) (-1044 2550127 2550439 2550864 "RDEEF" 2551312 NIL RDEEF (NIL T T) -7 NIL NIL NIL) (-1043 2543599 2547081 2547111 "RCFIELD" 2548406 T RCFIELD (NIL) -9 NIL 2549137 NIL) (-1042 2541555 2542167 2542863 "RCFIELD-" 2542938 NIL RCFIELD- (NIL T) -8 NIL NIL NIL) (-1041 2537607 2539628 2539671 "RCAGG" 2540755 NIL RCAGG (NIL T) -9 NIL 2541220 NIL) (-1040 2537217 2537329 2537492 "RCAGG-" 2537497 NIL RCAGG- (NIL T T) -8 NIL NIL NIL) (-1039 2536534 2536664 2536829 "RATRET" 2537101 NIL RATRET (NIL T) -7 NIL NIL NIL) (-1038 2536075 2536154 2536275 "RATFACT" 2536462 NIL RATFACT (NIL T) -7 NIL NIL NIL) (-1037 2535353 2535503 2535655 "RANDSRC" 2535945 T RANDSRC (NIL) -7 NIL NIL NIL) (-1036 2535081 2535131 2535204 "RADUTIL" 2535302 T RADUTIL (NIL) -7 NIL NIL NIL) (-1035 2527205 2533912 2534223 "RADIX" 2534804 NIL RADIX (NIL NIL) -8 NIL NIL NIL) (-1034 2516799 2527047 2527177 "RADFF" 2527182 NIL RADFF (NIL T T T NIL NIL) -8 NIL NIL NIL) (-1033 2516428 2516521 2516551 "RADCAT" 2516711 T RADCAT (NIL) -9 NIL NIL NIL) (-1032 2516198 2516258 2516358 "RADCAT-" 2516363 NIL RADCAT- (NIL T) -8 NIL NIL NIL) (-1031 2514109 2515968 2516060 "QUEUE" 2516141 NIL QUEUE (NIL T) -8 NIL NIL NIL) (-1030 2513734 2513783 2513914 "QUATCT2" 2514060 NIL QUATCT2 (NIL T T T T) -7 NIL NIL NIL) (-1029 2506105 2510157 2510199 "QUATCAT" 2510990 NIL QUATCAT (NIL T) -9 NIL 2511756 NIL) (-1028 2501986 2503281 2504671 "QUATCAT-" 2504767 NIL QUATCAT- (NIL T T) -8 NIL NIL NIL) (-1027 2497825 2501919 2501967 "QUAT" 2501972 NIL QUAT (NIL T) -8 NIL NIL NIL) (-1026 2495081 2496873 2496916 "QUAGG" 2497297 NIL QUAGG (NIL T) -9 NIL 2497472 NIL) (-1025 2494629 2494903 2494973 "QQUTAST" 2495033 T QQUTAST (NIL) -8 NIL NIL NIL) (-1024 2493540 2494142 2494307 "QFORM" 2494510 NIL QFORM (NIL NIL T) -8 NIL NIL NIL) (-1023 2493165 2493214 2493345 "QFCAT2" 2493491 NIL QFCAT2 (NIL T T T T) -7 NIL NIL NIL) (-1022 2482841 2489012 2489054 "QFCAT" 2489722 NIL QFCAT (NIL T) -9 NIL 2490723 NIL) (-1021 2478156 2479609 2481203 "QFCAT-" 2481299 NIL QFCAT- (NIL T T) -8 NIL NIL NIL) (-1020 2477587 2477721 2477853 "QEQUAT" 2478046 T QEQUAT (NIL) -8 NIL NIL NIL) (-1019 2470605 2471786 2472972 "QCMPACK" 2476520 NIL QCMPACK (NIL T T T T T) -7 NIL NIL NIL) (-1018 2469834 2470016 2470252 "QALGSET2" 2470423 NIL QALGSET2 (NIL NIL NIL) -7 NIL NIL NIL) (-1017 2467284 2467820 2468250 "QALGSET" 2469489 NIL QALGSET (NIL T T T T) -8 NIL NIL NIL) (-1016 2465951 2466193 2466512 "PWFFINTB" 2467057 NIL PWFFINTB (NIL T T T T) -7 NIL NIL NIL) (-1015 2464096 2464294 2464650 "PUSHVAR" 2465765 NIL PUSHVAR (NIL T T T T) -7 NIL NIL NIL) (-1014 2459823 2461039 2461082 "PTRANFN" 2462993 NIL PTRANFN (NIL T) -9 NIL NIL NIL) (-1013 2458160 2458505 2458829 "PTPACK" 2459534 NIL PTPACK (NIL T) -7 NIL NIL NIL) (-1012 2457783 2457846 2457957 "PTFUNC2" 2458097 NIL PTFUNC2 (NIL T T) -7 NIL NIL NIL) (-1011 2451699 2456572 2456615 "PTCAT" 2456915 NIL PTCAT (NIL T) -9 NIL 2457068 NIL) (-1010 2451348 2451389 2451515 "PSQFR" 2451658 NIL PSQFR (NIL T T T T) -7 NIL NIL NIL) (-1009 2449920 2450236 2450572 "PSEUDLIN" 2451046 NIL PSEUDLIN (NIL T) -7 NIL NIL NIL) (-1008 2436440 2439015 2441341 "PSETPK" 2447680 NIL PSETPK (NIL T T T T) -7 NIL NIL NIL) (-1007 2429148 2432176 2432274 "PSETCAT" 2435315 NIL PSETCAT (NIL T T T T) -9 NIL 2436129 NIL) (-1006 2426873 2427615 2428439 "PSETCAT-" 2428444 NIL PSETCAT- (NIL T T T T T) -8 NIL NIL NIL) (-1005 2426186 2426381 2426411 "PSCURVE" 2426683 T PSCURVE (NIL) -9 NIL 2426850 NIL) (-1004 2421902 2423676 2423743 "PSCAT" 2424595 NIL PSCAT (NIL T T T) -9 NIL 2424835 NIL) (-1003 2420896 2421178 2421581 "PSCAT-" 2421586 NIL PSCAT- (NIL T T T T) -8 NIL NIL NIL) (-1002 2419095 2419955 2420220 "PRTITION" 2420653 T PRTITION (NIL) -8 NIL NIL NIL) (-1001 2418506 2418812 2418906 "PRTDAST" 2419023 T PRTDAST (NIL) -8 NIL NIL NIL) (-1000 2407350 2409772 2411962 "PRS" 2416368 NIL PRS (NIL T T) -7 NIL NIL NIL) (-999 2404970 2406672 2406712 "PRQAGG" 2406895 NIL PRQAGG (NIL T) -9 NIL 2406997 NIL) (-998 2404149 2404598 2404626 "PROPLOG" 2404765 T PROPLOG (NIL) -9 NIL 2404880 NIL) (-997 2403747 2403810 2403933 "PROPFUN2" 2404072 NIL PROPFUN2 (NIL T T) -8 NIL NIL NIL) (-996 2403044 2403183 2403355 "PROPFUN1" 2403608 NIL PROPFUN1 (NIL T) -8 NIL NIL NIL) (-995 2401023 2401791 2402088 "PROPFRML" 2402780 NIL PROPFRML (NIL T) -8 NIL NIL NIL) (-994 2400468 2400599 2400727 "PROPERTY" 2400915 T PROPERTY (NIL) -8 NIL NIL NIL) (-993 2394356 2398634 2399454 "PRODUCT" 2399694 NIL PRODUCT (NIL T T) -8 NIL NIL NIL) (-992 2394146 2394184 2394243 "PRINT" 2394317 T PRINT (NIL) -7 NIL NIL NIL) (-991 2393462 2393603 2393755 "PRIMES" 2394026 NIL PRIMES (NIL T) -7 NIL NIL NIL) (-990 2391509 2391928 2392394 "PRIMELT" 2393041 NIL PRIMELT (NIL T) -7 NIL NIL NIL) (-989 2391226 2391287 2391315 "PRIMCAT" 2391439 T PRIMCAT (NIL) -9 NIL NIL NIL) (-988 2390215 2390411 2390639 "PRIMARR2" 2391044 NIL PRIMARR2 (NIL T T) -7 NIL NIL NIL) (-987 2385937 2390153 2390198 "PRIMARR" 2390203 NIL PRIMARR (NIL T) -8 NIL NIL NIL) (-986 2385574 2385636 2385747 "PREASSOC" 2385875 NIL PREASSOC (NIL T T) -7 NIL NIL NIL) (-985 2382532 2385032 2385266 "PR" 2385385 NIL PR (NIL T T) -8 NIL NIL NIL) (-984 2381983 2382140 2382168 "PPCURVE" 2382373 T PPCURVE (NIL) -9 NIL 2382509 NIL) (-983 2381530 2381778 2381861 "PORTNUM" 2381920 T PORTNUM (NIL) -8 NIL NIL NIL) (-982 2378867 2379288 2379880 "POLYROOT" 2381111 NIL POLYROOT (NIL T T T T T) -7 NIL NIL NIL) (-981 2378244 2378308 2378542 "POLYLIFT" 2378803 NIL POLYLIFT (NIL T T T T T) -7 NIL NIL NIL) (-980 2374465 2374968 2375597 "POLYCATQ" 2377789 NIL POLYCATQ (NIL T T T T T) -7 NIL NIL NIL) (-979 2360106 2366212 2366277 "POLYCAT" 2369791 NIL POLYCAT (NIL T T T) -9 NIL 2371669 NIL) (-978 2353225 2355417 2357801 "POLYCAT-" 2357806 NIL POLYCAT- (NIL T T T T) -8 NIL NIL NIL) (-977 2352806 2352880 2353000 "POLY2UP" 2353151 NIL POLY2UP (NIL NIL T) -7 NIL NIL NIL) (-976 2352432 2352495 2352604 "POLY2" 2352743 NIL POLY2 (NIL T T) -7 NIL NIL NIL) (-975 2345640 2352036 2352196 "POLY" 2352305 NIL POLY (NIL T) -8 NIL NIL NIL) (-974 2344301 2344564 2344840 "POLUTIL" 2345414 NIL POLUTIL (NIL T T) -7 NIL NIL NIL) (-973 2342620 2342933 2343264 "POLTOPOL" 2344023 NIL POLTOPOL (NIL NIL T) -7 NIL NIL NIL) (-972 2337616 2342554 2342601 "POINT" 2342606 NIL POINT (NIL T) -8 NIL NIL NIL) (-971 2335749 2336160 2336535 "PNTHEORY" 2337261 T PNTHEORY (NIL) -7 NIL NIL NIL) (-970 2334195 2334504 2334903 "PMTOOLS" 2335447 NIL PMTOOLS (NIL T T T) -7 NIL NIL NIL) (-969 2333782 2333866 2333983 "PMSYM" 2334111 NIL PMSYM (NIL T) -7 NIL NIL NIL) (-968 2333284 2333359 2333534 "PMQFCAT" 2333707 NIL PMQFCAT (NIL T T T) -7 NIL NIL NIL) (-967 2332665 2332763 2332925 "PMPREDFS" 2333185 NIL PMPREDFS (NIL T T T) -7 NIL NIL NIL) (-966 2332008 2332130 2332286 "PMPRED" 2332542 NIL PMPRED (NIL T) -7 NIL NIL NIL) (-965 2330662 2330880 2331258 "PMPLCAT" 2331770 NIL PMPLCAT (NIL T T T T T) -7 NIL NIL NIL) (-964 2330188 2330273 2330425 "PMLSAGG" 2330577 NIL PMLSAGG (NIL T T T) -7 NIL NIL NIL) (-963 2329655 2329737 2329919 "PMKERNEL" 2330106 NIL PMKERNEL (NIL T T) -7 NIL NIL NIL) (-962 2329266 2329347 2329460 "PMINS" 2329574 NIL PMINS (NIL T) -7 NIL NIL NIL) (-961 2328702 2328777 2328986 "PMFS" 2329191 NIL PMFS (NIL T T T) -7 NIL NIL NIL) (-960 2327918 2328048 2328253 "PMDOWN" 2328579 NIL PMDOWN (NIL T T T) -7 NIL NIL NIL) (-959 2327167 2327301 2327464 "PMASSFS" 2327805 NIL PMASSFS (NIL T T) -7 NIL NIL NIL) (-958 2326310 2326492 2326673 "PMASS" 2327006 T PMASS (NIL) -7 NIL NIL NIL) (-957 2325959 2326033 2326127 "PLOTTOOL" 2326236 T PLOTTOOL (NIL) -7 NIL NIL NIL) (-956 2321611 2322805 2323727 "PLOT3D" 2325057 T PLOT3D (NIL) -8 NIL NIL NIL) (-955 2320499 2320700 2320935 "PLOT1" 2321415 NIL PLOT1 (NIL T) -7 NIL NIL NIL) (-954 2314920 2316310 2317458 "PLOT" 2319371 T PLOT (NIL) -8 NIL NIL NIL) (-953 2290095 2294986 2299837 "PLEQN" 2310186 NIL PLEQN (NIL T T T T) -7 NIL NIL NIL) (-952 2289782 2289835 2289938 "PINTERPA" 2290042 NIL PINTERPA (NIL T T) -7 NIL NIL NIL) (-951 2289088 2289222 2289402 "PINTERP" 2289647 NIL PINTERP (NIL NIL T) -7 NIL NIL NIL) (-950 2287173 2288346 2288374 "PID" 2288556 T PID (NIL) -9 NIL 2288690 NIL) (-949 2286918 2286961 2287036 "PICOERCE" 2287130 NIL PICOERCE (NIL T) -7 NIL NIL NIL) (-948 2286014 2286682 2286769 "PI" 2286809 T PI (NIL) -8 NIL NIL 2286876) (-947 2285322 2285473 2285649 "PGROEB" 2285870 NIL PGROEB (NIL T) -7 NIL NIL NIL) (-946 2280761 2281720 2282626 "PGE" 2284436 T PGE (NIL) -7 NIL NIL NIL) (-945 2278842 2279131 2279497 "PGCD" 2280478 NIL PGCD (NIL T T T T) -7 NIL NIL NIL) (-944 2278168 2278283 2278444 "PFRPAC" 2278726 NIL PFRPAC (NIL T) -7 NIL NIL NIL) (-943 2274419 2276716 2277069 "PFR" 2277847 NIL PFR (NIL T) -8 NIL NIL NIL) (-942 2272772 2273052 2273377 "PFOTOOLS" 2274166 NIL PFOTOOLS (NIL T T) -7 NIL NIL NIL) (-941 2271287 2271544 2271895 "PFOQ" 2272529 NIL PFOQ (NIL T T T) -7 NIL NIL NIL) (-940 2269770 2270000 2270356 "PFO" 2271071 NIL PFO (NIL T T T T T) -7 NIL NIL NIL) (-939 2266848 2268361 2268389 "PFECAT" 2268974 T PFECAT (NIL) -9 NIL 2269358 NIL) (-938 2266275 2266447 2266661 "PFECAT-" 2266666 NIL PFECAT- (NIL T) -8 NIL NIL NIL) (-937 2264848 2265130 2265431 "PFBRU" 2266024 NIL PFBRU (NIL T T) -7 NIL NIL NIL) (-936 2262678 2263066 2263498 "PFBR" 2264499 NIL PFBR (NIL T T T T) -7 NIL NIL NIL) (-935 2258603 2262567 2262636 "PF" 2262641 NIL PF (NIL NIL) -8 NIL NIL NIL) (-934 2253657 2254810 2255680 "PERMGRP" 2257766 NIL PERMGRP (NIL T) -8 NIL NIL NIL) (-933 2251569 2252681 2252722 "PERMCAT" 2253122 NIL PERMCAT (NIL T) -9 NIL 2253420 NIL) (-932 2251216 2251263 2251387 "PERMAN" 2251522 NIL PERMAN (NIL NIL T) -7 NIL NIL NIL) (-931 2247018 2248725 2249373 "PERM" 2250601 NIL PERM (NIL T) -8 NIL NIL NIL) (-930 2244259 2246683 2246805 "PENDTREE" 2246929 NIL PENDTREE (NIL T) -8 NIL NIL NIL) (-929 2243140 2243403 2243444 "PDSPC" 2243977 NIL PDSPC (NIL T) -9 NIL 2244222 NIL) (-928 2242195 2242461 2242823 "PDSPC-" 2242828 NIL PDSPC- (NIL T T) -8 NIL NIL NIL) (-927 2240909 2241845 2241886 "PDRING" 2241891 NIL PDRING (NIL T) -9 NIL 2241919 NIL) (-926 2239652 2240414 2240468 "PDMOD" 2240473 NIL PDMOD (NIL T T) -9 NIL 2240577 NIL) (-925 2236819 2237645 2238313 "PDEPROB" 2239004 T PDEPROB (NIL) -8 NIL NIL NIL) (-924 2234328 2234868 2235423 "PDEPACK" 2236284 T PDEPACK (NIL) -7 NIL NIL NIL) (-923 2233216 2233430 2233681 "PDECOMP" 2234127 NIL PDECOMP (NIL T T) -7 NIL NIL NIL) (-922 2230733 2231624 2231652 "PDECAT" 2232439 T PDECAT (NIL) -9 NIL 2233152 NIL) (-921 2230350 2230417 2230471 "PDDOM" 2230636 NIL PDDOM (NIL T T) -9 NIL 2230716 NIL) (-920 2230163 2230199 2230306 "PDDOM-" 2230311 NIL PDDOM- (NIL T T T) -8 NIL NIL NIL) (-919 2229908 2229947 2230037 "PCOMP" 2230124 NIL PCOMP (NIL T T) -7 NIL NIL NIL) (-918 2227948 2228709 2229006 "PBWLB" 2229637 NIL PBWLB (NIL T) -8 NIL NIL NIL) (-917 2227574 2227637 2227746 "PATTERN2" 2227885 NIL PATTERN2 (NIL T T) -7 NIL NIL NIL) (-916 2225283 2225719 2226176 "PATTERN1" 2227163 NIL PATTERN1 (NIL T T) -7 NIL NIL NIL) (-915 2217462 2219356 2220694 "PATTERN" 2223966 NIL PATTERN (NIL T) -8 NIL NIL NIL) (-914 2217020 2217093 2217225 "PATRES2" 2217389 NIL PATRES2 (NIL T T T) -7 NIL NIL NIL) (-913 2214286 2214969 2215450 "PATRES" 2216585 NIL PATRES (NIL T T) -8 NIL NIL NIL) (-912 2212139 2212574 2212981 "PATMATCH" 2213953 NIL PATMATCH (NIL T T T) -7 NIL NIL NIL) (-911 2211593 2211844 2211885 "PATMAB" 2211992 NIL PATMAB (NIL T) -9 NIL 2212075 NIL) (-910 2210039 2210447 2210705 "PATLRES" 2211398 NIL PATLRES (NIL T T T) -8 NIL NIL NIL) (-909 2209577 2209708 2209749 "PATAB" 2209754 NIL PATAB (NIL T) -9 NIL 2209926 NIL) (-908 2207717 2208154 2208577 "PARTPERM" 2209174 T PARTPERM (NIL) -7 NIL NIL NIL) (-907 2207326 2207401 2207503 "PARSURF" 2207648 NIL PARSURF (NIL T) -8 NIL NIL NIL) (-906 2206952 2207015 2207124 "PARSU2" 2207263 NIL PARSU2 (NIL T T) -7 NIL NIL NIL) (-905 2206710 2206756 2206823 "PARSER" 2206905 T PARSER (NIL) -7 NIL NIL NIL) (-904 2206319 2206394 2206496 "PARSCURV" 2206641 NIL PARSCURV (NIL T) -8 NIL NIL NIL) (-903 2205945 2206008 2206117 "PARSC2" 2206256 NIL PARSC2 (NIL T T) -7 NIL NIL NIL) (-902 2205572 2205642 2205739 "PARPCURV" 2205881 NIL PARPCURV (NIL T) -8 NIL NIL NIL) (-901 2205198 2205261 2205370 "PARPC2" 2205509 NIL PARPC2 (NIL T T) -7 NIL NIL NIL) (-900 2204187 2204571 2204753 "PARAMAST" 2205036 T PARAMAST (NIL) -8 NIL NIL NIL) (-899 2203695 2203793 2203912 "PAN2EXPR" 2204088 T PAN2EXPR (NIL) -7 NIL NIL NIL) (-898 2202388 2202816 2203044 "PALETTE" 2203487 T PALETTE (NIL) -8 NIL NIL NIL) (-897 2200733 2201393 2201753 "PAIR" 2202074 NIL PAIR (NIL T T) -8 NIL NIL NIL) (-896 2193645 2199990 2200185 "PADICRC" 2200587 NIL PADICRC (NIL NIL T) -8 NIL NIL NIL) (-895 2185881 2192989 2193174 "PADICRAT" 2193492 NIL PADICRAT (NIL NIL) -8 NIL NIL NIL) (-894 2182671 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NIL) (-858 2118471 2118751 2118792 "OPERCAT" 2119004 NIL OPERCAT (NIL T) -9 NIL 2119101 NIL) (-857 2118214 2118282 2118399 "OPERCAT-" 2118404 NIL OPERCAT- (NIL T T) -8 NIL NIL NIL) (-856 2115123 2116525 2117029 "OP" 2117743 NIL OP (NIL T) -8 NIL NIL NIL) (-855 2114416 2114543 2114717 "ONECOMP2" 2114995 NIL ONECOMP2 (NIL T T) -7 NIL NIL NIL) (-854 2111029 2113213 2113582 "ONECOMP" 2114080 NIL ONECOMP (NIL T) -8 NIL NIL NIL) (-853 2110430 2110554 2110684 "OMSERVER" 2110919 T OMSERVER (NIL) -7 NIL NIL NIL) (-852 2106944 2109870 2109910 "OMSAGG" 2109971 NIL OMSAGG (NIL T) -9 NIL 2110035 NIL) (-851 2105519 2105830 2106112 "OMPKG" 2106682 T OMPKG (NIL) -7 NIL NIL NIL) (-850 2103866 2105068 2105237 "OMLO" 2105400 NIL OMLO (NIL T T) -8 NIL NIL NIL) (-849 2102802 2102973 2103193 "OMEXPR" 2103692 NIL OMEXPR (NIL T) -7 NIL NIL NIL) (-848 2101887 2102223 2102383 "OMERRK" 2102662 T OMERRK (NIL) -8 NIL NIL NIL) (-847 2101124 2101433 2101569 "OMERR" 2101771 T OMERR (NIL) -8 NIL NIL NIL) (-846 2100515 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2028337 2029046 2029074 "ODECAT" 2029679 T ODECAT (NIL) -9 NIL 2030210 NIL) (-821 2027969 2028018 2028145 "OCTCT2" 2028288 NIL OCTCT2 (NIL T T T T) -7 NIL NIL NIL) (-820 2024462 2027674 2027796 "OCT" 2027879 NIL OCT (NIL T) -8 NIL NIL NIL) (-819 2023685 2024255 2024283 "OCAMON" 2024288 T OCAMON (NIL) -9 NIL 2024309 NIL) (-818 2017949 2020728 2020768 "OC" 2021865 NIL OC (NIL T) -9 NIL 2022723 NIL) (-817 2014984 2015924 2016914 "OC-" 2017008 NIL OC- (NIL T T) -8 NIL NIL NIL) (-816 2014404 2014829 2014857 "OASGP" 2014862 T OASGP (NIL) -9 NIL 2014882 NIL) (-815 2013530 2014127 2014155 "OAMONS" 2014195 T OAMONS (NIL) -9 NIL 2014238 NIL) (-814 2012821 2013350 2013378 "OAMON" 2013383 T OAMON (NIL) -9 NIL 2013403 NIL) (-813 2011932 2012570 2012598 "OAGROUP" 2012603 T OAGROUP (NIL) -9 NIL 2012623 NIL) (-812 2011614 2011670 2011759 "NUMTUBE" 2011876 NIL NUMTUBE (NIL T) -7 NIL NIL NIL) (-811 2005133 2006705 2008241 "NUMQUAD" 2010098 T NUMQUAD (NIL) -7 NIL NIL NIL) (-810 2000813 2001847 2002882 "NUMODE" 2004118 T NUMODE (NIL) -7 NIL NIL NIL) (-809 1998094 1999034 1999062 "NUMINT" 1999985 T NUMINT (NIL) -9 NIL 2000749 NIL) (-808 1997006 1997239 1997457 "NUMFMT" 1997896 T NUMFMT (NIL) -7 NIL NIL NIL) (-807 1983189 1986310 1988842 "NUMERIC" 1994513 NIL NUMERIC (NIL T) -7 NIL NIL NIL) (-806 1976893 1982637 1982732 "NTSCAT" 1982737 NIL NTSCAT (NIL T T T T) -9 NIL 1982776 NIL) (-805 1976073 1976252 1976445 "NTPOLFN" 1976732 NIL NTPOLFN (NIL T) -7 NIL NIL NIL) (-804 1975699 1975762 1975871 "NSUP2" 1976010 NIL NSUP2 (NIL T T) -7 NIL NIL NIL) (-803 1962460 1972524 1973336 "NSUP" 1974920 NIL NSUP (NIL T) -8 NIL NIL NIL) (-802 1951296 1962234 1962367 "NSMP" 1962372 NIL NSMP (NIL T T) -8 NIL NIL NIL) (-801 1949704 1950029 1950386 "NREP" 1950984 NIL NREP (NIL T) -7 NIL NIL NIL) (-800 1948283 1948547 1948905 "NPCOEF" 1949447 NIL NPCOEF (NIL T T T T T) -7 NIL NIL NIL) (-799 1947331 1947464 1947680 "NORMRETR" 1948164 NIL NORMRETR (NIL T T T T NIL) -7 NIL NIL NIL) (-798 1945342 1945662 1946071 "NORMPK" 1947039 NIL NORMPK (NIL T T T T T) -7 NIL NIL NIL) (-797 1945021 1945055 1945179 "NORMMA" 1945308 NIL NORMMA (NIL T T T T) -7 NIL NIL NIL) (-796 1944804 1944839 1944908 "NONE1" 1944985 NIL NONE1 (NIL T) -7 NIL NIL NIL) (-795 1944568 1944761 1944790 "NONE" 1944795 T NONE (NIL) -8 NIL NIL NIL) (-794 1944059 1944127 1944306 "NODE1" 1944500 NIL NODE1 (NIL T T) -7 NIL NIL NIL) (-793 1942151 1943182 1943437 "NNI" 1943784 T NNI (NIL) -8 NIL NIL 1944019) (-792 1940547 1940884 1941248 "NLINSOL" 1941819 NIL NLINSOL (NIL T) -7 NIL NIL NIL) (-791 1936728 1937783 1938682 "NIPROB" 1939668 T NIPROB (NIL) -8 NIL NIL NIL) (-790 1935467 1935719 1936021 "NFINTBAS" 1936490 NIL NFINTBAS (NIL T T) -7 NIL NIL NIL) (-789 1934551 1935117 1935158 "NETCLT" 1935330 NIL NETCLT (NIL T) -9 NIL 1935412 NIL) (-788 1933223 1933490 1933771 "NCODIV" 1934319 NIL NCODIV (NIL T T) -7 NIL NIL NIL) (-787 1932979 1933022 1933097 "NCNTFRAC" 1933180 NIL NCNTFRAC (NIL T) -7 NIL NIL NIL) (-786 1931135 1931523 1931943 "NCEP" 1932604 NIL NCEP (NIL T) -7 NIL NIL NIL) (-785 1929798 1930745 1930773 "NASRING" 1930883 T NASRING (NIL) -9 NIL 1930963 NIL) (-784 1929581 1929637 1929731 "NASRING-" 1929736 NIL NASRING- (NIL T) -8 NIL NIL NIL) (-783 1928548 1929199 1929227 "NARNG" 1929344 T NARNG (NIL) -9 NIL 1929435 NIL) (-782 1928222 1928307 1928441 "NARNG-" 1928446 NIL NARNG- (NIL T) -8 NIL NIL NIL) (-781 1927059 1927308 1927543 "NAGSP" 1928007 T NAGSP (NIL) -7 NIL NIL NIL) (-780 1918103 1920015 1921688 "NAGS" 1925406 T NAGS (NIL) -7 NIL NIL NIL) (-779 1916627 1916959 1917290 "NAGF07" 1917792 T NAGF07 (NIL) -7 NIL NIL NIL) (-778 1911099 1912456 1913763 "NAGF04" 1915340 T NAGF04 (NIL) -7 NIL NIL NIL) (-777 1903971 1905681 1907314 "NAGF02" 1909486 T NAGF02 (NIL) -7 NIL NIL NIL) (-776 1899135 1900295 1901412 "NAGF01" 1902874 T NAGF01 (NIL) -7 NIL NIL NIL) (-775 1892715 1894329 1895914 "NAGE04" 1897570 T NAGE04 (NIL) -7 NIL NIL NIL) (-774 1883776 1886005 1888135 "NAGE02" 1890605 T NAGE02 (NIL) -7 NIL NIL NIL) (-773 1879669 1880676 1881640 "NAGE01" 1882832 T NAGE01 (NIL) -7 NIL NIL NIL) (-772 1877446 1877998 1878556 "NAGD03" 1879131 T NAGD03 (NIL) -7 NIL NIL NIL) (-771 1869142 1871124 1873078 "NAGD02" 1875512 T NAGD02 (NIL) -7 NIL NIL NIL) (-770 1862881 1864378 1865818 "NAGD01" 1867722 T NAGD01 (NIL) -7 NIL NIL NIL) (-769 1859018 1859912 1860749 "NAGC06" 1862064 T NAGC06 (NIL) -7 NIL NIL NIL) (-768 1857465 1857815 1858171 "NAGC05" 1858682 T NAGC05 (NIL) -7 NIL NIL NIL) (-767 1856829 1856960 1857104 "NAGC02" 1857341 T NAGC02 (NIL) -7 NIL NIL NIL) (-766 1855630 1856357 1856397 "NAALG" 1856476 NIL NAALG (NIL T) -9 NIL 1856537 NIL) (-765 1855459 1855494 1855584 "NAALG-" 1855589 NIL NAALG- (NIL T T) -8 NIL NIL NIL) (-764 1849331 1850517 1851704 "MULTSQFR" 1854355 NIL MULTSQFR (NIL T T T T) -7 NIL NIL NIL) (-763 1848638 1848725 1848909 "MULTFACT" 1849243 NIL MULTFACT (NIL T T T T) -7 NIL NIL NIL) (-762 1840776 1845221 1845274 "MTSCAT" 1846344 NIL MTSCAT (NIL T T) -9 NIL 1846860 NIL) (-761 1840482 1840542 1840634 "MTHING" 1840716 NIL MTHING (NIL T) -7 NIL NIL NIL) (-760 1840268 1840307 1840367 "MSYSCMD" 1840442 T MSYSCMD (NIL) -7 NIL NIL NIL) (-759 1837013 1839829 1839870 "MSETAGG" 1839875 NIL MSETAGG (NIL T) -9 NIL 1839909 NIL) (-758 1832727 1835768 1836088 "MSET" 1836726 NIL MSET (NIL T) -8 NIL NIL NIL) (-757 1828319 1830106 1830851 "MRING" 1832027 NIL MRING (NIL T T) -8 NIL NIL NIL) (-756 1827879 1827952 1828083 "MRF2" 1828246 NIL MRF2 (NIL T T T) -7 NIL NIL NIL) (-755 1827491 1827532 1827676 "MRATFAC" 1827838 NIL MRATFAC (NIL T T T T) -7 NIL NIL NIL) (-754 1825061 1825398 1825829 "MPRFF" 1827196 NIL MPRFF (NIL T T T T) -7 NIL NIL NIL) (-753 1818388 1824915 1825012 "MPOLY" 1825017 NIL MPOLY (NIL NIL T) -8 NIL NIL NIL) (-752 1817872 1817913 1818121 "MPCPF" 1818347 NIL MPCPF (NIL T T T T) -7 NIL NIL NIL) (-751 1817380 1817429 1817613 "MPC3" 1817823 NIL MPC3 (NIL T T T T T T T) -7 NIL NIL NIL) (-750 1816563 1816656 1816877 "MPC2" 1817295 NIL MPC2 (NIL T T T T T T T) -7 NIL NIL NIL) (-749 1814840 1815201 1815591 "MONOTOOL" 1816223 NIL MONOTOOL (NIL T T) -7 NIL NIL NIL) (-748 1813985 1814368 1814396 "MONOID" 1814615 T MONOID (NIL) -9 NIL 1814762 NIL) (-747 1813501 1813650 1813831 "MONOID-" 1813836 NIL MONOID- (NIL T) -8 NIL NIL NIL) (-746 1802453 1809321 1809380 "MONOGEN" 1810054 NIL MONOGEN (NIL T T) -9 NIL 1810510 NIL) (-745 1799503 1800406 1801406 "MONOGEN-" 1801525 NIL MONOGEN- (NIL T T T) -8 NIL NIL NIL) (-744 1798220 1798768 1798796 "MONADWU" 1799188 T MONADWU (NIL) -9 NIL 1799426 NIL) (-743 1797550 1797751 1797999 "MONADWU-" 1798004 NIL MONADWU- (NIL T) -8 NIL NIL NIL) (-742 1796835 1797139 1797167 "MONAD" 1797374 T MONAD (NIL) -9 NIL 1797486 NIL) (-741 1796502 1796598 1796730 "MONAD-" 1796735 NIL MONAD- (NIL T) -8 NIL NIL NIL) (-740 1794641 1795415 1795694 "MOEBIUS" 1796255 NIL MOEBIUS (NIL T) -8 NIL NIL NIL) (-739 1793809 1794309 1794349 "MODULE" 1794354 NIL MODULE (NIL T) -9 NIL 1794393 NIL) (-738 1793347 1793473 1793663 "MODULE-" 1793668 NIL MODULE- (NIL T T) -8 NIL NIL NIL) (-737 1790877 1791711 1792038 "MODRING" 1793171 NIL MODRING (NIL T T NIL NIL NIL) -8 NIL NIL NIL) (-736 1787599 1788982 1789503 "MODOP" 1790406 NIL MODOP (NIL T T) -8 NIL NIL NIL) (-735 1786085 1786666 1786943 "MODMONOM" 1787462 NIL MODMONOM (NIL T T NIL) -8 NIL NIL NIL) (-734 1774825 1784376 1784790 "MODMON" 1785722 NIL MODMON (NIL T T) -8 NIL NIL NIL) (-733 1771651 1773669 1773945 "MODFIELD" 1774700 NIL MODFIELD (NIL T T NIL NIL NIL) -8 NIL NIL NIL) (-732 1770562 1770932 1771122 "MMLFORM" 1771481 T MMLFORM (NIL) -8 NIL NIL NIL) (-731 1770082 1770131 1770310 "MMAP" 1770513 NIL MMAP (NIL T T T T T T) -7 NIL NIL NIL) (-730 1767975 1768914 1768955 "MLO" 1769378 NIL MLO (NIL T) -9 NIL 1769620 NIL) (-729 1765323 1765857 1766459 "MLIFT" 1767456 NIL MLIFT (NIL T T T T) -7 NIL NIL NIL) (-728 1764702 1764798 1764952 "MKUCFUNC" 1765234 NIL MKUCFUNC (NIL T T T) -7 NIL NIL NIL) (-727 1764295 1764371 1764494 "MKRECORD" 1764625 NIL MKRECORD (NIL T T) -7 NIL NIL NIL) (-726 1763318 1763504 1763732 "MKFUNC" 1764106 NIL MKFUNC (NIL T) -7 NIL NIL NIL) (-725 1762694 1762810 1762966 "MKFLCFN" 1763201 NIL MKFLCFN (NIL T) -7 NIL NIL NIL) (-724 1761959 1762073 1762258 "MKBCFUNC" 1762587 NIL MKBCFUNC (NIL T T T T) -7 NIL NIL NIL) (-723 1757942 1761513 1761649 "MINT" 1761843 T MINT (NIL) -8 NIL NIL NIL) (-722 1756724 1756997 1757274 "MHROWRED" 1757697 NIL MHROWRED (NIL T) -7 NIL NIL NIL) (-721 1751468 1755259 1755664 "MFLOAT" 1756339 T MFLOAT (NIL) -8 NIL NIL NIL) (-720 1750813 1750901 1751072 "MFINFACT" 1751380 NIL MFINFACT (NIL T T T T) -7 NIL NIL NIL) (-719 1747092 1747976 1748860 "MESH" 1749949 T MESH (NIL) -7 NIL NIL NIL) (-718 1745446 1745794 1746147 "MDDFACT" 1746779 NIL MDDFACT (NIL T) -7 NIL NIL NIL) (-717 1741982 1744577 1744618 "MDAGG" 1744873 NIL MDAGG (NIL T) -9 NIL 1745016 NIL) (-716 1729684 1741275 1741482 "MCMPLX" 1741795 T MCMPLX (NIL) -8 NIL NIL NIL) (-715 1728803 1728967 1729168 "MCDEN" 1729533 NIL MCDEN (NIL T T) -7 NIL NIL NIL) (-714 1726651 1726963 1727343 "MCALCFN" 1728533 NIL MCALCFN (NIL T T T T) -7 NIL NIL NIL) (-713 1725528 1725816 1726049 "MAYBE" 1726457 NIL MAYBE (NIL T) -8 NIL NIL NIL) (-712 1723086 1723663 1724225 "MATSTOR" 1724999 NIL MATSTOR (NIL T) -7 NIL NIL NIL) (-711 1718508 1722458 1722706 "MATRIX" 1722871 NIL MATRIX (NIL T) -8 NIL NIL NIL) (-710 1714208 1714981 1715717 "MATLIN" 1717865 NIL MATLIN (NIL T T T T) -7 NIL NIL NIL) (-709 1712784 1712955 1713288 "MATCAT2" 1714043 NIL MATCAT2 (NIL T T T T T T T T) -7 NIL NIL NIL) (-708 1702123 1705841 1705918 "MATCAT" 1710950 NIL MATCAT (NIL T T T) -9 NIL 1712422 NIL) (-707 1698076 1699386 1700799 "MATCAT-" 1700804 NIL MATCAT- (NIL T T T T) -8 NIL NIL NIL) (-706 1696152 1696512 1696896 "MAPPKG3" 1697751 NIL MAPPKG3 (NIL T T T) -7 NIL NIL NIL) (-705 1695109 1695306 1695528 "MAPPKG2" 1695976 NIL MAPPKG2 (NIL T T) -7 NIL NIL NIL) (-704 1693566 1693892 1694219 "MAPPKG1" 1694815 NIL MAPPKG1 (NIL T) -7 NIL NIL NIL) (-703 1692567 1692972 1693149 "MAPPAST" 1693409 T MAPPAST (NIL) -8 NIL NIL NIL) (-702 1692172 1692236 1692359 "MAPHACK3" 1692503 NIL MAPHACK3 (NIL T T T) -7 NIL NIL NIL) (-701 1691752 1691825 1691939 "MAPHACK2" 1692104 NIL MAPHACK2 (NIL T T) -7 NIL NIL NIL) (-700 1691178 1691293 1691435 "MAPHACK1" 1691643 NIL MAPHACK1 (NIL T) -7 NIL NIL NIL) (-699 1689101 1689878 1690182 "MAGMA" 1690906 NIL MAGMA (NIL T) -8 NIL NIL NIL) (-698 1688520 1688825 1688916 "MACROAST" 1689030 T MACROAST (NIL) -8 NIL NIL NIL) (-697 1684763 1686759 1687220 "M3D" 1688092 NIL M3D (NIL T) -8 NIL NIL NIL) (-696 1678235 1683074 1683115 "LZSTAGG" 1683897 NIL LZSTAGG (NIL T) -9 NIL 1684192 NIL) (-695 1673917 1675366 1676823 "LZSTAGG-" 1676828 NIL LZSTAGG- (NIL T T) -8 NIL NIL NIL) (-694 1670830 1671808 1672295 "LWORD" 1673462 NIL LWORD (NIL T) -8 NIL NIL NIL) (-693 1670352 1670634 1670709 "LSTAST" 1670775 T LSTAST (NIL) -8 NIL NIL NIL) (-692 1662280 1670123 1670257 "LSQM" 1670262 NIL LSQM (NIL NIL T) -8 NIL NIL NIL) (-691 1661498 1661643 1661871 "LSPP" 1662135 NIL LSPP (NIL T T T T) -7 NIL NIL NIL) (-690 1658235 1658951 1659681 "LSMP1" 1660800 NIL LSMP1 (NIL T) -7 NIL NIL NIL) (-689 1656017 1656348 1656804 "LSMP" 1657924 NIL LSMP (NIL T T T T) -7 NIL NIL NIL) (-688 1649145 1655107 1655148 "LSAGG" 1655210 NIL LSAGG (NIL T) -9 NIL 1655288 NIL) (-687 1645654 1646764 1647977 "LSAGG-" 1647982 NIL LSAGG- (NIL T T) -8 NIL NIL NIL) (-686 1642949 1644798 1645047 "LPOLY" 1645449 NIL LPOLY (NIL T T) -8 NIL NIL NIL) (-685 1642525 1642616 1642739 "LPEFRAC" 1642858 NIL LPEFRAC (NIL T) -7 NIL NIL NIL) (-684 1642208 1642287 1642315 "LOGIC" 1642426 T LOGIC (NIL) -9 NIL 1642508 NIL) (-683 1642064 1642093 1642164 "LOGIC-" 1642169 NIL LOGIC- (NIL T) -8 NIL NIL NIL) (-682 1641239 1641397 1641590 "LODOOPS" 1641920 NIL LODOOPS (NIL T T) -7 NIL NIL NIL) (-681 1639763 1640012 1640365 "LODOF" 1640986 NIL LODOF (NIL T T) -7 NIL NIL NIL) (-680 1635639 1638398 1638439 "LODOCAT" 1638877 NIL LODOCAT (NIL T) -9 NIL 1639088 NIL) (-679 1635354 1635430 1635557 "LODOCAT-" 1635562 NIL LODOCAT- (NIL T T) -8 NIL NIL NIL) (-678 1632340 1635195 1635313 "LODO2" 1635318 NIL LODO2 (NIL T T) -8 NIL NIL NIL) (-677 1629447 1632277 1632322 "LODO1" 1632327 NIL LODO1 (NIL T) -8 NIL NIL NIL) (-676 1626542 1629363 1629429 "LODO" 1629434 NIL LODO (NIL T NIL) -8 NIL NIL NIL) (-675 1625411 1625588 1625893 "LODEEF" 1626365 NIL LODEEF (NIL T T T) -7 NIL NIL NIL) (-674 1623588 1624505 1624758 "LO" 1625243 NIL LO (NIL T T T) -8 NIL NIL NIL) (-673 1618560 1621754 1621795 "LNAGG" 1622657 NIL LNAGG (NIL T) -9 NIL 1623092 NIL) (-672 1617653 1617921 1618263 "LNAGG-" 1618268 NIL LNAGG- (NIL T T) -8 NIL NIL NIL) (-671 1613633 1614578 1615217 "LMOPS" 1617068 NIL LMOPS (NIL T T NIL) -8 NIL NIL NIL) (-670 1612932 1613410 1613451 "LMODULE" 1613456 NIL LMODULE (NIL T) -9 NIL 1613482 NIL) (-669 1609887 1612577 1612700 "LMDICT" 1612842 NIL LMDICT (NIL T) -8 NIL NIL NIL) (-668 1609463 1609677 1609718 "LLINSET" 1609779 NIL LLINSET (NIL T) -9 NIL 1609823 NIL) (-667 1609108 1609371 1609431 "LITERAL" 1609436 NIL LITERAL (NIL T) -8 NIL NIL NIL) (-666 1608627 1608707 1608846 "LIST3" 1609028 NIL LIST3 (NIL T T T) -7 NIL NIL NIL) (-665 1606725 1607073 1607472 "LIST2MAP" 1608274 NIL LIST2MAP (NIL T T) -7 NIL NIL NIL) (-664 1605714 1605910 1606138 "LIST2" 1606543 NIL LIST2 (NIL T T) -7 NIL NIL NIL) (-663 1598168 1604648 1604952 "LIST" 1605443 NIL LIST (NIL T) -8 NIL NIL NIL) (-662 1597751 1597987 1598028 "LINSET" 1598033 NIL LINSET (NIL T) -9 NIL 1598067 NIL) (-661 1596565 1597259 1597426 "LINFORM" 1597636 NIL LINFORM (NIL T NIL) -8 NIL NIL NIL) (-660 1594864 1595592 1595633 "LINEXP" 1596123 NIL LINEXP (NIL T) -9 NIL 1596396 NIL) (-659 1593440 1594344 1594525 "LINELT" 1594735 NIL LINELT (NIL T NIL) -8 NIL NIL NIL) (-658 1591997 1592277 1592588 "LINDEP" 1593192 NIL LINDEP (NIL T T) -7 NIL NIL NIL) (-657 1591133 1591729 1591839 "LINBASIS" 1591927 NIL LINBASIS (NIL NIL) -8 NIL NIL NIL) (-656 1587870 1588619 1589396 "LIMITRF" 1590388 NIL LIMITRF (NIL T) -7 NIL NIL NIL) (-655 1586155 1586469 1586878 "LIMITPS" 1587565 NIL LIMITPS (NIL T T) -7 NIL NIL NIL) (-654 1584983 1585558 1585598 "LIECAT" 1585738 NIL LIECAT (NIL T) -9 NIL 1585889 NIL) (-653 1584818 1584851 1584939 "LIECAT-" 1584944 NIL LIECAT- (NIL T T) -8 NIL NIL NIL) (-652 1578838 1584329 1584557 "LIE" 1584639 NIL LIE (NIL T T) -8 NIL NIL NIL) (-651 1571023 1578378 1578534 "LIB" 1578702 T LIB (NIL) -8 NIL NIL NIL) (-650 1566592 1567541 1568476 "LGROBP" 1570140 NIL LGROBP (NIL NIL T) -7 NIL NIL NIL) (-649 1565216 1566124 1566152 "LFCAT" 1566359 T LFCAT (NIL) -9 NIL 1566498 NIL) (-648 1563154 1563488 1563838 "LF" 1564937 NIL LF (NIL T T) -7 NIL NIL NIL) (-647 1560014 1560686 1561374 "LEXTRIPK" 1562518 NIL LEXTRIPK (NIL T NIL) -7 NIL NIL NIL) (-646 1556602 1557584 1558087 "LEXP" 1559594 NIL LEXP (NIL T T NIL) -8 NIL NIL NIL) (-645 1556018 1556323 1556415 "LETAST" 1556530 T LETAST (NIL) -8 NIL NIL NIL) (-644 1554404 1554729 1555130 "LEADCDET" 1555700 NIL LEADCDET (NIL T T T T) -7 NIL NIL NIL) (-643 1553582 1553668 1553897 "LAZM3PK" 1554325 NIL LAZM3PK (NIL T T T T T T) -7 NIL NIL NIL) (-642 1548093 1551659 1552197 "LAUPOL" 1553094 NIL LAUPOL (NIL T T) -8 NIL NIL NIL) (-641 1547666 1547716 1547877 "LAPLACE" 1548043 NIL LAPLACE (NIL T T) -7 NIL NIL NIL) (-640 1546514 1547230 1547271 "LALG" 1547333 NIL LALG (NIL T) -9 NIL 1547392 NIL) (-639 1546210 1546287 1546423 "LALG-" 1546428 NIL LALG- (NIL T T) -8 NIL NIL NIL) (-638 1543947 1545311 1545562 "LA" 1546043 NIL LA (NIL T T T) -8 NIL NIL NIL) (-637 1543776 1543806 1543847 "KVTFROM" 1543909 NIL KVTFROM (NIL T) -9 NIL NIL NIL) (-636 1542533 1543143 1543328 "KTVLOGIC" 1543611 T KTVLOGIC (NIL) -8 NIL NIL NIL) (-635 1542362 1542392 1542433 "KRCFROM" 1542495 NIL KRCFROM (NIL T) -9 NIL NIL NIL) (-634 1541254 1541453 1541752 "KOVACIC" 1542162 NIL KOVACIC (NIL T T) -7 NIL NIL NIL) (-633 1541083 1541113 1541154 "KONVERT" 1541216 NIL KONVERT (NIL T) -9 NIL NIL NIL) (-632 1540912 1540942 1540983 "KOERCE" 1541045 NIL KOERCE (NIL T) -9 NIL NIL NIL) (-631 1540396 1540489 1540621 "KERNEL2" 1540826 NIL KERNEL2 (NIL T T) -7 NIL NIL NIL) (-630 1538083 1538989 1539366 "KERNEL" 1540052 NIL KERNEL (NIL T) -8 NIL NIL NIL) (-629 1531554 1536560 1536614 "KDAGG" 1536991 NIL KDAGG (NIL T T) -9 NIL 1537197 NIL) (-628 1531065 1531207 1531412 "KDAGG-" 1531417 NIL KDAGG- (NIL T T T) -8 NIL NIL NIL) (-627 1523765 1530726 1530881 "KAFILE" 1530943 NIL KAFILE (NIL T) -8 NIL NIL NIL) (-626 1523369 1523654 1523717 "JVMOP" 1523722 T JVMOP (NIL) -8 NIL NIL NIL) (-625 1522105 1522609 1522858 "JVMMDACC" 1523140 T JVMMDACC (NIL) -8 NIL NIL NIL) (-624 1521041 1521495 1521700 "JVMFDACC" 1521920 T JVMFDACC (NIL) -8 NIL NIL NIL) (-623 1519622 1520117 1520417 "JVMCSTTG" 1520761 T JVMCSTTG (NIL) -8 NIL NIL NIL) (-622 1518758 1519162 1519323 "JVMCFACC" 1519481 T JVMCFACC (NIL) -8 NIL NIL NIL) (-621 1518436 1518675 1518724 "JVMBCODE" 1518729 T JVMBCODE (NIL) -8 NIL NIL NIL) (-620 1512455 1517947 1518175 "JORDAN" 1518257 NIL JORDAN (NIL T T) -8 NIL NIL NIL) (-619 1511768 1512104 1512225 "JOINAST" 1512354 T JOINAST (NIL) -8 NIL NIL NIL) (-618 1507803 1509945 1509999 "IXAGG" 1510928 NIL IXAGG (NIL T T) -9 NIL 1511387 NIL) (-617 1506656 1507028 1507447 "IXAGG-" 1507452 NIL IXAGG- (NIL T T T) -8 NIL NIL NIL) (-616 1501745 1506578 1506637 "IVECTOR" 1506642 NIL IVECTOR (NIL T NIL) -8 NIL NIL NIL) (-615 1500470 1500748 1501014 "ITUPLE" 1501512 NIL ITUPLE (NIL T) -8 NIL NIL NIL) (-614 1498942 1499149 1499444 "ITRIGMNP" 1500292 NIL ITRIGMNP (NIL T T T) -7 NIL NIL NIL) (-613 1497669 1497891 1498174 "ITFUN3" 1498718 NIL ITFUN3 (NIL T T T) -7 NIL NIL NIL) (-612 1497267 1497330 1497453 "ITFUN2" 1497592 NIL ITFUN2 (NIL T T) -8 NIL NIL NIL) (-611 1496372 1496747 1496921 "ITFORM" 1497113 T ITFORM (NIL) -8 NIL NIL NIL) (-610 1494141 1495392 1495670 "ITAYLOR" 1496127 NIL ITAYLOR (NIL T) -8 NIL NIL NIL) (-609 1482538 1488278 1489441 "ISUPS" 1493011 NIL ISUPS (NIL T) -8 NIL NIL NIL) (-608 1481630 1481782 1482018 "ISUMP" 1482385 NIL ISUMP (NIL T T T T) -7 NIL NIL NIL) (-607 1476480 1481575 1481616 "ISTRING" 1481621 NIL ISTRING (NIL NIL) -8 NIL NIL NIL) (-606 1475896 1476201 1476293 "ISAST" 1476408 T ISAST (NIL) -8 NIL NIL NIL) (-605 1475093 1475187 1475403 "IRURPK" 1475810 NIL IRURPK (NIL T T T T T) -7 NIL NIL NIL) (-604 1474005 1474230 1474470 "IRSN" 1474873 T IRSN (NIL) -7 NIL NIL NIL) (-603 1472050 1472431 1472860 "IRRF2F" 1473643 NIL IRRF2F (NIL T) -7 NIL NIL NIL) (-602 1471791 1471835 1471911 "IRREDFFX" 1472006 NIL IRREDFFX (NIL T) -7 NIL NIL NIL) (-601 1470364 1470665 1470964 "IROOT" 1471524 NIL IROOT (NIL T) -7 NIL NIL NIL) (-600 1469503 1469857 1470008 "IRFORM" 1470233 T IRFORM (NIL) -8 NIL NIL NIL) (-599 1468585 1468716 1468930 "IR2F" 1469386 NIL IR2F (NIL T T) -7 NIL NIL NIL) (-598 1466174 1466693 1467259 "IR2" 1468063 NIL IR2 (NIL T T) -7 NIL NIL NIL) (-597 1462614 1463858 1464550 "IR" 1465514 NIL IR (NIL T) -8 NIL NIL NIL) (-596 1462399 1462439 1462499 "IPRNTPK" 1462574 T IPRNTPK (NIL) -7 NIL NIL NIL) (-595 1458352 1462288 1462357 "IPF" 