diff options
author | dos-reis <gdr@axiomatics.org> | 2010-06-29 00:15:40 +0000 |
---|---|---|
committer | dos-reis <gdr@axiomatics.org> | 2010-06-29 00:15:40 +0000 |
commit | 322c78e4fbe48f8449bf0e22c001c2fc9719b4c4 (patch) | |
tree | 33ae31fa99b354a93564895e11508b3563de07b2 /src/share/algebra | |
parent | 1c92e6f09b84c2b8951a6bcedb34964908167c37 (diff) | |
download | open-axiom-322c78e4fbe48f8449bf0e22c001c2fc9719b4c4.tar.gz |
* algebra/indexedp.spad.pamphlet (IndexedDirectProductCategory)
[support]: New.
(IndexedDirectProductObject): Implement.
Diffstat (limited to 'src/share/algebra')
-rw-r--r-- | src/share/algebra/browse.daase | 642 | ||||
-rw-r--r-- | src/share/algebra/category.daase | 1540 | ||||
-rw-r--r-- | src/share/algebra/compress.daase | 1313 | ||||
-rw-r--r-- | src/share/algebra/interp.daase | 9032 | ||||
-rw-r--r-- | src/share/algebra/operation.daase | 27891 |
5 files changed, 20211 insertions, 20207 deletions
diff --git a/src/share/algebra/browse.daase b/src/share/algebra/browse.daase index f274ebea..09f5d135 100644 --- a/src/share/algebra/browse.daase +++ b/src/share/algebra/browse.daase @@ -1,5 +1,5 @@ -(2293192 . 3486658188) +(2293439 . 3486753495) (-18 A S) ((|constructor| (NIL "One-dimensional-array aggregates serves as models for one-dimensional arrays. Categorically,{} these aggregates are finite linear aggregates with the \\spadatt{shallowlyMutable} property,{} that is,{} any component of the array may be changed without affecting the identity of the overall array. Array data structures are typically represented by a fixed area in storage and therefore cannot efficiently grow or shrink on demand as can list structures (see however \\spadtype{FlexibleArray} for a data structure which is a cross between a list and an array). Iteration over,{} and access to,{} elements of arrays is extremely fast (and often can be optimized to open-code). Insertion and deletion however is generally slow since an entirely new data structure must be created for the result."))) NIL @@ -56,7 +56,7 @@ NIL ((|constructor| (NIL "This domain represents the syntax for an add-expression.")) (|body| (((|SpadAst|) $) "base(\\spad{d}) returns the actual body of the add-domain expression \\spad{`d'}.")) (|base| (((|SpadAst|) $) "\\spad{base(d)} returns the base domain(\\spad{s}) of the add-domain expression."))) NIL NIL -(-32 R -1966) +(-32 R -1955) ((|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 -1057) (QUOTE (-576))))) @@ -88,11 +88,11 @@ NIL ((|constructor| (NIL "Factorization of univariate polynomials with coefficients in \\spadtype{AlgebraicNumber}.")) (|doublyTransitive?| (((|Boolean|) |#1|) "\\spad{doublyTransitive?(p)} is \\spad{true} if \\spad{p} is irreducible over over the field \\spad{K} generated by its coefficients,{} and if \\spad{p(X) / (X - a)} is irreducible over \\spad{K(a)} where \\spad{p(a) = 0}.")) (|split| (((|Factored| |#1|) |#1|) "\\spad{split(p)} returns a prime factorisation of \\spad{p} over its splitting field.")) (|factor| (((|Factored| |#1|) |#1|) "\\spad{factor(p)} returns a prime factorisation of \\spad{p} over the field generated by its coefficients.") (((|Factored| |#1|) |#1| (|List| (|AlgebraicNumber|))) "\\spad{factor(p, [a1,...,an])} returns a prime factorisation of \\spad{p} over the field generated by its coefficients and a1,{}...,{}an."))) NIL NIL -(-40 -1966 UP UPUP -3290) +(-40 -1955 UP UPUP -3878) ((|constructor| (NIL "Function field defined by \\spad{f}(\\spad{x},{} \\spad{y}) = 0.")) (|knownInfBasis| (((|Void|) (|NonNegativeInteger|)) "\\spad{knownInfBasis(n)} \\undocumented{}"))) ((-4455 |has| (-419 |#2|) (-374)) (-4460 |has| (-419 |#2|) (-374)) (-4454 |has| (-419 |#2|) (-374)) ((-4464 "*") . T) (-4456 . T) (-4457 . T) (-4459 . T)) -((|HasCategory| (-419 |#2|) (QUOTE (-146))) (|HasCategory| (-419 |#2|) (QUOTE (-148))) (|HasCategory| (-419 |#2|) (QUOTE (-360))) (-2781 (|HasCategory| (-419 |#2|) (QUOTE (-374))) (|HasCategory| (-419 |#2|) (QUOTE (-360)))) (|HasCategory| (-419 |#2|) (QUOTE (-374))) (|HasCategory| (-419 |#2|) (QUOTE (-379))) (-2781 (-12 (|HasCategory| (-419 |#2|) (QUOTE (-238))) (|HasCategory| (-419 |#2|) (QUOTE (-374)))) (|HasCategory| (-419 |#2|) (QUOTE (-360)))) (-2781 (-12 (|HasCategory| (-419 |#2|) (QUOTE (-238))) (|HasCategory| (-419 |#2|) (QUOTE (-374)))) (-12 (|HasCategory| (-419 |#2|) (QUOTE (-237))) (|HasCategory| (-419 |#2|) (QUOTE (-374)))) (|HasCategory| (-419 |#2|) (QUOTE (-360)))) (-2781 (-12 (|HasCategory| (-419 |#2|) (LIST (QUOTE -915) (QUOTE (-1195)))) (|HasCategory| (-419 |#2|) (QUOTE (-374)))) (-12 (|HasCategory| (-419 |#2|) (LIST (QUOTE -915) (QUOTE (-1195)))) (|HasCategory| (-419 |#2|) (QUOTE (-360))))) (-2781 (-12 (|HasCategory| (-419 |#2|) (LIST (QUOTE -915) (QUOTE (-1195)))) (|HasCategory| (-419 |#2|) (QUOTE (-374)))) (-12 (|HasCategory| (-419 |#2|) (LIST (QUOTE -917) (QUOTE (-1195)))) (|HasCategory| (-419 |#2|) (QUOTE (-374))))) (|HasCategory| (-419 |#2|) (LIST (QUOTE -651) (QUOTE (-576)))) (-2781 (|HasCategory| (-419 |#2|) (LIST (QUOTE -1057) (LIST (QUOTE -419) (QUOTE (-576))))) (|HasCategory| (-419 |#2|) (QUOTE (-374)))) (|HasCategory| (-419 |#2|) (LIST (QUOTE -1057) (LIST (QUOTE -419) (QUOTE (-576))))) (|HasCategory| (-419 |#2|) (LIST (QUOTE -1057) (QUOTE (-576)))) (|HasCategory| |#1| (QUOTE (-374))) (|HasCategory| |#1| (QUOTE (-379))) (-12 (|HasCategory| (-419 |#2|) (QUOTE (-237))) (|HasCategory| (-419 |#2|) (QUOTE (-374)))) (-12 (|HasCategory| (-419 |#2|) (LIST (QUOTE -917) (QUOTE (-1195)))) (|HasCategory| (-419 |#2|) (QUOTE (-374)))) (-12 (|HasCategory| (-419 |#2|) (QUOTE (-238))) (|HasCategory| (-419 |#2|) (QUOTE (-374)))) (-12 (|HasCategory| (-419 |#2|) (LIST (QUOTE -915) (QUOTE (-1195)))) (|HasCategory| (-419 |#2|) (QUOTE (-374))))) -(-41 R -1966) +((|HasCategory| (-419 |#2|) (QUOTE (-146))) (|HasCategory| (-419 |#2|) (QUOTE (-148))) (|HasCategory| (-419 |#2|) (QUOTE (-360))) (-2755 (|HasCategory| (-419 |#2|) (QUOTE (-374))) (|HasCategory| (-419 |#2|) (QUOTE (-360)))) (|HasCategory| (-419 |#2|) (QUOTE (-374))) (|HasCategory| (-419 |#2|) (QUOTE (-379))) (-2755 (-12 (|HasCategory| (-419 |#2|) (QUOTE (-238))) (|HasCategory| (-419 |#2|) (QUOTE (-374)))) (|HasCategory| (-419 |#2|) (QUOTE (-360)))) (-2755 (-12 (|HasCategory| (-419 |#2|) (QUOTE (-238))) (|HasCategory| (-419 |#2|) (QUOTE (-374)))) (-12 (|HasCategory| (-419 |#2|) (QUOTE (-237))) (|HasCategory| (-419 |#2|) (QUOTE (-374)))) (|HasCategory| (-419 |#2|) (QUOTE (-360)))) (-2755 (-12 (|HasCategory| (-419 |#2|) (LIST (QUOTE -915) (QUOTE (-1195)))) (|HasCategory| (-419 |#2|) (QUOTE (-374)))) (-12 (|HasCategory| (-419 |#2|) (LIST (QUOTE -915) (QUOTE (-1195)))) (|HasCategory| (-419 |#2|) (QUOTE (-360))))) (-2755 (-12 (|HasCategory| (-419 |#2|) (LIST (QUOTE -915) (QUOTE (-1195)))) (|HasCategory| (-419 |#2|) (QUOTE (-374)))) (-12 (|HasCategory| (-419 |#2|) (LIST (QUOTE -917) (QUOTE (-1195)))) (|HasCategory| (-419 |#2|) (QUOTE (-374))))) (|HasCategory| (-419 |#2|) (LIST (QUOTE -651) (QUOTE (-576)))) (-2755 (|HasCategory| (-419 |#2|) (LIST (QUOTE -1057) (LIST (QUOTE -419) (QUOTE (-576))))) (|HasCategory| (-419 |#2|) (QUOTE (-374)))) (|HasCategory| (-419 |#2|) (LIST (QUOTE -1057) (LIST (QUOTE -419) (QUOTE (-576))))) (|HasCategory| (-419 |#2|) (LIST (QUOTE -1057) (QUOTE (-576)))) (|HasCategory| |#1| (QUOTE (-374))) (|HasCategory| |#1| (QUOTE (-379))) (-12 (|HasCategory| (-419 |#2|) (QUOTE (-237))) (|HasCategory| (-419 |#2|) (QUOTE (-374)))) (-12 (|HasCategory| (-419 |#2|) (LIST (QUOTE -917) (QUOTE (-1195)))) (|HasCategory| (-419 |#2|) (QUOTE (-374)))) (-12 (|HasCategory| (-419 |#2|) (QUOTE (-238))) (|HasCategory| (-419 |#2|) (QUOTE (-374)))) (-12 (|HasCategory| (-419 |#2|) (LIST (QUOTE -915) (QUOTE (-1195)))) (|HasCategory| (-419 |#2|) (QUOTE (-374))))) +(-41 R -1955) ((|constructor| (NIL "AlgebraicManipulations provides functions to simplify and expand expressions involving algebraic operators.")) (|rootKerSimp| ((|#2| (|BasicOperator|) |#2| (|NonNegativeInteger|)) "\\spad{rootKerSimp(op,f,n)} should be local but conditional.")) (|rootSimp| ((|#2| |#2|) "\\spad{rootSimp(f)} transforms every radical of the form \\spad{(a * b**(q*n+r))**(1/n)} appearing in \\spad{f} into \\spad{b**q * (a * b**r)**(1/n)}. This transformation is not in general valid for all complex numbers \\spad{b}.")) (|rootProduct| ((|#2| |#2|) "\\spad{rootProduct(f)} combines every product of the form \\spad{(a**(1/n))**m * (a**(1/s))**t} into a single power of a root of \\spad{a},{} and transforms every radical power of the form \\spad{(a**(1/n))**m} into a simpler form.")) (|rootPower| ((|#2| |#2|) "\\spad{rootPower(f)} transforms every radical power of the form \\spad{(a**(1/n))**m} into a simpler form if \\spad{m} and \\spad{n} have a common factor.")) (|ratPoly| (((|SparseUnivariatePolynomial| |#2|) |#2|) "\\spad{ratPoly(f)} returns a polynomial \\spad{p} such that \\spad{p} has no algebraic coefficients,{} and \\spad{p(f) = 0}.")) (|ratDenom| ((|#2| |#2| (|List| (|Kernel| |#2|))) "\\spad{ratDenom(f, [a1,...,an])} removes the \\spad{ai}\\spad{'s} which are algebraic from the denominators in \\spad{f}.") ((|#2| |#2| (|List| |#2|)) "\\spad{ratDenom(f, [a1,...,an])} removes the \\spad{ai}\\spad{'s} which are algebraic kernels from the denominators in \\spad{f}.") ((|#2| |#2| |#2|) "\\spad{ratDenom(f, a)} removes \\spad{a} from the denominators in \\spad{f} if \\spad{a} is an algebraic kernel.") ((|#2| |#2|) "\\spad{ratDenom(f)} rationalizes the denominators appearing in \\spad{f} by moving all the algebraic quantities into the numerators.")) (|rootSplit| ((|#2| |#2|) "\\spad{rootSplit(f)} transforms every radical of the form \\spad{(a/b)**(1/n)} appearing in \\spad{f} into \\spad{a**(1/n) / b**(1/n)}. This transformation is not in general valid for all complex numbers \\spad{a} and \\spad{b}.")) (|coerce| (($ (|SparseMultivariatePolynomial| |#1| (|Kernel| $))) "\\spad{coerce(x)} \\undocumented")) (|denom| (((|SparseMultivariatePolynomial| |#1| (|Kernel| $)) $) "\\spad{denom(x)} \\undocumented")) (|numer| (((|SparseMultivariatePolynomial| |#1| (|Kernel| $)) $) "\\spad{numer(x)} \\undocumented"))) NIL ((-12 (|HasCategory| |#1| (QUOTE (-464))) (|HasCategory| |#1| (LIST (QUOTE -1057) (QUOTE (-576)))) (|HasCategory| |#2| (LIST (QUOTE -442) (|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."))) ((-4462 . T) (-4463 . T)) -((-2781 (-12 (|HasCategory| (-2 (|:| -4300 |#1|) (|:| -4391 |#2|)) (QUOTE (-862))) (|HasCategory| (-2 (|:| -4300 |#1|) (|:| -4391 |#2|)) (LIST (QUOTE -319) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -4300) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -4391) (|devaluate| |#2|)))))) (-12 (|HasCategory| (-2 (|:| -4300 |#1|) (|:| -4391 |#2|)) (QUOTE (-1119))) (|HasCategory| (-2 (|:| -4300 |#1|) (|:| -4391 |#2|)) (LIST (QUOTE -319) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -4300) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -4391) (|devaluate| |#2|))))))) (-2781 (|HasCategory| (-2 (|:| -4300 |#1|) (|:| -4391 |#2|)) (QUOTE (-862))) (|HasCategory| (-2 (|:| -4300 |#1|) (|:| -4391 |#2|)) (QUOTE (-1119))) (|HasCategory| (-2 (|:| -4300 |#1|) (|:| -4391 |#2|)) (LIST (QUOTE -625) (QUOTE (-874)))) (|HasCategory| |#2| (QUOTE (-1119))) (|HasCategory| |#2| (LIST (QUOTE -625) (QUOTE (-874))))) (|HasCategory| (-2 (|:| -4300 |#1|) (|:| -4391 |#2|)) (LIST (QUOTE -626) (QUOTE (-548)))) (-12 (|HasCategory| |#2| (QUOTE (-1119))) (|HasCategory| |#2| (LIST (QUOTE -319) (|devaluate| |#2|)))) (-2781 (|HasCategory| (-2 (|:| -4300 |#1|) (|:| -4391 |#2|)) (QUOTE (-102))) (|HasCategory| (-2 (|:| -4300 |#1|) (|:| -4391 |#2|)) (QUOTE (-862))) (|HasCategory| (-2 (|:| -4300 |#1|) (|:| -4391 |#2|)) (QUOTE (-1119))) (|HasCategory| |#2| (QUOTE (-102))) (|HasCategory| |#2| (QUOTE (-1119)))) (-2781 (|HasCategory| (-2 (|:| -4300 |#1|) (|:| -4391 |#2|)) (QUOTE (-862))) (|HasCategory| (-2 (|:| -4300 |#1|) (|:| -4391 |#2|)) (QUOTE (-1119))) (|HasCategory| |#2| (QUOTE (-1119)))) (|HasCategory| (-2 (|:| -4300 |#1|) (|:| -4391 |#2|)) (QUOTE (-862))) (|HasCategory| |#1| (QUOTE (-862))) (|HasCategory| |#2| (QUOTE (-1119))) (|HasCategory| (-576) (QUOTE (-862))) (|HasCategory| (-2 (|:| -4300 |#1|) (|:| -4391 |#2|)) (QUOTE (-1119))) (-2781 (|HasCategory| (-2 (|:| -4300 |#1|) (|:| -4391 |#2|)) (QUOTE (-1119))) (|HasCategory| |#2| (QUOTE (-1119)))) (-2781 (|HasCategory| (-2 (|:| -4300 |#1|) (|:| -4391 |#2|)) (LIST (QUOTE -625) (QUOTE (-874)))) (|HasCategory| |#2| (LIST (QUOTE -625) (QUOTE (-874))))) (-2781 (|HasCategory| (-2 (|:| -4300 |#1|) (|:| -4391 |#2|)) (QUOTE (-102))) (|HasCategory| |#2| (QUOTE (-102)))) (|HasCategory| |#2| (QUOTE (-102))) (|HasCategory| |#2| (LIST (QUOTE -625) (QUOTE (-874)))) (|HasCategory| (-2 (|:| -4300 |#1|) (|:| -4391 |#2|)) (LIST (QUOTE -625) (QUOTE (-874)))) (|HasCategory| (-2 (|:| -4300 |#1|) (|:| -4391 |#2|)) (QUOTE (-102))) (-12 (|HasCategory| (-2 (|:| -4300 |#1|) (|:| -4391 |#2|)) (QUOTE (-1119))) (|HasCategory| (-2 (|:| -4300 |#1|) (|:| -4391 |#2|)) (LIST (QUOTE -319) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -4300) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -4391) (|devaluate| |#2|))))))) +((-2755 (-12 (|HasCategory| (-2 (|:| -4298 |#1|) (|:| -4437 |#2|)) (QUOTE (-862))) (|HasCategory| (-2 (|:| -4298 |#1|) (|:| -4437 |#2|)) (LIST (QUOTE -319) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -4298) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -4437) (|devaluate| |#2|)))))) (-12 (|HasCategory| (-2 (|:| -4298 |#1|) (|:| -4437 |#2|)) (QUOTE (-1119))) (|HasCategory| (-2 (|:| -4298 |#1|) (|:| -4437 |#2|)) (LIST (QUOTE -319) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -4298) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -4437) (|devaluate| |#2|))))))) (-2755 (|HasCategory| (-2 (|:| -4298 |#1|) (|:| -4437 |#2|)) (QUOTE (-862))) (|HasCategory| (-2 (|:| -4298 |#1|) (|:| -4437 |#2|)) (QUOTE (-1119))) (|HasCategory| (-2 (|:| -4298 |#1|) (|:| -4437 |#2|)) (LIST (QUOTE -625) (QUOTE (-874)))) (|HasCategory| |#2| (QUOTE (-1119))) (|HasCategory| |#2| (LIST (QUOTE -625) (QUOTE (-874))))) (|HasCategory| (-2 (|:| -4298 |#1|) (|:| -4437 |#2|)) (LIST (QUOTE -626) (QUOTE (-548)))) (-12 (|HasCategory| |#2| (QUOTE (-1119))) (|HasCategory| |#2| (LIST (QUOTE -319) (|devaluate| |#2|)))) (-2755 (|HasCategory| (-2 (|:| -4298 |#1|) (|:| -4437 |#2|)) (QUOTE (-102))) (|HasCategory| (-2 (|:| -4298 |#1|) (|:| -4437 |#2|)) (QUOTE (-862))) (|HasCategory| (-2 (|:| -4298 |#1|) (|:| -4437 |#2|)) (QUOTE (-1119))) (|HasCategory| |#2| (QUOTE (-102))) (|HasCategory| |#2| (QUOTE (-1119)))) (-2755 (|HasCategory| (-2 (|:| -4298 |#1|) (|:| -4437 |#2|)) (QUOTE (-862))) (|HasCategory| (-2 (|:| -4298 |#1|) (|:| -4437 |#2|)) (QUOTE (-1119))) (|HasCategory| |#2| (QUOTE (-1119)))) (|HasCategory| (-2 (|:| -4298 |#1|) (|:| -4437 |#2|)) (QUOTE (-862))) (|HasCategory| |#1| (QUOTE (-862))) (|HasCategory| |#2| (QUOTE (-1119))) (|HasCategory| (-576) (QUOTE (-862))) (|HasCategory| (-2 (|:| -4298 |#1|) (|:| -4437 |#2|)) (QUOTE (-1119))) (-2755 (|HasCategory| (-2 (|:| -4298 |#1|) (|:| -4437 |#2|)) (QUOTE (-1119))) (|HasCategory| |#2| (QUOTE (-1119)))) (-2755 (|HasCategory| (-2 (|:| -4298 |#1|) (|:| -4437 |#2|)) (LIST (QUOTE -625) (QUOTE (-874)))) (|HasCategory| |#2| (LIST (QUOTE -625) (QUOTE (-874))))) (-2755 (|HasCategory| (-2 (|:| -4298 |#1|) (|:| -4437 |#2|)) (QUOTE (-102))) (|HasCategory| |#2| (QUOTE (-102)))) (|HasCategory| |#2| (QUOTE (-102))) (|HasCategory| |#2| (LIST (QUOTE -625) (QUOTE (-874)))) (|HasCategory| (-2 (|:| -4298 |#1|) (|:| -4437 |#2|)) (LIST (QUOTE -625) (QUOTE (-874)))) (|HasCategory| (-2 (|:| -4298 |#1|) (|:| -4437 |#2|)) (QUOTE (-102))) (-12 (|HasCategory| (-2 (|:| -4298 |#1|) (|:| -4437 |#2|)) (QUOTE (-1119))) (|HasCategory| (-2 (|:| -4298 |#1|) (|:| -4437 |#2|)) (LIST (QUOTE -319) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -4298) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -4437) (|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| $) "\\spad{leadingCoefficient(p)} returns the coefficient highest degree term of \\spad{p}."))) NIL @@ -144,7 +144,7 @@ NIL ((|constructor| (NIL "\\spad{ApplyUnivariateSkewPolynomial} (internal) allows univariate skew polynomials to be applied to appropriate modules.")) (|apply| ((|#2| |#3| (|Mapping| |#2| |#2|) |#2|) "\\spad{apply(p, f, m)} returns \\spad{p(m)} where the action is given by \\spad{x m = f(m)}. \\spad{f} must be an \\spad{R}-pseudo linear map on \\spad{M}."))) NIL NIL -(-54 |Base| R -1966) +(-54 |Base| R -1955) ((|constructor| (NIL "This package apply rewrite rules to expressions,{} calling the pattern matcher.")) (|localUnquote| ((|#3| |#3| (|List| (|Symbol|))) "\\spad{localUnquote(f,ls)} is a local function.")) (|applyRules| ((|#3| (|List| (|RewriteRule| |#1| |#2| |#3|)) |#3| (|PositiveInteger|)) "\\spad{applyRules([r1,...,rn], expr, n)} applies the rules \\spad{r1},{}...,{}\\spad{rn} to \\spad{f} a most \\spad{n} times.") ((|#3| (|List| (|RewriteRule| |#1| |#2| |#3|)) |#3|) "\\spad{applyRules([r1,...,rn], expr)} applies the rules \\spad{r1},{}...,{}\\spad{rn} to \\spad{f} an unlimited number of times,{} \\spadignore{i.e.} until none of \\spad{r1},{}...,{}\\spad{rn} is applicable to the expression."))) NIL NIL @@ -167,64 +167,64 @@ NIL (-59 S) ((|constructor| (NIL "This is the domain of 1-based one dimensional arrays")) (|oneDimensionalArray| (($ (|NonNegativeInteger|) |#1|) "\\spad{oneDimensionalArray(n,s)} creates an array from \\spad{n} copies of element \\spad{s}") (($ (|List| |#1|)) "\\spad{oneDimensionalArray(l)} creates an array from a list of elements \\spad{l}"))) ((-4463 . T) (-4462 . T)) -((-2781 (-12 (|HasCategory| |#1| (QUOTE (-862))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1119))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|))))) (-2781 (-12 (|HasCategory| |#1| (QUOTE (-1119))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-874))))) (|HasCategory| |#1| (LIST (QUOTE -626) (QUOTE (-548)))) (-2781 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-862))) (|HasCategory| |#1| (QUOTE (-1119)))) (-2781 (|HasCategory| |#1| (QUOTE (-862))) (|HasCategory| |#1| (QUOTE (-1119)))) (|HasCategory| |#1| (QUOTE (-862))) (|HasCategory| (-576) (QUOTE (-862))) (|HasCategory| |#1| (QUOTE (-1119))) (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-874)))) (|HasCategory| |#1| (QUOTE (-102))) (-12 (|HasCategory| |#1| (QUOTE (-1119))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|))))) +((-2755 (-12 (|HasCategory| |#1| (QUOTE (-862))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1119))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|))))) (-2755 (-12 (|HasCategory| |#1| (QUOTE (-1119))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-874))))) (|HasCategory| |#1| (LIST (QUOTE -626) (QUOTE (-548)))) (-2755 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-862))) (|HasCategory| |#1| (QUOTE (-1119)))) (-2755 (|HasCategory| |#1| (QUOTE (-862))) (|HasCategory| |#1| (QUOTE (-1119)))) (|HasCategory| |#1| (QUOTE (-862))) (|HasCategory| (-576) (QUOTE (-862))) (|HasCategory| |#1| (QUOTE (-1119))) (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-874)))) (|HasCategory| |#1| (QUOTE (-102))) (-12 (|HasCategory| |#1| (QUOTE (-1119))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|))))) (-60 R) ((|constructor| (NIL "\\indented{1}{A TwoDimensionalArray is a two dimensional array with} 1-based indexing for both rows and columns.")) (|shallowlyMutable| ((|attribute|) "One may destructively alter TwoDimensionalArray\\spad{'s}."))) ((-4462 . T) (-4463 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1119))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1119))) (-2781 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-1119)))) (-2781 (-12 (|HasCategory| |#1| (QUOTE (-1119))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-874))))) (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-874)))) (|HasCategory| |#1| (QUOTE (-102)))) -(-61 -2648) +((-12 (|HasCategory| |#1| (QUOTE (-1119))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1119))) (-2755 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-1119)))) (-2755 (-12 (|HasCategory| |#1| (QUOTE (-1119))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-874))))) (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-874)))) (|HasCategory| |#1| (QUOTE (-102)))) +(-61 -2624) ((|constructor| (NIL "\\spadtype{ASP10} produces Fortran for Type 10 ASPs,{} needed for NAG routine \\axiomOpFrom{d02kef}{d02Package}. This ASP computes the values of a set of functions,{} for example:\\begin{verbatim} SUBROUTINE COEFFN(P,Q,DQDL,X,ELAM,JINT) DOUBLE PRECISION ELAM,P,Q,X,DQDL INTEGER JINT P=1.0D0 Q=((-1.0D0*X**3)+ELAM*X*X-2.0D0)/(X*X) DQDL=1.0D0 RETURN END\\end{verbatim}")) (|coerce| (($ (|Vector| (|FortranExpression| (|construct| (QUOTE JINT) (QUOTE X) (QUOTE ELAM)) (|construct|) (|MachineFloat|)))) "\\spad{coerce(f)} takes objects from the appropriate instantiation of \\spadtype{FortranExpression} and turns them into an ASP."))) NIL NIL -(-62 -2648) +(-62 -2624) ((|constructor| (NIL "\\spadtype{Asp12} produces Fortran for Type 12 ASPs,{} needed for NAG routine \\axiomOpFrom{d02kef}{d02Package} etc.,{} for example:\\begin{verbatim} SUBROUTINE MONIT (MAXIT,IFLAG,ELAM,FINFO) DOUBLE PRECISION ELAM,FINFO(15) INTEGER MAXIT,IFLAG IF(MAXIT.EQ.-1)THEN PRINT*,\"Output from Monit\" ENDIF PRINT*,MAXIT,IFLAG,ELAM,(FINFO(I),I=1,4) RETURN END\\end{verbatim}")) (|outputAsFortran| (((|Void|)) "\\spad{outputAsFortran()} generates the default code for \\spadtype{ASP12}."))) NIL NIL -(-63 -2648) +(-63 -2624) ((|constructor| (NIL "\\spadtype{Asp19} produces Fortran for Type 19 ASPs,{} evaluating a set of functions and their jacobian at a given point,{} for example:\\begin{verbatim} SUBROUTINE LSFUN2(M,N,XC,FVECC,FJACC,LJC) DOUBLE PRECISION FVECC(M),FJACC(LJC,N),XC(N) INTEGER M,N,LJC INTEGER I,J DO 25003 I=1,LJC DO 25004 J=1,N FJACC(I,J)=0.0D025004 CONTINUE25003 CONTINUE FVECC(1)=((XC(1)-0.14D0)*XC(3)+(15.0D0*XC(1)-2.1D0)*XC(2)+1.0D0)/( &XC(3)+15.0D0*XC(2)) FVECC(2)=((XC(1)-0.18D0)*XC(3)+(7.0D0*XC(1)-1.26D0)*XC(2)+1.0D0)/( &XC(3)+7.0D0*XC(2)) FVECC(3)=((XC(1)-0.22D0)*XC(3)+(4.333333333333333D0*XC(1)-0.953333 &3333333333D0)*XC(2)+1.0D0)/(XC(3)+4.333333333333333D0*XC(2)) FVECC(4)=((XC(1)-0.25D0)*XC(3)+(3.0D0*XC(1)-0.75D0)*XC(2)+1.0D0)/( &XC(3)+3.0D0*XC(2)) FVECC(5)=((XC(1)-0.29D0)*XC(3)+(2.2D0*XC(1)-0.6379999999999999D0)* &XC(2)+1.0D0)/(XC(3)+2.2D0*XC(2)) FVECC(6)=((XC(1)-0.32D0)*XC(3)+(1.666666666666667D0*XC(1)-0.533333 &3333333333D0)*XC(2)+1.0D0)/(XC(3)+1.666666666666667D0*XC(2)) FVECC(7)=((XC(1)-0.35D0)*XC(3)+(1.285714285714286D0*XC(1)-0.45D0)* &XC(2)+1.0D0)/(XC(3)+1.285714285714286D0*XC(2)) FVECC(8)=((XC(1)-0.39D0)*XC(3)+(XC(1)-0.39D0)*XC(2)+1.0D0)/(XC(3)+ &XC(2)) FVECC(9)=((XC(1)-0.37D0)*XC(3)+(XC(1)-0.37D0)*XC(2)+1.285714285714 &286D0)/(XC(3)+XC(2)) FVECC(10)=((XC(1)-0.58D0)*XC(3)+(XC(1)-0.58D0)*XC(2)+1.66666666666 &6667D0)/(XC(3)+XC(2)) FVECC(11)=((XC(1)-0.73D0)*XC(3)+(XC(1)-0.73D0)*XC(2)+2.2D0)/(XC(3) &+XC(2)) FVECC(12)=((XC(1)-0.96D0)*XC(3)+(XC(1)-0.96D0)*XC(2)+3.0D0)/(XC(3) &+XC(2)) FVECC(13)=((XC(1)-1.34D0)*XC(3)+(XC(1)-1.34D0)*XC(2)+4.33333333333 &3333D0)/(XC(3)+XC(2)) FVECC(14)=((XC(1)-2.1D0)*XC(3)+(XC(1)-2.1D0)*XC(2)+7.0D0)/(XC(3)+X &C(2)) FVECC(15)=((XC(1)-4.39D0)*XC(3)+(XC(1)-4.39D0)*XC(2)+15.0D0)/(XC(3 &)+XC(2)) FJACC(1,1)=1.0D0 FJACC(1,2)=-15.0D0/(XC(3)**2+30.0D0*XC(2)*XC(3)+225.0D0*XC(2)**2) FJACC(1,3)=-1.0D0/(XC(3)**2+30.0D0*XC(2)*XC(3)+225.0D0*XC(2)**2) FJACC(2,1)=1.0D0 FJACC(2,2)=-7.0D0/(XC(3)**2+14.0D0*XC(2)*XC(3)+49.0D0*XC(2)**2) FJACC(2,3)=-1.0D0/(XC(3)**2+14.0D0*XC(2)*XC(3)+49.0D0*XC(2)**2) FJACC(3,1)=1.0D0 FJACC(3,2)=((-0.1110223024625157D-15*XC(3))-4.333333333333333D0)/( &XC(3)**2+8.666666666666666D0*XC(2)*XC(3)+18.77777777777778D0*XC(2) &**2) FJACC(3,3)=(0.1110223024625157D-15*XC(2)-1.0D0)/(XC(3)**2+8.666666 &666666666D0*XC(2)*XC(3)+18.77777777777778D0*XC(2)**2) FJACC(4,1)=1.0D0 FJACC(4,2)=-3.0D0/(XC(3)**2+6.0D0*XC(2)*XC(3)+9.0D0*XC(2)**2) FJACC(4,3)=-1.0D0/(XC(3)**2+6.0D0*XC(2)*XC(3)+9.0D0*XC(2)**2) FJACC(5,1)=1.0D0 FJACC(5,2)=((-0.1110223024625157D-15*XC(3))-2.2D0)/(XC(3)**2+4.399 &999999999999D0*XC(2)*XC(3)+4.839999999999998D0*XC(2)**2) FJACC(5,3)=(0.1110223024625157D-15*XC(2)-1.0D0)/(XC(3)**2+4.399999 &999999999D0*XC(2)*XC(3)+4.839999999999998D0*XC(2)**2) FJACC(6,1)=1.0D0 FJACC(6,2)=((-0.2220446049250313D-15*XC(3))-1.666666666666667D0)/( &XC(3)**2+3.333333333333333D0*XC(2)*XC(3)+2.777777777777777D0*XC(2) &**2) FJACC(6,3)=(0.2220446049250313D-15*XC(2)-1.0D0)/(XC(3)**2+3.333333 &333333333D0*XC(2)*XC(3)+2.777777777777777D0*XC(2)**2) FJACC(7,1)=1.0D0 FJACC(7,2)=((-0.5551115123125783D-16*XC(3))-1.285714285714286D0)/( &XC(3)**2+2.571428571428571D0*XC(2)*XC(3)+1.653061224489796D0*XC(2) &**2) FJACC(7,3)=(0.5551115123125783D-16*XC(2)-1.0D0)/(XC(3)**2+2.571428 &571428571D0*XC(2)*XC(3)+1.653061224489796D0*XC(2)**2) FJACC(8,1)=1.0D0 FJACC(8,2)=-1.0D0/(XC(3)**2+2.0D0*XC(2)*XC(3)+XC(2)**2) FJACC(8,3)=-1.0D0/(XC(3)**2+2.0D0*XC(2)*XC(3)+XC(2)**2) FJACC(9,1)=1.0D0 FJACC(9,2)=-1.285714285714286D0/(XC(3)**2+2.0D0*XC(2)*XC(3)+XC(2)* &*2) FJACC(9,3)=-1.285714285714286D0/(XC(3)**2+2.0D0*XC(2)*XC(3)+XC(2)* &*2) FJACC(10,1)=1.0D0 FJACC(10,2)=-1.666666666666667D0/(XC(3)**2+2.0D0*XC(2)*XC(3)+XC(2) &**2) FJACC(10,3)=-1.666666666666667D0/(XC(3)**2+2.0D0*XC(2)*XC(3)+XC(2) &**2) FJACC(11,1)=1.0D0 FJACC(11,2)=-2.2D0/(XC(3)**2+2.0D0*XC(2)*XC(3)+XC(2)**2) FJACC(11,3)=-2.2D0/(XC(3)**2+2.0D0*XC(2)*XC(3)+XC(2)**2) FJACC(12,1)=1.0D0 FJACC(12,2)=-3.0D0/(XC(3)**2+2.0D0*XC(2)*XC(3)+XC(2)**2) FJACC(12,3)=-3.0D0/(XC(3)**2+2.0D0*XC(2)*XC(3)+XC(2)**2) FJACC(13,1)=1.0D0 FJACC(13,2)=-4.333333333333333D0/(XC(3)**2+2.0D0*XC(2)*XC(3)+XC(2) &**2) FJACC(13,3)=-4.333333333333333D0/(XC(3)**2+2.0D0*XC(2)*XC(3)+XC(2) &**2) FJACC(14,1)=1.0D0 FJACC(14,2)=-7.0D0/(XC(3)**2+2.0D0*XC(2)*XC(3)+XC(2)**2) FJACC(14,3)=-7.0D0/(XC(3)**2+2.0D0*XC(2)*XC(3)+XC(2)**2) FJACC(15,1)=1.0D0 FJACC(15,2)=-15.0D0/(XC(3)**2+2.0D0*XC(2)*XC(3)+XC(2)**2) FJACC(15,3)=-15.0D0/(XC(3)**2+2.0D0*XC(2)*XC(3)+XC(2)**2) RETURN END\\end{verbatim}")) (|coerce| (($ (|Vector| (|FortranExpression| (|construct|) (|construct| (QUOTE XC)) (|MachineFloat|)))) "\\spad{coerce(f)} takes objects from the appropriate instantiation of \\spadtype{FortranExpression} and turns them into an ASP."))) NIL NIL -(-64 -2648) +(-64 -2624) ((|constructor| (NIL "\\spadtype{Asp1} produces Fortran for Type 1 ASPs,{} needed for various NAG routines. Type 1 ASPs take a univariate expression (in the symbol \\spad{X}) and turn it into a Fortran Function like the following:\\begin{verbatim} DOUBLE PRECISION FUNCTION F(X) DOUBLE PRECISION X F=DSIN(X) RETURN END\\end{verbatim}")) (|coerce| (($ (|FortranExpression| (|construct| (QUOTE X)) (|construct|) (|MachineFloat|))) "\\spad{coerce(f)} takes an object from the appropriate instantiation of \\spadtype{FortranExpression} and turns it into an ASP."))) NIL NIL -(-65 -2648) +(-65 -2624) ((|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 -2648) +(-66 -2624) ((|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 -2648) +(-67 -2624) ((|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 -2648) +(-68 -2624) ((|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 -2648) +(-69 -2624) ((|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 -2648) +(-70 -2624) ((|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 -2648) +(-71 -2624) ((|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 -2648) +(-72 -2624) ((|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 -2648) +(-73 -2624) ((|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 -2648) +(-74 -2624) ((|constructor| (NIL "\\spadtype{Asp35} produces Fortran for Type 35 ASPs,{} needed for NAG routines \\axiomOpFrom{c05pbf}{c05Package},{} \\axiomOpFrom{c05pcf}{c05Package},{} for example:\\begin{verbatim} SUBROUTINE FCN(N,X,FVEC,FJAC,LDFJAC,IFLAG) DOUBLE PRECISION X(N),FVEC(N),FJAC(LDFJAC,N) INTEGER LDFJAC,N,IFLAG IF(IFLAG.EQ.1)THEN FVEC(1)=(-1.0D0*X(2))+X(1) FVEC(2)=(-1.0D0*X(3))+2.0D0*X(2) FVEC(3)=3.0D0*X(3) ELSEIF(IFLAG.EQ.2)THEN FJAC(1,1)=1.0D0 FJAC(1,2)=-1.0D0 FJAC(1,3)=0.0D0 FJAC(2,1)=0.0D0 FJAC(2,2)=2.0D0 FJAC(2,3)=-1.0D0 FJAC(3,1)=0.0D0 FJAC(3,2)=0.0D0 FJAC(3,3)=3.0D0 ENDIF END\\end{verbatim}")) (|coerce| (($ (|Vector| (|FortranExpression| (|construct|) (|construct| (QUOTE X)) (|MachineFloat|)))) "\\spad{coerce(f)} takes objects from the appropriate instantiation of \\spadtype{FortranExpression} and turns them into an ASP."))) NIL NIL @@ -236,55 +236,55 @@ NIL ((|constructor| (NIL "\\spadtype{Asp42} produces Fortran for Type 42 ASPs,{} needed for NAG routines \\axiomOpFrom{d02raf}{d02Package} and \\axiomOpFrom{d02saf}{d02Package} in particular. These ASPs are in fact three Fortran routines which return a vector of functions,{} and their derivatives \\spad{wrt} \\spad{Y}(\\spad{i}) and also a continuation parameter EPS,{} for example:\\begin{verbatim} SUBROUTINE G(EPS,YA,YB,BC,N) DOUBLE PRECISION EPS,YA(N),YB(N),BC(N) INTEGER N BC(1)=YA(1) BC(2)=YA(2) BC(3)=YB(2)-1.0D0 RETURN END SUBROUTINE JACOBG(EPS,YA,YB,AJ,BJ,N) DOUBLE PRECISION EPS,YA(N),AJ(N,N),BJ(N,N),YB(N) INTEGER N AJ(1,1)=1.0D0 AJ(1,2)=0.0D0 AJ(1,3)=0.0D0 AJ(2,1)=0.0D0 AJ(2,2)=1.0D0 AJ(2,3)=0.0D0 AJ(3,1)=0.0D0 AJ(3,2)=0.0D0 AJ(3,3)=0.0D0 BJ(1,1)=0.0D0 BJ(1,2)=0.0D0 BJ(1,3)=0.0D0 BJ(2,1)=0.0D0 BJ(2,2)=0.0D0 BJ(2,3)=0.0D0 BJ(3,1)=0.0D0 BJ(3,2)=1.0D0 BJ(3,3)=0.0D0 RETURN END SUBROUTINE JACGEP(EPS,YA,YB,BCEP,N) DOUBLE PRECISION EPS,YA(N),YB(N),BCEP(N) INTEGER N BCEP(1)=0.0D0 BCEP(2)=0.0D0 BCEP(3)=0.0D0 RETURN END\\end{verbatim}")) (|coerce| (($ (|Vector| (|FortranExpression| (|construct| (QUOTE EPS)) (|construct| (QUOTE YA) (QUOTE YB)) (|MachineFloat|)))) "\\spad{coerce(f)} takes objects from the appropriate instantiation of \\spadtype{FortranExpression} and turns them into an ASP."))) NIL NIL -(-77 -2648) +(-77 -2624) ((|constructor| (NIL "\\spadtype{Asp49} produces Fortran for Type 49 ASPs,{} needed for NAG routines \\axiomOpFrom{e04dgf}{e04Package},{} \\axiomOpFrom{e04ucf}{e04Package},{} for example:\\begin{verbatim} SUBROUTINE OBJFUN(MODE,N,X,OBJF,OBJGRD,NSTATE,IUSER,USER) DOUBLE PRECISION X(N),OBJF,OBJGRD(N),USER(*) INTEGER N,IUSER(*),MODE,NSTATE OBJF=X(4)*X(9)+((-1.0D0*X(5))+X(3))*X(8)+((-1.0D0*X(3))+X(1))*X(7) &+(-1.0D0*X(2)*X(6)) OBJGRD(1)=X(7) OBJGRD(2)=-1.0D0*X(6) OBJGRD(3)=X(8)+(-1.0D0*X(7)) OBJGRD(4)=X(9) OBJGRD(5)=-1.0D0*X(8) OBJGRD(6)=-1.0D0*X(2) OBJGRD(7)=(-1.0D0*X(3))+X(1) OBJGRD(8)=(-1.0D0*X(5))+X(3) OBJGRD(9)=X(4) RETURN END\\end{verbatim}")) (|coerce| (($ (|FortranExpression| (|construct|) (|construct| (QUOTE X)) (|MachineFloat|))) "\\spad{coerce(f)} takes an object from the appropriate instantiation of \\spadtype{FortranExpression} and turns it into an ASP."))) NIL NIL -(-78 -2648) +(-78 -2624) ((|constructor| (NIL "\\spadtype{Asp4} produces Fortran for Type 4 ASPs,{} which take an expression in \\spad{X}(1) .. \\spad{X}(NDIM) and produce a real function of the form:\\begin{verbatim} DOUBLE PRECISION FUNCTION FUNCTN(NDIM,X) DOUBLE PRECISION X(NDIM) INTEGER NDIM FUNCTN=(4.0D0*X(1)*X(3)**2*DEXP(2.0D0*X(1)*X(3)))/(X(4)**2+(2.0D0* &X(2)+2.0D0)*X(4)+X(2)**2+2.0D0*X(2)+1.0D0) RETURN END\\end{verbatim}")) (|coerce| (($ (|FortranExpression| (|construct|) (|construct| (QUOTE X)) (|MachineFloat|))) "\\spad{coerce(f)} takes an object from the appropriate instantiation of \\spadtype{FortranExpression} and turns it into an ASP."))) NIL NIL -(-79 -2648) +(-79 -2624) ((|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 -2648) +(-80 -2624) ((|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 -2648) +(-81 -2624) ((|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 -2648) +(-82 -2624) ((|constructor| (NIL "\\spadtype{Asp73} produces Fortran for Type 73 ASPs,{} needed for NAG routine \\axiomOpFrom{d03eef}{d03Package},{} for example:\\begin{verbatim} SUBROUTINE PDEF(X,Y,ALPHA,BETA,GAMMA,DELTA,EPSOLN,PHI,PSI) DOUBLE PRECISION ALPHA,EPSOLN,PHI,X,Y,BETA,DELTA,GAMMA,PSI ALPHA=DSIN(X) BETA=Y GAMMA=X*Y DELTA=DCOS(X)*DSIN(Y) EPSOLN=Y+X PHI=X PSI=Y RETURN END\\end{verbatim}")) (|coerce| (($ (|Vector| (|FortranExpression| (|construct| (QUOTE X) (QUOTE Y)) (|construct|) (|MachineFloat|)))) "\\spad{coerce(f)} takes objects from the appropriate instantiation of \\spadtype{FortranExpression} and turns them into an ASP."))) NIL NIL -(-83 -2648) +(-83 -2624) ((|constructor| (NIL "\\spadtype{Asp74} produces Fortran for Type 74 ASPs,{} needed for NAG routine \\axiomOpFrom{d03eef}{d03Package},{} for example:\\begin{verbatim} SUBROUTINE BNDY(X,Y,A,B,C,IBND) DOUBLE PRECISION A,B,C,X,Y INTEGER IBND IF(IBND.EQ.0)THEN A=0.0D0 B=1.0D0 C=-1.0D0*DSIN(X) ELSEIF(IBND.EQ.1)THEN A=1.0D0 B=0.0D0 C=DSIN(X)*DSIN(Y) ELSEIF(IBND.EQ.2)THEN A=1.0D0 B=0.0D0 C=DSIN(X)*DSIN(Y) ELSEIF(IBND.EQ.3)THEN A=0.0D0 B=1.0D0 C=-1.0D0*DSIN(Y) ENDIF END\\end{verbatim}")) (|coerce| (($ (|Matrix| (|FortranExpression| (|construct| (QUOTE X) (QUOTE Y)) (|construct|) (|MachineFloat|)))) "\\spad{coerce(f)} takes objects from the appropriate instantiation of \\spadtype{FortranExpression} and turns them into an ASP."))) NIL NIL -(-84 -2648) +(-84 -2624) ((|constructor| (NIL "\\spadtype{Asp77} produces Fortran for Type 77 ASPs,{} needed for NAG routine \\axiomOpFrom{d02gbf}{d02Package},{} for example:\\begin{verbatim} SUBROUTINE FCNF(X,F) DOUBLE PRECISION X DOUBLE PRECISION F(2,2) F(1,1)=0.0D0 F(1,2)=1.0D0 F(2,1)=0.0D0 F(2,2)=-10.0D0 RETURN END\\end{verbatim}")) (|coerce| (($ (|Matrix| (|FortranExpression| (|construct| (QUOTE X)) (|construct|) (|MachineFloat|)))) "\\spad{coerce(f)} takes objects from the appropriate instantiation of \\spadtype{FortranExpression} and turns them into an ASP."))) NIL NIL -(-85 -2648) +(-85 -2624) ((|constructor| (NIL "\\spadtype{Asp78} produces Fortran for Type 78 ASPs,{} needed for NAG routine \\axiomOpFrom{d02gbf}{d02Package},{} for example:\\begin{verbatim} SUBROUTINE FCNG(X,G) DOUBLE PRECISION G(*),X G(1)=0.0D0 G(2)=0.0D0 END\\end{verbatim}")) (|coerce| (($ (|Vector| (|FortranExpression| (|construct| (QUOTE X)) (|construct|) (|MachineFloat|)))) "\\spad{coerce(f)} takes objects from the appropriate instantiation of \\spadtype{FortranExpression} and turns them into an ASP."))) NIL NIL -(-86 -2648) +(-86 -2624) ((|constructor| (NIL "\\spadtype{Asp7} produces Fortran for Type 7 ASPs,{} needed for NAG routines \\axiomOpFrom{d02bbf}{d02Package},{} \\axiomOpFrom{d02gaf}{d02Package}. These represent a vector of functions of the scalar \\spad{X} and the array \\spad{Z},{} and look like:\\begin{verbatim} SUBROUTINE FCN(X,Z,F) DOUBLE PRECISION F(*),X,Z(*) F(1)=DTAN(Z(3)) F(2)=((-0.03199999999999999D0*DCOS(Z(3))*DTAN(Z(3)))+(-0.02D0*Z(2) &**2))/(Z(2)*DCOS(Z(3))) F(3)=-0.03199999999999999D0/(X*Z(2)**2) RETURN END\\end{verbatim}")) (|coerce| (($ (|Vector| (|FortranExpression| (|construct| (QUOTE X)) (|construct| (QUOTE Y)) (|MachineFloat|)))) "\\spad{coerce(f)} takes objects from the appropriate instantiation of \\spadtype{FortranExpression} and turns them into an ASP."))) NIL NIL -(-87 -2648) +(-87 -2624) ((|constructor| (NIL "\\spadtype{Asp80} produces Fortran for Type 80 ASPs,{} needed for NAG routine \\axiomOpFrom{d02kef}{d02Package},{} for example:\\begin{verbatim} SUBROUTINE BDYVAL(XL,XR,ELAM,YL,YR) DOUBLE PRECISION ELAM,XL,YL(3),XR,YR(3) YL(1)=XL YL(2)=2.0D0 YR(1)=1.0D0 YR(2)=-1.0D0*DSQRT(XR+(-1.0D0*ELAM)) RETURN END\\end{verbatim}")) (|coerce| (($ (|Matrix| (|FortranExpression| (|construct| (QUOTE XL) (QUOTE XR) (QUOTE ELAM)) (|construct|) (|MachineFloat|)))) "\\spad{coerce(f)} takes objects from the appropriate instantiation of \\spadtype{FortranExpression} and turns them into an ASP."))) NIL NIL -(-88 -2648) +(-88 -2624) ((|constructor| (NIL "\\spadtype{Asp8} produces Fortran for Type 8 ASPs,{} needed for NAG routine \\axiomOpFrom{d02bbf}{d02Package}. This ASP prints intermediate values of the computed solution of an ODE and might look like:\\begin{verbatim} SUBROUTINE OUTPUT(XSOL,Y,COUNT,M,N,RESULT,FORWRD) DOUBLE PRECISION Y(N),RESULT(M,N),XSOL INTEGER M,N,COUNT LOGICAL FORWRD DOUBLE PRECISION X02ALF,POINTS(8) EXTERNAL X02ALF INTEGER I POINTS(1)=1.0D0 POINTS(2)=2.0D0 POINTS(3)=3.0D0 POINTS(4)=4.0D0 POINTS(5)=5.0D0 POINTS(6)=6.0D0 POINTS(7)=7.0D0 POINTS(8)=8.0D0 COUNT=COUNT+1 DO 25001 I=1,N RESULT(COUNT,I)=Y(I)25001 CONTINUE IF(COUNT.EQ.M)THEN IF(FORWRD)THEN XSOL=X02ALF() ELSE XSOL=-X02ALF() ENDIF ELSE XSOL=POINTS(COUNT) ENDIF END\\end{verbatim}"))) NIL NIL -(-89 -2648) +(-89 -2624) ((|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}."))) ((-4462 . T) (-4463 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1119))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1119))) (-2781 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-1119)))) (-2781 (-12 (|HasCategory| |#1| (QUOTE (-1119))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-874))))) (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-874)))) (|HasCategory| |#1| (QUOTE (-102)))) +((-12 (|HasCategory| |#1| (QUOTE (-1119))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1119))) (-2755 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-1119)))) (-2755 (-12 (|HasCategory| |#1| (QUOTE (-1119))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-874))))) (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-874)))) (|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 \\spad{pl} and \\spad{pr}. Then \\spad{mapDown!(l,pl,f)} and \\spad{mapDown!(l,pr,f)} are evaluated.") (($ $ |#1| (|Mapping| |#1| |#1| |#1|)) "\\spad{mapDown!(t,p,f)} returns \\spad{t} after traversing \\spad{t} in \"preorder\" (node then left then right) fashion replacing the successive interior nodes as follows. The root value \\spad{x} is replaced by \\spad{q} \\spad{:=} \\spad{f}(\\spad{p},{}\\spad{x}). The mapDown!(\\spad{l},{}\\spad{q},{}\\spad{f}) and mapDown!(\\spad{r},{}\\spad{q},{}\\spad{f}) are evaluated for the left and right subtrees \\spad{l} and \\spad{r} of \\spad{t}.")) (|mapUp!| (($ $ $ (|Mapping| |#1| |#1| |#1| |#1| |#1|)) "\\spad{mapUp!(t,t1,f)} traverses \\spad{t} in an \"endorder\" (left then right then node) fashion returning \\spad{t} with the value at each successive interior node of \\spad{t} replaced by \\spad{f}(\\spad{l},{}\\spad{r},{}\\spad{l1},{}\\spad{r1}) where \\spad{l} and \\spad{r} are the values at the immediate left and right nodes. Values \\spad{l1} and \\spad{r1} are values at the corresponding nodes of a balanced binary tree \\spad{t1},{} of identical shape at \\spad{t}.") ((|#1| $ (|Mapping| |#1| |#1| |#1|)) "\\spad{mapUp!(t,f)} traverses balanced binary tree \\spad{t} in an \"endorder\" (left then right then node) fashion returning \\spad{t} with the value at each successive interior node of \\spad{t} replaced by \\spad{f}(\\spad{l},{}\\spad{r}) where \\spad{l} and \\spad{r} are the values at the immediate left and right nodes.")) (|setleaves!| (($ $ (|List| |#1|)) "\\spad{setleaves!(t, ls)} sets the leaves of \\spad{t} in left-to-right order to the elements of \\spad{ls}.")) (|balancedBinaryTree| (($ (|NonNegativeInteger|) |#1|) "\\spad{balancedBinaryTree(n, s)} creates a balanced binary tree with \\spad{n} nodes each with value \\spad{s}."))) ((-4462 . T) (-4463 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1119))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1119))) (-2781 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-1119)))) (-2781 (-12 (|HasCategory| |#1| (QUOTE (-1119))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-874))))) (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-874)))) (|HasCategory| |#1| (QUOTE (-102)))) +((-12 (|HasCategory| |#1| (QUOTE (-1119))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1119))) (-2755 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-1119)))) (-2755 (-12 (|HasCategory| |#1| (QUOTE (-1119))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-874))))) (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-874)))) (|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."))) ((-4454 . T) (-4460 . T) (-4455 . T) ((-4464 "*") . T) (-4456 . T) (-4457 . T) (-4459 . T)) -((|HasCategory| (-576) (QUOTE (-926))) (|HasCategory| (-576) (LIST (QUOTE -1057) (QUOTE (-1195)))) (|HasCategory| (-576) (QUOTE (-146))) (|HasCategory| (-576) (QUOTE (-148))) (|HasCategory| (-576) (LIST (QUOTE -626) (QUOTE (-548)))) (|HasCategory| (-576) (QUOTE (-1041))) (|HasCategory| (-576) (QUOTE (-832))) (-2781 (|HasCategory| (-576) (QUOTE (-832))) (|HasCategory| (-576) (QUOTE (-862)))) (|HasCategory| (-576) (LIST (QUOTE -1057) (QUOTE (-576)))) (|HasCategory| (-576) (QUOTE (-1171))) (|HasCategory| (-576) (LIST (QUOTE -899) (QUOTE (-390)))) (|HasCategory| (-576) (LIST (QUOTE -899) (QUOTE (-576)))) (|HasCategory| (-576) (LIST (QUOTE -626) (LIST (QUOTE -905) (QUOTE (-390))))) (|HasCategory| (-576) (LIST (QUOTE -626) (LIST (QUOTE -905) (QUOTE (-576))))) (|HasCategory| (-576) (QUOTE (-237))) (|HasCategory| (-576) (LIST (QUOTE -917) (QUOTE (-1195)))) (|HasCategory| (-576) (QUOTE (-238))) (|HasCategory| (-576) (LIST (QUOTE -915) (QUOTE (-1195)))) (|HasCategory| (-576) (LIST (QUOTE -526) (QUOTE (-1195)) (QUOTE (-576)))) (|HasCategory| (-576) (LIST (QUOTE -319) (QUOTE (-576)))) (|HasCategory| (-576) (LIST (QUOTE -296) (QUOTE (-576)) (QUOTE (-576)))) (|HasCategory| (-576) (QUOTE (-317))) (|HasCategory| (-576) (QUOTE (-557))) (|HasCategory| (-576) (QUOTE (-862))) (|HasCategory| (-576) (LIST (QUOTE -651) (QUOTE (-576)))) (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| (-576) (QUOTE (-926)))) (-2781 (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| (-576) (QUOTE (-926)))) (|HasCategory| (-576) (QUOTE (-146))))) +((|HasCategory| (-576) (QUOTE (-926))) (|HasCategory| (-576) (LIST (QUOTE -1057) (QUOTE (-1195)))) (|HasCategory| (-576) (QUOTE (-146))) (|HasCategory| (-576) (QUOTE (-148))) (|HasCategory| (-576) (LIST (QUOTE -626) (QUOTE (-548)))) (|HasCategory| (-576) (QUOTE (-1041))) (|HasCategory| (-576) (QUOTE (-832))) (-2755 (|HasCategory| (-576) (QUOTE (-832))) (|HasCategory| (-576) (QUOTE (-862)))) (|HasCategory| (-576) (LIST (QUOTE -1057) (QUOTE (-576)))) (|HasCategory| (-576) (QUOTE (-1171))) (|HasCategory| (-576) (LIST (QUOTE -899) (QUOTE (-390)))) (|HasCategory| (-576) (LIST (QUOTE -899) (QUOTE (-576)))) (|HasCategory| (-576) (LIST (QUOTE -626) (LIST (QUOTE -905) (QUOTE (-390))))) (|HasCategory| (-576) (LIST (QUOTE -626) (LIST (QUOTE -905) (QUOTE (-576))))) (|HasCategory| (-576) (QUOTE (-237))) (|HasCategory| (-576) (LIST (QUOTE -917) (QUOTE (-1195)))) (|HasCategory| (-576) (QUOTE (-238))) (|HasCategory| (-576) (LIST (QUOTE -915) (QUOTE (-1195)))) (|HasCategory| (-576) (LIST (QUOTE -526) (QUOTE (-1195)) (QUOTE (-576)))) (|HasCategory| (-576) (LIST (QUOTE -319) (QUOTE (-576)))) (|HasCategory| (-576) (LIST (QUOTE -296) (QUOTE (-576)) (QUOTE (-576)))) (|HasCategory| (-576) (QUOTE (-317))) (|HasCategory| (-576) (QUOTE (-557))) (|HasCategory| (-576) (QUOTE (-862))) (|HasCategory| (-576) (LIST (QUOTE -651) (QUOTE (-576)))) (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| (-576) (QUOTE (-926)))) (-2755 (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| (-576) (QUOTE (-926)))) (|HasCategory| (-576) (QUOTE (-146))))) (-109) ((|constructor| (NIL "\\indented{1}{Author: Gabriel Dos Reis} Date Created: October 24,{} 2007 Date Last Modified: January 18,{} 2008. A `Binding' is a name asosciated with a collection of properties.")) (|binding| (($ (|Identifier|) (|List| (|Property|))) "\\spad{binding(n,props)} constructs a binding with name \\spad{`n'} and property list `props'.")) (|properties| (((|List| (|Property|)) $) "\\spad{properties(b)} returns the properties associated with binding \\spad{b}.")) (|name| (((|Identifier|) $) "\\spad{name(b)} returns the name of binding \\spad{b}"))) NIL @@ -392,7 +392,7 @@ NIL ((|constructor| (NIL "A basic operator is an object that can be applied to a list of arguments from a set,{} the result being a kernel over that set.")) (|setProperties| (($ $ (|AssociationList| (|String|) (|None|))) "\\spad{setProperties(op, l)} sets the property list of \\spad{op} to \\spad{l}. Argument \\spad{op} is modified \"in place\",{} \\spadignore{i.e.} no copy is made.")) (|setProperty| (($ $ (|Identifier|) (|None|)) "\\spad{setProperty(op, p, v)} attaches property \\spad{p} to \\spad{op},{} and sets its value to \\spad{v}. Argument \\spad{op} is modified \"in place\",{} \\spadignore{i.e.} no copy is made.") (($ $ (|String|) (|None|)) "\\spad{setProperty(op, s, v)} attaches property \\spad{s} to \\spad{op},{} and sets its value to \\spad{v}. Argument \\spad{op} is modified \"in place\",{} \\spadignore{i.e.} no copy is made.")) (|property| (((|Maybe| (|None|)) $ (|Identifier|)) "\\spad{property(op, p)} returns the value of property \\spad{p} if it is attached to \\spad{op},{} otherwise \\spad{nothing}.") (((|Union| (|None|) "failed") $ (|String|)) "\\spad{property(op, s)} returns the value of property \\spad{s} if it is attached to \\spad{op},{} and \"failed\" otherwise.")) (|deleteProperty!| (($ $ (|Identifier|)) "\\spad{deleteProperty!(op, p)} unattaches property \\spad{p} from \\spad{op}. Argument \\spad{op} is modified \"in place\",{} \\spadignore{i.e.} no copy is made.") (($ $ (|String|)) "\\spad{deleteProperty!(op, s)} unattaches property \\spad{s} from \\spad{op}. Argument \\spad{op} is modified \"in place\",{} \\spadignore{i.e.} no copy is made.")) (|assert| (($ $ (|Identifier|)) "\\spad{assert(op, p)} attaches property \\spad{p} to \\spad{op}. Argument \\spad{op} is modified \"in place\",{} \\spadignore{i.e.} no copy is made.")) (|has?| (((|Boolean|) $ (|Identifier|)) "\\spad{has?(op,p)} tests if property \\spad{s} is attached to \\spad{op}.")) (|input| (((|Union| (|Mapping| (|InputForm|) (|List| (|InputForm|))) "failed") $) "\\spad{input(op)} returns the \"\\%input\" property of \\spad{op} if it has one attached,{} \"failed\" otherwise.") (($ $ (|Mapping| (|InputForm|) (|List| (|InputForm|)))) "\\spad{input(op, foo)} attaches foo as the \"\\%input\" property of \\spad{op}. If \\spad{op} has a \"\\%input\" property \\spad{f},{} then \\spad{op(a1,...,an)} gets converted to InputForm as \\spad{f(a1,...,an)}.")) (|display| (($ $ (|Mapping| (|OutputForm|) (|OutputForm|))) "\\spad{display(op, foo)} attaches foo as the \"\\%display\" property of \\spad{op}. If \\spad{op} has a \"\\%display\" property \\spad{f},{} then \\spad{op(a)} gets converted to OutputForm as \\spad{f(a)}. Argument \\spad{op} must be unary.") (($ $ (|Mapping| (|OutputForm|) (|List| (|OutputForm|)))) "\\spad{display(op, foo)} attaches foo as the \"\\%display\" property of \\spad{op}. If \\spad{op} has a \"\\%display\" property \\spad{f},{} then \\spad{op(a1,...,an)} gets converted to OutputForm as \\spad{f(a1,...,an)}.") (((|Union| (|Mapping| (|OutputForm|) (|List| (|OutputForm|))) "failed") $) "\\spad{display(op)} returns the \"\\%display\" property of \\spad{op} if it has one attached,{} and \"failed\" otherwise.")) (|comparison| (($ $ (|Mapping| (|Boolean|) $ $)) "\\spad{comparison(op, foo?)} attaches foo? as the \"\\%less?\" property to \\spad{op}. If op1 and op2 have the same name,{} and one of them has a \"\\%less?\" property \\spad{f},{} then \\spad{f(op1, op2)} is called to decide whether \\spad{op1 < op2}.")) (|equality| (($ $ (|Mapping| (|Boolean|) $ $)) "\\spad{equality(op, foo?)} attaches foo? as the \"\\%equal?\" property to \\spad{op}. If op1 and op2 have the same name,{} and one of them has an \"\\%equal?\" property \\spad{f},{} then \\spad{f(op1, op2)} is called to decide whether op1 and op2 should be considered equal.")) (|weight| (($ $ (|NonNegativeInteger|)) "\\spad{weight(op, n)} attaches the weight \\spad{n} to \\spad{op}.") (((|NonNegativeInteger|) $) "\\spad{weight(op)} returns the weight attached to \\spad{op}.")) (|nary?| (((|Boolean|) $) "\\spad{nary?(op)} tests if \\spad{op} has arbitrary arity.")) (|unary?| (((|Boolean|) $) "\\spad{unary?(op)} tests if \\spad{op} is unary.")) (|nullary?| (((|Boolean|) $) "\\spad{nullary?(op)} tests if \\spad{op} is nullary.")) (|operator| (($ (|Symbol|) (|Arity|)) "\\spad{operator(f, a)} makes \\spad{f} into an operator of arity \\spad{a}.") (($ (|Symbol|) (|NonNegativeInteger|)) "\\spad{operator(f, n)} makes \\spad{f} into an \\spad{n}-ary operator.") (($ (|Symbol|)) "\\spad{operator(f)} makes \\spad{f} into an operator with arbitrary arity.")) (|copy| (($ $) "\\spad{copy(op)} returns a copy of \\spad{op}.")) (|properties| (((|AssociationList| (|String|) (|None|)) $) "\\spad{properties(op)} returns the list of all the properties currently attached to \\spad{op}."))) NIL NIL -(-116 -1966 UP) +(-116 -1955 UP) ((|constructor| (NIL "\\spadtype{BoundIntegerRoots} provides functions to find lower bounds on the integer roots of a polynomial.")) (|integerBound| (((|Integer|) |#2|) "\\spad{integerBound(p)} returns a lower bound on the negative integer roots of \\spad{p},{} and 0 if \\spad{p} has no negative integer roots."))) NIL NIL @@ -403,7 +403,7 @@ NIL (-118 |p|) ((|constructor| (NIL "Stream-based implementation of \\spad{Qp:} numbers are represented as sum(\\spad{i} = \\spad{k}..,{} a[\\spad{i}] * p^i),{} where the a[\\spad{i}] lie in -(\\spad{p} - 1)\\spad{/2},{}...,{}(\\spad{p} - 1)\\spad{/2}."))) ((-4454 . T) (-4460 . T) (-4455 . T) ((-4464 "*") . T) (-4456 . T) (-4457 . T) (-4459 . T)) -((|HasCategory| (-117 |#1|) (QUOTE (-926))) (|HasCategory| (-117 |#1|) (LIST (QUOTE -1057) (QUOTE (-1195)))) (|HasCategory| (-117 |#1|) (QUOTE (-146))) (|HasCategory| (-117 |#1|) (QUOTE (-148))) (|HasCategory| (-117 |#1|) (LIST (QUOTE -626) (QUOTE (-548)))) (|HasCategory| (-117 |#1|) (QUOTE (-1041))) (|HasCategory| (-117 |#1|) (QUOTE (-832))) (-2781 (|HasCategory| (-117 |#1|) (QUOTE (-832))) (|HasCategory| (-117 |#1|) (QUOTE (-862)))) (|HasCategory| (-117 |#1|) (LIST (QUOTE -1057) (QUOTE (-576)))) (|HasCategory| (-117 |#1|) (QUOTE (-1171))) (|HasCategory| (-117 |#1|) (LIST (QUOTE -899) (QUOTE (-390)))) (|HasCategory| (-117 |#1|) (LIST (QUOTE -899) (QUOTE (-576)))) (|HasCategory| (-117 |#1|) (LIST (QUOTE -626) (LIST (QUOTE -905) (QUOTE (-390))))) (|HasCategory| (-117 |#1|) (LIST (QUOTE -626) (LIST (QUOTE -905) (QUOTE (-576))))) (|HasCategory| (-117 |#1|) (LIST (QUOTE -651) (QUOTE (-576)))) (|HasCategory| (-117 |#1|) (QUOTE (-237))) (|HasCategory| (-117 |#1|) (LIST (QUOTE -917) (QUOTE (-1195)))) (|HasCategory| (-117 |#1|) (QUOTE (-238))) (|HasCategory| (-117 |#1|) (LIST (QUOTE -915) (QUOTE (-1195)))) (|HasCategory| (-117 |#1|) (LIST (QUOTE -526) (QUOTE (-1195)) (LIST (QUOTE -117) (|devaluate| |#1|)))) (|HasCategory| (-117 |#1|) (LIST (QUOTE -319) (LIST (QUOTE -117) (|devaluate| |#1|)))) (|HasCategory| (-117 |#1|) (LIST (QUOTE -296) (LIST (QUOTE -117) (|devaluate| |#1|)) (LIST (QUOTE -117) (|devaluate| |#1|)))) (|HasCategory| (-117 |#1|) (QUOTE (-317))) (|HasCategory| (-117 |#1|) (QUOTE (-557))) (|HasCategory| (-117 |#1|) (QUOTE (-862))) (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| (-117 |#1|) (QUOTE (-926)))) (-2781 (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| (-117 |#1|) (QUOTE (-926)))) (|HasCategory| (-117 |#1|) (QUOTE (-146))))) +((|HasCategory| (-117 |#1|) (QUOTE (-926))) (|HasCategory| (-117 |#1|) (LIST (QUOTE -1057) (QUOTE (-1195)))) (|HasCategory| (-117 |#1|) (QUOTE (-146))) (|HasCategory| (-117 |#1|) (QUOTE (-148))) (|HasCategory| (-117 |#1|) (LIST (QUOTE -626) (QUOTE (-548)))) (|HasCategory| (-117 |#1|) (QUOTE (-1041))) (|HasCategory| (-117 |#1|) (QUOTE (-832))) (-2755 (|HasCategory| (-117 |#1|) (QUOTE (-832))) (|HasCategory| (-117 |#1|) (QUOTE (-862)))) (|HasCategory| (-117 |#1|) (LIST (QUOTE -1057) (QUOTE (-576)))) (|HasCategory| (-117 |#1|) (QUOTE (-1171))) (|HasCategory| (-117 |#1|) (LIST (QUOTE -899) (QUOTE (-390)))) (|HasCategory| (-117 |#1|) (LIST (QUOTE -899) (QUOTE (-576)))) (|HasCategory| (-117 |#1|) (LIST (QUOTE -626) (LIST (QUOTE -905) (QUOTE (-390))))) (|HasCategory| (-117 |#1|) (LIST (QUOTE -626) (LIST (QUOTE -905) (QUOTE (-576))))) (|HasCategory| (-117 |#1|) (LIST (QUOTE -651) (QUOTE (-576)))) (|HasCategory| (-117 |#1|) (QUOTE (-237))) (|HasCategory| (-117 |#1|) (LIST (QUOTE -917) (QUOTE (-1195)))) (|HasCategory| (-117 |#1|) (QUOTE (-238))) (|HasCategory| (-117 |#1|) (LIST (QUOTE -915) (QUOTE (-1195)))) (|HasCategory| (-117 |#1|) (LIST (QUOTE -526) (QUOTE (-1195)) (LIST (QUOTE -117) (|devaluate| |#1|)))) (|HasCategory| (-117 |#1|) (LIST (QUOTE -319) (LIST (QUOTE -117) (|devaluate| |#1|)))) (|HasCategory| (-117 |#1|) (LIST (QUOTE -296) (LIST (QUOTE -117) (|devaluate| |#1|)) (LIST (QUOTE -117) (|devaluate| |#1|)))) (|HasCategory| (-117 |#1|) (QUOTE (-317))) (|HasCategory| (-117 |#1|) (QUOTE (-557))) (|HasCategory| (-117 |#1|) (QUOTE (-862))) (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| (-117 |#1|) (QUOTE (-926)))) (-2755 (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| (-117 |#1|) (QUOTE (-926)))) (|HasCategory| (-117 |#1|) (QUOTE (-146))))) (-119 A S) ((|constructor| (NIL "A binary-recursive aggregate has 0,{} 1 or 2 children and serves as a model for a binary tree or a doubly-linked aggregate structure")) (|setright!| (($ $ $) "\\spad{setright!(a,x)} sets the right child of \\spad{t} to be \\spad{x}.")) (|setleft!| (($ $ $) "\\spad{setleft!(a,b)} sets the left child of \\axiom{a} to be \\spad{b}.")) (|setelt| (($ $ "right" $) "\\spad{setelt(a,\"right\",b)} (also written \\axiom{\\spad{b} . right \\spad{:=} \\spad{b}}) is equivalent to \\axiom{setright!(a,{}\\spad{b})}.") (($ $ "left" $) "\\spad{setelt(a,\"left\",b)} (also written \\axiom{a . left \\spad{:=} \\spad{b}}) is equivalent to \\axiom{setleft!(a,{}\\spad{b})}.")) (|right| (($ $) "\\spad{right(a)} returns the right child.")) (|elt| (($ $ "right") "\\spad{elt(a,\"right\")} (also written: \\axiom{a . right}) is equivalent to \\axiom{right(a)}.") (($ $ "left") "\\spad{elt(u,\"left\")} (also written: \\axiom{a . left}) is equivalent to \\axiom{left(a)}.")) (|left| (($ $) "\\spad{left(u)} returns the left child."))) NIL @@ -419,7 +419,7 @@ NIL (-122 S) ((|constructor| (NIL "BinarySearchTree(\\spad{S}) is the domain of a binary trees where elements are ordered across the tree. A binary search tree is either empty or has a value which is an \\spad{S},{} and a right and left which are both BinaryTree(\\spad{S}) Elements are ordered across the tree.")) (|split| (((|Record| (|:| |less| $) (|:| |greater| $)) |#1| $) "\\spad{split(x,b)} splits binary tree \\spad{b} into two trees,{} one with elements greater than \\spad{x},{} the other with elements less than \\spad{x}.")) (|insertRoot!| (($ |#1| $) "\\spad{insertRoot!(x,b)} inserts element \\spad{x} as a root of binary search tree \\spad{b}.")) (|insert!| (($ |#1| $) "\\spad{insert!(x,b)} inserts element \\spad{x} as leaves into binary search tree \\spad{b}.")) (|binarySearchTree| (($ (|List| |#1|)) "\\spad{binarySearchTree(l)} \\undocumented"))) ((-4462 . T) (-4463 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1119))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1119))) (-2781 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-1119)))) (-2781 (-12 (|HasCategory| |#1| (QUOTE (-1119))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-874))))) (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-874)))) (|HasCategory| |#1| (QUOTE (-102)))) +((-12 (|HasCategory| |#1| (QUOTE (-1119))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1119))) (-2755 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-1119)))) (-2755 (-12 (|HasCategory| |#1| (QUOTE (-1119))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-874))))) (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-874)))) (|HasCategory| |#1| (QUOTE (-102)))) (-123 S) ((|constructor| (NIL "The bit aggregate category models aggregates representing large quantities of Boolean data.")) (|xor| (($ $ $) "\\spad{xor(a,b)} returns the logical {\\em exclusive-or} of bit aggregates \\axiom{a} and \\axiom{\\spad{b}}.")) (|nor| (($ $ $) "\\spad{nor(a,b)} returns the logical {\\em nor} of bit aggregates \\axiom{a} and \\axiom{\\spad{b}}.")) (|nand| (($ $ $) "\\spad{nand(a,b)} returns the logical {\\em nand} of bit aggregates \\axiom{a} and \\axiom{\\spad{b}}."))) NIL @@ -439,15 +439,15 @@ NIL (-127 S) ((|constructor| (NIL "\\spadtype{BinaryTournament(S)} is the domain of binary trees where elements are ordered down the tree. A binary search tree is either empty or is a node containing a \\spadfun{value} of type \\spad{S},{} and a \\spadfun{right} and a \\spadfun{left} which are both \\spadtype{BinaryTree(S)}")) (|insert!| (($ |#1| $) "\\spad{insert!(x,b)} inserts element \\spad{x} as leaves into binary tournament \\spad{b}.")) (|binaryTournament| (($ (|List| |#1|)) "\\spad{binaryTournament(ls)} creates a binary tournament with the elements of \\spad{ls} as values at the nodes."))) ((-4462 . T) (-4463 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1119))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1119))) (-2781 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-1119)))) (-2781 (-12 (|HasCategory| |#1| (QUOTE (-1119))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-874))))) (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-874)))) (|HasCategory| |#1| (QUOTE (-102)))) +((-12 (|HasCategory| |#1| (QUOTE (-1119))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1119))) (-2755 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-1119)))) (-2755 (-12 (|HasCategory| |#1| (QUOTE (-1119))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-874))))) (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-874)))) (|HasCategory| |#1| (QUOTE (-102)))) (-128 S) ((|constructor| (NIL "\\spadtype{BinaryTree(S)} is the domain of all binary trees. A binary tree over \\spad{S} is either empty or has a \\spadfun{value} which is an \\spad{S} and a \\spadfun{right} and \\spadfun{left} which are both binary trees.")) (|binaryTree| (($ $ |#1| $) "\\spad{binaryTree(l,v,r)} creates a binary tree with value \\spad{v} with left subtree \\spad{l} and right subtree \\spad{r}.") (($ |#1|) "\\spad{binaryTree(v)} is an non-empty binary tree with value \\spad{v},{} and left and right empty."))) ((-4462 . T) (-4463 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1119))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1119))) (-2781 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-1119)))) (-2781 (-12 (|HasCategory| |#1| (QUOTE (-1119))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-874))))) (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-874)))) (|HasCategory| |#1| (QUOTE (-102)))) +((-12 (|HasCategory| |#1| (QUOTE (-1119))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1119))) (-2755 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-1119)))) (-2755 (-12 (|HasCategory| |#1| (QUOTE (-1119))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-874))))) (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-874)))) (|HasCategory| |#1| (QUOTE (-102)))) (-129) ((|constructor| (NIL "ByteBuffer provides datatype for buffers of bytes. This domain differs from PrimitiveArray Byte in that it is not as rigid as PrimitiveArray Byte. That is,{} the typical use of ByteBuffer is to pre-allocate a vector of Byte of some capacity \\spad{`n'}. The array can then store up to \\spad{`n'} bytes. The actual interesting bytes count (the length of the buffer) is therefore different from the capacity. The length is no more than the capacity,{} but it can be set dynamically as needed. This functionality is used for example when reading bytes from input/output devices where we use buffers to transfer data in and out of the system. Note: a value of type ByteBuffer is 0-based indexed,{} as opposed \\indented{6}{Vector,{} but not unlike PrimitiveArray Byte.}")) (|finiteAggregate| ((|attribute|) "A ByteBuffer object is a finite aggregate")) (|setLength!| (((|NonNegativeInteger|) $ (|NonNegativeInteger|)) "\\spad{setLength!(buf,n)} sets the number of active bytes in the `buf'. Error if \\spad{`n'} is more than the capacity.")) (|capacity| (((|NonNegativeInteger|) $) "\\spad{capacity(buf)} returns the pre-allocated maximum size of `buf'.")) (|byteBuffer| (($ (|NonNegativeInteger|)) "\\spad{byteBuffer(n)} creates a buffer of capacity \\spad{n},{} and length 0."))) ((-4463 . T) (-4462 . T)) -((-2781 (-12 (|HasCategory| (-130) (QUOTE (-862))) (|HasCategory| (-130) (LIST (QUOTE -319) (QUOTE (-130))))) (-12 (|HasCategory| (-130) (QUOTE (-1119))) (|HasCategory| (-130) (LIST (QUOTE -319) (QUOTE (-130)))))) (-2781 (-12 (|HasCategory| (-130) (QUOTE (-1119))) (|HasCategory| (-130) (LIST (QUOTE -319) (QUOTE (-130))))) (|HasCategory| (-130) (LIST (QUOTE -625) (QUOTE (-874))))) (|HasCategory| (-130) (LIST (QUOTE -626) (QUOTE (-548)))) (-2781 (|HasCategory| (-130) (QUOTE (-102))) (|HasCategory| (-130) (QUOTE (-862))) (|HasCategory| (-130) (QUOTE (-1119)))) (-2781 (|HasCategory| (-130) (QUOTE (-862))) (|HasCategory| (-130) (QUOTE (-1119)))) (|HasCategory| (-130) (QUOTE (-862))) (|HasCategory| (-576) (QUOTE (-862))) (|HasCategory| (-130) (QUOTE (-1119))) (|HasCategory| (-130) (LIST (QUOTE -625) (QUOTE (-874)))) (|HasCategory| (-130) (QUOTE (-102))) (-12 (|HasCategory| (-130) (QUOTE (-1119))) (|HasCategory| (-130) (LIST (QUOTE -319) (QUOTE (-130)))))) +((-2755 (-12 (|HasCategory| (-130) (QUOTE (-862))) (|HasCategory| (-130) (LIST (QUOTE -319) (QUOTE (-130))))) (-12 (|HasCategory| (-130) (QUOTE (-1119))) (|HasCategory| (-130) (LIST (QUOTE -319) (QUOTE (-130)))))) (-2755 (-12 (|HasCategory| (-130) (QUOTE (-1119))) (|HasCategory| (-130) (LIST (QUOTE -319) (QUOTE (-130))))) (|HasCategory| (-130) (LIST (QUOTE -625) (QUOTE (-874))))) (|HasCategory| (-130) (LIST (QUOTE -626) (QUOTE (-548)))) (-2755 (|HasCategory| (-130) (QUOTE (-102))) (|HasCategory| (-130) (QUOTE (-862))) (|HasCategory| (-130) (QUOTE (-1119)))) (-2755 (|HasCategory| (-130) (QUOTE (-862))) (|HasCategory| (-130) (QUOTE (-1119)))) (|HasCategory| (-130) (QUOTE (-862))) (|HasCategory| (-576) (QUOTE (-862))) (|HasCategory| (-130) (QUOTE (-1119))) (|HasCategory| (-130) (LIST (QUOTE -625) (QUOTE (-874)))) (|HasCategory| (-130) (QUOTE (-102))) (-12 (|HasCategory| (-130) (QUOTE (-1119))) (|HasCategory| (-130) (LIST (QUOTE -319) (QUOTE (-130)))))) (-130) ((|constructor| (NIL "Byte is the datatype of 8-bit sized unsigned integer values.")) (|sample| (($) "\\spad{sample} gives a sample datum of type Byte.")) (|bitior| (($ $ $) "bitor(\\spad{x},{}\\spad{y}) returns the bitwise `inclusive or' of \\spad{`x'} and \\spad{`y'}.")) (|bitand| (($ $ $) "\\spad{bitand(x,y)} returns the bitwise `and' of \\spad{`x'} and \\spad{`y'}.")) (|byte| (($ (|NonNegativeInteger|)) "\\spad{byte(x)} injects the unsigned integer value \\spad{`v'} into the Byte algebra. \\spad{`v'} must be non-negative and less than 256."))) NIL @@ -472,11 +472,11 @@ NIL ((|constructor| (NIL "Members of the domain CardinalNumber are values indicating the cardinality of sets,{} both finite and infinite. Arithmetic operations are defined on cardinal numbers as follows. \\blankline If \\spad{x = \\#X} and \\spad{y = \\#Y} then \\indented{2}{\\spad{x+y\\space{2}= \\#(X+Y)}\\space{3}\\tab{30}disjoint union} \\indented{2}{\\spad{x-y\\space{2}= \\#(X-Y)}\\space{3}\\tab{30}relative complement} \\indented{2}{\\spad{x*y\\space{2}= \\#(X*Y)}\\space{3}\\tab{30}cartesian product} \\indented{2}{\\spad{x**y = \\#(X**Y)}\\space{2}\\tab{30}\\spad{X**Y = \\{g| g:Y->X\\}}} \\blankline The non-negative integers have a natural construction as cardinals \\indented{2}{\\spad{0 = \\#\\{\\}},{} \\spad{1 = \\{0\\}},{} \\spad{2 = \\{0, 1\\}},{} ...,{} \\spad{n = \\{i| 0 <= i < n\\}}.} \\blankline That \\spad{0} acts as a zero for the multiplication of cardinals is equivalent to the axiom of choice. \\blankline The generalized continuum hypothesis asserts \\center{\\spad{2**Aleph i = Aleph(i+1)}} and is independent of the axioms of set theory [Goedel 1940]. \\blankline Three commonly encountered cardinal numbers are \\indented{3}{\\spad{a = \\#Z}\\space{7}\\tab{30}countable infinity} \\indented{3}{\\spad{c = \\#R}\\space{7}\\tab{30}the continuum} \\indented{3}{\\spad{f = \\#\\{g| g:[0,1]->R\\}}} \\blankline In this domain,{} these values are obtained using \\indented{3}{\\spad{a := Aleph 0},{} \\spad{c := 2**a},{} \\spad{f := 2**c}.} \\blankline")) (|generalizedContinuumHypothesisAssumed| (((|Boolean|) (|Boolean|)) "\\spad{generalizedContinuumHypothesisAssumed(bool)} is used to dictate whether the hypothesis is to be assumed.")) (|generalizedContinuumHypothesisAssumed?| (((|Boolean|)) "\\spad{generalizedContinuumHypothesisAssumed?()} tests if the hypothesis is currently assumed.")) (|countable?| (((|Boolean|) $) "\\spad{countable?(\\spad{a})} determines whether \\spad{a} is a countable cardinal,{} \\spadignore{i.e.} an integer or \\spad{Aleph 0}.")) (|finite?| (((|Boolean|) $) "\\spad{finite?(\\spad{a})} determines whether \\spad{a} is a finite cardinal,{} \\spadignore{i.e.} an integer.")) (|Aleph| (($ (|NonNegativeInteger|)) "\\spad{Aleph(n)} provides the named (infinite) cardinal number.")) (** (($ $ $) "\\spad{x**y} returns \\spad{\\#(X**Y)} where \\spad{X**Y} is defined \\indented{1}{as \\spad{\\{g| g:Y->X\\}}.}")) (- (((|Union| $ "failed") $ $) "\\spad{x - y} returns an element \\spad{z} such that \\spad{z+y=x} or \"failed\" if no such element exists.")) (|commutative| ((|attribute| "*") "a domain \\spad{D} has \\spad{commutative(\"*\")} if it has an operation \\spad{\"*\": (D,D) -> D} which is commutative."))) (((-4464 "*") . T)) NIL -(-136 |minix| -2695 S T$) +(-136 |minix| -2701 S T$) ((|constructor| (NIL "This package provides functions to enable conversion of tensors given conversion of the components.")) (|map| (((|CartesianTensor| |#1| |#2| |#4|) (|Mapping| |#4| |#3|) (|CartesianTensor| |#1| |#2| |#3|)) "\\spad{map(f,ts)} does a componentwise conversion of the tensor \\spad{ts} to a tensor with components of type \\spad{T}.")) (|reshape| (((|CartesianTensor| |#1| |#2| |#4|) (|List| |#4|) (|CartesianTensor| |#1| |#2| |#3|)) "\\spad{reshape(lt,ts)} organizes the list of components \\spad{lt} into a tensor with the same shape as \\spad{ts}."))) NIL NIL -(-137 |minix| -2695 R) +(-137 |minix| -2701 R) ((|constructor| (NIL "CartesianTensor(minix,{}dim,{}\\spad{R}) provides Cartesian tensors with components belonging to a commutative ring \\spad{R}. These tensors can have any number of indices. Each index takes values from \\spad{minix} to \\spad{minix + dim - 1}.")) (|sample| (($) "\\spad{sample()} returns an object of type \\%.")) (|unravel| (($ (|List| |#3|)) "\\spad{unravel(t)} produces a tensor from a list of components such that \\indented{2}{\\spad{unravel(ravel(t)) = t}.}")) (|ravel| (((|List| |#3|) $) "\\spad{ravel(t)} produces a list of components from a tensor such that \\indented{2}{\\spad{unravel(ravel(t)) = t}.}")) (|leviCivitaSymbol| (($) "\\spad{leviCivitaSymbol()} is the rank \\spad{dim} tensor defined by \\spad{leviCivitaSymbol()(i1,...idim) = +1/0/-1} if \\spad{i1,...,idim} is an even/is nota /is an odd permutation of \\spad{minix,...,minix+dim-1}.")) (|kroneckerDelta| (($) "\\spad{kroneckerDelta()} is the rank 2 tensor defined by \\indented{3}{\\spad{kroneckerDelta()(i,j)}} \\indented{6}{\\spad{= 1\\space{2}if i = j}} \\indented{6}{\\spad{= 0 if\\space{2}i \\~= j}}")) (|reindex| (($ $ (|List| (|Integer|))) "\\spad{reindex(t,[i1,...,idim])} permutes the indices of \\spad{t}. For example,{} if \\spad{r = reindex(t, [4,1,2,3])} for a rank 4 tensor \\spad{t},{} then \\spad{r} is the rank for tensor given by \\indented{4}{\\spad{r(i,j,k,l) = t(l,i,j,k)}.}")) (|transpose| (($ $ (|Integer|) (|Integer|)) "\\spad{transpose(t,i,j)} exchanges the \\spad{i}\\spad{-}th and \\spad{j}\\spad{-}th indices of \\spad{t}. For example,{} if \\spad{r = transpose(t,2,3)} for a rank 4 tensor \\spad{t},{} then \\spad{r} is the rank 4 tensor given by \\indented{4}{\\spad{r(i,j,k,l) = t(i,k,j,l)}.}") (($ $) "\\spad{transpose(t)} exchanges the first and last indices of \\spad{t}. For example,{} if \\spad{r = transpose(t)} for a rank 4 tensor \\spad{t},{} then \\spad{r} is the rank 4 tensor given by \\indented{4}{\\spad{r(i,j,k,l) = t(l,j,k,i)}.}")) (|contract| (($ $ (|Integer|) (|Integer|)) "\\spad{contract(t,i,j)} is the contraction of tensor \\spad{t} which sums along the \\spad{i}\\spad{-}th and \\spad{j}\\spad{-}th indices. For example,{} if \\spad{r = contract(t,1,3)} for a rank 4 tensor \\spad{t},{} then \\spad{r} is the rank 2 \\spad{(= 4 - 2)} tensor given by \\indented{4}{\\spad{r(i,j) = sum(h=1..dim,t(h,i,h,j))}.}") (($ $ (|Integer|) $ (|Integer|)) "\\spad{contract(t,i,s,j)} is the inner product of tenors \\spad{s} and \\spad{t} which sums along the \\spad{k1}\\spad{-}th index of \\spad{t} and the \\spad{k2}\\spad{-}th index of \\spad{s}. For example,{} if \\spad{r = contract(s,2,t,1)} for rank 3 tensors rank 3 tensors \\spad{s} and \\spad{t},{} then \\spad{r} is the rank 4 \\spad{(= 3 + 3 - 2)} tensor given by \\indented{4}{\\spad{r(i,j,k,l) = sum(h=1..dim,s(i,h,j)*t(h,k,l))}.}")) (* (($ $ $) "\\spad{s*t} is the inner product of the tensors \\spad{s} and \\spad{t} which contracts the last index of \\spad{s} with the first index of \\spad{t},{} \\spadignore{i.e.} \\indented{4}{\\spad{t*s = contract(t,rank t, s, 1)}} \\indented{4}{\\spad{t*s = sum(k=1..N, t[i1,..,iN,k]*s[k,j1,..,jM])}} This is compatible with the use of \\spad{M*v} to denote the matrix-vector inner product.")) (|product| (($ $ $) "\\spad{product(s,t)} is the outer product of the tensors \\spad{s} and \\spad{t}. For example,{} if \\spad{r = product(s,t)} for rank 2 tensors \\spad{s} and \\spad{t},{} then \\spad{r} is a rank 4 tensor given by \\indented{4}{\\spad{r(i,j,k,l) = s(i,j)*t(k,l)}.}")) (|elt| ((|#3| $ (|List| (|Integer|))) "\\spad{elt(t,[i1,...,iN])} gives a component of a rank \\spad{N} tensor.") ((|#3| $ (|Integer|) (|Integer|) (|Integer|) (|Integer|)) "\\spad{elt(t,i,j,k,l)} gives a component of a rank 4 tensor.") ((|#3| $ (|Integer|) (|Integer|) (|Integer|)) "\\spad{elt(t,i,j,k)} gives a component of a rank 3 tensor.") ((|#3| $ (|Integer|) (|Integer|)) "\\spad{elt(t,i,j)} gives a component of a rank 2 tensor.") ((|#3| $) "\\spad{elt(t)} gives the component of a rank 0 tensor.")) (|rank| (((|NonNegativeInteger|) $) "\\spad{rank(t)} returns the tensorial rank of \\spad{t} (that is,{} the number of indices). This is the same as the graded module degree.")) (|coerce| (($ (|List| $)) "\\spad{coerce([t_1,...,t_dim])} allows tensors to be constructed using lists.") (($ (|List| |#3|)) "\\spad{coerce([r_1,...,r_dim])} allows tensors to be constructed using lists.") (($ (|SquareMatrix| |#2| |#3|)) "\\spad{coerce(m)} views a matrix as a rank 2 tensor.") (($ (|DirectProduct| |#2| |#3|)) "\\spad{coerce(v)} views a vector as a rank 1 tensor."))) NIL NIL @@ -499,7 +499,7 @@ NIL (-142) ((|constructor| (NIL "This domain allows classes of characters to be defined and manipulated efficiently.")) (|alphanumeric| (($) "\\spad{alphanumeric()} returns the class of all characters for which \\spadfunFrom{alphanumeric?}{Character} is \\spad{true}.")) (|alphabetic| (($) "\\spad{alphabetic()} returns the class of all characters for which \\spadfunFrom{alphabetic?}{Character} is \\spad{true}.")) (|lowerCase| (($) "\\spad{lowerCase()} returns the class of all characters for which \\spadfunFrom{lowerCase?}{Character} is \\spad{true}.")) (|upperCase| (($) "\\spad{upperCase()} returns the class of all characters for which \\spadfunFrom{upperCase?}{Character} is \\spad{true}.")) (|hexDigit| (($) "\\spad{hexDigit()} returns the class of all characters for which \\spadfunFrom{hexDigit?}{Character} is \\spad{true}.")) (|digit| (($) "\\spad{digit()} returns the class of all characters for which \\spadfunFrom{digit?}{Character} is \\spad{true}.")) (|charClass| (($ (|List| (|Character|))) "\\spad{charClass(l)} creates a character class which contains exactly the characters given in the list \\spad{l}.") (($ (|String|)) "\\spad{charClass(s)} creates a character class which contains exactly the characters given in the string \\spad{s}."))) ((-4462 . T) (-4452 . T) (-4463 . T)) -((-2781 (-12 (|HasCategory| (-145) (QUOTE (-379))) (|HasCategory| (-145) (LIST (QUOTE -319) (QUOTE (-145))))) (-12 (|HasCategory| (-145) (QUOTE (-1119))) (|HasCategory| (-145) (LIST (QUOTE -319) (QUOTE (-145)))))) (|HasCategory| (-145) (LIST (QUOTE -626) (QUOTE (-548)))) (|HasCategory| (-145) (QUOTE (-379))) (|HasCategory| (-145) (QUOTE (-862))) (|HasCategory| (-145) (QUOTE (-1119))) (|HasCategory| (-145) (LIST (QUOTE -625) (QUOTE (-874)))) (|HasCategory| (-145) (QUOTE (-102))) (-12 (|HasCategory| (-145) (QUOTE (-1119))) (|HasCategory| (-145) (LIST (QUOTE -319) (QUOTE (-145)))))) +((-2755 (-12 (|HasCategory| (-145) (QUOTE (-379))) (|HasCategory| (-145) (LIST (QUOTE -319) (QUOTE (-145))))) (-12 (|HasCategory| (-145) (QUOTE (-1119))) (|HasCategory| (-145) (LIST (QUOTE -319) (QUOTE (-145)))))) (|HasCategory| (-145) (LIST (QUOTE -626) (QUOTE (-548)))) (|HasCategory| (-145) (QUOTE (-379))) (|HasCategory| (-145) (QUOTE (-862))) (|HasCategory| (-145) (QUOTE (-1119))) (|HasCategory| (-145) (LIST (QUOTE -625) (QUOTE (-874)))) (|HasCategory| (-145) (QUOTE (-102))) (-12 (|HasCategory| (-145) (QUOTE (-1119))) (|HasCategory| (-145) (LIST (QUOTE -319) (QUOTE (-145)))))) (-143 R Q A) ((|constructor| (NIL "CommonDenominator provides functions to compute the common denominator of a finite linear aggregate of elements of the quotient field of an integral domain.")) (|splitDenominator| (((|Record| (|:| |num| |#3|) (|:| |den| |#1|)) |#3|) "\\spad{splitDenominator([q1,...,qn])} returns \\spad{[[p1,...,pn], d]} such that \\spad{qi = pi/d} and \\spad{d} is a common denominator for the \\spad{qi}\\spad{'s}.")) (|clearDenominator| ((|#3| |#3|) "\\spad{clearDenominator([q1,...,qn])} returns \\spad{[p1,...,pn]} such that \\spad{qi = pi/d} where \\spad{d} is a common denominator for the \\spad{qi}\\spad{'s}.")) (|commonDenominator| ((|#1| |#3|) "\\spad{commonDenominator([q1,...,qn])} returns a common denominator \\spad{d} for \\spad{q1},{}...,{}\\spad{qn}."))) NIL @@ -524,7 +524,7 @@ NIL ((|constructor| (NIL "Rings of Characteristic Zero."))) ((-4459 . T)) NIL -(-149 -1966 UP UPUP) +(-149 -1955 UP UPUP) ((|constructor| (NIL "Tools to send a point to infinity on an algebraic curve.")) (|chvar| (((|Record| (|:| |func| |#3|) (|:| |poly| |#3|) (|:| |c1| (|Fraction| |#2|)) (|:| |c2| (|Fraction| |#2|)) (|:| |deg| (|NonNegativeInteger|))) |#3| |#3|) "\\spad{chvar(f(x,y), p(x,y))} returns \\spad{[g(z,t), q(z,t), c1(z), c2(z), n]} such that under the change of variable \\spad{x = c1(z)},{} \\spad{y = t * c2(z)},{} one gets \\spad{f(x,y) = g(z,t)}. The algebraic relation between \\spad{x} and \\spad{y} is \\spad{p(x, y) = 0}. The algebraic relation between \\spad{z} and \\spad{t} is \\spad{q(z, t) = 0}.")) (|eval| ((|#3| |#3| (|Fraction| |#2|) (|Fraction| |#2|)) "\\spad{eval(p(x,y), f(x), g(x))} returns \\spad{p(f(x), y * g(x))}.")) (|goodPoint| ((|#1| |#3| |#3|) "\\spad{goodPoint(p, q)} returns an integer a such that a is neither a pole of \\spad{p(x,y)} nor a branch point of \\spad{q(x,y) = 0}.")) (|rootPoly| (((|Record| (|:| |exponent| (|NonNegativeInteger|)) (|:| |coef| (|Fraction| |#2|)) (|:| |radicand| |#2|)) (|Fraction| |#2|) (|NonNegativeInteger|)) "\\spad{rootPoly(g, n)} returns \\spad{[m, c, P]} such that \\spad{c * g ** (1/n) = P ** (1/m)} thus if \\spad{y**n = g},{} then \\spad{z**m = P} where \\spad{z = c * y}.")) (|radPoly| (((|Union| (|Record| (|:| |radicand| (|Fraction| |#2|)) (|:| |deg| (|NonNegativeInteger|))) "failed") |#3|) "\\spad{radPoly(p(x, y))} returns \\spad{[c(x), n]} if \\spad{p} is of the form \\spad{y**n - c(x)},{} \"failed\" otherwise.")) (|mkIntegral| (((|Record| (|:| |coef| (|Fraction| |#2|)) (|:| |poly| |#3|)) |#3|) "\\spad{mkIntegral(p(x,y))} returns \\spad{[c(x), q(x,z)]} such that \\spad{z = c * y} is integral. The algebraic relation between \\spad{x} and \\spad{y} is \\spad{p(x, y) = 0}. The algebraic relation between \\spad{x} and \\spad{z} is \\spad{q(x, z) = 0}."))) NIL NIL @@ -564,7 +564,7 @@ NIL ((|constructor| (NIL "Color() specifies a domain of 27 colors provided in the \\Language{} system (the colors mix additively).")) (|color| (($ (|Integer|)) "\\spad{color(i)} returns a color of the indicated hue \\spad{i}.")) (|numberOfHues| (((|PositiveInteger|)) "\\spad{numberOfHues()} returns the number of total hues,{} set in totalHues.")) (|hue| (((|Integer|) $) "\\spad{hue(c)} returns the hue index of the indicated color \\spad{c}.")) (|blue| (($) "\\spad{blue()} returns the position of the blue hue from total hues.")) (|green| (($) "\\spad{green()} returns the position of the green hue from total hues.")) (|yellow| (($) "\\spad{yellow()} returns the position of the yellow hue from total hues.")) (|red| (($) "\\spad{red()} returns the position of the red hue from total hues.")) (+ (($ $ $) "\\spad{c1 + c2} additively mixes the two colors \\spad{c1} and \\spad{c2}.")) (* (($ (|DoubleFloat|) $) "\\spad{s * c},{} returns the color \\spad{c},{} whose weighted shade has been scaled by \\spad{s}.") (($ (|PositiveInteger|) $) "\\spad{s * c},{} returns the color \\spad{c},{} whose weighted shade has been scaled by \\spad{s}."))) NIL NIL -(-159 R -1966) +(-159 R -1955) ((|constructor| (NIL "Provides combinatorial functions over an integral domain.")) (|ipow| ((|#2| (|List| |#2|)) "\\spad{ipow(l)} should be local but conditional.")) (|iidprod| ((|#2| (|List| |#2|)) "\\spad{iidprod(l)} should be local but conditional.")) (|iidsum| ((|#2| (|List| |#2|)) "\\spad{iidsum(l)} should be local but conditional.")) (|iipow| ((|#2| (|List| |#2|)) "\\spad{iipow(l)} should be local but conditional.")) (|iiperm| ((|#2| (|List| |#2|)) "\\spad{iiperm(l)} should be local but conditional.")) (|iibinom| ((|#2| (|List| |#2|)) "\\spad{iibinom(l)} should be local but conditional.")) (|iifact| ((|#2| |#2|) "\\spad{iifact(x)} should be local but conditional.")) (|product| ((|#2| |#2| (|SegmentBinding| |#2|)) "\\spad{product(f(n), n = a..b)} returns \\spad{f}(a) * ... * \\spad{f}(\\spad{b}) as a formal product.") ((|#2| |#2| (|Symbol|)) "\\spad{product(f(n), n)} returns the formal product \\spad{P}(\\spad{n}) which verifies \\spad{P}(\\spad{n+1})\\spad{/P}(\\spad{n}) = \\spad{f}(\\spad{n}).")) (|summation| ((|#2| |#2| (|SegmentBinding| |#2|)) "\\spad{summation(f(n), n = a..b)} returns \\spad{f}(a) + ... + \\spad{f}(\\spad{b}) as a formal sum.") ((|#2| |#2| (|Symbol|)) "\\spad{summation(f(n), n)} returns the formal sum \\spad{S}(\\spad{n}) which verifies \\spad{S}(\\spad{n+1}) - \\spad{S}(\\spad{n}) = \\spad{f}(\\spad{n}).")) (|factorials| ((|#2| |#2| (|Symbol|)) "\\spad{factorials(f, x)} rewrites the permutations and binomials in \\spad{f} involving \\spad{x} in terms of factorials.") ((|#2| |#2|) "\\spad{factorials(f)} rewrites the permutations and binomials in \\spad{f} in terms of factorials.")) (|factorial| ((|#2| |#2|) "\\spad{factorial(n)} returns the factorial of \\spad{n},{} \\spadignore{i.e.} \\spad{n!}.")) (|permutation| ((|#2| |#2| |#2|) "\\spad{permutation(n, r)} returns the number of permutations of \\spad{n} objects taken \\spad{r} at a time,{} \\spadignore{i.e.} \\spad{n!/}(\\spad{n}-\\spad{r})!.")) (|binomial| ((|#2| |#2| |#2|) "\\spad{binomial(n, r)} returns the number of subsets of \\spad{r} objects taken among \\spad{n} objects,{} \\spadignore{i.e.} \\spad{n!/}(\\spad{r!} * (\\spad{n}-\\spad{r})!).")) (** ((|#2| |#2| |#2|) "\\spad{a ** b} is the formal exponential a**b.")) (|operator| (((|BasicOperator|) (|BasicOperator|)) "\\spad{operator(op)} returns a copy of \\spad{op} with the domain-dependent properties appropriate for \\spad{F}; error if \\spad{op} is not a combinatorial operator.")) (|belong?| (((|Boolean|) (|BasicOperator|)) "\\spad{belong?(op)} is \\spad{true} if \\spad{op} is a combinatorial operator."))) NIL NIL @@ -598,7 +598,7 @@ NIL ((|HasCategory| |#2| (QUOTE (-926))) (|HasCategory| |#2| (QUOTE (-557))) (|HasCategory| |#2| (QUOTE (-1021))) (|HasCategory| |#2| (QUOTE (-1221))) (|HasCategory| |#2| (QUOTE (-1079))) (|HasCategory| |#2| (QUOTE (-1041))) (|HasCategory| |#2| (QUOTE (-146))) (|HasCategory| |#2| (QUOTE (-148))) (|HasCategory| |#2| (LIST (QUOTE -626) (QUOTE (-548)))) (|HasCategory| |#2| (QUOTE (-374))) (|HasAttribute| |#2| (QUOTE -4458)) (|HasAttribute| |#2| (QUOTE -4461)) (|HasCategory| |#2| (QUOTE (-317))) (|HasCategory| |#2| (QUOTE (-568)))) (-167 R) ((|constructor| (NIL "This category represents the extension of a ring by a square root of \\spad{-1}.")) (|rationalIfCan| (((|Union| (|Fraction| (|Integer|)) "failed") $) "\\spad{rationalIfCan(x)} returns \\spad{x} as a rational number,{} or \"failed\" if \\spad{x} is not a rational number.")) (|rational| (((|Fraction| (|Integer|)) $) "\\spad{rational(x)} returns \\spad{x} as a rational number. Error: if \\spad{x} is not a rational number.")) (|rational?| (((|Boolean|) $) "\\spad{rational?(x)} tests if \\spad{x} is a rational number.")) (|polarCoordinates| (((|Record| (|:| |r| |#1|) (|:| |phi| |#1|)) $) "\\spad{polarCoordinates(x)} returns (\\spad{r},{} phi) such that \\spad{x} = \\spad{r} * exp(\\%\\spad{i} * phi).")) (|argument| ((|#1| $) "\\spad{argument(x)} returns the angle made by (0,{}1) and (0,{}\\spad{x}).")) (|abs| (($ $) "\\spad{abs(x)} returns the absolute value of \\spad{x} = sqrt(norm(\\spad{x})).")) (|exquo| (((|Union| $ "failed") $ |#1|) "\\spad{exquo(x, r)} returns the exact quotient of \\spad{x} by \\spad{r},{} or \"failed\" if \\spad{r} does not divide \\spad{x} exactly.")) (|norm| ((|#1| $) "\\spad{norm(x)} returns \\spad{x} * conjugate(\\spad{x})")) (|real| ((|#1| $) "\\spad{real(x)} returns real part of \\spad{x}.")) (|imag| ((|#1| $) "\\spad{imag(x)} returns imaginary part of \\spad{x}.")) (|conjugate| (($ $) "\\spad{conjugate(x + \\%i y)} returns \\spad{x} - \\%\\spad{i} \\spad{y}.")) (|imaginary| (($) "\\spad{imaginary()} = sqrt(\\spad{-1}) = \\%\\spad{i}.")) (|complex| (($ |#1| |#1|) "\\spad{complex(x,y)} constructs \\spad{x} + \\%i*y.") ((|attribute|) "indicates that \\% has sqrt(\\spad{-1})"))) -((-4455 -2781 (|has| |#1| (-568)) (-12 (|has| |#1| (-317)) (|has| |#1| (-926)))) (-4460 |has| |#1| (-374)) (-4454 |has| |#1| (-374)) (-4458 |has| |#1| (-6 -4458)) (-4461 |has| |#1| (-6 -4461)) (-4172 . T) ((-4464 "*") . T) (-4456 . T) (-4457 . T) (-4459 . T)) +((-4455 -2755 (|has| |#1| (-568)) (-12 (|has| |#1| (-317)) (|has| |#1| (-926)))) (-4460 |has| |#1| (-374)) (-4454 |has| |#1| (-374)) (-4458 |has| |#1| (-6 -4458)) (-4461 |has| |#1| (-6 -4461)) (-4175 . T) ((-4464 "*") . T) (-4456 . T) (-4457 . T) (-4459 . T)) NIL (-168 RR PR) ((|constructor| (NIL "\\indented{1}{Author:} Date Created: Date Last Updated: Basic Functions: Related Constructors: Complex,{} UnivariatePolynomial Also See: AMS Classifications: Keywords: complex,{} polynomial factorization,{} factor References:")) (|factor| (((|Factored| |#2|) |#2|) "\\spad{factor(p)} factorizes the polynomial \\spad{p} with complex coefficients."))) @@ -614,8 +614,8 @@ NIL NIL (-171 R) ((|constructor| (NIL "\\spadtype {Complex(R)} creates the domain of elements of the form \\spad{a + b * i} where \\spad{a} and \\spad{b} come from the ring \\spad{R},{} and \\spad{i} is a new element such that \\spad{i**2 = -1}."))) -((-4455 -2781 (|has| |#1| (-568)) (-12 (|has| |#1| (-317)) (|has| |#1| (-926)))) (-4460 |has| |#1| (-374)) (-4454 |has| |#1| (-374)) (-4458 |has| |#1| (-6 -4458)) (-4461 |has| |#1| (-6 -4461)) (-4172 . T) ((-4464 "*") . T) (-4456 . T) (-4457 . T) (-4459 . T)) -((|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-148))) (|HasCategory| |#1| (QUOTE (-360))) (-2781 (|HasCategory| |#1| (QUOTE (-374))) (|HasCategory| |#1| (QUOTE (-360)))) (|HasCategory| |#1| (QUOTE (-568))) (|HasCategory| |#1| (QUOTE (-374))) (|HasCategory| |#1| (QUOTE (-379))) (-2781 (|HasCategory| |#1| (QUOTE (-238))) (|HasCategory| |#1| (QUOTE (-360)))) (-2781 (-12 (|HasCategory| |#1| (QUOTE (-238))) (|HasCategory| |#1| (QUOTE (-374)))) (|HasCategory| |#1| (QUOTE (-237))) (|HasCategory| |#1| (QUOTE (-360)))) (|HasCategory| |#1| (LIST (QUOTE -915) (QUOTE (-1195)))) (-2781 (|HasCategory| |#1| (LIST (QUOTE -917) (QUOTE (-1195)))) (-12 (|HasCategory| |#1| (QUOTE (-374))) (|HasCategory| |#1| (LIST (QUOTE -915) (QUOTE (-1195)))))) (|HasCategory| |#1| (LIST (QUOTE -651) (QUOTE (-576)))) (-2781 (|HasCategory| |#1| (LIST (QUOTE -1057) (LIST (QUOTE -419) (QUOTE (-576))))) (|HasCategory| |#1| (QUOTE (-374)))) (|HasCategory| |#1| (LIST (QUOTE -1057) (LIST (QUOTE -419) (QUOTE (-576))))) (|HasCategory| |#1| (LIST (QUOTE -1057) (QUOTE (-576)))) (-2781 (-12 (|HasCategory| |#1| (QUOTE (-317))) (|HasCategory| |#1| (QUOTE (-926)))) (|HasCategory| |#1| (QUOTE (-374))) (-12 (|HasCategory| |#1| (QUOTE (-360))) (|HasCategory| |#1| (QUOTE (-926))))) (-2781 (-12 (|HasCategory| |#1| (QUOTE (-317))) (|HasCategory| |#1| (QUOTE (-926)))) (-12 (|HasCategory| |#1| (QUOTE (-374))) (|HasCategory| |#1| (QUOTE (-926)))) (-12 (|HasCategory| |#1| (QUOTE (-360))) (|HasCategory| |#1| (QUOTE (-926))))) (-2781 (|HasCategory| |#1| (QUOTE (-374))) (|HasCategory| |#1| (QUOTE (-568)))) (-12 (|HasCategory| |#1| (QUOTE (-1021))) (|HasCategory| |#1| (QUOTE (-1221)))) (|HasCategory| |#1| (QUOTE (-1221))) (|HasCategory| |#1| (QUOTE (-1041))) (|HasCategory| |#1| (LIST (QUOTE -626) (QUOTE (-548)))) (-2781 (|HasCategory| |#1| (QUOTE (-317))) (|HasCategory| |#1| (QUOTE (-374))) (|HasCategory| |#1| (QUOTE (-360))) (|HasCategory| |#1| (QUOTE (-568)))) (-2781 (|HasCategory| |#1| (QUOTE (-317))) (|HasCategory| |#1| (QUOTE (-374))) (|HasCategory| |#1| (QUOTE (-360)))) (|HasCategory| |#1| (LIST (QUOTE -626) (LIST (QUOTE -905) (QUOTE (-390))))) (|HasCategory| |#1| (LIST (QUOTE -626) (LIST (QUOTE -905) (QUOTE (-576))))) (|HasCategory| |#1| (LIST (QUOTE -899) (QUOTE (-390)))) (|HasCategory| |#1| (LIST (QUOTE -899) (QUOTE (-576)))) (|HasCategory| |#1| (LIST (QUOTE -526) (QUOTE (-1195)) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -296) (|devaluate| |#1|) (|devaluate| |#1|))) (|HasCategory| |#1| (QUOTE (-840))) (|HasCategory| |#1| (QUOTE (-1079))) (-12 (|HasCategory| |#1| (QUOTE (-1079))) (|HasCategory| |#1| (QUOTE (-1221)))) (|HasCategory| |#1| (QUOTE (-557))) (|HasCategory| |#1| (QUOTE (-317))) (|HasCategory| |#1| (QUOTE (-926))) (-2781 (-12 (|HasCategory| |#1| (QUOTE (-317))) (|HasCategory| |#1| (QUOTE (-926)))) (|HasCategory| |#1| (QUOTE (-374)))) (-2781 (-12 (|HasCategory| |#1| (QUOTE (-317))) (|HasCategory| |#1| (QUOTE (-926)))) (|HasCategory| |#1| (QUOTE (-568)))) (-2781 (-12 (|HasCategory| |#1| (QUOTE (-238))) (|HasCategory| |#1| (QUOTE (-374)))) (|HasCategory| |#1| (QUOTE (-237)))) (|HasCategory| |#1| (QUOTE (-237))) (|HasCategory| |#1| (LIST (QUOTE -917) (QUOTE (-1195)))) (|HasCategory| |#1| (QUOTE (-238))) (-12 (|HasCategory| |#1| (QUOTE (-317))) (|HasCategory| |#1| (QUOTE (-926)))) (|HasAttribute| |#1| (QUOTE -4458)) (|HasAttribute| |#1| (QUOTE -4461)) (-12 (|HasCategory| |#1| (QUOTE (-237))) (|HasCategory| |#1| (QUOTE (-374)))) (-12 (|HasCategory| |#1| (QUOTE (-374))) (|HasCategory| |#1| (LIST (QUOTE -917) (QUOTE (-1195))))) (-12 (|HasCategory| |#1| (QUOTE (-238))) (|HasCategory| |#1| (QUOTE (-374)))) (-12 (|HasCategory| |#1| (QUOTE (-374))) (|HasCategory| |#1| (LIST (QUOTE -915) (QUOTE (-1195))))) (-2781 (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-317))) (|HasCategory| |#1| (QUOTE (-926)))) (|HasCategory| |#1| (QUOTE (-146)))) (-2781 (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-317))) (|HasCategory| |#1| (QUOTE (-926)))) (|HasCategory| |#1| (QUOTE (-360))))) +((-4455 -2755 (|has| |#1| (-568)) (-12 (|has| |#1| (-317)) (|has| |#1| (-926)))) (-4460 |has| |#1| (-374)) (-4454 |has| |#1| (-374)) (-4458 |has| |#1| (-6 -4458)) (-4461 |has| |#1| (-6 -4461)) (-4175 . T) ((-4464 "*") . T) (-4456 . T) (-4457 . T) (-4459 . T)) +((|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-148))) (|HasCategory| |#1| (QUOTE (-360))) (-2755 (|HasCategory| |#1| (QUOTE (-374))) (|HasCategory| |#1| (QUOTE (-360)))) (|HasCategory| |#1| (QUOTE (-568))) (|HasCategory| |#1| (QUOTE (-374))) (|HasCategory| |#1| (QUOTE (-379))) (-2755 (|HasCategory| |#1| (QUOTE (-238))) (|HasCategory| |#1| (QUOTE (-360)))) (-2755 (-12 (|HasCategory| |#1| (QUOTE (-238))) (|HasCategory| |#1| (QUOTE (-374)))) (|HasCategory| |#1| (QUOTE (-237))) (|HasCategory| |#1| (QUOTE (-360)))) (|HasCategory| |#1| (LIST (QUOTE -915) (QUOTE (-1195)))) (-2755 (|HasCategory| |#1| (LIST (QUOTE -917) (QUOTE (-1195)))) (-12 (|HasCategory| |#1| (QUOTE (-374))) (|HasCategory| |#1| (LIST (QUOTE -915) (QUOTE (-1195)))))) (|HasCategory| |#1| (LIST (QUOTE -651) (QUOTE (-576)))) (-2755 (|HasCategory| |#1| (LIST (QUOTE -1057) (LIST (QUOTE -419) (QUOTE (-576))))) (|HasCategory| |#1| (QUOTE (-374)))) (|HasCategory| |#1| (LIST (QUOTE -1057) (LIST (QUOTE -419) (QUOTE (-576))))) (|HasCategory| |#1| (LIST (QUOTE -1057) (QUOTE (-576)))) (-2755 (-12 (|HasCategory| |#1| (QUOTE (-317))) (|HasCategory| |#1| (QUOTE (-926)))) (|HasCategory| |#1| (QUOTE (-374))) (-12 (|HasCategory| |#1| (QUOTE (-360))) (|HasCategory| |#1| (QUOTE (-926))))) (-2755 (-12 (|HasCategory| |#1| (QUOTE (-317))) (|HasCategory| |#1| (QUOTE (-926)))) (-12 (|HasCategory| |#1| (QUOTE (-374))) (|HasCategory| |#1| (QUOTE (-926)))) (-12 (|HasCategory| |#1| (QUOTE (-360))) (|HasCategory| |#1| (QUOTE (-926))))) (-2755 (|HasCategory| |#1| (QUOTE (-374))) (|HasCategory| |#1| (QUOTE (-568)))) (-12 (|HasCategory| |#1| (QUOTE (-1021))) (|HasCategory| |#1| (QUOTE (-1221)))) (|HasCategory| |#1| (QUOTE (-1221))) (|HasCategory| |#1| (QUOTE (-1041))) (|HasCategory| |#1| (LIST (QUOTE -626) (QUOTE (-548)))) (-2755 (|HasCategory| |#1| (QUOTE (-317))) (|HasCategory| |#1| (QUOTE (-374))) (|HasCategory| |#1| (QUOTE (-360))) (|HasCategory| |#1| (QUOTE (-568)))) (-2755 (|HasCategory| |#1| (QUOTE (-317))) (|HasCategory| |#1| (QUOTE (-374))) (|HasCategory| |#1| (QUOTE (-360)))) (|HasCategory| |#1| (LIST (QUOTE -626) (LIST (QUOTE -905) (QUOTE (-390))))) (|HasCategory| |#1| (LIST (QUOTE -626) (LIST (QUOTE -905) (QUOTE (-576))))) (|HasCategory| |#1| (LIST (QUOTE -899) (QUOTE (-390)))) (|HasCategory| |#1| (LIST (QUOTE -899) (QUOTE (-576)))) (|HasCategory| |#1| (LIST (QUOTE -526) (QUOTE (-1195)) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -296) (|devaluate| |#1|) (|devaluate| |#1|))) (|HasCategory| |#1| (QUOTE (-840))) (|HasCategory| |#1| (QUOTE (-1079))) (-12 (|HasCategory| |#1| (QUOTE (-1079))) (|HasCategory| |#1| (QUOTE (-1221)))) (|HasCategory| |#1| (QUOTE (-557))) (|HasCategory| |#1| (QUOTE (-317))) (|HasCategory| |#1| (QUOTE (-926))) (-2755 (-12 (|HasCategory| |#1| (QUOTE (-317))) (|HasCategory| |#1| (QUOTE (-926)))) (|HasCategory| |#1| (QUOTE (-374)))) (-2755 (-12 (|HasCategory| |#1| (QUOTE (-317))) (|HasCategory| |#1| (QUOTE (-926)))) (|HasCategory| |#1| (QUOTE (-568)))) (-2755 (-12 (|HasCategory| |#1| (QUOTE (-238))) (|HasCategory| |#1| (QUOTE (-374)))) (|HasCategory| |#1| (QUOTE (-237)))) (|HasCategory| |#1| (QUOTE (-237))) (|HasCategory| |#1| (LIST (QUOTE -917) (QUOTE (-1195)))) (|HasCategory| |#1| (QUOTE (-238))) (-12 (|HasCategory| |#1| (QUOTE (-317))) (|HasCategory| |#1| (QUOTE (-926)))) (|HasAttribute| |#1| (QUOTE -4458)) (|HasAttribute| |#1| (QUOTE -4461)) (-12 (|HasCategory| |#1| (QUOTE (-237))) (|HasCategory| |#1| (QUOTE (-374)))) (-12 (|HasCategory| |#1| (QUOTE (-374))) (|HasCategory| |#1| (LIST (QUOTE -917) (QUOTE (-1195))))) (-12 (|HasCategory| |#1| (QUOTE (-238))) (|HasCategory| |#1| (QUOTE (-374)))) (-12 (|HasCategory| |#1| (QUOTE (-374))) (|HasCategory| |#1| (LIST (QUOTE -915) (QUOTE (-1195))))) (-2755 (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-317))) (|HasCategory| |#1| (QUOTE (-926)))) (|HasCategory| |#1| (QUOTE (-146)))) (-2755 (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-317))) (|HasCategory| |#1| (QUOTE (-926)))) (|HasCategory| |#1| (QUOTE (-360))))) (-172 R S CS) ((|constructor| (NIL "This package supports converting complex expressions to patterns")) (|convert| (((|Pattern| |#1|) |#3|) "\\spad{convert(cs)} converts the complex expression \\spad{cs} to a pattern"))) NIL @@ -688,7 +688,7 @@ NIL ((|constructor| (NIL "This domain provides implementations for constructors.")) (|findConstructor| (((|Maybe| $) (|Identifier|)) "\\spad{findConstructor(s)} attempts to find a constructor named \\spad{s}. If successful,{} returns that constructor; otherwise,{} returns \\spad{nothing}."))) NIL NIL -(-190 R -1966) +(-190 R -1955) ((|constructor| (NIL "\\spadtype{ComplexTrigonometricManipulations} provides function that compute the real and imaginary parts of complex functions.")) (|complexForm| (((|Complex| (|Expression| |#1|)) |#2|) "\\spad{complexForm(f)} returns \\spad{[real f, imag f]}.")) (|trigs| ((|#2| |#2|) "\\spad{trigs(f)} rewrites all the complex logs and exponentials appearing in \\spad{f} in terms of trigonometric functions.")) (|real?| (((|Boolean|) |#2|) "\\spad{real?(f)} returns \\spad{true} if \\spad{f = real f}.")) (|imag| (((|Expression| |#1|) |#2|) "\\spad{imag(f)} returns the imaginary part of \\spad{f} where \\spad{f} is a complex function.")) (|real| (((|Expression| |#1|) |#2|) "\\spad{real(f)} returns the real part of \\spad{f} where \\spad{f} is a complex function.")) (|complexElementary| ((|#2| |#2| (|Symbol|)) "\\spad{complexElementary(f, x)} rewrites the kernels of \\spad{f} involving \\spad{x} in terms of the 2 fundamental complex transcendental elementary functions: \\spad{log, exp}.") ((|#2| |#2|) "\\spad{complexElementary(f)} rewrites \\spad{f} in terms of the 2 fundamental complex transcendental elementary functions: \\spad{log, exp}.")) (|complexNormalize| ((|#2| |#2| (|Symbol|)) "\\spad{complexNormalize(f, x)} rewrites \\spad{f} using the least possible number of complex independent kernels involving \\spad{x}.") ((|#2| |#2|) "\\spad{complexNormalize(f)} rewrites \\spad{f} using the least possible number of complex independent kernels."))) NIL NIL @@ -796,23 +796,23 @@ NIL ((|constructor| (NIL "\\indented{1}{This domain implements a simple view of a database whose fields are} indexed by symbols")) (- (($ $ $) "\\spad{db1-db2} returns the difference of databases \\spad{db1} and \\spad{db2} \\spadignore{i.e.} consisting of elements in \\spad{db1} but not in \\spad{db2}")) (+ (($ $ $) "\\spad{db1+db2} returns the merge of databases \\spad{db1} and \\spad{db2}")) (|fullDisplay| (((|Void|) $ (|PositiveInteger|) (|PositiveInteger|)) "\\spad{fullDisplay(db,start,end )} prints full details of entries in the range \\axiom{\\spad{start}..end} in \\axiom{\\spad{db}}.") (((|Void|) $) "\\spad{fullDisplay(db)} prints full details of each entry in \\axiom{\\spad{db}}.") (((|Void|) $) "\\spad{fullDisplay(x)} displays \\spad{x} in detail")) (|display| (((|Void|) $) "\\spad{display(db)} prints a summary line for each entry in \\axiom{\\spad{db}}.") (((|Void|) $) "\\spad{display(x)} displays \\spad{x} in some form")) (|elt| (((|DataList| (|String|)) $ (|Symbol|)) "\\spad{elt(db,s)} returns the \\axiom{\\spad{s}} field of each element of \\axiom{\\spad{db}}.") (($ $ (|QueryEquation|)) "\\spad{elt(db,q)} returns all elements of \\axiom{\\spad{db}} which satisfy \\axiom{\\spad{q}}.") (((|String|) $ (|Symbol|)) "\\spad{elt(x,s)} returns an element of \\spad{x} indexed by \\spad{s}"))) NIL NIL -(-217 -1966 UP UPUP R) +(-217 -1955 UP UPUP R) ((|constructor| (NIL "This package provides functions for computing the residues of a function on an algebraic curve.")) (|doubleResultant| ((|#2| |#4| (|Mapping| |#2| |#2|)) "\\spad{doubleResultant(f, ')} returns \\spad{p}(\\spad{x}) whose roots are rational multiples of the residues of \\spad{f} at all its finite poles. Argument ' is the derivation to use."))) NIL NIL -(-218 -1966 FP) +(-218 -1955 FP) ((|constructor| (NIL "Package for the factorization of a univariate polynomial with coefficients in a finite field. The algorithm used is the \"distinct degree\" algorithm of Cantor-Zassenhaus,{} modified to use trace instead of the norm and a table for computing Frobenius as suggested by Naudin and Quitte .")) (|irreducible?| (((|Boolean|) |#2|) "\\spad{irreducible?(p)} tests whether the polynomial \\spad{p} is irreducible.")) (|tracePowMod| ((|#2| |#2| (|NonNegativeInteger|) |#2|) "\\spad{tracePowMod(u,k,v)} produces the sum of \\spad{u**(q**i)} for \\spad{i} running and \\spad{q=} size \\spad{F}")) (|trace2PowMod| ((|#2| |#2| (|NonNegativeInteger|) |#2|) "\\spad{trace2PowMod(u,k,v)} produces the sum of \\spad{u**(2**i)} for \\spad{i} running from 1 to \\spad{k} all computed modulo the polynomial \\spad{v}.")) (|exptMod| ((|#2| |#2| (|NonNegativeInteger|) |#2|) "\\spad{exptMod(u,k,v)} raises the polynomial \\spad{u} to the \\spad{k}th power modulo the polynomial \\spad{v}.")) (|separateFactors| (((|List| |#2|) (|List| (|Record| (|:| |deg| (|NonNegativeInteger|)) (|:| |prod| |#2|)))) "\\spad{separateFactors(lfact)} takes the list produced by \\spadfunFrom{separateDegrees}{DistinctDegreeFactorization} and produces the complete list of factors.")) (|separateDegrees| (((|List| (|Record| (|:| |deg| (|NonNegativeInteger|)) (|:| |prod| |#2|))) |#2|) "\\spad{separateDegrees(p)} splits the square free polynomial \\spad{p} into factors each of which is a product of irreducibles of the same degree.")) (|distdfact| (((|Record| (|:| |cont| |#1|) (|:| |factors| (|List| (|Record| (|:| |irr| |#2|) (|:| |pow| (|Integer|)))))) |#2| (|Boolean|)) "\\spad{distdfact(p,sqfrflag)} produces the complete factorization of the polynomial \\spad{p} returning an internal data structure. If argument \\spad{sqfrflag} is \\spad{true},{} the polynomial is assumed square free.")) (|factorSquareFree| (((|Factored| |#2|) |#2|) "\\spad{factorSquareFree(p)} produces the complete factorization of the square free polynomial \\spad{p}.")) (|factor| (((|Factored| |#2|) |#2|) "\\spad{factor(p)} produces the complete factorization of the polynomial \\spad{p}."))) NIL NIL (-219) ((|constructor| (NIL "This domain allows rational numbers to be presented as repeating decimal expansions.")) (|decimal| (($ (|Fraction| (|Integer|))) "\\spad{decimal(r)} converts a rational number to a decimal expansion.")) (|fractionPart| (((|Fraction| (|Integer|)) $) "\\spad{fractionPart(d)} returns the fractional part of a decimal expansion."))) ((-4454 . T) (-4460 . T) (-4455 . T) ((-4464 "*") . T) (-4456 . T) (-4457 . T) (-4459 . T)) -((|HasCategory| (-576) (QUOTE (-926))) (|HasCategory| (-576) (LIST (QUOTE -1057) (QUOTE (-1195)))) (|HasCategory| (-576) (QUOTE (-146))) (|HasCategory| (-576) (QUOTE (-148))) (|HasCategory| (-576) (LIST (QUOTE -626) (QUOTE (-548)))) (|HasCategory| (-576) (QUOTE (-1041))) (|HasCategory| (-576) (QUOTE (-832))) (-2781 (|HasCategory| (-576) (QUOTE (-832))) (|HasCategory| (-576) (QUOTE (-862)))) (|HasCategory| (-576) (LIST (QUOTE -1057) (QUOTE (-576)))) (|HasCategory| (-576) (QUOTE (-1171))) (|HasCategory| (-576) (LIST (QUOTE -899) (QUOTE (-390)))) (|HasCategory| (-576) (LIST (QUOTE -899) (QUOTE (-576)))) (|HasCategory| (-576) (LIST (QUOTE -626) (LIST (QUOTE -905) (QUOTE (-390))))) (|HasCategory| (-576) (LIST (QUOTE -626) (LIST (QUOTE -905) (QUOTE (-576))))) (|HasCategory| (-576) (QUOTE (-237))) (|HasCategory| (-576) (LIST (QUOTE -917) (QUOTE (-1195)))) (|HasCategory| (-576) (QUOTE (-238))) (|HasCategory| (-576) (LIST (QUOTE -915) (QUOTE (-1195)))) (|HasCategory| (-576) (LIST (QUOTE -526) (QUOTE (-1195)) (QUOTE (-576)))) (|HasCategory| (-576) (LIST (QUOTE -319) (QUOTE (-576)))) (|HasCategory| (-576) (LIST (QUOTE -296) (QUOTE (-576)) (QUOTE (-576)))) (|HasCategory| (-576) (QUOTE (-317))) (|HasCategory| (-576) (QUOTE (-557))) (|HasCategory| (-576) (QUOTE (-862))) (|HasCategory| (-576) (LIST (QUOTE -651) (QUOTE (-576)))) (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| (-576) (QUOTE (-926)))) (-2781 (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| (-576) (QUOTE (-926)))) (|HasCategory| (-576) (QUOTE (-146))))) +((|HasCategory| (-576) (QUOTE (-926))) (|HasCategory| (-576) (LIST (QUOTE -1057) (QUOTE (-1195)))) (|HasCategory| (-576) (QUOTE (-146))) (|HasCategory| (-576) (QUOTE (-148))) (|HasCategory| (-576) (LIST (QUOTE -626) (QUOTE (-548)))) (|HasCategory| (-576) (QUOTE (-1041))) (|HasCategory| (-576) (QUOTE (-832))) (-2755 (|HasCategory| (-576) (QUOTE (-832))) (|HasCategory| (-576) (QUOTE (-862)))) (|HasCategory| (-576) (LIST (QUOTE -1057) (QUOTE (-576)))) (|HasCategory| (-576) (QUOTE (-1171))) (|HasCategory| (-576) (LIST (QUOTE -899) (QUOTE (-390)))) (|HasCategory| (-576) (LIST (QUOTE -899) (QUOTE (-576)))) (|HasCategory| (-576) (LIST (QUOTE -626) (LIST (QUOTE -905) (QUOTE (-390))))) (|HasCategory| (-576) (LIST (QUOTE -626) (LIST (QUOTE -905) (QUOTE (-576))))) (|HasCategory| (-576) (QUOTE (-237))) (|HasCategory| (-576) (LIST (QUOTE -917) (QUOTE (-1195)))) (|HasCategory| (-576) (QUOTE (-238))) (|HasCategory| (-576) (LIST (QUOTE -915) (QUOTE (-1195)))) (|HasCategory| (-576) (LIST (QUOTE -526) (QUOTE (-1195)) (QUOTE (-576)))) (|HasCategory| (-576) (LIST (QUOTE -319) (QUOTE (-576)))) (|HasCategory| (-576) (LIST (QUOTE -296) (QUOTE (-576)) (QUOTE (-576)))) (|HasCategory| (-576) (QUOTE (-317))) (|HasCategory| (-576) (QUOTE (-557))) (|HasCategory| (-576) (QUOTE (-862))) (|HasCategory| (-576) (LIST (QUOTE -651) (QUOTE (-576)))) (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| (-576) (QUOTE (-926)))) (-2755 (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| (-576) (QUOTE (-926)))) (|HasCategory| (-576) (QUOTE (-146))))) (-220) ((|constructor| (NIL "This domain represents the syntax of a definition.")) (|body| (((|SpadAst|) $) "\\spad{body(d)} returns the right hand side of the definition \\spad{`d'}.")) (|signature| (((|Signature|) $) "\\spad{signature(d)} returns the signature of the operation being defined. Note that this list may be partial in that it contains only the types actually specified in the definition.")) (|head| (((|HeadAst|) $) "\\spad{head(d)} returns the head of the definition \\spad{`d'}. This is a list of identifiers starting with the name of the operation followed by the name of the parameters,{} if any."))) NIL NIL -(-221 R -1966) +(-221 R -1955) ((|constructor| (NIL "\\spadtype{ElementaryFunctionDefiniteIntegration} provides functions to compute definite integrals of elementary functions.")) (|innerint| (((|Union| (|:| |f1| (|OrderedCompletion| |#2|)) (|:| |f2| (|List| (|OrderedCompletion| |#2|))) (|:| |fail| "failed") (|:| |pole| "potentialPole")) |#2| (|Symbol|) (|OrderedCompletion| |#2|) (|OrderedCompletion| |#2|) (|Boolean|)) "\\spad{innerint(f, x, a, b, ignore?)} should be local but conditional")) (|integrate| (((|Union| (|:| |f1| (|OrderedCompletion| |#2|)) (|:| |f2| (|List| (|OrderedCompletion| |#2|))) (|:| |fail| "failed") (|:| |pole| "potentialPole")) |#2| (|SegmentBinding| (|OrderedCompletion| |#2|)) (|String|)) "\\spad{integrate(f, x = a..b, \"noPole\")} returns the integral of \\spad{f(x)dx} from a to \\spad{b}. If it is not possible to check whether \\spad{f} has a pole for \\spad{x} between a and \\spad{b} (because of parameters),{} then this function will assume that \\spad{f} has no such pole. Error: if \\spad{f} has a pole for \\spad{x} between a and \\spad{b} or if the last argument is not \"noPole\".") (((|Union| (|:| |f1| (|OrderedCompletion| |#2|)) (|:| |f2| (|List| (|OrderedCompletion| |#2|))) (|:| |fail| "failed") (|:| |pole| "potentialPole")) |#2| (|SegmentBinding| (|OrderedCompletion| |#2|))) "\\spad{integrate(f, x = a..b)} returns the integral of \\spad{f(x)dx} from a to \\spad{b}. Error: if \\spad{f} has a pole for \\spad{x} between a and \\spad{b}."))) NIL NIL @@ -827,18 +827,18 @@ NIL (-224 S) ((|constructor| (NIL "Linked list implementation of a Dequeue")) (|dequeue| (($ (|List| |#1|)) "\\spad{dequeue([x,y,...,z])} creates a dequeue with first (top or front) element \\spad{x},{} second element \\spad{y},{}...,{}and last (bottom or back) element \\spad{z}."))) ((-4462 . T) (-4463 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1119))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1119))) (-2781 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-1119)))) (-2781 (-12 (|HasCategory| |#1| (QUOTE (-1119))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-874))))) (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-874)))) (|HasCategory| |#1| (QUOTE (-102)))) +((-12 (|HasCategory| |#1| (QUOTE (-1119))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1119))) (-2755 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-1119)))) (-2755 (-12 (|HasCategory| |#1| (QUOTE (-1119))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-874))))) (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-874)))) (|HasCategory| |#1| (QUOTE (-102)))) (-225 |CoefRing| |listIndVar|) ((|constructor| (NIL "The deRham complex of Euclidean space,{} that is,{} the class of differential forms of arbitary degree over a coefficient ring. See Flanders,{} Harley,{} Differential Forms,{} With Applications to the Physical Sciences,{} New York,{} Academic Press,{} 1963.")) (|exteriorDifferential| (($ $) "\\spad{exteriorDifferential(df)} returns the exterior derivative (gradient,{} curl,{} divergence,{} ...) of the differential form \\spad{df}.")) (|totalDifferential| (($ (|Expression| |#1|)) "\\spad{totalDifferential(x)} returns the total differential (gradient) form for element \\spad{x}.")) (|map| (($ (|Mapping| (|Expression| |#1|) (|Expression| |#1|)) $) "\\spad{map(f,df)} replaces each coefficient \\spad{x} of differential form \\spad{df} by \\spad{f(x)}.")) (|degree| (((|Integer|) $) "\\spad{degree(df)} returns the homogeneous degree of differential form \\spad{df}.")) (|retractable?| (((|Boolean|) $) "\\spad{retractable?(df)} tests if differential form \\spad{df} is a 0-form,{} \\spadignore{i.e.} if degree(\\spad{df}) = 0.")) (|homogeneous?| (((|Boolean|) $) "\\spad{homogeneous?(df)} tests if all of the terms of differential form \\spad{df} have the same degree.")) (|generator| (($ (|NonNegativeInteger|)) "\\spad{generator(n)} returns the \\spad{n}th basis term for a differential form.")) (|coefficient| (((|Expression| |#1|) $ $) "\\spad{coefficient(df,u)},{} where \\spad{df} is a differential form,{} returns the coefficient of \\spad{df} containing the basis term \\spad{u} if such a term exists,{} and 0 otherwise.")) (|reductum| (($ $) "\\spad{reductum(df)},{} where \\spad{df} is a differential form,{} returns \\spad{df} minus the leading term of \\spad{df} if \\spad{df} has two or more terms,{} and 0 otherwise.")) (|leadingBasisTerm| (($ $) "\\spad{leadingBasisTerm(df)} returns the leading basis term of differential form \\spad{df}.")) (|leadingCoefficient| (((|Expression| |#1|) $) "\\spad{leadingCoefficient(df)} returns the leading coefficient of differential form \\spad{df}."))) ((-4459 . T)) NIL -(-226 R -1966) +(-226 R -1955) ((|constructor| (NIL "\\spadtype{DefiniteIntegrationTools} provides common tools used by the definite integration of both rational and elementary functions.")) (|checkForZero| (((|Union| (|Boolean|) "failed") (|SparseUnivariatePolynomial| |#2|) (|OrderedCompletion| |#2|) (|OrderedCompletion| |#2|) (|Boolean|)) "\\spad{checkForZero(p, a, b, incl?)} is \\spad{true} if \\spad{p} has a zero between a and \\spad{b},{} \\spad{false} otherwise,{} \"failed\" if this cannot be determined. Check for a and \\spad{b} inclusive if incl? is \\spad{true},{} exclusive otherwise.") (((|Union| (|Boolean|) "failed") (|Polynomial| |#1|) (|Symbol|) (|OrderedCompletion| |#2|) (|OrderedCompletion| |#2|) (|Boolean|)) "\\spad{checkForZero(p, x, a, b, incl?)} is \\spad{true} if \\spad{p} has a zero for \\spad{x} between a and \\spad{b},{} \\spad{false} otherwise,{} \"failed\" if this cannot be determined. Check for a and \\spad{b} inclusive if incl? is \\spad{true},{} exclusive otherwise.")) (|computeInt| (((|Union| (|OrderedCompletion| |#2|) "failed") (|Kernel| |#2|) |#2| (|OrderedCompletion| |#2|) (|OrderedCompletion| |#2|) (|Boolean|)) "\\spad{computeInt(x, g, a, b, eval?)} returns the integral of \\spad{f} for \\spad{x} between a and \\spad{b},{} assuming that \\spad{g} is an indefinite integral of \\spad{f} and \\spad{f} has no pole between a and \\spad{b}. If \\spad{eval?} is \\spad{true},{} then \\spad{g} can be evaluated safely at \\spad{a} and \\spad{b},{} provided that they are finite values. Otherwise,{} limits must be computed.")) (|ignore?| (((|Boolean|) (|String|)) "\\spad{ignore?(s)} is \\spad{true} if \\spad{s} is the string that tells the integrator to assume that the function has no pole in the integration interval."))) NIL NIL (-227) ((|constructor| (NIL "\\indented{1}{\\spadtype{DoubleFloat} is intended to make accessible} hardware floating point arithmetic in \\Language{},{} either native double precision,{} or IEEE. On most machines,{} there will be hardware support for the arithmetic operations: \\spadfunFrom{+}{DoubleFloat},{} \\spadfunFrom{*}{DoubleFloat},{} \\spadfunFrom{/}{DoubleFloat} and possibly also the \\spadfunFrom{sqrt}{DoubleFloat} operation. The operations \\spadfunFrom{exp}{DoubleFloat},{} \\spadfunFrom{log}{DoubleFloat},{} \\spadfunFrom{sin}{DoubleFloat},{} \\spadfunFrom{cos}{DoubleFloat},{} \\spadfunFrom{atan}{DoubleFloat} are normally coded in software based on minimax polynomial/rational approximations. Note that under Lisp/VM,{} \\spadfunFrom{atan}{DoubleFloat} is not available at this time. Some general comments about the accuracy of the operations: the operations \\spadfunFrom{+}{DoubleFloat},{} \\spadfunFrom{*}{DoubleFloat},{} \\spadfunFrom{/}{DoubleFloat} and \\spadfunFrom{sqrt}{DoubleFloat} are expected to be fully accurate. The operations \\spadfunFrom{exp}{DoubleFloat},{} \\spadfunFrom{log}{DoubleFloat},{} \\spadfunFrom{sin}{DoubleFloat},{} \\spadfunFrom{cos}{DoubleFloat} and \\spadfunFrom{atan}{DoubleFloat} are not expected to be fully accurate. In particular,{} \\spadfunFrom{sin}{DoubleFloat} and \\spadfunFrom{cos}{DoubleFloat} will lose all precision for large arguments. \\blankline The \\spadtype{Float} domain provides an alternative to the \\spad{DoubleFloat} domain. It provides an arbitrary precision model of floating point arithmetic. This means that accuracy problems like those above are eliminated by increasing the working precision where necessary. \\spadtype{Float} provides some special functions such as \\spadfunFrom{erf}{DoubleFloat},{} the error function in addition to the elementary functions. The disadvantage of \\spadtype{Float} is that it is much more expensive than small floats when the latter can be used.")) (|rationalApproximation| (((|Fraction| (|Integer|)) $ (|NonNegativeInteger|) (|NonNegativeInteger|)) "\\spad{rationalApproximation(f, n, b)} computes a rational approximation \\spad{r} to \\spad{f} with relative error \\spad{< b**(-n)} (that is,{} \\spad{|(r-f)/f| < b**(-n)}).") (((|Fraction| (|Integer|)) $ (|NonNegativeInteger|)) "\\spad{rationalApproximation(f, n)} computes a rational approximation \\spad{r} to \\spad{f} with relative error \\spad{< 10**(-n)}.")) (|Beta| (($ $ $) "\\spad{Beta(x,y)} is \\spad{Gamma(x) * Gamma(y)/Gamma(x+y)}.")) (|Gamma| (($ $) "\\spad{Gamma(x)} is the Euler Gamma function.")) (|atan| (($ $ $) "\\spad{atan(x,y)} computes the arc tangent from \\spad{x} with phase \\spad{y}.")) (|log10| (($ $) "\\spad{log10(x)} computes the logarithm with base 10 for \\spad{x}.")) (|log2| (($ $) "\\spad{log2(x)} computes the logarithm with base 2 for \\spad{x}.")) (|exp1| (($) "\\spad{exp1()} returns the natural log base \\spad{2.718281828...}.")) (** (($ $ $) "\\spad{x ** y} returns the \\spad{y}th power of \\spad{x} (equal to \\spad{exp(y log x)}).")) (/ (($ $ (|Integer|)) "\\spad{x / i} computes the division from \\spad{x} by an integer \\spad{i}."))) -((-4161 . T) (-4454 . T) (-4460 . T) (-4455 . T) ((-4464 "*") . T) (-4456 . T) (-4457 . T) (-4459 . T)) +((-4163 . T) (-4454 . T) (-4460 . T) (-4455 . T) ((-4464 "*") . T) (-4456 . T) (-4457 . T) (-4459 . T)) NIL (-228) ((|constructor| (NIL "This package provides special functions for double precision real and complex floating point.")) (|hypergeometric0F1| (((|Complex| (|DoubleFloat|)) (|Complex| (|DoubleFloat|)) (|Complex| (|DoubleFloat|))) "\\spad{hypergeometric0F1(c,z)} is the hypergeometric function \\spad{0F1(; c; z)}.") (((|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|)) "\\spad{hypergeometric0F1(c,z)} is the hypergeometric function \\spad{0F1(; c; z)}.")) (|airyBi| (((|Complex| (|DoubleFloat|)) (|Complex| (|DoubleFloat|))) "\\spad{airyBi(x)} is the Airy function \\spad{Bi(x)}. This function satisfies the differential equation: \\indented{2}{\\spad{Bi''(x) - x * Bi(x) = 0}.}") (((|DoubleFloat|) (|DoubleFloat|)) "\\spad{airyBi(x)} is the Airy function \\spad{Bi(x)}. This function satisfies the differential equation: \\indented{2}{\\spad{Bi''(x) - x * Bi(x) = 0}.}")) (|airyAi| (((|DoubleFloat|) (|DoubleFloat|)) "\\spad{airyAi(x)} is the Airy function \\spad{Ai(x)}. This function satisfies the differential equation: \\indented{2}{\\spad{Ai''(x) - x * Ai(x) = 0}.}") (((|Complex| (|DoubleFloat|)) (|Complex| (|DoubleFloat|))) "\\spad{airyAi(x)} is the Airy function \\spad{Ai(x)}. This function satisfies the differential equation: \\indented{2}{\\spad{Ai''(x) - x * Ai(x) = 0}.}")) (|besselK| (((|Complex| (|DoubleFloat|)) (|Complex| (|DoubleFloat|)) (|Complex| (|DoubleFloat|))) "\\spad{besselK(v,x)} is the modified Bessel function of the first kind,{} \\spad{K(v,x)}. This function satisfies the differential equation: \\indented{2}{\\spad{x^2 w''(x) + x w'(x) - (x^2+v^2)w(x) = 0}.} Note: The default implmentation uses the relation \\indented{2}{\\spad{K(v,x) = \\%pi/2*(I(-v,x) - I(v,x))/sin(v*\\%pi)}} so is not valid for integer values of \\spad{v}.") (((|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|)) "\\spad{besselK(v,x)} is the modified Bessel function of the first kind,{} \\spad{K(v,x)}. This function satisfies the differential equation: \\indented{2}{\\spad{x^2 w''(x) + x w'(x) - (x^2+v^2)w(x) = 0}.} Note: The default implmentation uses the relation \\indented{2}{\\spad{K(v,x) = \\%pi/2*(I(-v,x) - I(v,x))/sin(v*\\%pi)}.} so is not valid for integer values of \\spad{v}.")) (|besselI| (((|Complex| (|DoubleFloat|)) (|Complex| (|DoubleFloat|)) (|Complex| (|DoubleFloat|))) "\\spad{besselI(v,x)} is the modified Bessel function of the first kind,{} \\spad{I(v,x)}. This function satisfies the differential equation: \\indented{2}{\\spad{x^2 w''(x) + x w'(x) - (x^2+v^2)w(x) = 0}.}") (((|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|)) "\\spad{besselI(v,x)} is the modified Bessel function of the first kind,{} \\spad{I(v,x)}. This function satisfies the differential equation: \\indented{2}{\\spad{x^2 w''(x) + x w'(x) - (x^2+v^2)w(x) = 0}.}")) (|besselY| (((|Complex| (|DoubleFloat|)) (|Complex| (|DoubleFloat|)) (|Complex| (|DoubleFloat|))) "\\spad{besselY(v,x)} is the Bessel function of the second kind,{} \\spad{Y(v,x)}. This function satisfies the differential equation: \\indented{2}{\\spad{x^2 w''(x) + x w'(x) + (x^2-v^2)w(x) = 0}.} Note: The default implmentation uses the relation \\indented{2}{\\spad{Y(v,x) = (J(v,x) cos(v*\\%pi) - J(-v,x))/sin(v*\\%pi)}} so is not valid for integer values of \\spad{v}.") (((|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|)) "\\spad{besselY(v,x)} is the Bessel function of the second kind,{} \\spad{Y(v,x)}. This function satisfies the differential equation: \\indented{2}{\\spad{x^2 w''(x) + x w'(x) + (x^2-v^2)w(x) = 0}.} Note: The default implmentation uses the relation \\indented{2}{\\spad{Y(v,x) = (J(v,x) cos(v*\\%pi) - J(-v,x))/sin(v*\\%pi)}} so is not valid for integer values of \\spad{v}.")) (|besselJ| (((|Complex| (|DoubleFloat|)) (|Complex| (|DoubleFloat|)) (|Complex| (|DoubleFloat|))) "\\spad{besselJ(v,x)} is the Bessel function of the first kind,{} \\spad{J(v,x)}. This function satisfies the differential equation: \\indented{2}{\\spad{x^2 w''(x) + x w'(x) + (x^2-v^2)w(x) = 0}.}") (((|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|)) "\\spad{besselJ(v,x)} is the Bessel function of the first kind,{} \\spad{J(v,x)}. This function satisfies the differential equation: \\indented{2}{\\spad{x^2 w''(x) + x w'(x) + (x^2-v^2)w(x) = 0}.}")) (|polygamma| (((|Complex| (|DoubleFloat|)) (|NonNegativeInteger|) (|Complex| (|DoubleFloat|))) "\\spad{polygamma(n, x)} is the \\spad{n}-th derivative of \\spad{digamma(x)}.") (((|DoubleFloat|) (|NonNegativeInteger|) (|DoubleFloat|)) "\\spad{polygamma(n, x)} is the \\spad{n}-th derivative of \\spad{digamma(x)}.")) (|digamma| (((|Complex| (|DoubleFloat|)) (|Complex| (|DoubleFloat|))) "\\spad{digamma(x)} is the function,{} \\spad{psi(x)},{} defined by \\indented{2}{\\spad{psi(x) = Gamma'(x)/Gamma(x)}.}") (((|DoubleFloat|) (|DoubleFloat|)) "\\spad{digamma(x)} is the function,{} \\spad{psi(x)},{} defined by \\indented{2}{\\spad{psi(x) = Gamma'(x)/Gamma(x)}.}")) (|logGamma| (((|Complex| (|DoubleFloat|)) (|Complex| (|DoubleFloat|))) "\\spad{logGamma(x)} is the natural log of \\spad{Gamma(x)}. This can often be computed even if \\spad{Gamma(x)} cannot.") (((|DoubleFloat|) (|DoubleFloat|)) "\\spad{logGamma(x)} is the natural log of \\spad{Gamma(x)}. This can often be computed even if \\spad{Gamma(x)} cannot.")) (|Beta| (((|Complex| (|DoubleFloat|)) (|Complex| (|DoubleFloat|)) (|Complex| (|DoubleFloat|))) "\\spad{Beta(x, y)} is the Euler beta function,{} \\spad{B(x,y)},{} defined by \\indented{2}{\\spad{Beta(x,y) = integrate(t^(x-1)*(1-t)^(y-1), t=0..1)}.} This is related to \\spad{Gamma(x)} by \\indented{2}{\\spad{Beta(x,y) = Gamma(x)*Gamma(y) / Gamma(x + y)}.}") (((|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|)) "\\spad{Beta(x, y)} is the Euler beta function,{} \\spad{B(x,y)},{} defined by \\indented{2}{\\spad{Beta(x,y) = integrate(t^(x-1)*(1-t)^(y-1), t=0..1)}.} This is related to \\spad{Gamma(x)} by \\indented{2}{\\spad{Beta(x,y) = Gamma(x)*Gamma(y) / Gamma(x + y)}.}")) (|Gamma| (((|Complex| (|DoubleFloat|)) (|Complex| (|DoubleFloat|))) "\\spad{Gamma(x)} is the Euler gamma function,{} \\spad{Gamma(x)},{} defined by \\indented{2}{\\spad{Gamma(x) = integrate(t^(x-1)*exp(-t), t=0..\\%infinity)}.}") (((|DoubleFloat|) (|DoubleFloat|)) "\\spad{Gamma(x)} is the Euler gamma function,{} \\spad{Gamma(x)},{} defined by \\indented{2}{\\spad{Gamma(x) = integrate(t^(x-1)*exp(-t), t=0..\\%infinity)}.}"))) @@ -847,7 +847,7 @@ NIL (-229 R) ((|constructor| (NIL "\\indented{1}{A Denavit-Hartenberg Matrix is a 4x4 Matrix of the form:} \\indented{1}{\\spad{nx ox ax px}} \\indented{1}{\\spad{ny oy ay py}} \\indented{1}{\\spad{nz oz az pz}} \\indented{2}{\\spad{0\\space{2}0\\space{2}0\\space{2}1}} (\\spad{n},{} \\spad{o},{} and a are the direction cosines)")) (|translate| (($ |#1| |#1| |#1|) "\\spad{translate(X,Y,Z)} returns a dhmatrix for translation by \\spad{X},{} \\spad{Y},{} and \\spad{Z}")) (|scale| (($ |#1| |#1| |#1|) "\\spad{scale(sx,sy,sz)} returns a dhmatrix for scaling in the \\spad{X},{} \\spad{Y} and \\spad{Z} directions")) (|rotatez| (($ |#1|) "\\spad{rotatez(r)} returns a dhmatrix for rotation about axis \\spad{Z} for \\spad{r} degrees")) (|rotatey| (($ |#1|) "\\spad{rotatey(r)} returns a dhmatrix for rotation about axis \\spad{Y} for \\spad{r} degrees")) (|rotatex| (($ |#1|) "\\spad{rotatex(r)} returns a dhmatrix for rotation about axis \\spad{X} for \\spad{r} degrees")) (|identity| (($) "\\spad{identity()} create the identity dhmatrix")) (* (((|Point| |#1|) $ (|Point| |#1|)) "\\spad{t*p} applies the dhmatrix \\spad{t} to point \\spad{p}"))) ((-4462 . T) (-4463 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1119))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1119))) (-2781 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-1119)))) (-2781 (-12 (|HasCategory| |#1| (QUOTE (-1119))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-874))))) (|HasCategory| |#1| (QUOTE (-317))) (|HasCategory| |#1| (QUOTE (-568))) (|HasAttribute| |#1| (QUOTE (-4464 "*"))) (|HasCategory| |#1| (QUOTE (-374))) (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-874)))) (|HasCategory| |#1| (QUOTE (-102)))) +((-12 (|HasCategory| |#1| (QUOTE (-1119))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1119))) (-2755 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-1119)))) (-2755 (-12 (|HasCategory| |#1| (QUOTE (-1119))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-874))))) (|HasCategory| |#1| (QUOTE (-317))) (|HasCategory| |#1| (QUOTE (-568))) (|HasAttribute| |#1| (QUOTE (-4464 "*"))) (|HasCategory| |#1| (QUOTE (-374))) (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-874)))) (|HasCategory| |#1| (QUOTE (-102)))) (-230 A S) ((|constructor| (NIL "A dictionary is an aggregate in which entries can be inserted,{} searched for and removed. Duplicates are thrown away on insertion. This category models the usual notion of dictionary which involves large amounts of data where copying is impractical. Principal operations are thus destructive (non-copying) ones."))) NIL @@ -896,22 +896,22 @@ NIL ((|constructor| (NIL "any solution of a homogeneous linear Diophantine equation can be represented as a sum of minimal solutions,{} which form a \"basis\" (a minimal solution cannot be represented as a nontrivial sum of solutions) in the case of an inhomogeneous linear Diophantine equation,{} each solution is the sum of a inhomogeneous solution and any number of homogeneous solutions therefore,{} it suffices to compute two sets: \\indented{3}{1. all minimal inhomogeneous solutions} \\indented{3}{2. all minimal homogeneous solutions} the algorithm implemented is a completion procedure,{} which enumerates all solutions in a recursive depth-first-search it can be seen as finding monotone paths in a graph for more details see Reference")) (|dioSolve| (((|Record| (|:| |varOrder| (|List| (|Symbol|))) (|:| |inhom| (|Union| (|List| (|Vector| (|NonNegativeInteger|))) "failed")) (|:| |hom| (|List| (|Vector| (|NonNegativeInteger|))))) (|Equation| (|Polynomial| (|Integer|)))) "\\spad{dioSolve(u)} computes a basis of all minimal solutions for linear homogeneous Diophantine equation \\spad{u},{} then all minimal solutions of inhomogeneous equation"))) NIL NIL -(-242 S -2695 R) +(-242 S -2701 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 (-374))) (|HasCategory| |#3| (QUOTE (-805))) (|HasCategory| |#3| (QUOTE (-862))) (|HasAttribute| |#3| (QUOTE -4459)) (|HasCategory| |#3| (QUOTE (-174))) (|HasCategory| |#3| (QUOTE (-379))) (|HasCategory| |#3| (QUOTE (-738))) (|HasCategory| |#3| (QUOTE (-21))) (|HasCategory| |#3| (QUOTE (-23))) (|HasCategory| |#3| (QUOTE (-132))) (|HasCategory| |#3| (QUOTE (-25))) (|HasCategory| |#3| (QUOTE (-1068))) (|HasCategory| |#3| (QUOTE (-1119)))) -(-243 -2695 R) +(-243 -2701 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"))) ((-4456 |has| |#2| (-1068)) (-4457 |has| |#2| (-1068)) (-4459 |has| |#2| (-6 -4459)) (-4462 . T)) NIL -(-244 -2695 A B) +(-244 -2701 A B) ((|constructor| (NIL "\\indented{2}{This package provides operations which all take as arguments} direct products of elements of some type \\spad{A} and functions from \\spad{A} to another type \\spad{B}. The operations all iterate over their vector argument and either return a value of type \\spad{B} or a direct product over \\spad{B}.")) (|map| (((|DirectProduct| |#1| |#3|) (|Mapping| |#3| |#2|) (|DirectProduct| |#1| |#2|)) "\\spad{map(f, v)} applies the function \\spad{f} to every element of the vector \\spad{v} producing a new vector containing the values.")) (|reduce| ((|#3| (|Mapping| |#3| |#2| |#3|) (|DirectProduct| |#1| |#2|) |#3|) "\\spad{reduce(func,vec,ident)} combines the elements in \\spad{vec} using the binary function \\spad{func}. Argument \\spad{ident} is returned if the vector is empty.")) (|scan| (((|DirectProduct| |#1| |#3|) (|Mapping| |#3| |#2| |#3|) (|DirectProduct| |#1| |#2|) |#3|) "\\spad{scan(func,vec,ident)} creates a new vector whose elements are the result of applying reduce to the binary function \\spad{func},{} increasing initial subsequences of the vector \\spad{vec},{} and the element \\spad{ident}."))) NIL NIL -(-245 -2695 R) +(-245 -2701 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."))) ((-4456 |has| |#2| (-1068)) (-4457 |has| |#2| (-1068)) (-4459 |has| |#2| (-6 -4459)) (-4462 . 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(|sayLength| (((|Integer|) (|List| (|String|))) "\\spad{sayLength(l)} returns the length of a list of strings \\spad{l} as an integer.") (((|Integer|) (|String|)) "\\spad{sayLength(s)} returns the length of a string \\spad{s} as an integer.")) (|say| (((|Void|) (|List| (|String|))) "\\spad{say(l)} sends a list of strings \\spad{l} to output.") (((|Void|) (|String|)) "\\spad{say(s)} sends a string \\spad{s} to output.")) (|center| (((|List| (|String|)) (|List| (|String|)) (|Integer|) (|String|)) "\\spad{center(l,i,s)} takes a list of strings \\spad{l},{} and centers them within a list of strings which is \\spad{i} characters long,{} in which the remaining spaces are filled with strings composed of as many repetitions as possible of the last string parameter \\spad{s}.") (((|String|) (|String|) (|Integer|) (|String|)) "\\spad{center(s,i,s)} takes the first string \\spad{s},{} and centers it within a string of length \\spad{i},{} in which the other elements of the string are composed of as many replications as possible of the second indicated string,{} \\spad{s} which must have a length greater than that of an empty string.")) (|copies| (((|String|) (|Integer|) (|String|)) "\\spad{copies(i,s)} will take a string \\spad{s} and create a new string composed of \\spad{i} copies of \\spad{s}.")) (|newLine| (((|String|)) "\\spad{newLine()} sends a new line command to output.")) (|bright| (((|List| (|String|)) (|List| (|String|))) "\\spad{bright(l)} sets the font property of a list of strings,{} \\spad{l},{} to bold-face type.") (((|List| (|String|)) (|String|)) "\\spad{bright(s)} sets the font property of the string \\spad{s} to bold-face type."))) NIL @@ -931,7 +931,7 @@ NIL (-250 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}"))) ((-4463 . T) (-4462 . T)) -((-2781 (-12 (|HasCategory| |#1| (QUOTE (-862))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1119))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|))))) (-2781 (-12 (|HasCategory| |#1| (QUOTE (-1119))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-874))))) (|HasCategory| |#1| (LIST (QUOTE -626) (QUOTE (-548)))) (-2781 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-862))) (|HasCategory| |#1| (QUOTE (-1119)))) (-2781 (|HasCategory| |#1| (QUOTE (-862))) (|HasCategory| |#1| (QUOTE (-1119)))) (|HasCategory| |#1| (QUOTE (-862))) (|HasCategory| (-576) (QUOTE (-862))) (|HasCategory| |#1| (QUOTE (-1119))) (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-874)))) (|HasCategory| |#1| (QUOTE (-102))) (-12 (|HasCategory| |#1| (QUOTE (-1119))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|))))) +((-2755 (-12 (|HasCategory| |#1| (QUOTE (-862))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1119))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|))))) (-2755 (-12 (|HasCategory| |#1| (QUOTE (-1119))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-874))))) (|HasCategory| |#1| (LIST (QUOTE -626) (QUOTE (-548)))) (-2755 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-862))) (|HasCategory| |#1| (QUOTE (-1119)))) (-2755 (|HasCategory| |#1| (QUOTE (-862))) (|HasCategory| |#1| (QUOTE (-1119)))) (|HasCategory| |#1| (QUOTE (-862))) (|HasCategory| (-576) (QUOTE (-862))) (|HasCategory| |#1| (QUOTE (-1119))) (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-874)))) (|HasCategory| |#1| (QUOTE (-102))) (-12 (|HasCategory| |#1| (QUOTE (-1119))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|))))) (-251 M) ((|constructor| (NIL "DiscreteLogarithmPackage implements help functions for discrete logarithms in monoids using small cyclic groups.")) (|shanksDiscLogAlgorithm| (((|Union| (|NonNegativeInteger|) "failed") |#1| |#1| (|NonNegativeInteger|)) "\\spad{shanksDiscLogAlgorithm(b,a,p)} computes \\spad{s} with \\spad{b**s = a} for assuming that \\spad{a} and \\spad{b} are elements in a 'small' cyclic group of order \\spad{p} by Shank\\spad{'s} algorithm. Note: this is a subroutine of the function \\spadfun{discreteLog}.")) (** ((|#1| |#1| (|Integer|)) "\\spad{x ** n} returns \\spad{x} raised to the integer power \\spad{n}"))) NIL @@ -943,7 +943,7 @@ NIL (-253 |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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T)) -((|HasCategory| |#2| (QUOTE (-926))) (-2781 (|HasCategory| |#2| (QUOTE (-174))) (|HasCategory| |#2| (QUOTE (-464))) (|HasCategory| |#2| (QUOTE (-568))) (|HasCategory| |#2| (QUOTE (-926)))) (-2781 (|HasCategory| |#2| (QUOTE (-464))) (|HasCategory| |#2| (QUOTE (-568))) (|HasCategory| |#2| (QUOTE (-926)))) (-2781 (|HasCategory| |#2| (QUOTE (-464))) (|HasCategory| |#2| (QUOTE (-926)))) (|HasCategory| |#2| (QUOTE (-568))) (|HasCategory| |#2| (QUOTE (-174))) (-2781 (|HasCategory| |#2| (QUOTE (-174))) (|HasCategory| |#2| (QUOTE (-568)))) (-12 (|HasCategory| (-876 |#1|) (LIST (QUOTE -899) (QUOTE (-390)))) (|HasCategory| |#2| (LIST (QUOTE -899) (QUOTE (-390))))) (-12 (|HasCategory| (-876 |#1|) (LIST (QUOTE -899) (QUOTE (-576)))) (|HasCategory| |#2| (LIST (QUOTE -899) (QUOTE (-576))))) (-12 (|HasCategory| (-876 |#1|) (LIST (QUOTE -626) (LIST (QUOTE -905) (QUOTE (-390))))) (|HasCategory| |#2| (LIST (QUOTE -626) (LIST (QUOTE -905) (QUOTE (-390)))))) (-12 (|HasCategory| (-876 |#1|) (LIST (QUOTE -626) (LIST (QUOTE -905) (QUOTE (-576))))) (|HasCategory| |#2| (LIST (QUOTE -626) (LIST (QUOTE -905) (QUOTE (-576)))))) (-12 (|HasCategory| (-876 |#1|) (LIST (QUOTE -626) (QUOTE (-548)))) (|HasCategory| |#2| (LIST (QUOTE -626) (QUOTE (-548))))) (|HasCategory| |#2| (LIST (QUOTE -651) (QUOTE (-576)))) (|HasCategory| |#2| (QUOTE (-148))) (|HasCategory| |#2| (QUOTE (-146))) (|HasCategory| |#2| (LIST (QUOTE -38) (LIST (QUOTE -419) (QUOTE (-576))))) (|HasCategory| |#2| (LIST (QUOTE -1057) (QUOTE (-576)))) (-2781 (|HasCategory| |#2| (LIST (QUOTE -38) (LIST (QUOTE -419) (QUOTE (-576))))) (|HasCategory| |#2| (LIST (QUOTE -1057) (LIST (QUOTE -419) (QUOTE (-576)))))) (|HasCategory| |#2| (LIST (QUOTE -1057) (LIST (QUOTE -419) (QUOTE (-576))))) (|HasCategory| |#2| (QUOTE (-374))) (|HasAttribute| |#2| (QUOTE -4460)) (|HasCategory| |#2| (QUOTE (-464))) (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| |#2| (QUOTE (-926)))) (-2781 (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| |#2| (QUOTE (-926)))) (|HasCategory| |#2| (QUOTE (-146))))) +((|HasCategory| |#2| (QUOTE (-926))) (-2755 (|HasCategory| |#2| (QUOTE (-174))) (|HasCategory| |#2| (QUOTE (-464))) (|HasCategory| |#2| (QUOTE (-568))) (|HasCategory| |#2| (QUOTE (-926)))) (-2755 (|HasCategory| |#2| (QUOTE (-464))) (|HasCategory| |#2| (QUOTE (-568))) (|HasCategory| |#2| (QUOTE (-926)))) (-2755 (|HasCategory| |#2| (QUOTE (-464))) (|HasCategory| |#2| (QUOTE (-926)))) (|HasCategory| |#2| (QUOTE (-568))) (|HasCategory| |#2| (QUOTE (-174))) (-2755 (|HasCategory| |#2| (QUOTE (-174))) (|HasCategory| |#2| (QUOTE (-568)))) (-12 (|HasCategory| (-876 |#1|) (LIST (QUOTE -899) (QUOTE (-390)))) (|HasCategory| |#2| (LIST (QUOTE -899) (QUOTE (-390))))) (-12 (|HasCategory| (-876 |#1|) (LIST (QUOTE -899) (QUOTE (-576)))) (|HasCategory| |#2| (LIST (QUOTE -899) (QUOTE (-576))))) (-12 (|HasCategory| (-876 |#1|) (LIST (QUOTE -626) (LIST (QUOTE -905) (QUOTE (-390))))) (|HasCategory| |#2| (LIST (QUOTE -626) (LIST (QUOTE -905) (QUOTE (-390)))))) (-12 (|HasCategory| (-876 |#1|) (LIST (QUOTE -626) (LIST (QUOTE -905) (QUOTE (-576))))) (|HasCategory| |#2| (LIST (QUOTE -626) (LIST (QUOTE -905) (QUOTE (-576)))))) (-12 (|HasCategory| (-876 |#1|) (LIST (QUOTE -626) (QUOTE (-548)))) (|HasCategory| |#2| (LIST (QUOTE -626) (QUOTE (-548))))) (|HasCategory| |#2| (LIST (QUOTE -651) (QUOTE (-576)))) (|HasCategory| |#2| (QUOTE (-148))) (|HasCategory| |#2| (QUOTE (-146))) (|HasCategory| |#2| (LIST (QUOTE -38) (LIST (QUOTE -419) (QUOTE (-576))))) (|HasCategory| |#2| (LIST (QUOTE -1057) (QUOTE (-576)))) (-2755 (|HasCategory| |#2| (LIST (QUOTE -38) (LIST (QUOTE -419) (QUOTE (-576))))) (|HasCategory| |#2| (LIST (QUOTE -1057) (LIST (QUOTE -419) (QUOTE (-576)))))) (|HasCategory| |#2| (LIST (QUOTE -1057) (LIST (QUOTE -419) (QUOTE (-576))))) (|HasCategory| |#2| (QUOTE (-374))) (|HasAttribute| |#2| (QUOTE -4460)) (|HasCategory| |#2| (QUOTE (-464))) (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| |#2| (QUOTE (-926)))) (-2755 (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| |#2| (QUOTE (-926)))) (|HasCategory| |#2| (QUOTE (-146))))) (-254) ((|showSummary| (((|Void|) $) "\\spad{showSummary(d)} prints out implementation detail information of domain \\spad{`d'}.")) (|reflect| (($ (|ConstructorCall| (|DomainConstructor|))) "\\spad{reflect cc} returns the domain object designated by the ConstructorCall syntax `cc'. The constructor implied by `cc' must be known to the system since it is instantiated.")) (|reify| (((|ConstructorCall| (|DomainConstructor|)) $) "\\spad{reify(d)} returns the abstract syntax for the domain \\spad{`x'}.")) (|constructor| (NIL "\\indented{1}{Author: Gabriel Dos Reis} Date Create: October 18,{} 2007. Date Last Updated: December 20,{} 2008. Basic Operations: coerce,{} reify Related Constructors: Type,{} Syntax,{} OutputForm Also See: Type,{} ConstructorCall") (((|DomainConstructor|) $) "\\spad{constructor(d)} returns the domain constructor that is instantiated to the domain object \\spad{`d'}."))) 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category constructor specifying basic functions in an ordinary differential polynomial ring with a given ordered set of differential indeterminates. In addition,{} it implements defaults for the basic functions. The functions \\spadfun{order} and \\spadfun{weight} are extended from the set of derivatives of differential indeterminates to the set of differential polynomials. Other operations provided on differential polynomials are \\spadfun{leader},{} \\spadfun{initial},{} \\spadfun{separant},{} \\spadfun{differentialVariables},{} and \\spadfun{isobaric?}. Furthermore,{} if the ground ring is a differential ring,{} then evaluation (substitution of differential indeterminates by elements of the ground ring or by differential polynomials) is provided by \\spadfun{eval}. A convenient way of referencing derivatives is provided by the functions \\spadfun{makeVariable}. \\blankline To construct a domain using this constructor,{} one needs to provide a ground ring \\spad{R},{} an ordered set \\spad{S} of differential indeterminates,{} a ranking \\spad{V} on the set of derivatives of the differential indeterminates,{} and a set \\spad{E} of exponents in bijection with the set of differential monomials in the given differential indeterminates. \\blankline")) (|separant| (($ $) "\\spad{separant(p)} returns the partial derivative of the differential polynomial \\spad{p} with respect to its leader.")) (|initial| (($ $) "\\spad{initial(p)} returns the leading coefficient when the differential polynomial \\spad{p} is written as a univariate polynomial in its leader.")) (|leader| ((|#4| $) "\\spad{leader(p)} returns the derivative of the highest rank appearing in the differential polynomial \\spad{p} Note: an error occurs if \\spad{p} is in the ground ring.")) (|isobaric?| (((|Boolean|) $) "\\spad{isobaric?(p)} returns \\spad{true} if every differential monomial appearing in the differential polynomial \\spad{p} has same weight,{} and returns \\spad{false} otherwise.")) (|weight| (((|NonNegativeInteger|) $ |#3|) "\\spad{weight(p, s)} returns the maximum weight of all differential monomials appearing in the differential polynomial \\spad{p} when \\spad{p} is viewed as a differential polynomial in the differential indeterminate \\spad{s} alone.") (((|NonNegativeInteger|) $) "\\spad{weight(p)} returns the maximum weight of all differential monomials appearing in the differential polynomial \\spad{p}.")) (|weights| (((|List| (|NonNegativeInteger|)) $ |#3|) "\\spad{weights(p, s)} returns a list of weights of differential monomials appearing in the differential polynomial \\spad{p} when \\spad{p} is viewed as a differential polynomial in the differential indeterminate \\spad{s} alone.") (((|List| (|NonNegativeInteger|)) $) "\\spad{weights(p)} returns a list of weights of differential monomials appearing in differential polynomial \\spad{p}.")) (|degree| (((|NonNegativeInteger|) $ |#3|) "\\spad{degree(p, s)} returns the maximum degree of the differential polynomial \\spad{p} viewed as a differential polynomial in the differential indeterminate \\spad{s} alone.")) (|order| (((|NonNegativeInteger|) $) "\\spad{order(p)} returns the order of the differential polynomial \\spad{p},{} which is the maximum number of differentiations of a differential indeterminate,{} among all those appearing in \\spad{p}.") (((|NonNegativeInteger|) $ |#3|) "\\spad{order(p,s)} returns the order of the differential polynomial \\spad{p} in differential indeterminate \\spad{s}.")) (|differentialVariables| (((|List| |#3|) $) "\\spad{differentialVariables(p)} returns a list of differential indeterminates occurring in a differential polynomial \\spad{p}.")) (|makeVariable| (((|Mapping| $ (|NonNegativeInteger|)) $) "\\spad{makeVariable(p)} views \\spad{p} as an element of a differential ring,{} in such a way that the \\spad{n}-th derivative of \\spad{p} may be simply referenced as \\spad{z}.\\spad{n} where \\spad{z} \\spad{:=} makeVariable(\\spad{p}). Note: In the interpreter,{} \\spad{z} is given as an internal map,{} which may be ignored.") (((|Mapping| $ (|NonNegativeInteger|)) |#3|) "\\spad{makeVariable(s)} views \\spad{s} as a differential indeterminate,{} in such a way that the \\spad{n}-th derivative of \\spad{s} may be simply referenced as \\spad{z}.\\spad{n} where \\spad{z} :=makeVariable(\\spad{s}). Note: In the interpreter,{} \\spad{z} is given as an internal map,{} which may be ignored."))) NIL @@ -1023,7 +1023,7 @@ NIL (-273 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"))) (((-4464 "*") |has| |#1| (-174)) (-4455 |has| |#1| (-568)) (-4460 |has| |#1| (-6 -4460)) (-4457 . T) (-4456 . T) (-4459 . 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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 @@ -1068,11 +1068,11 @@ NIL ((|constructor| (NIL "A domain used in the construction of the exterior algebra on a set \\spad{X} over a ring \\spad{R}. This domain represents the set of all ordered subsets of the set \\spad{X},{} assumed to be in correspondance with {1,{}2,{}3,{} ...}. The ordered subsets are themselves ordered lexicographically and are in bijective correspondance with an ordered basis of the exterior algebra. In this domain we are dealing strictly with the exponents of basis elements which can only be 0 or 1. \\blankline The multiplicative identity element of the exterior algebra corresponds to the empty subset of \\spad{X}. A coerce from List Integer to an ordered basis element is provided to allow the convenient input of expressions. Another exported function forgets the ordered structure and simply returns the list corresponding to an ordered subset.")) (|Nul| (($ (|NonNegativeInteger|)) "\\spad{Nul()} gives the basis element 1 for the algebra generated by \\spad{n} generators.")) (|exponents| (((|List| (|Integer|)) $) "\\spad{exponents(x)} converts a domain element into a list of zeros and ones corresponding to the exponents in the basis element that \\spad{x} represents.")) (|degree| (((|NonNegativeInteger|) $) "\\spad{degree(x)} gives the numbers of 1\\spad{'s} in \\spad{x},{} \\spadignore{i.e.} the number of non-zero exponents in the basis element that \\spad{x} represents.")) (|coerce| (($ (|List| (|Integer|))) "\\spad{coerce(l)} converts a list of 0\\spad{'s} and 1\\spad{'s} into a basis element,{} where 1 (respectively 0) designates that the variable of the corresponding index of \\spad{l} is (respectively,{} is not) present. Error: if an element of \\spad{l} is not 0 or 1."))) NIL NIL -(-285 R -1966) +(-285 R -1955) ((|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 -(-286 R -1966) +(-286 R -1955) ((|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 @@ -1124,7 +1124,7 @@ 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 -(-299 S R |Mod| -3046 -1512 |exactQuo|) +(-299 S R |Mod| -2634 -2331 |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| $) "\\spad{modulus(x)} \\undocumented"))) ((-4455 . T) ((-4464 "*") . T) (-4456 . T) (-4457 . T) (-4459 . T)) NIL @@ -1146,21 +1146,21 @@ NIL NIL (-304 S) ((|constructor| (NIL "Equations as mathematical objects. All properties of the basis domain,{} \\spadignore{e.g.} being an abelian group are carried over the equation domain,{} by performing the structural operations on the left and on the right hand side.")) (|subst| (($ $ $) "\\spad{subst(eq1,eq2)} substitutes \\spad{eq2} into both sides of \\spad{eq1} the \\spad{lhs} of \\spad{eq2} should be a kernel")) (|inv| (($ $) "\\spad{inv(x)} returns the multiplicative inverse of \\spad{x}.")) (/ (($ $ $) "\\spad{e1/e2} produces a new equation by dividing the left and right hand sides of equations e1 and e2.")) (|factorAndSplit| (((|List| $) $) "\\spad{factorAndSplit(eq)} make the right hand side 0 and factors the new left hand side. Each factor is equated to 0 and put into the resulting list without repetitions.")) (|rightOne| (((|Union| $ "failed") $) "\\spad{rightOne(eq)} divides by the right hand side.") (((|Union| $ "failed") $) "\\spad{rightOne(eq)} divides by the right hand side,{} if possible.")) (|leftOne| (((|Union| $ "failed") $) "\\spad{leftOne(eq)} divides by the left hand side.") (((|Union| $ "failed") $) "\\spad{leftOne(eq)} divides by the left hand side,{} if possible.")) (* (($ $ |#1|) "\\spad{eqn*x} produces a new equation by multiplying both sides of equation eqn by \\spad{x}.") (($ |#1| $) "\\spad{x*eqn} produces a new equation by multiplying both sides of equation eqn by \\spad{x}.")) (- (($ $ |#1|) "\\spad{eqn-x} produces a new equation by subtracting \\spad{x} from both sides of equation eqn.") (($ |#1| $) "\\spad{x-eqn} produces a new equation by subtracting both sides of equation eqn from \\spad{x}.")) (|rightZero| (($ $) "\\spad{rightZero(eq)} subtracts the right hand side.")) (|leftZero| (($ $) "\\spad{leftZero(eq)} subtracts the left hand side.")) (+ (($ $ |#1|) "\\spad{eqn+x} produces a new equation by adding \\spad{x} to both sides of equation eqn.") (($ |#1| $) "\\spad{x+eqn} produces a new equation by adding \\spad{x} to both sides of equation eqn.")) (|eval| (($ $ (|List| $)) "\\spad{eval(eqn, [x1=v1, ... xn=vn])} replaces \\spad{xi} by \\spad{vi} in equation \\spad{eqn}.") (($ $ $) "\\spad{eval(eqn, x=f)} replaces \\spad{x} by \\spad{f} in equation \\spad{eqn}.")) (|map| (($ (|Mapping| |#1| |#1|) $) "\\spad{map(f,eqn)} constructs a new equation by applying \\spad{f} to both sides of \\spad{eqn}.")) (|rhs| ((|#1| $) "\\spad{rhs(eqn)} returns the right hand side of equation \\spad{eqn}.")) (|lhs| ((|#1| $) "\\spad{lhs(eqn)} returns the left hand side of equation \\spad{eqn}.")) (|swap| (($ $) "\\spad{swap(eq)} interchanges left and right hand side of equation \\spad{eq}.")) (|equation| (($ |#1| |#1|) "\\spad{equation(a,b)} creates an equation.")) 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Thus keys are considered equal only if they are the same instance of a structure."))) ((-4462 . T) (-4463 . 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Typically,{} these functions would be called in user functions. The simple forms of the functions take one argument which is either a string (an error message) or a list of strings which all together make up a message. The list can contain formatting codes (see below). The more sophisticated versions takes two arguments where the first argument is the name of the function from which the error was invoked and the second argument is either a string or a list of strings,{} as above. When you use the one argument version in an interpreter function,{} the system will automatically insert the name of the function as the new first argument. Thus in the user interpreter function \\indented{2}{\\spad{f x == if x < 0 then error \"negative argument\" else x}} the call to error will actually be of the form \\indented{2}{\\spad{error(\"f\",\"negative argument\")}} because the interpreter will have created a new first argument. \\blankline Formatting codes: error messages may contain the following formatting codes (they should either start or end a string or else have blanks around them): \\indented{3}{\\spad{\\%l}\\space{6}start a new line} \\indented{3}{\\spad{\\%b}\\space{6}start printing in a bold font (where available)} \\indented{3}{\\spad{\\%d}\\space{6}stop\\space{2}printing in a bold font (where available)} \\indented{3}{\\spad{ \\%ceon}\\space{2}start centering message lines} \\indented{3}{\\spad{\\%ceoff}\\space{2}stop\\space{2}centering message lines} \\indented{3}{\\spad{\\%rjon}\\space{3}start displaying lines \"ragged left\"} \\indented{3}{\\spad{\\%rjoff}\\space{2}stop\\space{2}displaying lines \"ragged left\"} \\indented{3}{\\spad{\\%i}\\space{6}indent\\space{3}following lines 3 additional spaces} \\indented{3}{\\spad{\\%u}\\space{6}unindent following lines 3 additional spaces} \\indented{3}{\\spad{\\%xN}\\space{5}insert \\spad{N} blanks (eg,{} \\spad{\\%x10} inserts 10 blanks)} \\blankline")) (|error| (((|Exit|) (|String|) (|List| (|String|))) "\\spad{error(nam,lmsg)} displays error messages \\spad{lmsg} preceded by a message containing the name \\spad{nam} of the function in which the error is contained.") (((|Exit|) (|String|) (|String|)) "\\spad{error(nam,msg)} displays error message \\spad{msg} preceded by a message containing the name \\spad{nam} of the function in which the error is contained.") (((|Exit|) (|List| (|String|))) "\\spad{error(lmsg)} displays error message \\spad{lmsg} and terminates.") (((|Exit|) (|String|)) "\\spad{error(msg)} displays error message \\spad{msg} and terminates."))) NIL NIL -(-307 -1966 S) +(-307 -1955 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 -(-308 E -1966) +(-308 E -1955) ((|constructor| (NIL "This package allows a mapping \\spad{E} \\spad{->} \\spad{F} to be lifted to a kernel over \\spad{E}; This lifting can fail if the operator of the kernel cannot be applied in \\spad{F}; Do not use this package with \\spad{E} = \\spad{F},{} since this may drop some properties of the operators.")) (|map| ((|#2| (|Mapping| |#2| |#1|) (|Kernel| |#1|)) "\\spad{map(f, k)} returns \\spad{g = op(f(a1),...,f(an))} where \\spad{k = op(a1,...,an)}."))) NIL NIL @@ -1208,7 +1208,7 @@ NIL ((|constructor| (NIL "This category provides \\spadfun{eval} operations. A domain may belong to this category if it is possible to make ``evaluation\\spad{''} substitutions.")) (|eval| (($ $ (|List| (|Equation| |#1|))) "\\spad{eval(f, [x1 = v1,...,xn = vn])} replaces \\spad{xi} by \\spad{vi} in \\spad{f}.") (($ $ (|Equation| |#1|)) "\\spad{eval(f,x = v)} replaces \\spad{x} by \\spad{v} in \\spad{f}."))) NIL NIL -(-320 -1966) +(-320 -1955) ((|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 @@ -1223,7 +1223,7 @@ NIL (-323 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.")) 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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 @@ -1234,9 +1234,9 @@ NIL NIL (-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."))) -((-4459 -2781 (-12 (|has| |#1| (-568)) (-2781 (|has| |#1| (-1068)) (|has| |#1| (-485)))) (|has| |#1| (-1068)) (|has| |#1| (-485))) (-4457 |has| |#1| (-174)) (-4456 |has| |#1| (-174)) ((-4464 "*") |has| |#1| (-568)) (-4455 |has| |#1| (-568)) (-4460 |has| |#1| (-568)) (-4454 |has| |#1| (-568))) -((-2781 (|HasCategory| |#1| (LIST (QUOTE -1057) (LIST (QUOTE -419) 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(|HasCategory| |#1| (QUOTE (-25))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-148))) (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-568))) (|HasCategory| |#1| (QUOTE (-1068)))) (-2755 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-148))) (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-568))) (|HasCategory| |#1| (QUOTE (-1068)))) (-2755 (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-148))) (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-568))) (|HasCategory| |#1| (QUOTE (-1068)))) (-12 (|HasCategory| |#1| (QUOTE (-464))) (|HasCategory| |#1| (QUOTE (-568)))) (-2755 (|HasCategory| |#1| (QUOTE (-485))) (|HasCategory| |#1| (QUOTE (-568)))) (-12 (|HasCategory| |#1| (QUOTE (-1068))) (|HasCategory| |#1| (LIST (QUOTE -651) (QUOTE (-576))))) (-2755 (|HasCategory| |#1| (QUOTE (-21))) (-12 (|HasCategory| |#1| (QUOTE (-1068))) (|HasCategory| |#1| (LIST (QUOTE -651) (QUOTE (-576)))))) (-2755 (|HasCategory| |#1| (QUOTE (-25))) (-12 (|HasCategory| |#1| (QUOTE (-1068))) (|HasCategory| |#1| (LIST (QUOTE -651) (QUOTE (-576))))) (|HasCategory| |#1| (QUOTE (-1131)))) (-2755 (|HasCategory| |#1| (QUOTE (-25))) (-12 (|HasCategory| |#1| (QUOTE (-1068))) (|HasCategory| |#1| (LIST (QUOTE -651) (QUOTE (-576)))))) (-2755 (|HasCategory| |#1| (QUOTE (-485))) (|HasCategory| |#1| (QUOTE (-1068)))) (-2755 (-12 (|HasCategory| |#1| (LIST (QUOTE -1057) (LIST (QUOTE -419) (QUOTE (-576))))) (|HasCategory| |#1| (QUOTE (-568)))) (-12 (|HasCategory| |#1| (QUOTE (-568))) (|HasCategory| |#1| (LIST (QUOTE -1057) (QUOTE (-576)))))) (|HasCategory| |#1| (QUOTE (-25))) (|HasCategory| |#1| (QUOTE (-1131))) (|HasCategory| |#1| (LIST (QUOTE -1057) (LIST (QUOTE -419) (QUOTE (-576))))) (|HasCategory| $ (QUOTE (-1068))) (|HasCategory| $ (LIST (QUOTE -1057) (QUOTE (-576))))) +(-327 R -1955) ((|constructor| (NIL "Taylor series solutions of explicit ODE\\spad{'s}.")) (|seriesSolve| (((|Any|) |#2| (|BasicOperator|) (|Equation| |#2|) (|List| |#2|)) "\\spad{seriesSolve(eq, y, x = a, [b0,...,bn])} is equivalent to \\spad{seriesSolve(eq = 0, y, x = a, [b0,...,b(n-1)])}.") (((|Any|) |#2| (|BasicOperator|) (|Equation| |#2|) (|Equation| |#2|)) "\\spad{seriesSolve(eq, y, x = a, y a = b)} is equivalent to \\spad{seriesSolve(eq=0, y, x=a, y a = b)}.") (((|Any|) |#2| (|BasicOperator|) (|Equation| |#2|) |#2|) "\\spad{seriesSolve(eq, y, x = a, b)} is equivalent to \\spad{seriesSolve(eq = 0, y, x = a, y a = b)}.") (((|Any|) (|Equation| |#2|) (|BasicOperator|) (|Equation| |#2|) |#2|) "\\spad{seriesSolve(eq,y, x=a, b)} is equivalent to \\spad{seriesSolve(eq, y, x=a, y a = b)}.") (((|Any|) (|List| |#2|) (|List| (|BasicOperator|)) (|Equation| |#2|) (|List| (|Equation| |#2|))) "\\spad{seriesSolve([eq1,...,eqn], [y1,...,yn], x = a,[y1 a = b1,..., yn a = bn])} is equivalent to \\spad{seriesSolve([eq1=0,...,eqn=0], [y1,...,yn], x = a, [y1 a = b1,..., yn a = bn])}.") (((|Any|) (|List| |#2|) (|List| (|BasicOperator|)) (|Equation| |#2|) (|List| |#2|)) "\\spad{seriesSolve([eq1,...,eqn], [y1,...,yn], x=a, [b1,...,bn])} is equivalent to \\spad{seriesSolve([eq1=0,...,eqn=0], [y1,...,yn], x=a, [b1,...,bn])}.") (((|Any|) (|List| (|Equation| |#2|)) (|List| (|BasicOperator|)) (|Equation| |#2|) (|List| |#2|)) "\\spad{seriesSolve([eq1,...,eqn], [y1,...,yn], x=a, [b1,...,bn])} is equivalent to \\spad{seriesSolve([eq1,...,eqn], [y1,...,yn], x = a, [y1 a = b1,..., yn a = bn])}.") (((|Any|) (|List| (|Equation| |#2|)) (|List| (|BasicOperator|)) (|Equation| |#2|) (|List| (|Equation| |#2|))) "\\spad{seriesSolve([eq1,...,eqn],[y1,...,yn],x = a,[y1 a = b1,...,yn a = bn])} returns a taylor series solution of \\spad{[eq1,...,eqn]} around \\spad{x = a} with initial conditions \\spad{yi(a) = bi}. Note: eqi must be of the form \\spad{fi(x, y1 x, y2 x,..., yn x) y1'(x) + gi(x, y1 x, y2 x,..., yn x) = h(x, y1 x, y2 x,..., yn x)}.") (((|Any|) (|Equation| |#2|) (|BasicOperator|) (|Equation| |#2|) (|List| |#2|)) "\\spad{seriesSolve(eq,y,x=a,[b0,...,b(n-1)])} returns a Taylor series solution of \\spad{eq} around \\spad{x = a} with initial conditions \\spad{y(a) = b0},{} \\spad{y'(a) = b1},{} \\spad{y''(a) = b2},{} ...,{}\\spad{y(n-1)(a) = b(n-1)} \\spad{eq} must be of the form \\spad{f(x, y x, y'(x),..., y(n-1)(x)) y(n)(x) + g(x,y x,y'(x),...,y(n-1)(x)) = h(x,y x, y'(x),..., y(n-1)(x))}.") (((|Any|) (|Equation| |#2|) (|BasicOperator|) (|Equation| |#2|) (|Equation| |#2|)) "\\spad{seriesSolve(eq,y,x=a, y a = b)} returns a Taylor series solution of \\spad{eq} around \\spad{x} = a with initial condition \\spad{y(a) = b}. Note: \\spad{eq} must be of the form \\spad{f(x, y x) y'(x) + g(x, y x) = h(x, y x)}."))) NIL NIL @@ -1247,7 +1247,7 @@ NIL (-329 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."))) (((-4464 "*") |has| |#1| (-174)) (-4455 |has| |#1| (-568)) (-4460 |has| |#1| (-374)) (-4454 |has| |#1| (-374)) (-4456 . T) (-4457 . T) (-4459 . T)) -((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -419) (QUOTE (-576))))) (|HasCategory| |#1| (QUOTE (-568))) (|HasCategory| |#1| (QUOTE (-174))) (-2781 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-568)))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-148))) (-12 (|HasCategory| |#1| (LIST (QUOTE -915) (QUOTE (-1195)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -419) (QUOTE (-576))) (|devaluate| |#1|))))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -419) (QUOTE (-576))) (|devaluate| |#1|)))) (|HasCategory| (-419 (-576)) (QUOTE (-1131))) (|HasCategory| |#1| (QUOTE (-374))) (-2781 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-374))) (|HasCategory| |#1| (QUOTE (-568)))) (-2781 (|HasCategory| |#1| (QUOTE (-374))) (|HasCategory| |#1| (QUOTE (-568)))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -419) (QUOTE (-576)))))) (|HasSignature| |#1| (LIST (QUOTE -3581) (LIST (|devaluate| |#1|) (QUOTE (-1195)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -419) (QUOTE (-576)))))) (-2781 (-12 (|HasCategory| |#1| (LIST (QUOTE -29) (QUOTE (-576)))) (|HasCategory| |#1| (QUOTE (-976))) (|HasCategory| |#1| (QUOTE (-1221))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -419) (QUOTE (-576)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -419) (QUOTE (-576))))) (|HasSignature| |#1| (LIST (QUOTE -4121) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1195))))) (|HasSignature| |#1| (LIST (QUOTE -1934) (LIST (LIST (QUOTE -656) (QUOTE (-1195))) (|devaluate| |#1|))))))) +((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -419) (QUOTE (-576))))) (|HasCategory| |#1| (QUOTE (-568))) (|HasCategory| |#1| (QUOTE (-174))) (-2755 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-568)))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-148))) (-12 (|HasCategory| |#1| (LIST (QUOTE -915) (QUOTE (-1195)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -419) (QUOTE (-576))) (|devaluate| |#1|))))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -419) (QUOTE (-576))) (|devaluate| |#1|)))) (|HasCategory| (-419 (-576)) (QUOTE (-1131))) (|HasCategory| |#1| (QUOTE (-374))) (-2755 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-374))) (|HasCategory| |#1| (QUOTE (-568)))) (-2755 (|HasCategory| |#1| (QUOTE (-374))) (|HasCategory| |#1| (QUOTE (-568)))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -419) (QUOTE (-576)))))) (|HasSignature| |#1| (LIST (QUOTE -3567) (LIST (|devaluate| |#1|) (QUOTE (-1195)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -419) (QUOTE (-576)))))) (-2755 (-12 (|HasCategory| |#1| (LIST (QUOTE -29) (QUOTE (-576)))) (|HasCategory| |#1| (QUOTE (-976))) (|HasCategory| |#1| (QUOTE (-1221))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -419) (QUOTE (-576)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -419) (QUOTE (-576))))) (|HasSignature| |#1| (LIST (QUOTE -1589) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1195))))) (|HasSignature| |#1| (LIST (QUOTE -1962) (LIST (LIST (QUOTE -656) (QUOTE (-1195))) (|devaluate| |#1|))))))) (-330 M) ((|constructor| (NIL "computes various functions on factored arguments.")) (|log| (((|List| (|Record| (|:| |coef| (|NonNegativeInteger|)) (|:| |logand| |#1|))) (|Factored| |#1|)) "\\spad{log(f)} returns \\spad{[(a1,b1),...,(am,bm)]} such that the logarithm of \\spad{f} is equal to \\spad{a1*log(b1) + ... + am*log(bm)}.")) (|nthRoot| (((|Record| (|:| |exponent| (|NonNegativeInteger|)) (|:| |coef| |#1|) (|:| |radicand| (|List| |#1|))) (|Factored| |#1|) (|NonNegativeInteger|)) "\\spad{nthRoot(f, n)} returns \\spad{(p, r, [r1,...,rm])} such that the \\spad{n}th-root of \\spad{f} is equal to \\spad{r * \\spad{p}th-root(r1 * ... * rm)},{} where \\spad{r1},{}...,{}\\spad{rm} are distinct factors of \\spad{f},{} each of which has an exponent smaller than \\spad{p} in \\spad{f}."))) NIL @@ -1279,12 +1279,12 @@ NIL (-337 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."))) ((-4463 . T) (-4462 . T)) -((-2781 (-12 (|HasCategory| |#1| (QUOTE (-862))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1119))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|))))) (-2781 (-12 (|HasCategory| |#1| (QUOTE (-1119))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-874))))) (|HasCategory| |#1| (LIST (QUOTE -626) (QUOTE (-548)))) (-2781 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-862))) (|HasCategory| |#1| (QUOTE (-1119)))) (-2781 (|HasCategory| |#1| (QUOTE (-862))) (|HasCategory| |#1| (QUOTE (-1119)))) (|HasCategory| |#1| (QUOTE (-862))) (|HasCategory| (-576) (QUOTE (-862))) (|HasCategory| |#1| (QUOTE (-1119))) (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-874)))) (|HasCategory| |#1| (QUOTE (-102))) (-12 (|HasCategory| |#1| (QUOTE (-1119))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|))))) -(-338 S -1966) +((-2755 (-12 (|HasCategory| |#1| (QUOTE (-862))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1119))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|))))) (-2755 (-12 (|HasCategory| |#1| (QUOTE (-1119))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-874))))) (|HasCategory| |#1| (LIST (QUOTE -626) (QUOTE (-548)))) (-2755 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-862))) (|HasCategory| |#1| (QUOTE (-1119)))) (-2755 (|HasCategory| |#1| (QUOTE (-862))) (|HasCategory| |#1| (QUOTE (-1119)))) (|HasCategory| |#1| (QUOTE (-862))) (|HasCategory| (-576) (QUOTE (-862))) (|HasCategory| |#1| (QUOTE (-1119))) (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-874)))) (|HasCategory| |#1| (QUOTE (-102))) (-12 (|HasCategory| |#1| (QUOTE (-1119))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|))))) +(-338 S -1955) ((|constructor| (NIL "FiniteAlgebraicExtensionField {\\em F} is the category of fields which are finite algebraic extensions of the field {\\em F}. If {\\em F} is finite then any finite algebraic extension of {\\em F} is finite,{} too. Let {\\em K} be a finite algebraic extension of the finite field {\\em F}. The exponentiation of elements of {\\em K} defines a \\spad{Z}-module structure on the multiplicative group of {\\em K}. The additive group of {\\em K} becomes a module over the ring of polynomials over {\\em F} via the operation \\spadfun{linearAssociatedExp}(a:K,{}f:SparseUnivariatePolynomial \\spad{F}) which is linear over {\\em F},{} \\spadignore{i.e.