1462362 NIL IPF (NIL NIL) -8 NIL NIL NIL) (-594 1456373 1458277 1458334 "IPADIC" 1458339 NIL IPADIC (NIL NIL NIL) -8 NIL NIL NIL) (-593 1455631 1455933 1456063 "IP4ADDR" 1456263 T IP4ADDR (NIL) -8 NIL NIL NIL) (-592 1454969 1455260 1455392 "IOMODE" 1455519 T IOMODE (NIL) -8 NIL NIL NIL) (-591 1453940 1454566 1454693 "IOBFILE" 1454862 T IOBFILE (NIL) -8 NIL NIL NIL) (-590 1453350 1453844 1453872 "IOBCON" 1453877 T IOBCON (NIL) -9 NIL 1453898 NIL) (-589 1452855 1452919 1453102 "INVLAPLA" 1453286 NIL INVLAPLA (NIL T T) -7 NIL NIL NIL) (-588 1442425 1444857 1447243 "INTTR" 1450519 NIL INTTR (NIL T T) -7 NIL NIL NIL) (-587 1438718 1439502 1440367 "INTTOOLS" 1441610 NIL INTTOOLS (NIL T T) -7 NIL NIL NIL) (-586 1438298 1438395 1438512 "INTSLPE" 1438621 T INTSLPE (NIL) -7 NIL NIL NIL) (-585 1435765 1438221 1438280 "INTRVL" 1438285 NIL INTRVL (NIL T) -8 NIL NIL NIL) (-584 1433343 1433879 1434454 "INTRF" 1435250 NIL INTRF (NIL T) -7 NIL NIL NIL) (-583 1432736 1432851 1432993 "INTRET" 1433241 NIL INTRET (NIL T) -7 NIL NIL NIL) (-582 1430709 1431122 1431592 "INTRAT" 1432344 NIL INTRAT (NIL T T) -7 NIL NIL NIL) (-581 1427954 1428555 1429174 "INTPM" 1430194 NIL INTPM (NIL T T) -7 NIL NIL NIL) (-580 1424671 1425298 1426036 "INTPAF" 1427340 NIL INTPAF (NIL T T T) -7 NIL NIL NIL) (-579 1419772 1420812 1421863 "INTPACK" 1423640 T INTPACK (NIL) -7 NIL NIL NIL) (-578 1419018 1419176 1419384 "INTHERTR" 1419614 NIL INTHERTR (NIL T T) -7 NIL NIL NIL) (-577 1418451 1418537 1418725 "INTHERAL" 1418932 NIL INTHERAL (NIL T T T T) -7 NIL NIL NIL) (-576 1416219 1416740 1417197 "INTHEORY" 1418014 T INTHEORY (NIL) -7 NIL NIL NIL) (-575 1407551 1409246 1411018 "INTG0" 1414571 NIL INTG0 (NIL T T T) -7 NIL NIL NIL) (-574 1388076 1392914 1397724 "INTFTBL" 1402761 T INTFTBL (NIL) -8 NIL NIL NIL) (-573 1387301 1387463 1387636 "INTFACT" 1387935 NIL INTFACT (NIL T) -7 NIL NIL NIL) (-572 1384698 1385174 1385731 "INTEF" 1386855 NIL INTEF (NIL T T) -7 NIL NIL NIL) (-571 1382895 1383790 1383818 "INTDOM" 1384119 T INTDOM (NIL) -9 NIL 1384326 NIL) (-570 1382234 1382438 1382680 "INTDOM-" 1382685 NIL INTDOM- (NIL T) -8 NIL NIL NIL) (-569 1378102 1380523 1380577 "INTCAT" 1381376 NIL INTCAT (NIL T) -9 NIL 1381697 NIL) (-568 1377556 1377677 1377805 "INTBIT" 1377994 T INTBIT (NIL) -7 NIL NIL NIL) (-567 1376237 1376409 1376716 "INTALG" 1377401 NIL INTALG (NIL T T T T T) -7 NIL NIL NIL) (-566 1375714 1375810 1375967 "INTAF" 1376141 NIL INTAF (NIL T T) -7 NIL NIL NIL) (-565 1368681 1375524 1375664 "INTABL" 1375669 NIL INTABL (NIL T T T) -8 NIL NIL NIL) (-564 1367922 1368484 1368549 "INT8" 1368583 T INT8 (NIL) -8 NIL NIL 1368628) (-563 1367162 1367724 1367789 "INT64" 1367823 T INT64 (NIL) -8 NIL NIL 1367868) (-562 1366402 1366964 1367029 "INT32" 1367063 T INT32 (NIL) -8 NIL NIL 1367108) (-561 1365642 1366204 1366269 "INT16" 1366303 T INT16 (NIL) -8 NIL NIL 1366348) (-560 1361830 1365439 1365548 "INT" 1365553 T INT (NIL) -8 NIL NIL NIL) (-559 1355925 1359378 1359406 "INS" 1360340 T INS (NIL) -9 NIL 1361005 NIL) (-558 1352979 1353936 1354910 "INS-" 1354983 NIL INS- (NIL T) -8 NIL NIL NIL) (-557 1351736 1351981 1352279 "INPSIGN" 1352732 NIL INPSIGN (NIL T T) -7 NIL NIL NIL) (-556 1350830 1350971 1351168 "INPRODPF" 1351616 NIL INPRODPF (NIL T T) -7 NIL NIL NIL) (-555 1349700 1349841 1350078 "INPRODFF" 1350710 NIL INPRODFF (NIL T T T T) -7 NIL NIL NIL) (-554 1348688 1348852 1349112 "INNMFACT" 1349536 NIL INNMFACT (NIL T T T T) -7 NIL NIL NIL) (-553 1347867 1347982 1348170 "INMODGCD" 1348587 NIL INMODGCD (NIL T T NIL NIL) -7 NIL NIL NIL) (-552 1346351 1346620 1346944 "INFSP" 1347612 NIL INFSP (NIL T T T) -7 NIL NIL NIL) (-551 1345511 1345652 1345835 "INFPROD0" 1346231 NIL INFPROD0 (NIL T T) -7 NIL NIL NIL) (-550 1345109 1345181 1345279 "INFORM1" 1345446 NIL INFORM1 (NIL T) -7 NIL NIL NIL) (-549 1341676 1343174 1343689 "INFORM" 1344602 T INFORM (NIL) -8 NIL NIL NIL) (-548 1341181 1341288 1341402 "INFINITY" 1341582 T INFINITY (NIL) -7 NIL NIL NIL) (-547 1340255 1340901 1341002 "INETCLTS" 1341100 T INETCLTS (NIL) -8 NIL NIL NIL) (-546 1338853 1339121 1339442 "INEP" 1340003 NIL INEP (NIL T T T) -7 NIL NIL NIL) (-545 1337914 1338750 1338815 "INDE" 1338820 NIL INDE (NIL T) -8 NIL NIL NIL) (-544 1337466 1337546 1337663 "INCRMAPS" 1337841 NIL INCRMAPS (NIL T) -7 NIL NIL NIL) (-543 1336188 1336735 1336941 "INBFILE" 1337280 T INBFILE (NIL) -8 NIL NIL NIL) (-542 1331367 1332424 1333368 "INBFF" 1335276 NIL INBFF (NIL T) -7 NIL NIL NIL) (-541 1330221 1330544 1330572 "INBCON" 1331085 T INBCON (NIL) -9 NIL 1331351 NIL) (-540 1329431 1329696 1329972 "INBCON-" 1329977 NIL INBCON- (NIL T) -8 NIL NIL NIL) (-539 1328850 1329155 1329246 "INAST" 1329360 T INAST (NIL) -8 NIL NIL NIL) (-538 1328217 1328529 1328635 "IMPTAST" 1328764 T IMPTAST (NIL) -8 NIL NIL NIL) (-537 1324138 1328061 1328165 "IMATRIX" 1328170 NIL IMATRIX (NIL T NIL NIL) -8 NIL NIL NIL) (-536 1322830 1322969 1323285 "IMATQF" 1323994 NIL IMATQF (NIL T T T T T T T T) -7 NIL NIL NIL) (-535 1321010 1321277 1321614 "IMATLIN" 1322586 NIL IMATLIN (NIL T T T T) -7 NIL NIL NIL) (-534 1314925 1320934 1320992 "ILIST" 1320997 NIL ILIST (NIL T NIL) -8 NIL NIL NIL) (-533 1312591 1314785 1314898 "IIARRAY2" 1314903 NIL IIARRAY2 (NIL T NIL NIL T T) -8 NIL NIL NIL) (-532 1307391 1312502 1312566 "IFF" 1312571 NIL IFF (NIL NIL NIL) -8 NIL NIL NIL) (-531 1306672 1307008 1307124 "IFAST" 1307295 T IFAST (NIL) -8 NIL NIL NIL) (-530 1301184 1305964 1306152 "IFARRAY" 1306529 NIL IFARRAY (NIL T NIL) -8 NIL NIL NIL) (-529 1300222 1301088 1301161 "IFAMON" 1301166 NIL IFAMON (NIL T T NIL) -8 NIL NIL NIL) (-528 1299794 1299871 1299925 "IEVALAB" 1300132 NIL IEVALAB (NIL T T) -9 NIL NIL NIL) (-527 1299457 1299537 1299697 "IEVALAB-" 1299702 NIL IEVALAB- (NIL T T T) -8 NIL NIL NIL) (-526 1298521 1299346 1299421 "IDPOAMS" 1299426 NIL IDPOAMS (NIL T T) -8 NIL NIL NIL) (-525 1297654 1298410 1298485 "IDPOAM" 1298490 NIL IDPOAM (NIL T T) -8 NIL NIL NIL) (-524 1297035 1297569 1297631 "IDPO" 1297636 NIL IDPO (NIL T T) -8 NIL NIL NIL) (-523 1295515 1296042 1296094 "IDPC" 1296606 NIL IDPC (NIL T T) -9 NIL 1296887 NIL) (-522 1294847 1295407 1295480 "IDPAM" 1295485 NIL IDPAM (NIL T T) -8 NIL NIL NIL) (-521 1294062 1294739 1294812 "IDPAG" 1294817 NIL IDPAG (NIL T T) -8 NIL NIL NIL) (-520 1293606 1293868 1293958 "IDENT" 1293992 T IDENT (NIL) -8 NIL NIL NIL) (-519 1289825 1290709 1291604 "IDECOMP" 1292763 NIL IDECOMP (NIL NIL NIL) -7 NIL NIL NIL) (-518 1282460 1283748 1284795 "IDEAL" 1288861 NIL IDEAL (NIL T T T T) -8 NIL NIL NIL) (-517 1281602 1281732 1281932 "ICDEN" 1282344 NIL ICDEN (NIL T T T T) -7 NIL NIL NIL) (-516 1280577 1281082 1281229 "ICARD" 1281475 T ICARD (NIL) -8 NIL NIL NIL) (-515 1278607 1278950 1279355 "IBPTOOLS" 1280254 NIL IBPTOOLS (NIL T T T T) -7 NIL NIL NIL) (-514 1273722 1278227 1278340 "IBITS" 1278526 NIL IBITS (NIL NIL) -8 NIL NIL NIL) (-513 1270397 1271021 1271716 "IBATOOL" 1273139 NIL IBATOOL (NIL T T T) -7 NIL NIL NIL) (-512 1268158 1268638 1269171 "IBACHIN" 1269932 NIL IBACHIN (NIL T T T) -7 NIL NIL NIL) (-511 1265748 1268004 1268107 "IARRAY2" 1268112 NIL IARRAY2 (NIL T NIL NIL) -8 NIL NIL NIL) (-510 1261461 1265674 1265731 "IARRAY1" 1265736 NIL IARRAY1 (NIL T NIL) -8 NIL NIL NIL) (-509 1254471 1259873 1260354 "IAN" 1261000 T IAN (NIL) -8 NIL NIL NIL) (-508 1253976 1254039 1254212 "IALGFACT" 1254408 NIL IALGFACT (NIL T T T T) -7 NIL NIL NIL) (-507 1253468 1253617 1253645 "HYPCAT" 1253852 T HYPCAT (NIL) -9 NIL NIL NIL) (-506 1252970 1253123 1253309 "HYPCAT-" 1253314 NIL HYPCAT- (NIL T) -8 NIL NIL NIL) (-505 1252517 1252765 1252848 "HOSTNAME" 1252907 T HOSTNAME (NIL) -8 NIL NIL NIL) (-504 1252350 1252399 1252440 "HOMOTOP" 1252445 NIL HOMOTOP (NIL T) -9 NIL 1252478 NIL) (-503 1248783 1250282 1250323 "HOAGG" 1251304 NIL HOAGG (NIL T) -9 NIL 1252033 NIL) (-502 1247299 1247776 1248302 "HOAGG-" 1248307 NIL HOAGG- (NIL T T) -8 NIL NIL NIL) (-501 1240335 1246892 1247042 "HEXADEC" 1247169 T HEXADEC (NIL) -8 NIL NIL NIL) (-500 1239047 1239305 1239568 "HEUGCD" 1240112 NIL HEUGCD (NIL T) -7 NIL NIL NIL) (-499 1237979 1238884 1239014 "HELLFDIV" 1239019 NIL HELLFDIV (NIL T T T T) -8 NIL NIL NIL) (-498 1235989 1237756 1237844 "HEAP" 1237923 NIL HEAP (NIL T) -8 NIL NIL NIL) (-497 1235186 1235541 1235675 "HEADAST" 1235875 T HEADAST (NIL) -8 NIL NIL NIL) (-496 1228573 1235101 1235163 "HDP" 1235168 NIL HDP (NIL NIL T) -8 NIL NIL NIL) (-495 1221585 1228208 1228360 "HDMP" 1228474 NIL HDMP (NIL NIL T) -8 NIL NIL NIL) (-494 1220891 1221049 1221213 "HB" 1221441 T HB (NIL) -7 NIL NIL NIL) (-493 1213901 1220737 1220841 "HASHTBL" 1220846 NIL HASHTBL (NIL T T NIL) -8 NIL NIL NIL) (-492 1213317 1213622 1213714 "HASAST" 1213829 T HASAST (NIL) -8 NIL NIL NIL) (-491 1210723 1212939 1213121 "HACKPI" 1213155 T HACKPI (NIL) -8 NIL NIL NIL) (-490 1205895 1210576 1210689 "GTSET" 1210694 NIL GTSET (NIL T T T T) -8 NIL NIL NIL) (-489 1198934 1205773 1205871 "GSTBL" 1205876 NIL GSTBL (NIL T T T NIL) -8 NIL NIL NIL) (-488 1190683 1198099 1198355 "GSERIES" 1198734 NIL GSERIES (NIL T NIL NIL) -8 NIL NIL NIL) (-487 1189714 1190227 1190255 "GROUP" 1190458 T GROUP (NIL) -9 NIL 1190592 NIL) (-486 1189038 1189239 1189490 "GROUP-" 1189495 NIL GROUP- (NIL T) -8 NIL NIL NIL) (-485 1187387 1187726 1188113 "GROEBSOL" 1188715 NIL GROEBSOL (NIL NIL T T) -7 NIL NIL NIL) (-484 1186215 1186575 1186626 "GRMOD" 1187155 NIL GRMOD (NIL T T) -9 NIL 1187323 NIL) (-483 1185971 1186019 1186147 "GRMOD-" 1186152 NIL GRMOD- (NIL T T T) -8 NIL NIL NIL) (-482 1181111 1182325 1183325 "GRIMAGE" 1184991 T GRIMAGE (NIL) -8 NIL NIL NIL) (-481 1179505 1179838 1180162 "GRDEF" 1180807 T GRDEF (NIL) -7 NIL NIL NIL) (-480 1178937 1179065 1179206 "GRAY" 1179384 T GRAY (NIL) -7 NIL NIL NIL) (-479 1178014 1178516 1178567 "GRALG" 1178720 NIL GRALG (NIL T T) -9 NIL 1178813 NIL) (-478 1177651 1177748 1177911 "GRALG-" 1177916 NIL GRALG- (NIL T T T) -8 NIL NIL NIL) (-477 1174132 1177234 1177413 "GPOLSET" 1177557 NIL GPOLSET (NIL T T T T) -8 NIL NIL NIL) (-476 1173480 1173543 1173801 "GOSPER" 1174069 NIL GOSPER (NIL T T T T T) -7 NIL NIL NIL) (-475 1169050 1169918 1170444 "GMODPOL" 1173179 NIL GMODPOL (NIL NIL T T T NIL T) -8 NIL NIL NIL) (-474 1168037 1168239 1168477 "GHENSEL" 1168862 NIL GHENSEL (NIL T T) -7 NIL NIL NIL) (-473 1162109 1163036 1164056 "GENUPS" 1167121 NIL GENUPS (NIL T T) -7 NIL NIL NIL) (-472 1161800 1161857 1161946 "GENUFACT" 1162052 NIL GENUFACT (NIL T) -7 NIL NIL NIL) (-471 1161200 1161289 1161454 "GENPGCD" 1161718 NIL GENPGCD (NIL T T T T) -7 NIL NIL NIL) (-470 1160668 1160709 1160922 "GENMFACT" 1161159 NIL GENMFACT (NIL T T T T T) -7 NIL NIL NIL) (-469 1159204 1159491 1159798 "GENEEZ" 1160411 NIL GENEEZ (NIL T T) -7 NIL NIL NIL) (-468 1152376 1158815 1158977 "GDMP" 1159127 NIL GDMP (NIL NIL T T) -8 NIL NIL NIL) (-467 1141114 1146147 1147253 "GCNAALG" 1151359 NIL GCNAALG (NIL T NIL NIL NIL) -8 NIL NIL NIL) (-466 1139241 1140289 1140317 "GCDDOM" 1140572 T GCDDOM (NIL) -9 NIL 1140729 NIL) (-465 1138681 1138838 1139053 "GCDDOM-" 1139058 NIL GCDDOM- (NIL T) -8 NIL NIL NIL) (-464 1127153 1129627 1132019 "GBINTERN" 1136372 NIL GBINTERN (NIL T T T T) -7 NIL NIL NIL) (-463 1124954 1125282 1125703 "GBF" 1126828 NIL GBF (NIL T T T T) -7 NIL NIL NIL) (-462 1123711 1123900 1124167 "GBEUCLID" 1124770 NIL GBEUCLID (NIL T T T T) -7 NIL NIL NIL) (-461 1122361 1122568 1122872 "GB" 1123490 NIL GB (NIL T T T T) -7 NIL NIL NIL) (-460 1121692 1121835 1121984 "GAUSSFAC" 1122232 T GAUSSFAC (NIL) -7 NIL NIL NIL) (-459 1120013 1120361 1120675 "GALUTIL" 1121411 NIL GALUTIL (NIL T) -7 NIL NIL NIL) (-458 1118273 1118595 1118919 "GALPOLYU" 1119740 NIL GALPOLYU (NIL T T) -7 NIL NIL NIL) (-457 1115572 1115928 1116335 "GALFACTU" 1117970 NIL GALFACTU (NIL T T T) -7 NIL NIL NIL) (-456 1107186 1108877 1110485 "GALFACT" 1114004 NIL GALFACT (NIL T) -7 NIL NIL NIL) (-455 1104472 1105232 1105260 "FVFUN" 1106416 T FVFUN (NIL) -9 NIL 1107136 NIL) (-454 1103702 1103920 1103948 "FVC" 1104239 T FVC (NIL) -9 NIL 1104422 NIL) (-453 1103303 1103527 1103595 "FUNDESC" 1103654 T FUNDESC (NIL) -8 NIL NIL NIL) (-452 1102876 1103100 1103181 "FUNCTION" 1103255 NIL FUNCTION (NIL NIL) -8 NIL NIL NIL) (-451 1101553 1102177 1102380 "FTEM" 1102693 T FTEM (NIL) -8 NIL NIL NIL) (-450 1099183 1099875 1100341 "FT" 1101107 T FT (NIL) -8 NIL NIL NIL) (-449 1097452 1097763 1098160 "FSUPFACT" 1098874 NIL FSUPFACT (NIL T T T) -7 NIL NIL NIL) (-448 1095771 1096138 1096470 "FST" 1097140 T FST (NIL) -8 NIL NIL NIL) (-447 1094952 1095076 1095264 "FSRED" 1095653 NIL FSRED (NIL T T) -7 NIL NIL NIL) (-446 1093641 1093907 1094254 "FSPRMELT" 1094667 NIL FSPRMELT (NIL T T) -7 NIL NIL NIL) (-445 1090851 1091385 1091871 "FSPECF" 1093204 NIL FSPECF (NIL T T) -7 NIL NIL NIL) (-444 1090373 1090433 1090603 "FSINT" 1090792 NIL FSINT (NIL T T) -7 NIL NIL NIL) (-443 1088509 1089366 1089669 "FSERIES" 1090152 NIL FSERIES (NIL T T) -8 NIL NIL NIL) (-442 1087533 1087667 1087891 "FSCINT" 1088389 NIL FSCINT (NIL T T) -7 NIL NIL NIL) (-441 1086557 1086718 1086945 "FSAGG2" 1087386 NIL FSAGG2 (NIL T T T T) -7 NIL NIL NIL) (-440 1082421 1085501 1085542 "FSAGG" 1085912 NIL FSAGG (NIL T) -9 NIL 1086171 NIL) (-439 1080021 1080784 1081580 "FSAGG-" 1081675 NIL FSAGG- (NIL T T) -8 NIL NIL NIL) (-438 1077681 1077979 1078527 "FS2UPS" 1079739 NIL FS2UPS (NIL T T T T T NIL) -7 NIL NIL NIL) (-437 1076547 1076730 1077032 "FS2EXPXP" 1077506 NIL FS2EXPXP (NIL T T NIL NIL) -7 NIL NIL NIL) (-436 1076175 1076224 1076353 "FS2" 1076498 NIL FS2 (NIL T T T T) -7 NIL NIL NIL) (-435 1056399 1065949 1065990 "FS" 1069874 NIL FS (NIL T) -9 NIL 1072163 NIL) (-434 1044460 1048035 1052092 "FS-" 1052392 NIL FS- (NIL T T) -8 NIL NIL NIL) (-433 1043874 1044001 1044153 "FRUTIL" 1044340 NIL FRUTIL (NIL T) -7 NIL NIL NIL) (-432 1038385 1041563 1041603 "FRNAALG" 1042923 NIL FRNAALG (NIL T) -9 NIL 1043521 NIL) (-431 1033866 1035134 1036409 "FRNAALG-" 1037159 NIL FRNAALG- (NIL T T) -8 NIL NIL NIL) (-430 1033498 1033547 1033674 "FRNAAF2" 1033817 NIL FRNAAF2 (NIL T T T T) -7 NIL NIL NIL) (-429 1031785 1032347 1032643 "FRMOD" 1033310 NIL FRMOD (NIL T T T T NIL) -8 NIL NIL NIL) (-428 1030970 1031063 1031354 "FRIDEAL2" 1031692 NIL FRIDEAL2 (NIL T T T T T T T T) -7 NIL NIL NIL) (-427 1028575 1029345 1029663 "FRIDEAL" 1030761 NIL FRIDEAL (NIL T T T T) -8 NIL NIL NIL) (-426 1027666 1028122 1028163 "FRETRCT" 1028168 NIL FRETRCT (NIL T) -9 NIL 1028344 NIL) (-425 1026724 1027009 1027360 "FRETRCT-" 1027365 NIL FRETRCT- (NIL T T) -8 NIL NIL NIL) (-424 1023538 1025008 1025067 "FRAMALG" 1025949 NIL FRAMALG (NIL T T) -9 NIL 1026241 NIL) (-423 1021576 1022127 1022757 "FRAMALG-" 1022980 NIL FRAMALG- (NIL T T T) -8 NIL NIL NIL) (-422 1021206 1021269 1021376 "FRAC2" 1021513 NIL FRAC2 (NIL T T) -7 NIL NIL NIL) (-421 1014177 1020679 1020956 "FRAC" 1020961 NIL FRAC (NIL T) -8 NIL NIL NIL) (-420 1013807 1013870 1013977 "FR2" 1014114 NIL FR2 (NIL T T) -7 NIL NIL NIL) (-419 1004724 1009302 1010660 "FR" 1012481 NIL FR (NIL T) -8 NIL NIL NIL) (-418 998636 1002103 1002131 "FPS" 1003250 T FPS (NIL) -9 NIL 1003807 NIL) (-417 998061 998194 998358 "FPS-" 998504 NIL FPS- (NIL T) -8 NIL NIL NIL) (-416 995013 997018 997046 "FPC" 997271 T FPC (NIL) -9 NIL 997413 NIL) (-415 994794 994846 994943 "FPC-" 994948 NIL FPC- (NIL T) -8 NIL NIL NIL) (-414 993552 994282 994323 "FPATMAB" 994328 NIL FPATMAB (NIL T) -9 NIL 994480 NIL) (-413 991695 992294 992641 "FPARFRAC" 993268 NIL FPARFRAC (NIL T T) -8 NIL NIL NIL) (-412 986987 987587 988269 "FORTRAN" 991127 NIL FORTRAN (NIL NIL NIL NIL NIL) -8 NIL NIL NIL) (-411 984561 985225 985253 "FORTFN" 986313 T FORTFN (NIL) -9 NIL 986937 NIL) (-410 984313 984375 984403 "FORTCAT" 984462 T FORTCAT (NIL) -9 NIL 984524 NIL) (-409 981999 982529 983068 "FORT" 983794 T FORT (NIL) -7 NIL NIL NIL) (-408 981781 981817 981886 "FORMULA1" 981963 NIL FORMULA1 (NIL T) -7 NIL NIL NIL) (-407 979785 980397 980787 "FORMULA" 981411 T FORMULA (NIL) -8 NIL NIL NIL) (-406 979302 979360 979533 "FORDER" 979727 NIL FORDER (NIL T T T T) -7 NIL NIL NIL) (-405 978362 978562 978755 "FOP" 979129 T FOP (NIL) -7 NIL NIL NIL) (-404 976775 977642 977816 "FNLA" 978244 NIL FNLA (NIL NIL NIL T) -8 NIL NIL NIL) (-403 975394 975905 975933 "FNCAT" 976393 T FNCAT (NIL) -9 NIL 976653 NIL) (-402 974837 975353 975381 "FNAME" 975386 T FNAME (NIL) -8 NIL NIL NIL) (-401 973163 974336 974364 "FMTC" 974369 T FMTC (NIL) -9 NIL 974405 NIL) (-400 971712 973099 973145 "FMONOID" 973150 NIL FMONOID (NIL T) -8 NIL NIL NIL) (-399 968301 969667 969708 "FMONCAT" 970925 NIL FMONCAT (NIL T) -9 NIL 971530 NIL) (-398 965623 966371 966399 "FMFUN" 967543 T FMFUN (NIL) -9 NIL 968251 NIL) (-397 962496 963548 963602 "FMCAT" 964797 NIL FMCAT (NIL T T) -9 NIL 965292 NIL) (-396 961729 961946 961974 "FMC" 962264 T FMC (NIL) -9 NIL 962446 NIL) (-395 960397 961495 961595 "FM1" 961674 NIL FM1 (NIL T T) -8 NIL NIL NIL) (-394 959415 960139 960288 "FM" 960293 NIL FM (NIL T T) -8 NIL NIL NIL) (-393 957153 957605 958099 "FLOATRP" 958966 NIL FLOATRP (NIL T) -7 NIL NIL NIL) (-392 954555 955091 955669 "FLOATCP" 956620 NIL FLOATCP (NIL T) -7 NIL NIL NIL) (-391 947211 952284 952905 "FLOAT" 953954 T FLOAT (NIL) -8 NIL NIL NIL) (-390 945729 946803 946844 "FLINEXP" 946849 NIL FLINEXP (NIL T) -9 NIL 946942 NIL) (-389 944859 945118 945446 "FLINEXP-" 945451 NIL FLINEXP- (NIL T T) -8 NIL NIL NIL) (-388 943917 944079 944303 "FLASORT" 944711 NIL FLASORT (NIL T T) -7 NIL NIL NIL) (-387 940835 941887 941939 "FLALG" 943166 NIL FLALG (NIL T T) -9 NIL 943633 NIL) (-386 939859 940020 940247 "FLAGG2" 940688 NIL FLAGG2 (NIL T T T T) -7 NIL NIL NIL) (-385 933114 937268 937309 "FLAGG" 938571 NIL FLAGG (NIL T) -9 NIL 939223 NIL) (-384 931768 932179 932669 "FLAGG-" 932674 NIL FLAGG- (NIL T T) -8 NIL NIL NIL) (-383 928399 929613 929672 "FINRALG" 930800 NIL FINRALG (NIL T T) -9 NIL 931308 NIL) (-382 927523 927788 928127 "FINRALG-" 928132 NIL FINRALG- (NIL T T T) -8 NIL NIL NIL) (-381 926829 927128 927156 "FINITE" 927352 T FINITE (NIL) -9 NIL 927459 NIL) (-380 918780 921359 921399 "FINAALG" 925066 NIL FINAALG (NIL T) -9 NIL 926519 NIL) (-379 913896 915162 916306 "FINAALG-" 917685 NIL FINAALG- (NIL T T) -8 NIL NIL NIL) (-378 912456 912878 912932 "FILECAT" 913616 NIL FILECAT (NIL T T) -9 NIL 913832 NIL) (-377 911734 912211 912314 "FILE" 912386 NIL FILE (NIL T) -8 NIL NIL NIL) (-376 909130 910964 910992 "FIELD" 911032 T FIELD (NIL) -9 NIL 911112 NIL) (-375 907672 908135 908646 "FIELD-" 908651 NIL FIELD- (NIL T) -8 NIL NIL NIL) (-374 905355 906307 906654 "FGROUP" 907358 NIL FGROUP (NIL T) -8 NIL NIL NIL) (-373 904427 904609 904829 "FGLMICPK" 905187 NIL FGLMICPK (NIL T NIL) -7 NIL NIL NIL) (-372 899661 904352 904409 "FFX" 904414 NIL FFX (NIL T NIL) -8 NIL NIL NIL) (-371 899256 899323 899458 "FFSLPE" 899594 NIL FFSLPE (NIL T T T) -7 NIL NIL NIL) (-370 898754 898796 899005 "FFPOLY2" 899214 NIL FFPOLY2 (NIL T T) -7 NIL NIL NIL) (-369 894630 895526 896322 "FFPOLY" 897990 NIL FFPOLY (NIL T) -7 NIL NIL NIL) (-368 889878 894549 894612 "FFP" 894617 NIL FFP (NIL T NIL) -8 NIL NIL NIL) (-367 884388 889221 889411 "FFNBX" 889732 NIL FFNBX (NIL T NIL) -8 NIL NIL NIL) (-366 878700 883523 883781 "FFNBP" 884242 NIL FFNBP (NIL T NIL) -8 NIL NIL NIL) (-365 872717 877984 878195 "FFNB" 878533 NIL FFNB (NIL NIL NIL) -8 NIL NIL NIL) (-364 871537 871747 872062 "FFINTBAS" 872514 NIL FFINTBAS (NIL T T T) -7 NIL NIL NIL) (-363 867109 869784 869812 "FFIELDC" 870432 T FFIELDC (NIL) -9 NIL 870808 NIL) (-362 865687 866142 866639 "FFIELDC-" 866644 NIL FFIELDC- (NIL T) -8 NIL NIL NIL) (-361 865244 865302 865426 "FFHOM" 865629 NIL FFHOM (NIL T T T) -7 NIL NIL NIL) (-360 862903 863426 863943 "FFF" 864759 NIL FFF (NIL T) -7 NIL NIL NIL) (-359 857917 862645 862746 "FFCGX" 862846 NIL FFCGX (NIL T NIL) -8 NIL NIL NIL) (-358 852935 857649 857756 "FFCGP" 857860 NIL FFCGP (NIL T NIL) -8 NIL NIL NIL) (-357 847514 852662 852770 "FFCG" 852871 NIL FFCG (NIL NIL NIL) -8 NIL NIL NIL) (-356 846919 846968 847203 "FFCAT2" 847465 NIL FFCAT2 (NIL T T T T T T T T) -7 NIL NIL NIL) (-355 825580 836651 836737 "FFCAT" 841902 NIL FFCAT (NIL T T T) -9 NIL 843353 NIL) (-354 820591 821825 823139 "FFCAT-" 824369 NIL FFCAT- (NIL T T T T) -8 NIL NIL NIL) (-353 815391 820502 820566 "FF" 820571 NIL FF (NIL NIL NIL) -8 NIL NIL NIL) (-352 804044 808363 809583 "FEXPR" 814243 NIL FEXPR (NIL NIL NIL T) -8 NIL NIL NIL) (-351 802972 803441 803482 "FEVALAB" 803566 NIL FEVALAB (NIL T) -9 NIL 803827 NIL) (-350 802089 802341 802679 "FEVALAB-" 802684 NIL FEVALAB- (NIL T T) -8 NIL NIL NIL) (-349 798951 799836 799951 "FDIVCAT" 801519 NIL FDIVCAT (NIL T T T T) -9 NIL 801956 NIL) (-348 798707 798740 798910 "FDIVCAT-" 798915 NIL FDIVCAT- (NIL T T T T T) -8 NIL NIL NIL) (-347 797921 798014 798291 "FDIV2" 798614 NIL FDIV2 (NIL T T T T T T T T) -7 NIL NIL NIL) (-346 796331 797304 797507 "FDIV" 797820 NIL FDIV (NIL T T T T) -8 NIL NIL NIL) (-345 795239 795626 795828 "FCTRDATA" 796149 T FCTRDATA (NIL) -8 NIL NIL NIL) (-344 793895 794184 794473 "FCPAK1" 794970 T FCPAK1 (NIL) -7 NIL NIL NIL) (-343 792898 793395 793536 "FCOMP" 793786 NIL FCOMP (NIL T) -8 NIL NIL NIL) (-342 776212 780048 783586 "FC" 789380 T FC (NIL) -8 NIL NIL NIL) (-341 767901 772533 772573 "FAXF" 774375 NIL FAXF (NIL T) -9 NIL 775067 NIL) (-340 765022 765835 766660 "FAXF-" 767125 NIL FAXF- (NIL T T) -8 NIL NIL NIL) (-339 759591 764398 764574 "FARRAY" 764879 NIL FARRAY (NIL T) -8 NIL NIL NIL) (-338 754150 756538 756591 "FAMR" 757614 NIL FAMR (NIL T T) -9 NIL 758074 NIL) (-337 752974 753342 753777 "FAMR-" 753782 NIL FAMR- (NIL T T T) -8 NIL NIL NIL) (-336 752001 752896 752949 "FAMONOID" 752954 NIL FAMONOID (NIL T) -8 NIL NIL NIL) (-335 749631 750483 750536 "FAMONC" 751477 NIL FAMONC (NIL T T) -9 NIL 751863 NIL) (-334 748105 749385 749522 "FAGROUP" 749527 NIL FAGROUP (NIL T) -8 NIL NIL NIL) (-333 745858 746219 746622 "FACUTIL" 747786 NIL FACUTIL (NIL T T T T) -7 NIL NIL NIL) (-332 744945 745142 745364 "FACTFUNC" 745668 NIL FACTFUNC (NIL T) -7 NIL NIL NIL) (-331 736703 744248 744447 "EXPUPXS" 744801 NIL EXPUPXS (NIL T NIL NIL) -8 NIL NIL NIL) (-330 734156 734726 735312 "EXPRTUBE" 736137 T EXPRTUBE (NIL) -7 NIL NIL NIL) (-329 730367 731019 731749 "EXPRODE" 733495 NIL EXPRODE (NIL T T) -7 NIL NIL NIL) (-328 724801 725508 726314 "EXPR2UPS" 729665 NIL EXPR2UPS (NIL T T) -7 NIL NIL NIL) (-327 724427 724490 724599 "EXPR2" 724738 NIL EXPR2 (NIL T T) -7 NIL NIL NIL) (-326 708721 723076 723505 "EXPR" 724031 NIL EXPR (NIL T) -8 NIL NIL NIL) (-325 699038 707872 708163 "EXPEXPAN" 708557 NIL EXPEXPAN (NIL T T NIL NIL) -8 NIL NIL NIL) (-324 698458 698762 698853 "EXITAST" 698967 T EXITAST (NIL) -8 NIL NIL NIL) (-323 698222 698415 698444 "EXIT" 698449 T EXIT (NIL) -8 NIL NIL NIL) (-322 697843 697911 698024 "EVALCYC" 698154 NIL EVALCYC (NIL T) -7 NIL NIL NIL) (-321 697360 697502 697543 "EVALAB" 697713 NIL EVALAB (NIL T) -9 NIL 697817 NIL) (-320 696817 696963 697184 "EVALAB-" 697189 NIL EVALAB- (NIL T T) -8 NIL NIL NIL) (-319 693925 695473 695501 "EUCDOM" 696056 T EUCDOM (NIL) -9 NIL 696406 NIL) (-318 692264 692772 693362 "EUCDOM-" 693367 NIL EUCDOM- (NIL T) -8 NIL NIL NIL) (-317 691890 691953 692062 "ESTOOLS2" 692201 NIL ESTOOLS2 (NIL T T) -7 NIL NIL NIL) (-316 691635 691683 691763 "ESTOOLS1" 691842 NIL ESTOOLS1 (NIL T) -7 NIL NIL NIL) (-315 678952 681933 684683 "ESTOOLS" 688905 T ESTOOLS (NIL) -7 NIL NIL NIL) (-314 678691 678729 678811 "ESCONT1" 678914 NIL ESCONT1 (NIL NIL NIL) -7 NIL NIL NIL) (-313 674999 675826 676606 "ESCONT" 677931 T ESCONT (NIL) -7 NIL NIL NIL) (-312 674668 674724 674824 "ES2" 674943 NIL ES2 (NIL T T) -7 NIL NIL NIL) (-311 674292 674356 674465 "ES1" 674604 NIL ES1 (NIL T T) -7 NIL NIL NIL) (-310 667993 669923 669951 "ES" 672719 T ES (NIL) -9 NIL 674129 NIL) (-309 662670 664227 666044 "ES-" 666208 NIL ES- (NIL T) -8 NIL NIL NIL) (-308 661862 662015 662191 "ERROR" 662514 T ERROR (NIL) -7 NIL NIL NIL) (-307 654878 661721 661812 "EQTBL" 661817 NIL EQTBL (NIL T T) -8 NIL NIL NIL) (-306 654504 654567 654676 "EQ2" 654815 NIL EQ2 (NIL T T) -7 NIL NIL NIL) (-305 646763 649818 651267 "EQ" 653088 NIL -1490 (NIL T) -8 NIL NIL NIL) (-304 642006 643101 644194 "EP" 645702 NIL EP (NIL T) -7 NIL NIL NIL) (-303 640546 640897 641203 "ENV" 641720 T ENV (NIL) -8 NIL NIL NIL) (-302 639506 640180 640208 "ENTIRER" 640213 T ENTIRER (NIL) -9 NIL 640259 NIL) (-301 635918 637688 638049 "EMR" 639314 NIL EMR (NIL T T T NIL NIL NIL) -8 NIL NIL NIL) (-300 635022 635233 635287 "ELTAGG" 635667 NIL ELTAGG (NIL T T) -9 NIL 635878 NIL) (-299 634729 634803 634944 "ELTAGG-" 634949 NIL ELTAGG- (NIL T T T) -8 NIL NIL NIL) (-298 634487 634522 634576 "ELTAB" 634660 NIL ELTAB (NIL T T) -9 NIL 634712 NIL) (-297 633589 633759 633958 "ELFUTS" 634338 NIL ELFUTS (NIL T T) -7 NIL NIL NIL) (-296 633313 633387 633415 "ELEMFUN" 633520 T ELEMFUN (NIL) -9 NIL NIL NIL) (-295 633177 633204 633272 "ELEMFUN-" 633277 NIL ELEMFUN- (NIL T) -8 NIL NIL NIL) (-294 627588 631219 631260 "ELAGG" 632200 NIL ELAGG (NIL T) -9 NIL 632663 NIL) (-293 625765 626307 626970 "ELAGG-" 626975 NIL ELAGG- (NIL T T) -8 NIL NIL NIL) (-292 625047 625214 625370 "ELABOR" 625629 T ELABOR (NIL) -8 NIL NIL NIL) (-291 623653 623987 624281 "ELABEXPR" 624773 T ELABEXPR (NIL) -8 NIL NIL NIL) (-290 616165 618290 619119 "EFUPXS" 622928 NIL EFUPXS (NIL T T T T) -8 NIL NIL NIL) (-289 609291 611414 612225 "EFULS" 615440 NIL EFULS (NIL T T T) -8 NIL NIL NIL) (-288 606728 607134 607606 "EFSTRUC" 608923 NIL EFSTRUC (NIL T T) -7 NIL NIL NIL) (-287 596165 598085 599633 "EF" 605243 NIL EF (NIL T T) -7 NIL NIL NIL) (-286 595143 595650 595799 "EAB" 596036 T EAB (NIL) -8 NIL NIL NIL) (-285 594265 595102 595130 "E04UCFA" 595135 T E04UCFA (NIL) -8 NIL NIL NIL) (-284 593387 594224 594252 "E04NAFA" 594257 T E04NAFA (NIL) -8 NIL NIL NIL) (-283 592509 593346 593374 "E04MBFA" 593379 T E04MBFA (NIL) -8 NIL NIL NIL) (-282 591631 592468 592496 "E04JAFA" 592501 T E04JAFA (NIL) -8 NIL NIL NIL) (-281 590755 591590 591618 "E04GCFA" 591623 T E04GCFA (NIL) -8 NIL NIL NIL) (-280 589879 590714 590742 "E04FDFA" 590747 T E04FDFA (NIL) -8 NIL NIL NIL) (-279 589001 589838 589866 "E04DGFA" 589871 T E04DGFA (NIL) -8 NIL NIL NIL) (-278 583078 584526 585890 "E04AGNT" 587657 T E04AGNT (NIL) -7 NIL NIL NIL) (-277 581698 582379 582419 "DVARCAT" 582760 NIL DVARCAT (NIL T) -9 NIL 582923 NIL) (-276 580848 581114 581428 "DVARCAT-" 581433 NIL DVARCAT- (NIL T T) -8 NIL NIL NIL) (-275 572809 580647 580776 "DSMP" 580781 NIL DSMP (NIL T T T) -8 NIL NIL NIL) (-274 571160 571951 571992 "DSEXT" 572355 NIL DSEXT (NIL T) -9 NIL 572649 NIL) (-273 569349 569873 570539 "DSEXT-" 570544 NIL DSEXT- (NIL T T) -8 NIL NIL NIL) (-272 569008 569073 569171 "DROPT1" 569284 NIL DROPT1 (NIL T) -7 NIL NIL NIL) (-271 564027 565249 566386 "DROPT0" 567891 T DROPT0 (NIL) -7 NIL NIL NIL) (-270 558610 559972 561040 "DROPT" 562979 T DROPT (NIL) -8 NIL NIL NIL) (-269 556919 557280 557666 "DRAWPT" 558244 T DRAWPT (NIL) -7 NIL NIL NIL) (-268 556546 556605 556723 "DRAWHACK" 556860 NIL DRAWHACK (NIL T) -7 NIL NIL NIL) (-267 555247 555546 555837 "DRAWCX" 556275 T DRAWCX (NIL) -7 NIL NIL NIL) (-266 554756 554831 554982 "DRAWCURV" 555173 NIL DRAWCURV (NIL T T) -7 NIL NIL NIL) (-265 545074 547186 549301 "DRAWCFUN" 552661 T DRAWCFUN (NIL) -7 NIL NIL NIL) (-264 539565 540584 541663 "DRAW" 544048 NIL DRAW (NIL T) -7 NIL NIL NIL) (-263 536036 538230 538271 "DQAGG" 538900 NIL DQAGG (NIL T) -9 NIL 539174 NIL) (-262 522612 530247 530330 "DPOLCAT" 532182 NIL DPOLCAT (NIL T T T T) -9 NIL 532727 NIL) (-261 517131 518797 520755 "DPOLCAT-" 520760 NIL DPOLCAT- (NIL T T T T T) -8 NIL NIL NIL) (-260 509988 516992 517090 "DPMO" 517095 NIL DPMO (NIL NIL T T) -8 NIL NIL NIL) (-259 502742 509768 509935 "DPMM" 509940 NIL DPMM (NIL NIL T T T) -8 NIL NIL NIL) (-258 502264 502526 502615 "DOMTMPLT" 502673 T DOMTMPLT (NIL) -8 NIL NIL NIL) (-257 501613 502066 502146 "DOMCTOR" 502204 T DOMCTOR (NIL) -8 NIL NIL NIL) (-256 500765 501093 501244 "DOMAIN" 501482 T DOMAIN (NIL) -8 NIL NIL NIL) (-255 493777 500400 500552 "DMP" 500666 NIL DMP (NIL NIL T) -8 NIL NIL NIL) (-254 491554 492844 492885 "DMEXT" 492890 NIL DMEXT (NIL T) -9 NIL 493066 NIL) (-253 491148 491210 491354 "DLP" 491492 NIL DLP (NIL T) -7 NIL NIL NIL) (-252 484271 490475 490665 "DLIST" 490990 NIL DLIST (NIL T) -8 NIL NIL NIL) (-251 480809 483096 483137 "DLAGG" 483687 NIL DLAGG (NIL T) -9 NIL 483917 NIL) (-250 479321 480135 480163 "DIVRING" 480255 T DIVRING (NIL) -9 NIL 480338 NIL) (-249 478504 478748 479048 "DIVRING-" 479053 NIL DIVRING- (NIL T) -8 NIL NIL NIL) (-248 476546 476963 477369 "DISPLAY" 478118 T DISPLAY (NIL) -7 NIL NIL NIL) (-247 475376 475597 475862 "DIRPROD2" 476339 NIL DIRPROD2 (NIL NIL T T) -7 NIL NIL NIL) (-246 468783 475290 475353 "DIRPROD" 475358 NIL DIRPROD (NIL NIL T) -8 NIL NIL NIL) (-245 456995 463494 463547 "DIRPCAT" 463805 NIL DIRPCAT (NIL NIL T) -9 NIL 464680 NIL) (-244 454195 454963 455844 "DIRPCAT-" 456181 NIL DIRPCAT- (NIL T NIL T) -8 NIL NIL NIL) (-243 453476 453642 453828 "DIOSP" 454029 T DIOSP (NIL) -7 NIL NIL NIL) (-242 449890 452360 452401 "DIOPS" 452835 NIL DIOPS (NIL T) -9 NIL 453064 NIL) (-241 449409 449553 449744 "DIOPS-" 449749 NIL DIOPS- (NIL T T) -8 NIL NIL NIL) (-240 448316 449088 449116 "DIFRING" 449121 T DIFRING (NIL) -9 NIL 449143 NIL) (-239 447964 448062 448090 "DIFFSPC" 448209 T DIFFSPC (NIL) -9 NIL 448284 NIL) (-238 447585 447687 447839 "DIFFSPC-" 447844 NIL DIFFSPC- (NIL T) -8 NIL NIL NIL) (-237 446521 447119 447160 "DIFFMOD" 447165 NIL DIFFMOD (NIL T) -9 NIL 447263 NIL) (-236 446217 446274 446315 "DIFFDOM" 446436 NIL DIFFDOM (NIL T) -9 NIL 446504 NIL) (-235 446064 446094 446178 "DIFFDOM-" 446183 NIL DIFFDOM- (NIL T T) -8 NIL NIL NIL) (-234 443804 445268 445309 "DIFEXT" 445314 NIL DIFEXT (NIL T) -9 NIL 445467 NIL) (-233 440838 443308 443349 "DIAGG" 443354 NIL DIAGG (NIL T) -9 NIL 443374 NIL) (-232 440186 440379 440631 "DIAGG-" 440636 NIL DIAGG- (NIL T T) -8 NIL NIL NIL) (-231 435036 439145 439422 "DHMATRIX" 439955 NIL DHMATRIX (NIL T) -8 NIL NIL NIL) (-230 430504 431557 432567 "DFSFUN" 434046 T DFSFUN (NIL) -7 NIL NIL NIL) (-229 424738 429435 429747 "DFLOAT" 430212 T DFLOAT (NIL) -8 NIL NIL NIL) (-228 422977 423282 423671 "DFINTTLS" 424446 NIL DFINTTLS (NIL T T) -7 NIL NIL NIL) (-227 419796 420998 421398 "DERHAM" 422643 NIL DERHAM (NIL T NIL) -8 NIL NIL NIL) (-226 417332 419571 419660 "DEQUEUE" 419740 NIL DEQUEUE (NIL T) -8 NIL NIL NIL) (-225 416574 416719 416902 "DEGRED" 417194 NIL DEGRED (NIL T T) -7 NIL NIL NIL) (-224 412980 413749 414595 "DEFINTRF" 415802 NIL DEFINTRF (NIL T) -7 NIL NIL NIL) (-223 410517 411004 411596 "DEFINTEF" 412499 NIL DEFINTEF (NIL T T) -7 NIL NIL NIL) (-222 409801 410137 410252 "DEFAST" 410422 T DEFAST (NIL) -8 NIL NIL NIL) (-221 402837 409394 409544 "DECIMAL" 409671 T DECIMAL (NIL) -8 NIL NIL NIL) (-220 400295 400807 401313 "DDFACT" 402381 NIL DDFACT (NIL T T) -7 NIL NIL NIL) (-219 399885 399934 400085 "DBLRESP" 400246 NIL DBLRESP (NIL T T T T) -7 NIL NIL NIL) (-218 399086 399655 399746 "DBASIS" 399834 NIL DBASIS (NIL NIL) -8 NIL NIL NIL) (-217 396870 397316 397677 "DBASE" 398852 NIL DBASE (NIL T) -8 NIL NIL NIL) (-216 396058 396350 396496 "DATAARY" 396769 NIL DATAARY (NIL NIL T) -8 NIL NIL NIL) (-215 395116 396017 396045 "D03FAFA" 396050 T D03FAFA (NIL) -8 NIL NIL NIL) (-214 394175 395075 395103 "D03EEFA" 395108 T D03EEFA (NIL) -8 NIL NIL NIL) (-213 392101 392591 393080 "D03AGNT" 393706 T D03AGNT (NIL) -7 NIL NIL NIL) (-212 391342 392060 392088 "D02EJFA" 392093 T D02EJFA (NIL) -8 NIL NIL NIL) (-211 390583 391301 391329 "D02CJFA" 391334 T D02CJFA (NIL) -8 NIL NIL NIL) (-210 389824 390542 390570 "D02BHFA" 390575 T D02BHFA (NIL) -8 NIL NIL NIL) (-209 389065 389783 389811 "D02BBFA" 389816 T D02BBFA (NIL) -8 NIL NIL NIL) (-208 382196 383851 385457 "D02AGNT" 387479 T D02AGNT (NIL) -7 NIL NIL NIL) (-207 379946 380487 381033 "D01WGTS" 381670 T D01WGTS (NIL) -7 NIL NIL NIL) (-206 378953 379905 379933 "D01TRNS" 379938 T D01TRNS (NIL) -8 NIL NIL NIL) (-205 377961 378912 378940 "D01GBFA" 378945 T D01GBFA (NIL) -8 NIL NIL NIL) (-204 376969 377920 377948 "D01FCFA" 377953 T D01FCFA (NIL) -8 NIL NIL NIL) (-203 375977 376928 376956 "D01ASFA" 376961 T D01ASFA (NIL) -8 NIL NIL NIL) (-202 374985 375936 375964 "D01AQFA" 375969 T D01AQFA (NIL) -8 NIL NIL NIL) (-201 373993 374944 374972 "D01APFA" 374977 T D01APFA (NIL) -8 NIL NIL NIL) (-200 373001 373952 373980 "D01ANFA" 373985 T D01ANFA (NIL) -8 NIL NIL NIL) (-199 372009 372960 372988 "D01AMFA" 372993 T D01AMFA (NIL) -8 NIL NIL NIL) (-198 371017 371968 371996 "D01ALFA" 372001 T D01ALFA (NIL) -8 NIL NIL NIL) (-197 370025 370976 371004 "D01AKFA" 371009 T D01AKFA (NIL) -8 NIL NIL NIL) (-196 369033 369984 370012 "D01AJFA" 370017 T D01AJFA (NIL) -8 NIL NIL NIL) (-195 362256 363881 365442 "D01AGNT" 367492 T D01AGNT (NIL) -7 NIL NIL NIL) (-194 361575 361721 361873 "CYCLOTOM" 362124 T CYCLOTOM (NIL) -7 NIL NIL NIL) (-193 358230 359023 359750 "CYCLES" 360868 T CYCLES (NIL) -7 NIL NIL NIL) (-192 357530 357676 357847 "CVMP" 358091 NIL CVMP (NIL T) -7 NIL NIL NIL) (-191 355317 355629 355998 "CTRIGMNP" 357258 NIL CTRIGMNP (NIL T T) -7 NIL NIL NIL) (-190 354790 355048 355149 "CTORKIND" 355236 T CTORKIND (NIL) -8 NIL NIL NIL) (-189 353995 354383 354411 "CTORCAT" 354593 T CTORCAT (NIL) -9 NIL 354706 NIL) (-188 353569 353704 353863 "CTORCAT-" 353868 NIL CTORCAT- (NIL T) -8 NIL NIL NIL) (-187 352983 353243 353351 "CTORCALL" 353493 NIL CTORCALL (NIL T) -8 NIL NIL NIL) (-186 352341 352777 352850 "CTOR" 352930 T CTOR (NIL) -8 NIL NIL NIL) (-185 351697 351814 351967 "CSTTOOLS" 352238 NIL CSTTOOLS (NIL T T) -7 NIL NIL NIL) (-184 347394 348153 348911 "CRFP" 351009 NIL CRFP (NIL T T) -7 NIL NIL NIL) (-183 346809 347115 347207 "CRCEAST" 347322 T CRCEAST (NIL) -8 NIL NIL NIL) (-182 345832 346041 346269 "CRAPACK" 346613 NIL CRAPACK (NIL T) -7 NIL NIL NIL) (-181 345212 345317 345521 "CPMATCH" 345708 NIL CPMATCH (NIL T T T) -7 NIL NIL NIL) (-180 344931 344965 345071 "CPIMA" 345178 NIL CPIMA (NIL T T T) -7 NIL NIL NIL) (-179 341189 341951 342670 "COORDSYS" 344266 NIL COORDSYS (NIL T) -7 NIL NIL NIL) (-178 340577 340722 340864 "CONTOUR" 341067 T CONTOUR (NIL) -8 NIL NIL NIL) (-177 336042 338580 339072 "CONTFRAC" 340117 NIL CONTFRAC (NIL T) -8 NIL NIL NIL) (-176 335916 335943 335971 "CONDUIT" 336008 T CONDUIT (NIL) -9 NIL NIL NIL) (-175 334870 335544 335572 "COMRING" 335577 T COMRING (NIL) -9 NIL 335629 NIL) (-174 333852 334228 334412 "COMPPROP" 334706 T COMPPROP (NIL) -8 NIL NIL NIL) (-173 333507 333548 333676 "COMPLPAT" 333811 NIL COMPLPAT (NIL T T T) -7 NIL NIL NIL) (-172 333137 333200 333307 "COMPLEX2" 333444 NIL COMPLEX2 (NIL T T) -7 NIL NIL NIL) (-171 321520 332946 333055 "COMPLEX" 333060 NIL COMPLEX (NIL T) -8 NIL NIL NIL) (-170 320841 320980 321140 "COMPILER" 321380 T COMPILER (NIL) -8 NIL NIL NIL) (-169 320553 320594 320692 "COMPFACT" 320800 NIL COMPFACT (NIL T T) -7 NIL NIL NIL) (-168 301926 314257 314297 "COMPCAT" 315301 NIL COMPCAT (NIL T) -9 NIL 316649 NIL) (-167 290814 294365 297992 "COMPCAT-" 298348 NIL COMPCAT- (NIL T T) -8 NIL NIL NIL) (-166 290537 290571 290674 "COMMUPC" 290780 NIL COMMUPC (NIL T T T) -7 NIL NIL NIL) (-165 290325 290365 290424 "COMMONOP" 290498 T COMMONOP (NIL) -7 NIL NIL NIL) (-164 289847 290129 290204 "COMMAAST" 290270 T COMMAAST (NIL) -8 NIL NIL NIL) (-163 289354 289598 289685 "COMM" 289780 T COMM (NIL) -8 NIL NIL NIL) (-162 288549 288797 288825 "COMBOPC" 289163 T COMBOPC (NIL) -9 NIL 289338 NIL) (-161 287403 287655 287897 "COMBINAT" 288339 NIL COMBINAT (NIL T) -7 NIL NIL NIL) (-160 283746 284434 285061 "COMBF" 286825 NIL COMBF (NIL T T) -7 NIL NIL NIL) (-159 282408 282862 283097 "COLOR" 283531 T COLOR (NIL) -8 NIL NIL NIL) (-158 281824 282129 282221 "COLONAST" 282336 T COLONAST (NIL) -8 NIL NIL NIL) (-157 281458 281511 281636 "CMPLXRT" 281771 NIL CMPLXRT (NIL T T) -7 NIL NIL NIL) (-156 280846 281158 281257 "CLLCTAST" 281379 T CLLCTAST (NIL) -8 NIL NIL NIL) (-155 276306 277376 278456 "CLIP" 279786 T CLIP (NIL) -7 NIL NIL NIL) (-154 274479 275407 275647 "CLIF" 276133 NIL CLIF (NIL NIL T NIL) -8 NIL NIL NIL) (-153 270461 272597 272638 "CLAGG" 273567 NIL CLAGG (NIL T) -9 NIL 274103 NIL) (-152 268805 269340 269923 "CLAGG-" 269928 NIL CLAGG- (NIL T T) -8 NIL NIL NIL) (-151 268343 268434 268574 "CINTSLPE" 268714 NIL CINTSLPE (NIL T T) -7 NIL NIL NIL) (-150 265808 266315 266863 "CHVAR" 267871 NIL CHVAR (NIL T T T) -7 NIL NIL NIL) (-149 264848 265522 265550 "CHARZ" 265555 T CHARZ (NIL) -9 NIL 265570 NIL) (-148 264596 264642 264720 "CHARPOL" 264802 NIL CHARPOL (NIL T) -7 NIL NIL NIL) (-147 263514 264227 264255 "CHARNZ" 264302 T CHARNZ (NIL) -9 NIL 264358 NIL) (-146 260458 261568 262097 "CHAR" 263005 T CHAR (NIL) -8 NIL NIL NIL) (-145 260166 260245 260273 "CFCAT" 260384 T CFCAT (NIL) -9 NIL NIL NIL) (-144 259389 259518 259701 "CDEN" 260050 NIL CDEN (NIL T T T) -7 NIL NIL NIL) (-143 254986 258542 258822 "CCLASS" 259129 T CCLASS (NIL) -8 NIL NIL NIL) (-142 254207 254394 254571 "CATEGORY" 254829 T -10 (NIL) -8 NIL NIL NIL) (-141 253702 254126 254174 "CATCTOR" 254179 T CATCTOR (NIL) -8 NIL NIL NIL) (-140 253093 253405 253503 "CATAST" 253624 T CATAST (NIL) -8 NIL NIL NIL) (-139 252509 252814 252906 "CASEAST" 253021 T CASEAST (NIL) -8 NIL NIL NIL) (-138 251605 251765 251986 "CARTEN2" 252356 NIL CARTEN2 (NIL NIL NIL T T) -7 NIL NIL NIL) (-137 246503 247762 248506 "CARTEN" 250917 NIL CARTEN (NIL NIL NIL T) -8 NIL NIL NIL) (-136 244633 245653 245910 "CARD" 246266 T CARD (NIL) -8 NIL NIL NIL) (-135 244155 244437 244512 "CAPSLAST" 244578 T CAPSLAST (NIL) -8 NIL NIL NIL) (-134 243597 243853 243881 "CACHSET" 244013 T CACHSET (NIL) -9 NIL 244091 NIL) (-133 242987 243375 243403 "CABMON" 243453 T CABMON (NIL) -9 NIL 243509 NIL) (-132 242424 242691 242801 "BYTEORD" 242897 T BYTEORD (NIL) -8 NIL NIL NIL) (-131 237351 241929 242101 "BYTEBUF" 242272 T BYTEBUF (NIL) -8 NIL NIL NIL) (-130 236109 236866 237015 "BYTE" 237178 T BYTE (NIL) -8 NIL NIL 237307) (-129 233371 235801 235908 "BTREE" 236035 NIL BTREE (NIL T) -8 NIL NIL NIL) (-128 230573 233019 233141 "BTOURN" 233281 NIL BTOURN (NIL T) -8 NIL NIL NIL) (-127 227680 230015 230056 "BTCAT" 230124 NIL BTCAT (NIL T) -9 NIL 230201 NIL) (-126 227329 227427 227576 "BTCAT-" 227581 NIL BTCAT- (NIL T T) -8 NIL NIL NIL) (-125 222218 226575 226603 "BTAGG" 226717 T BTAGG (NIL) -9 NIL 226827 NIL) (-124 221672 221833 222039 "BTAGG-" 222044 NIL BTAGG- (NIL T) -8 NIL NIL NIL) (-123 218408 220950 221165 "BSTREE" 221489 NIL BSTREE (NIL T) -8 NIL NIL NIL) (-122 217516 217672 217856 "BRILL" 218264 NIL BRILL (NIL T) -7 NIL NIL NIL) (-121 213911 216214 216255 "BRAGG" 216904 NIL BRAGG (NIL T) -9 NIL 217162 NIL) (-120 212344 212846 213401 "BRAGG-" 213406 NIL BRAGG- (NIL T T) -8 NIL NIL NIL) (-119 204580 211688 211873 "BPADICRT" 212191 NIL BPADICRT (NIL NIL) -8 NIL NIL NIL) (-118 202589 204517 204562 "BPADIC" 204567 NIL BPADIC (NIL NIL) -8 NIL NIL NIL) (-117 202281 202317 202431 "BOUNDZRO" 202553 NIL BOUNDZRO (NIL T T) -7 NIL NIL NIL) (-116 200008 200466 200941 "BOP1" 201839 NIL BOP1 (NIL T) -7 NIL NIL NIL) (-115 194990 196434 197346 "BOP" 199116 T BOP (NIL) -8 NIL NIL NIL) (-114 193655 194578 194720 "BOOLEAN" 194868 T BOOLEAN (NIL) -8 NIL NIL NIL) (-113 193248 193405 193433 "BOOLE" 193544 T BOOLE (NIL) -9 NIL 193625 NIL) (-112 193116 193143 193209 "BOOLE-" 193214 NIL BOOLE- (NIL T) -8 NIL NIL NIL) (-111 192285 192785 192839 "BMODULE" 192844 NIL BMODULE (NIL T T) -9 NIL 192909 NIL) (-110 187606 192083 192156 "BITS" 192232 T BITS (NIL) -8 NIL NIL NIL) (-109 187003 187146 187286 "BINDING" 187486 T BINDING (NIL) -8 NIL NIL NIL) (-108 180042 186598 186747 "BINARY" 186874 T BINARY (NIL) -8 NIL NIL NIL) (-107 177649 179269 179310 "BGAGG" 179570 NIL BGAGG (NIL T) -9 NIL 179707 NIL) (-106 177474 177512 177603 "BGAGG-" 177608 NIL BGAGG- (NIL T T) -8 NIL NIL NIL) (-105 176497 176858 177063 "BFUNCT" 177289 T BFUNCT (NIL) -8 NIL NIL NIL) (-104 175167 175365 175653 "BEZOUT" 176321 NIL BEZOUT (NIL T T T T T) -7 NIL NIL NIL) (-103 171365 174019 174349 "BBTREE" 174870 NIL BBTREE (NIL T) -8 NIL NIL NIL) (-102 170948 171044 171072 "BASTYPE" 171249 T BASTYPE (NIL) -9 NIL 171348 NIL) (-101 170606 170705 170840 "BASTYPE-" 170845 NIL BASTYPE- (NIL T) -8 NIL NIL NIL) (-100 170028 170116 170268 "BALFACT" 170517 NIL BALFACT (NIL T T) -7 NIL NIL NIL) (-99 168764 169443 169629 "AUTOMOR" 169873 NIL AUTOMOR (NIL T) -8 NIL NIL NIL) (-98 168490 168495 168521 "ATTREG" 168526 T ATTREG (NIL) -9 NIL NIL NIL) (-97 166652 167187 167539 "ATTRBUT" 168156 T ATTRBUT (NIL) -8 NIL NIL NIL) (-96 166206 166480 166546 "ATTRAST" 166604 T ATTRAST (NIL) -8 NIL NIL NIL) (-95 165706 165855 165881 "ATRIG" 166082 T ATRIG (NIL) -9 NIL NIL NIL) (-94 165503 165556 165643 "ATRIG-" 165648 NIL ATRIG- (NIL T) -8 NIL NIL NIL) (-93 165086 165320 165346 "ASTCAT" 165351 T ASTCAT (NIL) -9 NIL 165381 NIL) (-92 164795 164872 164991 "ASTCAT-" 164996 NIL ASTCAT- (NIL T) -8 NIL NIL NIL) (-91 162769 164571 164659 "ASTACK" 164738 NIL ASTACK (NIL T) -8 NIL NIL NIL) (-90 161258 161571 161936 "ASSOCEQ" 162451 NIL ASSOCEQ (NIL T T) -7 NIL NIL NIL) (-89 160182 160917 161041 "ASP9" 161165 NIL ASP9 (NIL NIL) -8 NIL NIL NIL) (-88 158942 159787 159929 "ASP80" 160071 NIL ASP80 (NIL NIL) -8 NIL NIL NIL) (-87 158669 158890 158929 "ASP8" 158934 NIL ASP8 (NIL NIL) -8 NIL NIL NIL) (-86 157515 158346 158464 "ASP78" 158582 NIL ASP78 (NIL NIL) -8 NIL NIL NIL) (-85 156376 157195 157312 "ASP77" 157429 NIL ASP77 (NIL NIL) -8 NIL NIL NIL) (-84 155180 156014 156145 "ASP74" 156276 NIL ASP74 (NIL NIL) -8 NIL NIL NIL) (-83 153972 154815 154947 "ASP73" 155079 NIL ASP73 (NIL NIL) -8 NIL NIL NIL) (-82 152762 153607 153739 "ASP7" 153871 NIL ASP7 (NIL NIL) -8 NIL NIL NIL) (-81 151758 152588 152688 "ASP6" 152693 NIL ASP6 (NIL NIL) -8 NIL NIL NIL) (-80 150597 151435 151553 "ASP55" 151671 NIL ASP55 (NIL NIL) -8 NIL NIL NIL) (-79 149438 150271 150390 "ASP50" 150509 NIL ASP50 (NIL NIL) -8 NIL NIL NIL) (-78 148418 149139 149249 "ASP49" 149359 NIL ASP49 (NIL NIL) -8 NIL NIL NIL) (-77 147094 147957 148125 "ASP42" 148307 NIL ASP42 (NIL NIL NIL NIL) -8 NIL NIL NIL) (-76 145763 146627 146797 "ASP41" 146981 NIL ASP41 (NIL NIL NIL NIL) -8 NIL NIL NIL) (-75 144743 145464 145574 "ASP4" 145684 NIL ASP4 (NIL NIL) -8 NIL NIL NIL) (-74 143585 144420 144538 "ASP35" 144656 NIL ASP35 (NIL NIL) -8 NIL NIL NIL) (-73 143314 143533 143572 "ASP34" 143577 NIL ASP34 (NIL NIL) -8 NIL NIL NIL) (-72 143033 143118 143194 "ASP33" 143269 NIL ASP33 (NIL NIL) -8 NIL NIL NIL) (-71 141819 142668 142800 "ASP31" 142932 NIL ASP31 (NIL NIL) -8 NIL NIL NIL) (-70 141548 141767 141806 "ASP30" 141811 NIL ASP30 (NIL NIL) -8 NIL NIL NIL) (-69 141265 141352 141428 "ASP29" 141503 NIL ASP29 (NIL NIL) -8 NIL NIL NIL) (-68 140994 141213 141252 "ASP28" 141257 NIL ASP28 (NIL NIL) -8 NIL NIL NIL) (-67 140723 140942 140981 "ASP27" 140986 NIL ASP27 (NIL NIL) -8 NIL NIL NIL) (-66 139699 140421 140532 "ASP24" 140643 NIL ASP24 (NIL NIL) -8 NIL NIL NIL) (-65 138668 139501 139613 "ASP20" 139618 NIL ASP20 (NIL NIL) -8 NIL NIL NIL) (-64 137503 138342 138461 "ASP19" 138580 NIL ASP19 (NIL NIL) -8 NIL NIL NIL) (-63 137222 137307 137383 "ASP12" 137458 NIL ASP12 (NIL NIL) -8 NIL NIL NIL) (-62 135966 136821 136965 "ASP10" 137109 NIL ASP10 (NIL NIL) -8 NIL NIL NIL) (-61 134946 135667 135777 "ASP1" 135887 NIL ASP1 (NIL NIL) -8 NIL NIL NIL) (-60 132558 134790 134881 "ARRAY2" 134886 NIL ARRAY2 (NIL T) -8 NIL NIL NIL) (-59 131572 131763 131984 "ARRAY12" 132381 NIL ARRAY12 (NIL T T) -7 NIL NIL NIL) (-58 126932 131220 131334 "ARRAY1" 131489 NIL ARRAY1 (NIL T) -8 NIL NIL NIL) (-57 120977 123134 123209 "ARR2CAT" 125839 NIL ARR2CAT (NIL T T T) -9 NIL 126597 NIL) (-56 118267 119155 120109 "ARR2CAT-" 120114 NIL ARR2CAT- (NIL T T T T) -8 NIL NIL NIL) (-55 117518 117894 118019 "ARITY" 118160 T ARITY (NIL) -8 NIL NIL NIL) (-54 116276 116446 116745 "APPRULE" 117354 NIL APPRULE (NIL T T T) -7 NIL NIL NIL) (-53 115921 115975 116094 "APPLYORE" 116222 NIL APPLYORE (NIL T T T) -7 NIL NIL NIL) (-52 115175 115322 115479 "ANY1" 115795 NIL ANY1 (NIL T) -7 NIL NIL NIL) (-51 114475 114768 114888 "ANY" 115073 T ANY (NIL) -8 NIL NIL NIL) (-50 111801 112912 113239 "ANTISYM" 114199 NIL ANTISYM (NIL T NIL) -8 NIL NIL NIL) (-49 111245 111508 111604 "ANON" 111723 T ANON (NIL) -8 NIL NIL NIL) (-48 104401 109784 110238 "AN" 110809 T AN (NIL) -8 NIL NIL NIL) (-47 100057 101673 101724 "AMR" 102472 NIL AMR (NIL T T) -9 NIL 103072 NIL) (-46 99109 99390 99753 "AMR-" 99758 NIL AMR- (NIL T T T) -8 NIL NIL NIL) (-45 82578 99026 99087 "ALIST" 99092 NIL ALIST (NIL T T) -8 NIL NIL NIL) (-44 78875 82172 82341 "ALGSC" 82496 NIL ALGSC (NIL T NIL NIL NIL) -8 NIL NIL NIL) (-43 75325 75985 76592 "ALGPKG" 78315 NIL ALGPKG (NIL T T) -7 NIL NIL NIL) (-42 74590 74703 74887 "ALGMFACT" 75211 NIL ALGMFACT (NIL T T T) -7 NIL NIL NIL) (-41 70573 71204 71798 "ALGMANIP" 74174 NIL ALGMANIP (NIL T T) -7 NIL NIL NIL) (-40 59912 70199 70349 "ALGFF" 70506 NIL ALGFF (NIL T T T NIL) -8 NIL NIL NIL) (-39 59084 59239 59418 "ALGFACT" 59770 NIL ALGFACT (NIL T) -7 NIL NIL NIL) (-38 57873 58611 58649 "ALGEBRA" 58654 NIL ALGEBRA (NIL T) -9 NIL 58695 NIL) (-37 57573 57650 57782 "ALGEBRA-" 57787 NIL ALGEBRA- (NIL T T) -8 NIL NIL NIL) (-36 38527 55410 55462 "ALAGG" 55598 NIL ALAGG (NIL T T) -9 NIL 55759 NIL) (-35 38027 38176 38202 "AHYP" 38403 T AHYP (NIL) -9 NIL NIL NIL) (-34 36912 37206 37232 "AGG" 37731 T AGG (NIL) -9 NIL 38010 NIL) (-33 36310 36508 36722 "AGG-" 36727 NIL AGG- (NIL T) -8 NIL NIL NIL) (-32 34070 34539 34944 "AF" 35952 NIL AF (NIL T T) -7 NIL NIL NIL) (-31 33490 33795 33885 "ADDAST" 33998 T ADDAST (NIL) -8 NIL NIL NIL) (-30 32722 33017 33173 "ACPLOT" 33352 T ACPLOT (NIL) -8 NIL NIL NIL) (-29 20273 29654 29692 "ACFS" 30299 NIL ACFS (NIL T) -9 NIL 30538 NIL) (-28 18180 18790 19552 "ACFS-" 19557 NIL ACFS- (NIL T T) -8 NIL NIL NIL) (-27 13882 16213 16239 "ACF" 17118 T ACF (NIL) -9 NIL 17531 NIL) (-26 12514 12920 13413 "ACF-" 13418 NIL ACF- (NIL T) -8 NIL NIL NIL) (-25 12024 12267 12293 "ABELSG" 12385 T ABELSG (NIL) -9 NIL 12450 NIL) (-24 11885 11916 11982 "ABELSG-" 11987 NIL ABELSG- (NIL T) -8 NIL NIL NIL) (-23 11154 11501 11527 "ABELMON" 11697 T ABELMON (NIL) -9 NIL 11809 NIL) (-22 10794 10902 11040 "ABELMON-" 11045 NIL ABELMON- (NIL T) -8 NIL NIL NIL) (-21 10044 10500 10526 "ABELGRP" 10598 T ABELGRP (NIL) -9 NIL 10673 NIL) (-20 9471 9636 9852 "ABELGRP-" 9857 NIL ABELGRP- (NIL T) -8 NIL NIL NIL) (-19 4579 8733 8772 "A1AGG" 8777 NIL A1AGG (NIL T) -9 NIL 8817 NIL) (-18 30 1497 3059 "A1AGG-" 3064 NIL A1AGG- (NIL T T) -8 NIL NIL NIL))
\ No newline at end of file +((-3 3473038 3473043 3473048 NIL NIL NIL NIL (NIL) -8 NIL NIL NIL) (-2 3473023 3473028 3473033 NIL NIL NIL NIL (NIL) -8 NIL NIL NIL) (-1 3473008 3473013 3473018 NIL NIL NIL NIL (NIL) -8 NIL NIL NIL) (0 3472993 3472998 3473003 NIL NIL NIL NIL (NIL) -8 NIL NIL NIL) (-1327 3471980 3472868 3472945 "ZMOD" 3472950 NIL ZMOD (NIL NIL) -8 NIL NIL NIL) (-1326 3471016 3471198 3471421 "ZLINDEP" 3471812 NIL ZLINDEP (NIL T) -7 NIL NIL NIL) (-1325 3460178 3462084 3464056 "ZDSOLVE" 3469146 NIL ZDSOLVE (NIL T NIL NIL) -7 NIL NIL NIL) (-1324 3459412 3459565 3459754 "YSTREAM" 3460024 NIL YSTREAM (NIL T) -7 NIL NIL NIL) (-1323 3458772 3459081 3459196 "YDIAGRAM" 3459319 T YDIAGRAM (NIL) -8 NIL NIL NIL) (-1322 3456220 3458073 3458277 "XRPOLY" 3458615 NIL XRPOLY (NIL T T) -8 NIL NIL NIL) (-1321 3452487 3454091 3454666 "XPR" 3455692 NIL XPR (NIL T T) -8 NIL NIL NIL) (-1320 3449818 3451494 3451549 "XPOLYC" 3451837 NIL XPOLYC (NIL T T) -9 NIL 3451950 NIL) (-1319 3447213 3449149 3449353 "XPOLY" 3449649 NIL XPOLY (NIL T) -8 NIL NIL NIL) (-1318 3443159 3445730 3446118 "XPBWPOLY" 3446871 NIL XPBWPOLY (NIL T T) -8 NIL NIL NIL) (-1317 3438051 3439630 3439685 "XFALG" 3441857 NIL XFALG (NIL T T) -9 NIL 3442646 NIL) (-1316 3433314 3436027 3436069 "XF" 3436690 NIL XF (NIL T) -9 NIL 3437090 NIL) (-1315 3432911 3433023 3433192 "XF-" 3433197 NIL XF- (NIL T T) -8 NIL NIL NIL) (-1314 3432026 3432148 3432353 "XEXPPKG" 3432803 NIL XEXPPKG (NIL T T T) -7 NIL NIL NIL) (-1313 3429767 3431876 3431972 "XDPOLY" 3431977 NIL XDPOLY (NIL T T) -8 NIL NIL NIL) (-1312 3428422 3429160 3429203 "XALG" 3429208 NIL XALG (NIL T) -9 NIL 3429319 NIL) (-1311 3421332 3426399 3426893 "WUTSET" 3428014 NIL WUTSET (NIL T T T T) -8 NIL NIL NIL) (-1310 3419434 3420384 3420707 "WP" 3421143 NIL WP (NIL T T T T NIL NIL NIL) -8 NIL NIL NIL) (-1309 3418982 3419256 3419326 "WHILEAST" 3419386 T WHILEAST (NIL) -8 NIL NIL NIL) (-1308 3418394 3418699 3418793 "WHEREAST" 3418910 T WHEREAST (NIL) -8 NIL NIL NIL) (-1307 3417268 3417478 3417773 "WFFINTBS" 3418191 NIL WFFINTBS (NIL T T T T) -7 NIL NIL NIL) (-1306 3415136 3415599 3416061 "WEIER" 3416840 NIL WEIER (NIL T) -7 NIL NIL NIL) (-1305 3414060 3414618 3414660 "VSPACE" 3414796 NIL VSPACE (NIL T) -9 NIL 3414870 NIL) (-1304 3413892 3413925 3414016 "VSPACE-" 3414021 NIL VSPACE- (NIL T T) -8 NIL NIL NIL) (-1303 3413689 3413743 3413811 "VOID" 3413846 T VOID (NIL) -8 NIL NIL NIL) (-1302 3409957 3410752 3411489 "VIEWDEF" 3412974 T VIEWDEF (NIL) -7 NIL NIL NIL) (-1301 3398901 3401505 3403678 "VIEW3D" 3407806 T VIEW3D (NIL) -8 NIL NIL NIL) (-1300 3390918 3392812 3394391 "VIEW2D" 3397344 T VIEW2D (NIL) -8 NIL NIL NIL) (-1299 3389018 3389413 3389819 "VIEW" 3390534 T VIEW (NIL) -7 NIL NIL NIL) (-1298 3387571 3387854 3388172 "VECTOR2" 3388748 NIL VECTOR2 (NIL T T) -7 NIL NIL NIL) (-1297 3382477 3387341 3387433 "VECTOR" 3387514 NIL VECTOR (NIL T) -8 NIL NIL NIL) (-1296 3375422 3380181 3380224 "VECTCAT" 3381219 NIL VECTCAT (NIL T) -9 NIL 3381806 NIL) (-1295 3374364 3374690 3375080 "VECTCAT-" 3375085 NIL VECTCAT- (NIL T T) -8 NIL NIL NIL) (-1294 3373770 3374015 3374135 "VARIABLE" 3374279 NIL VARIABLE (NIL NIL) -8 NIL NIL NIL) (-1293 3373703 3373708 3373738 "UTYPE" 3373743 T UTYPE (NIL) -9 NIL NIL NIL) (-1292 3372511 3372687 3372949 "UTSODETL" 3373529 NIL UTSODETL (NIL T T T T) -7 NIL NIL NIL) (-1291 3369903 3370411 3370935 "UTSODE" 3372052 NIL UTSODE (NIL T T) -7 NIL NIL NIL) (-1290 3359906 3365836 3365879 "UTSCAT" 3366991 NIL UTSCAT (NIL T) -9 NIL 3367749 NIL) (-1289 3357032 3357976 3358965 "UTSCAT-" 3358970 NIL UTSCAT- (NIL T T) -8 NIL NIL NIL) (-1288 3356653 3356702 3356835 "UTS2" 3356983 NIL UTS2 (NIL T T T T) -7 NIL NIL NIL) (-1287 3347963 3354414 3354894 "UTS" 3356231 NIL UTS (NIL T NIL NIL) -8 NIL NIL NIL) (-1286 3341830 3344773 3344816 "URAGG" 3346886 NIL URAGG (NIL T) -9 NIL 3347609 NIL) (-1285 3338553 3339632 3340755 "URAGG-" 3340760 NIL URAGG- (NIL T T) -8 NIL NIL NIL) (-1284 3333922 3337188 3337653 "UPXSSING" 3338217 NIL UPXSSING (NIL T T NIL NIL) -8 NIL NIL NIL) (-1283 3326337 3333826 3333898 "UPXSCONS" 3333903 NIL UPXSCONS (NIL T T) -8 NIL NIL NIL) (-1282 3315081 3322539 3322601 "UPXSCCA" 3323175 NIL UPXSCCA (NIL T T) -9 NIL 3323408 NIL) (-1281 3314701 3314804 3314978 "UPXSCCA-" 3314983 NIL UPXSCCA- (NIL T T T) -8 NIL NIL NIL) (-1280 3303345 3310528 3310571 "UPXSCAT" 3311219 NIL UPXSCAT (NIL T) -9 NIL 3311828 NIL) (-1279 3302769 3302854 3303033 "UPXS2" 3303260 NIL UPXS2 (NIL T T NIL NIL NIL NIL) -7 NIL NIL NIL) (-1278 3294247 3302151 3302415 "UPXS" 3302563 NIL UPXS (NIL T NIL NIL) -8 NIL NIL NIL) (-1277 3292883 3293154 3293505 "UPSQFREE" 3293990 NIL UPSQFREE (NIL T T) -7 NIL NIL NIL) (-1276 3285707 3289149 3289204 "UPSCAT" 3290284 NIL UPSCAT (NIL T T) -9 NIL 3291050 NIL) (-1275 3284863 3285118 3285445 "UPSCAT-" 3285450 NIL UPSCAT- (NIL T T T) -8 NIL NIL NIL) (-1274 3284484 3284533 3284666 "UPOLYC2" 3284814 NIL UPOLYC2 (NIL T T T T) -7 NIL NIL NIL) (-1273 3268611 3277611 3277654 "UPOLYC" 3279755 NIL UPOLYC (NIL T) -9 NIL 3280976 NIL) (-1272 3259459 3262365 3265512 "UPOLYC-" 3265517 NIL UPOLYC- (NIL T T) -8 NIL NIL NIL) (-1271 3258780 3258905 3259069 "UPMP" 3259348 NIL UPMP (NIL T T) -7 NIL NIL NIL) (-1270 3258327 3258414 3258553 "UPDIVP" 3258693 NIL UPDIVP (NIL T T) -7 NIL NIL NIL) (-1269 3256865 3257144 3257460 "UPDECOMP" 3258076 NIL UPDECOMP (NIL T T) -7 NIL NIL NIL) (-1268 3256078 3256208 3256394 "UPCDEN" 3256749 NIL UPCDEN (NIL T T T) -7 NIL NIL NIL) (-1267 3255591 3255666 3255815 "UP2" 3256003 NIL UP2 (NIL NIL T NIL T) -7 NIL NIL NIL) (-1266 3246166 3255274 3255403 "UP" 3255510 NIL UP (NIL NIL T) -8 NIL NIL NIL) (-1265 3245371 3245508 3245713 "UNISEG2" 3246009 NIL UNISEG2 (NIL T T) -7 NIL NIL NIL) (-1264 3243724 3244575 3244852 "UNISEG" 3245129 NIL UNISEG (NIL T) -8 NIL NIL NIL) (-1263 3242766 3242964 3243190 "UNIFACT" 3243540 NIL UNIFACT (NIL T) -7 NIL NIL NIL) (-1262 3229476 3242670 3242742 "ULSCONS" 3242747 NIL ULSCONS (NIL T T) -8 NIL NIL NIL) (-1261 3209272 3222556 3222618 "ULSCCAT" 3223256 NIL ULSCCAT (NIL T T) -9 NIL 3223545 NIL) (-1260 3208268 3208567 3208955 "ULSCCAT-" 3208960 NIL ULSCCAT- (NIL T T T) -8 NIL NIL NIL) (-1259 3196709 3203814 3203857 "ULSCAT" 3204720 NIL ULSCAT (NIL T) -9 NIL 3205451 NIL) (-1258 3196133 3196218 3196397 "ULS2" 3196624 NIL ULS2 (NIL T T NIL NIL NIL NIL) -7 NIL NIL NIL) (-1257 3177943 3195445 3195687 "ULS" 3195949 NIL ULS (NIL T NIL NIL) -8 NIL NIL NIL) (-1256 3176862 3177562 3177676 "UINT8" 3177787 T UINT8 (NIL) -8 NIL NIL 3177879) (-1255 3175780 3176480 3176594 "UINT64" 3176705 T UINT64 (NIL) -8 NIL NIL 3176797) (-1254 3174698 3175398 3175512 "UINT32" 3175623 T UINT32 (NIL) -8 NIL NIL 3175715) (-1253 3173616 3174316 3174430 "UINT16" 3174541 T UINT16 (NIL) -8 NIL NIL 3174633) (-1252 3171695 3172862 3172892 "UFD" 3173104 T UFD (NIL) -9 NIL 3173218 NIL) (-1251 3171477 3171535 3171630 "UFD-" 3171635 NIL UFD- (NIL T) -8 NIL NIL NIL) (-1250 3170535 3170742 3170958 "UDVO" 3171283 T UDVO (NIL) -7 NIL NIL NIL) (-1249 3168301 3168760 3169231 "UDPO" 3170099 NIL UDPO (NIL T) -7 NIL NIL NIL) (-1248 3168013 3168256 3168287 "TYPEAST" 3168292 T TYPEAST (NIL) -8 NIL NIL NIL) (-1247 3167946 3167951 3167981 "TYPE" 3167986 T TYPE (NIL) -9 NIL NIL NIL) (-1246 3166899 3167119 3167359 "TWOFACT" 3167740 NIL TWOFACT (NIL T) -7 NIL NIL NIL) (-1245 3165874 3166308 3166543 "TUPLE" 3166699 NIL TUPLE (NIL T) -8 NIL NIL NIL) (-1244 3163511 3164084 3164623 "TUBETOOL" 3165357 T TUBETOOL (NIL) -7 NIL NIL NIL) (-1243 3162317 3162558 3162800 "TUBE" 3163304 NIL TUBE (NIL T) -8 NIL NIL NIL) (-1242 3150452 3155074 3155171 "TSETCAT" 3160440 NIL TSETCAT (NIL T T T T) -9 NIL 3161972 NIL) (-1241 3144920 3146784 3148675 "TSETCAT-" 3148680 NIL TSETCAT- (NIL T T T T T) -8 NIL NIL NIL) (-1240 3139099 3143892 3144175 "TS" 3144672 NIL TS (NIL T) -8 NIL NIL NIL) (-1239 3133572 3134585 3135514 "TRMANIP" 3138235 NIL TRMANIP (NIL T T) -7 NIL NIL NIL) (-1238 3133001 3133076 3133239 "TRIMAT" 3133504 NIL TRIMAT (NIL T T T T) -7 NIL NIL NIL) (-1237 3130813 3131104 3131461 "TRIGMNIP" 3132750 NIL TRIGMNIP (NIL T T) -7 NIL NIL NIL) (-1236 3130297 3130446 3130476 "TRIGCAT" 3130689 T TRIGCAT (NIL) -9 NIL NIL NIL) (-1235 3129942 3130045 3130186 "TRIGCAT-" 3130191 NIL TRIGCAT- (NIL T) -8 NIL NIL NIL) (-1234 3126556 3128800 3129081 "TREE" 3129696 NIL TREE (NIL T) -8 NIL NIL NIL) (-1233 3125662 3126358 3126388 "TRANFUN" 3126423 T TRANFUN (NIL) -9 NIL 3126489 NIL) (-1232 3124881 3125132 3125412 "TRANFUN-" 3125417 NIL TRANFUN- (NIL T) -8 NIL NIL NIL) (-1231 3124679 3124717 3124778 "TOPSP" 3124842 T TOPSP (NIL) -7 NIL NIL NIL) (-1230 3124009 3124142 3124296 "TOOLSIGN" 3124560 NIL TOOLSIGN (NIL T) -7 NIL NIL NIL) (-1229 3122523 3123186 3123425 "TEXTFILE" 3123792 T TEXTFILE (NIL) -8 NIL NIL NIL) (-1228 3122298 3122335 3122407 "TEX1" 3122486 NIL TEX1 (NIL T) -7 NIL NIL NIL) (-1227 3120102 3120751 3121180 "TEX" 3121891 T TEX (NIL) -8 NIL NIL NIL) (-1226 3119738 3119813 3119903 "TEMUTL" 3120034 T TEMUTL (NIL) -7 NIL NIL NIL) (-1225 3117832 3118172 3118497 "TBCMPPK" 3119461 NIL TBCMPPK (NIL T T) -7 NIL NIL NIL) (-1224 3109152 3115918 3115974 "TBAGG" 3116374 NIL TBAGG (NIL T T) -9 NIL 3116585 NIL) (-1223 3104036 3105710 3107464 "TBAGG-" 3107469 NIL TBAGG- (NIL T T T) -8 NIL NIL NIL) (-1222 3103402 3103527 3103672 "TANEXP" 3103925 NIL TANEXP (NIL T) -7 NIL NIL NIL) (-1221 3102853 3103177 3103267 "TALGOP" 3103347 NIL TALGOP (NIL T) -8 NIL NIL NIL) (-1220 3102247 3102364 3102502 "TABLEAU" 3102750 NIL TABLEAU (NIL T) -8 NIL NIL NIL) (-1219 3095261 3102104 3102197 "TABLE" 3102202 NIL TABLE (NIL T T) -8 NIL NIL NIL) (-1218 3089791 3091089 3092337 "TABLBUMP" 3094047 NIL TABLBUMP (NIL T) -7 NIL NIL NIL) (-1217 3089001 3089160 3089341 "SYSTEM" 3089632 T SYSTEM (NIL) -8 NIL NIL NIL) (-1216 3085406 3086159 3086942 "SYSSOLP" 3088252 NIL SYSSOLP (NIL T) -7 NIL NIL NIL) (-1215 3085168 3085361 3085392 "SYSPTR" 3085397 T SYSPTR (NIL) -8 NIL NIL NIL) (-1214 3084007 3084699 3084825 "SYSNNI" 3085011 NIL SYSNNI (NIL NIL) -8 NIL NIL 3085103) (-1213 3083214 3083769 3083848 "SYSINT" 3083908 NIL SYSINT (NIL NIL) -8 NIL NIL 3083953) (-1212 3079312 3080492 3081202 "SYNTAX" 3082526 T SYNTAX (NIL) -8 NIL NIL NIL) (-1211 3076392 3077072 3077704 "SYMTAB" 3078702 T SYMTAB (NIL) -8 NIL NIL NIL) (-1210 3071491 3072543 3073526 "SYMS" 3075431 T SYMS (NIL) -8 NIL NIL NIL) (-1209 3068390 3070942 3071175 "SYMPOLY" 3071293 NIL SYMPOLY (NIL T) -8 NIL NIL NIL) (-1208 3067895 3067982 3068105 "SYMFUNC" 3068302 NIL SYMFUNC (NIL T) -7 NIL NIL NIL) (-1207 3063693 3065207 3066020 "SYMBOL" 3067104 T SYMBOL (NIL) -8 NIL NIL NIL) (-1206 3057166 3058921 3060641 "SWITCH" 3061995 T SWITCH (NIL) -8 NIL NIL NIL) (-1205 3049920 3056122 3056416 "SUTS" 3056930 NIL SUTS (NIL T NIL NIL) -8 NIL NIL NIL) (-1204 3041398 3049302 3049566 "SUPXS" 3049714 NIL SUPXS (NIL T NIL NIL) -8 NIL NIL NIL) (-1203 3040545 3040684 3040901 "SUPFRACF" 3041266 NIL SUPFRACF (NIL T T T T) -7 NIL NIL NIL) (-1202 3040160 3040225 3040338 "SUP2" 3040480 NIL SUP2 (NIL T T) -7 NIL NIL NIL) (-1201 3030683 3039778 3039904 "SUP" 3040069 NIL SUP (NIL T) -8 NIL NIL NIL) (-1200 3029107 3029405 3029761 "SUMRF" 3030382 NIL SUMRF (NIL T) -7 NIL NIL NIL) (-1199 3028430 3028508 3028700 "SUMFS" 3029028 NIL SUMFS (NIL T T) -7 NIL NIL NIL) (-1198 3010275 3027742 3027984 "SULS" 3028246 NIL SULS (NIL T NIL NIL) -8 NIL NIL NIL) (-1197 3009823 3010097 3010167 "SUCHTAST" 3010227 T SUCHTAST (NIL) -8 NIL NIL NIL) (-1196 3009064 3009348 3009488 "SUCH" 3009731 NIL SUCH (NIL T T) -8 NIL NIL NIL) (-1195 3002703 3003970 3004929 "SUBSPACE" 3008152 NIL SUBSPACE (NIL NIL T) -8 NIL NIL NIL) (-1194 3002123 3002223 3002387 "SUBRESP" 3002591 NIL SUBRESP (NIL T T) -7 NIL NIL NIL) (-1193 2996134 2997416 2998563 "STTFNC" 3001023 NIL STTFNC (NIL T) -7 NIL NIL NIL) (-1192 2989328 2990799 2992110 "STTF" 2994870 NIL STTF (NIL T) -7 NIL NIL NIL) (-1191 2980445 2982510 2984304 "STTAYLOR" 2987569 NIL STTAYLOR (NIL T) -7 NIL NIL NIL) (-1190 2973199 2980309 2980392 "STRTBL" 2980397 NIL STRTBL (NIL T) -8 NIL NIL NIL) (-1189 2967596 2972908 2973007 "STRING" 2973122 T STRING (NIL) -8 NIL NIL NIL) (-1188 2967100 2967183 2967327 "STREAM3" 2967513 NIL STREAM3 (NIL T T T) -7 NIL NIL NIL) (-1187 2966064 2966265 2966500 "STREAM2" 2966913 NIL STREAM2 (NIL T T) -7 NIL NIL NIL) (-1186 2965746 2965804 2965897 "STREAM1" 2966006 NIL STREAM1 (NIL T) -7 NIL NIL NIL) (-1185 2957860 2963365 2963976 "STREAM" 2965170 NIL STREAM (NIL T) -8 NIL NIL NIL) (-1184 2956852 2957057 2957288 "STINPROD" 2957676 NIL STINPROD (NIL T) -7 NIL NIL NIL) (-1183 2955967 2956341 2956489 "STEPAST" 2956726 T STEPAST (NIL) -8 NIL NIL NIL) (-1182 2955463 2955715 2955745 "STEP" 2955825 T STEP (NIL) -9 NIL 2955903 NIL) (-1181 2948519 2955362 2955439 "STBL" 2955444 NIL STBL (NIL T T NIL) -8 NIL NIL NIL) (-1180 2943069 2947682 2947725 "STAGG" 2947878 NIL STAGG (NIL T) -9 NIL 2947967 NIL) (-1179 2940621 2941373 2942245 "STAGG-" 2942250 NIL STAGG- (NIL T T) -8 NIL NIL NIL) (-1178 2938593 2940391 2940483 "STACK" 2940564 NIL STACK (NIL T) -8 NIL NIL NIL) (-1177 2930600 2936734 2937190 "SREGSET" 2938223 NIL SREGSET (NIL T T T T) -8 NIL NIL NIL) (-1176 2922947 2924394 2925907 "SRDCMPK" 2929206 NIL SRDCMPK (NIL T T T T T) -7 NIL NIL NIL) (-1175 2915247 2920306 2920336 "SRAGG" 2921639 T SRAGG (NIL) -9 NIL 2922247 NIL) (-1174 2914198 2914519 2914898 "SRAGG-" 2914903 NIL SRAGG- (NIL T) -8 NIL NIL NIL) (-1173 2907782 2913145 2913566 "SQMATRIX" 2913824 NIL SQMATRIX (NIL NIL T) -8 NIL NIL NIL) (-1172 2901194 2904500 2905227 "SPLTREE" 2907127 NIL SPLTREE (NIL T T) -8 NIL NIL NIL) (-1171 2897019 2897850 2898496 "SPLNODE" 2900620 NIL SPLNODE (NIL T T) -8 NIL NIL NIL) (-1170 2895994 2896299 2896329 "SPFCAT" 2896773 T SPFCAT (NIL) -9 NIL NIL NIL) (-1169 2894689 2894941 2895205 "SPECOUT" 2895752 T SPECOUT (NIL) -7 NIL NIL NIL) (-1168 2885335 2887653 2887683 "SPADXPT" 2892361 T SPADXPT (NIL) -9 NIL 2894527 NIL) (-1167 2885090 2885136 2885205 "SPADPRSR" 2885288 T SPADPRSR (NIL) -7 NIL NIL NIL) (-1166 2882693 2885045 2885076 "SPADAST" 2885081 T SPADAST (NIL) -8 NIL NIL NIL) (-1165 2874294 2876397 2876440 "SPACEC" 2880813 NIL SPACEC (NIL T) -9 NIL 2882629 NIL) (-1164 2872094 2874226 2874275 "SPACE3" 2874280 NIL SPACE3 (NIL T) -8 NIL NIL NIL) (-1163 2870826 2871017 2871308 "SORTPAK" 2871899 NIL SORTPAK (NIL T T) -7 NIL NIL NIL) (-1162 2868888 2869221 2869633 "SOLVETRA" 2870490 NIL SOLVETRA (NIL T) -7 NIL NIL NIL) (-1161 2867926 2868160 2868421 "SOLVESER" 2868661 NIL SOLVESER (NIL T) -7 NIL NIL NIL) (-1160 2863158 2864118 2865113 "SOLVERAD" 2866978 NIL SOLVERAD (NIL T) -7 NIL NIL NIL) (-1159 2858883 2859582 2860311 "SOLVEFOR" 2862525 NIL SOLVEFOR (NIL T T) -7 NIL NIL NIL) (-1158 2852487 2858231 2858328 "SNTSCAT" 2858333 NIL SNTSCAT (NIL T T T T) -9 NIL 2858403 NIL) (-1157 2846031 2850810 2851201 "SMTS" 2852177 NIL SMTS (NIL T T T) -8 NIL NIL NIL) (-1156 2839746 2845919 2845996 "SMP" 2846001 NIL SMP (NIL T T) -8 NIL NIL NIL) (-1155 2837875 2838206 2838604 "SMITH" 2839443 NIL SMITH (NIL T T T T) -7 NIL NIL NIL) (-1154 2829400 2834454 2834557 "SMATCAT" 2835908 NIL SMATCAT (NIL NIL T T T) -9 NIL 2836458 NIL) (-1153 2826172 2827163 2828341 "SMATCAT-" 2828346 NIL SMATCAT- (NIL T NIL T T T) -8 NIL NIL NIL) (-1152 2823641 2825380 2825423 "SKAGG" 2825684 NIL SKAGG (NIL T) -9 NIL 2825819 NIL) (-1151 2819131 2823110 2823294 "SINT" 2823446 T SINT (NIL) -8 NIL NIL 2823608) (-1150 2818897 2818941 2819007 "SIMPAN" 2819087 T SIMPAN (NIL) -7 NIL NIL NIL) (-1149 2817717 2817956 2818231 "SIGNRF" 2818656 NIL SIGNRF (NIL T) -7 NIL NIL NIL) (-1148 2816532 2816701 2816985 "SIGNEF" 2817546 NIL SIGNEF (NIL T T) -7 NIL NIL NIL) (-1147 2815772 2816115 2816239 "SIGAST" 2816430 T SIGAST (NIL) -8 NIL NIL NIL) (-1146 2814997 2815307 2815447 "SIG" 2815654 T SIG (NIL) -8 NIL NIL NIL) (-1145 2812649 2813141 2813647 "SHP" 2814538 NIL SHP (NIL T NIL) -7 NIL NIL NIL) (-1144 2806022 2812550 2812626 "SHDP" 2812631 NIL SHDP (NIL NIL NIL T) -8 NIL NIL NIL) (-1143 2805533 2805773 2805803 "SGROUP" 2805896 T SGROUP (NIL) -9 NIL 2805958 NIL) (-1142 2805385 2805417 2805490 "SGROUP-" 2805495 NIL SGROUP- (NIL T) -8 NIL NIL NIL) (-1141 2802104 2802874 2803597 "SGCF" 2804684 T SGCF (NIL) -7 NIL NIL NIL) (-1140 2795806 2801550 2801647 "SFRTCAT" 2801652 NIL SFRTCAT (NIL T T T T) -9 NIL 2801691 NIL) (-1139 2789125 2790245 2791381 "SFRGCD" 2794789 NIL SFRGCD (NIL T T T T T) -7 NIL NIL NIL) (-1138 2782143 2783324 2784510 "SFQCMPK" 2788058 NIL SFQCMPK (NIL T T T T T) -7 NIL NIL NIL) (-1137 2781745 2781852 2781963 "SFORT" 2782084 NIL SFORT (NIL T T) -8 NIL NIL NIL) (-1136 2780671 2781585 2781706 "SEXOF" 2781711 NIL SEXOF (NIL T T T T T) -8 NIL NIL NIL) (-1135 2776260 2777167 2777262 "SEXCAT" 2779884 NIL SEXCAT (NIL T T T T T) -9 NIL 2780444 NIL) (-1134 2775175 2776141 2776209 "SEX" 2776214 T SEX (NIL) -8 NIL NIL NIL) (-1133 2773297 2773888 2774193 "SETMN" 2774916 NIL SETMN (NIL NIL NIL) -8 NIL NIL NIL) (-1132 2772827 2773015 2773045 "SETCAT" 2773162 T SETCAT (NIL) -9 NIL 2773247 NIL) (-1131 2772595 2772659 2772758 "SETCAT-" 2772763 NIL SETCAT- (NIL T) -8 NIL NIL NIL) (-1130 2768698 2771056 2771099 "SETAGG" 2771969 NIL SETAGG (NIL T) -9 NIL 2772309 NIL) (-1129 2768120 2768272 2768509 "SETAGG-" 2768514 NIL SETAGG- (NIL T T) -8 NIL NIL NIL) (-1128 2764929 2768054 2768102 "SET" 2768107 NIL SET (NIL T) -8 NIL NIL NIL) (-1127 2764312 2764625 2764726 "SEQAST" 2764850 T SEQAST (NIL) -8 NIL NIL NIL) (-1126 2763439 2763805 2763866 "SEGXCAT" 2764152 NIL SEGXCAT (NIL T T) -9 NIL 2764272 NIL) (-1125 2762364 2762632 2762675 "SEGCAT" 2763197 NIL SEGCAT (NIL T) -9 NIL 2763418 NIL) (-1124 2761979 2762044 2762157 "SEGBIND2" 2762299 NIL SEGBIND2 (NIL T T) -7 NIL NIL NIL) (-1123 2760869 2761342 2761550 "SEGBIND" 2761806 NIL SEGBIND (NIL T) -8 NIL NIL NIL) (-1122 2760388 2760670 2760747 "SEGAST" 2760814 T SEGAST (NIL) -8 NIL NIL NIL) (-1121 2759597 2759733 2759937 "SEG2" 2760232 NIL SEG2 (NIL T T) -7 NIL NIL NIL) (-1120 2758513 2759263 2759445 "SEG" 2759450 NIL SEG (NIL T) -8 NIL NIL NIL) (-1119 2757746 2758448 2758495 "SDVAR" 2758500 NIL SDVAR (NIL T) -8 NIL NIL NIL) (-1118 2749097 2757516 2757646 "SDPOL" 2757651 NIL SDPOL (NIL T) -8 NIL NIL NIL) (-1117 2747666 2747956 2748275 "SCPKG" 2748812 NIL SCPKG (NIL T) -7 NIL NIL NIL) (-1116 2746788 2747002 2747194 "SCOPE" 2747496 T SCOPE (NIL) -8 NIL NIL NIL) (-1115 2745984 2746142 2746321 "SCACHE" 2746643 NIL SCACHE (NIL T) -7 NIL NIL NIL) (-1114 2745568 2745802 2745832 "SASTCAT" 2745837 T SASTCAT (NIL) -9 NIL 2745850 NIL) (-1113 2744971 2745403 2745479 "SAOS" 2745514 T SAOS (NIL) -8 NIL NIL NIL) (-1112 2744530 2744571 2744744 "SAERFFC" 2744930 NIL SAERFFC (NIL T T T) -7 NIL NIL NIL) (-1111 2744117 2744158 2744317 "SAEFACT" 2744489 NIL SAEFACT (NIL T T T) -7 NIL NIL NIL) (-1110 2737144 2744014 2744094 "SAE" 2744099 NIL SAE (NIL T T NIL) -8 NIL NIL NIL) (-1109 2735447 2735779 2736180 "RURPK" 2736810 NIL RURPK (NIL T NIL) -7 NIL NIL NIL) (-1108 2734024 2734390 2734695 "RULESET" 2735281 NIL RULESET (NIL T T T) -8 NIL NIL NIL) (-1107 2733594 2733818 2733901 "RULECOLD" 2733976 NIL RULECOLD (NIL NIL) -8 NIL NIL NIL) (-1106 2730709 2731347 2731805 "RULE" 2733275 NIL RULE (NIL T T T) -8 NIL NIL NIL) (-1105 2730493 2730527 2730598 "RTVALUE" 2730660 T RTVALUE (NIL) -8 NIL NIL NIL) (-1104 2729904 2730210 2730304 "RSTRCAST" 2730421 T RSTRCAST (NIL) -8 NIL NIL NIL) (-1103 2724674 2725547 2726467 "RSETGCD" 2729103 NIL RSETGCD (NIL T T T T T) -7 NIL NIL NIL) (-1102 2713238 2718982 2719079 "RSETCAT" 2723198 NIL RSETCAT (NIL T T T T) -9 NIL 2724295 NIL) (-1101 2711057 2711704 2712528 "RSETCAT-" 2712533 NIL RSETCAT- (NIL T T T T T) -8 NIL NIL NIL) (-1100 2703365 2704819 2706339 "RSDCMPK" 2709656 NIL RSDCMPK (NIL T T T T T) -7 NIL NIL NIL) (-1099 2701234 2701797 2701871 "RRCC" 2702957 NIL RRCC (NIL T T) -9 NIL 2703301 NIL) (-1098 2700555 2700759 2701038 "RRCC-" 2701043 NIL RRCC- (NIL T T T) -8 NIL NIL NIL) (-1097 2699938 2700251 2700352 "RPTAST" 2700476 T RPTAST (NIL) -8 NIL NIL NIL) (-1096 2672317 2683050 2683117 "RPOLCAT" 2693783 NIL RPOLCAT (NIL T T T) -9 NIL 2696943 NIL) (-1095 2663287 2666155 2669277 "RPOLCAT-" 2669282 NIL RPOLCAT- (NIL T T T T) -8 NIL NIL NIL) (-1094 2653740 2661498 2661980 "ROUTINE" 2662827 T ROUTINE (NIL) -8 NIL NIL NIL) (-1093 2649789 2653366 2653506 "ROMAN" 2653622 T ROMAN (NIL) -8 NIL NIL NIL) (-1092 2647901 2648649 2648909 "ROIRC" 2649594 NIL ROIRC (NIL T T) -8 NIL NIL NIL) (-1091 2643614 2646390 2646420 "RNS" 2646724 T RNS (NIL) -9 NIL 2646998 NIL) (-1090 2642021 2642506 2643040 "RNS-" 2643115 NIL RNS- (NIL T) -8 NIL NIL NIL) (-1089 2640982 2641386 2641588 "RNGBIND" 2641872 NIL RNGBIND (NIL T T) -8 NIL NIL NIL) (-1088 2640275 2640779 2640809 "RNG" 2640814 T RNG (NIL) -9 NIL 2640835 NIL) (-1087 2639570 2640048 2640091 "RMODULE" 2640096 NIL RMODULE (NIL T) -9 NIL 2640123 NIL) (-1086 2638394 2638500 2638836 "RMCAT2" 2639471 NIL RMCAT2 (NIL NIL NIL T T T T T T T T) -7 NIL NIL NIL) (-1085 2634896 2637740 2638037 "RMATRIX" 2638156 NIL RMATRIX (NIL NIL NIL T) -8 NIL NIL NIL) (-1084 2627395 2629983 2630098 "RMATCAT" 2633457 NIL RMATCAT (NIL NIL NIL T T T) -9 NIL 2634439 NIL) (-1083 2626734 2626917 2627224 "RMATCAT-" 2627229 NIL RMATCAT- (NIL T NIL NIL T T T) -8 NIL NIL NIL) (-1082 2626307 2626521 2626564 "RLINSET" 2626626 NIL RLINSET (NIL T) -9 NIL 2626670 NIL) (-1081 2625868 2625949 2626077 "RINTERP" 2626226 NIL RINTERP (NIL NIL T) -7 NIL NIL NIL) (-1080 2624792 2625466 2625496 "RING" 2625552 T RING (NIL) -9 NIL 2625644 NIL) (-1079 2624572 2624628 2624725 "RING-" 2624730 NIL RING- (NIL T) -8 NIL NIL NIL) (-1078 2623383 2623650 2623908 "RIDIST" 2624336 T RIDIST (NIL) -7 NIL NIL NIL) (-1077 2614008 2622851 2623057 "RGCHAIN" 2623231 NIL RGCHAIN (NIL T NIL) -8 NIL NIL NIL) (-1076 2613266 2613750 2613791 "RGBCSPC" 2613849 NIL RGBCSPC (NIL T) -9 NIL 2613901 NIL) (-1075 2612332 2612791 2612832 "RGBCMDL" 2613064 NIL RGBCMDL (NIL T) -9 NIL 2613178 NIL) (-1074 2611972 2612041 2612144 "RFFACTOR" 2612263 NIL RFFACTOR (NIL T) -7 NIL NIL NIL) (-1073 2611691 2611732 2611829 "RFFACT" 2611931 NIL RFFACT (NIL T) -7 NIL NIL NIL) (-1072 2609742 2610172 2610554 "RFDIST" 2611331 T RFDIST (NIL) -7 NIL NIL NIL) (-1071 2606682 2607350 2608020 "RF" 2609106 NIL RF (NIL T) -7 NIL NIL NIL) (-1070 2606129 2606227 2606390 "RETSOL" 2606584 NIL RETSOL (NIL T T) -7 NIL NIL NIL) (-1069 2605747 2605845 2605888 "RETRACT" 2606021 NIL RETRACT (NIL T) -9 NIL 2606108 NIL) (-1068 2605590 2605621 2605708 "RETRACT-" 2605713 NIL RETRACT- (NIL T T) -8 NIL NIL NIL) (-1067 2605138 2605412 2605482 "RETAST" 2605542 T RETAST (NIL) -8 NIL NIL NIL) (-1066 2597488 2604791 2604918 "RESULT" 2605033 T RESULT (NIL) -8 NIL NIL NIL) (-1065 2595923 2596757 2596956 "RESRING" 2597391 NIL RESRING (NIL T T T T NIL) -8 NIL NIL NIL) (-1064 2595547 2595608 2595706 "RESLATC" 2595860 NIL RESLATC (NIL T) -7 NIL NIL NIL) (-1063 2595246 2595287 2595394 "REPSQ" 2595506 NIL REPSQ (NIL T) -7 NIL NIL NIL) (-1062 2594937 2594978 2595089 "REPDB" 2595205 NIL REPDB (NIL T) -7 NIL NIL NIL) (-1061 2588769 2590226 2591449 "REP2" 2593749 NIL REP2 (NIL T) -7 NIL NIL NIL) (-1060 2585072 2585827 2586635 "REP1" 2587996 NIL REP1 (NIL T) -7 NIL NIL NIL) (-1059 2582452 2583074 2583676 "REP" 2584492 T REP (NIL) -7 NIL NIL NIL) (-1058 2574460 2580593 2581049 "REGSET" 2582082 NIL REGSET (NIL T T T T) -8 NIL NIL NIL) (-1057 2573169 2573608 2573858 "REF" 2574245 NIL REF (NIL T) -8 NIL NIL NIL) (-1056 2572534 2572649 2572816 "REDORDER" 2573053 NIL REDORDER (NIL T T) -7 NIL NIL NIL) (-1055 2567898 2571747 2571974 "RECLOS" 2572362 NIL RECLOS (NIL T) -8 NIL NIL NIL) (-1054 2566932 2567131 2567346 "REALSOLV" 2567705 T REALSOLV (NIL) -7 NIL NIL NIL) (-1053 2563379 2564217 2565101 "REAL0Q" 2566097 NIL REAL0Q (NIL T) -7 NIL NIL NIL) (-1052 2558932 2559968 2561029 "REAL0" 2562360 NIL REAL0 (NIL T) -7 NIL NIL NIL) (-1051 2558766 2558819 2558849 "REAL" 2558854 T REAL (NIL) -9 NIL 2558889 NIL) (-1050 2558177 2558483 2558577 "RDUCEAST" 2558694 T RDUCEAST (NIL) -8 NIL NIL NIL) (-1049 2557576 2557654 2557861 "RDIV" 2558099 NIL RDIV (NIL T T T T T) -7 NIL NIL NIL) (-1048 2556626 2556818 2557031 "RDIST" 2557398 NIL RDIST (NIL T) -7 NIL NIL NIL) (-1047 2555211 2555510 2555882 "RDETRS" 2556334 NIL RDETRS (NIL T T) -7 NIL NIL NIL) (-1046 2553005 2553477 2554015 "RDETR" 2554753 NIL RDETR (NIL T T) -7 NIL NIL NIL) (-1045 2551624 2551908 2552305 "RDEEFS" 2552721 NIL RDEEFS (NIL T T) -7 NIL NIL NIL) (-1044 2550127 2550439 2550864 "RDEEF" 2551312 NIL RDEEF (NIL T T) -7 NIL NIL NIL) (-1043 2543599 2547081 2547111 "RCFIELD" 2548406 T RCFIELD (NIL) -9 NIL 2549137 NIL) (-1042 2541555 2542167 2542863 "RCFIELD-" 2542938 NIL RCFIELD- (NIL T) -8 NIL NIL NIL) (-1041 2537607 2539628 2539671 "RCAGG" 2540755 NIL RCAGG (NIL T) -9 NIL 2541220 NIL) (-1040 2537217 2537329 2537492 "RCAGG-" 2537497 NIL RCAGG- (NIL T T) -8 NIL NIL NIL) (-1039 2536534 2536664 2536829 "RATRET" 2537101 NIL RATRET (NIL T) -7 NIL NIL NIL) (-1038 2536075 2536154 2536275 "RATFACT" 2536462 NIL RATFACT (NIL T) -7 NIL NIL NIL) (-1037 2535353 2535503 2535655 "RANDSRC" 2535945 T RANDSRC (NIL) -7 NIL NIL NIL) (-1036 2535081 2535131 2535204 "RADUTIL" 2535302 T RADUTIL (NIL) -7 NIL NIL NIL) (-1035 2527205 2533912 2534223 "RADIX" 2534804 NIL RADIX (NIL NIL) -8 NIL NIL NIL) (-1034 2516799 2527047 2527177 "RADFF" 2527182 NIL RADFF (NIL T T T NIL NIL) -8 NIL NIL NIL) (-1033 2516428 2516521 2516551 "RADCAT" 2516711 T RADCAT (NIL) -9 NIL NIL NIL) (-1032 2516198 2516258 2516358 "RADCAT-" 2516363 NIL RADCAT- (NIL T) -8 NIL NIL NIL) (-1031 2514109 2515968 2516060 "QUEUE" 2516141 NIL QUEUE (NIL T) -8 NIL NIL NIL) (-1030 2513734 2513783 2513914 "QUATCT2" 2514060 NIL QUATCT2 (NIL T T T T) -7 NIL NIL NIL) (-1029 2506105 2510157 2510199 "QUATCAT" 2510990 NIL QUATCAT (NIL T) -9 NIL 2511756 NIL) (-1028 2501986 2503281 2504671 "QUATCAT-" 2504767 NIL QUATCAT- (NIL T T) -8 NIL NIL NIL) (-1027 2497825 2501919 2501967 "QUAT" 2501972 NIL QUAT (NIL T) -8 NIL NIL NIL) (-1026 2495081 2496873 2496916 "QUAGG" 2497297 NIL QUAGG (NIL T) -9 NIL 2497472 NIL) (-1025 2494629 2494903 2494973 "QQUTAST" 2495033 T QQUTAST (NIL) -8 NIL NIL NIL) (-1024 2493540 2494142 2494307 "QFORM" 2494510 NIL QFORM (NIL NIL T) -8 NIL NIL NIL) (-1023 2493165 2493214 2493345 "QFCAT2" 2493491 NIL QFCAT2 (NIL T T T T) -7 NIL NIL NIL) (-1022 2482841 2489012 2489054 "QFCAT" 2489722 NIL QFCAT (NIL T) -9 NIL 2490723 NIL) (-1021 2478156 2479609 2481203 "QFCAT-" 2481299 NIL QFCAT- (NIL T T) -8 NIL NIL NIL) (-1020 2477587 2477721 2477853 "QEQUAT" 2478046 T QEQUAT (NIL) -8 NIL NIL NIL) (-1019 2470605 2471786 2472972 "QCMPACK" 2476520 NIL QCMPACK (NIL T T T T T) -7 NIL NIL NIL) (-1018 2469834 2470016 2470252 "QALGSET2" 2470423 NIL QALGSET2 (NIL NIL NIL) -7 NIL NIL NIL) (-1017 2467284 2467820 2468250 "QALGSET" 2469489 NIL QALGSET (NIL T T T T) -8 NIL NIL NIL) (-1016 2465951 2466193 2466512 "PWFFINTB" 2467057 NIL PWFFINTB (NIL T T T T) -7 NIL NIL NIL) (-1015 2464096 2464294 2464650 "PUSHVAR" 2465765 NIL PUSHVAR (NIL T T T T) -7 NIL NIL NIL) (-1014 2459823 2461039 2461082 "PTRANFN" 2462993 NIL PTRANFN (NIL T) -9 NIL NIL NIL) (-1013 2458160 2458505 2458829 "PTPACK" 2459534 NIL PTPACK (NIL T) -7 NIL NIL NIL) (-1012 2457783 2457846 2457957 "PTFUNC2" 2458097 NIL PTFUNC2 (NIL T T) -7 NIL NIL NIL) (-1011 2451699 2456572 2456615 "PTCAT" 2456915 NIL PTCAT (NIL T) -9 NIL 2457068 NIL) (-1010 2451348 2451389 2451515 "PSQFR" 2451658 NIL PSQFR (NIL T T T T) -7 NIL NIL NIL) (-1009 2449920 2450236 2450572 "PSEUDLIN" 2451046 NIL PSEUDLIN (NIL T) -7 NIL NIL NIL) (-1008 2436440 2439015 2441341 "PSETPK" 2447680 NIL PSETPK (NIL T T T T) -7 NIL NIL NIL) (-1007 2429148 2432176 2432274 "PSETCAT" 2435315 NIL PSETCAT (NIL T T T T) -9 NIL 2436129 NIL) (-1006 2426873 2427615 2428439 "PSETCAT-" 2428444 NIL PSETCAT- (NIL T T T T T) -8 NIL NIL NIL) (-1005 2426186 2426381 2426411 "PSCURVE" 2426683 T PSCURVE (NIL) -9 NIL 2426850 NIL) (-1004 2421902 2423676 2423743 "PSCAT" 2424595 NIL PSCAT (NIL T T T) -9 NIL 2424835 NIL) (-1003 2420896 2421178 2421581 "PSCAT-" 2421586 NIL PSCAT- (NIL T T T T) -8 NIL NIL NIL) (-1002 2419095 2419955 2420220 "PRTITION" 2420653 T PRTITION (NIL) -8 NIL NIL NIL) (-1001 2418506 2418812 2418906 "PRTDAST" 2419023 T PRTDAST (NIL) -8 NIL NIL NIL) (-1000 2407350 2409772 2411962 "PRS" 2416368 NIL PRS (NIL T T) -7 NIL NIL NIL) (-999 2404970 2406672 2406712 "PRQAGG" 2406895 NIL PRQAGG (NIL T) -9 NIL 2406997 NIL) (-998 2404149 2404598 2404626 "PROPLOG" 2404765 T PROPLOG (NIL) -9 NIL 2404880 NIL) (-997 2403747 2403810 2403933 "PROPFUN2" 2404072 NIL PROPFUN2 (NIL T T) -8 NIL NIL NIL) (-996 2403044 2403183 2403355 "PROPFUN1" 2403608 NIL PROPFUN1 (NIL T) -8 NIL NIL NIL) (-995 2401023 2401791 2402088 "PROPFRML" 2402780 NIL PROPFRML (NIL T) -8 NIL NIL NIL) (-994 2400468 2400599 2400727 "PROPERTY" 2400915 T PROPERTY (NIL) -8 NIL NIL NIL) (-993 2394356 2398634 2399454 "PRODUCT" 2399694 NIL PRODUCT (NIL T T) -8 NIL NIL NIL) (-992 2394146 2394184 2394243 "PRINT" 2394317 T PRINT (NIL) -7 NIL NIL NIL) (-991 2393462 2393603 2393755 "PRIMES" 2394026 NIL PRIMES (NIL T) -7 NIL NIL NIL) (-990 2391509 2391928 2392394 "PRIMELT" 2393041 NIL PRIMELT (NIL T) -7 NIL NIL NIL) (-989 2391226 2391287 2391315 "PRIMCAT" 2391439 T PRIMCAT (NIL) -9 NIL NIL NIL) (-988 2390215 2390411 2390639 "PRIMARR2" 2391044 NIL PRIMARR2 (NIL T T) -7 NIL NIL NIL) (-987 2385937 2390153 2390198 "PRIMARR" 2390203 NIL PRIMARR (NIL T) -8 NIL NIL NIL) (-986 2385574 2385636 2385747 "PREASSOC" 2385875 NIL PREASSOC (NIL T T) -7 NIL NIL NIL) (-985 2382532 2385032 2385266 "PR" 2385385 NIL PR (NIL T T) -8 NIL NIL NIL) (-984 2381983 2382140 2382168 "PPCURVE" 2382373 T PPCURVE (NIL) -9 NIL 2382509 NIL) (-983 2381530 2381778 2381861 "PORTNUM" 2381920 T PORTNUM (NIL) -8 NIL NIL NIL) (-982 2378867 2379288 2379880 "POLYROOT" 2381111 NIL POLYROOT (NIL T T T T T) -7 NIL NIL NIL) (-981 2378244 2378308 2378542 "POLYLIFT" 2378803 NIL POLYLIFT (NIL T T T T T) -7 NIL NIL NIL) (-980 2374465 2374968 2375597 "POLYCATQ" 2377789 NIL POLYCATQ (NIL T T T T T) -7 NIL NIL NIL) (-979 2360106 2366212 2366277 "POLYCAT" 2369791 NIL POLYCAT (NIL T T T) -9 NIL 2371669 NIL) (-978 2353225 2355417 2357801 "POLYCAT-" 2357806 NIL POLYCAT- (NIL T T T T) -8 NIL NIL NIL) (-977 2352806 2352880 2353000 "POLY2UP" 2353151 NIL POLY2UP (NIL NIL T) -7 NIL NIL NIL) (-976 2352432 2352495 2352604 "POLY2" 2352743 NIL POLY2 (NIL T T) -7 NIL NIL NIL) (-975 2345640 2352036 2352196 "POLY" 2352305 NIL POLY (NIL T) -8 NIL NIL NIL) (-974 2344301 2344564 2344840 "POLUTIL" 2345414 NIL POLUTIL (NIL T T) -7 NIL NIL NIL) (-973 2342620 2342933 2343264 "POLTOPOL" 2344023 NIL POLTOPOL (NIL NIL T) -7 NIL NIL NIL) (-972 2337616 2342554 2342601 "POINT" 2342606 NIL POINT (NIL T) -8 NIL NIL NIL) (-971 2335749 2336160 2336535 "PNTHEORY" 2337261 T PNTHEORY (NIL) -7 NIL NIL NIL) (-970 2334195 2334504 2334903 "PMTOOLS" 2335447 NIL PMTOOLS (NIL T T T) -7 NIL NIL NIL) (-969 2333782 2333866 2333983 "PMSYM" 2334111 NIL PMSYM (NIL T) -7 NIL NIL NIL) (-968 2333284 2333359 2333534 "PMQFCAT" 2333707 NIL PMQFCAT (NIL T T T) -7 NIL NIL NIL) (-967 2332665 2332763 2332925 "PMPREDFS" 2333185 NIL PMPREDFS (NIL T T T) -7 NIL NIL NIL) (-966 2332008 2332130 2332286 "PMPRED" 2332542 NIL PMPRED (NIL T) -7 NIL NIL NIL) (-965 2330662 2330880 2331258 "PMPLCAT" 2331770 NIL PMPLCAT (NIL T T T T T) -7 NIL NIL NIL) (-964 2330188 2330273 2330425 "PMLSAGG" 2330577 NIL PMLSAGG (NIL T T T) -7 NIL NIL NIL) (-963 2329655 2329737 2329919 "PMKERNEL" 2330106 NIL PMKERNEL (NIL T T) -7 NIL NIL NIL) (-962 2329266 2329347 2329460 "PMINS" 2329574 NIL PMINS (NIL T) -7 NIL NIL NIL) (-961 2328702 2328777 2328986 "PMFS" 2329191 NIL PMFS (NIL T T T) -7 NIL NIL NIL) (-960 2327918 2328048 2328253 "PMDOWN" 2328579 NIL PMDOWN (NIL T T T) -7 NIL NIL NIL) (-959 2327167 2327301 2327464 "PMASSFS" 2327805 NIL PMASSFS (NIL T T) -7 NIL NIL NIL) (-958 2326310 2326492 2326673 "PMASS" 2327006 T PMASS (NIL) -7 NIL NIL NIL) (-957 2325959 2326033 2326127 "PLOTTOOL" 2326236 T PLOTTOOL (NIL) -7 NIL NIL NIL) (-956 2321611 2322805 2323727 "PLOT3D" 2325057 T PLOT3D (NIL) -8 NIL NIL NIL) (-955 2320499 2320700 2320935 "PLOT1" 2321415 NIL PLOT1 (NIL T) -7 NIL NIL NIL) (-954 2314920 2316310 2317458 "PLOT" 2319371 T PLOT (NIL) -8 NIL NIL NIL) (-953 2290095 2294986 2299837 "PLEQN" 2310186 NIL PLEQN (NIL T T T T) -7 NIL NIL NIL) (-952 2289782 2289835 2289938 "PINTERPA" 2290042 NIL PINTERPA (NIL T T) -7 NIL NIL NIL) (-951 2289088 2289222 2289402 "PINTERP" 2289647 NIL PINTERP (NIL NIL T) -7 NIL NIL NIL) (-950 2287173 2288346 2288374 "PID" 2288556 T PID (NIL) -9 NIL 2288690 NIL) (-949 2286918 2286961 2287036 "PICOERCE" 2287130 NIL PICOERCE (NIL T) -7 NIL NIL NIL) (-948 2286014 2286682 2286769 "PI" 2286809 T PI (NIL) -8 NIL NIL 2286876) (-947 2285322 2285473 2285649 "PGROEB" 2285870 NIL PGROEB (NIL T) -7 NIL NIL NIL) (-946 2280761 2281720 2282626 "PGE" 2284436 T PGE (NIL) -7 NIL NIL NIL) (-945 2278842 2279131 2279497 "PGCD" 2280478 NIL PGCD (NIL T T T T) -7 NIL NIL NIL) (-944 2278168 2278283 2278444 "PFRPAC" 2278726 NIL PFRPAC (NIL T) -7 NIL NIL NIL) (-943 2274419 2276716 2277069 "PFR" 2277847 NIL PFR (NIL T) -8 NIL NIL NIL) (-942 2272772 2273052 2273377 "PFOTOOLS" 2274166 NIL PFOTOOLS (NIL T T) -7 NIL NIL NIL) (-941 2271287 2271544 2271895 "PFOQ" 2272529 NIL PFOQ (NIL T T T) -7 NIL NIL NIL) (-940 2269770 2270000 2270356 "PFO" 2271071 NIL PFO (NIL T T T T T) -7 NIL NIL NIL) (-939 2266848 2268361 2268389 "PFECAT" 2268974 T PFECAT (NIL) -9 NIL 2269358 NIL) (-938 2266275 2266447 2266661 "PFECAT-" 2266666 NIL PFECAT- (NIL T) -8 NIL NIL NIL) (-937 2264848 2265130 2265431 "PFBRU" 2266024 NIL PFBRU (NIL T T) -7 NIL NIL NIL) (-936 2262678 2263066 2263498 "PFBR" 2264499 NIL PFBR (NIL T T T T) -7 NIL NIL NIL) (-935 2258603 2262567 2262636 "PF" 2262641 NIL PF (NIL NIL) -8 NIL NIL NIL) (-934 2253657 2254810 2255680 "PERMGRP" 2257766 NIL PERMGRP (NIL T) -8 NIL NIL NIL) (-933 2251569 2252681 2252722 "PERMCAT" 2253122 NIL PERMCAT (NIL T) -9 NIL 2253420 NIL) (-932 2251216 2251263 2251387 "PERMAN" 2251522 NIL PERMAN (NIL NIL T) -7 NIL NIL NIL) (-931 2247018 2248725 2249373 "PERM" 2250601 NIL PERM (NIL T) -8 NIL NIL NIL) (-930 2244259 2246683 2246805 "PENDTREE" 2246929 NIL PENDTREE (NIL T) -8 NIL NIL NIL) (-929 2243140 2243403 2243444 "PDSPC" 2243977 NIL PDSPC (NIL T) -9 NIL 2244222 NIL) (-928 2242195 2242461 2242823 "PDSPC-" 2242828 NIL PDSPC- (NIL T T) -8 NIL NIL NIL) (-927 2240909 2241845 2241886 "PDRING" 2241891 NIL PDRING (NIL T) -9 NIL 2241919 NIL) (-926 2239652 2240414 2240468 "PDMOD" 2240473 NIL PDMOD (NIL T T) -9 NIL 2240577 NIL) (-925 2236819 2237645 2238313 "PDEPROB" 2239004 T PDEPROB (NIL) -8 NIL NIL NIL) (-924 2234328 2234868 2235423 "PDEPACK" 2236284 T PDEPACK (NIL) -7 NIL NIL NIL) (-923 2233216 2233430 2233681 "PDECOMP" 2234127 NIL PDECOMP (NIL T T) -7 NIL NIL NIL) (-922 2230733 2231624 2231652 "PDECAT" 2232439 T PDECAT (NIL) -9 NIL 2233152 NIL) (-921 2230350 2230417 2230471 "PDDOM" 2230636 NIL PDDOM (NIL T T) -9 NIL 2230716 NIL) (-920 2230163 2230199 2230306 "PDDOM-" 2230311 NIL PDDOM- (NIL T T T) -8 NIL NIL NIL) (-919 2229908 2229947 2230037 "PCOMP" 2230124 NIL PCOMP (NIL T T) -7 NIL NIL NIL) (-918 2227948 2228709 2229006 "PBWLB" 2229637 NIL PBWLB (NIL T) -8 NIL NIL NIL) (-917 2227574 2227637 2227746 "PATTERN2" 2227885 NIL PATTERN2 (NIL T T) -7 NIL NIL NIL) (-916 2225283 2225719 2226176 "PATTERN1" 2227163 NIL PATTERN1 (NIL T T) -7 NIL NIL NIL) (-915 2217462 2219356 2220694 "PATTERN" 2223966 NIL PATTERN (NIL T) -8 NIL NIL NIL) (-914 2217020 2217093 2217225 "PATRES2" 2217389 NIL PATRES2 (NIL T T T) -7 NIL NIL NIL) (-913 2214286 2214969 2215450 "PATRES" 2216585 NIL PATRES (NIL T T) -8 NIL NIL NIL) (-912 2212139 2212574 2212981 "PATMATCH" 2213953 NIL PATMATCH (NIL T T T) -7 NIL NIL NIL) (-911 2211593 2211844 2211885 "PATMAB" 2211992 NIL PATMAB (NIL T) -9 NIL 2212075 NIL) (-910 2210039 2210447 2210705 "PATLRES" 2211398 NIL PATLRES (NIL T T T) -8 NIL NIL NIL) (-909 2209577 2209708 2209749 "PATAB" 2209754 NIL PATAB (NIL T) -9 NIL 2209926 NIL) (-908 2207717 2208154 2208577 "PARTPERM" 2209174 T PARTPERM (NIL) -7 NIL NIL NIL) (-907 2207326 2207401 2207503 "PARSURF" 2207648 NIL PARSURF (NIL T) -8 NIL NIL NIL) (-906 2206952 2207015 2207124 "PARSU2" 2207263 NIL PARSU2 (NIL T T) -7 NIL NIL NIL) (-905 2206710 2206756 2206823 "PARSER" 2206905 T PARSER (NIL) -7 NIL NIL NIL) (-904 2206319 2206394 2206496 "PARSCURV" 2206641 NIL PARSCURV (NIL T) -8 NIL NIL NIL) (-903 2205945 2206008 2206117 "PARSC2" 2206256 NIL PARSC2 (NIL T T) -7 NIL NIL NIL) (-902 2205572 2205642 2205739 "PARPCURV" 2205881 NIL PARPCURV (NIL T) -8 NIL NIL NIL) (-901 2205198 2205261 2205370 "PARPC2" 2205509 NIL PARPC2 (NIL T T) -7 NIL NIL NIL) (-900 2204187 2204571 2204753 "PARAMAST" 2205036 T PARAMAST (NIL) -8 NIL NIL NIL) (-899 2203695 2203793 2203912 "PAN2EXPR" 2204088 T PAN2EXPR (NIL) -7 NIL NIL NIL) (-898 2202388 2202816 2203044 "PALETTE" 2203487 T PALETTE (NIL) -8 NIL NIL NIL) (-897 2200733 2201393 2201753 "PAIR" 2202074 NIL PAIR (NIL T T) -8 NIL NIL NIL) (-896 2193645 2199990 2200185 "PADICRC" 2200587 NIL PADICRC (NIL NIL T) -8 NIL NIL NIL) (-895 2185881 2192989 2193174 "PADICRAT" 2193492 NIL PADICRAT (NIL NIL) -8 NIL NIL NIL) (-894 2182671 2184541 2184581 "PADICCT" 2185162 NIL PADICCT (NIL NIL) -9 NIL 2185444 NIL) (-893 2180680 2182608 2182653 "PADIC" 2182658 NIL PADIC (NIL NIL) -8 NIL NIL NIL) (-892 2179625 2179837 2180105 "PADEPAC" 2180467 NIL PADEPAC (NIL T NIL NIL) -7 NIL NIL NIL) (-891 2178825 2178970 2179176 "PADE" 2179487 NIL PADE (NIL T T T) -7 NIL NIL NIL) (-890 2177058 2178033 2178313 "OWP" 2178629 NIL OWP (NIL T NIL NIL NIL) -8 NIL NIL NIL) (-889 2176503 2176764 2176861 "OVERSET" 2176981 T OVERSET (NIL) -8 NIL NIL NIL) (-888 2175423 2176108 2176280 "OVAR" 2176371 NIL OVAR (NIL NIL) -8 NIL NIL NIL) (-887 2163659 2166532 2168732 "OUTFORM" 2173243 T OUTFORM (NIL) -8 NIL NIL NIL) (-886 2162941 2163256 2163383 "OUTBFILE" 2163552 T OUTBFILE (NIL) -8 NIL NIL NIL) (-885 2162218 2162413 2162441 "OUTBCON" 2162759 T OUTBCON (NIL) -9 NIL 2162925 NIL) (-884 2161801 2161931 2162088 "OUTBCON-" 2162093 NIL OUTBCON- (NIL T) -8 NIL NIL NIL) (-883 2161041 2161186 2161347 "OUT" 2161660 T OUT (NIL) -7 NIL NIL NIL) (-882 2160337 2160770 2160859 "OSI" 2160972 T OSI (NIL) -8 NIL NIL NIL) (-881 2159756 2160178 2160206 "OSGROUP" 2160211 T OSGROUP (NIL) -9 NIL 2160233 NIL) (-880 2158467 2158728 2159013 "ORTHPOL" 2159503 NIL ORTHPOL (NIL T) -7 NIL NIL NIL) (-879 2155718 2158302 2158423 "OREUP" 2158428 NIL OREUP (NIL NIL T NIL NIL) -8 NIL NIL NIL) (-878 2152821 2155409 2155536 "ORESUP" 2155660 NIL ORESUP (NIL T NIL NIL) -8 NIL NIL NIL) (-877 2150321 2150849 2151410 "OREPCTO" 2152310 NIL OREPCTO (NIL T T) -7 NIL NIL NIL) (-876 2143699 2146194 2146235 "OREPCAT" 2148583 NIL OREPCAT (NIL T) -9 NIL 2149687 NIL) (-875 2140672 2141628 2142686 "OREPCAT-" 2142691 NIL OREPCAT- (NIL T T) -8 NIL NIL NIL) (-874 2139864 2140142 2140170 "ORDTYPE" 2140479 T ORDTYPE (NIL) -9 NIL 2140642 NIL) (-873 2139165 2139381 2139636 "ORDTYPE-" 2139641 NIL ORDTYPE- (NIL T) -8 NIL NIL NIL) (-872 2138521 2138904 2139062 "ORDSTRCT" 2139067 NIL ORDSTRCT (NIL T NIL) -8 NIL NIL NIL) (-871 2138019 2138389 2138417 "ORDSET" 2138422 T ORDSET (NIL) -9 NIL 2138444 NIL) (-870 2136377 2137348 2137376 "ORDRING" 2137578 T ORDRING (NIL) -9 NIL 2137703 NIL) (-869 2135998 2136116 2136260 "ORDRING-" 2136265 NIL ORDRING- (NIL T) -8 NIL NIL NIL) (-868 2135249 2135814 2135842 "ORDMON" 2135847 T ORDMON (NIL) -9 NIL 2135868 NIL) (-867 2134393 2134558 2134753 "ORDFUNS" 2135098 NIL ORDFUNS (NIL NIL T) -7 NIL NIL NIL) (-866 2133608 2134123 2134151 "ORDFIN" 2134216 T ORDFIN (NIL) -9 NIL 2134290 NIL) (-865 2132862 2133001 2133187 "ORDCOMP2" 2133468 NIL ORDCOMP2 (NIL T T) -7 NIL NIL NIL) (-864 2129209 2131448 2131857 "ORDCOMP" 2132486 NIL ORDCOMP (NIL T) -8 NIL NIL NIL) (-863 2125730 2126700 2127514 "OPTPROB" 2128415 T OPTPROB (NIL) -8 NIL NIL NIL) (-862 2122472 2123171 2123875 "OPTPACK" 2125046 T OPTPACK (NIL) -7 NIL NIL NIL) (-861 2120085 2120911 2120939 "OPTCAT" 2121758 T OPTCAT (NIL) -9 NIL 2122408 NIL) (-860 2119403 2119762 2119867 "OPSIG" 2120000 T OPSIG (NIL) -8 NIL NIL NIL) (-859 2119165 2119210 2119276 "OPQUERY" 2119357 T OPQUERY (NIL) -7 NIL NIL NIL) (-858 2118471 2118751 2118792 "OPERCAT" 2119004 NIL OPERCAT (NIL T) -9 NIL 2119101 NIL) (-857 2118214 2118282 2118399 "OPERCAT-" 2118404 NIL OPERCAT- (NIL T T) -8 NIL NIL NIL) (-856 2115123 2116525 2117029 "OP" 2117743 NIL OP (NIL T) -8 NIL NIL NIL) (-855 2114416 2114543 2114717 "ONECOMP2" 2114995 NIL ONECOMP2 (NIL T T) -7 NIL NIL NIL) (-854 2111029 2113213 2113582 "ONECOMP" 2114080 NIL ONECOMP (NIL T) -8 NIL NIL NIL) (-853 2110430 2110554 2110684 "OMSERVER" 2110919 T OMSERVER (NIL) -7 NIL NIL NIL) (-852 2106944 2109870 2109910 "OMSAGG" 2109971 NIL OMSAGG (NIL T) -9 NIL 2110035 NIL) (-851 2105519 2105830 2106112 "OMPKG" 2106682 T OMPKG (NIL) -7 NIL NIL NIL) (-850 2103866 2105068 2105237 "OMLO" 2105400 NIL OMLO (NIL T T) -8 NIL NIL NIL) (-849 2102802 2102973 2103193 "OMEXPR" 2103692 NIL OMEXPR (NIL T) -7 NIL NIL NIL) (-848 2101887 2102223 2102383 "OMERRK" 2102662 T OMERRK (NIL) -8 NIL NIL NIL) (-847 2101124 2101433 2101569 "OMERR" 2101771 T OMERR (NIL) -8 NIL NIL NIL) (-846 2100515 2100801 2100909 "OMENC" 2101036 T OMENC (NIL) -8 NIL NIL NIL) (-845 2094152 2095595 2096766 "OMDEV" 2099364 T OMDEV (NIL) -8 NIL NIL NIL) (-844 2093185 2093392 2093586 "OMCONN" 2093978 T OMCONN (NIL) -8 NIL NIL NIL) (-843 2092591 2092718 2092746 "OM" 2093045 T OM (NIL) -9 NIL NIL NIL) (-842 2090869 2092061 2092089 "OINTDOM" 2092094 T OINTDOM (NIL) -9 NIL 2092115 NIL) (-841 2087944 2089557 2089894 "OFMONOID" 2090564 NIL OFMONOID (NIL T) -8 NIL NIL NIL) (-840 2087178 2087881 2087926 "ODVAR" 2087931 NIL ODVAR (NIL T) -8 NIL NIL NIL) (-839 2084315 2086923 2087078 "ODR" 2087083 NIL ODR (NIL T T NIL) -8 NIL NIL NIL) (-838 2075720 2084091 2084217 "ODPOL" 2084222 NIL ODPOL (NIL T) -8 NIL NIL NIL) (-837 2069063 2075592 2075697 "ODP" 2075702 NIL ODP (NIL NIL T NIL) -8 NIL NIL NIL) (-836 2067805 2068044 2068319 "ODETOOLS" 2068837 NIL ODETOOLS (NIL T T) -7 NIL NIL NIL) (-835 2064748 2065430 2066146 "ODESYS" 2067138 NIL ODESYS (NIL T T) -7 NIL NIL NIL) (-834 2059578 2060538 2061563 "ODERTRIC" 2063823 NIL ODERTRIC (NIL T T) -7 NIL NIL NIL) (-833 2058998 2059086 2059280 "ODERED" 2059490 NIL ODERED (NIL T T T T T) -7 NIL NIL NIL) (-832 2055850 2056434 2057111 "ODERAT" 2058421 NIL ODERAT (NIL T T) -7 NIL NIL NIL) (-831 2052767 2053274 2053871 "ODEPRRIC" 2055379 NIL ODEPRRIC (NIL T T T T) -7 NIL NIL NIL) (-830 2050662 2051306 2051792 "ODEPROB" 2052301 T ODEPROB (NIL) -8 NIL NIL NIL) (-829 2047128 2047667 2048314 "ODEPRIM" 2050141 NIL ODEPRIM (NIL T T T T) -7 NIL NIL NIL) (-828 2046371 2046479 2046739 "ODEPAL" 2047020 NIL ODEPAL (NIL T T T T) -7 NIL NIL NIL) (-827 2042473 2043324 2044188 "ODEPACK" 2045527 T ODEPACK (NIL) -7 NIL NIL NIL) (-826 2041516 2041641 2041863 "ODEINT" 2042362 NIL ODEINT (NIL T T) -7 NIL NIL NIL) (-825 2035581 2037042 2038489 "ODEIFTBL" 2040089 T ODEIFTBL (NIL) -8 NIL NIL NIL) (-824 2030931 2031765 2032717 "ODEEF" 2034740 NIL ODEEF (NIL T T) -7 NIL NIL NIL) (-823 2030274 2030369 2030592 "ODECONST" 2030836 NIL ODECONST (NIL T T T) -7 NIL NIL NIL) (-822 2028337 2029046 2029074 "ODECAT" 2029679 T ODECAT (NIL) -9 NIL 2030210 NIL) (-821 2027969 2028018 2028145 "OCTCT2" 2028288 NIL OCTCT2 (NIL T T T T) -7 NIL NIL NIL) (-820 2024462 2027674 2027796 "OCT" 2027879 NIL OCT (NIL T) -8 NIL NIL NIL) (-819 2023685 2024255 2024283 "OCAMON" 2024288 T OCAMON (NIL) -9 NIL 2024309 NIL) (-818 2017949 2020728 2020768 "OC" 2021865 NIL OC (NIL T) -9 NIL 2022723 NIL) (-817 2014984 2015924 2016914 "OC-" 2017008 NIL OC- (NIL T T) -8 NIL NIL NIL) (-816 2014404 2014829 2014857 "OASGP" 2014862 T OASGP (NIL) -9 NIL 2014882 NIL) (-815 2013530 2014127 2014155 "OAMONS" 2014195 T OAMONS (NIL) -9 NIL 2014238 NIL) (-814 2012821 2013350 2013378 "OAMON" 2013383 T OAMON (NIL) -9 NIL 2013403 NIL) (-813 2011932 2012570 2012598 "OAGROUP" 2012603 T OAGROUP (NIL) -9 NIL 2012623 NIL) (-812 2011614 2011670 2011759 "NUMTUBE" 2011876 NIL NUMTUBE (NIL T) -7 NIL NIL NIL) (-811 2005133 2006705 2008241 "NUMQUAD" 2010098 T NUMQUAD (NIL) -7 NIL NIL NIL) (-810 2000813 2001847 2002882 "NUMODE" 2004118 T NUMODE (NIL) -7 NIL NIL NIL) (-809 1998094 1999034 1999062 "NUMINT" 1999985 T NUMINT (NIL) -9 NIL 2000749 NIL) (-808 1997006 1997239 1997457 "NUMFMT" 1997896 T NUMFMT (NIL) -7 NIL NIL NIL) (-807 1983189 1986310 1988842 "NUMERIC" 1994513 NIL NUMERIC (NIL T) -7 NIL NIL NIL) (-806 1976893 1982637 1982732 "NTSCAT" 1982737 NIL NTSCAT (NIL T T T T) -9 NIL 1982776 NIL) (-805 1976073 1976252 1976445 "NTPOLFN" 1976732 NIL NTPOLFN (NIL T) -7 NIL NIL NIL) (-804 1975699 1975762 1975871 "NSUP2" 1976010 NIL NSUP2 (NIL T T) -7 NIL NIL NIL) (-803 1962460 1972524 1973336 "NSUP" 1974920 NIL NSUP (NIL T) -8 NIL NIL NIL) (-802 1951296 1962234 1962367 "NSMP" 1962372 NIL NSMP (NIL T T) -8 NIL NIL NIL) (-801 1949704 1950029 1950386 "NREP" 1950984 NIL NREP (NIL T) -7 NIL NIL NIL) (-800 1948283 1948547 1948905 "NPCOEF" 1949447 NIL NPCOEF (NIL T T T T T) -7 NIL NIL NIL) (-799 1947331 1947464 1947680 "NORMRETR" 1948164 NIL NORMRETR (NIL T T T T NIL) -7 NIL NIL NIL) (-798 1945342 1945662 1946071 "NORMPK" 1947039 NIL NORMPK (NIL T T T T T) -7 NIL NIL NIL) (-797 1945021 1945055 1945179 "NORMMA" 1945308 NIL NORMMA (NIL T T T T) -7 NIL NIL NIL) (-796 1944804 1944839 1944908 "NONE1" 1944985 NIL NONE1 (NIL T) -7 NIL NIL NIL) (-795 1944568 1944761 1944790 "NONE" 1944795 T NONE (NIL) -8 NIL NIL NIL) (-794 1944059 1944127 1944306 "NODE1" 1944500 NIL NODE1 (NIL T T) -7 NIL NIL NIL) (-793 1942151 1943182 1943437 "NNI" 1943784 T NNI (NIL) -8 NIL NIL 1944019) (-792 1940547 1940884 1941248 "NLINSOL" 1941819 NIL NLINSOL (NIL T) -7 NIL NIL NIL) (-791 1936728 1937783 1938682 "NIPROB" 1939668 T NIPROB (NIL) -8 NIL NIL NIL) (-790 1935467 1935719 1936021 "NFINTBAS" 1936490 NIL NFINTBAS (NIL T T) -7 NIL NIL NIL) (-789 1934551 1935117 1935158 "NETCLT" 1935330 NIL NETCLT (NIL T) -9 NIL 1935412 NIL) (-788 1933223 1933490 1933771 "NCODIV" 1934319 NIL NCODIV (NIL T T) -7 NIL NIL NIL) (-787 1932979 1933022 1933097 "NCNTFRAC" 1933180 NIL NCNTFRAC (NIL T) -7 NIL NIL NIL) (-786 1931135 1931523 1931943 "NCEP" 1932604 NIL NCEP (NIL T) -7 NIL NIL NIL) (-785 1929798 1930745 1930773 "NASRING" 1930883 T NASRING (NIL) -9 NIL 1930963 NIL) (-784 1929581 1929637 1929731 "NASRING-" 1929736 NIL NASRING- (NIL T) -8 NIL NIL NIL) (-783 1928548 1929199 1929227 "NARNG" 1929344 T NARNG (NIL) -9 NIL 1929435 NIL) (-782 1928222 1928307 1928441 "NARNG-" 1928446 NIL NARNG- (NIL T) -8 NIL NIL NIL) (-781 1927059 1927308 1927543 "NAGSP" 1928007 T NAGSP (NIL) -7 NIL NIL NIL) (-780 1918103 1920015 1921688 "NAGS" 1925406 T NAGS (NIL) -7 NIL NIL NIL) (-779 1916627 1916959 1917290 "NAGF07" 1917792 T NAGF07 (NIL) -7 NIL NIL NIL) (-778 1911099 1912456 1913763 "NAGF04" 1915340 T NAGF04 (NIL) -7 NIL NIL NIL) (-777 1903971 1905681 1907314 "NAGF02" 1909486 T NAGF02 (NIL) -7 NIL NIL NIL) (-776 1899135 1900295 1901412 "NAGF01" 1902874 T NAGF01 (NIL) -7 NIL NIL NIL) (-775 1892715 1894329 1895914 "NAGE04" 1897570 T NAGE04 (NIL) -7 NIL NIL NIL) (-774 1883776 1886005 1888135 "NAGE02" 1890605 T NAGE02 (NIL) -7 NIL NIL NIL) (-773 1879669 1880676 1881640 "NAGE01" 1882832 T NAGE01 (NIL) -7 NIL NIL NIL) (-772 1877446 1877998 1878556 "NAGD03" 1879131 T NAGD03 (NIL) -7 NIL NIL NIL) (-771 1869142 1871124 1873078 "NAGD02" 1875512 T NAGD02 (NIL) -7 NIL NIL NIL) (-770 1862881 1864378 1865818 "NAGD01" 1867722 T NAGD01 (NIL) -7 NIL NIL NIL) (-769 1859018 1859912 1860749 "NAGC06" 1862064 T NAGC06 (NIL) -7 NIL NIL NIL) (-768 1857465 1857815 1858171 "NAGC05" 1858682 T NAGC05 (NIL) -7 NIL NIL NIL) (-767 1856829 1856960 1857104 "NAGC02" 1857341 T NAGC02 (NIL) -7 NIL NIL NIL) (-766 1855630 1856357 1856397 "NAALG" 1856476 NIL NAALG (NIL T) -9 NIL 1856537 NIL) (-765 1855459 1855494 1855584 "NAALG-" 1855589 NIL NAALG- (NIL T T) -8 NIL NIL NIL) (-764 1849331 1850517 1851704 "MULTSQFR" 1854355 NIL MULTSQFR (NIL T T T T) -7 NIL NIL NIL) (-763 1848638 1848725 1848909 "MULTFACT" 1849243 NIL MULTFACT (NIL T T T T) -7 NIL NIL NIL) (-762 1840776 1845221 1845274 "MTSCAT" 1846344 NIL MTSCAT (NIL T T) -9 NIL 1846860 NIL) (-761 1840482 1840542 1840634 "MTHING" 1840716 NIL MTHING (NIL T) -7 NIL NIL NIL) (-760 1840268 1840307 1840367 "MSYSCMD" 1840442 T MSYSCMD (NIL) -7 NIL NIL NIL) (-759 1837013 1839829 1839870 "MSETAGG" 1839875 NIL MSETAGG (NIL T) -9 NIL 1839909 NIL) (-758 1832727 1835768 1836088 "MSET" 1836726 NIL MSET (NIL T) -8 NIL NIL NIL) (-757 1828319 1830106 1830851 "MRING" 1832027 NIL MRING (NIL T T) -8 NIL NIL NIL) (-756 1827879 1827952 1828083 "MRF2" 1828246 NIL MRF2 (NIL T T T) -7 NIL NIL NIL) (-755 1827491 1827532 1827676 "MRATFAC" 1827838 NIL MRATFAC (NIL T T T T) -7 NIL NIL NIL) (-754 1825061 1825398 1825829 "MPRFF" 1827196 NIL MPRFF (NIL T T T T) -7 NIL NIL NIL) (-753 1818388 1824915 1825012 "MPOLY" 1825017 NIL MPOLY (NIL NIL T) -8 NIL NIL NIL) (-752 1817872 1817913 1818121 "MPCPF" 1818347 NIL MPCPF (NIL T T T T) -7 NIL NIL NIL) (-751 1817380 1817429 1817613 "MPC3" 1817823 NIL MPC3 (NIL T T T T T T T) -7 NIL NIL NIL) (-750 1816563 1816656 1816877 "MPC2" 1817295 NIL MPC2 (NIL T T T T T T T) -7 NIL NIL NIL) (-749 1814840 1815201 1815591 "MONOTOOL" 1816223 NIL MONOTOOL (NIL T T) -7 NIL NIL NIL) (-748 1813985 1814368 1814396 "MONOID" 1814615 T MONOID (NIL) -9 NIL 1814762 NIL) (-747 1813501 1813650 1813831 "MONOID-" 1813836 NIL MONOID- (NIL T) -8 NIL NIL NIL) (-746 1802453 1809321 1809380 "MONOGEN" 1810054 NIL MONOGEN (NIL T T) -9 NIL 1810510 NIL) (-745 1799503 1800406 1801406 "MONOGEN-" 1801525 NIL MONOGEN- (NIL T T T) -8 NIL NIL NIL) (-744 1798220 1798768 1798796 "MONADWU" 1799188 T MONADWU (NIL) -9 NIL 1799426 NIL) (-743 1797550 1797751 1797999 "MONADWU-" 1798004 NIL MONADWU- (NIL T) -8 NIL NIL NIL) (-742 1796835 1797139 1797167 "MONAD" 1797374 T MONAD (NIL) -9 NIL 1797486 NIL) (-741 1796502 1796598 1796730 "MONAD-" 1796735 NIL MONAD- (NIL T) -8 NIL NIL NIL) (-740 1794641 1795415 1795694 "MOEBIUS" 1796255 NIL MOEBIUS (NIL T) -8 NIL NIL NIL) (-739 1793809 1794309 1794349 "MODULE" 1794354 NIL MODULE (NIL T) -9 NIL 1794393 NIL) (-738 1793347 1793473 1793663 "MODULE-" 1793668 NIL MODULE- (NIL T T) -8 NIL NIL NIL) (-737 1790877 1791711 1792038 "MODRING" 1793171 NIL MODRING (NIL T T NIL NIL NIL) -8 NIL NIL NIL) (-736 1787599 1788982 1789503 "MODOP" 1790406 NIL MODOP (NIL T T) -8 NIL NIL NIL) (-735 1786085 1786666 1786943 "MODMONOM" 1787462 NIL MODMONOM (NIL T T NIL) -8 NIL NIL NIL) (-734 1774825 1784376 1784790 "MODMON" 1785722 NIL MODMON (NIL T T) -8 NIL NIL NIL) (-733 1771651 1773669 1773945 "MODFIELD" 1774700 NIL MODFIELD (NIL T T NIL NIL NIL) -8 NIL NIL NIL) (-732 1770562 1770932 1771122 "MMLFORM" 1771481 T MMLFORM (NIL) -8 NIL NIL NIL) (-731 1770082 1770131 1770310 "MMAP" 1770513 NIL MMAP (NIL T T T T T T) -7 NIL NIL NIL) (-730 1767975 1768914 1768955 "MLO" 1769378 NIL MLO (NIL T) -9 NIL 1769620 NIL) (-729 1765323 1765857 1766459 "MLIFT" 1767456 NIL MLIFT (NIL T T T T) -7 NIL NIL NIL) (-728 1764702 1764798 1764952 "MKUCFUNC" 1765234 NIL MKUCFUNC (NIL T T T) -7 NIL NIL NIL) (-727 1764295 1764371 1764494 "MKRECORD" 1764625 NIL MKRECORD (NIL T T) -7 NIL NIL NIL) (-726 1763318 1763504 1763732 "MKFUNC" 1764106 NIL MKFUNC (NIL T) -7 NIL NIL NIL) (-725 1762694 1762810 1762966 "MKFLCFN" 1763201 NIL MKFLCFN (NIL T) -7 NIL NIL NIL) (-724 1761959 1762073 1762258 "MKBCFUNC" 1762587 NIL MKBCFUNC (NIL T T T T) -7 NIL NIL NIL) (-723 1757942 1761513 1761649 "MINT" 1761843 T MINT (NIL) -8 NIL NIL NIL) (-722 1756724 1756997 1757274 "MHROWRED" 1757697 NIL MHROWRED (NIL T) -7 NIL NIL NIL) (-721 1751468 1755259 1755664 "MFLOAT" 1756339 T MFLOAT (NIL) -8 NIL NIL NIL) (-720 1750813 1750901 1751072 "MFINFACT" 1751380 NIL MFINFACT (NIL T T T T) -7 NIL NIL NIL) (-719 1747092 1747976 1748860 "MESH" 1749949 T MESH (NIL) -7 NIL NIL NIL) (-718 1745446 1745794 1746147 "MDDFACT" 1746779 NIL MDDFACT (NIL T) -7 NIL NIL NIL) (-717 1741982 1744577 1744618 "MDAGG" 1744873 NIL MDAGG (NIL T) -9 NIL 1745016 NIL) (-716 1729684 1741275 1741482 "MCMPLX" 1741795 T MCMPLX (NIL) -8 NIL NIL NIL) (-715 1728803 1728967 1729168 "MCDEN" 1729533 NIL MCDEN (NIL T T) -7 NIL NIL NIL) (-714 1726651 1726963 1727343 "MCALCFN" 1728533 NIL MCALCFN (NIL T T T T) -7 NIL NIL NIL) (-713 1725528 1725816 1726049 "MAYBE" 1726457 NIL MAYBE (NIL T) -8 NIL NIL NIL) (-712 1723086 1723663 1724225 "MATSTOR" 1724999 NIL MATSTOR (NIL T) -7 NIL NIL NIL) (-711 1718508 1722458 1722706 "MATRIX" 1722871 NIL MATRIX (NIL T) -8 NIL NIL NIL) (-710 1714208 1714981 1715717 "MATLIN" 1717865 NIL MATLIN (NIL T T T T) -7 NIL NIL NIL) (-709 1712784 1712955 1713288 "MATCAT2" 1714043 NIL MATCAT2 (NIL T T T T T T T T) -7 NIL NIL NIL) (-708 1702123 1705841 1705918 "MATCAT" 1710950 NIL MATCAT (NIL T T T) -9 NIL 1712422 NIL) (-707 1698076 1699386 1700799 "MATCAT-" 1700804 NIL MATCAT- (NIL T T T T) -8 NIL NIL NIL) (-706 1696152 1696512 1696896 "MAPPKG3" 1697751 NIL MAPPKG3 (NIL T T T) -7 NIL NIL NIL) (-705 1695109 1695306 1695528 "MAPPKG2" 1695976 NIL MAPPKG2 (NIL T T) -7 NIL NIL NIL) (-704 1693566 1693892 1694219 "MAPPKG1" 1694815 NIL MAPPKG1 (NIL T) -7 NIL NIL NIL) (-703 1692567 1692972 1693149 "MAPPAST" 1693409 T MAPPAST (NIL) -8 NIL NIL NIL) (-702 1692172 1692236 1692359 "MAPHACK3" 1692503 NIL MAPHACK3 (NIL T T T) -7 NIL NIL NIL) (-701 1691752 1691825 1691939 "MAPHACK2" 1692104 NIL MAPHACK2 (NIL T T) -7 NIL NIL NIL) (-700 1691178 1691293 1691435 "MAPHACK1" 1691643 NIL MAPHACK1 (NIL T) -7 NIL NIL NIL) (-699 1689101 1689878 1690182 "MAGMA" 1690906 NIL MAGMA (NIL T) -8 NIL NIL NIL) (-698 1688520 1688825 1688916 "MACROAST" 1689030 T MACROAST (NIL) -8 NIL NIL NIL) (-697 1684763 1686759 1687220 "M3D" 1688092 NIL M3D (NIL T) -8 NIL NIL NIL) (-696 1678235 1683074 1683115 "LZSTAGG" 1683897 NIL LZSTAGG (NIL T) -9 NIL 1684192 NIL) (-695 1673917 1675366 1676823 "LZSTAGG-" 1676828 NIL LZSTAGG- (NIL T T) -8 NIL NIL NIL) (-694 1670830 1671808 1672295 "LWORD" 1673462 NIL LWORD (NIL T) -8 NIL NIL NIL) (-693 1670352 1670634 1670709 "LSTAST" 1670775 T LSTAST (NIL) -8 NIL NIL NIL) (-692 1662280 1670123 1670257 "LSQM" 1670262 NIL LSQM (NIL NIL T) -8 NIL NIL NIL) (-691 1661498 1661643 1661871 "LSPP" 1662135 NIL LSPP (NIL T T T T) -7 NIL NIL NIL) (-690 1658235 1658951 1659681 "LSMP1" 1660800 NIL LSMP1 (NIL T) -7 NIL NIL NIL) (-689 1656017 1656348 1656804 "LSMP" 1657924 NIL LSMP (NIL T T T T) -7 NIL NIL NIL) (-688 1649145 1655107 1655148 "LSAGG" 1655210 NIL LSAGG (NIL T) -9 NIL 1655288 NIL) (-687 1645654 1646764 1647977 "LSAGG-" 1647982 NIL LSAGG- (NIL T T) -8 NIL NIL NIL) (-686 1642949 1644798 1645047 "LPOLY" 1645449 NIL LPOLY (NIL T T) -8 NIL NIL NIL) (-685 1642525 1642616 1642739 "LPEFRAC" 1642858 NIL LPEFRAC (NIL T) -7 NIL NIL NIL) (-684 1642208 1642287 1642315 "LOGIC" 1642426 T LOGIC (NIL) -9 NIL 1642508 NIL) (-683 1642064 1642093 1642164 "LOGIC-" 1642169 NIL LOGIC- (NIL T) -8 NIL NIL NIL) (-682 1641239 1641397 1641590 "LODOOPS" 1641920 NIL LODOOPS (NIL T T) -7 NIL NIL NIL) (-681 1639763 1640012 1640365 "LODOF" 1640986 NIL LODOF (NIL T T) -7 NIL NIL NIL) (-680 1635639 1638398 1638439 "LODOCAT" 1638877 NIL LODOCAT (NIL T) -9 NIL 1639088 NIL) (-679 1635354 1635430 1635557 "LODOCAT-" 1635562 NIL LODOCAT- (NIL T T) -8 NIL NIL NIL) (-678 1632340 1635195 1635313 "LODO2" 1635318 NIL LODO2 (NIL T T) -8 NIL NIL NIL) (-677 1629447 1632277 1632322 "LODO1" 1632327 NIL LODO1 (NIL T) -8 NIL NIL NIL) (-676 1626542 1629363 1629429 "LODO" 1629434 NIL LODO (NIL T NIL) -8 NIL NIL NIL) (-675 1625411 1625588 1625893 "LODEEF" 1626365 NIL LODEEF (NIL T T T) -7 NIL NIL NIL) (-674 1623588 1624505 1624758 "LO" 1625243 NIL LO (NIL T T T) -8 NIL NIL NIL) (-673 1618560 1621754 1621795 "LNAGG" 1622657 NIL LNAGG (NIL T) -9 NIL 1623092 NIL) (-672 1617653 1617921 1618263 "LNAGG-" 1618268 NIL LNAGG- (NIL T T) -8 NIL NIL NIL) (-671 1613633 1614578 1615217 "LMOPS" 1617068 NIL LMOPS (NIL T T NIL) -8 NIL NIL NIL) (-670 1612932 1613410 1613451 "LMODULE" 1613456 NIL LMODULE (NIL T) -9 NIL 1613482 NIL) (-669 1609887 1612577 1612700 "LMDICT" 1612842 NIL LMDICT (NIL T) -8 NIL NIL NIL) (-668 1609463 1609677 1609718 "LLINSET" 1609779 NIL LLINSET (NIL T) -9 NIL 1609823 NIL) (-667 1609108 1609371 1609431 "LITERAL" 1609436 NIL LITERAL (NIL T) -8 NIL NIL NIL) (-666 1608627 1608707 1608846 "LIST3" 1609028 NIL LIST3 (NIL T T T) -7 NIL NIL NIL) (-665 1606725 1607073 1607472 "LIST2MAP" 1608274 NIL LIST2MAP (NIL T T) -7 NIL NIL NIL) (-664 1605714 1605910 1606138 "LIST2" 1606543 NIL LIST2 (NIL T T) -7 NIL NIL NIL) (-663 1598168 1604648 1604952 "LIST" 1605443 NIL LIST (NIL T) -8 NIL NIL NIL) (-662 1597751 1597987 1598028 "LINSET" 1598033 NIL LINSET (NIL T) -9 NIL 1598067 NIL) (-661 1596565 1597259 1597426 "LINFORM" 1597636 NIL LINFORM (NIL T NIL) -8 NIL NIL NIL) (-660 1594864 1595592 1595633 "LINEXP" 1596123 NIL LINEXP (NIL T) -9 NIL 1596396 NIL) (-659 1593440 1594344 1594525 "LINELT" 1594735 NIL LINELT (NIL T NIL) -8 NIL NIL NIL) (-658 1591997 1592277 1592588 "LINDEP" 1593192 NIL LINDEP (NIL T T) -7 NIL NIL NIL) (-657 1591133 1591729 1591839 "LINBASIS" 1591927 NIL LINBASIS (NIL NIL) -8 NIL NIL NIL) (-656 1587870 1588619 1589396 "LIMITRF" 1590388 NIL LIMITRF (NIL T) -7 NIL NIL NIL) (-655 1586155 1586469 1586878 "LIMITPS" 1587565 NIL LIMITPS (NIL T T) -7 NIL NIL NIL) (-654 1584983 1585558 1585598 "LIECAT" 1585738 NIL LIECAT (NIL T) -9 NIL 1585889 NIL) (-653 1584818 1584851 1584939 "LIECAT-" 1584944 NIL LIECAT- (NIL T T) -8 NIL NIL NIL) (-652 1578838 1584329 1584557 "LIE" 1584639 NIL LIE (NIL T T) -8 NIL NIL NIL) (-651 1571023 1578378 1578534 "LIB" 1578702 T LIB (NIL) -8 NIL NIL NIL) (-650 1566592 1567541 1568476 "LGROBP" 1570140 NIL LGROBP (NIL NIL T) -7 NIL NIL NIL) (-649 1565216 1566124 1566152 "LFCAT" 1566359 T LFCAT (NIL) -9 NIL 1566498 NIL) (-648 1563154 1563488 1563838 "LF" 1564937 NIL LF (NIL T T) -7 NIL NIL NIL) (-647 1560014 1560686 1561374 "LEXTRIPK" 1562518 NIL LEXTRIPK (NIL T NIL) -7 NIL NIL NIL) (-646 1556602 1557584 1558087 "LEXP" 1559594 NIL LEXP (NIL T T NIL) -8 NIL NIL NIL) (-645 1556018 1556323 1556415 "LETAST" 1556530 T LETAST (NIL) -8 NIL NIL NIL) (-644 1554404 1554729 1555130 "LEADCDET" 1555700 NIL LEADCDET (NIL T T T T) -7 NIL NIL NIL) (-643 1553582 1553668 1553897 "LAZM3PK" 1554325 NIL LAZM3PK (NIL T T T T T T) -7 NIL NIL NIL) (-642 1548093 1551659 1552197 "LAUPOL" 1553094 NIL LAUPOL (NIL T T) -8 NIL NIL NIL) (-641 1547666 1547716 1547877 "LAPLACE" 1548043 NIL LAPLACE (NIL T T) -7 NIL NIL NIL) (-640 1546514 1547230 1547271 "LALG" 1547333 NIL LALG (NIL T) -9 NIL 1547392 NIL) (-639 1546210 1546287 1546423 "LALG-" 1546428 NIL LALG- (NIL T T) -8 NIL NIL NIL) (-638 1543947 1545311 1545562 "LA" 1546043 NIL LA (NIL T T T) -8 NIL NIL NIL) (-637 1543776 1543806 1543847 "KVTFROM" 1543909 NIL KVTFROM (NIL T) -9 NIL NIL NIL) (-636 1542533 1543143 1543328 "KTVLOGIC" 1543611 T KTVLOGIC (NIL) -8 NIL NIL NIL) (-635 1542362 1542392 1542433 "KRCFROM" 1542495 NIL KRCFROM (NIL T) -9 NIL NIL NIL) (-634 1541254 1541453 1541752 "KOVACIC" 1542162 NIL KOVACIC (NIL T T) -7 NIL NIL NIL) (-633 1541083 1541113 1541154 "KONVERT" 1541216 NIL KONVERT (NIL T) -9 NIL NIL NIL) (-632 1540912 1540942 1540983 "KOERCE" 1541045 NIL KOERCE (NIL T) -9 NIL NIL NIL) (-631 1540396 1540489 1540621 "KERNEL2" 1540826 NIL KERNEL2 (NIL T T) -7 NIL NIL NIL) (-630 1538083 1538989 1539366 "KERNEL" 1540052 NIL KERNEL (NIL T) -8 NIL NIL NIL) (-629 1531554 1536560 1536614 "KDAGG" 1536991 NIL KDAGG (NIL T T) -9 NIL 1537197 NIL) (-628 1531065 1531207 1531412 "KDAGG-" 1531417 NIL KDAGG- (NIL T T T) -8 NIL NIL NIL) (-627 1523765 1530726 1530881 "KAFILE" 1530943 NIL KAFILE (NIL T) -8 NIL NIL NIL) (-626 1523369 1523654 1523717 "JVMOP" 1523722 T JVMOP (NIL) -8 NIL NIL NIL) (-625 1522105 1522609 1522858 "JVMMDACC" 1523140 T JVMMDACC (NIL) -8 NIL NIL NIL) (-624 1521041 1521495 1521700 "JVMFDACC" 1521920 T JVMFDACC (NIL) -8 NIL NIL NIL) (-623 1519622 1520117 1520417 "JVMCSTTG" 1520761 T JVMCSTTG (NIL) -8 NIL NIL NIL) (-622 1518758 1519162 1519323 "JVMCFACC" 1519481 T JVMCFACC (NIL) -8 NIL NIL NIL) (-621 1518436 1518675 1518724 "JVMBCODE" 1518729 T JVMBCODE (NIL) -8 NIL NIL NIL) (-620 1512455 1517947 1518175 "JORDAN" 1518257 NIL JORDAN (NIL T T) -8 NIL NIL NIL) (-619 1511768 1512104 1512225 "JOINAST" 1512354 T JOINAST (NIL) -8 NIL NIL NIL) (-618 1507803 1509945 1509999 "IXAGG" 1510928 NIL IXAGG (NIL T T) -9 NIL 1511387 NIL) (-617 1506656 1507028 1507447 "IXAGG-" 1507452 NIL IXAGG- (NIL T T T) -8 NIL NIL NIL) (-616 1501745 1506578 1506637 "IVECTOR" 1506642 NIL IVECTOR (NIL T NIL) -8 NIL NIL NIL) (-615 1500470 1500748 1501014 "ITUPLE" 1501512 NIL ITUPLE (NIL T) -8 NIL NIL NIL) (-614 1498942 1499149 1499444 "ITRIGMNP" 1500292 NIL ITRIGMNP (NIL T T T) -7 NIL NIL NIL) (-613 1497669 1497891 1498174 "ITFUN3" 1498718 NIL ITFUN3 (NIL T T T) -7 NIL NIL NIL) (-612 1497267 1497330 1497453 "ITFUN2" 1497592 NIL ITFUN2 (NIL T T) -8 NIL NIL NIL) (-611 1496372 1496747 1496921 "ITFORM" 1497113 T ITFORM (NIL) -8 NIL NIL NIL) (-610 1494141 1495392 1495670 "ITAYLOR" 1496127 NIL ITAYLOR (NIL T) -8 NIL NIL NIL) (-609 1482538 1488278 1489441 "ISUPS" 1493011 NIL ISUPS (NIL T) -8 NIL NIL NIL) (-608 1481630 1481782 1482018 "ISUMP" 1482385 NIL ISUMP (NIL T T T T) -7 NIL NIL NIL) (-607 1476480 1481575 1481616 "ISTRING" 1481621 NIL ISTRING (NIL NIL) -8 NIL NIL NIL) (-606 1475896 1476201 1476293 "ISAST" 1476408 T ISAST (NIL) -8 NIL NIL NIL) (-605 1475093 1475187 1475403 "IRURPK" 1475810 NIL IRURPK (NIL T T T T T) -7 NIL NIL NIL) (-604 1474005 1474230 1474470 "IRSN" 1474873 T IRSN (NIL) -7 NIL NIL NIL) (-603 1472050 1472431 1472860 "IRRF2F" 1473643 NIL IRRF2F (NIL T) -7 NIL NIL NIL) (-602 1471791 1471835 1471911 "IRREDFFX" 1472006 NIL IRREDFFX (NIL T) -7 NIL NIL NIL) (-601 1470364 1470665 1470964 "IROOT" 1471524 NIL IROOT (NIL T) -7 NIL NIL NIL) (-600 1469503 1469857 1470008 "IRFORM" 1470233 T IRFORM (NIL) -8 NIL NIL NIL) (-599 1468585 1468716 1468930 "IR2F" 1469386 NIL IR2F (NIL T T) -7 NIL NIL NIL) (-598 1466174 1466693 1467259 "IR2" 1468063 NIL IR2 (NIL T T) -7 NIL NIL NIL) (-597 1462614 1463858 1464550 "IR" 1465514 NIL IR (NIL T) -8 NIL NIL NIL) (-596 1462399 1462439 1462499 "IPRNTPK" 1462574 T IPRNTPK (NIL) -7 NIL NIL NIL) (-595 1458352 1462288 1462357 "IPF" 1462362 NIL IPF (NIL NIL) -8 NIL NIL NIL) (-594 1456373 1458277 1458334 "IPADIC" 1458339 NIL IPADIC (NIL NIL NIL) -8 NIL NIL NIL) (-593 1455631 1455933 1456063 "IP4ADDR" 1456263 T IP4ADDR (NIL) -8 NIL NIL NIL) (-592 1454969 1455260 1455392 "IOMODE" 1455519 T IOMODE (NIL) -8 NIL NIL NIL) (-591 1453940 1454566 1454693 "IOBFILE" 1454862 T IOBFILE (NIL) -8 NIL NIL NIL) (-590 1453350 1453844 1453872 "IOBCON" 1453877 T IOBCON (NIL) -9 NIL 1453898 NIL) (-589 1452855 1452919 1453102 "INVLAPLA" 1453286 NIL INVLAPLA (NIL T T) -7 NIL NIL NIL) (-588 1442425 1444857 1447243 "INTTR" 1450519 NIL INTTR (NIL T T) -7 NIL NIL NIL) (-587 1438718 1439502 1440367 "INTTOOLS" 1441610 NIL INTTOOLS (NIL T T) -7 NIL NIL NIL) (-586 1438298 1438395 1438512 "INTSLPE" 1438621 T INTSLPE (NIL) -7 NIL NIL NIL) (-585 1435765 1438221 1438280 "INTRVL" 1438285 NIL INTRVL (NIL T) -8 NIL NIL NIL) (-584 1433343 1433879 1434454 "INTRF" 1435250 NIL INTRF (NIL T) -7 NIL NIL NIL) (-583 1432736 1432851 1432993 "INTRET" 1433241 NIL INTRET (NIL T) -7 NIL NIL NIL) (-582 1430709 1431122 1431592 "INTRAT" 1432344 NIL INTRAT (NIL T T) -7 NIL NIL NIL) (-581 1427954 1428555 1429174 "INTPM" 1430194 NIL INTPM (NIL T T) -7 NIL NIL NIL) (-580 1424671 1425298 1426036 "INTPAF" 1427340 NIL INTPAF (NIL T T T) -7 NIL NIL NIL) (-579 1419772 1420812 1421863 "INTPACK" 1423640 T INTPACK (NIL) -7 NIL NIL NIL) (-578 1419018 1419176 1419384 "INTHERTR" 1419614 NIL INTHERTR (NIL T T) -7 NIL NIL NIL) (-577 1418451 1418537 1418725 "INTHERAL" 1418932 NIL INTHERAL (NIL T T T T) -7 NIL NIL NIL) (-576 1416219 1416740 1417197 "INTHEORY" 1418014 T INTHEORY (NIL) -7 NIL NIL NIL) (-575 1407551 1409246 1411018 "INTG0" 1414571 NIL INTG0 (NIL T T T) -7 NIL NIL NIL) (-574 1388076 1392914 1397724 "INTFTBL" 1402761 T INTFTBL (NIL) -8 NIL NIL NIL) (-573 1387301 1387463 1387636 "INTFACT" 1387935 NIL INTFACT (NIL T) -7 NIL NIL NIL) (-572 1384698 1385174 1385731 "INTEF" 1386855 NIL INTEF (NIL T T) -7 NIL NIL NIL) (-571 1382895 1383790 1383818 "INTDOM" 1384119 T INTDOM (NIL) -9 NIL 1384326 NIL) (-570 1382234 1382438 1382680 "INTDOM-" 1382685 NIL INTDOM- (NIL T) -8 NIL NIL NIL) (-569 1378102 1380523 1380577 "INTCAT" 1381376 NIL INTCAT (NIL T) -9 NIL 1381697 NIL) (-568 1377556 1377677 1377805 "INTBIT" 1377994 T INTBIT (NIL) -7 NIL NIL NIL) (-567 1376237 1376409 1376716 "INTALG" 1377401 NIL INTALG (NIL T T T T T) -7 NIL NIL NIL) (-566 1375714 1375810 1375967 "INTAF" 1376141 NIL INTAF (NIL T T) -7 NIL NIL NIL) (-565 1368681 1375524 1375664 "INTABL" 1375669 NIL INTABL (NIL T T T) -8 NIL NIL NIL) (-564 1367922 1368484 1368549 "INT8" 1368583 T INT8 (NIL) -8 NIL NIL 1368628) (-563 1367162 1367724 1367789 "INT64" 1367823 T INT64 (NIL) -8 NIL NIL 1367868) (-562 1366402 1366964 1367029 "INT32" 1367063 T INT32 (NIL) -8 NIL NIL 1367108) (-561 1365642 1366204 1366269 "INT16" 1366303 T INT16 (NIL) -8 NIL NIL 1366348) (-560 1361830 1365439 1365548 "INT" 1365553 T INT (NIL) -8 NIL NIL NIL) (-559 1355925 1359378 1359406 "INS" 1360340 T INS (NIL) -9 NIL 1361005 NIL) (-558 1352979 1353936 1354910 "INS-" 1354983 NIL INS- (NIL T) -8 NIL NIL NIL) (-557 1351736 1351981 1352279 "INPSIGN" 1352732 NIL INPSIGN (NIL T T) -7 NIL NIL NIL) (-556 1350830 1350971 1351168 "INPRODPF" 1351616 NIL INPRODPF (NIL T T) -7 NIL NIL NIL) (-555 1349700 1349841 1350078 "INPRODFF" 1350710 NIL INPRODFF (NIL T T T T) -7 NIL NIL NIL) (-554 1348688 1348852 1349112 "INNMFACT" 1349536 NIL INNMFACT (NIL T T T T) -7 NIL NIL NIL) (-553 1347867 1347982 1348170 "INMODGCD" 1348587 NIL INMODGCD (NIL T T NIL NIL) -7 NIL NIL NIL) (-552 1346351 1346620 1346944 "INFSP" 1347612 NIL INFSP (NIL T T T) -7 NIL NIL NIL) (-551 1345511 1345652 1345835 "INFPROD0" 1346231 NIL INFPROD0 (NIL T T) -7 NIL NIL NIL) (-550 1345109 1345181 1345279 "INFORM1" 1345446 NIL INFORM1 (NIL T) -7 NIL NIL NIL) (-549 1341676 1343174 1343689 "INFORM" 1344602 T INFORM (NIL) -8 NIL NIL NIL) (-548 1341181 1341288 1341402 "INFINITY" 1341582 T INFINITY (NIL) -7 NIL NIL NIL) (-547 1340255 1340901 1341002 "INETCLTS" 1341100 T INETCLTS (NIL) -8 NIL NIL NIL) (-546 1338853 1339121 1339442 "INEP" 1340003 NIL INEP (NIL T T T) -7 NIL NIL NIL) (-545 1337914 1338750 1338815 "INDE" 1338820 NIL INDE (NIL T) -8 NIL NIL NIL) (-544 1337466 1337546 1337663 "INCRMAPS" 1337841 NIL INCRMAPS (NIL T) -7 NIL NIL NIL) (-543 1336188 1336735 1336941 "INBFILE" 1337280 T INBFILE (NIL) -8 NIL NIL NIL) (-542 1331367 1332424 1333368 "INBFF" 1335276 NIL INBFF (NIL T) -7 NIL NIL NIL) (-541 1330221 1330544 1330572 "INBCON" 1331085 T INBCON (NIL) -9 NIL 1331351 NIL) (-540 1329431 1329696 1329972 "INBCON-" 1329977 NIL INBCON- (NIL T) -8 NIL NIL NIL) (-539 1328850 1329155 1329246 "INAST" 1329360 T INAST (NIL) -8 NIL NIL NIL) (-538 1328217 1328529 1328635 "IMPTAST" 1328764 T IMPTAST (NIL) -8 NIL NIL NIL) (-537 1324138 1328061 1328165 "IMATRIX" 1328170 NIL IMATRIX (NIL T NIL NIL) -8 NIL NIL NIL) (-536 1322830 1322969 1323285 "IMATQF" 1323994 NIL IMATQF (NIL T T T T T T T T) -7 NIL NIL NIL) (-535 1321010 1321277 1321614 "IMATLIN" 1322586 NIL IMATLIN (NIL T T T T) -7 NIL NIL NIL) (-534 1314925 1320934 1320992 "ILIST" 1320997 NIL ILIST (NIL T NIL) -8 NIL NIL NIL) (-533 1312591 1314785 1314898 "IIARRAY2" 1314903 NIL IIARRAY2 (NIL T NIL NIL T T) -8 NIL NIL NIL) (-532 1307391 1312502 1312566 "IFF" 1312571 NIL IFF (NIL NIL NIL) -8 NIL NIL NIL) (-531 1306672 1307008 1307124 "IFAST" 1307295 T IFAST (NIL) -8 NIL NIL NIL) (-530 1301184 1305964 1306152 "IFARRAY" 1306529 NIL IFARRAY (NIL T NIL) -8 NIL NIL NIL) (-529 1300222 1301088 1301161 "IFAMON" 1301166 NIL IFAMON (NIL T T NIL) -8 NIL NIL NIL) (-528 1299794 1299871 1299925 "IEVALAB" 1300132 NIL IEVALAB (NIL T T) -9 NIL NIL NIL) (-527 1299457 1299537 1299697 "IEVALAB-" 1299702 NIL IEVALAB- (NIL T T T) -8 NIL NIL NIL) (-526 1298521 1299346 1299421 "IDPOAMS" 1299426 NIL IDPOAMS (NIL T T) -8 NIL NIL NIL) (-525 1297654 1298410 1298485 "IDPOAM" 1298490 NIL IDPOAM (NIL T T) -8 NIL NIL NIL) (-524 1297035 1297569 1297631 "IDPO" 1297636 NIL IDPO (NIL T T) -8 NIL NIL NIL) (-523 1295515 1296042 1296094 "IDPC" 1296606 NIL IDPC (NIL T T) -9 NIL 1296887 NIL) (-522 1294847 1295407 1295480 "IDPAM" 1295485 NIL IDPAM (NIL T T) -8 NIL NIL NIL) (-521 1294062 1294739 1294812 "IDPAG" 1294817 NIL IDPAG (NIL T T) -8 NIL NIL NIL) (-520 1293606 1293868 1293958 "IDENT" 1293992 T IDENT (NIL) -8 NIL NIL NIL) (-519 1289825 1290709 1291604 "IDECOMP" 1292763 NIL IDECOMP (NIL NIL NIL) -7 NIL NIL NIL) (-518 1282460 1283748 1284795 "IDEAL" 1288861 NIL IDEAL (NIL T T T T) -8 NIL NIL NIL) (-517 1281602 1281732 1281932 "ICDEN" 1282344 NIL ICDEN (NIL T T T T) -7 NIL NIL NIL) (-516 1280577 1281082 1281229 "ICARD" 1281475 T ICARD (NIL) -8 NIL NIL NIL) (-515 1278607 1278950 1279355 "IBPTOOLS" 1280254 NIL IBPTOOLS (NIL T T T T) -7 NIL NIL NIL) (-514 1273722 1278227 1278340 "IBITS" 1278526 NIL IBITS (NIL NIL) -8 NIL NIL NIL) (-513 1270397 1271021 1271716 "IBATOOL" 1273139 NIL IBATOOL (NIL T T T) -7 NIL NIL NIL) (-512 1268158 1268638 1269171 "IBACHIN" 1269932 NIL IBACHIN (NIL T T T) -7 NIL NIL NIL) (-511 1265748 1268004 1268107 "IARRAY2" 1268112 NIL IARRAY2 (NIL T NIL NIL) -8 NIL NIL NIL) (-510 1261461 1265674 1265731 "IARRAY1" 1265736 NIL IARRAY1 (NIL T NIL) -8 NIL NIL NIL) (-509 1254471 1259873 1260354 "IAN" 1261000 T IAN (NIL) -8 NIL NIL NIL) (-508 1253976 1254039 1254212 "IALGFACT" 1254408 NIL IALGFACT (NIL T T T T) -7 NIL NIL NIL) (-507 1253468 1253617 1253645 "HYPCAT" 1253852 T HYPCAT (NIL) -9 NIL NIL NIL) (-506 1252970 1253123 1253309 "HYPCAT-" 1253314 NIL HYPCAT- (NIL T) -8 NIL NIL NIL) (-505 1252517 1252765 1252848 "HOSTNAME" 1252907 T HOSTNAME (NIL) -8 NIL NIL NIL) (-504 1252350 1252399 1252440 "HOMOTOP" 1252445 NIL HOMOTOP (NIL T) -9 NIL 1252478 NIL) (-503 1248783 1250282 1250323 "HOAGG" 1251304 NIL HOAGG (NIL T) -9 NIL 1252033 NIL) (-502 1247299 1247776 1248302 "HOAGG-" 1248307 NIL HOAGG- (NIL T T) -8 NIL NIL NIL) (-501 1240335 1246892 1247042 "HEXADEC" 1247169 T HEXADEC (NIL) -8 NIL NIL NIL) (-500 1239047 1239305 1239568 "HEUGCD" 1240112 NIL HEUGCD (NIL T) -7 NIL NIL NIL) (-499 1237979 1238884 1239014 "HELLFDIV" 1239019 NIL HELLFDIV (NIL T T T T) -8 NIL NIL NIL) (-498 1235989 1237756 1237844 "HEAP" 1237923 NIL HEAP (NIL T) -8 NIL NIL NIL) (-497 1235186 1235541 1235675 "HEADAST" 1235875 T HEADAST (NIL) -8 NIL NIL NIL) (-496 1228573 1235101 1235163 "HDP" 1235168 NIL HDP (NIL NIL T) -8 NIL NIL NIL) (-495 1221585 1228208 1228360 "HDMP" 1228474 NIL HDMP (NIL NIL T) -8 NIL NIL NIL) (-494 1220891 1221049 1221213 "HB" 1221441 T HB (NIL) -7 NIL NIL NIL) (-493 1213901 1220737 1220841 "HASHTBL" 1220846 NIL HASHTBL (NIL T T NIL) -8 NIL NIL NIL) (-492 1213317 1213622 1213714 "HASAST" 1213829 T HASAST (NIL) -8 NIL NIL NIL) (-491 1210723 1212939 1213121 "HACKPI" 1213155 T HACKPI (NIL) -8 NIL NIL NIL) (-490 1205895 1210576 1210689 "GTSET" 1210694 NIL GTSET (NIL T T T T) -8 NIL NIL NIL) (-489 1198934 1205773 1205871 "GSTBL" 1205876 NIL GSTBL (NIL T T T NIL) -8 NIL NIL NIL) (-488 1190683 1198099 1198355 "GSERIES" 1198734 NIL GSERIES (NIL T NIL NIL) -8 NIL NIL NIL) (-487 1189714 1190227 1190255 "GROUP" 1190458 T GROUP (NIL) -9 NIL 1190592 NIL) (-486 1189038 1189239 1189490 "GROUP-" 1189495 NIL GROUP- (NIL T) -8 NIL NIL NIL) (-485 1187387 1187726 1188113 "GROEBSOL" 1188715 NIL GROEBSOL (NIL NIL T T) -7 NIL NIL NIL) (-484 1186215 1186575 1186626 "GRMOD" 1187155 NIL GRMOD (NIL T T) -9 NIL 1187323 NIL) (-483 1185971 1186019 1186147 "GRMOD-" 1186152 NIL GRMOD- (NIL T T T) -8 NIL NIL NIL) (-482 1181111 1182325 1183325 "GRIMAGE" 1184991 T GRIMAGE (NIL) -8 NIL NIL NIL) (-481 1179505 1179838 1180162 "GRDEF" 1180807 T GRDEF (NIL) -7 NIL NIL NIL) (-480 1178937 1179065 1179206 "GRAY" 1179384 T GRAY (NIL) -7 NIL NIL NIL) (-479 1178014 1178516 1178567 "GRALG" 1178720 NIL GRALG (NIL T T) -9 NIL 1178813 NIL) (-478 1177651 1177748 1177911 "GRALG-" 1177916 NIL GRALG- (NIL T T T) -8 NIL NIL NIL) (-477 1174132 1177234 1177413 "GPOLSET" 1177557 NIL GPOLSET (NIL T T T T) -8 NIL NIL NIL) (-476 1173480 1173543 1173801 "GOSPER" 1174069 NIL GOSPER (NIL T T T T T) -7 NIL NIL NIL) (-475 1169050 1169918 1170444 "GMODPOL" 1173179 NIL GMODPOL (NIL NIL T T T NIL T) -8 NIL NIL NIL) (-474 1168037 1168239 1168477 "GHENSEL" 1168862 NIL GHENSEL (NIL T T) -7 NIL NIL NIL) (-473 1162109 1163036 1164056 "GENUPS" 1167121 NIL GENUPS (NIL T T) -7 NIL NIL NIL) (-472 1161800 1161857 1161946 "GENUFACT" 1162052 NIL GENUFACT (NIL T) -7 NIL NIL NIL) (-471 1161200 1161289 1161454 "GENPGCD" 1161718 NIL GENPGCD (NIL T T T T) -7 NIL NIL NIL) (-470 1160668 1160709 1160922 "GENMFACT" 1161159 NIL GENMFACT (NIL T T T T T) -7 NIL NIL NIL) (-469 1159204 1159491 1159798 "GENEEZ" 1160411 NIL GENEEZ (NIL T T) -7 NIL NIL NIL) (-468 1152376 1158815 1158977 "GDMP" 1159127 NIL GDMP (NIL NIL T T) -8 NIL NIL NIL) (-467 1141114 1146147 1147253 "GCNAALG" 1151359 NIL GCNAALG (NIL T NIL NIL NIL) -8 NIL NIL NIL) (-466 1139241 1140289 1140317 "GCDDOM" 1140572 T GCDDOM (NIL) -9 NIL 1140729 NIL) (-465 1138681 1138838 1139053 "GCDDOM-" 1139058 NIL GCDDOM- (NIL T) -8 NIL NIL NIL) (-464 1127153 1129627 1132019 "GBINTERN" 1136372 NIL GBINTERN (NIL T T T T) -7 NIL NIL NIL) (-463 1124954 1125282 1125703 "GBF" 1126828 NIL GBF (NIL T T T T) -7 NIL NIL NIL) (-462 1123711 1123900 1124167 "GBEUCLID" 1124770 NIL GBEUCLID (NIL T T T T) -7 NIL NIL NIL) (-461 1122361 1122568 1122872 "GB" 1123490 NIL GB (NIL T T T T) -7 NIL NIL NIL) (-460 1121692 1121835 1121984 "GAUSSFAC" 1122232 T GAUSSFAC (NIL) -7 NIL NIL NIL) (-459 1120013 1120361 1120675 "GALUTIL" 1121411 NIL GALUTIL (NIL T) -7 NIL NIL NIL) (-458 1118273 1118595 1118919 "GALPOLYU" 1119740 NIL GALPOLYU (NIL T T) -7 NIL NIL NIL) (-457 1115572 1115928 1116335 "GALFACTU" 1117970 NIL GALFACTU (NIL T T T) -7 NIL NIL NIL) (-456 1107186 1108877 1110485 "GALFACT" 1114004 NIL GALFACT (NIL T) -7 NIL NIL NIL) (-455 1104472 1105232 1105260 "FVFUN" 1106416 T FVFUN (NIL) -9 NIL 1107136 NIL) (-454 1103702 1103920 1103948 "FVC" 1104239 T FVC (NIL) -9 NIL 1104422 NIL) (-453 1103303 1103527 1103595 "FUNDESC" 1103654 T FUNDESC (NIL) -8 NIL NIL NIL) (-452 1102876 1103100 1103181 "FUNCTION" 1103255 NIL FUNCTION (NIL NIL) -8 NIL NIL NIL) (-451 1101553 1102177 1102380 "FTEM" 1102693 T FTEM (NIL) -8 NIL NIL NIL) (-450 1099183 1099875 1100341 "FT" 1101107 T FT (NIL) -8 NIL NIL NIL) (-449 1097452 1097763 1098160 "FSUPFACT" 1098874 NIL FSUPFACT (NIL T T T) -7 NIL NIL NIL) (-448 1095771 1096138 1096470 "FST" 1097140 T FST (NIL) -8 NIL NIL NIL) (-447 1094952 1095076 1095264 "FSRED" 1095653 NIL FSRED (NIL T T) -7 NIL NIL NIL) (-446 1093641 1093907 1094254 "FSPRMELT" 1094667 NIL FSPRMELT (NIL T T) -7 NIL NIL NIL) (-445 1090851 1091385 1091871 "FSPECF" 1093204 NIL FSPECF (NIL T T) -7 NIL NIL NIL) (-444 1090373 1090433 1090603 "FSINT" 1090792 NIL FSINT (NIL T T) -7 NIL NIL NIL) (-443 1088509 1089366 1089669 "FSERIES" 1090152 NIL FSERIES (NIL T T) -8 NIL NIL NIL) (-442 1087533 1087667 1087891 "FSCINT" 1088389 NIL FSCINT (NIL T T) -7 NIL NIL NIL) (-441 1086557 1086718 1086945 "FSAGG2" 1087386 NIL FSAGG2 (NIL T T T T) -7 NIL NIL NIL) (-440 1082421 1085501 1085542 "FSAGG" 1085912 NIL FSAGG (NIL T) -9 NIL 1086171 NIL) (-439 1080021 1080784 1081580 "FSAGG-" 1081675 NIL FSAGG- (NIL T T) -8 NIL NIL NIL) (-438 1077681 1077979 1078527 "FS2UPS" 1079739 NIL FS2UPS (NIL T T T T T NIL) -7 NIL NIL NIL) (-437 1076547 1076730 1077032 "FS2EXPXP" 1077506 NIL FS2EXPXP (NIL T T NIL NIL) -7 NIL NIL NIL) (-436 1076175 1076224 1076353 "FS2" 1076498 NIL FS2 (NIL T T T T) -7 NIL NIL NIL) (-435 1056399 1065949 1065990 "FS" 1069874 NIL FS (NIL T) -9 NIL 1072163 NIL) (-434 1044460 1048035 1052092 "FS-" 1052392 NIL FS- (NIL T T) -8 NIL NIL NIL) (-433 1043874 1044001 1044153 "FRUTIL" 1044340 NIL FRUTIL (NIL T) -7 NIL NIL NIL) (-432 1038385 1041563 1041603 "FRNAALG" 1042923 NIL FRNAALG (NIL T) -9 NIL 1043521 NIL) (-431 1033866 1035134 1036409 "FRNAALG-" 1037159 NIL FRNAALG- (NIL T T) -8 NIL NIL NIL) (-430 1033498 1033547 1033674 "FRNAAF2" 1033817 NIL FRNAAF2 (NIL T T T T) -7 NIL NIL NIL) (-429 1031785 1032347 1032643 "FRMOD" 1033310 NIL FRMOD (NIL T T T T NIL) -8 NIL NIL NIL) (-428 1030970 1031063 1031354 "FRIDEAL2" 1031692 NIL FRIDEAL2 (NIL T T T T T T T T) -7 NIL NIL NIL) (-427 1028575 1029345 1029663 "FRIDEAL" 1030761 NIL FRIDEAL (NIL T T T T) -8 NIL NIL NIL) (-426 1027666 1028122 1028163 "FRETRCT" 1028168 NIL FRETRCT (NIL T) -9 NIL 1028344 NIL) (-425 1026724 1027009 1027360 "FRETRCT-" 1027365 NIL FRETRCT- (NIL T T) -8 NIL NIL NIL) (-424 1023538 1025008 1025067 "FRAMALG" 1025949 NIL FRAMALG (NIL T T) -9 NIL 1026241 NIL) (-423 1021576 1022127 1022757 "FRAMALG-" 1022980 NIL FRAMALG- (NIL T T T) -8 NIL NIL NIL) (-422 1021206 1021269 1021376 "FRAC2" 1021513 NIL FRAC2 (NIL T T) -7 NIL NIL NIL) (-421 1014177 1020679 1020956 "FRAC" 1020961 NIL FRAC (NIL T) -8 NIL NIL NIL) (-420 1013807 1013870 1013977 "FR2" 1014114 NIL FR2 (NIL T T) -7 NIL NIL NIL) (-419 1004724 1009302 1010660 "FR" 1012481 NIL FR (NIL T) -8 NIL NIL NIL) (-418 998636 1002103 1002131 "FPS" 1003250 T FPS (NIL) -9 NIL 1003807 NIL) (-417 998061 998194 998358 "FPS-" 998504 NIL FPS- (NIL T) -8 NIL NIL NIL) (-416 995013 997018 997046 "FPC" 997271 T FPC (NIL) -9 NIL 997413 NIL) (-415 994794 994846 994943 "FPC-" 994948 NIL FPC- (NIL T) -8 NIL NIL NIL) (-414 993552 994282 994323 "FPATMAB" 994328 NIL FPATMAB (NIL T) -9 NIL 994480 NIL) (-413 991695 992294 992641 "FPARFRAC" 993268 NIL FPARFRAC (NIL T T) -8 NIL NIL NIL) (-412 986987 987587 988269 "FORTRAN" 991127 NIL FORTRAN (NIL NIL NIL NIL NIL) -8 NIL NIL NIL) (-411 984561 985225 985253 "FORTFN" 986313 T FORTFN (NIL) -9 NIL 986937 NIL) (-410 984313 984375 984403 "FORTCAT" 984462 T FORTCAT (NIL) -9 NIL 984524 NIL) (-409 981999 982529 983068 "FORT" 983794 T FORT (NIL) -7 NIL NIL NIL) (-408 981781 981817 981886 "FORMULA1" 981963 NIL FORMULA1 (NIL T) -7 NIL NIL NIL) (-407 979785 980397 980787 "FORMULA" 981411 T FORMULA (NIL) -8 NIL NIL NIL) (-406 979302 979360 979533 "FORDER" 979727 NIL FORDER (NIL T T T T) -7 NIL NIL NIL) (-405 978362 978562 978755 "FOP" 979129 T FOP (NIL) -7 NIL NIL NIL) (-404 976775 977642 977816 "FNLA" 978244 NIL FNLA (NIL NIL NIL T) -8 NIL NIL NIL) (-403 975394 975905 975933 "FNCAT" 976393 T FNCAT (NIL) -9 NIL 976653 NIL) (-402 974837 975353 975381 "FNAME" 975386 T FNAME (NIL) -8 NIL NIL NIL) (-401 973163 974336 974364 "FMTC" 974369 T FMTC (NIL) -9 NIL 974405 NIL) (-400 971712 973099 973145 "FMONOID" 973150 NIL FMONOID (NIL T) -8 NIL NIL NIL) (-399 968301 969667 969708 "FMONCAT" 970925 NIL FMONCAT (NIL T) -9 NIL 971530 NIL) (-398 965623 966371 966399 "FMFUN" 967543 T FMFUN (NIL) -9 NIL 968251 NIL) (-397 962496 963548 963602 "FMCAT" 964797 NIL FMCAT (NIL T T) -9 NIL 965292 NIL) (-396 961729 961946 961974 "FMC" 962264 T FMC (NIL) -9 NIL 962446 NIL) (-395 960397 961495 961595 "FM1" 961674 NIL FM1 (NIL T T) -8 NIL NIL NIL) (-394 959415 960139 960288 "FM" 960293 NIL FM (NIL T T) -8 NIL NIL NIL) (-393 957153 957605 958099 "FLOATRP" 958966 NIL FLOATRP (NIL T) -7 NIL NIL NIL) (-392 954555 955091 955669 "FLOATCP" 956620 NIL FLOATCP (NIL T) -7 NIL NIL NIL) (-391 947211 952284 952905 "FLOAT" 953954 T FLOAT (NIL) -8 NIL NIL NIL) (-390 945729 946803 946844 "FLINEXP" 946849 NIL FLINEXP (NIL T) -9 NIL 946942 NIL) (-389 944859 945118 945446 "FLINEXP-" 945451 NIL FLINEXP- (NIL T T) -8 NIL NIL NIL) (-388 943917 944079 944303 "FLASORT" 944711 NIL FLASORT (NIL T T) -7 NIL NIL NIL) (-387 940835 941887 941939 "FLALG" 943166 NIL FLALG (NIL T T) -9 NIL 943633 NIL) (-386 939859 940020 940247 "FLAGG2" 940688 NIL FLAGG2 (NIL T T T T) -7 NIL NIL NIL) (-385 933114 937268 937309 "FLAGG" 938571 NIL FLAGG (NIL T) -9 NIL 939223 NIL) (-384 931768 932179 932669 "FLAGG-" 932674 NIL FLAGG- (NIL T T) -8 NIL NIL NIL) (-383 928399 929613 929672 "FINRALG" 930800 NIL FINRALG (NIL T T) -9 NIL 931308 NIL) (-382 927523 927788 928127 "FINRALG-" 928132 NIL FINRALG- (NIL T T T) -8 NIL NIL NIL) (-381 926829 927128 927156 "FINITE" 927352 T FINITE (NIL) -9 NIL 927459 NIL) (-380 918780 921359 921399 "FINAALG" 925066 NIL FINAALG (NIL T) -9 NIL 926519 NIL) (-379 913896 915162 916306 "FINAALG-" 917685 NIL FINAALG- (NIL T T) -8 NIL NIL NIL) (-378 912456 912878 912932 "FILECAT" 913616 NIL FILECAT (NIL T T) -9 NIL 913832 NIL) (-377 911734 912211 912314 "FILE" 912386 NIL FILE (NIL T) -8 NIL NIL NIL) (-376 909130 910964 910992 "FIELD" 911032 T FIELD (NIL) -9 NIL 911112 NIL) (-375 907672 908135 908646 "FIELD-" 908651 NIL FIELD- (NIL T) -8 NIL NIL NIL) (-374 905355 906307 906654 "FGROUP" 907358 NIL FGROUP (NIL T) -8 NIL NIL NIL) (-373 904427 904609 904829 "FGLMICPK" 905187 NIL FGLMICPK (NIL T NIL) -7 NIL NIL NIL) (-372 899661 904352 904409 "FFX" 904414 NIL FFX (NIL T NIL) -8 NIL NIL NIL) (-371 899256 899323 899458 "FFSLPE" 899594 NIL FFSLPE (NIL T T T) -7 NIL NIL NIL) (-370 898754 898796 899005 "FFPOLY2" 899214 NIL FFPOLY2 (NIL T T) -7 NIL NIL NIL) (-369 894630 895526 896322 "FFPOLY" 897990 NIL FFPOLY (NIL T) -7 NIL NIL NIL) (-368 889878 894549 894612 "FFP" 894617 NIL FFP (NIL T NIL) -8 NIL NIL NIL) (-367 884388 889221 889411 "FFNBX" 889732 NIL FFNBX (NIL T NIL) -8 NIL NIL NIL) (-366 878700 883523 883781 "FFNBP" 884242 NIL FFNBP (NIL T NIL) -8 NIL NIL NIL) (-365 872717 877984 878195 "FFNB" 878533 NIL FFNB (NIL NIL NIL) -8 NIL NIL NIL) (-364 871537 871747 872062 "FFINTBAS" 872514 NIL FFINTBAS (NIL T T T) -7 NIL NIL NIL) (-363 867109 869784 869812 "FFIELDC" 870432 T FFIELDC (NIL) -9 NIL 870808 NIL) (-362 865687 866142 866639 "FFIELDC-" 866644 NIL FFIELDC- (NIL T) -8 NIL NIL NIL) (-361 865244 865302 865426 "FFHOM" 865629 NIL FFHOM (NIL T T T) -7 NIL NIL NIL) (-360 862903 863426 863943 "FFF" 864759 NIL FFF (NIL T) -7 NIL NIL NIL) (-359 857917 862645 862746 "FFCGX" 862846 NIL FFCGX (NIL T NIL) -8 NIL NIL NIL) (-358 852935 857649 857756 "FFCGP" 857860 NIL FFCGP (NIL T NIL) -8 NIL NIL NIL) (-357 847514 852662 852770 "FFCG" 852871 NIL FFCG (NIL NIL NIL) -8 NIL NIL NIL) (-356 846919 846968 847203 "FFCAT2" 847465 NIL FFCAT2 (NIL T T T T T T T T) -7 NIL NIL NIL) (-355 825580 836651 836737 "FFCAT" 841902 NIL FFCAT (NIL T T T) -9 NIL 843353 NIL) (-354 820591 821825 823139 "FFCAT-" 824369 NIL FFCAT- (NIL T T T T) -8 NIL NIL NIL) (-353 815391 820502 820566 "FF" 820571 NIL FF (NIL NIL NIL) -8 NIL NIL NIL) (-352 804044 808363 809583 "FEXPR" 814243 NIL FEXPR (NIL NIL NIL T) -8 NIL NIL NIL) (-351 802972 803441 803482 "FEVALAB" 803566 NIL FEVALAB (NIL T) -9 NIL 803827 NIL) (-350 802089 802341 802679 "FEVALAB-" 802684 NIL FEVALAB- (NIL T T) -8 NIL NIL NIL) (-349 798951 799836 799951 "FDIVCAT" 801519 NIL FDIVCAT (NIL T T T T) -9 NIL 801956 NIL) (-348 798707 798740 798910 "FDIVCAT-" 798915 NIL FDIVCAT- (NIL T T T T T) -8 NIL NIL NIL) (-347 797921 798014 798291 "FDIV2" 798614 NIL FDIV2 (NIL T T T T T T T T) -7 NIL NIL NIL) (-346 796331 797304 797507 "FDIV" 797820 NIL FDIV (NIL T T T T) -8 NIL NIL NIL) (-345 795239 795626 795828 "FCTRDATA" 796149 T FCTRDATA (NIL) -8 NIL NIL NIL) (-344 793895 794184 794473 "FCPAK1" 794970 T FCPAK1 (NIL) -7 NIL NIL NIL) (-343 792898 793395 793536 "FCOMP" 793786 NIL FCOMP (NIL T) -8 NIL NIL NIL) (-342 776212 780048 783586 "FC" 789380 T FC (NIL) -8 NIL NIL NIL) (-341 767901 772533 772573 "FAXF" 774375 NIL FAXF (NIL T) -9 NIL 775067 NIL) (-340 765022 765835 766660 "FAXF-" 767125 NIL FAXF- (NIL T T) -8 NIL NIL NIL) (-339 759591 764398 764574 "FARRAY" 764879 NIL FARRAY (NIL T) -8 NIL NIL NIL) (-338 754150 756538 756591 "FAMR" 757614 NIL FAMR (NIL T T) -9 NIL 758074 NIL) (-337 752974 753342 753777 "FAMR-" 753782 NIL FAMR- (NIL T T T) -8 NIL NIL NIL) (-336 752001 752896 752949 "FAMONOID" 752954 NIL FAMONOID (NIL T) -8 NIL NIL NIL) (-335 749631 750483 750536 "FAMONC" 751477 NIL FAMONC (NIL T T) -9 NIL 751863 NIL) (-334 748105 749385 749522 "FAGROUP" 749527 NIL FAGROUP (NIL T) -8 NIL NIL NIL) (-333 745858 746219 746622 "FACUTIL" 747786 NIL FACUTIL (NIL T T T T) -7 NIL NIL NIL) (-332 744945 745142 745364 "FACTFUNC" 745668 NIL FACTFUNC (NIL T) -7 NIL NIL NIL) (-331 736703 744248 744447 "EXPUPXS" 744801 NIL EXPUPXS (NIL T NIL NIL) -8 NIL NIL NIL) (-330 734156 734726 735312 "EXPRTUBE" 736137 T EXPRTUBE (NIL) -7 NIL NIL NIL) (-329 730367 731019 731749 "EXPRODE" 733495 NIL EXPRODE (NIL T T) -7 NIL NIL NIL) (-328 724801 725508 726314 "EXPR2UPS" 729665 NIL EXPR2UPS (NIL T T) -7 NIL NIL NIL) (-327 724427 724490 724599 "EXPR2" 724738 NIL EXPR2 (NIL T T) -7 NIL NIL NIL) (-326 708721 723076 723505 "EXPR" 724031 NIL EXPR (NIL T) -8 NIL NIL NIL) (-325 699038 707872 708163 "EXPEXPAN" 708557 NIL EXPEXPAN (NIL T T NIL NIL) -8 NIL NIL NIL) (-324 698458 698762 698853 "EXITAST" 698967 T EXITAST (NIL) -8 NIL NIL NIL) (-323 698222 698415 698444 "EXIT" 698449 T EXIT (NIL) -8 NIL NIL NIL) (-322 697843 697911 698024 "EVALCYC" 698154 NIL EVALCYC (NIL T) -7 NIL NIL NIL) (-321 697360 697502 697543 "EVALAB" 697713 NIL EVALAB (NIL T) -9 NIL 697817 NIL) (-320 696817 696963 697184 "EVALAB-" 697189 NIL EVALAB- (NIL T T) -8 NIL NIL NIL) (-319 693925 695473 695501 "EUCDOM" 696056 T EUCDOM (NIL) -9 NIL 696406 NIL) (-318 692264 692772 693362 "EUCDOM-" 693367 NIL EUCDOM- (NIL T) -8 NIL NIL NIL) (-317 691890 691953 692062 "ESTOOLS2" 692201 NIL ESTOOLS2 (NIL T T) -7 NIL