} for elements {\\em a} from {\\em K},{} {\\em c,d} from {\\em F} and {\\em f,g} univariate polynomials over {\\em F} we have \\spadfun{linearAssociatedExp}(a,{}cf+dg) equals {\\em c} times \\spadfun{linearAssociatedExp}(a,{}\\spad{f}) plus {\\em d} times \\spadfun{linearAssociatedExp}(a,{}\\spad{g}). Therefore \\spadfun{linearAssociatedExp} is defined completely by its action on monomials from {\\em F[X]}: \\spadfun{linearAssociatedExp}(a,{}monomial(1,{}\\spad{k})\\spad{\\$}SUP(\\spad{F})) is defined to be \\spadfun{Frobenius}(a,{}\\spad{k}) which is {\\em a**(q**k)} where {\\em q=size()\\$F}. The operations order and discreteLog associated with the multiplicative exponentiation have additive analogues associated to the operation \\spadfun{linearAssociatedExp}. These are the functions \\spadfun{linearAssociatedOrder} and \\spadfun{linearAssociatedLog},{} respectively.")) (|linearAssociatedLog| (((|Union| (|SparseUnivariatePolynomial| |#2|) "failed") $ $) "\\spad{linearAssociatedLog(b,a)} returns a polynomial {\\em g},{} such that the \\spadfun{linearAssociatedExp}(\\spad{b},{}\\spad{g}) equals {\\em a}. If there is no such polynomial {\\em g},{} then \\spadfun{linearAssociatedLog} fails.") (((|SparseUnivariatePolynomial| |#2|) $) "\\spad{linearAssociatedLog(a)} returns a polynomial {\\em g},{} such that \\spadfun{linearAssociatedExp}(normalElement(),{}\\spad{g}) equals {\\em a}.")) (|linearAssociatedOrder| (((|SparseUnivariatePolynomial| |#2|) $) "\\spad{linearAssociatedOrder(a)} retruns the monic polynomial {\\em g} of least degree,{} such that \\spadfun{linearAssociatedExp}(a,{}\\spad{g}) is 0.")) (|linearAssociatedExp| (($ $ (|SparseUnivariatePolynomial| |#2|)) "\\spad{linearAssociatedExp(a,f)} is linear over {\\em F},{} \\spadignore{i.e.} for elements {\\em a} from {\\em \\$},{} {\\em c,d} form {\\em F} and {\\em f,g} univariate polynomials over {\\em F} we have \\spadfun{linearAssociatedExp}(a,{}cf+dg) equals {\\em c} times \\spadfun{linearAssociatedExp}(a,{}\\spad{f}) plus {\\em d} times \\spadfun{linearAssociatedExp}(a,{}\\spad{g}). Therefore \\spadfun{linearAssociatedExp} is defined completely by its action on monomials from {\\em F[X]}: \\spadfun{linearAssociatedExp}(a,{}monomial(1,{}\\spad{k})\\spad{\\$}SUP(\\spad{F})) is defined to be \\spadfun{Frobenius}(a,{}\\spad{k}) which is {\\em a**(q**k)},{} where {\\em q=size()\\$F}.")) (|generator| (($) "\\spad{generator()} returns a root of the defining polynomial. This element generates the field as an algebra over the ground field.")) (|normal?| (((|Boolean|) $) "\\spad{normal?(a)} tests whether the element \\spad{a} is normal over the ground field \\spad{F},{} \\spadignore{i.e.} \\spad{a**(q**i), 0 <= i <= extensionDegree()-1} is an \\spad{F}-basis,{} where \\spad{q = size()\\$F}. Implementation according to Lidl/Niederreiter: Theorem 2.39.")) (|normalElement| (($) "\\spad{normalElement()} returns a element,{} normal over the ground field \\spad{F},{} \\spadignore{i.e.} \\spad{a**(q**i), 0 <= i < extensionDegree()} is an \\spad{F}-basis,{} where \\spad{q = size()\\$F}. At the first call,{} the element is computed by \\spadfunFrom{createNormalElement}{FiniteAlgebraicExtensionField} then cached in a global variable. On subsequent calls,{} the element is retrieved by referencing the global variable.")) (|createNormalElement| (($) "\\spad{createNormalElement()} computes a normal element over the ground field \\spad{F},{} that is,{} \\spad{a**(q**i), 0 <= i < extensionDegree()} is an \\spad{F}-basis,{} where \\spad{q = size()\\$F}. Reference: Such an element exists Lidl/Niederreiter: Theorem 2.35.")) (|trace| (($ $ (|PositiveInteger|)) "\\spad{trace(a,d)} computes the trace of \\spad{a} with respect to the field of extension degree \\spad{d} over the ground field of size \\spad{q}. Error: if \\spad{d} does not divide the extension degree of \\spad{a}. Note: \\spad{trace(a,d) = reduce(+,[a**(q**(d*i)) for i in 0..n/d])}.") ((|#2| $) "\\spad{trace(a)} computes the trace of \\spad{a} with respect to the field considered as an algebra with 1 over the ground field \\spad{F}.")) (|norm| (($ $ (|PositiveInteger|)) "\\spad{norm(a,d)} computes the norm of \\spad{a} with respect to the field of extension degree \\spad{d} over the ground field of size. Error: if \\spad{d} does not divide the extension degree of \\spad{a}. Note: norm(a,{}\\spad{d}) = reduce(*,{}[a**(\\spad{q**}(d*i)) for \\spad{i} in 0..\\spad{n/d}])") ((|#2| $) "\\spad{norm(a)} computes the norm of \\spad{a} with respect to the field considered as an algebra with 1 over the ground field \\spad{F}.")) (|degree| (((|PositiveInteger|) $) "\\spad{degree(a)} returns the degree of the minimal polynomial of an element \\spad{a} over the ground field \\spad{F}.")) (|extensionDegree| (((|PositiveInteger|)) "\\spad{extensionDegree()} returns the degree of field extension.")) (|definingPolynomial| (((|SparseUnivariatePolynomial| |#2|)) "\\spad{definingPolynomial()} returns the polynomial used to define the field extension.")) (|minimalPolynomial| (((|SparseUnivariatePolynomial| $) $ (|PositiveInteger|)) "\\spad{minimalPolynomial(x,n)} computes the minimal polynomial of \\spad{x} over the field of extension degree \\spad{n} over the ground field \\spad{F}.") (((|SparseUnivariatePolynomial| |#2|) $) "\\spad{minimalPolynomial(a)} returns the minimal polynomial of an element \\spad{a} over the ground field \\spad{F}.")) (|represents| (($ (|Vector| |#2|)) "\\spad{represents([a1,..,an])} returns \\spad{a1*v1 + ... + an*vn},{} where \\spad{v1},{}...,{}\\spad{vn} are the elements of the fixed basis.")) (|coordinates| (((|Matrix| |#2|) (|Vector| $)) "\\spad{coordinates([v1,...,vm])} returns the coordinates of the \\spad{vi}\\spad{'s} with to the fixed basis. The coordinates of \\spad{vi} are contained in the \\spad{i}th row of the matrix returned by this function.") (((|Vector| |#2|) $) "\\spad{coordinates(a)} returns the coordinates of \\spad{a} with respect to the fixed \\spad{F}-vectorspace basis.")) (|basis| (((|Vector| $) (|PositiveInteger|)) "\\spad{basis(n)} returns a fixed basis of a subfield of \\spad{\\$} as \\spad{F}-vectorspace.") (((|Vector| $)) "\\spad{basis()} returns a fixed basis of \\spad{\\$} as \\spad{F}-vectorspace."))) NIL ((|HasCategory| |#2| (QUOTE (-379)))) -(-339 -1966) +(-339 -1955) ((|constructor| (NIL "FiniteAlgebraicExtensionField {\\em F} is the category of fields which are finite algebraic extensions of the field {\\em F}. If {\\em F} is finite then any finite algebraic extension of {\\em F} is finite,{} too. Let {\\em K} be a finite algebraic extension of the finite field {\\em F}. The exponentiation of elements of {\\em K} defines a \\spad{Z}-module structure on the multiplicative group of {\\em K}. The additive group of {\\em K} becomes a module over the ring of polynomials over {\\em F} via the operation \\spadfun{linearAssociatedExp}(a:K,{}f:SparseUnivariatePolynomial \\spad{F}) which is linear over {\\em F},{} \\spadignore{i.e.} for elements {\\em a} from {\\em K},{} {\\em c,d} from {\\em F} and {\\em f,g} univariate polynomials over {\\em F} we have \\spadfun{linearAssociatedExp}(a,{}cf+dg) equals {\\em c} times \\spadfun{linearAssociatedExp}(a,{}\\spad{f}) plus {\\em d} times \\spadfun{linearAssociatedExp}(a,{}\\spad{g}). Therefore \\spadfun{linearAssociatedExp} is defined completely by its action on monomials from {\\em F[X]}: \\spadfun{linearAssociatedExp}(a,{}monomial(1,{}\\spad{k})\\spad{\\$}SUP(\\spad{F})) is defined to be \\spadfun{Frobenius}(a,{}\\spad{k}) which is {\\em a**(q**k)} where {\\em q=size()\\$F}. The operations order and discreteLog associated with the multiplicative exponentiation have additive analogues associated to the operation \\spadfun{linearAssociatedExp}. These are the functions \\spadfun{linearAssociatedOrder} and \\spadfun{linearAssociatedLog},{} respectively.")) (|linearAssociatedLog| (((|Union| (|SparseUnivariatePolynomial| |#1|) "failed") $ $) "\\spad{linearAssociatedLog(b,a)} returns a polynomial {\\em g},{} such that the \\spadfun{linearAssociatedExp}(\\spad{b},{}\\spad{g}) equals {\\em a}. If there is no such polynomial {\\em g},{} then \\spadfun{linearAssociatedLog} fails.") (((|SparseUnivariatePolynomial| |#1|) $) "\\spad{linearAssociatedLog(a)} returns a polynomial {\\em g},{} such that \\spadfun{linearAssociatedExp}(normalElement(),{}\\spad{g}) equals {\\em a}.")) (|linearAssociatedOrder| (((|SparseUnivariatePolynomial| |#1|) $) "\\spad{linearAssociatedOrder(a)} retruns the monic polynomial {\\em g} of least degree,{} such that \\spadfun{linearAssociatedExp}(a,{}\\spad{g}) is 0.")) (|linearAssociatedExp| (($ $ (|SparseUnivariatePolynomial| |#1|)) "\\spad{linearAssociatedExp(a,f)} is linear over {\\em F},{} \\spadignore{i.e.} for elements {\\em a} from {\\em \\$},{} {\\em c,d} form {\\em F} and {\\em f,g} univariate polynomials over {\\em F} we have \\spadfun{linearAssociatedExp}(a,{}cf+dg) equals {\\em c} times \\spadfun{linearAssociatedExp}(a,{}\\spad{f}) plus {\\em d} times \\spadfun{linearAssociatedExp}(a,{}\\spad{g}). Therefore \\spadfun{linearAssociatedExp} is defined completely by its action on monomials from {\\em F[X]}: \\spadfun{linearAssociatedExp}(a,{}monomial(1,{}\\spad{k})\\spad{\\$}SUP(\\spad{F})) is defined to be \\spadfun{Frobenius}(a,{}\\spad{k}) which is {\\em a**(q**k)},{} where {\\em q=size()\\$F}.")) (|generator| (($) "\\spad{generator()} returns a root of the defining polynomial. This element generates the field as an algebra over the ground field.")) (|normal?| (((|Boolean|) $) "\\spad{normal?(a)} tests whether the element \\spad{a} is normal over the ground field \\spad{F},{} \\spadignore{i.e.} \\spad{a**(q**i), 0 <= i <= extensionDegree()-1} is an \\spad{F}-basis,{} where \\spad{q = size()\\$F}. Implementation according to Lidl/Niederreiter: Theorem 2.39.")) (|normalElement| (($) "\\spad{normalElement()} returns a element,{} normal over the ground field \\spad{F},{} \\spadignore{i.e.} \\spad{a**(q**i), 0 <= i < extensionDegree()} is an \\spad{F}-basis,{} where \\spad{q = size()\\$F}. At the first call,{} the element is computed by \\spadfunFrom{createNormalElement}{FiniteAlgebraicExtensionField} then cached in a global variable. On subsequent calls,{} the element is retrieved by referencing the global variable.")) (|createNormalElement| (($) "\\spad{createNormalElement()} computes a normal element over the ground field \\spad{F},{} that is,{} \\spad{a**(q**i), 0 <= i < extensionDegree()} is an \\spad{F}-basis,{} where \\spad{q = size()\\$F}. Reference: Such an element exists Lidl/Niederreiter: Theorem 2.35.")) (|trace| (($ $ (|PositiveInteger|)) "\\spad{trace(a,d)} computes the trace of \\spad{a} with respect to the field of extension degree \\spad{d} over the ground field of size \\spad{q}. Error: if \\spad{d} does not divide the extension degree of \\spad{a}. Note: \\spad{trace(a,d) = reduce(+,[a**(q**(d*i)) for i in 0..n/d])}.") ((|#1| $) "\\spad{trace(a)} computes the trace of \\spad{a} with respect to the field considered as an algebra with 1 over the ground field \\spad{F}.")) (|norm| (($ $ (|PositiveInteger|)) "\\spad{norm(a,d)} computes the norm of \\spad{a} with respect to the field of extension degree \\spad{d} over the ground field of size. Error: if \\spad{d} does not divide the extension degree of \\spad{a}. Note: norm(a,{}\\spad{d}) = reduce(*,{}[a**(\\spad{q**}(d*i)) for \\spad{i} in 0..\\spad{n/d}])") ((|#1| $) "\\spad{norm(a)} computes the norm of \\spad{a} with respect to the field considered as an algebra with 1 over the ground field \\spad{F}.")) (|degree| (((|PositiveInteger|) $) "\\spad{degree(a)} returns the degree of the minimal polynomial of an element \\spad{a} over the ground field \\spad{F}.")) (|extensionDegree| (((|PositiveInteger|)) "\\spad{extensionDegree()} returns the degree of field extension.")) (|definingPolynomial| (((|SparseUnivariatePolynomial| |#1|)) "\\spad{definingPolynomial()} returns the polynomial used to define the field extension.")) (|minimalPolynomial| (((|SparseUnivariatePolynomial| $) $ (|PositiveInteger|)) "\\spad{minimalPolynomial(x,n)} computes the minimal polynomial of \\spad{x} over the field of extension degree \\spad{n} over the ground field \\spad{F}.") (((|SparseUnivariatePolynomial| |#1|) $) "\\spad{minimalPolynomial(a)} returns the minimal polynomial of an element \\spad{a} over the ground field \\spad{F}.")) (|represents| (($ (|Vector| |#1|)) "\\spad{represents([a1,..,an])} returns \\spad{a1*v1 + ... + an*vn},{} where \\spad{v1},{}...,{}\\spad{vn} are the elements of the fixed basis.")) (|coordinates| (((|Matrix| |#1|) (|Vector| $)) "\\spad{coordinates([v1,...,vm])} returns the coordinates of the \\spad{vi}\\spad{'s} with to the fixed basis. The coordinates of \\spad{vi} are contained in the \\spad{i}th row of the matrix returned by this function.") (((|Vector| |#1|) $) "\\spad{coordinates(a)} returns the coordinates of \\spad{a} with respect to the fixed \\spad{F}-vectorspace basis.")) (|basis| (((|Vector| $) (|PositiveInteger|)) "\\spad{basis(n)} returns a fixed basis of a subfield of \\spad{\\$} as \\spad{F}-vectorspace.") (((|Vector| $)) "\\spad{basis()} returns a fixed basis of \\spad{\\$} as \\spad{F}-vectorspace."))) ((-4454 . T) (-4460 . T) (-4455 . T) ((-4464 "*") . T) (-4456 . T) (-4457 . T) (-4459 . T)) NIL @@ -1308,15 +1308,15 @@ NIL ((|constructor| (NIL "\\indented{1}{Lift a map to finite divisors.} Author: Manuel Bronstein Date Created: 1988 Date Last Updated: 19 May 1993")) (|map| (((|FiniteDivisor| |#5| |#6| |#7| |#8|) (|Mapping| |#5| |#1|) (|FiniteDivisor| |#1| |#2| |#3| |#4|)) "\\spad{map(f,d)} \\undocumented{}"))) NIL NIL -(-345 S -1966 UP UPUP R) +(-345 S -1955 UP UPUP R) ((|constructor| (NIL "This category describes finite rational divisors on a curve,{} that is finite formal sums SUM(\\spad{n} * \\spad{P}) where the \\spad{n}\\spad{'s} are integers and the \\spad{P}\\spad{'s} are finite rational points on the curve.")) (|generator| (((|Union| |#5| "failed") $) "\\spad{generator(d)} returns \\spad{f} if \\spad{(f) = d},{} \"failed\" if \\spad{d} is not principal.")) (|principal?| (((|Boolean|) $) "\\spad{principal?(D)} tests if the argument is the divisor of a function.")) (|reduce| (($ $) "\\spad{reduce(D)} converts \\spad{D} to some reduced form (the reduced forms can be differents in different implementations).")) (|decompose| (((|Record| (|:| |id| (|FractionalIdeal| |#3| (|Fraction| |#3|) |#4| |#5|)) (|:| |principalPart| |#5|)) $) "\\spad{decompose(d)} returns \\spad{[id, f]} where \\spad{d = (id) + div(f)}.")) (|divisor| (($ |#5| |#3| |#3| |#3| |#2|) "\\spad{divisor(h, d, d', g, r)} returns the sum of all the finite points where \\spad{h/d} has residue \\spad{r}. \\spad{h} must be integral. \\spad{d} must be squarefree. \\spad{d'} is some derivative of \\spad{d} (not necessarily dd/dx). \\spad{g = gcd(d,discriminant)} contains the ramified zeros of \\spad{d}") (($ |#2| |#2| (|Integer|)) "\\spad{divisor(a, b, n)} makes the divisor \\spad{nP} where \\spad{P:} \\spad{(x = a, y = b)}. \\spad{P} is allowed to be singular if \\spad{n} is a multiple of the rank.") (($ |#2| |#2|) "\\spad{divisor(a, b)} makes the divisor \\spad{P:} \\spad{(x = a, y = b)}. Error: if \\spad{P} is singular.") (($ |#5|) "\\spad{divisor(g)} returns the divisor of the function \\spad{g}.") (($ (|FractionalIdeal| |#3| (|Fraction| |#3|) |#4| |#5|)) "\\spad{divisor(I)} makes a divisor \\spad{D} from an ideal \\spad{I}.")) (|ideal| (((|FractionalIdeal| |#3| (|Fraction| |#3|) |#4| |#5|) $) "\\spad{ideal(D)} returns the ideal corresponding to a divisor \\spad{D}."))) NIL NIL -(-346 -1966 UP UPUP R) +(-346 -1955 UP UPUP R) ((|constructor| (NIL "This category describes finite rational divisors on a curve,{} that is finite formal sums SUM(\\spad{n} * \\spad{P}) where the \\spad{n}\\spad{'s} are integers and the \\spad{P}\\spad{'s} are finite rational points on the curve.")) (|generator| (((|Union| |#4| "failed") $) "\\spad{generator(d)} returns \\spad{f} if \\spad{(f) = d},{} \"failed\" if \\spad{d} is not principal.")) (|principal?| (((|Boolean|) $) "\\spad{principal?(D)} tests if the argument is the divisor of a function.")) (|reduce| (($ $) "\\spad{reduce(D)} converts \\spad{D} to some reduced form (the reduced forms can be differents in different implementations).")) (|decompose| (((|Record| (|:| |id| (|FractionalIdeal| |#2| (|Fraction| |#2|) |#3| |#4|)) (|:| |principalPart| |#4|)) $) "\\spad{decompose(d)} returns \\spad{[id, f]} where \\spad{d = (id) + div(f)}.")) (|divisor| (($ |#4| |#2| |#2| |#2| |#1|) "\\spad{divisor(h, d, d', g, r)} returns the sum of all the finite points where \\spad{h/d} has residue \\spad{r}. \\spad{h} must be integral. \\spad{d} must be squarefree. \\spad{d'} is some derivative of \\spad{d} (not necessarily dd/dx). \\spad{g = gcd(d,discriminant)} contains the ramified zeros of \\spad{d}") (($ |#1| |#1| (|Integer|)) "\\spad{divisor(a, b, n)} makes the divisor \\spad{nP} where \\spad{P:} \\spad{(x = a, y = b)}. \\spad{P} is allowed to be singular if \\spad{n} is a multiple of the rank.") (($ |#1| |#1|) "\\spad{divisor(a, b)} makes the divisor \\spad{P:} \\spad{(x = a, y = b)}. Error: if \\spad{P} is singular.") (($ |#4|) "\\spad{divisor(g)} returns the divisor of the function \\spad{g}.") (($ (|FractionalIdeal| |#2| (|Fraction| |#2|) |#3| |#4|)) "\\spad{divisor(I)} makes a divisor \\spad{D} from an ideal \\spad{I}.")) (|ideal| (((|FractionalIdeal| |#2| (|Fraction| |#2|) |#3| |#4|) $) "\\spad{ideal(D)} returns the ideal corresponding to a divisor \\spad{D}."))) NIL NIL -(-347 -1966 UP UPUP R) +(-347 -1955 UP UPUP R) ((|constructor| (NIL "This domains implements finite rational divisors on a curve,{} that is finite formal sums SUM(\\spad{n} * \\spad{P}) where the \\spad{n}\\spad{'s} are integers and the \\spad{P}\\spad{'s} are finite rational points on the curve.")) (|lSpaceBasis| (((|Vector| |#4|) $) "\\spad{lSpaceBasis(d)} returns a basis for \\spad{L(d) = {f | (f) >= -d}} as a module over \\spad{K[x]}.")) (|finiteBasis| (((|Vector| |#4|) $) "\\spad{finiteBasis(d)} returns a basis for \\spad{d} as a module over {\\em K[x]}."))) NIL NIL @@ -1336,26 +1336,26 @@ NIL ((|constructor| (NIL "Lifts a map from rings to function fields over them.")) (|map| ((|#8| (|Mapping| |#5| |#1|) |#4|) "\\spad{map(f, p)} lifts \\spad{f} to \\spad{F1} and applies it to \\spad{p}."))) NIL NIL -(-352 S -1966 UP UPUP) +(-352 S -1955 UP UPUP) ((|constructor| (NIL "This category is a model for the function field of a plane algebraic curve.")) (|rationalPoints| (((|List| (|List| |#2|))) "\\spad{rationalPoints()} returns the list of all the affine rational points.")) (|nonSingularModel| (((|List| (|Polynomial| |#2|)) (|Symbol|)) "\\spad{nonSingularModel(u)} returns the equations in u1,{}...,{}un of an affine non-singular model for the curve.")) (|algSplitSimple| (((|Record| (|:| |num| $) (|:| |den| |#3|) (|:| |derivden| |#3|) (|:| |gd| |#3|)) $ (|Mapping| |#3| |#3|)) "\\spad{algSplitSimple(f, D)} returns \\spad{[h,d,d',g]} such that \\spad{f=h/d},{} \\spad{h} is integral at all the normal places \\spad{w}.\\spad{r}.\\spad{t}. \\spad{D},{} \\spad{d' = Dd},{} \\spad{g = gcd(d, discriminant())} and \\spad{D} is the derivation to use. \\spad{f} must have at most simple finite poles.")) (|hyperelliptic| (((|Union| |#3| "failed")) "\\spad{hyperelliptic()} returns \\spad{p(x)} if the curve is the hyperelliptic defined by \\spad{y**2 = p(x)},{} \"failed\" otherwise.")) (|elliptic| (((|Union| |#3| "failed")) "\\spad{elliptic()} returns \\spad{p(x)} if the curve is the elliptic defined by \\spad{y**2 = p(x)},{} \"failed\" otherwise.")) (|elt| ((|#2| $ |#2| |#2|) "\\spad{elt(f,a,b)} or \\spad{f}(a,{} \\spad{b}) returns the value of \\spad{f} at the point \\spad{(x = a, y = b)} if it is not singular.")) (|primitivePart| (($ $) "\\spad{primitivePart(f)} removes the content of the denominator and the common content of the numerator of \\spad{f}.")) (|differentiate| (($ $ (|Mapping| |#3| |#3|)) "\\spad{differentiate(x, d)} extends the derivation \\spad{d} from UP to \\$ and applies it to \\spad{x}.")) (|integralDerivationMatrix| (((|Record| (|:| |num| (|Matrix| |#3|)) (|:| |den| |#3|)) (|Mapping| |#3| |#3|)) "\\spad{integralDerivationMatrix(d)} extends the derivation \\spad{d} from UP to \\$ and returns (\\spad{M},{} \\spad{Q}) such that the i^th row of \\spad{M} divided by \\spad{Q} form the coordinates of \\spad{d(wi)} with respect to \\spad{(w1,...,wn)} where \\spad{(w1,...,wn)} is the integral basis returned by integralBasis().")) (|integralRepresents| (($ (|Vector| |#3|) |#3|) "\\spad{integralRepresents([A1,...,An], D)} returns \\spad{(A1 w1+...+An wn)/D} where \\spad{(w1,...,wn)} is the integral basis of \\spad{integralBasis()}.")) (|integralCoordinates| (((|Record| (|:| |num| (|Vector| |#3|)) (|:| |den| |#3|)) $) "\\spad{integralCoordinates(f)} returns \\spad{[[A1,...,An], D]} such that \\spad{f = (A1 w1 +...+ An wn) / D} where \\spad{(w1,...,wn)} is the integral basis returned by \\spad{integralBasis()}.")) (|represents| (($ (|Vector| |#3|) |#3|) "\\spad{represents([A0,...,A(n-1)],D)} returns \\spad{(A0 + A1 y +...+ A(n-1)*y**(n-1))/D}.")) (|yCoordinates| (((|Record| (|:| |num| (|Vector| |#3|)) (|:| |den| |#3|)) $) "\\spad{yCoordinates(f)} returns \\spad{[[A1,...,An], D]} such that \\spad{f = (A1 + A2 y +...+ An y**(n-1)) / D}.")) (|inverseIntegralMatrixAtInfinity| (((|Matrix| (|Fraction| |#3|))) "\\spad{inverseIntegralMatrixAtInfinity()} returns \\spad{M} such that \\spad{M (v1,...,vn) = (1, y, ..., y**(n-1))} where \\spad{(v1,...,vn)} is the local integral basis at infinity returned by \\spad{infIntBasis()}.")) (|integralMatrixAtInfinity| (((|Matrix| (|Fraction| |#3|))) "\\spad{integralMatrixAtInfinity()} returns \\spad{M} such that \\spad{(v1,...,vn) = M (1, y, ..., y**(n-1))} where \\spad{(v1,...,vn)} is the local integral basis at infinity returned by \\spad{infIntBasis()}.")) (|inverseIntegralMatrix| (((|Matrix| (|Fraction| |#3|))) "\\spad{inverseIntegralMatrix()} returns \\spad{M} such that \\spad{M (w1,...,wn) = (1, y, ..., y**(n-1))} where \\spad{(w1,...,wn)} is the integral basis of \\spadfunFrom{integralBasis}{FunctionFieldCategory}.")) (|integralMatrix| (((|Matrix| (|Fraction| |#3|))) "\\spad{integralMatrix()} returns \\spad{M} such that \\spad{(w1,...,wn) = M (1, y, ..., y**(n-1))},{} where \\spad{(w1,...,wn)} is the integral basis of \\spadfunFrom{integralBasis}{FunctionFieldCategory}.")) (|reduceBasisAtInfinity| (((|Vector| $) (|Vector| $)) "\\spad{reduceBasisAtInfinity(b1,...,bn)} returns \\spad{(x**i * bj)} for all \\spad{i},{}\\spad{j} such that \\spad{x**i*bj} is locally integral at infinity.")) (|normalizeAtInfinity| (((|Vector| $) (|Vector| $)) "\\spad{normalizeAtInfinity(v)} makes \\spad{v} normal at infinity.")) (|complementaryBasis| (((|Vector| $) (|Vector| $)) "\\spad{complementaryBasis(b1,...,bn)} returns the complementary basis \\spad{(b1',...,bn')} of \\spad{(b1,...,bn)}.")) (|integral?| (((|Boolean|) $ |#3|) "\\spad{integral?(f, p)} tests whether \\spad{f} is locally integral at \\spad{p(x) = 0}.") (((|Boolean|) $ |#2|) "\\spad{integral?(f, a)} tests whether \\spad{f} is locally integral at \\spad{x = a}.") (((|Boolean|) $) "\\spad{integral?()} tests if \\spad{f} is integral over \\spad{k[x]}.")) (|integralAtInfinity?| (((|Boolean|) $) "\\spad{integralAtInfinity?()} tests if \\spad{f} is locally integral at infinity.")) (|integralBasisAtInfinity| (((|Vector| $)) "\\spad{integralBasisAtInfinity()} returns the local integral basis at infinity.")) (|integralBasis| (((|Vector| $)) "\\spad{integralBasis()} returns the integral basis for the curve.")) (|ramified?| (((|Boolean|) |#3|) "\\spad{ramified?(p)} tests whether \\spad{p(x) = 0} is ramified.") (((|Boolean|) |#2|) "\\spad{ramified?(a)} tests whether \\spad{x = a} is ramified.")) (|ramifiedAtInfinity?| (((|Boolean|)) "\\spad{ramifiedAtInfinity?()} tests if infinity is ramified.")) (|singular?| (((|Boolean|) |#3|) "\\spad{singular?(p)} tests whether \\spad{p(x) = 0} is singular.") (((|Boolean|) |#2|) "\\spad{singular?(a)} tests whether \\spad{x = a} is singular.")) (|singularAtInfinity?| (((|Boolean|)) "\\spad{singularAtInfinity?()} tests if there is a singularity at infinity.")) (|branchPoint?| (((|Boolean|) |#3|) "\\spad{branchPoint?(p)} tests whether \\spad{p(x) = 0} is a branch point.") (((|Boolean|) |#2|) "\\spad{branchPoint?(a)} tests whether \\spad{x = a} is a branch point.")) (|branchPointAtInfinity?| (((|Boolean|)) "\\spad{branchPointAtInfinity?()} tests if there is a branch point at infinity.")) (|rationalPoint?| (((|Boolean|) |#2| |#2|) "\\spad{rationalPoint?(a, b)} tests if \\spad{(x=a,y=b)} is on the curve.")) (|absolutelyIrreducible?| (((|Boolean|)) "\\spad{absolutelyIrreducible?()} tests if the curve absolutely irreducible?")) (|genus| (((|NonNegativeInteger|)) "\\spad{genus()} returns the genus of one absolutely irreducible component")) (|numberOfComponents| (((|NonNegativeInteger|)) "\\spad{numberOfComponents()} returns the number of absolutely irreducible components."))) NIL ((|HasCategory| |#2| (QUOTE (-379))) (|HasCategory| |#2| (QUOTE (-374)))) -(-353 -1966 UP UPUP) +(-353 -1955 UP UPUP) ((|constructor| (NIL "This category is a model for the function field of a plane algebraic curve.")) (|rationalPoints| (((|List| (|List| |#1|))) "\\spad{rationalPoints()} returns the list of all the affine rational points.")) (|nonSingularModel| (((|List| (|Polynomial| |#1|)) (|Symbol|)) "\\spad{nonSingularModel(u)} returns the equations in u1,{}...,{}un of an affine non-singular model for the curve.")) (|algSplitSimple| (((|Record| (|:| |num| $) (|:| |den| |#2|) (|:| |derivden| |#2|) (|:| |gd| |#2|)) $ (|Mapping| |#2| |#2|)) "\\spad{algSplitSimple(f, D)} returns \\spad{[h,d,d',g]} such that \\spad{f=h/d},{} \\spad{h} is integral at all the normal places \\spad{w}.\\spad{r}.\\spad{t}. \\spad{D},{} \\spad{d' = Dd},{} \\spad{g = gcd(d, discriminant())} and \\spad{D} is the derivation to use. \\spad{f} must have at most simple finite poles.")) (|hyperelliptic| (((|Union| |#2| "failed")) "\\spad{hyperelliptic()} returns \\spad{p(x)} if the curve is the hyperelliptic defined by \\spad{y**2 = p(x)},{} \"failed\" otherwise.")) (|elliptic| (((|Union| |#2| "failed")) "\\spad{elliptic()} returns \\spad{p(x)} if the curve is the elliptic defined by \\spad{y**2 = p(x)},{} \"failed\" otherwise.")) (|elt| ((|#1| $ |#1| |#1|) "\\spad{elt(f,a,b)} or \\spad{f}(a,{} \\spad{b}) returns the value of \\spad{f} at the point \\spad{(x = a, y = b)} if it is not singular.")) (|primitivePart| (($ $) "\\spad{primitivePart(f)} removes the content of the denominator and the common content of the numerator of \\spad{f}.")) (|differentiate| (($ $ (|Mapping| |#2| |#2|)) "\\spad{differentiate(x, d)} extends the derivation \\spad{d} from UP to \\$ and applies it to \\spad{x}.")) (|integralDerivationMatrix| (((|Record| (|:| |num| (|Matrix| |#2|)) (|:| |den| |#2|)) (|Mapping| |#2| |#2|)) "\\spad{integralDerivationMatrix(d)} extends the derivation \\spad{d} from UP to \\$ and returns (\\spad{M},{} \\spad{Q}) such that the i^th row of \\spad{M} divided by \\spad{Q} form the coordinates of \\spad{d(wi)} with respect to \\spad{(w1,...,wn)} where \\spad{(w1,...,wn)} is the integral basis returned by integralBasis().")) (|integralRepresents| (($ (|Vector| |#2|) |#2|) "\\spad{integralRepresents([A1,...,An], D)} returns \\spad{(A1 w1+...+An wn)/D} where \\spad{(w1,...,wn)} is the integral basis of \\spad{integralBasis()}.")) (|integralCoordinates| (((|Record| (|:| |num| (|Vector| |#2|)) (|:| |den| |#2|)) $) "\\spad{integralCoordinates(f)} returns \\spad{[[A1,...,An], D]} such that \\spad{f = (A1 w1 +...+ An wn) / D} where \\spad{(w1,...,wn)} is the integral basis returned by \\spad{integralBasis()}.")) (|represents| (($ (|Vector| |#2|) |#2|) "\\spad{represents([A0,...,A(n-1)],D)} returns \\spad{(A0 + A1 y +...+ A(n-1)*y**(n-1))/D}.")) (|yCoordinates| (((|Record| (|:| |num| (|Vector| |#2|)) (|:| |den| |#2|)) $) "\\spad{yCoordinates(f)} returns \\spad{[[A1,...,An], D]} such that \\spad{f = (A1 + A2 y +...+ An y**(n-1)) / D}.")) (|inverseIntegralMatrixAtInfinity| (((|Matrix| (|Fraction| |#2|))) "\\spad{inverseIntegralMatrixAtInfinity()} returns \\spad{M} such that \\spad{M (v1,...,vn) = (1, y, ..., y**(n-1))} where \\spad{(v1,...,vn)} is the local integral basis at infinity returned by \\spad{infIntBasis()}.")) (|integralMatrixAtInfinity| (((|Matrix| (|Fraction| |#2|))) "\\spad{integralMatrixAtInfinity()} returns \\spad{M} such that \\spad{(v1,...,vn) = M (1, y, ..., y**(n-1))} where \\spad{(v1,...,vn)} is the local integral basis at infinity returned by \\spad{infIntBasis()}.")) (|inverseIntegralMatrix| (((|Matrix| (|Fraction| |#2|))) "\\spad{inverseIntegralMatrix()} returns \\spad{M} such that \\spad{M (w1,...,wn) = (1, y, ..., y**(n-1))} where \\spad{(w1,...,wn)} is the integral basis of \\spadfunFrom{integralBasis}{FunctionFieldCategory}.")) (|integralMatrix| (((|Matrix| (|Fraction| |#2|))) "\\spad{integralMatrix()} returns \\spad{M} such that \\spad{(w1,...,wn) = M (1, y, ..., y**(n-1))},{} where \\spad{(w1,...,wn)} is the integral basis of \\spadfunFrom{integralBasis}{FunctionFieldCategory}.")) (|reduceBasisAtInfinity| (((|Vector| $) (|Vector| $)) "\\spad{reduceBasisAtInfinity(b1,...,bn)} returns \\spad{(x**i * bj)} for all \\spad{i},{}\\spad{j} such that \\spad{x**i*bj} is locally integral at infinity.")) (|normalizeAtInfinity| (((|Vector| $) (|Vector| $)) "\\spad{normalizeAtInfinity(v)} makes \\spad{v} normal at infinity.")) (|complementaryBasis| (((|Vector| $) (|Vector| $)) "\\spad{complementaryBasis(b1,...,bn)} returns the complementary basis \\spad{(b1',...,bn')} of \\spad{(b1,...,bn)}.")) (|integral?| (((|Boolean|) $ |#2|) "\\spad{integral?(f, p)} tests whether \\spad{f} is locally integral at \\spad{p(x) = 0}.") (((|Boolean|) $ |#1|) "\\spad{integral?(f, a)} tests whether \\spad{f} is locally integral at \\spad{x = a}.") (((|Boolean|) $) "\\spad{integral?()} tests if \\spad{f} is integral over \\spad{k[x]}.")) (|integralAtInfinity?| (((|Boolean|) $) "\\spad{integralAtInfinity?()} tests if \\spad{f} is locally integral at infinity.")) (|integralBasisAtInfinity| (((|Vector| $)) "\\spad{integralBasisAtInfinity()} returns the local integral basis at infinity.")) (|integralBasis| (((|Vector| $)) "\\spad{integralBasis()} returns the integral basis for the curve.")) (|ramified?| (((|Boolean|) |#2|) "\\spad{ramified?(p)} tests whether \\spad{p(x) = 0} is ramified.") (((|Boolean|) |#1|) "\\spad{ramified?(a)} tests whether \\spad{x = a} is ramified.")) (|ramifiedAtInfinity?| (((|Boolean|)) "\\spad{ramifiedAtInfinity?()} tests if infinity is ramified.")) (|singular?| (((|Boolean|) |#2|) "\\spad{singular?(p)} tests whether \\spad{p(x) = 0} is singular.") (((|Boolean|) |#1|) "\\spad{singular?(a)} tests whether \\spad{x = a} is singular.")) (|singularAtInfinity?| (((|Boolean|)) "\\spad{singularAtInfinity?()} tests if there is a singularity at infinity.")) (|branchPoint?| (((|Boolean|) |#2|) "\\spad{branchPoint?(p)} tests whether \\spad{p(x) = 0} is a branch point.") (((|Boolean|) |#1|) "\\spad{branchPoint?(a)} tests whether \\spad{x = a} is a branch point.")) (|branchPointAtInfinity?| (((|Boolean|)) "\\spad{branchPointAtInfinity?()} tests if there is a branch point at infinity.")) (|rationalPoint?| (((|Boolean|) |#1| |#1|) "\\spad{rationalPoint?(a, b)} tests if \\spad{(x=a,y=b)} is on the curve.")) (|absolutelyIrreducible?| (((|Boolean|)) "\\spad{absolutelyIrreducible?()} tests if the curve absolutely irreducible?")) (|genus| (((|NonNegativeInteger|)) "\\spad{genus()} returns the genus of one absolutely irreducible component")) (|numberOfComponents| (((|NonNegativeInteger|)) "\\spad{numberOfComponents()} returns the number of absolutely irreducible components."))) ((-4455 |has| (-419 |#2|) (-374)) (-4460 |has| (-419 |#2|) (-374)) (-4454 |has| (-419 |#2|) (-374)) ((-4464 "*") . T) (-4456 . T) (-4457 . T) (-4459 . T)) NIL (-354 |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."))) ((-4454 . T) (-4460 . T) (-4455 . T) ((-4464 "*") . T) (-4456 . T) (-4457 . T) (-4459 . T)) -((-2781 (|HasCategory| (-927 |#1|) (QUOTE (-146))) (|HasCategory| (-927 |#1|) (QUOTE (-379)))) (|HasCategory| (-927 |#1|) (QUOTE (-148))) (|HasCategory| (-927 |#1|) (QUOTE (-379))) (|HasCategory| (-927 |#1|) (QUOTE (-146)))) +((-2755 (|HasCategory| (-927 |#1|) (QUOTE (-146))) (|HasCategory| (-927 |#1|) (QUOTE (-379)))) (|HasCategory| (-927 |#1|) (QUOTE (-148))) (|HasCategory| (-927 |#1|) (QUOTE (-379))) (|HasCategory| (-927 |#1|) (QUOTE (-146)))) (-355 GF |defpol|) ((|constructor| (NIL "FiniteFieldCyclicGroupExtensionByPolynomial(\\spad{GF},{}defpol) implements a finite extension field of the ground field {\\em GF}. Its elements are represented by powers of a primitive element,{} \\spadignore{i.e.} a generator of the multiplicative (cyclic) group. As primitive element we choose the root of the extension polynomial {\\em defpol},{} which MUST be primitive (user responsibility). Zech logarithms are stored in a table of size half of the field size,{} and use \\spadtype{SingleInteger} for representing field elements,{} hence,{} there are restrictions on the size of the field.")) (|getZechTable| (((|PrimitiveArray| (|SingleInteger|))) "\\spad{getZechTable()} returns the zech logarithm table of the field it is used to perform additions in the field quickly."))) ((-4454 . T) (-4460 . T) (-4455 . T) ((-4464 "*") . T) (-4456 . T) (-4457 . T) (-4459 . T)) -((-2781 (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-379)))) (|HasCategory| |#1| (QUOTE (-148))) (|HasCategory| |#1| (QUOTE (-379))) (|HasCategory| |#1| (QUOTE (-146)))) +((-2755 (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-379)))) (|HasCategory| |#1| (QUOTE (-148))) (|HasCategory| |#1| (QUOTE (-379))) (|HasCategory| |#1| (QUOTE (-146)))) (-356 GF |extdeg|) ((|constructor| (NIL "FiniteFieldCyclicGroupExtension(\\spad{GF},{}\\spad{n}) implements a extension of degree \\spad{n} over the ground field {\\em GF}. Its elements are represented by powers of a primitive element,{} \\spadignore{i.e.} a generator of the multiplicative (cyclic) group. As primitive element we choose the root of the extension polynomial,{} which is created by {\\em createPrimitivePoly} from \\spadtype{FiniteFieldPolynomialPackage}. Zech logarithms are stored in a table of size half of the field size,{} and use \\spadtype{SingleInteger} for representing field elements,{} hence,{} there are restrictions on the size of the field.")) (|getZechTable| (((|PrimitiveArray| (|SingleInteger|))) "\\spad{getZechTable()} returns the zech logarithm table of the field. This table is used to perform additions in the field quickly."))) ((-4454 . T) (-4460 . T) (-4455 . T) ((-4464 "*") . T) (-4456 . T) (-4457 . T) (-4459 . T)) -((-2781 (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-379)))) (|HasCategory| |#1| (QUOTE (-148))) (|HasCategory| |#1| (QUOTE (-379))) (|HasCategory| |#1| (QUOTE (-146)))) +((-2755 (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-379)))) (|HasCategory| |#1| (QUOTE (-148))) (|HasCategory| |#1| (QUOTE (-379))) (|HasCategory| |#1| (QUOTE (-146)))) (-357 GF) ((|constructor| (NIL "FiniteFieldFunctions(\\spad{GF}) is a package with functions concerning finite extension fields of the finite ground field {\\em GF},{} \\spadignore{e.g.} Zech logarithms.")) (|createLowComplexityNormalBasis| (((|Union| (|SparseUnivariatePolynomial| |#1|) (|Vector| (|List| (|Record| (|:| |value| |#1|) (|:| |index| (|SingleInteger|)))))) (|PositiveInteger|)) "\\spad{createLowComplexityNormalBasis(n)} tries to find a a low complexity normal basis of degree {\\em n} over {\\em GF} and returns its multiplication matrix If no low complexity basis is found it calls \\axiomFunFrom{createNormalPoly}{FiniteFieldPolynomialPackage}(\\spad{n}) to produce a normal polynomial of degree {\\em n} over {\\em GF}")) (|createLowComplexityTable| (((|Union| (|Vector| (|List| (|Record| (|:| |value| |#1|) (|:| |index| (|SingleInteger|))))) "failed") (|PositiveInteger|)) "\\spad{createLowComplexityTable(n)} tries to find a low complexity normal basis of degree {\\em n} over {\\em GF} and returns its multiplication matrix Fails,{} if it does not find a low complexity basis")) (|sizeMultiplication| (((|NonNegativeInteger|) (|Vector| (|List| (|Record| (|:| |value| |#1|) (|:| |index| (|SingleInteger|)))))) "\\spad{sizeMultiplication(m)} returns the number of entries of the multiplication table {\\em m}.")) (|createMultiplicationMatrix| (((|Matrix| |#1|) (|Vector| (|List| (|Record| (|:| |value| |#1|) (|:| |index| (|SingleInteger|)))))) "\\spad{createMultiplicationMatrix(m)} forms the multiplication table {\\em m} into a matrix over the ground field.")) (|createMultiplicationTable| (((|Vector| (|List| (|Record| (|:| |value| |#1|) (|:| |index| (|SingleInteger|))))) (|SparseUnivariatePolynomial| |#1|)) "\\spad{createMultiplicationTable(f)} generates a multiplication table for the normal basis of the field extension determined by {\\em f}. This is needed to perform multiplications between elements represented as coordinate vectors to this basis. See \\spadtype{FFNBP},{} \\spadtype{FFNBX}.")) (|createZechTable| (((|PrimitiveArray| (|SingleInteger|)) (|SparseUnivariatePolynomial| |#1|)) "\\spad{createZechTable(f)} generates a Zech logarithm table for the cyclic group representation of a extension of the ground field by the primitive polynomial {\\em f(x)},{} \\spadignore{i.e.} \\spad{Z(i)},{} defined by {\\em x**Z(i) = 1+x**i} is stored at index \\spad{i}. This is needed in particular to perform addition of field elements in finite fields represented in this way. See \\spadtype{FFCGP},{} \\spadtype{FFCGX}."))) NIL @@ -1372,31 +1372,31 @@ NIL ((|constructor| (NIL "FiniteFieldCategory is the category of finite fields")) (|representationType| (((|Union| "prime" "polynomial" "normal" "cyclic")) "\\spad{representationType()} returns the type of the representation,{} one of: \\spad{prime},{} \\spad{polynomial},{} \\spad{normal},{} or \\spad{cyclic}.")) (|order| (((|PositiveInteger|) $) "\\spad{order(b)} computes the order of an element \\spad{b} in the multiplicative group of the field. Error: if \\spad{b} equals 0.")) (|discreteLog| (((|NonNegativeInteger|) $) "\\spad{discreteLog(a)} computes the discrete logarithm of \\spad{a} with respect to \\spad{primitiveElement()} of the field.")) (|primitive?| (((|Boolean|) $) "\\spad{primitive?(b)} tests whether the element \\spad{b} is a generator of the (cyclic) multiplicative group of the field,{} \\spadignore{i.e.} is a primitive element. Implementation Note: see \\spad{ch}.IX.1.3,{} th.2 in \\spad{D}. Lipson.")) (|primitiveElement| (($) "\\spad{primitiveElement()} returns a primitive element stored in a global variable in the domain. At first call,{} the primitive element is computed by calling \\spadfun{createPrimitiveElement}.")) (|createPrimitiveElement| (($) "\\spad{createPrimitiveElement()} computes a generator of the (cyclic) multiplicative group of the field.")) (|tableForDiscreteLogarithm| (((|Table| (|PositiveInteger|) (|NonNegativeInteger|)) (|Integer|)) "\\spad{tableForDiscreteLogarithm(a,n)} returns a table of the discrete logarithms of \\spad{a**0} up to \\spad{a**(n-1)} which,{} called with key \\spad{lookup(a**i)} returns \\spad{i} for \\spad{i} in \\spad{0..n-1}. Error: if not called for prime divisors of order of \\indented{7}{multiplicative group.}")) (|factorsOfCyclicGroupSize| (((|List| (|Record| (|:| |factor| (|Integer|)) (|:| |exponent| (|Integer|))))) "\\spad{factorsOfCyclicGroupSize()} returns the factorization of size()\\spad{-1}")) (|conditionP| (((|Union| (|Vector| $) "failed") (|Matrix| $)) "\\spad{conditionP(mat)},{} given a matrix representing a homogeneous system of equations,{} returns a vector whose characteristic'th powers is a non-trivial solution,{} or \"failed\" if no such vector exists.")) (|charthRoot| (($ $) "\\spad{charthRoot(a)} takes the characteristic'th root of {\\em a}. Note: such a root is alway defined in finite fields."))) ((-4454 . T) (-4460 . T) (-4455 . T) ((-4464 "*") . T) (-4456 . T) (-4457 . T) (-4459 . T)) NIL -(-361 R UP -1966) +(-361 R UP -1955) ((|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 (-362 |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."))) ((-4454 . T) (-4460 . T) (-4455 . T) ((-4464 "*") . T) (-4456 . T) (-4457 . T) (-4459 . T)) -((-2781 (|HasCategory| (-927 |#1|) (QUOTE (-146))) (|HasCategory| (-927 |#1|) (QUOTE (-379)))) (|HasCategory| (-927 |#1|) (QUOTE (-148))) (|HasCategory| (-927 |#1|) (QUOTE (-379))) (|HasCategory| (-927 |#1|) (QUOTE (-146)))) +((-2755 (|HasCategory| (-927 |#1|) (QUOTE (-146))) (|HasCategory| (-927 |#1|) (QUOTE (-379)))) (|HasCategory| (-927 |#1|) (QUOTE (-148))) (|HasCategory| (-927 |#1|) (QUOTE (-379))) (|HasCategory| (-927 |#1|) (QUOTE (-146)))) (-363 GF |uni|) ((|constructor| (NIL "FiniteFieldNormalBasisExtensionByPolynomial(\\spad{GF},{}uni) implements a finite extension of the ground field {\\em GF}. The elements are represented by coordinate vectors with respect to. a normal basis,{} \\spadignore{i.e.} a basis consisting of the conjugates (\\spad{q}-powers) of an element,{} in this case called normal element,{} where \\spad{q} is the size of {\\em GF}. The normal element is chosen as a root of the extension polynomial,{} which MUST be normal over {\\em GF} (user responsibility)")) (|sizeMultiplication| (((|NonNegativeInteger|)) "\\spad{sizeMultiplication()} returns the number of entries in the multiplication table of the field. Note: the time of multiplication of field elements depends on this size.")) (|getMultiplicationMatrix| (((|Matrix| |#1|)) "\\spad{getMultiplicationMatrix()} returns the multiplication table in form of a matrix.")) (|getMultiplicationTable| (((|Vector| (|List| (|Record| (|:| |value| |#1|) (|:| |index| (|SingleInteger|)))))) "\\spad{getMultiplicationTable()} returns the multiplication table for the normal basis of the field. This table is used to perform multiplications between field elements."))) ((-4454 . T) (-4460 . T) (-4455 . T) ((-4464 "*") . T) (-4456 . T) (-4457 . T) (-4459 . T)) -((-2781 (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-379)))) (|HasCategory| |#1| (QUOTE (-148))) (|HasCategory| |#1| (QUOTE (-379))) (|HasCategory| |#1| (QUOTE (-146)))) +((-2755 (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-379)))) (|HasCategory| |#1| (QUOTE (-148))) (|HasCategory| |#1| (QUOTE (-379))) (|HasCategory| |#1| (QUOTE (-146)))) (-364 GF |extdeg|) ((|constructor| (NIL "FiniteFieldNormalBasisExtensionByPolynomial(\\spad{GF},{}\\spad{n}) implements a finite extension field of degree \\spad{n} over the ground field {\\em GF}. The elements are represented by coordinate vectors with respect to a normal basis,{} \\spadignore{i.e.} a basis consisting of the conjugates (\\spad{q}-powers) of an element,{} in this case called normal element. This is chosen as a root of the extension polynomial,{} created by {\\em createNormalPoly} from \\spadtype{FiniteFieldPolynomialPackage}")) (|sizeMultiplication| (((|NonNegativeInteger|)) "\\spad{sizeMultiplication()} returns the number of entries in the multiplication table of the field. Note: the time of multiplication of field elements depends on this size.")) (|getMultiplicationMatrix| (((|Matrix| |#1|)) "\\spad{getMultiplicationMatrix()} returns the multiplication table in form of a matrix.")) (|getMultiplicationTable| (((|Vector| (|List| (|Record| (|:| |value| |#1|) (|:| |index| (|SingleInteger|)))))) "\\spad{getMultiplicationTable()} returns the multiplication table for the normal basis of the field. This table is used to perform multiplications between field elements."))) ((-4454 . T) (-4460 . T) (-4455 . T) ((-4464 "*") . T) (-4456 . T) (-4457 . T) (-4459 . T)) -((-2781 (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-379)))) (|HasCategory| |#1| (QUOTE (-148))) (|HasCategory| |#1| (QUOTE (-379))) (|HasCategory| |#1| (QUOTE (-146)))) +((-2755 (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-379)))) (|HasCategory| |#1| (QUOTE (-148))) (|HasCategory| |#1| (QUOTE (-379))) (|HasCategory| |#1| (QUOTE (-146)))) (-365 |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}."))) ((-4454 . T) (-4460 . T) (-4455 . T) ((-4464 "*") . T) (-4456 . T) (-4457 . T) (-4459 . T)) -((-2781 (|HasCategory| (-927 |#1|) (QUOTE (-146))) (|HasCategory| (-927 |#1|) (QUOTE (-379)))) (|HasCategory| (-927 |#1|) (QUOTE (-148))) (|HasCategory| (-927 |#1|) (QUOTE (-379))) (|HasCategory| (-927 |#1|) (QUOTE (-146)))) +((-2755 (|HasCategory| (-927 |#1|) (QUOTE (-146))) (|HasCategory| (-927 |#1|) (QUOTE (-379)))) (|HasCategory| (-927 |#1|) (QUOTE (-148))) (|HasCategory| (-927 |#1|) (QUOTE (-379))) (|HasCategory| (-927 |#1|) (QUOTE (-146)))) (-366 GF |defpol|) ((|constructor| (NIL "FiniteFieldExtensionByPolynomial(\\spad{GF},{} defpol) implements the extension of the finite field {\\em GF} generated by the extension polynomial {\\em defpol} which MUST be irreducible. Note: the user has the responsibility to ensure that {\\em defpol} is irreducible."))) ((-4454 . T) (-4460 . T) (-4455 . T) ((-4464 "*") . T) (-4456 . T) (-4457 . T) (-4459 . T)) -((-2781 (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-379)))) (|HasCategory| |#1| (QUOTE (-148))) (|HasCategory| |#1| (QUOTE (-379))) (|HasCategory| |#1| (QUOTE (-146)))) -(-367 -1966 GF) +((-2755 (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-379)))) (|HasCategory| |#1| (QUOTE (-148))) (|HasCategory| |#1| (QUOTE (-379))) (|HasCategory| |#1| (QUOTE (-146)))) +(-367 -1955 GF) ((|constructor| (NIL "FiniteFieldPolynomialPackage2(\\spad{F},{}\\spad{GF}) exports some functions concerning finite fields,{} which depend on a finite field {\\em GF} and an algebraic extension \\spad{F} of {\\em GF},{} \\spadignore{e.g.} a zero of a polynomial over {\\em GF} in \\spad{F}.")) (|rootOfIrreduciblePoly| ((|#1| (|SparseUnivariatePolynomial| |#2|)) "\\spad{rootOfIrreduciblePoly(f)} computes one root of the monic,{} irreducible polynomial \\spad{f},{} which degree must divide the extension degree of {\\em F} over {\\em GF},{} \\spadignore{i.e.} \\spad{f} splits into linear factors over {\\em F}.")) (|Frobenius| ((|#1| |#1|) "\\spad{Frobenius(x)} \\undocumented{}")) (|basis| (((|Vector| |#1|) (|PositiveInteger|)) "\\spad{basis(n)} \\undocumented{}")) (|lookup| (((|PositiveInteger|) |#1|) "\\spad{lookup(x)} \\undocumented{}")) (|coerce| ((|#1| |#2|) "\\spad{coerce(x)} \\undocumented{}"))) NIL NIL @@ -1404,14 +1404,14 @@ NIL ((|constructor| (NIL "This package provides a number of functions for generating,{} counting and testing irreducible,{} normal,{} primitive,{} random polynomials over finite fields.")) (|reducedQPowers| (((|PrimitiveArray| (|SparseUnivariatePolynomial| |#1|)) (|SparseUnivariatePolynomial| |#1|)) "\\spad{reducedQPowers(f)} generates \\spad{[x,x**q,x**(q**2),...,x**(q**(n-1))]} reduced modulo \\spad{f} where \\spad{q = size()\\$GF} and \\spad{n = degree f}.")) (|leastAffineMultiple| (((|SparseUnivariatePolynomial| |#1|) (|SparseUnivariatePolynomial| |#1|)) "\\spad{leastAffineMultiple(f)} computes the least affine polynomial which is divisible by the polynomial \\spad{f} over the finite field {\\em GF},{} \\spadignore{i.e.} a polynomial whose exponents are 0 or a power of \\spad{q},{} the size of {\\em GF}.")) (|random| (((|SparseUnivariatePolynomial| |#1|) (|PositiveInteger|) (|PositiveInteger|)) "\\spad{random(m,n)}\\$FFPOLY(\\spad{GF}) generates a random monic polynomial of degree \\spad{d} over the finite field {\\em GF},{} \\spad{d} between \\spad{m} and \\spad{n}.") (((|SparseUnivariatePolynomial| |#1|) (|PositiveInteger|)) "\\spad{random(n)}\\$FFPOLY(\\spad{GF}) generates a random monic polynomial of degree \\spad{n} over the finite field {\\em GF}.")) (|nextPrimitiveNormalPoly| (((|Union| (|SparseUnivariatePolynomial| |#1|) "failed") (|SparseUnivariatePolynomial| |#1|)) "\\spad{nextPrimitiveNormalPoly(f)} yields the next primitive normal polynomial over a finite field {\\em GF} of the same degree as \\spad{f} in the following order,{} or \"failed\" if there are no greater ones. Error: if \\spad{f} has degree 0. Note: the input polynomial \\spad{f} is made monic. Also,{} \\spad{f < g} if the {\\em lookup} of the constant term of \\spad{f} is less than this number for \\spad{g} or,{} in case these numbers are equal,{} if the {\\em lookup} of the coefficient of the term of degree {\\em n-1} of \\spad{f} is less than this number for \\spad{g}. If these numbers are equals,{} \\spad{f < g} if the number of monomials of \\spad{f} is less than that for \\spad{g},{} or if the lists of exponents for \\spad{f} are lexicographically less than those for \\spad{g}. If these lists are also equal,{} the lists of coefficients are coefficients according to the lexicographic ordering induced by the ordering of the elements of {\\em GF} given by {\\em lookup}. This operation is equivalent to nextNormalPrimitivePoly(\\spad{f}).")) (|nextNormalPrimitivePoly| (((|Union| (|SparseUnivariatePolynomial| |#1|) "failed") (|SparseUnivariatePolynomial| |#1|)) "\\spad{nextNormalPrimitivePoly(f)} yields the next normal primitive polynomial over a finite field {\\em GF} of the same degree as \\spad{f} in the following order,{} or \"failed\" if there are no greater ones. Error: if \\spad{f} has degree 0. Note: the input polynomial \\spad{f} is made monic. Also,{} \\spad{f < g} if the {\\em lookup} of the constant term of \\spad{f} is less than this number for \\spad{g} or if {\\em lookup} of the coefficient of the term of degree {\\em n-1} of \\spad{f} is less than this number for \\spad{g}. Otherwise,{} \\spad{f < g} if the number of monomials of \\spad{f} is less than that for \\spad{g} or if the lists of exponents for \\spad{f} are lexicographically less than those for \\spad{g}. If these lists are also equal,{} the lists of coefficients are compared according to the lexicographic ordering induced by the ordering of the elements of {\\em GF} given by {\\em lookup}. This operation is equivalent to nextPrimitiveNormalPoly(\\spad{f}).")) (|nextNormalPoly| (((|Union| (|SparseUnivariatePolynomial| |#1|) "failed") (|SparseUnivariatePolynomial| |#1|)) "\\spad{nextNormalPoly(f)} yields the next normal polynomial over a finite field {\\em GF} of the same degree as \\spad{f} in the following order,{} or \"failed\" if there are no greater ones. Error: if \\spad{f} has degree 0. Note: the input polynomial \\spad{f} is made monic. Also,{} \\spad{f < g} if the {\\em lookup} of the coefficient of the term of degree {\\em n-1} of \\spad{f} is less than that for \\spad{g}. In case these numbers are equal,{} \\spad{f < g} if if the number of monomials of \\spad{f} is less that for \\spad{g} or if the list of exponents of \\spad{f} are lexicographically less than the corresponding list for \\spad{g}. If these lists are also equal,{} the lists of coefficients are compared according to the lexicographic ordering induced by the ordering of the elements of {\\em GF} given by {\\em lookup}.")) (|nextPrimitivePoly| (((|Union| (|SparseUnivariatePolynomial| |#1|) "failed") (|SparseUnivariatePolynomial| |#1|)) "\\spad{nextPrimitivePoly(f)} yields the next primitive polynomial over a finite field {\\em GF} of the same degree as \\spad{f} in the following order,{} or \"failed\" if there are no greater ones. Error: if \\spad{f} has degree 0. Note: the input polynomial \\spad{f} is made monic. Also,{} \\spad{f < g} if the {\\em lookup} of the constant term of \\spad{f} is less than this number for \\spad{g}. If these values are equal,{} then \\spad{f < g} if if the number of monomials of \\spad{f} is less than that for \\spad{g} or if the lists of exponents of \\spad{f} are lexicographically less than the corresponding list for \\spad{g}. If these lists are also equal,{} the lists of coefficients are compared according to the lexicographic ordering induced by the ordering of the elements of {\\em GF} given by {\\em lookup}.")) (|nextIrreduciblePoly| (((|Union| (|SparseUnivariatePolynomial| |#1|) "failed") (|SparseUnivariatePolynomial| |#1|)) "\\spad{nextIrreduciblePoly(f)} yields the next monic irreducible polynomial over a finite field {\\em GF} of the same degree as \\spad{f} in the following order,{} or \"failed\" if there are no greater ones. Error: if \\spad{f} has degree 0. Note: the input polynomial \\spad{f} is made monic. Also,{} \\spad{f < g} if the number of monomials of \\spad{f} is less than this number for \\spad{g}. If \\spad{f} and \\spad{g} have the same number of monomials,{} the lists of exponents are compared lexicographically. If these lists are also equal,{} the lists of coefficients are compared according to the lexicographic ordering induced by the ordering of the elements of {\\em GF} given by {\\em lookup}.")) (|createPrimitiveNormalPoly| (((|SparseUnivariatePolynomial| |#1|) (|PositiveInteger|)) "\\spad{createPrimitiveNormalPoly(n)}\\$FFPOLY(\\spad{GF}) generates a normal and primitive polynomial of degree \\spad{n} over the field {\\em GF}. polynomial of degree \\spad{n} over the field {\\em GF}.")) (|createNormalPrimitivePoly| (((|SparseUnivariatePolynomial| |#1|) (|PositiveInteger|)) "\\spad{createNormalPrimitivePoly(n)}\\$FFPOLY(\\spad{GF}) generates a normal and primitive polynomial of degree \\spad{n} over the field {\\em GF}. Note: this function is equivalent to createPrimitiveNormalPoly(\\spad{n})")) (|createNormalPoly| (((|SparseUnivariatePolynomial| |#1|) (|PositiveInteger|)) "\\spad{createNormalPoly(n)}\\$FFPOLY(\\spad{GF}) generates a normal polynomial of degree \\spad{n} over the finite field {\\em GF}.")) (|createPrimitivePoly| (((|SparseUnivariatePolynomial| |#1|) (|PositiveInteger|)) "\\spad{createPrimitivePoly(n)}\\$FFPOLY(\\spad{GF}) generates a primitive polynomial of degree \\spad{n} over the finite field {\\em GF}.")) (|createIrreduciblePoly| (((|SparseUnivariatePolynomial| |#1|) (|PositiveInteger|)) "\\spad{createIrreduciblePoly(n)}\\$FFPOLY(\\spad{GF}) generates a monic irreducible univariate polynomial of degree \\spad{n} over the finite field {\\em GF}.")) (|numberOfNormalPoly| (((|PositiveInteger|) (|PositiveInteger|)) "\\spad{numberOfNormalPoly(n)}\\$FFPOLY(\\spad{GF}) yields the number of normal polynomials of degree \\spad{n} over the finite field {\\em GF}.")) (|numberOfPrimitivePoly| (((|PositiveInteger|) (|PositiveInteger|)) "\\spad{numberOfPrimitivePoly(n)}\\$FFPOLY(\\spad{GF}) yields the number of primitive polynomials of degree \\spad{n} over the finite field {\\em GF}.")) (|numberOfIrreduciblePoly| (((|PositiveInteger|) (|PositiveInteger|)) "\\spad{numberOfIrreduciblePoly(n)}\\$FFPOLY(\\spad{GF}) yields the number of monic irreducible univariate polynomials of degree \\spad{n} over the finite field {\\em GF}.")) (|normal?| (((|Boolean|) (|SparseUnivariatePolynomial| |#1|)) "\\spad{normal?(f)} tests whether the polynomial \\spad{f} over a finite field is normal,{} \\spadignore{i.e.} its roots are linearly independent over the field.")) (|primitive?| (((|Boolean|) (|SparseUnivariatePolynomial| |#1|)) "\\spad{primitive?(f)} tests whether the polynomial \\spad{f} over a finite field is primitive,{} \\spadignore{i.e.} all its roots are primitive."))) NIL NIL -(-369 -1966 FP FPP) +(-369 -1955 FP FPP) ((|constructor| (NIL "This package solves linear diophantine equations for Bivariate polynomials over finite fields")) (|solveLinearPolynomialEquation| (((|Union| (|List| |#3|) "failed") (|List| |#3|) |#3|) "\\spad{solveLinearPolynomialEquation([f1, ..., fn], g)} (where the \\spad{fi} are relatively prime to each other) returns a list of \\spad{ai} such that \\spad{g/prod fi = sum ai/fi} or returns \"failed\" if no such list of \\spad{ai}\\spad{'s} exists."))) NIL NIL (-370 GF |n|) ((|constructor| (NIL "FiniteFieldExtensionByPolynomial(\\spad{GF},{} \\spad{n}) implements an extension of the finite field {\\em GF} of degree \\spad{n} generated by the extension polynomial constructed by \\spadfunFrom{createIrreduciblePoly}{FiniteFieldPolynomialPackage} from \\spadtype{FiniteFieldPolynomialPackage}."))) ((-4454 . T) (-4460 . T) (-4455 . T) ((-4464 "*") . T) (-4456 . T) (-4457 . T) (-4459 . T)) -((-2781 (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-379)))) (|HasCategory| |#1| (QUOTE (-148))) (|HasCategory| |#1| (QUOTE (-379))) (|HasCategory| |#1| (QUOTE (-146)))) +((-2755 (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-379)))) (|HasCategory| |#1| (QUOTE (-148))) (|HasCategory| |#1| (QUOTE (-379))) (|HasCategory| |#1| (QUOTE (-146)))) (-371 R |ls|) ((|constructor| (NIL "This is just an interface between several packages and domains. The goal is to compute lexicographical Groebner bases of sets of polynomial with type \\spadtype{Polynomial R} by the {\\em FGLM} algorithm if this is possible (\\spadignore{i.e.} if the input system generates a zero-dimensional ideal).")) (|groebner| (((|List| (|Polynomial| |#1|)) (|List| (|Polynomial| |#1|))) "\\axiom{groebner(\\spad{lq1})} returns the lexicographical Groebner basis of \\axiom{\\spad{lq1}}. If \\axiom{\\spad{lq1}} generates a zero-dimensional ideal then the {\\em FGLM} strategy is used,{} otherwise the {\\em Sugar} strategy is used.")) (|fglmIfCan| (((|Union| (|List| (|Polynomial| |#1|)) "failed") (|List| (|Polynomial| |#1|))) "\\axiom{fglmIfCan(\\spad{lq1})} returns the lexicographical Groebner basis of \\axiom{\\spad{lq1}} by using the {\\em FGLM} strategy,{} if \\axiom{zeroDimensional?(\\spad{lq1})} holds.")) (|zeroDimensional?| (((|Boolean|) (|List| (|Polynomial| |#1|))) "\\axiom{zeroDimensional?(\\spad{lq1})} returns \\spad{true} iff \\axiom{\\spad{lq1}} generates a zero-dimensional ideal \\spad{w}.\\spad{r}.\\spad{t}. the variables of \\axiom{\\spad{ls}}."))) NIL @@ -1490,7 +1490,7 @@ NIL NIL (-390) ((|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}."))) -((-4445 . T) (-4453 . T) (-4161 . T) (-4454 . T) (-4460 . T) (-4455 . T) ((-4464 "*") . T) (-4456 . T) (-4457 . T) (-4459 . T)) +((-4445 . T) (-4453 . T) (-4163 . T) (-4454 . T) (-4460 . T) (-4455 . T) ((-4464 "*") . T) (-4456 . T) (-4457 . T) (-4459 . T)) NIL (-391 |Par|) ((|constructor| (NIL "\\indented{3}{This is a package for the approximation of real solutions for} systems of polynomial equations over the rational numbers. The results are expressed as either rational numbers or floats depending on the type of the precision parameter which can be either a rational number or a floating point number.")) (|realRoots| (((|List| |#1|) (|Fraction| (|Polynomial| (|Integer|))) |#1|) "\\spad{realRoots(rf, eps)} finds the real zeros of a univariate rational function with precision given by eps.") (((|List| (|List| |#1|)) (|List| (|Fraction| (|Polynomial| (|Integer|)))) (|List| (|Symbol|)) |#1|) "\\spad{realRoots(lp,lv,eps)} computes the list of the real solutions of the list \\spad{lp} of rational functions with rational coefficients with respect to the variables in \\spad{lv},{} with precision \\spad{eps}. Each solution is expressed as a list of numbers in order corresponding to the variables in \\spad{lv}.")) (|solve| (((|List| (|Equation| (|Polynomial| |#1|))) (|Equation| (|Fraction| (|Polynomial| (|Integer|)))) |#1|) "\\spad{solve(eq,eps)} finds all of the real solutions of the univariate equation \\spad{eq} of rational functions with respect to the unique variables appearing in \\spad{eq},{} with precision \\spad{eps}.") (((|List| (|Equation| (|Polynomial| |#1|))) (|Fraction| (|Polynomial| (|Integer|))) |#1|) "\\spad{solve(p,eps)} finds all of the real solutions of the univariate rational function \\spad{p} with rational coefficients with respect to the unique variable appearing in \\spad{p},{} with precision \\spad{eps}.") (((|List| (|List| (|Equation| (|Polynomial| |#1|)))) (|List| (|Equation| (|Fraction| (|Polynomial| (|Integer|))))) |#1|) "\\spad{solve(leq,eps)} finds all of the real solutions of the system \\spad{leq} of equationas of rational functions with respect to all the variables appearing in \\spad{lp},{} with precision \\spad{eps}.") (((|List| (|List| (|Equation| (|Polynomial| |#1|)))) (|List| (|Fraction| (|Polynomial| (|Integer|)))) |#1|) "\\spad{solve(lp,eps)} finds all of the real solutions of the system \\spad{lp} of rational functions over the rational numbers with respect to all the variables appearing in \\spad{lp},{} with precision \\spad{eps}."))) @@ -1544,7 +1544,7 @@ 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 -(-404 -1966 UP UPUP R) +(-404 -1955 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 @@ -1568,11 +1568,11 @@ NIL ((|constructor| (NIL "provides an interface to the boot code for calling Fortran")) (|setLegalFortranSourceExtensions| (((|List| (|String|)) (|List| (|String|))) "\\spad{setLegalFortranSourceExtensions(l)} \\undocumented{}")) (|outputAsFortran| (((|Void|) (|FileName|)) "\\spad{outputAsFortran(fn)} \\undocumented{}")) (|linkToFortran| (((|SExpression|) (|Symbol|) (|List| (|Symbol|)) (|TheSymbolTable|) (|List| (|Symbol|))) "\\spad{linkToFortran(s,l,t,lv)} \\undocumented{}") (((|SExpression|) (|Symbol|) (|List| (|Union| (|:| |array| (|List| (|Symbol|))) (|:| |scalar| (|Symbol|)))) (|List| (|List| (|Union| (|:| |array| (|List| (|Symbol|))) (|:| |scalar| (|Symbol|))))) (|List| (|Symbol|)) (|Symbol|)) "\\spad{linkToFortran(s,l,ll,lv,t)} \\undocumented{}") (((|SExpression|) (|Symbol|) (|List| (|Union| (|:| |array| (|List| (|Symbol|))) (|:| |scalar| (|Symbol|)))) (|List| (|List| (|Union| (|:| |array| (|List| (|Symbol|))) (|:| |scalar| (|Symbol|))))) (|List| (|Symbol|))) "\\spad{linkToFortran(s,l,ll,lv)} \\undocumented{}"))) NIL NIL -(-410 -2648 |returnType| -1867 |symbols|) +(-410 -2624 |returnType| -1924 |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 -(-411 -1966 UP) +(-411 -1955 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 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| $) "\\spad{p + x} returns the sum of \\spad{p} and \\spad{x}"))) NIL NIL @@ -1594,7 +1594,7 @@ NIL ((|HasAttribute| |#1| (QUOTE -4445)) (|HasAttribute| |#1| (QUOTE -4453))) (-416) ((|constructor| (NIL "This category is intended as a model for floating point systems. A floating point system is a model for the real numbers. In fact,{} it is an approximation in the sense that not all real numbers are exactly representable by floating point numbers. A floating point system is characterized by the following: \\blankline \\indented{2}{1: \\spadfunFrom{base}{FloatingPointSystem} of the \\spadfunFrom{exponent}{FloatingPointSystem}.} \\indented{9}{(actual implemenations are usually binary or decimal)} \\indented{2}{2: \\spadfunFrom{precision}{FloatingPointSystem} of the \\spadfunFrom{mantissa}{FloatingPointSystem} (arbitrary or fixed)} \\indented{2}{3: rounding error for operations} \\blankline Because a Float is an approximation to the real numbers,{} even though it is defined to be a join of a Field and OrderedRing,{} some of the attributes do not hold. In particular associative(\\spad{\"+\"}) does not hold. Algorithms defined over a field need special considerations when the field is a floating point system.")) (|max| (($) "\\spad{max()} returns the maximum floating point number.")) (|min| (($) "\\spad{min()} returns the minimum floating point number.")) (|decreasePrecision| (((|PositiveInteger|) (|Integer|)) "\\spad{decreasePrecision(n)} decreases the current \\spadfunFrom{precision}{FloatingPointSystem} precision by \\spad{n} decimal digits.")) (|increasePrecision| (((|PositiveInteger|) (|Integer|)) "\\spad{increasePrecision(n)} increases the current \\spadfunFrom{precision}{FloatingPointSystem} by \\spad{n} decimal digits.")) (|precision| (((|PositiveInteger|) (|PositiveInteger|)) "\\spad{precision(n)} set the precision in the base to \\spad{n} decimal digits.") (((|PositiveInteger|)) "\\spad{precision()} returns the precision in digits base.")) (|digits| (((|PositiveInteger|) (|PositiveInteger|)) "\\spad{digits(d)} set the \\spadfunFrom{precision}{FloatingPointSystem} to \\spad{d} digits.") (((|PositiveInteger|)) "\\spad{digits()} returns ceiling\\spad{'s} precision in decimal digits.")) (|bits| (((|PositiveInteger|) (|PositiveInteger|)) "\\spad{bits(n)} set the \\spadfunFrom{precision}{FloatingPointSystem} to \\spad{n} bits.") (((|PositiveInteger|)) "\\spad{bits()} returns ceiling\\spad{'s} precision in bits.")) (|mantissa| (((|Integer|) $) "\\spad{mantissa(x)} returns the mantissa part of \\spad{x}.")) (|exponent| (((|Integer|) $) "\\spad{exponent(x)} returns the \\spadfunFrom{exponent}{FloatingPointSystem} part of \\spad{x}.")) (|base| (((|PositiveInteger|)) "\\spad{base()} returns the base of the \\spadfunFrom{exponent}{FloatingPointSystem}.")) (|order| (((|Integer|) $) "\\spad{order x} is the order of magnitude of \\spad{x}. Note: \\spad{base ** order x <= |x| < base ** (1 + order x)}.")) (|float| (($ (|Integer|) (|Integer|) (|PositiveInteger|)) "\\spad{float(a,e,b)} returns \\spad{a * b ** e}.") (($ (|Integer|) (|Integer|)) "\\spad{float(a,e)} returns \\spad{a * base() ** e}.")) (|approximate| ((|attribute|) "\\spad{approximate} means \"is an approximation to the real numbers\"."))) -((-4161 . T) (-4454 . T) (-4460 . T) (-4455 . T) ((-4464 "*") . T) (-4456 . T) (-4457 . T) (-4459 . T)) +((-4163 . T) (-4454 . T) (-4460 . T) (-4455 . T) ((-4464 "*") . T) (-4456 . T) (-4457 . T) (-4459 . T)) NIL (-417 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."))) @@ -1607,7 +1607,7 @@ NIL (-419 S) ((|constructor| (NIL "Fraction takes an IntegralDomain \\spad{S} and produces the domain of Fractions with numerators and denominators from \\spad{S}. If \\spad{S} is also a GcdDomain,{} then \\spad{gcd}\\spad{'s} between numerator and denominator will be cancelled during all operations.")) (|canonical| ((|attribute|) "\\spad{canonical} means that equal elements are in fact identical."))) ((-4449 -12 (|has| |#1| (-6 -4460)) (|has| |#1| (-464)) (|has| |#1| (-6 -4449))) (-4454 . T) (-4460 . T) (-4455 . T) ((-4464 "*") . T) (-4456 . T) (-4457 . T) (-4459 . T)) -((|HasCategory| |#1| (QUOTE (-926))) (|HasCategory| |#1| (LIST (QUOTE -1057) (QUOTE (-1195)))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-148))) (-2781 (-12 (|HasCategory| |#1| (QUOTE (-557))) (|HasCategory| |#1| (QUOTE (-840)))) (|HasCategory| |#1| (LIST (QUOTE -626) (QUOTE (-548))))) (|HasCategory| |#1| (QUOTE (-1041))) (|HasCategory| |#1| (QUOTE (-832))) (-2781 (|HasCategory| |#1| (QUOTE (-832))) (|HasCategory| |#1| (QUOTE (-862)))) (-2781 (-12 (|HasCategory| |#1| (QUOTE (-557))) (|HasCategory| |#1| (QUOTE (-840)))) (|HasCategory| |#1| (LIST (QUOTE -1057) (QUOTE (-576))))) (|HasCategory| |#1| (QUOTE (-1171))) (|HasCategory| |#1| (LIST (QUOTE -899) (QUOTE (-390)))) (-2781 (-12 (|HasCategory| |#1| (QUOTE (-557))) (|HasCategory| |#1| (QUOTE (-840)))) (|HasCategory| |#1| (LIST (QUOTE -899) (QUOTE (-576))))) (|HasCategory| |#1| (LIST (QUOTE -626) (LIST (QUOTE -905) (QUOTE (-390))))) (-2781 (|HasCategory| |#1| (LIST (QUOTE -626) (LIST (QUOTE -905) (QUOTE (-576))))) (-12 (|HasCategory| |#1| (QUOTE (-557))) (|HasCategory| |#1| (QUOTE (-840))))) (-2781 (|HasCategory| |#1| (LIST (QUOTE -651) (QUOTE (-576)))) (-12 (|HasCategory| |#1| (QUOTE (-557))) (|HasCategory| |#1| (QUOTE (-840))))) (|HasCategory| |#1| (QUOTE (-237))) (|HasCategory| |#1| (LIST (QUOTE -917) (QUOTE (-1195)))) (|HasCategory| |#1| (QUOTE (-238))) (|HasCategory| |#1| (LIST (QUOTE -915) (QUOTE (-1195)))) (|HasCategory| |#1| (LIST (QUOTE -526) (QUOTE (-1195)) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -296) (|devaluate| |#1|) (|devaluate| |#1|))) (-12 (|HasCategory| |#1| (QUOTE (-557))) (|HasCategory| |#1| (QUOTE (-840)))) (|HasCategory| |#1| (QUOTE (-317))) (|HasCategory| |#1| (QUOTE (-557))) (-12 (|HasAttribute| |#1| (QUOTE -4460)) (|HasAttribute| |#1| (QUOTE -4449)) (|HasCategory| |#1| (QUOTE (-464)))) (|HasCategory| |#1| (LIST (QUOTE -626) (QUOTE (-548)))) (|HasCategory| |#1| (QUOTE (-862))) (|HasCategory| |#1| (LIST (QUOTE -1057) (QUOTE (-576)))) (|HasCategory| |#1| (LIST (QUOTE -899) (QUOTE (-576)))) (|HasCategory| |#1| (LIST (QUOTE -626) (LIST (QUOTE -905) (QUOTE (-576))))) (|HasCategory| |#1| (LIST (QUOTE -651) (QUOTE (-576)))) (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-926)))) (-2781 (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-926)))) (|HasCategory| |#1| (QUOTE (-146))))) +((|HasCategory| |#1| (QUOTE (-926))) (|HasCategory| |#1| (LIST (QUOTE -1057) (QUOTE (-1195)))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-148))) (-2755 (-12 (|HasCategory| |#1| (QUOTE (-557))) (|HasCategory| |#1| (QUOTE (-840)))) (|HasCategory| |#1| (LIST (QUOTE -626) (QUOTE (-548))))) (|HasCategory| |#1| (QUOTE (-1041))) (|HasCategory| |#1| (QUOTE (-832))) (-2755 (|HasCategory| |#1| (QUOTE (-832))) (|HasCategory| |#1| (QUOTE (-862)))) (-2755 (-12 (|HasCategory| |#1| (QUOTE (-557))) (|HasCategory| |#1| (QUOTE (-840)))) (|HasCategory| |#1| (LIST (QUOTE -1057) (QUOTE (-576))))) (|HasCategory| |#1| (QUOTE (-1171))) (|HasCategory| |#1| (LIST (QUOTE -899) (QUOTE (-390)))) (-2755 (-12 (|HasCategory| |#1| (QUOTE (-557))) (|HasCategory| |#1| (QUOTE (-840)))) (|HasCategory| |#1| (LIST (QUOTE -899) (QUOTE (-576))))) (|HasCategory| |#1| (LIST (QUOTE -626) (LIST (QUOTE -905) (QUOTE (-390))))) (-2755 (|HasCategory| |#1| (LIST (QUOTE -626) (LIST (QUOTE -905) (QUOTE (-576))))) (-12 (|HasCategory| |#1| (QUOTE (-557))) (|HasCategory| |#1| (QUOTE (-840))))) (-2755 (|HasCategory| |#1| (LIST (QUOTE -651) (QUOTE (-576)))) (-12 (|HasCategory| |#1| (QUOTE (-557))) (|HasCategory| |#1| (QUOTE (-840))))) (|HasCategory| |#1| (QUOTE (-237))) (|HasCategory| |#1| (LIST (QUOTE -917) (QUOTE (-1195)))) (|HasCategory| |#1| (QUOTE (-238))) (|HasCategory| |#1| (LIST (QUOTE -915) (QUOTE (-1195)))) (|HasCategory| |#1| (LIST (QUOTE -526) (QUOTE (-1195)) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -296) (|devaluate| |#1|) (|devaluate| |#1|))) (-12 (|HasCategory| |#1| (QUOTE (-557))) (|HasCategory| |#1| (QUOTE (-840)))) (|HasCategory| |#1| (QUOTE (-317))) (|HasCategory| |#1| (QUOTE (-557))) (-12 (|HasAttribute| |#1| (QUOTE -4460)) (|HasAttribute| |#1| (QUOTE -4449)) (|HasCategory| |#1| (QUOTE (-464)))) (|HasCategory| |#1| (LIST (QUOTE -626) (QUOTE (-548)))) (|HasCategory| |#1| (QUOTE (-862))) (|HasCategory| |#1| (LIST (QUOTE -1057) (QUOTE (-576)))) (|HasCategory| |#1| (LIST (QUOTE -899) (QUOTE (-576)))) (|HasCategory| |#1| (LIST (QUOTE -626) (LIST (QUOTE -905) (QUOTE (-576))))) (|HasCategory| |#1| (LIST (QUOTE -651) (QUOTE (-576)))) (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-926)))) (-2755 (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-926)))) (|HasCategory| |#1| (QUOTE (-146))))) (-420 S R UP) ((|constructor| (NIL "A \\spadtype{FramedAlgebra} is a \\spadtype{FiniteRankAlgebra} together with a fixed \\spad{R}-module basis.")) (|regularRepresentation| (((|Matrix| |#2|) $) "\\spad{regularRepresentation(a)} returns the matrix of the linear map defined by left multiplication by \\spad{a} with respect to the fixed basis.")) (|discriminant| ((|#2|) "\\spad{discriminant()} = determinant(traceMatrix()).")) (|traceMatrix| (((|Matrix| |#2|)) "\\spad{traceMatrix()} is the \\spad{n}-by-\\spad{n} matrix ( \\spad{Tr(vi * vj)} ),{} where \\spad{v1},{} ...,{} \\spad{vn} are the elements of the fixed basis.")) (|convert| (($ (|Vector| |#2|)) "\\spad{convert([a1,..,an])} returns \\spad{a1*v1 + ... + an*vn},{} where \\spad{v1},{} ...,{} \\spad{vn} are the elements of the fixed basis.") (((|Vector| |#2|) $) "\\spad{convert(a)} returns the coordinates of \\spad{a} with respect to the fixed \\spad{R}-module basis.")) (|represents| (($ (|Vector| |#2|)) "\\spad{represents([a1,..,an])} returns \\spad{a1*v1 + ... + an*vn},{} where \\spad{v1},{} ...,{} \\spad{vn} are the elements of the fixed basis.")) (|coordinates| (((|Matrix| |#2|) (|Vector| $)) "\\spad{coordinates([v1,...,vm])} returns the coordinates of the \\spad{vi}\\spad{'s} with to the fixed basis. The coordinates of \\spad{vi} are contained in the \\spad{i}th row of the matrix returned by this function.") (((|Vector| |#2|) $) "\\spad{coordinates(a)} returns the coordinates of \\spad{a} with respect to the fixed \\spad{R}-module basis.")) (|basis| (((|Vector| $)) "\\spad{basis()} returns the fixed \\spad{R}-module basis."))) NIL @@ -1628,11 +1628,11 @@ NIL ((|constructor| (NIL "\\indented{1}{Lifting of morphisms to fractional ideals.} Author: Manuel Bronstein Date Created: 1 Feb 1989 Date Last Updated: 27 Feb 1990 Keywords: ideal,{} algebra,{} module.")) (|map| (((|FractionalIdeal| |#5| |#6| |#7| |#8|) (|Mapping| |#5| |#1|) (|FractionalIdeal| |#1| |#2| |#3| |#4|)) "\\spad{map(f,i)} \\undocumented{}"))) NIL NIL -(-425 R -1966 UP A) +(-425 R -1955 UP A) ((|constructor| (NIL "Fractional ideals in a framed algebra.")) (|randomLC| ((|#4| (|NonNegativeInteger|) (|Vector| |#4|)) "\\spad{randomLC(n,x)} should be local but conditional.")) (|minimize| (($ $) "\\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)}."))) ((-4459 . T)) NIL -(-426 R -1966 UP A |ibasis|) +(-426 R -1955 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 -1057) (|devaluate| |#2|)))) @@ -1651,7 +1651,7 @@ NIL (-430 R) ((|constructor| (NIL "\\spadtype{Factored} creates a domain whose objects are kept in factored form as long as possible. Thus certain operations like multiplication and \\spad{gcd} are relatively easy to do. Others,{} like addition require somewhat more work,{} and unless the argument domain provides a factor function,{} the result may not be completely factored. Each object consists of a unit and a list of factors,{} where a factor has a member of \\spad{R} (the \"base\"),{} and exponent and a flag indicating what is known about the base. A flag may be one of \"nil\",{} \"sqfr\",{} \"irred\" or \"prime\",{} which respectively mean that nothing is known about the base,{} it is square-free,{} it is irreducible,{} or it is prime. The current restriction to integral domains allows simplification to be performed without worrying about multiplication order.")) (|rationalIfCan| (((|Union| (|Fraction| (|Integer|)) "failed") $) "\\spad{rationalIfCan(u)} returns a rational number if \\spad{u} really is one,{} and \"failed\" otherwise.")) (|rational| (((|Fraction| (|Integer|)) $) "\\spad{rational(u)} assumes spadvar{\\spad{u}} is actually a rational number and does the conversion to rational number (see \\spadtype{Fraction Integer}).")) (|rational?| (((|Boolean|) $) "\\spad{rational?(u)} tests if \\spadvar{\\spad{u}} is actually a rational number (see \\spadtype{Fraction Integer}).")) (|map| (($ (|Mapping| |#1| |#1|) $) "\\spad{map(fn,u)} maps the function \\userfun{\\spad{fn}} across the factors of \\spadvar{\\spad{u}} and creates a new factored object. Note: this clears the information flags (sets them to \"nil\") because the effect of \\userfun{\\spad{fn}} is clearly not known in general.")) (|unitNormalize| (($ $) "\\spad{unitNormalize(u)} normalizes the unit part of the factorization. For example,{} when working with factored integers,{} this operation will ensure that the bases are all positive integers.")) (|unit| ((|#1| $) "\\spad{unit(u)} extracts the unit part of the factorization.")) (|flagFactor| (($ |#1| (|Integer|) (|Union| "nil" "sqfr" "irred" "prime")) "\\spad{flagFactor(base,exponent,flag)} creates a factored object with a single factor whose \\spad{base} is asserted to be properly described by the information \\spad{flag}.")) (|sqfrFactor| (($ |#1| (|Integer|)) "\\spad{sqfrFactor(base,exponent)} creates a factored object with a single factor whose \\spad{base} is asserted to be square-free (flag = \"sqfr\").")) (|primeFactor| (($ |#1| (|Integer|)) "\\spad{primeFactor(base,exponent)} creates a factored object with a single factor whose \\spad{base} is asserted to be prime (flag = \"prime\").")) (|numberOfFactors| (((|NonNegativeInteger|) $) "\\spad{numberOfFactors(u)} returns the number of factors in \\spadvar{\\spad{u}}.")) (|nthFlag| (((|Union| "nil" "sqfr" "irred" "prime") $ (|Integer|)) "\\spad{nthFlag(u,n)} returns the information flag of the \\spad{n}th factor of \\spadvar{\\spad{u}}. If \\spadvar{\\spad{n}} is not a valid index for a factor (for example,{} less than 1 or too big),{} \"nil\" is returned.")) (|nthFactor| ((|#1| $ (|Integer|)) "\\spad{nthFactor(u,n)} returns the base of the \\spad{n}th factor of \\spadvar{\\spad{u}}. If \\spadvar{\\spad{n}} is not a valid index for a factor (for example,{} less than 1 or too big),{} 1 is returned. If \\spadvar{\\spad{u}} consists only of a unit,{} the unit is returned.")) (|nthExponent| (((|Integer|) $ (|Integer|)) "\\spad{nthExponent(u,n)} returns the exponent of the \\spad{n}th factor of \\spadvar{\\spad{u}}. If \\spadvar{\\spad{n}} is not a valid index for a factor (for example,{} less than 1 or too big),{} 0 is returned.")) (|irreducibleFactor| (($ |#1| (|Integer|)) "\\spad{irreducibleFactor(base,exponent)} creates a factored object with a single factor whose \\spad{base} is asserted to be irreducible (flag = \"irred\").")) (|factors| (((|List| (|Record| (|:| |factor| |#1|) (|:| |exponent| (|Integer|)))) $) "\\spad{factors(u)} returns a list of the factors in a form suitable for iteration. That is,{} it returns a list where each element is a record containing a base and exponent. The original object is the product of all the factors and the unit (which can be extracted by \\axiom{unit(\\spad{u})}).")) (|nilFactor| (($ |#1| (|Integer|)) "\\spad{nilFactor(base,exponent)} creates a factored object with a single factor with no information about the kind of \\spad{base} (flag = \"nil\").")) (|factorList| (((|List| (|Record| (|:| |flg| (|Union| "nil" "sqfr" "irred" "prime")) (|:| |fctr| |#1|) (|:| |xpnt| (|Integer|)))) $) "\\spad{factorList(u)} returns the list of factors with flags (for use by factoring code).")) (|makeFR| (($ |#1| (|List| (|Record| (|:| |flg| (|Union| "nil" "sqfr" "irred" "prime")) (|:| |fctr| |#1|) (|:| |xpnt| (|Integer|))))) "\\spad{makeFR(unit,listOfFactors)} creates a factored object (for use by factoring code).")) (|exponent| (((|Integer|) $) "\\spad{exponent(u)} returns the exponent of the first factor of \\spadvar{\\spad{u}},{} or 0 if the factored form consists solely of a unit.")) (|expand| ((|#1| $) "\\spad{expand(f)} multiplies the unit and factors together,{} yielding an \"unfactored\" object. Note: this is purposely not called \\spadfun{coerce} which would cause the interpreter to do this automatically."))) ((-4455 . T) ((-4464 "*") . T) (-4456 . T) (-4457 . T) (-4459 . T)) -((|HasCategory| |#1| (LIST (QUOTE -526) (QUOTE (-1195)) (QUOTE $))) (|HasCategory| |#1| (LIST (QUOTE -319) (QUOTE $))) (|HasCategory| |#1| (LIST (QUOTE -296) (QUOTE $) (QUOTE $))) (|HasCategory| |#1| (LIST (QUOTE -626) (QUOTE (-548)))) (|HasCategory| |#1| (QUOTE (-1240))) (-2781 (|HasCategory| |#1| (QUOTE (-464))) (|HasCategory| |#1| (QUOTE (-1240)))) (|HasCategory| |#1| (QUOTE (-1041))) (|HasCategory| |#1| (LIST (QUOTE -1057) (LIST (QUOTE -419) (QUOTE (-576))))) (|HasCategory| |#1| (LIST (QUOTE -1057) (QUOTE (-576)))) (|HasCategory| |#1| (LIST (QUOTE -526) (QUOTE (-1195)) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -296) (|devaluate| |#1|) (|devaluate| |#1|))) (|HasCategory| |#1| (QUOTE (-237))) (|HasCategory| |#1| (LIST (QUOTE -917) (QUOTE (-1195)))) (|HasCategory| |#1| (QUOTE (-238))) (|HasCategory| |#1| (LIST (QUOTE -915) (QUOTE (-1195)))) (|HasCategory| |#1| (QUOTE (-557))) (|HasCategory| |#1| (QUOTE (-464)))) +((|HasCategory| |#1| (LIST (QUOTE -526) (QUOTE (-1195)) (QUOTE $))) (|HasCategory| |#1| (LIST (QUOTE -319) (QUOTE $))) (|HasCategory| |#1| (LIST (QUOTE -296) (QUOTE $) (QUOTE $))) (|HasCategory| |#1| (LIST (QUOTE -626) (QUOTE (-548)))) (|HasCategory| |#1| (QUOTE (-1240))) (-2755 (|HasCategory| |#1| (QUOTE (-464))) (|HasCategory| |#1| (QUOTE (-1240)))) (|HasCategory| |#1| (QUOTE (-1041))) (|HasCategory| |#1| (LIST (QUOTE -1057) (LIST (QUOTE -419) (QUOTE (-576))))) (|HasCategory| |#1| (LIST (QUOTE -1057) (QUOTE (-576)))) (|HasCategory| |#1| (LIST (QUOTE -526) (QUOTE (-1195)) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -296) (|devaluate| |#1|) (|devaluate| |#1|))) (|HasCategory| |#1| (QUOTE (-237))) (|HasCategory| |#1| (LIST (QUOTE -917) (QUOTE (-1195)))) (|HasCategory| |#1| (QUOTE (-238))) (|HasCategory| |#1| (LIST (QUOTE -915) (QUOTE (-1195)))) (|HasCategory| |#1| (QUOTE (-557))) (|HasCategory| |#1| (QUOTE (-464)))) (-431 R) ((|constructor| (NIL "\\spadtype{FactoredFunctionUtilities} implements some utility functions for manipulating factored objects.")) (|mergeFactors| (((|Factored| |#1|) (|Factored| |#1|) (|Factored| |#1|)) "\\spad{mergeFactors(u,v)} is used when the factorizations of \\spadvar{\\spad{u}} and \\spadvar{\\spad{v}} are known to be disjoint,{} \\spadignore{e.g.} resulting from a content/primitive part split. Essentially,{} it creates a new factored object by multiplying the units together and appending the lists of factors.")) (|refine| (((|Factored| |#1|) (|Factored| |#1|) (|Mapping| (|Factored| |#1|) |#1|)) "\\spad{refine(u,fn)} is used to apply the function \\userfun{\\spad{fn}} to each factor of \\spadvar{\\spad{u}} and then build a new factored object from the results. For example,{} if \\spadvar{\\spad{u}} were created by calling \\spad{nilFactor(10,2)} then \\spad{refine(u,factor)} would create a factored object equal to that created by \\spad{factor(100)} or \\spad{primeFactor(2,2) * primeFactor(5,2)}."))) NIL @@ -1680,7 +1680,7 @@ NIL ((|constructor| (NIL "A finite-set aggregate models the notion of a finite set,{} that is,{} a collection of elements characterized by membership,{} but not by order or multiplicity. See \\spadtype{Set} for an example.")) (|min| ((|#1| $) "\\spad{min(u)} returns the smallest element of aggregate \\spad{u}.")) (|max| ((|#1| $) "\\spad{max(u)} returns the largest element of aggregate \\spad{u}.")) (|universe| (($) "\\spad{universe()}\\$\\spad{D} returns the universal set for finite set aggregate \\spad{D}.")) (|complement| (($ $) "\\spad{complement(u)} returns the complement of the set \\spad{u},{} \\spadignore{i.e.} the set of all values not in \\spad{u}.")) (|cardinality| (((|NonNegativeInteger|) $) "\\spad{cardinality(u)} returns the number of elements of \\spad{u}. Note: \\axiom{cardinality(\\spad{u}) = \\#u}."))) ((-4462 . T) (-4452 . T) (-4463 . T)) NIL -(-438 R -1966) +(-438 R -1955) ((|constructor| (NIL "\\spadtype{FunctionSpaceComplexIntegration} provides functions for the indefinite integration of complex-valued functions.")) (|complexIntegrate| ((|#2| |#2| (|Symbol|)) "\\spad{complexIntegrate(f, x)} returns the integral of \\spad{f(x)dx} where \\spad{x} is viewed as a complex variable.")) (|internalIntegrate0| (((|IntegrationResult| |#2|) |#2| (|Symbol|)) "\\spad{internalIntegrate0 should} be a local function,{} but is conditional.")) (|internalIntegrate| (((|IntegrationResult| |#2|) |#2| (|Symbol|)) "\\spad{internalIntegrate(f, x)} returns the integral of \\spad{f(x)dx} where \\spad{x} is viewed as a complex variable."))) NIL NIL @@ -1688,7 +1688,7 @@ NIL ((|constructor| (NIL "\\indented{1}{Author: James Davenport} Date Created: 17 April 1992 Date Last Updated: Basic Functions: Related Constructors: Also See: AMS Classifications: Keywords: References: Description:")) (|makeCos| (($ |#2| |#1|) "\\spad{makeCos(e,r)} makes a sin expression with given argument and coefficient")) (|makeSin| (($ |#2| |#1|) "\\spad{makeSin(e,r)} makes a sin expression with given argument and coefficient")) (|coerce| (($ (|FourierComponent| |#2|)) "\\spad{coerce(c)} converts sin/cos terms into Fourier Series") (($ |#1|) "\\spad{coerce(r)} converts coefficients into Fourier Series"))) ((-4449 -12 (|has| |#1| (-6 -4449)) (|has| |#2| (-6 -4449))) (-4456 . T) (-4457 . T) (-4459 . T)) ((-12 (|HasAttribute| |#1| (QUOTE -4449)) (|HasAttribute| |#2| (QUOTE -4449)))) -(-440 R -1966) +(-440 R -1955) ((|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 @@ -1698,17 +1698,17 @@ NIL ((|HasCategory| |#2| (LIST (QUOTE -1057) (QUOTE (-576)))) (|HasCategory| |#2| (QUOTE (-568))) (|HasCategory| |#2| (QUOTE (-174))) (|HasCategory| |#2| (QUOTE (-146))) (|HasCategory| |#2| (QUOTE (-148))) (|HasCategory| |#2| (QUOTE (-1068))) (|HasCategory| |#2| (QUOTE (-21))) (|HasCategory| |#2| (QUOTE (-25))) (|HasCategory| |#2| (QUOTE (-485))) (|HasCategory| |#2| (QUOTE (-1131))) (|HasCategory| |#2| (LIST (QUOTE -626) (QUOTE (-548))))) (-442 R) ((|constructor| (NIL "A space of formal functions with arguments in an arbitrary ordered set.")) (|univariate| (((|Fraction| (|SparseUnivariatePolynomial| $)) $ (|Kernel| $)) "\\spad{univariate(f, k)} returns \\spad{f} viewed as a univariate fraction in \\spad{k}.")) (/ (($ (|SparseMultivariatePolynomial| |#1| (|Kernel| $)) (|SparseMultivariatePolynomial| |#1| (|Kernel| $))) "\\spad{p1/p2} returns the quotient of \\spad{p1} and \\spad{p2} as an element of \\%.")) (|denominator| (($ $) "\\spad{denominator(f)} returns the denominator of \\spad{f} converted to \\%.")) (|denom| (((|SparseMultivariatePolynomial| |#1| (|Kernel| $)) $) "\\spad{denom(f)} returns the denominator of \\spad{f} viewed as a polynomial in the kernels over \\spad{R}.")) (|convert| (($ (|Factored| $)) "\\spad{convert(f1\\^e1 ... fm\\^em)} returns \\spad{(f1)\\^e1 ... (fm)\\^em} as an element of \\%,{} using formal kernels created using a \\spadfunFrom{paren}{ExpressionSpace}.")) (|isPower| (((|Union| (|Record| (|:| |val| $) (|:| |exponent| (|Integer|))) "failed") $) "\\spad{isPower(p)} returns \\spad{[x, n]} if \\spad{p = x**n} and \\spad{n <> 0}.")) (|numerator| (($ $) "\\spad{numerator(f)} returns the numerator of \\spad{f} converted to \\%.")) (|numer| (((|SparseMultivariatePolynomial| |#1| (|Kernel| $)) $) "\\spad{numer(f)} returns the numerator of \\spad{f} viewed as a polynomial in the kernels over \\spad{R} if \\spad{R} is an integral domain. If not,{} then numer(\\spad{f}) = \\spad{f} viewed as a polynomial in the kernels over \\spad{R}.")) (|coerce| (($ (|Fraction| (|Polynomial| (|Fraction| |#1|)))) "\\spad{coerce(f)} returns \\spad{f} as an element of \\%.") (($ (|Polynomial| (|Fraction| |#1|))) "\\spad{coerce(p)} returns \\spad{p} as an element of \\%.") (($ (|Fraction| |#1|)) "\\spad{coerce(q)} returns \\spad{q} as an element of \\%.") (($ (|SparseMultivariatePolynomial| |#1| (|Kernel| $))) "\\spad{coerce(p)} returns \\spad{p} as an element of \\%.")) (|isMult| (((|Union| (|Record| (|:| |coef| (|Integer|)) (|:| |var| (|Kernel| $))) "failed") $) "\\spad{isMult(p)} returns \\spad{[n, x]} if \\spad{p = n * x} and \\spad{n <> 0}.")) (|isPlus| (((|Union| (|List| $) "failed") $) "\\spad{isPlus(p)} returns \\spad{[m1,...,mn]} if \\spad{p = m1 +...+ mn} and \\spad{n > 1}.")) (|isExpt| (((|Union| (|Record| (|:| |var| (|Kernel| $)) (|:| |exponent| (|Integer|))) "failed") $ (|Symbol|)) "\\spad{isExpt(p,f)} returns \\spad{[x, n]} if \\spad{p = x**n} and \\spad{n <> 0} and \\spad{x = f(a)}.") (((|Union| (|Record| (|:| |var| (|Kernel| $)) (|:| |exponent| (|Integer|))) "failed") $ (|BasicOperator|)) "\\spad{isExpt(p,op)} returns \\spad{[x, n]} if \\spad{p = x**n} and \\spad{n <> 0} and \\spad{x = op(a)}.") (((|Union| (|Record| (|:| |var| (|Kernel| $)) (|:| |exponent| (|Integer|))) "failed") $) "\\spad{isExpt(p)} returns \\spad{[x, n]} if \\spad{p = x**n} and \\spad{n <> 0}.")) (|isTimes| (((|Union| (|List| $) "failed") $) "\\spad{isTimes(p)} returns \\spad{[a1,...,an]} if \\spad{p = a1*...*an} and \\spad{n > 1}.")) (** (($ $ (|NonNegativeInteger|)) "\\spad{x**n} returns \\spad{x} * \\spad{x} * \\spad{x} * ... * \\spad{x} (\\spad{n} times).")) (|eval| (($ $ (|Symbol|) (|NonNegativeInteger|) (|Mapping| $ $)) "\\spad{eval(x, s, n, f)} replaces every \\spad{s(a)**n} in \\spad{x} by \\spad{f(a)} for any \\spad{a}.") (($ $ (|Symbol|) (|NonNegativeInteger|) (|Mapping| $ (|List| $))) "\\spad{eval(x, s, n, f)} replaces every \\spad{s(a1,...,am)**n} in \\spad{x} by \\spad{f(a1,...,am)} for any a1,{}...,{}am.") (($ $ (|List| (|Symbol|)) (|List| (|NonNegativeInteger|)) (|List| (|Mapping| $ (|List| $)))) "\\spad{eval(x, [s1,...,sm], [n1,...,nm], [f1,...,fm])} replaces every \\spad{si(a1,...,an)**ni} in \\spad{x} by \\spad{fi(a1,...,an)} for any a1,{}...,{}am.") (($ $ (|List| (|Symbol|)) (|List| (|NonNegativeInteger|)) (|List| (|Mapping| $ $))) "\\spad{eval(x, [s1,...,sm], [n1,...,nm], [f1,...,fm])} replaces every \\spad{si(a)**ni} in \\spad{x} by \\spad{fi(a)} for any \\spad{a}.") (($ $ (|List| (|BasicOperator|)) (|List| $) (|Symbol|)) "\\spad{eval(x, [s1,...,sm], [f1,...,fm], y)} replaces every \\spad{si(a)} in \\spad{x} by \\spad{fi(y)} with \\spad{y} replaced by \\spad{a} for any \\spad{a}.") (($ $ (|BasicOperator|) $ (|Symbol|)) "\\spad{eval(x, s, f, y)} replaces every \\spad{s(a)} in \\spad{x} by \\spad{f(y)} with \\spad{y} replaced by \\spad{a} for any \\spad{a}.") (($ $) "\\spad{eval(f)} unquotes all the quoted operators in \\spad{f}.") (($ $ (|List| (|Symbol|))) "\\spad{eval(f, [foo1,...,foon])} unquotes all the \\spad{fooi}\\spad{'s} in \\spad{f}.") (($ $ (|Symbol|)) "\\spad{eval(f, foo)} unquotes all the foo\\spad{'s} in \\spad{f}.")) (|applyQuote| (($ (|Symbol|) (|List| $)) "\\spad{applyQuote(foo, [x1,...,xn])} returns \\spad{'foo(x1,...,xn)}.") (($ (|Symbol|) $ $ $ $) "\\spad{applyQuote(foo, x, y, z, t)} returns \\spad{'foo(x,y,z,t)}.") (($ (|Symbol|) $ $ $) "\\spad{applyQuote(foo, x, y, z)} returns \\spad{'foo(x,y,z)}.") (($ (|Symbol|) $ $) "\\spad{applyQuote(foo, x, y)} returns \\spad{'foo(x,y)}.") (($ (|Symbol|) $) "\\spad{applyQuote(foo, x)} returns \\spad{'foo(x)}.")) (|variables| (((|List| (|Symbol|)) $) "\\spad{variables(f)} returns the list of all the variables of \\spad{f}.")) (|ground| ((|#1| $) "\\spad{ground(f)} returns \\spad{f} as an element of \\spad{R}. An error occurs if \\spad{f} is not an element of \\spad{R}.")) (|ground?| (((|Boolean|) $) "\\spad{ground?(f)} tests if \\spad{f} is an element of \\spad{R}."))) -((-4459 -2781 (|has| |#1| (-1068)) (|has| |#1| (-485))) (-4457 |has| |#1| (-174)) (-4456 |has| |#1| (-174)) ((-4464 "*") |has| |#1| (-568)) (-4455 |has| |#1| (-568)) (-4460 |has| |#1| (-568)) (-4454 |has| |#1| (-568))) +((-4459 -2755 (|has| |#1| (-1068)) (|has| |#1| (-485))) (-4457 |has| |#1| (-174)) (-4456 |has| |#1| (-174)) ((-4464 "*") |has| |#1| (-568)) (-4455 |has| |#1| (-568)) (-4460 |has| |#1| (-568)) (-4454 |has| |#1| (-568))) NIL -(-443 R -1966) +(-443 R -1955) ((|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 -(-444 R -1966) +(-444 R -1955) ((|constructor| (NIL "FunctionsSpacePrimitiveElement provides functions to compute primitive elements in functions spaces.")) (|primitiveElement| (((|Record| (|:| |primelt| |#2|) (|:| |pol1| (|SparseUnivariatePolynomial| |#2|)) (|:| |pol2| (|SparseUnivariatePolynomial| |#2|)) (|:| |prim| (|SparseUnivariatePolynomial| |#2|))) |#2| |#2|) "\\spad{primitiveElement(a1, a2)} returns \\spad{[a, q1, q2, q]} such that \\spad{k(a1, a2) = k(a)},{} \\spad{ai = qi(a)},{} and \\spad{q(a) = 0}. The minimal polynomial for a2 may involve \\spad{a1},{} but the minimal polynomial for \\spad{a1} may not involve a2; This operations uses \\spadfun{resultant}.") (((|Record| (|:| |primelt| |#2|) (|:| |poly| (|List| (|SparseUnivariatePolynomial| |#2|))) (|:| |prim| (|SparseUnivariatePolynomial| |#2|))) (|List| |#2|)) "\\spad{primitiveElement([a1,...,an])} returns \\spad{[a, [q1,...,qn], q]} such that then \\spad{k(a1,...,an) = k(a)},{} \\spad{ai = qi(a)},{} and \\spad{q(a) = 0}. This operation uses the technique of \\spadglossSee{groebner bases}{Groebner basis}."))) NIL ((|HasCategory| |#2| (QUOTE (-27)))) -(-445 R -1966) +(-445 R -1955) ((|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 @@ -1716,7 +1716,7 @@ 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 -(-447 R -1966 UP) +(-447 R -1955 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 -1057) (QUOTE (-48))))) @@ -1748,7 +1748,7 @@ NIL ((|constructor| (NIL "\\spadtype{GaloisGroupFactorizer} provides functions to factor resolvents.")) (|btwFact| (((|Record| (|:| |contp| (|Integer|)) (|:| |factors| (|List| (|Record| (|:| |irr| |#1|) (|:| |pow| (|Integer|)))))) |#1| (|Boolean|) (|Set| (|NonNegativeInteger|)) (|NonNegativeInteger|)) "\\spad{btwFact(p,sqf,pd,r)} returns the factorization of \\spad{p},{} the result is a Record such that \\spad{contp=}content \\spad{p},{} \\spad{factors=}List of irreducible factors of \\spad{p} with exponent. If \\spad{sqf=true} the polynomial is assumed to be square free (\\spadignore{i.e.} without repeated factors). \\spad{pd} is the \\spadtype{Set} of possible degrees. \\spad{r} is a lower bound for the number of factors of \\spad{p}. Please do not use this function in your code because its design may change.")) (|henselFact| (((|Record| (|:| |contp| (|Integer|)) (|:| |factors| (|List| (|Record| (|:| |irr| |#1|) (|:| |pow| (|Integer|)))))) |#1| (|Boolean|)) "\\spad{henselFact(p,sqf)} returns the factorization of \\spad{p},{} the result is a Record such that \\spad{contp=}content \\spad{p},{} \\spad{factors=}List of irreducible factors of \\spad{p} with exponent. If \\spad{sqf=true} the polynomial is assumed to be square free (\\spadignore{i.e.} without repeated factors).")) (|factorOfDegree| (((|Union| |#1| "failed") (|PositiveInteger|) |#1| (|List| (|NonNegativeInteger|)) (|NonNegativeInteger|) (|Boolean|)) "\\spad{factorOfDegree(d,p,listOfDegrees,r,sqf)} returns a factor of \\spad{p} of degree \\spad{d} knowing that \\spad{p} has for possible splitting of its degree \\spad{listOfDegrees},{} and that \\spad{p} has at least \\spad{r} factors. If \\spad{sqf=true} the polynomial is assumed to be square free (\\spadignore{i.e.} without repeated factors).") (((|Union| |#1| "failed") (|PositiveInteger|) |#1| (|List| (|NonNegativeInteger|)) (|NonNegativeInteger|)) "\\spad{factorOfDegree(d,p,listOfDegrees,r)} returns a factor of \\spad{p} of degree \\spad{d} knowing that \\spad{p} has for possible splitting of its degree \\spad{listOfDegrees},{} and that \\spad{p} has at least \\spad{r} factors.") (((|Union| |#1| "failed") (|PositiveInteger|) |#1| (|List| (|NonNegativeInteger|))) "\\spad{factorOfDegree(d,p,listOfDegrees)} returns a factor of \\spad{p} of degree \\spad{d} knowing that \\spad{p} has for possible splitting of its degree \\spad{listOfDegrees}.") (((|Union| |#1| "failed") (|PositiveInteger|) |#1| (|NonNegativeInteger|)) "\\spad{factorOfDegree(d,p,r)} returns a factor of \\spad{p} of degree \\spad{d} knowing that \\spad{p} has at least \\spad{r} factors.") (((|Union| |#1| "failed") (|PositiveInteger|) |#1|) "\\spad{factorOfDegree(d,p)} returns a factor of \\spad{p} of degree \\spad{d}.")) (|factorSquareFree| (((|Factored| |#1|) |#1| (|NonNegativeInteger|) (|NonNegativeInteger|)) "\\spad{factorSquareFree(p,d,r)} factorizes the polynomial \\spad{p} using the single factor bound algorithm,{} knowing that \\spad{d} divides the degree of all factors of \\spad{p} and that \\spad{p} has at least \\spad{r} factors. \\spad{f} is supposed not having any repeated factor (this is not checked).") (((|Factored| |#1|) |#1| (|List| (|NonNegativeInteger|)) (|NonNegativeInteger|)) "\\spad{factorSquareFree(p,listOfDegrees,r)} factorizes the polynomial \\spad{p} using the single factor bound algorithm,{} knowing that \\spad{p} has for possible splitting of its degree \\spad{listOfDegrees} and that \\spad{p} has at least \\spad{r} factors. \\spad{f} is supposed not having any repeated factor (this is not checked).") (((|Factored| |#1|) |#1| (|List| (|NonNegativeInteger|))) "\\spad{factorSquareFree(p,listOfDegrees)} factorizes the polynomial \\spad{p} using the single factor bound algorithm and knowing that \\spad{p} has for possible splitting of its degree \\spad{listOfDegrees}. \\spad{f} is supposed not having any repeated factor (this is not checked).") (((|Factored| |#1|) |#1| (|NonNegativeInteger|)) "\\spad{factorSquareFree(p,r)} factorizes the polynomial \\spad{p} using the single factor bound algorithm and knowing that \\spad{p} has at least \\spad{r} factors. \\spad{f} is supposed not having any repeated factor (this is not checked).") (((|Factored| |#1|) |#1|) "\\spad{factorSquareFree(p)} returns the factorization of \\spad{p} which is supposed not having any repeated factor (this is not checked).")) (|factor| (((|Factored| |#1|) |#1| (|NonNegativeInteger|) (|NonNegativeInteger|)) "\\spad{factor(p,d,r)} factorizes the polynomial \\spad{p} using the single factor bound algorithm,{} knowing that \\spad{d} divides the degree of all factors of \\spad{p} and that \\spad{p} has at least \\spad{r} factors.") (((|Factored| |#1|) |#1| (|List| (|NonNegativeInteger|)) (|NonNegativeInteger|)) "\\spad{factor(p,listOfDegrees,r)} factorizes the polynomial \\spad{p} using the single factor bound algorithm,{} knowing that \\spad{p} has for possible splitting of its degree \\spad{listOfDegrees} and that \\spad{p} has at least \\spad{r} factors.") (((|Factored| |#1|) |#1| (|List| (|NonNegativeInteger|))) "\\spad{factor(p,listOfDegrees)} factorizes the polynomial \\spad{p} using the single factor bound algorithm and knowing that \\spad{p} has for possible splitting of its degree \\spad{listOfDegrees}.") (((|Factored| |#1|) |#1| (|NonNegativeInteger|)) "\\spad{factor(p,r)} factorizes the polynomial \\spad{p} using the single factor bound algorithm and knowing that \\spad{p} has at least \\spad{r} factors.") (((|Factored| |#1|) |#1|) "\\spad{factor(p)} returns the factorization of \\spad{p} over the integers.")) (|tryFunctionalDecomposition| (((|Boolean|) (|Boolean|)) "\\spad{tryFunctionalDecomposition(b)} chooses whether factorizers have to look for functional decomposition of polynomials (\\spad{true}) or not (\\spad{false}). Returns the previous value.")) (|tryFunctionalDecomposition?| (((|Boolean|)) "\\spad{tryFunctionalDecomposition?()} returns \\spad{true} if factorizers try functional decomposition of polynomials before factoring them.")) (|eisensteinIrreducible?| (((|Boolean|) |#1|) "\\spad{eisensteinIrreducible?(p)} returns \\spad{true} if \\spad{p} can be shown to be irreducible by Eisenstein\\spad{'s} criterion,{} \\spad{false} is inconclusive.")) (|useEisensteinCriterion| (((|Boolean|) (|Boolean|)) "\\spad{useEisensteinCriterion(b)} chooses whether factorizers check Eisenstein\\spad{'s} criterion before factoring: \\spad{true} for using it,{} \\spad{false} else. Returns the previous value.")) (|useEisensteinCriterion?| (((|Boolean|)) "\\spad{useEisensteinCriterion?()} returns \\spad{true} if factorizers check Eisenstein\\spad{'s} criterion before factoring.")) (|useSingleFactorBound| (((|Boolean|) (|Boolean|)) "\\spad{useSingleFactorBound(b)} chooses the algorithm to be used by the factorizers: \\spad{true} for algorithm with single factor bound,{} \\spad{false} for algorithm with overall bound. Returns the previous value.")) (|useSingleFactorBound?| (((|Boolean|)) "\\spad{useSingleFactorBound?()} returns \\spad{true} if algorithm with single factor bound is used for factorization,{} \\spad{false} for algorithm with overall bound.")) (|modularFactor| (((|Record| (|:| |prime| (|Integer|)) (|:| |factors| (|List| |#1|))) |#1|) "\\spad{modularFactor(f)} chooses a \"good\" prime and returns the factorization of \\spad{f} modulo this prime in a form that may be used by \\spadfunFrom{completeHensel}{GeneralHenselPackage}. If prime is zero it means that \\spad{f} has been proved to be irreducible over the integers or that \\spad{f} is a unit (\\spadignore{i.e.} 1 or \\spad{-1}). \\spad{f} shall be primitive (\\spadignore{i.e.} content(\\spad{p})\\spad{=1}) and square free (\\spadignore{i.e.} without repeated factors).")) (|numberOfFactors| (((|NonNegativeInteger|) (|List| (|Record| (|:| |factor| |#1|) (|:| |degree| (|Integer|))))) "\\spad{numberOfFactors(ddfactorization)} returns the number of factors of the polynomial \\spad{f} modulo \\spad{p} where \\spad{ddfactorization} is the distinct degree factorization of \\spad{f} computed by \\spadfunFrom{ddFact}{ModularDistinctDegreeFactorizer} for some prime \\spad{p}.")) (|stopMusserTrials| (((|PositiveInteger|) (|PositiveInteger|)) "\\spad{stopMusserTrials(n)} sets to \\spad{n} the bound on the number of factors for which \\spadfun{modularFactor} stops to look for an other prime. You will have to remember that the step of recombining the extraneous factors may take up to \\spad{2**n} trials. Returns the previous value.") (((|PositiveInteger|)) "\\spad{stopMusserTrials()} returns the bound on the number of factors for which \\spadfun{modularFactor} stops to look for an other prime. You will have to remember that the step of recombining the extraneous factors may take up to \\spad{2**stopMusserTrials()} trials.")) (|musserTrials| (((|PositiveInteger|) (|PositiveInteger|)) "\\spad{musserTrials(n)} sets to \\spad{n} the number of primes to be tried in \\spadfun{modularFactor} and returns the previous value.") (((|PositiveInteger|)) "\\spad{musserTrials()} returns the number of primes that are tried in \\spadfun{modularFactor}.")) (|degreePartition| (((|Multiset| (|NonNegativeInteger|)) (|List| (|Record| (|:| |factor| |#1|) (|:| |degree| (|Integer|))))) "\\spad{degreePartition(ddfactorization)} returns the degree partition of the polynomial \\spad{f} modulo \\spad{p} where \\spad{ddfactorization} is the distinct degree factorization of \\spad{f} computed by \\spadfunFrom{ddFact}{ModularDistinctDegreeFactorizer} for some prime \\spad{p}.")) (|makeFR| (((|Factored| |#1|) (|Record| (|:| |contp| (|Integer|)) (|:| |factors| (|List| (|Record| (|:| |irr| |#1|) (|:| |pow| (|Integer|))))))) "\\spad{makeFR(flist)} turns the final factorization of henselFact into a \\spadtype{Factored} object."))) NIL NIL -(-455 R UP -1966) +(-455 R UP -1955) ((|constructor| (NIL "\\spadtype{GaloisGroupFactorizationUtilities} provides functions that will be used by the factorizer.")) (|length| ((|#3| |#2|) "\\spad{length(p)} returns the sum of the absolute values of the coefficients of the polynomial \\spad{p}.")) (|height| ((|#3| |#2|) "\\spad{height(p)} returns the maximal absolute value of the coefficients of the polynomial \\spad{p}.")) (|infinityNorm| ((|#3| |#2|) "\\spad{infinityNorm(f)} returns the maximal absolute value of the coefficients of the polynomial \\spad{f}.")) (|quadraticNorm| ((|#3| |#2|) "\\spad{quadraticNorm(f)} returns the \\spad{l2} norm of the polynomial \\spad{f}.")) (|norm| ((|#3| |#2| (|PositiveInteger|)) "\\spad{norm(f,p)} returns the \\spad{lp} norm of the polynomial \\spad{f}.")) (|singleFactorBound| (((|Integer|) |#2|) "\\spad{singleFactorBound(p,r)} returns a bound on the infinite norm of the factor of \\spad{p} with smallest Bombieri\\spad{'s} norm. \\spad{p} shall be of degree higher or equal to 2.") (((|Integer|) |#2| (|NonNegativeInteger|)) "\\spad{singleFactorBound(p,r)} returns a bound on the infinite norm of the factor of \\spad{p} with smallest Bombieri\\spad{'s} norm. \\spad{r} is a lower bound for the number of factors of \\spad{p}. \\spad{p} shall be of degree higher or equal to 2.")) (|rootBound| (((|Integer|) |#2|) "\\spad{rootBound(p)} returns a bound on the largest norm of the complex roots of \\spad{p}.")) (|bombieriNorm| ((|#3| |#2| (|PositiveInteger|)) "\\spad{bombieriNorm(p,n)} returns the \\spad{n}th Bombieri\\spad{'s} norm of \\spad{p}.") ((|#3| |#2|) "\\spad{bombieriNorm(p)} returns quadratic Bombieri\\spad{'s} norm of \\spad{p}.")) (|beauzamyBound| (((|Integer|) |#2|) "\\spad{beauzamyBound(p)} returns a bound on the larger coefficient of any factor of \\spad{p}."))) NIL NIL @@ -1795,7 +1795,7 @@ NIL (-466 |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"))) (((-4464 "*") |has| |#2| (-174)) (-4455 |has| |#2| (-568)) (-4460 |has| |#2| (-6 -4460)) (-4457 . T) (-4456 . T) (-4459 . 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A table containing the solutions of \\spad{Af+Bg=x**k} is used. The operations are performed modulus a prime which are in principle big enough,{} but the solutions are tested and,{} in case of failure,{} a hensel lifting process is used to get to the right solutions. It will be used in the factorization of multivariate polynomials over finite field,{} with \\spad{R=F[x]}.")) (|testModulus| (((|Boolean|) |#1| (|List| |#2|)) "\\spad{testModulus(p,lp)} returns \\spad{true} if the the prime \\spad{p} is valid for the list of polynomials \\spad{lp},{} \\spadignore{i.e.} preserves the degree and they remain relatively prime.")) (|solveid| (((|Union| (|List| |#2|) "failed") |#2| |#1| (|Vector| (|List| |#2|))) "\\spad{solveid(h,table)} computes the coefficients of the extended euclidean algorithm for a list of polynomials whose tablePow is \\spad{table} and with right side \\spad{h}.")) (|tablePow| (((|Union| (|Vector| (|List| |#2|)) "failed") (|NonNegativeInteger|) |#1| (|List| |#2|)) "\\spad{tablePow(maxdeg,prime,lpol)} constructs the table with the coefficients of the Extended Euclidean Algorithm for \\spad{lpol}. Here the right side is \\spad{x**k},{} for \\spad{k} less or equal to \\spad{maxdeg}. The operation returns \"failed\" when the elements are not coprime modulo \\spad{prime}.")) (|compBound| (((|NonNegativeInteger|) |#2| (|List| |#2|)) "\\spad{compBound(p,lp)} computes a bound for the coefficients of the solution polynomials. Given a polynomial right hand side \\spad{p},{} and a list \\spad{lp} of left hand side polynomials. Exported because it depends on the valuation.")) (|reduction| ((|#2| |#2| |#1|) "\\spad{reduction(p,prime)} reduces the polynomial \\spad{p} modulo \\spad{prime} of \\spad{R}. Note: this function is exported only because it\\spad{'s} conditional."))) NIL @@ -1860,7 +1860,7 @@ NIL ((|constructor| (NIL "GradedModule(\\spad{R},{}\\spad{E}) denotes ``E-graded \\spad{R}-module\\spad{''},{} \\spadignore{i.e.} collection of \\spad{R}-modules indexed by an abelian monoid \\spad{E}. An element \\spad{g} of \\spad{G[s]} for some specific \\spad{s} in \\spad{E} is said to be an element of \\spad{G} with {\\em degree} \\spad{s}. Sums are defined in each module \\spad{G[s]} so two elements of \\spad{G} have a sum if they have the same degree. \\blankline Morphisms can be defined and composed by degree to give the mathematical category of graded modules.")) (+ (($ $ $) "\\spad{g+h} is the sum of \\spad{g} and \\spad{h} in the module of elements of the same degree as \\spad{g} and \\spad{h}. Error: if \\spad{g} and \\spad{h} have different degrees.")) (- (($ $ $) "\\spad{g-h} is the difference of \\spad{g} and \\spad{h} in the module of elements of the same degree as \\spad{g} and \\spad{h}. Error: if \\spad{g} and \\spad{h} have different degrees.") (($ $) "\\spad{-g} is the additive inverse of \\spad{g} in the module of elements of the same grade as \\spad{g}.")) (* (($ $ |#1|) "\\spad{g*r} is right module multiplication.") (($ |#1| $) "\\spad{r*g} is left module multiplication.")) ((|Zero|) (($) "0 denotes the zero of degree 0.")) (|degree| ((|#2| $) "\\spad{degree(g)} names the degree of \\spad{g}. The set of all elements of a given degree form an \\spad{R}-module."))) NIL NIL -(-483 |lv| -1966 R) +(-483 |lv| -1955 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 @@ -1875,11 +1875,11 @@ NIL (-486 |Coef| |var| |cen|) ((|constructor| (NIL "This is a category of univariate Puiseux series constructed from univariate Laurent series. A Puiseux series is represented by a pair \\spad{[r,f(x)]},{} where \\spad{r} is a positive rational number and \\spad{f(x)} is a Laurent series. This pair represents the Puiseux series \\spad{f(x\\^r)}.")) (|integrate| (($ $ (|Variable| |#2|)) "\\spad{integrate(f(x))} returns an anti-derivative of the power series \\spad{f(x)} with constant coefficient 0. We may integrate a series when we can divide coefficients by integers.")) (|coerce| (($ (|UnivariatePuiseuxSeries| |#1| |#2| |#3|)) "\\spad{coerce(f)} converts a Puiseux series to a general power series.") (($ (|Variable| |#2|)) "\\spad{coerce(var)} converts the series variable \\spad{var} into a Puiseux series."))) (((-4464 "*") |has| |#1| (-174)) (-4455 |has| |#1| (-568)) (-4460 |has| |#1| (-374)) (-4454 |has| |#1| (-374)) (-4456 . T) (-4457 . T) (-4459 . 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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)}"))) ((-4463 . T) (-4462 . T)) @@ -1895,7 +1895,7 @@ NIL (-491 |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."))) ((-4462 . T) (-4463 . 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Hall as given in Serre\\spad{'s} book Lie Groups \\spad{--} Lie Algebras")) (|generate| (((|Vector| (|List| (|Integer|))) (|NonNegativeInteger|) (|NonNegativeInteger|)) "\\spad{generate(numberOfGens, maximalWeight)} generates a vector of elements of the form [left,{}weight,{}right] which represents a \\spad{P}. Hall basis element for the free lie algebra on \\spad{numberOfGens} generators. We only generate those basis elements of weight less than or equal to maximalWeight")) (|inHallBasis?| (((|Boolean|) (|Integer|) (|Integer|) (|Integer|) (|Integer|)) "\\spad{inHallBasis?(numberOfGens, leftCandidate, rightCandidate, left)} tests to see if a new element should be added to the \\spad{P}. Hall basis being constructed. The list \\spad{[leftCandidate,wt,rightCandidate]} is included in the basis if in the unique factorization of \\spad{rightCandidate},{} we have left factor leftOfRight,{} and leftOfRight \\spad{<=} \\spad{leftCandidate}")) (|lfunc| (((|Integer|) (|Integer|) (|Integer|)) "\\spad{lfunc(d,n)} computes the rank of the \\spad{n}th factor in the lower central series of the free \\spad{d}-generated free Lie algebra; This rank is \\spad{d} if \\spad{n} = 1 and binom(\\spad{d},{}2) if \\spad{n} = 2"))) NIL @@ -1903,11 +1903,11 @@ NIL (-493 |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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(|parameters| (((|List| (|ParameterAst|)) $) "\\spad{parameters(h)} gives the parameters specified in the definition header \\spad{`h'}.")) (|name| (((|Identifier|) $) "\\spad{name(h)} returns the name of the operation defined defined.")) (|headAst| (($ (|Identifier|) (|List| (|ParameterAst|))) "\\spad{headAst(f,[x1,..,xn])} constructs a function definition header."))) NIL @@ -1915,8 +1915,8 @@ NIL (-496 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}."))) ((-4462 . T) (-4463 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1119))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1119))) (-2781 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-1119)))) (-2781 (-12 (|HasCategory| |#1| (QUOTE (-1119))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-874))))) (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-874)))) (|HasCategory| |#1| (QUOTE (-102)))) -(-497 -1966 UP UPUP R) +((-12 (|HasCategory| |#1| (QUOTE (-1119))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1119))) (-2755 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-1119)))) (-2755 (-12 (|HasCategory| |#1| (QUOTE (-1119))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-874))))) (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-874)))) (|HasCategory| |#1| (QUOTE (-102)))) +(-497 -1955 UP UPUP R) ((|constructor| (NIL "This domains implements finite rational divisors on an hyperelliptic curve,{} that is finite formal sums SUM(\\spad{n} * \\spad{P}) where the \\spad{n}\\spad{'s} are integers and the \\spad{P}\\spad{'s} are finite rational points on the curve. The equation of the curve must be \\spad{y^2} = \\spad{f}(\\spad{x}) and \\spad{f} must have odd degree."))) NIL NIL @@ -1927,7 +1927,7 @@ NIL (-499) ((|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."))) ((-4454 . T) (-4460 . T) (-4455 . T) ((-4464 "*") . T) (-4456 . T) (-4457 . T) (-4459 . 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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|) $) "\\spad{map(f,u)} returns a copy of \\spad{u} with each element \\spad{x} replaced by \\spad{f}(\\spad{x}). For collections,{} \\axiom{map(\\spad{f},{}\\spad{u}) = [\\spad{f}(\\spad{x}) for \\spad{x} in \\spad{u}]}."))) NIL @@ -1952,7 +1952,7 @@ NIL ((|constructor| (NIL "Category for the hyperbolic trigonometric functions.")) (|tanh| (($ $) "\\spad{tanh(x)} returns the hyperbolic tangent of \\spad{x}.")) (|sinh| (($ $) "\\spad{sinh(x)} returns the hyperbolic sine of \\spad{x}.")) (|sech| (($ $) "\\spad{sech(x)} returns the hyperbolic secant of \\spad{x}.")) (|csch| (($ $) "\\spad{csch(x)} returns the hyperbolic cosecant of \\spad{x}.")) (|coth| (($ $) "\\spad{coth(x)} returns the hyperbolic cotangent of \\spad{x}.")) (|cosh| (($ $) "\\spad{cosh(x)} returns the hyperbolic cosine of \\spad{x}."))) NIL NIL -(-506 -1966 UP |AlExt| |AlPol|) +(-506 -1955 UP |AlExt| |AlPol|) ((|constructor| (NIL "Factorization of univariate polynomials with coefficients in an algebraic extension of a field over which we can factor UP\\spad{'s}.")) (|factor| (((|Factored| |#4|) |#4| (|Mapping| (|Factored| |#2|) |#2|)) "\\spad{factor(p, f)} returns a prime factorisation of \\spad{p}; \\spad{f} is a factorisation map for elements of UP."))) NIL NIL @@ -1963,16 +1963,16 @@ NIL (-508 S |mn|) ((|constructor| (NIL "\\indented{1}{Author Micheal Monagan Aug/87} This is the basic one dimensional array data type."))) ((-4463 . T) (-4462 . T)) -((-2781 (-12 (|HasCategory| |#1| (QUOTE (-862))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1119))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|))))) (-2781 (-12 (|HasCategory| |#1| (QUOTE (-1119))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-874))))) (|HasCategory| |#1| (LIST (QUOTE -626) (QUOTE (-548)))) (-2781 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-862))) (|HasCategory| |#1| (QUOTE (-1119)))) (-2781 (|HasCategory| |#1| (QUOTE (-862))) (|HasCategory| |#1| (QUOTE (-1119)))) (|HasCategory| |#1| (QUOTE (-862))) (|HasCategory| (-576) (QUOTE (-862))) (|HasCategory| |#1| (QUOTE (-1119))) (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-874)))) (|HasCategory| |#1| (QUOTE (-102))) (-12 (|HasCategory| |#1| (QUOTE (-1119))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|))))) +((-2755 (-12 (|HasCategory| |#1| (QUOTE (-862))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1119))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|))))) (-2755 (-12 (|HasCategory| |#1| (QUOTE (-1119))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-874))))) (|HasCategory| |#1| (LIST (QUOTE -626) (QUOTE (-548)))) (-2755 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-862))) (|HasCategory| |#1| (QUOTE (-1119)))) (-2755 (|HasCategory| |#1| (QUOTE (-862))) (|HasCategory| |#1| (QUOTE (-1119)))) (|HasCategory| |#1| (QUOTE (-862))) (|HasCategory| (-576) (QUOTE (-862))) (|HasCategory| |#1| (QUOTE (-1119))) (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-874)))) (|HasCategory| |#1| (QUOTE (-102))) (-12 (|HasCategory| |#1| (QUOTE (-1119))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|))))) (-509 R |mnRow| |mnCol|) ((|constructor| (NIL "\\indented{1}{An IndexedTwoDimensionalArray is a 2-dimensional array where} the minimal row and column indices are parameters of the type. Rows and columns are returned as IndexedOneDimensionalArray\\spad{'s} with minimal indices matching those of the IndexedTwoDimensionalArray. The index of the 'first' row may be obtained by calling the function 'minRowIndex'. The index of the 'first' column may be obtained by calling the function 'minColIndex'. The index of the first element of a 'Row' is the same as the index of the first column in an array and vice versa."))) ((-4462 . T) (-4463 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1119))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1119))) (-2781 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-1119)))) (-2781 (-12 (|HasCategory| |#1| (QUOTE (-1119))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-874))))) (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-874)))) (|HasCategory| |#1| (QUOTE (-102)))) +((-12 (|HasCategory| |#1| (QUOTE (-1119))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1119))) (-2755 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-1119)))) (-2755 (-12 (|HasCategory| |#1| (QUOTE (-1119))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-874))))) (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-874)))) (|HasCategory| |#1| (QUOTE (-102)))) (-510 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 -(-511 R UP -1966) +(-511 R UP -1955) ((|constructor| (NIL "This package contains functions used in the packages FunctionFieldIntegralBasis and NumberFieldIntegralBasis.")) (|moduleSum| (((|Record| (|:| |basis| (|Matrix| |#1|)) (|:| |basisDen| |#1|) (|:| |basisInv| (|Matrix| |#1|))) (|Record| (|:| |basis| (|Matrix| |#1|)) (|:| |basisDen| |#1|) (|:| |basisInv| (|Matrix| |#1|))) (|Record| (|:| |basis| (|Matrix| |#1|)) (|:| |basisDen| |#1|) (|:| |basisInv| (|Matrix| |#1|)))) "\\spad{moduleSum(m1,m2)} returns the sum of two modules in the framed algebra \\spad{F}. Each module \\spad{mi} is represented as follows: \\spad{F} is a framed algebra with \\spad{R}-module basis \\spad{w1,w2,...,wn} and \\spad{mi} is a record \\spad{[basis,basisDen,basisInv]}. If \\spad{basis} is the matrix \\spad{(aij, i = 1..n, j = 1..n)},{} then a basis \\spad{v1,...,vn} for \\spad{mi} is given by \\spad{vi = (1/basisDen) * sum(aij * wj, j = 1..n)},{} \\spadignore{i.e.} the \\spad{i}th row of 'basis' contains the coordinates of the \\spad{i}th basis vector. Similarly,{} the \\spad{i}th row of the matrix \\spad{basisInv} contains the coordinates of \\spad{wi} with respect to the basis \\spad{v1,...,vn}: if \\spad{basisInv} is the matrix \\spad{(bij, i = 1..n, j = 1..n)},{} then \\spad{wi = sum(bij * vj, j = 1..n)}.")) (|idealiserMatrix| (((|Matrix| |#1|) (|Matrix| |#1|) (|Matrix| |#1|)) "\\spad{idealiserMatrix(m1, m2)} returns the matrix representing the linear conditions on the Ring associatied with an ideal defined by \\spad{m1} and \\spad{m2}.")) (|idealiser| (((|Matrix| |#1|) (|Matrix| |#1|) (|Matrix| |#1|) |#1|) "\\spad{idealiser(m1,m2,d)} computes the order of an ideal defined by \\spad{m1} and \\spad{m2} where \\spad{d} is the known part of the denominator") (((|Matrix| |#1|) (|Matrix| |#1|) (|Matrix| |#1|)) "\\spad{idealiser(m1,m2)} computes the order of an ideal defined by \\spad{m1} and \\spad{m2}")) (|leastPower| (((|NonNegativeInteger|) (|NonNegativeInteger|) (|NonNegativeInteger|)) "\\spad{leastPower(p,n)} returns \\spad{e},{} where \\spad{e} is the smallest integer such that \\spad{p **e >= n}")) (|divideIfCan!| ((|#1| (|Matrix| |#1|) (|Matrix| |#1|) |#1| (|Integer|)) "\\spad{divideIfCan!(matrix,matrixOut,prime,n)} attempts to divide the entries of \\spad{matrix} by \\spad{prime} and store the result in \\spad{matrixOut}. If it is successful,{} 1 is returned and if not,{} \\spad{prime} is returned. Here both \\spad{matrix} and \\spad{matrixOut} are \\spad{n}-by-\\spad{n} upper triangular matrices.")) (|matrixGcd| ((|#1| (|Matrix| |#1|) |#1| (|NonNegativeInteger|)) "\\spad{matrixGcd(mat,sing,n)} is \\spad{gcd(sing,g)} where \\spad{g} is the \\spad{gcd} of the entries of the \\spad{n}-by-\\spad{n} upper-triangular matrix \\spad{mat}.")) (|diagonalProduct| ((|#1| (|Matrix| |#1|)) "\\spad{diagonalProduct(m)} returns the product of the elements on the diagonal of the matrix \\spad{m}")) (|squareFree| (((|Factored| $) $) "\\spad{squareFree(x)} returns a square-free factorisation of \\spad{x}"))) NIL NIL @@ -1992,7 +1992,7 @@ NIL ((|constructor| (NIL "InnerCommonDenominator provides functions to compute the common denominator of a finite linear aggregate of elements of the quotient field of an integral domain.")) (|splitDenominator| (((|Record| (|:| |num| |#3|) (|:| |den| |#1|)) |#4|) "\\spad{splitDenominator([q1,...,qn])} returns \\spad{[[p1,...,pn], d]} such that \\spad{qi = pi/d} and \\spad{d} is a common denominator for the \\spad{qi}\\spad{'s}.")) (|clearDenominator| ((|#3| |#4|) "\\spad{clearDenominator([q1,...,qn])} returns \\spad{[p1,...,pn]} such that \\spad{qi = pi/d} where \\spad{d} is a common denominator for the \\spad{qi}\\spad{'s}.")) (|commonDenominator| ((|#1| |#4|) "\\spad{commonDenominator([q1,...,qn])} returns a common denominator \\spad{d} for \\spad{q1},{}...,{}\\spad{qn}."))) NIL NIL -(-516 -1966 |Expon| |VarSet| |DPoly|) +(-516 -1955 |Expon| |VarSet| |DPoly|) ((|constructor| (NIL "This domain represents polynomial ideals with coefficients in any field and supports the basic ideal operations,{} including intersection sum and quotient. An ideal is represented by a list of polynomials (the generators of the ideal) and a boolean that is \\spad{true} if the generators are a Groebner basis. The algorithms used are based on Groebner basis computations. The ordering is determined by the datatype of the input polynomials. Users may use refinements of total degree orderings.")) (|relationsIdeal| (((|SuchThat| (|List| (|Polynomial| |#1|)) (|List| (|Equation| (|Polynomial| |#1|)))) (|List| |#4|)) "\\spad{relationsIdeal(polyList)} returns the ideal of relations among the polynomials in \\spad{polyList}.")) (|saturate| (($ $ |#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}.")) (* (($ $ $) "\\spad{I*J} computes the product of the ideal \\spad{I} and \\spad{J}."))) NIL ((|HasCategory| |#3| (LIST (QUOTE -626) (QUOTE (-1195))))) @@ -2013,7 +2013,7 @@ NIL NIL NIL (-521 A S) -((|constructor| (NIL "This category represents the direct product of some set with respect to an ordered indexing set.")) (|reductum| (($ $) "\\spad{reductum(z)} returns a new element created by removing the leading coefficient/support pair from the element \\spad{z}. Error: if \\spad{z} has no support.")) (|leadingSupport| ((|#2| $) "\\spad{leadingSupport(z)} returns the index of leading (with respect to the ordering on the indexing set) monomial of \\spad{z}. Error: if \\spad{z} has no support.")) (|leadingCoefficient| ((|#1| $) "\\spad{leadingCoefficient(z)} returns the coefficient of the leading (with respect to the ordering on the indexing set) monomial of \\spad{z}. Error: if \\spad{z} has no support.")) (|monomial| (($ |#1| |#2|) "\\spad{monomial(a,s)} constructs a direct product element with the \\spad{s} component set to \\spad{a}")) (|map| (($ (|Mapping| |#1| |#1|) $) "\\spad{map(f,z)} returns the new element created by applying the function \\spad{f} to each component of the direct product element \\spad{z}."))) +((|constructor| (NIL "This category represents the direct product of some set with respect to an ordered indexing set.")) (|support| (((|List| (|Pair| |#2| |#1|)) $) "\\spad{support x} returns the list of terms in \\spad{x}. Each term is a pair of an index (the first component) and the corresponding value (the second component).")) (|reductum| (($ $) "\\spad{reductum(z)} returns a new element created by removing the leading coefficient/support pair from the element \\spad{z}. Error: if \\spad{z} has no support.")) (|leadingSupport| ((|#2| $) "\\spad{leadingSupport(z)} returns the index of leading (with respect to the ordering on the indexing set) monomial of \\spad{z}. Error: if \\spad{z} has no support.")) (|leadingCoefficient| ((|#1| $) "\\spad{leadingCoefficient(z)} returns the coefficient of the leading (with respect to the ordering on the indexing set) monomial of \\spad{z}. Error: if \\spad{z} has no support.")) (|monomial| (($ |#1| |#2|) "\\spad{monomial(a,s)} constructs a direct product element with the \\spad{s} component set to \\spad{a}")) (|map| (($ (|Mapping| |#1| |#1|) $) "\\spad{map(f,z)} returns the new element created by applying the function \\spad{f} to each component of the direct product element \\spad{z}."))) NIL NIL (-522 A S) @@ -2025,7 +2025,7 @@ NIL NIL NIL (-524 A S) -((|constructor| (NIL "\\indented{1}{Indexed direct products of objects over a set \\spad{A}} of generators indexed by an ordered set \\spad{S}. All items have finite support."))) +((|constructor| (NIL "\\indented{1}{Data Last Updated: June 28,{} 2010} Indexed direct products of objects over a set \\spad{A} of generators indexed by an ordered set \\spad{S}. All items have finite support."))) NIL NIL (-525 S A B) @@ -2043,7 +2043,7 @@ NIL (-528 S |mn|) ((|constructor| (NIL "\\indented{1}{Author: Michael Monagan July/87,{} modified \\spad{SMW} June/91} A FlexibleArray is the notion of an array intended to allow for growth at the end only. Hence the following efficient operations \\indented{2}{\\spad{append(x,a)} meaning append item \\spad{x} at the end of the array \\spad{a}} \\indented{2}{\\spad{delete(a,n)} meaning delete the last item from the array \\spad{a}} Flexible arrays support the other operations inherited from \\spadtype{ExtensibleLinearAggregate}. However,{} these are not efficient. Flexible arrays combine the \\spad{O(1)} access time property of arrays with growing and shrinking at the end in \\spad{O(1)} (average) time. This is done by using an ordinary array which may have zero or more empty slots at the end. When the array becomes full it is copied into a new larger (50\\% larger) array. Conversely,{} when the array becomes less than 1/2 full,{} it is copied into a smaller array. Flexible arrays provide for an efficient implementation of many data structures in particular heaps,{} stacks and sets.")) (|shrinkable| (((|Boolean|) (|Boolean|)) "\\spad{shrinkable(b)} sets the shrinkable attribute of flexible arrays to \\spad{b} and returns the previous value")) (|physicalLength!| (($ $ (|Integer|)) "\\spad{physicalLength!(x,n)} changes the physical length of \\spad{x} to be \\spad{n} and returns the new array.")) (|physicalLength| (((|NonNegativeInteger|) $) "\\spad{physicalLength(x)} returns the number of elements \\spad{x} can accomodate before growing")) (|flexibleArray| (($ (|List| |#1|)) "\\spad{flexibleArray(l)} creates a flexible array from the list of elements \\spad{l}"))) ((-4463 . T) (-4462 . T)) -((-2781 (-12 (|HasCategory| |#1| (QUOTE (-862))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1119))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|))))) (-2781 (-12 (|HasCategory| |#1| (QUOTE (-1119))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-874))))) (|HasCategory| |#1| (LIST (QUOTE -626) (QUOTE (-548)))) (-2781 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-862))) (|HasCategory| |#1| (QUOTE (-1119)))) (-2781 (|HasCategory| |#1| (QUOTE (-862))) (|HasCategory| |#1| (QUOTE (-1119)))) (|HasCategory| |#1| (QUOTE (-862))) (|HasCategory| (-576) (QUOTE (-862))) (|HasCategory| |#1| (QUOTE (-1119))) (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-874)))) (|HasCategory| |#1| (QUOTE (-102))) (-12 (|HasCategory| |#1| (QUOTE (-1119))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|))))) +((-2755 (-12 (|HasCategory| |#1| (QUOTE (-862))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1119))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|))))) (-2755 (-12 (|HasCategory| |#1| (QUOTE (-1119))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-874))))) (|HasCategory| |#1| (LIST (QUOTE -626) (QUOTE (-548)))) (-2755 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-862))) (|HasCategory| |#1| (QUOTE (-1119)))) (-2755 (|HasCategory| |#1| (QUOTE (-862))) (|HasCategory| |#1| (QUOTE (-1119)))) (|HasCategory| |#1| (QUOTE (-862))) (|HasCategory| (-576) (QUOTE (-862))) (|HasCategory| |#1| (QUOTE (-1119))) (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-874)))) (|HasCategory| |#1| (QUOTE (-102))) (-12 (|HasCategory| |#1| (QUOTE (-1119))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|))))) (-529) ((|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 @@ -2051,15 +2051,15 @@ NIL (-530 |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}."))) ((-4454 . T) (-4460 . T) (-4455 . T) ((-4464 "*") . T) (-4456 . T) (-4457 . T) (-4459 . T)) -((-2781 (|HasCategory| (-593 |#1|) (QUOTE (-146))) (|HasCategory| (-593 |#1|) (QUOTE (-379)))) (|HasCategory| (-593 |#1|) (QUOTE (-148))) (|HasCategory| (-593 |#1|) (QUOTE (-379))) (|HasCategory| (-593 |#1|) (QUOTE (-146)))) +((-2755 (|HasCategory| (-593 |#1|) (QUOTE (-146))) (|HasCategory| (-593 |#1|) (QUOTE (-379)))) (|HasCategory| (-593 |#1|) (QUOTE (-148))) (|HasCategory| (-593 |#1|) (QUOTE (-379))) (|HasCategory| (-593 |#1|) (QUOTE (-146)))) (-531 R |mnRow| |mnCol| |Row| |Col|) ((|constructor| (NIL "\\indented{1}{This is an internal type which provides an implementation of} 2-dimensional arrays as PrimitiveArray\\spad{'s} of PrimitiveArray\\spad{'s}."))) ((-4462 . T) (-4463 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1119))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1119))) (-2781 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-1119)))) (-2781 (-12 (|HasCategory| |#1| (QUOTE (-1119))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-874))))) (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-874)))) (|HasCategory| |#1| (QUOTE (-102)))) +((-12 (|HasCategory| |#1| (QUOTE (-1119))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1119))) (-2755 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-1119)))) (-2755 (-12 (|HasCategory| |#1| (QUOTE (-1119))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-874))))) (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-874)))) (|HasCategory| |#1| (QUOTE (-102)))) (-532 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."))) ((-4463 . T) (-4462 . T)) -((-2781 (-12 (|HasCategory| |#1| (QUOTE (-862))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1119))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|))))) (-2781 (-12 (|HasCategory| |#1| (QUOTE (-1119))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-874))))) (|HasCategory| |#1| (LIST (QUOTE -626) (QUOTE (-548)))) (-2781 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-862))) (|HasCategory| |#1| (QUOTE (-1119)))) (-2781 (|HasCategory| |#1| (QUOTE (-862))) (|HasCategory| |#1| (QUOTE (-1119)))) (|HasCategory| |#1| (QUOTE (-862))) (|HasCategory| (-576) (QUOTE (-862))) (|HasCategory| |#1| (QUOTE (-1119))) (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-874)))) (|HasCategory| |#1| (QUOTE (-102))) (-12 (|HasCategory| |#1| (QUOTE (-1119))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|))))) +((-2755 (-12 (|HasCategory| |#1| (QUOTE (-862))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1119))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|))))) (-2755 (-12 (|HasCategory| |#1| (QUOTE (-1119))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-874))))) (|HasCategory| |#1| (LIST (QUOTE -626) (QUOTE (-548)))) (-2755 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-862))) (|HasCategory| |#1| (QUOTE (-1119)))) (-2755 (|HasCategory| |#1| (QUOTE (-862))) (|HasCategory| |#1| (QUOTE (-1119)))) (|HasCategory| |#1| (QUOTE (-862))) (|HasCategory| (-576) (QUOTE (-862))) (|HasCategory| |#1| (QUOTE (-1119))) (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-874)))) (|HasCategory| |#1| (QUOTE (-102))) (-12 (|HasCategory| |#1| (QUOTE (-1119))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|))))) (-533 R |Row| |Col| M) ((|constructor| (NIL "\\spadtype{InnerMatrixLinearAlgebraFunctions} is an internal package which provides standard linear algebra functions on domains in \\spad{MatrixCategory}")) (|inverse| (((|Union| |#4| "failed") |#4|) "\\spad{inverse(m)} returns the inverse of the matrix \\spad{m}. If the matrix is not invertible,{} \"failed\" is returned. Error: if the matrix is not square.")) (|generalizedInverse| ((|#4| |#4|) "\\spad{generalizedInverse(m)} returns the generalized (Moore--Penrose) inverse of the matrix \\spad{m},{} \\spadignore{i.e.} the matrix \\spad{h} such that m*h*m=h,{} h*m*h=m,{} \\spad{m*h} and \\spad{h*m} are both symmetric matrices.")) (|determinant| ((|#1| |#4|) "\\spad{determinant(m)} returns the determinant of the matrix \\spad{m}. an error message is returned if the matrix is not square.")) (|nullSpace| (((|List| |#3|) |#4|) "\\spad{nullSpace(m)} returns a basis for the null space of the matrix \\spad{m}.")) (|nullity| (((|NonNegativeInteger|) |#4|) "\\spad{nullity(m)} returns the mullity of the matrix \\spad{m}. This is the dimension of the null space of the matrix \\spad{m}.")) (|rank| (((|NonNegativeInteger|) |#4|) "\\spad{rank(m)} returns the rank of the matrix \\spad{m}.")) (|rowEchelon| ((|#4| |#4|) "\\spad{rowEchelon(m)} returns the row echelon form of the matrix \\spad{m}."))) NIL @@ -2071,7 +2071,7 @@ NIL (-535 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."))) ((-4462 . T) (-4463 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1119))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1119))) (-2781 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-1119)))) (-2781 (-12 (|HasCategory| |#1| (QUOTE (-1119))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-874))))) (|HasCategory| |#1| (QUOTE (-317))) (|HasCategory| |#1| (QUOTE (-568))) (|HasAttribute| |#1| (QUOTE (-4464 "*"))) (|HasCategory| |#1| (QUOTE (-374))) (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-874)))) (|HasCategory| |#1| (QUOTE (-102)))) +((-12 (|HasCategory| |#1| (QUOTE (-1119))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1119))) (-2755 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-1119)))) (-2755 (-12 (|HasCategory| |#1| (QUOTE (-1119))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-874))))) (|HasCategory| |#1| (QUOTE (-317))) (|HasCategory| |#1| (QUOTE (-568))) (|HasAttribute| |#1| (QUOTE (-4464 "*"))) (|HasCategory| |#1| (QUOTE (-374))) (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-874)))) (|HasCategory| |#1| (QUOTE (-102)))) (-536) ((|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 @@ -2104,7 +2104,7 @@ NIL ((|constructor| (NIL "\\indented{2}{IndexedExponents of an ordered set of variables gives a representation} for the degree of polynomials in commuting variables. It gives an ordered pairing of non negative integer exponents with variables"))) NIL NIL -(-544 K -1966 |Par|) +(-544 K -1955 |Par|) ((|constructor| (NIL "This package is the inner package to be used by NumericRealEigenPackage and NumericComplexEigenPackage for the computation of numeric eigenvalues and eigenvectors.")) (|innerEigenvectors| (((|List| (|Record| (|:| |outval| |#2|) (|:| |outmult| (|Integer|)) (|:| |outvect| (|List| (|Matrix| |#2|))))) (|Matrix| |#1|) |#3| (|Mapping| (|Factored| (|SparseUnivariatePolynomial| |#1|)) (|SparseUnivariatePolynomial| |#1|))) "\\spad{innerEigenvectors(m,eps,factor)} computes explicitly the eigenvalues and the correspondent eigenvectors of the matrix \\spad{m}. The parameter \\spad{eps} determines the type of the output,{} \\spad{factor} is the univariate factorizer to \\spad{br} used to reduce the characteristic polynomial into irreducible factors.")) (|solve1| (((|List| |#2|) (|SparseUnivariatePolynomial| |#1|) |#3|) "\\spad{solve1(pol, eps)} finds the roots of the univariate polynomial polynomial \\spad{pol} to precision eps. If \\spad{K} is \\spad{Fraction Integer} then only the real roots are returned,{} if \\spad{K} is \\spad{Complex Fraction Integer} then all roots are found.")) (|charpol| (((|SparseUnivariatePolynomial| |#1|) (|Matrix| |#1|)) "\\spad{charpol(m)} computes the characteristic polynomial of a matrix \\spad{m} with entries in \\spad{K}. This function returns a polynomial over \\spad{K},{} while the general one (that is in EiegenPackage) returns Fraction \\spad{P} \\spad{K}"))) NIL NIL @@ -2128,7 +2128,7 @@ 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 -(-550 K -1966 |Par|) +(-550 K -1955 |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 @@ -2179,12 +2179,12 @@ NIL (-562 |Key| |Entry| |addDom|) ((|constructor| (NIL "This domain is used to provide a conditional \"add\" domain for the implementation of \\spadtype{Table}."))) ((-4462 . T) (-4463 . T)) -((-12 (|HasCategory| (-2 (|:| -4300 |#1|) (|:| -4391 |#2|)) (QUOTE (-1119))) (|HasCategory| (-2 (|:| -4300 |#1|) (|:| -4391 |#2|)) (LIST (QUOTE -319) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -4300) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -4391) (|devaluate| |#2|)))))) (-2781 (|HasCategory| (-2 (|:| -4300 |#1|) (|:| -4391 |#2|)) (QUOTE (-1119))) (|HasCategory| |#2| (QUOTE (-1119)))) (-2781 (|HasCategory| (-2 (|:| -4300 |#1|) (|:| -4391 |#2|)) (QUOTE (-102))) (|HasCategory| (-2 (|:| -4300 |#1|) (|:| -4391 |#2|)) (QUOTE (-1119))) (|HasCategory| |#2| (QUOTE (-102))) (|HasCategory| |#2| (QUOTE (-1119)))) (-2781 (|HasCategory| (-2 (|:| -4300 |#1|) (|:| -4391 |#2|)) (QUOTE (-1119))) (|HasCategory| (-2 (|:| -4300 |#1|) (|:| -4391 |#2|)) (LIST (QUOTE -625) (QUOTE (-874)))) (|HasCategory| |#2| (QUOTE (-1119))) (|HasCategory| |#2| (LIST (QUOTE -625) (QUOTE (-874))))) (|HasCategory| (-2 (|:| -4300 |#1|) (|:| -4391 |#2|)) (LIST (QUOTE -626) (QUOTE (-548)))) (-12 (|HasCategory| |#2| (QUOTE (-1119))) (|HasCategory| |#2| (LIST (QUOTE -319) (|devaluate| |#2|)))) (|HasCategory| (-2 (|:| -4300 |#1|) (|:| -4391 |#2|)) (QUOTE (-1119))) (|HasCategory| |#1| (QUOTE (-862))) (|HasCategory| |#2| (QUOTE (-1119))) (-2781 (|HasCategory| (-2 (|:| -4300 |#1|) (|:| -4391 |#2|)) (LIST (QUOTE -625) (QUOTE (-874)))) (|HasCategory| |#2| (LIST (QUOTE -625) (QUOTE (-874))))) (-2781 (|HasCategory| (-2 (|:| -4300 |#1|) (|:| -4391 |#2|)) (QUOTE (-102))) (|HasCategory| |#2| (QUOTE (-102)))) (|HasCategory| |#2| (QUOTE (-102))) (|HasCategory| |#2| (LIST (QUOTE -625) (QUOTE (-874)))) (|HasCategory| (-2 (|:| -4300 |#1|) (|:| -4391 |#2|)) (LIST (QUOTE -625) (QUOTE (-874)))) (|HasCategory| (-2 (|:| -4300 |#1|) (|:| -4391 |#2|)) (QUOTE (-102)))) -(-563 R -1966) +((-12 (|HasCategory| (-2 (|:| -4298 |#1|) (|:| -4437 |#2|)) (QUOTE (-1119))) (|HasCategory| (-2 (|:| -4298 |#1|) (|:| -4437 |#2|)) (LIST (QUOTE -319) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -4298) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -4437) (|devaluate| |#2|)))))) (-2755 (|HasCategory| (-2 (|:| -4298 |#1|) (|:| -4437 |#2|)) (QUOTE (-1119))) (|HasCategory| |#2| (QUOTE (-1119)))) (-2755 (|HasCategory| (-2 (|:| -4298 |#1|) (|:| -4437 |#2|)) (QUOTE (-102))) (|HasCategory| (-2 (|:| -4298 |#1|) (|:| -4437 |#2|)) (QUOTE (-1119))) (|HasCategory| |#2| (QUOTE (-102))) (|HasCategory| |#2| (QUOTE (-1119)))) (-2755 (|HasCategory| (-2 (|:| -4298 |#1|) (|:| -4437 |#2|)) (QUOTE (-1119))) (|HasCategory| (-2 (|:| -4298 |#1|) (|:| -4437 |#2|)) (LIST (QUOTE -625) (QUOTE (-874)))) (|HasCategory| |#2| (QUOTE (-1119))) (|HasCategory| |#2| (LIST (QUOTE -625) (QUOTE (-874))))) (|HasCategory| (-2 (|:| -4298 |#1|) (|:| -4437 |#2|)) (LIST (QUOTE -626) (QUOTE (-548)))) (-12 (|HasCategory| |#2| (QUOTE (-1119))) (|HasCategory| |#2| (LIST (QUOTE -319) (|devaluate| |#2|)))) (|HasCategory| (-2 (|:| -4298 |#1|) (|:| -4437 |#2|)) (QUOTE (-1119))) (|HasCategory| |#1| (QUOTE (-862))) (|HasCategory| |#2| (QUOTE (-1119))) (-2755 (|HasCategory| (-2 (|:| -4298 |#1|) (|:| -4437 |#2|)) (LIST (QUOTE -625) (QUOTE (-874)))) (|HasCategory| |#2| (LIST (QUOTE -625) (QUOTE (-874))))) (-2755 (|HasCategory| (-2 (|:| -4298 |#1|) (|:| -4437 |#2|)) (QUOTE (-102))) (|HasCategory| |#2| (QUOTE (-102)))) (|HasCategory| |#2| (QUOTE (-102))) (|HasCategory| |#2| (LIST (QUOTE -625) (QUOTE (-874)))) (|HasCategory| (-2 (|:| -4298 |#1|) (|:| -4437 |#2|)) (LIST (QUOTE -625) (QUOTE (-874)))) (|HasCategory| (-2 (|:| -4298 |#1|) (|:| -4437 |#2|)) (QUOTE (-102)))) +(-563 R -1955) ((|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 -(-564 R0 -1966 UP UPUP R) +(-564 R0 -1955 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 @@ -2194,7 +2194,7 @@ NIL NIL (-566 R) ((|constructor| (NIL "\\indented{1}{+ Author: Mike Dewar} + Date Created: November 1996 + Date Last Updated: + Basic Functions: + Related Constructors: + Also See: + AMS Classifications: + Keywords: + References: + Description: + This category implements of interval arithmetic and transcendental + functions over intervals.")) (|contains?| (((|Boolean|) $ |#1|) "\\spad{contains?(i,f)} returns \\spad{true} if \\axiom{\\spad{f}} is contained within the interval \\axiom{\\spad{i}},{} \\spad{false} otherwise.")) (|negative?| (((|Boolean|) $) "\\spad{negative?(u)} returns \\axiom{\\spad{true}} if every element of \\spad{u} is negative,{} \\axiom{\\spad{false}} otherwise.")) (|positive?| (((|Boolean|) $) "\\spad{positive?(u)} returns \\axiom{\\spad{true}} if every element of \\spad{u} is positive,{} \\axiom{\\spad{false}} otherwise.")) (|width| ((|#1| $) "\\spad{width(u)} returns \\axiom{sup(\\spad{u}) - inf(\\spad{u})}.")) (|sup| ((|#1| $) "\\spad{sup(u)} returns the supremum of \\axiom{\\spad{u}}.")) (|inf| ((|#1| $) "\\spad{inf(u)} returns the infinum of \\axiom{\\spad{u}}.")) (|qinterval| (($ |#1| |#1|) "\\spad{qinterval(inf,sup)} creates a new interval \\axiom{[\\spad{inf},{}\\spad{sup}]},{} without checking the ordering on the elements.")) (|interval| (($ (|Fraction| (|Integer|))) "\\spad{interval(f)} creates a new interval around \\spad{f}.") (($ |#1|) "\\spad{interval(f)} creates a new interval around \\spad{f}.") (($ |#1| |#1|) "\\spad{interval(inf,sup)} creates a new interval,{} either \\axiom{[\\spad{inf},{}\\spad{sup}]} if \\axiom{\\spad{inf} \\spad{<=} \\spad{sup}} or \\axiom{[\\spad{sup},{}in]} otherwise."))) -((-4161 . T) (-4455 . T) ((-4464 "*") . T) (-4456 . T) (-4457 . T) (-4459 . T)) +((-4163 . T) (-4455 . T) ((-4464 "*") . T) (-4456 . T) (-4457 . T) (-4459 . T)) NIL (-567 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."))) @@ -2204,7 +2204,7 @@ 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."))) ((-4455 . T) ((-4464 "*") . T) (-4456 . T) (-4457 . T) (-4459 . T)) NIL -(-569 R -1966) +(-569 R -1955) ((|constructor| (NIL "This package provides functions for integration,{} limited integration,{} extended integration and the risch differential equation for elemntary functions.")) (|lfextlimint| (((|Union| (|Record| (|:| |ratpart| |#2|) (|:| |coeff| |#2|)) "failed") |#2| (|Symbol|) (|Kernel| |#2|) (|List| (|Kernel| |#2|))) "\\spad{lfextlimint(f,x,k,[k1,...,kn])} returns functions \\spad{[h, c]} such that \\spad{dh/dx = f - c dk/dx}. Value \\spad{h} is looked for in a field containing \\spad{f} and \\spad{k1},{}...,{}\\spad{kn} (the \\spad{ki}\\spad{'s} must be logs).")) (|lfintegrate| (((|IntegrationResult| |#2|) |#2| (|Symbol|)) "\\spad{lfintegrate(f, x)} = \\spad{g} such that \\spad{dg/dx = f}.")) (|lfinfieldint| (((|Union| |#2| "failed") |#2| (|Symbol|)) "\\spad{lfinfieldint(f, x)} returns a function \\spad{g} such that \\spad{dg/dx = f} if \\spad{g} exists,{} \"failed\" otherwise.")) (|lflimitedint| (((|Union| (|Record| (|:| |mainpart| |#2|) (|:| |limitedlogs| (|List| (|Record| (|:| |coeff| |#2|) (|:| |logand| |#2|))))) "failed") |#2| (|Symbol|) (|List| |#2|)) "\\spad{lflimitedint(f,x,[g1,...,gn])} returns functions \\spad{[h,[[ci, gi]]]} such that the \\spad{gi}\\spad{'s} are among \\spad{[g1,...,gn]},{} and \\spad{d(h+sum(ci log(gi)))/dx = f},{} if possible,{} \"failed\" otherwise.")) (|lfextendedint| (((|Union| (|Record| (|:| |ratpart| |#2|) (|:| |coeff| |#2|)) "failed") |#2| (|Symbol|) |#2|) "\\spad{lfextendedint(f, x, g)} returns functions \\spad{[h, c]} such that \\spad{dh/dx = f - cg},{} if (\\spad{h},{} \\spad{c}) exist,{} \"failed\" otherwise."))) NIL NIL @@ -2216,7 +2216,7 @@ 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 -(-572 R -1966 L) +(-572 R -1955 L) ((|constructor| (NIL "This internal package rationalises integrands on curves of the form: \\indented{2}{\\spad{y\\^2 = a x\\^2 + b x + c}} \\indented{2}{\\spad{y\\^2 = (a x + b) / (c x + d)}} \\indented{2}{\\spad{f(x, y) = 0} where \\spad{f} has degree 1 in \\spad{x}} The rationalization is done for integration,{} limited integration,{} extended integration and the risch differential equation.")) (|palgLODE0| (((|Record| (|:| |particular| (|Union| |#2| "failed")) (|:| |basis| (|List| |#2|))) |#3| |#2| (|Kernel| |#2|) (|Kernel| |#2|) (|Kernel| |#2|) |#2| (|Fraction| (|SparseUnivariatePolynomial| |#2|))) "\\spad{palgLODE0(op,g,x,y,z,t,c)} returns the solution of \\spad{op f = g} Argument \\spad{y} is an algebraic function of \\spad{x} satisfying \\spad{f(x,y)dx = c f(t,y) dy}; \\spad{c} and \\spad{t} are rational functions of \\spad{y}.") (((|Record| (|:| |particular| (|Union| |#2| "failed")) (|:| |basis| (|List| |#2|))) |#3| |#2| (|Kernel| |#2|) (|Kernel| |#2|) |#2| (|SparseUnivariatePolynomial| |#2|)) "\\spad{palgLODE0(op, g, x, y, d, p)} returns the solution of \\spad{op f = g}. Argument \\spad{y} is an algebraic function of \\spad{x} satisfying \\spad{d(x)\\^2y(x)\\^2 = P(x)}.")) (|lift| (((|SparseUnivariatePolynomial| (|Fraction| (|SparseUnivariatePolynomial| |#2|))) (|SparseUnivariatePolynomial| |#2|) (|Kernel| |#2|)) "\\spad{lift(u,k)} \\undocumented")) (|multivariate| ((|#2| (|SparseUnivariatePolynomial| (|Fraction| (|SparseUnivariatePolynomial| |#2|))) (|Kernel| |#2|) |#2|) "\\spad{multivariate(u,k,f)} \\undocumented")) (|univariate| (((|SparseUnivariatePolynomial| (|Fraction| (|SparseUnivariatePolynomial| |#2|))) |#2| (|Kernel| |#2|) (|Kernel| |#2|) (|SparseUnivariatePolynomial| |#2|)) "\\spad{univariate(f,k,k,p)} \\undocumented")) (|palgRDE0| (((|Union| |#2| "failed") |#2| |#2| (|Kernel| |#2|) (|Kernel| |#2|) (|Mapping| (|Union| |#2| "failed") |#2| |#2| (|Symbol|)) (|Kernel| |#2|) |#2| (|Fraction| (|SparseUnivariatePolynomial| |#2|))) "\\spad{palgRDE0(f, g, x, y, foo, t, c)} returns a function \\spad{z(x,y)} such that \\spad{dz/dx + n * df/dx z(x,y) = g(x,y)} if such a \\spad{z} exists,{} and \"failed\" otherwise. Argument \\spad{y} is an algebraic function of \\spad{x} satisfying \\spad{f(x,y)dx = c f(t,y) dy}; \\spad{c} and \\spad{t} are rational functions of \\spad{y}. Argument \\spad{foo},{} called by \\spad{foo(a, b, x)},{} is a function that solves \\spad{du/dx + n * da/dx u(x) = u(x)} for an unknown \\spad{u(x)} not involving \\spad{y}.") (((|Union| |#2| "failed") |#2| |#2| (|Kernel| |#2|) (|Kernel| |#2|) (|Mapping| (|Union| |#2| "failed") |#2| |#2| (|Symbol|)) |#2| (|SparseUnivariatePolynomial| |#2|)) "\\spad{palgRDE0(f, g, x, y, foo, d, p)} returns a function \\spad{z(x,y)} such that \\spad{dz/dx + n * df/dx z(x,y) = g(x,y)} if such a \\spad{z} exists,{} and \"failed\" otherwise. Argument \\spad{y} is an algebraic function of \\spad{x} satisfying \\spad{d(x)\\^2y(x)\\^2 = P(x)}. Argument \\spad{foo},{} called by \\spad{foo(a, b, x)},{} is a function that solves \\spad{du/dx + n * da/dx u(x) = u(x)} for an unknown \\spad{u(x)} not involving \\spad{y}.")) (|palglimint0| (((|Union| (|Record| (|:| |mainpart| |#2|) (|:| |limitedlogs| (|List| (|Record| (|:| |coeff| |#2|) (|:| |logand| |#2|))))) "failed") |#2| (|Kernel| |#2|) (|Kernel| |#2|) (|List| |#2|) (|Kernel| |#2|) |#2| (|Fraction| (|SparseUnivariatePolynomial| |#2|))) "\\spad{palglimint0(f, x, y, [u1,...,un], z, t, c)} returns functions \\spad{[h,[[ci, ui]]]} such that the \\spad{ui}\\spad{'s} are among \\spad{[u1,...,un]} and \\spad{d(h + sum(ci log(ui)))/dx = f(x,y)} if such functions exist,{} and \"failed\" otherwise. Argument \\spad{y} is an algebraic function of \\spad{x} satisfying \\spad{f(x,y)dx = c f(t,y) dy}; \\spad{c} and \\spad{t} are rational functions of \\spad{y}.") (((|Union| (|Record| (|:| |mainpart| |#2|) (|:| |limitedlogs| (|List| (|Record| (|:| |coeff| |#2|) (|:| |logand| |#2|))))) "failed") |#2| (|Kernel| |#2|) (|Kernel| |#2|) (|List| |#2|) |#2| (|SparseUnivariatePolynomial| |#2|)) "\\spad{palglimint0(f, x, y, [u1,...,un], d, p)} returns functions \\spad{[h,[[ci, ui]]]} such that the \\spad{ui}\\spad{'s} are among \\spad{[u1,...,un]} and \\spad{d(h + sum(ci log(ui)))/dx = f(x,y)} if such functions exist,{} and \"failed\" otherwise. Argument \\spad{y} is an algebraic function of \\spad{x} satisfying \\spad{d(x)\\^2y(x)\\^2 = P(x)}.")) (|palgextint0| (((|Union| (|Record| (|:| |ratpart| |#2|) (|:| |coeff| |#2|)) "failed") |#2| (|Kernel| |#2|) (|Kernel| |#2|) |#2| (|Kernel| |#2|) |#2| (|Fraction| (|SparseUnivariatePolynomial| |#2|))) "\\spad{palgextint0(f, x, y, g, z, t, c)} returns functions \\spad{[h, d]} such that \\spad{dh/dx = f(x,y) - d g},{} where \\spad{y} is an algebraic function of \\spad{x} satisfying \\spad{f(x,y)dx = c f(t,y) dy},{} and \\spad{c} and \\spad{t} are rational functions of \\spad{y}. Argument \\spad{z} is a dummy variable not appearing in \\spad{f(x,y)}. The operation returns \"failed\" if no such functions exist.") (((|Union| (|Record| (|:| |ratpart| |#2|) (|:| |coeff| |#2|)) "failed") |#2| (|Kernel| |#2|) (|Kernel| |#2|) |#2| |#2| (|SparseUnivariatePolynomial| |#2|)) "\\spad{palgextint0(f, x, y, g, d, p)} returns functions \\spad{[h, c]} such that \\spad{dh/dx = f(x,y) - c g},{} where \\spad{y} is an algebraic function of \\spad{x} satisfying \\spad{d(x)\\^2 y(x)\\^2 = P(x)},{} or \"failed\" if no such functions exist.")) (|palgint0| (((|IntegrationResult| |#2|) |#2| (|Kernel| |#2|) (|Kernel| |#2|) (|Kernel| |#2|) |#2| (|Fraction| (|SparseUnivariatePolynomial| |#2|))) "\\spad{palgint0(f, x, y, z, t, c)} returns the integral of \\spad{f(x,y)dx} where \\spad{y} is an algebraic function of \\spad{x} satisfying \\spad{f(x,y)dx = c f(t,y) dy}; \\spad{c} and \\spad{t} are rational functions of \\spad{y}. Argument \\spad{z} is a dummy variable not appearing in \\spad{f(x,y)}.") (((|IntegrationResult| |#2|) |#2| (|Kernel| |#2|) (|Kernel| |#2|) |#2| (|SparseUnivariatePolynomial| |#2|)) "\\spad{palgint0(f, x, y, d, p)} returns the integral of \\spad{f(x,y)dx} where \\spad{y} is an algebraic function of \\spad{x} satisfying \\spad{d(x)\\^2 y(x)\\^2 = P(x)}."))) NIL ((|HasCategory| |#3| (LIST (QUOTE -668) (|devaluate| |#2|)))) @@ -2224,11 +2224,11 @@ 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 -(-574 -1966 UP UPUP R) +(-574 -1955 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 -(-575 -1966 UP) +(-575 -1955 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 @@ -2240,15 +2240,15 @@ NIL ((|measure| (((|Record| (|:| |measure| (|Float|)) (|:| |name| (|String|)) (|:| |explanations| (|List| (|String|))) (|:| |extra| (|Result|))) (|NumericalIntegrationProblem|) (|RoutinesTable|)) "\\spad{measure(prob,R)} is a top level ANNA function for identifying the most appropriate numerical routine from those in the routines table provided for solving the numerical integration problem defined by \\axiom{\\spad{prob}}. \\blankline It calls each \\axiom{domain} listed in \\axiom{\\spad{R}} of \\axiom{category} \\axiomType{NumericalIntegrationCategory} in turn to calculate all measures and returns the best \\spadignore{i.e.} the name of the most appropriate domain and any other relevant information.") (((|Record| (|:| |measure| (|Float|)) (|:| |name| (|String|)) (|:| |explanations| (|List| (|String|))) (|:| |extra| (|Result|))) (|NumericalIntegrationProblem|)) "\\spad{measure(prob)} is a top level ANNA function for identifying the most appropriate numerical routine for solving the numerical integration problem defined by \\axiom{\\spad{prob}}. \\blankline It calls each \\axiom{domain} of \\axiom{category} \\axiomType{NumericalIntegrationCategory} in turn to calculate all measures and returns the best \\spadignore{i.e.} the name of the most appropriate domain and any other relevant information.")) (|integrate| (((|Union| (|Result|) "failed") (|Expression| (|Float|)) (|SegmentBinding| (|OrderedCompletion| (|Float|))) (|Symbol|)) "\\spad{integrate(exp, x = a..b, numerical)} is a top level ANNA function to integrate an expression,{} {\\spad{\\tt} \\spad{exp}},{} over a given range,{} {\\spad{\\tt} a} to {\\spad{\\tt} \\spad{b}}. \\blankline It iterates over the \\axiom{domains} of \\axiomType{NumericalIntegrationCategory} to get the name and other relevant information of the the (domain of the) numerical routine likely to be the most appropriate,{} \\spadignore{i.e.} have the best \\axiom{measure}. \\blankline It then performs the integration of the given expression on that \\axiom{domain}.\\newline \\blankline Default values for the absolute and relative error are used. \\blankline It is an error if the last argument is not {\\spad{\\tt} numerical}.") (((|Union| (|Result|) "failed") (|Expression| (|Float|)) (|SegmentBinding| (|OrderedCompletion| (|Float|))) (|String|)) "\\spad{integrate(exp, x = a..b, \"numerical\")} is a top level ANNA function to integrate an expression,{} {\\spad{\\tt} \\spad{exp}},{} over a given range,{} {\\spad{\\tt} a} to {\\spad{\\tt} \\spad{b}}. \\blankline It iterates over the \\axiom{domains} of \\axiomType{NumericalIntegrationCategory} to get the name and other relevant information of the the (domain of the) numerical routine likely to be the most appropriate,{} \\spadignore{i.e.} have the best \\axiom{measure}. \\blankline It then performs the integration of the given expression on that \\axiom{domain}.\\newline \\blankline Default values for the absolute and relative error are used. \\blankline It is an error of the last argument is not {\\spad{\\tt} \"numerical\"}.") (((|Result|) (|Expression| (|Float|)) (|List| (|Segment| (|OrderedCompletion| (|Float|)))) (|Float|) (|Float|) (|RoutinesTable|)) "\\spad{integrate(exp, [a..b,c..d,...], epsabs, epsrel, routines)} is a top level ANNA function to integrate a multivariate expression,{} {\\spad{\\tt} \\spad{exp}},{} over a given set of ranges to the required absolute and relative accuracy,{} using the routines available in the RoutinesTable provided. \\blankline It iterates over the \\axiom{domains} of \\axiomType{NumericalIntegrationCategory} to get the name and other relevant information of the the (domain of the) numerical routine likely to be the most appropriate,{} \\spadignore{i.e.} have the best \\axiom{measure}. \\blankline It then performs the integration of the given expression on that \\axiom{domain}.") (((|Result|) (|Expression| (|Float|)) (|List| (|Segment| (|OrderedCompletion| (|Float|)))) (|Float|) (|Float|)) "\\spad{integrate(exp, [a..b,c..d,...], epsabs, epsrel)} is a top level ANNA function to integrate a multivariate expression,{} {\\spad{\\tt} \\spad{exp}},{} over a given set of ranges to the required absolute and relative accuracy. \\blankline It iterates over the \\axiom{domains} of \\axiomType{NumericalIntegrationCategory} to get the name and other relevant information of the the (domain of the) numerical routine likely to be the most appropriate,{} \\spadignore{i.e.} have the best \\axiom{measure}. \\blankline It then performs the integration of the given expression on that \\axiom{domain}.") (((|Result|) (|Expression| (|Float|)) (|List| (|Segment| (|OrderedCompletion| (|Float|)))) (|Float|)) "\\spad{integrate(exp, [a..b,c..d,...], epsrel)} is a top level ANNA function to integrate a multivariate expression,{} {\\spad{\\tt} \\spad{exp}},{} over a given set of ranges to the required relative accuracy. \\blankline It iterates over the \\axiom{domains} of \\axiomType{NumericalIntegrationCategory} to get the name and other relevant information of the the (domain of the) numerical routine likely to be the most appropriate,{} \\spadignore{i.e.} have the best \\axiom{measure}. \\blankline It then performs the integration of the given expression on that \\axiom{domain}. \\blankline If epsrel = 0,{} a default absolute accuracy is used.") (((|Result|) (|Expression| (|Float|)) (|List| (|Segment| (|OrderedCompletion| (|Float|))))) "\\spad{integrate(exp, [a..b,c..d,...])} is a top level ANNA function to integrate a multivariate expression,{} {\\spad{\\tt} \\spad{exp}},{} over a given set of ranges. \\blankline It iterates over the \\axiom{domains} of \\axiomType{NumericalIntegrationCategory} to get the name and other relevant information of the the (domain of the) numerical routine likely to be the most appropriate,{} \\spadignore{i.e.} have the best \\axiom{measure}. \\blankline It then performs the integration of the given expression on that \\axiom{domain}. \\blankline Default values for the absolute and relative error are used.") (((|Result|) (|Expression| (|Float|)) (|Segment| (|OrderedCompletion| (|Float|)))) "\\spad{integrate(exp, a..b)} is a top level ANNA function to integrate an expression,{} {\\spad{\\tt} \\spad{exp}},{} over a given range {\\spad{\\tt} a} to {\\spad{\\tt} \\spad{b}}. \\blankline It iterates over the \\axiom{domains} of \\axiomType{NumericalIntegrationCategory} to get the name and other relevant information of the the (domain of the) numerical routine likely to be the most appropriate,{} \\spadignore{i.e.} have the best \\axiom{measure}. \\blankline It then performs the integration of the given expression on that \\axiom{domain}. \\blankline Default values for the absolute and relative error are used.") (((|Result|) (|Expression| (|Float|)) (|Segment| (|OrderedCompletion| (|Float|))) (|Float|)) "\\spad{integrate(exp, a..b, epsrel)} is a top level ANNA function to integrate an expression,{} {\\spad{\\tt} \\spad{exp}},{} over a given range {\\spad{\\tt} a} to {\\spad{\\tt} \\spad{b}} to the required relative accuracy. \\blankline It iterates over the \\axiom{domains} of \\axiomType{NumericalIntegrationCategory} to get the name and other relevant information of the the (domain of the) numerical routine likely to be the most appropriate,{} \\spadignore{i.e.} have the best \\axiom{measure}. \\blankline It then performs the integration of the given expression on that \\axiom{domain}. \\blankline If epsrel = 0,{} a default absolute accuracy is used.") (((|Result|) (|Expression| (|Float|)) (|Segment| (|OrderedCompletion| (|Float|))) (|Float|) (|Float|)) "\\spad{integrate(exp, a..b, epsabs, epsrel)} is a top level ANNA function to integrate an expression,{} {\\spad{\\tt} \\spad{exp}},{} over a given range {\\spad{\\tt} a} to {\\spad{\\tt} \\spad{b}} to the required absolute and relative accuracy. \\blankline It iterates over the \\axiom{domains} of \\axiomType{NumericalIntegrationCategory} to get the name and other relevant information of the the (domain of the) numerical routine likely to be the most appropriate,{} \\spadignore{i.e.} have the best \\axiom{measure}. \\blankline It then performs the integration of the given expression on that \\axiom{domain}.") (((|Result|) (|NumericalIntegrationProblem|)) "\\spad{integrate(IntegrationProblem)} is a top level ANNA function to integrate an expression over a given range or ranges to the required absolute and relative accuracy. \\blankline It iterates over the \\axiom{domains} of \\axiomType{NumericalIntegrationCategory} to get the name and other relevant information of the the (domain of the) numerical routine likely to be the most appropriate,{} \\spadignore{i.e.} have the best \\axiom{measure}. \\blankline It then performs the integration of the given expression on that \\axiom{domain}.") (((|Result|) (|Expression| (|Float|)) (|Segment| (|OrderedCompletion| (|Float|))) (|Float|) (|Float|) (|RoutinesTable|)) "\\spad{integrate(exp, a..b, epsrel, routines)} is a top level ANNA function to integrate an expression,{} {\\spad{\\tt} \\spad{exp}},{} over a given range {\\spad{\\tt} a} to {\\spad{\\tt} \\spad{b}} to the required absolute and relative accuracy using the routines available in the RoutinesTable provided. \\blankline It iterates over the \\axiom{domains} of \\axiomType{NumericalIntegrationCategory} to get the name and other relevant information of the the (domain of the) numerical routine likely to be the most appropriate,{} \\spadignore{i.e.} have the best \\axiom{measure}. \\blankline It then performs the integration of the given expression on that \\axiom{domain}."))) NIL NIL -(-578 R -1966 L) +(-578 R -1955 L) ((|constructor| (NIL "This package provides functions for integration,{} limited integration,{} extended integration and the risch differential equation for pure algebraic integrands.")) (|palgLODE| (((|Record| (|:| |particular| (|Union| |#2| "failed")) (|:| |basis| (|List| |#2|))) |#3| |#2| (|Kernel| |#2|) (|Kernel| |#2|) (|Symbol|)) "\\spad{palgLODE(op, g, kx, y, x)} returns the solution of \\spad{op f = g}. \\spad{y} is an algebraic function of \\spad{x}.")) (|palgRDE| (((|Union| |#2| "failed") |#2| |#2| |#2| (|Kernel| |#2|) (|Kernel| |#2|) (|Mapping| (|Union| |#2| "failed") |#2| |#2| (|Symbol|))) "\\spad{palgRDE(nfp, f, g, x, y, foo)} returns a function \\spad{z(x,y)} such that \\spad{dz/dx + n * df/dx z(x,y) = g(x,y)} if such a \\spad{z} exists,{} \"failed\" otherwise; \\spad{y} is an algebraic function of \\spad{x}; \\spad{foo(a, b, x)} is a function that solves \\spad{du/dx + n * da/dx u(x) = u(x)} for an unknown \\spad{u(x)} not involving \\spad{y}. \\spad{nfp} is \\spad{n * df/dx}.")) (|palglimint| (((|Union| (|Record| (|:| |mainpart| |#2|) (|:| |limitedlogs| (|List| (|Record| (|:| |coeff| |#2|) (|:| |logand| |#2|))))) "failed") |#2| (|Kernel| |#2|) (|Kernel| |#2|) (|List| |#2|)) "\\spad{palglimint(f, x, y, [u1,...,un])} returns functions \\spad{[h,[[ci, ui]]]} such that the \\spad{ui}\\spad{'s} are among \\spad{[u1,...,un]} and \\spad{d(h + sum(ci log(ui)))/dx = f(x,y)} if such functions exist,{} \"failed\" otherwise; \\spad{y} is an algebraic function of \\spad{x}.")) (|palgextint| (((|Union| (|Record| (|:| |ratpart| |#2|) (|:| |coeff| |#2|)) "failed") |#2| (|Kernel| |#2|) (|Kernel| |#2|) |#2|) "\\spad{palgextint(f, x, y, g)} returns functions \\spad{[h, c]} such that \\spad{dh/dx = f(x,y) - c g},{} where \\spad{y} is an algebraic function of \\spad{x}; returns \"failed\" if no such functions exist.")) (|palgint| (((|IntegrationResult| |#2|) |#2| (|Kernel| |#2|) (|Kernel| |#2|)) "\\spad{palgint(f, x, y)} returns the integral of \\spad{f(x,y)dx} where \\spad{y} is an algebraic function of \\spad{x}."))) NIL ((|HasCategory| |#3| (LIST (QUOTE -668) (|devaluate| |#2|)))) -(-579 R -1966) +(-579 R -1955) ((|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 -626) (LIST (QUOTE -905) (QUOTE (-576))))) (|HasCategory| |#1| (LIST (QUOTE -899) (QUOTE (-576)))) (|HasCategory| |#2| (QUOTE (-1158)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -626) (LIST (QUOTE -905) (QUOTE (-576))))) (|HasCategory| |#1| (LIST (QUOTE -899) (QUOTE (-576)))) (|HasCategory| |#2| (QUOTE (-641))))) -(-580 -1966 UP) +(-580 -1955 UP) ((|constructor| (NIL "This package provides functions for the base case of the Risch algorithm.")) (|limitedint| (((|Union| (|Record| (|:| |mainpart| (|Fraction| |#2|)) (|:| |limitedlogs| (|List| (|Record| (|:| |coeff| (|Fraction| |#2|)) (|:| |logand| (|Fraction| |#2|)))))) "failed") (|Fraction| |#2|) (|List| (|Fraction| |#2|))) "\\spad{limitedint(f, [g1,...,gn])} returns fractions \\spad{[h,[[ci, gi]]]} such that the \\spad{gi}\\spad{'s} are among \\spad{[g1,...,gn]},{} \\spad{ci' = 0},{} and \\spad{(h+sum(ci log(gi)))' = f},{} if possible,{} \"failed\" otherwise.")) (|extendedint| (((|Union| (|Record| (|:| |ratpart| (|Fraction| |#2|)) (|:| |coeff| (|Fraction| |#2|))) "failed") (|Fraction| |#2|) (|Fraction| |#2|)) "\\spad{extendedint(f, g)} returns fractions \\spad{[h, c]} such that \\spad{c' = 0} and \\spad{h' = f - cg},{} if \\spad{(h, c)} exist,{} \"failed\" otherwise.")) (|infieldint| (((|Union| (|Fraction| |#2|) "failed") (|Fraction| |#2|)) "\\spad{infieldint(f)} returns \\spad{g} such that \\spad{g' = f} or \"failed\" if the integral of \\spad{f} is not a rational function.")) (|integrate| (((|IntegrationResult| (|Fraction| |#2|)) (|Fraction| |#2|)) "\\spad{integrate(f)} returns \\spad{g} such that \\spad{g' = f}."))) NIL NIL @@ -2256,27 +2256,27 @@ 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 -(-582 -1966) +(-582 -1955) ((|constructor| (NIL "This package provides functions for the integration of rational functions.")) (|extendedIntegrate| (((|Union| (|Record| (|:| |ratpart| (|Fraction| (|Polynomial| |#1|))) (|:| |coeff| (|Fraction| (|Polynomial| |#1|)))) "failed") (|Fraction| (|Polynomial| |#1|)) (|Symbol|) (|Fraction| (|Polynomial| |#1|))) "\\spad{extendedIntegrate(f, x, g)} returns fractions \\spad{[h, c]} such that \\spad{dc/dx = 0} and \\spad{dh/dx = f - cg},{} if \\spad{(h, c)} exist,{} \"failed\" otherwise.")) (|limitedIntegrate| (((|Union| (|Record| (|:| |mainpart| (|Fraction| (|Polynomial| |#1|))) (|:| |limitedlogs| (|List| (|Record| (|:| |coeff| (|Fraction| (|Polynomial| |#1|))) (|:| |logand| (|Fraction| (|Polynomial| |#1|))))))) "failed") (|Fraction| (|Polynomial| |#1|)) (|Symbol|) (|List| (|Fraction| (|Polynomial| |#1|)))) "\\spad{limitedIntegrate(f, x, [g1,...,gn])} returns fractions \\spad{[h, [[ci,gi]]]} such that the \\spad{gi}\\spad{'s} are among \\spad{[g1,...,gn]},{} \\spad{dci/dx = 0},{} and \\spad{d(h + sum(ci log(gi)))/dx = f} if possible,{} \"failed\" otherwise.")) (|infieldIntegrate| (((|Union| (|Fraction| (|Polynomial| |#1|)) "failed") (|Fraction| (|Polynomial| |#1|)) (|Symbol|)) "\\spad{infieldIntegrate(f, x)} returns a fraction \\spad{g} such that \\spad{dg/dx = f} if \\spad{g} exists,{} \"failed\" otherwise.")) (|internalIntegrate| (((|IntegrationResult| (|Fraction| (|Polynomial| |#1|))) (|Fraction| (|Polynomial| |#1|)) (|Symbol|)) "\\spad{internalIntegrate(f, x)} returns \\spad{g} such that \\spad{dg/dx = f}."))) NIL NIL (-583 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."))) -((-4161 . T) (-4455 . T) ((-4464 "*") . T) (-4456 . T) (-4457 . T) (-4459 . T)) +((-4163 . T) (-4455 . T) ((-4464 "*") . T) (-4456 . T) (-4457 . T) (-4459 . T)) NIL (-584) ((|constructor| (NIL "This package provides the implementation for the \\spadfun{solveLinearPolynomialEquation} operation over the integers. It uses a lifting technique from the package GenExEuclid")) (|solveLinearPolynomialEquation| (((|Union| (|List| (|SparseUnivariatePolynomial| (|Integer|))) "failed") (|List| (|SparseUnivariatePolynomial| (|Integer|))) (|SparseUnivariatePolynomial| (|Integer|))) "\\spad{solveLinearPolynomialEquation([f1, ..., fn], g)} (where the \\spad{fi} are relatively prime to each other) returns a list of \\spad{ai} such that \\spad{g/prod fi = sum ai/fi} or returns \"failed\" if no such list of \\spad{ai}\\spad{'s} exists."))) NIL NIL -(-585 R -1966) +(-585 R -1955) ((|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 -626) (LIST (QUOTE -905) (QUOTE (-576))))) (|HasCategory| |#1| (QUOTE (-464))) (|HasCategory| |#1| (LIST (QUOTE -899) (QUOTE (-576)))) (|HasCategory| |#2| (QUOTE (-294))) (|HasCategory| |#2| (QUOTE (-641))) (|HasCategory| |#2| (LIST (QUOTE -1057) (QUOTE (-1195))))) (-12 (|HasCategory| |#1| (QUOTE (-464))) (|HasCategory| |#2| (QUOTE (-294)))) (|HasCategory| |#1| (QUOTE (-568)))) -(-586 -1966 UP) +(-586 -1955 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 -(-587 R -1966) +(-587 R -1955) ((|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 @@ -2308,11 +2308,11 @@ NIL ((|constructor| (NIL "A package to print strings without line-feed nor carriage-return.")) (|iprint| (((|Void|) (|String|)) "\\axiom{iprint(\\spad{s})} prints \\axiom{\\spad{s}} at the current position of the cursor."))) NIL NIL -(-595 R -1966) +(-595 R -1955) ((|constructor| (NIL "This package allows a sum of logs over the roots of a polynomial to be expressed as explicit logarithms and arc tangents,{} provided that the indexing polynomial can be factored into quadratics.")) (|complexExpand| ((|#2| (|IntegrationResult| |#2|)) "\\spad{complexExpand(i)} returns the expanded complex function corresponding to \\spad{i}.")) (|expand| (((|List| |#2|) (|IntegrationResult| |#2|)) "\\spad{expand(i)} returns the list of possible real functions corresponding to \\spad{i}.")) (|split| (((|IntegrationResult| |#2|) (|IntegrationResult| |#2|)) "\\spad{split(u(x) + sum_{P(a)=0} Q(a,x))} returns \\spad{u(x) + sum_{P1(a)=0} Q(a,x) + ... + sum_{Pn(a)=0} Q(a,x)} where \\spad{P1},{}...,{}\\spad{Pn} are the factors of \\spad{P}."))) NIL NIL -(-596 E -1966) +(-596 E -1955) ((|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 @@ -2320,7 +2320,7 @@ NIL ((|constructor| (NIL "This domain provides representations for the intermediate form data structure used by the Spad elaborator.")) (|irDef| (($ (|Identifier|) (|InternalTypeForm|) $) "\\spad{irDef(f,ts,e)} returns an IR representation for a definition of a function named \\spad{f},{} with signature \\spad{ts} and body \\spad{e}.")) (|irCtor| (($ (|Identifier|) (|InternalTypeForm|)) "\\spad{irCtor(n,t)} returns an IR for a constructor reference of type designated by the type form \\spad{t}")) (|irVar| (($ (|Identifier|) (|InternalTypeForm|)) "\\spad{irVar(x,t)} returns an IR for a variable reference of type designated by the type form \\spad{t}"))) NIL NIL -(-598 -1966) +(-598 -1955) ((|constructor| (NIL "If a function \\spad{f} has an elementary integral \\spad{g},{} then \\spad{g} can be written in the form \\spad{g = h + c1 log(u1) + c2 log(u2) + ... + cn log(un)} where \\spad{h},{} which is in the same field than \\spad{f},{} is called the rational part of the integral,{} and \\spad{c1 log(u1) + ... cn log(un)} is called the logarithmic part of the integral. This domain manipulates integrals represented in that form,{} by keeping both parts separately. The logs are not explicitly computed.")) (|differentiate| ((|#1| $ (|Symbol|)) "\\spad{differentiate(ir,x)} differentiates \\spad{ir} with respect to \\spad{x}") ((|#1| $ (|Mapping| |#1| |#1|)) "\\spad{differentiate(ir,D)} differentiates \\spad{ir} with respect to the derivation \\spad{D}.")) (|integral| (($ |#1| (|Symbol|)) "\\spad{integral(f,x)} returns the formal integral of \\spad{f} with respect to \\spad{x}") (($ |#1| |#1|) "\\spad{integral(f,x)} returns the formal integral of \\spad{f} with respect to \\spad{x}")) (|elem?| (((|Boolean|) $) "\\spad{elem?(ir)} tests if an integration result is elementary over \\spad{F?}")) (|notelem| (((|List| (|Record| (|:| |integrand| |#1|) (|:| |intvar| |#1|))) $) "\\spad{notelem(ir)} returns the non-elementary part of an integration result")) (|logpart| (((|List| (|Record| (|:| |scalar| (|Fraction| (|Integer|))) (|:| |coeff| (|SparseUnivariatePolynomial| |#1|)) (|:| |logand| (|SparseUnivariatePolynomial| |#1|)))) $) "\\spad{logpart(ir)} returns the logarithmic part of an integration result")) (|ratpart| ((|#1| $) "\\spad{ratpart(ir)} returns the rational part of an integration result")) (|mkAnswer| (($ |#1| (|List| (|Record| (|:| |scalar| (|Fraction| (|Integer|))) (|:| |coeff| (|SparseUnivariatePolynomial| |#1|)) (|:| |logand| (|SparseUnivariatePolynomial| |#1|)))) (|List| (|Record| (|:| |integrand| |#1|) (|:| |intvar| |#1|)))) "\\spad{mkAnswer(r,l,ne)} creates an integration result from a rational part \\spad{r},{} a logarithmic part \\spad{l},{} and a non-elementary part \\spad{ne}."))) ((-4457 . T) (-4456 . T)) ((|HasCategory| |#1| (LIST (QUOTE -915) (QUOTE (-1195)))) (|HasCategory| |#1| (LIST (QUOTE -1057) (QUOTE (-1195))))) @@ -2351,7 +2351,7 @@ NIL (-605 |mn|) ((|constructor| (NIL "This domain implements low-level strings"))) ((-4463 . T) (-4462 . T)) -((-2781 (-12 (|HasCategory| (-145) (QUOTE (-862))) (|HasCategory| (-145) (LIST (QUOTE -319) (QUOTE (-145))))) (-12 (|HasCategory| (-145) (QUOTE (-1119))) (|HasCategory| (-145) (LIST (QUOTE -319) (QUOTE (-145)))))) (-2781 (|HasCategory| (-145) (LIST (QUOTE -625) (QUOTE (-874)))) (-12 (|HasCategory| (-145) (QUOTE (-1119))) (|HasCategory| (-145) (LIST (QUOTE -319) (QUOTE (-145)))))) (|HasCategory| (-145) (LIST (QUOTE -626) (QUOTE (-548)))) (-2781 (|HasCategory| (-145) (QUOTE (-102))) (|HasCategory| (-145) (QUOTE (-862))) (|HasCategory| (-145) (QUOTE (-1119)))) (-2781 (|HasCategory| (-145) (QUOTE (-862))) (|HasCategory| (-145) (QUOTE (-1119)))) (|HasCategory| (-145) (QUOTE (-862))) (|HasCategory| (-576) (QUOTE (-862))) (|HasCategory| (-145) (QUOTE (-1119))) (|HasCategory| (-145) (LIST (QUOTE -625) (QUOTE (-874)))) (|HasCategory| (-145) (QUOTE (-102))) (-12 (|HasCategory| (-145) (QUOTE (-1119))) (|HasCategory| (-145) (LIST (QUOTE -319) (QUOTE (-145)))))) +((-2755 (-12 (|HasCategory| (-145) (QUOTE (-862))) (|HasCategory| (-145) (LIST (QUOTE -319) (QUOTE (-145))))) (-12 (|HasCategory| (-145) (QUOTE (-1119))) (|HasCategory| (-145) (LIST (QUOTE -319) (QUOTE (-145)))))) (-2755 (|HasCategory| (-145) (LIST (QUOTE -625) (QUOTE (-874)))) (-12 (|HasCategory| (-145) (QUOTE (-1119))) (|HasCategory| (-145) (LIST (QUOTE -319) (QUOTE (-145)))))) (|HasCategory| (-145) (LIST (QUOTE -626) (QUOTE (-548)))) (-2755 (|HasCategory| (-145) (QUOTE (-102))) (|HasCategory| (-145) (QUOTE (-862))) (|HasCategory| (-145) (QUOTE (-1119)))) (-2755 (|HasCategory| (-145) (QUOTE (-862))) (|HasCategory| (-145) (QUOTE (-1119)))) (|HasCategory| (-145) (QUOTE (-862))) (|HasCategory| (-576) (QUOTE (-862))) (|HasCategory| (-145) (QUOTE (-1119))) (|HasCategory| (-145) (LIST (QUOTE -625) (QUOTE (-874)))) (|HasCategory| (-145) (QUOTE (-102))) (-12 (|HasCategory| (-145) (QUOTE (-1119))) (|HasCategory| (-145) (LIST (QUOTE -319) (QUOTE (-145)))))) (-606 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 @@ -2359,7 +2359,7 @@ NIL (-607 |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}."))) (((-4464 "*") |has| |#1| (-174)) (-4455 |has| |#1| (-568)) (-4456 . T) (-4457 . T) (-4459 . T)) -((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -419) (QUOTE (-576))))) (|HasCategory| |#1| (QUOTE (-568))) (-2781 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-568)))) (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-148))) (-12 (|HasCategory| |#1| (LIST (QUOTE -915) (QUOTE (-1195)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (QUOTE (-576)) (|devaluate| |#1|))))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (QUOTE (-576)) (|devaluate| |#1|)))) (|HasCategory| (-576) (QUOTE (-1131))) (|HasCategory| |#1| (QUOTE (-374))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-576))))) (|HasSignature| |#1| (LIST (QUOTE -3581) (LIST (|devaluate| |#1|) (QUOTE (-1195)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-576)))))) +((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -419) (QUOTE (-576))))) (|HasCategory| |#1| (QUOTE (-568))) (-2755 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-568)))) (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-148))) (-12 (|HasCategory| |#1| (LIST (QUOTE -915) (QUOTE (-1195)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (QUOTE (-576)) (|devaluate| |#1|))))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (QUOTE (-576)) (|devaluate| |#1|)))) (|HasCategory| (-576) (QUOTE (-1131))) (|HasCategory| |#1| (QUOTE (-374))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-576))))) (|HasSignature| |#1| (LIST (QUOTE -3567) (LIST (|devaluate| |#1|) (QUOTE (-1195)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-576)))))) (-608 |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.}"))) (((-4464 "*") |has| |#1| (-568)) (-4455 |has| |#1| (-568)) (-4456 . T) (-4457 . T) (-4459 . T)) @@ -2376,7 +2376,7 @@ 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 -(-612 R -1966 FG) +(-612 R -1955 FG) ((|constructor| (NIL "This package provides transformations from trigonometric functions to exponentials and logarithms,{} and back. \\spad{F} and \\spad{FG} should be the same type of function space.")) (|trigs2explogs| ((|#3| |#3| (|List| (|Kernel| |#3|)) (|List| (|Symbol|))) "\\spad{trigs2explogs(f, [k1,...,kn], [x1,...,xm])} rewrites all the trigonometric functions appearing in \\spad{f} and involving one of the \\spad{xi's} in terms of complex logarithms and exponentials. A kernel of the form \\spad{tan(u)} is expressed using \\spad{exp(u)**2} if it is one of the \\spad{ki's},{} in terms of \\spad{exp(2*u)} otherwise.")) (|explogs2trigs| (((|Complex| |#2|) |#3|) "\\spad{explogs2trigs(f)} rewrites all the complex logs and exponentials appearing in \\spad{f} in terms of trigonometric functions.")) (F2FG ((|#3| |#2|) "\\spad{F2FG(a + sqrt(-1) b)} returns \\spad{a + i b}.")) (FG2F ((|#2| |#3|) "\\spad{FG2F(a + i b)} returns \\spad{a + sqrt(-1) b}.")) (GF2FG ((|#3| (|Complex| |#2|)) "\\spad{GF2FG(a + i b)} returns \\spad{a + i b} viewed as a function with the \\spad{i} pushed down into the coefficient domain."))) NIL NIL @@ -2387,7 +2387,7 @@ NIL (-614 R |mn|) ((|constructor| (NIL "\\indented{2}{This type represents vector like objects with varying lengths} and a user-specified initial index."))) ((-4463 . T) (-4462 . T)) -((-2781 (-12 (|HasCategory| |#1| (QUOTE (-862))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1119))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|))))) (-2781 (-12 (|HasCategory| |#1| (QUOTE (-1119))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-874))))) (|HasCategory| |#1| (LIST (QUOTE -626) (QUOTE (-548)))) (-2781 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-862))) (|HasCategory| |#1| (QUOTE (-1119)))) (-2781 (|HasCategory| |#1| (QUOTE (-862))) (|HasCategory| |#1| (QUOTE (-1119)))) (|HasCategory| |#1| (QUOTE (-862))) (|HasCategory| (-576) (QUOTE (-862))) (|HasCategory| |#1| (QUOTE (-1119))) (|HasCategory| |#1| (QUOTE (-25))) (|HasCategory| |#1| (QUOTE (-23))) (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-738))) (|HasCategory| |#1| (QUOTE (-1068))) (-12 (|HasCategory| |#1| (QUOTE (-1021))) (|HasCategory| |#1| (QUOTE (-1068)))) (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-874)))) (|HasCategory| |#1| (QUOTE (-102))) (-12 (|HasCategory| |#1| (QUOTE (-1119))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|))))) +((-2755 (-12 (|HasCategory| |#1| (QUOTE (-862))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1119))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|))))) (-2755 (-12 (|HasCategory| |#1| (QUOTE (-1119))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-874))))) (|HasCategory| |#1| (LIST (QUOTE -626) (QUOTE (-548)))) (-2755 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-862))) (|HasCategory| |#1| (QUOTE (-1119)))) (-2755 (|HasCategory| |#1| (QUOTE (-862))) (|HasCategory| |#1| (QUOTE (-1119)))) (|HasCategory| |#1| (QUOTE (-862))) (|HasCategory| (-576) (QUOTE (-862))) (|HasCategory| |#1| (QUOTE (-1119))) (|HasCategory| |#1| (QUOTE (-25))) (|HasCategory| |#1| (QUOTE (-23))) (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-738))) (|HasCategory| |#1| (QUOTE (-1068))) (-12 (|HasCategory| |#1| (QUOTE (-1021))) (|HasCategory| |#1| (QUOTE (-1068)))) (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-874)))) (|HasCategory| |#1| (QUOTE (-102))) (-12 (|HasCategory| |#1| (QUOTE (-1119))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|))))) (-615 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|) $) "\\spad{entries(u)} returns a list of all the entries of aggregate \\spad{u} in no assumed order."))) NIL @@ -2406,12 +2406,12 @@ NIL NIL (-619 R A) ((|constructor| (NIL "\\indented{1}{AssociatedJordanAlgebra takes an algebra \\spad{A} and uses \\spadfun{*\\$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)."))) -((-4459 -2781 (-2697 (|has| |#2| (-378 |#1|)) (|has| |#1| (-568))) (-12 (|has| |#2| (-429 |#1|)) (|has| |#1| (-568)))) (-4457 . T) (-4456 . T)) -((-2781 (|HasCategory| |#2| (LIST (QUOTE -378) (|devaluate| |#1|))) (|HasCategory| |#2| (LIST (QUOTE -429) (|devaluate| |#1|)))) (|HasCategory| |#2| (LIST (QUOTE -429) (|devaluate| |#1|))) (-12 (|HasCategory| |#1| (QUOTE (-374))) (|HasCategory| |#2| (LIST (QUOTE -429) (|devaluate| |#1|)))) (-2781 (-12 (|HasCategory| |#1| (QUOTE (-568))) (|HasCategory| |#2| (LIST (QUOTE -378) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-568))) (|HasCategory| |#2| (LIST (QUOTE -429) (|devaluate| |#1|))))) (|HasCategory| |#2| (LIST (QUOTE -378) (|devaluate| |#1|)))) +((-4459 -2755 (-2669 (|has| |#2| (-378 |#1|)) (|has| |#1| (-568))) (-12 (|has| |#2| (-429 |#1|)) (|has| |#1| (-568)))) (-4457 . T) (-4456 . T)) +((-2755 (|HasCategory| |#2| (LIST (QUOTE -378) (|devaluate| |#1|))) (|HasCategory| |#2| (LIST (QUOTE -429) (|devaluate| |#1|)))) (|HasCategory| |#2| (LIST (QUOTE -429) (|devaluate| |#1|))) (-12 (|HasCategory| |#1| (QUOTE (-374))) (|HasCategory| |#2| (LIST (QUOTE -429) (|devaluate| |#1|)))) (-2755 (-12 (|HasCategory| |#1| (QUOTE (-568))) (|HasCategory| |#2| (LIST (QUOTE -378) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-568))) (|HasCategory| |#2| (LIST (QUOTE -429) (|devaluate| |#1|))))) (|HasCategory| |#2| (LIST (QUOTE -378) (|devaluate| |#1|)))) (-620 |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."))) ((-4462 . T) (-4463 . T)) -((-12 (|HasCategory| (-2 (|:| -4300 (-1177)) (|:| -4391 |#1|)) (QUOTE (-1119))) (|HasCategory| (-2 (|:| -4300 (-1177)) (|:| -4391 |#1|)) (LIST (QUOTE -319) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -4300) (QUOTE (-1177))) (LIST (QUOTE |:|) (QUOTE -4391) (|devaluate| |#1|)))))) (|HasCategory| (-2 (|:| -4300 (-1177)) (|:| -4391 |#1|)) (LIST (QUOTE -626) (QUOTE (-548)))) (-12 (|HasCategory| |#1| (QUOTE (-1119))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1119))) (|HasCategory| (-1177) (QUOTE (-862))) (|HasCategory| (-2 (|:| -4300 (-1177)) (|:| -4391 |#1|)) (QUOTE (-1119))) (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-874)))) (|HasCategory| (-2 (|:| -4300 (-1177)) (|:| -4391 |#1|)) (LIST (QUOTE -625) (QUOTE (-874)))) (|HasCategory| (-2 (|:| -4300 (-1177)) (|:| -4391 |#1|)) (QUOTE (-102)))) +((-12 (|HasCategory| (-2 (|:| -4298 (-1177)) (|:| -4437 |#1|)) (QUOTE (-1119))) (|HasCategory| (-2 (|:| -4298 (-1177)) (|:| -4437 |#1|)) (LIST (QUOTE -319) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -4298) (QUOTE (-1177))) (LIST (QUOTE |:|) (QUOTE -4437) (|devaluate| |#1|)))))) (|HasCategory| (-2 (|:| -4298 (-1177)) (|:| -4437 |#1|)) (LIST (QUOTE -626) (QUOTE (-548)))) (-12 (|HasCategory| |#1| (QUOTE (-1119))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1119))) (|HasCategory| (-1177) (QUOTE (-862))) (|HasCategory| (-2 (|:| -4298 (-1177)) (|:| -4437 |#1|)) (QUOTE (-1119))) (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-874)))) (|HasCategory| (-2 (|:| -4298 (-1177)) (|:| -4437 |#1|)) (LIST (QUOTE -625) (QUOTE (-874)))) (|HasCategory| (-2 (|:| -4298 (-1177)) (|:| -4437 |#1|)) (QUOTE (-102)))) (-621 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 @@ -2436,7 +2436,7 @@ 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| $) "\\spad{convert(a)} transforms a into an element of \\spad{S}."))) NIL NIL -(-627 -1966 UP) +(-627 -1955 UP) ((|constructor| (NIL "\\spadtype{Kovacic} provides a modified Kovacic\\spad{'s} algorithm for solving explicitely irreducible 2nd order linear ordinary differential equations.")) (|kovacic| (((|Union| (|SparseUnivariatePolynomial| (|Fraction| |#2|)) "failed") (|Fraction| |#2|) (|Fraction| |#2|) (|Fraction| |#2|) (|Mapping| (|Factored| |#2|) |#2|)) "\\spad{kovacic(a_0,a_1,a_2,ezfactor)} returns either \"failed\" or \\spad{P}(\\spad{u}) such that \\spad{\\$e^{\\int(-a_1/2a_2)} e^{\\int u}\\$} is a solution of \\indented{5}{\\spad{\\$a_2 y'' + a_1 y' + a0 y = 0\\$}} whenever \\spad{u} is a solution of \\spad{P u = 0}. The equation must be already irreducible over the rational functions. Argument \\spad{ezfactor} is a factorisation in \\spad{UP},{} not necessarily into irreducibles.") (((|Union| (|SparseUnivariatePolynomial| (|Fraction| |#2|)) "failed") (|Fraction| |#2|) (|Fraction| |#2|) (|Fraction| |#2|)) "\\spad{kovacic(a_0,a_1,a_2)} returns either \"failed\" or \\spad{P}(\\spad{u}) such that \\spad{\\$e^{\\int(-a_1/2a_2)} e^{\\int u}\\$} is a solution of \\indented{5}{\\spad{a_2 y'' + a_1 y' + a0 y = 0}} whenever \\spad{u} is a solution of \\spad{P u = 0}. The equation must be already irreducible over the rational functions."))) NIL NIL @@ -2464,7 +2464,7 @@ NIL ((|constructor| (NIL "LocalAlgebra produces the localization of an algebra,{} \\spadignore{i.e.} fractions whose numerators come from some \\spad{R} algebra.")) (|denom| ((|#3| $) "\\spad{denom x} returns the denominator of \\spad{x}.")) (|numer| ((|#1| $) "\\spad{numer x} returns the numerator of \\spad{x}.")) (/ (($ |#1| |#3|) "\\spad{a / d} divides the element \\spad{a} by \\spad{d}.") (($ $ |#3|) "\\spad{x / d} divides the element \\spad{x} by \\spad{d}."))) ((-4456 . T) (-4457 . T) (-4459 . T)) ((|HasCategory| |#1| (QUOTE (-860)))) -(-634 R -1966) +(-634 R -1955) ((|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 @@ -2496,18 +2496,18 @@ 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 -(-642 R -1966) +(-642 R -1955) ((|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 -(-643 |lv| -1966) +(-643 |lv| -1955) ((|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 (-644) ((|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."))) ((-4463 . T)) -((-12 (|HasCategory| (-2 (|:| -4300 (-1177)) (|:| -4391 (-52))) (QUOTE (-1119))) (|HasCategory| (-2 (|:| -4300 (-1177)) (|:| -4391 (-52))) (LIST (QUOTE -319) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -4300) (QUOTE (-1177))) (LIST (QUOTE |:|) (QUOTE -4391) (QUOTE (-52))))))) (-2781 (|HasCategory| (-2 (|:| -4300 (-1177)) (|:| -4391 (-52))) (QUOTE (-1119))) (|HasCategory| (-52) (QUOTE (-1119)))) (-2781 (|HasCategory| (-2 (|:| -4300 (-1177)) (|:| -4391 (-52))) (QUOTE (-102))) (|HasCategory| (-2 (|:| -4300 (-1177)) (|:| -4391 (-52))) (QUOTE (-1119))) (|HasCategory| (-52) (QUOTE (-102))) (|HasCategory| (-52) (QUOTE (-1119)))) (-2781 (|HasCategory| (-2 (|:| -4300 (-1177)) (|:| -4391 (-52))) (QUOTE (-1119))) (|HasCategory| (-2 (|:| -4300 (-1177)) (|:| -4391 (-52))) (LIST (QUOTE -625) (QUOTE (-874)))) (|HasCategory| (-52) (QUOTE (-1119))) (|HasCategory| (-52) (LIST (QUOTE -625) (QUOTE (-874))))) (|HasCategory| (-2 (|:| -4300 (-1177)) (|:| -4391 (-52))) (LIST (QUOTE -626) (QUOTE (-548)))) (-12 (|HasCategory| (-52) (QUOTE (-1119))) (|HasCategory| (-52) (LIST (QUOTE -319) (QUOTE (-52))))) (|HasCategory| (-1177) (QUOTE (-862))) (-2781 (|HasCategory| (-2 (|:| -4300 (-1177)) (|:| -4391 (-52))) (LIST (QUOTE -625) (QUOTE (-874)))) (|HasCategory| (-52) (LIST (QUOTE -625) (QUOTE (-874))))) (-2781 (|HasCategory| (-2 (|:| -4300 (-1177)) (|:| -4391 (-52))) (QUOTE (-102))) (|HasCategory| (-52) (QUOTE (-102)))) (|HasCategory| (-52) (QUOTE (-1119))) (|HasCategory| (-52) (QUOTE (-102))) (|HasCategory| (-52) (LIST (QUOTE -625) (QUOTE (-874)))) (|HasCategory| (-2 (|:| -4300 (-1177)) (|:| -4391 (-52))) (LIST (QUOTE -625) (QUOTE (-874)))) (|HasCategory| (-2 (|:| -4300 (-1177)) (|:| -4391 (-52))) (QUOTE (-102))) (|HasCategory| (-2 (|:| -4300 (-1177)) (|:| -4391 (-52))) (QUOTE (-1119)))) +((-12 (|HasCategory| (-2 (|:| -4298 (-1177)) (|:| -4437 (-52))) (QUOTE (-1119))) (|HasCategory| (-2 (|:| -4298 (-1177)) (|:| -4437 (-52))) (LIST (QUOTE -319) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -4298) (QUOTE (-1177))) (LIST (QUOTE |:|) (QUOTE -4437) (QUOTE (-52))))))) (-2755 (|HasCategory| (-2 (|:| -4298 (-1177)) (|:| -4437 (-52))) (QUOTE (-1119))) (|HasCategory| (-52) (QUOTE (-1119)))) (-2755 (|HasCategory| (-2 (|:| -4298 (-1177)) (|:| -4437 (-52))) (QUOTE (-102))) (|HasCategory| (-2 (|:| -4298 (-1177)) (|:| -4437 (-52))) (QUOTE (-1119))) (|HasCategory| (-52) (QUOTE (-102))) (|HasCategory| (-52) (QUOTE (-1119)))) (-2755 (|HasCategory| (-2 (|:| -4298 (-1177)) (|:| -4437 (-52))) (QUOTE (-1119))) (|HasCategory| (-2 (|:| -4298 (-1177)) (|:| -4437 (-52))) (LIST (QUOTE -625) (QUOTE (-874)))) (|HasCategory| (-52) (QUOTE (-1119))) (|HasCategory| (-52) (LIST (QUOTE -625) (QUOTE (-874))))) (|HasCategory| (-2 (|:| -4298 (-1177)) (|:| -4437 (-52))) (LIST (QUOTE -626) (QUOTE (-548)))) (-12 (|HasCategory| (-52) (QUOTE (-1119))) (|HasCategory| (-52) (LIST (QUOTE -319) (QUOTE (-52))))) (|HasCategory| (-1177) (QUOTE (-862))) (-2755 (|HasCategory| (-2 (|:| -4298 (-1177)) (|:| -4437 (-52))) (LIST (QUOTE -625) (QUOTE (-874)))) (|HasCategory| (-52) (LIST (QUOTE -625) (QUOTE (-874))))) (-2755 (|HasCategory| (-2 (|:| -4298 (-1177)) (|:| -4437 (-52))) (QUOTE (-102))) (|HasCategory| (-52) (QUOTE (-102)))) (|HasCategory| (-52) (QUOTE (-1119))) (|HasCategory| (-52) (QUOTE (-102))) (|HasCategory| (-52) (LIST (QUOTE -625) (QUOTE (-874)))) (|HasCategory| (-2 (|:| -4298 (-1177)) (|:| -4437 (-52))) (LIST (QUOTE -625) (QUOTE (-874)))) (|HasCategory| (-2 (|:| -4298 (-1177)) (|:| -4437 (-52))) (QUOTE (-102))) (|HasCategory| (-2 (|:| -4298 (-1177)) (|:| -4437 (-52))) (QUOTE (-1119)))) (-645 S R) ((|constructor| (NIL "\\axiom{JacobiIdentity} means that \\axiom{[\\spad{x},{}[\\spad{y},{}\\spad{z}]]+[\\spad{y},{}[\\spad{z},{}\\spad{x}]]+[\\spad{z},{}[\\spad{x},{}\\spad{y}]] = 0} holds.")) (/ (($ $ |#2|) "\\axiom{\\spad{x/r}} returns the division of \\axiom{\\spad{x}} by \\axiom{\\spad{r}}.")) (|construct| (($ $ $) "\\axiom{construct(\\spad{x},{}\\spad{y})} returns the Lie bracket of \\axiom{\\spad{x}} and \\axiom{\\spad{y}}."))) NIL @@ -2518,8 +2518,8 @@ NIL NIL (-647 R A) ((|constructor| (NIL "AssociatedLieAlgebra takes an algebra \\spad{A} and uses \\spadfun{*\\$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)."))) -((-4459 -2781 (-2697 (|has| |#2| (-378 |#1|)) (|has| |#1| (-568))) (-12 (|has| |#2| (-429 |#1|)) (|has| |#1| (-568)))) (-4457 . T) (-4456 . T)) -((-2781 (|HasCategory| |#2| (LIST (QUOTE -378) (|devaluate| |#1|))) (|HasCategory| |#2| (LIST (QUOTE -429) (|devaluate| |#1|)))) (|HasCategory| |#2| (LIST (QUOTE -429) (|devaluate| |#1|))) (-12 (|HasCategory| |#1| (QUOTE (-374))) (|HasCategory| |#2| (LIST (QUOTE -429) (|devaluate| |#1|)))) (-2781 (-12 (|HasCategory| |#1| (QUOTE (-568))) (|HasCategory| |#2| (LIST (QUOTE -378) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-568))) (|HasCategory| |#2| (LIST (QUOTE -429) (|devaluate| |#1|))))) (|HasCategory| |#2| (LIST (QUOTE -378) (|devaluate| |#1|)))) +((-4459 -2755 (-2669 (|has| |#2| (-378 |#1|)) (|has| |#1| (-568))) (-12 (|has| |#2| (-429 |#1|)) (|has| |#1| (-568)))) (-4457 . T) (-4456 . T)) +((-2755 (|HasCategory| |#2| (LIST (QUOTE -378) (|devaluate| |#1|))) (|HasCategory| |#2| (LIST (QUOTE -429) (|devaluate| |#1|)))) (|HasCategory| |#2| (LIST (QUOTE -429) (|devaluate| |#1|))) (-12 (|HasCategory| |#1| (QUOTE (-374))) (|HasCategory| |#2| (LIST (QUOTE -429) (|devaluate| |#1|)))) (-2755 (-12 (|HasCategory| |#1| (QUOTE (-568))) (|HasCategory| |#2| (LIST (QUOTE -378) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-568))) (|HasCategory| |#2| (LIST (QUOTE -429) (|devaluate| |#1|))))) (|HasCategory| |#2| (LIST (QUOTE -378) (|devaluate| |#1|)))) (-648 R FE) ((|constructor| (NIL "PowerSeriesLimitPackage implements limits of expressions in one or more variables as one of the variables approaches a limiting value. Included are two-sided limits,{} left- and right- hand limits,{} and limits at plus or minus infinity.")) (|complexLimit| (((|Union| (|OnePointCompletion| |#2|) "failed") |#2| (|Equation| (|OnePointCompletion| |#2|))) "\\spad{complexLimit(f(x),x = a)} computes the complex limit \\spad{lim(x -> a,f(x))}.")) (|limit| (((|Union| (|OrderedCompletion| |#2|) "failed") |#2| (|Equation| |#2|) (|String|)) "\\spad{limit(f(x),x=a,\"left\")} computes the left hand real limit \\spad{lim(x -> a-,f(x))}; \\spad{limit(f(x),x=a,\"right\")} computes the right hand real limit \\spad{lim(x -> a+,f(x))}.") (((|Union| (|OrderedCompletion| |#2|) (|Record| (|:| |leftHandLimit| (|Union| (|OrderedCompletion| |#2|) "failed")) (|:| |rightHandLimit| (|Union| (|OrderedCompletion| |#2|) "failed"))) "failed") |#2| (|Equation| (|OrderedCompletion| |#2|))) "\\spad{limit(f(x),x = a)} computes the real limit \\spad{lim(x -> a,f(x))}."))) NIL @@ -2531,7 +2531,7 @@ NIL (-650 S R) ((|constructor| (NIL "Test for linear dependence.")) (|solveLinear| (((|Union| (|Vector| (|Fraction| |#1|)) "failed") (|Vector| |#2|) |#2|) "\\spad{solveLinear([v1,...,vn], u)} returns \\spad{[c1,...,cn]} such that \\spad{c1*v1 + ... + cn*vn = u},{} \"failed\" if no such \\spad{ci}\\spad{'s} exist in the quotient field of \\spad{S}.") (((|Union| (|Vector| |#1|) "failed") (|Vector| |#2|) |#2|) "\\spad{solveLinear([v1,...,vn], u)} returns \\spad{[c1,...,cn]} such that \\spad{c1*v1 + ... + cn*vn = u},{} \"failed\" if no such \\spad{ci}\\spad{'s} exist in \\spad{S}.")) (|linearDependence| (((|Union| (|Vector| |#1|) "failed") (|Vector| |#2|)) "\\spad{linearDependence([v1,...,vn])} returns \\spad{[c1,...,cn]} if \\spad{c1*v1 + ... + cn*vn = 0} and not all the \\spad{ci}\\spad{'s} are 0,{} \"failed\" if the \\spad{vi}\\spad{'s} are linearly independent over \\spad{S}.")) (|linearlyDependent?| (((|Boolean|) (|Vector| |#2|)) "\\spad{linearlyDependent?([v1,...,vn])} returns \\spad{true} if the \\spad{vi}\\spad{'s} are linearly dependent over \\spad{S},{} \\spad{false} otherwise."))) NIL -((-2684 (|HasCategory| |#1| (QUOTE (-374)))) (|HasCategory| |#1| (QUOTE (-374)))) +((-2658 (|HasCategory| |#1| (QUOTE (-374)))) (|HasCategory| |#1| (QUOTE (-374)))) (-651 R) ((|constructor| (NIL "An extension of left-module with an explicit linear dependence test.")) (|reducedSystem| (((|Record| (|:| |mat| (|Matrix| |#1|)) (|:| |vec| (|Vector| |#1|))) (|Matrix| $) (|Vector| $)) "\\spad{reducedSystem(A, v)} returns a matrix \\spad{B} and a vector \\spad{w} such that \\spad{A x = v} and \\spad{B x = w} have the same solutions in \\spad{R}.") (((|Matrix| |#1|) (|Matrix| $)) "\\spad{reducedSystem(A)} returns a matrix \\spad{B} such that \\spad{A x = 0} and \\spad{B x = 0} have the same solutions in \\spad{R}.")) (|leftReducedSystem| (((|Record| (|:| |mat| (|Matrix| |#1|)) (|:| |vec| (|Vector| |#1|))) (|Vector| $) $) "\\spad{reducedSystem([v1,...,vn],u)} returns a matrix \\spad{M} with coefficients in \\spad{R} and a vector \\spad{w} such that the system of equations \\spad{c1*v1 + ... + cn*vn = u} has the same solution as \\spad{c * M = w} where \\spad{c} is the row vector \\spad{[c1,...cn]}.") (((|Matrix| |#1|) (|Vector| $)) "\\spad{leftReducedSystem [v1,...,vn]} returns a matrix \\spad{M} with coefficients in \\spad{R} such that the system of equations \\spad{c1*v1 + ... + cn*vn = 0\\$\\%} has the same solution as \\spad{c * M = 0} where \\spad{c} is the row vector \\spad{[c1,...cn]}."))) NIL @@ -2555,7 +2555,7 @@ NIL (-656 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."))) ((-4463 . T) (-4462 . T)) -((-2781 (-12 (|HasCategory| |#1| (QUOTE (-862))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1119))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|))))) (-2781 (-12 (|HasCategory| |#1| (QUOTE (-1119))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-874))))) (|HasCategory| |#1| (LIST (QUOTE -626) (QUOTE (-548)))) (-2781 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-862))) (|HasCategory| |#1| (QUOTE (-1119)))) (-2781 (|HasCategory| |#1| (QUOTE (-862))) (|HasCategory| |#1| (QUOTE (-1119)))) (|HasCategory| |#1| (QUOTE (-862))) (|HasCategory| |#1| (QUOTE (-840))) (|HasCategory| (-576) (QUOTE (-862))) (|HasCategory| |#1| (QUOTE (-1119))) (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-874)))) (|HasCategory| |#1| (QUOTE (-102))) (-12 (|HasCategory| |#1| (QUOTE (-1119))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|))))) +((-2755 (-12 (|HasCategory| |#1| (QUOTE (-862))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1119))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|))))) (-2755 (-12 (|HasCategory| |#1| (QUOTE (-1119))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-874))))) (|HasCategory| |#1| (LIST (QUOTE -626) (QUOTE (-548)))) (-2755 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-862))) (|HasCategory| |#1| (QUOTE (-1119)))) (-2755 (|HasCategory| |#1| (QUOTE (-862))) (|HasCategory| |#1| (QUOTE (-1119)))) (|HasCategory| |#1| (QUOTE (-862))) (|HasCategory| |#1| (QUOTE (-840))) (|HasCategory| (-576) (QUOTE (-862))) (|HasCategory| |#1| (QUOTE (-1119))) (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-874)))) (|HasCategory| |#1| (QUOTE (-102))) (-12 (|HasCategory| |#1| (QUOTE (-1119))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|))))) (-657 T$) ((|constructor| (NIL "This domain represents AST for Spad literals."))) NIL @@ -2567,7 +2567,7 @@ NIL (-659 S) ((|substitute| (($ |#1| |#1| $) "\\spad{substitute(x,y,d)} replace \\spad{x}\\spad{'s} with \\spad{y}\\spad{'s} in dictionary \\spad{d}.")) (|duplicates?| (((|Boolean|) $) "\\spad{duplicates?(d)} tests if dictionary \\spad{d} has duplicate entries."))) ((-4462 . T) (-4463 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1119))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1119))) (-2781 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-1119)))) (-2781 (-12 (|HasCategory| |#1| (QUOTE (-1119))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-874))))) (|HasCategory| |#1| (LIST (QUOTE -626) (QUOTE (-548)))) (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-874)))) (|HasCategory| |#1| (QUOTE (-102)))) +((-12 (|HasCategory| |#1| (QUOTE (-1119))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1119))) (-2755 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-1119)))) (-2755 (-12 (|HasCategory| |#1| (QUOTE (-1119))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-874))))) (|HasCategory| |#1| (LIST (QUOTE -626) (QUOTE (-548)))) (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-874)))) (|HasCategory| |#1| (QUOTE (-102)))) (-660 R) ((|constructor| (NIL "The category of left modules over an \\spad{rng} (ring not necessarily with unit). This is an abelian group which supports left multiplation by elements of the \\spad{rng}. \\blankline"))) NIL @@ -2584,7 +2584,7 @@ NIL ((|constructor| (NIL "A linear aggregate is an aggregate whose elements are indexed by integers. Examples of linear aggregates are strings,{} lists,{} and arrays. Most of the exported operations for linear aggregates are non-destructive but are not always efficient for a particular aggregate. For example,{} \\spadfun{concat} of two lists needs only to copy its first argument,{} whereas \\spadfun{concat} of two arrays needs to copy both arguments. Most of the operations exported here apply to infinite objects (\\spadignore{e.g.} streams) as well to finite ones. For finite linear aggregates,{} see \\spadtype{FiniteLinearAggregate}.")) (|setelt| ((|#1| $ (|UniversalSegment| (|Integer|)) |#1|) "\\spad{setelt(u,i..j,x)} (also written: \\axiom{\\spad{u}(\\spad{i}..\\spad{j}) \\spad{:=} \\spad{x}}) destructively replaces each element in the segment \\axiom{\\spad{u}(\\spad{i}..\\spad{j})} by \\spad{x}. The value \\spad{x} is returned. Note: \\spad{u} is destructively change so that \\axiom{\\spad{u}.\\spad{k} \\spad{:=} \\spad{x} for \\spad{k} in \\spad{i}..\\spad{j}}; its length remains unchanged.")) (|insert| (($ $ $ (|Integer|)) "\\spad{insert(v,u,k)} returns a copy of \\spad{u} having \\spad{v} inserted beginning at the \\axiom{\\spad{i}}th element. Note: \\axiom{insert(\\spad{v},{}\\spad{u},{}\\spad{k}) = concat( \\spad{u}(0..\\spad{k}-1),{} \\spad{v},{} \\spad{u}(\\spad{k}..) )}.") (($ |#1| $ (|Integer|)) "\\spad{insert(x,u,i)} returns a copy of \\spad{u} having \\spad{x} as its \\axiom{\\spad{i}}th element. Note: \\axiom{insert(\\spad{x},{}a,{}\\spad{k}) = concat(concat(a(0..\\spad{k}-1),{}\\spad{x}),{}a(\\spad{k}..))}.")) (|delete| (($ $ (|UniversalSegment| (|Integer|))) "\\spad{delete(u,i..j)} returns a copy of \\spad{u} with the \\axiom{\\spad{i}}th through \\axiom{\\spad{j}}th element deleted. Note: \\axiom{delete(a,{}\\spad{i}..\\spad{j}) = concat(a(0..\\spad{i}-1),{}a(\\spad{j+1}..))}.") (($ $ (|Integer|)) "\\spad{delete(u,i)} returns a copy of \\spad{u} with the \\axiom{\\spad{i}}th element deleted. Note: for lists,{} \\axiom{delete(a,{}\\spad{i}) \\spad{==} concat(a(0..\\spad{i} - 1),{}a(\\spad{i} + 1,{}..))}.")) (|map| (($ (|Mapping| |#1| |#1| |#1|) $ $) "\\spad{map(f,u,v)} returns a new collection \\spad{w} with elements \\axiom{\\spad{z} = \\spad{f}(\\spad{x},{}\\spad{y})} for corresponding elements \\spad{x} and \\spad{y} from \\spad{u} and \\spad{v}. Note: for linear aggregates,{} \\axiom{\\spad{w}.\\spad{i} = \\spad{f}(\\spad{u}.\\spad{i},{}\\spad{v}.\\spad{i})}.")) (|concat| (($ (|List| $)) "\\spad{concat(u)},{} where \\spad{u} is a lists of aggregates \\axiom{[a,{}\\spad{b},{}...,{}\\spad{c}]},{} returns a single aggregate consisting of the elements of \\axiom{a} followed by those of \\spad{b} followed ... by the elements of \\spad{c}. Note: \\axiom{concat(a,{}\\spad{b},{}...,{}\\spad{c}) = concat(a,{}concat(\\spad{b},{}...,{}\\spad{c}))}.") (($ $ $) "\\spad{concat(u,v)} returns an aggregate consisting of the elements of \\spad{u} followed by the elements of \\spad{v}. Note: if \\axiom{\\spad{w} = concat(\\spad{u},{}\\spad{v})} then \\axiom{\\spad{w}.\\spad{i} = \\spad{u}.\\spad{i} for \\spad{i} in indices \\spad{u}} and \\axiom{\\spad{w}.(\\spad{j} + maxIndex \\spad{u}) = \\spad{v}.\\spad{j} for \\spad{j} in indices \\spad{v}}.") (($ |#1| $) "\\spad{concat(x,u)} returns aggregate \\spad{u} with additional element at the front. Note: for lists: \\axiom{concat(\\spad{x},{}\\spad{u}) \\spad{==} concat([\\spad{x}],{}\\spad{u})}.") (($ $ |#1|) "\\spad{concat(u,x)} returns aggregate \\spad{u} with additional element \\spad{x} at the end. Note: for lists,{} \\axiom{concat(\\spad{u},{}\\spad{x}) \\spad{==} concat(\\spad{u},{}[\\spad{x}])}")) (|new| (($ (|NonNegativeInteger|) |#1|) "\\spad{new(n,x)} returns \\axiom{fill!(new \\spad{n},{}\\spad{x})}."))) NIL NIL -(-664 R -1966 L) +(-664 R -1955 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 @@ -2604,11 +2604,11 @@ NIL ((|constructor| (NIL "\\spad{LinearOrdinaryDifferentialOperatorCategory} is the category of differential operators with coefficients in a ring A with a given derivation. Multiplication of operators corresponds to functional composition: \\indented{4}{\\spad{(L1 * L2).(f) = L1 L2 f}}")) (|directSum| (($ $ $) "\\spad{directSum(a,b)} computes an operator \\spad{c} of minimal order such that the nullspace of \\spad{c} is generated by all the sums of a solution of \\spad{a} by a solution of \\spad{b}.")) (|symmetricSquare| (($ $) "\\spad{symmetricSquare(a)} computes \\spad{symmetricProduct(a,a)} using a more efficient method.")) (|symmetricPower| (($ $ (|NonNegativeInteger|)) "\\spad{symmetricPower(a,n)} computes an operator \\spad{c} of minimal order such that the nullspace of \\spad{c} is generated by all the products of \\spad{n} solutions of \\spad{a}.")) (|symmetricProduct| (($ $ $) "\\spad{symmetricProduct(a,b)} computes an operator \\spad{c} of minimal order such that the nullspace of \\spad{c} is generated by all the products of a solution of \\spad{a} by a solution of \\spad{b}.")) (|adjoint| (($ $) "\\spad{adjoint(a)} returns the adjoint operator of a.")) (D (($) "\\spad{D()} provides the operator corresponding to a derivation in the ring \\spad{A}."))) ((-4456 . T) (-4457 . T) (-4459 . T)) NIL -(-669 -1966 UP) +(-669 -1955 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)))) -(-670 A -4138) +(-670 A -3801) ((|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}}"))) ((-4456 . T) (-4457 . T) (-4459 . T)) ((|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (LIST (QUOTE -1057) (LIST (QUOTE -419) (QUOTE (-576))))) (|HasCategory| |#1| (LIST (QUOTE -1057) (QUOTE (-576)))) (|HasCategory| |#1| (QUOTE (-568))) (|HasCategory| |#1| (QUOTE (-464))) (|HasCategory| |#1| (QUOTE (-374)))) @@ -2644,11 +2644,11 @@ 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}."))) ((-4463 . T) (-4462 . T)) NIL -(-679 -1966) +(-679 -1955) ((|constructor| (NIL "This package solves linear system in the matrix form \\spad{AX = B}. It is essentially a particular instantiation of the package \\spadtype{LinearSystemMatrixPackage} for Matrix and Vector. This package\\spad{'s} existence makes it easier to use \\spadfun{solve} in the AXIOM interpreter.")) (|rank| (((|NonNegativeInteger|) (|Matrix| |#1|) (|Vector| |#1|)) "\\spad{rank(A,B)} computes the rank of the complete matrix \\spad{(A|B)} of the linear system \\spad{AX = B}.")) (|hasSolution?| (((|Boolean|) (|Matrix| |#1|) (|Vector| |#1|)) "\\spad{hasSolution?(A,B)} tests if the linear system \\spad{AX = B} has a solution.")) (|particularSolution| (((|Union| (|Vector| |#1|) "failed") (|Matrix| |#1|) (|Vector| |#1|)) "\\spad{particularSolution(A,B)} finds a particular solution of the linear system \\spad{AX = B}.")) (|solve| (((|List| (|Record| (|:| |particular| (|Union| (|Vector| |#1|) "failed")) (|:| |basis| (|List| (|Vector| |#1|))))) (|List| (|List| |#1|)) (|List| (|Vector| |#1|))) "\\spad{solve(A,LB)} finds a particular soln of the systems \\spad{AX = B} and a basis of the associated homogeneous systems \\spad{AX = 0} where \\spad{B} varies in the list of column vectors \\spad{LB}.") (((|List| (|Record| (|:| |particular| (|Union| (|Vector| |#1|) "failed")) (|:| |basis| (|List| (|Vector| |#1|))))) (|Matrix| |#1|) (|List| (|Vector| |#1|))) "\\spad{solve(A,LB)} finds a particular soln of the systems \\spad{AX = B} and a basis of the associated homogeneous systems \\spad{AX = 0} where \\spad{B} varies in the list of column vectors \\spad{LB}.") (((|Record| (|:| |particular| (|Union| (|Vector| |#1|) "failed")) (|:| |basis| (|List| (|Vector| |#1|)))) (|List| (|List| |#1|)) (|Vector| |#1|)) "\\spad{solve(A,B)} finds a particular solution of the system \\spad{AX = B} and a basis of the associated homogeneous system \\spad{AX = 0}.") (((|Record| (|:| |particular| (|Union| (|Vector| |#1|) "failed")) (|:| |basis| (|List| (|Vector| |#1|)))) (|Matrix| |#1|) (|Vector| |#1|)) "\\spad{solve(A,B)} finds a particular solution of the system \\spad{AX = B} and a basis of the associated homogeneous system \\spad{AX = 0}."))) NIL NIL -(-680 -1966 |Row| |Col| M) +(-680 -1955 |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 @@ -2659,7 +2659,7 @@ NIL (-682 |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."))) ((-4459 . T) (-4462 . T) (-4456 . T) (-4457 . T)) -((|HasCategory| |#2| (LIST (QUOTE -915) (QUOTE (-1195)))) (|HasCategory| |#2| (LIST (QUOTE -917) (QUOTE (-1195)))) (|HasCategory| |#2| (QUOTE (-238))) (|HasCategory| |#2| (QUOTE (-237))) (|HasAttribute| |#2| (QUOTE (-4464 "*"))) (|HasCategory| |#2| (LIST (QUOTE -651) (QUOTE (-576)))) (|HasCategory| |#2| (LIST (QUOTE -1057) (LIST (QUOTE -419) (QUOTE (-576))))) (|HasCategory| |#2| (LIST (QUOTE -1057) (QUOTE (-576)))) (-2781 (-12 (|HasCategory| |#2| (QUOTE (-238))) (|HasCategory| |#2| (LIST (QUOTE -319) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-1119))) (|HasCategory| |#2| (LIST (QUOTE -319) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (LIST (QUOTE -319) (|devaluate| |#2|))) (|HasCategory| |#2| (LIST (QUOTE -651) (QUOTE (-576))))) (-12 (|HasCategory| |#2| (LIST (QUOTE -319) (|devaluate| |#2|))) (|HasCategory| |#2| (LIST (QUOTE -915) (QUOTE (-1195)))))) (|HasCategory| |#2| (QUOTE (-317))) (|HasCategory| |#2| (QUOTE (-1119))) (|HasCategory| |#2| (QUOTE (-374))) (|HasCategory| |#2| (QUOTE (-568))) (-2781 (|HasAttribute| |#2| (QUOTE (-4464 "*"))) (|HasCategory| |#2| (LIST (QUOTE -915) (QUOTE (-1195)))) (|HasCategory| |#2| (QUOTE (-238)))) (|HasCategory| |#2| (LIST (QUOTE -625) (QUOTE (-874)))) (|HasCategory| |#2| (QUOTE (-102))) (-12 (|HasCategory| |#2| (QUOTE (-1119))) (|HasCategory| |#2| (LIST (QUOTE -319) (|devaluate| |#2|)))) (|HasCategory| |#2| (QUOTE (-174)))) +((|HasCategory| |#2| (LIST (QUOTE -915) (QUOTE (-1195)))) (|HasCategory| |#2| (LIST (QUOTE -917) (QUOTE (-1195)))) (|HasCategory| |#2| (QUOTE (-238))) (|HasCategory| |#2| (QUOTE (-237))) (|HasAttribute| |#2| (QUOTE (-4464 "*"))) (|HasCategory| |#2| (LIST (QUOTE -651) (QUOTE (-576)))) (|HasCategory| |#2| (LIST (QUOTE -1057) (LIST (QUOTE -419) (QUOTE (-576))))) (|HasCategory| |#2| (LIST (QUOTE -1057) (QUOTE (-576)))) (-2755 (-12 (|HasCategory| |#2| (QUOTE (-238))) (|HasCategory| |#2| (LIST (QUOTE -319) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-1119))) (|HasCategory| |#2| (LIST (QUOTE -319) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (LIST (QUOTE -319) (|devaluate| |#2|))) (|HasCategory| |#2| (LIST (QUOTE -651) (QUOTE (-576))))) (-12 (|HasCategory| |#2| (LIST (QUOTE -319) (|devaluate| |#2|))) (|HasCategory| |#2| (LIST (QUOTE -915) (QUOTE (-1195)))))) (|HasCategory| |#2| (QUOTE (-317))) (|HasCategory| |#2| (QUOTE (-1119))) (|HasCategory| |#2| (QUOTE (-374))) (|HasCategory| |#2| (QUOTE (-568))) (-2755 (|HasAttribute| |#2| (QUOTE (-4464 "*"))) (|HasCategory| |#2| (LIST (QUOTE -915) (QUOTE (-1195)))) (|HasCategory| |#2| (QUOTE (-238)))) (|HasCategory| |#2| (LIST (QUOTE -625) (QUOTE (-874)))) (|HasCategory| |#2| (QUOTE (-102))) (-12 (|HasCategory| |#2| (QUOTE (-1119))) (|HasCategory| |#2| (LIST (QUOTE -319) (|devaluate| |#2|)))) (|HasCategory| |#2| (QUOTE (-174)))) (-683) ((|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 @@ -2679,7 +2679,7 @@ NIL (-687 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 -((-2781 (-12 (|HasCategory| |#1| (QUOTE (-1068))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1119))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|))))) (|HasCategory| |#1| (QUOTE (-1119))) (-2781 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-1119)))) (-2781 (-12 (|HasCategory| |#1| (QUOTE (-1119))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-874))))) (|HasCategory| |#1| (QUOTE (-1068))) (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-874)))) (|HasCategory| |#1| (QUOTE (-102))) (-12 (|HasCategory| |#1| (QUOTE (-1119))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|))))) +((-2755 (-12 (|HasCategory| |#1| (QUOTE (-1068))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1119))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|))))) (|HasCategory| |#1| (QUOTE (-1119))) (-2755 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-1119)))) (-2755 (-12 (|HasCategory| |#1| (QUOTE (-1119))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-874))))) (|HasCategory| |#1| (QUOTE (-1068))) (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-874)))) (|HasCategory| |#1| (QUOTE (-102))) (-12 (|HasCategory| |#1| (QUOTE (-1119))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|))))) (-688) ((|constructor| (NIL "This domain represents the syntax of a macro definition.")) (|body| (((|SpadAst|) $) "\\spad{body(m)} returns the right hand side of the definition \\spad{`m'}.")) (|head| (((|HeadAst|) $) "\\spad{head(m)} returns the head of the macro definition \\spad{`m'}. This is a list of identifiers starting with the name of the macro followed by the name of the parameters,{} if any."))) NIL @@ -2735,7 +2735,7 @@ NIL (-701 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."))) ((-4462 . T) (-4463 . T)) -((-2781 (-12 (|HasCategory| |#1| (QUOTE (-374))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1119))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|))))) (|HasCategory| |#1| (QUOTE (-1119))) (-2781 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-1119)))) (-2781 (-12 (|HasCategory| |#1| (QUOTE (-1119))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-874))))) (|HasCategory| |#1| (LIST (QUOTE -626) (QUOTE (-548)))) (|HasCategory| |#1| (QUOTE (-317))) (|HasCategory| |#1| (QUOTE (-568))) (|HasAttribute| |#1| (QUOTE (-4464 "*"))) (|HasCategory| |#1| (QUOTE (-374))) (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-874)))) (|HasCategory| |#1| (QUOTE (-102))) (-12 (|HasCategory| |#1| (QUOTE (-1119))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|))))) +((-2755 (-12 (|HasCategory| |#1| (QUOTE (-374))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1119))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|))))) (|HasCategory| |#1| (QUOTE (-1119))) (-2755 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-1119)))) (-2755 (-12 (|HasCategory| |#1| (QUOTE (-1119))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-874))))) (|HasCategory| |#1| (LIST (QUOTE -626) (QUOTE (-548)))) (|HasCategory| |#1| (QUOTE (-317))) (|HasCategory| |#1| (QUOTE (-568))) (|HasAttribute| |#1| (QUOTE (-4464 "*"))) (|HasCategory| |#1| (QUOTE (-374))) (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-874)))) (|HasCategory| |#1| (QUOTE (-102))) (-12 (|HasCategory| |#1| (QUOTE (-1119))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|))))) (-702 R) ((|constructor| (NIL "This package provides standard arithmetic operations on matrices. The functions in this package store the results of computations in existing matrices,{} rather than creating new matrices. This package works only for matrices of type Matrix and uses the internal representation of this type.")) (** (((|Matrix| |#1|) (|Matrix| |#1|) (|NonNegativeInteger|)) "\\spad{x ** n} computes the \\spad{n}-th power of a square matrix. The power \\spad{n} is assumed greater than 1.")) (|power!| (((|Matrix| |#1|) (|Matrix| |#1|) (|Matrix| |#1|) (|Matrix| |#1|) (|Matrix| |#1|) (|NonNegativeInteger|)) "\\spad{power!(a,b,c,m,n)} computes \\spad{m} \\spad{**} \\spad{n} and stores the result in \\spad{a}. The matrices \\spad{b} and \\spad{c} are used to store intermediate results. Error: if \\spad{a},{} \\spad{b},{} \\spad{c},{} and \\spad{m} are not square and of the same dimensions.")) (|times!| (((|Matrix| |#1|) (|Matrix| |#1|) (|Matrix| |#1|) (|Matrix| |#1|)) "\\spad{times!(c,a,b)} computes the matrix product \\spad{a * b} and stores the result in the matrix \\spad{c}. Error: if \\spad{a},{} \\spad{b},{} and \\spad{c} do not have compatible dimensions.")) (|rightScalarTimes!| (((|Matrix| |#1|) (|Matrix| |#1|) (|Matrix| |#1|) |#1|) "\\spad{rightScalarTimes!(c,a,r)} computes the scalar product \\spad{a * r} and stores the result in the matrix \\spad{c}. Error: if \\spad{a} and \\spad{c} do not have the same dimensions.")) (|leftScalarTimes!| (((|Matrix| |#1|) (|Matrix| |#1|) |#1| (|Matrix| |#1|)) "\\spad{leftScalarTimes!(c,r,a)} computes the scalar product \\spad{r * a} and stores the result in the matrix \\spad{c}. Error: if \\spad{a} and \\spad{c} do not have the same dimensions.")) (|minus!| (((|Matrix| |#1|) (|Matrix| |#1|) (|Matrix| |#1|) (|Matrix| |#1|)) "\\spad{!minus!(c,a,b)} computes the matrix difference \\spad{a - b} and stores the result in the matrix \\spad{c}. Error: if \\spad{a},{} \\spad{b},{} and \\spad{c} do not have the same dimensions.") (((|Matrix| |#1|) (|Matrix| |#1|) (|Matrix| |#1|)) "\\spad{minus!(c,a)} computes \\spad{-a} and stores the result in the matrix \\spad{c}. Error: if a and \\spad{c} do not have the same dimensions.")) (|plus!| (((|Matrix| |#1|) (|Matrix| |#1|) (|Matrix| |#1|) (|Matrix| |#1|)) "\\spad{plus!(c,a,b)} computes the matrix sum \\spad{a + b} and stores the result in the matrix \\spad{c}. Error: if \\spad{a},{} \\spad{b},{} and \\spad{c} do not have the same dimensions.")) (|copy!| (((|Matrix| |#1|) (|Matrix| |#1|) (|Matrix| |#1|)) "\\spad{copy!(c,a)} copies the matrix \\spad{a} into the matrix \\spad{c}. Error: if \\spad{a} and \\spad{c} do not have the same dimensions."))) NIL @@ -2744,7 +2744,7 @@ NIL ((|constructor| (NIL "This domain implements the notion of optional value,{} where a computation may fail to produce expected value.")) (|nothing| (($) "\\spad{nothing} represents failure or absence of value.")) (|autoCoerce| ((|#1| $) "\\spad{autoCoerce} is a courtesy coercion function used by the compiler in case it knows that \\spad{`x'} really is a \\spadtype{T}.")) (|case| (((|Boolean|) $ (|[\|\|]| |nothing|)) "\\spad{x case nothing} holds if the value for \\spad{x} is missing.") (((|Boolean|) $ (|[\|\|]| |#1|)) "\\spad{x case T} returns \\spad{true} if \\spad{x} is actually a data of type \\spad{T}.")) (|just| (($ |#1|) "\\spad{just x} injects the value \\spad{`x'} into \\%."))) NIL NIL -(-704 S -1966 FLAF FLAS) +(-704 S -1955 FLAF FLAS) ((|constructor| (NIL "\\indented{1}{\\spadtype{MultiVariableCalculusFunctions} Package provides several} \\indented{1}{functions for multivariable calculus.} These include gradient,{} hessian and jacobian,{} divergence and laplacian. Various forms for banded and sparse storage of matrices are included.")) (|bandedJacobian| (((|Matrix| |#2|) |#3| |#4| (|NonNegativeInteger|) (|NonNegativeInteger|)) "\\spad{bandedJacobian(vf,xlist,kl,ku)} computes the jacobian,{} the matrix of first partial derivatives,{} of the vector field \\spad{vf},{} \\spad{vf} a vector function of the variables listed in \\spad{xlist},{} \\spad{kl} is the number of nonzero subdiagonals,{} \\spad{ku} is the number of nonzero superdiagonals,{} kl+ku+1 being actual bandwidth. Stores the nonzero band in a matrix,{} dimensions kl+ku+1 by \\#xlist. The upper triangle is in the top \\spad{ku} rows,{} the diagonal is in row ku+1,{} the lower triangle in the last \\spad{kl} rows. Entries in a column in the band store correspond to entries in same column of full store. (The notation conforms to LAPACK/NAG-\\spad{F07} conventions.)")) (|jacobian| (((|Matrix| |#2|) |#3| |#4|) "\\spad{jacobian(vf,xlist)} computes the jacobian,{} the matrix of first partial derivatives,{} of the vector field \\spad{vf},{} \\spad{vf} a vector function of the variables listed in \\spad{xlist}.")) (|bandedHessian| (((|Matrix| |#2|) |#2| |#4| (|NonNegativeInteger|)) "\\spad{bandedHessian(v,xlist,k)} computes the hessian,{} the matrix of second partial derivatives,{} of the scalar field \\spad{v},{} \\spad{v} a function of the variables listed in \\spad{xlist},{} \\spad{k} is the semi-bandwidth,{} the number of nonzero subdiagonals,{} 2*k+1 being actual bandwidth. Stores the nonzero band in lower triangle in a matrix,{} dimensions \\spad{k+1} by \\#xlist,{} whose rows are the vectors formed by diagonal,{} subdiagonal,{} etc. of the real,{} full-matrix,{} hessian. (The notation conforms to LAPACK/NAG-\\spad{F07} conventions.)")) (|hessian| (((|Matrix| |#2|) |#2| |#4|) "\\spad{hessian(v,xlist)} computes the hessian,{} the matrix of second partial derivatives,{} of the scalar field \\spad{v},{} \\spad{v} a function of the variables listed in \\spad{xlist}.")) (|laplacian| ((|#2| |#2| |#4|) "\\spad{laplacian(v,xlist)} computes the laplacian of the scalar field \\spad{v},{} \\spad{v} a function of the variables listed in \\spad{xlist}.")) (|divergence| ((|#2| |#3| |#4|) "\\spad{divergence(vf,xlist)} computes the divergence of the vector field \\spad{vf},{} \\spad{vf} a vector function of the variables listed in \\spad{xlist}.")) (|gradient| (((|Vector| |#2|) |#2| |#4|) "\\spad{gradient(v,xlist)} computes the gradient,{} the vector of first partial derivatives,{} of the scalar field \\spad{v},{} \\spad{v} a function of the variables listed in \\spad{xlist}."))) NIL NIL @@ -2754,8 +2754,8 @@ NIL NIL (-706) ((|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"))) -((-4455 . T) (-4460 |has| (-711) (-374)) (-4454 |has| (-711) (-374)) (-4172 . T) (-4461 |has| (-711) (-6 -4461)) (-4458 |has| (-711) (-6 -4458)) ((-4464 "*") . T) (-4456 . T) (-4457 . T) (-4459 . T)) -((|HasCategory| (-711) (QUOTE (-148))) (|HasCategory| (-711) (QUOTE (-146))) (|HasCategory| (-711) (LIST (QUOTE -1057) (LIST (QUOTE -419) (QUOTE (-576))))) (|HasCategory| (-711) (LIST (QUOTE -651) (QUOTE (-576)))) (|HasCategory| (-711) (QUOTE (-379))) (|HasCategory| (-711) (QUOTE (-374))) (-2781 (|HasCategory| (-711) (LIST (QUOTE -1057) (LIST (QUOTE -419) (QUOTE (-576))))) (|HasCategory| (-711) (QUOTE (-374)))) (|HasCategory| (-711) (LIST (QUOTE -915) (QUOTE (-1195)))) (|HasCategory| (-711) (QUOTE (-238))) (|HasCategory| (-711) (QUOTE (-237))) (-2781 (-12 (|HasCategory| (-711) (LIST (QUOTE -915) (QUOTE (-1195)))) (|HasCategory| (-711) (QUOTE (-374)))) (|HasCategory| (-711) (LIST (QUOTE -917) (QUOTE (-1195))))) (-2781 (|HasCategory| (-711) (QUOTE (-374))) (|HasCategory| (-711) (QUOTE (-360)))) (|HasCategory| (-711) (QUOTE (-360))) (|HasCategory| (-711) (LIST (QUOTE -296) (QUOTE (-711)) (QUOTE (-711)))) (|HasCategory| (-711) (LIST (QUOTE -319) (QUOTE (-711)))) (|HasCategory| (-711) (LIST (QUOTE -526) (QUOTE (-1195)) (QUOTE (-711)))) (|HasCategory| (-711) (LIST (QUOTE -899) (QUOTE (-576)))) (|HasCategory| (-711) (LIST (QUOTE -899) (QUOTE (-390)))) (|HasCategory| (-711) (LIST (QUOTE -626) (LIST (QUOTE -905) (QUOTE (-576))))) (|HasCategory| (-711) (LIST (QUOTE -626) (LIST (QUOTE -905) (QUOTE (-390))))) (-2781 (|HasCategory| (-711) (QUOTE (-317))) (|HasCategory| (-711) (QUOTE (-374))) (|HasCategory| (-711) (QUOTE (-360)))) (|HasCategory| (-711) (LIST (QUOTE -626) (QUOTE (-548)))) (|HasCategory| (-711) (QUOTE (-1041))) (|HasCategory| (-711) (QUOTE (-1221))) (-12 (|HasCategory| (-711) (QUOTE (-1021))) (|HasCategory| (-711) (QUOTE (-1221)))) (-2781 (-12 (|HasCategory| (-711) (QUOTE (-317))) (|HasCategory| (-711) (QUOTE (-926)))) (|HasCategory| (-711) (QUOTE (-374))) (-12 (|HasCategory| (-711) (QUOTE (-360))) (|HasCategory| (-711) (QUOTE (-926))))) (-2781 (-12 (|HasCategory| (-711) (QUOTE (-317))) (|HasCategory| (-711) (QUOTE (-926)))) (-12 (|HasCategory| (-711) (QUOTE (-374))) (|HasCategory| (-711) (QUOTE (-926)))) (-12 (|HasCategory| (-711) (QUOTE (-360))) (|HasCategory| (-711) (QUOTE (-926))))) (|HasCategory| (-711) (QUOTE (-557))) (-12 (|HasCategory| (-711) (QUOTE (-1079))) (|HasCategory| (-711) (QUOTE (-1221)))) (|HasCategory| (-711) (QUOTE (-1079))) (|HasCategory| (-711) (QUOTE (-317))) (|HasCategory| (-711) (QUOTE (-926))) (-2781 (-12 (|HasCategory| (-711) (QUOTE (-317))) (|HasCategory| (-711) (QUOTE (-926)))) (|HasCategory| (-711) (QUOTE (-374)))) (-2781 (-12 (|HasCategory| (-711) (QUOTE (-238))) (|HasCategory| (-711) (QUOTE (-374)))) (|HasCategory| (-711) (QUOTE (-237)))) (-2781 (-12 (|HasCategory| (-711) (QUOTE (-317))) (|HasCategory| (-711) (QUOTE (-926)))) (|HasCategory| (-711) (QUOTE (-568)))) (-12 (|HasCategory| (-711) (QUOTE (-237))) (|HasCategory| (-711) (QUOTE (-374)))) (-12 (|HasCategory| (-711) (LIST (QUOTE -917) (QUOTE (-1195)))) (|HasCategory| (-711) (QUOTE (-374)))) (-12 (|HasCategory| (-711) (QUOTE (-238))) (|HasCategory| (-711) (QUOTE (-374)))) (-12 (|HasCategory| (-711) (LIST (QUOTE -915) (QUOTE (-1195)))) (|HasCategory| (-711) (QUOTE (-374)))) (|HasCategory| (-711) (LIST (QUOTE -1057) (QUOTE (-576)))) (|HasCategory| (-711) (QUOTE (-568))) (|HasAttribute| (-711) (QUOTE -4461)) (|HasAttribute| (-711) (QUOTE -4458)) (-12 (|HasCategory| (-711) (QUOTE (-317))) (|HasCategory| (-711) (QUOTE (-926)))) (|HasCategory| (-711) (LIST (QUOTE -917) (QUOTE (-1195)))) (-2781 (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| (-711) (QUOTE (-317))) (|HasCategory| (-711) (QUOTE (-926)))) (|HasCategory| (-711) (QUOTE (-146)))) (-2781 (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| (-711) (QUOTE (-317))) (|HasCategory| (-711) (QUOTE (-926)))) (|HasCategory| (-711) (QUOTE (-360))))) +((-4455 . T) (-4460 |has| (-711) (-374)) (-4454 |has| (-711) (-374)) (-4175 . T) (-4461 |has| (-711) (-6 -4461)) (-4458 |has| (-711) (-6 -4458)) ((-4464 "*") . T) (-4456 . T) (-4457 . T) (-4459 . T)) +((|HasCategory| (-711) (QUOTE (-148))) (|HasCategory| (-711) (QUOTE (-146))) (|HasCategory| (-711) (LIST (QUOTE -1057) (LIST (QUOTE -419) (QUOTE (-576))))) (|HasCategory| (-711) (LIST (QUOTE -651) (QUOTE (-576)))) (|HasCategory| (-711) (QUOTE (-379))) (|HasCategory| (-711) (QUOTE (-374))) (-2755 (|HasCategory| (-711) (LIST (QUOTE -1057) (LIST (QUOTE -419) (QUOTE (-576))))) (|HasCategory| (-711) (QUOTE (-374)))) (|HasCategory| (-711) (LIST (QUOTE -915) (QUOTE (-1195)))) (|HasCategory| (-711) (QUOTE (-238))) (|HasCategory| (-711) (QUOTE (-237))) (-2755 (-12 (|HasCategory| (-711) (LIST (QUOTE -915) (QUOTE (-1195)))) (|HasCategory| (-711) (QUOTE (-374)))) (|HasCategory| (-711) (LIST (QUOTE -917) (QUOTE (-1195))))) (-2755 (|HasCategory| (-711) (QUOTE (-374))) (|HasCategory| (-711) (QUOTE (-360)))) (|HasCategory| (-711) (QUOTE (-360))) (|HasCategory| (-711) (LIST (QUOTE -296) (QUOTE (-711)) (QUOTE (-711)))) (|HasCategory| (-711) (LIST (QUOTE -319) (QUOTE (-711)))) (|HasCategory| (-711) (LIST (QUOTE -526) (QUOTE (-1195)) (QUOTE (-711)))) (|HasCategory| (-711) (LIST (QUOTE -899) (QUOTE (-576)))) (|HasCategory| (-711) (LIST (QUOTE -899) (QUOTE (-390)))) (|HasCategory| (-711) (LIST (QUOTE -626) (LIST (QUOTE -905) (QUOTE (-576))))) (|HasCategory| (-711) (LIST (QUOTE -626) (LIST (QUOTE -905) (QUOTE (-390))))) (-2755 (|HasCategory| (-711) (QUOTE (-317))) (|HasCategory| (-711) (QUOTE (-374))) (|HasCategory| (-711) (QUOTE (-360)))) (|HasCategory| (-711) (LIST (QUOTE -626) (QUOTE (-548)))) (|HasCategory| (-711) (QUOTE (-1041))) (|HasCategory| (-711) (QUOTE (-1221))) (-12 (|HasCategory| (-711) (QUOTE (-1021))) (|HasCategory| (-711) (QUOTE (-1221)))) (-2755 (-12 (|HasCategory| (-711) (QUOTE (-317))) (|HasCategory| (-711) (QUOTE (-926)))) (|HasCategory| (-711) (QUOTE (-374))) (-12 (|HasCategory| (-711) (QUOTE (-360))) (|HasCategory| (-711) (QUOTE (-926))))) (-2755 (-12 (|HasCategory| (-711) (QUOTE (-317))) (|HasCategory| (-711) (QUOTE (-926)))) (-12 (|HasCategory| (-711) (QUOTE (-374))) (|HasCategory| (-711) (QUOTE (-926)))) (-12 (|HasCategory| (-711) (QUOTE (-360))) (|HasCategory| (-711) (QUOTE (-926))))) (|HasCategory| (-711) (QUOTE (-557))) (-12 (|HasCategory| (-711) (QUOTE (-1079))) (|HasCategory| (-711) (QUOTE (-1221)))) (|HasCategory| (-711) (QUOTE (-1079))) (|HasCategory| (-711) (QUOTE (-317))) (|HasCategory| (-711) (QUOTE (-926))) (-2755 (-12 (|HasCategory| (-711) (QUOTE (-317))) (|HasCategory| (-711) (QUOTE (-926)))) (|HasCategory| (-711) (QUOTE (-374)))) (-2755 (-12 (|HasCategory| (-711) (QUOTE (-238))) (|HasCategory| (-711) (QUOTE (-374)))) (|HasCategory| (-711) (QUOTE (-237)))) (-2755 (-12 (|HasCategory| (-711) (QUOTE (-317))) (|HasCategory| (-711) (QUOTE (-926)))) (|HasCategory| (-711) (QUOTE (-568)))) (-12 (|HasCategory| (-711) (QUOTE (-237))) (|HasCategory| (-711) (QUOTE (-374)))) (-12 (|HasCategory| (-711) (LIST (QUOTE -917) (QUOTE (-1195)))) (|HasCategory| (-711) (QUOTE (-374)))) (-12 (|HasCategory| (-711) (QUOTE (-238))) (|HasCategory| (-711) (QUOTE (-374)))) (-12 (|HasCategory| (-711) (LIST (QUOTE -915) (QUOTE (-1195)))) (|HasCategory| (-711) (QUOTE (-374)))) (|HasCategory| (-711) (LIST (QUOTE -1057) (QUOTE (-576)))) (|HasCategory| (-711) (QUOTE (-568))) (|HasAttribute| (-711) (QUOTE -4461)) (|HasAttribute| (-711) (QUOTE -4458)) (-12 (|HasCategory| (-711) (QUOTE (-317))) (|HasCategory| (-711) (QUOTE (-926)))) (|HasCategory| (-711) (LIST (QUOTE -917) (QUOTE (-1195)))) (-2755 (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| (-711) (QUOTE (-317))) (|HasCategory| (-711) (QUOTE (-926)))) (|HasCategory| (-711) (QUOTE (-146)))) (-2755 (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| (-711) (QUOTE (-317))) (|HasCategory| (-711) (QUOTE (-926)))) (|HasCategory| (-711) (QUOTE (-360))))) (-707 S) ((|constructor| (NIL "A multi-dictionary is a dictionary which may contain duplicates. As for any dictionary,{} its size is assumed large so that copying (non-destructive) operations are generally to be avoided.")) (|duplicates| (((|List| (|Record| (|:| |entry| |#1|) (|:| |count| (|NonNegativeInteger|)))) $) "\\spad{duplicates(d)} returns a list of values which have duplicates in \\spad{d}")) (|removeDuplicates!| (($ $) "\\spad{removeDuplicates!(d)} destructively removes any duplicate values in dictionary \\spad{d}.")) (|insert!| (($ |#1| $ (|NonNegativeInteger|)) "\\spad{insert!(x,d,n)} destructively inserts \\spad{n} copies of \\spad{x} into dictionary \\spad{d}."))) ((-4463 . T)) @@ -2768,13 +2768,13 @@ NIL ((|constructor| (NIL "\\indented{1}{<description of package>} Author: Jim Wen Date Created: \\spad{??} Date Last Updated: October 1991 by Jon Steinbach Keywords: Examples: References:")) (|ptFunc| (((|Mapping| (|Point| (|DoubleFloat|)) (|DoubleFloat|) (|DoubleFloat|)) (|Mapping| (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|)) (|Mapping| (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|)) (|Mapping| (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|)) (|Mapping| (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|))) "\\spad{ptFunc(a,b,c,d)} is an internal function exported in order to compile packages.")) (|meshPar1Var| (((|ThreeSpace| (|DoubleFloat|)) (|Expression| (|Integer|)) (|Expression| (|Integer|)) (|Expression| (|Integer|)) (|Mapping| (|DoubleFloat|) (|DoubleFloat|)) (|Segment| (|DoubleFloat|)) (|List| (|DrawOption|))) "\\spad{meshPar1Var(s,t,u,f,s1,l)} \\undocumented")) (|meshFun2Var| (((|ThreeSpace| (|DoubleFloat|)) (|Mapping| (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|)) (|Union| (|Mapping| (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|)) "undefined") (|Segment| (|DoubleFloat|)) (|Segment| (|DoubleFloat|)) (|List| (|DrawOption|))) "\\spad{meshFun2Var(f,g,s1,s2,l)} \\undocumented")) (|meshPar2Var| (((|ThreeSpace| (|DoubleFloat|)) (|ThreeSpace| (|DoubleFloat|)) (|Mapping| (|Point| (|DoubleFloat|)) (|DoubleFloat|) (|DoubleFloat|)) (|Segment| (|DoubleFloat|)) (|Segment| (|DoubleFloat|)) (|List| (|DrawOption|))) "\\spad{meshPar2Var(sp,f,s1,s2,l)} \\undocumented") (((|ThreeSpace| (|DoubleFloat|)) (|Mapping| (|Point| (|DoubleFloat|)) (|DoubleFloat|) (|DoubleFloat|)) (|Segment| (|DoubleFloat|)) (|Segment| (|DoubleFloat|)) (|List| (|DrawOption|))) "\\spad{meshPar2Var(f,s1,s2,l)} \\undocumented") (((|ThreeSpace| (|DoubleFloat|)) (|Mapping| (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|)) (|Mapping| (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|)) (|Mapping| (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|)) (|Union| (|Mapping| (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|)) "undefined") (|Segment| (|DoubleFloat|)) (|Segment| (|DoubleFloat|)) (|List| (|DrawOption|))) "\\spad{meshPar2Var(f,g,h,j,s1,s2,l)} \\undocumented"))) NIL NIL -(-710 OV E -1966 PG) +(-710 OV E -1955 PG) ((|constructor| (NIL "Package for factorization of multivariate polynomials over finite fields.")) (|factor| (((|Factored| (|SparseUnivariatePolynomial| |#4|)) (|SparseUnivariatePolynomial| |#4|)) "\\spad{factor(p)} produces the complete factorization of the multivariate polynomial \\spad{p} over a finite field. \\spad{p} is represented as a univariate polynomial with multivariate coefficients over a finite field.") (((|Factored| |#4|) |#4|) "\\spad{factor(p)} produces the complete factorization of the multivariate polynomial \\spad{p} over a finite field."))) NIL NIL (-711) ((|constructor| (NIL "A domain which models the floating point representation used by machines in the AXIOM-NAG link.")) (|changeBase| (($ (|Integer|) (|Integer|) (|PositiveInteger|)) "\\spad{changeBase(exp,man,base)} \\undocumented{}")) (|exponent| (((|Integer|) $) "\\spad{exponent(u)} returns the exponent of \\spad{u}")) (|mantissa| (((|Integer|) $) "\\spad{mantissa(u)} returns the mantissa of \\spad{u}")) (|coerce| (($ (|MachineInteger|)) "\\spad{coerce(u)} transforms a MachineInteger into a MachineFloat") (((|Float|) $) "\\spad{coerce(u)} transforms a MachineFloat to a standard Float")) (|minimumExponent| (((|Integer|)) "\\spad{minimumExponent()} returns the minimum exponent in the model") (((|Integer|) (|Integer|)) "\\spad{minimumExponent(e)} sets the minimum exponent in the model to \\spad{e}")) (|maximumExponent| (((|Integer|)) "\\spad{maximumExponent()} returns the maximum exponent in the model") (((|Integer|) (|Integer|)) "\\spad{maximumExponent(e)} sets the maximum exponent in the model to \\spad{e}")) (|base| (((|PositiveInteger|) (|PositiveInteger|)) "\\spad{base(b)} sets the base of the model to \\spad{b}")) (|precision| (((|PositiveInteger|)) "\\spad{precision()} returns the number of digits in the model") (((|PositiveInteger|) (|PositiveInteger|)) "\\spad{precision(p)} sets the number of digits in the model to \\spad{p}"))) -((-4161 . T) (-4454 . T) (-4460 . T) (-4455 . T) ((-4464 "*") . T) (-4456 . T) (-4457 . T) (-4459 . T)) +((-4163 . T) (-4454 . T) (-4460 . T) (-4455 . T) ((-4464 "*") . T) (-4456 . T) (-4457 . T) (-4459 . T)) NIL (-712 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."))) @@ -2800,7 +2800,7 @@ NIL ((|constructor| (NIL "MakeRecord is used internally by the interpreter to create record types which are used for doing parallel iterations on streams.")) (|makeRecord| (((|Record| (|:| |part1| |#1|) (|:| |part2| |#2|)) |#1| |#2|) "\\spad{makeRecord(a,b)} creates a record object with type Record(part1:S,{} part2:R),{} where part1 is \\spad{a} and part2 is \\spad{b}."))) NIL NIL -(-718 S -1992 I) +(-718 S -2014 I) ((|constructor| (NIL "transforms top-level objects into compiled functions.")) (|compiledFunction| (((|Mapping| |#3| |#2|) |#1| (|Symbol|)) "\\spad{compiledFunction(expr, x)} returns a function \\spad{f: D -> I} defined by \\spad{f(x) == expr}. Function \\spad{f} is compiled and directly applicable to objects of type \\spad{D}.")) (|unaryFunction| (((|Mapping| |#3| |#2|) (|Symbol|)) "\\spad{unaryFunction(a)} is a local function"))) NIL NIL @@ -2820,14 +2820,14 @@ NIL ((|constructor| (NIL "\\spadtype{MathMLFormat} provides a coercion from \\spadtype{OutputForm} to MathML format.")) (|display| (((|Void|) (|String|)) "prints the string returned by coerce,{} adding <math ...> tags.")) (|exprex| (((|String|) (|OutputForm|)) "coverts \\spadtype{OutputForm} to \\spadtype{String} with the structure preserved with braces. Actually this is not quite accurate. The function \\spadfun{precondition} is first applied to the \\spadtype{OutputForm} expression before \\spadfun{exprex}. The raw \\spadtype{OutputForm} and the nature of the \\spadfun{precondition} function is still obscure to me at the time of this writing (2007-02-14).")) (|coerceL| (((|String|) (|OutputForm|)) "coerceS(\\spad{o}) changes \\spad{o} in the standard output format to MathML format and displays result as one long string.")) (|coerceS| (((|String|) (|OutputForm|)) "\\spad{coerceS(o)} changes \\spad{o} in the standard output format to MathML format and displays formatted result.")) (|coerce| (((|String|) (|OutputForm|)) "coerceS(\\spad{o}) changes \\spad{o} in the standard output format to MathML format."))) NIL NIL -(-723 R |Mod| -3046 -1512 |exactQuo|) +(-723 R |Mod| -2634 -2331 |exactQuo|) ((|constructor| (NIL "\\indented{1}{These domains are used for the factorization and gcds} of univariate polynomials over the integers in order to work modulo different primes. See \\spadtype{ModularRing},{} \\spadtype{EuclideanModularRing}")) (|exQuo| (((|Union| $ "failed") $ $) "\\spad{exQuo(x,y)} \\undocumented")) (|reduce| (($ |#1| |#2|) "\\spad{reduce(r,m)} \\undocumented")) (|coerce| ((|#1| $) "\\spad{coerce(x)} \\undocumented")) (|modulus| ((|#2| $) "\\spad{modulus(x)} \\undocumented"))) ((-4454 . T) (-4460 . T) (-4455 . T) ((-4464 "*") . T) (-4456 . T) (-4457 . T) (-4459 . T)) NIL (-724 R |Rep|) ((|constructor| (NIL "This package \\undocumented")) (|frobenius| (($ $) "\\spad{frobenius(x)} \\undocumented")) (|computePowers| (((|PrimitiveArray| $)) "\\spad{computePowers()} \\undocumented")) (|pow| (((|PrimitiveArray| $)) "\\spad{pow()} \\undocumented")) (|An| (((|Vector| |#1|) $) "\\spad{An(x)} \\undocumented")) (|UnVectorise| (($ (|Vector| |#1|)) "\\spad{UnVectorise(v)} \\undocumented")) (|Vectorise| (((|Vector| |#1|) $) "\\spad{Vectorise(x)} \\undocumented")) (|lift| ((|#2| $) "\\spad{lift(x)} \\undocumented")) (|reduce| (($ |#2|) "\\spad{reduce(x)} \\undocumented")) (|modulus| ((|#2|) "\\spad{modulus()} \\undocumented")) (|setPoly| ((|#2| |#2|) "\\spad{setPoly(x)} \\undocumented"))) (((-4464 "*") |has| |#1| (-174)) (-4455 |has| |#1| (-568)) (-4458 |has| |#1| (-374)) (-4460 |has| |#1| (-6 -4460)) (-4457 . T) (-4456 . T) (-4459 . T)) -((|HasCategory| |#1| (QUOTE (-926))) (|HasCategory| |#1| (QUOTE (-568))) (|HasCategory| |#1| (QUOTE (-174))) (-2781 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-568)))) (-12 (|HasCategory| (-1101) (LIST (QUOTE -899) (QUOTE (-390)))) (|HasCategory| |#1| (LIST (QUOTE -899) (QUOTE (-390))))) (-12 (|HasCategory| (-1101) (LIST (QUOTE -899) (QUOTE (-576)))) (|HasCategory| |#1| (LIST (QUOTE -899) (QUOTE (-576))))) (-12 (|HasCategory| (-1101) (LIST (QUOTE -626) (LIST (QUOTE -905) (QUOTE (-390))))) (|HasCategory| |#1| (LIST (QUOTE -626) (LIST (QUOTE -905) (QUOTE (-390)))))) (-12 (|HasCategory| (-1101) (LIST (QUOTE -626) (LIST (QUOTE -905) (QUOTE (-576))))) (|HasCategory| |#1| (LIST (QUOTE -626) (LIST (QUOTE -905) (QUOTE (-576)))))) (-12 (|HasCategory| (-1101) (LIST (QUOTE -626) (QUOTE (-548)))) (|HasCategory| |#1| (LIST (QUOTE -626) (QUOTE (-548))))) (|HasCategory| |#1| (LIST (QUOTE -651) (QUOTE (-576)))) (|HasCategory| |#1| (QUOTE (-148))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -419) (QUOTE (-576))))) (|HasCategory| |#1| (LIST (QUOTE -1057) (QUOTE (-576)))) (-2781 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -419) (QUOTE (-576))))) (|HasCategory| |#1| (LIST (QUOTE -1057) (LIST (QUOTE -419) (QUOTE (-576)))))) (|HasCategory| |#1| (LIST (QUOTE -1057) (LIST (QUOTE -419) (QUOTE (-576))))) (-2781 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-374))) (|HasCategory| |#1| (QUOTE (-464))) (|HasCategory| |#1| (QUOTE (-568))) (|HasCategory| |#1| (QUOTE (-926)))) (-2781 (|HasCategory| |#1| (QUOTE (-374))) (|HasCategory| |#1| (QUOTE (-464))) (|HasCategory| |#1| (QUOTE (-568))) (|HasCategory| |#1| (QUOTE (-926)))) (-2781 (|HasCategory| |#1| (QUOTE (-374))) (|HasCategory| |#1| (QUOTE (-464))) (|HasCategory| |#1| (QUOTE (-926)))) (|HasCategory| |#1| (QUOTE (-374))) (|HasCategory| |#1| (QUOTE (-1171))) (|HasCategory| |#1| (LIST (QUOTE -917) (QUOTE (-1195)))) (|HasCategory| |#1| (LIST (QUOTE -915) (QUOTE (-1195)))) (|HasCategory| |#1| (QUOTE (-379))) (|HasCategory| |#1| (QUOTE (-360))) (|HasCategory| |#1| (QUOTE (-237))) (|HasCategory| |#1| (QUOTE (-238))) (|HasAttribute| |#1| (QUOTE -4460)) (|HasCategory| |#1| (QUOTE (-464))) (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-926)))) (-2781 (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-926)))) (|HasCategory| |#1| (QUOTE (-146))))) +((|HasCategory| |#1| (QUOTE (-926))) (|HasCategory| |#1| (QUOTE (-568))) (|HasCategory| |#1| (QUOTE (-174))) (-2755 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-568)))) (-12 (|HasCategory| (-1101) (LIST (QUOTE -899) (QUOTE (-390)))) (|HasCategory| |#1| (LIST (QUOTE -899) (QUOTE (-390))))) (-12 (|HasCategory| (-1101) (LIST (QUOTE -899) (QUOTE (-576)))) (|HasCategory| |#1| (LIST (QUOTE -899) (QUOTE (-576))))) (-12 (|HasCategory| (-1101) (LIST (QUOTE -626) (LIST (QUOTE -905) (QUOTE (-390))))) (|HasCategory| |#1| (LIST (QUOTE -626) (LIST (QUOTE -905) (QUOTE (-390)))))) (-12 (|HasCategory| (-1101) (LIST (QUOTE -626) (LIST (QUOTE -905) (QUOTE (-576))))) (|HasCategory| |#1| (LIST (QUOTE -626) (LIST (QUOTE -905) (QUOTE (-576)))))) (-12 (|HasCategory| (-1101) (LIST (QUOTE -626) (QUOTE (-548)))) (|HasCategory| |#1| (LIST (QUOTE -626) (QUOTE (-548))))) (|HasCategory| |#1| (LIST (QUOTE -651) (QUOTE (-576)))) (|HasCategory| |#1| (QUOTE (-148))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -419) (QUOTE (-576))))) (|HasCategory| |#1| (LIST (QUOTE -1057) (QUOTE (-576)))) (-2755 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -419) (QUOTE (-576))))) (|HasCategory| |#1| (LIST (QUOTE -1057) (LIST (QUOTE -419) (QUOTE (-576)))))) (|HasCategory| |#1| (LIST (QUOTE -1057) (LIST (QUOTE -419) (QUOTE (-576))))) (-2755 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-374))) (|HasCategory| |#1| (QUOTE (-464))) (|HasCategory| |#1| (QUOTE (-568))) (|HasCategory| |#1| (QUOTE (-926)))) (-2755 (|HasCategory| |#1| (QUOTE (-374))) (|HasCategory| |#1| (QUOTE (-464))) (|HasCategory| |#1| (QUOTE (-568))) (|HasCategory| |#1| (QUOTE (-926)))) (-2755 (|HasCategory| |#1| (QUOTE (-374))) (|HasCategory| |#1| (QUOTE (-464))) (|HasCategory| |#1| (QUOTE (-926)))) (|HasCategory| |#1| (QUOTE (-374))) (|HasCategory| |#1| (QUOTE (-1171))) (|HasCategory| |#1| (LIST (QUOTE -917) (QUOTE (-1195)))) (|HasCategory| |#1| (LIST (QUOTE -915) (QUOTE (-1195)))) (|HasCategory| |#1| (QUOTE (-379))) (|HasCategory| |#1| (QUOTE (-360))) (|HasCategory| |#1| (QUOTE (-237))) (|HasCategory| |#1| (QUOTE (-238))) (|HasAttribute| |#1| (QUOTE -4460)) (|HasCategory| |#1| (QUOTE (-464))) (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-926)))) (-2755 (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-926)))) (|HasCategory| |#1| (QUOTE (-146))))) (-725 IS E |ff|) ((|constructor| (NIL "This package \\undocumented")) (|construct| (($ |#1| |#2|) "\\spad{construct(i,e)} \\undocumented")) (|index| ((|#1| $) "\\spad{index(x)} \\undocumented")) (|exponent| ((|#2| $) "\\spad{exponent(x)} \\undocumented"))) NIL @@ -2836,7 +2836,7 @@ NIL ((|constructor| (NIL "Algebra of ADDITIVE operators on a module.")) (|makeop| (($ |#1| (|FreeGroup| (|BasicOperator|))) "\\spad{makeop should} be local but conditional")) (|opeval| ((|#2| (|BasicOperator|) |#2|) "\\spad{opeval should} be local but conditional")) (** (($ $ (|Integer|)) "\\spad{op**n} \\undocumented") (($ (|BasicOperator|) (|Integer|)) "\\spad{op**n} \\undocumented")) (|evaluateInverse| (($ $ (|Mapping| |#2| |#2|)) "\\spad{evaluateInverse(x,f)} \\undocumented")) (|evaluate| (($ $ (|Mapping| |#2| |#2|)) "\\spad{evaluate(f, u +-> g u)} attaches the map \\spad{g} to \\spad{f}. \\spad{f} must be a basic operator \\spad{g} MUST be additive,{} \\spadignore{i.e.} \\spad{g(a + b) = g(a) + g(b)} for any \\spad{a},{} \\spad{b} in \\spad{M}. This implies that \\spad{g(n a) = n g(a)} for any \\spad{a} in \\spad{M} and integer \\spad{n > 0}.")) (|conjug| ((|#1| |#1|) "\\spad{conjug(x)}should be local but conditional")) (|adjoint| (($ $ $) "\\spad{adjoint(op1, op2)} sets the adjoint of \\spad{op1} to be op2. \\spad{op1} must be a basic operator") (($ $) "\\spad{adjoint(op)} returns the adjoint of the operator \\spad{op}."))) ((-4457 |has| |#1| (-174)) (-4456 |has| |#1| (-174)) (-4459 . T)) ((|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-148)))) -(-727 R |Mod| -3046 -1512 |exactQuo|) +(-727 R |Mod| -2634 -2331 |exactQuo|) ((|constructor| (NIL "These domains are used for the factorization and gcds of univariate polynomials over the integers in order to work modulo different primes. See \\spadtype{EuclideanModularRing} ,{}\\spadtype{ModularField}")) (|inv| (($ $) "\\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"))) ((-4459 . T)) NIL @@ -2848,7 +2848,7 @@ NIL ((|constructor| (NIL "The category of modules over a commutative ring. \\blankline"))) ((-4457 . T) (-4456 . T)) NIL -(-730 -1966) +(-730 -1955) ((|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]]}."))) ((-4459 . T)) NIL @@ -2884,7 +2884,7 @@ 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 -(-739 -1966 UP) +(-739 -1955 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 @@ -2903,7 +2903,7 @@ NIL (-743 |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."))) (((-4464 "*") |has| |#2| (-174)) (-4455 |has| |#2| (-568)) (-4460 |has| |#2| (-6 -4460)) (-4457 . T) (-4456 . T) (-4459 . 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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 @@ -3036,11 +3036,11 @@ 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 -(-777 -1966) +(-777 -1955) ((|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 -(-778 P -1966) +(-778 P -1955) ((|constructor| (NIL "This package provides a division and related operations for \\spadtype{MonogenicLinearOperator}\\spad{s} over a \\spadtype{Field}. Since the multiplication is in general non-commutative,{} these operations all have left- and right-hand versions. This package provides the operations based on left-division.")) (|leftLcm| ((|#1| |#1| |#1|) "\\spad{leftLcm(a,b)} computes the value \\spad{m} of lowest degree such that \\spad{m = a*aa = b*bb} for some values \\spad{aa} and \\spad{bb}. The value \\spad{m} is computed using left-division.")) (|leftGcd| ((|#1| |#1| |#1|) "\\spad{leftGcd(a,b)} computes the value \\spad{g} of highest degree such that \\indented{3}{\\spad{a = aa*g}} \\indented{3}{\\spad{b = bb*g}} for some values \\spad{aa} and \\spad{bb}. The value \\spad{g} is computed using left-division.")) (|leftExactQuotient| (((|Union| |#1| "failed") |#1| |#1|) "\\spad{leftExactQuotient(a,b)} computes the value \\spad{q},{} if it exists,{} \\indented{1}{such that \\spad{a = b*q}.}")) (|leftRemainder| ((|#1| |#1| |#1|) "\\spad{leftRemainder(a,b)} computes the pair \\spad{[q,r]} such that \\spad{a = b*q + r} and the degree of \\spad{r} is less than the degree of \\spad{b}. The value \\spad{r} is returned.")) (|leftQuotient| ((|#1| |#1| |#1|) "\\spad{leftQuotient(a,b)} computes the pair \\spad{[q,r]} such that \\spad{a = b*q + r} and the degree of \\spad{r} is less than the degree of \\spad{b}. The value \\spad{q} is returned.")) (|leftDivide| (((|Record| (|:| |quotient| |#1|) (|:| |remainder| |#1|)) |#1| |#1|) "\\spad{leftDivide(a,b)} returns the pair \\spad{[q,r]} such that \\spad{a = b*q + r} and the degree of \\spad{r} is less than the degree of \\spad{b}. This process is called ``left division\\spad{''}."))) NIL NIL @@ -3048,7 +3048,7 @@ NIL NIL NIL NIL -(-780 UP -1966) +(-780 UP -1955) ((|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 @@ -3064,7 +3064,7 @@ 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."))) (((-4464 "*") . T)) NIL -(-784 R -1966) +(-784 R -1955) ((|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 @@ -3084,7 +3084,7 @@ NIL ((|constructor| (NIL "A package for computing normalized assocites of univariate polynomials with coefficients in a tower of simple extensions of a field.\\newline References : \\indented{1}{[1] \\spad{D}. LAZARD \"A new method for solving algebraic systems of} \\indented{5}{positive dimension\" Discr. App. Math. 33:147-160,{}1991} \\indented{1}{[2] \\spad{M}. MORENO MAZA and \\spad{R}. RIOBOO \"Computations of \\spad{gcd} over} \\indented{5}{algebraic towers of simple extensions\" In proceedings of AAECC11} \\indented{5}{Paris,{} 1995.} \\indented{1}{[3] \\spad{M}. MORENO MAZA \"Calculs de pgcd au-dessus des tours} \\indented{5}{d'extensions simples et resolution des systemes d'equations} \\indented{5}{algebriques\" These,{} Universite \\spad{P}.etM. Curie,{} Paris,{} 1997.}")) (|normInvertible?| (((|List| (|Record| (|:| |val| (|Boolean|)) (|:| |tower| |#5|))) |#4| |#5|) "\\axiom{normInvertible?(\\spad{p},{}\\spad{ts})} is an internal subroutine,{} exported only for developement.")) (|outputArgs| (((|Void|) (|String|) (|String|) |#4| |#5|) "\\axiom{outputArgs(\\spad{s1},{}\\spad{s2},{}\\spad{p},{}\\spad{ts})} is an internal subroutine,{} exported only for developement.")) (|normalize| (((|List| (|Record| (|:| |val| |#4|) (|:| |tower| |#5|))) |#4| |#5|) "\\axiom{normalize(\\spad{p},{}\\spad{ts})} normalizes \\axiom{\\spad{p}} \\spad{w}.\\spad{r}.\\spad{t} \\spad{ts}.")) (|normalizedAssociate| ((|#4| |#4| |#5|) "\\axiom{normalizedAssociate(\\spad{p},{}\\spad{ts})} returns a normalized polynomial \\axiom{\\spad{n}} \\spad{w}.\\spad{r}.\\spad{t}. \\spad{ts} such that \\axiom{\\spad{n}} and \\axiom{\\spad{p}} are associates \\spad{w}.\\spad{r}.\\spad{t} \\spad{ts} and assuming that \\axiom{\\spad{p}} is invertible \\spad{w}.\\spad{r}.\\spad{t} \\spad{ts}.")) (|recip| (((|Record| (|:| |num| |#4|) (|:| |den| |#4|)) |#4| |#5|) "\\axiom{recip(\\spad{p},{}\\spad{ts})} returns the inverse of \\axiom{\\spad{p}} \\spad{w}.\\spad{r}.\\spad{t} \\spad{ts} assuming that \\axiom{\\spad{p}} is invertible \\spad{w}.\\spad{r}.\\spad{t} \\spad{ts}."))) NIL NIL -(-789 -1966 |ExtF| |SUEx| |ExtP| |n|) +(-789 -1955 |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 @@ -3099,7 +3099,7 @@ NIL (-792 R |VarSet|) ((|constructor| (NIL "A post-facto extension for \\axiomType{\\spad{SMP}} in order to speed up operations related to pseudo-division and \\spad{gcd}. This domain is based on the \\axiomType{NSUP} constructor which is itself a post-facto extension of the \\axiomType{SUP} constructor."))) (((-4464 "*") |has| |#1| (-174)) (-4455 |has| |#1| (-568)) (-4460 |has| |#1| (-6 -4460)) (-4457 . T) (-4456 . T) (-4459 . 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(-576))))))) (-12 (|HasCategory| |#2| (LIST (QUOTE -626) (QUOTE (-1195)))) (-2658 (|HasCategory| |#1| (LIST (QUOTE -38) (QUOTE (-576))))) (-2658 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -419) (QUOTE (-576))))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -419) (QUOTE (-576))))) (|HasCategory| |#2| (LIST (QUOTE -626) (QUOTE (-1195)))) (-2658 (|HasCategory| |#1| (LIST (QUOTE -1011) (QUOTE (-576))))))) (|HasAttribute| |#1| (QUOTE -4460)) (|HasCategory| |#1| (QUOTE (-464))) (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-926)))) (-2755 (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-926)))) (|HasCategory| |#1| (QUOTE (-146))))) (-793 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 @@ -3107,7 +3107,7 @@ NIL (-794 R) ((|constructor| (NIL "A post-facto extension for \\axiomType{SUP} in order to speed up operations related to pseudo-division and \\spad{gcd} for both \\axiomType{SUP} and,{} consequently,{} \\axiomType{NSMP}.")) (|halfExtendedResultant2| (((|Record| (|:| |resultant| |#1|) (|:| |coef2| $)) $ $) "\\axiom{halfExtendedResultant2(a,{}\\spad{b})} returns \\axiom{[\\spad{r},{}ca]} such that \\axiom{extendedResultant(a,{}\\spad{b})} returns \\axiom{[\\spad{r},{}ca,{} \\spad{cb}]}")) (|halfExtendedResultant1| (((|Record| (|:| |resultant| |#1|) (|:| |coef1| $)) $ $) "\\axiom{halfExtendedResultant1(a,{}\\spad{b})} returns \\axiom{[\\spad{r},{}ca]} such that \\axiom{extendedResultant(a,{}\\spad{b})} returns \\axiom{[\\spad{r},{}ca,{} \\spad{cb}]}")) (|extendedResultant| (((|Record| (|:| |resultant| |#1|) (|:| |coef1| $) (|:| |coef2| $)) $ $) "\\axiom{extendedResultant(a,{}\\spad{b})} returns \\axiom{[\\spad{r},{}ca,{}\\spad{cb}]} such that \\axiom{\\spad{r}} is the resultant of \\axiom{a} and \\axiom{\\spad{b}} and \\axiom{\\spad{r} = ca * a + \\spad{cb} * \\spad{b}}")) (|halfExtendedSubResultantGcd2| (((|Record| (|:| |gcd| $) (|:| |coef2| $)) $ $) "\\axiom{halfExtendedSubResultantGcd2(a,{}\\spad{b})} returns \\axiom{[\\spad{g},{}\\spad{cb}]} such that \\axiom{extendedSubResultantGcd(a,{}\\spad{b})} returns \\axiom{[\\spad{g},{}ca,{} \\spad{cb}]}")) (|halfExtendedSubResultantGcd1| (((|Record| (|:| |gcd| $) (|:| |coef1| $)) $ $) "\\axiom{halfExtendedSubResultantGcd1(a,{}\\spad{b})} returns \\axiom{[\\spad{g},{}ca]} such that \\axiom{extendedSubResultantGcd(a,{}\\spad{b})} returns \\axiom{[\\spad{g},{}ca,{} \\spad{cb}]}")) (|extendedSubResultantGcd| (((|Record| (|:| |gcd| $) (|:| |coef1| $) (|:| |coef2| $)) $ $) "\\axiom{extendedSubResultantGcd(a,{}\\spad{b})} returns \\axiom{[\\spad{g},{}ca,{} \\spad{cb}]} such that \\axiom{\\spad{g}} is a \\spad{gcd} of \\axiom{a} and \\axiom{\\spad{b}} in \\axiom{\\spad{R^}(\\spad{-1}) \\spad{P}} and \\axiom{\\spad{g} = ca * a + \\spad{cb} * \\spad{b}}")) (|lastSubResultant| (($ $ $) "\\axiom{lastSubResultant(a,{}\\spad{b})} returns \\axiom{resultant(a,{}\\spad{b})} if \\axiom{a} and \\axiom{\\spad{b}} has no non-trivial \\spad{gcd} in \\axiom{\\spad{R^}(\\spad{-1}) \\spad{P}} otherwise the non-zero sub-resultant with smallest index.")) (|subResultantsChain| (((|List| $) $ $) "\\axiom{subResultantsChain(a,{}\\spad{b})} returns the list of the non-zero sub-resultants of \\axiom{a} and \\axiom{\\spad{b}} sorted by increasing degree.")) (|lazyPseudoQuotient| (($ $ $) "\\axiom{lazyPseudoQuotient(a,{}\\spad{b})} returns \\axiom{\\spad{q}} if \\axiom{lazyPseudoDivide(a,{}\\spad{b})} returns \\axiom{[\\spad{c},{}\\spad{g},{}\\spad{q},{}\\spad{r}]}")) (|lazyPseudoDivide| (((|Record| (|:| |coef| |#1|) (|:| |gap| (|NonNegativeInteger|)) (|:| |quotient| $) (|:| |remainder| $)) $ $) "\\axiom{lazyPseudoDivide(a,{}\\spad{b})} returns \\axiom{[\\spad{c},{}\\spad{g},{}\\spad{q},{}\\spad{r}]} such that \\axiom{\\spad{c^n} * a = \\spad{q*b} \\spad{+r}} and \\axiom{lazyResidueClass(a,{}\\spad{b})} returns \\axiom{[\\spad{r},{}\\spad{c},{}\\spad{n}]} where \\axiom{\\spad{n} + \\spad{g} = max(0,{} degree(\\spad{b}) - degree(a) + 1)}.")) (|lazyPseudoRemainder| (($ $ $) "\\axiom{lazyPseudoRemainder(a,{}\\spad{b})} returns \\axiom{\\spad{r}} if \\axiom{lazyResidueClass(a,{}\\spad{b})} returns \\axiom{[\\spad{r},{}\\spad{c},{}\\spad{n}]}. This lazy pseudo-remainder is computed by means of the \\axiomOpFrom{fmecg}{NewSparseUnivariatePolynomial} operation.")) (|lazyResidueClass| (((|Record| (|:| |polnum| $) (|:| |polden| |#1|) (|:| |power| (|NonNegativeInteger|))) $ $) "\\axiom{lazyResidueClass(a,{}\\spad{b})} returns \\axiom{[\\spad{r},{}\\spad{c},{}\\spad{n}]} such that \\axiom{\\spad{r}} is reduced \\spad{w}.\\spad{r}.\\spad{t}. \\axiom{\\spad{b}} and \\axiom{\\spad{b}} divides \\axiom{\\spad{c^n} * a - \\spad{r}} where \\axiom{\\spad{c}} is \\axiom{leadingCoefficient(\\spad{b})} and \\axiom{\\spad{n}} is as small as possible with the previous properties.")) (|monicModulo| (($ $ $) "\\axiom{monicModulo(a,{}\\spad{b})} returns \\axiom{\\spad{r}} such that \\axiom{\\spad{r}} is reduced \\spad{w}.\\spad{r}.\\spad{t}. \\axiom{\\spad{b}} and \\axiom{\\spad{b}} divides \\axiom{a \\spad{-r}} where \\axiom{\\spad{b}} is monic.")) (|fmecg| (($ $ (|NonNegativeInteger|) |#1| $) "\\axiom{fmecg(\\spad{p1},{}\\spad{e},{}\\spad{r},{}\\spad{p2})} returns \\axiom{\\spad{p1} - \\spad{r} * X**e * \\spad{p2}} where \\axiom{\\spad{X}} is \\axiom{monomial(1,{}1)}"))) (((-4464 "*") |has| |#1| (-174)) (-4455 |has| |#1| (-568)) (-4458 |has| |#1| (-374)) (-4460 |has| |#1| (-6 -4460)) (-4457 . T) (-4456 . T) (-4459 . T)) -((|HasCategory| |#1| (QUOTE (-926))) (|HasCategory| |#1| (QUOTE (-568))) (|HasCategory| |#1| (QUOTE (-174))) (-2781 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-568)))) (-12 (|HasCategory| (-1101) (LIST (QUOTE -899) (QUOTE (-390)))) (|HasCategory| |#1| (LIST (QUOTE -899) (QUOTE (-390))))) (-12 (|HasCategory| (-1101) (LIST (QUOTE -899) (QUOTE (-576)))) (|HasCategory| |#1| (LIST (QUOTE -899) (QUOTE (-576))))) (-12 (|HasCategory| (-1101) (LIST (QUOTE -626) (LIST (QUOTE -905) (QUOTE (-390))))) (|HasCategory| |#1| (LIST (QUOTE -626) (LIST (QUOTE -905) (QUOTE (-390)))))) (-12 (|HasCategory| (-1101) (LIST (QUOTE -626) (LIST (QUOTE -905) (QUOTE (-576))))) (|HasCategory| |#1| (LIST (QUOTE -626) (LIST (QUOTE -905) (QUOTE (-576)))))) (-12 (|HasCategory| (-1101) (LIST (QUOTE -626) (QUOTE (-548)))) (|HasCategory| |#1| (LIST (QUOTE -626) (QUOTE (-548))))) (|HasCategory| |#1| (LIST (QUOTE -651) (QUOTE (-576)))) (|HasCategory| |#1| (QUOTE (-148))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -419) (QUOTE (-576))))) (|HasCategory| |#1| (LIST (QUOTE -1057) (QUOTE (-576)))) (-2781 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -419) (QUOTE (-576))))) (|HasCategory| |#1| (LIST (QUOTE -1057) (LIST (QUOTE -419) (QUOTE (-576)))))) (|HasCategory| |#1| (LIST (QUOTE -1057) (LIST (QUOTE -419) (QUOTE (-576))))) (-2781 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-374))) (|HasCategory| |#1| (QUOTE (-464))) (|HasCategory| |#1| (QUOTE (-568))) (|HasCategory| |#1| (QUOTE (-926)))) (-2781 (|HasCategory| |#1| (QUOTE (-374))) (|HasCategory| |#1| (QUOTE (-464))) (|HasCategory| |#1| (QUOTE (-568))) (|HasCategory| |#1| (QUOTE (-926)))) (-2781 (|HasCategory| |#1| (QUOTE (-374))) (|HasCategory| |#1| (QUOTE (-464))) (|HasCategory| |#1| (QUOTE (-926)))) (|HasCategory| |#1| (QUOTE (-374))) (|HasCategory| |#1| (QUOTE (-1171))) (|HasCategory| |#1| (LIST (QUOTE -917) (QUOTE (-1195)))) (|HasCategory| |#1| (LIST (QUOTE -915) (QUOTE (-1195)))) (|HasCategory| |#1| (QUOTE (-237))) (|HasCategory| |#1| (QUOTE (-238))) (|HasAttribute| |#1| (QUOTE -4460)) (|HasCategory| |#1| (QUOTE (-464))) (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-926)))) (-2781 (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-926)))) (|HasCategory| |#1| (QUOTE (-146))))) +((|HasCategory| |#1| (QUOTE (-926))) (|HasCategory| |#1| (QUOTE (-568))) (|HasCategory| |#1| (QUOTE (-174))) (-2755 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-568)))) (-12 (|HasCategory| (-1101) (LIST (QUOTE -899) (QUOTE (-390)))) (|HasCategory| |#1| (LIST (QUOTE -899) (QUOTE (-390))))) (-12 (|HasCategory| (-1101) (LIST (QUOTE -899) (QUOTE (-576)))) (|HasCategory| |#1| (LIST (QUOTE -899) (QUOTE (-576))))) (-12 (|HasCategory| (-1101) (LIST (QUOTE -626) (LIST (QUOTE -905) (QUOTE (-390))))) (|HasCategory| |#1| (LIST (QUOTE -626) (LIST (QUOTE -905) (QUOTE (-390)))))) (-12 (|HasCategory| (-1101) (LIST (QUOTE -626) (LIST (QUOTE -905) (QUOTE (-576))))) (|HasCategory| |#1| (LIST (QUOTE -626) (LIST (QUOTE -905) (QUOTE (-576)))))) (-12 (|HasCategory| (-1101) (LIST (QUOTE -626) (QUOTE (-548)))) (|HasCategory| |#1| (LIST (QUOTE -626) (QUOTE (-548))))) (|HasCategory| |#1| (LIST (QUOTE -651) (QUOTE (-576)))) (|HasCategory| |#1| (QUOTE (-148))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -419) (QUOTE (-576))))) (|HasCategory| |#1| (LIST (QUOTE -1057) (QUOTE (-576)))) (-2755 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -419) (QUOTE (-576))))) (|HasCategory| |#1| (LIST (QUOTE -1057) (LIST (QUOTE -419) (QUOTE (-576)))))) (|HasCategory| |#1| (LIST (QUOTE -1057) (LIST (QUOTE -419) (QUOTE (-576))))) (-2755 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-374))) (|HasCategory| |#1| (QUOTE (-464))) (|HasCategory| |#1| (QUOTE (-568))) (|HasCategory| |#1| (QUOTE (-926)))) (-2755 (|HasCategory| |#1| (QUOTE (-374))) (|HasCategory| |#1| (QUOTE (-464))) (|HasCategory| |#1| (QUOTE (-568))) (|HasCategory| |#1| (QUOTE (-926)))) (-2755 (|HasCategory| |#1| (QUOTE (-374))) (|HasCategory| |#1| (QUOTE (-464))) (|HasCategory| |#1| (QUOTE (-926)))) (|HasCategory| |#1| (QUOTE (-374))) (|HasCategory| |#1| (QUOTE (-1171))) (|HasCategory| |#1| (LIST (QUOTE -917) (QUOTE (-1195)))) (|HasCategory| |#1| (LIST (QUOTE -915) (QUOTE (-1195)))) (|HasCategory| |#1| (QUOTE (-237))) (|HasCategory| |#1| (QUOTE (-238))) (|HasAttribute| |#1| (QUOTE -4460)) (|HasCategory| |#1| (QUOTE (-464))) (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-926)))) (-2755 (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-926)))) (|HasCategory| |#1| (QUOTE (-146))))) (-795 R) ((|constructor| (NIL "This package provides polynomials as functions on a ring.")) (|eulerE| ((|#1| (|NonNegativeInteger|) |#1|) "\\spad{eulerE(n,r)} \\undocumented")) (|bernoulliB| ((|#1| (|NonNegativeInteger|) |#1|) "\\spad{bernoulliB(n,r)} \\undocumented")) (|cyclotomic| ((|#1| (|NonNegativeInteger|) |#1|) "\\spad{cyclotomic(n,r)} \\undocumented"))) NIL @@ -3168,23 +3168,23 @@ NIL ((|constructor| (NIL "OctonionCategory gives the categorial frame for the octonions,{} and eight-dimensional non-associative algebra,{} doubling the the quaternions in the same way as doubling the Complex numbers to get the quaternions.")) (|inv| (($ $) "\\spad{inv(o)} returns the inverse of \\spad{o} if it exists.")) (|rationalIfCan| (((|Union| (|Fraction| (|Integer|)) "failed") $) "\\spad{rationalIfCan(o)} returns the real part if all seven imaginary parts are 0,{} and \"failed\" otherwise.")) (|rational| (((|Fraction| (|Integer|)) $) "\\spad{rational(o)} returns the real part if all seven imaginary parts are 0. Error: if \\spad{o} is not rational.")) (|rational?| (((|Boolean|) $) "\\spad{rational?(o)} tests if \\spad{o} is rational,{} \\spadignore{i.e.} that all seven imaginary parts are 0.")) (|abs| ((|#1| $) "\\spad{abs(o)} computes the absolute value of an octonion,{} equal to the square root of the \\spadfunFrom{norm}{Octonion}.")) (|octon| (($ |#1| |#1| |#1| |#1| |#1| |#1| |#1| |#1|) "\\spad{octon(re,ri,rj,rk,rE,rI,rJ,rK)} constructs an octonion from scalars.")) (|norm| ((|#1| $) "\\spad{norm(o)} returns the norm of an octonion,{} equal to the sum of the squares of its coefficients.")) (|imagK| ((|#1| $) "\\spad{imagK(o)} extracts the imaginary \\spad{K} part of octonion \\spad{o}.")) (|imagJ| ((|#1| $) "\\spad{imagJ(o)} extracts the imaginary \\spad{J} part of octonion \\spad{o}.")) (|imagI| ((|#1| $) "\\spad{imagI(o)} extracts the imaginary \\spad{I} part of octonion \\spad{o}.")) (|imagE| ((|#1| $) "\\spad{imagE(o)} extracts the imaginary \\spad{E} part of octonion \\spad{o}.")) (|imagk| ((|#1| $) "\\spad{imagk(o)} extracts the \\spad{k} part of octonion \\spad{o}.")) (|imagj| ((|#1| $) "\\spad{imagj(o)} extracts the \\spad{j} part of octonion \\spad{o}.")) (|imagi| ((|#1| $) "\\spad{imagi(o)} extracts the \\spad{i} part of octonion \\spad{o}.")) (|real| ((|#1| $) "\\spad{real(o)} extracts real part of octonion \\spad{o}.")) (|conjugate| (($ $) "\\spad{conjugate(o)} negates the imaginary parts \\spad{i},{}\\spad{j},{}\\spad{k},{}\\spad{E},{}\\spad{I},{}\\spad{J},{}\\spad{K} of octonian \\spad{o}."))) ((-4456 . T) (-4457 . T) (-4459 . T)) NIL -(-810 -2781 R OS S) +(-810 -2755 R OS S) ((|constructor| (NIL "OctonionCategoryFunctions2 implements functions between two octonion domains defined over different rings. The function map is used to coerce between octonion types.")) (|map| ((|#3| (|Mapping| |#4| |#2|) |#1|) "\\spad{map(f,u)} maps \\spad{f} onto the component parts of the octonion \\spad{u}."))) NIL NIL (-811 R) ((|constructor| (NIL "Octonion implements octonions (Cayley-Dixon algebra) over a commutative ring,{} an eight-dimensional non-associative algebra,{} doubling the quaternions in the same way as doubling the complex numbers to get the quaternions the main constructor function is {\\em octon} which takes 8 arguments: the real part,{} the \\spad{i} imaginary part,{} the \\spad{j} imaginary part,{} the \\spad{k} imaginary part,{} (as with quaternions) and in addition the imaginary parts \\spad{E},{} \\spad{I},{} \\spad{J},{} \\spad{K}.")) (|octon| (($ (|Quaternion| |#1|) (|Quaternion| |#1|)) "\\spad{octon(qe,qE)} constructs an octonion from two quaternions using the relation {\\em O = Q + QE}."))) ((-4456 . T) (-4457 . T) (-4459 . T)) -((|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-148))) (|HasCategory| |#1| (LIST (QUOTE -626) (QUOTE (-548)))) (|HasCategory| |#1| (QUOTE (-862))) (|HasCategory| |#1| (QUOTE (-379))) (|HasCategory| |#1| (LIST (QUOTE -526) (QUOTE (-1195)) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -296) (|devaluate| |#1|) (|devaluate| |#1|))) (-2781 (|HasCategory| (-1018 |#1|) (LIST (QUOTE -1057) (LIST (QUOTE -419) (QUOTE (-576))))) (|HasCategory| |#1| (LIST (QUOTE -1057) (LIST (QUOTE -419) (QUOTE (-576)))))) (-2781 (|HasCategory| (-1018 |#1|) (LIST (QUOTE -1057) (QUOTE (-576)))) (|HasCategory| |#1| (LIST (QUOTE -1057) (QUOTE (-576))))) (|HasCategory| |#1| (QUOTE (-1079))) (|HasCategory| |#1| (QUOTE (-557))) (|HasCategory| |#1| (QUOTE (-374))) (|HasCategory| (-1018 |#1|) (LIST (QUOTE -1057) (LIST (QUOTE -419) (QUOTE (-576))))) (|HasCategory| (-1018 |#1|) (LIST (QUOTE -1057) (QUOTE (-576)))) (|HasCategory| |#1| (LIST (QUOTE -1057) (LIST (QUOTE -419) (QUOTE (-576))))) (|HasCategory| |#1| (LIST (QUOTE -1057) (QUOTE (-576))))) +((|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-148))) (|HasCategory| |#1| (LIST (QUOTE -626) (QUOTE (-548)))) (|HasCategory| |#1| (QUOTE (-862))) (|HasCategory| |#1| (QUOTE (-379))) (|HasCategory| |#1| (LIST (QUOTE -526) (QUOTE (-1195)) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -296) (|devaluate| |#1|) (|devaluate| |#1|))) (-2755 (|HasCategory| (-1018 |#1|) (LIST (QUOTE -1057) (LIST (QUOTE -419) (QUOTE (-576))))) (|HasCategory| |#1| (LIST (QUOTE -1057) (LIST (QUOTE -419) (QUOTE (-576)))))) (-2755 (|HasCategory| (-1018 |#1|) (LIST (QUOTE -1057) (QUOTE (-576)))) (|HasCategory| |#1| (LIST (QUOTE -1057) (QUOTE (-576))))) (|HasCategory| |#1| (QUOTE (-1079))) (|HasCategory| |#1| (QUOTE (-557))) (|HasCategory| |#1| (QUOTE (-374))) (|HasCategory| (-1018 |#1|) (LIST (QUOTE -1057) (LIST (QUOTE -419) (QUOTE (-576))))) (|HasCategory| (-1018 |#1|) (LIST (QUOTE -1057) (QUOTE (-576)))) (|HasCategory| |#1| (LIST (QUOTE -1057) (LIST (QUOTE -419) (QUOTE (-576))))) (|HasCategory| |#1| (LIST (QUOTE -1057) (QUOTE (-576))))) (-812) ((|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 -(-813 R -1966 L) +(-813 R -1955 L) ((|constructor| (NIL "Solution of linear ordinary differential equations,{} constant coefficient case.")) (|constDsolve| (((|Record| (|:| |particular| |#2|) (|:| |basis| (|List| |#2|))) |#3| |#2| (|Symbol|)) "\\spad{constDsolve(op, g, x)} returns \\spad{[f, [y1,...,ym]]} where \\spad{f} is a particular solution of the equation \\spad{op y = g},{} and the \\spad{yi}\\spad{'s} form a basis for the solutions of \\spad{op y = 0}."))) NIL NIL -(-814 R -1966) +(-814 R -1955) ((|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 @@ -3192,7 +3192,7 @@ NIL ((|constructor| (NIL "\\axiom{ODEIntensityFunctionsTable()} provides a dynamic table and a set of functions to store details found out about sets of ODE\\spad{'s}.")) (|showIntensityFunctions| (((|Union| (|Record| (|:| |stiffness| (|Float|)) (|:| |stability| (|Float|)) (|:| |expense| (|Float|)) (|:| |accuracy| (|Float|)) (|:| |intermediateResults| (|Float|))) "failed") (|Record| (|:| |xinit| (|DoubleFloat|)) (|:| |xend| (|DoubleFloat|)) (|:| |fn| (|Vector| (|Expression| (|DoubleFloat|)))) (|:| |yinit| (|List| (|DoubleFloat|))) (|:| |intvals| (|List| (|DoubleFloat|))) (|:| |g| (|Expression| (|DoubleFloat|))) (|:| |abserr| (|DoubleFloat|)) (|:| |relerr| (|DoubleFloat|)))) "\\spad{showIntensityFunctions(k)} returns the entries in the table of intensity functions \\spad{k}.")) (|insert!| (($ (|Record| (|:| |key| (|Record| (|:| |xinit| (|DoubleFloat|)) (|:| |xend| (|DoubleFloat|)) (|:| |fn| (|Vector| (|Expression| (|DoubleFloat|)))) (|:| |yinit| (|List| (|DoubleFloat|))) (|:| |intvals| (|List| (|DoubleFloat|))) (|:| |g| (|Expression| (|DoubleFloat|))) (|:| |abserr| (|DoubleFloat|)) (|:| |relerr| (|DoubleFloat|)))) (|:| |entry| (|Record| (|:| |stiffness| (|Float|)) (|:| |stability| (|Float|)) (|:| |expense| (|Float|)) (|:| |accuracy| (|Float|)) (|:| |intermediateResults| (|Float|)))))) "\\spad{insert!(r)} inserts an entry \\spad{r} into theIFTable")) (|iFTable| (($ (|List| (|Record| (|:| |key| (|Record| (|:| |xinit| (|DoubleFloat|)) (|:| |xend| (|DoubleFloat|)) (|:| |fn| (|Vector| (|Expression| (|DoubleFloat|)))) (|:| |yinit| (|List| (|DoubleFloat|))) (|:| |intvals| (|List| (|DoubleFloat|))) (|:| |g| (|Expression| (|DoubleFloat|))) (|:| |abserr| (|DoubleFloat|)) (|:| |relerr| (|DoubleFloat|)))) (|:| |entry| (|Record| (|:| |stiffness| (|Float|)) (|:| |stability| (|Float|)) (|:| |expense| (|Float|)) (|:| |accuracy| (|Float|)) (|:| |intermediateResults| (|Float|))))))) "\\spad{iFTable(l)} creates an intensity-functions table from the elements of \\spad{l}.")) (|keys| (((|List| (|Record| (|:| |xinit| (|DoubleFloat|)) (|:| |xend| (|DoubleFloat|)) (|:| |fn| (|Vector| (|Expression| (|DoubleFloat|)))) (|:| |yinit| (|List| (|DoubleFloat|))) (|:| |intvals| (|List| (|DoubleFloat|))) (|:| |g| (|Expression| (|DoubleFloat|))) (|:| |abserr| (|DoubleFloat|)) (|:| |relerr| (|DoubleFloat|)))) $) "\\spad{keys(tab)} returns the list of keys of \\spad{f}")) (|clearTheIFTable| (((|Void|)) "\\spad{clearTheIFTable()} clears the current table of intensity functions.")) (|showTheIFTable| (($) "\\spad{showTheIFTable()} returns the current table of intensity functions."))) NIL NIL -(-816 R -1966) +(-816 R -1955) ((|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 @@ -3200,11 +3200,11 @@ NIL ((|measure| (((|Record| (|:| |measure| (|Float|)) (|:| |name| (|String|)) (|:| |explanations| (|List| (|String|)))) (|NumericalODEProblem|) (|RoutinesTable|)) "\\spad{measure(prob,R)} is a top level ANNA function for identifying the most appropriate numerical routine from those in the routines table provided for solving the numerical ODE problem defined by \\axiom{\\spad{prob}}. \\blankline It calls each \\axiom{domain} listed in \\axiom{\\spad{R}} of \\axiom{category} \\axiomType{OrdinaryDifferentialEquationsSolverCategory} in turn to calculate all measures and returns the best \\spadignore{i.e.} the name of the most appropriate domain and any other relevant information. It predicts the likely most effective NAG numerical Library routine to solve the input set of ODEs by checking various attributes of the system of ODEs and calculating a measure of compatibility of each routine to these attributes.") (((|Record| (|:| |measure| (|Float|)) (|:| |name| (|String|)) (|:| |explanations| (|List| (|String|)))) (|NumericalODEProblem|)) "\\spad{measure(prob)} is a top level ANNA function for identifying the most appropriate numerical routine from those in the routines table provided for solving the numerical ODE problem defined by \\axiom{\\spad{prob}}. \\blankline It calls each \\axiom{domain} of \\axiom{category} \\axiomType{OrdinaryDifferentialEquationsSolverCategory} in turn to calculate all measures and returns the best \\spadignore{i.e.} the name of the most appropriate domain and any other relevant information. It predicts the likely most effective NAG numerical Library routine to solve the input set of ODEs by checking various attributes of the system of ODEs and calculating a measure of compatibility of each routine to these attributes.")) (|solve| (((|Result|) (|Vector| (|Expression| (|Float|))) (|Float|) (|Float|) (|List| (|Float|)) (|Expression| (|Float|)) (|List| (|Float|)) (|Float|) (|Float|)) "\\spad{solve(f,xStart,xEnd,yInitial,G,intVals,epsabs,epsrel)} is a top level ANNA function to solve numerically a system of ordinary differential equations,{} \\axiom{\\spad{f}},{} \\spadignore{i.e.} equations for the derivatives \\spad{Y}[1]'..\\spad{Y}[\\spad{n}]' defined in terms of \\spad{X},{}\\spad{Y}[1]..\\spad{Y}[\\spad{n}] from \\axiom{\\spad{xStart}} to \\axiom{\\spad{xEnd}} with the initial values for \\spad{Y}[1]..\\spad{Y}[\\spad{n}] (\\axiom{\\spad{yInitial}}) to an absolute error requirement \\axiom{\\spad{epsabs}} and relative error \\axiom{\\spad{epsrel}}. The values of \\spad{Y}[1]..\\spad{Y}[\\spad{n}] will be output for the values of \\spad{X} in \\axiom{\\spad{intVals}}. The calculation will stop if the function \\spad{G}(\\spad{X},{}\\spad{Y}[1],{}..,{}\\spad{Y}[\\spad{n}]) evaluates to zero before \\spad{X} = \\spad{xEnd}. \\blankline It iterates over the \\axiom{domains} of \\axiomType{OrdinaryDifferentialEquationsSolverCategory} contained in the table of routines \\axiom{\\spad{R}} to get the name and other relevant information of the the (domain of the) numerical routine likely to be the most appropriate,{} \\spadignore{i.e.} have the best \\axiom{measure}. \\blankline The method used to perform the numerical process will be one of the routines contained in the NAG numerical Library. The function predicts the likely most effective routine by checking various attributes of the system of ODE\\spad{'s} and calculating a measure of compatibility of each routine to these attributes. \\blankline It then calls the resulting `best' routine.") (((|Result|) (|Vector| (|Expression| (|Float|))) (|Float|) (|Float|) (|List| (|Float|)) (|Expression| (|Float|)) (|List| (|Float|)) (|Float|)) "\\spad{solve(f,xStart,xEnd,yInitial,G,intVals,tol)} is a top level ANNA function to solve numerically a system of ordinary differential equations,{} \\axiom{\\spad{f}},{} \\spadignore{i.e.} equations for the derivatives \\spad{Y}[1]'..\\spad{Y}[\\spad{n}]' defined in terms of \\spad{X},{}\\spad{Y}[1]..\\spad{Y}[\\spad{n}] from \\axiom{\\spad{xStart}} to \\axiom{\\spad{xEnd}} with the initial values for \\spad{Y}[1]..\\spad{Y}[\\spad{n}] (\\axiom{\\spad{yInitial}}) to a tolerance \\axiom{\\spad{tol}}. The values of \\spad{Y}[1]..\\spad{Y}[\\spad{n}] will be output for the values of \\spad{X} in \\axiom{\\spad{intVals}}. The calculation will stop if the function \\spad{G}(\\spad{X},{}\\spad{Y}[1],{}..,{}\\spad{Y}[\\spad{n}]) evaluates to zero before \\spad{X} = \\spad{xEnd}. \\blankline It iterates over the \\axiom{domains} of \\axiomType{OrdinaryDifferentialEquationsSolverCategory} contained in the table of routines \\axiom{\\spad{R}} to get the name and other relevant information of the the (domain of the) numerical routine likely to be the most appropriate,{} \\spadignore{i.e.} have the best \\axiom{measure}. \\blankline The method used to perform the numerical process will be one of the routines contained in the NAG numerical Library. The function predicts the likely most effective routine by checking various attributes of the system of ODE\\spad{'s} and calculating a measure of compatibility of each routine to these attributes. \\blankline It then calls the resulting `best' routine.") (((|Result|) (|Vector| (|Expression| (|Float|))) (|Float|) (|Float|) (|List| (|Float|)) (|List| (|Float|)) (|Float|)) "\\spad{solve(f,xStart,xEnd,yInitial,intVals,tol)} is a top level ANNA function to solve numerically a system of ordinary differential equations,{} \\axiom{\\spad{f}},{} \\spadignore{i.e.} equations for the derivatives \\spad{Y}[1]'..\\spad{Y}[\\spad{n}]' defined in terms of \\spad{X},{}\\spad{Y}[1]..\\spad{Y}[\\spad{n}] from \\axiom{\\spad{xStart}} to \\axiom{\\spad{xEnd}} with the initial values for \\spad{Y}[1]..\\spad{Y}[\\spad{n}] (\\axiom{\\spad{yInitial}}) to a tolerance \\axiom{\\spad{tol}}. The values of \\spad{Y}[1]..\\spad{Y}[\\spad{n}] will be output for the values of \\spad{X} in \\axiom{\\spad{intVals}}. \\blankline It iterates over the \\axiom{domains} of \\axiomType{OrdinaryDifferentialEquationsSolverCategory} contained in the table of routines \\axiom{\\spad{R}} to get the name and other relevant information of the the (domain of the) numerical routine likely to be the most appropriate,{} \\spadignore{i.e.} have the best \\axiom{measure}. \\blankline The method used to perform the numerical process will be one of the routines contained in the NAG numerical Library. The function predicts the likely most effective routine by checking various attributes of the system of ODE\\spad{'s} and calculating a measure of compatibility of each routine to these attributes. \\blankline It then calls the resulting `best' routine.") (((|Result|) (|Vector| (|Expression| (|Float|))) (|Float|) (|Float|) (|List| (|Float|)) (|Expression| (|Float|)) (|Float|)) "\\spad{solve(f,xStart,xEnd,yInitial,G,tol)} is a top level ANNA function to solve numerically a system of ordinary differential equations,{} \\axiom{\\spad{f}},{} \\spadignore{i.e.} equations for the derivatives \\spad{Y}[1]'..\\spad{Y}[\\spad{n}]' defined in terms of \\spad{X},{}\\spad{Y}[1]..\\spad{Y}[\\spad{n}] from \\axiom{\\spad{xStart}} to \\axiom{\\spad{xEnd}} with the initial values for \\spad{Y}[1]..\\spad{Y}[\\spad{n}] (\\axiom{\\spad{yInitial}}) to a tolerance \\axiom{\\spad{tol}}. The calculation will stop if the function \\spad{G}(\\spad{X},{}\\spad{Y}[1],{}..,{}\\spad{Y}[\\spad{n}]) evaluates to zero before \\spad{X} = \\spad{xEnd}. \\blankline It iterates over the \\axiom{domains} of \\axiomType{OrdinaryDifferentialEquationsSolverCategory} contained in the table of routines \\axiom{\\spad{R}} to get the name and other relevant information of the the (domain of the) numerical routine likely to be the most appropriate,{} \\spadignore{i.e.} have the best \\axiom{measure}. \\blankline The method used to perform the numerical process will be one of the routines contained in the NAG numerical Library. The function predicts the likely most effective routine by checking various attributes of the system of ODE\\spad{'s} and calculating a measure of compatibility of each routine to these attributes. \\blankline It then calls the resulting `best' routine.") (((|Result|) (|Vector| (|Expression| (|Float|))) (|Float|) (|Float|) (|List| (|Float|)) (|Float|)) "\\spad{solve(f,xStart,xEnd,yInitial,tol)} is a top level ANNA function to solve numerically a system of ordinary differential equations,{} \\axiom{\\spad{f}},{} \\spadignore{i.e.} equations for the derivatives \\spad{Y}[1]'..\\spad{Y}[\\spad{n}]' defined in terms of \\spad{X},{}\\spad{Y}[1]..\\spad{Y}[\\spad{n}] from \\axiom{\\spad{xStart}} to \\axiom{\\spad{xEnd}} with the initial values for \\spad{Y}[1]..\\spad{Y}[\\spad{n}] (\\axiom{\\spad{yInitial}}) to a tolerance \\axiom{\\spad{tol}}. \\blankline It iterates over the \\axiom{domains} of \\axiomType{OrdinaryDifferentialEquationsSolverCategory} contained in the table of routines \\axiom{\\spad{R}} to get the name and other relevant information of the the (domain of the) numerical routine likely to be the most appropriate,{} \\spadignore{i.e.} have the best \\axiom{measure}. \\blankline The method used to perform the numerical process will be one of the routines contained in the NAG numerical Library. The function predicts the likely most effective routine by checking various attributes of the system of ODE\\spad{'s} and calculating a measure of compatibility of each routine to these attributes. \\blankline It then calls the resulting `best' routine.") (((|Result|) (|Vector| (|Expression| (|Float|))) (|Float|) (|Float|) (|List| (|Float|))) "\\spad{solve(f,xStart,xEnd,yInitial)} is a top level ANNA function to solve numerically a system of ordinary differential equations \\spadignore{i.e.} equations for the derivatives \\spad{Y}[1]'..\\spad{Y}[\\spad{n}]' defined in terms of \\spad{X},{}\\spad{Y}[1]..\\spad{Y}[\\spad{n}],{} together with a starting value for \\spad{X} and \\spad{Y}[1]..\\spad{Y}[\\spad{n}] (called the initial conditions) and a final value of \\spad{X}. A default value is used for the accuracy requirement. \\blankline It iterates over the \\axiom{domains} of \\axiomType{OrdinaryDifferentialEquationsSolverCategory} contained in the table of routines \\axiom{\\spad{R}} to get the name and other relevant information of the the (domain of the) numerical routine likely to be the most appropriate,{} \\spadignore{i.e.} have the best \\axiom{measure}. \\blankline The method used to perform the numerical process will be one of the routines contained in the NAG numerical Library. The function predicts the likely most effective routine by checking various attributes of the system of ODE\\spad{'s} and calculating a measure of compatibility of each routine to these attributes. \\blankline It then calls the resulting `best' routine.") (((|Result|) (|NumericalODEProblem|) (|RoutinesTable|)) "\\spad{solve(odeProblem,R)} is a top level ANNA function to solve numerically a system of ordinary differential equations \\spadignore{i.e.} equations for the derivatives \\spad{Y}[1]'..\\spad{Y}[\\spad{n}]' defined in terms of \\spad{X},{}\\spad{Y}[1]..\\spad{Y}[\\spad{n}],{} together with starting values for \\spad{X} and \\spad{Y}[1]..\\spad{Y}[\\spad{n}] (called the initial conditions),{} a final value of \\spad{X},{} an accuracy requirement and any intermediate points at which the result is required. \\blankline It iterates over the \\axiom{domains} of \\axiomType{OrdinaryDifferentialEquationsSolverCategory} contained in the table of routines \\axiom{\\spad{R}} to get the name and other relevant information of the the (domain of the) numerical routine likely to be the most appropriate,{} \\spadignore{i.e.} have the best \\axiom{measure}. \\blankline The method used to perform the numerical process will be one of the routines contained in the NAG numerical Library. The function predicts the likely most effective routine by checking various attributes of the system of ODE\\spad{'s} and calculating a measure of compatibility of each routine to these attributes. \\blankline It then calls the resulting `best' routine.") (((|Result|) (|NumericalODEProblem|)) "\\spad{solve(odeProblem)} is a top level ANNA function to solve numerically a system of ordinary differential equations \\spadignore{i.e.} equations for the derivatives \\spad{Y}[1]'..\\spad{Y}[\\spad{n}]' defined in terms of \\spad{X},{}\\spad{Y}[1]..\\spad{Y}[\\spad{n}],{} together with starting values for \\spad{X} and \\spad{Y}[1]..\\spad{Y}[\\spad{n}] (called the initial conditions),{} a final value of \\spad{X},{} an accuracy requirement and any intermediate points at which the result is required. \\blankline It iterates over the \\axiom{domains} of \\axiomType{OrdinaryDifferentialEquationsSolverCategory} to get the name and other relevant information of the the (domain of the) numerical routine likely to be the most appropriate,{} \\spadignore{i.e.} have the best \\axiom{measure}. \\blankline The method used to perform the numerical process will be one of the routines contained in the NAG numerical Library. The function predicts the likely most effective routine by checking various attributes of the system of ODE\\spad{'s} and calculating a measure of compatibility of each routine to these attributes. \\blankline It then calls the resulting `best' routine."))) NIL NIL -(-818 -1966 UP UPUP R) +(-818 -1955 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 -(-819 -1966 UP L LQ) +(-819 -1955 UP L LQ) ((|constructor| (NIL "\\spad{PrimitiveRatDE} provides functions for in-field solutions of linear \\indented{1}{ordinary differential equations,{} in the transcendental case.} \\indented{1}{The derivation to use is given by the parameter \\spad{L}.}")) (|splitDenominator| (((|Record| (|:| |eq| |#3|) (|:| |rh| (|List| (|Fraction| |#2|)))) |#4| (|List| (|Fraction| |#2|))) "\\spad{splitDenominator(op, [g1,...,gm])} returns \\spad{op0, [h1,...,hm]} such that the equations \\spad{op y = c1 g1 + ... + cm gm} and \\spad{op0 y = c1 h1 + ... + cm hm} have the same solutions.")) (|indicialEquation| ((|#2| |#4| |#1|) "\\spad{indicialEquation(op, a)} returns the indicial equation of \\spad{op} at \\spad{a}.") ((|#2| |#3| |#1|) "\\spad{indicialEquation(op, a)} returns the indicial equation of \\spad{op} at \\spad{a}.")) (|indicialEquations| (((|List| (|Record| (|:| |center| |#2|) (|:| |equation| |#2|))) |#4| |#2|) "\\spad{indicialEquations(op, p)} returns \\spad{[[d1,e1],...,[dq,eq]]} where the \\spad{d_i}\\spad{'s} are the affine singularities of \\spad{op} above the roots of \\spad{p},{} and the \\spad{e_i}\\spad{'s} are the indicial equations at each \\spad{d_i}.") (((|List| (|Record| (|:| |center| |#2|) (|:| |equation| |#2|))) |#4|) "\\spad{indicialEquations op} returns \\spad{[[d1,e1],...,[dq,eq]]} where the \\spad{d_i}\\spad{'s} are the affine singularities of \\spad{op},{} and the \\spad{e_i}\\spad{'s} are the indicial equations at each \\spad{d_i}.") (((|List| (|Record| (|:| |center| |#2|) (|:| |equation| |#2|))) |#3| |#2|) "\\spad{indicialEquations(op, p)} returns \\spad{[[d1,e1],...,[dq,eq]]} where the \\spad{d_i}\\spad{'s} are the affine singularities of \\spad{op} above the roots of \\spad{p},{} and the \\spad{e_i}\\spad{'s} are the indicial equations at each \\spad{d_i}.") (((|List| (|Record| (|:| |center| |#2|) (|:| |equation| |#2|))) |#3|) "\\spad{indicialEquations op} returns \\spad{[[d1,e1],...,[dq,eq]]} where the \\spad{d_i}\\spad{'s} are the affine singularities of \\spad{op},{} and the \\spad{e_i}\\spad{'s} are the indicial equations at each \\spad{d_i}.")) (|denomLODE| ((|#2| |#3| (|List| (|Fraction| |#2|))) "\\spad{denomLODE(op, [g1,...,gm])} returns a polynomial \\spad{d} such that any rational solution of \\spad{op y = c1 g1 + ... + cm gm} is of the form \\spad{p/d} for some polynomial \\spad{p}.") (((|Union| |#2| "failed") |#3| (|Fraction| |#2|)) "\\spad{denomLODE(op, g)} returns a polynomial \\spad{d} such that any rational solution of \\spad{op y = g} is of the form \\spad{p/d} for some polynomial \\spad{p},{} and \"failed\",{} if the equation has no rational solution."))) NIL NIL @@ -3212,38 +3212,38 @@ 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 -(-821 -1966 UP L LQ) +(-821 -1955 UP L LQ) ((|constructor| (NIL "In-field solution of Riccati equations,{} primitive case.")) (|changeVar| ((|#3| |#3| (|Fraction| |#2|)) "\\spad{changeVar(+/[ai D^i], a)} returns the operator \\spad{+/[ai (D+a)^i]}.") ((|#3| |#3| |#2|) "\\spad{changeVar(+/[ai D^i], a)} returns the operator \\spad{+/[ai (D+a)^i]}.")) (|singRicDE| (((|List| (|Record| (|:| |frac| (|Fraction| |#2|)) (|:| |eq| |#3|))) |#3| (|Mapping| (|List| |#2|) |#2| (|SparseUnivariatePolynomial| |#2|)) (|Mapping| (|Factored| |#2|) |#2|)) "\\spad{singRicDE(op, zeros, ezfactor)} returns \\spad{[[f1, L1], [f2, L2], ... , [fk, Lk]]} such that the singular part of any rational solution of the associated Riccati equation of \\spad{op y=0} must be one of the \\spad{fi}\\spad{'s} (up to the constant coefficient),{} in which case the equation for \\spad{z=y e^{-int p}} is \\spad{Li z=0}. \\spad{zeros(C(x),H(x,y))} returns all the \\spad{P_i(x)}\\spad{'s} such that \\spad{H(x,P_i(x)) = 0 modulo C(x)}. Argument \\spad{ezfactor} is a factorisation in \\spad{UP},{} not necessarily into irreducibles.")) (|polyRicDE| (((|List| (|Record| (|:| |poly| |#2|) (|:| |eq| |#3|))) |#3| (|Mapping| (|List| |#1|) |#2|)) "\\spad{polyRicDE(op, zeros)} returns \\spad{[[p1, L1], [p2, L2], ... , [pk, Lk]]} such that the polynomial part of any rational solution of the associated Riccati equation of \\spad{op y=0} must be one of the \\spad{pi}\\spad{'s} (up to the constant coefficient),{} in which case the equation for \\spad{z=y e^{-int p}} is \\spad{Li z =0}. \\spad{zeros} is a zero finder in \\spad{UP}.")) (|constantCoefficientRicDE| (((|List| (|Record| (|:| |constant| |#1|) (|:| |eq| |#3|))) |#3| (|Mapping| (|List| |#1|) |#2|)) "\\spad{constantCoefficientRicDE(op, ric)} returns \\spad{[[a1, L1], [a2, L2], ... , [ak, Lk]]} such that any rational solution with no polynomial part of the associated Riccati equation of \\spad{op y = 0} must be one of the \\spad{ai}\\spad{'s} in which case the equation for \\spad{z = y e^{-int ai}} is \\spad{Li z = 0}. \\spad{ric} is a Riccati equation solver over \\spad{F},{} whose input is the associated linear equation.")) (|leadingCoefficientRicDE| (((|List| (|Record| (|:| |deg| (|NonNegativeInteger|)) (|:| |eq| |#2|))) |#3|) "\\spad{leadingCoefficientRicDE(op)} returns \\spad{[[m1, p1], [m2, p2], ... , [mk, pk]]} such that the polynomial part of any rational solution of the associated Riccati equation of \\spad{op y = 0} must have degree \\spad{mj} for some \\spad{j},{} and its leading coefficient is then a zero of \\spad{pj}. In addition,{}\\spad{m1>m2> ... >mk}.")) (|denomRicDE| ((|#2| |#3|) "\\spad{denomRicDE(op)} returns a polynomial \\spad{d} such that any rational solution of the associated Riccati equation of \\spad{op y = 0} is of the form \\spad{p/d + q'/q + r} for some polynomials \\spad{p} and \\spad{q} and a reduced \\spad{r}. Also,{} \\spad{deg(p) < deg(d)} and {\\spad{gcd}(\\spad{d},{}\\spad{q}) = 1}."))) NIL NIL -(-822 -1966 UP) +(-822 -1955 UP) ((|constructor| (NIL "\\spad{RationalLODE} provides functions for in-field solutions of linear \\indented{1}{ordinary differential equations,{} in the rational case.}")) (|indicialEquationAtInfinity| ((|#2| (|LinearOrdinaryDifferentialOperator2| |#2| (|Fraction| |#2|))) "\\spad{indicialEquationAtInfinity op} returns the indicial equation of \\spad{op} at infinity.") ((|#2| (|LinearOrdinaryDifferentialOperator1| (|Fraction| |#2|))) "\\spad{indicialEquationAtInfinity op} returns the indicial equation of \\spad{op} at infinity.")) (|ratDsolve| (((|Record| (|:| |basis| (|List| (|Fraction| |#2|))) (|:| |mat| (|Matrix| |#1|))) (|LinearOrdinaryDifferentialOperator2| |#2| (|Fraction| |#2|)) (|List| (|Fraction| |#2|))) "\\spad{ratDsolve(op, [g1,...,gm])} returns \\spad{[[h1,...,hq], M]} such that any rational solution of \\spad{op y = c1 g1 + ... + cm gm} is of the form \\spad{d1 h1 + ... + dq hq} where \\spad{M [d1,...,dq,c1,...,cm] = 0}.") (((|Record| (|:| |particular| (|Union| (|Fraction| |#2|) "failed")) (|:| |basis| (|List| (|Fraction| |#2|)))) (|LinearOrdinaryDifferentialOperator2| |#2| (|Fraction| |#2|)) (|Fraction| |#2|)) "\\spad{ratDsolve(op, g)} returns \\spad{[\"failed\", []]} if the equation \\spad{op y = g} has no rational solution. Otherwise,{} it returns \\spad{[f, [y1,...,ym]]} where \\spad{f} is a particular rational solution and the \\spad{yi}\\spad{'s} form a basis for the rational solutions of the homogeneous equation.") (((|Record| (|:| |basis| (|List| (|Fraction| |#2|))) (|:| |mat| (|Matrix| |#1|))) (|LinearOrdinaryDifferentialOperator1| (|Fraction| |#2|)) (|List| (|Fraction| |#2|))) "\\spad{ratDsolve(op, [g1,...,gm])} returns \\spad{[[h1,...,hq], M]} such that any rational solution of \\spad{op y = c1 g1 + ... + cm gm} is of the form \\spad{d1 h1 + ... + dq hq} where \\spad{M [d1,...,dq,c1,...,cm] = 0}.") (((|Record| (|:| |particular| (|Union| (|Fraction| |#2|) "failed")) (|:| |basis| (|List| (|Fraction| |#2|)))) (|LinearOrdinaryDifferentialOperator1| (|Fraction| |#2|)) (|Fraction| |#2|)) "\\spad{ratDsolve(op, g)} returns \\spad{[\"failed\", []]} if the equation \\spad{op y = g} has no rational solution. Otherwise,{} it returns \\spad{[f, [y1,...,ym]]} where \\spad{f} is a particular rational solution and the \\spad{yi}\\spad{'s} form a basis for the rational solutions of the homogeneous equation."))) NIL NIL -(-823 -1966 L UP A LO) +(-823 -1955 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 -(-824 -1966 UP) +(-824 -1955 UP) ((|constructor| (NIL "In-field solution of Riccati equations,{} rational case.")) (|polyRicDE| (((|List| (|Record| (|:| |poly| |#2|) (|:| |eq| (|LinearOrdinaryDifferentialOperator2| |#2| (|Fraction| |#2|))))) (|LinearOrdinaryDifferentialOperator2| |#2| (|Fraction| |#2|)) (|Mapping| (|List| |#1|) |#2|)) "\\spad{polyRicDE(op, zeros)} returns \\spad{[[p1, L1], [p2, L2], ... , [pk,Lk]]} such that the polynomial part of any rational solution of the associated Riccati equation of \\spad{op y = 0} must be one of the \\spad{pi}\\spad{'s} (up to the constant coefficient),{} in which case the equation for \\spad{z = y e^{-int p}} is \\spad{Li z = 0}. \\spad{zeros} is a zero finder in \\spad{UP}.")) (|singRicDE| (((|List| (|Record| (|:| |frac| (|Fraction| |#2|)) (|:| |eq| (|LinearOrdinaryDifferentialOperator2| |#2| (|Fraction| |#2|))))) (|LinearOrdinaryDifferentialOperator2| |#2| (|Fraction| |#2|)) (|Mapping| (|Factored| |#2|) |#2|)) "\\spad{singRicDE(op, ezfactor)} returns \\spad{[[f1,L1], [f2,L2],..., [fk,Lk]]} such that the singular \\spad{++} part of any rational solution of the associated Riccati equation of \\spad{op y = 0} must be one of the \\spad{fi}\\spad{'s} (up to the constant coefficient),{} in which case the equation for \\spad{z = y e^{-int ai}} is \\spad{Li z = 0}. Argument \\spad{ezfactor} is a factorisation in \\spad{UP},{} not necessarily into irreducibles.")) (|ricDsolve| (((|List| (|Fraction| |#2|)) (|LinearOrdinaryDifferentialOperator2| |#2| (|Fraction| |#2|)) (|Mapping| (|Factored| |#2|) |#2|)) "\\spad{ricDsolve(op, ezfactor)} returns the rational solutions of the associated Riccati equation of \\spad{op y = 0}. Argument \\spad{ezfactor} is a factorisation in \\spad{UP},{} not necessarily into irreducibles.") (((|List| (|Fraction| |#2|)) (|LinearOrdinaryDifferentialOperator2| |#2| (|Fraction| |#2|))) "\\spad{ricDsolve(op)} returns the rational solutions of the associated Riccati equation of \\spad{op y = 0}.") (((|List| (|Fraction| |#2|)) (|LinearOrdinaryDifferentialOperator1| (|Fraction| |#2|)) (|Mapping| (|Factored| |#2|) |#2|)) "\\spad{ricDsolve(op, ezfactor)} returns the rational solutions of the associated Riccati equation of \\spad{op y = 0}. Argument \\spad{ezfactor} is a factorisation in \\spad{UP},{} not necessarily into irreducibles.") (((|List| (|Fraction| |#2|)) (|LinearOrdinaryDifferentialOperator1| (|Fraction| |#2|))) "\\spad{ricDsolve(op)} returns the rational solutions of the associated Riccati equation of \\spad{op y = 0}.") (((|List| (|Fraction| |#2|)) (|LinearOrdinaryDifferentialOperator2| |#2| (|Fraction| |#2|)) (|Mapping| (|List| |#1|) |#2|) (|Mapping| (|Factored| |#2|) |#2|)) "\\spad{ricDsolve(op, zeros, ezfactor)} returns the rational solutions of the associated Riccati equation of \\spad{op y = 0}. \\spad{zeros} is a zero finder in \\spad{UP}. Argument \\spad{ezfactor} is a factorisation in \\spad{UP},{} not necessarily into irreducibles.") (((|List| (|Fraction| |#2|)) (|LinearOrdinaryDifferentialOperator2| |#2| (|Fraction| |#2|)) (|Mapping| (|List| |#1|) |#2|)) "\\spad{ricDsolve(op, zeros)} returns the rational solutions of the associated Riccati equation of \\spad{op y = 0}. \\spad{zeros} is a zero finder in \\spad{UP}.") (((|List| (|Fraction| |#2|)) (|LinearOrdinaryDifferentialOperator1| (|Fraction| |#2|)) (|Mapping| (|List| |#1|) |#2|) (|Mapping| (|Factored| |#2|) |#2|)) "\\spad{ricDsolve(op, zeros, ezfactor)} returns the rational solutions of the associated Riccati equation of \\spad{op y = 0}. \\spad{zeros} is a zero finder in \\spad{UP}. Argument \\spad{ezfactor} is a factorisation in \\spad{UP},{} not necessarily into irreducibles.") (((|List| (|Fraction| |#2|)) (|LinearOrdinaryDifferentialOperator1| (|Fraction| |#2|)) (|Mapping| (|List| |#1|) |#2|)) "\\spad{ricDsolve(op, zeros)} returns the rational solutions of the associated Riccati equation of \\spad{op y = 0}. \\spad{zeros} is a zero finder in \\spad{UP}."))) NIL ((|HasCategory| |#1| (QUOTE (-27)))) -(-825 -1966 LO) +(-825 -1955 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 -(-826 -1966 LODO) +(-826 -1955 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}. 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The ranking on the differential indeterminate is orderly. This is analogous to the domain \\spadtype{Polynomial}. \\blankline"))) (((-4464 "*") |has| |#1| (-174)) (-4455 |has| |#1| (-568)) (-4460 |has| |#1| (-6 -4460)) (-4457 . T) (-4456 . T) (-4459 . 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(((-4464 "*") |has| |#2| (-374)) (-4455 |has| |#2| (-374)) (-4460 |has| |#2| (-374)) (-4454 |has| |#2| (-374)) (-4459 . T) (-4457 . T) (-4456 . T)) @@ -3311,7 +3311,7 @@ NIL (-845 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."))) ((-4459 |has| |#1| (-860))) -((|HasCategory| |#1| (QUOTE (-860))) (|HasCategory| |#1| (QUOTE (-21))) (-2781 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-860)))) (|HasCategory| |#1| (LIST (QUOTE -1057) (LIST (QUOTE -419) (QUOTE (-576))))) (-2781 (|HasCategory| |#1| (QUOTE (-860))) (|HasCategory| |#1| (LIST (QUOTE -1057) (QUOTE (-576))))) (|HasCategory| |#1| (LIST (QUOTE -1057) (QUOTE (-576)))) (|HasCategory| |#1| (QUOTE (-557)))) +((|HasCategory| |#1| (QUOTE (-860))) (|HasCategory| |#1| (QUOTE (-21))) (-2755 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-860)))) (|HasCategory| |#1| (LIST (QUOTE -1057) (LIST (QUOTE -419) (QUOTE (-576))))) (-2755 (|HasCategory| |#1| (QUOTE (-860))) (|HasCategory| |#1| (LIST (QUOTE -1057) (QUOTE (-576))))) (|HasCategory| |#1| (LIST (QUOTE -1057) (QUOTE (-576)))) (|HasCategory| |#1| (QUOTE (-557)))) (-846 A S) ((|constructor| (NIL "This category specifies the interface for operators used to build terms,{} in the sense of Universal Algebra. The domain parameter \\spad{S} provides representation for the `external name' of an operator.")) (|is?| (((|Boolean|) $ |#2|) "\\spad{is?(op,n)} holds if the name of the operator \\spad{op} is \\spad{n}.")) (|arity| (((|Arity|) $) "\\spad{arity(op)} returns the arity of the operator \\spad{op}.")) (|name| ((|#2| $) "\\spad{name(op)} returns the externam name of \\spad{op}."))) NIL @@ -3351,12 +3351,12 @@ NIL (-855 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| (($) "\\spad{plusInfinity()} returns +infinity."))) ((-4459 |has| |#1| (-860))) -((|HasCategory| |#1| (QUOTE (-860))) (|HasCategory| |#1| (QUOTE (-21))) (-2781 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-860)))) (|HasCategory| |#1| (LIST (QUOTE -1057) (LIST (QUOTE -419) (QUOTE (-576))))) (-2781 (|HasCategory| |#1| (QUOTE (-860))) (|HasCategory| |#1| (LIST (QUOTE -1057) (QUOTE (-576))))) (|HasCategory| |#1| (LIST (QUOTE -1057) (QUOTE (-576)))) (|HasCategory| |#1| (QUOTE (-557)))) +((|HasCategory| |#1| (QUOTE (-860))) (|HasCategory| |#1| (QUOTE (-21))) (-2755 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-860)))) (|HasCategory| |#1| (LIST (QUOTE -1057) (LIST (QUOTE -419) (QUOTE (-576))))) (-2755 (|HasCategory| |#1| (QUOTE (-860))) (|HasCategory| |#1| (LIST (QUOTE -1057) (QUOTE (-576))))) (|HasCategory| |#1| (LIST (QUOTE -1057) (QUOTE (-576)))) (|HasCategory| |#1| (QUOTE (-557)))) (-856) ((|constructor| (NIL "Ordered finite sets.")) (|max| (($) "\\spad{max} is the maximum value of \\%.")) (|min| (($) "\\spad{min} is the minimum value of \\%."))) NIL NIL -(-857 -2695 S) +(-857 -2701 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 @@ -3392,11 +3392,11 @@ NIL ((|constructor| (NIL "\\spad{UnivariateSkewPolynomialCategoryOps} provides products and \\indented{1}{divisions of univariate skew polynomials.