NIL NIL) (-316 691635 691683 691763 "ESTOOLS1" 691842 NIL ESTOOLS1 (NIL T) -7 NIL NIL NIL) (-315 678952 681933 684683 "ESTOOLS" 688905 T ESTOOLS (NIL) -7 NIL NIL NIL) (-314 678691 678729 678811 "ESCONT1" 678914 NIL ESCONT1 (NIL NIL NIL) -7 NIL NIL NIL) (-313 674999 675826 676606 "ESCONT" 677931 T ESCONT (NIL) -7 NIL NIL NIL) (-312 674668 674724 674824 "ES2" 674943 NIL ES2 (NIL T T) -7 NIL NIL NIL) (-311 674292 674356 674465 "ES1" 674604 NIL ES1 (NIL T T) -7 NIL NIL NIL) (-310 667993 669923 669951 "ES" 672719 T ES (NIL) -9 NIL 674129 NIL) (-309 662670 664227 666044 "ES-" 666208 NIL ES- (NIL T) -8 NIL NIL NIL) (-308 661862 662015 662191 "ERROR" 662514 T ERROR (NIL) -7 NIL NIL NIL) (-307 654878 661721 661812 "EQTBL" 661817 NIL EQTBL (NIL T T) -8 NIL NIL NIL) (-306 654504 654567 654676 "EQ2" 654815 NIL EQ2 (NIL T T) -7 NIL NIL NIL) (-305 646763 649818 651267 "EQ" 653088 NIL -1492 (NIL T) -8 NIL NIL NIL) (-304 642006 643101 644194 "EP" 645702 NIL EP (NIL T) -7 NIL NIL NIL) (-303 640546 640897 641203 "ENV" 641720 T ENV (NIL) -8 NIL NIL NIL) (-302 639506 640180 640208 "ENTIRER" 640213 T ENTIRER (NIL) -9 NIL 640259 NIL) (-301 635918 637688 638049 "EMR" 639314 NIL EMR (NIL T T T NIL NIL NIL) -8 NIL NIL NIL) (-300 635022 635233 635287 "ELTAGG" 635667 NIL ELTAGG (NIL T T) -9 NIL 635878 NIL) (-299 634729 634803 634944 "ELTAGG-" 634949 NIL ELTAGG- (NIL T T T) -8 NIL NIL NIL) (-298 634487 634522 634576 "ELTAB" 634660 NIL ELTAB (NIL T T) -9 NIL 634712 NIL) (-297 633589 633759 633958 "ELFUTS" 634338 NIL ELFUTS (NIL T T) -7 NIL NIL NIL) (-296 633313 633387 633415 "ELEMFUN" 633520 T ELEMFUN (NIL) -9 NIL NIL NIL) (-295 633177 633204 633272 "ELEMFUN-" 633277 NIL ELEMFUN- (NIL T) -8 NIL NIL NIL) (-294 627588 631219 631260 "ELAGG" 632200 NIL ELAGG (NIL T) -9 NIL 632663 NIL) (-293 625765 626307 626970 "ELAGG-" 626975 NIL ELAGG- (NIL T T) -8 NIL NIL NIL) (-292 625047 625214 625370 "ELABOR" 625629 T ELABOR (NIL) -8 NIL NIL NIL) (-291 623653 623987 624281 "ELABEXPR" 624773 T ELABEXPR (NIL) -8 NIL NIL NIL) (-290 616165 618290 619119 "EFUPXS" 622928 NIL EFUPXS (NIL T T T T) -8 NIL NIL NIL) (-289 609291 611414 612225 "EFULS" 615440 NIL EFULS (NIL T T T) -8 NIL NIL NIL) (-288 606728 607134 607606 "EFSTRUC" 608923 NIL EFSTRUC (NIL T T) -7 NIL NIL NIL) (-287 596165 598085 599633 "EF" 605243 NIL EF (NIL T T) -7 NIL NIL NIL) (-286 595143 595650 595799 "EAB" 596036 T EAB (NIL) -8 NIL NIL NIL) (-285 594265 595102 595130 "E04UCFA" 595135 T E04UCFA (NIL) -8 NIL NIL NIL) (-284 593387 594224 594252 "E04NAFA" 594257 T E04NAFA (NIL) -8 NIL NIL NIL) (-283 592509 593346 593374 "E04MBFA" 593379 T E04MBFA (NIL) -8 NIL NIL NIL) (-282 591631 592468 592496 "E04JAFA" 592501 T E04JAFA (NIL) -8 NIL NIL NIL) (-281 590755 591590 591618 "E04GCFA" 591623 T E04GCFA (NIL) -8 NIL NIL NIL) (-280 589879 590714 590742 "E04FDFA" 590747 T E04FDFA (NIL) -8 NIL NIL NIL) (-279 589001 589838 589866 "E04DGFA" 589871 T E04DGFA (NIL) -8 NIL NIL NIL) (-278 583078 584526 585890 "E04AGNT" 587657 T E04AGNT (NIL) -7 NIL NIL NIL) (-277 581698 582379 582419 "DVARCAT" 582760 NIL DVARCAT (NIL T) -9 NIL 582923 NIL) (-276 580848 581114 581428 "DVARCAT-" 581433 NIL DVARCAT- (NIL T T) -8 NIL NIL NIL) (-275 572809 580647 580776 "DSMP" 580781 NIL DSMP (NIL T T T) -8 NIL NIL NIL) (-274 571160 571951 571992 "DSEXT" 572355 NIL DSEXT (NIL T) -9 NIL 572649 NIL) (-273 569349 569873 570539 "DSEXT-" 570544 NIL DSEXT- (NIL T T) -8 NIL NIL NIL) (-272 569008 569073 569171 "DROPT1" 569284 NIL DROPT1 (NIL T) -7 NIL NIL NIL) (-271 564027 565249 566386 "DROPT0" 567891 T DROPT0 (NIL) -7 NIL NIL NIL) (-270 558610 559972 561040 "DROPT" 562979 T DROPT (NIL) -8 NIL NIL NIL) (-269 556919 557280 557666 "DRAWPT" 558244 T DRAWPT (NIL) -7 NIL NIL NIL) (-268 556546 556605 556723 "DRAWHACK" 556860 NIL DRAWHACK (NIL T) -7 NIL NIL NIL) (-267 555247 555546 555837 "DRAWCX" 556275 T DRAWCX (NIL) -7 NIL NIL NIL) (-266 554756 554831 554982 "DRAWCURV" 555173 NIL DRAWCURV (NIL T T) -7 NIL NIL NIL) (-265 545074 547186 549301 "DRAWCFUN" 552661 T DRAWCFUN (NIL) -7 NIL NIL NIL) (-264 539565 540584 541663 "DRAW" 544048 NIL DRAW (NIL T) -7 NIL NIL NIL) (-263 536036 538230 538271 "DQAGG" 538900 NIL DQAGG (NIL T) -9 NIL 539174 NIL) (-262 522612 530247 530330 "DPOLCAT" 532182 NIL DPOLCAT (NIL T T T T) -9 NIL 532727 NIL) (-261 517131 518797 520755 "DPOLCAT-" 520760 NIL DPOLCAT- (NIL T T T T T) -8 NIL NIL NIL) (-260 509988 516992 517090 "DPMO" 517095 NIL DPMO (NIL NIL T T) -8 NIL NIL NIL) (-259 502742 509768 509935 "DPMM" 509940 NIL DPMM (NIL NIL T T T) -8 NIL NIL NIL) (-258 502264 502526 502615 "DOMTMPLT" 502673 T DOMTMPLT (NIL) -8 NIL NIL NIL) (-257 501613 502066 502146 "DOMCTOR" 502204 T DOMCTOR (NIL) -8 NIL NIL NIL) (-256 500765 501093 501244 "DOMAIN" 501482 T DOMAIN (NIL) -8 NIL NIL NIL) (-255 493777 500400 500552 "DMP" 500666 NIL DMP (NIL NIL T) -8 NIL NIL NIL) (-254 491554 492844 492885 "DMEXT" 492890 NIL DMEXT (NIL T) -9 NIL 493066 NIL) (-253 491148 491210 491354 "DLP" 491492 NIL DLP (NIL T) -7 NIL NIL NIL) (-252 484271 490475 490665 "DLIST" 490990 NIL DLIST (NIL T) -8 NIL NIL NIL) (-251 480809 483096 483137 "DLAGG" 483687 NIL DLAGG (NIL T) -9 NIL 483917 NIL) (-250 479321 480135 480163 "DIVRING" 480255 T DIVRING (NIL) -9 NIL 480338 NIL) (-249 478504 478748 479048 "DIVRING-" 479053 NIL DIVRING- (NIL T) -8 NIL NIL NIL) (-248 476546 476963 477369 "DISPLAY" 478118 T DISPLAY (NIL) -7 NIL NIL NIL) (-247 475376 475597 475862 "DIRPROD2" 476339 NIL DIRPROD2 (NIL NIL T T) -7 NIL NIL NIL) (-246 468783 475290 475353 "DIRPROD" 475358 NIL DIRPROD (NIL NIL T) -8 NIL NIL NIL) (-245 456995 463494 463547 "DIRPCAT" 463805 NIL DIRPCAT (NIL NIL T) -9 NIL 464680 NIL) (-244 454195 454963 455844 "DIRPCAT-" 456181 NIL DIRPCAT- (NIL T NIL T) -8 NIL NIL NIL) (-243 453476 453642 453828 "DIOSP" 454029 T DIOSP (NIL) -7 NIL NIL NIL) (-242 449890 452360 452401 "DIOPS" 452835 NIL DIOPS (NIL T) -9 NIL 453064 NIL) (-241 449409 449553 449744 "DIOPS-" 449749 NIL DIOPS- (NIL T T) -8 NIL NIL NIL) (-240 448316 449088 449116 "DIFRING" 449121 T DIFRING (NIL) -9 NIL 449143 NIL) (-239 447964 448062 448090 "DIFFSPC" 448209 T DIFFSPC (NIL) -9 NIL 448284 NIL) (-238 447585 447687 447839 "DIFFSPC-" 447844 NIL DIFFSPC- (NIL T) -8 NIL NIL NIL) (-237 446521 447119 447160 "DIFFMOD" 447165 NIL DIFFMOD (NIL T) -9 NIL 447263 NIL) (-236 446217 446274 446315 "DIFFDOM" 446436 NIL DIFFDOM (NIL T) -9 NIL 446504 NIL) (-235 446064 446094 446178 "DIFFDOM-" 446183 NIL DIFFDOM- (NIL T T) -8 NIL NIL NIL) (-234 443804 445268 445309 "DIFEXT" 445314 NIL DIFEXT (NIL T) -9 NIL 445467 NIL) (-233 440838 443308 443349 "DIAGG" 443354 NIL DIAGG (NIL T) -9 NIL 443374 NIL) (-232 440186 440379 440631 "DIAGG-" 440636 NIL DIAGG- (NIL T T) -8 NIL NIL NIL) (-231 435036 439145 439422 "DHMATRIX" 439955 NIL DHMATRIX (NIL T) -8 NIL NIL NIL) (-230 430504 431557 432567 "DFSFUN" 434046 T DFSFUN (NIL) -7 NIL NIL NIL) (-229 424738 429435 429747 "DFLOAT" 430212 T DFLOAT (NIL) -8 NIL NIL NIL) (-228 422977 423282 423671 "DFINTTLS" 424446 NIL DFINTTLS (NIL T T) -7 NIL NIL NIL) (-227 419796 420998 421398 "DERHAM" 422643 NIL DERHAM (NIL T NIL) -8 NIL NIL NIL) (-226 417332 419571 419660 "DEQUEUE" 419740 NIL DEQUEUE (NIL T) -8 NIL NIL NIL) (-225 416574 416719 416902 "DEGRED" 417194 NIL DEGRED (NIL T T) -7 NIL NIL NIL) (-224 412980 413749 414595 "DEFINTRF" 415802 NIL DEFINTRF (NIL T) -7 NIL NIL NIL) (-223 410517 411004 411596 "DEFINTEF" 412499 NIL DEFINTEF (NIL T T) -7 NIL NIL NIL) (-222 409801 410137 410252 "DEFAST" 410422 T DEFAST (NIL) -8 NIL NIL NIL) (-221 402837 409394 409544 "DECIMAL" 409671 T DECIMAL (NIL) -8 NIL NIL NIL) (-220 400295 400807 401313 "DDFACT" 402381 NIL DDFACT (NIL T T) -7 NIL NIL NIL) (-219 399885 399934 400085 "DBLRESP" 400246 NIL DBLRESP (NIL T T T T) -7 NIL NIL NIL) (-218 399086 399655 399746 "DBASIS" 399834 NIL DBASIS (NIL NIL) -8 NIL NIL NIL) (-217 396870 397316 397677 "DBASE" 398852 NIL DBASE (NIL T) -8 NIL NIL NIL) (-216 396058 396350 396496 "DATAARY" 396769 NIL DATAARY (NIL NIL T) -8 NIL NIL NIL) (-215 395116 396017 396045 "D03FAFA" 396050 T D03FAFA (NIL) -8 NIL NIL NIL) (-214 394175 395075 395103 "D03EEFA" 395108 T D03EEFA (NIL) -8 NIL NIL NIL) (-213 392101 392591 393080 "D03AGNT" 393706 T D03AGNT (NIL) -7 NIL NIL NIL) (-212 391342 392060 392088 "D02EJFA" 392093 T D02EJFA (NIL) -8 NIL NIL NIL) (-211 390583 391301 391329 "D02CJFA" 391334 T D02CJFA (NIL) -8 NIL NIL NIL) (-210 389824 390542 390570 "D02BHFA" 390575 T D02BHFA (NIL) -8 NIL NIL NIL) (-209 389065 389783 389811 "D02BBFA" 389816 T D02BBFA (NIL) -8 NIL NIL NIL) (-208 382196 383851 385457 "D02AGNT" 387479 T D02AGNT (NIL) -7 NIL NIL NIL) (-207 379946 380487 381033 "D01WGTS" 381670 T D01WGTS (NIL) -7 NIL NIL NIL) (-206 378953 379905 379933 "D01TRNS" 379938 T D01TRNS (NIL) -8 NIL NIL NIL) (-205 377961 378912 378940 "D01GBFA" 378945 T D01GBFA (NIL) -8 NIL NIL NIL) (-204 376969 377920 377948 "D01FCFA" 377953 T D01FCFA (NIL) -8 NIL NIL NIL) (-203 375977 376928 376956 "D01ASFA" 376961 T D01ASFA (NIL) -8 NIL NIL NIL) (-202 374985 375936 375964 "D01AQFA" 375969 T D01AQFA (NIL) -8 NIL NIL NIL) (-201 373993 374944 374972 "D01APFA" 374977 T D01APFA (NIL) -8 NIL NIL NIL) (-200 373001 373952 373980 "D01ANFA" 373985 T D01ANFA (NIL) -8 NIL NIL NIL) (-199 372009 372960 372988 "D01AMFA" 372993 T D01AMFA (NIL) -8 NIL NIL NIL) (-198 371017 371968 371996 "D01ALFA" 372001 T D01ALFA (NIL) -8 NIL NIL NIL) (-197 370025 370976 371004 "D01AKFA" 371009 T D01AKFA (NIL) -8 NIL NIL NIL) (-196 369033 369984 370012 "D01AJFA" 370017 T D01AJFA (NIL) -8 NIL NIL NIL) (-195 362256 363881 365442 "D01AGNT" 367492 T D01AGNT (NIL) -7 NIL NIL NIL) (-194 361575 361721 361873 "CYCLOTOM" 362124 T CYCLOTOM (NIL) -7 NIL NIL NIL) (-193 358230 359023 359750 "CYCLES" 360868 T CYCLES (NIL) -7 NIL NIL NIL) (-192 357530 357676 357847 "CVMP" 358091 NIL CVMP (NIL T) -7 NIL NIL NIL) (-191 355317 355629 355998 "CTRIGMNP" 357258 NIL CTRIGMNP (NIL T T) -7 NIL NIL NIL) (-190 354790 355048 355149 "CTORKIND" 355236 T CTORKIND (NIL) -8 NIL NIL NIL) (-189 353995 354383 354411 "CTORCAT" 354593 T CTORCAT (NIL) -9 NIL 354706 NIL) (-188 353569 353704 353863 "CTORCAT-" 353868 NIL CTORCAT- (NIL T) -8 NIL NIL NIL) (-187 352983 353243 353351 "CTORCALL" 353493 NIL CTORCALL (NIL T) -8 NIL NIL NIL) (-186 352341 352777 352850 "CTOR" 352930 T CTOR (NIL) -8 NIL NIL NIL) (-185 351697 351814 351967 "CSTTOOLS" 352238 NIL CSTTOOLS (NIL T T) -7 NIL NIL NIL) (-184 347394 348153 348911 "CRFP" 351009 NIL CRFP (NIL T T) -7 NIL NIL NIL) (-183 346809 347115 347207 "CRCEAST" 347322 T CRCEAST (NIL) -8 NIL NIL NIL) (-182 345832 346041 346269 "CRAPACK" 346613 NIL CRAPACK (NIL T) -7 NIL NIL NIL) (-181 345212 345317 345521 "CPMATCH" 345708 NIL CPMATCH (NIL T T T) -7 NIL NIL NIL) (-180 344931 344965 345071 "CPIMA" 345178 NIL CPIMA (NIL T T T) -7 NIL NIL NIL) (-179 341189 341951 342670 "COORDSYS" 344266 NIL COORDSYS (NIL T) -7 NIL NIL NIL) (-178 340577 340722 340864 "CONTOUR" 341067 T CONTOUR (NIL) -8 NIL NIL NIL) (-177 336042 338580 339072 "CONTFRAC" 340117 NIL CONTFRAC (NIL T) -8 NIL NIL NIL) (-176 335916 335943 335971 "CONDUIT" 336008 T CONDUIT (NIL) -9 NIL NIL NIL) (-175 334870 335544 335572 "COMRING" 335577 T COMRING (NIL) -9 NIL 335629 NIL) (-174 333852 334228 334412 "COMPPROP" 334706 T COMPPROP (NIL) -8 NIL NIL NIL) (-173 333507 333548 333676 "COMPLPAT" 333811 NIL COMPLPAT (NIL T T T) -7 NIL NIL NIL) (-172 333137 333200 333307 "COMPLEX2" 333444 NIL COMPLEX2 (NIL T T) -7 NIL NIL NIL) (-171 321520 332946 333055 "COMPLEX" 333060 NIL COMPLEX (NIL T) -8 NIL NIL NIL) (-170 320841 320980 321140 "COMPILER" 321380 T COMPILER (NIL) -8 NIL NIL NIL) (-169 320553 320594 320692 "COMPFACT" 320800 NIL COMPFACT (NIL T T) -7 NIL NIL NIL) (-168 301926 314257 314297 "COMPCAT" 315301 NIL COMPCAT (NIL T) -9 NIL 316649 NIL) (-167 290814 294365 297992 "COMPCAT-" 298348 NIL COMPCAT- (NIL T T) -8 NIL NIL NIL) (-166 290537 290571 290674 "COMMUPC" 290780 NIL COMMUPC (NIL T T T) -7 NIL NIL NIL) (-165 290325 290365 290424 "COMMONOP" 290498 T COMMONOP (NIL) -7 NIL NIL NIL) (-164 289847 290129 290204 "COMMAAST" 290270 T COMMAAST (NIL) -8 NIL NIL NIL) (-163 289354 289598 289685 "COMM" 289780 T COMM (NIL) -8 NIL NIL NIL) (-162 288549 288797 288825 "COMBOPC" 289163 T COMBOPC (NIL) -9 NIL 289338 NIL) (-161 287403 287655 287897 "COMBINAT" 288339 NIL COMBINAT (NIL T) -7 NIL NIL NIL) (-160 283746 284434 285061 "COMBF" 286825 NIL COMBF (NIL T T) -7 NIL NIL NIL) (-159 282408 282862 283097 "COLOR" 283531 T COLOR (NIL) -8 NIL NIL NIL) (-158 281824 282129 282221 "COLONAST" 282336 T COLONAST (NIL) -8 NIL NIL NIL) (-157 281458 281511 281636 "CMPLXRT" 281771 NIL CMPLXRT (NIL T T) -7 NIL NIL NIL) (-156 280846 281158 281257 "CLLCTAST" 281379 T CLLCTAST (NIL) -8 NIL NIL NIL) (-155 276306 277376 278456 "CLIP" 279786 T CLIP (NIL) -7 NIL NIL NIL) (-154 274479 275407 275647 "CLIF" 276133 NIL CLIF (NIL NIL T NIL) -8 NIL NIL NIL) (-153 270461 272597 272638 "CLAGG" 273567 NIL CLAGG (NIL T) -9 NIL 274103 NIL) (-152 268805 269340 269923 "CLAGG-" 269928 NIL CLAGG- (NIL T T) -8 NIL NIL NIL) (-151 268343 268434 268574 "CINTSLPE" 268714 NIL CINTSLPE (NIL T T) -7 NIL NIL NIL) (-150 265808 266315 266863 "CHVAR" 267871 NIL CHVAR (NIL T T T) -7 NIL NIL NIL) (-149 264848 265522 265550 "CHARZ" 265555 T CHARZ (NIL) -9 NIL 265570 NIL) (-148 264596 264642 264720 "CHARPOL" 264802 NIL CHARPOL (NIL T) -7 NIL NIL NIL) (-147 263514 264227 264255 "CHARNZ" 264302 T CHARNZ (NIL) -9 NIL 264358 NIL) (-146 260458 261568 262097 "CHAR" 263005 T CHAR (NIL) -8 NIL NIL NIL) (-145 260166 260245 260273 "CFCAT" 260384 T CFCAT (NIL) -9 NIL NIL NIL) (-144 259389 259518 259701 "CDEN" 260050 NIL CDEN (NIL T T T) -7 NIL NIL NIL) (-143 254986 258542 258822 "CCLASS" 259129 T CCLASS (NIL) -8 NIL NIL NIL) (-142 254207 254394 254571 "CATEGORY" 254829 T -10 (NIL) -8 NIL NIL NIL) (-141 253702 254126 254174 "CATCTOR" 254179 T CATCTOR (NIL) -8 NIL NIL NIL) (-140 253093 253405 253503 "CATAST" 253624 T CATAST (NIL) -8 NIL NIL NIL) (-139 252509 252814 252906 "CASEAST" 253021 T CASEAST (NIL) -8 NIL NIL NIL) (-138 251605 251765 251986 "CARTEN2" 252356 NIL CARTEN2 (NIL NIL NIL T T) -7 NIL NIL NIL) (-137 246503 247762 248506 "CARTEN" 250917 NIL CARTEN (NIL NIL NIL T) -8 NIL NIL NIL) (-136 244633 245653 245910 "CARD" 246266 T CARD (NIL) -8 NIL NIL NIL) (-135 244155 244437 244512 "CAPSLAST" 244578 T CAPSLAST (NIL) -8 NIL NIL NIL) (-134 243597 243853 243881 "CACHSET" 244013 T CACHSET (NIL) -9 NIL 244091 NIL) (-133 242987 243375 243403 "CABMON" 243453 T CABMON (NIL) -9 NIL 243509 NIL) (-132 242424 242691 242801 "BYTEORD" 242897 T BYTEORD (NIL) -8 NIL NIL NIL) (-131 237351 241929 242101 "BYTEBUF" 242272 T BYTEBUF (NIL) -8 NIL NIL NIL) (-130 236109 236866 237015 "BYTE" 237178 T BYTE (NIL) -8 NIL NIL 237307) (-129 233371 235801 235908 "BTREE" 236035 NIL BTREE (NIL T) -8 NIL NIL NIL) (-128 230573 233019 233141 "BTOURN" 233281 NIL BTOURN (NIL T) -8 NIL NIL NIL) (-127 227680 230015 230056 "BTCAT" 230124 NIL BTCAT (NIL T) -9 NIL 230201 NIL) (-126 227329 227427 227576 "BTCAT-" 227581 NIL BTCAT- (NIL T T) -8 NIL NIL NIL) (-125 222218 226575 226603 "BTAGG" 226717 T BTAGG (NIL) -9 NIL 226827 NIL) (-124 221672 221833 222039 "BTAGG-" 222044 NIL BTAGG- (NIL T) -8 NIL NIL NIL) (-123 218408 220950 221165 "BSTREE" 221489 NIL BSTREE (NIL T) -8 NIL NIL NIL) (-122 217516 217672 217856 "BRILL" 218264 NIL BRILL (NIL T) -7 NIL NIL NIL) (-121 213911 216214 216255 "BRAGG" 216904 NIL BRAGG (NIL T) -9 NIL 217162 NIL) (-120 212344 212846 213401 "BRAGG-" 213406 NIL BRAGG- (NIL T T) -8 NIL NIL NIL) (-119 204580 211688 211873 "BPADICRT" 212191 NIL BPADICRT (NIL NIL) -8 NIL NIL NIL) (-118 202589 204517 204562 "BPADIC" 204567 NIL BPADIC (NIL NIL) -8 NIL NIL NIL) (-117 202281 202317 202431 "BOUNDZRO" 202553 NIL BOUNDZRO (NIL T T) -7 NIL NIL NIL) (-116 200008 200466 200941 "BOP1" 201839 NIL BOP1 (NIL T) -7 NIL NIL NIL) (-115 194990 196434 197346 "BOP" 199116 T BOP (NIL) -8 NIL NIL NIL) (-114 193655 194578 194720 "BOOLEAN" 194868 T BOOLEAN (NIL) -8 NIL NIL NIL) (-113 193248 193405 193433 "BOOLE" 193544 T BOOLE (NIL) -9 NIL 193625 NIL) (-112 193116 193143 193209 "BOOLE-" 193214 NIL BOOLE- (NIL T) -8 NIL NIL NIL) (-111 192285 192785 192839 "BMODULE" 192844 NIL BMODULE (NIL T T) -9 NIL 192909 NIL) (-110 187606 192083 192156 "BITS" 192232 T BITS (NIL) -8 NIL NIL NIL) (-109 187003 187146 187286 "BINDING" 187486 T BINDING (NIL) -8 NIL NIL NIL) (-108 180042 186598 186747 "BINARY" 186874 T BINARY (NIL) -8 NIL NIL NIL) (-107 177649 179269 179310 "BGAGG" 179570 NIL BGAGG (NIL T) -9 NIL 179707 NIL) (-106 177474 177512 177603 "BGAGG-" 177608 NIL BGAGG- (NIL T T) -8 NIL NIL NIL) (-105 176497 176858 177063 "BFUNCT" 177289 T BFUNCT (NIL) -8 NIL NIL NIL) (-104 175167 175365 175653 "BEZOUT" 176321 NIL BEZOUT (NIL T T T T T) -7 NIL NIL NIL) (-103 171365 174019 174349 "BBTREE" 174870 NIL BBTREE (NIL T) -8 NIL NIL NIL) (-102 170948 171044 171072 "BASTYPE" 171249 T BASTYPE (NIL) -9 NIL 171348 NIL) (-101 170606 170705 170840 "BASTYPE-" 170845 NIL BASTYPE- (NIL T) -8 NIL NIL NIL) (-100 170028 170116 170268 "BALFACT" 170517 NIL BALFACT (NIL T T) -7 NIL NIL NIL) (-99 168764 169443 169629 "AUTOMOR" 169873 NIL AUTOMOR (NIL T) -8 NIL NIL NIL) (-98 168490 168495 168521 "ATTREG" 168526 T ATTREG (NIL) -9 NIL NIL NIL) (-97 166652 167187 167539 "ATTRBUT" 168156 T ATTRBUT (NIL) -8 NIL NIL NIL) (-96 166206 166480 166546 "ATTRAST" 166604 T ATTRAST (NIL) -8 NIL NIL NIL) (-95 165706 165855 165881 "ATRIG" 166082 T ATRIG (NIL) -9 NIL NIL NIL) (-94 165503 165556 165643 "ATRIG-" 165648 NIL ATRIG- (NIL T) -8 NIL NIL NIL) (-93 165086 165320 165346 "ASTCAT" 165351 T ASTCAT (NIL) -9 NIL 165381 NIL) (-92 164795 164872 164991 "ASTCAT-" 164996 NIL ASTCAT- (NIL T) -8 NIL NIL NIL) (-91 162769 164571 164659 "ASTACK" 164738 NIL ASTACK (NIL T) -8 NIL NIL NIL) (-90 161258 161571 161936 "ASSOCEQ" 162451 NIL ASSOCEQ (NIL T T) -7 NIL NIL NIL) (-89 160182 160917 161041 "ASP9" 161165 NIL ASP9 (NIL NIL) -8 NIL NIL NIL) (-88 158942 159787 159929 "ASP80" 160071 NIL ASP80 (NIL NIL) -8 NIL NIL NIL) (-87 158669 158890 158929 "ASP8" 158934 NIL ASP8 (NIL NIL) -8 NIL NIL NIL) (-86 157515 158346 158464 "ASP78" 158582 NIL ASP78 (NIL NIL) -8 NIL NIL NIL) (-85 156376 157195 157312 "ASP77" 157429 NIL ASP77 (NIL NIL) -8 NIL NIL NIL) (-84 155180 156014 156145 "ASP74" 156276 NIL ASP74 (NIL NIL) -8 NIL NIL NIL) (-83 153972 154815 154947 "ASP73" 155079 NIL ASP73 (NIL NIL) -8 NIL NIL NIL) (-82 152762 153607 153739 "ASP7" 153871 NIL ASP7 (NIL NIL) -8 NIL NIL NIL) (-81 151758 152588 152688 "ASP6" 152693 NIL ASP6 (NIL NIL) -8 NIL NIL NIL) (-80 150597 151435 151553 "ASP55" 151671 NIL ASP55 (NIL NIL) -8 NIL NIL NIL) (-79 149438 150271 150390 "ASP50" 150509 NIL ASP50 (NIL NIL) -8 NIL NIL NIL) (-78 148418 149139 149249 "ASP49" 149359 NIL ASP49 (NIL NIL) -8 NIL NIL NIL) (-77 147094 147957 148125 "ASP42" 148307 NIL ASP42 (NIL NIL NIL NIL) -8 NIL NIL NIL) (-76 145763 146627 146797 "ASP41" 146981 NIL ASP41 (NIL NIL NIL NIL) -8 NIL NIL NIL) (-75 144743 145464 145574 "ASP4" 145684 NIL ASP4 (NIL NIL) -8 NIL NIL NIL) (-74 143585 144420 144538 "ASP35" 144656 NIL ASP35 (NIL NIL) -8 NIL NIL NIL) (-73 143314 143533 143572 "ASP34" 143577 NIL ASP34 (NIL NIL) -8 NIL NIL NIL) (-72 143033 143118 143194 "ASP33" 143269 NIL ASP33 (NIL NIL) -8 NIL NIL NIL) (-71 141819 142668 142800 "ASP31" 142932 NIL ASP31 (NIL NIL) -8 NIL NIL NIL) (-70 141548 141767 141806 "ASP30" 141811 NIL ASP30 (NIL NIL) -8 NIL NIL NIL) (-69 141265 141352 141428 "ASP29" 141503 NIL ASP29 (NIL NIL) -8 NIL NIL NIL) (-68 140994 141213 141252 "ASP28" 141257 NIL ASP28 (NIL NIL) -8 NIL NIL NIL) (-67 140723 140942 140981 "ASP27" 140986 NIL ASP27 (NIL NIL) -8 NIL NIL NIL) (-66 139699 140421 140532 "ASP24" 140643 NIL ASP24 (NIL NIL) -8 NIL NIL NIL) (-65 138668 139501 139613 "ASP20" 139618 NIL ASP20 (NIL NIL) -8 NIL NIL NIL) (-64 137503 138342 138461 "ASP19" 138580 NIL ASP19 (NIL NIL) -8 NIL NIL NIL) (-63 137222 137307 137383 "ASP12" 137458 NIL ASP12 (NIL NIL) -8 NIL NIL NIL) (-62 135966 136821 136965 "ASP10" 137109 NIL ASP10 (NIL NIL) -8 NIL NIL NIL) (-61 134946 135667 135777 "ASP1" 135887 NIL ASP1 (NIL NIL) -8 NIL NIL NIL) (-60 132558 134790 134881 "ARRAY2" 134886 NIL ARRAY2 (NIL T) -8 NIL NIL NIL) (-59 131572 131763 131984 "ARRAY12" 132381 NIL ARRAY12 (NIL T T) -7 NIL NIL NIL) (-58 126932 131220 131334 "ARRAY1" 131489 NIL ARRAY1 (NIL T) -8 NIL NIL NIL) (-57 120977 123134 123209 "ARR2CAT" 125839 NIL ARR2CAT (NIL T T T) -9 NIL 126597 NIL) (-56 118267 119155 120109 "ARR2CAT-" 120114 NIL ARR2CAT- (NIL T T T T) -8 NIL NIL NIL) (-55 117518 117894 118019 "ARITY" 118160 T ARITY (NIL) -8 NIL NIL NIL) (-54 116276 116446 116745 "APPRULE" 117354 NIL APPRULE (NIL T T T) -7 NIL NIL NIL) (-53 115921 115975 116094 "APPLYORE" 116222 NIL APPLYORE (NIL T T T) -7 NIL NIL NIL) (-52 115175 115322 115479 "ANY1" 115795 NIL ANY1 (NIL T) -7 NIL NIL NIL) (-51 114475 114768 114888 "ANY" 115073 T ANY (NIL) -8 NIL NIL NIL) (-50 111801 112912 113239 "ANTISYM" 114199 NIL ANTISYM (NIL T NIL) -8 NIL NIL NIL) (-49 111245 111508 111604 "ANON" 111723 T ANON (NIL) -8 NIL NIL NIL) (-48 104401 109784 110238 "AN" 110809 T AN (NIL) -8 NIL NIL NIL) (-47 100057 101673 101724 "AMR" 102472 NIL AMR (NIL T T) -9 NIL 103072 NIL) (-46 99109 99390 99753 "AMR-" 99758 NIL AMR- (NIL T T T) -8 NIL NIL NIL) (-45 82578 99026 99087 "ALIST" 99092 NIL ALIST (NIL T T) -8 NIL NIL NIL) (-44 78875 82172 82341 "ALGSC" 82496 NIL ALGSC (NIL T NIL NIL NIL) -8 NIL NIL NIL) (-43 75325 75985 76592 "ALGPKG" 78315 NIL ALGPKG (NIL T T) -7 NIL NIL NIL) (-42 74590 74703 74887 "ALGMFACT" 75211 NIL ALGMFACT (NIL T T T) -7 NIL NIL NIL) (-41 70573 71204 71798 "ALGMANIP" 74174 NIL ALGMANIP (NIL T T) -7 NIL NIL NIL) (-40 59912 70199 70349 "ALGFF" 70506 NIL ALGFF (NIL T T T NIL) -8 NIL NIL NIL) (-39 59084 59239 59418 "ALGFACT" 59770 NIL ALGFACT (NIL T) -7 NIL NIL NIL) (-38 57873 58611 58649 "ALGEBRA" 58654 NIL ALGEBRA (NIL T) -9 NIL 58695 NIL) (-37 57573 57650 57782 "ALGEBRA-" 57787 NIL ALGEBRA- (NIL T T) -8 NIL NIL NIL) (-36 38527 55410 55462 "ALAGG" 55598 NIL ALAGG (NIL T T) -9 NIL 55759 NIL) (-35 38027 38176 38202 "AHYP" 38403 T AHYP (NIL) -9 NIL NIL NIL) (-34 36912 37206 37232 "AGG" 37731 T AGG (NIL) -9 NIL 38010 NIL) (-33 36310 36508 36722 "AGG-" 36727 NIL AGG- (NIL T) -8 NIL NIL NIL) (-32 34070 34539 34944 "AF" 35952 NIL AF (NIL T T) -7 NIL NIL NIL) (-31 33490 33795 33885 "ADDAST" 33998 T ADDAST (NIL) -8 NIL NIL NIL) (-30 32722 33017 33173 "ACPLOT" 33352 T ACPLOT (NIL) -8 NIL NIL NIL) (-29 20273 29654 29692 "ACFS" 30299 NIL ACFS (NIL T) -9 NIL 30538 NIL) (-28 18180 18790 19552 "ACFS-" 19557 NIL ACFS- (NIL T T) -8 NIL NIL NIL) (-27 13882 16213 16239 "ACF" 17118 T ACF (NIL) -9 NIL 17531 NIL) (-26 12514 12920 13413 "ACF-" 13418 NIL ACF- (NIL T) -8 NIL NIL NIL) (-25 12024 12267 12293 "ABELSG" 12385 T ABELSG (NIL) -9 NIL 12450 NIL) (-24 11885 11916 11982 "ABELSG-" 11987 NIL ABELSG- (NIL T) -8 NIL NIL NIL) (-23 11154 11501 11527 "ABELMON" 11697 T ABELMON (NIL) -9 NIL 11809 NIL) (-22 10794 10902 11040 "ABELMON-" 11045 NIL ABELMON- (NIL T) -8 NIL NIL NIL) (-21 10044 10500 10526 "ABELGRP" 10598 T ABELGRP (NIL) -9 NIL 10673 NIL) (-20 9471 9636 9852 "ABELGRP-" 9857 NIL ABELGRP- (NIL T) -8 NIL NIL NIL) (-19 4579 8733 8772 "A1AGG" 8777 NIL A1AGG (NIL T) -9 NIL 8817 NIL) (-18 30 1497 3059 "A1AGG-" 3064 NIL A1AGG- (NIL T T) -8 NIL NIL NIL))
\ No newline at end of file diff --git a/src/share/algebra/operation.daase b/src/share/algebra/operation.daase index 80ceb27f..bc095dde 100644 --- a/src/share/algebra/operation.daase +++ b/src/share/algebra/operation.daase @@ -1,74 +1,48 @@ -(733360 . 3507509288) +(733360 . 3507527189) (((*1 *2 *3 *4) - (-12 (-5 *4 (-305 (-864 *3))) (-4 *3 (-13 (-27) (-1233) (-435 *5))) - (-4 *5 (-13 (-466) (-1069 (-560)) (-660 (-560)))) - (-5 *2 - (-3 (-864 *3) - (-2 (|:| |leftHandLimit| (-3 (-864 *3) "failed")) - (|:| |rightHandLimit| (-3 (-864 *3) "failed"))) - "failed")) - (-5 *1 (-655 *5 *3)))) - ((*1 *2 *3 *4 *5) - (|partial| -12 (-5 *4 (-305 *3)) (-5 *5 (-1189)) - (-4 *3 (-13 (-27) (-1233) (-435 *6))) - (-4 *6 (-13 (-466) (-1069 (-560)) (-660 (-560)))) - (-5 *2 (-864 *3)) (-5 *1 (-655 *6 *3)))) - ((*1 *2 *3 *4) - (-12 (-5 *4 (-305 (-864 (-975 *5)))) (-4 *5 (-466)) - (-5 *2 - (-3 (-864 (-421 (-975 *5))) - (-2 (|:| |leftHandLimit| (-3 (-864 (-421 (-975 *5))) "failed")) - (|:| |rightHandLimit| (-3 (-864 (-421 (-975 *5))) "failed"))) - "failed")) - (-5 *1 (-656 *5)) (-5 *3 (-421 (-975 *5))))) - ((*1 *2 *3 *4) - (-12 (-5 *4 (-305 (-421 (-975 *5)))) (-5 *3 (-421 (-975 *5))) - (-4 *5 (-466)) - (-5 *2 - (-3 (-864 *3) - (-2 (|:| |leftHandLimit| (-3 (-864 *3) "failed")) - (|:| |rightHandLimit| (-3 (-864 *3) "failed"))) - "failed")) - (-5 *1 (-656 *5)))) - ((*1 *2 *3 *4 *5) - (|partial| -12 (-5 *4 (-305 (-421 (-975 *6)))) (-5 *5 (-1189)) - (-5 *3 (-421 (-975 *6))) (-4 *6 (-466)) (-5 *2 (-864 *3)) - (-5 *1 (-656 *6))))) -(((*1 *2 *1) (|partial| -12 (-5 *2 (-630 *1)) (-4 *1 (-310))))) + (-12 (-5 *3 (-229)) (-5 *4 (-560)) (-5 *2 (-1066)) (-5 *1 (-780))))) +(((*1 *1 *2 *3) + (-12 (-5 *3 (-1189)) (-4 *1 (-378 *2 *4)) (-4 *2 (-1132)) + (-4 *4 (-1132)))) + ((*1 *1 *2) + (-12 (-4 *1 (-378 *2 *3)) (-4 *2 (-1132)) (-4 *3 (-1132))))) +(((*1 *2 *1 *3) (-12 (-5 *3 (-1207)) (-5 *2 (-391)) (-5 *1 (-1094))))) (((*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 (-1155 *4 *5 *6 *3)) (-4 *3 (-708 *4 *5 *6))))) -(((*1 *2 *1) - (-12 (-5 *2 (-1185 (-421 *3))) (-5 *1 (-177 *3)) (-4 *3 (-319))))) -(((*1 *2 *3 *4) - (-12 (-5 *3 (-663 *8)) (-5 *4 (-663 *9)) (-4 *8 (-1096 *5 *6 *7)) - (-4 *9 (-1102 *5 *6 *7 *8)) (-4 *5 (-466)) (-4 *6 (-815)) - (-4 *7 (-871)) (-5 *2 (-793)) (-5 *1 (-1100 *5 *6 *7 *8 *9)))) - ((*1 *2 *3 *4) - (-12 (-5 *3 (-663 *8)) (-5 *4 (-663 *9)) (-4 *8 (-1096 *5 *6 *7)) - (-4 *9 (-1140 *5 *6 *7 *8)) (-4 *5 (-466)) (-4 *6 (-815)) - (-4 *7 (-871)) (-5 *2 (-793)) (-5 *1 (-1176 *5 *6 *7 *8 *9))))) -(((*1 *1 *1 *1) (-12 (-4 *1 (-1273 *2)) (-4 *2 (-1080))))) -(((*1 *2 *1) - (-12 (-4 *1 (-1242 *3 *4 *5 *6)) (-4 *3 (-571)) (-4 *4 (-815)) - (-4 *5 (-871)) (-4 *6 (-1096 *3 *4 *5)) (-5 *2 (-663 *6))))) + (-12 (-5 *2 (-663 (-1189))) (-5 *1 (-248)) (-5 *3 (-1189)))) + ((*1 *2 *2) (-12 (-5 *2 (-663 (-1189))) (-5 *1 (-248)))) + ((*1 *1 *2) (-12 (-5 *2 (-159)) (-5 *1 (-898))))) (((*1 *2 *1) - (-12 (-4 *1 (-1165 *3)) (-4 *3 (-1080)) (-5 *2 (-663 (-972 *3))))) - ((*1 *1 *2) - (-12 (-5 *2 (-663 (-972 *3))) (-4 *3 (-1080)) (-4 *1 (-1165 *3)))) - ((*1 *1 *1 *2) - (-12 (-5 *2 (-663 (-663 *3))) (-4 *1 (-1165 *3)) (-4 *3 (-1080)))) - ((*1 *1 *1 *2) - (-12 (-5 *2 (-663 (-972 *3))) (-4 *1 (-1165 *3)) (-4 *3 (-1080))))) -(((*1 *1 *2 *3) - (-12 (-5 *2 (-482)) (-5 *3 (-663 (-270))) (-5 *1 (-1300)))) - ((*1 *1 *1) (-5 *1 (-1300)))) -(((*1 *1 *1) - (-12 (-5 *1 (-1172 *2 *3)) (-4 *2 (-13 (-1132) (-34))) - (-4 *3 (-13 (-1132) (-34)))))) + (-12 (-5 *2 (-663 (-560))) (-5 *1 (-1035 *3)) (-14 *3 (-560))))) +(((*1 *2 *1) (-12 (-5 *2 (-1303)) (-5 *1 (-845))))) +(((*1 *2 *1) (-12 (-4 *1 (-380 *3)) (-4 *3 (-175)) (-5 *2 (-1201 *3))))) +(((*1 *2) + (-12 (-4 *4 (-175)) (-5 *2 (-114)) (-5 *1 (-379 *3 *4)) + (-4 *3 (-380 *4)))) + ((*1 *2) (-12 (-4 *1 (-380 *3)) (-4 *3 (-175)) (-5 *2 (-114))))) +(((*1 *2 *1) (-12 (-4 *1 (-1165 *3)) (-4 *3 (-1080)) (-5 *2 (-114))))) +(((*1 *2 *3) + (-12 (-5 *3 (-1297 (-663 (-2 (|:| -1420 *4) (|:| -3998 (-1151)))))) + (-4 *4 (-363)) (-5 *2 (-793)) (-5 *1 (-360 *4)))) + ((*1 *2) + (-12 (-5 *2 (-793)) (-5 *1 (-365 *3 *4)) (-14 *3 (-948)) + (-14 *4 (-948)))) + ((*1 *2) + (-12 (-5 *2 (-793)) (-5 *1 (-366 *3 *4)) (-4 *3 (-363)) + (-14 *4 + (-3 (-1201 *3) + (-1297 (-663 (-2 (|:| -1420 *3) (|:| -3998 (-1151))))))))) + ((*1 *2) + (-12 (-5 *2 (-793)) (-5 *1 (-367 *3 *4)) (-4 *3 (-363)) + (-14 *4 (-948))))) +(((*1 *2) + (-12 (-4 *3 (-466)) (-4 *4 (-815)) (-4 *5 (-871)) + (-4 *6 (-1096 *3 *4 *5)) (-5 *2 (-1303)) + (-5 *1 (-1103 *3 *4 *5 *6 *7)) (-4 *7 (-1102 *3 *4 *5 *6)))) + ((*1 *2) + (-12 (-4 *3 (-466)) (-4 *4 (-815)) (-4 *5 (-871)) + (-4 *6 (-1096 *3 *4 *5)) (-5 *2 (-1303)) + (-5 *1 (-1139 *3 *4 *5 *6 *7)) (-4 *7 (-1102 *3 *4 *5 *6))))) (((*1 *2 *3) (-12 (-5 *3 (-948)) (-5 *2 (-1201 *4)) (-5 *1 (-369 *4)) (-4 *4 (-363)))) @@ -86,94 +60,68 @@ (-12 (-5 *3 (-560)) (-5 *2 (-931 *4)) (-5 *1 (-934 *4)) (-4 *4 (-1132)))) ((*1 *1) (-12 (-4 *1 (-1022 *2)) (-4 *2 (-559)) (-4 *2 (-571))))) -(((*1 *2 *2) - (-12 (-5 *2 (-663 *6)) (-4 *6 (-1096 *3 *4 *5)) (-4 *3 (-571)) - (-4 *4 (-815)) (-4 *5 (-871)) (-5 *1 (-1008 *3 *4 *5 *6))))) -(((*1 *2 *1) - (-12 (-5 *2 (-114)) (-5 *1 (-1195 *3 *4)) (-14 *3 (-948)) - (-4 *4 (-1080))))) -(((*1 *2 *1 *3) - (-12 (-5 *3 (-972 (-229))) (-5 *2 (-1303)) (-5 *1 (-482))))) -(((*1 *1 *1 *2 *3) - (-12 (-5 *3 (-663 *6)) (-4 *6 (-871)) (-4 *4 (-376)) (-4 *5 (-815)) - (-5 *1 (-518 *4 *5 *6 *2)) (-4 *2 (-979 *4 *5 *6)))) - ((*1 *1 *1 *2) - (-12 (-4 *3 (-376)) (-4 *4 (-815)) (-4 *5 (-871)) - (-5 *1 (-518 *3 *4 *5 *2)) (-4 *2 (-979 *3 *4 *5))))) -(((*1 *1 *2 *3 *1) - (-12 (-5 *2 (-1123 (-975 (-560)))) (-5 *3 (-975 (-560))) - (-5 *1 (-342)))) - ((*1 *1 *2 *1) (-12 (-5 *2 (-1123 (-975 (-560)))) (-5 *1 (-342))))) -(((*1 *2 *3 *4 *4 *4 *4 *5 *5 *5) - (-12 (-5 *3 (-1 (-391) (-391))) (-5 *4 (-391)) - (-5 *2 - (-2 (|:| -1399 *4) (|:| -2747 *4) (|:| |totalpts| (-560)) - (|:| |success| (-114)))) - (-5 *1 (-811)) (-5 *5 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points") - (|:| |lowerSingular| - "There is a singularity at the lower end point") - (|:| |upperSingular| - "There is a singularity at the upper end point") - (|:| |bothSingular| "There are singularities at both end points") - (|:| |notEvaluated| "End point continuity not yet evaluated"))) - (-5 *1 (-195))))) -(((*1 *2 *3 *4) - (-12 (-5 *4 (-1 (-1185 *3))) (-5 *2 (-1185 *3)) (-5 *1 (-1191 *3)) - (-4 *3 (-38 (-421 (-560)))) (-4 *3 (-1080))))) -(((*1 *2 *1) (-12 (-5 *2 (-1166)) (-5 *1 (-539))))) -(((*1 *1 *1 *2) - (-12 (-5 *2 (-793)) (-4 *1 (-1317 *3 *4)) (-4 *3 (-871)) - (-4 *4 (-1080)) (-4 *4 (-175)))) - ((*1 *1 *1 *1) - (-12 (-4 *1 (-1317 *2 *3)) (-4 *2 (-871)) (-4 *3 (-1080)) - (-4 *3 (-175))))) -(((*1 *2 *3 *4) - (-12 (-5 *3 (-1201 *5)) (-4 *5 (-376)) (-5 *2 (-663 *6)) - (-5 *1 (-546 *5 *6 *4)) (-4 *6 (-376)) (-4 *4 (-13 (-376) (-870)))))) -(((*1 *1 *2 *2 *3) (-12 (-5 *2 (-1189)) (-5 *3 (-846)) (-5 *1 (-845))))) + (-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| (-1185 (-229))) + (|:| |notEvaluated| + "Internal singularities not yet evaluated"))) + (|:| -2016 + (-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 (-1066)) (-5 *1 (-315))))) +(((*1 *2 *1) + (-12 (-4 *1 (-1135 *3 *4 *5 *6 *7)) (-4 *3 (-1132)) (-4 *4 (-1132)) + (-4 *5 (-1132)) (-4 *6 (-1132)) (-4 *7 (-1132)) (-5 *2 (-114))))) +(((*1 *2 *3) (-12 (-5 *3 (-975 (-229))) (-5 *2 (-229)) (-5 *1 (-315))))) +(((*1 *2 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singularity at the lower end point") - (|:| |upperSingular| - "There is a singularity at the upper end point") - (|:| |bothSingular| - "There are singularities at both end points") - (|:| |notEvaluated| - "End point continuity not yet evaluated"))) - (|:| |singularitiesStream| - (-3 (|:| |str| (-1185 (-229))) - (|:| |notEvaluated| - "Internal singularities not yet evaluated"))) - (|:| -1580 - (-3 (|:| |finite| "The range is finite") - (|:| |lowerInfinite| - "The bottom of range is infinite") - (|:| |upperInfinite| "The top of range is infinite") - (|:| |bothInfinite| - "Both top and bottom points are infinite") - (|:| |notEvaluated| "Range not yet evaluated")))))))) - (-5 *1 (-574)))) - ((*1 *2 *1) - (-12 (-4 *1 (-618 *3 *4)) (-4 *3 (-1132)) (-4 *4 (-1247)) - (-5 *2 (-663 *4))))) -(((*1 *2) - (-12 (-4 *3 (-815)) (-4 *4 (-871)) (-4 *2 (-939)) - (-5 *1 (-471 *3 *4 *2 *5)) (-4 *5 (-979 *2 *3 *4)))) - ((*1 *2) - (-12 (-4 *3 (-815)) (-4 *4 (-871)) (-4 *2 (-939)) - (-5 *1 (-936 *2 *3 *4 *5)) 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*3)) (-4 *3 (-649)) (-4 *3 (-13 (-27) (-1233) (-435 *5)))))) +(((*1 *2 *2 *2) + (-12 (-4 *3 (-1247)) (-5 *1 (-185 *3 *2)) (-4 *2 (-696 *3))))) +(((*1 *2 *3) + (-12 (-4 *4 (-1080)) (-5 *2 (-114)) (-5 *1 (-458 *4 *3)) + (-4 *3 (-1273 *4)))) + ((*1 *2 *1) + (-12 (-4 *1 (-1096 *3 *4 *5)) (-4 *3 (-1080)) (-4 *4 (-815)) + (-4 *5 (-871)) (-5 *2 (-114))))) +(((*1 *2 *3 *4) + (-12 (-5 *3 (-1297 *1)) (-5 *4 (-1 *5 *5)) (-4 *5 (-376)) + (-4 *1 (-746 *5 *6)) (-4 *5 (-175)) (-4 *6 (-1273 *5)) + (-5 *2 (-711 *5))))) +(((*1 *2) (-12 (-5 *2 (-114)) (-5 *1 (-956))))) +(((*1 *2 *1 *3 *4) + (-12 (-5 *3 (-482)) (-5 *4 (-948)) (-5 *2 (-1303)) (-5 *1 (-1300))))) +(((*1 *1 *2) (-12 (-5 *2 (-421 (-560))) (-5 *1 (-501))))) +(((*1 *2) + (-12 (-5 *2 (-114)) (-5 *1 (-1225 *3 *4)) (-4 *3 (-1132)) + (-4 *4 (-1132))))) +(((*1 *1 *1) + (|partial| -12 (-4 *1 (-380 *2)) (-4 *2 (-175)) (-4 *2 (-571)))) + ((*1 *1 *1) (|partial| -4 *1 (-744)))) +(((*1 *2 *3 *4 *5 *6 *3 *3 *3 *3 *6 *3 *7 *8) + (-12 (-5 *3 (-560)) (-5 *4 (-711 (-229))) (-5 *5 (-114)) + (-5 *6 (-229)) (-5 *7 (-3 (|:| |fn| (-402)) (|:| |fp| (-68 APROD)))) + (-5 *8 (-3 (|:| |fn| (-402)) (|:| |fp| (-73 