}")) (|rightDivide| (((|Record| (|:| |quotient| |#2|) (|:| |remainder| |#2|)) |#2| |#2| (|Automorphism| |#1|)) "\\spad{rightDivide(a, b, sigma)} returns the pair \\spad{[q,r]} such that \\spad{a = q*b + r} and the degree of \\spad{r} is less than the degree of \\spad{b}. This process is called ``right division\\spad{''}. \\spad{\\sigma} is the morphism to use.")) (|leftDivide| (((|Record| (|:| |quotient| |#2|) (|:| |remainder| |#2|)) |#2| |#2| (|Automorphism| |#1|)) "\\spad{leftDivide(a, b, sigma)} returns the pair \\spad{[q,r]} such that \\spad{a = b*q + r} and the degree of \\spad{r} is less than the degree of \\spad{b}. This process is called ``left division\\spad{''}. \\spad{\\sigma} is the morphism to use.")) (|monicRightDivide| (((|Record| (|:| |quotient| |#2|) (|:| |remainder| |#2|)) |#2| |#2| (|Automorphism| |#1|)) "\\spad{monicRightDivide(a, b, sigma)} returns the pair \\spad{[q,r]} such that \\spad{a = q*b + r} and the degree of \\spad{r} is less than the degree of \\spad{b}. \\spad{b} must be monic. This process is called ``right division\\spad{''}. \\spad{\\sigma} is the morphism to use.")) (|monicLeftDivide| (((|Record| (|:| |quotient| |#2|) (|:| |remainder| |#2|)) |#2| |#2| (|Automorphism| |#1|)) "\\spad{monicLeftDivide(a, b, sigma)} returns the pair \\spad{[q,r]} such that \\spad{a = b*q + r} and the degree of \\spad{r} is less than the degree of \\spad{b}. \\spad{b} must be monic. This process is called ``left division\\spad{''}. \\spad{\\sigma} is the morphism to use.")) (|apply| ((|#1| |#2| |#1| |#1| (|Automorphism| |#1|) (|Mapping| |#1| |#1|)) "\\spad{apply(p, c, m, sigma, delta)} returns \\spad{p(m)} where the action is given by \\spad{x m = c sigma(m) + delta(m)}.")) (|times| ((|#2| |#2| |#2| (|Automorphism| |#1|) (|Mapping| |#1| |#1|)) "\\spad{times(p, q, sigma, delta)} returns \\spad{p * q}. \\spad{\\sigma} and \\spad{\\delta} are the maps to use."))) NIL ((|HasCategory| |#1| (QUOTE (-374))) (|HasCategory| |#1| (QUOTE (-568)))) -(-866 R |sigma| -3574) +(-866 R |sigma| -3640) ((|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."))) ((-4456 . T) (-4457 . T) (-4459 . T)) ((|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (LIST (QUOTE -1057) (LIST (QUOTE -419) (QUOTE (-576))))) (|HasCategory| |#1| (LIST (QUOTE -1057) (QUOTE (-576)))) (|HasCategory| |#1| (QUOTE (-568))) (|HasCategory| |#1| (QUOTE (-464))) (|HasCategory| |#1| (QUOTE (-374)))) -(-867 |x| R |sigma| -3574) +(-867 |x| R |sigma| -3640) ((|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}."))) ((-4456 . T) (-4457 . T) (-4459 . T)) ((|HasCategory| |#2| (QUOTE (-174))) (|HasCategory| |#2| (LIST (QUOTE -1057) (LIST (QUOTE -419) (QUOTE (-576))))) (|HasCategory| |#2| (LIST (QUOTE -1057) (QUOTE (-576)))) (|HasCategory| |#2| (QUOTE (-568))) (|HasCategory| |#2| (QUOTE (-464))) (|HasCategory| |#2| (QUOTE (-374)))) @@ -3463,15 +3463,15 @@ NIL (-883 |p|) ((|constructor| (NIL "Stream-based implementation of \\spad{Qp:} numbers are represented as sum(\\spad{i} = \\spad{k}..,{} a[\\spad{i}] * p^i) where the a[\\spad{i}] lie in 0,{}1,{}...,{}(\\spad{p} - 1)."))) ((-4454 . T) (-4460 . T) (-4455 . T) ((-4464 "*") . T) (-4456 . T) (-4457 . T) (-4459 . T)) -((|HasCategory| (-882 |#1|) (QUOTE (-926))) (|HasCategory| (-882 |#1|) (LIST (QUOTE -1057) (QUOTE (-1195)))) (|HasCategory| (-882 |#1|) (QUOTE (-146))) (|HasCategory| (-882 |#1|) (QUOTE (-148))) (|HasCategory| (-882 |#1|) (LIST (QUOTE -626) (QUOTE (-548)))) (|HasCategory| (-882 |#1|) (QUOTE (-1041))) (|HasCategory| (-882 |#1|) (QUOTE (-832))) (-2781 (|HasCategory| (-882 |#1|) (QUOTE (-832))) (|HasCategory| (-882 |#1|) (QUOTE (-862)))) (|HasCategory| (-882 |#1|) (LIST (QUOTE -1057) (QUOTE (-576)))) (|HasCategory| (-882 |#1|) (QUOTE (-1171))) (|HasCategory| (-882 |#1|) (LIST (QUOTE -899) (QUOTE (-390)))) (|HasCategory| (-882 |#1|) (LIST (QUOTE -899) (QUOTE (-576)))) (|HasCategory| (-882 |#1|) (LIST (QUOTE -626) (LIST (QUOTE -905) (QUOTE (-390))))) (|HasCategory| (-882 |#1|) (LIST (QUOTE -626) (LIST (QUOTE -905) (QUOTE (-576))))) (|HasCategory| (-882 |#1|) (LIST (QUOTE -651) (QUOTE (-576)))) (|HasCategory| (-882 |#1|) (QUOTE (-237))) (|HasCategory| (-882 |#1|) (LIST (QUOTE -917) (QUOTE (-1195)))) (|HasCategory| (-882 |#1|) (QUOTE (-238))) (|HasCategory| (-882 |#1|) (LIST (QUOTE -915) (QUOTE (-1195)))) (|HasCategory| (-882 |#1|) (LIST (QUOTE -526) (QUOTE (-1195)) (LIST (QUOTE -882) (|devaluate| |#1|)))) (|HasCategory| (-882 |#1|) (LIST (QUOTE -319) (LIST (QUOTE -882) (|devaluate| |#1|)))) (|HasCategory| (-882 |#1|) (LIST (QUOTE -296) (LIST (QUOTE -882) (|devaluate| |#1|)) (LIST (QUOTE -882) (|devaluate| |#1|)))) (|HasCategory| (-882 |#1|) (QUOTE (-317))) (|HasCategory| (-882 |#1|) (QUOTE (-557))) (|HasCategory| (-882 |#1|) (QUOTE (-862))) (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| (-882 |#1|) (QUOTE (-926)))) (-2781 (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| (-882 |#1|) (QUOTE (-926)))) (|HasCategory| (-882 |#1|) (QUOTE (-146))))) +((|HasCategory| (-882 |#1|) (QUOTE (-926))) (|HasCategory| (-882 |#1|) (LIST (QUOTE -1057) (QUOTE (-1195)))) (|HasCategory| (-882 |#1|) (QUOTE (-146))) (|HasCategory| (-882 |#1|) (QUOTE (-148))) (|HasCategory| (-882 |#1|) (LIST (QUOTE -626) (QUOTE (-548)))) (|HasCategory| (-882 |#1|) (QUOTE (-1041))) (|HasCategory| (-882 |#1|) (QUOTE (-832))) (-2755 (|HasCategory| (-882 |#1|) (QUOTE (-832))) (|HasCategory| (-882 |#1|) (QUOTE (-862)))) (|HasCategory| (-882 |#1|) (LIST (QUOTE -1057) (QUOTE (-576)))) (|HasCategory| (-882 |#1|) (QUOTE (-1171))) (|HasCategory| (-882 |#1|) (LIST (QUOTE -899) (QUOTE (-390)))) (|HasCategory| (-882 |#1|) (LIST (QUOTE -899) (QUOTE (-576)))) (|HasCategory| (-882 |#1|) (LIST (QUOTE -626) (LIST (QUOTE -905) (QUOTE (-390))))) (|HasCategory| (-882 |#1|) (LIST (QUOTE -626) (LIST (QUOTE -905) (QUOTE (-576))))) (|HasCategory| (-882 |#1|) (LIST (QUOTE -651) (QUOTE (-576)))) (|HasCategory| (-882 |#1|) (QUOTE (-237))) (|HasCategory| (-882 |#1|) (LIST (QUOTE -917) (QUOTE (-1195)))) (|HasCategory| (-882 |#1|) (QUOTE (-238))) (|HasCategory| (-882 |#1|) (LIST (QUOTE -915) (QUOTE (-1195)))) (|HasCategory| (-882 |#1|) (LIST (QUOTE -526) (QUOTE (-1195)) (LIST (QUOTE -882) (|devaluate| |#1|)))) (|HasCategory| (-882 |#1|) (LIST (QUOTE -319) (LIST (QUOTE -882) (|devaluate| |#1|)))) (|HasCategory| (-882 |#1|) (LIST (QUOTE -296) (LIST (QUOTE -882) (|devaluate| |#1|)) (LIST (QUOTE -882) (|devaluate| |#1|)))) (|HasCategory| (-882 |#1|) (QUOTE (-317))) (|HasCategory| (-882 |#1|) (QUOTE (-557))) (|HasCategory| (-882 |#1|) (QUOTE (-862))) (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| (-882 |#1|) (QUOTE (-926)))) (-2755 (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| (-882 |#1|) (QUOTE (-926)))) (|HasCategory| (-882 |#1|) (QUOTE (-146))))) (-884 |p| PADIC) ((|constructor| (NIL "This is the category of stream-based representations of \\spad{Qp}.")) (|removeZeroes| (($ (|Integer|) $) "\\spad{removeZeroes(n,x)} removes up to \\spad{n} leading zeroes from the \\spad{p}-adic rational \\spad{x}.") (($ $) "\\spad{removeZeroes(x)} removes leading zeroes from the representation of the \\spad{p}-adic rational \\spad{x}. A \\spad{p}-adic rational is represented by (1) an exponent and (2) a \\spad{p}-adic integer which may have leading zero digits. When the \\spad{p}-adic integer has a leading zero digit,{} a 'leading zero' is removed from the \\spad{p}-adic rational as follows: the number is rewritten by increasing the exponent by 1 and dividing the \\spad{p}-adic integer by \\spad{p}. Note: \\spad{removeZeroes(f)} removes all leading zeroes from \\spad{f}.")) (|continuedFraction| (((|ContinuedFraction| (|Fraction| (|Integer|))) $) "\\spad{continuedFraction(x)} converts the \\spad{p}-adic rational number \\spad{x} to a continued fraction.")) (|approximate| (((|Fraction| (|Integer|)) $ (|Integer|)) "\\spad{approximate(x,n)} returns a rational number \\spad{y} such that \\spad{y = x (mod p^n)}."))) ((-4454 . T) (-4460 . T) (-4455 . T) ((-4464 "*") . T) (-4456 . T) (-4457 . T) (-4459 . T)) -((|HasCategory| |#2| (QUOTE (-926))) (|HasCategory| |#2| (LIST (QUOTE -1057) (QUOTE (-1195)))) (|HasCategory| |#2| (QUOTE (-146))) (|HasCategory| |#2| (QUOTE (-148))) (|HasCategory| |#2| (LIST (QUOTE -626) (QUOTE (-548)))) (|HasCategory| |#2| (QUOTE (-1041))) (|HasCategory| |#2| (QUOTE (-832))) (-2781 (|HasCategory| |#2| (QUOTE (-832))) (|HasCategory| |#2| (QUOTE (-862)))) (|HasCategory| |#2| (LIST (QUOTE -1057) (QUOTE (-576)))) (|HasCategory| |#2| (QUOTE (-1171))) (|HasCategory| |#2| (LIST (QUOTE -899) (QUOTE (-390)))) (|HasCategory| |#2| (LIST (QUOTE -899) (QUOTE (-576)))) (|HasCategory| |#2| (LIST (QUOTE -626) (LIST (QUOTE -905) (QUOTE (-390))))) (|HasCategory| |#2| (LIST (QUOTE -626) (LIST (QUOTE -905) (QUOTE (-576))))) (|HasCategory| |#2| (LIST (QUOTE -651) (QUOTE (-576)))) (|HasCategory| |#2| (QUOTE (-237))) (|HasCategory| |#2| (LIST (QUOTE -917) (QUOTE (-1195)))) (|HasCategory| |#2| (QUOTE (-238))) (|HasCategory| |#2| (LIST (QUOTE -915) (QUOTE (-1195)))) (|HasCategory| |#2| (LIST (QUOTE -526) (QUOTE (-1195)) (|devaluate| |#2|))) (|HasCategory| |#2| (LIST (QUOTE -319) (|devaluate| |#2|))) (|HasCategory| |#2| (LIST (QUOTE -296) (|devaluate| |#2|) (|devaluate| |#2|))) (|HasCategory| |#2| (QUOTE (-317))) (|HasCategory| |#2| (QUOTE (-557))) (|HasCategory| |#2| (QUOTE (-862))) (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| |#2| (QUOTE (-926)))) (-2781 (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| |#2| (QUOTE (-926)))) (|HasCategory| |#2| (QUOTE (-146))))) +((|HasCategory| |#2| (QUOTE (-926))) (|HasCategory| |#2| (LIST (QUOTE -1057) (QUOTE (-1195)))) (|HasCategory| |#2| (QUOTE (-146))) (|HasCategory| |#2| (QUOTE (-148))) (|HasCategory| |#2| (LIST (QUOTE -626) (QUOTE (-548)))) (|HasCategory| |#2| (QUOTE (-1041))) (|HasCategory| |#2| (QUOTE (-832))) (-2755 (|HasCategory| |#2| (QUOTE (-832))) (|HasCategory| |#2| (QUOTE (-862)))) (|HasCategory| |#2| (LIST (QUOTE -1057) (QUOTE (-576)))) (|HasCategory| |#2| (QUOTE (-1171))) (|HasCategory| |#2| (LIST (QUOTE -899) (QUOTE (-390)))) (|HasCategory| |#2| (LIST (QUOTE -899) (QUOTE (-576)))) (|HasCategory| |#2| (LIST (QUOTE -626) (LIST (QUOTE -905) (QUOTE (-390))))) (|HasCategory| |#2| (LIST (QUOTE -626) (LIST (QUOTE -905) (QUOTE (-576))))) (|HasCategory| |#2| (LIST (QUOTE -651) (QUOTE (-576)))) (|HasCategory| |#2| (QUOTE (-237))) (|HasCategory| |#2| (LIST (QUOTE -917) (QUOTE (-1195)))) (|HasCategory| |#2| (QUOTE (-238))) (|HasCategory| |#2| (LIST (QUOTE -915) (QUOTE (-1195)))) (|HasCategory| |#2| (LIST (QUOTE -526) (QUOTE (-1195)) (|devaluate| |#2|))) (|HasCategory| |#2| (LIST (QUOTE -319) (|devaluate| |#2|))) (|HasCategory| |#2| (LIST (QUOTE -296) (|devaluate| |#2|) (|devaluate| |#2|))) (|HasCategory| |#2| (QUOTE (-317))) (|HasCategory| |#2| (QUOTE (-557))) (|HasCategory| |#2| (QUOTE (-862))) (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| |#2| (QUOTE (-926)))) (-2755 (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| |#2| (QUOTE (-926)))) (|HasCategory| |#2| (QUOTE (-146))))) (-885 S T$) ((|constructor| (NIL "\\indented{1}{This domain provides a very simple representation} of the notion of `pair of objects'. It does not try to achieve all possible imaginable things.")) (|second| ((|#2| $) "\\spad{second(p)} extracts the second components of \\spad{`p'}.")) (|first| ((|#1| $) "\\spad{first(p)} extracts the first component of \\spad{`p'}.")) (|construct| (($ |#1| |#2|) "\\spad{construct(s,t)} is same as pair(\\spad{s},{}\\spad{t}),{} with syntactic sugar.")) (|pair| (($ |#1| |#2|) "\\spad{pair(s,t)} returns a pair object composed of \\spad{`s'} and \\spad{`t'}."))) NIL -((-12 (|HasCategory| |#1| (QUOTE (-1119))) (|HasCategory| |#2| (QUOTE (-1119)))) (-2781 (-12 (|HasCategory| |#1| (QUOTE (-1119))) (|HasCategory| |#2| (QUOTE (-1119)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-874)))) (|HasCategory| |#2| (LIST (QUOTE -625) (QUOTE (-874)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-874)))) (|HasCategory| |#2| (LIST (QUOTE -625) (QUOTE (-874)))))) +((-12 (|HasCategory| |#1| (QUOTE (-1119))) (|HasCategory| |#2| (QUOTE (-1119)))) (-2755 (-12 (|HasCategory| |#1| (QUOTE (-1119))) (|HasCategory| |#2| (QUOTE (-1119)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-874)))) (|HasCategory| |#2| (LIST (QUOTE -625) (QUOTE (-874)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-874)))) (|HasCategory| |#2| (LIST (QUOTE -625) (QUOTE (-874)))))) (-886) ((|constructor| (NIL "This domain describes four groups of color shades (palettes).")) (|coerce| (($ (|Color|)) "\\spad{coerce(c)} sets the average shade for the palette to that of the indicated color \\spad{c}.")) (|shade| (((|Integer|) $) "\\spad{shade(p)} returns the shade index of the indicated palette \\spad{p}.")) (|hue| (((|Color|) $) "\\spad{hue(p)} returns the hue field of the indicated palette \\spad{p}.")) (|light| (($ (|Color|)) "\\spad{light(c)} sets the shade of a hue,{} \\spad{c},{} to it\\spad{'s} highest value.")) (|pastel| (($ (|Color|)) "\\spad{pastel(c)} sets the shade of a hue,{} \\spad{c},{} above bright,{} but below light.")) (|bright| (($ (|Color|)) "\\spad{bright(c)} sets the shade of a hue,{} \\spad{c},{} above dim,{} but below pastel.")) (|dim| (($ (|Color|)) "\\spad{dim(c)} sets the shade of a hue,{} \\spad{c},{} above dark,{} but below bright.")) (|dark| (($ (|Color|)) "\\spad{dark(c)} sets the shade of the indicated hue of \\spad{c} to it\\spad{'s} lowest value."))) NIL @@ -3531,7 +3531,7 @@ NIL (-900 |Base| |Subject| |Pat|) ((|constructor| (NIL "This package provides the top-level pattern macthing functions.")) (|Is| (((|PatternMatchResult| |#1| |#2|) |#2| |#3|) "\\spad{Is(expr, pat)} matches the pattern pat on the expression \\spad{expr} and returns a match of the form \\spad{[v1 = e1,...,vn = en]}; returns an empty match if \\spad{expr} is exactly equal to pat. returns a \\spadfun{failed} match if pat does not match \\spad{expr}.") (((|List| (|Equation| (|Polynomial| |#2|))) |#2| |#3|) "\\spad{Is(expr, pat)} matches the pattern pat on the expression \\spad{expr} and returns a list of matches \\spad{[v1 = e1,...,vn = en]}; returns an empty list if either \\spad{expr} is exactly equal to pat or if pat does not match \\spad{expr}.") (((|List| (|Equation| |#2|)) |#2| |#3|) "\\spad{Is(expr, pat)} matches the pattern pat on the expression \\spad{expr} and returns a list of matches \\spad{[v1 = e1,...,vn = en]}; returns an empty list if either \\spad{expr} is exactly equal to pat or if pat does not match \\spad{expr}.") (((|PatternMatchListResult| |#1| |#2| (|List| |#2|)) (|List| |#2|) |#3|) "\\spad{Is([e1,...,en], pat)} matches the pattern pat on the list of expressions \\spad{[e1,...,en]} and returns the result.")) (|is?| (((|Boolean|) (|List| |#2|) |#3|) "\\spad{is?([e1,...,en], pat)} tests if the list of expressions \\spad{[e1,...,en]} matches the pattern pat.") (((|Boolean|) |#2| |#3|) "\\spad{is?(expr, pat)} tests if the expression \\spad{expr} matches the pattern pat."))) NIL -((-12 (-2684 (|HasCategory| |#2| (QUOTE (-1068)))) (-2684 (|HasCategory| |#2| (LIST (QUOTE -1057) (QUOTE (-1195)))))) (-12 (|HasCategory| |#2| (QUOTE (-1068))) (-2684 (|HasCategory| |#2| (LIST (QUOTE -1057) (QUOTE (-1195)))))) (|HasCategory| |#2| (LIST (QUOTE -1057) (QUOTE (-1195))))) +((-12 (-2658 (|HasCategory| |#2| (QUOTE (-1068)))) (-2658 (|HasCategory| |#2| (LIST (QUOTE -1057) (QUOTE (-1195)))))) (-12 (|HasCategory| |#2| (QUOTE (-1068))) (-2658 (|HasCategory| |#2| (LIST (QUOTE -1057) (QUOTE (-1195)))))) (|HasCategory| |#2| (LIST (QUOTE -1057) (QUOTE (-1195))))) (-901 R A B) ((|constructor| (NIL "Lifts maps to pattern matching results.")) (|map| (((|PatternMatchResult| |#1| |#3|) (|Mapping| |#3| |#2|) (|PatternMatchResult| |#1| |#2|)) "\\spad{map(f, [(v1,a1),...,(vn,an)])} returns the matching result [(\\spad{v1},{}\\spad{f}(a1)),{}...,{}(\\spad{vn},{}\\spad{f}(an))]."))) NIL @@ -3540,7 +3540,7 @@ NIL ((|constructor| (NIL "A PatternMatchResult is an object internally returned by the pattern matcher; It is either a failed match,{} or a list of matches of the form (var,{} expr) meaning that the variable var matches the expression expr.")) (|satisfy?| (((|Union| (|Boolean|) "failed") $ (|Pattern| |#1|)) "\\spad{satisfy?(r, p)} returns \\spad{true} if the matches satisfy the top-level predicate of \\spad{p},{} \\spad{false} if they don\\spad{'t},{} and \"failed\" if not enough variables of \\spad{p} are matched in \\spad{r} to decide.")) (|construct| (($ (|List| (|Record| (|:| |key| (|Symbol|)) (|:| |entry| |#2|)))) "\\spad{construct([v1,e1],...,[vn,en])} returns the match result containing the matches (\\spad{v1},{}e1),{}...,{}(\\spad{vn},{}en).")) (|destruct| (((|List| (|Record| (|:| |key| (|Symbol|)) (|:| |entry| |#2|))) $) "\\spad{destruct(r)} returns the list of matches (var,{} expr) in \\spad{r}. Error: if \\spad{r} is a failed match.")) (|addMatchRestricted| (($ (|Pattern| |#1|) |#2| $ |#2|) "\\spad{addMatchRestricted(var, expr, r, val)} adds the match (\\spad{var},{} \\spad{expr}) in \\spad{r},{} provided that \\spad{expr} satisfies the predicates attached to \\spad{var},{} that \\spad{var} is not matched to another expression already,{} and that either \\spad{var} is an optional pattern variable or that \\spad{expr} is not equal to val (usually an identity).")) (|insertMatch| (($ (|Pattern| |#1|) |#2| $) "\\spad{insertMatch(var, expr, r)} adds the match (\\spad{var},{} \\spad{expr}) in \\spad{r},{} without checking predicates or previous matches for \\spad{var}.")) (|addMatch| (($ (|Pattern| |#1|) |#2| $) "\\spad{addMatch(var, expr, r)} adds the match (\\spad{var},{} \\spad{expr}) in \\spad{r},{} provided that \\spad{expr} satisfies the predicates attached to \\spad{var},{} and that \\spad{var} is not matched to another expression already.")) (|getMatch| (((|Union| |#2| "failed") (|Pattern| |#1|) $) "\\spad{getMatch(var, r)} returns the expression that \\spad{var} matches in the result \\spad{r},{} and \"failed\" if \\spad{var} is not matched in \\spad{r}.")) (|union| (($ $ $) "\\spad{union(a, b)} makes the set-union of two match results.")) (|new| (($) "\\spad{new()} returns a new empty match result.")) (|failed| (($) "\\spad{failed()} returns a failed match.")) (|failed?| (((|Boolean|) $) "\\spad{failed?(r)} tests if \\spad{r} is a failed match."))) NIL NIL -(-903 R -1992) +(-903 R -2014) ((|constructor| (NIL "Tools for patterns.")) (|badValues| (((|List| |#2|) (|Pattern| |#1|)) "\\spad{badValues(p)} returns the list of \"bad values\" for \\spad{p}; \\spad{p} is not allowed to match any of its \"bad values\".")) (|addBadValue| (((|Pattern| |#1|) (|Pattern| |#1|) |#2|) "\\spad{addBadValue(p, v)} adds \\spad{v} to the list of \"bad values\" for \\spad{p}; \\spad{p} is not allowed to match any of its \"bad values\".")) (|satisfy?| (((|Boolean|) (|List| |#2|) (|Pattern| |#1|)) "\\spad{satisfy?([v1,...,vn], p)} returns \\spad{f(v1,...,vn)} where \\spad{f} is the top-level predicate attached to \\spad{p}.") (((|Boolean|) |#2| (|Pattern| |#1|)) "\\spad{satisfy?(v, p)} returns \\spad{f}(\\spad{v}) where \\spad{f} is the predicate attached to \\spad{p}.")) (|predicate| (((|Mapping| (|Boolean|) |#2|) (|Pattern| |#1|)) "\\spad{predicate(p)} returns the predicate attached to \\spad{p},{} the constant function \\spad{true} if \\spad{p} has no predicates attached to it.")) (|suchThat| (((|Pattern| |#1|) (|Pattern| |#1|) (|List| (|Symbol|)) (|Mapping| (|Boolean|) (|List| |#2|))) "\\spad{suchThat(p, [a1,...,an], f)} returns a copy of \\spad{p} with the top-level predicate set to \\spad{f(a1,...,an)}.") (((|Pattern| |#1|) (|Pattern| |#1|) (|List| (|Mapping| (|Boolean|) |#2|))) "\\spad{suchThat(p, [f1,...,fn])} makes a copy of \\spad{p} and adds the predicate \\spad{f1} and ... and \\spad{fn} to the copy,{} which is returned.") (((|Pattern| |#1|) (|Pattern| |#1|) (|Mapping| (|Boolean|) |#2|)) "\\spad{suchThat(p, f)} makes a copy of \\spad{p} and adds the predicate \\spad{f} to the copy,{} which is returned."))) NIL NIL @@ -3572,7 +3572,7 @@ 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 -(-911 UP -1966) +(-911 UP -1955) ((|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 @@ -3603,7 +3603,7 @@ NIL (-918 S) ((|constructor| (NIL "\\indented{1}{A PendantTree(\\spad{S})is either a leaf? and is an \\spad{S} or has} a left and a right both PendantTree(\\spad{S})\\spad{'s}")) (|ptree| (($ $ $) "\\spad{ptree(x,y)} \\undocumented") (($ |#1|) "\\spad{ptree(s)} is a leaf? pendant tree"))) NIL -((-12 (|HasCategory| |#1| (QUOTE (-1119))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1119))) (-2781 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-1119)))) (-2781 (-12 (|HasCategory| |#1| (QUOTE (-1119))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-874))))) (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-874)))) (|HasCategory| |#1| (QUOTE (-102)))) +((-12 (|HasCategory| |#1| (QUOTE (-1119))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1119))) (-2755 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-1119)))) (-2755 (-12 (|HasCategory| |#1| (QUOTE (-1119))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-874))))) (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-874)))) (|HasCategory| |#1| (QUOTE (-102)))) (-919 |n| R) ((|constructor| (NIL "Permanent implements the functions {\\em permanent},{} the permanent for square matrices.")) (|permanent| ((|#2| (|SquareMatrix| |#1| |#2|)) "\\spad{permanent(x)} computes the permanent of a square matrix \\spad{x}. The {\\em permanent} is equivalent to the \\spadfun{determinant} except that coefficients have no change of sign. This function is much more difficult to compute than the {\\em determinant}. The formula used is by \\spad{H}.\\spad{J}. Ryser,{} improved by [Nijenhuis and Wilf,{} \\spad{Ch}. 19]. Note: permanent(\\spad{x}) choose one of three algorithms,{} depending on the underlying ring \\spad{R} and on \\spad{n},{} the number of rows (and columns) of \\spad{x:}\\begin{items} \\item 1. if 2 has an inverse in \\spad{R} we can use the algorithm of \\indented{3}{[Nijenhuis and Wilf,{} \\spad{ch}.19,{}\\spad{p}.158]; if 2 has no inverse,{}} \\indented{3}{some modifications are necessary:} \\item 2. if {\\em n > 6} and \\spad{R} is an integral domain with characteristic \\indented{3}{different from 2 (the algorithm works if and only 2 is not a} \\indented{3}{zero-divisor of \\spad{R} and {\\em characteristic()\\$R ~= 2},{}} \\indented{3}{but how to check that for any given \\spad{R} ?),{}} \\indented{3}{the local function {\\em permanent2} is called;} \\item 3. else,{} the local function {\\em permanent3} is called \\indented{3}{(works for all commutative rings \\spad{R}).} \\end{items}"))) NIL @@ -3619,7 +3619,7 @@ NIL (-922 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."))) ((-4459 . T)) -((-2781 (|HasCategory| |#1| (QUOTE (-379))) (|HasCategory| |#1| (QUOTE (-862)))) (|HasCategory| |#1| (QUOTE (-379))) (|HasCategory| |#1| (QUOTE (-862)))) +((-2755 (|HasCategory| |#1| (QUOTE (-379))) (|HasCategory| |#1| (QUOTE (-862)))) (|HasCategory| |#1| (QUOTE (-379))) (|HasCategory| |#1| (QUOTE (-862)))) (-923 R E |VarSet| S) ((|constructor| (NIL "PolynomialFactorizationByRecursion(\\spad{R},{}\\spad{E},{}\\spad{VarSet},{}\\spad{S}) is used for factorization of sparse univariate polynomials over a domain \\spad{S} of multivariate polynomials over \\spad{R}.")) (|factorSFBRlcUnit| (((|Factored| (|SparseUnivariatePolynomial| |#4|)) (|List| |#3|) (|SparseUnivariatePolynomial| |#4|)) "\\spad{factorSFBRlcUnit(p)} returns the square free factorization of polynomial \\spad{p} (see \\spadfun{factorSquareFreeByRecursion}{PolynomialFactorizationByRecursionUnivariate}) in the case where the leading coefficient of \\spad{p} is a unit.")) (|bivariateSLPEBR| (((|Union| (|List| (|SparseUnivariatePolynomial| |#4|)) "failed") (|List| (|SparseUnivariatePolynomial| |#4|)) (|SparseUnivariatePolynomial| |#4|) |#3|) "\\spad{bivariateSLPEBR(lp,p,v)} implements the bivariate case of \\spadfunFrom{solveLinearPolynomialEquationByRecursion}{PolynomialFactorizationByRecursionUnivariate}; its implementation depends on \\spad{R}")) (|randomR| ((|#1|) "\\spad{randomR produces} a random element of \\spad{R}")) (|factorSquareFreeByRecursion| (((|Factored| (|SparseUnivariatePolynomial| |#4|)) (|SparseUnivariatePolynomial| |#4|)) "\\spad{factorSquareFreeByRecursion(p)} returns the square free factorization of \\spad{p}. This functions performs the recursion step for factorSquareFreePolynomial,{} as defined in \\spadfun{PolynomialFactorizationExplicit} category (see \\spadfun{factorSquareFreePolynomial}).")) (|factorByRecursion| (((|Factored| (|SparseUnivariatePolynomial| |#4|)) (|SparseUnivariatePolynomial| |#4|)) "\\spad{factorByRecursion(p)} factors polynomial \\spad{p}. This function performs the recursion step for factorPolynomial,{} as defined in \\spadfun{PolynomialFactorizationExplicit} category (see \\spadfun{factorPolynomial})")) (|solveLinearPolynomialEquationByRecursion| (((|Union| (|List| (|SparseUnivariatePolynomial| |#4|)) "failed") (|List| (|SparseUnivariatePolynomial| |#4|)) (|SparseUnivariatePolynomial| |#4|)) "\\spad{solveLinearPolynomialEquationByRecursion([p1,...,pn],p)} returns the list of polynomials \\spad{[q1,...,qn]} such that \\spad{sum qi/pi = p / prod pi},{} a recursion step for solveLinearPolynomialEquation as defined in \\spadfun{PolynomialFactorizationExplicit} category (see \\spadfun{solveLinearPolynomialEquation}). If no such list of \\spad{qi} exists,{} then \"failed\" is returned."))) NIL @@ -3640,7 +3640,7 @@ NIL ((|constructor| (NIL "PrimeField(\\spad{p}) implements the field with \\spad{p} elements if \\spad{p} is a prime number. Error: if \\spad{p} is not prime. Note: this domain does not check that argument is a prime."))) ((-4454 . T) (-4460 . T) (-4455 . T) ((-4464 "*") . T) (-4456 . T) (-4457 . T) (-4459 . T)) ((|HasCategory| $ (QUOTE (-148))) (|HasCategory| $ (QUOTE (-146))) (|HasCategory| $ (QUOTE (-379)))) -(-928 R0 -1966 UP UPUP R) +(-928 R0 -1955 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 @@ -3668,7 +3668,7 @@ NIL ((|constructor| (NIL "PermutationGroupExamples provides permutation groups for some classes of groups: symmetric,{} alternating,{} dihedral,{} cyclic,{} direct products of cyclic,{} which are in fact the finite abelian groups of symmetric groups called Young subgroups. Furthermore,{} Rubik\\spad{'s} group as permutation group of 48 integers and a list of sporadic simple groups derived from the atlas of finite groups.")) (|youngGroup| (((|PermutationGroup| (|Integer|)) (|Partition|)) "\\spad{youngGroup(lambda)} constructs the direct product of the symmetric groups given by the parts of the partition {\\em lambda}.") (((|PermutationGroup| (|Integer|)) (|List| (|Integer|))) "\\spad{youngGroup([n1,...,nk])} constructs the direct product of the symmetric groups {\\em Sn1},{}...,{}{\\em Snk}.")) (|rubiksGroup| (((|PermutationGroup| (|Integer|))) "\\spad{rubiksGroup constructs} the permutation group representing Rubic\\spad{'s} Cube acting on integers {\\em 10*i+j} for {\\em 1 <= i <= 6},{} {\\em 1 <= j <= 8}. The faces of Rubik\\spad{'s} Cube are labelled in the obvious way Front,{} Right,{} Up,{} Down,{} Left,{} Back and numbered from 1 to 6 in this given ordering,{} the pieces on each face (except the unmoveable center piece) are clockwise numbered from 1 to 8 starting with the piece in the upper left corner. The moves of the cube are represented as permutations on these pieces,{} represented as a two digit integer {\\em ij} where \\spad{i} is the numer of theface (1 to 6) and \\spad{j} is the number of the piece on this face. The remaining ambiguities are resolved by looking at the 6 generators,{} which represent a 90 degree turns of the faces,{} or from the following pictorial description. Permutation group representing Rubic\\spad{'s} Cube acting on integers 10*i+j for 1 \\spad{<=} \\spad{i} \\spad{<=} 6,{} 1 \\spad{<=} \\spad{j} \\spad{<=8}. \\blankline\\begin{verbatim}Rubik's Cube: +-----+ +-- B where: marks Side # : / U /|/ / / | F(ront) <-> 1 L --> +-----+ R| R(ight) <-> 2 | | + U(p) <-> 3 | F | / D(own) <-> 4 | |/ L(eft) <-> 5 +-----+ B(ack) <-> 6 ^ | DThe Cube's surface: The pieces on each side +---+ (except the unmoveable center |567| piece) are clockwise numbered |4U8| from 1 to 8 starting with the |321| piece in the upper left +---+---+---+ corner (see figure on the |781|123|345| left). The moves of the cube |6L2|8F4|2R6| are represented as |543|765|187| permutations on these pieces. +---+---+---+ Each of the pieces is |123| represented as a two digit |8D4| integer ij where i is the |765| # of the side ( 1 to 6 for +---+ F to B (see table above )) |567| and j is the # of the piece. |4B8| |321| +---+\\end{verbatim}")) (|janko2| (((|PermutationGroup| (|Integer|))) "\\spad{janko2 constructs} the janko group acting on the integers 1,{}...,{}100.") (((|PermutationGroup| (|Integer|)) (|List| (|Integer|))) "\\spad{janko2(li)} constructs the janko group acting on the 100 integers given in the list {\\em li}. Note: duplicates in the list will be removed. Error: if {\\em li} has less or more than 100 different entries")) (|mathieu24| (((|PermutationGroup| (|Integer|))) "\\spad{mathieu24 constructs} the mathieu group acting on the integers 1,{}...,{}24.") (((|PermutationGroup| (|Integer|)) (|List| (|Integer|))) "\\spad{mathieu24(li)} constructs the mathieu group acting on the 24 integers given in the list {\\em li}. Note: duplicates in the list will be removed. Error: if {\\em li} has less or more than 24 different entries.")) (|mathieu23| (((|PermutationGroup| (|Integer|))) "\\spad{mathieu23 constructs} the mathieu group acting on the integers 1,{}...,{}23.") (((|PermutationGroup| (|Integer|)) (|List| (|Integer|))) "\\spad{mathieu23(li)} constructs the mathieu group acting on the 23 integers given in the list {\\em li}. Note: duplicates in the list will be removed. Error: if {\\em li} has less or more than 23 different entries.")) (|mathieu22| (((|PermutationGroup| (|Integer|))) "\\spad{mathieu22 constructs} the mathieu group acting on the integers 1,{}...,{}22.") (((|PermutationGroup| (|Integer|)) (|List| (|Integer|))) "\\spad{mathieu22(li)} constructs the mathieu group acting on the 22 integers given in the list {\\em li}. Note: duplicates in the list will be removed. Error: if {\\em li} has less or more than 22 different entries.")) (|mathieu12| (((|PermutationGroup| (|Integer|))) "\\spad{mathieu12 constructs} the mathieu group acting on the integers 1,{}...,{}12.") (((|PermutationGroup| (|Integer|)) (|List| (|Integer|))) "\\spad{mathieu12(li)} constructs the mathieu group acting on the 12 integers given in the list {\\em li}. Note: duplicates in the list will be removed Error: if {\\em li} has less or more than 12 different entries.")) (|mathieu11| (((|PermutationGroup| (|Integer|))) "\\spad{mathieu11 constructs} the mathieu group acting on the integers 1,{}...,{}11.") (((|PermutationGroup| (|Integer|)) (|List| (|Integer|))) "\\spad{mathieu11(li)} constructs the mathieu group acting on the 11 integers given in the list {\\em li}. Note: duplicates in the list will be removed. error,{} if {\\em li} has less or more than 11 different entries.")) (|dihedralGroup| (((|PermutationGroup| (|Integer|)) (|List| (|Integer|))) "\\spad{dihedralGroup([i1,...,ik])} constructs the dihedral group of order 2k acting on the integers out of {\\em i1},{}...,{}{\\em ik}. Note: duplicates in the list will be removed.") (((|PermutationGroup| (|Integer|)) (|PositiveInteger|)) "\\spad{dihedralGroup(n)} constructs the dihedral group of order 2n acting on integers 1,{}...,{}\\spad{N}.")) (|cyclicGroup| (((|PermutationGroup| (|Integer|)) (|List| (|Integer|))) "\\spad{cyclicGroup([i1,...,ik])} constructs the cyclic group of order \\spad{k} acting on the integers {\\em i1},{}...,{}{\\em ik}. Note: duplicates in the list will be removed.") (((|PermutationGroup| (|Integer|)) (|PositiveInteger|)) "\\spad{cyclicGroup(n)} constructs the cyclic group of order \\spad{n} acting on the integers 1,{}...,{}\\spad{n}.")) (|abelianGroup| (((|PermutationGroup| (|Integer|)) (|List| (|PositiveInteger|))) "\\spad{abelianGroup([n1,...,nk])} constructs the abelian group that is the direct product of cyclic groups with order {\\em ni}.")) (|alternatingGroup| (((|PermutationGroup| (|Integer|)) (|List| (|Integer|))) "\\spad{alternatingGroup(li)} constructs the alternating group acting on the integers in the list {\\em li},{} generators are in general the {\\em n-2}-cycle {\\em (li.3,...,li.n)} and the 3-cycle {\\em (li.1,li.2,li.3)},{} if \\spad{n} is odd and product of the 2-cycle {\\em (li.1,li.2)} with {\\em n-2}-cycle {\\em (li.3,...,li.n)} and the 3-cycle {\\em (li.1,li.2,li.3)},{} if \\spad{n} is even. Note: duplicates in the list will be removed.") (((|PermutationGroup| (|Integer|)) (|PositiveInteger|)) "\\spad{alternatingGroup(n)} constructs the alternating group {\\em An} acting on the integers 1,{}...,{}\\spad{n},{} generators are in general the {\\em n-2}-cycle {\\em (3,...,n)} and the 3-cycle {\\em (1,2,3)} if \\spad{n} is odd and the product of the 2-cycle {\\em (1,2)} with {\\em n-2}-cycle {\\em (3,...,n)} and the 3-cycle {\\em (1,2,3)} if \\spad{n} is even.")) (|symmetricGroup| (((|PermutationGroup| (|Integer|)) (|List| (|Integer|))) "\\spad{symmetricGroup(li)} constructs the symmetric group acting on the integers in the list {\\em li},{} generators are the cycle given by {\\em li} and the 2-cycle {\\em (li.1,li.2)}. Note: duplicates in the list will be removed.") (((|PermutationGroup| (|Integer|)) (|PositiveInteger|)) "\\spad{symmetricGroup(n)} constructs the symmetric group {\\em Sn} acting on the integers 1,{}...,{}\\spad{n},{} generators are the {\\em n}-cycle {\\em (1,...,n)} and the 2-cycle {\\em (1,2)}."))) NIL NIL -(-935 -1966) +(-935 -1955) ((|constructor| (NIL "Groebner functions for \\spad{P} \\spad{F} \\indented{2}{This package is an interface package to the groebner basis} package which allows you to compute groebner bases for polynomials in either lexicographic ordering or total degree ordering refined by reverse lex. The input is the ordinary polynomial type which is internally converted to a type with the required ordering. The resulting grobner basis is converted back to ordinary polynomials. The ordering among the variables is controlled by an explicit list of variables which is passed as a second argument. The coefficient domain is allowed to be any \\spad{gcd} domain,{} but the groebner basis is computed as if the polynomials were over a field.")) (|totalGroebner| (((|List| (|Polynomial| |#1|)) (|List| (|Polynomial| |#1|)) (|List| (|Symbol|))) "\\spad{totalGroebner(lp,lv)} computes Groebner basis for the list of polynomials \\spad{lp} with the terms ordered first by total degree and then refined by reverse lexicographic ordering. The variables are ordered by their position in the list \\spad{lv}.")) (|lexGroebner| (((|List| (|Polynomial| |#1|)) (|List| (|Polynomial| |#1|)) (|List| (|Symbol|))) "\\spad{lexGroebner(lp,lv)} computes Groebner basis for the list of polynomials \\spad{lp} in lexicographic order. The variables are ordered by their position in the list \\spad{lv}."))) NIL NIL @@ -3684,11 +3684,11 @@ NIL ((|constructor| (NIL "\\spadtype{PositiveInteger} provides functions for \\indented{2}{positive integers.}")) (|commutative| ((|attribute| "*") "\\spad{commutative(\"*\")} means multiplication is commutative : x*y = \\spad{y*x}")) (|gcd| (($ $ $) "\\spad{gcd(a,b)} computes the greatest common divisor of two positive integers \\spad{a} and \\spad{b}."))) (((-4464 "*") . T)) NIL -(-939 -1966 P) +(-939 -1955 P) ((|constructor| (NIL "This package exports interpolation algorithms")) (|LagrangeInterpolation| ((|#2| (|List| |#1|) (|List| |#1|)) "\\spad{LagrangeInterpolation(l1,l2)} \\undocumented"))) NIL NIL -(-940 |xx| -1966) +(-940 |xx| -1955) ((|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 @@ -3712,7 +3712,7 @@ NIL ((|constructor| (NIL "This package exports plotting tools")) (|calcRanges| (((|List| (|Segment| (|DoubleFloat|))) (|List| (|List| (|Point| (|DoubleFloat|))))) "\\spad{calcRanges(l)} \\undocumented"))) NIL NIL -(-946 R -1966) +(-946 R -1955) ((|constructor| (NIL "Attaching assertions to symbols for pattern matching; Date Created: 21 Mar 1989 Date Last Updated: 23 May 1990")) (|multiple| ((|#2| |#2|) "\\spad{multiple(x)} tells the pattern matcher that \\spad{x} should preferably match a multi-term quantity in a sum or product. For matching on lists,{} multiple(\\spad{x}) tells the pattern matcher that \\spad{x} should match a list instead of an element of a list. Error: if \\spad{x} is not a symbol.")) (|optional| ((|#2| |#2|) "\\spad{optional(x)} tells the pattern matcher that \\spad{x} can match an identity (0 in a sum,{} 1 in a product or exponentiation). Error: if \\spad{x} is not a symbol.")) (|constant| ((|#2| |#2|) "\\spad{constant(x)} tells the pattern matcher that \\spad{x} should match only the symbol \\spad{'x} and no other quantity. Error: if \\spad{x} is not a symbol.")) (|assert| ((|#2| |#2| (|Identifier|)) "\\spad{assert(x, s)} makes the assertion \\spad{s} about \\spad{x}. Error: if \\spad{x} is not a symbol."))) NIL NIL @@ -3724,7 +3724,7 @@ 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 -(-949 S R -1966) +(-949 S R -1955) ((|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 @@ -3744,11 +3744,11 @@ 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 -899) (|devaluate| |#1|)))) -(-954 R -1966 -1992) +(-954 R -1955 -2014) ((|constructor| (NIL "Attaching predicates to symbols for pattern matching. Date Created: 21 Mar 1989 Date Last Updated: 23 May 1990")) (|suchThat| ((|#2| |#2| (|List| (|Mapping| (|Boolean|) |#3|))) "\\spad{suchThat(x, [f1, f2, ..., fn])} attaches the predicate \\spad{f1} and \\spad{f2} and ... and \\spad{fn} to \\spad{x}. Error: if \\spad{x} is not a symbol.") ((|#2| |#2| (|Mapping| (|Boolean|) |#3|)) "\\spad{suchThat(x, foo)} attaches the predicate foo to \\spad{x}; error if \\spad{x} is not a symbol."))) NIL NIL -(-955 -1992) +(-955 -2014) ((|constructor| (NIL "Attaching predicates to symbols for pattern matching. Date Created: 21 Mar 1989 Date Last Updated: 23 May 1990")) (|suchThat| (((|Expression| (|Integer|)) (|Symbol|) (|List| (|Mapping| (|Boolean|) |#1|))) "\\spad{suchThat(x, [f1, f2, ..., fn])} attaches the predicate \\spad{f1} and \\spad{f2} and ... and \\spad{fn} to \\spad{x}.") (((|Expression| (|Integer|)) (|Symbol|) (|Mapping| (|Boolean|) |#1|)) "\\spad{suchThat(x, foo)} attaches the predicate foo to \\spad{x}."))) NIL NIL @@ -3771,7 +3771,7 @@ NIL (-960 R) ((|constructor| (NIL "This domain implements points in coordinate space"))) ((-4463 . T) (-4462 . T)) -((-2781 (-12 (|HasCategory| |#1| (QUOTE (-862))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1119))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|))))) (-2781 (-12 (|HasCategory| |#1| (QUOTE (-1119))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-874))))) (|HasCategory| |#1| (LIST (QUOTE -626) (QUOTE (-548)))) (-2781 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-862))) (|HasCategory| |#1| (QUOTE (-1119)))) (-2781 (|HasCategory| |#1| (QUOTE (-862))) (|HasCategory| |#1| (QUOTE (-1119)))) (|HasCategory| |#1| (QUOTE (-862))) (|HasCategory| (-576) (QUOTE (-862))) (|HasCategory| |#1| (QUOTE (-1119))) (|HasCategory| |#1| (QUOTE (-25))) (|HasCategory| |#1| (QUOTE (-23))) (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-738))) (|HasCategory| |#1| (QUOTE (-1068))) (-12 (|HasCategory| |#1| (QUOTE (-1021))) (|HasCategory| |#1| (QUOTE (-1068)))) (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-874)))) (|HasCategory| |#1| (QUOTE (-102))) (-12 (|HasCategory| |#1| (QUOTE (-1119))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|))))) +((-2755 (-12 (|HasCategory| |#1| (QUOTE (-862))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1119))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|))))) (-2755 (-12 (|HasCategory| |#1| (QUOTE (-1119))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-874))))) (|HasCategory| |#1| (LIST (QUOTE -626) (QUOTE (-548)))) (-2755 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-862))) (|HasCategory| |#1| (QUOTE (-1119)))) (-2755 (|HasCategory| |#1| (QUOTE (-862))) (|HasCategory| |#1| (QUOTE (-1119)))) (|HasCategory| |#1| (QUOTE (-862))) (|HasCategory| (-576) (QUOTE (-862))) (|HasCategory| |#1| (QUOTE (-1119))) (|HasCategory| |#1| (QUOTE (-25))) (|HasCategory| |#1| (QUOTE (-23))) (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-738))) (|HasCategory| |#1| (QUOTE (-1068))) (-12 (|HasCategory| |#1| (QUOTE (-1021))) (|HasCategory| |#1| (QUOTE (-1068)))) (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-874)))) (|HasCategory| |#1| (QUOTE (-102))) (-12 (|HasCategory| |#1| (QUOTE (-1119))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|))))) (-961 |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 @@ -3796,7 +3796,7 @@ NIL ((|constructor| (NIL "The category for general multi-variate polynomials over a ring \\spad{R},{} in variables from VarSet,{} with exponents from the \\spadtype{OrderedAbelianMonoidSup}.")) (|canonicalUnitNormal| ((|attribute|) "we can choose a unique representative for each associate class. This normalization is chosen to be normalization of leading coefficient (by default).")) (|squareFreePart| (($ $) "\\spad{squareFreePart(p)} returns product of all the irreducible factors of polynomial \\spad{p} each taken with multiplicity one.")) (|squareFree| (((|Factored| $) $) "\\spad{squareFree(p)} returns the square free factorization of the polynomial \\spad{p}.")) (|primitivePart| (($ $ |#3|) "\\spad{primitivePart(p,v)} returns the unitCanonical associate of the polynomial \\spad{p} with its content with respect to the variable \\spad{v} divided out.") (($ $) "\\spad{primitivePart(p)} returns the unitCanonical associate of the polynomial \\spad{p} with its content divided out.")) (|content| (($ $ |#3|) "\\spad{content(p,v)} is the \\spad{gcd} of the coefficients of the polynomial \\spad{p} when \\spad{p} is viewed as a univariate polynomial with respect to the variable \\spad{v}. Thus,{} for polynomial 7*x**2*y + 14*x*y**2,{} the \\spad{gcd} of the coefficients with respect to \\spad{x} is 7*y.")) (|discriminant| (($ $ |#3|) "\\spad{discriminant(p,v)} returns the disriminant of the polynomial \\spad{p} with respect to the variable \\spad{v}.")) (|resultant| (($ $ $ |#3|) "\\spad{resultant(p,q,v)} returns the resultant of the polynomials \\spad{p} and \\spad{q} with respect to the variable \\spad{v}.")) (|primitiveMonomials| (((|List| $) $) "\\spad{primitiveMonomials(p)} gives the list of monomials of the polynomial \\spad{p} with their coefficients removed. Note: \\spad{primitiveMonomials(sum(a_(i) X^(i))) = [X^(1),...,X^(n)]}.")) (|variables| (((|List| |#3|) $) "\\spad{variables(p)} returns the list of those variables actually appearing in the polynomial \\spad{p}.")) (|totalDegree| (((|NonNegativeInteger|) $ (|List| |#3|)) "\\spad{totalDegree(p, lv)} returns the maximum sum (over all monomials of polynomial \\spad{p}) of the variables in the list \\spad{lv}.") (((|NonNegativeInteger|) $) "\\spad{totalDegree(p)} returns the largest sum over all monomials of all exponents of a monomial.")) (|isExpt| (((|Union| (|Record| (|:| |var| |#3|) (|:| |exponent| (|NonNegativeInteger|))) "failed") $) "\\spad{isExpt(p)} returns \\spad{[x, n]} if polynomial \\spad{p} has the form \\spad{x**n} and \\spad{n > 0}.")) (|isTimes| (((|Union| (|List| $) "failed") $) "\\spad{isTimes(p)} returns \\spad{[a1,...,an]} if polynomial \\spad{p = a1 ... an} and \\spad{n >= 2},{} and,{} for each \\spad{i},{} \\spad{ai} is either a nontrivial constant in \\spad{R} or else of the form \\spad{x**e},{} where \\spad{e > 0} is an integer and \\spad{x} in a member of VarSet.")) (|isPlus| (((|Union| (|List| $) "failed") $) "\\spad{isPlus(p)} returns \\spad{[m1,...,mn]} if polynomial \\spad{p = m1 + ... + mn} and \\spad{n >= 2} and each \\spad{mi} is a nonzero monomial.")) (|multivariate| (($ (|SparseUnivariatePolynomial| $) |#3|) "\\spad{multivariate(sup,v)} converts an anonymous univariable polynomial \\spad{sup} to a polynomial in the variable \\spad{v}.") (($ (|SparseUnivariatePolynomial| |#1|) |#3|) "\\spad{multivariate(sup,v)} converts an anonymous univariable polynomial \\spad{sup} to a polynomial in the variable \\spad{v}.")) (|monomial| (($ $ (|List| |#3|) (|List| (|NonNegativeInteger|))) "\\spad{monomial(a,[v1..vn],[e1..en])} returns \\spad{a*prod(vi**ei)}.") (($ $ |#3| (|NonNegativeInteger|)) "\\spad{monomial(a,x,n)} creates the monomial \\spad{a*x**n} where \\spad{a} is a polynomial,{} \\spad{x} is a variable and \\spad{n} is a nonnegative integer.")) (|monicDivide| (((|Record| (|:| |quotient| $) (|:| |remainder| $)) $ $ |#3|) "\\spad{monicDivide(a,b,v)} divides the polynomial a by the polynomial \\spad{b},{} with each viewed as a univariate polynomial in \\spad{v} returning both the quotient and remainder. Error: if \\spad{b} is not monic with respect to \\spad{v}.")) (|minimumDegree| (((|List| (|NonNegativeInteger|)) $ (|List| |#3|)) "\\spad{minimumDegree(p, lv)} gives the list of minimum degrees of the polynomial \\spad{p} with respect to each of the variables in the list \\spad{lv}") (((|NonNegativeInteger|) $ |#3|) "\\spad{minimumDegree(p,v)} gives the minimum degree of polynomial \\spad{p} with respect to \\spad{v},{} \\spadignore{i.e.} viewed a univariate polynomial in \\spad{v}")) (|mainVariable| (((|Union| |#3| "failed") $) "\\spad{mainVariable(p)} returns the biggest variable which actually occurs in the polynomial \\spad{p},{} or \"failed\" if no variables are present. fails precisely if polynomial satisfies ground?")) (|univariate| (((|SparseUnivariatePolynomial| |#1|) $) "\\spad{univariate(p)} converts the multivariate polynomial \\spad{p},{} which should actually involve only one variable,{} into a univariate polynomial in that variable,{} whose coefficients are in the ground ring. Error: if polynomial is genuinely multivariate") (((|SparseUnivariatePolynomial| $) $ |#3|) "\\spad{univariate(p,v)} converts the multivariate polynomial \\spad{p} into a univariate polynomial in \\spad{v},{} whose coefficients are still multivariate polynomials (in all the other variables).")) (|monomials| (((|List| $) $) "\\spad{monomials(p)} returns the list of non-zero monomials of polynomial \\spad{p},{} \\spadignore{i.e.} \\spad{monomials(sum(a_(i) X^(i))) = [a_(1) X^(1),...,a_(n) X^(n)]}.")) (|coefficient| (($ $ (|List| |#3|) (|List| (|NonNegativeInteger|))) "\\spad{coefficient(p, lv, ln)} views the polynomial \\spad{p} as a polynomial in the variables of \\spad{lv} and returns the coefficient of the term \\spad{lv**ln},{} \\spadignore{i.e.} \\spad{prod(lv_i ** ln_i)}.") (($ $ |#3| (|NonNegativeInteger|)) "\\spad{coefficient(p,v,n)} views the polynomial \\spad{p} as a univariate polynomial in \\spad{v} and returns the coefficient of the \\spad{v**n} term.")) (|degree| (((|List| (|NonNegativeInteger|)) $ (|List| |#3|)) "\\spad{degree(p,lv)} gives the list of degrees of polynomial \\spad{p} with respect to each of the variables in the list \\spad{lv}.") (((|NonNegativeInteger|) $ |#3|) "\\spad{degree(p,v)} gives the degree of polynomial \\spad{p} with respect to the variable \\spad{v}."))) (((-4464 "*") |has| |#1| (-174)) (-4455 |has| |#1| (-568)) (-4460 |has| |#1| (-6 -4460)) (-4457 . T) (-4456 . T) (-4459 . T)) NIL -(-967 E V R P -1966) +(-967 E V R P -1955) ((|constructor| (NIL "This package transforms multivariate polynomials or fractions into univariate polynomials or fractions,{} and back.")) (|isPower| (((|Union| (|Record| (|:| |val| |#5|) (|:| |exponent| (|Integer|))) "failed") |#5|) "\\spad{isPower(p)} returns \\spad{[x, n]} if \\spad{p = x**n} and \\spad{n <> 0},{} \"failed\" otherwise.")) (|isExpt| (((|Union| (|Record| (|:| |var| |#2|) (|:| |exponent| (|Integer|))) "failed") |#5|) "\\spad{isExpt(p)} returns \\spad{[x, n]} if \\spad{p = x**n} and \\spad{n <> 0},{} \"failed\" otherwise.")) (|isTimes| (((|Union| (|List| |#5|) "failed") |#5|) "\\spad{isTimes(p)} returns \\spad{[a1,...,an]} if \\spad{p = a1 ... an} and \\spad{n > 1},{} \"failed\" otherwise.")) (|isPlus| (((|Union| (|List| |#5|) "failed") |#5|) "\\spad{isPlus(p)} returns [\\spad{m1},{}...,{}\\spad{mn}] if \\spad{p = m1 + ... + mn} and \\spad{n > 1},{} \"failed\" otherwise.")) (|multivariate| ((|#5| (|Fraction| (|SparseUnivariatePolynomial| |#5|)) |#2|) "\\spad{multivariate(f, v)} applies both the numerator and denominator of \\spad{f} to \\spad{v}.")) (|univariate| (((|SparseUnivariatePolynomial| |#5|) |#5| |#2| (|SparseUnivariatePolynomial| |#5|)) "\\spad{univariate(f, x, p)} returns \\spad{f} viewed as a univariate polynomial in \\spad{x},{} using the side-condition \\spad{p(x) = 0}.") (((|Fraction| (|SparseUnivariatePolynomial| |#5|)) |#5| |#2|) "\\spad{univariate(f, v)} returns \\spad{f} viewed as a univariate rational function in \\spad{v}.")) (|mainVariable| (((|Union| |#2| "failed") |#5|) "\\spad{mainVariable(f)} returns the highest variable appearing in the numerator or the denominator of \\spad{f},{} \"failed\" if \\spad{f} has no variables.")) (|variables| (((|List| |#2|) |#5|) "\\spad{variables(f)} returns the list of variables appearing in the numerator or the denominator of \\spad{f}."))) NIL NIL @@ -3807,8 +3807,8 @@ NIL (-969 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}."))) (((-4464 "*") |has| |#1| (-174)) (-4455 |has| |#1| (-568)) (-4460 |has| |#1| (-6 -4460)) (-4457 . T) (-4456 . T) (-4459 . T)) -((|HasCategory| |#1| (QUOTE (-926))) (-2781 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-464))) (|HasCategory| |#1| (QUOTE (-568))) (|HasCategory| |#1| (QUOTE (-926)))) (-2781 (|HasCategory| |#1| (QUOTE (-464))) (|HasCategory| |#1| (QUOTE (-568))) (|HasCategory| |#1| (QUOTE (-926)))) (-2781 (|HasCategory| |#1| (QUOTE (-464))) (|HasCategory| |#1| (QUOTE (-926)))) (|HasCategory| |#1| (QUOTE (-568))) (|HasCategory| |#1| (QUOTE (-174))) (-2781 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-568)))) (-12 (|HasCategory| (-1195) (LIST (QUOTE -899) (QUOTE (-390)))) (|HasCategory| |#1| (LIST (QUOTE -899) (QUOTE (-390))))) (-12 (|HasCategory| (-1195) (LIST (QUOTE -899) (QUOTE (-576)))) (|HasCategory| |#1| (LIST (QUOTE -899) (QUOTE (-576))))) (-12 (|HasCategory| (-1195) (LIST (QUOTE -626) (LIST (QUOTE -905) (QUOTE (-390))))) (|HasCategory| |#1| (LIST (QUOTE -626) (LIST (QUOTE -905) (QUOTE (-390)))))) (-12 (|HasCategory| (-1195) (LIST (QUOTE -626) (LIST (QUOTE -905) (QUOTE (-576))))) (|HasCategory| |#1| (LIST (QUOTE -626) (LIST (QUOTE -905) (QUOTE (-576)))))) (-12 (|HasCategory| (-1195) (LIST (QUOTE -626) (QUOTE (-548)))) (|HasCategory| |#1| (LIST (QUOTE -626) (QUOTE (-548))))) (|HasCategory| |#1| (LIST (QUOTE -651) (QUOTE (-576)))) (|HasCategory| |#1| (QUOTE (-148))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -419) (QUOTE (-576))))) (|HasCategory| |#1| (LIST (QUOTE -1057) (QUOTE (-576)))) (-2781 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -419) (QUOTE (-576))))) (|HasCategory| |#1| (LIST (QUOTE -1057) (LIST (QUOTE -419) (QUOTE (-576)))))) (|HasCategory| |#1| (LIST (QUOTE -1057) (LIST (QUOTE -419) (QUOTE (-576))))) (|HasCategory| |#1| (QUOTE (-374))) (|HasAttribute| |#1| (QUOTE -4460)) (|HasCategory| |#1| (QUOTE (-464))) (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-926)))) (-2781 (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-926)))) (|HasCategory| |#1| (QUOTE (-146))))) -(-970 E V R P -1966) +((|HasCategory| |#1| (QUOTE (-926))) (-2755 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-464))) (|HasCategory| |#1| (QUOTE (-568))) (|HasCategory| |#1| (QUOTE (-926)))) (-2755 (|HasCategory| |#1| (QUOTE (-464))) (|HasCategory| |#1| (QUOTE (-568))) (|HasCategory| |#1| (QUOTE (-926)))) (-2755 (|HasCategory| |#1| (QUOTE (-464))) (|HasCategory| |#1| (QUOTE (-926)))) (|HasCategory| |#1| (QUOTE (-568))) (|HasCategory| |#1| (QUOTE (-174))) (-2755 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-568)))) (-12 (|HasCategory| (-1195) (LIST (QUOTE -899) (QUOTE (-390)))) (|HasCategory| |#1| (LIST (QUOTE -899) (QUOTE (-390))))) (-12 (|HasCategory| (-1195) (LIST (QUOTE -899) (QUOTE (-576)))) (|HasCategory| |#1| (LIST (QUOTE -899) (QUOTE (-576))))) (-12 (|HasCategory| (-1195) (LIST (QUOTE -626) (LIST (QUOTE -905) (QUOTE (-390))))) (|HasCategory| |#1| (LIST (QUOTE -626) (LIST (QUOTE -905) (QUOTE (-390)))))) (-12 (|HasCategory| (-1195) (LIST (QUOTE -626) (LIST (QUOTE -905) (QUOTE (-576))))) (|HasCategory| |#1| (LIST (QUOTE -626) (LIST (QUOTE -905) (QUOTE (-576)))))) (-12 (|HasCategory| (-1195) (LIST (QUOTE -626) (QUOTE (-548)))) (|HasCategory| |#1| (LIST (QUOTE -626) (QUOTE (-548))))) (|HasCategory| |#1| (LIST (QUOTE -651) (QUOTE (-576)))) (|HasCategory| |#1| (QUOTE (-148))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -419) (QUOTE (-576))))) (|HasCategory| |#1| (LIST (QUOTE -1057) (QUOTE (-576)))) (-2755 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -419) (QUOTE (-576))))) (|HasCategory| |#1| (LIST (QUOTE -1057) (LIST (QUOTE -419) (QUOTE (-576)))))) (|HasCategory| |#1| (LIST (QUOTE -1057) (LIST (QUOTE -419) (QUOTE (-576))))) (|HasCategory| |#1| (QUOTE (-374))) (|HasAttribute| |#1| (QUOTE -4460)) (|HasCategory| |#1| (QUOTE (-464))) (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-926)))) (-2755 (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-926)))) (|HasCategory| |#1| (QUOTE (-146))))) +(-970 E V R P -1955) ((|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 (-464)))) @@ -3831,12 +3831,12 @@ NIL (-975 S) ((|constructor| (NIL "\\indented{1}{This provides a fast array type with no bound checking on elt\\spad{'s}.} Minimum index is 0 in this type,{} cannot be changed"))) ((-4463 . T) (-4462 . T)) -((-2781 (-12 (|HasCategory| |#1| (QUOTE (-862))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1119))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|))))) (-2781 (-12 (|HasCategory| |#1| (QUOTE (-1119))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-874))))) (|HasCategory| |#1| (LIST (QUOTE -626) (QUOTE (-548)))) (-2781 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-862))) (|HasCategory| |#1| (QUOTE (-1119)))) (-2781 (|HasCategory| |#1| (QUOTE (-862))) (|HasCategory| |#1| (QUOTE (-1119)))) (|HasCategory| |#1| (QUOTE (-862))) (|HasCategory| (-576) (QUOTE (-862))) (|HasCategory| |#1| (QUOTE (-1119))) (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-874)))) (|HasCategory| |#1| (QUOTE (-102))) (-12 (|HasCategory| |#1| (QUOTE (-1119))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|))))) +((-2755 (-12 (|HasCategory| |#1| (QUOTE (-862))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1119))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|))))) (-2755 (-12 (|HasCategory| |#1| (QUOTE (-1119))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-874))))) (|HasCategory| |#1| (LIST (QUOTE -626) (QUOTE (-548)))) (-2755 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-862))) (|HasCategory| |#1| (QUOTE (-1119)))) (-2755 (|HasCategory| |#1| (QUOTE (-862))) (|HasCategory| |#1| (QUOTE (-1119)))) (|HasCategory| |#1| (QUOTE (-862))) (|HasCategory| (-576) (QUOTE (-862))) (|HasCategory| |#1| (QUOTE (-1119))) (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-874)))) (|HasCategory| |#1| (QUOTE (-102))) (-12 (|HasCategory| |#1| (QUOTE (-1119))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|))))) (-976) ((|constructor| (NIL "Category for the functions defined by integrals.")) (|integral| (($ $ (|SegmentBinding| $)) "\\spad{integral(f, x = a..b)} returns the formal definite integral of \\spad{f} \\spad{dx} for \\spad{x} between \\spad{a} and \\spad{b}.") (($ $ (|Symbol|)) "\\spad{integral(f, x)} returns the formal integral of \\spad{f} \\spad{dx}."))) NIL NIL -(-977 -1966) +(-977 -1955) ((|constructor| (NIL "PrimitiveElement provides functions to compute primitive elements in algebraic extensions.")) (|primitiveElement| (((|Record| (|:| |coef| (|List| (|Integer|))) (|:| |poly| (|List| (|SparseUnivariatePolynomial| |#1|))) (|:| |prim| (|SparseUnivariatePolynomial| |#1|))) (|List| (|Polynomial| |#1|)) (|List| (|Symbol|)) (|Symbol|)) "\\spad{primitiveElement([p1,...,pn], [a1,...,an], a)} returns \\spad{[[c1,...,cn], [q1,...,qn], q]} such that then \\spad{k(a1,...,an) = k(a)},{} where \\spad{a = a1 c1 + ... + an cn},{} \\spad{ai = qi(a)},{} and \\spad{q(a) = 0}. The \\spad{pi}\\spad{'s} are the defining polynomials for the \\spad{ai}\\spad{'s}. This operation uses the technique of \\spadglossSee{groebner bases}{Groebner basis}.") (((|Record| (|:| |coef| (|List| (|Integer|))) (|:| |poly| (|List| (|SparseUnivariatePolynomial| |#1|))) (|:| |prim| (|SparseUnivariatePolynomial| |#1|))) (|List| (|Polynomial| |#1|)) (|List| (|Symbol|))) "\\spad{primitiveElement([p1,...,pn], [a1,...,an])} returns \\spad{[[c1,...,cn], [q1,...,qn], q]} such that then \\spad{k(a1,...,an) = k(a)},{} where \\spad{a = a1 c1 + ... + an cn},{} \\spad{ai = qi(a)},{} and \\spad{q(a) = 0}. The \\spad{pi}\\spad{'s} are the defining polynomials for the \\spad{ai}\\spad{'s}. This operation uses the technique of \\spadglossSee{groebner bases}{Groebner basis}.") (((|Record| (|:| |coef1| (|Integer|)) (|:| |coef2| (|Integer|)) (|:| |prim| (|SparseUnivariatePolynomial| |#1|))) (|Polynomial| |#1|) (|Symbol|) (|Polynomial| |#1|) (|Symbol|)) "\\spad{primitiveElement(p1, a1, p2, a2)} returns \\spad{[c1, c2, q]} such that \\spad{k(a1, a2) = k(a)} where \\spad{a = c1 a1 + c2 a2, and q(a) = 0}. The \\spad{pi}\\spad{'s} are the defining polynomials for the \\spad{ai}\\spad{'s}. The \\spad{p2} may involve \\spad{a1},{} but \\spad{p1} must not involve a2. This operation uses \\spadfun{resultant}."))) NIL NIL @@ -3851,11 +3851,11 @@ NIL (-980 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}"))) (((-4464 "*") |has| |#1| (-174)) (-4455 |has| |#1| (-568)) (-4460 |has| |#1| (-6 -4460)) (-4456 . T) (-4457 . T) (-4459 . T)) -((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -419) (QUOTE (-576))))) (|HasCategory| |#1| (QUOTE (-568))) (-2781 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-568)))) (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-148))) (-2781 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -419) (QUOTE (-576))))) (|HasCategory| |#1| (LIST (QUOTE -1057) (LIST (QUOTE -419) (QUOTE (-576)))))) (|HasCategory| |#1| (LIST (QUOTE -1057) (LIST (QUOTE -419) (QUOTE (-576))))) (|HasCategory| |#1| (LIST (QUOTE -1057) (QUOTE (-576)))) (|HasCategory| |#1| (QUOTE (-374))) (|HasCategory| |#1| (QUOTE (-464))) (-12 (|HasCategory| |#1| (QUOTE (-568))) (|HasCategory| |#2| (QUOTE (-132)))) (|HasAttribute| |#1| (QUOTE -4460))) +((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -419) (QUOTE (-576))))) (|HasCategory| |#1| (QUOTE (-568))) (-2755 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-568)))) (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-148))) (-2755 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -419) (QUOTE (-576))))) (|HasCategory| |#1| (LIST (QUOTE -1057) (LIST (QUOTE -419) (QUOTE (-576)))))) (|HasCategory| |#1| (LIST (QUOTE -1057) (LIST (QUOTE -419) (QUOTE (-576))))) (|HasCategory| |#1| (LIST (QUOTE -1057) (QUOTE (-576)))) (|HasCategory| |#1| (QUOTE (-374))) (|HasCategory| |#1| (QUOTE (-464))) (-12 (|HasCategory| |#1| (QUOTE (-568))) (|HasCategory| |#2| (QUOTE (-132)))) (|HasAttribute| |#1| (QUOTE -4460))) (-981 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"))) ((-4459 -12 (|has| |#2| (-485)) (|has| |#1| (-485)))) -((-2781 (-12 (|HasCategory| |#1| (QUOTE (-805))) (|HasCategory| |#2| (QUOTE (-805)))) (-12 (|HasCategory| |#1| (QUOTE (-862))) (|HasCategory| |#2| (QUOTE (-862))))) (-12 (|HasCategory| |#1| (QUOTE (-805))) (|HasCategory| |#2| (QUOTE (-805)))) (-2781 (-12 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#2| (QUOTE (-21)))) (-12 (|HasCategory| |#1| (QUOTE (-132))) (|HasCategory| |#2| (QUOTE (-132)))) (-12 (|HasCategory| |#1| (QUOTE (-805))) (|HasCategory| |#2| (QUOTE (-805))))) (-12 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#2| (QUOTE (-21)))) (-2781 (-12 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#2| (QUOTE (-21)))) (-12 (|HasCategory| |#1| (QUOTE (-23))) (|HasCategory| |#2| (QUOTE (-23)))) (-12 (|HasCategory| |#1| (QUOTE (-132))) (|HasCategory| |#2| (QUOTE (-132)))) (-12 (|HasCategory| |#1| (QUOTE (-805))) (|HasCategory| |#2| (QUOTE (-805))))) (-12 (|HasCategory| |#1| (QUOTE (-485))) (|HasCategory| |#2| (QUOTE (-485)))) (-2781 (-12 (|HasCategory| |#1| (QUOTE (-485))) (|HasCategory| |#2| (QUOTE (-485)))) (-12 (|HasCategory| |#1| (QUOTE (-738))) (|HasCategory| |#2| (QUOTE (-738))))) (-12 (|HasCategory| |#1| (QUOTE (-379))) (|HasCategory| |#2| (QUOTE (-379)))) (-2781 (-12 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#2| (QUOTE (-21)))) (-12 (|HasCategory| |#1| (QUOTE (-23))) (|HasCategory| |#2| (QUOTE (-23)))) (-12 (|HasCategory| |#1| (QUOTE (-132))) (|HasCategory| |#2| (QUOTE (-132)))) (-12 (|HasCategory| |#1| (QUOTE (-485))) (|HasCategory| |#2| (QUOTE (-485)))) (-12 (|HasCategory| |#1| (QUOTE (-738))) (|HasCategory| |#2| (QUOTE (-738)))) (-12 (|HasCategory| |#1| (QUOTE (-805))) (|HasCategory| |#2| (QUOTE (-805))))) (-12 (|HasCategory| |#1| (QUOTE (-738))) (|HasCategory| |#2| (QUOTE (-738)))) (-12 (|HasCategory| |#1| (QUOTE (-23))) (|HasCategory| |#2| (QUOTE (-23)))) (-12 (|HasCategory| |#1| (QUOTE (-132))) (|HasCategory| |#2| (QUOTE (-132)))) (-12 (|HasCategory| |#1| (QUOTE (-862))) (|HasCategory| |#2| (QUOTE (-862))))) +((-2755 (-12 (|HasCategory| |#1| (QUOTE (-805))) (|HasCategory| |#2| (QUOTE (-805)))) (-12 (|HasCategory| |#1| (QUOTE (-862))) (|HasCategory| |#2| (QUOTE (-862))))) (-12 (|HasCategory| |#1| (QUOTE (-805))) (|HasCategory| |#2| (QUOTE (-805)))) (-2755 (-12 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#2| (QUOTE (-21)))) (-12 (|HasCategory| |#1| (QUOTE (-132))) (|HasCategory| |#2| (QUOTE (-132)))) (-12 (|HasCategory| |#1| (QUOTE (-805))) (|HasCategory| |#2| (QUOTE (-805))))) (-12 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#2| (QUOTE (-21)))) (-2755 (-12 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#2| (QUOTE (-21)))) (-12 (|HasCategory| |#1| (QUOTE (-23))) (|HasCategory| |#2| (QUOTE (-23)))) (-12 (|HasCategory| |#1| (QUOTE (-132))) (|HasCategory| |#2| (QUOTE (-132)))) (-12 (|HasCategory| |#1| (QUOTE (-805))) (|HasCategory| |#2| (QUOTE (-805))))) (-12 (|HasCategory| |#1| (QUOTE (-485))) (|HasCategory| |#2| (QUOTE (-485)))) (-2755 (-12 (|HasCategory| |#1| (QUOTE (-485))) (|HasCategory| |#2| (QUOTE (-485)))) (-12 (|HasCategory| |#1| (QUOTE (-738))) (|HasCategory| |#2| (QUOTE (-738))))) (-12 (|HasCategory| |#1| (QUOTE (-379))) (|HasCategory| |#2| (QUOTE (-379)))) (-2755 (-12 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#2| (QUOTE (-21)))) (-12 (|HasCategory| |#1| (QUOTE (-23))) (|HasCategory| |#2| (QUOTE (-23)))) (-12 (|HasCategory| |#1| (QUOTE (-132))) (|HasCategory| |#2| (QUOTE (-132)))) (-12 (|HasCategory| |#1| (QUOTE (-485))) (|HasCategory| |#2| (QUOTE (-485)))) (-12 (|HasCategory| |#1| (QUOTE (-738))) (|HasCategory| |#2| (QUOTE (-738)))) (-12 (|HasCategory| |#1| (QUOTE (-805))) (|HasCategory| |#2| (QUOTE (-805))))) (-12 (|HasCategory| |#1| (QUOTE (-738))) (|HasCategory| |#2| (QUOTE (-738)))) (-12 (|HasCategory| |#1| (QUOTE (-23))) (|HasCategory| |#2| (QUOTE (-23)))) (-12 (|HasCategory| |#1| (QUOTE (-132))) (|HasCategory| |#2| (QUOTE (-132)))) (-12 (|HasCategory| |#1| (QUOTE (-862))) (|HasCategory| |#2| (QUOTE (-862))))) (-982) ((|constructor| (NIL "\\indented{1}{Author: Gabriel Dos Reis} Date Created: October 24,{} 2007 Date Last Modified: January 18,{} 2008. An `Property' is a pair of name and value.")) (|property| (($ (|Identifier|) (|SExpression|)) "\\spad{property(n,val)} constructs a property with name \\spad{`n'} and value `val'.")) (|value| (((|SExpression|) $) "\\spad{value(p)} returns value of property \\spad{p}")) (|name| (((|Identifier|) $) "\\spad{name(p)} returns the name of property \\spad{p}"))) NIL @@ -3944,7 +3944,7 @@ 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 -(-1004 K R UP -1966) +(-1004 K R UP -1955) ((|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 @@ -4003,11 +4003,11 @@ NIL (-1018 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.}"))) ((-4455 |has| |#1| (-300)) (-4456 . T) (-4457 . T) (-4459 . T)) -((|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-148))) (|HasCategory| |#1| (LIST (QUOTE -626) (QUOTE (-548)))) (|HasCategory| |#1| (QUOTE (-374))) (-2781 (|HasCategory| |#1| (QUOTE (-300))) (|HasCategory| |#1| (QUOTE (-374)))) (|HasCategory| |#1| (QUOTE (-300))) (|HasCategory| |#1| (QUOTE (-862))) (|HasCategory| |#1| (LIST (QUOTE -651) (QUOTE (-576)))) (|HasCategory| |#1| (LIST (QUOTE -526) (QUOTE (-1195)) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -296) (|devaluate| |#1|) (|devaluate| |#1|))) (|HasCategory| |#1| (QUOTE (-237))) (|HasCategory| |#1| (LIST (QUOTE -917) (QUOTE (-1195)))) (|HasCategory| |#1| (QUOTE (-238))) (|HasCategory| |#1| (LIST (QUOTE -915) (QUOTE (-1195)))) (-2781 (|HasCategory| |#1| (LIST (QUOTE -1057) (LIST (QUOTE -419) (QUOTE (-576))))) (|HasCategory| |#1| (QUOTE (-374)))) (|HasCategory| |#1| (LIST (QUOTE -1057) (LIST (QUOTE -419) (QUOTE (-576))))) (|HasCategory| |#1| (LIST (QUOTE -1057) (QUOTE (-576)))) (|HasCategory| |#1| (QUOTE (-1079))) (|HasCategory| |#1| (QUOTE (-557)))) +((|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-148))) (|HasCategory| |#1| (LIST (QUOTE -626) (QUOTE (-548)))) (|HasCategory| |#1| (QUOTE (-374))) (-2755 (|HasCategory| |#1| (QUOTE (-300))) (|HasCategory| |#1| (QUOTE (-374)))) (|HasCategory| |#1| (QUOTE (-300))) (|HasCategory| |#1| (QUOTE (-862))) (|HasCategory| |#1| (LIST (QUOTE -651) (QUOTE (-576)))) (|HasCategory| |#1| (LIST (QUOTE -526) (QUOTE (-1195)) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -296) (|devaluate| |#1|) (|devaluate| |#1|))) (|HasCategory| |#1| (QUOTE (-237))) (|HasCategory| |#1| (LIST (QUOTE -917) (QUOTE (-1195)))) (|HasCategory| |#1| (QUOTE (-238))) (|HasCategory| |#1| (LIST (QUOTE -915) (QUOTE (-1195)))) (-2755 (|HasCategory| |#1| (LIST (QUOTE -1057) (LIST (QUOTE -419) (QUOTE (-576))))) (|HasCategory| |#1| (QUOTE (-374)))) (|HasCategory| |#1| (LIST (QUOTE -1057) (LIST (QUOTE -419) (QUOTE (-576))))) (|HasCategory| |#1| (LIST (QUOTE -1057) (QUOTE (-576)))) (|HasCategory| |#1| (QUOTE (-1079))) (|HasCategory| |#1| (QUOTE (-557)))) (-1019 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}."))) ((-4462 . T) (-4463 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1119))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1119))) (-2781 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-1119)))) (-2781 (-12 (|HasCategory| |#1| (QUOTE (-1119))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-874))))) (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-874)))) (|HasCategory| |#1| (QUOTE (-102)))) +((-12 (|HasCategory| |#1| (QUOTE (-1119))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1119))) (-2755 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-1119)))) (-2755 (-12 (|HasCategory| |#1| (QUOTE (-1119))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-874))))) (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-874)))) (|HasCategory| |#1| (QUOTE (-102)))) (-1020 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| (($ $) "\\spad{sqrt(x)} returns the square root of \\spad{x}."))) NIL @@ -4016,14 +4016,14 @@ NIL ((|constructor| (NIL "The \\spad{RadicalCategory} is a model for the rational numbers.")) (** (($ $ (|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 -(-1022 -1966 UP UPUP |radicnd| |n|) +(-1022 -1955 UP UPUP |radicnd| |n|) ((|constructor| (NIL "Function field defined by y**n = \\spad{f}(\\spad{x})."))) ((-4455 |has| (-419 |#2|) (-374)) (-4460 |has| (-419 |#2|) (-374)) (-4454 |has| (-419 |#2|) (-374)) ((-4464 "*") . T) (-4456 . T) (-4457 . T) (-4459 . T)) -((|HasCategory| (-419 |#2|) (QUOTE (-146))) (|HasCategory| (-419 |#2|) (QUOTE (-148))) (|HasCategory| (-419 |#2|) (QUOTE (-360))) (-2781 (|HasCategory| (-419 |#2|) (QUOTE (-374))) (|HasCategory| (-419 |#2|) (QUOTE (-360)))) (|HasCategory| (-419 |#2|) (QUOTE (-374))) (|HasCategory| (-419 |#2|) (QUOTE (-379))) (-2781 (-12 (|HasCategory| (-419 |#2|) (QUOTE (-238))) (|HasCategory| (-419 |#2|) (QUOTE (-374)))) (|HasCategory| (-419 |#2|) (QUOTE (-360)))) (-2781 (-12 (|HasCategory| (-419 |#2|) (QUOTE (-238))) (|HasCategory| (-419 |#2|) (QUOTE (-374)))) (-12 (|HasCategory| (-419 |#2|) (QUOTE (-237))) (|HasCategory| (-419 |#2|) (QUOTE (-374)))) (|HasCategory| (-419 |#2|) (QUOTE (-360)))) (-2781 (-12 (|HasCategory| (-419 |#2|) (LIST (QUOTE -915) (QUOTE (-1195)))) (|HasCategory| (-419 |#2|) (QUOTE (-374)))) (-12 (|HasCategory| (-419 |#2|) (LIST (QUOTE -915) (QUOTE (-1195)))) (|HasCategory| (-419 |#2|) (QUOTE (-360))))) (-2781 (-12 (|HasCategory| (-419 |#2|) (LIST (QUOTE -915) (QUOTE (-1195)))) (|HasCategory| (-419 |#2|) (QUOTE (-374)))) (-12 (|HasCategory| (-419 |#2|) (LIST (QUOTE -917) (QUOTE (-1195)))) (|HasCategory| (-419 |#2|) (QUOTE (-374))))) (|HasCategory| (-419 |#2|) (LIST (QUOTE -651) (QUOTE (-576)))) (-2781 (|HasCategory| (-419 |#2|) (LIST (QUOTE -1057) (LIST (QUOTE -419) (QUOTE (-576))))) (|HasCategory| (-419 |#2|) (QUOTE (-374)))) (|HasCategory| (-419 |#2|) (LIST (QUOTE -1057) (LIST (QUOTE -419) (QUOTE (-576))))) (|HasCategory| (-419 |#2|) (LIST (QUOTE -1057) (QUOTE (-576)))) (|HasCategory| |#1| (QUOTE (-374))) (|HasCategory| |#1| (QUOTE (-379))) (-12 (|HasCategory| (-419 |#2|) (QUOTE (-237))) (|HasCategory| (-419 |#2|) (QUOTE (-374)))) (-12 (|HasCategory| (-419 |#2|) (LIST (QUOTE -917) (QUOTE (-1195)))) (|HasCategory| (-419 |#2|) (QUOTE (-374)))) (-12 (|HasCategory| (-419 |#2|) (QUOTE (-238))) (|HasCategory| (-419 |#2|) (QUOTE (-374)))) (-12 (|HasCategory| (-419 |#2|) (LIST (QUOTE -915) (QUOTE (-1195)))) (|HasCategory| (-419 |#2|) (QUOTE (-374))))) +((|HasCategory| (-419 |#2|) (QUOTE (-146))) (|HasCategory| (-419 |#2|) (QUOTE (-148))) (|HasCategory| (-419 |#2|) (QUOTE (-360))) (-2755 (|HasCategory| (-419 |#2|) (QUOTE (-374))) (|HasCategory| (-419 |#2|) (QUOTE (-360)))) (|HasCategory| (-419 |#2|) (QUOTE (-374))) (|HasCategory| (-419 |#2|) (QUOTE (-379))) (-2755 (-12 (|HasCategory| (-419 |#2|) (QUOTE (-238))) (|HasCategory| (-419 |#2|) (QUOTE (-374)))) (|HasCategory| (-419 |#2|) (QUOTE (-360)))) (-2755 (-12 (|HasCategory| (-419 |#2|) (QUOTE (-238))) (|HasCategory| (-419 |#2|) (QUOTE (-374)))) (-12 (|HasCategory| (-419 |#2|) (QUOTE (-237))) (|HasCategory| (-419 |#2|) (QUOTE (-374)))) (|HasCategory| (-419 |#2|) (QUOTE (-360)))) (-2755 (-12 (|HasCategory| (-419 |#2|) (LIST (QUOTE -915) (QUOTE (-1195)))) (|HasCategory| (-419 |#2|) (QUOTE (-374)))) (-12 (|HasCategory| (-419 |#2|) (LIST (QUOTE -915) (QUOTE (-1195)))) (|HasCategory| (-419 |#2|) (QUOTE (-360))))) (-2755 (-12 (|HasCategory| (-419 |#2|) (LIST (QUOTE -915) (QUOTE (-1195)))) (|HasCategory| (-419 |#2|) (QUOTE (-374)))) (-12 (|HasCategory| (-419 |#2|) (LIST (QUOTE -917) (QUOTE (-1195)))) (|HasCategory| (-419 |#2|) (QUOTE (-374))))) (|HasCategory| (-419 |#2|) (LIST (QUOTE -651) (QUOTE (-576)))) (-2755 (|HasCategory| (-419 |#2|) (LIST (QUOTE -1057) (LIST (QUOTE -419) (QUOTE (-576))))) (|HasCategory| (-419 |#2|) (QUOTE (-374)))) (|HasCategory| (-419 |#2|) (LIST (QUOTE -1057) (LIST (QUOTE -419) (QUOTE (-576))))) (|HasCategory| (-419 |#2|) (LIST (QUOTE -1057) (QUOTE (-576)))) (|HasCategory| |#1| (QUOTE (-374))) (|HasCategory| |#1| (QUOTE (-379))) (-12 (|HasCategory| (-419 |#2|) (QUOTE (-237))) (|HasCategory| (-419 |#2|) (QUOTE (-374)))) (-12 (|HasCategory| (-419 |#2|) (LIST (QUOTE -917) (QUOTE (-1195)))) (|HasCategory| (-419 |#2|) (QUOTE (-374)))) (-12 (|HasCategory| (-419 |#2|) (QUOTE (-238))) (|HasCategory| (-419 |#2|) (QUOTE (-374)))) (-12 (|HasCategory| (-419 |#2|) (LIST (QUOTE -915) (QUOTE (-1195)))) (|HasCategory| (-419 |#2|) (QUOTE (-374))))) (-1023 |bb|) ((|constructor| (NIL "This domain allows rational numbers to be presented as repeating decimal expansions or more generally as repeating expansions in any base.")) (|fractRadix| (($ (|List| (|Integer|)) (|List| (|Integer|))) "\\spad{fractRadix(pre,cyc)} creates a fractional radix expansion from a list of prefix ragits and a list of cyclic ragits. For example,{} \\spad{fractRadix([1],[6])} will return \\spad{0.16666666...}.")) (|wholeRadix| (($ (|List| (|Integer|))) "\\spad{wholeRadix(l)} creates an integral radix expansion from a list of ragits. For example,{} \\spad{wholeRadix([1,3,4])} will return \\spad{134}.")) (|cycleRagits| (((|List| (|Integer|)) $) "\\spad{cycleRagits(rx)} returns the cyclic part of the ragits of the fractional part of a radix expansion. For example,{} if \\spad{x = 3/28 = 0.10 714285 714285 ...},{} then \\spad{cycleRagits(x) = [7,1,4,2,8,5]}.")) (|prefixRagits| (((|List| (|Integer|)) $) "\\spad{prefixRagits(rx)} returns the non-cyclic part of the ragits of the fractional part of a radix expansion. For example,{} if \\spad{x = 3/28 = 0.10 714285 714285 ...},{} then \\spad{prefixRagits(x)=[1,0]}.")) (|fractRagits| (((|Stream| (|Integer|)) $) "\\spad{fractRagits(rx)} returns the ragits of the fractional part of a radix expansion.")) (|wholeRagits| (((|List| (|Integer|)) $) "\\spad{wholeRagits(rx)} returns the ragits of the integer part of a radix expansion.")) (|fractionPart| (((|Fraction| (|Integer|)) $) "\\spad{fractionPart(rx)} returns the fractional part of a radix expansion."))) ((-4454 . T) (-4460 . T) (-4455 . T) ((-4464 "*") . T) (-4456 . T) (-4457 . T) (-4459 . T)) -((|HasCategory| (-576) (QUOTE (-926))) (|HasCategory| (-576) (LIST (QUOTE -1057) (QUOTE (-1195)))) (|HasCategory| (-576) (QUOTE (-146))) (|HasCategory| (-576) (QUOTE (-148))) (|HasCategory| (-576) (LIST (QUOTE -626) (QUOTE (-548)))) (|HasCategory| (-576) (QUOTE (-1041))) (|HasCategory| (-576) (QUOTE (-832))) (-2781 (|HasCategory| (-576) (QUOTE (-832))) (|HasCategory| (-576) (QUOTE (-862)))) (|HasCategory| (-576) (LIST (QUOTE -1057) (QUOTE (-576)))) (|HasCategory| (-576) (QUOTE (-1171))) (|HasCategory| (-576) (LIST (QUOTE -899) (QUOTE (-390)))) (|HasCategory| (-576) (LIST (QUOTE -899) (QUOTE (-576)))) (|HasCategory| (-576) (LIST (QUOTE -626) (LIST (QUOTE -905) (QUOTE (-390))))) (|HasCategory| (-576) (LIST (QUOTE -626) (LIST (QUOTE -905) (QUOTE (-576))))) (|HasCategory| (-576) (QUOTE (-237))) (|HasCategory| (-576) (LIST (QUOTE -917) (QUOTE (-1195)))) (|HasCategory| (-576) (QUOTE (-238))) (|HasCategory| (-576) (LIST (QUOTE -915) (QUOTE (-1195)))) (|HasCategory| (-576) (LIST (QUOTE -526) (QUOTE (-1195)) (QUOTE (-576)))) (|HasCategory| (-576) (LIST (QUOTE -319) (QUOTE (-576)))) (|HasCategory| (-576) (LIST (QUOTE -296) (QUOTE (-576)) (QUOTE (-576)))) (|HasCategory| (-576) (QUOTE (-317))) (|HasCategory| (-576) (QUOTE (-557))) (|HasCategory| (-576) (QUOTE (-862))) (|HasCategory| (-576) (LIST (QUOTE -651) (QUOTE (-576)))) (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| (-576) (QUOTE (-926)))) (-2781 (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| (-576) (QUOTE (-926)))) (|HasCategory| (-576) (QUOTE (-146))))) +((|HasCategory| (-576) (QUOTE (-926))) (|HasCategory| (-576) (LIST (QUOTE -1057) (QUOTE (-1195)))) (|HasCategory| (-576) (QUOTE (-146))) (|HasCategory| (-576) (QUOTE (-148))) (|HasCategory| (-576) (LIST (QUOTE -626) (QUOTE (-548)))) (|HasCategory| (-576) (QUOTE (-1041))) (|HasCategory| (-576) (QUOTE (-832))) (-2755 (|HasCategory| (-576) (QUOTE (-832))) (|HasCategory| (-576) (QUOTE (-862)))) (|HasCategory| (-576) (LIST (QUOTE -1057) (QUOTE (-576)))) (|HasCategory| (-576) (QUOTE (-1171))) (|HasCategory| (-576) (LIST (QUOTE -899) (QUOTE (-390)))) (|HasCategory| (-576) (LIST (QUOTE -899) (QUOTE (-576)))) (|HasCategory| (-576) (LIST (QUOTE -626) (LIST (QUOTE -905) (QUOTE (-390))))) (|HasCategory| (-576) (LIST (QUOTE -626) (LIST (QUOTE -905) (QUOTE (-576))))) (|HasCategory| (-576) (QUOTE (-237))) (|HasCategory| (-576) (LIST (QUOTE -917) (QUOTE (-1195)))) (|HasCategory| (-576) (QUOTE (-238))) (|HasCategory| (-576) (LIST (QUOTE -915) (QUOTE (-1195)))) (|HasCategory| (-576) (LIST (QUOTE -526) (QUOTE (-1195)) (QUOTE (-576)))) (|HasCategory| (-576) (LIST (QUOTE -319) (QUOTE (-576)))) (|HasCategory| (-576) (LIST (QUOTE -296) (QUOTE (-576)) (QUOTE (-576)))) (|HasCategory| (-576) (QUOTE (-317))) (|HasCategory| (-576) (QUOTE (-557))) (|HasCategory| (-576) (QUOTE (-862))) (|HasCategory| (-576) (LIST (QUOTE -651) (QUOTE (-576)))) (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| (-576) (QUOTE (-926)))) (-2755 (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| (-576) (QUOTE (-926)))) (|HasCategory| (-576) (QUOTE (-146))))) (-1024) ((|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 @@ -4056,19 +4056,19 @@ NIL ((|constructor| (NIL "\\axiomType{RealClosedField} provides common acces functions for all real closed fields.")) (|approximate| (((|Fraction| (|Integer|)) $ $) "\\axiom{approximate(\\spad{n},{}\\spad{p})} gives an approximation of \\axiom{\\spad{n}} that has precision \\axiom{\\spad{p}}")) (|rename| (($ $ (|OutputForm|)) "\\axiom{rename(\\spad{x},{}name)} gives a new number that prints as name")) (|rename!| (($ $ (|OutputForm|)) "\\axiom{rename!(\\spad{x},{}name)} changes the way \\axiom{\\spad{x}} is printed")) (|sqrt| (($ (|Integer|)) "\\axiom{sqrt(\\spad{x})} is \\axiom{\\spad{x} \\spad{**} (1/2)}") (($ (|Fraction| (|Integer|))) "\\axiom{sqrt(\\spad{x})} is \\axiom{\\spad{x} \\spad{**} (1/2)}") (($ $) "\\axiom{sqrt(\\spad{x})} is \\axiom{\\spad{x} \\spad{**} (1/2)}") (($ $ (|PositiveInteger|)) "\\axiom{sqrt(\\spad{x},{}\\spad{n})} is \\axiom{\\spad{x} \\spad{**} (1/n)}")) (|allRootsOf| (((|List| $) (|Polynomial| (|Integer|))) "\\axiom{allRootsOf(pol)} creates all the roots of \\axiom{pol} naming each uniquely") (((|List| $) (|Polynomial| (|Fraction| (|Integer|)))) "\\axiom{allRootsOf(pol)} creates all the roots of \\axiom{pol} naming each uniquely") (((|List| $) (|Polynomial| $)) "\\axiom{allRootsOf(pol)} creates all the roots of \\axiom{pol} naming each uniquely") (((|List| $) (|SparseUnivariatePolynomial| (|Integer|))) "\\axiom{allRootsOf(pol)} creates all the roots of \\axiom{pol} naming each uniquely") (((|List| $) (|SparseUnivariatePolynomial| (|Fraction| (|Integer|)))) "\\axiom{allRootsOf(pol)} creates all the roots of \\axiom{pol} naming each uniquely") (((|List| $) (|SparseUnivariatePolynomial| $)) "\\axiom{allRootsOf(pol)} creates all the roots of \\axiom{pol} naming each uniquely")) (|rootOf| (((|Union| $ "failed") (|SparseUnivariatePolynomial| $) (|PositiveInteger|)) "\\axiom{rootOf(pol,{}\\spad{n})} creates the \\spad{n}th root for the order of \\axiom{pol} and gives it unique name") (((|Union| $ "failed") (|SparseUnivariatePolynomial| $) (|PositiveInteger|) (|OutputForm|)) "\\axiom{rootOf(pol,{}\\spad{n},{}name)} creates the \\spad{n}th root for the order of \\axiom{pol} and names it \\axiom{name}")) (|mainValue| (((|Union| (|SparseUnivariatePolynomial| $) "failed") $) "\\axiom{mainValue(\\spad{x})} is the expression of \\axiom{\\spad{x}} in terms of \\axiom{SparseUnivariatePolynomial(\\$)}")) (|mainDefiningPolynomial| (((|Union| (|SparseUnivariatePolynomial| $) "failed") $) "\\axiom{mainDefiningPolynomial(\\spad{x})} is the defining polynomial for the main algebraic quantity of \\axiom{\\spad{x}}")) (|mainForm| (((|Union| (|OutputForm|) "failed") $) "\\axiom{mainForm(\\spad{x})} is the main algebraic quantity name of \\axiom{\\spad{x}}"))) ((-4455 . T) (-4460 . T) (-4454 . T) (-4457 . T) (-4456 . T) ((-4464 "*") . T) (-4459 . T)) NIL -(-1032 R -1966) +(-1032 R -1955) ((|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 -(-1033 R -1966) +(-1033 R -1955) ((|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 -(-1034 -1966 UP) +(-1034 -1955 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 -(-1035 -1966 UP) +(-1035 -1955 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 @@ -4103,8 +4103,8 @@ NIL (-1043 |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"))) ((-4455 . T) (-4460 . T) (-4454 . T) (-4457 . T) (-4456 . T) ((-4464 "*") . T) (-4459 . T)) -((-2781 (|HasCategory| (-419 (-576)) (LIST (QUOTE -1057) (QUOTE (-576)))) (|HasCategory| |#1| (LIST (QUOTE -1057) (QUOTE (-576))))) (|HasCategory| |#1| (LIST (QUOTE -1057) (LIST (QUOTE -419) (QUOTE (-576))))) (|HasCategory| |#1| (LIST (QUOTE -1057) (QUOTE (-576)))) (|HasCategory| (-419 (-576)) (LIST (QUOTE -1057) (LIST (QUOTE -419) (QUOTE (-576))))) (|HasCategory| (-419 (-576)) (LIST (QUOTE -1057) (QUOTE (-576))))) -(-1044 -1966 L) +((-2755 (|HasCategory| (-419 (-576)) (LIST (QUOTE -1057) (QUOTE (-576)))) (|HasCategory| |#1| (LIST (QUOTE -1057) (QUOTE (-576))))) (|HasCategory| |#1| (LIST (QUOTE -1057) (LIST (QUOTE -419) (QUOTE (-576))))) (|HasCategory| |#1| (LIST (QUOTE -1057) (QUOTE (-576)))) (|HasCategory| (-419 (-576)) (LIST (QUOTE -1057) (LIST (QUOTE -419) (QUOTE (-576))))) (|HasCategory| (-419 (-576)) (LIST (QUOTE -1057) (QUOTE (-576))))) +(-1044 -1955 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 @@ -4140,14 +4140,14 @@ 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 -(-1053 -1966 |Expon| |VarSet| |FPol| |LFPol|) +(-1053 -1955 |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"))) (((-4464 "*") . T) (-4456 . T) (-4457 . T) (-4459 . T)) NIL (-1054) ((|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.}"))) ((-4462 . T) (-4463 . T)) -((-12 (|HasCategory| (-2 (|:| -4300 (-1195)) (|:| -4391 (-52))) (QUOTE (-1119))) (|HasCategory| (-2 (|:| -4300 (-1195)) (|:| -4391 (-52))) (LIST (QUOTE -319) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -4300) (QUOTE (-1195))) (LIST (QUOTE |:|) (QUOTE -4391) (QUOTE (-52))))))) (-2781 (|HasCategory| (-2 (|:| -4300 (-1195)) (|:| -4391 (-52))) (QUOTE (-1119))) (|HasCategory| (-52) (QUOTE (-1119)))) (-2781 (|HasCategory| (-2 (|:| -4300 (-1195)) (|:| -4391 (-52))) (QUOTE (-102))) (|HasCategory| (-2 (|:| -4300 (-1195)) (|:| -4391 (-52))) (QUOTE (-1119))) (|HasCategory| (-52) (QUOTE (-102))) (|HasCategory| (-52) (QUOTE (-1119)))) (-2781 (|HasCategory| (-2 (|:| -4300 (-1195)) (|:| -4391 (-52))) (QUOTE (-1119))) (|HasCategory| (-2 (|:| -4300 (-1195)) (|:| -4391 (-52))) (LIST (QUOTE -625) (QUOTE (-874)))) (|HasCategory| (-52) (QUOTE (-1119))) (|HasCategory| (-52) (LIST (QUOTE -625) (QUOTE (-874))))) (|HasCategory| (-2 (|:| -4300 (-1195)) (|:| -4391 (-52))) (LIST (QUOTE -626) (QUOTE (-548)))) (-12 (|HasCategory| (-52) (QUOTE (-1119))) (|HasCategory| (-52) (LIST (QUOTE -319) (QUOTE (-52))))) (|HasCategory| (-2 (|:| -4300 (-1195)) (|:| -4391 (-52))) (QUOTE (-1119))) (|HasCategory| (-1195) (QUOTE (-862))) (|HasCategory| (-52) (QUOTE (-1119))) (-2781 (|HasCategory| (-2 (|:| -4300 (-1195)) (|:| -4391 (-52))) (LIST (QUOTE -625) (QUOTE (-874)))) (|HasCategory| (-52) (LIST (QUOTE -625) (QUOTE (-874))))) (-2781 (|HasCategory| (-2 (|:| -4300 (-1195)) (|:| -4391 (-52))) (QUOTE (-102))) (|HasCategory| (-52) (QUOTE (-102)))) (|HasCategory| (-52) (QUOTE (-102))) (|HasCategory| (-52) (LIST (QUOTE -625) (QUOTE (-874)))) (|HasCategory| (-2 (|:| -4300 (-1195)) (|:| -4391 (-52))) (LIST (QUOTE -625) (QUOTE (-874)))) (|HasCategory| (-2 (|:| -4300 (-1195)) (|:| -4391 (-52))) (QUOTE (-102)))) +((-12 (|HasCategory| (-2 (|:| -4298 (-1195)) (|:| -4437 (-52))) (QUOTE (-1119))) (|HasCategory| (-2 (|:| -4298 (-1195)) (|:| -4437 (-52))) (LIST (QUOTE -319) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -4298) (QUOTE (-1195))) (LIST (QUOTE |:|) (QUOTE -4437) (QUOTE (-52))))))) (-2755 (|HasCategory| (-2 (|:| -4298 (-1195)) (|:| -4437 (-52))) (QUOTE (-1119))) (|HasCategory| (-52) (QUOTE (-1119)))) (-2755 (|HasCategory| (-2 (|:| -4298 (-1195)) (|:| -4437 (-52))) (QUOTE (-102))) (|HasCategory| (-2 (|:| -4298 (-1195)) (|:| -4437 (-52))) (QUOTE (-1119))) (|HasCategory| (-52) (QUOTE (-102))) (|HasCategory| (-52) (QUOTE (-1119)))) (-2755 (|HasCategory| (-2 (|:| -4298 (-1195)) (|:| -4437 (-52))) (QUOTE (-1119))) (|HasCategory| (-2 (|:| -4298 (-1195)) (|:| -4437 (-52))) (LIST (QUOTE -625) (QUOTE (-874)))) (|HasCategory| (-52) (QUOTE (-1119))) (|HasCategory| (-52) (LIST (QUOTE -625) (QUOTE (-874))))) (|HasCategory| (-2 (|:| -4298 (-1195)) (|:| -4437 (-52))) (LIST (QUOTE -626) (QUOTE (-548)))) (-12 (|HasCategory| (-52) (QUOTE (-1119))) (|HasCategory| (-52) (LIST (QUOTE -319) (QUOTE (-52))))) (|HasCategory| (-2 (|:| -4298 (-1195)) (|:| -4437 (-52))) (QUOTE (-1119))) (|HasCategory| (-1195) (QUOTE (-862))) (|HasCategory| (-52) (QUOTE (-1119))) (-2755 (|HasCategory| (-2 (|:| -4298 (-1195)) (|:| -4437 (-52))) (LIST (QUOTE -625) (QUOTE (-874)))) (|HasCategory| (-52) (LIST (QUOTE -625) (QUOTE (-874))))) (-2755 (|HasCategory| (-2 (|:| -4298 (-1195)) (|:| -4437 (-52))) (QUOTE (-102))) (|HasCategory| (-52) (QUOTE (-102)))) (|HasCategory| (-52) (QUOTE (-102))) (|HasCategory| (-52) (LIST (QUOTE -625) (QUOTE (-874)))) (|HasCategory| (-2 (|:| -4298 (-1195)) (|:| -4437 (-52))) (LIST (QUOTE -625) (QUOTE (-874)))) (|HasCategory| (-2 (|:| -4298 (-1195)) (|:| -4437 (-52))) (QUOTE (-102)))) (-1055) ((|constructor| (NIL "This domain represents `return' expressions.")) (|expression| (((|SpadAst|) $) "\\spad{expression(e)} returns the expression returned by `e'."))) NIL @@ -4204,7 +4204,7 @@ NIL ((|constructor| (NIL "The category of rings with unity,{} always associative,{} but not necessarily commutative.")) (|unitsKnown| ((|attribute|) "recip truly yields reciprocal or \"failed\" if not a unit. Note: \\spad{recip(0) = \"failed\"}.")) (|characteristic| (((|NonNegativeInteger|)) "\\spad{characteristic()} returns the characteristic of the ring this is the smallest positive integer \\spad{n} such that \\spad{n*x=0} for all \\spad{x} in the ring,{} or zero if no such \\spad{n} exists."))) ((-4459 . T)) NIL -(-1069 |xx| -1966) +(-1069 |xx| -1955) ((|constructor| (NIL "This package exports rational interpolation algorithms"))) NIL NIL @@ -4223,7 +4223,7 @@ NIL (-1073 |m| |n| R) ((|constructor| (NIL "\\spadtype{RectangularMatrix} is a matrix domain where the number of rows and the number of columns are parameters of the domain.")) (|rectangularMatrix| (($ (|Matrix| |#3|)) "\\spad{rectangularMatrix(m)} converts a matrix of type \\spadtype{Matrix} to a matrix of type \\spad{RectangularMatrix}."))) ((-4462 . T) (-4457 . T) (-4456 . T)) -((|HasCategory| |#3| (QUOTE (-174))) (-2781 (-12 (|HasCategory| |#3| (QUOTE (-174))) (|HasCategory| |#3| (LIST (QUOTE -319) (|devaluate| |#3|)))) (-12 (|HasCategory| |#3| (QUOTE (-374))) (|HasCategory| |#3| (LIST (QUOTE -319) (|devaluate| |#3|)))) (-12 (|HasCategory| |#3| (QUOTE (-1119))) (|HasCategory| |#3| (LIST (QUOTE -319) (|devaluate| |#3|))))) (|HasCategory| |#3| (LIST (QUOTE -626) (QUOTE (-548)))) (-2781 (|HasCategory| |#3| (QUOTE (-174))) (|HasCategory| |#3| (QUOTE (-374)))) (|HasCategory| |#3| (QUOTE (-374))) (|HasCategory| |#3| (QUOTE (-1119))) (|HasCategory| |#3| (QUOTE (-317))) (|HasCategory| |#3| (QUOTE (-568))) (-12 (|HasCategory| |#3| (QUOTE (-1119))) (|HasCategory| |#3| (LIST (QUOTE -319) (|devaluate| |#3|)))) (|HasCategory| |#3| (QUOTE (-102))) (|HasCategory| |#3| (LIST (QUOTE -625) (QUOTE (-874))))) +((|HasCategory| |#3| (QUOTE (-174))) (-2755 (-12 (|HasCategory| |#3| (QUOTE (-174))) (|HasCategory| |#3| (LIST (QUOTE -319) (|devaluate| |#3|)))) (-12 (|HasCategory| |#3| (QUOTE (-374))) (|HasCategory| |#3| (LIST (QUOTE -319) (|devaluate| |#3|)))) (-12 (|HasCategory| |#3| (QUOTE (-1119))) (|HasCategory| |#3| (LIST (QUOTE -319) (|devaluate| |#3|))))) (|HasCategory| |#3| (LIST (QUOTE -626) (QUOTE (-548)))) (-2755 (|HasCategory| |#3| (QUOTE (-174))) (|HasCategory| |#3| (QUOTE (-374)))) (|HasCategory| |#3| (QUOTE (-374))) (|HasCategory| |#3| (QUOTE (-1119))) (|HasCategory| |#3| (QUOTE (-317))) (|HasCategory| |#3| (QUOTE (-568))) (-12 (|HasCategory| |#3| (QUOTE (-1119))) (|HasCategory| |#3| (LIST (QUOTE -319) (|devaluate| |#3|)))) (|HasCategory| |#3| (QUOTE (-102))) (|HasCategory| |#3| (LIST (QUOTE -625) (QUOTE (-874))))) (-1074 |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 @@ -4259,7 +4259,7 @@ NIL (-1082) ((|constructor| (NIL "\\axiomType{RoutinesTable} implements a database and associated tuning mechanisms for a set of known NAG routines")) (|recoverAfterFail| (((|Union| (|String|) "failed") $ (|String|) (|Integer|)) "\\spad{recoverAfterFail(routs,routineName,ifailValue)} acts on the instructions given by the ifail list")) (|showTheRoutinesTable| (($) "\\spad{showTheRoutinesTable()} returns the current table of NAG routines.")) (|deleteRoutine!| (($ $ (|Symbol|)) "\\spad{deleteRoutine!(R,s)} destructively deletes the given routine from the current database of NAG routines")) (|getExplanations| (((|List| (|String|)) $ (|String|)) "\\spad{getExplanations(R,s)} gets the explanations of the output parameters for the given NAG routine.")) (|getMeasure| (((|Float|) $ (|Symbol|)) "\\spad{getMeasure(R,s)} gets the current value of the maximum measure for the given NAG routine.")) (|changeMeasure| (($ $ (|Symbol|) (|Float|)) "\\spad{changeMeasure(R,s,newValue)} changes the maximum value for a measure of the given NAG routine.")) (|changeThreshhold| (($ $ (|Symbol|) (|Float|)) "\\spad{changeThreshhold(R,s,newValue)} changes the value below which,{} given a NAG routine generating a higher measure,{} the routines will make no attempt to generate a measure.")) (|selectMultiDimensionalRoutines| (($ $) "\\spad{selectMultiDimensionalRoutines(R)} chooses only those routines from the database which are designed for use with multi-dimensional expressions")) (|selectNonFiniteRoutines| (($ $) "\\spad{selectNonFiniteRoutines(R)} chooses only those routines from the database which are designed for use with non-finite expressions.")) (|selectSumOfSquaresRoutines| (($ $) "\\spad{selectSumOfSquaresRoutines(R)} chooses only those routines from the database which are designed for use with sums of squares")) (|selectFiniteRoutines| (($ $) "\\spad{selectFiniteRoutines(R)} chooses only those routines from the database which are designed for use with finite expressions")) (|selectODEIVPRoutines| (($ $) "\\spad{selectODEIVPRoutines(R)} chooses only those routines from the database which are for the solution of ODE\\spad{'s}")) (|selectPDERoutines| (($ $) "\\spad{selectPDERoutines(R)} chooses only those routines from the database which are for the solution of PDE\\spad{'s}")) (|selectOptimizationRoutines| (($ $) "\\spad{selectOptimizationRoutines(R)} chooses only those routines from the database which are for integration")) (|selectIntegrationRoutines| (($ $) "\\spad{selectIntegrationRoutines(R)} chooses only those routines from the database which are for integration")) (|routines| (($) "\\spad{routines()} initialises a database of known NAG routines")) (|concat| (($ $ $) "\\spad{concat(x,y)} merges two tables \\spad{x} and \\spad{y}"))) ((-4462 . T) (-4463 . T)) -((-12 (|HasCategory| (-2 (|:| -4300 (-1195)) (|:| -4391 (-52))) (QUOTE (-1119))) (|HasCategory| (-2 (|:| -4300 (-1195)) (|:| -4391 (-52))) (LIST (QUOTE -319) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -4300) (QUOTE (-1195))) (LIST (QUOTE |:|) (QUOTE -4391) (QUOTE (-52))))))) (-2781 (|HasCategory| (-2 (|:| -4300 (-1195)) (|:| -4391 (-52))) (QUOTE (-1119))) (|HasCategory| (-52) (QUOTE (-1119)))) (-2781 (|HasCategory| (-2 (|:| -4300 (-1195)) (|:| -4391 (-52))) (QUOTE (-102))) (|HasCategory| (-2 (|:| -4300 (-1195)) (|:| -4391 (-52))) (QUOTE (-1119))) (|HasCategory| (-52) (QUOTE (-102))) (|HasCategory| (-52) (QUOTE (-1119)))) (-2781 (|HasCategory| (-2 (|:| -4300 (-1195)) (|:| -4391 (-52))) (QUOTE (-1119))) (|HasCategory| (-2 (|:| -4300 (-1195)) (|:| -4391 (-52))) (LIST (QUOTE -625) (QUOTE (-874)))) (|HasCategory| (-52) (QUOTE (-1119))) (|HasCategory| (-52) (LIST (QUOTE -625) (QUOTE (-874))))) (|HasCategory| (-2 (|:| -4300 (-1195)) (|:| -4391 (-52))) (LIST (QUOTE -626) (QUOTE (-548)))) (-12 (|HasCategory| (-52) (QUOTE (-1119))) (|HasCategory| (-52) (LIST (QUOTE -319) (QUOTE (-52))))) (|HasCategory| (-2 (|:| -4300 (-1195)) (|:| -4391 (-52))) (QUOTE (-1119))) (|HasCategory| (-1195) (QUOTE (-862))) (|HasCategory| (-52) (QUOTE (-1119))) (-2781 (|HasCategory| (-2 (|:| -4300 (-1195)) (|:| -4391 (-52))) (LIST (QUOTE -625) (QUOTE (-874)))) (|HasCategory| (-52) (LIST (QUOTE -625) (QUOTE (-874))))) (-2781 (|HasCategory| (-2 (|:| -4300 (-1195)) (|:| -4391 (-52))) (QUOTE (-102))) (|HasCategory| (-52) (QUOTE (-102)))) (|HasCategory| (-52) (QUOTE (-102))) (|HasCategory| (-52) (LIST (QUOTE -625) (QUOTE (-874)))) (|HasCategory| (-2 (|:| -4300 (-1195)) (|:| -4391 (-52))) (LIST (QUOTE -625) (QUOTE (-874)))) (|HasCategory| (-2 (|:| -4300 (-1195)) (|:| -4391 (-52))) (QUOTE (-102)))) +((-12 (|HasCategory| (-2 (|:| -4298 (-1195)) (|:| -4437 (-52))) (QUOTE (-1119))) (|HasCategory| (-2 (|:| -4298 (-1195)) (|:| -4437 (-52))) (LIST (QUOTE -319) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -4298) (QUOTE (-1195))) (LIST (QUOTE |:|) (QUOTE -4437) (QUOTE (-52))))))) (-2755 (|HasCategory| (-2 (|:| -4298 (-1195)) (|:| -4437 (-52))) (QUOTE (-1119))) (|HasCategory| (-52) (QUOTE (-1119)))) (-2755 (|HasCategory| (-2 (|:| -4298 (-1195)) (|:| -4437 (-52))) (QUOTE (-102))) (|HasCategory| (-2 (|:| -4298 (-1195)) (|:| -4437 (-52))) (QUOTE (-1119))) (|HasCategory| (-52) (QUOTE (-102))) (|HasCategory| (-52) (QUOTE (-1119)))) (-2755 (|HasCategory| (-2 (|:| -4298 (-1195)) (|:| -4437 (-52))) (QUOTE (-1119))) (|HasCategory| (-2 (|:| -4298 (-1195)) (|:| -4437 (-52))) (LIST (QUOTE -625) (QUOTE (-874)))) (|HasCategory| (-52) (QUOTE (-1119))) (|HasCategory| (-52) (LIST (QUOTE -625) (QUOTE (-874))))) (|HasCategory| (-2 (|:| -4298 (-1195)) (|:| -4437 (-52))) (LIST (QUOTE -626) (QUOTE (-548)))) (-12 (|HasCategory| (-52) (QUOTE (-1119))) (|HasCategory| (-52) (LIST (QUOTE -319) (QUOTE (-52))))) (|HasCategory| (-2 (|:| -4298 (-1195)) (|:| -4437 (-52))) (QUOTE (-1119))) (|HasCategory| (-1195) (QUOTE (-862))) (|HasCategory| (-52) (QUOTE (-1119))) (-2755 (|HasCategory| (-2 (|:| -4298 (-1195)) (|:| -4437 (-52))) (LIST (QUOTE -625) (QUOTE (-874)))) (|HasCategory| (-52) (LIST (QUOTE -625) (QUOTE (-874))))) (-2755 (|HasCategory| (-2 (|:| -4298 (-1195)) (|:| -4437 (-52))) (QUOTE (-102))) (|HasCategory| (-52) (QUOTE (-102)))) (|HasCategory| (-52) (QUOTE (-102))) (|HasCategory| (-52) (LIST (QUOTE -625) (QUOTE (-874)))) (|HasCategory| (-2 (|:| -4298 (-1195)) (|:| -4437 (-52))) (LIST (QUOTE -625) (QUOTE (-874)))) (|HasCategory| (-2 (|:| -4298 (-1195)) (|:| -4437 (-52))) (QUOTE (-102)))) (-1083 S R E V) ((|constructor| (NIL "A category for general multi-variate polynomials with coefficients in a ring,{} variables in an ordered set,{} and exponents from an ordered abelian monoid,{} with a \\axiomOp{sup} operation. When not constant,{} such a polynomial is viewed as a univariate polynomial in its main variable \\spad{w}. \\spad{r}. \\spad{t}. to the total ordering on the elements in the ordered set,{} so that some operations usually defined for univariate polynomials make sense here.")) (|mainSquareFreePart| (($ $) "\\axiom{mainSquareFreePart(\\spad{p})} returns the square free part of \\axiom{\\spad{p}} viewed as a univariate polynomial in its main variable and with coefficients in the polynomial ring generated by its other variables over \\axiom{\\spad{R}}.")) (|mainPrimitivePart| (($ $) "\\axiom{mainPrimitivePart(\\spad{p})} returns the primitive part of \\axiom{\\spad{p}} viewed as a univariate polynomial in its main variable and with coefficients in the polynomial ring generated by its other variables over \\axiom{\\spad{R}}.")) (|mainContent| (($ $) "\\axiom{mainContent(\\spad{p})} returns the content of \\axiom{\\spad{p}} viewed as a univariate polynomial in its main variable and with coefficients in the polynomial ring generated by its other variables over \\axiom{\\spad{R}}.")) (|primitivePart!| (($ $) "\\axiom{primitivePart!(\\spad{p})} replaces \\axiom{\\spad{p}} by its primitive part.")) (|gcd| ((|#2| |#2| $) "\\axiom{\\spad{gcd}(\\spad{r},{}\\spad{p})} returns the \\spad{gcd} of \\axiom{\\spad{r}} and the content of \\axiom{\\spad{p}}.")) (|nextsubResultant2| (($ $ $ $ $) "\\axiom{nextsubResultant2(\\spad{p},{}\\spad{q},{}\\spad{z},{}\\spad{s})} is the multivariate version of the operation \\axiomOpFrom{next_sousResultant2}{PseudoRemainderSequence} from the \\axiomType{PseudoRemainderSequence} constructor.")) (|LazardQuotient2| (($ $ $ $ (|NonNegativeInteger|)) "\\axiom{LazardQuotient2(\\spad{p},{}a,{}\\spad{b},{}\\spad{n})} returns \\axiom{(a**(\\spad{n}-1) * \\spad{p}) exquo \\spad{b**}(\\spad{n}-1)} assuming that this quotient does not fail.")) (|LazardQuotient| (($ $ $ (|NonNegativeInteger|)) "\\axiom{LazardQuotient(a,{}\\spad{b},{}\\spad{n})} returns \\axiom{a**n exquo \\spad{b**}(\\spad{n}-1)} assuming that this quotient does not fail.")) (|lastSubResultant| (($ $ $) "\\axiom{lastSubResultant(a,{}\\spad{b})} returns the last non-zero subresultant of \\axiom{a} and \\axiom{\\spad{b}} where \\axiom{a} and \\axiom{\\spad{b}} are assumed to have the same main variable \\axiom{\\spad{v}} and are viewed as univariate polynomials in \\axiom{\\spad{v}}.")) (|subResultantChain| (((|List| $) $ $) "\\axiom{subResultantChain(a,{}\\spad{b})},{} where \\axiom{a} and \\axiom{\\spad{b}} are not contant polynomials with the same main variable,{} returns the subresultant chain of \\axiom{a} and \\axiom{\\spad{b}}.")) (|resultant| (($ $ $) "\\axiom{resultant(a,{}\\spad{b})} computes the resultant of \\axiom{a} and \\axiom{\\spad{b}} where \\axiom{a} and \\axiom{\\spad{b}} are assumed to have the same main variable \\axiom{\\spad{v}} and are viewed as univariate polynomials in \\axiom{\\spad{v}}.")) (|halfExtendedSubResultantGcd2| (((|Record| (|:| |gcd| $) (|:| |coef2| $)) $ $) "\\axiom{halfExtendedSubResultantGcd2(a,{}\\spad{b})} returns \\axiom{[\\spad{g},{}\\spad{cb}]} if \\axiom{extendedSubResultantGcd(a,{}\\spad{b})} returns \\axiom{[\\spad{g},{}ca,{}\\spad{cb}]} otherwise produces an error.")) (|halfExtendedSubResultantGcd1| (((|Record| (|:| |gcd| $) (|:| |coef1| $)) $ $) "\\axiom{halfExtendedSubResultantGcd1(a,{}\\spad{b})} returns \\axiom{[\\spad{g},{}ca]} if \\axiom{extendedSubResultantGcd(a,{}\\spad{b})} returns \\axiom{[\\spad{g},{}ca,{}\\spad{cb}]} otherwise produces an error.")) (|extendedSubResultantGcd| (((|Record| (|:| |gcd| $) (|:| |coef1| $) (|:| |coef2| $)) $ $) "\\axiom{extendedSubResultantGcd(a,{}\\spad{b})} returns \\axiom{[ca,{}\\spad{cb},{}\\spad{r}]} such that \\axiom{\\spad{r}} is \\axiom{subResultantGcd(a,{}\\spad{b})} and we have \\axiom{ca * a + \\spad{cb} * \\spad{cb} = \\spad{r}} .")) (|subResultantGcd| (($ $ $) "\\axiom{subResultantGcd(a,{}\\spad{b})} computes a \\spad{gcd} of \\axiom{a} and \\axiom{\\spad{b}} where \\axiom{a} and \\axiom{\\spad{b}} are assumed to have the same main variable \\axiom{\\spad{v}} and are viewed as univariate polynomials in \\axiom{\\spad{v}} with coefficients in the fraction field of the polynomial ring generated by their other variables over \\axiom{\\spad{R}}.")) (|exactQuotient!| (($ $ $) "\\axiom{exactQuotient!(a,{}\\spad{b})} replaces \\axiom{a} by \\axiom{exactQuotient(a,{}\\spad{b})}") (($ $ |#2|) "\\axiom{exactQuotient!(\\spad{p},{}\\spad{r})} replaces \\axiom{\\spad{p}} by \\axiom{exactQuotient(\\spad{p},{}\\spad{r})}.")) (|exactQuotient| (($ $ $) "\\axiom{exactQuotient(a,{}\\spad{b})} computes the exact quotient of \\axiom{a} by \\axiom{\\spad{b}},{} which is assumed to be a divisor of \\axiom{a}. No error is returned if this exact quotient fails!") (($ $ |#2|) "\\axiom{exactQuotient(\\spad{p},{}\\spad{r})} computes the exact quotient of \\axiom{\\spad{p}} by \\axiom{\\spad{r}},{} which is assumed to be a divisor of \\axiom{\\spad{p}}. No error is returned if this exact quotient fails!")) (|primPartElseUnitCanonical!| (($ $) "\\axiom{primPartElseUnitCanonical!(\\spad{p})} replaces \\axiom{\\spad{p}} by \\axiom{primPartElseUnitCanonical(\\spad{p})}.")) (|primPartElseUnitCanonical| (($ $) "\\axiom{primPartElseUnitCanonical(\\spad{p})} returns \\axiom{primitivePart(\\spad{p})} if \\axiom{\\spad{R}} is a \\spad{gcd}-domain,{} otherwise \\axiom{unitCanonical(\\spad{p})}.")) (|convert| (($ (|Polynomial| |#2|)) "\\axiom{convert(\\spad{p})} returns \\axiom{\\spad{p}} as an element of the current domain if all its variables belong to \\axiom{\\spad{V}},{} otherwise an error is produced.") (($ (|Polynomial| (|Integer|))) "\\axiom{convert(\\spad{p})} returns the same as \\axiom{retract(\\spad{p})}.") (($ (|Polynomial| (|Integer|))) "\\axiom{convert(\\spad{p})} returns the same as \\axiom{retract(\\spad{p})}") (($ (|Polynomial| (|Fraction| (|Integer|)))) "\\axiom{convert(\\spad{p})} returns the same as \\axiom{retract(\\spad{p})}.")) (|retract| (($ (|Polynomial| |#2|)) "\\axiom{retract(\\spad{p})} returns \\axiom{\\spad{p}} as an element of the current domain if \\axiom{retractIfCan(\\spad{p})} does not return \"failed\",{} otherwise an error is produced.") (($ (|Polynomial| |#2|)) "\\axiom{retract(\\spad{p})} returns \\axiom{\\spad{p}} as an element of the current domain if \\axiom{retractIfCan(\\spad{p})} does not return \"failed\",{} otherwise an error is produced.") (($ (|Polynomial| (|Integer|))) "\\axiom{retract(\\spad{p})} returns \\axiom{\\spad{p}} as an element of the current domain if \\axiom{retractIfCan(\\spad{p})} does not return \"failed\",{} otherwise an error is produced.") (($ (|Polynomial| |#2|)) "\\axiom{retract(\\spad{p})} returns \\axiom{\\spad{p}} as an element of the current domain if \\axiom{retractIfCan(\\spad{p})} does not return \"failed\",{} otherwise an error is produced.") (($ (|Polynomial| (|Integer|))) "\\axiom{retract(\\spad{p})} returns \\axiom{\\spad{p}} as an element of the current domain if \\axiom{retractIfCan(\\spad{p})} does not return \"failed\",{} otherwise an error is produced.") (($ (|Polynomial| (|Fraction| (|Integer|)))) "\\axiom{retract(\\spad{p})} returns \\axiom{\\spad{p}} as an element of the current domain if \\axiom{retractIfCan(\\spad{p})} does not return \"failed\",{} otherwise an error is produced.")) (|retractIfCan| (((|Union| $ "failed") (|Polynomial| |#2|)) "\\axiom{retractIfCan(\\spad{p})} returns \\axiom{\\spad{p}} as an element of the current domain if all its variables belong to \\axiom{\\spad{V}}.") (((|Union| $ "failed") (|Polynomial| |#2|)) "\\axiom{retractIfCan(\\spad{p})} returns \\axiom{\\spad{p}} as an element of the current domain if all its variables belong to \\axiom{\\spad{V}}.") (((|Union| $ "failed") (|Polynomial| (|Integer|))) "\\axiom{retractIfCan(\\spad{p})} returns \\axiom{\\spad{p}} as an element of the current domain if all its variables belong to \\axiom{\\spad{V}}.") (((|Union| $ "failed") (|Polynomial| |#2|)) "\\axiom{retractIfCan(\\spad{p})} returns \\axiom{\\spad{p}} as an element of the current domain if all its variables belong to \\axiom{\\spad{V}}.") (((|Union| $ "failed") (|Polynomial| (|Integer|))) "\\axiom{retractIfCan(\\spad{p})} returns \\axiom{\\spad{p}} as an element of the current domain if all its variables belong to \\axiom{\\spad{V}}.") (((|Union| $ "failed") (|Polynomial| (|Fraction| (|Integer|)))) "\\axiom{retractIfCan(\\spad{p})} returns \\axiom{\\spad{p}} as an element of the current domain if all its variables belong to \\axiom{\\spad{V}}.")) (|initiallyReduce| (($ $ $) "\\axiom{initiallyReduce(a,{}\\spad{b})} returns a polynomial \\axiom{\\spad{r}} such that \\axiom{initiallyReduced?(\\spad{r},{}\\spad{b})} holds and there exists an integer \\axiom{\\spad{e}} such that \\axiom{init(\\spad{b})^e a - \\spad{r}} is zero modulo \\axiom{\\spad{b}}.")) (|headReduce| (($ $ $) "\\axiom{headReduce(a,{}\\spad{b})} returns a polynomial \\axiom{\\spad{r}} such that \\axiom{headReduced?(\\spad{r},{}\\spad{b})} holds and there exists an integer \\axiom{\\spad{e}} such that \\axiom{init(\\spad{b})^e a - \\spad{r}} is zero modulo \\axiom{\\spad{b}}.")) (|lazyResidueClass| (((|Record| (|:| |polnum| $) (|:| |polden| $) (|:| |power| (|NonNegativeInteger|))) $ $) "\\axiom{lazyResidueClass(a,{}\\spad{b})} returns \\axiom{[\\spad{p},{}\\spad{q},{}\\spad{n}]} where \\axiom{\\spad{p} / q**n} represents the residue class of \\axiom{a} modulo \\axiom{\\spad{b}} and \\axiom{\\spad{p}} is reduced \\spad{w}.\\spad{r}.\\spad{t}. \\axiom{\\spad{b}} and \\axiom{\\spad{q}} is \\axiom{init(\\spad{b})}.")) (|monicModulo| (($ $ $) "\\axiom{monicModulo(a,{}\\spad{b})} computes \\axiom{a mod \\spad{b}},{} if \\axiom{\\spad{b}} is monic as univariate polynomial in its main variable.")) (|pseudoDivide| (((|Record| (|:| |quotient| $) (|:| |remainder| $)) $ $) "\\axiom{pseudoDivide(a,{}\\spad{b})} computes \\axiom{[pquo(a,{}\\spad{b}),{}prem(a,{}\\spad{b})]},{} both polynomials viewed as univariate polynomials in the main variable of \\axiom{\\spad{b}},{} if \\axiom{\\spad{b}} is not a constant polynomial.")) (|lazyPseudoDivide| (((|Record| (|:| |coef| $) (|:| |gap| (|NonNegativeInteger|)) (|:| |quotient| $) (|:| |remainder| $)) $ $ |#4|) "\\axiom{lazyPseudoDivide(a,{}\\spad{b},{}\\spad{v})} returns \\axiom{[\\spad{c},{}\\spad{g},{}\\spad{q},{}\\spad{r}]} such that \\axiom{\\spad{r} = lazyPrem(a,{}\\spad{b},{}\\spad{v})},{} \\axiom{(c**g)\\spad{*r} = prem(a,{}\\spad{b},{}\\spad{v})} and \\axiom{\\spad{q}} is the pseudo-quotient computed in this lazy pseudo-division.") (((|Record| (|:| |coef| $) (|:| |gap| (|NonNegativeInteger|)) (|:| |quotient| $) (|:| |remainder| $)) $ $) "\\axiom{lazyPseudoDivide(a,{}\\spad{b})} returns \\axiom{[\\spad{c},{}\\spad{g},{}\\spad{q},{}\\spad{r}]} such that \\axiom{[\\spad{c},{}\\spad{g},{}\\spad{r}] = lazyPremWithDefault(a,{}\\spad{b})} and \\axiom{\\spad{q}} is the pseudo-quotient computed in this lazy pseudo-division.")) (|lazyPremWithDefault| (((|Record| (|:| |coef| $) (|:| |gap| (|NonNegativeInteger|)) (|:| |remainder| $)) $ $ |#4|) "\\axiom{lazyPremWithDefault(a,{}\\spad{b},{}\\spad{v})} returns \\axiom{[\\spad{c},{}\\spad{g},{}\\spad{r}]} such that \\axiom{\\spad{r} = lazyPrem(a,{}\\spad{b},{}\\spad{v})} and \\axiom{(c**g)\\spad{*r} = prem(a,{}\\spad{b},{}\\spad{v})}.") (((|Record| (|:| |coef| $) (|:| |gap| (|NonNegativeInteger|)) (|:| |remainder| $)) $ $) "\\axiom{lazyPremWithDefault(a,{}\\spad{b})} returns \\axiom{[\\spad{c},{}\\spad{g},{}\\spad{r}]} such that \\axiom{\\spad{r} = lazyPrem(a,{}\\spad{b})} and \\axiom{(c**g)\\spad{*r} = prem(a,{}\\spad{b})}.")) (|lazyPquo| (($ $ $ |#4|) "\\axiom{lazyPquo(a,{}\\spad{b},{}\\spad{v})} returns the polynomial \\axiom{\\spad{q}} such that \\axiom{lazyPseudoDivide(a,{}\\spad{b},{}\\spad{v})} returns \\axiom{[\\spad{c},{}\\spad{g},{}\\spad{q},{}\\spad{r}]}.") (($ $ $) "\\axiom{lazyPquo(a,{}\\spad{b})} returns the polynomial \\axiom{\\spad{q}} such that \\axiom{lazyPseudoDivide(a,{}\\spad{b})} returns \\axiom{[\\spad{c},{}\\spad{g},{}\\spad{q},{}\\spad{r}]}.")) (|lazyPrem| (($ $ $ |#4|) "\\axiom{lazyPrem(a,{}\\spad{b},{}\\spad{v})} returns the polynomial \\axiom{\\spad{r}} reduced \\spad{w}.\\spad{r}.\\spad{t}. \\axiom{\\spad{b}} viewed as univariate polynomials in the variable \\axiom{\\spad{v}} such that \\axiom{\\spad{b}} divides \\axiom{init(\\spad{b})^e a - \\spad{r}} where \\axiom{\\spad{e}} is the number of steps of this pseudo-division.") (($ $ $) "\\axiom{lazyPrem(a,{}\\spad{b})} returns the polynomial \\axiom{\\spad{r}} reduced \\spad{w}.\\spad{r}.\\spad{t}. \\axiom{\\spad{b}} and such that \\axiom{\\spad{b}} divides \\axiom{init(\\spad{b})^e a - \\spad{r}} where \\axiom{\\spad{e}} is the number of steps of this pseudo-division.")) (|pquo| (($ $ $ |#4|) "\\axiom{pquo(a,{}\\spad{b},{}\\spad{v})} computes the pseudo-quotient of \\axiom{a} by \\axiom{\\spad{b}},{} both viewed as univariate polynomials in \\axiom{\\spad{v}}.") (($ $ $) "\\axiom{pquo(a,{}\\spad{b})} computes the pseudo-quotient of \\axiom{a} by \\axiom{\\spad{b}},{} both viewed as univariate polynomials in the main variable of \\axiom{\\spad{b}}.")) (|prem| (($ $ $ |#4|) "\\axiom{prem(a,{}\\spad{b},{}\\spad{v})} computes the pseudo-remainder of \\axiom{a} by \\axiom{\\spad{b}},{} both viewed as univariate polynomials in \\axiom{\\spad{v}}.") (($ $ $) "\\axiom{prem(a,{}\\spad{b})} computes the pseudo-remainder of \\axiom{a} by \\axiom{\\spad{b}},{} both viewed as univariate polynomials in the main variable of \\axiom{\\spad{b}}.")) (|normalized?| (((|Boolean|) $ (|List| $)) "\\axiom{normalized?(\\spad{q},{}\\spad{lp})} returns \\spad{true} iff \\axiom{normalized?(\\spad{q},{}\\spad{p})} holds for every \\axiom{\\spad{p}} in \\axiom{\\spad{lp}}.") (((|Boolean|) $ $) "\\axiom{normalized?(a,{}\\spad{b})} returns \\spad{true} iff \\axiom{a} and its iterated initials have degree zero \\spad{w}.\\spad{r}.\\spad{t}. the main variable of \\axiom{\\spad{b}}")) (|initiallyReduced?| (((|Boolean|) $ (|List| $)) "\\axiom{initiallyReduced?(\\spad{q},{}\\spad{lp})} returns \\spad{true} iff \\axiom{initiallyReduced?(\\spad{q},{}\\spad{p})} holds for every \\axiom{\\spad{p}} in \\axiom{\\spad{lp}}.") (((|Boolean|) $ $) "\\axiom{initiallyReduced?(a,{}\\spad{b})} returns \\spad{false} iff there exists an iterated initial of \\axiom{a} which is not reduced \\spad{w}.\\spad{r}.\\spad{t} \\axiom{\\spad{b}}.")) (|headReduced?| (((|Boolean|) $ (|List| $)) "\\axiom{headReduced?(\\spad{q},{}\\spad{lp})} returns \\spad{true} iff \\axiom{headReduced?(\\spad{q},{}\\spad{p})} holds for every \\axiom{\\spad{p}} in \\axiom{\\spad{lp}}.") (((|Boolean|) $ $) "\\axiom{headReduced?(a,{}\\spad{b})} returns \\spad{true} iff \\axiom{degree(head(a),{}mvar(\\spad{b})) < mdeg(\\spad{b})}.")) (|reduced?| (((|Boolean|) $ (|List| $)) "\\axiom{reduced?(\\spad{q},{}\\spad{lp})} returns \\spad{true} iff \\axiom{reduced?(\\spad{q},{}\\spad{p})} holds for every \\axiom{\\spad{p}} in \\axiom{\\spad{lp}}.") (((|Boolean|) $ $) "\\axiom{reduced?(a,{}\\spad{b})} returns \\spad{true} iff \\axiom{degree(a,{}mvar(\\spad{b})) < mdeg(\\spad{b})}.")) (|supRittWu?| (((|Boolean|) $ $) "\\axiom{supRittWu?(a,{}\\spad{b})} returns \\spad{true} if \\axiom{a} is greater than \\axiom{\\spad{b}} \\spad{w}.\\spad{r}.\\spad{t}. the Ritt and Wu Wen Tsun ordering using the refinement of Lazard.")) (|infRittWu?| (((|Boolean|) $ $) "\\axiom{infRittWu?(a,{}\\spad{b})} returns \\spad{true} if \\axiom{a} is less than \\axiom{\\spad{b}} \\spad{w}.\\spad{r}.\\spad{t}. the Ritt and Wu Wen Tsun ordering using the refinement of Lazard.")) (|RittWuCompare| (((|Union| (|Boolean|) "failed") $ $) "\\axiom{RittWuCompare(a,{}\\spad{b})} returns \\axiom{\"failed\"} if \\axiom{a} and \\axiom{\\spad{b}} have same rank \\spad{w}.\\spad{r}.\\spad{t}. Ritt and Wu Wen Tsun ordering using the refinement of Lazard,{} otherwise returns \\axiom{infRittWu?(a,{}\\spad{b})}.")) (|mainMonomials| (((|List| $) $) "\\axiom{mainMonomials(\\spad{p})} returns an error if \\axiom{\\spad{p}} is \\axiom{\\spad{O}},{} otherwise,{} if \\axiom{\\spad{p}} belongs to \\axiom{\\spad{R}} returns [1],{} otherwise returns the list of the monomials of \\axiom{\\spad{p}},{} where \\axiom{\\spad{p}} is viewed as a univariate polynomial in its main variable.")) (|mainCoefficients| (((|List| $) $) "\\axiom{mainCoefficients(\\spad{p})} returns an error if \\axiom{\\spad{p}} is \\axiom{\\spad{O}},{} otherwise,{} if \\axiom{\\spad{p}} belongs to \\axiom{\\spad{R}} returns [\\spad{p}],{} otherwise returns the list of the coefficients of \\axiom{\\spad{p}},{} where \\axiom{\\spad{p}} is viewed as a univariate polynomial in its main variable.")) (|leastMonomial| (($ $) "\\axiom{leastMonomial(\\spad{p})} returns an error if \\axiom{\\spad{p}} is \\axiom{\\spad{O}},{} otherwise,{} if \\axiom{\\spad{p}} belongs to \\axiom{\\spad{R}} returns \\axiom{1},{} otherwise,{} the monomial of \\axiom{\\spad{p}} with lowest degree,{} where \\axiom{\\spad{p}} is viewed as a univariate polynomial in its main variable.")) (|mainMonomial| (($ $) "\\axiom{mainMonomial(\\spad{p})} returns an error if \\axiom{\\spad{p}} is \\axiom{\\spad{O}},{} otherwise,{} if \\axiom{\\spad{p}} belongs to \\axiom{\\spad{R}} returns \\axiom{1},{} otherwise,{} \\axiom{mvar(\\spad{p})} raised to the power \\axiom{mdeg(\\spad{p})}.")) (|quasiMonic?| (((|Boolean|) $) "\\axiom{quasiMonic?(\\spad{p})} returns \\spad{false} if \\axiom{\\spad{p}} belongs to \\axiom{\\spad{R}},{} otherwise returns \\spad{true} iff the initial of \\axiom{\\spad{p}} lies in the base ring \\axiom{\\spad{R}}.")) (|monic?| (((|Boolean|) $) "\\axiom{monic?(\\spad{p})} returns \\spad{false} if \\axiom{\\spad{p}} belongs to \\axiom{\\spad{R}},{} otherwise returns \\spad{true} iff \\axiom{\\spad{p}} is monic as a univariate polynomial in its main variable.")) (|reductum| (($ $ |#4|) "\\axiom{reductum(\\spad{p},{}\\spad{v})} returns the reductum of \\axiom{\\spad{p}},{} where \\axiom{\\spad{p}} is viewed as a univariate polynomial in \\axiom{\\spad{v}}.")) (|leadingCoefficient| (($ $ |#4|) "\\axiom{leadingCoefficient(\\spad{p},{}\\spad{v})} returns the leading coefficient of \\axiom{\\spad{p}},{} where \\axiom{\\spad{p}} is viewed as A univariate polynomial in \\axiom{\\spad{v}}.")) (|deepestInitial| (($ $) "\\axiom{deepestInitial(\\spad{p})} returns an error if \\axiom{\\spad{p}} belongs to \\axiom{\\spad{R}},{} otherwise returns the last term of \\axiom{iteratedInitials(\\spad{p})}.")) (|iteratedInitials| (((|List| $) $) "\\axiom{iteratedInitials(\\spad{p})} returns \\axiom{[]} if \\axiom{\\spad{p}} belongs to \\axiom{\\spad{R}},{} otherwise returns the list of the iterated initials of \\axiom{\\spad{p}}.")) (|deepestTail| (($ $) "\\axiom{deepestTail(\\spad{p})} returns \\axiom{0} if \\axiom{\\spad{p}} belongs to \\axiom{\\spad{R}},{} otherwise returns tail(\\spad{p}),{} if \\axiom{tail(\\spad{p})} belongs to \\axiom{\\spad{R}} or \\axiom{mvar(tail(\\spad{p})) < mvar(\\spad{p})},{} otherwise returns \\axiom{deepestTail(tail(\\spad{p}))}.")) (|tail| (($ $) "\\axiom{tail(\\spad{p})} returns its reductum,{} where \\axiom{\\spad{p}} is viewed as a univariate polynomial in its main variable.")) (|head| (($ $) "\\axiom{head(\\spad{p})} returns \\axiom{\\spad{p}} if \\axiom{\\spad{p}} belongs to \\axiom{\\spad{R}},{} otherwise returns its leading term (monomial in the AXIOM sense),{} where \\axiom{\\spad{p}} is viewed as a univariate polynomial in its main variable.")) (|init| (($ $) "\\axiom{init(\\spad{p})} returns an error if \\axiom{\\spad{p}} belongs to \\axiom{\\spad{R}},{} otherwise returns its leading coefficient,{} where \\axiom{\\spad{p}} is viewed as a univariate polynomial in its main variable.")) (|mdeg| (((|NonNegativeInteger|) $) "\\axiom{mdeg(\\spad{p})} returns an error if \\axiom{\\spad{p}} is \\axiom{0},{} otherwise,{} if \\axiom{\\spad{p}} belongs to \\axiom{\\spad{R}} returns \\axiom{0},{} otherwise,{} returns the degree of \\axiom{\\spad{p}} in its main variable.")) (|mvar| ((|#4| $) "\\axiom{mvar(\\spad{p})} returns an error if \\axiom{\\spad{p}} belongs to \\axiom{\\spad{R}},{} otherwise returns its main variable \\spad{w}. \\spad{r}. \\spad{t}. to the total ordering on the elements in \\axiom{\\spad{V}}."))) NIL @@ -4308,11 +4308,11 @@ NIL ((|constructor| (NIL "This domain implements named rules")) (|name| (((|Symbol|) $) "\\spad{name(x)} returns the symbol"))) NIL NIL -(-1095 |Base| R -1966) +(-1095 |Base| R -1955) ((|constructor| (NIL "\\indented{1}{Rules for the pattern matcher} Author: Manuel Bronstein Date Created: 24 Oct 1988 Date Last Updated: 26 October 1993 Keywords: pattern,{} matching,{} rule.")) (|quotedOperators| (((|List| (|Symbol|)) $) "\\spad{quotedOperators(r)} returns the list of operators on the right hand side of \\spad{r} that are considered quoted,{} that is they are not evaluated during any rewrite,{} but just applied formally to their arguments.")) (|elt| ((|#3| $ |#3| (|PositiveInteger|)) "\\spad{elt(r,f,n)} or \\spad{r}(\\spad{f},{} \\spad{n}) applies the rule \\spad{r} to \\spad{f} at most \\spad{n} times.")) (|rhs| ((|#3| $) "\\spad{rhs(r)} returns the right hand side of the rule \\spad{r}.")) (|lhs| ((|#3| $) "\\spad{lhs(r)} returns the left hand side of the rule \\spad{r}.")) (|pattern| (((|Pattern| |#1|) $) "\\spad{pattern(r)} returns the pattern corresponding to the left hand side of the rule \\spad{r}.")) (|suchThat| (($ $ (|List| (|Symbol|)) (|Mapping| (|Boolean|) (|List| |#3|))) "\\spad{suchThat(r, [a1,...,an], f)} returns the rewrite rule \\spad{r} with the predicate \\spad{f(a1,...,an)} attached to it.")) (|rule| (($ |#3| |#3| (|List| (|Symbol|))) "\\spad{rule(f, g, [f1,...,fn])} creates the rewrite rule \\spad{f == eval(eval(g, g is f), [f1,...,fn])},{} that is a rule with left-hand side \\spad{f} and right-hand side \\spad{g}; The symbols \\spad{f1},{}...,{}\\spad{fn} are the operators that are considered quoted,{} that is they are not evaluated during any rewrite,{} but just applied formally to their arguments.") (($ |#3| |#3|) "\\spad{rule(f, g)} creates the rewrite rule: \\spad{f == eval(g, g is f)},{} with left-hand side \\spad{f} and right-hand side \\spad{g}."))) NIL NIL -(-1096 |Base| R -1966) +(-1096 |Base| R -1955) ((|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 @@ -4327,7 +4327,7 @@ NIL (-1099 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."))) ((-4455 |has| |#1| (-374)) (-4460 |has| |#1| (-374)) (-4454 |has| |#1| (-374)) ((-4464 "*") . T) (-4456 . T) (-4457 . T) (-4459 . T)) -((|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-148))) (|HasCategory| |#1| (QUOTE (-360))) (-2781 (|HasCategory| |#1| (QUOTE (-374))) (|HasCategory| |#1| (QUOTE (-360)))) (|HasCategory| |#1| (QUOTE (-374))) (|HasCategory| |#1| (QUOTE (-379))) (-2781 (-12 (|HasCategory| |#1| (QUOTE (-238))) (|HasCategory| |#1| (QUOTE (-374)))) (|HasCategory| |#1| (QUOTE (-360)))) (-2781 (-12 (|HasCategory| |#1| (QUOTE (-238))) (|HasCategory| |#1| (QUOTE (-374)))) (-12 (|HasCategory| |#1| (QUOTE (-237))) (|HasCategory| |#1| (QUOTE (-374)))) (|HasCategory| |#1| (QUOTE (-360)))) (-2781 (-12 (|HasCategory| |#1| (QUOTE (-374))) (|HasCategory| |#1| (LIST (QUOTE -915) (QUOTE (-1195))))) (-12 (|HasCategory| |#1| (QUOTE (-360))) (|HasCategory| |#1| (LIST (QUOTE -915) (QUOTE (-1195)))))) (-2781 (-12 (|HasCategory| |#1| (QUOTE (-374))) (|HasCategory| |#1| (LIST (QUOTE -915) (QUOTE (-1195))))) (-12 (|HasCategory| |#1| (QUOTE (-374))) (|HasCategory| |#1| (LIST (QUOTE -917) (QUOTE (-1195)))))) (|HasCategory| |#1| (LIST (QUOTE -651) (QUOTE (-576)))) (-2781 (|HasCategory| |#1| (LIST (QUOTE -1057) (LIST (QUOTE -419) (QUOTE (-576))))) (|HasCategory| |#1| (QUOTE (-374)))) (|HasCategory| |#1| (LIST (QUOTE -1057) (LIST (QUOTE -419) (QUOTE (-576))))) (|HasCategory| |#1| (LIST (QUOTE -1057) (QUOTE (-576)))) (-2781 (-12 (|HasCategory| |#1| (QUOTE (-237))) (|HasCategory| |#1| (QUOTE (-374)))) (|HasCategory| |#1| (QUOTE (-360)))) (-12 (|HasCategory| |#1| (QUOTE (-374))) (|HasCategory| |#1| (LIST (QUOTE -917) (QUOTE (-1195))))) (-12 (|HasCategory| |#1| (QUOTE (-237))) (|HasCategory| |#1| (QUOTE (-374)))) (-12 (|HasCategory| |#1| (QUOTE (-238))) (|HasCategory| |#1| (QUOTE (-374)))) (-12 (|HasCategory| |#1| (QUOTE (-374))) (|HasCategory| |#1| (LIST (QUOTE -915) (QUOTE (-1195)))))) +((|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-148))) (|HasCategory| |#1| (QUOTE (-360))) (-2755 (|HasCategory| |#1| (QUOTE (-374))) (|HasCategory| |#1| (QUOTE (-360)))) (|HasCategory| |#1| (QUOTE (-374))) (|HasCategory| |#1| (QUOTE (-379))) (-2755 (-12 (|HasCategory| |#1| (QUOTE (-238))) (|HasCategory| |#1| (QUOTE (-374)))) (|HasCategory| |#1| (QUOTE (-360)))) (-2755 (-12 (|HasCategory| |#1| (QUOTE (-238))) (|HasCategory| |#1| (QUOTE (-374)))) (-12 (|HasCategory| |#1| (QUOTE (-237))) (|HasCategory| |#1| (QUOTE (-374)))) (|HasCategory| |#1| (QUOTE (-360)))) (-2755 (-12 (|HasCategory| |#1| (QUOTE (-374))) (|HasCategory| |#1| (LIST (QUOTE -915) (QUOTE (-1195))))) (-12 (|HasCategory| |#1| (QUOTE (-360))) (|HasCategory| |#1| (LIST (QUOTE -915) (QUOTE (-1195)))))) (-2755 (-12 (|HasCategory| |#1| (QUOTE (-374))) (|HasCategory| |#1| (LIST (QUOTE -915) (QUOTE (-1195))))) (-12 (|HasCategory| |#1| (QUOTE (-374))) (|HasCategory| |#1| (LIST (QUOTE -917) (QUOTE (-1195)))))) (|HasCategory| |#1| (LIST (QUOTE -651) (QUOTE (-576)))) (-2755 (|HasCategory| |#1| (LIST (QUOTE -1057) (LIST (QUOTE -419) (QUOTE (-576))))) (|HasCategory| |#1| (QUOTE (-374)))) (|HasCategory| |#1| (LIST (QUOTE -1057) (LIST (QUOTE -419) (QUOTE (-576))))) (|HasCategory| |#1| (LIST (QUOTE -1057) (QUOTE (-576)))) (-2755 (-12 (|HasCategory| |#1| (QUOTE (-237))) (|HasCategory| |#1| (QUOTE (-374)))) (|HasCategory| |#1| (QUOTE (-360)))) (-12 (|HasCategory| |#1| (QUOTE (-374))) (|HasCategory| |#1| (LIST (QUOTE -917) (QUOTE (-1195))))) (-12 (|HasCategory| |#1| (QUOTE (-237))) (|HasCategory| |#1| (QUOTE (-374)))) (-12 (|HasCategory| |#1| (QUOTE (-238))) (|HasCategory| |#1| (QUOTE (-374)))) (-12 (|HasCategory| |#1| (QUOTE (-374))) (|HasCategory| |#1| (LIST (QUOTE -915) (QUOTE (-1195)))))) (-1100 UP SAE UPA) ((|constructor| (NIL "Factorization of univariate polynomials with coefficients in an algebraic extension of \\spadtype{Fraction Polynomial Integer}.")) (|factor| (((|Factored| |#3|) |#3|) "\\spad{factor(p)} returns a prime factorisation of \\spad{p}."))) NIL @@ -4355,7 +4355,7 @@ NIL (-1106 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"))) (((-4464 "*") |has| |#1| (-174)) (-4455 |has| |#1| (-568)) (-4460 |has| |#1| (-6 -4460)) (-4457 . T) (-4456 . T) (-4459 . 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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 @@ -4415,7 +4415,7 @@ NIL (-1121 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. 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(|#| (((|Integer|) $) "\\spad{\\#((a1,...,an))} returns \\spad{n}.")) (|cdr| (($ $) "\\spad{cdr((a1,...,an))} returns \\spad{(a2,...,an)}.")) (|car| (($ $) "\\spad{car((a1,...,an))} returns a1.")) (|expr| ((|#5| $) "\\spad{expr(s)} returns \\spad{s} as an element of Expr; Error: if \\spad{s} is not an atom that also belongs to Expr.")) (|float| ((|#4| $) "\\spad{float(s)} returns \\spad{s} as an element of \\spad{Flt}; Error: if \\spad{s} is not an atom that also belongs to \\spad{Flt}.")) (|integer| ((|#3| $) "\\spad{integer(s)} returns \\spad{s} as an element of Int. Error: if \\spad{s} is not an atom that also belongs to Int.")) (|symbol| ((|#2| $) "\\spad{symbol(s)} returns \\spad{s} as an element of \\spad{Sym}. Error: if \\spad{s} is not an atom that also belongs to \\spad{Sym}.")) (|string| ((|#1| $) "\\spad{string(s)} returns \\spad{s} as an element of \\spad{Str}. Error: if \\spad{s} is not an atom that also belongs to \\spad{Str}.")) 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(|UnivariatePolynomial| |#2| |#1|)) "\\spad{SturmHabichtMultiple(p1,p2)} computes \\spad{c_}{+}\\spad{-c_}{-} where \\spad{c_}{+} is the number of real roots of \\spad{p1} with p2>0 and \\spad{c_}{-} is the number of real roots of \\spad{p1} with p2<0. If p2=1 what you get is the number of real roots of \\spad{p1}.")) (|countRealRoots| (((|Integer|) (|UnivariatePolynomial| |#2| |#1|)) "\\spad{countRealRoots(p)} says how many real roots \\spad{p} has")) (|SturmHabicht| (((|Integer|) (|UnivariatePolynomial| |#2| |#1|) (|UnivariatePolynomial| |#2| |#1|)) "\\spad{SturmHabicht(p1,p2)} computes \\spad{c_}{+}\\spad{-c_}{-} where \\spad{c_}{+} is the number of real roots of \\spad{p1} with p2>0 and \\spad{c_}{-} is the number of real roots of \\spad{p1} with p2<0. If p2=1 what you get is the number of real roots of \\spad{p1}.")) (|SturmHabichtCoefficients| (((|List| |#1|) (|UnivariatePolynomial| |#2| |#1|) (|UnivariatePolynomial| |#2| |#1|)) "\\spad{SturmHabichtCoefficients(p1,p2)} computes the principal Sturm-Habicht coefficients of \\spad{p1} and \\spad{p2}")) (|SturmHabichtSequence| (((|List| (|UnivariatePolynomial| |#2| |#1|)) (|UnivariatePolynomial| |#2| |#1|) (|UnivariatePolynomial| |#2| |#1|)) "\\spad{SturmHabichtSequence(p1,p2)} computes the Sturm-Habicht sequence of \\spad{p1} and \\spad{p2}")) (|subresultantSequence| (((|List| (|UnivariatePolynomial| |#2| |#1|)) (|UnivariatePolynomial| |#2| |#1|) (|UnivariatePolynomial| |#2| |#1|)) "\\spad{subresultantSequence(p1,p2)} computes the (standard) subresultant sequence of \\spad{p1} and \\spad{p2}"))) NIL @@ -4468,7 +4468,7 @@ NIL ((|constructor| (NIL "This domain represents a signature AST. A signature AST \\indented{2}{is a description of an exported operation,{} \\spadignore{e.g.} its name,{} result} \\indented{2}{type,{} and the list of its argument types.}")) (|signature| (((|Signature|) $) "\\spad{signature(s)} returns AST of the declared signature for \\spad{`s'}.")) (|name| (((|Identifier|) $) "\\spad{name(s)} returns the name of the signature \\spad{`s'}.")) (|signatureAst| (($ (|Identifier|) (|Signature|)) "\\spad{signatureAst(n,s,t)} builds the signature AST \\spad{n:} \\spad{s} \\spad{->} \\spad{t}"))) NIL NIL -(-1135 R -1966) +(-1135 R -1955) ((|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 @@ -4507,16 +4507,16 @@ NIL (-1144 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."))) (((-4464 "*") |has| |#1| (-174)) (-4455 |has| |#1| (-568)) (-4460 |has| |#1| (-6 -4460)) (-4457 . T) (-4456 . T) (-4459 . T)) -((|HasCategory| |#1| (QUOTE (-926))) (-2781 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-464))) (|HasCategory| |#1| (QUOTE (-568))) (|HasCategory| |#1| (QUOTE (-926)))) (-2781 (|HasCategory| |#1| (QUOTE (-464))) (|HasCategory| |#1| (QUOTE (-568))) (|HasCategory| |#1| (QUOTE (-926)))) (-2781 (|HasCategory| |#1| (QUOTE (-464))) (|HasCategory| |#1| (QUOTE (-926)))) (|HasCategory| |#1| (QUOTE (-568))) (|HasCategory| |#1| (QUOTE (-174))) (-2781 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-568)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -899) (QUOTE (-390)))) (|HasCategory| |#2| (LIST (QUOTE -899) (QUOTE (-390))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -899) (QUOTE (-576)))) (|HasCategory| |#2| (LIST (QUOTE -899) (QUOTE (-576))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -626) (LIST (QUOTE -905) (QUOTE (-390))))) (|HasCategory| |#2| (LIST (QUOTE -626) (LIST (QUOTE -905) (QUOTE (-390)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -626) (LIST (QUOTE -905) (QUOTE (-576))))) (|HasCategory| |#2| (LIST (QUOTE -626) (LIST (QUOTE -905) (QUOTE (-576)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -626) (QUOTE (-548)))) (|HasCategory| |#2| (LIST (QUOTE -626) (QUOTE (-548))))) (|HasCategory| |#1| (LIST (QUOTE -651) (QUOTE (-576)))) (|HasCategory| |#1| (QUOTE (-148))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -419) (QUOTE (-576))))) (|HasCategory| |#1| (LIST (QUOTE -1057) (QUOTE (-576)))) (-2781 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -419) (QUOTE (-576))))) (|HasCategory| |#1| (LIST (QUOTE -1057) (LIST (QUOTE -419) (QUOTE (-576)))))) (|HasCategory| |#1| (LIST (QUOTE -1057) (LIST (QUOTE -419) (QUOTE (-576))))) (|HasCategory| |#1| (QUOTE (-374))) (|HasAttribute| |#1| (QUOTE -4460)) (|HasCategory| |#1| (QUOTE (-464))) (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-926)))) (-2781 (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-926)))) (|HasCategory| |#1| (QUOTE (-146))))) +((|HasCategory| |#1| (QUOTE (-926))) (-2755 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-464))) (|HasCategory| |#1| (QUOTE (-568))) (|HasCategory| |#1| (QUOTE (-926)))) (-2755 (|HasCategory| |#1| (QUOTE (-464))) (|HasCategory| |#1| (QUOTE (-568))) (|HasCategory| |#1| (QUOTE (-926)))) (-2755 (|HasCategory| |#1| (QUOTE (-464))) (|HasCategory| |#1| (QUOTE (-926)))) (|HasCategory| |#1| (QUOTE (-568))) (|HasCategory| |#1| (QUOTE (-174))) (-2755 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-568)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -899) (QUOTE (-390)))) (|HasCategory| |#2| (LIST (QUOTE -899) (QUOTE (-390))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -899) (QUOTE (-576)))) (|HasCategory| |#2| (LIST (QUOTE -899) (QUOTE (-576))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -626) (LIST (QUOTE -905) (QUOTE (-390))))) (|HasCategory| |#2| (LIST (QUOTE -626) (LIST (QUOTE -905) (QUOTE (-390)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -626) (LIST (QUOTE -905) (QUOTE (-576))))) (|HasCategory| |#2| (LIST (QUOTE -626) (LIST (QUOTE -905) (QUOTE (-576)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -626) (QUOTE (-548)))) (|HasCategory| |#2| (LIST (QUOTE -626) (QUOTE (-548))))) (|HasCategory| |#1| (LIST (QUOTE -651) (QUOTE (-576)))) (|HasCategory| |#1| (QUOTE (-148))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -419) (QUOTE (-576))))) (|HasCategory| |#1| (LIST (QUOTE -1057) (QUOTE (-576)))) (-2755 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -419) (QUOTE (-576))))) (|HasCategory| |#1| (LIST (QUOTE -1057) (LIST (QUOTE -419) (QUOTE (-576)))))) (|HasCategory| |#1| (LIST (QUOTE -1057) (LIST (QUOTE -419) (QUOTE (-576))))) (|HasCategory| |#1| (QUOTE (-374))) (|HasAttribute| |#1| (QUOTE -4460)) (|HasCategory| |#1| (QUOTE (-464))) (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-926)))) (-2755 (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-926)))) (|HasCategory| |#1| (QUOTE (-146))))) (-1145 |Coef| |Var| SMP) ((|constructor| (NIL "This domain provides multivariate Taylor series with variables from an arbitrary ordered set. A Taylor series is represented by a stream of polynomials from the polynomial domain \\spad{SMP}. The \\spad{n}th element of the stream is a form of degree \\spad{n}. SMTS is an internal domain.")) (|fintegrate| (($ (|Mapping| $) |#2| |#1|) "\\spad{fintegrate(f,v,c)} is the integral of \\spad{f()} with respect \\indented{1}{to \\spad{v} and having \\spad{c} as the constant of integration.} \\indented{1}{The evaluation of \\spad{f()} is delayed.}")) (|integrate| (($ $ |#2| |#1|) "\\spad{integrate(s,v,c)} is the integral of \\spad{s} with respect \\indented{1}{to \\spad{v} and having \\spad{c} as the constant of integration.}")) (|csubst| (((|Mapping| (|Stream| |#3|) |#3|) (|List| |#2|) (|List| (|Stream| |#3|))) "\\spad{csubst(a,b)} is for internal use only")) (* (($ |#3| $) "\\spad{smp*ts} multiplies a TaylorSeries by a monomial \\spad{SMP}.")) (|coerce| (($ |#3|) "\\spad{coerce(poly)} regroups the terms by total degree and forms a series.") (($ |#2|) "\\spad{coerce(var)} converts a variable to a Taylor series")) (|coefficient| ((|#3| $ (|NonNegativeInteger|)) "\\spad{coefficient(s, n)} gives the terms of total degree \\spad{n}."))) (((-4464 "*") |has| |#1| (-174)) (-4455 |has| |#1| (-568)) (-4457 . T) (-4456 . T) (-4459 . T)) -((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -419) (QUOTE (-576))))) (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-148))) (|HasCategory| |#1| (QUOTE (-146))) (-2781 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-568)))) (|HasCategory| |#1| (QUOTE (-568))) (|HasCategory| |#1| (QUOTE (-374)))) +((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -419) (QUOTE (-576))))) (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-148))) (|HasCategory| |#1| (QUOTE (-146))) (-2755 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-568)))) (|HasCategory| |#1| (QUOTE (-568))) (|HasCategory| |#1| (QUOTE (-374)))) (-1146 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}"))) ((-4463 . T) (-4462 . T)) NIL -(-1147 UP -1966) +(-1147 UP -1955) ((|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 @@ -4571,11 +4571,11 @@ NIL (-1160 V C) ((|constructor| (NIL "This domain exports a modest implementation of splitting trees. Spliiting trees are needed when the evaluation of some quantity under some hypothesis requires to split the hypothesis into sub-cases. For instance by adding some new hypothesis on one hand and its negation on another hand. The computations are terminated is a splitting tree \\axiom{a} when \\axiom{status(value(a))} is \\axiom{\\spad{true}}. Thus,{} if for the splitting tree \\axiom{a} the flag \\axiom{status(value(a))} is \\axiom{\\spad{true}},{} then \\axiom{status(value(\\spad{d}))} is \\axiom{\\spad{true}} for any subtree \\axiom{\\spad{d}} of \\axiom{a}. This property of splitting trees is called the termination condition. If no vertex in a splitting tree \\axiom{a} is equal to another,{} \\axiom{a} is said to satisfy the no-duplicates condition. The splitting tree \\axiom{a} will satisfy this condition if nodes are added to \\axiom{a} by mean of \\axiom{splitNodeOf!} and if \\axiom{construct} is only used to create the root of \\axiom{a} with no children.")) (|splitNodeOf!| (($ $ $ (|List| (|SplittingNode| |#1| |#2|)) (|Mapping| (|Boolean|) |#2| |#2|)) "\\axiom{splitNodeOf!(\\spad{l},{}a,{}\\spad{ls},{}sub?)} returns \\axiom{a} where the children list of \\axiom{\\spad{l}} has been set to \\axiom{[[\\spad{s}]\\$\\% for \\spad{s} in \\spad{ls} | not subNodeOf?(\\spad{s},{}a,{}sub?)]}. Thus,{} if \\axiom{\\spad{l}} is not a node of \\axiom{a},{} this latter splitting tree is unchanged.") (($ $ $ (|List| (|SplittingNode| |#1| |#2|))) "\\axiom{splitNodeOf!(\\spad{l},{}a,{}\\spad{ls})} returns \\axiom{a} where the children list of \\axiom{\\spad{l}} has been set to \\axiom{[[\\spad{s}]\\$\\% for \\spad{s} in \\spad{ls} | not nodeOf?(\\spad{s},{}a)]}. Thus,{} if \\axiom{\\spad{l}} is not a node of \\axiom{a},{} this latter splitting tree is unchanged.")) (|remove!| (($ (|SplittingNode| |#1| |#2|) $) "\\axiom{remove!(\\spad{s},{}a)} replaces a by remove(\\spad{s},{}a)")) (|remove| (($ (|SplittingNode| |#1| |#2|) $) "\\axiom{remove(\\spad{s},{}a)} returns the splitting tree obtained from a by removing every sub-tree \\axiom{\\spad{b}} such that \\axiom{value(\\spad{b})} and \\axiom{\\spad{s}} have the same value,{} condition and status.")) (|subNodeOf?| (((|Boolean|) (|SplittingNode| |#1| |#2|) $ (|Mapping| (|Boolean|) |#2| |#2|)) "\\axiom{subNodeOf?(\\spad{s},{}a,{}sub?)} returns \\spad{true} iff for some node \\axiom{\\spad{n}} in \\axiom{a} we have \\axiom{\\spad{s} = \\spad{n}} or \\axiom{status(\\spad{n})} and \\axiom{subNode?(\\spad{s},{}\\spad{n},{}sub?)}.")) (|nodeOf?| (((|Boolean|) (|SplittingNode| |#1| |#2|) $) "\\axiom{nodeOf?(\\spad{s},{}a)} returns \\spad{true} iff some node of \\axiom{a} is equal to \\axiom{\\spad{s}}")) (|result| (((|List| (|Record| (|:| |val| |#1|) (|:| |tower| |#2|))) $) "\\axiom{result(a)} where \\axiom{\\spad{ls}} is the leaves list of \\axiom{a} returns \\axiom{[[value(\\spad{s}),{}condition(\\spad{s})]\\$\\spad{VT} for \\spad{s} in \\spad{ls}]} if the computations are terminated in \\axiom{a} else an error is produced.")) (|conditions| (((|List| |#2|) $) "\\axiom{conditions(a)} returns the list of the conditions of the leaves of a")) (|construct| (($ |#1| |#2| |#1| (|List| |#2|)) "\\axiom{construct(\\spad{v1},{}\\spad{t},{}\\spad{v2},{}\\spad{lt})} creates a splitting tree with value (\\spadignore{i.e.} root vertex) given by \\axiom{[\\spad{v},{}\\spad{t}]\\$\\spad{S}} and with children list given by \\axiom{[[[\\spad{v},{}\\spad{t}]\\$\\spad{S}]\\$\\% for \\spad{s} in \\spad{ls}]}.") (($ |#1| |#2| (|List| (|SplittingNode| |#1| |#2|))) "\\axiom{construct(\\spad{v},{}\\spad{t},{}\\spad{ls})} creates a splitting tree with value (\\spadignore{i.e.} root vertex) given by \\axiom{[\\spad{v},{}\\spad{t}]\\$\\spad{S}} and with children list given by \\axiom{[[\\spad{s}]\\$\\% for \\spad{s} in \\spad{ls}]}.") (($ |#1| |#2| (|List| $)) "\\axiom{construct(\\spad{v},{}\\spad{t},{}la)} creates a splitting tree with value (\\spadignore{i.e.} root vertex) given by \\axiom{[\\spad{v},{}\\spad{t}]\\$\\spad{S}} and with \\axiom{la} as children list.") (($ (|SplittingNode| |#1| |#2|)) "\\axiom{construct(\\spad{s})} creates a splitting tree with value (\\spadignore{i.e.} root vertex) given by \\axiom{\\spad{s}} and no children. Thus,{} if the status of \\axiom{\\spad{s}} is \\spad{false},{} \\axiom{[\\spad{s}]} represents the starting point of the evaluation \\axiom{value(\\spad{s})} under the hypothesis \\axiom{condition(\\spad{s})}.")) (|updateStatus!| (($ $) "\\axiom{updateStatus!(a)} returns a where the status of the vertices are updated to satisfy the \"termination condition\".")) (|extractSplittingLeaf| (((|Union| $ "failed") $) "\\axiom{extractSplittingLeaf(a)} returns the left most leaf (as a tree) whose status is \\spad{false} if any,{} else \"failed\" is returned."))) ((-4462 . T) (-4463 . T)) -((-12 (|HasCategory| (-1159 |#1| |#2|) (LIST (QUOTE -319) (LIST (QUOTE -1159) (|devaluate| |#1|) (|devaluate| |#2|)))) (|HasCategory| (-1159 |#1| |#2|) (QUOTE (-1119)))) (|HasCategory| (-1159 |#1| |#2|) (QUOTE (-1119))) (-2781 (|HasCategory| (-1159 |#1| |#2|) (QUOTE (-102))) (|HasCategory| (-1159 |#1| |#2|) (QUOTE (-1119)))) (-2781 (|HasCategory| (-1159 |#1| |#2|) (LIST (QUOTE -625) (QUOTE (-874)))) (-12 (|HasCategory| (-1159 |#1| |#2|) (LIST (QUOTE -319) (LIST (QUOTE -1159) (|devaluate| |#1|) (|devaluate| |#2|)))) (|HasCategory| (-1159 |#1| |#2|) (QUOTE (-1119))))) (|HasCategory| (-1159 |#1| |#2|) (LIST (QUOTE -625) (QUOTE (-874)))) (|HasCategory| (-1159 |#1| |#2|) (QUOTE (-102)))) +((-12 (|HasCategory| (-1159 |#1| |#2|) (LIST (QUOTE -319) (LIST (QUOTE -1159) (|devaluate| |#1|) (|devaluate| |#2|)))) (|HasCategory| (-1159 |#1| |#2|) (QUOTE (-1119)))) (|HasCategory| (-1159 |#1| |#2|) (QUOTE (-1119))) (-2755 (|HasCategory| (-1159 |#1| |#2|) (QUOTE (-102))) (|HasCategory| (-1159 |#1| |#2|) (QUOTE (-1119)))) (-2755 (|HasCategory| (-1159 |#1| |#2|) (LIST (QUOTE -625) (QUOTE (-874)))) (-12 (|HasCategory| (-1159 |#1| |#2|) (LIST (QUOTE -319) (LIST (QUOTE -1159) (|devaluate| |#1|) (|devaluate| |#2|)))) (|HasCategory| (-1159 |#1| |#2|) (QUOTE (-1119))))) (|HasCategory| (-1159 |#1| |#2|) (LIST (QUOTE -625) (QUOTE (-874)))) (|HasCategory| (-1159 |#1| |#2|) (QUOTE (-102)))) (-1161 |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}."))) ((-4459 . T) (-4451 |has| |#2| (-6 (-4464 "*"))) (-4462 . T) (-4456 . T) (-4457 . T)) -((|HasCategory| |#2| (LIST (QUOTE -915) (QUOTE (-1195)))) (|HasCategory| |#2| (LIST (QUOTE -917) (QUOTE (-1195)))) (|HasCategory| |#2| (QUOTE (-238))) (|HasCategory| |#2| (QUOTE (-237))) (|HasAttribute| |#2| (QUOTE (-4464 "*"))) (|HasCategory| |#2| (LIST (QUOTE -651) (QUOTE (-576)))) (|HasCategory| |#2| (LIST (QUOTE -1057) (LIST (QUOTE -419) (QUOTE (-576))))) (|HasCategory| |#2| (LIST (QUOTE -1057) (QUOTE (-576)))) (-2781 (-12 (|HasCategory| |#2| (QUOTE (-238))) (|HasCategory| |#2| (LIST (QUOTE -319) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-1119))) (|HasCategory| |#2| (LIST (QUOTE -319) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (LIST (QUOTE -319) (|devaluate| |#2|))) (|HasCategory| |#2| (LIST (QUOTE -651) (QUOTE (-576))))) (-12 (|HasCategory| |#2| (LIST (QUOTE -319) (|devaluate| |#2|))) (|HasCategory| |#2| (LIST (QUOTE -915) (QUOTE (-1195)))))) (|HasCategory| |#2| (LIST (QUOTE -626) (QUOTE (-548)))) (|HasCategory| |#2| (QUOTE (-317))) (|HasCategory| |#2| (QUOTE (-568))) (|HasCategory| |#2| (QUOTE (-1119))) (|HasCategory| |#2| (QUOTE (-374))) (-2781 (|HasAttribute| |#2| (QUOTE (-4464 "*"))) (|HasCategory| |#2| (LIST (QUOTE -915) (QUOTE (-1195)))) (|HasCategory| |#2| (QUOTE (-238)))) (|HasCategory| |#2| (LIST (QUOTE -625) (QUOTE (-874)))) (|HasCategory| |#2| (QUOTE (-102))) (-12 (|HasCategory| |#2| (QUOTE (-1119))) (|HasCategory| |#2| (LIST (QUOTE -319) (|devaluate| |#2|)))) (|HasCategory| |#2| (QUOTE (-174)))) +((|HasCategory| |#2| (LIST (QUOTE -915) (QUOTE (-1195)))) (|HasCategory| |#2| (LIST (QUOTE -917) (QUOTE (-1195)))) (|HasCategory| |#2| (QUOTE (-238))) (|HasCategory| |#2| (QUOTE (-237))) (|HasAttribute| |#2| (QUOTE (-4464 "*"))) (|HasCategory| |#2| (LIST (QUOTE -651) (QUOTE (-576)))) (|HasCategory| |#2| (LIST (QUOTE -1057) (LIST (QUOTE -419) (QUOTE (-576))))) (|HasCategory| |#2| (LIST (QUOTE -1057) (QUOTE (-576)))) (-2755 (-12 (|HasCategory| |#2| (QUOTE (-238))) (|HasCategory| |#2| (LIST (QUOTE -319) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-1119))) (|HasCategory| |#2| (LIST (QUOTE -319) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (LIST (QUOTE -319) (|devaluate| |#2|))) (|HasCategory| |#2| (LIST (QUOTE -651) (QUOTE (-576))))) (-12 (|HasCategory| |#2| (LIST (QUOTE -319) (|devaluate| |#2|))) (|HasCategory| |#2| (LIST (QUOTE -915) (QUOTE (-1195)))))) (|HasCategory| |#2| (LIST (QUOTE -626) (QUOTE (-548)))) (|HasCategory| |#2| (QUOTE (-317))) (|HasCategory| |#2| (QUOTE (-568))) (|HasCategory| |#2| (QUOTE (-1119))) (|HasCategory| |#2| (QUOTE (-374))) (-2755 (|HasAttribute| |#2| (QUOTE (-4464 "*"))) (|HasCategory| |#2| (LIST (QUOTE -915) (QUOTE (-1195)))) (|HasCategory| |#2| (QUOTE (-238)))) (|HasCategory| |#2| (LIST (QUOTE -625) (QUOTE (-874)))) (|HasCategory| |#2| (QUOTE (-102))) (-12 (|HasCategory| |#2| (QUOTE (-1119))) (|HasCategory| |#2| (LIST (QUOTE -319) (|devaluate| |#2|)))) (|HasCategory| |#2| (QUOTE (-174)))) (-1162 S) ((|constructor| (NIL "A string aggregate is a category for strings,{} that is,{} one dimensional arrays of characters.")) (|elt| (($ $ $) "\\spad{elt(s,t)} returns the concatenation of \\spad{s} and \\spad{t}. It is provided to allow juxtaposition of strings to work as concatenation. For example,{} \\axiom{\"smoo\" \"shed\"} returns \\axiom{\"smooshed\"}.")) (|rightTrim| (($ $ (|CharacterClass|)) "\\spad{rightTrim(s,cc)} returns \\spad{s} with all trailing occurences of characters in \\spad{cc} deleted. For example,{} \\axiom{rightTrim(\"(abc)\",{} charClass \"()\")} returns \\axiom{\"(abc\"}.") (($ $ (|Character|)) "\\spad{rightTrim(s,c)} returns \\spad{s} with all trailing occurrences of \\spad{c} deleted. For example,{} \\axiom{rightTrim(\" abc \",{} char \" \")} returns \\axiom{\" abc\"}.")) (|leftTrim| (($ $ (|CharacterClass|)) "\\spad{leftTrim(s,cc)} returns \\spad{s} with all leading characters in \\spad{cc} deleted. For example,{} \\axiom{leftTrim(\"(abc)\",{} charClass \"()\")} returns \\axiom{\"abc)\"}.") (($ $ (|Character|)) "\\spad{leftTrim(s,c)} returns \\spad{s} with all leading characters \\spad{c} deleted. For example,{} \\axiom{leftTrim(\" abc \",{} char \" \")} returns \\axiom{\"abc \"}.")) (|trim| (($ $ (|CharacterClass|)) "\\spad{trim(s,cc)} returns \\spad{s} with all characters in \\spad{cc} deleted from right and left ends. For example,{} \\axiom{trim(\"(abc)\",{} charClass \"()\")} returns \\axiom{\"abc\"}.") (($ $ (|Character|)) "\\spad{trim(s,c)} returns \\spad{s} with all characters \\spad{c} deleted from right and left ends. For example,{} \\axiom{trim(\" abc \",{} char \" \")} returns \\axiom{\"abc\"}.")) (|split| (((|List| $) $ (|CharacterClass|)) "\\spad{split(s,cc)} returns a list of substrings delimited by characters in \\spad{cc}.") (((|List| $) $ (|Character|)) "\\spad{split(s,c)} returns a list of substrings delimited by character \\spad{c}.")) (|coerce| (($ (|Character|)) "\\spad{coerce(c)} returns \\spad{c} as a string \\spad{s} with the character \\spad{c}.")) (|position| (((|Integer|) (|CharacterClass|) $ (|Integer|)) "\\spad{position(cc,t,i)} returns the position \\axiom{\\spad{j} \\spad{>=} \\spad{i}} in \\spad{t} of the first character belonging to \\spad{cc}.") (((|Integer|) $ $ (|Integer|)) "\\spad{position(s,t,i)} returns the position \\spad{j} of the substring \\spad{s} in string \\spad{t},{} where \\axiom{\\spad{j} \\spad{>=} \\spad{i}} is required.")) (|replace| (($ $ (|UniversalSegment| (|Integer|)) $) "\\spad{replace(s,i..j,t)} replaces the substring \\axiom{\\spad{s}(\\spad{i}..\\spad{j})} of \\spad{s} by string \\spad{t}.")) (|match?| (((|Boolean|) $ $ (|Character|)) "\\spad{match?(s,t,c)} tests if \\spad{s} matches \\spad{t} except perhaps for multiple and consecutive occurrences of character \\spad{c}. Typically \\spad{c} is the blank character.")) (|match| (((|NonNegativeInteger|) $ $ (|Character|)) "\\spad{match(p,s,wc)} tests if pattern \\axiom{\\spad{p}} matches subject \\axiom{\\spad{s}} where \\axiom{\\spad{wc}} is a wild card character. If no match occurs,{} the index \\axiom{0} is returned; otheriwse,{} the value returned is the first index of the first character in the subject matching the subject (excluding that matched by an initial wild-card). For example,{} \\axiom{match(\"*to*\",{}\"yorktown\",{}\\spad{\"*\"})} returns \\axiom{5} indicating a successful match starting at index \\axiom{5} of \\axiom{\"yorktown\"}.")) (|substring?| (((|Boolean|) $ $ (|Integer|)) "\\spad{substring?(s,t,i)} tests if \\spad{s} is a substring of \\spad{t} beginning at index \\spad{i}. Note: \\axiom{substring?(\\spad{s},{}\\spad{t},{}0) = prefix?(\\spad{s},{}\\spad{t})}.")) (|suffix?| (((|Boolean|) $ $) "\\spad{suffix?(s,t)} tests if the string \\spad{s} is the final substring of \\spad{t}. Note: \\axiom{suffix?(\\spad{s},{}\\spad{t}) \\spad{==} reduce(and,{}[\\spad{s}.\\spad{i} = \\spad{t}.(\\spad{n} - \\spad{m} + \\spad{i}) for \\spad{i} in 0..maxIndex \\spad{s}])} where \\spad{m} and \\spad{n} denote the maxIndex of \\spad{s} and \\spad{t} respectively.")) (|prefix?| (((|Boolean|) $ $) "\\spad{prefix?(s,t)} tests if the string \\spad{s} is the initial substring of \\spad{t}. Note: \\axiom{prefix?(\\spad{s},{}\\spad{t}) \\spad{==} reduce(and,{}[\\spad{s}.\\spad{i} = \\spad{t}.\\spad{i} for \\spad{i} in 0..maxIndex \\spad{s}])}.")) (|upperCase!| (($ $) "\\spad{upperCase!(s)} destructively replaces the alphabetic characters in \\spad{s} by upper case characters.")) (|upperCase| (($ $) "\\spad{upperCase(s)} returns the string with all characters in upper case.")) (|lowerCase!| (($ $) "\\spad{lowerCase!(s)} destructively replaces the alphabetic characters in \\spad{s} by lower case.")) (|lowerCase| (($ $) "\\spad{lowerCase(s)} returns the string with all characters in lower case."))) NIL @@ -4595,7 +4595,7 @@ NIL (-1166 S) ((|constructor| (NIL "Linked List implementation of a Stack")) (|stack| (($ (|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}."))) ((-4462 . T) (-4463 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1119))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1119))) (-2781 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-1119)))) (-2781 (-12 (|HasCategory| |#1| (QUOTE (-1119))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-874))))) (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-874)))) (|HasCategory| |#1| (QUOTE (-102)))) +((-12 (|HasCategory| |#1| (QUOTE (-1119))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1119))) (-2755 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-1119)))) (-2755 (-12 (|HasCategory| |#1| (QUOTE (-1119))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-874))))) (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-874)))) (|HasCategory| |#1| (QUOTE (-102)))) (-1167 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 @@ -4607,7 +4607,7 @@ NIL (-1169 |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."))) ((-4463 . T)) -((-12 (|HasCategory| (-2 (|:| -4300 |#1|) (|:| -4391 |#2|)) (QUOTE (-1119))) (|HasCategory| (-2 (|:| -4300 |#1|) (|:| -4391 |#2|)) (LIST (QUOTE -319) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -4300) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -4391) (|devaluate| |#2|)))))) (-2781 (|HasCategory| (-2 (|:| -4300 |#1|) (|:| -4391 |#2|)) (QUOTE (-1119))) (|HasCategory| |#2| (QUOTE (-1119)))) (-2781 (|HasCategory| (-2 (|:| -4300 |#1|) (|:| -4391 |#2|)) (QUOTE (-102))) (|HasCategory| (-2 (|:| -4300 |#1|) (|:| -4391 |#2|)) (QUOTE (-1119))) (|HasCategory| |#2| (QUOTE (-102))) (|HasCategory| |#2| (QUOTE (-1119)))) (-2781 (|HasCategory| (-2 (|:| -4300 |#1|) (|:| -4391 |#2|)) (QUOTE (-1119))) (|HasCategory| (-2 (|:| -4300 |#1|) (|:| -4391 |#2|)) (LIST (QUOTE -625) (QUOTE (-874)))) (|HasCategory| |#2| (QUOTE (-1119))) (|HasCategory| |#2| (LIST (QUOTE -625) (QUOTE (-874))))) (|HasCategory| (-2 (|:| -4300 |#1|) (|:| -4391 |#2|)) (LIST (QUOTE -626) (QUOTE (-548)))) (-12 (|HasCategory| |#2| (QUOTE (-1119))) (|HasCategory| |#2| (LIST (QUOTE -319) (|devaluate| |#2|)))) (|HasCategory| |#1| (QUOTE (-862))) (-2781 (|HasCategory| (-2 (|:| -4300 |#1|) (|:| -4391 |#2|)) (QUOTE (-102))) (|HasCategory| |#2| (QUOTE (-102)))) (-2781 (|HasCategory| (-2 (|:| -4300 |#1|) (|:| -4391 |#2|)) (LIST (QUOTE -625) (QUOTE (-874)))) (|HasCategory| |#2| (LIST (QUOTE -625) (QUOTE (-874))))) (|HasCategory| |#2| (QUOTE (-1119))) (|HasCategory| |#2| (QUOTE (-102))) (|HasCategory| |#2| (LIST (QUOTE -625) (QUOTE (-874)))) (|HasCategory| (-2 (|:| -4300 |#1|) (|:| -4391 |#2|)) (LIST (QUOTE -625) (QUOTE (-874)))) (|HasCategory| (-2 (|:| -4300 |#1|) (|:| -4391 |#2|)) (QUOTE (-102))) (|HasCategory| (-2 (|:| -4300 |#1|) (|:| -4391 |#2|)) (QUOTE (-1119)))) +((-12 (|HasCategory| (-2 (|:| -4298 |#1|) (|:| -4437 |#2|)) (QUOTE (-1119))) (|HasCategory| (-2 (|:| -4298 |#1|) (|:| -4437 |#2|)) (LIST (QUOTE -319) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -4298) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -4437) (|devaluate| |#2|)))))) (-2755 (|HasCategory| (-2 (|:| -4298 |#1|) (|:| -4437 |#2|)) (QUOTE (-1119))) (|HasCategory| |#2| (QUOTE (-1119)))) (-2755 (|HasCategory| (-2 (|:| -4298 |#1|) (|:| -4437 |#2|)) (QUOTE (-102))) (|HasCategory| (-2 (|:| -4298 |#1|) (|:| -4437 |#2|)) (QUOTE (-1119))) (|HasCategory| |#2| (QUOTE (-102))) (|HasCategory| |#2| (QUOTE (-1119)))) (-2755 (|HasCategory| (-2 (|:| -4298 |#1|) (|:| -4437 |#2|)) (QUOTE (-1119))) (|HasCategory| (-2 (|:| -4298 |#1|) (|:| -4437 |#2|)) (LIST (QUOTE -625) (QUOTE (-874)))) (|HasCategory| |#2| (QUOTE (-1119))) (|HasCategory| |#2| (LIST (QUOTE -625) (QUOTE (-874))))) (|HasCategory| (-2 (|:| -4298 |#1|) (|:| -4437 |#2|)) (LIST (QUOTE -626) (QUOTE (-548)))) (-12 (|HasCategory| |#2| (QUOTE (-1119))) (|HasCategory| |#2| (LIST (QUOTE -319) (|devaluate| |#2|)))) (|HasCategory| |#1| (QUOTE (-862))) (-2755 (|HasCategory| (-2 (|:| -4298 |#1|) (|:| -4437 |#2|)) (QUOTE (-102))) (|HasCategory| |#2| (QUOTE (-102)))) (-2755 (|HasCategory| (-2 (|:| -4298 |#1|) (|:| -4437 |#2|)) (LIST (QUOTE -625) (QUOTE (-874)))) (|HasCategory| |#2| (LIST (QUOTE -625) (QUOTE (-874))))) (|HasCategory| |#2| (QUOTE (-1119))) (|HasCategory| |#2| (QUOTE (-102))) (|HasCategory| |#2| (LIST (QUOTE -625) (QUOTE (-874)))) (|HasCategory| (-2 (|:| -4298 |#1|) (|:| -4437 |#2|)) (LIST (QUOTE -625) (QUOTE (-874)))) (|HasCategory| (-2 (|:| -4298 |#1|) (|:| -4437 |#2|)) (QUOTE (-102))) (|HasCategory| (-2 (|:| -4298 |#1|) (|:| -4437 |#2|)) (QUOTE (-1119)))) (-1170) ((|constructor| (NIL "This domain represents an arithmetic progression iterator syntax.")) (|step| (((|SpadAst|) $) "\\spad{step(i)} returns the Spad AST denoting the step of the arithmetic progression represented by the iterator \\spad{i}.")) (|upperBound| (((|Maybe| (|SpadAst|)) $) "If the set of values assumed by the iteration variable is bounded from above,{} \\spad{upperBound(i)} returns the upper bound. Otherwise,{} its returns \\spad{nothing}.")) (|lowerBound| (((|SpadAst|) $) "\\spad{lowerBound(i)} returns the lower bound on the values assumed by the iteration variable.")) (|iterationVar| (((|Identifier|) $) "\\spad{iterationVar(i)} returns the name of the iterating variable of the arithmetic progression iterator \\spad{i}."))) NIL @@ -4635,15 +4635,15 @@ NIL (-1176 S) ((|constructor| (NIL "A stream is an implementation of an infinite sequence using a list of terms that have been computed and a function closure to compute additional terms when needed.")) (|filterUntil| (($ (|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."))) ((-4463 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1119))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1119))) (-2781 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-1119)))) (-2781 (-12 (|HasCategory| |#1| (QUOTE (-1119))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-874))))) (|HasCategory| |#1| (LIST (QUOTE -626) (QUOTE (-548)))) (|HasCategory| (-576) (QUOTE (-862))) (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-874)))) (|HasCategory| |#1| (QUOTE (-102)))) +((-12 (|HasCategory| |#1| (QUOTE (-1119))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1119))) (-2755 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-1119)))) (-2755 (-12 (|HasCategory| |#1| (QUOTE (-1119))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-874))))) (|HasCategory| |#1| (LIST (QUOTE -626) (QUOTE (-548)))) (|HasCategory| (-576) (QUOTE (-862))) (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-874)))) (|HasCategory| |#1| (QUOTE (-102)))) (-1177) ((|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"))) ((-4463 . 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(|power| (((|Stream| |#1|) |#1| (|Stream| |#1|)) "\\spad{power(a,f)} returns the power series \\spad{f} raised to the power \\spad{a}.")) (|lazyGintegrate| (((|Stream| |#1|) (|Mapping| |#1| (|Integer|)) |#1| (|Mapping| (|Stream| |#1|))) "\\spad{lazyGintegrate(f,r,g)} is used for fixed point computations.")) (|mapdiv| (((|Stream| |#1|) (|Stream| |#1|) (|Stream| |#1|)) "\\spad{mapdiv([a0,a1,..],[b0,b1,..])} returns \\spad{[a0/b0,a1/b1,..]}.")) (|powern| (((|Stream| |#1|) (|Fraction| (|Integer|)) (|Stream| |#1|)) "\\spad{powern(r,f)} raises power series \\spad{f} to the power \\spad{r}.")) (|nlde| (((|Stream| |#1|) (|Stream| (|Stream| |#1|))) "\\spad{nlde(u)} solves a first order non-linear differential equation described by \\spad{u} of the form \\spad{[[b<0,0>,b<0,1>,...],[b<1,0>,b<1,1>,.],...]}. the differential equation has the form \\spad{y' = sum(i=0 to infinity,j=0 to infinity,b<i,j>*(x**i)*(y**j))}.")) (|lazyIntegrate| (((|Stream| |#1|) |#1| (|Mapping| (|Stream| |#1|))) "\\spad{lazyIntegrate(r,f)} is a local function used for fixed point computations.")) (|integrate| (((|Stream| |#1|) |#1| (|Stream| |#1|)) "\\spad{integrate(r,a)} returns the integral of the power series \\spad{a} with respect to the power series variableintegration where \\spad{r} denotes the constant of integration. Thus \\spad{integrate(a,[a0,a1,a2,...]) = [a,a0,a1/2,a2/3,...]}.")) (|invmultisect| (((|Stream| |#1|) (|Integer|) (|Integer|) (|Stream| |#1|)) "\\spad{invmultisect(a,b,st)} substitutes \\spad{x**((a+b)*n)} for \\spad{x**n} and multiplies by \\spad{x**b}.")) (|multisect| (((|Stream| |#1|) (|Integer|) (|Integer|) (|Stream| |#1|)) "\\spad{multisect(a,b,st)} selects the coefficients of \\spad{x**((a+b)*n+a)},{} and changes them to \\spad{x**n}.")) (|generalLambert| (((|Stream| |#1|) (|Stream| |#1|) (|Integer|) (|Integer|)) "\\spad{generalLambert(f(x),a,d)} returns \\spad{f(x**a) + f(x**(a + d)) + f(x**(a + 2 d)) + ...}. \\spad{f(x)} should have zero constant coefficient and \\spad{a} and \\spad{d} should be positive.")) (|evenlambert| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{evenlambert(st)} computes \\spad{f(x**2) + f(x**4) + f(x**6) + ...} if \\spad{st} is a stream representing \\spad{f(x)}. This function is used for computing infinite products. If \\spad{f(x)} is a power series with constant coefficient 1,{} then \\spad{prod(f(x**(2*n)),n=1..infinity) = exp(evenlambert(log(f(x))))}.")) (|oddlambert| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{oddlambert(st)} computes \\spad{f(x) + f(x**3) + f(x**5) + ...} if \\spad{st} is a stream representing \\spad{f(x)}. This function is used for computing infinite products. If \\spad{f}(\\spad{x}) is a power series with constant coefficient 1 then \\spad{prod(f(x**(2*n-1)),n=1..infinity) = exp(oddlambert(log(f(x))))}.")) (|lambert| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{lambert(st)} computes \\spad{f(x) + f(x**2) + f(x**3) + ...} if \\spad{st} is a stream representing \\spad{f(x)}. This function is used for computing infinite products. If \\spad{f(x)} is a power series with constant coefficient 1 then \\spad{prod(f(x**n),n = 1..infinity) = exp(lambert(log(f(x))))}.")) (|addiag| (((|Stream| |#1|) (|Stream| (|Stream| |#1|))) "\\spad{addiag(x)} performs diagonal addition of a stream of streams. if \\spad{x} = \\spad{[[a<0,0>,a<0,1>,..],[a<1,0>,a<1,1>,..],[a<2,0>,a<2,1>,..],..]} and \\spad{addiag(x) = [b<0,b<1>,...], then b<k> = sum(i+j=k,a<i,j>)}.")) (|revert| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{revert(a)} computes the inverse of a power series \\spad{a} with respect to composition. the series should have constant coefficient 0 and first order coefficient should be invertible.")) (|lagrange| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{lagrange(g)} produces the power series for \\spad{f} where \\spad{f} is implicitly defined as \\spad{f(z) = z*g(f(z))}.")) (|compose| (((|Stream| |#1|) (|Stream| |#1|) (|Stream| |#1|)) "\\spad{compose(a,b)} composes the power series \\spad{a} with the power series \\spad{b}.")) (|eval| (((|Stream| |#1|) (|Stream| |#1|) |#1|) "\\spad{eval(a,r)} returns a stream of partial sums of the power series \\spad{a} evaluated at the power series variable equal to \\spad{r}.")) (|coerce| (((|Stream| |#1|) |#1|) "\\spad{coerce(r)} converts a ring element \\spad{r} to a stream with one element.")) (|gderiv| (((|Stream| |#1|) (|Mapping| |#1| (|Integer|)) (|Stream| |#1|)) "\\spad{gderiv(f,[a0,a1,a2,..])} returns \\spad{[f(0)*a0,f(1)*a1,f(2)*a2,..]}.")) (|deriv| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{deriv(a)} returns the derivative of the power series with respect to the power series variable. Thus \\spad{deriv([a0,a1,a2,...])} returns \\spad{[a1,2 a2,3 a3,...]}.")) (|mapmult| (((|Stream| |#1|) (|Stream| |#1|) (|Stream| |#1|)) "\\spad{mapmult([a0,a1,..],[b0,b1,..])} returns \\spad{[a0*b0,a1*b1,..]}.")) (|int| (((|Stream| |#1|) |#1|) "\\spad{int(r)} returns [\\spad{r},{}\\spad{r+1},{}\\spad{r+2},{}...],{} where \\spad{r} is a ring element.")) (|oddintegers| (((|Stream| (|Integer|)) (|Integer|)) "\\spad{oddintegers(n)} returns \\spad{[n,n+2,n+4,...]}.")) (|integers| (((|Stream| (|Integer|)) (|Integer|)) "\\spad{integers(n)} returns \\spad{[n,n+1,n+2,...]}.")) (|monom| (((|Stream| |#1|) |#1| (|Integer|)) "\\spad{monom(deg,coef)} is a monomial of degree \\spad{deg} with coefficient \\spad{coef}.")) (|recip| (((|Union| (|Stream| |#1|) "failed") (|Stream| |#1|)) "\\spad{recip(a)} returns the power series reciprocal of \\spad{a},{} or \"failed\" if not possible.")) (/ (((|Stream| |#1|) (|Stream| |#1|) (|Stream| |#1|)) "\\spad{a / b} returns the power series quotient of \\spad{a} by \\spad{b}. An error message is returned if \\spad{b} is not invertible. This function is used in fixed point computations.")) (|exquo| (((|Union| (|Stream| |#1|) "failed") (|Stream| |#1|) (|Stream| |#1|)) "\\spad{exquo(a,b)} returns the power series quotient of \\spad{a} by \\spad{b},{} if the quotient exists,{} and \"failed\" otherwise")) (* (((|Stream| |#1|) (|Stream| |#1|) |#1|) "\\spad{a * r} returns the power series scalar multiplication of \\spad{a} by \\spad{r:} \\spad{[a0,a1,...] * r = [a0 * r,a1 * r,...]}") (((|Stream| |#1|) |#1| (|Stream| |#1|)) "\\spad{r * a} returns the power series scalar multiplication of \\spad{r} by \\spad{a}: \\spad{r * [a0,a1,...] = [r * a0,r * a1,...]}") (((|Stream| |#1|) (|Stream| |#1|) (|Stream| |#1|)) "\\spad{a * b} returns the power series (Cauchy) product of \\spad{a} and \\spad{b:} \\spad{[a0,a1,...] * [b0,b1,...] = [c0,c1,...]} where \\spad{ck = sum(i + j = k,ai * bk)}.")) (- (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{- a} returns the power series negative of \\spad{a}: \\spad{- [a0,a1,...] = [- a0,- a1,...]}") (((|Stream| |#1|) (|Stream| |#1|) (|Stream| |#1|)) "\\spad{a - b} returns the power series difference of \\spad{a} and \\spad{b}: \\spad{[a0,a1,..] - [b0,b1,..] = [a0 - b0,a1 - b1,..]}")) (+ (((|Stream| |#1|) (|Stream| |#1|) (|Stream| |#1|)) "\\spad{a + b} returns the power series sum of \\spad{a} and \\spad{b}: \\spad{[a0,a1,..] + [b0,b1,..] = [a0 + b0,a1 + b1,..]}"))) NIL @@ -4674,9 +4674,9 @@ NIL NIL (-1186 |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}(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 @@ -4695,15 +4695,15 @@ NIL (-1191 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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\\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."))) (((-4464 "*") |has| |#1| (-174)) (-4455 |has| |#1| (-568)) (-4460 |has| |#1| (-374)) (-4454 |has| |#1| (-374)) (-4456 . T) (-4457 . T) (-4459 . T)) -((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -419) (QUOTE (-576))))) (|HasCategory| |#1| (QUOTE (-568))) (|HasCategory| |#1| (QUOTE (-174))) (-2781 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-568)))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-148))) (-12 (|HasCategory| |#1| (LIST (QUOTE -915) (QUOTE (-1195)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -419) (QUOTE (-576))) (|devaluate| |#1|))))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -419) (QUOTE (-576))) (|devaluate| |#1|)))) (|HasCategory| (-419 (-576)) (QUOTE (-1131))) (|HasCategory| |#1| (QUOTE (-374))) (-2781 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-374))) (|HasCategory| |#1| (QUOTE (-568)))) (-2781 (|HasCategory| |#1| (QUOTE (-374))) (|HasCategory| |#1| (QUOTE (-568)))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -419) (QUOTE (-576)))))) (|HasSignature| |#1| (LIST (QUOTE -3581) (LIST (|devaluate| |#1|) (QUOTE (-1195)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -419) (QUOTE (-576)))))) (-2781 (-12 (|HasCategory| |#1| (LIST (QUOTE -29) (QUOTE (-576)))) (|HasCategory| |#1| (QUOTE (-976))) (|HasCategory| |#1| (QUOTE (-1221))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -419) (QUOTE (-576)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -419) (QUOTE (-576))))) (|HasSignature| |#1| (LIST (QUOTE -4121) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1195))))) (|HasSignature| |#1| (LIST (QUOTE -1934) (LIST (LIST (QUOTE -656) (QUOTE (-1195))) (|devaluate| |#1|))))))) +((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -419) (QUOTE (-576))))) (|HasCategory| |#1| (QUOTE (-568))) (|HasCategory| |#1| (QUOTE (-174))) (-2755 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-568)))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-148))) (-12 (|HasCategory| |#1| (LIST (QUOTE -915) (QUOTE (-1195)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -419) (QUOTE (-576))) (|devaluate| |#1|))))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -419) (QUOTE (-576))) (|devaluate| |#1|)))) (|HasCategory| (-419 (-576)) (QUOTE (-1131))) (|HasCategory| |#1| (QUOTE (-374))) (-2755 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-374))) (|HasCategory| |#1| (QUOTE (-568)))) (-2755 (|HasCategory| |#1| (QUOTE (-374))) (|HasCategory| |#1| (QUOTE (-568)))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -419) (QUOTE (-576)))))) (|HasSignature| |#1| (LIST (QUOTE -3567) (LIST (|devaluate| |#1|) (QUOTE (-1195)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -419) (QUOTE (-576)))))) (-2755 (-12 (|HasCategory| |#1| (LIST (QUOTE -29) (QUOTE (-576)))) (|HasCategory| |#1| (QUOTE (-976))) (|HasCategory| |#1| (QUOTE (-1221))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -419) (QUOTE (-576)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -419) (QUOTE (-576))))) (|HasSignature| |#1| (LIST (QUOTE -1589) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1195))))) (|HasSignature| |#1| (LIST (QUOTE -1962) (LIST (LIST (QUOTE -656) (QUOTE (-1195))) (|devaluate| |#1|))))))) (-1193 |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}."))) (((-4464 "*") |has| |#1| (-174)) (-4455 |has| |#1| (-568)) (-4456 . T) (-4457 . T) (-4459 . 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(NOT (($ $) "\\spad{NOT(x)} returns the \\axiomType{Switch} expression representing \\spad{\\~~x}.") (($ (|Union| (|:| I (|Expression| (|Integer|))) (|:| F (|Expression| (|Float|))) (|:| CF (|Expression| (|Complex| (|Float|)))) (|:| |switch| $))) "\\spad{NOT(x)} returns the \\axiomType{Switch} expression representing \\spad{\\~~x}.")) (AND (($ (|Union| (|:| I (|Expression| (|Integer|))) (|:| F (|Expression| (|Float|))) (|:| CF (|Expression| (|Complex| (|Float|)))) (|:| |switch| $)) (|Union| (|:| I (|Expression| (|Integer|))) (|:| F (|Expression| (|Float|))) (|:| CF (|Expression| (|Complex| (|Float|)))) (|:| |switch| $))) "\\spad{AND(x,y)} returns the \\axiomType{Switch} expression representing \\spad{x and y}.")) (EQ (($ (|Union| (|:| I (|Expression| (|Integer|))) (|:| F (|Expression| (|Float|))) (|:| CF (|Expression| (|Complex| (|Float|)))) (|:| |switch| $)) (|Union| (|:| I (|Expression| (|Integer|))) (|:| F (|Expression| (|Float|))) (|:| CF (|Expression| (|Complex| (|Float|)))) (|:| |switch| $))) "\\spad{EQ(x,y)} returns the \\axiomType{Switch} expression representing \\spad{x = y}.")) (OR (($ (|Union| (|:| I (|Expression| (|Integer|))) (|:| F (|Expression| (|Float|))) (|:| CF (|Expression| (|Complex| (|Float|)))) (|:| |switch| $)) (|Union| (|:| I (|Expression| (|Integer|))) (|:| F (|Expression| (|Float|))) (|:| CF (|Expression| (|Complex| (|Float|)))) (|:| |switch| $))) "\\spad{OR(x,y)} returns the \\axiomType{Switch} expression representing \\spad{x or y}.")) (GE (($ (|Union| (|:| I (|Expression| (|Integer|))) (|:| F (|Expression| (|Float|))) (|:| CF (|Expression| (|Complex| (|Float|)))) (|:| |switch| $)) (|Union| (|:| I (|Expression| (|Integer|))) (|:| F (|Expression| (|Float|))) (|:| CF (|Expression| (|Complex| (|Float|)))) (|:| |switch| $))) "\\spad{GE(x,y)} returns the \\axiomType{Switch} expression representing \\spad{x>=y}.")) (LE (($ (|Union| (|:| I (|Expression| (|Integer|))) (|:| F (|Expression| (|Float|))) (|:| CF (|Expression| (|Complex| (|Float|)))) (|:| |switch| $)) (|Union| (|:| I (|Expression| (|Integer|))) (|:| F (|Expression| (|Float|))) (|:| CF (|Expression| (|Complex| (|Float|)))) (|:| |switch| $))) "\\spad{LE(x,y)} returns the \\axiomType{Switch} expression representing \\spad{x<=y}.")) (GT (($ (|Union| (|:| I (|Expression| (|Integer|))) (|:| F (|Expression| (|Float|))) (|:| CF (|Expression| (|Complex| (|Float|)))) (|:| |switch| $)) (|Union| (|:| I (|Expression| (|Integer|))) (|:| F (|Expression| (|Float|))) (|:| CF (|Expression| (|Complex| (|Float|)))) (|:| |switch| $))) "\\spad{GT(x,y)} returns the \\axiomType{Switch} expression representing \\spad{x>y}.")) (LT (($ (|Union| (|:| I (|Expression| (|Integer|))) (|:| F (|Expression| (|Float|))) (|:| CF (|Expression| (|Complex| (|Float|)))) (|:| |switch| $)) (|Union| (|:| I (|Expression| (|Integer|))) (|:| F (|Expression| (|Float|))) (|:| CF (|Expression| (|Complex| (|Float|)))) (|:| |switch| $))) "\\spad{LT(x,y)} returns the \\axiomType{Switch} expression representing \\spad{x<y}.")) (|coerce| (($ (|Symbol|)) "\\spad{coerce(s)} \\undocumented{}"))) NIL @@ -4719,7 +4719,7 @@ NIL (-1197 R) ((|constructor| (NIL "This domain implements symmetric polynomial"))) (((-4464 "*") |has| |#1| (-174)) (-4455 |has| |#1| (-568)) (-4460 |has| |#1| (-6 -4460)) (-4456 . T) (-4457 . T) (-4459 . T)) -((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -419) (QUOTE (-576))))) (|HasCategory| |#1| (QUOTE (-568))) (-2781 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-568)))) (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-148))) (-2781 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -419) (QUOTE (-576))))) (|HasCategory| |#1| (LIST (QUOTE -1057) (LIST (QUOTE -419) (QUOTE (-576)))))) (|HasCategory| |#1| (LIST (QUOTE -1057) (LIST (QUOTE -419) (QUOTE (-576))))) (|HasCategory| |#1| (LIST (QUOTE -1057) (QUOTE (-576)))) (|HasCategory| |#1| (QUOTE (-374))) (|HasCategory| |#1| (QUOTE (-464))) (-12 (|HasCategory| (-990) (QUOTE (-132))) (|HasCategory| |#1| (QUOTE (-568)))) (|HasAttribute| |#1| (QUOTE -4460))) +((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -419) (QUOTE (-576))))) (|HasCategory| |#1| (QUOTE (-568))) (-2755 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-568)))) (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-148))) (-2755 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -419) (QUOTE (-576))))) (|HasCategory| |#1| (LIST (QUOTE -1057) (LIST (QUOTE -419) (QUOTE (-576)))))) (|HasCategory| |#1| (LIST (QUOTE -1057) (LIST (QUOTE -419) (QUOTE (-576))))) (|HasCategory| |#1| (LIST (QUOTE -1057) (QUOTE (-576)))) (|HasCategory| |#1| (QUOTE (-374))) (|HasCategory| |#1| (QUOTE (-464))) (-12 (|HasCategory| (-990) (QUOTE (-132))) (|HasCategory| |#1| (QUOTE (-568)))) (|HasAttribute| |#1| (QUOTE -4460))) (-1198) ((|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 @@ -4763,7 +4763,7 @@ NIL (-1208 |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}"))) ((-4462 . T) (-4463 . T)) -((-12 (|HasCategory| (-2 (|:| -4300 |#1|) (|:| -4391 |#2|)) (QUOTE (-1119))) (|HasCategory| (-2 (|:| -4300 |#1|) (|:| -4391 |#2|)) (LIST (QUOTE -319) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -4300) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -4391) (|devaluate| |#2|)))))) (-2781 (|HasCategory| (-2 (|:| -4300 |#1|) (|:| -4391 |#2|)) (QUOTE (-1119))) (|HasCategory| |#2| (QUOTE (-1119)))) (-2781 (|HasCategory| (-2 (|:| -4300 |#1|) (|:| -4391 |#2|)) (QUOTE (-102))) (|HasCategory| (-2 (|:| -4300 |#1|) (|:| -4391 |#2|)) (QUOTE (-1119))) (|HasCategory| |#2| (QUOTE (-102))) (|HasCategory| |#2| (QUOTE (-1119)))) (-2781 (|HasCategory| (-2 (|:| -4300 |#1|) (|:| -4391 |#2|)) (QUOTE (-1119))) (|HasCategory| (-2 (|:| -4300 |#1|) (|:| -4391 |#2|)) (LIST (QUOTE -625) (QUOTE (-874)))) (|HasCategory| |#2| (QUOTE (-1119))) (|HasCategory| |#2| (LIST (QUOTE -625) (QUOTE (-874))))) (|HasCategory| (-2 (|:| -4300 |#1|) (|:| -4391 |#2|)) (LIST (QUOTE -626) (QUOTE (-548)))) (-12 (|HasCategory| |#2| (QUOTE (-1119))) (|HasCategory| |#2| (LIST (QUOTE -319) (|devaluate| |#2|)))) (|HasCategory| (-2 (|:| -4300 |#1|) (|:| -4391 |#2|)) (QUOTE (-1119))) (|HasCategory| |#1| (QUOTE (-862))) (|HasCategory| |#2| (QUOTE (-1119))) (-2781 (|HasCategory| (-2 (|:| -4300 |#1|) (|:| -4391 |#2|)) (LIST (QUOTE -625) (QUOTE (-874)))) (|HasCategory| |#2| (LIST (QUOTE -625) (QUOTE (-874))))) (-2781 (|HasCategory| (-2 (|:| -4300 |#1|) (|:| -4391 |#2|)) (QUOTE (-102))) (|HasCategory| |#2| (QUOTE (-102)))) (|HasCategory| |#2| (QUOTE (-102))) (|HasCategory| |#2| (LIST (QUOTE -625) (QUOTE (-874)))) (|HasCategory| (-2 (|:| -4300 |#1|) (|:| -4391 |#2|)) (LIST (QUOTE -625) (QUOTE (-874)))) (|HasCategory| (-2 (|:| -4300 |#1|) (|:| -4391 |#2|)) (QUOTE (-102)))) +((-12 (|HasCategory| (-2 (|:| -4298 |#1|) (|:| -4437 |#2|)) (QUOTE (-1119))) (|HasCategory| (-2 (|:| -4298 |#1|) (|:| -4437 |#2|)) (LIST (QUOTE -319) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -4298) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -4437) (|devaluate| |#2|)))))) (-2755 (|HasCategory| (-2 (|:| -4298 |#1|) (|:| -4437 |#2|)) (QUOTE (-1119))) (|HasCategory| |#2| (QUOTE (-1119)))) (-2755 (|HasCategory| (-2 (|:| -4298 |#1|) (|:| -4437 |#2|)) (QUOTE (-102))) (|HasCategory| (-2 (|:| -4298 |#1|) (|:| -4437 |#2|)) (QUOTE (-1119))) (|HasCategory| |#2| (QUOTE (-102))) (|HasCategory| |#2| (QUOTE (-1119)))) (-2755 (|HasCategory| (-2 (|:| -4298 |#1|) (|:| -4437 |#2|)) (QUOTE (-1119))) (|HasCategory| (-2 (|:| -4298 |#1|) (|:| -4437 |#2|)) (LIST (QUOTE -625) (QUOTE (-874)))) (|HasCategory| |#2| (QUOTE (-1119))) (|HasCategory| |#2| (LIST (QUOTE -625) (QUOTE (-874))))) (|HasCategory| (-2 (|:| -4298 |#1|) (|:| -4437 |#2|)) (LIST (QUOTE -626) (QUOTE (-548)))) (-12 (|HasCategory| |#2| (QUOTE (-1119))) (|HasCategory| |#2| (LIST (QUOTE -319) (|devaluate| |#2|)))) (|HasCategory| (-2 (|:| -4298 |#1|) (|:| -4437 |#2|)) (QUOTE (-1119))) (|HasCategory| |#1| (QUOTE (-862))) (|HasCategory| |#2| (QUOTE (-1119))) (-2755 (|HasCategory| (-2 (|:| -4298 |#1|) (|:| -4437 |#2|)) (LIST (QUOTE -625) (QUOTE (-874)))) (|HasCategory| |#2| (LIST (QUOTE -625) (QUOTE (-874))))) (-2755 (|HasCategory| (-2 (|:| -4298 |#1|) (|:| -4437 |#2|)) (QUOTE (-102))) (|HasCategory| |#2| (QUOTE (-102)))) (|HasCategory| |#2| (QUOTE (-102))) (|HasCategory| |#2| (LIST (QUOTE -625) (QUOTE (-874)))) (|HasCategory| (-2 (|:| -4298 |#1|) (|:| -4437 |#2|)) (LIST (QUOTE -625) (QUOTE (-874)))) (|HasCategory| (-2 (|:| -4298 |#1|) (|:| -4437 |#2|)) (QUOTE (-102)))) (-1209 S) ((|constructor| (NIL "\\indented{1}{Author: Gabriel Dos Reis} Date Created: April 17,{} 2010 Date Last Modified: April 17,{} 2010")) (|operator| (($ |#1| (|Arity|)) "\\spad{operator(n,a)} returns an operator named \\spad{n} and with arity \\spad{a}."))) NIL @@ -4819,7 +4819,7 @@ NIL (-1222 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| $)) "\\spad{tree(nd,ls)} creates a tree with value \\spad{nd},{} and children \\spad{ls}."))) ((-4463 . T) (-4462 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1119))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1119))) (-2781 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-1119)))) (-2781 (-12 (|HasCategory| |#1| (QUOTE (-1119))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-874))))) (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-874)))) (|HasCategory| |#1| (QUOTE (-102)))) +((-12 (|HasCategory| |#1| (QUOTE (-1119))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1119))) (-2755 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-1119)))) (-2755 (-12 (|HasCategory| |#1| (QUOTE (-1119))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-874))))) (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-874)))) (|HasCategory| |#1| (QUOTE (-102)))) (-1223 S) ((|constructor| (NIL "Category for the trigonometric functions.")) (|tan| (($ $) "\\spad{tan(x)} returns the tangent of \\spad{x}.")) (|sin| (($ $) "\\spad{sin(x)} returns the sine of \\spad{x}.")) (|sec| (($ $) "\\spad{sec(x)} returns the secant of \\spad{x}.")) (|csc| (($ $) "\\spad{csc(x)} returns the cosecant of \\spad{x}.")) (|cot| (($ $) "\\spad{cot(x)} returns the cotangent of \\spad{x}.")) (|cos| (($ $) "\\spad{cos(x)} returns the cosine of \\spad{x}."))) NIL @@ -4828,7 +4828,7 @@ NIL ((|constructor| (NIL "Category for the trigonometric functions.")) (|tan| (($ $) "\\spad{tan(x)} returns the tangent of \\spad{x}.")) (|sin| (($ $) "\\spad{sin(x)} returns the sine of \\spad{x}.")) (|sec| (($ $) "\\spad{sec(x)} returns the secant of \\spad{x}.")) (|csc| (($ $) "\\spad{csc(x)} returns the cosecant of \\spad{x}.")) (|cot| (($ $) "\\spad{cot(x)} returns the cotangent of \\spad{x}.")) (|cos| (($ $) "\\spad{cos(x)} returns the cosine of \\spad{x}."))) NIL NIL -(-1225 R -1966) +(-1225 R -1955) ((|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 @@ -4836,7 +4836,7 @@ NIL ((|constructor| (NIL "This package provides functions that compute \"fraction-free\" inverses of upper and lower triangular matrices over a integral domain. By \"fraction-free inverses\" we mean the following: given a matrix \\spad{B} with entries in \\spad{R} and an element \\spad{d} of \\spad{R} such that \\spad{d} * inv(\\spad{B}) also has entries in \\spad{R},{} we return \\spad{d} * inv(\\spad{B}). Thus,{} it is not necessary to pass to the quotient field in any of our computations.")) (|LowTriBddDenomInv| ((|#4| |#4| |#1|) "\\spad{LowTriBddDenomInv(B,d)} returns \\spad{M},{} where \\spad{B} is a non-singular lower triangular matrix and \\spad{d} is an element of \\spad{R} such that \\spad{M = d * inv(B)} has entries in \\spad{R}.")) (|UpTriBddDenomInv| ((|#4| |#4| |#1|) "\\spad{UpTriBddDenomInv(B,d)} returns \\spad{M},{} where \\spad{B} is a non-singular upper triangular matrix and \\spad{d} is an element of \\spad{R} such that \\spad{M = d * inv(B)} has entries in \\spad{R}."))) NIL NIL -(-1227 R -1966) +(-1227 R -1955) ((|constructor| (NIL "TranscendentalManipulations provides functions to simplify and expand expressions involving transcendental operators.")) (|expandTrigProducts| ((|#2| |#2|) "\\spad{expandTrigProducts(e)} replaces \\axiom{sin(\\spad{x})*sin(\\spad{y})} by \\spad{(cos(x-y)-cos(x+y))/2},{} \\axiom{cos(\\spad{x})*cos(\\spad{y})} by \\spad{(cos(x-y)+cos(x+y))/2},{} and \\axiom{sin(\\spad{x})*cos(\\spad{y})} by \\spad{(sin(x-y)+sin(x+y))/2}. Note that this operation uses the pattern matcher and so is relatively expensive. To avoid getting into an infinite loop the transformations are applied at most ten times.")) (|removeSinhSq| ((|#2| |#2|) "\\spad{removeSinhSq(f)} converts every \\spad{sinh(u)**2} appearing in \\spad{f} into \\spad{1 - cosh(x)**2},{} and also reduces higher powers of \\spad{sinh(u)} with that formula.")) (|removeCoshSq| ((|#2| |#2|) "\\spad{removeCoshSq(f)} converts every \\spad{cosh(u)**2} appearing in \\spad{f} into \\spad{1 - sinh(x)**2},{} and also reduces higher powers of \\spad{cosh(u)} with that formula.")) (|removeSinSq| ((|#2| |#2|) "\\spad{removeSinSq(f)} converts every \\spad{sin(u)**2} appearing in \\spad{f} into \\spad{1 - cos(x)**2},{} and also reduces higher powers of \\spad{sin(u)} with that formula.")) (|removeCosSq| ((|#2| |#2|) "\\spad{removeCosSq(f)} converts every \\spad{cos(u)**2} appearing in \\spad{f} into \\spad{1 - sin(x)**2},{} and also reduces higher powers of \\spad{cos(u)} with that formula.")) (|coth2tanh| ((|#2| |#2|) "\\spad{coth2tanh(f)} converts every \\spad{coth(u)} appearing in \\spad{f} into \\spad{1/tanh(u)}.")) (|cot2tan| ((|#2| |#2|) "\\spad{cot2tan(f)} converts every \\spad{cot(u)} appearing in \\spad{f} into \\spad{1/tan(u)}.")) (|tanh2coth| ((|#2| |#2|) "\\spad{tanh2coth(f)} converts every \\spad{tanh(u)} appearing in \\spad{f} into \\spad{1/coth(u)}.")) (|tan2cot| ((|#2| |#2|) "\\spad{tan2cot(f)} converts every \\spad{tan(u)} appearing in \\spad{f} into \\spad{1/cot(u)}.")) (|tanh2trigh| ((|#2| |#2|) "\\spad{tanh2trigh(f)} converts every \\spad{tanh(u)} appearing in \\spad{f} into \\spad{sinh(u)/cosh(u)}.")) (|tan2trig| ((|#2| |#2|) "\\spad{tan2trig(f)} converts every \\spad{tan(u)} appearing in \\spad{f} into \\spad{sin(u)/cos(u)}.")) (|sinh2csch| ((|#2| |#2|) "\\spad{sinh2csch(f)} converts every \\spad{sinh(u)} appearing in \\spad{f} into \\spad{1/csch(u)}.")) (|sin2csc| ((|#2| |#2|) "\\spad{sin2csc(f)} converts every \\spad{sin(u)} appearing in \\spad{f} into \\spad{1/csc(u)}.")) (|sech2cosh| ((|#2| |#2|) "\\spad{sech2cosh(f)} converts every \\spad{sech(u)} appearing in \\spad{f} into \\spad{1/cosh(u)}.")) (|sec2cos| ((|#2| |#2|) "\\spad{sec2cos(f)} converts every \\spad{sec(u)} appearing in \\spad{f} into \\spad{1/cos(u)}.")) (|csch2sinh| ((|#2| |#2|) "\\spad{csch2sinh(f)} converts every \\spad{csch(u)} appearing in \\spad{f} into \\spad{1/sinh(u)}.")) (|csc2sin| ((|#2| |#2|) "\\spad{csc2sin(f)} converts every \\spad{csc(u)} appearing in \\spad{f} into \\spad{1/sin(u)}.")) (|coth2trigh| ((|#2| |#2|) "\\spad{coth2trigh(f)} converts every \\spad{coth(u)} appearing in \\spad{f} into \\spad{cosh(u)/sinh(u)}.")) (|cot2trig| ((|#2| |#2|) "\\spad{cot2trig(f)} converts every \\spad{cot(u)} appearing in \\spad{f} into \\spad{cos(u)/sin(u)}.")) (|cosh2sech| ((|#2| |#2|) "\\spad{cosh2sech(f)} converts every \\spad{cosh(u)} appearing in \\spad{f} into \\spad{1/sech(u)}.")) (|cos2sec| ((|#2| |#2|) "\\spad{cos2sec(f)} converts every \\spad{cos(u)} appearing in \\spad{f} into \\spad{1/sec(u)}.")) (|expandLog| ((|#2| |#2|) "\\spad{expandLog(f)} converts every \\spad{log(a/b)} appearing in \\spad{f} into \\spad{log(a) - log(b)},{} and every \\spad{log(a*b)} into \\spad{log(a) + log(b)}..")) (|expandPower| ((|#2| |#2|) "\\spad{expandPower(f)} converts every power \\spad{(a/b)**c} appearing in \\spad{f} into \\spad{a**c * b**(-c)}.")) (|simplifyLog| ((|#2| |#2|) "\\spad{simplifyLog(f)} converts every \\spad{log(a) - log(b)} appearing in \\spad{f} into \\spad{log(a/b)},{} every \\spad{log(a) + log(b)} into \\spad{log(a*b)} and every \\spad{n*log(a)} into \\spad{log(a^n)}.")) (|simplifyExp| ((|#2| |#2|) "\\spad{simplifyExp(f)} converts every product \\spad{exp(a)*exp(b)} appearing in \\spad{f} into \\spad{exp(a+b)}.")) (|htrigs| ((|#2| |#2|) "\\spad{htrigs(f)} converts all the exponentials in \\spad{f} into hyperbolic sines and cosines.")) (|simplify| ((|#2| |#2|) "\\spad{simplify(f)} performs the following simplifications on \\spad{f:}\\begin{items} \\item 1. rewrites trigs and hyperbolic trigs in terms of \\spad{sin} ,{}\\spad{cos},{} \\spad{sinh},{} \\spad{cosh}. \\item 2. rewrites \\spad{sin**2} and \\spad{sinh**2} in terms of \\spad{cos} and \\spad{cosh},{} \\item 3. rewrites \\spad{exp(a)*exp(b)} as \\spad{exp(a+b)}. \\item 4. rewrites \\spad{(a**(1/n))**m * (a**(1/s))**t} as a single power of a single radical of \\spad{a}. \\end{items}")) (|expand| ((|#2| |#2|) "\\spad{expand(f)} performs the following expansions on \\spad{f:}\\begin{items} \\item 1. logs of products are expanded into sums of logs,{} \\item 2. trigonometric and hyperbolic trigonometric functions of sums are expanded into sums of products of trigonometric and hyperbolic trigonometric functions. \\item 3. formal powers of the form \\spad{(a/b)**c} are expanded into \\spad{a**c * b**(-c)}. \\end{items}"))) NIL ((-12 (|HasCategory| |#1| (LIST (QUOTE -626) (LIST (QUOTE -905) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -899) (|devaluate| |#1|))) (|HasCategory| |#2| (LIST (QUOTE -626) (LIST (QUOTE -905) (|devaluate| |#1|)))) (|HasCategory| |#2| (LIST (QUOTE -899) (|devaluate| |#1|))))) @@ -4851,7 +4851,7 @@ NIL (-1230 |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}."))) (((-4464 "*") |has| |#1| (-174)) (-4455 |has| |#1| (-568)) (-4457 . T) (-4456 . T) (-4459 . T)) -((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -419) (QUOTE (-576))))) (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-148))) (|HasCategory| |#1| (QUOTE (-146))) (-2781 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-568)))) (|HasCategory| |#1| (QUOTE (-568))) (|HasCategory| |#1| (QUOTE (-374)))) +((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -419) (QUOTE (-576))))) (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-148))) (|HasCategory| |#1| (QUOTE (-146))) (-2755 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-568)))) (|HasCategory| |#1| (QUOTE (-568))) (|HasCategory| |#1| (QUOTE (-374)))) (-1231 |Curve|) ((|constructor| (NIL "\\indented{2}{Package for constructing tubes around 3-dimensional parametric curves.} Domain of tubes around 3-dimensional parametric curves.")) (|tube| (($ |#1| (|List| (|List| (|Point| (|DoubleFloat|)))) (|Boolean|)) "\\spad{tube(c,ll,b)} creates a tube of the domain \\spadtype{TubePlot} from a space curve \\spad{c} of the category \\spadtype{PlottableSpaceCurveCategory},{} a list of lists of points (loops) \\spad{ll} and a boolean \\spad{b} which if \\spad{true} indicates a closed tube,{} or if \\spad{false} an open tube.")) (|setClosed| (((|Boolean|) $ (|Boolean|)) "\\spad{setClosed(t,b)} declares the given tube plot \\spad{t} to be closed if \\spad{b} is \\spad{true},{} or if \\spad{b} is \\spad{false},{} \\spad{t} is set to be open.")) (|open?| (((|Boolean|) $) "\\spad{open?(t)} tests whether the given tube plot \\spad{t} is open.")) (|closed?| (((|Boolean|) $) "\\spad{closed?(t)} tests whether the given tube plot \\spad{t} is closed.")) (|listLoops| (((|List| (|List| (|Point| (|DoubleFloat|)))) $) "\\spad{listLoops(t)} returns the list of lists of points,{} or the 'loops',{} of the given tube plot \\spad{t}.")) (|getCurve| ((|#1| $) "\\spad{getCurve(t)} returns the \\spadtype{PlottableSpaceCurveCategory} representing the parametric curve of the given tube plot \\spad{t}."))) NIL @@ -4864,7 +4864,7 @@ NIL ((|constructor| (NIL "\\indented{1}{This domain is used to interface with the interpreter\\spad{'s} notion} of comma-delimited sequences of values.")) (|length| (((|NonNegativeInteger|) $) "\\spad{length(x)} returns the number of elements in tuple \\spad{x}")) (|select| ((|#1| $ (|NonNegativeInteger|)) "\\spad{select(x,n)} returns the \\spad{n}-th element of tuple \\spad{x}. tuples are 0-based"))) NIL ((|HasCategory| |#1| (QUOTE (-1119))) (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-874))))) -(-1234 -1966) +(-1234 -1955) ((|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 @@ -4927,11 +4927,11 @@ NIL (-1249 |Coef| UTS) ((|constructor| (NIL "This package enables one to construct a univariate Laurent series domain from a univariate Taylor series domain. Univariate Laurent series are represented by a pair \\spad{[n,f(x)]},{} where \\spad{n} is an arbitrary integer and \\spad{f(x)} is a Taylor series. This pair represents the Laurent series \\spad{x**n * f(x)}."))) (((-4464 "*") |has| |#1| (-174)) (-4455 |has| |#1| (-568)) (-4460 |has| |#1| (-374)) (-4454 |has| |#1| (-374)) (-4456 . T) (-4457 . T) (-4459 . 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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 @@ -4967,7 +4967,7 @@ NIL (-1259 |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}"))) (((-4464 "*") |has| |#2| (-174)) (-4455 |has| |#2| (-568)) (-4458 |has| |#2| (-374)) (-4460 |has| |#2| (-6 -4460)) (-4457 . T) (-4456 . T) (-4459 . T)) -((|HasCategory| |#2| (QUOTE (-926))) (|HasCategory| |#2| (QUOTE (-568))) (|HasCategory| |#2| (QUOTE (-174))) (-2781 (|HasCategory| |#2| (QUOTE (-174))) (|HasCategory| |#2| (QUOTE (-568)))) (-12 (|HasCategory| (-1101) (LIST (QUOTE -899) (QUOTE (-390)))) (|HasCategory| |#2| (LIST (QUOTE -899) (QUOTE (-390))))) (-12 (|HasCategory| (-1101) (LIST (QUOTE -899) (QUOTE (-576)))) (|HasCategory| |#2| (LIST (QUOTE -899) (QUOTE (-576))))) (-12 (|HasCategory| (-1101) (LIST (QUOTE -626) (LIST (QUOTE -905) (QUOTE (-390))))) (|HasCategory| |#2| (LIST (QUOTE -626) (LIST (QUOTE -905) (QUOTE (-390)))))) (-12 (|HasCategory| (-1101) (LIST (QUOTE -626) (LIST (QUOTE -905) (QUOTE (-576))))) (|HasCategory| |#2| (LIST (QUOTE -626) (LIST (QUOTE -905) (QUOTE (-576)))))) (-12 (|HasCategory| (-1101) (LIST (QUOTE -626) (QUOTE (-548)))) (|HasCategory| |#2| (LIST (QUOTE -626) (QUOTE (-548))))) (|HasCategory| |#2| (LIST (QUOTE -651) (QUOTE (-576)))) (|HasCategory| |#2| (QUOTE (-148))) (|HasCategory| |#2| (QUOTE (-146))) (|HasCategory| |#2| (LIST (QUOTE -38) (LIST (QUOTE -419) (QUOTE (-576))))) (|HasCategory| |#2| (LIST (QUOTE -1057) (QUOTE (-576)))) (-2781 (|HasCategory| |#2| (LIST (QUOTE -38) (LIST (QUOTE -419) (QUOTE (-576))))) (|HasCategory| |#2| (LIST (QUOTE -1057) (LIST (QUOTE -419) (QUOTE (-576)))))) (|HasCategory| |#2| (LIST (QUOTE -1057) (LIST (QUOTE -419) (QUOTE (-576))))) (-2781 (|HasCategory| |#2| (QUOTE (-174))) (|HasCategory| |#2| (QUOTE (-374))) (|HasCategory| |#2| (QUOTE (-464))) (|HasCategory| |#2| (QUOTE (-568))) (|HasCategory| |#2| (QUOTE (-926)))) (-2781 (|HasCategory| |#2| (QUOTE (-374))) (|HasCategory| |#2| (QUOTE (-464))) (|HasCategory| |#2| (QUOTE (-568))) (|HasCategory| |#2| (QUOTE (-926)))) (-2781 (|HasCategory| |#2| (QUOTE (-374))) (|HasCategory| |#2| (QUOTE (-464))) (|HasCategory| |#2| (QUOTE (-926)))) (|HasCategory| |#2| (QUOTE (-374))) (|HasCategory| |#2| (QUOTE (-1171))) (|HasCategory| |#2| (LIST (QUOTE -917) (QUOTE (-1195)))) (|HasCategory| |#2| (LIST (QUOTE -915) (QUOTE (-1195)))) (|HasCategory| |#2| (QUOTE (-237))) (|HasCategory| |#2| (QUOTE (-238))) (|HasAttribute| |#2| (QUOTE -4460)) (|HasCategory| |#2| (QUOTE (-464))) (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| |#2| (QUOTE (-926)))) (-2781 (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| |#2| (QUOTE (-926)))) (|HasCategory| |#2| (QUOTE (-146))))) +((|HasCategory| |#2| (QUOTE (-926))) (|HasCategory| |#2| (QUOTE (-568))) (|HasCategory| |#2| (QUOTE (-174))) (-2755 (|HasCategory| |#2| (QUOTE (-174))) (|HasCategory| |#2| (QUOTE (-568)))) (-12 (|HasCategory| (-1101) (LIST (QUOTE -899) (QUOTE (-390)))) (|HasCategory| |#2| (LIST (QUOTE -899) (QUOTE (-390))))) (-12 (|HasCategory| (-1101) (LIST (QUOTE -899) (QUOTE (-576)))) (|HasCategory| |#2| (LIST (QUOTE -899) (QUOTE (-576))))) (-12 (|HasCategory| (-1101) (LIST (QUOTE -626) (LIST (QUOTE -905) (QUOTE (-390))))) (|HasCategory| |#2| (LIST (QUOTE -626) (LIST (QUOTE -905) (QUOTE (-390)))))) (-12 (|HasCategory| (-1101) (LIST (QUOTE -626) (LIST (QUOTE -905) (QUOTE (-576))))) (|HasCategory| |#2| (LIST (QUOTE -626) (LIST (QUOTE -905) (QUOTE (-576)))))) (-12 (|HasCategory| (-1101) (LIST (QUOTE -626) (QUOTE (-548)))) (|HasCategory| |#2| (LIST (QUOTE -626) (QUOTE (-548))))) (|HasCategory| |#2| (LIST (QUOTE -651) (QUOTE (-576)))) (|HasCategory| |#2| (QUOTE (-148))) (|HasCategory| |#2| (QUOTE (-146))) (|HasCategory| |#2| (LIST (QUOTE -38) (LIST (QUOTE -419) (QUOTE (-576))))) (|HasCategory| |#2| (LIST (QUOTE -1057) (QUOTE (-576)))) (-2755 (|HasCategory| |#2| (LIST (QUOTE -38) (LIST (QUOTE -419) (QUOTE (-576))))) (|HasCategory| |#2| (LIST (QUOTE -1057) (LIST (QUOTE -419) (QUOTE (-576)))))) (|HasCategory| |#2| (LIST (QUOTE -1057) (LIST (QUOTE -419) (QUOTE (-576))))) (-2755 (|HasCategory| |#2| (QUOTE (-174))) (|HasCategory| |#2| (QUOTE (-374))) (|HasCategory| |#2| (QUOTE (-464))) (|HasCategory| |#2| (QUOTE (-568))) (|HasCategory| |#2| (QUOTE (-926)))) (-2755 (|HasCategory| |#2| (QUOTE (-374))) (|HasCategory| |#2| (QUOTE (-464))) (|HasCategory| |#2| (QUOTE (-568))) (|HasCategory| |#2| (QUOTE (-926)))) (-2755 (|HasCategory| |#2| (QUOTE (-374))) (|HasCategory| |#2| (QUOTE (-464))) (|HasCategory| |#2| (QUOTE (-926)))) (|HasCategory| |#2| (QUOTE (-374))) (|HasCategory| |#2| (QUOTE (-1171))) (|HasCategory| |#2| (LIST (QUOTE -917) (QUOTE (-1195)))) (|HasCategory| |#2| (LIST (QUOTE -915) (QUOTE (-1195)))) (|HasCategory| |#2| (QUOTE (-237))) (|HasCategory| |#2| (QUOTE (-238))) (|HasAttribute| |#2| (QUOTE -4460)) (|HasCategory| |#2| (QUOTE (-464))) (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| |#2| (QUOTE (-926)))) (-2755 (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| |#2| (QUOTE (-926)))) (|HasCategory| |#2| (QUOTE (-146))))) (-1260 R PR S PS) ((|constructor| (NIL "Mapping from polynomials over \\spad{R} to polynomials over \\spad{S} given a map from \\spad{R} to \\spad{S} assumed to send zero to zero.")) (|map| ((|#4| (|Mapping| |#3| |#1|) |#2|) "\\spad{map(f, p)} takes a function \\spad{f} from \\spad{R} to \\spad{S},{} and applies it to each (non-zero) coefficient of a polynomial \\spad{p} over \\spad{R},{} getting a new polynomial over \\spad{S}. Note: since the map is not applied to zero elements,{} it may map zero to zero."))) NIL @@ -4983,7 +4983,7 @@ NIL (-1263 S |Coef| |Expon|) ((|constructor| (NIL "\\spadtype{UnivariatePowerSeriesCategory} is the most general univariate power series category with exponents in an ordered abelian monoid. Note: this category exports a substitution function if it is possible to multiply exponents. Note: this category exports a derivative operation if it is possible to multiply coefficients by exponents.")) (|eval| (((|Stream| |#2|) $ |#2|) "\\spad{eval(f,a)} evaluates a power series at a value in the ground ring by returning a stream of partial sums.")) (|extend| (($ $ |#3|) "\\spad{extend(f,n)} causes all terms of \\spad{f} of degree \\spad{<=} \\spad{n} to be computed.")) (|approximate| ((|#2| $ |#3|) "\\spad{approximate(f)} returns a truncated power series with the series variable viewed as an element of the coefficient domain.")) (|truncate| (($ $ |#3| |#3|) "\\spad{truncate(f,k1,k2)} returns a (finite) power series consisting of the sum of all terms of \\spad{f} of degree \\spad{d} with \\spad{k1 <= d <= k2}.") (($ $ |#3|) "\\spad{truncate(f,k)} returns a (finite) power series consisting of the sum of all terms of \\spad{f} of degree \\spad{<= k}.")) (|order| ((|#3| $ |#3|) "\\spad{order(f,n) = min(m,n)},{} where \\spad{m} is the degree of the lowest order non-zero term in \\spad{f}.") ((|#3| $) "\\spad{order(f)} is the degree of the lowest order non-zero term in \\spad{f}. This will result in an infinite loop if \\spad{f} has no non-zero terms.")) (|multiplyExponents| (($ $ (|PositiveInteger|)) "\\spad{multiplyExponents(f,n)} multiplies all exponents of the power series \\spad{f} by the positive integer \\spad{n}.")) (|center| ((|#2| $) "\\spad{center(f)} returns the point about which the series \\spad{f} is expanded.")) (|variable| (((|Symbol|) $) "\\spad{variable(f)} returns the (unique) power series variable of the power series \\spad{f}.")) (|terms| (((|Stream| (|Record| (|:| |k| |#3|) (|:| |c| |#2|))) $) "\\spad{terms(f(x))} returns a stream of non-zero terms,{} where a a term is an exponent-coefficient pair. The terms in the stream are ordered by increasing order of exponents."))) NIL -((|HasCategory| |#2| (LIST (QUOTE -915) (QUOTE (-1195)))) (|HasSignature| |#2| (LIST (QUOTE *) (LIST (|devaluate| |#2|) (|devaluate| |#3|) (|devaluate| |#2|)))) (|HasCategory| |#3| (QUOTE (-1131))) (|HasSignature| |#2| (LIST (QUOTE **) (LIST (|devaluate| |#2|) (|devaluate| |#2|) (|devaluate| |#3|)))) (|HasSignature| |#2| (LIST (QUOTE -3581) (LIST (|devaluate| |#2|) (QUOTE (-1195)))))) +((|HasCategory| |#2| (LIST (QUOTE -915) (QUOTE (-1195)))) (|HasSignature| |#2| (LIST (QUOTE *) (LIST (|devaluate| |#2|) (|devaluate| |#3|) (|devaluate| |#2|)))) (|HasCategory| |#3| (QUOTE (-1131))) (|HasSignature| |#2| (LIST (QUOTE **) (LIST (|devaluate| |#2|) (|devaluate| |#2|) (|devaluate| |#3|)))) (|HasSignature| |#2| (LIST (QUOTE -3567) (LIST (|devaluate| |#2|) (QUOTE (-1195)))))) (-1264 |Coef| |Expon|) ((|constructor| (NIL "\\spadtype{UnivariatePowerSeriesCategory} is the most general univariate power series category with exponents in an ordered abelian monoid. Note: this category exports a substitution function if it is possible to multiply exponents. Note: this category exports a derivative operation if it is possible to multiply coefficients by exponents.")) (|eval| (((|Stream| |#1|) $ |#1|) "\\spad{eval(f,a)} evaluates a power series at a value in the ground ring by returning a stream of partial sums.")) (|extend| (($ $ |#2|) "\\spad{extend(f,n)} causes all terms of \\spad{f} of degree \\spad{<=} \\spad{n} to be computed.")) (|approximate| ((|#1| $ |#2|) "\\spad{approximate(f)} returns a truncated power series with the series variable viewed as an element of the coefficient domain.")) (|truncate| (($ $ |#2| |#2|) "\\spad{truncate(f,k1,k2)} returns a (finite) power series consisting of the sum of all terms of \\spad{f} of degree \\spad{d} with \\spad{k1 <= d <= k2}.") (($ $ |#2|) "\\spad{truncate(f,k)} returns a (finite) power series consisting of the sum of all terms of \\spad{f} of degree \\spad{<= k}.")) (|order| ((|#2| $ |#2|) "\\spad{order(f,n) = min(m,n)},{} where \\spad{m} is the degree of the lowest order non-zero term in \\spad{f}.") ((|#2| $) "\\spad{order(f)} is the degree of the lowest order non-zero term in \\spad{f}. This will result in an infinite loop if \\spad{f} has no non-zero terms.")) (|multiplyExponents| (($ $ (|PositiveInteger|)) "\\spad{multiplyExponents(f,n)} multiplies all exponents of the power series \\spad{f} by the positive integer \\spad{n}.")) (|center| ((|#1| $) "\\spad{center(f)} returns the point about which the series \\spad{f} is expanded.")) (|variable| (((|Symbol|) $) "\\spad{variable(f)} returns the (unique) power series variable of the power series \\spad{f}.")) (|terms| (((|Stream| (|Record| (|:| |k| |#2|) (|:| |c| |#1|))) $) "\\spad{terms(f(x))} returns a stream of non-zero terms,{} where a a term is an exponent-coefficient pair. The terms in the stream are ordered by increasing order of exponents."))) (((-4464 "*") |has| |#1| (-174)) (-4455 |has| |#1| (-568)) (-4456 . T) (-4457 . T) (-4459 . T)) @@ -5011,15 +5011,15 @@ NIL (-1270 |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)}."))) (((-4464 "*") |has| |#1| (-174)) (-4455 |has| |#1| (-568)) (-4460 |has| |#1| (-374)) (-4454 |has| |#1| (-374)) (-4456 . T) (-4457 . T) (-4459 . T)) -((|HasCategory| |#1| (QUOTE (-568))) (|HasCategory| |#1| (QUOTE (-174))) (-2781 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-568)))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-148))) (-12 (|HasCategory| |#1| (LIST (QUOTE -915) (QUOTE (-1195)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -419) (QUOTE (-576))) (|devaluate| |#1|))))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -419) (QUOTE (-576))) (|devaluate| |#1|)))) (|HasCategory| (-419 (-576)) (QUOTE (-1131))) (|HasCategory| |#1| (QUOTE (-374))) (-2781 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-374))) (|HasCategory| |#1| (QUOTE (-568)))) (-2781 (|HasCategory| |#1| (QUOTE (-374))) (|HasCategory| |#1| (QUOTE (-568)))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -419) (QUOTE (-576)))))) (|HasSignature| |#1| (LIST (QUOTE -3581) (LIST (|devaluate| |#1|) (QUOTE (-1195)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -419) (QUOTE (-576)))))) (-2781 (-12 (|HasCategory| |#1| (LIST (QUOTE -29) (QUOTE (-576)))) (|HasCategory| |#1| (QUOTE (-976))) (|HasCategory| |#1| (QUOTE (-1221))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -419) (QUOTE (-576)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -419) (QUOTE (-576))))) (|HasSignature| |#1| (LIST (QUOTE -4121) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1195))))) (|HasSignature| |#1| (LIST (QUOTE -1934) (LIST (LIST (QUOTE -656) (QUOTE (-1195))) (|devaluate| |#1|)))))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -419) (QUOTE (-576)))))) +((|HasCategory| |#1| (QUOTE (-568))) (|HasCategory| |#1| (QUOTE (-174))) (-2755 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-568)))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-148))) (-12 (|HasCategory| |#1| (LIST (QUOTE -915) (QUOTE (-1195)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -419) (QUOTE (-576))) (|devaluate| |#1|))))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -419) (QUOTE (-576))) (|devaluate| |#1|)))) (|HasCategory| (-419 (-576)) (QUOTE (-1131))) (|HasCategory| |#1| (QUOTE (-374))) (-2755 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-374))) (|HasCategory| |#1| (QUOTE (-568)))) (-2755 (|HasCategory| |#1| (QUOTE (-374))) (|HasCategory| |#1| (QUOTE (-568)))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -419) (QUOTE (-576)))))) (|HasSignature| |#1| (LIST (QUOTE -3567) (LIST (|devaluate| |#1|) (QUOTE (-1195)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -419) (QUOTE (-576)))))) (-2755 (-12 (|HasCategory| |#1| (LIST (QUOTE -29) (QUOTE (-576)))) (|HasCategory| |#1| (QUOTE (-976))) (|HasCategory| |#1| (QUOTE (-1221))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -419) (QUOTE (-576)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -419) (QUOTE (-576))))) (|HasSignature| |#1| (LIST (QUOTE -1589) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1195))))) (|HasSignature| |#1| (LIST (QUOTE -1962) (LIST (LIST (QUOTE -656) (QUOTE (-1195))) (|devaluate| |#1|)))))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -419) (QUOTE (-576)))))) (-1271 |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."))) (((-4464 "*") |has| |#1| (-174)) (-4455 |has| |#1| (-568)) (-4460 |has| |#1| (-374)) (-4454 |has| |#1| (-374)) (-4456 . T) (-4457 . T) (-4459 . T)) -((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -419) (QUOTE (-576))))) (|HasCategory| |#1| (QUOTE (-568))) (|HasCategory| |#1| (QUOTE (-174))) (-2781 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-568)))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-148))) (-12 (|HasCategory| |#1| (LIST (QUOTE -915) (QUOTE (-1195)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -419) (QUOTE (-576))) (|devaluate| |#1|))))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -419) (QUOTE (-576))) (|devaluate| |#1|)))) (|HasCategory| (-419 (-576)) (QUOTE (-1131))) (|HasCategory| |#1| (QUOTE (-374))) (-2781 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-374))) (|HasCategory| |#1| (QUOTE (-568)))) (-2781 (|HasCategory| |#1| (QUOTE (-374))) (|HasCategory| |#1| (QUOTE (-568)))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -419) (QUOTE (-576)))))) (|HasSignature| |#1| (LIST (QUOTE -3581) (LIST (|devaluate| |#1|) (QUOTE (-1195)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -419) (QUOTE (-576)))))) (-2781 (-12 (|HasCategory| |#1| (LIST (QUOTE -29) (QUOTE (-576)))) (|HasCategory| |#1| (QUOTE (-976))) (|HasCategory| |#1| (QUOTE (-1221))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -419) (QUOTE (-576)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -419) (QUOTE (-576))))) (|HasSignature| |#1| (LIST (QUOTE -4121) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1195))))) (|HasSignature| |#1| (LIST (QUOTE -1934) (LIST (LIST (QUOTE -656) (QUOTE (-1195))) (|devaluate| |#1|))))))) +((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -419) (QUOTE (-576))))) (|HasCategory| |#1| (QUOTE (-568))) (|HasCategory| |#1| (QUOTE (-174))) (-2755 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-568)))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-148))) (-12 (|HasCategory| |#1| (LIST (QUOTE -915) (QUOTE (-1195)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -419) (QUOTE (-576))) (|devaluate| |#1|))))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -419) (QUOTE (-576))) (|devaluate| |#1|)))) (|HasCategory| (-419 (-576)) (QUOTE (-1131))) (|HasCategory| |#1| (QUOTE (-374))) (-2755 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-374))) (|HasCategory| |#1| (QUOTE (-568)))) (-2755 (|HasCategory| |#1| (QUOTE (-374))) (|HasCategory| |#1| (QUOTE (-568)))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -419) (QUOTE (-576)))))) (|HasSignature| |#1| (LIST (QUOTE -3567) (LIST (|devaluate| |#1|) (QUOTE (-1195)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -419) (QUOTE (-576)))))) (-2755 (-12 (|HasCategory| |#1| (LIST (QUOTE -29) (QUOTE (-576)))) (|HasCategory| |#1| (QUOTE (-976))) (|HasCategory| |#1| (QUOTE (-1221))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -419) (QUOTE (-576)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -419) (QUOTE (-576))))) (|HasSignature| |#1| (LIST (QUOTE -1589) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1195))))) (|HasSignature| |#1| (LIST (QUOTE -1962) (LIST (LIST (QUOTE -656) (QUOTE (-1195))) (|devaluate| |#1|))))))) (-1272 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))}."))) (((-4464 "*") |has| (-1271 |#2| |#3| |#4|) (-174)) (-4455 |has| (-1271 |#2| |#3| |#4|) (-568)) (-4456 . T) (-4457 . T) (-4459 . T)) -((|HasCategory| (-1271 |#2| |#3| |#4|) (LIST (QUOTE -38) (LIST (QUOTE -419) (QUOTE (-576))))) (|HasCategory| (-1271 |#2| |#3| |#4|) (QUOTE (-146))) (|HasCategory| (-1271 |#2| |#3| |#4|) (QUOTE (-148))) (|HasCategory| (-1271 |#2| |#3| |#4|) (QUOTE (-174))) (-2781 (|HasCategory| (-1271 |#2| |#3| |#4|) (LIST (QUOTE -38) (LIST (QUOTE -419) (QUOTE (-576))))) (|HasCategory| (-1271 |#2| |#3| |#4|) (LIST (QUOTE -1057) (LIST (QUOTE -419) (QUOTE (-576)))))) (|HasCategory| (-1271 |#2| |#3| |#4|) (LIST (QUOTE -1057) (LIST (QUOTE -419) (QUOTE (-576))))) (|HasCategory| (-1271 |#2| |#3| |#4|) (LIST (QUOTE -1057) (QUOTE (-576)))) (|HasCategory| (-1271 |#2| |#3| |#4|) (QUOTE (-374))) (|HasCategory| (-1271 |#2| |#3| |#4|) (QUOTE (-464))) (|HasCategory| (-1271 |#2| |#3| |#4|) (QUOTE (-568)))) +((|HasCategory| (-1271 |#2| |#3| |#4|) (LIST (QUOTE -38) (LIST (QUOTE -419) (QUOTE (-576))))) (|HasCategory| (-1271 |#2| |#3| |#4|) (QUOTE (-146))) (|HasCategory| (-1271 |#2| |#3| |#4|) (QUOTE (-148))) (|HasCategory| (-1271 |#2| |#3| |#4|) (QUOTE (-174))) (-2755 (|HasCategory| (-1271 |#2| |#3| |#4|) (LIST (QUOTE -38) (LIST (QUOTE -419) (QUOTE (-576))))) (|HasCategory| (-1271 |#2| |#3| |#4|) (LIST (QUOTE -1057) (LIST (QUOTE -419) (QUOTE (-576)))))) (|HasCategory| (-1271 |#2| |#3| |#4|) (LIST (QUOTE -1057) (LIST (QUOTE -419) (QUOTE (-576))))) (|HasCategory| (-1271 |#2| |#3| |#4|) (LIST (QUOTE -1057) (QUOTE (-576)))) (|HasCategory| (-1271 |#2| |#3| |#4|) (QUOTE (-374))) (|HasCategory| (-1271 |#2| |#3| |#4|) (QUOTE (-464))) (|HasCategory| (-1271 |#2| |#3| |#4|) (QUOTE (-568)))) (-1273 A S) ((|constructor| (NIL "A unary-recursive aggregate is a one where nodes may have either 0 or 1 children. This aggregate models,{} though not precisely,{} a linked list possibly with a single cycle. A node with one children models a non-empty list,{} with the \\spadfun{value} of the list designating the head,{} or \\spadfun{first},{} of the list,{} and the child designating the tail,{} or \\spadfun{rest},{} of the list. A node with no child then designates the empty list. Since these aggregates are recursive aggregates,{} they may be cyclic.")) (|split!| (($ $ (|Integer|)) "\\spad{split!(u,n)} splits \\spad{u} into two aggregates: \\axiom{\\spad{v} = rest(\\spad{u},{}\\spad{n})} and \\axiom{\\spad{w} = first(\\spad{u},{}\\spad{n})},{} returning \\axiom{\\spad{v}}. Note: afterwards \\axiom{rest(\\spad{u},{}\\spad{n})} returns \\axiom{empty()}.")) (|setlast!| ((|#2| $ |#2|) "\\spad{setlast!(u,x)} destructively changes the last element of \\spad{u} to \\spad{x}.")) (|setrest!| (($ $ $) "\\spad{setrest!(u,v)} destructively changes the rest of \\spad{u} to \\spad{v}.")) (|setelt| ((|#2| $ "last" |#2|) "\\spad{setelt(u,\"last\",x)} (also written: \\axiom{\\spad{u}.last \\spad{:=} \\spad{b}}) is equivalent to \\axiom{setlast!(\\spad{u},{}\\spad{v})}.") (($ $ "rest" $) "\\spad{setelt(u,\"rest\",v)} (also written: \\axiom{\\spad{u}.rest \\spad{:=} \\spad{v}}) is equivalent to \\axiom{setrest!(\\spad{u},{}\\spad{v})}.") ((|#2| $ "first" |#2|) "\\spad{setelt(u,\"first\",x)} (also written: \\axiom{\\spad{u}.first \\spad{:=} \\spad{x}}) is equivalent to \\axiom{setfirst!(\\spad{u},{}\\spad{x})}.")) (|setfirst!| ((|#2| $ |#2|) "\\spad{setfirst!(u,x)} destructively changes the first element of a to \\spad{x}.")) (|cycleSplit!| (($ $) "\\spad{cycleSplit!(u)} splits the aggregate by dropping off the cycle. The value returned is the cycle entry,{} or nil if none exists. For example,{} if \\axiom{\\spad{w} = concat(\\spad{u},{}\\spad{v})} is the cyclic list where \\spad{v} is the head of the cycle,{} \\axiom{cycleSplit!(\\spad{w})} will drop \\spad{v} off \\spad{w} thus destructively changing \\spad{w} to \\spad{u},{} and returning \\spad{v}.")) (|concat!| (($ $ |#2|) "\\spad{concat!(u,x)} destructively adds element \\spad{x} to the end of \\spad{u}. Note: \\axiom{concat!(a,{}\\spad{x}) = setlast!(a,{}[\\spad{x}])}.") (($ $ $) "\\spad{concat!(u,v)} destructively concatenates \\spad{v} to the end of \\spad{u}. Note: \\axiom{concat!(\\spad{u},{}\\spad{v}) = setlast!(\\spad{u},{}\\spad{v})}.")) (|cycleTail| (($ $) "\\spad{cycleTail(u)} returns the last node in the cycle,{} or empty if none exists.")) (|cycleLength| (((|NonNegativeInteger|) $) "\\spad{cycleLength(u)} returns the length of a top-level cycle contained in aggregate \\spad{u},{} or 0 is \\spad{u} has no such cycle.")) (|cycleEntry| (($ $) "\\spad{cycleEntry(u)} returns the head of a top-level cycle contained in aggregate \\spad{u},{} or \\axiom{empty()} if none exists.")) (|third| ((|#2| $) "\\spad{third(u)} returns the third element of \\spad{u}. Note: \\axiom{third(\\spad{u}) = first(rest(rest(\\spad{u})))}.")) (|second| ((|#2| $) "\\spad{second(u)} returns the second element of \\spad{u}. Note: \\axiom{second(\\spad{u}) = first(rest(\\spad{u}))}.")) (|tail| (($ $) "\\spad{tail(u)} returns the last node of \\spad{u}. Note: if \\spad{u} is \\axiom{shallowlyMutable},{} \\axiom{setrest(tail(\\spad{u}),{}\\spad{v}) = concat(\\spad{u},{}\\spad{v})}.")) (|last| (($ $ (|NonNegativeInteger|)) "\\spad{last(u,n)} returns a copy of the last \\spad{n} (\\axiom{\\spad{n} \\spad{>=} 0}) nodes of \\spad{u}. Note: \\axiom{last(\\spad{u},{}\\spad{n})} is a list of \\spad{n} elements.") ((|#2| $) "\\spad{last(u)} resturn the last element of \\spad{u}. Note: for lists,{} \\axiom{last(\\spad{u}) = \\spad{u} . (maxIndex \\spad{u}) = \\spad{u} . (\\# \\spad{u} - 1)}.")) (|rest| (($ $ (|NonNegativeInteger|)) "\\spad{rest(u,n)} returns the \\axiom{\\spad{n}}th (\\spad{n} \\spad{>=} 0) node of \\spad{u}. Note: \\axiom{rest(\\spad{u},{}0) = \\spad{u}}.") (($ $) "\\spad{rest(u)} returns an aggregate consisting of all but the first element of \\spad{u} (equivalently,{} the next node of \\spad{u}).")) (|elt| ((|#2| $ "last") "\\spad{elt(u,\"last\")} (also written: \\axiom{\\spad{u} . last}) is equivalent to last \\spad{u}.") (($ $ "rest") "\\spad{elt(\\%,\"rest\")} (also written: \\axiom{\\spad{u}.rest}) is equivalent to \\axiom{rest \\spad{u}}.") ((|#2| $ "first") "\\spad{elt(u,\"first\")} (also written: \\axiom{\\spad{u} . first}) is equivalent to first \\spad{u}.")) (|first| (($ $ (|NonNegativeInteger|)) "\\spad{first(u,n)} returns a copy of the first \\spad{n} (\\axiom{\\spad{n} \\spad{>=} 0}) elements of \\spad{u}.") ((|#2| $) "\\spad{first(u)} returns the first element of \\spad{u} (equivalently,{} the value at the current node).")) (|concat| (($ |#2| $) "\\spad{concat(x,u)} returns aggregate consisting of \\spad{x} followed by the elements of \\spad{u}. Note: if \\axiom{\\spad{v} = concat(\\spad{x},{}\\spad{u})} then \\axiom{\\spad{x} = first \\spad{v}} and \\axiom{\\spad{u} = rest \\spad{v}}.") (($ $ $) "\\spad{concat(u,v)} returns an aggregate \\spad{w} consisting of the elements of \\spad{u} followed by the elements of \\spad{v}. Note: \\axiom{\\spad{v} = rest(\\spad{w},{}\\#a)}."))) NIL @@ -5035,7 +5035,7 @@ NIL (-1276 S |Coef|) ((|constructor| (NIL "\\spadtype{UnivariateTaylorSeriesCategory} is the category of Taylor series in one variable.")) (|integrate| (($ $ (|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 (-576)))) (|HasCategory| |#2| (QUOTE (-976))) (|HasCategory| |#2| (QUOTE (-1221))) (|HasSignature| |#2| (LIST (QUOTE -1934) (LIST (LIST (QUOTE -656) (QUOTE (-1195))) (|devaluate| |#2|)))) (|HasSignature| |#2| (LIST (QUOTE -4121) (LIST (|devaluate| |#2|) (|devaluate| |#2|) (QUOTE (-1195))))) (|HasCategory| |#2| (LIST (QUOTE -38) (LIST (QUOTE -419) (QUOTE (-576))))) (|HasCategory| |#2| (QUOTE (-374)))) +((|HasCategory| |#2| (LIST (QUOTE -29) (QUOTE (-576)))) (|HasCategory| |#2| (QUOTE (-976))) (|HasCategory| |#2| (QUOTE (-1221))) (|HasSignature| |#2| (LIST (QUOTE -1962) (LIST (LIST (QUOTE -656) (QUOTE (-1195))) (|devaluate| |#2|)))) (|HasSignature| |#2| (LIST (QUOTE -1589) (LIST (|devaluate| |#2|) (|devaluate| |#2|) (QUOTE (-1195))))) (|HasCategory| |#2| (LIST (QUOTE -38) (LIST (QUOTE -419) (QUOTE (-576))))) (|HasCategory| |#2| (QUOTE (-374)))) (-1277 |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."))) (((-4464 "*") |has| |#1| (-174)) (-4455 |has| |#1| (-568)) (-4456 . T) (-4457 . T) (-4459 . T)) @@ -5043,12 +5043,12 @@ NIL (-1278 |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}."))) (((-4464 "*") |has| |#1| (-174)) (-4455 |has| |#1| (-568)) (-4456 . T) (-4457 . T) (-4459 . T)) -((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -419) (QUOTE (-576))))) (|HasCategory| |#1| (QUOTE (-568))) (-2781 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-568)))) (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-148))) (-12 (|HasCategory| |#1| (LIST (QUOTE -915) (QUOTE (-1195)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (QUOTE (-783)) (|devaluate| |#1|))))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (QUOTE (-783)) (|devaluate| |#1|)))) (|HasCategory| (-783) (QUOTE (-1131))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-783))))) (|HasSignature| |#1| (LIST (QUOTE -3581) (LIST (|devaluate| |#1|) (QUOTE (-1195)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-783))))) (|HasCategory| |#1| (QUOTE (-374))) (-2781 (-12 (|HasCategory| |#1| (LIST (QUOTE -29) (QUOTE (-576)))) (|HasCategory| |#1| (QUOTE (-976))) (|HasCategory| |#1| (QUOTE (-1221))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -419) (QUOTE (-576)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -419) (QUOTE (-576))))) (|HasSignature| |#1| (LIST (QUOTE -4121) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1195))))) (|HasSignature| |#1| (LIST (QUOTE -1934) (LIST (LIST (QUOTE -656) (QUOTE (-1195))) (|devaluate| |#1|))))))) +((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -419) (QUOTE (-576))))) (|HasCategory| |#1| (QUOTE (-568))) (-2755 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-568)))) (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-148))) (-12 (|HasCategory| |#1| (LIST (QUOTE -915) (QUOTE (-1195)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (QUOTE (-783)) (|devaluate| |#1|))))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (QUOTE (-783)) (|devaluate| |#1|)))) (|HasCategory| (-783) (QUOTE (-1131))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-783))))) (|HasSignature| |#1| (LIST (QUOTE -3567) (LIST (|devaluate| |#1|) (QUOTE (-1195)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-783))))) (|HasCategory| |#1| (QUOTE (-374))) (-2755 (-12 (|HasCategory| |#1| (LIST (QUOTE -29) (QUOTE (-576)))) (|HasCategory| |#1| (QUOTE (-976))) (|HasCategory| |#1| (QUOTE (-1221))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -419) (QUOTE (-576)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -419) (QUOTE (-576))))) (|HasSignature| |#1| (LIST (QUOTE -1589) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1195))))) (|HasSignature| |#1| (LIST (QUOTE -1962) (LIST (LIST (QUOTE -656) (QUOTE (-1195))) (|devaluate| |#1|))))))) (-1279 |Coef| UTS) ((|constructor| (NIL "\\indented{1}{This package provides Taylor series solutions to regular} linear or non-linear ordinary differential equations of arbitrary order.")) (|mpsode| (((|List| |#2|) (|List| |#1|) (|List| (|Mapping| |#2| (|List| |#2|)))) "\\spad{mpsode(r,f)} solves the system of differential equations \\spad{dy[i]/dx =f[i] [x,y[1],y[2],...,y[n]]},{} \\spad{y[i](a) = r[i]} for \\spad{i} in 1..\\spad{n}.")) (|ode| ((|#2| (|Mapping| |#2| (|List| |#2|)) (|List| |#1|)) "\\spad{ode(f,cl)} is the solution to \\spad{y<n>=f(y,y',..,y<n-1>)} such that \\spad{y<i>(a) = cl.i} for \\spad{i} in 1..\\spad{n}.")) (|ode2| ((|#2| (|Mapping| |#2| |#2| |#2|) |#1| |#1|) "\\spad{ode2(f,c0,c1)} is the solution to \\spad{y'' = f(y,y')} such that \\spad{y(a) = c0} and \\spad{y'(a) = c1}.")) (|ode1| ((|#2| (|Mapping| |#2| |#2|) |#1|) "\\spad{ode1(f,c)} is the solution to \\spad{y' = f(y)} such that \\spad{y(a) = c}.")) (|fixedPointExquo| ((|#2| |#2| |#2|) "\\spad{fixedPointExquo(f,g)} computes the exact quotient of \\spad{f} and \\spad{g} using a fixed point computation.")) (|stFuncN| (((|Mapping| (|Stream| |#1|) (|List| (|Stream| |#1|))) (|Mapping| |#2| (|List| |#2|))) "\\spad{stFuncN(f)} is a local function xported due to compiler problem. This function is of no interest to the top-level user.")) (|stFunc2| (((|Mapping| (|Stream| |#1|) (|Stream| |#1|) (|Stream| |#1|)) (|Mapping| |#2| |#2| |#2|)) "\\spad{stFunc2(f)} is a local function exported due to compiler problem. This function is of no interest to the top-level user.")) (|stFunc1| (((|Mapping| (|Stream| |#1|) (|Stream| |#1|)) (|Mapping| |#2| |#2|)) "\\spad{stFunc1(f)} is a local function exported due to compiler problem. This function is of no interest to the top-level user."))) NIL NIL -(-1280 -1966 UP L UTS) +(-1280 -1955 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 (-568)))) @@ -5075,7 +5075,7 @@ NIL (-1286 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."))) ((-4463 . T) (-4462 . T)) -((-2781 (-12 (|HasCategory| |#1| (QUOTE (-862))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1119))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|))))) (-2781 (-12 (|HasCategory| |#1| (QUOTE (-1119))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-874))))) (|HasCategory| |#1| (LIST (QUOTE -626) (QUOTE (-548)))) (-2781 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-862))) (|HasCategory| |#1| (QUOTE (-1119)))) (-2781 (|HasCategory| |#1| (QUOTE (-862))) (|HasCategory| |#1| (QUOTE (-1119)))) (|HasCategory| |#1| (QUOTE (-862))) (|HasCategory| (-576) (QUOTE (-862))) (|HasCategory| |#1| (QUOTE (-1119))) (|HasCategory| |#1| (QUOTE (-25))) (|HasCategory| |#1| (QUOTE (-23))) (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-738))) (|HasCategory| |#1| (QUOTE (-1068))) (-12 (|HasCategory| |#1| (QUOTE (-1021))) (|HasCategory| |#1| (QUOTE (-1068)))) (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-874)))) (|HasCategory| |#1| (QUOTE (-102))) (-12 (|HasCategory| |#1| (QUOTE (-1119))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|))))) +((-2755 (-12 (|HasCategory| |#1| (QUOTE (-862))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1119))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|))))) (-2755 (-12 (|HasCategory| |#1| (QUOTE (-1119))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-874))))) (|HasCategory| |#1| (LIST (QUOTE -626) (QUOTE (-548)))) (-2755 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-862))) (|HasCategory| |#1| (QUOTE (-1119)))) (-2755 (|HasCategory| |#1| (QUOTE (-862))) (|HasCategory| |#1| (QUOTE (-1119)))) (|HasCategory| |#1| (QUOTE (-862))) (|HasCategory| (-576) (QUOTE (-862))) (|HasCategory| |#1| (QUOTE (-1119))) (|HasCategory| |#1| (QUOTE (-25))) (|HasCategory| |#1| (QUOTE (-23))) (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-738))) (|HasCategory| |#1| (QUOTE (-1068))) (-12 (|HasCategory| |#1| (QUOTE (-1021))) (|HasCategory| |#1| (QUOTE (-1068)))) (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-874)))) (|HasCategory| |#1| (QUOTE (-102))) (-12 (|HasCategory| |#1| (QUOTE (-1119))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|))))) (-1287) ((|constructor| (NIL "TwoDimensionalViewport creates viewports to display graphs.")) (|coerce| (((|OutputForm|) $) "\\spad{coerce(v)} returns the given two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport} as output of the domain \\spadtype{OutputForm}.")) (|key| (((|Integer|) $) "\\spad{key(v)} returns the process ID number of the given two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport}.")) (|reset| (((|Void|) $) "\\spad{reset(v)} sets the current state of the graph characteristics of the given two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport},{} back to their initial settings.")) (|write| (((|String|) $ (|String|) (|List| (|String|))) "\\spad{write(v,s,lf)} takes the given two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport},{} and creates a directory indicated by \\spad{s},{} which contains the graph data files for \\spad{v} and the optional file types indicated by the list \\spad{lf}.") (((|String|) $ (|String|) (|String|)) "\\spad{write(v,s,f)} takes the given two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport},{} and creates a directory indicated by \\spad{s},{} which contains the graph data files for \\spad{v} and an optional file type \\spad{f}.") (((|String|) $ (|String|)) "\\spad{write(v,s)} takes the given two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport},{} and creates a directory indicated by \\spad{s},{} which contains the graph data files for \\spad{v}.")) (|resize| (((|Void|) $ (|PositiveInteger|) (|PositiveInteger|)) "\\spad{resize(v,w,h)} displays the two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport},{} with a width of \\spad{w} and a height of \\spad{h},{} keeping the upper left-hand corner position unchanged.")) (|update| (((|Void|) $ (|GraphImage|) (|PositiveInteger|)) "\\spad{update(v,gr,n)} drops the graph \\spad{gr} in slot \\spad{n} of viewport \\spad{v}. The graph \\spad{gr} must have been transmitted already and acquired an integer key.")) (|move| (((|Void|) $ (|NonNegativeInteger|) (|NonNegativeInteger|)) "\\spad{move(v,x,y)} displays the two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport},{} with the upper left-hand corner of the viewport window at the screen coordinate position \\spad{x},{} \\spad{y}.")) (|show| (((|Void|) $ (|PositiveInteger|) (|String|)) "\\spad{show(v,n,s)} displays the graph in field \\spad{n} of the given two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport},{} if \\spad{s} is \"on\",{} or does not display the graph if \\spad{s} is \"off\".")) (|translate| (((|Void|) $ (|PositiveInteger|) (|Float|) (|Float|)) "\\spad{translate(v,n,dx,dy)} displays the graph in field \\spad{n} of the given two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport},{} translated by \\spad{dx} in the \\spad{x}-coordinate direction from the center of the viewport,{} and by \\spad{dy} in the \\spad{y}-coordinate direction from the center. Setting \\spad{dx} and \\spad{dy} to \\spad{0} places the center of the graph at the center of the viewport.")) (|scale| (((|Void|) $ (|PositiveInteger|) (|Float|) (|Float|)) "\\spad{scale(v,n,sx,sy)} displays the graph in field \\spad{n} of the given two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport},{} scaled by the factor \\spad{sx} in the \\spad{x}-coordinate direction and by the factor \\spad{sy} in the \\spad{y}-coordinate direction.")) (|dimensions| (((|Void|) $ (|NonNegativeInteger|) (|NonNegativeInteger|) (|PositiveInteger|) (|PositiveInteger|)) "\\spad{dimensions(v,x,y,width,height)} sets the position of the upper left-hand corner of the two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport},{} to the window coordinate \\spad{x},{} \\spad{y},{} and sets the dimensions of the window to that of \\spad{width},{} \\spad{height}. The new dimensions are not displayed until the function \\spadfun{makeViewport2D} is executed again for \\spad{v}.")) (|close| (((|Void|) $) "\\spad{close(v)} closes the viewport window of the given two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport},{} and terminates the corresponding process ID.")) (|controlPanel| (((|Void|) $ (|String|)) "\\spad{controlPanel(v,s)} displays the control panel of the given two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport},{} if \\spad{s} is \"on\",{} or hides the control panel if \\spad{s} is \"off\".")) (|connect| (((|Void|) $ (|PositiveInteger|) (|String|)) "\\spad{connect(v,n,s)} displays the lines connecting the graph points in field \\spad{n} of the given two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport},{} if \\spad{s} is \"on\",{} or does not display the lines if \\spad{s} is \"off\".")) (|region| (((|Void|) $ (|PositiveInteger|) (|String|)) "\\spad{region(v,n,s)} displays the bounding box of the graph in field \\spad{n} of the given two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport},{} if \\spad{s} is \"on\",{} or does not display the bounding box if \\spad{s} is \"off\".")) (|points| (((|Void|) $ (|PositiveInteger|) (|String|)) "\\spad{points(v,n,s)} displays the points of the graph in field \\spad{n} of the given two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport},{} if \\spad{s} is \"on\",{} or does not display the points if \\spad{s} is \"off\".")) (|units| (((|Void|) $ (|PositiveInteger|) (|Palette|)) "\\spad{units(v,n,c)} displays the units of the graph in field \\spad{n} of the given two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport},{} with the units color set to the given palette color \\spad{c}.") (((|Void|) $ (|PositiveInteger|) (|String|)) "\\spad{units(v,n,s)} displays the units of the graph in field \\spad{n} of the given two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport},{} if \\spad{s} is \"on\",{} or does not display the units if \\spad{s} is \"off\".")) (|axes| (((|Void|) $ (|PositiveInteger|) (|Palette|)) "\\spad{axes(v,n,c)} displays the axes of the graph in field \\spad{n} of the given two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport},{} with the axes color set to the given palette color \\spad{c}.") (((|Void|) $ (|PositiveInteger|) (|String|)) "\\spad{axes(v,n,s)} displays the axes of the graph in field \\spad{n} of the given two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport},{} if \\spad{s} is \"on\",{} or does not display the axes if \\spad{s} is \"off\".")) (|getGraph| (((|GraphImage|) $ (|PositiveInteger|)) "\\spad{getGraph(v,n)} returns the graph which is of the domain \\spadtype{GraphImage} which is located in graph field \\spad{n} of the given two-dimensional viewport,{} \\spad{v},{} which is of the domain \\spadtype{TwoDimensionalViewport}.")) (|putGraph| (((|Void|) $ (|GraphImage|) (|PositiveInteger|)) "\\spad{putGraph(v,gi,n)} sets the graph field indicated by \\spad{n},{} of the indicated two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport},{} to be the graph,{} \\spad{gi} of domain \\spadtype{GraphImage}. The contents of viewport,{} \\spad{v},{} will contain \\spad{gi} when the function \\spadfun{makeViewport2D} is called to create the an updated viewport \\spad{v}.")) (|title| (((|Void|) $ (|String|)) "\\spad{title(v,s)} changes the title which is shown in the two-dimensional viewport window,{} \\spad{v} of domain \\spadtype{TwoDimensionalViewport}.")) (|graphs| (((|Vector| (|Union| (|GraphImage|) "undefined")) $) "\\spad{graphs(v)} returns a vector,{} or list,{} which is a union of all the graphs,{} of the domain \\spadtype{GraphImage},{} which are allocated for the two-dimensional viewport,{} \\spad{v},{} of domain \\spadtype{TwoDimensionalViewport}. Those graphs which have no data are labeled \"undefined\",{} otherwise their contents are shown.")) (|graphStates| (((|Vector| (|Record| (|:| |scaleX| (|DoubleFloat|)) (|:| |scaleY| (|DoubleFloat|)) (|:| |deltaX| (|DoubleFloat|)) (|:| |deltaY| (|DoubleFloat|)) (|:| |points| (|Integer|)) (|:| |connect| (|Integer|)) (|:| |spline| (|Integer|)) (|:| |axes| (|Integer|)) (|:| |axesColor| (|Palette|)) (|:| |units| (|Integer|)) (|:| |unitsColor| (|Palette|)) (|:| |showing| (|Integer|)))) $) "\\spad{graphStates(v)} returns and shows a listing of a record containing the current state of the characteristics of each of the ten graph records in the given two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport}.")) (|graphState| (((|Void|) $ (|PositiveInteger|) (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|) (|Integer|) (|Integer|) (|Integer|) (|Integer|) (|Palette|) (|Integer|) (|Palette|) (|Integer|)) "\\spad{graphState(v,num,sX,sY,dX,dY,pts,lns,box,axes,axesC,un,unC,cP)} sets the state of the characteristics for the graph indicated by \\spad{num} in the given two-dimensional viewport \\spad{v},{} of domain \\spadtype{TwoDimensionalViewport},{} to the values given as parameters. The scaling of the graph in the \\spad{x} and \\spad{y} component directions is set to be \\spad{sX} and \\spad{sY}; the window translation in the \\spad{x} and \\spad{y} component directions is set to be \\spad{dX} and \\spad{dY}; The graph points,{} lines,{} bounding \\spad{box},{} \\spad{axes},{} or units will be shown in the viewport if their given parameters \\spad{pts},{} \\spad{lns},{} \\spad{box},{} \\spad{axes} or \\spad{un} are set to be \\spad{1},{} but will not be shown if they are set to \\spad{0}. The color of the \\spad{axes} and the color of the units are indicated by the palette colors \\spad{axesC} and \\spad{unC} respectively. To display the control panel when the viewport window is displayed,{} set \\spad{cP} to \\spad{1},{} otherwise set it to \\spad{0}.")) (|options| (($ $ (|List| (|DrawOption|))) "\\spad{options(v,lopt)} takes the given two-dimensional viewport,{} \\spad{v},{} of the domain \\spadtype{TwoDimensionalViewport} and returns \\spad{v} with it\\spad{'s} draw options modified to be those which are indicated in the given list,{} \\spad{lopt} of domain \\spadtype{DrawOption}.") (((|List| (|DrawOption|)) $) "\\spad{options(v)} takes the given two-dimensional viewport,{} \\spad{v},{} of the domain \\spadtype{TwoDimensionalViewport} and returns a list containing the draw options from the domain \\spadtype{DrawOption} for \\spad{v}.")) (|makeViewport2D| (($ (|GraphImage|) (|List| (|DrawOption|))) "\\spad{makeViewport2D(gi,lopt)} creates and displays a viewport window of the domain \\spadtype{TwoDimensionalViewport} whose graph field is assigned to be the given graph,{} \\spad{gi},{} of domain \\spadtype{GraphImage},{} and whose options field is set to be the list of options,{} \\spad{lopt} of domain \\spadtype{DrawOption}.") (($ $) "\\spad{makeViewport2D(v)} takes the given two-dimensional viewport,{} \\spad{v},{} of the domain \\spadtype{TwoDimensionalViewport} and displays a viewport window on the screen which contains the contents of \\spad{v}.")) (|viewport2D| (($) "\\spad{viewport2D()} returns an undefined two-dimensional viewport of the domain \\spadtype{TwoDimensionalViewport} whose contents are empty.")) (|getPickedPoints| (((|List| (|Point| (|DoubleFloat|))) $) "\\spad{getPickedPoints(x)} returns a list of small floats for the points the user interactively picked on the viewport for full integration into the system,{} some design issues need to be addressed: \\spadignore{e.g.} how to go through the GraphImage interface,{} how to default to graphs,{} etc."))) NIL @@ -5108,7 +5108,7 @@ NIL ((|constructor| (NIL "This package implements the Weierstrass preparation theorem \\spad{f} or multivariate power series. weierstrass(\\spad{v},{}\\spad{p}) where \\spad{v} is a variable,{} and \\spad{p} is a TaylorSeries(\\spad{R}) in which the terms of lowest degree \\spad{s} must include c*v**s where \\spad{c} is a constant,{}\\spad{s>0},{} is a list of TaylorSeries coefficients A[\\spad{i}] of the equivalent polynomial A = A[0] + A[1]\\spad{*v} + A[2]*v**2 + ... + A[\\spad{s}-1]*v**(\\spad{s}-1) + v**s such that p=A*B ,{} \\spad{B} being a TaylorSeries of minimum degree 0")) (|qqq| (((|Mapping| (|Stream| (|TaylorSeries| |#1|)) (|Stream| (|TaylorSeries| |#1|))) (|NonNegativeInteger|) (|TaylorSeries| |#1|) (|Stream| (|TaylorSeries| |#1|))) "\\spad{qqq(n,s,st)} is used internally.")) (|weierstrass| (((|List| (|TaylorSeries| |#1|)) (|Symbol|) (|TaylorSeries| |#1|)) "\\spad{weierstrass(v,ts)} where \\spad{v} is a variable and \\spad{ts} is \\indented{1}{a TaylorSeries,{} impements the Weierstrass Preparation} \\indented{1}{Theorem. The result is a list of TaylorSeries that} \\indented{1}{are the coefficients of the equivalent series.}")) (|clikeUniv| (((|Mapping| (|SparseUnivariatePolynomial| (|Polynomial| |#1|)) (|Polynomial| |#1|)) (|Symbol|)) "\\spad{clikeUniv(v)} is used internally.")) (|sts2stst| (((|Stream| (|Stream| (|Polynomial| |#1|))) (|Symbol|) (|Stream| (|Polynomial| |#1|))) "\\spad{sts2stst(v,s)} is used internally.")) (|cfirst| (((|Mapping| (|Stream| (|Polynomial| |#1|)) (|Stream| (|Polynomial| |#1|))) (|NonNegativeInteger|)) "\\spad{cfirst n} is used internally.")) (|crest| (((|Mapping| (|Stream| (|Polynomial| |#1|)) (|Stream| (|Polynomial| |#1|))) (|NonNegativeInteger|)) "\\spad{crest n} is used internally."))) NIL NIL -(-1295 K R UP -1966) +(-1295 K R UP -1955) ((|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 @@ -5144,11 +5144,11 @@ NIL ((|constructor| (NIL "This category specifies opeations for polynomials and formal series with non-commutative variables.")) (|varList| (((|List| |#1|) $) "\\spad{varList(x)} returns the list of variables which appear in \\spad{x}.")) (|map| (($ (|Mapping| |#2| |#2|) $) "\\spad{map(fn,x)} returns \\spad{Sum(fn(r_i) w_i)} if \\spad{x} writes \\spad{Sum(r_i w_i)}.")) (|sh| (($ $ (|NonNegativeInteger|)) "\\spad{sh(x,n)} returns the shuffle power of \\spad{x} to the \\spad{n}.") (($ $ $) "\\spad{sh(x,y)} returns the shuffle-product of \\spad{x} by \\spad{y}. This multiplication is associative and commutative.")) (|quasiRegular| (($ $) "\\spad{quasiRegular(x)} return \\spad{x} minus its constant term.")) (|quasiRegular?| (((|Boolean|) $) "\\spad{quasiRegular?(x)} return \\spad{true} if \\spad{constant(x)} is zero.")) (|constant| ((|#2| $) "\\spad{constant(x)} returns the constant term of \\spad{x}.")) (|constant?| (((|Boolean|) $) "\\spad{constant?(x)} returns \\spad{true} if \\spad{x} is constant.")) (|coerce| (($ |#1|) "\\spad{coerce(v)} returns \\spad{v}.")) (|mirror| (($ $) "\\spad{mirror(x)} returns \\spad{Sum(r_i mirror(w_i))} if \\spad{x} writes \\spad{Sum(r_i w_i)}.")) (|monomial?| (((|Boolean|) $) "\\spad{monomial?(x)} returns \\spad{true} if \\spad{x} is a monomial")) (|monom| (($ (|OrderedFreeMonoid| |#1|) |#2|) "\\spad{monom(w,r)} returns the product of the word \\spad{w} by the coefficient \\spad{r}.")) (|rquo| (($ $ $) "\\spad{rquo(x,y)} returns the right simplification of \\spad{x} by \\spad{y}.") (($ $ (|OrderedFreeMonoid| |#1|)) "\\spad{rquo(x,w)} returns the right simplification of \\spad{x} by \\spad{w}.") (($ $ |#1|) "\\spad{rquo(x,v)} returns the right simplification of \\spad{x} by the variable \\spad{v}.")) (|lquo| (($ $ $) "\\spad{lquo(x,y)} returns the left simplification of \\spad{x} by \\spad{y}.") (($ $ (|OrderedFreeMonoid| |#1|)) "\\spad{lquo(x,w)} returns the left simplification of \\spad{x} by the word \\spad{w}.") (($ $ |#1|) "\\spad{lquo(x,v)} returns the left simplification of \\spad{x} by the variable \\spad{v}.")) (|coef| ((|#2| $ $) "\\spad{coef(x,y)} returns scalar product of \\spad{x} by \\spad{y},{} the set of words being regarded as an orthogonal basis.") ((|#2| $ (|OrderedFreeMonoid| |#1|)) "\\spad{coef(x,w)} returns the coefficient of the word \\spad{w} in \\spad{x}.")) (|mindegTerm| (((|Record| (|:| |k| (|OrderedFreeMonoid| |#1|)) (|:| |c| |#2|)) $) "\\spad{mindegTerm(x)} returns the term whose word is \\spad{mindeg(x)}.")) (|mindeg| (((|OrderedFreeMonoid| |#1|) $) "\\spad{mindeg(x)} returns the little word which appears in \\spad{x}. Error if \\spad{x=0}.")) (* (($ $ |#2|) "\\spad{x * r} returns the product of \\spad{x} by \\spad{r}. Usefull if \\spad{R} is a non-commutative Ring.") (($ |#1| $) "\\spad{v * x} returns the product of a variable \\spad{x} by \\spad{x}."))) ((-4455 |has| |#2| (-6 -4455)) (-4457 . T) (-4456 . T) (-4459 . T)) NIL -(-1304 S -1966) +(-1304 S -1955) ((|constructor| (NIL "ExtensionField {\\em F} is the category of fields which extend the field \\spad{F}")) (|Frobenius| (($ $ (|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|) $) "\\spad{algebraic?(a)} tests whether an element \\spad{a} is algebraic with respect to the ground field \\spad{F}."))) NIL ((|HasCategory| |#2| (QUOTE (-379))) (|HasCategory| |#2| (QUOTE (-146))) (|HasCategory| |#2| (QUOTE (-148)))) -(-1305 -1966) +(-1305 -1955) ((|constructor| (NIL "ExtensionField {\\em F} is the category of fields which extend the field \\spad{F}")) (|Frobenius| (($ $ (|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}."))) ((-4454 . T) (-4460 . T) (-4455 . T) ((-4464 "*") . T) (-4456 . T) (-4457 . T) (-4459 . T)) NIL @@ -5208,4 +5208,4 @@ NIL NIL NIL NIL -((-3 NIL 2293172 2293177 2293182 2293187) (-2 NIL 2293152 2293157 2293162 2293167) (-1 NIL 2293132 2293137 2293142 2293147) (0 NIL 2293112 2293117 2293122 2293127) (-1315 "ZMOD.spad" 2292921 2292934 2293050 2293107) (-1314 "ZLINDEP.spad" 2291987 2291998 2292911 2292916) (-1313 "ZDSOLVE.spad" 2281932 2281954 2291977 2291982) (-1312 "YSTREAM.spad" 2281427 2281438 2281922 2281927) (-1311 "YDIAGRAM.spad" 2281061 2281070 2281417 2281422) (-1310 "XRPOLY.spad" 2280281 2280301 2280917 2280986) (-1309 "XPR.spad" 2278076 2278089 2279999 2280098) (-1308 "XPOLY.spad" 2277631 2277642 2277932 2278001) (-1307 "XPOLYC.spad" 2276950 2276966 2277557 2277626) (-1306 "XPBWPOLY.spad" 2275387 2275407 2276730 2276799) (-1305 "XF.spad" 2273850 2273865 2275289 2275382) (-1304 "XF.spad" 2272293 2272310 2273734 2273739) (-1303 "XFALG.spad" 2269341 2269357 2272219 2272288) (-1302 "XEXPPKG.spad" 2268592 2268618 2269331 2269336) (-1301 "XDPOLY.spad" 2268206 2268222 2268448 2268517) (-1300 "XALG.spad" 2267866 2267877 2268162 2268201) (-1299 "WUTSET.spad" 2263669 2263686 2267476 2267503) (-1298 "WP.spad" 2262868 2262912 2263527 2263594) (-1297 "WHILEAST.spad" 2262666 2262675 2262858 2262863) (-1296 "WHEREAST.spad" 2262337 2262346 2262656 2262661) (-1295 "WFFINTBS.spad" 2260000 2260022 2262327 2262332) (-1294 "WEIER.spad" 2258222 2258233 2259990 2259995) (-1293 "VSPACE.spad" 2257895 2257906 2258190 2258217) (-1292 "VSPACE.spad" 2257588 2257601 2257885 2257890) (-1291 "VOID.spad" 2257265 2257274 2257578 2257583) (-1290 "VIEW.spad" 2254945 2254954 2257255 2257260) (-1289 "VIEWDEF.spad" 2250146 2250155 2254935 2254940) (-1288 "VIEW3D.spad" 2234107 2234116 2250136 2250141) (-1287 "VIEW2D.spad" 2221998 2222007 2234097 2234102) (-1286 "VECTOR.spad" 2220519 2220530 2220770 2220797) (-1285 "VECTOR2.spad" 2219158 2219171 2220509 2220514) (-1284 "VECTCAT.spad" 2217062 2217073 2219126 2219153) (-1283 "VECTCAT.spad" 2214773 2214786 2216839 2216844) (-1282 "VARIABLE.spad" 2214553 2214568 2214763 2214768) (-1281 "UTYPE.spad" 2214197 2214206 2214543 2214548) (-1280 "UTSODETL.spad" 2213492 2213516 2214153 2214158) (-1279 "UTSODE.spad" 2211708 2211728 2213482 2213487) (-1278 "UTS.spad" 2206655 2206683 2210175 2210272) (-1277 "UTSCAT.spad" 2204134 2204150 2206553 2206650) (-1276 "UTSCAT.spad" 2201257 2201275 2203678 2203683) (-1275 "UTS2.spad" 2200852 2200887 2201247 2201252) (-1274 "URAGG.spad" 2195525 2195536 2200842 2200847) (-1273 "URAGG.spad" 2190162 2190175 2195481 2195486) (-1272 "UPXSSING.spad" 2187807 2187833 2189243 2189376) (-1271 "UPXS.spad" 2185103 2185131 2185939 2186088) (-1270 "UPXSCONS.spad" 2182862 2182882 2183235 2183384) (-1269 "UPXSCCA.spad" 2181433 2181453 2182708 2182857) (-1268 "UPXSCCA.spad" 2180146 2180168 2181423 2181428) (-1267 "UPXSCAT.spad" 2178735 2178751 2179992 2180141) (-1266 "UPXS2.spad" 2178278 2178331 2178725 2178730) (-1265 "UPSQFREE.spad" 2176692 2176706 2178268 2178273) (-1264 "UPSCAT.spad" 2174479 2174503 2176590 2176687) (-1263 "UPSCAT.spad" 2171972 2171998 2174085 2174090) (-1262 "UPOLYC.spad" 2167012 2167023 2171814 2171967) (-1261 "UPOLYC.spad" 2161944 2161957 2166748 2166753) (-1260 "UPOLYC2.spad" 2161415 2161434 2161934 2161939) (-1259 "UP.spad" 2158521 2158536 2158908 2159061) (-1258 "UPMP.spad" 2157421 2157434 2158511 2158516) (-1257 "UPDIVP.spad" 2156986 2157000 2157411 2157416) (-1256 "UPDECOMP.spad" 2155231 2155245 2156976 2156981) (-1255 "UPCDEN.spad" 2154440 2154456 2155221 2155226) (-1254 "UP2.spad" 2153804 2153825 2154430 2154435) (-1253 "UNISEG.spad" 2153157 2153168 2153723 2153728) (-1252 "UNISEG2.spad" 2152654 2152667 2153113 2153118) (-1251 "UNIFACT.spad" 2151757 2151769 2152644 2152649) (-1250 "ULS.spad" 2141541 2141569 2142486 2142915) (-1249 "ULSCONS.spad" 2132675 2132695 2133045 2133194) (-1248 "ULSCCAT.spad" 2130412 2130432 2132521 2132670) (-1247 "ULSCCAT.spad" 2128257 2128279 2130368 2130373) (-1246 "ULSCAT.spad" 2126489 2126505 2128103 2128252) (-1245 "ULS2.spad" 2126003 2126056 2126479 2126484) (-1244 "UINT8.spad" 2125880 2125889 2125993 2125998) (-1243 "UINT64.spad" 2125756 2125765 2125870 2125875) (-1242 "UINT32.spad" 2125632 2125641 2125746 2125751) (-1241 "UINT16.spad" 2125508 2125517 2125622 2125627) (-1240 "UFD.spad" 2124573 2124582 2125434 2125503) (-1239 "UFD.spad" 2123700 2123711 2124563 2124568) (-1238 "UDVO.spad" 2122581 2122590 2123690 2123695) (-1237 "UDPO.spad" 2120074 2120085 2122537 2122542) (-1236 "TYPE.spad" 2120006 2120015 2120064 2120069) (-1235 "TYPEAST.spad" 2119925 2119934 2119996 2120001) (-1234 "TWOFACT.spad" 2118577 2118592 2119915 2119920) (-1233 "TUPLE.spad" 2118063 2118074 2118476 2118481) (-1232 "TUBETOOL.spad" 2114930 2114939 2118053 2118058) (-1231 "TUBE.spad" 2113577 2113594 2114920 2114925) (-1230 "TS.spad" 2112176 2112192 2113142 2113239) (-1229 "TSETCAT.spad" 2099303 2099320 2112144 2112171) (-1228 "TSETCAT.spad" 2086416 2086435 2099259 2099264) (-1227 "TRMANIP.spad" 2080782 2080799 2086122 2086127) (-1226 "TRIMAT.spad" 2079745 2079770 2080772 2080777) (-1225 "TRIGMNIP.spad" 2078272 2078289 2079735 2079740) (-1224 "TRIGCAT.spad" 2077784 2077793 2078262 2078267) (-1223 "TRIGCAT.spad" 2077294 2077305 2077774 2077779) (-1222 "TREE.spad" 2075752 2075763 2076784 2076811) (-1221 "TRANFUN.spad" 2075591 2075600 2075742 2075747) (-1220 "TRANFUN.spad" 2075428 2075439 2075581 2075586) (-1219 "TOPSP.spad" 2075102 2075111 2075418 2075423) (-1218 "TOOLSIGN.spad" 2074765 2074776 2075092 2075097) (-1217 "TEXTFILE.spad" 2073326 2073335 2074755 2074760) (-1216 "TEX.spad" 2070472 2070481 2073316 2073321) (-1215 "TEX1.spad" 2070028 2070039 2070462 2070467) (-1214 "TEMUTL.spad" 2069583 2069592 2070018 2070023) (-1213 "TBCMPPK.spad" 2067676 2067699 2069573 2069578) (-1212 "TBAGG.spad" 2066726 2066749 2067656 2067671) (-1211 "TBAGG.spad" 2065784 2065809 2066716 2066721) (-1210 "TANEXP.spad" 2065192 2065203 2065774 2065779) (-1209 "TALGOP.spad" 2064916 2064927 2065182 2065187) (-1208 "TABLE.spad" 2062885 2062908 2063155 2063182) (-1207 "TABLEAU.spad" 2062366 2062377 2062875 2062880) (-1206 "TABLBUMP.spad" 2059169 2059180 2062356 2062361) (-1205 "SYSTEM.spad" 2058397 2058406 2059159 2059164) (-1204 "SYSSOLP.spad" 2055880 2055891 2058387 2058392) (-1203 "SYSPTR.spad" 2055779 2055788 2055870 2055875) (-1202 "SYSNNI.spad" 2054961 2054972 2055769 2055774) (-1201 "SYSINT.spad" 2054365 2054376 2054951 2054956) (-1200 "SYNTAX.spad" 2050571 2050580 2054355 2054360) (-1199 "SYMTAB.spad" 2048639 2048648 2050561 2050566) (-1198 "SYMS.spad" 2044662 2044671 2048629 2048634) (-1197 "SYMPOLY.spad" 2043669 2043680 2043751 2043878) (-1196 "SYMFUNC.spad" 2043170 2043181 2043659 2043664) (-1195 "SYMBOL.spad" 2040673 2040682 2043160 2043165) (-1194 "SWITCH.spad" 2037444 2037453 2040663 2040668) (-1193 "SUTS.spad" 2034492 2034520 2035911 2036008) (-1192 "SUPXS.spad" 2031775 2031803 2032624 2032773) (-1191 "SUP.spad" 2028495 2028506 2029268 2029421) (-1190 "SUPFRACF.spad" 2027600 2027618 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1577112 1577117) (-967 "POLYCATQ.spad" 1574505 1574527 1576377 1576382) (-966 "POLYCAT.spad" 1567975 1567996 1574373 1574500) (-965 "POLYCAT.spad" 1560783 1560806 1567183 1567188) (-964 "POLY2UP.spad" 1560235 1560249 1560773 1560778) (-963 "POLY2.spad" 1559832 1559844 1560225 1560230) (-962 "POLUTIL.spad" 1558773 1558802 1559788 1559793) (-961 "POLTOPOL.spad" 1557521 1557536 1558763 1558768) (-960 "POINT.spad" 1556206 1556216 1556293 1556320) (-959 "PNTHEORY.spad" 1552908 1552916 1556196 1556201) (-958 "PMTOOLS.spad" 1551683 1551697 1552898 1552903) (-957 "PMSYM.spad" 1551232 1551242 1551673 1551678) (-956 "PMQFCAT.spad" 1550823 1550837 1551222 1551227) (-955 "PMPRED.spad" 1550302 1550316 1550813 1550818) (-954 "PMPREDFS.spad" 1549756 1549778 1550292 1550297) (-953 "PMPLCAT.spad" 1548836 1548854 1549688 1549693) (-952 "PMLSAGG.spad" 1548421 1548435 1548826 1548831) (-951 "PMKERNEL.spad" 1548000 1548012 1548411 1548416) (-950 "PMINS.spad" 1547580 1547590 1547990 1547995) (-949 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417166) (-301 "ENV.spad" 412175 412183 413487 413492) (-300 "ENTIRER.spad" 411843 411851 412119 412170) (-299 "EMR.spad" 411131 411172 411769 411838) (-298 "ELTAGG.spad" 409385 409404 411121 411126) (-297 "ELTAGG.spad" 407603 407624 409341 409346) (-296 "ELTAB.spad" 407078 407091 407593 407598) (-295 "ELFUTS.spad" 406465 406484 407068 407073) (-294 "ELEMFUN.spad" 406154 406162 406455 406460) (-293 "ELEMFUN.spad" 405841 405851 406144 406149) (-292 "ELAGG.spad" 403812 403822 405821 405836) (-291 "ELAGG.spad" 401720 401732 403731 403736) (-290 "ELABOR.spad" 401066 401074 401710 401715) (-289 "ELABEXPR.spad" 399998 400006 401056 401061) (-288 "EFUPXS.spad" 396774 396804 399954 399959) (-287 "EFULS.spad" 393610 393633 396730 396735) (-286 "EFSTRUC.spad" 391625 391641 393600 393605) (-285 "EF.spad" 386401 386417 391615 391620) (-284 "EAB.spad" 384677 384685 386391 386396) (-283 "E04UCFA.spad" 384213 384221 384667 384672) (-282 "E04NAFA.spad" 383790 383798 384203 384208) (-281 "E04MBFA.spad" 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332382 332409) (-260 "DPOLCAT.spad" 325941 325957 330460 330587) (-259 "DPOLCAT.spad" 321376 321394 325897 325902) (-258 "DPMO.spad" 313136 313152 313274 313487) (-257 "DPMM.spad" 304909 304927 305034 305247) (-256 "DOMTMPLT.spad" 304680 304688 304899 304904) (-255 "DOMCTOR.spad" 304435 304443 304670 304675) (-254 "DOMAIN.spad" 303522 303530 304425 304430) (-253 "DMP.spad" 300782 300797 301352 301479) (-252 "DMEXT.spad" 300649 300659 300750 300777) (-251 "DLP.spad" 300001 300011 300639 300644) (-250 "DLIST.spad" 298427 298437 299031 299058) (-249 "DLAGG.spad" 296844 296854 298417 298422) (-248 "DIVRING.spad" 296386 296394 296788 296839) (-247 "DIVRING.spad" 295972 295982 296376 296381) (-246 "DISPLAY.spad" 294162 294170 295962 295967) (-245 "DIRPROD.spad" 281709 281725 282349 282448) (-244 "DIRPROD2.spad" 280527 280545 281699 281704) (-243 "DIRPCAT.spad" 279720 279736 280423 280522) (-242 "DIRPCAT.spad" 278540 278558 279245 279250) (-241 "DIOSP.spad" 277365 277373 278530 278535) (-240 "DIOPS.spad" 276361 276371 277345 277360) (-239 "DIOPS.spad" 275331 275343 276317 276322) (-238 "DIFRING.spad" 275169 275177 275311 275326) (-237 "DIFFSPC.spad" 274748 274756 275159 275164) (-236 "DIFFSPC.spad" 274325 274335 274738 274743) (-235 "DIFFMOD.spad" 273814 273824 274293 274320) (-234 "DIFFDOM.spad" 272979 272990 273804 273809) (-233 "DIFFDOM.spad" 272142 272155 272969 272974) (-232 "DIFEXT.spad" 271961 271971 272122 272137) (-231 "DIAGG.spad" 271591 271601 271941 271956) (-230 "DIAGG.spad" 271229 271241 271581 271586) (-229 "DHMATRIX.spad" 269424 269434 270569 270596) (-228 "DFSFUN.spad" 263064 263072 269414 269419) (-227 "DFLOAT.spad" 259795 259803 262954 263059) (-226 "DFINTTLS.spad" 258026 258042 259785 259790) (-225 "DERHAM.spad" 255940 255972 258006 258021) (-224 "DEQUEUE.spad" 255147 255157 255430 255457) (-223 "DEGRED.spad" 254764 254778 255137 255142) (-222 "DEFINTRF.spad" 252301 252311 254754 254759) (-221 "DEFINTEF.spad" 250811 250827 252291 252296) (-220 "DEFAST.spad" 250179 250187 250801 250806) (-219 "DECIMAL.spad" 248188 248196 248549 248642) (-218 "DDFACT.spad" 246001 246018 248178 248183) (-217 "DBLRESP.spad" 245601 245625 245991 245996) (-216 "DBASE.spad" 244265 244275 245591 245596) (-215 "DATAARY.spad" 243727 243740 244255 244260) (-214 "D03FAFA.spad" 243555 243563 243717 243722) (-213 "D03EEFA.spad" 243375 243383 243545 243550) (-212 "D03AGNT.spad" 242461 242469 243365 243370) (-211 "D02EJFA.spad" 241923 241931 242451 242456) (-210 "D02CJFA.spad" 241401 241409 241913 241918) (-209 "D02BHFA.spad" 240891 240899 241391 241396) (-208 "D02BBFA.spad" 240381 240389 240881 240886) (-207 "D02AGNT.spad" 235195 235203 240371 240376) (-206 "D01WGTS.spad" 233514 233522 235185 235190) (-205 "D01TRNS.spad" 233491 233499 233504 233509) (-204 "D01GBFA.spad" 233013 233021 233481 233486) (-203 "D01FCFA.spad" 232535 232543 233003 233008) (-202 "D01ASFA.spad" 232003 232011 232525 232530) (-201 "D01AQFA.spad" 231449 231457 231993 231998) (-200 "D01APFA.spad" 230873 230881 231439 231444) (-199 "D01ANFA.spad" 230367 230375 230863 230868) (-198 "D01AMFA.spad" 229877 229885 230357 230362) (-197 "D01ALFA.spad" 229417 229425 229867 229872) (-196 "D01AKFA.spad" 228943 228951 229407 229412) (-195 "D01AJFA.spad" 228466 228474 228933 228938) (-194 "D01AGNT.spad" 224533 224541 228456 228461) (-193 "CYCLOTOM.spad" 224039 224047 224523 224528) (-192 "CYCLES.spad" 220831 220839 224029 224034) (-191 "CVMP.spad" 220248 220258 220821 220826) (-190 "CTRIGMNP.spad" 218748 218764 220238 220243) (-189 "CTOR.spad" 218439 218447 218738 218743) (-188 "CTORKIND.spad" 218042 218050 218429 218434) (-187 "CTORCAT.spad" 217291 217299 218032 218037) (-186 "CTORCAT.spad" 216538 216548 217281 217286) (-185 "CTORCALL.spad" 216127 216137 216528 216533) (-184 "CSTTOOLS.spad" 215372 215385 216117 216122) (-183 "CRFP.spad" 209096 209109 215362 215367) (-182 "CRCEAST.spad" 208816 208824 209086 209091) (-181 "CRAPACK.spad" 207867 207877 208806 208811) (-180 "CPMATCH.spad" 207371 207386 207792 207797) (-179 "CPIMA.spad" 207076 207095 207361 207366) (-178 "COORDSYS.spad" 202085 202095 207066 207071) (-177 "CONTOUR.spad" 201496 201504 202075 202080) (-176 "CONTFRAC.spad" 197246 197256 201398 201491) (-175 "CONDUIT.spad" 197004 197012 197236 197241) (-174 "COMRING.spad" 196678 196686 196942 196999) (-173 "COMPPROP.spad" 196196 196204 196668 196673) (-172 "COMPLPAT.spad" 195963 195978 196186 196191) (-171 "COMPLEX.spad" 191340 191350 191584 191845) (-170 "COMPLEX2.spad" 191055 191067 191330 191335) (-169 "COMPILER.spad" 190604 190612 191045 191050) (-168 "COMPFACT.spad" 190206 190220 190594 190599) (-167 "COMPCAT.spad" 188278 188288 189940 190201) (-166 "COMPCAT.spad" 186078 186090 187742 187747) (-165 "COMMUPC.spad" 185826 185844 186068 186073) (-164 "COMMONOP.spad" 185359 185367 185816 185821) (-163 "COMM.spad" 185170 185178 185349 185354) (-162 "COMMAAST.spad" 184933 184941 185160 185165) (-161 "COMBOPC.spad" 183848 183856 184923 184928) (-160 "COMBINAT.spad" 182615 182625 183838 183843) (-159 "COMBF.spad" 179997 180013 182605 182610) (-158 "COLOR.spad" 178834 178842 179987 179992) (-157 "COLONAST.spad" 178500 178508 178824 178829) (-156 "CMPLXRT.spad" 178211 178228 178490 178495) (-155 "CLLCTAST.spad" 177873 177881 178201 178206) (-154 "CLIP.spad" 173981 173989 177863 177868) (-153 "CLIF.spad" 172636 172652 173937 173976) (-152 "CLAGG.spad" 169141 169151 172626 172631) (-151 "CLAGG.spad" 165517 165529 169004 169009) (-150 "CINTSLPE.spad" 164848 164861 165507 165512) (-149 "CHVAR.spad" 162986 163008 164838 164843) (-148 "CHARZ.spad" 162901 162909 162966 162981) (-147 "CHARPOL.spad" 162411 162421 162891 162896) (-146 "CHARNZ.spad" 162164 162172 162391 162406) (-145 "CHAR.spad" 160038 160046 162154 162159) (-144 "CFCAT.spad" 159366 159374 160028 160033) (-143 "CDEN.spad" 158562 158576 159356 159361) (-142 "CCLASS.spad" 156673 156681 157935 157974) (-141 "CATEGORY.spad" 155715 155723 156663 156668) (-140 "CATCTOR.spad" 155606 155614 155705 155710) (-139 "CATAST.spad" 155224 155232 155596 155601) (-138 "CASEAST.spad" 154938 154946 155214 155219) (-137 "CARTEN.spad" 150305 150329 154928 154933) (-136 "CARTEN2.spad" 149695 149722 150295 150300) (-135 "CARD.spad" 146990 146998 149669 149690) (-134 "CAPSLAST.spad" 146764 146772 146980 146985) (-133 "CACHSET.spad" 146388 146396 146754 146759) (-132 "CABMON.spad" 145943 145951 146378 146383) (-131 "BYTEORD.spad" 145618 145626 145933 145938) (-130 "BYTE.spad" 145045 145053 145608 145613) (-129 "BYTEBUF.spad" 142743 142751 144053 144080) (-128 "BTREE.spad" 141699 141709 142233 142260) (-127 "BTOURN.spad" 140587 140597 141189 141216) (-126 "BTCAT.spad" 139979 139989 140555 140582) (-125 "BTCAT.spad" 139391 139403 139969 139974) (-124 "BTAGG.spad" 138857 138865 139359 139386) (-123 "BTAGG.spad" 138343 138353 138847 138852) (-122 "BSTREE.spad" 136967 136977 137833 137860) (-121 "BRILL.spad" 135164 135175 136957 136962) (-120 "BRAGG.spad" 134104 134114 135154 135159) (-119 "BRAGG.spad" 133008 133020 134060 134065) (-118 "BPADICRT.spad" 130882 130894 131137 131230) (-117 "BPADIC.spad" 130546 130558 130808 130877) (-116 "BOUNDZRO.spad" 130202 130219 130536 130541) (-115 "BOP.spad" 125384 125392 130192 130197) (-114 "BOP1.spad" 122850 122860 125374 125379) (-113 "BOOLE.spad" 122500 122508 122840 122845) (-112 "BOOLEAN.spad" 121938 121946 122490 122495) (-111 "BMODULE.spad" 121650 121662 121906 121933) (-110 "BITS.spad" 121033 121041 121248 121275) (-109 "BINDING.spad" 120446 120454 121023 121028) (-108 "BINARY.spad" 118460 118468 118816 118909) (-107 "BGAGG.spad" 117665 117675 118440 118455) (-106 "BGAGG.spad" 116878 116890 117655 117660) (-105 "BFUNCT.spad" 116442 116450 116858 116873) (-104 "BEZOUT.spad" 115582 115609 116392 116397) (-103 "BBTREE.spad" 112310 112320 115072 115099) (-102 "BASTYPE.spad" 111982 111990 112300 112305) (-101 "BASTYPE.spad" 111652 111662 111972 111977) (-100 "BALFACT.spad" 111111 111124 111642 111647) (-99 "AUTOMOR.spad" 110562 110571 111091 111106) (-98 "ATTREG.spad" 107285 107292 110314 110557) (-97 "ATTRBUT.spad" 103308 103315 107265 107280) (-96 "ATTRAST.spad" 103025 103032 103298 103303) (-95 "ATRIG.spad" 102495 102502 103015 103020) (-94 "ATRIG.spad" 101963 101972 102485 102490) (-93 "ASTCAT.spad" 101867 101874 101953 101958) (-92 "ASTCAT.spad" 101769 101778 101857 101862) (-91 "ASTACK.spad" 100991 101000 101259 101286) (-90 "ASSOCEQ.spad" 99817 99828 100947 100952) (-89 "ASP9.spad" 98898 98911 99807 99812) (-88 "ASP8.spad" 97941 97954 98888 98893) (-87 "ASP80.spad" 97263 97276 97931 97936) (-86 "ASP7.spad" 96423 96436 97253 97258) (-85 "ASP78.spad" 95874 95887 96413 96418) (-84 "ASP77.spad" 95243 95256 95864 95869) (-83 "ASP74.spad" 94335 94348 95233 95238) (-82 "ASP73.spad" 93606 93619 94325 94330) (-81 "ASP6.spad" 92473 92486 93596 93601) (-80 "ASP55.spad" 90982 90995 92463 92468) (-79 "ASP50.spad" 88799 88812 90972 90977) (-78 "ASP4.spad" 88094 88107 88789 88794) (-77 "ASP49.spad" 87093 87106 88084 88089) (-76 "ASP42.spad" 85500 85539 87083 87088) (-75 "ASP41.spad" 84079 84118 85490 85495) (-74 "ASP35.spad" 83067 83080 84069 84074) (-73 "ASP34.spad" 82368 82381 83057 83062) (-72 "ASP33.spad" 81928 81941 82358 82363) (-71 "ASP31.spad" 81068 81081 81918 81923) (-70 "ASP30.spad" 79960 79973 81058 81063) (-69 "ASP29.spad" 79426 79439 79950 79955) (-68 "ASP28.spad" 70699 70712 79416 79421) (-67 "ASP27.spad" 69596 69609 70689 70694) (-66 "ASP24.spad" 68683 68696 69586 69591) (-65 "ASP20.spad" 68147 68160 68673 68678) (-64 "ASP1.spad" 67528 67541 68137 68142) (-63 "ASP19.spad" 62214 62227 67518 67523) (-62 "ASP12.spad" 61628 61641 62204 62209) (-61 "ASP10.spad" 60899 60912 61618 61623) (-60 "ARRAY2.spad" 60142 60151 60389 60416) (-59 "ARRAY1.spad" 58826 58835 59172 59199) (-58 "ARRAY12.spad" 57539 57550 58816 58821) (-57 "ARR2CAT.spad" 53313 53334 57507 57534) (-56 "ARR2CAT.spad" 49107 49130 53303 53308) (-55 "ARITY.spad" 48479 48486 49097 49102) (-54 "APPRULE.spad" 47739 47761 48469 48474) (-53 "APPLYORE.spad" 47358 47371 47729 47734) (-52 "ANY.spad" 46217 46224 47348 47353) (-51 "ANY1.spad" 45288 45297 46207 46212) (-50 "ANTISYM.spad" 43733 43749 45268 45283) (-49 "ANON.spad" 43426 43433 43723 43728) (-48 "AN.spad" 41735 41742 43242 43335) (-47 "AMR.spad" 39920 39931 41633 41730) (-46 "AMR.spad" 37942 37955 39657 39662) (-45 "ALIST.spad" 34842 34863 35192 35219) (-44 "ALGSC.spad" 33977 34003 34714 34767) (-43 "ALGPKG.spad" 29760 29771 33933 33938) (-42 "ALGMFACT.spad" 28953 28967 29750 29755) (-41 "ALGMANIP.spad" 26427 26442 28786 28791) (-40 "ALGFF.spad" 24068 24095 24285 24441) (-39 "ALGFACT.spad" 23195 23205 24058 24063) (-38 "ALGEBRA.spad" 23028 23037 23151 23190) (-37 "ALGEBRA.spad" 22893 22904 23018 23023) (-36 "ALAGG.spad" 22405 22426 22861 22888) (-35 "AHYP.spad" 21786 21793 22395 22400) (-34 "AGG.spad" 20103 20110 21776 21781) (-33 "AGG.spad" 18384 18393 20059 20064) (-32 "AF.spad" 16815 16830 18319 18324) (-31 "ADDAST.spad" 16493 16500 16805 16810) (-30 "ACPLOT.spad" 15084 15091 16483 16488) (-29 "ACFS.spad" 12893 12902 14986 15079) (-28 "ACFS.spad" 10788 10799 12883 12888) (-27 "ACF.spad" 7470 7477 10690 10783) (-26 "ACF.spad" 4238 4247 7460 7465) (-25 "ABELSG.spad" 3779 3786 4228 4233) (-24 "ABELSG.spad" 3318 3327 3769 3774) (-23 "ABELMON.spad" 2861 2868 3308 3313) (-22 "ABELMON.spad" 2402 2411 2851 2856) (-21 "ABELGRP.spad" 2067 2074 2392 2397) (-20 "ABELGRP.spad" 1730 1739 2057 2062) (-19 "A1AGG.spad" 870 879 1698 1725) (-18 "A1AGG.spad" 30 41 860 865))
\ No newline at end of file +((-3 NIL 2293419 2293424 2293429 2293434) (-2 NIL 2293399 2293404 2293409 2293414) (-1 NIL 2293379 2293384 2293389 2293394) (0 NIL 2293359 2293364 2293369 2293374) (-1315 "ZMOD.spad" 2293168 2293181 2293297 2293354) (-1314 "ZLINDEP.spad" 2292234 2292245 2293158 2293163) (-1313 "ZDSOLVE.spad" 2282179 2282201 2292224 2292229) (-1312 "YSTREAM.spad" 2281674 2281685 2282169 2282174) (-1311 "YDIAGRAM.spad" 2281308 2281317 2281664 2281669) (-1310 "XRPOLY.spad" 2280528 2280548 2281164 2281233) (-1309 "XPR.spad" 2278323 2278336 2280246 2280345) (-1308 "XPOLY.spad" 2277878 2277889 2278179 2278248) (-1307 "XPOLYC.spad" 2277197 2277213 2277804 2277873) (-1306 "XPBWPOLY.spad" 2275634 2275654 2276977 2277046) (-1305 "XF.spad" 2274097 2274112 2275536 2275629) (-1304 "XF.spad" 2272540 2272557 2273981 2273986) (-1303 "XFALG.spad" 2269588 2269604 2272466 2272535) (-1302 "XEXPPKG.spad" 2268839 2268865 2269578 2269583) (-1301 "XDPOLY.spad" 2268453 2268469 2268695 2268764) (-1300 "XALG.spad" 2268113 2268124 2268409 2268448) (-1299 "WUTSET.spad" 2263916 2263933 2267723 2267750) (-1298 "WP.spad" 2263115 2263159 2263774 2263841) (-1297 "WHILEAST.spad" 2262913 2262922 2263105 2263110) (-1296 "WHEREAST.spad" 2262584 2262593 2262903 2262908) (-1295 "WFFINTBS.spad" 2260247 2260269 2262574 2262579) (-1294 "WEIER.spad" 2258469 2258480 2260237 2260242) (-1293 "VSPACE.spad" 2258142 2258153 2258437 2258464) (-1292 "VSPACE.spad" 2257835 2257848 2258132 2258137) (-1291 "VOID.spad" 2257512 2257521 2257825 2257830) (-1290 "VIEW.spad" 2255192 2255201 2257502 2257507) (-1289 "VIEWDEF.spad" 2250393 2250402 2255182 2255187) (-1288 "VIEW3D.spad" 2234354 2234363 2250383 2250388) (-1287 "VIEW2D.spad" 2222245 2222254 2234344 2234349) (-1286 "VECTOR.spad" 2220766 2220777 2221017 2221044) (-1285 "VECTOR2.spad" 2219405 2219418 2220756 2220761) (-1284 "VECTCAT.spad" 2217309 2217320 2219373 2219400) (-1283 "VECTCAT.spad" 2215020 2215033 2217086 2217091) (-1282 "VARIABLE.spad" 2214800 2214815 2215010 2215015) (-1281 "UTYPE.spad" 2214444 2214453 2214790 2214795) (-1280 "UTSODETL.spad" 2213739 2213763 2214400 2214405) (-1279 "UTSODE.spad" 2211955 2211975 2213729 2213734) (-1278 "UTS.spad" 2206902 2206930 2210422 2210519) (-1277 "UTSCAT.spad" 2204381 2204397 2206800 2206897) (-1276 "UTSCAT.spad" 2201504 2201522 2203925 2203930) (-1275 "UTS2.spad" 2201099 2201134 2201494 2201499) (-1274 "URAGG.spad" 2195772 2195783 2201089 2201094) (-1273 "URAGG.spad" 2190409 2190422 2195728 2195733) (-1272 "UPXSSING.spad" 2188054 2188080 2189490 2189623) (-1271 "UPXS.spad" 2185350 2185378 2186186 2186335) (-1270 "UPXSCONS.spad" 2183109 2183129 2183482 2183631) (-1269 "UPXSCCA.spad" 2181680 2181700 2182955 2183104) (-1268 "UPXSCCA.spad" 2180393 2180415 2181670 2181675) (-1267 "UPXSCAT.spad" 2178982 2178998 2180239 2180388) (-1266 "UPXS2.spad" 2178525 2178578 2178972 2178977) (-1265 "UPSQFREE.spad" 2176939 2176953 2178515 2178520) (-1264 "UPSCAT.spad" 2174726 2174750 2176837 2176934) (-1263 "UPSCAT.spad" 2172219 2172245 2174332 2174337) (-1262 "UPOLYC.spad" 2167259 2167270 2172061 2172214) (-1261 "UPOLYC.spad" 2162191 2162204 2166995 2167000) (-1260 "UPOLYC2.spad" 2161662 2161681 2162181 2162186) (-1259 "UP.spad" 2158768 2158783 2159155 2159308) (-1258 "UPMP.spad" 2157668 2157681 2158758 2158763) (-1257 "UPDIVP.spad" 2157233 2157247 2157658 2157663) (-1256 "UPDECOMP.spad" 2155478 2155492 2157223 2157228) (-1255 "UPCDEN.spad" 2154687 2154703 2155468 2155473) (-1254 "UP2.spad" 2154051 2154072 2154677 2154682) (-1253 "UNISEG.spad" 2153404 2153415 2153970 2153975) (-1252 "UNISEG2.spad" 2152901 2152914 2153360 2153365) (-1251 "UNIFACT.spad" 2152004 2152016 2152891 2152896) (-1250 "ULS.spad" 2141788 2141816 2142733 2143162) (-1249 "ULSCONS.spad" 2132922 2132942 2133292 2133441) (-1248 "ULSCCAT.spad" 2130659 2130679 2132768 2132917) (-1247 "ULSCCAT.spad" 2128504 2128526 2130615 2130620) (-1246 "ULSCAT.spad" 2126736 2126752 2128350 2128499) (-1245 "ULS2.spad" 2126250 2126303 2126726 2126731) (-1244 "UINT8.spad" 2126127 2126136 2126240 2126245) (-1243 "UINT64.spad" 2126003 2126012 2126117 2126122) (-1242 "UINT32.spad" 2125879 2125888 2125993 2125998) (-1241 "UINT16.spad" 2125755 2125764 2125869 2125874) (-1240 "UFD.spad" 2124820 2124829 2125681 2125750) (-1239 "UFD.spad" 2123947 2123958 2124810 2124815) (-1238 "UDVO.spad" 2122828 2122837 2123937 2123942) (-1237 "UDPO.spad" 2120321 2120332 2122784 2122789) (-1236 "TYPE.spad" 2120253 2120262 2120311 2120316) (-1235 "TYPEAST.spad" 2120172 2120181 2120243 2120248) (-1234 "TWOFACT.spad" 2118824 2118839 2120162 2120167) (-1233 "TUPLE.spad" 2118310 2118321 2118723 2118728) (-1232 "TUBETOOL.spad" 2115177 2115186 2118300 2118305) (-1231 "TUBE.spad" 2113824 2113841 2115167 2115172) (-1230 "TS.spad" 2112423 2112439 2113389 2113486) (-1229 "TSETCAT.spad" 2099550 2099567 2112391 2112418) (-1228 "TSETCAT.spad" 2086663 2086682 2099506 2099511) (-1227 "TRMANIP.spad" 2081029 2081046 2086369 2086374) (-1226 "TRIMAT.spad" 2079992 2080017 2081019 2081024) (-1225 "TRIGMNIP.spad" 2078519 2078536 2079982 2079987) (-1224 "TRIGCAT.spad" 2078031 2078040 2078509 2078514) (-1223 "TRIGCAT.spad" 2077541 2077552 2078021 2078026) (-1222 "TREE.spad" 2075999 2076010 2077031 2077058) (-1221 "TRANFUN.spad" 2075838 2075847 2075989 2075994) (-1220 "TRANFUN.spad" 2075675 2075686 2075828 2075833) (-1219 "TOPSP.spad" 2075349 2075358 2075665 2075670) (-1218 "TOOLSIGN.spad" 2075012 2075023 2075339 2075344) (-1217 "TEXTFILE.spad" 2073573 2073582 2075002 2075007) (-1216 "TEX.spad" 2070719 2070728 2073563 2073568) (-1215 "TEX1.spad" 2070275 2070286 2070709 2070714) (-1214 "TEMUTL.spad" 2069830 2069839 2070265 2070270) (-1213 "TBCMPPK.spad" 2067923 2067946 2069820 2069825) (-1212 "TBAGG.spad" 2066973 2066996 2067903 2067918) (-1211 "TBAGG.spad" 2066031 2066056 2066963 2066968) (-1210 "TANEXP.spad" 2065439 2065450 2066021 2066026) (-1209 "TALGOP.spad" 2065163 2065174 2065429 2065434) (-1208 "TABLE.spad" 2063132 2063155 2063402 2063429) (-1207 "TABLEAU.spad" 2062613 2062624 2063122 2063127) (-1206 "TABLBUMP.spad" 2059416 2059427 2062603 2062608) (-1205 "SYSTEM.spad" 2058644 2058653 2059406 2059411) (-1204 "SYSSOLP.spad" 2056127 2056138 2058634 2058639) (-1203 "SYSPTR.spad" 2056026 2056035 2056117 2056122) (-1202 "SYSNNI.spad" 2055208 2055219 2056016 2056021) (-1201 "SYSINT.spad" 2054612 2054623 2055198 2055203) (-1200 "SYNTAX.spad" 2050818 2050827 2054602 2054607) (-1199 "SYMTAB.spad" 2048886 2048895 2050808 2050813) (-1198 "SYMS.spad" 2044909 2044918 2048876 2048881) (-1197 "SYMPOLY.spad" 2043916 2043927 2043998 2044125) (-1196 "SYMFUNC.spad" 2043417 2043428 2043906 2043911) (-1195 "SYMBOL.spad" 2040920 2040929 2043407 2043412) (-1194 "SWITCH.spad" 2037691 2037700 2040910 2040915) (-1193 "SUTS.spad" 2034739 2034767 2036158 2036255) (-1192 "SUPXS.spad" 2032022 2032050 2032871 2033020) (-1191 "SUP.spad" 2028742 2028753 2029515 2029668) (-1190 "SUPFRACF.spad" 2027847 2027865 2028732 2028737) (-1189 "SUP2.spad" 2027239 2027252 2027837 2027842) (-1188 "SUMRF.spad" 2026213 2026224 2027229 2027234) (-1187 "SUMFS.spad" 2025850 2025867 2026203 2026208) (-1186 "SULS.spad" 2015621 2015649 2016579 2017008) (-1185 "SUCHTAST.spad" 2015390 2015399 2015611 2015616) (-1184 "SUCH.spad" 2015072 2015087 2015380 2015385) (-1183 "SUBSPACE.spad" 2007187 2007202 2015062 2015067) (-1182 "SUBRESP.spad" 2006357 2006371 2007143 2007148) (-1181 "STTF.spad" 2002456 2002472 2006347 2006352) (-1180 "STTFNC.spad" 1998924 1998940 2002446 2002451) (-1179 "STTAYLOR.spad" 1991559 1991570 1998805 1998810) (-1178 "STRTBL.spad" 1989610 1989627 1989759 1989786) (-1177 "STRING.spad" 1988397 1988406 1988618 1988645) (-1176 "STREAM.spad" 1985198 1985209 1987805 1987820) (-1175 "STREAM3.spad" 1984771 1984786 1985188 1985193) (-1174 "STREAM2.spad" 1983899 1983912 1984761 1984766) (-1173 "STREAM1.spad" 1983605 1983616 1983889 1983894) (-1172 "STINPROD.spad" 1982541 1982557 1983595 1983600) (-1171 "STEP.spad" 1981742 1981751 1982531 1982536) (-1170 "STEPAST.spad" 1980976 1980985 1981732 1981737) (-1169 "STBL.spad" 1979060 1979088 1979227 1979242) (-1168 "STAGG.spad" 1978135 1978146 1979050 1979055) (-1167 "STAGG.spad" 1977208 1977221 1978125 1978130) (-1166 "STACK.spad" 1976448 1976459 1976698 1976725) (-1165 "SREGSET.spad" 1974116 1974133 1976058 1976085) (-1164 "SRDCMPK.spad" 1972677 1972697 1974106 1974111) (-1163 "SRAGG.spad" 1967820 1967829 1972645 1972672) (-1162 "SRAGG.spad" 1962983 1962994 1967810 1967815) (-1161 "SQMATRIX.spad" 1960526 1960544 1961442 1961529) (-1160 "SPLTREE.spad" 1954922 1954935 1959806 1959833) (-1159 "SPLNODE.spad" 1951510 1951523 1954912 1954917) (-1158 "SPFCAT.spad" 1950319 1950328 1951500 1951505) (-1157 "SPECOUT.spad" 1948871 1948880 1950309 1950314) (-1156 "SPADXPT.spad" 1940466 1940475 1948861 1948866) (-1155 "spad-parser.spad" 1939931 1939940 1940456 1940461) (-1154 "SPADAST.spad" 1939632 1939641 1939921 1939926) (-1153 "SPACEC.spad" 1923831 1923842 1939622 1939627) (-1152 "SPACE3.spad" 1923607 1923618 1923821 1923826) (-1151 "SORTPAK.spad" 1923156 1923169 1923563 1923568) (-1150 "SOLVETRA.spad" 1920919 1920930 1923146 1923151) (-1149 "SOLVESER.spad" 1919447 1919458 1920909 1920914) (-1148 "SOLVERAD.spad" 1915473 1915484 1919437 1919442) (-1147 "SOLVEFOR.spad" 1913935 1913953 1915463 1915468) (-1146 "SNTSCAT.spad" 1913535 1913552 1913903 1913930) (-1145 "SMTS.spad" 1911807 1911833 1913100 1913197) (-1144 "SMP.spad" 1909282 1909302 1909672 1909799) (-1143 "SMITH.spad" 1908127 1908152 1909272 1909277) (-1142 "SMATCAT.spad" 1906237 1906267 1908071 1908122) (-1141 "SMATCAT.spad" 1904279 1904311 1906115 1906120) (-1140 "SKAGG.spad" 1903242 1903253 1904247 1904274) (-1139 "SINT.spad" 1902182 1902191 1903108 1903237) (-1138 "SIMPAN.spad" 1901910 1901919 1902172 1902177) (-1137 "SIG.spad" 1901240 1901249 1901900 1901905) (-1136 "SIGNRF.spad" 1900358 1900369 1901230 1901235) (-1135 "SIGNEF.spad" 1899637 1899654 1900348 1900353) (-1134 "SIGAST.spad" 1899022 1899031 1899627 1899632) (-1133 "SHP.spad" 1896950 1896965 1898978 1898983) (-1132 "SHDP.spad" 1884628 1884655 1885137 1885236) (-1131 "SGROUP.spad" 1884236 1884245 1884618 1884623) (-1130 "SGROUP.spad" 1883842 1883853 1884226 1884231) (-1129 "SGCF.spad" 1876981 1876990 1883832 1883837) (-1128 "SFRTCAT.spad" 1875911 1875928 1876949 1876976) (-1127 "SFRGCD.spad" 1874974 1874994 1875901 1875906) (-1126 "SFQCMPK.spad" 1869611 1869631 1874964 1874969) (-1125 "SFORT.spad" 1869050 1869064 1869601 1869606) (-1124 "SEXOF.spad" 1868893 1868933 1869040 1869045) (-1123 "SEX.spad" 1868785 1868794 1868883 1868888) (-1122 "SEXCAT.spad" 1866557 1866597 1868775 1868780) (-1121 "SET.spad" 1864845 1864856 1865942 1865981) (-1120 "SETMN.spad" 1863295 1863312 1864835 1864840) (-1119 "SETCAT.spad" 1862617 1862626 1863285 1863290) (-1118 "SETCAT.spad" 1861937 1861948 1862607 1862612) (-1117 "SETAGG.spad" 1858486 1858497 1861917 1861932) (-1116 "SETAGG.spad" 1855043 1855056 1858476 1858481) (-1115 "SEQAST.spad" 1854746 1854755 1855033 1855038) (-1114 "SEGXCAT.spad" 1853902 1853915 1854736 1854741) (-1113 "SEG.spad" 1853715 1853726 1853821 1853826) (-1112 "SEGCAT.spad" 1852640 1852651 1853705 1853710) (-1111 "SEGBIND.spad" 1852398 1852409 1852587 1852592) (-1110 "SEGBIND2.spad" 1852096 1852109 1852388 1852393) (-1109 "SEGAST.spad" 1851810 1851819 1852086 1852091) (-1108 "SEG2.spad" 1851245 1851258 1851766 1851771) (-1107 "SDVAR.spad" 1850521 1850532 1851235 1851240) (-1106 "SDPOL.spad" 1847854 1847865 1848145 1848272) (-1105 "SCPKG.spad" 1845943 1845954 1847844 1847849) (-1104 "SCOPE.spad" 1845096 1845105 1845933 1845938) (-1103 "SCACHE.spad" 1843792 1843803 1845086 1845091) (-1102 "SASTCAT.spad" 1843701 1843710 1843782 1843787) (-1101 "SAOS.spad" 1843573 1843582 1843691 1843696) (-1100 "SAERFFC.spad" 1843286 1843306 1843563 1843568) (-1099 "SAE.spad" 1840756 1840772 1841367 1841502) (-1098 "SAEFACT.spad" 1840457 1840477 1840746 1840751) (-1097 "RURPK.spad" 1838116 1838132 1840447 1840452) (-1096 "RULESET.spad" 1837569 1837593 1838106 1838111) (-1095 "RULE.spad" 1835809 1835833 1837559 1837564) (-1094 "RULECOLD.spad" 1835661 1835674 1835799 1835804) (-1093 "RTVALUE.spad" 1835396 1835405 1835651 1835656) (-1092 "RSTRCAST.spad" 1835113 1835122 1835386 1835391) (-1091 "RSETGCD.spad" 1831491 1831511 1835103 1835108) (-1090 "RSETCAT.spad" 1821427 1821444 1831459 1831486) (-1089 "RSETCAT.spad" 1811383 1811402 1821417 1821422) (-1088 "RSDCMPK.spad" 1809835 1809855 1811373 1811378) (-1087 "RRCC.spad" 1808219 1808249 1809825 1809830) (-1086 "RRCC.spad" 1806601 1806633 1808209 1808214) (-1085 "RPTAST.spad" 1806303 1806312 1806591 1806596) (-1084 "RPOLCAT.spad" 1785663 1785678 1806171 1806298) (-1083 "RPOLCAT.spad" 1764736 1764753 1785246 1785251) (-1082 "ROUTINE.spad" 1760157 1760166 1762921 1762948) (-1081 "ROMAN.spad" 1759485 1759494 1760023 1760152) (-1080 "ROIRC.spad" 1758565 1758597 1759475 1759480) (-1079 "RNS.spad" 1757468 1757477 1758467 1758560) (-1078 "RNS.spad" 1756457 1756468 1757458 1757463) (-1077 "RNG.spad" 1756192 1756201 1756447 1756452) (-1076 "RNGBIND.spad" 1755352 1755366 1756147 1756152) (-1075 "RMODULE.spad" 1755117 1755128 1755342 1755347) (-1074 "RMCAT2.spad" 1754537 1754594 1755107 1755112) (-1073 "RMATRIX.spad" 1753325 1753344 1753668 1753707) (-1072 "RMATCAT.spad" 1748904 1748935 1753281 1753320) (-1071 "RMATCAT.spad" 1744373 1744406 1748752 1748757) (-1070 "RLINSET.spad" 1744077 1744088 1744363 1744368) (-1069 "RINTERP.spad" 1743965 1743985 1744067 1744072) (-1068 "RING.spad" 1743435 1743444 1743945 1743960) (-1067 "RING.spad" 1742913 1742924 1743425 1743430) (-1066 "RIDIST.spad" 1742305 1742314 1742903 1742908) (-1065 "RGCHAIN.spad" 1740833 1740849 1741735 1741762) (-1064 "RGBCSPC.spad" 1740614 1740626 1740823 1740828) (-1063 "RGBCMDL.spad" 1740144 1740156 1740604 1740609) (-1062 "RF.spad" 1737786 1737797 1740134 1740139) (-1061 "RFFACTOR.spad" 1737248 1737259 1737776 1737781) (-1060 "RFFACT.spad" 1736983 1736995 1737238 1737243) (-1059 "RFDIST.spad" 1735979 1735988 1736973 1736978) (-1058 "RETSOL.spad" 1735398 1735411 1735969 1735974) (-1057 "RETRACT.spad" 1734826 1734837 1735388 1735393) (-1056 "RETRACT.spad" 1734252 1734265 1734816 1734821) (-1055 "RETAST.spad" 1734064 1734073 1734242 1734247) (-1054 "RESULT.spad" 1731662 1731671 1732249 1732276) (-1053 "RESRING.spad" 1731009 1731056 1731600 1731657) (-1052 "RESLATC.spad" 1730333 1730344 1730999 1731004) (-1051 "REPSQ.spad" 1730064 1730075 1730323 1730328) (-1050 "REP.spad" 1727618 1727627 1730054 1730059) (-1049 "REPDB.spad" 1727325 1727336 1727608 1727613) (-1048 "REP2.spad" 1716983 1716994 1727167 1727172) (-1047 "REP1.spad" 1711179 1711190 1716933 1716938) (-1046 "REGSET.spad" 1708940 1708957 1710789 1710816) (-1045 "REF.spad" 1708275 1708286 1708895 1708900) (-1044 "REDORDER.spad" 1707481 1707498 1708265 1708270) (-1043 "RECLOS.spad" 1706264 1706284 1706968 1707061) (-1042 "REALSOLV.spad" 1705404 1705413 1706254 1706259) (-1041 "REAL.spad" 1705276 1705285 1705394 1705399) (-1040 "REAL0Q.spad" 1702574 1702589 1705266 1705271) (-1039 "REAL0.spad" 1699418 1699433 1702564 1702569) (-1038 "RDUCEAST.spad" 1699139 1699148 1699408 1699413) (-1037 "RDIV.spad" 1698794 1698819 1699129 1699134) (-1036 "RDIST.spad" 1698361 1698372 1698784 1698789) (-1035 "RDETRS.spad" 1697225 1697243 1698351 1698356) (-1034 "RDETR.spad" 1695364 1695382 1697215 1697220) (-1033 "RDEEFS.spad" 1694463 1694480 1695354 1695359) (-1032 "RDEEF.spad" 1693473 1693490 1694453 1694458) (-1031 "RCFIELD.spad" 1690659 1690668 1693375 1693468) (-1030 "RCFIELD.spad" 1687931 1687942 1690649 1690654) (-1029 "RCAGG.spad" 1685859 1685870 1687921 1687926) (-1028 "RCAGG.spad" 1683714 1683727 1685778 1685783) (-1027 "RATRET.spad" 1683074 1683085 1683704 1683709) (-1026 "RATFACT.spad" 1682766 1682778 1683064 1683069) (-1025 "RANDSRC.spad" 1682085 1682094 1682756 1682761) (-1024 "RADUTIL.spad" 1681841 1681850 1682075 1682080) (-1023 "RADIX.spad" 1678665 1678679 1680211 1680304) (-1022 "RADFF.spad" 1676404 1676441 1676523 1676679) (-1021 "RADCAT.spad" 1675999 1676008 1676394 1676399) (-1020 "RADCAT.spad" 1675592 1675603 1675989 1675994) (-1019 "QUEUE.spad" 1674823 1674834 1675082 1675109) (-1018 "QUAT.spad" 1673311 1673322 1673654 1673719) (-1017 "QUATCT2.spad" 1672931 1672950 1673301 1673306) (-1016 "QUATCAT.spad" 1671101 1671112 1672861 1672926) (-1015 "QUATCAT.spad" 1669022 1669035 1670784 1670789) (-1014 "QUAGG.spad" 1667849 1667860 1668990 1669017) (-1013 "QQUTAST.spad" 1667617 1667626 1667839 1667844) (-1012 "QFORM.spad" 1667235 1667250 1667607 1667612) (-1011 "QFCAT.spad" 1665937 1665948 1667137 1667230) (-1010 "QFCAT.spad" 1664230 1664243 1665432 1665437) (-1009 "QFCAT2.spad" 1663922 1663939 1664220 1664225) (-1008 "QEQUAT.spad" 1663480 1663489 1663912 1663917) (-1007 "QCMPACK.spad" 1658226 1658246 1663470 1663475) (-1006 "QALGSET.spad" 1654304 1654337 1658140 1658145) (-1005 "QALGSET2.spad" 1652299 1652318 1654294 1654299) (-1004 "PWFFINTB.spad" 1649714 1649736 1652289 1652294) (-1003 "PUSHVAR.spad" 1649052 1649072 1649704 1649709) (-1002 "PTRANFN.spad" 1645179 1645190 1649042 1649047) (-1001 "PTPACK.spad" 1642266 1642277 1645169 1645174) (-1000 "PTFUNC2.spad" 1642088 1642103 1642256 1642261) (-999 "PTCAT.spad" 1641343 1641353 1642056 1642083) (-998 "PSQFR.spad" 1640650 1640674 1641333 1641338) (-997 "PSEUDLIN.spad" 1639536 1639546 1640640 1640645) (-996 "PSETPK.spad" 1624969 1624985 1639414 1639419) (-995 "PSETCAT.spad" 1618889 1618912 1624949 1624964) (-994 "PSETCAT.spad" 1612783 1612808 1618845 1618850) (-993 "PSCURVE.spad" 1611766 1611774 1612773 1612778) (-992 "PSCAT.spad" 1610549 1610578 1611664 1611761) (-991 "PSCAT.spad" 1609422 1609453 1610539 1610544) (-990 "PRTITION.spad" 1608120 1608128 1609412 1609417) (-989 "PRTDAST.spad" 1607839 1607847 1608110 1608115) (-988 "PRS.spad" 1597401 1597418 1607795 1607800) (-987 "PRQAGG.spad" 1596836 1596846 1597369 1597396) (-986 "PROPLOG.spad" 1596408 1596416 1596826 1596831) (-985 "PROPFUN2.spad" 1596031 1596044 1596398 1596403) (-984 "PROPFUN1.spad" 1595429 1595440 1596021 1596026) (-983 "PROPFRML.spad" 1593997 1594008 1595419 1595424) (-982 "PROPERTY.spad" 1593485 1593493 1593987 1593992) (-981 "PRODUCT.spad" 1591167 1591179 1591451 1591506) (-980 "PR.spad" 1589559 1589571 1590258 1590385) (-979 "PRINT.spad" 1589311 1589319 1589549 1589554) (-978 "PRIMES.spad" 1587564 1587574 1589301 1589306) (-977 "PRIMELT.spad" 1585645 1585659 1587554 1587559) (-976 "PRIMCAT.spad" 1585272 1585280 1585635 1585640) (-975 "PRIMARR.spad" 1584124 1584134 1584302 1584329) (-974 "PRIMARR2.spad" 1582891 1582903 1584114 1584119) (-973 "PREASSOC.spad" 1582273 1582285 1582881 1582886) (-972 "PPCURVE.spad" 1581410 1581418 1582263 1582268) (-971 "PORTNUM.spad" 1581185 1581193 1581400 1581405) (-970 "POLYROOT.spad" 1580034 1580056 1581141 1581146) (-969 "POLY.spad" 1577369 1577379 1577884 1578011) (-968 "POLYLIFT.spad" 1576634 1576657 1577359 1577364) (-967 "POLYCATQ.spad" 1574752 1574774 1576624 1576629) (-966 "POLYCAT.spad" 1568222 1568243 1574620 1574747) (-965 "POLYCAT.spad" 1561030 1561053 1567430 1567435) (-964 "POLY2UP.spad" 1560482 1560496 1561020 1561025) (-963 "POLY2.spad" 1560079 1560091 1560472 1560477) (-962 "POLUTIL.spad" 1559020 1559049 1560035 1560040) (-961 "POLTOPOL.spad" 1557768 1557783 1559010 1559015) (-960 "POINT.spad" 1556453 1556463 1556540 1556567) (-959 "PNTHEORY.spad" 1553155 1553163 1556443 1556448) (-958 "PMTOOLS.spad" 1551930 1551944 1553145 1553150) (-957 "PMSYM.spad" 1551479 1551489 1551920 1551925) (-956 "PMQFCAT.spad" 1551070 1551084 1551469 1551474) (-955 "PMPRED.spad" 1550549 1550563 1551060 1551065) (-954 "PMPREDFS.spad" 1550003 1550025 1550539 1550544) (-953 "PMPLCAT.spad" 1549083 1549101 1549935 1549940) (-952 "PMLSAGG.spad" 1548668 1548682 1549073 1549078) (-951 "PMKERNEL.spad" 1548247 1548259 1548658 1548663) (-950 "PMINS.spad" 1547827 1547837 1548237 1548242) (-949 "PMFS.spad" 1547404 1547422 1547817 1547822) (-948 "PMDOWN.spad" 1546694 1546708 1547394 1547399) (-947 "PMASS.spad" 1545704 1545712 1546684 1546689) (-946 "PMASSFS.spad" 1544671 1544687 1545694 1545699) (-945 "PLOTTOOL.spad" 1544451 1544459 1544661 1544666) (-944 "PLOT.spad" 1539374 1539382 1544441 1544446) (-943 "PLOT3D.spad" 1535838 1535846 1539364 1539369) (-942 "PLOT1.spad" 1534995 1535005 1535828 1535833) (-941 "PLEQN.spad" 1522285 1522312 1534985 1534990) (-940 "PINTERP.spad" 1521907 1521926 1522275 1522280) (-939 "PINTERPA.spad" 1521691 1521707 1521897 1521902) (-938 "PI.spad" 1521300 1521308 1521665 1521686) (-937 "PID.spad" 1520270 1520278 1521226 1521295) (-936 "PICOERCE.spad" 1519927 1519937 1520260 1520265) (-935 "PGROEB.spad" 1518528 1518542 1519917 1519922) (-934 "PGE.spad" 1510145 1510153 1518518 1518523) (-933 "PGCD.spad" 1509035 1509052 1510135 1510140) (-932 "PFRPAC.spad" 1508184 1508194 1509025 1509030) (-931 "PFR.spad" 1504847 1504857 1508086 1508179) (-930 "PFOTOOLS.spad" 1504105 1504121 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"PARSCURV.spad" 1448309 1448337 1448865 1448870) (-891 "PARSC2.spad" 1448100 1448116 1448299 1448304) (-890 "PARPCURV.spad" 1447562 1447590 1448090 1448095) (-889 "PARPC2.spad" 1447353 1447369 1447552 1447557) (-888 "PARAMAST.spad" 1446481 1446489 1447343 1447348) (-887 "PAN2EXPR.spad" 1445893 1445901 1446471 1446476) (-886 "PALETTE.spad" 1444863 1444871 1445883 1445888) (-885 "PAIR.spad" 1443850 1443863 1444451 1444456) (-884 "PADICRC.spad" 1441091 1441109 1442262 1442355) (-883 "PADICRAT.spad" 1438999 1439011 1439220 1439313) (-882 "PADIC.spad" 1438694 1438706 1438925 1438994) (-881 "PADICCT.spad" 1437243 1437255 1438620 1438689) (-880 "PADEPAC.spad" 1435932 1435951 1437233 1437238) (-879 "PADE.spad" 1434684 1434700 1435922 1435927) (-878 "OWP.spad" 1433924 1433954 1434542 1434609) (-877 "OVERSET.spad" 1433497 1433505 1433914 1433919) (-876 "OVAR.spad" 1433278 1433301 1433487 1433492) (-875 "OUT.spad" 1432364 1432372 1433268 1433273) (-874 "OUTFORM.spad" 1421756 1421764 1432354 1432359) (-873 "OUTBFILE.spad" 1421174 1421182 1421746 1421751) (-872 "OUTBCON.spad" 1420180 1420188 1421164 1421169) (-871 "OUTBCON.spad" 1419184 1419194 1420170 1420175) (-870 "OSI.spad" 1418659 1418667 1419174 1419179) (-869 "OSGROUP.spad" 1418577 1418585 1418649 1418654) (-868 "ORTHPOL.spad" 1417062 1417072 1418494 1418499) (-867 "OREUP.spad" 1416515 1416543 1416742 1416781) (-866 "ORESUP.spad" 1415816 1415840 1416195 1416234) (-865 "OREPCTO.spad" 1413673 1413685 1415736 1415741) (-864 "OREPCAT.spad" 1407820 1407830 1413629 1413668) (-863 "OREPCAT.spad" 1401857 1401869 1407668 1407673) (-862 "ORDSET.spad" 1401029 1401037 1401847 1401852) (-861 "ORDSET.spad" 1400199 1400209 1401019 1401024) (-860 "ORDRING.spad" 1399589 1399597 1400179 1400194) (-859 "ORDRING.spad" 1398987 1398997 1399579 1399584) (-858 "ORDMON.spad" 1398842 1398850 1398977 1398982) (-857 "ORDFUNS.spad" 1397974 1397990 1398832 1398837) (-856 "ORDFIN.spad" 1397794 1397802 1397964 1397969) (-855 "ORDCOMP.spad" 1396259 1396269 1397341 1397370) (-854 "ORDCOMP2.spad" 1395552 1395564 1396249 1396254) (-853 "OPTPROB.spad" 1394190 1394198 1395542 1395547) (-852 "OPTPACK.spad" 1386599 1386607 1394180 1394185) (-851 "OPTCAT.spad" 1384278 1384286 1386589 1386594) (-850 "OPSIG.spad" 1383932 1383940 1384268 1384273) (-849 "OPQUERY.spad" 1383481 1383489 1383922 1383927) (-848 "OP.spad" 1383223 1383233 1383303 1383370) (-847 "OPERCAT.spad" 1382689 1382699 1383213 1383218) (-846 "OPERCAT.spad" 1382153 1382165 1382679 1382684) (-845 "ONECOMP.spad" 1380898 1380908 1381700 1381729) (-844 "ONECOMP2.spad" 1380322 1380334 1380888 1380893) (-843 "OMSERVER.spad" 1379328 1379336 1380312 1380317) (-842 "OMSAGG.spad" 1379116 1379126 1379284 1379323) (-841 "OMPKG.spad" 1377732 1377740 1379106 1379111) (-840 "OM.spad" 1376705 1376713 1377722 1377727) (-839 "OMLO.spad" 1376130 1376142 1376591 1376630) (-838 "OMEXPR.spad" 1375964 1375974 1376120 1376125) (-837 "OMERR.spad" 1375509 1375517 1375954 1375959) (-836 "OMERRK.spad" 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"ODEPACK.spad" 1318545 1318553 1331869 1331874) (-816 "ODEINT.spad" 1317980 1317996 1318535 1318540) (-815 "ODEIFTBL.spad" 1315375 1315383 1317970 1317975) (-814 "ODEEF.spad" 1310866 1310882 1315365 1315370) (-813 "ODECONST.spad" 1310403 1310421 1310856 1310861) (-812 "ODECAT.spad" 1309001 1309009 1310393 1310398) (-811 "OCT.spad" 1307137 1307147 1307851 1307890) (-810 "OCTCT2.spad" 1306783 1306804 1307127 1307132) (-809 "OC.spad" 1304579 1304589 1306739 1306778) (-808 "OC.spad" 1302100 1302112 1304262 1304267) (-807 "OCAMON.spad" 1301948 1301956 1302090 1302095) (-806 "OASGP.spad" 1301763 1301771 1301938 1301943) (-805 "OAMONS.spad" 1301285 1301293 1301753 1301758) (-804 "OAMON.spad" 1301146 1301154 1301275 1301280) (-803 "OAGROUP.spad" 1301008 1301016 1301136 1301141) (-802 "NUMTUBE.spad" 1300599 1300615 1300998 1301003) (-801 "NUMQUAD.spad" 1288575 1288583 1300589 1300594) (-800 "NUMODE.spad" 1279929 1279937 1288565 1288570) (-799 "NUMINT.spad" 1277495 1277503 1279919 1279924) (-798 "NUMFMT.spad" 1276335 1276343 1277485 1277490) (-797 "NUMERIC.spad" 1268449 1268459 1276140 1276145) (-796 "NTSCAT.spad" 1266957 1266973 1268417 1268444) (-795 "NTPOLFN.spad" 1266508 1266518 1266874 1266879) (-794 "NSUP.spad" 1259461 1259471 1264001 1264154) (-793 "NSUP2.spad" 1258853 1258865 1259451 1259456) (-792 "NSMP.spad" 1255083 1255102 1255391 1255518) (-791 "NREP.spad" 1253461 1253475 1255073 1255078) (-790 "NPCOEF.spad" 1252707 1252727 1253451 1253456) (-789 "NORMRETR.spad" 1252305 1252344 1252697 1252702) (-788 "NORMPK.spad" 1250207 1250226 1252295 1252300) (-787 "NORMMA.spad" 1249895 1249921 1250197 1250202) (-786 "NONE.spad" 1249636 1249644 1249885 1249890) (-785 "NONE1.spad" 1249312 1249322 1249626 1249631) (-784 "NODE1.spad" 1248799 1248815 1249302 1249307) (-783 "NNI.spad" 1247694 1247702 1248773 1248794) (-782 "NLINSOL.spad" 1246320 1246330 1247684 1247689) (-781 "NIPROB.spad" 1244861 1244869 1246310 1246315) (-780 "NFINTBAS.spad" 1242421 1242438 1244851 1244856) (-779 "NETCLT.spad" 1242395 1242406 1242411 1242416) (-778 "NCODIV.spad" 1240611 1240627 1242385 1242390) (-777 "NCNTFRAC.spad" 1240253 1240267 1240601 1240606) (-776 "NCEP.spad" 1238419 1238433 1240243 1240248) (-775 "NASRING.spad" 1238015 1238023 1238409 1238414) (-774 "NASRING.spad" 1237609 1237619 1238005 1238010) (-773 "NARNG.spad" 1236961 1236969 1237599 1237604) (-772 "NARNG.spad" 1236311 1236321 1236951 1236956) (-771 "NAGSP.spad" 1235388 1235396 1236301 1236306) (-770 "NAGS.spad" 1225049 1225057 1235378 1235383) (-769 "NAGF07.spad" 1223480 1223488 1225039 1225044) (-768 "NAGF04.spad" 1217882 1217890 1223470 1223475) (-767 "NAGF02.spad" 1211951 1211959 1217872 1217877) (-766 "NAGF01.spad" 1207712 1207720 1211941 1211946) (-765 "NAGE04.spad" 1201412 1201420 1207702 1207707) (-764 "NAGE02.spad" 1192072 1192080 1201402 1201407) (-763 "NAGE01.spad" 1188074 1188082 1192062 1192067) (-762 "NAGD03.spad" 1186078 1186086 1188064 1188069) (-761 "NAGD02.spad" 1178825 1178833 1186068 1186073) (-760 "NAGD01.spad" 1173118 1173126 1178815 1178820) (-759 "NAGC06.spad" 1168993 1169001 1173108 1173113) (-758 "NAGC05.spad" 1167494 1167502 1168983 1168988) (-757 "NAGC02.spad" 1166761 1166769 1167484 1167489) (-756 "NAALG.spad" 1166302 1166312 1166729 1166756) (-755 "NAALG.spad" 1165863 1165875 1166292 1166297) (-754 "MULTSQFR.spad" 1162821 1162838 1165853 1165858) (-753 "MULTFACT.spad" 1162204 1162221 1162811 1162816) (-752 "MTSCAT.spad" 1160298 1160319 1162102 1162199) (-751 "MTHING.spad" 1159957 1159967 1160288 1160293) (-750 "MSYSCMD.spad" 1159391 1159399 1159947 1159952) (-749 "MSET.spad" 1157313 1157323 1159061 1159100) (-748 "MSETAGG.spad" 1157158 1157168 1157281 1157308) (-747 "MRING.spad" 1154135 1154147 1156866 1156933) (-746 "MRF2.spad" 1153705 1153719 1154125 1154130) (-745 "MRATFAC.spad" 1153251 1153268 1153695 1153700) (-744 "MPRFF.spad" 1151291 1151310 1153241 1153246) (-743 "MPOLY.spad" 1148762 1148777 1149121 1149248) (-742 "MPCPF.spad" 1148026 1148045 1148752 1148757) (-741 "MPC3.spad" 1147843 1147883 1148016 1148021) (-740 "MPC2.spad" 1147489 1147522 1147833 1147838) (-739 "MONOTOOL.spad" 1145840 1145857 1147479 1147484) (-738 "MONOID.spad" 1145159 1145167 1145830 1145835) (-737 "MONOID.spad" 1144476 1144486 1145149 1145154) (-736 "MONOGEN.spad" 1143224 1143237 1144336 1144471) (-735 "MONOGEN.spad" 1141994 1142009 1143108 1143113) (-734 "MONADWU.spad" 1140024 1140032 1141984 1141989) (-733 "MONADWU.spad" 1138052 1138062 1140014 1140019) (-732 "MONAD.spad" 1137212 1137220 1138042 1138047) (-731 "MONAD.spad" 1136370 1136380 1137202 1137207) (-730 "MOEBIUS.spad" 1135106 1135120 1136350 1136365) (-729 "MODULE.spad" 1134976 1134986 1135074 1135101) (-728 "MODULE.spad" 1134866 1134878 1134966 1134971) (-727 "MODRING.spad" 1134201 1134240 1134846 1134861) (-726 "MODOP.spad" 1132866 1132878 1134023 1134090) (-725 "MODMONOM.spad" 1132597 1132615 1132856 1132861) (-724 "MODMON.spad" 1129299 1129315 1130018 1130171) (-723 "MODFIELD.spad" 1128661 1128700 1129201 1129294) (-722 "MMLFORM.spad" 1127521 1127529 1128651 1128656) (-721 "MMAP.spad" 1127263 1127297 1127511 1127516) (-720 "MLO.spad" 1125722 1125732 1127219 1127258) (-719 "MLIFT.spad" 1124334 1124351 1125712 1125717) (-718 "MKUCFUNC.spad" 1123869 1123887 1124324 1124329) (-717 "MKRECORD.spad" 1123473 1123486 1123859 1123864) (-716 "MKFUNC.spad" 1122880 1122890 1123463 1123468) (-715 "MKFLCFN.spad" 1121848 1121858 1122870 1122875) (-714 "MKBCFUNC.spad" 1121343 1121361 1121838 1121843) (-713 "MINT.spad" 1120782 1120790 1121245 1121338) (-712 "MHROWRED.spad" 1119293 1119303 1120772 1120777) (-711 "MFLOAT.spad" 1117813 1117821 1119183 1119288) (-710 "MFINFACT.spad" 1117213 1117235 1117803 1117808) (-709 "MESH.spad" 1114995 1115003 1117203 1117208) (-708 "MDDFACT.spad" 1113206 1113216 1114985 1114990) (-707 "MDAGG.spad" 1112497 1112507 1113186 1113201) (-706 "MCMPLX.spad" 1107928 1107936 1108542 1108743) (-705 "MCDEN.spad" 1107138 1107150 1107918 1107923) (-704 "MCALCFN.spad" 1104260 1104286 1107128 1107133) (-703 "MAYBE.spad" 1103544 1103555 1104250 1104255) (-702 "MATSTOR.spad" 1100852 1100862 1103534 1103539) (-701 "MATRIX.spad" 1099439 1099449 1099923 1099950) (-700 "MATLIN.spad" 1096783 1096807 1099323 1099328) (-699 "MATCAT.spad" 1088305 1088327 1096751 1096778) (-698 "MATCAT.spad" 1079699 1079723 1088147 1088152) (-697 "MATCAT2.spad" 1078981 1079029 1079689 1079694) (-696 "MAPPKG3.spad" 1077896 1077910 1078971 1078976) (-695 "MAPPKG2.spad" 1077234 1077246 1077886 1077891) (-694 "MAPPKG1.spad" 1076062 1076072 1077224 1077229) (-693 "MAPPAST.spad" 1075377 1075385 1076052 1076057) (-692 "MAPHACK3.spad" 1075189 1075203 1075367 1075372) (-691 "MAPHACK2.spad" 1074958 1074970 1075179 1075184) (-690 "MAPHACK1.spad" 1074602 1074612 1074948 1074953) (-689 "MAGMA.spad" 1072392 1072409 1074592 1074597) (-688 "MACROAST.spad" 1071971 1071979 1072382 1072387) (-687 "M3D.spad" 1069574 1069584 1071232 1071237) (-686 "LZSTAGG.spad" 1066812 1066822 1069564 1069569) (-685 "LZSTAGG.spad" 1064048 1064060 1066802 1066807) (-684 "LWORD.spad" 1060753 1060770 1064038 1064043) (-683 "LSTAST.spad" 1060537 1060545 1060743 1060748) (-682 "LSQM.spad" 1058694 1058708 1059088 1059139) (-681 "LSPP.spad" 1058229 1058246 1058684 1058689) (-680 "LSMP.spad" 1057079 1057107 1058219 1058224) (-679 "LSMP1.spad" 1054897 1054911 1057069 1057074) (-678 "LSAGG.spad" 1054566 1054576 1054865 1054892) (-677 "LSAGG.spad" 1054255 1054267 1054556 1054561) (-676 "LPOLY.spad" 1053209 1053228 1054111 1054180) (-675 "LPEFRAC.spad" 1052480 1052490 1053199 1053204) (-674 "LO.spad" 1051881 1051895 1052414 1052441) (-673 "LOGIC.spad" 1051483 1051491 1051871 1051876) (-672 "LOGIC.spad" 1051083 1051093 1051473 1051478) (-671 "LODOOPS.spad" 1050013 1050025 1051073 1051078) (-670 "LODO.spad" 1049397 1049413 1049693 1049732) (-669 "LODOF.spad" 1048443 1048460 1049354 1049359) (-668 "LODOCAT.spad" 1047109 1047119 1048399 1048438) (-667 "LODOCAT.spad" 1045773 1045785 1047065 1047070) (-666 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(-647 "LIE.spad" 1015501 1015513 1016775 1016920) (-646 "LIECAT.spad" 1014977 1014987 1015427 1015496) (-645 "LIECAT.spad" 1014481 1014493 1014933 1014938) (-644 "LIB.spad" 1012232 1012240 1012678 1012693) (-643 "LGROBP.spad" 1009585 1009604 1012222 1012227) (-642 "LF.spad" 1008540 1008556 1009575 1009580) (-641 "LFCAT.spad" 1007599 1007607 1008530 1008535) (-640 "LEXTRIPK.spad" 1003102 1003117 1007589 1007594) (-639 "LEXP.spad" 1001105 1001132 1003082 1003097) (-638 "LETAST.spad" 1000804 1000812 1001095 1001100) (-637 "LEADCDET.spad" 999202 999219 1000794 1000799) (-636 "LAZM3PK.spad" 997906 997928 999192 999197) (-635 "LAUPOL.spad" 996506 996519 997406 997475) (-634 "LAPLACE.spad" 996089 996105 996496 996501) (-633 "LA.spad" 995529 995543 996011 996050) (-632 "LALG.spad" 995305 995315 995509 995524) (-631 "LALG.spad" 995089 995101 995295 995300) (-630 "KVTFROM.spad" 994824 994834 995079 995084) (-629 "KTVLOGIC.spad" 994336 994344 994814 994819) (-628 "KRCFROM.spad" 994074 994084 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85500 85539 87083 87088) (-75 "ASP41.spad" 84079 84118 85490 85495) (-74 "ASP35.spad" 83067 83080 84069 84074) (-73 "ASP34.spad" 82368 82381 83057 83062) (-72 "ASP33.spad" 81928 81941 82358 82363) (-71 "ASP31.spad" 81068 81081 81918 81923) (-70 "ASP30.spad" 79960 79973 81058 81063) (-69 "ASP29.spad" 79426 79439 79950 79955) (-68 "ASP28.spad" 70699 70712 79416 79421) (-67 "ASP27.spad" 69596 69609 70689 70694) (-66 "ASP24.spad" 68683 68696 69586 69591) (-65 "ASP20.spad" 68147 68160 68673 68678) (-64 "ASP1.spad" 67528 67541 68137 68142) (-63 "ASP19.spad" 62214 62227 67518 67523) (-62 "ASP12.spad" 61628 61641 62204 62209) (-61 "ASP10.spad" 60899 60912 61618 61623) (-60 "ARRAY2.spad" 60142 60151 60389 60416) (-59 "ARRAY1.spad" 58826 58835 59172 59199) (-58 "ARRAY12.spad" 57539 57550 58816 58821) (-57 "ARR2CAT.spad" 53313 53334 57507 57534) (-56 "ARR2CAT.spad" 49107 49130 53303 53308) (-55 "ARITY.spad" 48479 48486 49097 49102) (-54 "APPRULE.spad" 47739 47761 48469 48474) (-53 "APPLYORE.spad" 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\ No newline at end of file diff --git a/src/share/algebra/category.daase b/src/share/algebra/category.daase index c3aa62cb..b74acbfe 100644 --- a/src/share/algebra/category.daase +++ b/src/share/algebra/category.daase @@ -1,15 +1,15 @@ -(203818 . 3486658196) -(((|#2| |#2|) -12 (|has| |#2| (-319 |#2|)) (|has| |#2| (-1119))) ((#0=(-2 (|:| -4300 |#1|) (|:| -4391 |#2|)) #0#) |has| (-2 (|:| -4300 |#1|) (|:| -4391 |#2|)) (-319 (-2 (|:| -4300 |#1|) (|:| -4391 |#2|))))) -((((-576)) . T) (($) -2781 (|has| |#1| (-317)) (|has| |#1| (-374)) (|has| |#1| (-360)) (|has| |#1| (-568))) (((-419 (-576))) -2781 (|has| |#1| (-374)) (|has| |#1| (-360)) (|has| |#1| (-1057 (-419 (-576))))) ((|#1|) . T)) +(203818 . 3486753502) +(((|#2| |#2|) -12 (|has| |#2| (-319 |#2|)) (|has| |#2| (-1119))) ((#0=(-2 (|:| -4298 |#1|) (|:| -4437 |#2|)) #0#) |has| (-2 (|:| -4298 |#1|) (|:| -4437 |#2|)) (-319 (-2 (|:| -4298 |#1|) (|:| -4437 |#2|))))) +((((-576)) . T) (($) -2755 (|has| |#1| (-317)) (|has| |#1| (-374)) (|has| |#1| (-360)) (|has| |#1| (-568))) (((-419 (-576))) -2755 (|has| |#1| (-374)) (|has| |#1| (-360)) (|has| |#1| (-1057 (-419 (-576))))) ((|#1|) . T)) (((|#2| |#2|) . T)) ((((-576)) . T)) -((($ $) -2781 (|has| |#2| (-174)) (|has| |#2| (-374)) (|has| |#2| (-464)) (|has| |#2| (-568)) (|has| |#2| (-926))) ((|#2| |#2|) . T) ((#0=(-419 (-576)) #0#) |has| |#2| (-38 (-419 (-576))))) +((($ $) -2755 (|has| |#2| (-174)) (|has| |#2| (-374)) (|has| |#2| (-464)) (|has| |#2| (-568)) (|has| |#2| (-926))) ((|#2| |#2|) . T) ((#0=(-419 (-576)) #0#) |has| |#2| (-38 (-419 (-576))))) ((($) . T)) (((|#1|) . T)) ((($) . T) (((-576)) |has| |#1| (-651 (-576))) ((|#1|) . T) (((-419 (-576))) |has| |#1| (-38 (-419 (-576))))) (((|#2|) . T)) -((($) -2781 (|has| |#2| (-174)) (|has| |#2| (-374)) (|has| |#2| (-464)) (|has| |#2| (-568)) (|has| |#2| (-926))) ((|#2|) . T) (((-419 (-576))) |has| |#2| (-38 (-419 (-576))))) +((($) -2755 (|has| |#2| (-174)) (|has| |#2| (-374)) (|has| |#2| (-464)) (|has| |#2| (-568)) (|has| |#2| (-926))) ((|#2|) . T) (((-419 (-576))) |has| |#2| (-38 (-419 (-576))))) (|has| |#1| (-926)) ((((-874)) . T)) ((((-874)) . T)) @@ -24,19 +24,19 @@ ((((-227)) . T) (((-874)) . T)) (((|#1|) -12 (|has| |#1| (-319 |#1|)) (|has| |#1| (-1119)))) (((|#1|) . T)) -(-2781 (|has| |#1| (-21)) (|has| |#1| (-860))) -((($ $) . T) ((#0=(-419 (-576)) #0#) -2781 (|has| |#1| (-374)) (|has| |#1| (-360))) ((|#1| |#1|) . T)) -(-2781 (|has| |#1| (-832)) (|has| |#1| (-862))) +(-2755 (|has| |#1| (-21)) (|has| |#1| (-860))) +((($ $) . T) ((#0=(-419 (-576)) #0#) -2755 (|has| |#1| (-374)) (|has| |#1| (-360))) ((|#1| |#1|) . T)) +(-2755 (|has| |#1| (-832)) (|has| |#1| (-862))) ((((-419 (-576))) |has| |#1| (-1057 (-419 (-576)))) (((-576)) |has| |#1| (-1057 (-576))) ((|#1|) . T)) ((((-874)) . T)) ((((-874)) . 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T)) (|has| |#4| (-379)) (|has| |#3| (-379)) @@ -72,13 +72,13 @@ (|has| |#1| (-146)) (|has| |#1| (-148)) (|has| |#1| (-568)) -((((-576)) . T) (((-419 (-576))) -2781 (|has| |#2| (-38 (-419 (-576)))) (|has| |#2| (-1057 (-419 (-576))))) ((|#2|) . T) (($) -2781 (|has| |#2| (-464)) (|has| |#2| (-568)) (|has| |#2| (-926))) (((-876 |#1|)) . T)) -(-2781 (|has| |#1| (-374)) (|has| |#1| (-568))) -(-2781 (|has| |#1| (-374)) (|has| |#1| (-568))) -((((-2 (|:| -3227 |#1|) (|:| -2795 |#2|))) . T)) +((((-576)) . T) (((-419 (-576))) -2755 (|has| |#2| (-38 (-419 (-576)))) (|has| |#2| (-1057 (-419 (-576))))) ((|#2|) . T) (($) -2755 (|has| |#2| (-464)) (|has| |#2| (-568)) (|has| |#2| (-926))) (((-876 |#1|)) . T)) +(-2755 (|has| |#1| (-374)) (|has| |#1| (-568))) +(-2755 (|has| |#1| (-374)) (|has| |#1| (-568))) +((((-2 (|:| -3222 |#1|) (|:| -1567 |#2|))) . T)) ((($) . T)) -((((-576)) . T) (((-419 (-576))) -2781 (|has| |#1| (-38 (-419 (-576)))) (|has| |#1| (-1057 (-419 (-576))))) ((|#1|) . T) (($) -2781 (|has| |#1| (-464)) (|has| |#1| (-568)) (|has| |#1| (-926))) (((-1195)) . T)) -((((-874)) -2781 (|has| |#1| (-625 (-874))) (|has| |#1| (-862)) (|has| |#1| (-1119)))) +((((-576)) . T) (((-419 (-576))) -2755 (|has| |#1| (-38 (-419 (-576)))) (|has| |#1| (-1057 (-419 (-576))))) ((|#1|) . T) (($) -2755 (|has| |#1| (-464)) (|has| |#1| (-568)) (|has| |#1| (-926))) (((-1195)) . T)) +((((-874)) -2755 (|has| |#1| (-625 (-874))) (|has| |#1| (-862)) (|has| |#1| (-1119)))) ((((-548)) |has| |#1| (-626 (-548)))) ((((-1195)) . T)) ((((-576)) . T) (($) . T)) @@ -98,12 +98,12 @@ ((((-874)) . T)) (((|#1| |#2|) . T)) (((|#1|) . T)) -(((#0=(-419 (-576)) #0#) |has| |#2| (-38 (-419 (-576)))) ((|#2| |#2|) . T) (($ $) -2781 (|has| |#2| (-174)) (|has| |#2| (-464)) (|has| |#2| (-568)) (|has| |#2| (-926)))) +(((#0=(-419 (-576)) #0#) |has| |#2| (-38 (-419 (-576)))) ((|#2| |#2|) . 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T) (($) -2781 (|has| |#1| (-174)) (|has| |#1| (-464)) (|has| |#1| (-568)) (|has| |#1| (-926)))) +(((#0=(-419 (-576)) #0#) |has| |#1| (-38 (-419 (-576)))) ((|#1| |#1|) . T) (($ $) -2755 (|has| |#1| (-174)) (|has| |#1| (-464)) (|has| |#1| (-568)) (|has| |#1| (-926)))) +((((-419 (-576))) |has| |#1| (-38 (-419 (-576)))) ((|#1|) . T) (($) -2755 (|has| |#1| (-174)) (|has| |#1| (-464)) (|has| |#1| (-568)) (|has| |#1| (-926)))) ((($ $) . T)) ((($) . T)) ((((-576)) . T) (($) . T) ((|#1|) . T) (((-419 (-576))) |has| |#1| (-38 (-419 (-576))))) @@ -127,30 +127,30 @@ (|has| |#1| (-379)) (((|#1|) . T)) ((((-874)) . T)) -((((-419 (-576))) -2781 (|has| |#1| (-38 (-419 (-576)))) (|has| |#1| (-374))) (((-1278 |#1| |#2| |#3|)) |has| |#1| (-374)) (($) . T) ((|#1|) . T)) -(((|#1|) . T) (((-419 (-576))) -2781 (|has| |#1| (-38 (-419 (-576)))) (|has| |#1| (-374))) (($) . T)) +((((-419 (-576))) -2755 (|has| |#1| (-38 (-419 (-576)))) (|has| |#1| (-374))) (((-1278 |#1| |#2| |#3|)) |has| |#1| (-374)) (($) . 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T)) ((((-419 (-576))) . T) (($) . T)) @@ -223,7 +223,7 @@ (((|#1|) . T)) (|has| |#2| (-374)) ((((-1253 (-576)) $) . T) (((-576) |#1|) . T)) -((($) -2781 (|has| (-419 |#2|) (-238)) (|has| (-419 |#2|) (-237)))) +((($) -2755 (|has| (-419 |#2|) (-238)) (|has| (-419 |#2|) (-237)))) ((($) . T) (((-576)) . T) (((-419 (-576))) . T)) (((|#1| |#2|) . T)) ((((-874)) . T)) @@ -236,13 +236,13 @@ ((((-874)) . T)) ((((-874)) . T)) (((|#1| |#1|) . T)) -(((#0=(-419 (-576)) #0#) |has| |#1| (-38 (-419 (-576)))) ((|#1| |#1|) . T) (($ $) -2781 (|has| |#1| (-174)) (|has| |#1| (-464)) (|has| |#1| (-568)) (|has| |#1| (-926)))) -((($ $) -2781 (|has| |#1| (-174)) (|has| |#1| (-374)) (|has| |#1| (-464)) (|has| |#1| (-568)) (|has| |#1| (-926))) ((|#1| |#1|) . T) ((#0=(-419 (-576)) #0#) |has| |#1| (-38 (-419 (-576))))) +(((#0=(-419 (-576)) #0#) |has| |#1| (-38 (-419 (-576)))) ((|#1| |#1|) . 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T) (($) -2755 (|has| |#1| (-174)) (|has| |#1| (-464)) (|has| |#1| (-568)) (|has| |#1| (-926)))) +((($) -2755 (|has| |#1| (-174)) (|has| |#1| (-374)) (|has| |#1| (-464)) (|has| |#1| (-568)) (|has| |#1| (-926))) ((|#1|) . T) (((-419 (-576))) |has| |#1| (-38 (-419 (-576))))) +(((|#2|) -2755 (|has| |#2| (-174)) (|has| |#2| (-374)) (|has| |#2| (-1068))) (($) |has| |#2| (-1068)) (((-576)) -12 (|has| |#2| (-651 (-576))) (|has| |#2| (-1068)))) ((((-874)) . T)) ((((-874)) . T)) ((((-874)) . T)) @@ -253,10 +253,10 @@ ((((-171 (-227))) |has| |#1| (-1041)) (((-171 (-390))) |has| |#1| (-1041)) (((-548)) |has| |#1| (-626 (-548))) (((-1191 |#1|)) . T) (((-905 (-576))) |has| |#1| (-626 (-905 (-576)))) (((-905 (-390))) |has| |#1| (-626 (-905 (-390))))) (((|#1| |#1|) -12 (|has| |#1| (-319 |#1|)) (|has| |#1| (-1119)))) (((|#1|) . 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T)) -((((-2 (|:| -3227 |#1|) (|:| -2795 |#2|))) . T) (((-874)) . T)) +((((-2 (|:| -3222 |#1|) (|:| -1567 |#2|))) . T) (((-874)) . T)) ((((-548)) |has| |#1| (-626 (-548))) (((-905 (-390))) |has| |#1| (-626 (-905 (-390)))) (((-905 (-576))) |has| |#1| (-626 (-905 (-576))))) -(((|#4|) -2781 (|has| |#4| (-174)) (|has| |#4| (-374)) (|has| |#4| (-1068)))) -(((|#3|) -2781 (|has| |#3| (-174)) (|has| |#3| (-374)) (|has| |#3| (-1068)))) -((((-2 (|:| -3227 |#1|) (|:| -2795 |#2|))) . T)) +(((|#4|) -2755 (|has| |#4| (-174)) (|has| |#4| (-374)) (|has| |#4| (-1068)))) +(((|#3|) -2755 (|has| |#3| (-174)) (|has| |#3| (-374)) (|has| |#3| (-1068)))) +((((-2 (|:| -3222 |#1|) (|:| -1567 |#2|))) . T)) ((((-874)) . T)) ((((-874)) . T)) ((((-548)) . T) (((-576)) . T) (((-905 (-576))) . T) (((-390)) . T) (((-227)) . T)) @@ -321,15 +321,15 @@ (((|#1|) . T) (((-576)) |has| |#1| (-1057 (-576))) (((-419 (-576))) |has| |#1| (-1057 (-419 (-576))))) ((($) . 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T)) @@ -343,15 +343,15 @@ (|has| |#1| (-1119)) ((((-927 |#1|)) . T) (($) . T) (((-419 (-576))) . T)) (((|#1|) . T)) -((((-874)) -2781 (|has| |#1| (-625 (-874))) (|has| |#1| (-862)) (|has| |#1| (-1119)))) +((((-874)) -2755 (|has| |#1| (-625 (-874))) (|has| |#1| (-862)) (|has| |#1| (-1119)))) ((((-548)) |has| |#1| (-626 (-548)))) ((((-874)) . T) (((-1200)) . T)) -((((-419 (-576))) |has| |#2| (-38 (-419 (-576)))) ((|#2|) |has| |#2| (-174)) (($) -2781 (|has| |#2| (-464)) (|has| |#2| (-568)) (|has| |#2| (-926)))) +((((-419 (-576))) |has| |#2| (-38 (-419 (-576)))) ((|#2|) |has| |#2| (-174)) (($) -2755 (|has| |#2| (-464)) (|has| |#2| (-568)) (|has| |#2| (-926)))) ((((-1200)) . 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T)) (((|#1| (-990)) . T)) ((((-576)) . T) ((|#2|) . T)) @@ -362,7 +362,7 @@ (((|#1|) . T)) (((|#2| |#2|) . T)) (|has| |#1| (-1171)) -((((-2 (|:| -4300 (-1177)) (|:| -4391 |#1|))) . T)) +((((-2 (|:| -4298 (-1177)) (|:| -4437 |#1|))) . T)) (|has| (-1272 |#1| |#2| |#3| |#4|) (-146)) (|has| (-1272 |#1| |#2| |#3| |#4|) (-148)) (|has| |#1| (-146)) @@ -374,27 +374,27 @@ (((|#2|) . T)) (((|#1|) . T)) (((|#2|) . T) (((-576)) |has| |#2| (-651 (-576)))) -((((-1144 |#1| (-1195))) . T) (((-576)) . T) (((-830 (-1195))) . T) (($) -2781 (|has| |#1| (-464)) (|has| |#1| (-568)) (|has| |#1| (-926))) ((|#1|) . T) (((-419 (-576))) -2781 (|has| |#1| (-38 (-419 (-576)))) (|has| |#1| (-1057 (-419 (-576))))) (((-1195)) . T)) +((((-1144 |#1| (-1195))) . T) (((-576)) . T) (((-830 (-1195))) . T) (($) -2755 (|has| |#1| (-464)) (|has| |#1| (-568)) (|has| |#1| (-926))) ((|#1|) . T) (((-419 (-576))) -2755 (|has| |#1| (-38 (-419 (-576)))) (|has| |#1| (-1057 (-419 (-576))))) (((-1195)) . 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T)) -((($) -2781 (|has| |#1| (-174)) (|has| |#1| (-464)) (|has| |#1| (-568)) (|has| |#1| (-926))) ((|#1|) . T) (((-419 (-576))) |has| |#1| (-38 (-419 (-576))))) +((($) -2755 (|has| |#1| (-174)) (|has| |#1| (-464)) (|has| |#1| (-568)) (|has| |#1| (-926))) ((|#1|) . T) (((-419 (-576))) |has| |#1| (-38 (-419 (-576))))) ((((-874)) . T)) ((((-874)) . T)) (|has| (-1271 |#2| |#3| |#4|) (-148)) @@ -405,18 +405,18 @@ ((((-874)) . T)) (((|#1|) . T)) (((|#1|) . T)) -(-2781 (|has| |#1| (-21)) (|has| |#1| (-174)) (|has| |#1| (-374)) (|has| |#1| (-915 (-1195))) (|has| |#1| (-1068))) +(-2755 (|has| |#1| (-21)) (|has| |#1| (-174)) (|has| |#1| (-374)) (|has| |#1| (-915 (-1195))) (|has| |#1| (-1068))) (((|#1|) . T)) ((($) . T)) ((((-576) |#1|) . T)) (((|#2|) |has| |#2| (-174))) (((|#1|) . T)) (((|#1|) |has| |#1| (-174))) -(-2781 (|has| |#1| (-21)) (|has| |#1| (-860))) +(-2755 (|has| |#1| (-21)) (|has| |#1| (-860))) ((((-874)) |has| |#1| (-1119))) -((($) -2781 (|has| |#1| (-238)) (|has| |#1| (-237)))) -(-2781 (|has| |#1| (-485)) (|has| |#1| (-738)) (|has| |#1| (-915 (-1195))) (|has| |#1| (-1068)) (|has| |#1| (-1131))) -(-2781 (|has| |#1| (-374)) (|has| |#1| (-360))) +((($) -2755 (|has| |#1| (-238)) (|has| |#1| (-237)))) +(-2755 (|has| |#1| (-485)) (|has| |#1| (-738)) (|has| |#1| (-915 (-1195))) (|has| |#1| (-1068)) (|has| |#1| (-1131))) +(-2755 (|has| |#1| (-374)) (|has| |#1| (-360))) ((((-927 |#1|)) . T)) ((((-419 |#2|) |#3|) . T)) (|has| |#1| (-15 * (|#1| (-576) |#1|))) @@ -427,7 +427,7 @@ ((((-874)) . T)) ((((-419 (-576))) |has| |#1| (-38 (-419 (-576)))) ((|#1|) |has| |#1| (-174)) (($) |has| |#1| (-568))) (|has| |#1| (-374)) -(-2781 (-12 (|has| (-1278 |#1| |#2| |#3|) (-238)) (|has| |#1| (-374))) (|has| |#1| (-15 * (|#1| (-576) |#1|)))) +(-2755 (-12 (|has| (-1278 |#1| |#2| |#3|) (-238)) (|has| |#1| (-374))) (|has| |#1| (-15 * (|#1| (-576) |#1|)))) (|has| |#1| (-15 * (|#1| (-419 (-576)) |#1|))) (|has| |#1| (-374)) (|has| |#1| (-15 * (|#1| (-783) |#1|))) @@ -441,23 +441,23 @@ ((((-1253 (-576)) $) . T) (((-576) |#1|) . T)) ((((-874)) . T)) (((|#2|) . T)) -(-2781 (|has| |#2| (-374)) (|has| |#2| (-464)) (|has| |#2| (-568)) (|has| |#2| (-926))) +(-2755 (|has| |#2| (-374)) (|has| |#2| (-464)) (|has| |#2| (-568)) (|has| |#2| (-926))) ((((-576)) . T) (((-419 (-576))) |has| |#1| (-38 (-419 (-576)))) ((|#1|) |has| |#1| (-174)) (($) |has| |#1| (-568))) ((($) |has| |#1| (-568)) (((-576)) . T)) (|has| |#2| (-805)) (|has| |#2| (-805)) -((((-1278 |#1| |#2| |#3|)) . 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T)) -((($ (-1195)) -2781 (|has| (-419 |#2|) (-915 (-1195))) (|has| (-419 |#2|) (-917 (-1195))))) +((($ (-1195)) -2755 (|has| (-419 |#2|) (-915 (-1195))) (|has| (-419 |#2|) (-917 (-1195))))) (((#0=(-711) (-1191 #0#)) . T)) ((((-593 |#1|)) . T) (((-419 (-576))) . T) (($) . T)) ((((-419 (-576))) . T) (($) . T)) @@ -465,18 +465,18 @@ ((((-874)) . T) (((-1286 |#3|)) . T)) ((((-593 |#1|)) . T) (($) . T) (((-419 (-576))) . T)) ((($) . T) (((-419 (-576))) . T)) -((((-419 (-576))) |has| |#1| (-38 (-419 (-576)))) ((|#1|) . T) (($) -2781 (|has| |#1| (-174)) (|has| |#1| (-568)))) +((((-419 (-576))) |has| |#1| (-38 (-419 (-576)))) ((|#1|) . T) (($) -2755 (|has| |#1| (-174)) (|has| |#1| (-568)))) ((($) |has| |#1| (-568)) ((|#1|) . T)) ((((-874)) . T)) ((($) . T) (((-576)) . T) (((-419 (-576))) . T)) ((($) . 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T) (($) -2755 (|has| |#1| (-174)) (|has| |#1| (-374)) (|has| |#1| (-568))) (((-419 (-576))) -2755 (|has| |#1| (-38 (-419 (-576)))) (|has| |#1| (-374)))) (((|#3|) |has| |#3| (-1068))) -((($) -2781 (|has| |#1| (-174)) (|has| |#1| (-568))) ((|#1|) . T) (((-419 (-576))) |has| |#1| (-38 (-419 (-576))))) -((($ $) -2781 (|has| |#1| (-174)) (|has| |#1| (-568))) ((|#1| |#1|) . T) ((#0=(-419 (-576)) #0#) |has| |#1| (-38 (-419 (-576))))) +((($) -2755 (|has| |#1| (-174)) (|has| |#1| (-568))) ((|#1|) . T) (((-419 (-576))) |has| |#1| (-38 (-419 (-576))))) +((($ $) -2755 (|has| |#1| (-174)) (|has| |#1| (-568))) ((|#1| |#1|) . T) ((#0=(-419 (-576)) #0#) |has| |#1| (-38 (-419 (-576))))) (|has| (-1113 |#1|) (-1119)) (((|#2| (-831 |#1|)) . T)) ((($) . T) (((-576)) . T) (((-419 (-576))) |has| |#2| (-38 (-419 (-576)))) ((|#2|) . T)) @@ -484,20 +484,20 @@ (((|#1|) . T) (((-419 (-576))) . T) (((-576)) . T) (($) . T)) (((|#1|) . T) (((-419 (-576))) . T) (((-576)) . T) (($) . T)) (((|#1|) . 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T)) (((|#3|) |has| |#3| (-1119)) (((-576)) -12 (|has| |#3| (-1057 (-576))) (|has| |#3| (-1119))) (((-419 (-576))) -12 (|has| |#3| (-1057 (-419 (-576)))) (|has| |#3| (-1119)))) -((((-2 (|:| -4300 |#1|) (|:| -4391 |#2|))) . T)) +((((-2 (|:| -4298 |#1|) (|:| -4437 |#2|))) . T)) (((|#1|) . T)) -((((-874)) -2781 (|has| |#1| (-625 (-874))) (|has| |#1| (-862)) (|has| |#1| (-1119)))) +((((-874)) -2755 (|has| |#1| (-625 (-874))) (|has| |#1| (-862)) (|has| |#1| (-1119)))) ((((-548)) |has| |#1| (-626 (-548)))) (((|#1|) |has| |#1| (-174))) -((((-2 (|:| -4300 (-1195)) (|:| -4391 (-52)))) . T)) +((((-2 (|:| -4298 (-1195)) (|:| -4437 (-52)))) . T)) (|has| |#1| (-374)) ((((-1200)) . T)) (((|#1|) . T)) -(-2781 (|has| |#1| (-21)) (|has| |#1| (-860))) +(-2755 (|has| |#1| (-21)) (|has| |#1| (-860))) ((($) . T)) ((((-1195) |#1|) |has| |#1| (-526 (-1195) |#1|)) ((|#1| |#1|) |has| |#1| (-319 |#1|))) (|has| |#2| (-832)) (|has| |#1| (-38 (-419 (-576)))) (|has| |#1| (-860)) -((((-2 (|:| -4300 |#1|) (|:| -4391 |#2|))) . T)) +((((-2 (|:| -4298 |#1|) (|:| -4437 |#2|))) . T)) (((|#1| |#2|) . T)) (((|#1| |#2| |#3| (-543 |#3|)) . T)) ((((-874)) . T)) @@ -530,12 +530,12 @@ (|has| |#1| (-379)) ((((-419 (-576))) . T)) (((|#1|) . T)) -(-2781 (|has| |#2| (-464)) (|has| |#2| (-568)) (|has| |#2| (-926))) +(-2755 (|has| |#2| (-464)) (|has| |#2| (-568)) (|has| |#2| (-926))) ((((-419 (-576))) . T)) ((((-1177) |#1|) . T)) (|has| |#1| (-379)) -(-2781 (|has| |#1| (-464)) (|has| |#1| (-568)) (|has| |#1| (-926))) -(-2781 (|has| |#1| (-862)) (|has| |#1| (-1119))) +(-2755 (|has| |#1| (-464)) (|has| |#1| (-568)) (|has| |#1| (-926))) +(-2755 (|has| |#1| (-862)) (|has| |#1| (-1119))) ((((-576)) . T)) ((((-576)) . T)) (((|#1|) . T) (((-576)) . T)) @@ -552,12 +552,12 @@ ((((-576) |#3|) . T)) (((|#1|) . T) (((-576)) |has| |#1| (-651 (-576)))) (|has| |#2| (-1068)) -((((-2 (|:| -4300 |#1|) (|:| -4391 |#2|))) . T)) -(-2781 (|has| |#2| (-174)) (|has| |#2| (-374)) (|has| |#2| (-464)) (|has| |#2| (-568)) (|has| |#2| (-926))) +((((-2 (|:| -4298 |#1|) (|:| -4437 |#2|))) . T)) +(-2755 (|has| |#2| (-174)) (|has| |#2| (-374)) (|has| |#2| (-464)) (|has| |#2| (-568)) (|has| |#2| (-926))) ((((-874)) . T)) ((((-1272 |#1| |#2| |#3| |#4|)) . T)) ((((-419 (-576))) . T) (((-576)) . T)) -((((-874)) -2781 (|has| |#1| (-625 (-874))) (|has| |#1| (-1119)))) +((((-874)) -2755 (|has| |#1| (-625 (-874))) (|has| |#1| (-1119)))) (((|#1| |#1|) . T)) (((|#1|) . T)) (((|#1|) -12 (|has| |#1| (-319 |#1|)) (|has| |#1| (-1119)))) @@ -566,9 +566,9 @@ ((($) . T) (((-576)) . T) (((-419 (-576))) . T)) ((((-576)) . T)) ((((-576)) . T)) -((($) . T) (((-576)) . T) (((-419 (-576))) -2781 (|has| |#1| (-38 (-419 (-576)))) (|has| |#1| (-374))) ((|#1|) . T)) +((($) . T) (((-576)) . 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T)) @@ -826,8 +826,8 @@ (|has| |#3| (-1068)) (|has| |#3| (-805)) (|has| |#3| (-805)) -((((-419 (-576))) -2781 (|has| |#1| (-38 (-419 (-576)))) (|has| |#1| (-374))) (($) -2781 (|has| |#1| (-374)) (|has| |#1| (-568))) ((|#2|) |has| |#1| (-374)) ((|#1|) |has| |#1| (-174))) -(((|#1|) |has| |#1| (-174)) (((-419 (-576))) -2781 (|has| |#1| (-38 (-419 (-576)))) (|has| |#1| (-374))) (($) -2781 (|has| |#1| (-374)) (|has| |#1| (-568)))) +((((-419 (-576))) -2755 (|has| |#1| (-38 (-419 (-576)))) (|has| |#1| (-374))) (($) -2755 (|has| |#1| (-374)) (|has| |#1| (-568))) ((|#2|) |has| |#1| (-374)) ((|#1|) |has| |#1| (-174))) +(((|#1|) |has| |#1| (-174)) (((-419 (-576))) -2755 (|has| |#1| (-38 (-419 (-576)))) (|has| |#1| (-374))) (($) -2755 (|has| |#1| (-374)) (|has| |#1| (-568)))) (((|#2|) . T)) ((((-874)) . T)) ((((-874)) . T)) @@ -841,37 +841,37 @@ ((((-419 (-576))) . T) (($) . T)) (((|#1| |#1|) -12 (|has| |#1| (-319 |#1|)) (|has| |#1| (-1119)))) ((($) . T) (((-419 (-576))) . 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T)) (|has| (-419 |#2|) (-148)) (|has| (-419 |#2|) (-146)) @@ -884,15 +884,15 @@ (|has| |#1| (-568)) (|has| |#1| (-38 (-419 (-576)))) (|has| |#1| (-38 (-419 (-576)))) -((((-2 (|:| -4300 |#1|) (|:| -4391 |#2|))) . T)) +((((-2 (|:| -4298 |#1|) (|:| -4437 |#2|))) . T)) ((((-874)) . T)) -((((-2 (|:| -4300 (-1177)) (|:| -4391 |#1|))) . T)) +((((-2 (|:| -4298 (-1177)) (|:| -4437 |#1|))) . T)) (|has| |#1| (-38 (-419 (-576)))) -((((-400) (-2 (|:| -4300 (-1177)) (|:| -4391 |#1|))) . T)) +((((-400) (-2 (|:| -4298 (-1177)) (|:| -4437 |#1|))) . T)) (|has| |#1| (-38 (-419 (-576)))) (|has| |#2| (-1171)) -(-2781 (|has| |#1| (-374)) (|has| |#1| (-568))) -(-2781 (|has| |#1| (-374)) (|has| |#1| (-568))) +(-2755 (|has| |#1| (-374)) (|has| |#1| (-568))) +(-2755 (|has| |#1| (-374)) (|has| |#1| (-568))) ((((-874)) . T) (((-1200)) . T)) ((((-874)) . T) (((-1200)) . T)) ((((-1200)) . T)) @@ -910,7 +910,7 @@ ((((-400) (-1177)) . T)) (|has| |#1| (-568)) ((((-1253 (-576)) $) . T) (((-576) |#1|) . 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T)) -((((-1195)) -2781 (|has| |#1| (-915 (-1195))) (|has| |#1| (-917 (-1195))))) +((((-1195)) -2755 (|has| |#1| (-915 (-1195))) (|has| |#1| (-917 (-1195))))) (((|#3|) . T)) ((($ $) . T) ((#0=(-876 |#1|) $) . T) ((#0# |#2|) . T)) (|has| |#1| (-840)) @@ -1194,10 +1194,10 @@ ((($) . T) (((-576)) . T) (((-419 (-576))) |has| |#1| (-38 (-419 (-576)))) ((|#1|) . T)) ((((-576)) . T) (($) . T) ((|#1|) . T) (((-419 (-576))) |has| |#1| (-38 (-419 (-576))))) (|has| (-1113 |#1|) (-1119)) -(((|#2| |#2|) -2781 (|has| |#2| (-174)) (|has| |#2| (-374)) (|has| |#2| (-1068)))) -(((|#2|) -2781 (|has| |#2| (-174)) (|has| |#2| (-374)))) -((((-576) (-2 (|:| -4300 |#1|) (|:| -4391 |#2|))) . T) ((|#1| |#2|) . T)) -(((|#2|) -2781 (|has| |#2| (-174)) (|has| |#2| (-374)) (|has| |#2| (-1068)))) +(((|#2| |#2|) -2755 (|has| |#2| (-174)) (|has| |#2| (-374)) (|has| |#2| (-1068)))) +(((|#2|) -2755 (|has| |#2| (-174)) (|has| |#2| (-374)))) +((((-576) (-2 (|:| -4298 |#1|) (|:| -4437 |#2|))) . T) ((|#1| |#2|) . 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T)) -((($) -2781 (|has| |#1| (-317)) (|has| |#1| (-374)) (|has| |#1| (-360)) (|has| |#1| (-568))) (((-419 (-576))) -2781 (|has| |#1| (-374)) (|has| |#1| (-360))) ((|#1|) . T)) -((($) -2781 (|has| (-419 |#2|) (-238)) (|has| (-419 |#2|) (-237)))) +((($) -2755 (|has| |#1| (-317)) (|has| |#1| (-374)) (|has| |#1| (-360)) (|has| |#1| (-568))) (((-419 (-576))) -2755 (|has| |#1| (-374)) (|has| |#1| (-360))) ((|#1|) . T)) +((($) -2755 (|has| (-419 |#2|) (-238)) (|has| (-419 |#2|) (-237)))) ((((-576) |#2|) . T)) -((($ (-1195)) -2781 (|has| |#2| (-915 (-1195))) (|has| |#2| (-917 (-1195))))) +((($ (-1195)) -2755 (|has| |#2| (-915 (-1195))) (|has| |#2| (-917 (-1195))))) (((|#1| |#2|) . T)) (((|#1| |#2|) . T)) (|has| |#2| (-379)) @@ -1262,42 +1262,42 @@ ((((-874)) . 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T)) (((|#1|) |has| |#1| (-319 |#1|))) @@ -1307,21 +1307,21 @@ (|has| |#1| (-379)) ((((-1195) $) |has| |#1| (-526 (-1195) $)) (($ $) |has| |#1| (-319 $)) ((|#1| |#1|) |has| |#1| (-319 |#1|)) (((-1195) |#1|) |has| |#1| (-526 (-1195) |#1|))) ((((-1195)) |has| |#1| (-915 (-1195)))) -(-2781 (-12 (|has| |#1| (-238)) (|has| |#1| (-374))) (|has| |#1| (-360))) +(-2755 (-12 (|has| |#1| (-238)) (|has| |#1| (-374))) (|has| |#1| (-360))) (((|#1| |#4|) . T)) (((|#1| |#3|) . T)) ((($) . T)) ((((-400) |#1|) . T)) -(-2781 (|has| |#1| (-374)) (|has| |#1| (-360))) -(-2781 (|has| |#1| (-102)) (|has| |#1| (-1119))) +(-2755 (|has| |#1| (-374)) (|has| |#1| (-360))) +(-2755 (|has| |#1| (-102)) (|has| |#1| (-1119))) (((|#2|) . T) (((-874)) . T)) ((((-874)) . T)) (((|#2|) . T)) ((((-927 |#1|)) . T)) ((((-874)) . T) (((-1200)) . T)) ((((-1200)) . T)) -((((-419 (-576))) |has| |#2| (-38 (-419 (-576)))) ((|#2|) |has| |#2| (-174)) (($) -2781 (|has| |#2| (-464)) (|has| |#2| (-568)) (|has| |#2| (-926)))) -((((-419 (-576))) |has| |#1| (-38 (-419 (-576)))) ((|#1|) |has| |#1| (-174)) (($) -2781 (|has| |#1| (-464)) (|has| |#1| (-568)) (|has| |#1| (-926)))) +((((-419 (-576))) |has| |#2| (-38 (-419 (-576)))) ((|#2|) |has| |#2| (-174)) (($) -2755 (|has| |#2| (-464)) (|has| |#2| (-568)) (|has| |#2| (-926)))) +((((-419 (-576))) |has| |#1| (-38 (-419 (-576)))) ((|#1|) |has| |#1| (-174)) (($) -2755 (|has| |#1| (-464)) (|has| |#1| (-568)) (|has| |#1| (-926)))) (((|#1| |#2|) . T)) ((($) . T)) ((((-576)) . T) (($) . T) (((-419 (-576))) . T)) @@ -1330,7 +1330,7 @@ (((|#1|) . T) (((-419 (-576))) . T) (($) . T) (((-576)) . T)) (((|#1| |#1|) . T)) (((#0=(-882 |#1|)) |has| #0# (-319 #0#))) -((((-576)) . T) (($) -2781 (|has| |#1| (-374)) (|has| |#1| (-360))) (((-419 (-576))) -2781 (|has| |#1| (-374)) (|has| |#1| (-360)) (|has| |#1| (-1057 (-419 (-576))))) ((|#1|) . T)) +((((-576)) . T) (($) -2755 (|has| |#1| (-374)) (|has| |#1| (-360))) (((-419 (-576))) -2755 (|has| |#1| (-374)) (|has| |#1| (-360)) (|has| |#1| (-1057 (-419 (-576))))) ((|#1|) . T)) (((|#1| |#2|) . T)) (|has| |#2| (-805)) (|has| |#2| (-805)) @@ -1339,7 +1339,7 @@ (-12 (|has| |#1| (-805)) (|has| |#2| (-805))) (|has| |#2| (-1068)) ((($) . T) (((-576)) . T) ((|#2|) . T)) -(((|#2|) . T) (((-2 (|:| -4300 |#1|) (|:| -4391 |#2|))) . T)) +(((|#2|) . T) (((-2 (|:| -4298 |#1|) (|:| -4437 |#2|))) . T)) (((|#2|) . T) (($) . T)) (|has| |#1| (-1221)) (((#0=(-576) #0#) . T) ((#1=(-419 (-576)) #1#) . T) (($ $) . T)) @@ -1353,14 +1353,14 @@ (((|#1| |#1|) . T) (($ $) . T) ((#0=(-419 (-576)) #0#) . T)) (|has| |#1| (-374)) ((((-576)) . T) (((-419 (-576))) . T) (($) . 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T) (((-419 (-576))) |has| |#2| (-38 (-419 (-576))))) +((($) -2755 (|has| |#2| (-174)) (|has| |#2| (-374)) (|has| |#2| (-464)) (|has| |#2| (-568)) (|has| |#2| (-926))) ((|#2|) . T) (((-419 (-576))) |has| |#2| (-38 (-419 (-576))))) ((((-576)) |has| #0=(-419 |#2|) (-651 (-576))) ((#0#) . T)) ((($) . T) (((-576)) . T)) ((((-576) (-145)) . T)) -((((-576) (-2 (|:| -4300 |#1|) (|:| -4391 |#2|))) . T) ((|#1| |#2|) . T)) +((((-576) (-2 (|:| -4298 |#1|) (|:| -4437 |#2|))) . T) ((|#1| |#2|) . T)) ((((-419 (-576))) . T) (($) . T)) (((|#1|) . T)) -((((-2 (|:| -4300 |#1|) (|:| -4391 |#2|))) . T)) +((((-2 (|:| -4298 |#1|) (|:| -4437 |#2|))) . T)) ((((-874)) . T)) ((((-927 |#1|)) . T)) (|has| |#1| (-374)) @@ -1401,11 +1401,11 @@ (|has| |#1| (-374)) (|has| |#1| (-15 * (|#1| (-419 (-576)) |#1|))) (|has| |#1| (-860)) -((($) -2781 (|has| |#1| (-317)) (|has| |#1| (-374)) (|has| |#1| (-360)) (|has| |#1| (-568))) (((-419 (-576))) -2781 (|has| |#1| (-374)) (|has| |#1| (-360))) ((|#1|) . 