MSOLVE)))) + (-5 *2 (-1066)) (-5 *1 (-778))))) +(((*1 *2 *3 *3 *2) + (-12 (-5 *2 (-1066)) (-5 *3 (-1207)) (-5 *1 (-195))))) +(((*1 *2 *3) + (|partial| -12 + (-5 *3 + (-2 (|:| |var| (-1207)) (|:| |fn| (-326 (-229))) + (|:| -2016 (-1120 (-864 (-229)))) (|:| |abserr| (-229)) + (|:| |relerr| (-229)))) + (-5 *2 + (-2 + (|:| |endPointContinuity| + (-3 (|:| |continuous| "Continuous at the end points") + (|:| |lowerSingular| + "There is a singularity at the lower end point") + (|:| |upperSingular| + "There is a singularity at the upper end point") + (|:| |bothSingular| + "There are singularities at both end points") + (|:| |notEvaluated| + "End point continuity not yet evaluated"))) + (|:| |singularitiesStream| + (-3 (|:| |str| (-1185 (-229))) + (|:| |notEvaluated| + "Internal singularities not yet evaluated"))) + (|:| -2016 + (-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 *3) (-12 (-5 *3 (-863)) (-5 *2 (-1066)) (-5 *1 (-862)))) + ((*1 *2 *3 *4) + (-12 (-5 *3 (-663 (-326 (-391)))) (-5 *4 (-663 (-391))) + (-5 *2 (-1066)) (-5 *1 (-862))))) +(((*1 *2 *1) + (-12 (-4 *2 (-730 *3)) (-5 *1 (-850 *2 *3)) (-4 *3 (-1080))))) (((*1 *2 *3 *4) (-12 (-5 *4 (-1207)) (-4 *5 (-13 (-571) (-1069 (-560)) (-660 (-560)))) @@ -3479,10 +3912,180 @@ (-2 (|:| |func| *3) (|:| |kers| (-663 (-630 *3))) (|:| |vals| (-663 *3)))) (-5 *1 (-288 *5 *3)) (-4 *3 (-13 (-27) (-1233) (-435 *5)))))) +(((*1 *2) + (-12 (-5 *2 (-114)) (-5 *1 (-1225 *3 *4)) (-4 *3 (-1132)) + (-4 *4 (-1132))))) +(((*1 *2 *3) (-12 (-5 *3 (-1189)) (-5 *2 (-1303)) (-5 *1 (-596))))) +(((*1 *2) (-12 (-4 *1 (-380 *3)) (-4 *3 (-175)) (-5 *2 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- (-5 *1 (-575 *7 *4 *3)) (-4 *3 (-680 *4)) (-4 *3 (-1132))))) +(((*1 *2 *3) + (-12 (-5 *3 (-1207)) (-5 *2 (-326 (-560))) (-5 *1 (-958)))) + ((*1 *2 *2) + (-12 (-4 *3 (-1132)) (-5 *1 (-959 *3 *2)) (-4 *2 (-435 *3))))) (((*1 *1 *1) (-4 *1 (-250))) ((*1 *1 *1) (-12 (-4 *2 (-175)) (-5 *1 (-301 *2 *3 *4 *5 *6 *7)) @@ -9764,7 +9310,7 @@ (-14 *6 (-1 (-3 *4 "failed") *4 *4)) (-14 *7 (-1 (-3 *3 "failed") *3 *3 *4)))) ((*1 *1 *1) - (-2181 (-12 (-5 *1 (-305 *2)) (-4 *2 (-376)) (-4 *2 (-1247))) + (-2173 (-12 (-5 *1 (-305 *2)) (-4 *2 (-376)) (-4 *2 (-1247))) (-12 (-5 *1 (-305 *2)) (-4 *2 (-487)) (-4 *2 (-1247))))) ((*1 *1 *1) (-4 *1 (-487))) ((*1 *2 *2) (-12 (-5 *2 (-1297 *3)) (-4 *3 (-363)) (-5 *1 (-542 *3)))) @@ -9773,14 +9319,13 @@ (-14 *4 (-1 *2 *2 *3)) (-14 *5 (-1 (-3 *3 "failed") *3 *3)) (-14 *6 (-1 (-3 *2 "failed") *2 *2 *3)))) ((*1 *1 *1) (-12 (-4 *1 (-818 *2)) (-4 *2 (-175)) (-4 *2 (-376))))) -(((*1 *2 *2) (|partial| -12 (-4 *1 (-1014 *2)) (-4 *2 (-1233))))) -(((*1 *2 *2) - (-12 (-5 *2 (-1297 *1)) (-4 *1 (-355 *3 *4 *5)) (-4 *3 (-1252)) - (-4 *4 (-1273 *3)) (-4 *5 (-1273 (-421 *4)))))) +(((*1 *2 *1) (-12 (-5 *2 (-114)) (-5 *1 (-1243 *3)) (-4 *3 (-1005))))) +(((*1 *2 *1) (-12 (-5 *2 (-520)) (-5 *1 (-539)))) + ((*1 *2 *1) (-12 (-5 *2 (-520)) (-5 *1 (-1183))))) (((*1 *2 *3) (-12 (-5 *3 (-1189)) (-5 *2 (-1303)) (-5 *1 (-760))))) -(((*1 *2 *3 *2) - (-12 (-5 *3 (-793)) (-5 *1 (-805 *2)) (-4 *2 (-38 (-421 (-560)))) - (-4 *2 (-175))))) +(((*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 (-1066)) (-5 *1 (-778))))) (((*1 *1 *2 *3) (-12 (-5 *2 (-1207)) (-5 *3 (-663 *1)) (-4 *1 (-435 *4)) (-4 *4 (-1132)))) @@ -9792,87 +9337,114 @@ (-12 (-5 *2 (-1207)) (-4 *1 (-435 *3)) (-4 *3 (-1132)))) ((*1 *1 *2 *1) (-12 (-5 *2 (-1207)) (-4 *1 (-435 *3)) (-4 *3 (-1132))))) +(((*1 *2 *2) (-12 (-5 *2 (-560)) (-5 *1 (-954))))) (((*1 *2 *3) - (-12 (-5 *3 (-975 *5)) (-4 *5 (-1080)) (-5 *2 (-495 *4 *5)) - (-5 *1 (-973 *4 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((*1 *1 *2) + (-12 (-5 *2 (-1207)) (-5 *1 (-467 *3 *4 *5 *6)) (-4 *3 (-175)) + (-14 *4 (-948)) (-14 *5 (-663 *2)) (-14 *6 (-1297 (-711 *3))))) + ((*1 *1) + (-12 (-5 *1 (-467 *2 *3 *4 *5)) (-4 *2 (-175)) (-14 *3 (-948)) + (-14 *4 (-663 (-1207))) (-14 *5 (-1297 (-711 *2)))))) (((*1 *2 *3) (-12 (-5 *3 (-1207)) (-4 *4 (-13 (-466) (-1069 (-560)) (-660 (-560)))) (-5 *2 (-51)) @@ -9907,39 +9479,49 @@ ((*1 *1 *2 *3) (-12 (-5 *2 (-421 (-560))) (-4 *4 (-1080)) (-4 *1 (-1282 *4 *3)) (-4 *3 (-1259 *4))))) -(((*1 *1 *1 *2) - (-12 (-5 *2 (-1 *4 *4)) (-4 *4 (-670 *3)) (-4 *3 (-1080)) - (-5 *1 (-736 *3 *4)))) - ((*1 *1 *1 *2) - (-12 (-5 *2 (-1 *3 *3)) (-4 *3 (-1080)) (-5 *1 (-856 *3))))) -(((*1 *2 *1 *3) (-12 (-5 *3 (-1207)) (-5 *2 (-1303)) (-5 *1 (-845))))) -(((*1 *1 *2 *1) - (-12 (-5 *2 (-1 *3 *3)) (-4 *1 (-57 *3 *4 *5)) (-4 *3 (-1247)) - (-4 *4 (-385 *3)) (-4 *5 (-385 *3)))) - ((*1 *1 *2 *1) - (-12 (-5 *2 (-1 *3 *3)) (|has| *1 (-6 -4509)) (-4 *1 (-503 *3)) - (-4 *3 (-1247))))) -(((*1 *2 *1) - 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+ (-12 (-4 *4 (-13 (-376) (-870))) + (-5 *2 (-2 (|:| |start| *3) (|:| -1450 (-419 *3)))) + (-5 *1 (-184 *4 *3)) (-4 *3 (-1273 (-171 *4)))))) +(((*1 *1 *2) + (-12 (-5 *2 (-1195 3 *3)) (-4 *3 (-1080)) (-4 *1 (-1165 *3)))) + ((*1 *1) (-12 (-4 *1 (-1165 *2)) (-4 *2 (-1080))))) +(((*1 *2 *3 *3 *2 *4) + (-12 (-5 *3 (-711 *2)) (-5 *4 (-560)) + (-4 *2 (-13 (-319) (-10 -8 (-15 -2535 ((-419 $) $))))) + (-4 *5 (-1273 *2)) (-5 *1 (-513 *2 *5 *6)) (-4 *6 (-424 *2 *5))))) +(((*1 *2 *2) (-12 (-5 *2 (-1189)) (-5 *1 (-887))))) (((*1 *2 *3) (-12 (-5 *3 (-1207)) (-4 *4 (-13 (-466) (-1069 (-560)) (-660 (-560)))) (-5 *2 (-51)) @@ -9974,7 +9556,12 @@ (-4 *3 (-1290 *4)))) ((*1 *2 *1) (-12 (-4 *1 (-1282 *3 *2)) (-4 *3 (-1080)) (-4 *2 (-1259 *3))))) -(((*1 *2 *1) (-12 (-4 *1 (-1005)) (-5 *2 (-1120 (-229)))))) +(((*1 *1 *2 *1) + (-12 (-5 *2 (-1 *3 *3)) (-4 *1 (-57 *3 *4 *5)) (-4 *3 (-1247)) + (-4 *4 (-385 *3)) (-4 *5 (-385 *3)))) + ((*1 *1 *2 *1) + (-12 (-5 *2 (-1 *3 *3)) (|has| *1 (-6 -4509)) (-4 *1 (-503 *3)) + (-4 *3 (-1247))))) (((*1 *1 *1) (-4 *1 (-35))) ((*1 *2 *2) (-12 (-4 *3 (-571)) (-5 *1 (-287 *3 *2)) @@ -9995,32 +9582,29 @@ (-12 (-4 *3 (-1132)) (-5 *1 (-910 *2 *3 *4)) (-4 *2 (-1132)) (-4 *4 (-688 *3)))) ((*1 *1) (-12 (-5 *1 (-913 *2 *3)) (-4 *2 (-1132)) (-4 *3 (-1132))))) -(((*1 *2 *3 *3 *4) - (-12 (-5 *3 (-663 (-495 *5 *6))) (-5 *4 (-888 *5)) - (-14 *5 (-663 (-1207))) (-5 *2 (-495 *5 *6)) (-5 *1 (-650 *5 *6)) - (-4 *6 (-466)))) - ((*1 *2 *3 *4) - (-12 (-5 *3 (-663 (-495 *5 *6))) (-5 *4 (-888 *5)) - (-14 *5 (-663 (-1207))) (-5 *2 (-495 *5 *6)) (-5 *1 (-650 *5 *6)) - (-4 *6 (-466))))) (((*1 *2 *3) - (-12 (-4 *4 (-466)) (-4 *5 (-815)) (-4 *6 (-871)) (-5 *2 (-793)) - (-5 *1 (-464 *4 *5 *6 *3)) (-4 *3 (-979 *4 *5 *6))))) + (-12 (-5 *3 (-663 (-560))) (-5 *2 (-934 (-560))) (-5 *1 (-946)))) + ((*1 *2) (-12 (-5 *2 (-934 (-560))) (-5 *1 (-946))))) +(((*1 *2 *3 *3 *3 *3 *4 *3 *3 *3 *3 *3 *3 *5 *5 *4 *3 *6 *7) + (-12 (-5 *3 (-560)) (-5 *5 (-711 (-229))) + (-5 *6 (-3 (|:| |fn| (-402)) (|:| |fp| (-76 FCN JACOBF JACEPS)))) + (-5 *7 (-3 (|:| |fn| (-402)) (|:| |fp| (-77 G JACOBG JACGEP)))) + (-5 *4 (-229)) (-5 *2 (-1066)) (-5 *1 (-771))))) +(((*1 *2 *1) (-12 (-4 *1 (-403)) (-5 *2 (-114))))) +(((*1 *2 *3 *3) + (-12 (-5 *3 (-1266 *5 *4)) (-4 *4 (-466)) (-4 *4 (-842)) + (-14 *5 (-1207)) (-5 *2 (-560)) (-5 *1 (-1145 *4 *5))))) (((*1 *2 *3) - (-12 (-5 *3 (-305 (-975 (-560)))) - (-5 *2 - (-2 (|:| |varOrder| (-663 (-1207))) - (|:| |inhom| (-3 (-663 (-1297 (-793))) "failed")) - (|:| |hom| (-663 (-1297 (-793)))))) - (-5 *1 (-243))))) -(((*1 *2 *1 *3 *3 *4 *4) - (-12 (-5 *3 (-793)) (-5 *4 (-948)) (-5 *2 (-1303)) (-5 *1 (-1300)))) - ((*1 *2 *1 *3 *3 *4 *4) - (-12 (-5 *3 (-793)) (-5 *4 (-948)) (-5 *2 (-1303)) (-5 *1 (-1301))))) + (-12 (-5 *3 (-663 *2)) (-4 *2 (-435 *4)) (-5 *1 (-160 *4 *2)) + (-4 *4 (-571))))) (((*1 *2 *3 *4) - (-12 (-5 *3 (-663 *5)) (-5 *4 (-948)) (-4 *5 (-871)) - (-5 *2 (-663 (-694 *5))) (-5 *1 (-694 *5))))) -(((*1 *2 *2) (|partial| -12 (-4 *1 (-1014 *2)) (-4 *2 (-1233))))) + (-12 (-5 *3 (-1 *5 *7)) (-5 *4 (-1201 *7)) (-4 *5 (-1080)) + (-4 *7 (-1080)) (-4 *2 (-1273 *5)) (-5 *1 (-515 *5 *2 *6 *7)) + (-4 *6 (-1273 *2)))) + ((*1 *2 *3 *4) + (-12 (-5 *3 (-1 *7 *5)) (-4 *5 (-1080)) (-4 *7 (-1080)) + (-4 *4 (-1273 *5)) (-5 *2 (-1201 *7)) (-5 *1 (-515 *5 *4 *6 *7)) + (-4 *6 (-1273 *4))))) (((*1 *2 *3) (-12 (-5 *3 (-1207)) (-4 *4 (-13 (-466) (-1069 (-560)) (-660 (-560)))) (-5 *2 (-51)) @@ -10063,16 +9647,31 @@ (-5 *1 (-473 *7 *3)))) ((*1 *2 *1) (-12 (-4 *1 (-1261 *3 *2)) (-4 *3 (-1080)) (-4 *2 (-1290 *3))))) -(((*1 *2) (-12 (-5 *2 (-1189)) (-5 *1 (-1217))))) -(((*1 *2 *1) (-12 (-5 *2 (-114)) (-5 *1 (-915 *3)) (-4 *3 (-1132))))) -(((*1 *2 *1) (-12 (-4 *1 (-984)) (-5 *2 (-1120 (-229))))) - ((*1 *2 *1) (-12 (-4 *1 (-1005)) (-5 *2 (-1120 (-229)))))) -(((*1 *1 *2 *1) - (-12 (-5 *2 (-1 *3 (-560))) (-4 *3 (-1080)) (-5 *1 (-609 *3)))) - ((*1 *1 *2 *1) - (-12 (-5 *2 (-1 *3 (-560))) (-4 *1 (-1259 *3)) (-4 *3 (-1080)))) - ((*1 *1 *2 *1) - (-12 (-5 *2 (-1 *3 (-560))) (-4 *1 (-1290 *3)) (-4 *3 (-1080))))) +(((*1 *2 *1) + (-12 (-5 *2 (-1185 (-2 (|:| |k| (-560)) (|:| |c| *3)))) + (-5 *1 (-609 *3)) (-4 *3 (-1080))))) +(((*1 *2 *1 *1 *3) (-12 (-4 *1 (-1175)) (-5 *3 (-146)) (-5 *2 (-114))))) +(((*1 *2 *3 *1) + (-12 (-4 *4 (-376)) (-4 *5 (-815)) (-4 *6 (-871)) (-5 *2 (-114)) + (-5 *1 (-518 *4 *5 *6 *3)) (-4 *3 (-979 *4 *5 *6))))) +(((*1 *1 *2 *2 *3) + (-12 (-5 *2 (-793)) (-4 *3 (-1247)) (-4 *1 (-57 *3 *4 *5)) + (-4 *4 (-385 *3)) (-4 *5 (-385 *3)))) + ((*1 *1) (-5 *1 (-174))) + ((*1 *1) (-12 (-5 *1 (-216 *2 *3)) (-14 *2 (-948)) (-4 *3 (-1132)))) + ((*1 *1 *2 *2 *2) (-12 (-5 *2 (-1189)) (-4 *1 (-403)))) + ((*1 *1) (-5 *1 (-407))) + ((*1 *1 *2 *3) (-12 (-5 *2 (-793)) (-4 *1 (-673 *3)) (-4 *3 (-1247)))) + ((*1 *1) + (-12 (-4 *3 (-1132)) (-5 *1 (-910 *2 *3 *4)) (-4 *2 (-1132)) + (-4 *4 (-688 *3)))) + ((*1 *1) (-12 (-5 *1 (-913 *2 *3)) (-4 *2 (-1132)) (-4 *3 (-1132)))) + ((*1 *1 *2) + (-12 (-5 *1 (-1173 *3 *2)) (-14 *3 (-793)) (-4 *2 (-1080)))) + ((*1 *1) (-12 (-5 *1 (-1195 *2 *3)) (-14 *2 (-948)) (-4 *3 (-1080)))) + ((*1 *1 *1) (-5 *1 (-1207))) ((*1 *1) (-5 *1 (-1207))) + ((*1 *1) (-5 *1 (-1227)))) +(((*1 *2 *1) (-12 (-4 *1 (-1005)) (-5 *2 (-1120 (-229)))))) (((*1 *1 *1) (-4 *1 (-35))) ((*1 *2 *2) (-12 (-4 *3 (-571)) (-5 *1 (-287 *3 *2)) @@ -10089,27 +9688,40 @@ ((*1 *2 *2) (-12 (-5 *2 (-1185 *3)) (-4 *3 (-38 (-421 (-560)))) (-5 *1 (-1193 *3))))) -(((*1 *1 *1 *2) (-12 (-5 *2 (-663 (-1212))) (-5 *1 (-1212)))) - ((*1 *1 *2 *3) - (-12 (-5 *2 (-520)) (-5 *3 (-663 (-1212))) (-5 *1 (-1212))))) -(((*1 *2 *1) (-12 (-4 *1 (-1022 *2)) (-4 *2 (-571)) (-4 *2 (-559)))) - ((*1 *1 *1) (-4 *1 (-1091)))) (((*1 *2 *3 *4) - (-12 (-4 *5 (-1132)) (-4 *3 (-927 *5)) (-5 *2 (-1297 *3)) - (-5 *1 (-714 *5 *3 *6 *4)) (-4 *6 (-385 *3)) - (-4 *4 (-13 (-385 *5) (-10 -7 (-6 -4508))))))) -(((*1 *2 *3) - (-12 (-5 *3 (-948)) (-5 *2 (-1201 *4)) (-5 *1 (-369 *4)) - (-4 *4 (-363))))) -(((*1 *2 *2) - (-12 (-4 *3 (-466)) (-5 *1 (-1239 *3 *2)) - (-4 *2 (-13 (-435 *3) (-1233)))))) + (-12 (-4 *5 (-466)) (-4 *6 (-815)) (-4 *7 (-871)) + (-4 *3 (-1096 *5 *6 *7)) (-5 *2 (-114)) + (-5 *1 (-1103 *5 *6 *7 *3 *4)) (-4 *4 (-1102 *5 *6 *7 *3)))) + ((*1 *2 *3 *4) + (-12 (-4 *5 (-466)) (-4 *6 (-815)) (-4 *7 (-871)) + (-4 *3 (-1096 *5 *6 *7)) + (-5 *2 (-663 (-2 (|:| |val| (-114)) (|:| -3611 *4)))) + (-5 *1 (-1103 *5 *6 *7 *3 *4)) (-4 *4 (-1102 *5 *6 *7 *3))))) (((*1 *2 *2) (-12 (-4 *3 (-466)) (-5 *1 (-1239 *3 *2)) (-4 *2 (-13 (-435 *3) (-1233)))))) -(((*1 *2 *3 *4 *4 *4 *3) - (-12 (-5 *3 (-560)) (-5 *4 (-711 (-229))) (-5 *2 (-1066)) - (-5 *1 (-773))))) +(((*1 *1 *2) (-12 (-5 *2 (-663 *3)) (-4 *3 (-871)) (-5 *1 (-498 *3))))) +(((*1 *1) (-5 *1 (-143)))) +(((*1 *2 *1) + (-12 (-4 *3 (-1132)) (-4 *4 (-13 (-1080) (-911 *3) (-633 (-915 *3)))) + (-5 *2 (-663 (-1207))) (-5 *1 (-1106 *3 *4 *5)) + (-4 *5 (-13 (-435 *4) (-911 *3) (-633 (-915 *3))))))) +(((*1 *2 *3) + (|partial| -12 (-5 *3 (-948)) + (-5 *2 (-1297 (-663 (-2 (|:| -1420 *4) (|:| -3998 (-1151)))))) + (-5 *1 (-360 *4)) (-4 *4 (-363))))) +(((*1 *2 *3) + (-12 (-5 *3 (-663 (-663 (-972 (-229))))) + (-5 *2 (-663 (-1120 (-229)))) (-5 *1 (-957))))) +(((*1 *2) (-12 (-5 *2 (-898)) (-5 *1 (-1302)))) + ((*1 *2 *2) (-12 (-5 *2 (-898)) (-5 *1 (-1302))))) +(((*1 *2 *2 *2) + (-12 (-4 *2 (-13 (-376) (-10 -8 (-15 ** ($ $ (-421 (-560))))))) + (-5 *1 (-1159 *3 *2)) (-4 *3 (-1273 *2))))) +(((*1 *1 *2) + (-12 (-5 *2 (-663 (-2 (|:| -3835 *3) (|:| -2923 *4)))) + (-4 *3 (-1132)) (-4 *4 (-1132)) (-4 *1 (-1224 *3 *4)))) + ((*1 *1) (-12 (-4 *1 (-1224 *2 *3)) (-4 *2 (-1132)) (-4 *3 (-1132))))) (((*1 *2 *1) (-12 (-4 *1 (-984)) (-5 *2 (-1120 (-229))))) ((*1 *2 *1) (-12 (-4 *1 (-1005)) (-5 *2 (-1120 (-229)))))) (((*1 *1 *1) (-4 *1 (-35))) @@ -10128,44 +9740,38 @@ ((*1 *2 *2) (-12 (-5 *2 (-1185 *3)) (-4 *3 (-38 (-421 (-560)))) (-5 *1 (-1193 *3))))) -(((*1 *2 *3 *4 *5 *5 *2) - (|partial| -12 (-5 *2 (-114)) (-5 *3 (-975 *6)) (-5 *4 (-1207)) - (-5 *5 (-864 *7)) - (-4 *6 (-13 (-466) (-1069 (-560)) (-660 (-560)))) - (-4 *7 (-13 (-1233) (-29 *6))) (-5 *1 (-228 *6 *7)))) - ((*1 *2 *3 *4 *4 *2) - (|partial| -12 (-5 *2 (-114)) (-5 *3 (-1201 *6)) (-5 *4 (-864 *6)) - (-4 *6 (-13 (-1233) (-29 *5))) - (-4 *5 (-13 (-466) (-1069 (-560)) (-660 (-560)))) - (-5 *1 (-228 *5 *6))))) +(((*1 *2 *3 *4 *4 *3 *5 *3 *3 *3 *6) + (-12 (-5 *3 (-560)) (-5 *4 (-711 (-229))) (-5 *5 (-229)) + (-5 *6 (-3 (|:| |fn| (-402)) (|:| |fp| (-75 FUNCTN)))) + (-5 *2 (-1066)) (-5 *1 (-770))))) +(((*1 *2 *3 *4) + (-12 (-5 *3 (-419 *5)) (-4 *5 (-571)) + (-5 *2 + (-2 (|:| -4417 (-793)) (|:| -2326 *5) (|:| |radicand| (-663 *5)))) + (-5 *1 (-332 *5)) (-5 *4 (-793)))) + ((*1 *1 *1 *2) (-12 (-4 *1 (-1033)) (-5 *2 (-560))))) +(((*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 (-793)) (-5 *1 (-1195 *3 *4)) (-14 *3 (-948)) - (-4 *4 (-1080))))) -(((*1 *2 *3) - (-12 (-5 *3 (-711 (-421 (-975 (-560))))) - (-5 *2 (-663 (-711 (-326 (-560))))) (-5 *1 (-1059))))) -(((*1 *2 *3 *2) - (-12 (-5 *3 (-115)) (-4 *4 (-1080)) (-5 *1 (-736 *4 *2)) - (-4 *2 (-670 *4)))) - ((*1 *2 *3 *2) (-12 (-5 *3 (-115)) (-5 *1 (-856 *2)) (-4 *2 (-1080))))) -(((*1 *2 *3 *2) - (|partial| -12 (-5 *3 (-948)) (-5 *1 (-456 *2)) - (-4 *2 (-1273 (-560))))) - ((*1 *2 *3 *2 *4) - (|partial| -12 (-5 *3 (-948)) (-5 *4 (-793)) (-5 *1 (-456 *2)) - (-4 *2 (-1273 (-560))))) - ((*1 *2 *3 *2 *4) - (|partial| -12 (-5 *3 (-948)) (-5 *4 (-663 (-793))) (-5 *1 (-456 *2)) - (-4 *2 (-1273 (-560))))) - ((*1 *2 *3 *2 *4 *5) - (|partial| -12 (-5 *3 (-948)) (-5 *4 (-663 (-793))) (-5 *5 (-793)) - (-5 *1 (-456 *2)) (-4 *2 (-1273 (-560))))) - ((*1 *2 *3 *2 *4 *5 *6) - (|partial| -12 (-5 *3 (-948)) (-5 *4 (-663 (-793))) (-5 *5 (-793)) - (-5 *6 (-114)) (-5 *1 (-456 *2)) (-4 *2 (-1273 (-560))))) + (-12 (-5 *2 (-177 (-421 (-560)))) (-5 *1 (-119 *3)) (-14 *3 (-560)))) + ((*1 *1 *2 *3 *3) + (-12 (-5 *3 (-1185 *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 (-5 *2 (-177 (-560))) (-5 *1 (-787 *3)) (-4 *3 (-418)))) + ((*1 *2 *1) + (-12 (-5 *2 (-177 (-421 (-560)))) (-5 *1 (-895 *3)) (-14 *3 (-560)))) + ((*1 *2 *1) + (-12 (-14 *3 (-560)) (-5 *2 (-177 (-421 (-560)))) + (-5 *1 (-896 *3 *4)) (-4 *4 (-894 *3))))) +(((*1 *2 *3 *4) + (-12 (-4 *5 (-376)) (-4 *6 (-13 (-385 *5) (-10 -7 (-6 -4509)))) + (-4 *4 (-13 (-385 *5) (-10 -7 (-6 -4509)))) (-5 *2 (-114)) + (-5 *1 (-689 *5 *6 *4 *3)) (-4 *3 (-708 *5 *6 *4)))) ((*1 *2 *3 *4) - (-12 (-5 *3 (-948)) (-5 *4 (-419 *2)) (-4 *2 (-1273 *5)) - (-5 *1 (-458 *5 *2)) (-4 *5 (-1080))))) + (-12 (-5 *3 (-711 *5)) (-5 *4 (-1297 *5)) (-4 *5 (-376)) + (-5 *2 (-114)) (-5 *1 (-690 *5))))) (((*1 *1 *2 *1) (-12 (-5 *2 (-1 (-114) *3)) (|has| *1 (-6 -4508)) (-4 *1 (-153 *3)) (-4 *3 (-1247)))) @@ -10178,21 +9784,23 @@ (-4 *5 (-815)) (-4 *3 (-871)) (-4 *2 (-1096 *4 *5 *3)))) ((*1 *2 *1 *3) (-12 (-5 *3 (-793)) (-5 *1 (-1245 *2)) (-4 *2 (-1247))))) -(((*1 *2 *3 *3 *3 *3 *3 *3 *3 *3 *4 *5 *5 *5 *5 *5 *5 *6 *6 *6 *3 *3 *5 - *7 *3 *8) - (-12 (-5 *5 (-711 (-229))) (-5 *6 (-114)) (-5 *7 (-711 (-560))) - (-5 *8 (-3 (|:| |fn| (-402)) (|:| |fp| (-65 QPHESS)))) - (-5 *3 (-560)) (-5 *4 (-229)) (-5 *2 (-1066)) (-5 *1 (-775))))) -(((*1 *2 *1) (-12 (-5 *2 (-114)) (-5 *1 (-1212))))) -(((*1 *2 *3) - (-12 (-5 *2 (-114)) (-5 *1 (-456 *3)) (-4 *3 (-1273 (-560)))))) -(((*1 *2 *1 *1 *3) (-12 (-4 *1 (-1175)) (-5 *3 (-146)) (-5 *2 (-114))))) -(((*1 *2 *1 *3 *2) - (-12 (-5 *3 (-793)) (-5 *1 (-216 *4 *2)) (-14 *4 (-948)) - (-4 *2 (-1132))))) -(((*1 *2 *3 *4) - (|partial| -12 (-5 *3 (-1297 *4)) (-4 *4 (-13 (-1080) (-660 (-560)))) - (-5 *2 (-1297 (-421 (-560)))) (-5 *1 (-1326 *4))))) +(((*1 *1 *1 *1) (-4 *1 (-487))) ((*1 *1 *1 *1) (-4 *1 (-783)))) +(((*1 *1 *1 *1 *2) + (-12 (-5 *2 (-793)) (-4 *1 (-1096 *3 *4 *5)) (-4 *3 (-1080)) + (-4 *4 (-815)) (-4 *5 (-871)) (-4 *3 (-571))))) +(((*1 *1 *1) + (-12 (-4 *2 (-363)) (-4 *2 (-1080)) (-5 *1 (-734 *2 *3)) + (-4 *3 (-1273 *2))))) +(((*1 *2 *1) (-12 (-4 *1 (-984)) (-5 *2 (-1120 (-229))))) + ((*1 *2 *1) (-12 (-4 *1 (-1005)) (-5 *2 (-1120 (-229)))))) +(((*1 *2 *1) (-12 (-5 *2 (-114)) (-5 *1 (-291)))) + ((*1 *2 *1) (-12 (-5 *2 (-114)) (-5 *1 (-915 *3)) (-4 *3 (-1132)))) + ((*1 *2 *1) + (-12 (-4 *1 (-1317 *3 *4)) (-4 *3 (-871)) (-4 *4 (-1080)) + (-5 *2 (-114)))) + ((*1 *2 *1) + (-12 (-5 *2 (-114)) (-5 *1 (-1321 *3 *4)) (-4 *3 (-1080)) + (-4 *4 (-868))))) (((*1 *1 *1) (-4 *1 (-35))) ((*1 *2 *2) (-12 (-4 *3 (-571)) (-5 *1 (-287 *3 *2)) @@ -10209,48 +9817,32 @@ ((*1 *2 *2) (-12 (-5 *2 (-1185 *3)) (-4 *3 (-38 (-421 (-560)))) (-5 *1 (-1193 *3))))) -(((*1 *2 *3 *3 *4) - (|partial| -12 (-5 *4 (-1 *6 *6)) (-4 *6 (-1273 *5)) - (-4 *5 (-13 (-376) (-149) (-1069 (-560)))) - (-5 *2 - (-2 (|:| |a| *6) (|:| |b| (-421 *6)) (|:| |c| (-421 *6)) - (|:| -4063 *6))) - (-5 *1 (-1046 *5 *6)) (-5 *3 (-421 *6))))) -(((*1 *2 *3) - (-12 (-5 *3 (-663 (-948))) (-5 *2 (-934 (-560))) (-5 *1 (-946))))) -(((*1 *1) (-5 *1 (-1301)))) +(((*1 *2 *3 *4) + (-12 (-5 *3 (-663 *6)) (-5 *4 (-663 (-1185 *7))) (-4 *6 (-871)) + (-4 *7 (-979 *5 (-545 *6) *6)) (-4 *5 (-1080)) + (-5 *2 (-1 (-1185 *7) *7)) (-5 *1 (-1157 *5 *6 *7))))) +(((*1 *2 *2) + (-12 (-4 *3 (-571)) (-5 *1 (-287 *3 *2)) + (-4 *2 (-13 (-435 *3) (-1033)))))) (((*1 *1 *2 *1) (-12 (-5 *2 (-1 (-114) *3)) (-4 *3 (-1247)) (-5 *1 (-615 *3)))) ((*1 *1 *2 *1) (-12 (-5 *2 (-1 (-114) *3)) (-4 *3 (-1247)) (-5 *1 (-1185 *3))))) -(((*1 *2 *3 *4) - (-12 (-5 *3 (-305 (-421 (-975 *5)))) (-5 *4 (-1207)) - (-4 *5 (-13 (-319) (-149))) - (-5 *2 (-1196 (-663 (-326 *5)) (-663 (-305 (-326 *5))))) - (-5 *1 (-1160 *5)))) - ((*1 *2 *3 *4) - (-12 (-5 *3 (-421 (-975 *5))) (-5 *4 (-1207)) - (-4 *5 (-13 (-319) (-149))) - (-5 *2 (-1196 (-663 (-326 *5)) (-663 (-305 (-326 *5))))) - (-5 *1 (-1160 *5))))) +(((*1 *2 *3 *3 *4 *4 *4 *4 *3) + (-12 (-5 *3 (-560)) (-5 *4 (-711 (-229))) (-5 *2 (-1066)) + (-5 *1 (-774))))) +(((*1 *2 *1) (-12 (-4 *1 (-569 *2)) (-4 *2 (-13 (-418) (-1233))))) + ((*1 *2) (-12 (-5 *2 (-560)) (-5 *1 (-887)))) + ((*1 *2 *1) (-12 (-5 *2 (-560)) (-5 *1 (-887))))) +(((*1 *2 *3 *4 *4 *4 *4 *5 *5 *4) + (-12 (-5 *3 (-1189)) (-5 *4 (-560)) (-5 *5 (-711 (-229))) + (-5 *2 (-1066)) (-5 *1 (-776))))) (((*1 *2 *3) - (-12 (-4 *4 (-13 (-571) (-1069 (-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) (-1069 (-560)))) (-5 *2 (-1201 (-421 (-560)))) - (-5 *1 (-447 *5 *3))))) -(((*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 (-1247)))) - ((*1 *2 *1 *3) - (-12 (-5 *3 (-793)) (-4 *2 (-1132)) (-5 *1 (-216 *4 *2)) - (-14 *4 (-948)))) - ((*1 *2 *1 *3) - (-12 (-4 *1 (-300 *3 *2)) (-4 *3 (-1132)) (-4 *2 (-1247)))) - ((*1 *2 *1 *3 *3) - (-12 (-5 *3 (-560)) (-4 *1 (-1084 *4 *5 *2 *6 *7)) - (-4 *6 (-245 *5 *2)) (-4 *7 (-245 *4 *2)) (-4 *2 (-1080))))) + (-12 (-5 *3 (-1207)) (-5 *2 (-1 *6 *5)) (-5 *1 (-728 *4 *5 *6)) + (-4 *4 (-633 (-549))) (-4 *5 (-1247)) (-4 *6 (-1247))))) +(((*1 *2 *1 *3 *2) + (-12 (-5 *3 (-793)) (-5 *1 (-216 *4 *2)) (-14 *4 (-948)) + (-4 *2 (-1132))))) (((*1 *1 *1) (-4 *1 (-35))) ((*1 *2 *2) (-12 (-4 *3 (-571)) (-5 *1 (-287 *3 *2)) @@ -10267,45 +9859,44 @@ ((*1 *2 *2) (-12 (-5 *2 (-1185 *3)) (-4 *3 (-38 (-421 (-560)))) (-5 *1 (-1193 *3))))) -(((*1 *2 *1) - (-12 (-4 *1 (-338 *3 *4)) (-4 *3 (-1080)) (-4 *4 (-814)) - (-5 *2 (-793)))) - ((*1 *2 *1) - (-12 (-4 *1 (-397 *3 *4)) (-4 *3 (-1080)) (-4 *4 (-1132)) - (-5 *2 (-793)))) - ((*1 *2 *1) - (-12 (-5 *2 (-793)) (-5 *1 (-757 *3 *4)) (-4 *3 (-1080)) - (-4 *4 (-748))))) -(((*1 *2 *3 *3 *4 *5 *3 *6) - (-12 (-5 *3 (-560)) (-5 *4 (-711 (-229))) (-5 *5 (-229)) - (-5 *6 (-3 (|:| |fn| (-402)) (|:| |fp| (-81 FCN)))) (-5 *2 (-1066)) - (-5 *1 (-768))))) -(((*1 *1 *1) (-12 (-4 *1 (-680 *2)) (-4 *2 (-1080)) (-4 *2 (-376))))) -(((*1 *2 *1) - (-12 (-5 *2 (-663 (-2 (|:| |k| (-1207)) (|:| |c| (-1319 *3))))) - (-5 *1 (-1319 *3)) (-4 *3 (-1080)))) - ((*1 *2 *1) - (-12 (-5 *2 (-663 (-2 (|:| |k| *3) (|:| |c| (-1322 *3 *4))))) - (-5 *1 (-1322 *3 *4)) (-4 *3 (-871)) (-4 *4 (-1080))))) (((*1 *2 *3 *4) - (-12 (-5 *3 (-1207)) (-4 *5 (-376)) (-5 *2 (-1185 (-1185 (-975 *5)))) - (-5 *1 (-1306 *5)) (-5 *4 (-1185 (-975 *5)))))) + (-12 (-5 *3 (-1 *6 *4 *5)) (-4 *4 (-1132)) (-4 *5 (-1132)) + (-4 *6 (-1132)) (-5 *2 (-1 *6 *5)) (-5 *1 (-706 *4 *5 *6))))) +(((*1 *2 *1) (-12 (-5 *2 (-345)) (-5 *1 (-257))))) +(((*1 *1 *1 *2 *3) + (-12 (-5 *3 (-1 (-663 *2) *2 *2 *2)) (-4 *2 (-1132)) + (-5 *1 (-103 *2)))) + ((*1 *1 *1 *2 *3) + (-12 (-5 *3 (-1 *2 *2 *2)) (-4 *2 (-1132)) (-5 *1 (-103 *2))))) +(((*1 *2 *3 *4) + (-12 (-4 *5 (-1132)) (-4 *2 (-927 *5)) (-5 *1 (-714 *5 *2 *3 *4)) + (-4 *3 (-385 *2)) (-4 *4 (-13 (-385 *5) (-10 -7 (-6 -4508))))))) +(((*1 *2 *3) + (-12 (-4 *4 (-571)) (-5 *2 (-793)) (-5 *1 (-43 *4 *3)) + (-4 *3 (-432 *4))))) +(((*1 *2 *3 *4 *4) + (-12 (-5 *3 (-1 *2 *2 *2)) (-4 *2 (-1290 *4)) (-5 *1 (-1291 *4 *2)) + (-4 *4 (-38 (-421 (-560))))))) (((*1 *1 *2 *1) (-12 (-5 *2 (-1 (-114) *3)) (-4 *3 (-1247)) (-5 *1 (-615 *3)))) ((*1 *1 *2 *1) (-12 (-5 *2 (-1 (-114) *3)) (-4 *3 (-1247)) (-5 *1 (-1185 *3))))) -(((*1 *1) - (-12 (-5 *1 (-137 *2 *3 *4)) (-14 *2 (-560)) (-14 *3 (-793)) - (-4 *4 (-175))))) -(((*1 *2 *1) (-12 (-4 *1 (-569 *2)) (-4 *2 (-13 (-418) (-1233))))) - ((*1 *2) (-12 (-5 *2 (-560)) (-5 *1 (-887)))) - ((*1 *2 *1) (-12 (-5 *2 (-560)) (-5 *1 (-887))))) -(((*1 *2 *3 *1) - (-12 (-4 *1 (-1242 *4 *5 *3 *6)) (-4 *4 (-571)) (-4 *5 (-815)) - (-4 *3 (-871)) (-4 *6 (-1096 *4 *5 *3)) (-5 *2 (-114)))) - ((*1 *2 *1) (-12 (-4 *1 (-1316 *3)) (-4 *3 (-376)) (-5 *2 (-114))))) -(((*1 *2 *1) - (-12 (-5 *2 (-663 (-51))) (-5 *1 (-915 *3)) (-4 *3 (-1132))))) +(((*1 *2 *3 *3 *3 *3 *3 *4 *4 *4 *5) + (-12 (-5 *3 (-229)) (-5 *4 (-560)) + (-5 *5 (-3 (|:| |fn| (-402)) (|:| |fp| (-61 G)))) (-5 *2 (-1066)) + (-5 *1 (-770))))) +(((*1 *2 *2) (-12 (-5 *2 (-326 (-229))) (-5 *1 (-278))))) +(((*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 (-1247)))) + ((*1 *2 *1 *3) + (-12 (-5 *3 (-793)) (-4 *2 (-1132)) (-5 *1 (-216 *4 *2)) + (-14 *4 (-948)))) + ((*1 *2 *1 *3) + (-12 (-4 *1 (-300 *3 *2)) (-4 *3 (-1132)) (-4 *2 (-1247)))) + ((*1 *2 *1 *3 *3) + (-12 (-5 *3 (-560)) (-4 *1 (-1084 *4 *5 *2 *6 *7)) + (-4 *6 (-245 *5 *2)) (-4 *7 (-245 *4 *2)) (-4 *2 (-1080))))) (((*1 *2 *2) (-12 (-4 *3 (-571)) (-5 *1 (-287 *3 *2)) (-4 *2 (-13 (-435 *3) (-1033))))) @@ -10322,18 +9913,15 @@ ((*1 *2 *2) (-12 (-5 *2 (-1185 *3)) (-4 *3 (-38 (-421 (-560)))) (-5 *1 (-1193 *3))))) -(((*1 *2 *3) - (-12 (-5 *3 (-663 *2)) (-4 *2 (-1273 *4)) (-5 *1 (-553 *4 *2 *5 *6)) - (-4 *4 (-319)) (-14 *5 *4) (-14 *6 (-1 *4 *4 (-793)))))) -(((*1 *2 *3) - (-12 (-5 *3 |RationalNumber|) (-5 *2 (-1 (-560))) (-5 *1 (-1078))))) -(((*1 *2 *2 *2) - (-12 (-5 *2 (-711 *3)) - (-4 *3 (-13 (-319) (-10 -8 (-15 -2617 ((-419 $) $))))) - (-4 *4 (-1273 *3)) (-5 *1 (-513 *3 *4 *5)) (-4 *5 (-424 *3 *4))))) -(((*1 *2 *1 *3 *4) - (-12 (-5 *3 (-948)) (-5 *4 (-1189)) (-5 *2 (-1303)) (-5 *1 (-1300))))) -(((*1 *2 *3 *3) (-12 (-5 *3 (-1151)) (-5 *2 (-1303)) (-5 *1 (-853))))) +(((*1 *1 *1 *1) (-12 (-4 *1 (-876 *2)) (-4 *2 (-1080)) (-4 *2 (-376))))) +(((*1 *1) (-5 *1 (-624)))) +(((*1 *2 *2) (-12 (-5 *2 (-402)) (-5 *1 (-451)))) + ((*1 *2 *2 *2) (-12 (-5 *2 (-402)) (-5 *1 (-451))))) +(((*1 *2 *3 *2) (-12 (-5 *3 (-793)) (-5 *1 (-880 *2)) (-4 *2 (-175)))) + ((*1 *2 *3 *3 *2) + (-12 (-5 *3 (-793)) (-5 *1 (-880 *2)) (-4 *2 (-175))))) +(((*1 *1 *2 *3) (-12 (-5 *2 (-793)) (-5 *1 (-58 *3)) (-4 *3 (-1247)))) + ((*1 *1 *2) (-12 (-5 *2 (-663 *3)) (-4 *3 (-1247)) (-5 *1 (-58 *3))))) (((*1 *2 *3 *4) (-12 (-5 *4 (-948)) (-4 *6 (-571)) (-5 *2 (-663 (-326 *6))) (-5 *1 (-225 *5 *6)) (-5 *3 (-326 *6)) (-4 *5 (-1080)))) @@ -10359,22 +9947,28 @@ ((*1 *2 *1) (-12 (-5 *2 (-1313 *3 *4)) (-5 *1 (-1322 *3 *4)) (-4 *3 (-871)) (-4 *4 (-1080))))) -(((*1 *2 *2 *3) - (|partial| -12 (-5 *2 (-663 (-1201 *5))) (-5 *3 (-1201 *5)) - (-4 *5 (-168 *4)) (-4 *4 (-559)) (-5 *1 (-151 *4 *5)))) - ((*1 *2 *2 *3) - (|partial| -12 (-5 *2 (-663 *3)) (-4 *3 (-1273 *5)) - (-4 *5 (-1273 *4)) (-4 *4 (-363)) (-5 *1 (-371 *4 *5 *3)))) - ((*1 *2 *2 *3) - (|partial| -12 (-5 *2 (-663 (-1201 (-560)))) (-5 *3 (-1201 (-560))) - (-5 *1 (-586)))) - ((*1 *2 *2 *3) - (|partial| -12 (-5 *2 (-663 (-1201 *1))) (-5 *3 (-1201 *1)) - (-4 *1 (-939))))) +(((*1 *2 *3 *4) + (-12 (-5 *3 (-1201 (-975 *6))) (-4 *6 (-571)) + (-4 *2 (-979 (-421 (-975 *6)) *5 *4)) (-5 *1 (-754 *5 *4 *6 *2)) + (-4 *5 (-815)) + (-4 *4 (-13 (-871) (-10 -8 (-15 -2106 ((-1207) $)))))))) +(((*1 *2 *1) (-12 (-5 *2 (-1166)) (-5 *1 (-139)))) + ((*1 *2 *1) (-12 (-5 *2 (-1248)) (-5 *1 (-158)))) + ((*1 *2 *1) (-12 (-5 *1 (-305 *2)) (-4 *2 (-1247)))) + ((*1 *2 *1) (-12 (-5 *2 (-1166)) (-5 *1 (-492)))) + ((*1 *2 *1) (-12 (-5 *2 (-1166)) (-5 *1 (-606)))) + ((*1 *2 *1) (-12 (-5 *2 (-1166)) (-5 *1 (-645)))) + ((*1 *2 *1) + (-12 (-4 *3 (-1132)) + (-4 *2 (-13 (-435 *4) (-911 *3) (-633 (-915 *3)))) + (-5 *1 (-1106 *3 *4 *2)) + (-4 *4 (-13 (-1080) (-911 *3) (-633 (-915 *3)))))) + ((*1 *2 *1) + (-12 (-4 *2 (-1132)) (-5 *1 (-1196 *3 *2)) (-4 *3 (-1132))))) (((*1 *2 *3) (-12 (-5 *3 - (-2 (|:| |lfn| (-663 (-326 (-229)))) (|:| -1986 (-663 (-229))))) + (-2 (|:| |lfn| (-663 (-326 (-229)))) (|:| -1981 (-663 (-229))))) (-5 *2 (-663 (-1207))) (-5 *1 (-278)))) ((*1 *2 *3) (-12 (-5 *3 (-1201 *7)) (-4 *7 (-979 *6 *4 *5)) (-4 *4 (-815)) @@ -10396,7 +9990,7 @@ (-5 *1 (-980 *4 *5 *6 *7 *3)) (-4 *3 (-13 (-376) - (-10 -8 (-15 -4272 ($ *7)) (-15 -2167 (*7 $)) (-15 -2180 (*7 $))))))) + (-10 -8 (-15 -2383 ($ *7)) (-15 -2158 (*7 $)) (-15 -2171 (*7 $))))))) ((*1 *2 *1) (-12 (-4 *1 (-1004 *3 *4 *5)) (-4 *3 (-1080)) (-4 *4 (-814)) (-4 *5 (-871)) (-5 *2 (-663 *5)))) @@ -10406,8 +10000,15 @@ ((*1 *2 *3) (-12 (-5 *3 (-421 (-975 *4))) (-4 *4 (-571)) (-5 *2 (-663 (-1207))) (-5 *1 (-1071 *4))))) -(((*1 *1) (-12 (-4 *1 (-1076 *2)) (-4 *2 (-23))))) -(((*1 *1) (-5 *1 (-624)))) +(((*1 *2 *3) + (-12 (-4 *4 (-939)) (-4 *5 (-815)) (-4 *6 (-871)) + (-4 *7 (-979 *4 *5 *6)) (-5 *2 (-419 (-1201 *7))) + (-5 *1 (-936 *4 *5 *6 *7)) (-5 *3 (-1201 *7)))) + ((*1 *2 *3) + (-12 (-4 *4 (-939)) (-4 *5 (-1273 *4)) (-5 *2 (-419 (-1201 *5))) + (-5 *1 (-937 *4 *5)) (-5 *3 (-1201 *5))))) +(((*1 *2 *1) + (-12 (-5 *2 (-1128 (-1128 *3))) (-5 *1 (-934 *3)) (-4 *3 (-1132))))) (((*1 *2 *2) (-12 (-4 *3 (-571)) (-5 *1 (-287 *3 *2)) (-4 *2 (-13 (-435 *3) (-1033))))) @@ -10424,24 +10025,95 @@ ((*1 *2 *2) (-12 (-5 *2 (-1185 *3)) (-4 *3 (-38 (-421 (-560)))) (-5 *1 (-1193 *3))))) +(((*1 *1 *2) + (-12 (-5 *2 (-711 *5)) (-4 *5 (-1080)) (-5 *1 (-1085 *3 *4 *5)) + (-14 *3 (-793)) (-14 *4 (-793))))) +(((*1 *1 *2) + (-12 + (-5 *2 + (-663 + (-2 + (|:| -3835 + (-2 (|:| |var| (-1207)) (|:| |fn| (-326 (-229))) + (|:| -2016 (-1120 (-864 (-229)))) (|:| |abserr| (-229)) + (|:| |relerr| (-229)))) + (|:| -2923 + (-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| (-1185 (-229))) + (|:| |notEvaluated| + "Internal singularities not yet evaluated"))) + (|:| -2016 + (-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 (-5 *2 (-887)) (-5 *1 (-404 *3 *4 *5)) (-14 *3 (-793)) - (-14 *4 (-793)) (-4 *5 (-175))))) -(((*1 *2 *2) (-12 (-5 *2 (-560)) (-5 *1 (-954))))) -(((*1 *2 *1) - (-12 (-4 *3 (-376)) (-4 *4 (-1273 *3)) (-4 *5 (-1273 (-421 *4))) - (-5 *2 (-1297 *6)) (-5 *1 (-346 *3 *4 *5 *6)) - (-4 *6 (-355 *3 *4 *5))))) -(((*1 *2 *1 *3 *3 *3 *2) - (-12 (-5 *3 (-793)) (-5 *1 (-697 *2)) (-4 *2 (-1132))))) -(((*1 *2 *1) (-12 (-4 *1 (-403)) (-5 *2 (-114))))) -(((*1 *2 *2) - (-12 (-4 *3 (-466)) (-5 *1 (-1239 *3 *2)) - (-4 *2 (-13 (-435 *3) (-1233)))))) + (|partial| -12 (-4 *3 (-25)) (-4 *3 (-1132)) + (-5 *2 (-2 (|:| -2326 (-560)) (|:| |var| (-630 *1)))) + (-4 *1 (-435 *3))))) +(((*1 *2 *2 *2 *3) + (-12 (-5 *2 (-711 *3)) (-4 *3 (-1080)) (-5 *1 (-712 *3))))) +(((*1 *2 *3 *4) + (-12 (-5 *4 (-560)) (-4 *2 (-435 *3)) (-5 *1 (-32 *3 *2)) + (-4 *3 (-1069 *4)) (-4 *3 (-571))))) +(((*1 *2 *3) + (-12 + (-5 *2 + (-663 (-2 (|:| -2788 (-421 (-560))) (|:| -2802 (-421 (-560)))))) + (-5 *1 (-1052 *3)) (-4 *3 (-1273 (-560))))) + ((*1 *2 *3 *4) + (-12 + (-5 *2 + (-663 (-2 (|:| -2788 (-421 (-560))) (|:| -2802 (-421 (-560)))))) + (-5 *1 (-1052 *3)) (-4 *3 (-1273 (-560))) + (-5 *4 (-2 (|:| -2788 (-421 (-560))) (|:| -2802 (-421 (-560))))))) + ((*1 *2 *3 *4) + (-12 + (-5 *2 + (-663 (-2 (|:| -2788 (-421 (-560))) (|:| -2802 (-421 (-560)))))) + (-5 *1 (-1052 *3)) (-4 *3 (-1273 (-560))) (-5 *4 (-421 (-560))))) + ((*1 *2 *3 *4 *5) + (-12 (-5 *5 (-421 (-560))) + (-5 *2 (-663 (-2 (|:| -2788 *5) (|:| -2802 *5)))) (-5 *1 (-1052 *3)) + (-4 *3 (-1273 (-560))) (-5 *4 (-2 (|:| -2788 *5) (|:| -2802 *5))))) + ((*1 *2 *3) + (-12 + (-5 *2 + (-663 (-2 (|:| -2788 (-421 (-560))) (|:| -2802 (-421 (-560)))))) + (-5 *1 (-1053 *3)) (-4 *3 (-1273 (-421 (-560)))))) + ((*1 *2 *3 *4) + (-12 + (-5 *2 + (-663 (-2 (|:| -2788 (-421 (-560))) (|:| -2802 (-421 (-560)))))) + (-5 *1 (-1053 *3)) (-4 *3 (-1273 (-421 (-560)))) + (-5 *4 (-2 (|:| -2788 (-421 (-560))) (|:| -2802 (-421 (-560))))))) + ((*1 *2 *3 *4) + (-12 (-5 *4 (-421 (-560))) + (-5 *2 (-663 (-2 (|:| -2788 *4) (|:| -2802 *4)))) (-5 *1 (-1053 *3)) + (-4 *3 (-1273 *4)))) + ((*1 *2 *3 *4 *5) + (-12 (-5 *5 (-421 (-560))) + (-5 *2 (-663 (-2 (|:| -2788 *5) (|:| -2802 *5)))) (-5 *1 (-1053 *3)) + (-4 *3 (-1273 *5)) (-5 *4 (-2 (|:| -2788 *5) (|:| -2802 *5)))))) (((*1 *2 *3) (-12 (-5 *2 (-1 *3 *3)) (-5 *1 (-544 *3)) (-4 *3 (-13 (-748) (-25)))))) (((*1 *2 *1) (-12 (-5 *2 (-1166)) (-5 *1 (-139)))) - ((*1 *2 *1) (-12 (-5 *2 (-1248)) (-5 *1 (-158)))) + ((*1 *2 *1) (-12 (-5 *2 (-1166)) (-5 *1 (-158)))) ((*1 *2 *1) (-12 (-5 *1 (-305 *2)) (-4 *2 (-1247)))) ((*1 *2 *1) (-12 (-5 *2 (-1166)) (-5 *1 (-492)))) ((*1 *2 *1) (-12 (-5 *2 (-1166)) (-5 *1 (-606)))) @@ -10452,7 +10124,7 @@ (-5 *1 (-1106 *3 *4 *2)) (-4 *4 (-13 (-1080) (-911 *3) (-633 (-915 *3)))))) ((*1 *2 *1) - (-12 (-4 *2 (-1132)) (-5 *1 (-1196 *3 *2)) (-4 *3 (-1132))))) + (-12 (-4 *2 (-1132)) (-5 *1 (-1196 *2 *3)) (-4 *3 (-1132))))) (((*1 *2 *3 *4 *2) (-12 (-5 *3 (-1201 (-421 (-1201 *2)))) (-5 *4 (-630 *2)) (-4 *2 (-13 (-435 *5) (-27) (-1233))) @@ -10469,17 +10141,18 @@ (-4 *6 (-1080)) (-4 *2 (-13 (-376) - (-10 -8 (-15 -4272 ($ *7)) (-15 -2167 (*7 $)) (-15 -2180 (*7 $))))) + (-10 -8 (-15 -2383 ($ *7)) (-15 -2158 (*7 $)) (-15 -2171 (*7 $))))) (-5 *1 (-980 *5 *4 *6 *7 *2)) (-4 *7 (-979 *6 *5 *4)))) ((*1 *2 *3 *4) (-12 (-5 *3 (-421 (-1201 (-421 (-975 *5))))) (-5 *4 (-1207)) (-5 *2 (-421 (-975 *5))) (-5 *1 (-1071 *5)) (-4 *5 (-571))))) -(((*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 *2) - (-12 (-4 *3 (-571)) (-5 *1 (-287 *3 *2)) - (-4 *2 (-13 (-435 *3) (-1033)))))) +(((*1 *2 *3) + (|partial| -12 (-5 *3 (-711 (-421 (-975 (-560))))) + (-5 *2 (-711 (-326 (-560)))) (-5 *1 (-1059))))) +(((*1 *2 *1) + (-12 (-4 *3 (-13 (-376) (-149))) + (-5 *2 (-663 (-2 (|:| -4417 (-793)) (|:| -3954 *4) (|:| |num| *4)))) + (-5 *1 (-413 *3 *4)) (-4 *4 (-1273 *3))))) (((*1 *2 *2) (-12 (-4 *3 (-571)) (-5 *1 (-287 *3 *2)) (-4 *2 (-13 (-435 *3) (-1033))))) @@ -10496,42 +10169,77 @@ ((*1 *2 *2) (-12 (-5 *2 (-1185 *3)) (-4 *3 (-38 (-421 (-560)))) (-5 *1 (-1193 *3))))) -(((*1 *1 *1 *2 *3) - (-12 (-5 *3 (-1 (-663 *2) *2 *2 *2)) (-4 *2 (-1132)) - (-5 *1 (-103 *2)))) - ((*1 *1 *1 *2 *3) - (-12 (-5 *3 (-1 *2 *2 *2)) (-4 *2 (-1132)) (-5 *1 (-103 *2))))) -(((*1 *2 *2) (-12 (-5 *2 (-402)) (-5 *1 (-451)))) - ((*1 *2 *2 *2) (-12 (-5 *2 (-402)) (-5 *1 (-451))))) -(((*1 *2 *1) - (|partial| -12 (-4 *3 (-25)) (-4 *3 (-1132)) - (-5 *2 (-2 (|:| -2338 (-560)) (|:| |var| (-630 *1)))) - (-4 *1 (-435 *3))))) +(((*1 *2 *3) + (-12 (-5 *3 (-255 *4 *5)) (-14 *4 (-663 (-1207))) (-4 *5 (-1080)) + (-5 *2 (-975 *5)) (-5 *1 (-973 *4 *5))))) +(((*1 *2 *1 *3 *4) + (-12 (-5 *3 (-948)) (-5 *4 (-898)) (-5 *2 (-1303)) (-5 *1 (-1300)))) + ((*1 *2 *1 *3 *4) + (-12 (-5 *3 (-948)) (-5 *4 (-1189)) (-5 *2 (-1303)) (-5 *1 (-1300)))) + ((*1 *2 *1 *3) (-12 (-5 *3 (-1189)) (-5 *2 (-1303)) (-5 *1 (-1301))))) (((*1 *2 *2 *2 *3) (-12 (-5 *2 (-1297 (-560))) (-5 *3 (-560)) (-5 *1 (-1141)))) ((*1 *2 *3 *2 *4) (-12 (-5 *2 (-1297 (-560))) (-5 *3 (-663 (-560))) (-5 *4 (-560)) (-5 *1 (-1141))))) -(((*1 *2 *1) - (-12 (-5 *2 (-114)) (-5 *1 (-50 *3 *4)) (-4 *3 (-1080)) - (-14 *4 (-663 (-1207))))) - ((*1 *2 *1) - (-12 (-5 *2 (-114)) (-5 *1 (-227 *3 *4)) (-4 *3 (-13 (-1080) (-871))) - (-14 *4 (-663 (-1207)))))) -(((*1 *2 *2) (|partial| -12 (-4 *1 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(-5 *2 (-1066)) + (-5 *1 (-769))))) (((*1 *2 *2) (-12 (-4 *3 (-571)) (-5 *1 (-287 *3 *2)) (-4 *2 (-13 (-435 *3) (-1033))))) @@ -10826,44 +10476,39 @@ ((*1 *2 *2) (-12 (-5 *2 (-1185 *3)) (-4 *3 (-38 (-421 (-560)))) (-5 *1 (-1193 *3))))) -(((*1 *2 *3 *4 *5) - (-12 (-5 *4 (-1 (-663 *7) *7 (-1201 *7))) (-5 *5 (-1 (-419 *7) *7)) - (-4 *7 (-1273 *6)) (-4 *6 (-13 (-376) (-149) (-1069 (-421 (-560))))) - (-5 *2 (-663 (-2 (|:| |frac| (-421 *7)) (|:| -2524 *3)))) - (-5 *1 (-831 *6 *7 *3 *8)) (-4 *3 (-680 *7)) - (-4 *8 (-680 (-421 *7))))) - ((*1 *2 *3 *4) - (-12 (-5 *4 (-1 (-419 *6) *6)) (-4 *6 (-1273 *5)) - (-4 *5 (-13 (-376) (-149) (-1069 (-560)) (-1069 (-421 (-560))))) - (-5 *2 - (-663 (-2 (|:| |frac| (-421 *6)) (|:| -2524 (-678 *6 (-421 *6)))))) - (-5 *1 (-834 *5 *6)) (-5 *3 (-678 *6 (-421 *6)))))) -(((*1 *2 *3 *4 *3 *3 *3 *3 *4 *3) - (-12 (-5 *3 (-560)) (-5 *4 (-711 (-171 (-229)))) (-5 *2 (-1066)) - (-5 *1 (-778))))) +(((*1 *2 *1) (-12 (-4 *1 (-310)) (-5 *2 (-663 (-115)))))) +(((*1 *1 *1 *2) + (-12 (-5 *2 (-114)) (-5 *1 (-1171 *3 *4)) (-4 *3 (-13 (-1132) (-34))) + (-4 *4 (-13 (-1132) (-34)))))) +(((*1 *2 *1) (-12 (-5 *2 (-1303)) (-5 *1 (-845))))) (((*1 *2 *1) - (-12 (-4 *1 (-1007 *3 *4 *2 *5)) (-4 *3 (-1080)) (-4 *4 (-815)) - (-4 *5 (-1096 *3 *4 *2)) (-4 *2 (-871)))) + (-12 (-4 *1 (-57 *3 *4 *5)) (-4 *3 (-1247)) (-4 *4 (-385 *3)) + (-4 *5 (-385 *3)) (-5 *2 (-560)))) ((*1 *2 *1) - (-12 (-4 *1 (-1096 *3 *4 *2)) (-4 *3 (-1080)) (-4 *4 (-815)) - (-4 *2 (-871))))) -(((*1 *2 *3 *4) - (-12 (-5 *3 (-663 (-1297 *5))) (-5 *4 (-560)) (-5 *2 (-1297 *5)) - (-5 *1 (-1061 *5)) (-4 *5 (-376)) (-4 *5 (-381)) (-4 *5 (-1080))))) -(((*1 *1) (-5 *1 (-146)))) + (-12 (-4 *1 (-1084 *3 *4 *5 *6 *7)) (-4 *5 (-1080)) + (-4 *6 (-245 *4 *5)) (-4 *7 (-245 *3 *5)) (-5 *2 (-560))))) +(((*1 *2 *3) + (-12 (-5 *3 (-663 (-2 (|:| |den| (-560)) (|:| |gcdnum| (-560))))) + (-4 *4 (-1273 (-421 *2))) (-5 *2 (-560)) (-5 *1 (-942 *4 *5)) + (-4 *5 (-1273 (-421 *4)))))) +(((*1 *1 *1) + (-12 (-5 *1 (-609 *2)) (-4 *2 (-38 (-421 (-560)))) (-4 *2 (-1080))))) (((*1 *1 *1 *2) (-12 (-5 *2 (-663 (-887))) (-5 *1 (-887))))) +(((*1 *2 *3 *4 *4 *2 *2 *2 *2) + (-12 (-5 *2 (-560)) + (-5 *3 + (-2 (|:| |lcmfij| *6) (|:| |totdeg| (-793)) (|:| |poli| *4) + (|:| |polj| *4))) + (-4 *6 (-815)) (-4 *4 (-979 *5 *6 *7)) (-4 *5 (-466)) (-4 *7 (-871)) + (-5 *1 (-464 *5 *6 *7 *4))))) +(((*1 *2 *1) (-12 (-5 *2 (-114)) (-5 *1 (-146))))) +(((*1 *2 *3 *3) + (-12 (|has| *2 (-6 (-4510 "*"))) (-4 *5 (-385 *2)) (-4 *6 (-385 *2)) + (-4 *2 (-1080)) (-5 *1 (-104 *2 *3 *4 *5 *6)) (-4 *3 (-1273 *2)) + (-4 *4 (-708 *2 *5 *6))))) (((*1 *2 *3) - (|partial| -12 (-5 *3 (-1189)) (-5 *2 (-391)) (-5 *1 (-808))))) -(((*1 *2 *3 *4 *4 *5 *6) - (-12 (-5 *3 (-663 (-663 (-972 (-229))))) (-5 *4 (-898)) - (-5 *5 (-948)) (-5 *6 (-663 (-270))) (-5 *2 (-482)) (-5 *1 (-1299)))) - ((*1 *2 *3) - (-12 (-5 *3 (-663 (-663 (-972 (-229))))) (-5 *2 (-482)) - (-5 *1 (-1299)))) - ((*1 *2 *3 *4) - (-12 (-5 *3 (-663 (-663 (-972 (-229))))) (-5 *4 (-663 (-270))) - (-5 *2 (-482)) (-5 *1 (-1299))))) -(((*1 *2 *2) (-12 (-5 *2 (-1189)) (-5 *1 (-781))))) + (-12 (-4 *4 (-571)) (-5 *2 (-793)) (-5 *1 (-43 *4 *3)) + (-4 *3 (-432 *4))))) (((*1 *1 *1) (-4 *1 (-95))) ((*1 *2 *2) (-12 (-4 *3 (-571)) (-5 *1 (-287 *3 *2)) @@ -10880,47 +10525,84 @@ ((*1 *2 *2) (-12 (-5 *2 (-1185 *3)) (-4 *3 (-38 (-421 (-560)))) (-5 *1 (-1193 *3))))) -(((*1 *1 *1) - (-12 (-4 *1 (-1096 *2 *3 *4)) (-4 *2 (-1080)) (-4 *3 (-815)) - (-4 *4 (-871)) (-4 *2 (-571))))) -(((*1 *2 *3 *4 *4 *4 *4 *5 *5) - (-12 (-5 *3 (-1 (-391) (-391))) (-5 *4 (-391)) - (-5 *2 - (-2 (|:| -1399 *4) (|:| -2747 *4) (|:| |totalpts| (-560)) - (|:| |success| (-114)))) - (-5 *1 (-811)) (-5 *5 (-560))))) (((*1 *2 *3 *4) - (-12 (-5 *3 (-663 *6)) (-5 *4 (-663 (-1207))) (-4 *6 (-376)) - (-5 *2 (-663 (-305 (-975 *6)))) (-5 *1 (-552 *5 *6 *7)) - (-4 *5 (-466)) (-4 *7 (-13 (-376) (-870)))))) -(((*1 *2 *2) - (-12 (-4 *3 (-466)) (-5 *1 (-1239 *3 *2)) - (-4 *2 (-13 (-435 *3) (-1233)))))) -(((*1 *1 *1) (-4 *1 (-34))) ((*1 *1 *1) 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+ ((*1 *2 *1 *3 *2) + (-12 (-5 *3 "value") (|has| *1 (-6 -4509)) (-4 *1 (-1041 *2)) + (-4 *2 (-1247)))) + ((*1 *2 *1 *2) (-12 (-5 *1 (-1057 *2)) (-4 *2 (-1247)))) + ((*1 *2 *1 *3 *2) + (-12 (-4 *1 (-1224 *3 *2)) (-4 *3 (-1132)) (-4 *2 (-1132)))) + ((*1 *2 *1 *3 *2) + (-12 (-5 *3 "last") (|has| *1 (-6 -4509)) (-4 *1 (-1286 *2)) + (-4 *2 (-1247)))) + ((*1 *1 *1 *2 *1) + (-12 (-5 *2 "rest") (|has| *1 (-6 -4509)) (-4 *1 (-1286 *3)) + (-4 *3 (-1247)))) + ((*1 *2 *1 *3 *2) + (-12 (-5 *3 "first") (|has| *1 (-6 -4509)) (-4 *1 (-1286 *2)) + (-4 *2 (-1247))))) +(((*1 *1 *2) (-12 (-5 *2 (-114)) (-5 *1 (-270)))) + ((*1 *2 *3 *2) + (-12 (-5 *2 (-114)) (-5 *3 (-663 (-270))) (-5 *1 (-271))))) (((*1 *2 *1) - (-12 (-5 *2 (-421 (-975 *3))) (-5 *1 (-467 *3 *4 *5 *6)) - (-4 *3 (-571)) (-4 *3 (-175)) (-14 *4 (-948)) - (-14 *5 (-663 (-1207))) (-14 *6 (-1297 (-711 *3)))))) -(((*1 *2) (-12 (-5 *2 (-663 (-948))) (-5 *1 (-1302)))) - ((*1 *2 *2) (-12 (-5 *2 (-663 (-948))) (-5 *1 (-1302))))) + (-12 (-4 *1 (-380 *3)) (-4 *3 (-175)) (-4 *3 (-571)) + (-5 *2 (-1201 *3))))) +(((*1 *2 *1) (-12 (-5 *2 (-663 (-187 (-141)))) (-5 *1 (-142))))) (((*1 *2 *1) (-12 (-5 *2 (-793)) (-5 *1 (-915 *3)) (-4 *3 (-1132)))) ((*1 *2 *1) (-12 (-4 *1 (-1152 *3)) (-4 *3 (-1247)) (-5 *2 (-793))))) (((*1 *2 *1) - (-12 (-5 *2 (-663 (-2 (|:| -3819 (-1207)) (|:| -2913 *4)))) + (-12 (-5 *2 (-663 (-2 (|:| -3835 (-1207)) (|:| -2923 *4)))) (-5 *1 (-913 *3 *4)) (-4 *3 (-1132)) (-4 *4 (-1132)))) ((*1 *2 *1) (-12 (-4 *3 (-1132)) (-4 *4 (-1132)) (-4 *5 (-1132)) (-4 *6 (-1132)) (-4 *7 (-1132)) (-5 *2 (-663 *1)) (-4 *1 (-1135 *3 *4 *5 *6 *7))))) -(((*1 *1 *1) - (-12 (-5 *1 (-609 *2)) (-4 *2 (-38 (-421 (-560)))) (-4 *2 (-1080))))) -(((*1 *2 *1) (-12 (-5 *2 (-663 (-663 (-972 (-229))))) (-5 *1 (-482))))) -(((*1 *2 *1) (-12 (-5 *2 (-114)) (-5 *1 (-291))))) +(((*1 *2 *1 *3 *3) + (-12 (-5 *3 (-159)) (-5 *2 (-1303)) (-5 *1 (-1301))))) +(((*1 *2 *3 *4 *4 *5 *3 *3 *3 *3 *3) + (-12 (-5 *3 (-560)) (-5 *5 (-711 (-229))) (-5 *4 (-229)) + (-5 *2 (-1066)) (-5 *1 (-774))))) +(((*1 *2 *3 *3 *4 *4 *4 *4) + (-12 (-5 *3 (-229)) (-5 *4 (-560)) (-5 *2 (-1066)) (-5 *1 (-770))))) (((*1 *1 *1) (-4 *1 (-95))) ((*1 *2 *2) (-12 (-4 *3 (-571)) (-5 *1 (-287 *3 *2)) @@ -10937,42 +10619,54 @@ ((*1 *2 *2) (-12 (-5 *2 (-1185 *3)) (-4 *3 (-38 (-421 (-560)))) (-5 *1 (-1193 *3))))) -(((*1 *2 *3 *3) - (-12 (-5 *3 (-1297 *5)) (-4 *5 (-814)) (-5 *2 (-114)) - (-5 *1 (-867 *4 *5)) (-14 *4 (-793))))) -(((*1 *2 *1) - (-12 (-5 *2 (-1297 (-793))) (-5 *1 (-697 *3)) (-4 *3 (-1132))))) -(((*1 *2 *2) - (-12 - (-5 *2 - (-2 (|:| |fn| (-326 (-229))) (|:| -1986 (-663 (-229))) - (|:| |lb| (-663 (-864 (-229)))) (|:| |cf| (-663 (-326 (-229)))) - (|:| |ub| (-663 (-864 (-229)))))) - (-5 *1 (-278))))) -(((*1 *2 *1) - (-12 (-4 *3 (-1080)) (-4 *4 (-1132)) (-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 (-1080)) - (-4 *4 (-748)))) +(((*1 *2 *3 *4 *5 *6 *7 *6) + (|partial| -12 + (-5 *5 + (-2 (|:| |contp| *3) + (|:| -1450 (-663 (-2 (|:| |irr| *10) (|:| -2817 (-560))))))) + (-5 *6 (-663 *3)) (-5 *7 (-663 *8)) (-4 *8 (-871)) (-4 *3 (-319)) + (-4 *10 (-979 *3 *9 *8)) (-4 *9 (-815)) + (-5 *2 + (-2 (|:| |polfac| (-663 *10)) (|:| |correct| *3) + (|:| |corrfact| (-663 (-1201 *3))))) + (-5 *1 (-644 *8 *9 *3 *10)) (-5 *4 (-663 (-1201 *3)))))) +(((*1 *1) (-5 *1 (-846)))) +(((*1 *2 *3 *4) + (-12 (-5 *3 (-229)) (-5 *4 (-560)) (-5 *2 (-1066)) (-5 *1 (-780))))) +(((*1 *2 *3) + (-12 (-5 *3 (-1266 *5 *4)) (-4 *4 (-466)) (-4 *4 (-842)) + (-14 *5 (-1207)) (-5 *2 (-560)) (-5 *1 (-1145 *4 *5))))) +(((*1 *2 *1) (-12 (-5 *2 (-114)) (-5 *1 (-610 *3)) (-4 *3 (-1080)))) ((*1 *2 *1) - (-12 (-4 *3 (-1080)) (-4 *4 (-815)) (-4 *5 (-871)) (-5 *2 (-663 *1)) - (-4 *1 (-979 *3 *4 *5))))) -(((*1 *2 *3 *3) (-12 (-5 *3 (-1189)) (-5 *2 (-391)) (-5 *1 (-97))))) -(((*1 *1 *2) - (-12 (-5 *2 (-663 (-663 *3))) (-4 *3 (-1132)) (-5 *1 (-931 *3))))) + (-12 (-4 *1 (-1004 *3 *4 *5)) (-4 *3 (-1080)) (-4 *4 (-814)) + (-4 *5 (-871)) (-5 *2 (-114))))) +(((*1 *2 *3 *3 *2) + (-12 (-5 *2 (-1185 *4)) (-5 *3 (-560)) (-4 *4 (-1080)) + (-5 *1 (-1191 *4)))) + ((*1 *1 *2 *2 *1) + (-12 (-5 *2 (-560)) (-5 *1 (-1287 *3 *4 *5)) (-4 *3 (-1080)) + (-14 *4 (-1207)) (-14 *5 *3)))) (((*1 *1 *2) (-12 (-5 *2 (-663 (-887))) (-5 *1 (-887)))) ((*1 *1 *1) (-5 *1 (-887))) ((*1 *1 *2) (-12 (-5 *2 (-663 *3)) (-4 *3 (-1132)) (-4 *1 (-1130 *3)))) ((*1 *1) (-12 (-4 *1 (-1130 *2)) (-4 *2 (-1132))))) -(((*1 *2 *3 *3) (-12 (-5 *3 (-1189)) (-5 *2 (-323)) (-5 *1 (-851))))) -(((*1 *2 *2 *2) - (-12 (-5 *2 (-663 *6)) (-4 *6 (-1096 *3 *4 *5)) (-4 *3 (-466)) - (-4 *3 (-571)) (-4 *4 (-815)) (-4 *5 (-871)) - (-5 *1 (-1008 *3 *4 *5 *6))))) -(((*1 *2 *2 *2) - (-12 (-5 *2 (-711 *3)) (-4 *3 (-1080)) (-5 *1 (-712 *3))))) +(((*1 *2 *2 *3) + (-12 (-4 *3 (-571)) (-4 *4 (-385 *3)) (-4 *5 (-385 *3)) + (-5 *1 (-1238 *3 *4 *5 *2)) (-4 *2 (-708 *3 *4 *5))))) +(((*1 *2 *3) + (-12 + (-5 *3 + (-518 (-421 (-560)) (-246 *5 (-793)) (-888 *4) + (-255 *4 (-421 (-560))))) + (-14 *4 (-663 (-1207))) (-14 *5 (-793)) (-5 *2 (-114)) + (-5 *1 (-519 *4 *5))))) +(((*1 *2 *1 *3) + (-12 (-4 *1 (-262 *4 *3 *5 *6)) (-4 *4 (-1080)) (-4 *3 (-871)) + (-4 *5 (-277 *3)) (-4 *6 (-815)) (-5 *2 (-663 (-793))))) + ((*1 *2 *1) + (-12 (-4 *1 (-262 *3 *4 *5 *6)) (-4 *3 (-1080)) (-4 *4 (-871)) + (-4 *5 (-277 *4)) (-4 *6 (-815)) (-5 *2 (-663 (-793)))))) (((*1 *1 *1) (-4 *1 (-95))) ((*1 *2 *2) (-12 (-4 *3 (-571)) (-5 *1 (-287 *3 *2)) @@ -10989,72 +10683,48 @@ ((*1 *2 *2) (-12 (-5 *2 (-1185 *3)) (-4 *3 (-38 (-421 (-560)))) (-5 *1 (-1193 *3))))) -(((*1 *2) - (-12 (-4 *4 (-175)) (-5 *2 (-114)) (-5 *1 (-379 *3 *4)) - (-4 *3 (-380 *4)))) - ((*1 *2) (-12 (-4 *1 (-380 *3)) (-4 *3 (-175)) (-5 *2 (-114))))) -(((*1 *1 *1) (-5 *1 (-1094)))) -(((*1 *1) (-5 *1 (-623)))) -(((*1 *2 *3 *3 *2) - (-12 (-5 *2 (-1185 *4)) (-5 *3 (-560)) (-4 *4 (-1080)) - (-5 *1 (-1191 *4)))) - ((*1 *1 *2 *2 *1) - (-12 (-5 *2 (-560)) (-5 *1 (-1287 *3 *4 *5)) (-4 *3 (-1080)) - (-14 *4 (-1207)) (-14 *5 *3)))) -(((*1 *2 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(-13 (-571) (-1069 (-560)))) (-5 *2 (-326 *4)) @@ -11207,12 +10864,15 @@ ((*1 *2 *2) (-12 (-4 *3 (-13 (-466) (-1069 (-560)) (-660 (-560)))) (-5 *1 (-1237 *3 *2)) (-4 *2 (-13 (-27) (-1233) (-435 *3)))))) -(((*1 *1 *1) (|partial| -4 *1 (-1182)))) -(((*1 *1 *2) (-12 (-5 *2 (-421 (-560))) (-5 *1 (-108)))) - ((*1 *1 *1 *2) (-12 (-5 *2 (-663 (-549))) (-5 *1 (-549))))) -(((*1 *2 *3 *4) - (-12 (-5 *3 (-1207)) (-5 *4 (-975 (-560))) (-5 *2 (-342)) - (-5 *1 (-344))))) +(((*1 *2 *2 *2) + (-12 (-4 *3 (-1080)) (-5 *1 (-1271 *3 *2)) (-4 *2 (-1273 *3))))) +(((*1 *1 *1 *1) (-5 *1 (-887)))) +(((*1 *2 *2) + (-12 (-5 *2 (-972 *3)) (-4 *3 (-13 (-376) (-1233) (-1033))) + (-5 *1 (-179 *3))))) +(((*1 *2 *2 *1) + (-12 (-4 *1 (-1242 *3 *4 *5 *2)) (-4 *3 (-571)) (-4 *4 (-815)) + (-4 *5 (-871)) (-4 *2 (-1096 *3 *4 *5))))) (((*1 *1 *1) (-4 *1 (-95))) ((*1 *2 *2) (-12 (-4 *3 (-571)) (-5 *1 (-287 *3 *2)) @@ -11232,58 +10892,24 @@ ((*1 *2 *2) (-12 (-5 *2 (-1185 *3)) (-4 *3 (-38 (-421 (-560)))) (-5 *1 (-1193 *3))))) 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(-560)))) (-5 *2 (-326 *4)) @@ -11293,42 +10919,15 @@ ((*1 *2 *2) (-12 (-4 *3 (-13 (-466) (-1069 (-560)) (-660 (-560)))) (-5 *1 (-1237 *3 *2)) (-4 *2 (-13 (-27) (-1233) (-435 *3)))))) -(((*1 *2 *3 *3) - (-12 (-4 *4 (-842)) (-14 *5 (-1207)) (-5 *2 (-663 (-1266 *5 *4))) - (-5 *1 (-1145 *4 *5)) (-5 *3 (-1266 *5 *4))))) -(((*1 *1 *1 *1) - (-12 (-4 *1 (-1096 *2 *3 *4)) (-4 *2 (-1080)) (-4 *3 (-815)) - (-4 *4 (-871)))) - ((*1 *2 *2 *1) - (-12 (-4 *1 (-1242 *3 *4 *5 *2)) (-4 *3 (-571)) (-4 *4 (-815)) - (-4 *5 (-871)) (-4 *2 (-1096 *3 *4 *5))))) -(((*1 *2 *2) - (-12 (-4 *3 (-13 (-466) (-1069 (-560)))) (-4 *3 (-571)) - (-5 *1 (-41 *3 *2)) (-4 *2 (-435 *3)) - (-4 *2 - (-13 (-376) (-310) - (-10 -8 (-15 -2167 ((-1156 *3 (-630 $)) $)) - (-15 -2180 ((-1156 *3 (-630 $)) $)) - (-15 -4272 ($ (-1156 *3 (-630 $)))))))))) +(((*1 *2 *1) + (-12 (-5 *2 (-793)) (-5 *1 (-1195 *3 *4)) (-14 *3 (-948)) + (-4 *4 (-1080))))) +(((*1 *2 *2 *2 *3) + (-12 (-5 *3 (-793)) (-4 *4 (-571)) (-5 *1 (-1000 *4 *2)) + (-4 *2 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*4)) (-4 *4 (-1273 (-560)))))) (((*1 *2 *2) (-12 (-4 *3 (-571)) (-5 *1 (-287 *3 *2)) (-4 *2 (-13 (-435 *3) (-1033))))) @@ -11345,19 +10944,36 @@ (-12 (-5 *2 (-1185 *3)) (-4 *3 (-38 (-421 (-560)))) (-5 *1 (-1193 *3)))) ((*1 *1 *1) (-4 *1 (-1236)))) -(((*1 *1) (-5 *1 (-1210)))) -(((*1 *2 *1) (-12 (-5 *2 (-663 (-187 (-141)))) (-5 *1 (-142))))) -(((*1 *2 *3 *1) - (-12 (-4 *1 (-629 *3 *4)) (-4 *3 (-1132)) (-4 *4 (-1132)) - (-5 *2 (-114))))) +(((*1 *1 *2 *2 *3) (-12 (-5 *2 (-560)) (-5 *3 (-948)) (-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 (-1009 *5))))) +(((*1 *2 *3 *3) + (-12 (-4 *4 (-13 (-319) (-149))) (-4 *5 (-13 (-871) (-633 (-1207)))) + (-4 *6 (-815)) (-5 *2 (-663 (-663 (-560)))) + (-5 *1 (-953 *4 *5 *6 *7)) (-5 *3 (-560)) (-4 *7 (-979 *4 *6 *5))))) +(((*1 *1) (-4 *1 (-998)))) +(((*1 *2 *3 *4 *4) + (-12 (-5 *4 (-114)) (-4 *5 (-466)) (-4 *6 (-815)) (-4 *7 (-871)) + (-4 *8 (-1096 *5 *6 *7)) + (-5 *2 + (-2 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(-845))))) (((*1 *1 *1) (-12 (-5 *1 (-352 *2 *3 *4)) (-14 *2 (-663 (-1207))) (-14 *3 (-663 (-1207))) (-4 *4 (-401)))) @@ -11367,29 +10983,26 @@ ((*1 *1 *2) (-12 (-5 *2 (-421 (-560))) (-4 *1 (-1043)))) ((*1 *1 *1 *2) (-12 (-4 *1 (-1043)) (-5 *2 (-948)))) ((*1 *1 *1) (-4 *1 (-1043)))) -(((*1 *2 *3 *4) - (-12 (-5 *4 (-560)) (-4 *5 (-363)) (-5 *2 (-419 (-1201 (-1201 *5)))) - (-5 *1 (-1246 *5)) (-5 *3 (-1201 (-1201 *5)))))) -(((*1 *2 *3 *4) - (-12 (-4 *5 (-815)) (-4 *4 (-871)) (-4 *6 (-319)) (-5 *2 (-419 *3)) - (-5 *1 (-764 *5 *4 *6 *3)) (-4 *3 (-979 *6 *5 *4))))) -(((*1 *2 *3 *3 *4) - (-12 (-5 *4 (-114)) (-4 *5 (-13 (-376) (-870))) - (-5 *2 (-663 (-2 (|:| -1448 (-663 *3)) (|:| -2747 *5)))) - (-5 *1 (-184 *5 *3)) (-4 *3 (-1273 (-171 *5))))) - ((*1 *2 *3 *3) - (-12 (-4 *4 (-13 (-376) (-870))) - (-5 *2 (-663 (-2 (|:| -1448 (-663 *3)) (|:| -2747 *4)))) - (-5 *1 (-184 *4 *3)) (-4 *3 (-1273 (-171 *4)))))) +(((*1 *1 *1 *1) (-4 *1 (-998)))) +(((*1 *2 *1) (-12 (-5 *2 (-1248)) (-5 *1 (-183)))) + 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(-1156 *3 (-630 $)))))))))) (((*1 *2 *2) (-12 (-4 *3 (-571)) (-5 *1 (-287 *3 *2)) (-4 *2 (-13 (-435 *3) (-1033))))) @@ -11406,135 +11019,62 @@ (-12 (-5 *2 (-1185 *3)) (-4 *3 (-38 (-421 (-560)))) (-5 *1 (-1193 *3)))) ((*1 *1 *1) (-4 *1 (-1236)))) -(((*1 *2 *1 *3) - (-12 (-5 *3 (-948)) (-4 *4 (-381)) (-4 *4 (-376)) (-5 *2 (-1201 *1)) - (-4 *1 (-341 *4)))) - ((*1 *2 *1) (-12 (-4 *1 (-341 *3)) (-4 *3 (-376)) (-5 *2 (-1201 *3)))) - ((*1 *2 *1) - (-12 (-4 *1 (-383 *3 *2)) (-4 *3 (-175)) (-4 *3 (-376)) - (-4 *2 (-1273 *3)))) +(((*1 *2 *2 *3) + (-12 (-5 *3 (-1 (-114) *2)) (-4 *2 (-134)) (-5 *1 (-1115 *2)))) + ((*1 *2 *2 *3) + (-12 (-5 *3 (-1 (-560) *2 *2)) (-4 *2 (-134)) (-5 *1 (-1115 *2))))) +(((*1 *1 *2) (-12 (-5 *2 (-663 *1)) (-4 *1 (-466)))) + ((*1 *1 *1 *1) (-4 *1 (-466))) ((*1 *2 *3) - (-12 (-5 *3 (-1297 *4)) (-4 *4 (-363)) (-5 *2 (-1201 *4)) - (-5 *1 (-542 *4))))) -(((*1 *2 *3) - (-12 (-5 *3 (-663 (-229))) (-5 *2 (-663 (-1189))) (-5 *1 (-195)))) + (-12 (-5 *3 (-663 *2)) (-5 *1 (-500 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(-560)) - (-5 *1 (-953 *7 *8 *9 *10)))) - ((*1 *2 *3 *4 *5) - (-12 (-5 *3 (-711 *9)) (-5 *4 (-948)) (-5 *5 (-1189)) - (-4 *9 (-979 *6 *8 *7)) (-4 *6 (-13 (-319) (-149))) - (-4 *7 (-13 (-871) (-633 (-1207)))) (-4 *8 (-815)) (-5 *2 (-560)) - (-5 *1 (-953 *6 *7 *8 *9))))) -(((*1 *2 *2) - (-12 (-4 *3 (-571)) (-5 *1 (-287 *3 *2)) - (-4 *2 (-13 (-435 *3) (-1033)))))) + (-12 (-5 *3 (-1120 (-560))) (-5 *2 (-1 (-560))) (-5 *1 (-1078))))) +(((*1 *2 *3 *4 *5) + (-12 (-5 *4 (-1 *7 *7)) + (-5 *5 + (-1 (-2 (|:| |ans| *6) (|:| -2802 *6) (|:| |sol?| (-114))) (-560) + *6)) + (-4 *6 (-376)) (-4 *7 (-1273 *6)) + (-5 *2 (-2 (|:| |answer| (-597 (-421 *7))) (|:| |a0| *6))) + (-5 *1 (-588 *6 *7)) (-5 *3 (-421 *7))))) (((*1 *1 *1) (-4 *1 (-559)))) -(((*1 *2 *3) - (-12 - (-5 *3 - (-2 (|:| |xinit| (-229)) (|:| |xend| (-229)) - (|:| |fn| (-1297 (-326 (-229)))) (|:| |yinit| (-663 (-229))) - (|:| |intvals| (-663 (-229))) (|:| |g| (-326 (-229))) - (|:| |abserr| (-229)) (|:| |relerr| (-229)))) - (-5 *2 (-391)) (-5 *1 (-208))))) +(((*1 *2 *3 *4) + (-12 (-5 *3 (-3 (-421 (-975 *5)) (-1196 (-1207) (-975 *5)))) + (-4 *5 (-466)) (-5 *2 (-663 (-711 (-421 (-975 *5))))) + (-5 *1 (-304 *5)) (-5 *4 (-711 (-421 (-975 *5))))))) +(((*1 *2) (-12 (-5 *2 (-1303)) (-5 *1 (-1210)))) + ((*1 *2 *3) (-12 (-5 *3 (-1207)) (-5 *2 (-1303)) (-5 *1 (-1210)))) + ((*1 *2 *3 *1) (-12 (-5 *3 (-1207)) (-5 *2 (-1303)) (-5 *1 (-1210))))) (((*1 *2 *3 *4) (-12 (-5 *4 (-663 (-48))) (-5 *2 (-419 *3)) (-5 *1 (-39 *3)) (-4 *3 (-1273 (-48))))) @@ -11583,8 +11123,8 @@ (-12 (-4 *4 (-13 (-871) - (-10 -8 (-15 -2112 ((-1207) $)) - (-15 -4244 ((-3 $ "failed") (-1207)))))) + (-10 -8 (-15 -2106 ((-1207) $)) + (-15 -4254 ((-3 $ "failed") (-1207)))))) (-4 *5 (-815)) (-4 *7 (-571)) (-5 *2 (-419 *3)) (-5 *1 (-470 *4 *5 *6 *7 *3)) (-4 *6 (-571)) (-4 *3 (-979 *7 *5 *4)))) @@ -11633,13 +11173,13 @@ (-12 (-4 *4 (-815)) (-4 *5 (-13 (-871) - (-10 -8 (-15 -2112 ((-1207) $)) - (-15 -4244 ((-3 $ "failed") (-1207)))))) + (-10 -8 (-15 -2106 ((-1207) $)) + (-15 -4254 ((-3 $ "failed") (-1207)))))) (-4 *6 (-319)) (-5 *2 (-419 *3)) (-5 *1 (-752 *4 *5 *6 *3)) (-4 *3 (-979 (-975 *6) *4 *5)))) ((*1 *2 *3) (-12 (-4 *4 (-815)) - (-4 *5 (-13 (-871) (-10 -8 (-15 -2112 ((-1207) $))))) (-4 *6 (-571)) + (-4 *5 (-13 (-871) (-10 -8 (-15 -2106 ((-1207) $))))) (-4 *6 (-571)) (-5 *2 (-419 *3)) (-5 *1 (-754 *4 *5 *6 *3)) (-4 *3 (-979 (-421 (-975 *6)) *4 *5)))) ((*1 *2 *3) @@ -11675,16 +11215,17 @@ ((*1 *2 *1) (-12 (-5 *2 (-419 *1)) (-4 *1 (-1252)))) ((*1 *2 *3) (-12 (-5 *2 (-419 *3)) (-5 *1 (-1263 *3)) (-4 *3 (-1273 (-560)))))) -(((*1 *2 *1 *3) - (-12 (-5 *3 (-663 (-972 *4))) (-4 *1 (-1165 *4)) (-4 *4 (-1080)) - (-5 *2 (-793))))) -(((*1 *2 *2 *3 *4) - (-12 (-5 *3 (-663 (-630 *2))) (-5 *4 (-663 (-1207))) - (-4 *2 (-13 (-435 (-171 *5)) (-1033) (-1233))) (-4 *5 (-571)) - (-5 *1 (-614 *5 *6 *2)) (-4 *6 (-13 (-435 *5) (-1033) (-1233)))))) -(((*1 *2 *1) - (-12 (-4 *1 (-355 *3 *4 *5)) (-4 *3 (-1252)) (-4 *4 (-1273 *3)) - (-4 *5 (-1273 (-421 *4))) (-5 *2 (-114))))) +(((*1 *2 *1 *3 *4) + (-12 (-5 *3 (-1189)) (-5 *4 (-1151)) (-5 *2 (-114)) (-5 *1 (-844))))) +(((*1 *2 *2) (-12 (-5 *2 (-391)) (-5 *1 (-1301)))) + ((*1 *2) (-12 (-5 *2 (-391)) (-5 *1 (-1301))))) +(((*1 *2 *3 *4) + (-12 (-5 *3 (-677 *4)) (-4 *4 (-355 *5 *6 *7)) + (-4 *5 (-13 (-376) (-149) (-1069 (-560)) (-1069 (-421 (-560))))) + (-4 *6 (-1273 *5)) (-4 *7 (-1273 (-421 *6))) + (-5 *2 + (-2 (|:| |particular| (-3 *4 "failed")) (|:| -4157 (-663 *4)))) + (-5 *1 (-828 *5 *6 *7 *4))))) (((*1 *2 *2) (-12 (-4 *3 (-571)) (-5 *1 (-287 *3 *2)) (-4 *2 (-13 (-435 *3) (-1033))))) @@ -11701,61 +11242,77 @@ (-12 (-5 *2 (-1185 *3)) (-4 *3 (-38 (-421 (-560)))) (-5 *1 (-1193 *3)))) ((*1 *1 *1) (-4 *1 (-1236)))) -(((*1 *1 *1 *1 *1 *1) - (-12 (-4 *1 (-1096 *2 *3 *4)) (-4 *2 (-1080)) (-4 *3 (-815)) - (-4 *4 (-871)) (-4 *2 (-571))))) -(((*1 *2 *3 *3 *4) - (-12 (-4 *5 (-466)) (-4 *6 (-815)) (-4 *7 (-871)) - (-4 *3 (-1096 *5 *6 *7)) - (-5 *2 (-663 (-2 (|:| |val| *3) (|:| -3622 *4)))) - (-5 *1 (-1139 *5 *6 *7 *3 *4)) (-4 *4 (-1102 *5 *6 *7 *3))))) -(((*1 *1) (-4 *1 (-998)))) -(((*1 *2 *3 *3 *4 *4) - (|partial| -12 (-5 *3 (-793)) (-4 *5 (-376)) (-5 *2 (-421 *6)) - (-5 *1 (-891 *5 *4 *6)) (-4 *4 (-1290 *5)) (-4 *6 (-1273 *5)))) - ((*1 *2 *3 *3 *4 *4) - (|partial| -12 (-5 *3 (-793)) (-5 *4 (-1287 *5 *6 *7)) (-4 *5 (-376)) - (-14 *6 (-1207)) (-14 *7 *5) (-5 *2 (-421 (-1266 *6 *5))) - (-5 *1 (-892 *5 *6 *7)))) - ((*1 *2 *3 *3 *4) - (|partial| -12 (-5 *3 (-793)) (-5 *4 (-1287 *5 *6 *7)) (-4 *5 (-376)) - (-14 *6 (-1207)) (-14 *7 *5) (-5 *2 (-421 (-1266 *6 *5))) - (-5 *1 (-892 *5 *6 *7))))) -(((*1 *2 *1) (-12 (-4 *1 (-440 *3)) (-4 *3 (-1132)) (-5 *2 (-793))))) +(((*1 *2) (-12 (-5 *2 (-934 (-560))) (-5 *1 (-946))))) +(((*1 *2 *3 *3 *3 *3 *4 *3) + (-12 (-5 *3 (-560)) (-5 *4 (-711 (-229))) (-5 *2 (-1066)) + (-5 *1 (-777))))) +(((*1 *1 *1 *1) (-12 (-5 *1 (-663 *2)) (-4 *2 (-1247))))) +(((*1 *1 *1 *2) + (-12 (-5 *2 (-793)) (-4 *1 (-387 *3 *4)) (-4 *3 (-871)) + (-4 *4 (-175)))) + ((*1 *1 *1 *2) + (-12 (-5 *2 (-793)) (-4 *1 (-1320 *3 *4)) (-4 *3 (-871)) + (-4 *4 (-1080))))) +(((*1 *2 *1 *1) + (-12 (-5 *2 (-421 (-560))) (-5 *1 (-1055 *3)) + (-4 *3 (-13 (-870) (-376) (-1051))))) + ((*1 *2 *3 *1 *2) + (-12 (-4 *2 (-13 (-870) (-376))) (-5 *1 (-1092 *2 *3)) + (-4 *3 (-1273 *2)))) + ((*1 *2 *3 *1 *2) + (-12 (-4 *1 (-1099 *2 *3)) (-4 *2 (-13 (-870) (-376))) + (-4 *3 (-1273 *2))))) (((*1 *2 *1) (-12 (-5 *2 (-114)) (-5 *1 (-887))))) -(((*1 *2 *3 *4 *5) - (-12 (-5 *3 (-326 (-229))) (-5 *4 (-1207)) - (-5 *5 (-1120 (-864 (-229)))) (-5 *2 (-663 (-229))) (-5 *1 (-195)))) - ((*1 *2 *3 *4 *5) - (-12 (-5 *3 (-326 (-229))) (-5 *4 (-1207)) - (-5 *5 (-1120 (-864 (-229)))) (-5 *2 (-663 (-229))) (-5 *1 (-313))))) +(((*1 *2 *3) + (-12 (-4 *4 (-13 (-571) (-1069 (-560)))) (-4 *5 (-435 *4)) + (-5 *2 (-419 *3)) (-5 *1 (-449 *4 *5 *3)) (-4 *3 (-1273 *5))))) (((*1 *2 *1) (-12 (-4 *3 (-1132)) (-4 *4 (-13 (-1080) (-911 *3) (-633 (-915 *3)))) (-5 *2 (-663 (-1106 *3 *4 *5))) (-5 *1 (-1108 *3 *4 *5)) (-4 *5 (-13 (-435 *4) (-911 *3) (-633 (-915 *3))))))) -(((*1 *2) - (-12 (-4 *3 (-466)) (-4 *4 (-815)) (-4 *5 (-871)) - (-4 *6 (-1096 *3 *4 *5)) (-5 *2 (-1303)) - (-5 *1 (-1019 *3 *4 *5 *6 *7)) (-4 *7 (-1102 *3 *4 *5 *6)))) - ((*1 *2) - (-12 (-4 *3 (-466)) (-4 *4 (-815)) (-4 *5 (-871)) - (-4 *6 (-1096 *3 *4 *5)) (-5 *2 (-1303)) - (-5 *1 (-1138 *3 *4 *5 *6 *7)) (-4 *7 (-1102 *3 *4 *5 *6))))) -(((*1 *1 *1) - (-12 (-4 *2 (-376)) (-4 *3 (-815)) (-4 *4 (-871)) - (-5 *1 (-518 *2 *3 *4 *5)) (-4 *5 (-979 *2 *3 *4))))) -(((*1 *1 *2) - (-12 (-5 *2 (-1 *3 *3 (-560))) (-4 *3 (-1080)) (-5 *1 (-99 *3)))) - ((*1 *1 *2 *2) - (-12 (-5 *2 (-1 *3 *3)) (-4 *3 (-1080)) (-5 *1 (-99 *3)))) - ((*1 *1 *2) (-12 (-5 *2 (-1 *3 *3)) (-4 *3 (-1080)) (-5 *1 (-99 *3))))) -(((*1 *2 *1) (-12 (-5 *2 (-1248)) (-5 *1 (-183)))) - ((*1 *2 *1) (-12 (-5 *2 (-1248)) (-5 *1 (-703)))) - ((*1 *2 *1) (-12 (-5 *2 (-1248)) (-5 *1 (-1001)))) - ((*1 *2 *1) (-12 (-5 *2 (-1248)) (-5 *1 (-1104)))) - ((*1 *2 *1) (-12 (-5 *2 (-1212)) (-5 *1 (-1146))))) -(((*1 *2 *2) - (-12 (-5 *2 (-663 *3)) (-4 *3 (-1273 (-560))) (-5 *1 (-500 *3))))) +(((*1 *2 *1) + (-12 + (-5 *2 + (-663 + (-2 + (|:| -3835 + (-2 (|:| |var| (-1207)) (|:| |fn| (-326 (-229))) + (|:| -2016 (-1120 (-864 (-229)))) (|:| |abserr| (-229)) + (|:| |relerr| (-229)))) + (|:| -2923 + (-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| (-1185 (-229))) + (|:| |notEvaluated| + "Internal singularities not yet evaluated"))) + (|:| -2016 + (-3 (|:| |finite| "The range is finite") + (|:| |lowerInfinite| + "The bottom of range is infinite") + (|:| |upperInfinite| "The top of range is infinite") + (|:| |bothInfinite| + "Both top and bottom points are infinite") + (|:| |notEvaluated| "Range not yet evaluated")))))))) + (-5 *1 (-574)))) + ((*1 *2 *1) + (-12 (-4 *1 (-618 *3 *4)) (-4 *3 (-1132)) (-4 *4 (-1247)) + (-5 *2 (-663 *4))))) +(((*1 *1 *1 *2) + (-12 (-5 *2 (-663 (-51))) (-5 *1 (-915 *3)) (-4 *3 (-1132))))) +(((*1 *1 *2) (-12 (-5 *2 (-1189)) (-5 *1 (-342))))) +(((*1 *2 *3) (-12 (-5 *3 (-948)) (-5 *2 (-934 (-560))) (-5 *1 (-946)))) + ((*1 *2 *3) + (-12 (-5 *3 (-663 (-560))) (-5 *2 (-934 (-560))) (-5 *1 (-946))))) (((*1 *2 *2) (-12 (-4 *3 (-571)) (-5 *1 (-287 *3 *2)) (-4 *2 (-13 (-435 *3) (-1033))))) @@ -11775,68 +11332,31 @@ (-12 (-5 *2 (-1185 *3)) (-4 *3 (-38 (-421 (-560)))) (-5 *1 (-1193 *3)))) ((*1 *1 *1) (-4 *1 (-1236)))) -(((*1 *1 *2) (-12 (-5 *2 (-663 *1)) (-4 *1 (-466)))) - ((*1 *1 *1 *1) (-4 *1 (-466))) - ((*1 *2 *3) - (-12 (-5 *3 (-663 *2)) (-5 *1 (-500 *2)) (-4 *2 (-1273 (-560))))) - ((*1 *2 *2 *2 *3) - (-12 (-5 *3 (-560)) (-5 *1 (-718 *2)) (-4 *2 (-1273 *3)))) - ((*1 *1 *1 *1) (-5 *1 (-793))) - ((*1 *2 *2 *2) - (-12 (-4 *3 (-815)) (-4 *4 (-871)) (-4 *5 (-319)) - (-5 *1 (-945 *3 *4 *5 *2)) (-4 *2 (-979 *5 *3 *4)))) - ((*1 *2 *3) - (-12 (-5 *3 (-663 *2)) (-4 *2 (-979 *6 *4 *5)) - (-5 *1 (-945 *4 *5 *6 *2)) (-4 *4 (-815)) (-4 *5 (-871)) - (-4 *6 (-319)))) - ((*1 *2 *2 *2) - (-12 (-5 *2 (-1201 *6)) (-4 *6 (-979 *5 *3 *4)) (-4 *3 (-815)) - (-4 *4 (-871)) (-4 *5 (-319)) (-5 *1 (-945 *3 *4 *5 *6)))) - ((*1 *2 *3) - (-12 (-5 *3 (-663 (-1201 *7))) (-4 *4 (-815)) (-4 *5 (-871)) - (-4 *6 (-319)) (-5 *2 (-1201 *7)) (-5 *1 (-945 *4 *5 *6 *7)) - (-4 *7 (-979 *6 *4 *5)))) - ((*1 *1 *1 *1) (-5 *1 (-948))) - ((*1 *2 *2 *2) - (-12 (-4 *3 (-466)) (-4 *3 (-571)) (-5 *1 (-1000 *3 *2)) - (-4 *2 (-1273 *3)))) - ((*1 *2 *2 *1) - (-12 (-4 *1 (-1096 *2 *3 *4)) (-4 *2 (-1080)) (-4 *3 (-815)) - (-4 *4 (-871)) (-4 *2 (-466))))) (((*1 *2 *3) - (-12 (-5 *3 (-972 *2)) (-5 *1 (-1013 *2)) (-4 *2 (-1080))))) -(((*1 *2 *3 *4) - (-12 (-4 *2 (-1273 *4)) (-5 *1 (-829 *4 *2 *3 *5)) - (-4 *4 (-13 (-376) (-149) (-1069 (-421 (-560))))) (-4 *3 (-680 *2)) - (-4 *5 (-680 (-421 *2))))) - ((*1 *2 *3 *4) - (-12 (-4 *2 (-1273 *4)) (-5 *1 (-829 *4 *2 *5 *3)) - (-4 *4 (-13 (-376) (-149) (-1069 (-421 (-560))))) (-4 *5 (-680 *2)) - (-4 *3 (-680 (-421 *2)))))) -(((*1 *2 *3 *1) (-12 (-5 *3 (-1207)) (-5 *2 (-1211)) (-5 *1 (-1210))))) -(((*1 *2 *3 *4) - (-12 (-5 *3 (-229)) (-5 *4 (-560)) (-5 *2 (-1066)) (-5 *1 (-780))))) -(((*1 *2 *2) - (-12 (-5 *2 (-114)) (-5 *1 (-456 *3)) (-4 *3 (-1273 (-560)))))) + (-12 (-4 *4 (-466)) (-4 *5 (-815)) (-4 *6 (-871)) (-5 *2 (-560)) + (-5 *1 (-464 *4 *5 *6 *3)) (-4 *3 (-979 *4 *5 *6))))) +(((*1 *2 *2) (|partial| -12 (-5 *1 (-601 *2)) (-4 *2 (-559))))) +(((*1 *2 *1) (-12 (-5 *2 (-114)) (-5 *1 (-146))))) +(((*1 *2 *2 *2 *2 *2) (-12 (-5 *2 (-560)) (-5 *1 (-1078))))) +(((*1 *2 *1) (-12 (-5 *2 (-114)) (-5 *1 (-915 *3)) (-4 *3 (-1132))))) (((*1 *2 *1) (-12 (-4 *1 (-1125 *2)) (-4 *2 (-1247))))) -(((*1 *2 *3 *4 *5 *6) - (-12 (-5 *4 (-114)) (-5 *5 (-1128 (-793))) (-5 *6 (-793)) - (-5 *2 - (-2 (|:| |contp| (-560)) - (|:| -1448 (-663 (-2 (|:| |irr| *3) (|:| -1831 (-560))))))) - (-5 *1 (-456 *3)) (-4 *3 (-1273 (-560)))))) -(((*1 *2 *2 *2) (-12 (-5 *2 (-229)) (-5 *1 (-230)))) - ((*1 *2 *2 *2) (-12 (-5 *2 (-171 (-229))) (-5 *1 (-230)))) - ((*1 *2 *2 *2) - (-12 (-4 *3 (-571)) (-5 *1 (-445 *3 *2)) (-4 *2 (-435 *3)))) - ((*1 *1 *1 *1) (-4 *1 (-1170)))) -(((*1 *2 *1) (-12 (-4 *1 (-818 *2)) (-4 *2 (-175))))) +(((*1 *2) + (-12 (-4 *3 (-815)) (-4 *4 (-871)) (-4 *2 (-939)) + (-5 *1 (-471 *3 *4 *2 *5)) (-4 *5 (-979 *2 *3 *4)))) + ((*1 *2) + (-12 (-4 *3 (-815)) (-4 *4 (-871)) (-4 *2 (-939)) + (-5 *1 (-936 *2 *3 *4 *5)) (-4 *5 (-979 *2 *3 *4)))) + ((*1 *2) (-12 (-4 *2 (-939)) (-5 *1 (-937 *2 *3)) (-4 *3 (-1273 *2))))) +(((*1 *2 *1) (-12 (-5 *2 (-1151)) (-5 *1 (-864 *3)) (-4 *3 (-1132))))) +(((*1 *2 *1) + (-12 (-4 *1 (-618 *2 *3)) (-4 *3 (-1247)) (-4 *2 (-1132)) + (-4 *2 (-871))))) (((*1 *1 *1 *2) (-12 (-4 *1 (-47 *2 *3)) (-4 *2 (-1080)) (-4 *3 (-814)) (-4 *2 (-376)))) ((*1 *1 *1 *2) (-12 (-5 *2 (-560)) (-5 *1 (-229)))) ((*1 *1 *1 *1) - (-2181 (-12 (-5 *1 (-305 *2)) (-4 *2 (-376)) (-4 *2 (-1247))) + (-2173 (-12 (-5 *1 (-305 *2)) (-4 *2 (-376)) (-4 *2 (-1247))) (-12 (-5 *1 (-305 *2)) (-4 *2 (-487)) (-4 *2 (-1247))))) ((*1 *1 *1 *1) (-4 *1 (-376))) ((*1 *1 *1 *2) (-12 (-5 *2 (-560)) (-5 *1 (-391)))) @@ -11884,12 +11404,9 @@ ((*1 *1 *1 *2) (-12 (-5 *1 (-1321 *2 *3)) (-4 *2 (-376)) (-4 *2 (-1080)) (-4 *3 (-868))))) -(((*1 *2 *2 *2 *2 *3 *3 *4) - (|partial| -12 (-5 *3 (-630 *2)) - (-5 *4 (-1 (-3 *2 "failed") *2 *2 (-1207))) - (-4 *2 (-13 (-435 *5) (-27) (-1233))) - (-4 *5 (-13 (-466) (-1069 (-560)) (-149) (-660 (-560)))) - (-5 *1 (-580 *5 *2 *6)) (-4 *6 (-1132))))) +(((*1 *2 *1) (-12 (-5 *2 (-663 (-1248))) (-5 *1 (-703)))) + ((*1 *2 *1) (-12 (-5 *2 (-663 (-1212))) (-5 *1 (-1146))))) +(((*1 *1) (-12 (-5 *1 (-231 *2)) (-4 *2 (-13 (-376) (-1233)))))) (((*1 *2 *2) (-12 (-4 *3 (-571)) (-5 *1 (-287 *3 *2)) (-4 *2 (-13 (-435 *3) (-1033))))) @@ -11910,41 +11427,35 @@ (-12 (-5 *2 (-1185 *3)) (-4 *3 (-38 (-421 (-560)))) (-5 *1 (-1193 *3)))) ((*1 *1 *1) (-4 *1 (-1236)))) -(((*1 *1 *1 *1) (-12 (-5 *1 (-663 *2)) (-4 *2 (-1247))))) -(((*1 *2 *1 *2) - (-12 (|has| *1 (-6 -4509)) (-4 *1 (-1286 *2)) (-4 *2 (-1247))))) -(((*1 *2 *3 *3) - (-12 (-4 *4 (-466)) (-4 *5 (-815)) (-4 *6 (-871)) - (-4 *7 (-1096 *4 *5 *6)) (-5 *2 (-114)) - (-5 *1 (-1019 *4 *5 *6 *7 *3)) (-4 *3 (-1102 *4 *5 *6 *7)))) - ((*1 *2 *3 *3) - (-12 (-4 *4 (-466)) (-4 *5 (-815)) (-4 *6 (-871)) - (-4 *7 (-1096 *4 *5 *6)) (-5 *2 (-114)) - (-5 *1 (-1138 *4 *5 *6 *7 *3)) (-4 *3 (-1102 *4 *5 *6 *7))))) -(((*1 *2 *2 *3) - (-12 (-5 *3 (-1 (-114) *4 *4)) (-4 *4 (-1247)) (-5 *1 (-1163 *4 *2)) - (-4 *2 (-13 (-618 (-560) *4) (-10 -7 (-6 -4508) (-6 -4509)))))) - ((*1 *2 *2) - (-12 (-4 *3 (-871)) (-4 *3 (-1247)) (-5 *1 (-1163 *3 *2)) - (-4 *2 (-13 (-618 (-560) *3) (-10 -7 (-6 -4508) (-6 -4509))))))) -(((*1 *2 *3 *4) - (-12 (-5 *4 (-1207)) - (-4 *5 (-13 (-319) (-149) (-1069 (-560)) (-660 (-560)))) - (-5 *2 (-597 *3)) (-5 *1 (-442 *5 *3)) - (-4 *3 (-13 (-1233) (-29 *5)))))) +(((*1 *2 *3 *4 *4 *4 *4) + (-12 (-5 *3 (-711 (-229))) (-5 *4 (-560)) (-5 *2 (-1066)) + (-5 *1 (-777))))) +(((*1 *1 *2) (-12 (-5 *2 (-663 *1)) (-4 *1 (-466)))) + ((*1 *1 *1 *1) (-4 *1 (-466)))) +(((*1 *2 *3 *4 *4 *4 *4) + (-12 (-5 *4 (-229)) + (-5 *2 + (-2 (|:| |brans| (-663 (-663 (-972 *4)))) + (|:| |xValues| (-1120 *4)) (|:| |yValues| (-1120 *4)))) + (-5 *1 (-155)) (-5 *3 (-663 (-663 (-972 *4))))))) (((*1 *2 *3 *4 *5) - (-12 (-5 *5 (-114)) (-4 *4 (-13 (-376) (-870))) (-5 *2 (-419 *3)) - (-5 *1 (-184 *4 *3)) (-4 *3 (-1273 (-171 *4))))) - ((*1 *2 *3 *4) - (-12 (-4 *4 (-13 (-376) (-870))) (-5 *2 (-419 *3)) - (-5 *1 (-184 *4 *3)) (-4 *3 (-1273 (-171 *4)))))) + (-12 (-5 *3 (-1 *4 (-560))) (-5 *5 (-1 (-1185 *4))) (-4 *4 (-376)) + (-4 *4 (-1080)) (-5 *2 (-1185 *4)) (-5 *1 (-1191 *4))))) +(((*1 *2 *2) + (-12 (-4 *3 (-571)) (-5 *1 (-287 *3 *2)) + (-4 *2 (-13 (-435 *3) (-1033)))))) +(((*1 *2 *3) + (-12 (-4 *4 (-571)) (-5 *2 (-663 *3)) (-5 *1 (-43 *4 *3)) + (-4 *3 (-432 *4))))) (((*1 *2 *1) (-12 (-4 *1 (-1125 *3)) (-4 *3 (-1247)) (-5 *2 (-560))))) -(((*1 *1 *1) - (-12 (|has| *1 (-6 -4509)) (-4 *1 (-385 *2)) (-4 *2 (-1247)) - (-4 *2 (-871)))) - ((*1 *1 *2 *1) - (-12 (-5 *2 (-1 (-114) *3 *3)) (|has| *1 (-6 -4509)) - (-4 *1 (-385 *3)) (-4 *3 (-1247))))) +(((*1 *2 *3 *2) + (-12 + (-5 *2 + (-663 + (-2 (|:| |lcmfij| *3) (|:| |totdeg| (-793)) (|:| |poli| *6) + (|:| |polj| *6)))) + (-4 *3 (-815)) (-4 *6 (-979 *4 *3 *5)) (-4 *4 (-466)) (-4 *5 (-871)) + (-5 *1 (-464 *4 *3 *5 *6))))) (((*1 *2 *1 *3) (-12 (-5 *3 (-630 *1)) (-4 *1 (-435 *4)) (-4 *4 (-1132)) (-4 *4 (-571)) (-5 *2 (-421 (-1201 *1))))) @@ -11968,28 +11479,27 @@ (-5 *1 (-980 *5 *4 *6 *7 *3)) (-4 *3 (-13 (-376) - (-10 -8 (-15 -4272 ($ *7)) (-15 -2167 (*7 $)) (-15 -2180 (*7 $))))))) + (-10 -8 (-15 -2383 ($ *7)) (-15 -2158 (*7 $)) (-15 -2171 (*7 $))))))) ((*1 *2 *3 *4 *2) (-12 (-5 *2 (-1201 *3)) (-4 *3 (-13 (-376) - (-10 -8 (-15 -4272 ($ *7)) (-15 -2167 (*7 $)) 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(-12 (-4 *4 (-1252)) (-4 *5 (-1273 *4)) (-4 *6 (-1273 (-421 *5))) + (-5 *2 (-793)) (-5 *1 (-354 *3 *4 *5 *6)) (-4 *3 (-355 *4 *5 *6)))) ((*1 *2) - (|partial| -12 (-4 *1 (-355 *3 *2 *4)) (-4 *3 (-1252)) - (-4 *4 (-1273 (-421 *2))) (-4 *2 (-1273 *3))))) + (-12 (-4 *1 (-355 *3 *4 *5)) (-4 *3 (-1252)) (-4 *4 (-1273 *3)) + (-4 *5 (-1273 (-421 *4))) (-5 *2 (-793)))) + ((*1 *2 *1) (-12 (-4 *1 (-1165 *3)) (-4 *3 (-1080)) (-5 *2 (-793))))) +(((*1 *2 *3 *3) + (-12 (-5 *2 (-663 *3)) (-5 *1 (-991 *3)) (-4 *3 (-559))))) +(((*1 *1 *2) + (-12 (-5 *2 (-948)) (-5 *1 (-154 *3 *4 *5)) (-14 *3 *2) + (-4 *4 (-376)) (-14 *5 (-1024 *3 *4))))) (((*1 *1 *1) (-5 *1 (-48))) ((*1 *2 *3 *4 *2) (-12 (-5 *3 (-1 *2 *5 *2)) (-5 *4 (-58 *5)) (-4 *5 (-1247)) @@ -14705,7 +14749,7 @@ (-4 *2 (-1247)))) ((*1 *2 *3) (-12 (-4 *4 (-1080)) - (-5 *2 (-2 (|:| -4117 (-1201 *4)) (|:| |deg| (-948)))) + (-5 *2 (-2 (|:| -4397 (-1201 *4)) (|:| |deg| (-948)))) (-5 *1 (-225 *4 *5)) (-5 *3 (-1201 *4)) (-4 *5 (-571)))) ((*1 *2 *3 *4 *2) (-12 (-5 *3 (-1 *2 *6 *2)) (-5 *4 (-246 *5 *6)) (-14 *5 (-793)) @@ -14772,55 +14816,57 @@ ((*1 *2 *3 *4 *2) (-12 (-5 *3 (-1 *2 *5 *2)) (-5 *4 (-1297 *5)) (-4 *5 (-1247)) (-4 *2 (-1247)) (-5 *1 (-1298 *5 *2))))) -(((*1 *2 *3 *2) - (-12 (-5 *2 (-663 (-663 (-663 *4)))) (-5 *3 (-663 *4)) (-4 *4 (-871)) - (-5 *1 (-1218 *4))))) +(((*1 *2 *2 *3 *4 *4) + (-12 (-5 *4 (-560)) (-4 *3 (-175)) (-4 *5 (-385 *3)) + (-4 *6 (-385 *3)) (-5 *1 (-710 *3 *5 *6 *2)) + (-4 *2 (-708 *3 *5 *6))))) (((*1 *2 *3) - (-12 (-5 *3 (-1297 *4)) (-4 *4 (-13 (-1080) (-660 (-560)))) - (-5 *2 (-114)) (-5 *1 (-1326 *4))))) -(((*1 *1 *2) - (-12 - (-5 *2 - (-2 (|:| |mval| (-711 *3)) (|:| |invmval| (-711 *3)) - (|:| |genIdeal| (-518 *3 *4 *5 *6)))) - (-4 *3 (-376)) (-4 *4 (-815)) (-4 *5 (-871)) - (-5 *1 (-518 *3 *4 *5 *6)) (-4 *6 (-979 *3 *4 *5))))) -(((*1 *2 *3 *4 *4) - (-12 (-5 *4 (-114)) (-4 *5 (-466)) (-4 *6 (-815)) (-4 *7 (-871)) - (-4 *8 (-1096 *5 *6 *7)) - (-5 *2 - (-2 (|:| |val| (-663 *8)) - (|:| |towers| (-663 (-1058 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