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T)) -(((|#2|) -2781 (|has| |#2| (-174)) (|has| |#2| (-374)) (|has| |#2| (-1068)))) +(((|#2|) -2755 (|has| |#2| (-174)) (|has| |#2| (-374)) (|has| |#2| (-1068)))) (|has| $ (-148)) ((((-419 |#2|)) . T)) ((((-419 (-576))) |has| #0=(-419 |#2|) (-1057 (-419 (-576)))) (((-576)) |has| #0# (-1057 (-576))) ((#0#) . T)) @@ -1548,11 +1548,11 @@ (|has| |#2| (-148)) (|has| |#1| (-148)) (|has| |#1| (-146)) -(-2781 (|has| |#1| (-146)) (|has| |#1| (-379))) +(-2755 (|has| |#1| (-146)) (|has| |#1| (-379))) (|has| |#1| (-148)) -(-2781 (|has| |#1| (-146)) (|has| |#1| (-379))) +(-2755 (|has| |#1| (-146)) (|has| |#1| (-379))) (|has| |#1| (-148)) -(-2781 (|has| |#1| (-146)) (|has| |#1| (-379))) +(-2755 (|has| |#1| (-146)) (|has| |#1| (-379))) (|has| |#1| (-148)) (((|#1|) . T)) (|has| |#2| (-238)) @@ -1589,9 +1589,9 @@ ((((-874)) . T)) ((((-874)) . T)) ((((-1018 |#1|)) . T) ((|#1|) . T)) -((((-1195)) -2781 (|has| |#1| (-915 (-1195))) (|has| |#1| (-917 (-1195)))) (((-830 (-1195))) . 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T)) -((((-576)) -2781 (|has| |#2| (-21)) (|has| |#2| (-174)) (|has| |#2| (-374)) (|has| |#2| (-1068))) ((|#2|) -2781 (|has| |#2| (-174)) (|has| |#2| (-374)) (|has| |#2| (-738)) (|has| |#2| (-1068))) (($) |has| |#2| (-1068))) +((((-576)) -2755 (|has| |#2| (-21)) (|has| |#2| (-174)) (|has| |#2| (-374)) (|has| |#2| (-1068))) ((|#2|) -2755 (|has| |#2| (-174)) (|has| |#2| (-374)) (|has| |#2| (-738)) (|has| |#2| (-1068))) (($) |has| |#2| (-1068))) (((|#1|) . T)) ((((-576) |#3|) . T)) ((((-576) (-145)) . T)) @@ -1653,7 +1653,7 @@ ((((-576)) . T) (($) . T)) (((|#1|) -12 (|has| |#1| (-319 |#1|)) (|has| |#1| (-1119)))) (((|#1|) . T)) -((($ (-1195)) -2781 (|has| |#1| (-915 (-1195))) (|has| |#1| (-917 (-1195))))) +((($ (-1195)) -2755 (|has| |#1| (-915 (-1195))) (|has| |#1| (-917 (-1195))))) (((|#2|) . T) (((-576)) |has| |#2| (-651 (-576)))) ((((-145)) . T)) ((((-874)) . T)) @@ -1664,26 +1664,26 @@ (((|#1|) . T)) (((|#1|) -12 (|has| |#1| (-319 |#1|)) (|has| |#1| (-1119)))) (((|#1| |#2|) . T)) -(-2781 (|has| |#2| (-238)) (|has| |#2| (-237))) +(-2755 (|has| |#2| (-238)) (|has| |#2| (-237))) ((((-576) (-145)) . T) (((-1253 (-576)) $) . T)) -(((#0=(-2 (|:| -4300 |#1|) (|:| -4391 |#2|)) #0#) |has| (-2 (|:| -4300 |#1|) (|:| -4391 |#2|)) (-319 (-2 (|:| -4300 |#1|) (|:| -4391 |#2|)))) ((|#2| |#2|) -12 (|has| |#2| (-319 |#2|)) (|has| |#2| (-1119)))) -((($) -2781 (|has| |#1| (-464)) (|has| |#1| (-568)) (|has| |#1| (-926))) ((|#1|) |has| |#1| (-174)) (((-419 (-576))) |has| |#1| (-38 (-419 (-576))))) +(((#0=(-2 (|:| -4298 |#1|) (|:| -4437 |#2|)) #0#) |has| (-2 (|:| -4298 |#1|) (|:| -4437 |#2|)) (-319 (-2 (|:| -4298 |#1|) (|:| -4437 |#2|)))) ((|#2| |#2|) -12 (|has| |#2| (-319 |#2|)) (|has| |#2| (-1119)))) +((($) -2755 (|has| |#1| (-464)) (|has| |#1| (-568)) (|has| |#1| (-926))) ((|#1|) |has| |#1| (-174)) (((-419 (-576))) |has| |#1| (-38 (-419 (-576))))) (|has| |#1| (-862)) (((|#2| (-783) (-1101)) . T)) (((|#1| |#2|) . 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T)) -(-2781 (|has| |#1| (-148)) (-12 (|has| |#1| (-374)) (|has| |#2| (-148)))) +(-2755 (|has| |#1| (-148)) (-12 (|has| |#1| (-374)) (|has| |#2| (-148)))) (((|#4|) . T)) -(-2781 (|has| |#1| (-146)) (-12 (|has| |#1| (-374)) (|has| |#2| (-146)))) +(-2755 (|has| |#1| (-146)) (-12 (|has| |#1| (-374)) (|has| |#2| (-146)))) ((((-1177) |#1|) . T)) (|has| |#1| (-146)) (|has| |#1| (-148)) @@ -1697,24 +1697,24 @@ (((|#3|) . T)) ((((-1278 |#1| |#2| |#3|)) |has| |#1| (-374))) ((($) . T) (((-576)) . T) (((-419 (-576))) |has| |#1| (-38 (-419 (-576)))) ((|#1|) . T)) -((((-419 (-576))) -2781 (|has| |#1| (-38 (-419 (-576)))) (|has| |#1| (-374))) (((-1193 |#1| |#2| |#3|)) |has| |#1| (-374)) (((-576)) . T) (($) . T) ((|#1|) . T)) -(((|#1|) . T) (((-419 (-576))) -2781 (|has| |#1| (-38 (-419 (-576)))) (|has| |#1| (-374))) (((-576)) . T) (($) . T)) +((((-419 (-576))) -2755 (|has| |#1| (-38 (-419 (-576)))) (|has| |#1| (-374))) (((-1193 |#1| |#2| |#3|)) |has| |#1| (-374)) (((-576)) . T) (($) . T) ((|#1|) . 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T)) -(((|#4|) -2781 (|has| |#4| (-174)) (|has| |#4| (-374)) (|has| |#4| (-738)))) -(((|#3|) -2781 (|has| |#3| (-174)) (|has| |#3| (-374)) (|has| |#3| (-738)))) +(((|#4|) -2755 (|has| |#4| (-174)) (|has| |#4| (-374)) (|has| |#4| (-738)))) +(((|#3|) -2755 (|has| |#3| (-174)) (|has| |#3| (-374)) (|has| |#3| (-738)))) (|has| |#2| (-374)) (((|#1|) |has| |#1| (-174))) -(((|#4|) -2781 (|has| |#4| (-174)) (|has| |#4| (-374)) (|has| |#4| (-738)) (|has| |#4| (-1068)))) -(((|#3|) -2781 (|has| |#3| (-174)) (|has| |#3| (-374)) (|has| |#3| (-738)) (|has| |#3| (-1068)))) +(((|#4|) -2755 (|has| |#4| (-174)) (|has| |#4| (-374)) (|has| |#4| (-738)) (|has| |#4| (-1068)))) +(((|#3|) -2755 (|has| |#3| (-174)) (|has| |#3| (-374)) (|has| |#3| (-738)) (|has| |#3| (-1068)))) (((|#2|) |has| |#2| (-1068))) (((|#2|) |has| |#2| (-1068))) ((((-1177) |#1|) . T)) @@ -1726,8 +1726,8 @@ ((((-400) (-1177)) . T)) ((($ (-1195)) . 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T)) (|has| |#2| (-148)) (|has| |#1| (-485)) -(-2781 (|has| |#1| (-485)) (|has| |#1| (-738)) (|has| |#1| (-915 (-1195))) (|has| |#1| (-1068))) +(-2755 (|has| |#1| (-485)) (|has| |#1| (-738)) (|has| |#1| (-915 (-1195))) (|has| |#1| (-1068))) (|has| |#1| (-374)) ((((-874)) . T)) (|has| |#1| (-38 (-419 (-576)))) @@ -1747,8 +1747,8 @@ (|has| |#1| (-860)) ((((-874)) . T)) (((|#2|) . 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T)) ((((-874)) . T)) -(-2781 (|has| |#1| (-102)) (|has| |#1| (-1119))) +(-2755 (|has| |#1| (-102)) (|has| |#1| (-1119))) (((|#2| (-494 (-3500 |#1|) (-783)) (-876 |#1|)) . T)) ((((-419 (-576))) . #0=(|has| |#2| (-374))) (($) . #0#)) (((|#1| (-543 (-1195)) (-1195)) . T)) @@ -1778,19 +1778,19 @@ (((|#2|) |has| |#2| (-174))) (((|#1|) . T)) (((|#2|) . T)) -(((|#1|) . T) (((-2 (|:| -4300 (-1177)) (|:| -4391 |#1|))) . T)) -((((-2 (|:| -4300 |#1|) (|:| -4391 |#2|))) . T)) +(((|#1|) . T) (((-2 (|:| -4298 (-1177)) (|:| -4437 |#1|))) . T)) +((((-2 (|:| -4298 |#1|) (|:| -4437 |#2|))) . T)) (((|#2|) . T)) -((((-2 (|:| -4300 (-1195)) (|:| -4391 (-52)))) . T)) +((((-2 (|:| -4298 (-1195)) (|:| -4437 (-52)))) . T)) ((((-1193 |#1| |#2| |#3|)) |has| |#1| (-374))) ((((-1193 |#1| |#2| |#3|)) |has| |#1| (-374))) -((((-2 (|:| -4300 |#1|) (|:| -4391 |#2|))) . T)) +((((-2 (|:| -4298 |#1|) (|:| -4437 |#2|))) . T)) ((((-1195) (-52)) . T)) ((((-419 (-576)) |#1|) . T) (($ $) . T)) (((|#1| (-576)) . T)) ((((-927 |#1|)) . T)) -(((|#1|) -2781 (|has| |#1| (-174)) (|has| |#1| (-374)) (|has| |#1| (-1068))) (($) -2781 (|has| |#1| (-915 (-1195))) (|has| |#1| (-1068)))) -((((-1195)) -2781 (-12 (|has| |#2| (-915 (-1195))) (|has| |#2| (-1068))) (-12 (|has| |#2| (-917 (-1195))) (|has| |#2| (-1068))))) +(((|#1|) -2755 (|has| |#1| (-174)) (|has| |#1| (-374)) (|has| |#1| (-1068))) (($) -2755 (|has| |#1| (-915 (-1195))) (|has| |#1| (-1068)))) +((((-1195)) -2755 (-12 (|has| |#2| (-915 (-1195))) (|has| |#2| (-1068))) (-12 (|has| |#2| (-917 (-1195))) (|has| |#2| (-1068))))) (((|#1|) . T) (((-576)) |has| |#1| (-1057 (-576))) (((-419 (-576))) |has| |#1| (-1057 (-419 (-576))))) (|has| |#1| (-862)) (|has| |#1| (-862)) @@ -1810,15 +1810,15 @@ (((|#4| |#4|) -12 (|has| |#4| (-319 |#4|)) (|has| |#4| (-1119)))) (((|#1|) |has| |#1| (-174))) (((|#4| |#4|) -12 (|has| |#4| (-319 |#4|)) (|has| |#4| (-1119)))) -(((|#3|) -2781 (|has| |#3| (-174)) (|has| |#3| (-374)))) -((($) -2781 (|has| |#1| (-464)) (|has| |#1| (-568)) (|has| |#1| (-926))) ((|#1|) |has| |#1| (-174)) (((-419 (-576))) |has| |#1| (-38 (-419 (-576))))) -(-2781 (|has| |#2| (-374)) (|has| |#2| (-464)) (|has| |#2| (-926))) -((($) -2781 (|has| |#1| (-174)) (|has| |#1| (-464)) (|has| |#1| (-568)) (|has| |#1| (-926))) ((|#1|) . 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T)) @@ -1827,7 +1827,7 @@ (|has| |#1| (-832)) (|has| |#1| (-832)) (((|#1|) . T)) -(-2781 (|has| |#1| (-317)) (|has| |#1| (-374)) (|has| |#1| (-360))) +(-2755 (|has| |#1| (-317)) (|has| |#1| (-374)) (|has| |#1| (-360))) (|has| |#1| (-860)) (|has| |#1| (-860)) (|has| |#1| (-860)) @@ -1836,14 +1836,14 @@ ((((-576)) . T) (($) . T) (((-419 (-576))) . T)) (|has| |#1| (-38 (-419 (-576)))) (|has| |#1| (-38 (-419 (-576)))) -(-2781 (|has| |#1| (-374)) (|has| |#1| (-360))) +(-2755 (|has| |#1| (-374)) (|has| |#1| (-360))) (|has| |#1| (-38 (-419 (-576)))) (|has| |#1| (-38 (-419 (-576)))) -((((-2 (|:| -4300 |#1|) (|:| -4391 |#2|))) . T)) +((((-2 (|:| -4298 |#1|) (|:| -4437 |#2|))) . T)) ((((-1195)) |has| |#1| (-915 (-1195))) (((-1101)) . T)) (((|#1|) . 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T)) (|has| |#1| (-146)) (|has| |#1| (-148)) @@ -1893,31 +1893,31 @@ ((((-419 (-576))) |has| |#1| (-38 (-419 (-576)))) ((|#1|) |has| |#1| (-174)) (($) |has| |#1| (-568))) ((($) |has| |#1| (-568))) (((|#2|) . T)) -((((-419 (-576))) |has| |#1| (-38 (-419 (-576)))) ((|#1|) . T) (($) -2781 (|has| |#1| (-174)) (|has| |#1| (-568)))) +((((-419 (-576))) |has| |#1| (-38 (-419 (-576)))) ((|#1|) . T) (($) -2755 (|has| |#1| (-174)) (|has| |#1| (-568)))) ((($) |has| |#1| (-568)) ((|#1|) . T)) ((($) |has| |#1| (-860))) ((((-1193 |#1| |#2| |#3|)) |has| |#1| (-374))) (|has| |#1| (-926)) ((((-1195)) . T)) ((((-874)) . T)) -((($) -2781 (|has| |#1| (-174)) (|has| |#1| (-374)) (|has| |#1| (-568))) (((-419 (-576))) -2781 (|has| |#1| (-38 (-419 (-576)))) (|has| |#1| (-374))) (((-1278 |#1| |#2| |#3|)) |has| |#1| (-374)) ((|#1|) . 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T) (($ (-1195)) -12 (|has| |#1| (-15 * (|#1| (-783) |#1|))) (|has| |#1| (-915 (-1195))))) (|has| |#1| (-926)) @@ -2248,7 +2248,7 @@ (((|#2|) |has| |#2| (-1068))) (|has| |#1| (-374)) ((($) . T)) -(((|#2|) -12 (|has| |#2| (-319 |#2|)) (|has| |#2| (-1119))) (((-2 (|:| -4300 |#1|) (|:| -4391 |#2|))) |has| (-2 (|:| -4300 |#1|) (|:| -4391 |#2|)) (-319 (-2 (|:| -4300 |#1|) (|:| -4391 |#2|))))) +(((|#2|) -12 (|has| |#2| (-319 |#2|)) (|has| |#2| (-1119))) (((-2 (|:| -4298 |#1|) (|:| -4437 |#2|))) |has| (-2 (|:| -4298 |#1|) (|:| -4437 |#2|)) (-319 (-2 (|:| -4298 |#1|) (|:| -4437 |#2|))))) (((|#1|) |has| |#1| (-174))) ((($ (-876 |#1|)) . T)) (((|#1| |#1|) . T)) @@ -2259,7 +2259,7 @@ (((|#1|) . T)) ((((-419 |#2|)) . T) (((-419 (-576))) . T) (($) . T) (((-576)) . T)) ((((-656 $)) . T) (((-1177)) . T) (((-1195)) . T) (((-576)) . T) (((-227)) . T) (((-874)) . 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T)) (((|#3|) |has| |#3| (-1068))) @@ -2334,15 +2334,15 @@ ((($) . T)) ((((-1195)) |has| |#2| (-915 (-1195)))) ((((-874)) . T)) -((((-2 (|:| -4300 |#1|) (|:| -4391 |#2|))) . T)) +((((-2 (|:| -4298 |#1|) (|:| -4437 |#2|))) . T)) ((((-419 (-576))) . T) (($) . T)) (|has| |#1| (-485)) (|has| |#1| (-379)) (|has| |#1| (-379)) (|has| |#1| (-379)) (|has| |#1| (-374)) -(-2781 (|has| |#1| (-146)) (|has| |#1| (-148)) (|has| |#1| (-174)) (|has| |#1| (-485)) (|has| |#1| (-568)) (|has| |#1| (-1068)) (|has| |#1| (-1131))) -((($) -2781 (|has| |#1| (-238)) (|has| |#1| (-237)) (|has| |#1| (-360)))) +(-2755 (|has| |#1| (-146)) (|has| |#1| (-148)) (|has| |#1| (-174)) (|has| |#1| (-485)) (|has| |#1| (-568)) (|has| |#1| (-1068)) (|has| |#1| (-1131))) +((($) -2755 (|has| |#1| (-238)) (|has| |#1| (-237)) (|has| |#1| (-360)))) ((((-117 |#1|)) . T)) ((((-117 |#1|)) . T)) (|has| |#1| (-360)) @@ -2353,7 +2353,7 @@ (|has| |#1| (-38 (-419 (-576)))) (((|#2|) . T) (((-874)) . T)) (((|#2|) . T) (((-874)) . 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T)) +((($) -2755 (|has| |#1| (-374)) (|has| |#1| (-360))) (((-419 (-576))) -2755 (|has| |#1| (-374)) (|has| |#1| (-360))) ((|#1|) . T)) ((((-576)) . T)) -((((-2 (|:| -4300 (-1177)) (|:| -4391 (-52)))) |has| (-2 (|:| -4300 (-1177)) (|:| -4391 (-52))) (-319 (-2 (|:| -4300 (-1177)) (|:| -4391 (-52)))))) +((((-2 (|:| -4298 (-1177)) (|:| -4437 (-52)))) |has| (-2 (|:| -4298 (-1177)) (|:| -4437 (-52))) (-319 (-2 (|:| -4298 (-1177)) (|:| -4437 (-52)))))) (((|#1|) -12 (|has| |#1| (-319 |#1|)) (|has| |#1| (-1119)))) (|has| |#1| (-860)) ((((-576) $) . T) (((-656 (-576)) $) . T)) @@ -2547,56 +2547,56 @@ (|has| |#1| (-38 (-419 (-576)))) ((((-1177)) . T) (((-518)) . T) (((-227)) . T) (((-576)) . 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T)) @@ -2609,11 +2609,11 @@ (|has| |#2| (-146)) (|has| |#2| (-148)) ((((-927 |#1|)) . T) (((-419 (-576))) . T) (($) . T)) -(-2781 (|has| |#1| (-102)) (|has| |#1| (-1119))) +(-2755 (|has| |#1| (-102)) (|has| |#1| (-1119))) ((((-576)) . T) ((|#1|) . T)) (((|#2|) . T) (($) . T) (((-576)) . T)) (((|#2|) . T)) -((((-1195)) -2781 (|has| |#2| (-915 (-1195))) (|has| |#2| (-917 (-1195))))) +((((-1195)) -2755 (|has| |#2| (-915 (-1195))) (|has| |#2| (-917 (-1195))))) (((|#1| |#1|) . T)) (((|#3|) |has| |#3| (-374))) ((((-419 |#2|)) . T)) @@ -2622,10 +2622,10 @@ ((((-874)) . T)) ((((-874)) . T)) ((((-548)) |has| |#1| (-626 (-548)))) -((((-2 (|:| -4300 |#1|) (|:| -4391 |#2|))) . T)) +((((-2 (|:| -4298 |#1|) (|:| -4437 |#2|))) . T)) ((((-576)) . T) (($) . T) (((-419 (-576))) . T)) ((((-1195) |#1|) |has| |#1| (-526 (-1195) |#1|)) ((|#1| |#1|) |has| |#1| (-319 |#1|))) -(((|#1|) -2781 (|has| |#1| (-174)) (|has| |#1| (-374)))) +(((|#1|) -2755 (|has| |#1| (-174)) (|has| |#1| (-374)))) (((|#1|) . T) (((-419 (-576))) . T) (($) . T)) ((((-576)) . T) (((-419 (-576))) . T) (($) . T)) (((|#1|) . T) (((-419 (-576))) . T) (($) . T)) @@ -2635,14 +2635,14 @@ (((|#1|) . T) (($) . T) (((-419 (-576))) . T)) (((|#1|) . T) (($) . T) (((-419 (-576))) . T)) (((|#2|) |has| |#2| (-374))) -((($) -2781 (|has| |#1| (-374)) (|has| |#1| (-360))) (((-419 (-576))) -2781 (|has| |#1| (-374)) (|has| |#1| (-360))) ((|#1|) . T)) +((($) -2755 (|has| |#1| (-374)) (|has| |#1| (-360))) (((-419 (-576))) -2755 (|has| |#1| (-374)) (|has| |#1| (-360))) ((|#1|) . T)) (((|#2|) . T)) ((((-419 (-576))) . T) (((-711)) . T) (($) . T)) -((($) . T) (((-419 (-576))) -2781 (|has| |#1| (-374)) (|has| |#1| (-360))) ((|#1|) . T)) +((($) . T) (((-419 (-576))) -2755 (|has| |#1| (-374)) (|has| |#1| (-360))) ((|#1|) . 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T)) (((|#1| |#1|) -12 (|has| |#1| (-319 |#1|)) (|has| |#1| (-1119)))) (|has| |#1| (-38 (-419 (-576)))) @@ -2660,13 +2660,13 @@ (|has| |#1| (-146)) (|has| |#1| (-148)) ((($ $) . T)) -(-2781 (|has| |#1| (-21)) (|has| |#1| (-25)) (|has| |#1| (-174)) (|has| |#1| (-374)) (|has| |#1| (-485)) (|has| |#1| (-738)) (|has| |#1| (-915 (-1195))) (|has| |#1| (-1068)) (|has| |#1| (-1131)) (|has| |#1| (-1119))) +(-2755 (|has| |#1| (-21)) (|has| |#1| (-25)) (|has| |#1| (-174)) (|has| |#1| (-374)) (|has| |#1| (-485)) (|has| |#1| (-738)) (|has| |#1| (-915 (-1195))) (|has| |#1| (-1068)) (|has| |#1| (-1131)) (|has| |#1| (-1119))) (|has| |#1| (-568)) (((|#2|) . T)) ((((-576)) . T)) -((((-2 (|:| -4300 |#1|) (|:| -4391 |#2|))) . T)) +((((-2 (|:| -4298 |#1|) (|:| -4437 |#2|))) . T)) (((|#1|) . 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T) (((-576)) . T)) -((((-2 (|:| -4300 (-1177)) (|:| -4391 (-52)))) . T)) +((((-2 (|:| -4298 (-1177)) (|:| -4437 (-52)))) . T)) (((|#1|) . T)) -((((-2 (|:| -4300 |#1|) (|:| -4391 |#2|))) . T)) +((((-2 (|:| -4298 |#1|) (|:| -4437 |#2|))) . T)) ((((-874)) . T)) (((|#1| |#2|) . T)) ((($) . T) (((-576)) . T)) (((|#1| (-419 (-576))) . T)) (((|#1|) . T)) -(-2781 (|has| |#1| (-300)) (|has| |#1| (-374))) +(-2755 (|has| |#1| (-300)) (|has| |#1| (-374))) ((((-145)) . T)) ((((-576)) |has| #0=(-419 |#2|) (-651 (-576))) ((#0#) . T) (((-419 (-576))) . T) (($) . T)) (|has| |#1| (-860)) @@ -2842,7 +2842,7 @@ ((((-874)) . T)) ((((-874)) . T)) ((((-189)) . T) (((-874)) . T)) -((((-2 (|:| -4300 |#1|) (|:| -4391 |#2|))) . T)) +((((-2 (|:| -4298 |#1|) (|:| -4437 |#2|))) . T)) (((|#2| |#2|) . T) ((|#1| |#1|) . T)) ((((-874)) . T)) ((((-874)) . T)) @@ -2857,10 +2857,10 @@ ((((-1177)) . 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T)) -(-2781 (|has| |#1| (-374)) (|has| |#1| (-360))) +(-2755 (|has| |#1| (-374)) (|has| |#1| (-360))) (((#0=(-419 (-576)) #0#) . T) ((#1=(-711) #1#) . T) (($ $) . T)) ((((-326 |#1|)) . T) (($) . T)) (((|#1|) . T) (((-419 (-576))) |has| |#1| (-374))) ((((-874)) . T)) (|has| |#1| (-1119)) (((|#1|) . T)) -(((|#1|) -2781 (|has| |#2| (-378 |#1|)) (|has| |#2| (-429 |#1|)))) -(((|#1|) -2781 (|has| |#2| (-378 |#1|)) (|has| |#2| (-429 |#1|)))) +(((|#1|) -2755 (|has| |#2| (-378 |#1|)) (|has| |#2| (-429 |#1|)))) +(((|#1|) -2755 (|has| |#2| (-378 |#1|)) (|has| |#2| (-429 |#1|)))) (((|#2|) . T)) ((((-419 (-576))) . T) (((-711)) . T) (($) . T)) ((((-591)) . T)) (((|#3| |#3|) . T)) -((($ (-1195)) -2781 (|has| |#2| (-915 (-1195))) (|has| |#2| (-917 (-1195))))) +((($ (-1195)) -2755 (|has| |#2| (-915 (-1195))) (|has| |#2| (-917 (-1195))))) (|has| |#2| (-238)) ((((-876 |#1|)) . T)) ((((-1195)) |has| |#1| (-915 (-1195))) ((|#3|) . T)) @@ -2968,10 +2968,10 @@ (|has| |#1| (-1119)) (((|#2|) . T)) (((|#1|) . T)) -((($) -2781 (|has| |#1| (-238)) (|has| |#1| (-237)))) +((($) -2755 (|has| |#1| (-238)) (|has| |#1| (-237)))) ((((-576)) . T)) (((|#2|) . T) (((-419 (-576))) |has| |#1| (-1057 (-419 (-576)))) ((|#1|) . T) (($) . T) (((-576)) . T)) -(-2781 (|has| |#1| (-174)) (|has| |#1| (-374)) (|has| |#1| (-464)) (|has| |#1| (-568)) (|has| |#1| (-926))) +(-2755 (|has| |#1| (-174)) (|has| |#1| (-374)) (|has| |#1| (-464)) (|has| |#1| (-568)) (|has| |#1| (-926))) (((|#2|) . T) (((-576)) |has| |#2| (-651 (-576)))) (((|#1| |#2|) . T)) ((($) . T)) @@ -3014,7 +3014,7 @@ (|has| |#2| (-1041)) ((($) . T)) (|has| |#1| (-926)) -((((-2 (|:| -4300 |#1|) (|:| -4391 |#2|))) . T)) +((((-2 (|:| -4298 |#1|) (|:| -4437 |#2|))) . T)) (((|#4|) . T)) ((($) . T)) (((|#2|) . T)) @@ -3024,16 +3024,16 @@ (|has| |#1| (-374)) ((((-927 |#1|)) . T)) ((($) . T) (((-576)) . T) ((|#1|) . T) (((-419 (-576))) . 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T)) -(-2781 (-12 (|has| |#3| (-238)) (|has| |#3| (-1068))) (-12 (|has| |#3| (-237)) (|has| |#3| (-1068)))) +(-2755 (-12 (|has| |#3| (-238)) (|has| |#3| (-1068))) (-12 (|has| |#3| (-237)) (|has| |#3| (-1068)))) ((($) . T) (((-419 (-576))) . T)) ((($) . T) (((-576)) . T) (((-419 (-576))) . T) (((-624 $)) . T)) ((((-576)) . T) (($) . T)) @@ -3042,14 +3042,14 @@ (((|#2| (-245 (-3500 |#1|) (-783))) . T)) (((|#1| (-543 |#3|)) . T)) ((((-419 (-576))) . T)) -(-2781 (|has| |#1| (-464)) (|has| |#1| (-568)) (|has| |#1| (-926))) +(-2755 (|has| |#1| (-464)) (|has| |#1| (-568)) (|has| |#1| (-926))) ((((-1177)) . T) (((-874)) . T)) -(((#0=(-2 (|:| -4300 (-1195)) (|:| -4391 (-52))) #0#) |has| (-2 (|:| -4300 (-1195)) (|:| -4391 (-52))) (-319 (-2 (|:| -4300 (-1195)) (|:| -4391 (-52)))))) +(((#0=(-2 (|:| -4298 (-1195)) (|:| -4437 (-52))) #0#) |has| (-2 (|:| -4298 (-1195)) (|:| -4437 (-52))) (-319 (-2 (|:| -4298 (-1195)) (|:| -4437 (-52)))))) ((((-1177)) . T)) (|has| |#1| (-926)) (|has| |#2| (-374)) (((|#1|) . T) (($) . T) (((-576)) . T)) -(-2781 (|has| |#2| (-21)) (|has| |#2| (-132)) (|has| |#2| (-174)) (|has| |#2| (-374)) (|has| |#2| (-805)) (|has| |#2| (-1068))) +(-2755 (|has| |#2| (-21)) (|has| |#2| (-132)) (|has| |#2| (-174)) (|has| |#2| (-374)) (|has| |#2| (-805)) (|has| |#2| (-1068))) ((((-171 (-390))) . T) (((-227)) . T) (((-390)) . T)) ((((-874)) . T)) (((|#1|) . T)) @@ -3066,11 +3066,11 @@ (|has| |#1| (-38 (-419 (-576)))) (|has| |#1| (-38 (-419 (-576)))) (|has| |#1| (-38 (-419 (-576)))) -(-2781 (|has| |#1| (-317)) (|has| |#1| (-374)) (|has| |#1| (-360))) +(-2755 (|has| |#1| (-317)) (|has| |#1| (-374)) (|has| |#1| (-360))) (|has| |#1| (-38 (-419 (-576)))) (-12 (|has| |#1| (-557)) (|has| |#1| (-840))) ((((-874)) . T)) -((((-1195)) -2781 (-12 (|has| |#1| (-15 * (|#1| (-576) |#1|))) (|has| |#1| (-915 (-1195)))) (-12 (|has| |#1| (-374)) (|has| |#2| (-915 (-1195)))))) +((((-1195)) -2755 (-12 (|has| |#1| (-15 * (|#1| (-576) |#1|))) (|has| |#1| (-915 (-1195)))) (-12 (|has| |#1| (-374)) (|has| |#2| (-915 (-1195)))))) (|has| |#1| (-374)) ((((-1195)) -12 (|has| |#1| (-15 * (|#1| (-419 (-576)) |#1|))) (|has| |#1| (-915 (-1195))))) (|has| |#1| (-374)) @@ -3083,11 +3083,11 @@ ((((-576) |#1|) . T)) ((((-1195)) |has| |#1| (-915 (-1195)))) (((|#1|) . T)) -(-2781 (-12 (|has| |#1| (-238)) (|has| |#1| (-374))) (-12 (|has| |#1| (-237)) (|has| |#1| (-374))) (|has| |#1| (-360))) +(-2755 (-12 (|has| |#1| (-238)) (|has| |#1| (-374))) (-12 (|has| |#1| (-237)) (|has| |#1| (-374))) (|has| |#1| (-360))) (((|#2|) |has| |#1| (-374))) (((|#2|) |has| |#1| (-374))) ((((-576)) . T) (($) . T)) -((((-2 (|:| -4300 |#1|) (|:| -4391 |#2|))) . T)) +((((-2 (|:| -4298 |#1|) (|:| -4437 |#2|))) . T)) (((|#1|) . T)) (((|#1|) . T)) (((|#1|) |has| |#1| (-174))) @@ -3119,34 +3119,34 @@ (((|#1| |#1|) -12 (|has| |#1| (-319 |#1|)) (|has| |#1| (-1119)))) (((|#2|) |has| |#1| (-374))) ((((-390)) -12 (|has| |#1| (-374)) (|has| |#2| (-899 (-390)))) (((-576)) -12 (|has| |#1| (-374)) (|has| |#2| (-899 (-576))))) -(-2781 (|has| |#1| (-374)) (|has| |#1| (-568))) +(-2755 (|has| |#1| (-374)) (|has| |#1| (-568))) (((|#1|) . T)) ((($) . T) (((-576)) . T) ((|#2|) . T)) (|has| |#1| (-374)) (((|#3|) . T)) ((((-1177)) . T) (((-518)) . T) (((-227)) . T) (((-576)) . T)) (((|#1|) . T)) -(-2781 (|has| |#1| (-374)) (|has| |#1| (-568))) +(-2755 (|has| |#1| (-374)) (|has| |#1| (-568))) (|has| |#1| (-374)) (|has| |#1| (-568)) (((|#4| |#4|) -12 (|has| |#4| (-319 |#4|)) (|has| |#4| (-1119)))) ((((-419 |#2|)) . T) (((-419 (-576))) . T) (($) . T) (((-576)) . 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T)) (|has| |#1| (-148)) -(-2781 (|has| |#1| (-146)) (|has| |#1| (-379))) +(-2755 (|has| |#1| (-146)) (|has| |#1| (-379))) (|has| |#1| (-148)) -(-2781 (|has| |#1| (-146)) (|has| |#1| (-379))) +(-2755 (|has| |#1| (-146)) (|has| |#1| (-379))) (|has| |#1| (-148)) ((($) . T)) ((((-593 |#1|)) . T)) @@ -3162,7 +3162,7 @@ ((((-419 (-576))) |has| |#2| (-1057 (-576))) (((-576)) |has| |#2| (-1057 (-576))) (((-1195)) |has| |#2| (-1057 (-1195))) ((|#2|) . T)) (((#0=(-419 |#2|) #0#) . T) ((#1=(-419 (-576)) #1#) . T) (($ $) . T)) (((|#1|) . T)) -(-2781 (|has| |#1| (-146)) (|has| |#1| (-360))) +(-2755 (|has| |#1| (-146)) (|has| |#1| (-360))) (|has| |#1| (-148)) ((((-874)) . T)) ((($) . T)) @@ -3182,15 +3182,15 @@ ((((-419 |#2|)) . T)) ((((-874)) . T)) (((|#1|) . T)) -((((-1195)) -2781 (|has| |#1| (-915 (-1195))) (|has| |#1| (-917 (-1195))))) -(-2781 (|has| |#1| (-102)) (|has| |#1| (-1119))) +((((-1195)) -2755 (|has| |#1| (-915 (-1195))) (|has| |#1| (-917 (-1195))))) +(-2755 (|has| |#1| (-102)) (|has| |#1| (-1119))) (|has| |#1| (-803)) (|has| |#1| (-803)) ((((-874)) . T)) ((((-927 |#1|)) . T) (((-419 (-576))) . T) (($) . T) (((-576)) . T)) ((((-874)) . T)) ((((-548)) |has| |#1| (-626 (-548)))) -((((-874)) -2781 (|has| |#1| (-625 (-874))) (|has| |#1| (-862)) (|has| |#1| (-1119)))) +((((-874)) -2755 (|has| |#1| (-625 (-874))) (|has| |#1| (-862)) (|has| |#1| (-1119)))) ((((-115)) . T) ((|#1|) . T)) (((|#1|) . T)) (((|#1|) . T)) @@ -3199,7 +3199,7 @@ ((((-1272 |#1| |#2| |#3| |#4|)) . T) (($) . T) (((-419 (-576))) . T)) (((|#1|) |has| |#1| (-174)) (($) |has| |#1| (-568)) (((-419 (-576))) |has| |#1| (-568))) ((((-874)) . T)) -(-2781 (-12 (|has| |#2| (-238)) (|has| |#2| (-1068))) (-12 (|has| |#2| (-237)) (|has| |#2| (-1068)))) +(-2755 (-12 (|has| |#2| (-238)) (|has| |#2| (-1068))) (-12 (|has| |#2| (-237)) (|has| |#2| (-1068)))) ((((-874)) . T)) (((|#2|) . T)) (((|#2|) . T)) @@ -3212,10 +3212,10 @@ ((((-874)) . T)) (((|#2|) . T)) ((((-576)) . T)) -((((-1195)) -2781 (|has| (-419 |#2|) (-915 (-1195))) (|has| (-419 |#2|) (-917 (-1195))))) +((((-1195)) -2755 (|has| (-419 |#2|) (-915 (-1195))) (|has| (-419 |#2|) (-917 (-1195))))) ((((-874)) . T)) ((((-576)) . T)) -(-2781 (|has| |#2| (-805)) (|has| |#2| (-862))) +(-2755 (|has| |#2| (-805)) (|has| |#2| (-862))) ((((-171 (-390))) . T) (((-227)) . T) (((-390)) . T)) ((((-874)) . T)) ((((-874)) . T)) @@ -3227,10 +3227,10 @@ (((|#1|) . T) (($) . T) (((-419 (-576))) . 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T)) (|has| |#1| (-568)) @@ -3262,15 +3262,15 @@ (((|#1|) . T)) (((|#1|) . T)) ((((-419 |#2|)) . T) (((-419 (-576))) . T) (($) . T)) -(-2781 (|has| |#1| (-374)) (|has| |#1| (-568))) +(-2755 (|has| |#1| (-374)) (|has| |#1| (-568))) (|has| |#1| (-374)) -(-2781 (|has| |#1| (-374)) (|has| |#1| (-568))) +(-2755 (|has| |#1| (-374)) (|has| |#1| (-568))) (|has| |#1| (-374)) (|has| |#1| (-568)) ((($) . T)) (|has| |#1| (-1119)) ((((-792 |#1| (-876 |#2|))) |has| (-792 |#1| (-876 |#2|)) (-319 (-792 |#1| (-876 |#2|))))) -(-2781 (|has| |#2| (-464)) (|has| |#2| (-568)) (|has| |#2| (-926))) +(-2755 (|has| |#2| (-464)) (|has| |#2| (-568)) (|has| |#2| (-926))) (((|#1|) . T)) (((|#2| |#3|) . T)) (((|#1|) . T)) @@ -3279,17 +3279,17 @@ (((|#1| (-783)) . T)) (|has| |#1| (-238)) (((|#1| (-543 (-1107 (-1195)))) . 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T) (((-419 (-576))) |has| |#2| (-38 (-419 (-576)))) ((|#2|) . T) (((-576)) |has| |#2| (-651 (-576)))) @@ -3331,29 +3331,29 @@ (((|#1|) . T) (((-419 (-576))) . T) (($) . T)) (((|#1|) . T) (((-419 (-576))) . T) (($) . T)) (((|#1|) . T) (((-419 (-576))) . T) (($) . T)) -((($ $) -2781 (|has| |#1| (-174)) (|has| |#1| (-464)) (|has| |#1| (-568)) (|has| |#1| (-926))) ((|#1| |#1|) . T) ((#0=(-419 (-576)) #0#) |has| |#1| (-38 (-419 (-576))))) -((($ $) -2781 (|has| |#1| (-174)) (|has| |#1| (-374)) (|has| |#1| (-464)) (|has| |#1| (-568)) (|has| |#1| (-926))) ((|#1| |#1|) . T) ((#0=(-419 (-576)) #0#) |has| |#1| (-38 (-419 (-576))))) +((($ $) -2755 (|has| |#1| (-174)) (|has| |#1| (-464)) (|has| |#1| (-568)) (|has| |#1| (-926))) ((|#1| |#1|) . T) ((#0=(-419 (-576)) #0#) |has| |#1| (-38 (-419 (-576))))) +((($ $) -2755 (|has| |#1| (-174)) (|has| |#1| (-374)) (|has| |#1| (-464)) (|has| |#1| (-568)) (|has| |#1| (-926))) ((|#1| |#1|) . 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T)) -((((-2 (|:| -4300 (-1177)) (|:| -4391 |#1|))) . T)) +((((-2 (|:| -4298 (-1177)) (|:| -4437 |#1|))) . T)) (((|#1|) . T)) (((|#1|) . T)) (((|#1|) . T)) (((|#1| |#1|) . T)) (((|#1|) . T)) (((|#1|) . T)) -(-2781 (|has| |#1| (-102)) (|has| |#1| (-1119))) +(-2755 (|has| |#1| (-102)) (|has| |#1| (-1119))) (((|#1|) . T)) (((|#1|) . T) (($) . T) (((-419 (-576))) . T)) ((((-1195)) . T) ((|#1|) . T)) @@ -3365,15 +3365,15 @@ (((#0=(-419 (-576)) #0#) . T)) ((((-419 (-576))) . T)) (((|#1|) |has| |#1| (-174))) -(-2781 (|has| |#2| (-21)) (|has| |#2| (-174)) (|has| |#2| (-374)) (|has| |#2| (-1068))) +(-2755 (|has| |#2| (-21)) (|has| |#2| (-174)) (|has| |#2| (-374)) (|has| |#2| (-1068))) (((|#1|) . T)) (((|#1|) . 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T)) @@ -3440,7 +3440,7 @@ (|has| |#1| (-374)) (|has| |#1| (-374)) (((|#4|) -12 (|has| |#4| (-319 |#4|)) (|has| |#4| (-1119)))) -(((|#2|) -2781 (|has| |#2| (-6 (-4464 "*"))) (|has| |#2| (-174)))) +(((|#2|) -2755 (|has| |#2| (-6 (-4464 "*"))) (|has| |#2| (-174)))) (((|#2|) . T)) (|has| |#1| (-374)) (((|#2|) . T)) @@ -3454,12 +3454,12 @@ (((|#2| (-783)) . T)) ((((-1195)) . T)) ((((-882 |#1|)) . T)) -(-2781 (|has| |#3| (-21)) (|has| |#3| (-174)) (|has| |#3| (-374)) (|has| |#3| (-1068))) -(-2781 (|has| |#3| (-21)) (|has| |#3| (-23)) (|has| |#3| (-25)) (|has| |#3| (-132)) (|has| |#3| (-174)) (|has| |#3| (-374)) (|has| |#3| (-805)) (|has| |#3| (-1068))) +(-2755 (|has| |#3| (-21)) (|has| |#3| (-174)) (|has| |#3| (-374)) (|has| |#3| (-1068))) +(-2755 (|has| |#3| (-21)) (|has| |#3| (-23)) (|has| |#3| (-25)) (|has| |#3| (-132)) (|has| |#3| (-174)) (|has| |#3| (-374)) (|has| |#3| (-805)) (|has| |#3| (-1068))) ((((-874)) . T)) (((|#1|) . T)) -(-2781 (|has| |#2| (-805)) (|has| |#2| (-862))) -(-2781 (-12 (|has| |#1| (-805)) (|has| |#2| (-805))) (-12 (|has| |#1| (-862)) (|has| |#2| (-862)))) +(-2755 (|has| |#2| (-805)) (|has| |#2| (-862))) +(-2755 (-12 (|has| |#1| (-805)) (|has| |#2| (-805))) (-12 (|has| |#1| (-862)) (|has| |#2| (-862)))) ((((-882 |#1|)) . T)) (((|#1|) . T)) (|has| |#1| (-379)) @@ -3477,7 +3477,7 @@ (((|#1|) . T)) ((((-874)) . T)) ((($) . T) ((|#2|) . T) (((-419 (-576))) . T) (((-576)) |has| |#2| (-651 (-576)))) -(-2781 (|has| |#1| (-102)) (|has| |#1| (-1119))) +(-2755 (|has| |#1| (-102)) (|has| |#1| (-1119))) (((|#1|) -12 (|has| |#1| (-319 |#1|)) (|has| |#1| (-1119)))) (((|#1| |#1|) -12 (|has| |#1| (-319 |#1|)) (|has| |#1| (-1119)))) (((|#1| |#1|) -12 (|has| |#1| (-319 |#1|)) (|has| |#1| (-1119)))) @@ -3486,7 +3486,7 @@ (((|#1|) . T)) ((((-874)) . T)) (|has| |#2| (-926)) -((((-2 (|:| -4300 (-1195)) (|:| -4391 (-52)))) . T)) +((((-2 (|:| -4298 (-1195)) (|:| -4437 (-52)))) . T)) ((((-548)) |has| |#2| (-626 (-548))) (((-905 (-390))) |has| |#2| (-626 (-905 (-390)))) (((-905 (-576))) |has| |#2| (-626 (-905 (-576))))) ((((-874)) . T)) ((((-874)) . T)) @@ -3496,7 +3496,7 @@ ((((-1191 |#1|)) . T) (((-874)) . T)) ((((-874)) . T)) ((((-419 (-576))) |has| |#2| (-1057 (-419 (-576)))) (((-576)) |has| |#2| (-1057 (-576))) ((|#2|) . T) (((-876 |#1|)) . T)) -((((-1195)) -2781 (|has| |#1| (-915 (-1195))) (|has| |#1| (-917 (-1195)))) (((-1101)) . T)) +((((-1195)) -2755 (|has| |#1| (-915 (-1195))) (|has| |#1| (-917 (-1195)))) (((-1101)) . T)) ((((-117 |#1|)) . T) (($) . T) (((-419 (-576))) . T)) ((((-419 (-576))) |has| |#1| (-1057 (-419 (-576)))) (((-576)) |has| |#1| (-1057 (-576))) ((|#1|) . T) (((-1195)) . T)) ((((-874)) . T)) @@ -3515,10 +3515,10 @@ ((((-656 |#1|)) . T)) ((($) |has| |#1| (-15 * (|#1| (-419 (-576)) |#1|)))) ((($) . T) (((-576)) . T) (((-1272 |#1| |#2| |#3| |#4|)) . T) (((-419 (-576))) . 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T)) @@ -3532,16 +3532,16 @@ ((((-419 |#2|) |#3|) . T)) ((((-874)) . T)) (((|#1|) . T)) -(-2781 (|has| |#1| (-102)) (|has| |#1| (-1119))) +(-2755 (|has| |#1| (-102)) (|has| |#1| (-1119))) (((|#2| (-494 (-3500 |#1|) (-783))) . T)) ((((-576) |#1|) . T)) ((((-1177)) . T) (((-874)) . T)) (((|#2| |#2|) . T)) (((|#1| (-543 (-1195))) . T)) -(-2781 (|has| |#2| (-21)) (|has| |#2| (-132)) (|has| |#2| (-174)) (|has| |#2| (-374)) (|has| |#2| (-805)) (|has| |#2| (-1068))) +(-2755 (|has| |#2| (-21)) (|has| |#2| (-132)) (|has| |#2| (-174)) (|has| |#2| (-374)) (|has| |#2| (-805)) (|has| |#2| (-1068))) ((((-576)) . T)) (((|#2|) . T)) -((($) -2781 (-12 (|has| |#2| (-238)) (|has| |#2| (-1068))) (-12 (|has| |#2| (-237)) (|has| |#2| (-1068))))) +((($) -2755 (-12 (|has| |#2| (-238)) (|has| |#2| (-1068))) (-12 (|has| |#2| (-237)) (|has| |#2| (-1068))))) (((|#2|) . T)) ((((-1195)) |has| |#1| (-915 (-1195))) (((-1101)) . T)) (((|#1|) . T) (((-576)) |has| |#1| (-651 (-576)))) @@ -3550,9 +3550,9 @@ ((($) . T) (((-419 (-576))) . T)) ((($) . T)) ((($) . T)) -(-2781 (|has| |#1| (-862)) (|has| |#1| (-1119))) +(-2755 (|has| |#1| (-862)) (|has| |#1| (-1119))) (((|#1|) . T)) -((($) -2781 (|has| |#1| (-374)) (|has| |#1| (-464)) (|has| |#1| (-568)) (|has| |#1| (-926))) ((|#1|) |has| |#1| (-174)) (((-419 (-576))) |has| |#1| (-38 (-419 (-576))))) +((($) -2755 (|has| |#1| (-374)) (|has| |#1| (-464)) (|has| |#1| (-568)) (|has| |#1| (-926))) ((|#1|) |has| |#1| (-174)) (((-419 (-576))) |has| |#1| (-38 (-419 (-576))))) ((((-874)) . T)) ((((-145)) . T)) (((|#1|) . T) (((-419 (-576))) . T)) @@ -3561,7 +3561,7 @@ ((((-874)) . T)) (((|#1|) . T)) (|has| |#1| (-1171)) -((($ (-1195)) -2781 (|has| (-419 |#2|) (-915 (-1195))) (|has| (-419 |#2|) (-917 (-1195))))) +((($ (-1195)) -2755 (|has| (-419 |#2|) (-915 (-1195))) (|has| (-419 |#2|) (-917 (-1195))))) (((|#1|) . T)) (((|#1| (-543 (-876 |#2|)) (-876 |#2|) (-792 |#1| (-876 |#2|))) . T)) ((((-419 $) (-419 $)) |has| |#1| (-568)) (($ $) . T) ((|#1| |#1|) . T)) @@ -3586,14 +3586,14 @@ (|has| |#1| (-1119)) (|has| |#1| (-1119)) (|has| |#2| (-374)) -(((|#1|) . T) (($) -2781 (|has| |#1| (-300)) (|has| |#1| (-374))) (((-419 (-576))) |has| |#1| (-374))) +(((|#1|) . T) (($) -2755 (|has| |#1| (-300)) (|has| |#1| (-374))) (((-419 (-576))) |has| |#1| (-374))) (|has| |#1| (-374)) (|has| |#1| (-374)) (|has| |#1| (-38 (-419 (-576)))) -((($) -2781 (|has| |#2| (-238)) (|has| |#2| (-237)))) +((($) -2755 (|has| |#2| (-238)) (|has| |#2| (-237)))) ((((-576)) . T)) (|has| |#1| (-1119)) -((($ (-1195)) -2781 (|has| |#2| (-915 (-1195))) (|has| |#2| (-917 (-1195))))) +((($ (-1195)) -2755 (|has| |#2| (-915 (-1195))) (|has| |#2| (-917 (-1195))))) ((((-1195)) -12 (|has| |#4| (-915 (-1195))) (|has| |#4| (-1068)))) ((((-1195)) -12 (|has| |#3| (-915 (-1195))) (|has| |#3| (-1068)))) (((|#1|) . T)) @@ -3605,25 +3605,25 @@ (|has| |#1| (-379)) (((|#1|) . T) (($) . T)) (((|#1| (-543 |#2|)) . 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T) (($) -2755 (|has| |#2| (-174)) (|has| |#2| (-464)) (|has| |#2| (-568)) (|has| |#2| (-926)))) +((($) -2755 (|has| |#1| (-174)) (|has| |#1| (-464)) (|has| |#1| (-568)) (|has| |#1| (-926))) ((|#1|) . T) (((-419 (-576))) |has| |#1| (-38 (-419 (-576))))) (((|#1|) . T) (($) . T) (((-419 (-576))) . T)) (((|#1|) . T) (($) . T) (((-419 (-576))) . T)) (((|#1|) . T) (($) . T) (((-419 (-576))) . T)) @@ -3664,11 +3664,11 @@ (((|#1|) . 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T) (((-576)) |has| |#1| (-1057 (-576))) (((-419 (-576))) |has| |#1| (-1057 (-419 (-576)))) (((-1195)) . T)) ((($) . T)) @@ -3749,12 +3749,12 @@ (((#0=(-1272 |#1| |#2| |#3| |#4|)) |has| #0# (-319 #0#))) ((($) . T)) (((|#1|) . T)) -((($ $) -2781 (|has| |#1| (-174)) (|has| |#1| (-374)) (|has| |#1| (-568))) ((#0=(-419 (-576)) #0#) -2781 (|has| |#1| (-38 (-419 (-576)))) (|has| |#1| (-374))) ((|#2| |#2|) |has| |#1| (-374)) ((|#1| |#1|) . T)) -(((|#1| |#1|) . T) (($ $) -2781 (|has| |#1| (-174)) (|has| |#1| (-374)) (|has| |#1| (-568))) ((#0=(-419 (-576)) #0#) -2781 (|has| |#1| (-38 (-419 (-576)))) (|has| |#1| (-374)))) +((($ $) -2755 (|has| |#1| (-174)) (|has| |#1| (-374)) (|has| |#1| (-568))) ((#0=(-419 (-576)) #0#) -2755 (|has| |#1| (-38 (-419 (-576)))) (|has| |#1| (-374))) ((|#2| |#2|) |has| |#1| (-374)) ((|#1| |#1|) . T)) +(((|#1| |#1|) . 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T)) (|has| |#2| (-1068)) ((((-1195)) -12 (|has| |#2| (-915 (-1195))) (|has| |#2| (-1068)))) -(-2781 (-12 (|has| |#1| (-485)) (|has| |#2| (-485))) (-12 (|has| |#1| (-738)) (|has| |#2| (-738)))) +(-2755 (-12 (|has| |#1| (-485)) (|has| |#2| (-485))) (-12 (|has| |#1| (-738)) (|has| |#2| (-738)))) (|has| |#1| (-146)) (|has| |#1| (-148)) (|has| |#1| (-374)) @@ -3946,7 +3946,7 @@ (((|#1| |#2|) . T)) ((((-576)) . T) ((|#2|) |has| |#2| (-174))) ((((-115)) . T) ((|#1|) . T) (((-576)) . T)) -(-2781 (|has| |#1| (-360)) (|has| |#1| (-379))) +(-2755 (|has| |#1| (-360)) (|has| |#1| (-379))) (((|#1| |#2|) . T)) ((((-227)) . T)) ((((-419 (-576))) . T) (($) . T) (((-576)) . T)) @@ -3955,11 +3955,11 @@ ((($) . T) (((-419 (-576))) |has| |#1| (-38 (-419 (-576)))) ((|#1|) . T) (((-576)) |has| |#1| (-651 (-576)))) ((($) . T) (((-576)) |has| |#1| (-651 (-576))) ((|#1|) . T) (((-419 (-576))) |has| |#1| (-38 (-419 (-576))))) (((|#2|) |has| |#2| (-1119)) (((-576)) -12 (|has| |#2| (-1057 (-576))) (|has| |#2| (-1119))) (((-419 (-576))) -12 (|has| |#2| (-1057 (-419 (-576)))) (|has| |#2| (-1119)))) -(-2781 (|has| |#2| (-238)) (|has| |#2| (-237))) +(-2755 (|has| |#2| (-238)) (|has| |#2| (-237))) (((|#1|) . T)) (((|#1|) . T)) ((((-548)) |has| |#1| (-626 (-548)))) -((((-874)) -2781 (|has| |#1| (-625 (-874))) (|has| |#1| (-862)) (|has| |#1| (-1119)))) +((((-874)) -2755 (|has| |#1| (-625 (-874))) (|has| |#1| (-862)) (|has| |#1| (-1119)))) ((((-576) $) . T) (((-656 (-576)) $) . T)) ((($) . T) (((-419 (-576))) . T)) (|has| |#1| (-926)) @@ -3971,14 +3971,14 @@ (((|#1| |#1|) |has| |#1| (-174))) (((|#1|) . T) (((-576)) . T)) ((((-1200)) . T)) -(-2781 (|has| |#1| (-374)) (|has| |#1| (-568))) -(-2781 (|has| |#1| (-21)) (|has| |#1| (-860))) +(-2755 (|has| |#1| (-374)) (|has| |#1| (-568))) +(-2755 (|has| |#1| (-21)) (|has| |#1| (-860))) (((|#2|) . T)) -(-2781 (|has| |#1| (-21)) (|has| |#1| (-860))) +(-2755 (|has| |#1| (-21)) (|has| |#1| (-860))) (((|#1|) |has| |#1| (-174))) (((|#1|) . T)) (((|#1|) . T)) -((((-874)) -2781 (-12 (|has| |#1| (-625 (-874))) (|has| |#2| (-625 (-874)))) (-12 (|has| |#1| (-1119)) (|has| |#2| (-1119))))) +((((-874)) -2755 (-12 (|has| |#1| (-625 (-874))) (|has| |#2| (-625 (-874)))) (-12 (|has| |#1| (-1119)) (|has| |#2| (-1119))))) ((((-419 |#2|) |#3|) . T)) ((((-419 (-576))) . T) (($) . T)) (|has| |#1| (-38 (-419 (-576)))) @@ -4002,7 +4002,7 @@ ((((-1200)) . T)) ((((-576)) . T)) (((|#2|) . T)) -((((-1195)) -2781 (-12 (|has| (-1193 |#1| |#2| |#3|) (-915 (-1195))) (|has| |#1| (-374))) (-12 (|has| |#1| (-15 * (|#1| (-576) |#1|))) (|has| |#1| (-915 (-1195)))))) +((((-1195)) -2755 (-12 (|has| (-1193 |#1| |#2| |#3|) (-915 (-1195))) (|has| |#1| (-374))) (-12 (|has| |#1| (-15 * (|#1| (-576) |#1|))) (|has| |#1| (-915 (-1195)))))) ((((-1195)) -12 (|has| |#1| (-15 * (|#1| (-419 (-576)) |#1|))) (|has| |#1| (-915 (-1195))))) ((((-1195)) -12 (|has| |#1| (-15 * (|#1| (-783) |#1|))) (|has| |#1| (-915 (-1195))))) (((|#1| |#1|) . T) (($ $) . T)) @@ -4017,11 +4017,11 @@ ((((-1193 |#1| |#2| |#3|)) |has| |#1| (-374))) ((((-1159 |#1| |#2|)) . T)) ((((-1193 |#1| |#2| |#3|)) |has| |#1| (-374))) -(((|#2|) . T) (((-2 (|:| -4300 |#1|) (|:| -4391 |#2|))) . T)) -((((-2 (|:| -4300 (-1195)) (|:| -4391 (-52)))) . T)) +(((|#2|) . T) (((-2 (|:| -4298 |#1|) (|:| -4437 |#2|))) . T)) +((((-2 (|:| -4298 (-1195)) (|:| -4437 (-52)))) . T)) ((($) . T)) (|has| |#1| (-1041)) -(((|#2|) . T) (((-2 (|:| -4300 |#1|) (|:| -4391 |#2|))) . T)) +(((|#2|) . T) (((-2 (|:| -4298 |#1|) (|:| -4437 |#2|))) . T)) ((($) . T)) ((((-874)) . T)) ((((-548)) |has| |#2| (-626 (-548))) (((-905 (-576))) |has| |#2| (-626 (-905 (-576)))) (((-905 (-390))) |has| |#2| (-626 (-905 (-390)))) (((-390)) . #0=(|has| |#2| (-1041))) (((-227)) . #0#)) @@ -4030,7 +4030,7 @@ (((|#1|) . T)) (|has| |#1| (-38 (-419 (-576)))) (|has| |#1| (-38 (-419 (-576)))) -((((-1195)) -2781 (|has| |#2| (-915 (-1195))) (|has| |#2| (-917 (-1195))))) +((((-1195)) -2755 (|has| |#2| (-915 (-1195))) (|has| |#2| (-917 (-1195))))) ((((-874)) . T)) (((|#2|) . T)) ((((-874)) . T)) @@ -4040,15 +4040,15 @@ ((((-1193 |#1| |#2| |#3|)) . T)) ((((-1193 |#1| |#2| |#3|)) . T) (((-1186 |#1| |#2| |#3|)) . T)) ((((-874)) . T)) -((((-874)) -2781 (|has| |#1| (-625 (-874))) (|has| |#1| (-1119)))) +((((-874)) -2755 (|has| |#1| (-625 (-874))) (|has| |#1| (-1119)))) ((((-576) |#1|) . T)) ((((-1193 |#1| |#2| |#3|)) |has| |#1| (-374))) (((|#1| |#2| |#3| |#4|) . T)) (((|#1|) . T)) (((|#2|) . T)) (|has| |#2| (-374)) -(((|#3|) . T) ((|#2|) . T) ((|#4|) -2781 (|has| |#4| (-174)) (|has| |#4| (-374)) (|has| |#4| (-1068))) (($) |has| |#4| (-1068)) (((-576)) -12 (|has| |#4| (-651 (-576))) (|has| |#4| (-1068)))) -(((|#2|) . T) ((|#3|) -2781 (|has| |#3| (-174)) (|has| |#3| (-374)) (|has| |#3| (-1068))) (($) |has| |#3| (-1068)) (((-576)) -12 (|has| |#3| (-651 (-576))) (|has| |#3| (-1068)))) +(((|#3|) . T) ((|#2|) . T) ((|#4|) -2755 (|has| |#4| (-174)) (|has| |#4| (-374)) (|has| |#4| (-1068))) (($) |has| |#4| (-1068)) (((-576)) -12 (|has| |#4| (-651 (-576))) (|has| |#4| (-1068)))) +(((|#2|) . T) ((|#3|) -2755 (|has| |#3| (-174)) (|has| |#3| (-374)) (|has| |#3| (-1068))) (($) |has| |#3| (-1068)) (((-576)) -12 (|has| |#3| (-651 (-576))) (|has| |#3| (-1068)))) (((|#1|) . T)) (((|#1|) . T)) ((((-117 |#1|)) . T)) @@ -4062,7 +4062,7 @@ ((((-189)) . T) (((-874)) . T)) ((((-874)) . T)) (((|#1|) . T)) -((((-874)) -2781 (|has| |#1| (-625 (-874))) (|has| |#1| (-1119)))) +((((-874)) -2755 (|has| |#1| (-625 (-874))) (|has| |#1| (-1119)))) ((((-130)) . T) (((-874)) . T)) ((((-576) |#1|) . T) (((-1253 (-576)) $) . T)) ((((-130)) . T)) @@ -4071,14 +4071,14 @@ (((|#1|) . T)) (((|#2| $) -12 (|has| |#1| (-374)) (|has| |#2| (-296 |#2| |#2|))) (($ $) . T) (((-576) |#1|) . T)) ((($ $) . T) (((-419 (-576)) |#1|) . T)) -(-2781 (|has| |#1| (-374)) (|has| |#1| (-464)) (|has| |#1| (-926))) +(-2755 (|has| |#1| (-374)) (|has| |#1| (-464)) (|has| |#1| (-926))) ((($ (-1195)) |has| |#1| (-1068))) -(-2781 (|has| |#1| (-862)) (|has| |#1| (-1119))) +(-2755 (|has| |#1| (-862)) (|has| |#1| (-1119))) ((((-874)) . T)) ((((-874)) . T)) ((((-874)) . T)) (((|#1| (-543 |#2|)) . T)) -((((-2 (|:| -4300 (-1195)) (|:| -4391 (-52)))) . T)) +((((-2 (|:| -4298 (-1195)) (|:| -4437 (-52)))) . T)) ((((-576) (-130)) . T)) (((|#1| (-576)) . T)) (((|#1| (-419 (-576))) . T)) @@ -4093,8 +4093,8 @@ ((((-1200)) . T)) ((((-874)) . T) (((-1200)) . T)) ((((-874)) . T) (((-1200)) . T)) -(-2781 (|has| |#2| (-464)) (|has| |#2| (-568)) (|has| |#2| (-926))) -(-2781 (|has| |#1| (-464)) (|has| |#1| (-568)) (|has| |#1| (-926))) +(-2755 (|has| |#2| (-464)) (|has| |#2| (-568)) (|has| |#2| (-926))) +(-2755 (|has| |#1| (-464)) (|has| |#1| (-568)) (|has| |#1| (-926))) ((($) . T)) (((|#2| (-543 (-876 |#1|))) . T)) ((((-1200)) . T)) @@ -4109,7 +4109,7 @@ ((((-1200)) . T)) ((((-874)) . T) (((-1200)) . T)) ((((-1200)) . T)) -((((-874)) -2781 (|has| |#1| (-625 (-874))) (|has| |#1| (-1119)))) +((((-874)) -2755 (|has| |#1| (-625 (-874))) (|has| |#1| (-1119)))) (((|#1| |#2|) . T)) (((|#1|) . T)) ((((-1177) |#1|) . T)) @@ -4117,7 +4117,7 @@ ((((-419 |#2|)) . T)) (|has| |#1| (-568)) (|has| |#1| (-568)) -((((-2 (|:| -4300 |#1|) (|:| -4391 |#2|))) . T)) +((((-2 (|:| -4298 |#1|) (|:| -4437 |#2|))) . T)) (((|#2| (-783)) . T)) ((($) . T) ((|#2|) . T)) ((($) . T) (((-419 (-576))) . T)) @@ -4127,14 +4127,14 @@ ((((-576)) . 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197595) ((-1186 . -388) 197547) ((-1106 . -1077) T) ((-449 . -102) T) ((-185 . -1119) T) ((-258 . -34) T) ((-257 . -34) T) ((-794 . -1077) T) ((-792 . -1077) T) ((-743 . -915) 197524) ((-466 . -1077) T) ((-59 . -501) 197508) ((-1053 . -1075) 197482) ((-531 . -501) 197466) ((-528 . -501) 197450) ((-509 . -501) 197434) ((-508 . -501) 197418) ((-250 . -526) 197351) ((-1053 . -111) 197318) ((-1193 . -915) 197231) ((-1192 . -915) 197137) ((-682 . -1131) T) ((-1186 . -915) 196970) ((-657 . -93) T) ((-1145 . -915) 196954) ((-365 . -1171) T) ((-332 . -1075) 196936) ((-31 . -502) 196917) ((-258 . -806) 196896) ((-258 . -805) 196875) ((-257 . -806) 196854) ((-257 . -805) 196833) ((-31 . -625) 196799) ((-50 . -1077) T) ((-258 . -738) 196777) ((-257 . -738) 196755) ((-1230 . -1119) T) ((-682 . -23) T) ((-593 . -1077) T) ((-530 . -1077) T) ((-390 . -1075) 196720) ((-332 . -111) 196695) ((-73 . -394) T) ((-73 . -407) T) ((-1043 . -38) 196632) ((-706 . -412) 196614) ((-99 . -102) T) ((-723 . -1119) 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191589) ((-370 . -568) T) ((-219 . -937) T) ((-219 . -832) T) ((-326 . -652) 191499) ((-323 . -652) 191428) ((-364 . -568) T) ((-356 . -568) T) ((-495 . -628) 191409) ((-108 . -568) T) ((-670 . -729) 191379) ((-1186 . -1041) NIL) ((-220 . -628) 191360) ((-329 . -23) T) ((-67 . -1236) T) ((-1019 . -625) 191292) ((-706 . -272) 191274) ((-706 . -232) 191256) ((-1315 . -1171) T) ((-726 . -111) 191221) ((-1310 . -21) T) ((-656 . -34) T) ((-250 . -501) 191205) ((-1310 . -25) T) ((-1308 . -132) T) ((-1306 . -132) T) ((-1299 . -102) T) ((-1121 . -1117) 191189) ((-173 . -1119) T) ((-1282 . -625) 191155) ((-1278 . -1236) T) ((-1271 . -1236) T) ((-1271 . -1057) 191090) ((-1250 . -1236) T) ((-969 . -926) 191069) ((-1250 . -899) NIL) ((-1250 . -897) 191021) ((-1250 . -1057) 190987) ((-527 . -628) 190971) ((-1230 . -526) 190938) ((-1208 . -626) NIL) ((-1208 . -625) 190920) ((-493 . -926) 190899) ((-1161 . -1142) 190844) ((-1106 . -729) 190693) ((-1081 . -660) 190665) ((-969 . -660) 190554) ((-794 . 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. -625) 188871) ((-1139 . -652) 188858) ((-1139 . -1070) 188845) ((-831 . -738) T) ((-831 . -869) T) ((-614 . -298) 188822) ((-593 . -729) 188787) ((-491 . -626) NIL) ((-491 . -625) 188769) ((-530 . -729) 188714) ((-326 . -102) T) ((-323 . -102) T) ((-299 . -23) T) ((-153 . -132) T) ((-927 . -625) 188696) ((-927 . -626) 188678) ((-398 . -738) T) ((-884 . -1075) 188630) ((-884 . -111) 188568) ((-726 . -1068) T) ((-724 . -1262) 188552) ((-706 . -360) NIL) ((-115 . -102) T) ((-140 . -102) T) ((-137 . -102) T) ((-531 . -625) 188484) ((-390 . -807) T) ((-169 . -1236) T) ((-225 . -1119) T) ((-390 . -804) T) ((-59 . -626) 188445) ((-227 . -806) T) ((-227 . -803) T) ((-59 . -625) 188357) ((-227 . -738) T) ((-528 . -626) 188318) ((-528 . -625) 188230) ((-509 . -625) 188162) ((-508 . -626) 188123) ((-508 . -625) 188035) ((-1099 . -374) 187986) ((-40 . -423) 187963) ((-77 . -1236) T) ((-883 . -926) NIL) ((-370 . -339) 187947) ((-370 . -374) T) ((-364 . -339) 187931) ((-364 . -374) T) ((-356 . -339) 187915) ((-356 . -374) T) ((-326 . -294) 187894) ((-108 . -374) T) ((-70 . -1236) T) ((-1250 . -349) 187846) ((-883 . -660) 187791) ((-1250 . -388) 187743) ((-981 . -132) 187598) ((-827 . -132) 187469) ((-975 . -663) 187453) ((-1106 . -174) 187364) ((-975 . -384) 187348) ((-1081 . -806) T) ((-1081 . -803) T) ((-884 . -628) 187246) ((-794 . -174) 187137) ((-792 . -174) 187048) ((-828 . -47) 187010) ((-1081 . -738) T) ((-337 . -501) 186994) ((-969 . -738) T) ((-1299 . -319) 186932) ((-1278 . -915) 186845) ((-466 . -174) 186756) ((-250 . -296) 186708) ((-1271 . -915) 186614) ((-1270 . -1075) 186449) ((-1250 . -915) 186282) ((-493 . -738) T) ((-1249 . -1075) 186090) ((-1230 . -300) 186069) ((-1205 . -1236) T) ((-1202 . -379) T) ((-1201 . -379) T) ((-1165 . -152) 186053) ((-1139 . -102) T) ((-1137 . -1119) T) ((-1099 . -23) T) ((-1099 . -1131) T) ((-1094 . -102) T) ((-1076 . -625) 186020) ((-1022 . -421) 185992) ((-944 . -972) T) ((-749 . -319) 185930) ((-75 . -1236) T) ((-676 . -393) 185902) ((-171 . -926) 185855) ((-30 . -972) T) ((-112 . -856) T) ((-1 . -625) 185837) ((-1018 . -909) 185758) ((-129 . -663) 185740) ((-50 . -632) 185724) ((-706 . -658) 185659) ((-607 . -915) 185572) ((-450 . -102) T) ((-129 . -384) 185554) ((-142 . -319) NIL) ((-884 . -1068) T) ((-845 . -862) 185533) ((-81 . -1236) T) ((-723 . -300) T) ((-40 . -1077) T) ((-593 . -174) T) ((-530 . -174) T) ((-523 . -625) 185515) ((-171 . -660) 185389) ((-519 . -625) 185371) ((-362 . -148) 185353) ((-362 . -146) T) ((-370 . -1131) T) ((-364 . -1131) T) ((-356 . -1131) T) ((-1023 . -317) T) ((-931 . -317) T) ((-884 . -248) T) ((-108 . -1131) T) ((-884 . -238) 185332) ((-1270 . -111) 185153) ((-1249 . -111) 184942) ((-250 . -1274) 184926) ((-576 . -860) T) ((-370 . -23) T) ((-365 . -360) T) ((-326 . -319) 184913) ((-323 . -319) 184854) ((-364 . -23) T) ((-329 . -132) T) ((-356 . -23) T) ((-1023 . -1041) T) ((-31 . -628) 184835) ((-108 . -23) T) ((-666 . -1070) 184819) ((-250 . -616) 184796) ((-343 . 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T) ((-1301 . -1236) T) ((-666 . -102) T) ((-1270 . -248) 182921) ((-1270 . -238) 182873) ((-1249 . -238) 182778) ((-1249 . -248) 182757) ((-1022 . -414) NIL) ((-682 . -651) 182705) ((-326 . -38) 182615) ((-323 . -38) 182544) ((-69 . -625) 182526) ((-329 . -505) 182492) ((-48 . -658) 182442) ((-1208 . -298) 182421) ((-1244 . -862) T) ((-1132 . -1131) 182399) ((-83 . -1236) T) ((-61 . -625) 182381) ((-491 . -298) 182360) ((-1301 . -1057) 182337) ((-1183 . -1119) T) ((-1132 . -23) 182189) ((-828 . -915) 182125) ((-1259 . -738) T) ((-1121 . -1236) T) ((-486 . -628) 181951) ((-362 . -237) T) ((-1106 . -300) 181882) ((-983 . -1119) T) ((-906 . -102) T) ((-794 . -300) 181793) ((-337 . -19) 181777) ((-59 . -298) 181754) ((-792 . -300) 181685) ((-867 . -738) T) ((-118 . -860) NIL) ((-528 . -298) 181662) ((-337 . -616) 181639) ((-508 . -298) 181616) ((-466 . -300) 181547) ((-1054 . -319) 181398) ((-888 . -502) 181379) ((-888 . -625) 181345) ((-693 . -502) 181326) ((-583 . -738) T) ((-688 . -502) 181307) ((-693 . -625) 181257) ((-688 . -625) 181223) ((-674 . -625) 181205) ((-490 . -502) 181186) ((-490 . -625) 181152) ((-250 . -626) 181113) ((-250 . -502) 181090) ((-139 . -502) 181071) ((-138 . -502) 181052) ((-134 . -502) 181033) ((-250 . -625) 180925) ((-215 . -102) T) ((-139 . -625) 180891) ((-138 . -625) 180857) ((-134 . -625) 180823) ((-1166 . -34) T) ((-960 . -1236) T) ((-354 . -729) 180768) ((-682 . -25) T) ((-682 . -21) T) ((-1195 . -628) 180749) ((-341 . -1236) T) ((-486 . -1068) T) ((-647 . -429) 180714) ((-619 . -429) 180679) ((-1139 . -1171) T) ((-1271 . -317) 180658) ((-724 . -1070) 180481) ((-593 . -300) T) ((-530 . -300) T) ((-1250 . -317) 180460) ((-486 . -238) 180412) ((-486 . -248) 180391) ((-451 . -1236) T) ((-724 . -652) 180220) ((-1250 . -1041) NIL) ((-1099 . -132) T) ((-884 . -807) 180199) ((-145 . -102) T) ((-40 . -1119) T) ((-884 . -804) 180178) ((-656 . -1029) 180162) ((-592 . -1077) T) ((-576 . -1077) T) ((-507 . -1077) T) ((-419 . -464) T) ((-370 . 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-1075) 178455) ((-724 . -102) T) ((-711 . -1077) T) ((-609 . -628) 178436) ((-597 . -628) 178417) ((-548 . -630) 178320) ((-354 . -174) T) ((-153 . -21) T) ((-153 . -25) T) ((-88 . -625) 178302) ((-927 . -111) 178258) ((-40 . -729) 178203) ((-882 . -1119) T) ((-676 . -628) 178180) ((-657 . -628) 178161) ((-366 . -628) 178098) ((-363 . -628) 178035) ((-355 . -628) 177972) ((-559 . -1119) T) ((-337 . -626) 177933) ((-337 . -625) 177845) ((-273 . -628) 177598) ((-253 . -628) 177383) ((-188 . -1236) T) ((-1249 . -804) 177336) ((-1249 . -807) 177289) ((-258 . -388) 177258) ((-257 . -388) 177227) ((-666 . -38) 177197) ((-620 . -34) T) ((-494 . -1131) 177175) ((-487 . -34) T) ((-1132 . -132) 177046) ((-981 . -25) 176857) ((-927 . -628) 176807) ((-886 . -625) 176789) ((-981 . -21) 176744) ((-827 . -25) 176577) ((-827 . -21) 176488) ((-1242 . -379) T) ((-635 . -1077) T) ((-1197 . -568) 176467) ((-1191 . -47) 176444) ((-366 . -1068) T) ((-363 . -1068) T) ((-494 . -23) 176296) ((-355 . -1068) T) 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-1236) T) ((-874 . -1236) T) ((-40 . -174) T) ((-706 . -423) 175335) ((-724 . -319) 175322) ((-848 . -660) 175282) ((-839 . -660) 175256) ((-329 . -25) T) ((-329 . -21) T) ((-670 . -296) 175235) ((-592 . -1119) T) ((-576 . -1119) T) ((-507 . -1119) T) ((-1191 . -1236) T) ((-250 . -298) 175212) ((-1144 . -1236) T) ((-866 . -1236) T) ((-323 . -272) 175173) ((-323 . -232) 175134) ((-1191 . -899) NIL) ((-55 . -1119) T) ((-1144 . -899) 174993) ((-130 . -862) T) ((-1191 . -1057) 174873) ((-1144 . -1057) 174756) ((-185 . -625) 174738) ((-866 . -1057) 174634) ((-794 . -296) 174561) ((-829 . -1131) T) ((-1053 . -738) T) ((-1065 . -995) 174490) ((-614 . -663) 174474) ((-1022 . -909) 174381) ((-1018 . -102) T) ((-829 . -23) T) ((-724 . -1171) 174359) ((-706 . -1077) T) ((-614 . -384) 174343) ((-362 . -464) T) ((-354 . -300) T) ((-1287 . -1119) T) ((-254 . -1119) T) ((-411 . -102) T) ((-299 . -21) T) ((-299 . -25) T) ((-372 . -738) T) ((-722 . -1119) T) ((-711 . -1119) T) ((-372 . -485) T) ((-1230 . -625) 174325) ((-1191 . -388) 174309) ((-1144 . -388) 174293) ((-1043 . -423) 174255) ((-142 . -231) 174237) ((-390 . -806) T) ((-390 . -803) T) ((-882 . -174) T) ((-390 . -738) T) ((-723 . -625) 174219) ((-724 . -38) 174048) ((-1286 . -1284) 174032) ((-362 . -414) T) ((-1286 . -1119) 173982) ((-1209 . -1119) T) ((-592 . -729) 173969) ((-576 . -729) 173956) ((-507 . -729) 173921) ((-1272 . -658) 173811) ((-326 . -641) 173790) ((-848 . -738) T) ((-839 . -738) T) ((-1134 . -1236) T) ((-656 . -1236) T) ((-1099 . -651) 173738) ((-1191 . -915) 173681) ((-1144 . -915) 173665) ((-827 . -234) 173556) ((-674 . -1075) 173540) ((-108 . -651) 173522) ((-494 . -132) 173393) ((-1197 . -1131) T) ((-831 . -1236) T) ((-969 . -47) 173362) ((-635 . -1119) T) ((-674 . -111) 173341) ((-503 . -625) 173307) ((-337 . -298) 173284) ((-398 . -1236) T) ((-334 . -1236) T) ((-493 . -47) 173241) ((-1197 . -23) T) ((-118 . -1119) T) ((-103 . -102) 173191) ((-1298 . -1131) T) ((-560 . -862) T) ((-227 . -1236) T) 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T) ((-48 . -1077) T) ((-592 . -174) T) ((-576 . -174) T) ((-507 . -174) T) ((-1081 . -1236) T) ((-969 . -1236) T) ((-725 . -1236) T) ((-670 . -625) 172173) ((-493 . -1236) T) ((-749 . -748) 172157) ((-347 . -625) 172139) ((-68 . -394) T) ((-68 . -407) T) ((-1121 . -107) 172123) ((-1081 . -899) 172105) ((-969 . -899) 172030) ((-665 . -1131) T) ((-635 . -729) 172017) ((-493 . -899) NIL) ((-1165 . -102) T) ((-1113 . -630) 172001) ((-1081 . -1057) 171983) ((-97 . -625) 171965) ((-489 . -148) T) ((-969 . -1057) 171845) ((-118 . -729) 171790) ((-724 . -917) 171697) ((-665 . -23) T) ((-493 . -1057) 171573) ((-1106 . -626) NIL) ((-1106 . -625) 171555) ((-794 . -626) NIL) ((-794 . -625) 171516) ((-792 . -626) 171150) ((-792 . -625) 171064) ((-1132 . -651) 170970) ((-473 . -625) 170952) ((-466 . -625) 170934) ((-466 . -626) 170795) ((-1054 . -231) 170741) ((-884 . -926) 170720) ((-127 . -34) T) ((-829 . -132) T) ((-661 . -625) 170702) ((-590 . -102) T) ((-366 . -1305) 170686) ((-363 . -1305) 170670) ((-355 . -1305) 170654) ((-128 . -526) 170587) ((-122 . -526) 170520) ((-523 . -804) T) ((-523 . -807) T) ((-522 . -806) T) ((-103 . -319) 170458) ((-224 . -102) 170408) ((-711 . -174) T) ((-706 . -1119) T) ((-884 . -660) 170324) ((-65 . -395) T) ((-284 . -625) 170306) ((-65 . -407) T) ((-969 . -388) 170290) ((-882 . -300) T) ((-50 . -625) 170272) ((-1018 . -38) 170220) ((-1139 . -658) 170192) ((-593 . -625) 170174) ((-493 . -388) 170158) ((-593 . -626) 170140) ((-530 . -625) 170122) ((-927 . -1305) 170109) ((-883 . -1236) T) ((-713 . -464) T) ((-507 . -526) 170075) ((-1297 . -1236) T) ((-1296 . -1236) T) ((-499 . -374) T) ((-366 . -379) 170054) ((-363 . -379) 170033) ((-355 . -379) 170012) ((-726 . -738) T) ((-219 . -374) T) ((-117 . -464) T) ((-1309 . -1300) 169996) ((-883 . -897) 169973) ((-883 . -899) NIL) ((-981 . -862) 169872) ((-827 . -862) 169823) ((-1243 . -102) T) ((-666 . -668) 169807) ((-1222 . -34) T) ((-173 . -625) 169789) ((-1132 . -25) 169622) ((-1132 . -21) 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168628) ((-1099 . -234) 168501) ((-499 . -1131) T) ((-365 . -1119) T) ((-219 . -1131) T) ((-76 . -453) T) ((-76 . -407) T) ((-171 . -1057) 168397) ((-304 . -909) 168354) ((-329 . -862) T) ((-1249 . -660) 168162) ((-884 . -806) 168141) ((-884 . -803) 168120) ((-884 . -738) T) ((-499 . -23) T) ((-370 . -234) 168093) ((-364 . -234) 168066) ((-356 . -234) 168039) ((-176 . -464) T) ((-86 . -453) T) ((-224 . -319) 167977) ((-86 . -407) T) ((-225 . -625) 167959) ((-108 . -234) 167946) ((-219 . -23) T) ((-1310 . -1303) 167925) ((-689 . -1057) 167909) ((-592 . -300) T) ((-576 . -300) T) ((-507 . -300) T) ((-1259 . -1236) T) ((-137 . -482) 167864) ((-867 . -1236) T) ((-666 . -658) 167823) ((-48 . -1119) T) ((-724 . -272) 167807) ((-724 . -232) 167791) ((-883 . -915) NIL) ((-583 . -1236) T) ((-1259 . -899) NIL) ((-902 . -102) T) ((-898 . -102) T) ((-400 . -1119) T) ((-171 . -388) 167775) ((-171 . -349) 167759) ((-1259 . -1057) 167639) ((-867 . -1057) 167535) ((-1161 . -102) T) ((-1018 . -917) 167458) ((-674 . -804) 167437) ((-665 . -132) T) ((-674 . -807) 167416) ((-118 . -526) 167324) ((-583 . -1057) 167306) ((-304 . -1293) 167276) ((-878 . -102) T) ((-980 . -568) 167255) ((-1230 . -1075) 167138) ((-1022 . -1070) 167083) ((-494 . -651) 166989) ((-921 . -1119) T) ((-1043 . -729) 166926) ((-723 . -1075) 166891) ((-1022 . -652) 166836) ((-629 . -102) T) ((-614 . -34) T) ((-1166 . -1236) T) ((-1230 . -111) 166705) ((-486 . -660) 166602) ((-365 . -729) 166547) ((-171 . -915) 166506) ((-711 . -300) T) ((-706 . -174) T) ((-723 . -111) 166462) ((-1315 . -1077) T) ((-1259 . -388) 166446) ((-430 . -1240) 166424) ((-1137 . -625) 166406) ((-323 . -860) NIL) ((-430 . -568) T) ((-227 . -317) T) ((-1249 . -803) 166359) ((-1249 . -806) 166312) ((-1270 . -738) T) ((-1249 . -738) T) ((-48 . -729) 166277) ((-227 . -1041) T) ((-1272 . -423) 166243) ((-362 . -1293) 166220) ((-1259 . -915) 166163) ((-730 . -738) T) ((-343 . -625) 166145) ((-1230 . -628) 166027) ((-1132 . -234) 165918) ((-112 . 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. -1119) T) ((-250 . -678) 165043) ((-250 . -663) 165027) ((-670 . -111) 165006) ((-598 . -628) 164990) ((-326 . -423) 164974) ((-250 . -384) 164958) ((-1178 . -240) 164905) ((-1018 . -272) 164889) ((-1018 . -232) 164873) ((-74 . -1236) T) ((-48 . -174) T) ((-713 . -399) T) ((-713 . -144) T) ((-1309 . -102) T) ((-1217 . -1236) T) ((-1216 . -628) 164855) ((-1107 . -1236) T) ((-1106 . -1075) 164698) ((-1095 . -1236) T) ((-273 . -926) 164677) ((-253 . -926) 164656) ((-794 . -1075) 164479) ((-792 . -1075) 164322) ((-620 . -1236) T) ((-1183 . -625) 164304) ((-1106 . -111) 164133) ((-1065 . -102) T) ((-487 . -1236) T) ((-473 . -1075) 164104) ((-466 . -1075) 163947) ((-676 . -660) 163931) ((-883 . -317) T) ((-794 . -111) 163740) ((-792 . -111) 163569) ((-366 . -660) 163521) ((-363 . -660) 163473) ((-355 . -660) 163425) ((-273 . -660) 163314) ((-253 . -660) 163203) ((-1177 . -862) T) ((-1107 . -1057) 163187) ((-473 . -111) 163148) ((-466 . -111) 162977) ((-1095 . -1057) 162954) ((-1019 . -34) 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. -317) 161262) ((-430 . -23) T) ((-40 . -625) 161244) ((-40 . -626) 161228) ((-108 . -1011) 161210) ((-117 . -881) 161194) ((-661 . -628) 161178) ((-48 . -526) 161144) ((-1222 . -1029) 161128) ((-1200 . -625) 161095) ((-1208 . -34) T) ((-971 . -625) 161061) ((-938 . -625) 161043) ((-1132 . -862) 160994) ((-783 . -625) 160976) ((-684 . -625) 160958) ((-529 . -1236) T) ((-1259 . -317) 160937) ((-1176 . -319) 160875) ((-1160 . -34) T) ((-491 . -34) T) ((-1111 . -1236) T) ((-489 . -464) T) ((-1053 . -1236) T) ((-1106 . -1068) T) ((-50 . -628) 160844) ((-794 . -1068) T) ((-792 . -1068) T) ((-659 . -240) 160828) ((-644 . -240) 160774) ((-1197 . -21) T) ((-593 . -628) 160724) ((-530 . -628) 160654) ((-494 . -234) 160545) ((-1197 . -25) T) ((-1106 . -336) 160506) ((-466 . -1068) T) ((-1106 . -238) 160485) ((-794 . -336) 160462) ((-794 . -238) T) ((-792 . -336) 160434) ((-743 . -1240) 160413) ((-531 . -34) T) ((-337 . -663) 160397) ((-528 . -34) T) ((-59 . -34) T) ((-509 . -34) T) ((-508 . 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159644) ((-1139 . -1077) T) ((-103 . -126) 159628) ((-304 . -652) 159570) ((-811 . -23) T) ((-1308 . -1303) 159546) ((-1306 . -1303) 159525) ((-1286 . -296) 159477) ((-419 . -319) 159442) ((-1272 . -1119) T) ((-1161 . -917) 159365) ((-882 . -625) 159347) ((-848 . -1057) 159316) ((-205 . -799) T) ((-204 . -799) T) ((-203 . -799) T) ((-202 . -799) T) ((-201 . -799) T) ((-200 . -799) T) ((-199 . -799) T) ((-198 . -799) T) ((-197 . -799) T) ((-196 . -799) T) ((-559 . -625) 159298) ((-507 . -1021) T) ((-283 . -851) T) ((-282 . -851) T) ((-281 . -851) T) ((-280 . -851) T) ((-48 . -300) T) ((-279 . -851) T) ((-278 . -851) T) ((-277 . -851) T) ((-195 . -799) T) ((-624 . -862) T) ((-666 . -423) 159282) ((-682 . -237) 159233) ((-225 . -628) 159195) ((-110 . -862) T) ((-665 . -21) T) ((-665 . -25) T) ((-1309 . -38) 159165) ((-118 . -296) 159116) ((-1286 . -19) 159100) ((-1286 . -616) 159077) ((-1299 . -1119) T) ((-362 . -1070) 159022) ((-1096 . -1119) T) ((-1006 . -1119) T) ((-980 . -132) T) 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. -1236) T) ((-657 . -1236) T) ((-794 . -926) 150067) ((-792 . -926) 150046) ((-1208 . -1236) T) ((-366 . -1236) T) ((-363 . -1236) T) ((-355 . -1236) T) ((-273 . -1236) T) ((-253 . -1236) T) ((-466 . -926) 150025) ((-749 . -501) 150009) ((-1106 . -660) 149898) ((-711 . -628) 149833) ((-794 . -660) 149722) ((-635 . -1075) 149709) ((-491 . -1236) T) ((-354 . -379) T) ((-142 . -501) 149691) ((-792 . -660) 149580) ((-1160 . -1236) T) ((-561 . -862) T) ((-473 . -660) 149551) ((-273 . -899) 149410) ((-253 . -899) NIL) ((-118 . -1075) 149355) ((-466 . -660) 149244) ((-676 . -1057) 149221) ((-635 . -111) 149206) ((-402 . -1070) 149190) ((-366 . -1057) 149174) ((-363 . -1057) 149158) ((-355 . -1057) 149142) ((-273 . -1057) 148986) ((-253 . -1057) 148862) ((-927 . -1236) T) ((-118 . -111) 148791) ((-59 . -1236) T) ((-402 . -652) 148775) ((-633 . -1070) 148759) ((-531 . -1236) T) ((-528 . -1236) T) ((-509 . -1236) T) ((-508 . -1236) T) ((-449 . -625) 148741) ((-446 . -625) 148723) ((-633 . -652) 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-1236) T) ((-605 . -862) T) ((-1161 . -1119) T) ((-1161 . -1072) 142286) ((-103 . -526) 142219) ((-944 . -625) 142201) ((-354 . -738) T) ((-30 . -625) 142183) ((-878 . -1119) T) ((-855 . -1077) 142162) ((-40 . -660) 142069) ((-227 . -1240) T) ((-419 . -1077) T) ((-1177 . -152) 142051) ((-1018 . -300) 142002) ((-886 . -1236) T) ((-629 . -1119) T) ((-227 . -568) T) ((-329 . -1267) 141986) ((-329 . -1264) 141956) ((-713 . -658) 141928) ((-1208 . -1212) 141907) ((-1094 . -625) 141889) ((-1208 . -107) 141839) ((-659 . -152) 141823) ((-644 . -152) 141769) ((-117 . -658) 141741) ((-491 . -1212) 141720) ((-499 . -148) T) ((-499 . -146) NIL) ((-1139 . -626) 141635) ((-450 . -625) 141617) ((-219 . -148) T) ((-219 . -146) NIL) ((-1139 . -625) 141599) ((-130 . -102) T) ((-52 . -102) T) ((-1250 . -651) 141551) ((-491 . -107) 141501) ((-1012 . -23) T) ((-1310 . -38) 141471) ((-1191 . -1131) T) ((-1144 . -1131) T) ((-1081 . -1240) T) ((-245 . -234) 141362) ((-321 . -102) T) ((-866 . -1131) T) ((-969 . -1240) 141341) ((-493 . -1240) 141320) ((-1081 . -568) T) ((-969 . -568) 141251) ((-1191 . -23) T) ((-1170 . -1102) T) ((-1144 . -23) T) ((-866 . -23) T) ((-493 . -568) 141182) ((-1161 . -729) 141114) ((-682 . -1070) 141098) ((-1165 . -526) 141031) ((-682 . -652) 141015) ((-1054 . -626) NIL) ((-1054 . -625) 140997) ((-96 . -1102) T) ((-1315 . -1075) 140984) ((-878 . -729) 140954) ((-1315 . -111) 140939) ((-1230 . -47) 140908) ((-1186 . -862) NIL) ((-258 . -132) T) ((-257 . -132) T) ((-1123 . -1119) T) ((-1022 . -1119) T) ((-62 . -625) 140890) ((-1099 . -909) 140759) ((-1043 . -804) T) ((-1043 . -807) T) ((-1278 . -25) T) ((-1278 . -21) T) ((-1271 . -21) T) ((-1271 . -25) T) ((-882 . -660) 140746) ((-1250 . -21) T) ((-1250 . -25) T) ((-1046 . -152) 140730) ((-1023 . -234) 140717) ((-884 . -832) 140696) ((-884 . -937) T) ((-724 . -296) 140623) ((-608 . -21) T) ((-350 . -658) 140582) ((-108 . -909) NIL) ((-608 . -25) T) ((-607 . -21) T) ((-176 . -658) 140499) ((-40 . -738) T) ((-224 . -526) 140432) ((-607 . -25) T) ((-488 . -152) 140416) ((-475 . -152) 140400) ((-185 . -1236) T) ((-938 . -806) T) ((-938 . -738) T) ((-783 . -805) T) ((-783 . -806) T) ((-518 . -1119) T) ((-514 . -1119) T) ((-783 . -738) T) ((-227 . -374) T) ((-1308 . -1070) 140384) ((-1306 . -1070) 140368) ((-1308 . -652) 140338) ((-1176 . -1119) 140316) ((-883 . -1240) T) ((-1306 . -652) 140286) ((-666 . -625) 140268) ((-883 . -568) T) ((-706 . -379) NIL) ((-44 . -1070) 140252) ((-1315 . -628) 140234) ((-1309 . -1119) T) ((-682 . -102) T) ((-370 . -1293) 140218) ((-364 . -1293) 140202) ((-44 . -652) 140186) ((-356 . -1293) 140170) ((-560 . -102) T) ((-1230 . -1236) T) ((-532 . -862) 140149) ((-723 . -1236) T) ((-499 . -237) T) ((-219 . -237) T) ((-1065 . -1119) T) ((-829 . -464) 140128) ((-153 . -1070) 140112) ((-1065 . -1090) 140041) ((-1046 . -995) 140010) ((-831 . -1131) T) ((-1022 . -729) 139955) ((-153 . -652) 139939) ((-398 . -1131) T) ((-488 . -995) 139908) ((-475 . -995) 139877) ((-110 . 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-34) T) ((-794 . -47) 138509) ((-792 . -47) 138481) ((-1259 . -568) 138392) ((-1216 . -1236) T) ((-365 . -379) T) ((-493 . -1131) T) ((-1191 . -132) T) ((-1144 . -132) T) ((-466 . -47) 138371) ((-883 . -374) T) ((-866 . -132) T) ((-153 . -102) T) ((-1081 . -23) T) ((-969 . -23) T) ((-583 . -568) T) ((-828 . -25) T) ((-828 . -21) T) ((-1161 . -526) 138304) ((-604 . -1102) T) ((-598 . -1057) 138288) ((-1272 . -628) 138162) ((-493 . -23) T) ((-362 . -1077) T) ((-1230 . -915) 138143) ((-682 . -319) 138081) ((-1278 . -234) 138034) ((-1132 . -1293) 138004) ((-711 . -660) 137969) ((-1023 . -862) T) ((-1022 . -174) T) ((-980 . -146) 137948) ((-647 . -1119) T) ((-619 . -1119) T) ((-980 . -148) 137927) ((-747 . -148) 137906) ((-747 . -146) 137885) ((-670 . -1236) T) ((-990 . -862) T) ((-1271 . -234) 137831) ((-1250 . -234) 137648) ((-845 . -658) 137565) ((-486 . -937) 137544) ((-347 . -1236) T) ((-329 . -1070) 137379) ((-326 . -1075) 137289) ((-323 . -1075) 137218) ((-1018 . -296) 137176) ((-419 . -729) 137128) ((-329 . -652) 136969) ((-607 . -234) 136922) ((-713 . -860) T) ((-1272 . -1068) T) ((-326 . -111) 136818) ((-323 . -111) 136731) ((-97 . -1236) T) ((-981 . -102) T) ((-827 . -102) 136463) ((-724 . -626) NIL) ((-724 . -625) 136445) ((-1272 . -336) 136389) ((-670 . -1057) 136285) ((-1106 . -1236) T) ((-1054 . -298) 136260) ((-592 . -738) T) ((-576 . -806) T) ((-171 . -374) 136211) ((-576 . -803) T) ((-576 . -738) T) ((-507 . -738) T) ((-794 . -1236) T) ((-792 . -1236) T) ((-1165 . -501) 136195) ((-473 . -1236) T) ((-466 . -1236) T) ((-1308 . -1307) 136171) ((-1106 . -899) NIL) ((-883 . -1131) T) ((-118 . -926) NIL) ((-1306 . -1307) 136150) ((-661 . -1236) T) ((-794 . -899) NIL) ((-792 . -899) 136009) ((-1301 . -25) T) ((-1301 . -21) T) ((-1233 . -102) 135987) ((-1125 . -407) T) ((-635 . -660) 135974) ((-466 . -899) NIL) ((-687 . -102) 135924) ((-1106 . -1057) 135751) ((-883 . -23) T) ((-794 . -1057) 135610) ((-792 . -1057) 135467) ((-118 . -660) 135412) ((-466 . -1057) 135288) ((-284 . -1236) T) ((-326 . -628) 134852) ((-323 . -628) 134735) ((-50 . -1236) T) ((-402 . -658) 134704) ((-661 . -1057) 134688) ((-639 . -102) T) ((-593 . -1236) T) ((-530 . -1236) T) ((-224 . -501) 134672) ((-1286 . -34) T) ((-633 . -658) 134631) ((-299 . -1070) 134618) ((-137 . -628) 134602) ((-299 . -652) 134589) ((-647 . -729) 134573) ((-619 . -729) 134557) ((-682 . -38) 134517) ((-329 . -102) T) ((-1139 . -1075) 134504) ((-85 . -625) 134486) ((-50 . -1057) 134470) ((-1106 . -388) 134454) ((-794 . -388) 134438) ((-711 . -738) T) ((-711 . -806) T) ((-711 . -803) T) ((-60 . -57) 134400) ((-593 . -1057) 134387) ((-530 . -1057) 134364) ((-173 . -1236) T) ((-334 . -132) T) ((-326 . -1068) 134254) ((-323 . -1068) T) ((-171 . -1131) T) ((-792 . -388) 134238) ((-45 . -152) 134188) ((-1023 . -1011) 134170) ((-466 . -388) 134154) ((-419 . -174) T) ((-326 . -248) 134133) ((-323 . -248) T) ((-323 . -238) NIL) ((-304 . -1119) 133915) ((-227 . -132) T) ((-1139 . -111) 133900) ((-171 . -23) T) ((-811 . -148) 133879) ((-811 . -146) 133858) ((-258 . -651) 133764) ((-257 . -651) 133670) ((-329 . -294) 133636) ((-1176 . -526) 133569) ((-489 . -658) 133519) ((-494 . -909) 133386) ((-1152 . -1119) T) ((-227 . -1079) T) ((-827 . -319) 133324) ((-1106 . -915) 133259) ((-794 . -915) 133202) ((-792 . -915) 133186) ((-1308 . -38) 133156) ((-1306 . -38) 133126) ((-1259 . -1131) T) ((-867 . -1131) T) ((-466 . -915) 133103) ((-870 . -1119) T) ((-1259 . -23) T) ((-1139 . -628) 133075) ((-1081 . -132) T) ((-583 . -1131) T) ((-867 . -23) T) ((-635 . -738) T) ((-366 . -937) T) ((-363 . -937) T) ((-299 . -102) T) ((-355 . -937) T) ((-989 . -1102) T) ((-969 . -132) T) ((-828 . -234) 133020) ((-118 . -806) NIL) ((-118 . -803) NIL) ((-118 . -738) T) ((-1065 . -526) 132921) ((-706 . -926) NIL) ((-583 . -23) T) ((-493 . -132) T) ((-430 . -237) 132872) ((-687 . -319) 132810) ((-225 . -1236) T) ((-647 . -773) T) ((-619 . -773) T) ((-1250 . -862) NIL) ((-1099 . -1070) 132720) ((-1022 . -300) T) ((-706 . -660) 132670) ((-258 . -25) T) ((-362 . -1119) T) ((-258 . -21) T) ((-257 . -25) T) ((-257 . -21) T) ((-153 . -38) 132654) ((-2 . -102) T) ((-927 . -937) T) ((-1099 . -652) 132522) ((-494 . -1293) 132492) ((-1139 . -1068) T) ((-723 . -317) T) ((-370 . -1070) 132444) ((-364 . -1070) 132396) ((-356 . -1070) 132348) ((-370 . -652) 132300) ((-225 . -1057) 132277) ((-364 . -652) 132229) ((-108 . -1070) 132179) ((-356 . -652) 132131) ((-304 . -729) 132073) ((-713 . -1077) T) ((-499 . -464) T) ((-419 . -526) 131985) ((-108 . -652) 131935) ((-219 . -464) T) ((-1139 . -238) T) ((-305 . -152) 131885) ((-1018 . -626) 131846) ((-1018 . -625) 131828) ((-1008 . -625) 131810) ((-117 . -1077) T) ((-666 . -1075) 131794) ((-227 . -505) T) ((-411 . -625) 131776) ((-411 . -626) 131753) ((-1073 . -1293) 131723) ((-666 . -111) 131702) ((-682 . -917) 131625) ((-1161 . -501) 131609) ((-1310 . -658) 131568) ((-392 . -658) 131537) ((-63 . -453) T) ((-63 . -407) T) ((-1178 . -102) T) ((-883 . -132) T) ((-496 . -102) 131487) ((-1137 . -1236) T) ((-1315 . -379) T) ((-1099 . -102) T) ((-1080 . -102) T) ((-362 . -729) 131432) ((-743 . -148) 131411) ((-743 . -146) 131390) ((-666 . -628) 131308) ((-1043 . -660) 131245) ((-535 . -1119) 131223) ((-370 . -102) T) ((-364 . -102) T) ((-356 . -102) T) ((-108 . -102) T) ((-516 . -1119) T) ((-365 . -660) 131168) ((-1191 . -651) 131116) ((-1144 . -651) 131064) ((-396 . -521) 131043) ((-845 . -860) 131022) ((-706 . -738) T) ((-390 . -1240) T) ((-343 . -1236) T) ((-1250 . -1011) 130974) ((-350 . -1077) T) ((-112 . -1236) T) ((-176 . -1077) T) ((-103 . -625) 130906) ((-1193 . -146) 130885) ((-1193 . -148) 130864) ((-390 . -568) T) ((-1192 . -148) 130843) ((-1192 . -146) 130822) ((-1186 . -146) 130729) ((-419 . -300) T) ((-1186 . -148) 130636) ((-1145 . -148) 130615) ((-1145 . -146) 130594) ((-329 . -38) 130435) ((-171 . -132) T) ((-323 . -807) NIL) ((-323 . -804) NIL) ((-666 . -1068) T) ((-48 . -660) 130385) ((-1132 . -1070) 130286) ((-906 . -628) 130263) ((-1132 . -652) 130185) ((-1185 . -102) T) ((-1013 . -102) T) ((-1012 . -21) T) ((-128 . -1029) 130169) ((-122 . -1029) 130153) ((-1012 . -25) T) ((-918 . -120) 130137) ((-1177 . -102) T) ((-1259 . -132) T) ((-1191 . -25) T) ((-1191 . -21) T) ((-354 . -1236) T) ((-1144 . -25) T) ((-867 . -132) T) ((-406 . -1236) T) ((-1144 . -21) T) ((-866 . -25) T) ((-866 . -21) T) ((-794 . -317) 130116) ((-1178 . -319) 129911) ((-1176 . -501) 129895) ((-1169 . -152) 129845) ((-659 . -102) 129795) ((-644 . -102) T) ((-1165 . -625) 129757) ((-583 . -132) T) ((-633 . -860) 129736) ((-1165 . -626) 129697) ((-1043 . -803) T) ((-1043 . -806) T) ((-1043 . -738) T) ((-827 . -917) 129566) ((-724 . -1075) 129389) ((-496 . -319) 129327) ((-465 . -429) 129297) ((-362 . -174) T) ((-299 . -38) 129284) ((-258 . -234) 129175) ((-257 . -234) 129066) ((-283 . -102) T) ((-282 . -102) T) ((-281 . -102) T) ((-280 . -102) T) ((-279 . -102) T) ((-278 . -102) T) ((-354 . -1057) 129043) ((-277 . -102) T) ((-214 . -102) T) ((-213 . -102) T) ((-211 . -102) T) ((-210 . -102) T) ((-209 . -102) T) ((-208 . -102) T) ((-205 . -102) T) ((-204 . -102) T) ((-203 . -102) T) ((-202 . -102) T) ((-201 . -102) T) ((-200 . -102) T) ((-199 . -102) T) ((-198 . -102) T) ((-197 . -102) T) ((-196 . -102) T) ((-195 . -102) T) ((-724 . -111) 128852) ((-365 . -738) T) ((-682 . -272) 128836) ((-682 . -232) 128820) ((-593 . -317) T) ((-530 . -317) T) ((-304 . -526) 128769) ((-1183 . -1236) T) ((-108 . -319) NIL) ((-72 . -407) T) ((-1132 . -102) 128501) ((-845 . -423) 128485) ((-1139 . -807) T) ((-1139 . -804) T) ((-713 . -1119) T) ((-590 . -625) 128467) ((-390 . -374) T) ((-171 . -505) 128445) ((-224 . -625) 128377) ((-135 . -1119) T) ((-117 . -1119) T) ((-983 . -1236) T) ((-48 . -738) T) ((-1065 . -501) 128342) ((-142 . -437) 128324) ((-142 . -379) T) ((-1046 . -102) T) ((-524 . -521) 128303) ((-724 . -628) 128059) ((-1243 . -625) 128041) ((-1200 . -1236) T) ((-1193 . -237) 128000) ((-488 . -102) T) ((-475 . -102) T) 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126511) ((-1023 . -148) T) ((-1023 . -146) NIL) ((-390 . -1131) T) ((-334 . -25) T) ((-332 . -23) T) ((-960 . -862) 126490) ((-724 . -336) 126467) ((-493 . -651) 126415) ((-40 . -1057) 126303) ((-724 . -238) T) ((-713 . -729) 126290) ((-350 . -1119) T) ((-176 . -1119) T) ((-341 . -862) T) ((-430 . -464) 126240) ((-390 . -23) T) ((-370 . -38) 126205) ((-364 . -38) 126170) ((-356 . -38) 126135) ((-80 . -453) T) ((-80 . -407) T) ((-227 . -25) T) ((-227 . -21) T) ((-848 . -1131) T) ((-108 . -38) 126085) ((-839 . -1131) T) ((-786 . -1119) T) ((-117 . -729) 126072) ((-684 . -1057) 126056) ((-624 . -102) T) ((-848 . -23) T) ((-839 . -23) T) ((-1176 . -296) 126008) ((-1132 . -319) 125946) ((-494 . -1070) 125847) ((-1121 . -240) 125831) ((-64 . -408) T) ((-64 . -407) T) ((-1170 . -102) T) ((-110 . -102) T) ((-494 . -652) 125753) ((-40 . -388) 125730) ((-96 . -102) T) ((-665 . -864) 125714) ((-1191 . -234) 125701) ((-1154 . -1102) T) ((-1081 . -21) T) ((-1081 . -25) T) ((-1073 . -1070) 125685) ((-827 . -272) 125654) ((-827 . -232) 125623) ((-969 . -25) T) ((-969 . -21) T) ((-1139 . -379) T) ((-1073 . -652) 125565) ((-633 . -1077) T) ((-1046 . -319) 125503) ((-902 . -625) 125485) ((-682 . -658) 125444) ((-493 . -25) T) ((-493 . -21) T) ((-396 . -1070) 125428) ((-898 . -625) 125410) ((-882 . -1236) T) ((-535 . -526) 125343) ((-258 . -862) 125294) ((-257 . -862) 125245) ((-396 . -652) 125215) ((-883 . -651) 125192) ((-488 . -319) 125130) ((-559 . -1236) T) ((-475 . -319) 125068) ((-362 . -300) T) ((-1176 . -1274) 125052) ((-1161 . -625) 125014) ((-1161 . -626) 124975) ((-1159 . -102) T) ((-1018 . -1075) 124871) ((-40 . -915) 124823) ((-1176 . -616) 124800) ((-1315 . -660) 124787) ((-1082 . -152) 124733) ((-499 . -909) NIL) ((-878 . -502) 124710) ((-1018 . -111) 124592) ((-884 . -1240) T) ((-219 . -909) NIL) ((-350 . -729) 124576) ((-878 . -625) 124538) ((-176 . -729) 124470) ((-884 . -568) T) ((-419 . -296) 124428) ((-245 . -237) 124325) ((-108 . -412) 124307) ((-84 . -395) T) 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123147) ((-1018 . -248) 123126) ((-1018 . -238) 123105) ((-1278 . -148) 123084) ((-1271 . -148) 123063) ((-845 . -1119) T) ((-1271 . -146) 123042) ((-1270 . -1240) 123021) ((-1250 . -146) 122928) ((-1250 . -148) 122835) ((-1249 . -1240) 122814) ((-390 . -132) T) ((-227 . -234) 122801) ((-176 . -174) T) ((-576 . -899) 122783) ((0 . -1119) T) ((-171 . -21) T) ((-171 . -25) T) ((-55 . -1236) T) ((-49 . -1119) T) ((-1272 . -660) 122688) ((-1270 . -568) 122639) ((-726 . -1131) T) ((-1249 . -568) 122590) ((-576 . -1057) 122572) ((-607 . -148) 122551) ((-607 . -146) 122530) ((-507 . -1057) 122473) ((-1154 . -1156) T) ((-87 . -395) T) ((-87 . -407) T) ((-884 . -374) T) ((-848 . -132) T) ((-839 . -132) T) ((-981 . -658) 122417) ((-726 . -23) T) ((-518 . -625) 122383) ((-514 . -625) 122365) ((-827 . -658) 122144) ((-1310 . -1077) T) ((-390 . -1079) T) ((-1045 . -1119) 122122) ((-55 . -1057) 122104) ((-918 . -34) T) ((-494 . -319) 122042) ((-604 . -102) T) ((-1176 . -626) 122003) ((-1176 . -625) 121935) ((-1197 . -1070) 121818) ((-45 . -102) T) ((-829 . -102) T) ((-1197 . -652) 121715) ((-1287 . -1236) T) ((-1259 . -25) T) ((-1259 . -21) T) ((-1081 . -234) 121702) ((-867 . -25) T) ((-254 . -1236) T) ((-44 . -378) 121686) ((-867 . -21) T) ((-743 . -464) 121637) ((-1309 . -625) 121619) ((-722 . -1236) T) ((-711 . -1236) T) ((-1298 . -1070) 121589) ((-1073 . -319) 121527) ((-683 . -1102) T) ((-618 . -1102) T) ((-402 . -1119) T) ((-583 . -25) T) ((-583 . -21) T) ((-182 . -1102) T) ((-162 . -1102) T) ((-157 . -1102) T) ((-155 . -1102) T) ((-1298 . -652) 121497) ((-633 . -1119) T) ((-711 . -899) 121479) ((-1286 . -1236) T) ((-229 . -319) 121417) ((-145 . -379) T) ((-1209 . -1236) T) ((-1065 . -626) 121359) ((-1065 . -625) 121302) ((-323 . -926) NIL) ((-1244 . -856) T) ((-1132 . -917) 121171) ((-711 . -1057) 121116) ((-723 . -937) T) ((-486 . -1240) 121095) ((-1192 . -464) 121074) ((-1186 . -464) 121053) ((-340 . -102) T) ((-884 . -1131) T) ((-329 . -658) 120935) ((-326 . -660) 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119485) ((-633 . -729) 119469) ((-1124 . -1236) T) ((-45 . -319) 119273) ((-828 . -146) 119252) ((-828 . -148) 119231) ((-299 . -658) 119203) ((-1309 . -393) 119182) ((-831 . -862) T) ((-1288 . -1119) T) ((-1178 . -231) 119129) ((-398 . -862) 119108) ((-1278 . -35) 119074) ((-1278 . -1224) 119040) ((-1278 . -1221) 119006) ((-1271 . -1221) 118972) ((-527 . -132) T) ((-1271 . -1224) 118938) ((-1250 . -1221) 118904) ((-1250 . -1224) 118870) ((-1278 . -95) 118836) ((-1271 . -95) 118802) ((-430 . -909) 118723) ((-647 . -625) 118692) ((-619 . -625) 118661) ((-227 . -862) T) ((-1271 . -35) 118627) ((-1270 . -1131) T) ((-1250 . -95) 118593) ((-1139 . -660) 118565) ((-1250 . -35) 118531) ((-1249 . -1131) T) ((-605 . -152) 118513) ((-1099 . -360) 118492) ((-176 . -300) T) ((-118 . -388) 118469) ((-118 . -349) 118446) ((-171 . -234) 118371) ((-882 . -317) T) ((-323 . -806) NIL) ((-323 . -803) NIL) ((-326 . -738) 118220) ((-323 . -738) T) ((-486 . -374) 118199) ((-370 . -360) 118178) ((-364 . -360) 118157) ((-356 . -360) 118136) ((-326 . -485) 118115) ((-1270 . -23) T) ((-1249 . -23) T) ((-730 . -1131) T) ((-726 . -132) T) ((-665 . -102) T) ((-489 . -729) 118080) ((-45 . -292) 118030) ((-105 . -1119) T) ((-68 . -625) 118012) ((-989 . -102) T) ((-876 . -102) T) ((-635 . -915) 117971) ((-1310 . -1119) T) ((-392 . -1119) T) ((-1259 . -234) 117958) ((-1235 . -1119) T) ((-82 . -1236) T) ((-1132 . -272) 117927) ((-1081 . -862) T) ((-118 . -915) NIL) ((-794 . -937) 117906) ((-725 . -862) T) ((-543 . -1119) T) ((-512 . -1119) T) ((-366 . -1240) T) ((-363 . -1240) T) ((-355 . -1240) T) ((-273 . -1240) 117885) ((-253 . -1240) 117864) ((-545 . -872) T) ((-1132 . -232) 117833) ((-1177 . -840) T) ((-1161 . -1075) 117817) ((-402 . -773) T) ((-706 . -1236) T) ((-703 . -1057) 117801) ((-366 . -568) T) ((-363 . -568) T) ((-355 . -568) T) ((-273 . -568) 117732) ((-253 . -568) 117663) ((-537 . -1102) T) ((-1161 . -111) 117642) ((-465 . -756) 117612) ((-878 . -1075) 117582) ((-829 . -38) 117524) ((-706 . -897) 117506) ((-706 . -899) 117488) ((-305 . -319) 117292) ((-1176 . -298) 117269) ((-927 . -1240) T) ((-1099 . -658) 117164) ((-1023 . -464) T) ((-682 . -423) 117148) ((-878 . -111) 117113) ((-931 . -464) T) ((-706 . -1057) 117058) ((-927 . -568) T) ((-545 . -625) 117040) ((-593 . -937) T) ((-499 . -1070) 116990) ((-486 . -1131) T) ((-530 . -937) T) ((-494 . -917) 116859) ((-65 . -625) 116841) ((-219 . -1070) 116791) ((-499 . -652) 116741) ((-370 . -658) 116678) ((-364 . -658) 116615) ((-356 . -658) 116552) ((-644 . -231) 116498) ((-219 . -652) 116448) ((-108 . -658) 116398) ((-486 . -23) T) ((-1139 . -806) T) ((-884 . -132) T) ((-1139 . -803) T) ((-1301 . -1303) 116377) ((-1139 . -738) T) ((-666 . -660) 116351) ((-304 . -625) 116092) ((-1161 . -628) 116010) ((-1054 . -34) T) ((-828 . -237) 115961) ((-592 . -317) T) ((-576 . -317) T) ((-507 . -317) T) ((-1310 . -729) 115931) ((-706 . -388) 115913) ((-706 . -349) 115895) ((-489 . -174) T) ((-392 . -729) 115865) ((-878 . -628) 115800) ((-883 . -862) NIL) ((-576 . -1041) T) ((-507 . -1041) T) ((-1152 . -625) 115782) ((-1132 . -243) 115761) ((-216 . -102) T) ((-1169 . -102) T) ((-71 . -625) 115743) ((-1043 . -1236) T) ((-1161 . -1068) T) ((-1197 . -38) 115640) ((-870 . -625) 115622) ((-576 . -557) T) ((-682 . -1077) T) ((-743 . -966) 115575) ((-365 . -1236) T) ((-1161 . -238) 115554) ((-1101 . -1119) T) ((-1053 . -25) T) ((-1053 . -21) T) ((-1022 . -1075) 115499) ((-922 . -102) T) ((-878 . -1068) T) ((-706 . -915) NIL) ((-366 . -339) 115483) ((-366 . -374) T) ((-363 . -339) 115467) ((-363 . -374) T) ((-355 . -339) 115451) ((-355 . -374) T) ((-499 . -102) T) ((-1298 . -38) 115421) ((-558 . -862) T) ((-535 . -699) 115371) ((-219 . -102) T) ((-1043 . -1057) 115251) ((-1022 . -111) 115180) ((-1193 . -992) 115149) ((-1192 . -992) 115111) ((-532 . -152) 115095) ((-1099 . -381) 115074) ((-362 . -625) 115056) ((-332 . -21) T) ((-365 . -1057) 115033) ((-332 . -25) T) ((-1186 . -992) 115002) ((-48 . -1236) T) 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. -628) 112547) ((-512 . -526) NIL) ((-494 . -243) 112526) ((-419 . -628) 112424) ((-980 . -1070) 112307) ((-747 . -1070) 112277) ((-980 . -652) 112174) ((-1191 . -146) 112153) ((-747 . -652) 112123) ((-465 . -1070) 112093) ((-1191 . -148) 112072) ((-1144 . -148) 112051) ((-1144 . -146) 112030) ((-647 . -1075) 112014) ((-619 . -1075) 111998) ((-465 . -652) 111968) ((-1193 . -1277) 111952) ((-1193 . -1264) 111929) ((-1192 . -1269) 111890) ((-682 . -1119) T) ((-682 . -1072) 111830) ((-1192 . -1264) 111800) ((-560 . -1119) T) ((-499 . -1171) T) ((-1192 . -1267) 111784) ((-1186 . -1248) 111745) ((-830 . -275) 111729) ((-219 . -1171) T) ((-354 . -937) T) ((-99 . -1236) T) ((-647 . -111) 111708) ((-619 . -111) 111687) ((-1186 . -1264) 111664) ((-855 . -1068) 111643) ((-1186 . -1246) 111627) ((-527 . -25) T) ((-507 . -312) T) ((-523 . -23) T) ((-522 . -25) T) ((-520 . -25) T) ((-519 . -23) T) ((-430 . -1070) 111601) ((-419 . -1068) T) ((-329 . -1077) T) ((-706 . -317) T) ((-430 . -652) 111575) ((-108 . -860) T) ((-724 . -738) T) ((-419 . -248) T) ((-419 . -238) 111554) ((-390 . -234) 111541) ((-499 . -38) 111491) ((-219 . -38) 111441) ((-486 . -505) 111407) ((-1243 . -379) T) ((-1177 . -1163) T) ((-1120 . -102) T) ((-839 . -234) 111380) ((-713 . -625) 111362) ((-713 . -626) 111277) ((-726 . -21) T) ((-726 . -25) T) ((-1154 . -102) T) ((-494 . -658) 111056) ((-245 . -909) 110923) ((-135 . -625) 110905) ((-117 . -625) 110887) ((-158 . -25) T) ((-1308 . -1119) T) ((-884 . -651) 110835) ((-1306 . -1119) T) ((-877 . -1236) T) ((-980 . -102) T) ((-747 . -102) T) ((-727 . -102) T) ((-465 . -102) T) ((-828 . -464) 110786) ((-44 . -1119) T) ((-1107 . -862) T) ((-1082 . -319) 110637) ((-676 . -132) T) ((-1073 . -658) 110606) ((-682 . -729) 110590) ((-299 . -1077) T) ((-366 . -132) T) ((-363 . -132) T) ((-355 . -132) T) ((-273 . -132) T) ((-253 . -132) T) ((-396 . -658) 110559) ((-1315 . -1236) T) ((-430 . -102) T) ((-153 . -1119) T) ((-45 . -231) 110509) ((-1023 . -909) NIL) ((-811 . -1070) 110493) ((-975 . -862) 110472) ((-1018 . -660) 110374) ((-811 . -652) 110358) ((-245 . -1293) 110328) ((-1043 . -317) T) ((-304 . -1075) 110249) ((-927 . -132) T) ((-40 . -937) T) ((-499 . -412) 110231) ((-365 . -317) T) ((-219 . -412) 110213) ((-1099 . -423) 110197) ((-304 . -111) 110113) ((-1202 . -862) T) ((-1201 . -862) T) ((-884 . -25) T) ((-884 . -21) T) ((-1272 . -47) 110057) ((-350 . -625) 110039) ((-1191 . -237) T) ((-227 . -148) T) ((-176 . -625) 110021) ((-786 . -625) 110003) ((-129 . -862) T) ((-620 . -240) 109950) ((-487 . -240) 109900) ((-1308 . -729) 109870) ((-48 . -317) T) ((-1306 . -729) 109840) ((-65 . -628) 109769) ((-981 . -1119) T) ((-827 . -1119) 109521) ((-322 . -102) T) ((-918 . -1236) T) ((-48 . -1041) T) ((-1249 . -651) 109429) ((-701 . -102) 109379) ((-44 . -729) 109363) ((-562 . -102) T) ((-304 . -628) 109294) ((-67 . -394) T) ((-499 . -917) NIL) ((-67 . -407) T) ((-219 . -917) NIL) ((-674 . -23) T) ((-829 . -658) 109230) ((-682 . -773) T) 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106274) ((-1193 . -652) 106171) ((-1192 . -652) 106012) ((-723 . -1240) T) ((-1186 . -652) 105808) ((-1176 . -663) 105792) ((-1145 . -652) 105689) ((-831 . -397) 105673) ((-723 . -568) T) ((-607 . -909) 105584) ((-326 . -897) 105568) ((-326 . -899) 105493) ((-323 . -897) 105454) ((-140 . -1236) T) ((-137 . -1236) T) ((-115 . -1236) T) ((-323 . -899) NIL) ((-811 . -319) 105419) ((-329 . -729) 105260) ((-398 . -397) 105244) ((-334 . -333) 105221) ((-497 . -102) T) ((-486 . -25) T) ((-486 . -21) T) ((-430 . -38) 105195) ((-326 . -1057) 104858) ((-227 . -1221) T) ((-227 . -1224) T) ((-3 . -625) 104840) ((-323 . -1057) 104770) ((-884 . -234) 104715) ((-2 . -1119) T) ((-2 . |RecordCategory|) T) ((-1132 . -1077) 104693) ((-845 . -625) 104675) ((-1081 . -237) T) ((-592 . -937) T) ((-576 . -832) T) ((-576 . -937) T) ((-507 . -937) T) ((-137 . -1057) 104659) ((-227 . -95) T) ((-171 . -148) 104638) ((-75 . -453) T) ((0 . -625) 104620) ((-75 . -407) T) ((-171 . -146) 104571) ((-227 . -35) T) ((-49 . -625) 104553) ((-489 . -1077) T) ((-499 . -272) 104535) ((-499 . -232) 104517) ((-496 . -987) 104501) ((-219 . -272) 104483) ((-219 . -232) 104465) ((-81 . -453) T) ((-81 . -407) T) ((-1165 . -34) T) ((-743 . -102) T) ((-665 . -658) 104424) ((-1045 . -625) 104391) ((-512 . -296) 104341) ((-326 . -388) 104310) ((-323 . -388) 104271) ((-323 . -349) 104232) ((-1104 . -625) 104214) ((-828 . -966) 104161) ((-674 . -132) T) ((-1259 . -146) 104140) ((-1259 . -148) 104119) ((-1193 . -102) T) ((-1192 . -102) T) ((-1186 . -102) T) ((-1178 . -1119) T) ((-1145 . -102) T) ((-1094 . -1236) T) ((-224 . -34) T) ((-299 . -729) 104106) ((-1178 . -622) 104082) ((-605 . -319) NIL) ((-1278 . -1277) 104066) ((-1169 . -231) 104016) ((-496 . -1119) 103994) ((-450 . -1236) T) ((-402 . -625) 103976) ((-522 . -862) T) ((-1139 . -1236) T) ((-1278 . -1264) 103953) ((-1271 . -1269) 103914) ((-1271 . -1264) 103884) ((-1271 . -1267) 103868) ((-1250 . -1248) 103829) ((-1250 . -1264) 103806) ((-1250 . -1246) 103790) 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-1119) T) ((-280 . -1119) T) ((-279 . -1119) T) ((-278 . -1119) T) ((-277 . -1119) T) ((-214 . -1119) T) ((-213 . -1119) T) ((-171 . -1224) 100186) ((-171 . -1221) 100164) ((-211 . -1119) T) ((-210 . -1119) T) ((-117 . -1068) T) ((-209 . -1119) T) ((-208 . -1119) T) ((-205 . -1119) T) ((-204 . -1119) T) ((-203 . -1119) T) ((-202 . -1119) T) ((-201 . -1119) T) ((-200 . -1119) T) ((-199 . -1119) T) ((-198 . -1119) T) ((-197 . -1119) T) ((-196 . -1119) T) ((-195 . -1119) T) ((-245 . -102) 99896) ((-171 . -35) 99874) ((-171 . -95) 99852) ((-666 . -1057) 99748) ((-494 . -1077) 99726) ((-1132 . -1119) 99478) ((-1161 . -34) T) ((-682 . -501) 99462) ((-73 . -1236) T) ((-105 . -625) 99444) ((-906 . -1236) T) ((-1310 . -625) 99426) ((-392 . -625) 99408) ((-350 . -628) 99360) ((-176 . -628) 99277) ((-1235 . -502) 99258) ((-743 . -38) 99107) ((-583 . -1224) T) ((-583 . -1221) T) ((-543 . -625) 99089) ((-532 . -319) 99027) ((-512 . -625) 99009) ((-512 . -626) 98991) ((-1235 . -625) 98957) ((-1186 . 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95998) ((-299 . -300) T) ((-1250 . -1070) 95788) ((-1101 . -625) 95770) ((-1101 . -626) 95751) ((-419 . -926) 95730) ((-1230 . -132) T) ((-50 . -1131) T) ((-1186 . -412) 95682) ((-1043 . -937) T) ((-1022 . -738) T) ((-855 . -660) 95655) ((-724 . -899) NIL) ((-608 . -1070) 95615) ((-593 . -1131) T) ((-530 . -1131) T) ((-607 . -1070) 95498) ((-1176 . -34) T) ((-1023 . -319) NIL) ((-827 . -501) 95482) ((-608 . -652) 95455) ((-365 . -937) T) ((-607 . -652) 95352) ((-927 . -234) 95339) ((-419 . -660) 95255) ((-50 . -23) T) ((-723 . -132) T) ((-724 . -1057) 95135) ((-593 . -23) T) ((-108 . -526) NIL) ((-530 . -23) T) ((-171 . -421) 95106) ((-1159 . -1119) T) ((-1301 . -1300) 95090) ((-743 . -917) 95067) ((-713 . -807) T) ((-713 . -804) T) ((-1139 . -317) T) ((-390 . -148) T) ((-290 . -625) 95049) ((-289 . -625) 95031) ((-1249 . -1011) 95001) ((-48 . -937) T) ((-687 . -501) 94985) ((-258 . -1293) 94955) ((-257 . -1293) 94925) ((-1107 . -237) T) ((-1195 . -862) T) ((-1139 . -1041) T) ((-1065 . -34) T) ((-848 . -148) 94904) ((-848 . -146) 94883) ((-749 . -107) 94867) ((-624 . -133) T) ((-1197 . -1077) T) ((-494 . -1119) 94619) ((-1193 . -917) 94532) ((-1192 . -917) 94438) ((-1186 . -917) 94199) ((-883 . -464) T) ((-85 . -1236) T) ((-142 . -107) 94181) ((-1145 . -917) 94165) ((-724 . -388) 94149) ((-845 . -628) 94017) ((-1309 . -738) T) ((-1298 . -1077) T) ((-1278 . -102) T) ((-1139 . -557) T) ((-591 . -102) T) ((-130 . -502) 93999) ((-1271 . -102) T) ((-402 . -1075) 93983) ((-1191 . -966) 93952) ((-44 . -296) 93929) ((-130 . -625) 93896) ((-52 . -625) 93878) ((-1144 . -966) 93845) ((-665 . -423) 93829) ((-1250 . -102) T) ((-1177 . -526) NIL) ((-674 . -25) T) ((-633 . -1075) 93813) ((-674 . -21) T) ((-980 . -658) 93723) ((-747 . -658) 93668) ((-727 . -658) 93640) ((-402 . -111) 93619) ((-224 . -261) 93603) ((-1073 . -1072) 93543) ((-1073 . -1119) T) ((-1023 . -1171) T) ((-830 . -1119) T) ((-465 . -658) 93458) ((-647 . -660) 93442) ((-633 . -111) 93421) ((-619 . -660) 93405) 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. -296) 92189) ((-489 . -111) 92145) ((-665 . -1077) T) ((-1191 . -909) 92048) ((-1144 . -909) 92030) ((-828 . -1070) 91873) ((-1297 . -1102) T) ((-1259 . -464) 91804) ((-828 . -652) 91653) ((-1296 . -1102) T) ((-1106 . -132) T) ((-1073 . -729) 91595) ((-1046 . -526) 91528) ((-794 . -132) T) ((-792 . -132) T) ((-583 . -464) T) ((-633 . -1068) T) ((-604 . -1119) T) ((-545 . -175) T) ((-473 . -132) T) ((-466 . -132) T) ((-390 . -237) T) ((-1018 . -1236) T) ((-45 . -1119) T) ((-396 . -729) 91498) ((-829 . -1119) T) ((-488 . -526) 91431) ((-475 . -526) 91364) ((-1311 . -628) 91346) ((-465 . -378) 91316) ((-45 . -622) 91295) ((-411 . -1236) T) ((-326 . -312) T) ((-839 . -237) 91274) ((-489 . -628) 91224) ((-1250 . -319) 91109) ((-682 . -625) 91071) ((-59 . -862) 91050) ((-1023 . -412) 91032) ((-560 . -625) 91014) ((-811 . -658) 90973) ((-827 . -616) 90950) ((-528 . -862) 90929) ((-508 . -862) 90908) ((-1018 . -1057) 90804) ((-40 . -1240) T) ((-245 . -917) 90673) ((-50 . -132) T) ((-593 . -132) T) ((-530 . -132) T) ((-304 . -660) 90533) ((-354 . -339) 90510) ((-354 . -374) T) ((-332 . -333) 90487) ((-329 . -296) 90445) ((-40 . -568) T) ((-390 . -1221) T) ((-390 . -1224) T) ((-1054 . -1212) 90420) ((-1208 . -240) 90370) ((-1186 . -232) 90322) ((-1186 . -272) 90274) ((-340 . -1119) T) ((-390 . -95) T) ((-390 . -35) T) ((-1054 . -107) 90220) ((-489 . -1068) T) ((-1310 . -1075) 90204) ((-491 . -240) 90154) ((-1178 . -501) 90088) ((-1301 . -1070) 90072) ((-392 . -1075) 90056) ((-1301 . -652) 90026) ((-489 . -248) T) ((-828 . -102) T) ((-726 . -148) 90005) ((-726 . -146) 89984) ((-496 . -501) 89968) ((-497 . -346) 89937) ((-524 . -1119) T) ((-1310 . -111) 89916) ((-1018 . -388) 89900) ((-425 . -102) T) ((-392 . -111) 89879) ((-1018 . -349) 89863) ((-288 . -1002) 89847) ((-287 . -1002) 89831) ((-1023 . -917) NIL) ((-1308 . -625) 89813) ((-1306 . -625) 89795) ((-110 . -526) NIL) ((-1191 . -1262) 89779) ((-866 . -864) 89763) ((-1197 . -1119) T) ((-103 . -1236) T) ((-969 . -966) 89724) ((-829 . -729) 89666) ((-1250 . -1171) NIL) ((-493 . -966) 89611) ((-1081 . -144) T) ((-60 . -102) 89561) ((-44 . -625) 89543) ((-78 . -625) 89525) ((-362 . -660) 89470) ((-1298 . -1119) T) ((-523 . -862) T) ((-299 . -296) 89449) ((-354 . -1131) T) ((-305 . -1119) T) ((-1018 . -915) 89408) ((-305 . -622) 89387) ((-1310 . -628) 89336) ((-1278 . -38) 89233) ((-1271 . -38) 89074) ((-1250 . -38) 88870) ((-499 . -1077) T) ((-392 . -628) 88854) ((-219 . -1077) T) ((-354 . -23) T) ((-153 . -625) 88836) ((-845 . -807) 88815) ((-845 . -804) 88794) ((-1235 . -628) 88775) ((-608 . -38) 88748) ((-607 . -38) 88645) ((-882 . -568) T) ((-225 . -132) T) ((-329 . -1021) 88611) ((-79 . -625) 88593) ((-724 . -317) 88572) ((-304 . -738) 88474) ((-836 . -102) T) ((-876 . -856) T) ((-304 . -485) 88453) ((-1301 . -102) T) ((-40 . -374) T) ((-884 . -148) 88432) ((-497 . -658) 88414) ((-884 . -146) 88393) ((-1177 . -501) 88375) ((-1310 . -1068) T) ((-494 . -526) 88308) ((-1165 . -1236) T) ((-981 . -625) 88290) ((-659 . -501) 88274) ((-644 . -501) 88205) ((-827 . -625) 87898) ((-48 . -27) T) ((-1197 . -729) 87795) ((-969 . -909) 87774) ((-665 . -1119) T) ((-873 . -872) T) ((-448 . -375) 87748) ((-743 . -658) 87658) ((-493 . -909) 87633) ((-1121 . -102) T) ((-989 . -1119) T) ((-876 . -1119) T) ((-828 . -319) 87620) ((-545 . -539) T) ((-545 . -588) T) ((-1306 . -393) 87592) ((-1073 . -526) 87525) ((-1178 . -296) 87501) ((-245 . -272) 87470) ((-245 . -232) 87439) ((-258 . -1070) 87340) ((-257 . -1070) 87241) ((-1298 . -729) 87211) ((-1185 . -93) T) ((-1013 . -93) T) ((-829 . -174) 87190) ((-258 . -652) 87112) ((-257 . -652) 87034) ((-1233 . -502) 87011) ((-590 . -1236) T) ((-229 . -526) 86944) ((-633 . -807) 86923) ((-633 . -804) 86902) ((-1233 . -625) 86814) ((-224 . -1236) T) ((-687 . -625) 86746) ((-1193 . -658) 86656) ((-1176 . -1029) 86640) ((-960 . -102) 86570) ((-362 . -738) T) ((-873 . -625) 86552) ((-1192 . -658) 86434) ((-1186 . -658) 86271) ((-1145 . -658) 86181) ((-1250 . -412) 86133) ((-1132 . -501) 86117) ((-60 . -319) 86055) ((-341 . -102) T) ((-1230 . -21) T) ((-1230 . -25) T) ((-40 . -1131) T) ((-723 . -21) T) ((-639 . -625) 86037) ((-527 . -333) 86016) ((-723 . -25) T) ((-451 . -102) T) ((-108 . -296) NIL) ((-938 . -1131) T) ((-40 . -23) T) ((-783 . -1131) T) ((-576 . -1240) T) ((-507 . -1240) T) ((-1023 . -272) 85998) ((-329 . -625) 85980) ((-1023 . -232) 85962) ((-171 . -167) 85946) ((-592 . -568) T) ((-576 . -568) T) ((-507 . -568) T) ((-783 . -23) T) ((-1270 . -148) 85925) ((-1270 . -146) 85904) ((-1178 . -616) 85880) ((-1249 . -146) 85805) ((-1046 . -501) 85789) ((-1243 . -1236) T) ((-1249 . -148) 85714) ((-1301 . -1307) 85693) ((-883 . -909) NIL) ((-488 . -501) 85677) ((-475 . -501) 85661) ((-535 . -34) T) ((-665 . -729) 85631) ((-1278 . -917) 85544) ((-1271 . -917) 85450) ((-1250 . -917) 85211) ((-112 . -986) T) ((-1197 . -174) 85162) ((-674 . -862) 85141) ((-376 . -102) T) ((-607 . -917) 85054) ((-245 . -243) 85033) ((-258 . -102) T) 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-616) 83758) ((-670 . -21) T) ((-670 . -25) T) ((-605 . -1163) T) ((-1132 . -296) 83735) ((-347 . -25) T) ((-347 . -21) T) ((-902 . -1236) T) ((-898 . -1236) T) ((-1308 . -1075) 83719) ((-245 . -658) 83498) ((-507 . -374) T) ((-1306 . -1075) 83482) ((-1301 . -38) 83452) ((-1270 . -1221) 83418) ((-1270 . -1224) 83384) ((-1259 . -909) 83287) ((-1191 . -1070) 83110) ((-1161 . -1236) T) ((-1144 . -1070) 82953) ((-866 . -1070) 82937) ((-644 . -616) 82912) ((-1270 . -95) 82878) ((-1270 . -237) 82830) ((-1253 . -102) 82808) ((-1191 . -652) 82637) ((-1144 . -652) 82486) ((-866 . -652) 82456) ((-1250 . -232) 82408) ((-1106 . -25) T) ((-561 . -1119) T) ((-1106 . -21) T) ((-980 . -1077) T) ((-543 . -804) T) ((-543 . -807) T) ((-118 . -1240) T) ((-878 . -1236) T) ((-635 . -568) T) ((-794 . -25) T) ((-794 . -21) T) ((-792 . -21) T) ((-792 . -25) T) ((-747 . -1077) T) ((-727 . -1077) T) ((-682 . -1075) 82392) ((-529 . -1102) T) ((-473 . -25) T) ((-118 . -568) T) ((-473 . -21) T) ((-466 . -25) T) 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. -1236) T) ((-487 . -622) 28181) ((-195 . -1236) T) ((-283 . -1236) T) ((-282 . -1236) T) ((-281 . -1236) T) ((-280 . -1236) T) ((-491 . -231) 28131) ((-279 . -1236) T) ((-278 . -1236) T) ((-277 . -1236) T) ((-439 . -1068) T) ((-931 . -248) T) ((-878 . -132) T) ((-48 . -237) T) ((-711 . -464) T) ((-855 . -1131) 28110) ((-108 . -915) NIL) ((-1230 . -294) 28076) ((-1132 . -1236) T) ((-884 . -860) 28055) ((-1018 . -25) T) ((-922 . -738) T) ((-171 . -526) 27967) ((-1018 . -21) T) ((-922 . -485) T) ((-419 . -1131) T) ((-499 . -806) T) ((-499 . -803) T) ((-927 . -360) T) ((-499 . -738) T) ((-219 . -806) T) ((-219 . -803) T) ((-724 . -234) 27954) ((-219 . -738) T) ((-855 . -23) 27906) ((-1203 . -1119) T) ((-670 . -1070) 27890) ((-1202 . -1119) T) ((-536 . -628) 27871) ((-1201 . -1119) T) ((-329 . -317) 27850) ((-1054 . -240) 27796) ((-670 . -652) 27766) ((-419 . -23) T) ((-960 . -626) 27727) ((-960 . -625) 27639) ((-656 . -501) 27623) ((-45 . -1029) 27573) ((-1132 . -1057) 27400) ((-629 . 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. -1075) 24877) ((-1250 . -1075) 24667) ((-1271 . -111) 24488) ((-1250 . -111) 24257) ((-1230 . -319) 24244) ((-1022 . -132) T) ((-927 . -658) 24194) ((-376 . -625) 24176) ((-362 . -568) T) ((-299 . -317) T) ((-608 . -1075) 24136) ((-607 . -1075) 24019) ((-593 . -1070) 23984) ((-530 . -1070) 23929) ((-372 . -1119) T) ((-332 . -1119) T) ((-258 . -625) 23890) ((-257 . -625) 23851) ((-593 . -652) 23816) ((-530 . -652) 23761) ((-706 . -421) 23728) ((-647 . -23) T) ((-619 . -23) T) ((-40 . -909) 23635) ((-670 . -102) T) ((-608 . -111) 23588) ((-607 . -111) 23457) ((-390 . -1119) T) ((-347 . -102) T) ((-171 . -300) 23368) ((-1249 . -860) 23321) ((-726 . -1077) T) ((-624 . -1236) T) ((-1166 . -526) 23254) ((-1209 . -847) 23238) ((-1132 . -915) 23170) ((-848 . -1119) T) ((-839 . -1119) T) ((-837 . -1119) T) ((-97 . -102) T) ((-145 . -862) T) ((-624 . -897) 23154) ((-1170 . -1236) T) ((-110 . -1236) T) ((-1106 . -102) T) ((-1082 . -34) T) ((-794 . -102) T) ((-792 . -102) T) ((-1278 . -628) 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20288) ((-426 . -1236) T) ((-396 . -1236) T) ((-1092 . -1119) T) ((-229 . -1236) T) ((-1085 . -1119) T) ((-1055 . -1119) T) ((-1038 . -1119) T) ((-794 . -319) 20275) ((-792 . -319) 20262) ((-1191 . -625) 20244) ((-828 . -111) 20073) ((-1144 . -625) 20055) ((-638 . -1119) T) ((-589 . -175) T) ((-541 . -175) T) ((-466 . -319) 20042) ((-495 . -1119) T) ((-1144 . -626) 19790) ((-1053 . -174) T) ((-960 . -298) 19767) ((-220 . -1119) T) ((-866 . -625) 19749) ((-620 . -526) 19532) ((-81 . -628) 19473) ((-830 . -1057) 19457) ((-487 . -526) 19249) ((-980 . -738) T) ((-747 . -738) T) ((-727 . -738) T) ((-362 . -1131) T) ((-1198 . -625) 19231) ((-225 . -102) T) ((-494 . -388) 19200) ((-527 . -1119) T) ((-522 . -1119) T) ((-520 . -1119) T) ((-811 . -660) 19174) ((-1043 . -464) T) ((-975 . -526) 19107) ((-362 . -23) T) ((-647 . -132) T) ((-619 . -132) T) ((-365 . -464) T) ((-245 . -379) 19086) ((-390 . -174) T) ((-1270 . -1077) T) ((-1249 . -1077) T) ((-227 . -1021) T) ((-828 . -628) 18823) ((-711 . -399) T) ((-430 . -738) T) ((-713 . -1240) T) ((-1161 . -651) 18771) ((-592 . -881) 18755) ((-1301 . -1075) 18739) ((-1178 . -1212) 18715) ((-713 . -568) T) ((-127 . -1119) 18693) ((-726 . -1119) T) ((-670 . -38) 18663) ((-494 . -915) 18595) ((-255 . -1119) T) ((-189 . -1119) T) ((-365 . -414) T) ((-326 . -148) 18574) ((-326 . -146) 18553) ((-117 . -568) T) ((-129 . -526) NIL) ((-323 . -148) 18509) ((-323 . -146) 18465) ((-48 . -464) T) ((-163 . -1119) T) ((-158 . -1119) T) ((-1178 . -107) 18412) ((-794 . -1171) 18390) ((-1301 . -111) 18369) ((-701 . -34) T) ((-604 . -1236) T) ((-562 . -34) T) ((-496 . -107) 18353) ((-258 . -298) 18330) ((-257 . -298) 18307) ((-1242 . -856) T) ((-883 . -296) 18258) ((-45 . -1236) T) ((-1230 . -917) 18239) ((-829 . -1236) T) ((-828 . -1068) T) ((-674 . -658) 18208) ((-1197 . -47) 18185) ((-828 . -336) 18147) ((-1106 . -38) 17996) ((-828 . -238) 17975) ((-794 . -38) 17804) ((-792 . -38) 17653) ((-1134 . -502) 17634) ((-466 . -38) 17483) ((-1134 . -625) 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\ No newline at end of file diff --git a/src/share/algebra/compress.daase b/src/share/algebra/compress.daase index 4a05c0f7..1ff2fc66 100644 --- a/src/share/algebra/compress.daase +++ b/src/share/algebra/compress.daase @@ -1,5 +1,5 @@ -(30 . 3486658186) +(30 . 3486753493) (4465 |Enumeration| |Mapping| |Record| |Union| |ofCategory| |isDomain| ATTRIBUTE |package| |domain| |category| CATEGORY |nobranch| AND |Join| |ofType| SIGNATURE "failed" "algebra" |OneDimensionalArrayAggregate&| @@ -488,661 +488,662 @@ |XPolynomial| |XPolynomialRing| |XRecursivePolynomial| |YoungDiagram| |ParadoxicalCombinatorsForStreams| |ZeroDimensionalSolvePackage| |IntegerLinearDependence| |IntegerMod| |Enumeration| |Mapping| - |Record| |Union| |linearlyDependent?| |f02aaf| |updatF| |sequence| - |doublyTransitive?| |match| |save| |primitive?| |string| LODO2FUN - |arbitrary| |lp| |addmod| |coordinates| |cAtanh| |trim| - |numberOfPrimitivePoly| |reopen!| |generic| - |purelyAlgebraicLeadingMonomial?| |bernoulli| 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|algebraicDecompose| |cosh2sech| |extendIfCan| |chvar| |rhs| - |composites| |dominantTerm| |symmetricRemainder| |f04maf| - |BumInSepFFE| |writable?| |genericRightNorm| |multiplyExponents| - |selectPolynomials| |reflect| |removeRedundantFactorsInPols| - |clikeUniv| |polyRDE| |untab| |viewDeltaYDefault| |scalarMatrix| - |basisOfCenter| |UnVectorise| |solveRetract| |currentEnv| - |schwerpunkt| |singular?| |rightTraceMatrix| |patternMatchTimes| - |changeBase| |rightRegularRepresentation| |relativeApprox| |s01eaf| - |Beta| |clearTable!| |kroneckerDelta| |quasiAlgebraicSet| |laplacian| - |setref| |makeObject| |null?| |basisOfRightAnnihilator| |sparsityIF| - |pseudoRemainder| |hasTopPredicate?| |qelt| |genericPosition| - |identityMatrix| |unvectorise| |isEquiv| |linear| |space| |coef| - |rightCharacteristicPolynomial| |zeroSquareMatrix| |aQuartic| - |qsetelt| |increment| |insertTop!| |maximumExponent| |inrootof| - |imports| |indicialEquation| |compiledFunction| |corrPoly| |debug3D| - |rightFactorCandidate| |xRange| |f07fdf| |df2mf| |coefChoose| |s13acf| - |polynomial| |viewWriteAvailable| |removeZero| |partialDenominators| - |alternating| |leftCharacteristicPolynomial| |e02bcf| |yRange| - |fillPascalTriangle| |transform| |trapezoidalo| |addMatchRestricted| - |negative?| |ipow| |rootPoly| |besselI| |argscript| - |expenseOfEvaluation| |zRange| |isExpt| |nextsubResultant2| - |semiResultantEuclideannaif| |slex| |scaleRoots| |sort| |preprocess| - |simplifyPower| |floor| |branchPoint?| |map!| |separant| - |purelyAlgebraic?| |sdf2lst| |palgLODE0| |unitCanonical| |dec| - |normDeriv2| |getCurve| |generalLambert| |qsetelt!| |primitivePart| - |integralDerivationMatrix| |monicRightDivide| |sinIfCan| |fintegrate| - |rootNormalize| |showIntensityFunctions| |selectfirst| - |selectODEIVPRoutines| |curry| |kind| |padicallyExpand| |fractRadix| - |length| |binomThmExpt| |selectOrPolynomials| |fortranLiteral| - |bipolarCylindrical| |recoverAfterFail| |rquo| |c06ekf| |op| - |lazyIntegrate| |sign| |scripts| |c06fqf| |maxRowIndex| |setPoly| - |random| |exportedOperators| |numberOfOperations| |leftReducedSystem| - |univariate| |palgint| |trace2PowMod| |OMgetEndAtp| |push| |nullity| - |getConstant| SEGMENT |numFunEvals3D| |constDsolve| |leftExtendedGcd| - |e01baf| |s17aff| |tableau| |solveInField| |userOrdered?| |logpart| - |mpsode| |coerceS| |gderiv| |quote| |acsch| |bezoutMatrix| |concat!| - |groebner| |definingInequation| |moebiusMu| |setButtonValue| |factor| - |OMputEndObject| |listBranches| |resultantnaif| |cap| |categoryMode| - |OMsupportsCD?| |orthonormalBasis| |solveLinear| |comp| - |complexEigenvectors| |mathieu24| |OMputFloat| |sqrt| - |lineColorDefault| |innerSolve| |integralCoordinates| - |expressIdealMember| |depth| |algebraicSort| |removeCosSq| - |toseSquareFreePart| |generalizedContinuumHypothesisAssumed?| - |dfRange| |localIntegralBasis| |real| |addPoint2| |one?| |union| - |hostPlatform| |viewThetaDefault| |equality| |quasiComponent| - |doubleResultant| |createMultiplicationTable| |s19adf| |meshPar2Var| - |imag| |d01bbf| |createRandomElement| |curryRight| - |complexEigenvalues| |permutationRepresentation| |dimension| - |algSplitSimple| |directProduct| |oddlambert| |getSyntaxFormsFromFile| - |SturmHabicht| |pol| |divideExponents| |realRoots| |unexpand| - |critpOrder| |triangularSystems| |physicalLength!| |writeByte!| - |rectangularMatrix| |jacobi| |unitVector| |localReal?| - |var2StepsDefault| |hcrf| |e02gaf| |gramschmidt| |brace| - |algebraicCoefficients?| |nextColeman| |cSinh| |squareTop| |arguments| - |numeric| |ricDsolve| |split!| |FormatRoman| |child| |copy| |reindex| - |eof?| |genericRightDiscriminant| |destruct| - |basisOfCommutingElements| |returnTypeOf| |dihedral| |setLabelValue| - |low| |every?| |radical| |symbolIfCan| |setIntersection| |Lazard| - |leftGcd| |coth2tanh| |external?| |exponential1| |prinb| - |externalList| |palginfieldint| |leftTraceMatrix| |leadingIndex| - |factorSquareFreeByRecursion| |primitivePart!| |block| - |selectOptimizationRoutines| |cycleElt| |copy!| |prinpolINFO| - |euclideanSize| |perfectNthPower?| |d02raf| |bernoulliB| - |explogs2trigs| |invertIfCan| |rightPower| |removeSinhSq| - |parabolicCylindrical| |adaptive?| |pr2dmp| |monomial| - |createGenericMatrix| |mindegTerm| |match?| |mapGen| |s17akf| - |exprHasAlgebraicWeight| |subPolSet?| |autoCoerce| |nary?| - |iflist2Result| |multivariate| |seed| |hasoln| |pair?| |setRow!| - |explicitlyFinite?| |ideal| |bivariatePolynomials| |variables| - |hasPredicate?| |cyclicGroup| |setleft!| |exprHasLogarithmicWeights| - |e02ddf| |integral?| |nthFlag| |e01bff| |f01brf| |row| |operation| - |birth| |viewWriteDefault| |condition| |pleskenSplit| |quasiMonic?| - |rightRank| |fibonacci| |getDatabase| |cTan| |paren| |rootPower| - |identitySquareMatrix| |OMputBind| |rCoord| |semiResultantEuclidean2| - |close| |rroot| |size?| |decreasePrecision| |s21baf| F |imagi| - |leftMult| |makeGraphImage| |OMUnknownSymbol?| |setPrologue!| - |interpret| |rewriteSetByReducingWithParticularGenerators| - |commaSeparate| |rightExtendedGcd| |cycle| |makeRecord| |trunc| - |applyRules| |bothWays| |irreducibleRepresentation| |debug| |display| - |mightHaveRoots| |parametric?| |conditionsForIdempotents| |randomR| - |mapDown!| |elementary| |zeroDimPrimary?| |f01ref| D |taylor| |lquo| - |weight| |rightFactorIfCan| |firstUncouplingMatrix| |anfactor| - |readUInt8!| |linSolve| |sturmVariationsOf| |removeConstantTerm| - |bezoutDiscriminant| |laurent| |cyclicSubmodule| |palgLODE| |isOp| - |makeCos| |leadingExponent| |twist| |df2st| |getZechTable| |putGraph| - |puiseux| |ldf2lst| |denominator| |d02gaf| |logIfCan| |laurentIfCan| - |cAsin| |adjoint| |supRittWu?| |removeDuplicates| |leftExactQuotient| - |OMclose| |startTableGcd!| |topPredicate| |identification| |recip| - |eigenvectors| |rk4qc| |redmat| |cCosh| |extend| |seriesSolve| |inv| - |input| |enumerate| |rischNormalize| |d02ejf| - |selectSumOfSquaresRoutines| |light| |isOr| |radicalSimplify| - |numberOfDivisors| |taylorQuoByVar| |ground?| |headAst| |library| - |e02dcf| |triangular?| |credPol| |OMputEndApp| EQ |rationalPower| - |bezoutResultant| |findCycle| |ground| |mathieu12| |setMaxPoints3D| - |iicot| |SFunction| |logGamma| |basisOfRightNucleus| |predicates| - |zoom| |exp1| |initials| |leadingMonomial| F2FG |principalIdeal| - |cycleSplit!| |implies| |ceiling| |decrease| |hMonic| |cAcot| - |normalizedDivide| |Lazard2| |leadingCoefficient| |maxIndex| |scale| - |partialFraction| |f02wef| |leftLcm| |noLinearFactor?| |iicsch| |size| - |multiple?| |isAnd| |internalSubQuasiComponent?| |primitiveMonomials| - |print| |set| |bumptab| |s17dhf| |lazyPremWithDefault| |OMbindTCP| - |euler| |jordanAdmissible?| |makeFR| |jacobiIdentity?| |tanSum| - |resolve| |reductum| |quotientByP| |overlap| |gcdprim| |reify| - |f04qaf| |tubeRadiusDefault| |uncouplingMatrices| |toseInvertibleSet| - |maxrank| |fortran| |univariatePolynomialsGcds| |symmetricSquare| - |f01maf| |kmax| |rightGcd| |nextNormalPoly| |iifact| |selectsecond| - |square?| |mainMonomial| |digits| |lowerCase!| |makeTerm| |transpose| - |mergeFactors| |pmComplexintegrate| |resultantEuclidean| |chebyshevT| - |forLoop| |colorFunction| |s17ajf| |pushdterm| |tRange| - |symmetricGroup| |generator| |categories| |polCase| |screenResolution| - |subNodeOf?| |testModulus| |alternatingGroup| |returns| |f02ajf| - |sylvesterMatrix| |numberOfVariables| |nthFactor| |eq?| |getGoodPrime| - |transcendent?| |makeEq| |bfKeys| |cAsinh| |unparse| |true| |s19acf| - |optpair| |category| |clearDenominator| |OMgetAttr| |cAcoth| - |triangulate| |presub| |postfix| |byteBuffer| |sncndn| |goodnessOfFit| - |defineProperty| |domain| |pointPlot| |graphCurves| |lazyEvaluate| - |laguerreL| |iicosh| |binaryTournament| |pomopo!| |selectPDERoutines| - |basisOfLeftNucloid| |ReduceOrder| |package| |interpolate| |node| - |resetBadValues| |OMopenString| |overlabel| |characteristicSet| - |insert| |members| |linearPart| |create| |singularitiesOf| |exptMod| - |incrementKthElement| |bigEndian| |operators| |splitSquarefree| - |search| |const| |flatten| |show| |normalizeAtInfinity| |divisor| - |fortranLogical| |fractionFreeGauss!| |c06gcf| |tube| |updatD| - |fortranComplex| |c06gqf| |explicitEntries?| |setDifference| |baseRDE| - |listYoungTableaus| |homogeneous?| |prinshINFO| |wholePart| |f01qcf| - |validExponential| |monicCompleteDecompose| |dot| |isQuotient| |trace| - |torsionIfCan| |nonSingularModel| |subset?| |factorList| |pop!| - |viewDefaults| |readIfCan!| |divideIfCan!| |argument| - |radicalEigenvalues| |getPickedPoints| |messagePrint| - |lastSubResultantEuclidean| |iiacoth| |cSin| |cyclotomic| |incr| - |computeCycleEntry| |rootProduct| |nullSpace| |isTimes| |script| - |safeCeiling| |fortranCompilerName| |tanh2trigh| |OMreceive| - |cycleRagits| |monomRDE| |hi| |changeNameToObjf| |plotPolar| |resize| - |partialNumerators| |radicalEigenvectors| |genericRightTrace| - |decomposeFunc| |complementaryBasis| |numberOfComputedEntries| - |directory| |removeCoshSq| |setOfMinN| |ratpart| |bsolve| |divisors| - |iiacsch| |generalizedContinuumHypothesisAssumed| |upperCase!| - |patternMatch| |order| |primlimitedint| |commutativeEquality| - |integralBasis| |e01sef| |upDateBranches| |tex| |height| |rischDEsys| - |solid| |numerator| |iiasec| |thenBranch| - |combineFeatureCompatibility| |setLength!| |pushdown| |cot2tan| - |clearTheIFTable| |removeRoughlyRedundantFactorsInPol| - |SturmHabichtSequence| |sts2stst| |monomialIntPoly| - |setScreenResolution| |d01gaf| |makeVariable| |disjunction| - |primPartElseUnitCanonical!| |elements| |units| |outerProduct| - |ParCond| |integralRepresents| |clearTheSymbolTable| |pointLists| - |showRegion| |s18aff| |normalDeriv| |setLegalFortranSourceExtensions| - |contours| |signatureAst| |cyclicEntries| |gcdcofactprim| |s14baf| - |generateIrredPoly| |squareFreePart| |removeZeroes| |equation| - |fortranCharacter| |point| |hypergeometric0F1| |genericLeftTrace| - |idealiserMatrix| |OMgetBVar| |integral| |lowerCase| |compBound| - |hitherPlane| |quadratic?| |sinh2csch| |noValueMode| |head| - |pushucoef| |comment| |dictionary| |bfEntry| |extractSplittingLeaf| - |internalIntegrate| |dimensionsOf| |normalElement| |center| - |getButtonValue| |rootKerSimp| |invertibleElseSplit?| |exprToUPS| - |log10| |OMParseError?| |limitedIntegrate| |perfectSqrt| |iiacosh| - |host| |increase| |exactQuotient!| |series| |mkcomm| - |numberOfImproperPartitions| |code| |makeSin| |jordanAlgebra?| - |bitand| |f04atf| |setCondition!| |figureUnits| |ScanRoman| - |multMonom| |declare| |leftFactorIfCan| |rowEchelonLocal| - |reducedDiscriminant| |deepestInitial| |primaryDecomp| |bitior| - |genericLeftTraceForm| |setchildren!| |ratDenom| |d03eef| |rational| - |stiffnessAndStabilityOfODEIF| |elColumn2!| |lazyPquo| - |computeCycleLength| |bipolar| |normal?| |gethi| |resetNew| |factors| - |rule| |coerceL| |generate| |changeMeasure| |point?| |close!| - |conjugate| |noKaratsuba| |makeop| |sin?| |f04asf| |inverseLaplace| - |c06eaf| |asimpson| |min| |monicLeftDivide| |resultantReduitEuclidean| - |associates?| |lazyPrem| |e02agf| |inRadical?| |sizePascalTriangle| - |superscript| |sizeMultiplication| |coHeight| |quasiMonicPolynomials| - |incrementBy| |palglimint0| |e01bhf| |rightRecip| |matrix| - |triangSolve| |stFunc2| |representationType| |indicialEquations| - |f02aef| |endOfFile?| |numberOfNormalPoly| |expand| |outputSpacing| - |powers| |color| |genericRightTraceForm| |transcendentalDecompose| - |rightOne| |removeRoughlyRedundantFactorsInContents| |listLoops| - |cycleTail| |expPot| |filterWhile| |components| |shiftRoots| - |saturate| |showTheFTable| |interpretString| |mappingAst| |cos2sec| - |cExp| |currentCategoryFrame| |rename| |filterUntil| |commutative?| - |intChoose| |withPredicates| |roughBase?| |OMputEndAtp| |mkIntegral| - |s21bcf| |OMencodingXML| |smith| |parseString| |select| |OMgetEndAttr| - |inspect| |content| |splitNodeOf!| |meshPar1Var| |lllp| |htrigs| - |minIndex| |rk4| |internalInfRittWu?| |properties| |digit| - |complexNormalize| |resultantReduit| |lift| |leadingSupport| - |direction| |reciprocalPolynomial| |generalTwoFactor| |complexLimit| - |extractProperty| |socf2socdf| |f01rdf| |LazardQuotient2| |primes| - |translate| |reduce| |semiDiscriminantEuclidean| |rightAlternative?| - |newSubProgram| |belong?| |result| |f02awf| |eigenMatrix| - |stoseInvertibleSetreg| |qqq| |groebnerFactorize| |returnType!| - |musserTrials| |scripted?| |mainKernel| |pointSizeDefault| |vspace| - |getOperands| |imagk| Y |mainSquareFreePart| |cTanh| |torsion?| - |coshIfCan| |diagonals| |edf2fi| |primlimintfrac| |leastMonomial| - |shiftRight| |sylvesterSequence| |vectorise| |evaluateInverse| - |hostByteOrder| |trailingCoefficient| |tubePoints| |unit| |f02aff| - |boundOfCauchy| |label| |cross| |charpol| |leadingTerm| |character?| - |pmintegrate| |retractable?| |nextPrimitiveNormalPoly| |meshFun2Var| - |appendPoint| |reverseLex| |palgRDE| |lastSubResultant| |univcase| - |closedCurve| |hermite| |clipPointsDefault| - |semiSubResultantGcdEuclidean2| |goto| |coefficients| |upperCase?| - |constantLeft| |distFact| |semiLastSubResultantEuclidean| |c06fpf| - |putProperties| |extractClosed| |getMultiplicationTable| |setEmpty!| - |rewriteIdealWithHeadRemainder| |complement| |acosIfCan| - |exactQuotient| |lazyResidueClass| |setRealSteps| |poisson| |polyPart| - |factorPolynomial| |componentUpperBound| |nand| |iCompose| |epilogue| - |rightDiscriminant| |OMputApp| |yellow| |outputGeneral| |key?| - |OMlistCDs| |outputAsFortran| |thetaCoord| |quotedOperators| UTS2UP - |parents| |f02bbf| |currentSubProgram| |isPlus| |norm| |swapRows!| - |d02kef| |approxSqrt| |addMatch| |constructor| |setAdaptive3D| - |createNormalElement| |finite?| |lookup| |pointData| |coerceImages| - |f04adf| |byte| |linearDependence| |outlineRender| |tanNa| |option| - |fill!| |factorSFBRlcUnit| |setMinPoints3D| |sPol| |showSummary| - |tubeRadius| |getMatch| |lookupFunction| |halfExtendedResultant1| - |screenResolution3D| |cSec| |limitPlus| |mainVariables| - |deleteRoutine!| |chiSquare1| |mesh| |primeFactor| |element?| - |largest| |decimal| |LyndonCoordinates| |member?| |modifyPoint| - |iidsum| |showAttributes| |c05nbf| |dmpToHdmp| |swap!| |region| - |factorset| |cyclicEqual?| |localAbs| |ode2| |outputList| - |numberOfComposites| |littleEndian| |atom?| |module| - |dimensionOfIrreducibleRepresentation| |padicFraction| |subSet| - |basis| |cAtan| |ef2edf| |stack| |rightTrim| |semicolonSeparate| - |semiIndiceSubResultantEuclidean| |name| |f02akf| |double| - |lazyIrreducibleFactors| |radicalEigenvector| |readBytes!| |bat1| - |initTable!| |polynomialZeros| |leftTrim| |brillhartTrials| |sinhcosh| - |body| |deleteProperty!| |unitNormal| |stopTableInvSet!| |coleman| - |nthExponent| |safeFloor| |int| |setClosed| |tanQ| - |createNormalPrimitivePoly| |null| |determinant| |changeName| |e02bdf| - |mapdiv| |critT| |separateDegrees| |fixedPoint| |imagJ| |loopPoints| - |uniform01| |signature| |cCsc| |not| |mathieu22| |string?| - |var1StepsDefault| |fixedDivisor| BY |factorsOfDegree| - |minimalPolynomial| |subResultantGcd| |pushuconst| |totalDegree| |dim| - |frst| |and| |polygon| |vector| |d02cjf| |s18adf| |ignore?| |output| - |twoFactor| |partialQuotients| |printStats!| |balancedBinaryTree| - |monomRDEsys| |escape| |or| |binary| |differentiate| |cdr| - |reduceByQuasiMonic| |firstSubsetGray| |setColumn!| |positive?| - |processTemplate| |restorePrecision| |shift| |elaboration| |xor| - |asinhIfCan| |zeroOf| |s19aaf| |swap| |minordet| |cAcsc| |terms| |nor| - |e04ycf| |declare!| |permutation| |case| |lepol| |nonQsign| |atoms| - |assert| |cAsec| |cot2trig| |irForm| |port| |realSolve| |tanAn| - |cycleLength| |pattern| |setClipValue| |Zero| |internalAugment| - |makeSketch| |fixPredicate| |bringDown| |extendedResultant| |s15aef| - |hconcat| |setAttributeButtonStep| |totalGroebner| |One| - |swapColumns!| |insertionSort!| |move| |internalSubPolSet?| |simplify| - |palgint0| |t| |superHeight| |writeInt8!| |quadratic| |minPoly| NOT - |qualifier| |f04faf| |iFTable| |genericRightMinimalPolynomial| - |semiResultantEuclidean1| |ldf2vmf| |nextPrimitivePoly| |algint| - |entries| |conjugates| OR |heapSort| |OMgetError| |nextSublist| - |genericLeftMinimalPolynomial| |LazardQuotient| - |sumOfKthPowerDivisors| |airyBi| |att2Result| |zeroMatrix| - |getProperty| |message| AND |monicDivide| |exponent| - |subresultantVector| |exprex| |buildSyntax| |select!| |genus| - |leftNorm| |symmetricTensors| |palgextint| |OMgetType| |writeUInt8!| - |badValues| |style| |cscIfCan| |paraboloidal| |logical?| - |removeSuperfluousCases| |useEisensteinCriterion| |front| - |complexExpand| |segment| |elt| |setelt!| |alphanumeric?| - |degreeSubResultantEuclidean| |rotate!| |getGraph| |elliptic?| - |categoryFrame| |physicalLength| |complexForm| |cond| |mkAnswer| - |e02adf| |commutator| |bandedHessian| |dihedralGroup| |Frobenius| - |systemSizeIF| |symbol?| |ruleset| |connectTo| |adaptive3D?| - |stosePrepareSubResAlgo| |readLine!| |linear?| |rur| |mvar| - |dualSignature| |PDESolve| |leftRecip| |coordinate| - |absolutelyIrreducible?| |more?| |binding| |dmp2rfi| - |stiffnessAndStabilityFactor| |leftFactor| |ffactor| |normInvertible?| - |radicalRoots| |fortranDoubleComplex| |s13aaf| |cons| - |prolateSpheroidal| |matrixGcd| |ref| |degreeSubResultant| |second| - |leadingCoefficientRicDE| |gcdPolynomial| |c06ecf| |totalLex| |prod| - |minPol| |nthr| |suchThat| |basisOfLeftAnnihilator| |leftDivide| - |badNum| |OMconnectTCP| |hasHi| |recolor| |third| |revert| - |linkToFortran| |root?| |rationalApproximation| |critMonD1| - |singleFactorBound| |halfExtendedSubResultantGcd1| |moduloP| - |selectMultiDimensionalRoutines| |computePowers| |makingStats?| - |cartesian| |elseBranch| |semiSubResultantGcdEuclidean1| |taylorIfCan| - |resultant| |void| |lazy?| |property| |top!| |dual| |setEpilogue!| - |quoByVar| * |ran| |clipBoolean| |component| |multinomial| |satisfy?| - |systemCommand| |minPoints3D| |rewriteSetWithReduction| |nlde| - |graphs| |reducedContinuedFraction| |OMsetEncoding| |cCot| - |createIrreduciblePoly| |patternVariable| |has?| - |certainlySubVariety?| |var1Steps| |beauzamyBound| |leftRemainder| - |padecf| |antisymmetricTensors| |squareFreeFactors| - |internalDecompose| |ratPoly| |constantOpIfCan| |elaborate| - |rational?| |subHeight| |leaves| |source| |power!| |cubic| |children| - |mergeDifference| |replaceKthElement| |middle| |discriminant| - |removeRoughlyRedundantFactorsInPols| = |getlo| |monomials| |clip| - |makeUnit| |basisOfCentroid| |sorted?| |s14aaf| |f02fjf| |normal| - |LagrangeInterpolation| |showArrayValues| |macroExpand| |typeLists| - |startPolynomial| |rationalFunction| |partitions| |polygamma| - |plusInfinity| |unknownEndian| |monicRightFactorIfCan| - |functionIsFracPolynomial?| |iterationVar| |iicos| |schema| |expr| < - |radicalSolve| |countable?| |f04arf| |shellSort| |f02agf| - |minusInfinity| |outputFloating| |bitTruth| |sqfrFactor| |printHeader| - |chineseRemainder| |char| > |prime?| |bottom!| |infix| |invmod| - |showTheSymbolTable| |extractIfCan| |lagrange| |zeroDimensional?| - |mirror| |subtractIfCan| |ratDsolve| <= |myDegree| |quadraticForm| - |useNagFunctions| |d03edf| |target| |rotatey| |transcendenceDegree| - |c06frf| |printInfo!| |matrixDimensions| >= |nextsousResultant2| - |algintegrate| |OMputInteger| |shanksDiscLogAlgorithm| - |bandedJacobian| |lSpaceBasis| |jacobian| |toScale| |OMgetBind| - |PollardSmallFactor| |variable| |henselFact| |s18aef| |zag| - |rightUnits| |addiag| |cylindrical| |tablePow| |coerceListOfPairs| - |mathieu23| |harmonic| |iterators| |Hausdorff| |univariatePolynomials| - |inGroundField?| |e04ucf| |f01qdf| |type| |reduceBasisAtInfinity| - |coefficient| |factorial| |lifting1| |initiallyReduced?| - |completeHensel| + |contains?| |elRow1!| |quotient| |Si| |makeMulti| - |nextItem| |reduction| |removeRedundantFactors| |stopMusserTrials| - |prevPrime| - |float| |f04jgf| |quartic| |comparison| - |eisensteinIrreducible?| |rst| |algebraic?| |nonLinearPart| FG2F - |expintegrate| |variationOfParameters| |jokerMode| / |mapUnivariate| - |contract| |deepCopy| |splitDenominator| |leftZero| |lfinfieldint| - |symbol| |bumptab1| |antisymmetric?| |magnitude| - |createLowComplexityNormalBasis| |id| |rationalIfCan| |regime| |scan| - |leftRank| |newLine| |factorAndSplit| |fullDisplay| |getVariableOrder| - |expression| |tubePointsDefault| |computeBasis| |lo| |substitute| - |solid?| |callForm?| |rightTrace| |stFuncN| |number?| |zeroDimPrime?| - |extendedint| |e02ajf| |integer| |c06ebf| |iitan| |getProperties| - |fracPart| |d01anf| |linears| |value| |polar| - |standardBasisOfCyclicSubmodule| |OMencodingUnknown| |coth2trigh| - |mainForm| |s20acf| |mappingMode| |insertMatch| |delete!| - |outputFixed| |removeDuplicates!| |extensionDegree| |qinterval| - |f02adf| |even?| |viewDeltaXDefault| |orbits| |orbit| |perfectNthRoot| - |queue| |cAcsch| 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|stoseInvertible?reg| |vark| |diff| |denomLODE| |encodingDirectory| - |separateFactors| |relerror| |cosIfCan| |maxdeg| |realEigenvalues| - |convert| |acotIfCan| |exponentialOrder| |invertible?| |bitCoef| - |e02dff| |divergence| |irVar| |expint| |tValues| |normalizedAssociate| - |legendre| |internalLastSubResultant| |drawComplexVectorField| |pquo| - |approximate| |mainContent| |whatInfinity| |divideIfCan| - |rightExactQuotient| |leftTrace| UP2UTS |readable?| |box| - |positiveRemainder| |writeBytes!| |complex| |stop| |diagonal| |sort!| - |primextintfrac| |unitsColorDefault| |reduced?| |singRicDE| RF2UTS - |plus!| |prepareSubResAlgo| |ellipticCylindrical| |interReduce| - |subCase?| |shufflein| |janko2| |fortranReal| |integers| |drawToScale| - |geometric| |e04dgf| |simplifyLog| |open?| |branchIfCan| |acscIfCan| - |f2st| |secIfCan| |numerators| |OMmakeConn| |failed| |difference| - |numberOfHues| |linearDependenceOverZ| |cCoth| |left| |empty?| - |setleaves!| |linearPolynomials| 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|conditions| |elaborateFile| |conjug| |showAll?| |write| - |UpTriBddDenomInv| |makeSUP| |nil| |infinite| |arbitraryExponent| + |Record| |Union| |f02aaf| |psolve| |difference| + |resultantEuclideannaif| |arg2| |alphabetic?| |s17dhf| |systemSizeIF| + |string| |qualifier| |balancedFactorisation| |insertRoot!| |stFuncN| + |curve?| |power| |swap| |shellSort| |recur| |say| |removeCosSq| + |generalizedEigenvectors| |factorOfDegree| |sts2stst| |BasicMethod| + |sechIfCan| |conditions| |tanh2coth| |ipow| |low| |commutative?| + |subscriptedVariables| |nextNormalPrimitivePoly| |c05nbf| |presub| + |pop!| |title| |match| |primlimintfrac| |s18acf| |bivariate?| |reset| + |f07adf| |ord| |internalDecompose| |writeLine!| |mix| |monomRDE| |sum| + |invertibleElseSplit?| |changeWeightLevel| |diagonal| |inc| + |zeroSquareMatrix| |groebnerIdeal| |trigs2explogs| + |degreeSubResultant| |symmetricTensors| |binary| |numberOfMonomials| + |companionBlocks| |write| |rewriteIdealWithQuasiMonicGenerators| + |clipPointsDefault| |gcdcofactprim| |getMatch| |moduloP| |roman| |e| + |lexTriangular| |setProperties| |save| |modularGcdPrimitive| |s17ajf| + |lp| |rightPower| |makeResult| |B1solve| |cyclicGroup| |unexpand| + |sign| |critBonD| |nothing| |rk4qc| |setVariableOrder| + |nextsousResultant2| |univariatePolynomials| |extractProperty| + |alphabetic| |splitSquarefree| |orbit| |createPrimitiveNormalPoly| + |leftRank| |extendedIntegrate| |numberOfHues| |divisorCascade| + |e04mbf| |noKaratsuba| |top| |polyRicDE| |symbol?| |f04faf| |mapDown!| + |d01ajf| |build| |factorPolynomial| |toseLastSubResultant| + |tanintegrate| |continue| |sinhcosh| |csch2sinh| |toseSquareFreePart| + |deleteRoutine!| |scalarMatrix| |updatF| |leastPower| |choosemon| + |maxIndex| |intChoose| |numerator| |unrankImproperPartitions0| + |d01gbf| |postfix| |expt| |diophantineSystem| |OMgetApp| |polygamma| + |RittWuCompare| ** |hash| |rename!| |null?| |generalizedInverse| + |stoseInvertibleSet| |viewDefaults| |totolex| |removeZero| |split!| + |sort!| |count| |createIrreduciblePoly| |testDim| |changeNameToObjf| + |environment| |palgextint| |cdr| |readInt16!| |child?| + |listConjugateBases| |ParCond| |stoseInvertibleSetsqfreg| |bumprow| + |sup| |head| |pushdterm| FG2F |tValues| |powerSum| |cyclotomic| + |constant| |c06fqf| |redpps| |pointSizeDefault| |positiveSolve| + |measure2Result| |imagi| |retractable?| |rootOf| |eulerPhi| + |strongGenerators| |laguerre| |mantissa| |iiabs| |elementary| + |coerceImages| |heap| |maxPoints| |makeop| |entry?| |adjoint| + |LazardQuotient2| |newLine| |mapSolve| |nary?| |oddintegers| + |stoseSquareFreePart| |overlabel| |insertMatch| |mainMonomial| + |clipSurface| |rotatex| |xn| |s18aef| |zeroSetSplit| |getCode| + |pointColorPalette| |f01mcf| |swapColumns!| |rarrow| |chiSquare1| + |getMultiplicationTable| |traceMatrix| |scale| |categoryFrame| + |semicolonSeparate| |setOrder| |basisOfRightAnnihilator| + |basisOfCenter| |directSum| |wholePart| |infinityNorm| |unknownEndian| + |omError| |orthonormalBasis| |iiasec| |integralRepresents| + |leftFactor| |cyclicParents| |edf2ef| |reduceByQuasiMonic| + |partialDenominators| |FormatRoman| |nullary| |outputAsTex| + |taylorRep| |initializeGroupForWordProblem| |mainVariable?| |unparse| + |dn| |rowEchLocal| |vspace| |components| |empty?| |lowerCase?| + |normalizedAssociate| |cycleElt| |computeCycleEntry| |nullary?| + |maxRowIndex| |pushucoef| |showScalarValues| |pquo| |iiacot| + |categories| |patternVariable| |stoseLastSubResultant| |newReduc| + |myDegree| |exponent| |numer| |sin?| |retractIfCan| |permutationGroup| + |repeating| |flexibleArray| |factorAndSplit| |expintegrate| + |iflist2Result| |nextPrimitiveNormalPoly| |algSplitSimple| |denom| + |binomial| |delete!| |partition| |digits| |zeroDimPrimary?| |leftMult| + |f04mbf| |zag| |llprop| |integrate| |inf| |mainExpression| + |inverseColeman| |f04adf| |mesh| |pdf2df| |nthRootIfCan| + |complexNormalize| |pi| |expintfldpoly| |supRittWu?| + |characteristicSet| |extractTop!| |subscript| |printingInfo?| + |goodPoint| |setEmpty!| |branchIfCan| |infinity| |partialFraction| + |physicalLength| |semiIndiceSubResultantEuclidean| |insertionSort!| + |concat| |step| |sparsityIF| |linearlyDependentOverZ?| |e02baf| + |e04fdf| |leftOne| |firstSubsetGray| |moebius| |extractPoint| + |solveLinear| |UnVectorise| |OMgetEndObject| |f01qcf| |acothIfCan| + |bombieriNorm| |integer?| |atanhIfCan| |child| |shiftRoots| + |thenBranch| |clearTheSymbolTable| |rootProduct| |complexRoots| + |kernel| |s19acf| |doubleFloatFormat| |alternating| + |monicRightFactorIfCan| |consnewpol| |formula| |eigenvalues| + |inputOutputBinaryFile| |closed?| |ffactor| |e04gcf| |list| |ptree| + |setPoly| |dictionary| |qPot| |mainContent| |lhs| |has?| |fullDisplay| + |recolor| |copy!| |draw| |subresultantVector| |f04asf| |clearCache| + |getOperands| |axesColorDefault| |rangeIsFinite| |rhs| |range| + |f01ref| |quadraticForm| |pseudoDivide| |readByte!| |upperCase| + |rootSimp| |surface| |f02axf| |primeFactor| |makeGraphImage| + |tubePlot| |meshFun2Var| |oddlambert| |singularAtInfinity?| + |ParCondList| |prepareDecompose| |lowerCase!| |currentEnv| |nrows| + |safetyMargin| |variationOfParameters| |rightUnits| |outputArgs| + |resultantReduit| |f02wef| |removeDuplicates| |indices| |f2df| |ncols| + |limit| |pseudoRemainder| |lyndon?| |seed| |makeObject| |acscIfCan| + |isList| |outputFixed| |members| |move| |pointLists| + |linearDependence| |setPosition| |rewriteIdealWithHeadRemainder| + |rotatez| |coef| |setColumn!| |mapExponents| |getRef| + |complexEigenvectors| |iiGamma| |traverse| |validExponential| |plot| + |linearAssociatedExp| |OMputAtp| |f02akf| |complexForm| |freeOf?| + |numFunEvals| |solveRetract| |iicoth| |besselJ| |exprex| |e02daf| + |reindex| |prindINFO| |saturate| |combineFeatureCompatibility| + |mapExpon| |numberOfIrreduciblePoly| |mapMatrixIfCan| |optpair| + |exportedOperators| |functionIsFracPolynomial?| + |leftCharacteristicPolynomial| |whatInfinity| |kind| |s13adf| + |getVariableOrder| |normInvertible?| |nullSpace| |stFunc1| |iiasin| + |bfEntry| |normalDenom| |dAndcExp| |op| |palglimint| |lquo| + |useNagFunctions| |revert| |getSyntaxFormsFromFile| |kernels| + |inverseLaplace| |UP2ifCan| |imagk| |makeTerm| |numericalOptimization| + |makeCrit| |certainlySubVariety?| |prinpolINFO| |characteristicSerie| + |leadingSupport| |s19abf| |operator| |evenlambert| |colorDef| |froot| + |goodnessOfFit| |element?| |jokerMode| |appendPoint| |hasoln| + |wordInStrongGenerators| SEGMENT |leftLcm| |expenseOfEvaluationIF| + |setValue!| |OMputSymbol| |OMUnknownSymbol?| |hasTopPredicate?| + |addiag| |generalSqFr| |f2st| |sort| |linearPart| |getOrder| + |removeDuplicates!| |univariate| |internalSubPolSet?| |normFactors| + |typeList| |derivative| |OMunhandledSymbol| |inverse| |dec| + |LyndonWordsList1| |leftExactQuotient| |yCoord| |mathieu24| + |showRegion| |outlineRender| |pointColor| |complement| + |makeFloatFunction| |positive?| |mkAnswer| |lazyIrreducibleFactors| + |crushedSet| |union| |overset?| |back| |factorGroebnerBasis| |f02xef| + |clearDenominator| |nativeModuleExtension| |factor| |deref| + |subTriSet?| |showTheFTable| |setLength!| |compound?| |iomode| + |OMputEndAttr| |OMgetInteger| |random| |convergents| |variable?| + |eof?| |sqrt| |collectQuasiMonic| |schwerpunkt| |weight| |isTimes| + |monicCompleteDecompose| |comp| |buildSyntax| |numberOfOperations| + |e02bcf| |real| |iterationVar| |divideIfCan| |var1Steps| + |tubePointsDefault| |asinIfCan| |radicalRoots| |SturmHabicht| |c06eaf| + |s17ahf| |imag| |rdHack1| |simpson| |super| |properties| |e02bef| + |setStatus| |factorials| |quasiRegular?| |OMwrite| |copy| + |directProduct| |fortranLinkerArgs| |mainSquareFreePart| + |extractSplittingLeaf| |d02bbf| |rootDirectory| |largest| |translate| + |euclideanSize| |linkToFortran| |direction| |ScanFloatIgnoreSpaces| + |iipow| |dflist| |transpose| |genericPosition| |OMgetEndBind| |depth| + |cylindrical| |d03edf| |secIfCan| |noLinearFactor?| |rootRadius| + |zeroDim?| |brace| |scanOneDimSubspaces| |mapUnivariate| |s18aff| + |reverseLex| |pair?| |select!| |inverseIntegralMatrixAtInfinity| + |lifting| |destruct| |OMclose| |simplify| |setPrologue!| + |initiallyReduce| |parabolic| |Is| |tan2trig| |processTemplate| + |multiplyCoefficients| |extensionDegree| |insertBottom!| |match?| + |anticoord| |symmetricProduct| |iisin| |acosIfCan| |autoCoerce| + |conditionP| |nextPrime| |create| |OMputFloat| |arguments| + |totalDifferential| |tanNa| |powmod| |OMReadError?| |iiatan| + |radicalEigenvector| |palgextint0| |computeBasis| + |generalInfiniteProduct| |getMultiplicationMatrix| |tanIfCan| + |implies| |expand| |createNormalPoly| |e02adf| |monomial| + |interpretString| |singular?| |rightFactorIfCan| |safeCeiling| + |headReduce| |baseRDEsys| |filterWhile| |iicos| |fillPascalTriangle| + |multivariate| |rightExactQuotient| |close| |decimal| + |createZechTable| F |root?| |dot| |filterUntil| |twoFactor| |iiasinh| + |genericRightDiscriminant| |variables| |specialTrigs| + |fortranDoubleComplex| |fixedPointExquo| |OMreadStr| |select| + |internalIntegrate| |cTanh| |mergeFactors| |display| |applyRules| + |rewriteSetWithReduction| |setRow!| |vertConcat| |fortranLiteral| + |d01apf| |LiePolyIfCan| |d03faf| |virtualDegree| |bumptab1| |rotatey| + |po| |factors| |minus!| |listRepresentation| |palgint0| + |palgintegrate| |rCoord| |tablePow| |perfectNthPower?| |totalfract| + |nthExpon| |predicate| |quartic| |tanAn| |palgRDE| |isImplies| + |unravel| |ldf2lst| |qqq| |debug| |taylor| |lineColorDefault| |reseed| + |position!| |s01eaf| |showTheRoutinesTable| |exactQuotient| |cn| + |setAdaptive| |copyInto!| |standardBasisOfCyclicSubmodule| D |laurent| + |input| |mappingAst| |simplifyPower| |addMatch| |prefixRagits| + |optional?| |expandTrigProducts| |ceiling| |iisinh| |roughSubIdeal?| + |puiseux| |library| |d02bhf| |rightAlternative?| + |stripCommentsAndBlanks| |endOfFile?| EQ |partialQuotients| + |mapUnivariateIfCan| |dimensionOfIrreducibleRepresentation| + |leftTrace| |car| |exponentialOrder| |removeRedundantFactorsInPols| + |bandedJacobian| |viewport3D| |max| |selectPDERoutines| |rotate| |inv| + |upperBound| |OMsupportsSymbol?| |bothWays| |derivationCoordinates| + |pr2dmp| |unrankImproperPartitions1| |fractionPart| |rationalPoints| + |f07fdf| |ground?| |discreteLog| |e02ahf| |antisymmetric?| + |integralBasis| |associatorDependence| |leftTraceMatrix| |rootsOf| + |compBound| |setelt!| |ground| |set| |radicalSimplify| |lyndon| + |f07fef| |mapdiv| |extractIfCan| |bipolarCylindrical| + |showArrayValues| |countRealRootsMultiple| |OMputEndObject| + |leadingMonomial| |paraboloidal| |nlde| |cycleLength| |graeffe| + |wronskianMatrix| |coerceL| |algebraicCoefficients?| |univariateSolve| + |refine| |leadingCoefficient| |parameters| |pile| |comparison| |Beta| + |inR?| |cross| |size| |problemPoints| |groebnerFactorize| |cyclicCopy| + |transcendentalDecompose| |primitiveMonomials| |setfirst!| + |numberOfNormalPoly| |semiResultantEuclidean2| |setFieldInfo| + |roughEqualIdeals?| |decrease| |irreducibleFactor| |cRationalPower| + |OMencodingUnknown| |print| |reductum| |rightNorm| |floor| |universe| + |substring?| |lSpaceBasis| |groebgen| |fortranReal| |list?| |compdegd| + |denominator| |resolve| |seriesToOutputForm| |interval| + |setAdaptive3D| |invertible?| |f02bjf| |createGenericMatrix| + |trivialIdeal?| |semiDegreeSubResultantEuclidean| |padicFraction| + |chiSquare| |groebSolve| |e04naf| |irreducibleRepresentation| + |suffix?| |newSubProgram| |infiniteProduct| |true| |setImagSteps| + |showFortranOutputStack| |eq?| |category| |printStats!| + |basisOfLeftNucloid| |mapmult| |rightGcd| |OMgetType| |domain| + |fortranTypeOf| |magnitude| |clikeUniv| |critT| |setDifference| + |accuracyIF| |optional| |maxrow| |f01qef| |OMserve| |df2ef| + |setClipValue| |numberOfDivisors| |e01sef| |prefix?| + |absolutelyIrreducible?| |zero?| |package| |innerEigenvectors| + |recoverAfterFail| |alphanumeric?| |df2mf| |extendedResultant| + |insert| |subResultantsChain| |s17def| |SturmHabichtMultiple| + |unitNormalize| |OMgetObject| |sumOfKthPowerDivisors| |changeMeasure| + |putProperty| |collect| |listBranches| |show| |increasePrecision| + |integralLastSubResultant| |clearTable!| |LiePoly| |curryLeft| + |d01bbf| |symFunc| |nextColeman| |hitherPlane| |rightOne| |search| + |logical?| |bitCoef| |graphs| |leadingIndex| |getPickedPoints| |lllp| + |node| |f01rcf| |binaryTree| |typeLists| |sin2csc| |trace| |e01sbf| + |createLowComplexityNormalBasis| |eisensteinIrreducible?| |lagrange| + |modifyPointData| |viewPhiDefault| |hMonic| |stirling1| + |approxNthRoot| |points| |branchPoint?| |rroot| |mightHaveRoots| + |charpol| |jacobian| |integers| |extractIndex| |d02gaf| |returnType!| + |multiEuclideanTree| |createNormalElement| |principal?| |ODESolve| + |infix?| |minset| |mindegTerm| |probablyZeroDim?| |balancedBinaryTree| + |rk4f| |closedCurve?| |critMTonD1| |leftMinimalPolynomial| |mask| + |f07aef| |internalAugment| |separateDegrees| |empty| + |OMencodingBinary| |minimize| |primitiveElement| |coth2trigh| + |nextIrreduciblePoly| |flatten| |taylorQuoByVar| |kroneckerDelta| + |d01akf| |fortranInteger| |symmetricDifference| |getGoodPrime| + |gensym| |sub| |ReduceOrder| |nextNormalPoly| |redPo| + |reducedContinuedFraction| |makeVariable| |notelem| |setMaxPoints| + |sequences| |rquo| |multiEuclidean| |subSet| |s15aef| |isQuotient| + |removeSuperfluousCases| |trapezoidal| |polyRDE| |nsqfree| |baseRDE| + |airyBi| |rubiksGroup| |degreeSubResultantEuclidean| |laurentRep| + |s18dcf| |contractSolve| |e02dff| |cotIfCan| |optAttributes| + |messagePrint| |createRandomElement| |point?| |startPolynomial| + |quadratic?| |resultantnaif| |separant| |round| |upDateBranches| + |more?| |monomial?| |e04jaf| |check| |cSinh| |coefChoose| |doubleRank| + |curve| |exprToXXP| |parametric?| |zeroDimensional?| |sturmSequence| + |directory| |htrigs| |createLowComplexityTable| |musserTrials| + |decompose| |removeRoughlyRedundantFactorsInContents| |size?| + |setCondition!| |toScale| |rationalIfCan| + |factorSquareFreeByRecursion| |shiftLeft| |drawToScale| |cAcot| + |frobenius| |OMgetVariable| |subQuasiComponent?| |height| |units| + |makeSketch| |log10| |s17adf| |leadingTerm| |explimitedint| |mapGen| + |slex| |merge| |equation| |monomRDEsys| |rootBound| |basis| |hexDigit| + |headAst| |bitand| |rst| |FormatArabic| |idealiser| |subNode?| + |csc2sin| |youngDiagram| |fortranLiteralLine| |cothIfCan| |fprindINFO| + |leaves| |skewSFunction| |outerProduct| |bitior| + |solveLinearPolynomialEquationByRecursion| |finite?| + |quasiAlgebraicSet| |fixedPoint| |linear| |transcendent?| + |particularSolution| |logIfCan| |interpolate| |iifact| + |useEisensteinCriterion| |disjunction| |csubst| |flexible?| |augment| + |att2Result| |c06ekf| |mainForm| |viewpoint| |macroExpand| + |irreducibleFactors| |mulmod| |green| |untab| |collectUnder| + |listYoungTableaus| |polynomial| |mainCoefficients| |hyperelliptic| + |dmpToP| |rotate!| |curveColor| |comment| |f01bsf| |divergence| + |rischDEsys| |coercePreimagesImages| |aQuadratic| |curryRight| + |center| |close!| |unprotectedRemoveRedundantFactors| |ode1| |hconcat| + |purelyAlgebraic?| |createPrimitivePoly| |controlPanel| |binding| + |lastSubResultantEuclidean| |minIndex| |iisqrt2| |squareTop| + |rightLcm| |cap| |extractBottom!| |figureUnits| + |conditionsForIdempotents| |numericIfCan| |merge!| |rule| |ridHack1| + |declare| |normalizedDivide| |s13acf| |rationalFunction| |coord| + |common| |slash| |OMsetEncoding| |regime| |s17akf| |primitivePart!| + |geometric| |pseudoQuotient| |evaluate| |powern| |listLoops| + |setright!| |blankSeparate| |decreasePrecision| |length| |OMgetBind| + |mirror| |lowerPolynomial| |escape| |scripted?| |sinh2csch| |legendre| + |lookup| |primintfldpoly| |scripts| |fixPredicate| |innerint| |solve| + |pascalTriangle| |socf2socdf| |nthRoot| |leftScalarTimes!| |s17dgf| + |iiacsc| |e02dcf| |laplacian| |algebraic?| |character?| |symmetric?| + |makeEq| |any?| |cycles| |replace| |characteristic| |matrix| + |selectsecond| |nextSubsetGray| |OMgetEndError| |monicModulo| + |iiacoth| |nilFactor| |zeroMatrix| |lazyIntegrate| |primeFrobenius| + |s20acf| |stoseInvertible?sqfreg| |ScanFloatIgnoreSpacesIfCan| + |iisqrt3| |primPartElseUnitCanonical!| |intersect| |sample| |mesh?| + |conjugate| |resetBadValues| |laurentIfCan| |setAttributeButtonStep| + |front| |irVar| |viewDeltaYDefault| |homogeneous?| |var2Steps| + |complexEigenvalues| Y |selectIntegrationRoutines| |cAtan| |se2rfi| + |bracket| |solid| |sdf2lst| |exprHasAlgebraicWeight| |complexSolve| + |label| |usingTable?| |fullPartialFraction| |checkForZero| |remainder| + |getGraph| |categoryMode| |neglist| |randomR| |PollardSmallFactor| + |intPatternMatch| |rk4| |Lazard2| |quickSort| |ricDsolve| |setlast!| + |cCot| |scan| |putProperties| |dmp2rfi| |e04dgf| |currentScope| + |partitions| |viewWriteAvailable| |cycleTail| |binaryFunction| + |setref| |result| |subtractIfCan| |lieAlgebra?| |bfKeys| |distribute| + |mainKernel| |in?| |expextendedint| |nonLinearPart| |elements| |block| + |call| |delay| |noValueMode| |zeroSetSplitIntoTriangularSystems| + |internalLastSubResultant| |isobaric?| |trueEqual| |prologue| + |pmintegrate| |numeric| |getProperty| |perspective| |d02gbf| + |updateStatus!| |extension| |radical| |s21baf| |expint| |cSin| + |showAllElements| |s17aef| |oddInfiniteProduct| |ef2edf| + |leftRegularRepresentation| |constructor| |times!| |matrixConcat3D| + |pointData| |setsubMatrix!| |OMgetString| |euclideanGroebner| |zoom| + |OMopenString| |internal?| |pole?| |bindings| |option| + |sortConstraints| |prem| |permutationRepresentation| |unary?| + |symbolTable| |showSummary| |cAsin| |tab1| |square?| |palglimint0| + |compactFraction| |prinshINFO| |subPolSet?| |overbar| |totalDegree| + |elliptic?| |mappingMode| |totalGroebner| |clipBoolean| |denomLODE| + |addPointLast| |henselFact| |internalInfRittWu?| + |pushFortranOutputStack| |integerIfCan| |showAttributes| |divide| + |tensorProduct| |autoReduced?| |duplicates?| |setTopPredicate| + |stiffnessAndStabilityFactor| |makeRecord| |selectAndPolynomials| + |simplifyLog| |popFortranOutputStack| |selectODEIVPRoutines| + |OMsupportsCD?| |biRank| |tanSum| |generic?| |extractClosed| |cAsinh| + |errorInfo| |outputAsFortran| |mainDefiningPolynomial| + |argumentListOf| |expPot| |linearAssociatedLog| |lepol| |name| + |parents| |ratDsolve| |charthRoot| |sinhIfCan| |lazyPquo| |imports| + |over| |uniform| |rightTrim| |reduction| |tanhIfCan| |body| + |selectOptimizationRoutines| |shape| |iteratedInitials| |HenselLift| + |hypergeometric0F1| |setnext!| |drawComplexVectorField| |leftTrim| + |cTan| |makeSUP| |null| |octon| |exp1| |readUInt16!| |isNot| + |hasSolution?| |stack| |solveInField| |isPlus| |setProperty| |c02agf| + |not| |monicDivide| |removeSinSq| |edf2df| |graphCurves| |maxint| BY + |intcompBasis| |e01bhf| |increase| |c06gcf| |and| |dimension| |frst| + |getProperties| |s20adf| |outputList| |wholeRadix| |zCoord| + |numberOfComponents| |redPol| |Vectorise| |principalAncestors| |or| + |rowEch| |structuralConstants| |cubic| |encodingDirectory| |writable?| + |lexico| |rur| |digit| |xor| |OMgetAtp| |leadingExponent| |makeUnit| + |antiAssociative?| |mainMonomials| |iidprod| |alternative?| + |quotientByP| |external?| |signature| |dim| |case| |open?| + |basisOfNucleus| |curry| |unitVector| |assert| |cardinality| + |semiSubResultantGcdEuclidean1| |port| |weighted| |upperCase!| + |d02ejf| |prime?| |pattern| |Zero| |create3Space| |computeCycleLength| + |repeating?| |ode2| |uncouplingMatrices| |factorial| |component| + |nonQsign| |trailingCoefficient| |listexp| |One| |printCode| + |primextendedint| |acschIfCan| |deepExpand| |internalIntegrate0| + |sncndn| |t| |parametersOf| |factorSquareFree| |exQuo| |setClosed| + |shift| |OMreadFile| NOT |basisOfLeftAnnihilator| |permutations| + |printStatement| |indicialEquation| |addmod| |output| |bytes| |paren| + |userOrdered?| |integerBound| |leftAlternative?| |smith| |reducedForm| + OR |leader| |vector| |genericLeftTrace| |lazyEvaluate| + |constantKernel| |e01bff| |intermediateResultsIF| + |removeRedundantFactors| |roughBasicSet| |rischDE| |message| + |prepareSubResAlgo| AND |initials| |differentiate| |leadingIdeal| + |children| |bezoutMatrix| |OMputApp| |rightRecip| |algDsolve| + |realElementary| |imagK| |solveid| |enterInCache| |capacity| |c06fpf| + |mdeg| |trigs| |wordInGenerators| |fortran| |atanh| |separateFactors| + |norm| |exactQuotient!| |tube| |OMputEndBind| |OMgetAttr| |elt| + |polygon| |basisOfCentroid| |approximants| |e01bgf| |OMcloseConn| + |acoth| |powerAssociative?| |overlap| |errorKind| |pastel| + |putColorInfo| |alternatingGroup| |chebyshevU| |localReal?| |fracPart| + |monomialIntegrate| |readLineIfCan!| |asech| |level| |conjunction| + |stopTable!| |tanQ| |mvar| |complex?| |radix| |padicallyExpand| + |belong?| |twist| |imagE| |supDimElseRittWu?| |genericRightNorm| + |e01sff| |bottom!| |setScreenResolution3D| |reciprocalPolynomial| + |conjugates| |bipolar| |coerceP| |split| |toseInvertibleSet| + |decomposeFunc| |multiple| |cons| |varselect| |atoms| |exponential1| + |selectSumOfSquaresRoutines| |equality| |pol| |weierstrass| + |raisePolynomial| |numberOfComposites| |discriminantEuclidean| |lex| + |applyQuote| |tubePoints| |patternMatch| |shallowCopy| |cond| + |diagonalProduct| |parseString| |quatern| |retract| |sumOfDivisors| + |exists?| |cAsech| |elRow2!| |taylorIfCan| |multinomial| |triangSolve| + |pack!| |rdregime| |numerators| |nextPartition| F2FG |isMult| + |compiledFunction| |yellow| |leftDivide| |ellipticCylindrical| |mat| + |relerror| |multisect| |prime| |crest| |scaleRoots| |second| * + |minrank| |idealiserMatrix| |laguerreL| |functorData| |concat!| + |ruleset| |rootPower| |bag| |mkcomm| |gcdprim| |returns| |asechIfCan| + |cAcoth| |third| |someBasis| |mergeDifference| |endSubProgram| + |lifting1| |arity| |stopMusserTrials| |compose| |interactiveEnv| + |updatD| |e01daf| |reduceLODE| |d02cjf| |index?| |failed?| |f01brf| + |f04axf| |source| |void| |unit?| |cAsec| |sizeLess?| |primintegrate| + |genus| |heapSort| |clearTheFTable| = |sorted?| |numberOfFactors| + |ramified?| |Ei| |suchThat| |swapRows!| |assign| |dualSignature| + |OMconnInDevice| |OMputAttr| |real?| |df2st| |fractRadix| + |exprToGenUPS| |var2StepsDefault| |maxrank| |script| |mapUp!| + |patternMatchTimes| |light| |polygon?| |push!| |divideExponents| + |polarCoordinates| < |d01anf| |f02awf| |badNum| |coordinates| + |plusInfinity| |fi2df| |factor1| |createNormalPrimitivePoly| |prinb| + |before?| |quasiComponent| |char| |normal?| > |littleEndian| |aCubic| + |outputAsScript| |algebraicDecompose| |systemCommand| |minusInfinity| + |multiplyExponents| |stFunc2| |infix| |imagI| |attributeData| + |generalTwoFactor| |Aleph| |multiset| <= |rightRankPolynomial| + |normal01| |complementaryBasis| |tex| |target| |differentialVariables| + |cosIfCan| |toroidal| |unit| |OMmakeConn| |OMgetEndAttr| |cup| >= + |pureLex| |digamma| |groebner| |linGenPos| |reify| |leftNorm| |order| + |nodes| |sec2cos| |primes| |interReduce| |expr| |principalIdeal| + |iicosh| |corrPoly| |reducedQPowers| |outputSpacing| |setleaves!| + |cCsch| |satisfy?| |quasiRegular| |phiCoord| |normal| + |brillhartIrreducible?| |triangulate| |s18adf| + |radicalOfLeftTraceForm| |hermiteH| |laplace| |resultant| |iiacos| + |sqfree| |ddFact| |numberOfImproperPartitions| |subResultantChain| + |stoseInternalLastSubResultant| + |makeViewport3D| |lfintegrate| + |OMgetBVar| |row| |changeThreshhold| |type| |identitySquareMatrix| + |cot2trig| |purelyTranscendental?| |stopTableGcd!| |getStream| + |OMputVariable| |complexIntegrate| |point| - |float| |d01amf| + |replaceKthElement| |addBadValue| |initiallyReduced?| |prevPrime| + |changeBase| |oneDimensionalArray| |gradient| |f02ajf| |variable| + |binomThmExpt| / |hcrf| |d01alf| |outputGeneral| + |univariatePolynomialsGcds| |representationType| |d02kef| + |fortranComplex| |determinant| |OMgetError| |iterators| |gethi| + |getZechTable| |s14aaf| |complexNumericIfCan| |stronglyReduced?| + |weights| |hue| |product| |rangePascalTriangle| |linearPolynomials| + |doubleResultant| |startTable!| |series| |outputMeasure| |linears| + |vedf2vef| |OMconnectTCP| |changeVar| |maxdeg| |PDESolve| + |toseInvertible?| |inspect| |univariate?| |highCommonTerms| + |eigenMatrix| |cAtanh| |definingInequation| |irForm| + |selectPolynomials| |leviCivitaSymbol| |invmod| |id| |c06gbf| + |normalizeIfCan| |squareMatrix| |idealSimplify| |atom?| |value| + |cosh2sech| |branchPointAtInfinity?| |makeSin| |f04qaf| |symbol| + |externalList| |lo| |subCase?| |cycleSplit!| |associatedSystem| + |checkRur| |numberOfComputedEntries| |powers| |primlimitedint| + |f02aff| |OMgetEndBVar| |expression| |separate| |sylvesterMatrix| + |ignore?| |min| |binaryTournament| |debug3D| |finiteBound| + |commonDenominator| |parabolicCylindrical| |denomRicDE| |minPoints3D| + |integer| |ode| |gcdcofact| |column| |indicialEquationAtInfinity| GE + |drawComplex| |nthFractionalTerm| |qfactor| |lazy?| + |rightRegularRepresentation| |minRowIndex| |OMputInteger| + |stoseIntegralLastSubResultant| |realRoots| |minGbasis| |iprint| GT + |e02gaf| |integral| |cAcosh| |dimensions| |f04jgf| |indicialEquations| + |changeName| |constantIfCan| |OMencodingSGML| |selectOrPolynomials| LE + |f02fjf| |routines| |completeHensel| |symmetricSquare| |OMputBind| + |factorSquareFreePolynomial| |squareFreePolynomial| + |primPartElseUnitCanonical| |nextSublist| |equiv| LT + |exteriorDifferential| |stoseInvertibleSetreg| |makeYoungTableau| + |birth| |basisOfMiddleNucleus| |realEigenvalues| |rationalPoint?| + |c06gqf| |createMultiplicationTable| |extract!| |resetNew| |polar| + |remove!| |sumSquares| |hasHi| |nthCoef| |approxSqrt| |c02aff| + |inconsistent?| |normalize| |moebiusMu| |definingPolynomial| + |isAbsolutelyIrreducible?| |putGraph| |key?| |measure| |iiperm| + |listOfMonoms| |realSolve| |jordanAlgebra?| |keys| |content| |s14abf| + |spherical| |module| |critM| |squareFreeLexTriangular| |reflect| + |relativeApprox| |useSingleFactorBound?| |leftRecip| |shufflein| + |pomopo!| |headRemainder| |color| |trim| |option?| + |commutativeEquality| |oblateSpheroidal| |palginfieldint| + |genericLeftMinimalPolynomial| |index| |genericLeftTraceForm| + |lexGroebner| |expIfCan| |numberOfChildren| |extendIfCan| |f02aef| + |shade| |shanksDiscLogAlgorithm| |showTheSymbolTable| |s17acf| |iicsc| + |identity| |rightFactorCandidate| |OMputBVar| |monic?| |acotIfCan| + |findBinding| |adaptive?| |boundOfCauchy| |wordsForStrongGenerators| + |clipParametric| |complexExpand| |c05adf| |f01maf| |removeCoshSq| + |zerosOf| |exponential| |pair| |numberOfVariables| |setMaxPoints3D| + |tree| |open| |LagrangeInterpolation| |lowerCase| |ip4Address| + |pushNewContour| |getConstant| |s17dlf| |bright| |e02bdf| |odd?| + |bivariateSLPEBR| |closed| |gramschmidt| |stoseInvertible?| + |setButtonValue| |property| |inRadical?| |setOfMinN| |double?| + |mapBivariate| |s19adf| |var1StepsDefault| |cyclotomicDecomposition| + |mathieu11| |genericRightTraceForm| |contains?| |rightMult| + |isConnected?| |eval| |fortranDouble| |unmakeSUP| |infLex?| + |monicRightDivide| |hdmpToP| |viewWriteDefault| |pleskenSplit| + |completeEchelonBasis| |explicitEntries?| |f04atf| |splitNodeOf!| + |operations| |OMgetEndApp| |isAtom| |lowerBound| |cCos| |intensity| + |elRow1!| |lazyPremWithDefault| |factorByRecursion| |float?| |janko2| + |setchildren!| |monomialIntPoly| |drawStyle| |inputBinaryFile| + |interpret| |OMlistCDs| |error| |factorsOfCyclicGroupSize| + |bubbleSort!| |coordinate| |deepestTail| |constant?| |composite| + |number?| |meatAxe| |numberOfPrimitivePoly| |associative?| |palgRDE0| + |thetaCoord| |nthFactor| |iicot| |ratPoly| |removeConstantTerm| |kmax| + |atanIfCan| |optimize| |reopen!| |minordet| |inHallBasis?| |every?| + |precision| |complete| |function| |OMputEndBVar| |OMgetSymbol| + |removeRedundantFactorsInContents| |chvar| |bringDown| |ranges| + |wholeRagits| |rootPoly| |f02agf| |LazardQuotient| |OMsend| + |critpOrder| |dmpToHdmp| |top!| |lprop| |sizePascalTriangle| + |composites| |pdf2ef| |LyndonWordsList| |width| |symbolTableOf| + |fixedDivisor| |represents| |middle| |exprToUPS| |ratpart| + |numFunEvals3D| |leastMonomial| |rules| |double| |meshPar2Var| + |selectFiniteRoutines| |lookupFunction| |aQuartic| + |leadingCoefficientRicDE| |mainValue| |expandPower| |squareFree| + |iiatanh| |pushup| |meshPar1Var| |sinIfCan| |resetAttributeButtons| + |basicSet| |completeEval| |algintegrate| |df2fi| |lazyVariations| + |iibinom| |e01bef| |semiResultantReduitEuclidean| |ratDenom| + |subMatrix| |s14baf| |selectMultiDimensionalRoutines| |removeSinhSq| + |finiteBasis| |dual| |perfectNthRoot| |fglmIfCan| |youngGroup| + |constantRight| |createThreeSpace| |setleft!| |s17dcf| + |checkPrecision| |mr| |quotient| |OMbindTCP| |const| |redmat| + |iFTable| |ocf2ocdf| |splitLinear| |setScreenResolution| + |semiSubResultantGcdEuclidean2| |inGroundField?| |cAcsc| |quasiMonic?| + |deleteProperty!| |connectTo| |generalizedContinuumHypothesisAssumed?| + |SFunction| |bezoutDiscriminant| |mainCharacterization| |complexZeros| + |LyndonBasis| |subst| |rem| |vconcat| |rewriteIdealWithRemainder| + |doubleDisc| |node?| |outputBinaryFile| |hclf| |constantOpIfCan| + |zeroDimPrime?| |componentUpperBound| |lllip| |outputFloating| |quo| + |quotedOperators| |latex| |s18def| |withPredicates| |declare!| + |varList| |factorsOfDegree| |generalizedEigenvector| + |nextLatticePermutation| |iiexp| |sequence| |generic| |s15adf| + |symbolIfCan| |besselI| |primextintfrac| |lcm| |irDef| |swap!| + |triangularSystems| |setTex!| |readIfCan!| |delete| |div| + |constDsolve| |subspace| |OMParseError?| |firstDenom| |enterPointData| + |write!| |quoted?| |discriminant| |cyclic| |dequeue| |exquo| + |superscript| |dominantTerm| |setvalue!| |shiftRight| |simpsono| |any| + |arrayStack| |fintegrate| |increment| |append| |backOldPos| + |gcdPolynomial| ~= |linearAssociatedOrder| |tan2cot| |limitedint| + |aromberg| |tRange| |preprocess| |euclideanNormalForm| |d03eef| + |halfExtendedResultant1| |gcd| |goto| |plotPolar| |objects| |#| + |infieldIntegrate| |bsolve| |whileLoop| |setUnion| |yCoordinates| + |eigenvector| |generateIrredPoly| |lazyGintegrate| |eulerE| |false| + |computePowers| |normalise| |base| ~ |euler| |extendedSubResultantGcd| + |zeroVector| |randomLC| |genericRightMinimalPolynomial| |algebraicOf| + |signAround| |numberOfCycles| |central?| |continuedFraction| |ravel| + |leftDiscriminant| |setEpilogue!| |normalizeAtInfinity| |cCosh| + |dfRange| |segment| |part?| |symmetricPower| |d01gaf| + |exprHasLogarithmicWeights| |addPoint| |init| |rightRank| |terms| + |adaptive3D?| |queue| |reshape| |roughBase?| |logGamma| |extendedint| + |high| |divideIfCan!| |e04ucf| |/\\| |find| |elaborateFile| + |unitNormal| |subResultantGcdEuclidean| |lastSubResultantElseSplit| + GF2FG |elaborate| |cyclicSubmodule| |nand| |mindeg| |\\/| |Si| + |leftExtendedGcd| |bitTruth| |less?| |unitsColorDefault| |apply| + |coerce| |minimalPolynomial| |readInt8!| |besselY| |c06ecf| + |atrapezoidal| |sizeMultiplication| UTS2UP |setIntersection| + |argscript| |c06gsf| |first| |construct| |presuper| |physicalLength!| + |region| |doublyTransitive?| |xCoord| |showTheIFTable| + |purelyAlgebraicLeadingMonomial?| |limitedIntegrate| |reverse!| + |symmetricGroup| |rest| |repSq| |removeRoughlyRedundantFactorsInPols| + |airyAi| |generalPosition| |logpart| |plus| |stoseInvertible?reg| + |Gamma| |OMconnOutDevice| |OMopenFile| |qroot| |update| + |rootNormalize| |insertTop!| |shallowExpand| |ptFunc| |enqueue!| + |jordanAdmissible?| |symmetricRemainder| |GospersMethod| + |sylvesterSequence| |numberOfFractionalTerms| |realEigenvectors| + |linearMatrix| |screenResolution3D| |midpoints| |coefficients| + |divisors| |asecIfCan| |cAcsch| |hdmpToDmp| |semiResultantEuclidean1| + |rational| |karatsubaDivide| |squareFreePart| |bitLength| |resize| + |nor| |just| |divisor| |extend| |localIntegralBasis| |times| + |viewport2D| |rightQuotient| |completeHermite| |lfunc| |pToHdmp| + |previous| |delta| |lazyPseudoQuotient| |closeComponent| + |cyclePartition| |halfExtendedSubResultantGcd2| |OMputEndAtp| + |typeForm| |startStats!| |characteristicPolynomial| |rational?| + |iiasech| |makingStats?| |conjug| |quoByVar| |box| |reorder| + |stopTableInvSet!| |position| |infRittWu?| |basisOfRightNucleus| + |palgLODE| |pointColorDefault| |argument| |e02ddf| |fibonacci| + |e01baf| |setPredicates| |stosePrepareSubResAlgo| |reduced?| + |datalist| |lift| |ListOfTerms| |isOr| |getlo| |e02ajf| + |integralAtInfinity?| |f01qdf| |makeMulti| |c05pbf| + |expenseOfEvaluation| |sqfrFactor| |bat| |monom| |reduce| |dark| + |indiceSubResultantEuclidean| |digit?| |writeByte!| |localUnquote| + |totalLex| |f02bbf| |coHeight| |perfectSqrt| |Lazard| |weakBiRank| + |loadNativeModule| |stirling2| |subResultantGcd| + |inverseIntegralMatrix| |factorset| |iCompose| |mpsode| + |tryFunctionalDecomposition?| |vark| |antiCommutator| |rightDivide| + |root| |polCase| |lazyPseudoRemainder| |cscIfCan| |gbasis| |cSec| + |upperCase?| |primitive?| |badValues| |imaginary| |makeFR| + |genericLeftDiscriminant| |vectorise| |irreducible?| + |showIntensityFunctions| |associatedEquations| |maximumExponent| + |diag| |opeval| |lambda| |wrregime| |bernoulli| |seriesSolve| |c06fuf| + |ldf2vmf| |rank| |stiffnessAndStabilityOfODEIF| |pdct| |lambert| + |rightScalarTimes!| |truncate| |e04ycf| |f04maf| |npcoef| |isOpen?| + |addPoint2| |log| |mainVariable| |parent| |removeZeroes| + |partialNumerators| |expandLog| |iiacsch| |s17agf| |fortranLogical| + |OMUnknownCD?| |mkIntegral| |setelt| |leftRankPolynomial| + |basisOfRightNucloid| |defineProperty| |innerSolve1| |shuffle| + |e02def| |showAll?| |lflimitedint| |coleman| |karatsuba| |byteBuffer| + |OMputString| |whitePoint| |subHeight| |cartesian| + |radicalEigenvalues| |ran| |s17aff| |is?| |removeSquaresIfCan| + |singRicDE| |predicates| |c06ebf| |nodeOf?| |kovacic| |degree| + |halfExtendedResultant2| |quasiMonicPolynomials| |isExpt| |readLine!| + |blue| |pushuconst| |isOp| |monomials| |reduceBasisAtInfinity| |prod| + |iExquo| |argumentList!| |iiacosh| |leftGcd| |submod| + |semiResultantEuclideannaif| |aLinear| |lfextlimint| + |rectangularMatrix| |integral?| |coerceS| |diff| |getDatabase| + |printHeader| |cyclic?| |screenResolution| |byte| |lists| |f01rdf| + |lazyPseudoDivide| |internalZeroSetSplit| |cyclicEqual?| + |constantLeft| |epilogue| |rightUnit| |nextItem| + |cyclotomicFactorization| |evaluateInverse| |nextPrimitivePoly| + |selectfirst| |adaptive| |limitPlus| |e02aef| |viewPosDefault| |erf| + |jacobiIdentity?| |Ci| |fixedPoints| |bounds| |zero| |d01asf| + |getBadValues| |domainTemplate| |reverse| |inrootof| |normalized?| + |graphImage| |red| |permutation| |currentSubProgram| |imagj| + |enumerate| |one?| |writeUInt8!| |fortranCharacter| |elColumn2!| |li| + |pow| LODO2FUN |viewZoomDefault| |nthExponent| |OMputError| + |monicDecomposeIfCan| |shrinkable| |And| |s21bcf| |constantOperator| + |OMputObject| |pointPlot| |read!| |unknown| |dilog| + |fractionFreeGauss!| |deriv| |UpTriBddDenomInv| |sincos| |Or| + |moreAlgebraic?| |ScanRoman| |linearDependenceOverZ| + |solveLinearPolynomialEquationByFractions| |complexElementary| + |minPol| |lyndonIfCan| |sin| |ramifiedAtInfinity?| |relationsIdeal| + |BumInSepFFE| |modulus| |Not| RF2UTS + |removeSuperfluousQuasiComponents| |iitan| |power!| + |radicalEigenvectors| |gderiv| |cos| + |generalizedContinuumHypothesisAssumed| |tableau| |flagFactor| + |nextsubResultant2| |packageCall| |int| |makeViewport2D| + |removeIrreducibleRedundantFactors| |eyeDistance| |computeInt| + |infieldint| |tan| |host| |linear?| |e02akf| |calcRanges| |clip| + |makeCos| |elseBranch| |distFact| |cot| |normalForm| + |chineseRemainder| |lighting| |subNodeOf?| |triangular?| + |rightMinimalPolynomial| |jacobi| |extendedEuclidean| |nthFlag| |sec| + |functionIsContinuousAtEndPoints| |sumOfSquares| |coth2tanh| |algint| + |palgLODE0| |localAbs| |mainVariables| |rightRemainder| |coefficient| + |csc| |leftReducedSystem| |rischNormalize| |infinite?| |cLog| + |multMonom| |leadingBasisTerm| |newTypeLists| |asin| |asimpson| |test| + |status| |hostByteOrder| |operation| |hostPlatform| |s21bdf| |remove| + |beauzamyBound| |getOperator| |rightDiscriminant| |tubeRadiusDefault| + |acos| |setrest!| |safeFloor| |indiceSubResultant| |OMencodingXML| + |curveColorPalette| |Nul| |pushdown| |arbitrary| |e01saf| |atan| + |splitConstant| |sn| |makeSeries| |graphState| |OMread| |parts| + |credPol| |last| |identityMatrix| |sech2cosh| |scopes| |nthr| |acot| + |iicsch| |plus!| |assoc| |roughUnitIdeal?| |normalDeriv| + |subresultantSequence| |quote| |diagonal?| |asec| |degreePartition| + |explicitlyEmpty?| |qinterval| |condition| |tower| |testModulus| + |elem?| |contract| |reducedSystem| |noncommutativeJordanAlgebra?| + |genericRightTrace| |acsc| |restorePrecision| |singularitiesOf| + |startTableGcd!| |axes| |imagJ| |fill!| |substitute| |prefix| + |semiLastSubResultantEuclidean| |fmecg| |sinh| |leftQuotient| + |readBytes!| |e02zaf| |entries| |unitCanonical| + |rewriteSetByReducingWithParticularGenerators| |besselK| |cosh| + |useSingleFactorBound| |solveLinearPolynomialEquation| + |definingEquations| |setMinPoints| |solve1| |An| + |firstUncouplingMatrix| |basisOfLeftNucleus| |f04mcf| |obj| |tanh| + |palgint| |eq| |fortranCarriageReturn| |polyred| |minPoints| + |leftFactorIfCan| |LyndonCoordinates| |cschIfCan| |elliptic| + |leftUnit| |cache| |coth| |clearFortranOutputStack| |iter| |transform| + |commutator| |complexNumeric| |viewThetaDefault| + |rationalApproximation| |fTable| |rightTraceMatrix| |d01aqf| + |complexLimit| |torsionIfCan| |sech| |monicLeftDivide| + |basisOfCommutingElements| |dimensionsOf| |style| |modTree| + |OMputEndApp| |s13aaf| |mainPrimitivePart| |fortranCompilerName| + |startTableInvSet!| |csch| |bit?| |maxPoints3D| |schema| + |pmComplexintegrate| |makeprod| |unvectorise| |cot2tan| |outputForm| + |printTypes| |asinh| |setErrorBound| |constantToUnaryFunction| + |simplifyExp| |perfectSquare?| |superHeight| + |setLegalFortranSourceExtensions| |tryFunctionalDecomposition| + |leftRemainder| |semiDiscriminantEuclidean| |exponents| |KrullNumber| + |acosh| |multiple?| |voidMode| |torsion?| |SturmHabichtCoefficients| + |minimumDegree| |loopPoints| |minColIndex| |sh| |d02raf| + |coerceListOfPairs| |elaboration| |ksec| |f02adf| |innerSolve| + |normDeriv2| |commaSeparate| |graphStates| |explicitlyFinite?| + |transcendenceDegree| |invmultisect| |exp| |rightZero| |topPredicate| + |lintgcd| |modularFactor| |tableForDiscreteLogarithm| |deepCopy| + |readInt32!| |lastSubResultant| |factorFraction| |scalarTypeOf| + |exptMod| |cos2sec| |map| |rowEchelonLocal| |solid?| + |antiCommutative?| |createPrimitiveElement| |lazyResidueClass| + |trace2PowMod| |cosSinInfo| |chainSubResultants| |bat1| UP2UTS |table| + |generator| |mkPrim| |anfactor| |factorSFBRlcUnit| |cSech| |cAcos| + |nil| |leastAffineMultiple| |cCoth| |dioSolve| |RemainderList| + |alphanumeric| |new| |wreath| |member?| |cycleEntry| |charClass| + |maxColIndex| |compile| |resultantReduitEuclidean| |bandedHessian| + |trapezoidalo| |resultantEuclidean| |rationalPower| |clearTheIFTable| + |algebraicVariables| |nonSingularModel| |viewSizeDefault| + |plenaryPower| |normalElement| |radicalSolve| |completeSmith| + |uniform01| |acoshIfCan| |allRootsOf| |unaryFunction| |abs| + |approximate| |stop| |isAnd| |modularGcd| |returnTypeOf| |droot| + |convert| |possiblyInfinite?| |padecf| |isEquiv| |prolateSpheroidal| + |tanh2trigh| |complex| |insert!| |d01fcf| |coshIfCan| |writeInt8!| + |getCurve| |hex| |possiblyNewVariety?| |findConstructor| |critMonD1| + |iroot| |useEisensteinCriterion?| |showClipRegion| + |integralCoordinates| |rombergo| |rightExtendedGcd| |contours| |ideal| + |c06frf| |failed| |asinhIfCan| |identification| |hspace| |cExp| + |reducedDiscriminant| |iisech| |splitDenominator| |bernoulliB| + |mathieu23| |distdfact| |even?| |leaf?| |areEquivalent?| + |karatsubaOnce| |topFortranOutputStack| |ScanArabic| |setRealSteps| + |lfextendedint| |OMgetEndAtp| |incrementKthElement| |initTable!| + |readable?| |incr| |bezoutResultant| |callForm?| |setMinPoints3D| + |leftUnits| |univcase| |associates?| |nil?| |drawCurves| |copies| |hi| + |selectNonFiniteRoutines| |conical| |readUInt8!| |getIdentifier| + |generators| |rk4a| |log2| |quadraticNorm| |gcdPrimitive| |left| + |cCsc| |f02abf| |invertibleSet| |supersub| |univariatePolynomial| + |romberg| |addMatchRestricted| |dihedralGroup| |chebyshevT| |right| + |setStatus!| |mapCoef| |integralMatrix| |lieAdmissible?| |OMreceive| + |integralBasisAtInfinity| |countable?| |abelianGroup| |OMlistSymbols| + |generalLambert| |removeRoughlyRedundantFactorsInPol| |modifyPoint| + |countRealRoots| |medialSet| |internalSubQuasiComponent?| + |getButtonValue| |dihedral| |quadratic| |morphism| |setFormula!| + |singleFactorBound| |groebner?| |matrixGcd| |qelt| |zeroOf| |iilog| + |HermiteIntegrate| |expressIdealMember| |qsetelt| |deepestInitial| + |space| |antisymmetricTensors| |cPower| |subset?| |initial| + |rowEchelon| |LowTriBddDenomInv| |diagonals| |OMputEndError| + |leftZero| |cfirst| |harmonic| |pade| |xRange| |midpoint| |rootSplit| + |next| |leftPower| |isPower| |currentCategoryFrame| |key| |btwFact| + |critB| |cycle| |signatureAst| |yRange| |bivariatePolynomials| |push| + |irCtor| |recip| |positiveRemainder| |tracePowMod| |OMgetFloat| + |edf2efi| |explogs2trigs| |zRange| |poisson| |summation| |bigEndian| + |viewDeltaXDefault| |minimumExponent| |filename| |sPol| |findCycle| + |map!| |diagonalMatrix| |printInfo!| |solveLinearlyOverQ| |lazyPrem| + |setprevious!| |firstNumer| |simpleBounds?| |clipWithRanges| + |constantCoefficientRicDE| |qsetelt!| |realZeros| |linearlyDependent?| + |closedCurve| |repeatUntilLoop| |polynomialZeros| |permanent| + |forLoop| |parse| |mathieu22| |rspace| |support| |getMeasure| |tab| + |functionIsOscillatory| |regularRepresentation| |code| |Frobenius| + |minPoly| |generate| |primitivePart| |rightTrace| + |SturmHabichtSequence| |sayLength| |rootOfIrreduciblePoly| |bumptab| + |knownInfBasis| |setLabelValue| |randnum| |primaryDecomp| |linSolve| + |listOfLists| |factorList| |hessian| |s19aaf| |f04arf| |s21bbf| + |algebraicSort| |incrementBy| |connect| |iidsum| |squareFreeFactors| + |horizConcat| |aspFilename| |numericalIntegration| |edf2fi| + |negative?| |fractRagits| |collectUpper| |legendreP| |dequeue!| + |cycleRagits| |ref| |acsch| |iitanh| |rootKerSimp| |distance| |rename| + |rightCharacteristicPolynomial| |mathieu12| |lfinfieldint| |printInfo| + |readUInt32!| |halfExtendedSubResultantGcd1| |e02agf| |moduleSum| + |squareFreePrim| |writeBytes!| |getExplanations| |associator| |trunc| + |matrixDimensions| |hasPredicate?| |nullity| |evenInfiniteProduct| + |stronglyReduce| |doubleComplex?| |string?| |tubeRadius| + |cyclicEntries| |invertIfCan| |Hausdorff| |eigenvectors| |e02bbf| + |operators| |options| |colorFunction| |denominators| |headReduced?| + |iisec| |bits| |tail| |hermite| |dom| |duplicates| |genericLeftNorm| + |orbits| |pToDmp| |integralDerivationMatrix| + |exprHasWeightCosWXorSinWX| |sturmVariationsOf| |radPoly| |polyPart| + |arg1| |createMultiplicationMatrix| |entry| |brillhartTrials| + |hexDigit?| |resetVariableOrder| |binarySearchTree| + |integralMatrixAtInfinity| |nil| |infinite| |arbitraryExponent| |approximate| |complex| |shallowMutable| |canonical| |noetherian| |central| |partiallyOrderedSet| |arbitraryPrecision| |canonicalsClosed| |noZeroDivisors| |rightUnitary| |leftUnitary| diff --git a/src/share/algebra/interp.daase b/src/share/algebra/interp.daase index c9569497..fa2d51ab 100644 --- a/src/share/algebra/interp.daase +++ b/src/share/algebra/interp.daase @@ -1,5083 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T) ((-23) . T) ((-25) . T) ((-38 #0=(-419 (-576))) -2755 (|has| |#1| (-360)) (|has| |#1| (-374))) ((-38 |#1|) . T) ((-38 $) -2755 (|has| |#1| (-568)) (|has| |#1| (-360)) (|has| |#1| (-374)) (|has| |#1| (-317))) ((-35) |has| |#1| (-1221)) ((-95) |has| |#1| (-1221)) ((-102) . T) ((-111 #0# #0#) -2755 (|has| |#1| (-360)) (|has| |#1| (-374))) ((-111 |#1| |#1|) . T) ((-111 $ $) . T) ((-132) . T) ((-146) -2755 (|has| |#1| (-360)) (|has| |#1| (-146))) ((-148) |has| |#1| (-148)) ((-628 #0#) -2755 (|has| |#1| (-1057 (-419 (-576)))) (|has| |#1| (-360)) (|has| |#1| (-374))) ((-628 (-576)) . T) ((-628 |#1|) . T) ((-628 $) -2755 (|has| |#1| (-568)) (|has| |#1| (-360)) (|has| |#1| (-374)) (|has| |#1| (-317))) ((-625 (-874)) . T) ((-174) . T) ((-626 (-171 (-227))) |has| |#1| (-1041)) ((-626 (-171 (-390))) |has| |#1| (-1041)) ((-626 (-548)) |has| |#1| (-626 (-548))) ((-626 (-905 (-390))) |has| |#1| (-626 (-905 (-390)))) ((-626 (-905 (-576))) |has| |#1| (-626 (-905 (-576)))) ((-626 #1=(-1191 |#1|)) . T) ((-234 $) -2755 (|has| |#1| (-360)) (|has| |#1| (-237)) (|has| |#1| (-238))) ((-232 |#1|) . T) ((-238) -2755 (|has| |#1| (-360)) (|has| |#1| (-238))) ((-237) -2755 (|has| |#1| (-360)) (|has| |#1| (-237)) (|has| |#1| (-238))) ((-272 |#1|) . T) ((-248) -2755 (|has| |#1| (-360)) (|has| |#1| (-374))) ((-294) |has| |#1| (-1221)) ((-296 |#1| $) |has| |#1| (-296 |#1| |#1|)) ((-300) -2755 (|has| |#1| (-568)) (|has| |#1| (-360)) (|has| |#1| (-374)) (|has| |#1| (-317))) ((-317) -2755 (|has| |#1| (-360)) (|has| |#1| (-374)) (|has| |#1| (-317))) ((-319 |#1|) |has| |#1| (-319 |#1|)) ((-374) -2755 (|has| |#1| (-360)) (|has| |#1| (-374))) ((-414) |has| |#1| (-360)) ((-379) -2755 (|has| |#1| (-379)) (|has| |#1| (-360))) ((-360) |has| |#1| (-360)) ((-381 |#1| #1#) . T) ((-421 |#1| #1#) . T) ((-349 |#1|) . T) ((-388 |#1|) . T) ((-412 |#1|) . T) ((-423 |#1|) . T) ((-464) -2755 (|has| |#1| (-360)) (|has| |#1| (-374)) (|has| |#1| (-317))) ((-505) |has| |#1| (-1221)) ((-526 (-1195) |#1|) |has| |#1| (-526 (-1195) |#1|)) ((-526 |#1| |#1|) |has| |#1| (-319 |#1|)) ((-568) -2755 (|has| |#1| (-568)) (|has| |#1| (-360)) (|has| |#1| (-374)) (|has| |#1| (-317))) ((-658 #0#) -2755 (|has| |#1| (-360)) (|has| |#1| (-374))) ((-658 (-576)) . T) ((-658 |#1|) . T) ((-658 $) . T) ((-660 #0#) -2755 (|has| |#1| (-360)) (|has| |#1| (-374))) ((-660 #2=(-576)) |has| |#1| (-651 (-576))) ((-660 |#1|) . T) ((-660 $) . T) ((-652 #0#) -2755 (|has| |#1| (-360)) (|has| |#1| (-374))) ((-652 |#1|) . T) ((-652 $) -2755 (|has| |#1| (-568)) (|has| |#1| (-360)) (|has| |#1| (-374)) (|has| |#1| (-317))) ((-651 #2#) |has| |#1| (-651 (-576))) ((-651 |#1|) . T) ((-729 #0#) -2755 (|has| |#1| (-360)) (|has| |#1| (-374))) ((-729 |#1|) . T) ((-729 $) -2755 (|has| |#1| (-568)) (|has| |#1| (-360)) (|has| |#1| (-374)) (|has| |#1| (-317))) ((-736 |#1| #1#) . T) ((-738) . T) ((-909 $ #3=(-1195)) -2755 (|has| |#1| (-917 (-1195))) (|has| |#1| (-915 (-1195)))) ((-915 (-1195)) |has| |#1| (-915 (-1195))) ((-917 #3#) -2755 (|has| |#1| (-917 (-1195))) (|has| |#1| (-915 (-1195)))) ((-899 (-390)) |has| |#1| (-899 (-390))) ((-899 (-576)) |has| |#1| (-899 (-576))) ((-897 |#1|) . T) ((-926) -12 (|has| |#1| (-317)) (|has| |#1| (-926))) ((-937) -2755 (|has| |#1| (-360)) (|has| |#1| (-374)) (|has| |#1| (-317))) ((-1021) -12 (|has| |#1| (-1021)) (|has| |#1| (-1221))) ((-1057 (-419 (-576))) |has| |#1| (-1057 (-419 (-576)))) ((-1057 (-576)) |has| |#1| (-1057 (-576))) ((-1057 |#1|) . T) ((-1070 #0#) -2755 (|has| |#1| (-360)) (|has| |#1| (-374))) ((-1070 |#1|) . T) ((-1070 $) . T) ((-1075 #0#) -2755 (|has| |#1| (-360)) (|has| |#1| (-374))) ((-1075 |#1|) . T) ((-1075 $) . T) ((-1068) . T) ((-1077) . T) ((-1131) . T) ((-1119) . T) ((-1171) |has| |#1| (-360)) ((-1221) |has| |#1| (-1221)) ((-1224) |has| |#1| (-1221)) ((-1236) . 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T) ((-234 $) -2781 (-12 (|has| |#2| (-237)) (|has| |#2| (-1068))) (-12 (|has| |#2| (-238)) (|has| |#2| (-1068)))) ((-232 |#2|) |has| |#2| (-1068)) ((-238) -12 (|has| |#2| (-238)) (|has| |#2| (-1068))) ((-237) -2781 (-12 (|has| |#2| (-237)) (|has| |#2| (-1068))) (-12 (|has| |#2| (-238)) (|has| |#2| (-1068)))) ((-272 |#2|) |has| |#2| (-1068)) ((-296 #1=(-576) |#2|) . T) ((-298 #1# |#2|) . T) ((-319 |#2|) -12 (|has| |#2| (-319 |#2|)) (|has| |#2| (-1119))) ((-379) |has| |#2| (-379)) ((-388 |#2|) |has| |#2| (-1068)) ((-423 |#2|) |has| |#2| (-1119)) ((-501 |#2|) . T) ((-616 #1# |#2|) . T) ((-526 |#2| |#2|) -12 (|has| |#2| (-319 |#2|)) (|has| |#2| (-1119))) ((-658 (-576)) -2781 (|has| |#2| (-1068)) (|has| |#2| (-374)) (|has| |#2| (-174)) (|has| |#2| (-21))) ((-658 |#2|) -2781 (|has| |#2| (-1068)) (|has| |#2| (-738)) (|has| |#2| (-374)) (|has| |#2| (-174))) ((-658 $) |has| |#2| (-1068)) ((-660 #2=(-576)) -12 (|has| |#2| (-651 (-576))) (|has| |#2| (-1068))) ((-660 |#2|) -2781 (|has| |#2| (-1068)) (|has| |#2| (-374)) (|has| |#2| (-174))) ((-660 $) |has| |#2| (-1068)) ((-652 |#2|) -2781 (|has| |#2| (-738)) (|has| |#2| (-374)) (|has| |#2| (-174))) ((-651 #2#) -12 (|has| |#2| (-651 (-576))) (|has| |#2| (-1068))) ((-651 |#2|) |has| |#2| (-1068)) ((-729 |#2|) -2781 (|has| |#2| (-374)) (|has| |#2| (-174))) ((-738) |has| |#2| (-1068)) ((-804) |has| |#2| (-805)) ((-805) |has| |#2| (-805)) ((-806) |has| |#2| (-805)) ((-807) |has| |#2| (-805)) ((-862) -2781 (|has| |#2| (-862)) (|has| |#2| (-805))) ((-909 $ #3=(-1195)) -2781 (-12 (|has| |#2| (-917 (-1195))) (|has| |#2| (-1068))) (-12 (|has| |#2| (-915 (-1195))) (|has| |#2| (-1068)))) ((-915 (-1195)) -12 (|has| |#2| (-915 (-1195))) (|has| |#2| (-1068))) ((-917 #3#) -2781 (-12 (|has| |#2| (-917 (-1195))) (|has| |#2| (-1068))) (-12 (|has| |#2| (-915 (-1195))) (|has| |#2| (-1068)))) ((-1057 #0#) -12 (|has| |#2| (-1057 (-419 (-576)))) (|has| |#2| (-1119))) ((-1057 (-576)) -12 (|has| |#2| (-1057 (-576))) (|has| |#2| (-1119))) ((-1057 |#2|) |has| |#2| (-1119)) ((-1070 |#2|) -2781 (|has| |#2| (-1068)) (|has| |#2| (-738)) (|has| |#2| (-374)) (|has| |#2| (-174))) ((-1075 |#2|) -2781 (|has| |#2| (-1068)) (|has| |#2| (-374)) (|has| |#2| (-174))) ((-1068) |has| |#2| (-1068)) ((-1077) |has| |#2| (-1068)) ((-1131) |has| |#2| (-1068)) ((-1119) -2781 (|has| |#2| (-1119)) (|has| |#2| (-1068)) (|has| |#2| (-862)) (|has| |#2| (-805)) (|has| |#2| (-738)) (|has| |#2| (-379)) (|has| |#2| (-374)) (|has| |#2| (-174)) (|has| |#2| (-132)) (|has| |#2| (-25)) (|has| |#2| (-23)) (|has| |#2| (-21))) ((-1236) . T) ((-1293 |#2|) |has| |#2| (-374))) -((-3078 (((-245 |#1| |#3|) (-1 |#3| |#2| |#3|) (-245 |#1| |#2|) |#3|) 21)) (-2488 ((|#3| (-1 |#3| |#2| |#3|) (-245 |#1| |#2|) |#3|) 23)) (-4096 (((-245 |#1| |#3|) (-1 |#3| |#2|) (-245 |#1| |#2|)) 18))) -(((-244 |#1| |#2| |#3|) (-10 -7 (-15 -3078 ((-245 |#1| |#3|) (-1 |#3| |#2| |#3|) (-245 |#1| |#2|) |#3|)) (-15 -2488 (|#3| (-1 |#3| |#2| |#3|) (-245 |#1| |#2|) |#3|)) (-15 -4096 ((-245 |#1| |#3|) (-1 |#3| |#2|) (-245 |#1| |#2|)))) (-783) (-1236) (-1236)) (T -244)) -((-4096 (*1 *2 *3 *4) (-12 (-5 *3 (-1 *7 *6)) (-5 *4 (-245 *5 *6)) (-14 *5 (-783)) (-4 *6 (-1236)) (-4 *7 (-1236)) (-5 *2 (-245 *5 *7)) (-5 *1 (-244 *5 *6 *7)))) (-2488 (*1 *2 *3 *4 *2) (-12 (-5 *3 (-1 *2 *6 *2)) (-5 *4 (-245 *5 *6)) (-14 *5 (-783)) (-4 *6 (-1236)) (-4 *2 (-1236)) (-5 *1 (-244 *5 *6 *2)))) (-3078 (*1 *2 *3 *4 *5) (-12 (-5 *3 (-1 *5 *7 *5)) (-5 *4 (-245 *6 *7)) (-14 *6 (-783)) (-4 *7 (-1236)) (-4 *5 (-1236)) (-5 *2 (-245 *6 *5)) (-5 *1 (-244 *6 *7 *5))))) -(-10 -7 (-15 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NIL (-12 (|has| |#2| (-917 (-1195))) (|has| |#2| (-1068)))) (($ $ (-1195)) NIL (-12 (|has| |#2| (-917 (-1195))) (|has| |#2| (-1068)))) (($ $ (-1 |#2| |#2|)) NIL (|has| |#2| (-1068))) (($ $ (-1 |#2| |#2|) (-783)) NIL (|has| |#2| (-1068)))) (-1434 (((-783) (-1 (-112) |#2|) $) NIL (|has| $ (-6 -4462))) (((-783) |#2| $) NIL (-12 (|has| $ (-6 -4462)) (|has| |#2| (-1119))))) (-1873 (($ $) NIL)) (-3581 (((-1286 |#2|) $) 9) (($ (-576)) NIL (-2781 (-12 (|has| |#2| (-1057 (-576))) (|has| |#2| (-1119))) (|has| |#2| (-1068)))) (($ (-419 (-576))) NIL (-12 (|has| |#2| (-1057 (-419 (-576)))) (|has| |#2| (-1119)))) (($ |#2|) 12 (|has| |#2| (-1119))) (((-874) $) NIL (|has| |#2| (-625 (-874))))) (-1543 (((-783)) NIL (|has| |#2| (-1068)) CONST)) (-3565 (((-112) $ $) NIL (|has| |#2| (-1119)))) (-1447 (((-112) (-1 (-112) |#2|) $) NIL (|has| $ (-6 -4462)))) (-2748 (($) 36 (|has| |#2| (-23)) CONST)) (-2758 (($) 40 (|has| |#2| (-1068)) CONST)) (-1992 (($ $ (-783)) NIL (-12 (|has| |#2| (-237)) (|has| |#2| 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(|has| |#2| (-1068))) (($ $ |#2|) 44 (|has| |#2| (-738))) (($ |#2| $) 45 (|has| |#2| (-738))) (($ (-576) $) NIL (|has| |#2| (-21))) (($ (-783) $) NIL (|has| |#2| (-23))) (($ (-938) $) NIL (|has| |#2| (-25)))) (-3500 (((-783) $) NIL (|has| $ (-6 -4462))))) +((-1869 (*1 *1 *2) (-12 (-5 *2 (-1286 *4)) (-4 *4 (-1236)) (-4 *1 (-243 *3 *4)))) (-2706 (*1 *1 *2) (-12 (-5 *2 (-938)) (-4 *1 (-243 *3 *4)) (-4 *4 (-1068)) (-4 *4 (-1236)))) (-1957 (*1 *2 *1 *1) (-12 (-4 *1 (-243 *3 *2)) (-4 *2 (-1236)) (-4 *2 (-1068))))) +(-13 (-616 (-576) |t#2|) (-625 (-1286 |t#2|)) (-10 -8 (-6 -4462) (-15 -1869 ($ (-1286 |t#2|))) (IF (|has| |t#2| (-1119)) (-6 (-423 |t#2|)) |%noBranch|) (IF (|has| |t#2| (-1068)) (PROGN (-6 (-111 |t#2| |t#2|)) (-6 (-232 |t#2|)) (-6 (-388 |t#2|)) (-15 -2706 ($ (-938))) (-15 -1957 (|t#2| $ $))) |%noBranch|) (IF (|has| |t#2| (-25)) (-6 (-25)) |%noBranch|) (IF (|has| |t#2| (-132)) (-6 (-132)) |%noBranch|) (IF (|has| |t#2| (-23)) (-6 (-23)) |%noBranch|) (IF (|has| |t#2| (-21)) (-6 (-21)) |%noBranch|) (IF (|has| |t#2| (-738)) (-6 (-652 |t#2|)) |%noBranch|) (IF (|has| |t#2| (-379)) (-6 (-379)) |%noBranch|) (IF (|has| |t#2| (-174)) (-6 (-729 |t#2|)) |%noBranch|) (IF (|has| |t#2| (-6 -4459)) (-6 -4459) |%noBranch|) (IF (|has| |t#2| (-862)) (-6 (-862)) |%noBranch|) (IF (|has| |t#2| (-805)) (-6 (-805)) |%noBranch|) (IF (|has| |t#2| (-374)) (-6 (-1293 |t#2|)) |%noBranch|))) +(((-21) -2755 (|has| |#2| (-1068)) (|has| |#2| (-374)) (|has| |#2| (-174)) (|has| |#2| (-21))) ((-23) -2755 (|has| |#2| (-1068)) (|has| |#2| (-805)) (|has| |#2| (-374)) (|has| |#2| (-174)) (|has| |#2| (-132)) (|has| |#2| (-23)) (|has| |#2| (-21))) ((-25) -2755 (|has| |#2| (-1068)) (|has| |#2| (-805)) (|has| |#2| (-374)) (|has| |#2| (-174)) (|has| |#2| (-132)) (|has| |#2| (-25)) (|has| |#2| (-23)) (|has| |#2| (-21))) ((-34) . T) ((-102) -2755 (|has| |#2| (-1119)) (|has| |#2| (-1068)) (|has| |#2| (-862)) (|has| |#2| (-805)) (|has| |#2| (-738)) (|has| |#2| (-379)) (|has| |#2| (-374)) (|has| |#2| (-174)) (|has| |#2| (-132)) (|has| |#2| (-102)) (|has| |#2| (-25)) (|has| |#2| (-23)) (|has| |#2| (-21))) ((-111 |#2| |#2|) -2755 (|has| |#2| (-1068)) (|has| |#2| (-374)) (|has| |#2| (-174))) ((-132) -2755 (|has| |#2| (-1068)) (|has| |#2| (-805)) (|has| |#2| (-374)) (|has| |#2| (-174)) (|has| |#2| (-132)) (|has| |#2| (-21))) ((-628 #0=(-419 (-576))) -12 (|has| |#2| (-1057 (-419 (-576)))) (|has| |#2| (-1119))) ((-628 (-576)) -2755 (|has| |#2| (-1068)) (-12 (|has| |#2| (-1057 (-576))) (|has| |#2| (-1119)))) ((-628 |#2|) |has| |#2| (-1119)) ((-625 (-874)) -2755 (|has| |#2| (-1119)) (|has| |#2| (-1068)) (|has| |#2| (-862)) (|has| |#2| (-805)) (|has| |#2| (-738)) (|has| |#2| (-379)) (|has| |#2| (-374)) (|has| |#2| (-174)) (|has| |#2| (-625 (-874))) (|has| |#2| (-132)) (|has| |#2| (-25)) (|has| |#2| (-23)) (|has| |#2| (-21))) ((-625 (-1286 |#2|)) . T) ((-234 $) -2755 (-12 (|has| |#2| (-237)) (|has| |#2| (-1068))) (-12 (|has| |#2| (-238)) (|has| |#2| (-1068)))) ((-232 |#2|) |has| |#2| (-1068)) ((-238) -12 (|has| |#2| (-238)) (|has| |#2| (-1068))) ((-237) -2755 (-12 (|has| |#2| (-237)) (|has| |#2| (-1068))) (-12 (|has| |#2| (-238)) (|has| |#2| (-1068)))) ((-272 |#2|) |has| |#2| (-1068)) ((-296 #1=(-576) |#2|) . T) ((-298 #1# |#2|) . T) ((-319 |#2|) -12 (|has| |#2| (-319 |#2|)) (|has| |#2| (-1119))) ((-379) |has| |#2| (-379)) ((-388 |#2|) |has| |#2| (-1068)) ((-423 |#2|) |has| |#2| (-1119)) ((-501 |#2|) . T) ((-616 #1# |#2|) . T) ((-526 |#2| |#2|) -12 (|has| |#2| (-319 |#2|)) (|has| |#2| (-1119))) ((-658 (-576)) -2755 (|has| |#2| (-1068)) (|has| |#2| (-374)) (|has| |#2| (-174)) (|has| |#2| (-21))) ((-658 |#2|) -2755 (|has| |#2| (-1068)) (|has| |#2| (-738)) (|has| |#2| (-374)) (|has| |#2| (-174))) ((-658 $) |has| |#2| (-1068)) ((-660 #2=(-576)) -12 (|has| |#2| (-651 (-576))) (|has| |#2| (-1068))) ((-660 |#2|) -2755 (|has| |#2| (-1068)) (|has| |#2| (-374)) (|has| |#2| (-174))) ((-660 $) |has| |#2| (-1068)) ((-652 |#2|) -2755 (|has| |#2| (-738)) (|has| |#2| (-374)) (|has| |#2| (-174))) ((-651 #2#) -12 (|has| |#2| (-651 (-576))) (|has| |#2| (-1068))) ((-651 |#2|) |has| |#2| (-1068)) ((-729 |#2|) -2755 (|has| |#2| (-374)) (|has| |#2| (-174))) ((-738) |has| |#2| (-1068)) ((-804) |has| |#2| (-805)) ((-805) |has| |#2| (-805)) ((-806) |has| |#2| (-805)) ((-807) |has| |#2| (-805)) ((-862) -2755 (|has| |#2| (-862)) (|has| |#2| (-805))) ((-909 $ #3=(-1195)) -2755 (-12 (|has| |#2| (-917 (-1195))) (|has| |#2| (-1068))) (-12 (|has| |#2| (-915 (-1195))) (|has| |#2| (-1068)))) ((-915 (-1195)) -12 (|has| |#2| (-915 (-1195))) (|has| |#2| (-1068))) ((-917 #3#) -2755 (-12 (|has| |#2| (-917 (-1195))) (|has| |#2| (-1068))) (-12 (|has| |#2| (-915 (-1195))) (|has| |#2| (-1068)))) ((-1057 #0#) -12 (|has| |#2| (-1057 (-419 (-576)))) (|has| |#2| (-1119))) ((-1057 (-576)) -12 (|has| |#2| (-1057 (-576))) (|has| |#2| (-1119))) ((-1057 |#2|) |has| |#2| (-1119)) ((-1070 |#2|) -2755 (|has| |#2| (-1068)) (|has| |#2| (-738)) (|has| |#2| (-374)) (|has| |#2| (-174))) ((-1075 |#2|) -2755 (|has| |#2| (-1068)) (|has| |#2| (-374)) (|has| |#2| (-174))) ((-1068) |has| |#2| (-1068)) ((-1077) |has| |#2| (-1068)) ((-1131) |has| |#2| (-1068)) ((-1119) -2755 (|has| |#2| (-1119)) (|has| |#2| (-1068)) (|has| |#2| (-862)) (|has| |#2| (-805)) (|has| |#2| (-738)) (|has| |#2| (-379)) (|has| |#2| (-374)) (|has| |#2| (-174)) (|has| |#2| (-132)) (|has| |#2| (-25)) (|has| |#2| (-23)) (|has| |#2| (-21))) ((-1236) . 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T) ((-568) -2781 (|has| |#1| (-926)) (|has| |#1| (-568)) (|has| |#1| (-464))) ((-658 #0#) |has| |#1| (-38 (-419 (-576)))) ((-658 (-576)) . T) ((-658 |#1|) . T) ((-658 $) . T) ((-660 #0#) |has| |#1| (-38 (-419 (-576)))) ((-660 #1=(-576)) |has| |#1| (-651 (-576))) ((-660 |#1|) . T) ((-660 $) . T) ((-652 #0#) |has| |#1| (-38 (-419 (-576)))) ((-652 |#1|) |has| |#1| (-174)) ((-652 $) -2781 (|has| |#1| (-926)) (|has| |#1| (-568)) (|has| |#1| (-464))) ((-651 #1#) |has| |#1| (-651 (-576))) ((-651 |#1|) . T) ((-729 #0#) |has| |#1| (-38 (-419 (-576)))) ((-729 |#1|) |has| |#1| (-174)) ((-729 $) -2781 (|has| |#1| (-926)) (|has| |#1| (-568)) (|has| |#1| (-464))) ((-738) . T) ((-909 $ #2=(-1195)) -2781 (|has| |#1| (-917 (-1195))) (|has| |#1| (-915 (-1195)))) ((-909 $ |#3|) . T) ((-915 (-1195)) |has| |#1| (-915 (-1195))) ((-915 |#3|) . T) ((-917 #2#) -2781 (|has| |#1| (-917 (-1195))) (|has| |#1| (-915 (-1195)))) ((-917 |#3|) . T) ((-899 (-390)) -12 (|has| |#1| (-899 (-390))) (|has| |#3| (-899 (-390)))) ((-899 (-576)) -12 (|has| |#1| (-899 (-576))) (|has| |#3| (-899 (-576)))) ((-966 |#1| |#4| |#3|) . T) ((-926) |has| |#1| (-926)) ((-1057 (-419 (-576))) |has| |#1| (-1057 (-419 (-576)))) ((-1057 (-576)) |has| |#1| (-1057 (-576))) ((-1057 |#1|) . T) ((-1057 |#2|) . T) ((-1057 |#3|) . T) ((-1070 #0#) |has| |#1| (-38 (-419 (-576)))) ((-1070 |#1|) . T) ((-1070 $) -2781 (|has| |#1| (-926)) (|has| |#1| (-568)) (|has| |#1| (-464)) (|has| |#1| (-174))) ((-1075 #0#) |has| |#1| (-38 (-419 (-576)))) ((-1075 |#1|) . T) ((-1075 $) -2781 (|has| |#1| (-926)) (|has| |#1| (-568)) (|has| |#1| (-464)) (|has| |#1| (-174))) ((-1068) . T) ((-1077) . T) ((-1131) . T) ((-1119) . T) ((-1236) . T) ((-1240) |has| |#1| (-926))) -((-3488 (((-112) $ $) 20 (|has| |#1| (-102)))) (-2898 ((|#1| $) 55)) (-1371 ((|#1| $) 45)) (-1963 (((-112) $ (-783)) 8)) (-3321 (($) 7 T CONST)) (-2820 (($ $) 61)) (-4237 (($ $) 49)) (-3857 ((|#1| |#1| $) 47)) (-2231 ((|#1| $) 46)) (-3904 (((-656 |#1|) $) 31 (|has| $ (-6 -4462)))) (-2848 (((-112) $ (-783)) 9)) (-2192 (((-656 |#1|) $) 30 (|has| $ (-6 -4462)))) (-2621 (((-112) |#1| $) 28 (-12 (|has| |#1| (-1119)) (|has| $ (-6 -4462))))) (-1726 (($ (-1 |#1| |#1|) $) 35 (|has| $ (-6 -4463)))) (-4096 (($ (-1 |#1| |#1|) $) 36)) (-4373 (((-112) $ (-783)) 10)) (-1750 (((-783) $) 62)) (-4435 (((-1177) $) 22 (|has| |#1| (-1119)))) (-2463 ((|#1| $) 40)) (-1683 ((|#1| |#1| $) 53)) (-1380 ((|#1| |#1| $) 52)) (-3180 (($ |#1| $) 41)) (-2282 (((-783) $) 56)) (-1423 (((-1139) $) 21 (|has| |#1| (-1119)))) (-2813 ((|#1| $) 63)) (-3834 ((|#1| $) 51)) (-3926 ((|#1| $) 50)) (-3665 ((|#1| $) 42)) (-1883 (((-112) (-1 (-112) |#1|) $) 33 (|has| $ (-6 -4462)))) (-3289 (($ $ (-656 (-304 |#1|))) 27 (-12 (|has| |#1| (-319 |#1|)) (|has| |#1| (-1119)))) (($ $ (-304 |#1|)) 26 (-12 (|has| |#1| (-319 |#1|)) (|has| |#1| (-1119)))) (($ $ |#1| |#1|) 25 (-12 (|has| |#1| (-319 |#1|)) (|has| |#1| (-1119)))) (($ $ (-656 |#1|) (-656 |#1|)) 24 (-12 (|has| |#1| (-319 |#1|)) (|has| |#1| (-1119))))) (-2152 (((-112) $ $) 14)) (-1619 ((|#1| |#1| $) 59)) (-4207 (((-112) $) 11)) (-4247 (($) 12)) (-4014 ((|#1| $) 60)) (-3943 (($) 58) (($ (-656 |#1|)) 57)) (-1815 (((-783) $) 44)) (-1434 (((-783) (-1 (-112) |#1|) $) 32 (|has| $ (-6 -4462))) (((-783) |#1| $) 29 (-12 (|has| |#1| (-1119)) (|has| $ (-6 -4462))))) (-1873 (($ $) 13)) (-3581 (((-874) $) 18 (|has| |#1| (-625 (-874))))) (-2983 ((|#1| $) 54)) (-3565 (((-112) $ $) 23 (|has| |#1| (-1119)))) (-3573 (($ (-656 |#1|)) 43)) (-4030 ((|#1| $) 64)) (-1447 (((-112) (-1 (-112) |#1|) $) 34 (|has| $ (-6 -4462)))) (-2942 (((-112) $ $) 19 (|has| |#1| (-102)))) (-3500 (((-783) $) 6 (|has| $ (-6 -4462))))) +((-2261 (*1 *2 *3) (-12 (-4 *4 (-1068)) (-4 *3 (-862)) (-4 *5 (-275 *3)) (-4 *6 (-805)) (-5 *2 (-1 *1 (-783))) (-4 *1 (-260 *4 *3 *5 *6)))) (-2982 (*1 *2 *1) (-12 (-4 *1 (-260 *3 *4 *5 *6)) (-4 *3 (-1068)) (-4 *4 (-862)) (-4 *5 (-275 *4)) (-4 *6 (-805)) (-5 *2 (-656 *4)))) (-2996 (*1 *2 *1 *3) (-12 (-4 *1 (-260 *4 *3 *5 *6)) (-4 *4 (-1068)) (-4 *3 (-862)) (-4 *5 (-275 *3)) (-4 *6 (-805)) (-5 *2 (-783)))) (-2996 (*1 *2 *1) (-12 (-4 *1 (-260 *3 *4 *5 *6)) (-4 *3 (-1068)) (-4 *4 (-862)) (-4 *5 (-275 *4)) (-4 *6 (-805)) (-5 *2 (-783)))) (-3779 (*1 *2 *1 *3) (-12 (-4 *1 (-260 *4 *3 *5 *6)) (-4 *4 (-1068)) (-4 *3 (-862)) (-4 *5 (-275 *3)) (-4 *6 (-805)) (-5 *2 (-783)))) (-3070 (*1 *2 *1) (-12 (-4 *1 (-260 *3 *4 *5 *6)) (-4 *3 (-1068)) (-4 *4 (-862)) (-4 *5 (-275 *4)) (-4 *6 (-805)) (-5 *2 (-656 (-783))))) (-1841 (*1 *2 *1) (-12 (-4 *1 (-260 *3 *4 *5 *6)) (-4 *3 (-1068)) (-4 *4 (-862)) (-4 *5 (-275 *4)) (-4 *6 (-805)) (-5 *2 (-783)))) (-3070 (*1 *2 *1 *3) (-12 (-4 *1 (-260 *4 *3 *5 *6)) (-4 *4 (-1068)) (-4 *3 (-862)) (-4 *5 (-275 *3)) (-4 *6 (-805)) (-5 *2 (-656 (-783))))) (-1841 (*1 *2 *1 *3) (-12 (-4 *1 (-260 *4 *3 *5 *6)) (-4 *4 (-1068)) (-4 *3 (-862)) (-4 *5 (-275 *3)) (-4 *6 (-805)) (-5 *2 (-783)))) (-2542 (*1 *2 *1) (-12 (-4 *1 (-260 *3 *4 *5 *6)) (-4 *3 (-1068)) (-4 *4 (-862)) (-4 *5 (-275 *4)) (-4 *6 (-805)) (-5 *2 (-112)))) (-2756 (*1 *2 *1) (-12 (-4 *1 (-260 *3 *4 *2 *5)) (-4 *3 (-1068)) (-4 *4 (-862)) (-4 *5 (-805)) (-4 *2 (-275 *4)))) (-4282 (*1 *1 *1) (-12 (-4 *1 (-260 *2 *3 *4 *5)) (-4 *2 (-1068)) (-4 *3 (-862)) (-4 *4 (-275 *3)) (-4 *5 (-805)))) (-2290 (*1 *1 *1) (-12 (-4 *1 (-260 *2 *3 *4 *5)) (-4 *2 (-1068)) (-4 *3 (-862)) (-4 *4 (-275 *3)) (-4 *5 (-805)))) (-2261 (*1 *2 *1) (-12 (-4 *3 (-238)) (-4 *3 (-1068)) (-4 *4 (-862)) (-4 *5 (-275 *4)) (-4 *6 (-805)) (-5 *2 (-1 *1 (-783))) (-4 *1 (-260 *3 *4 *5 *6))))) +(-13 (-966 |t#1| |t#4| |t#3|) (-232 |t#1|) (-1057 |t#2|) (-10 -8 (-15 -2261 ((-1 $ (-783)) |t#2|)) (-15 -2982 ((-656 |t#2|) $)) (-15 -2996 ((-783) $ |t#2|)) (-15 -2996 ((-783) $)) (-15 -3779 ((-783) $ |t#2|)) (-15 -3070 ((-656 (-783)) $)) (-15 -1841 ((-783) $)) (-15 -3070 ((-656 (-783)) $ |t#2|)) (-15 -1841 ((-783) $ |t#2|)) (-15 -2542 ((-112) $)) (-15 -2756 (|t#3| $)) (-15 -4282 ($ $)) (-15 -2290 ($ $)) (IF (|has| |t#1| (-238)) (PROGN (-6 (-526 |t#2| |t#1|)) (-6 (-526 |t#2| $)) (-6 (-319 $)) (-15 -2261 ((-1 $ (-783)) $))) |%noBranch|))) +(((-21) . T) ((-23) . T) ((-47 |#1| |#4|) . T) ((-25) . T) ((-38 #0=(-419 (-576))) |has| |#1| (-38 (-419 (-576)))) ((-38 |#1|) |has| |#1| (-174)) ((-38 $) -2755 (|has| |#1| (-926)) (|has| |#1| (-568)) (|has| |#1| (-464))) ((-102) . T) ((-111 #0# #0#) |has| |#1| (-38 (-419 (-576)))) ((-111 |#1| |#1|) . T) ((-111 $ $) -2755 (|has| |#1| (-926)) (|has| |#1| (-568)) (|has| |#1| (-464)) (|has| |#1| (-174))) ((-132) . T) ((-146) |has| |#1| (-146)) ((-148) |has| |#1| (-148)) ((-628 #0#) -2755 (|has| |#1| (-1057 (-419 (-576)))) (|has| |#1| (-38 (-419 (-576))))) ((-628 (-576)) . T) ((-628 |#1|) . T) ((-628 |#2|) . T) ((-628 |#3|) . T) ((-628 $) -2755 (|has| |#1| (-926)) (|has| |#1| (-568)) (|has| |#1| (-464))) ((-625 (-874)) . T) ((-174) -2755 (|has| |#1| (-926)) (|has| |#1| (-568)) (|has| |#1| (-464)) (|has| |#1| (-174))) ((-626 (-548)) -12 (|has| |#1| (-626 (-548))) (|has| |#3| (-626 (-548)))) ((-626 (-905 (-390))) -12 (|has| |#1| (-626 (-905 (-390)))) (|has| |#3| (-626 (-905 (-390))))) ((-626 (-905 (-576))) -12 (|has| |#1| (-626 (-905 (-576)))) (|has| |#3| (-626 (-905 (-576))))) ((-234 $) -2755 (|has| |#1| (-237)) (|has| |#1| (-238))) ((-232 |#1|) . T) ((-238) |has| |#1| (-238)) ((-237) -2755 (|has| |#1| (-237)) (|has| |#1| (-238))) ((-272 |#1|) . T) ((-300) -2755 (|has| |#1| (-926)) (|has| |#1| (-568)) (|has| |#1| (-464))) ((-319 $) . T) ((-336 |#1| |#4|) . T) ((-388 |#1|) . T) ((-423 |#1|) . T) ((-464) -2755 (|has| |#1| (-926)) (|has| |#1| (-464))) ((-526 |#2| |#1|) |has| |#1| (-238)) ((-526 |#2| $) |has| |#1| (-238)) ((-526 |#3| |#1|) . T) ((-526 |#3| $) . T) ((-526 $ $) . T) ((-568) -2755 (|has| |#1| (-926)) (|has| |#1| (-568)) (|has| |#1| (-464))) ((-658 #0#) |has| |#1| (-38 (-419 (-576)))) ((-658 (-576)) . T) ((-658 |#1|) . T) ((-658 $) . T) ((-660 #0#) |has| |#1| (-38 (-419 (-576)))) ((-660 #1=(-576)) |has| |#1| (-651 (-576))) ((-660 |#1|) . T) ((-660 $) . T) ((-652 #0#) |has| |#1| (-38 (-419 (-576)))) ((-652 |#1|) |has| |#1| (-174)) ((-652 $) -2755 (|has| |#1| (-926)) (|has| |#1| (-568)) (|has| |#1| (-464))) ((-651 #1#) |has| |#1| (-651 (-576))) ((-651 |#1|) . T) ((-729 #0#) |has| |#1| (-38 (-419 (-576)))) ((-729 |#1|) |has| |#1| (-174)) ((-729 $) -2755 (|has| |#1| (-926)) (|has| |#1| (-568)) (|has| |#1| (-464))) ((-738) . T) ((-909 $ #2=(-1195)) -2755 (|has| |#1| (-917 (-1195))) (|has| |#1| (-915 (-1195)))) ((-909 $ |#3|) . T) ((-915 (-1195)) |has| |#1| (-915 (-1195))) ((-915 |#3|) . T) ((-917 #2#) -2755 (|has| |#1| (-917 (-1195))) (|has| |#1| (-915 (-1195)))) ((-917 |#3|) . T) ((-899 (-390)) -12 (|has| |#1| (-899 (-390))) (|has| |#3| (-899 (-390)))) ((-899 (-576)) -12 (|has| |#1| (-899 (-576))) (|has| |#3| (-899 (-576)))) ((-966 |#1| |#4| |#3|) . T) ((-926) |has| |#1| (-926)) ((-1057 (-419 (-576))) |has| |#1| (-1057 (-419 (-576)))) ((-1057 (-576)) |has| |#1| (-1057 (-576))) ((-1057 |#1|) . T) ((-1057 |#2|) . T) ((-1057 |#3|) . T) ((-1070 #0#) |has| |#1| (-38 (-419 (-576)))) ((-1070 |#1|) . T) ((-1070 $) -2755 (|has| |#1| (-926)) (|has| |#1| (-568)) (|has| |#1| (-464)) (|has| |#1| (-174))) ((-1075 #0#) |has| |#1| (-38 (-419 (-576)))) ((-1075 |#1|) . T) ((-1075 $) -2755 (|has| |#1| (-926)) (|has| |#1| (-568)) (|has| |#1| (-464)) (|has| |#1| (-174))) ((-1068) . T) ((-1077) . T) ((-1131) . T) ((-1119) . T) ((-1236) . T) ((-1240) |has| |#1| (-926))) +((-3486 (((-112) $ $) 20 (|has| |#1| (-102)))) (-3351 ((|#1| $) 55)) (-1417 ((|#1| $) 45)) (-2311 (((-112) $ (-783)) 8)) (-2478 (($) 7 T CONST)) (-2382 (($ $) 61)) (-3588 (($ $) 49)) (-2944 ((|#1| |#1| $) 47)) (-1354 ((|#1| $) 46)) (-3964 (((-656 |#1|) $) 31 (|has| $ (-6 -4462)))) (-2293 (((-112) $ (-783)) 9)) (-1706 (((-656 |#1|) $) 30 (|has| $ (-6 -4462)))) (-4140 (((-112) |#1| $) 28 (-12 (|has| |#1| (-1119)) (|has| $ (-6 -4462))))) (-4322 (($ (-1 |#1| |#1|) $) 35 (|has| $ (-6 -4463)))) (-4114 (($ (-1 |#1| |#1|) $) 36)) (-3564 (((-112) $ (-783)) 10)) (-2432 (((-783) $) 62)) (-3440 (((-1177) $) 22 (|has| |#1| (-1119)))) (-3086 ((|#1| $) 40)) (-3604 ((|#1| |#1| $) 53)) (-1913 ((|#1| |#1| $) 52)) (-4176 (($ |#1| $) 41)) (-2322 (((-783) $) 56)) (-1448 (((-1139) $) 21 (|has| |#1| (-1119)))) (-2484 ((|#1| $) 63)) (-1602 ((|#1| $) 51)) (-2406 ((|#1| $) 50)) (-3180 ((|#1| $) 42)) (-3334 (((-112) (-1 (-112) |#1|) $) 33 (|has| $ (-6 -4462)))) (-3282 (($ $ (-656 (-304 |#1|))) 27 (-12 (|has| |#1| (-319 |#1|)) (|has| |#1| (-1119)))) (($ $ (-304 |#1|)) 26 (-12 (|has| |#1| (-319 |#1|)) (|has| |#1| (-1119)))) (($ $ |#1| |#1|) 25 (-12 (|has| |#1| (-319 |#1|)) (|has| |#1| (-1119)))) (($ $ (-656 |#1|) (-656 |#1|)) 24 (-12 (|has| |#1| (-319 |#1|)) (|has| |#1| (-1119))))) (-2140 (((-112) $ $) 14)) (-3607 ((|#1| |#1| $) 59)) (-1551 (((-112) $) 11)) (-2242 (($) 12)) (-4382 ((|#1| $) 60)) (-3472 (($) 58) (($ (-656 |#1|)) 57)) (-1886 (((-783) $) 44)) (-1458 (((-783) (-1 (-112) |#1|) $) 32 (|has| $ (-6 -4462))) (((-783) |#1| $) 29 (-12 (|has| |#1| (-1119)) (|has| $ (-6 -4462))))) (-1868 (($ $) 13)) (-3567 (((-874) $) 18 (|has| |#1| (-625 (-874))))) (-2827 ((|#1| $) 54)) (-2957 (((-112) $ $) 23 (|has| |#1| (-1119)))) (-2890 (($ (-656 |#1|)) 43)) (-1820 ((|#1| $) 64)) (-2458 (((-112) (-1 (-112) |#1|) $) 34 (|has| $ (-6 -4462)))) (-2922 (((-112) $ $) 19 (|has| |#1| (-102)))) (-3500 (((-783) $) 6 (|has| $ (-6 -4462))))) (((-261 |#1|) (-141) (-1236)) (T -261)) -((-3943 (*1 *1) (-12 (-4 *1 (-261 *2)) (-4 *2 (-1236)))) (-3943 (*1 *1 *2) (-12 (-5 *2 (-656 *3)) (-4 *3 (-1236)) (-4 *1 (-261 *3)))) (-2282 (*1 *2 *1) (-12 (-4 *1 (-261 *3)) (-4 *3 (-1236)) (-5 *2 (-783)))) (-2898 (*1 *2 *1) (-12 (-4 *1 (-261 *2)) (-4 *2 (-1236)))) (-2983 (*1 *2 *1) (-12 (-4 *1 (-261 *2)) (-4 *2 (-1236)))) (-1683 (*1 *2 *2 *1) (-12 (-4 *1 (-261 *2)) (-4 *2 (-1236)))) (-1380 (*1 *2 *2 *1) (-12 (-4 *1 (-261 *2)) (-4 *2 (-1236)))) (-3834 (*1 *2 *1) (-12 (-4 *1 (-261 *2)) (-4 *2 (-1236)))) (-3926 (*1 *2 *1) (-12 (-4 *1 (-261 *2)) (-4 *2 (-1236)))) (-4237 (*1 *1 *1) (-12 (-4 *1 (-261 *2)) (-4 *2 (-1236))))) -(-13 (-1140 |t#1|) (-1014 |t#1|) (-10 -8 (-15 -3943 ($)) (-15 -3943 ($ (-656 |t#1|))) (-15 -2282 ((-783) $)) (-15 -2898 (|t#1| $)) (-15 -2983 (|t#1| $)) (-15 -1683 (|t#1| |t#1| $)) (-15 -1380 (|t#1| |t#1| $)) (-15 -3834 (|t#1| $)) (-15 -3926 (|t#1| $)) (-15 -4237 ($ $)))) -(((-34) . 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T) ((-23) . T) ((-25) . T) ((-38 #0=(-419 (-576))) . T) ((-38 |#1|) . T) ((-38 $) . T) ((-102) . T) ((-111 #0# #0#) . T) ((-111 |#1| |#1|) . T) ((-111 $ $) . T) ((-132) . T) ((-146) |has| |#1| (-146)) ((-148) |has| |#1| (-148)) ((-628 #0#) . T) ((-628 (-576)) . T) ((-628 #1=(-1195)) |has| |#1| (-1057 (-1195))) ((-628 |#1|) . T) ((-628 $) . T) ((-625 (-874)) . T) ((-174) . T) ((-626 (-227)) |has| |#1| (-1041)) ((-626 (-390)) |has| |#1| (-1041)) ((-626 (-548)) |has| |#1| (-626 (-548))) ((-626 (-905 (-390))) |has| |#1| (-626 (-905 (-390)))) ((-626 (-905 (-576))) |has| |#1| (-626 (-905 (-576)))) ((-234 $) -2755 (|has| |#1| (-237)) (|has| |#1| (-238))) ((-232 |#1|) . T) ((-238) |has| |#1| (-238)) ((-237) -2755 (|has| |#1| (-237)) (|has| |#1| (-238))) ((-272 |#1|) . T) ((-248) . T) ((-296 |#1| $) |has| |#1| (-296 |#1| |#1|)) ((-300) . T) ((-317) . T) ((-319 |#1|) |has| |#1| (-319 |#1|)) ((-374) . T) ((-349 |#1|) . T) ((-388 |#1|) . T) ((-412 |#1|) . T) ((-464) . 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T) ((-660 |#2|) |has| |#1| (-374)) ((-660 $) . T) ((-652 #1#) -2781 (|has| |#1| (-374)) (|has| |#1| (-38 (-419 (-576))))) ((-652 |#1|) |has| |#1| (-174)) ((-652 |#2|) |has| |#1| (-374)) ((-652 $) -2781 (|has| |#1| (-568)) (|has| |#1| (-374))) ((-651 #3#) -12 (|has| |#1| (-374)) (|has| |#2| (-651 (-576)))) ((-651 |#2|) |has| |#1| (-374)) ((-729 #1#) -2781 (|has| |#1| (-374)) (|has| |#1| (-38 (-419 (-576))))) ((-729 |#1|) |has| |#1| (-174)) ((-729 |#2|) |has| |#1| (-374)) ((-729 $) -2781 (|has| |#1| (-568)) (|has| |#1| (-374))) ((-738) . 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T) ((-937) |has| |#1| (-374)) ((-1011 |#2|) |has| |#1| (-374)) ((-1021) |has| |#1| (-38 (-419 (-576)))) ((-1041) -12 (|has| |#1| (-374)) (|has| |#2| (-1041))) ((-1057 (-419 (-576))) -12 (|has| |#1| (-374)) (|has| |#2| (-1057 (-576)))) ((-1057 (-576)) -12 (|has| |#1| (-374)) (|has| |#2| (-1057 (-576)))) ((-1057 #2#) -12 (|has| |#1| (-374)) (|has| |#2| (-1057 (-1195)))) ((-1057 |#2|) . T) ((-1070 #1#) -2781 (|has| |#1| (-374)) (|has| |#1| (-38 (-419 (-576))))) ((-1070 |#1|) . T) ((-1070 |#2|) |has| |#1| (-374)) ((-1070 $) -2781 (|has| |#1| (-568)) (|has| |#1| (-374)) (|has| |#1| (-174))) ((-1075 #1#) -2781 (|has| |#1| (-374)) (|has| |#1| (-38 (-419 (-576))))) ((-1075 |#1|) . T) ((-1075 |#2|) |has| |#1| (-374)) ((-1075 $) -2781 (|has| |#1| (-568)) (|has| |#1| (-374)) (|has| |#1| (-174))) ((-1068) . T) ((-1077) . T) ((-1131) . T) ((-1119) . T) ((-1171) -12 (|has| |#1| (-374)) (|has| |#2| (-1171))) ((-1221) |has| |#1| (-38 (-419 (-576)))) ((-1224) |has| |#1| (-38 (-419 (-576)))) ((-1236) . T) ((-1240) |has| |#1| (-374)) ((-1246 |#1|) . T) ((-1264 |#1| #0#) . 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T) ((-23) . T) ((-47 |#1| #0=(-576)) . T) ((-25) . T) ((-38 #1=(-419 (-576))) -2755 (|has| |#1| (-374)) (|has| |#1| (-38 (-419 (-576))))) ((-38 |#1|) |has| |#1| (-174)) ((-38 |#2|) |has| |#1| (-374)) ((-38 $) -2755 (|has| |#1| (-568)) (|has| |#1| (-374))) ((-35) |has| |#1| (-38 (-419 (-576)))) ((-95) |has| |#1| (-38 (-419 (-576)))) ((-102) . T) ((-111 #1# #1#) -2755 (|has| |#1| (-374)) (|has| |#1| (-38 (-419 (-576))))) ((-111 |#1| |#1|) . T) ((-111 |#2| |#2|) |has| |#1| (-374)) ((-111 $ $) -2755 (|has| |#1| (-568)) (|has| |#1| (-374)) (|has| |#1| (-174))) ((-132) . T) ((-146) -2755 (-12 (|has| |#1| (-374)) (|has| |#2| (-146))) (|has| |#1| (-146))) ((-148) -2755 (-12 (|has| |#1| (-374)) (|has| |#2| (-148))) (|has| |#1| (-148))) ((-628 #1#) -2755 (|has| |#1| (-374)) (|has| |#1| (-38 (-419 (-576))))) ((-628 (-576)) . T) ((-628 #2=(-1195)) -12 (|has| |#1| (-374)) (|has| |#2| (-1057 (-1195)))) ((-628 |#1|) |has| |#1| (-174)) ((-628 |#2|) . T) ((-628 $) -2755 (|has| |#1| (-568)) (|has| |#1| (-374))) ((-625 (-874)) . T) ((-174) -2755 (|has| |#1| (-568)) (|has| |#1| (-374)) (|has| |#1| (-174))) ((-626 (-227)) -12 (|has| |#1| (-374)) (|has| |#2| (-1041))) ((-626 (-390)) -12 (|has| |#1| (-374)) (|has| |#2| (-1041))) ((-626 (-548)) -12 (|has| |#1| (-374)) (|has| |#2| (-626 (-548)))) ((-626 (-905 (-390))) -12 (|has| |#1| (-374)) (|has| |#2| (-626 (-905 (-390))))) ((-626 (-905 (-576))) -12 (|has| |#1| (-374)) (|has| |#2| (-626 (-905 (-576))))) ((-234 $) -2755 (-12 (|has| |#1| (-374)) (|has| |#2| (-237))) (-12 (|has| |#1| (-374)) (|has| |#2| (-238))) (|has| |#1| (-15 * (|#1| (-576) |#1|)))) ((-232 |#2|) |has| |#1| (-374)) ((-238) -2755 (-12 (|has| |#1| (-374)) (|has| |#2| (-238))) (|has| |#1| (-15 * (|#1| (-576) |#1|)))) ((-237) -2755 (-12 (|has| |#1| (-374)) (|has| |#2| (-237))) (-12 (|has| |#1| (-374)) (|has| |#2| (-238))) (|has| |#1| (-15 * (|#1| (-576) |#1|)))) ((-272 |#2|) |has| |#1| (-374)) ((-248) |has| |#1| (-374)) ((-294) |has| |#1| (-38 (-419 (-576)))) ((-296 #0# |#1|) . T) ((-296 |#2| $) -12 (|has| |#1| (-374)) (|has| |#2| (-296 |#2| |#2|))) ((-296 $ $) |has| (-576) (-1131)) ((-300) -2755 (|has| |#1| (-568)) (|has| |#1| (-374))) ((-317) |has| |#1| (-374)) ((-319 |#2|) -12 (|has| |#1| (-374)) (|has| |#2| (-319 |#2|))) ((-374) |has| |#1| (-374)) ((-349 |#2|) |has| |#1| (-374)) ((-388 |#2|) |has| |#1| (-374)) ((-412 |#2|) |has| |#1| (-374)) ((-464) |has| |#1| (-374)) ((-505) |has| |#1| (-38 (-419 (-576)))) ((-526 (-1195) |#2|) -12 (|has| |#1| (-374)) (|has| |#2| (-526 (-1195) |#2|))) ((-526 |#2| |#2|) -12 (|has| |#1| (-374)) (|has| |#2| (-319 |#2|))) ((-568) -2755 (|has| |#1| (-568)) (|has| |#1| (-374))) ((-658 #1#) -2755 (|has| |#1| (-374)) (|has| |#1| (-38 (-419 (-576))))) ((-658 (-576)) . T) ((-658 |#1|) . T) ((-658 |#2|) |has| |#1| (-374)) ((-658 $) . T) ((-660 #1#) -2755 (|has| |#1| (-374)) (|has| |#1| (-38 (-419 (-576))))) ((-660 #3=(-576)) -12 (|has| |#1| (-374)) (|has| |#2| (-651 (-576)))) ((-660 |#1|) . T) ((-660 |#2|) |has| |#1| (-374)) ((-660 $) . T) ((-652 #1#) -2755 (|has| |#1| (-374)) (|has| |#1| (-38 (-419 (-576))))) ((-652 |#1|) |has| |#1| (-174)) ((-652 |#2|) |has| |#1| (-374)) ((-652 $) -2755 (|has| |#1| (-568)) (|has| |#1| (-374))) ((-651 #3#) -12 (|has| |#1| (-374)) (|has| |#2| (-651 (-576)))) ((-651 |#2|) |has| |#1| (-374)) ((-729 #1#) -2755 (|has| |#1| (-374)) (|has| |#1| (-38 (-419 (-576))))) ((-729 |#1|) |has| |#1| (-174)) ((-729 |#2|) |has| |#1| (-374)) ((-729 $) -2755 (|has| |#1| (-568)) (|has| |#1| (-374))) ((-738) . T) ((-803) -12 (|has| |#1| (-374)) (|has| |#2| (-832))) ((-804) -12 (|has| |#1| (-374)) (|has| |#2| (-832))) ((-806) -12 (|has| |#1| (-374)) (|has| |#2| (-832))) ((-807) -12 (|has| |#1| (-374)) (|has| |#2| (-832))) ((-832) -12 (|has| |#1| (-374)) (|has| |#2| (-832))) ((-860) -12 (|has| |#1| (-374)) (|has| |#2| (-832))) ((-862) -2755 (-12 (|has| |#1| (-374)) (|has| |#2| (-862))) (-12 (|has| |#1| (-374)) (|has| |#2| (-832)))) ((-909 $ #4=(-1195)) -2755 (-12 (|has| |#1| (-374)) (|has| |#2| (-917 (-1195)))) (-12 (|has| |#1| (-374)) (|has| |#2| (-915 (-1195)))) (-12 (|has| |#1| (-15 * (|#1| (-576) |#1|))) (|has| |#1| (-915 (-1195))))) ((-915 (-1195)) -2755 (-12 (|has| |#1| (-374)) (|has| |#2| (-915 (-1195)))) (-12 (|has| |#1| (-15 * (|#1| (-576) |#1|))) (|has| |#1| (-915 (-1195))))) ((-917 #4#) -2755 (-12 (|has| |#1| (-374)) (|has| |#2| (-917 (-1195)))) (-12 (|has| |#1| (-374)) (|has| |#2| (-915 (-1195)))) (-12 (|has| |#1| (-15 * (|#1| (-576) |#1|))) (|has| |#1| (-915 (-1195))))) ((-899 (-390)) -12 (|has| |#1| (-374)) (|has| |#2| (-899 (-390)))) ((-899 (-576)) -12 (|has| |#1| (-374)) (|has| |#2| (-899 (-576)))) ((-897 |#2|) |has| |#1| (-374)) ((-926) -12 (|has| |#1| (-374)) (|has| |#2| (-926))) ((-992 |#1| #0# (-1101)) . T) ((-937) |has| |#1| (-374)) ((-1011 |#2|) |has| |#1| (-374)) ((-1021) |has| |#1| (-38 (-419 (-576)))) ((-1041) -12 (|has| |#1| (-374)) (|has| |#2| (-1041))) ((-1057 (-419 (-576))) -12 (|has| |#1| (-374)) (|has| |#2| (-1057 (-576)))) ((-1057 (-576)) -12 (|has| |#1| (-374)) (|has| |#2| (-1057 (-576)))) ((-1057 #2#) -12 (|has| |#1| (-374)) (|has| |#2| (-1057 (-1195)))) ((-1057 |#2|) . T) ((-1070 #1#) -2755 (|has| |#1| (-374)) (|has| |#1| (-38 (-419 (-576))))) ((-1070 |#1|) . T) ((-1070 |#2|) |has| |#1| (-374)) ((-1070 $) -2755 (|has| |#1| (-568)) (|has| |#1| (-374)) (|has| |#1| (-174))) ((-1075 #1#) -2755 (|has| |#1| (-374)) (|has| |#1| (-38 (-419 (-576))))) ((-1075 |#1|) . T) ((-1075 |#2|) |has| |#1| (-374)) ((-1075 $) -2755 (|has| |#1| (-568)) (|has| |#1| (-374)) (|has| |#1| (-174))) ((-1068) . T) ((-1077) . T) ((-1131) . T) ((-1119) . T) ((-1171) -12 (|has| |#1| (-374)) (|has| |#2| (-1171))) ((-1221) |has| |#1| (-38 (-419 (-576)))) ((-1224) |has| |#1| (-38 (-419 (-576)))) ((-1236) . T) ((-1240) |has| |#1| (-374)) ((-1246 |#1|) . T) ((-1264 |#1| #0#) . 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T) ((-23) . T) ((-47 |#1| #0=(-783)) . T) ((-25) . T) ((-38 #1=(-419 (-576))) |has| |#1| (-38 (-419 (-576)))) ((-38 |#1|) |has| |#1| (-174)) ((-38 $) -2781 (|has| |#1| (-926)) (|has| |#1| (-568)) (|has| |#1| (-464)) (|has| |#1| (-374))) ((-102) . T) ((-111 #1# #1#) |has| |#1| (-38 (-419 (-576)))) ((-111 |#1| |#1|) . T) ((-111 $ $) -2781 (|has| |#1| (-926)) (|has| |#1| (-568)) (|has| |#1| (-464)) (|has| |#1| (-374)) (|has| |#1| (-174))) ((-132) . T) ((-146) |has| |#1| (-146)) ((-148) |has| |#1| (-148)) ((-628 #1#) -2781 (|has| |#1| (-1057 (-419 (-576)))) (|has| |#1| (-38 (-419 (-576))))) ((-628 (-576)) . T) ((-628 #2=(-1101)) . T) ((-628 |#1|) . T) ((-628 $) -2781 (|has| |#1| (-926)) (|has| |#1| (-568)) (|has| |#1| (-464)) (|has| |#1| (-374))) ((-625 (-874)) . T) ((-174) -2781 (|has| |#1| (-926)) (|has| |#1| (-568)) (|has| |#1| (-464)) (|has| |#1| (-374)) (|has| |#1| (-174))) ((-626 (-548)) -12 (|has| (-1101) (-626 (-548))) (|has| |#1| (-626 (-548)))) ((-626 (-905 (-390))) -12 (|has| (-1101) (-626 (-905 (-390)))) (|has| |#1| (-626 (-905 (-390))))) ((-626 (-905 (-576))) -12 (|has| (-1101) (-626 (-905 (-576)))) (|has| |#1| (-626 (-905 (-576))))) ((-234 $) . T) ((-232 |#1|) . T) ((-238) . T) ((-237) . T) ((-272 |#1|) . T) ((-296 (-419 $) (-419 $)) |has| |#1| (-568)) ((-296 |#1| |#1|) . T) ((-296 $ $) . T) ((-300) -2781 (|has| |#1| (-926)) (|has| |#1| (-568)) (|has| |#1| (-464)) (|has| |#1| (-374))) ((-317) |has| |#1| (-374)) ((-319 $) . T) ((-336 |#1| #0#) . T) ((-388 |#1|) . T) ((-423 |#1|) . T) ((-464) -2781 (|has| |#1| (-926)) (|has| |#1| (-464)) (|has| |#1| (-374))) ((-526 #2# |#1|) . T) ((-526 #2# $) . T) ((-526 $ $) . T) ((-568) -2781 (|has| |#1| (-926)) (|has| |#1| (-568)) (|has| |#1| (-464)) (|has| |#1| (-374))) ((-658 #1#) |has| |#1| (-38 (-419 (-576)))) ((-658 (-576)) . T) ((-658 |#1|) . T) ((-658 $) . T) ((-660 #1#) |has| |#1| (-38 (-419 (-576)))) ((-660 #3=(-576)) |has| |#1| (-651 (-576))) ((-660 |#1|) . T) ((-660 $) . T) ((-652 #1#) |has| |#1| (-38 (-419 (-576)))) ((-652 |#1|) |has| |#1| (-174)) ((-652 $) -2781 (|has| |#1| (-926)) (|has| |#1| (-568)) (|has| |#1| (-464)) (|has| |#1| (-374))) ((-651 #3#) |has| |#1| (-651 (-576))) ((-651 |#1|) . T) ((-729 #1#) |has| |#1| (-38 (-419 (-576)))) ((-729 |#1|) |has| |#1| (-174)) ((-729 $) -2781 (|has| |#1| (-926)) (|has| |#1| (-568)) (|has| |#1| (-464)) (|has| |#1| (-374))) ((-738) . T) ((-909 $ #2#) . T) ((-909 $ #4=(-1195)) -2781 (|has| |#1| (-917 (-1195))) (|has| |#1| (-915 (-1195)))) ((-915 #2#) . T) ((-915 (-1195)) |has| |#1| (-915 (-1195))) ((-917 #2#) . T) ((-917 #4#) -2781 (|has| |#1| (-917 (-1195))) (|has| |#1| (-915 (-1195)))) ((-899 (-390)) -12 (|has| (-1101) (-899 (-390))) (|has| |#1| (-899 (-390)))) ((-899 (-576)) -12 (|has| (-1101) (-899 (-576))) (|has| |#1| (-899 (-576)))) ((-966 |#1| #0# #2#) . T) ((-926) |has| |#1| (-926)) ((-937) |has| |#1| (-374)) ((-1057 (-419 (-576))) |has| |#1| (-1057 (-419 (-576)))) ((-1057 (-576)) |has| |#1| (-1057 (-576))) ((-1057 #2#) . T) ((-1057 |#1|) . T) ((-1070 #1#) |has| |#1| (-38 (-419 (-576)))) ((-1070 |#1|) . T) ((-1070 $) -2781 (|has| |#1| (-926)) (|has| |#1| (-568)) (|has| |#1| (-464)) (|has| |#1| (-374)) (|has| |#1| (-174))) ((-1075 #1#) |has| |#1| (-38 (-419 (-576)))) ((-1075 |#1|) . T) ((-1075 $) -2781 (|has| |#1| (-926)) (|has| |#1| (-568)) (|has| |#1| (-464)) (|has| |#1| (-374)) (|has| |#1| (-174))) ((-1068) . T) ((-1077) . T) ((-1131) . T) ((-1119) . T) ((-1171) |has| |#1| (-1171)) ((-1236) . T) ((-1240) |has| |#1| (-926))) -((-1934 (((-656 (-1101)) $) 34)) (-2105 (($ $) 31)) (-1915 (($ |#2| |#3|) NIL) (($ $ (-1101) |#3|) 28) (($ $ (-656 (-1101)) (-656 |#3|)) 27)) (-2069 (($ $) 14)) (-2080 ((|#2| $) 12)) (-3972 ((|#3| $) 10))) -(((-1263 |#1| |#2| |#3|) (-10 -8 (-15 -1934 ((-656 (-1101)) |#1|)) (-15 -1915 (|#1| |#1| (-656 (-1101)) (-656 |#3|))) (-15 -1915 (|#1| |#1| (-1101) |#3|)) (-15 -2105 (|#1| |#1|)) (-15 -1915 (|#1| |#2| |#3|)) (-15 -3972 (|#3| |#1|)) (-15 -2069 (|#1| |#1|)) (-15 -2080 (|#2| |#1|))) (-1264 |#2| |#3|) (-1068) (-804)) (T -1263)) -NIL -(-10 -8 (-15 -1934 ((-656 (-1101)) |#1|)) (-15 -1915 (|#1| |#1| (-656 (-1101)) (-656 |#3|))) (-15 -1915 (|#1| |#1| (-1101) |#3|)) (-15 -2105 (|#1| |#1|)) (-15 -1915 (|#1| |#2| |#3|)) (-15 -3972 (|#3| |#1|)) (-15 -2069 (|#1| |#1|)) (-15 -2080 (|#2| |#1|))) -((-3488 (((-112) $ $) 6)) (-4385 (((-112) $) 17)) (-1934 (((-656 (-1101)) $) 86)) (-3015 (((-1195) $) 118)) (-2662 (((-2 (|:| -2523 $) (|:| -4449 $) (|:| |associate| $)) 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(-576))))))) +(-13 (-966 |t#1| (-783) (-1101)) (-296 |t#1| |t#1|) (-296 $ $) (-238) (-232 |t#1|) (-10 -8 (-15 -3718 ((-1286 |t#1|) $ (-783))) (-15 -2646 ((-1191 |t#1|) $)) (-15 -3284 ($ (-1191 |t#1|))) (-15 -2968 ($ $ (-783))) (-15 -2945 ((-3 $ "failed") $ (-783))) (-15 -2659 ((-2 (|:| -3405 $) (|:| -2503 $)) $ $)) (-15 -3624 ((-2 (|:| -3405 $) (|:| -2503 $)) $ (-783))) (-15 -3477 ($ $ (-783))) (-15 -2316 ($ $ (-783))) (-15 -1699 ($ $ $)) (-15 -2770 ($ $ (-1 |t#1| |t#1|) $)) (IF (|has| |t#1| (-1171)) (-6 (-1171)) |%noBranch|) (IF (|has| |t#1| (-174)) (PROGN (-15 -3470 (|t#1| $)) (-15 -3019 (|t#1| $ $))) |%noBranch|) (IF (|has| |t#1| (-568)) (PROGN (-6 (-296 (-419 $) (-419 $))) (-15 -2794 ((-419 $) (-419 $) (-419 $))) (-15 -2996 ((-783) $ $)) (-15 -3697 ($ $ $)) (-15 -3317 ((-3 $ "failed") $ $)) (-15 -3317 ((-3 (-419 $) "failed") (-419 $) $)) (-15 -2425 ($ $ $)) (-15 -1671 ((-2 (|:| -1713 |t#1|) (|:| -3405 $) (|:| -2503 $)) $ $))) |%noBranch|) (IF (|has| |t#1| (-464)) (-15 -3120 ((-2 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T) ((-23) . T) ((-47 |#1| #0=(-783)) . T) ((-25) . T) ((-38 #1=(-419 (-576))) |has| |#1| (-38 (-419 (-576)))) ((-38 |#1|) |has| |#1| (-174)) ((-38 $) -2755 (|has| |#1| (-926)) (|has| |#1| (-568)) (|has| |#1| (-464)) (|has| |#1| (-374))) ((-102) . T) ((-111 #1# #1#) |has| |#1| (-38 (-419 (-576)))) ((-111 |#1| |#1|) . T) ((-111 $ $) -2755 (|has| |#1| (-926)) (|has| |#1| (-568)) (|has| |#1| (-464)) (|has| |#1| (-374)) (|has| |#1| (-174))) ((-132) . T) ((-146) |has| |#1| (-146)) ((-148) |has| |#1| (-148)) ((-628 #1#) -2755 (|has| |#1| (-1057 (-419 (-576)))) (|has| |#1| (-38 (-419 (-576))))) ((-628 (-576)) . T) ((-628 #2=(-1101)) . T) ((-628 |#1|) . T) ((-628 $) -2755 (|has| |#1| (-926)) (|has| |#1| (-568)) (|has| |#1| (-464)) (|has| |#1| (-374))) ((-625 (-874)) . T) ((-174) -2755 (|has| |#1| (-926)) (|has| |#1| (-568)) (|has| |#1| (-464)) (|has| |#1| (-374)) (|has| |#1| (-174))) ((-626 (-548)) -12 (|has| (-1101) (-626 (-548))) (|has| |#1| (-626 (-548)))) ((-626 (-905 (-390))) -12 (|has| (-1101) (-626 (-905 (-390)))) (|has| |#1| (-626 (-905 (-390))))) ((-626 (-905 (-576))) -12 (|has| (-1101) (-626 (-905 (-576)))) (|has| |#1| (-626 (-905 (-576))))) ((-234 $) . T) ((-232 |#1|) . T) ((-238) . T) ((-237) . T) ((-272 |#1|) . T) ((-296 (-419 $) (-419 $)) |has| |#1| (-568)) ((-296 |#1| |#1|) . T) ((-296 $ $) . T) ((-300) -2755 (|has| |#1| (-926)) (|has| |#1| (-568)) (|has| |#1| (-464)) (|has| |#1| (-374))) ((-317) |has| |#1| (-374)) ((-319 $) . T) ((-336 |#1| #0#) . T) ((-388 |#1|) . T) ((-423 |#1|) . T) ((-464) -2755 (|has| |#1| (-926)) (|has| |#1| (-464)) (|has| |#1| (-374))) ((-526 #2# |#1|) . T) ((-526 #2# $) . T) ((-526 $ $) . T) ((-568) -2755 (|has| |#1| (-926)) (|has| |#1| (-568)) (|has| |#1| (-464)) (|has| |#1| (-374))) ((-658 #1#) |has| |#1| (-38 (-419 (-576)))) ((-658 (-576)) . T) ((-658 |#1|) . T) ((-658 $) . T) ((-660 #1#) |has| |#1| (-38 (-419 (-576)))) ((-660 #3=(-576)) |has| |#1| (-651 (-576))) ((-660 |#1|) . T) ((-660 $) . T) ((-652 #1#) |has| |#1| (-38 (-419 (-576)))) ((-652 |#1|) |has| |#1| (-174)) ((-652 $) -2755 (|has| |#1| (-926)) (|has| |#1| (-568)) (|has| |#1| (-464)) (|has| |#1| (-374))) ((-651 #3#) |has| |#1| (-651 (-576))) ((-651 |#1|) . T) ((-729 #1#) |has| |#1| (-38 (-419 (-576)))) ((-729 |#1|) |has| |#1| (-174)) ((-729 $) -2755 (|has| |#1| (-926)) (|has| |#1| (-568)) (|has| |#1| (-464)) (|has| |#1| (-374))) ((-738) . T) ((-909 $ #2#) . T) ((-909 $ #4=(-1195)) -2755 (|has| |#1| (-917 (-1195))) (|has| |#1| (-915 (-1195)))) ((-915 #2#) . T) ((-915 (-1195)) |has| |#1| (-915 (-1195))) ((-917 #2#) . 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T) ((-652 #1#) -2781 (|has| |#1| (-374)) (|has| |#1| (-38 (-419 (-576))))) ((-652 |#1|) |has| |#1| (-174)) ((-652 $) -2781 (|has| |#1| (-568)) (|has| |#1| (-374))) ((-729 #1#) -2781 (|has| |#1| (-374)) (|has| |#1| (-38 (-419 (-576))))) ((-729 |#1|) |has| |#1| (-174)) ((-729 $) -2781 (|has| |#1| (-568)) (|has| |#1| (-374))) ((-738) . T) ((-909 $ #2=(-1195)) -12 (|has| |#1| (-15 * (|#1| (-419 (-576)) |#1|))) (|has| |#1| (-915 (-1195)))) ((-915 #2#) -12 (|has| |#1| (-15 * (|#1| (-419 (-576)) |#1|))) (|has| |#1| (-915 (-1195)))) ((-917 #2#) -12 (|has| |#1| (-15 * (|#1| (-419 (-576)) |#1|))) (|has| |#1| (-915 (-1195)))) ((-992 |#1| #0# (-1101)) . T) ((-937) |has| |#1| (-374)) ((-1021) |has| |#1| (-38 (-419 (-576)))) ((-1057 |#2|) . T) ((-1070 #1#) -2781 (|has| |#1| (-374)) (|has| |#1| (-38 (-419 (-576))))) ((-1070 |#1|) . T) ((-1070 $) -2781 (|has| |#1| (-568)) (|has| |#1| (-374)) (|has| |#1| (-174))) ((-1075 #1#) -2781 (|has| |#1| (-374)) (|has| |#1| (-38 (-419 (-576))))) ((-1075 |#1|) . 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T) ((-23) . T) ((-47 |#1| #0=(-783)) . T) ((-25) . T) ((-38 #1=(-419 (-576))) |has| |#1| (-38 (-419 (-576)))) ((-38 |#1|) |has| |#1| (-174)) ((-38 $) |has| |#1| (-568)) ((-35) |has| |#1| (-38 (-419 (-576)))) ((-95) |has| |#1| (-38 (-419 (-576)))) ((-102) . T) ((-111 #1# #1#) |has| |#1| (-38 (-419 (-576)))) ((-111 |#1| |#1|) . T) ((-111 $ $) -2781 (|has| |#1| (-568)) (|has| |#1| (-174))) ((-132) . T) ((-146) |has| |#1| (-146)) ((-148) |has| |#1| (-148)) ((-628 #1#) |has| |#1| (-38 (-419 (-576)))) ((-628 (-576)) . T) ((-628 |#1|) |has| |#1| (-174)) ((-628 $) |has| |#1| (-568)) ((-625 (-874)) . T) ((-174) -2781 (|has| |#1| (-568)) (|has| |#1| (-174))) ((-234 $) |has| |#1| (-15 * (|#1| (-783) |#1|))) ((-238) |has| |#1| (-15 * (|#1| (-783) |#1|))) ((-237) |has| |#1| (-15 * (|#1| (-783) |#1|))) ((-294) |has| |#1| (-38 (-419 (-576)))) ((-296 #0# |#1|) . 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NIL NIL NIL) (-1301 3220118 3221859 3221955 "XDPOLY" 3221960 NIL XDPOLY (NIL T T) -8 NIL NIL NIL) (-1300 3218911 3219511 3219554 "XALG" 3219559 NIL XALG (NIL T) -9 NIL 3219670 NIL) (-1299 3212353 3216888 3217382 "WUTSET" 3218503 NIL WUTSET (NIL T T T T) -8 NIL NIL NIL) (-1298 3210609 3211405 3211728 "WP" 3212164 NIL WP (NIL T T T T NIL NIL NIL) -8 NIL NIL NIL) (-1297 3210211 3210431 3210501 "WHILEAST" 3210561 T WHILEAST (NIL) -8 NIL NIL NIL) (-1296 3209683 3209928 3210022 "WHEREAST" 3210139 T WHEREAST (NIL) -8 NIL NIL NIL) (-1295 3208569 3208767 3209062 "WFFINTBS" 3209480 NIL WFFINTBS (NIL T T T T) -7 NIL NIL NIL) (-1294 3206473 3206900 3207362 "WEIER" 3208141 NIL WEIER (NIL T) -7 NIL NIL NIL) (-1293 3205505 3205955 3205997 "VSPACE" 3206133 NIL VSPACE (NIL T) -9 NIL 3206207 NIL) (-1292 3205343 3205370 3205461 "VSPACE-" 3205466 NIL VSPACE- (NIL T T) -8 NIL NIL NIL) (-1291 3205152 3205194 3205262 "VOID" 3205297 T VOID (NIL) -8 NIL NIL NIL) (-1290 3203288 3203647 3204053 "VIEW" 3204768 T VIEW (NIL) -7 NIL NIL NIL) (-1289 3199712 3200351 3201088 "VIEWDEF" 3202573 T VIEWDEF (NIL) -7 NIL NIL NIL) (-1288 3189016 3191260 3193433 "VIEW3D" 3197561 T VIEW3D (NIL) -8 NIL NIL NIL) (-1287 3181267 3182927 3184506 "VIEW2D" 3187459 T VIEW2D (NIL) -8 NIL NIL NIL) (-1286 3176622 3181037 3181129 "VECTOR" 3181210 NIL VECTOR (NIL T) -8 NIL NIL NIL) (-1285 3175199 3175458 3175776 "VECTOR2" 3176352 NIL VECTOR2 (NIL T T) -7 NIL NIL NIL) (-1284 3168623 3172930 3172973 "VECTCAT" 3173968 NIL VECTCAT (NIL T) -9 NIL 3174555 NIL) (-1283 3167637 3167891 3168281 "VECTCAT-" 3168286 NIL VECTCAT- (NIL T T) -8 NIL NIL NIL) (-1282 3167091 3167288 3167408 "VARIABLE" 3167552 NIL VARIABLE (NIL NIL) -8 NIL NIL NIL) (-1281 3167024 3167029 3167059 "UTYPE" 3167064 T UTYPE (NIL) -9 NIL NIL NIL) (-1280 3165854 3166008 3166270 "UTSODETL" 3166850 NIL UTSODETL (NIL T T T T) -7 NIL NIL NIL) (-1279 3163294 3163754 3164278 "UTSODE" 3165395 NIL UTSODE (NIL T T) -7 NIL NIL NIL) (-1278 3155242 3161055 3161535 "UTS" 3162872 NIL UTS (NIL T NIL NIL) -8 NIL NIL NIL) (-1277 3145806 3151176 3151219 "UTSCAT" 3152331 NIL UTSCAT (NIL T) -9 NIL 3153089 NIL) (-1276 3143154 3143876 3144865 "UTSCAT-" 3144870 NIL UTSCAT- (NIL T T) -8 NIL NIL NIL) (-1275 3142781 3142824 3142957 "UTS2" 3143105 NIL UTS2 (NIL T T T T) -7 NIL NIL NIL) (-1274 3136981 3139591 3139634 "URAGG" 3141704 NIL URAGG (NIL T) -9 NIL 3142427 NIL) (-1273 3133920 3134783 3135906 "URAGG-" 3135911 NIL URAGG- (NIL T T) -8 NIL NIL NIL) (-1272 3129629 3132555 3133020 "UPXSSING" 3133584 NIL UPXSSING (NIL T T NIL NIL) -8 NIL NIL NIL) (-1271 3121805 3129011 3129275 "UPXS" 3129423 NIL UPXS (NIL T NIL NIL) -8 NIL NIL NIL) (-1270 3114878 3121709 3121781 "UPXSCONS" 3121786 NIL UPXSCONS (NIL T T) -8 NIL NIL NIL) (-1269 3104285 3111081 3111143 "UPXSCCA" 3111717 NIL UPXSCCA (NIL T T) -9 NIL 3111950 NIL) (-1268 3103923 3104008 3104182 "UPXSCCA-" 3104187 NIL UPXSCCA- (NIL T T T) -8 NIL NIL NIL) (-1267 3093182 3099751 3099794 "UPXSCAT" 3100442 NIL UPXSCAT (NIL T) -9 NIL 3101051 NIL) (-1266 3092612 3092691 3092870 "UPXS2" 3093097 NIL UPXS2 (NIL T T NIL NIL NIL NIL) -7 NIL NIL NIL) (-1265 3091266 3091519 3091870 "UPSQFREE" 3092355 NIL UPSQFREE (NIL T T) -7 NIL NIL NIL) (-1264 3084474 3087534 3087589 "UPSCAT" 3088669 NIL UPSCAT (NIL T T) -9 NIL 3089434 NIL) (-1263 3083678 3083885 3084212 "UPSCAT-" 3084217 NIL UPSCAT- (NIL T T T) -8 NIL NIL NIL) (-1262 3068760 3076805 3076848 "UPOLYC" 3078949 NIL UPOLYC (NIL T) -9 NIL 3080170 NIL) (-1261 3060088 3062514 3065661 "UPOLYC-" 3065666 NIL UPOLYC- (NIL T T) -8 NIL NIL NIL) (-1260 3059715 3059758 3059891 "UPOLYC2" 3060039 NIL UPOLYC2 (NIL T T T T) -7 NIL NIL NIL) (-1259 3051250 3059398 3059527 "UP" 3059634 NIL UP (NIL NIL T) -8 NIL NIL NIL) (-1258 3050589 3050696 3050860 "UPMP" 3051139 NIL UPMP (NIL T T) -7 NIL NIL NIL) (-1257 3050142 3050223 3050362 "UPDIVP" 3050502 NIL UPDIVP (NIL T T) -7 NIL NIL NIL) (-1256 3048710 3048959 3049275 "UPDECOMP" 3049891 NIL UPDECOMP (NIL T T) -7 NIL NIL NIL) (-1255 3047941 3048053 3048239 "UPCDEN" 3048594 NIL UPCDEN (NIL T T T) -7 NIL NIL NIL) (-1254 3047460 3047529 3047678 "UP2" 3047866 NIL UP2 (NIL NIL T NIL T) -7 NIL NIL NIL) (-1253 3045927 3046664 3046941 "UNISEG" 3047218 NIL UNISEG (NIL T) -8 NIL NIL NIL) (-1252 3045142 3045269 3045474 "UNISEG2" 3045770 NIL UNISEG2 (NIL T T) -7 NIL NIL NIL) (-1251 3044202 3044382 3044608 "UNIFACT" 3044958 NIL UNIFACT (NIL T) -7 NIL NIL NIL) (-1250 3026954 3043514 3043756 "ULS" 3044018 NIL ULS (NIL T NIL NIL) -8 NIL NIL NIL) (-1249 3014584 3026858 3026930 "ULSCONS" 3026935 NIL ULSCONS (NIL T T) -8 NIL NIL NIL) (-1248 2995412 3007772 3007834 "ULSCCAT" 3008472 NIL ULSCCAT (NIL T T) -9 NIL 3008761 NIL) (-1247 2994462 2994707 2995095 "ULSCCAT-" 2995100 NIL ULSCCAT- (NIL T T T) -8 NIL NIL NIL) (-1246 2983526 2990009 2990052 "ULSCAT" 2990915 NIL ULSCAT (NIL T) -9 NIL 2991646 NIL) (-1245 2982956 2983035 2983214 "ULS2" 2983441 NIL ULS2 (NIL T T NIL NIL NIL NIL) -7 NIL NIL NIL) (-1244 2982075 2982585 2982692 "UINT8" 2982803 T UINT8 (NIL) -8 NIL NIL 2982888) (-1243 2981193 2981703 2981810 "UINT64" 2981921 T UINT64 (NIL) -8 NIL NIL 2982006) (-1242 2980311 2980821 2980928 "UINT32" 2981039 T UINT32 (NIL) -8 NIL NIL 2981124) (-1241 2979429 2979939 2980046 "UINT16" 2980157 T UINT16 (NIL) -8 NIL NIL 2980242) (-1240 2977718 2978675 2978705 "UFD" 2978917 T UFD (NIL) -9 NIL 2979031 NIL) (-1239 2977512 2977558 2977653 "UFD-" 2977658 NIL UFD- (NIL T) -8 NIL NIL NIL) (-1238 2976594 2976777 2976993 "UDVO" 2977318 T UDVO (NIL) -7 NIL NIL NIL) (-1237 2974410 2974819 2975290 "UDPO" 2976158 NIL UDPO (NIL T) -7 NIL NIL NIL) (-1236 2974343 2974348 2974378 "TYPE" 2974383 T TYPE (NIL) -9 NIL NIL NIL) (-1235 2974103 2974298 2974329 "TYPEAST" 2974334 T TYPEAST (NIL) -8 NIL NIL NIL) (-1234 2973074 2973276 2973516 "TWOFACT" 2973897 NIL TWOFACT (NIL T) -7 NIL NIL NIL) (-1233 2972097 2972483 2972718 "TUPLE" 2972874 NIL TUPLE (NIL T) -8 NIL NIL NIL) (-1232 2969788 2970307 2970846 "TUBETOOL" 2971580 T TUBETOOL (NIL) -7 NIL NIL NIL) (-1231 2968637 2968842 2969083 "TUBE" 2969581 NIL TUBE (NIL T) -8 NIL NIL NIL) (-1230 2963366 2967609 2967892 "TS" 2968389 NIL TS (NIL T) -8 NIL NIL NIL) (-1229 2952006 2956125 2956222 "TSETCAT" 2961491 NIL TSETCAT (NIL T T T T) -9 NIL 2963022 NIL) (-1228 2946738 2948338 2950229 "TSETCAT-" 2950234 NIL TSETCAT- (NIL T T T T T) -8 NIL NIL NIL) (-1227 2941377 2942224 2943153 "TRMANIP" 2945874 NIL TRMANIP (NIL T T) -7 NIL NIL NIL) (-1226 2940818 2940881 2941044 "TRIMAT" 2941309 NIL TRIMAT (NIL T T T T) -7 NIL NIL NIL) (-1225 2938684 2938921 2939278 "TRIGMNIP" 2940567 NIL TRIGMNIP (NIL T T) -7 NIL NIL NIL) (-1224 2938204 2938317 2938347 "TRIGCAT" 2938560 T TRIGCAT (NIL) -9 NIL NIL NIL) (-1223 2937873 2937952 2938093 "TRIGCAT-" 2938098 NIL TRIGCAT- (NIL T) -8 NIL NIL NIL) (-1222 2934720 2936731 2937012 "TREE" 2937627 NIL TREE (NIL T) -8 NIL NIL NIL) (-1221 2933994 2934522 2934552 "TRANFUN" 2934587 T TRANFUN (NIL) -9 NIL 2934653 NIL) (-1220 2933273 2933464 2933744 "TRANFUN-" 2933749 NIL TRANFUN- (NIL T) -8 NIL NIL NIL) (-1219 2933077 2933109 2933170 "TOPSP" 2933234 T TOPSP (NIL) -7 NIL NIL NIL) (-1218 2932425 2932540 2932694 "TOOLSIGN" 2932958 NIL TOOLSIGN (NIL T) -7 NIL NIL NIL) (-1217 2931059 2931602 2931841 "TEXTFILE" 2932208 T TEXTFILE (NIL) -8 NIL NIL NIL) (-1216 2928971 2929512 2929941 "TEX" 2930652 T TEX (NIL) -8 NIL NIL NIL) (-1215 2928752 2928783 2928855 "TEX1" 2928934 NIL TEX1 (NIL T) -7 NIL NIL NIL) (-1214 2928400 2928463 2928553 "TEMUTL" 2928684 T TEMUTL (NIL) -7 NIL NIL NIL) (-1213 2926554 2926834 2927159 "TBCMPPK" 2928123 NIL TBCMPPK (NIL T T) -7 NIL NIL NIL) (-1212 2918261 2924640 2924696 "TBAGG" 2925096 NIL TBAGG (NIL T T) -9 NIL 2925307 NIL) (-1211 2913331 2914819 2916573 "TBAGG-" 2916578 NIL TBAGG- (NIL T T T) -8 NIL NIL NIL) (-1210 2912715 2912822 2912967 "TANEXP" 2913220 NIL TANEXP (NIL T) -7 NIL NIL NIL) (-1209 2912226 2912490 2912580 "TALGOP" 2912660 NIL TALGOP (NIL T) -8 NIL NIL NIL) (-1208 2905620 2912083 2912176 "TABLE" 2912181 NIL TABLE (NIL T T) -8 NIL NIL NIL) (-1207 2905032 2905131 2905269 "TABLEAU" 2905517 NIL TABLEAU (NIL T) -8 NIL NIL NIL) (-1206 2899640 2900860 2902108 "TABLBUMP" 2903818 NIL TABLBUMP (NIL T) -7 NIL NIL NIL) (-1205 2898862 2899009 2899190 "SYSTEM" 2899481 T SYSTEM (NIL) -8 NIL NIL NIL) (-1204 2895321 2896020 2896803 "SYSSOLP" 2898113 NIL SYSSOLP (NIL T) -7 NIL NIL NIL) (-1203 2895119 2895276 2895307 "SYSPTR" 2895312 T SYSPTR (NIL) -8 NIL NIL NIL) (-1202 2894155 2894660 2894779 "SYSNNI" 2894965 NIL SYSNNI (NIL NIL) -8 NIL NIL 2895050) (-1201 2893454 2893913 2893992 "SYSINT" 2894052 NIL SYSINT (NIL NIL) -8 NIL NIL 2894097) (-1200 2889786 2890732 2891442 "SYNTAX" 2892766 T SYNTAX (NIL) -8 NIL NIL NIL) (-1199 2886944 2887546 2888178 "SYMTAB" 2889176 T SYMTAB (NIL) -8 NIL NIL NIL) (-1198 2882193 2883095 2884078 "SYMS" 2885983 T SYMS (NIL) -8 NIL NIL NIL) (-1197 2879428 2881651 2881881 "SYMPOLY" 2881998 NIL SYMPOLY (NIL T) -8 NIL NIL NIL) (-1196 2878945 2879020 2879143 "SYMFUNC" 2879340 NIL SYMFUNC (NIL T) -7 NIL NIL NIL) (-1195 2874965 2876257 2877070 "SYMBOL" 2878154 T SYMBOL (NIL) -8 NIL NIL NIL) (-1194 2868504 2870193 2871913 "SWITCH" 2873267 T SWITCH (NIL) -8 NIL NIL NIL) (-1193 2861848 2867460 2867754 "SUTS" 2868268 NIL SUTS (NIL T NIL NIL) -8 NIL NIL NIL) (-1192 2854024 2861230 2861494 "SUPXS" 2861642 NIL SUPXS (NIL T NIL NIL) -8 NIL NIL NIL) (-1191 2845507 2853642 2853768 "SUP" 2853933 NIL SUP (NIL T) -8 NIL NIL NIL) (-1190 2844666 2844793 2845010 "SUPFRACF" 2845375 NIL SUPFRACF (NIL T T T T) -7 NIL NIL NIL) (-1189 2844287 2844346 2844459 "SUP2" 2844601 NIL SUP2 (NIL T T) -7 NIL NIL NIL) (-1188 2842735 2843009 2843365 "SUMRF" 2843986 NIL SUMRF (NIL T) -7 NIL NIL NIL) (-1187 2842070 2842136 2842328 "SUMFS" 2842656 NIL SUMFS (NIL T T) -7 NIL NIL NIL) (-1186 2824857 2841382 2841624 "SULS" 2841886 NIL SULS (NIL T NIL NIL) -8 NIL NIL NIL) (-1185 2824459 2824679 2824749 "SUCHTAST" 2824809 T SUCHTAST (NIL) -8 NIL NIL NIL) (-1184 2823754 2823984 2824124 "SUCH" 2824367 NIL SUCH (NIL T T) -8 NIL NIL NIL) (-1183 2817621 2818660 2819619 "SUBSPACE" 2822842 NIL SUBSPACE (NIL NIL T) -8 NIL NIL NIL) (-1182 2817051 2817141 2817305 "SUBRESP" 2817509 NIL SUBRESP (NIL T T) -7 NIL NIL NIL) (-1181 2810419 2811716 2813027 "STTF" 2815787 NIL STTF (NIL T) -7 NIL NIL NIL) (-1180 2804592 2805712 2806859 "STTFNC" 2809319 NIL STTFNC (NIL T) -7 NIL NIL NIL) (-1179 2795905 2797774 2799568 "STTAYLOR" 2802833 NIL STTAYLOR (NIL T) -7 NIL NIL NIL) (-1178 2789039 2795769 2795852 "STRTBL" 2795857 NIL STRTBL (NIL T) -8 NIL NIL NIL) (-1177 2783999 2788748 2788847 "STRING" 2788962 T STRING (NIL) -8 NIL NIL NIL) (-1176 2776754 2781618 2782229 "STREAM" 2783423 NIL STREAM (NIL T) -8 NIL NIL NIL) (-1175 2776264 2776341 2776485 "STREAM3" 2776671 NIL STREAM3 (NIL T T T) -7 NIL NIL NIL) (-1174 2775246 2775429 2775664 "STREAM2" 2776077 NIL STREAM2 (NIL T T) -7 NIL NIL NIL) (-1173 2774934 2774986 2775079 "STREAM1" 2775188 NIL STREAM1 (NIL T) -7 NIL NIL NIL) (-1172 2773950 2774131 2774362 "STINPROD" 2774750 NIL STINPROD (NIL T) -7 NIL NIL NIL) (-1171 2773488 2773698 2773728 "STEP" 2773808 T STEP (NIL) -9 NIL 2773886 NIL) (-1170 2772675 2772977 2773125 "STEPAST" 2773362 T STEPAST (NIL) -8 NIL NIL NIL) (-1169 2766111 2772574 2772651 "STBL" 2772656 NIL STBL (NIL T T NIL) -8 NIL NIL NIL) (-1168 2761180 2765274 2765317 "STAGG" 2765470 NIL STAGG (NIL T) -9 NIL 2765559 NIL) (-1167 2758882 2759484 2760356 "STAGG-" 2760361 NIL STAGG- (NIL T T) -8 NIL NIL NIL) (-1166 2757031 2758652 2758744 "STACK" 2758825 NIL STACK (NIL T) -8 NIL NIL NIL) (-1165 2749726 2755172 2755628 "SREGSET" 2756661 NIL SREGSET (NIL T T T T) -8 NIL NIL NIL) (-1164 2742151 2743520 2745033 "SRDCMPK" 2748332 NIL SRDCMPK (NIL T T T T T) -7 NIL NIL NIL) (-1163 2735016 2739539 2739569 "SRAGG" 2740872 T SRAGG (NIL) -9 NIL 2741480 NIL) (-1162 2734033 2734288 2734667 "SRAGG-" 2734672 NIL SRAGG- (NIL T) -8 NIL NIL NIL) (-1161 2728217 2732980 2733401 "SQMATRIX" 2733659 NIL SQMATRIX (NIL NIL T) -8 NIL NIL NIL) (-1160 2721904 2724935 2725662 "SPLTREE" 2727562 NIL SPLTREE (NIL T T) -8 NIL NIL NIL) (-1159 2717867 2718560 2719206 "SPLNODE" 2721330 NIL SPLNODE (NIL T T) -8 NIL NIL NIL) (-1158 2716914 2717147 2717177 "SPFCAT" 2717621 T SPFCAT (NIL) -9 NIL NIL NIL) (-1157 2715651 2715861 2716125 "SPECOUT" 2716672 T SPECOUT (NIL) -7 NIL NIL NIL) (-1156 2706747 2708619 2708649 "SPADXPT" 2713325 T SPADXPT (NIL) -9 NIL 2715489 NIL) (-1155 2706508 2706548 2706617 "SPADPRSR" 2706700 T SPADPRSR (NIL) -7 NIL NIL NIL) (-1154 2704557 2706463 2706494 "SPADAST" 2706499 T SPADAST (NIL) -8 NIL NIL NIL) (-1153 2696488 2698261 2698304 "SPACEC" 2702677 NIL SPACEC (NIL T) -9 NIL 2704493 NIL) (-1152 2694618 2696420 2696469 "SPACE3" 2696474 NIL SPACE3 (NIL T) -8 NIL NIL NIL) (-1151 2693370 2693541 2693832 "SORTPAK" 2694423 NIL SORTPAK (NIL T T) -7 NIL NIL NIL) (-1150 2691462 2691765 2692177 "SOLVETRA" 2693034 NIL SOLVETRA (NIL T) -7 NIL NIL NIL) (-1149 2690512 2690734 2690995 "SOLVESER" 2691235 NIL SOLVESER (NIL T) -7 NIL NIL NIL) (-1148 2685816 2686704 2687699 "SOLVERAD" 2689564 NIL SOLVERAD (NIL T) -7 NIL NIL NIL) (-1147 2681631 2682240 2682969 "SOLVEFOR" 2685183 NIL SOLVEFOR (NIL T T) -7 NIL NIL NIL) (-1146 2675901 2680980 2681077 "SNTSCAT" 2681082 NIL SNTSCAT (NIL T T T T) -9 NIL 2681152 NIL) (-1145 2670007 2674224 2674615 "SMTS" 2675591 NIL SMTS (NIL T T T) -8 NIL NIL NIL) (-1144 2664416 2669895 2669972 "SMP" 2669977 NIL SMP (NIL T T) -8 NIL NIL NIL) (-1143 2662575 2662876 2663274 "SMITH" 2664113 NIL SMITH (NIL T T T T) -7 NIL NIL NIL) (-1142 2654679 2659154 2659257 "SMATCAT" 2660608 NIL SMATCAT (NIL NIL T T T) -9 NIL 2661158 NIL) (-1141 2651619 2652442 2653620 "SMATCAT-" 2653625 NIL SMATCAT- (NIL T NIL T T T) -8 NIL NIL NIL) (-1140 2649259 2650827 2650870 "SKAGG" 2651131 NIL SKAGG (NIL T) -9 NIL 2651266 NIL) (-1139 2645449 2648732 2648916 "SINT" 2649068 T SINT (NIL) -8 NIL NIL 2649230) (-1138 2645221 2645259 2645325 "SIMPAN" 2645405 T SIMPAN (NIL) -7 NIL NIL NIL) (-1137 2644500 2644756 2644896 "SIG" 2645103 T SIG (NIL) -8 NIL NIL NIL) (-1136 2643338 2643559 2643834 "SIGNRF" 2644259 NIL SIGNRF (NIL T) -7 NIL NIL NIL) (-1135 2642171 2642322 2642606 "SIGNEF" 2643167 NIL SIGNEF (NIL T T) -7 NIL NIL NIL) (-1134 2641477 2641754 2641878 "SIGAST" 2642069 T SIGAST (NIL) -8 NIL NIL NIL) (-1133 2639167 2639621 2640127 "SHP" 2641018 NIL SHP (NIL T NIL) -7 NIL NIL NIL) (-1132 2632995 2639068 2639144 "SHDP" 2639149 NIL SHDP (NIL NIL NIL T) -8 NIL NIL NIL) (-1131 2632554 2632746 2632776 "SGROUP" 2632869 T SGROUP (NIL) -9 NIL 2632931 NIL) (-1130 2632412 2632438 2632511 "SGROUP-" 2632516 NIL SGROUP- (NIL T) -8 NIL NIL NIL) (-1129 2629203 2629901 2630624 "SGCF" 2631711 T SGCF (NIL) -7 NIL NIL NIL) (-1128 2623571 2628650 2628747 "SFRTCAT" 2628752 NIL SFRTCAT (NIL T T T T) -9 NIL 2628791 NIL) (-1127 2616992 2618010 2619146 "SFRGCD" 2622554 NIL SFRGCD (NIL T T T T T) -7 NIL NIL NIL) (-1126 2610118 2611191 2612377 "SFQCMPK" 2615925 NIL SFQCMPK (NIL T T T T T) -7 NIL NIL NIL) (-1125 2609738 2609827 2609938 "SFORT" 2610059 NIL SFORT (NIL T T) -8 NIL NIL NIL) (-1124 2608856 2609578 2609699 "SEXOF" 2609704 NIL SEXOF (NIL T T T T T) -8 NIL NIL NIL) (-1123 2607963 2608737 2608805 "SEX" 2608810 T SEX (NIL) -8 NIL NIL NIL) (-1122 2603744 2604459 2604554 "SEXCAT" 2607176 NIL SEXCAT (NIL T T T T T) -9 NIL 2607736 NIL) (-1121 2600897 2603678 2603726 "SET" 2603731 NIL SET (NIL T) -8 NIL NIL NIL) (-1120 2599121 2599610 2599915 "SETMN" 2600638 NIL SETMN (NIL NIL NIL) -8 NIL NIL NIL) (-1119 2598603 2598755 2598785 "SETCAT" 2598961 T SETCAT (NIL) -9 NIL 2599071 NIL) (-1118 2598295 2598373 2598503 "SETCAT-" 2598508 NIL SETCAT- (NIL T) -8 NIL NIL NIL) (-1117 2594656 2596756 2596799 "SETAGG" 2597669 NIL SETAGG (NIL T) -9 NIL 2598009 NIL) (-1116 2594114 2594230 2594467 "SETAGG-" 2594472 NIL SETAGG- (NIL T T) -8 NIL NIL NIL) (-1115 2593557 2593810 2593911 "SEQAST" 2594035 T SEQAST (NIL) -8 NIL NIL NIL) (-1114 2592756 2593050 2593111 "SEGXCAT" 2593397 NIL SEGXCAT (NIL T T) -9 NIL 2593517 NIL) (-1113 2591762 2592422 2592604 "SEG" 2592609 NIL SEG (NIL T) -8 NIL NIL NIL) (-1112 2590741 2590955 2590998 "SEGCAT" 2591520 NIL SEGCAT (NIL T) -9 NIL 2591741 NIL) (-1111 2589673 2590104 2590312 "SEGBIND" 2590568 NIL SEGBIND (NIL T) -8 NIL NIL NIL) (-1110 2589294 2589353 2589466 "SEGBIND2" 2589608 NIL SEGBIND2 (NIL T T) -7 NIL NIL NIL) (-1109 2588867 2589095 2589172 "SEGAST" 2589239 T SEGAST (NIL) -8 NIL NIL NIL) (-1108 2588086 2588212 2588416 "SEG2" 2588711 NIL SEG2 (NIL T T) -7 NIL NIL NIL) (-1107 2587457 2588021 2588068 "SDVAR" 2588073 NIL SDVAR (NIL T) -8 NIL NIL NIL) (-1106 2579708 2587227 2587357 "SDPOL" 2587362 NIL SDPOL (NIL T) -8 NIL NIL NIL) (-1105 2578301 2578567 2578886 "SCPKG" 2579423 NIL SCPKG (NIL T) -7 NIL NIL NIL) (-1104 2577465 2577637 2577829 "SCOPE" 2578131 T SCOPE (NIL) -8 NIL NIL NIL) (-1103 2576685 2576819 2576998 "SCACHE" 2577320 NIL SCACHE (NIL T) -7 NIL NIL NIL) (-1102 2576317 2576503 2576533 "SASTCAT" 2576538 T SASTCAT (NIL) -9 NIL 2576551 NIL) (-1101 2575804 2576152 2576228 "SAOS" 2576263 T SAOS (NIL) -8 NIL NIL NIL) (-1100 2575369 2575404 2575577 "SAERFFC" 2575763 NIL SAERFFC (NIL T T T) -7 NIL NIL NIL) (-1099 2569032 2575266 2575346 "SAE" 2575351 NIL SAE (NIL T T NIL) -8 NIL NIL NIL) (-1098 2568625 2568660 2568819 "SAEFACT" 2568991 NIL SAEFACT (NIL T T T) -7 NIL NIL NIL) (-1097 2566946 2567260 2567661 "RURPK" 2568291 NIL RURPK (NIL T NIL) -7 NIL NIL NIL) (-1096 2565583 2565889 2566194 "RULESET" 2566780 NIL RULESET (NIL T T T) -8 NIL NIL NIL) (-1095 2562806 2563336 2563794 "RULE" 2565264 NIL RULE (NIL T T T) -8 NIL NIL NIL) (-1094 2562418 2562600 2562683 "RULECOLD" 2562758 NIL RULECOLD (NIL NIL) -8 NIL NIL NIL) (-1093 2562208 2562236 2562307 "RTVALUE" 2562369 T RTVALUE (NIL) -8 NIL NIL NIL) (-1092 2561679 2561925 2562019 "RSTRCAST" 2562136 T RSTRCAST (NIL) -8 NIL NIL NIL) (-1091 2556527 2557322 2558242 "RSETGCD" 2560878 NIL RSETGCD (NIL T T T T T) -7 NIL NIL NIL) (-1090 2545757 2550836 2550933 "RSETCAT" 2555052 NIL RSETCAT (NIL T T T T) -9 NIL 2556149 NIL) (-1089 2543684 2544223 2545047 "RSETCAT-" 2545052 NIL RSETCAT- (NIL T T T T T) -8 NIL NIL NIL) (-1088 2536070 2537446 2538966 "RSDCMPK" 2542283 NIL RSDCMPK (NIL T T T T T) -7 NIL NIL NIL) (-1087 2534035 2534502 2534576 "RRCC" 2535662 NIL RRCC (NIL T T) -9 NIL 2536006 NIL) (-1086 2533386 2533560 2533839 "RRCC-" 2533844 NIL RRCC- (NIL T T T) -8 NIL NIL NIL) (-1085 2532829 2533082 2533183 "RPTAST" 2533307 T RPTAST (NIL) -8 NIL NIL NIL) (-1084 2506305 2515941 2516008 "RPOLCAT" 2526674 NIL RPOLCAT (NIL T T T) -9 NIL 2529834 NIL) (-1083 2497803 2500143 2503265 "RPOLCAT-" 2503270 NIL RPOLCAT- (NIL T T T T) -8 NIL NIL NIL) (-1082 2488738 2496014 2496496 "ROUTINE" 2497343 T ROUTINE (NIL) -8 NIL NIL NIL) (-1081 2485399 2488364 2488504 "ROMAN" 2488620 T ROMAN (NIL) -8 NIL NIL NIL) (-1080 2483643 2484259 2484519 "ROIRC" 2485204 NIL ROIRC (NIL T T) -8 NIL NIL NIL) (-1079 2479861 2482145 2482175 "RNS" 2482479 T RNS (NIL) -9 NIL 2482753 NIL) (-1078 2478370 2478753 2479287 "RNS-" 2479362 NIL RNS- (NIL T) -8 NIL NIL NIL) (-1077 2477759 2478167 2478197 "RNG" 2478202 T RNG (NIL) -9 NIL 2478223 NIL) (-1076 2476762 2477124 2477326 "RNGBIND" 2477610 NIL RNGBIND (NIL T T) -8 NIL NIL NIL) (-1075 2476147 2476535 2476578 "RMODULE" 2476583 NIL RMODULE (NIL T) -9 NIL 2476610 NIL) (-1074 2474983 2475077 2475413 "RMCAT2" 2476048 NIL RMCAT2 (NIL NIL NIL T T T T T T T T) -7 NIL NIL NIL) (-1073 2471833 2474329 2474626 "RMATRIX" 2474745 NIL RMATRIX (NIL NIL NIL T) -8 NIL NIL NIL) (-1072 2464660 2466920 2467035 "RMATCAT" 2470394 NIL RMATCAT (NIL NIL NIL T T T) -9 NIL 2471376 NIL) (-1071 2464035 2464182 2464489 "RMATCAT-" 2464494 NIL RMATCAT- (NIL T NIL NIL T T T) -8 NIL NIL NIL) (-1070 2463650 2463822 2463865 "RLINSET" 2463927 NIL RLINSET (NIL T) -9 NIL 2463971 NIL) (-1069 2463217 2463292 2463420 "RINTERP" 2463569 NIL RINTERP (NIL NIL T) -7 NIL NIL NIL) (-1068 2462261 2462815 2462845 "RING" 2462901 T RING (NIL) -9 NIL 2462993 NIL) (-1067 2462053 2462097 2462194 "RING-" 2462199 NIL RING- (NIL T) -8 NIL NIL NIL) (-1066 2460894 2461131 2461389 "RIDIST" 2461817 T RIDIST (NIL) -7 NIL NIL NIL) (-1065 2452183 2460362 2460568 "RGCHAIN" 2460742 NIL RGCHAIN (NIL T NIL) -8 NIL NIL NIL) (-1064 2451519 2451925 2451966 "RGBCSPC" 2452024 NIL RGBCSPC (NIL T) -9 NIL 2452076 NIL) (-1063 2450663 2451044 2451085 "RGBCMDL" 2451317 NIL RGBCMDL (NIL T) -9 NIL 2451431 NIL) (-1062 2447657 2448271 2448941 "RF" 2450027 NIL RF (NIL T) -7 NIL NIL NIL) (-1061 2447303 2447366 2447469 "RFFACTOR" 2447588 NIL RFFACTOR (NIL T) -7 NIL NIL NIL) (-1060 2447028 2447063 2447160 "RFFACT" 2447262 NIL RFFACT (NIL T) -7 NIL NIL NIL) (-1059 2445145 2445509 2445891 "RFDIST" 2446668 T RFDIST (NIL) -7 NIL NIL NIL) (-1058 2444598 2444690 2444853 "RETSOL" 2445047 NIL RETSOL (NIL T T) -7 NIL NIL NIL) (-1057 2444234 2444314 2444357 "RETRACT" 2444490 NIL RETRACT (NIL T) -9 NIL 2444577 NIL) (-1056 2444083 2444108 2444195 "RETRACT-" 2444200 NIL RETRACT- (NIL T T) -8 NIL NIL NIL) (-1055 2443685 2443905 2443975 "RETAST" 2444035 T RETAST (NIL) -8 NIL NIL NIL) (-1054 2436427 2443338 2443465 "RESULT" 2443580 T RESULT (NIL) -8 NIL NIL NIL) (-1053 2435018 2435696 2435895 "RESRING" 2436330 NIL RESRING (NIL T T T T NIL) -8 NIL NIL NIL) (-1052 2434654 2434703 2434801 "RESLATC" 2434955 NIL RESLATC (NIL T) -7 NIL NIL NIL) (-1051 2434359 2434394 2434501 "REPSQ" 2434613 NIL REPSQ (NIL T) -7 NIL NIL NIL) (-1050 2431781 2432361 2432963 "REP" 2433779 T REP (NIL) -7 NIL NIL NIL) (-1049 2431478 2431513 2431624 "REPDB" 2431740 NIL REPDB (NIL T) -7 NIL NIL NIL) (-1048 2425378 2426767 2427990 "REP2" 2430290 NIL REP2 (NIL T) -7 NIL NIL NIL) (-1047 2421755 2422436 2423244 "REP1" 2424605 NIL REP1 (NIL T) -7 NIL NIL NIL) (-1046 2414451 2419896 2420352 "REGSET" 2421385 NIL REGSET (NIL T T T T) -8 NIL NIL NIL) (-1045 2413216 2413599 2413849 "REF" 2414236 NIL REF (NIL T) -8 NIL NIL NIL) (-1044 2412593 2412696 2412863 "REDORDER" 2413100 NIL REDORDER (NIL T T) -7 NIL NIL NIL) (-1043 2408561 2411806 2412033 "RECLOS" 2412421 NIL RECLOS (NIL T) -8 NIL NIL NIL) (-1042 2407613 2407794 2408009 "REALSOLV" 2408368 T REALSOLV (NIL) -7 NIL NIL NIL) (-1041 2407459 2407500 2407530 "REAL" 2407535 T REAL (NIL) -9 NIL 2407570 NIL) (-1040 2403942 2404744 2405628 "REAL0Q" 2406624 NIL REAL0Q (NIL T) -7 NIL NIL NIL) (-1039 2399543 2400531 2401592 "REAL0" 2402923 NIL REAL0 (NIL T) -7 NIL NIL NIL) (-1038 2399014 2399260 2399354 "RDUCEAST" 2399471 T RDUCEAST (NIL) -8 NIL NIL NIL) (-1037 2398419 2398491 2398698 "RDIV" 2398936 NIL RDIV (NIL T T T T T) -7 NIL NIL NIL) (-1036 2397487 2397661 2397874 "RDIST" 2398241 NIL RDIST (NIL T) -7 NIL NIL NIL) (-1035 2396084 2396371 2396743 "RDETRS" 2397195 NIL RDETRS (NIL T T) -7 NIL NIL NIL) (-1034 2393896 2394350 2394888 "RDETR" 2395626 NIL RDETR (NIL T T) -7 NIL NIL NIL) (-1033 2392521 2392799 2393196 "RDEEFS" 2393612 NIL RDEEFS (NIL T T) -7 NIL NIL NIL) (-1032 2391030 2391336 2391761 "RDEEF" 2392209 NIL RDEEF (NIL T T) -7 NIL NIL NIL) (-1031 2385077 2387997 2388027 "RCFIELD" 2389322 T RCFIELD (NIL) -9 NIL 2390053 NIL) (-1030 2383141 2383645 2384341 "RCFIELD-" 2384416 NIL RCFIELD- (NIL T) -8 NIL NIL NIL) (-1029 2379384 2381214 2381257 "RCAGG" 2382341 NIL RCAGG (NIL T) -9 NIL 2382806 NIL) (-1028 2379012 2379106 2379269 "RCAGG-" 2379274 NIL RCAGG- (NIL T T) -8 NIL NIL NIL) (-1027 2378347 2378459 2378624 "RATRET" 2378896 NIL RATRET (NIL T) -7 NIL NIL NIL) (-1026 2377900 2377967 2378088 "RATFACT" 2378275 NIL RATFACT (NIL T) -7 NIL NIL NIL) (-1025 2377208 2377328 2377480 "RANDSRC" 2377770 T RANDSRC (NIL) -7 NIL NIL NIL) (-1024 2376942 2376986 2377059 "RADUTIL" 2377157 T RADUTIL (NIL) -7 NIL NIL NIL) (-1023 2369770 2375773 2376084 "RADIX" 2376665 NIL RADIX (NIL NIL) -8 NIL NIL NIL) (-1022 2360230 2369612 2369742 "RADFF" 2369747 NIL RADFF (NIL T T T NIL NIL) -8 NIL NIL NIL) (-1021 2359877 2359952 2359982 "RADCAT" 2360142 T RADCAT (NIL) -9 NIL NIL NIL) (-1020 2359659 2359707 2359807 "RADCAT-" 2359812 NIL RADCAT- (NIL T) -8 NIL NIL NIL) (-1019 2357759 2359429 2359521 "QUEUE" 2359602 NIL QUEUE (NIL T) -8 NIL NIL NIL) (-1018 2354020 2357692 2357740 "QUAT" 2357745 NIL QUAT (NIL T) -8 NIL NIL NIL) (-1017 2353651 2353694 2353825 "QUATCT2" 2353971 NIL QUATCT2 (NIL T T T T) -7 NIL NIL NIL) (-1016 2346477 2350101 2350143 "QUATCAT" 2350934 NIL QUATCAT (NIL T) -9 NIL 2351700 NIL) (-1015 2342616 2343653 2345043 "QUATCAT-" 2345139 NIL QUATCAT- (NIL T T) -8 NIL NIL NIL) (-1014 2340055 2341664 2341707 "QUAGG" 2342088 NIL QUAGG (NIL T) -9 NIL 2342263 NIL) (-1013 2339657 2339877 2339947 "QQUTAST" 2340007 T QQUTAST (NIL) -8 NIL NIL NIL) (-1012 2338670 2339170 2339335 "QFORM" 2339538 NIL QFORM (NIL NIL T) -8 NIL NIL NIL) (-1011 2329057 2334572 2334614 "QFCAT" 2335282 NIL QFCAT (NIL T) -9 NIL 2336283 NIL) (-1010 2324624 2325825 2327419 "QFCAT-" 2327515 NIL QFCAT- (NIL T T) -8 NIL NIL NIL) (-1009 2324255 2324298 2324429 "QFCAT2" 2324575 NIL QFCAT2 (NIL T T T T) -7 NIL NIL NIL) (-1008 2323710 2323820 2323952 "QEQUAT" 2324145 T QEQUAT (NIL) -8 NIL NIL NIL) (-1007 2316836 2317909 2319095 "QCMPACK" 2322643 NIL QCMPACK (NIL T T T T T) -7 NIL NIL NIL) (-1006 2314374 2314822 2315252 "QALGSET" 2316491 NIL QALGSET (NIL T T T T) -8 NIL NIL NIL) (-1005 2313609 2313785 2314021 "QALGSET2" 2314192 NIL QALGSET2 (NIL NIL NIL) -7 NIL NIL NIL) (-1004 2312294 2312518 2312837 "PWFFINTB" 2313382 NIL PWFFINTB (NIL T T T T) -7 NIL NIL NIL) (-1003 2310469 2310637 2310993 "PUSHVAR" 2312108 NIL PUSHVAR (NIL T T T T) -7 NIL NIL NIL) (-1002 2306358 2307412 2307455 "PTRANFN" 2309366 NIL PTRANFN (NIL T) -9 NIL NIL NIL) (-1001 2304749 2305040 2305364 "PTPACK" 2306069 NIL PTPACK (NIL T) -7 NIL NIL NIL) (-1000 2304378 2304435 2304546 "PTFUNC2" 2304686 NIL PTFUNC2 (NIL T T) -7 NIL NIL NIL) (-999 2298805 2303200 2303241 "PTCAT" 2303537 NIL PTCAT (NIL T) -9 NIL 2303690 NIL) (-998 2298463 2298498 2298622 "PSQFR" 2298764 NIL PSQFR (NIL T T T T) -7 NIL NIL NIL) (-997 2297058 2297356 2297690 "PSEUDLIN" 2298161 NIL PSEUDLIN (NIL T) -7 NIL NIL NIL) (-996 2283821 2286192 2288516 "PSETPK" 2294818 NIL PSETPK (NIL T T T T) -7 NIL NIL NIL) (-995 2276839 2279579 2279675 "PSETCAT" 2282696 NIL PSETCAT (NIL T T T T) -9 NIL 2283510 NIL) (-994 2274675 2275309 2276130 "PSETCAT-" 2276135 NIL PSETCAT- (NIL T T T T T) -8 NIL NIL NIL) (-993 2274024 2274189 2274217 "PSCURVE" 2274485 T PSCURVE (NIL) -9 NIL 2274652 NIL) (-992 2270008 2271524 2271589 "PSCAT" 2272433 NIL PSCAT (NIL T T T) -9 NIL 2272673 NIL) (-991 2269071 2269287 2269687 "PSCAT-" 2269692 NIL PSCAT- (NIL T T T T) -8 NIL NIL NIL) (-990 2267430 2268140 2268403 "PRTITION" 2268828 T PRTITION (NIL) -8 NIL NIL NIL) (-989 2266905 2267151 2267243 "PRTDAST" 2267358 T PRTDAST (NIL) -8 NIL NIL NIL) (-988 2255995 2258209 2260397 "PRS" 2264767 NIL PRS (NIL T T) -7 NIL NIL NIL) (-987 2253780 2255317 2255357 "PRQAGG" 2255540 NIL PRQAGG (NIL T) -9 NIL 2255642 NIL) (-986 2253116 2253421 2253449 "PROPLOG" 2253588 T PROPLOG (NIL) -9 NIL 2253703 NIL) (-985 2252720 2252777 2252900 "PROPFUN2" 2253039 NIL PROPFUN2 (NIL T T) -8 NIL NIL NIL) (-984 2252035 2252156 2252328 "PROPFUN1" 2252581 NIL PROPFUN1 (NIL T) -8 NIL NIL NIL) (-983 2250216 2250782 2251079 "PROPFRML" 2251771 NIL PROPFRML (NIL T) -8 NIL NIL NIL) (-982 2249685 2249792 2249920 "PROPERTY" 2250108 T PROPERTY (NIL) -8 NIL NIL NIL) (-981 2243743 2247851 2248671 "PRODUCT" 2248911 NIL PRODUCT (NIL T T) -8 NIL NIL NIL) (-980 2241021 2243201 2243435 "PR" 2243554 NIL PR (NIL T T) -8 NIL NIL NIL) (-979 2240817 2240849 2240908 "PRINT" 2240982 T PRINT (NIL) -7 NIL NIL NIL) (-978 2240157 2240274 2240426 "PRIMES" 2240697 NIL PRIMES (NIL T) -7 NIL NIL NIL) (-977 2238222 2238623 2239089 "PRIMELT" 2239736 NIL PRIMELT (NIL T) -7 NIL NIL NIL) (-976 2237951 2238000 2238028 "PRIMCAT" 2238152 T PRIMCAT (NIL) -9 NIL NIL NIL) (-975 2234068 2237889 2237934 "PRIMARR" 2237939 NIL PRIMARR (NIL T) -8 NIL NIL NIL) (-974 2233075 2233253 2233481 "PRIMARR2" 2233886 NIL PRIMARR2 (NIL T T) -7 NIL NIL NIL) (-973 2232718 2232774 2232885 "PREASSOC" 2233013 NIL PREASSOC (NIL T T) -7 NIL NIL NIL) (-972 2232193 2232326 2232354 "PPCURVE" 2232559 T PPCURVE (NIL) -9 NIL 2232695 NIL) (-971 2231788 2231988 2232071 "PORTNUM" 2232130 T PORTNUM (NIL) -8 NIL NIL NIL) (-970 2229147 2229546 2230138 "POLYROOT" 2231369 NIL POLYROOT (NIL T T T T T) -7 NIL NIL NIL) (-969 2223053 2228751 2228911 "POLY" 2229020 NIL POLY (NIL T) -8 NIL NIL NIL) (-968 2222436 2222494 2222728 "POLYLIFT" 2222989 NIL POLYLIFT (NIL T T T T T) -7 NIL NIL NIL) (-967 2218711 2219160 2219789 "POLYCATQ" 2221981 NIL POLYCATQ (NIL T T T T T) -7 NIL NIL NIL) (-966 2205053 2210458 2210523 "POLYCAT" 2214037 NIL POLYCAT (NIL T T T) -9 NIL 2215915 NIL) (-965 2198502 2200364 2202748 "POLYCAT-" 2202753 NIL POLYCAT- (NIL T T T T) -8 NIL NIL NIL) (-964 2198089 2198157 2198277 "POLY2UP" 2198428 NIL POLY2UP (NIL NIL T) -7 NIL NIL NIL) (-963 2197721 2197778 2197887 "POLY2" 2198026 NIL POLY2 (NIL T T) -7 NIL NIL NIL) (-962 2196406 2196645 2196921 "POLUTIL" 2197495 NIL POLUTIL (NIL T T) -7 NIL NIL NIL) (-961 2194761 2195038 2195369 "POLTOPOL" 2196128 NIL POLTOPOL (NIL NIL T) -7 NIL NIL NIL) (-960 2190228 2194697 2194743 "POINT" 2194748 NIL POINT (NIL T) -8 NIL NIL NIL) (-959 2188415 2188772 2189147 "PNTHEORY" 2189873 T PNTHEORY (NIL) -7 NIL NIL NIL) (-958 2186873 2187170 2187569 "PMTOOLS" 2188113 NIL PMTOOLS (NIL T T T) -7 NIL NIL NIL) (-957 2186466 2186544 2186661 "PMSYM" 2186789 NIL PMSYM (NIL T) -7 NIL NIL NIL) (-956 2185974 2186043 2186218 "PMQFCAT" 2186391 NIL PMQFCAT (NIL T T T) -7 NIL NIL NIL) (-955 2185329 2185439 2185595 "PMPRED" 2185851 NIL PMPRED (NIL T) -7 NIL NIL NIL) (-954 2184722 2184808 2184970 "PMPREDFS" 2185230 NIL PMPREDFS (NIL T T T) -7 NIL NIL NIL) (-953 2183386 2183594 2183972 "PMPLCAT" 2184484 NIL PMPLCAT (NIL T T T T T) -7 NIL NIL NIL) (-952 2182918 2182997 2183149 "PMLSAGG" 2183301 NIL PMLSAGG (NIL T T T) -7 NIL NIL NIL) (-951 2182391 2182467 2182649 "PMKERNEL" 2182836 NIL PMKERNEL (NIL T T) -7 NIL NIL NIL) (-950 2182008 2182083 2182196 "PMINS" 2182310 NIL PMINS (NIL T) -7 NIL NIL NIL) (-949 2181450 2181519 2181728 "PMFS" 2181933 NIL PMFS (NIL T T T) -7 NIL NIL NIL) (-948 2180678 2180796 2181001 "PMDOWN" 2181327 NIL PMDOWN (NIL T T T) -7 NIL NIL NIL) (-947 2179845 2180003 2180184 "PMASS" 2180517 T PMASS (NIL) -7 NIL NIL NIL) (-946 2179118 2179228 2179391 "PMASSFS" 2179732 NIL PMASSFS (NIL T T) -7 NIL NIL NIL) (-945 2178773 2178841 2178935 "PLOTTOOL" 2179044 T PLOTTOOL (NIL) -7 NIL NIL NIL) (-944 2173380 2174584 2175732 "PLOT" 2177645 T PLOT (NIL) -8 NIL NIL NIL) (-943 2169184 2170228 2171149 "PLOT3D" 2172479 T PLOT3D (NIL) -8 NIL NIL NIL) (-942 2168096 2168273 2168508 "PLOT1" 2168988 NIL PLOT1 (NIL T) -7 NIL NIL NIL) (-941 2143487 2148162 2153013 "PLEQN" 2163362 NIL PLEQN (NIL T T T T) -7 NIL NIL NIL) (-940 2142805 2142927 2143107 "PINTERP" 2143352 NIL PINTERP (NIL NIL T) -7 NIL NIL NIL) (-939 2142498 2142545 2142648 "PINTERPA" 2142752 NIL PINTERPA (NIL T T) -7 NIL NIL NIL) (-938 2141714 2142262 2142349 "PI" 2142389 T PI (NIL) -8 NIL NIL 2142456) (-937 2139997 2140972 2141000 "PID" 2141182 T PID (NIL) -9 NIL 2141316 NIL) (-936 2139748 2139785 2139860 "PICOERCE" 2139954 NIL PICOERCE (NIL T) -7 NIL NIL NIL) (-935 2139068 2139207 2139383 "PGROEB" 2139604 NIL PGROEB (NIL T) -7 NIL NIL NIL) (-934 2134655 2135469 2136374 "PGE" 2138183 T PGE (NIL) -7 NIL NIL NIL) (-933 2132778 2133025 2133391 "PGCD" 2134372 NIL PGCD (NIL T T T T) -7 NIL NIL NIL) (-932 2132116 2132219 2132380 "PFRPAC" 2132662 NIL PFRPAC (NIL T) -7 NIL NIL NIL) (-931 2128756 2130664 2131017 "PFR" 2131795 NIL PFR (NIL T) -8 NIL NIL NIL) (-930 2127145 2127389 2127714 "PFOTOOLS" 2128503 NIL PFOTOOLS (NIL T T) -7 NIL NIL NIL) (-929 2125678 2125917 2126268 "PFOQ" 2126902 NIL PFOQ (NIL T T T) -7 NIL NIL NIL) (-928 2124179 2124391 2124747 "PFO" 2125462 NIL PFO (NIL T T T T T) -7 NIL NIL NIL) (-927 2120732 2124068 2124137 "PF" 2124142 NIL PF (NIL NIL) -8 NIL NIL NIL) (-926 2118052 2119323 2119351 "PFECAT" 2119936 T PFECAT (NIL) -9 NIL 2120320 NIL) (-925 2117497 2117651 2117865 "PFECAT-" 2117870 NIL PFECAT- (NIL T) -8 NIL NIL NIL) (-924 2116100 2116352 2116653 "PFBRU" 2117246 NIL PFBRU (NIL T T) -7 NIL NIL NIL) (-923 2113966 2114318 2114750 "PFBR" 2115751 NIL PFBR (NIL T T T T) -7 NIL NIL NIL) (-922 2110012 2111478 2112125 "PERM" 2113352 NIL PERM (NIL T) -8 NIL NIL NIL) (-921 2105246 2106219 2107089 "PERMGRP" 2109175 NIL PERMGRP (NIL T) -8 NIL NIL NIL) (-920 2103365 2104325 2104366 "PERMCAT" 2104766 NIL PERMCAT (NIL T) -9 NIL 2105064 NIL) (-919 2103018 2103059 2103183 "PERMAN" 2103318 NIL PERMAN (NIL NIL T) -7 NIL NIL NIL) (-918 2100508 2102683 2102805 "PENDTREE" 2102929 NIL PENDTREE (NIL T) -8 NIL NIL NIL) (-917 2099437 2099652 2099693 "PDSPC" 2100226 NIL PDSPC (NIL T) -9 NIL 2100471 NIL) (-916 2098540 2098758 2099120 "PDSPC-" 2099125 NIL PDSPC- (NIL T T) -8 NIL NIL NIL) (-915 2097422 2098190 2098231 "PDRING" 2098236 NIL PDRING (NIL T) -9 NIL 2098264 NIL) (-914 2096309 2096927 2096981 "PDMOD" 2096986 NIL PDMOD (NIL T T) -9 NIL 2097090 NIL) (-913 2093524 2094302 2094970 "PDEPROB" 2095661 T PDEPROB (NIL) -8 NIL NIL NIL) (-912 2091069 2091573 2092128 "PDEPACK" 2092989 T PDEPACK (NIL) -7 NIL NIL NIL) (-911 2089981 2090171 2090422 "PDECOMP" 2090868 NIL PDECOMP (NIL T T) -7 NIL NIL NIL) (-910 2087546 2088389 2088417 "PDECAT" 2089204 T PDECAT (NIL) -9 NIL 2089917 NIL) (-909 2087175 2087230 2087284 "PDDOM" 2087449 NIL PDDOM (NIL T T) -9 NIL 2087529 NIL) (-908 2086994 2087024 2087131 "PDDOM-" 2087136 NIL PDDOM- (NIL T T T) -8 NIL NIL NIL) (-907 2086745 2086778 2086868 "PCOMP" 2086955 NIL PCOMP (NIL T T) -7 NIL NIL NIL) (-906 2084923 2085546 2085843 "PBWLB" 2086474 NIL PBWLB (NIL T) -8 NIL NIL NIL) (-905 2077396 2078996 2080334 "PATTERN" 2083606 NIL PATTERN (NIL T) -8 NIL NIL NIL) (-904 2077028 2077085 2077194 "PATTERN2" 2077333 NIL PATTERN2 (NIL T T) -7 NIL NIL NIL) (-903 2074785 2075173 2075630 "PATTERN1" 2076617 NIL PATTERN1 (NIL T T) -7 NIL NIL NIL) (-902 2072153 2072734 2073215 "PATRES" 2074350 NIL PATRES (NIL T T) -8 NIL NIL NIL) (-901 2071717 2071784 2071916 "PATRES2" 2072080 NIL PATRES2 (NIL T T T) -7 NIL NIL NIL) (-900 2069600 2070005 2070412 "PATMATCH" 2071384 NIL PATMATCH (NIL T T T) -7 NIL NIL NIL) (-899 2069096 2069305 2069346 "PATMAB" 2069453 NIL PATMAB (NIL T) -9 NIL 2069536 NIL) (-898 2067614 2067950 2068208 "PATLRES" 2068901 NIL PATLRES (NIL T T T) -8 NIL NIL NIL) (-897 2067160 2067283 2067324 "PATAB" 2067329 NIL PATAB (NIL T) -9 NIL 2067501 NIL) (-896 2065342 2065737 2066160 "PARTPERM" 2066757 T PARTPERM (NIL) -7 NIL NIL NIL) (-895 2064963 2065026 2065128 "PARSURF" 2065273 NIL PARSURF (NIL T) -8 NIL NIL NIL) (-894 2064595 2064652 2064761 "PARSU2" 2064900 NIL PARSU2 (NIL T T) -7 NIL NIL NIL) (-893 2064359 2064399 2064466 "PARSER" 2064548 T PARSER (NIL) -7 NIL NIL NIL) (-892 2063980 2064043 2064145 "PARSCURV" 2064290 NIL PARSCURV (NIL T) -8 NIL NIL NIL) (-891 2063612 2063669 2063778 "PARSC2" 2063917 NIL PARSC2 (NIL T T) -7 NIL NIL NIL) (-890 2063251 2063309 2063406 "PARPCURV" 2063548 NIL PARPCURV (NIL T) -8 NIL NIL NIL) (-889 2062883 2062940 2063049 "PARPC2" 2063188 NIL PARPC2 (NIL T T) -7 NIL NIL NIL) (-888 2061944 2062256 2062438 "PARAMAST" 2062721 T PARAMAST (NIL) -8 NIL NIL NIL) (-887 2061464 2061550 2061669 "PAN2EXPR" 2061845 T PAN2EXPR (NIL) -7 NIL NIL NIL) (-886 2060241 2060585 2060813 "PALETTE" 2061256 T PALETTE (NIL) -8 NIL NIL NIL) (-885 2058634 2059246 2059606 "PAIR" 2059927 NIL PAIR (NIL T T) -8 NIL NIL NIL) (-884 2052226 2057891 2058086 "PADICRC" 2058488 NIL PADICRC (NIL NIL T) -8 NIL NIL NIL) (-883 2045142 2051570 2051755 "PADICRAT" 2052073 NIL PADICRAT (NIL NIL) -8 NIL NIL NIL) (-882 2043457 2045079 2045124 "PADIC" 2045129 NIL PADIC (NIL NIL) -8 NIL NIL NIL) (-881 2040553 2042117 2042157 "PADICCT" 2042738 NIL PADICCT (NIL NIL) -9 NIL 2043020 NIL) (-880 2039510 2039710 2039978 "PADEPAC" 2040340 NIL PADEPAC (NIL T NIL NIL) -7 NIL NIL NIL) (-879 2038722 2038855 2039061 "PADE" 2039372 NIL PADE (NIL T T T) -7 NIL NIL NIL) (-878 2037109 2037930 2038210 "OWP" 2038526 NIL OWP (NIL T NIL NIL NIL) -8 NIL NIL NIL) (-877 2036602 2036815 2036912 "OVERSET" 2037032 T OVERSET (NIL) -8 NIL NIL NIL) (-876 2035648 2036207 2036379 "OVAR" 2036470 NIL OVAR (NIL NIL) -8 NIL NIL NIL) (-875 2034912 2035033 2035194 "OUT" 2035507 T OUT (NIL) -7 NIL NIL NIL) (-874 2023784 2026021 2028221 "OUTFORM" 2032732 T OUTFORM (NIL) -8 NIL NIL NIL) (-873 2023120 2023381 2023508 "OUTBFILE" 2023677 T OUTBFILE (NIL) -8 NIL NIL NIL) (-872 2022427 2022592 2022620 "OUTBCON" 2022938 T OUTBCON (NIL) -9 NIL 2023104 NIL) (-871 2022028 2022140 2022297 "OUTBCON-" 2022302 NIL OUTBCON- (NIL T) -8 NIL NIL NIL) (-870 2021408 2021757 2021846 "OSI" 2021959 T OSI (NIL) -8 NIL NIL NIL) (-869 2020924 2021262 2021290 "OSGROUP" 2021295 T OSGROUP (NIL) -9 NIL 2021317 NIL) (-868 2019669 2019896 2020181 "ORTHPOL" 2020671 NIL ORTHPOL (NIL T) -7 NIL NIL NIL) (-867 2017220 2019504 2019625 "OREUP" 2019630 NIL OREUP (NIL NIL T NIL NIL) -8 NIL NIL NIL) (-866 2014623 2016911 2017038 "ORESUP" 2017162 NIL ORESUP (NIL T NIL NIL) -8 NIL NIL NIL) (-865 2012151 2012651 2013212 "OREPCTO" 2014112 NIL OREPCTO (NIL T T) -7 NIL NIL NIL) (-864 2005823 2008024 2008065 "OREPCAT" 2010413 NIL OREPCAT (NIL T) -9 NIL 2011517 NIL) (-863 2002970 2003752 2004810 "OREPCAT-" 2004815 NIL OREPCAT- (NIL T T) -8 NIL NIL NIL) (-862 2002107 2002405 2002433 "ORDSET" 2002742 T ORDSET (NIL) -9 NIL 2002906 NIL) (-861 2001538 2001686 2001910 "ORDSET-" 2001915 NIL ORDSET- (NIL T) -8 NIL NIL NIL) (-860 2000089 2000880 2000908 "ORDRING" 2001110 T ORDRING (NIL) -9 NIL 2001235 NIL) (-859 1999734 1999828 1999972 "ORDRING-" 1999977 NIL ORDRING- (NIL T) -8 NIL NIL NIL) (-858 1999100 1999563 1999591 "ORDMON" 1999596 T ORDMON (NIL) -9 NIL 1999617 NIL) (-857 1998262 1998409 1998604 "ORDFUNS" 1998949 NIL ORDFUNS (NIL NIL T) -7 NIL NIL NIL) (-856 1997586 1998005 1998033 "ORDFIN" 1998098 T ORDFIN (NIL) -9 NIL 1998172 NIL) (-855 1994145 1996172 1996581 "ORDCOMP" 1997210 NIL ORDCOMP (NIL T) -8 NIL NIL NIL) (-854 1993411 1993538 1993724 "ORDCOMP2" 1994005 NIL ORDCOMP2 (NIL T T) -7 NIL NIL NIL) (-853 1989992 1990902 1991716 "OPTPROB" 1992617 T OPTPROB (NIL) -8 NIL NIL NIL) (-852 1986794 1987433 1988137 "OPTPACK" 1989308 T OPTPACK (NIL) -7 NIL NIL NIL) (-851 1984467 1985233 1985261 "OPTCAT" 1986080 T OPTCAT (NIL) -9 NIL 1986730 NIL) (-850 1983851 1984144 1984249 "OPSIG" 1984382 T OPSIG (NIL) -8 NIL NIL NIL) (-849 1983619 1983658 1983724 "OPQUERY" 1983805 T OPQUERY (NIL) -7 NIL NIL NIL) (-848 1980750 1981930 1982434 "OP" 1983148 NIL OP (NIL T) -8 NIL NIL NIL) (-847 1980110 1980336 1980377 "OPERCAT" 1980589 NIL OPERCAT (NIL T) -9 NIL 1980686 NIL) (-846 1979865 1979921 1980038 "OPERCAT-" 1980043 NIL OPERCAT- (NIL T T) -8 NIL NIL NIL) (-845 1976678 1978662 1979031 "ONECOMP" 1979529 NIL ONECOMP (NIL T) -8 NIL NIL NIL) (-844 1975983 1976098 1976272 "ONECOMP2" 1976550 NIL ONECOMP2 (NIL T T) -7 NIL NIL NIL) (-843 1975402 1975508 1975638 "OMSERVER" 1975873 T OMSERVER (NIL) -7 NIL NIL NIL) (-842 1972264 1974842 1974882 "OMSAGG" 1974943 NIL OMSAGG (NIL T) -9 NIL 1975007 NIL) (-841 1970887 1971150 1971432 "OMPKG" 1972002 T OMPKG (NIL) -7 NIL NIL NIL) (-840 1970317 1970420 1970448 "OM" 1970747 T OM (NIL) -9 NIL NIL NIL) (-839 1968864 1969866 1970035 "OMLO" 1970198 NIL OMLO (NIL T T) -8 NIL NIL NIL) (-838 1967824 1967971 1968191 "OMEXPR" 1968690 NIL OMEXPR (NIL T) -7 NIL NIL NIL) (-837 1967115 1967370 1967506 "OMERR" 1967708 T OMERR (NIL) -8 NIL NIL NIL) (-836 1966266 1966536 1966696 "OMERRK" 1966975 T OMERRK (NIL) -8 NIL NIL NIL) (-835 1965717 1965943 1966051 "OMENC" 1966178 T OMENC (NIL) -8 NIL NIL NIL) (-834 1959612 1960797 1961968 "OMDEV" 1964566 T OMDEV (NIL) -8 NIL NIL NIL) (-833 1958681 1958852 1959046 "OMCONN" 1959438 T OMCONN (NIL) -8 NIL NIL NIL) (-832 1957188 1958164 1958192 "OINTDOM" 1958197 T OINTDOM (NIL) -9 NIL 1958218 NIL) (-831 1954526 1955876 1956213 "OFMONOID" 1956883 NIL OFMONOID (NIL T) -8 NIL NIL NIL) (-830 1953898 1954463 1954508 "ODVAR" 1954513 NIL ODVAR (NIL T) -8 NIL NIL NIL) (-829 1951321 1953643 1953798 "ODR" 1953803 NIL ODR (NIL T T NIL) -8 NIL NIL NIL) (-828 1943626 1951097 1951223 "ODPOL" 1951228 NIL ODPOL (NIL T) -8 NIL NIL NIL) (-827 1937424 1943498 1943603 "ODP" 1943608 NIL ODP (NIL NIL T NIL) -8 NIL NIL NIL) (-826 1936190 1936405 1936680 "ODETOOLS" 1937198 NIL ODETOOLS (NIL T T) -7 NIL NIL NIL) (-825 1933157 1933815 1934531 "ODESYS" 1935523 NIL ODESYS (NIL T T) -7 NIL NIL NIL) (-824 1928039 1928947 1929972 "ODERTRIC" 1932232 NIL ODERTRIC (NIL T T) -7 NIL NIL NIL) (-823 1927465 1927547 1927741 "ODERED" 1927951 NIL ODERED (NIL T T T T T) -7 NIL NIL NIL) (-822 1924353 1924901 1925578 "ODERAT" 1926888 NIL ODERAT (NIL T T) -7 NIL NIL NIL) (-821 1921312 1921777 1922374 "ODEPRRIC" 1923882 NIL ODEPRRIC (NIL T T T T) -7 NIL NIL NIL) (-820 1919255 1919851 1920337 "ODEPROB" 1920846 T ODEPROB (NIL) -8 NIL NIL NIL) (-819 1915775 1916260 1916907 "ODEPRIM" 1918734 NIL ODEPRIM (NIL T T T T) -7 NIL NIL NIL) (-818 1915024 1915126 1915386 "ODEPAL" 1915667 NIL ODEPAL (NIL T T T T) -7 NIL NIL NIL) (-817 1911186 1911977 1912841 "ODEPACK" 1914180 T ODEPACK (NIL) -7 NIL NIL NIL) (-816 1910247 1910354 1910576 "ODEINT" 1911075 NIL ODEINT (NIL T T) -7 NIL NIL NIL) (-815 1904348 1905773 1907220 "ODEIFTBL" 1908820 T ODEIFTBL (NIL) -8 NIL NIL NIL) (-814 1899746 1900532 1901484 "ODEEF" 1903507 NIL ODEEF (NIL T T) -7 NIL NIL NIL) (-813 1899095 1899184 1899407 "ODECONST" 1899651 NIL ODECONST (NIL T T T) -7 NIL NIL NIL) (-812 1897206 1897867 1897895 "ODECAT" 1898500 T ODECAT (NIL) -9 NIL 1899031 NIL) (-811 1894061 1896911 1897033 "OCT" 1897116 NIL OCT (NIL T) -8 NIL NIL NIL) (-810 1893699 1893742 1893869 "OCTCT2" 1894012 NIL OCTCT2 (NIL T T T T) -7 NIL NIL NIL) (-809 1888334 1890769 1890809 "OC" 1891906 NIL OC (NIL T) -9 NIL 1892764 NIL) (-808 1885561 1886309 1887299 "OC-" 1887393 NIL OC- (NIL T T) -8 NIL NIL NIL) (-807 1884899 1885367 1885395 "OCAMON" 1885400 T OCAMON (NIL) -9 NIL 1885421 NIL) (-806 1884416 1884757 1884785 "OASGP" 1884790 T OASGP (NIL) -9 NIL 1884810 NIL) (-805 1883663 1884152 1884180 "OAMONS" 1884220 T OAMONS (NIL) -9 NIL 1884263 NIL) (-804 1883063 1883496 1883524 "OAMON" 1883529 T OAMON (NIL) -9 NIL 1883549 NIL) (-803 1882307 1882825 1882853 "OAGROUP" 1882858 T OAGROUP (NIL) -9 NIL 1882878 NIL) (-802 1881997 1882047 1882135 "NUMTUBE" 1882251 NIL NUMTUBE (NIL T) -7 NIL NIL NIL) (-801 1875570 1877088 1878624 "NUMQUAD" 1880481 T NUMQUAD (NIL) -7 NIL NIL NIL) (-800 1871326 1872314 1873339 "NUMODE" 1874565 T NUMODE (NIL) -7 NIL NIL NIL) (-799 1868667 1869547 1869575 "NUMINT" 1870498 T NUMINT (NIL) -9 NIL 1871262 NIL) (-798 1867615 1867812 1868030 "NUMFMT" 1868469 T NUMFMT (NIL) -7 NIL NIL NIL) (-797 1853974 1856919 1859451 "NUMERIC" 1865122 NIL NUMERIC (NIL T) -7 NIL NIL NIL) (-796 1848344 1853423 1853518 "NTSCAT" 1853523 NIL NTSCAT (NIL T T T T) -9 NIL 1853562 NIL) (-795 1847538 1847703 1847896 "NTPOLFN" 1848183 NIL NTPOLFN (NIL T) -7 NIL NIL NIL) (-794 1835339 1844363 1845175 "NSUP" 1846759 NIL NSUP (NIL T) -8 NIL NIL NIL) (-793 1834971 1835028 1835137 "NSUP2" 1835276 NIL NSUP2 (NIL T T) -7 NIL NIL NIL) (-792 1824921 1834745 1834878 "NSMP" 1834883 NIL NSMP (NIL T T) -8 NIL NIL NIL) (-791 1823353 1823654 1824011 "NREP" 1824609 NIL NREP (NIL T) -7 NIL NIL NIL) (-790 1821944 1822196 1822554 "NPCOEF" 1823096 NIL NPCOEF (NIL T T T T T) -7 NIL NIL NIL) (-789 1821010 1821125 1821341 "NORMRETR" 1821825 NIL NORMRETR (NIL T T T T NIL) -7 NIL NIL NIL) (-788 1819051 1819341 1819750 "NORMPK" 1820718 NIL NORMPK (NIL T T T T T) -7 NIL NIL NIL) (-787 1818736 1818764 1818888 "NORMMA" 1819017 NIL NORMMA (NIL T T T T) -7 NIL NIL NIL) (-786 1818536 1818693 1818722 "NONE" 1818727 T NONE (NIL) -8 NIL NIL NIL) (-785 1818325 1818354 1818423 "NONE1" 1818500 NIL NONE1 (NIL T) -7 NIL NIL NIL) (-784 1817822 1817884 1818063 "NODE1" 1818257 NIL NODE1 (NIL T T) -7 NIL NIL NIL) (-783 1816103 1816954 1817209 "NNI" 1817556 T NNI (NIL) -8 NIL NIL 1817791) (-782 1814523 1814836 1815200 "NLINSOL" 1815771 NIL NLINSOL (NIL T) -7 NIL NIL NIL) (-781 1810764 1811759 1812658 "NIPROB" 1813644 T NIPROB (NIL) -8 NIL NIL NIL) (-780 1809521 1809755 1810057 "NFINTBAS" 1810526 NIL NFINTBAS (NIL T T) -7 NIL NIL NIL) (-779 1808695 1809171 1809212 "NETCLT" 1809384 NIL NETCLT (NIL T) -9 NIL 1809466 NIL) (-778 1807403 1807634 1807915 "NCODIV" 1808463 NIL NCODIV (NIL T T) -7 NIL NIL NIL) (-777 1807165 1807202 1807277 "NCNTFRAC" 1807360 NIL NCNTFRAC (NIL T) -7 NIL NIL NIL) (-776 1805345 1805709 1806129 "NCEP" 1806790 NIL NCEP (NIL T) -7 NIL NIL NIL) (-775 1804182 1804955 1804983 "NASRING" 1805093 T NASRING (NIL) -9 NIL 1805173 NIL) (-774 1803977 1804021 1804115 "NASRING-" 1804120 NIL NASRING- (NIL T) -8 NIL NIL NIL) (-773 1803070 1803595 1803623 "NARNG" 1803740 T NARNG (NIL) -9 NIL 1803831 NIL) (-772 1802762 1802829 1802963 "NARNG-" 1802968 NIL NARNG- (NIL T) -8 NIL NIL NIL) (-771 1801641 1801848 1802083 "NAGSP" 1802547 T NAGSP (NIL) -7 NIL NIL NIL) (-770 1792913 1794597 1796270 "NAGS" 1799988 T NAGS (NIL) -7 NIL NIL NIL) (-769 1791461 1791769 1792100 "NAGF07" 1792602 T NAGF07 (NIL) -7 NIL NIL NIL) (-768 1785999 1787290 1788597 "NAGF04" 1790174 T NAGF04 (NIL) -7 NIL NIL NIL) (-767 1778967 1780581 1782214 "NAGF02" 1784386 T NAGF02 (NIL) -7 NIL NIL NIL) (-766 1774191 1775291 1776408 "NAGF01" 1777870 T NAGF01 (NIL) -7 NIL NIL NIL) (-765 1767819 1769385 1770970 "NAGE04" 1772626 T NAGE04 (NIL) -7 NIL NIL NIL) (-764 1758988 1761109 1763239 "NAGE02" 1765709 T NAGE02 (NIL) -7 NIL NIL NIL) (-763 1754941 1755888 1756852 "NAGE01" 1758044 T NAGE01 (NIL) -7 NIL NIL NIL) (-762 1752736 1753270 1753828 "NAGD03" 1754403 T NAGD03 (NIL) -7 NIL NIL NIL) (-761 1744486 1746414 1748368 "NAGD02" 1750802 T NAGD02 (NIL) -7 NIL NIL NIL) (-760 1738297 1739722 1741162 "NAGD01" 1743066 T NAGD01 (NIL) -7 NIL NIL NIL) (-759 1734506 1735328 1736165 "NAGC06" 1737480 T NAGC06 (NIL) -7 NIL NIL NIL) (-758 1732971 1733303 1733659 "NAGC05" 1734170 T NAGC05 (NIL) -7 NIL NIL NIL) (-757 1732347 1732466 1732610 "NAGC02" 1732847 T NAGC02 (NIL) -7 NIL NIL NIL) (-756 1731292 1731875 1731915 "NAALG" 1731994 NIL NAALG (NIL T) -9 NIL 1732055 NIL) (-755 1731127 1731156 1731246 "NAALG-" 1731251 NIL NAALG- (NIL T T) -8 NIL NIL NIL) (-754 1725077 1726185 1727372 "MULTSQFR" 1730023 NIL MULTSQFR (NIL T T T T) -7 NIL NIL NIL) (-753 1724396 1724471 1724655 "MULTFACT" 1724989 NIL MULTFACT (NIL T T T T) -7 NIL NIL NIL) (-752 1717067 1720981 1721034 "MTSCAT" 1722104 NIL MTSCAT (NIL T T) -9 NIL 1722619 NIL) (-751 1716779 1716833 1716925 "MTHING" 1717007 NIL MTHING (NIL T) -7 NIL NIL NIL) (-750 1716571 1716604 1716664 "MSYSCMD" 1716739 T MSYSCMD (NIL) -7 NIL NIL NIL) (-749 1712653 1715326 1715646 "MSET" 1716284 NIL MSET (NIL T) -8 NIL NIL NIL) (-748 1709722 1712214 1712255 "MSETAGG" 1712260 NIL MSETAGG (NIL T) -9 NIL 1712294 NIL) (-747 1705564 1707101 1707846 "MRING" 1709022 NIL MRING (NIL T T) -8 NIL NIL NIL) (-746 1705130 1705197 1705328 "MRF2" 1705491 NIL MRF2 (NIL T T T) -7 NIL NIL NIL) (-745 1704748 1704783 1704927 "MRATFAC" 1705089 NIL MRATFAC (NIL T T T T) -7 NIL NIL NIL) (-744 1702360 1702655 1703086 "MPRFF" 1704453 NIL MPRFF (NIL T T T T) -7 NIL NIL NIL) (-743 1696381 1702214 1702311 "MPOLY" 1702316 NIL MPOLY (NIL NIL T) -8 NIL NIL NIL) (-742 1695871 1695906 1696114 "MPCPF" 1696340 NIL MPCPF (NIL T T T T) -7 NIL NIL NIL) (-741 1695385 1695428 1695612 "MPC3" 1695822 NIL MPC3 (NIL T T T T T T T) -7 NIL NIL NIL) (-740 1694580 1694661 1694882 "MPC2" 1695300 NIL MPC2 (NIL T T T T T T T) -7 NIL NIL NIL) (-739 1692881 1693218 1693608 "MONOTOOL" 1694240 NIL MONOTOOL (NIL T T) -7 NIL NIL NIL) (-738 1692092 1692409 1692437 "MONOID" 1692656 T MONOID (NIL) -9 NIL 1692803 NIL) (-737 1691638 1691757 1691938 "MONOID-" 1691943 NIL MONOID- (NIL T) -8 NIL NIL NIL) (-736 1681228 1687458 1687517 "MONOGEN" 1688191 NIL MONOGEN (NIL T T) -9 NIL 1688647 NIL) (-735 1678446 1679181 1680181 "MONOGEN-" 1680300 NIL MONOGEN- (NIL T T T) -8 NIL NIL NIL) (-734 1677265 1677711 1677739 "MONADWU" 1678131 T MONADWU (NIL) -9 NIL 1678369 NIL) (-733 1676637 1676796 1677044 "MONADWU-" 1677049 NIL MONADWU- (NIL T) -8 NIL NIL NIL) (-732 1675982 1676226 1676254 "MONAD" 1676461 T MONAD (NIL) -9 NIL 1676573 NIL) (-731 1675667 1675745 1675877 "MONAD-" 1675882 NIL MONAD- (NIL T) -8 NIL NIL NIL) (-730 1673956 1674580 1674859 "MOEBIUS" 1675420 NIL MOEBIUS (NIL T) -8 NIL NIL NIL) (-729 1673220 1673624 1673664 "MODULE" 1673669 NIL MODULE (NIL T) -9 NIL 1673708 NIL) (-728 1672788 1672884 1673074 "MODULE-" 1673079 NIL MODULE- (NIL T T) -8 NIL NIL NIL) (-727 1670468 1671152 1671479 "MODRING" 1672612 NIL MODRING (NIL T T NIL NIL NIL) -8 NIL NIL NIL) (-726 1667412 1668573 1669094 "MODOP" 1669997 NIL MODOP (NIL T T) -8 NIL NIL NIL) (-725 1666000 1666479 1666756 "MODMONOM" 1667275 NIL MODMONOM (NIL T T NIL) -8 NIL NIL NIL) (-724 1655768 1664291 1664705 "MODMON" 1665637 NIL MODMON (NIL T T) -8 NIL NIL NIL) (-723 1652924 1654612 1654888 "MODFIELD" 1655643 NIL MODFIELD (NIL T T NIL NIL NIL) -8 NIL NIL NIL) (-722 1651901 1652205 1652395 "MMLFORM" 1652754 T MMLFORM (NIL) -8 NIL NIL NIL) (-721 1651427 1651470 1651649 "MMAP" 1651852 NIL MMAP (NIL T T T T T T) -7 NIL NIL NIL) (-720 1649492 1650259 1650300 "MLO" 1650723 NIL MLO (NIL T) -9 NIL 1650965 NIL) (-719 1646858 1647374 1647976 "MLIFT" 1648973 NIL MLIFT (NIL T T T T) -7 NIL NIL NIL) (-718 1646249 1646333 1646487 "MKUCFUNC" 1646769 NIL MKUCFUNC (NIL T T T) -7 NIL NIL NIL) (-717 1645848 1645918 1646041 "MKRECORD" 1646172 NIL MKRECORD (NIL T T) -7 NIL NIL NIL) (-716 1644895 1645057 1645285 "MKFUNC" 1645659 NIL MKFUNC (NIL T) -7 NIL NIL NIL) (-715 1644283 1644387 1644543 "MKFLCFN" 1644778 NIL MKFLCFN (NIL T) -7 NIL NIL NIL) (-714 1643560 1643662 1643847 "MKBCFUNC" 1644176 NIL MKBCFUNC (NIL T T T T) -7 NIL NIL NIL) (-713 1640149 1643114 1643250 "MINT" 1643444 T MINT (NIL) -8 NIL NIL NIL) (-712 1638961 1639204 1639481 "MHROWRED" 1639904 NIL MHROWRED (NIL T) -7 NIL NIL NIL) (-711 1634341 1637496 1637901 "MFLOAT" 1638576 T MFLOAT (NIL) -8 NIL NIL NIL) (-710 1633698 1633774 1633945 "MFINFACT" 1634253 NIL MFINFACT (NIL T T T T) -7 NIL NIL NIL) (-709 1630013 1630861 1631745 "MESH" 1632834 T MESH (NIL) -7 NIL NIL NIL) (-708 1628403 1628715 1629068 "MDDFACT" 1629700 NIL MDDFACT (NIL T) -7 NIL NIL NIL) (-707 1625172 1627534 1627575 "MDAGG" 1627830 NIL MDAGG (NIL T) -9 NIL 1627973 NIL) (-706 1613866 1624465 1624672 "MCMPLX" 1624985 T MCMPLX (NIL) -8 NIL NIL NIL) (-705 1613003 1613149 1613350 "MCDEN" 1613715 NIL MCDEN (NIL T T) -7 NIL NIL NIL) (-704 1610893 1611163 1611543 "MCALCFN" 1612733 NIL MCALCFN (NIL T T T T) -7 NIL NIL NIL) (-703 1609818 1610058 1610291 "MAYBE" 1610699 NIL MAYBE (NIL T) -8 NIL NIL NIL) (-702 1607430 1607953 1608515 "MATSTOR" 1609289 NIL MATSTOR (NIL T) -7 NIL NIL NIL) (-701 1603341 1606802 1607050 "MATRIX" 1607215 NIL MATRIX (NIL T) -8 NIL NIL NIL) (-700 1599107 1599814 1600550 "MATLIN" 1602698 NIL MATLIN (NIL T T T T) -7 NIL NIL NIL) (-699 1588932 1592164 1592241 "MATCAT" 1597273 NIL MATCAT (NIL T T T) -9 NIL 1598745 NIL) (-698 1585125 1586195 1587608 "MATCAT-" 1587613 NIL MATCAT- (NIL T T T T) -8 NIL NIL NIL) (-697 1583719 1583872 1584205 "MATCAT2" 1584960 NIL MATCAT2 (NIL T T T T T T T T) -7 NIL NIL NIL) (-696 1581831 1582155 1582539 "MAPPKG3" 1583394 NIL MAPPKG3 (NIL T T T) -7 NIL NIL NIL) (-695 1580812 1580985 1581207 "MAPPKG2" 1581655 NIL MAPPKG2 (NIL T T) -7 NIL NIL NIL) (-694 1579311 1579595 1579922 "MAPPKG1" 1580518 NIL MAPPKG1 (NIL T) -7 NIL NIL NIL) (-693 1578390 1578717 1578894 "MAPPAST" 1579154 T MAPPAST (NIL) -8 NIL NIL NIL) (-692 1578001 1578059 1578182 "MAPHACK3" 1578326 NIL MAPHACK3 (NIL T T T) -7 NIL NIL NIL) (-691 1577593 1577654 1577768 "MAPHACK2" 1577933 NIL MAPHACK2 (NIL T T) -7 NIL NIL NIL) (-690 1577031 1577134 1577276 "MAPHACK1" 1577484 NIL MAPHACK1 (NIL T) -7 NIL NIL NIL) (-689 1575110 1575731 1576035 "MAGMA" 1576759 NIL MAGMA (NIL T) -8 NIL NIL NIL) (-688 1574589 1574834 1574925 "MACROAST" 1575039 T MACROAST (NIL) -8 NIL NIL NIL) (-687 1571009 1572828 1573289 "M3D" 1574161 NIL M3D (NIL T) -8 NIL NIL NIL) (-686 1565058 1569320 1569361 "LZSTAGG" 1570143 NIL LZSTAGG (NIL T) -9 NIL 1570438 NIL) (-685 1561016 1562189 1563646 "LZSTAGG-" 1563651 NIL LZSTAGG- (NIL T T) -8 NIL NIL NIL) (-684 1558103 1558907 1559394 "LWORD" 1560561 NIL LWORD (NIL T) -8 NIL NIL NIL) (-683 1557679 1557907 1557982 "LSTAST" 1558048 T LSTAST (NIL) -8 NIL NIL NIL) (-682 1550569 1557450 1557584 "LSQM" 1557589 NIL LSQM (NIL NIL T) -8 NIL NIL NIL) (-681 1549793 1549932 1550160 "LSPP" 1550424 NIL LSPP (NIL T T T T) -7 NIL NIL NIL) (-680 1547605 1547906 1548362 "LSMP" 1549482 NIL LSMP (NIL T T T T) -7 NIL NIL NIL) (-679 1544384 1545058 1545788 "LSMP1" 1546907 NIL LSMP1 (NIL T) -7 NIL NIL NIL) (-678 1538212 1543501 1543542 "LSAGG" 1543604 NIL LSAGG (NIL T) -9 NIL 1543682 NIL) (-677 1534907 1535831 1537044 "LSAGG-" 1537049 NIL LSAGG- (NIL T T) -8 NIL NIL NIL) (-676 1532506 1534051 1534300 "LPOLY" 1534702 NIL LPOLY (NIL T T) -8 NIL NIL NIL) (-675 1532088 1532173 1532296 "LPEFRAC" 1532415 NIL LPEFRAC (NIL T) -7 NIL NIL NIL) (-674 1530409 1531182 1531435 "LO" 1531920 NIL LO (NIL T T T) -8 NIL NIL NIL) (-673 1530047 1530159 1530187 "LOGIC" 1530298 T LOGIC (NIL) -9 NIL 1530379 NIL) (-672 1529909 1529932 1530003 "LOGIC-" 1530008 NIL LOGIC- (NIL T) -8 NIL NIL NIL) (-671 1529102 1529242 1529435 "LODOOPS" 1529765 NIL LODOOPS (NIL T T) -7 NIL NIL NIL) (-670 1526525 1529018 1529084 "LODO" 1529089 NIL LODO (NIL T NIL) -8 NIL NIL NIL) (-669 1525063 1525298 1525651 "LODOF" 1526272 NIL LODOF (NIL T T) -7 NIL NIL NIL) (-668 1521267 1523698 1523739 "LODOCAT" 1524177 NIL LODOCAT (NIL T) -9 NIL 1524388 NIL) (-667 1521000 1521058 1521185 "LODOCAT-" 1521190 NIL LODOCAT- (NIL T T) -8 NIL NIL NIL) (-666 1518320 1520841 1520959 "LODO2" 1520964 NIL LODO2 (NIL T T) -8 NIL NIL NIL) (-665 1515755 1518257 1518302 "LODO1" 1518307 NIL LODO1 (NIL T) -8 NIL NIL NIL) (-664 1514636 1514801 1515106 "LODEEF" 1515578 NIL LODEEF (NIL T T T) -7 NIL NIL NIL) (-663 1509913 1512802 1512843 "LNAGG" 1513705 NIL LNAGG (NIL T) -9 NIL 1514140 NIL) (-662 1509060 1509274 1509616 "LNAGG-" 1509621 NIL LNAGG- (NIL T T) -8 NIL NIL NIL) (-661 1505196 1505985 1506624 "LMOPS" 1508475 NIL LMOPS (NIL T T NIL) -8 NIL NIL NIL) (-660 1504585 1504973 1505014 "LMODULE" 1505019 NIL LMODULE (NIL T) -9 NIL 1505045 NIL) (-659 1501785 1504230 1504353 "LMDICT" 1504495 NIL LMDICT (NIL T) -8 NIL NIL NIL) (-658 1501403 1501575 1501616 "LLINSET" 1501677 NIL LLINSET (NIL T) -9 NIL 1501721 NIL) (-657 1501102 1501311 1501371 "LITERAL" 1501376 NIL LITERAL (NIL T) -8 NIL NIL NIL) (-656 1494267 1500036 1500340 "LIST" 1500831 NIL LIST (NIL T) -8 NIL NIL NIL) (-655 1493792 1493866 1494005 "LIST3" 1494187 NIL LIST3 (NIL T T T) -7 NIL NIL NIL) (-654 1492799 1492977 1493205 "LIST2" 1493610 NIL LIST2 (NIL T T) -7 NIL NIL NIL) (-653 1490933 1491245 1491644 "LIST2MAP" 1492446 NIL LIST2MAP (NIL T T) -7 NIL NIL NIL) (-652 1490564 1490752 1490793 "LINSET" 1490798 NIL LINSET (NIL T) -9 NIL 1490832 NIL) (-651 1488977 1489591 1489632 "LINEXP" 1490122 NIL LINEXP (NIL T) -9 NIL 1490395 NIL) (-650 1487554 1487814 1488125 "LINDEP" 1488729 NIL LINDEP (NIL T T) -7 NIL NIL NIL) (-649 1484321 1485040 1485817 "LIMITRF" 1486809 NIL LIMITRF (NIL T) -7 NIL NIL NIL) (-648 1482624 1482920 1483329 "LIMITPS" 1484016 NIL LIMITPS (NIL T T) -7 NIL NIL NIL) (-647 1477052 1482135 1482363 "LIE" 1482445 NIL LIE (NIL T T) -8 NIL NIL NIL) (-646 1475986 1476455 1476495 "LIECAT" 1476635 NIL LIECAT (NIL T) -9 NIL 1476786 NIL) (-645 1475827 1475854 1475942 "LIECAT-" 1475947 NIL LIECAT- (NIL T T) -8 NIL NIL NIL) (-644 1468418 1475367 1475523 "LIB" 1475691 T LIB (NIL) -8 NIL NIL NIL) (-643 1464053 1464936 1465871 "LGROBP" 1467535 NIL LGROBP (NIL NIL T) -7 NIL NIL NIL) (-642 1462051 1462325 1462675 "LF" 1463774 NIL LF (NIL T T) -7 NIL NIL NIL) (-641 1460891 1461583 1461611 "LFCAT" 1461818 T LFCAT (NIL) -9 NIL 1461957 NIL) (-640 1457793 1458423 1459111 "LEXTRIPK" 1460255 NIL LEXTRIPK (NIL T NIL) -7 NIL NIL NIL) (-639 1454537 1455363 1455866 "LEXP" 1457373 NIL LEXP (NIL T T NIL) -8 NIL NIL NIL) (-638 1454013 1454258 1454350 "LETAST" 1454465 T LETAST (NIL) -8 NIL NIL NIL) (-637 1452411 1452724 1453125 "LEADCDET" 1453695 NIL LEADCDET (NIL T T T T) -7 NIL NIL NIL) (-636 1451601 1451675 1451904 "LAZM3PK" 1452332 NIL LAZM3PK (NIL T T T T T T) -7 NIL NIL NIL) (-635 1446518 1449678 1450216 "LAUPOL" 1451113 NIL LAUPOL (NIL T T) -8 NIL NIL NIL) (-634 1446097 1446141 1446302 "LAPLACE" 1446468 NIL LAPLACE (NIL T T) -7 NIL NIL NIL) (-633 1444036 1445198 1445449 "LA" 1445930 NIL LA (NIL T T T) -8 NIL NIL NIL) (-632 1443016 1443600 1443641 "LALG" 1443703 NIL LALG (NIL T) -9 NIL 1443762 NIL) (-631 1442730 1442789 1442925 "LALG-" 1442930 NIL LALG- (NIL T T) -8 NIL NIL NIL) (-630 1442565 1442589 1442630 "KVTFROM" 1442692 NIL KVTFROM (NIL T) -9 NIL NIL NIL) (-629 1441488 1441932 1442117 "KTVLOGIC" 1442400 T KTVLOGIC (NIL) -8 NIL NIL NIL) (-628 1441323 1441347 1441388 "KRCFROM" 1441450 NIL KRCFROM (NIL T) -9 NIL NIL NIL) (-627 1440227 1440414 1440713 "KOVACIC" 1441123 NIL KOVACIC (NIL T T) -7 NIL NIL NIL) (-626 1440062 1440086 1440127 "KONVERT" 1440189 NIL KONVERT (NIL T) -9 NIL NIL NIL) (-625 1439897 1439921 1439962 "KOERCE" 1440024 NIL KOERCE (NIL T) -9 NIL NIL NIL) (-624 1437728 1438490 1438867 "KERNEL" 1439553 NIL KERNEL (NIL T) -8 NIL NIL NIL) (-623 1437224 1437305 1437437 "KERNEL2" 1437642 NIL KERNEL2 (NIL T T) -7 NIL NIL NIL) (-622 1430934 1435701 1435755 "KDAGG" 1436132 NIL KDAGG (NIL T T) -9 NIL 1436338 NIL) (-621 1430463 1430587 1430792 "KDAGG-" 1430797 NIL KDAGG- (NIL T T T) -8 NIL NIL NIL) (-620 1423611 1430124 1430279 "KAFILE" 1430341 NIL KAFILE (NIL T) -8 NIL NIL NIL) (-619 1418039 1423122 1423350 "JORDAN" 1423432 NIL JORDAN (NIL T T) -8 NIL NIL NIL) (-618 1417418 1417688 1417809 "JOINAST" 1417938 T JOINAST (NIL) -8 NIL NIL NIL) (-617 1417264 1417323 1417378 "JAVACODE" 1417383 T JAVACODE (NIL) -8 NIL NIL NIL) (-616 1413490 1415441 1415495 "IXAGG" 1416424 NIL IXAGG (NIL T T) -9 NIL 1416883 NIL) (-615 1412409 1412715 1413134 "IXAGG-" 1413139 NIL IXAGG- (NIL T T T) -8 NIL NIL NIL) (-614 1407941 1412331 1412390 "IVECTOR" 1412395 NIL IVECTOR (NIL T NIL) -8 NIL NIL NIL) (-613 1406707 1406944 1407210 "ITUPLE" 1407708 NIL ITUPLE (NIL T) -8 NIL NIL NIL) (-612 1405209 1405386 1405681 "ITRIGMNP" 1406529 NIL ITRIGMNP (NIL T T T) -7 NIL NIL NIL) (-611 1403954 1404158 1404441 "ITFUN3" 1404985 NIL ITFUN3 (NIL T T T) -7 NIL NIL NIL) (-610 1403586 1403643 1403752 "ITFUN2" 1403891 NIL ITFUN2 (NIL T T) -7 NIL NIL NIL) (-609 1402745 1403066 1403240 "ITFORM" 1403432 T ITFORM (NIL) -8 NIL NIL NIL) (-608 1400706 1401765 1402043 "ITAYLOR" 1402500 NIL ITAYLOR (NIL T) -8 NIL NIL NIL) (-607 1389651 1394843 1396006 "ISUPS" 1399576 NIL ISUPS (NIL T) -8 NIL NIL NIL) (-606 1388755 1388895 1389131 "ISUMP" 1389498 NIL ISUMP (NIL T T T T) -7 NIL NIL NIL) (-605 1384132 1388700 1388741 "ISTRING" 1388746 NIL ISTRING (NIL NIL) -8 NIL NIL NIL) (-604 1383608 1383853 1383945 "ISAST" 1384060 T ISAST (NIL) -8 NIL NIL NIL) (-603 1382817 1382899 1383115 "IRURPK" 1383522 NIL IRURPK (NIL T T T T T) -7 NIL NIL NIL) (-602 1381753 1381954 1382194 "IRSN" 1382597 T IRSN (NIL) -7 NIL NIL NIL) (-601 1379824 1380179 1380608 "IRRF2F" 1381391 NIL IRRF2F (NIL T) -7 NIL NIL NIL) (-600 1379571 1379609 1379685 "IRREDFFX" 1379780 NIL IRREDFFX (NIL T) -7 NIL NIL NIL) (-599 1378186 1378445 1378744 "IROOT" 1379304 NIL IROOT (NIL T) -7 NIL NIL NIL) (-598 1374790 1375870 1376562 "IR" 1377526 NIL IR (NIL T) -8 NIL NIL NIL) (-597 1373995 1374283 1374434 "IRFORM" 1374659 T IRFORM (NIL) -8 NIL NIL NIL) (-596 1371608 1372103 1372669 "IR2" 1373473 NIL IR2 (NIL T T) -7 NIL NIL NIL) (-595 1370708 1370821 1371035 "IR2F" 1371491 NIL IR2F (NIL T T) -7 NIL NIL NIL) (-594 1370499 1370533 1370593 "IPRNTPK" 1370668 T IPRNTPK (NIL) -7 NIL NIL NIL) (-593 1367080 1370388 1370457 "IPF" 1370462 NIL IPF (NIL NIL) -8 NIL NIL NIL) (-592 1365407 1367005 1367062 "IPADIC" 1367067 NIL IPADIC (NIL NIL NIL) -8 NIL NIL NIL) (-591 1364719 1364967 1365097 "IP4ADDR" 1365297 T IP4ADDR (NIL) -8 NIL NIL NIL) (-590 1364093 1364348 1364480 "IOMODE" 1364607 T IOMODE (NIL) -8 NIL NIL NIL) (-589 1363166 1363690 1363817 "IOBFILE" 1363986 T IOBFILE (NIL) -8 NIL NIL NIL) (-588 1362654 1363070 1363098 "IOBCON" 1363103 T IOBCON (NIL) -9 NIL 1363124 NIL) (-587 1362165 1362223 1362406 "INVLAPLA" 1362590 NIL INVLAPLA (NIL T T) -7 NIL NIL NIL) (-586 1351813 1354167 1356553 "INTTR" 1359829 NIL INTTR (NIL T T) -7 NIL NIL NIL) (-585 1348148 1348890 1349755 "INTTOOLS" 1350998 NIL INTTOOLS (NIL T T) -7 NIL NIL NIL) (-584 1347734 1347825 1347942 "INTSLPE" 1348051 T INTSLPE (NIL) -7 NIL NIL NIL) (-583 1345687 1347657 1347716 "INTRVL" 1347721 NIL INTRVL (NIL T) -8 NIL NIL NIL) (-582 1343289 1343801 1344376 "INTRF" 1345172 NIL INTRF (NIL T) -7 NIL NIL NIL) (-581 1342700 1342797 1342939 "INTRET" 1343187 NIL INTRET (NIL T) -7 NIL NIL NIL) (-580 1340697 1341086 1341556 "INTRAT" 1342308 NIL INTRAT (NIL T T) -7 NIL NIL NIL) (-579 1337960 1338543 1339162 "INTPM" 1340182 NIL INTPM (NIL T T) -7 NIL NIL NIL) (-578 1334705 1335304 1336042 "INTPAF" 1337346 NIL INTPAF (NIL T T T) -7 NIL NIL NIL) (-577 1329884 1330846 1331897 "INTPACK" 1333674 T INTPACK (NIL) -7 NIL NIL NIL) (-576 1326696 1329681 1329790 "INT" 1329795 T INT (NIL) -8 NIL NIL NIL) (-575 1325948 1326100 1326308 "INTHERTR" 1326538 NIL INTHERTR (NIL T T) -7 NIL NIL NIL) (-574 1325387 1325467 1325655 "INTHERAL" 1325862 NIL INTHERAL (NIL T T T T) -7 NIL NIL NIL) (-573 1323233 1323676 1324133 "INTHEORY" 1324950 T INTHEORY (NIL) -7 NIL NIL NIL) (-572 1314639 1316260 1318032 "INTG0" 1321585 NIL INTG0 (NIL T T T) -7 NIL NIL NIL) (-571 1295212 1300002 1304812 "INTFTBL" 1309849 T INTFTBL (NIL) -8 NIL NIL NIL) (-570 1294461 1294599 1294772 "INTFACT" 1295071 NIL INTFACT (NIL T) -7 NIL NIL NIL) (-569 1291888 1292334 1292891 "INTEF" 1294015 NIL INTEF (NIL T T) -7 NIL NIL NIL) (-568 1290241 1290980 1291008 "INTDOM" 1291309 T INTDOM (NIL) -9 NIL 1291516 NIL) (-567 1289610 1289784 1290026 "INTDOM-" 1290031 NIL INTDOM- (NIL T) -8 NIL NIL NIL) (-566 1285984 1287912 1287966 "INTCAT" 1288765 NIL INTCAT (NIL T) -9 NIL 1289086 NIL) (-565 1285456 1285559 1285687 "INTBIT" 1285876 T INTBIT (NIL) -7 NIL NIL NIL) (-564 1284155 1284309 1284616 "INTALG" 1285301 NIL INTALG (NIL T T T T T) -7 NIL NIL NIL) (-563 1283638 1283728 1283885 "INTAF" 1284059 NIL INTAF (NIL T T) -7 NIL NIL NIL) (-562 1276985 1283448 1283588 "INTABL" 1283593 NIL INTABL (NIL T T T) -8 NIL NIL NIL) (-561 1276318 1276784 1276849 "INT8" 1276883 T INT8 (NIL) -8 NIL NIL 1276928) (-560 1275650 1276116 1276181 "INT64" 1276215 T INT64 (NIL) -8 NIL NIL 1276260) (-559 1274982 1275448 1275513 "INT32" 1275547 T INT32 (NIL) -8 NIL NIL 1275592) (-558 1274314 1274780 1274845 "INT16" 1274879 T INT16 (NIL) -8 NIL NIL 1274924) (-557 1269023 1271875 1271903 "INS" 1272837 T INS (NIL) -9 NIL 1273502 NIL) (-556 1266263 1267034 1268008 "INS-" 1268081 NIL INS- (NIL T) -8 NIL NIL NIL) (-555 1265038 1265265 1265563 "INPSIGN" 1266016 NIL INPSIGN (NIL T T) -7 NIL NIL NIL) (-554 1264156 1264273 1264470 "INPRODPF" 1264918 NIL INPRODPF (NIL T T) -7 NIL NIL NIL) (-553 1263050 1263167 1263404 "INPRODFF" 1264036 NIL INPRODFF (NIL T T T T) -7 NIL NIL NIL) (-552 1262050 1262202 1262462 "INNMFACT" 1262886 NIL INNMFACT (NIL T T T T) -7 NIL NIL NIL) (-551 1261247 1261344 1261532 "INMODGCD" 1261949 NIL INMODGCD (NIL T T NIL NIL) -7 NIL NIL NIL) (-550 1259755 1260000 1260324 "INFSP" 1260992 NIL INFSP (NIL T T T) -7 NIL NIL NIL) (-549 1258939 1259056 1259239 "INFPROD0" 1259635 NIL INFPROD0 (NIL T T) -7 NIL NIL NIL) (-548 1255794 1257004 1257519 "INFORM" 1258432 T INFORM (NIL) -8 NIL NIL NIL) (-547 1255404 1255464 1255562 "INFORM1" 1255729 NIL INFORM1 (NIL T) -7 NIL NIL NIL) (-546 1254927 1255016 1255130 "INFINITY" 1255310 T INFINITY (NIL) -7 NIL NIL NIL) (-545 1254103 1254647 1254748 "INETCLTS" 1254846 T INETCLTS (NIL) -8 NIL NIL NIL) (-544 1252719 1252969 1253290 "INEP" 1253851 NIL INEP (NIL T T T) -7 NIL NIL NIL) (-543 1251968 1252616 1252681 "INDE" 1252686 NIL INDE (NIL T) -8 NIL NIL NIL) (-542 1251532 1251600 1251717 "INCRMAPS" 1251895 NIL INCRMAPS (NIL T) -7 NIL NIL NIL) (-541 1250350 1250801 1251007 "INBFILE" 1251346 T INBFILE (NIL) -8 NIL NIL NIL) (-540 1245649 1246586 1247530 "INBFF" 1249438 NIL INBFF (NIL T) -7 NIL NIL NIL) (-539 1244557 1244826 1244854 "INBCON" 1245367 T INBCON (NIL) -9 NIL 1245633 NIL) (-538 1243809 1244032 1244308 "INBCON-" 1244313 NIL INBCON- (NIL T) -8 NIL NIL NIL) (-537 1243288 1243533 1243624 "INAST" 1243738 T INAST (NIL) -8 NIL NIL NIL) (-536 1242715 1242967 1243073 "IMPTAST" 1243202 T IMPTAST (NIL) -8 NIL NIL NIL) (-535 1239115 1242559 1242663 "IMATRIX" 1242668 NIL IMATRIX (NIL T NIL NIL) -8 NIL NIL NIL) (-534 1237823 1237946 1238262 "IMATQF" 1238971 NIL IMATQF (NIL T T T T T T T T) -7 NIL NIL NIL) (-533 1236043 1236270 1236607 "IMATLIN" 1237579 NIL IMATLIN (NIL T T T T) -7 NIL NIL NIL) (-532 1230623 1235967 1236025 "ILIST" 1236030 NIL ILIST (NIL T NIL) -8 NIL NIL NIL) (-531 1228530 1230483 1230596 "IIARRAY2" 1230601 NIL IIARRAY2 (NIL T NIL NIL T T) -8 NIL NIL NIL) (-530 1223928 1228441 1228505 "IFF" 1228510 NIL IFF (NIL NIL NIL) -8 NIL NIL NIL) (-529 1223275 1223545 1223661 "IFAST" 1223832 T IFAST (NIL) -8 NIL NIL NIL) (-528 1218272 1222567 1222755 "IFARRAY" 1223132 NIL IFARRAY (NIL T NIL) -8 NIL NIL NIL) (-527 1217452 1218176 1218249 "IFAMON" 1218254 NIL IFAMON (NIL T T NIL) -8 NIL NIL NIL) (-526 1217036 1217101 1217155 "IEVALAB" 1217362 NIL IEVALAB (NIL T T) -9 NIL NIL NIL) (-525 1216711 1216779 1216939 "IEVALAB-" 1216944 NIL IEVALAB- (NIL T T T) -8 NIL NIL NIL) (-524 1216342 1216625 1216688 "IDPO" 1216693 NIL IDPO (NIL T T) -8 NIL NIL NIL) (-523 1215592 1216231 1216306 "IDPOAMS" 1216311 NIL IDPOAMS (NIL T T) -8 NIL NIL NIL) (-522 1214899 1215481 1215556 "IDPOAM" 1215561 NIL IDPOAM (NIL T T) -8 NIL NIL NIL) (-521 1213944 1214220 1214273 "IDPC" 1214686 NIL IDPC (NIL T T) -9 NIL 1214835 NIL) (-520 1213413 1213836 1213909 "IDPAM" 1213914 NIL IDPAM (NIL T T) -8 NIL NIL NIL) (-519 1212789 1213305 1213378 "IDPAG" 1213383 NIL IDPAG (NIL T T) -8 NIL NIL NIL) (-518 1212434 1212625 1212700 "IDENT" 1212734 T IDENT (NIL) -8 NIL NIL NIL) (-517 1208689 1209537 1210432 "IDECOMP" 1211591 NIL IDECOMP (NIL NIL NIL) -7 NIL NIL NIL) (-516 1201526 1202612 1203659 "IDEAL" 1207725 NIL IDEAL (NIL T T T T) -8 NIL NIL NIL) (-515 1200686 1200798 1200998 "ICDEN" 1201410 NIL ICDEN (NIL T T T T) -7 NIL NIL NIL) (-514 1199757 1200166 1200313 "ICARD" 1200559 T ICARD (NIL) -8 NIL NIL NIL) (-513 1197817 1198130 1198535 "IBPTOOLS" 1199434 NIL IBPTOOLS (NIL T T T T) -7 NIL NIL NIL) (-512 1193424 1197437 1197550 "IBITS" 1197736 NIL IBITS (NIL NIL) -8 NIL NIL NIL) (-511 1190147 1190723 1191418 "IBATOOL" 1192841 NIL IBATOOL (NIL T T T) -7 NIL NIL NIL) (-510 1187926 1188388 1188921 "IBACHIN" 1189682 NIL IBACHIN (NIL T T T) -7 NIL NIL NIL) (-509 1185757 1187772 1187875 "IARRAY2" 1187880 NIL IARRAY2 (NIL T NIL NIL) -8 NIL NIL NIL) (-508 1181865 1185683 1185740 "IARRAY1" 1185745 NIL IARRAY1 (NIL T NIL) -8 NIL NIL NIL) (-507 1175725 1180277 1180758 "IAN" 1181404 T IAN (NIL) -8 NIL NIL NIL) (-506 1175236 1175293 1175466 "IALGFACT" 1175662 NIL IALGFACT (NIL T T T T) -7 NIL NIL NIL) (-505 1174764 1174877 1174905 "HYPCAT" 1175112 T HYPCAT (NIL) -9 NIL NIL NIL) (-504 1174302 1174419 1174605 "HYPCAT-" 1174610 NIL HYPCAT- (NIL T) -8 NIL NIL NIL) (-503 1173897 1174097 1174180 "HOSTNAME" 1174239 T HOSTNAME (NIL) -8 NIL NIL NIL) (-502 1173742 1173779 1173820 "HOMOTOP" 1173825 NIL HOMOTOP (NIL T) -9 NIL 1173858 NIL) (-501 1170298 1171674 1171715 "HOAGG" 1172696 NIL HOAGG (NIL T) -9 NIL 1173425 NIL) (-500 1168892 1169291 1169817 "HOAGG-" 1169822 NIL HOAGG- (NIL T T) -8 NIL NIL NIL) (-499 1162608 1168485 1168635 "HEXADEC" 1168762 T HEXADEC (NIL) -8 NIL NIL NIL) (-498 1161356 1161578 1161841 "HEUGCD" 1162385 NIL HEUGCD (NIL T) -7 NIL NIL NIL) (-497 1160432 1161193 1161323 "HELLFDIV" 1161328 NIL HELLFDIV (NIL T T T T) -8 NIL NIL NIL) (-496 1158613 1160209 1160297 "HEAP" 1160376 NIL HEAP (NIL T) -8 NIL NIL NIL) (-495 1157876 1158165 1158299 "HEADAST" 1158499 T HEADAST (NIL) -8 NIL NIL NIL) (-494 1151718 1157791 1157853 "HDP" 1157858 NIL HDP (NIL NIL T) -8 NIL NIL NIL) (-493 1145430 1151353 1151505 "HDMP" 1151619 NIL HDMP (NIL NIL T) -8 NIL NIL NIL) (-492 1144754 1144894 1145058 "HB" 1145286 T HB (NIL) -7 NIL NIL NIL) (-491 1138144 1144600 1144704 "HASHTBL" 1144709 NIL HASHTBL (NIL T T NIL) -8 NIL NIL NIL) (-490 1137620 1137865 1137957 "HASAST" 1138072 T HASAST (NIL) -8 NIL NIL NIL) (-489 1135398 1137242 1137424 "HACKPI" 1137458 T HACKPI (NIL) -8 NIL NIL NIL) (-488 1131066 1135251 1135364 "GTSET" 1135369 NIL GTSET (NIL T T T T) -8 NIL NIL NIL) (-487 1124485 1130944 1131042 "GSTBL" 1131047 NIL GSTBL (NIL T T T NIL) -8 NIL NIL NIL) (-486 1116872 1123650 1123906 "GSERIES" 1124285 NIL GSERIES (NIL T NIL NIL) -8 NIL NIL NIL) (-485 1115999 1116416 1116444 "GROUP" 1116647 T GROUP (NIL) -9 NIL 1116781 NIL) (-484 1115365 1115524 1115775 "GROUP-" 1115780 NIL GROUP- (NIL T) -8 NIL NIL NIL) (-483 1113732 1114053 1114440 "GROEBSOL" 1115042 NIL GROEBSOL (NIL NIL T T) -7 NIL NIL NIL) (-482 1112632 1112920 1112971 "GRMOD" 1113500 NIL GRMOD (NIL T T) -9 NIL 1113668 NIL) (-481 1112400 1112436 1112564 "GRMOD-" 1112569 NIL GRMOD- (NIL T T T) -8 NIL NIL NIL) (-480 1107690 1108754 1109754 "GRIMAGE" 1111420 T GRIMAGE (NIL) -8 NIL NIL NIL) (-479 1106156 1106417 1106741 "GRDEF" 1107386 T GRDEF (NIL) -7 NIL NIL NIL) (-478 1105600 1105716 1105857 "GRAY" 1106035 T GRAY (NIL) -7 NIL NIL NIL) (-477 1104773 1105179 1105230 "GRALG" 1105383 NIL GRALG (NIL T T) -9 NIL 1105476 NIL) (-476 1104434 1104507 1104670 "GRALG-" 1104675 NIL GRALG- (NIL T T T) -8 NIL NIL NIL) (-475 1101211 1104019 1104197 "GPOLSET" 1104341 NIL GPOLSET (NIL T T T T) -8 NIL NIL NIL) (-474 1100565 1100622 1100880 "GOSPER" 1101148 NIL GOSPER (NIL T T T T T) -7 NIL NIL NIL) (-473 1096297 1097003 1097529 "GMODPOL" 1100264 NIL GMODPOL (NIL NIL T T T NIL T) -8 NIL NIL NIL) (-472 1095302 1095486 1095724 "GHENSEL" 1096109 NIL GHENSEL (NIL T T) -7 NIL NIL NIL) (-471 1089458 1090301 1091321 "GENUPS" 1094386 NIL GENUPS (NIL T T) -7 NIL NIL NIL) (-470 1089155 1089206 1089295 "GENUFACT" 1089401 NIL GENUFACT (NIL T) -7 NIL NIL NIL) (-469 1088567 1088644 1088809 "GENPGCD" 1089073 NIL GENPGCD (NIL T T T T) -7 NIL NIL NIL) (-468 1088041 1088076 1088289 "GENMFACT" 1088526 NIL GENMFACT (NIL T T T T T) -7 NIL NIL NIL) (-467 1086607 1086864 1087171 "GENEEZ" 1087784 NIL GENEEZ (NIL T T) -7 NIL NIL NIL) (-466 1080479 1086218 1086380 "GDMP" 1086530 NIL GDMP (NIL NIL T T) -8 NIL NIL NIL) (-465 1069822 1074250 1075356 "GCNAALG" 1079462 NIL GCNAALG (NIL T NIL NIL NIL) -8 NIL NIL NIL) (-464 1068135 1068997 1069025 "GCDDOM" 1069280 T GCDDOM (NIL) -9 NIL 1069437 NIL) (-463 1067605 1067732 1067947 "GCDDOM-" 1067952 NIL GCDDOM- (NIL T) -8 NIL NIL NIL) (-462 1066277 1066462 1066766 "GB" 1067384 NIL GB (NIL T T T T) -7 NIL NIL NIL) (-461 1054893 1057223 1059615 "GBINTERN" 1063968 NIL GBINTERN (NIL T T T T) -7 NIL NIL NIL) (-460 1052730 1053022 1053443 "GBF" 1054568 NIL GBF (NIL T T T T) -7 NIL NIL NIL) (-459 1051511 1051676 1051943 "GBEUCLID" 1052546 NIL GBEUCLID (NIL T T T T) -7 NIL NIL NIL) (-458 1050860 1050985 1051134 "GAUSSFAC" 1051382 T GAUSSFAC (NIL) -7 NIL NIL NIL) (-457 1049227 1049529 1049843 "GALUTIL" 1050579 NIL GALUTIL (NIL T) -7 NIL NIL NIL) (-456 1047535 1047809 1048133 "GALPOLYU" 1048954 NIL GALPOLYU (NIL T T) -7 NIL NIL NIL) (-455 1044900 1045190 1045597 "GALFACTU" 1047232 NIL GALFACTU (NIL T T T) -7 NIL NIL NIL) (-454 1036706 1038205 1039813 "GALFACT" 1043332 NIL GALFACT (NIL T) -7 NIL NIL NIL) (-453 1034094 1034752 1034780 "FVFUN" 1035936 T FVFUN (NIL) -9 NIL 1036656 NIL) (-452 1033360 1033542 1033570 "FVC" 1033861 T FVC (NIL) -9 NIL 1034044 NIL) (-451 1033003 1033185 1033253 "FUNDESC" 1033312 T FUNDESC (NIL) -8 NIL NIL NIL) (-450 1032618 1032800 1032881 "FUNCTION" 1032955 NIL FUNCTION (NIL NIL) -8 NIL NIL NIL) (-449 1030362 1030940 1031406 "FT" 1032172 T FT (NIL) -8 NIL NIL NIL) (-448 1029153 1029663 1029866 "FTEM" 1030179 T FTEM (NIL) -8 NIL NIL NIL) (-447 1027444 1027733 1028130 "FSUPFACT" 1028844 NIL FSUPFACT (NIL T T T) -7 NIL NIL NIL) (-446 1025841 1026130 1026462 "FST" 1027132 T FST (NIL) -8 NIL NIL NIL) (-445 1025040 1025146 1025334 "FSRED" 1025723 NIL FSRED (NIL T T) -7 NIL NIL NIL) (-444 1023739 1023995 1024342 "FSPRMELT" 1024755 NIL FSPRMELT (NIL T T) -7 NIL NIL NIL) (-443 1021045 1021483 1021969 "FSPECF" 1023302 NIL FSPECF (NIL T T) -7 NIL NIL NIL) (-442 1002110 1010819 1010860 "FS" 1014744 NIL FS (NIL T) -9 NIL 1017033 NIL) (-441 990753 993746 997803 "FS-" 998103 NIL FS- (NIL T T) -8 NIL NIL NIL) (-440 990281 990335 990505 "FSINT" 990694 NIL FSINT (NIL T T) -7 NIL NIL NIL) (-439 988573 989274 989577 "FSERIES" 990060 NIL FSERIES (NIL T T) -8 NIL NIL NIL) (-438 987615 987731 987955 "FSCINT" 988453 NIL FSCINT (NIL T T) -7 NIL NIL NIL) (-437 983823 986559 986600 "FSAGG" 986970 NIL FSAGG (NIL T) -9 NIL 987229 NIL) (-436 981585 982186 982982 "FSAGG-" 983077 NIL FSAGG- (NIL T T) -8 NIL NIL NIL) (-435 980627 980770 980997 "FSAGG2" 981438 NIL FSAGG2 (NIL T T T T) -7 NIL NIL NIL) (-434 978305 978585 979133 "FS2UPS" 980345 NIL FS2UPS (NIL T T T T T NIL) -7 NIL NIL NIL) (-433 977939 977982 978111 "FS2" 978256 NIL FS2 (NIL T T T T) -7 NIL NIL NIL) (-432 976817 976988 977290 "FS2EXPXP" 977764 NIL FS2EXPXP (NIL T T NIL NIL) -7 NIL NIL NIL) (-431 976243 976358 976510 "FRUTIL" 976697 NIL FRUTIL (NIL T) -7 NIL NIL NIL) (-430 967656 971738 973096 "FR" 974917 NIL FR (NIL T) -8 NIL NIL NIL) (-429 962670 965345 965385 "FRNAALG" 966705 NIL FRNAALG (NIL T) -9 NIL 967303 NIL) (-428 958343 959419 960694 "FRNAALG-" 961444 NIL FRNAALG- (NIL T T) -8 NIL NIL NIL) (-427 957981 958024 958151 "FRNAAF2" 958294 NIL FRNAAF2 (NIL T T T T) -7 NIL NIL NIL) (-426 956356 956830 957126 "FRMOD" 957793 NIL FRMOD (NIL T T T T NIL) -8 NIL NIL NIL) (-425 954099 954731 955049 "FRIDEAL" 956147 NIL FRIDEAL (NIL T T T T) -8 NIL NIL NIL) (-424 953290 953377 953668 "FRIDEAL2" 954006 NIL FRIDEAL2 (NIL T T T T T T T T) -7 NIL NIL NIL) (-423 952423 952837 952878 "FRETRCT" 952883 NIL FRETRCT (NIL T) -9 NIL 953059 NIL) (-422 951535 951766 952117 "FRETRCT-" 952122 NIL FRETRCT- (NIL T T) -8 NIL NIL NIL) (-421 948609 949819 949878 "FRAMALG" 950760 NIL FRAMALG (NIL T T) -9 NIL 951052 NIL) (-420 946743 947198 947828 "FRAMALG-" 948051 NIL FRAMALG- (NIL T T T) -8 NIL NIL NIL) (-419 940386 946216 946493 "FRAC" 946498 NIL FRAC (NIL T) -8 NIL NIL NIL) (-418 940022 940079 940186 "FRAC2" 940323 NIL FRAC2 (NIL T T) -7 NIL NIL NIL) (-417 939658 939715 939822 "FR2" 939959 NIL FR2 (NIL T T) -7 NIL NIL NIL) (-416 934157 937050 937078 "FPS" 938197 T FPS (NIL) -9 NIL 938754 NIL) (-415 933606 933715 933879 "FPS-" 934025 NIL FPS- (NIL T) -8 NIL NIL NIL) (-414 930894 932563 932591 "FPC" 932816 T FPC (NIL) -9 NIL 932958 NIL) (-413 930687 930727 930824 "FPC-" 930829 NIL FPC- (NIL T) -8 NIL NIL NIL) (-412 929477 930175 930216 "FPATMAB" 930221 NIL FPATMAB (NIL T) -9 NIL 930373 NIL) (-411 927716 928219 928566 "FPARFRAC" 929193 NIL FPARFRAC (NIL T T) -8 NIL NIL NIL) (-410 923110 923608 924290 "FORTRAN" 927148 NIL FORTRAN (NIL NIL NIL NIL NIL) -8 NIL NIL NIL) (-409 920826 921326 921865 "FORT" 922591 T FORT (NIL) -7 NIL NIL NIL) (-408 918502 919064 919092 "FORTFN" 920152 T FORTFN (NIL) -9 NIL 920776 NIL) (-407 918266 918316 918344 "FORTCAT" 918403 T FORTCAT (NIL) -9 NIL 918465 NIL) (-406 916372 916882 917272 "FORMULA" 917896 T FORMULA (NIL) -8 NIL NIL NIL) (-405 916160 916190 916259 "FORMULA1" 916336 NIL FORMULA1 (NIL T) -7 NIL NIL NIL) (-404 915683 915735 915908 "FORDER" 916102 NIL FORDER (NIL T T T T) -7 NIL NIL NIL) (-403 914779 914943 915136 "FOP" 915510 T FOP (NIL) -7 NIL NIL NIL) (-402 913360 914059 914233 "FNLA" 914661 NIL FNLA (NIL NIL NIL T) -8 NIL NIL NIL) (-401 912075 912490 912518 "FNCAT" 912978 T FNCAT (NIL) -9 NIL 913238 NIL) (-400 911614 912034 912062 "FNAME" 912067 T FNAME (NIL) -8 NIL NIL NIL) (-399 910163 911126 911154 "FMTC" 911159 T FMTC (NIL) -9 NIL 911195 NIL) (-398 908909 910099 910145 "FMONOID" 910150 NIL FMONOID (NIL T) -8 NIL NIL NIL) (-397 905723 906891 906932 "FMONCAT" 908149 NIL FMONCAT (NIL T) -9 NIL 908754 NIL) (-396 904915 905465 905614 "FM" 905619 NIL FM (NIL T T) -8 NIL NIL NIL) (-395 902339 902985 903013 "FMFUN" 904157 T FMFUN (NIL) -9 NIL 904865 NIL) (-394 901608 901789 901817 "FMC" 902107 T FMC (NIL) -9 NIL 902289 NIL) (-393 898673 899533 899587 "FMCAT" 900782 NIL FMCAT (NIL T T) -9 NIL 901277 NIL) (-392 897539 898439 898539 "FM1" 898618 NIL FM1 (NIL T T) -8 NIL NIL NIL) (-391 895313 895729 896223 "FLOATRP" 897090 NIL FLOATRP (NIL T) -7 NIL NIL NIL) (-390 888891 893042 893663 "FLOAT" 894712 T FLOAT (NIL) -8 NIL NIL NIL) (-389 886329 886829 887407 "FLOATCP" 888358 NIL FLOATCP (NIL T) -7 NIL NIL NIL) (-388 884977 885921 885962 "FLINEXP" 885967 NIL FLINEXP (NIL T) -9 NIL 886060 NIL) (-387 884131 884366 884694 "FLINEXP-" 884699 NIL FLINEXP- (NIL T T) -8 NIL NIL NIL) (-386 883207 883351 883575 "FLASORT" 883983 NIL FLASORT (NIL T T) -7 NIL NIL NIL) (-385 880309 881177 881229 "FLALG" 882456 NIL FLALG (NIL T T) -9 NIL 882923 NIL) (-384 873995 877745 877786 "FLAGG" 879048 NIL FLAGG (NIL T) -9 NIL 879700 NIL) (-383 872721 873060 873550 "FLAGG-" 873555 NIL FLAGG- (NIL T T) -8 NIL NIL NIL) (-382 871763 871906 872133 "FLAGG2" 872574 NIL FLAGG2 (NIL T T T T) -7 NIL NIL NIL) (-381 868600 869608 869667 "FINRALG" 870795 NIL FINRALG (NIL T T) -9 NIL 871303 NIL) (-380 867760 867989 868328 "FINRALG-" 868333 NIL FINRALG- (NIL T T T) -8 NIL NIL NIL) (-379 867126 867365 867393 "FINITE" 867589 T FINITE (NIL) -9 NIL 867696 NIL) (-378 859469 861656 861696 "FINAALG" 865363 NIL FINAALG (NIL T) -9 NIL 866816 NIL) (-377 854801 855851 856995 "FINAALG-" 858374 NIL FINAALG- (NIL T T) -8 NIL NIL NIL) (-376 854169 854556 854659 "FILE" 854731 NIL FILE (NIL T) -8 NIL NIL NIL) (-375 852813 853151 853205 "FILECAT" 853889 NIL FILECAT (NIL T T) -9 NIL 854105 NIL) (-374 850515 852043 852071 "FIELD" 852111 T FIELD (NIL) -9 NIL 852191 NIL) (-373 849135 849520 850031 "FIELD-" 850036 NIL FIELD- (NIL T) -8 NIL NIL NIL) (-372 846985 847770 848117 "FGROUP" 848821 NIL FGROUP (NIL T) -8 NIL NIL NIL) (-371 846075 846239 846459 "FGLMICPK" 846817 NIL FGLMICPK (NIL T NIL) -7 NIL NIL NIL) (-370 841907 846000 846057 "FFX" 846062 NIL FFX (NIL T NIL) -8 NIL NIL NIL) (-369 841508 841569 841704 "FFSLPE" 841840 NIL FFSLPE (NIL T T T) -7 NIL NIL NIL) (-368 837498 838280 839076 "FFPOLY" 840744 NIL FFPOLY (NIL T) -7 NIL NIL NIL) (-367 837002 837038 837247 "FFPOLY2" 837456 NIL FFPOLY2 (NIL T T) -7 NIL NIL NIL) (-366 832848 836921 836984 "FFP" 836989 NIL FFP (NIL T NIL) -8 NIL NIL NIL) (-365 828246 832759 832823 "FF" 832828 NIL FF (NIL NIL NIL) -8 NIL NIL NIL) (-364 823372 827589 827779 "FFNBX" 828100 NIL FFNBX (NIL T NIL) -8 NIL NIL NIL) (-363 818300 822507 822765 "FFNBP" 823226 NIL FFNBP (NIL T NIL) -8 NIL NIL NIL) (-362 812933 817584 817795 "FFNB" 818133 NIL FFNB (NIL NIL NIL) -8 NIL NIL NIL) (-361 811765 811963 812278 "FFINTBAS" 812730 NIL FFINTBAS (NIL T T T) -7 NIL NIL NIL) (-360 807791 810012 810040 "FFIELDC" 810660 T FFIELDC (NIL) -9 NIL 811036 NIL) (-359 806453 806824 807321 "FFIELDC-" 807326 NIL FFIELDC- (NIL T) -8 NIL NIL NIL) (-358 806022 806068 806192 "FFHOM" 806395 NIL FFHOM (NIL T T T) -7 NIL NIL NIL) (-357 803717 804204 804721 "FFF" 805537 NIL FFF (NIL T) -7 NIL NIL NIL) (-356 799335 803459 803560 "FFCGX" 803660 NIL FFCGX (NIL T NIL) -8 NIL NIL NIL) (-355 794957 799067 799174 "FFCGP" 799278 NIL FFCGP (NIL T NIL) -8 NIL NIL NIL) (-354 790140 794684 794792 "FFCG" 794893 NIL FFCG (NIL NIL NIL) -8 NIL NIL NIL) (-353 769669 779872 779958 "FFCAT" 785123 NIL FFCAT (NIL T T T) -9 NIL 786574 NIL) (-352 764866 765914 767228 "FFCAT-" 768458 NIL FFCAT- (NIL T T T T) -8 NIL NIL NIL) (-351 764277 764320 764555 "FFCAT2" 764817 NIL FFCAT2 (NIL T T T T T T T T) -7 NIL NIL NIL) (-350 753600 757249 758469 "FEXPR" 763129 NIL FEXPR (NIL NIL NIL T) -8 NIL NIL NIL) (-349 752562 752997 753038 "FEVALAB" 753122 NIL FEVALAB (NIL T) -9 NIL 753383 NIL) (-348 751721 751931 752269 "FEVALAB-" 752274 NIL FEVALAB- (NIL T T) -8 NIL NIL NIL) (-347 750287 751104 751307 "FDIV" 751620 NIL FDIV (NIL T T T T) -8 NIL NIL NIL) (-346 747293 748034 748149 "FDIVCAT" 749717 NIL FDIVCAT (NIL T T T T) -9 NIL 750154 NIL) (-345 747055 747082 747252 "FDIVCAT-" 747257 NIL FDIVCAT- (NIL T T T T T) -8 NIL NIL NIL) (-344 746275 746362 746639 "FDIV2" 746962 NIL FDIV2 (NIL T T T T T T T T) -7 NIL NIL NIL) (-343 745249 745570 745772 "FCTRDATA" 746093 T FCTRDATA (NIL) -8 NIL NIL NIL) (-342 743935 744194 744483 "FCPAK1" 744980 T FCPAK1 (NIL) -7 NIL NIL NIL) (-341 743034 743435 743576 "FCOMP" 743826 NIL FCOMP (NIL T) -8 NIL NIL NIL) (-340 726739 730184 733722 "FC" 739516 T FC (NIL) -8 NIL NIL NIL) (-339 719032 723060 723100 "FAXF" 724902 NIL FAXF (NIL T) -9 NIL 725594 NIL) (-338 716309 716966 717791 "FAXF-" 718256 NIL FAXF- (NIL T T) -8 NIL NIL NIL) (-337 711363 715685 715861 "FARRAY" 716166 NIL FARRAY (NIL T) -8 NIL NIL NIL) (-336 706243 708310 708363 "FAMR" 709386 NIL FAMR (NIL T T) -9 NIL 709846 NIL) (-335 705133 705435 705870 "FAMR-" 705875 NIL FAMR- (NIL T T T) -8 NIL NIL NIL) (-334 704302 705055 705108 "FAMONOID" 705113 NIL FAMONOID (NIL T) -8 NIL NIL NIL) (-333 702074 702784 702837 "FAMONC" 703778 NIL FAMONC (NIL T T) -9 NIL 704164 NIL) (-332 700738 701828 701965 "FAGROUP" 701970 NIL FAGROUP (NIL T) -8 NIL NIL NIL) (-331 698533 698852 699255 "FACUTIL" 700419 NIL FACUTIL (NIL T T T T) -7 NIL NIL NIL) (-330 697632 697817 698039 "FACTFUNC" 698343 NIL FACTFUNC (NIL T) -7 NIL NIL NIL) (-329 690054 696935 697134 "EXPUPXS" 697488 NIL EXPUPXS (NIL T NIL NIL) -8 NIL NIL NIL) (-328 687537 688077 688663 "EXPRTUBE" 689488 T EXPRTUBE (NIL) -7 NIL NIL NIL) (-327 683808 684400 685130 "EXPRODE" 686876 NIL EXPRODE (NIL T T) -7 NIL NIL NIL) (-326 669292 682457 682886 "EXPR" 683412 NIL EXPR (NIL T) -8 NIL NIL NIL) (-325 663846 664433 665239 "EXPR2UPS" 668590 NIL EXPR2UPS (NIL T T) -7 NIL NIL NIL) (-324 663478 663535 663644 "EXPR2" 663783 NIL EXPR2 (NIL T T) -7 NIL NIL NIL) (-323 654475 662629 662920 "EXPEXPAN" 663314 NIL EXPEXPAN (NIL T T NIL NIL) -8 NIL NIL NIL) (-322 654275 654432 654461 "EXIT" 654466 T EXIT (NIL) -8 NIL NIL NIL) (-321 653755 653999 654090 "EXITAST" 654204 T EXITAST (NIL) -8 NIL NIL NIL) (-320 653382 653444 653557 "EVALCYC" 653687 NIL EVALCYC (NIL T) -7 NIL NIL NIL) (-319 652923 653041 653082 "EVALAB" 653252 NIL EVALAB (NIL T) -9 NIL 653356 NIL) (-318 652404 652526 652747 "EVALAB-" 652752 NIL EVALAB- (NIL T T) -8 NIL NIL NIL) (-317 649758 651060 651088 "EUCDOM" 651643 T EUCDOM (NIL) -9 NIL 651993 NIL) (-316 648163 648605 649195 "EUCDOM-" 649200 NIL EUCDOM- (NIL T) -8 NIL NIL NIL) (-315 635702 638461 641211 "ESTOOLS" 645433 T ESTOOLS (NIL) -7 NIL NIL NIL) (-314 635334 635391 635500 "ESTOOLS2" 635639 NIL ESTOOLS2 (NIL T T) -7 NIL NIL NIL) (-313 635085 635127 635207 "ESTOOLS1" 635286 NIL ESTOOLS1 (NIL T) -7 NIL NIL NIL) (-312 629108 630716 630744 "ES" 633512 T ES (NIL) -9 NIL 634922 NIL) (-311 624055 625342 627159 "ES-" 627323 NIL ES- (NIL T) -8 NIL NIL NIL) (-310 620429 621190 621970 "ESCONT" 623295 T ESCONT (NIL) -7 NIL NIL NIL) (-309 620174 620206 620288 "ESCONT1" 620391 NIL ESCONT1 (NIL NIL NIL) -7 NIL NIL NIL) (-308 619849 619899 619999 "ES2" 620118 NIL ES2 (NIL T T) -7 NIL NIL NIL) (-307 619479 619537 619646 "ES1" 619785 NIL ES1 (NIL T T) -7 NIL NIL NIL) (-306 618695 618824 619000 "ERROR" 619323 T ERROR (NIL) -7 NIL NIL NIL) (-305 612091 618554 618645 "EQTBL" 618650 NIL EQTBL (NIL T T) -8 NIL NIL NIL) (-304 604594 607405 608854 "EQ" 610675 NIL -2054 (NIL T) -8 NIL NIL NIL) (-303 604226 604283 604392 "EQ2" 604531 NIL EQ2 (NIL T T) -7 NIL NIL NIL) (-302 599517 600564 601657 "EP" 603165 NIL EP (NIL T) -7 NIL NIL NIL) (-301 598117 598408 598714 "ENV" 599231 T ENV (NIL) -8 NIL NIL NIL) (-300 597197 597751 597779 "ENTIRER" 597784 T ENTIRER (NIL) -9 NIL 597830 NIL) (-299 593891 595379 595740 "EMR" 597005 NIL EMR (NIL T T T NIL NIL NIL) -8 NIL NIL NIL) (-298 593021 593206 593260 "ELTAGG" 593640 NIL ELTAGG (NIL T T) -9 NIL 593851 NIL) (-297 592740 592802 592943 "ELTAGG-" 592948 NIL ELTAGG- (NIL T T T) -8 NIL NIL NIL) (-296 592504 592533 592587 "ELTAB" 592671 NIL ELTAB (NIL T T) -9 NIL 592723 NIL) (-295 591630 591776 591975 "ELFUTS" 592355 NIL ELFUTS (NIL T T) -7 NIL NIL NIL) (-294 591372 591428 591456 "ELEMFUN" 591561 T ELEMFUN (NIL) -9 NIL NIL NIL) (-293 591242 591263 591331 "ELEMFUN-" 591336 NIL ELEMFUN- (NIL T) -8 NIL NIL NIL) (-292 586030 589284 589325 "ELAGG" 590265 NIL ELAGG (NIL T) -9 NIL 590728 NIL) (-291 584315 584749 585412 "ELAGG-" 585417 NIL ELAGG- (NIL T T) -8 NIL NIL NIL) (-290 583627 583764 583920 "ELABOR" 584179 T ELABOR (NIL) -8 NIL NIL NIL) (-289 582288 582567 582861 "ELABEXPR" 583353 T ELABEXPR (NIL) -8 NIL NIL NIL) (-288 575122 576925 577754 "EFUPXS" 581563 NIL EFUPXS (NIL T T T T) -8 NIL NIL NIL) (-287 568570 570371 571182 "EFULS" 574397 NIL EFULS (NIL T T T) -8 NIL NIL NIL) (-286 566055 566413 566885 "EFSTRUC" 568202 NIL EFSTRUC (NIL T T) -7 NIL NIL NIL) (-285 555846 557412 558960 "EF" 564570 NIL EF (NIL T T) -7 NIL NIL NIL) (-284 554920 555331 555480 "EAB" 555717 T EAB (NIL) -8 NIL NIL NIL) (-283 554102 554879 554907 "E04UCFA" 554912 T E04UCFA (NIL) -8 NIL NIL NIL) (-282 553284 554061 554089 "E04NAFA" 554094 T E04NAFA (NIL) -8 NIL NIL NIL) (-281 552466 553243 553271 "E04MBFA" 553276 T E04MBFA (NIL) -8 NIL NIL NIL) (-280 551648 552425 552453 "E04JAFA" 552458 T E04JAFA (NIL) -8 NIL NIL NIL) (-279 550832 551607 551635 "E04GCFA" 551640 T E04GCFA (NIL) -8 NIL NIL NIL) (-278 550016 550791 550819 "E04FDFA" 550824 T E04FDFA (NIL) -8 NIL NIL NIL) (-277 549198 549975 550003 "E04DGFA" 550008 T E04DGFA (NIL) -8 NIL NIL NIL) (-276 543371 544723 546087 "E04AGNT" 547854 T E04AGNT (NIL) -7 NIL NIL NIL) (-275 542142 542685 542725 "DVARCAT" 543066 NIL DVARCAT (NIL T) -9 NIL 543229 NIL) (-274 541346 541558 541872 "DVARCAT-" 541877 NIL DVARCAT- (NIL T T) -8 NIL NIL NIL) (-273 534207 541145 541274 "DSMP" 541279 NIL DSMP (NIL T T T) -8 NIL NIL NIL) (-272 532630 533349 533390 "DSEXT" 533753 NIL DSEXT (NIL T) -9 NIL 534047 NIL) (-271 530915 531343 532009 "DSEXT-" 532014 NIL DSEXT- (NIL T T) -8 NIL NIL NIL) (-270 525696 526860 527928 "DROPT" 529867 T DROPT (NIL) -8 NIL NIL NIL) (-269 525361 525420 525518 "DROPT1" 525631 NIL DROPT1 (NIL T) -7 NIL NIL NIL) (-268 520476 521602 522739 "DROPT0" 524244 T DROPT0 (NIL) -7 NIL NIL NIL) (-267 518821 519146 519532 "DRAWPT" 520110 T DRAWPT (NIL) -7 NIL NIL NIL) (-266 513408 514331 515410 "DRAW" 517795 NIL DRAW (NIL T) -7 NIL NIL NIL) (-265 513041 513094 513212 "DRAWHACK" 513349 NIL DRAWHACK (NIL T) -7 NIL NIL NIL) (-264 511772 512041 512332 "DRAWCX" 512770 T DRAWCX (NIL) -7 NIL NIL NIL) (-263 511287 511356 511507 "DRAWCURV" 511698 NIL DRAWCURV (NIL T T) -7 NIL NIL NIL) (-262 501755 503717 505832 "DRAWCFUN" 509192 T DRAWCFUN (NIL) -7 NIL NIL NIL) (-261 498493 500420 500461 "DQAGG" 501090 NIL DQAGG (NIL T) -9 NIL 501364 NIL) (-260 485958 492704 492787 "DPOLCAT" 494639 NIL DPOLCAT (NIL T T T T) -9 NIL 495184 NIL) (-259 480795 482143 484101 "DPOLCAT-" 484106 NIL DPOLCAT- (NIL T T T T T) -8 NIL NIL NIL) (-258 474142 480656 480754 "DPMO" 480759 NIL DPMO (NIL NIL T T) -8 NIL NIL NIL) (-257 467392 473922 474089 "DPMM" 474094 NIL DPMM (NIL NIL T T T) -8 NIL NIL NIL) (-256 466962 467176 467265 "DOMTMPLT" 467323 T DOMTMPLT (NIL) -8 NIL NIL NIL) (-255 466395 466764 466844 "DOMCTOR" 466902 T DOMCTOR (NIL) -8 NIL NIL NIL) (-254 465607 465875 466026 "DOMAIN" 466264 T DOMAIN (NIL) -8 NIL NIL NIL) (-253 459319 465242 465394 "DMP" 465508 NIL DMP (NIL NIL T) -8 NIL NIL NIL) (-252 457264 458386 458427 "DMEXT" 458432 NIL DMEXT (NIL T) -9 NIL 458608 NIL) (-251 456864 456920 457064 "DLP" 457202 NIL DLP (NIL T) -7 NIL NIL NIL) (-250 450688 456191 456381 "DLIST" 456706 NIL DLIST (NIL T) -8 NIL NIL NIL) (-249 447459 449513 449554 "DLAGG" 450104 NIL DLAGG (NIL T) -9 NIL 450334 NIL) (-248 446121 446785 446813 "DIVRING" 446905 T DIVRING (NIL) -9 NIL 446988 NIL) (-247 445358 445548 445848 "DIVRING-" 445853 NIL DIVRING- (NIL T) -8 NIL NIL NIL) (-246 443460 443817 444223 "DISPLAY" 444972 T DISPLAY (NIL) -7 NIL NIL NIL) (-245 437322 443374 443437 "DIRPROD" 443442 NIL DIRPROD (NIL NIL T) -8 NIL NIL NIL) (-244 436170 436373 436638 "DIRPROD2" 437115 NIL DIRPROD2 (NIL NIL T T) -7 NIL NIL NIL) (-243 424899 430936 430989 "DIRPCAT" 431247 NIL DIRPCAT (NIL NIL T) -9 NIL 432122 NIL) (-242 422225 422867 423748 "DIRPCAT-" 424085 NIL DIRPCAT- (NIL T NIL T) -8 NIL NIL NIL) (-241 421512 421672 421858 "DIOSP" 422059 T DIOSP (NIL) -7 NIL NIL NIL) (-240 418141 420396 420437 "DIOPS" 420871 NIL DIOPS (NIL T) -9 NIL 421100 NIL) (-239 417690 417804 417995 "DIOPS-" 418000 NIL DIOPS- (NIL T T) -8 NIL NIL NIL) (-238 416741 417369 417397 "DIFRING" 417402 T DIFRING (NIL) -9 NIL 417424 NIL) (-237 416413 416487 416515 "DIFFSPC" 416634 T DIFFSPC (NIL) -9 NIL 416709 NIL) (-236 416058 416136 416288 "DIFFSPC-" 416293 NIL DIFFSPC- (NIL T) -8 NIL NIL NIL) (-235 415114 415592 415633 "DIFFMOD" 415638 NIL DIFFMOD (NIL T) -9 NIL 415736 NIL) (-234 414822 414867 414908 "DIFFDOM" 415029 NIL DIFFDOM (NIL T) -9 NIL 415097 NIL) (-233 414675 414699 414783 "DIFFDOM-" 414788 NIL DIFFDOM- (NIL T T) -8 NIL NIL NIL) (-232 412607 413879 413920 "DIFEXT" 413925 NIL DIFEXT (NIL T) -9 NIL 414078 NIL) (-231 409856 412111 412152 "DIAGG" 412157 NIL DIAGG (NIL T) -9 NIL 412177 NIL) (-230 409240 409397 409649 "DIAGG-" 409654 NIL DIAGG- (NIL T T) -8 NIL NIL NIL) (-229 404611 408199 408476 "DHMATRIX" 409009 NIL DHMATRIX (NIL T) -8 NIL NIL NIL) (-228 400223 401132 402142 "DFSFUN" 403621 T DFSFUN (NIL) -7 NIL NIL NIL) (-227 395301 399154 399466 "DFLOAT" 399931 T DFLOAT (NIL) -8 NIL NIL NIL) (-226 393564 393845 394234 "DFINTTLS" 395009 NIL DFINTTLS (NIL T T) -7 NIL NIL NIL) (-225 390593 391585 391985 "DERHAM" 393230 NIL DERHAM (NIL T NIL) -8 NIL NIL NIL) (-224 388396 390368 390457 "DEQUEUE" 390537 NIL DEQUEUE (NIL T) -8 NIL NIL NIL) (-223 387650 387783 387966 "DEGRED" 388258 NIL DEGRED (NIL T T) -7 NIL NIL NIL) (-222 384080 384825 385671 "DEFINTRF" 386878 NIL DEFINTRF (NIL T) -7 NIL NIL NIL) (-221 381635 382104 382696 "DEFINTEF" 383599 NIL DEFINTEF (NIL T T) -7 NIL NIL NIL) (-220 380985 381255 381370 "DEFAST" 381540 T DEFAST (NIL) -8 NIL NIL NIL) (-219 374701 380578 380728 "DECIMAL" 380855 T DECIMAL (NIL) -8 NIL NIL NIL) (-218 372213 372671 373177 "DDFACT" 374245 NIL DDFACT (NIL T T) -7 NIL NIL NIL) (-217 371809 371852 372003 "DBLRESP" 372164 NIL DBLRESP (NIL T T T T) -7 NIL NIL NIL) (-216 369677 370039 370400 "DBASE" 371575 NIL DBASE (NIL T) -8 NIL NIL NIL) (-215 368919 369157 369303 "DATAARY" 369576 NIL DATAARY (NIL NIL T) -8 NIL NIL NIL) (-214 368025 368878 368906 "D03FAFA" 368911 T D03FAFA (NIL) -8 NIL NIL NIL) (-213 367132 367984 368012 "D03EEFA" 368017 T D03EEFA (NIL) -8 NIL NIL NIL) (-212 365082 365548 366037 "D03AGNT" 366663 T D03AGNT (NIL) -7 NIL NIL NIL) (-211 364371 365041 365069 "D02EJFA" 365074 T D02EJFA (NIL) -8 NIL NIL NIL) (-210 363660 364330 364358 "D02CJFA" 364363 T D02CJFA (NIL) -8 NIL NIL NIL) (-209 362949 363619 363647 "D02BHFA" 363652 T D02BHFA (NIL) -8 NIL NIL NIL) (-208 362238 362908 362936 "D02BBFA" 362941 T D02BBFA (NIL) -8 NIL NIL NIL) (-207 355435 357024 358630 "D02AGNT" 360652 T D02AGNT (NIL) -7 NIL NIL NIL) (-206 353203 353726 354272 "D01WGTS" 354909 T D01WGTS (NIL) -7 NIL NIL NIL) (-205 352270 353162 353190 "D01TRNS" 353195 T D01TRNS (NIL) -8 NIL NIL NIL) (-204 351338 352229 352257 "D01GBFA" 352262 T D01GBFA (NIL) -8 NIL NIL NIL) (-203 350406 351297 351325 "D01FCFA" 351330 T D01FCFA (NIL) -8 NIL NIL NIL) (-202 349474 350365 350393 "D01ASFA" 350398 T D01ASFA (NIL) -8 NIL NIL NIL) (-201 348542 349433 349461 "D01AQFA" 349466 T D01AQFA (NIL) -8 NIL NIL NIL) (-200 347610 348501 348529 "D01APFA" 348534 T D01APFA (NIL) -8 NIL NIL NIL) (-199 346678 347569 347597 "D01ANFA" 347602 T D01ANFA (NIL) -8 NIL NIL NIL) (-198 345746 346637 346665 "D01AMFA" 346670 T D01AMFA (NIL) -8 NIL NIL NIL) (-197 344814 345705 345733 "D01ALFA" 345738 T D01ALFA (NIL) -8 NIL NIL NIL) (-196 343882 344773 344801 "D01AKFA" 344806 T D01AKFA (NIL) -8 NIL NIL NIL) (-195 342950 343841 343869 "D01AJFA" 343874 T D01AJFA (NIL) -8 NIL NIL NIL) (-194 336245 337798 339359 "D01AGNT" 341409 T D01AGNT (NIL) -7 NIL NIL NIL) (-193 335582 335710 335862 "CYCLOTOM" 336113 T CYCLOTOM (NIL) -7 NIL NIL NIL) (-192 332315 333030 333757 "CYCLES" 334875 T CYCLES (NIL) -7 NIL NIL NIL) (-191 331627 331761 331932 "CVMP" 332176 NIL CVMP (NIL T) -7 NIL NIL NIL) (-190 329468 329726 330095 "CTRIGMNP" 331355 NIL CTRIGMNP (NIL T T) -7 NIL NIL NIL) (-189 328904 329262 329335 "CTOR" 329415 T CTOR (NIL) -8 NIL NIL NIL) (-188 328413 328635 328736 "CTORKIND" 328823 T CTORKIND (NIL) -8 NIL NIL NIL) (-187 327690 328006 328034 "CTORCAT" 328216 T CTORCAT (NIL) -9 NIL 328329 NIL) (-186 327288 327399 327558 "CTORCAT-" 327563 NIL CTORCAT- (NIL T) -8 NIL NIL NIL) (-185 326750 326962 327070 "CTORCALL" 327212 NIL CTORCALL (NIL T) -8 NIL NIL NIL) (-184 326124 326223 326376 "CSTTOOLS" 326647 NIL CSTTOOLS (NIL T T) -7 NIL NIL NIL) (-183 321923 322580 323338 "CRFP" 325436 NIL CRFP (NIL T T) -7 NIL NIL NIL) (-182 321398 321644 321736 "CRCEAST" 321851 T CRCEAST (NIL) -8 NIL NIL NIL) (-181 320445 320630 320858 "CRAPACK" 321202 NIL CRAPACK (NIL T) -7 NIL NIL NIL) (-180 319829 319930 320134 "CPMATCH" 320321 NIL CPMATCH (NIL T T T) -7 NIL NIL NIL) (-179 319554 319582 319688 "CPIMA" 319795 NIL CPIMA (NIL T T T) -7 NIL NIL NIL) (-178 315902 316574 317293 "COORDSYS" 318889 NIL COORDSYS (NIL T) -7 NIL NIL NIL) (-177 315314 315435 315577 "CONTOUR" 315780 T CONTOUR (NIL) -8 NIL NIL NIL) (-176 311205 313317 313809 "CONTFRAC" 314854 NIL CONTFRAC (NIL T) -8 NIL NIL NIL) (-175 311085 311106 311134 "CONDUIT" 311171 T CONDUIT (NIL) -9 NIL NIL NIL) (-174 310159 310713 310741 "COMRING" 310746 T COMRING (NIL) -9 NIL 310798 NIL) (-173 309213 309517 309701 "COMPPROP" 309995 T COMPPROP (NIL) -8 NIL NIL NIL) (-172 308874 308909 309037 "COMPLPAT" 309172 NIL COMPLPAT (NIL T T T) -7 NIL NIL NIL) (-171 298177 308683 308792 "COMPLEX" 308797 NIL COMPLEX (NIL T) -8 NIL NIL NIL) (-170 297813 297870 297977 "COMPLEX2" 298114 NIL COMPLEX2 (NIL T T) -7 NIL NIL NIL) (-169 297152 297273 297433 "COMPILER" 297673 T COMPILER (NIL) -8 NIL NIL NIL) (-168 296870 296905 297003 "COMPFACT" 297111 NIL COMPFACT (NIL T T) -7 NIL NIL NIL) (-167 279149 290574 290614 "COMPCAT" 291618 NIL COMPCAT (NIL T) -9 NIL 292966 NIL) (-166 268661 271588 275215 "COMPCAT-" 275571 NIL COMPCAT- (NIL T T) -8 NIL NIL NIL) (-165 268390 268418 268521 "COMMUPC" 268627 NIL COMMUPC (NIL T T T) -7 NIL NIL NIL) (-164 268184 268218 268277 "COMMONOP" 268351 T COMMONOP (NIL) -7 NIL NIL NIL) (-163 267740 267935 268022 "COMM" 268117 T COMM (NIL) -8 NIL NIL NIL) (-162 267316 267544 267619 "COMMAAST" 267685 T COMMAAST (NIL) -8 NIL NIL NIL) (-161 266565 266759 266787 "COMBOPC" 267125 T COMBOPC (NIL) -9 NIL 267300 NIL) (-160 265461 265671 265913 "COMBINAT" 266355 NIL COMBINAT (NIL T) -7 NIL NIL NIL) (-159 261918 262492 263119 "COMBF" 264883 NIL COMBF (NIL T T) -7 NIL NIL NIL) (-158 260676 261034 261269 "COLOR" 261703 T COLOR (NIL) -8 NIL NIL NIL) (-157 260152 260397 260489 "COLONAST" 260604 T COLONAST (NIL) -8 NIL NIL NIL) (-156 259792 259839 259964 "CMPLXRT" 260099 NIL CMPLXRT (NIL T T) -7 NIL NIL NIL) (-155 259240 259492 259591 "CLLCTAST" 259713 T CLLCTAST (NIL) -8 NIL NIL NIL) (-154 254742 255770 256850 "CLIP" 258180 T CLIP (NIL) -7 NIL NIL NIL) (-153 253083 253843 254083 "CLIF" 254569 NIL CLIF (NIL NIL T NIL) -8 NIL NIL NIL) (-152 249232 251201 251242 "CLAGG" 252171 NIL CLAGG (NIL T) -9 NIL 252707 NIL) (-151 247654 248111 248694 "CLAGG-" 248699 NIL CLAGG- (NIL T T) -8 NIL NIL NIL) (-150 247198 247283 247423 "CINTSLPE" 247563 NIL CINTSLPE (NIL T T) -7 NIL NIL NIL) (-149 244699 245170 245718 "CHVAR" 246726 NIL CHVAR (NIL T T T) -7 NIL NIL NIL) (-148 243859 244413 244441 "CHARZ" 244446 T CHARZ (NIL) -9 NIL 244461 NIL) (-147 243613 243653 243731 "CHARPOL" 243813 NIL CHARPOL (NIL T) -7 NIL NIL NIL) (-146 242657 243244 243272 "CHARNZ" 243319 T CHARNZ (NIL) -9 NIL 243375 NIL) (-145 240563 241311 241664 "CHAR" 242324 T CHAR (NIL) -8 NIL NIL NIL) (-144 240289 240350 240378 "CFCAT" 240489 T CFCAT (NIL) -9 NIL NIL NIL) (-143 239530 239641 239824 "CDEN" 240173 NIL CDEN (NIL T T T) -7 NIL NIL NIL) (-142 235495 238683 238963 "CCLASS" 239270 T CCLASS (NIL) -8 NIL NIL NIL) (-141 234746 234903 235080 "CATEGORY" 235338 T -10 (NIL) -8 NIL NIL NIL) (-140 234319 234665 234713 "CATCTOR" 234718 T CATCTOR (NIL) -8 NIL NIL NIL) (-139 233770 234022 234120 "CATAST" 234241 T CATAST (NIL) -8 NIL NIL NIL) (-138 233246 233491 233583 "CASEAST" 233698 T CASEAST (NIL) -8 NIL NIL NIL) (-137 228384 229403 230147 "CARTEN" 232558 NIL CARTEN (NIL NIL NIL T) -8 NIL NIL NIL) (-136 227492 227640 227861 "CARTEN2" 228231 NIL CARTEN2 (NIL NIL NIL T T) -7 NIL NIL NIL) (-135 225808 226642 226899 "CARD" 227255 T CARD (NIL) -8 NIL NIL NIL) (-134 225384 225612 225687 "CAPSLAST" 225753 T CAPSLAST (NIL) -8 NIL NIL NIL) (-133 224874 225082 225110 "CACHSET" 225242 T CACHSET (NIL) -9 NIL 225320 NIL) (-132 224330 224652 224680 "CABMON" 224730 T CABMON (NIL) -9 NIL 224786 NIL) (-131 223803 224034 224144 "BYTEORD" 224240 T BYTEORD (NIL) -8 NIL NIL NIL) (-130 222780 223332 223474 "BYTE" 223637 T BYTE (NIL) -8 NIL NIL 223759) (-129 218132 222285 222457 "BYTEBUF" 222628 T BYTEBUF (NIL) -8 NIL NIL NIL) (-128 215643 217824 217931 "BTREE" 218058 NIL BTREE (NIL T) -8 NIL NIL NIL) (-127 213094 215291 215413 "BTOURN" 215553 NIL BTOURN (NIL T) -8 NIL NIL NIL) (-126 210438 212536 212577 "BTCAT" 212645 NIL BTCAT (NIL T) -9 NIL 212722 NIL) (-125 210105 210185 210334 "BTCAT-" 210339 NIL BTCAT- (NIL T T) -8 NIL NIL NIL) (-124 205484 209364 209392 "BTAGG" 209506 T BTAGG (NIL) -9 NIL 209616 NIL) (-123 204974 205099 205305 "BTAGG-" 205310 NIL BTAGG- (NIL T) -8 NIL NIL NIL) (-122 201971 204252 204467 "BSTREE" 204791 NIL BSTREE (NIL T) -8 NIL NIL NIL) (-121 201109 201235 201419 "BRILL" 201827 NIL BRILL (NIL T) -7 NIL NIL NIL) (-120 197735 199807 199848 "BRAGG" 200497 NIL BRAGG (NIL T) -9 NIL 200755 NIL) (-119 196264 196670 197225 "BRAGG-" 197230 NIL BRAGG- (NIL T T) -8 NIL NIL NIL) (-118 189180 195608 195793 "BPADICRT" 196111 NIL BPADICRT (NIL NIL) -8 NIL NIL NIL) (-117 187495 189117 189162 "BPADIC" 189167 NIL BPADIC (NIL NIL) -8 NIL NIL NIL) (-116 187193 187223 187337 "BOUNDZRO" 187459 NIL BOUNDZRO (NIL T T) -7 NIL NIL NIL) (-115 182421 183619 184531 "BOP" 186301 T BOP (NIL) -8 NIL NIL NIL) (-114 180202 180606 181081 "BOP1" 181979 NIL BOP1 (NIL T) -7 NIL NIL NIL) (-113 179903 179964 179992 "BOOLE" 180103 T BOOLE (NIL) -9 NIL 180185 NIL) (-112 178728 179477 179626 "BOOLEAN" 179774 T BOOLEAN (NIL) -8 NIL NIL NIL) (-111 177993 178397 178451 "BMODULE" 178456 NIL BMODULE (NIL T T) -9 NIL 178521 NIL) (-110 173794 177791 177864 "BITS" 177940 T BITS (NIL) -8 NIL NIL NIL) (-109 173215 173334 173474 "BINDING" 173674 T BINDING (NIL) -8 NIL NIL NIL) (-108 166934 172810 172959 "BINARY" 173086 T BINARY (NIL) -8 NIL NIL NIL) (-107 164688 166161 166202 "BGAGG" 166462 NIL BGAGG (NIL T) -9 NIL 166599 NIL) (-106 164519 164551 164642 "BGAGG-" 164647 NIL BGAGG- (NIL T T) -8 NIL NIL NIL) (-105 163590 163903 164108 "BFUNCT" 164334 T BFUNCT (NIL) -8 NIL NIL NIL) (-104 162280 162458 162746 "BEZOUT" 163414 NIL BEZOUT (NIL T T T T T) -7 NIL NIL NIL) (-103 158751 161132 161462 "BBTREE" 161983 NIL BBTREE (NIL T) -8 NIL NIL NIL) (-102 158460 158513 158541 "BASTYPE" 158660 T BASTYPE (NIL) -9 NIL 158734 NIL) (-101 158312 158341 158414 "BASTYPE-" 158419 NIL BASTYPE- (NIL T) -8 NIL NIL NIL) (-100 157746 157822 157974 "BALFACT" 158223 NIL BALFACT (NIL T T) -7 NIL NIL NIL) (-99 156602 157161 157347 "AUTOMOR" 157591 NIL AUTOMOR (NIL T) -8 NIL NIL NIL) (-98 156328 156333 156359 "ATTREG" 156364 T ATTREG (NIL) -9 NIL NIL NIL) (-97 154580 155025 155377 "ATTRBUT" 155994 T ATTRBUT (NIL) -8 NIL NIL NIL) (-96 154188 154408 154474 "ATTRAST" 154532 T ATTRAST (NIL) -8 NIL NIL NIL) (-95 153724 153837 153863 "ATRIG" 154064 T ATRIG (NIL) -9 NIL NIL NIL) (-94 153533 153574 153661 "ATRIG-" 153666 NIL ATRIG- (NIL T) -8 NIL NIL NIL) (-93 153164 153350 153376 "ASTCAT" 153381 T ASTCAT (NIL) -9 NIL 153411 NIL) (-92 152891 152950 153069 "ASTCAT-" 153074 NIL ASTCAT- (NIL T) -8 NIL NIL NIL) (-91 151042 152667 152755 "ASTACK" 152834 NIL ASTACK (NIL T) -8 NIL NIL NIL) (-90 149547 149844 150209 "ASSOCEQ" 150724 NIL ASSOCEQ (NIL T T) -7 NIL NIL NIL) (-89 148579 149206 149330 "ASP9" 149454 NIL ASP9 (NIL NIL) -8 NIL NIL NIL) (-88 148342 148527 148566 "ASP8" 148571 NIL ASP8 (NIL NIL) -8 NIL NIL NIL) (-87 147210 147947 148089 "ASP80" 148231 NIL ASP80 (NIL NIL) -8 NIL NIL NIL) (-86 146108 146845 146977 "ASP7" 147109 NIL ASP7 (NIL NIL) -8 NIL NIL NIL) (-85 145062 145785 145903 "ASP78" 146021 NIL ASP78 (NIL NIL) -8 NIL NIL NIL) (-84 144031 144742 144859 "ASP77" 144976 NIL ASP77 (NIL NIL) -8 NIL NIL NIL) (-83 142943 143669 143800 "ASP74" 143931 NIL ASP74 (NIL NIL) -8 NIL NIL NIL) (-82 141843 142578 142710 "ASP73" 142842 NIL ASP73 (NIL NIL) -8 NIL NIL NIL) (-81 140947 141669 141769 "ASP6" 141774 NIL ASP6 (NIL NIL) -8 NIL NIL NIL) (-80 139894 140624 140742 "ASP55" 140860 NIL ASP55 (NIL NIL) -8 NIL NIL NIL) (-79 138843 139568 139687 "ASP50" 139806 NIL ASP50 (NIL NIL) -8 NIL NIL NIL) (-78 137931 138544 138654 "ASP4" 138764 NIL ASP4 (NIL NIL) -8 NIL NIL NIL) (-77 137019 137632 137742 "ASP49" 137852 NIL ASP49 (NIL NIL) -8 NIL NIL NIL) (-76 135803 136558 136726 "ASP42" 136908 NIL ASP42 (NIL NIL NIL NIL) -8 NIL NIL NIL) (-75 134580 135336 135506 "ASP41" 135690 NIL ASP41 (NIL NIL NIL NIL) -8 NIL NIL NIL) (-74 133530 134257 134375 "ASP35" 134493 NIL ASP35 (NIL NIL) -8 NIL NIL NIL) (-73 133295 133478 133517 "ASP34" 133522 NIL ASP34 (NIL NIL) -8 NIL NIL NIL) (-72 133032 133099 133175 "ASP33" 133250 NIL ASP33 (NIL NIL) -8 NIL NIL NIL) (-71 131926 132667 132799 "ASP31" 132931 NIL ASP31 (NIL NIL) -8 NIL NIL NIL) (-70 131691 131874 131913 "ASP30" 131918 NIL ASP30 (NIL NIL) -8 NIL NIL NIL) (-69 131426 131495 131571 "ASP29" 131646 NIL ASP29 (NIL NIL) -8 NIL NIL NIL) (-68 131191 131374 131413 "ASP28" 131418 NIL ASP28 (NIL NIL) -8 NIL NIL NIL) (-67 130956 131139 131178 "ASP27" 131183 NIL ASP27 (NIL NIL) -8 NIL NIL NIL) (-66 130040 130654 130765 "ASP24" 130876 NIL ASP24 (NIL NIL) -8 NIL NIL NIL) (-65 129117 129842 129954 "ASP20" 129959 NIL ASP20 (NIL NIL) -8 NIL NIL NIL) (-64 128205 128818 128928 "ASP1" 129038 NIL ASP1 (NIL NIL) -8 NIL NIL NIL) (-63 127148 127879 127998 "ASP19" 128117 NIL ASP19 (NIL NIL) -8 NIL NIL NIL) (-62 126885 126952 127028 "ASP12" 127103 NIL ASP12 (NIL NIL) -8 NIL NIL NIL) (-61 125737 126484 126628 "ASP10" 126772 NIL ASP10 (NIL NIL) -8 NIL NIL NIL) (-60 123590 125581 125672 "ARRAY2" 125677 NIL ARRAY2 (NIL T) -8 NIL NIL NIL) (-59 119357 123238 123352 "ARRAY1" 123507 NIL ARRAY1 (NIL T) -8 NIL NIL NIL) (-58 118389 118562 118783 "ARRAY12" 119180 NIL ARRAY12 (NIL T T) -7 NIL NIL NIL) (-57 112675 114591 114666 "ARR2CAT" 117296 NIL ARR2CAT (NIL T T T) -9 NIL 118054 NIL) (-56 110109 110853 111807 "ARR2CAT-" 111812 NIL ARR2CAT- (NIL T T T T) -8 NIL NIL NIL) (-55 109426 109736 109861 "ARITY" 110002 T ARITY (NIL) -8 NIL NIL NIL) (-54 108202 108354 108653 "APPRULE" 109262 NIL APPRULE (NIL T T T) -7 NIL NIL NIL) (-53 107853 107901 108020 "APPLYORE" 108148 NIL APPLYORE (NIL T T T) -7 NIL NIL NIL) (-52 107207 107446 107566 "ANY" 107751 T ANY (NIL) -8 NIL NIL NIL) (-51 106485 106608 106765 "ANY1" 107081 NIL ANY1 (NIL T) -7 NIL NIL NIL) (-50 104015 104922 105249 "ANTISYM" 106209 NIL ANTISYM (NIL T NIL) -8 NIL NIL NIL) (-49 103507 103722 103818 "ANON" 103937 T ANON (NIL) -8 NIL NIL NIL) (-48 97507 102046 102500 "AN" 103071 T AN (NIL) -8 NIL NIL NIL) (-47 93391 94779 94830 "AMR" 95578 NIL AMR (NIL T T) -9 NIL 96178 NIL) (-46 92503 92724 93087 "AMR-" 93092 NIL AMR- (NIL T T T) -8 NIL NIL NIL) (-45 76946 92420 92481 "ALIST" 92486 NIL ALIST (NIL T T) -8 NIL NIL NIL) (-44 73751 76540 76709 "ALGSC" 76864 NIL ALGSC (NIL T NIL NIL NIL) -8 NIL NIL NIL) (-43 70307 70861 71468 "ALGPKG" 73191 NIL ALGPKG (NIL T T) -7 NIL NIL NIL) (-42 69584 69685 69869 "ALGMFACT" 70193 NIL ALGMFACT (NIL T T T) -7 NIL NIL NIL) (-41 65619 66198 66792 "ALGMANIP" 69168 NIL ALGMANIP (NIL T T) -7 NIL NIL NIL) (-40 55830 65245 65395 "ALGFF" 65552 NIL ALGFF (NIL T T T NIL) -8 NIL NIL NIL) (-39 55026 55157 55336 "ALGFACT" 55688 NIL ALGFACT (NIL T) -7 NIL NIL NIL) (-38 53953 54553 54591 "ALGEBRA" 54596 NIL ALGEBRA (NIL T) -9 NIL 54637 NIL) (-37 53671 53730 53862 "ALGEBRA-" 53867 NIL ALGEBRA- (NIL T T) -8 NIL NIL NIL) (-36 35666 51569 51621 "ALAGG" 51757 NIL ALAGG (NIL T T) -9 NIL 51918 NIL) (-35 35202 35315 35341 "AHYP" 35542 T AHYP (NIL) -9 NIL NIL NIL) (-34 34133 34381 34407 "AGG" 34906 T AGG (NIL) -9 NIL 35185 NIL) (-33 33567 33729 33943 "AGG-" 33948 NIL AGG- (NIL T) -8 NIL NIL NIL) (-32 31373 31796 32201 "AF" 33209 NIL AF (NIL T T) -7 NIL NIL NIL) (-31 30853 31098 31188 "ADDAST" 31301 T ADDAST (NIL) -8 NIL NIL NIL) (-30 30121 30380 30536 "ACPLOT" 30715 T ACPLOT (NIL) -8 NIL NIL NIL) (-29 18744 27053 27091 "ACFS" 27698 NIL ACFS (NIL T) -9 NIL 27937 NIL) (-28 16771 17261 18023 "ACFS-" 18028 NIL ACFS- (NIL T T) -8 NIL NIL NIL) (-27 12875 14804 14830 "ACF" 15709 T ACF (NIL) -9 NIL 16122 NIL) (-26 11579 11913 12406 "ACF-" 12411 NIL ACF- (NIL T) -8 NIL NIL NIL) (-25 11137 11332 11358 "ABELSG" 11450 T ABELSG (NIL) -9 NIL 11515 NIL) (-24 11004 11029 11095 "ABELSG-" 11100 NIL ABELSG- (NIL T) -8 NIL NIL NIL) (-23 10333 10620 10646 "ABELMON" 10816 T ABELMON (NIL) -9 NIL 10928 NIL) (-22 9997 10081 10219 "ABELMON-" 10224 NIL ABELMON- (NIL T) -8 NIL NIL NIL) (-21 9331 9703 9729 "ABELGRP" 9801 T ABELGRP (NIL) -9 NIL 9876 NIL) (-20 8794 8923 9139 "ABELGRP-" 9144 NIL ABELGRP- (NIL T) -8 NIL NIL NIL) (-19 4333 8083 8122 "A1AGG" 8127 NIL A1AGG (NIL T) -9 NIL 8167 NIL) (-18 30 1251 2813 "A1AGG-" 2818 NIL A1AGG- (NIL T T) -8 NIL NIL NIL))
\ No newline at end of file +((-3 3260686 3260691 3260696 NIL NIL NIL NIL (NIL) -8 NIL NIL NIL) (-2 3260671 3260676 3260681 NIL NIL NIL NIL (NIL) -8 NIL NIL NIL) (-1 3260656 3260661 3260666 NIL NIL NIL NIL (NIL) -8 NIL NIL NIL) (0 3260641 3260646 3260651 NIL NIL NIL NIL (NIL) -8 NIL NIL NIL) (-1315 3259784 3260516 3260593 "ZMOD" 3260598 NIL ZMOD (NIL NIL) -8 NIL NIL NIL) (-1314 3258838 3259002 3259225 "ZLINDEP" 3259616 NIL ZLINDEP (NIL T) -7 NIL NIL NIL) (-1313 3248138 3249906 3251878 "ZDSOLVE" 3256968 NIL ZDSOLVE (NIL T NIL NIL) -7 NIL NIL NIL) (-1312 3247384 3247525 3247714 "YSTREAM" 3247984 NIL YSTREAM (NIL T) -7 NIL NIL NIL) (-1311 3246812 3247058 3247171 "YDIAGRAM" 3247293 T YDIAGRAM (NIL) -8 NIL NIL NIL) (-1310 3244586 3246113 3246317 "XRPOLY" 3246655 NIL XRPOLY (NIL T T) -8 NIL NIL NIL) (-1309 3241139 3242457 3243032 "XPR" 3244058 NIL XPR (NIL T T) -8 NIL NIL NIL) (-1308 3238860 3240470 3240674 "XPOLY" 3240970 NIL XPOLY (NIL T) -8 NIL NIL NIL) (-1307 3236499 3237867 3237922 "XPOLYC" 3238210 NIL XPOLYC (NIL T T) -9 NIL 3238323 NIL) (-1306 3232875 3235016 3235404 "XPBWPOLY" 3236157 NIL XPBWPOLY (NIL T T) -8 NIL NIL NIL) (-1305 3228556 3230851 3230893 "XF" 3231514 NIL XF (NIL T) -9 NIL 3231914 NIL) (-1304 3228177 3228265 3228434 "XF-" 3228439 NIL XF- (NIL T T) -8 NIL NIL NIL) (-1303 3223359 3224648 3224703 "XFALG" 3226875 NIL XFALG (NIL T T) -9 NIL 3227664 NIL) (-1302 3222492 3222596 3222801 "XEXPPKG" 3223251 NIL XEXPPKG (NIL T T T) -7 NIL NIL NIL) (-1301 3220601 3222342 3222438 "XDPOLY" 3222443 NIL XDPOLY (NIL T T) -8 NIL NIL NIL) (-1300 3219394 3219994 3220037 "XALG" 3220042 NIL XALG (NIL T) -9 NIL 3220153 NIL) (-1299 3212836 3217371 3217865 "WUTSET" 3218986 NIL WUTSET (NIL T T T T) -8 NIL NIL NIL) (-1298 3211092 3211888 3212211 "WP" 3212647 NIL WP (NIL T T T T NIL NIL NIL) -8 NIL NIL NIL) (-1297 3210694 3210914 3210984 "WHILEAST" 3211044 T WHILEAST (NIL) -8 NIL NIL NIL) (-1296 3210166 3210411 3210505 "WHEREAST" 3210622 T WHEREAST (NIL) -8 NIL NIL NIL) (-1295 3209052 3209250 3209545 "WFFINTBS" 3209963 NIL WFFINTBS (NIL T T T T) -7 NIL NIL NIL) (-1294 3206956 3207383 3207845 "WEIER" 3208624 NIL WEIER (NIL T) -7 NIL NIL NIL) (-1293 3205988 3206438 3206480 "VSPACE" 3206616 NIL VSPACE (NIL T) -9 NIL 3206690 NIL) (-1292 3205826 3205853 3205944 "VSPACE-" 3205949 NIL VSPACE- (NIL T T) -8 NIL NIL NIL) (-1291 3205635 3205677 3205745 "VOID" 3205780 T VOID (NIL) -8 NIL NIL NIL) (-1290 3203771 3204130 3204536 "VIEW" 3205251 T VIEW (NIL) -7 NIL NIL NIL) (-1289 3200195 3200834 3201571 "VIEWDEF" 3203056 T VIEWDEF (NIL) -7 NIL NIL NIL) (-1288 3189499 3191743 3193916 "VIEW3D" 3198044 T VIEW3D (NIL) -8 NIL NIL NIL) (-1287 3181750 3183410 3184989 "VIEW2D" 3187942 T VIEW2D (NIL) -8 NIL NIL NIL) (-1286 3177105 3181520 3181612 "VECTOR" 3181693 NIL VECTOR (NIL T) -8 NIL NIL NIL) (-1285 3175682 3175941 3176259 "VECTOR2" 3176835 NIL VECTOR2 (NIL T T) -7 NIL NIL NIL) (-1284 3169106 3173413 3173456 "VECTCAT" 3174451 NIL VECTCAT (NIL T) -9 NIL 3175038 NIL) (-1283 3168120 3168374 3168764 "VECTCAT-" 3168769 NIL VECTCAT- (NIL T T) -8 NIL NIL NIL) (-1282 3167574 3167771 3167891 "VARIABLE" 3168035 NIL VARIABLE (NIL NIL) -8 NIL NIL NIL) (-1281 3167507 3167512 3167542 "UTYPE" 3167547 T UTYPE (NIL) -9 NIL NIL NIL) (-1280 3166337 3166491 3166753 "UTSODETL" 3167333 NIL UTSODETL (NIL T T T T) -7 NIL NIL NIL) (-1279 3163777 3164237 3164761 "UTSODE" 3165878 NIL UTSODE (NIL T T) -7 NIL NIL NIL) (-1278 3155725 3161538 3162018 "UTS" 3163355 NIL UTS (NIL T NIL NIL) -8 NIL NIL NIL) (-1277 3146289 3151659 3151702 "UTSCAT" 3152814 NIL UTSCAT (NIL T) -9 NIL 3153572 NIL) (-1276 3143637 3144359 3145348 "UTSCAT-" 3145353 NIL UTSCAT- (NIL T T) -8 NIL NIL NIL) (-1275 3143264 3143307 3143440 "UTS2" 3143588 NIL UTS2 (NIL T T T T) -7 NIL NIL NIL) (-1274 3137464 3140074 3140117 "URAGG" 3142187 NIL URAGG (NIL T) -9 NIL 3142910 NIL) (-1273 3134403 3135266 3136389 "URAGG-" 3136394 NIL URAGG- (NIL T T) -8 NIL NIL NIL) (-1272 3130112 3133038 3133503 "UPXSSING" 3134067 NIL UPXSSING (NIL T T NIL NIL) -8 NIL NIL NIL) (-1271 3122288 3129494 3129758 "UPXS" 3129906 NIL UPXS (NIL T NIL NIL) -8 NIL NIL NIL) (-1270 3115361 3122192 3122264 "UPXSCONS" 3122269 NIL UPXSCONS (NIL T T) -8 NIL NIL NIL) (-1269 3104768 3111564 3111626 "UPXSCCA" 3112200 NIL UPXSCCA (NIL T T) -9 NIL 3112433 NIL) (-1268 3104406 3104491 3104665 "UPXSCCA-" 3104670 NIL UPXSCCA- (NIL T T T) -8 NIL NIL NIL) (-1267 3093665 3100234 3100277 "UPXSCAT" 3100925 NIL UPXSCAT (NIL T) -9 NIL 3101534 NIL) (-1266 3093095 3093174 3093353 "UPXS2" 3093580 NIL UPXS2 (NIL T T NIL NIL NIL NIL) -7 NIL NIL NIL) (-1265 3091749 3092002 3092353 "UPSQFREE" 3092838 NIL UPSQFREE (NIL T T) -7 NIL NIL NIL) (-1264 3084957 3088017 3088072 "UPSCAT" 3089152 NIL UPSCAT (NIL T T) -9 NIL 3089917 NIL) (-1263 3084161 3084368 3084695 "UPSCAT-" 3084700 NIL UPSCAT- (NIL T T T) -8 NIL NIL NIL) (-1262 3069243 3077288 3077331 "UPOLYC" 3079432 NIL UPOLYC (NIL T) -9 NIL 3080653 NIL) (-1261 3060571 3062997 3066144 "UPOLYC-" 3066149 NIL UPOLYC- (NIL T T) -8 NIL NIL NIL) (-1260 3060198 3060241 3060374 "UPOLYC2" 3060522 NIL UPOLYC2 (NIL T T T T) -7 NIL NIL NIL) (-1259 3051733 3059881 3060010 "UP" 3060117 NIL UP (NIL NIL T) -8 NIL NIL NIL) (-1258 3051072 3051179 3051343 "UPMP" 3051622 NIL UPMP (NIL T T) -7 NIL NIL NIL) (-1257 3050625 3050706 3050845 "UPDIVP" 3050985 NIL UPDIVP (NIL T T) -7 NIL NIL NIL) (-1256 3049193 3049442 3049758 "UPDECOMP" 3050374 NIL UPDECOMP (NIL T T) -7 NIL NIL NIL) (-1255 3048424 3048536 3048722 "UPCDEN" 3049077 NIL UPCDEN (NIL T T T) -7 NIL NIL NIL) (-1254 3047943 3048012 3048161 "UP2" 3048349 NIL UP2 (NIL NIL T NIL T) -7 NIL NIL NIL) (-1253 3046410 3047147 3047424 "UNISEG" 3047701 NIL UNISEG (NIL T) -8 NIL NIL NIL) (-1252 3045625 3045752 3045957 "UNISEG2" 3046253 NIL UNISEG2 (NIL T T) -7 NIL NIL NIL) (-1251 3044685 3044865 3045091 "UNIFACT" 3045441 NIL UNIFACT (NIL T) -7 NIL NIL NIL) (-1250 3027437 3043997 3044239 "ULS" 3044501 NIL ULS (NIL T NIL NIL) -8 NIL NIL NIL) (-1249 3015067 3027341 3027413 "ULSCONS" 3027418 NIL ULSCONS (NIL T T) -8 NIL NIL NIL) (-1248 2995895 3008255 3008317 "ULSCCAT" 3008955 NIL ULSCCAT (NIL T T) -9 NIL 3009244 NIL) (-1247 2994945 2995190 2995578 "ULSCCAT-" 2995583 NIL ULSCCAT- (NIL T T T) -8 NIL NIL NIL) (-1246 2984009 2990492 2990535 "ULSCAT" 2991398 NIL ULSCAT (NIL T) -9 NIL 2992129 NIL) (-1245 2983439 2983518 2983697 "ULS2" 2983924 NIL ULS2 (NIL T T NIL NIL NIL NIL) -7 NIL NIL NIL) (-1244 2982558 2983068 2983175 "UINT8" 2983286 T UINT8 (NIL) -8 NIL NIL 2983371) (-1243 2981676 2982186 2982293 "UINT64" 2982404 T UINT64 (NIL) -8 NIL NIL 2982489) (-1242 2980794 2981304 2981411 "UINT32" 2981522 T UINT32 (NIL) -8 NIL NIL 2981607) (-1241 2979912 2980422 2980529 "UINT16" 2980640 T UINT16 (NIL) -8 NIL NIL 2980725) (-1240 2978201 2979158 2979188 "UFD" 2979400 T UFD (NIL) -9 NIL 2979514 NIL) (-1239 2977995 2978041 2978136 "UFD-" 2978141 NIL UFD- (NIL T) -8 NIL NIL NIL) (-1238 2977077 2977260 2977476 "UDVO" 2977801 T UDVO (NIL) -7 NIL NIL NIL) (-1237 2974893 2975302 2975773 "UDPO" 2976641 NIL UDPO (NIL T) -7 NIL NIL NIL) (-1236 2974826 2974831 2974861 "TYPE" 2974866 T TYPE (NIL) -9 NIL NIL NIL) (-1235 2974586 2974781 2974812 "TYPEAST" 2974817 T TYPEAST (NIL) -8 NIL NIL NIL) (-1234 2973557 2973759 2973999 "TWOFACT" 2974380 NIL TWOFACT (NIL T) -7 NIL NIL NIL) (-1233 2972580 2972966 2973201 "TUPLE" 2973357 NIL TUPLE (NIL T) -8 NIL NIL NIL) (-1232 2970271 2970790 2971329 "TUBETOOL" 2972063 T TUBETOOL (NIL) -7 NIL NIL NIL) (-1231 2969120 2969325 2969566 "TUBE" 2970064 NIL TUBE (NIL T) -8 NIL NIL NIL) (-1230 2963849 2968092 2968375 "TS" 2968872 NIL TS (NIL T) -8 NIL NIL NIL) (-1229 2952489 2956608 2956705 "TSETCAT" 2961974 NIL TSETCAT (NIL T T T T) -9 NIL 2963505 NIL) (-1228 2947221 2948821 2950712 "TSETCAT-" 2950717 NIL TSETCAT- (NIL T T T T T) -8 NIL NIL NIL) (-1227 2941860 2942707 2943636 "TRMANIP" 2946357 NIL TRMANIP (NIL T T) -7 NIL NIL NIL) (-1226 2941301 2941364 2941527 "TRIMAT" 2941792 NIL TRIMAT (NIL T T T T) -7 NIL NIL NIL) (-1225 2939167 2939404 2939761 "TRIGMNIP" 2941050 NIL TRIGMNIP (NIL T T) -7 NIL NIL NIL) (-1224 2938687 2938800 2938830 "TRIGCAT" 2939043 T TRIGCAT (NIL) -9 NIL NIL NIL) (-1223 2938356 2938435 2938576 "TRIGCAT-" 2938581 NIL TRIGCAT- (NIL T) -8 NIL NIL NIL) (-1222 2935203 2937214 2937495 "TREE" 2938110 NIL TREE (NIL T) -8 NIL NIL NIL) (-1221 2934477 2935005 2935035 "TRANFUN" 2935070 T TRANFUN (NIL) -9 NIL 2935136 NIL) (-1220 2933756 2933947 2934227 "TRANFUN-" 2934232 NIL TRANFUN- (NIL T) -8 NIL NIL NIL) (-1219 2933560 2933592 2933653 "TOPSP" 2933717 T TOPSP (NIL) -7 NIL NIL NIL) (-1218 2932908 2933023 2933177 "TOOLSIGN" 2933441 NIL TOOLSIGN (NIL T) -7 NIL NIL NIL) (-1217 2931542 2932085 2932324 "TEXTFILE" 2932691 T TEXTFILE (NIL) -8 NIL NIL NIL) (-1216 2929454 2929995 2930424 "TEX" 2931135 T TEX (NIL) -8 NIL NIL NIL) (-1215 2929235 2929266 2929338 "TEX1" 2929417 NIL TEX1 (NIL T) -7 NIL NIL NIL) (-1214 2928883 2928946 2929036 "TEMUTL" 2929167 T TEMUTL (NIL) -7 NIL NIL NIL) (-1213 2927037 2927317 2927642 "TBCMPPK" 2928606 NIL TBCMPPK (NIL T T) -7 NIL NIL NIL) (-1212 2918744 2925123 2925179 "TBAGG" 2925579 NIL TBAGG (NIL T T) -9 NIL 2925790 NIL) (-1211 2913814 2915302 2917056 "TBAGG-" 2917061 NIL TBAGG- (NIL T T T) -8 NIL NIL NIL) (-1210 2913198 2913305 2913450 "TANEXP" 2913703 NIL TANEXP (NIL T) -7 NIL NIL NIL) (-1209 2912709 2912973 2913063 "TALGOP" 2913143 NIL TALGOP (NIL T) -8 NIL NIL NIL) (-1208 2906103 2912566 2912659 "TABLE" 2912664 NIL TABLE (NIL T T) -8 NIL NIL NIL) (-1207 2905515 2905614 2905752 "TABLEAU" 2906000 NIL TABLEAU (NIL T) -8 NIL NIL NIL) (-1206 2900123 2901343 2902591 "TABLBUMP" 2904301 NIL TABLBUMP (NIL T) -7 NIL NIL NIL) (-1205 2899345 2899492 2899673 "SYSTEM" 2899964 T SYSTEM (NIL) -8 NIL NIL NIL) (-1204 2895804 2896503 2897286 "SYSSOLP" 2898596 NIL SYSSOLP (NIL T) -7 NIL NIL NIL) (-1203 2895602 2895759 2895790 "SYSPTR" 2895795 T SYSPTR (NIL) -8 NIL NIL NIL) (-1202 2894638 2895143 2895262 "SYSNNI" 2895448 NIL SYSNNI (NIL NIL) -8 NIL NIL 2895533) (-1201 2893937 2894396 2894475 "SYSINT" 2894535 NIL SYSINT (NIL NIL) -8 NIL NIL 2894580) (-1200 2890269 2891215 2891925 "SYNTAX" 2893249 T SYNTAX (NIL) -8 NIL NIL NIL) (-1199 2887427 2888029 2888661 "SYMTAB" 2889659 T SYMTAB (NIL) -8 NIL NIL NIL) (-1198 2882676 2883578 2884561 "SYMS" 2886466 T SYMS (NIL) -8 NIL NIL NIL) (-1197 2879911 2882134 2882364 "SYMPOLY" 2882481 NIL SYMPOLY (NIL T) -8 NIL NIL NIL) (-1196 2879428 2879503 2879626 "SYMFUNC" 2879823 NIL SYMFUNC (NIL T) -7 NIL NIL NIL) (-1195 2875448 2876740 2877553 "SYMBOL" 2878637 T SYMBOL (NIL) -8 NIL NIL NIL) (-1194 2868987 2870676 2872396 "SWITCH" 2873750 T SWITCH (NIL) -8 NIL NIL NIL) (-1193 2862331 2867943 2868237 "SUTS" 2868751 NIL SUTS (NIL T NIL NIL) -8 NIL NIL NIL) (-1192 2854507 2861713 2861977 "SUPXS" 2862125 NIL SUPXS (NIL T NIL NIL) -8 NIL NIL NIL) (-1191 2845990 2854125 2854251 "SUP" 2854416 NIL SUP (NIL T) -8 NIL NIL NIL) (-1190 2845149 2845276 2845493 "SUPFRACF" 2845858 NIL SUPFRACF (NIL T T T T) -7 NIL NIL NIL) (-1189 2844770 2844829 2844942 "SUP2" 2845084 NIL SUP2 (NIL T T) -7 NIL NIL NIL) (-1188 2843218 2843492 2843848 "SUMRF" 2844469 NIL SUMRF (NIL T) -7 NIL NIL NIL) (-1187 2842553 2842619 2842811 "SUMFS" 2843139 NIL SUMFS (NIL T T) -7 NIL NIL NIL) (-1186 2825340 2841865 2842107 "SULS" 2842369 NIL SULS (NIL T NIL NIL) -8 NIL NIL NIL) (-1185 2824942 2825162 2825232 "SUCHTAST" 2825292 T SUCHTAST (NIL) -8 NIL NIL NIL) (-1184 2824237 2824467 2824607 "SUCH" 2824850 NIL SUCH (NIL T T) -8 NIL NIL NIL) (-1183 2818104 2819143 2820102 "SUBSPACE" 2823325 NIL SUBSPACE (NIL NIL T) -8 NIL NIL NIL) (-1182 2817534 2817624 2817788 "SUBRESP" 2817992 NIL SUBRESP (NIL T T) -7 NIL NIL NIL) (-1181 2810902 2812199 2813510 "STTF" 2816270 NIL STTF (NIL T) -7 NIL NIL NIL) (-1180 2805075 2806195 2807342 "STTFNC" 2809802 NIL STTFNC (NIL T) -7 NIL NIL NIL) (-1179 2796388 2798257 2800051 "STTAYLOR" 2803316 NIL STTAYLOR (NIL T) -7 NIL NIL NIL) (-1178 2789522 2796252 2796335 "STRTBL" 2796340 NIL STRTBL (NIL T) -8 NIL NIL NIL) (-1177 2784482 2789231 2789330 "STRING" 2789445 T STRING (NIL) -8 NIL NIL NIL) (-1176 2777237 2782101 2782712 "STREAM" 2783906 NIL STREAM (NIL T) -8 NIL NIL NIL) (-1175 2776747 2776824 2776968 "STREAM3" 2777154 NIL STREAM3 (NIL T T T) -7 NIL NIL NIL) (-1174 2775729 2775912 2776147 "STREAM2" 2776560 NIL STREAM2 (NIL T T) -7 NIL NIL NIL) (-1173 2775417 2775469 2775562 "STREAM1" 2775671 NIL STREAM1 (NIL T) -7 NIL NIL NIL) (-1172 2774433 2774614 2774845 "STINPROD" 2775233 NIL STINPROD (NIL T) -7 NIL NIL NIL) (-1171 2773971 2774181 2774211 "STEP" 2774291 T STEP (NIL) -9 NIL 2774369 NIL) (-1170 2773158 2773460 2773608 "STEPAST" 2773845 T STEPAST (NIL) -8 NIL NIL NIL) (-1169 2766594 2773057 2773134 "STBL" 2773139 NIL STBL (NIL T T NIL) -8 NIL NIL NIL) (-1168 2761663 2765757 2765800 "STAGG" 2765953 NIL STAGG (NIL T) -9 NIL 2766042 NIL) (-1167 2759365 2759967 2760839 "STAGG-" 2760844 NIL STAGG- (NIL T T) -8 NIL NIL NIL) (-1166 2757514 2759135 2759227 "STACK" 2759308 NIL STACK (NIL T) -8 NIL NIL NIL) (-1165 2750209 2755655 2756111 "SREGSET" 2757144 NIL SREGSET (NIL T T T T) -8 NIL NIL NIL) (-1164 2742634 2744003 2745516 "SRDCMPK" 2748815 NIL SRDCMPK (NIL T T T T T) -7 NIL NIL NIL) (-1163 2735499 2740022 2740052 "SRAGG" 2741355 T SRAGG (NIL) -9 NIL 2741963 NIL) (-1162 2734516 2734771 2735150 "SRAGG-" 2735155 NIL SRAGG- (NIL T) -8 NIL NIL NIL) (-1161 2728700 2733463 2733884 "SQMATRIX" 2734142 NIL SQMATRIX (NIL NIL T) -8 NIL NIL NIL) (-1160 2722387 2725418 2726145 "SPLTREE" 2728045 NIL SPLTREE (NIL T T) -8 NIL NIL NIL) (-1159 2718350 2719043 2719689 "SPLNODE" 2721813 NIL SPLNODE (NIL T T) -8 NIL NIL NIL) (-1158 2717397 2717630 2717660 "SPFCAT" 2718104 T SPFCAT (NIL) -9 NIL NIL NIL) (-1157 2716134 2716344 2716608 "SPECOUT" 2717155 T SPECOUT (NIL) -7 NIL NIL NIL) (-1156 2707230 2709102 2709132 "SPADXPT" 2713808 T SPADXPT (NIL) -9 NIL 2715972 NIL) (-1155 2706991 2707031 2707100 "SPADPRSR" 2707183 T SPADPRSR (NIL) -7 NIL NIL NIL) (-1154 2705040 2706946 2706977 "SPADAST" 2706982 T SPADAST (NIL) -8 NIL NIL NIL) (-1153 2696971 2698744 2698787 "SPACEC" 2703160 NIL SPACEC (NIL T) -9 NIL 2704976 NIL) (-1152 2695101 2696903 2696952 "SPACE3" 2696957 NIL SPACE3 (NIL T) -8 NIL NIL NIL) (-1151 2693853 2694024 2694315 "SORTPAK" 2694906 NIL SORTPAK (NIL T T) -7 NIL NIL NIL) (-1150 2691945 2692248 2692660 "SOLVETRA" 2693517 NIL SOLVETRA (NIL T) -7 NIL NIL NIL) (-1149 2690995 2691217 2691478 "SOLVESER" 2691718 NIL SOLVESER (NIL T) -7 NIL NIL NIL) (-1148 2686299 2687187 2688182 "SOLVERAD" 2690047 NIL SOLVERAD (NIL T) -7 NIL NIL NIL) (-1147 2682114 2682723 2683452 "SOLVEFOR" 2685666 NIL SOLVEFOR (NIL T T) -7 NIL NIL NIL) (-1146 2676384 2681463 2681560 "SNTSCAT" 2681565 NIL SNTSCAT (NIL T T T T) -9 NIL 2681635 NIL) (-1145 2670490 2674707 2675098 "SMTS" 2676074 NIL SMTS (NIL T T T) -8 NIL NIL NIL) (-1144 2664899 2670378 2670455 "SMP" 2670460 NIL SMP (NIL T T) -8 NIL NIL NIL) (-1143 2663058 2663359 2663757 "SMITH" 2664596 NIL SMITH (NIL T T T T) -7 NIL NIL NIL) (-1142 2655162 2659637 2659740 "SMATCAT" 2661091 NIL SMATCAT (NIL NIL T T T) -9 NIL 2661641 NIL) (-1141 2652102 2652925 2654103 "SMATCAT-" 2654108 NIL SMATCAT- (NIL T NIL T T T) -8 NIL NIL NIL) (-1140 2649742 2651310 2651353 "SKAGG" 2651614 NIL SKAGG (NIL T) -9 NIL 2651749 NIL) (-1139 2645932 2649215 2649399 "SINT" 2649551 T SINT (NIL) -8 NIL NIL 2649713) (-1138 2645704 2645742 2645808 "SIMPAN" 2645888 T SIMPAN (NIL) -7 NIL NIL NIL) (-1137 2644983 2645239 2645379 "SIG" 2645586 T SIG (NIL) -8 NIL NIL NIL) (-1136 2643821 2644042 2644317 "SIGNRF" 2644742 NIL SIGNRF (NIL T) -7 NIL NIL NIL) (-1135 2642654 2642805 2643089 "SIGNEF" 2643650 NIL SIGNEF (NIL T T) -7 NIL NIL NIL) (-1134 2641960 2642237 2642361 "SIGAST" 2642552 T SIGAST (NIL) -8 NIL NIL NIL) (-1133 2639650 2640104 2640610 "SHP" 2641501 NIL SHP (NIL T NIL) -7 NIL NIL NIL) (-1132 2633478 2639551 2639627 "SHDP" 2639632 NIL SHDP (NIL NIL NIL T) -8 NIL NIL NIL) (-1131 2633037 2633229 2633259 "SGROUP" 2633352 T SGROUP (NIL) -9 NIL 2633414 NIL) (-1130 2632895 2632921 2632994 "SGROUP-" 2632999 NIL SGROUP- (NIL T) -8 NIL NIL NIL) (-1129 2629686 2630384 2631107 "SGCF" 2632194 T SGCF (NIL) -7 NIL NIL NIL) (-1128 2624054 2629133 2629230 "SFRTCAT" 2629235 NIL SFRTCAT (NIL T T T T) -9 NIL 2629274 NIL) (-1127 2617475 2618493 2619629 "SFRGCD" 2623037 NIL SFRGCD (NIL T T T T T) -7 NIL NIL NIL) (-1126 2610601 2611674 2612860 "SFQCMPK" 2616408 NIL SFQCMPK (NIL T T T T T) -7 NIL NIL NIL) (-1125 2610221 2610310 2610421 "SFORT" 2610542 NIL SFORT (NIL T T) -8 NIL NIL NIL) (-1124 2609339 2610061 2610182 "SEXOF" 2610187 NIL SEXOF (NIL T T T T T) -8 NIL NIL NIL) (-1123 2608446 2609220 2609288 "SEX" 2609293 T SEX (NIL) -8 NIL NIL NIL) (-1122 2604227 2604942 2605037 "SEXCAT" 2607659 NIL SEXCAT (NIL T T T T T) -9 NIL 2608219 NIL) (-1121 2601380 2604161 2604209 "SET" 2604214 NIL SET (NIL T) -8 NIL NIL NIL) (-1120 2599604 2600093 2600398 "SETMN" 2601121 NIL SETMN (NIL NIL NIL) -8 NIL NIL NIL) (-1119 2599086 2599238 2599268 "SETCAT" 2599444 T SETCAT (NIL) -9 NIL 2599554 NIL) (-1118 2598778 2598856 2598986 "SETCAT-" 2598991 NIL SETCAT- (NIL T) -8 NIL NIL NIL) (-1117 2595139 2597239 2597282 "SETAGG" 2598152 NIL SETAGG (NIL T) -9 NIL 2598492 NIL) (-1116 2594597 2594713 2594950 "SETAGG-" 2594955 NIL SETAGG- (NIL T T) -8 NIL NIL NIL) (-1115 2594040 2594293 2594394 "SEQAST" 2594518 T SEQAST (NIL) -8 NIL NIL NIL) (-1114 2593239 2593533 2593594 "SEGXCAT" 2593880 NIL SEGXCAT (NIL T T) -9 NIL 2594000 NIL) (-1113 2592245 2592905 2593087 "SEG" 2593092 NIL SEG (NIL T) -8 NIL NIL NIL) (-1112 2591224 2591438 2591481 "SEGCAT" 2592003 NIL SEGCAT (NIL T) -9 NIL 2592224 NIL) (-1111 2590156 2590587 2590795 "SEGBIND" 2591051 NIL SEGBIND (NIL T) -8 NIL NIL NIL) (-1110 2589777 2589836 2589949 "SEGBIND2" 2590091 NIL SEGBIND2 (NIL T T) -7 NIL NIL NIL) (-1109 2589350 2589578 2589655 "SEGAST" 2589722 T SEGAST (NIL) -8 NIL NIL NIL) (-1108 2588569 2588695 2588899 "SEG2" 2589194 NIL SEG2 (NIL T T) -7 NIL NIL NIL) (-1107 2587940 2588504 2588551 "SDVAR" 2588556 NIL SDVAR (NIL T) -8 NIL NIL NIL) (-1106 2580191 2587710 2587840 "SDPOL" 2587845 NIL SDPOL (NIL T) -8 NIL NIL NIL) (-1105 2578784 2579050 2579369 "SCPKG" 2579906 NIL SCPKG (NIL T) -7 NIL NIL NIL) (-1104 2577948 2578120 2578312 "SCOPE" 2578614 T SCOPE (NIL) -8 NIL NIL NIL) (-1103 2577168 2577302 2577481 "SCACHE" 2577803 NIL SCACHE (NIL T) -7 NIL NIL NIL) (-1102 2576800 2576986 2577016 "SASTCAT" 2577021 T SASTCAT (NIL) -9 NIL 2577034 NIL) (-1101 2576287 2576635 2576711 "SAOS" 2576746 T SAOS (NIL) -8 NIL NIL NIL) (-1100 2575852 2575887 2576060 "SAERFFC" 2576246 NIL SAERFFC (NIL T T T) -7 NIL NIL NIL) (-1099 2569515 2575749 2575829 "SAE" 2575834 NIL SAE (NIL T T NIL) -8 NIL NIL NIL) (-1098 2569108 2569143 2569302 "SAEFACT" 2569474 NIL SAEFACT (NIL T T T) -7 NIL NIL NIL) (-1097 2567429 2567743 2568144 "RURPK" 2568774 NIL RURPK (NIL T NIL) -7 NIL NIL NIL) (-1096 2566066 2566372 2566677 "RULESET" 2567263 NIL RULESET (NIL T T T) -8 NIL NIL NIL) (-1095 2563289 2563819 2564277 "RULE" 2565747 NIL RULE (NIL T T T) -8 NIL NIL NIL) (-1094 2562901 2563083 2563166 "RULECOLD" 2563241 NIL RULECOLD (NIL NIL) -8 NIL NIL NIL) (-1093 2562691 2562719 2562790 "RTVALUE" 2562852 T RTVALUE (NIL) -8 NIL NIL NIL) (-1092 2562162 2562408 2562502 "RSTRCAST" 2562619 T RSTRCAST (NIL) -8 NIL NIL NIL) (-1091 2557010 2557805 2558725 "RSETGCD" 2561361 NIL RSETGCD (NIL T T T T T) -7 NIL NIL NIL) (-1090 2546240 2551319 2551416 "RSETCAT" 2555535 NIL RSETCAT (NIL T T T T) -9 NIL 2556632 NIL) (-1089 2544167 2544706 2545530 "RSETCAT-" 2545535 NIL RSETCAT- (NIL T T T T T) -8 NIL NIL NIL) (-1088 2536553 2537929 2539449 "RSDCMPK" 2542766 NIL RSDCMPK (NIL T T T T T) -7 NIL NIL NIL) (-1087 2534518 2534985 2535059 "RRCC" 2536145 NIL RRCC (NIL T T) -9 NIL 2536489 NIL) (-1086 2533869 2534043 2534322 "RRCC-" 2534327 NIL RRCC- (NIL T T T) -8 NIL NIL NIL) (-1085 2533312 2533565 2533666 "RPTAST" 2533790 T RPTAST (NIL) -8 NIL NIL NIL) (-1084 2506788 2516424 2516491 "RPOLCAT" 2527157 NIL RPOLCAT (NIL T T T) -9 NIL 2530317 NIL) (-1083 2498286 2500626 2503748 "RPOLCAT-" 2503753 NIL RPOLCAT- (NIL T T T T) -8 NIL NIL NIL) (-1082 2489221 2496497 2496979 "ROUTINE" 2497826 T ROUTINE (NIL) -8 NIL NIL NIL) (-1081 2485882 2488847 2488987 "ROMAN" 2489103 T ROMAN (NIL) -8 NIL NIL NIL) (-1080 2484126 2484742 2485002 "ROIRC" 2485687 NIL ROIRC (NIL T T) -8 NIL NIL NIL) (-1079 2480344 2482628 2482658 "RNS" 2482962 T RNS (NIL) -9 NIL 2483236 NIL) (-1078 2478853 2479236 2479770 "RNS-" 2479845 NIL RNS- (NIL T) -8 NIL NIL NIL) (-1077 2478242 2478650 2478680 "RNG" 2478685 T RNG (NIL) -9 NIL 2478706 NIL) (-1076 2477245 2477607 2477809 "RNGBIND" 2478093 NIL RNGBIND (NIL T T) -8 NIL NIL NIL) (-1075 2476630 2477018 2477061 "RMODULE" 2477066 NIL RMODULE (NIL T) -9 NIL 2477093 NIL) (-1074 2475466 2475560 2475896 "RMCAT2" 2476531 NIL RMCAT2 (NIL NIL NIL T T T T T T T T) -7 NIL NIL NIL) (-1073 2472316 2474812 2475109 "RMATRIX" 2475228 NIL RMATRIX (NIL NIL NIL T) -8 NIL NIL NIL) (-1072 2465143 2467403 2467518 "RMATCAT" 2470877 NIL RMATCAT (NIL NIL NIL T T T) -9 NIL 2471859 NIL) (-1071 2464518 2464665 2464972 "RMATCAT-" 2464977 NIL RMATCAT- (NIL T NIL NIL T T T) -8 NIL NIL NIL) (-1070 2464133 2464305 2464348 "RLINSET" 2464410 NIL RLINSET (NIL T) -9 NIL 2464454 NIL) (-1069 2463700 2463775 2463903 "RINTERP" 2464052 NIL RINTERP (NIL NIL T) -7 NIL NIL NIL) (-1068 2462744 2463298 2463328 "RING" 2463384 T RING (NIL) -9 NIL 2463476 NIL) (-1067 2462536 2462580 2462677 "RING-" 2462682 NIL RING- (NIL T) -8 NIL NIL NIL) (-1066 2461377 2461614 2461872 "RIDIST" 2462300 T RIDIST (NIL) -7 NIL NIL NIL) (-1065 2452666 2460845 2461051 "RGCHAIN" 2461225 NIL RGCHAIN (NIL T NIL) -8 NIL NIL NIL) (-1064 2452002 2452408 2452449 "RGBCSPC" 2452507 NIL RGBCSPC (NIL T) -9 NIL 2452559 NIL) (-1063 2451146 2451527 2451568 "RGBCMDL" 2451800 NIL RGBCMDL (NIL T) -9 NIL 2451914 NIL) (-1062 2448140 2448754 2449424 "RF" 2450510 NIL RF (NIL T) -7 NIL NIL NIL) (-1061 2447786 2447849 2447952 "RFFACTOR" 2448071 NIL RFFACTOR (NIL T) -7 NIL NIL NIL) (-1060 2447511 2447546 2447643 "RFFACT" 2447745 NIL RFFACT (NIL T) -7 NIL NIL NIL) (-1059 2445628 2445992 2446374 "RFDIST" 2447151 T RFDIST (NIL) -7 NIL NIL NIL) (-1058 2445081 2445173 2445336 "RETSOL" 2445530 NIL RETSOL (NIL T T) -7 NIL NIL NIL) (-1057 2444717 2444797 2444840 "RETRACT" 2444973 NIL RETRACT (NIL T) -9 NIL 2445060 NIL) (-1056 2444566 2444591 2444678 "RETRACT-" 2444683 NIL RETRACT- (NIL T T) -8 NIL NIL NIL) (-1055 2444168 2444388 2444458 "RETAST" 2444518 T RETAST (NIL) -8 NIL NIL NIL) (-1054 2436910 2443821 2443948 "RESULT" 2444063 T RESULT (NIL) -8 NIL NIL NIL) (-1053 2435501 2436179 2436378 "RESRING" 2436813 NIL RESRING (NIL T T T T NIL) -8 NIL NIL NIL) (-1052 2435137 2435186 2435284 "RESLATC" 2435438 NIL RESLATC (NIL T) -7 NIL NIL NIL) (-1051 2434842 2434877 2434984 "REPSQ" 2435096 NIL REPSQ (NIL T) -7 NIL NIL NIL) (-1050 2432264 2432844 2433446 "REP" 2434262 T REP (NIL) -7 NIL NIL NIL) (-1049 2431961 2431996 2432107 "REPDB" 2432223 NIL REPDB (NIL T) -7 NIL NIL NIL) (-1048 2425861 2427250 2428473 "REP2" 2430773 NIL REP2 (NIL T) -7 NIL NIL NIL) (-1047 2422238 2422919 2423727 "REP1" 2425088 NIL REP1 (NIL T) -7 NIL NIL NIL) (-1046 2414934 2420379 2420835 "REGSET" 2421868 NIL REGSET (NIL T T T T) -8 NIL NIL NIL) (-1045 2413699 2414082 2414332 "REF" 2414719 NIL REF (NIL T) -8 NIL NIL NIL) (-1044 2413076 2413179 2413346 "REDORDER" 2413583 NIL REDORDER (NIL T T) -7 NIL NIL NIL) (-1043 2409044 2412289 2412516 "RECLOS" 2412904 NIL RECLOS (NIL T) -8 NIL NIL NIL) (-1042 2408096 2408277 2408492 "REALSOLV" 2408851 T REALSOLV (NIL) -7 NIL NIL NIL) (-1041 2407942 2407983 2408013 "REAL" 2408018 T REAL (NIL) -9 NIL 2408053 NIL) (-1040 2404425 2405227 2406111 "REAL0Q" 2407107 NIL REAL0Q (NIL T) -7 NIL NIL NIL) (-1039 2400026 2401014 2402075 "REAL0" 2403406 NIL REAL0 (NIL T) -7 NIL NIL NIL) (-1038 2399497 2399743 2399837 "RDUCEAST" 2399954 T RDUCEAST (NIL) -8 NIL NIL NIL) (-1037 2398902 2398974 2399181 "RDIV" 2399419 NIL RDIV (NIL T T T T T) -7 NIL NIL NIL) (-1036 2397970 2398144 2398357 "RDIST" 2398724 NIL RDIST (NIL T) -7 NIL NIL NIL) (-1035 2396567 2396854 2397226 "RDETRS" 2397678 NIL RDETRS (NIL T T) -7 NIL NIL NIL) (-1034 2394379 2394833 2395371 "RDETR" 2396109 NIL RDETR (NIL T T) -7 NIL NIL NIL) (-1033 2393004 2393282 2393679 "RDEEFS" 2394095 NIL RDEEFS (NIL T T) -7 NIL NIL NIL) (-1032 2391513 2391819 2392244 "RDEEF" 2392692 NIL RDEEF (NIL T T) -7 NIL NIL NIL) (-1031 2385560 2388480 2388510 "RCFIELD" 2389805 T RCFIELD (NIL) -9 NIL 2390536 NIL) (-1030 2383624 2384128 2384824 "RCFIELD-" 2384899 NIL RCFIELD- (NIL T) -8 NIL NIL NIL) (-1029 2379867 2381697 2381740 "RCAGG" 2382824 NIL RCAGG (NIL T) -9 NIL 2383289 NIL) (-1028 2379495 2379589 2379752 "RCAGG-" 2379757 NIL RCAGG- (NIL T T) -8 NIL NIL NIL) (-1027 2378830 2378942 2379107 "RATRET" 2379379 NIL RATRET (NIL T) -7 NIL NIL NIL) (-1026 2378383 2378450 2378571 "RATFACT" 2378758 NIL RATFACT (NIL T) -7 NIL NIL NIL) (-1025 2377691 2377811 2377963 "RANDSRC" 2378253 T RANDSRC (NIL) -7 NIL NIL NIL) (-1024 2377425 2377469 2377542 "RADUTIL" 2377640 T RADUTIL (NIL) -7 NIL NIL NIL) (-1023 2370253 2376256 2376567 "RADIX" 2377148 NIL RADIX (NIL NIL) -8 NIL NIL NIL) (-1022 2360713 2370095 2370225 "RADFF" 2370230 NIL RADFF (NIL T T T NIL NIL) -8 NIL NIL NIL) (-1021 2360360 2360435 2360465 "RADCAT" 2360625 T RADCAT (NIL) -9 NIL NIL NIL) (-1020 2360142 2360190 2360290 "RADCAT-" 2360295 NIL RADCAT- (NIL T) -8 NIL NIL NIL) (-1019 2358242 2359912 2360004 "QUEUE" 2360085 NIL QUEUE (NIL T) -8 NIL NIL NIL) (-1018 2354503 2358175 2358223 "QUAT" 2358228 NIL QUAT (NIL T) -8 NIL NIL NIL) (-1017 2354134 2354177 2354308 "QUATCT2" 2354454 NIL QUATCT2 (NIL T T T T) -7 NIL NIL NIL) (-1016 2346960 2350584 2350626 "QUATCAT" 2351417 NIL QUATCAT (NIL T) -9 NIL 2352183 NIL) (-1015 2343099 2344136 2345526 "QUATCAT-" 2345622 NIL QUATCAT- (NIL T T) -8 NIL NIL NIL) (-1014 2340538 2342147 2342190 "QUAGG" 2342571 NIL QUAGG (NIL T) -9 NIL 2342746 NIL) (-1013 2340140 2340360 2340430 "QQUTAST" 2340490 T QQUTAST (NIL) -8 NIL NIL NIL) (-1012 2339153 2339653 2339818 "QFORM" 2340021 NIL QFORM (NIL NIL T) -8 NIL NIL NIL) (-1011 2329540 2335055 2335097 "QFCAT" 2335765 NIL QFCAT (NIL T) -9 NIL 2336766 NIL) (-1010 2325107 2326308 2327902 "QFCAT-" 2327998 NIL QFCAT- (NIL T T) -8 NIL NIL NIL) (-1009 2324738 2324781 2324912 "QFCAT2" 2325058 NIL QFCAT2 (NIL T T T T) -7 NIL NIL NIL) (-1008 2324193 2324303 2324435 "QEQUAT" 2324628 T QEQUAT (NIL) -8 NIL NIL NIL) (-1007 2317319 2318392 2319578 "QCMPACK" 2323126 NIL QCMPACK (NIL T T T T T) -7 NIL NIL NIL) (-1006 2314857 2315305 2315735 "QALGSET" 2316974 NIL QALGSET (NIL T T T T) -8 NIL NIL NIL) (-1005 2314092 2314268 2314504 "QALGSET2" 2314675 NIL QALGSET2 (NIL NIL NIL) -7 NIL NIL NIL) (-1004 2312777 2313001 2313320 "PWFFINTB" 2313865 NIL PWFFINTB (NIL T T T T) -7 NIL NIL NIL) (-1003 2310952 2311120 2311476 "PUSHVAR" 2312591 NIL PUSHVAR (NIL T T T T) -7 NIL NIL NIL) (-1002 2306841 2307895 2307938 "PTRANFN" 2309849 NIL PTRANFN (NIL T) -9 NIL NIL NIL) (-1001 2305232 2305523 2305847 "PTPACK" 2306552 NIL PTPACK (NIL T) -7 NIL NIL NIL) (-1000 2304861 2304918 2305029 "PTFUNC2" 2305169 NIL PTFUNC2 (NIL T T) -7 NIL NIL NIL) (-999 2299288 2303683 2303724 "PTCAT" 2304020 NIL PTCAT (NIL T) -9 NIL 2304173 NIL) (-998 2298946 2298981 2299105 "PSQFR" 2299247 NIL PSQFR (NIL T T T T) -7 NIL NIL NIL) (-997 2297541 2297839 2298173 "PSEUDLIN" 2298644 NIL PSEUDLIN (NIL T) -7 NIL NIL NIL) (-996 2284304 2286675 2288999 "PSETPK" 2295301 NIL PSETPK (NIL T T T T) -7 NIL NIL NIL) (-995 2277322 2280062 2280158 "PSETCAT" 2283179 NIL PSETCAT (NIL T T T T) -9 NIL 2283993 NIL) (-994 2275158 2275792 2276613 "PSETCAT-" 2276618 NIL PSETCAT- (NIL T T T T T) -8 NIL NIL NIL) (-993 2274507 2274672 2274700 "PSCURVE" 2274968 T PSCURVE (NIL) -9 NIL 2275135 NIL) (-992 2270491 2272007 2272072 "PSCAT" 2272916 NIL PSCAT (NIL T T T) -9 NIL 2273156 NIL) (-991 2269554 2269770 2270170 "PSCAT-" 2270175 NIL PSCAT- (NIL T T T T) -8 NIL NIL NIL) (-990 2267913 2268623 2268886 "PRTITION" 2269311 T PRTITION (NIL) -8 NIL NIL NIL) (-989 2267388 2267634 2267726 "PRTDAST" 2267841 T PRTDAST (NIL) -8 NIL NIL NIL) (-988 2256478 2258692 2260880 "PRS" 2265250 NIL PRS (NIL T T) -7 NIL NIL NIL) (-987 2254263 2255800 2255840 "PRQAGG" 2256023 NIL PRQAGG (NIL T) -9 NIL 2256125 NIL) (-986 2253599 2253904 2253932 "PROPLOG" 2254071 T PROPLOG (NIL) -9 NIL 2254186 NIL) (-985 2253203 2253260 2253383 "PROPFUN2" 2253522 NIL PROPFUN2 (NIL T T) -8 NIL NIL NIL) (-984 2252518 2252639 2252811 "PROPFUN1" 2253064 NIL PROPFUN1 (NIL T) -8 NIL NIL NIL) (-983 2250699 2251265 2251562 "PROPFRML" 2252254 NIL PROPFRML (NIL T) -8 NIL NIL NIL) (-982 2250168 2250275 2250403 "PROPERTY" 2250591 T PROPERTY (NIL) -8 NIL NIL NIL) (-981 2244226 2248334 2249154 "PRODUCT" 2249394 NIL PRODUCT (NIL T T) -8 NIL NIL NIL) (-980 2241504 2243684 2243918 "PR" 2244037 NIL PR (NIL T T) -8 NIL NIL NIL) (-979 2241300 2241332 2241391 "PRINT" 2241465 T PRINT (NIL) -7 NIL NIL NIL) (-978 2240640 2240757 2240909 "PRIMES" 2241180 NIL PRIMES (NIL T) -7 NIL NIL NIL) (-977 2238705 2239106 2239572 "PRIMELT" 2240219 NIL PRIMELT (NIL T) -7 NIL NIL NIL) (-976 2238434 2238483 2238511 "PRIMCAT" 2238635 T PRIMCAT (NIL) -9 NIL NIL NIL) (-975 2234551 2238372 2238417 "PRIMARR" 2238422 NIL PRIMARR (NIL T) -8 NIL NIL NIL) (-974 2233558 2233736 2233964 "PRIMARR2" 2234369 NIL PRIMARR2 (NIL T T) -7 NIL NIL NIL) (-973 2233201 2233257 2233368 "PREASSOC" 2233496 NIL PREASSOC (NIL T T) -7 NIL NIL NIL) (-972 2232676 2232809 2232837 "PPCURVE" 2233042 T PPCURVE (NIL) -9 NIL 2233178 NIL) (-971 2232271 2232471 2232554 "PORTNUM" 2232613 T PORTNUM (NIL) -8 NIL NIL NIL) (-970 2229630 2230029 2230621 "POLYROOT" 2231852 NIL POLYROOT (NIL T T T T T) -7 NIL NIL NIL) (-969 2223536 2229234 2229394 "POLY" 2229503 NIL POLY (NIL T) -8 NIL NIL NIL) (-968 2222919 2222977 2223211 "POLYLIFT" 2223472 NIL POLYLIFT (NIL T T T T T) -7 NIL NIL NIL) (-967 2219194 2219643 2220272 "POLYCATQ" 2222464 NIL POLYCATQ (NIL T T T T T) -7 NIL NIL NIL) (-966 2205536 2210941 2211006 "POLYCAT" 2214520 NIL POLYCAT (NIL T T T) -9 NIL 2216398 NIL) (-965 2198985 2200847 2203231 "POLYCAT-" 2203236 NIL POLYCAT- (NIL T T T T) -8 NIL NIL NIL) (-964 2198572 2198640 2198760 "POLY2UP" 2198911 NIL POLY2UP (NIL NIL T) -7 NIL NIL NIL) (-963 2198204 2198261 2198370 "POLY2" 2198509 NIL POLY2 (NIL T T) -7 NIL NIL NIL) (-962 2196889 2197128 2197404 "POLUTIL" 2197978 NIL POLUTIL (NIL T T) -7 NIL NIL NIL) (-961 2195244 2195521 2195852 "POLTOPOL" 2196611 NIL POLTOPOL (NIL NIL T) -7 NIL NIL NIL) (-960 2190711 2195180 2195226 "POINT" 2195231 NIL POINT (NIL T) -8 NIL NIL NIL) (-959 2188898 2189255 2189630 "PNTHEORY" 2190356 T PNTHEORY (NIL) -7 NIL NIL NIL) (-958 2187356 2187653 2188052 "PMTOOLS" 2188596 NIL PMTOOLS (NIL T T T) -7 NIL NIL NIL) (-957 2186949 2187027 2187144 "PMSYM" 2187272 NIL PMSYM (NIL T) -7 NIL NIL NIL) (-956 2186457 2186526 2186701 "PMQFCAT" 2186874 NIL PMQFCAT (NIL T T T) -7 NIL NIL NIL) (-955 2185812 2185922 2186078 "PMPRED" 2186334 NIL PMPRED (NIL T) -7 NIL NIL NIL) (-954 2185205 2185291 2185453 "PMPREDFS" 2185713 NIL PMPREDFS (NIL T T T) -7 NIL NIL NIL) (-953 2183869 2184077 2184455 "PMPLCAT" 2184967 NIL PMPLCAT (NIL T T T T T) -7 NIL NIL NIL) (-952 2183401 2183480 2183632 "PMLSAGG" 2183784 NIL PMLSAGG (NIL T T T) -7 NIL NIL NIL) (-951 2182874 2182950 2183132 "PMKERNEL" 2183319 NIL PMKERNEL (NIL T T) -7 NIL NIL NIL) (-950 2182491 2182566 2182679 "PMINS" 2182793 NIL PMINS (NIL T) -7 NIL NIL NIL) (-949 2181933 2182002 2182211 "PMFS" 2182416 NIL PMFS (NIL T T T) -7 NIL NIL NIL) (-948 2181161 2181279 2181484 "PMDOWN" 2181810 NIL PMDOWN (NIL T T T) -7 NIL NIL NIL) (-947 2180328 2180486 2180667 "PMASS" 2181000 T PMASS (NIL) -7 NIL NIL NIL) (-946 2179601 2179711 2179874 "PMASSFS" 2180215 NIL PMASSFS (NIL T T) -7 NIL NIL NIL) (-945 2179256 2179324 2179418 "PLOTTOOL" 2179527 T PLOTTOOL (NIL) -7 NIL NIL NIL) (-944 2173863 2175067 2176215 "PLOT" 2178128 T PLOT (NIL) -8 NIL NIL NIL) (-943 2169667 2170711 2171632 "PLOT3D" 2172962 T PLOT3D (NIL) -8 NIL NIL NIL) (-942 2168579 2168756 2168991 "PLOT1" 2169471 NIL PLOT1 (NIL T) -7 NIL NIL NIL) (-941 2143970 2148645 2153496 "PLEQN" 2163845 NIL PLEQN (NIL T T T T) -7 NIL NIL NIL) (-940 2143288 2143410 2143590 "PINTERP" 2143835 NIL PINTERP (NIL NIL T) -7 NIL NIL NIL) (-939 2142981 2143028 2143131 "PINTERPA" 2143235 NIL PINTERPA (NIL T T) -7 NIL NIL NIL) (-938 2142197 2142745 2142832 "PI" 2142872 T PI (NIL) -8 NIL NIL 2142939) (-937 2140480 2141455 2141483 "PID" 2141665 T PID (NIL) -9 NIL 2141799 NIL) (-936 2140231 2140268 2140343 "PICOERCE" 2140437 NIL PICOERCE (NIL T) -7 NIL NIL NIL) (-935 2139551 2139690 2139866 "PGROEB" 2140087 NIL PGROEB (NIL T) -7 NIL NIL NIL) (-934 2135138 2135952 2136857 "PGE" 2138666 T PGE (NIL) -7 NIL NIL NIL) (-933 2133261 2133508 2133874 "PGCD" 2134855 NIL PGCD (NIL T T T T) -7 NIL NIL NIL) (-932 2132599 2132702 2132863 "PFRPAC" 2133145 NIL PFRPAC (NIL T) -7 NIL NIL NIL) (-931 2129239 2131147 2131500 "PFR" 2132278 NIL PFR (NIL T) -8 NIL NIL NIL) (-930 2127628 2127872 2128197 "PFOTOOLS" 2128986 NIL PFOTOOLS (NIL T T) -7 NIL NIL NIL) (-929 2126161 2126400 2126751 "PFOQ" 2127385 NIL PFOQ (NIL T T T) -7 NIL NIL NIL) (-928 2124662 2124874 2125230 "PFO" 2125945 NIL PFO (NIL T T T T T) -7 NIL NIL NIL) (-927 2121215 2124551 2124620 "PF" 2124625 NIL PF (NIL NIL) -8 NIL NIL NIL) (-926 2118535 2119806 2119834 "PFECAT" 2120419 T PFECAT (NIL) -9 NIL 2120803 NIL) (-925 2117980 2118134 2118348 "PFECAT-" 2118353 NIL PFECAT- (NIL T) -8 NIL NIL NIL) (-924 2116583 2116835 2117136 "PFBRU" 2117729 NIL PFBRU (NIL T T) -7 NIL NIL NIL) (-923 2114449 2114801 2115233 "PFBR" 2116234 NIL PFBR (NIL T T T T) -7 NIL NIL NIL) (-922 2110495 2111961 2112608 "PERM" 2113835 NIL PERM (NIL T) -8 NIL NIL NIL) (-921 2105729 2106702 2107572 "PERMGRP" 2109658 NIL PERMGRP (NIL T) -8 NIL NIL NIL) (-920 2103848 2104808 2104849 "PERMCAT" 2105249 NIL PERMCAT (NIL T) -9 NIL 2105547 NIL) (-919 2103501 2103542 2103666 "PERMAN" 2103801 NIL PERMAN (NIL NIL T) -7 NIL NIL NIL) (-918 2100991 2103166 2103288 "PENDTREE" 2103412 NIL PENDTREE (NIL T) -8 NIL NIL NIL) (-917 2099920 2100135 2100176 "PDSPC" 2100709 NIL PDSPC (NIL T) -9 NIL 2100954 NIL) (-916 2099023 2099241 2099603 "PDSPC-" 2099608 NIL PDSPC- (NIL T T) -8 NIL NIL NIL) (-915 2097905 2098673 2098714 "PDRING" 2098719 NIL PDRING (NIL T) -9 NIL 2098747 NIL) (-914 2096792 2097410 2097464 "PDMOD" 2097469 NIL PDMOD (NIL T T) -9 NIL 2097573 NIL) (-913 2094007 2094785 2095453 "PDEPROB" 2096144 T PDEPROB (NIL) -8 NIL NIL NIL) (-912 2091552 2092056 2092611 "PDEPACK" 2093472 T PDEPACK (NIL) -7 NIL NIL NIL) (-911 2090464 2090654 2090905 "PDECOMP" 2091351 NIL PDECOMP (NIL T T) -7 NIL NIL NIL) (-910 2088029 2088872 2088900 "PDECAT" 2089687 T PDECAT (NIL) -9 NIL 2090400 NIL) (-909 2087658 2087713 2087767 "PDDOM" 2087932 NIL PDDOM (NIL T T) -9 NIL 2088012 NIL) (-908 2087477 2087507 2087614 "PDDOM-" 2087619 NIL PDDOM- (NIL T T T) -8 NIL NIL NIL) (-907 2087228 2087261 2087351 "PCOMP" 2087438 NIL PCOMP (NIL T T) -7 NIL NIL NIL) (-906 2085406 2086029 2086326 "PBWLB" 2086957 NIL PBWLB (NIL T) -8 NIL NIL NIL) (-905 2077879 2079479 2080817 "PATTERN" 2084089 NIL PATTERN (NIL T) -8 NIL NIL NIL) (-904 2077511 2077568 2077677 "PATTERN2" 2077816 NIL PATTERN2 (NIL T T) -7 NIL NIL NIL) (-903 2075268 2075656 2076113 "PATTERN1" 2077100 NIL PATTERN1 (NIL T T) -7 NIL NIL NIL) (-902 2072636 2073217 2073698 "PATRES" 2074833 NIL PATRES (NIL T T) -8 NIL NIL NIL) (-901 2072200 2072267 2072399 "PATRES2" 2072563 NIL PATRES2 (NIL T T T) -7 NIL NIL NIL) (-900 2070083 2070488 2070895 "PATMATCH" 2071867 NIL PATMATCH (NIL T T T) -7 NIL NIL NIL) (-899 2069579 2069788 2069829 "PATMAB" 2069936 NIL PATMAB (NIL T) -9 NIL 2070019 NIL) (-898 2068097 2068433 2068691 "PATLRES" 2069384 NIL PATLRES (NIL T T T) -8 NIL NIL NIL) (-897 2067643 2067766 2067807 "PATAB" 2067812 NIL PATAB (NIL T) -9 NIL 2067984 NIL) (-896 2065825 2066220 2066643 "PARTPERM" 2067240 T PARTPERM (NIL) -7 NIL NIL NIL) (-895 2065446 2065509 2065611 "PARSURF" 2065756 NIL PARSURF (NIL T) -8 NIL NIL NIL) (-894 2065078 2065135 2065244 "PARSU2" 2065383 NIL PARSU2 (NIL T T) -7 NIL NIL NIL) (-893 2064842 2064882 2064949 "PARSER" 2065031 T PARSER (NIL) -7 NIL NIL NIL) (-892 2064463 2064526 2064628 "PARSCURV" 2064773 NIL PARSCURV (NIL T) -8 NIL NIL NIL) (-891 2064095 2064152 2064261 "PARSC2" 2064400 NIL PARSC2 (NIL T T) -7 NIL NIL NIL) (-890 2063734 2063792 2063889 "PARPCURV" 2064031 NIL PARPCURV (NIL T) -8 NIL NIL NIL) (-889 2063366 2063423 2063532 "PARPC2" 2063671 NIL PARPC2 (NIL T T) -7 NIL NIL NIL) (-888 2062427 2062739 2062921 "PARAMAST" 2063204 T PARAMAST (NIL) -8 NIL NIL NIL) (-887 2061947 2062033 2062152 "PAN2EXPR" 2062328 T PAN2EXPR (NIL) -7 NIL NIL NIL) (-886 2060724 2061068 2061296 "PALETTE" 2061739 T PALETTE (NIL) -8 NIL NIL NIL) (-885 2059117 2059729 2060089 "PAIR" 2060410 NIL PAIR (NIL T T) -8 NIL NIL NIL) (-884 2052709 2058374 2058569 "PADICRC" 2058971 NIL PADICRC (NIL NIL T) -8 NIL NIL NIL) (-883 2045625 2052053 2052238 "PADICRAT" 2052556 NIL PADICRAT (NIL NIL) -8 NIL NIL NIL) (-882 2043940 2045562 2045607 "PADIC" 2045612 NIL PADIC (NIL NIL) -8 NIL NIL NIL) (-881 2041036 2042600 2042640 "PADICCT" 2043221 NIL PADICCT (NIL NIL) -9 NIL 2043503 NIL) (-880 2039993 2040193 2040461 "PADEPAC" 2040823 NIL PADEPAC (NIL T NIL NIL) -7 NIL NIL NIL) (-879 2039205 2039338 2039544 "PADE" 2039855 NIL PADE (NIL T T T) -7 NIL NIL NIL) (-878 2037592 2038413 2038693 "OWP" 2039009 NIL OWP (NIL T NIL NIL NIL) -8 NIL NIL NIL) (-877 2037085 2037298 2037395 "OVERSET" 2037515 T OVERSET (NIL) -8 NIL NIL NIL) (-876 2036131 2036690 2036862 "OVAR" 2036953 NIL OVAR (NIL NIL) -8 NIL NIL NIL) (-875 2035395 2035516 2035677 "OUT" 2035990 T OUT (NIL) -7 NIL NIL NIL) (-874 2024267 2026504 2028704 "OUTFORM" 2033215 T OUTFORM (NIL) -8 NIL NIL NIL) (-873 2023603 2023864 2023991 "OUTBFILE" 2024160 T OUTBFILE (NIL) -8 NIL NIL NIL) (-872 2022910 2023075 2023103 "OUTBCON" 2023421 T OUTBCON (NIL) -9 NIL 2023587 NIL) (-871 2022511 2022623 2022780 "OUTBCON-" 2022785 NIL OUTBCON- (NIL T) -8 NIL NIL NIL) (-870 2021891 2022240 2022329 "OSI" 2022442 T OSI (NIL) -8 NIL NIL NIL) (-869 2021407 2021745 2021773 "OSGROUP" 2021778 T OSGROUP (NIL) -9 NIL 2021800 NIL) (-868 2020152 2020379 2020664 "ORTHPOL" 2021154 NIL ORTHPOL (NIL T) -7 NIL NIL NIL) (-867 2017703 2019987 2020108 "OREUP" 2020113 NIL OREUP (NIL NIL T NIL NIL) -8 NIL NIL NIL) (-866 2015106 2017394 2017521 "ORESUP" 2017645 NIL ORESUP (NIL T NIL NIL) -8 NIL NIL NIL) (-865 2012634 2013134 2013695 "OREPCTO" 2014595 NIL OREPCTO (NIL T T) -7 NIL NIL NIL) (-864 2006306 2008507 2008548 "OREPCAT" 2010896 NIL OREPCAT (NIL T) -9 NIL 2012000 NIL) (-863 2003453 2004235 2005293 "OREPCAT-" 2005298 NIL OREPCAT- (NIL T T) -8 NIL NIL NIL) (-862 2002590 2002888 2002916 "ORDSET" 2003225 T ORDSET (NIL) -9 NIL 2003389 NIL) (-861 2002021 2002169 2002393 "ORDSET-" 2002398 NIL ORDSET- (NIL T) -8 NIL NIL NIL) (-860 2000572 2001363 2001391 "ORDRING" 2001593 T ORDRING (NIL) -9 NIL 2001718 NIL) (-859 2000217 2000311 2000455 "ORDRING-" 2000460 NIL ORDRING- (NIL T) -8 NIL NIL NIL) (-858 1999583 2000046 2000074 "ORDMON" 2000079 T ORDMON (NIL) -9 NIL 2000100 NIL) (-857 1998745 1998892 1999087 "ORDFUNS" 1999432 NIL ORDFUNS (NIL NIL T) -7 NIL NIL NIL) (-856 1998069 1998488 1998516 "ORDFIN" 1998581 T ORDFIN (NIL) -9 NIL 1998655 NIL) (-855 1994628 1996655 1997064 "ORDCOMP" 1997693 NIL ORDCOMP (NIL T) -8 NIL NIL NIL) (-854 1993894 1994021 1994207 "ORDCOMP2" 1994488 NIL ORDCOMP2 (NIL T T) -7 NIL NIL NIL) (-853 1990475 1991385 1992199 "OPTPROB" 1993100 T OPTPROB (NIL) -8 NIL NIL NIL) (-852 1987277 1987916 1988620 "OPTPACK" 1989791 T OPTPACK (NIL) -7 NIL NIL NIL) (-851 1984950 1985716 1985744 "OPTCAT" 1986563 T OPTCAT (NIL) -9 NIL 1987213 NIL) (-850 1984334 1984627 1984732 "OPSIG" 1984865 T OPSIG (NIL) -8 NIL NIL NIL) (-849 1984102 1984141 1984207 "OPQUERY" 1984288 T OPQUERY (NIL) -7 NIL NIL NIL) (-848 1981233 1982413 1982917 "OP" 1983631 NIL OP (NIL T) -8 NIL NIL NIL) (-847 1980593 1980819 1980860 "OPERCAT" 1981072 NIL OPERCAT (NIL T) -9 NIL 1981169 NIL) (-846 1980348 1980404 1980521 "OPERCAT-" 1980526 NIL OPERCAT- (NIL T T) -8 NIL NIL NIL) (-845 1977161 1979145 1979514 "ONECOMP" 1980012 NIL ONECOMP (NIL T) -8 NIL NIL NIL) (-844 1976466 1976581 1976755 "ONECOMP2" 1977033 NIL ONECOMP2 (NIL T T) -7 NIL NIL NIL) (-843 1975885 1975991 1976121 "OMSERVER" 1976356 T OMSERVER (NIL) -7 NIL NIL NIL) (-842 1972747 1975325 1975365 "OMSAGG" 1975426 NIL OMSAGG (NIL T) -9 NIL 1975490 NIL) (-841 1971370 1971633 1971915 "OMPKG" 1972485 T OMPKG (NIL) -7 NIL NIL NIL) (-840 1970800 1970903 1970931 "OM" 1971230 T OM (NIL) -9 NIL NIL NIL) (-839 1969347 1970349 1970518 "OMLO" 1970681 NIL OMLO (NIL T T) -8 NIL NIL NIL) (-838 1968307 1968454 1968674 "OMEXPR" 1969173 NIL OMEXPR (NIL T) -7 NIL NIL NIL) (-837 1967598 1967853 1967989 "OMERR" 1968191 T OMERR (NIL) -8 NIL NIL NIL) (-836 1966749 1967019 1967179 "OMERRK" 1967458 T OMERRK (NIL) -8 NIL NIL NIL) (-835 1966200 1966426 1966534 "OMENC" 1966661 T OMENC (NIL) -8 NIL NIL NIL) (-834 1960095 1961280 1962451 "OMDEV" 1965049 T OMDEV (NIL) -8 NIL NIL NIL) (-833 1959164 1959335 1959529 "OMCONN" 1959921 T OMCONN (NIL) -8 NIL NIL NIL) (-832 1957671 1958647 1958675 "OINTDOM" 1958680 T OINTDOM (NIL) -9 NIL 1958701 NIL) (-831 1955009 1956359 1956696 "OFMONOID" 1957366 NIL OFMONOID (NIL T) -8 NIL NIL NIL) (-830 1954381 1954946 1954991 "ODVAR" 1954996 NIL ODVAR (NIL T) -8 NIL NIL NIL) (-829 1951804 1954126 1954281 "ODR" 1954286 NIL ODR (NIL T T NIL) -8 NIL NIL NIL) (-828 1944109 1951580 1951706 "ODPOL" 1951711 NIL ODPOL (NIL T) -8 NIL NIL NIL) (-827 1937907 1943981 1944086 "ODP" 1944091 NIL ODP (NIL NIL T NIL) -8 NIL NIL NIL) (-826 1936673 1936888 1937163 "ODETOOLS" 1937681 NIL ODETOOLS (NIL T T) -7 NIL NIL NIL) (-825 1933640 1934298 1935014 "ODESYS" 1936006 NIL ODESYS (NIL T T) -7 NIL NIL NIL) (-824 1928522 1929430 1930455 "ODERTRIC" 1932715 NIL ODERTRIC (NIL T T) -7 NIL NIL NIL) (-823 1927948 1928030 1928224 "ODERED" 1928434 NIL ODERED (NIL T T T T T) -7 NIL NIL NIL) (-822 1924836 1925384 1926061 "ODERAT" 1927371 NIL ODERAT (NIL T T) -7 NIL NIL NIL) (-821 1921795 1922260 1922857 "ODEPRRIC" 1924365 NIL ODEPRRIC (NIL T T T T) -7 NIL NIL NIL) (-820 1919738 1920334 1920820 "ODEPROB" 1921329 T ODEPROB (NIL) -8 NIL NIL NIL) (-819 1916258 1916743 1917390 "ODEPRIM" 1919217 NIL ODEPRIM (NIL T T T T) -7 NIL NIL NIL) (-818 1915507 1915609 1915869 "ODEPAL" 1916150 NIL ODEPAL (NIL T T T T) -7 NIL NIL NIL) (-817 1911669 1912460 1913324 "ODEPACK" 1914663 T ODEPACK (NIL) -7 NIL NIL NIL) (-816 1910730 1910837 1911059 "ODEINT" 1911558 NIL ODEINT (NIL T T) -7 NIL NIL NIL) (-815 1904831 1906256 1907703 "ODEIFTBL" 1909303 T ODEIFTBL (NIL) -8 NIL NIL NIL) (-814 1900229 1901015 1901967 "ODEEF" 1903990 NIL ODEEF (NIL T T) -7 NIL NIL NIL) (-813 1899578 1899667 1899890 "ODECONST" 1900134 NIL ODECONST (NIL T T T) -7 NIL NIL NIL) (-812 1897689 1898350 1898378 "ODECAT" 1898983 T ODECAT (NIL) -9 NIL 1899514 NIL) (-811 1894544 1897394 1897516 "OCT" 1897599 NIL OCT (NIL T) -8 NIL NIL NIL) (-810 1894182 1894225 1894352 "OCTCT2" 1894495 NIL OCTCT2 (NIL T T T T) -7 NIL NIL NIL) (-809 1888817 1891252 1891292 "OC" 1892389 NIL OC (NIL T) -9 NIL 1893247 NIL) (-808 1886044 1886792 1887782 "OC-" 1887876 NIL OC- (NIL T T) -8 NIL NIL NIL) (-807 1885382 1885850 1885878 "OCAMON" 1885883 T OCAMON (NIL) -9 NIL 1885904 NIL) (-806 1884899 1885240 1885268 "OASGP" 1885273 T OASGP (NIL) -9 NIL 1885293 NIL) (-805 1884146 1884635 1884663 "OAMONS" 1884703 T OAMONS (NIL) -9 NIL 1884746 NIL) (-804 1883546 1883979 1884007 "OAMON" 1884012 T OAMON (NIL) -9 NIL 1884032 NIL) (-803 1882790 1883308 1883336 "OAGROUP" 1883341 T OAGROUP (NIL) -9 NIL 1883361 NIL) (-802 1882480 1882530 1882618 "NUMTUBE" 1882734 NIL NUMTUBE (NIL T) -7 NIL NIL NIL) (-801 1876053 1877571 1879107 "NUMQUAD" 1880964 T NUMQUAD (NIL) -7 NIL NIL NIL) (-800 1871809 1872797 1873822 "NUMODE" 1875048 T NUMODE (NIL) -7 NIL NIL NIL) (-799 1869150 1870030 1870058 "NUMINT" 1870981 T NUMINT (NIL) -9 NIL 1871745 NIL) (-798 1868098 1868295 1868513 "NUMFMT" 1868952 T NUMFMT (NIL) -7 NIL NIL NIL) (-797 1854457 1857402 1859934 "NUMERIC" 1865605 NIL NUMERIC (NIL T) -7 NIL NIL NIL) (-796 1848827 1853906 1854001 "NTSCAT" 1854006 NIL NTSCAT (NIL T T T T) -9 NIL 1854045 NIL) (-795 1848021 1848186 1848379 "NTPOLFN" 1848666 NIL NTPOLFN (NIL T) -7 NIL NIL NIL) (-794 1835822 1844846 1845658 "NSUP" 1847242 NIL NSUP (NIL T) -8 NIL NIL NIL) (-793 1835454 1835511 1835620 "NSUP2" 1835759 NIL NSUP2 (NIL T T) -7 NIL NIL NIL) (-792 1825404 1835228 1835361 "NSMP" 1835366 NIL NSMP (NIL T T) -8 NIL NIL NIL) (-791 1823836 1824137 1824494 "NREP" 1825092 NIL NREP (NIL T) -7 NIL NIL NIL) (-790 1822427 1822679 1823037 "NPCOEF" 1823579 NIL NPCOEF (NIL T T T T T) -7 NIL NIL NIL) (-789 1821493 1821608 1821824 "NORMRETR" 1822308 NIL NORMRETR (NIL T T T T NIL) -7 NIL NIL NIL) (-788 1819534 1819824 1820233 "NORMPK" 1821201 NIL NORMPK (NIL T T T T T) -7 NIL NIL NIL) (-787 1819219 1819247 1819371 "NORMMA" 1819500 NIL NORMMA (NIL T T T T) -7 NIL NIL NIL) (-786 1819019 1819176 1819205 "NONE" 1819210 T NONE (NIL) -8 NIL NIL NIL) (-785 1818808 1818837 1818906 "NONE1" 1818983 NIL NONE1 (NIL T) -7 NIL NIL NIL) (-784 1818305 1818367 1818546 "NODE1" 1818740 NIL NODE1 (NIL T T) -7 NIL NIL NIL) (-783 1816586 1817437 1817692 "NNI" 1818039 T NNI (NIL) -8 NIL NIL 1818274) (-782 1815006 1815319 1815683 "NLINSOL" 1816254 NIL NLINSOL (NIL T) -7 NIL NIL NIL) (-781 1811247 1812242 1813141 "NIPROB" 1814127 T NIPROB (NIL) -8 NIL NIL NIL) (-780 1810004 1810238 1810540 "NFINTBAS" 1811009 NIL NFINTBAS (NIL T T) -7 NIL NIL NIL) (-779 1809178 1809654 1809695 "NETCLT" 1809867 NIL NETCLT (NIL T) -9 NIL 1809949 NIL) (-778 1807886 1808117 1808398 "NCODIV" 1808946 NIL NCODIV (NIL T T) -7 NIL NIL NIL) (-777 1807648 1807685 1807760 "NCNTFRAC" 1807843 NIL NCNTFRAC (NIL T) -7 NIL NIL NIL) (-776 1805828 1806192 1806612 "NCEP" 1807273 NIL NCEP (NIL T) -7 NIL NIL NIL) (-775 1804665 1805438 1805466 "NASRING" 1805576 T NASRING (NIL) -9 NIL 1805656 NIL) (-774 1804460 1804504 1804598 "NASRING-" 1804603 NIL NASRING- (NIL T) -8 NIL NIL NIL) (-773 1803553 1804078 1804106 "NARNG" 1804223 T NARNG (NIL) -9 NIL 1804314 NIL) (-772 1803245 1803312 1803446 "NARNG-" 1803451 NIL NARNG- (NIL T) -8 NIL NIL NIL) (-771 1802124 1802331 1802566 "NAGSP" 1803030 T NAGSP (NIL) -7 NIL NIL NIL) (-770 1793396 1795080 1796753 "NAGS" 1800471 T NAGS (NIL) -7 NIL NIL NIL) (-769 1791944 1792252 1792583 "NAGF07" 1793085 T NAGF07 (NIL) -7 NIL NIL NIL) (-768 1786482 1787773 1789080 "NAGF04" 1790657 T NAGF04 (NIL) -7 NIL NIL NIL) (-767 1779450 1781064 1782697 "NAGF02" 1784869 T NAGF02 (NIL) -7 NIL NIL NIL) (-766 1774674 1775774 1776891 "NAGF01" 1778353 T NAGF01 (NIL) -7 NIL NIL NIL) (-765 1768302 1769868 1771453 "NAGE04" 1773109 T NAGE04 (NIL) -7 NIL NIL NIL) (-764 1759471 1761592 1763722 "NAGE02" 1766192 T NAGE02 (NIL) -7 NIL NIL NIL) (-763 1755424 1756371 1757335 "NAGE01" 1758527 T NAGE01 (NIL) -7 NIL NIL NIL) (-762 1753219 1753753 1754311 "NAGD03" 1754886 T NAGD03 (NIL) -7 NIL NIL NIL) (-761 1744969 1746897 1748851 "NAGD02" 1751285 T NAGD02 (NIL) -7 NIL NIL NIL) (-760 1738780 1740205 1741645 "NAGD01" 1743549 T NAGD01 (NIL) -7 NIL NIL NIL) (-759 1734989 1735811 1736648 "NAGC06" 1737963 T NAGC06 (NIL) -7 NIL NIL NIL) (-758 1733454 1733786 1734142 "NAGC05" 1734653 T NAGC05 (NIL) -7 NIL NIL NIL) (-757 1732830 1732949 1733093 "NAGC02" 1733330 T NAGC02 (NIL) -7 NIL NIL NIL) (-756 1731775 1732358 1732398 "NAALG" 1732477 NIL NAALG (NIL T) -9 NIL 1732538 NIL) (-755 1731610 1731639 1731729 "NAALG-" 1731734 NIL NAALG- (NIL T T) -8 NIL NIL NIL) (-754 1725560 1726668 1727855 "MULTSQFR" 1730506 NIL MULTSQFR (NIL T T T T) -7 NIL NIL NIL) (-753 1724879 1724954 1725138 "MULTFACT" 1725472 NIL MULTFACT (NIL T T T T) -7 NIL NIL NIL) (-752 1717550 1721464 1721517 "MTSCAT" 1722587 NIL MTSCAT (NIL T T) -9 NIL 1723102 NIL) (-751 1717262 1717316 1717408 "MTHING" 1717490 NIL MTHING (NIL T) -7 NIL NIL NIL) (-750 1717054 1717087 1717147 "MSYSCMD" 1717222 T MSYSCMD (NIL) -7 NIL NIL NIL) (-749 1713136 1715809 1716129 "MSET" 1716767 NIL MSET (NIL T) -8 NIL NIL NIL) (-748 1710205 1712697 1712738 "MSETAGG" 1712743 NIL MSETAGG (NIL T) -9 NIL 1712777 NIL) (-747 1706047 1707584 1708329 "MRING" 1709505 NIL MRING (NIL T T) -8 NIL NIL NIL) (-746 1705613 1705680 1705811 "MRF2" 1705974 NIL MRF2 (NIL T T T) -7 NIL NIL NIL) (-745 1705231 1705266 1705410 "MRATFAC" 1705572 NIL MRATFAC (NIL T T T T) -7 NIL NIL NIL) (-744 1702843 1703138 1703569 "MPRFF" 1704936 NIL MPRFF (NIL T T T T) -7 NIL NIL NIL) (-743 1696864 1702697 1702794 "MPOLY" 1702799 NIL MPOLY (NIL NIL T) -8 NIL NIL NIL) (-742 1696354 1696389 1696597 "MPCPF" 1696823 NIL MPCPF (NIL T T T T) -7 NIL NIL NIL) (-741 1695868 1695911 1696095 "MPC3" 1696305 NIL MPC3 (NIL T T T T T T T) -7 NIL NIL NIL) (-740 1695063 1695144 1695365 "MPC2" 1695783 NIL MPC2 (NIL T T T T T T T) -7 NIL NIL NIL) (-739 1693364 1693701 1694091 "MONOTOOL" 1694723 NIL MONOTOOL (NIL T T) -7 NIL NIL NIL) (-738 1692575 1692892 1692920 "MONOID" 1693139 T MONOID (NIL) -9 NIL 1693286 NIL) (-737 1692121 1692240 1692421 "MONOID-" 1692426 NIL MONOID- (NIL T) -8 NIL NIL NIL) (-736 1681711 1687941 1688000 "MONOGEN" 1688674 NIL MONOGEN (NIL T T) -9 NIL 1689130 NIL) (-735 1678929 1679664 1680664 "MONOGEN-" 1680783 NIL MONOGEN- (NIL T T T) -8 NIL NIL NIL) (-734 1677748 1678194 1678222 "MONADWU" 1678614 T MONADWU (NIL) -9 NIL 1678852 NIL) (-733 1677120 1677279 1677527 "MONADWU-" 1677532 NIL MONADWU- (NIL T) -8 NIL NIL NIL) (-732 1676465 1676709 1676737 "MONAD" 1676944 T MONAD (NIL) -9 NIL 1677056 NIL) (-731 1676150 1676228 1676360 "MONAD-" 1676365 NIL MONAD- (NIL T) -8 NIL NIL NIL) (-730 1674439 1675063 1675342 "MOEBIUS" 1675903 NIL MOEBIUS (NIL T) -8 NIL NIL NIL) (-729 1673703 1674107 1674147 "MODULE" 1674152 NIL MODULE (NIL T) -9 NIL 1674191 NIL) (-728 1673271 1673367 1673557 "MODULE-" 1673562 NIL MODULE- (NIL T T) -8 NIL NIL NIL) (-727 1670951 1671635 1671962 "MODRING" 1673095 NIL MODRING (NIL T T NIL NIL NIL) -8 NIL NIL NIL) (-726 1667895 1669056 1669577 "MODOP" 1670480 NIL MODOP (NIL T T) -8 NIL NIL NIL) (-725 1666483 1666962 1667239 "MODMONOM" 1667758 NIL MODMONOM (NIL T T NIL) -8 NIL NIL NIL) (-724 1656251 1664774 1665188 "MODMON" 1666120 NIL MODMON (NIL T T) -8 NIL NIL NIL) (-723 1653407 1655095 1655371 "MODFIELD" 1656126 NIL MODFIELD (NIL T T NIL NIL NIL) -8 NIL NIL NIL) (-722 1652384 1652688 1652878 "MMLFORM" 1653237 T MMLFORM (NIL) -8 NIL NIL NIL) (-721 1651910 1651953 1652132 "MMAP" 1652335 NIL MMAP (NIL T T T T T T) -7 NIL NIL NIL) (-720 1649975 1650742 1650783 "MLO" 1651206 NIL MLO (NIL T) -9 NIL 1651448 NIL) (-719 1647341 1647857 1648459 "MLIFT" 1649456 NIL MLIFT (NIL T T T T) -7 NIL NIL NIL) (-718 1646732 1646816 1646970 "MKUCFUNC" 1647252 NIL MKUCFUNC (NIL T T T) -7 NIL NIL NIL) (-717 1646331 1646401 1646524 "MKRECORD" 1646655 NIL MKRECORD (NIL T T) -7 NIL NIL NIL) (-716 1645378 1645540 1645768 "MKFUNC" 1646142 NIL MKFUNC (NIL T) -7 NIL NIL NIL) (-715 1644766 1644870 1645026 "MKFLCFN" 1645261 NIL MKFLCFN (NIL T) -7 NIL NIL NIL) (-714 1644043 1644145 1644330 "MKBCFUNC" 1644659 NIL MKBCFUNC (NIL T T T T) -7 NIL NIL NIL) (-713 1640632 1643597 1643733 "MINT" 1643927 T MINT (NIL) -8 NIL NIL NIL) (-712 1639444 1639687 1639964 "MHROWRED" 1640387 NIL MHROWRED (NIL T) -7 NIL NIL NIL) (-711 1634824 1637979 1638384 "MFLOAT" 1639059 T MFLOAT (NIL) -8 NIL NIL NIL) (-710 1634181 1634257 1634428 "MFINFACT" 1634736 NIL MFINFACT (NIL T T T T) -7 NIL NIL NIL) (-709 1630496 1631344 1632228 "MESH" 1633317 T MESH (NIL) -7 NIL NIL NIL) (-708 1628886 1629198 1629551 "MDDFACT" 1630183 NIL MDDFACT (NIL T) -7 NIL NIL NIL) (-707 1625655 1628017 1628058 "MDAGG" 1628313 NIL MDAGG (NIL T) -9 NIL 1628456 NIL) (-706 1614349 1624948 1625155 "MCMPLX" 1625468 T MCMPLX (NIL) -8 NIL NIL NIL) (-705 1613486 1613632 1613833 "MCDEN" 1614198 NIL MCDEN (NIL T T) -7 NIL NIL NIL) (-704 1611376 1611646 1612026 "MCALCFN" 1613216 NIL MCALCFN (NIL T T T T) -7 NIL NIL NIL) (-703 1610301 1610541 1610774 "MAYBE" 1611182 NIL MAYBE (NIL T) -8 NIL NIL NIL) (-702 1607913 1608436 1608998 "MATSTOR" 1609772 NIL MATSTOR (NIL T) -7 NIL NIL NIL) (-701 1603824 1607285 1607533 "MATRIX" 1607698 NIL MATRIX (NIL T) -8 NIL NIL NIL) (-700 1599590 1600297 1601033 "MATLIN" 1603181 NIL MATLIN (NIL T T T T) -7 NIL NIL NIL) (-699 1589415 1592647 1592724 "MATCAT" 1597756 NIL MATCAT (NIL T T T) -9 NIL 1599228 NIL) (-698 1585608 1586678 1588091 "MATCAT-" 1588096 NIL MATCAT- (NIL T T T T) -8 NIL NIL NIL) (-697 1584202 1584355 1584688 "MATCAT2" 1585443 NIL MATCAT2 (NIL T T T T T T T T) -7 NIL NIL NIL) (-696 1582314 1582638 1583022 "MAPPKG3" 1583877 NIL MAPPKG3 (NIL T T T) -7 NIL NIL NIL) (-695 1581295 1581468 1581690 "MAPPKG2" 1582138 NIL MAPPKG2 (NIL T T) -7 NIL NIL NIL) (-694 1579794 1580078 1580405 "MAPPKG1" 1581001 NIL MAPPKG1 (NIL T) -7 NIL NIL NIL) (-693 1578873 1579200 1579377 "MAPPAST" 1579637 T MAPPAST (NIL) -8 NIL NIL NIL) (-692 1578484 1578542 1578665 "MAPHACK3" 1578809 NIL MAPHACK3 (NIL T T T) -7 NIL NIL NIL) (-691 1578076 1578137 1578251 "MAPHACK2" 1578416 NIL MAPHACK2 (NIL T T) -7 NIL NIL NIL) (-690 1577514 1577617 1577759 "MAPHACK1" 1577967 NIL MAPHACK1 (NIL T) -7 NIL NIL NIL) (-689 1575593 1576214 1576518 "MAGMA" 1577242 NIL MAGMA (NIL T) -8 NIL NIL NIL) (-688 1575072 1575317 1575408 "MACROAST" 1575522 T MACROAST (NIL) -8 NIL NIL NIL) (-687 1571492 1573311 1573772 "M3D" 1574644 NIL M3D (NIL T) -8 NIL NIL NIL) (-686 1565541 1569803 1569844 "LZSTAGG" 1570626 NIL LZSTAGG (NIL T) -9 NIL 1570921 NIL) (-685 1561499 1562672 1564129 "LZSTAGG-" 1564134 NIL LZSTAGG- (NIL T T) -8 NIL NIL NIL) (-684 1558586 1559390 1559877 "LWORD" 1561044 NIL LWORD (NIL T) -8 NIL NIL NIL) (-683 1558162 1558390 1558465 "LSTAST" 1558531 T LSTAST (NIL) -8 NIL NIL NIL) (-682 1551052 1557933 1558067 "LSQM" 1558072 NIL LSQM (NIL NIL T) -8 NIL NIL NIL) (-681 1550276 1550415 1550643 "LSPP" 1550907 NIL LSPP (NIL T T T T) -7 NIL NIL NIL) (-680 1548088 1548389 1548845 "LSMP" 1549965 NIL LSMP (NIL T T T T) -7 NIL NIL NIL) (-679 1544867 1545541 1546271 "LSMP1" 1547390 NIL LSMP1 (NIL T) -7 NIL NIL NIL) (-678 1538695 1543984 1544025 "LSAGG" 1544087 NIL LSAGG (NIL T) -9 NIL 1544165 NIL) (-677 1535390 1536314 1537527 "LSAGG-" 1537532 NIL LSAGG- (NIL T T) -8 NIL NIL NIL) (-676 1532989 1534534 1534783 "LPOLY" 1535185 NIL LPOLY (NIL T T) -8 NIL NIL NIL) (-675 1532571 1532656 1532779 "LPEFRAC" 1532898 NIL LPEFRAC (NIL T) -7 NIL NIL NIL) (-674 1530892 1531665 1531918 "LO" 1532403 NIL LO (NIL T T T) -8 NIL NIL NIL) (-673 1530530 1530642 1530670 "LOGIC" 1530781 T LOGIC (NIL) -9 NIL 1530862 NIL) (-672 1530392 1530415 1530486 "LOGIC-" 1530491 NIL LOGIC- (NIL T) -8 NIL NIL NIL) (-671 1529585 1529725 1529918 "LODOOPS" 1530248 NIL LODOOPS (NIL T T) -7 NIL NIL NIL) (-670 1527008 1529501 1529567 "LODO" 1529572 NIL LODO (NIL T NIL) -8 NIL NIL NIL) (-669 1525546 1525781 1526134 "LODOF" 1526755 NIL LODOF (NIL T T) -7 NIL NIL NIL) (-668 1521750 1524181 1524222 "LODOCAT" 1524660 NIL LODOCAT (NIL T) -9 NIL 1524871 NIL) (-667 1521483 1521541 1521668 "LODOCAT-" 1521673 NIL LODOCAT- (NIL T T) -8 NIL NIL NIL) (-666 1518803 1521324 1521442 "LODO2" 1521447 NIL LODO2 (NIL T T) -8 NIL NIL NIL) (-665 1516238 1518740 1518785 "LODO1" 1518790 NIL LODO1 (NIL T) -8 NIL NIL NIL) (-664 1515119 1515284 1515589 "LODEEF" 1516061 NIL LODEEF (NIL T T T) -7 NIL NIL NIL) (-663 1510396 1513285 1513326 "LNAGG" 1514188 NIL LNAGG (NIL T) -9 NIL 1514623 NIL) (-662 1509543 1509757 1510099 "LNAGG-" 1510104 NIL LNAGG- (NIL T T) -8 NIL NIL NIL) (-661 1505679 1506468 1507107 "LMOPS" 1508958 NIL LMOPS (NIL T T NIL) -8 NIL NIL NIL) (-660 1505068 1505456 1505497 "LMODULE" 1505502 NIL LMODULE (NIL T) -9 NIL 1505528 NIL) (-659 1502268 1504713 1504836 "LMDICT" 1504978 NIL LMDICT (NIL T) -8 NIL NIL NIL) (-658 1501886 1502058 1502099 "LLINSET" 1502160 NIL LLINSET (NIL T) -9 NIL 1502204 NIL) (-657 1501585 1501794 1501854 "LITERAL" 1501859 NIL LITERAL (NIL T) -8 NIL NIL NIL) (-656 1494750 1500519 1500823 "LIST" 1501314 NIL LIST (NIL T) -8 NIL NIL NIL) (-655 1494275 1494349 1494488 "LIST3" 1494670 NIL LIST3 (NIL T T T) -7 NIL NIL NIL) (-654 1493282 1493460 1493688 "LIST2" 1494093 NIL LIST2 (NIL T T) -7 NIL NIL NIL) (-653 1491416 1491728 1492127 "LIST2MAP" 1492929 NIL LIST2MAP (NIL T T) -7 NIL NIL NIL) (-652 1491047 1491235 1491276 "LINSET" 1491281 NIL LINSET (NIL T) -9 NIL 1491315 NIL) (-651 1489460 1490074 1490115 "LINEXP" 1490605 NIL LINEXP (NIL T) -9 NIL 1490878 NIL) (-650 1488037 1488297 1488608 "LINDEP" 1489212 NIL LINDEP (NIL T T) -7 NIL NIL NIL) (-649 1484804 1485523 1486300 "LIMITRF" 1487292 NIL LIMITRF (NIL T) -7 NIL NIL NIL) (-648 1483107 1483403 1483812 "LIMITPS" 1484499 NIL LIMITPS (NIL T T) -7 NIL NIL NIL) (-647 1477535 1482618 1482846 "LIE" 1482928 NIL LIE (NIL T T) -8 NIL NIL NIL) (-646 1476469 1476938 1476978 "LIECAT" 1477118 NIL LIECAT (NIL T) -9 NIL 1477269 NIL) (-645 1476310 1476337 1476425 "LIECAT-" 1476430 NIL LIECAT- (NIL T T) -8 NIL NIL NIL) (-644 1468901 1475850 1476006 "LIB" 1476174 T LIB (NIL) -8 NIL NIL NIL) (-643 1464536 1465419 1466354 "LGROBP" 1468018 NIL LGROBP (NIL NIL T) -7 NIL NIL NIL) (-642 1462534 1462808 1463158 "LF" 1464257 NIL LF (NIL T T) -7 NIL NIL NIL) (-641 1461374 1462066 1462094 "LFCAT" 1462301 T LFCAT (NIL) -9 NIL 1462440 NIL) (-640 1458276 1458906 1459594 "LEXTRIPK" 1460738 NIL LEXTRIPK (NIL T NIL) -7 NIL NIL NIL) (-639 1455020 1455846 1456349 "LEXP" 1457856 NIL LEXP (NIL T T NIL) -8 NIL NIL NIL) (-638 1454496 1454741 1454833 "LETAST" 1454948 T LETAST (NIL) -8 NIL NIL NIL) (-637 1452894 1453207 1453608 "LEADCDET" 1454178 NIL LEADCDET (NIL T T T T) -7 NIL NIL NIL) (-636 1452084 1452158 1452387 "LAZM3PK" 1452815 NIL LAZM3PK (NIL T T T T T T) -7 NIL NIL NIL) (-635 1447001 1450161 1450699 "LAUPOL" 1451596 NIL LAUPOL (NIL T T) -8 NIL NIL NIL) (-634 1446580 1446624 1446785 "LAPLACE" 1446951 NIL LAPLACE (NIL T T) -7 NIL NIL NIL) (-633 1444519 1445681 1445932 "LA" 1446413 NIL LA (NIL T T T) -8 NIL NIL NIL) (-632 1443499 1444083 1444124 "LALG" 1444186 NIL LALG (NIL T) -9 NIL 1444245 NIL) (-631 1443213 1443272 1443408 "LALG-" 1443413 NIL LALG- (NIL T T) -8 NIL NIL NIL) (-630 1443048 1443072 1443113 "KVTFROM" 1443175 NIL KVTFROM (NIL T) -9 NIL NIL NIL) (-629 1441971 1442415 1442600 "KTVLOGIC" 1442883 T KTVLOGIC (NIL) -8 NIL NIL NIL) (-628 1441806 1441830 1441871 "KRCFROM" 1441933 NIL KRCFROM (NIL T) -9 NIL NIL NIL) (-627 1440710 1440897 1441196 "KOVACIC" 1441606 NIL KOVACIC (NIL T T) -7 NIL NIL NIL) (-626 1440545 1440569 1440610 "KONVERT" 1440672 NIL KONVERT (NIL T) -9 NIL NIL NIL) (-625 1440380 1440404 1440445 "KOERCE" 1440507 NIL KOERCE (NIL T) -9 NIL NIL NIL) (-624 1438211 1438973 1439350 "KERNEL" 1440036 NIL KERNEL (NIL T) -8 NIL NIL NIL) (-623 1437707 1437788 1437920 "KERNEL2" 1438125 NIL KERNEL2 (NIL T T) -7 NIL NIL NIL) (-622 1431417 1436184 1436238 "KDAGG" 1436615 NIL KDAGG (NIL T T) -9 NIL 1436821 NIL) (-621 1430946 1431070 1431275 "KDAGG-" 1431280 NIL KDAGG- (NIL T T T) -8 NIL NIL NIL) (-620 1424094 1430607 1430762 "KAFILE" 1430824 NIL KAFILE (NIL T) -8 NIL NIL NIL) (-619 1418522 1423605 1423833 "JORDAN" 1423915 NIL JORDAN (NIL T T) -8 NIL NIL NIL) (-618 1417901 1418171 1418292 "JOINAST" 1418421 T JOINAST (NIL) -8 NIL NIL NIL) (-617 1417747 1417806 1417861 "JAVACODE" 1417866 T JAVACODE (NIL) -8 NIL NIL NIL) (-616 1413973 1415924 1415978 "IXAGG" 1416907 NIL IXAGG (NIL T T) -9 NIL 1417366 NIL) (-615 1412892 1413198 1413617 "IXAGG-" 1413622 NIL IXAGG- (NIL T T T) -8 NIL NIL NIL) (-614 1408424 1412814 1412873 "IVECTOR" 1412878 NIL IVECTOR (NIL T NIL) -8 NIL NIL NIL) (-613 1407190 1407427 1407693 "ITUPLE" 1408191 NIL ITUPLE (NIL T) -8 NIL NIL NIL) (-612 1405692 1405869 1406164 "ITRIGMNP" 1407012 NIL ITRIGMNP (NIL T T T) -7 NIL NIL NIL) (-611 1404437 1404641 1404924 "ITFUN3" 1405468 NIL ITFUN3 (NIL T T T) -7 NIL NIL NIL) (-610 1404069 1404126 1404235 "ITFUN2" 1404374 NIL ITFUN2 (NIL T T) -7 NIL NIL NIL) (-609 1403228 1403549 1403723 "ITFORM" 1403915 T ITFORM (NIL) -8 NIL NIL NIL) (-608 1401189 1402248 1402526 "ITAYLOR" 1402983 NIL ITAYLOR (NIL T) -8 NIL NIL NIL) (-607 1390134 1395326 1396489 "ISUPS" 1400059 NIL ISUPS (NIL T) -8 NIL NIL NIL) (-606 1389238 1389378 1389614 "ISUMP" 1389981 NIL ISUMP (NIL T T T T) -7 NIL NIL NIL) (-605 1384615 1389183 1389224 "ISTRING" 1389229 NIL ISTRING (NIL NIL) -8 NIL NIL NIL) (-604 1384091 1384336 1384428 "ISAST" 1384543 T ISAST (NIL) -8 NIL NIL NIL) (-603 1383300 1383382 1383598 "IRURPK" 1384005 NIL IRURPK (NIL T T T T T) -7 NIL NIL NIL) (-602 1382236 1382437 1382677 "IRSN" 1383080 T IRSN (NIL) -7 NIL NIL NIL) (-601 1380307 1380662 1381091 "IRRF2F" 1381874 NIL IRRF2F (NIL T) -7 NIL NIL NIL) (-600 1380054 1380092 1380168 "IRREDFFX" 1380263 NIL IRREDFFX (NIL T) -7 NIL NIL NIL) (-599 1378669 1378928 1379227 "IROOT" 1379787 NIL IROOT (NIL T) -7 NIL NIL NIL) (-598 1375273 1376353 1377045 "IR" 1378009 NIL IR (NIL T) -8 NIL NIL NIL) (-597 1374478 1374766 1374917 "IRFORM" 1375142 T IRFORM (NIL) -8 NIL NIL NIL) (-596 1372091 1372586 1373152 "IR2" 1373956 NIL IR2 (NIL T T) -7 NIL NIL NIL) (-595 1371191 1371304 1371518 "IR2F" 1371974 NIL IR2F (NIL T T) -7 NIL NIL NIL) (-594 1370982 1371016 1371076 "IPRNTPK" 1371151 T IPRNTPK (NIL) -7 NIL NIL NIL) (-593 1367563 1370871 1370940 "IPF" 1370945 NIL IPF (NIL NIL) -8 NIL NIL NIL) (-592 1365890 1367488 1367545 "IPADIC" 1367550 NIL IPADIC (NIL NIL NIL) -8 NIL NIL NIL) (-591 1365202 1365450 1365580 "IP4ADDR" 1365780 T IP4ADDR (NIL) -8 NIL NIL NIL) (-590 1364576 1364831 1364963 "IOMODE" 1365090 T IOMODE (NIL) -8 NIL NIL NIL) (-589 1363649 1364173 1364300 "IOBFILE" 1364469 T IOBFILE (NIL) -8 NIL NIL NIL) (-588 1363137 1363553 1363581 "IOBCON" 1363586 T IOBCON (NIL) -9 NIL 1363607 NIL) (-587 1362648 1362706 1362889 "INVLAPLA" 1363073 NIL INVLAPLA (NIL T T) -7 NIL NIL NIL) (-586 1352296 1354650 1357036 "INTTR" 1360312 NIL INTTR (NIL T T) -7 NIL NIL NIL) (-585 1348631 1349373 1350238 "INTTOOLS" 1351481 NIL INTTOOLS (NIL T T) -7 NIL NIL NIL) (-584 1348217 1348308 1348425 "INTSLPE" 1348534 T INTSLPE (NIL) -7 NIL NIL NIL) (-583 1346170 1348140 1348199 "INTRVL" 1348204 NIL INTRVL (NIL T) -8 NIL NIL NIL) (-582 1343772 1344284 1344859 "INTRF" 1345655 NIL INTRF (NIL T) -7 NIL NIL NIL) (-581 1343183 1343280 1343422 "INTRET" 1343670 NIL INTRET (NIL T) -7 NIL NIL NIL) (-580 1341180 1341569 1342039 "INTRAT" 1342791 NIL INTRAT (NIL T T) -7 NIL NIL NIL) (-579 1338443 1339026 1339645 "INTPM" 1340665 NIL INTPM (NIL T T) -7 NIL NIL NIL) (-578 1335188 1335787 1336525 "INTPAF" 1337829 NIL INTPAF (NIL T T T) -7 NIL NIL NIL) (-577 1330367 1331329 1332380 "INTPACK" 1334157 T INTPACK (NIL) -7 NIL NIL NIL) (-576 1327179 1330164 1330273 "INT" 1330278 T INT (NIL) -8 NIL NIL NIL) (-575 1326431 1326583 1326791 "INTHERTR" 1327021 NIL INTHERTR (NIL T T) -7 NIL NIL NIL) (-574 1325870 1325950 1326138 "INTHERAL" 1326345 NIL INTHERAL (NIL T T T T) -7 NIL NIL NIL) (-573 1323716 1324159 1324616 "INTHEORY" 1325433 T INTHEORY (NIL) -7 NIL NIL NIL) (-572 1315122 1316743 1318515 "INTG0" 1322068 NIL INTG0 (NIL T T T) -7 NIL NIL NIL) (-571 1295695 1300485 1305295 "INTFTBL" 1310332 T INTFTBL (NIL) -8 NIL NIL NIL) (-570 1294944 1295082 1295255 "INTFACT" 1295554 NIL INTFACT (NIL T) -7 NIL NIL NIL) (-569 1292371 1292817 1293374 "INTEF" 1294498 NIL INTEF (NIL T T) -7 NIL NIL NIL) (-568 1290724 1291463 1291491 "INTDOM" 1291792 T INTDOM (NIL) -9 NIL 1291999 NIL) (-567 1290093 1290267 1290509 "INTDOM-" 1290514 NIL INTDOM- (NIL T) -8 NIL NIL NIL) (-566 1286467 1288395 1288449 "INTCAT" 1289248 NIL INTCAT (NIL T) -9 NIL 1289569 NIL) (-565 1285939 1286042 1286170 "INTBIT" 1286359 T INTBIT (NIL) -7 NIL NIL NIL) (-564 1284638 1284792 1285099 "INTALG" 1285784 NIL INTALG (NIL T T T T T) -7 NIL NIL NIL) (-563 1284121 1284211 1284368 "INTAF" 1284542 NIL INTAF (NIL T T) -7 NIL NIL NIL) (-562 1277468 1283931 1284071 "INTABL" 1284076 NIL INTABL (NIL T T T) -8 NIL NIL NIL) (-561 1276801 1277267 1277332 "INT8" 1277366 T INT8 (NIL) -8 NIL NIL 1277411) (-560 1276133 1276599 1276664 "INT64" 1276698 T INT64 (NIL) -8 NIL NIL 1276743) (-559 1275465 1275931 1275996 "INT32" 1276030 T INT32 (NIL) -8 NIL NIL 1276075) (-558 1274797 1275263 1275328 "INT16" 1275362 T INT16 (NIL) -8 NIL NIL 1275407) (-557 1269506 1272358 1272386 "INS" 1273320 T INS (NIL) -9 NIL 1273985 NIL) (-556 1266746 1267517 1268491 "INS-" 1268564 NIL INS- (NIL T) -8 NIL NIL NIL) (-555 1265521 1265748 1266046 "INPSIGN" 1266499 NIL INPSIGN (NIL T T) -7 NIL NIL NIL) (-554 1264639 1264756 1264953 "INPRODPF" 1265401 NIL INPRODPF (NIL T T) -7 NIL NIL NIL) (-553 1263533 1263650 1263887 "INPRODFF" 1264519 NIL INPRODFF (NIL T T T T) -7 NIL NIL NIL) (-552 1262533 1262685 1262945 "INNMFACT" 1263369 NIL INNMFACT (NIL T T T T) -7 NIL NIL NIL) (-551 1261730 1261827 1262015 "INMODGCD" 1262432 NIL INMODGCD (NIL T T NIL NIL) -7 NIL NIL NIL) (-550 1260238 1260483 1260807 "INFSP" 1261475 NIL INFSP (NIL T T T) -7 NIL NIL NIL) (-549 1259422 1259539 1259722 "INFPROD0" 1260118 NIL INFPROD0 (NIL T T) -7 NIL NIL NIL) (-548 1256277 1257487 1258002 "INFORM" 1258915 T INFORM (NIL) -8 NIL NIL NIL) (-547 1255887 1255947 1256045 "INFORM1" 1256212 NIL INFORM1 (NIL T) -7 NIL NIL NIL) (-546 1255410 1255499 1255613 "INFINITY" 1255793 T INFINITY (NIL) -7 NIL NIL NIL) (-545 1254586 1255130 1255231 "INETCLTS" 1255329 T INETCLTS (NIL) -8 NIL NIL NIL) (-544 1253202 1253452 1253773 "INEP" 1254334 NIL INEP (NIL T T T) -7 NIL NIL NIL) (-543 1252407 1253099 1253164 "INDE" 1253169 NIL INDE (NIL T) -8 NIL NIL NIL) (-542 1251971 1252039 1252156 "INCRMAPS" 1252334 NIL INCRMAPS (NIL T) -7 NIL NIL NIL) (-541 1250789 1251240 1251446 "INBFILE" 1251785 T INBFILE (NIL) -8 NIL NIL NIL) (-540 1246088 1247025 1247969 "INBFF" 1249877 NIL INBFF (NIL T) -7 NIL NIL NIL) (-539 1244996 1245265 1245293 "INBCON" 1245806 T INBCON (NIL) -9 NIL 1246072 NIL) (-538 1244248 1244471 1244747 "INBCON-" 1244752 NIL INBCON- (NIL T) -8 NIL NIL NIL) (-537 1243727 1243972 1244063 "INAST" 1244177 T INAST (NIL) -8 NIL NIL NIL) (-536 1243154 1243406 1243512 "IMPTAST" 1243641 T IMPTAST (NIL) -8 NIL NIL NIL) (-535 1239554 1242998 1243102 "IMATRIX" 1243107 NIL IMATRIX (NIL T NIL NIL) -8 NIL NIL NIL) (-534 1238262 1238385 1238701 "IMATQF" 1239410 NIL IMATQF (NIL T T T T T T T T) -7 NIL NIL NIL) (-533 1236482 1236709 1237046 "IMATLIN" 1238018 NIL IMATLIN (NIL T T T T) -7 NIL NIL NIL) (-532 1231062 1236406 1236464 "ILIST" 1236469 NIL ILIST (NIL T NIL) -8 NIL NIL NIL) (-531 1228969 1230922 1231035 "IIARRAY2" 1231040 NIL IIARRAY2 (NIL T NIL NIL T T) -8 NIL NIL NIL) (-530 1224367 1228880 1228944 "IFF" 1228949 NIL IFF (NIL NIL NIL) -8 NIL NIL NIL) (-529 1223714 1223984 1224100 "IFAST" 1224271 T IFAST (NIL) -8 NIL NIL NIL) (-528 1218711 1223006 1223194 "IFARRAY" 1223571 NIL IFARRAY (NIL T NIL) -8 NIL NIL NIL) (-527 1217891 1218615 1218688 "IFAMON" 1218693 NIL IFAMON (NIL T T NIL) -8 NIL NIL NIL) (-526 1217475 1217540 1217594 "IEVALAB" 1217801 NIL IEVALAB (NIL T T) -9 NIL NIL NIL) (-525 1217150 1217218 1217378 "IEVALAB-" 1217383 NIL IEVALAB- (NIL T T T) -8 NIL NIL NIL) (-524 1216740 1217064 1217127 "IDPO" 1217132 NIL IDPO (NIL T T) -8 NIL NIL NIL) (-523 1215948 1216629 1216704 "IDPOAMS" 1216709 NIL IDPOAMS (NIL T T) -8 NIL NIL NIL) (-522 1215213 1215837 1215912 "IDPOAM" 1215917 NIL IDPOAM (NIL T T) -8 NIL NIL NIL) (-521 1214070 1214387 1214440 "IDPC" 1214958 NIL IDPC (NIL T T) -9 NIL 1215149 NIL) (-520 1213497 1213962 1214035 "IDPAM" 1214040 NIL IDPAM (NIL T T) -8 NIL NIL NIL) (-519 1212831 1213389 1213462 "IDPAG" 1213467 NIL IDPAG (NIL T T) -8 NIL NIL NIL) (-518 1212476 1212667 1212742 "IDENT" 1212776 T IDENT (NIL) -8 NIL NIL NIL) (-517 1208731 1209579 1210474 "IDECOMP" 1211633 NIL IDECOMP (NIL NIL NIL) -7 NIL NIL NIL) (-516 1201568 1202654 1203701 "IDEAL" 1207767 NIL IDEAL (NIL T T T T) -8 NIL NIL NIL) (-515 1200728 1200840 1201040 "ICDEN" 1201452 NIL ICDEN (NIL T T T T) -7 NIL NIL NIL) (-514 1199799 1200208 1200355 "ICARD" 1200601 T ICARD (NIL) -8 NIL NIL NIL) (-513 1197859 1198172 1198577 "IBPTOOLS" 1199476 NIL IBPTOOLS (NIL T T T T) -7 NIL NIL NIL) (-512 1193466 1197479 1197592 "IBITS" 1197778 NIL IBITS (NIL NIL) -8 NIL NIL NIL) (-511 1190189 1190765 1191460 "IBATOOL" 1192883 NIL IBATOOL (NIL T T T) -7 NIL NIL NIL) (-510 1187968 1188430 1188963 "IBACHIN" 1189724 NIL IBACHIN (NIL T T T) -7 NIL NIL NIL) (-509 1185799 1187814 1187917 "IARRAY2" 1187922 NIL IARRAY2 (NIL T NIL NIL) -8 NIL NIL NIL) (-508 1181907 1185725 1185782 "IARRAY1" 1185787 NIL IARRAY1 (NIL T NIL) -8 NIL NIL NIL) (-507 1175767 1180319 1180800 "IAN" 1181446 T IAN (NIL) -8 NIL NIL NIL) (-506 1175278 1175335 1175508 "IALGFACT" 1175704 NIL IALGFACT (NIL T T T T) -7 NIL NIL NIL) (-505 1174806 1174919 1174947 "HYPCAT" 1175154 T HYPCAT (NIL) -9 NIL NIL NIL) (-504 1174344 1174461 1174647 "HYPCAT-" 1174652 NIL HYPCAT- (NIL T) -8 NIL NIL NIL) (-503 1173939 1174139 1174222 "HOSTNAME" 1174281 T HOSTNAME (NIL) -8 NIL NIL NIL) (-502 1173784 1173821 1173862 "HOMOTOP" 1173867 NIL HOMOTOP (NIL T) -9 NIL 1173900 NIL) (-501 1170340 1171716 1171757 "HOAGG" 1172738 NIL HOAGG (NIL T) -9 NIL 1173467 NIL) (-500 1168934 1169333 1169859 "HOAGG-" 1169864 NIL HOAGG- (NIL T T) -8 NIL NIL NIL) (-499 1162650 1168527 1168677 "HEXADEC" 1168804 T HEXADEC (NIL) -8 NIL NIL NIL) (-498 1161398 1161620 1161883 "HEUGCD" 1162427 NIL HEUGCD (NIL T) -7 NIL NIL NIL) (-497 1160474 1161235 1161365 "HELLFDIV" 1161370 NIL HELLFDIV (NIL T T T T) -8 NIL NIL NIL) (-496 1158655 1160251 1160339 "HEAP" 1160418 NIL HEAP (NIL T) -8 NIL NIL NIL) (-495 1157918 1158207 1158341 "HEADAST" 1158541 T HEADAST (NIL) -8 NIL NIL NIL) (-494 1151760 1157833 1157895 "HDP" 1157900 NIL HDP (NIL NIL T) -8 NIL NIL NIL) (-493 1145472 1151395 1151547 "HDMP" 1151661 NIL HDMP (NIL NIL T) -8 NIL NIL NIL) (-492 1144796 1144936 1145100 "HB" 1145328 T HB (NIL) -7 NIL NIL NIL) (-491 1138186 1144642 1144746 "HASHTBL" 1144751 NIL HASHTBL (NIL T T NIL) -8 NIL NIL NIL) (-490 1137662 1137907 1137999 "HASAST" 1138114 T HASAST (NIL) -8 NIL NIL NIL) (-489 1135440 1137284 1137466 "HACKPI" 1137500 T HACKPI (NIL) -8 NIL NIL NIL) (-488 1131108 1135293 1135406 "GTSET" 1135411 NIL GTSET (NIL T T T T) -8 NIL NIL NIL) (-487 1124527 1130986 1131084 "GSTBL" 1131089 NIL GSTBL (NIL T T T NIL) -8 NIL NIL NIL) (-486 1116914 1123692 1123948 "GSERIES" 1124327 NIL GSERIES (NIL T NIL NIL) -8 NIL NIL NIL) (-485 1116041 1116458 1116486 "GROUP" 1116689 T GROUP (NIL) -9 NIL 1116823 NIL) (-484 1115407 1115566 1115817 "GROUP-" 1115822 NIL GROUP- (NIL T) -8 NIL NIL NIL) (-483 1113774 1114095 1114482 "GROEBSOL" 1115084 NIL GROEBSOL (NIL NIL T T) -7 NIL NIL NIL) (-482 1112674 1112962 1113013 "GRMOD" 1113542 NIL GRMOD (NIL T T) -9 NIL 1113710 NIL) (-481 1112442 1112478 1112606 "GRMOD-" 1112611 NIL GRMOD- (NIL T T T) -8 NIL NIL NIL) (-480 1107732 1108796 1109796 "GRIMAGE" 1111462 T GRIMAGE (NIL) -8 NIL NIL NIL) (-479 1106198 1106459 1106783 "GRDEF" 1107428 T GRDEF (NIL) -7 NIL NIL NIL) (-478 1105642 1105758 1105899 "GRAY" 1106077 T GRAY (NIL) -7 NIL NIL NIL) (-477 1104815 1105221 1105272 "GRALG" 1105425 NIL GRALG (NIL T T) -9 NIL 1105518 NIL) (-476 1104476 1104549 1104712 "GRALG-" 1104717 NIL GRALG- (NIL T T T) -8 NIL NIL NIL) (-475 1101253 1104061 1104239 "GPOLSET" 1104383 NIL GPOLSET (NIL T T T T) -8 NIL NIL NIL) (-474 1100607 1100664 1100922 "GOSPER" 1101190 NIL GOSPER (NIL T T T T T) -7 NIL NIL NIL) (-473 1096339 1097045 1097571 "GMODPOL" 1100306 NIL GMODPOL (NIL NIL T T T NIL T) -8 NIL NIL NIL) (-472 1095344 1095528 1095766 "GHENSEL" 1096151 NIL GHENSEL (NIL T T) -7 NIL NIL NIL) (-471 1089500 1090343 1091363 "GENUPS" 1094428 NIL GENUPS (NIL T T) -7 NIL NIL NIL) (-470 1089197 1089248 1089337 "GENUFACT" 1089443 NIL GENUFACT (NIL T) -7 NIL NIL NIL) (-469 1088609 1088686 1088851 "GENPGCD" 1089115 NIL GENPGCD (NIL T T T T) -7 NIL NIL NIL) (-468 1088083 1088118 1088331 "GENMFACT" 1088568 NIL GENMFACT (NIL T T T T T) -7 NIL NIL NIL) (-467 1086649 1086906 1087213 "GENEEZ" 1087826 NIL GENEEZ (NIL T T) -7 NIL NIL NIL) (-466 1080521 1086260 1086422 "GDMP" 1086572 NIL GDMP (NIL NIL T T) -8 NIL NIL NIL) (-465 1069864 1074292 1075398 "GCNAALG" 1079504 NIL GCNAALG (NIL T NIL NIL NIL) -8 NIL NIL NIL) (-464 1068177 1069039 1069067 "GCDDOM" 1069322 T GCDDOM (NIL) -9 NIL 1069479 NIL) (-463 1067647 1067774 1067989 "GCDDOM-" 1067994 NIL GCDDOM- (NIL T) -8 NIL NIL NIL) (-462 1066319 1066504 1066808 "GB" 1067426 NIL GB (NIL T T T T) -7 NIL NIL NIL) (-461 1054935 1057265 1059657 "GBINTERN" 1064010 NIL GBINTERN (NIL T T T T) -7 NIL NIL NIL) (-460 1052772 1053064 1053485 "GBF" 1054610 NIL GBF (NIL T T T T) -7 NIL NIL NIL) (-459 1051553 1051718 1051985 "GBEUCLID" 1052588 NIL GBEUCLID (NIL T T T T) -7 NIL NIL NIL) (-458 1050902 1051027 1051176 "GAUSSFAC" 1051424 T GAUSSFAC (NIL) -7 NIL NIL NIL) (-457 1049269 1049571 1049885 "GALUTIL" 1050621 NIL GALUTIL (NIL T) -7 NIL NIL NIL) (-456 1047577 1047851 1048175 "GALPOLYU" 1048996 NIL GALPOLYU (NIL T T) -7 NIL NIL NIL) (-455 1044942 1045232 1045639 "GALFACTU" 1047274 NIL GALFACTU (NIL T T T) -7 NIL NIL NIL) (-454 1036748 1038247 1039855 "GALFACT" 1043374 NIL GALFACT (NIL T) -7 NIL NIL NIL) (-453 1034136 1034794 1034822 "FVFUN" 1035978 T FVFUN (NIL) -9 NIL 1036698 NIL) (-452 1033402 1033584 1033612 "FVC" 1033903 T FVC (NIL) -9 NIL 1034086 NIL) (-451 1033045 1033227 1033295 "FUNDESC" 1033354 T FUNDESC (NIL) -8 NIL NIL NIL) (-450 1032660 1032842 1032923 "FUNCTION" 1032997 NIL FUNCTION (NIL NIL) -8 NIL NIL NIL) (-449 1030404 1030982 1031448 "FT" 1032214 T FT (NIL) -8 NIL NIL NIL) (-448 1029195 1029705 1029908 "FTEM" 1030221 T FTEM (NIL) -8 NIL NIL NIL) (-447 1027486 1027775 1028172 "FSUPFACT" 1028886 NIL FSUPFACT (NIL T T T) -7 NIL NIL NIL) (-446 1025883 1026172 1026504 "FST" 1027174 T FST (NIL) -8 NIL NIL NIL) (-445 1025082 1025188 1025376 "FSRED" 1025765 NIL FSRED (NIL T T) -7 NIL NIL NIL) (-444 1023781 1024037 1024384 "FSPRMELT" 1024797 NIL FSPRMELT (NIL T T) -7 NIL NIL NIL) (-443 1021087 1021525 1022011 "FSPECF" 1023344 NIL FSPECF (NIL T T) -7 NIL NIL NIL) (-442 1002152 1010861 1010902 "FS" 1014786 NIL FS (NIL T) -9 NIL 1017075 NIL) (-441 990795 993788 997845 "FS-" 998145 NIL FS- (NIL T T) -8 NIL NIL NIL) (-440 990323 990377 990547 "FSINT" 990736 NIL FSINT (NIL T T) -7 NIL NIL NIL) (-439 988615 989316 989619 "FSERIES" 990102 NIL FSERIES (NIL T T) -8 NIL NIL NIL) (-438 987657 987773 987997 "FSCINT" 988495 NIL FSCINT (NIL T T) -7 NIL NIL NIL) (-437 983865 986601 986642 "FSAGG" 987012 NIL FSAGG (NIL T) -9 NIL 987271 NIL) (-436 981627 982228 983024 "FSAGG-" 983119 NIL FSAGG- (NIL T T) -8 NIL NIL NIL) (-435 980669 980812 981039 "FSAGG2" 981480 NIL FSAGG2 (NIL T T T T) -7 NIL NIL NIL) (-434 978347 978627 979175 "FS2UPS" 980387 NIL FS2UPS (NIL T T T T T NIL) -7 NIL NIL NIL) (-433 977981 978024 978153 "FS2" 978298 NIL FS2 (NIL T T T T) -7 NIL NIL NIL) (-432 976859 977030 977332 "FS2EXPXP" 977806 NIL FS2EXPXP (NIL T T NIL NIL) -7 NIL NIL NIL) (-431 976285 976400 976552 "FRUTIL" 976739 NIL FRUTIL (NIL T) -7 NIL NIL NIL) (-430 967698 971780 973138 "FR" 974959 NIL FR (NIL T) -8 NIL NIL NIL) (-429 962712 965387 965427 "FRNAALG" 966747 NIL FRNAALG (NIL T) -9 NIL 967345 NIL) (-428 958385 959461 960736 "FRNAALG-" 961486 NIL FRNAALG- (NIL T T) -8 NIL NIL NIL) (-427 958023 958066 958193 "FRNAAF2" 958336 NIL FRNAAF2 (NIL T T T T) -7 NIL NIL NIL) (-426 956398 956872 957168 "FRMOD" 957835 NIL FRMOD (NIL T T T T NIL) -8 NIL NIL NIL) (-425 954141 954773 955091 "FRIDEAL" 956189 NIL FRIDEAL (NIL T T T T) -8 NIL NIL NIL) (-424 953332 953419 953710 "FRIDEAL2" 954048 NIL FRIDEAL2 (NIL T T T T T T T T) -7 NIL NIL NIL) (-423 952465 952879 952920 "FRETRCT" 952925 NIL FRETRCT (NIL T) -9 NIL 953101 NIL) (-422 951577 951808 952159 "FRETRCT-" 952164 NIL FRETRCT- (NIL T T) -8 NIL NIL NIL) (-421 948651 949861 949920 "FRAMALG" 950802 NIL FRAMALG (NIL T T) -9 NIL 951094 NIL) (-420 946785 947240 947870 "FRAMALG-" 948093 NIL FRAMALG- (NIL T T T) -8 NIL NIL NIL) (-419 940428 946258 946535 "FRAC" 946540 NIL FRAC (NIL T) -8 NIL NIL NIL) (-418 940064 940121 940228 "FRAC2" 940365 NIL FRAC2 (NIL T T) -7 NIL NIL NIL) (-417 939700 939757 939864 "FR2" 940001 NIL FR2 (NIL T T) -7 NIL NIL NIL) (-416 934199 937092 937120 "FPS" 938239 T FPS (NIL) -9 NIL 938796 NIL) (-415 933648 933757 933921 "FPS-" 934067 NIL FPS- (NIL T) -8 NIL NIL NIL) (-414 930936 932605 932633 "FPC" 932858 T FPC (NIL) -9 NIL 933000 NIL) (-413 930729 930769 930866 "FPC-" 930871 NIL FPC- (NIL T) -8 NIL NIL NIL) (-412 929519 930217 930258 "FPATMAB" 930263 NIL FPATMAB (NIL T) -9 NIL 930415 NIL) (-411 927758 928261 928608 "FPARFRAC" 929235 NIL FPARFRAC (NIL T T) -8 NIL NIL NIL) (-410 923152 923650 924332 "FORTRAN" 927190 NIL FORTRAN (NIL NIL NIL NIL NIL) -8 NIL NIL NIL) (-409 920868 921368 921907 "FORT" 922633 T FORT (NIL) -7 NIL NIL NIL) (-408 918544 919106 919134 "FORTFN" 920194 T FORTFN (NIL) -9 NIL 920818 NIL) (-407 918308 918358 918386 "FORTCAT" 918445 T FORTCAT (NIL) -9 NIL 918507 NIL) (-406 916414 916924 917314 "FORMULA" 917938 T FORMULA (NIL) -8 NIL NIL NIL) (-405 916202 916232 916301 "FORMULA1" 916378 NIL FORMULA1 (NIL T) -7 NIL NIL NIL) (-404 915725 915777 915950 "FORDER" 916144 NIL FORDER (NIL T T T T) -7 NIL NIL NIL) (-403 914821 914985 915178 "FOP" 915552 T FOP (NIL) -7 NIL NIL NIL) (-402 913402 914101 914275 "FNLA" 914703 NIL FNLA (NIL NIL NIL T) -8 NIL NIL NIL) (-401 912117 912532 912560 "FNCAT" 913020 T FNCAT (NIL) -9 NIL 913280 NIL) (-400 911656 912076 912104 "FNAME" 912109 T FNAME (NIL) -8 NIL NIL NIL) (-399 910205 911168 911196 "FMTC" 911201 T FMTC (NIL) -9 NIL 911237 NIL) (-398 908951 910141 910187 "FMONOID" 910192 NIL FMONOID (NIL T) -8 NIL NIL NIL) (-397 905765 906933 906974 "FMONCAT" 908191 NIL FMONCAT (NIL T) -9 NIL 908796 NIL) (-396 904915 905507 905656 "FM" 905661 NIL FM (NIL T T) -8 NIL NIL NIL) (-395 902339 902985 903013 "FMFUN" 904157 T FMFUN (NIL) -9 NIL 904865 NIL) (-394 901608 901789 901817 "FMC" 902107 T FMC (NIL) -9 NIL 902289 NIL) (-393 898673 899533 899587 "FMCAT" 900782 NIL FMCAT (NIL T T) -9 NIL 901277 NIL) (-392 897539 898439 898539 "FM1" 898618 NIL FM1 (NIL T T) -8 NIL NIL NIL) (-391 895313 895729 896223 "FLOATRP" 897090 NIL FLOATRP (NIL T) -7 NIL NIL NIL) (-390 888891 893042 893663 "FLOAT" 894712 T FLOAT (NIL) -8 NIL NIL NIL) (-389 886329 886829 887407 "FLOATCP" 888358 NIL FLOATCP (NIL T) -7 NIL NIL NIL) (-388 884977 885921 885962 "FLINEXP" 885967 NIL FLINEXP (NIL T) -9 NIL 886060 NIL) (-387 884131 884366 884694 "FLINEXP-" 884699 NIL FLINEXP- (NIL T T) -8 NIL NIL NIL) (-386 883207 883351 883575 "FLASORT" 883983 NIL FLASORT (NIL T T) -7 NIL NIL NIL) (-385 880309 881177 881229 "FLALG" 882456 NIL FLALG (NIL T T) -9 NIL 882923 NIL) (-384 873995 877745 877786 "FLAGG" 879048 NIL FLAGG (NIL T) -9 NIL 879700 NIL) (-383 872721 873060 873550 "FLAGG-" 873555 NIL FLAGG- (NIL T T) -8 NIL NIL NIL) (-382 871763 871906 872133 "FLAGG2" 872574 NIL FLAGG2 (NIL T T T T) -7 NIL NIL NIL) (-381 868600 869608 869667 "FINRALG" 870795 NIL FINRALG (NIL T T) -9 NIL 871303 NIL) (-380 867760 867989 868328 "FINRALG-" 868333 NIL FINRALG- (NIL T T T) -8 NIL NIL NIL) (-379 867126 867365 867393 "FINITE" 867589 T FINITE (NIL) -9 NIL 867696 NIL) (-378 859469 861656 861696 "FINAALG" 865363 NIL FINAALG (NIL T) -9 NIL 866816 NIL) (-377 854801 855851 856995 "FINAALG-" 858374 NIL FINAALG- (NIL T T) -8 NIL NIL NIL) (-376 854169 854556 854659 "FILE" 854731 NIL FILE (NIL T) -8 NIL NIL NIL) (-375 852813 853151 853205 "FILECAT" 853889 NIL FILECAT (NIL T T) -9 NIL 854105 NIL) (-374 850515 852043 852071 "FIELD" 852111 T FIELD (NIL) -9 NIL 852191 NIL) (-373 849135 849520 850031 "FIELD-" 850036 NIL FIELD- (NIL T) -8 NIL NIL NIL) (-372 846985 847770 848117 "FGROUP" 848821 NIL FGROUP (NIL T) -8 NIL NIL NIL) (-371 846075 846239 846459 "FGLMICPK" 846817 NIL FGLMICPK (NIL T NIL) -7 NIL NIL NIL) (-370 841907 846000 846057 "FFX" 846062 NIL FFX (NIL T NIL) -8 NIL NIL NIL) (-369 841508 841569 841704 "FFSLPE" 841840 NIL FFSLPE (NIL T T T) -7 NIL NIL NIL) (-368 837498 838280 839076 "FFPOLY" 840744 NIL FFPOLY (NIL T) -7 NIL NIL NIL) (-367 837002 837038 837247 "FFPOLY2" 837456 NIL FFPOLY2 (NIL T T) -7 NIL NIL NIL) (-366 832848 836921 836984 "FFP" 836989 NIL FFP (NIL T NIL) -8 NIL NIL NIL) (-365 828246 832759 832823 "FF" 832828 NIL FF (NIL NIL NIL) -8 NIL NIL NIL) (-364 823372 827589 827779 "FFNBX" 828100 NIL FFNBX (NIL T NIL) -8 NIL NIL NIL) (-363 818300 822507 822765 "FFNBP" 823226 NIL FFNBP (NIL T NIL) -8 NIL NIL NIL) (-362 812933 817584 817795 "FFNB" 818133 NIL FFNB (NIL NIL NIL) -8 NIL NIL NIL) (-361 811765 811963 812278 "FFINTBAS" 812730 NIL FFINTBAS (NIL T T T) -7 NIL NIL NIL) (-360 807791 810012 810040 "FFIELDC" 810660 T FFIELDC (NIL) -9 NIL 811036 NIL) (-359 806453 806824 807321 "FFIELDC-" 807326 NIL FFIELDC- (NIL T) -8 NIL NIL NIL) (-358 806022 806068 806192 "FFHOM" 806395 NIL FFHOM (NIL T T T) -7 NIL NIL NIL) (-357 803717 804204 804721 "FFF" 805537 NIL FFF (NIL T) -7 NIL NIL NIL) (-356 799335 803459 803560 "FFCGX" 803660 NIL FFCGX (NIL T NIL) -8 NIL NIL NIL) (-355 794957 799067 799174 "FFCGP" 799278 NIL FFCGP (NIL T NIL) -8 NIL NIL NIL) (-354 790140 794684 794792 "FFCG" 794893 NIL FFCG (NIL NIL NIL) -8 NIL NIL NIL) (-353 769669 779872 779958 "FFCAT" 785123 NIL FFCAT (NIL T T T) -9 NIL 786574 NIL) (-352 764866 765914 767228 "FFCAT-" 768458 NIL FFCAT- (NIL T T T T) -8 NIL NIL NIL) (-351 764277 764320 764555 "FFCAT2" 764817 NIL FFCAT2 (NIL T T T T T T T T) -7 NIL NIL NIL) (-350 753600 757249 758469 "FEXPR" 763129 NIL FEXPR (NIL NIL NIL T) -8 NIL NIL NIL) (-349 752562 752997 753038 "FEVALAB" 753122 NIL FEVALAB (NIL T) -9 NIL 753383 NIL) (-348 751721 751931 752269 "FEVALAB-" 752274 NIL FEVALAB- (NIL T T) -8 NIL NIL NIL) (-347 750287 751104 751307 "FDIV" 751620 NIL FDIV (NIL T T T T) -8 NIL NIL NIL) (-346 747293 748034 748149 "FDIVCAT" 749717 NIL FDIVCAT (NIL T T T T) -9 NIL 750154 NIL) (-345 747055 747082 747252 "FDIVCAT-" 747257 NIL FDIVCAT- (NIL T T T T T) -8 NIL NIL NIL) (-344 746275 746362 746639 "FDIV2" 746962 NIL FDIV2 (NIL T T T T T T T T) -7 NIL NIL NIL) (-343 745249 745570 745772 "FCTRDATA" 746093 T FCTRDATA (NIL) -8 NIL NIL NIL) (-342 743935 744194 744483 "FCPAK1" 744980 T FCPAK1 (NIL) -7 NIL NIL NIL) (-341 743034 743435 743576 "FCOMP" 743826 NIL FCOMP (NIL T) -8 NIL NIL NIL) (-340 726739 730184 733722 "FC" 739516 T FC (NIL) -8 NIL NIL NIL) (-339 719032 723060 723100 "FAXF" 724902 NIL FAXF (NIL T) -9 NIL 725594 NIL) (-338 716309 716966 717791 "FAXF-" 718256 NIL FAXF- (NIL T T) -8 NIL NIL NIL) (-337 711363 715685 715861 "FARRAY" 716166 NIL FARRAY (NIL T) -8 NIL NIL NIL) (-336 706243 708310 708363 "FAMR" 709386 NIL FAMR (NIL T T) -9 NIL 709846 NIL) (-335 705133 705435 705870 "FAMR-" 705875 NIL FAMR- (NIL T T T) -8 NIL NIL NIL) (-334 704302 705055 705108 "FAMONOID" 705113 NIL FAMONOID (NIL T) -8 NIL NIL NIL) (-333 702074 702784 702837 "FAMONC" 703778 NIL FAMONC (NIL T T) -9 NIL 704164 NIL) (-332 700738 701828 701965 "FAGROUP" 701970 NIL FAGROUP (NIL T) -8 NIL NIL NIL) (-331 698533 698852 699255 "FACUTIL" 700419 NIL FACUTIL (NIL T T T T) -7 NIL NIL NIL) (-330 697632 697817 698039 "FACTFUNC" 698343 NIL FACTFUNC (NIL T) -7 NIL NIL NIL) (-329 690054 696935 697134 "EXPUPXS" 697488 NIL EXPUPXS (NIL T NIL NIL) -8 NIL NIL NIL) (-328 687537 688077 688663 "EXPRTUBE" 689488 T EXPRTUBE (NIL) -7 NIL NIL NIL) (-327 683808 684400 685130 "EXPRODE" 686876 NIL EXPRODE (NIL T T) -7 NIL NIL NIL) (-326 669292 682457 682886 "EXPR" 683412 NIL EXPR (NIL T) -8 NIL NIL NIL) (-325 663846 664433 665239 "EXPR2UPS" 668590 NIL EXPR2UPS (NIL T T) -7 NIL NIL NIL) (-324 663478 663535 663644 "EXPR2" 663783 NIL EXPR2 (NIL T T) -7 NIL NIL NIL) (-323 654475 662629 662920 "EXPEXPAN" 663314 NIL EXPEXPAN (NIL T T NIL NIL) -8 NIL NIL NIL) (-322 654275 654432 654461 "EXIT" 654466 T EXIT (NIL) -8 NIL NIL NIL) (-321 653755 653999 654090 "EXITAST" 654204 T EXITAST (NIL) -8 NIL NIL NIL) (-320 653382 653444 653557 "EVALCYC" 653687 NIL EVALCYC (NIL T) -7 NIL NIL NIL) (-319 652923 653041 653082 "EVALAB" 653252 NIL EVALAB (NIL T) -9 NIL 653356 NIL) (-318 652404 652526 652747 "EVALAB-" 652752 NIL EVALAB- (NIL T T) -8 NIL NIL NIL) (-317 649758 651060 651088 "EUCDOM" 651643 T EUCDOM (NIL) -9 NIL 651993 NIL) (-316 648163 648605 649195 "EUCDOM-" 649200 NIL EUCDOM- (NIL T) -8 NIL NIL NIL) (-315 635702 638461 641211 "ESTOOLS" 645433 T ESTOOLS (NIL) -7 NIL NIL NIL) (-314 635334 635391 635500 "ESTOOLS2" 635639 NIL ESTOOLS2 (NIL T T) -7 NIL NIL NIL) (-313 635085 635127 635207 "ESTOOLS1" 635286 NIL ESTOOLS1 (NIL T) -7 NIL NIL NIL) (-312 629108 630716 630744 "ES" 633512 T ES (NIL) -9 NIL 634922 NIL) (-311 624055 625342 627159 "ES-" 627323 NIL ES- (NIL T) -8 NIL NIL NIL) (-310 620429 621190 621970 "ESCONT" 623295 T ESCONT (NIL) -7 NIL NIL NIL) (-309 620174 620206 620288 "ESCONT1" 620391 NIL ESCONT1 (NIL NIL NIL) -7 NIL NIL NIL) (-308 619849 619899 619999 "ES2" 620118 NIL ES2 (NIL T T) -7 NIL NIL NIL) (-307 619479 619537 619646 "ES1" 619785 NIL ES1 (NIL T T) -7 NIL NIL NIL) (-306 618695 618824 619000 "ERROR" 619323 T ERROR (NIL) -7 NIL NIL NIL) (-305 612091 618554 618645 "EQTBL" 618650 NIL EQTBL (NIL T T) -8 NIL NIL NIL) (-304 604594 607405 608854 "EQ" 610675 NIL -2032 (NIL T) -8 NIL NIL NIL) (-303 604226 604283 604392 "EQ2" 604531 NIL EQ2 (NIL T T) -7 NIL NIL NIL) (-302 599517 600564 601657 "EP" 603165 NIL EP (NIL T) -7 NIL NIL NIL) (-301 598117 598408 598714 "ENV" 599231 T ENV (NIL) -8 NIL NIL NIL) (-300 597197 597751 597779 "ENTIRER" 597784 T ENTIRER (NIL) -9 NIL 597830 NIL) (-299 593891 595379 595740 "EMR" 597005 NIL EMR (NIL T T T NIL NIL NIL) -8 NIL NIL NIL) (-298 593021 593206 593260 "ELTAGG" 593640 NIL ELTAGG (NIL T T) -9 NIL 593851 NIL) (-297 592740 592802 592943 "ELTAGG-" 592948 NIL ELTAGG- (NIL T T T) -8 NIL NIL NIL) (-296 592504 592533 592587 "ELTAB" 592671 NIL ELTAB (NIL T T) -9 NIL 592723 NIL) (-295 591630 591776 591975 "ELFUTS" 592355 NIL ELFUTS (NIL T T) -7 NIL NIL NIL) (-294 591372 591428 591456 "ELEMFUN" 591561 T ELEMFUN (NIL) -9 NIL NIL NIL) (-293 591242 591263 591331 "ELEMFUN-" 591336 NIL ELEMFUN- (NIL T) -8 NIL NIL NIL) (-292 586030 589284 589325 "ELAGG" 590265 NIL ELAGG (NIL T) -9 NIL 590728 NIL) (-291 584315 584749 585412 "ELAGG-" 585417 NIL ELAGG- (NIL T T) -8 NIL NIL NIL) (-290 583627 583764 583920 "ELABOR" 584179 T ELABOR (NIL) -8 NIL NIL NIL) (-289 582288 582567 582861 "ELABEXPR" 583353 T ELABEXPR (NIL) -8 NIL NIL NIL) (-288 575122 576925 577754 "EFUPXS" 581563 NIL EFUPXS (NIL T T T T) -8 NIL NIL NIL) (-287 568570 570371 571182 "EFULS" 574397 NIL EFULS (NIL T T T) -8 NIL NIL NIL) (-286 566055 566413 566885 "EFSTRUC" 568202 NIL EFSTRUC (NIL T T) -7 NIL NIL NIL) (-285 555846 557412 558960 "EF" 564570 NIL EF (NIL T T) -7 NIL NIL NIL) (-284 554920 555331 555480 "EAB" 555717 T EAB (NIL) -8 NIL NIL NIL) (-283 554102 554879 554907 "E04UCFA" 554912 T E04UCFA (NIL) -8 NIL NIL NIL) (-282 553284 554061 554089 "E04NAFA" 554094 T E04NAFA (NIL) -8 NIL NIL NIL) (-281 552466 553243 553271 "E04MBFA" 553276 T E04MBFA (NIL) -8 NIL NIL NIL) (-280 551648 552425 552453 "E04JAFA" 552458 T E04JAFA (NIL) -8 NIL NIL NIL) (-279 550832 551607 551635 "E04GCFA" 551640 T E04GCFA (NIL) -8 NIL NIL NIL) (-278 550016 550791 550819 "E04FDFA" 550824 T E04FDFA (NIL) -8 NIL NIL NIL) (-277 549198 549975 550003 "E04DGFA" 550008 T E04DGFA (NIL) -8 NIL NIL NIL) (-276 543371 544723 546087 "E04AGNT" 547854 T E04AGNT (NIL) -7 NIL NIL NIL) (-275 542142 542685 542725 "DVARCAT" 543066 NIL DVARCAT (NIL T) -9 NIL 543229 NIL) (-274 541346 541558 541872 "DVARCAT-" 541877 NIL DVARCAT- (NIL T T) -8 NIL NIL NIL) (-273 534207 541145 541274 "DSMP" 541279 NIL DSMP (NIL T T T) -8 NIL NIL NIL) (-272 532630 533349 533390 "DSEXT" 533753 NIL DSEXT (NIL T) -9 NIL 534047 NIL) (-271 530915 531343 532009 "DSEXT-" 532014 NIL DSEXT- (NIL T T) -8 NIL NIL NIL) (-270 525696 526860 527928 "DROPT" 529867 T DROPT (NIL) -8 NIL NIL NIL) (-269 525361 525420 525518 "DROPT1" 525631 NIL DROPT1 (NIL T) -7 NIL NIL NIL) (-268 520476 521602 522739 "DROPT0" 524244 T DROPT0 (NIL) -7 NIL NIL NIL) (-267 518821 519146 519532 "DRAWPT" 520110 T DRAWPT (NIL) -7 NIL NIL NIL) (-266 513408 514331 515410 "DRAW" 517795 NIL DRAW (NIL T) -7 NIL NIL NIL) (-265 513041 513094 513212 "DRAWHACK" 513349 NIL DRAWHACK (NIL T) -7 NIL NIL NIL) (-264 511772 512041 512332 "DRAWCX" 512770 T DRAWCX (NIL) -7 NIL NIL NIL) (-263 511287 511356 511507 "DRAWCURV" 511698 NIL DRAWCURV (NIL T T) -7 NIL NIL NIL) (-262 501755 503717 505832 "DRAWCFUN" 509192 T DRAWCFUN (NIL) -7 NIL NIL NIL) (-261 498493 500420 500461 "DQAGG" 501090 NIL DQAGG (NIL T) -9 NIL 501364 NIL) (-260 485958 492704 492787 "DPOLCAT" 494639 NIL DPOLCAT (NIL T T T T) -9 NIL 495184 NIL) (-259 480795 482143 484101 "DPOLCAT-" 484106 NIL DPOLCAT- (NIL T T T T T) -8 NIL NIL NIL) (-258 474142 480656 480754 "DPMO" 480759 NIL DPMO (NIL NIL T T) -8 NIL NIL NIL) (-257 467392 473922 474089 "DPMM" 474094 NIL DPMM (NIL NIL T T T) -8 NIL NIL NIL) (-256 466962 467176 467265 "DOMTMPLT" 467323 T DOMTMPLT (NIL) -8 NIL NIL NIL) (-255 466395 466764 466844 "DOMCTOR" 466902 T DOMCTOR (NIL) -8 NIL NIL NIL) (-254 465607 465875 466026 "DOMAIN" 466264 T DOMAIN (NIL) -8 NIL NIL NIL) (-253 459319 465242 465394 "DMP" 465508 NIL DMP (NIL NIL T) -8 NIL NIL NIL) (-252 457264 458386 458427 "DMEXT" 458432 NIL DMEXT (NIL T) -9 NIL 458608 NIL) (-251 456864 456920 457064 "DLP" 457202 NIL DLP (NIL T) -7 NIL NIL NIL) (-250 450688 456191 456381 "DLIST" 456706 NIL DLIST (NIL T) -8 NIL NIL NIL) (-249 447459 449513 449554 "DLAGG" 450104 NIL DLAGG (NIL T) -9 NIL 450334 NIL) (-248 446121 446785 446813 "DIVRING" 446905 T DIVRING (NIL) -9 NIL 446988 NIL) (-247 445358 445548 445848 "DIVRING-" 445853 NIL DIVRING- (NIL T) -8 NIL NIL NIL) (-246 443460 443817 444223 "DISPLAY" 444972 T DISPLAY (NIL) -7 NIL NIL NIL) (-245 437322 443374 443437 "DIRPROD" 443442 NIL DIRPROD (NIL NIL T) -8 NIL NIL NIL) (-244 436170 436373 436638 "DIRPROD2" 437115 NIL DIRPROD2 (NIL NIL T T) -7 NIL NIL NIL) (-243 424899 430936 430989 "DIRPCAT" 431247 NIL DIRPCAT (NIL NIL T) -9 NIL 432122 NIL) (-242 422225 422867 423748 "DIRPCAT-" 424085 NIL DIRPCAT- (NIL T NIL T) -8 NIL NIL NIL) (-241 421512 421672 421858 "DIOSP" 422059 T DIOSP (NIL) -7 NIL NIL NIL) (-240 418141 420396 420437 "DIOPS" 420871 NIL DIOPS (NIL T) -9 NIL 421100 NIL) (-239 417690 417804 417995 "DIOPS-" 418000 NIL DIOPS- (NIL T T) -8 NIL NIL NIL) (-238 416741 417369 417397 "DIFRING" 417402 T DIFRING (NIL) -9 NIL 417424 NIL) (-237 416413 416487 416515 "DIFFSPC" 416634 T DIFFSPC (NIL) -9 NIL 416709 NIL) (-236 416058 416136 416288 "DIFFSPC-" 416293 NIL DIFFSPC- (NIL T) -8 NIL NIL NIL) (-235 415114 415592 415633 "DIFFMOD" 415638 NIL DIFFMOD (NIL T) -9 NIL 415736 NIL) (-234 414822 414867 414908 "DIFFDOM" 415029 NIL DIFFDOM (NIL T) -9 NIL 415097 NIL) (-233 414675 414699 414783 "DIFFDOM-" 414788 NIL DIFFDOM- (NIL T T) -8 NIL NIL NIL) (-232 412607 413879 413920 "DIFEXT" 413925 NIL DIFEXT (NIL T) -9 NIL 414078 NIL) (-231 409856 412111 412152 "DIAGG" 412157 NIL DIAGG (NIL T) -9 NIL 412177 NIL) (-230 409240 409397 409649 "DIAGG-" 409654 NIL DIAGG- (NIL T T) -8 NIL NIL NIL) (-229 404611 408199 408476 "DHMATRIX" 409009 NIL DHMATRIX (NIL T) -8 NIL NIL NIL) (-228 400223 401132 402142 "DFSFUN" 403621 T DFSFUN (NIL) -7 NIL NIL NIL) (-227 395301 399154 399466 "DFLOAT" 399931 T DFLOAT (NIL) -8 NIL NIL NIL) (-226 393564 393845 394234 "DFINTTLS" 395009 NIL DFINTTLS (NIL T T) -7 NIL NIL NIL) (-225 390593 391585 391985 "DERHAM" 393230 NIL DERHAM (NIL T NIL) -8 NIL NIL NIL) (-224 388396 390368 390457 "DEQUEUE" 390537 NIL DEQUEUE (NIL T) -8 NIL NIL NIL) (-223 387650 387783 387966 "DEGRED" 388258 NIL DEGRED (NIL T T) -7 NIL NIL NIL) (-222 384080 384825 385671 "DEFINTRF" 386878 NIL DEFINTRF (NIL T) -7 NIL NIL NIL) (-221 381635 382104 382696 "DEFINTEF" 383599 NIL DEFINTEF (NIL T T) -7 NIL NIL NIL) (-220 380985 381255 381370 "DEFAST" 381540 T DEFAST (NIL) -8 NIL NIL NIL) (-219 374701 380578 380728 "DECIMAL" 380855 T DECIMAL (NIL) -8 NIL NIL NIL) (-218 372213 372671 373177 "DDFACT" 374245 NIL DDFACT (NIL T T) -7 NIL NIL NIL) (-217 371809 371852 372003 "DBLRESP" 372164 NIL DBLRESP (NIL T T T T) -7 NIL NIL NIL) (-216 369677 370039 370400 "DBASE" 371575 NIL DBASE (NIL T) -8 NIL NIL NIL) (-215 368919 369157 369303 "DATAARY" 369576 NIL DATAARY (NIL NIL T) -8 NIL NIL NIL) (-214 368025 368878 368906 "D03FAFA" 368911 T D03FAFA (NIL) -8 NIL NIL NIL) (-213 367132 367984 368012 "D03EEFA" 368017 T D03EEFA (NIL) -8 NIL NIL NIL) (-212 365082 365548 366037 "D03AGNT" 366663 T D03AGNT (NIL) -7 NIL NIL NIL) (-211 364371 365041 365069 "D02EJFA" 365074 T D02EJFA (NIL) -8 NIL NIL NIL) (-210 363660 364330 364358 "D02CJFA" 364363 T D02CJFA (NIL) -8 NIL NIL NIL) (-209 362949 363619 363647 "D02BHFA" 363652 T D02BHFA (NIL) -8 NIL NIL NIL) (-208 362238 362908 362936 "D02BBFA" 362941 T D02BBFA (NIL) -8 NIL NIL NIL) (-207 355435 357024 358630 "D02AGNT" 360652 T D02AGNT (NIL) -7 NIL NIL NIL) (-206 353203 353726 354272 "D01WGTS" 354909 T D01WGTS (NIL) -7 NIL NIL NIL) (-205 352270 353162 353190 "D01TRNS" 353195 T D01TRNS (NIL) -8 NIL NIL NIL) (-204 351338 352229 352257 "D01GBFA" 352262 T D01GBFA (NIL) -8 NIL NIL NIL) (-203 350406 351297 351325 "D01FCFA" 351330 T D01FCFA (NIL) -8 NIL NIL NIL) (-202 349474 350365 350393 "D01ASFA" 350398 T D01ASFA (NIL) -8 NIL NIL NIL) (-201 348542 349433 349461 "D01AQFA" 349466 T D01AQFA (NIL) -8 NIL NIL NIL) (-200 347610 348501 348529 "D01APFA" 348534 T D01APFA (NIL) -8 NIL NIL NIL) (-199 346678 347569 347597 "D01ANFA" 347602 T D01ANFA (NIL) -8 NIL NIL NIL) (-198 345746 346637 346665 "D01AMFA" 346670 T D01AMFA (NIL) -8 NIL NIL NIL) (-197 344814 345705 345733 "D01ALFA" 345738 T D01ALFA (NIL) -8 NIL NIL NIL) (-196 343882 344773 344801 "D01AKFA" 344806 T D01AKFA (NIL) -8 NIL NIL NIL) (-195 342950 343841 343869 "D01AJFA" 343874 T D01AJFA (NIL) -8 NIL NIL NIL) (-194 336245 337798 339359 "D01AGNT" 341409 T D01AGNT (NIL) -7 NIL NIL NIL) (-193 335582 335710 335862 "CYCLOTOM" 336113 T CYCLOTOM (NIL) -7 NIL NIL NIL) (-192 332315 333030 333757 "CYCLES" 334875 T CYCLES (NIL) -7 NIL NIL NIL) (-191 331627 331761 331932 "CVMP" 332176 NIL CVMP (NIL T) -7 NIL NIL NIL) (-190 329468 329726 330095 "CTRIGMNP" 331355 NIL CTRIGMNP (NIL T T) -7 NIL NIL NIL) (-189 328904 329262 329335 "CTOR" 329415 T CTOR (NIL) -8 NIL NIL NIL) (-188 328413 328635 328736 "CTORKIND" 328823 T CTORKIND (NIL) -8 NIL NIL NIL) (-187 327690 328006 328034 "CTORCAT" 328216 T CTORCAT (NIL) -9 NIL 328329 NIL) (-186 327288 327399 327558 "CTORCAT-" 327563 NIL CTORCAT- (NIL T) -8 NIL NIL NIL) (-185 326750 326962 327070 "CTORCALL" 327212 NIL CTORCALL (NIL T) -8 NIL NIL NIL) (-184 326124 326223 326376 "CSTTOOLS" 326647 NIL CSTTOOLS (NIL T T) -7 NIL NIL NIL) (-183 321923 322580 323338 "CRFP" 325436 NIL CRFP (NIL T T) -7 NIL NIL NIL) (-182 321398 321644 321736 "CRCEAST" 321851 T CRCEAST (NIL) -8 NIL NIL NIL) (-181 320445 320630 320858 "CRAPACK" 321202 NIL CRAPACK (NIL T) -7 NIL NIL NIL) (-180 319829 319930 320134 "CPMATCH" 320321 NIL CPMATCH (NIL T T T) -7 NIL NIL NIL) (-179 319554 319582 319688 "CPIMA" 319795 NIL CPIMA (NIL T T T) -7 NIL NIL NIL) (-178 315902 316574 317293 "COORDSYS" 318889 NIL COORDSYS (NIL T) -7 NIL NIL NIL) (-177 315314 315435 315577 "CONTOUR" 315780 T CONTOUR (NIL) -8 NIL NIL NIL) (-176 311205 313317 313809 "CONTFRAC" 314854 NIL CONTFRAC (NIL T) -8 NIL NIL NIL) (-175 311085 311106 311134 "CONDUIT" 311171 T CONDUIT (NIL) -9 NIL NIL NIL) (-174 310159 310713 310741 "COMRING" 310746 T COMRING (NIL) -9 NIL 310798 NIL) (-173 309213 309517 309701 "COMPPROP" 309995 T COMPPROP (NIL) -8 NIL NIL NIL) (-172 308874 308909 309037 "COMPLPAT" 309172 NIL COMPLPAT (NIL T T T) -7 NIL NIL NIL) (-171 298177 308683 308792 "COMPLEX" 308797 NIL COMPLEX (NIL T) -8 NIL NIL NIL) (-170 297813 297870 297977 "COMPLEX2" 298114 NIL COMPLEX2 (NIL T T) -7 NIL NIL NIL) (-169 297152 297273 297433 "COMPILER" 297673 T COMPILER (NIL) -8 NIL NIL NIL) (-168 296870 296905 297003 "COMPFACT" 297111 NIL COMPFACT (NIL T T) -7 NIL NIL NIL) (-167 279149 290574 290614 "COMPCAT" 291618 NIL COMPCAT (NIL T) -9 NIL 292966 NIL) (-166 268661 271588 275215 "COMPCAT-" 275571 NIL COMPCAT- (NIL T T) -8 NIL NIL NIL) (-165 268390 268418 268521 "COMMUPC" 268627 NIL COMMUPC (NIL T T T) -7 NIL NIL NIL) (-164 268184 268218 268277 "COMMONOP" 268351 T COMMONOP (NIL) -7 NIL NIL NIL) (-163 267740 267935 268022 "COMM" 268117 T COMM (NIL) -8 NIL NIL NIL) (-162 267316 267544 267619 "COMMAAST" 267685 T COMMAAST (NIL) -8 NIL NIL NIL) (-161 266565 266759 266787 "COMBOPC" 267125 T COMBOPC (NIL) -9 NIL 267300 NIL) (-160 265461 265671 265913 "COMBINAT" 266355 NIL COMBINAT (NIL T) -7 NIL NIL NIL) (-159 261918 262492 263119 "COMBF" 264883 NIL COMBF (NIL T T) -7 NIL NIL NIL) (-158 260676 261034 261269 "COLOR" 261703 T COLOR (NIL) -8 NIL NIL NIL) (-157 260152 260397 260489 "COLONAST" 260604 T COLONAST (NIL) -8 NIL NIL NIL) (-156 259792 259839 259964 "CMPLXRT" 260099 NIL CMPLXRT (NIL T T) -7 NIL NIL NIL) (-155 259240 259492 259591 "CLLCTAST" 259713 T CLLCTAST (NIL) -8 NIL NIL NIL) (-154 254742 255770 256850 "CLIP" 258180 T CLIP (NIL) -7 NIL NIL NIL) (-153 253083 253843 254083 "CLIF" 254569 NIL CLIF (NIL NIL T NIL) -8 NIL NIL NIL) (-152 249232 251201 251242 "CLAGG" 252171 NIL CLAGG (NIL T) -9 NIL 252707 NIL) (-151 247654 248111 248694 "CLAGG-" 248699 NIL CLAGG- (NIL T T) -8 NIL NIL NIL) (-150 247198 247283 247423 "CINTSLPE" 247563 NIL CINTSLPE (NIL T T) -7 NIL NIL NIL) (-149 244699 245170 245718 "CHVAR" 246726 NIL CHVAR (NIL T T T) -7 NIL NIL NIL) (-148 243859 244413 244441 "CHARZ" 244446 T CHARZ (NIL) -9 NIL 244461 NIL) (-147 243613 243653 243731 "CHARPOL" 243813 NIL CHARPOL (NIL T) -7 NIL NIL NIL) (-146 242657 243244 243272 "CHARNZ" 243319 T CHARNZ (NIL) -9 NIL 243375 NIL) (-145 240563 241311 241664 "CHAR" 242324 T CHAR (NIL) -8 NIL NIL NIL) (-144 240289 240350 240378 "CFCAT" 240489 T CFCAT (NIL) -9 NIL NIL NIL) (-143 239530 239641 239824 "CDEN" 240173 NIL CDEN (NIL T T T) -7 NIL NIL NIL) (-142 235495 238683 238963 "CCLASS" 239270 T CCLASS (NIL) -8 NIL NIL NIL) (-141 234746 234903 235080 "CATEGORY" 235338 T -10 (NIL) -8 NIL NIL NIL) (-140 234319 234665 234713 "CATCTOR" 234718 T CATCTOR (NIL) -8 NIL NIL NIL) (-139 233770 234022 234120 "CATAST" 234241 T CATAST (NIL) -8 NIL NIL NIL) (-138 233246 233491 233583 "CASEAST" 233698 T CASEAST (NIL) -8 NIL NIL NIL) (-137 228384 229403 230147 "CARTEN" 232558 NIL CARTEN (NIL NIL NIL T) -8 NIL NIL NIL) (-136 227492 227640 227861 "CARTEN2" 228231 NIL CARTEN2 (NIL NIL NIL T T) -7 NIL NIL NIL) (-135 225808 226642 226899 "CARD" 227255 T CARD (NIL) -8 NIL NIL NIL) (-134 225384 225612 225687 "CAPSLAST" 225753 T CAPSLAST (NIL) -8 NIL NIL NIL) (-133 224874 225082 225110 "CACHSET" 225242 T CACHSET (NIL) -9 NIL 225320 NIL) (-132 224330 224652 224680 "CABMON" 224730 T CABMON (NIL) -9 NIL 224786 NIL) (-131 223803 224034 224144 "BYTEORD" 224240 T BYTEORD (NIL) -8 NIL NIL NIL) (-130 222780 223332 223474 "BYTE" 223637 T BYTE (NIL) -8 NIL NIL 223759) (-129 218132 222285 222457 "BYTEBUF" 222628 T BYTEBUF (NIL) -8 NIL NIL NIL) (-128 215643 217824 217931 "BTREE" 218058 NIL BTREE (NIL T) -8 NIL NIL NIL) (-127 213094 215291 215413 "BTOURN" 215553 NIL BTOURN (NIL T) -8 NIL NIL NIL) (-126 210438 212536 212577 "BTCAT" 212645 NIL BTCAT (NIL T) -9 NIL 212722 NIL) (-125 210105 210185 210334 "BTCAT-" 210339 NIL BTCAT- (NIL T T) -8 NIL NIL NIL) (-124 205484 209364 209392 "BTAGG" 209506 T BTAGG (NIL) -9 NIL 209616 NIL) (-123 204974 205099 205305 "BTAGG-" 205310 NIL BTAGG- (NIL T) -8 NIL NIL NIL) (-122 201971 204252 204467 "BSTREE" 204791 NIL BSTREE (NIL T) -8 NIL NIL NIL) (-121 201109 201235 201419 "BRILL" 201827 NIL BRILL (NIL T) -7 NIL NIL NIL) (-120 197735 199807 199848 "BRAGG" 200497 NIL BRAGG (NIL T) -9 NIL 200755 NIL) (-119 196264 196670 197225 "BRAGG-" 197230 NIL BRAGG- (NIL T T) -8 NIL NIL NIL) (-118 189180 195608 195793 "BPADICRT" 196111 NIL BPADICRT (NIL NIL) -8 NIL NIL NIL) (-117 187495 189117 189162 "BPADIC" 189167 NIL BPADIC (NIL NIL) -8 NIL NIL NIL) (-116 187193 187223 187337 "BOUNDZRO" 187459 NIL BOUNDZRO (NIL T T) -7 NIL NIL NIL) (-115 182421 183619 184531 "BOP" 186301 T BOP (NIL) -8 NIL NIL NIL) (-114 180202 180606 181081 "BOP1" 181979 NIL BOP1 (NIL T) -7 NIL NIL NIL) (-113 179903 179964 179992 "BOOLE" 180103 T BOOLE (NIL) -9 NIL 180185 NIL) (-112 178728 179477 179626 "BOOLEAN" 179774 T BOOLEAN (NIL) -8 NIL NIL NIL) (-111 177993 178397 178451 "BMODULE" 178456 NIL BMODULE (NIL T T) -9 NIL 178521 NIL) (-110 173794 177791 177864 "BITS" 177940 T BITS (NIL) -8 NIL NIL NIL) (-109 173215 173334 173474 "BINDING" 173674 T BINDING (NIL) -8 NIL NIL NIL) (-108 166934 172810 172959 "BINARY" 173086 T BINARY (NIL) -8 NIL NIL NIL) (-107 164688 166161 166202 "BGAGG" 166462 NIL BGAGG (NIL T) -9 NIL 166599 NIL) (-106 164519 164551 164642 "BGAGG-" 164647 NIL BGAGG- (NIL T T) -8 NIL NIL NIL) (-105 163590 163903 164108 "BFUNCT" 164334 T BFUNCT (NIL) -8 NIL NIL NIL) (-104 162280 162458 162746 "BEZOUT" 163414 NIL BEZOUT (NIL T T T T T) -7 NIL NIL NIL) (-103 158751 161132 161462 "BBTREE" 161983 NIL BBTREE (NIL T) -8 NIL NIL NIL) (-102 158460 158513 158541 "BASTYPE" 158660 T BASTYPE (NIL) -9 NIL 158734 NIL) (-101 158312 158341 158414 "BASTYPE-" 158419 NIL BASTYPE- (NIL T) -8 NIL NIL NIL) (-100 157746 157822 157974 "BALFACT" 158223 NIL BALFACT (NIL T T) -7 NIL NIL NIL) (-99 156602 157161 157347 "AUTOMOR" 157591 NIL AUTOMOR (NIL T) -8 NIL NIL NIL) (-98 156328 156333 156359 "ATTREG" 156364 T ATTREG (NIL) -9 NIL NIL NIL) (-97 154580 155025 155377 "ATTRBUT" 155994 T ATTRBUT (NIL) -8 NIL NIL NIL) (-96 154188 154408 154474 "ATTRAST" 154532 T ATTRAST (NIL) -8 NIL NIL NIL) (-95 153724 153837 153863 "ATRIG" 154064 T ATRIG (NIL) -9 NIL NIL NIL) (-94 153533 153574 153661 "ATRIG-" 153666 NIL ATRIG- (NIL T) -8 NIL NIL NIL) (-93 153164 153350 153376 "ASTCAT" 153381 T ASTCAT (NIL) -9 NIL 153411 NIL) (-92 152891 152950 153069 "ASTCAT-" 153074 NIL ASTCAT- (NIL T) -8 NIL NIL NIL) (-91 151042 152667 152755 "ASTACK" 152834 NIL ASTACK (NIL T) -8 NIL NIL NIL) (-90 149547 149844 150209 "ASSOCEQ" 150724 NIL ASSOCEQ (NIL T T) -7 NIL NIL NIL) (-89 148579 149206 149330 "ASP9" 149454 NIL ASP9 (NIL NIL) -8 NIL NIL NIL) (-88 148342 148527 148566 "ASP8" 148571 NIL ASP8 (NIL NIL) -8 NIL NIL NIL) (-87 147210 147947 148089 "ASP80" 148231 NIL ASP80 (NIL NIL) -8 NIL NIL NIL) (-86 146108 146845 146977 "ASP7" 147109 NIL ASP7 (NIL NIL) -8 NIL NIL NIL) (-85 145062 145785 145903 "ASP78" 146021 NIL ASP78 (NIL NIL) -8 NIL NIL NIL) (-84 144031 144742 144859 "ASP77" 144976 NIL ASP77 (NIL NIL) -8 NIL NIL NIL) (-83 142943 143669 143800 "ASP74" 143931 NIL ASP74 (NIL NIL) -8 NIL NIL NIL) (-82 141843 142578 142710 "ASP73" 142842 NIL ASP73 (NIL NIL) -8 NIL NIL NIL) (-81 140947 141669 141769 "ASP6" 141774 NIL ASP6 (NIL NIL) -8 NIL NIL NIL) (-80 139894 140624 140742 "ASP55" 140860 NIL ASP55 (NIL NIL) -8 NIL NIL NIL) (-79 138843 139568 139687 "ASP50" 139806 NIL ASP50 (NIL NIL) -8 NIL NIL NIL) (-78 137931 138544 138654 "ASP4" 138764 NIL ASP4 (NIL NIL) -8 NIL NIL NIL) (-77 137019 137632 137742 "ASP49" 137852 NIL ASP49 (NIL NIL) -8 NIL NIL NIL) (-76 135803 136558 136726 "ASP42" 136908 NIL ASP42 (NIL NIL NIL NIL) -8 NIL NIL NIL) (-75 134580 135336 135506 "ASP41" 135690 NIL ASP41 (NIL NIL NIL NIL) -8 NIL NIL NIL) (-74 133530 134257 134375 "ASP35" 134493 NIL ASP35 (NIL NIL) -8 NIL NIL NIL) (-73 133295 133478 133517 "ASP34" 133522 NIL ASP34 (NIL NIL) -8 NIL NIL NIL) (-72 133032 133099 133175 "ASP33" 133250 NIL ASP33 (NIL NIL) -8 NIL NIL NIL) (-71 131926 132667 132799 "ASP31" 132931 NIL ASP31 (NIL NIL) -8 NIL NIL NIL) (-70 131691 131874 131913 "ASP30" 131918 NIL ASP30 (NIL NIL) -8 NIL NIL NIL) (-69 131426 131495 131571 "ASP29" 131646 NIL ASP29 (NIL NIL) -8 NIL NIL NIL) (-68 131191 131374 131413 "ASP28" 131418 NIL ASP28 (NIL NIL) -8 NIL NIL NIL) (-67 130956 131139 131178 "ASP27" 131183 NIL ASP27 (NIL NIL) -8 NIL NIL NIL) (-66 130040 130654 130765 "ASP24" 130876 NIL ASP24 (NIL NIL) -8 NIL NIL NIL) (-65 129117 129842 129954 "ASP20" 129959 NIL ASP20 (NIL NIL) -8 NIL NIL NIL) (-64 128205 128818 128928 "ASP1" 129038 NIL ASP1 (NIL NIL) -8 NIL NIL NIL) (-63 127148 127879 127998 "ASP19" 128117 NIL ASP19 (NIL NIL) -8 NIL NIL NIL) (-62 126885 126952 127028 "ASP12" 127103 NIL ASP12 (NIL NIL) -8 NIL NIL NIL) (-61 125737 126484 126628 "ASP10" 126772 NIL ASP10 (NIL NIL) -8 NIL NIL NIL) (-60 123590 125581 125672 "ARRAY2" 125677 NIL ARRAY2 (NIL T) -8 NIL NIL NIL) (-59 119357 123238 123352 "ARRAY1" 123507 NIL ARRAY1 (NIL T) -8 NIL NIL NIL) (-58 118389 118562 118783 "ARRAY12" 119180 NIL ARRAY12 (NIL T T) -7 NIL NIL NIL) (-57 112675 114591 114666 "ARR2CAT" 117296 NIL ARR2CAT (NIL T T T) -9 NIL 118054 NIL) (-56 110109 110853 111807 "ARR2CAT-" 111812 NIL ARR2CAT- (NIL T T T T) -8 NIL NIL NIL) (-55 109426 109736 109861 "ARITY" 110002 T ARITY (NIL) -8 NIL NIL NIL) (-54 108202 108354 108653 "APPRULE" 109262 NIL APPRULE (NIL T T T) -7 NIL NIL NIL) (-53 107853 107901 108020 "APPLYORE" 108148 NIL APPLYORE (NIL T T T) -7 NIL NIL NIL) (-52 107207 107446 107566 "ANY" 107751 T ANY (NIL) -8 NIL NIL NIL) (-51 106485 106608 106765 "ANY1" 107081 NIL ANY1 (NIL T) -7 NIL NIL NIL) (-50 104015 104922 105249 "ANTISYM" 106209 NIL ANTISYM (NIL T NIL) -8 NIL NIL NIL) (-49 103507 103722 103818 "ANON" 103937 T ANON (NIL) -8 NIL NIL NIL) (-48 97507 102046 102500 "AN" 103071 T AN (NIL) -8 NIL NIL NIL) (-47 93391 94779 94830 "AMR" 95578 NIL AMR (NIL T T) -9 NIL 96178 NIL) (-46 92503 92724 93087 "AMR-" 93092 NIL AMR- (NIL T T T) -8 NIL NIL NIL) (-45 76946 92420 92481 "ALIST" 92486 NIL ALIST (NIL T T) -8 NIL NIL NIL) (-44 73751 76540 76709 "ALGSC" 76864 NIL ALGSC (NIL T NIL NIL NIL) -8 NIL NIL NIL) (-43 70307 70861 71468 "ALGPKG" 73191 NIL ALGPKG (NIL T T) -7 NIL NIL NIL) (-42 69584 69685 69869 "ALGMFACT" 70193 NIL ALGMFACT (NIL T T T) -7 NIL NIL NIL) (-41 65619 66198 66792 "ALGMANIP" 69168 NIL ALGMANIP (NIL T T) -7 NIL NIL NIL) (-40 55830 65245 65395 "ALGFF" 65552 NIL ALGFF (NIL T T T NIL) -8 NIL NIL NIL) (-39 55026 55157 55336 "ALGFACT" 55688 NIL ALGFACT (NIL T) -7 NIL NIL NIL) (-38 53953 54553 54591 "ALGEBRA" 54596 NIL ALGEBRA (NIL T) -9 NIL 54637 NIL) (-37 53671 53730 53862 "ALGEBRA-" 53867 NIL ALGEBRA- (NIL T T) -8 NIL NIL NIL) (-36 35666 51569 51621 "ALAGG" 51757 NIL ALAGG (NIL T T) -9 NIL 51918 NIL) (-35 35202 35315 35341 "AHYP" 35542 T AHYP (NIL) -9 NIL NIL NIL) (-34 34133 34381 34407 "AGG" 34906 T AGG (NIL) -9 NIL 35185 NIL) (-33 33567 33729 33943 "AGG-" 33948 NIL AGG- (NIL T) -8 NIL NIL NIL) (-32 31373 31796 32201 "AF" 33209 NIL AF (NIL T T) -7 NIL NIL NIL) (-31 30853 31098 31188 "ADDAST" 31301 T ADDAST (NIL) -8 NIL NIL NIL) (-30 30121 30380 30536 "ACPLOT" 30715 T ACPLOT (NIL) -8 NIL NIL NIL) (-29 18744 27053 27091 "ACFS" 27698 NIL ACFS (NIL T) -9 NIL 27937 NIL) (-28 16771 17261 18023 "ACFS-" 18028 NIL ACFS- (NIL T T) -8 NIL NIL NIL) (-27 12875 14804 14830 "ACF" 15709 T ACF (NIL) -9 NIL 16122 NIL) (-26 11579 11913 12406 "ACF-" 12411 NIL ACF- (NIL T) -8 NIL NIL NIL) (-25 11137 11332 11358 "ABELSG" 11450 T ABELSG (NIL) -9 NIL 11515 NIL) (-24 11004 11029 11095 "ABELSG-" 11100 NIL ABELSG- (NIL T) -8 NIL NIL NIL) (-23 10333 10620 10646 "ABELMON" 10816 T ABELMON (NIL) -9 NIL 10928 NIL) (-22 9997 10081 10219 "ABELMON-" 10224 NIL ABELMON- (NIL T) -8 NIL NIL NIL) (-21 9331 9703 9729 "ABELGRP" 9801 T ABELGRP (NIL) -9 NIL 9876 NIL) (-20 8794 8923 9139 "ABELGRP-" 9144 NIL ABELGRP- (NIL T) -8 NIL NIL NIL) (-19 4333 8083 8122 "A1AGG" 8127 NIL A1AGG (NIL T) -9 NIL 8167 NIL) (-18 30 1251 2813 "A1AGG-" 2818 NIL A1AGG- (NIL T T) -8 NIL NIL NIL))
\ No newline at end of file diff --git a/src/share/algebra/operation.daase b/src/share/algebra/operation.daase index 2be65a1d..7641d07b 100644 --- a/src/share/algebra/operation.daase +++ b/src/share/algebra/operation.daase @@ -1,247 +1,20 @@ -(731430 . 3486658190) -(((*1 *2 *1) - (-12 (-4 *1 (-1262 *3)) (-4 *3 (-1068)) (-5 *2 (-1191 *3))))) -(((*1 *2 *2 *3) - (-12 (-4 *3 (-568)) (-4 *4 (-384 *3)) (-4 *5 (-384 *3)) - (-5 *1 (-1226 *3 *4 *5 *2)) (-4 *2 (-699 *3 *4 *5))))) -(((*1 *2 *1 *2 *3) - (-12 (-5 *3 (-656 (-1177))) (-5 *2 (-1177)) (-5 *1 (-1287)))) - ((*1 *2 *1 *2 *2) (-12 (-5 *2 (-1177)) (-5 *1 (-1287)))) - ((*1 *2 *1 *2) (-12 (-5 *2 (-1177)) (-5 *1 (-1287)))) - ((*1 *2 *1 *2 *3) - (-12 (-5 *3 (-656 (-1177))) (-5 *2 (-1177)) (-5 *1 (-1288)))) - ((*1 *2 *1 *2 *2) (-12 (-5 *2 (-1177)) (-5 *1 (-1288)))) - ((*1 *2 *1 *2) (-12 (-5 *2 (-1177)) (-5 *1 (-1288))))) +(731535 . 3486753497) (((*1 *2) - (-12 (-5 *2 (-112)) (-5 *1 (-1176 *3)) (-4 *3 (-1119)) - (-4 *3 (-1236))))) -(((*1 *2 *2) - 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(-5 *3 (-1113 (-227))) - (-5 *1 (-943)))) - ((*1 *1 *1 *2) (-12 (-5 *2 (-1113 (-227))) (-5 *1 (-944)))) - ((*1 *1 *2 *2 *3 *3 *3) - (-12 (-5 *2 (-1 (-227) (-227))) (-5 *3 (-1113 (-227))) - (-5 *1 (-944)))) - ((*1 *1 *2 *2 *3) - (-12 (-5 *2 (-1 (-227) (-227))) (-5 *3 (-1113 (-227))) - (-5 *1 (-944)))) - ((*1 *1 *2 *3 *3) - (-12 (-5 *2 (-656 (-1 (-227) (-227)))) (-5 *3 (-1113 (-227))) - (-5 *1 (-944)))) - ((*1 *1 *2 *3) - (-12 (-5 *2 (-656 (-1 (-227) (-227)))) (-5 *3 (-1113 (-227))) - (-5 *1 (-944)))) - ((*1 *1 *2 *3 *3) - (-12 (-5 *2 (-1 (-227) (-227))) (-5 *3 (-1113 (-227))) - (-5 *1 (-944)))) - ((*1 *1 *2 *3) - (-12 (-5 *2 (-1 (-227) (-227))) (-5 *3 (-1113 (-227))) - (-5 *1 (-944))))) -(((*1 *2 *3 *3 *3 *3 *4 *3 *5) - (-12 (-5 *3 (-576)) (-5 *4 (-701 (-227))) - (-5 *5 (-3 (|:| |fn| (-400)) (|:| |fp| (-79 LSFUN1)))) - (-5 *2 (-1054)) (-5 *1 (-765))))) -(((*1 *2 *1) - (-12 (-5 *2 (-656 (-1222 *3))) (-5 *1 (-1222 *3)) (-4 *3 (-1119))))) + (-12 (-4 *1 (-353 *3 *4 *5)) (-4 *3 (-1240)) (-4 *4 (-1262 *3)) + (-4 *5 (-1262 (-419 *4))) (-5 *2 (-701 (-419 *4)))))) +(((*1 *1 *2) (-12 (-5 *2 (-656 *3)) (-4 *3 (-862)) (-5 *1 (-122 *3))))) +(((*1 *2) (-12 (-5 *2 (-1291)) (-5 *1 (-1238))))) +(((*1 *2 *1) (-12 (-5 *2 (-112)) (-5 *1 (-145))))) +(((*1 *2) + (-12 (-5 *2 (-783)) (-5 *1 (-121 *3)) (-4 *3 (-1262 (-576))))) + ((*1 *2 *2) + (-12 (-5 *2 (-783)) (-5 *1 (-121 *3)) (-4 *3 (-1262 (-576)))))) (((*1 *2 *3) (-12 (-5 *3 (-2 (|:| |var| (-1195)) (|:| |fn| (-326 (-227))) - (|:| -4005 (-1113 (-855 (-227)))) (|:| |abserr| (-227)) + (|:| -1668 (-1113 (-855 (-227)))) (|:| |abserr| (-227)) (|:| |relerr| (-227)))) (-5 *2 (-2 @@ -259,7 +32,7 @@ (-3 (|:| |str| (-1176 (-227))) (|:| |notEvaluated| "Internal singularities not yet evaluated"))) - (|:| -4005 + (|:| -1668 (-3 (|:| |finite| "The range is finite") (|:| |lowerInfinite| "The bottom of range is infinite") (|:| |upperInfinite| "The top of range is infinite") @@ -267,480 +40,61 @@ "Both top and bottom points are infinite") (|:| 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"There are singularities at both end points") + (|:| |notEvaluated| + "End point continuity not yet evaluated"))) + (|:| |singularitiesStream| + (-3 (|:| |str| (-1176 (-227))) + (|:| |notEvaluated| + "Internal singularities not yet evaluated"))) + (|:| -1668 + (-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 (-571)))) + ((*1 *1 *2 *1 *3) + (-12 (-5 *3 (-783)) (-4 *1 (-707 *2)) (-4 *2 (-1119)))) + ((*1 *1 *2) + (-12 + (-5 *2 + (-2 + (|:| -4298 + (-2 (|:| |xinit| (-227)) (|:| |xend| (-227)) + (|:| |fn| (-1286 (-326 (-227)))) (|:| |yinit| (-656 (-227))) + (|:| |intvals| (-656 (-227))) (|:| |g| (-326 (-227))) + (|:| |abserr| (-227)) (|:| |relerr| (-227)))) + (|:| -4437 + (-2 (|:| |stiffness| (-390)) (|:| |stability| (-390)) + (|:| |expense| (-390)) (|:| 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*6))) + (-5 *2 (-2 (|:| -3363 *6) (|:| |coeff| *6))) (-5 *1 (-596 *5 *6)))) ((*1 *2 *3 *4) (|partial| -12 (-5 *3 (-1 *2 *5)) (-5 *4 (-3 *5 "failed")) @@ -2251,7 +1792,7 @@ (-4 *8 (-1068)) (-4 *6 (-805)) (-4 *2 (-13 (-1119) - (-10 -8 (-15 -3039 ($ $ $)) (-15 * ($ $ $)) (-15 ** ($ $ (-783)))))) + (-10 -8 (-15 -3026 ($ $ $)) (-15 * ($ $ $)) (-15 ** ($ $ (-783)))))) (-5 *1 (-968 *6 *7 *8 *5 *2)) (-4 *5 (-966 *8 *6 *7)))) ((*1 *2 *3 *4) (-12 (-5 *3 (-1 *6 *5)) (-5 *4 (-975 *5)) (-4 *5 (-1236)) @@ -2267,8 +1808,8 @@ (-4 *2 (-966 (-969 *4) *5 *6)) (-4 *5 (-805)) (-4 *6 (-13 (-862) - (-10 -8 (-15 -4146 ((-1195) $)) - (-15 -3015 ((-3 $ "failed") (-1195)))))) + (-10 -8 (-15 -4169 ((-1195) $)) + (-15 -3052 ((-3 $ "failed") (-1195)))))) (-5 *1 (-1003 *4 *5 *6 *2)))) ((*1 *2 *3 *4) (-12 (-5 *3 (-1 *6 *5)) (-4 *5 (-568)) (-4 *6 (-568)) @@ -2355,140 +1896,46 @@ ((*1 *1 *2 *1) (-12 (-5 *2 (-1 *3 *3)) (-4 *3 (-1068)) (-5 *1 (-1309 *3 *4)) (-4 *4 (-858))))) -(((*1 *2 *3) - (-12 (-5 *3 (-783)) (-5 *2 (-1 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(-1277 *3)) @@ -2701,53 +2159,51 @@ ((*1 *2 *2) (-12 (-4 *3 (-38 (-419 (-576)))) (-4 *4 (-1246 *3)) (-5 *1 (-288 *3 *4 *2 *5)) (-4 *2 (-1269 *3 *4)) (-4 *5 (-1002 *4)))) + ((*1 *1 *1) (-4 *1 (-505))) ((*1 *2 *2) (-12 (-5 *2 (-1176 *3)) (-4 *3 (-38 (-419 (-576)))) (-5 *1 (-1180 *3)))) ((*1 *2 *2) (-12 (-5 *2 (-1176 *3)) (-4 *3 (-38 (-419 (-576)))) (-5 *1 (-1181 *3))))) -(((*1 *1 *2) - (-12 (-5 *2 (-656 *1)) (-4 *3 (-1068)) (-4 *1 (-699 *3 *4 *5)) - (-4 *4 (-384 *3)) (-4 *5 (-384 *3)))) - ((*1 *1 *2) - (-12 (-5 *2 (-656 *3)) (-4 *3 (-1068)) (-4 *1 (-699 *3 *4 *5)) - (-4 *4 (-384 *3)) (-4 *5 (-384 *3)))) - ((*1 *1 *2) - (-12 (-5 *2 (-1286 *3)) (-4 *3 (-1068)) (-5 *1 (-701 *3)))) - ((*1 *1 *2) - (-12 (-5 *2 (-656 *4)) (-4 *4 (-1068)) (-4 *1 (-1142 *3 *4 *5 *6)) - (-4 *5 (-243 *3 *4)) (-4 *6 (-243 *3 *4))))) -(((*1 *2 *3) (-12 (-5 *3 (-1177)) (-5 *2 (-938)) (-5 *1 (-798))))) -(((*1 *2 *1) - (-12 - (-5 *2 - (-1286 - (-2 (|:| |scaleX| (-227)) (|:| |scaleY| (-227)) - (|:| |deltaX| (-227)) (|:| 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*1 (-1084 *2 *3 *4)) (-4 *2 (-1068)) (-4 *3 (-805)) + (-4 *4 (-862)) (-4 *2 (-464))))) (((*1 *2 *3 *4) - (-12 (-5 *4 (-1195)) - (-4 *5 (-13 (-464) (-148) (-1057 (-576)) (-651 (-576)))) - (-5 *2 (-598 *3)) (-5 *1 (-569 *5 *3)) - (-4 *3 (-13 (-27) (-1221) (-442 *5)))))) -(((*1 *2 *1) - (-12 (-4 *4 (-1119)) (-5 *2 (-112)) (-5 *1 (-898 *3 *4 *5)) - (-4 *3 (-1119)) (-4 *5 (-678 *4)))) - ((*1 *2 *1) - (-12 (-5 *2 (-112)) (-5 *1 (-902 *3 *4)) (-4 *3 (-1119)) - (-4 *4 (-1119))))) -(((*1 *1 *1) (-4 *1 (-35))) - ((*1 *2 *2) + (-12 (-5 *3 (-227)) (-5 *4 (-576)) (-5 *2 (-1054)) (-5 *1 (-770))))) +(((*1 *2 *1) (-12 (-5 *2 (-1291)) (-5 *1 (-834))))) +(((*1 *2 *3 *2) + (-12 (-5 *2 (-656 *3)) (-4 *3 (-317)) (-5 *1 (-181 *3))))) +(((*1 *2 *3 *2) + (-12 (-5 *2 (-1177)) (-5 *3 (-656 (-270))) (-5 *1 (-268)))) + ((*1 *1 *2) (-12 (-5 *2 (-1177)) (-5 *1 (-270))))) +(((*1 *2 *1) (-12 (-5 *2 (-656 (-969 (-576)))) (-5 *1 (-449)))) + ((*1 *2 *3 *4) + (-12 (-5 *3 (-1195)) (-5 *4 (-701 (-227))) (-5 *2 (-1123)) + (-5 *1 (-771)))) + ((*1 *2 *3 *4) + (-12 (-5 *3 (-1195)) (-5 *4 (-701 (-576))) (-5 *2 (-1123)) + (-5 *1 (-771))))) +(((*1 *2) + (-12 (-4 *3 (-568)) (-5 *2 (-656 *4)) (-5 *1 (-43 *3 *4)) + (-4 *4 (-429 *3))))) +(((*1 *2 *1 *1) + (-12 (-4 *3 (-568)) (-4 *3 (-1068)) + (-5 *2 (-2 (|:| -3405 *1) (|:| -2503 *1))) (-4 *1 (-864 *3)))) + ((*1 *2 *3 *3 *4) + (-12 (-5 *4 (-99 *5)) (-4 *5 (-568)) (-4 *5 (-1068)) + (-5 *2 (-2 (|:| -3405 *3) (|:| -2503 *3))) (-5 *1 (-865 *5 *3)) + (-4 *3 (-864 *5))))) +(((*1 *2 *2) (-12 (-4 *3 (-568)) (-5 *1 (-285 *3 *2)) (-4 *2 (-13 (-442 *3) (-1021))))) ((*1 *2 *2) @@ -2756,24 +2212,92 @@ ((*1 *2 *2) (-12 (-4 *3 (-38 (-419 (-576)))) (-4 *4 (-1246 *3)) (-5 *1 (-288 *3 *4 *2 *5)) (-4 *2 (-1269 *3 *4)) (-4 *5 (-1002 *4)))) + ((*1 *1 *1) (-4 *1 (-505))) ((*1 *2 *2) (-12 (-5 *2 (-1176 *3)) (-4 *3 (-38 (-419 (-576)))) (-5 *1 (-1180 *3)))) ((*1 *2 *2) (-12 (-5 *2 (-1176 *3)) (-4 *3 (-38 (-419 (-576)))) (-5 *1 (-1181 *3))))) -(((*1 *2 *2) - (-12 (-4 *3 (-13 (-568) (-1057 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(-112)) (-5 *1 (-1160 *4 *5))))) + (|partial| -12 (-5 *4 (-304 (-845 *3))) + (-4 *5 (-13 (-464) (-1057 (-576)) (-651 (-576)))) + (-5 *2 (-845 *3)) (-5 *1 (-648 *5 *3)) + (-4 *3 (-13 (-27) (-1221) (-442 *5))))) + ((*1 *2 *3 *4) + (-12 (-5 *4 (-304 (-845 (-969 *5)))) (-4 *5 (-464)) + (-5 *2 (-845 (-419 (-969 *5)))) (-5 *1 (-649 *5)) + (-5 *3 (-419 (-969 *5))))) + ((*1 *2 *3 *4) + (-12 (-5 *4 (-304 (-419 (-969 *5)))) (-5 *3 (-419 (-969 *5))) + (-4 *5 (-464)) (-5 *2 (-845 *3)) (-5 *1 (-649 *5))))) +(((*1 *2 *3 *3 *3 *3 *3 *4 *4 *4 *5) + (-12 (-5 *3 (-227)) (-5 *4 (-576)) + (-5 *5 (-3 (|:| |fn| (-400)) (|:| |fp| (-64 G)))) (-5 *2 (-1054)) + (-5 *1 (-760))))) +(((*1 *2 *3) + (-12 (-5 *3 (-1286 *1)) (-4 *1 (-378 *4)) (-4 *4 (-174)) + (-5 *2 (-701 *4)))) + ((*1 *2) + (-12 (-4 *4 (-174)) (-5 *2 (-701 *4)) (-5 *1 (-428 *3 *4)) + (-4 *3 (-429 *4)))) + ((*1 *2) (-12 (-4 *1 (-429 *3)) (-4 *3 (-174)) (-5 *2 (-701 *3))))) +(((*1 *1 *2) + (-12 + (-5 *2 + (-656 + (-2 + (|:| -4298 + (-2 (|:| |var| (-1195)) (|:| |fn| (-326 (-227))) + (|:| -1668 (-1113 (-855 (-227)))) (|:| |abserr| (-227)) + (|:| |relerr| (-227)))) + (|:| -4437 + (-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| (-1176 (-227))) + (|:| |notEvaluated| + "Internal singularities not yet evaluated"))) + (|:| -1668 + (-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 (-571))))) +(((*1 *2 *1 *3 *3) + (-12 (-5 *3 (-783)) (-5 *2 (-419 (-576))) (-5 *1 (-227)))) + ((*1 *2 *1 *3) + (-12 (-5 *3 (-783)) (-5 *2 (-419 (-576))) (-5 *1 (-227)))) + ((*1 *2 *1 *3 *3) + (-12 (-5 *3 (-783)) (-5 *2 (-419 (-576))) (-5 *1 (-390)))) + ((*1 *2 *1 *3) + (-12 (-5 *3 (-783)) (-5 *2 (-419 (-576))) (-5 *1 (-390))))) +(((*1 *2 *2) (-12 (-5 *2 (-390)) (-5 *1 (-1288)))) + ((*1 *2) (-12 (-5 *2 (-390)) (-5 *1 (-1288))))) (((*1 *2 *3) (-12 (-5 *2 (-171 (-390))) (-5 *1 (-797 *3)) (-4 *3 (-626 (-390))))) ((*1 *2 *3 *4) @@ -2822,173 +2346,14 @@ (-12 (-5 *3 (-326 (-171 *5))) (-5 *4 (-938)) (-4 *5 (-568)) (-4 *5 (-862)) (-4 *5 (-626 (-390))) (-5 *2 (-171 (-390))) (-5 *1 (-797 *5))))) -(((*1 *2) (-12 (-5 *2 (-886)) (-5 *1 (-1289)))) - ((*1 *2 *2) (-12 (-5 *2 (-886)) (-5 *1 (-1289))))) -(((*1 *2 *2 *2) (-12 (-5 *2 (-227)) (-5 *1 (-228)))) - ((*1 *2 *2 *2) (-12 (-5 *2 (-171 (-227))) (-5 *1 (-228)))) - ((*1 *2 *2 *2) - (-12 (-4 *3 (-568)) (-5 *1 (-443 *3 *2)) (-4 *2 (-442 *3)))) - ((*1 *1 *1 *1) (-4 *1 (-1158)))) -(((*1 *2 *3 *2 *4) - (-12 (-5 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(-1191 *1)) + (-4 *1 (-926))))) +(((*1 *2 *2) + (-12 (-5 *2 (-112)) (-5 *1 (-454 *3)) (-4 *3 (-1262 (-576)))))) (((*1 *2 *2) (-12 (-4 *3 (-568)) (-5 *1 (-285 *3 *2)) (-4 *2 (-13 (-442 *3) (-1021))))) @@ -3186,88 +2478,61 @@ ((*1 *2 *2) (-12 (-5 *2 (-1176 *3)) (-4 *3 (-38 (-419 (-576)))) (-5 *1 (-1181 *3))))) +(((*1 *2 *2 *2) (-12 (-5 *2 (-227)) (-5 *1 (-228)))) + ((*1 *2 *2 *2) (-12 (-5 *2 (-171 (-227))) (-5 *1 (-228)))) + ((*1 *2 *2 *2) + (-12 (-4 *3 (-568)) (-5 *1 (-443 *3 *2)) (-4 *2 (-442 *3)))) + ((*1 *1 *1 *1) (-4 *1 (-1158)))) +(((*1 *2 *2 *3 *4 *5) + (-12 (-5 *2 (-656 *9)) (-5 *3 (-1 (-112) *9)) + (-5 *4 (-1 (-112) *9 *9)) (-5 *5 (-1 *9 *9 *9)) + (-4 *9 (-1084 *6 *7 *8)) (-4 *6 (-568)) (-4 *7 (-805)) + (-4 *8 (-862)) (-5 *1 (-996 *6 *7 *8 *9))))) +(((*1 *1 *1) (-4 *1 (-568)))) +(((*1 *2 *1) + (-12 + (-5 *2 + (-656 + (-2 + (|:| -4298 + (-2 (|:| |var| (-1195)) (|:| |fn| (-326 (-227))) + (|:| -1668 (-1113 (-855 (-227)))) (|:| |abserr| (-227)) + (|:| |relerr| (-227)))) + (|:| -4437 + (-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| (-1176 (-227))) + (|:| |notEvaluated| + "Internal singularities not yet evaluated"))) + (|:| -1668 + (-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 (-571)))) + ((*1 *2 *1) + (-12 (-4 *1 (-616 *3 *4)) (-4 *3 (-1119)) (-4 *4 (-1236)) + (-5 *2 (-656 *4))))) +(((*1 *2 *3 *3 *4 *4 *3 *4 *4 *3 *3 *3) + (-12 (-5 *3 (-576)) (-5 *4 (-701 (-227))) (-5 *2 (-1054)) + (-5 *1 (-764))))) +(((*1 *2 *1 *3) (-12 (-4 *1 (-539)) (-5 *3 (-129)) (-5 *2 (-783))))) (((*1 *2 *2 *2) - (-12 (-4 *3 (-38 (-419 (-576)))) (-5 *1 (-1279 *3 *2)) - (-4 *2 (-1277 *3))))) -(((*1 *2 *2) - (-12 (-4 *3 (-568)) (-5 *1 (-159 *3 *2)) (-4 *2 (-442 *3)))) - ((*1 *2 *2 *3) - (-12 (-5 *3 (-1195)) (-4 *4 (-568)) (-5 *1 (-159 *4 *2)) - (-4 *2 (-442 *4)))) - ((*1 *1 *1 *2) (-12 (-4 *1 (-161)) (-5 *2 (-1195)))) - ((*1 *1 *1) (-4 *1 (-161)))) -(((*1 *2 *3) - (-12 (-5 *3 (-656 *7)) (-4 *7 (-1084 *4 *5 *6)) (-4 *4 (-568)) - (-4 *5 (-805)) (-4 *6 (-862)) (-5 *2 (-656 (-1299 *4 *5 *6 *7))) - (-5 *1 (-1299 *4 *5 *6 *7)))) - ((*1 *2 *3 *4 *5) - (-12 (-5 *3 (-656 *9)) (-5 *4 (-1 (-112) *9 *9)) - (-5 *5 (-1 *9 *9 *9)) (-4 *9 (-1084 *6 *7 *8)) (-4 *6 (-568)) - (-4 *7 (-805)) (-4 *8 (-862)) (-5 *2 (-656 (-1299 *6 *7 *8 *9))) - (-5 *1 (-1299 *6 *7 *8 *9))))) -(((*1 *2 *3 *3) - (-12 (-4 *4 (-568)) - (-5 *2 (-2 (|:| -1677 *4) (|:| -3042 *3) (|:| -3730 *3))) - (-5 *1 (-988 *4 *3)) (-4 *3 (-1262 *4)))) - ((*1 *2 *1 *1) - (-12 (-4 *3 (-1068)) (-4 *4 (-805)) (-4 *5 (-862)) - (-5 *2 (-2 (|:| -3042 *1) (|:| -3730 *1))) (-4 *1 (-1084 *3 *4 *5)))) - ((*1 *2 *1 *1) - (-12 (-4 *3 (-568)) (-4 *3 (-1068)) - (-5 *2 (-2 (|:| -1677 *3) (|:| -3042 *1) (|:| -3730 *1))) - (-4 *1 (-1262 *3))))) -(((*1 *2 *3 *4) - (-12 (-5 *3 (-656 (-938))) (-5 *4 (-656 (-576))) - (-5 *2 (-701 (-576))) (-5 *1 (-1129))))) -(((*1 *2 *3) - (|partial| -12 (-5 *3 (-969 (-171 *4))) (-4 *4 (-174)) - (-4 *4 (-626 (-390))) (-5 *2 (-171 (-390))) (-5 *1 (-797 *4)))) - ((*1 *2 *3 *4) - (|partial| -12 (-5 *3 (-969 (-171 *5))) (-5 *4 (-938)) (-4 *5 (-174)) - (-4 *5 (-626 (-390))) (-5 *2 (-171 (-390))) (-5 *1 (-797 *5)))) - ((*1 *2 *3) - (|partial| -12 (-5 *3 (-969 *4)) (-4 *4 (-1068)) - (-4 *4 (-626 (-390))) (-5 *2 (-171 (-390))) (-5 *1 (-797 *4)))) - ((*1 *2 *3 *4) - (|partial| -12 (-5 *3 (-969 *5)) (-5 *4 (-938)) (-4 *5 (-1068)) - (-4 *5 (-626 (-390))) (-5 *2 (-171 (-390))) (-5 *1 (-797 *5)))) - ((*1 *2 *3) - (|partial| -12 (-5 *3 (-419 (-969 *4))) (-4 *4 (-568)) - (-4 *4 (-626 (-390))) (-5 *2 (-171 (-390))) (-5 *1 (-797 *4)))) - ((*1 *2 *3 *4) - (|partial| -12 (-5 *3 (-419 (-969 *5))) (-5 *4 (-938)) (-4 *5 (-568)) - (-4 *5 (-626 (-390))) (-5 *2 (-171 (-390))) (-5 *1 (-797 *5)))) - ((*1 *2 *3) - (|partial| -12 (-5 *3 (-419 (-969 (-171 *4)))) (-4 *4 (-568)) - (-4 *4 (-626 (-390))) (-5 *2 (-171 (-390))) (-5 *1 (-797 *4)))) - ((*1 *2 *3 *4) - (|partial| -12 (-5 *3 (-419 (-969 (-171 *5)))) (-5 *4 (-938)) - (-4 *5 (-568)) (-4 *5 (-626 (-390))) (-5 *2 (-171 (-390))) - (-5 *1 (-797 *5)))) - ((*1 *2 *3) - (|partial| -12 (-5 *3 (-326 *4)) (-4 *4 (-568)) (-4 *4 (-862)) - (-4 *4 (-626 (-390))) (-5 *2 (-171 (-390))) (-5 *1 (-797 *4)))) - ((*1 *2 *3 *4) - (|partial| -12 (-5 *3 (-326 *5)) (-5 *4 (-938)) (-4 *5 (-568)) - (-4 *5 (-862)) (-4 *5 (-626 (-390))) (-5 *2 (-171 (-390))) - (-5 *1 (-797 *5)))) - ((*1 *2 *3) - (|partial| -12 (-5 *3 (-326 (-171 *4))) (-4 *4 (-568)) (-4 *4 (-862)) - (-4 *4 (-626 (-390))) (-5 *2 (-171 (-390))) (-5 *1 (-797 *4)))) - ((*1 *2 *3 *4) - (|partial| -12 (-5 *3 (-326 (-171 *5))) (-5 *4 (-938)) (-4 *5 (-568)) - (-4 *5 (-862)) (-4 *5 (-626 (-390))) (-5 *2 (-171 (-390))) - (-5 *1 (-797 *5))))) -(((*1 *2 *3) (-12 (-5 *3 (-874)) (-5 *2 (-1291)) (-5 *1 (-1157)))) - ((*1 *2 *3) - (-12 (-5 *3 (-656 (-874))) (-5 *2 (-1291)) (-5 *1 (-1157))))) -(((*1 *2 *2 *3 *4 *4) - (-12 (-5 *4 (-576)) (-4 *3 (-174)) (-4 *5 (-384 *3)) - (-4 *6 (-384 *3)) (-5 *1 (-700 *3 *5 *6 *2)) - (-4 *2 (-699 *3 *5 *6))))) -(((*1 *2 *3) - (-12 (-5 *2 (-624 *4)) (-5 *1 (-623 *3 *4)) (-4 *3 (-1119)) - (-4 *4 (-1119))))) + (-12 (-4 *3 (-374)) (-5 *1 (-778 *2 *3)) (-4 *2 (-720 *3)))) + ((*1 *1 *1 *1) (-12 (-4 *1 (-864 *2)) (-4 *2 (-1068)) (-4 *2 (-374))))) (((*1 *2 *2) (-12 (-4 *3 (-568)) (-5 *1 (-285 *3 *2)) (-4 *2 (-13 (-442 *3) (-1021))))) @@ -3287,46 +2552,60 @@ ((*1 *2 *2) (-12 (-5 *2 (-1176 *3)) (-4 *3 (-38 (-419 (-576)))) (-5 *1 (-1181 *3))))) +(((*1 *1 *1 *2 *3 *1) + (-12 (-5 *2 (-783)) (-5 *1 (-794 *3)) (-4 *3 (-1068)))) + ((*1 *1 *1 *2 *3 *1) + (-12 (-5 *1 (-980 *3 *2)) (-4 *2 (-132)) (-4 *3 (-568)) + (-4 *3 (-1068)) (-4 *2 (-804)))) + ((*1 *1 *1 *2 *3 *1) + (-12 (-5 *2 (-783)) (-5 *1 (-1191 *3)) (-4 *3 (-1068)))) + ((*1 *1 *1 *2 *3 *1) + (-12 (-5 *2 (-990)) (-4 *2 (-132)) (-5 *1 (-1197 *3)) (-4 *3 (-568)) + (-4 *3 (-1068)))) + ((*1 *1 *1 *2 *3 *1) + (-12 (-5 *2 (-783)) (-5 *1 (-1259 *4 *3)) (-14 *4 (-1195)) + (-4 *3 (-1068))))) +(((*1 *2 *3 *3) + (-12 (-4 *4 (-568)) + (-5 *2 (-2 (|:| |coef2| *3) (|:| |subResultant| *3))) + (-5 *1 (-988 *4 *3)) (-4 *3 (-1262 *4))))) (((*1 *1 *1 *2) (-12 (-5 *2 (-656 (-874))) (-5 *1 (-874))))) -(((*1 *2 *3 *4 *4 *4 *3) - (-12 (-5 *3 (-576)) (-5 *4 (-701 (-227))) (-5 *2 (-1054)) - (-5 *1 (-763))))) -(((*1 *2 *1) - (-12 (-4 *1 (-375 *3 *2)) (-4 *3 (-1119)) (-4 *2 (-1119))))) -(((*1 *1 *2 *1) - (-12 (|has| *1 (-6 -4462)) (-4 *1 (-152 *2)) (-4 *2 (-1236)) - (-4 *2 (-1119)))) - ((*1 *1 *2 *1) - (-12 (-5 *2 (-1 (-112) *3)) (|has| *1 (-6 -4462)) (-4 *1 (-152 *3)) - (-4 *3 (-1236)))) - ((*1 *1 *2 *1) - (-12 (-5 *2 (-1 (-112) *3)) (-4 *1 (-686 *3)) (-4 *3 (-1236)))) - ((*1 *1 *2 *1 *3) - (-12 (-5 *2 (-1 (-112) *4)) (-5 *3 (-576)) (-4 *4 (-1119)) - (-5 *1 (-749 *4)))) - ((*1 *1 *2 *1 *3) - (-12 (-5 *3 (-576)) (-5 *1 (-749 *2)) (-4 *2 (-1119)))) - ((*1 *1 *2 *1) - (-12 (-5 *2 (-1159 *3 *4)) (-4 *3 (-13 (-1119) (-34))) - (-4 *4 (-13 (-1119) (-34))) (-5 *1 (-1160 *3 *4))))) +(((*1 *1 *2 *2 *1) (-12 (-5 *1 (-659 *2)) (-4 *2 (-1119))))) +(((*1 *1 *1 *2) + (-12 (-4 *1 (-57 *2 *3 *4)) (-4 *2 (-1236)) (-4 *3 (-384 *2)) + (-4 *4 (-384 *2)))) + ((*1 *1 *1 *2) + (-12 (|has| *1 (-6 -4463)) (-4 *1 (-616 *3 *2)) (-4 *3 (-1119)) + (-4 *2 (-1236))))) +(((*1 *2 *1) (-12 (-4 *1 (-809 *2)) (-4 *2 (-174)))) + ((*1 *2 *1) (-12 (-4 *1 (-1016 *2)) (-4 *2 (-174))))) +(((*1 *2 *1 *3 *4) + (-12 (-5 *3 (-938)) (-5 *4 (-886)) (-5 *2 (-1291)) (-5 *1 (-1287)))) + ((*1 *2 *1 *3 *4) + (-12 (-5 *3 (-938)) (-5 *4 (-1177)) (-5 *2 (-1291)) (-5 *1 (-1287)))) + ((*1 *2 *1 *3) (-12 (-5 *3 (-1177)) (-5 *2 (-1291)) (-5 *1 (-1288))))) (((*1 *2 *3 *3 *3) - (|partial| -12 - (-4 *4 (-13 (-148) (-27) (-1057 (-576)) (-1057 (-419 (-576))))) - (-4 *5 (-1262 *4)) (-5 *2 (-1191 (-419 *5))) (-5 *1 (-627 *4 *5)) - (-5 *3 (-419 *5)))) - ((*1 *2 *3 *3 *3 *4) - (|partial| -12 (-5 *4 (-1 (-430 *6) *6)) (-4 *6 (-1262 *5)) - (-4 *5 (-13 (-148) (-27) (-1057 (-576)) (-1057 (-419 (-576))))) - (-5 *2 (-1191 (-419 *6))) (-5 *1 (-627 *5 *6)) (-5 *3 (-419 *6))))) -(((*1 *2 *1) - (-12 (-4 *1 (-353 *3 *4 *5)) (-4 *3 (-1240)) (-4 *4 (-1262 *3)) - (-4 *5 (-1262 (-419 *4))) (-5 *2 (-112))))) + (-12 (-5 *3 (-1177)) (-4 *4 (-464)) (-4 *5 (-805)) (-4 *6 (-862)) + (-4 *7 (-1084 *4 *5 *6)) (-5 *2 (-1291)) + (-5 *1 (-1091 *4 *5 *6 *7 *8)) (-4 *8 (-1090 *4 *5 *6 *7)))) + ((*1 *2 *3 *3 *3) + (-12 (-5 *3 (-1177)) (-4 *4 (-464)) (-4 *5 (-805)) (-4 *6 (-862)) + (-4 *7 (-1084 *4 *5 *6)) (-5 *2 (-1291)) + (-5 *1 (-1127 *4 *5 *6 *7 *8)) (-4 *8 (-1090 *4 *5 *6 *7))))) (((*1 *2 *3) - (-12 (-5 *3 (-960 *2)) (-5 *1 (-1001 *2)) (-4 *2 (-1068))))) -(((*1 *1 *2) (-12 (-5 *2 (-656 *3)) (-4 *3 (-1119)) (-5 *1 (-224 *3)))) - ((*1 *1 *2) (-12 (-5 *2 (-656 *3)) (-4 *3 (-1236)) (-4 *1 (-261 *3)))) - ((*1 *1) (-12 (-4 *1 (-261 *2)) (-4 *2 (-1236))))) -(((*1 *2 *1) (-12 (-5 *2 (-301)) (-5 *1 (-290))))) + (-12 + (-5 *3 + (-2 (|:| |var| (-1195)) (|:| |fn| (-326 (-227))) + (|:| -1668 (-1113 (-855 (-227)))) (|:| |abserr| (-227)) + (|:| |relerr| (-227)))) + (-5 *2 (-1176 (-227))) (-5 *1 (-194)))) + ((*1 *2 *3 *4 *5) + (-12 (-5 *3 (-326 (-227))) (-5 *4 (-656 (-1195))) + (-5 *5 (-1113 (-855 (-227)))) (-5 *2 (-1176 (-227))) (-5 *1 (-310)))) + ((*1 *2 *3 *4 *5) + (-12 (-5 *3 (-1286 (-326 (-227)))) (-5 *4 (-656 (-1195))) + (-5 *5 (-1113 (-855 (-227)))) (-5 *2 (-1176 (-227))) (-5 *1 (-310))))) +(((*1 *2) (-12 (-5 *2 (-1291)) (-5 *1 (-771))))) (((*1 *1 *1) (-4 *1 (-95))) ((*1 *2 *2) (-12 (-4 *3 (-568)) (-5 *1 (-285 *3 *2)) @@ -3343,42 +2622,52 @@ ((*1 *2 *2) (-12 (-5 *2 (-1176 *3)) (-4 *3 (-38 (-419 (-576)))) (-5 *1 (-1181 *3))))) -(((*1 *2 *2 *3) - (-12 (-4 *3 (-374)) (-5 *1 (-295 *3 *2)) (-4 *2 (-1277 *3))))) -(((*1 *2 *3) - (-12 (-5 *3 (-656 (-2 (|:| |den| (-576)) (|:| |gcdnum| (-576))))) - (-4 *4 (-1262 (-419 *2))) (-5 *2 (-576)) (-5 *1 (-930 *4 *5)) - (-4 *5 (-1262 (-419 *4)))))) -(((*1 *2 *3) - (-12 (-5 *3 (-1191 *4)) (-4 *4 (-360)) - (-4 *2 - (-13 (-414) - (-10 -7 (-15 -3581 (*2 *4)) (-15 -2591 ((-938) *2)) - (-15 -2641 ((-1286 *2) (-938))) (-15 -2832 (*2 *2))))) - (-5 *1 (-367 *2 *4))))) -(((*1 *2 *3) - (-12 (-5 *3 (-2 (|:| -4206 (-419 (-576))) (|:| -4216 (-419 (-576))))) - (-5 *2 (-419 (-576))) (-5 *1 (-1039 *4)) (-4 *4 (-1262 (-576)))))) -(((*1 *2 *3) (-12 (-5 *3 (-518)) (-5 *2 (-703 (-189))) (-5 *1 (-189))))) -(((*1 *2 *3) (-12 (-5 *3 (-1195)) (-5 *2 (-1291)) (-5 *1 (-1198)))) - ((*1 *2 *1) (-12 (-5 *2 (-1291)) (-5 *1 (-1199))))) -(((*1 *1 *1 *1) - (-12 (-4 *1 (-699 *2 *3 *4)) (-4 *2 (-1068)) (-4 *3 (-384 *2)) - (-4 *4 (-384 *2))))) (((*1 *2 *1) - (-12 (-4 *1 (-1303 *3 *4)) (-4 *3 (-862)) (-4 *4 (-1068)) - (-5 *2 (-112)))) - ((*1 *2 *1) - (-12 (-5 *2 (-112)) (-5 *1 (-1309 *3 *4)) (-4 *3 (-1068)) - (-4 *4 (-858))))) -(((*1 *2 *2) (-12 (-5 *2 (-938)) (-5 *1 (-368 *3)) (-4 *3 (-360))))) + (-12 (-5 *2 (-419 (-969 *3))) (-5 *1 (-465 *3 *4 *5 *6)) + (-4 *3 (-568)) (-4 *3 (-174)) (-14 *4 (-938)) + (-14 *5 (-656 (-1195))) (-14 *6 (-1286 (-701 *3)))))) +(((*1 *2) + (-12 (-4 *4 (-174)) (-5 *2 (-112)) (-5 *1 (-377 *3 *4)) + (-4 *3 (-378 *4)))) + ((*1 *2) (-12 (-4 *1 (-378 *3)) (-4 *3 (-174)) (-5 *2 (-112))))) (((*1 *2 *3 *4) - (-12 (-5 *3 (-419 (-969 (-171 (-576))))) (-5 *2 (-656 (-171 *4))) - (-5 *1 (-389 *4)) (-4 *4 (-13 (-374) (-860))))) - ((*1 *2 *3 *4 *5) - (-12 (-5 *3 (-656 (-419 (-969 (-171 (-576)))))) - (-5 *4 (-656 (-1195))) (-5 *2 (-656 (-656 (-171 *5)))) - (-5 *1 (-389 *5)) (-4 *5 (-13 (-374) (-860)))))) + (-12 (-5 *3 (-701 *1)) (-5 *4 (-1286 *1)) (-4 *1 (-651 *5)) + (-4 *5 (-1068)) + (-5 *2 (-2 (|:| -2875 (-701 *5)) (|:| |vec| (-1286 *5)))))) + ((*1 *2 *3) + (-12 (-5 *3 (-701 *1)) (-4 *1 (-651 *4)) (-4 *4 (-1068)) + (-5 *2 (-701 *4))))) +(((*1 *1 *1 *2 *2) + (-12 (-5 *2 (-576)) (-5 *1 (-137 *3 *4 *5)) (-14 *3 *2) + (-14 *4 (-783)) (-4 *5 (-174)))) + ((*1 *1 *1 *2 *1 *2) + (-12 (-5 *2 (-576)) (-5 *1 (-137 *3 *4 *5)) (-14 *3 *2) + (-14 *4 (-783)) (-4 *5 (-174)))) + ((*1 *2 *2 *3) + (-12 + (-5 *2 + (-516 (-419 (-576)) (-245 *5 (-783)) (-876 *4) + (-253 *4 (-419 (-576))))) + (-5 *3 (-656 (-876 *4))) (-14 *4 (-656 (-1195))) (-14 *5 (-783)) + (-5 *1 (-517 *4 *5))))) +(((*1 *2 *1) (-12 (-5 *2 (-112)) (-5 *1 (-598 *3)) (-4 *3 (-374))))) +(((*1 *2 *3 *4) + (-12 (-5 *4 (-656 *5)) (-4 *5 (-1262 *3)) (-4 *3 (-317)) + (-5 *2 (-112)) (-5 *1 (-467 *3 *5))))) +(((*1 *2 *1) (-12 (-5 *2 (-656 (-624 *1))) (-4 *1 (-312))))) +(((*1 *2 *1) (-12 (-5 *2 (-1154)) (-5 *1 (-529)))) + ((*1 *2 *1) + (-12 (-4 *2 (-13 (-1119) (-34))) (-5 *1 (-1159 *3 *2)) + (-4 *3 (-13 (-1119) (-34))))) + ((*1 *2 *1) (-12 (-5 *2 (-1154)) (-5 *1 (-1297))))) +(((*1 *1 *2 *2) (-12 (-4 *1 (-566 *2)) (-4 *2 (-13 (-416) (-1221)))))) +(((*1 *2 *1) (-12 (-4 *1 (-686 *3)) (-4 *3 (-1236)) (-5 *2 (-112))))) +(((*1 *2 *3) + (-12 (-5 *3 (-656 (-2 (|:| -1825 *4) (|:| -3779 (-576))))) + (-4 *4 (-1262 (-576))) (-5 *2 (-749 (-783))) (-5 *1 (-454 *4)))) + ((*1 *2 *3) + (-12 (-5 *3 (-430 *5)) (-4 *5 (-1262 *4)) (-4 *4 (-1068)) + (-5 *2 (-749 (-783))) (-5 *1 (-456 *4 *5))))) (((*1 *1 *1) (-4 *1 (-95))) ((*1 *2 *2) (-12 (-4 *3 (-568)) (-5 *1 (-285 *3 *2)) @@ -3395,40 +2684,32 @@ ((*1 *2 *2) (-12 (-5 *2 (-1176 *3)) (-4 *3 (-38 (-419 (-576)))) (-5 *1 (-1181 *3))))) +(((*1 *2 *1) + (-12 (-4 *1 (-699 *3 *4 *5)) (-4 *3 (-1068)) (-4 *4 (-384 *3)) + (-4 *5 (-384 *3)) (-5 *2 (-112)))) + ((*1 *2 *1) + (-12 (-4 *1 (-1072 *3 *4 *5 *6 *7)) (-4 *5 (-1068)) + (-4 *6 (-243 *4 *5)) (-4 *7 (-243 *3 *5)) (-5 *2 (-112))))) +(((*1 *1) (-5 *1 (-145))) ((*1 *1 *1) (-5 *1 (-874)))) +(((*1 *2 *3 *3) + (-12 (-4 *4 (-832)) (-14 *5 (-1195)) (-5 *2 (-656 (-1259 *5 *4))) + 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-(((*1 *2 *3) - (-12 - (-5 *3 - (-3 - (|:| |noa| - (-2 (|:| |fn| (-326 (-227))) (|:| -3475 (-656 (-227))) - (|:| |lb| (-656 (-855 (-227)))) - (|:| |cf| (-656 (-326 (-227)))) - (|:| |ub| (-656 (-855 (-227)))))) - (|:| |lsa| - (-2 (|:| |lfn| (-656 (-326 (-227)))) - (|:| -3475 (-656 (-227))))))) - (-5 *2 (-656 (-1177))) (-5 *1 (-276))))) -(((*1 *2 *1) (-12 (-5 *2 (-1291)) (-5 *1 (-834))))) -(((*1 *1) (-5 *1 (-1288)))) -(((*1 *2 *3) - (-12 (-5 *3 (-656 *2)) (-4 *2 (-442 *4)) (-5 *1 (-159 *4 *2)) - (-4 *4 (-568))))) -(((*1 *2 *2) (-12 (-5 *2 (-783)) (-5 *1 (-457 *3)) (-4 *3 (-1068)))) - ((*1 *2) (-12 (-5 *2 (-783)) (-5 *1 (-457 *3)) (-4 *3 (-1068))))) + (|partial| -12 (-4 *1 (-36 *3 *4)) (-4 *3 (-1119)) (-4 *4 (-1119)) + (-5 *2 (-2 (|:| -4298 *3) (|:| -4437 *4)))))) +(((*1 *2 *2 *2 *2) + (-12 (-5 *2 (-701 *3)) (-4 *3 (-1068)) (-5 *1 (-702 *3))))) +(((*1 *2 *2) + (-12 (-4 *3 (-568)) (-5 *1 (-285 *3 *2)) + (-4 *2 (-13 (-442 *3) (-1021)))))) (((*1 *1 *1) (-4 *1 (-95))) ((*1 *2 *2) (-12 (-4 *3 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(-34)))))) (((*1 *1 *1) (-5 *1 (-112)))) +(((*1 *2 *3 *4 *4 *4 *4 *5 *5 *5) + (-12 (-5 *3 (-1 (-390) (-390))) (-5 *4 (-390)) + (-5 *2 + (-2 (|:| -3102 *4) (|:| -3311 *4) (|:| |totalpts| (-576)) + (|:| |success| (-112)))) + (-5 *1 (-801)) (-5 *5 (-576))))) (((*1 *1 *1) (-4 *1 (-95))) ((*1 *2 *2) (-12 (-4 *3 (-568)) (-5 *1 (-285 *3 *2)) @@ -3632,34 +2928,37 @@ ((*1 *2 *2) (-12 (-5 *2 (-1176 *3)) (-4 *3 (-38 (-419 (-576)))) (-5 *1 (-1181 *3))))) -(((*1 *1 *2) (-12 (-5 *2 (-656 (-874))) (-5 *1 (-874))))) -(((*1 *2 *2 *2) (-12 (-5 *1 (-160 *2)) (-4 *2 (-557))))) -(((*1 *2 *1) (-12 (-4 *1 (-336 *3 *2)) (-4 *3 (-1068)) (-4 *2 (-804)))) - ((*1 *2 *1) (-12 (-4 *1 (-720 *3)) (-4 *3 (-1068)) (-5 *2 (-783)))) - ((*1 *2 *1) (-12 (-4 *1 (-864 *3)) (-4 *3 (-1068)) (-5 *2 (-783)))) - ((*1 *2 *1 *3) - (-12 (-5 *3 (-656 *6)) (-4 *1 (-966 *4 *5 *6)) (-4 *4 (-1068)) - (-4 *5 (-805)) (-4 *6 (-862)) (-5 *2 (-656 (-783))))) - ((*1 *2 *1 *3) - (-12 (-4 *1 (-966 *4 *5 *3)) (-4 *4 (-1068)) (-4 *5 (-805)) - (-4 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(-3500 *4) (-783))) + (-14 *6 + (-1 (-112) (-2 (|:| -3222 *5) (|:| -1567 *3)) + (-2 (|:| -3222 *5) (|:| -1567 *3)))) + (-5 *1 (-473 *4 *2 *5 *3 *6 *7)) (-4 *5 (-862)) + (-4 *7 (-966 *2 *3 (-876 *4)))))) +(((*1 *1 *1) + (-12 (-5 *1 (-607 *2)) (-4 *2 (-38 (-419 (-576)))) (-4 *2 (-1068))))) +(((*1 *2 *1) (-12 (-5 *2 (-112)) (-5 *1 (-845 *3)) (-4 *3 (-1119)))) + ((*1 *2 *1) (-12 (-5 *2 (-112)) (-5 *1 (-855 *3)) (-4 *3 (-1119))))) (((*1 *2 *3 *4) - (-12 (-5 *3 (-656 (-227))) (-5 *4 (-783)) (-5 *2 (-701 (-227))) - (-5 *1 (-315))))) + (-12 (-5 *4 (-1195)) + (-4 *5 (-13 (-568) (-1057 (-576)) (-651 (-576)))) + (-5 *2 + (-2 (|:| |func| *3) (|:| |kers| (-656 (-624 *3))) + (|:| |vals| (-656 *3)))) + (-5 *1 (-286 *5 *3)) (-4 *3 (-13 (-27) (-1221) (-442 *5)))))) +(((*1 *2 *3 *1) + (-12 (-5 *3 (-1286 *1)) (-4 *1 (-651 *4)) (-4 *4 (-1068)) + (-5 *2 (-2 (|:| -2875 (-701 *4)) (|:| |vec| (-1286 *4)))))) + ((*1 *2 *3) + (-12 (-5 *3 (-1286 *1)) (-4 *1 (-651 *4)) (-4 *4 (-1068)) + (-5 *2 (-701 *4))))) (((*1 *2 *2) (-12 (-4 *3 (-568)) (-5 *1 (-285 *3 *2)) (-4 *2 (-13 (-442 *3) (-1021))))) @@ -3676,38 +2975,99 @@ (-12 (-5 *2 (-1176 *3)) (-4 *3 (-38 (-419 (-576)))) (-5 *1 (-1181 *3)))) ((*1 *1 *1) (-4 *1 (-1224)))) -(((*1 *2 *3 *4) - (-12 (-5 *3 (-419 (-576))) (-5 *4 (-576)) (-5 *2 (-52)) - (-5 *1 (-1024))))) -(((*1 *2 *1) (-12 (-5 *2 (-576)) (-5 *1 (-834))))) -(((*1 *2 *3) - (-12 (-5 *3 (-1 *5 *5)) (-4 *5 (-1277 *4)) - (-4 *4 (-38 (-419 (-576)))) (-5 *2 (-1 (-1176 *4) (-1176 *4))) - (-5 *1 (-1279 *4 *5))))) -(((*1 *2 *3) - (-12 (-5 *3 (-701 (-419 (-969 *4)))) (-4 *4 (-464)) - (-5 *2 (-656 (-3 (-419 (-969 *4)) (-1184 (-1195) (-969 *4))))) - (-5 *1 (-302 *4))))) -(((*1 *2 *1) (-12 (-5 *2 (-112)) (-5 *1 (-115))))) -(((*1 *1 *2 *2 *2 *2 *2 *2 *2 *2) - (-12 (-4 *1 (-809 *2)) (-4 *2 (-174)))) - ((*1 *1 *2 *2) - (-12 (-5 *2 (-1018 *3)) (-4 *3 (-174)) (-5 *1 (-811 *3))))) -(((*1 *2 *2) - (-12 (-5 *2 (-656 *6)) (-4 *6 (-966 *3 *4 *5)) (-4 *3 (-317)) - (-4 *4 (-805)) (-4 *5 (-862)) (-5 *1 (-459 *3 *4 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"Continuous at the end points") + (|:| |lowerSingular| + "There is a singularity at the lower end point") + (|:| |upperSingular| + "There is a singularity at the upper end point") + (|:| |bothSingular| "There are singularities at both end points") + (|:| |notEvaluated| "End point continuity not yet evaluated"))) + (-5 *1 (-194))))) (((*1 *2 *2) (-12 (-4 *3 (-568)) (-5 *1 (-285 *3 *2)) (-4 *2 (-13 (-442 *3) (-1021))))) @@ -3724,36 +3084,55 @@ (-12 (-5 *2 (-1176 *3)) (-4 *3 (-38 (-419 (-576)))) (-5 *1 (-1181 *3)))) ((*1 *1 *1) (-4 *1 (-1224)))) +(((*1 *2 *1 *3) + (-12 (-5 *3 (-576)) (-5 *2 (-3 "nil" "sqfr" "irred" "prime")) + (-5 *1 (-430 *4)) (-4 *4 (-568))))) +(((*1 *2 *1 *1 *1) + (|partial| -12 (-5 *2 (-2 (|:| |coef1| *1) (|:| |coef2| *1))) + (-4 *1 (-317)))) + ((*1 *2 *1 *1) + (-12 (-5 *2 (-2 (|:| |coef1| *1) (|:| |coef2| *1) (|:| -4126 *1))) + (-4 *1 (-317))))) +(((*1 *2 *2 *2) (-12 (-5 *2 (-576)) (-5 *1 (-573))))) +(((*1 *2 *1) + (-12 (-4 *1 (-378 *3)) (-4 *3 (-174)) (-4 *3 (-568)) + (-5 *2 (-1191 *3))))) +(((*1 *2 *1) + (-12 (-4 *1 (-995 *3 *4 *5 *6)) (-4 *3 (-1068)) (-4 *4 (-805)) + (-4 *5 (-862)) (-4 *6 (-1084 *3 *4 *5)) (-4 *3 (-568)) + (-5 *2 (-112))))) +(((*1 *2 *3 *1 *4) + (-12 (-5 *3 (-1159 *5 *6)) (-5 *4 (-1 (-112) *6 *6)) + (-4 *5 (-13 (-1119) (-34))) (-4 *6 (-13 (-1119) (-34))) + (-5 *2 (-112)) (-5 *1 (-1160 *5 *6))))) +(((*1 *2 *1 *3 *3 *3) + (-12 (-5 *3 (-390)) (-5 *2 (-1291)) (-5 *1 (-1288))))) (((*1 *2 *3 *3) - (-12 (-5 *2 (-1176 (-656 (-576)))) (-5 *1 (-896)) - (-5 *3 (-656 (-576))))) - ((*1 *2 *3) - (-12 (-5 *2 (-1176 (-656 (-576)))) (-5 *1 (-896)) - (-5 *3 (-656 (-576)))))) -(((*1 *2 *3 *4 *5) - (-12 (-5 *3 (-701 *6)) (-5 *5 (-1 (-430 (-1191 *6)) (-1191 *6))) - (-4 *6 (-374)) - (-5 *2 + (-12 (-5 *3 (-656 *2)) (-5 *1 (-181 *2)) (-4 *2 (-317)))) + ((*1 *2 *3 *2) + (-12 (-5 *3 (-656 (-656 *4))) (-5 *2 (-656 *4)) (-4 *4 (-317)) + (-5 *1 (-181 *4)))) + ((*1 *2 *3 *4 *5) + (-12 (-5 *3 (-656 *8)) + (-5 *4 (-656 - (-2 (|:| |outval| *7) (|:| |outmult| (-576)) - (|:| |outvect| (-656 (-701 *7)))))) - (-5 *1 (-544 *6 *7 *4)) (-4 *7 (-374)) (-4 *4 (-13 (-374) (-860)))))) -(((*1 *2 *3 *1) (-12 (-5 *3 (-1195)) (-5 *2 (-1199)) (-5 *1 (-1198))))) -(((*1 *2 *2 *3 *4) - (|partial| -12 (-5 *2 (-656 (-1191 *7))) (-5 *3 (-1191 *7)) - (-4 *7 (-966 *5 *6 *4)) (-4 *5 (-926)) (-4 *6 (-805)) - (-4 *4 (-862)) (-5 *1 (-923 *5 *6 *4 *7))))) -(((*1 *1) (-5 *1 (-835)))) -(((*1 *2 *1) - (-12 (-5 *2 (-1176 (-2 (|:| |k| (-576)) (|:| |c| *3)))) - (-5 *1 (-607 *3)) (-4 *3 (-1068))))) -(((*1 *2 *2 *1) (-12 (-4 *1 (-1140 *2)) (-4 *2 (-1236))))) -(((*1 *2 *1) (-12 (-5 *2 (-112)) (-5 *1 (-446))))) -(((*1 *2) (-12 (-5 *2 (-576)) (-5 *1 (-479)))) - ((*1 *2 *2) (-12 (-5 *2 (-576)) (-5 *1 (-479)))) - ((*1 *2) (-12 (-5 *2 (-576)) (-5 *1 (-944))))) -(((*1 *1 *1) - (-12 (-5 *1 (-607 *2)) (-4 *2 (-38 (-419 (-576)))) (-4 *2 (-1068))))) + (-2 (|:| -2335 (-701 *7)) (|:| |basisDen| *7) + (|:| |basisInv| (-701 *7))))) + (-5 *5 (-783)) (-4 *8 (-1262 *7)) (-4 *7 (-1262 *6)) (-4 *6 (-360)) + (-5 *2 + (-2 (|:| -2335 (-701 *7)) (|:| |basisDen| *7) + (|:| |basisInv| (-701 *7)))) + (-5 *1 (-510 *6 *7 *8)))) + ((*1 *2 *2 *2 *2 *2) (-12 (-5 *2 (-576)) (-5 *1 (-573))))) +(((*1 *2 *2 *3) + (-12 (-5 *3 (-656 *2)) (-4 *2 (-966 *4 *5 *6)) (-4 *4 (-374)) + (-4 *4 (-464)) (-4 *5 (-805)) (-4 *6 (-862)) + (-5 *1 (-462 *4 *5 *6 *2)))) + ((*1 *2 *3 *4 *5) + (-12 (-5 *4 (-99 *6)) (-5 *5 (-1 *6 *6)) (-4 *6 (-374)) + (-5 *2 + (-2 (|:| R (-701 *6)) (|:| A (-701 *6)) (|:| |Ainv| (-701 *6)))) + (-5 *1 (-997 *6)) (-5 *3 (-701 *6))))) (((*1 *2 *2) (-12 (-4 *3 (-568)) (-5 *1 (-285 *3 *2)) (-4 *2 (-13 (-442 *3) (-1021))))) @@ -3770,31 +3149,60 @@ (-12 (-5 *2 (-1176 *3)) (-4 *3 (-38 (-419 (-576)))) (-5 *1 (-1181 *3)))) ((*1 *1 *1) (-4 *1 (-1224)))) -(((*1 *2 *1) - (-12 (-5 *2 (-656 (-52))) (-5 *1 (-905 *3)) (-4 *3 (-1119))))) -(((*1 *2 *3) - (-12 (-4 *4 (-360)) (-5 *2 (-112)) (-5 *1 (-218 *4 *3)) - (-4 *3 (-1262 *4))))) -(((*1 *2 *1) (-12 (-5 *2 (-576)) (-5 *1 (-931 *3)) (-4 *3 (-317))))) -(((*1 *2 *1) - (-12 (-4 *1 (-353 *3 *4 *5)) (-4 *3 (-1240)) (-4 *4 (-1262 *3)) - (-4 *5 (-1262 (-419 *4))) - (-5 *2 (-2 (|:| |num| (-1286 *4)) (|:| |den| *4)))))) -(((*1 *2 *2) - (-12 (-4 *3 (-568)) (-5 *1 (-443 *3 *2)) (-4 *2 (-442 *3))))) +(((*1 *2 *3 *4 *5 *6 *7 *6) + (|partial| -12 + (-5 *5 + (-2 (|:| |contp| *3) + (|:| -1984 (-656 (-2 (|:| |irr| *10) (|:| -3847 (-576))))))) + (-5 *6 (-656 *3)) (-5 *7 (-656 *8)) (-4 *8 (-862)) (-4 *3 (-317)) + (-4 *10 (-966 *3 *9 *8)) (-4 *9 (-805)) + (-5 *2 + (-2 (|:| |polfac| (-656 *10)) (|:| |correct| *3) + (|:| |corrfact| (-656 (-1191 *3))))) + (-5 *1 (-637 *8 *9 *3 *10)) (-5 *4 (-656 (-1191 *3)))))) +(((*1 *2 *1) (-12 (-5 *2 (-1154)) (-5 *1 (-529))))) +(((*1 *1 *2 *3) + (-12 (-5 *1 (-439 *3 *2)) (-4 *3 (-13 (-174) (-38 (-419 (-576))))) + (-4 *2 (-13 (-862) (-21)))))) (((*1 *2 *3) - (-12 (-5 *3 (-938)) (-5 *2 (-1191 *4)) (-5 *1 (-368 *4)) - (-4 *4 (-360))))) -(((*1 *1 *1) (-12 (-5 *1 (-512 *2)) (-14 *2 (-576)))) - ((*1 *1 *1) (-5 *1 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(-340))))) + (-5 *2 (-2 (|:| |localSymbols| (-1199)) (|:| -4348 (-656 (-340))))) (-4 *1 (-453)))) ((*1 *1 *2) (-12 (-5 *2 (-340)) (-4 *1 (-453)))) ((*1 *1 *2) (-12 (-5 *2 (-656 (-340))) (-4 *1 (-453)))) @@ -5426,7 +5310,7 @@ (-14 *4 (-1 *2 *2 *3)) (-14 *5 (-1 (-3 *3 "failed") *3 *3)) (-14 *6 (-1 (-3 *2 "failed") *2 *2 *3)))) ((*1 *1 *2) - (-12 (-5 *2 (-656 (-2 (|:| -1677 *3) (|:| -3660 *4)))) + (-12 (-5 *2 (-656 (-2 (|:| -1713 *3) (|:| -3682 *4)))) (-4 *3 (-1068)) (-4 *4 (-738)) (-5 *1 (-747 *3 *4)))) ((*1 *1 *2) (-12 (-5 *2 (-576)) (-4 *1 (-775)))) ((*1 *1 *2) @@ -5435,25 +5319,25 @@ (-3 (|:| |nia| (-2 (|:| |var| (-1195)) (|:| |fn| (-326 (-227))) - (|:| -4005 (-1113 (-855 (-227)))) (|:| |abserr| (-227)) + (|:| -1668 (-1113 (-855 (-227)))) (|:| |abserr| (-227)) (|:| |relerr| (-227)))) (|:| |mdnia| (-2 (|:| |fn| (-326 (-227))) - (|:| -4005 (-656 (-1113 (-855 (-227))))) + (|:| -1668 (-656 (-1113 (-855 (-227))))) (|:| |abserr| (-227)) (|:| |relerr| (-227)))))) (-5 *1 (-781)))) ((*1 *1 *2) (-12 (-5 *2 (-2 (|:| |fn| (-326 (-227))) - (|:| -4005 (-656 (-1113 (-855 (-227))))) (|:| |abserr| (-227)) + (|:| -1668 (-656 (-1113 (-855 (-227))))) (|:| |abserr| (-227)) (|:| |relerr| (-227)))) (-5 *1 (-781)))) ((*1 *1 *2) (-12 (-5 *2 (-2 (|:| |var| (-1195)) (|:| |fn| (-326 (-227))) - (|:| -4005 (-1113 (-855 (-227)))) (|:| |abserr| (-227)) + (|:| -1668 (-1113 (-855 (-227)))) (|:| |abserr| (-227)) (|:| |relerr| (-227)))) (-5 *1 (-781)))) ((*1 *2 *3) (-12 (-5 *2 (-786)) (-5 *1 (-785 *3)) (-4 *3 (-1236)))) @@ -5471,23 +5355,23 @@ (-5 *2 (-3 (|:| |noa| - (-2 (|:| |fn| (-326 (-227))) (|:| -3475 (-656 (-227))) + (-2 (|:| |fn| (-326 (-227))) (|:| -3537 (-656 (-227))) (|:| |lb| (-656 (-855 (-227)))) (|:| |cf| (-656 (-326 (-227)))) (|:| |ub| (-656 (-855 (-227)))))) (|:| |lsa| (-2 (|:| |lfn| (-656 (-326 (-227)))) - (|:| -3475 (-656 (-227))))))) + (|:| -3537 (-656 (-227))))))) (-5 *1 (-853)))) ((*1 *1 *2) (-12 (-5 *2 - (-2 (|:| |lfn| (-656 (-326 (-227)))) (|:| -3475 (-656 (-227))))) + (-2 (|:| 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(-1195))))) @@ -13315,8 +13150,8 @@ ((*1 *2 *1) (-12 (-14 *3 (-656 (-1195))) (-4 *5 (-243 (-3500 *3) (-783))) (-14 *6 - (-1 (-112) (-2 (|:| -3227 *4) (|:| -2795 *5)) - (-2 (|:| -3227 *4) (|:| -2795 *5)))) + (-1 (-112) (-2 (|:| -3222 *4) (|:| -1567 *5)) + (-2 (|:| -3222 *4) (|:| -1567 *5)))) (-4 *2 (-174)) (-5 *1 (-473 *3 *2 *4 *5 *6 *7)) (-4 *4 (-862)) (-4 *7 (-966 *2 *5 (-876 *3))))) ((*1 *2 *1) (-12 (-4 *1 (-521 *2 *3)) (-4 *3 (-862)) (-4 *2 (-1119)))) @@ -13333,34 +13168,81 @@ ((*1 *1 *1 *2) (-12 (-4 *1 (-1084 *3 *4 *2)) (-4 *3 (-1068)) (-4 *4 (-805)) (-4 *2 (-862))))) -(((*1 *2 *2 *3 *3 *4) - (-12 (-5 *4 (-783)) (-4 *3 (-568)) (-5 *1 (-988 *3 *2)) - (-4 *2 (-1262 *3))))) -(((*1 *2 *3 *3) - (-12 (-4 *3 (-317)) (-4 *3 (-174)) (-4 *4 (-384 *3)) - (-4 *5 (-384 *3)) (-5 *2 (-2 (|:| -3042 *3) (|:| -3730 *3))) - (-5 *1 (-700 *3 *4 *5 *6)) (-4 *6 (-699 *3 *4 *5)))) - ((*1 *2 *3 *3) - (-12 (-5 *2 (-2 (|:| -3042 *3) (|:| -3730 *3))) (-5 *1 (-712 *3)) - (-4 *3 (-317))))) -(((*1 *1 *1) - (-12 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*3) (|:| -3019 *4))) + (-5 *1 (-988 *4 *3)) (-4 *3 (-1262 *4))))) +(((*1 *1 *1 *2) (-12 (-4 *1 (-1117 *2)) (-4 *2 (-1119)))) + ((*1 *1 *1 *1) (-12 (-4 *1 (-1117 *2)) (-4 *2 (-1119))))) (((*1 *2 *3 *4) (-12 (-5 *3 (-701 *8)) (-4 *8 (-966 *5 *7 *6)) (-4 *5 (-13 (-317) (-148))) (-4 *6 (-13 (-862) (-626 (-1195)))) @@ -17006,7 +17422,7 @@ (|:| |wcond| (-656 (-969 *5))) (|:| |bsoln| (-2 (|:| |partsol| (-1286 (-419 (-969 *5)))) - (|:| -2641 (-656 (-1286 (-419 (-969 *5)))))))))) + (|:| -2335 (-656 (-1286 (-419 (-969 *5)))))))))) (-5 *1 (-941 *5 *6 *7 *8)) (-5 *4 (-656 *8)))) ((*1 *2 *3 *4) (-12 (-5 *3 (-701 *8)) (-5 *4 (-656 (-1195))) (-4 *8 (-966 *5 *7 *6)) @@ -17018,7 +17434,7 @@ (|:| |wcond| (-656 (-969 *5))) (|:| |bsoln| (-2 (|:| |partsol| (-1286 (-419 (-969 *5)))) - (|:| -2641 (-656 (-1286 (-419 (-969 *5)))))))))) + (|:| -2335 (-656 (-1286 (-419 (-969 *5)))))))))) (-5 *1 (-941 *5 *6 *7 *8)))) ((*1 *2 *3) (-12 (-5 *3 (-701 *7)) (-4 *7 (-966 *4 *6 *5)) @@ -17030,7 +17446,7 @@ (|:| |wcond| (-656 (-969 *4))) (|:| |bsoln| (-2 (|:| |partsol| (-1286 (-419 (-969 *4)))) - (|:| -2641 (-656 (-1286 (-419 (-969 *4)))))))))) + (|:| -2335 (-656 (-1286 (-419 (-969 *4)))))))))) (-5 *1 (-941 *4 *5 *6 *7)))) ((*1 *2 *3 *4 *5) (-12 (-5 *3 (-701 *9)) (-5 *5 (-938)) (-4 *9 (-966 *6 *8 *7)) @@ -17042,7 +17458,7 @@ (|:| |wcond| (-656 (-969 *6))) (|:| |bsoln| (-2 (|:| |partsol| (-1286 (-419 (-969 *6)))) - (|:| -2641 (-656 (-1286 (-419 (-969 *6)))))))))) + (|:| -2335 (-656 (-1286 (-419 (-969 *6)))))))))) (-5 *1 (-941 *6 *7 *8 *9)) (-5 *4 (-656 *9)))) ((*1 *2 *3 *4 *5) (-12 (-5 *3 (-701 *9)) (-5 *4 (-656 (-1195))) (-5 *5 (-938)) @@ -17054,7 +17470,7 @@ (|:| |wcond| (-656 (-969 *6))) (|:| |bsoln| (-2 (|:| |partsol| (-1286 (-419 (-969 *6)))) - (|:| -2641 (-656 (-1286 (-419 (-969 *6)))))))))) + (|:| -2335 (-656 (-1286 (-419 (-969 *6)))))))))) (-5 *1 (-941 *6 *7 *8 *9)))) ((*1 *2 *3 *4) (-12 (-5 *3 (-701 *8)) (-5 *4 (-938)) (-4 *8 (-966 *5 *7 *6)) @@ -17066,7 +17482,7 @@ (|:| |wcond| (-656 (-969 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